LMFDB - Embedded newform 216.2.t.a.61.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			61.29
Character	$\chi$	$=$	216.61
Dual form			216.2.t.a.85.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22374 + 0.708852i) q^{2} +(-0.741273 + 1.56541i) q^{3} +(0.995058 + 1.73489i) q^{4} +(-1.92794 + 0.339948i) q^{5} +(-2.01677 + 1.39020i) q^{6} +(1.11744 + 0.937647i) q^{7} +(-0.0120958 + 2.82840i) q^{8} +(-1.90103 - 2.32079i) q^{9} +O(q^{10})$	\(q+(1.22374 + 0.708852i) q^{2} +(-0.741273 + 1.56541i) q^{3} +(0.995058 + 1.73489i) q^{4} +(-1.92794 + 0.339948i) q^{5} +(-2.01677 + 1.39020i) q^{6} +(1.11744 + 0.937647i) q^{7} +(-0.0120958 + 2.82840i) q^{8} +(-1.90103 - 2.32079i) q^{9} +(-2.60027 - 0.950619i) q^{10} +(-0.757167 - 0.133509i) q^{11} +(-3.45343 + 0.271645i) q^{12} +(1.24934 - 3.43252i) q^{13} +(0.702804 + 1.93954i) q^{14} +(0.896973 - 3.27002i) q^{15} +(-2.01972 + 3.45264i) q^{16} +(2.40908 + 4.17264i) q^{17} +(-0.681258 - 4.18759i) q^{18} +(6.24367 + 3.60478i) q^{19} +(-2.50819 - 3.00651i) q^{20} +(-2.29614 + 1.05421i) q^{21} +(-0.831935 - 0.700099i) q^{22} +(1.35218 - 1.13461i) q^{23} +(-4.41865 - 2.11555i) q^{24} +(-1.09706 + 0.399298i) q^{25} +(3.96200 - 3.31490i) q^{26} +(5.04218 - 1.25555i) q^{27} +(-0.514797 + 2.87166i) q^{28} +(-2.25636 - 6.19930i) q^{29} +(3.41562 - 3.36582i) q^{30} +(6.71672 - 5.63600i) q^{31} +(-4.91901 + 2.79344i) q^{32} +(0.770264 - 1.08631i) q^{33} +(-0.00971330 + 6.81389i) q^{34} +(-2.47312 - 1.42786i) q^{35} +(2.13470 - 5.60741i) q^{36} +(-4.91459 + 2.83744i) q^{37} +(5.08534 + 8.83714i) q^{38} +(4.44721 + 4.50016i) q^{39} +(-0.938191 - 5.45711i) q^{40} +(0.331211 + 0.120551i) q^{41} +(-3.55714 - 0.337547i) q^{42} +(6.05852 + 1.06828i) q^{43} +(-0.521801 - 1.44646i) q^{44} +(4.45403 + 3.82811i) q^{45} +(2.45899 - 0.429972i) q^{46} +(1.39202 + 1.16804i) q^{47} +(-3.90764 - 5.72104i) q^{48} +(-0.846037 - 4.79812i) q^{49} +(-1.62556 - 0.289019i) q^{50} +(-8.31768 + 0.678130i) q^{51} +(7.19822 - 1.24809i) q^{52} -3.71259i q^{53} +(7.06030 + 2.03770i) q^{54} +1.50516 q^{55} +(-2.66556 + 3.14924i) q^{56} +(-10.2712 + 7.10178i) q^{57} +(1.63320 - 9.18573i) q^{58} +(-11.1189 + 1.96057i) q^{59} +(6.56568 - 1.69771i) q^{60} +(5.27287 - 6.28396i) q^{61} +(12.2146 - 2.13581i) q^{62} +(0.0517918 - 4.37585i) q^{63} +(-7.99971 - 0.0684238i) q^{64} +(-1.24177 + 7.04241i) q^{65} +(1.71263 - 0.783356i) q^{66} +(2.10768 - 5.79080i) q^{67} +(-4.84192 + 8.33151i) q^{68} +(0.773804 + 2.95778i) q^{69} +(-2.01431 - 3.50040i) q^{70} +(-3.64209 - 6.30828i) q^{71} +(6.58713 - 5.34880i) q^{72} +(0.685732 - 1.18772i) q^{73} +(-8.02548 - 0.0114404i) q^{74} +(0.188156 - 2.01334i) q^{75} +(-0.0411093 + 14.4191i) q^{76} +(-0.720908 - 0.859145i) q^{77} +(2.25226 + 8.65942i) q^{78} +(-16.2077 + 5.89913i) q^{79} +(2.72019 - 7.34310i) q^{80} +(-1.77217 + 8.82380i) q^{81} +(0.319862 + 0.382302i) q^{82} +(2.31520 + 6.36096i) q^{83} +(-4.11373 - 2.93455i) q^{84} +(-6.06304 - 7.22565i) q^{85} +(6.65678 + 5.60189i) q^{86} +(11.3770 + 1.06324i) q^{87} +(0.386776 - 2.13996i) q^{88} +(-6.47879 + 11.2216i) q^{89} +(2.73699 + 7.84184i) q^{90} +(4.61456 - 2.66421i) q^{91} +(3.31394 + 1.21688i) q^{92} +(3.84374 + 14.6922i) q^{93} +(0.875494 + 2.41611i) q^{94} +(-13.2629 - 4.82729i) q^{95} +(-0.726549 - 9.77098i) q^{96} +(1.57059 - 8.90723i) q^{97} +(2.36583 - 6.47134i) q^{98} +(1.12955 + 2.01103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	1.22374	+	0.708852i	0.865312	+	0.501234i
$2$	1.22374	+	0.708852i	0.865312	+	0.501234i
$3$	−0.741273	+	1.56541i	−0.427974	+	0.903791i
$3$	−0.741273	+	1.56541i	−0.427974	+	0.903791i
$4$	0.995058	+	1.73489i	0.497529	+	0.867447i
$5$	−1.92794	+	0.339948i	−0.862203	+	0.152030i	−0.587228	−	0.809422i	$-0.699781\pi$
$5$	−1.92794	+	0.339948i	−0.862203	+	0.152030i	−0.274975	+	0.961451i	$0.588670\pi$
$6$	−2.01677	+	1.39020i	−0.823342	+	0.567546i
$7$	1.11744	+	0.937647i	0.422354	+	0.354397i	0.829058	−	0.559163i	$-0.188877\pi$
$7$	1.11744	+	0.937647i	0.422354	+	0.354397i	−0.406704	+	0.913560i	$0.633322\pi$
$8$	−0.0120958	+	2.82840i	−0.00427653	+	0.999991i
$9$	−1.90103	−	2.32079i	−0.633676	−	0.773598i
$10$	−2.60027	−	0.950619i	−0.822276	−	0.300612i
$11$	−0.757167	−	0.133509i	−0.228295	−	0.0402545i	0.0583305	−	0.998297i	$-0.481422\pi$
$11$	−0.757167	−	0.133509i	−0.228295	−	0.0402545i	−0.286625	+	0.958043i	$0.592533\pi$
$12$	−3.45343	+	0.271645i	−0.996921	+	0.0784172i
$13$	1.24934	−	3.43252i	0.346503	−	0.952010i	−0.636959	−	0.770898i	$-0.719808\pi$
$13$	1.24934	−	3.43252i	0.346503	−	0.952010i	0.983462	−	0.181112i	$-0.0579697\pi$
$14$	0.702804	+	1.93954i	0.187832	+	0.518363i
$15$	0.896973	−	3.27002i	0.231597	−	0.844316i
$16$	−2.01972	+	3.45264i	−0.504930	+	0.863160i
$17$	2.40908	+	4.17264i	0.584287	+	1.01201i	0.994964	+	0.100233i	$0.0319589\pi$
$17$	2.40908	+	4.17264i	0.584287	+	1.01201i	−0.410677	+	0.911781i	$0.634708\pi$
$18$	−0.681258	−	4.18759i	−0.160574	−	0.987024i
$19$	6.24367	+	3.60478i	1.43240	+	0.826994i	0.997303	−	0.0733919i	$-0.0233824\pi$
$19$	6.24367	+	3.60478i	1.43240	+	0.826994i	0.435092	+	0.900386i	$0.356716\pi$
$20$	−2.50819	−	3.00651i	−0.560848	−	0.672276i
$21$	−2.29614	+	1.05421i	−0.501058	+	0.230047i
$22$	−0.831935	−	0.700099i	−0.177369	−	0.149262i
$23$	1.35218	−	1.13461i	0.281949	−	0.236583i	−0.490835	−	0.871253i	$-0.663308\pi$
$23$	1.35218	−	1.13461i	0.281949	−	0.236583i	0.772784	+	0.634669i	$0.218864\pi$
$24$	−4.41865	−	2.11555i	−0.901953	−	0.431835i
$25$	−1.09706	+	0.399298i	−0.219412	+	0.0798596i
$26$	3.96200	−	3.31490i	0.777013	−	0.650106i
$27$	5.04218	−	1.25555i	0.970368	−	0.241631i
$28$	−0.514797	+	2.87166i	−0.0972876	+	0.542693i
$29$	−2.25636	−	6.19930i	−0.418996	−	1.15118i	−0.952275	−	0.305242i	$-0.901263\pi$
$29$	−2.25636	−	6.19930i	−0.418996	−	1.15118i	0.533279	−	0.845939i	$-0.320960\pi$
$30$	3.41562	−	3.36582i	0.623604	−	0.614512i
$31$	6.71672	−	5.63600i	1.20636	−	1.01226i	0.206933	−	0.978355i	$-0.433652\pi$
$31$	6.71672	−	5.63600i	1.20636	−	1.01226i	0.999425	−	0.0339000i	$-0.0107928\pi$
$32$	−4.91901	+	2.79344i	−0.869567	+	0.493815i
$33$	0.770264	−	1.08631i	0.134086	−	0.189103i
$34$	−0.00971330	+	6.81389i	−0.00166582	+	1.16857i
$35$	−2.47312	−	1.42786i	−0.418034	−	0.241352i
$36$	2.13470	−	5.60741i	0.355783	−	0.934568i
$37$	−4.91459	+	2.83744i	−0.807953	+	0.466472i	−0.846245	−	0.532795i	$-0.821142\pi$
$37$	−4.91459	+	2.83744i	−0.807953	+	0.466472i	0.0382914	+	0.999267i	$0.487809\pi$
$38$	5.08534	+	8.83714i	0.824951	+	1.43357i
$39$	4.44721	+	4.50016i	0.712124	+	0.720602i
$40$	−0.938191	−	5.45711i	−0.148341	−	0.862845i
$41$	0.331211	+	0.120551i	0.0517264	+	0.0188269i	0.367754	−	0.929923i	$-0.380127\pi$
$41$	0.331211	+	0.120551i	0.0517264	+	0.0188269i	−0.316027	+	0.948750i	$0.602349\pi$
$42$	−3.55714	−	0.337547i	−0.548879	−	0.0520847i
$43$	6.05852	+	1.06828i	0.923916	+	0.162911i	0.615316	−	0.788281i	$-0.289028\pi$
$43$	6.05852	+	1.06828i	0.923916	+	0.162911i	0.308600	+	0.951192i	$0.400140\pi$
$44$	−0.521801	−	1.44646i	−0.0786645	−	0.218061i
$45$	4.45403	+	3.82811i	0.663967	+	0.570661i
$46$	2.45899	−	0.429972i	0.362558	−	0.0633959i
$47$	1.39202	+	1.16804i	0.203047	+	0.170377i	0.738641	−	0.674099i	$-0.235468\pi$
$47$	1.39202	+	1.16804i	0.203047	+	0.170377i	−0.535594	+	0.844475i	$0.679912\pi$
$48$	−3.90764	−	5.72104i	−0.564020	−	0.825761i
$49$	−0.846037	−	4.79812i	−0.120862	−	0.685445i
$50$	−1.62556	−	0.289019i	−0.229888	−	0.0408735i
$51$	−8.31768	+	0.678130i	−1.16471	+	0.0949572i
$52$	7.19822	−	1.24809i	0.998214	−	0.173079i
$53$		−	3.71259i		−	0.509963i	−0.966946	−	0.254981i	$-0.917931\pi$
$53$		−	3.71259i		−	0.509963i	0.966946	−	0.254981i	$-0.0820693\pi$
$54$	7.06030	+	2.03770i	0.960785	+	0.277295i
$55$	1.50516			0.202956
$56$	−2.66556	+	3.14924i	−0.356200	+	0.420835i
$57$	−10.2712	+	7.10178i	−1.36046	+	0.940654i
$58$	1.63320	−	9.18573i	0.214449	−	1.20615i
$59$	−11.1189	+	1.96057i	−1.44756	+	0.255244i	−0.841536	−	0.540201i	$-0.818348\pi$
$59$	−11.1189	+	1.96057i	−1.44756	+	0.255244i	−0.606025	+	0.795445i	$0.707237\pi$
$60$	6.56568	−	1.69771i	0.847626	−	0.219173i
$61$	5.27287	−	6.28396i	0.675122	−	0.804579i	−0.314349	−	0.949307i	$-0.601786\pi$
$61$	5.27287	−	6.28396i	0.675122	−	0.804579i	0.989471	+	0.144728i	$0.0462308\pi$
$62$	12.2146	−	2.13581i	1.55125	−	0.271248i
$63$	0.0517918	−	4.37585i	0.00652515	−	0.551306i
$64$	−7.99971	−	0.0684238i	−0.999963	−	0.00855298i
$65$	−1.24177	+	7.04241i	−0.154022	+	0.873504i
$66$	1.71263	−	0.783356i	0.210811	−	0.0964244i
$67$	2.10768	−	5.79080i	0.257494	−	0.707459i	−0.741826	−	0.670592i	$-0.766040\pi$
$67$	2.10768	−	5.79080i	0.257494	−	0.707459i	0.999320	−	0.0368670i	$-0.0117378\pi$
$68$	−4.84192	+	8.33151i	−0.587169	+	1.01034i
$69$	0.773804	+	2.95778i	0.0931551	+	0.356075i
$70$	−2.01431	−	3.50040i	−0.240756	−	0.418377i
$71$	−3.64209	−	6.30828i	−0.432237	−	0.748656i	0.564829	−	0.825208i	$-0.308942\pi$
$71$	−3.64209	−	6.30828i	−0.432237	−	0.748656i	−0.997066	+	0.0765523i	$0.975609\pi$
$72$	6.58713	−	5.34880i	0.776301	−	0.630362i
$73$	0.685732	−	1.18772i	0.0802588	−	0.139012i	−0.823102	−	0.567893i	$-0.807759\pi$
$73$	0.685732	−	1.18772i	0.0802588	−	0.139012i	0.903361	+	0.428881i	$0.141092\pi$
$74$	−8.02548	−	0.0114404i	−0.932943	−	0.00132992i
$75$	0.188156	−	2.01334i	0.0217264	−	0.232481i
$76$	−0.0411093	+	14.4191i	−0.00471556	+	1.65398i
$77$	−0.720908	−	0.859145i	−0.0821551	−	0.0979087i
$78$	2.25226	+	8.65942i	0.255019	+	0.980486i
$79$	−16.2077	+	5.89913i	−1.82351	+	0.663704i	−0.828979	+	0.559280i	$0.811078\pi$
$79$	−16.2077	+	5.89913i	−1.82351	+	0.663704i	−0.994533	+	0.104424i	$0.966700\pi$
$80$	2.72019	−	7.34310i	0.304126	−	0.820983i
$81$	−1.77217	+	8.82380i	−0.196908	+	0.980422i
$82$	0.319862	+	0.382302i	0.0353228	+	0.0422182i
$83$	2.31520	+	6.36096i	0.254126	+	0.698206i	0.999502	+	0.0315612i	$0.0100479\pi$
$83$	2.31520	+	6.36096i	0.254126	+	0.698206i	−0.745376	+	0.666645i	$0.767730\pi$
$84$	−4.11373	−	2.93455i	−0.448845	−	0.320186i
$85$	−6.06304	−	7.22565i	−0.657629	−	0.783732i
$86$	6.65678	+	5.60189i	0.717819	+	0.604067i
$87$	11.3770	+	1.06324i	1.21975	+	0.113991i
$88$	0.386776	−	2.13996i	0.0412304	−	0.228120i
$89$	−6.47879	+	11.2216i	−0.686750	+	1.18949i	0.286133	+	0.958190i	$0.407630\pi$
$89$	−6.47879	+	11.2216i	−0.686750	+	1.18949i	−0.972883	+	0.231297i	$0.925703\pi$
$90$	2.73699	+	7.84184i	0.288504	+	0.826602i
$91$	4.61456	−	2.66421i	0.483737	−	0.279286i
$92$	3.31394	+	1.21688i	0.345502	+	0.126869i
$93$	3.84374	+	14.6922i	0.398577	+	1.52351i
$94$	0.875494	+	2.41611i	0.0903003	+	0.249203i
$95$	−13.2629	−	4.82729i	−1.36074	−	0.495270i
$96$	−0.726549	−	9.77098i	−0.0741531	−	0.997247i
$97$	1.57059	−	8.90723i	0.159469	−	0.904393i	−0.795117	−	0.606456i	$-0.792591\pi$
$97$	1.57059	−	8.90723i	0.159469	−	0.904393i	0.954586	−	0.297936i	$-0.0962984\pi$
$98$	2.36583	−	6.47134i	0.238985	−	0.653704i
$99$	1.12955	+	2.01103i	0.113524	+	0.202117i
$100$	−1.78438	−	1.50596i	−0.178438	−	0.150596i
$101$	4.98136	−	5.93656i	0.495664	−	0.590709i	−0.458985	−	0.888444i	$-0.651787\pi$
$101$	4.98136	−	5.93656i	0.495664	−	0.590709i	0.954649	+	0.297735i	$0.0962311\pi$
$102$	−10.6593	−	5.06615i	−1.05543	−	0.501624i
$103$	0.625164	+	3.54548i	0.0615992	+	0.349347i	0.999993	+	0.00377840i	$0.00120270\pi$
$103$	0.625164	+	3.54548i	0.0615992	+	0.349347i	−0.938394	+	0.345568i	$0.887686\pi$
$104$	9.69343	+	3.57514i	0.950519	+	0.350571i
$105$	4.06844	−	2.81302i	0.397039	−	0.274523i
$106$	2.63167	−	4.54322i	0.255611	−	0.441277i
$107$			4.03180i			0.389769i	0.980826	+	0.194885i	$0.0624332\pi$
$107$			4.03180i			0.389769i	−0.980826	+	0.194885i	$0.937567\pi$
$108$	7.19551	+	7.49831i	0.692389	+	0.721525i
$109$			5.66517i			0.542625i	0.962491	+	0.271313i	$0.0874577\pi$
$109$			5.66517i			0.542625i	−0.962491	+	0.271313i	$0.912542\pi$
$110$	1.84192	+	1.06694i	0.175620	+	0.101728i
$111$	−0.798710	−	9.79667i	−0.0758102	−	0.929859i
$112$	−5.49428	+	1.96435i	−0.519161	+	0.185614i
$113$	−2.85140	−	16.1711i	−0.268237	−	1.52125i	−0.759656	−	0.650325i	$-0.774633\pi$
$113$	−2.85140	−	16.1711i	−0.268237	−	1.52125i	0.491419	−	0.870923i	$-0.336478\pi$
$114$	−17.6034	+	1.40992i	−1.64871	+	0.132052i
$115$	−2.22122	+	2.64714i	−0.207130	+	0.246848i
$116$	8.50993	−	10.0832i	0.790127	−	0.936203i
$117$	−10.3412	+	3.62587i	−0.956044	+	0.335212i
$118$	−14.9964	−	5.48246i	−1.38053	−	0.504701i
$119$	−1.22046	+	6.92156i	−0.111879	+	0.634498i
$120$	9.23808	+	2.57655i	0.843317	+	0.235206i
$121$	−9.78114	−	3.56004i	−0.889195	−	0.323640i
$122$	10.9070	−	3.95222i	0.987473	−	0.357818i
$123$	−0.434229	+	0.429120i	−0.0391531	+	0.0386925i
$124$	16.4614	+	6.04466i	1.47828	+	0.542826i
$125$	10.4564	−	6.03698i	0.935245	−	0.539964i
$126$	3.16521	−	5.31818i	0.281980	−	0.473781i
$127$	−5.35174	+	9.26949i	−0.474890	+	0.822534i	−0.999586	−	0.0287554i	$-0.990846\pi$
$127$	−5.35174	+	9.26949i	−0.474890	+	0.822534i	0.524696	+	0.851290i	$0.324179\pi$
$128$	−9.74102	−	5.75434i	−0.860993	−	0.508617i
$129$	−6.16332	+	8.69220i	−0.542650	+	0.765305i
$130$	−6.51162	+	7.73782i	−0.571107	+	0.678652i
$131$	−3.74449	−	4.46251i	−0.327158	−	0.389892i	0.577245	−	0.816571i	$-0.304128\pi$
$131$	−3.74449	−	4.46251i	−0.327158	−	0.389892i	−0.904403	+	0.426679i	$0.859683\pi$
$132$	2.65110	+	0.255384i	0.230748	+	0.0222283i
$133$	3.59694	+	9.88250i	0.311894	+	0.856922i
$134$	6.68407	−	5.59238i	0.577415	−	0.483108i
$135$	−9.29422	+	4.13472i	−0.799919	+	0.355860i
$136$	−11.8310	+	6.76336i	−1.01450	+	0.579953i
$137$	14.3574	−	5.22568i	1.22664	−	0.446460i	0.354194	−	0.935172i	$-0.384755\pi$
$137$	14.3574	−	5.22568i	1.22664	−	0.446460i	0.872445	+	0.488712i	$0.162533\pi$
$138$	−1.14970	+	4.16805i	−0.0978686	+	0.354808i
$139$	7.13743	+	8.50606i	0.605389	+	0.721475i	0.978485	−	0.206318i	$-0.0661481\pi$
$139$	7.13743	+	8.50606i	0.605389	+	0.721475i	−0.373096	+	0.927793i	$0.621704\pi$
$140$	0.0162834	−	5.71141i	0.00137620	−	0.482702i
$141$	−2.86033	+	1.31325i	−0.240884	+	0.110595i
$142$	0.0146848	−	10.3014i	0.00123232	−	0.864472i
$143$	−1.40423	+	2.43220i	−0.117427	+	0.203390i
$144$	11.8524	−	1.87622i	0.987701	−	0.156351i
$145$	6.45758	+	11.1849i	0.536273	+	0.928852i
$146$	1.68107	−	0.967375i	0.139127	−	0.0800606i
$147$	8.13817	+	2.23232i	0.671225	+	0.184118i
$148$	−9.81296	−	5.70288i	−0.806620	−	0.468774i
$149$	−3.51712	+	9.66320i	−0.288134	+	0.791640i	0.708194	+	0.706018i	$0.249510\pi$
$149$	−3.51712	+	9.66320i	−0.288134	+	0.791640i	−0.996328	+	0.0856226i	$0.972712\pi$
$150$	1.65742	−	2.33042i	0.135327	−	0.190278i
$151$	−3.51987	+	19.9622i	−0.286443	+	1.62450i	0.413641	+	0.910440i	$0.364257\pi$
$151$	−3.51987	+	19.9622i	−0.286443	+	1.62450i	−0.700085	+	0.714060i	$0.746854\pi$
$152$	−10.2713	+	17.6160i	−0.833112	+	1.42885i
$153$	5.10412	−	13.5233i	0.412644	−	1.09329i
$154$	−0.273195	−	1.56238i	−0.0220146	−	0.125900i
$155$	−11.0335	+	13.1492i	−0.886233	+	1.05617i
$156$	−3.38207	+	12.1934i	−0.270782	+	0.976250i
$157$	−6.73787	+	1.18807i	−0.537741	+	0.0948182i	−0.435921	−	0.899985i	$-0.643577\pi$
$157$	−6.73787	+	1.18807i	−0.537741	+	0.0948182i	−0.101819	+	0.994803i	$0.532466\pi$
$158$	−24.0156	−	4.26990i	−1.91058	−	0.339695i
$159$	5.81173	+	2.75204i	0.460900	+	0.218251i
$160$	8.53396	−	7.05780i	0.674669	−	0.557968i
$161$	2.57486			0.202927
$162$	−8.42344	+	9.54179i	−0.661808	+	0.749673i
$163$		−	10.4060i		−	0.815064i	−0.913191	−	0.407532i	$-0.866389\pi$
$163$		−	10.4060i		−	0.815064i	0.913191	−	0.407532i	$-0.133611\pi$
$164$	0.120431	+	0.694571i	0.00940406	+	0.0542369i
$165$	−1.11574	+	2.35620i	−0.0868599	+	0.183430i
$166$	−1.67579	+	9.42527i	−0.130066	+	0.731542i
$167$	−1.57073	−	8.90806i	−0.121547	−	0.689326i	−0.983299	−	0.181997i	$-0.941744\pi$
$167$	−1.57073	−	8.90806i	−0.121547	−	0.689326i	0.861752	−	0.507329i	$-0.169367\pi$
$168$	−2.95395	−	6.50714i	−0.227902	−	0.502037i
$169$	−0.262778	−	0.220497i	−0.0202137	−	0.0169613i
$170$	−2.29764	−	13.1401i	−0.176221	−	1.00780i
$171$	−3.50343	−	21.3431i	−0.267914	−	1.63215i
$172$	4.17523	+	11.5739i	0.318358	+	0.882502i
$173$	18.7971	+	3.31443i	1.42911	+	0.251991i	0.834051	−	0.551687i	$-0.186016\pi$
$173$	18.7971	+	3.31443i	1.42911	+	0.251991i	0.595063	+	0.803679i	$0.297127\pi$
$174$	13.1688	+	9.36576i	0.998325	+	0.710017i
$175$	−1.60031	−	0.582464i	−0.120972	−	0.0440301i
$176$	1.99023	−	2.34458i	0.150019	−	0.176729i
$177$	5.17306	−	18.8590i	0.388831	−	1.41753i
$178$	−15.8828	+	9.13976i	−1.19046	+	0.685054i
$179$	13.9615	−	8.06067i	1.04353	−	0.602483i	0.122699	−	0.992444i	$-0.460845\pi$
$179$	13.9615	−	8.06067i	1.04353	−	0.602483i	0.920831	+	0.389961i	$0.127512\pi$
$180$	−2.20935	+	11.5365i	−0.164675	+	0.859877i
$181$	−14.2617	−	8.23400i	−1.06006	−	0.612028i	−0.134614	−	0.990898i	$-0.542979\pi$
$181$	−14.2617	−	8.23400i	−1.06006	−	0.612028i	−0.925450	+	0.378870i	$0.876313\pi$
$182$	7.53553	+	0.0107420i	0.558571	+	0.000796251i
$183$	5.92836	+	12.9123i	0.438237	+	0.954508i
$184$	3.19279	+	3.83823i	0.235376	+	0.282958i
$185$	8.51046	−	7.14113i	0.625702	−	0.525026i
$186$	−5.71091	+	20.7041i	−0.418744	+	1.51810i
$187$	−1.26699	−	3.48102i	−0.0926514	−	0.254557i
$188$	−0.641292	+	3.57728i	−0.0467710	+	0.260900i
$189$	6.81162	+	3.32478i	0.495473	+	0.241842i
$190$	−12.8084	−	15.3087i	−0.929221	−	1.11061i
$191$	22.7306	−	8.27326i	1.64473	−	0.598632i	0.656871	−	0.754003i	$-0.271880\pi$
$191$	22.7306	−	8.27326i	1.64473	−	0.598632i	0.987856	+	0.155371i	$0.0496573\pi$
$192$	6.03708	−	12.4721i	0.435688	−	0.900098i
$193$	17.3461	−	14.5551i	1.24860	−	1.04770i	0.251798	−	0.967780i	$-0.418978\pi$
$193$	17.3461	−	14.5551i	1.24860	−	1.04770i	0.996801	−	0.0799198i	$-0.0254664\pi$
$194$	8.23589	−	9.78679i	0.591303	−	0.702650i
$195$	−10.1038	−	7.16423i	−0.723547	−	0.513041i
$196$	7.48237	−	6.24219i	0.534455	−	0.445871i
$197$	−18.9776	−	10.9567i	−1.35210	−	0.780634i	−0.363554	−	0.931573i	$-0.618437\pi$
$197$	−18.9776	−	10.9567i	−1.35210	−	0.780634i	−0.988543	+	0.150940i	$0.951770\pi$
$198$	−0.0432547	+	3.26166i	−0.00307398	+	0.231796i
$199$	0.103950	+	0.180046i	0.00736881	+	0.0127631i	0.869686	−	0.493605i	$-0.164321\pi$
$199$	0.103950	+	0.180046i	0.00736881	+	0.0127631i	−0.862317	+	0.506368i	$0.830988\pi$
$200$	−1.11610	−	3.10776i	−0.0789205	−	0.219752i
$201$	7.50263	+	7.59195i	0.529195	+	0.535495i
$202$	10.3040	−	3.73373i	0.724988	−	0.262704i
$203$	3.29140	−	9.04305i	0.231011	−	0.634698i
$204$	−9.45306	−	13.7555i	−0.661847	−	0.963080i
$205$	−0.679536	−	0.119821i	−0.0474609	−	0.00836863i
$206$	−1.74819	+	4.78188i	−0.121802	+	0.333169i
$207$	−5.20374	−	0.981199i	−0.361685	−	0.0681980i
$208$	9.32795	+	11.2462i	0.646777	+	0.779786i
$209$	−4.24623	−	3.56301i	−0.293718	−	0.246459i
$210$	6.97271	−	0.558472i	0.481163	−	0.0385382i
$211$	−11.2001	+	1.97488i	−0.771045	+	0.135956i	−0.545312	−	0.838233i	$-0.683589\pi$
$211$	−11.2001	+	1.97488i	−0.771045	+	0.135956i	−0.225733	+	0.974189i	$0.572478\pi$
$212$	6.44094	−	3.69424i	0.442366	−	0.253721i
$213$	12.5748	−	1.02521i	0.861614	−	0.0702463i
$214$	−2.85795	+	4.93386i	−0.195366	+	0.337272i
$215$	−12.0437			−0.821370
$216$	3.49022	+	14.2765i	0.237479	+	0.971393i
$217$	12.7901			0.868251
$218$	−4.01577	+	6.93267i	−0.271982	+	0.469540i
$219$	1.35096	+	1.95388i	0.0912894	+	0.132031i
$220$	1.49772	+	2.61130i	0.100976	+	0.176054i
$221$	17.3324	−	3.05617i	1.16590	−	0.205580i
$222$	5.96698	−	12.5547i	0.400477	−	0.842616i
$223$	−7.84787	−	6.58515i	−0.525532	−	0.440974i	0.341023	−	0.940055i	$-0.389227\pi$
$223$	−7.84787	−	6.58515i	−0.525532	−	0.440974i	−0.866555	+	0.499081i	$0.833671\pi$
$224$	−8.11599	−	1.49079i	−0.542272	−	0.0996075i
$225$	3.01224	+	1.78698i	0.200816	+	0.119132i
$226$	7.97355	−	21.8104i	0.530393	−	1.45080i
$227$	2.26203	+	0.398857i	0.150136	+	0.0264731i	0.248211	−	0.968706i	$-0.420157\pi$
$227$	2.26203	+	0.398857i	0.150136	+	0.0264731i	−0.0980748	+	0.995179i	$0.531268\pi$
$228$	−22.5413	−	10.7528i	−1.49284	−	0.712123i
$229$	2.18394	−	6.00032i	0.144319	−	0.396512i	−0.846381	−	0.532578i	$-0.821223\pi$
$229$	2.18394	−	6.00032i	0.144319	−	0.396512i	0.990700	+	0.136065i	$0.0434457\pi$
$230$	−4.59462	+	1.66489i	−0.302960	+	0.109780i
$231$	1.87931	−	0.491658i	0.123649	−	0.0323487i
$232$	17.5614	−	6.30691i	1.15296	−	0.414069i
$233$	7.33508	+	12.7047i	0.480537	+	0.832315i	0.999751	−	0.0223298i	$-0.00710837\pi$
$233$	7.33508	+	12.7047i	0.480537	+	0.832315i	−0.519213	+	0.854645i	$0.673775\pi$
$234$	−15.2251	−	2.89327i	−0.995296	−	0.189139i
$235$	−3.08081	−	1.77871i	−0.200970	−	0.116030i
$236$	−14.4654	−	17.3393i	−0.941614	−	1.12869i
$237$	2.77978	−	29.7446i	0.180566	−	1.93212i
$238$	−6.39988	+	7.60503i	−0.414842	+	0.492961i
$239$	−3.58395	+	3.00729i	−0.231827	+	0.194526i	−0.751300	−	0.659961i	$-0.770573\pi$
$239$	−3.58395	+	3.00729i	−0.231827	+	0.194526i	0.519473	+	0.854487i	$0.326128\pi$
$240$	9.47857	+	9.70145i	0.611839	+	0.626226i
$241$	−17.4776	+	6.36134i	−1.12583	+	0.409770i	−0.836778	−	0.547542i	$-0.815564\pi$
$241$	−17.4776	+	6.36134i	−1.12583	+	0.409770i	−0.289056	+	0.957312i	$0.593341\pi$
$242$	−9.44599	−	11.2899i	−0.607211	−	0.725744i
$243$	−12.4992	−	9.31502i	−0.801825	−	0.597559i
$244$	16.1488	+	2.89497i	1.03382	+	0.185331i
$245$	3.26222	+	8.96289i	0.208416	+	0.572618i
$246$	−0.835564	+	0.217325i	−0.0532736	+	0.0138562i
$247$	20.1739	−	16.9279i	1.28364	−	1.07710i
$248$	15.8596	+	19.0658i	1.00709	+	1.21068i
$249$	−11.6737	−	1.09096i	−0.739792	−	0.0691370i
$250$	17.0751	+	0.0243409i	1.07993	+	0.00153945i
$251$	−3.47397	−	2.00570i	−0.219275	−	0.126598i	0.386340	−	0.922357i	$-0.373739\pi$
$251$	−3.47397	−	2.00570i	−0.219275	−	0.126598i	−0.605615	+	0.795758i	$0.707073\pi$
$252$	7.64318	−	4.26437i	0.481475	−	0.268630i
$253$	−1.17531	+	0.678565i	−0.0738910	+	0.0426610i
$254$	−13.1198	+	7.54981i	−0.823210	+	0.473717i
$255$	15.8055	−	4.13498i	0.989778	−	0.258943i
$256$	−7.84146	−	13.9467i	−0.490091	−	0.871671i
$257$	19.6124	+	7.13834i	1.22339	+	0.445277i	0.871329	−	0.490700i	$-0.163259\pi$
$257$	19.6124	+	7.13834i	1.22339	+	0.445277i	0.352061	+	0.935977i	$0.385481\pi$
$258$	−13.7038	+	6.26807i	−0.853158	+	0.390233i
$259$	−8.15230	−	1.43747i	−0.506559	−	0.0893200i
$260$	−13.4535	+	4.85327i	−0.834349	+	0.300987i
$261$	−10.0979	+	17.0216i	−0.625044	+	1.05361i
$262$	−1.41901	−	8.11523i	−0.0876666	−	0.501360i
$263$	7.51180	+	6.30315i	0.463197	+	0.388669i	0.844306	−	0.535862i	$-0.180013\pi$
$263$	7.51180	+	6.30315i	0.463197	+	0.388669i	−0.381108	+	0.924530i	$0.624458\pi$
$264$	3.06321	+	2.19176i	0.188528	+	0.134893i
$265$	1.26209	+	7.15765i	0.0775294	+	0.439691i
$266$	−2.60353	+	14.6433i	−0.159633	+	0.897836i
$267$	−12.7639	−	18.4602i	−0.781136	−	1.12975i
$268$	12.1437	−	2.10558i	0.741795	−	0.128619i
$269$			29.3430i			1.78907i	0.446995	+	0.894537i	$0.352494\pi$
$269$			29.3430i			1.78907i	−0.446995	+	0.894537i	$0.647506\pi$
$270$	−14.3046	−	1.52842i	−0.870548	−	0.0930170i
$271$	−7.09190			−0.430802			−0.215401	−	0.976526i	$-0.569106\pi$
$271$	−7.09190			−0.430802			−0.215401	+	0.976526i	$0.569106\pi$
$272$	−19.2723	−	0.109893i	−1.16855	−	0.00666323i
$273$	0.749950	+	9.19859i	0.0453890	+	0.556724i
$274$	21.2740	+	3.78245i	1.28521	+	0.228506i
$275$	0.883970	−	0.155868i	0.0533054	−	0.00939918i
$276$	−4.36146	+	4.28563i	−0.262529	+	0.257965i
$277$	−5.91654	+	7.05106i	−0.355491	+	0.423657i	−0.913920	−	0.405895i	$-0.866960\pi$
$277$	−5.91654	+	7.05106i	−0.355491	+	0.423657i	0.558429	+	0.829552i	$0.311404\pi$
$278$	2.70479	+	15.4686i	0.162223	+	0.927742i
$279$	−25.8487	−	4.87393i	−1.54752	−	0.291795i
$280$	4.06847	−	6.97771i	0.243137	−	0.416998i
$281$	2.27862	−	12.9227i	0.135931	−	0.770904i	−0.838276	−	0.545247i	$-0.816436\pi$
$281$	2.27862	−	12.9227i	0.135931	−	0.770904i	0.974207	−	0.225657i	$-0.0724529\pi$
$282$	−4.43119	−	0.420488i	−0.263873	−	0.0250397i
$283$	−7.37385	+	20.2595i	−0.438330	+	1.20430i	0.502248	+	0.864724i	$0.332507\pi$
$283$	−7.37385	+	20.2595i	−0.438330	+	1.20430i	−0.940578	+	0.339578i	$0.889716\pi$
$284$	7.32012	−	12.5958i	0.434369	−	0.747420i
$285$	17.3881	−	17.1835i	1.02998	−	1.01786i
$286$	−3.44247	+	1.98097i	−0.203558	+	0.117137i
$287$	0.257075	+	0.445268i	0.0151747	+	0.0262833i
$288$	15.8342	+	6.10562i	0.933038	+	0.359777i
$289$	−3.10729	+	5.38198i	−0.182782	+	0.316587i
$290$	−0.0260367	+	18.2648i	−0.00152893	+	1.07254i
$291$	12.7793	+	9.06130i	0.749133	+	0.531183i
$292$	2.74292	+	0.00782015i	0.160517	+	0.000457640i
$293$	6.51334	+	7.76230i	0.380513	+	0.453478i	0.921976	−	0.387246i	$-0.126574\pi$
$293$	6.51334	+	7.76230i	0.380513	+	0.453478i	−0.541463	+	0.840725i	$0.682129\pi$
$294$	8.37659	+	8.50053i	0.488533	+	0.495761i
$295$	20.7702	−	7.55972i	1.20929	−	0.440144i
$296$	−7.96597	−	13.9347i	−0.463013	−	0.809941i
$297$	−3.98540	+	0.277487i	−0.231257	+	0.0161014i
$298$	−11.1538	+	9.33209i	−0.646122	+	0.540593i
$299$	−2.20526	−	6.05890i	−0.127533	−	0.350395i
$300$	3.68016	−	1.67696i	0.212474	−	0.0968194i
$301$	5.76839	+	6.87450i	0.332485	+	0.396240i
$302$	−18.4576	+	21.9334i	−1.06212	+	1.26212i
$303$	5.60061	+	12.1985i	0.321747	+	0.700785i
$304$	−25.0565	+	14.2765i	−1.43709	+	0.818813i
$305$	−8.02957	+	13.9076i	−0.459772	+	0.796349i
$306$	15.8321	−	12.9309i	0.905061	−	0.739208i
$307$	2.70392	−	1.56111i	0.154321	−	0.0890972i	−0.420851	−	0.907130i	$-0.638268\pi$
$307$	2.70392	−	1.56111i	0.154321	−	0.0890972i	0.575172	+	0.818033i	$0.304935\pi$
$308$	0.773181	−	2.10560i	0.0440561	−	0.119978i
$309$	−6.01356	−	1.64953i	−0.342099	−	0.0938384i
$310$	−22.8229	+	8.27005i	−1.29626	+	0.469707i
$311$	−23.9263	−	8.70847i	−1.35674	−	0.493812i	−0.441694	−	0.897166i	$-0.645622\pi$
$311$	−23.9263	−	8.70847i	−1.35674	−	0.493812i	−0.915044	+	0.403354i	$0.867844\pi$
$312$	−12.7820	+	12.5241i	−0.723641	+	0.709035i
$313$	5.59690	−	31.7416i	0.316355	−	1.79414i	−0.248161	−	0.968719i	$-0.579826\pi$
$313$	5.59690	−	31.7416i	0.316355	−	1.79414i	0.564516	−	0.825422i	$-0.309063\pi$
$314$	−9.08754	−	3.32227i	−0.512839	−	0.187487i
$315$	1.38771	+	8.45401i	0.0781888	+	0.476329i
$316$	−26.3620	−	22.2487i	−1.48298	−	1.25159i
$317$	6.34661	−	7.56360i	0.356461	−	0.424814i	−0.557777	−	0.829991i	$-0.688346\pi$
$317$	6.34661	−	7.56360i	0.356461	−	0.424814i	0.914238	+	0.405177i	$0.132790\pi$
$318$	5.16123	+	7.48742i	0.289427	+	0.419874i
$319$	0.880781	+	4.99516i	0.0493143	+	0.279675i
$320$	15.4462	−	2.58757i	0.863471	−	0.144650i
$321$	−6.31143	−	2.98867i	−0.352270	−	0.166811i
$322$	3.15094	+	1.82519i	0.175595	+	0.101714i
$323$			34.7368i			1.93281i
$324$	−17.0718	+	5.70565i	−0.948432	+	0.316981i
$325$			4.26454i			0.236554i
$326$	7.37634	−	12.7342i	0.408538	−	0.705285i
$327$	−8.86833	−	4.19944i	−0.490420	−	0.232229i
$328$	−0.344972	+	0.935338i	−0.0190479	+	0.0516454i
$329$	0.460292	+	2.61045i	0.0253767	+	0.143919i
$330$	−3.03556	+	2.09247i	−0.167102	+	0.115187i
$331$	−8.93218	+	10.6450i	−0.490957	+	0.585100i	−0.953461	−	0.301518i	$-0.902507\pi$
$331$	−8.93218	+	10.6450i	−0.490957	+	0.585100i	0.462503	+	0.886617i	$0.346951\pi$
$332$	−8.73184	+	10.3461i	−0.479222	+	0.567819i
$333$	15.9279	+	6.01169i	0.872843	+	0.329439i
$334$	4.39234	−	12.0145i	0.240338	−	0.657406i
$335$	−2.09491	+	11.8808i	−0.114457	+	0.649120i
$336$	0.997746	−	10.0569i	0.0544315	−	0.548651i
$337$	−19.1694	−	6.97710i	−1.04423	−	0.380067i	−0.237745	−	0.971328i	$-0.576408\pi$
$337$	−19.1694	−	6.97710i	−1.04423	−	0.380067i	−0.806480	+	0.591261i	$0.798630\pi$
$338$	−0.165271	−	0.456100i	−0.00898955	−	0.0248086i
$339$	27.4281	+	7.52357i	1.48969	+	0.408624i
$340$	6.50267	−	17.7087i	0.352657	−	0.960388i
$341$	−5.83814	+	3.37065i	−0.316153	+	0.182531i
$342$	10.8418	−	28.6017i	0.586257	−	1.54660i
$343$	8.65906	−	14.9979i	0.467545	−	0.809812i
$344$	−3.09481	+	17.1230i	−0.166861	+	0.923211i
$345$	−2.49734	−	5.43938i	−0.134452	−	0.292846i
$346$	20.6532	+	17.3803i	1.11032	+	0.934372i
$347$	7.86880	+	9.37767i	0.422419	+	0.503419i	0.934719	−	0.355387i	$-0.115651\pi$
$347$	7.86880	+	9.37767i	0.422419	+	0.503419i	−0.512300	+	0.858806i	$0.671206\pi$
$348$	9.47621	+	20.7960i	0.507978	+	1.11478i
$349$	4.50680	+	12.3823i	0.241243	+	0.662811i	0.999935	+	0.0113614i	$0.00361651\pi$
$349$	4.50680	+	12.3823i	0.241243	+	0.662811i	−0.758692	+	0.651449i	$0.774161\pi$
$350$	−1.54547	−	1.84716i	−0.0826089	−	0.0987350i
$351$	1.98966	−	18.8760i	0.106200	−	1.00753i
$352$	4.09747	−	1.45837i	0.218396	−	0.0777312i
$353$	−24.6091	+	8.95698i	−1.30981	+	0.476732i	−0.900179	−	0.435519i	$-0.856565\pi$
$353$	−24.6091	+	8.95698i	−1.30981	+	0.476732i	−0.409631	+	0.912251i	$0.634343\pi$
$354$	19.6987	−	19.4115i	1.04697	−	1.03171i
$355$	9.16623	+	10.9239i	0.486493	+	0.579780i
$356$	−25.9151	−	0.0738847i	−1.37350	−	0.00391588i
$357$	−9.93040	−	7.04128i	−0.525572	−	0.372664i
$358$	22.7990	+	0.0325003i	1.20496	+	0.00171769i
$359$	4.24628	−	7.35478i	0.224110	−	0.388170i	−0.731942	−	0.681367i	$-0.761386\pi$
$359$	4.24628	−	7.35478i	0.224110	−	0.388170i	0.956052	+	0.293197i	$0.0947191\pi$
$360$	−10.8813	+	12.5515i	−0.573495	+	0.661521i
$361$	16.4889	+	28.5597i	0.867838	+	1.50314i
$362$	−11.6159	−	20.1857i	−0.610516	−	1.06094i
$363$	12.8234	−	12.6726i	0.673055	−	0.665136i
$364$	9.21388	+	5.35472i	0.482939	+	0.280664i
$365$	−0.918287	+	2.52297i	−0.0480654	+	0.132058i
$366$	−1.89820	+	20.0036i	−0.0992206	+	1.04561i
$367$	−3.37974	+	19.1675i	−0.176421	+	1.00053i	0.760070	+	0.649841i	$0.225165\pi$
$367$	−3.37974	+	19.1675i	−0.176421	+	1.00053i	−0.936491	+	0.350692i	$0.885946\pi$
$368$	1.18639	+	6.96020i	0.0618449	+	0.362825i
$369$	−0.349867	−	0.997842i	−0.0182134	−	0.0519456i
$370$	15.4766	−	2.70619i	0.804588	−	0.140688i
$371$	3.48110	−	4.14861i	0.180729	−	0.215385i
$372$	−21.6648	+	21.2881i	−1.12327	+	1.10374i
$373$	−27.4736	+	4.84433i	−1.42253	+	0.250830i	−0.831367	−	0.555723i	$-0.812441\pi$
$373$	−27.4736	+	4.84433i	−1.42253	+	0.250830i	−0.591161	+	0.806554i	$0.701330\pi$
$374$	0.917070	−	5.15796i	0.0474206	−	0.266712i
$375$	1.69935	+	20.8436i	0.0877540	+	1.07636i
$376$	−3.32053	+	3.92306i	−0.171243	+	0.202316i
$377$	−24.0982			−1.24112
$378$	5.97885	+	8.89708i	0.307519	+	0.457616i
$379$			7.33693i			0.376873i	0.982085	+	0.188436i	$0.0603419\pi$
$379$			7.33693i			0.376873i	−0.982085	+	0.188436i	$0.939658\pi$
$380$	−4.82249	−	27.8131i	−0.247388	−	1.42678i
$381$	−10.5435	−	15.2489i	−0.540158	−	0.781225i
$382$	33.6807	+	5.98834i	1.72326	+	0.306390i
$383$	3.93614	+	22.3230i	0.201128	+	1.14065i	0.903418	+	0.428761i	$0.141050\pi$
$383$	3.93614	+	22.3230i	0.201128	+	1.14065i	−0.702291	+	0.711890i	$0.747839\pi$
$384$	16.2287	−	10.9832i	0.828166	−	0.560483i
$385$	1.68194	+	1.41131i	0.0857194	+	0.0719271i
$386$	31.5445	−	5.51579i	1.60557	−	0.280746i
$387$	−9.03817	−	16.0914i	−0.459436	−	0.817973i
$388$	17.0159	−	6.13841i	0.863853	−	0.311631i
$389$	−33.6046	−	5.92539i	−1.70382	−	0.300429i	−0.764794	−	0.644275i	$-0.777159\pi$
$389$	−33.6046	−	5.92539i	−1.70382	−	0.300429i	−0.939026	+	0.343846i	$0.888270\pi$
$390$	−7.28599	−	15.9292i	−0.368941	−	0.806607i
$391$	7.99184	+	2.90879i	0.404165	+	0.147104i
$392$	13.5812	−	2.33490i	0.685956	−	0.117930i
$393$	9.76136	−	2.55374i	0.492396	−	0.128819i
$394$	−15.4569	−	26.8604i	−0.778705	−	1.35321i
$395$	29.2422	−	16.8830i	1.47133	−	0.849475i
$396$	−2.36497	+	3.96075i	−0.118844	+	0.199035i
$397$	12.4146	+	7.16758i	0.623072	+	0.359731i	0.778064	−	0.628185i	$-0.216202\pi$
$397$	12.4146	+	7.16758i	0.623072	+	0.359731i	−0.154992	+	0.987916i	$0.549535\pi$
$398$	−0.000419122		0.294014i	−2.10087e−5		0.0147376i
$399$	−18.1365	−	1.69494i	−0.907961	−	0.0848532i
$400$	0.837126	−	4.59423i	0.0418563	−	0.229712i
$401$	0.749505	−	0.628909i	0.0374285	−	0.0314062i	−0.623882	−	0.781519i	$-0.714445\pi$
$401$	0.749505	−	0.628909i	0.0374285	−	0.0314062i	0.661310	+	0.750113i	$0.270001\pi$
$402$	3.79966	+	14.6088i	0.189510	+	0.728621i
$403$	−10.9542	−	30.0965i	−0.545670	−	1.49921i
$404$	15.2560	+	2.73492i	0.759016	+	0.136067i
$405$	0.417016	−	17.6142i	0.0207217	−	0.875258i
$406$	10.4380	−	8.73319i	0.518029	−	0.433421i
$407$	4.09999	−	1.49227i	0.203229	−	0.0739693i
$408$	−1.81742	−	23.5340i	−0.0899755	−	1.16510i
$409$	−20.5361	+	17.2318i	−1.01544	+	0.852059i	−0.989048	−	0.147592i	$-0.952848\pi$
$409$	−20.5361	+	17.2318i	−1.01544	+	0.852059i	−0.0263963	+	0.999652i	$0.508403\pi$
$410$	−0.746638	−	0.628319i	−0.0368738	−	0.0310305i
$411$	−2.46244	+	26.3490i	−0.121463	+	1.29970i
$412$	−5.52896	+	4.61255i	−0.272392	+	0.227244i
$413$	−14.2631	−	8.23481i	−0.701841	−	0.405208i
$414$	−5.67248	−	4.88941i	−0.278787	−	0.240301i
$415$	−6.62597	−	11.4765i	−0.325256	−	0.563360i
$416$	3.44303	+	20.3746i	0.168809	+	0.998945i
$417$	−18.6063	+	4.86771i	−0.911153	+	0.238373i
$418$	−2.67062	−	7.37013i	−0.130624	−	0.360485i
$419$	0.646349	−	1.77583i	0.0315762	−	0.0867550i	−0.922903	−	0.385033i	$-0.874190\pi$
$419$	0.646349	−	1.77583i	0.0315762	−	0.0867550i	0.954479	+	0.298278i	$0.0964123\pi$
$420$	8.92863	+	4.25920i	0.435673	+	0.207828i
$421$	−4.73822	−	0.835477i	−0.230927	−	0.0407186i	0.0569871	−	0.998375i	$-0.481851\pi$
$421$	−4.73822	−	0.835477i	−0.230927	−	0.0407186i	−0.287914	+	0.957656i	$0.592962\pi$
$422$	−15.1058	−	5.52247i	−0.735340	−	0.268830i
$423$	0.0645179	−	5.45107i	0.00313697	−	0.265040i
$424$	10.5007	+	0.0449069i	0.509958	+	0.00218087i
$425$	−4.30903	−	3.61571i	−0.209019	−	0.175388i
$426$	16.1150	+	7.65912i	0.780775	+	0.371085i
$427$	11.7843	−	2.07789i	0.570281	−	0.100556i
$428$	−6.99475	+	4.01188i	−0.338104	+	0.193921i
$429$	−2.76647	−	4.00112i	−0.133566	−	0.193176i
$430$	−14.7382	−	8.53717i	−0.710741	−	0.411699i
$431$	20.5298			0.988886			0.494443	−	0.869210i	$-0.335372\pi$
$431$	20.5298			0.988886			0.494443	+	0.869210i	$0.335372\pi$
$432$	−5.84882	+	19.9447i	−0.281402	+	0.959590i
$433$	3.08517			0.148264			0.0741319	−	0.997248i	$-0.476381\pi$
$433$	3.08517			0.148264			0.0741319	+	0.997248i	$0.476381\pi$
$434$	15.6517	+	9.06632i	0.751308	+	0.435197i
$435$	−22.2957	+	1.81774i	−1.06900	+	0.0871542i
$436$	−9.82848	+	5.63717i	−0.470699	+	0.269972i
$437$	12.5326	−	2.20984i	0.599516	−	0.105711i
$438$	0.268207	+	3.34866i	0.0128154	+	0.160005i
$439$	−15.9614	−	13.3932i	−0.761798	−	0.639224i	0.176796	−	0.984247i	$-0.443427\pi$
$439$	−15.9614	−	13.3932i	−0.761798	−	0.639224i	−0.938594	+	0.345023i	$0.887871\pi$
$440$	−0.0182062	+	4.25720i	−0.000867947	+	0.202954i
$441$	−9.52710	+	11.0848i	−0.453671	+	0.527850i
$442$	23.3767	+	8.54617i	1.11191	+	0.406500i
$443$	−13.3206	−	2.34878i	−0.632881	−	0.111594i	−0.152001	−	0.988380i	$-0.548572\pi$
$443$	−13.3206	−	2.34878i	−0.632881	−	0.111594i	−0.480880	+	0.876786i	$0.659683\pi$
$444$	16.2014	−	11.1339i	0.768886	−	0.528393i
$445$	8.67598	−	23.8371i	0.411281	−	1.12998i
$446$	−4.93583	−	13.6215i	−0.233718	−	0.644995i
$447$	−12.5197	−	12.6688i	−0.592164	−	0.599214i
$448$	−8.87507	−	7.57736i	−0.419308	−	0.357997i
$449$	−7.60426	−	13.1710i	−0.358867	−	0.621576i	0.628905	−	0.777482i	$-0.283504\pi$
$449$	−7.60426	−	13.1710i	−0.358867	−	0.621576i	−0.987772	+	0.155906i	$0.950170\pi$
$450$	2.41948	+	4.32202i	0.114055	+	0.203742i
$451$	−0.234687	−	0.135497i	−0.0110510	−	0.00638029i
$452$	25.2178	−	21.0380i	1.18615	−	0.989547i
$453$	−28.6399	−	20.3075i	−1.34562	−	0.954129i
$454$	2.48540	+	2.09154i	0.116645	+	0.0981609i
$455$	−7.99091	+	6.70517i	−0.374619	+	0.314343i
$456$	−19.9625	−	29.1371i	−0.934828	−	1.36447i
$457$	9.11474	−	3.31749i	0.426370	−	0.155186i	−0.119918	−	0.992784i	$-0.538263\pi$
$457$	9.11474	−	3.31749i	0.426370	−	0.155186i	0.546287	+	0.837598i	$0.316041\pi$
$458$	6.92590	−	5.79472i	0.323626	−	0.270769i
$459$	17.3860	+	18.0145i	0.811507	+	0.840844i
$460$	−6.80276	−	1.21952i	−0.317180	−	0.0568603i
$461$	−9.46327	−	26.0001i	−0.440748	−	1.21095i	−0.939001	−	0.343914i	$-0.888247\pi$
$461$	−9.46327	−	26.0001i	−0.440748	−	1.21095i	0.498253	−	0.867032i	$-0.333975\pi$
$462$	2.64829	+	0.730490i	0.123209	+	0.0339855i
$463$	−8.78407	+	7.37071i	−0.408230	+	0.342546i	−0.823665	−	0.567077i	$-0.808074\pi$
$463$	−8.78407	+	7.37071i	−0.408230	+	0.342546i	0.415434	+	0.909623i	$0.363630\pi$
$464$	25.9612	+	4.73045i	1.20522	+	0.219606i
$465$	−12.4051	−	27.0191i	−0.575273	−	1.25298i
$466$	−0.0295748	+	20.7467i	−0.00137002	+	0.961073i
$467$	12.4672	+	7.19795i	0.576914	+	0.333081i	0.759906	−	0.650033i	$-0.225245\pi$
$467$	12.4672	+	7.19795i	0.576914	+	0.333081i	−0.182992	+	0.983114i	$0.558578\pi$
$468$	−16.5806	−	14.3329i	−0.766438	−	0.662540i
$469$	7.78495	−	4.49464i	0.359476	−	0.207543i
$470$	−2.50926	−	4.36050i	−0.115743	−	0.201135i
$471$	3.13478	−	11.4282i	0.144443	−	0.526585i
$472$	−5.41078	−	31.4725i	−0.249051	−	1.44864i
$473$	−4.44469	−	1.61774i	−0.204367	−	0.0743836i
$474$	24.4863	−	34.4291i	1.12469	−	1.58138i
$475$	−8.28907	−	1.46159i	−0.380329	−	0.0670622i
$476$	−13.2226	+	4.76998i	−0.606057	+	0.218632i
$477$	−8.61615	+	7.05773i	−0.394506	+	0.323151i
$478$	−6.51754	+	1.13964i	−0.298105	+	0.0521259i
$479$	29.9827	+	25.1585i	1.36994	+	1.14952i	0.972769	+	0.231777i	$0.0744541\pi$
$479$	29.9827	+	25.1585i	1.36994	+	1.14952i	0.397176	+	0.917743i	$0.369990\pi$
$480$	4.72238	+	18.5909i	0.215546	+	0.848555i
$481$	3.59960	+	20.4143i	0.164128	+	0.930813i
$482$	−25.8973	−	4.60446i	−1.17959	−	0.209727i
$483$	−1.90867	+	4.03071i	−0.0868475	+	0.183404i
$484$	−3.55650	−	20.5117i	−0.161659	−	0.932350i
$485$			17.7066i			0.804014i
$486$	−8.69276	−	20.2592i	−0.394312	−	0.918977i
$487$	10.3483			0.468925			0.234463	−	0.972125i	$-0.424667\pi$
$487$	10.3483			0.468925			0.234463	+	0.972125i	$0.424667\pi$
$488$	17.7098	+	14.9898i	0.801684	+	0.678557i
$489$	16.2897	+	7.71372i	0.736648	+	0.348826i
$490$	−2.36126	+	13.2806i	−0.106671	+	0.599958i
$491$	11.1737	−	1.97022i	0.504261	−	0.0889147i	0.0842695	−	0.996443i	$-0.473144\pi$
$491$	11.1737	−	1.97022i	0.504261	−	0.0889147i	0.419991	+	0.907528i	$0.362033\pi$
$492$	−1.17656	−	0.326343i	−0.0530435	−	0.0147127i
$493$	20.4317	−	24.3496i	0.920198	−	1.09665i
$494$	36.6869	−	6.41499i	1.65062	−	0.288624i
$495$	−2.86136	−	3.49317i	−0.128608	−	0.157006i
$496$	5.89318	+	34.5736i	0.264612	+	1.55240i
$497$	1.84511	−	10.4642i	0.0827646	−	0.469381i
$498$	−13.5122	−	9.60999i	−0.605497	−	0.430634i
$499$	−0.767687	+	2.10920i	−0.0343664	+	0.0944208i	−0.955689	−	0.294378i	$-0.904888\pi$
$499$	−0.767687	+	2.10920i	−0.0343664	+	0.0944208i	0.921323	+	0.388799i	$0.127110\pi$
$500$	20.8782	+	12.1335i	0.933702	+	0.542628i
$501$	15.1091	+	4.14446i	0.675026	+	0.185161i
$502$	−2.82948	−	4.91697i	−0.126286	−	0.219455i
$503$	−11.9050	−	20.6201i	−0.530819	−	0.919405i	−0.999353	−	0.0359597i	$-0.988551\pi$
$503$	−11.9050	−	20.6201i	−0.530819	−	0.919405i	0.468535	−	0.883445i	$-0.344782\pi$
$504$	12.3760	+	0.199418i	0.551273	+	0.00888277i
$505$	−7.58566	+	13.1388i	−0.337557	+	0.584667i
$506$	−1.91927	−	0.00273595i	−0.0853219	−	0.000121628i
$507$	0.539958	−	0.247907i	0.0239804	−	0.0110099i
$508$	−21.4069	−	0.0610318i	−0.949777	−	0.00270785i
$509$	2.40142	+	2.86190i	0.106441	+	0.126851i	0.816635	−	0.577155i	$-0.195837\pi$
$509$	2.40142	+	2.86190i	0.106441	+	0.126851i	−0.710194	+	0.704006i	$0.751393\pi$
$510$	22.2728	+	6.14363i	0.986258	+	0.272045i
$511$	1.87993	−	0.684239i	0.0831633	−	0.0302689i
$512$	0.290293	−	22.6256i	0.0128293	−	0.999918i
$513$	36.0077	+	10.3367i	1.58978	+	0.456377i
$514$	18.9404	+	22.6378i	0.835425	+	0.998508i
$515$	−2.41056	−	6.62296i	−0.106222	−	0.291843i
$516$	−21.2129	−	2.04347i	−0.933846	−	0.0899588i
$517$	−0.898047	−	1.07025i	−0.0394961	−	0.0470696i
$518$	−8.95730	−	7.53785i	−0.393561	−	0.331194i
$519$	−19.1222	+	26.9683i	−0.839372	+	1.18378i
$520$	−19.9038	−	3.59740i	−0.872837	−	0.157756i
$521$	2.47837	−	4.29266i	0.108579	−	0.188065i	−0.806616	−	0.591076i	$-0.798703\pi$
$521$	2.47837	−	4.29266i	0.108579	−	0.188065i	0.915195	+	0.403011i	$0.132037\pi$
$522$	−24.4230	+	13.6720i	−1.06896	+	0.598409i
$523$	16.9347	−	9.77726i	0.740503	−	0.427530i	−0.0817489	−	0.996653i	$-0.526051\pi$
$523$	16.9347	−	9.77726i	0.740503	−	0.427530i	0.822252	+	0.569123i	$0.192717\pi$
$524$	4.01600	−	10.9368i	0.175440	−	0.477775i
$525$	2.09806	−	2.07337i	0.0915668	−	0.0904895i
$526$	4.72446	+	13.0381i	0.205996	+	0.568490i
$527$	39.6981	+	14.4489i	1.72928	+	0.629405i
$528$	2.19493	+	4.85349i	0.0955220	+	0.211221i
$529$	−3.45286	+	19.5822i	−0.150125	+	0.851399i
$530$	−3.52926	+	9.65371i	−0.153301	+	0.419330i
$531$	25.6875	+	22.0777i	1.11474	+	0.958088i
$532$	−13.5659	+	16.0740i	−0.588158	+	0.696895i
$533$	0.827586	−	0.986279i	0.0358467	−	0.0427205i
$534$	−2.53402	−	31.6381i	−0.109658	−	1.36912i
$535$	−1.37060	−	7.77309i	−0.0592564	−	0.336060i
$536$	16.3532	+	6.03141i	0.706352	+	0.260517i
$537$	2.26900	+	27.8306i	0.0979144	+	1.20098i
$538$	−20.7998	+	35.9081i	−0.896744	+	1.54811i
$539$			3.74593i			0.161349i
$540$	−16.4216	−	12.0102i	−0.706672	−	0.516837i
$541$			4.60230i			0.197869i	0.995094	+	0.0989343i	$0.0315434\pi$
$541$			4.60230i			0.197869i	−0.995094	+	0.0989343i	$0.968457\pi$
$542$	−8.67861	−	5.02711i	−0.372778	−	0.215933i
$543$	23.4614	−	16.2218i	1.00683	−	0.696144i
$544$	−23.5063	−	13.7957i	−1.00782	−	0.591485i
$545$	−1.92587	−	10.9221i	−0.0824951	−	0.467853i
$546$	−5.60270	+	11.7882i	−0.239773	+	0.504490i
$547$	−25.7121	+	30.6425i	−1.09937	+	1.31018i	−0.152594	+	0.988289i	$0.548763\pi$
$547$	−25.7121	+	30.6425i	−1.09937	+	1.31018i	−0.946777	+	0.321891i	$0.895682\pi$
$548$	23.3525	+	19.7088i	0.997569	+	0.841918i
$549$	−24.6077	−	0.291252i	−1.05023	−	0.0124303i
$550$	1.19223	+	0.435863i	0.0508370	+	0.0185852i
$551$	8.25917	−	46.8401i	0.351852	−	1.99545i
$552$	−8.37515	+	2.15285i	−0.356470	+	0.0916315i
$553$	−23.6425	−	8.60518i	−1.00538	−	0.365929i
$554$	−12.2384	+	4.43468i	−0.519962	+	0.188412i
$555$	4.87023	+	18.6159i	0.206730	+	0.790201i
$556$	−7.65497	+	20.8467i	−0.324643	+	0.884098i
$557$	−8.50694	+	4.91149i	−0.360451	+	0.208106i	−0.669278	−	0.743012i	$-0.733397\pi$
$557$	−8.50694	+	4.91149i	−0.360451	+	0.208106i	0.308828	+	0.951118i	$0.400063\pi$
$558$	−28.1770	−	24.2873i	−1.19283	−	1.02816i
$559$	11.2360	−	19.4614i	0.475233	−	0.823128i
$560$	9.92489	−	5.65493i	0.419403	−	0.238964i
$561$	6.38842	+	0.597028i	0.269719	+	0.0252065i
$562$	11.9487	−	14.1988i	0.504026	−	0.598939i
$563$	−23.6333	−	28.1650i	−0.996023	−	1.18701i	−0.982339	−	0.187108i	$-0.940089\pi$
$563$	−23.6333	−	28.1650i	−0.996023	−	1.18701i	−0.0136839	−	0.999906i	$-0.504356\pi$
$564$	−5.12454	−	3.65562i	−0.215782	−	0.153930i
$565$	10.9947	+	30.2076i	0.462549	+	1.27084i
$566$	−23.3846	+	19.5653i	−0.982929	+	0.822391i
$567$	−10.2539	+	8.19843i	−0.430624	+	0.344302i
$568$	17.8864	−	10.2250i	0.750497	−	0.429031i
$569$	−23.9481	+	8.71638i	−1.00395	+	0.365410i	−0.791108	−	0.611676i	$-0.790496\pi$
$569$	−23.9481	+	8.71638i	−1.00395	+	0.365410i	−0.212846	+	0.977086i	$0.568273\pi$
$570$	33.4590	−	8.70250i	1.40144	−	0.364508i
$571$	−6.05835	−	7.22006i	−0.253534	−	0.302150i	0.624233	−	0.781238i	$-0.285412\pi$
$571$	−6.05835	−	7.22006i	−0.253534	−	0.302150i	−0.877767	+	0.479089i	$0.840967\pi$
$572$	−5.61689	−	0.0160140i	−0.234854	−	0.000669577i
$573$	−3.89851	+	41.7155i	−0.162863	+	1.74269i
$574$	−0.00103652	+	0.727118i	−4.32634e−5	+	0.0303493i
$575$	−1.03038	+	1.78467i	−0.0429697	+	0.0744257i
$576$	15.0489	+	18.6958i	0.627037	+	0.778990i
$577$	−9.02461	−	15.6311i	−0.375699	−	0.650730i	0.614732	−	0.788736i	$-0.289264\pi$
$577$	−9.02461	−	15.6311i	−0.375699	−	0.650730i	−0.990431	+	0.138006i	$0.955931\pi$
$578$	−7.61753	+	4.38351i	−0.316847	+	0.182330i
$579$	9.92655	+	37.9431i	0.412533	+	1.57686i
$580$	−12.9789	+	22.3328i	−0.538919	+	0.927319i
$581$	−3.37723	+	9.27886i	−0.140111	+	0.384952i
$582$	9.21531	+	20.1472i	0.381987	+	0.835130i
$583$	−0.495664	+	2.81105i	−0.0205283	+	0.116422i
$584$	3.35106	+	1.95389i	0.138668	+	0.0808526i
$585$	18.7046	−	10.5059i	0.773341	−	0.434368i
$586$	2.46829	+	14.1160i	0.101964	+	0.583126i
$587$	5.58607	−	6.65722i	0.230562	−	0.274773i	−0.638343	−	0.769752i	$-0.720380\pi$
$587$	5.58607	−	6.65722i	0.230562	−	0.274773i	0.868905	+	0.494979i	$0.164824\pi$
$588$	4.22512	+	16.3402i	0.174241	+	0.673857i
$589$	62.2535	−	10.9770i	2.56511	−	0.452298i
$590$	30.7759	+	5.47187i	1.26702	+	0.225273i
$591$	31.2193	−	21.5858i	1.28419	−	0.887922i
$592$	0.129433	−	22.6991i	0.00531967	−	0.932929i
$593$	42.5626			1.74783			0.873917	−	0.486075i	$-0.161572\pi$
$593$	42.5626			1.74783			0.873917	+	0.486075i	$0.161572\pi$
$594$	−5.07378	−	2.48549i	−0.208180	−	0.101981i
$595$		−	13.7593i		−	0.564075i
$596$	−20.2644	+	3.51362i	−0.830061	+	0.143923i
$597$	−0.358902	+	0.0292608i	−0.0146889	+	0.00119757i
$598$	1.59621	−	8.97770i	0.0652739	−	0.367125i
$599$	1.29608	+	7.35045i	0.0529565	+	0.300331i	0.999770	−	0.0214519i	$-0.00682887\pi$
$599$	1.29608	+	7.35045i	0.0529565	+	0.300331i	−0.946813	+	0.321783i	$0.895718\pi$
$600$	5.69227	+	0.556535i	0.232386	+	0.0227204i
$601$	0.911576	+	0.764903i	0.0371840	+	0.0312011i	0.661190	−	0.750218i	$-0.270052\pi$
$601$	0.911576	+	0.764903i	0.0371840	+	0.0312011i	−0.624006	+	0.781419i	$0.714496\pi$
$602$	2.18598	+	12.5015i	0.0890940	+	0.509524i
$603$	−17.4460	+	6.11700i	−0.710457	+	0.249103i
$604$	−38.1348	+	13.7569i	−1.55168	+	0.559761i
$605$	20.0677	+	3.53848i	0.815869	+	0.143860i
$606$	−1.79326	+	18.8977i	−0.0728462	+	0.767668i
$607$	−7.43872	−	2.70747i	−0.301928	−	0.109893i	0.186613	−	0.982433i	$-0.440249\pi$
$607$	−7.43872	−	2.70747i	−0.301928	−	0.109893i	−0.488542	+	0.872540i	$0.662471\pi$
$608$	−40.7824	−	0.290685i	−1.65395	−	0.0117888i
$609$	11.7163	+	11.8558i	0.474767	+	0.480420i
$610$	−19.6845	+	11.3275i	−0.797003	+	0.458636i
$611$	5.74843	−	3.31886i	0.232557	−	0.134267i
$612$	28.5404	−	4.60134i	1.15368	−	0.185998i
$613$	13.9051	+	8.02810i	0.561621	+	0.324252i	0.753796	−	0.657109i	$-0.228221\pi$
$613$	13.9051	+	8.02810i	0.561621	+	0.324252i	−0.192175	+	0.981361i	$0.561554\pi$
$614$	4.41548	+	0.00629433i	0.178194	+	0.000254018i
$615$	0.691290	−	0.974935i	0.0278755	−	0.0393132i
$616$	2.43873	−	2.02863i	0.0982591	−	0.0817357i
$617$	−1.02353	+	0.858846i	−0.0412059	+	0.0345758i	−0.663158	−	0.748479i	$-0.730784\pi$
$617$	−1.02353	+	0.858846i	−0.0412059	+	0.0345758i	0.621952	+	0.783055i	$0.286340\pi$
$618$	−6.18973	−	6.28131i	−0.248987	−	0.252671i
$619$	−16.1849	−	44.4676i	−0.650526	−	1.78731i	−0.615792	−	0.787909i	$-0.711164\pi$
$619$	−16.1849	−	44.4676i	−0.650526	−	1.78731i	−0.0347344	−	0.999397i	$-0.511059\pi$
$620$	−33.7915	−	6.05774i	−1.35710	−	0.243285i
$621$	5.39337	−	7.41867i	0.216429	−	0.297701i
$622$	−23.1065	−	27.6171i	−0.926486	−	1.10734i
$623$	−17.7616	+	6.46469i	−0.711603	+	0.259002i
$624$	−24.5195	+	6.26556i	−0.981568	+	0.250823i
$625$	−13.6353	+	11.4414i	−0.545414	+	0.457656i
$626$	29.3492	−	34.8759i	1.17303	−	1.39392i
$627$	8.72519	−	4.00594i	0.348451	−	0.159982i
$628$	−8.76575	−	10.5073i	−0.349791	−	0.419287i
$629$	−23.6792	−	13.6712i	−0.944152	−	0.545107i
$630$	−4.29444	+	11.3292i	−0.171095	+	0.451364i
$631$	−11.3526	−	19.6633i	−0.451941	−	0.782785i	0.546565	−	0.837417i	$-0.315935\pi$
$631$	−11.3526	−	19.6633i	−0.451941	−	0.782785i	−0.998507	+	0.0546311i	$0.982602\pi$
$632$	−16.4891	−	45.9133i	−0.655900	−	1.82633i
$633$	5.21082	−	18.9967i	0.207111	−	0.755049i
$634$	13.1280	−	4.75704i	0.521381	−	0.188926i
$635$	7.16671	−	19.6904i	0.284402	−	0.781388i
$636$	1.00851	+	12.8212i	0.0399899	+	0.508392i
$637$	−17.5266	−	3.09042i	−0.694430	−	0.122447i
$638$	−2.46298	+	6.73709i	−0.0975104	+	0.266724i
$639$	−7.71651	+	20.4448i	−0.305261	+	0.808783i
$640$	20.7363	+	7.78260i	0.819675	+	0.307634i
$641$	−13.5874	−	11.4012i	−0.536669	−	0.450319i	0.333728	−	0.942670i	$-0.391693\pi$
$641$	−13.5874	−	11.4012i	−0.536669	−	0.450319i	−0.870397	+	0.492350i	$0.836138\pi$
$642$	−5.60500	−	8.13121i	−0.221212	−	0.320913i
$643$	−7.39349	+	1.30367i	−0.291571	+	0.0514118i	−0.317520	−	0.948251i	$-0.602850\pi$
$643$	−7.39349	+	1.30367i	−0.291571	+	0.0514118i	0.0259495	+	0.999663i	$0.491739\pi$
$644$	2.56213	+	4.46710i	0.100962	+	0.176029i
$645$	8.92763	−	18.8533i	0.351525	−	0.742347i
$646$	−24.6232	+	42.5086i	−0.968788	+	1.67248i
$647$	3.82983			0.150566			0.0752831	−	0.997162i	$-0.476014\pi$
$647$	3.82983			0.150566			0.0752831	+	0.997162i	$0.476014\pi$
$648$	−24.9358	−	5.11915i	−0.979571	−	0.201099i
$649$	8.68064			0.340745
$650$	−3.02293	+	5.21867i	−0.118569	+	0.204693i
$651$	−9.48098	+	20.0218i	−0.371589	+	0.784718i
$652$	18.0534	−	10.3546i	0.707025	−	0.405518i
$653$	−46.6926	+	8.23316i	−1.82722	+	0.322189i	−0.978436	−	0.206548i	$-0.933777\pi$
$653$	−46.6926	+	8.23316i	−1.82722	+	0.322189i	−0.848786	+	0.528737i	$0.822666\pi$
$654$	−7.87571	−	11.4253i	−0.307965	−	0.446766i
$655$	8.73620	+	7.33054i	0.341351	+	0.286428i
$656$	−1.08517	+	0.900073i	−0.0423688	+	0.0351419i
$657$	−4.06005	+	0.666452i	−0.158398	+	0.0260008i
$658$	−1.28714	+	3.52077i	−0.0501781	+	0.137254i
$659$	−9.03959	−	1.59392i	−0.352132	−	0.0620904i	−0.00521573	−	0.999986i	$-0.501660\pi$
$659$	−9.03959	−	1.59392i	−0.352132	−	0.0620904i	−0.346917	+	0.937896i	$0.612771\pi$
$660$	−5.19798	+	0.408870i	−0.202331	+	0.0159152i
$661$	−1.72239	+	4.73222i	−0.0669932	+	0.184062i	−0.968672	−	0.248345i	$-0.920113\pi$
$661$	−1.72239	+	4.73222i	−0.0669932	+	0.184062i	0.901679	+	0.432407i	$0.142336\pi$
$662$	−18.4763	+	6.69502i	−0.718103	+	0.260209i
$663$	−8.06388	+	29.3978i	−0.313175	+	1.14172i
$664$	−18.0193	+	6.47137i	−0.699286	+	0.251138i
$665$	−10.2942	−	17.8301i	−0.399193	−	0.691423i
$666$	15.2301	+	18.6472i	0.590155	+	0.722566i
$667$	−10.0848	−	5.82248i	−0.390486	−	0.225447i
$668$	13.8916	−	11.5891i	0.537481	−	0.448395i
$669$	16.1259	−	7.40376i	0.623463	−	0.286246i
$670$	−10.9854	+	13.0540i	−0.424402	+	0.504321i
$671$	−4.83141	+	4.05404i	−0.186515	+	0.156504i
$672$	8.34986	−	11.5998i	0.322103	−	0.447471i
$673$	20.4837	−	7.45546i	0.789589	−	0.287387i	0.0844237	−	0.996430i	$-0.473095\pi$
$673$	20.4837	−	7.45546i	0.789589	−	0.287387i	0.705165	+	0.709043i	$0.250873\pi$
$674$	−18.5126	−	22.1264i	−0.713078	−	0.852277i
$675$	−5.03025	+	3.39075i	−0.193614	+	0.130510i
$676$	0.121059	−	0.675298i	0.00465613	−	0.0259730i
$677$	3.09363	+	8.49967i	0.118898	+	0.326669i	0.984837	−	0.173480i	$-0.0555010\pi$
$677$	3.09363	+	8.49967i	0.118898	+	0.326669i	−0.865940	+	0.500148i	$0.833279\pi$
$678$	28.2316	+	28.6493i	1.08423	+	1.10027i
$679$	10.1069	−	8.48068i	0.387867	−	0.325459i
$680$	20.5104	−	17.0613i	0.786537	−	0.654272i
$681$	−2.30116	+	3.24535i	−0.0881806	+	0.124362i
$682$	−9.53363	−	0.0135903i	−0.365062	−	0.000520401i
$683$	−25.4905	−	14.7170i	−0.975367	−	0.563129i	−0.0744991	−	0.997221i	$-0.523736\pi$
$683$	−25.4905	−	14.7170i	−0.975367	−	0.563129i	−0.900868	+	0.434092i	$0.857069\pi$
$684$	33.5419	−	27.3157i	1.28250	−	1.04444i
$685$	−25.9039	+	14.9556i	−0.989736	+	0.571425i
$686$	21.2277	−	12.2155i	0.810478	−	0.466391i
$687$	7.77408	+	7.86664i	0.296600	+	0.300131i
$688$	−15.9249	+	18.7603i	−0.607132	+	0.715229i
$689$	−12.7435	−	4.63826i	−0.485490	−	0.176704i
$690$	0.799625	−	8.42661i	0.0304412	−	0.320795i
$691$	25.6679	+	4.52594i	0.976452	+	0.172175i	0.639033	−	0.769180i	$-0.279335\pi$
$691$	25.6679	+	4.52594i	0.976452	+	0.172175i	0.337419	+	0.941354i	$0.390446\pi$
$692$	12.9540	+	35.9090i	0.492436	+	1.36505i
$693$	−0.623431	+	3.30634i	−0.0236822	+	0.125597i
$694$	2.98195	+	17.0536i	0.113193	+	0.647346i
$695$	−16.6522	−	13.9728i	−0.631654	−	0.530020i
$696$	−3.14488	+	32.1660i	−0.119206	+	1.21925i
$697$	0.294896	+	1.67244i	0.0111700	+	0.0633481i
$698$	−3.26211	+	18.3473i	−0.123473	+	0.694457i
$699$	−25.3254	+	2.06475i	−0.957896	+	0.0780961i
$700$	−0.581884	−	3.35595i	−0.0219931	−	0.126843i
$701$			8.19846i			0.309652i	0.987942	+	0.154826i	$0.0494816\pi$
$701$			8.19846i			0.309652i	−0.987942	+	0.154826i	$0.950518\pi$
$702$	15.8151	−	21.6888i	0.596903	−	0.818593i
$703$	−40.9134			−1.54308
$704$	6.04798	+	1.11984i	0.227942	+	0.0422056i
$705$	5.06813	−	3.50423i	0.190877	−	0.131977i
$706$	−36.4642	−	6.48324i	−1.37235	−	0.244000i
$707$	11.1328	−	1.96301i	0.418692	−	0.0738266i
$708$	37.8659	−	9.79109i	1.42309	−	0.367972i
$709$	27.3414	−	32.5842i	1.02683	−	1.22372i	0.0524923	−	0.998621i	$-0.483284\pi$
$709$	27.3414	−	32.5842i	1.02683	−	1.22372i	0.974335	−	0.225104i	$-0.0722720\pi$
$710$	3.47363	+	19.8655i	0.130363	+	0.745537i
$711$	44.5020	+	26.4004i	1.66896	+	0.990092i
$712$	−31.6608	−	18.4604i	−1.18654	−	0.691831i
$713$	2.68754	−	15.2418i	0.100649	−	0.570809i
$714$	−7.16096	−	15.6558i	−0.267992	−	0.585905i
$715$	1.88045	−	5.16650i	0.0703249	−	0.193216i
$716$	27.8769	+	16.2009i	1.04181	+	0.605455i
$717$	−2.05097	−	7.83959i	−0.0765948	−	0.292775i
$718$	10.4098	−	5.99032i	0.388489	−	0.223557i
$719$	1.78626	+	3.09390i	0.0666164	+	0.115383i	0.897410	−	0.441198i	$-0.145446\pi$
$719$	1.78626	+	3.09390i	0.0666164	+	0.115383i	−0.830793	+	0.556581i	$0.812113\pi$
$720$	−22.2130	+	7.64645i	−0.827829	+	0.284966i
$721$	−2.62582	+	4.54806i	−0.0977908	+	0.169379i
$722$	−0.0664827	+	46.6377i	−0.00247423	+	1.73567i
$723$	2.99758	−	32.0752i	0.111481	−	1.19289i
$724$	0.0939013	−	32.9359i	0.00348981	−	1.22405i
$725$	4.95074	+	5.90006i	0.183866	+	0.219123i
$726$	24.6754	−	6.41794i	0.915792	−	0.238192i
$727$	37.9414	−	13.8096i	1.40717	−	0.512168i	0.476872	−	0.878973i	$-0.341771\pi$
$727$	37.9414	−	13.8096i	1.40717	−	0.512168i	0.930298	+	0.366805i	$0.119548\pi$
$728$	7.47965	+	13.0840i	0.277214	+	0.484927i
$729$	23.8472	−	12.6614i	0.883229	−	0.468942i
$730$	−2.91216	+	2.43652i	−0.107784	+	0.0901798i
$731$	10.1379	+	27.8536i	0.374963	+	1.03020i
$732$	−16.5025	+	23.1336i	−0.609950	+	0.855043i
$733$	6.40625	+	7.63467i	0.236620	+	0.281993i	0.871267	−	0.490809i	$-0.163299\pi$
$733$	6.40625	+	7.63467i	0.236620	+	0.281993i	−0.634647	+	0.772802i	$0.718854\pi$
$734$	−17.7228	+	21.0602i	−0.654160	+	0.777345i
$735$	−16.4488	−	1.53722i	−0.606724	−	0.0567012i
$736$	−3.48192	+	9.35842i	−0.128345	+	0.344956i
$737$	−2.36899	+	4.10321i	−0.0872629	+	0.151144i
$738$	0.279177	−	1.46910i	0.0102767	−	0.0540783i
$739$	8.10394	−	4.67881i	0.298108	−	0.172113i	−0.343484	−	0.939158i	$-0.611607\pi$
$739$	8.10394	−	4.67881i	0.298108	−	0.172113i	0.641593	+	0.767045i	$0.278274\pi$
$740$	20.8575	+	7.65893i	0.766737	+	0.281548i
$741$	11.5448	+	44.1287i	0.424109	+	1.62111i
$742$	7.20069	−	2.60922i	0.264346	−	0.0957874i
$743$	−2.25694	−	0.821460i	−0.0827992	−	0.0301364i	0.300288	−	0.953848i	$-0.402917\pi$
$743$	−2.25694	−	0.821460i	−0.0827992	−	0.0301364i	−0.383088	+	0.923712i	$0.625139\pi$
$744$	−41.6021	+	10.6939i	−1.52521	+	0.392058i
$745$	3.49581	−	19.8257i	0.128077	−	0.726359i
$746$	−37.0543	−	13.5465i	−1.35666	−	0.495973i
$747$	10.3612	−	17.4655i	0.379097	−	0.639028i
$748$	4.77848	−	5.66191i	0.174719	−	0.207020i
$749$	−3.78041	+	4.50532i	−0.138133	+	0.164621i
$750$	−12.6954	+	26.7116i	−0.463572	+	0.975369i
$751$	1.65762	+	9.40083i	0.0604874	+	0.343041i	1.00000		0.000526413i	$0.000167562\pi$
$751$	1.65762	+	9.40083i	0.0604874	+	0.343041i	−0.939512	+	0.342515i	$0.888721\pi$
$752$	−6.84432	+	2.44702i	−0.249587	+	0.0892338i
$753$	5.71490	−	3.95143i	0.208263	−	0.143998i
$754$	−29.4898	−	17.0820i	−1.07396	−	0.622091i
$755$		−	39.6825i		−	1.44420i
$756$	1.00982	+	15.1258i	0.0367268	+	0.550120i
$757$		−	23.4437i		−	0.852075i	−0.904706	−	0.426037i	$-0.859909\pi$
$757$		−	23.4437i		−	0.852075i	0.904706	−	0.426037i	$-0.140091\pi$
$758$	−5.20080	+	8.97846i	−0.188901	+	0.326112i
$759$	−0.191009	−	2.34284i	−0.00693319	−	0.0850399i
$760$	13.8139	−	37.4544i	0.501085	−	1.35861i
$761$	5.09011	+	28.8674i	0.184516	+	1.04644i	0.926575	+	0.376109i	$0.122738\pi$
$761$	5.09011	+	28.8674i	0.184516	+	1.04644i	−0.742059	+	0.670334i	$0.766151\pi$
$762$	−2.09321	−	26.1344i	−0.0758288	−	0.946749i
$763$	−5.31193	+	6.33052i	−0.192305	+	0.229180i
$764$	36.9715	+	31.2028i	1.33758	+	1.12888i
$765$	−5.24323	+	27.8073i	−0.189570	+	1.00537i
$766$	−11.0069	+	30.1076i	−0.397695	+	1.08783i
$767$	−7.16158	+	40.6153i	−0.258590	+	1.46654i
$768$	27.6451	−	1.93678i	0.997555	−	0.0698877i
$769$	29.5782	+	10.7656i	1.06662	+	0.388217i	0.814911	−	0.579587i	$-0.196786\pi$
$769$	29.5782	+	10.7656i	1.06662	+	0.388217i	0.251707	+	0.967804i	$0.419008\pi$
$770$	1.05783	+	2.91932i	0.0381217	+	0.105205i
$771$	−25.7126	+	25.4101i	−0.926017	+	0.915122i
$772$	42.5120	+	15.6105i	1.53004	+	0.561834i
$773$	30.7452	−	17.7508i	1.10583	−	0.638450i	0.168083	−	0.985773i	$-0.446242\pi$
$773$	30.7452	−	17.7508i	1.10583	−	0.638450i	0.937746	+	0.347323i	$0.112909\pi$
$774$	0.346105	−	26.0984i	0.0124405	−	0.938087i
$775$	−5.11822	+	8.86501i	−0.183852	+	0.318441i
$776$	25.1742	+	4.54999i	0.903702	+	0.163335i
$777$	8.29331	−	11.6961i	0.297521	−	0.419597i
$778$	−36.9229	−	31.0718i	−1.32375	−	1.11398i
$779$	1.63341	+	1.94662i	0.0585230	+	0.0697450i
$780$	2.37533	−	24.6578i	0.0850503	−	0.882892i
$781$	1.91546	+	5.26268i	0.0685405	+	0.188313i
$782$	7.71800	+	9.22463i	0.275995	+	0.329872i
$783$	−19.1605	−	28.4250i	−0.684742	−	1.01583i
$784$	18.2749	+	6.76979i	0.652676	+	0.241778i
$785$	12.5864	−	4.58106i	0.449226	−	0.163505i
$786$	13.7555	+	3.79426i	0.490644	+	0.135337i
$787$	11.6599	+	13.8958i	0.415632	+	0.495331i	0.932720	−	0.360601i	$-0.117428\pi$
$787$	11.6599	+	13.8958i	0.415632	+	0.495331i	−0.517088	+	0.855932i	$0.672984\pi$
$788$	0.124951	−	43.8267i	0.00445121	−	1.56126i
$789$	−15.4353	+	7.08671i	−0.549512	+	0.252294i
$790$	47.7522	+	0.0680715i	1.69895	+	0.00242188i
$791$	11.9765	−	20.7439i	0.425835	−	0.737568i
$792$	−5.70168	+	3.17050i	−0.202600	+	0.112659i
$793$	−14.9822	−	25.9500i	−0.532035	−	0.921512i
$794$	10.1115	+	17.5714i	0.358842	+	0.623584i
$795$	−12.1402	−	3.33009i	−0.430570	−	0.118106i
$796$	−0.208925	+	0.359498i	−0.00740516	+	0.0127421i
$797$	−1.32902	+	3.65146i	−0.0470764	+	0.129341i	−0.961003	−	0.276539i	$-0.910813\pi$
$797$	−1.32902	+	3.65146i	−0.0470764	+	0.129341i	0.913926	+	0.405880i	$0.133035\pi$
$798$	−20.9928	−	14.9303i	−0.743138	−	0.528525i
$799$	−1.52034	+	8.62230i	−0.0537859	+	0.305035i
$800$	4.28105	−	5.02873i	0.151358	−	0.177792i
$801$	38.3594	−	6.29664i	1.35536	−	0.222481i
$802$	1.36300	−	0.238331i	0.0481292	−	0.00841575i
$803$	−0.677785	+	0.807753i	−0.0239185	+	0.0285050i
$804$	−5.70569	+	20.5707i	−0.201224	+	0.725473i
$805$	−4.96418	+	0.875318i	−0.174964	+	0.0308509i
$806$	7.92889	−	44.5951i	0.279283	−	1.57080i
$807$	−45.9339	−	21.7512i	−1.61695	−	0.765677i
$808$	16.7307	+	14.1611i	0.588584	+	0.498186i
$809$	−3.93026			−0.138181			−0.0690904	−	0.997610i	$-0.522010\pi$
$809$	−3.93026			−0.138181			−0.0690904	+	0.997610i	$0.522010\pi$
$810$	12.9962	−	21.2596i	0.456640	−	0.746985i
$811$		−	25.0834i		−	0.880798i	−0.897802	−	0.440399i	$-0.854837\pi$
$811$		−	25.0834i		−	0.880798i	0.897802	−	0.440399i	$-0.145163\pi$
$812$	18.9639	−	3.28812i	0.665501	−	0.115390i
$813$	5.25703	−	11.1017i	0.184372	−	0.389355i
$814$	6.07511	+	1.08014i	0.212932	+	0.0378588i
$815$	3.53752	+	20.0623i	0.123914	+	0.702750i
$816$	14.4581	−	30.0876i	0.506133	−	1.05328i
$817$	33.9765	+	28.5097i	1.18869	+	0.997427i
$818$	−37.3456	+	6.53015i	−1.30576	+	0.228321i
$819$	−14.9555	−	5.64468i	−0.522588	−	0.197241i
$820$	−0.468302	−	1.29815i	−0.0163538	−	0.0453335i
$821$	−26.3780	−	4.65115i	−0.920598	−	0.162326i	−0.306786	−	0.951779i	$-0.599254\pi$
$821$	−26.3780	−	4.65115i	−0.920598	−	0.162326i	−0.613812	+	0.789452i	$0.710365\pi$
$822$	−21.6909	+	30.4987i	−0.756557	+	1.06376i
$823$	38.4958	+	14.0113i	1.34188	+	0.488404i	0.910404	−	0.413721i	$-0.135771\pi$
$823$	38.4958	+	14.0113i	1.34188	+	0.488404i	0.431475	+	0.902125i	$0.357993\pi$
$824$	−10.0356	+	1.72533i	−0.349607	+	0.0601047i
$825$	−0.411265	+	1.49932i	−0.0143184	+	0.0521995i
$826$	−11.6170	−	20.1877i	−0.404207	−	0.702418i
$827$	8.94467	−	5.16421i	0.311037	−	0.179577i	−0.336354	−	0.941736i	$-0.609194\pi$
$827$	8.94467	−	5.16421i	0.311037	−	0.179577i	0.647390	+	0.762159i	$0.275860\pi$
$828$	−3.47575	−	10.0043i	−0.120791	−	0.347673i
$829$	−7.72702	−	4.46120i	−0.268370	−	0.154944i	0.359776	−	0.933039i	$-0.382853\pi$
$829$	−7.72702	−	4.46120i	−0.268370	−	0.154944i	−0.628147	+	0.778095i	$0.716186\pi$
$830$	0.0267157	−	18.7411i	0.000927314	−	0.650512i
$831$	−6.65204	−	14.4886i	−0.230757	−	0.502603i
$832$	−10.2292	+	27.3737i	−0.354633	+	0.949011i
$833$	17.9827	−	15.0892i	0.623062	−	0.522811i
$834$	−26.2197	−	7.23230i	−0.907912	−	0.250434i
$835$	6.05656	+	16.6403i	0.209596	+	0.575860i
$836$	1.95620	−	10.9122i	0.0676567	−	0.377405i
$837$	26.7906	−	36.8509i	0.926020	−	1.27375i
$838$	2.04976	−	1.71498i	0.0708078	−	0.0592430i
$839$	−53.9056	+	19.6200i	−1.86103	+	0.677359i	−0.882828	+	0.469696i	$0.844364\pi$
$839$	−53.9056	+	19.6200i	−1.86103	+	0.677359i	−0.978200	+	0.207664i	$0.933414\pi$
$840$	7.90714	+	11.5412i	0.272822	+	0.398210i
$841$	−11.1249	+	9.33490i	−0.383617	+	0.321893i
$842$	−5.20610	−	4.38110i	−0.179414	−	0.150983i
$843$	18.5403	+	13.1462i	0.638561	+	0.452780i
$844$	−14.5709	−	17.4658i	−0.501552	−	0.601199i
$845$	0.581578	+	0.335774i	0.0200069	+	0.0115510i
$846$	3.94296	−	6.62494i	0.135562	−	0.227770i
$847$	−7.59182	−	13.1494i	−0.260858	−	0.451819i
$848$	12.8182	+	7.49838i	0.440180	+	0.257495i
$849$	−26.2484	−	26.5609i	−0.900843	−	0.911569i
$850$	−2.71011	−	7.47914i	−0.0929562	−	0.256532i
$851$	−3.42601	+	9.41289i	−0.117442	+	0.322670i
$852$	14.2913	+	20.7959i	0.489613	+	0.712455i
$853$	6.55578	+	1.15596i	0.224466	+	0.0395793i	0.284750	−	0.958602i	$-0.408090\pi$
$853$	6.55578	+	1.15596i	0.224466	+	0.0395793i	−0.0602840	+	0.998181i	$0.519201\pi$
$854$	15.8938	+	5.81053i	0.543873	+	0.198832i
$855$	14.0100	+	39.9572i	0.479131	+	1.36651i
$856$	−11.4036	−	0.0487681i	−0.389765	−	0.00166686i
$857$	−17.5716	−	14.7443i	−0.600234	−	0.503656i	0.291287	−	0.956636i	$-0.405916\pi$
$857$	−17.5716	−	14.7443i	−0.600234	−	0.503656i	−0.891521	+	0.452980i	$0.850361\pi$
$858$	−0.549230	−	6.85733i	−0.0187504	−	0.234105i
$859$	−9.67774	+	1.70645i	−0.330200	+	0.0582232i	−0.336291	−	0.941758i	$-0.609172\pi$
$859$	−9.67774	+	1.70645i	−0.330200	+	0.0582232i	0.00609046	+	0.999981i	$0.498061\pi$
$860$	−11.9841	−	20.8945i	−0.408655	−	0.712495i
$861$	−0.887590	+	0.0723641i	−0.0302490	+	0.00246616i
$862$	25.1230	+	14.5526i	0.855694	+	0.495663i
$863$	4.02004			0.136844			0.0684218	−	0.997656i	$-0.478204\pi$
$863$	4.02004			0.136844			0.0684218	+	0.997656i	$0.478204\pi$
$864$	−21.2953	+	20.2611i	−0.724479	+	0.689297i
$865$	−37.3664			−1.27050
$866$	3.77543	+	2.18693i	0.128294	+	0.0743149i
$867$	−6.12167	−	8.85370i	−0.207903	−	0.300687i
$868$	12.7269	+	22.1895i	0.431980	+	0.753162i
$869$	13.0596	−	2.30275i	0.443015	−	0.0781155i
$870$	−28.5726	−	13.5799i	−0.968702	−	0.460403i
$871$	−17.2439	−	14.4693i	−0.584286	−	0.490274i
$872$	−16.0234	−	0.0685251i	−0.542620	−	0.00232055i
$873$	−23.6576	+	13.2879i	−0.800688	+	0.449728i
$874$	16.9030	+	6.17951i	0.571754	+	0.209025i
$875$	17.3450	+	3.05838i	0.586367	+	0.103392i
$876$	−2.04549	+	4.28800i	−0.0691107	+	0.144878i
$877$	−8.74616	+	24.0299i	−0.295337	+	0.811431i	0.699926	+	0.714215i	$0.253216\pi$
$877$	−8.74616	+	24.0299i	−0.295337	+	0.811431i	−0.995263	+	0.0972163i	$0.969006\pi$
$878$	−10.0388	−	27.7041i	−0.338792	−	0.934968i
$879$	−16.9794	+	4.44208i	−0.572700	+	0.149828i
$880$	−3.04001	+	5.19679i	−0.102479	+	0.175184i
$881$	14.2403	+	24.6649i	0.479768	+	0.830982i	0.999731	−	0.0232066i	$-0.00738755\pi$
$881$	14.2403	+	24.6649i	0.479768	+	0.830982i	−0.519963	+	0.854189i	$0.674054\pi$
$882$	−19.5162	+	6.81161i	−0.657143	+	0.229359i
$883$	13.9721	+	8.06678i	0.470198	+	0.271469i	0.716323	−	0.697769i	$-0.245824\pi$
$883$	13.9721	+	8.06678i	0.470198	+	0.271469i	−0.246125	+	0.969238i	$0.579157\pi$
$884$	22.5489	+	27.0288i	0.758401	+	0.909079i
$885$	−3.56228	+	38.1177i	−0.119745	+	1.28131i
$886$	−14.6360	−	12.3166i	−0.491705	−	0.413785i
$887$	−24.5247	+	20.5787i	−0.823459	+	0.690964i	−0.953779	−	0.300508i	$-0.902844\pi$
$887$	−24.5247	+	20.5787i	−0.823459	+	0.690964i	0.130320	+	0.991472i	$0.458399\pi$
$888$	27.7186	−	2.14057i	0.930175	−	0.0718330i
$889$	−14.6718	+	5.34009i	−0.492076	+	0.179101i
$890$	27.5140	−	23.0203i	0.922273	−	0.771641i
$891$	2.51989	−	6.44449i	0.0844195	−	0.215899i
$892$	3.61545	−	20.1678i	0.121054	−	0.675269i
$893$	4.48076	+	12.3108i	0.149943	+	0.411965i
$894$	−6.34055	−	24.3779i	−0.212060	−	0.815320i
$895$	−24.1767	+	20.2867i	−0.808139	+	0.678110i
$896$	−5.48951	−	15.5638i	−0.183392	−	0.519950i
$897$	11.1194	+	1.03916i	0.371265	+	0.0346965i
$898$	0.0306601	−	21.5081i	0.00102314	−	0.717733i
$899$	−50.0946	−	28.9221i	−1.67075	−	0.964607i
$900$	−0.102871	+	7.00406i	−0.00342904	+	0.233469i
$901$	15.4913	−	8.94390i	0.516090	−	0.297964i
$902$	−0.191148	−	0.332171i	−0.00636453	−	0.0110601i
$903$	−15.0374	+	3.93403i	−0.500413	+	0.130916i
$904$	45.7728	−	7.86930i	1.52238	−	0.261729i
$905$	30.2949	+	11.0264i	1.00704	+	0.366531i
$906$	−20.6526	−	45.1524i	−0.686138	−	1.50009i
$907$	41.9059	+	7.38913i	1.39146	+	0.245352i	0.818630	−	0.574321i	$-0.194734\pi$
$907$	41.9059	+	7.38913i	1.39146	+	0.245352i	0.572831	+	0.819673i	$0.305845\pi$
$908$	1.55888	+	4.32127i	0.0517331	+	0.143406i
$909$	−23.2472	−	0.275150i	−0.771062	−	0.00912615i
$910$	−14.5317	+	2.54098i	−0.481722	+	0.0842327i
$911$	−12.0851	−	10.1406i	−0.400397	−	0.335973i	0.420250	−	0.907408i	$-0.361942\pi$
$911$	−12.0851	−	10.1406i	−0.400397	−	0.335973i	−0.820647	+	0.571435i	$0.806387\pi$
$912$	−3.77490	−	49.8065i	−0.125000	−	1.64926i
$913$	−0.903748	−	5.12541i	−0.0299097	−	0.169626i
$914$	13.5056	+	2.40127i	0.446727	+	0.0794268i
$915$	−15.8191	−	22.8789i	−0.522962	−	0.756354i
$916$	12.5831	−	2.18176i	0.415756	−	0.0720875i
$917$		−	8.49762i		−	0.280616i
$918$	8.50622	+	34.3690i	0.280747	+	1.13435i
$919$	7.16323			0.236293			0.118147	−	0.992996i	$-0.462305\pi$
$919$	7.16323			0.236293			0.118147	+	0.992996i	$0.462305\pi$
$920$	−7.46032	−	6.31452i	−0.245959	−	0.208183i
$921$	0.439436	+	5.38996i	0.0144799	+	0.177605i
$922$	6.84970	−	38.5253i	0.225583	−	1.26876i
$923$	−26.2035	+	4.62038i	−0.862499	+	0.152082i
$924$	2.72299	+	2.77117i	0.0895799	+	0.0911648i
$925$	4.25862	−	5.07523i	0.140023	−	0.166873i
$926$	−15.9741	+	2.79320i	−0.524942	+	0.0917901i
$927$	7.03988	−	8.19094i	0.231220	−	0.269026i
$928$	28.4164	+	24.1915i	0.932815	+	0.794123i
$929$	−3.55403	+	20.1559i	−0.116604	+	0.661294i	0.869340	+	0.494215i	$0.164545\pi$
$929$	−3.55403	+	20.1559i	−0.116604	+	0.661294i	−0.985944	+	0.167079i	$0.946567\pi$
$930$	3.97200	−	41.8577i	0.130247	−	1.37257i
$931$	12.0138	−	33.0076i	0.393736	−	1.08178i
$932$	−14.7425	+	25.3675i	−0.482908	+	0.830941i
$933$	31.3683	−	30.9992i	1.02695	−	1.01487i
$934$	10.1543	+	17.6458i	0.332259	+	0.577388i
$935$	3.62605	+	6.28050i	0.118584	+	0.205394i
$936$	−10.1303	−	29.2929i	−0.331120	−	0.957469i
$937$	11.3098	−	19.5891i	0.369475	−	0.639949i	−0.620009	−	0.784595i	$-0.712871\pi$
$937$	11.3098	−	19.5891i	0.369475	−	0.639949i	0.989483	+	0.144646i	$0.0462044\pi$
$938$	12.7128	+	0.0181222i	0.415086	+	0.000591711i
$939$	45.5398	+	32.2906i	1.48614	+	1.05376i
$940$	0.0202845	−	7.11479i	0.000661608	−	0.232059i
$941$	−5.01971	−	5.98225i	−0.163638	−	0.195016i	0.677994	−	0.735067i	$-0.262849\pi$
$941$	−5.01971	−	5.98225i	−0.163638	−	0.195016i	−0.841632	+	0.540051i	$0.818405\pi$
$942$	11.9371	−	11.7630i	0.388931	−	0.383260i
$943$	0.584635	−	0.212790i	0.0190383	−	0.00692939i
$944$	15.6880	−	42.3495i	0.510600	−	1.37836i
$945$	−14.2627	−	4.09438i	−0.463965	−	0.133190i
$946$	−4.29239	−	5.13031i	−0.139558	−	0.166801i
$947$	6.07943	+	16.7031i	0.197555	+	0.542778i	0.998428	−	0.0560568i	$-0.0178528\pi$
$947$	6.07943	+	16.7031i	0.197555	+	0.542778i	−0.800873	+	0.598835i	$0.795631\pi$
$948$	54.3699	−	24.7750i	1.76585	−	0.804655i
$949$	−3.22017	−	3.83765i	−0.104531	−	0.124575i
$950$	−9.10759	−	7.66432i	−0.295489	−	0.248663i
$951$	7.13558	+	15.5418i	0.231387	+	0.503976i
$952$	−19.5622	−	3.53567i	−0.634014	−	0.114592i
$953$	17.3067	−	29.9761i	0.560620	−	0.971022i	−0.436822	−	0.899548i	$-0.643896\pi$
$953$	17.3067	−	29.9761i	0.560620	−	0.971022i	0.997442	−	0.0714747i	$-0.0227705\pi$
$954$	−15.5468	+	2.52923i	−0.503345	+	0.0818868i
$955$	−41.0108	+	23.6776i	−1.32708	+	0.766189i
$956$	−8.78358	−	3.22535i	−0.284081	−	0.104315i
$957$	−8.47238	−	2.32399i	−0.273873	−	0.0751239i
$958$	18.8573	+	52.0406i	0.609251	+	1.68136i
$959$	20.9435	+	7.62281i	0.676301	+	0.246153i
$960$	−7.39927	+	26.0978i	−0.238810	+	0.842304i
$961$	7.96677	−	45.1818i	0.256993	−	1.45748i
$962$	−10.0658	+	27.5333i	−0.324534	+	0.887710i
$963$	9.35698	−	7.66457i	0.301525	−	0.246987i
$964$	−28.4275	−	23.9920i	−0.915589	−	0.772729i
$965$	−28.4943	+	33.9582i	−0.917264	+	1.09315i
$966$	−5.19288	+	3.57956i	−0.167078	+	0.115170i
$967$	0.884011	+	5.01348i	0.0284279	+	0.161223i	0.995717	−	0.0924542i	$-0.0294712\pi$
$967$	0.884011	+	5.01348i	0.0284279	+	0.161223i	−0.967289	+	0.253677i	$0.918360\pi$
$968$	10.1875	−	27.6219i	0.327440	−	0.887802i
$969$	−54.3774	−	25.7494i	−1.74685	−	0.827191i
$970$	−12.5513	+	21.6682i	−0.402999	+	0.695722i
$971$			26.0152i			0.834868i	0.908707	+	0.417434i	$0.137071\pi$
$971$			26.0152i			0.834868i	−0.908707	+	0.417434i	$0.862929\pi$
$972$	3.72315	−	30.9538i	0.119420	−	0.992844i
$973$			16.1974i			0.519266i
$974$	12.6636	+	7.33540i	0.405767	+	0.235041i
$975$	−6.67577	−	3.16119i	−0.213796	−	0.101239i
$976$	11.0465	+	30.8972i	0.353591	+	0.988995i
$977$	3.98395	+	22.5941i	0.127458	+	0.722850i	0.979818	+	0.199894i	$0.0640598\pi$
$977$	3.98395	+	22.5941i	0.127458	+	0.722850i	−0.852360	+	0.522956i	$0.824829\pi$
$978$	14.4665	+	20.9866i	0.462586	+	0.671076i
$979$	6.40371	−	7.63165i	0.204664	−	0.243909i
$980$	−12.3036	+	14.5782i	−0.393023	+	0.465684i
$981$	13.1477	−	10.7697i	0.419774	−	0.343849i
$982$	15.0702	+	5.50945i	0.480910	+	0.175814i
$983$	−0.658420	+	3.73409i	−0.0210003	+	0.119099i	−0.993506	−	0.113781i	$-0.963704\pi$
$983$	−0.658420	+	3.73409i	−0.0210003	+	0.119099i	0.972506	+	0.232880i	$0.0748149\pi$
$984$	−1.20847	−	1.23336i	−0.0385247	−	0.0393182i
$985$	40.3124	+	14.6725i	1.28446	+	0.467505i
$986$	42.2633	−	15.3144i	1.34594	−	0.487709i
$987$	−4.42763	−	1.21451i	−0.140933	−	0.0386581i
$988$	49.4424	+	18.1554i	1.57297	+	0.577599i
$989$	9.40431	−	5.42958i	0.299040	−	0.172651i
$990$	−1.02540	−	6.30300i	−0.0325895	−	0.200322i
$991$	−10.0747	+	17.4499i	−0.320034	+	0.554315i	−0.980495	−	0.196545i	$-0.937028\pi$
$991$	−10.0747	+	17.4499i	−0.320034	+	0.554315i	0.660461	+	0.750861i	$0.270361\pi$
$992$	−17.2958	+	46.4863i	−0.549143	+	1.47594i
$993$	−10.0426	−	21.8734i	−0.318691	−	0.694130i
$994$	9.67547	−	11.4974i	0.306887	−	0.364677i
$995$	−0.261616	−	0.311782i	−0.00829378	−	0.00988414i
$996$	−9.72331	−	21.3382i	−0.308095	−	0.676128i
$997$	10.2918	+	28.2764i	0.325944	+	0.895524i	0.989127	+	0.147066i	$0.0469830\pi$
$997$	10.2918	+	28.2764i	0.325944	+	0.895524i	−0.663183	+	0.748458i	$0.730795\pi$
$998$	−2.43456	+	2.03693i	−0.0770646	+	0.0644779i
$999$	−21.2177	+	20.4774i	−0.671298	+	0.647876i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.61.29	yes	204
3.2	odd	2		648.2.t.a.181.6		204
4.3	odd	2		864.2.bf.a.817.23		204
8.3	odd	2		864.2.bf.a.817.12		204
8.5	even	2	inner	216.2.t.a.61.22	✓	204
24.5	odd	2		648.2.t.a.181.13		204
27.4	even	9	inner	216.2.t.a.85.22	yes	204
27.23	odd	18		648.2.t.a.469.13		204
108.31	odd	18		864.2.bf.a.625.12		204
216.77	odd	18		648.2.t.a.469.6		204
216.85	even	18	inner	216.2.t.a.85.29	yes	204
216.139	odd	18		864.2.bf.a.625.23		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.61.22	✓	204	8.5	even	2	inner
216.2.t.a.61.29	yes	204	1.1	even	1	trivial
216.2.t.a.85.22	yes	204	27.4	even	9	inner
216.2.t.a.85.29	yes	204	216.85	even	18	inner
648.2.t.a.181.6		204	3.2	odd	2
648.2.t.a.181.13		204	24.5	odd	2
648.2.t.a.469.6		204	216.77	odd	18
648.2.t.a.469.13		204	27.23	odd	18
864.2.bf.a.625.12		204	108.31	odd	18
864.2.bf.a.625.23		204	216.139	odd	18
864.2.bf.a.817.12		204	8.3	odd	2
864.2.bf.a.817.23		204	4.3	odd	2

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22374 + 0.708852i) q^{2} +(-0.741273 + 1.56541i) q^{3} +(0.995058 + 1.73489i) q^{4} +(-1.92794 + 0.339948i) q^{5} +(-2.01677 + 1.39020i) q^{6} +(1.11744 + 0.937647i) q^{7} +(-0.0120958 + 2.82840i) q^{8} +(-1.90103 - 2.32079i) q^{9} +O(q^{10})\)	\(q+(1.22374 + 0.708852i) q^{2} +(-0.741273 + 1.56541i) q^{3} +(0.995058 + 1.73489i) q^{4} +(-1.92794 + 0.339948i) q^{5} +(-2.01677 + 1.39020i) q^{6} +(1.11744 + 0.937647i) q^{7} +(-0.0120958 + 2.82840i) q^{8} +(-1.90103 - 2.32079i) q^{9} +(-2.60027 - 0.950619i) q^{10} +(-0.757167 - 0.133509i) q^{11} +(-3.45343 + 0.271645i) q^{12} +(1.24934 - 3.43252i) q^{13} +(0.702804 + 1.93954i) q^{14} +(0.896973 - 3.27002i) q^{15} +(-2.01972 + 3.45264i) q^{16} +(2.40908 + 4.17264i) q^{17} +(-0.681258 - 4.18759i) q^{18} +(6.24367 + 3.60478i) q^{19} +(-2.50819 - 3.00651i) q^{20} +(-2.29614 + 1.05421i) q^{21} +(-0.831935 - 0.700099i) q^{22} +(1.35218 - 1.13461i) q^{23} +(-4.41865 - 2.11555i) q^{24} +(-1.09706 + 0.399298i) q^{25} +(3.96200 - 3.31490i) q^{26} +(5.04218 - 1.25555i) q^{27} +(-0.514797 + 2.87166i) q^{28} +(-2.25636 - 6.19930i) q^{29} +(3.41562 - 3.36582i) q^{30} +(6.71672 - 5.63600i) q^{31} +(-4.91901 + 2.79344i) q^{32} +(0.770264 - 1.08631i) q^{33} +(-0.00971330 + 6.81389i) q^{34} +(-2.47312 - 1.42786i) q^{35} +(2.13470 - 5.60741i) q^{36} +(-4.91459 + 2.83744i) q^{37} +(5.08534 + 8.83714i) q^{38} +(4.44721 + 4.50016i) q^{39} +(-0.938191 - 5.45711i) q^{40} +(0.331211 + 0.120551i) q^{41} +(-3.55714 - 0.337547i) q^{42} +(6.05852 + 1.06828i) q^{43} +(-0.521801 - 1.44646i) q^{44} +(4.45403 + 3.82811i) q^{45} +(2.45899 - 0.429972i) q^{46} +(1.39202 + 1.16804i) q^{47} +(-3.90764 - 5.72104i) q^{48} +(-0.846037 - 4.79812i) q^{49} +(-1.62556 - 0.289019i) q^{50} +(-8.31768 + 0.678130i) q^{51} +(7.19822 - 1.24809i) q^{52} -3.71259i q^{53} +(7.06030 + 2.03770i) q^{54} +1.50516 q^{55} +(-2.66556 + 3.14924i) q^{56} +(-10.2712 + 7.10178i) q^{57} +(1.63320 - 9.18573i) q^{58} +(-11.1189 + 1.96057i) q^{59} +(6.56568 - 1.69771i) q^{60} +(5.27287 - 6.28396i) q^{61} +(12.2146 - 2.13581i) q^{62} +(0.0517918 - 4.37585i) q^{63} +(-7.99971 - 0.0684238i) q^{64} +(-1.24177 + 7.04241i) q^{65} +(1.71263 - 0.783356i) q^{66} +(2.10768 - 5.79080i) q^{67} +(-4.84192 + 8.33151i) q^{68} +(0.773804 + 2.95778i) q^{69} +(-2.01431 - 3.50040i) q^{70} +(-3.64209 - 6.30828i) q^{71} +(6.58713 - 5.34880i) q^{72} +(0.685732 - 1.18772i) q^{73} +(-8.02548 - 0.0114404i) q^{74} +(0.188156 - 2.01334i) q^{75} +(-0.0411093 + 14.4191i) q^{76} +(-0.720908 - 0.859145i) q^{77} +(2.25226 + 8.65942i) q^{78} +(-16.2077 + 5.89913i) q^{79} +(2.72019 - 7.34310i) q^{80} +(-1.77217 + 8.82380i) q^{81} +(0.319862 + 0.382302i) q^{82} +(2.31520 + 6.36096i) q^{83} +(-4.11373 - 2.93455i) q^{84} +(-6.06304 - 7.22565i) q^{85} +(6.65678 + 5.60189i) q^{86} +(11.3770 + 1.06324i) q^{87} +(0.386776 - 2.13996i) q^{88} +(-6.47879 + 11.2216i) q^{89} +(2.73699 + 7.84184i) q^{90} +(4.61456 - 2.66421i) q^{91} +(3.31394 + 1.21688i) q^{92} +(3.84374 + 14.6922i) q^{93} +(0.875494 + 2.41611i) q^{94} +(-13.2629 - 4.82729i) q^{95} +(-0.726549 - 9.77098i) q^{96} +(1.57059 - 8.90723i) q^{97} +(2.36583 - 6.47134i) q^{98} +(1.12955 + 2.01103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

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