LMFDB - Embedded newform 216.2.t.a.13.30

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			13.30
Character	$\chi$	$=$	216.13
Dual form			216.2.t.a.133.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24074 - 0.678648i) q^{2} +(0.479138 + 1.66446i) q^{3} +(1.07887 - 1.68405i) q^{4} +(-2.25773 + 2.69066i) q^{5} +(1.72407 + 1.74000i) q^{6} +(3.36848 + 1.22603i) q^{7} +(0.195724 - 2.82165i) q^{8} +(-2.54085 + 1.59501i) q^{9} +O(q^{10})$	\(q+(1.24074 - 0.678648i) q^{2} +(0.479138 + 1.66446i) q^{3} +(1.07887 - 1.68405i) q^{4} +(-2.25773 + 2.69066i) q^{5} +(1.72407 + 1.74000i) q^{6} +(3.36848 + 1.22603i) q^{7} +(0.195724 - 2.82165i) q^{8} +(-2.54085 + 1.59501i) q^{9} +(-0.975248 + 4.87061i) q^{10} +(-1.86181 - 2.21882i) q^{11} +(3.31997 + 0.988849i) q^{12} +(1.53462 + 0.270594i) q^{13} +(5.01146 - 0.764832i) q^{14} +(-5.56026 - 2.46871i) q^{15} +(-1.67206 - 3.63376i) q^{16} +(3.86560 - 6.69542i) q^{17} +(-2.07009 + 3.70334i) q^{18} +(0.847303 - 0.489191i) q^{19} +(2.09540 + 6.70502i) q^{20} +(-0.426706 + 6.19414i) q^{21} +(-3.81583 - 1.48947i) q^{22} +(-6.90160 + 2.51198i) q^{23} +(4.79030 - 1.02618i) q^{24} +(-1.27406 - 7.22553i) q^{25} +(2.08770 - 0.705728i) q^{26} +(-3.87225 - 3.46492i) q^{27} +(5.69886 - 4.34997i) q^{28} +(5.11578 - 0.902050i) q^{29} +(-8.57422 + 0.710435i) q^{30} +(-2.11811 + 0.770928i) q^{31} +(-4.54064 - 3.37381i) q^{32} +(2.80108 - 4.16204i) q^{33} +(0.252376 - 10.9307i) q^{34} +(-10.9040 + 6.29540i) q^{35} +(-0.0551779 + 5.99975i) q^{36} +(-0.179911 - 0.103872i) q^{37} +(0.719295 - 1.18198i) q^{38} +(0.284900 + 2.68396i) q^{39} +(7.15020 + 6.89715i) q^{40} +(-1.00198 + 5.68249i) q^{41} +(3.67421 + 7.97491i) q^{42} +(-2.62405 - 3.12722i) q^{43} +(-5.74527 + 0.741561i) q^{44} +(1.44493 - 10.4377i) q^{45} +(-6.85834 + 7.80046i) q^{46} +(1.96476 + 0.715114i) q^{47} +(5.24710 - 4.52415i) q^{48} +(4.48123 + 3.76020i) q^{49} +(-6.48436 - 8.10037i) q^{50} +(12.9964 + 3.22611i) q^{51} +(2.11135 - 2.29244i) q^{52} -3.19246i q^{53} +(-7.15592 - 1.67117i) q^{54} +10.1736 q^{55} +(4.11871 - 9.26471i) q^{56} +(1.22021 + 1.17591i) q^{57} +(5.73518 - 4.59103i) q^{58} +(2.41918 - 2.88307i) q^{59} +(-10.1562 + 6.70034i) q^{60} +(-2.94263 + 8.08481i) q^{61} +(-2.10483 + 2.39397i) q^{62} +(-10.5144 + 2.25761i) q^{63} +(-7.92338 - 1.10453i) q^{64} +(-4.19283 + 3.51820i) q^{65} +(0.650851 - 7.06495i) q^{66} +(-2.94730 - 0.519689i) q^{67} +(-7.10494 - 13.7334i) q^{68} +(-7.48790 - 10.2838i) q^{69} +(-9.25662 + 15.2109i) q^{70} +(-4.82588 + 8.35866i) q^{71} +(4.00325 + 7.48157i) q^{72} +(1.70348 + 2.95051i) q^{73} +(-0.293715 - 0.00678153i) q^{74} +(11.4162 - 5.58264i) q^{75} +(0.0903106 - 1.95468i) q^{76} +(-3.55115 - 9.75670i) q^{77} +(2.17495 + 3.13675i) q^{78} +(-0.447375 - 2.53719i) q^{79} +(13.5523 + 3.70510i) q^{80} +(3.91188 - 8.10538i) q^{81} +(2.61322 + 7.73049i) q^{82} +(-6.28878 + 1.10888i) q^{83} +(9.97090 + 7.40129i) q^{84} +(9.28760 + 25.5175i) q^{85} +(-5.37805 - 2.09926i) q^{86} +(3.95259 + 8.08281i) q^{87} +(-6.62514 + 4.81910i) q^{88} +(4.56318 + 7.90366i) q^{89} +(-5.29072 - 13.9311i) q^{90} +(4.83758 + 2.79298i) q^{91} +(-3.21565 + 14.3328i) q^{92} +(-2.29804 - 3.15612i) q^{93} +(2.92307 - 0.446109i) q^{94} +(-0.596737 + 3.38427i) q^{95} +(3.43998 - 9.17423i) q^{96} +(7.10870 - 5.96491i) q^{97} +(8.11189 + 1.62425i) q^{98} +(8.26964 + 2.66809i) 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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	1.24074	−	0.678648i	0.877336	−	0.479877i
$2$	1.24074	−	0.678648i	0.877336	−	0.479877i
$3$	0.479138	+	1.66446i	0.276630	+	0.960976i
$3$	0.479138	+	1.66446i	0.276630	+	0.960976i
$4$	1.07887	−	1.68405i	0.539437	−	0.842026i
$5$	−2.25773	+	2.69066i	−1.00969	+	1.20330i	−0.0306692	+	0.999530i	$0.509764\pi$
$5$	−2.25773	+	2.69066i	−1.00969	+	1.20330i	−0.979019	+	0.203770i	$0.934681\pi$
$6$	1.72407	+	1.74000i	0.703848	+	0.710351i
$7$	3.36848	+	1.22603i	1.27317	+	0.463395i	0.888167	−	0.459521i	$-0.151979\pi$
$7$	3.36848	+	1.22603i	1.27317	+	0.463395i	0.385001	+	0.922916i	$0.374201\pi$
$8$	0.195724	−	2.82165i	0.0691988	−	0.997603i
$9$	−2.54085	+	1.59501i	−0.846951	+	0.531671i
$10$	−0.975248	+	4.87061i	−0.308400	+	1.54022i
$11$	−1.86181	−	2.21882i	−0.561358	−	0.669000i	0.408475	−	0.912769i	$-0.366061\pi$
$11$	−1.86181	−	2.21882i	−0.561358	−	0.669000i	−0.969833	+	0.243769i	$0.921616\pi$
$12$	3.31997	+	0.988849i	0.958392	+	0.285456i
$13$	1.53462	+	0.270594i	0.425626	+	0.0750494i	0.382358	−	0.924014i	$-0.375112\pi$
$13$	1.53462	+	0.270594i	0.425626	+	0.0750494i	0.0432679	+	0.999064i	$0.486223\pi$
$14$	5.01146	−	0.764832i	1.33937	−	0.204410i
$15$	−5.56026	−	2.46871i	−1.43565	−	0.637417i
$16$	−1.67206	−	3.63376i	−0.418016	−	0.908440i
$17$	3.86560	−	6.69542i	0.937546	−	1.62388i	0.167516	−	0.985869i	$-0.446425\pi$
$17$	3.86560	−	6.69542i	0.937546	−	1.62388i	0.770030	−	0.638008i	$-0.220241\pi$
$18$	−2.07009	+	3.70334i	−0.487925	+	0.872886i
$19$	0.847303	−	0.489191i	0.194385	−	0.112228i	−0.399649	−	0.916668i	$-0.630868\pi$
$19$	0.847303	−	0.489191i	0.194385	−	0.112228i	0.594034	+	0.804440i	$0.297535\pi$
$20$	2.09540	+	6.70502i	0.468546	+	1.49929i
$21$	−0.426706	+	6.19414i	−0.0931149	+	1.35167i
$22$	−3.81583	−	1.48947i	−0.813537	−	0.317555i
$23$	−6.90160	+	2.51198i	−1.43908	+	0.523783i	−0.939520	−	0.342495i	$-0.888728\pi$
$23$	−6.90160	+	2.51198i	−1.43908	+	0.523783i	−0.499563	+	0.866278i	$0.666506\pi$
$24$	4.79030	−	1.02618i	0.977815	−	0.209469i
$25$	−1.27406	−	7.22553i	−0.254811	−	1.44511i
$26$	2.08770	−	0.705728i	0.409432	−	0.138405i
$27$	−3.87225	−	3.46492i	−0.745215	−	0.666824i
$28$	5.69886	−	4.34997i	1.07698	−	0.822068i
$29$	5.11578	−	0.902050i	0.949977	−	0.167507i	0.322873	−	0.946442i	$-0.395351\pi$
$29$	5.11578	−	0.902050i	0.949977	−	0.167507i	0.627104	+	0.778936i	$0.284240\pi$
$30$	−8.57422	+	0.710435i	−1.56543	+	0.129707i
$31$	−2.11811	+	0.770928i	−0.380423	+	0.138463i	−0.525152	−	0.851009i	$-0.675991\pi$
$31$	−2.11811	+	0.770928i	−0.380423	+	0.138463i	0.144728	+	0.989471i	$0.453769\pi$
$32$	−4.54064	−	3.37381i	−0.802679	−	0.596411i
$33$	2.80108	−	4.16204i	0.487605	−	0.724517i
$34$	0.252376	−	10.9307i	0.0432821	−	1.87459i
$35$	−10.9040	+	6.29540i	−1.84310	+	1.06412i
$36$	−0.0551779	+	5.99975i	−0.00919632	+	0.999958i
$37$	−0.179911	−	0.103872i	−0.0295771	−	0.0170764i	0.485139	−	0.874437i	$-0.338769\pi$
$37$	−0.179911	−	0.103872i	−0.0295771	−	0.0170764i	−0.514716	+	0.857361i	$0.672103\pi$
$38$	0.719295	−	1.18198i	0.116685	−	0.191742i
$39$	0.284900	+	2.68396i	0.0456205	+	0.429778i
$40$	7.15020	+	6.89715i	1.13055	+	1.09053i
$41$	−1.00198	+	5.68249i	−0.156483	+	0.887457i	0.800935	+	0.598751i	$0.204336\pi$
$41$	−1.00198	+	5.68249i	−0.156483	+	0.887457i	−0.957418	+	0.288706i	$0.906775\pi$
$42$	3.67421	+	7.97491i	0.566943	+	1.23055i
$43$	−2.62405	−	3.12722i	−0.400164	−	0.476897i	0.527906	−	0.849303i	$-0.322977\pi$
$43$	−2.62405	−	3.12722i	−0.400164	−	0.476897i	−0.928070	+	0.372406i	$0.878533\pi$
$44$	−5.74527	+	0.741561i	−0.866133	+	0.111795i
$45$	1.44493	−	10.4377i	0.215398	−	1.55596i
$46$	−6.85834	+	7.80046i	−1.01121	+	1.15012i
$47$	1.96476	+	0.715114i	0.286589	+	0.104310i	0.481315	−	0.876548i	$-0.340159\pi$
$47$	1.96476	+	0.715114i	0.286589	+	0.104310i	−0.194725	+	0.980858i	$0.562382\pi$
$48$	5.24710	−	4.52415i	0.757353	−	0.653005i
$49$	4.48123	+	3.76020i	0.640176	+	0.537171i
$50$	−6.48436	−	8.10037i	−0.917028	−	1.14557i
$51$	12.9964	+	3.22611i	1.81986	+	0.451746i
$52$	2.11135	−	2.29244i	0.292792	−	0.317904i
$53$		−	3.19246i		−	0.438519i	−0.975667	−	0.219259i	$-0.929636\pi$
$53$		−	3.19246i		−	0.438519i	0.975667	−	0.219259i	$-0.0703641\pi$
$54$	−7.15592	−	1.67117i	−0.973797	−	0.227417i
$55$	10.1736			1.37180
$56$	4.11871	−	9.26471i	0.550386	−	1.23805i
$57$	1.22021	+	1.17591i	0.161621	+	0.155753i
$58$	5.73518	−	4.59103i	0.753066	−	0.602831i
$59$	2.41918	−	2.88307i	0.314951	−	0.375344i	−0.585225	−	0.810871i	$-0.698994\pi$
$59$	2.41918	−	2.88307i	0.314951	−	0.375344i	0.900176	+	0.435527i	$0.143438\pi$
$60$	−10.1562	+	6.70034i	−1.31117	+	0.865011i
$61$	−2.94263	+	8.08481i	−0.376765	+	1.03515i	0.595924	+	0.803041i	$0.296786\pi$
$61$	−2.94263	+	8.08481i	−0.376765	+	1.03515i	−0.972689	+	0.232113i	$0.925436\pi$
$62$	−2.10483	+	2.39397i	−0.267314	+	0.304035i
$63$	−10.5144	+	2.25761i	−1.32468	+	0.284433i
$64$	−7.92338	−	1.10453i	−0.990423	−	0.138066i
$65$	−4.19283	+	3.51820i	−0.520057	+	0.436379i
$66$	0.650851	−	7.06495i	0.0801143	−	0.869635i
$67$	−2.94730	−	0.519689i	−0.360070	−	0.0634901i	−0.00931341	−	0.999957i	$-0.502965\pi$
$67$	−2.94730	−	0.519689i	−0.360070	−	0.0634901i	−0.350757	+	0.936466i	$0.614076\pi$
$68$	−7.10494	−	13.7334i	−0.861600	−	1.66542i
$69$	−7.48790	−	10.2838i	−0.901437	−	1.23803i
$70$	−9.25662	+	15.2109i	−1.10638	+	1.81805i
$71$	−4.82588	+	8.35866i	−0.572726	+	0.991991i	0.423558	+	0.905869i	$0.360781\pi$
$71$	−4.82588	+	8.35866i	−0.572726	+	0.991991i	−0.996285	+	0.0861221i	$0.972552\pi$
$72$	4.00325	+	7.48157i	0.471788	+	0.881712i
$73$	1.70348	+	2.95051i	0.199377	+	0.345331i	0.948327	−	0.317296i	$-0.102775\pi$
$73$	1.70348	+	2.95051i	0.199377	+	0.345331i	−0.748950	+	0.662627i	$0.769442\pi$
$74$	−0.293715	−	0.00678153i	−0.0341436	−	0.000788337i
$75$	11.4162	−	5.58264i	1.31822	−	0.644628i
$76$	0.0903106	−	1.95468i	0.0103593	−	0.224217i
$77$	−3.55115	−	9.75670i	−0.404691	−	1.11188i
$78$	2.17495	+	3.13675i	0.246265	+	0.355167i
$79$	−0.447375	−	2.53719i	−0.0503336	−	0.285456i	0.949243	−	0.314543i	$-0.101851\pi$
$79$	−0.447375	−	2.53719i	−0.0503336	−	0.285456i	−0.999577	+	0.0290867i	$0.990740\pi$
$80$	13.5523	+	3.70510i	1.51519	+	0.414243i
$81$	3.91188	−	8.10538i	0.434653	−	0.900598i
$82$	2.61322	+	7.73049i	0.288582	+	0.853690i
$83$	−6.28878	+	1.10888i	−0.690283	+	0.121716i	−0.507776	−	0.861489i	$-0.669532\pi$
$83$	−6.28878	+	1.10888i	−0.690283	+	0.121716i	−0.182507	+	0.983205i	$0.558421\pi$
$84$	9.97090	+	7.40129i	1.08791	+	0.807547i
$85$	9.28760	+	25.5175i	1.00738	+	2.76776i
$86$	−5.37805	−	2.09926i	−0.579930	−	0.226369i
$87$	3.95259	+	8.08281i	0.423762	+	0.866568i
$88$	−6.62514	+	4.81910i	−0.706242	+	0.513718i
$89$	4.56318	+	7.90366i	0.483696	+	0.837786i	0.999825	−	0.0187248i	$-0.00596065\pi$
$89$	4.56318	+	7.90366i	0.483696	+	0.837786i	−0.516129	+	0.856511i	$0.672627\pi$
$90$	−5.29072	−	13.9311i	−0.557691	−	1.46846i
$91$	4.83758	+	2.79298i	0.507116	+	0.292784i
$92$	−3.21565	+	14.3328i	−0.335255	+	1.49429i
$93$	−2.29804	−	3.15612i	−0.238296	−	0.327275i
$94$	2.92307	−	0.446109i	0.301491	−	0.0460126i
$95$	−0.596737	+	3.38427i	−0.0612240	+	0.347218i
$96$	3.43998	−	9.17423i	0.351091	−	0.936341i
$97$	7.10870	−	5.96491i	0.721780	−	0.605645i	−0.206097	−	0.978531i	$-0.566076\pi$
$97$	7.10870	−	5.96491i	0.721780	−	0.605645i	0.927877	+	0.372887i	$0.121632\pi$
$98$	8.11189	+	1.62425i	0.819425	+	0.164074i
$99$	8.26964	+	2.66809i	0.831130	+	0.268153i
$100$	−13.5427	−	5.64986i	−1.35427	−	0.564986i
$101$	3.11369	−	8.55479i	0.309824	−	0.851234i	−0.682866	−	0.730543i	$-0.739267\pi$
$101$	3.11369	−	8.55479i	0.309824	−	0.851234i	0.992690	−	0.120691i	$-0.0385109\pi$
$102$	18.3146	−	4.81722i	1.81341	−	0.476976i
$103$	−5.51631	−	4.62874i	−0.543539	−	0.456083i	0.329207	−	0.944258i	$-0.393218\pi$
$103$	−5.51631	−	4.62874i	−0.543539	−	0.456083i	−0.872746	+	0.488175i	$0.837663\pi$
$104$	1.06388	−	4.27719i	0.104322	−	0.419413i
$105$	−15.7029	−	15.1328i	−1.53245	−	1.47681i
$106$	−2.16656	−	3.96102i	−0.210435	−	0.384728i
$107$			17.0166i			1.64505i	0.568727	+	0.822526i	$0.307436\pi$
$107$			17.0166i			1.64505i	−0.568727	+	0.822526i	$0.692564\pi$
$108$	−10.0128	+	2.78286i	−0.963480	+	0.267781i
$109$		−	6.48016i		−	0.620687i	−0.950625	−	0.310343i	$-0.899556\pi$
$109$		−	6.48016i		−	0.620687i	0.950625	−	0.310343i	$-0.100444\pi$
$110$	12.6228	−	6.90427i	1.20353	−	0.658297i
$111$	0.0866879	−	0.349223i	0.00822805	−	0.0331468i
$112$	−1.17723	−	14.2903i	−0.111237	−	1.35030i
$113$	9.90741	+	8.31330i	0.932010	+	0.782050i	0.976177	−	0.216975i	$-0.0696189\pi$
$113$	9.90741	+	8.31330i	0.932010	+	0.782050i	−0.0441669	+	0.999024i	$0.514063\pi$
$114$	2.31200	+	0.630907i	0.216539	+	0.0590898i
$115$	8.82308	−	24.2412i	0.822756	−	2.26050i
$116$	4.00018	−	9.58844i	0.371408	−	0.890264i
$117$	−4.33084	+	1.76019i	−0.400386	+	0.162730i
$118$	1.04499	−	5.21892i	0.0961991	−	0.480440i
$119$	21.2300	−	17.8141i	1.94615	−	1.63301i
$120$	−8.05409	+	15.2059i	−0.735235	+	1.38810i
$121$	0.453305	−	2.57082i	0.0412095	−	0.233711i
$122$	1.83570	+	12.0282i	0.166196	+	1.08898i
$123$	−9.93837	+	1.05495i	−0.896113	+	0.0951214i
$124$	−0.986888	+	4.39874i	−0.0886251	+	0.395018i
$125$	7.10875	+	4.10424i	0.635826	+	0.367094i
$126$	−11.5135	+	9.93666i	−1.02570	+	0.885228i
$127$	2.74777	+	4.75927i	0.243825	+	0.422317i	0.961801	−	0.273751i	$-0.0882645\pi$
$127$	2.74777	+	4.75927i	0.243825	+	0.422317i	−0.717976	+	0.696068i	$0.754931\pi$
$128$	−10.5804	+	4.00676i	−0.935188	+	0.354151i
$129$	3.94785	−	5.86600i	0.347589	−	0.516472i
$130$	−2.81459	+	7.21063i	−0.246856	+	0.632414i
$131$	−1.17365	−	3.22458i	−0.102542	−	0.281733i	0.877803	−	0.479022i	$-0.159008\pi$
$131$	−1.17365	−	3.22458i	−0.102542	−	0.281733i	−0.980345	+	0.197289i	$0.936786\pi$
$132$	−3.98708	−	9.20747i	−0.347031	−	0.801407i
$133$	3.45389	−	0.609014i	0.299490	−	0.0528082i
$134$	−4.00953	+	1.35538i	−0.346370	+	0.117087i
$135$	18.0654	−	2.59606i	1.55482	−	0.223433i
$136$	−18.1355	−	12.2178i	−1.55511	−	1.04767i
$137$	1.22217	+	6.93130i	0.104417	+	0.592181i	0.991451	+	0.130476i	$0.0416507\pi$
$137$	1.22217	+	6.93130i	0.104417	+	0.592181i	−0.887034	+	0.461704i	$0.847238\pi$
$138$	−16.2697	−	7.67794i	−1.38496	−	0.653590i
$139$	1.90997	+	5.24760i	0.162001	+	0.445095i	0.993960	−	0.109742i	$-0.0350026\pi$
$139$	1.90997	+	5.24760i	0.162001	+	0.445095i	−0.831959	+	0.554838i	$0.812780\pi$
$140$	−1.16221	+	25.1548i	−0.0982245	+	2.12597i
$141$	−0.248888	+	3.61290i	−0.0209601	+	0.304261i
$142$	−0.315070	+	13.6460i	−0.0264401	+	1.14515i
$143$	−2.25677	−	3.90884i	−0.188721	−	0.326874i
$144$	10.0444	+	6.56589i	0.837030	+	0.547158i
$145$	−9.12295	+	15.8014i	−0.757620	+	1.31224i
$146$	4.11593	+	2.50476i	0.340637	+	0.207295i
$147$	−4.11157	+	9.26048i	−0.339117	+	0.763791i
$148$	−0.369026	+	0.190915i	−0.0303338	+	0.0156931i
$149$	19.1032	+	3.36840i	1.56499	+	0.275950i	0.887931	−	0.459977i	$-0.152142\pi$
$149$	19.1032	+	3.36840i	1.56499	+	0.275950i	0.677061	+	0.735927i	$0.263253\pi$
$150$	10.3758	−	14.6742i	0.847184	−	1.19814i
$151$	−6.65033	+	5.58029i	−0.541196	+	0.454118i	−0.871947	−	0.489601i	$-0.837143\pi$
$151$	−6.65033	+	5.58029i	−0.541196	+	0.454118i	0.330751	+	0.943718i	$0.392698\pi$
$152$	−1.21449	−	2.48654i	−0.0985078	−	0.201685i
$153$	0.857342	+	23.1778i	0.0693120	+	1.87381i
$154$	−11.0274	−	9.69556i	−0.888615	−	0.781290i
$155$	2.70781	−	7.43965i	0.217497	−	0.597567i
$156$	4.82730	+	2.41587i	0.386493	+	0.193424i
$157$	0.181238	−	0.215991i	0.0144644	−	0.0172380i	−0.758764	−	0.651366i	$-0.774196\pi$
$157$	0.181238	−	0.215991i	0.0144644	−	0.0172380i	0.773228	+	0.634128i	$0.218641\pi$
$158$	−2.27693	−	2.84438i	−0.181143	−	0.226287i
$159$	5.31373	−	1.52963i	0.421406	−	0.121308i
$160$	19.3293	−	4.60016i	1.52812	−	0.363674i
$161$	−26.3277			−2.07491
$162$	−0.647079	−	12.7115i	−0.0508393	−	0.998707i
$163$		−	4.95712i		−	0.388271i	−0.980975	−	0.194136i	$-0.937810\pi$
$163$		−	4.95712i		−	0.388271i	0.980975	−	0.194136i	$-0.0621902\pi$
$164$	8.48861	+	7.81808i	0.662849	+	0.610489i
$165$	4.87454	+	16.9335i	0.379483	+	1.31827i
$166$	−7.05021	+	5.64370i	−0.547202	+	0.438036i
$167$	−7.82926	−	6.56953i	−0.605846	−	0.508365i	0.287473	−	0.957789i	$-0.407185\pi$
$167$	−7.82926	−	6.56953i	−0.605846	−	0.508365i	−0.893319	+	0.449424i	$0.851629\pi$
$168$	17.3942	+	2.41636i	1.34199	+	0.186426i
$169$	−9.93417	−	3.61574i	−0.764167	−	0.278134i
$170$	28.8409	+	25.3575i	2.21199	+	1.94483i
$171$	−1.37261	+	2.59442i	−0.104966	+	0.198400i
$172$	−8.09742	+	1.04516i	−0.617423	+	0.0796927i
$173$	−0.368911	−	0.439651i	−0.0280478	−	0.0334261i	0.751838	−	0.659348i	$-0.229167\pi$
$173$	−0.368911	−	0.439651i	−0.0280478	−	0.0334261i	−0.779886	+	0.625922i	$0.784723\pi$
$174$	10.3895	+	7.34625i	0.787628	+	0.556918i
$175$	4.56706	−	25.9011i	0.345238	−	1.95794i
$176$	−4.94960	+	10.4754i	−0.373090	+	0.789612i
$177$	5.95788	+	2.64525i	0.447822	+	0.198829i
$178$	11.0255	+	6.70960i	0.826398	+	0.502906i
$179$	−14.6677	−	8.46841i	−1.09632	−	0.632959i	−0.161066	−	0.986944i	$-0.551493\pi$
$179$	−14.6677	−	8.46841i	−1.09632	−	0.632959i	−0.935251	+	0.353985i	$0.884826\pi$
$180$	−16.0187	−	13.6943i	−1.19396	−	1.02071i
$181$	−4.72394	+	2.72737i	−0.351128	+	0.202724i	−0.665182	−	0.746681i	$-0.731646\pi$
$181$	−4.72394	+	2.72737i	−0.351128	+	0.202724i	0.314054	+	0.949405i	$0.398313\pi$
$182$	7.89763	+	0.182347i	0.585411	+	0.0135165i
$183$	−14.8668	−	1.02415i	−1.09898	−	0.0757075i
$184$	5.73710	+	19.9655i	0.422945	+	1.47188i
$185$	0.685673	−	0.249565i	0.0504117	−	0.0183484i
$186$	−4.99317	−	2.35637i	−0.366117	−	0.172777i
$187$	−22.0530	+	3.88853i	−1.61267	+	0.284358i
$188$	3.32401	−	2.53724i	0.242429	−	0.185047i
$189$	−8.79553	−	16.4190i	−0.639781	−	1.19431i
$190$	1.55633	+	4.60397i	0.112908	+	0.334007i
$191$	0.165326	+	0.937608i	0.0119625	+	0.0678430i	0.990205	−	0.139624i	$-0.0445893\pi$
$191$	0.165326	+	0.937608i	0.0119625	+	0.0678430i	−0.978242	+	0.207467i	$0.933478\pi$
$192$	−1.95795	−	13.7174i	−0.141303	−	0.989966i
$193$	−19.2158	+	6.99398i	−1.38318	+	0.503438i	−0.923142	−	0.384459i	$-0.874388\pi$
$193$	−19.2158	+	6.99398i	−1.38318	+	0.503438i	−0.460042	+	0.887897i	$0.652166\pi$
$194$	4.77198	−	12.2252i	0.342608	−	0.877719i
$195$	−7.86485	−	5.29309i	−0.563214	−	0.379046i
$196$	11.1670	−	3.48984i	0.797646	−	0.249275i
$197$	−8.81684	+	5.09041i	−0.628174	+	0.362676i	−0.780045	−	0.625724i	$-0.784804\pi$
$197$	−8.81684	+	5.09041i	−0.628174	+	0.362676i	0.151871	+	0.988400i	$0.451470\pi$
$198$	12.0712	−	2.30177i	0.857861	−	0.163580i
$199$	−7.33178	+	12.6990i	−0.519736	+	0.900210i	0.480000	+	0.877268i	$0.340636\pi$
$199$	−7.33178	+	12.6990i	−0.519736	+	0.900210i	−0.999737	+	0.0229415i	$0.992697\pi$
$200$	−20.6373	+	2.18073i	−1.45927	+	0.154201i
$201$	−0.547163	−	5.15467i	−0.0385939	−	0.363583i
$202$	−1.94241	−	12.7274i	−0.136668	−	0.895495i
$203$	18.3384	+	3.23355i	1.28710	+	0.226951i
$204$	19.4544	−	18.4061i	1.36208	−	1.28868i
$205$	−13.0275	−	15.5255i	−0.909877	−	1.08435i
$206$	−9.98560	−	1.99943i	−0.695730	−	0.139307i
$207$	13.5293	−	17.3907i	0.940352	−	1.20874i
$208$	−1.58270	−	6.02888i	−0.109741	−	0.418028i
$209$	−2.66295	−	0.969234i	−0.184200	−	0.0670433i
$210$	−29.7531	−	8.11915i	−2.05316	−	0.560274i
$211$	−0.485058	+	0.578070i	−0.0333928	+	0.0397960i	−0.782482	−	0.622673i	$-0.786047\pi$
$211$	−0.485058	+	0.578070i	−0.0333928	+	0.0397960i	0.749090	+	0.662469i	$0.230491\pi$
$212$	−5.37628	−	3.44427i	−0.369244	−	0.236553i
$213$	−16.2249	−	4.02753i	−1.11171	−	0.275962i
$214$	11.5483	+	21.1131i	0.789422	+	1.44326i
$215$	14.3387			0.977891
$216$	−10.5347	+	10.2480i	−0.716793	+	0.697286i
$217$	−8.07999			−0.548505
$218$	−4.39775	−	8.04020i	−0.297853	−	0.544551i
$219$	−4.09480	+	4.24907i	−0.276701	+	0.287126i
$220$	10.9760	−	17.1328i	0.740002	−	1.15509i
$221$	7.74396	−	9.22890i	0.520915	−	0.620803i
$222$	−0.129442	−	0.492126i	−0.00868760	−	0.0330293i
$223$	−5.75940	−	2.09625i	−0.385678	−	0.140375i	0.141902	−	0.989881i	$-0.454678\pi$
$223$	−5.75940	−	2.09625i	−0.385678	−	0.140375i	−0.527580	+	0.849505i	$0.676900\pi$
$224$	−11.1587	−	16.9316i	−0.745571	−	1.13129i
$225$	14.7620	+	16.3269i	0.984133	+	1.08846i
$226$	17.9343	+	3.59101i	1.19297	+	0.238870i
$227$	12.0866	+	14.4043i	0.802218	+	0.956047i	0.999706	−	0.0242588i	$-0.00772257\pi$
$227$	12.0866	+	14.4043i	0.802218	+	0.956047i	−0.197487	+	0.980305i	$0.563278\pi$
$228$	3.29675	−	0.786242i	0.218333	−	0.0520701i
$229$	−23.0759	−	4.06891i	−1.52490	−	0.268881i	−0.652543	−	0.757751i	$-0.726298\pi$
$229$	−23.0759	−	4.06891i	−1.52490	−	0.268881i	−0.872356	+	0.488870i	$0.837409\pi$
$230$	−5.50410	−	36.0648i	−0.362929	−	2.37804i
$231$	14.5382	−	10.5856i	0.956540	−	0.696478i
$232$	−1.54399	−	14.6115i	−0.101368	−	0.959291i
$233$	7.95771	−	13.7832i	0.521327	−	0.902964i	−0.478366	−	0.878161i	$-0.658771\pi$
$233$	7.95771	−	13.7832i	0.521327	−	0.902964i	0.999692	−	0.0248036i	$-0.00789605\pi$
$234$	−4.17890	+	5.12306i	−0.273183	+	0.334905i
$235$	−6.36002	+	3.67196i	−0.414882	+	0.239532i
$236$	−2.24525	−	7.18450i	−0.146153	−	0.467671i
$237$	4.00870	−	1.96030i	0.260393	−	0.127335i
$238$	14.2514	−	36.5103i	0.923782	−	2.36661i
$239$	−2.46978	+	0.898927i	−0.159757	+	0.0581468i	−0.420661	−	0.907218i	$-0.638202\pi$
$239$	−2.46978	+	0.898927i	−0.159757	+	0.0581468i	0.260904	+	0.965365i	$0.415979\pi$
$240$	0.326417	+	24.3325i	0.0210701	+	1.57065i
$241$	0.876791	+	4.97253i	0.0564791	+	0.320309i	0.999937	−	0.0111822i	$-0.00355947\pi$
$241$	0.876791	+	4.97253i	0.0564791	+	0.320309i	−0.943458	+	0.331491i	$0.892448\pi$
$242$	−1.18225	−	3.49735i	−0.0759977	−	0.224818i
$243$	15.3654	+	2.62756i	0.985692	+	0.168558i
$244$	10.4405	+	13.6780i	0.668386	+	0.875647i
$245$	−20.2348	+	3.56794i	−1.29276	+	0.227948i
$246$	−11.6150	+	8.05357i	−0.740545	+	0.513477i
$247$	1.43266	−	0.521445i	0.0911579	−	0.0331788i
$248$	1.76072	+	6.12744i	0.111806	+	0.389093i
$249$	−4.85888	−	9.93612i	−0.307919	−	0.629676i
$250$	11.6054	+	0.267956i	0.733993	+	0.0169470i
$251$	8.06637	−	4.65712i	0.509145	−	0.293955i	−0.223337	−	0.974741i	$-0.571695\pi$
$251$	8.06637	−	4.65712i	0.509145	−	0.293955i	0.732482	+	0.680786i	$0.238362\pi$
$252$	−7.54172	+	20.1424i	−0.475084	+	1.26885i
$253$	18.4231	+	10.6366i	1.15825	+	0.668717i
$254$	6.63913	+	4.04025i	0.416576	+	0.253508i
$255$	−38.0228	+	27.6852i	−2.38108	+	1.73372i
$256$	−10.4084	+	12.1517i	−0.650526	+	0.759484i
$257$	0.912908	−	5.17736i	0.0569456	−	0.322955i	−0.943006	−	0.332775i	$-0.892015\pi$
$257$	0.912908	−	5.17736i	0.0569456	−	0.322955i	0.999952	+	0.00982065i	$0.00312606\pi$
$258$	0.917314	−	9.95738i	0.0571095	−	0.619920i
$259$	−0.478677	−	0.570465i	−0.0297435	−	0.0354470i
$260$	1.40130	+	10.8566i	0.0869050	+	0.673300i
$261$	−11.5597	+	10.4517i	−0.715526	+	0.646945i
$262$	−3.64455	−	3.20437i	−0.225161	−	0.197966i
$263$	−19.7976	−	7.20575i	−1.22078	−	0.444326i	−0.350346	−	0.936620i	$-0.613936\pi$
$263$	−19.7976	−	7.20575i	−1.22078	−	0.444326i	−0.870429	+	0.492294i	$0.836158\pi$
$264$	−11.1956	−	8.71826i	−0.689039	−	0.536572i
$265$	8.58983	+	7.20773i	0.527669	+	0.442767i
$266$	3.87207	−	3.09960i	0.237412	−	0.190049i
$267$	−10.9689	+	11.3822i	−0.671288	+	0.696578i
$268$	−4.05495	+	4.40273i	−0.247696	+	0.268940i
$269$		−	1.52571i		−	0.0930241i	−0.998918	−	0.0465120i	$-0.985189\pi$
$269$		−	1.52571i		−	0.0930241i	0.998918	−	0.0465120i	$-0.0148106\pi$
$270$	20.6527	−	15.4811i	1.25688	−	0.942149i
$271$	31.4903			1.91290			0.956450	−	0.291897i	$-0.0942863\pi$
$271$	31.4903			1.91290			0.956450	+	0.291897i	$0.0942863\pi$
$272$	−30.7931	−	2.85151i	−1.86710	−	0.172898i
$273$	−2.33093	+	9.39018i	−0.141074	+	0.568319i
$274$	6.22031	+	7.77051i	0.375783	+	0.469434i
$275$	−13.6601	+	16.2795i	−0.823736	+	0.981690i
$276$	−25.3970	+	1.51504i	−1.52872	+	0.0911946i
$277$	−2.02751	+	5.57054i	−0.121821	+	0.334701i	−0.985581	−	0.169202i	$-0.945881\pi$
$277$	−2.02751	+	5.57054i	−0.121821	+	0.334701i	0.863760	+	0.503903i	$0.168103\pi$
$278$	5.93105	+	5.21471i	0.355721	+	0.312757i
$279$	4.15216	−	5.33722i	0.248583	−	0.319531i
$280$	15.6292	+	31.9993i	0.934025	+	1.91232i
$281$	20.9759	−	17.6009i	1.25132	−	1.04998i	0.254769	−	0.967002i	$-0.418001\pi$
$281$	20.9759	−	17.6009i	1.25132	−	1.04998i	0.996551	−	0.0829803i	$-0.0264438\pi$
$282$	2.14308	+	4.65158i	0.127619	+	0.276997i
$283$	32.5610	+	5.74138i	1.93555	+	0.341290i	0.999931	−	0.0117196i	$-0.00373056\pi$
$283$	32.5610	+	5.74138i	1.93555	+	0.341290i	0.935620	+	0.353010i	$0.114842\pi$
$284$	8.86991	+	17.1450i	0.526332	+	1.01737i
$285$	−5.91889	+	0.628284i	−0.350605	+	0.0372164i
$286$	−5.45279	−	3.31830i	−0.322430	−	0.196215i
$287$	−10.3420	+	17.9129i	−0.610471	+	1.05737i
$288$	16.9184	+	1.32999i	0.996924	+	0.0783702i
$289$	−21.3857	−	37.0412i	−1.25799	−	2.17889i
$290$	−0.595616	+	25.7967i	−0.0349758	+	1.51484i
$291$	13.3344	+	8.97414i	0.781677	+	0.526073i
$292$	6.80665	+	0.314483i	0.398329	+	0.0184037i
$293$	10.9273	+	30.0225i	0.638378	+	1.75393i	0.656760	+	0.754099i	$0.271926\pi$
$293$	10.9273	+	30.0225i	0.638378	+	1.75393i	−0.0183820	+	0.999831i	$0.505851\pi$
$294$	1.18321	+	14.2802i	0.0690063	+	0.832836i
$295$	2.29550	+	13.0184i	0.133649	+	0.757961i
$296$	−0.328302	+	0.487315i	−0.0190821	+	0.0283246i
$297$	−0.478630	+	15.0429i	−0.0277729	+	0.872876i
$298$	25.9880	−	8.78501i	1.50545	−	0.508902i
$299$	−11.2710	+	1.98739i	−0.651821	+	0.114934i
$300$	2.91514	−	25.2484i	0.168305	−	1.45772i
$301$	−5.00501	−	13.7512i	−0.288484	−	0.792604i
$302$	−4.46428	+	11.4369i	−0.256891	+	0.658121i
$303$	15.7310	+	1.08369i	0.903722	+	0.0622562i
$304$	−3.19435	−	2.26094i	−0.183208	−	0.129674i
$305$	−15.1098	−	26.1709i	−0.865185	−	1.49854i
$306$	16.7933	+	28.1757i	0.960008	+	1.61070i
$307$	0.965983	+	0.557711i	0.0551316	+	0.0318302i	0.527312	−	0.849671i	$-0.323200\pi$
$307$	0.965983	+	0.557711i	0.0551316	+	0.0318302i	−0.472181	+	0.881502i	$0.656533\pi$
$308$	−20.2620	−	4.54593i	−1.15454	−	0.259028i
$309$	5.06127	−	11.3995i	0.287926	−	0.648494i
$310$	−1.68921	−	11.0683i	−0.0959409	−	0.628639i
$311$	1.69867	−	9.63366i	0.0963230	−	0.546275i	−0.898011	−	0.439973i	$-0.854988\pi$
$311$	1.69867	−	9.63366i	0.0963230	−	0.546275i	0.994334	−	0.106302i	$-0.0339010\pi$
$312$	7.62895	−	0.278571i	0.431904	−	0.0157710i
$313$	14.1280	−	11.8548i	0.798563	−	0.670074i	−0.149286	−	0.988794i	$-0.547698\pi$
$313$	14.1280	−	11.8548i	0.798563	−	0.670074i	0.947849	+	0.318720i	$0.103253\pi$
$314$	0.0782874	−	0.390986i	0.00441801	−	0.0220646i
$315$	17.6641	−	33.3876i	0.995260	−	1.88118i
$316$	−4.75542	−	1.98390i	−0.267513	−	0.111603i
$317$	9.63709	−	26.4777i	0.541273	−	1.48713i	−0.303933	−	0.952693i	$-0.598300\pi$
$317$	9.63709	−	26.4777i	0.541273	−	1.48713i	0.845206	−	0.534441i	$-0.179478\pi$
$318$	5.55488	−	5.50403i	0.311502	−	0.308650i
$319$	−11.5261	−	9.67156i	−0.645339	−	0.541504i
$320$	20.8608	−	18.8254i	1.16615	−	1.05237i
$321$	−28.3234	+	8.15328i	−1.58086	+	0.455072i
$322$	−32.6658	+	17.8672i	−1.82039	+	0.995701i
$323$		−	7.56407i		−	0.420876i
$324$	−9.42947	−	15.3325i	−0.523859	−	0.851805i
$325$		−	11.4332i		−	0.634199i
$326$	−3.36414	−	6.15050i	−0.186322	−	0.340645i
$327$	10.7860	−	3.10489i	0.596465	−	0.171701i
$328$	15.8379	+	3.93943i	0.874501	+	0.217518i
$329$	5.74151	+	4.81770i	0.316540	+	0.265608i
$330$	17.5399	+	17.7020i	0.965541	+	0.974462i
$331$	−10.1053	+	27.7642i	−0.555439	+	1.52606i	0.270742	+	0.962652i	$0.412731\pi$
$331$	−10.1053	+	27.7642i	−0.555439	+	1.52606i	−0.826181	+	0.563405i	$0.809491\pi$
$332$	−4.91739	+	11.7870i	−0.269877	+	0.646895i
$333$	0.622803	−	0.0230374i	0.0341294	−	0.00126244i
$334$	−14.1725	−	2.83777i	−0.775483	−	0.155276i
$335$	8.05253	−	6.75687i	0.439956	−	0.369167i
$336$	23.2215	−	8.80645i	1.26684	−	0.480431i
$337$	−4.75555	+	26.9700i	−0.259051	+	1.46915i	0.526405	+	0.850234i	$0.323540\pi$
$337$	−4.75555	+	26.9700i	−0.259051	+	1.46915i	−0.785456	+	0.618918i	$0.787571\pi$
$338$	−14.7795	+	2.25561i	−0.803902	+	0.122689i
$339$	−9.09014	+	20.4737i	−0.493709	+	1.11198i
$340$	52.9929	+	11.8893i	2.87394	+	0.644789i
$341$	5.65407	+	3.26438i	0.306185	+	0.176776i
$342$	0.0576473	+	4.15052i	0.00311721	+	0.224434i
$343$	−2.06149	−	3.57061i	−0.111310	−	0.192795i
$344$	−9.33751	+	6.79207i	−0.503445	+	0.366204i
$345$	44.5760	+	3.07078i	2.39989	+	0.165325i
$346$	−0.756092	−	0.295132i	−0.0406477	−	0.0158664i
$347$	−4.52278	−	12.4262i	−0.242795	−	0.667075i	−0.999905	−	0.0137870i	$-0.995611\pi$
$347$	−4.52278	−	12.4262i	−0.242795	−	0.667075i	0.757110	−	0.653288i	$-0.226611\pi$
$348$	17.8762	+	2.06396i	0.958266	+	0.110640i
$349$	18.1196	−	3.19498i	0.969920	−	0.171023i	0.333826	−	0.942635i	$-0.391660\pi$
$349$	18.1196	−	3.19498i	0.969920	−	0.171023i	0.636094	+	0.771611i	$0.280549\pi$
$350$	−11.9112	−	35.2360i	−0.636680	−	1.88344i
$351$	−5.00484	−	6.36514i	−0.267139	−	0.339746i
$352$	0.967936	+	16.3563i	0.0515912	+	0.871793i
$353$	4.80481	+	27.2494i	0.255734	+	1.45034i	0.794181	+	0.607682i	$0.207900\pi$
$353$	4.80481	+	27.2494i	0.255734	+	1.45034i	−0.538446	+	0.842660i	$0.680989\pi$
$354$	9.18737	−	0.761239i	0.488303	−	0.0404594i
$355$	−11.5948	−	31.8564i	−0.615387	−	1.69076i
$356$	18.2333	+	0.842419i	0.966361	+	0.0446481i
$357$	39.8229	+	26.8011i	2.10765	+	1.41846i
$358$	−23.9459	−	0.552883i	−1.26558	−	0.0292208i
$359$	−10.2486	−	17.7511i	−0.540900	−	0.936866i	−0.998853	−	0.0478893i	$-0.984751\pi$
$359$	−10.2486	−	17.7511i	−0.540900	−	0.936866i	0.457953	−	0.888976i	$-0.348583\pi$
$360$	−29.1686	−	6.11999i	−1.53732	−	0.322552i
$361$	−9.02138	+	15.6255i	−0.474810	+	0.822395i
$362$	−4.01026	+	6.58985i	−0.210775	+	0.346355i
$363$	4.49622	−	0.477269i	0.235990	−	0.0250501i
$364$	9.92266	−	5.13346i	0.520088	−	0.269067i
$365$	−11.7848	−	2.07798i	−0.616845	−	0.108766i
$366$	−19.1408	+	8.81860i	−1.00051	+	0.460956i
$367$	−6.56209	+	5.50625i	−0.342538	+	0.287424i	−0.797786	−	0.602941i	$-0.793995\pi$
$367$	−6.56209	+	5.50625i	−0.342538	+	0.287424i	0.455247	+	0.890365i	$0.349551\pi$
$368$	20.6678	+	20.8786i	1.07738	+	1.08837i
$369$	−6.51777	−	16.0366i	−0.339301	−	0.834830i
$370$	0.681376	−	0.774975i	0.0354230	−	0.0402891i
$371$	3.91405	−	10.7538i	0.203207	−	0.558308i
$372$	−7.79438	+	0.464967i	−0.404120	+	0.0241074i
$373$	4.80331	−	5.72436i	0.248706	−	0.296396i	−0.627220	−	0.778842i	$-0.715807\pi$
$373$	4.80331	−	5.72436i	0.248706	−	0.296396i	0.875926	+	0.482446i	$0.160252\pi$
$374$	−24.7231	+	19.7909i	−1.27840	+	1.02336i
$375$	−3.42527	+	13.7987i	−0.176880	+	0.712563i
$376$	2.40235	−	5.40389i	0.123892	−	0.278684i
$377$	8.09486			0.416906
$378$	−22.0557	−	14.4027i	−1.13442	−	0.740793i
$379$		−	38.3104i		−	1.96787i	−0.178521	−	0.983936i	$-0.557131\pi$
$379$		−	38.3104i		−	1.96787i	0.178521	−	0.983936i	$-0.442869\pi$
$380$	5.05547	+	4.65613i	0.259340	+	0.238855i
$381$	−6.60506	+	6.85389i	−0.338387	+	0.351136i
$382$	0.841432	+	1.05113i	0.0430514	+	0.0537805i
$383$	−2.12705	−	1.78480i	−0.108687	−	0.0911992i	0.586825	−	0.809714i	$-0.300378\pi$
$383$	−2.12705	−	1.78480i	−0.108687	−	0.0911992i	−0.695512	+	0.718515i	$0.744822\pi$
$384$	−11.7386	−	15.6909i	−0.599032	−	0.800725i
$385$	34.2695	+	12.4731i	1.74654	+	0.635687i
$386$	−19.0954	+	21.7185i	−0.971929	+	1.10544i
$387$	11.6553	+	3.76042i	0.592471	+	0.191153i
$388$	−2.37583	−	18.4068i	−0.120614	−	0.934464i
$389$	−5.26382	−	6.27317i	−0.266886	−	0.318063i	0.615912	−	0.787815i	$-0.288788\pi$
$389$	−5.26382	−	6.27317i	−0.266886	−	0.318063i	−0.882798	+	0.469752i	$0.844343\pi$
$390$	−13.3504	−	1.22989i	−0.676023	−	0.0622779i
$391$	−9.86009	+	55.9194i	−0.498646	+	2.82796i
$392$	11.4870	−	11.9085i	0.580183	−	0.601469i
$393$	4.80484	−	3.49851i	0.242372	−	0.176476i
$394$	−7.48482	+	12.2994i	−0.377080	+	0.619635i
$395$	7.83676	+	4.52456i	0.394310	+	0.227655i
$396$	13.4151	−	11.0480i	0.674134	−	0.555182i
$397$	19.5557	−	11.2905i	0.981473	−	0.566654i	0.0787584	−	0.996894i	$-0.474904\pi$
$397$	19.5557	−	11.2905i	0.981473	−	0.566654i	0.902715	+	0.430240i	$0.141571\pi$
$398$	−0.478675	+	20.7319i	−0.0239938	+	1.03920i
$399$	2.66857	+	5.45706i	0.133596	+	0.273195i
$400$	−24.1255	+	16.7112i	−1.20628	+	0.835558i
$401$	31.8252	−	11.5834i	1.58927	−	0.578449i	0.612081	−	0.790795i	$-0.290333\pi$
$401$	31.8252	−	11.5834i	1.58927	−	0.578449i	0.977194	+	0.212347i	$0.0681106\pi$
$402$	−4.17710	−	6.02428i	−0.208335	−	0.300464i
$403$	−3.45909	+	0.609932i	−0.172310	+	0.0303829i
$404$	−11.0474	−	14.4732i	−0.549631	−	0.720067i
$405$	12.9769	+	28.8253i	0.644825	+	1.43234i
$406$	24.9476	−	8.43330i	1.23813	−	0.418538i
$407$	0.104488	+	0.592579i	0.00517927	+	0.0293731i
$408$	11.6467	−	36.0399i	0.576595	−	1.78424i
$409$	20.8066	−	7.57298i	1.02882	−	0.374460i	0.228189	−	0.973617i	$-0.426720\pi$
$409$	20.8066	−	7.57298i	1.02882	−	0.374460i	0.800631	+	0.599157i	$0.204498\pi$
$410$	−26.7001	−	10.4221i	−1.31862	−	0.514710i
$411$	−10.9513	+	5.35531i	−0.540187	+	0.264158i
$412$	−13.7464	+	4.29594i	−0.677239	+	0.211646i
$413$	11.6837	−	6.74559i	0.574918	−	0.331929i
$414$	4.98421	−	30.7590i	0.244961	−	1.51172i
$415$	11.2148	−	19.4245i	0.550511	−	0.953512i
$416$	−6.05521	−	6.40618i	−0.296881	−	0.314089i
$417$	−7.81928	+	5.69339i	−0.382912	+	0.278806i
$418$	−3.96180	+	0.604637i	−0.193778	+	0.0295737i
$419$	−12.3232	−	2.17290i	−0.602026	−	0.106153i	−0.135675	−	0.990753i	$-0.543320\pi$
$419$	−12.3232	−	2.17290i	−0.602026	−	0.106153i	−0.466350	+	0.884600i	$0.654431\pi$
$420$	−42.4260	+	10.1182i	−2.07017	+	0.493715i
$421$	19.2609	+	22.9542i	0.938717	+	1.11872i	0.992752	+	0.120180i	$0.0383472\pi$
$421$	19.2609	+	22.9542i	0.938717	+	1.11872i	−0.0540354	+	0.998539i	$0.517208\pi$
$422$	−0.209525	+	1.04642i	−0.0101995	+	0.0509388i
$423$	−6.13278	+	1.31681i	−0.298186	+	0.0640257i
$424$	−9.00801	−	0.624841i	−0.437467	−	0.0303450i
$425$	−53.3029	−	19.4007i	−2.58557	−	0.941071i
$426$	−22.8642	+	6.01390i	−1.10777	+	0.291374i
$427$	−19.8244	+	23.6258i	−0.959370	+	1.14333i
$428$	28.6568	+	18.3587i	1.38518	+	0.887402i
$429$	5.42480	−	5.62918i	0.261912	−	0.271779i
$430$	17.7906	−	9.73092i	0.857939	−	0.469267i
$431$	24.0142			1.15673			0.578363	−	0.815780i	$-0.303692\pi$
$431$	24.0142			1.15673			0.578363	+	0.815780i	$0.303692\pi$
$432$	−6.11603	+	19.8644i	−0.294258	+	0.955726i
$433$	1.02353			0.0491875			0.0245938	−	0.999698i	$-0.492171\pi$
$433$	1.02353			0.0491875			0.0245938	+	0.999698i	$0.492171\pi$
$434$	−10.0252	+	5.48347i	−0.481224	+	0.263215i
$435$	−30.6720	−	7.61373i	−1.47061	−	0.365050i
$436$	−10.9129	−	6.99128i	−0.522634	−	0.334821i
$437$	−4.61891	+	5.50460i	−0.220952	+	0.263321i
$438$	−2.19697	+	8.05093i	−0.104975	+	0.384688i
$439$	−7.30450	−	2.65862i	−0.348625	−	0.126889i	0.161772	−	0.986828i	$-0.448279\pi$
$439$	−7.30450	−	2.65862i	−0.348625	−	0.126889i	−0.510396	+	0.859939i	$0.670501\pi$
$440$	1.99121	−	28.7062i	0.0949272	−	1.36852i
$441$	−17.3837	−	2.40650i	−0.827795	−	0.114595i
$442$	3.34508	−	16.7061i	0.159109	−	0.794628i
$443$	4.33387	+	5.16490i	0.205908	+	0.245392i	0.859109	−	0.511793i	$-0.171019\pi$
$443$	4.33387	+	5.16490i	0.205908	+	0.245392i	−0.653200	+	0.757185i	$0.726574\pi$
$444$	−0.494584	−	0.522755i	−0.0234719	−	0.0248088i
$445$	−31.5685	−	5.56638i	−1.49649	−	0.263872i
$446$	−8.56854	+	1.30770i	−0.405732	+	0.0619215i
$447$	3.54648	+	33.4104i	0.167743	+	1.58026i
$448$	−25.3356	−	13.4349i	−1.19700	−	0.634738i
$449$	11.5307	−	19.9718i	0.544168	−	0.942526i	−0.454491	−	0.890751i	$-0.650179\pi$
$449$	11.5307	−	19.9718i	0.544168	−	0.942526i	0.998659	−	0.0517751i	$-0.0164879\pi$
$450$	29.3960	+	10.2392i	1.38574	+	0.482682i
$451$	14.4739	−	8.35653i	0.681551	−	0.393494i
$452$	24.6889	−	7.71558i	1.16127	−	0.362911i
$453$	−12.4746	−	8.39548i	−0.586108	−	0.394454i
$454$	24.7718	+	9.66942i	1.16260	+	0.453808i
$455$	−18.4369	+	6.71048i	−0.864335	+	0.314592i
$456$	3.55683	−	3.21286i	0.166564	−	0.150456i
$457$	−3.82459	−	21.6903i	−0.178907	−	1.01463i	−0.933537	−	0.358481i	$-0.883295\pi$
$457$	−3.82459	−	21.6903i	−0.178907	−	1.01463i	0.754630	−	0.656150i	$-0.227816\pi$
$458$	−31.3926	+	10.6120i	−1.46688	+	0.495865i
$459$	−38.1677	+	12.5324i	−1.78151	+	0.584960i
$460$	−31.3045	−	41.0117i	−1.45958	−	1.91218i
$461$	−28.7509	+	5.06955i	−1.33906	+	0.236113i	−0.796874	−	0.604145i	$-0.793515\pi$
$461$	−28.7509	+	5.06955i	−1.33906	+	0.236113i	−0.542187	+	0.840258i	$0.682404\pi$
$462$	10.8542	−	23.0002i	0.504984	−	1.07007i
$463$	−14.0257	+	5.10493i	−0.651829	+	0.237246i	−0.646705	−	0.762741i	$-0.723853\pi$
$463$	−14.0257	+	5.10493i	−0.651829	+	0.237246i	−0.00512418	+	0.999987i	$0.501631\pi$
$464$	−11.8317	−	17.0812i	−0.549275	−	0.792976i
$465$	13.6804	+	0.942425i	0.634414	+	0.0437039i
$466$	0.519540	−	22.5018i	0.0240672	−	1.04238i
$467$	23.0145	−	13.2874i	1.06498	−	0.614868i	0.138177	−	0.990408i	$-0.455876\pi$
$467$	23.0145	−	13.2874i	1.06498	−	0.614868i	0.926806	+	0.375539i	$0.122543\pi$
$468$	−1.70818	+	9.19238i	−0.0789604	+	0.424918i
$469$	−9.29079	−	5.36404i	−0.429009	−	0.247688i
$470$	−5.39917	+	8.87217i	−0.249045	+	0.409243i
$471$	0.446346	+	0.198174i	0.0205666	+	0.00913137i
$472$	−7.66152	−	7.39037i	−0.352650	−	0.340169i
$473$	−2.05326	+	11.6446i	−0.0944089	+	0.535420i
$474$	3.64340	−	5.15272i	0.167347	−	0.236672i
$475$	−4.61417	−	5.49896i	−0.211713	−	0.252310i
$476$	−7.09535	−	54.9715i	−0.325215	−	2.51962i
$477$	5.09202	+	8.11158i	0.233147	+	0.371404i
$478$	−2.45430	+	2.79145i	−0.112257	+	0.127678i
$479$	35.1455	+	12.7919i	1.60584	+	0.584478i	0.980611	−	0.195963i	$-0.0627832\pi$
$479$	35.1455	+	12.7919i	1.60584	+	0.584478i	0.625229	+	0.780441i	$0.285005\pi$
$480$	16.9182	+	29.9688i	0.772206	+	1.36788i
$481$	−0.247987	−	0.208086i	−0.0113072	−	0.00948790i
$482$	4.46247	+	5.57459i	0.203260	+	0.253915i
$483$	−12.6146	−	43.8213i	−0.573983	−	1.99394i
$484$	−3.84033	−	3.53698i	−0.174561	−	0.160772i
$485$			32.5943i			1.48003i
$486$	20.8477	−	7.16758i	0.945670	−	0.325128i
$487$	−10.6546			−0.482806			−0.241403	−	0.970425i	$-0.577608\pi$
$487$	−10.6546			−0.482806			−0.241403	+	0.970425i	$0.577608\pi$
$488$	22.2365	+	9.88546i	1.00660	+	0.447494i
$489$	8.25093	−	2.37514i	0.373120	−	0.107408i
$490$	−22.6848	+	18.1592i	−1.02479	+	0.820350i
$491$	24.5176	−	29.2189i	1.10646	−	1.31863i	0.163198	−	0.986593i	$-0.447819\pi$
$491$	24.5176	−	29.2189i	1.10646	−	1.31863i	0.943266	−	0.332038i	$-0.107736\pi$
$492$	−8.94566	+	17.8749i	−0.403301	+	0.805862i
$493$	13.7360	−	37.7393i	0.618637	−	1.69969i
$494$	1.42368	−	1.61925i	0.0640544	−	0.0728535i
$495$	−25.8496	+	16.2270i	−1.16185	+	0.729348i
$496$	6.34298	+	6.40765i	0.284808	+	0.287712i
$497$	−26.5038	+	22.2394i	−1.18886	+	0.997572i
$498$	−12.7717	−	9.03067i	−0.572315	−	0.404674i
$499$	22.8313	+	4.02577i	1.02207	+	0.180218i	0.659472	−	0.751729i	$-0.270780\pi$
$499$	22.8313	+	4.02577i	1.02207	+	0.180218i	0.362595	+	0.931947i	$0.381891\pi$
$500$	14.5812	−	7.54355i	0.652091	−	0.337358i
$501$	7.18342	−	16.1792i	0.320932	−	0.722833i
$502$	6.84773	−	11.2525i	0.305629	−	0.502224i
$503$	−6.01047	+	10.4104i	−0.267993	+	0.464178i	−0.968344	−	0.249621i	$-0.919694\pi$
$503$	−6.01047	+	10.4104i	−0.267993	+	0.464178i	0.700350	+	0.713800i	$0.253027\pi$
$504$	4.31228	+	30.1097i	0.192084	+	1.34119i
$505$	15.9882	+	27.6923i	0.711464	+	1.23229i
$506$	30.0768	+	0.694438i	1.33708	+	0.0308715i
$507$	1.25842	−	18.2675i	0.0558885	−	0.811287i
$508$	10.9794	+	0.507271i	0.487130	+	0.0225065i
$509$	4.03924	+	11.0977i	0.179036	+	0.491898i	0.996453	−	0.0841485i	$-0.0268170\pi$
$509$	4.03924	+	11.0977i	0.179036	+	0.491898i	−0.817417	+	0.576046i	$0.804595\pi$
$510$	−28.3879	+	60.1542i	−1.25704	+	2.66367i
$511$	2.12073	+	12.0273i	0.0938156	+	0.532055i
$512$	−4.66738	+	22.1408i	−0.206271	+	0.978495i
$513$	−4.97598	−	1.04157i	−0.219695	−	0.0459863i
$514$	−2.38092	−	7.04330i	−0.105018	−	0.310667i
$515$	24.9087	−	4.39208i	1.09761	−	0.193538i
$516$	−5.61941	−	12.9771i	−0.247381	−	0.571283i
$517$	−2.07130	−	5.69086i	−0.0910958	−	0.250284i
$518$	−0.981059	−	0.382946i	−0.0431053	−	0.0168257i
$519$	0.555023	−	0.824692i	0.0243628	−	0.0362000i
$520$	9.10649	+	12.5193i	0.399346	+	0.549007i
$521$	−6.22104	−	10.7752i	−0.272549	−	0.472069i	0.696965	−	0.717105i	$-0.254533\pi$
$521$	−6.22104	−	10.7752i	−0.272549	−	0.472069i	−0.969514	+	0.245037i	$0.921200\pi$
$522$	−7.24952	+	20.8128i	−0.317303	+	0.910952i
$523$	23.1897	+	13.3886i	1.01402	+	0.585442i	0.912365	−	0.409378i	$-0.134254\pi$
$523$	23.1897	+	13.3886i	1.01402	+	0.585442i	0.101651	+	0.994820i	$0.467588\pi$
$524$	−6.69657	−	1.50242i	−0.292541	−	0.0656337i
$525$	45.2996	−	4.80851i	1.97704	−	0.209860i
$526$	−29.4539	+	4.49516i	−1.28425	+	0.195998i
$527$	−3.02607	+	17.1617i	−0.131818	+	0.747576i
$528$	−19.8074	−	3.21925i	−0.862007	−	0.140100i
$529$	23.7030	−	19.8892i	1.03056	−	0.864746i
$530$	15.5493	+	3.11344i	0.675417	+	0.135239i
$531$	−1.54826	+	11.1841i	−0.0671888	+	0.485348i
$532$	2.70070	−	6.47358i	0.117090	−	0.280665i
$533$	−3.07530	+	8.44933i	−0.133206	+	0.365981i
$534$	−5.88511	+	21.5664i	−0.254674	+	0.933268i
$535$	−45.7858	−	38.4188i	−1.97949	−	1.66099i
$536$	−2.04324	+	8.21454i	−0.0882544	+	0.354814i
$537$	7.06747	−	28.4714i	0.304984	−	1.22863i
$538$	−1.03542	−	1.89301i	−0.0446401	−	0.0816134i
$539$		−	16.9438i		−	0.729823i
$540$	15.1184	−	33.2239i	0.650593	−	1.42973i
$541$		−	0.365364i		−	0.0157082i	−0.999969	−	0.00785412i	$-0.997500\pi$
$541$		−	0.365364i		−	0.0157082i	0.999969	−	0.00785412i	$-0.00250007\pi$
$542$	39.0713	−	21.3708i	1.67826	−	0.917956i
$543$	−6.80301	−	6.55602i	−0.291945	−	0.281346i
$544$	−40.1414	+	17.3597i	−1.72105	+	0.744290i
$545$	17.4359	+	14.6305i	0.746872	+	0.626700i
$546$	3.48054	+	13.2327i	0.148954	+	0.566305i
$547$	−12.8891	+	35.4125i	−0.551098	+	1.51413i	0.281116	+	0.959674i	$0.409296\pi$
$547$	−12.8891	+	35.4125i	−0.551098	+	1.51413i	−0.832214	+	0.554455i	$0.812927\pi$
$548$	12.9912	+	5.41979i	0.554958	+	0.231522i
$549$	−5.41857	−	25.2359i	−0.231259	−	1.07704i
$550$	−5.90061	+	29.4690i	−0.251603	+	1.25656i
$551$	3.89334	−	3.26690i	0.165862	−	0.139175i
$552$	−30.4829	+	19.1154i	−1.29744	+	0.813606i
$553$	1.60369	−	9.09498i	0.0681958	−	0.386758i
$554$	1.26482	+	8.28756i	0.0537371	+	0.352105i
$555$	0.743922	+	1.02170i	0.0315777	+	0.0433687i
$556$	10.8978	+	2.44501i	0.462171	+	0.103691i
$557$	−11.9876	−	6.92105i	−0.507931	−	0.293254i	0.224052	−	0.974577i	$-0.428072\pi$
$557$	−11.9876	−	6.92105i	−0.507931	−	0.293254i	−0.731983	+	0.681323i	$0.761405\pi$
$558$	1.52966	−	9.43996i	0.0647557	−	0.399625i
$559$	−3.18071	−	5.50914i	−0.134530	−	0.233012i
$560$	41.1081	+	29.0960i	1.73713	+	1.22953i
$561$	−17.0387	−	34.8431i	−0.719376	−	1.47108i
$562$	14.0809	−	36.0734i	0.593966	−	1.52167i
$563$	11.4866	+	31.5593i	0.484104	+	1.33007i	0.905945	+	0.423396i	$0.139162\pi$
$563$	11.4866	+	31.5593i	0.484104	+	1.33007i	−0.421840	+	0.906670i	$0.638616\pi$
$564$	5.81579	+	4.31700i	0.244889	+	0.181779i
$565$	−44.7365	+	7.88825i	−1.88208	+	0.331861i
$566$	44.2961	−	14.9739i	1.86191	−	0.629400i
$567$	23.1145	−	22.5068i	0.970718	−	0.945196i
$568$	22.6407	+	15.2529i	0.949981	+	0.639998i
$569$	3.95256	+	22.4161i	0.165700	+	0.939730i	0.948340	+	0.317256i	$0.102761\pi$
$569$	3.95256	+	22.4161i	0.165700	+	0.939730i	−0.782640	+	0.622474i	$0.786128\pi$
$570$	−6.91743	+	4.79638i	−0.289739	+	0.200898i
$571$	−6.29067	−	17.2835i	−0.263256	−	0.723291i	−0.998943	−	0.0459688i	$-0.985363\pi$
$571$	−6.29067	−	17.2835i	−0.263256	−	0.723291i	0.735686	−	0.677322i	$-0.236860\pi$
$572$	−9.01746	−	0.416627i	−0.377039	−	0.0174201i
$573$	−1.48140	+	0.724422i	−0.0618863	+	0.0302631i
$574$	−0.675208	+	29.2439i	−0.0281826	+	1.22062i
$575$	26.9434	+	46.6673i	1.12362	+	1.94616i
$576$	21.8939	−	9.83145i	0.912246	−	0.409644i
$577$	12.9321	−	22.3991i	0.538372	−	0.932487i	−0.460620	−	0.887597i	$-0.652373\pi$
$577$	12.9321	−	22.3991i	0.538372	−	0.932487i	0.998992	−	0.0448896i	$-0.0142936\pi$
$578$	−51.6721	−	31.4451i	−2.14928	−	1.30794i
$579$	−20.8482	−	28.6329i	−0.866423	−	1.18994i
$580$	16.7679	+	32.4113i	0.696249	+	1.34580i
$581$	−22.5432	−	3.97497i	−0.935249	−	0.164910i
$582$	22.6348	+	2.08521i	0.938243	+	0.0864347i
$583$	−7.08351	+	5.94377i	−0.293369	+	0.246166i
$584$	8.65871	−	4.22913i	0.358300	−	0.175003i
$585$	5.04180	−	15.6269i	0.208453	−	0.646091i
$586$	33.9326	+	29.8343i	1.40174	+	1.23244i
$587$	−3.00647	+	8.26020i	−0.124090	+	0.340935i	−0.986146	−	0.165878i	$-0.946954\pi$
$587$	−3.00647	+	8.26020i	−0.124090	+	0.340935i	0.862056	+	0.506813i	$0.169176\pi$
$588$	11.1593	+	16.9150i	0.460200	+	0.697562i
$589$	−1.41755	+	1.68937i	−0.0584091	+	0.0696092i
$590$	11.6830	+	14.5946i	0.480983	+	0.600851i
$591$	−12.6973	−	12.2363i	−0.522295	−	0.503333i
$592$	−0.0766221	+	0.827432i	−0.00314915	+	0.0340072i
$593$	0.714890			0.0293570			0.0146785	−	0.999892i	$-0.495328\pi$
$593$	0.714890			0.0293570			0.0146785	+	0.999892i	$0.495328\pi$
$594$	9.61496	+	18.9891i	0.394507	+	0.779133i
$595$			97.3420i			3.99063i
$596$	26.2825	−	28.5366i	1.07657	−	1.16891i
$597$	−24.6499	−	6.11888i	−1.00886	−	0.250429i
$598$	−12.6357	+	10.1149i	−0.516712	+	0.413629i
$599$	−25.2336	−	21.1735i	−1.03102	−	0.865127i	−0.0400464	−	0.999198i	$-0.512751\pi$
$599$	−25.2336	−	21.1735i	−1.03102	−	0.865127i	−0.990972	+	0.134071i	$0.957195\pi$
$600$	−13.5178	−	33.3050i	−0.551863	−	1.35967i
$601$	−25.3646	−	9.23196i	−1.03464	−	0.376580i	−0.231797	−	0.972764i	$-0.574460\pi$
$601$	−25.3646	−	9.23196i	−1.03464	−	0.376580i	−0.802847	+	0.596185i	$0.796683\pi$
$602$	−15.5421	−	13.6650i	−0.633449	−	0.556943i
$603$	8.31758	−	3.38053i	0.338718	−	0.137666i
$604$	2.22263	+	17.2199i	0.0904376	+	0.700669i
$605$	5.89376	+	7.02390i	0.239615	+	0.285562i
$606$	20.2535	−	9.33124i	0.822743	−	0.379056i
$607$	5.64934	−	32.0390i	0.229300	−	1.30042i	−0.624993	−	0.780630i	$-0.714898\pi$
$607$	5.64934	−	32.0390i	0.229300	−	1.30042i	0.854293	−	0.519792i	$-0.173991\pi$
$608$	−5.49774	−	0.637402i	−0.222963	−	0.0258500i
$609$	3.40449	+	32.0728i	0.137957	+	1.29966i
$610$	−36.5082	−	22.2171i	−1.47817	−	0.899545i
$611$	2.82165	+	1.62908i	0.114152	+	0.0659055i
$612$	39.9575	+	23.5621i	1.61519	+	0.952440i
$613$	−6.39944	+	3.69472i	−0.258471	+	0.149228i	−0.623637	−	0.781714i	$-0.714346\pi$
$613$	−6.39944	+	3.69472i	−0.258471	+	0.149228i	0.365166	+	0.930942i	$0.381012\pi$
$614$	1.57702	+	0.0364116i	0.0636435	+	0.00146945i
$615$	19.5997	−	29.1226i	0.790335	−	1.17433i
$616$	−28.2250	+	8.11047i	−1.13722	+	0.326780i
$617$	−28.4748	+	10.3640i	−1.14635	+	0.417238i	−0.844203	−	0.536023i	$-0.819926\pi$
$617$	−28.4748	+	10.3640i	−1.14635	+	0.417238i	−0.302149	+	0.953261i	$0.597704\pi$
$618$	−1.45651	−	17.5786i	−0.0585896	−	0.707116i
$619$	29.4542	−	5.19358i	1.18387	−	0.208748i	0.453153	−	0.891433i	$-0.350299\pi$
$619$	29.4542	−	5.19358i	1.18387	−	0.208748i	0.730713	+	0.682685i	$0.239188\pi$
$620$	−9.60737	−	12.5865i	−0.385841	−	0.505488i
$621$	35.4285	+	14.1865i	1.42170	+	0.569283i
$622$	−4.43025	−	13.1057i	−0.177637	−	0.525490i
$623$	5.68089	+	32.2179i	0.227600	+	1.29078i
$624$	9.27650	−	5.52301i	0.371357	−	0.221097i
$625$	7.37985	−	2.68605i	0.295194	−	0.107442i
$626$	9.48396	−	24.2967i	0.379055	−	0.971091i
$627$	0.337332	−	4.89677i	0.0134717	−	0.195558i
$628$	−0.168207	−	0.538241i	−0.00671220	−	0.0214782i
$629$	−1.39093	+	0.803052i	−0.0554599	+	0.0320198i
$630$	−0.741863	−	53.4131i	−0.0295565	−	2.12803i
$631$	3.83176	−	6.63679i	0.152540	−	0.264207i	−0.779621	−	0.626252i	$-0.784588\pi$
$631$	3.83176	−	6.63679i	0.152540	−	0.264207i	0.932160	+	0.362045i	$0.117921\pi$
$632$	−7.24662	+	0.765746i	−0.288255	+	0.0304597i
$633$	−1.19458	−	0.530385i	−0.0474804	−	0.0210809i
$634$	−6.01190	−	39.3921i	−0.238763	−	1.56446i
$635$	−19.0093	−	3.35185i	−0.754361	−	0.133014i
$636$	3.15687	−	10.5989i	0.125178	−	0.420273i
$637$	5.85948	+	6.98306i	0.232161	+	0.276679i
$638$	−20.8645	−	4.17772i	−0.826034	−	0.165398i
$639$	−1.07032	−	28.9355i	−0.0423412	−	1.14467i
$640$	13.1070	−	37.5146i	0.518099	−	1.48289i
$641$	21.7828	+	7.92830i	0.860370	+	0.313149i	0.734261	−	0.678867i	$-0.237529\pi$
$641$	21.7828	+	7.92830i	0.860370	+	0.313149i	0.126109	+	0.992016i	$0.459751\pi$
$642$	−29.6088	+	29.3377i	−1.16856	+	1.15787i
$643$	−23.2439	+	27.7010i	−0.916651	+	1.09242i	0.0787757	+	0.996892i	$0.474899\pi$
$643$	−23.2439	+	27.7010i	−0.916651	+	1.09242i	−0.995427	+	0.0955296i	$0.969546\pi$
$644$	−28.4042	+	44.3372i	−1.11928	+	1.74713i
$645$	6.87021	+	23.8662i	0.270514	+	0.939730i
$646$	−5.13334	−	9.38504i	−0.201968	−	0.369250i
$647$	−41.5981			−1.63539			−0.817694	−	0.575653i	$-0.804748\pi$
$647$	−41.5981			−1.63539			−0.817694	+	0.575653i	$0.804748\pi$
$648$	−22.1049	−	12.6243i	−0.868362	−	0.495931i
$649$	−10.9011			−0.427905
$650$	−7.75910	−	14.1856i	−0.304337	−	0.556405i
$651$	−3.87143	−	13.4488i	−0.151733	−	0.527101i
$652$	−8.34805	−	5.34811i	−0.326935	−	0.209448i
$653$	−23.0229	+	27.4376i	−0.900957	+	1.07372i	0.0959707	+	0.995384i	$0.469405\pi$
$653$	−23.0229	+	27.4376i	−0.900957	+	1.07372i	−0.996927	+	0.0783340i	$0.975040\pi$
$654$	11.2755	−	11.1722i	0.440905	−	0.436869i
$655$	11.3260	+	4.12233i	0.442544	+	0.161073i
$656$	22.3242	−	5.86054i	0.871613	−	0.228816i
$657$	−9.03439	−	4.77975i	−0.352465	−	0.186476i
$658$	10.3932	+	2.08105i	0.405171	+	0.0811277i
$659$	−1.10500	−	1.31688i	−0.0430446	−	0.0512985i	0.744093	−	0.668076i	$-0.232882\pi$
$659$	−1.10500	−	1.31688i	−0.0430446	−	0.0512985i	−0.787137	+	0.616778i	$0.788438\pi$
$660$	33.7759	+	10.0601i	1.31473	+	0.391590i
$661$	30.1408	+	5.31464i	1.17234	+	0.206716i	0.725709	−	0.688002i	$-0.241512\pi$
$661$	30.1408	+	5.31464i	1.17234	+	0.206716i	0.446633	+	0.894717i	$0.352623\pi$
$662$	6.30400	+	41.3061i	0.245012	+	1.60541i
$663$	19.0716	+	8.46760i	0.740678	+	0.328854i
$664$	1.89801	+	17.9618i	0.0736570	+	0.697051i
$665$	−6.15930	+	10.6682i	−0.238848	+	0.413696i
$666$	0.757103	−	0.451248i	0.0293371	−	0.0174855i
$667$	−33.0411	+	19.0763i	−1.27936	+	0.738638i
$668$	−19.5102	+	6.09719i	−0.754873	+	0.235907i
$669$	0.729578	−	10.5907i	0.0282071	−	0.409460i
$670$	5.40556	−	13.8484i	0.208835	−	0.535009i
$671$	23.4174	−	8.52323i	0.904019	−	0.329036i
$672$	22.8354	−	26.6857i	0.880894	−	1.02942i
$673$	−3.20023	−	18.1494i	−0.123360	−	0.699609i	−0.982268	−	0.187480i	$-0.939968\pi$
$673$	−3.20023	−	18.1494i	−0.123360	−	0.699609i	0.858908	−	0.512129i	$-0.171143\pi$
$674$	12.4028	+	36.6902i	0.477737	+	1.41325i
$675$	−20.1024	+	32.3936i	−0.773742	+	1.24683i
$676$	−16.8068	+	12.8287i	−0.646416	+	0.493413i
$677$	2.92669	−	0.516054i	0.112482	−	0.0198336i	−0.117124	−	0.993117i	$-0.537367\pi$
$677$	2.92669	−	0.516054i	0.112482	−	0.0198336i	0.229606	+	0.973284i	$0.426256\pi$
$678$	2.61593	+	31.5716i	0.100464	+	1.21250i
$679$	31.2587	−	11.3772i	1.19960	−	0.436618i
$680$	73.8191	−	21.2119i	2.83083	−	0.813441i
$681$	−18.1842	+	27.0194i	−0.696820	+	1.03538i
$682$	9.23060	+	0.213124i	0.353458	+	0.00816093i
$683$	−25.1540	+	14.5226i	−0.962489	+	0.555693i	−0.896938	−	0.442156i	$-0.854214\pi$
$683$	−25.1540	+	14.5226i	−0.962489	+	0.555693i	−0.0655509	+	0.997849i	$0.520880\pi$
$684$	2.88827	+	5.11060i	0.110436	+	0.195409i
$685$	−21.4091	−	12.3605i	−0.817999	−	0.472272i
$686$	−4.98096	−	3.03117i	−0.190174	−	0.115731i
$687$	−4.28401	−	40.3585i	−0.163445	−	1.53977i
$688$	−6.97599	+	14.7641i	−0.265957	+	0.562875i
$689$	0.863863	−	4.89921i	0.0329106	−	0.186645i
$690$	57.3912	−	26.4414i	2.18485	−	1.00661i
$691$	8.61717	+	10.2695i	0.327813	+	0.390672i	0.904628	−	0.426203i	$-0.140149\pi$
$691$	8.61717	+	10.2695i	0.327813	+	0.390672i	−0.576815	+	0.816875i	$0.695705\pi$
$692$	−1.13840	+	0.146938i	−0.0432756	+	0.00558573i
$693$	24.5850	+	19.1262i	0.933907	+	0.726545i
$694$	−14.0446	−	12.3484i	−0.533127	−	0.468737i
$695$	−18.4317	−	6.70859i	−0.699154	−	0.254471i
$696$	23.5804	−	9.57082i	0.893815	−	0.362781i
$697$	34.1734	+	28.6749i	1.29441	+	1.08614i
$698$	20.3135	−	16.2610i	0.768876	−	0.615487i
$699$	26.7543	+	6.64125i	1.01194	+	0.251195i
$700$	−38.6915	−	35.6352i	−1.46240	−	1.34688i
$701$		−	49.0807i		−	1.85375i	−0.375368	−	0.926876i	$-0.622484\pi$
$701$		−	49.0807i		−	1.85375i	0.375368	−	0.926876i	$-0.377516\pi$
$702$	−10.5294	−	4.50096i	−0.397406	−	0.169878i
$703$	−0.203252			−0.00766579
$704$	12.3011	+	19.6370i	0.463616	+	0.740098i
$705$	−9.15916	−	8.82663i	−0.344954	−	0.332430i
$706$	24.4543	+	30.5487i	0.920350	+	1.14972i
$707$	20.9768	−	24.9992i	0.788915	−	0.940192i
$708$	10.8825	−	7.17949i	0.408991	−	0.269822i
$709$	−5.93610	+	16.3093i	−0.222935	+	0.612509i	−0.999854	−	0.0170917i	$-0.994559\pi$
$709$	−5.93610	+	16.3093i	−0.222935	+	0.612509i	0.776919	+	0.629601i	$0.216782\pi$
$710$	−36.0054	−	31.6568i	−1.35126	−	1.18806i
$711$	5.18356	+	5.73306i	0.194399	+	0.215007i
$712$	23.1945	−	11.3287i	0.869249	−	0.424563i
$713$	12.6818	−	10.6413i	0.474936	−	0.398519i
$714$	67.5984	+	6.22743i	2.52981	+	0.233056i
$715$	15.6125	+	2.75291i	0.583876	+	0.102953i
$716$	−30.0859	+	15.5649i	−1.12436	+	0.581686i
$717$	−2.67960	−	3.68014i	−0.100071	−	0.137438i
$718$	−24.7626	−	15.0693i	−0.924131	−	0.562381i
$719$	−3.17441	+	5.49824i	−0.118386	+	0.205050i	−0.919128	−	0.393959i	$-0.871105\pi$
$719$	−3.17441	+	5.49824i	−0.118386	+	0.205050i	0.800742	+	0.599009i	$0.204439\pi$
$720$	−40.3440	+	12.2019i	−1.50353	+	0.454739i
$721$	−12.9067	−	22.3550i	−0.480669	−	0.832543i
$722$	−0.588985	+	25.5095i	−0.0219198	+	0.949366i
$723$	−7.85647	+	3.84191i	−0.292185	+	0.142882i
$724$	−0.503505	+	10.8978i	−0.0187126	+	0.405015i
$725$	−13.0356	−	35.8150i	−0.484129	−	1.33013i
$726$	5.25474	−	3.64352i	0.195022	−	0.135224i
$727$	4.81683	+	27.3176i	0.178646	+	1.01315i	0.933850	+	0.357664i	$0.116427\pi$
$727$	4.81683	+	27.3176i	0.178646	+	1.01315i	−0.755204	+	0.655490i	$0.772462\pi$
$728$	8.82762	−	13.1033i	0.327174	−	0.485640i
$729$	2.98868	+	26.8341i	0.110692	+	0.993855i
$730$	−16.0321	+	5.41950i	−0.593375	+	0.200585i
$731$	−31.0816	+	5.48052i	−1.14959	+	0.202704i
$732$	−17.7641	+	23.9315i	−0.656580	+	0.884533i
$733$	14.4845	+	39.7958i	0.534997	+	1.46989i	0.853055	+	0.521822i	$0.174747\pi$
$733$	14.4845	+	39.7958i	0.534997	+	1.46989i	−0.318057	+	0.948071i	$0.603030\pi$
$734$	−4.40505	+	11.2852i	−0.162593	+	0.416543i
$735$	−15.6340	−	31.9705i	−0.576668	−	1.17925i
$736$	39.8126	+	11.8787i	1.46751	+	0.437855i
$737$	4.33423	+	7.50711i	0.159653	+	0.276528i
$738$	−18.9700	−	15.4739i	−0.698297	−	0.569603i
$739$	−15.5782	−	8.99410i	−0.573055	−	0.330853i	0.185314	−	0.982679i	$-0.440670\pi$
$739$	−15.5782	−	8.99410i	−0.573055	−	0.330853i	−0.758369	+	0.651826i	$0.774003\pi$
$740$	0.319475	−	1.42396i	0.0117441	−	0.0523457i
$741$	1.55437	+	2.13476i	0.0571010	+	0.0784223i
$742$	−2.44170	−	15.9989i	−0.0896376	−	0.587338i
$743$	6.19561	−	35.1371i	0.227295	−	1.28905i	−0.630954	−	0.775820i	$-0.717336\pi$
$743$	6.19561	−	35.1371i	0.227295	−	1.28905i	0.858249	−	0.513233i	$-0.171553\pi$
$744$	−9.35525	+	5.86654i	−0.342980	+	0.215078i
$745$	−52.1930	+	43.7951i	−1.91220	+	1.60453i
$746$	2.07483	−	10.3622i	0.0759650	−	0.379387i
$747$	14.2102	−	12.8482i	0.519924	−	0.470091i
$748$	−17.2439	+	41.3336i	−0.630499	+	1.51131i
$749$	−20.8628	+	57.3200i	−0.762309	+	2.09443i
$750$	5.11461	+	19.4452i	0.186759	+	0.710038i
$751$	31.2673	+	26.2364i	1.14096	+	0.957380i	0.999470	−	0.0325599i	$-0.0103660\pi$
$751$	31.2673	+	26.2364i	1.14096	+	0.957380i	0.141491	+	0.989940i	$0.454810\pi$
$752$	−0.686649	−	8.33517i	−0.0250395	−	0.303952i
$753$	11.6165	+	11.1948i	0.423329	+	0.407959i
$754$	10.0436	−	5.49356i	0.365767	−	0.200064i
$755$		−	30.4926i		−	1.10974i
$756$	−37.1397	−	2.90191i	−1.35076	−	0.105541i
$757$		−	17.0327i		−	0.619062i	−0.950889	−	0.309531i	$-0.899828\pi$
$757$		−	17.0327i		−	0.619062i	0.950889	−	0.309531i	$-0.100172\pi$
$758$	−25.9993	−	47.5332i	−0.944336	−	1.72649i
$759$	−8.87696	+	35.7609i	−0.322213	+	1.29804i
$760$	9.43241	+	2.34616i	0.342149	+	0.0851043i
$761$	−21.2571	−	17.8368i	−0.770569	−	0.646584i	0.170286	−	0.985395i	$-0.445531\pi$
$761$	−21.2571	−	17.8368i	−0.770569	−	0.646584i	−0.940855	+	0.338811i	$0.889975\pi$
$762$	−3.54378	+	12.9864i	−0.128378	+	0.470448i
$763$	7.94486	−	21.8283i	0.287623	−	0.790238i
$764$	1.75735	+	0.733144i	0.0635786	+	0.0265242i
$765$	−64.2991	−	50.0223i	−2.32474	−	1.80856i
$766$	−3.85037	−	0.770962i	−0.139119	−	0.0278560i
$767$	4.49267	−	3.76979i	0.162221	−	0.136119i
$768$	−25.2132	−	11.5020i	−0.909802	−	0.415044i
$769$	2.25754	−	12.8032i	0.0814091	−	0.461694i	−0.916665	−	0.399657i	$-0.869129\pi$
$769$	2.25754	−	12.8032i	0.0814091	−	0.461694i	0.998074	−	0.0620369i	$-0.0197596\pi$
$770$	50.9844	−	7.78108i	1.83735	−	0.280411i
$771$	9.05491	−	0.961169i	0.326105	−	0.0346157i
$772$	−8.95320	+	39.9061i	−0.322233	+	1.43625i
$773$	−13.6541	−	7.88319i	−0.491104	−	0.283539i	0.233929	−	0.972254i	$-0.424842\pi$
$773$	−13.6541	−	7.88319i	−0.491104	−	0.283539i	−0.725032	+	0.688715i	$0.758175\pi$
$774$	17.0132	−	3.24413i	0.611526	−	0.116608i
$775$	8.26895	+	14.3222i	0.297029	+	0.514470i
$776$	−15.4395	−	21.2257i	−0.554247	−	0.761959i
$777$	0.720164	−	1.07007i	0.0258357	−	0.0383886i
$778$	−10.7883	−	4.21110i	−0.386780	−	0.150975i
$779$	1.93085	+	5.30495i	0.0691797	+	0.190070i
$780$	−17.3990	+	7.53424i	−0.622985	+	0.269769i
$781$	27.5313	−	4.85451i	0.985146	−	0.173708i
$782$	25.7157	+	76.0730i	0.919593	+	2.72036i
$783$	−22.9351	−	14.2328i	−0.819635	−	0.508639i
$784$	6.17076	−	22.5710i	0.220384	−	0.806107i
$785$	0.171972	+	0.975299i	0.00613793	+	0.0348099i
$786$	3.58730	−	7.60154i	0.127955	−	0.271138i
$787$	−8.90762	−	24.4735i	−0.317523	−	0.872386i	−0.991082	−	0.133253i	$-0.957458\pi$
$787$	−8.90762	−	24.4735i	−0.317523	−	0.872386i	0.673560	−	0.739133i	$-0.264764\pi$
$788$	−0.939751	+	20.3399i	−0.0334772	+	0.724580i
$789$	2.50789	−	36.4049i	0.0892831	−	1.29605i
$790$	12.7940	+	0.295398i	0.455189	+	0.0105098i
$791$	23.1806	+	40.1500i	0.824207	+	1.42757i
$792$	9.14697	−	22.8118i	0.325024	−	0.810582i
$793$	−6.70352	+	11.6108i	−0.238049	+	0.412313i
$794$	16.6013	−	27.2800i	0.589158	−	0.968132i
$795$	−7.88126	+	17.7509i	−0.279519	+	0.629560i
$796$	13.4757	+	26.0477i	0.477635	+	0.923238i
$797$	−21.2149	−	3.74076i	−0.751470	−	0.132504i	−0.215222	−	0.976565i	$-0.569048\pi$
$797$	−21.2149	−	3.74076i	−0.751470	−	0.132504i	−0.536248	+	0.844061i	$0.680159\pi$
$798$	7.01442	+	4.95977i	0.248308	+	0.175574i
$799$	12.3830	−	10.3905i	0.438078	−	0.367591i
$800$	−18.5925	+	37.1069i	−0.657345	+	1.31193i
$801$	−24.2008	−	12.8037i	−0.855093	−	0.452397i
$802$	31.6258	−	35.9701i	1.11674	−	1.27015i
$803$	3.37510	−	9.27301i	0.119105	−	0.327238i
$804$	−9.27106	−	4.63979i	−0.326965	−	0.163633i
$805$	59.4408	−	70.8388i	2.09501	−	2.49674i
$806$	−3.87791	+	3.10427i	−0.136594	+	0.109343i
$807$	2.53948	−	0.731025i	0.0893939	−	0.0257333i
$808$	−23.5292	−	10.4601i	−0.827754	−	0.367986i
$809$	20.6468			0.725903			0.362951	−	0.931808i	$-0.381769\pi$
$809$	20.6468			0.725903			0.362951	+	0.931808i	$0.381769\pi$
$810$	35.6631	+	26.9580i	1.25308	+	0.947207i
$811$		−	16.1001i		−	0.565351i	−0.959216	−	0.282675i	$-0.908778\pi$
$811$		−	16.1001i		−	0.565351i	0.959216	−	0.282675i	$-0.0912219\pi$
$812$	25.2303	−	27.3942i	0.885408	−	0.961347i
$813$	15.0882	+	52.4143i	0.529166	+	1.83825i
$814$	0.531795	+	0.664327i	0.0186394	+	0.0232846i
$815$	13.3379	+	11.1918i	0.467207	+	0.392033i
$816$	−10.0079	−	52.6201i	−0.350347	−	1.84207i
$817$	−3.75318	−	1.36604i	−0.131307	−	0.0477918i
$818$	20.6762	−	23.5165i	0.722926	−	0.822234i
$819$	−16.7464	+	0.619447i	−0.585167	+	0.0216452i
$820$	−40.2008	+	5.18884i	−1.40387	+	0.181202i
$821$	23.8617	+	28.4372i	0.832778	+	0.992466i	0.999979	+	0.00654316i	$0.00208277\pi$
$821$	23.8617	+	28.4372i	0.832778	+	0.992466i	−0.167201	+	0.985923i	$0.553473\pi$
$822$	−9.95332	+	14.0766i	−0.347162	+	0.490978i
$823$	3.10968	−	17.6359i	0.108397	−	0.614747i	−0.881413	−	0.472347i	$-0.843407\pi$
$823$	3.10968	−	17.6359i	0.108397	−	0.614747i	0.989809	−	0.142400i	$-0.0454820\pi$
$824$	−14.1403	+	14.6591i	−0.492602	+	0.510675i
$825$	−33.6416	−	14.9366i	−1.17125	−	0.520025i
$826$	9.91857	−	16.2987i	0.345111	−	0.567103i
$827$	−10.8864	−	6.28525i	−0.378556	−	0.218560i	0.298634	−	0.954368i	$-0.403469\pi$
$827$	−10.8864	−	6.28525i	−0.378556	−	0.218560i	−0.677190	+	0.735808i	$0.736802\pi$
$828$	−14.6904	−	41.5464i	−0.510527	−	1.44384i
$829$	−34.2984	+	19.8022i	−1.19123	+	0.687758i	−0.958586	−	0.284804i	$-0.908072\pi$
$829$	−34.2984	+	19.8022i	−1.19123	+	0.687758i	−0.232646	+	0.972562i	$0.574738\pi$
$830$	0.732185	−	31.7117i	0.0254145	−	1.10073i
$831$	−10.2434	−	0.705654i	−0.355340	−	0.0244789i
$832$	−11.8605	−	3.83905i	−0.411188	−	0.133095i
$833$	42.4987	−	15.4683i	1.47249	−	0.535944i
$834$	−5.83789	+	12.3706i	−0.202149	+	0.428357i
$835$	35.3527	−	6.23364i	1.22343	−	0.215724i
$836$	−4.50523	+	3.43886i	−0.155816	+	0.118936i
$837$	10.8730	+	4.35384i	0.375828	+	0.150491i
$838$	−16.7645	+	5.66707i	−0.579119	+	0.195766i
$839$	−0.761220	−	4.31709i	−0.0262802	−	0.149043i	0.968844	−	0.247672i	$-0.0796654\pi$
$839$	−0.761220	−	4.31709i	−0.0262802	−	0.149043i	−0.995124	+	0.0986290i	$0.968554\pi$
$840$	−45.7729	+	41.3463i	−1.57932	+	1.42658i
$841$	−1.89355	+	0.689197i	−0.0652950	+	0.0237654i
$842$	39.4755	+	15.4089i	1.36042	+	0.531024i
$843$	39.3464	+	26.4804i	1.35516	+	0.912032i
$844$	0.450183	+	1.44053i	0.0154959	+	0.0495850i
$845$	32.1574	−	18.5661i	1.10625	−	0.638693i
$846$	−6.71553	+	5.79582i	−0.230885	+	0.199264i
$847$	4.67884	−	8.10400i	0.160767	−	0.278457i
$848$	−11.6006	+	5.33800i	−0.398368	+	0.183308i
$849$	6.04491	+	56.9474i	0.207461	+	1.95443i
$850$	−79.3013	+	12.1027i	−2.72001	+	0.415120i
$851$	1.50259	+	0.264948i	0.0515083	+	0.00908230i
$852$	−24.2872	+	22.9784i	−0.832066	+	0.787228i
$853$	17.4553	+	20.8024i	0.597656	+	0.712259i	0.977058	−	0.212973i	$-0.0683146\pi$
$853$	17.4553	+	20.8024i	0.597656	+	0.712259i	−0.379402	+	0.925232i	$0.623870\pi$
$854$	−8.56334	+	42.7673i	−0.293031	+	1.46347i
$855$	−3.88172	−	9.55073i	−0.132752	−	0.326628i
$856$	48.0147	+	3.33055i	1.64111	+	0.113836i
$857$	−32.6078	−	11.8683i	−1.11386	−	0.405413i	−0.281453	−	0.959575i	$-0.590816\pi$
$857$	−32.6078	−	11.8683i	−1.11386	−	0.405413i	−0.832409	+	0.554162i	$0.813039\pi$
$858$	2.91054	−	10.6659i	0.0993644	−	0.364127i
$859$	9.80975	−	11.6908i	0.334704	−	0.398885i	−0.572274	−	0.820062i	$-0.693939\pi$
$859$	9.80975	−	11.6908i	0.334704	−	0.398885i	0.906978	+	0.421178i	$0.138383\pi$
$860$	15.4696	−	24.1471i	0.527510	−	0.823409i
$861$	−34.7706	−	8.63114i	−1.18498	−	0.294149i
$862$	29.7954	−	16.2972i	1.01484	−	0.555086i
$863$	−14.5657			−0.495821			−0.247911	−	0.968783i	$-0.579744\pi$
$863$	−14.5657			−0.495821			−0.247911	+	0.968783i	$0.579744\pi$
$864$	5.89252	+	28.7972i	0.200468	+	0.979700i
$865$	2.01585			0.0685411
$866$	1.26993	−	0.694614i	0.0431540	−	0.0236039i
$867$	51.4069	−	53.3436i	1.74587	−	1.81164i
$868$	−8.71729	+	13.6071i	−0.295884	+	0.461856i
$869$	−4.79665	+	5.71642i	−0.162715	+	0.193916i
$870$	−43.2230	+	11.3688i	−1.46540	+	0.385439i
$871$	−4.38236	−	1.59505i	−0.148491	−	0.0540461i
$872$	−18.2847	−	1.26832i	−0.619199	−	0.0429508i
$873$	−8.54807	+	26.4944i	−0.289309	+	0.896701i
$874$	−1.99518	+	9.96440i	−0.0674880	+	0.337051i
$875$	18.9138	+	22.5406i	0.639403	+	0.762011i
$876$	2.73788	+	11.4801i	0.0925044	+	0.387876i
$877$	−38.2453	−	6.74367i	−1.29145	−	0.227718i	−0.514616	−	0.857421i	$-0.672065\pi$
$877$	−38.2453	−	6.74367i	−1.29145	−	0.227718i	−0.776836	+	0.629703i	$0.783176\pi$
$878$	−10.8673	+	1.65853i	−0.366752	+	0.0559725i
$879$	−44.7355	+	32.5729i	−1.50889	+	1.09866i
$880$	−17.0108	−	36.9683i	−0.573435	−	1.24620i
$881$	−23.9111	+	41.4153i	−0.805586	+	1.39532i	0.110309	+	0.993897i	$0.464816\pi$
$881$	−23.9111	+	41.4153i	−0.805586	+	1.39532i	−0.915895	+	0.401419i	$0.868517\pi$
$882$	−23.2018	+	8.81158i	−0.781246	+	0.296701i
$883$	−11.1556	+	6.44070i	−0.375417	+	0.216747i	−0.675822	−	0.737065i	$-0.736211\pi$
$883$	−11.1556	+	6.44070i	−0.375417	+	0.216747i	0.300406	+	0.953812i	$0.402878\pi$
$884$	−7.18718	−	22.9980i	−0.241731	−	0.773508i
$885$	−20.5687	+	10.0584i	−0.691411	+	0.338108i
$886$	8.88236	+	3.46713i	0.298409	+	0.116481i
$887$	−14.2711	+	5.19425i	−0.479176	+	0.174406i	−0.570304	−	0.821433i	$-0.693175\pi$
$887$	−14.2711	+	5.19425i	−0.479176	+	0.174406i	0.0911287	+	0.995839i	$0.470953\pi$
$888$	−0.968417	−	0.312954i	−0.0324980	−	0.0105020i
$889$	3.42081	+	19.4004i	0.114730	+	0.650667i
$890$	−42.9459	+	14.5175i	−1.43955	+	0.486626i
$891$	−25.2676	+	6.41095i	−0.846496	+	0.214775i
$892$	−9.74386	+	7.43754i	−0.326249	+	0.249027i
$893$	2.01457	−	0.355224i	0.0674151	−	0.0118871i
$894$	27.0741	+	39.0468i	0.905495	+	1.30592i
$895$	55.9014	−	20.3464i	1.86858	−	0.680106i
$896$	−40.5525	+	0.524773i	−1.35476	+	0.0175314i
$897$	−8.70831	−	17.8080i	−0.290762	−	0.594590i
$898$	0.752813	−	32.6051i	0.0251217	−	1.08805i
$899$	−10.1404	+	5.85454i	−0.338200	+	0.195260i
$900$	43.4216	−	7.24532i	1.44739	−	0.241511i
$901$	−21.3749	−	12.3408i	−0.712101	−	0.411131i
$902$	12.2873	−	20.1910i	0.409121	−	0.672287i
$903$	20.4902	−	14.9193i	0.681870	−	0.496485i
$904$	25.3963	−	26.3281i	0.844669	−	0.875659i
$905$	3.32697	−	18.8682i	0.110592	−	0.627199i
$906$	−21.1753	−	1.95075i	−0.703503	−	0.0648095i
$907$	2.50247	+	2.98233i	0.0830931	+	0.0990265i	0.805989	−	0.591930i	$-0.201634\pi$
$907$	2.50247	+	2.98233i	0.0830931	+	0.0990265i	−0.722896	+	0.690957i	$0.757189\pi$
$908$	37.2975	−	4.81411i	1.23776	−	0.159762i
$909$	5.73356	+	26.7029i	0.190170	+	0.885678i
$910$	−18.3214	+	20.8381i	−0.607347	+	0.690777i
$911$	−41.5625	−	15.1275i	−1.37703	−	0.501196i	−0.455750	−	0.890108i	$-0.650629\pi$
$911$	−41.5625	−	15.1275i	−1.37703	−	0.501196i	−0.921275	+	0.388911i	$0.872851\pi$
$912$	2.23271	−	6.40016i	0.0739324	−	0.211931i
$913$	14.1689	+	11.8892i	0.468924	+	0.393474i
$914$	−19.4654	−	24.3165i	−0.643859	−	0.804319i
$915$	36.3208	−	37.6892i	1.20073	−	1.24597i
$916$	−31.7483	+	34.4712i	−1.04899	+	1.13896i
$917$		−	12.3009i		−	0.406210i
$918$	−38.8511	+	41.4518i	−1.28228	+	1.36811i
$919$	7.23703			0.238727			0.119364	−	0.992851i	$-0.461915\pi$
$919$	7.23703			0.238727			0.119364	+	0.992851i	$0.461915\pi$
$920$	−66.6732	−	29.6402i	−2.19815	−	0.977208i
$921$	−0.465448	+	1.87506i	−0.0153370	+	0.0617853i
$922$	−32.2319	+	25.8017i	−1.06150	+	0.849734i
$923$	−9.66768	+	11.5215i	−0.318216	+	0.379235i
$924$	−2.14179	−	35.9035i	−0.0704597	−	1.18114i
$925$	−0.521310	+	1.43229i	−0.0171406	+	0.0470934i
$926$	−13.9378	+	15.8524i	−0.458024	+	0.520942i
$927$	21.3990	+	2.96236i	0.702837	+	0.0972966i
$928$	−26.2723	−	13.1638i	−0.862429	−	0.432123i
$929$	−25.6672	+	21.5374i	−0.842115	+	0.706618i	−0.958038	−	0.286640i	$-0.907462\pi$
$929$	−25.6672	+	21.5374i	−0.842115	+	0.706618i	0.115924	+	0.993258i	$0.463017\pi$
$930$	17.6134	−	8.11488i	0.577567	−	0.266098i
$931$	5.63641	+	0.993852i	0.184726	+	0.0325722i
$932$	−14.6262	−	28.2715i	−0.479097	−	0.926063i
$933$	16.8487	−	1.78848i	0.551603	−	0.0585521i
$934$	19.5375	−	32.1050i	0.639287	−	1.05051i
$935$	39.3270	−	68.1163i	1.28613	−	2.22764i
$936$	4.11899	+	12.5646i	0.134633	+	0.410687i
$937$	5.94845	+	10.3030i	0.194327	+	0.336585i	0.946680	−	0.322176i	$-0.104414\pi$
$937$	5.94845	+	10.3030i	0.194327	+	0.336585i	−0.752352	+	0.658761i	$0.771081\pi$
$938$	−15.1678	−	0.350206i	−0.495245	−	0.0114346i
$939$	26.5011	+	17.8354i	0.864832	+	0.582037i
$940$	−0.677889	+	14.6722i	−0.0221103	+	0.478554i
$941$	−3.22856	−	8.87040i	−0.105248	−	0.289167i	0.875879	−	0.482531i	$-0.160282\pi$
$941$	−3.22856	−	8.87040i	−0.105248	−	0.289167i	−0.981127	+	0.193364i	$0.938060\pi$
$942$	0.688290	−	0.0570297i	0.0224257	−	0.00185813i
$943$	−7.35905	−	41.7352i	−0.239644	−	1.35909i
$944$	−14.5214	−	3.97006i	−0.472632	−	0.129214i
$945$	64.0359	+	13.4039i	2.08309	+	0.436030i
$946$	5.35503	+	15.8414i	0.174107	+	0.515048i
$947$	0.288825	−	0.0509277i	0.00938556	−	0.00165493i	−0.168953	−	0.985624i	$-0.554039\pi$
$947$	0.288825	−	0.0509277i	0.00938556	−	0.00165493i	0.178339	+	0.983969i	$0.442928\pi$
$948$	1.02363	−	8.86577i	0.0332459	−	0.287947i
$949$	1.81580	+	4.98886i	0.0589432	+	0.161945i
$950$	−9.45685	−	3.69138i	−0.306821	−	0.119764i
$951$	48.6885	+	3.35409i	1.57883	+	0.108764i
$952$	−46.1098	−	63.3902i	−1.49443	−	2.05449i
$953$	19.5621	+	33.8825i	0.633678	+	1.09756i	0.986793	+	0.161983i	$0.0517891\pi$
$953$	19.5621	+	33.8825i	0.633678	+	1.09756i	−0.353115	+	0.935580i	$0.614878\pi$
$954$	11.8228	+	6.60868i	0.382777	+	0.213964i
$955$	−2.89605	−	1.67203i	−0.0937138	−	0.0541057i
$956$	−1.15074	+	5.12907i	−0.0372177	+	0.165886i
$957$	10.5753	−	23.8188i	0.341852	−	0.769952i
$958$	52.2877	−	7.97998i	1.68934	−	0.257822i
$959$	−4.38109	+	24.8464i	−0.141473	+	0.802331i
$960$	41.3293	+	25.7020i	1.33390	+	0.829527i
$961$	−19.8553	+	16.6606i	−0.640494	+	0.537439i
$962$	−0.448905	−	0.0898846i	−0.0144733	−	0.00289800i
$963$	−27.1416	−	43.2366i	−0.874626	−	1.39328i
$964$	9.31995	+	3.88817i	0.300175	+	0.125230i
$965$	24.5657	−	67.4937i	0.790798	−	2.17270i
$966$	−45.3907	−	45.8101i	−1.46042	−	1.47391i
$967$	30.8304	+	25.8698i	0.991440	+	0.831917i	0.985776	−	0.168067i	$-0.0537525\pi$
$967$	30.8304	+	25.8698i	0.991440	+	0.831917i	0.00566438	+	0.999984i	$0.498197\pi$
$968$	−7.16522	−	1.78224i	−0.230299	−	0.0572832i
$969$	12.5901	−	3.62423i	0.404452	−	0.116427i
$970$	22.1200	+	40.4410i	0.710231	+	1.29848i
$971$			52.4570i			1.68342i	0.539927	+	0.841712i	$0.318452\pi$
$971$			52.4570i			1.68342i	−0.539927	+	0.841712i	$0.681548\pi$
$972$	21.0023	−	23.0413i	0.673649	−	0.739051i
$973$			20.0181i			0.641751i
$974$	−13.2196	+	7.23073i	−0.423583	+	0.231687i
$975$	19.0301	−	5.47807i	0.609450	−	0.175439i
$976$	34.2985	−	2.82550i	1.09787	−	0.0904421i
$977$	−35.9884	−	30.1979i	−1.15137	−	0.966116i	−0.151621	−	0.988439i	$-0.548449\pi$
$977$	−35.9884	−	30.1979i	−1.15137	−	0.966116i	−0.999751	+	0.0223228i	$0.992894\pi$
$978$	8.62537	−	8.54641i	0.275809	−	0.273284i
$979$	9.04103	−	24.8400i	0.288953	−	0.793891i
$980$	−15.8222	+	37.9258i	−0.505422	+	1.21150i
$981$	10.3359	+	16.4651i	0.330001	+	0.525691i
$982$	10.5906	−	52.8919i	0.337960	−	1.68785i
$983$	22.9807	−	19.2831i	0.732970	−	0.615035i	−0.197969	−	0.980208i	$-0.563435\pi$
$983$	22.9807	−	19.2831i	0.732970	−	0.615035i	0.930940	+	0.365173i	$0.118990\pi$
$984$	1.03151	+	28.2490i	0.0328835	+	0.900547i
$985$	6.20951	−	35.2159i	0.197851	−	1.12207i
$986$	−8.56890	−	56.1465i	−0.272890	−	1.78807i
$987$	−5.26789	+	11.8649i	−0.167679	+	0.377662i
$988$	0.667517	−	2.97525i	0.0212366	−	0.0946552i
$989$	25.9656	+	14.9913i	0.825659	+	0.476695i
$990$	−21.0602	+	37.6762i	−0.669337	+	1.19743i
$991$	−26.0323	−	45.0893i	−0.826945	−	1.43231i	−0.900424	−	0.435013i	$-0.856744\pi$
$991$	−26.0323	−	45.0893i	−0.826945	−	1.43231i	0.0734794	−	0.997297i	$-0.476590\pi$
$992$	12.2185	+	3.64559i	0.387939	+	0.115747i
$993$	−51.0542	−	3.51705i	−1.62016	−	0.111610i
$994$	−17.7917	+	45.5801i	−0.564318	+	1.44571i
$995$	−17.6155	−	48.3983i	−0.558450	−	1.53433i
$996$	−21.9751	−	2.53721i	−0.696306	−	0.0803944i
$997$	−10.3169	+	1.81914i	−0.326738	+	0.0576128i	−0.334611	−	0.942356i	$-0.608605\pi$
$997$	−10.3169	+	1.81914i	−0.326738	+	0.0576128i	0.00787296	+	0.999969i	$0.497494\pi$
$998$	31.0597	−	10.4995i	0.983179	−	0.332354i
$999$	0.336753	+	1.02559i	0.0106544	+	0.0324483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.13.30	yes	204
3.2	odd	2		648.2.t.a.253.5		204
4.3	odd	2		864.2.bf.a.337.14		204
8.3	odd	2		864.2.bf.a.337.21		204
8.5	even	2	inner	216.2.t.a.13.1	✓	204
24.5	odd	2		648.2.t.a.253.34		204
27.2	odd	18		648.2.t.a.397.34		204
27.25	even	9	inner	216.2.t.a.133.1	yes	204
108.79	odd	18		864.2.bf.a.241.21		204
216.29	odd	18		648.2.t.a.397.5		204
216.133	even	18	inner	216.2.t.a.133.30	yes	204
216.187	odd	18		864.2.bf.a.241.14		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.1	✓	204	8.5	even	2	inner
216.2.t.a.13.30	yes	204	1.1	even	1	trivial
216.2.t.a.133.1	yes	204	27.25	even	9	inner
216.2.t.a.133.30	yes	204	216.133	even	18	inner
648.2.t.a.253.5		204	3.2	odd	2
648.2.t.a.253.34		204	24.5	odd	2
648.2.t.a.397.5		204	216.29	odd	18
648.2.t.a.397.34		204	27.2	odd	18
864.2.bf.a.241.14		204	216.187	odd	18
864.2.bf.a.241.21		204	108.79	odd	18
864.2.bf.a.337.14		204	4.3	odd	2
864.2.bf.a.337.21		204	8.3	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)

\(f(q)\)	\(=\)	\(q+(1.24074 - 0.678648i) q^{2} +(0.479138 + 1.66446i) q^{3} +(1.07887 - 1.68405i) q^{4} +(-2.25773 + 2.69066i) q^{5} +(1.72407 + 1.74000i) q^{6} +(3.36848 + 1.22603i) q^{7} +(0.195724 - 2.82165i) q^{8} +(-2.54085 + 1.59501i) q^{9} +O(q^{10})\)	\(q+(1.24074 - 0.678648i) q^{2} +(0.479138 + 1.66446i) q^{3} +(1.07887 - 1.68405i) q^{4} +(-2.25773 + 2.69066i) q^{5} +(1.72407 + 1.74000i) q^{6} +(3.36848 + 1.22603i) q^{7} +(0.195724 - 2.82165i) q^{8} +(-2.54085 + 1.59501i) q^{9} +(-0.975248 + 4.87061i) q^{10} +(-1.86181 - 2.21882i) q^{11} +(3.31997 + 0.988849i) q^{12} +(1.53462 + 0.270594i) q^{13} +(5.01146 - 0.764832i) q^{14} +(-5.56026 - 2.46871i) q^{15} +(-1.67206 - 3.63376i) q^{16} +(3.86560 - 6.69542i) q^{17} +(-2.07009 + 3.70334i) q^{18} +(0.847303 - 0.489191i) q^{19} +(2.09540 + 6.70502i) q^{20} +(-0.426706 + 6.19414i) q^{21} +(-3.81583 - 1.48947i) q^{22} +(-6.90160 + 2.51198i) q^{23} +(4.79030 - 1.02618i) q^{24} +(-1.27406 - 7.22553i) q^{25} +(2.08770 - 0.705728i) q^{26} +(-3.87225 - 3.46492i) q^{27} +(5.69886 - 4.34997i) q^{28} +(5.11578 - 0.902050i) q^{29} +(-8.57422 + 0.710435i) q^{30} +(-2.11811 + 0.770928i) q^{31} +(-4.54064 - 3.37381i) q^{32} +(2.80108 - 4.16204i) q^{33} +(0.252376 - 10.9307i) q^{34} +(-10.9040 + 6.29540i) q^{35} +(-0.0551779 + 5.99975i) q^{36} +(-0.179911 - 0.103872i) q^{37} +(0.719295 - 1.18198i) q^{38} +(0.284900 + 2.68396i) q^{39} +(7.15020 + 6.89715i) q^{40} +(-1.00198 + 5.68249i) q^{41} +(3.67421 + 7.97491i) q^{42} +(-2.62405 - 3.12722i) q^{43} +(-5.74527 + 0.741561i) q^{44} +(1.44493 - 10.4377i) q^{45} +(-6.85834 + 7.80046i) q^{46} +(1.96476 + 0.715114i) q^{47} +(5.24710 - 4.52415i) q^{48} +(4.48123 + 3.76020i) q^{49} +(-6.48436 - 8.10037i) q^{50} +(12.9964 + 3.22611i) q^{51} +(2.11135 - 2.29244i) q^{52} -3.19246i q^{53} +(-7.15592 - 1.67117i) q^{54} +10.1736 q^{55} +(4.11871 - 9.26471i) q^{56} +(1.22021 + 1.17591i) q^{57} +(5.73518 - 4.59103i) q^{58} +(2.41918 - 2.88307i) q^{59} +(-10.1562 + 6.70034i) q^{60} +(-2.94263 + 8.08481i) q^{61} +(-2.10483 + 2.39397i) q^{62} +(-10.5144 + 2.25761i) q^{63} +(-7.92338 - 1.10453i) q^{64} +(-4.19283 + 3.51820i) q^{65} +(0.650851 - 7.06495i) q^{66} +(-2.94730 - 0.519689i) q^{67} +(-7.10494 - 13.7334i) q^{68} +(-7.48790 - 10.2838i) q^{69} +(-9.25662 + 15.2109i) q^{70} +(-4.82588 + 8.35866i) q^{71} +(4.00325 + 7.48157i) q^{72} +(1.70348 + 2.95051i) q^{73} +(-0.293715 - 0.00678153i) q^{74} +(11.4162 - 5.58264i) q^{75} +(0.0903106 - 1.95468i) q^{76} +(-3.55115 - 9.75670i) q^{77} +(2.17495 + 3.13675i) q^{78} +(-0.447375 - 2.53719i) q^{79} +(13.5523 + 3.70510i) q^{80} +(3.91188 - 8.10538i) q^{81} +(2.61322 + 7.73049i) q^{82} +(-6.28878 + 1.10888i) q^{83} +(9.97090 + 7.40129i) q^{84} +(9.28760 + 25.5175i) q^{85} +(-5.37805 - 2.09926i) q^{86} +(3.95259 + 8.08281i) q^{87} +(-6.62514 + 4.81910i) q^{88} +(4.56318 + 7.90366i) q^{89} +(-5.29072 - 13.9311i) q^{90} +(4.83758 + 2.79298i) q^{91} +(-3.21565 + 14.3328i) q^{92} +(-2.29804 - 3.15612i) q^{93} +(2.92307 - 0.446109i) q^{94} +(-0.596737 + 3.38427i) q^{95} +(3.43998 - 9.17423i) q^{96} +(7.10870 - 5.96491i) q^{97} +(8.11189 + 1.62425i) q^{98} +(8.26964 + 2.66809i) 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

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