LMFDB - Embedded newform 288.2.bf.a.11.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [288,2,Mod(11,288)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("288.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(288, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 15, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.484847 + 1.32850i) q^{2} +(0.622180 + 1.61644i) q^{3} +(-1.52985 - 1.28824i) q^{4} +(-0.0345958 - 0.262781i) q^{5} +(-2.44912 + 0.0428399i) q^{6} +(0.779563 + 2.90937i) q^{7} +(2.45318 - 1.40781i) q^{8} +(-2.22579 + 2.01144i) q^{9} +(0.365879 + 0.0814479i) q^{10} +(-0.904502 + 0.694049i) q^{11} +(1.13053 - 3.27443i) q^{12} +(-2.05487 + 2.67796i) q^{13} +(-4.24308 - 0.374946i) q^{14} +(0.403246 - 0.219419i) q^{15} +(0.680862 + 3.94163i) q^{16} -6.62015 q^{17} +(-1.59304 - 3.93220i) q^{18} +(5.15825 - 2.13662i) q^{19} +(-0.285599 + 0.446582i) q^{20} +(-4.21781 + 3.07027i) q^{21} +(-0.483502 - 1.53814i) q^{22} +(-1.36994 - 0.367075i) q^{23} +(3.80196 + 3.08952i) q^{24} +(4.76177 - 1.27591i) q^{25} +(-2.56139 - 4.02831i) q^{26} +(-4.63621 - 2.34638i) q^{27} +(2.55536 - 5.45516i) q^{28} +(5.03525 + 0.662903i) q^{29} +(0.0959865 + 0.642099i) q^{30} +(2.63335 - 1.52037i) q^{31} +(-5.56658 - 1.00656i) q^{32} +(-1.68465 - 1.03025i) q^{33} +(3.20976 - 8.79490i) q^{34} +(0.737557 - 0.305506i) q^{35} +(5.99633 - 0.209840i) q^{36} +(-2.21656 + 5.35125i) q^{37} +(0.337543 + 7.88870i) q^{38} +(-5.60728 - 1.65542i) q^{39} +(-0.454814 - 0.595944i) q^{40} +(1.95155 - 7.28329i) q^{41} +(-2.03388 - 7.09198i) q^{42} +(4.35237 + 5.67212i) q^{43} +(2.27785 + 0.103430i) q^{44} +(0.605570 + 0.515307i) q^{45} +(1.15187 - 1.64200i) q^{46} +(2.30774 + 1.33237i) q^{47} +(-5.94780 + 3.55298i) q^{48} +(-1.79453 + 1.03607i) q^{49} +(-0.613675 + 6.94466i) q^{50} +(-4.11892 - 10.7011i) q^{51} +(6.59351 - 1.44970i) q^{52} +(-4.56045 + 11.0099i) q^{53} +(5.36503 - 5.02159i) q^{54} +(0.213675 + 0.213675i) q^{55} +(6.00824 + 6.03972i) q^{56} +(6.66309 + 7.00867i) q^{57} +(-3.32200 + 6.36794i) q^{58} +(5.08348 - 0.669253i) q^{59} +(-0.899570 - 0.183801i) q^{60} +(-1.61461 + 12.2642i) q^{61} +(0.743041 + 4.23557i) q^{62} +(-7.58715 - 4.90759i) q^{63} +(4.03616 - 6.90720i) q^{64} +(0.774808 + 0.447335i) q^{65} +(2.18550 - 1.73855i) q^{66} +(4.48367 - 5.84323i) q^{67} +(10.1278 + 8.52836i) q^{68} +(-0.258994 - 2.44282i) q^{69} +(0.0482638 + 1.12797i) q^{70} +(3.28684 + 3.28684i) q^{71} +(-2.62853 + 8.06789i) q^{72} +(2.26326 - 2.26326i) q^{73} +(-6.03447 - 5.53925i) q^{74} +(5.02512 + 6.90329i) q^{75} +(-10.6438 - 3.37638i) q^{76} +(-2.72436 - 2.09048i) q^{77} +(4.91790 - 6.64667i) q^{78} +(7.66807 - 13.2815i) q^{79} +(1.01223 - 0.315281i) q^{80} +(0.908239 - 8.95406i) q^{81} +(8.72967 + 6.12392i) q^{82} +(1.17203 + 0.154301i) q^{83} +(10.4078 + 0.736513i) q^{84} +(0.229029 + 1.73965i) q^{85} +(-9.64568 + 3.03203i) q^{86} +(2.06128 + 8.55165i) q^{87} +(-1.24182 + 2.97599i) q^{88} +(7.53778 - 7.53778i) q^{89} +(-0.978196 + 0.554658i) q^{90} +(-9.39309 - 3.89075i) q^{91} +(1.62292 + 2.32638i) q^{92} +(4.09601 + 3.31073i) q^{93} +(-2.88896 + 2.41984i) q^{94} +(-0.739916 - 1.28157i) q^{95} +(-1.83637 - 9.62433i) q^{96} +(-0.177831 + 0.308013i) q^{97} +(-0.506355 - 2.88638i) q^{98} +(0.617192 - 3.36415i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21}+ \cdots - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.484847	+	1.32850i	−0.342839	+	0.939394i
$2$	−0.484847	+	1.32850i	−0.342839	+	0.939394i
$3$	0.622180	+	1.61644i	0.359216	+	0.933255i
$3$	0.622180	+	1.61644i	0.359216	+	0.933255i
$4$	−1.52985	−	1.28824i	−0.764923	−	0.644121i
$5$	−0.0345958	−	0.262781i	−0.0154717	−	0.117519i	0.981966	−	0.189056i	$-0.0605429\pi$
$5$	−0.0345958	−	0.262781i	−0.0154717	−	0.117519i	−0.997438	+	0.0715371i	$0.977210\pi$
$6$	−2.44912	+	0.0428399i	−0.999847	+	0.0174893i
$7$	0.779563	+	2.90937i	0.294647	+	1.09964i	0.941497	+	0.337021i	$0.109419\pi$
$7$	0.779563	+	2.90937i	0.294647	+	1.09964i	−0.646850	+	0.762617i	$0.723914\pi$
$8$	2.45318	−	1.40781i	0.867329	−	0.497735i
$9$	−2.22579	+	2.01144i	−0.741928	+	0.670479i
$10$	0.365879	+	0.0814479i	0.115701	+	0.0257561i
$11$	−0.904502	+	0.694049i	−0.272718	+	0.209264i	−0.736061	−	0.676915i	$-0.763316\pi$
$11$	−0.904502	+	0.694049i	−0.272718	+	0.209264i	0.463343	+	0.886179i	$0.346650\pi$
$12$	1.13053	−	3.27443i	0.326357	−	0.945247i
$13$	−2.05487	+	2.67796i	−0.569919	+	0.742734i	−0.986028	−	0.166582i	$-0.946727\pi$
$13$	−2.05487	+	2.67796i	−0.569919	+	0.742734i	0.416108	+	0.909315i	$0.363394\pi$
$14$	−4.24308	−	0.374946i	−1.13401	−	0.100209i
$15$	0.403246	−	0.219419i	0.104118	−	0.0566538i
$16$	0.680862	+	3.94163i	0.170215	+	0.985407i
$17$	−6.62015			−1.60562			−0.802812	−	0.596233i	$-0.796664\pi$
$17$	−6.62015			−1.60562			−0.802812	+	0.596233i	$0.796664\pi$
$18$	−1.59304	−	3.93220i	−0.375483	−	0.926829i
$19$	5.15825	−	2.13662i	1.18338	−	0.490174i	0.297789	−	0.954632i	$-0.403751\pi$
$19$	5.15825	−	2.13662i	1.18338	−	0.490174i	0.885595	+	0.464458i	$0.153751\pi$
$20$	−0.285599	+	0.446582i	−0.0638620	+	0.0998588i
$21$	−4.21781	+	3.07027i	−0.920401	+	0.669988i
$22$	−0.483502	−	1.53814i	−0.103083	−	0.327933i
$23$	−1.36994	−	0.367075i	−0.285653	−	0.0765404i	0.113148	−	0.993578i	$-0.463907\pi$
$23$	−1.36994	−	0.367075i	−0.285653	−	0.0765404i	−0.398800	+	0.917038i	$0.630573\pi$
$24$	3.80196	+	3.08952i	0.776072	+	0.630645i
$25$	4.76177	−	1.27591i	0.952354	−	0.255183i
$26$	−2.56139	−	4.02831i	−0.502329	−	0.790017i
$27$	−4.63621	−	2.34638i	−0.892240	−	0.451562i
$28$	2.55536	−	5.45516i	0.482918	−	1.03093i
$29$	5.03525	+	0.662903i	0.935022	+	0.123098i	0.582615	−	0.812749i	$-0.302030\pi$
$29$	5.03525	+	0.662903i	0.935022	+	0.123098i	0.352408	+	0.935847i	$0.385363\pi$
$30$	0.0959865	+	0.642099i	0.0175247	+	0.117231i
$31$	2.63335	−	1.52037i	0.472964	−	0.273066i	−0.244515	−	0.969645i	$-0.578629\pi$
$31$	2.63335	−	1.52037i	0.472964	−	0.273066i	0.717480	+	0.696579i	$0.245296\pi$
$32$	−5.56658	−	1.00656i	−0.984042	−	0.177936i
$33$	−1.68465	−	1.03025i	−0.293261	−	0.179344i
$34$	3.20976	−	8.79490i	0.550470	−	1.50831i
$35$	0.737557	−	0.305506i	0.124670	−	0.0516400i
$36$	5.99633	−	0.209840i	0.999388	−	0.0349733i
$37$	−2.21656	+	5.35125i	−0.364401	+	0.879741i	0.630245	+	0.776396i	$0.282954\pi$
$37$	−2.21656	+	5.35125i	−0.364401	+	0.879741i	−0.994646	+	0.103344i	$0.967046\pi$
$38$	0.337543	+	7.88870i	0.0547567	+	1.27972i
$39$	−5.60728	−	1.65542i	−0.897883	−	0.265079i
$40$	−0.454814	−	0.595944i	−0.0719125	−	0.0942270i
$41$	1.95155	−	7.28329i	0.304781	−	1.13746i	−0.628353	−	0.777929i	$-0.716271\pi$
$41$	1.95155	−	7.28329i	0.304781	−	1.13746i	0.933134	−	0.359530i	$-0.117063\pi$
$42$	−2.03388	−	7.09198i	−0.313834	−	1.09432i
$43$	4.35237	+	5.67212i	0.663731	+	0.864991i	0.996965	−	0.0778532i	$-0.0248066\pi$
$43$	4.35237	+	5.67212i	0.663731	+	0.864991i	−0.333234	+	0.942844i	$0.608140\pi$
$44$	2.27785	+	0.103430i	0.343399	+	0.0155926i
$45$	0.605570	+	0.515307i	0.0902731	+	0.0768174i
$46$	1.15187	−	1.64200i	0.169834	−	0.242099i
$47$	2.30774	+	1.33237i	0.336618	+	0.194347i	0.658776	−	0.752339i	$-0.271075\pi$
$47$	2.30774	+	1.33237i	0.336618	+	0.194347i	−0.322157	+	0.946686i	$0.604408\pi$
$48$	−5.94780	+	3.55298i	−0.858491	+	0.512828i
$49$	−1.79453	+	1.03607i	−0.256362	+	0.148011i
$50$	−0.613675	+	6.94466i	−0.0867868	+	0.982123i
$51$	−4.11892	−	10.7011i	−0.576765	−	1.49846i
$52$	6.59351	−	1.44970i	0.914355	−	0.201037i
$53$	−4.56045	+	11.0099i	−0.626426	+	1.51233i	0.217608	+	0.976036i	$0.430174\pi$
$53$	−4.56045	+	11.0099i	−0.626426	+	1.51233i	−0.844034	+	0.536290i	$0.819826\pi$
$54$	5.36503	−	5.02159i	0.730089	−	0.683352i
$55$	0.213675	+	0.213675i	0.0288119	+	0.0288119i
$56$	6.00824	+	6.03972i	0.802884	+	0.807092i
$57$	6.66309	+	7.00867i	0.882547	+	0.928321i
$58$	−3.32200	+	6.36794i	−0.436199	+	0.836152i
$59$	5.08348	−	0.669253i	0.661813	−	0.0871294i	0.207865	−	0.978157i	$-0.433348\pi$
$59$	5.08348	−	0.669253i	0.661813	−	0.0871294i	0.453948	+	0.891028i	$0.350015\pi$
$60$	−0.899570	−	0.183801i	−0.116134	−	0.0237286i
$61$	−1.61461	+	12.2642i	−0.206730	+	1.57027i	0.502047	+	0.864840i	$0.332580\pi$
$61$	−1.61461	+	12.2642i	−0.206730	+	1.57027i	−0.708778	+	0.705432i	$0.750753\pi$
$62$	0.743041	+	4.23557i	0.0943663	+	0.537918i
$63$	−7.58715	−	4.90759i	−0.955892	−	0.618298i
$64$	4.03616	−	6.90720i	0.504520	−	0.863400i
$65$	0.774808	+	0.447335i	0.0961031	+	0.0554851i
$66$	2.18550	−	1.73855i	0.269016	−	0.214001i
$67$	4.48367	−	5.84323i	0.547767	−	0.713864i	−0.434643	−	0.900603i	$-0.643125\pi$
$67$	4.48367	−	5.84323i	0.547767	−	0.713864i	0.982410	+	0.186739i	$0.0597919\pi$
$68$	10.1278	+	8.52836i	1.22818	+	1.03422i
$69$	−0.258994	−	2.44282i	−0.0311792	−	0.294081i
$70$	0.0482638	+	1.12797i	0.00576863	+	0.134818i
$71$	3.28684	+	3.28684i	0.390076	+	0.390076i	0.874714	−	0.484639i	$-0.161049\pi$
$71$	3.28684	+	3.28684i	0.390076	+	0.390076i	−0.484639	+	0.874714i	$0.661049\pi$
$72$	−2.62853	+	8.06789i	−0.309775	+	0.950810i
$73$	2.26326	−	2.26326i	0.264894	−	0.264894i	−0.562145	−	0.827039i	$-0.690024\pi$
$73$	2.26326	−	2.26326i	0.264894	−	0.264894i	0.827039	+	0.562145i	$0.190024\pi$
$74$	−6.03447	−	5.53925i	−0.701493	−	0.643925i
$75$	5.02512	+	6.90329i	0.580251	+	0.797124i
$76$	−10.6438	−	3.37638i	−1.22093	−	0.387298i
$77$	−2.72436	−	2.09048i	−0.310470	−	0.238232i
$78$	4.91790	−	6.64667i	0.556842	−	0.752587i
$79$	7.66807	−	13.2815i	0.862726	−	1.49428i	−0.00656230	−	0.999978i	$-0.502089\pi$
$79$	7.66807	−	13.2815i	0.862726	−	1.49428i	0.869288	−	0.494306i	$-0.164578\pi$
$80$	1.01223	−	0.315281i	0.113171	−	0.0352495i
$81$	0.908239	−	8.95406i	0.100915	−	0.994895i
$82$	8.72967	+	6.12392i	0.964031	+	0.676274i
$83$	1.17203	+	0.154301i	0.128647	+	0.0169367i	0.194575	−	0.980888i	$-0.437667\pi$
$83$	1.17203	+	0.154301i	0.128647	+	0.0169367i	−0.0659276	+	0.997824i	$0.521001\pi$
$84$	10.4078	+	0.736513i	1.13559	+	0.0803602i
$85$	0.229029	+	1.73965i	0.0248417	+	0.188692i
$86$	−9.64568	+	3.03203i	−1.04012	+	0.326953i
$87$	2.06128	+	8.55165i	0.220993	+	0.916833i
$88$	−1.24182	+	2.97599i	−0.132378	+	0.317242i
$89$	7.53778	−	7.53778i	0.799003	−	0.799003i	−0.183935	−	0.982938i	$-0.558884\pi$
$89$	7.53778	−	7.53778i	0.799003	−	0.799003i	0.982938	+	0.183935i	$0.0588836\pi$
$90$	−0.978196	+	0.554658i	−0.103111	+	0.0584660i
$91$	−9.39309	−	3.89075i	−0.984663	−	0.407861i
$92$	1.62292	+	2.32638i	0.169201	+	0.242542i
$93$	4.09601	+	3.31073i	0.424736	+	0.343307i
$94$	−2.88896	+	2.41984i	−0.297974	+	0.249588i
$95$	−0.739916	−	1.28157i	−0.0759138	−	0.131487i
$96$	−1.83637	−	9.62433i	−0.187423	−	0.982279i
$97$	−0.177831	+	0.308013i	−0.0180560	+	0.0312740i	−0.874912	−	0.484282i	$-0.839081\pi$
$97$	−0.177831	+	0.308013i	−0.0180560	+	0.0312740i	0.856856	+	0.515555i	$0.172414\pi$
$98$	−0.506355	−	2.88638i	−0.0511496	−	0.291569i
$99$	0.617192	−	3.36415i	0.0620301	−	0.338110i
$100$	−8.92847	−	4.18237i	−0.892847	−	0.418237i
$101$	6.60978	−	5.07186i	0.657698	−	0.504669i	−0.225153	−	0.974323i	$-0.572288\pi$
$101$	6.60978	−	5.07186i	0.657698	−	0.504669i	0.882850	+	0.469654i	$0.155621\pi$
$102$	16.2135	−	0.283607i	1.60538	−	0.0280812i
$103$	−0.263483	−	0.0706001i	−0.0259618	−	0.00695644i	0.245815	−	0.969317i	$-0.420944\pi$
$103$	−0.263483	−	0.0706001i	−0.0259618	−	0.00695644i	−0.271777	+	0.962360i	$0.587611\pi$
$104$	−1.27091	+	9.46239i	−0.124623	+	0.927863i
$105$	0.952727	+	1.00214i	0.0929766	+	0.0977989i
$106$	−12.4156	−	11.3967i	−1.20591	−	1.10694i
$107$	6.64771	+	2.75357i	0.642659	+	0.266198i	0.680121	−	0.733100i	$-0.261927\pi$
$107$	6.64771	+	2.75357i	0.642659	+	0.266198i	−0.0374621	+	0.999298i	$0.511927\pi$
$108$	4.06999	+	9.56218i	0.391635	+	0.920121i
$109$	1.54546	+	3.73107i	0.148028	+	0.357372i	0.980449	−	0.196772i	$-0.0630459\pi$
$109$	1.54546	+	3.73107i	0.148028	+	0.357372i	−0.832421	+	0.554144i	$0.813046\pi$
$110$	−0.387467	+	0.180268i	−0.0369436	+	0.0171879i
$111$	−10.0291	−	0.253508i	−0.951920	−	0.0240619i
$112$	−10.9369	+	5.05363i	−1.03344	+	0.477523i
$113$	−8.65034	−	14.9828i	−0.813756	−	1.40947i	−0.910218	−	0.414129i	$-0.864086\pi$
$113$	−8.65034	−	14.9828i	−0.813756	−	1.40947i	0.0964624	−	0.995337i	$-0.469247\pi$
$114$	−12.5416	+	5.45380i	−1.17463	+	0.510796i
$115$	−0.0490661	+	0.372694i	−0.00457543	+	0.0347539i
$116$	−6.84918	−	7.50076i	−0.635930	−	0.696428i
$117$	−0.812849	−	10.0938i	−0.0751479	−	0.933174i
$118$	−1.57561	+	7.07792i	−0.145046	+	0.651575i
$119$	−5.16083	−	19.2605i	−0.473092	−	1.76560i
$120$	0.680334	−	1.10597i	0.0621057	−	0.100960i
$121$	−2.51059	+	9.36965i	−0.228235	+	0.851786i
$122$	−15.5102	−	8.09129i	−1.40423	−	0.732551i
$123$	12.9872	−	1.37694i	1.17102	−	0.124154i
$124$	−5.98723	−	1.06647i	−0.537669	−	0.0957718i
$125$	−1.00717	−	2.43153i	−0.0900841	−	0.217482i
$126$	10.1984	−	7.70014i	0.908542	−	0.685983i
$127$			0.469475i			0.0416592i	0.999783	+	0.0208296i	$0.00663074\pi$
$127$			0.469475i			0.0416592i	−0.999783	+	0.0208296i	$0.993369\pi$
$128$	7.21933	+	8.71099i	0.638104	+	0.769950i
$129$	−6.46072	+	10.5645i	−0.568834	+	0.930148i
$130$	−0.969950	+	0.812446i	−0.0850703	+	0.0712562i
$131$	7.31034	+	5.60942i	0.638707	+	0.490097i	0.876616	−	0.481190i	$-0.159795\pi$
$131$	7.31034	+	5.60942i	0.638707	+	0.490097i	−0.237909	+	0.971287i	$0.576462\pi$
$132$	1.25005	+	3.74638i	0.108802	+	0.326080i
$133$	10.2374	+	13.3416i	0.887695	+	1.15687i
$134$	5.58886	+	8.78964i	0.482804	+	0.759309i
$135$	−0.456191	+	1.29948i	−0.0392627	+	0.111842i
$136$	−16.2404	+	9.31990i	−1.39260	+	0.799175i
$137$	−20.4598	+	5.48217i	−1.74799	+	0.468374i	−0.984196	−	0.177081i	$-0.943335\pi$
$137$	−20.4598	+	5.48217i	−1.74799	+	0.468374i	−0.763798	+	0.645455i	$0.776668\pi$
$138$	3.37087	+	0.840320i	0.286947	+	0.0715328i
$139$	6.59649	−	0.868444i	0.559507	−	0.0736605i	0.154531	−	0.987988i	$-0.450613\pi$
$139$	6.59649	−	0.868444i	0.559507	−	0.0736605i	0.404976	+	0.914327i	$0.367280\pi$
$140$	−1.52192	−	0.482775i	−0.128625	−	0.0408019i
$141$	−0.717880	+	4.55931i	−0.0604564	+	0.383963i
$142$	−5.96019	+	2.77296i	−0.500168	+	0.232702i
$143$		−	3.84841i		−	0.321820i
$144$	−9.44379	−	7.40371i	−0.786982	−	0.616975i
$145$		−	1.34610i		−	0.111788i
$146$	1.90941	+	4.10408i	0.158024	+	0.339656i
$147$	−2.79128	−	2.25614i	−0.230221	−	0.186083i
$148$	10.2847	−	5.33113i	0.845398	−	0.438216i
$149$	4.02528	−	0.529938i	0.329764	−	0.0434142i	0.0361734	−	0.999346i	$-0.488483\pi$
$149$	4.02528	−	0.529938i	0.329764	−	0.0434142i	0.293590	+	0.955931i	$0.405150\pi$
$150$	−11.6075	+	3.32885i	−0.947746	+	0.271800i
$151$	−18.3805	+	4.92505i	−1.49579	+	0.400795i	−0.911687	−	0.410886i	$-0.865219\pi$
$151$	−18.3805	+	4.92505i	−1.49579	+	0.400795i	−0.584101	+	0.811681i	$0.698553\pi$
$152$	9.64617	−	12.5033i	0.782407	−	1.01415i
$153$	14.7350	−	13.3160i	1.19126	−	1.07654i
$154$	4.09811	−	2.60576i	0.330235	−	0.209979i
$155$	−0.490627	−	0.639397i	−0.0394081	−	0.0513576i
$156$	6.44570	+	9.75607i	0.516069	+	0.781111i
$157$	−16.3433	−	12.5406i	−1.30434	−	1.00085i	−0.998815	−	0.0486661i	$-0.984503\pi$
$157$	−16.3433	−	12.5406i	−1.30434	−	1.00085i	−0.305520	−	0.952186i	$-0.598830\pi$
$158$	13.9267	+	16.6266i	1.10795	+	1.32274i
$159$	−20.6343	−	0.521579i	−1.63641	−	0.0413639i
$160$	−0.0719242	+	1.49761i	−0.00568611	+	0.118397i
$161$		−	4.27182i		−	0.336667i
$162$	11.4551	+	5.54795i	0.900001	+	0.435888i
$163$	−7.29151	−	17.6033i	−0.571115	−	1.37879i	−0.900607	−	0.434635i	$-0.856877\pi$
$163$	−7.29151	−	17.6033i	−0.571115	−	1.37879i	0.329492	−	0.944159i	$-0.393123\pi$
$164$	−12.3682	+	8.62824i	−0.965795	+	0.673752i
$165$	−0.212449	+	0.478338i	−0.0165392	+	0.0372385i
$166$	−0.773246	+	1.48224i	−0.0600155	+	0.115044i
$167$	−0.626404	+	2.33777i	−0.0484726	+	0.180902i	−0.985918	−	0.167231i	$-0.946518\pi$
$167$	−0.626404	+	2.33777i	−0.0484726	+	0.180902i	0.937445	+	0.348133i	$0.113184\pi$
$168$	−6.02468	+	13.4698i	−0.464814	+	1.03922i
$169$	0.415664	+	1.55128i	0.0319742	+	0.119329i
$170$	−2.42218	−	0.539198i	−0.185772	−	0.0413546i
$171$	−7.18349	+	15.1312i	−0.549335	+	1.15711i
$172$	0.648607	−	14.2844i	0.0494559	−	1.08917i
$173$	2.78766	−	21.1744i	0.211942	−	1.60986i	−0.472865	−	0.881135i	$-0.656780\pi$
$173$	2.78766	−	21.1744i	0.211942	−	1.60986i	0.684807	−	0.728725i	$-0.259887\pi$
$174$	−12.3603	−	1.40782i	−0.937032	−	0.106726i
$175$	7.42420	+	12.8591i	0.561217	+	0.972057i
$176$	−3.35152	−	3.09266i	−0.252631	−	0.233118i
$177$	4.24465	+	7.80077i	0.319047	+	0.586342i
$178$	6.35930	+	13.6686i	0.476650	+	1.02451i
$179$	0.878974	+	2.12203i	0.0656976	+	0.158608i	0.953318	−	0.301967i	$-0.0976432\pi$
$179$	0.878974	+	2.12203i	0.0656976	+	0.158608i	−0.887621	+	0.460575i	$0.847643\pi$
$180$	−0.262589	−	1.56846i	−0.0195723	−	0.116906i
$181$	−10.5272	−	4.36050i	−0.782478	−	0.324113i	−0.0445631	−	0.999007i	$-0.514190\pi$
$181$	−10.5272	−	4.36050i	−0.782478	−	0.324113i	−0.737915	+	0.674893i	$0.764190\pi$
$182$	9.72308	−	10.5923i	0.720723	−	0.785157i
$183$	−20.8290	+	5.02061i	−1.53972	+	0.371134i
$184$	−3.87748	+	1.02811i	−0.285852	+	0.0757936i
$185$	1.48289	+	0.397340i	0.109024	+	0.0292130i
$186$	−6.38426	+	3.83637i	−0.468116	+	0.281296i
$187$	5.98794	−	4.59471i	0.437882	−	0.335999i
$188$	−1.81407	−	5.01126i	−0.132304	−	0.365483i
$189$	3.21227	−	15.3176i	0.233658	−	1.11419i
$190$	2.06132	−	0.361615i	0.149544	−	0.0262343i
$191$	−4.80107	+	8.31569i	−0.347393	+	0.601703i	−0.985786	−	0.168009i	$-0.946266\pi$
$191$	−4.80107	+	8.31569i	−0.347393	+	0.601703i	0.638392	+	0.769711i	$0.279600\pi$
$192$	13.6763	+	2.22671i	0.987004	+	0.160699i
$193$	−13.3346	−	23.0963i	−0.959848	−	1.66251i	−0.722861	−	0.690993i	$-0.757173\pi$
$193$	−13.3346	−	23.0963i	−0.959848	−	1.66251i	−0.236987	−	0.971513i	$-0.576160\pi$
$194$	−0.322975	−	0.385589i	−0.0231883	−	0.0276836i
$195$	−0.241023	+	1.53076i	−0.0172600	+	0.109620i
$196$	4.08008	+	0.726759i	0.291434	+	0.0519114i
$197$	−1.38480	−	0.573602i	−0.0986628	−	0.0408675i	0.332806	−	0.942995i	$-0.392005\pi$
$197$	−1.38480	−	0.573602i	−0.0986628	−	0.0408675i	−0.431469	+	0.902128i	$0.642005\pi$
$198$	4.17005	+	2.45104i	0.296352	+	0.174188i
$199$	6.42238	−	6.42238i	0.455271	−	0.455271i	−0.441829	−	0.897099i	$-0.645670\pi$
$199$	6.42238	−	6.42238i	0.455271	−	0.455271i	0.897099	+	0.441829i	$0.145670\pi$
$200$	9.88523	−	9.83370i	0.698991	−	0.695347i
$201$	12.2349	+	3.61206i	0.862983	+	0.254775i
$202$	3.53326	+	11.2402i	0.248599	+	0.790857i
$203$	1.99666	+	15.1662i	0.140138	+	1.06446i
$204$	−7.48430	+	21.6772i	−0.524006	+	1.51771i
$205$	−1.98142	−	0.260859i	−0.138389	−	0.0182192i
$206$	0.221542	−	0.315808i	0.0154355	−	0.0220034i
$207$	3.78754	−	1.93852i	0.263252	−	0.134737i
$208$	−11.9546	−	6.27622i	−0.828904	−	0.435178i
$209$	−3.18273	+	5.51266i	−0.220154	+	0.381319i
$210$	−1.79327	+	0.779817i	−0.123748	+	0.0538125i
$211$	8.22670	+	6.31257i	0.566349	+	0.434575i	0.851837	−	0.523807i	$-0.175489\pi$
$211$	8.22670	+	6.31257i	0.566349	+	0.434575i	−0.285487	+	0.958382i	$0.592155\pi$
$212$	21.1602	−	10.9685i	1.45329	−	0.753319i
$213$	−3.26799	+	7.35799i	−0.223919	+	0.504161i
$214$	−6.88126	+	7.49645i	−0.470393	+	0.512447i
$215$	1.33995	−	1.33995i	0.0913840	−	0.0913840i
$216$	−14.6767	+	0.770803i	−0.998624	+	0.0524465i
$217$	6.47618	+	6.47618i	0.439632	+	0.439632i
$218$	−5.70605	+	0.244152i	−0.386463	+	0.0165360i
$219$	5.06658	+	2.25028i	0.342368	+	0.152060i
$220$	−0.0516247	−	0.602155i	−0.00348054	−	0.0405973i
$221$	13.6036	−	17.7285i	0.915076	−	1.19255i
$222$	5.19937	−	13.2008i	0.348959	−	0.885979i
$223$	18.1004	+	10.4503i	1.21209	+	0.699802i	0.963215	−	0.268733i	$-0.0866050\pi$
$223$	18.1004	+	10.4503i	1.21209	+	0.699802i	0.248878	+	0.968535i	$0.419938\pi$
$224$	−1.41105	−	16.9799i	−0.0942799	−	1.13452i
$225$	−8.03226	+	12.4179i	−0.535484	+	0.827861i
$226$	24.0988	−	4.22763i	1.60303	−	0.281218i
$227$	−1.35199	+	10.2694i	−0.0897349	+	0.681604i	0.886162	+	0.463375i	$0.153362\pi$
$227$	−1.35199	+	10.2694i	−0.0897349	+	0.681604i	−0.975897	+	0.218230i	$0.929972\pi$
$228$	−1.16463	−	19.3059i	−0.0771296	−	1.27856i
$229$	7.89688	−	1.03964i	0.521840	−	0.0687016i	0.134995	−	0.990846i	$-0.456898\pi$
$229$	7.89688	−	1.03964i	0.521840	−	0.0687016i	0.386845	+	0.922145i	$0.373565\pi$
$230$	−0.471336	−	0.245884i	−0.0310790	−	0.0162131i
$231$	1.68410	−	5.70443i	0.110805	−	0.375324i
$232$	13.2856	−	5.46244i	0.872242	−	0.358627i
$233$	1.21008	+	1.21008i	0.0792748	+	0.0792748i	0.745632	−	0.666358i	$-0.232148\pi$
$233$	1.21008	+	1.21008i	0.0792748	+	0.0792748i	−0.666358	+	0.745632i	$0.732148\pi$
$234$	13.8038	+	3.81409i	0.902382	+	0.249335i
$235$	0.270284	−	0.652524i	0.0176314	−	0.0425660i
$236$	−8.63911	−	5.52491i	−0.562358	−	0.359641i
$237$	26.2397	+	4.13154i	1.70445	+	0.268372i
$238$	28.0898	+	2.48220i	1.82079	+	0.160897i
$239$	15.6470	−	9.03378i	1.01212	−	0.584347i	0.100307	−	0.994957i	$-0.468017\pi$
$239$	15.6470	−	9.03378i	1.01212	−	0.584347i	0.911811	+	0.410610i	$0.134684\pi$
$240$	1.13942	+	1.44005i	0.0735494	+	0.0929549i
$241$	−12.1405	−	7.00930i	−0.782036	−	0.451509i	0.0551154	−	0.998480i	$-0.482447\pi$
$241$	−12.1405	−	7.00930i	−0.782036	−	0.451509i	−0.837151	+	0.546971i	$0.815781\pi$
$242$	−11.2304	−	7.87817i	−0.721915	−	0.506428i
$243$	15.0388	−	4.10291i	0.964741	−	0.263202i
$244$	18.2694	−	16.6824i	1.16958	−	1.06798i
$245$	0.334344	+	0.435725i	0.0213604	+	0.0278375i
$246$	−4.46756	+	17.9212i	−0.284841	+	1.14261i
$247$	−4.87777	+	18.2041i	−0.310365	+	1.15830i
$248$	4.31970	−	7.43699i	0.274301	−	0.472249i
$249$	0.479795	+	1.99053i	0.0304058	+	0.126145i
$250$	3.71862	−	0.159113i	0.235186	−	0.0100632i
$251$	−10.1807	+	24.5783i	−0.642597	+	1.55137i	0.180567	+	0.983563i	$0.442207\pi$
$251$	−10.1807	+	24.5783i	−0.642597	+	1.55137i	−0.823164	+	0.567804i	$0.807793\pi$
$252$	5.28502	+	17.2820i	0.332925	+	1.08866i
$253$	1.49388	−	0.618787i	0.0939196	−	0.0389028i
$254$	−0.623699	−	0.227623i	−0.0391344	−	0.0142824i
$255$	−2.66955	+	1.45259i	−0.167174	+	0.0909646i
$256$	−15.0729	+	5.36741i	−0.942053	+	0.335463i
$257$	15.6830	−	9.05459i	0.978279	−	0.564810i	0.0765289	−	0.997067i	$-0.475616\pi$
$257$	15.6830	−	9.05459i	0.978279	−	0.564810i	0.901750	+	0.432258i	$0.142283\pi$
$258$	−10.9025	−	13.7052i	−0.678757	−	0.853250i
$259$	−17.2967	−	2.27716i	−1.07477	−	0.141496i
$260$	−0.609060	−	1.68250i	−0.0377723	−	0.104344i
$261$	−12.5408	+	8.65261i	−0.776254	+	0.535583i
$262$	−10.9965	+	6.99210i	−0.679368	+	0.431974i
$263$	−13.7483	+	3.68384i	−0.847755	+	0.227155i	−0.656444	−	0.754374i	$-0.727940\pi$
$263$	−13.7483	+	3.68384i	−0.847755	+	0.227155i	−0.191310	+	0.981530i	$0.561274\pi$
$264$	−5.58316	−	0.155729i	−0.343620	−	0.00958443i
$265$	3.05096	+	0.817503i	0.187419	+	0.0502188i
$266$	−22.6880	+	7.13177i	−1.39109	+	0.437277i
$267$	16.8743	+	7.49455i	1.03269	+	0.458659i
$268$	−14.3868	+	3.16319i	−0.878815	+	0.193223i
$269$	−9.33715	+	3.86758i	−0.569296	+	0.235810i	−0.648715	−	0.761031i	$-0.724693\pi$
$269$	−9.33715	+	3.86758i	−0.569296	+	0.235810i	0.0794191	+	0.996841i	$0.474693\pi$
$270$	−1.50519	−	1.23610i	−0.0916027	−	0.0752268i
$271$	−1.06895			−0.0649338			−0.0324669	−	0.999473i	$-0.510336\pi$
$271$	−1.06895			−0.0649338			−0.0324669	+	0.999473i	$0.510336\pi$
$272$	−4.50741	−	26.0942i	−0.273302	−	1.58219i
$273$	0.444985	−	17.6041i	0.0269317	−	1.06545i
$274$	2.63676	−	29.8389i	0.159292	−	1.80263i
$275$	−3.42149	+	4.45897i	−0.206323	+	0.268886i
$276$	−2.75072	+	4.07079i	−0.165574	+	0.245033i
$277$	−13.4899	+	10.3512i	−0.810530	+	0.621941i	−0.928608	−	0.371063i	$-0.878993\pi$
$277$	−13.4899	+	10.3512i	−0.810530	+	0.621941i	0.118078	+	0.993004i	$0.462327\pi$
$278$	−2.04456	+	9.18453i	−0.122624	+	0.550851i
$279$	−2.80316	+	8.68084i	−0.167821	+	0.519708i
$280$	1.37926	−	1.78780i	0.0824268	−	0.106841i
$281$	−4.45151	−	16.6133i	−0.265555	−	0.991064i	−0.961910	−	0.273367i	$-0.911863\pi$
$281$	−4.45151	−	16.6133i	−0.265555	−	0.991064i	0.696355	−	0.717698i	$-0.254804\pi$
$282$	−5.70900	−	3.16427i	−0.339966	−	0.188430i
$283$	0.845916	+	6.42537i	0.0502845	+	0.381949i	0.998020	+	0.0628925i	$0.0200325\pi$
$283$	0.845916	+	6.42537i	0.0502845	+	0.381949i	−0.947736	+	0.319056i	$0.896634\pi$
$284$	−0.794113	−	9.26260i	−0.0471219	−	0.549634i
$285$	1.61123	−	1.99340i	0.0954411	−	0.118079i
$286$	5.11263	+	1.86589i	0.302316	+	0.110332i
$287$	22.7111			1.34060
$288$	14.4146	−	8.95645i	0.849391	−	0.527764i
$289$	26.8264			1.57803
$290$	1.78830	+	0.652653i	0.105013	+	0.0383251i
$291$	−0.608528	−	0.0958151i	−0.0356726	−	0.00561678i
$292$	−6.37806	+	0.546812i	−0.373248	+	0.0319998i
$293$	3.47402	+	26.3878i	0.202954	+	1.54159i	0.725045	+	0.688701i	$0.241819\pi$
$293$	3.47402	+	26.3878i	0.202954	+	1.54159i	−0.522091	+	0.852890i	$0.674848\pi$
$294$	4.35063	−	2.61434i	0.253734	−	0.152472i
$295$	−0.351734	−	1.31269i	−0.0204787	−	0.0764277i
$296$	2.09591	+	16.2481i	0.121823	+	0.944400i
$297$	5.82197	−	1.09545i	0.337825	−	0.0635646i
$298$	−1.24762	+	5.60454i	−0.0722727	+	0.324662i
$299$	3.79807	−	2.91436i	0.219648	−	0.168542i
$300$	1.20545	−	17.0346i	0.0695969	−	0.983490i
$301$	−13.1094	+	17.0844i	−0.755611	+	0.984731i
$302$	2.36880	−	26.8065i	0.136309	−	1.54254i
$303$	12.3109	+	7.52873i	0.707240	+	0.432514i
$304$	11.9338	+	18.8772i	0.684451	+	1.08268i
$305$	3.27866			0.187736
$306$	10.5462	+	26.0318i	0.602884	+	1.48814i
$307$	−5.20812	+	2.15728i	−0.297243	+	0.123122i	−0.526321	−	0.850286i	$-0.676429\pi$
$307$	−5.20812	+	2.15728i	−0.297243	+	0.123122i	0.229078	+	0.973408i	$0.426429\pi$
$308$	1.47482	+	6.70775i	0.0840354	+	0.382209i
$309$	−0.0498127	−	0.469832i	−0.00283375	−	0.0267278i
$310$	1.08732	−	0.341790i	0.0617556	−	0.0194124i
$311$	−19.6599	−	5.26787i	−1.11481	−	0.298713i	−0.346030	−	0.938223i	$-0.612471\pi$
$311$	−19.6599	−	5.26787i	−1.11481	−	0.298713i	−0.768783	+	0.639510i	$0.779137\pi$
$312$	−16.0862	+	3.83294i	−0.910699	+	0.216998i
$313$	−1.25379	+	0.335953i	−0.0708686	+	0.0189892i	−0.294079	−	0.955781i	$-0.595013\pi$
$313$	−1.25379	+	0.335953i	−0.0708686	+	0.0189892i	0.223211	+	0.974770i	$0.428346\pi$
$314$	24.5843	−	15.6318i	1.38737	−	0.882155i
$315$	−1.02714	+	2.16354i	−0.0578726	+	0.121902i
$316$	−28.8408	+	10.4403i	−1.62242	+	0.587313i
$317$	23.3733	+	3.07716i	1.31278	+	0.172830i	0.754212	−	0.656631i	$-0.228019\pi$
$317$	23.3733	+	3.07716i	1.31278	+	0.172830i	0.558565	+	0.829461i	$0.311352\pi$
$318$	10.6974	−	27.1599i	0.599880	−	1.52305i
$319$	−5.01448	+	2.89511i	−0.280757	+	0.162095i
$320$	−1.95471	−	0.821666i	−0.109272	−	0.0459325i
$321$	−0.314926	+	12.4589i	−0.0175775	+	0.695387i
$322$	5.67514	+	2.07118i	0.316263	+	0.115422i
$323$	−34.1484	+	14.1447i	−1.90007	+	0.787035i
$324$	−12.9245	+	12.5283i	−0.718026	+	0.696017i
$325$	−6.36799	+	15.3737i	−0.353233	+	0.852779i
$326$	26.9213	−	1.15191i	1.49103	−	0.0637985i
$327$	−5.06951	+	4.81954i	−0.280345	+	0.266521i
$328$	−5.46596	−	20.6146i	−0.301807	−	1.13825i
$329$	−2.07734	+	7.75273i	−0.114527	+	0.427422i
$330$	−0.532468	−	0.514160i	−0.0293114	−	0.0283036i
$331$	−22.0420	−	28.7257i	−1.21154	−	1.57891i	−0.684333	−	0.729170i	$-0.739906\pi$
$331$	−22.0420	−	28.7257i	−1.21154	−	1.57891i	−0.527206	−	0.849738i	$-0.676760\pi$
$332$	−1.59425	−	1.74592i	−0.0874960	−	0.0958197i
$333$	−5.83012	−	16.3692i	−0.319489	−	0.897028i
$334$	−2.80203	−	1.96564i	−0.153320	−	0.107555i
$335$	−1.69060	−	0.976071i	−0.0923676	−	0.0533285i
$336$	−14.9736	−	14.5346i	−0.816877	−	0.792927i
$337$	−0.235650	+	0.136053i	−0.0128367	+	0.00741126i	−0.506405	−	0.862296i	$-0.669026\pi$
$337$	−0.235650	+	0.136053i	−0.0128367	+	0.00741126i	0.493568	+	0.869707i	$0.335692\pi$
$338$	−2.26241	−	0.199922i	−0.123059	−	0.0108743i
$339$	18.8368	−	23.3048i	1.02308	−	1.26574i
$340$	1.89071	−	2.95644i	0.102538	−	0.160336i
$341$	−1.32667	+	3.20285i	−0.0718429	+	0.173444i
$342$	−16.6189	−	16.8796i	−0.898648	−	0.912744i
$343$	10.4954	+	10.4954i	0.566697	+	0.566697i
$344$	18.6624	+	7.78742i	1.00621	+	0.419870i
$345$	−0.632967	+	0.152570i	−0.0340778	+	0.00821409i
$346$	26.7787	+	13.9698i	1.43963	+	0.751019i
$347$	20.9301	−	2.75551i	1.12359	−	0.147923i	0.454246	−	0.890877i	$-0.349909\pi$
$347$	20.9301	−	2.75551i	1.12359	−	0.147923i	0.669343	+	0.742953i	$0.266576\pi$
$348$	7.86315	−	15.7381i	0.421509	−	0.843653i
$349$	3.12296	−	23.7212i	0.167168	−	1.26977i	−0.677918	−	0.735137i	$-0.737118\pi$
$349$	3.12296	−	23.7212i	0.167168	−	1.26977i	0.845086	−	0.534630i	$-0.179549\pi$
$350$	−20.6830	+	3.62839i	−1.10555	+	0.193946i
$351$	15.8104	−	7.59410i	0.843895	−	0.405343i
$352$	5.73359	−	2.95305i	0.305601	−	0.157398i
$353$	−11.5807	−	6.68611i	−0.616378	−	0.355866i	0.159080	−	0.987266i	$-0.449147\pi$
$353$	−11.5807	−	6.68611i	−0.616378	−	0.355866i	−0.775457	+	0.631400i	$0.782481\pi$
$354$	−12.4214	+	1.85685i	−0.660188	+	0.0986907i
$355$	0.750007	−	0.977429i	0.0398063	−	0.0518765i
$356$	−21.2421	+	1.82116i	−1.12583	+	0.0965212i
$357$	27.9225	−	20.3257i	1.47782	−	1.07575i
$358$	−3.24529	+	0.138860i	−0.171519	+	0.00733899i
$359$	9.45820	+	9.45820i	0.499185	+	0.499185i	0.911184	−	0.411999i	$-0.135169\pi$
$359$	9.45820	+	9.45820i	0.499185	+	0.499185i	−0.411999	+	0.911184i	$0.635169\pi$
$360$	2.21102	+	0.411613i	0.116531	+	0.0216939i
$361$	8.60742	−	8.60742i	0.453022	−	0.453022i
$362$	10.8970	−	11.8712i	0.572734	−	0.623937i
$363$	−16.7075	+	1.77137i	−0.876919	+	0.0929731i
$364$	9.35776	+	18.0528i	0.490480	+	0.946225i
$365$	−0.673040	−	0.516442i	−0.0352285	−	0.0270318i
$366$	3.42898	−	30.1056i	0.179236	−	1.57365i
$367$	17.9630	−	31.1128i	0.937661	−	1.62408i	0.167841	−	0.985814i	$-0.446320\pi$
$367$	17.9630	−	31.1128i	0.937661	−	1.62408i	0.769819	−	0.638262i	$-0.220346\pi$
$368$	0.514131	−	5.64973i	0.0268009	−	0.294512i
$369$	10.3061	+	20.1365i	0.536516	+	1.04826i
$370$	−1.24684	+	1.77738i	−0.0648203	+	0.0924015i
$371$	−35.5870	−	4.68512i	−1.84759	−	0.243239i
$372$	−2.00124	−	10.3416i	−0.103760	−	0.536185i
$373$	−4.50258	−	34.2005i	−0.233135	−	1.77083i	−0.562663	−	0.826687i	$-0.690223\pi$
$373$	−4.50258	−	34.2005i	−0.233135	−	1.77083i	0.329528	−	0.944146i	$-0.393110\pi$
$374$	3.20086	+	10.1827i	0.165512	+	0.526537i
$375$	3.30379	−	3.14088i	0.170607	−	0.162194i
$376$	7.53702	+	0.0196978i	0.388692	+	0.00101584i
$377$	−12.1220	+	12.1220i	−0.624316	+	0.624316i
$378$	18.7921	+	11.6942i	0.966559	+	0.601486i
$379$	−27.9266	−	11.5676i	−1.43449	−	0.594187i	−0.476038	−	0.879425i	$-0.657927\pi$
$379$	−27.9266	−	11.5676i	−1.43449	−	0.594187i	−0.958457	+	0.285238i	$0.907927\pi$
$380$	−0.519018	+	2.91380i	−0.0266251	+	0.149475i
$381$	−0.758880	+	0.292098i	−0.0388786	+	0.0149646i
$382$	−8.71965	−	10.4101i	−0.446136	−	0.532626i
$383$	13.9736	+	24.2030i	0.714017	+	1.23671i	0.963337	+	0.268293i	$0.0864595\pi$
$383$	13.9736	+	24.2030i	0.714017	+	1.23671i	−0.249320	+	0.968421i	$0.580207\pi$
$384$	−9.58911	+	17.0894i	−0.489342	+	0.872092i
$385$	−0.455086	+	0.788232i	−0.0231933	+	0.0401720i
$386$	37.1488	−	6.51696i	1.89082	−	0.331705i
$387$	−21.0966	−	3.87040i	−1.07240	−	0.196744i
$388$	0.668850	−	0.242122i	0.0339557	−	0.0122919i
$389$	−18.0693	+	13.8651i	−0.916151	+	0.702987i	−0.955109	−	0.296254i	$-0.904263\pi$
$389$	−18.0693	+	13.8651i	−0.916151	+	0.702987i	0.0389586	+	0.999241i	$0.487596\pi$
$390$	−1.91676	−	1.06238i	−0.0970588	−	0.0537959i
$391$	9.06922	+	2.43009i	0.458650	+	0.122895i
$392$	−2.94372	+	5.06803i	−0.148680	+	0.255974i
$393$	−4.51897	+	15.3068i	−0.227952	+	0.772127i
$394$	1.43345	−	1.56160i	0.0722161	−	0.0786723i
$395$	−3.75541	−	1.55554i	−0.188955	−	0.0782677i
$396$	−5.27806	+	4.35155i	−0.265232	+	0.218673i
$397$	4.54017	+	10.9609i	0.227864	+	0.550113i	0.995917	−	0.0902734i	$-0.0287741\pi$
$397$	4.54017	+	10.9609i	0.227864	+	0.550113i	−0.768053	+	0.640387i	$0.778774\pi$
$398$	5.41829	+	11.6460i	0.271594	+	0.583763i
$399$	−15.1965	+	24.8491i	−0.760777	+	1.24401i
$400$	8.27128	+	17.9004i	0.413564	+	0.895021i
$401$	11.6633	+	20.2014i	0.582437	+	1.00881i	0.995190	+	0.0979670i	$0.0312340\pi$
$401$	11.6633	+	20.2014i	0.582437	+	1.00881i	−0.412753	+	0.910843i	$0.635433\pi$
$402$	−10.7307	+	14.5028i	−0.535198	+	0.723335i
$403$	−1.33972	+	10.1762i	−0.0667363	+	0.506912i
$404$	−16.6457	−	0.755828i	−0.828156	−	0.0376039i
$405$	−2.38438	+	0.0711045i	−0.118481	+	0.00353321i
$406$	−21.1164	−	4.70070i	−1.04799	−	0.233292i
$407$	−1.70915	−	6.37862i	−0.0847193	−	0.316177i
$408$	−25.1696	−	20.4531i	−1.24608	−	1.01258i
$409$	−0.194109	+	0.724424i	−0.00959807	+	0.0358205i	−0.970559	−	0.240864i	$-0.922569\pi$
$409$	−0.194109	+	0.724424i	−0.00959807	+	0.0358205i	0.960961	+	0.276685i	$0.0892358\pi$
$410$	1.30724	−	2.50585i	0.0645600	−	0.123755i
$411$	−21.5913	−	29.6612i	−1.06502	−	1.46308i
$412$	0.312139	+	0.447438i	0.0153780	+	0.0220437i
$413$	5.91000	+	14.2680i	0.290812	+	0.702083i
$414$	0.738956	+	5.97165i	0.0363177	+	0.293491i
$415$		−	0.313326i		−	0.0153806i
$416$	14.1342	−	12.8388i	0.692984	−	0.629472i
$417$	5.50799	+	10.1225i	0.269728	+	0.495702i
$418$	−5.78045	−	6.90107i	−0.282731	−	0.337542i
$419$	0.850799	+	0.652841i	0.0415642	+	0.0318934i	0.629335	−	0.777134i	$-0.283327\pi$
$419$	0.850799	+	0.652841i	0.0415642	+	0.0318934i	−0.587770	+	0.809028i	$0.699994\pi$
$420$	−0.166526	−	2.76046i	−0.00812563	−	0.134697i
$421$	11.9771	+	15.6089i	0.583729	+	0.760731i	0.988091	−	0.153868i	$-0.0491732\pi$
$421$	11.9771	+	15.6089i	0.583729	+	0.760731i	−0.404362	+	0.914599i	$0.632507\pi$
$422$	−12.3750	+	7.86858i	−0.602404	+	0.383036i
$423$	−7.81652	+	1.67629i	−0.380052	+	0.0815042i
$424$	4.31222	+	33.4295i	0.209420	+	1.62348i
$425$	−31.5237	+	8.44674i	−1.52912	+	0.409727i
$426$	−8.19065	−	7.90903i	−0.396838	−	0.383194i
$427$	−36.9398	+	4.86322i	−1.78764	+	0.235348i
$428$	−6.62271	−	12.7764i	−0.320121	−	0.617571i
$429$	6.22074	−	2.39440i	0.300340	−	0.115603i
$430$	1.13046	+	2.42980i	0.0545156	+	0.117176i
$431$		−	1.14937i		−	0.0553631i	−0.999617	−	0.0276815i	$-0.991188\pi$
$431$		−	1.14937i		−	0.0553631i	0.999617	−	0.0276815i	$-0.00881243\pi$
$432$	6.09195	−	19.8718i	0.293099	−	0.956082i
$433$		−	13.4381i		−	0.645792i	−0.946434	−	0.322896i	$-0.895344\pi$
$433$		−	13.4381i		−	0.645792i	0.946434	−	0.322896i	$-0.104656\pi$
$434$	−11.7436	+	5.46367i	−0.563710	+	0.262265i
$435$	2.17590	−	0.837517i	0.104326	−	0.0401559i
$436$	2.44221	−	7.69889i	0.116960	−	0.368710i
$437$	−7.85080	+	1.03358i	−0.375555	+	0.0494427i
$438$	−5.44602	+	5.63993i	−0.260221	+	0.269486i
$439$	18.5478	−	4.96986i	0.885237	−	0.237199i	0.212572	−	0.977145i	$-0.431816\pi$
$439$	18.5478	−	4.96986i	0.885237	−	0.237199i	0.672665	+	0.739947i	$0.265149\pi$
$440$	0.824995	+	0.223369i	0.0393301	+	0.0106487i
$441$	1.91025	−	5.91567i	0.0909641	−	0.281699i
$442$	16.9568	+	26.6680i	0.806551	+	1.26847i
$443$	15.7477	+	20.5228i	0.748196	+	0.975068i	0.999973	+	0.00728264i	$0.00231816\pi$
$443$	15.7477	+	20.5228i	0.748196	+	0.975068i	−0.251778	+	0.967785i	$0.581015\pi$
$444$	15.0164	+	13.3077i	0.712647	+	0.631558i
$445$	−2.24156	−	1.72001i	−0.106260	−	0.0815363i
$446$	−22.6591	+	18.9797i	−1.07294	+	0.898713i
$447$	3.36106	+	6.17693i	0.158973	+	0.292159i
$448$	23.2420	+	6.35808i	1.09808	+	0.300391i
$449$			28.8086i			1.35956i	0.733414	+	0.679782i	$0.237926\pi$
$449$			28.8086i			1.35956i	−0.733414	+	0.679782i	$0.762074\pi$
$450$	−12.6028	−	16.6917i	−0.594103	−	0.786854i
$451$	3.28978	+	7.94222i	0.154909	+	0.373985i
$452$	−6.06782	+	34.0652i	−0.285406	+	1.60229i
$453$	−19.3971	−	26.6469i	−0.911354	−	1.25198i
$454$	−12.9874	−	6.77522i	−0.609531	−	0.317977i
$455$	−0.697453	+	2.60293i	−0.0326971	+	0.122027i
$456$	26.2126	+	7.81317i	1.22752	+	0.365885i
$457$	2.55106	+	9.52070i	0.119334	+	0.445360i	0.999575	−	0.0291677i	$-0.00928569\pi$
$457$	2.55106	+	9.52070i	0.119334	+	0.445360i	−0.880241	+	0.474527i	$0.842619\pi$
$458$	−2.44761	+	10.9951i	−0.114369	+	0.513767i
$459$	30.6925	+	15.5334i	1.43260	+	0.725038i
$460$	0.555183	−	0.506955i	0.0258856	−	0.0236369i
$461$	2.43585	−	18.5021i	0.113449	−	0.861730i	−0.836202	−	0.548421i	$-0.815229\pi$
$461$	2.43585	−	18.5021i	0.113449	−	0.861730i	0.949651	−	0.313309i	$-0.101438\pi$
$462$	6.76183	+	5.00311i	0.314589	+	0.232766i
$463$	−12.7222	−	22.0354i	−0.591249	−	1.02407i	−0.994065	−	0.108792i	$-0.965302\pi$
$463$	−12.7222	−	22.0354i	−0.591249	−	1.02407i	0.402816	−	0.915281i	$-0.368032\pi$
$464$	0.815392	+	20.2984i	0.0378536	+	0.942331i
$465$	0.728292	−	1.19089i	0.0337737	−	0.0552262i
$466$	−2.19429	+	1.02089i	−0.101649	+	0.0472918i
$467$	0.653601	+	1.57793i	0.0302451	+	0.0730181i	0.938280	−	0.345875i	$-0.112418\pi$
$467$	0.653601	+	1.57793i	0.0302451	+	0.0730181i	−0.908035	+	0.418894i	$0.862418\pi$
$468$	−11.7598	+	16.4891i	−0.543595	+	0.762211i
$469$	20.4954	+	8.48948i	0.946390	+	0.392008i
$470$	0.735835	+	0.675448i	0.0339415	+	0.0311561i
$471$	10.1028	−	34.2205i	0.465512	−	1.57680i
$472$	11.5285	−	8.79836i	0.530643	−	0.404977i
$473$	−7.87347	−	2.10969i	−0.362022	−	0.0970036i
$474$	−18.2110	+	32.8564i	−0.836460	+	1.50914i
$475$	21.8363	−	16.7556i	1.00192	−	0.768799i
$476$	−16.9169	+	36.1140i	−0.775384	+	1.65528i
$477$	−11.9951	−	33.6787i	−0.549220	−	1.54204i
$478$	4.41503	+	25.1671i	0.201939	+	1.15111i
$479$	3.28151	−	5.68375i	0.149936	−	0.259697i	−0.781267	−	0.624196i	$-0.785426\pi$
$479$	3.28151	−	5.68375i	0.149936	−	0.259697i	0.931204	+	0.364499i	$0.118760\pi$
$480$	−2.46556	+	0.815524i	−0.112537	+	0.0372234i
$481$	−9.77571	−	16.9320i	−0.445734	−	0.772034i
$482$	15.1982	−	12.7302i	0.692257	−	0.579846i
$483$	6.90517	−	2.65784i	0.314196	−	0.120936i
$484$	15.9112	−	11.0999i	0.723236	−	0.504540i
$485$	0.0870921	+	0.0360747i	0.00395465	+	0.00163807i
$486$	−1.84079	+	21.9684i	−0.0835000	+	0.996508i
$487$	−24.6314	+	24.6314i	−1.11616	+	1.11616i	−0.123856	+	0.992300i	$0.539526\pi$
$487$	−24.6314	+	24.6314i	−1.11616	+	1.11616i	−0.992300	+	0.123856i	$0.960474\pi$
$488$	13.3047	+	32.3594i	0.602276	+	1.46484i
$489$	23.9181	−	22.7387i	1.08161	−	1.02828i
$490$	−0.740969	+	0.232917i	−0.0334735	+	0.0105221i
$491$	−3.63549	−	27.6143i	−0.164067	−	1.24622i	−0.853201	−	0.521582i	$-0.825342\pi$
$491$	−3.63549	−	27.6143i	−0.164067	−	1.24622i	0.689134	−	0.724634i	$-0.257991\pi$
$492$	−21.6423	−	14.6242i	−0.975711	−	0.659310i
$493$	−33.3341	−	4.38852i	−1.50129	−	0.197649i
$494$	−21.8192	−	15.3063i	−0.981694	−	0.688665i
$495$	−0.905388	−	0.0458007i	−0.0406942	−	0.00205859i
$496$	7.78567	+	9.34454i	0.349587	+	0.419582i
$497$	−7.00032	+	12.1249i	−0.314007	+	0.543877i
$498$	−2.87705	−	0.327691i	−0.128924	−	0.0146842i
$499$	18.6348	+	14.2990i	0.834207	+	0.640110i	0.934941	−	0.354804i	$-0.115452\pi$
$499$	18.6348	+	14.2990i	0.834207	+	0.640110i	−0.100734	+	0.994913i	$0.532119\pi$
$500$	−1.59158	+	5.01734i	−0.0711775	+	0.224382i
$501$	−4.16862	+	0.441967i	−0.186240	+	0.0197456i
$502$	−27.7163	−	25.4417i	−1.23704	−	1.13552i
$503$	20.8337	−	20.8337i	0.928930	−	0.928930i	−0.0687068	−	0.997637i	$-0.521887\pi$
$503$	20.8337	−	20.8337i	0.928930	−	0.928930i	0.997637	+	0.0687068i	$0.0218873\pi$
$504$	−25.5216	−	1.35794i	−1.13682	−	0.0604873i
$505$	−1.56146	−	1.56146i	−0.0694840	−	0.0694840i
$506$	0.0977558	+	2.28465i	0.00434578	+	0.101565i
$507$	−2.24894	+	1.63707i	−0.0998789	+	0.0727049i
$508$	0.604797	−	0.718224i	0.0268335	−	0.0318661i
$509$	−8.00983	+	10.4386i	−0.355030	+	0.462684i	−0.936389	−	0.350963i	$-0.885854\pi$
$509$	−8.00983	+	10.4386i	−0.355030	+	0.462684i	0.581360	+	0.813647i	$0.302521\pi$
$510$	−0.635446	−	4.25079i	−0.0281380	−	0.188228i
$511$	8.34900	+	4.82030i	0.369338	+	0.213237i
$512$	0.177406	−	22.6267i	0.00784031	−	0.999969i
$513$	−28.9281	−	2.19741i	−1.27721	−	0.0970182i
$514$	4.42520	+	25.2250i	0.195187	+	1.11263i
$515$	−0.00943696	+	0.0716808i	−0.000415842	+	0.00315863i
$516$	23.4935	−	7.83902i	1.03424	−	0.345094i
$517$	−3.01209	+	0.396549i	−0.132471	+	0.0174402i
$518$	11.4115	−	21.8747i	0.501392	−	0.961119i
$519$	35.9617	−	8.66818i	1.57854	−	0.380491i
$520$	2.53050	+	0.00661340i	0.110970	+	0.000290017i
$521$	−11.1752	−	11.1752i	−0.489592	−	0.489592i	0.418585	−	0.908178i	$-0.362526\pi$
$521$	−11.1752	−	11.1752i	−0.489592	−	0.489592i	−0.908178	+	0.418585i	$0.862526\pi$
$522$	−5.41467	−	20.8557i	−0.236994	−	0.912827i
$523$	4.41161	−	10.6506i	0.192906	−	0.465717i	−0.797600	−	0.603187i	$-0.793897\pi$
$523$	4.41161	−	10.6506i	0.192906	−	0.465717i	0.990506	+	0.137470i	$0.0438971\pi$
$524$	−3.95740	−	17.9990i	−0.172880	−	0.786292i
$525$	−16.1668	+	20.0015i	−0.705578	+	0.872936i
$526$	1.77181	−	20.0507i	0.0772548	−	0.874254i
$527$	−17.4332	+	10.0651i	−0.759403	+	0.438441i
$528$	2.91386	−	7.34174i	0.126810	−	0.319508i
$529$	−18.1766	−	10.4943i	−0.790286	−	0.456272i
$530$	−2.56531	+	3.65685i	−0.111430	+	0.158844i
$531$	−9.96858	+	11.7147i	−0.432600	+	0.508376i
$532$	1.52562	−	33.5989i	0.0661438	−	1.45670i
$533$	15.4942	+	20.1924i	0.671128	+	0.874631i
$534$	−18.1380	+	18.7838i	−0.784907	+	0.812855i
$535$	0.493604	−	1.84215i	0.0213404	−	0.0796433i
$536$	2.77309	−	20.6466i	0.119779	−	0.891798i
$537$	−2.88326	+	2.74110i	−0.124422	+	0.118287i
$538$	−0.610999	−	14.2796i	−0.0263420	−	0.615639i
$539$	0.904073	−	2.18263i	0.0389412	−	0.0940123i
$540$	2.37195	−	1.40033i	0.102073	−	0.0602604i
$541$	−4.88193	+	2.02216i	−0.209891	+	0.0869396i	−0.485152	−	0.874430i	$-0.661236\pi$
$541$	−4.88193	+	2.02216i	−0.209891	+	0.0869396i	0.275261	+	0.961369i	$0.411236\pi$
$542$	0.518275	−	1.42010i	0.0222618	−	0.0609985i
$543$	0.498710	−	19.7296i	0.0214017	−	0.846678i
$544$	36.8516	+	6.66357i	1.58000	+	0.285698i
$545$	0.926988	−	0.535197i	0.0397078	−	0.0229253i
$546$	23.1714	+	9.12648i	0.991646	+	0.390577i
$547$	−2.53143	−	0.333269i	−0.108236	−	0.0142495i	0.0762136	−	0.997092i	$-0.475717\pi$
$547$	−2.53143	−	0.333269i	−0.108236	−	0.0142495i	−0.184450	+	0.982842i	$0.559050\pi$
$548$	38.3627	+	17.9702i	1.63877	+	0.767651i
$549$	−21.0749	−	30.5452i	−0.899456	−	1.30364i
$550$	−4.26486	−	6.70738i	−0.181854	−	0.286004i
$551$	27.3895	−	7.33899i	1.16683	−	0.312651i
$552$	−4.07438	−	5.62806i	−0.173417	−	0.239546i
$553$	44.6185	+	11.9555i	1.89737	+	0.508399i
$554$	−7.21103	−	22.9401i	−0.306367	−	0.974632i
$555$	0.280347	+	2.64423i	0.0119001	+	0.112241i
$556$	−11.2104	−	7.16929i	−0.475426	−	0.304046i
$557$	19.4433	−	8.05366i	0.823838	−	0.341245i	0.0693774	−	0.997590i	$-0.477899\pi$
$557$	19.4433	−	8.05366i	0.823838	−	0.341245i	0.754460	+	0.656346i	$0.227899\pi$
$558$	−10.1734	−	7.93288i	−0.430676	−	0.335826i
$559$	−24.1333			−1.02073
$560$	1.70637	+	2.69917i	0.0721071	+	0.114061i
$561$	11.1527	+	6.82044i	0.470866	+	0.287959i
$562$	24.2291	+	2.14104i	1.02204	+	0.0903144i
$563$	11.2281	−	14.6327i	0.473206	−	0.616694i	−0.494377	−	0.869248i	$-0.664604\pi$
$563$	11.2281	−	14.6327i	0.473206	−	0.616694i	0.967583	+	0.252554i	$0.0812704\pi$
$564$	6.97174	−	6.05024i	0.293563	−	0.254761i
$565$	−3.63794	+	2.79149i	−0.153049	+	0.117439i
$566$	−8.94627	−	1.99152i	−0.376040	−	0.0837098i
$567$	26.7587	−	4.33785i	1.12376	−	0.182173i
$568$	12.6904	+	3.43596i	0.532478	+	0.144170i
$569$	0.0592096	+	0.220973i	0.00248220	+	0.00926368i	0.967156	−	0.254184i	$-0.0818070\pi$
$569$	0.0592096	+	0.220973i	0.00248220	+	0.00926368i	−0.964674	+	0.263448i	$0.915140\pi$
$570$	1.86704	+	3.10702i	0.0782018	+	0.130139i
$571$	2.55267	+	19.3894i	0.106826	+	0.811422i	0.958046	+	0.286614i	$0.0925297\pi$
$571$	2.55267	+	19.3894i	0.106826	+	0.811422i	−0.851220	+	0.524808i	$0.824137\pi$
$572$	−4.95768	+	5.88747i	−0.207291	+	0.246168i
$573$	−16.4290	−	2.58680i	−0.686331	−	0.108065i
$574$	−11.0114	+	30.1718i	−0.459608	+	1.25935i
$575$	−6.99170			−0.291574
$576$	4.90978	+	23.4924i	0.204574	+	0.978851i
$577$	14.9051			0.620507			0.310254	−	0.950654i	$-0.399586\pi$
$577$	14.9051			0.620507			0.310254	+	0.950654i	$0.399586\pi$
$578$	−13.0067	+	35.6390i	−0.541008	+	1.48239i
$579$	29.0373	−	35.9247i	1.20675	−	1.49298i
$580$	−1.73410	+	2.05933i	−0.0720048	+	0.0855090i
$581$	0.464755	+	3.53016i	0.0192813	+	0.146456i
$582$	0.422334	−	0.761977i	0.0175063	−	0.0315850i
$583$	−3.51647	−	13.1237i	−0.145637	−	0.543526i
$584$	2.36594	−	8.73840i	0.0979034	−	0.361598i
$585$	−2.62434	+	0.562805i	−0.108503	+	0.0232691i
$586$	−36.7407	−	8.17879i	−1.51774	−	0.337863i
$587$	21.3266	−	16.3645i	0.880243	−	0.675434i	−0.0663737	−	0.997795i	$-0.521143\pi$
$587$	21.3266	−	16.3645i	0.880243	−	0.675434i	0.946617	+	0.322360i	$0.104476\pi$
$588$	1.36377	+	7.04739i	0.0562411	+	0.290629i
$589$	10.3351	−	13.4689i	0.425849	−	0.554977i
$590$	1.91445	+	0.169173i	0.0788167	+	0.00696476i
$591$	0.0656029	−	2.59533i	0.00269854	−	0.106758i
$592$	−22.6018	−	5.09340i	−0.928929	−	0.209337i
$593$	11.8751			0.487652			0.243826	−	0.969819i	$-0.421597\pi$
$593$	11.8751			0.487652			0.243826	+	0.969819i	$0.421597\pi$
$594$	−1.36745	+	8.26564i	−0.0561073	+	0.339143i
$595$	−4.88274	+	2.02250i	−0.200173	+	0.0829143i
$596$	−6.84075	−	4.37481i	−0.280208	−	0.179199i
$597$	14.3773	+	6.38555i	0.588424	+	0.261343i
$598$	2.03026	+	6.45877i	0.0830234	+	0.264119i
$599$	−40.3284	−	10.8060i	−1.64777	−	0.441520i	−0.688786	−	0.724965i	$-0.741856\pi$
$599$	−40.3284	−	10.8060i	−1.64777	−	0.441520i	−0.958988	+	0.283445i	$0.908523\pi$
$600$	22.0460	+	9.86060i	0.900025	+	0.402557i
$601$	−8.99022	+	2.40892i	−0.366719	+	0.0982620i	−0.437472	−	0.899232i	$-0.644126\pi$
$601$	−8.99022	+	2.40892i	−0.366719	+	0.0982620i	0.0707537	+	0.997494i	$0.477460\pi$
$602$	−16.3407	−	25.6992i	−0.665998	−	1.04742i
$603$	1.77361	+	22.0244i	0.0722269	+	0.896902i
$604$	34.4641	+	16.1440i	1.40232	+	0.656891i
$605$	2.54902	+	0.335585i	0.103632	+	0.0136435i
$606$	−15.9708	+	12.7047i	−0.648771	+	0.516095i
$607$	35.1470	−	20.2921i	1.42657	−	0.823632i	0.429724	−	0.902960i	$-0.358611\pi$
$607$	35.1470	−	20.2921i	1.42657	−	0.823632i	0.996849	+	0.0793280i	$0.0252774\pi$
$608$	−30.8645	+	6.70158i	−1.25172	+	0.271785i
$609$	−23.2730	+	12.6636i	−0.943069	+	0.513154i
$610$	−1.58965	+	4.35572i	−0.0643630	+	0.176358i
$611$	−8.31016	+	3.44218i	−0.336193	+	0.139256i
$612$	−39.6966	+	1.38917i	−1.60464	+	0.0561539i
$613$	11.7152	−	28.2829i	0.473171	−	1.14234i	−0.489583	−	0.871957i	$-0.662851\pi$
$613$	11.7152	−	28.2829i	0.473171	−	1.14234i	0.962754	−	0.270379i	$-0.0871489\pi$
$614$	−0.340806	−	7.96496i	−0.0137538	−	0.321440i
$615$	−0.811137	−	3.36516i	−0.0327082	−	0.135696i
$616$	−9.62633	−	1.29293i	−0.387856	−	0.0520938i
$617$	−5.17000	+	19.2947i	−0.208136	+	0.776776i	0.780334	+	0.625363i	$0.215049\pi$
$617$	−5.17000	+	19.2947i	−0.208136	+	0.776776i	−0.988471	+	0.151413i	$0.951618\pi$
$618$	0.648325	+	0.161620i	0.0260795	+	0.00650132i
$619$	−6.37543	−	8.30863i	−0.256250	−	0.333952i	0.647458	−	0.762101i	$-0.275832\pi$
$619$	−6.37543	−	8.30863i	−0.256250	−	0.333952i	−0.903708	+	0.428150i	$0.859166\pi$
$620$	−0.0731150	+	1.61023i	−0.00293637	+	0.0646682i
$621$	5.49004	+	4.91624i	0.220308	+	0.197282i
$622$	16.5304	−	23.5642i	0.662811	−	0.944839i
$623$	27.8064	+	16.0540i	1.11404	+	0.643191i
$624$	2.70725	−	23.2289i	0.108377	−	0.929901i
$625$	20.7423	−	11.9756i	0.829693	−	0.479023i
$626$	0.161583	−	1.82855i	0.00645816	−	0.0730837i
$627$	−10.8911	−	1.71485i	−0.434950	−	0.0684845i
$628$	8.84732	+	40.2394i	0.353047	+	1.60572i
$629$	14.6740	−	35.4261i	0.585090	−	1.41253i
$630$	−2.37627	−	2.41354i	−0.0946728	−	0.0961578i
$631$	22.7060	+	22.7060i	0.903913	+	0.903913i	0.995772	−	0.0918593i	$-0.0292810\pi$
$631$	22.7060	+	22.7060i	0.903913	+	0.903913i	−0.0918593	+	0.995772i	$0.529281\pi$
$632$	0.113365	−	43.3770i	0.00450940	−	1.72545i
$633$	−5.08543	+	17.2256i	−0.202128	+	0.684654i
$634$	−15.4205	+	29.5596i	−0.612427	+	1.17396i
$635$	0.123369	−	0.0162418i	0.00489575	−	0.000644538i
$636$	30.8954	+	27.3799i	1.22508	+	1.08568i
$637$	0.912970	−	6.93470i	0.0361732	−	0.274763i
$638$	−1.41491	−	8.06545i	−0.0560169	−	0.319314i
$639$	−13.9271	−	0.704526i	−0.550946	−	0.0278706i
$640$	2.03932	−	2.19846i	0.0806114	−	0.0869019i
$641$	27.5561	+	15.9095i	1.08840	+	0.628389i	0.933150	−	0.359486i	$-0.117048\pi$
$641$	27.5561	+	15.9095i	1.08840	+	0.628389i	0.155251	+	0.987875i	$0.450381\pi$
$642$	−16.3990	−	6.45903i	−0.647216	−	0.254918i
$643$	21.8644	−	28.4942i	0.862247	−	1.12370i	−0.128996	−	0.991645i	$-0.541175\pi$
$643$	21.8644	−	28.4942i	0.862247	−	1.12370i	0.991242	−	0.132056i	$-0.0421580\pi$
$644$	−5.50314	+	6.53523i	−0.216854	+	0.257524i
$645$	2.99965	+	1.33227i	0.118111	+	0.0524580i
$646$	−2.23459	−	52.2244i	−0.0879186	−	2.05474i
$647$	−24.1345	−	24.1345i	−0.948824	−	0.948824i	0.0499284	−	0.998753i	$-0.484101\pi$
$647$	−24.1345	−	24.1345i	−0.948824	−	0.948824i	−0.998753	+	0.0499284i	$0.984101\pi$
$648$	−10.3775	−	23.2445i	−0.407667	−	0.913131i
$649$	−4.13353	+	4.13353i	−0.162255	+	0.162255i
$650$	−17.3365	−	15.9138i	−0.679994	−	0.624190i
$651$	−6.43904	+	14.4977i	−0.252366	+	0.568211i
$652$	−11.5224	+	36.3235i	−0.451251	+	1.42254i
$653$	−2.66142	−	2.04218i	−0.104150	−	0.0799168i	0.555374	−	0.831601i	$-0.312575\pi$
$653$	−2.66142	−	2.04218i	−0.104150	−	0.0799168i	−0.659523	+	0.751684i	$0.729242\pi$
$654$	−3.94485	−	9.07161i	−0.154256	−	0.354728i
$655$	1.22114	−	2.11508i	0.0477140	−	0.0826430i
$656$	30.0367	+	2.73337i	1.17274	+	0.106720i
$657$	−0.485124	+	9.58992i	−0.0189265	+	0.374139i
$658$	−9.29235	−	6.51864i	−0.362253	−	0.254123i
$659$	−31.3084	−	4.12183i	−1.21960	−	0.160564i	−0.506884	−	0.862014i	$-0.669203\pi$
$659$	−31.3084	−	4.12183i	−1.21960	−	0.160564i	−0.712718	+	0.701451i	$0.752536\pi$
$660$	0.941230	−	0.458097i	0.0366373	−	0.0178314i
$661$	0.0570210	+	0.433117i	0.00221786	+	0.0168463i	0.992518	−	0.122098i	$-0.0389623\pi$
$661$	0.0570210	+	0.433117i	0.00221786	+	0.0168463i	−0.990300	+	0.138945i	$0.955629\pi$
$662$	48.8492	−	15.3553i	1.89858	−	0.596802i
$663$	37.1211	+	10.9591i	1.44166	+	0.425616i
$664$	3.09243	−	1.27147i	0.120009	−	0.0493425i
$665$	3.15176	−	3.15176i	0.122220	−	0.122220i
$666$	24.5733	+	0.191226i	0.952196	+	0.00740984i
$667$	−6.65466	−	2.75645i	−0.257670	−	0.106730i
$668$	3.96992	−	2.76947i	0.153601	−	0.107154i
$669$	−5.63058	+	35.7602i	−0.217691	+	1.38257i
$670$	2.11640	−	1.77273i	0.0817636	−	0.0684865i
$671$	−7.05155	−	12.2136i	−0.272222	−	0.471502i
$672$	26.5692	−	12.8454i	1.02493	−	0.495524i
$673$	−4.03557	+	6.98981i	−0.155560	+	0.269438i	−0.933263	−	0.359194i	$-0.883051\pi$
$673$	−4.03557	+	6.98981i	−0.155560	+	0.269438i	0.777703	+	0.628632i	$0.216385\pi$
$674$	−0.0664923	−	0.379027i	−0.00256119	−	0.0145996i
$675$	−25.0704	−	5.25753i	−0.964959	−	0.202363i
$676$	1.36252	−	2.90870i	0.0524047	−	0.111873i
$677$	16.1027	−	12.3561i	0.618878	−	0.474882i	−0.251107	−	0.967959i	$-0.580795\pi$
$677$	16.1027	−	12.3561i	0.618878	−	0.474882i	0.869985	+	0.493077i	$0.164128\pi$
$678$	21.8275	+	36.3241i	0.838282	+	1.39502i
$679$	−1.03475	−	0.277261i	−0.0397102	−	0.0106403i
$680$	3.01094	+	3.94524i	0.115464	+	0.151293i
$681$	−17.4411	+	4.20399i	−0.668345	+	0.161097i
$682$	−3.61177	−	3.31537i	−0.138302	−	0.126952i
$683$	2.59322	+	1.07415i	0.0992269	+	0.0411011i	0.431745	−	0.901996i	$-0.357898\pi$
$683$	2.59322	+	1.07415i	0.0992269	+	0.0411011i	−0.332518	+	0.943097i	$0.607898\pi$
$684$	30.4822	−	13.8943i	1.16552	−	0.531261i
$685$	2.14843	+	5.18677i	0.0820874	+	0.198176i
$686$	−19.0318	+	8.85449i	−0.726637	+	0.338066i
$687$	6.59380	+	12.1180i	0.251569	+	0.462331i
$688$	−19.3940	+	21.0174i	−0.739391	+	0.801280i
$689$	−20.1130	−	34.8367i	−0.766243	−	1.32717i
$690$	0.104202	−	0.914872i	0.00396691	−	0.0348286i
$691$	−2.01546	+	15.3089i	−0.0766717	+	0.582380i	0.909383	+	0.415959i	$0.136554\pi$
$691$	−2.01546	+	15.3089i	−0.0766717	+	0.582380i	−0.986055	+	0.166420i	$0.946779\pi$
$692$	−31.5425	+	28.8024i	−1.19906	+	1.09490i
$693$	10.2687	−	0.826932i	0.390076	−	0.0314126i
$694$	−6.48722	+	29.1418i	−0.246251	+	1.10621i
$695$	−0.456421	−	1.70339i	−0.0173130	−	0.0646132i
$696$	17.0958	+	18.0768i	0.648013	+	0.685200i
$697$	−12.9196	+	48.2165i	−0.489363	+	1.82633i
$698$	29.9996	+	15.6500i	1.13550	+	0.592362i
$699$	−1.20314	+	2.70891i	−0.0455068	+	0.102460i
$700$	5.20775	−	29.2366i	0.196834	−	1.10504i
$701$	−3.78858	−	9.14644i	−0.143093	−	0.345456i	0.836043	−	0.548664i	$-0.184863\pi$
$701$	−3.78858	−	9.14644i	−0.143093	−	0.345456i	−0.979136	+	0.203208i	$0.934863\pi$
$702$	2.42318	+	24.6861i	0.0914570	+	0.931717i
$703$			32.3391i			1.21969i
$704$	1.14322	+	9.04887i	0.0430868	+	0.341042i
$705$	1.22293	+	0.0309124i	0.0460584	+	0.00116423i
$706$	14.4974	−	12.1432i	0.545616	−	0.457017i
$707$	19.9087	+	15.2764i	0.748742	+	0.574530i
$708$	3.55562	−	17.4021i	0.133629	−	0.654012i
$709$	2.79341	+	3.64044i	0.104909	+	0.136720i	0.842857	−	0.538138i	$-0.180872\pi$
$709$	2.79341	+	3.64044i	0.104909	+	0.136720i	−0.737948	+	0.674857i	$0.764205\pi$
$710$	0.934879	+	1.47029i	0.0350854	+	0.0551790i
$711$	9.64741	+	44.9856i	0.361806	+	1.68709i
$712$	7.87977	−	29.1033i	0.295307	−	1.09069i
$713$	−4.16563	+	1.11618i	−0.156004	+	0.0418012i
$714$	13.4646	+	46.9500i	0.503899	+	1.75706i
$715$	−1.01129	+	0.133139i	−0.0378200	+	0.00497910i
$716$	1.38899	−	4.37871i	0.0519092	−	0.163640i
$717$	24.3378	+	19.6718i	0.908913	+	0.734658i
$718$	−17.1510	+	7.97948i	−0.640071	+	0.297792i
$719$		−	51.3863i		−	1.91639i	−0.286124	−	0.958193i	$-0.592367\pi$
$719$		−	51.3863i		−	1.91639i	0.286124	−	0.958193i	$-0.407633\pi$
$720$	−1.61884	+	2.73778i	−0.0603305	+	0.102031i
$721$		−	0.821607i		−	0.0305983i
$722$	7.26171	+	15.6083i	0.270253	+	0.580880i
$723$	3.77660	−	23.9854i	0.140453	−	0.892028i
$724$	10.4876	+	20.2324i	0.389768	+	0.751933i
$725$	24.8225	−	3.26795i	0.921885	−	0.121368i
$726$	5.74733	−	23.0549i	0.213303	−	0.855647i
$727$	−20.4427	+	5.47760i	−0.758177	+	0.203153i	−0.617142	−	0.786852i	$-0.711710\pi$
$727$	−20.4427	+	5.47760i	−0.758177	+	0.203153i	−0.141035	+	0.990005i	$0.545043\pi$
$728$	−28.5203	+	3.67897i	−1.05703	+	0.136352i
$729$	15.9890	+	21.7567i	0.592184	+	0.805803i
$730$	1.01242	−	0.643741i	0.0374712	−	0.0238259i
$731$	−28.8134	−	37.5503i	−1.06570	−	1.38885i
$732$	38.3330	+	19.1520i	1.41683	+	0.707880i
$733$	7.07162	+	5.42625i	0.261196	+	0.200423i	0.731055	−	0.682319i	$-0.239028\pi$
$733$	7.07162	+	5.42625i	0.261196	+	0.200423i	−0.469858	+	0.882742i	$0.655695\pi$
$734$	32.6242	+	38.9489i	1.20418	+	1.43763i
$735$	−0.496304	+	0.811548i	−0.0183064	+	0.0299344i
$736$	7.25641	+	3.42228i	0.267475	+	0.126147i
$737$			8.39710i			0.309311i
$738$	−31.7483	+	3.92865i	−1.16867	+	0.144616i
$739$	6.91091	+	16.6844i	0.254222	+	0.613746i	0.998536	−	0.0540833i	$-0.0172236\pi$
$739$	6.91091	+	16.6844i	0.254222	+	0.613746i	−0.744315	+	0.667829i	$0.767224\pi$
$740$	−1.75673	−	2.51819i	−0.0645786	−	0.0925706i
$741$	−32.4608	+	3.44157i	−1.19248	+	0.126429i
$742$	23.4785	−	45.0059i	0.861921	−	1.65222i
$743$	1.20425	−	4.49432i	0.0441796	−	0.164880i	−0.940312	−	0.340315i	$-0.889466\pi$
$743$	1.20425	−	4.49432i	0.0441796	−	0.164880i	0.984491	+	0.175434i	$0.0561330\pi$
$744$	14.7091	+	2.35541i	0.539262	+	0.0863537i
$745$	−0.278515	−	1.03943i	−0.0102040	−	0.0380819i
$746$	47.6185	+	10.6003i	1.74344	+	0.388105i
$747$	−2.91906	+	2.01403i	−0.106803	+	0.0736894i
$748$	−15.0797	−	0.684721i	−0.551370	−	0.0250359i
$749$	−2.82885	+	21.4872i	−0.103364	+	0.785127i
$750$	2.57084	+	5.91194i	0.0938740	+	0.215874i
$751$	12.6948	+	21.9881i	0.463241	+	0.802357i	0.999120	−	0.0419377i	$-0.0133531\pi$
$751$	12.6948	+	21.9881i	0.463241	+	0.802357i	−0.535879	+	0.844295i	$0.680020\pi$
$752$	−3.68047	+	10.0034i	−0.134213	+	0.364787i
$753$	−46.0636	−	1.16436i	−1.67865	−	0.0424317i
$754$	−10.2268	−	21.9815i	−0.372440	−	0.800519i
$755$	1.93010	+	4.65967i	0.0702435	+	0.169583i
$756$	−24.6471	+	19.2954i	−0.896406	+	0.701768i
$757$	−5.75348	−	2.38317i	−0.209114	−	0.0866178i	0.275668	−	0.961253i	$-0.411101\pi$
$757$	−5.75348	−	2.38317i	−0.209114	−	0.0866178i	−0.484782	+	0.874635i	$0.661101\pi$
$758$	28.9077	−	31.4921i	1.04998	−	1.14385i
$759$	1.92970	+	2.02978i	0.0700436	+	0.0736764i
$760$	−3.61935	−	2.10227i	−0.131288	−	0.0762572i
$761$	−8.21213	−	2.20043i	−0.297689	−	0.0797657i	0.106883	−	0.994272i	$-0.465913\pi$
$761$	−8.21213	−	2.20043i	−0.297689	−	0.0797657i	−0.404572	+	0.914506i	$0.632580\pi$
$762$	−0.0201122	−	1.14980i	−0.000728589	−	0.0416528i
$763$	−9.65028	+	7.40492i	−0.349363	+	0.268076i
$764$	18.0575	−	6.53680i	0.653299	−	0.236493i
$765$	−4.00897	−	3.41141i	−0.144945	−	0.123340i
$766$	−38.9288	+	6.82924i	−1.40655	+	0.246750i
$767$	−8.65368	+	14.9886i	−0.312466	+	0.541208i
$768$	−18.0541	−	21.0249i	−0.651473	−	0.758672i
$769$	−6.57551	−	11.3891i	−0.237119	−	0.410702i	0.722767	−	0.691091i	$-0.242870\pi$
$769$	−6.57551	−	11.3891i	−0.237119	−	0.410702i	−0.959886	+	0.280389i	$0.909537\pi$
$770$	−0.826522	−	0.986756i	−0.0297858	−	0.0355602i
$771$	24.3939	+	19.7171i	0.878524	+	0.710095i
$772$	−9.35365	+	52.5120i	−0.336645	+	1.88995i
$773$	−29.2765	−	12.1267i	−1.05300	−	0.436168i	−0.212040	−	0.977261i	$-0.568011\pi$
$773$	−29.2765	−	12.1267i	−1.05300	−	0.436168i	−0.840963	+	0.541093i	$0.818011\pi$
$774$	15.3705	−	26.1503i	0.552480	−	0.939954i
$775$	10.5996	−	10.5996i	0.380748	−	0.380748i
$776$	−0.00262905	+	1.00596i	−9.43775e−5	+	0.0361119i
$777$	−7.08077	−	29.3760i	−0.254021	−	1.05386i
$778$	−9.65895	−	30.7276i	−0.346290	−	1.10164i
$779$	−5.49501	−	41.7388i	−0.196879	−	1.49545i
$780$	2.34071	−	2.03133i	0.0838110	−	0.0727332i
$781$	−5.25418	−	0.691726i	−0.188009	−	0.0247519i
$782$	−7.62557	+	10.8703i	−0.272690	+	0.388720i
$783$	−21.7891	−	14.8880i	−0.778678	−	0.532053i
$784$	−5.30565	−	6.36796i	−0.189487	−	0.227427i
$785$	−2.73003	+	4.72855i	−0.0974390	+	0.168769i
$786$	−18.1442	−	13.4249i	−0.647181	−	0.478852i
$787$	−4.75669	−	3.64994i	−0.169558	−	0.130106i	0.520497	−	0.853864i	$-0.325747\pi$
$787$	−4.75669	−	3.64994i	−0.169558	−	0.130106i	−0.690054	+	0.723757i	$0.742413\pi$
$788$	1.37959	+	2.66148i	0.0491459	+	0.0948113i
$789$	−14.5086	−	19.9313i	−0.516520	−	0.709574i
$790$	3.88734	−	4.23487i	0.138305	−	0.150670i
$791$	36.8471	−	36.8471i	1.31013	−	1.31013i
$792$	−3.22200	−	9.12175i	−0.114489	−	0.324127i
$793$	−29.5253	−	29.5253i	−1.04847	−	1.04847i
$794$	−16.7629	+	0.717255i	−0.594894	+	0.0254544i
$795$	0.576799	+	5.44035i	0.0204569	+	0.192949i
$796$	−18.0988	+	1.55167i	−0.641497	+	0.0549976i
$797$	−25.3211	+	32.9991i	−0.896919	+	1.16889i	0.0880434	+	0.996117i	$0.471939\pi$
$797$	−25.3211	+	32.9991i	−0.896919	+	1.16889i	−0.984962	+	0.172771i	$0.944728\pi$
$798$	−25.6441	−	32.2366i	−0.907792	−	1.14116i
$799$	−15.2776	−	8.82052i	−0.540482	−	0.312048i
$800$	−27.7911	+	2.30947i	−0.982563	+	0.0816522i
$801$	−1.61571	+	31.9393i	−0.0570882	+	1.12852i
$802$	−32.4926	+	5.70013i	−1.14735	+	0.201279i
$803$	−0.476310	+	3.61793i	−0.0168086	+	0.127674i
$804$	−14.0643	−	21.2874i	−0.496010	−	0.750749i
$805$	−1.12255	+	0.147787i	−0.0395648	+	0.00520881i
$806$	−12.8696	−	6.71372i	−0.453311	−	0.236481i
$807$	−12.0611	−	12.6867i	−0.424571	−	0.446592i
$808$	9.07476	−	21.7475i	0.319249	−	0.765073i
$809$	27.0808	+	27.0808i	0.952111	+	0.952111i	0.998905	−	0.0467934i	$-0.0149002\pi$
$809$	27.0808	+	27.0808i	0.952111	+	0.952111i	−0.0467934	+	0.998905i	$0.514900\pi$
$810$	1.06160	−	3.20213i	0.0373007	−	0.112511i
$811$	−20.6708	+	49.9036i	−0.725848	+	1.75235i	−0.0698911	+	0.997555i	$0.522265\pi$
$811$	−20.6708	+	49.9036i	−0.725848	+	1.75235i	−0.655957	+	0.754798i	$0.727735\pi$
$812$	16.4831	−	25.7741i	0.578444	−	0.904494i
$813$	−0.665076	−	1.72789i	−0.0233252	−	0.0605998i
$814$	9.30270	+	0.822048i	0.326060	+	0.0288128i
$815$	−4.37355	+	2.52507i	−0.153199	+	0.0884493i
$816$	39.3754	−	23.5212i	1.37841	−	0.823408i
$817$	34.5698	+	19.9589i	1.20944	+	0.698273i
$818$	−0.868288	−	0.609109i	−0.0303590	−	0.0212970i
$819$	28.7330	−	10.2336i	1.00401	−	0.357593i
$820$	2.69522	+	2.95163i	0.0941213	+	0.103075i
$821$	10.6012	+	13.8157i	0.369984	+	0.482172i	0.940827	−	0.338887i	$-0.110050\pi$
$821$	10.6012	+	13.8157i	0.369984	+	0.482172i	−0.570843	+	0.821059i	$0.693384\pi$
$822$	49.8734	−	14.3030i	1.73954	−	0.498873i
$823$	−9.82579	+	36.6703i	−0.342505	+	1.27825i	0.552994	+	0.833185i	$0.313485\pi$
$823$	−9.82579	+	36.6703i	−0.342505	+	1.27825i	−0.895499	+	0.445063i	$0.853181\pi$
$824$	−0.745762	+	0.197739i	−0.0259799	+	0.00688856i
$825$	−9.33646	−	2.75637i	−0.325054	−	0.0959643i
$826$	−21.8206	+	0.933661i	−0.759234	+	0.0324862i
$827$	−8.01205	+	19.3428i	−0.278606	+	0.672615i	−0.999798	−	0.0201210i	$-0.993595\pi$
$827$	−8.01205	+	19.3428i	−0.278606	+	0.672615i	0.721191	+	0.692736i	$0.243595\pi$
$828$	−8.29165	−	1.91363i	−0.288155	−	0.0665033i
$829$	−19.1561	+	7.93471i	−0.665318	+	0.275584i	−0.689675	−	0.724119i	$-0.742246\pi$
$829$	−19.1561	+	7.93471i	−0.665318	+	0.275584i	0.0243563	+	0.999703i	$0.492246\pi$
$830$	0.416255	+	0.151915i	0.0144484	+	0.00527305i
$831$	−25.1252	−	15.3654i	−0.871584	−	0.533020i
$832$	10.2034	+	25.0021i	0.353741	+	0.866792i
$833$	11.8801	−	6.85897i	0.411621	−	0.237649i
$834$	−16.1184	+	2.40951i	−0.558133	+	0.0834346i
$835$	0.635993	+	0.0837301i	0.0220094	+	0.00289760i
$836$	11.9707	−	4.33339i	0.414017	−	0.149873i
$837$	−15.7762	+	0.869895i	−0.545304	+	0.0300680i
$838$	−1.27981	+	0.813762i	−0.0442103	+	0.0281109i
$839$	4.59959	−	1.23246i	0.158795	−	0.0425491i	−0.178546	−	0.983932i	$-0.557139\pi$
$839$	4.59959	−	1.23246i	0.158795	−	0.0425491i	0.337341	+	0.941383i	$0.390473\pi$
$840$	3.74803	+	1.11717i	0.129319	+	0.0385461i
$841$	−3.09755	−	0.829987i	−0.106812	−	0.0286202i
$842$	−26.5435	+	8.34373i	−0.914751	+	0.287544i
$843$	24.0848	−	17.5321i	0.829524	−	0.603836i
$844$	−4.45347	−	20.2553i	−0.153295	−	0.697214i
$845$	0.393266	−	0.162896i	0.0135288	−	0.00560380i
$846$	1.56285	−	11.1970i	0.0537319	−	0.384962i
$847$	−29.2169			−1.00391
$848$	−46.5019	−	10.4794i	−1.59688	−	0.359863i
$849$	−9.85994	+	5.36511i	−0.338392	+	0.184130i
$850$	4.06263	−	45.9747i	0.139347	−	1.57692i
$851$	5.00087	−	6.51726i	0.171428	−	0.223409i
$852$	14.4784	−	7.04664i	0.496022	−	0.241414i
$853$	21.4402	−	16.4516i	0.734098	−	0.563293i	−0.172642	−	0.984985i	$-0.555230\pi$
$853$	21.4402	−	16.4516i	0.734098	−	0.563293i	0.906739	+	0.421692i	$0.138564\pi$
$854$	11.4494	−	51.4326i	0.391789	−	1.75999i
$855$	4.22470	+	1.36421i	0.144482	+	0.0466550i
$856$	20.1845	−	2.60369i	0.689893	−	0.0889925i
$857$	−4.43416	−	16.5485i	−0.151468	−	0.565286i	−0.999382	−	0.0351522i	$-0.988808\pi$
$857$	−4.43416	−	16.5485i	−0.151468	−	0.565286i	0.847914	−	0.530134i	$-0.177858\pi$
$858$	0.164865	+	9.42519i	0.00562841	+	0.321771i
$859$	−2.95798	−	22.4681i	−0.100925	−	0.766600i	−0.964817	−	0.262923i	$-0.915313\pi$
$859$	−2.95798	−	22.4681i	−0.100925	−	0.766600i	0.863892	−	0.503677i	$-0.168020\pi$
$860$	−3.77611	+	0.323738i	−0.128764	+	0.0110394i
$861$	14.1304	+	36.7113i	0.481563	+	1.25112i
$862$	1.52694	+	0.557267i	0.0520078	+	0.0189806i
$863$	−37.9392			−1.29147			−0.645733	−	0.763564i	$-0.723448\pi$
$863$	−37.9392			−1.29147			−0.645733	+	0.763564i	$0.723448\pi$
$864$	23.4461	+	17.7280i	0.797653	+	0.603117i
$865$	−5.66067			−0.192469
$866$	17.8525	+	6.51541i	0.606653	+	0.221402i
$867$	16.6909	+	43.3634i	0.566851	+	1.47270i
$868$	−1.56467	−	18.2504i	−0.0531084	−	0.619460i
$869$	2.28222	+	17.3352i	0.0774189	+	0.588055i
$870$	0.0576668	+	3.29676i	0.00195509	+	0.111771i
$871$	6.43458	+	24.0142i	0.218028	+	0.813690i
$872$	9.04391	+	6.97727i	0.306266	+	0.236280i
$873$	−0.223734	−	1.04327i	−0.00757226	−	0.0353092i
$874$	2.43333	−	10.9310i	0.0823085	−	0.369745i
$875$	6.28905	−	4.82576i	0.212609	−	0.163140i
$876$	−4.85219	−	9.96956i	−0.163940	−	0.336840i
$877$	8.94330	−	11.6551i	0.301994	−	0.393566i	−0.617564	−	0.786521i	$-0.711880\pi$
$877$	8.94330	−	11.6551i	0.301994	−	0.393566i	0.919558	+	0.392955i	$0.128547\pi$
$878$	−2.39035	+	27.0504i	−0.0806705	+	0.912907i
$879$	−40.4929	+	22.0335i	−1.36579	+	0.743171i
$880$	−0.696744	+	0.987710i	−0.0234872	+	0.0332957i
$881$	39.5715			1.33320			0.666598	−	0.745417i	$-0.267750\pi$
$881$	39.5715			1.33320			0.666598	+	0.745417i	$0.267750\pi$
$882$	6.93281	+	5.40597i	0.233440	+	0.182028i
$883$	−7.71952	+	3.19753i	−0.259782	+	0.107605i	−0.508774	−	0.860900i	$-0.669901\pi$
$883$	−7.71952	+	3.19753i	−0.259782	+	0.107605i	0.248991	+	0.968506i	$0.419901\pi$
$884$	−43.6500	+	9.59722i	−1.46811	+	0.322790i
$885$	1.90305	−	1.38529i	0.0639702	−	0.0465659i
$886$	−34.8999	+	10.9705i	−1.17248	+	0.368560i
$887$	6.06787	+	1.62588i	0.203739	+	0.0545918i	0.359245	−	0.933243i	$-0.383034\pi$
$887$	6.06787	+	1.62588i	0.203739	+	0.0545918i	−0.155506	+	0.987835i	$0.549701\pi$
$888$	−24.9601	+	13.4971i	−0.837605	+	0.452934i
$889$	−1.36588	+	0.365985i	−0.0458100	+	0.0122748i
$890$	3.37186	−	2.14398i	0.113025	−	0.0718664i
$891$	5.39305	+	8.72933i	0.180674	+	0.292443i
$892$	−14.2283	−	39.3050i	−0.476400	−	1.31603i
$893$	14.7507	+	1.94196i	0.493613	+	0.0649853i
$894$	−9.83567	+	1.47032i	−0.328954	+	0.0491749i
$895$	0.527220	−	0.304391i	0.0176230	−	0.0101747i
$896$	−19.7156	+	27.7945i	−0.658651	+	0.928547i
$897$	7.07398	+	4.32611i	0.236193	+	0.144445i
$898$	−38.2724	−	13.9678i	−1.27717	−	0.466111i
$899$	14.2675	−	5.90977i	0.475846	−	0.197102i
$900$	28.2854	−	8.65000i	0.942847	−	0.288333i
$901$	30.1909	−	72.8872i	1.00580	−	2.42823i
$902$	−12.1463	+	0.519718i	−0.404428	+	0.0173047i
$903$	−35.7724	−	10.5610i	−1.19043	−	0.351446i
$904$	−42.3138	−	24.5775i	−1.40733	−	0.817436i
$905$	−0.781660	+	2.91719i	−0.0259832	+	0.0969708i
$906$	44.8051	−	12.8494i	1.48855	−	0.426894i
$907$	13.0875	+	17.0560i	0.434565	+	0.566336i	0.958380	−	0.285496i	$-0.0921584\pi$
$907$	13.0875	+	17.0560i	0.434565	+	0.566336i	−0.523815	+	0.851832i	$0.675492\pi$
$908$	15.2978	−	13.9689i	0.507676	−	0.463575i
$909$	−4.51021	+	24.5840i	−0.149594	+	0.815401i
$910$	−3.11984	−	2.18859i	−0.103422	−	0.0725511i
$911$	41.5522	+	23.9902i	1.37668	+	0.794829i	0.991759	−	0.128118i	$-0.0408937\pi$
$911$	41.5522	+	23.9902i	1.37668	+	0.794829i	0.384926	+	0.922948i	$0.374227\pi$
$912$	−23.0889	+	31.0353i	−0.764551	+	1.02768i
$913$	−1.16720	+	0.673882i	−0.0386286	+	0.0223022i
$914$	−13.8852	−	1.22698i	−0.459280	−	0.0405850i
$915$	2.03992	+	5.29977i	0.0674375	+	0.175205i
$916$	−13.4203	−	8.58260i	−0.443420	−	0.283577i
$917$	−10.6210	+	25.6414i	−0.350736	+	0.846753i
$918$	−35.5174	+	33.2437i	−1.17225	+	1.09721i
$919$	−19.6503	−	19.6503i	−0.648203	−	0.648203i	0.304356	−	0.952558i	$-0.401559\pi$
$919$	−19.6503	−	19.6503i	−0.648203	−	0.648203i	−0.952558	+	0.304356i	$0.901559\pi$
$920$	0.404313	+	0.983359i	0.0133298	+	0.0324204i
$921$	−6.72750	−	7.07643i	−0.221679	−	0.233176i
$922$	23.3991	+	12.2067i	0.770609	+	0.402008i
$923$	−15.5561	+	2.04799i	−0.512034	+	0.0674106i
$924$	−9.92510	+	6.55738i	−0.326512	+	0.215722i
$925$	−3.72703	+	28.3096i	−0.122544	+	0.930814i
$926$	35.4425	−	6.21763i	1.16471	−	0.204324i
$927$	0.728465	−	0.372839i	0.0239259	−	0.0122456i
$928$	−27.3619	−	8.75838i	−0.898198	−	0.287508i
$929$	12.4296	+	7.17623i	0.407802	+	0.235445i	0.689845	−	0.723957i	$-0.257679\pi$
$929$	12.4296	+	7.17623i	0.407802	+	0.235445i	−0.282043	+	0.959402i	$0.591012\pi$
$930$	1.22899	+	1.54494i	0.0403003	+	0.0506605i
$931$	−7.04296	+	9.17857i	−0.230824	+	0.300815i
$932$	−0.292360	−	3.41011i	−0.00957655	−	0.111702i
$933$	−3.71680	−	35.0568i	−0.121683	−	1.14771i
$934$	−2.41319	+	0.103256i	−0.0789619	+	0.00337864i
$935$	−1.41456	−	1.41456i	−0.0462611	−	0.0462611i
$936$	−16.2042	−	23.6176i	−0.529651	−	0.771965i
$937$	18.7763	−	18.7763i	0.613394	−	0.613394i	−0.330435	−	0.943829i	$-0.607195\pi$
$937$	18.7763	−	18.7763i	0.613394	−	0.613394i	0.943829	+	0.330435i	$0.107195\pi$
$938$	−21.2154	+	23.1121i	−0.692709	+	0.754638i
$939$	−1.32313	−	1.81766i	−0.0431788	−	0.0593172i
$940$	−1.25410	+	0.650070i	−0.0409043	+	0.0212030i
$941$	−3.06173	−	2.34935i	−0.0998096	−	0.0765866i	0.557651	−	0.830075i	$-0.311703\pi$
$941$	−3.06173	−	2.34935i	−0.0998096	−	0.0765866i	−0.657461	+	0.753489i	$0.728369\pi$
$942$	40.5638	+	30.0133i	1.32164	+	0.977887i
$943$	−5.34702	+	9.26131i	−0.174123	+	0.301590i
$944$	6.09910	+	19.5815i	0.198509	+	0.637325i
$945$	−4.13631	−	0.314199i	−0.134554	−	0.0102209i
$946$	6.62016	−	9.43706i	0.215240	−	0.306825i
$947$	21.4607	+	2.82535i	0.697378	+	0.0918116i	0.470876	−	0.882199i	$-0.343938\pi$
$947$	21.4607	+	2.82535i	0.697378	+	0.0918116i	0.226502	+	0.974011i	$0.427271\pi$
$948$	−34.8203	−	40.1237i	−1.13091	−	1.30316i
$949$	1.41021	+	10.7116i	0.0457774	+	0.347714i
$950$	11.6726	+	37.1335i	0.378709	+	1.20477i
$951$	9.56835	+	39.6962i	0.310275	+	1.28724i
$952$	−39.7755	−	39.9839i	−1.28913	−	1.29589i
$953$	33.7540	−	33.7540i	1.09340	−	1.09340i	0.0982373	−	0.995163i	$-0.468680\pi$
$953$	33.7540	−	33.7540i	1.09340	−	1.09340i	0.995163	−	0.0982373i	$-0.0313204\pi$
$954$	50.5581	+	0.393436i	1.63688	+	0.0127379i
$955$	2.35130	+	0.973941i	0.0760864	+	0.0315160i
$956$	−35.5752	−	6.33679i	−1.15058	−	0.204946i
$957$	−7.79970	−	6.30435i	−0.252128	−	0.203791i
$958$	5.95985	+	7.11526i	0.192554	+	0.229883i
$959$	−31.8993	−	55.2513i	−1.03008	−	1.78416i
$960$	0.111993	−	3.67091i	0.00361456	−	0.118478i
$961$	−10.8770	+	18.8395i	−0.350870	+	0.607724i
$962$	27.2340	−	4.77763i	0.878059	−	0.154037i
$963$	−20.3350	+	7.24260i	−0.655287	+	0.233389i
$964$	9.54337	+	26.3630i	0.307371	+	0.849096i
$965$	−5.60794	+	4.30312i	−0.180526	+	0.138522i
$966$	0.183004	+	10.4622i	0.00588807	+	0.336615i
$967$	−50.2128	−	13.4545i	−1.61474	−	0.432667i	−0.665286	−	0.746588i	$-0.731691\pi$
$967$	−50.2128	−	13.4545i	−1.61474	−	0.432667i	−0.949449	+	0.313921i	$0.898357\pi$
$968$	7.03173	+	26.5198i	0.226008	+	0.852380i
$969$	−44.1107	−	46.3985i	−1.41704	−	1.49053i
$970$	−0.0901518	+	0.0982115i	−0.00289460	+	0.00315338i
$971$	−22.5790	−	9.35251i	−0.724593	−	0.300136i	−0.0102652	−	0.999947i	$-0.503268\pi$
$971$	−22.5790	−	9.35251i	−0.724593	−	0.300136i	−0.714328	+	0.699811i	$0.753268\pi$
$972$	−28.2926	−	13.0968i	−0.907487	−	0.420081i
$973$	7.66900	+	18.5146i	0.245857	+	0.593551i
$974$	−20.7805	−	44.6654i	−0.665849	−	1.43117i
$975$	−28.8128	−	0.728308i	−0.922747	−	0.0233245i
$976$	−49.4403	+	1.98603i	−1.58255	+	0.0635712i
$977$	18.3789	+	31.8332i	0.587994	+	1.01844i	0.994495	+	0.104785i	$0.0334155\pi$
$977$	18.3789	+	31.8332i	0.587994	+	1.01844i	−0.406501	+	0.913650i	$0.633251\pi$
$978$	18.6119	+	42.8000i	0.595142	+	1.36859i
$979$	−1.58635	+	12.0495i	−0.0507000	+	0.385105i
$980$	0.0498252	−	1.09731i	0.00159161	−	0.0350522i
$981$	−10.9447	−	5.19596i	−0.349437	−	0.165894i
$982$	38.4484	+	8.55895i	1.22694	+	0.273127i
$983$	9.93099	+	37.0629i	0.316749	+	1.18212i	0.922350	+	0.386356i	$0.126266\pi$
$983$	9.93099	+	37.0629i	0.316749	+	1.18212i	−0.605601	+	0.795769i	$0.707067\pi$
$984$	29.9215	−	21.6614i	0.953864	−	0.690540i
$985$	−0.102824	+	0.383743i	−0.00327623	+	0.0122271i
$986$	21.9921	−	42.1568i	0.700372	−	1.34254i
$987$	−13.8243	+	1.46569i	−0.440034	+	0.0466534i
$988$	30.9135	−	21.5657i	0.983491	−	0.686097i
$989$	−3.88040	−	9.36813i	−0.123390	−	0.297889i
$990$	0.499821	−	1.18061i	0.0158854	−	0.0375221i
$991$		−	7.63952i		−	0.242677i	−0.992611	−	0.121339i	$-0.961281\pi$
$991$		−	7.63952i		−	0.242677i	0.992611	−	0.121339i	$-0.0387187\pi$
$992$	−16.1891	+	5.81263i	−0.514005	+	0.184551i
$993$	32.7194	−	53.5022i	1.03832	−	1.69784i
$994$	−12.7139	−	15.1787i	−0.403261	−	0.481439i
$995$	−1.90987	−	1.46549i	−0.0605468	−	0.0464592i
$996$	1.83027	−	3.66329i	0.0579943	−	0.116076i
$997$	32.1606	+	41.9125i	1.01854	+	1.32738i	0.943922	+	0.330169i	$0.107106\pi$
$997$	32.1606	+	41.9125i	1.01854	+	1.32738i	0.0746143	+	0.997212i	$0.476227\pi$
$998$	−28.0312	+	17.8236i	−0.887314	+	0.564195i
$999$	22.8325	−	19.6087i	0.722390	−	0.620391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.19	✓	368
3.2	odd	2		864.2.bn.a.683.28		368
9.4	even	3		864.2.bn.a.395.12		368
9.5	odd	6	inner	288.2.bf.a.203.35	yes	368
32.3	odd	8	inner	288.2.bf.a.227.35	yes	368
96.35	even	8		864.2.bn.a.35.12		368
288.67	odd	24		864.2.bn.a.611.28		368
288.131	even	24	inner	288.2.bf.a.131.19	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.19	✓	368	1.1	even	1	trivial
288.2.bf.a.131.19	yes	368	288.131	even	24	inner
288.2.bf.a.203.35	yes	368	9.5	odd	6	inner
288.2.bf.a.227.35	yes	368	32.3	odd	8	inner
864.2.bn.a.35.12		368	96.35	even	8
864.2.bn.a.395.12		368	9.4	even	3
864.2.bn.a.611.28		368	288.67	odd	24
864.2.bn.a.683.28		368	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.484847 + 1.32850i) q^{2} +(0.622180 + 1.61644i) q^{3} +(-1.52985 - 1.28824i) q^{4} +(-0.0345958 - 0.262781i) q^{5} +(-2.44912 + 0.0428399i) q^{6} +(0.779563 + 2.90937i) q^{7} +(2.45318 - 1.40781i) q^{8} +(-2.22579 + 2.01144i) q^{9} +(0.365879 + 0.0814479i) q^{10} +(-0.904502 + 0.694049i) q^{11} +(1.13053 - 3.27443i) q^{12} +(-2.05487 + 2.67796i) q^{13} +(-4.24308 - 0.374946i) q^{14} +(0.403246 - 0.219419i) q^{15} +(0.680862 + 3.94163i) q^{16} -6.62015 q^{17} +(-1.59304 - 3.93220i) q^{18} +(5.15825 - 2.13662i) q^{19} +(-0.285599 + 0.446582i) q^{20} +(-4.21781 + 3.07027i) q^{21} +(-0.483502 - 1.53814i) q^{22} +(-1.36994 - 0.367075i) q^{23} +(3.80196 + 3.08952i) q^{24} +(4.76177 - 1.27591i) q^{25} +(-2.56139 - 4.02831i) q^{26} +(-4.63621 - 2.34638i) q^{27} +(2.55536 - 5.45516i) q^{28} +(5.03525 + 0.662903i) q^{29} +(0.0959865 + 0.642099i) q^{30} +(2.63335 - 1.52037i) q^{31} +(-5.56658 - 1.00656i) q^{32} +(-1.68465 - 1.03025i) q^{33} +(3.20976 - 8.79490i) q^{34} +(0.737557 - 0.305506i) q^{35} +(5.99633 - 0.209840i) q^{36} +(-2.21656 + 5.35125i) q^{37} +(0.337543 + 7.88870i) q^{38} +(-5.60728 - 1.65542i) q^{39} +(-0.454814 - 0.595944i) q^{40} +(1.95155 - 7.28329i) q^{41} +(-2.03388 - 7.09198i) q^{42} +(4.35237 + 5.67212i) q^{43} +(2.27785 + 0.103430i) q^{44} +(0.605570 + 0.515307i) q^{45} +(1.15187 - 1.64200i) q^{46} +(2.30774 + 1.33237i) q^{47} +(-5.94780 + 3.55298i) q^{48} +(-1.79453 + 1.03607i) q^{49} +(-0.613675 + 6.94466i) q^{50} +(-4.11892 - 10.7011i) q^{51} +(6.59351 - 1.44970i) q^{52} +(-4.56045 + 11.0099i) q^{53} +(5.36503 - 5.02159i) q^{54} +(0.213675 + 0.213675i) q^{55} +(6.00824 + 6.03972i) q^{56} +(6.66309 + 7.00867i) q^{57} +(-3.32200 + 6.36794i) q^{58} +(5.08348 - 0.669253i) q^{59} +(-0.899570 - 0.183801i) q^{60} +(-1.61461 + 12.2642i) q^{61} +(0.743041 + 4.23557i) q^{62} +(-7.58715 - 4.90759i) q^{63} +(4.03616 - 6.90720i) q^{64} +(0.774808 + 0.447335i) q^{65} +(2.18550 - 1.73855i) q^{66} +(4.48367 - 5.84323i) q^{67} +(10.1278 + 8.52836i) q^{68} +(-0.258994 - 2.44282i) q^{69} +(0.0482638 + 1.12797i) q^{70} +(3.28684 + 3.28684i) q^{71} +(-2.62853 + 8.06789i) q^{72} +(2.26326 - 2.26326i) q^{73} +(-6.03447 - 5.53925i) q^{74} +(5.02512 + 6.90329i) q^{75} +(-10.6438 - 3.37638i) q^{76} +(-2.72436 - 2.09048i) q^{77} +(4.91790 - 6.64667i) q^{78} +(7.66807 - 13.2815i) q^{79} +(1.01223 - 0.315281i) q^{80} +(0.908239 - 8.95406i) q^{81} +(8.72967 + 6.12392i) q^{82} +(1.17203 + 0.154301i) q^{83} +(10.4078 + 0.736513i) q^{84} +(0.229029 + 1.73965i) q^{85} +(-9.64568 + 3.03203i) q^{86} +(2.06128 + 8.55165i) q^{87} +(-1.24182 + 2.97599i) q^{88} +(7.53778 - 7.53778i) q^{89} +(-0.978196 + 0.554658i) q^{90} +(-9.39309 - 3.89075i) q^{91} +(1.62292 + 2.32638i) q^{92} +(4.09601 + 3.31073i) q^{93} +(-2.88896 + 2.41984i) q^{94} +(-0.739916 - 1.28157i) q^{95} +(-1.83637 - 9.62433i) q^{96} +(-0.177831 + 0.308013i) q^{97} +(-0.506355 - 2.88638i) q^{98} +(0.617192 - 3.36415i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21}+ \cdots - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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