LMFDB - Embedded newform 216.2.t.a.13.1

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			13.1
Character	$\chi$	$=$	216.13
Dual form			216.2.t.a.133.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39803 - 0.213362i) q^{2} +(-0.479138 - 1.66446i) q^{3} +(1.90895 + 0.596572i) q^{4} +(2.25773 - 2.69066i) q^{5} +(0.314714 + 2.42919i) q^{6} +(3.36848 + 1.22603i) q^{7} +(-2.54148 - 1.24132i) q^{8} +(-2.54085 + 1.59501i) q^{9} +O(q^{10})$	\(q+(-1.39803 - 0.213362i) q^{2} +(-0.479138 - 1.66446i) q^{3} +(1.90895 + 0.596572i) q^{4} +(2.25773 - 2.69066i) q^{5} +(0.314714 + 2.42919i) q^{6} +(3.36848 + 1.22603i) q^{7} +(-2.54148 - 1.24132i) q^{8} +(-2.54085 + 1.59501i) q^{9} +(-3.73045 + 3.27990i) q^{10} +(1.86181 + 2.21882i) q^{11} +(0.0783185 - 3.46322i) q^{12} +(-1.53462 - 0.270594i) q^{13} +(-4.44764 - 2.43273i) q^{14} +(-5.56026 - 2.46871i) q^{15} +(3.28820 + 2.27766i) q^{16} +(3.86560 - 6.69542i) q^{17} +(3.89249 - 1.68775i) q^{18} +(-0.847303 + 0.489191i) q^{19} +(5.91507 - 3.78944i) q^{20} +(0.426706 - 6.19414i) q^{21} +(-2.12945 - 3.49921i) q^{22} +(-6.90160 + 2.51198i) q^{23} +(-0.848411 + 4.82496i) 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} +(7.24666 + 4.63766i) q^{30} +(-2.11811 + 0.770928i) q^{31} +(-4.11103 - 3.88580i) q^{32} +(2.80108 - 4.16204i) q^{33} +(-6.83276 + 8.53559i) q^{34} +(10.9040 - 6.29540i) q^{35} +(-5.80191 + 1.52900i) q^{36} +(0.179911 + 0.103872i) q^{37} +(1.28893 - 0.503119i) q^{38} +(0.284900 + 2.68396i) q^{39} +(-9.07795 + 4.03569i) q^{40} +(-1.00198 + 5.68249i) q^{41} +(-1.91814 + 8.56853i) q^{42} +(2.62405 + 3.12722i) q^{43} +(2.23043 + 5.34633i) q^{44} +(-1.44493 + 10.4377i) q^{45} +(10.1846 - 2.03927i) q^{46} +(1.96476 + 0.715114i) q^{47} +(2.21556 - 6.56439i) q^{48} +(4.48123 + 3.76020i) q^{49} +(0.239508 + 10.3733i) q^{50} +(-12.9964 - 3.22611i) q^{51} +(-2.76808 - 1.43206i) q^{52} +3.19246i q^{53} +(-4.67423 - 5.67024i) q^{54} +10.1736 q^{55} +(-7.03904 - 7.29730i) q^{56} +(1.22021 + 1.17591i) q^{57} +(7.34446 - 0.169575i) q^{58} +(-2.41918 + 2.88307i) q^{59} +(-9.14151 - 8.02974i) q^{60} +(2.94263 - 8.08481i) q^{61} +(3.12566 - 0.625853i) q^{62} +(-10.5144 + 2.25761i) q^{63} +(4.91824 + 6.30959i) q^{64} +(-4.19283 + 3.51820i) q^{65} +(-4.80400 + 5.22099i) q^{66} +(2.94730 + 0.519689i) q^{67} +(11.3736 - 10.4751i) q^{68} +(7.48790 + 10.2838i) q^{69} +(-16.5872 + 6.47464i) q^{70} +(-4.82588 + 8.35866i) q^{71} +(8.43745 - 0.899673i) q^{72} +(1.70348 + 2.95051i) q^{73} +(-0.229358 - 0.183601i) q^{74} +(-11.4162 + 5.58264i) q^{75} +(-1.90930 + 0.428365i) q^{76} +(3.55115 + 9.75670i) q^{77} +(0.174359 - 3.81303i) 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} +(4.50981 - 11.5698i) q^{84} +(-9.28760 - 25.5175i) q^{85} +(-3.00126 - 4.93181i) q^{86} +(3.95259 + 8.08281i) q^{87} +(-1.97749 - 7.95020i) q^{88} +(4.56318 + 7.90366i) q^{89} +(4.24706 - 14.2839i) q^{90} +(-4.83758 - 2.79298i) q^{91} +(-14.6734 + 0.677944i) q^{92} +(2.29804 + 3.15612i) q^{93} +(-2.59420 - 1.41895i) q^{94} +(-0.596737 + 3.38427i) q^{95} +(-4.49801 + 8.70448i) q^{96} +(7.10870 - 5.96491i) q^{97} +(-5.46259 - 6.21298i) 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 $

$2$	−1.39803	−	0.213362i	−0.988554	−	0.150870i
$2$	−1.39803	−	0.213362i	−0.988554	−	0.150870i
$3$	−0.479138	−	1.66446i	−0.276630	−	0.960976i
$3$	−0.479138	−	1.66446i	−0.276630	−	0.960976i
$4$	1.90895	+	0.596572i	0.954477	+	0.298286i
$5$	2.25773	−	2.69066i	1.00969	−	1.20330i	0.0306692	−	0.999530i	$-0.490236\pi$
$5$	2.25773	−	2.69066i	1.00969	−	1.20330i	0.979019	−	0.203770i	$-0.0653194\pi$
$6$	0.314714	+	2.42919i	0.128482	+	0.991712i
$7$	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	$0.374201\pi$
$8$	−2.54148	−	1.24132i	−0.898549	−	0.438874i
$9$	−2.54085	+	1.59501i	−0.846951	+	0.531671i
$10$	−3.73045	+	3.27990i	−1.17967	+	1.03719i
$11$	1.86181	+	2.21882i	0.561358	+	0.669000i	0.969833	−	0.243769i	$-0.0783839\pi$
$11$	1.86181	+	2.21882i	0.561358	+	0.669000i	−0.408475	+	0.912769i	$0.633939\pi$
$12$	0.0783185	−	3.46322i	0.0226086	−	0.999744i
$13$	−1.53462	−	0.270594i	−0.425626	−	0.0750494i	−0.0432679	−	0.999064i	$-0.513777\pi$
$13$	−1.53462	−	0.270594i	−0.425626	−	0.0750494i	−0.382358	+	0.924014i	$0.624888\pi$
$14$	−4.44764	−	2.43273i	−1.18868	−	0.650173i
$15$	−5.56026	−	2.46871i	−1.43565	−	0.637417i
$16$	3.28820	+	2.27766i	0.822051	+	0.569414i
$17$	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	$-0.220241\pi$
$18$	3.89249	−	1.68775i	0.917470	−	0.397805i
$19$	−0.847303	+	0.489191i	−0.194385	+	0.112228i	−0.594034	−	0.804440i	$-0.702465\pi$
$19$	−0.847303	+	0.489191i	−0.194385	+	0.112228i	0.399649	+	0.916668i	$0.369132\pi$
$20$	5.91507	−	3.78944i	1.32265	−	0.847345i
$21$	0.426706	−	6.19414i	0.0931149	−	1.35167i
$22$	−2.12945	−	3.49921i	−0.454000	−	0.746035i
$23$	−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	$0.666506\pi$
$24$	−0.848411	+	4.82496i	−0.173181	+	0.984890i
$25$	−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	−0.627104	−	0.778936i	$-0.715760\pi$
$29$	−5.11578	+	0.902050i	−0.949977	+	0.167507i	−0.322873	+	0.946442i	$0.604649\pi$
$30$	7.24666	+	4.63766i	1.32305	+	0.846718i
$31$	−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	$0.453769\pi$
$32$	−4.11103	−	3.88580i	−0.726734	−	0.686919i
$33$	2.80108	−	4.16204i	0.487605	−	0.724517i
$34$	−6.83276	+	8.53559i	−1.17181	+	1.46384i
$35$	10.9040	−	6.29540i	1.84310	−	1.06412i
$36$	−5.80191	+	1.52900i	−0.966985	+	0.254833i
$37$	0.179911	+	0.103872i	0.0295771	+	0.0170764i	0.514716	−	0.857361i	$-0.327897\pi$
$37$	0.179911	+	0.103872i	0.0295771	+	0.0170764i	−0.485139	+	0.874437i	$0.661231\pi$
$38$	1.28893	−	0.503119i	0.209092	−	0.0816167i
$39$	0.284900	+	2.68396i	0.0456205	+	0.429778i
$40$	−9.07795	+	4.03569i	−1.43535	+	0.638098i
$41$	−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	$0.906775\pi$
$42$	−1.91814	+	8.56853i	−0.295976	+	1.32215i
$43$	2.62405	+	3.12722i	0.400164	+	0.476897i	0.928070	−	0.372406i	$-0.121467\pi$
$43$	2.62405	+	3.12722i	0.400164	+	0.476897i	−0.527906	+	0.849303i	$0.677023\pi$
$44$	2.23043	+	5.34633i	0.336249	+	0.805990i
$45$	−1.44493	+	10.4377i	−0.215398	+	1.55596i
$46$	10.1846	−	2.03927i	1.50163	−	0.300673i
$47$	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	$0.562382\pi$
$48$	2.21556	−	6.56439i	0.319789	−	0.947489i
$49$	4.48123	+	3.76020i	0.640176	+	0.537171i
$50$	0.239508	+	10.3733i	0.0338715	+	1.46701i
$51$	−12.9964	−	3.22611i	−1.81986	−	0.451746i
$52$	−2.76808	−	1.43206i	−0.383864	−	0.198591i
$53$			3.19246i			0.438519i	0.975667	+	0.219259i	$0.0703641\pi$
$53$			3.19246i			0.438519i	−0.975667	+	0.219259i	$0.929636\pi$
$54$	−4.67423	−	5.67024i	−0.636082	−	0.771622i
$55$	10.1736			1.37180
$56$	−7.03904	−	7.29730i	−0.940631	−	0.975142i
$57$	1.22021	+	1.17591i	0.161621	+	0.155753i
$58$	7.34446	−	0.169575i	0.964375	−	0.0222663i
$59$	−2.41918	+	2.88307i	−0.314951	+	0.375344i	−0.900176	−	0.435527i	$-0.856562\pi$
$59$	−2.41918	+	2.88307i	−0.314951	+	0.375344i	0.585225	+	0.810871i	$0.301006\pi$
$60$	−9.14151	−	8.02974i	−1.18016	−	1.03663i
$61$	2.94263	−	8.08481i	0.376765	−	1.03515i	−0.595924	−	0.803041i	$-0.703214\pi$
$61$	2.94263	−	8.08481i	0.376765	−	1.03515i	0.972689	−	0.232113i	$-0.0745639\pi$
$62$	3.12566	−	0.625853i	0.396959	−	0.0794834i
$63$	−10.5144	+	2.25761i	−1.32468	+	0.284433i
$64$	4.91824	+	6.30959i	0.614780	+	0.788699i
$65$	−4.19283	+	3.51820i	−0.520057	+	0.436379i
$66$	−4.80400	+	5.22099i	−0.591331	+	0.642659i
$67$	2.94730	+	0.519689i	0.360070	+	0.0634901i	0.350757	−	0.936466i	$-0.385924\pi$
$67$	2.94730	+	0.519689i	0.360070	+	0.0634901i	0.00931341	+	0.999957i	$0.497035\pi$
$68$	11.3736	−	10.4751i	1.37925	−	1.27030i
$69$	7.48790	+	10.2838i	0.901437	+	1.23803i
$70$	−16.5872	+	6.47464i	−1.98255	+	0.773868i
$71$	−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	$0.972552\pi$
$72$	8.43745	−	0.899673i	0.994363	−	0.106027i
$73$	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	$0.769442\pi$
$74$	−0.229358	−	0.183601i	−0.0266623	−	0.0213432i
$75$	−11.4162	+	5.58264i	−1.31822	+	0.644628i
$76$	−1.90930	+	0.428365i	−0.219012	+	0.0491368i
$77$	3.55115	+	9.75670i	0.404691	+	1.11188i
$78$	0.174359	−	3.81303i	0.0197423	−	0.431741i
$79$	−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	0.182507	−	0.983205i	$-0.441579\pi$
$83$	6.28878	−	1.10888i	0.690283	−	0.121716i	0.507776	+	0.861489i	$0.330468\pi$
$84$	4.50981	−	11.5698i	0.492061	−	1.26237i
$85$	−9.28760	−	25.5175i	−1.00738	−	2.76776i
$86$	−3.00126	−	4.93181i	−0.323634	−	0.531811i
$87$	3.95259	+	8.08281i	0.423762	+	0.866568i
$88$	−1.97749	−	7.95020i	−0.210801	−	0.847494i
$89$	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	$0.672627\pi$
$90$	4.24706	−	14.2839i	0.447679	−	1.50565i
$91$	−4.83758	−	2.79298i	−0.507116	−	0.292784i
$92$	−14.6734	+	0.677944i	−1.52981	+	0.0706806i
$93$	2.29804	+	3.15612i	0.238296	+	0.327275i
$94$	−2.59420	−	1.41895i	−0.267572	−	0.146354i
$95$	−0.596737	+	3.38427i	−0.0612240	+	0.347218i
$96$	−4.49801	+	8.70448i	−0.459076	+	0.888397i
$97$	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	$0.121632\pi$
$98$	−5.46259	−	6.21298i	−0.551805	−	0.627606i
$99$	−8.26964	−	2.66809i	−0.831130	−	0.268153i
$100$	1.87844	−	14.5533i	0.187844	−	1.45533i
$101$	−3.11369	+	8.55479i	−0.309824	+	0.851234i	0.682866	+	0.730543i	$0.260733\pi$
$101$	−3.11369	+	8.55479i	−0.309824	+	0.851234i	−0.992690	+	0.120691i	$0.961489\pi$
$102$	17.4810	+	7.28313i	1.73088	+	0.721137i
$103$	−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	$0.837663\pi$
$104$	3.56430	+	2.59266i	0.349509	+	0.254232i
$105$	−15.7029	−	15.1328i	−1.53245	−	1.47681i
$106$	0.681151	−	4.46315i	0.0661593	−	0.433499i
$107$		−	17.0166i		−	1.64505i	−0.568727	−	0.822526i	$-0.692564\pi$
$107$		−	17.0166i		−	1.64505i	0.568727	−	0.822526i	$-0.307436\pi$
$108$	5.32487	+	8.92444i	0.512386	+	0.858755i
$109$			6.48016i			0.620687i	0.950625	+	0.310343i	$0.100444\pi$
$109$			6.48016i			0.620687i	−0.950625	+	0.310343i	$0.899556\pi$
$110$	−14.2229	−	2.17066i	−1.35610	−	0.206964i
$111$	0.0866879	−	0.349223i	0.00822805	−	0.0331468i
$112$	8.28379	+	11.7037i	0.782745	+	1.10589i
$113$	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	$0.514063\pi$
$114$	−1.45499	−	1.90430i	−0.136273	−	0.178354i
$115$	−8.82308	+	24.2412i	−0.822756	+	2.26050i
$116$	−10.3039	−	1.32996i	−0.956696	−	0.123484i
$117$	4.33084	−	1.76019i	0.400386	−	0.162730i
$118$	3.99722	−	3.51445i	0.367974	−	0.323531i
$119$	21.2300	−	17.8141i	1.94615	−	1.63301i
$120$	11.0668	+	13.1762i	1.01026	+	1.20282i
$121$	0.453305	−	2.57082i	0.0412095	−	0.233711i
$122$	−5.83887	+	10.6749i	−0.528626	+	0.966463i
$123$	9.93837	−	1.05495i	0.896113	−	0.0951214i
$124$	−4.50328	+	0.208062i	−0.404407	+	0.0186845i
$125$	−7.10875	−	4.10424i	−0.635826	−	0.367094i
$126$	15.1810	−	0.912836i	1.35243	−	0.0813219i
$127$	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	$0.754931\pi$
$128$	−5.52960	−	9.87034i	−0.488752	−	0.872423i
$129$	3.94785	−	5.86600i	0.347589	−	0.516472i
$130$	6.61234	−	4.02395i	0.579940	−	0.352924i
$131$	1.17365	+	3.22458i	0.102542	+	0.281733i	0.980345	−	0.197289i	$-0.0632138\pi$
$131$	1.17365	+	3.22458i	0.102542	+	0.281733i	−0.877803	+	0.479022i	$0.840992\pi$
$132$	7.83008	−	6.27409i	0.681521	−	0.546089i
$133$	−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	$0.847238\pi$
$138$	−8.27409	−	15.9747i	−0.704337	−	1.35986i
$139$	−1.90997	−	5.24760i	−0.162001	−	0.445095i	0.831959	−	0.554838i	$-0.187220\pi$
$139$	−1.90997	−	5.24760i	−0.162001	−	0.445095i	−0.993960	+	0.109742i	$0.964997\pi$
$140$	24.5708	−	5.51263i	2.07661	−	0.465902i
$141$	0.248888	−	3.61290i	0.0209601	−	0.304261i
$142$	8.53012	−	10.6560i	0.715832	−	0.894229i
$143$	−2.25677	−	3.90884i	−0.188721	−	0.326874i
$144$	−11.9877	−	0.542468i	−0.998978	−	0.0452056i
$145$	−9.12295	+	15.8014i	−0.757620	+	1.31224i
$146$	−1.75198	−	4.48835i	−0.144995	−	0.371458i
$147$	4.11157	−	9.26048i	0.339117	−	0.763791i
$148$	0.281474	+	0.305616i	0.0231370	+	0.0251214i
$149$	−19.1032	−	3.36840i	−1.56499	−	0.275950i	−0.677061	−	0.735927i	$-0.736747\pi$
$149$	−19.1032	−	3.36840i	−1.56499	−	0.275950i	−0.887931	+	0.459977i	$0.847858\pi$
$150$	17.1512	−	5.36890i	1.40039	−	0.438369i
$151$	−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	$0.392698\pi$
$152$	2.76065	−	0.191493i	0.223918	−	0.0155321i
$153$	0.857342	+	23.1778i	0.0693120	+	1.87381i
$154$	−2.88289	−	14.3978i	−0.232310	−	1.16021i
$155$	−2.70781	+	7.43965i	−0.217497	+	0.597567i
$156$	−1.05732	+	5.29352i	−0.0846530	+	0.423821i
$157$	−0.181238	+	0.215991i	−0.0144644	+	0.0172380i	−0.773228	−	0.634128i	$-0.781359\pi$
$157$	−0.181238	+	0.215991i	−0.0144644	+	0.0172380i	0.758764	+	0.651366i	$0.225804\pi$
$158$	0.0841013	+	3.64251i	0.00669074	+	0.289783i
$159$	5.31373	−	1.52963i	0.421406	−	0.121308i
$160$	−19.7370	+	2.28828i	−1.56034	+	0.180905i
$161$	−26.3277			−2.07491
$162$	−7.19829	+	10.4969i	−0.565551	+	0.824713i
$163$			4.95712i			0.388271i	0.980975	+	0.194136i	$0.0621902\pi$
$163$			4.95712i			0.388271i	−0.980975	+	0.194136i	$0.937810\pi$
$164$	−5.30274	+	10.2499i	−0.414075	+	0.800380i
$165$	−4.87454	−	16.9335i	−0.379483	−	1.31827i
$166$	−9.02847	+	0.208457i	−0.700745	+	0.0161794i
$167$	−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	$0.851629\pi$
$168$	−8.77339	+	15.2126i	−0.676882	+	1.17368i
$169$	−9.93417	−	3.61574i	−0.764167	−	0.278134i
$170$	7.53984	+	37.6557i	0.578279	+	2.88806i
$171$	1.37261	−	2.59442i	0.104966	−	0.198400i
$172$	3.14358	+	7.53516i	0.239695	+	0.574550i
$173$	0.368911	+	0.439651i	0.0280478	+	0.0334261i	0.779886	−	0.625922i	$-0.215277\pi$
$173$	0.368911	+	0.439651i	0.0280478	+	0.0334261i	−0.751838	+	0.659348i	$0.770833\pi$
$174$	−3.80126	−	12.1433i	−0.288173	−	0.920582i
$175$	4.56706	−	25.9011i	0.345238	−	1.95794i
$176$	1.06831	+	11.5365i	0.0805266	+	0.869597i
$177$	5.95788	+	2.64525i	0.447822	+	0.198829i
$178$	−4.69310	−	12.0231i	−0.351763	−	0.901172i
$179$	14.6677	+	8.46841i	1.09632	+	0.632959i	0.935251	−	0.353985i	$-0.115174\pi$
$179$	14.6677	+	8.46841i	1.09632	+	0.632959i	0.161066	+	0.986944i	$0.448507\pi$
$180$	−8.98513	+	19.0630i	−0.669712	+	1.42087i
$181$	4.72394	−	2.72737i	0.351128	−	0.202724i	−0.314054	−	0.949405i	$-0.601687\pi$
$181$	4.72394	−	2.72737i	0.351128	−	0.202724i	0.665182	+	0.746681i	$0.268354\pi$
$182$	6.16714	+	4.93681i	0.457139	+	0.365941i
$183$	−14.8668	−	1.02415i	−1.09898	−	0.0757075i
$184$	20.6584	+	2.18297i	1.52296	+	0.160930i
$185$	0.685673	−	0.249565i	0.0504117	−	0.0183484i
$186$	−2.53933	−	4.90266i	−0.186193	−	0.359480i
$187$	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	$0.933478\pi$
$192$	8.14554	−	11.2094i	0.587854	−	0.808967i
$193$	−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	$0.652166\pi$
$194$	−11.2108	+	6.82237i	−0.804891	+	0.489818i
$195$	7.86485	+	5.29309i	0.563214	+	0.379046i
$196$	6.31123	+	9.85142i	0.450802	+	0.703673i
$197$	8.81684	−	5.09041i	0.628174	−	0.362676i	−0.151871	−	0.988400i	$-0.548530\pi$
$197$	8.81684	−	5.09041i	0.628174	−	0.362676i	0.780045	+	0.625724i	$0.215196\pi$
$198$	10.9919	+	5.49449i	0.781161	+	0.390476i
$199$	−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	$0.992697\pi$
$200$	−5.73122	+	19.9451i	−0.405258	+	1.41033i
$201$	−0.547163	−	5.15467i	−0.0385939	−	0.363583i
$202$	6.17829	−	11.2955i	0.434703	−	0.794747i
$203$	−18.3384	−	3.23355i	−1.28710	−	0.226951i
$204$	−22.8849	−	13.9118i	−1.60227	−	0.974020i
$205$	13.0275	+	15.5255i	0.909877	+	1.08435i
$206$	6.72435	+	7.64807i	0.468508	+	0.532866i
$207$	13.5293	−	17.3907i	0.940352	−	1.20874i
$208$	−4.42981	−	4.38510i	−0.307152	−	0.304052i
$209$	−2.66295	−	0.969234i	−0.184200	−	0.0670433i
$210$	18.7243	+	24.5065i	1.29210	+	1.69111i
$211$	0.485058	−	0.578070i	0.0333928	−	0.0397960i	−0.749090	−	0.662469i	$-0.769509\pi$
$211$	0.485058	−	0.578070i	0.0333928	−	0.0397960i	0.782482	+	0.622673i	$0.213953\pi$
$212$	−1.90453	+	6.09426i	−0.130804	+	0.418556i
$213$	16.2249	+	4.02753i	1.11171	+	0.275962i
$214$	−3.63069	+	23.7896i	−0.248189	+	1.62622i
$215$	14.3387			0.977891
$216$	−5.54017	−	13.6127i	−0.376961	−	0.926229i
$217$	−8.07999			−0.548505
$218$	1.38262	−	9.05943i	0.0936430	−	0.613582i
$219$	4.09480	−	4.24907i	0.276701	−	0.287126i
$220$	19.4209	+	6.06927i	1.30935	+	0.409190i
$221$	−7.74396	+	9.22890i	−0.520915	+	0.620803i
$222$	−0.195703	+	0.469727i	−0.0131347	+	0.0315260i
$223$	−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	$0.676900\pi$
$224$	−9.08383	−	18.1295i	−0.606939	−	1.21133i
$225$	14.7620	+	16.3269i	0.984133	+	1.08846i
$226$	−12.0771	−	13.7361i	−0.803354	−	0.913710i
$227$	−12.0866	−	14.4043i	−0.802218	−	0.956047i	0.197487	−	0.980305i	$-0.436722\pi$
$227$	−12.0866	−	14.4043i	−0.802218	−	0.956047i	−0.999706	+	0.0242588i	$0.992277\pi$
$228$	1.62781	+	2.97271i	0.107805	+	0.196872i
$229$	23.0759	+	4.06891i	1.52490	+	0.268881i	0.872356	−	0.488870i	$-0.162591\pi$
$229$	23.0759	+	4.06891i	1.52490	+	0.268881i	0.652543	+	0.757751i	$0.273702\pi$
$230$	17.5071	−	32.0073i	1.15438	−	2.11050i
$231$	14.5382	−	10.5856i	0.956540	−	0.696478i
$232$	14.1214	+	4.05779i	0.927115	+	0.266407i
$233$	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	$-0.00789605\pi$
$234$	−6.43019	+	1.53676i	−0.420354	+	0.100461i
$235$	6.36002	−	3.67196i	0.414882	−	0.239532i
$236$	−6.33807	+	4.06043i	−0.412573	+	0.264312i
$237$	−4.00870	+	1.96030i	−0.260393	+	0.127335i
$238$	−33.4809	+	20.3749i	−2.17025	+	1.32071i
$239$	−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	$0.415979\pi$
$240$	−12.6604	−	20.7820i	−0.817225	−	1.34147i
$241$	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
$246$	−14.1192	−	0.645629i	−0.900206	−	0.0411638i
$247$	1.43266	−	0.521445i	0.0911579	−	0.0331788i
$248$	6.34010	+	0.669955i	0.402597	+	0.0425422i
$249$	−4.85888	−	9.93612i	−0.307919	−	0.629676i
$250$	9.06253	+	7.25457i	0.573164	+	0.458819i
$251$	−8.06637	+	4.65712i	−0.509145	+	0.293955i	−0.732482	−	0.680786i	$-0.761638\pi$
$251$	−8.06637	+	4.65712i	−0.509145	+	0.293955i	0.223337	+	0.974741i	$0.428305\pi$
$252$	−21.4182	−	1.96289i	−1.34922	−	0.123651i
$253$	−18.4231	−	10.6366i	−1.15825	−	0.668717i
$254$	−2.82600	−	7.23985i	−0.177319	−	0.454269i
$255$	−38.0228	+	27.6852i	−2.38108	+	1.73372i
$256$	5.62457	+	14.9788i	0.351535	+	0.936175i
$257$	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	$0.00312606\pi$
$258$	−6.77078	+	7.35849i	−0.421531	+	0.458120i
$259$	0.478677	+	0.570465i	0.0297435	+	0.0354470i
$260$	−10.1028	+	4.21476i	−0.626548	+	0.261388i
$261$	11.5597	−	10.4517i	0.715526	−	0.646945i
$262$	−0.952790	−	4.75845i	−0.0588636	−	0.293978i
$263$	−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	$0.836158\pi$
$264$	−12.2853	+	7.10069i	−0.756108	+	0.437017i
$265$	8.58983	+	7.20773i	0.527669	+	0.442767i
$266$	4.95857	−	0.114487i	0.304029	−	0.00701968i
$267$	10.9689	−	11.3822i	0.671288	−	0.696578i
$268$	5.31623	+	2.75034i	0.324741	+	0.168004i
$269$			1.52571i			0.0930241i	0.998918	+	0.0465120i	$0.0148106\pi$
$269$			1.52571i			0.0930241i	−0.998918	+	0.0465120i	$0.985189\pi$
$270$	−25.8098	−	0.225125i	−1.57074	−	0.0137007i
$271$	31.4903			1.91290			0.956450	−	0.291897i	$-0.0942863\pi$
$271$	31.4903			1.91290			0.956450	+	0.291897i	$0.0942863\pi$
$272$	27.9607	−	13.2114i	1.69537	−	0.801058i
$273$	−2.33093	+	9.39018i	−0.141074	+	0.568319i
$274$	−0.229755	−	9.95090i	−0.0138800	−	0.601156i
$275$	13.6601	−	16.2795i	0.823736	−	0.981690i
$276$	8.15899	+	24.0985i	0.491114	+	1.45056i
$277$	2.02751	−	5.57054i	0.121821	−	0.334701i	−0.863760	−	0.503903i	$-0.831897\pi$
$277$	2.02751	−	5.57054i	0.121821	−	0.334701i	0.985581	+	0.169202i	$0.0541190\pi$
$278$	1.55055	+	7.74379i	0.0929956	+	0.464442i
$279$	4.15216	−	5.33722i	0.248583	−	0.319531i
$280$	−35.5268	+	2.46432i	−2.12313	+	0.147271i
$281$	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	$-0.0264438\pi$
$282$	−1.11881	+	4.99782i	−0.0666240	+	0.297616i
$283$	−32.5610	−	5.74138i	−1.93555	−	0.341290i	−0.935620	−	0.353010i	$-0.885158\pi$
$283$	−32.5610	−	5.74138i	−1.93555	−	0.341290i	−0.999931	+	0.0117196i	$0.996269\pi$
$284$	−14.1989	+	13.0773i	−0.842551	+	0.775996i
$285$	5.91889	−	0.628284i	0.350605	−	0.0372164i
$286$	2.32102	+	5.94617i	0.137245	+	0.351604i
$287$	−10.3420	+	17.9129i	−0.610471	+	1.05737i
$288$	16.6434	+	3.31611i	0.980723	+	0.195404i
$289$	−21.3857	−	37.0412i	−1.25799	−	2.17889i
$290$	16.1255	−	20.1443i	0.946925	−	1.18291i
$291$	−13.3344	−	8.97414i	−0.781677	−	0.526073i
$292$	1.49167	+	6.64863i	0.0872932	+	0.389082i
$293$	−10.9273	−	30.0225i	−0.638378	−	1.75393i	−0.656760	−	0.754099i	$-0.728074\pi$
$293$	−10.9273	−	30.0225i	−0.638378	−	1.75393i	0.0183820	−	0.999831i	$-0.494149\pi$
$294$	−7.72392	+	12.0691i	−0.450468	+	0.703886i
$295$	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
$300$	−25.1234	+	3.84644i	−1.45050	+	0.222074i
$301$	5.00501	+	13.7512i	0.288484	+	0.792604i
$302$	10.4880	−	6.38246i	0.603514	−	0.367269i
$303$	15.7310	+	1.08369i	0.903722	+	0.0622562i
$304$	−3.90031	−	0.321306i	−0.223698	−	0.0184282i
$305$	−15.1098	−	26.1709i	−0.865185	−	1.49854i
$306$	3.74667	−	32.5860i	0.214183	−	1.86282i
$307$	−0.965983	−	0.557711i	−0.0551316	−	0.0318302i	0.472181	−	0.881502i	$-0.343467\pi$
$307$	−0.965983	−	0.557711i	−0.0551316	−	0.0318302i	−0.527312	+	0.849671i	$0.676800\pi$
$308$	0.958402	+	20.7436i	0.0546100	+	1.18198i
$309$	−5.06127	+	11.3995i	−0.287926	+	0.648494i
$310$	5.37293	−	9.82308i	0.305162	−	0.557914i
$311$	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	$-0.0339010\pi$
$312$	2.60759	−	7.17489i	0.147626	−	0.406198i
$313$	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	$0.103253\pi$
$314$	0.299460	−	0.263292i	0.0168995	−	0.0148584i
$315$	−17.6641	+	33.3876i	−0.995260	+	1.88118i
$316$	0.659598	−	5.11027i	0.0371053	−	0.287475i
$317$	−9.63709	+	26.4777i	−0.541273	+	1.48713i	0.303933	+	0.952693i	$0.401700\pi$
$317$	−9.63709	+	26.4777i	−0.541273	+	1.48713i	−0.845206	+	0.534441i	$0.820522\pi$
$318$	−7.75510	+	1.00471i	−0.434884	+	0.0563416i
$319$	−11.5261	−	9.67156i	−0.645339	−	0.541504i
$320$	28.0810	+	1.01204i	1.56978	+	0.0565750i
$321$	−28.3234	+	8.15328i	−1.58086	+	0.455072i
$322$	36.8068	+	5.61733i	2.05116	+	0.313042i
$323$			7.56407i			0.420876i
$324$	12.3030	−	13.1391i	0.683502	−	0.729949i
$325$			11.4332i			0.634199i
$326$	1.05766	−	6.93018i	0.0585785	−	0.383827i
$327$	10.7860	−	3.10489i	0.596465	−	0.171701i
$328$	9.60031	−	13.1982i	0.530088	−	0.728747i
$329$	5.74151	+	4.81770i	0.316540	+	0.265608i
$330$	3.20177	+	24.7135i	0.176251	+	1.36043i
$331$	10.1053	−	27.7642i	0.555439	−	1.52606i	−0.270742	−	0.962652i	$-0.587269\pi$
$331$	10.1053	−	27.7642i	0.555439	−	1.52606i	0.826181	−	0.563405i	$-0.190509\pi$
$332$	12.6665	+	1.63491i	0.695165	+	0.0897272i
$333$	−0.622803	+	0.0230374i	−0.0341294	+	0.00126244i
$334$	9.54382	+	10.8548i	0.522214	+	0.593950i
$335$	8.05253	−	6.75687i	0.439956	−	0.369167i
$336$	15.5112	−	19.3957i	0.846207	−	1.05812i
$337$	−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	$0.787571\pi$
$338$	13.1168	+	7.17448i	0.713458	+	0.390240i
$339$	9.09014	−	20.4737i	0.493709	−	1.11198i
$340$	−2.50658	−	54.2524i	−0.135939	−	2.94225i
$341$	−5.65407	−	3.26438i	−0.306185	−	0.176776i
$342$	−2.47249	+	3.33420i	−0.133697	+	0.180293i
$343$	−2.06149	−	3.57061i	−0.111310	−	0.192795i
$344$	−2.78708	−	11.2051i	−0.150270	−	0.604137i
$345$	44.5760	+	3.07078i	2.39989	+	0.165325i
$346$	−0.421943	−	0.693356i	−0.0226838	−	0.0372750i
$347$	4.52278	+	12.4262i	0.242795	+	0.667075i	0.999905	+	0.0137870i	$0.00438867\pi$
$347$	4.52278	+	12.4262i	0.242795	+	0.667075i	−0.757110	+	0.653288i	$0.773389\pi$
$348$	2.72334	+	17.7877i	0.145986	+	0.953521i
$349$	−18.1196	+	3.19498i	−0.969920	+	0.171023i	−0.636094	−	0.771611i	$-0.719451\pi$
$349$	−18.1196	+	3.19498i	−0.969920	+	0.171023i	−0.333826	+	0.942635i	$0.608340\pi$
$350$	−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	$0.680989\pi$
$354$	−7.76488	−	4.96931i	−0.412698	−	0.264116i
$355$	11.5948	+	31.8564i	0.615387	+	1.69076i
$356$	3.99579	+	17.8100i	0.211777	+	0.943927i
$357$	−39.8229	−	26.8011i	−2.10765	−	1.41846i
$358$	−18.6990	−	14.9686i	−0.988274	−	0.791115i
$359$	−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	$-0.348583\pi$
$360$	16.6288	−	24.7335i	0.876414	−	1.30357i
$361$	−9.02138	+	15.6255i	−0.474810	+	0.822395i
$362$	−7.18611	+	2.80502i	−0.377693	+	0.147429i
$363$	−4.49622	+	0.477269i	−0.235990	+	0.0250501i
$364$	−7.56850	−	8.21763i	−0.396697	−	0.430721i
$365$	11.7848	+	2.07798i	0.616845	+	0.108766i
$366$	20.5656	+	4.60380i	1.07498	+	0.240644i
$367$	−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	$0.349551\pi$
$368$	−28.4153	−	7.45957i	−1.48125	−	0.388857i
$369$	−6.51777	−	16.0366i	−0.339301	−	0.834830i
$370$	−1.01184	+	0.202601i	−0.0526029	+	0.0105327i
$371$	−3.91405	+	10.7538i	−0.203207	+	0.558308i
$372$	2.50400	+	7.39584i	0.129827	+	0.383457i
$373$	−4.80331	+	5.72436i	−0.248706	+	0.296396i	−0.875926	−	0.482446i	$-0.839748\pi$
$373$	−4.80331	+	5.72436i	−0.248706	+	0.296396i	0.627220	+	0.778842i	$0.284193\pi$
$374$	−31.6603	+	0.730999i	−1.63711	+	0.0377991i
$375$	−3.42527	+	13.7987i	−0.176880	+	0.712563i
$376$	−4.10571	−	4.25634i	−0.211736	−	0.219504i
$377$	8.09486			0.416906
$378$	−8.79318	−	24.8308i	−0.452273	−	1.27716i
$379$			38.3104i			1.96787i	0.178521	+	0.983936i	$0.442869\pi$
$379$			38.3104i			1.96787i	−0.178521	+	0.983936i	$0.557131\pi$
$380$	−3.15810	+	6.10441i	−0.162007	+	0.313149i
$381$	6.60506	−	6.85389i	0.338387	−	0.351136i
$382$	−0.0310793	−	1.34608i	−0.00159015	−	0.0688712i
$383$	−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	$0.744822\pi$
$384$	−13.7793	+	13.9330i	−0.703174	+	0.711018i
$385$	34.2695	+	12.4731i	1.74654	+	0.635687i
$386$	28.3565	−	5.67784i	1.44331	−	0.288994i
$387$	−11.6553	−	3.76042i	−0.592471	−	0.191153i
$388$	17.1287	−	7.14588i	0.869577	−	0.362777i
$389$	5.26382	+	6.27317i	0.266886	+	0.318063i	0.882798	−	0.469752i	$-0.155657\pi$
$389$	5.26382	+	6.27317i	0.266886	+	0.318063i	−0.615912	+	0.787815i	$0.711212\pi$
$390$	−9.86592	−	9.07795i	−0.499580	−	0.459680i
$391$	−9.86009	+	55.9194i	−0.498646	+	2.82796i
$392$	−6.72134	−	15.1191i	−0.339479	−	0.763630i
$393$	4.80484	−	3.49851i	0.242372	−	0.176476i
$394$	−13.4123	+	5.23534i	−0.675701	+	0.263752i
$395$	−7.83676	−	4.52456i	−0.394310	−	0.227655i
$396$	−14.1947	−	10.0267i	−0.713308	−	0.503860i
$397$	−19.5557	+	11.2905i	−0.981473	+	0.566654i	−0.902715	−	0.430240i	$-0.858429\pi$
$397$	−19.5557	+	11.2905i	−0.981473	+	0.566654i	−0.0787584	+	0.996894i	$0.525096\pi$
$398$	12.9595	−	16.1892i	0.649602	−	0.811493i
$399$	2.66857	+	5.45706i	0.133596	+	0.273195i
$400$	12.2679	−	26.6609i	0.613396	−	1.33304i
$401$	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	$0.0681106\pi$
$402$	−0.334864	+	7.32311i	−0.0167015	+	0.365243i
$403$	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
$408$	29.0255	+	24.3318i	1.43698	+	1.20460i
$409$	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	$0.204498\pi$
$410$	−14.9002	−	24.4847i	−0.735867	−	1.20921i
$411$	10.9513	−	5.35531i	0.540187	−	0.264158i
$412$	−7.76901	−	12.1269i	−0.382752	−	0.597451i
$413$	−11.6837	+	6.74559i	−0.574918	+	0.331929i
$414$	−22.6249	+	21.4260i	−1.11195	+	1.05303i
$415$	11.2148	−	19.4245i	0.550511	−	0.953512i
$416$	5.25738	+	7.07564i	0.257764	+	0.346912i
$417$	−7.81928	+	5.69339i	−0.382912	+	0.278806i
$418$	3.51607	+	1.92319i	0.171977	+	0.0940661i
$419$	12.3232	+	2.17290i	0.602026	+	0.106153i	0.466350	−	0.884600i	$-0.345569\pi$
$419$	12.3232	+	2.17290i	0.602026	+	0.106153i	0.135675	+	0.990753i	$0.456680\pi$
$420$	−20.9484	−	38.2558i	−1.02217	−	1.86669i
$421$	−19.2609	−	22.9542i	−0.938717	−	1.11872i	−0.992752	−	0.120180i	$-0.961653\pi$
$421$	−19.2609	−	22.9542i	−0.938717	−	1.11872i	0.0540354	−	0.998539i	$-0.482792\pi$
$422$	−0.801462	+	0.704663i	−0.0390146	+	0.0343025i
$423$	−6.13278	+	1.31681i	−0.298186	+	0.0640257i
$424$	3.96288	−	8.11358i	0.192454	−	0.394030i
$425$	−53.3029	−	19.4007i	−2.58557	−	0.941071i
$426$	−21.8235	−	9.09237i	−1.05735	−	0.440527i
$427$	19.8244	−	23.6258i	0.959370	−	1.14333i
$428$	10.1516	−	32.4838i	0.490696	−	1.57016i
$429$	−5.42480	+	5.62918i	−0.261912	+	0.271779i
$430$	−20.0459	−	3.05934i	−0.966697	−	0.147534i
$431$	24.0142			1.15673			0.578363	−	0.815780i	$-0.303692\pi$
$431$	24.0142			1.15673			0.578363	+	0.815780i	$0.303692\pi$
$432$	4.84086	+	20.2130i	0.232906	+	0.972499i
$433$	1.02353			0.0491875			0.0245938	−	0.999698i	$-0.492171\pi$
$433$	1.02353			0.0491875			0.0245938	+	0.999698i	$0.492171\pi$
$434$	11.2960	+	1.72397i	0.542227	+	0.0827530i
$435$	30.6720	+	7.61373i	1.47061	+	0.365050i
$436$	−3.86588	+	12.3703i	−0.185142	+	0.592431i
$437$	4.61891	−	5.50460i	0.220952	−	0.263321i
$438$	−6.63123	+	5.06664i	−0.316853	+	0.242093i
$439$	−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	$0.670501\pi$
$440$	−25.8559	−	12.6287i	−1.23263	−	0.602048i
$441$	−17.3837	−	2.40650i	−0.827795	−	0.114595i
$442$	12.7954	−	11.2500i	0.608613	−	0.535106i
$443$	−4.33387	−	5.16490i	−0.205908	−	0.245392i	0.653200	−	0.757185i	$-0.273426\pi$
$443$	−4.33387	−	5.16490i	−0.205908	−	0.245392i	−0.859109	+	0.511793i	$0.828981\pi$
$444$	0.373820	−	0.614935i	0.0177407	−	0.0291835i
$445$	31.5685	+	5.56638i	1.49649	+	0.263872i
$446$	7.60453	+	4.15945i	0.360085	+	0.196956i
$447$	3.54648	+	33.4104i	0.167743	+	1.58026i
$448$	8.83128	+	27.2836i	0.417239	+	1.28903i
$449$	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	$-0.0164879\pi$
$450$	−17.1541	−	25.9751i	−0.808653	−	1.22448i
$451$	−14.4739	+	8.35653i	−0.681551	+	0.393494i
$452$	13.9533	+	21.7802i	0.656308	+	1.02445i
$453$	12.4746	+	8.39548i	0.586108	+	0.394454i
$454$	13.8241	+	22.7164i	0.648797	+	1.06613i
$455$	−18.4369	+	6.71048i	−0.864335	+	0.314592i
$456$	−1.64146	−	4.50324i	−0.0768685	−	0.210883i
$457$	−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	0.542187	−	0.840258i	$-0.317596\pi$
$461$	28.7509	−	5.06955i	1.33906	−	0.236113i	0.796874	+	0.604145i	$0.206485\pi$
$462$	−22.5833	+	11.6970i	−1.05067	+	0.544193i
$463$	−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	$0.501631\pi$
$464$	−18.8763	−	8.68587i	−0.876310	−	0.403231i
$465$	13.6804	+	0.942425i	0.634414	+	0.0437039i
$466$	−14.0659	+	17.5713i	−0.651590	+	0.813976i
$467$	−23.0145	+	13.2874i	−1.06498	+	0.614868i	−0.926806	−	0.375539i	$-0.877457\pi$
$467$	−23.0145	+	13.2874i	−1.06498	+	0.614868i	−0.138177	+	0.990408i	$0.544124\pi$
$468$	9.31745	−	0.776466i	0.430699	−	0.0358921i
$469$	9.29079	+	5.36404i	0.429009	+	0.247688i
$470$	−9.67493	+	3.77651i	−0.446271	+	0.174197i
$471$	0.446346	+	0.198174i	0.0205666	+	0.00913137i
$472$	9.72713	−	4.32428i	0.447727	−	0.199041i
$473$	−2.05326	+	11.6446i	−0.0944089	+	0.535420i
$474$	6.02252	−	1.88525i	0.276623	−	0.0865923i
$475$	4.61417	+	5.49896i	0.211713	+	0.252310i
$476$	51.1544	−	21.3410i	2.34466	−	0.978164i
$477$	−5.09202	−	8.11158i	−0.233147	−	0.371404i
$478$	3.64462	−	0.729765i	0.166701	−	0.0333787i
$479$	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	$0.285005\pi$
$480$	13.2655	+	31.7550i	0.605484	+	1.44941i
$481$	−0.247987	−	0.208086i	−0.0113072	−	0.00948790i
$482$	−0.164826	−	7.13880i	−0.00750764	−	0.325163i
$483$	12.6146	+	43.8213i	0.573983	+	1.99394i
$484$	2.39902	−	4.63714i	0.109046	−	0.210779i
$485$		−	32.5943i		−	1.48003i
$486$	20.9206	+	6.95180i	0.948979	+	0.315340i
$487$	−10.6546			−0.482806			−0.241403	−	0.970425i	$-0.577608\pi$
$487$	−10.6546			−0.482806			−0.241403	+	0.970425i	$0.577608\pi$
$488$	−17.5145	+	16.8946i	−0.792844	+	0.764784i
$489$	8.25093	−	2.37514i	0.373120	−	0.107408i
$490$	−29.0501	+	0.670732i	−1.31235	+	0.0303006i
$491$	−24.5176	+	29.2189i	−1.10646	+	1.31863i	−0.163198	+	0.986593i	$0.552181\pi$
$491$	−24.5176	+	29.2189i	−1.10646	+	1.31863i	−0.943266	+	0.332038i	$0.892264\pi$
$492$	19.6012	+	3.91511i	0.883692	+	0.176507i
$493$	−13.7360	+	37.7393i	−0.618637	+	1.69969i
$494$	−2.11415	+	0.423319i	−0.0951201	+	0.0190460i
$495$	−25.8496	+	16.2270i	−1.16185	+	0.729348i
$496$	−8.72068	−	2.28935i	−0.391570	−	0.102795i
$497$	−26.5038	+	22.2394i	−1.18886	+	0.997572i
$498$	4.67285	+	14.9277i	0.209395	+	0.668924i
$499$	−22.8313	−	4.02577i	−1.02207	−	0.180218i	−0.362595	−	0.931947i	$-0.618109\pi$
$499$	−22.8313	−	4.02577i	−1.02207	−	0.180218i	−0.659472	+	0.751729i	$0.729220\pi$
$500$	−11.1218	−	12.0757i	−0.497382	−	0.540041i
$501$	−7.18342	+	16.1792i	−0.320932	+	0.722833i
$502$	12.2707	−	4.78972i	0.547666	−	0.213776i
$503$	−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	$0.253027\pi$
$504$	29.5244	+	7.31402i	1.31512	+	0.325792i
$505$	15.9882	+	27.6923i	0.711464	+	1.23229i
$506$	23.4865	+	18.8010i	1.04410	+	0.835807i
$507$	−1.25842	+	18.2675i	−0.0558885	+	0.811287i
$508$	2.40611	+	10.7245i	0.106754	+	0.475821i
$509$	−4.03924	−	11.0977i	−0.179036	−	0.491898i	0.817417	−	0.576046i	$-0.195405\pi$
$509$	−4.03924	−	11.0977i	−0.179036	−	0.491898i	−0.996453	+	0.0841485i	$0.973183\pi$
$510$	59.0638	−	30.5920i	2.61539	−	1.35464i
$511$	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
$516$	11.0358	−	8.84274i	0.485822	−	0.389280i
$517$	2.07130	+	5.69086i	0.0910958	+	0.250284i
$518$	−0.547487	−	0.899657i	−0.0240552	−	0.0395286i
$519$	0.555023	−	0.824692i	0.0243628	−	0.0362000i
$520$	15.0232	−	3.73679i	0.658812	−	0.163869i
$521$	−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	$0.921200\pi$
$522$	−18.3907	+	12.1454i	−0.804940	+	0.531588i
$523$	−23.1897	−	13.3886i	−1.01402	−	0.585442i	−0.101651	−	0.994820i	$-0.532412\pi$
$523$	−23.1897	−	13.3886i	−1.01402	−	0.585442i	−0.912365	+	0.409378i	$0.865746\pi$
$524$	0.316750	+	6.85573i	0.0138373	+	0.299494i
$525$	−45.2996	+	4.80851i	−1.97704	+	0.209860i
$526$	26.1402	+	14.2979i	1.13977	+	0.623418i
$527$	−3.02607	+	17.1617i	−0.131818	+	0.747576i
$528$	18.6902	−	7.30573i	0.813386	−	0.317941i
$529$	23.7030	−	19.8892i	1.03056	−	0.864746i
$530$	−10.4710	−	11.9093i	−0.454829	−	0.517308i
$531$	1.54826	−	11.1841i	0.0671888	−	0.485348i
$532$	−6.95663	−	0.897915i	−0.301608	−	0.0389295i
$533$	3.07530	−	8.44933i	0.133206	−	0.365981i
$534$	−17.7634	+	13.5722i	−0.768697	+	0.587327i
$535$	−45.7858	−	38.4188i	−1.97949	−	1.66099i
$536$	−6.84541	−	4.97933i	−0.295677	−	0.215074i
$537$	7.06747	−	28.4714i	0.304984	−	1.22863i
$538$	0.325529	−	2.13298i	0.0140345	−	0.0919593i
$539$			16.9438i			0.729823i
$540$	36.0348	+	5.82157i	1.55069	+	0.250521i
$541$			0.365364i			0.0157082i	0.999969	+	0.00785412i	$0.00250007\pi$
$541$			0.365364i			0.0157082i	−0.999969	+	0.00785412i	$0.997500\pi$
$542$	−44.0243	−	6.71884i	−1.89100	−	0.288599i
$543$	−6.80301	−	6.55602i	−0.291945	−	0.281346i
$544$	−41.9087	+	12.5041i	−1.79682	+	0.536109i
$545$	17.4359	+	14.6305i	0.746872	+	0.626700i
$546$	5.26221	−	12.6304i	0.225202	−	0.540530i
$547$	12.8891	−	35.4125i	0.551098	−	1.51413i	−0.281116	−	0.959674i	$-0.590704\pi$
$547$	12.8891	−	35.4125i	0.551098	−	1.51413i	0.832214	−	0.554455i	$-0.187073\pi$
$548$	−1.80194	+	13.9606i	−0.0769752	+	0.596369i
$549$	5.41857	+	25.2359i	0.231259	+	1.07704i
$550$	−22.5706	+	19.8446i	−0.962415	+	0.846177i
$551$	3.89334	−	3.26690i	0.165862	−	0.139175i
$552$	−6.26478	−	35.4311i	−0.266647	−	1.50805i
$553$	1.60369	−	9.09498i	0.0681958	−	0.386758i
$554$	−4.02306	+	7.35517i	−0.170923	+	0.312491i
$555$	−0.743922	−	1.02170i	−0.0315777	−	0.0433687i
$556$	−0.515472	−	11.1569i	−0.0218609	−	0.473156i
$557$	11.9876	+	6.92105i	0.507931	+	0.293254i	0.731983	−	0.681323i	$-0.238595\pi$
$557$	11.9876	+	6.92105i	0.507931	+	0.293254i	−0.224052	+	0.974577i	$0.571928\pi$
$558$	−6.94359	+	6.57566i	−0.293946	+	0.278370i
$559$	−3.18071	−	5.50914i	−0.134530	−	0.233012i
$560$	50.1932	+	4.13490i	2.12105	+	0.174731i
$561$	−17.0387	−	34.8431i	−0.719376	−	1.47108i
$562$	−33.0803	+	20.1311i	−1.39541	+	0.849177i
$563$	−11.4866	−	31.5593i	−0.484104	−	1.33007i	−0.905945	−	0.423396i	$-0.860838\pi$
$563$	−11.4866	−	31.5593i	−0.484104	−	1.33007i	0.421840	−	0.906670i	$-0.361384\pi$
$564$	2.63047	−	6.74838i	0.110763	−	0.284158i
$565$	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	$0.786128\pi$
$570$	−8.40882	−	0.384511i	−0.352207	−	0.0161054i
$571$	6.29067	+	17.2835i	0.263256	+	0.723291i	0.998943	+	0.0459688i	$0.0146375\pi$
$571$	6.29067	+	17.2835i	0.263256	+	0.723291i	−0.735686	+	0.677322i	$0.763140\pi$
$572$	−1.97616	−	8.80812i	−0.0826275	−	0.368286i
$573$	1.48140	−	0.724422i	0.0618863	−	0.0302631i
$574$	18.2804	−	22.8362i	0.763009	−	0.953163i
$575$	26.9434	+	46.6673i	1.12362	+	1.94616i
$576$	−22.5604	−	8.18709i	−0.940017	−	0.341129i
$577$	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	$-0.0142936\pi$
$578$	21.9946	+	56.3475i	0.914856	+	2.34375i
$579$	20.8482	+	28.6329i	0.866423	+	1.18994i
$580$	−26.8420	+	24.7217i	−1.11455	+	1.02651i
$581$	22.5432	+	3.97497i	0.935249	+	0.164910i
$582$	16.7271	+	15.3911i	0.693361	+	0.637983i
$583$	−7.08351	+	5.94377i	−0.293369	+	0.246166i
$584$	−0.666822	−	9.61323i	−0.0275933	−	0.397798i
$585$	5.04180	−	15.6269i	0.208453	−	0.646091i
$586$	8.87096	+	44.3036i	0.366456	+	1.83017i
$587$	3.00647	−	8.26020i	0.124090	−	0.340935i	−0.862056	−	0.506813i	$-0.830824\pi$
$587$	3.00647	−	8.26020i	0.124090	−	0.340935i	0.986146	+	0.165878i	$0.0530458\pi$
$588$	13.3733	−	15.2250i	0.551507	−	0.627867i
$589$	1.41755	−	1.68937i	0.0584091	−	0.0696092i
$590$	−0.431526	−	18.6898i	−0.0177657	−	0.769448i
$591$	−12.6973	−	12.2363i	−0.522295	−	0.503333i
$592$	0.355000	+	0.751326i	0.0145904	+	0.0308793i
$593$	0.714890			0.0293570			0.0146785	−	0.999892i	$-0.495328\pi$
$593$	0.714890			0.0293570			0.0146785	+	0.999892i	$0.495328\pi$
$594$	3.87872	−	20.9282i	0.159146	−	0.858695i
$595$		−	97.3420i		−	3.99063i
$596$	−34.4575	−	17.8265i	−1.41144	−	0.730203i
$597$	24.6499	+	6.11888i	1.00886	+	0.250429i
$598$	−16.1812	+	0.373606i	−0.661700	+	0.0152779i
$599$	−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	$0.957195\pi$
$600$	35.9438	−	0.0170447i	1.46740	−	0.000695847i
$601$	−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	$0.796683\pi$
$602$	−4.06316	−	20.2924i	−0.165602	−	0.827055i
$603$	−8.31758	+	3.38053i	−0.338718	+	0.137666i
$604$	−16.0242	+	6.68511i	−0.652016	+	0.272013i
$605$	−5.89376	−	7.02390i	−0.239615	−	0.285562i
$606$	−21.7611	−	4.87142i	−0.883985	−	0.197888i
$607$	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	$-0.173991\pi$
$608$	5.38419	+	1.28137i	0.218358	+	0.0519666i
$609$	3.40449	+	32.0728i	0.137957	+	1.29966i
$610$	15.5400	+	39.8115i	0.629196	+	1.61192i
$611$	−2.82165	−	1.62908i	−0.114152	−	0.0659055i
$612$	−12.1906	+	44.7567i	−0.492775	+	1.80918i
$613$	6.39944	−	3.69472i	0.258471	−	0.149228i	−0.365166	−	0.930942i	$-0.618988\pi$
$613$	6.39944	−	3.69472i	0.258471	−	0.149228i	0.623637	+	0.781714i	$0.285654\pi$
$614$	1.23147	+	0.985798i	0.0496983	+	0.0397836i
$615$	19.5997	−	29.1226i	0.790335	−	1.17433i
$616$	3.08603	−	29.2046i	0.124340	−	1.17669i
$617$	−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	$0.597704\pi$
$618$	9.50801	−	14.8569i	0.382468	−	0.597632i
$619$	−29.4542	+	5.19358i	−1.18387	+	0.208748i	−0.730713	−	0.682685i	$-0.760812\pi$
$619$	−29.4542	+	5.19358i	−1.18387	+	0.208748i	−0.453153	+	0.891433i	$0.649701\pi$
$620$	−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
$624$	−5.17633	+	9.47432i	−0.207219	+	0.379276i
$625$	7.37985	−	2.68605i	0.295194	−	0.107442i
$626$	−22.2807	+	13.5590i	−0.890516	+	0.541925i
$627$	−0.337332	+	4.89677i	−0.0134717	+	0.195558i
$628$	−0.474829	+	0.304195i	−0.0189477	+	0.0121387i
$629$	1.39093	−	0.803052i	0.0554599	−	0.0320198i
$630$	31.8186	−	42.9079i	1.26768	−	1.70949i
$631$	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	$0.117921\pi$
$632$	−2.01247	+	7.00355i	−0.0800519	+	0.278586i
$633$	−1.19458	−	0.530385i	−0.0474804	−	0.0210809i
$634$	19.1222	−	34.9603i	0.759441	−	1.38845i
$635$	19.0093	+	3.35185i	0.754361	+	0.133014i
$636$	11.0562	+	0.250029i	0.438407	+	0.00991429i
$637$	−5.85948	−	6.98306i	−0.232161	−	0.276679i
$638$	14.0503	+	15.9803i	0.556255	+	0.632668i
$639$	−1.07032	−	28.9355i	−0.0423412	−	1.14467i
$640$	−39.0421	−	7.40629i	−1.54327	−	0.292760i
$641$	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	$0.459751\pi$
$642$	41.3364	−	5.35535i	1.63142	−	0.211359i
$643$	23.2439	−	27.7010i	0.916651	−	1.09242i	−0.0787757	−	0.996892i	$-0.525101\pi$
$643$	23.2439	−	27.7010i	0.916651	−	1.09242i	0.995427	−	0.0955296i	$-0.0304545\pi$
$644$	−50.2583	−	15.7063i	−1.98045	−	0.618917i
$645$	−6.87021	−	23.8662i	−0.270514	−	0.939730i
$646$	1.61389	−	10.5748i	0.0634975	−	0.416058i
$647$	−41.5981			−1.63539			−0.817694	−	0.575653i	$-0.804748\pi$
$647$	−41.5981			−1.63539			−0.817694	+	0.575653i	$0.804748\pi$
$648$	−20.0033	+	15.7438i	−0.785805	+	0.618474i
$649$	−10.9011			−0.427905
$650$	2.43941	−	15.9839i	0.0956815	−	0.626939i
$651$	3.87143	+	13.4488i	0.151733	+	0.527101i
$652$	−2.95728	+	9.46291i	−0.115816	+	0.370596i
$653$	23.0229	−	27.4376i	0.900957	−	1.07372i	−0.0959707	−	0.995384i	$-0.530595\pi$
$653$	23.0229	−	27.4376i	0.900957	−	1.07372i	0.996927	−	0.0783340i	$-0.0249601\pi$
$654$	−15.7415	+	2.03940i	−0.615542	+	0.0797468i
$655$	11.3260	+	4.12233i	0.442544	+	0.161073i
$656$	−16.2375	+	16.4030i	−0.633967	+	0.640431i
$657$	−9.03439	−	4.77975i	−0.352465	−	0.186476i
$658$	−6.99886	−	7.96029i	−0.272844	−	0.310324i
$659$	1.10500	+	1.31688i	0.0430446	+	0.0512985i	0.787137	−	0.616778i	$-0.211562\pi$
$659$	1.10500	+	1.31688i	0.0430446	+	0.0512985i	−0.744093	+	0.668076i	$0.767118\pi$
$660$	0.796778	−	35.2333i	0.0310146	−	1.37145i
$661$	−30.1408	−	5.31464i	−1.17234	−	0.206716i	−0.446633	−	0.894717i	$-0.647377\pi$
$661$	−30.1408	−	5.31464i	−1.17234	−	0.206716i	−0.725709	+	0.688002i	$0.758488\pi$
$662$	−20.0513	+	36.6589i	−0.779317	+	1.42479i
$663$	19.0716	+	8.46760i	0.740678	+	0.328854i
$664$	−17.3593	−	4.98820i	−0.673671	−	0.193580i
$665$	−6.15930	+	10.6682i	−0.238848	+	0.413696i
$666$	0.875610	+	0.100676i	0.0339292	+	0.00390111i
$667$	33.0411	−	19.0763i	1.27936	−	0.738638i
$668$	−11.0265	−	17.2116i	−0.426628	−	0.665938i
$669$	−0.729578	+	10.5907i	−0.0282071	+	0.409460i
$670$	−12.6993	+	7.72818i	−0.490617	+	0.298565i
$671$	23.4174	−	8.52323i	0.904019	−	0.329036i
$672$	−25.8234	+	23.8062i	−0.996160	+	0.918344i
$673$	−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	−0.229606	−	0.973284i	$-0.573744\pi$
$677$	−2.92669	+	0.516054i	−0.112482	+	0.0198336i	0.117124	+	0.993117i	$0.462633\pi$
$678$	−17.0766	+	26.6833i	−0.655822	+	1.02476i
$679$	31.2587	−	11.3772i	1.19960	−	0.436618i
$680$	−8.07114	+	76.3810i	−0.309514	+	2.92908i
$681$	−18.1842	+	27.0194i	−0.696820	+	1.03538i
$682$	7.20805	+	5.77005i	0.276010	+	0.220947i
$683$	25.1540	−	14.5226i	0.962489	−	0.555693i	0.0655509	−	0.997849i	$-0.479120\pi$
$683$	25.1540	−	14.5226i	0.962489	−	0.555693i	0.896938	+	0.442156i	$0.145786\pi$
$684$	4.16800	−	4.13377i	0.159368	−	0.158059i
$685$	21.4091	+	12.3605i	0.817999	+	0.472272i
$686$	2.12018	+	5.43164i	0.0809490	+	0.207381i
$687$	−4.28401	−	40.3585i	−0.163445	−	1.53977i
$688$	1.50568	+	16.2596i	0.0574034	+	0.619893i
$689$	0.863863	−	4.89921i	0.0329106	−	0.186645i
$690$	−61.6632	−	13.8039i	−2.34748	−	0.525504i
$691$	−8.61717	−	10.2695i	−0.327813	−	0.390672i	0.576815	−	0.816875i	$-0.304295\pi$
$691$	−8.61717	−	10.2695i	−0.327813	−	0.390672i	−0.904628	+	0.426203i	$0.859851\pi$
$692$	0.441951	+	1.05936i	0.0168004	+	0.0402707i
$693$	−24.5850	−	19.1262i	−0.933907	−	0.726545i
$694$	−3.67167	−	18.3372i	−0.139375	−	0.696070i
$695$	−18.4317	−	6.70859i	−0.699154	−	0.254471i
$696$	−0.0120679	−	25.4487i	−0.000457432	−	0.964632i
$697$	34.1734	+	28.6749i	1.29441	+	1.08614i
$698$	26.0134	−	0.600618i	0.984621	−	0.0227337i
$699$	−26.7543	−	6.64125i	−1.01194	−	0.251195i
$700$	24.1702	−	46.7194i	0.913547	−	1.76583i
$701$			49.0807i			1.85375i	0.375368	+	0.926876i	$0.377516\pi$
$701$			49.0807i			1.85375i	−0.375368	+	0.926876i	$0.622484\pi$
$702$	5.63881	+	9.96647i	0.212823	+	0.376160i
$703$	−0.203252			−0.00766579
$704$	−4.84301	+	22.6600i	−0.182528	+	0.854030i
$705$	−9.15916	−	8.82663i	−0.344954	−	0.332430i
$706$	−0.903249	−	39.1206i	−0.0339942	−	1.47232i
$707$	−20.9768	+	24.9992i	−0.788915	+	0.940192i
$708$	9.79523	+	8.60396i	0.368127	+	0.323356i
$709$	5.93610	−	16.3093i	0.222935	−	0.612509i	−0.776919	−	0.629601i	$-0.783218\pi$
$709$	5.93610	−	16.3093i	0.222935	−	0.612509i	0.999854	+	0.0170917i	$0.00544071\pi$
$710$	−9.41285	−	47.0100i	−0.353258	−	1.76425i
$711$	5.18356	+	5.73306i	0.194399	+	0.215007i
$712$	−1.78625	−	25.7514i	−0.0669424	−	0.965073i
$713$	12.6818	−	10.6413i	0.474936	−	0.398519i
$714$	49.9551	+	45.9653i	1.86952	+	1.72021i
$715$	−15.6125	−	2.75291i	−0.583876	−	0.102953i
$716$	22.9480	+	24.9162i	0.857606	+	0.931160i
$717$	2.67960	+	3.68014i	0.100071	+	0.137438i
$718$	10.5404	+	27.0031i	0.393363	+	1.00775i
$719$	−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	$0.204439\pi$
$720$	−28.5247	+	31.0302i	−1.06305	+	1.15643i
$721$	−12.9067	−	22.3550i	−0.480669	−	0.832543i
$722$	15.9460	−	19.9200i	0.593449	−	0.741347i
$723$	7.85647	−	3.84191i	0.292185	−	0.142882i
$724$	10.6448	−	2.38825i	0.395613	−	0.0887585i
$725$	13.0356	+	35.8150i	0.484129	+	1.33013i
$726$	6.38766	+	0.292089i	0.237068	+	0.0108404i
$727$	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
$732$	−27.7690	−	10.8242i	−1.02637	−	0.400072i
$733$	−14.4845	−	39.7958i	−0.534997	−	1.46989i	−0.853055	−	0.521822i	$-0.825253\pi$
$733$	−14.4845	−	39.7958i	−0.534997	−	1.46989i	0.318057	−	0.948071i	$-0.396970\pi$
$734$	10.3488	−	6.29777i	0.381981	−	0.232455i
$735$	−15.6340	−	31.9705i	−0.576668	−	1.17925i
$736$	38.1337	+	16.4914i	1.40563	+	0.607882i
$737$	4.33423	+	7.50711i	0.159653	+	0.276528i
$738$	5.69041	+	23.8102i	0.209467	+	0.876464i
$739$	15.5782	+	8.99410i	0.573055	+	0.330853i	0.758369	−	0.651826i	$-0.225997\pi$
$739$	15.5782	+	8.99410i	0.573055	+	0.330853i	−0.185314	+	0.982679i	$0.559330\pi$
$740$	1.45780	−	0.0673537i	0.0535898	−	0.00247597i
$741$	−1.55437	−	2.13476i	−0.0571010	−	0.0784223i
$742$	7.76639	−	14.1989i	0.285113	−	0.521259i
$743$	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	$-0.171553\pi$
$744$	−1.92267	−	10.8738i	−0.0704884	−	0.398654i
$745$	−52.1930	+	43.7951i	−1.91220	+	1.60453i
$746$	7.93651	−	6.97796i	0.290576	−	0.255481i
$747$	−14.2102	+	12.8482i	−0.519924	+	0.470091i
$748$	44.4179	+	5.73316i	1.62408	+	0.209625i
$749$	20.8628	−	57.3200i	0.762309	−	2.09443i
$750$	7.73274	−	18.5602i	0.282360	−	0.677721i
$751$	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	$0.454810\pi$
$752$	4.83174	+	6.82648i	0.176196	+	0.248936i
$753$	11.6165	+	11.1948i	0.423329	+	0.407959i
$754$	−11.3168	−	1.72714i	−0.412134	−	0.0628986i
$755$			30.4926i			1.10974i
$756$	6.99514	+	36.5903i	0.254411	+	1.33078i
$757$			17.0327i			0.619062i	0.950889	+	0.309531i	$0.100172\pi$
$757$			17.0327i			0.619062i	−0.950889	+	0.309531i	$0.899828\pi$
$758$	8.17399	−	53.5589i	0.296893	−	1.94535i
$759$	−8.87696	+	35.7609i	−0.322213	+	1.29804i
$760$	5.71756	−	7.86030i	0.207398	−	0.285123i
$761$	−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	$0.889975\pi$
$762$	−10.6964	+	8.17265i	−0.387490	+	0.296064i
$763$	−7.94486	+	21.8283i	−0.287623	+	0.790238i
$764$	−0.243752	+	1.88848i	−0.00881864	+	0.0683228i
$765$	64.2991	+	50.0223i	2.32474	+	1.80856i
$766$	2.59286	+	2.94903i	0.0936837	+	0.106553i
$767$	4.49267	−	3.76979i	0.162221	−	0.136119i
$768$	22.2367	−	16.5388i	0.802396	−	0.596792i
$769$	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	$-0.0197596\pi$
$770$	−45.2484	−	24.7495i	−1.63064	−	0.891910i
$771$	−9.05491	+	0.961169i	−0.326105	+	0.0346157i
$772$	−40.8545	+	1.88757i	−1.47039	+	0.0679352i
$773$	13.6541	+	7.88319i	0.491104	+	0.283539i	0.725032	−	0.688715i	$-0.241825\pi$
$773$	13.6541	+	7.88319i	0.491104	+	0.283539i	−0.233929	+	0.972254i	$0.575158\pi$
$774$	15.4921	+	7.74397i	0.556851	+	0.278351i
$775$	8.26895	+	14.3222i	0.297029	+	0.514470i
$776$	−25.4710	+	6.33551i	−0.914356	+	0.227432i
$777$	0.720164	−	1.07007i	0.0258357	−	0.0383886i
$778$	−6.02050	−	9.89316i	−0.215845	−	0.354687i
$779$	−1.93085	−	5.30495i	−0.0691797	−	0.190070i
$780$	11.8559	+	14.7962i	0.424510	+	0.529790i
$781$	−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
$786$	−7.46374	+	3.86584i	−0.266223	+	0.137890i
$787$	8.90762	+	24.4735i	0.317523	+	0.872386i	0.991082	+	0.133253i	$0.0425423\pi$
$787$	8.90762	+	24.4735i	0.317523	+	0.872386i	−0.673560	+	0.739133i	$0.735236\pi$
$788$	19.8677	−	4.45746i	0.707759	−	0.158791i
$789$	−2.50789	+	36.4049i	−0.0892831	+	1.29605i
$790$	9.99063	+	7.99752i	0.355451	+	0.284539i
$791$	23.1806	+	40.1500i	0.824207	+	1.42757i
$792$	17.7052	+	17.0462i	0.629126	+	0.605710i
$793$	−6.70352	+	11.6108i	−0.238049	+	0.412313i
$794$	29.7484	−	11.6120i	1.05573	−	0.412093i
$795$	7.88126	−	17.7509i	0.279519	−	0.629560i
$796$	−21.5719	+	19.8679i	−0.764596	+	0.704199i
$797$	21.2149	+	3.74076i	0.751470	+	0.132504i	0.536248	−	0.844061i	$-0.319841\pi$
$797$	21.2149	+	3.74076i	0.751470	+	0.132504i	0.215222	+	0.976565i	$0.430952\pi$
$798$	−2.56640	−	8.19848i	−0.0908495	−	0.290223i
$799$	12.3830	−	10.3905i	0.438078	−	0.367591i
$800$	−22.8393	+	34.6551i	−0.807491	+	1.22524i
$801$	−24.2008	−	12.8037i	−0.855093	−	0.452397i
$802$	−46.9639	+	9.40363i	−1.65835	+	0.332054i
$803$	−3.37510	+	9.27301i	−0.119105	+	0.327238i
$804$	2.03062	−	10.1664i	0.0716146	−	0.358543i
$805$	−59.4408	+	70.8388i	−2.09501	+	2.49674i
$806$	−4.96604	+	0.114660i	−0.174921	+	0.00403873i
$807$	2.53948	−	0.731025i	0.0893939	−	0.0257333i
$808$	18.5326	−	17.8767i	0.651976	−	0.628902i
$809$	20.6468			0.725903			0.362951	−	0.931808i	$-0.381769\pi$
$809$	20.6468			0.725903			0.362951	+	0.931808i	$0.381769\pi$
$810$	11.9918	+	43.0673i	0.421347	+	1.51323i
$811$			16.1001i			0.565351i	0.959216	+	0.282675i	$0.0912219\pi$
$811$			16.1001i			0.565351i	−0.959216	+	0.282675i	$0.908778\pi$
$812$	−33.0780	−	17.1129i	−1.16081	−	0.600543i
$813$	−15.0882	−	52.4143i	−0.529166	−	1.83825i
$814$	−0.0196425	−	0.850735i	−0.000688468	−	0.0298183i
$815$	13.3379	+	11.1918i	0.467207	+	0.392033i
$816$	−35.3869	−	40.2095i	−1.23879	−	1.40761i
$817$	−3.75318	−	1.36604i	−0.131307	−	0.0477918i
$818$	−30.7040	+	6.14788i	−1.07354	+	0.214956i
$819$	16.7464	−	0.619447i	0.585167	−	0.0216452i
$820$	15.6067	+	37.4093i	0.545010	+	1.30639i
$821$	−23.8617	−	28.4372i	−0.832778	−	0.992466i	−0.999979	−	0.00654316i	$-0.997917\pi$
$821$	−23.8617	−	28.4372i	−0.832778	−	0.992466i	0.167201	−	0.985923i	$-0.446527\pi$
$822$	−16.4528	+	5.15027i	−0.573857	+	0.179636i
$823$	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	$-0.0454820\pi$
$824$	8.27385	+	18.6114i	0.288233	+	0.648358i
$825$	−33.6416	−	14.9366i	−1.17125	−	0.520025i
$826$	17.7734	−	6.93765i	0.618415	−	0.241392i
$827$	10.8864	+	6.28525i	0.378556	+	0.218560i	0.677190	−	0.735808i	$-0.263198\pi$
$827$	10.8864	+	6.28525i	0.378556	+	0.218560i	−0.298634	+	0.954368i	$0.596531\pi$
$828$	36.2016	−	25.1268i	1.25809	−	0.873217i
$829$	34.2984	−	19.8022i	1.19123	−	0.687758i	0.232646	−	0.972562i	$-0.425262\pi$
$829$	34.2984	−	19.8022i	1.19123	−	0.687758i	0.958586	+	0.284804i	$0.0919285\pi$
$830$	−19.8230	+	24.7632i	−0.688066	+	0.859543i
$831$	−10.2434	−	0.705654i	−0.355340	−	0.0244789i
$832$	−5.84028	−	11.0137i	−0.202475	−	0.381830i
$833$	42.4987	−	15.4683i	1.47249	−	0.535944i
$834$	12.1463	−	6.29117i	0.420592	−	0.217845i
$835$	−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	$0.968554\pi$
$840$	21.1240	+	57.9522i	0.728847	+	1.99954i
$841$	−1.89355	+	0.689197i	−0.0652950	+	0.0237654i
$842$	22.0296	+	36.2001i	0.759191	+	1.24754i
$843$	−39.3464	−	26.4804i	−1.35516	−	0.912032i
$844$	1.27081	−	0.814136i	0.0437432	−	0.0280237i
$845$	−32.1574	+	18.5661i	−1.10625	+	0.638693i
$846$	8.85474	−	0.532436i	0.304432	−	0.0183055i
$847$	4.67884	−	8.10400i	0.160767	−	0.278457i
$848$	−7.27133	+	10.4975i	−0.249699	+	0.360485i
$849$	6.04491	+	56.9474i	0.207461	+	1.95443i
$850$	70.3795	+	38.4955i	2.41400	+	1.32038i
$851$	−1.50259	−	0.264948i	−0.0515083	−	0.00908230i
$852$	28.5699	+	17.3677i	0.978789	+	0.595007i
$853$	−17.4553	−	20.8024i	−0.597656	−	0.712259i	0.379402	−	0.925232i	$-0.376130\pi$
$853$	−17.4553	−	20.8024i	−0.597656	−	0.712259i	−0.977058	+	0.212973i	$0.931685\pi$
$854$	−32.7559	+	28.7997i	−1.12088	+	0.985506i
$855$	−3.88172	−	9.55073i	−0.132752	−	0.326628i
$856$	−21.1230	+	43.2472i	−0.721970	+	1.47816i
$857$	−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	$0.813039\pi$
$858$	8.78507	−	6.71229i	0.299917	−	0.229154i
$859$	−9.80975	+	11.6908i	−0.334704	+	0.398885i	−0.906978	−	0.421178i	$-0.861617\pi$
$859$	−9.80975	+	11.6908i	−0.334704	+	0.398885i	0.572274	+	0.820062i	$0.306061\pi$
$860$	27.3719	+	8.55406i	0.933374	+	0.291691i
$861$	34.7706	+	8.63114i	1.18498	+	0.294149i
$862$	−33.5725	−	5.12373i	−1.14349	−	0.174515i
$863$	−14.5657			−0.495821			−0.247911	−	0.968783i	$-0.579744\pi$
$863$	−14.5657			−0.495821			−0.247911	+	0.968783i	$0.579744\pi$
$864$	−2.45495	−	29.2912i	−0.0835192	−	0.996506i
$865$	2.01585			0.0685411
$866$	−1.43092	−	0.218382i	−0.0486245	−	0.00742092i
$867$	−51.4069	+	53.3436i	−1.74587	+	1.81164i
$868$	−15.4243	−	4.82030i	−0.523536	−	0.163611i
$869$	4.79665	−	5.71642i	0.162715	−	0.193916i
$870$	−41.2557	−	17.1884i	−1.39870	−	0.582742i
$871$	−4.38236	−	1.59505i	−0.148491	−	0.0540461i
$872$	8.04396	−	16.4692i	0.272403	−	0.557717i
$873$	−8.54807	+	26.4944i	−0.289309	+	0.896701i
$874$	−7.63183	+	6.71008i	−0.258151	+	0.226972i
$875$	−18.9138	−	22.5406i	−0.639403	−	0.762011i
$876$	10.3517	−	5.66843i	0.349750	−	0.191519i
$877$	38.2453	+	6.74367i	1.29145	+	0.227718i	0.776836	−	0.629703i	$-0.216824\pi$
$877$	38.2453	+	6.74367i	1.29145	+	0.227718i	0.514616	+	0.857421i	$0.327935\pi$
$878$	9.64463	+	5.27532i	0.325490	+	0.178034i
$879$	−44.7355	+	32.5729i	−1.50889	+	1.09866i
$880$	33.4528	+	23.1719i	1.12769	+	0.781124i
$881$	−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	$0.868517\pi$
$882$	23.7894	+	7.07338i	0.801031	+	0.238173i
$883$	11.1556	−	6.44070i	0.375417	−	0.216747i	−0.300406	−	0.953812i	$-0.597122\pi$
$883$	11.1556	−	6.44070i	0.375417	−	0.216747i	0.675822	+	0.737065i	$0.263789\pi$
$884$	−20.2886	+	12.9977i	−0.682378	+	0.437160i
$885$	20.5687	−	10.0584i	0.691411	−	0.338108i
$886$	4.95687	+	8.14535i	0.166529	+	0.273648i
$887$	−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	$0.470953\pi$
$888$	−0.653814	+	0.779936i	−0.0219406	+	0.0261729i
$889$	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
$894$	2.17045	−	47.4652i	0.0725906	−	1.58748i
$895$	55.9014	−	20.3464i	1.86858	−	0.680106i
$896$	−6.52506	−	40.0275i	−0.217987	−	1.33723i
$897$	−8.70831	−	17.8080i	−0.290762	−	0.594590i
$898$	−20.3815	+	25.4608i	−0.680138	+	0.849639i
$899$	10.1404	−	5.85454i	0.338200	−	0.195260i
$900$	18.4398	+	39.9738i	0.614660	+	1.33246i
$901$	21.3749	+	12.3408i	0.712101	+	0.411131i
$902$	22.0179	−	8.59446i	0.733116	−	0.286164i
$903$	20.4902	−	14.9193i	0.681870	−	0.496485i
$904$	−14.8600	−	33.4264i	−0.494236	−	1.11174i
$905$	3.32697	−	18.8682i	0.110592	−	0.627199i
$906$	−15.6485	−	14.3987i	−0.519888	−	0.478365i
$907$	−2.50247	−	2.98233i	−0.0830931	−	0.0990265i	0.722896	−	0.690957i	$-0.242811\pi$
$907$	−2.50247	−	2.98233i	−0.0830931	−	0.0990265i	−0.805989	+	0.591930i	$0.798366\pi$
$908$	−14.4796	−	34.7077i	−0.480523	−	1.15181i
$909$	−5.73356	−	26.7029i	−0.190170	−	0.885678i
$910$	27.2070	−	5.44769i	0.901904	−	0.180589i
$911$	−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	$0.872851\pi$
$912$	1.33399	+	6.64587i	0.0441727	+	0.220067i
$913$	14.1689	+	11.8892i	0.468924	+	0.393474i
$914$	0.718978	+	31.1397i	0.0237817	+	1.03001i
$915$	−36.3208	+	37.6892i	−1.20073	+	1.24597i
$916$	41.6235	+	21.5338i	1.37528	+	0.711497i
$917$			12.3009i			0.406210i
$918$	−56.0333	+	9.37701i	−1.84937	+	0.309488i
$919$	7.23703			0.238727			0.119364	−	0.992851i	$-0.461915\pi$
$919$	7.23703			0.238727			0.119364	+	0.992851i	$0.461915\pi$
$920$	52.5148	−	50.6563i	1.73136	−	1.67009i
$921$	−0.465448	+	1.87506i	−0.0153370	+	0.0617853i
$922$	−41.2761	+	0.953017i	−1.35936	+	0.0313859i
$923$	9.66768	−	11.5215i	0.318216	−	0.379235i
$924$	34.0677	−	11.5343i	1.12074	−	0.379450i
$925$	0.521310	−	1.43229i	0.0171406	−	0.0470934i
$926$	20.6975	−	4.14427i	0.680161	−	0.136189i
$927$	21.3990	+	2.96236i	0.702837	+	0.0972966i
$928$	24.5363	+	16.1706i	0.805444	+	0.530824i
$929$	−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	$0.463017\pi$
$930$	−18.9245	−	4.23642i	−0.620559	−	0.138918i
$931$	−5.63641	−	0.993852i	−0.184726	−	0.0325722i
$932$	23.4135	−	21.5640i	0.766936	−	0.706354i
$933$	−16.8487	+	1.78848i	−0.551603	+	0.0585521i
$934$	35.0099	−	13.6657i	1.14556	−	0.447156i
$935$	39.3270	−	68.1163i	1.28613	−	2.22764i
$936$	−13.1917	−	0.902474i	−0.431184	−	0.0294983i
$937$	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	$0.771081\pi$
$938$	−11.8443	−	9.48137i	−0.386730	−	0.309578i
$939$	−26.5011	−	17.8354i	−0.864832	−	0.582037i
$940$	14.3316	−	3.21539i	0.467444	−	0.104874i
$941$	3.22856	+	8.87040i	0.105248	+	0.289167i	0.981127	−	0.193364i	$-0.0619399\pi$
$941$	3.22856	+	8.87040i	0.105248	+	0.289167i	−0.875879	+	0.482531i	$0.839718\pi$
$942$	−0.581721	−	0.372286i	−0.0189535	−	0.0121297i
$943$	−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	−0.178339	−	0.983969i	$-0.557072\pi$
$947$	−0.288825	+	0.0509277i	−0.00938556	+	0.00165493i	0.168953	+	0.985624i	$0.445961\pi$
$948$	−8.82187	+	1.35065i	−0.286521	+	0.0438670i
$949$	−1.81580	−	4.98886i	−0.0589432	−	0.161945i
$950$	−5.27746	−	8.67218i	−0.171224	−	0.281363i
$951$	48.6885	+	3.35409i	1.57883	+	0.108764i
$952$	−76.0686	+	18.9209i	−2.46540	+	0.613229i
$953$	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	$0.614878\pi$
$954$	5.38807	+	12.4266i	0.174445	+	0.402328i
$955$	2.89605	+	1.67203i	0.0937138	+	0.0541057i
$956$	−5.25097	+	0.242607i	−0.169829	+	0.00784647i
$957$	−10.5753	+	23.8188i	−0.341852	+	0.769952i
$958$	−46.4051	−	25.3822i	−1.49928	−	0.820061i
$959$	−4.38109	+	24.8464i	−0.141473	+	0.802331i
$960$	−11.7702	−	47.2246i	−0.379881	−	1.52417i
$961$	−19.8553	+	16.6606i	−0.640494	+	0.537439i
$962$	0.302295	+	0.343821i	0.00974637	+	0.0110852i
$963$	27.1416	+	43.2366i	0.874626	+	1.39328i
$964$	−1.29272	+	10.0154i	−0.0416357	+	0.322574i
$965$	−24.5657	+	67.4937i	−0.790798	+	2.17270i
$966$	−8.28569	−	63.9549i	−0.266588	−	2.05771i
$967$	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	$0.498197\pi$
$968$	−4.34328	+	5.97099i	−0.139598	+	0.191915i
$969$	12.5901	−	3.62423i	0.404452	−	0.116427i
$970$	−6.95439	+	45.5676i	−0.223292	+	1.46309i
$971$		−	52.4570i		−	1.68342i	−0.539927	−	0.841712i	$-0.681548\pi$
$971$		−	52.4570i		−	1.68342i	0.539927	−	0.841712i	$-0.318452\pi$
$972$	−27.7643	−	14.1825i	−0.890541	−	0.454903i
$973$		−	20.0181i		−	0.641751i
$974$	14.8954	+	2.27329i	0.477280	+	0.0728410i
$975$	19.0301	−	5.47807i	0.609450	−	0.175439i
$976$	28.0904	−	19.8822i	0.899152	−	0.636414i
$977$	−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	$0.992894\pi$
$978$	−12.0418	+	1.56008i	−0.385053	+	0.0498857i
$979$	−9.04103	+	24.8400i	−0.288953	+	0.793891i
$980$	40.7559	+	5.26049i	1.30190	+	0.168040i
$981$	−10.3359	−	16.4651i	−0.330001	−	0.525691i
$982$	40.5104	−	35.6177i	1.29274	−	1.13661i
$983$	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	$0.118990\pi$
$984$	−26.5677	−	9.65559i	−0.846947	−	0.307809i
$985$	6.20951	−	35.2159i	0.197851	−	1.12207i
$986$	27.2554	−	49.8297i	0.867988	−	1.58690i
$987$	5.26789	−	11.8649i	0.167679	−	0.377662i
$988$	3.04596	−	0.140730i	0.0969048	−	0.00447722i
$989$	−25.9656	−	14.9913i	−0.825659	−	0.476695i
$990$	39.6006	−	17.1704i	1.25859	−	0.545711i
$991$	−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	$-0.476590\pi$
$992$	11.7033	+	5.06124i	0.371579	+	0.160694i
$993$	−51.0542	−	3.51705i	−1.62016	−	0.111610i
$994$	41.7981	−	25.4363i	1.32576	−	0.806790i
$995$	17.6155	+	48.3983i	0.558450	+	1.53433i
$996$	−3.34777	−	21.8663i	−0.106078	−	0.692859i
$997$	10.3169	−	1.81914i	0.326738	−	0.0576128i	−0.00787296	−	0.999969i	$-0.502506\pi$
$997$	10.3169	−	1.81914i	0.326738	−	0.0576128i	0.334611	+	0.942356i	$0.391395\pi$
$998$	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.13.1	✓	204
3.2	odd	2		648.2.t.a.253.34		204
4.3	odd	2		864.2.bf.a.337.21		204
8.3	odd	2		864.2.bf.a.337.14		204
8.5	even	2	inner	216.2.t.a.13.30	yes	204
24.5	odd	2		648.2.t.a.253.5		204
27.2	odd	18		648.2.t.a.397.5		204
27.25	even	9	inner	216.2.t.a.133.30	yes	204
108.79	odd	18		864.2.bf.a.241.14		204
216.29	odd	18		648.2.t.a.397.34		204
216.133	even	18	inner	216.2.t.a.133.1	yes	204
216.187	odd	18		864.2.bf.a.241.21		204

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

\(f(q)\)	\(=\)	\(q+(-1.39803 - 0.213362i) q^{2} +(-0.479138 - 1.66446i) q^{3} +(1.90895 + 0.596572i) q^{4} +(2.25773 - 2.69066i) q^{5} +(0.314714 + 2.42919i) q^{6} +(3.36848 + 1.22603i) q^{7} +(-2.54148 - 1.24132i) q^{8} +(-2.54085 + 1.59501i) q^{9} +O(q^{10})\)	\(q+(-1.39803 - 0.213362i) q^{2} +(-0.479138 - 1.66446i) q^{3} +(1.90895 + 0.596572i) q^{4} +(2.25773 - 2.69066i) q^{5} +(0.314714 + 2.42919i) q^{6} +(3.36848 + 1.22603i) q^{7} +(-2.54148 - 1.24132i) q^{8} +(-2.54085 + 1.59501i) q^{9} +(-3.73045 + 3.27990i) q^{10} +(1.86181 + 2.21882i) q^{11} +(0.0783185 - 3.46322i) q^{12} +(-1.53462 - 0.270594i) q^{13} +(-4.44764 - 2.43273i) q^{14} +(-5.56026 - 2.46871i) q^{15} +(3.28820 + 2.27766i) q^{16} +(3.86560 - 6.69542i) q^{17} +(3.89249 - 1.68775i) q^{18} +(-0.847303 + 0.489191i) q^{19} +(5.91507 - 3.78944i) q^{20} +(0.426706 - 6.19414i) q^{21} +(-2.12945 - 3.49921i) q^{22} +(-6.90160 + 2.51198i) q^{23} +(-0.848411 + 4.82496i) 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} +(7.24666 + 4.63766i) q^{30} +(-2.11811 + 0.770928i) q^{31} +(-4.11103 - 3.88580i) q^{32} +(2.80108 - 4.16204i) q^{33} +(-6.83276 + 8.53559i) q^{34} +(10.9040 - 6.29540i) q^{35} +(-5.80191 + 1.52900i) q^{36} +(0.179911 + 0.103872i) q^{37} +(1.28893 - 0.503119i) q^{38} +(0.284900 + 2.68396i) q^{39} +(-9.07795 + 4.03569i) q^{40} +(-1.00198 + 5.68249i) q^{41} +(-1.91814 + 8.56853i) q^{42} +(2.62405 + 3.12722i) q^{43} +(2.23043 + 5.34633i) q^{44} +(-1.44493 + 10.4377i) q^{45} +(10.1846 - 2.03927i) q^{46} +(1.96476 + 0.715114i) q^{47} +(2.21556 - 6.56439i) q^{48} +(4.48123 + 3.76020i) q^{49} +(0.239508 + 10.3733i) q^{50} +(-12.9964 - 3.22611i) q^{51} +(-2.76808 - 1.43206i) q^{52} +3.19246i q^{53} +(-4.67423 - 5.67024i) q^{54} +10.1736 q^{55} +(-7.03904 - 7.29730i) q^{56} +(1.22021 + 1.17591i) q^{57} +(7.34446 - 0.169575i) q^{58} +(-2.41918 + 2.88307i) q^{59} +(-9.14151 - 8.02974i) q^{60} +(2.94263 - 8.08481i) q^{61} +(3.12566 - 0.625853i) q^{62} +(-10.5144 + 2.25761i) q^{63} +(4.91824 + 6.30959i) q^{64} +(-4.19283 + 3.51820i) q^{65} +(-4.80400 + 5.22099i) q^{66} +(2.94730 + 0.519689i) q^{67} +(11.3736 - 10.4751i) q^{68} +(7.48790 + 10.2838i) q^{69} +(-16.5872 + 6.47464i) q^{70} +(-4.82588 + 8.35866i) q^{71} +(8.43745 - 0.899673i) q^{72} +(1.70348 + 2.95051i) q^{73} +(-0.229358 - 0.183601i) q^{74} +(-11.4162 + 5.58264i) q^{75} +(-1.90930 + 0.428365i) q^{76} +(3.55115 + 9.75670i) q^{77} +(0.174359 - 3.81303i) 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} +(4.50981 - 11.5698i) q^{84} +(-9.28760 - 25.5175i) q^{85} +(-3.00126 - 4.93181i) q^{86} +(3.95259 + 8.08281i) q^{87} +(-1.97749 - 7.95020i) q^{88} +(4.56318 + 7.90366i) q^{89} +(4.24706 - 14.2839i) q^{90} +(-4.83758 - 2.79298i) q^{91} +(-14.6734 + 0.677944i) q^{92} +(2.29804 + 3.15612i) q^{93} +(-2.59420 - 1.41895i) q^{94} +(-0.596737 + 3.38427i) q^{95} +(-4.49801 + 8.70448i) q^{96} +(7.10870 - 5.96491i) q^{97} +(-5.46259 - 6.21298i) 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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