LMFDB - Embedded newform 216.2.v.b.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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([9, 9, 13]))

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

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

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (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:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38842 - 0.268854i) q^{2} +(-1.38044 - 1.04613i) q^{3} +(1.85543 + 0.746566i) q^{4} +(-3.21396 - 1.16979i) q^{5} +(1.63538 + 1.82361i) q^{6} +(0.199218 + 0.0351275i) q^{7} +(-2.37541 - 1.53539i) q^{8} +(0.811221 + 2.88824i) q^{9} +O(q^{10})$	\(q+(-1.38842 - 0.268854i) q^{2} +(-1.38044 - 1.04613i) q^{3} +(1.85543 + 0.746566i) q^{4} +(-3.21396 - 1.16979i) q^{5} +(1.63538 + 1.82361i) q^{6} +(0.199218 + 0.0351275i) q^{7} +(-2.37541 - 1.53539i) q^{8} +(0.811221 + 2.88824i) q^{9} +(4.14784 + 2.48825i) q^{10} +(1.37658 + 3.78212i) q^{11} +(-1.78031 - 2.97162i) q^{12} +(-1.09713 - 1.30751i) q^{13} +(-0.267155 - 0.102332i) q^{14} +(3.21293 + 4.97704i) q^{15} +(2.88528 + 2.77041i) q^{16} +(1.57350 - 0.908459i) q^{17} +(-0.349802 - 4.22820i) q^{18} +(-3.24004 + 5.61192i) q^{19} +(-5.08997 - 4.56990i) q^{20} +(-0.238260 - 0.256900i) q^{21} +(-0.894435 - 5.62128i) q^{22} +(1.37566 + 7.80173i) q^{23} +(1.67289 + 4.60450i) q^{24} +(5.13093 + 4.30536i) q^{25} +(1.17176 + 2.11035i) q^{26} +(1.90163 - 4.83568i) q^{27} +(0.343411 + 0.213906i) q^{28} +(3.08543 + 2.58898i) q^{29} +(-3.12280 - 7.77405i) q^{30} +(-7.51214 + 1.32459i) q^{31} +(-3.26115 - 4.62222i) q^{32} +(2.05631 - 6.66106i) q^{33} +(-2.42892 + 0.838284i) q^{34} +(-0.599188 - 0.345941i) q^{35} +(-0.651094 + 5.96457i) q^{36} +(-1.53384 + 0.885560i) q^{37} +(6.00733 - 6.92061i) q^{38} +(0.146696 + 2.95269i) q^{39} +(5.83840 + 7.71341i) q^{40} +(-6.61260 - 7.88059i) q^{41} +(0.261737 + 0.420742i) q^{42} +(3.47909 - 1.26628i) q^{43} +(-0.269450 + 8.04518i) q^{44} +(0.771390 - 10.2316i) q^{45} +(0.187536 - 11.2020i) q^{46} +(-0.523875 + 2.97105i) q^{47} +(-1.08474 - 6.84276i) q^{48} +(-6.53939 - 2.38014i) q^{49} +(-5.96638 - 7.35713i) q^{50} +(-3.12248 - 0.392012i) q^{51} +(-1.05952 - 3.24509i) q^{52} -9.46508 q^{53} +(-3.94036 + 6.20270i) q^{54} -13.7659i q^{55} +(-0.419290 - 0.389320i) q^{56} +(10.3435 - 4.35740i) q^{57} +(-3.58782 - 4.42413i) q^{58} +(1.23077 - 3.38152i) q^{59} +(2.24568 + 11.6332i) q^{60} +(8.13039 + 1.43361i) q^{61} +(10.7861 + 0.180575i) q^{62} +(0.0601532 + 0.603885i) q^{63} +(3.28515 + 7.29437i) q^{64} +(1.99664 + 5.48571i) q^{65} +(-4.64588 + 8.69553i) q^{66} +(-1.26475 + 1.06125i) q^{67} +(3.59775 - 0.510867i) q^{68} +(6.26262 - 12.2089i) q^{69} +(0.738918 + 0.641406i) q^{70} +(2.24594 + 3.89008i) q^{71} +(2.50759 - 8.10629i) q^{72} +(-4.05026 + 7.01525i) q^{73} +(2.36770 - 0.817154i) q^{74} +(-2.57896 - 11.3109i) q^{75} +(-10.2014 + 7.99364i) q^{76} +(0.141383 + 0.801822i) q^{77} +(0.590166 - 4.13902i) q^{78} +(0.380899 - 0.453938i) q^{79} +(-6.03238 - 12.2792i) q^{80} +(-7.68384 + 4.68600i) q^{81} +(7.06236 + 12.7194i) q^{82} +(-8.02454 + 9.56328i) q^{83} +(-0.250284 - 0.654537i) q^{84} +(-6.11986 + 1.07910i) q^{85} +(-5.17089 + 0.822771i) q^{86} +(-1.55083 - 6.80168i) q^{87} +(2.53709 - 11.0977i) q^{88} +(10.7122 + 6.18471i) q^{89} +(-3.82183 + 13.9985i) q^{90} +(-0.172639 - 0.299020i) q^{91} +(-3.27207 + 15.5026i) q^{92} +(11.7557 + 6.03016i) q^{93} +(1.52614 - 3.98422i) q^{94} +(16.9781 - 14.2463i) q^{95} +(-0.333631 + 9.79228i) q^{96} +(-8.24324 + 3.00029i) q^{97} +(8.43953 + 5.06279i) q^{98} +(-9.80695 + 7.04402i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−1.38842	−	0.268854i	−0.981763	−	0.190109i
$2$	−1.38842	−	0.268854i	−0.981763	−	0.190109i
$3$	−1.38044	−	1.04613i	−0.796997	−	0.603984i
$3$	−1.38044	−	1.04613i	−0.796997	−	0.603984i
$4$	1.85543	+	0.746566i	0.927717	+	0.373283i
$5$	−3.21396	−	1.16979i	−1.43733	−	0.523144i	−0.498306	−	0.867001i	$-0.666044\pi$
$5$	−3.21396	−	1.16979i	−1.43733	−	0.523144i	−0.939022	+	0.343857i	$0.888266\pi$
$6$	1.63538	+	1.82361i	0.667639	+	0.744485i
$7$	0.199218	+	0.0351275i	0.0752973	+	0.0132770i	0.211170	−	0.977449i	$-0.432273\pi$
$7$	0.199218	+	0.0351275i	0.0752973	+	0.0132770i	−0.135873	+	0.990726i	$0.543384\pi$
$8$	−2.37541	−	1.53539i	−0.839834	−	0.542843i
$9$	0.811221	+	2.88824i	0.270407	+	0.962746i
$10$	4.14784	+	2.48825i	1.31166	+	0.786852i
$11$	1.37658	+	3.78212i	0.415054	+	1.14035i	0.954469	+	0.298311i	$0.0964234\pi$
$11$	1.37658	+	3.78212i	0.415054	+	1.14035i	−0.539414	+	0.842040i	$0.681354\pi$
$12$	−1.78031	−	2.97162i	−0.513931	−	0.857832i
$13$	−1.09713	−	1.30751i	−0.304290	−	0.362639i	0.592131	−	0.805842i	$-0.298287\pi$
$13$	−1.09713	−	1.30751i	−0.304290	−	0.362639i	−0.896422	+	0.443202i	$0.853842\pi$
$14$	−0.267155	−	0.102332i	−0.0714001	−	0.0273495i
$15$	3.21293	+	4.97704i	0.829574	+	1.28507i
$16$	2.88528	+	2.77041i	0.721319	+	0.692603i
$17$	1.57350	−	0.908459i	0.381629	−	0.220334i	−0.296898	−	0.954909i	$-0.595952\pi$
$17$	1.57350	−	0.908459i	0.381629	−	0.220334i	0.678527	+	0.734576i	$0.262619\pi$
$18$	−0.349802	−	4.22820i	−0.0824492	−	0.996595i
$19$	−3.24004	+	5.61192i	−0.743317	+	1.28746i	0.207661	+	0.978201i	$0.433415\pi$
$19$	−3.24004	+	5.61192i	−0.743317	+	1.28746i	−0.950977	+	0.309261i	$0.899918\pi$
$20$	−5.08997	−	4.56990i	−1.13815	−	1.02186i
$21$	−0.238260	−	0.256900i	−0.0519927	−	0.0560601i
$22$	−0.894435	−	5.62128i	−0.190694	−	1.19846i
$23$	1.37566	+	7.80173i	0.286844	+	1.62677i	0.698623	+	0.715490i	$0.253796\pi$
$23$	1.37566	+	7.80173i	0.286844	+	1.62677i	−0.411779	+	0.911284i	$0.635092\pi$
$24$	1.67289	+	4.60450i	0.341477	+	0.939890i
$25$	5.13093	+	4.30536i	1.02619	+	0.861072i
$26$	1.17176	+	2.11035i	0.229800	+	0.413874i
$27$	1.90163	−	4.83568i	0.365970	−	0.930627i
$28$	0.343411	+	0.213906i	0.0648986	+	0.0404245i
$29$	3.08543	+	2.58898i	0.572949	+	0.480761i	0.882623	−	0.470081i	$-0.155775\pi$
$29$	3.08543	+	2.58898i	0.572949	+	0.480761i	−0.309674	+	0.950843i	$0.600220\pi$
$30$	−3.12280	−	7.77405i	−0.570143	−	1.41934i
$31$	−7.51214	+	1.32459i	−1.34922	+	0.237904i	−0.801117	−	0.598507i	$-0.795761\pi$
$31$	−7.51214	+	1.32459i	−1.34922	+	0.237904i	−0.548103	+	0.836411i	$0.684650\pi$
$32$	−3.26115	−	4.62222i	−0.576495	−	0.817101i
$33$	2.05631	−	6.66106i	0.357957	−	1.15954i
$34$	−2.42892	+	0.838284i	−0.416557	+	0.143764i
$35$	−0.599188	−	0.345941i	−0.101281	−	0.0584747i
$36$	−0.651094	+	5.96457i	−0.108516	+	0.994095i
$37$	−1.53384	+	0.885560i	−0.252161	+	0.145585i	−0.620753	−	0.784006i	$-0.713173\pi$
$37$	−1.53384	+	0.885560i	−0.252161	+	0.145585i	0.368592	+	0.929591i	$0.379840\pi$
$38$	6.00733	−	6.92061i	0.974518	−	1.12267i
$39$	0.146696	+	2.95269i	0.0234902	+	0.472809i
$40$	5.83840	+	7.71341i	0.923132	+	1.21960i
$41$	−6.61260	−	7.88059i	−1.03271	−	1.23074i	−0.972584	−	0.232551i	$-0.925293\pi$
$41$	−6.61260	−	7.88059i	−1.03271	−	1.23074i	−0.0601305	−	0.998191i	$-0.519152\pi$
$42$	0.261737	+	0.420742i	0.0403870	+	0.0649220i
$43$	3.47909	−	1.26628i	0.530556	−	0.193107i	−0.0628305	−	0.998024i	$-0.520013\pi$
$43$	3.47909	−	1.26628i	0.530556	−	0.193107i	0.593387	+	0.804918i	$0.297791\pi$
$44$	−0.269450	+	8.04518i	−0.0406211	+	1.21286i
$45$	0.771390	−	10.2316i	0.114992	−	1.52524i
$46$	0.187536	−	11.2020i	0.0276507	−	1.65164i
$47$	−0.523875	+	2.97105i	−0.0764151	+	0.433371i	0.922466	+	0.386078i	$0.126171\pi$
$47$	−0.523875	+	2.97105i	−0.0764151	+	0.433371i	−0.998881	+	0.0472931i	$0.984941\pi$
$48$	−1.08474	−	6.84276i	−0.156568	−	0.987667i
$49$	−6.53939	−	2.38014i	−0.934199	−	0.340021i
$50$	−5.96638	−	7.35713i	−0.843774	−	1.04046i
$51$	−3.12248	−	0.392012i	−0.437235	−	0.0548927i
$52$	−1.05952	−	3.24509i	−0.146928	−	0.450013i
$53$	−9.46508			−1.30013			−0.650064	−	0.759879i	$-0.725258\pi$
$53$	−9.46508			−1.30013			−0.650064	+	0.759879i	$0.725258\pi$
$54$	−3.94036	+	6.20270i	−0.536216	+	0.844081i
$55$		−	13.7659i		−	1.85619i
$56$	−0.419290	−	0.389320i	−0.0560300	−	0.0520250i
$57$	10.3435	−	4.35740i	1.37003	−	0.577152i
$58$	−3.58782	−	4.42413i	−0.471103	−	0.580916i
$59$	1.23077	−	3.38152i	0.160233	−	0.440237i	−0.833432	−	0.552623i	$-0.813627\pi$
$59$	1.23077	−	3.38152i	0.160233	−	0.440237i	0.993665	+	0.112386i	$0.0358493\pi$
$60$	2.24568	+	11.6332i	0.289917	+	1.50185i
$61$	8.13039	+	1.43361i	1.04099	+	0.183555i	0.667908	−	0.744244i	$-0.267190\pi$
$61$	8.13039	+	1.43361i	1.04099	+	0.183555i	0.373082	+	0.927798i	$0.378301\pi$
$62$	10.7861	+	0.180575i	1.36984	+	0.0229330i
$63$	0.0601532	+	0.603885i	0.00757859	+	0.0760824i
$64$	3.28515	+	7.29437i	0.410644	+	0.911796i
$65$	1.99664	+	5.48571i	0.247652	+	0.680419i
$66$	−4.64588	+	8.69553i	−0.571868	+	1.07035i
$67$	−1.26475	+	1.06125i	−0.154514	+	0.129653i	−0.716767	−	0.697312i	$-0.754379\pi$
$67$	−1.26475	+	1.06125i	−0.154514	+	0.129653i	0.562253	+	0.826965i	$0.309935\pi$
$68$	3.59775	−	0.510867i	0.436291	−	0.0619517i
$69$	6.26262	−	12.2089i	0.753931	−	1.46978i
$70$	0.738918	+	0.641406i	0.0883176	+	0.0766627i
$71$	2.24594	+	3.89008i	0.266544	+	0.461668i	0.967967	−	0.251078i	$-0.0807849\pi$
$71$	2.24594	+	3.89008i	0.266544	+	0.461668i	−0.701423	+	0.712745i	$0.747452\pi$
$72$	2.50759	−	8.10629i	0.295523	−	0.955336i
$73$	−4.05026	+	7.01525i	−0.474047	+	0.821073i	−0.999558	−	0.0297132i	$-0.990541\pi$
$73$	−4.05026	+	7.01525i	−0.474047	+	0.821073i	0.525512	+	0.850786i	$0.323874\pi$
$74$	2.36770	−	0.817154i	0.275239	−	0.0949922i
$75$	−2.57896	−	11.3109i	−0.297793	−	1.30607i
$76$	−10.2014	+	7.99364i	−1.17018	+	0.916934i
$77$	0.141383	+	0.801822i	0.0161121	+	0.0913761i
$78$	0.590166	−	4.13902i	0.0668232	−	0.468652i
$79$	0.380899	−	0.453938i	0.0428545	−	0.0510720i	−0.744191	−	0.667966i	$-0.767165\pi$
$79$	0.380899	−	0.453938i	0.0428545	−	0.0510720i	0.787046	+	0.616894i	$0.211609\pi$
$80$	−6.03238	−	12.2792i	−0.674441	−	1.37285i
$81$	−7.68384	+	4.68600i	−0.853760	+	0.520666i
$82$	7.06236	+	12.7194i	0.779907	+	1.40462i
$83$	−8.02454	+	9.56328i	−0.880808	+	1.04971i	0.117586	+	0.993063i	$0.462484\pi$
$83$	−8.02454	+	9.56328i	−0.880808	+	1.04971i	−0.998394	+	0.0566436i	$0.981960\pi$
$84$	−0.250284	−	0.654537i	−0.0273082	−	0.0714159i
$85$	−6.11986	+	1.07910i	−0.663792	+	0.117044i
$86$	−5.17089	+	0.822771i	−0.557592	+	0.0887217i
$87$	−1.55083	−	6.80168i	−0.166266	−	0.729217i
$88$	2.53709	−	11.0977i	0.270455	−	1.18302i
$89$	10.7122	+	6.18471i	1.13549	+	0.655578i	0.945311	−	0.326171i	$-0.105759\pi$
$89$	10.7122	+	6.18471i	1.13549	+	0.655578i	0.190183	+	0.981749i	$0.439092\pi$
$90$	−3.82183	+	13.9985i	−0.402857	+	1.47557i
$91$	−0.172639	−	0.299020i	−0.0180975	−	0.0313458i
$92$	−3.27207	+	15.5026i	−0.341137	+	1.61626i
$93$	11.7557	+	6.03016i	1.21901	+	0.625299i
$94$	1.52614	−	3.98422i	0.157409	−	0.410941i
$95$	16.9781	−	14.2463i	1.74192	−	1.46164i
$96$	−0.333631	+	9.79228i	−0.0340510	+	0.999420i
$97$	−8.24324	+	3.00029i	−0.836974	+	0.304634i	−0.724718	−	0.689046i	$-0.758030\pi$
$97$	−8.24324	+	3.00029i	−0.836974	+	0.304634i	−0.112256	+	0.993679i	$0.535808\pi$
$98$	8.43953	+	5.06279i	0.852521	+	0.511419i
$99$	−9.80695	+	7.04402i	−0.985636	+	0.707951i
$100$	6.30587	+	11.8189i	0.630587	+	1.18189i
$101$	−1.79803	+	10.1971i	−0.178910	+	1.01465i	0.754623	+	0.656159i	$0.227820\pi$
$101$	−1.79803	+	10.1971i	−0.178910	+	1.01465i	−0.933533	+	0.358491i	$0.883291\pi$
$102$	4.22993	+	1.38377i	0.418826	+	0.137014i
$103$	−2.22000	+	6.09941i	−0.218744	+	0.600993i	−0.999722	−	0.0235646i	$-0.992498\pi$
$103$	−2.22000	+	6.09941i	−0.218744	+	0.600993i	0.780979	+	0.624558i	$0.214721\pi$
$104$	0.598600	+	4.79041i	0.0586975	+	0.469739i
$105$	0.465242	+	1.10438i	0.0454030	+	0.107776i
$106$	13.1415	+	2.54473i	1.27642	+	0.247166i
$107$		−	2.26037i		−	0.218518i	−0.994013	−	0.109259i	$-0.965152\pi$
$107$		−	2.26037i		−	0.218518i	0.994013	−	0.109259i	$-0.0348478\pi$
$108$	7.13851	−	7.55259i	0.686904	−	0.726748i
$109$		−	3.00655i		−	0.287975i	−0.989580	−	0.143987i	$-0.954008\pi$
$109$		−	3.00655i		−	0.287975i	0.989580	−	0.143987i	$-0.0459925\pi$
$110$	−3.70102	+	19.1129i	−0.352878	+	1.82234i
$111$	3.04378	+	0.382131i	0.288902	+	0.0362703i
$112$	0.477482	+	0.653268i	0.0451178	+	0.0617281i
$113$	1.92611	−	5.29194i	0.181193	−	0.497824i	−0.815530	−	0.578715i	$-0.803554\pi$
$113$	1.92611	−	5.29194i	0.181193	−	0.497824i	0.996723	+	0.0808910i	$0.0257766\pi$
$114$	−15.5326	+	3.26902i	−1.45476	+	0.306172i
$115$	4.70506	−	26.6837i	0.438749	−	2.48827i
$116$	3.79196	+	7.10716i	0.352075	+	0.659883i
$117$	2.88639	−	4.22947i	0.266847	−	0.391014i
$118$	−2.61797	+	4.36408i	−0.241004	+	0.401746i
$119$	0.345381	−	0.125708i	0.0316610	−	0.0115237i
$120$	0.00968508	−	16.7556i	0.000884123	−	1.52957i
$121$	−3.98297	+	3.34211i	−0.362088	+	0.303828i
$122$	−10.9030	−	4.17634i	−0.987110	−	0.378108i
$123$	0.884160	+	17.7963i	0.0797220	+	1.60464i
$124$	−14.9272	−	3.15061i	−1.34050	−	0.282933i
$125$	−2.90369	−	5.02934i	−0.259714	−	0.449838i
$126$	0.0788391	−	0.854621i	0.00702354	−	0.0761357i
$127$	−9.60934	−	5.54795i	−0.852691	−	0.492301i	0.00886716	−	0.999961i	$-0.497177\pi$
$127$	−9.60934	−	5.54795i	−0.852691	−	0.492301i	−0.861558	+	0.507660i	$0.830511\pi$
$128$	−2.60006	−	11.0109i	−0.229815	−	0.973234i
$129$	−6.12737	−	1.89155i	−0.539485	−	0.166542i
$130$	−1.29732	−	8.15329i	−0.113782	−	0.715091i
$131$	7.26270	−	1.28061i	0.634545	−	0.111887i	0.152883	−	0.988244i	$-0.451144\pi$
$131$	7.26270	−	1.28061i	0.634545	−	0.111887i	0.481662	+	0.876357i	$0.340033\pi$
$132$	8.78827	−	10.8240i	0.764921	−	0.942108i
$133$	−0.842608	+	1.00418i	−0.0730633	+	0.0870735i
$134$	2.04134	−	1.13344i	0.176345	−	0.0979139i
$135$	−11.7685	+	13.3172i	−1.01287	+	1.14616i
$136$	−5.13254	−	0.257970i	−0.440112	−	0.0221207i
$137$	7.46073	−	8.89135i	0.637413	−	0.759640i	−0.346546	−	0.938033i	$-0.612646\pi$
$137$	7.46073	−	8.89135i	0.637413	−	0.759640i	0.983959	+	0.178393i	$0.0570900\pi$
$138$	−11.9776	+	15.2674i	−1.01960	+	1.29965i
$139$	1.37040	+	7.77191i	0.116236	+	0.659205i	0.986131	+	0.165969i	$0.0530751\pi$
$139$	1.37040	+	7.77191i	0.116236	+	0.659205i	−0.869895	+	0.493236i	$0.835814\pi$
$140$	−0.853486	−	1.08920i	−0.0721327	−	0.0920546i
$141$	3.83128	−	3.55330i	0.322652	−	0.299242i
$142$	−2.07245	−	6.00490i	−0.173916	−	0.503920i
$143$	3.43488	−	5.94939i	0.287239	−	0.497513i
$144$	−5.66101	+	10.5808i	−0.471751	+	0.881732i
$145$	−6.88789	−	11.9302i	−0.572008	−	0.990747i
$146$	7.50955	−	8.65121i	0.621495	−	0.715979i
$147$	6.53729	+	10.1267i	0.539186	+	0.835237i
$148$	−3.50706	+	0.497990i	−0.288279	+	0.0409345i
$149$	−5.38903	+	4.52193i	−0.441486	+	0.370451i	−0.836265	−	0.548325i	$-0.815266\pi$
$149$	−5.38903	+	4.52193i	−0.441486	+	0.370451i	0.394779	+	0.918776i	$0.370821\pi$
$150$	0.539704	+	16.3977i	0.0440667	+	1.33887i
$151$	−2.14375	−	5.88990i	−0.174456	−	0.479313i	0.821390	−	0.570367i	$-0.193199\pi$
$151$	−2.14375	−	5.88990i	−0.174456	−	0.479313i	−0.995846	+	0.0910533i	$0.970977\pi$
$152$	16.3129	−	8.35588i	1.32315	−	0.677751i
$153$	3.90030	+	3.80767i	0.315320	+	0.307832i
$154$	0.0192740	−	1.15128i	0.00155314	−	0.0927727i
$155$	25.6932	+	4.53041i	2.06373	+	0.363891i
$156$	−1.93219	+	5.58804i	−0.154699	+	0.447401i
$157$	1.70377	−	4.68108i	0.135976	−	0.373591i	−0.852952	−	0.521990i	$-0.825190\pi$
$157$	1.70377	−	4.68108i	0.135976	−	0.373591i	0.988928	+	0.148399i	$0.0474120\pi$
$158$	−0.650892	+	0.527851i	−0.0517822	+	0.0419936i
$159$	13.0660	+	9.90171i	1.03620	+	0.785257i
$160$	5.07420	+	18.6705i	0.401151	+	1.47603i
$161$			1.60257i			0.126300i
$162$	11.9283	−	4.44031i	0.937173	−	0.348864i
$163$	6.53033			0.511495			0.255747	−	0.966744i	$-0.417679\pi$
$163$	6.53033			0.511495			0.255747	+	0.966744i	$0.417679\pi$
$164$	−6.38587	−	19.5587i	−0.498652	−	1.52728i
$165$	−14.4009	+	19.0030i	−1.12111	+	1.47938i
$166$	13.7126	−	11.1204i	1.06430	−	0.863114i
$167$	11.5164	+	4.19163i	0.891167	+	0.324358i	0.746708	−	0.665152i	$-0.231633\pi$
$167$	11.5164	+	4.19163i	0.891167	+	0.324358i	0.144460	+	0.989511i	$0.453856\pi$
$168$	0.171525	+	0.976064i	0.0132334	+	0.0753050i
$169$	1.75154	−	9.93346i	0.134734	−	0.764113i
$170$	8.78707	+	0.147108i	0.673938	+	0.0112826i
$171$	−18.8369	−	4.80551i	−1.44050	−	0.367487i
$172$	7.40059	+	0.247861i	0.564290	+	0.0188992i
$173$	−22.9308	+	8.34612i	−1.74339	+	0.634543i	−0.999433	−	0.0336797i	$-0.989277\pi$
$173$	−22.9308	+	8.34612i	−1.74339	+	0.634543i	−0.743961	+	0.668223i	$0.767055\pi$
$174$	0.324545	+	9.86056i	0.0246037	+	0.747527i
$175$	0.870937	+	1.03794i	0.0658367	+	0.0784611i
$176$	−6.50621	+	14.7262i	−0.490424	+	1.11003i
$177$	−5.23652	+	3.38043i	−0.393601	+	0.254089i
$178$	−13.2103	−	11.4670i	−0.990155	−	0.859489i
$179$	−12.4964	+	7.21481i	−0.934026	+	0.539260i	−0.888083	−	0.459684i	$-0.847963\pi$
$179$	−12.4964	+	7.21481i	−0.934026	+	0.539260i	−0.0459437	+	0.998944i	$0.514629\pi$
$180$	9.06986	−	18.4083i	0.676028	−	1.37207i
$181$	17.7079	+	10.2237i	1.31622	+	0.759919i	0.983118	−	0.182973i	$-0.0585721\pi$
$181$	17.7079	+	10.2237i	1.31622	+	0.759919i	0.333100	+	0.942892i	$0.391905\pi$
$182$	0.159303	+	0.461581i	0.0118084	+	0.0342146i
$183$	−9.72376	−	10.4845i	−0.718801	−	0.775034i
$184$	8.71096	−	20.6445i	0.642181	−	1.52193i
$185$	5.96560	−	1.05190i	0.438600	−	0.0773370i
$186$	−14.7007	−	11.5330i	−1.07791	−	0.845640i
$187$	5.60194	+	4.70059i	0.409655	+	0.343741i
$188$	−3.19010	+	5.12147i	−0.232662	+	0.373522i
$189$	0.548705	−	0.896555i	0.0399124	−	0.0652148i
$190$	−27.4030	+	15.2153i	−1.98802	+	1.10383i
$191$	−15.9522	−	13.3855i	−1.15426	−	0.968538i	−0.154448	−	0.988001i	$-0.549360\pi$
$191$	−15.9522	−	13.3855i	−1.15426	−	0.968538i	−0.999811	+	0.0194633i	$0.993804\pi$
$192$	3.09591	−	13.5061i	0.223428	−	0.974720i
$193$	0.989078	+	5.60934i	0.0711954	+	0.403769i	0.999490	+	0.0319244i	$0.0101636\pi$
$193$	0.989078	+	5.60934i	0.0711954	+	0.403769i	−0.928295	+	0.371845i	$0.878725\pi$
$194$	12.2517	−	1.94945i	0.879623	−	0.139962i
$195$	2.98254	−	9.66143i	0.213584	−	0.691869i
$196$	−10.3565	−	9.29830i	−0.739749	−	0.664164i
$197$	13.4024	−	23.2137i	0.954885	−	1.65391i	0.220254	−	0.975443i	$-0.429312\pi$
$197$	13.4024	−	23.2137i	0.954885	−	1.65391i	0.734631	−	0.678467i	$-0.237355\pi$
$198$	15.5100	−	7.14344i	1.10225	−	0.507662i
$199$	22.2890	−	12.8685i	1.58002	−	0.912226i	0.585168	−	0.810912i	$-0.301029\pi$
$199$	22.2890	−	12.8685i	1.58002	−	0.912226i	0.994854	−	0.101314i	$-0.0323048\pi$
$200$	−5.57765	−	18.1050i	−0.394400	−	1.28022i
$201$	2.85613	−	0.141899i	0.201456	−	0.0100088i
$202$	5.23795	−	13.6745i	0.368541	−	0.962134i
$203$	0.523728	+	0.624155i	0.0367585	+	0.0438071i
$204$	−5.50090	−	3.05849i	−0.385140	−	0.214137i
$205$	12.0340	+	33.0633i	0.840494	+	2.30924i
$206$	4.72216	−	7.87171i	0.329008	−	0.548448i
$207$	−21.4173	+	10.3021i	−1.48861	+	0.716049i
$208$	0.456812	−	6.81205i	0.0316742	−	0.472331i
$209$	−25.6851	−	4.52898i	−1.77668	−	0.313276i
$210$	−0.349036	−	1.65843i	−0.0240857	−	0.114442i
$211$	−2.22400	−	0.809471i	−0.153107	−	0.0557263i	0.264330	−	0.964432i	$-0.414849\pi$
$211$	−2.22400	−	0.809471i	−0.153107	−	0.0557263i	−0.417437	+	0.908706i	$0.637071\pi$
$212$	−17.5618	−	7.06631i	−1.20615	−	0.485316i
$213$	0.969152	−	7.71956i	0.0664052	−	0.528936i
$214$	−0.607709	+	3.13835i	−0.0415421	+	0.214533i
$215$	−12.6629			−0.863606
$216$	−11.9418	+	8.56697i	−0.812538	+	0.582908i
$217$	−1.54308			−0.104751
$218$	−0.808322	+	4.17436i	−0.0547465	+	0.282723i
$219$	12.9300	−	5.44703i	0.873729	−	0.368076i
$220$	10.2771	−	25.5417i	0.692885	−	1.72202i
$221$	−2.91416	−	1.06067i	−0.196028	−	0.0713482i
$222$	−4.12331	−	1.34889i	−0.276739	−	0.0905316i
$223$	−19.7258	−	3.47820i	−1.32094	−	0.232917i	−0.531664	−	0.846955i	$-0.678433\pi$
$223$	−19.7258	−	3.47820i	−1.32094	−	0.232917i	−0.789277	+	0.614038i	$0.789544\pi$
$224$	−0.487313	−	1.03539i	−0.0325599	−	0.0691796i
$225$	−8.27259	+	18.3119i	−0.551506	+	1.22080i
$226$	−4.09701	+	6.82961i	−0.272529	+	0.454299i
$227$	−8.81116	−	24.2085i	−0.584817	−	1.60677i	−0.779843	−	0.625975i	$-0.784701\pi$
$227$	−8.81116	−	24.2085i	−0.584817	−	1.60677i	0.195026	−	0.980798i	$-0.437521\pi$
$228$	22.4447	−	0.362778i	1.48644	−	0.0240256i
$229$	−1.43440	−	1.70946i	−0.0947880	−	0.112964i	0.716565	−	0.697520i	$-0.245713\pi$
$229$	−1.43440	−	1.70946i	−0.0947880	−	0.112964i	−0.811353	+	0.584556i	$0.801269\pi$
$230$	−13.7066	+	35.7833i	−0.903788	+	2.35948i
$231$	0.643641	−	1.25477i	0.0423484	−	0.0825579i
$232$	−3.35406	−	10.8872i	−0.220205	−	0.714781i
$233$	−7.43882	+	4.29480i	−0.487333	+	0.281362i	−0.723467	−	0.690358i	$-0.757453\pi$
$233$	−7.43882	+	4.29480i	−0.487333	+	0.281362i	0.236134	+	0.971720i	$0.424119\pi$
$234$	−5.14464	+	5.09627i	−0.336316	+	0.333154i
$235$	5.15920	−	8.93600i	0.336549	−	0.582921i
$236$	4.80815	−	5.35534i	0.312984	−	0.348603i
$237$	−1.00069	+	0.228163i	−0.0650016	+	0.0148208i
$238$	−0.513332	+	0.0816793i	−0.0332744	+	0.00529448i
$239$	0.254336	+	1.44241i	0.0164516	+	0.0933018i	0.991928	−	0.126802i	$-0.0404714\pi$
$239$	0.254336	+	1.44241i	0.0164516	+	0.0933018i	−0.975476	+	0.220104i	$0.929360\pi$
$240$	−4.51826	+	23.2613i	−0.291653	+	1.50151i
$241$	1.54665	+	1.29779i	0.0996285	+	0.0835982i	0.691241	−	0.722624i	$-0.257064\pi$
$241$	1.54665	+	1.29779i	0.0996285	+	0.0835982i	−0.591613	+	0.806222i	$0.701509\pi$
$242$	6.42858	−	3.56942i	0.413245	−	0.229451i
$243$	15.5092	+	1.56957i	0.994918	+	0.100688i
$244$	14.0151	+	8.72984i	0.897227	+	0.558871i
$245$	18.2331	+	15.2994i	1.16487	+	0.977442i
$246$	3.55703	−	24.9465i	0.226788	−	1.59053i
$247$	10.8924	−	1.92063i	0.693068	−	0.122207i
$248$	19.8782	+	8.38762i	1.26227	+	0.532614i
$249$	21.0818	−	4.80680i	1.33601	−	0.304618i
$250$	2.67939	+	7.76352i	0.169460	+	0.491008i
$251$	−0.0195920	−	0.0113115i	−0.00123664	−	0.000713973i	0.499382	−	0.866382i	$-0.333561\pi$
$251$	−0.0195920	−	0.0113115i	−0.00123664	−	0.000713973i	−0.500618	+	0.865668i	$0.666894\pi$
$252$	−0.339230	+	1.16538i	−0.0213695	+	0.0734119i
$253$	−27.6134	+	15.9426i	−1.73604	+	1.00230i
$254$	11.8502	+	10.2864i	0.743550	+	0.645427i
$255$	9.57697	+	4.91255i	0.599733	+	0.307636i
$256$	0.649655	+	15.9868i	0.0406034	+	0.999175i
$257$	−10.5865	−	12.6165i	−0.660369	−	0.786997i	0.327070	−	0.945000i	$-0.393939\pi$
$257$	−10.5865	−	12.6165i	−0.660369	−	0.786997i	−0.987439	+	0.158003i	$0.949494\pi$
$258$	7.99882	+	4.27364i	0.497985	+	0.266065i
$259$	−0.336675	+	0.122540i	−0.0209200	+	0.00761425i
$260$	−0.390819	+	11.6690i	−0.0242376	+	0.723681i
$261$	−4.97463	+	11.0117i	−0.307922	+	0.681606i
$262$	−10.4280	−	0.174579i	−0.644243	−	0.0107855i
$263$	−1.02766	+	5.82816i	−0.0633684	+	0.359380i	0.936592	+	0.350423i	$0.113962\pi$
$263$	−1.02766	+	5.82816i	−0.0633684	+	0.359380i	−0.999960	+	0.00895677i	$0.997149\pi$
$264$	−15.1119	+	12.6655i	−0.930074	+	0.779509i
$265$	30.4204	+	11.0721i	1.86871	+	0.680155i
$266$	1.43987	−	1.16769i	0.0882843	−	0.0715956i
$267$	−8.31756	−	19.7440i	−0.509026	−	1.20831i
$268$	−3.13897	+	1.02487i	−0.191743	+	0.0626037i
$269$	4.98736			0.304085			0.152042	−	0.988374i	$-0.451415\pi$
$269$	4.98736			0.304085			0.152042	+	0.988374i	$0.451415\pi$
$270$	19.9200	−	15.3259i	1.21229	−	0.932703i
$271$			7.03519i			0.427358i	0.976904	+	0.213679i	$0.0685446\pi$
$271$			7.03519i			0.427358i	−0.976904	+	0.213679i	$0.931455\pi$
$272$	7.05678	+	1.73808i	0.427880	+	0.105386i
$273$	−0.0744961	+	0.593382i	−0.00450871	+	0.0359131i
$274$	−12.7491	+	10.3391i	−0.770203	+	0.624608i
$275$	−9.22026	+	25.3325i	−0.556003	+	1.52760i
$276$	20.7347	−	17.9774i	1.24808	−	1.08211i
$277$	22.4822	+	3.96421i	1.35082	+	0.238187i	0.801786	−	0.597611i	$-0.203883\pi$
$277$	22.4822	+	3.96421i	1.35082	+	0.238187i	0.549037	+	0.835798i	$0.314994\pi$
$278$	0.186819	−	11.1591i	0.0112047	−	0.669281i
$279$	−9.91974	−	20.6223i	−0.593879	−	1.23463i
$280$	0.892162	+	1.74174i	0.0533169	+	0.104089i
$281$	8.38379	+	23.0343i	0.500135	+	1.37411i	0.891143	+	0.453722i	$0.149904\pi$
$281$	8.38379	+	23.0343i	0.500135	+	1.37411i	−0.391008	+	0.920387i	$0.627874\pi$
$282$	−6.27476	+	3.90343i	−0.373656	+	0.232446i
$283$	−8.31451	+	6.97670i	−0.494246	+	0.414722i	−0.855545	−	0.517728i	$-0.826778\pi$
$283$	−8.31451	+	6.97670i	−0.494246	+	0.414722i	0.361299	+	0.932450i	$0.382333\pi$
$284$	1.26299	+	8.89453i	0.0749447	+	0.527793i
$285$	−38.3408	+	1.90485i	−2.27111	+	0.112834i
$286$	−6.36858	+	7.33678i	−0.376582	+	0.433833i
$287$	−1.04052	−	1.80224i	−0.0614202	−	0.106383i
$288$	10.7046	−	13.1686i	0.630772	−	0.775968i
$289$	−6.84941	+	11.8635i	−0.402906	+	0.697854i
$290$	6.35582	+	18.4160i	0.373227	+	1.08142i
$291$	14.5180	+	4.48178i	0.851059	+	0.262727i
$292$	−12.7523	+	9.99256i	−0.746274	+	0.584770i
$293$	2.84714	+	16.1469i	0.166332	+	0.943313i	0.947681	+	0.319219i	$0.103421\pi$
$293$	2.84714	+	16.1469i	0.166332	+	0.943313i	−0.781349	+	0.624094i	$0.785468\pi$
$294$	−6.35391	−	15.8177i	−0.370568	−	0.922508i
$295$	−7.91132	+	9.42834i	−0.460615	+	0.548939i
$296$	5.00317	+	0.251467i	0.290803	+	0.0146162i
$297$	20.9069	+	0.535518i	1.21314	+	0.0310739i
$298$	8.69799	−	4.82949i	0.503861	−	0.279765i
$299$	8.69159	−	10.3582i	0.502648	−	0.599032i
$300$	3.65925	−	22.9120i	0.211267	−	1.32283i
$301$	0.737579	−	0.130055i	0.0425133	−	0.00749625i
$302$	1.39291	+	8.75403i	0.0801527	+	0.503738i
$303$	13.1496	−	12.1955i	0.755423	−	0.700614i
$304$	−24.8957	+	7.21569i	−1.42787	+	0.413848i
$305$	−24.4538	−	14.1184i	−1.40022	−	0.808416i
$306$	−4.39155	−	6.33527i	−0.251048	−	0.362163i
$307$	7.29100	+	12.6284i	0.416119	+	0.720740i	0.995545	−	0.0942851i	$-0.0300565\pi$
$307$	7.29100	+	12.6284i	0.416119	+	0.720740i	−0.579426	+	0.815025i	$0.696723\pi$
$308$	−0.336287	+	1.59328i	−0.0191617	+	0.0907856i
$309$	9.44536	−	6.09745i	0.537328	−	0.346872i
$310$	−34.4550	−	13.1978i	−1.95691	−	0.749587i
$311$	18.0464	−	15.1428i	1.02332	−	0.858667i	0.0332788	−	0.999446i	$-0.489405\pi$
$311$	18.0464	−	15.1428i	1.02332	−	0.858667i	0.990041	+	0.140779i	$0.0449606\pi$
$312$	4.18507	−	7.23908i	0.236933	−	0.409832i
$313$	4.27277	−	1.55516i	0.241511	−	0.0879028i	−0.218429	−	0.975853i	$-0.570093\pi$
$313$	4.27277	−	1.55516i	0.241511	−	0.0879028i	0.459940	+	0.887950i	$0.347871\pi$
$314$	−3.62409	+	6.04125i	−0.204519	+	0.340928i
$315$	0.513087	−	2.01123i	0.0289092	−	0.113320i
$316$	1.04563	−	0.557886i	0.0588212	−	0.0313835i
$317$	1.85951	−	10.5458i	0.104440	−	0.592310i	−0.887002	−	0.461765i	$-0.847216\pi$
$317$	1.85951	−	10.5458i	0.104440	−	0.592310i	0.991442	−	0.130545i	$-0.0416726\pi$
$318$	−15.4790	−	17.2606i	−0.868017	−	0.967926i
$319$	−5.54450	+	15.2334i	−0.310432	+	0.852906i
$320$	−2.02550	−	27.2867i	−0.113229	−	1.52538i
$321$	−2.36464	+	3.12030i	−0.131981	+	0.174158i
$322$	0.430857	−	2.22504i	0.0240107	−	0.123997i
$323$			11.7738i			0.655111i
$324$	−17.7553	+	2.95807i	−0.986404	+	0.164337i
$325$		−	11.4323i		−	0.634151i
$326$	−9.06685	−	1.75570i	−0.502166	−	0.0972395i
$327$	−3.14524	+	4.15035i	−0.173932	+	0.229515i
$328$	3.60786	+	28.8726i	0.199210	+	1.59422i
$329$	−0.208731	+	0.573483i	−0.0115077	+	0.0316172i
$330$	25.1036	−	22.5124i	1.38191	−	1.23927i
$331$	−2.53127	+	14.3556i	−0.139131	+	0.789053i	0.832762	+	0.553631i	$0.186758\pi$
$331$	−2.53127	+	14.3556i	−0.139131	+	0.789053i	−0.971893	+	0.235422i	$0.924353\pi$
$332$	−22.0286	+	11.7532i	−1.20898	+	0.645040i
$333$	−3.80199	−	3.71170i	−0.208348	−	0.203400i
$334$	−14.8627	−	8.91600i	−0.813252	−	0.487862i
$335$	5.30631	−	1.93134i	0.289915	−	0.105520i
$336$	0.0242700	−	1.40131i	0.00132404	−	0.0764475i
$337$	19.2969	−	16.1920i	1.05117	−	0.882035i	0.0579523	−	0.998319i	$-0.481543\pi$
$337$	19.2969	−	16.1920i	1.05117	−	0.882035i	0.993216	+	0.116285i	$0.0370984\pi$
$338$	−5.10253	+	13.3209i	−0.277541	+	0.724564i
$339$	−8.19494	+	5.29024i	−0.445088	+	0.287326i
$340$	−12.1606	−	2.56669i	−0.659502	−	0.139198i
$341$	−15.3508	−	26.5884i	−0.831293	−	1.43984i
$342$	24.8617	+	11.7365i	1.34436	+	0.634636i
$343$	−2.44548	−	1.41190i	−0.132044	−	0.0762354i
$344$	−10.2085	−	2.33381i	−0.550406	−	0.125831i
$345$	−34.4097	+	31.9131i	−1.85255	+	1.71814i
$346$	34.0815	−	5.42291i	1.83223	−	0.291537i
$347$	−8.71967	+	1.53751i	−0.468097	+	0.0825380i	−0.402721	−	0.915323i	$-0.631936\pi$
$347$	−8.71967	+	1.53751i	−0.468097	+	0.0825380i	−0.0653753	+	0.997861i	$0.520824\pi$
$348$	2.20045	−	13.7779i	0.117956	−	0.738572i
$349$	19.6221	−	23.3847i	1.05035	−	1.25175i	0.0834696	−	0.996510i	$-0.473400\pi$
$349$	19.6221	−	23.3847i	1.05035	−	1.25175i	0.966877	−	0.255244i	$-0.0821557\pi$
$350$	−0.930174	−	1.67526i	−0.0497199	−	0.0895463i
$351$	−8.40906	+	2.81897i	−0.448843	+	0.150466i
$352$	12.9926	−	18.6969i	0.692506	−	0.996548i
$353$	−8.90806	+	10.6162i	−0.474128	+	0.565044i	−0.949107	−	0.314953i	$-0.898011\pi$
$353$	−8.90806	+	10.6162i	−0.474128	+	0.565044i	0.474979	+	0.879997i	$0.342456\pi$
$354$	8.17935	−	3.28561i	0.434727	−	0.174628i
$355$	−2.66780	−	15.1298i	−0.141592	−	0.803008i
$356$	15.2585	+	19.4727i	0.808701	+	1.03205i
$357$	−0.608284	−	0.187781i	−0.0321938	−	0.00993842i
$358$	19.2900	−	6.65750i	1.01951	−	0.351860i
$359$	−9.49643	+	16.4483i	−0.501202	+	0.868108i	0.498797	+	0.866719i	$0.333775\pi$
$359$	−9.49643	+	16.4483i	−0.501202	+	0.868108i	−0.999999	+	0.00138897i	$0.999558\pi$
$360$	−17.5419	+	23.1200i	−0.924541	+	1.21853i
$361$	−11.4957	−	19.9112i	−0.605039	−	1.04796i
$362$	−21.8374	−	18.9556i	−1.14775	−	0.996284i
$363$	8.99452	−	0.446868i	0.472090	−	0.0234545i
$364$	−0.0970827	−	0.683699i	−0.00508852	−	0.0358355i
$365$	21.2237	−	17.8088i	1.11090	−	0.932156i
$366$	10.6819	+	17.1711i	0.558352	+	0.897550i
$367$	6.89218	+	18.9361i	0.359769	+	0.988456i	0.979109	+	0.203334i	$0.0651777\pi$
$367$	6.89218	+	18.9361i	0.359769	+	0.988456i	−0.619341	+	0.785122i	$0.712600\pi$
$368$	−17.6449	+	26.3213i	−0.919801	+	1.37209i
$369$	17.3967	−	25.4917i	0.905638	−	1.32704i
$370$	−8.56559	−	0.143400i	−0.445304	−	0.00745499i
$371$	−1.88561	−	0.332485i	−0.0978962	−	0.0172617i
$372$	17.3101	+	19.9650i	0.897487	+	1.03514i
$373$	−4.70270	+	12.9206i	−0.243496	+	0.669001i	0.756393	+	0.654118i	$0.226960\pi$
$373$	−4.70270	+	12.9206i	−0.243496	+	0.669001i	−0.999889	+	0.0148833i	$0.995262\pi$
$374$	−6.51409	−	8.03251i	−0.336836	−	0.415351i
$375$	−1.25298	+	9.98034i	−0.0647037	+	0.515383i
$376$	5.80613	−	6.25310i	0.299429	−	0.322479i
$377$		−	6.87469i		−	0.354065i
$378$	−1.00288	+	1.09728i	−0.0515824	+	0.0564377i
$379$	−23.0899			−1.18605			−0.593026	−	0.805184i	$-0.702067\pi$
$379$	−23.0899			−1.18605			−0.593026	+	0.805184i	$0.702067\pi$
$380$	42.1376	−	13.7579i	2.16161	−	0.705763i
$381$	7.46121	+	17.7112i	0.382249	+	0.907374i
$382$	18.5496	+	22.8735i	0.949081	+	1.17031i
$383$	1.72830	+	0.629049i	0.0883119	+	0.0321429i	0.385798	−	0.922583i	$-0.373926\pi$
$383$	1.72830	+	0.629049i	0.0883119	+	0.0321429i	−0.297486	+	0.954726i	$0.596148\pi$
$384$	−7.92961	+	17.9199i	−0.404656	+	0.914469i
$385$	0.483562	−	2.74241i	0.0246446	−	0.139766i
$386$	0.134836	−	8.05406i	0.00686296	−	0.409941i
$387$	6.47964	+	9.02120i	0.329379	+	0.458573i
$388$	−17.5347	−	0.587274i	−0.890190	−	0.0298143i
$389$	27.9217	−	10.1627i	1.41569	−	0.515268i	0.482894	−	0.875679i	$-0.339586\pi$
$389$	27.9217	−	10.1627i	1.41569	−	0.515268i	0.932794	+	0.360411i	$0.117364\pi$
$390$	−6.73854	+	12.6123i	−0.341219	+	0.638648i
$391$	9.25214	+	11.0263i	0.467901	+	0.557623i
$392$	11.8793	+	15.6943i	0.599995	+	0.792684i
$393$	−11.3654	−	5.82993i	−0.573308	−	0.294081i
$394$	−24.8494	+	28.6272i	−1.25189	+	1.44222i
$395$	−1.75521	+	1.01337i	−0.0883140	+	0.0509881i
$396$	−23.4550	+	5.74818i	−1.17866	+	0.288857i
$397$	−13.2935	−	7.67501i	−0.667182	−	0.385198i	0.127826	−	0.991797i	$-0.459200\pi$
$397$	−13.2935	−	7.67501i	−0.667182	−	0.385198i	−0.795008	+	0.606599i	$0.792533\pi$
$398$	−34.4063	+	11.8745i	−1.72463	+	0.595214i
$399$	2.21367	−	0.504732i	0.110822	−	0.0252682i
$400$	2.87654	+	26.6369i	0.143827	+	1.33185i
$401$	16.6682	−	2.93905i	0.832368	−	0.146769i	0.258804	−	0.965930i	$-0.416672\pi$
$401$	16.6682	−	2.93905i	0.832368	−	0.146769i	0.573564	+	0.819161i	$0.305560\pi$
$402$	−4.00366	−	0.570866i	−0.199684	−	0.0284722i
$403$	9.97375	+	8.36897i	0.496828	+	0.416888i
$404$	−10.9489	+	17.5777i	−0.544730	+	0.874525i
$405$	30.1772	−	6.07216i	1.49952	−	0.301728i
$406$	−0.559349	−	1.00740i	−0.0277600	−	0.0499963i
$407$	−5.46074	−	4.58210i	−0.270679	−	0.227126i
$408$	6.81529	+	5.72542i	0.337407	+	0.283451i
$409$	0.249722	+	1.41624i	0.0123480	+	0.0700287i	0.990359	−	0.138524i	$-0.0442358\pi$
$409$	0.249722	+	1.41624i	0.0123480	+	0.0700287i	−0.978011	+	0.208553i	$0.933125\pi$
$410$	−7.81914	−	49.1412i	−0.386160	−	2.42691i
$411$	−19.6006	+	4.46906i	−0.966826	+	0.220443i
$412$	−8.67269	+	9.65968i	−0.427273	+	0.475898i
$413$	0.363977	−	0.630426i	0.0179101	−	0.0310212i
$414$	32.5060	−	8.54561i	1.59758	−	0.419994i
$415$	36.9776	−	21.3490i	1.81516	−	1.04798i
$416$	−2.46570	+	9.33519i	−0.120891	+	0.457695i
$417$	6.23869	−	12.1623i	0.305510	−	0.595589i
$418$	34.4442	+	13.1937i	1.68472	+	0.645324i
$419$	−17.2769	−	20.5898i	−0.844029	−	1.00588i	−0.999836	−	0.0180876i	$-0.994242\pi$
$419$	−17.2769	−	20.5898i	−0.844029	−	1.00588i	0.155807	−	0.987788i	$-0.450202\pi$
$420$	0.0387340	+	2.39644i	0.00189003	+	0.116934i
$421$	−13.1300	−	36.0744i	−0.639917	−	1.75816i	−0.651986	−	0.758231i	$-0.726064\pi$
$421$	−13.1300	−	36.0744i	−0.639917	−	1.75816i	0.0120688	−	0.999927i	$-0.496158\pi$
$422$	2.87023	+	1.72182i	0.139720	+	0.0838169i
$423$	−9.00607	+	0.897096i	−0.437890	+	0.0436183i
$424$	22.4835	+	14.5326i	1.09189	+	0.705765i
$425$	11.9847	+	2.11323i	0.581345	+	0.102507i
$426$	−3.42103	+	10.4575i	−0.165749	+	0.506665i
$427$	1.56936	+	0.571201i	0.0759467	+	0.0276424i
$428$	1.68751	−	4.19396i	0.0815691	−	0.202723i
$429$	−10.9655	+	4.61943i	−0.529418	+	0.223028i
$430$	17.5815	+	3.40448i	0.847856	+	0.164179i
$431$	−7.70543			−0.371157			−0.185579	−	0.982629i	$-0.559416\pi$
$431$	−7.70543			−0.371157			−0.185579	+	0.982629i	$0.559416\pi$
$432$	18.8836	−	8.68397i	0.908536	−	0.417808i
$433$	−18.8564			−0.906183			−0.453091	−	0.891464i	$-0.649679\pi$
$433$	−18.8564			−0.906183			−0.453091	+	0.891464i	$0.649679\pi$
$434$	2.14245	+	0.414864i	0.102841	+	0.0199141i
$435$	−2.97221	+	23.6745i	−0.142507	+	1.13511i
$436$	2.24459	−	5.57845i	0.107496	−	0.267159i
$437$	−48.2399	−	17.5579i	−2.30763	−	0.839907i
$438$	−19.4168	+	4.08649i	−0.927769	+	0.195260i
$439$	16.3164	+	2.87702i	0.778738	+	0.137313i	0.548868	−	0.835909i	$-0.315059\pi$
$439$	16.3164	+	2.87702i	0.778738	+	0.137313i	0.229870	+	0.973221i	$0.426170\pi$
$440$	−21.1360	+	32.6996i	−1.00762	+	1.55889i
$441$	1.56953	−	20.8182i	0.0747397	−	0.991341i
$442$	3.76092	+	2.25614i	0.178889	+	0.107314i
$443$	−2.23622	−	6.14396i	−0.106246	−	0.291908i	0.875166	−	0.483824i	$-0.160752\pi$
$443$	−2.23622	−	6.14396i	−0.106246	−	0.291908i	−0.981411	+	0.191915i	$0.938530\pi$
$444$	5.36224	+	2.98140i	0.254481	+	0.141491i
$445$	−27.1939	−	32.4084i	−1.28911	−	1.53631i
$446$	26.4527	+	10.1326i	1.25257	+	0.479792i
$447$	12.1698	−	0.604620i	0.575610	−	0.0285975i
$448$	0.398228	+	1.56857i	0.0188145	+	0.0741079i
$449$	9.04053	−	5.21955i	0.426649	−	0.246326i	−0.271269	−	0.962504i	$-0.587443\pi$
$449$	9.04053	−	5.21955i	0.426649	−	0.246326i	0.697918	+	0.716178i	$0.254110\pi$
$450$	16.4091	−	23.2006i	0.773532	−	1.09369i
$451$	20.7026	−	35.8579i	0.974846	−	1.68848i
$452$	7.52456	−	8.38089i	0.353925	−	0.394204i
$453$	−3.20229	+	10.3733i	−0.150457	+	0.487380i
$454$	5.72507	+	35.9805i	0.268691	+	1.68865i
$455$	0.205066	+	1.16299i	0.00961366	+	0.0545218i
$456$	−31.2603	−	5.53067i	−1.46390	−	0.258997i
$457$	20.6728	+	17.3466i	0.967034	+	0.811438i	0.982083	−	0.188449i	$-0.0603460\pi$
$457$	20.6728	+	17.3466i	0.967034	+	0.811438i	−0.0150490	+	0.999887i	$0.504790\pi$
$458$	1.53196	+	2.75909i	0.0715840	+	0.128924i
$459$	−1.40080	−	9.33648i	−0.0653836	−	0.435790i
$460$	28.6511	−	45.9972i	1.33586	−	2.14463i
$461$	−3.79701	−	3.18607i	−0.176844	−	0.148390i	0.550069	−	0.835119i	$-0.314601\pi$
$461$	−3.79701	−	3.18607i	−0.176844	−	0.148390i	−0.726913	+	0.686729i	$0.759046\pi$
$462$	−1.23100	+	1.56911i	−0.0572711	+	0.0730015i
$463$	−2.96473	+	0.522762i	−0.137783	+	0.0242948i	−0.242114	−	0.970248i	$-0.577841\pi$
$463$	−2.96473	+	0.522762i	−0.137783	+	0.0242948i	0.104331	+	0.994543i	$0.466730\pi$
$464$	1.72977	+	16.0178i	0.0803028	+	0.743608i
$465$	−30.7285	−	33.1324i	−1.42500	−	1.53648i
$466$	11.4829	−	3.96305i	0.531935	−	0.183585i
$467$	−29.0602	−	16.7779i	−1.34475	−	0.776390i	−0.357247	−	0.934010i	$-0.616284\pi$
$467$	−29.0602	−	16.7779i	−1.34475	−	0.776390i	−0.987500	+	0.157620i	$0.949618\pi$
$468$	8.51309	−	5.69262i	0.393518	−	0.263141i
$469$	−0.289241	+	0.166993i	−0.0133559	+	0.00771104i
$470$	−9.56564	+	11.0199i	−0.441230	+	0.508309i
$471$	−7.24898	+	4.67957i	−0.334015	+	0.215623i
$472$	−8.11555	+	6.14279i	−0.373548	+	0.282745i
$473$	9.57848	+	11.4152i	0.440419	+	0.524871i
$474$	1.45072	−	0.0477481i	0.0666337	−	0.00219314i
$475$	−40.7858	+	14.8448i	−1.87138	+	0.681126i
$476$	0.734681	+	0.0246060i	0.0336741	+	0.00112782i
$477$	−7.67827	−	27.3374i	−0.351564	−	1.25169i
$478$	0.0346723	−	2.07106i	0.00158587	−	0.0947279i
$479$	2.69060	−	15.2592i	0.122937	−	0.697208i	−0.859575	−	0.511009i	$-0.829272\pi$
$479$	2.69060	−	15.2592i	0.122937	−	0.697208i	0.982512	−	0.186199i	$-0.0596170\pi$
$480$	12.5271	−	31.0817i	0.571784	−	1.41868i
$481$	2.84070	+	1.03393i	0.129525	+	0.0471432i
$482$	−1.79849	−	2.21771i	−0.0819188	−	0.101014i
$483$	1.67650	−	2.21225i	0.0762833	−	0.100661i
$484$	−9.88524	+	3.22751i	−0.449329	+	0.146705i
$485$	30.0031			1.36237
$486$	−21.1114	−	6.34895i	−0.957632	−	0.287994i
$487$			42.9742i			1.94735i	0.227945	+	0.973674i	$0.426799\pi$
$487$			42.9742i			1.94735i	−0.227945	+	0.973674i	$0.573201\pi$
$488$	−17.1119	−	15.8887i	−0.774618	−	0.719249i
$489$	−9.01471	−	6.83157i	−0.407659	−	0.308934i
$490$	−21.2020	−	26.1441i	−0.957807	−	1.18107i
$491$	−4.27635	+	11.7492i	−0.192989	+	0.530233i	−0.998013	−	0.0630092i	$-0.979930\pi$
$491$	−4.27635	+	11.7492i	−0.192989	+	0.530233i	0.805024	+	0.593243i	$0.202152\pi$
$492$	−11.6456	+	33.6800i	−0.525025	+	1.51841i
$493$	7.20689	+	1.27077i	0.324582	+	0.0572325i
$494$	−15.6397	−	0.261829i	−0.703661	−	0.0117802i
$495$	39.7592	−	11.1672i	1.78704	−	0.501927i
$496$	−25.3443	−	16.9899i	−1.13799	−	0.762869i
$497$	0.310783	+	0.853868i	0.0139405	+	0.0383012i
$498$	−30.5628	+	1.00593i	−1.36955	+	0.0450767i
$499$	0.451535	−	0.378883i	0.0202135	−	0.0169611i	−0.632625	−	0.774458i	$-0.718023\pi$
$499$	0.451535	−	0.378883i	0.0202135	−	0.0169611i	0.652838	+	0.757497i	$0.273578\pi$
$500$	−1.63287	−	11.4994i	−0.0730244	−	0.514270i
$501$	−11.5127	−	17.8340i	−0.514350	−	0.796763i
$502$	0.0241609	+	0.0209725i	0.00107835	+	0.000936047i
$503$	5.40120	+	9.35516i	0.240828	+	0.417126i	0.960950	−	0.276721i	$-0.0892478\pi$
$503$	5.40120	+	9.35516i	0.240828	+	0.417126i	−0.720123	+	0.693847i	$0.755914\pi$
$504$	0.784312	−	1.52683i	0.0349360	−	0.0680106i
$505$	17.7072	−	30.6698i	0.787961	−	1.36479i
$506$	42.6253	−	14.7111i	1.89492	−	0.653988i
$507$	−12.8096	+	11.8802i	−0.568894	+	0.527618i
$508$	−13.6876	−	17.4679i	−0.607288	−	0.775011i
$509$	4.10539	+	23.2828i	0.181968	+	1.03199i	0.929789	+	0.368093i	$0.119989\pi$
$509$	4.10539	+	23.2828i	0.181968	+	1.03199i	−0.747821	+	0.663901i	$0.768900\pi$
$510$	−11.9761	−	9.39550i	−0.530312	−	0.416040i
$511$	−1.05331	+	1.25529i	−0.0465958	+	0.0555307i
$512$	3.39612	−	22.3711i	0.150089	−	0.988673i
$513$	20.9760	+	26.3396i	0.926115	+	1.16292i
$514$	11.3066	+	20.3633i	0.498711	+	0.898187i
$515$	14.2700	−	17.0064i	0.628812	−	0.749389i
$516$	−9.95676	−	8.08414i	−0.438322	−	0.355884i
$517$	−11.9580	+	2.10852i	−0.525912	+	0.0927325i
$518$	0.500393	−	0.0796204i	0.0219860	−	0.00349832i
$519$	40.3856	+	12.4673i	1.77273	+	0.547253i
$520$	3.67988	−	16.0964i	0.161374	−	0.705875i
$521$	29.7943	+	17.2017i	1.30531	+	0.753622i	0.981310	−	0.192434i	$-0.0616382\pi$
$521$	29.7943	+	17.2017i	1.30531	+	0.753622i	0.324002	+	0.946056i	$0.394972\pi$
$522$	9.86742	−	13.9514i	0.431885	−	0.610637i
$523$	15.1865	+	26.3038i	0.664059	+	1.15018i	0.979539	+	0.201252i	$0.0645011\pi$
$523$	15.1865	+	26.3038i	0.664059	+	1.15018i	−0.315480	+	0.948932i	$0.602166\pi$
$524$	14.4315	+	3.04600i	0.630444	+	0.133065i
$525$	−0.116452	−	2.34393i	−0.00508236	−	0.102297i
$526$	2.99375	−	7.81566i	0.130534	−	0.340779i
$527$	−10.6170	+	8.90871i	−0.462483	+	0.388070i
$528$	24.3869	−	13.5222i	1.06130	−	0.588478i
$529$	−37.3617	+	13.5985i	−1.62442	+	0.591241i
$530$	−39.2596	−	23.5514i	−1.70533	−	1.02301i
$531$	10.7651	+	0.811606i	0.467164	+	0.0352207i
$532$	−2.31309	+	1.23413i	−0.100285	+	0.0535063i
$533$	−3.04907	+	17.2921i	−0.132070	+	0.749005i
$534$	6.24003	+	29.6492i	0.270032	+	1.28305i
$535$	−2.64415	+	7.26473i	−0.114316	+	0.314082i
$536$	4.63375	−	0.579024i	0.200148	−	0.0250100i
$537$	24.7982	+	3.11329i	1.07012	+	0.134348i
$538$	−6.92456	−	1.34087i	−0.298539	−	0.0578091i
$539$		−	28.0092i		−	1.20644i
$540$	−31.7778	+	15.9232i	−1.36750	+	0.685225i
$541$		−	4.15389i		−	0.178590i	−0.996005	−	0.0892948i	$-0.971539\pi$
$541$		−	4.15389i		−	0.178590i	0.996005	−	0.0892948i	$-0.0284613\pi$
$542$	1.89144	−	9.76782i	0.0812443	−	0.419564i
$543$	−13.7494	−	32.6379i	−0.590042	−	1.40063i
$544$	−9.33050	−	4.31043i	−0.400042	−	0.184808i
$545$	−3.51702	+	9.66293i	−0.150652	+	0.413914i
$546$	0.262965	−	0.803836i	0.0112539	−	0.0344010i
$547$	2.83365	−	16.0704i	0.121158	−	0.687122i	−0.862358	−	0.506300i	$-0.831013\pi$
$547$	2.83365	−	16.0704i	0.121158	−	0.687122i	0.983516	−	0.180823i	$-0.0578760\pi$
$548$	20.4809	−	10.9274i	0.874900	−	0.466795i
$549$	2.45494	+	24.6455i	0.104774	+	1.05184i
$550$	19.6124	−	32.6933i	0.836274	−	1.39404i
$551$	−24.5260	+	8.92675i	−1.04484	+	0.380292i
$552$	−33.6218	+	19.3856i	−1.43104	+	0.825108i
$553$	0.0918277	−	0.0770526i	0.00390491	−	0.00327661i
$554$	−30.1490	−	11.5484i	−1.28091	−	0.490646i
$555$	−9.33557	−	4.78872i	−0.396273	−	0.203270i
$556$	−3.25956	+	15.4434i	−0.138236	+	0.654945i
$557$	14.8098	+	25.6513i	0.627511	+	1.08688i	0.988049	+	0.154137i	$0.0492598\pi$
$557$	14.8098	+	25.6513i	0.627511	+	1.08688i	−0.360538	+	0.932745i	$0.617407\pi$
$558$	8.22840	+	31.2994i	0.348336	+	1.32501i
$559$	−5.47271	−	3.15967i	−0.231471	−	0.133640i
$560$	−0.770424	−	2.65813i	−0.0325563	−	0.112327i
$561$	−2.81571	−	12.3492i	−0.118879	−	0.521385i
$562$	−5.44738	−	34.2353i	−0.229784	−	1.44413i
$563$	22.0013	−	3.87943i	0.927246	−	0.163498i	0.310421	−	0.950599i	$-0.399530\pi$
$563$	22.0013	−	3.87943i	0.927246	−	0.163498i	0.616824	+	0.787101i	$0.288419\pi$
$564$	9.76147	−	3.73262i	0.411032	−	0.157172i
$565$	−12.3809	+	14.7550i	−0.520868	+	0.620746i
$566$	13.4198	−	7.45122i	0.564075	−	0.313198i
$567$	−1.69537	+	0.663621i	−0.0711987	+	0.0278695i
$568$	0.637766	−	12.6889i	0.0267601	−	0.532416i
$569$	−1.10991	+	1.32274i	−0.0465299	+	0.0554522i	−0.788807	−	0.614640i	$-0.789301\pi$
$569$	−1.10991	+	1.32274i	−0.0465299	+	0.0554522i	0.742278	+	0.670093i	$0.233746\pi$
$570$	53.7453	+	7.66333i	2.25114	+	0.320982i
$571$	2.73361	+	15.5031i	0.114398	+	0.648783i	0.987047	+	0.160434i	$0.0512894\pi$
$571$	2.73361	+	15.5031i	0.114398	+	0.648783i	−0.872649	+	0.488349i	$0.837599\pi$
$572$	10.8148	−	8.47434i	0.452190	−	0.354330i
$573$	8.01805	+	35.1659i	0.334959	+	1.46907i
$574$	0.960147	+	2.78202i	0.0400758	+	0.116119i
$575$	−26.5309	+	45.9528i	−1.10641	+	1.91637i
$576$	−18.4029	+	15.4056i	−0.766787	+	0.641902i
$577$	9.83883	+	17.0414i	0.409596	+	0.709441i	0.994844	−	0.101413i	$-0.0323364\pi$
$577$	9.83883	+	17.0414i	0.409596	+	0.709441i	−0.585248	+	0.810854i	$0.699003\pi$
$578$	12.6994	−	14.6301i	0.528226	−	0.608531i
$579$	4.50274	−	8.77806i	0.187128	−	0.364804i
$580$	−3.87336	−	27.2779i	−0.160833	−	1.13265i
$581$	−1.93457	+	1.62330i	−0.0802594	+	0.0673456i
$582$	−18.9521	−	10.1258i	−0.785592	−	0.419729i
$583$	−13.0294	−	35.7981i	−0.539624	−	1.48260i
$584$	20.3922	−	10.4454i	0.843834	−	0.432233i
$585$	−14.2243	+	10.2169i	−0.588104	+	0.422416i
$586$	0.388135	−	23.1842i	0.0160337	−	0.957731i
$587$	−1.96505	−	0.346492i	−0.0811063	−	0.0143012i	0.132948	−	0.991123i	$-0.457556\pi$
$587$	−1.96505	−	0.346492i	−0.0811063	−	0.0143012i	−0.214054	+	0.976822i	$0.568667\pi$
$588$	4.56926	+	23.6700i	0.188433	+	0.976133i
$589$	16.9061	−	46.4492i	0.696605	−	1.91391i
$590$	13.5191	−	10.9635i	0.556573	−	0.451362i
$591$	−42.7858	+	18.0244i	−1.75997	+	0.741425i
$592$	−6.87890	−	1.69427i	−0.282721	−	0.0696339i
$593$			21.4365i			0.880291i	0.897927	+	0.440145i	$0.145073\pi$
$593$			21.4365i			0.880291i	−0.897927	+	0.440145i	$0.854927\pi$
$594$	−28.8836	−	6.36442i	−1.18511	−	0.261135i
$595$	−1.25709			−0.0515358
$596$	−13.3749	+	4.36688i	−0.547858	+	0.178875i
$597$	−44.2307	−	5.55294i	−1.81024	−	0.227267i
$598$	−14.8525	+	12.0448i	−0.607362	+	0.492550i
$599$	−39.6839	−	14.4438i	−1.62144	−	0.590156i	−0.637785	−	0.770215i	$-0.720149\pi$
$599$	−39.6839	−	14.4438i	−1.62144	−	0.590156i	−0.983656	+	0.180059i	$0.942371\pi$
$600$	−11.2406	+	30.8278i	−0.458894	+	1.25854i
$601$	−3.07096	+	17.4163i	−0.125267	+	0.710424i	0.855882	+	0.517171i	$0.173015\pi$
$601$	−3.07096	+	17.4163i	−0.125267	+	0.710424i	−0.981149	+	0.193253i	$0.938096\pi$
$602$	−1.05904	−	0.0177297i	−0.0431631	−	0.000722609i
$603$	−4.09115	−	2.79200i	−0.166605	−	0.113699i
$604$	0.419615	−	12.5288i	0.0170739	−	0.509789i
$605$	16.7107	−	6.08218i	0.679385	−	0.247276i
$606$	−21.5360	+	13.3972i	−0.874839	+	0.544224i
$607$	25.0286	+	29.8279i	1.01588	+	1.21068i	0.977395	+	0.211420i	$0.0678087\pi$
$607$	25.0286	+	29.8279i	1.01588	+	1.21068i	0.0384848	+	0.999259i	$0.487747\pi$
$608$	36.5058	−	3.32511i	1.48050	−	0.134851i
$609$	−0.0700268	−	1.40950i	−0.00283763	−	0.0571156i
$610$	30.1564	+	26.1768i	1.22100	+	1.05987i
$611$	4.45944	−	2.57466i	0.180410	−	0.104160i
$612$	4.39407	+	9.97672i	0.177620	+	0.403285i
$613$	−2.98975	−	1.72613i	−0.120755	−	0.0697178i	0.438406	−	0.898777i	$-0.355543\pi$
$613$	−2.98975	−	1.72613i	−0.120755	−	0.0697178i	−0.559161	+	0.829059i	$0.688877\pi$
$614$	−6.72780	−	19.4937i	−0.271512	−	0.786704i
$615$	17.9762	−	58.2310i	0.724872	−	2.34810i
$616$	0.895268	−	2.12173i	0.0360714	−	0.0854871i
$617$	3.45250	−	0.608769i	0.138992	−	0.0245081i	−0.103719	−	0.994607i	$-0.533074\pi$
$617$	3.45250	−	0.608769i	0.138992	−	0.0245081i	0.242711	+	0.970099i	$0.421963\pi$
$618$	−14.7535	+	5.92641i	−0.593472	+	0.238395i
$619$	−5.42408	−	4.55134i	−0.218012	−	0.182934i	0.527241	−	0.849716i	$-0.323227\pi$
$619$	−5.42408	−	4.55134i	−0.218012	−	0.182934i	−0.745253	+	0.666782i	$0.767671\pi$
$620$	44.2898	+	27.5876i	1.77872	+	1.10794i
$621$	40.3427	+	8.18382i	1.61890	+	0.328405i
$622$	−29.1273	+	16.1727i	−1.16790	+	0.648466i
$623$	1.91682	+	1.60840i	0.0767956	+	0.0644391i
$624$	−7.75690	+	8.92573i	−0.310524	+	0.357315i
$625$	−2.36634	−	13.4202i	−0.0946535	−	0.536807i
$626$	−6.35052	+	1.01047i	−0.253818	+	0.0403864i
$627$	30.7188	+	33.1220i	1.22679	+	1.32276i
$628$	6.65598	−	7.41346i	0.265602	−	0.295829i
$629$	−1.60899	+	2.78685i	−0.0641546	+	0.111119i
$630$	−1.25311	+	2.65449i	−0.0499251	+	0.105758i
$631$	−6.49028	+	3.74717i	−0.258374	+	0.149172i	−0.623593	−	0.781749i	$-0.714328\pi$
$631$	−6.49028	+	3.74717i	−0.258374	+	0.149172i	0.365219	+	0.930922i	$0.380994\pi$
$632$	−1.60176	+	0.493460i	−0.0637147	+	0.0196288i
$633$	2.22329	+	3.44402i	0.0883677	+	0.136888i
$634$	−5.41706	+	14.1421i	−0.215139	+	0.561653i
$635$	24.3941	+	29.0718i	0.968051	+	1.15368i
$636$	16.8508	+	28.1266i	0.668176	+	1.11529i
$637$	4.06252	+	11.1617i	0.160963	+	0.442242i
$638$	11.7937	−	19.6597i	0.466916	−	0.778335i
$639$	−9.41353	+	9.64252i	−0.372393	+	0.381452i
$640$	−4.52391	+	38.4301i	−0.178823	+	1.51908i
$641$	21.3252	+	3.76021i	0.842295	+	0.148519i	0.578116	−	0.815955i	$-0.303788\pi$
$641$	21.3252	+	3.76021i	0.842295	+	0.148519i	0.264178	+	0.964474i	$0.414899\pi$
$642$	4.12202	−	3.69655i	0.162683	−	0.145891i
$643$	−22.2522	−	8.09915i	−0.877543	−	0.319399i	−0.136325	−	0.990664i	$-0.543529\pi$
$643$	−22.2522	−	8.09915i	−0.877543	−	0.319399i	−0.741218	+	0.671265i	$0.765751\pi$
$644$	−1.19642	+	2.97346i	−0.0471457	+	0.117171i
$645$	17.4804	+	13.2471i	0.688291	+	0.521604i
$646$	3.16543	−	16.3470i	0.124542	−	0.643163i
$647$	18.8024			0.739198			0.369599	−	0.929191i	$-0.379495\pi$
$647$	18.8024			0.739198			0.369599	+	0.929191i	$0.379495\pi$
$648$	25.4471	+	0.666533i	0.999657	+	0.0261839i
$649$	14.4836			0.568530
$650$	−3.07363	+	15.8729i	−0.120558	+	0.622586i
$651$	2.13013	+	1.61427i	0.0834864	+	0.0632681i
$652$	12.1166	+	4.87532i	0.474522	+	0.190932i
$653$	−10.1057	−	3.67818i	−0.395467	−	0.143938i	0.136629	−	0.990622i	$-0.456373\pi$
$653$	−10.1057	−	3.67818i	−0.395467	−	0.143938i	−0.532096	+	0.846684i	$0.678595\pi$
$654$	5.48276	−	4.91683i	0.214393	−	0.192263i
$655$	−24.8401	−	4.37998i	−0.970582	−	0.171140i
$656$	2.75328	−	41.0573i	0.107497	−	1.60302i
$657$	−23.5474	−	6.00719i	−0.918671	−	0.234363i
$658$	0.443990	−	0.740119i	0.0173085	−	0.0288528i
$659$	8.25777	+	22.6880i	0.321677	+	0.883800i	0.990143	+	0.140058i	$0.0447289\pi$
$659$	8.25777	+	22.6880i	0.321677	+	0.883800i	−0.668466	+	0.743742i	$0.733049\pi$
$660$	−40.9069	+	24.5075i	−1.59230	+	0.953954i
$661$	1.20921	+	1.44108i	0.0470329	+	0.0560516i	0.789048	−	0.614331i	$-0.210574\pi$
$661$	1.20921	+	1.44108i	0.0470329	+	0.0560516i	−0.742015	+	0.670383i	$0.766130\pi$
$662$	7.37403	−	19.2511i	0.286600	−	0.748213i
$663$	2.91322	+	4.51278i	0.113140	+	0.175262i
$664$	33.7450	−	10.3959i	1.30956	−	0.403439i
$665$	3.88279	−	2.24173i	0.150568	−	0.0869305i
$666$	4.28086	+	6.17558i	0.165880	+	0.239299i
$667$	−15.9540	+	27.6332i	−0.617743	+	1.06996i
$668$	18.2386	+	16.3751i	0.705674	+	0.633571i
$669$	23.5917	+	25.4373i	0.912107	+	0.983461i
$670$	−7.88665	+	1.25489i	−0.304688	+	0.0484807i
$671$	5.77005	+	32.7236i	0.222750	+	1.26328i
$672$	−0.410444	+	1.93908i	−0.0158332	+	0.0748016i
$673$	−20.7393	−	17.4023i	−0.799439	−	0.670809i	0.148623	−	0.988894i	$-0.452516\pi$
$673$	−20.7393	−	17.4023i	−0.799439	−	0.670809i	−0.948062	+	0.318085i	$0.896960\pi$
$674$	−31.1455	+	17.2933i	−1.19968	+	0.666113i
$675$	30.5765	−	16.6243i	1.17689	−	0.639870i
$676$	10.6659	−	17.1233i	0.410225	−	0.658587i
$677$	18.1567	+	15.2353i	0.697820	+	0.585540i	0.921153	−	0.389202i	$-0.127249\pi$
$677$	18.1567	+	15.2353i	0.697820	+	0.585540i	−0.223333	+	0.974742i	$0.571694\pi$
$678$	12.8003	−	5.14184i	0.491594	−	0.197471i
$679$	−1.74759	+	0.308148i	−0.0670665	+	0.0118256i
$680$	16.1940	+	6.83308i	0.621012	+	0.262037i
$681$	−13.1620	+	42.6359i	−0.504367	+	1.63381i
$682$	14.1650	+	41.0431i	0.542407	+	1.57162i
$683$	18.0209	+	10.4044i	0.689551	+	0.398113i	0.803444	−	0.595380i	$-0.202999\pi$
$683$	18.0209	+	10.4044i	0.689551	+	0.398113i	−0.113893	+	0.993493i	$0.536332\pi$
$684$	−31.3631	−	22.9793i	−1.19920	−	0.878637i
$685$	−34.3795	+	19.8490i	−1.31357	+	0.758392i
$686$	3.01577	+	2.61779i	0.115143	+	0.0999478i
$687$	0.191792	+	3.86037i	0.00731731	+	0.147282i
$688$	13.5463	+	5.98492i	0.516447	+	0.228173i
$689$	10.3845	+	12.3757i	0.395617	+	0.471478i
$690$	56.3551	−	35.0577i	2.14540	−	1.33462i
$691$	17.7551	−	6.46235i	0.675438	−	0.245839i	0.0185503	−	0.999828i	$-0.494095\pi$
$691$	17.7551	−	6.46235i	0.675438	−	0.245839i	0.656887	+	0.753989i	$0.271873\pi$
$692$	−48.7775	−	1.63366i	−1.85424	−	0.0621024i
$693$	−2.20116	+	1.05880i	−0.0836152	+	0.0402206i
$694$	12.5200	+	0.209601i	0.475251	+	0.00795635i
$695$	4.68707	−	26.5817i	0.177791	−	1.00830i
$696$	−6.75939	+	18.5379i	−0.256214	+	0.702678i
$697$	−17.5641	−	6.39281i	−0.665288	−	0.242145i
$698$	−33.5308	+	27.1924i	−1.26916	+	1.02925i
$699$	14.7618	+	1.85327i	0.558341	+	0.0700969i
$700$	0.841074	+	2.57605i	0.0317896	+	0.0973654i
$701$	7.59328			0.286794			0.143397	−	0.989665i	$-0.454197\pi$
$701$	7.59328			0.286794			0.143397	+	0.989665i	$0.454197\pi$
$702$	12.4332	−	1.65312i	0.469262	−	0.0623929i
$703$		−	11.4770i		−	0.432864i
$704$	−23.0659	+	22.4661i	−0.869329	+	0.846723i
$705$	−16.4702	+	6.93840i	−0.620303	+	0.261315i
$706$	15.2224	−	12.3448i	0.572901	−	0.464603i
$707$	−0.716398	+	1.96829i	−0.0269429	+	0.0740251i
$708$	−12.2397	+	2.36276i	−0.459998	+	0.0887981i
$709$	−47.1054	−	8.30595i	−1.76908	−	0.311937i	−0.808202	−	0.588906i	$-0.799559\pi$
$709$	−47.1054	−	8.30595i	−1.76908	−	0.311937i	−0.960879	+	0.276969i	$0.910670\pi$
$710$	−0.363687	+	21.7239i	−0.0136489	+	0.815282i
$711$	1.62007	+	0.731884i	0.0607575	+	0.0274478i
$712$	−15.9500	−	31.1387i	−0.597751	−	1.16697i
$713$	−20.6682	−	56.7855i	−0.774032	−	2.12663i
$714$	0.794070	+	0.424259i	0.0297173	+	0.0158775i
$715$	−17.9991	+	15.1030i	−0.673128	+	0.564821i
$716$	−28.5726	+	4.05721i	−1.06781	+	0.151625i
$717$	1.15786	−	2.25723i	0.0432409	−	0.0842978i
$718$	17.6073	−	20.2840i	0.657097	−	0.756994i
$719$	3.52716	+	6.10922i	0.131541	+	0.227835i	0.924271	−	0.381738i	$-0.124674\pi$
$719$	3.52716	+	6.10922i	0.131541	+	0.227835i	−0.792730	+	0.609573i	$0.791341\pi$
$720$	30.5715	−	27.3841i	1.13933	−	1.02054i
$721$	−0.656522	+	1.13713i	−0.0244502	+	0.0423489i
$722$	10.6077	+	30.7359i	0.394779	+	1.14387i
$723$	−0.777393	−	3.40952i	−0.0289116	−	0.126801i
$724$	25.2232	+	32.1894i	0.937413	+	1.19631i
$725$	4.68461	+	26.5677i	0.173982	+	0.986701i
$726$	−12.6083	−	1.79777i	−0.467940	−	0.0667216i
$727$	−18.2911	+	21.7985i	−0.678380	+	0.808462i	−0.989898	−	0.141778i	$-0.954718\pi$
$727$	−18.2911	+	21.7985i	−0.678380	+	0.808462i	0.311518	+	0.950240i	$0.399163\pi$
$728$	−0.0490234	+	0.975364i	−0.00181693	+	0.0361494i
$729$	−19.7676	−	18.3914i	−0.732132	−	0.681163i
$730$	−34.2555	+	19.0201i	−1.26785	+	0.703965i
$731$	4.32397	−	5.15310i	0.159928	−	0.190594i
$732$	−10.2145	−	26.7127i	−0.377538	−	0.987329i
$733$	14.2179	−	2.50701i	0.525152	−	0.0925984i	0.0952137	−	0.995457i	$-0.469647\pi$
$733$	14.2179	−	2.50701i	0.525152	−	0.0925984i	0.429938	+	0.902858i	$0.358535\pi$
$734$	−4.47821	−	28.1443i	−0.165294	−	1.03883i
$735$	−9.16451	−	40.1941i	−0.338038	−	1.48258i
$736$	31.5751	−	31.8012i	1.16387	−	1.17221i
$737$	−5.75483	−	3.32255i	−0.211982	−	0.122388i
$738$	−31.0076	+	30.7160i	−1.14140	+	1.13067i
$739$	−7.63499	−	13.2242i	−0.280858	−	0.486460i	0.690738	−	0.723105i	$-0.257286\pi$
$739$	−7.63499	−	13.2242i	−0.280858	−	0.486460i	−0.971596	+	0.236645i	$0.923952\pi$
$740$	11.8541	+	2.50199i	0.435765	+	0.0919751i
$741$	−17.0455	−	8.74359i	−0.626184	−	0.321204i
$742$	2.52864	+	0.968585i	0.0928293	+	0.0355579i
$743$	9.41012	−	7.89602i	0.345224	−	0.289677i	−0.453645	−	0.891182i	$-0.649877\pi$
$743$	9.41012	−	7.89602i	0.345224	−	0.289677i	0.798869	+	0.601505i	$0.205432\pi$
$744$	−18.6661	−	32.3738i	−0.684331	−	1.18688i
$745$	22.6098	−	8.22931i	0.828360	−	0.301498i
$746$	10.0031	−	16.6749i	0.366239	−	0.610510i
$747$	−34.1307	−	15.4189i	−1.24878	−	0.564147i
$748$	6.88474	+	12.9039i	0.251731	+	0.471812i
$749$	0.0794011	−	0.450306i	0.00290125	−	0.0164538i
$750$	4.42292	−	13.5201i	0.161502	−	0.493683i
$751$	8.22636	−	22.6017i	0.300184	−	0.824749i	−0.694283	−	0.719702i	$-0.744278\pi$
$751$	8.22636	−	22.6017i	0.300184	−	0.824749i	0.994467	−	0.105047i	$-0.0334993\pi$
$752$	−9.74254	+	7.12094i	−0.355274	+	0.259674i
$753$	0.0152123	+	0.0361106i	0.000554367	+	0.00131594i
$754$	−1.84829	+	9.54498i	−0.0673107	+	0.347608i
$755$			21.4376i			0.780196i
$756$	1.68742	−	1.25385i	0.0613710	−	0.0456022i
$757$		−	2.57077i		−	0.0934361i	−0.998908	−	0.0467180i	$-0.985124\pi$
$757$		−	2.57077i		−	0.0934361i	0.998908	−	0.0467180i	$-0.0148762\pi$
$758$	32.0586	+	6.20783i	1.16442	+	0.225478i
$759$	54.7966	+	6.87944i	1.98899	+	0.249708i
$760$	−62.2037	+	7.77284i	−2.25636	+	0.281951i
$761$	−8.41063	+	23.1080i	−0.304885	+	0.837665i	0.688748	+	0.725001i	$0.258161\pi$
$761$	−8.41063	+	23.1080i	−0.304885	+	0.837665i	−0.993633	+	0.112664i	$0.964062\pi$
$762$	−5.59758	−	26.5966i	−0.202779	−	0.963495i
$763$	0.105613	−	0.598958i	0.00382343	−	0.0216837i
$764$	−19.6051	−	36.7452i	−0.709287	−	1.32939i
$765$	−8.08125	−	16.8002i	−0.292178	−	0.607414i
$766$	−2.23049	−	1.33805i	−0.0805908	−	0.0483456i
$767$	−5.77171	+	2.10073i	−0.208404	+	0.0758530i
$768$	15.8275	−	22.7484i	0.571125	−	0.820863i
$769$	17.5940	−	14.7631i	0.634455	−	0.532371i	−0.267855	−	0.963459i	$-0.586315\pi$
$769$	17.5940	−	14.7631i	0.634455	−	0.532371i	0.902310	+	0.431088i	$0.141870\pi$
$770$	−1.40870	+	3.67762i	−0.0507659	+	0.132532i
$771$	1.41551	+	28.4912i	0.0509782	+	1.02609i
$772$	−2.35257	+	11.1462i	−0.0846710	+	0.401160i
$773$	−1.98617	−	3.44015i	−0.0714375	−	0.123733i	0.828094	−	0.560589i	$-0.189425\pi$
$773$	−1.98617	−	3.44015i	−0.0714375	−	0.123733i	−0.899532	+	0.436856i	$0.856092\pi$
$774$	−6.57109	−	14.2673i	−0.236193	−	0.512828i
$775$	−44.2471	−	25.5461i	−1.58940	−	0.917642i
$776$	24.1877	+	5.52966i	0.868287	+	0.198503i
$777$	0.592952	+	0.183048i	0.0212720	+	0.00656680i
$778$	−41.4994	+	6.60322i	−1.48783	+	0.236737i
$779$	65.6503	−	11.5759i	2.35217	−	0.414751i
$780$	12.7468	−	15.6995i	0.456409	−	0.562132i
$781$	−11.6210	+	13.8494i	−0.415833	+	0.495571i
$782$	−9.88143	−	17.7966i	−0.353359	−	0.636405i
$783$	18.3868	−	9.99683i	0.657091	−	0.357258i
$784$	−12.2740	−	24.9842i	−0.438357	−	0.892292i
$785$	−10.9517	+	13.0518i	−0.390884	+	0.465837i
$786$	14.2126	+	11.1500i	0.506946	+	0.397709i
$787$	2.43923	+	13.8335i	0.0869490	+	0.493112i	0.996919	+	0.0784382i	$0.0249933\pi$
$787$	2.43923	+	13.8335i	0.0869490	+	0.493112i	−0.909970	+	0.414674i	$0.863896\pi$
$788$	42.1980	−	33.0657i	1.50324	−	1.17792i
$789$	7.51564	−	6.97035i	0.267564	−	0.248151i
$790$	2.70942	−	0.935090i	0.0963967	−	0.0332690i
$791$	0.569609	−	0.986591i	0.0202529	−	0.0350791i
$792$	34.1109	−	1.67494i	1.21208	−	0.0595163i
$793$	−7.04567	−	12.2035i	−0.250199	−	0.433358i
$794$	16.3936	+	14.2302i	0.581785	+	0.505010i
$795$	−30.4106	−	47.1081i	−1.07855	−	1.67075i
$796$	50.9629	−	7.23655i	1.80633	−	0.256493i
$797$	18.0786	−	15.1698i	0.640378	−	0.537341i	−0.263756	−	0.964589i	$-0.584961\pi$
$797$	18.0786	−	15.1698i	0.640378	−	0.537341i	0.904134	+	0.427248i	$0.140517\pi$
$798$	−3.20921	+	0.105626i	−0.113605	+	0.00373913i
$799$	1.87476	+	5.15085i	0.0663241	+	0.182224i
$800$	3.16760	−	37.7567i	0.111991	−	1.33490i
$801$	−9.17293	+	35.9566i	−0.324109	+	1.27046i
$802$	−23.9326	−	0.400665i	−0.845090	−	0.0141480i
$803$	−32.1080	−	5.66151i	−1.13307	−	0.199790i
$804$	5.40529	+	1.86900i	0.190630	+	0.0659147i
$805$	1.87466	−	5.15060i	0.0660732	−	0.181535i
$806$	−11.5977	−	14.3011i	−0.408513	−	0.503736i
$807$	−6.88474	−	5.21743i	−0.242354	−	0.183662i
$808$	19.9276	−	21.4617i	0.701050	−	0.755018i
$809$			30.1592i			1.06034i	0.847891	+	0.530170i	$0.177872\pi$
$809$			30.1592i			1.06034i	−0.847891	+	0.530170i	$0.822128\pi$
$810$	−43.5312	+	0.317466i	−1.52953	+	0.0111546i
$811$	−19.2303			−0.675266			−0.337633	−	0.941278i	$-0.609626\pi$
$811$	−19.2303			−0.675266			−0.337633	+	0.941278i	$0.609626\pi$
$812$	0.505770	+	1.54908i	0.0177491	+	0.0543619i
$813$	7.35973	−	9.71165i	0.258117	−	0.340602i
$814$	6.34990	+	7.83004i	0.222564	+	0.274443i
$815$	−20.9882	−	7.63909i	−0.735185	−	0.267586i
$816$	−7.92319	−	9.78162i	−0.277367	−	0.342425i
$817$	−4.16611	+	23.6272i	−0.145754	+	0.826610i
$818$	0.0340433	−	2.03348i	0.00119029	−	0.0710991i
$819$	0.723592	−	0.741194i	0.0252844	−	0.0258994i
$820$	−2.35553	+	70.3309i	−0.0822587	+	2.45606i
$821$	4.28889	−	1.56103i	0.149683	−	0.0544802i	−0.266092	−	0.963948i	$-0.585733\pi$
$821$	4.28889	−	1.56103i	0.149683	−	0.0544802i	0.415775	+	0.909467i	$0.363510\pi$
$822$	28.4154	−	0.935250i	0.991102	−	0.0326206i
$823$	−9.86833	−	11.7606i	−0.343988	−	0.409949i	0.566118	−	0.824324i	$-0.308445\pi$
$823$	−9.86833	−	11.7606i	−0.343988	−	0.409949i	−0.910106	+	0.414375i	$0.864000\pi$
$824$	14.6384	−	11.0800i	0.509953	−	0.385991i
$825$	39.2291	−	25.3243i	1.36578	−	0.881679i
$826$	−0.674846	+	0.777441i	−0.0234809	+	0.0270506i
$827$	30.5131	−	17.6168i	1.06104	−	0.612594i	0.135324	−	0.990801i	$-0.456793\pi$
$827$	30.5131	−	17.6168i	1.06104	−	0.612594i	0.925721	+	0.378207i	$0.123459\pi$
$828$	−47.4297	+	3.12553i	−1.64829	+	0.108620i
$829$	32.1764	+	18.5771i	1.11753	+	0.645208i	0.940770	−	0.339045i	$-0.110104\pi$
$829$	32.1764	+	18.5771i	1.11753	+	0.645208i	0.176763	+	0.984253i	$0.443437\pi$
$830$	−57.0803	+	19.6999i	−1.98129	+	0.683793i
$831$	−26.8882	−	28.9917i	−0.932741	−	1.00571i
$832$	5.93323	−	12.2983i	0.205698	−	0.426366i
$833$	−12.4520	+	2.19562i	−0.431435	+	0.0760737i
$834$	−11.9318	+	15.2091i	−0.413165	+	0.526647i
$835$	−32.1100	−	26.9435i	−1.11121	−	0.932418i
$836$	−44.2759	−	27.5789i	−1.53131	−	0.953835i
$837$	−7.88004	+	38.8452i	−0.272374	+	1.34269i
$838$	18.4519	+	33.2322i	0.637411	+	1.14799i
$839$	−12.7067	−	10.6622i	−0.438683	−	0.368099i	0.396533	−	0.918020i	$-0.370213\pi$
$839$	−12.7067	−	10.6622i	−0.438683	−	0.368099i	−0.835216	+	0.549921i	$0.814658\pi$
$840$	0.590513	−	3.33768i	0.0203746	−	0.115161i
$841$	−2.21876	−	12.5832i	−0.0765090	−	0.433904i
$842$	8.53125	+	53.6166i	0.294006	+	1.84775i
$843$	12.5236	−	40.5679i	0.431334	−	1.39723i
$844$	−3.52217	−	3.16229i	−0.121238	−	0.108850i
$845$	−17.2494	+	29.8769i	−0.593398	+	1.02779i
$846$	12.7454	+	1.17577i	0.438196	+	0.0404238i
$847$	−0.910879	+	0.525896i	−0.0312982	+	0.0180700i
$848$	−27.3094	−	26.2222i	−0.937808	−	0.900473i
$849$	18.7762	−	0.932843i	0.644398	−	0.0320151i
$850$	−16.0717	−	6.15621i	−0.551256	−	0.211156i
$851$	−9.01893	−	10.7483i	−0.309165	−	0.368449i
$852$	7.56136	−	13.5996i	0.259048	−	0.465915i
$853$	−6.77920	−	18.6257i	−0.232115	−	0.637732i	0.767880	−	0.640593i	$-0.221311\pi$
$853$	−6.77920	−	18.6257i	−0.232115	−	0.637732i	−0.999996	+	0.00286126i	$0.999089\pi$
$854$	−2.02537	−	1.21500i	−0.0693067	−	0.0415764i
$855$	54.9198	+	37.4799i	1.87822	+	1.28179i
$856$	−3.47055	+	5.36930i	−0.118621	+	0.183519i
$857$	−17.6147	−	3.10595i	−0.601708	−	0.106097i	−0.135507	−	0.990776i	$-0.543266\pi$
$857$	−17.6147	−	3.10595i	−0.601708	−	0.106097i	−0.466201	+	0.884679i	$0.654377\pi$
$858$	16.4667	−	3.46561i	0.562163	−	0.118314i
$859$	7.25730	+	2.64144i	0.247616	+	0.0901249i	0.462847	−	0.886438i	$-0.346828\pi$
$859$	7.25730	+	2.64144i	0.247616	+	0.0901249i	−0.215231	+	0.976563i	$0.569050\pi$
$860$	−23.4953	−	9.45373i	−0.801182	−	0.322369i
$861$	−0.449000	+	3.57641i	−0.0153019	+	0.121884i
$862$	10.6984	+	2.07164i	0.364389	+	0.0705602i
$863$	8.69446			0.295963			0.147981	−	0.988990i	$-0.452722\pi$
$863$	8.69446			0.295963			0.147981	+	0.988990i	$0.452722\pi$
$864$	−28.5531	+	6.98009i	−0.971395	+	0.237468i
$865$	83.4618			2.83779
$866$	26.1807	+	5.06963i	0.889657	+	0.172273i
$867$	21.8660	−	9.21148i	0.742607	−	0.312838i
$868$	−2.86309	−	1.15201i	−0.0971796	−	0.0391019i
$869$	2.24118	+	0.815725i	0.0760270	+	0.0276716i
$870$	10.4917	−	32.0711i	0.355701	−	1.08731i
$871$	2.77521	+	0.489344i	0.0940344	+	0.0165808i
$872$	−4.61622	+	7.14178i	−0.156325	+	0.241851i
$873$	−15.3526	−	21.3745i	−0.519608	−	0.723418i
$874$	62.2568	+	37.3472i	2.10587	+	1.26329i
$875$	−0.401800	−	1.10394i	−0.0135833	−	0.0373198i
$876$	28.0573	−	0.453496i	0.947970	−	0.0153222i
$877$	27.2022	+	32.4183i	0.918553	+	1.09469i	0.995223	+	0.0976318i	$0.0311268\pi$
$877$	27.2022	+	32.4183i	0.918553	+	1.09469i	−0.0766700	+	0.997057i	$0.524429\pi$
$878$	−21.8805	−	8.38124i	−0.738432	−	0.282853i
$879$	12.9615	−	25.2683i	0.437180	−	0.852279i
$880$	38.1372	−	39.7184i	1.28560	−	1.33891i
$881$	23.5185	−	13.5784i	0.792359	−	0.457468i	−0.0484336	−	0.998826i	$-0.515423\pi$
$881$	23.5185	−	13.5784i	0.792359	−	0.457468i	0.840792	+	0.541358i	$0.182090\pi$
$882$	−7.77622	+	28.4824i	−0.261839	+	0.959053i
$883$	4.48989	−	7.77672i	0.151097	−	0.261707i	−0.780534	−	0.625113i	$-0.785053\pi$
$883$	4.48989	−	7.77672i	0.151097	−	0.261707i	0.931631	+	0.363406i	$0.118386\pi$
$884$	−4.61517	−	4.14361i	−0.155225	−	0.139365i
$885$	20.7844	−	4.73897i	0.698659	−	0.159299i
$886$	1.45299	+	9.13163i	0.0488141	+	0.306783i
$887$	1.66173	+	9.42413i	0.0557954	+	0.316431i	0.999913	−	0.0131769i	$-0.00419445\pi$
$887$	1.66173	+	9.42413i	0.0557954	+	0.316431i	−0.944118	+	0.329608i	$0.893083\pi$
$888$	−6.64350	−	5.58110i	−0.222941	−	0.187290i
$889$	−1.71947	−	1.44280i	−0.0576691	−	0.0483901i
$890$	29.0435	+	52.3078i	0.973540	+	1.75336i
$891$	−28.3004	−	22.6106i	−0.948100	−	0.757482i
$892$	−34.0033	−	21.1802i	−1.13852	−	0.709166i
$893$	−14.9759	−	12.5663i	−0.501149	−	0.420514i
$894$	−17.0593	−	2.43242i	−0.570549	−	0.0813523i
$895$	48.6028	−	8.56999i	1.62461	−	0.286463i
$896$	−0.131193	−	2.28490i	−0.00438285	−	0.0763332i
$897$	−22.8343	+	5.20637i	−0.762414	+	0.173836i
$898$	−13.9554	+	4.81636i	−0.465697	+	0.160724i
$899$	−26.6075	−	15.3618i	−0.887409	−	0.512346i
$900$	−29.0203	+	27.8006i	−0.967345	+	0.926686i
$901$	−14.8933	+	8.59864i	−0.496167	+	0.286462i
$902$	−38.3845	+	44.2199i	−1.27806	+	1.47236i
$903$	−1.15424	−	0.592071i	−0.0384106	−	0.0197029i
$904$	−12.7005	+	9.61320i	−0.422412	+	0.319730i
$905$	−44.9530	−	53.5729i	−1.49429	−	1.78082i
$906$	7.23504	−	13.5416i	0.240368	−	0.449888i
$907$	22.4084	−	8.15601i	0.744060	−	0.270816i	0.0579560	−	0.998319i	$-0.481542\pi$
$907$	22.4084	−	8.15601i	0.744060	−	0.270816i	0.686104	+	0.727503i	$0.259319\pi$
$908$	1.72469	−	51.4954i	0.0572358	−	1.70893i
$909$	−30.9103	+	3.07898i	−1.02523	+	0.102123i
$910$	0.0279556	−	1.66985i	0.000926720	−	0.0553551i
$911$	−4.55164	+	25.8136i	−0.150802	+	0.855243i	0.811721	+	0.584045i	$0.198531\pi$
$911$	−4.55164	+	25.8136i	−0.150802	+	0.855243i	−0.962524	+	0.271198i	$0.912580\pi$
$912$	41.9156	+	16.0834i	1.38796	+	0.532574i
$913$	−47.2159	−	17.1852i	−1.56262	−	0.568746i
$914$	−24.0389	−	29.6423i	−0.795137	−	0.980481i
$915$	18.9872	+	45.0714i	0.627698	+	1.49001i
$916$	−1.38522	−	4.24266i	−0.0457690	−	0.140181i
$917$	1.49185			0.0492651
$918$	−0.565252	+	13.3396i	−0.0186561	+	0.440272i
$919$			28.4248i			0.937649i	0.883291	+	0.468824i	$0.155322\pi$
$919$			28.4248i			0.937649i	−0.883291	+	0.468824i	$0.844678\pi$
$920$	−52.1463	+	56.1606i	−1.71921	+	1.85156i
$921$	3.14616	−	25.0600i	0.103670	−	0.825756i
$922$	4.41527	+	5.44446i	0.145409	+	0.179304i
$923$	2.62224	−	7.20454i	0.0863120	−	0.237140i
$924$	2.13100	−	1.84763i	0.0701049	−	0.0607824i
$925$	−11.6827	−	2.05997i	−0.384123	−	0.0677313i
$926$	4.25685	+	0.0712654i	0.139889	+	0.00234193i
$927$	−19.4175	−	1.46393i	−0.637753	−	0.0480819i
$928$	1.90480	−	22.7046i	0.0625281	−	0.745314i
$929$	0.817461	+	2.24596i	0.0268200	+	0.0736874i	0.952380	−	0.304913i	$-0.0986275\pi$
$929$	0.817461	+	2.24596i	0.0268200	+	0.0736874i	−0.925560	+	0.378601i	$0.876405\pi$
$930$	33.7564	+	54.2633i	1.10692	+	1.77936i
$931$	34.5451	−	28.9868i	1.13217	−	0.950003i
$932$	−17.0086	+	2.41516i	−0.557135	+	0.0791112i
$933$	−40.7533	+	2.02471i	−1.33420	+	0.0662861i
$934$	35.8370	+	31.1078i	1.17262	+	1.01788i
$935$	−12.5057	−	21.6606i	−0.408982	−	0.708377i
$936$	−13.3503	+	5.61498i	−0.436367	+	0.183531i
$937$	−25.1607	+	43.5796i	−0.821965	+	1.42368i	0.0822523	+	0.996612i	$0.473789\pi$
$937$	−25.1607	+	43.5796i	−0.821965	+	1.42368i	−0.904217	+	0.427073i	$0.859545\pi$
$938$	0.446486	−	0.154094i	0.0145783	−	0.00503134i
$939$	−7.52519	−	2.32307i	−0.245575	−	0.0758105i
$940$	16.2439	−	12.7285i	0.529817	−	0.415157i
$941$	−7.57703	−	42.9715i	−0.247004	−	1.40083i	−0.815792	−	0.578346i	$-0.803698\pi$
$941$	−7.57703	−	42.9715i	−0.247004	−	1.40083i	0.568787	−	0.822485i	$-0.307413\pi$
$942$	11.3228	−	4.54831i	0.368916	−	0.148192i
$943$	52.3856	−	62.4307i	1.70591	−	2.03302i
$944$	12.9193	−	6.34688i	0.420488	−	0.206573i
$945$	−2.81230	+	2.23962i	−0.0914840	+	0.0728550i
$946$	−10.2300	−	18.4243i	−0.332605	−	0.599026i
$947$	−19.4528	+	23.1830i	−0.632132	+	0.753345i	−0.983105	−	0.183040i	$-0.941406\pi$
$947$	−19.4528	+	23.1830i	−0.632132	+	0.753345i	0.350974	+	0.936385i	$0.385851\pi$
$948$	−2.02705	−	0.323737i	−0.0658354	−	0.0105145i
$949$	13.6162	−	2.40091i	0.442001	−	0.0779367i
$950$	60.6190	−	9.64544i	1.96674	−	0.312939i
$951$	−13.5992	+	12.6125i	−0.440984	+	0.408989i
$952$	−1.01343	−	0.231686i	−0.0328455	−	0.00750897i
$953$	27.2578	+	15.7373i	0.882965	+	0.509780i	0.871635	−	0.490156i	$-0.163060\pi$
$953$	27.2578	+	15.7373i	0.882965	+	0.509780i	0.0113304	+	0.999936i	$0.496393\pi$
$954$	3.31091	+	40.0202i	0.107195	+	1.29570i
$955$	35.6115	+	61.6810i	1.15236	+	1.99595i
$956$	−0.604952	+	2.86618i	−0.0195655	+	0.0926989i
$957$	23.5899	−	15.2285i	0.762555	−	0.492267i
$958$	−7.83818	+	20.4628i	−0.253240	+	0.661122i
$959$	1.79864	−	1.50924i	0.0580812	−	0.0487359i
$960$	−25.7494	+	39.7866i	−0.831059	+	1.28411i
$961$	25.5472	−	9.29843i	0.824104	−	0.299949i
$962$	−3.66612	−	2.19927i	−0.118201	−	0.0709073i
$963$	6.52848	−	1.83366i	0.210377	−	0.0590888i
$964$	1.90082	+	3.56265i	0.0612213	+	0.114745i
$965$	3.38287	−	19.1852i	0.108899	−	0.617594i
$966$	−2.92246	+	2.62080i	−0.0940286	+	0.0843229i
$967$	2.57740	−	7.08136i	0.0828837	−	0.227721i	−0.891327	−	0.453361i	$-0.850225\pi$
$967$	2.57740	−	7.08136i	0.0828837	−	0.227721i	0.974211	+	0.225640i	$0.0724472\pi$
$968$	14.5926	−	1.82346i	0.469025	−	0.0586084i
$969$	12.3169	−	16.2530i	0.395676	−	0.522121i
$970$	−41.6570	−	8.06647i	−1.33753	−	0.258999i
$971$		−	15.5087i		−	0.497696i	−0.968543	−	0.248848i	$-0.919948\pi$
$971$		−	15.5087i		−	0.497696i	0.968543	−	0.248848i	$-0.0800520\pi$
$972$	27.6046	+	14.4909i	0.885418	+	0.464796i
$973$			1.59644i			0.0511796i
$974$	11.5538	−	59.6664i	0.370207	−	1.91183i
$975$	−11.9597	+	15.7816i	−0.383017	+	0.505416i
$976$	19.4868	+	26.6609i	0.623756	+	0.853394i
$977$	−7.54941	+	20.7418i	−0.241527	+	0.663590i	0.758403	+	0.651786i	$0.225980\pi$
$977$	−7.54941	+	20.7418i	−0.241527	+	0.663590i	−0.999930	+	0.0118046i	$0.996242\pi$
$978$	10.6795	+	11.9088i	0.341494	+	0.380800i
$979$	−8.64507	+	49.0287i	−0.276298	+	1.56696i
$980$	22.4083	+	41.9992i	0.715808	+	1.34162i
$981$	8.68362	−	2.43897i	0.277247	−	0.0778704i
$982$	9.09620	−	15.1631i	0.290272	−	0.483875i
$983$	13.7881	−	5.01845i	0.439771	−	0.160064i	−0.112639	−	0.993636i	$-0.535930\pi$
$983$	13.7881	−	5.01845i	0.439771	−	0.160064i	0.552410	+	0.833572i	$0.313708\pi$
$984$	25.2241	−	43.6311i	0.804114	−	1.39091i
$985$	−70.2301	+	58.9300i	−2.23772	+	1.87767i
$986$	−9.66455	−	3.70196i	−0.307782	−	0.117895i
$987$	0.888079	−	0.573299i	0.0282679	−	0.0182483i
$988$	21.6441	+	4.56831i	0.688589	+	0.145337i
$989$	14.6652	+	25.4010i	0.466328	+	0.807703i
$990$	−58.2049	+	4.81534i	−1.84987	+	0.153042i
$991$	10.0032	+	5.77533i	0.317761	+	0.183460i	0.650394	−	0.759597i	$-0.274604\pi$
$991$	10.0032	+	5.77533i	0.317761	+	0.183460i	−0.332633	+	0.943056i	$0.607937\pi$
$992$	30.6208	+	30.4031i	0.972210	+	0.965298i
$993$	18.5121	−	17.1689i	0.587463	−	0.544840i
$994$	−0.201932	−	1.26909i	−0.00640488	−	0.0402529i
$995$	−86.6893	+	15.2857i	−2.74824	+	0.484588i
$996$	42.7046	+	6.82029i	1.35315	+	0.216109i
$997$	27.6917	−	33.0016i	0.877004	−	1.04517i	−0.121612	−	0.992578i	$-0.538806\pi$
$997$	27.6917	−	33.0016i	0.877004	−	1.04517i	0.998616	−	0.0525950i	$-0.0167492\pi$
$998$	−0.728786	+	0.404653i	−0.0230693	+	0.0128091i
$999$	1.36549	+	9.10114i	0.0432022	+	0.287947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.3	✓	192
3.2	odd	2		648.2.v.b.35.30		192
4.3	odd	2		864.2.bh.b.335.25		192
8.3	odd	2	inner	216.2.v.b.11.20	yes	192
8.5	even	2		864.2.bh.b.335.26		192
24.11	even	2		648.2.v.b.35.13		192
27.5	odd	18	inner	216.2.v.b.59.20	yes	192
27.22	even	9		648.2.v.b.611.13		192
108.59	even	18		864.2.bh.b.815.26		192
216.5	odd	18		864.2.bh.b.815.25		192
216.59	even	18	inner	216.2.v.b.59.3	yes	192
216.211	odd	18		648.2.v.b.611.30		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.3	✓	192	1.1	even	1	trivial
216.2.v.b.11.20	yes	192	8.3	odd	2	inner
216.2.v.b.59.3	yes	192	216.59	even	18	inner
216.2.v.b.59.20	yes	192	27.5	odd	18	inner
648.2.v.b.35.13		192	24.11	even	2
648.2.v.b.35.30		192	3.2	odd	2
648.2.v.b.611.13		192	27.22	even	9
648.2.v.b.611.30		192	216.211	odd	18
864.2.bh.b.335.25		192	4.3	odd	2
864.2.bh.b.335.26		192	8.5	even	2
864.2.bh.b.815.25		192	216.5	odd	18
864.2.bh.b.815.26		192	108.59	even	18

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.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38842 - 0.268854i) q^{2} +(-1.38044 - 1.04613i) q^{3} +(1.85543 + 0.746566i) q^{4} +(-3.21396 - 1.16979i) q^{5} +(1.63538 + 1.82361i) q^{6} +(0.199218 + 0.0351275i) q^{7} +(-2.37541 - 1.53539i) q^{8} +(0.811221 + 2.88824i) q^{9} +O(q^{10})\)	\(q+(-1.38842 - 0.268854i) q^{2} +(-1.38044 - 1.04613i) q^{3} +(1.85543 + 0.746566i) q^{4} +(-3.21396 - 1.16979i) q^{5} +(1.63538 + 1.82361i) q^{6} +(0.199218 + 0.0351275i) q^{7} +(-2.37541 - 1.53539i) q^{8} +(0.811221 + 2.88824i) q^{9} +(4.14784 + 2.48825i) q^{10} +(1.37658 + 3.78212i) q^{11} +(-1.78031 - 2.97162i) q^{12} +(-1.09713 - 1.30751i) q^{13} +(-0.267155 - 0.102332i) q^{14} +(3.21293 + 4.97704i) q^{15} +(2.88528 + 2.77041i) q^{16} +(1.57350 - 0.908459i) q^{17} +(-0.349802 - 4.22820i) q^{18} +(-3.24004 + 5.61192i) q^{19} +(-5.08997 - 4.56990i) q^{20} +(-0.238260 - 0.256900i) q^{21} +(-0.894435 - 5.62128i) q^{22} +(1.37566 + 7.80173i) q^{23} +(1.67289 + 4.60450i) q^{24} +(5.13093 + 4.30536i) q^{25} +(1.17176 + 2.11035i) q^{26} +(1.90163 - 4.83568i) q^{27} +(0.343411 + 0.213906i) q^{28} +(3.08543 + 2.58898i) q^{29} +(-3.12280 - 7.77405i) q^{30} +(-7.51214 + 1.32459i) q^{31} +(-3.26115 - 4.62222i) q^{32} +(2.05631 - 6.66106i) q^{33} +(-2.42892 + 0.838284i) q^{34} +(-0.599188 - 0.345941i) q^{35} +(-0.651094 + 5.96457i) q^{36} +(-1.53384 + 0.885560i) q^{37} +(6.00733 - 6.92061i) q^{38} +(0.146696 + 2.95269i) q^{39} +(5.83840 + 7.71341i) q^{40} +(-6.61260 - 7.88059i) q^{41} +(0.261737 + 0.420742i) q^{42} +(3.47909 - 1.26628i) q^{43} +(-0.269450 + 8.04518i) q^{44} +(0.771390 - 10.2316i) q^{45} +(0.187536 - 11.2020i) q^{46} +(-0.523875 + 2.97105i) q^{47} +(-1.08474 - 6.84276i) q^{48} +(-6.53939 - 2.38014i) q^{49} +(-5.96638 - 7.35713i) q^{50} +(-3.12248 - 0.392012i) q^{51} +(-1.05952 - 3.24509i) q^{52} -9.46508 q^{53} +(-3.94036 + 6.20270i) q^{54} -13.7659i q^{55} +(-0.419290 - 0.389320i) q^{56} +(10.3435 - 4.35740i) q^{57} +(-3.58782 - 4.42413i) q^{58} +(1.23077 - 3.38152i) q^{59} +(2.24568 + 11.6332i) q^{60} +(8.13039 + 1.43361i) q^{61} +(10.7861 + 0.180575i) q^{62} +(0.0601532 + 0.603885i) q^{63} +(3.28515 + 7.29437i) q^{64} +(1.99664 + 5.48571i) q^{65} +(-4.64588 + 8.69553i) q^{66} +(-1.26475 + 1.06125i) q^{67} +(3.59775 - 0.510867i) q^{68} +(6.26262 - 12.2089i) q^{69} +(0.738918 + 0.641406i) q^{70} +(2.24594 + 3.89008i) q^{71} +(2.50759 - 8.10629i) q^{72} +(-4.05026 + 7.01525i) q^{73} +(2.36770 - 0.817154i) q^{74} +(-2.57896 - 11.3109i) q^{75} +(-10.2014 + 7.99364i) q^{76} +(0.141383 + 0.801822i) q^{77} +(0.590166 - 4.13902i) q^{78} +(0.380899 - 0.453938i) q^{79} +(-6.03238 - 12.2792i) q^{80} +(-7.68384 + 4.68600i) q^{81} +(7.06236 + 12.7194i) q^{82} +(-8.02454 + 9.56328i) q^{83} +(-0.250284 - 0.654537i) q^{84} +(-6.11986 + 1.07910i) q^{85} +(-5.17089 + 0.822771i) q^{86} +(-1.55083 - 6.80168i) q^{87} +(2.53709 - 11.0977i) q^{88} +(10.7122 + 6.18471i) q^{89} +(-3.82183 + 13.9985i) q^{90} +(-0.172639 - 0.299020i) q^{91} +(-3.27207 + 15.5026i) q^{92} +(11.7557 + 6.03016i) q^{93} +(1.52614 - 3.98422i) q^{94} +(16.9781 - 14.2463i) q^{95} +(-0.333631 + 9.79228i) q^{96} +(-8.24324 + 3.00029i) q^{97} +(8.43953 + 5.06279i) q^{98} +(-9.80695 + 7.04402i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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