LMFDB - Embedded newform 162.2.g.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	162.31
Dual form			162.2.g.b.115.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.396080 + 0.918216i) q^{2} +(-1.57515 - 0.720348i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(0.193287 - 3.31862i) q^{5} +(0.0375499 - 1.73164i) q^{6} +(2.86227 - 0.678371i) q^{7} +(-0.939693 - 0.342020i) q^{8} +(1.96220 + 2.26931i) q^{9} +O(q^{10})$	\(q+(0.396080 + 0.918216i) q^{2} +(-1.57515 - 0.720348i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(0.193287 - 3.31862i) q^{5} +(0.0375499 - 1.73164i) q^{6} +(2.86227 - 0.678371i) q^{7} +(-0.939693 - 0.342020i) q^{8} +(1.96220 + 2.26931i) q^{9} +(3.12376 - 1.13696i) q^{10} +(5.02852 - 3.30731i) q^{11} +(1.60490 - 0.651390i) q^{12} +(-6.08473 + 0.711203i) q^{13} +(1.75658 + 2.35949i) q^{14} +(-2.69501 + 5.08809i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(-0.253735 - 0.212909i) q^{17} +(-1.30653 + 2.70055i) q^{18} +(-0.285511 + 0.239572i) q^{19} +(2.28123 + 2.41796i) q^{20} +(-4.99717 - 0.993295i) q^{21} +(5.02852 + 3.30731i) q^{22} +(0.697536 + 0.165319i) q^{23} +(1.23378 + 1.21564i) q^{24} +(-6.00966 - 0.702429i) q^{25} +(-3.06308 - 5.30540i) q^{26} +(-1.45606 - 4.98797i) q^{27} +(-1.47078 + 2.54747i) q^{28} +(0.233421 - 0.313539i) q^{29} +(-5.73940 - 0.459319i) q^{30} +(2.28811 + 7.64280i) q^{31} +(0.893633 - 0.448799i) q^{32} +(-10.3031 + 1.58723i) q^{33} +(0.0949972 - 0.317313i) q^{34} +(-1.69801 - 9.62990i) q^{35} +(-2.99718 - 0.130046i) q^{36} +(-0.453355 + 2.57110i) q^{37} +(-0.333064 - 0.167271i) q^{38} +(10.0967 + 3.26287i) q^{39} +(-1.31666 + 3.05237i) q^{40} +(-0.132020 + 0.306057i) q^{41} +(-1.06722 - 4.98191i) q^{42} +(7.96817 + 4.00176i) q^{43} +(-1.04513 + 5.92723i) q^{44} +(7.91025 - 6.07315i) q^{45} +(0.124481 + 0.705968i) q^{46} +(-2.04511 + 6.83114i) q^{47} +(-0.627542 + 1.61437i) q^{48} +(1.47698 - 0.741765i) q^{49} +(-1.73532 - 5.79638i) q^{50} +(0.246303 + 0.518142i) q^{51} +(3.65828 - 4.91393i) q^{52} +(-3.45123 + 5.97770i) q^{53} +(4.00332 - 3.31261i) q^{54} +(-10.0037 - 17.3270i) q^{55} +(-2.92167 - 0.341494i) q^{56} +(0.622298 - 0.171695i) q^{57} +(0.380350 + 0.0901447i) q^{58} +(-9.06502 - 5.96216i) q^{59} +(-1.85151 - 5.45194i) q^{60} +(4.99910 + 5.29874i) q^{61} +(-6.11147 + 5.12813i) q^{62} +(7.15577 + 5.16429i) q^{63} +(0.766044 + 0.642788i) q^{64} +(1.18411 + 20.3303i) q^{65} +(-5.53826 - 8.83180i) q^{66} +(0.734568 + 0.986697i) q^{67} +(0.328988 - 0.0384532i) q^{68} +(-0.979637 - 0.762871i) q^{69} +(8.16978 - 5.37335i) q^{70} +(12.1389 - 4.41819i) q^{71} +(-1.06771 - 2.80357i) q^{72} +(-0.412642 - 0.150189i) q^{73} +(-2.54039 + 0.602084i) q^{74} +(8.96013 + 5.43548i) q^{75} +(0.0216710 - 0.372077i) q^{76} +(12.1494 - 12.8776i) q^{77} +(1.00307 + 10.5633i) q^{78} +(0.525833 + 1.21902i) q^{79} -3.32424 q^{80} +(-1.29956 + 8.90568i) q^{81} -0.333317 q^{82} +(-1.98870 - 4.61033i) q^{83} +(4.15176 - 2.95317i) q^{84} +(-0.755608 + 0.800897i) q^{85} +(-0.518454 + 8.90152i) q^{86} +(-0.593531 + 0.325727i) q^{87} +(-5.85643 + 1.38800i) q^{88} +(1.65643 + 0.602892i) q^{89} +(8.70955 + 4.85786i) q^{90} +(-16.9337 + 6.16336i) q^{91} +(-0.598927 + 0.393920i) q^{92} +(1.90137 - 13.6868i) q^{93} +(-7.08249 + 0.827825i) q^{94} +(0.739862 + 0.993807i) q^{95} +(-1.73090 + 0.0631998i) q^{96} +(-0.696419 - 11.9570i) q^{97} +(1.26610 + 1.06239i) q^{98} +(17.3723 + 4.92169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.396080	+	0.918216i	0.280071	+	0.649277i
$2$	0.396080	+	0.918216i	0.280071	+	0.649277i
$3$	−1.57515	−	0.720348i	−0.909414	−	0.415893i
$3$	−1.57515	−	0.720348i	−0.909414	−	0.415893i
$4$	−0.686242	+	0.727374i	−0.343121	+	0.363687i
$5$	0.193287	−	3.31862i	0.0864407	−	1.48413i	−0.624581	−	0.780960i	$-0.714730\pi$
$5$	0.193287	−	3.31862i	0.0864407	−	1.48413i	0.711022	−	0.703170i	$-0.248233\pi$
$6$	0.0375499	−	1.73164i	0.0153297	−	0.706941i
$7$	2.86227	−	0.678371i	1.08184	−	0.256400i	0.349219	−	0.937041i	$-0.386447\pi$
$7$	2.86227	−	0.678371i	1.08184	−	0.256400i	0.732617	+	0.680641i	$0.238299\pi$
$8$	−0.939693	−	0.342020i	−0.332232	−	0.120922i
$9$	1.96220	+	2.26931i	0.654066	+	0.756438i
$10$	3.12376	−	1.13696i	0.987821	−	0.359537i
$11$	5.02852	−	3.30731i	1.51616	−	0.997192i	0.527075	−	0.849818i	$-0.323289\pi$
$11$	5.02852	−	3.30731i	1.51616	−	0.997192i	0.989081	−	0.147373i	$-0.0470819\pi$
$12$	1.60490	−	0.651390i	0.463294	−	0.188040i
$13$	−6.08473	+	0.711203i	−1.68760	+	0.197252i	−0.905041	−	0.425324i	$-0.860160\pi$
$13$	−6.08473	+	0.711203i	−1.68760	+	0.197252i	−0.782559	+	0.622576i	$0.786086\pi$
$14$	1.75658	+	2.35949i	0.469465	+	0.630601i
$15$	−2.69501	+	5.08809i	−0.695850	+	1.31374i
$16$	−0.0581448	−	0.998308i	−0.0145362	−	0.249577i
$17$	−0.253735	−	0.212909i	−0.0615398	−	0.0516381i	0.611499	−	0.791245i	$-0.290567\pi$
$17$	−0.253735	−	0.212909i	−0.0615398	−	0.0516381i	−0.673039	+	0.739607i	$0.735011\pi$
$18$	−1.30653	+	2.70055i	−0.307953	+	0.636526i
$19$	−0.285511	+	0.239572i	−0.0655007	+	0.0549616i	−0.674950	−	0.737863i	$-0.735835\pi$
$19$	−0.285511	+	0.239572i	−0.0655007	+	0.0549616i	0.609450	+	0.792825i	$0.291390\pi$
$20$	2.28123	+	2.41796i	0.510099	+	0.540673i
$21$	−4.99717	−	0.993295i	−1.09047	−	0.216755i
$22$	5.02852	+	3.30731i	1.07208	+	0.705121i
$23$	0.697536	+	0.165319i	0.145446	+	0.0344714i	0.302694	−	0.953088i	$-0.402114\pi$
$23$	0.697536	+	0.165319i	0.145446	+	0.0344714i	−0.157248	+	0.987559i	$0.550262\pi$
$24$	1.23378	+	1.21564i	0.251845	+	0.248141i
$25$	−6.00966	−	0.702429i	−1.20193	−	0.140486i
$26$	−3.06308	−	5.30540i	−0.600719	−	1.04048i
$27$	−1.45606	−	4.98797i	−0.280219	−	0.959936i
$28$	−1.47078	+	2.54747i	−0.277951	+	0.481426i
$29$	0.233421	−	0.313539i	0.0433453	−	0.0582228i	−0.779922	−	0.625877i	$-0.784741\pi$
$29$	0.233421	−	0.313539i	0.0433453	−	0.0582228i	0.823267	+	0.567654i	$0.192149\pi$
$30$	−5.73940	−	0.459319i	−1.04787	−	0.0838597i
$31$	2.28811	+	7.64280i	0.410956	+	1.37269i	0.873816	+	0.486257i	$0.161638\pi$
$31$	2.28811	+	7.64280i	0.410956	+	1.37269i	−0.462860	+	0.886431i	$0.653177\pi$
$32$	0.893633	−	0.448799i	0.157973	−	0.0793372i
$33$	−10.3031	+	1.58723i	−1.79354	+	0.276301i
$34$	0.0949972	−	0.317313i	0.0162919	−	0.0544187i
$35$	−1.69801	−	9.62990i	−0.287016	−	1.62775i
$36$	−2.99718	−	0.130046i	−0.499530	−	0.0216743i
$37$	−0.453355	+	2.57110i	−0.0745310	+	0.422687i	0.924597	+	0.380946i	$0.124402\pi$
$37$	−0.453355	+	2.57110i	−0.0745310	+	0.422687i	−0.999128	+	0.0417409i	$0.986710\pi$
$38$	−0.333064	−	0.167271i	−0.0540301	−	0.0271349i
$39$	10.0967	+	3.26287i	1.61676	+	0.522477i
$40$	−1.31666	+	3.05237i	−0.208183	+	0.482622i
$41$	−0.132020	+	0.306057i	−0.0206181	+	0.0477981i	−0.928214	−	0.372047i	$-0.878656\pi$
$41$	−0.132020	+	0.306057i	−0.0206181	+	0.0477981i	0.907596	+	0.419845i	$0.137915\pi$
$42$	−1.06722	−	4.98191i	−0.164675	−	0.768725i
$43$	7.96817	+	4.00176i	1.21513	+	0.610263i	0.936680	−	0.350186i	$-0.113882\pi$
$43$	7.96817	+	4.00176i	1.21513	+	0.610263i	0.278454	+	0.960450i	$0.410178\pi$
$44$	−1.04513	+	5.92723i	−0.157559	+	0.893563i
$45$	7.91025	−	6.07315i	1.17919	−	0.905332i
$46$	0.124481	+	0.705968i	0.0183538	+	0.104089i
$47$	−2.04511	+	6.83114i	−0.298310	+	0.996425i	0.669092	+	0.743179i	$0.266683\pi$
$47$	−2.04511	+	6.83114i	−0.298310	+	0.996425i	−0.967402	+	0.253245i	$0.918502\pi$
$48$	−0.627542	+	1.61437i	−0.0905779	+	0.233014i
$49$	1.47698	−	0.741765i	0.210997	−	0.105966i
$50$	−1.73532	−	5.79638i	−0.245412	−	0.819733i
$51$	0.246303	+	0.518142i	0.0344892	+	0.0725543i
$52$	3.65828	−	4.91393i	0.507313	−	0.681439i
$53$	−3.45123	+	5.97770i	−0.474062	+	0.821100i	−0.999559	−	0.0296958i	$-0.990546\pi$
$53$	−3.45123	+	5.97770i	−0.474062	+	0.821100i	0.525497	+	0.850796i	$0.323879\pi$
$54$	4.00332	−	3.31261i	0.544783	−	0.450790i
$55$	−10.0037	−	17.3270i	−1.34890	−	2.33637i
$56$	−2.92167	−	0.341494i	−0.390425	−	0.0456341i
$57$	0.622298	−	0.171695i	0.0824254	−	0.0227415i
$58$	0.380350	+	0.0901447i	0.0499424	+	0.0118366i
$59$	−9.06502	−	5.96216i	−1.18016	−	0.776207i	−0.201063	−	0.979578i	$-0.564440\pi$
$59$	−9.06502	−	5.96216i	−1.18016	−	0.776207i	−0.979102	+	0.203372i	$0.934810\pi$
$60$	−1.85151	−	5.45194i	−0.239029	−	0.703842i
$61$	4.99910	+	5.29874i	0.640069	+	0.678434i	0.963466	−	0.267830i	$-0.0863064\pi$
$61$	4.99910	+	5.29874i	0.640069	+	0.678434i	−0.323397	+	0.946263i	$0.604825\pi$
$62$	−6.11147	+	5.12813i	−0.776158	+	0.651274i
$63$	7.15577	+	5.16429i	0.901543	+	0.650639i
$64$	0.766044	+	0.642788i	0.0957556	+	0.0803485i
$65$	1.18411	+	20.3303i	0.146871	+	2.52167i
$66$	−5.53826	−	8.83180i	−0.681713	−	1.08712i
$67$	0.734568	+	0.986697i	0.0897418	+	0.120544i	0.844726	−	0.535198i	$-0.179763\pi$
$67$	0.734568	+	0.986697i	0.0897418	+	0.120544i	−0.754985	+	0.655742i	$0.772356\pi$
$68$	0.328988	−	0.0384532i	0.0398957	−	0.00466314i
$69$	−0.979637	−	0.762871i	−0.117934	−	0.0918389i
$70$	8.16978	−	5.37335i	0.976475	−	0.642238i
$71$	12.1389	−	4.41819i	1.44062	−	0.524343i	0.500665	−	0.865641i	$-0.333089\pi$
$71$	12.1389	−	4.41819i	1.44062	−	0.524343i	0.939955	+	0.341298i	$0.110867\pi$
$72$	−1.06771	−	2.80357i	−0.125831	−	0.330404i
$73$	−0.412642	−	0.150189i	−0.0482961	−	0.0175783i	0.317759	−	0.948171i	$-0.397070\pi$
$73$	−0.412642	−	0.150189i	−0.0482961	−	0.0175783i	−0.366055	+	0.930593i	$0.619292\pi$
$74$	−2.54039	+	0.602084i	−0.295315	+	0.0699908i
$75$	8.96013	+	5.43548i	1.03463	+	0.627635i
$76$	0.0216710	−	0.372077i	0.00248584	−	0.0426802i
$77$	12.1494	−	12.8776i	1.38455	−	1.46754i
$78$	1.00307	+	10.5633i	0.113575	+	1.19606i
$79$	0.525833	+	1.21902i	0.0591609	+	0.137150i	0.945232	−	0.326399i	$-0.105835\pi$
$79$	0.525833	+	1.21902i	0.0591609	+	0.137150i	−0.886071	+	0.463549i	$0.846576\pi$
$80$	−3.32424			−0.371661
$81$	−1.29956	+	8.90568i	−0.144396	+	0.989520i
$82$	−0.333317			−0.0368087
$83$	−1.98870	−	4.61033i	−0.218288	−	0.506049i	0.773522	−	0.633770i	$-0.218493\pi$
$83$	−1.98870	−	4.61033i	−0.218288	−	0.506049i	−0.991810	+	0.127720i	$0.959234\pi$
$84$	4.15176	−	2.95317i	0.452994	−	0.322217i
$85$	−0.755608	+	0.800897i	−0.0819571	+	0.0868695i
$86$	−0.518454	+	8.90152i	−0.0559064	+	0.959875i
$87$	−0.593531	+	0.325727i	−0.0636332	+	0.0349216i
$88$	−5.85643	+	1.38800i	−0.624298	+	0.147961i
$89$	1.65643	+	0.602892i	0.175582	+	0.0639064i	0.428315	−	0.903629i	$-0.359107\pi$
$89$	1.65643	+	0.602892i	0.175582	+	0.0639064i	−0.252734	+	0.967536i	$0.581330\pi$
$90$	8.70955	+	4.85786i	0.918068	+	0.512064i
$91$	−16.9337	+	6.16336i	−1.77513	+	0.646095i
$92$	−0.598927	+	0.393920i	−0.0624425	+	0.0410691i
$93$	1.90137	−	13.6868i	0.197163	−	1.41925i
$94$	−7.08249	+	0.827825i	−0.730503	+	0.0853836i
$95$	0.739862	+	0.993807i	0.0759082	+	0.101962i
$96$	−1.73090	+	0.0631998i	−0.176659	+	0.00645030i
$97$	−0.696419	−	11.9570i	−0.0707106	−	1.21405i	−0.827907	−	0.560866i	$-0.810468\pi$
$97$	−0.696419	−	11.9570i	−0.0707106	−	1.21405i	0.757196	−	0.653188i	$-0.226569\pi$
$98$	1.26610	+	1.06239i	0.127896	+	0.107317i
$99$	17.3723	+	4.92169i	1.74598	+	0.494649i
$100$	4.63501	−	3.88923i	0.463501	−	0.388923i
$101$	4.08642	+	4.33136i	0.406614	+	0.430986i	0.898027	−	0.439941i	$-0.145001\pi$
$101$	4.08642	+	4.33136i	0.406614	+	0.430986i	−0.491412	+	0.870927i	$0.663519\pi$
$102$	−0.378211	+	0.431384i	−0.0374484	+	0.0427134i
$103$	2.28704	+	1.50421i	0.225348	+	0.148214i	0.657163	−	0.753748i	$-0.271756\pi$
$103$	2.28704	+	1.50421i	0.225348	+	0.148214i	−0.431815	+	0.901962i	$0.642127\pi$
$104$	5.96102	+	1.41279i	0.584526	+	0.138535i
$105$	−4.26225	+	16.3917i	−0.415953	+	1.59967i
$106$	−6.85578	−	0.801326i	−0.665892	−	0.0778316i
$107$	−1.73880	−	3.01170i	−0.168097	−	0.291152i	0.769654	−	0.638461i	$-0.220429\pi$
$107$	−1.73880	−	3.01170i	−0.168097	−	0.291152i	−0.937751	+	0.347309i	$0.887095\pi$
$108$	4.62733	+	2.36385i	0.445265	+	0.227462i
$109$	3.05632	−	5.29371i	0.292743	−	0.507045i	−0.681715	−	0.731618i	$-0.738765\pi$
$109$	3.05632	−	5.29371i	0.292743	−	0.507045i	0.974457	+	0.224573i	$0.0720987\pi$
$110$	11.9476	−	16.0485i	1.13916	−	1.53016i
$111$	2.56619	−	3.72330i	0.243572	−	0.353400i
$112$	−0.843649	−	2.81798i	−0.0797173	−	0.266274i
$113$	−4.71089	+	2.36590i	−0.443163	+	0.222565i	−0.656365	−	0.754443i	$-0.727907\pi$
$113$	−4.71089	+	2.36590i	−0.443163	+	0.222565i	0.213202	+	0.977008i	$0.431611\pi$
$114$	0.404133	+	0.503399i	0.0378505	+	0.0471476i
$115$	0.683455	−	2.28290i	0.0637325	−	0.212882i
$116$	0.0678768	+	0.384948i	0.00630220	+	0.0357415i
$117$	−13.5534	−	12.4126i	−1.25301	−	1.14755i
$118$	1.88408	−	10.6851i	0.173443	−	0.983647i
$119$	−0.870690	−	0.437277i	−0.0798160	−	0.0400851i
$120$	4.27271	−	3.85949i	0.390044	−	0.352321i
$121$	9.99085	−	23.1614i	0.908259	−	2.10558i
$122$	−2.88534	+	6.68898i	−0.261227	+	0.605592i
$123$	0.428419	−	0.386986i	0.0386293	−	0.0348933i
$124$	−7.12937	−	3.58050i	−0.640236	−	0.321539i
$125$	−0.606441	+	3.43930i	−0.0542417	+	0.307620i
$126$	−1.90768	+	8.61602i	−0.169949	+	0.767576i
$127$	0.883746	+	5.01197i	0.0784198	+	0.444741i	0.998584	+	0.0532069i	$0.0169443\pi$
$127$	0.883746	+	5.01197i	0.0784198	+	0.444741i	−0.920164	+	0.391534i	$0.871945\pi$
$128$	−0.286803	+	0.957990i	−0.0253501	+	0.0846751i
$129$	−9.66840	−	12.0432i	−0.851255	−	1.06035i
$130$	−18.1987	+	9.13971i	−1.59613	+	0.801605i
$131$	1.34349	+	4.48758i	0.117381	+	0.392081i	0.996407	−	0.0846931i	$-0.0269910\pi$
$131$	1.34349	+	4.48758i	0.117381	+	0.392081i	−0.879026	+	0.476775i	$0.841806\pi$
$132$	5.91590	−	8.58342i	0.514913	−	0.747091i
$133$	−0.654691	+	0.879402i	−0.0567689	+	0.0762538i
$134$	−0.615053	+	1.06530i	−0.0531325	+	0.0920282i
$135$	−16.8346	+	3.86800i	−1.44889	+	0.332904i
$136$	0.165614	+	0.286852i	0.0142013	+	0.0245973i
$137$	−15.4437	−	1.80511i	−1.31944	−	0.154221i	−0.572936	−	0.819600i	$-0.694196\pi$
$137$	−15.4437	−	1.80511i	−1.31944	−	0.154221i	−0.746505	+	0.665380i	$0.768270\pi$
$138$	0.312466	−	1.20168i	0.0265989	−	0.102293i
$139$	8.65408	+	2.05105i	0.734029	+	0.173968i	0.580597	−	0.814191i	$-0.302819\pi$
$139$	8.65408	+	2.05105i	0.734029	+	0.173968i	0.153432	+	0.988159i	$0.450967\pi$
$140$	8.16978	+	5.37335i	0.690472	+	0.454131i
$141$	8.14216	−	9.28689i	0.685693	−	0.782097i
$142$	8.86482	+	9.39616i	0.743919	+	0.788508i
$143$	−28.2450	+	23.7004i	−2.36197	+	1.98193i
$144$	2.15138	−	2.09083i	0.179282	−	0.174236i
$145$	−0.995399	−	0.835239i	−0.0826634	−	0.0693628i
$146$	−0.0255328	−	0.438382i	−0.00211311	−	0.0362807i
$147$	−2.86079	+	0.104455i	−0.235954	+	0.00861532i
$148$	−1.55904	−	2.09416i	−0.128152	−	0.172139i
$149$	−5.97912	+	0.698858i	−0.489828	+	0.0572527i	−0.357422	−	0.933943i	$-0.616344\pi$
$149$	−5.97912	+	0.698858i	−0.489828	+	0.0572527i	−0.132406	+	0.991196i	$0.542270\pi$
$150$	−1.44202	+	10.3802i	−0.117740	+	0.847541i
$151$	−15.0719	+	9.91297i	−1.22654	+	0.806706i	−0.986453	−	0.164046i	$-0.947546\pi$
$151$	−15.0719	+	9.91297i	−1.22654	+	0.806706i	−0.240085	+	0.970752i	$0.577175\pi$
$152$	0.350231	−	0.127474i	0.0284075	−	0.0103395i
$153$	−0.0147212	−	0.993574i	−0.00119014	−	0.0803257i
$154$	16.6366	+	6.05522i	1.34061	+	0.487943i
$155$	25.8058	−	6.11609i	2.07277	−	0.491256i
$156$	−9.30209	+	5.10494i	−0.744763	+	0.408722i
$157$	−0.606618	+	10.4152i	−0.0484134	+	0.831226i	0.883474	+	0.468479i	$0.155198\pi$
$157$	−0.606618	+	10.4152i	−0.0484134	+	0.831226i	−0.931888	+	0.362747i	$0.881839\pi$
$158$	−0.911050	+	0.965657i	−0.0724793	+	0.0768235i
$159$	9.74222	−	6.92969i	0.772608	−	0.549560i
$160$	−1.31666	−	3.05237i	−0.104091	−	0.241311i
$161$	2.10868			0.166188
$162$	−8.69207	+	2.33408i	−0.682913	+	0.183383i
$163$	−18.8787			−1.47869			−0.739346	−	0.673326i	$-0.764865\pi$
$163$	−18.8787			−1.47869			−0.739346	+	0.673326i	$0.764865\pi$
$164$	−0.132020	−	0.306057i	−0.0103090	−	0.0238991i
$165$	3.27594	+	34.4988i	0.255031	+	2.68573i
$166$	3.44559	−	3.65212i	0.267430	−	0.283459i
$167$	0.339011	−	5.82060i	0.0262335	−	0.450411i	−0.959458	−	0.281852i	$-0.909051\pi$
$167$	0.339011	−	5.82060i	0.0262335	−	0.450411i	0.985691	−	0.168560i	$-0.0539116\pi$
$168$	4.35608	+	2.64252i	0.336079	+	0.203875i
$169$	23.8685	−	5.65695i	1.83604	−	0.435150i
$170$	−1.03468	−	0.376592i	−0.0793561	−	0.0288833i
$171$	−1.10389	−	0.177826i	−0.0844168	−	0.0135987i
$172$	−8.37887	+	3.04966i	−0.638883	+	0.232534i
$173$	−19.9947	+	13.1507i	−1.52017	+	0.999828i	−0.531947	+	0.846778i	$0.678539\pi$
$173$	−19.9947	+	13.1507i	−1.52017	+	0.999828i	−0.988218	+	0.153051i	$0.951090\pi$
$174$	−0.534173	−	0.415976i	−0.0404956	−	0.0315351i
$175$	−17.6778	+	2.06624i	−1.33631	+	0.156193i
$176$	−3.59410	−	4.82771i	−0.270915	−	0.363902i
$177$	9.98394	+	15.9213i	0.750439	+	1.19672i
$178$	0.102494	+	1.75976i	0.00768226	+	0.131899i
$179$	5.79434	+	4.86203i	0.433090	+	0.363405i	0.833116	−	0.553098i	$-0.186555\pi$
$179$	5.79434	+	4.86203i	0.433090	+	0.363405i	−0.400026	+	0.916504i	$0.630999\pi$
$180$	−1.01089	+	9.92135i	−0.0753473	+	0.739494i
$181$	3.57502	−	2.99980i	0.265729	−	0.222973i	−0.500181	−	0.865921i	$-0.666733\pi$
$181$	3.57502	−	2.99980i	0.265729	−	0.222973i	0.765910	+	0.642948i	$0.222289\pi$
$182$	−12.3664	−	13.1076i	−0.916657	−	0.971600i
$183$	−4.05740	−	11.9474i	−0.299932	−	0.883177i
$184$	−0.598927	−	0.393920i	−0.0441535	−	0.0290402i
$185$	8.44487	+	2.00147i	0.620879	+	0.147151i
$186$	13.3205	−	3.67520i	0.976709	−	0.269478i
$187$	−1.98007	−	0.231437i	−0.144797	−	0.0169243i
$188$	−3.56535	−	6.17537i	−0.260030	−	0.450385i
$189$	−7.55134	−	13.2892i	−0.549279	−	0.966646i
$190$	−0.619485	+	1.07298i	−0.0449422	+	0.0778422i
$191$	−6.01138	+	8.07468i	−0.434968	+	0.584263i	−0.964519	−	0.264015i	$-0.914953\pi$
$191$	−6.01138	+	8.07468i	−0.434968	+	0.584263i	0.529551	+	0.848278i	$0.322361\pi$
$192$	−0.743604	−	1.56431i	−0.0536650	−	0.112894i
$193$	−4.53054	−	15.1331i	−0.326115	−	1.08930i	−0.951156	−	0.308709i	$-0.900103\pi$
$193$	−4.53054	−	15.1331i	−0.326115	−	1.08930i	0.625041	−	0.780592i	$-0.285082\pi$
$194$	10.7033	−	5.37541i	0.768453	−	0.385932i
$195$	12.7798	−	32.8763i	0.915179	−	2.35432i
$196$	−0.474022	+	1.58334i	−0.0338587	+	0.113096i
$197$	−1.60575	−	9.10664i	−0.114405	−	0.648821i	−0.987043	−	0.160455i	$-0.948704\pi$
$197$	−1.60575	−	9.10664i	−0.114405	−	0.648821i	0.872639	−	0.488367i	$-0.162407\pi$
$198$	2.36163	+	17.9009i	0.167834	+	1.27216i
$199$	−0.0962211	+	0.545697i	−0.00682093	+	0.0386834i	−0.988028	−	0.154273i	$-0.950696\pi$
$199$	−0.0962211	+	0.545697i	−0.00682093	+	0.0386834i	0.981207	+	0.192956i	$0.0618076\pi$
$200$	5.40699	+	2.71549i	0.382332	+	0.192014i
$201$	−0.446291	−	2.08334i	−0.0314789	−	0.146948i
$202$	−2.35857	+	5.46778i	−0.165948	+	0.384712i
$203$	0.455419	−	1.05578i	0.0319642	−	0.0741013i
$204$	−0.545906	−	0.176416i	−0.0382210	−	0.0123516i
$205$	0.990169	+	0.497281i	0.0691564	+	0.0347316i
$206$	−0.475339	+	2.69578i	−0.0331184	+	0.187824i
$207$	0.993543	+	1.90732i	0.0690560	+	0.132568i
$208$	1.06380	+	6.03308i	0.0737609	+	0.418319i
$209$	−0.643358	+	2.14897i	−0.0445020	+	0.148647i
$210$	−16.7393	+	2.57875i	−1.15512	+	0.177951i
$211$	11.3871	−	5.71883i	0.783923	−	0.393701i	−0.0113631	−	0.999935i	$-0.503617\pi$
$211$	11.3871	−	5.71883i	0.783923	−	0.393701i	0.795286	+	0.606235i	$0.207321\pi$
$212$	−1.97964	−	6.61247i	−0.135963	−	0.454147i
$213$	−22.3032	−	1.78490i	−1.52819	−	0.122300i
$214$	2.07668	−	2.78947i	0.141959	−	0.190684i
$215$	14.8205	−	25.6698i	1.01075	−	1.75067i
$216$	−0.337737	+	5.18516i	−0.0229801	+	0.352806i
$217$	11.7338	+	20.3236i	0.796544	+	1.37965i
$218$	6.07131	+	0.709635i	0.411201	+	0.0480625i
$219$	0.541785	+	0.533817i	0.0366104	+	0.0360720i
$220$	19.4682	+	4.61404i	1.31254	+	0.311079i
$221$	1.69533	+	1.11504i	0.114040	+	0.0750055i
$222$	4.43521	+	0.881593i	0.297672	+	0.0591687i
$223$	9.49130	+	10.0602i	0.635585	+	0.673680i	0.962471	−	0.271383i	$-0.0874810\pi$
$223$	9.49130	+	10.0602i	0.635585	+	0.673680i	−0.326887	+	0.945064i	$0.606000\pi$
$224$	2.25337	−	1.89080i	0.150559	−	0.126334i
$225$	−10.1981	−	15.0161i	−0.679874	−	1.00107i
$226$	−4.03829	−	3.38853i	−0.268623	−	0.225402i
$227$	−1.10287	−	18.9355i	−0.0731997	−	1.25679i	−0.812318	−	0.583215i	$-0.801794\pi$
$227$	−1.10287	−	18.9355i	−0.0731997	−	1.25679i	0.739118	−	0.673576i	$-0.235243\pi$
$228$	−0.302160	+	0.570467i	−0.0200111	+	0.0377801i
$229$	−0.390581	−	0.524641i	−0.0258103	−	0.0346693i	0.789031	−	0.614354i	$-0.210583\pi$
$229$	−0.390581	−	0.524641i	−0.0258103	−	0.0346693i	−0.814841	+	0.579684i	$0.803176\pi$
$230$	2.36690	−	0.276651i	0.156069	−	0.0182418i
$231$	−28.4135	+	11.5324i	−1.86947	+	0.758775i
$232$	−0.326581	+	0.214796i	−0.0214411	+	0.0141020i
$233$	8.18822	−	2.98027i	0.536428	−	0.195244i	−0.0595782	−	0.998224i	$-0.518976\pi$
$233$	8.18822	−	2.98027i	0.536428	−	0.195244i	0.596006	+	0.802980i	$0.296753\pi$
$234$	6.02926	−	17.3613i	0.394145	−	1.13495i
$235$	22.2746	+	8.10731i	1.45304	+	0.528862i
$236$	10.5575	−	2.50218i	0.687235	−	0.162878i
$237$	0.0498510	−	2.29892i	0.00323817	−	0.149331i
$238$	0.0566521	−	0.972678i	0.00367221	−	0.0630494i
$239$	3.50926	−	3.71960i	0.226995	−	0.240601i	−0.603859	−	0.797091i	$-0.706371\pi$
$239$	3.50926	−	3.71960i	0.226995	−	0.240601i	0.830854	+	0.556490i	$0.187852\pi$
$240$	5.23618	+	2.39461i	0.337994	+	0.154571i
$241$	1.10816	+	2.56900i	0.0713826	+	0.165484i	0.950172	−	0.311727i	$-0.100907\pi$
$241$	1.10816	+	2.56900i	0.0713826	+	0.165484i	−0.878789	+	0.477210i	$0.841648\pi$
$242$	25.2243			1.62148
$243$	8.46219	−	13.0917i	0.542850	−	0.839830i
$244$	−7.28475			−0.466358
$245$	−2.17615	−	5.04489i	−0.139029	−	0.322306i
$246$	0.525025	+	0.240104i	0.0334744	+	0.0153085i
$247$	1.56687	−	1.66079i	0.0996977	−	0.105673i
$248$	0.463877	−	7.96446i	0.0294562	−	0.505744i
$249$	−0.188537	+	8.69452i	−0.0119480	+	0.550993i
$250$	−3.39822	+	0.805392i	−0.214922	+	0.0509375i
$251$	5.23170	+	1.90418i	0.330222	+	0.120191i	0.501810	−	0.864978i	$-0.332668\pi$
$251$	5.23170	+	1.90418i	0.330222	+	0.120191i	−0.171588	+	0.985169i	$0.554890\pi$
$252$	−8.66696	+	1.66097i	−0.545967	+	0.104631i
$253$	4.05434	−	1.47566i	0.254894	−	0.0927738i
$254$	−4.25204	+	2.79661i	−0.266797	+	0.175475i
$255$	1.76712	−	0.717233i	0.110661	−	0.0449149i
$256$	−0.993238	+	0.116093i	−0.0620774	+	0.00725581i
$257$	5.02711	+	6.75258i	0.313582	+	0.421214i	0.930772	−	0.365600i	$-0.119136\pi$
$257$	5.02711	+	6.75258i	0.313582	+	0.421214i	−0.617190	+	0.786814i	$0.711729\pi$
$258$	7.22883	−	13.6478i	0.450048	−	0.849673i
$259$	0.446536	+	7.66673i	0.0277464	+	0.476387i
$260$	−15.6003	−	13.0902i	−0.967492	−	0.811822i
$261$	1.16954	−	0.0855200i	0.0723926	−	0.00529356i
$262$	−3.58844	+	3.01106i	−0.221694	+	0.186024i
$263$	−10.2726	−	10.8883i	−0.633435	−	0.671402i	0.328556	−	0.944485i	$-0.393438\pi$
$263$	−10.2726	−	10.8883i	−0.633435	−	0.671402i	−0.961990	+	0.273083i	$0.911957\pi$
$264$	10.2246	+	2.03236i	0.629281	+	0.125083i
$265$	19.1706	+	12.6087i	1.17764	+	0.774547i
$266$	−1.06679	−	0.252834i	−0.0654091	−	0.0155023i
$267$	−2.17484	−	2.14285i	−0.133098	−	0.131141i
$268$	−1.22179	−	0.142807i	−0.0746326	−	0.00872330i
$269$	13.7136	+	23.7527i	0.836135	+	1.44823i	0.893103	+	0.449852i	$0.148523\pi$
$269$	13.7136	+	23.7527i	0.836135	+	1.44823i	−0.0569680	+	0.998376i	$0.518143\pi$
$270$	−10.2195	−	13.9258i	−0.621939	−	0.847496i
$271$	3.19636	−	5.53625i	0.194165	−	0.336303i	−0.752462	−	0.658636i	$-0.771134\pi$
$271$	3.19636	−	5.53625i	0.194165	−	0.336303i	0.946626	+	0.322333i	$0.104467\pi$
$272$	−0.197796	+	0.265686i	−0.0119931	+	0.0161096i
$273$	31.1129	+	2.48993i	1.88304	+	0.150697i
$274$	−4.45945	−	14.8956i	−0.269405	−	0.899875i
$275$	−32.5429	+	16.3436i	−1.96241	+	0.985558i
$276$	1.22716	−	0.189048i	0.0738663	−	0.0113794i
$277$	−8.35954	+	27.9228i	−0.502276	+	1.67772i	0.211528	+	0.977372i	$0.432156\pi$
$277$	−8.35954	+	27.9228i	−0.502276	+	1.67772i	−0.713804	+	0.700346i	$0.753029\pi$
$278$	1.54439	+	8.75869i	0.0926266	+	0.525312i
$279$	−12.8542	+	20.1891i	−0.769561	+	1.20869i
$280$	−1.69801	+	9.62990i	−0.101476	+	0.575496i
$281$	−13.7103	−	6.88559i	−0.817890	−	0.410760i	−0.00989646	−	0.999951i	$-0.503150\pi$
$281$	−13.7103	−	6.88559i	−0.817890	−	0.410760i	−0.807994	+	0.589191i	$0.799446\pi$
$282$	11.7523	+	3.79791i	0.699840	+	0.226162i
$283$	7.68577	−	17.8176i	0.456872	−	1.05915i	−0.521679	−	0.853142i	$-0.674694\pi$
$283$	7.68577	−	17.8176i	0.456872	−	1.05915i	0.978551	−	0.206006i	$-0.0660467\pi$
$284$	−5.11653	+	11.8615i	−0.303610	+	0.703848i
$285$	−0.449507	−	2.09835i	−0.0266265	−	0.124296i
$286$	−32.9494	−	16.5478i	−1.94834	−	0.978491i
$287$	−0.170257	+	0.965577i	−0.0100500	+	0.0569962i
$288$	2.77195	+	1.14730i	0.163339	+	0.0676053i
$289$	−2.93297	−	16.6337i	−0.172528	−	0.978452i
$290$	0.372672	−	1.24481i	0.0218841	−	0.0730979i
$291$	−7.51627	+	19.3358i	−0.440611	+	1.13349i
$292$	0.392416	−	0.197079i	0.0229644	−	0.0115332i
$293$	−4.01512	−	13.4114i	−0.234566	−	0.783505i	−0.991511	−	0.130026i	$-0.958494\pi$
$293$	−4.01512	−	13.4114i	−0.234566	−	0.783505i	0.756945	−	0.653479i	$-0.226691\pi$
$294$	−1.22901	−	2.58545i	−0.0716775	−	0.150787i
$295$	−21.5383	+	28.9309i	−1.25401	+	1.68442i
$296$	1.30538	−	2.26099i	0.0758738	−	0.131417i
$297$	−23.8186	−	20.2665i	−1.38210	−	1.17598i
$298$	−3.00991	−	5.21332i	−0.174359	−	0.301999i
$299$	−4.36189	−	0.509832i	−0.252255	−	0.0294844i
$300$	−10.1024	+	2.78731i	−0.583264	+	0.160925i
$301$	25.5217	+	6.04876i	1.47105	+	0.348645i
$302$	−15.0719	−	9.91297i	−0.867293	−	0.570428i
$303$	−3.31665	−	9.76618i	−0.190536	−	0.561053i
$304$	0.255768	+	0.271098i	0.0146693	+	0.0155485i
$305$	18.5507	−	15.5659i	1.06221	−	0.891302i
$306$	0.906485	−	0.407052i	0.0518203	−	0.0232696i
$307$	15.4132	+	12.9332i	0.879679	+	0.738138i	0.966113	−	0.258119i	$-0.0831028\pi$
$307$	15.4132	+	12.9332i	0.879679	+	0.738138i	−0.0864343	+	0.996258i	$0.527547\pi$
$308$	1.02941	+	17.6743i	0.0586562	+	1.00709i
$309$	−2.51887	−	4.01682i	−0.143294	−	0.228509i
$310$	15.8370	+	21.2728i	0.899483	+	1.20822i
$311$	−7.96648	+	0.931148i	−0.451738	+	0.0528006i	−0.338920	−	0.940815i	$-0.610062\pi$
$311$	−7.96648	+	0.931148i	−0.451738	+	0.0528006i	−0.112818	+	0.993616i	$0.535988\pi$
$312$	−8.37181	−	6.51936i	−0.473960	−	0.369086i
$313$	25.3797	−	16.6925i	1.43455	−	0.943516i	0.435485	−	0.900196i	$-0.356577\pi$
$313$	25.3797	−	16.6925i	1.43455	−	0.943516i	0.999061	−	0.0433196i	$-0.0137934\pi$
$314$	−9.80370	+	3.56826i	−0.553255	+	0.201368i
$315$	18.5214	−	22.7491i	1.04356	−	1.28177i
$316$	−1.24753	−	0.454064i	−0.0701791	−	0.0255431i
$317$	26.0843	−	6.18210i	1.46504	−	0.347221i	0.580722	−	0.814102i	$-0.302770\pi$
$317$	26.0843	−	6.18210i	1.46504	−	0.347221i	0.884321	+	0.466880i	$0.154622\pi$
$318$	10.2216	+	6.20075i	0.573202	+	0.347721i
$319$	0.136792	−	2.34864i	0.00765891	−	0.131498i
$320$	2.28123	−	2.41796i	0.127525	−	0.135168i
$321$	0.569408	+	5.99642i	0.0317813	+	0.334688i
$322$	0.835207	+	1.93623i	0.0465443	+	0.107902i
$323$	0.123451			0.00686901
$324$	−5.58594	−	7.05671i	−0.310330	−	0.392040i
$325$	37.0667			2.05609
$326$	−7.47746	−	17.3347i	−0.414138	−	0.960080i
$327$	−8.62748	+	6.13677i	−0.477101	+	0.339364i
$328$	0.228736	−	0.242446i	0.0126298	−	0.0133868i
$329$	−1.21961	+	20.9399i	−0.0672394	+	1.15446i
$330$	−30.3798	+	16.6723i	−1.67235	+	0.917780i
$331$	−23.3438	+	5.53258i	−1.28309	+	0.304098i	−0.814937	−	0.579549i	$-0.803229\pi$
$331$	−23.3438	+	5.53258i	−1.28309	+	0.304098i	−0.468154	+	0.883647i	$0.655081\pi$
$332$	4.71816	+	1.71727i	0.258943	+	0.0942475i
$333$	−6.72421	+	4.01621i	−0.368484	+	0.220087i
$334$	5.47884	−	1.99413i	0.299789	−	0.109114i
$335$	3.41645	−	2.24703i	0.186661	−	0.122769i
$336$	−0.701055	+	5.04647i	−0.0382457	+	0.275307i
$337$	−28.5732	+	3.33973i	−1.55648	+	0.181927i	−0.850374	−	0.526178i	$-0.823624\pi$
$337$	−28.5732	+	3.33973i	−1.55648	+	0.181927i	−0.706107	+	0.708105i	$0.749550\pi$
$338$	14.6481	+	19.6759i	0.796754	+	1.07023i
$339$	9.12463	−	0.333165i	0.495582	−	0.0180950i
$340$	−0.0640222	−	1.09922i	−0.00347209	−	0.0596135i
$341$	36.7829	+	30.8645i	1.99191	+	1.67141i
$342$	−0.273947	−	1.08405i	−0.0148134	−	0.0586184i
$343$	−12.0492	+	10.1105i	−0.650598	+	0.545917i
$344$	−6.11894	−	6.48570i	−0.329911	−	0.349686i
$345$	−2.72103	+	3.10359i	−0.146495	+	0.167091i
$346$	−19.9947	−	13.1507i	−1.07492	−	0.706985i
$347$	−10.5355	−	2.49696i	−0.565576	−	0.134044i	−0.0621258	−	0.998068i	$-0.519788\pi$
$347$	−10.5355	−	2.49696i	−0.565576	−	0.134044i	−0.503450	+	0.864024i	$0.667936\pi$
$348$	0.170381	−	0.655246i	0.00913336	−	0.0351249i
$349$	−19.1454	−	2.23777i	−1.02483	−	0.119785i	−0.412963	−	0.910748i	$-0.635506\pi$
$349$	−19.1454	−	2.23777i	−1.02483	−	0.119785i	−0.611865	+	0.790963i	$0.709580\pi$
$350$	−8.89906	−	15.4136i	−0.475675	−	0.823893i
$351$	12.4072	+	29.3149i	0.662247	+	1.56471i
$352$	3.00933	−	5.21232i	0.160398	−	0.277817i
$353$	12.5332	−	16.8350i	0.667075	−	0.896037i	−0.331806	−	0.943348i	$-0.607658\pi$
$353$	12.5332	−	16.8350i	0.667075	−	0.896037i	0.998880	+	0.0473112i	$0.0150652\pi$
$354$	−10.6647	+	15.4735i	−0.566824	+	0.822408i
$355$	−12.3160	−	41.1383i	−0.653665	−	2.18339i
$356$	−1.57524	+	0.791116i	−0.0834876	+	0.0419291i
$357$	1.05648	+	1.31598i	0.0559147	+	0.0696489i
$358$	−2.16937	+	7.24621i	−0.114655	+	0.382974i
$359$	−1.91261	−	10.8469i	−0.100944	−	0.572479i	−0.992763	−	0.120088i	$-0.961682\pi$
$359$	−1.91261	−	10.8469i	−0.100944	−	0.572479i	0.891820	−	0.452391i	$-0.149429\pi$
$360$	−9.51034	+	3.00143i	−0.501239	+	0.158189i
$361$	−3.27519	+	18.5745i	−0.172379	+	0.977608i
$362$	4.17045	+	2.09448i	0.219194	+	0.110083i
$363$	−32.4214	+	29.2858i	−1.70168	+	1.53711i
$364$	7.13753	−	16.5467i	0.374108	−	0.867281i
$365$	−0.578180	+	1.34037i	−0.0302633	+	0.0701582i
$366$	9.36324	−	8.45769i	0.489424	−	0.442091i
$367$	33.0903	+	16.6186i	1.72730	+	0.867483i	0.978928	+	0.204205i	$0.0654609\pi$
$367$	33.0903	+	16.6186i	1.72730	+	0.867483i	0.748373	+	0.663278i	$0.230835\pi$
$368$	0.124481	−	0.705968i	0.00648903	−	0.0368011i
$369$	−0.953589	+	0.300950i	−0.0496419	+	0.0156668i
$370$	1.50706	+	8.54696i	0.0783483	+	0.444335i
$371$	−5.82325	+	19.4510i	−0.302328	+	1.00985i
$372$	8.65062	+	10.7755i	0.448514	+	0.558681i
$373$	−28.2445	+	14.1849i	−1.46244	+	0.734467i	−0.989215	−	0.146473i	$-0.953208\pi$
$373$	−28.2445	+	14.1849i	−1.46244	+	0.734467i	−0.473229	+	0.880939i	$0.656912\pi$
$374$	−0.571756	−	1.90980i	−0.0295648	−	0.0987534i
$375$	3.43273	−	4.98056i	0.177265	−	0.257195i
$376$	4.25816	−	5.71971i	0.219598	−	0.294971i
$377$	−1.19732	+	2.07381i	−0.0616649	+	0.106807i
$378$	9.21141	−	12.1973i	0.473784	−	0.627363i
$379$	−7.42062	−	12.8529i	−0.381172	−	0.660209i	0.610058	−	0.792357i	$-0.291146\pi$
$379$	−7.42062	−	12.8529i	−0.381172	−	0.660209i	−0.991230	+	0.132148i	$0.957813\pi$
$380$	−1.23059	−	0.143836i	−0.0631281	−	0.00737862i
$381$	2.21833	−	8.53122i	0.113649	−	0.437067i
$382$	−9.79529	−	2.32153i	−0.501170	−	0.118780i
$383$	−6.05315	−	3.98122i	−0.309301	−	0.203431i	0.385362	−	0.922765i	$-0.374076\pi$
$383$	−6.05315	−	3.98122i	−0.309301	−	0.203431i	−0.694664	+	0.719335i	$0.744447\pi$
$384$	1.14184	−	1.30238i	0.0582695	−	0.0664618i
$385$	−40.3875	−	42.8083i	−2.05834	−	2.18171i
$386$	12.1010	−	10.1539i	0.615923	−	0.516820i
$387$	6.55387	+	25.9345i	0.333152	+	1.31833i
$388$	9.17515	+	7.69887i	0.465798	+	0.390851i
$389$	−1.19265	−	20.4770i	−0.0604696	−	1.03822i	−0.882961	−	0.469446i	$-0.844454\pi$
$389$	−1.19265	−	20.4770i	−0.0604696	−	1.03822i	0.822492	−	0.568777i	$-0.192583\pi$
$390$	35.2494	−	1.28705i	1.78492	−	0.0651723i
$391$	−0.141792	−	0.190459i	−0.00717071	−	0.00963193i
$392$	−1.64160	+	0.191876i	−0.0829134	+	0.00969119i
$393$	1.11641	−	8.03639i	0.0563157	−	0.405382i
$394$	7.72586	−	5.08138i	0.389223	−	0.255996i
$395$	4.14709	−	1.50942i	0.208663	−	0.0759470i
$396$	−15.5015	+	9.25867i	−0.778979	+	0.465266i
$397$	−19.6226	−	7.14204i	−0.984830	−	0.358449i	−0.201114	−	0.979568i	$-0.564456\pi$
$397$	−19.6226	−	7.14204i	−0.984830	−	0.358449i	−0.783716	+	0.621119i	$0.786678\pi$
$398$	−0.539179	+	0.127788i	−0.0270266	+	0.00640542i
$399$	1.66471	−	0.913586i	0.0833398	−	0.0457365i
$400$	−0.351809	+	6.04034i	−0.0175905	+	0.302017i
$401$	−18.7706	+	19.8957i	−0.937361	+	0.993545i	−0.999990	−	0.00449194i	$-0.998570\pi$
$401$	−18.7706	+	19.8957i	−0.937361	+	0.993545i	0.0626286	+	0.998037i	$0.480052\pi$
$402$	1.73619	−	1.23496i	0.0865933	−	0.0615942i
$403$	−19.3581	−	44.8771i	−0.964295	−	2.23549i
$404$	−5.95479			−0.296262
$405$	29.3033	+	6.03410i	1.45609	+	0.299837i
$406$	1.14982			0.0570645
$407$	6.22373	+	14.4282i	0.308499	+	0.715181i
$408$	−0.0542338	−	0.571134i	−0.00268497	−	0.0282754i
$409$	−17.8934	+	18.9659i	−0.884774	+	0.937805i	−0.998447	−	0.0557130i	$-0.982257\pi$
$409$	−17.8934	+	18.9659i	−0.884774	+	0.937805i	0.113673	+	0.993518i	$0.463738\pi$
$410$	−0.0644260	+	1.10615i	−0.00318177	+	0.0546289i
$411$	23.0258	+	13.9681i	1.13578	+	0.688997i
$412$	−2.66358	+	0.631280i	−0.131225	+	0.0311009i
$413$	−29.9911	−	10.9159i	−1.47576	−	0.537135i
$414$	−1.35781	+	1.66774i	−0.0667325	+	0.0819648i
$415$	−15.6843	+	5.70862i	−0.769912	+	0.280225i
$416$	−5.11833	+	3.36638i	−0.250947	+	0.165050i
$417$	−12.1540	−	9.46467i	−0.595184	−	0.463487i
$418$	−2.22804	+	0.260420i	−0.108977	+	0.0127376i
$419$	1.42703	+	1.91683i	0.0697148	+	0.0936433i	0.835613	−	0.549319i	$-0.185113\pi$
$419$	1.42703	+	1.91683i	0.0697148	+	0.0936433i	−0.765898	+	0.642962i	$0.777705\pi$
$420$	−8.99795	−	14.3489i	−0.439055	−	0.700155i
$421$	−1.95309	−	33.5332i	−0.0951877	−	1.63431i	−0.621072	−	0.783754i	$-0.713302\pi$
$421$	−1.95309	−	33.5332i	−0.0951877	−	1.63431i	0.525884	−	0.850556i	$-0.323735\pi$
$422$	9.76134	+	8.19074i	0.475175	+	0.398719i
$423$	−19.5149	+	8.76306i	−0.948847	+	0.426074i
$424$	5.28758	−	4.43681i	0.256788	−	0.215471i
$425$	1.37531	+	1.45774i	0.0667123	+	0.0707109i
$426$	−7.19492	−	21.1861i	−0.348595	−	1.02647i
$427$	17.9033	+	11.7752i	0.866401	+	0.569841i
$428$	3.38387	+	0.801992i	0.163565	+	0.0387657i
$429$	61.5627	−	16.9854i	2.97227	−	0.820064i
$430$	29.4405	+	3.44110i	1.41975	+	0.165945i
$431$	−14.5851	−	25.2622i	−0.702541	−	1.21684i	−0.967572	−	0.252596i	$-0.918716\pi$
$431$	−14.5851	−	25.2622i	−0.702541	−	1.21684i	0.265031	−	0.964240i	$-0.414618\pi$
$432$	−4.89487	+	1.74362i	−0.235505	+	0.0838901i
$433$	5.39771	−	9.34910i	0.259397	−	0.449289i	−0.706683	−	0.707530i	$-0.749809\pi$
$433$	5.39771	−	9.34910i	0.259397	−	0.449289i	0.966081	+	0.258241i	$0.0831428\pi$
$434$	−14.0139	+	18.8240i	−0.672689	+	0.903579i
$435$	0.966241	+	2.03266i	0.0463277	+	0.0974586i
$436$	1.75313	+	5.85585i	0.0839595	+	0.280444i
$437$	−0.238760	+	0.119910i	−0.0114214	+	0.00573606i
$438$	−0.275569	+	0.708910i	−0.0131672	+	0.0338730i
$439$	5.37441	−	17.9518i	0.256507	−	0.856792i	−0.728614	−	0.684925i	$-0.759835\pi$
$439$	5.37441	−	17.9518i	0.256507	−	0.856792i	0.985120	−	0.171867i	$-0.0549798\pi$
$440$	3.47426	+	19.7035i	0.165629	+	0.939329i
$441$	4.58142	+	1.89623i	0.218163	+	0.0902967i
$442$	−0.352359	+	1.99832i	−0.0167600	+	0.0950506i
$443$	15.3004	+	7.68417i	0.726946	+	0.365086i	0.773471	−	0.633831i	$-0.218519\pi$
$443$	15.3004	+	7.68417i	0.726946	+	0.365086i	−0.0465256	+	0.998917i	$0.514815\pi$
$444$	0.947203	+	4.42166i	0.0449523	+	0.209843i
$445$	2.32094	−	5.38053i	0.110023	−	0.255062i
$446$	−5.47812	+	12.6997i	−0.259396	+	0.601349i
$447$	9.92143	+	3.20624i	0.469267	+	0.151650i
$448$	2.62867	+	1.32017i	0.124193	+	0.0623722i
$449$	0.580276	−	3.29091i	0.0273849	−	0.155308i	−0.968049	−	0.250761i	$-0.919319\pi$
$449$	0.580276	−	3.29091i	0.0273849	−	0.155308i	0.995434	+	0.0954537i	$0.0304302\pi$
$450$	9.74876	−	15.3116i	0.459561	−	0.721798i
$451$	0.348360	+	1.97565i	0.0164036	+	0.0930296i
$452$	1.51192	−	5.05016i	0.0711146	−	0.237539i
$453$	30.8814	−	4.75738i	1.45093	−	0.223521i
$454$	16.9500	−	8.51262i	0.795504	−	0.399517i
$455$	17.1807	+	57.3877i	0.805446	+	2.69038i
$456$	−0.643492	−	0.0514980i	−0.0301343	−	0.00241161i
$457$	−14.6603	+	19.6922i	−0.685781	+	0.921164i	−0.999599	−	0.0283195i	$-0.990984\pi$
$457$	−14.6603	+	19.6922i	−0.685781	+	0.921164i	0.313818	+	0.949483i	$0.398392\pi$
$458$	0.327033	−	0.566437i	0.0152812	−	0.0264679i
$459$	−0.692531	+	1.57563i	−0.0323246	+	0.0735443i
$460$	1.19151	+	2.06375i	0.0555542	+	0.0962228i
$461$	−27.2892	−	3.18964i	−1.27098	−	0.148557i	−0.546271	−	0.837609i	$-0.683953\pi$
$461$	−27.2892	−	3.18964i	−1.27098	−	0.148557i	−0.724712	+	0.689052i	$0.758027\pi$
$462$	−21.8432	−	21.5220i	−1.01624	−	1.00129i
$463$	5.17053	+	1.22544i	0.240295	+	0.0569509i	0.348999	−	0.937123i	$-0.386522\pi$
$463$	5.17053	+	1.22544i	0.240295	+	0.0569509i	−0.108704	+	0.994074i	$0.534670\pi$
$464$	−0.326581	−	0.214796i	−0.0151611	−	0.00997164i
$465$	−45.0537	−	8.95540i	−2.08932	−	0.415297i
$466$	5.97972	+	6.33813i	0.277005	+	0.293608i
$467$	4.85482	−	4.07368i	0.224654	−	0.188507i	−0.523513	−	0.852018i	$-0.675379\pi$
$467$	4.85482	−	4.07368i	0.224654	−	0.188507i	0.748167	+	0.663511i	$0.230934\pi$
$468$	18.3295	−	1.34031i	0.847282	−	0.0619558i
$469$	2.77188	+	2.32588i	0.127994	+	0.107399i
$470$	1.37828	+	23.6641i	0.0635751	+	1.09154i
$471$	8.45811	−	15.9686i	0.389729	−	0.735793i
$472$	6.47915	+	8.70301i	0.298227	+	0.400589i
$473$	53.3032	−	6.23025i	2.45088	−	0.286467i
$474$	2.13065	−	0.864782i	0.0978640	−	0.0397207i
$475$	1.88411	−	1.23920i	0.0864487	−	0.0568582i
$476$	0.915568	−	0.333239i	0.0419650	−	0.0152740i
$477$	−20.3372	+	3.89751i	−0.931179	+	0.178455i
$478$	4.80535	+	1.74900i	0.219791	+	0.0799975i
$479$	−11.9470	+	2.83148i	−0.545871	+	0.129374i	−0.494293	−	0.869295i	$-0.664573\pi$
$479$	−11.9470	+	2.83148i	−0.545871	+	0.129374i	−0.0515777	+	0.998669i	$0.516425\pi$
$480$	−0.124825	+	5.75640i	−0.00569745	+	0.262742i
$481$	0.929965	−	15.9669i	0.0424028	−	0.728027i
$482$	−1.91997	+	2.03505i	−0.0874524	+	0.0926942i
$483$	−3.32149	−	1.51899i	−0.151133	−	0.0691163i
$484$	9.99085	+	23.1614i	0.454130	+	1.05279i
$485$	−39.8154			−1.80793
$486$	15.3727	+	2.58478i	0.697318	+	0.117248i
$487$	36.9221			1.67310			0.836551	−	0.547889i	$-0.184568\pi$
$487$	36.9221			1.67310			0.836551	+	0.547889i	$0.184568\pi$
$488$	−2.88534	−	6.68898i	−0.130613	−	0.302796i
$489$	29.7367	+	13.5992i	1.34474	+	0.614978i
$490$	3.77037	−	3.99636i	0.170328	−	0.180537i
$491$	1.53285	−	26.3181i	0.0691767	−	1.18772i	−0.767877	−	0.640597i	$-0.778687\pi$
$491$	1.53285	−	26.3181i	0.0691767	−	1.18772i	0.837054	−	0.547121i	$-0.184276\pi$
$492$	−0.0125160	+	0.577187i	−0.000564266	+	0.0260216i
$493$	−0.125983	+	0.0298584i	−0.00567397	+	0.00134476i
$494$	2.14557	+	0.780923i	0.0965337	+	0.0351354i
$495$	19.6910	−	56.7006i	0.885047	−	2.54850i
$496$	7.49683	−	2.72862i	0.336618	−	0.122519i
$497$	31.7476	−	20.8807i	1.42407	−	0.936628i
$498$	−8.05812	+	3.27061i	−0.361093	+	0.146559i
$499$	−14.5973	+	1.70618i	−0.653463	+	0.0763789i	−0.436363	−	0.899770i	$-0.643734\pi$
$499$	−14.5973	+	1.70618i	−0.653463	+	0.0763789i	−0.217100	+	0.976149i	$0.569660\pi$
$500$	−2.08549	−	2.80130i	−0.0932659	−	0.125278i
$501$	−4.72685	+	8.92411i	−0.211180	+	0.398700i
$502$	0.323719	+	5.55804i	0.0144483	+	0.248068i
$503$	−22.9501	−	19.2574i	−1.02329	−	0.858644i	−0.0332546	−	0.999447i	$-0.510587\pi$
$503$	−22.9501	−	19.2574i	−1.02329	−	0.858644i	−0.990038	+	0.140803i	$0.955032\pi$
$504$	−4.95794	−	7.30026i	−0.220844	−	0.325180i
$505$	15.1640	−	12.7241i	0.674787	−	0.566214i
$506$	2.96081	+	3.13828i	0.131624	+	0.139514i
$507$	−41.6715	−	8.28311i	−1.85070	−	0.367866i
$508$	−4.25204	−	2.79661i	−0.188654	−	0.124080i
$509$	−3.42340	−	0.811361i	−0.151740	−	0.0359630i	0.154044	−	0.988064i	$-0.450770\pi$
$509$	−3.42340	−	0.811361i	−0.151740	−	0.0359630i	−0.305784	+	0.952101i	$0.598918\pi$
$510$	1.35850	+	1.33852i	0.0601552	+	0.0592705i
$511$	−1.28298	−	0.149959i	−0.0567556	−	0.00663378i
$512$	−0.500000	−	0.866025i	−0.0220971	−	0.0382733i
$513$	1.61070	+	1.07529i	0.0711142	+	0.0474752i
$514$	−4.20919	+	7.29053i	−0.185659	+	0.321571i
$515$	5.43394	−	7.29905i	0.239448	−	0.321635i
$516$	15.3948	+	1.23203i	0.677718	+	0.0542371i
$517$	12.3088	+	41.1144i	0.541342	+	1.80821i
$518$	−6.86285	+	3.44665i	−0.301536	+	0.151437i
$519$	40.9677	−	6.31121i	1.79828	−	0.277031i
$520$	5.84069	−	19.5093i	0.256131	−	0.855538i
$521$	6.86950	+	38.9589i	0.300958	+	1.70682i	0.641944	+	0.766751i	$0.278128\pi$
$521$	6.86950	+	38.9589i	0.300958	+	1.70682i	−0.340986	+	0.940068i	$0.610761\pi$
$522$	0.541756	+	1.04002i	0.0237120	+	0.0455202i
$523$	−1.46216	+	8.29230i	−0.0639357	+	0.362597i	0.936008	+	0.351979i	$0.114491\pi$
$523$	−1.46216	+	8.29230i	−0.0639357	+	0.362597i	−0.999944	+	0.0106183i	$0.996620\pi$
$524$	−4.18611	−	2.10234i	−0.182871	−	0.0918412i
$525$	29.3336	+	9.47952i	1.28022	+	0.413720i
$526$	5.92905	−	13.7451i	0.258519	−	0.599314i
$527$	1.04665	−	2.42641i	0.0455928	−	0.105696i
$528$	2.18361	+	10.1934i	0.0950296	+	0.443610i
$529$	−20.0943	−	10.0917i	−0.873666	−	0.438772i
$530$	−3.98443	+	22.5968i	−0.173072	+	0.981543i
$531$	−4.25736	−	32.2703i	−0.184754	−	1.40041i
$532$	−0.190378	−	1.07969i	−0.00825393	−	0.0468104i
$533$	0.585638	−	1.95617i	0.0253668	−	0.0847311i
$534$	1.10619	−	2.84571i	0.0478697	−	0.123146i
$535$	−10.3308	+	5.18830i	−0.446638	+	0.224310i
$536$	−0.352798	−	1.17843i	−0.0152386	−	0.0509004i
$537$	−5.62461	−	11.8324i	−0.242720	−	0.510605i
$538$	−16.3784	+	22.0000i	−0.706124	+	0.948489i
$539$	4.97376	−	8.61480i	0.214235	−	0.371066i
$540$	8.73913	−	14.8994i	0.376072	−	0.641169i
$541$	−3.31994	−	5.75031i	−0.142735	−	0.247225i	0.785790	−	0.618493i	$-0.212256\pi$
$541$	−3.31994	−	5.75031i	−0.142735	−	0.247225i	−0.928526	+	0.371268i	$0.878923\pi$
$542$	6.34949	+	0.742149i	0.272734	+	0.0318780i
$543$	−7.79209	+	2.14987i	−0.334391	+	0.0922599i
$544$	−0.322300	−	0.0763864i	−0.0138185	−	0.00327504i
$545$	−16.9770	−	11.1660i	−0.727216	−	0.478298i
$546$	10.0369	+	29.5545i	0.429539	+	1.26482i
$547$	11.7320	+	12.4352i	0.501623	+	0.531689i	0.927863	−	0.372921i	$-0.121644\pi$
$547$	11.7320	+	12.4352i	0.501623	+	0.531689i	−0.426240	+	0.904610i	$0.640162\pi$
$548$	11.9111	−	9.99458i	0.508816	−	0.426947i
$549$	−2.21527	+	21.7417i	−0.0945453	+	0.927913i
$550$	−27.8966	−	23.4080i	−1.18951	−	0.998120i
$551$	0.00847092	+	0.145440i	0.000360873	+	0.00619596i
$552$	0.659640	+	1.05192i	0.0280762	+	0.0447727i
$553$	2.33202	+	3.13245i	0.0991677	+	0.133205i
$554$	−28.9502	+	3.38379i	−1.22998	+	0.143764i
$555$	−11.8602	−	9.23586i	−0.503437	−	0.392041i
$556$	−7.43067	+	4.88723i	−0.315131	+	0.207265i
$557$	−27.7299	+	10.0929i	−1.17495	+	0.427649i	−0.854417	−	0.519587i	$-0.826086\pi$
$557$	−27.7299	+	10.0929i	−1.17495	+	0.427649i	−0.320538	+	0.947236i	$0.603864\pi$
$558$	−23.6293	−	3.80643i	−1.00031	−	0.161139i
$559$	−51.3302	−	18.6827i	−2.17104	−	0.790193i
$560$	−9.51487	+	2.25507i	−0.402077	+	0.0952940i
$561$	2.95219	+	1.79089i	0.124642	+	0.0756113i
$562$	0.892073	−	15.3163i	0.0376298	−	0.646079i
$563$	−11.0582	+	11.7210i	−0.466046	+	0.493980i	−0.917178	−	0.398477i	$-0.869539\pi$
$563$	−11.0582	+	11.7210i	−0.466046	+	0.493980i	0.451132	+	0.892457i	$0.351020\pi$
$564$	1.16755	+	12.2954i	0.0491627	+	0.517731i
$565$	6.94095	+	16.0909i	0.292008	+	0.676951i
$566$	19.4046			0.815637
$567$	2.32166	+	26.3720i	0.0975004	+	1.10752i
$568$	−12.9179			−0.542024
$569$	15.2873	+	35.4399i	0.640876	+	1.48572i	0.860143	+	0.510053i	$0.170374\pi$
$569$	15.2873	+	35.4399i	0.640876	+	1.48572i	−0.219267	+	0.975665i	$0.570367\pi$
$570$	1.74870	−	1.24386i	0.0732450	−	0.0520996i
$571$	−14.1739	+	15.0234i	−0.593159	+	0.628711i	−0.952516	−	0.304489i	$-0.901514\pi$
$571$	−14.1739	+	15.0234i	−0.593159	+	0.628711i	0.359357	+	0.933200i	$0.382996\pi$
$572$	2.14387	−	36.8089i	0.0896398	−	1.53906i
$573$	15.2854	−	8.38855i	0.638557	−	0.350437i
$574$	−0.954044	+	0.226113i	−0.0398210	+	0.00943776i
$575$	−4.07583	−	1.48348i	−0.169974	−	0.0618654i
$576$	0.0444445	+	2.99967i	0.00185185	+	0.124986i
$577$	36.8361	−	13.4072i	1.53351	−	0.558151i	0.569030	−	0.822317i	$-0.307319\pi$
$577$	36.8361	−	13.4072i	1.53351	−	0.558151i	0.964477	+	0.264166i	$0.0850968\pi$
$578$	14.1116	−	9.28136i	0.586966	−	0.386054i
$579$	−3.76478	+	27.1004i	−0.156459	+	1.12625i
$580$	1.29062	−	0.150851i	0.0535899	−	0.00626376i
$581$	−8.81971	−	11.8469i	−0.365903	−	0.491494i
$582$	−20.7315	+	0.756963i	−0.859348	+	0.0313771i
$583$	2.41554	+	41.4733i	0.100042	+	1.71765i
$584$	0.336389	+	0.282264i	0.0139199	+	0.0116802i
$585$	−43.8125	+	42.5793i	−1.81142	+	1.76044i
$586$	10.7243	−	8.99875i	0.443016	−	0.371735i
$587$	19.2706	+	20.4256i	0.795382	+	0.843055i	0.990470	−	0.137731i	$-0.0439808\pi$
$587$	19.2706	+	20.4256i	0.795382	+	0.843055i	−0.195088	+	0.980786i	$0.562499\pi$
$588$	1.88721	−	2.15254i	0.0778274	−	0.0887694i
$589$	−2.48428	−	1.63394i	−0.102363	−	0.0673252i
$590$	−35.0957	−	8.31783i	−1.44487	−	0.342440i
$591$	−4.03066	+	15.5010i	−0.165799	+	0.637627i
$592$	2.59311	+	0.303091i	0.106576	+	0.0124570i
$593$	19.1361	+	33.1448i	0.785827	+	1.36109i	0.928504	+	0.371323i	$0.121096\pi$
$593$	19.1361	+	33.1448i	0.785827	+	1.36109i	−0.142677	+	0.989769i	$0.545571\pi$
$594$	9.17494	−	29.8978i	0.376452	−	1.22672i
$595$	−1.61945	+	2.80497i	−0.0663909	+	0.114992i
$596$	3.59479	−	4.82864i	0.147248	−	0.197789i
$597$	0.544654	−	0.790242i	0.0222912	−	0.0323424i
$598$	−1.25952	−	4.20710i	−0.0515057	−	0.172041i
$599$	42.1825	−	21.1848i	1.72353	−	0.865589i	0.742980	−	0.669314i	$-0.233412\pi$
$599$	42.1825	−	21.1848i	1.72353	−	0.865589i	0.980549	−	0.196275i	$-0.0628846\pi$
$600$	−6.56072	−	8.17222i	−0.267840	−	0.333630i
$601$	6.44817	−	21.5384i	0.263026	−	0.878570i	−0.719823	−	0.694158i	$-0.755777\pi$
$601$	6.44817	−	21.5384i	0.263026	−	0.878570i	0.982849	−	0.184412i	$-0.0590379\pi$
$602$	4.55457	+	25.8303i	0.185630	+	1.05276i
$603$	−0.797755	+	3.60306i	−0.0324871	+	0.146728i
$604$	3.13256	−	17.7656i	0.127462	−	0.722873i
$605$	−74.9327	−	37.6326i	−3.04645	−	1.52998i
$606$	7.65381	−	6.91359i	0.310915	−	0.280845i
$607$	12.3108	−	28.5396i	0.499680	−	1.15839i	−0.462659	−	0.886536i	$-0.653105\pi$
$607$	12.3108	−	28.5396i	0.499680	−	1.15839i	0.962339	−	0.271852i	$-0.0876360\pi$
$608$	−0.147622	+	0.342226i	−0.00598687	+	0.0138791i
$609$	−1.47788	+	1.33495i	−0.0598868	+	0.0540950i
$610$	21.6404	+	10.8682i	0.876196	+	0.440042i
$611$	7.58561	−	43.0201i	0.306881	−	1.74041i
$612$	0.732802	+	0.671124i	0.0296218	+	0.0271286i
$613$	4.37659	+	24.8209i	0.176769	+	1.00251i	0.936082	+	0.351781i	$0.114424\pi$
$613$	4.37659	+	24.8209i	0.176769	+	1.00251i	−0.759313	+	0.650725i	$0.774465\pi$
$614$	−5.77063	+	19.2753i	−0.232884	+	0.777886i
$615$	−1.20145	−	1.49656i	−0.0484471	−	0.0603471i
$616$	−15.8211	+	7.94566i	−0.637451	+	0.320140i
$617$	−9.56432	−	31.9471i	−0.385045	−	1.28614i	−0.902596	−	0.430488i	$-0.858342\pi$
$617$	−9.56432	−	31.9471i	−0.385045	−	1.28614i	0.517551	−	0.855652i	$-0.326844\pi$
$618$	2.69063	−	3.90385i	0.108233	−	0.157036i
$619$	13.5345	−	18.1800i	0.543998	−	0.730716i	−0.442084	−	0.896973i	$-0.645761\pi$
$619$	13.5345	−	18.1800i	0.543998	−	0.730716i	0.986082	+	0.166257i	$0.0531682\pi$
$620$	−13.2603	+	22.9676i	−0.532548	+	0.922400i
$621$	−0.191048	−	3.72001i	−0.00766650	−	0.149279i
$622$	−4.01036	−	6.94614i	−0.160801	−	0.278515i
$623$	5.15014	+	0.601965i	0.206336	+	0.0241172i
$624$	2.67028	−	10.2693i	0.106897	−	0.411102i
$625$	−18.1409	−	4.29947i	−0.725636	−	0.171979i
$626$	25.3797	+	16.6925i	1.01438	+	0.667166i
$627$	2.56139	−	2.92150i	0.102292	−	0.116674i
$628$	−7.15948	−	7.58860i	−0.285694	−	0.302818i
$629$	0.662443	−	0.555856i	0.0264133	−	0.0221634i
$630$	28.2245	+	7.99621i	1.12449	+	0.318577i
$631$	1.88019	+	1.57766i	0.0748491	+	0.0628058i	0.679445	−	0.733727i	$-0.262221\pi$
$631$	1.88019	+	1.57766i	0.0748491	+	0.0628058i	−0.604596	+	0.796533i	$0.706665\pi$
$632$	−0.0771927	−	1.32535i	−0.00307056	−	0.0527195i
$633$	−22.0560	+	0.805325i	−0.876647	+	0.0320088i
$634$	16.0080	+	21.5025i	0.635758	+	0.853972i
$635$	16.8036	−	1.96406i	0.666832	−	0.0779415i
$636$	−1.64504	+	11.8417i	−0.0652302	+	0.469553i
$637$	−8.45946	+	5.56387i	−0.335176	+	0.220449i
$638$	2.21074	−	0.804642i	0.0875239	−	0.0318561i
$639$	33.8451	+	18.8776i	1.33889	+	0.746785i
$640$	3.12376	+	1.13696i	0.123478	+	0.0449422i
$641$	−0.914672	+	0.216781i	−0.0361274	+	0.00856234i	−0.248640	−	0.968596i	$-0.579984\pi$
$641$	−0.914672	+	0.216781i	−0.0361274	+	0.00856234i	0.212512	+	0.977158i	$0.431835\pi$
$642$	−5.28048	+	2.89790i	−0.208404	+	0.114371i
$643$	2.21590	−	38.0456i	0.0873866	−	1.50037i	−0.614973	−	0.788548i	$-0.710833\pi$
$643$	2.21590	−	38.0456i	0.0873866	−	1.50037i	0.702360	−	0.711822i	$-0.252130\pi$
$644$	−1.44707	+	1.53380i	−0.0570224	+	0.0604402i
$645$	−41.8356	+	29.7579i	−1.64728	+	1.17172i
$646$	0.0488965	+	0.113355i	0.00192381	+	0.00445989i
$647$	−15.8871			−0.624585			−0.312292	−	0.949986i	$-0.601097\pi$
$647$	−15.8871			−0.624585			−0.312292	+	0.949986i	$0.601097\pi$
$648$	4.26711	−	7.92413i	0.167628	−	0.311289i
$649$	−65.3024			−2.56334
$650$	14.6814	+	34.0353i	0.575851	+	1.33497i
$651$	−3.84249	−	40.4651i	−0.150599	−	1.58595i
$652$	12.9553	−	13.7318i	0.507370	−	0.537781i
$653$	0.995104	−	17.0853i	0.0389414	−	0.668599i	−0.921201	−	0.389087i	$-0.872790\pi$
$653$	0.995104	−	17.0853i	0.0389414	−	0.668599i	0.960142	−	0.279511i	$-0.0901725\pi$
$654$	−9.05205	−	5.49124i	−0.353963	−	0.214725i
$655$	15.1522	−	3.59114i	0.592047	−	0.140318i
$656$	0.313216	+	0.114001i	0.0122290	+	0.00445100i
$657$	−0.468859	−	1.23112i	−0.0182919	−	0.0480304i
$658$	−19.7104	+	7.17401i	−0.768393	+	0.279672i
$659$	−1.84544	+	1.21376i	−0.0718881	+	0.0472815i	−0.584944	−	0.811074i	$-0.698884\pi$
$659$	−1.84544	+	1.21376i	−0.0718881	+	0.0472815i	0.513056	+	0.858355i	$0.328513\pi$
$660$	−27.3416	−	21.2917i	−1.06427	−	0.828778i
$661$	−20.7712	+	2.42780i	−0.807905	+	0.0944306i	−0.510011	−	0.860168i	$-0.670359\pi$
$661$	−20.7712	+	2.42780i	−0.807905	+	0.0944306i	−0.297895	+	0.954599i	$0.596284\pi$
$662$	−14.3261	−	19.2433i	−0.556800	−	0.747912i
$663$	−1.86719	−	2.97758i	−0.0725156	−	0.115640i
$664$	0.291943	+	5.01247i	0.0113296	+	0.194522i
$665$	2.79185	+	2.34264i	0.108263	+	0.0908438i
$666$	−6.35107	−	4.58354i	−0.246099	−	0.177608i
$667$	0.214654	−	0.180116i	0.00831143	−	0.00697412i
$668$	4.00110	+	4.24092i	0.154807	+	0.164086i
$669$	−7.70339	−	22.6834i	−0.297830	−	0.876989i
$670$	3.41645	+	2.24703i	0.131989	+	0.0868105i
$671$	42.6627	+	10.1112i	1.64697	+	0.390340i
$672$	−4.91142	+	1.35508i	−0.189462	+	0.0522735i
$673$	48.9509	+	5.72154i	1.88692	+	0.220549i	0.979751	−	0.200219i	$-0.0641654\pi$
$673$	48.9509	+	5.72154i	1.88692	+	0.220549i	0.907168	+	0.420768i	$0.138240\pi$
$674$	−14.3839	−	24.9136i	−0.554046	−	0.959635i
$675$	5.24674	+	30.9988i	0.201947	+	1.19314i
$676$	−12.2649	+	21.2434i	−0.471726	+	0.817053i
$677$	−5.72803	+	7.69408i	−0.220146	+	0.295708i	−0.898452	−	0.439072i	$-0.855307\pi$
$677$	−5.72803	+	7.69408i	−0.220146	+	0.295708i	0.678306	+	0.734780i	$0.262715\pi$
$678$	3.92000	+	8.24642i	0.150547	+	0.316702i
$679$	−10.1046	−	33.7519i	−0.387781	−	1.29528i
$680$	0.983962	−	0.494164i	0.0377332	−	0.0189503i
$681$	−11.9029	+	30.6207i	−0.456122	+	1.17339i
$682$	−13.7713	+	45.9995i	−0.527332	+	1.76141i
$683$	4.55983	+	25.8601i	0.174477	+	0.989508i	0.938746	+	0.344610i	$0.111989\pi$
$683$	4.55983	+	25.8601i	0.174477	+	0.989508i	−0.764269	+	0.644898i	$0.776900\pi$
$684$	0.886883	−	0.680911i	0.0339108	−	0.0260353i
$685$	−8.97552	+	50.9027i	−0.342937	+	1.94489i
$686$	−14.0561	−	7.05924i	−0.536665	−	0.269523i
$687$	0.237299	+	1.10774i	0.00905354	+	0.0422630i
$688$	3.53169	−	8.18737i	0.134644	−	0.312141i
$689$	16.7484	−	38.8272i	0.638064	−	1.47920i
$690$	−3.92751	−	1.26922i	−0.149518	−	0.0483185i
$691$	−5.25149	−	2.63740i	−0.199776	−	0.100331i	0.346099	−	0.938198i	$-0.387506\pi$
$691$	−5.25149	−	2.63740i	−0.199776	−	0.100331i	−0.545875	+	0.837867i	$0.683803\pi$
$692$	4.15570	−	23.5681i	0.157976	−	0.895926i
$693$	53.0629	+	2.30237i	2.01569	+	0.0874598i
$694$	−1.88015	−	10.6629i	−0.0713696	−	0.404757i
$695$	8.47939	−	28.3231i	0.321641	−	1.07436i
$696$	0.669142	−	0.103084i	0.0253638	−	0.00390737i
$697$	0.0986606	−	0.0495492i	0.00373704	−	0.00187681i
$698$	−5.52833	−	18.4659i	−0.209250	−	0.698945i
$699$	−15.0445	−	1.20400i	−0.569036	−	0.0455393i
$700$	10.6283	−	14.2763i	0.401712	−	0.539593i
$701$	7.90660	−	13.6946i	0.298628	−	0.517239i	−0.677194	−	0.735804i	$-0.736804\pi$
$701$	7.90660	−	13.6946i	0.298628	−	0.517239i	0.975822	+	0.218565i	$0.0701376\pi$
$702$	−22.0032	+	23.0035i	−0.830457	+	0.868213i
$703$	−0.486526	−	0.842689i	−0.0183497	−	0.0317826i
$704$	5.97797	+	0.698724i	0.225303	+	0.0263342i
$705$	−29.2458	−	28.8157i	−1.10146	−	1.08526i
$706$	20.4223	+	4.84018i	0.768604	+	0.182162i
$707$	14.6347	+	9.62540i	0.550395	+	0.362000i
$708$	−18.4321	−	3.66378i	−0.692721	−	0.137693i
$709$	1.29478	+	1.37239i	0.0486265	+	0.0515411i	0.751230	−	0.660040i	$-0.229461\pi$
$709$	1.29478	+	1.37239i	0.0486265	+	0.0515411i	−0.702604	+	0.711581i	$0.747979\pi$
$710$	32.8957	−	27.6028i	1.23455	−	1.03591i
$711$	−1.73455	+	3.58523i	−0.0650505	+	0.134457i
$712$	−1.35034	−	1.13307i	−0.0506060	−	0.0424635i
$713$	0.332535	+	5.70940i	0.0124535	+	0.213819i
$714$	−0.789902	+	1.49131i	−0.0295614	+	0.0558107i
$715$	73.1931	+	98.3154i	2.73727	+	3.67679i
$716$	−7.51283	+	0.878124i	−0.280768	+	0.0328170i
$717$	−8.20702	+	3.33104i	−0.306497	+	0.124400i
$718$	9.20229	−	6.05244i	0.343426	−	0.225875i
$719$	−44.0317	+	16.0262i	−1.64211	+	0.597678i	−0.987405	−	0.158211i	$-0.949427\pi$
$719$	−44.0317	+	16.0262i	−1.64211	+	0.597678i	−0.654700	+	0.755888i	$0.727205\pi$
$720$	−6.52282	−	7.54374i	−0.243091	−	0.281139i
$721$	7.56653	+	2.75399i	0.281792	+	0.102564i
$722$	−18.3527	+	4.34967i	−0.683016	+	0.161878i
$723$	0.105057	−	4.84481i	0.00390713	−	0.180180i
$724$	−0.271354	+	4.65896i	−0.0100848	+	0.173149i
$725$	−1.62302	+	1.72030i	−0.0602775	+	0.0638904i
$726$	−39.7321	−	18.1703i	−1.47460	−	0.674363i
$727$	10.9506	+	25.3865i	0.406137	+	0.941531i	0.991422	+	0.130703i	$0.0417235\pi$
$727$	10.9506	+	25.3865i	0.406137	+	0.941531i	−0.585285	+	0.810828i	$0.699017\pi$
$728$	18.0204			0.667882
$729$	−22.7598	+	14.5256i	−0.842954	+	0.537985i
$730$	−1.45976			−0.0540280
$731$	−1.16979	−	2.71188i	−0.0432663	−	0.100303i
$732$	11.4746	+	5.24756i	0.424113	+	0.193955i
$733$	−33.3583	+	35.3577i	−1.23212	+	1.30597i	−0.295614	+	0.955307i	$0.595524\pi$
$733$	−33.3583	+	35.3577i	−1.23212	+	1.30597i	−0.936503	+	0.350660i	$0.885957\pi$
$734$	−2.15305	+	36.9664i	−0.0794703	+	1.36445i
$735$	−0.206308	+	9.51405i	−0.00760978	+	0.350931i
$736$	0.697536	−	0.165319i	0.0257115	−	0.00609374i
$737$	6.95711	+	2.53218i	0.256268	+	0.0932740i
$738$	−0.654034	−	0.756401i	−0.0240753	−	0.0278435i
$739$	9.67296	−	3.52067i	0.355826	−	0.129510i	−0.157921	−	0.987452i	$-0.550479\pi$
$739$	9.67296	−	3.52067i	0.355826	−	0.129510i	0.513747	+	0.857942i	$0.328257\pi$
$740$	−7.25104	+	4.76908i	−0.266554	+	0.175315i
$741$	−3.66440	+	1.48730i	−0.134615	+	0.0546372i
$742$	−20.1667	+	2.35715i	−0.740342	+	0.0865336i
$743$	6.81356	+	9.15220i	0.249965	+	0.335762i	0.909341	−	0.416052i	$-0.136587\pi$
$743$	6.81356	+	9.15220i	0.249965	+	0.335762i	−0.659375	+	0.751814i	$0.729179\pi$
$744$	−6.46786	+	12.2111i	−0.237123	+	0.447680i
$745$	1.16356	+	19.9775i	0.0426294	+	0.731918i
$746$	−24.2119	−	20.3162i	−0.886460	−	0.743828i
$747$	6.56005	−	13.5594i	0.240020	−	0.496111i
$748$	1.52715	−	1.28143i	0.0558380	−	0.0468537i
$749$	−7.01997	−	7.44074i	−0.256504	−	0.271879i
$750$	5.93287	+	1.17928i	0.216638	+	0.0430614i
$751$	27.3381	+	17.9805i	0.997581	+	0.656119i	0.939627	−	0.342200i	$-0.111172\pi$
$751$	27.3381	+	17.9805i	0.997581	+	0.656119i	0.0579539	+	0.998319i	$0.481542\pi$
$752$	6.93850	+	1.64445i	0.253021	+	0.0599671i
$753$	−6.86905	−	6.76803i	−0.250322	−	0.246641i
$754$	−2.37844	−	0.278000i	−0.0866177	−	0.0101242i
$755$	29.9841	+	51.9340i	1.09123	+	1.89007i
$756$	14.8482	+	3.62695i	0.540025	+	0.131911i
$757$	1.03503	−	1.79273i	0.0376190	−	0.0651580i	−0.846603	−	0.532225i	$-0.821356\pi$
$757$	1.03503	−	1.79273i	0.0376190	−	0.0651580i	0.884222	+	0.467067i	$0.154689\pi$
$758$	8.86258	−	11.9045i	0.321903	−	0.432391i
$759$	−7.44918	−	0.596150i	−0.270388	−	0.0216389i
$760$	−0.355341	−	1.18692i	−0.0128896	−	0.0430541i
$761$	27.1676	−	13.6441i	0.984826	−	0.494598i	0.117895	−	0.993026i	$-0.462385\pi$
$761$	27.1676	−	13.6441i	0.984826	−	0.494598i	0.866931	+	0.498428i	$0.166089\pi$
$762$	8.71214	−	1.34213i	0.315607	−	0.0486204i
$763$	5.15693	−	17.2253i	0.186693	−	0.623599i
$764$	−1.74805	−	9.91370i	−0.0632423	−	0.358665i
$765$	−3.30014	−	0.143191i	−0.119317	−	0.00517709i
$766$	1.25809	−	7.13498i	0.0454566	−	0.257797i
$767$	59.3985	+	29.8310i

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.396080 + 0.918216i) q^{2} +(-1.57515 - 0.720348i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(0.193287 - 3.31862i) q^{5} +(0.0375499 - 1.73164i) q^{6} +(2.86227 - 0.678371i) q^{7} +(-0.939693 - 0.342020i) q^{8} +(1.96220 + 2.26931i) q^{9} +O(q^{10})\)	\(q+(0.396080 + 0.918216i) q^{2} +(-1.57515 - 0.720348i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(0.193287 - 3.31862i) q^{5} +(0.0375499 - 1.73164i) q^{6} +(2.86227 - 0.678371i) q^{7} +(-0.939693 - 0.342020i) q^{8} +(1.96220 + 2.26931i) q^{9} +(3.12376 - 1.13696i) q^{10} +(5.02852 - 3.30731i) q^{11} +(1.60490 - 0.651390i) q^{12} +(-6.08473 + 0.711203i) q^{13} +(1.75658 + 2.35949i) q^{14} +(-2.69501 + 5.08809i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(-0.253735 - 0.212909i) q^{17} +(-1.30653 + 2.70055i) q^{18} +(-0.285511 + 0.239572i) q^{19} +(2.28123 + 2.41796i) q^{20} +(-4.99717 - 0.993295i) q^{21} +(5.02852 + 3.30731i) q^{22} +(0.697536 + 0.165319i) q^{23} +(1.23378 + 1.21564i) q^{24} +(-6.00966 - 0.702429i) q^{25} +(-3.06308 - 5.30540i) q^{26} +(-1.45606 - 4.98797i) q^{27} +(-1.47078 + 2.54747i) q^{28} +(0.233421 - 0.313539i) q^{29} +(-5.73940 - 0.459319i) q^{30} +(2.28811 + 7.64280i) q^{31} +(0.893633 - 0.448799i) q^{32} +(-10.3031 + 1.58723i) q^{33} +(0.0949972 - 0.317313i) q^{34} +(-1.69801 - 9.62990i) q^{35} +(-2.99718 - 0.130046i) q^{36} +(-0.453355 + 2.57110i) q^{37} +(-0.333064 - 0.167271i) q^{38} +(10.0967 + 3.26287i) q^{39} +(-1.31666 + 3.05237i) q^{40} +(-0.132020 + 0.306057i) q^{41} +(-1.06722 - 4.98191i) q^{42} +(7.96817 + 4.00176i) q^{43} +(-1.04513 + 5.92723i) q^{44} +(7.91025 - 6.07315i) q^{45} +(0.124481 + 0.705968i) q^{46} +(-2.04511 + 6.83114i) q^{47} +(-0.627542 + 1.61437i) q^{48} +(1.47698 - 0.741765i) q^{49} +(-1.73532 - 5.79638i) q^{50} +(0.246303 + 0.518142i) q^{51} +(3.65828 - 4.91393i) q^{52} +(-3.45123 + 5.97770i) q^{53} +(4.00332 - 3.31261i) q^{54} +(-10.0037 - 17.3270i) q^{55} +(-2.92167 - 0.341494i) q^{56} +(0.622298 - 0.171695i) q^{57} +(0.380350 + 0.0901447i) q^{58} +(-9.06502 - 5.96216i) q^{59} +(-1.85151 - 5.45194i) q^{60} +(4.99910 + 5.29874i) q^{61} +(-6.11147 + 5.12813i) q^{62} +(7.15577 + 5.16429i) q^{63} +(0.766044 + 0.642788i) q^{64} +(1.18411 + 20.3303i) q^{65} +(-5.53826 - 8.83180i) q^{66} +(0.734568 + 0.986697i) q^{67} +(0.328988 - 0.0384532i) q^{68} +(-0.979637 - 0.762871i) q^{69} +(8.16978 - 5.37335i) q^{70} +(12.1389 - 4.41819i) q^{71} +(-1.06771 - 2.80357i) q^{72} +(-0.412642 - 0.150189i) q^{73} +(-2.54039 + 0.602084i) q^{74} +(8.96013 + 5.43548i) q^{75} +(0.0216710 - 0.372077i) q^{76} +(12.1494 - 12.8776i) q^{77} +(1.00307 + 10.5633i) q^{78} +(0.525833 + 1.21902i) q^{79} -3.32424 q^{80} +(-1.29956 + 8.90568i) q^{81} -0.333317 q^{82} +(-1.98870 - 4.61033i) q^{83} +(4.15176 - 2.95317i) q^{84} +(-0.755608 + 0.800897i) q^{85} +(-0.518454 + 8.90152i) q^{86} +(-0.593531 + 0.325727i) q^{87} +(-5.85643 + 1.38800i) q^{88} +(1.65643 + 0.602892i) q^{89} +(8.70955 + 4.85786i) q^{90} +(-16.9337 + 6.16336i) q^{91} +(-0.598927 + 0.393920i) q^{92} +(1.90137 - 13.6868i) q^{93} +(-7.08249 + 0.827825i) q^{94} +(0.739862 + 0.993807i) q^{95} +(-1.73090 + 0.0631998i) q^{96} +(-0.696419 - 11.9570i) q^{97} +(1.26610 + 1.06239i) q^{98} +(17.3723 + 4.92169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

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