LMFDB - Embedded newform 243.2.g.a.208.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(10,243)] 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("243.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.g (of order $27$, degree $18$, not 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			208.3
Character	$\chi$	$=$	243.208
Dual form			243.2.g.a.118.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.658400 - 0.156044i) q^{2} +(-1.37812 - 0.692120i) q^{4} +(-0.563225 + 0.756542i) q^{5} +(1.22035 + 0.802640i) q^{7} +(1.83603 + 1.54061i) q^{8} +(0.488880 - 0.410219i) q^{10} +(6.07936 - 0.710575i) q^{11} +(1.50478 - 5.02631i) q^{13} +(-0.678234 - 0.718886i) q^{14} +(0.873392 + 1.17317i) q^{16} +(0.00536485 + 0.0304256i) q^{17} +(0.634963 - 3.60105i) q^{19} +(1.29981 - 0.652790i) q^{20} +(-4.11353 - 0.480802i) q^{22} +(0.0873480 - 0.0574497i) q^{23} +(1.17888 + 3.93774i) q^{25} +(-1.77507 + 3.07451i) q^{26} +(-1.12628 - 1.95077i) q^{28} +(0.351839 - 0.372928i) q^{29} +(0.475004 + 8.15551i) q^{31} +(-2.29059 - 5.31019i) q^{32} +(0.00121550 - 0.0208694i) q^{34} +(-1.29456 + 0.471183i) q^{35} +(5.42328 + 1.97391i) q^{37} +(-0.979980 + 2.27185i) q^{38} +(-2.19963 + 0.521322i) q^{40} +(-4.26774 + 1.01147i) q^{41} +(0.545274 - 1.26409i) q^{43} +(-8.86991 - 3.22838i) q^{44} +(-0.0664745 + 0.0241947i) q^{46} +(0.326176 - 5.60023i) q^{47} +(-1.92752 - 4.46850i) q^{49} +(-0.161716 - 2.77656i) q^{50} +(-5.55259 + 5.88540i) q^{52} +(4.89106 + 8.47157i) q^{53} +(-2.88646 + 4.99950i) q^{55} +(1.00405 + 3.35376i) q^{56} +(-0.289844 + 0.190633i) q^{58} +(-5.61120 - 0.655856i) q^{59} +(1.53507 - 0.770942i) q^{61} +(0.959872 - 5.44370i) q^{62} +(0.171556 + 0.972942i) q^{64} +(2.95509 + 3.96937i) q^{65} +(-1.87870 - 1.99130i) q^{67} +(0.0136647 - 0.0456434i) q^{68} +(0.925866 - 0.108218i) q^{70} +(-1.66448 + 1.39666i) q^{71} +(-6.38204 - 5.35517i) q^{73} +(-3.26267 - 2.14589i) q^{74} +(-3.36742 + 4.52323i) q^{76} +(7.98930 + 4.01238i) q^{77} +(-12.2728 - 2.90871i) q^{79} -1.37947 q^{80} +2.96771 q^{82} +(-17.3440 - 4.11059i) q^{83} +(-0.0260399 - 0.0130777i) q^{85} +(-0.556260 + 0.747187i) q^{86} +(12.2566 + 8.06128i) q^{88} +(10.6853 + 8.96604i) q^{89} +(5.87068 - 4.92609i) q^{91} +(-0.160139 + 0.0187175i) q^{92} +(-1.08863 + 3.63629i) q^{94} +(2.36672 + 2.50858i) q^{95} +(-4.18690 - 5.62398i) q^{97} +(0.571800 + 3.24284i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{27}\right)$

Coefficient data

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

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

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

$2$	−0.658400	−	0.156044i	−0.465559	−	0.110339i	−0.00885983	−	0.999961i	$-0.502820\pi$
$2$	−0.658400	−	0.156044i	−0.465559	−	0.110339i	−0.456699	+	0.889621i	$0.650968\pi$
$3$		0			0
$3$		0			0
$4$	−1.37812	−	0.692120i	−0.689062	−	0.346060i
$5$	−0.563225	+	0.756542i	−0.251882	+	0.338336i	−0.910022	−	0.414559i	$-0.863936\pi$
$5$	−0.563225	+	0.756542i	−0.251882	+	0.338336i	0.658141	+	0.752895i	$0.271343\pi$
$6$		0			0
$7$	1.22035	+	0.802640i	0.461251	+	0.303369i	0.758784	−	0.651342i	$-0.225794\pi$
$7$	1.22035	+	0.802640i	0.461251	+	0.303369i	−0.297534	+	0.954711i	$0.596164\pi$
$8$	1.83603	+	1.54061i	0.649133	+	0.544688i
$9$		0			0
$10$	0.488880	−	0.410219i	0.154598	−	0.129723i
$11$	6.07936	−	0.710575i	1.83299	−	0.214246i	0.871751	−	0.489948i	$-0.162984\pi$
$11$	6.07936	−	0.710575i	1.83299	−	0.214246i	0.961243	+	0.275702i	$0.0889103\pi$
$12$		0			0
$13$	1.50478	−	5.02631i	0.417351	−	1.39405i	−0.448516	−	0.893775i	$-0.648047\pi$
$13$	1.50478	−	5.02631i	0.417351	−	1.39405i	0.865867	−	0.500274i	$-0.166767\pi$
$14$	−0.678234	−	0.718886i	−0.181266	−	0.192130i
$15$		0			0
$16$	0.873392	+	1.17317i	0.218348	+	0.293292i
$17$	0.00536485	+	0.0304256i	0.00130117	+	0.00737929i	0.985451	−	0.169957i	$-0.0543630\pi$
$17$	0.00536485	+	0.0304256i	0.00130117	+	0.00737929i	−0.984150	+	0.177337i	$0.943252\pi$
$18$		0			0
$19$	0.634963	−	3.60105i	0.145670	−	0.826138i	−0.821156	−	0.570704i	$-0.806670\pi$
$19$	0.634963	−	3.60105i	0.145670	−	0.826138i	0.966826	−	0.255434i	$-0.0822184\pi$
$20$	1.29981	−	0.652790i	0.290647	−	0.145968i
$21$		0			0
$22$	−4.11353	−	0.480802i	−0.877007	−	0.102507i
$23$	0.0873480	−	0.0574497i	0.0182133	−	0.0119791i	−0.540370	−	0.841428i	$-0.681716\pi$
$23$	0.0873480	−	0.0574497i	0.0182133	−	0.0119791i	0.558583	+	0.829449i	$0.311345\pi$
$24$		0			0
$25$	1.17888	+	3.93774i	0.235776	+	0.787548i
$26$	−1.77507	+	3.07451i	−0.348120	+	0.602961i
$27$		0			0
$28$	−1.12628	−	1.95077i	−0.212846	−	0.368661i
$29$	0.351839	−	0.372928i	0.0653349	−	0.0692509i	−0.693882	−	0.720089i	$-0.744101\pi$
$29$	0.351839	−	0.372928i	0.0653349	−	0.0692509i	0.759216	+	0.650838i	$0.225582\pi$
$30$		0			0
$31$	0.475004	+	8.15551i	0.0853133	+	1.46477i	0.721059	+	0.692874i	$0.243656\pi$
$31$	0.475004	+	8.15551i	0.0853133	+	1.46477i	−0.635746	+	0.771898i	$0.719307\pi$
$32$	−2.29059	−	5.31019i	−0.404924	−	0.938718i
$33$		0			0
$34$	0.00121550	−	0.0208694i	0.000208457	−	0.00357906i
$35$	−1.29456	+	0.471183i	−0.218821	+	0.0796444i
$36$		0			0
$37$	5.42328	+	1.97391i	0.891581	+	0.324509i	0.746874	−	0.664965i	$-0.231554\pi$
$37$	5.42328	+	1.97391i	0.891581	+	0.324509i	0.144707	+	0.989475i	$0.453776\pi$
$38$	−0.979980	+	2.27185i	−0.158974	+	0.368543i
$39$		0			0
$40$	−2.19963	+	0.521322i	−0.347792	+	0.0824282i
$41$	−4.26774	+	1.01147i	−0.666509	+	0.157966i	−0.549924	−	0.835215i	$-0.685343\pi$
$41$	−4.26774	+	1.01147i	−0.666509	+	0.157966i	−0.116586	+	0.993181i	$0.537195\pi$
$42$		0			0
$43$	0.545274	−	1.26409i	0.0831534	−	0.192771i	−0.871567	−	0.490277i	$-0.836896\pi$
$43$	0.545274	−	1.26409i	0.0831534	−	0.192771i	0.954720	+	0.297506i	$0.0961548\pi$
$44$	−8.86991	−	3.22838i	−1.33719	−	0.486697i
$45$		0			0
$46$	−0.0664745	+	0.0241947i	−0.00980113	+	0.00356732i
$47$	0.326176	−	5.60023i	0.0475777	−	0.816877i	−0.887143	−	0.461494i	$-0.847313\pi$
$47$	0.326176	−	5.60023i	0.0475777	−	0.816877i	0.934721	−	0.355383i	$-0.115649\pi$
$48$		0			0
$49$	−1.92752	−	4.46850i	−0.275361	−	0.638358i
$50$	−0.161716	−	2.77656i	−0.0228702	−	0.392666i
$51$		0			0
$52$	−5.55259	+	5.88540i	−0.770005	+	0.816158i
$53$	4.89106	+	8.47157i	0.671839	+	1.16366i	0.977382	+	0.211481i	$0.0678288\pi$
$53$	4.89106	+	8.47157i	0.671839	+	1.16366i	−0.305543	+	0.952178i	$0.598838\pi$
$54$		0			0
$55$	−2.88646	+	4.99950i	−0.389211	+	0.674132i
$56$	1.00405	+	3.35376i	0.134172	+	0.448165i
$57$		0			0
$58$	−0.289844	+	0.190633i	−0.0380583	+	0.0250314i
$59$	−5.61120	−	0.655856i	−0.730517	−	0.0853851i	−0.257300	−	0.966331i	$-0.582833\pi$
$59$	−5.61120	−	0.655856i	−0.730517	−	0.0853851i	−0.473216	+	0.880946i	$0.656907\pi$
$60$		0			0
$61$	1.53507	−	0.770942i	0.196546	−	0.0987090i	−0.347804	−	0.937567i	$-0.613073\pi$
$61$	1.53507	−	0.770942i	0.196546	−	0.0987090i	0.544350	+	0.838858i	$0.316776\pi$
$62$	0.959872	−	5.44370i	0.121904	−	0.691351i
$63$		0			0
$64$	0.171556	+	0.972942i	0.0214445	+	0.121618i
$65$	2.95509	+	3.96937i	0.366534	+	0.492340i
$66$		0			0
$67$	−1.87870	−	1.99130i	−0.229520	−	0.243277i	0.602371	−	0.798216i	$-0.294223\pi$
$67$	−1.87870	−	1.99130i	−0.229520	−	0.243277i	−0.831891	+	0.554940i	$0.812741\pi$
$68$	0.0136647	−	0.0456434i	0.00165709	−	0.00553508i
$69$		0			0
$70$	0.925866	−	0.108218i	0.110662	−	0.0129345i
$71$	−1.66448	+	1.39666i	−0.197537	+	0.165753i	−0.736191	−	0.676774i	$-0.763377\pi$
$71$	−1.66448	+	1.39666i	−0.197537	+	0.165753i	0.538654	+	0.842527i	$0.318933\pi$
$72$		0			0
$73$	−6.38204	−	5.35517i	−0.746961	−	0.626775i	0.187736	−	0.982219i	$-0.439885\pi$
$73$	−6.38204	−	5.35517i	−0.746961	−	0.626775i	−0.934697	+	0.355445i	$0.884329\pi$
$74$	−3.26267	−	2.14589i	−0.379277	−	0.249455i
$75$		0			0
$76$	−3.36742	+	4.52323i	−0.386269	+	0.518850i
$77$	7.98930	+	4.01238i	0.910466	+	0.457253i
$78$		0			0
$79$	−12.2728	−	2.90871i	−1.38080	−	0.327256i	−0.527891	−	0.849312i	$-0.677017\pi$
$79$	−12.2728	−	2.90871i	−1.38080	−	0.327256i	−0.852911	+	0.522056i	$0.825165\pi$
$80$	−1.37947			−0.154229
$81$		0			0
$82$	2.96771			0.327729
$83$	−17.3440	−	4.11059i	−1.90375	−	0.451196i	−0.999719	−	0.0237250i	$-0.992447\pi$
$83$	−17.3440	−	4.11059i	−1.90375	−	0.451196i	−0.904029	−	0.427471i	$-0.859404\pi$
$84$		0			0
$85$	−0.0260399	−	0.0130777i	−0.00282442	−	0.00141848i
$86$	−0.556260	+	0.747187i	−0.0599831	+	0.0805713i
$87$		0			0
$88$	12.2566	+	8.06128i	1.30656	+	0.859335i
$89$	10.6853	+	8.96604i	1.13264	+	0.950399i	0.999173	−	0.0406545i	$-0.0129443\pi$
$89$	10.6853	+	8.96604i	1.13264	+	0.950399i	0.133468	+	0.991053i	$0.457389\pi$
$90$		0			0
$91$	5.87068	−	4.92609i	0.615415	−	0.516394i
$92$	−0.160139	+	0.0187175i	−0.0166956	+	0.00195143i
$93$		0			0
$94$	−1.08863	+	3.63629i	−0.112284	+	0.375055i
$95$	2.36672	+	2.50858i	0.242820	+	0.257375i
$96$		0			0
$97$	−4.18690	−	5.62398i	−0.425115	−	0.571029i	0.537031	−	0.843562i	$-0.319546\pi$
$97$	−4.18690	−	5.62398i	−0.425115	−	0.571029i	−0.962146	+	0.272534i	$0.912138\pi$
$98$	0.571800	+	3.24284i	0.0577605	+	0.327576i
$99$		0			0
$100$	1.10074	−	6.24263i	0.110074	−	0.624263i
$101$	7.76637	−	3.90042i	0.772782	−	0.388106i	−0.0182867	−	0.999833i	$-0.505821\pi$
$101$	7.76637	−	3.90042i	0.772782	−	0.388106i	0.791069	+	0.611727i	$0.209525\pi$
$102$		0			0
$103$	5.09302	+	0.595289i	0.501830	+	0.0586556i	0.363243	−	0.931695i	$-0.381670\pi$
$103$	5.09302	+	0.595289i	0.501830	+	0.0586556i	0.138588	+	0.990350i	$0.455744\pi$
$104$	10.5064	−	6.91017i	1.03024	−	0.677598i
$105$		0			0
$106$	−1.89834	−	6.34090i	−0.184383	−	0.615882i
$107$	4.97642	−	8.61941i	0.481089	−	0.833270i	−0.518676	−	0.854971i	$-0.673575\pi$
$107$	4.97642	−	8.61941i	0.481089	−	0.833270i	0.999765	+	0.0217011i	$0.00690820\pi$
$108$		0			0
$109$	6.36856	+	11.0307i	0.609997	+	1.05655i	0.991240	+	0.132071i	$0.0421627\pi$
$109$	6.36856	+	11.0307i	0.609997	+	1.05655i	−0.381243	+	0.924475i	$0.624504\pi$
$110$	2.68059	−	2.84126i	0.255584	−	0.270903i
$111$		0			0
$112$	0.124216	+	2.13270i	0.0117373	+	0.201521i
$113$	−2.27623	−	5.27688i	−0.214129	−	0.496408i	0.776969	−	0.629539i	$-0.216756\pi$
$113$	−2.27623	−	5.27688i	−0.214129	−	0.496408i	−0.991098	+	0.133131i	$0.957497\pi$
$114$		0			0
$115$	−0.00573345	+	0.0984395i	−0.000534647	+	0.00917953i
$116$	−0.742989	+	0.270426i	−0.0689848	+	0.0251084i
$117$		0			0
$118$	3.59207	+	1.30741i	0.330677	+	0.120357i
$119$	−0.0178738	+	0.0414361i	−0.00163849	+	0.00379844i
$120$		0			0
$121$	25.7502	−	6.10290i	2.34092	−	0.554809i
$122$	−1.13099	+	0.268050i	−0.102395	+	0.0242681i
$123$		0			0
$124$	4.98998	−	11.5681i	0.448113	−	1.03884i
$125$	−8.07451	−	2.93888i	−0.722206	−	0.262862i
$126$		0			0
$127$	−9.96192	+	3.62584i	−0.883977	+	0.321741i	−0.743814	−	0.668387i	$-0.766985\pi$
$127$	−9.96192	+	3.62584i	−0.883977	+	0.321741i	−0.140163	+	0.990128i	$0.544763\pi$
$128$	−0.633653	+	10.8794i	−0.0560075	+	0.961612i
$129$		0			0
$130$	−1.32623	−	3.07456i	−0.116318	−	0.269656i
$131$	0.829365	+	14.2396i	0.0724619	+	1.24412i	0.817037	+	0.576585i	$0.195615\pi$
$131$	0.829365	+	14.2396i	0.0724619	+	1.24412i	−0.744575	+	0.667538i	$0.767348\pi$
$132$		0			0
$133$	3.66523	−	3.88491i	0.317815	−	0.336865i
$134$	0.926205	+	1.60423i	0.0800119	+	0.138585i
$135$		0			0
$136$	−0.0370239	+	0.0641273i	−0.00317478	+	0.00549887i
$137$	1.53043	+	5.11200i	0.130754	+	0.436748i	0.998145	−	0.0608786i	$-0.0193902\pi$
$137$	1.53043	+	5.11200i	0.130754	+	0.436748i	−0.867391	+	0.497626i	$0.834205\pi$
$138$		0			0
$139$	3.42061	−	2.24977i	0.290133	−	0.190823i	−0.396096	−	0.918209i	$-0.629635\pi$
$139$	3.42061	−	2.24977i	0.290133	−	0.190823i	0.686229	+	0.727386i	$0.259265\pi$
$140$	2.11019	+	0.246645i	0.178343	+	0.0208453i
$141$		0			0
$142$	1.31383	−	0.659830i	0.110254	−	0.0553717i
$143$	5.57652	−	31.6260i	0.466332	−	2.64470i
$144$		0			0
$145$	0.0839709	+	0.476223i	0.00697341	+	0.0395482i
$146$	3.36629	+	4.52172i	0.278596	+	0.374220i
$147$		0			0
$148$	−6.10777	−	6.47386i	−0.502056	−	0.532148i
$149$	−5.41385	+	18.0835i	−0.443520	+	1.48146i	0.385746	+	0.922605i	$0.373944\pi$
$149$	−5.41385	+	18.0835i	−0.443520	+	1.48146i	−0.829266	+	0.558855i	$0.811241\pi$
$150$		0			0
$151$	3.05960	−	0.357617i	0.248987	−	0.0291024i	0.00931618	−	0.999957i	$-0.497035\pi$
$151$	3.05960	−	0.357617i	0.248987	−	0.0291024i	0.239671	+	0.970854i	$0.422960\pi$
$152$	6.71362	−	5.63340i	0.544547	−	0.456929i
$153$		0			0
$154$	−4.63405	−	3.88843i	−0.373422	−	0.313338i
$155$	−6.43752	−	4.23402i	−0.517074	−	0.340085i
$156$		0			0
$157$	−2.04742	+	2.75017i	−0.163402	+	0.219487i	−0.876281	−	0.481800i	$-0.839983\pi$
$157$	−2.04742	+	2.75017i	−0.163402	+	0.219487i	0.712879	+	0.701287i	$0.247391\pi$
$158$	7.62654	+	3.83019i	0.606735	+	0.304714i
$159$		0			0
$160$	5.30750	+	1.25790i	0.419595	+	0.0994458i
$161$	0.152707			0.0120350
$162$		0			0
$163$	−19.7151			−1.54420			−0.772101	−	0.635500i	$-0.780794\pi$
$163$	−19.7151			−1.54420			−0.772101	+	0.635500i	$0.780794\pi$
$164$	6.58154	+	1.55985i	0.513932	+	0.121804i
$165$		0			0
$166$	10.7778	+	5.41283i	0.836522	+	0.420117i
$167$	11.5505	−	15.5151i	0.893808	−	1.20059i	−0.0851164	−	0.996371i	$-0.527126\pi$
$167$	11.5505	−	15.5151i	0.893808	−	1.20059i	0.978925	−	0.204222i	$-0.0654664\pi$
$168$		0			0
$169$	−12.1381	−	7.98337i	−0.933702	−	0.614106i
$170$	0.0151039	+	0.0126737i	0.00115842	+	0.000972029i
$171$		0			0
$172$	−1.62635	+	1.36467i	−0.124008	+	0.104055i
$173$	−6.12562	+	0.715983i	−0.465723	+	0.0544352i	−0.345719	−	0.938338i	$-0.612365\pi$
$173$	−6.12562	+	0.715983i	−0.465723	+	0.0544352i	−0.120004	+	0.992773i	$0.538291\pi$
$174$		0			0
$175$	−1.72193	+	5.75166i	−0.130166	+	0.434784i
$176$	6.14328	+	6.51150i	0.463067	+	0.490823i
$177$		0			0
$178$	−5.63611	−	7.57061i	−0.422445	−	0.567441i
$179$	0.601129	+	3.40917i	0.0449305	+	0.254814i	0.998997	−	0.0447821i	$-0.0142593\pi$
$179$	0.601129	+	3.40917i	0.0449305	+	0.254814i	−0.954066	+	0.299596i	$0.903148\pi$
$180$		0			0
$181$	−3.31327	+	18.7905i	−0.246273	+	1.39668i	0.571244	+	0.820780i	$0.306461\pi$
$181$	−3.31327	+	18.7905i	−0.246273	+	1.39668i	−0.817517	+	0.575904i	$0.804650\pi$
$182$	−4.63394	+	2.32725i	−0.343490	+	0.172507i
$183$		0			0
$184$	0.248881	+	0.0290900i	0.0183477	+	0.00214454i
$185$	−4.54787	+	2.99118i	−0.334366	+	0.219916i
$186$		0			0
$187$	0.0542345	+	0.181156i	0.00396602	+	0.0132474i
$188$	−4.32554	+	7.49206i	−0.315473	+	0.546415i
$189$		0			0
$190$	−1.16680	−	2.02096i	−0.0846486	−	0.146616i
$191$	−13.6753	+	14.4949i	−0.989508	+	1.04882i	0.00929782	+	0.999957i	$0.497040\pi$
$191$	−13.6753	+	14.4949i	−0.989508	+	1.04882i	−0.998806	+	0.0488602i	$0.984441\pi$
$192$		0			0
$193$	0.623160	+	10.6992i	0.0448561	+	0.770149i	0.943480	+	0.331429i	$0.107531\pi$
$193$	0.623160	+	10.6992i	0.0448561	+	0.770149i	−0.898624	+	0.438720i	$0.855432\pi$
$194$	1.87907	+	4.35616i	0.134909	+	0.312754i
$195$		0			0
$196$	−0.436373	+	7.49223i	−0.0311695	+	0.535160i
$197$	−22.2725	+	8.10651i	−1.58685	+	0.577565i	−0.976679	−	0.214707i	$-0.931120\pi$
$197$	−22.2725	+	8.10651i	−1.58685	+	0.577565i	−0.610169	+	0.792272i	$0.708898\pi$
$198$		0			0
$199$	−8.20833	−	2.98759i	−0.581873	−	0.211785i	0.0342781	−	0.999412i	$-0.489087\pi$
$199$	−8.20833	−	2.98759i	−0.581873	−	0.211785i	−0.616151	+	0.787628i	$0.711309\pi$
$200$	−3.90206	+	9.04599i	−0.275917	+	0.639648i
$201$		0			0
$202$	−5.72201	+	1.35614i	−0.402599	+	0.0954177i
$203$	0.728695	−	0.172704i	0.0511443	−	0.0121214i
$204$		0			0
$205$	1.63848	−	3.79841i	0.114436	−	0.265293i
$206$	−3.26035	−	1.18667i	−0.227160	−	0.0826793i
$207$		0			0
$208$	7.21098	−	2.62458i	0.499991	−	0.181982i
$209$	1.30135	−	22.3433i	0.0900161	−	1.54552i
$210$		0			0
$211$	−2.88269	−	6.68284i	−0.198453	−	0.460065i	0.789709	−	0.613482i	$-0.210232\pi$
$211$	−2.88269	−	6.68284i	−0.198453	−	0.460065i	−0.988162	+	0.153416i	$0.950972\pi$
$212$	−0.877150	−	15.0601i	−0.0602429	−	1.03433i
$213$		0			0
$214$	−4.62148	+	4.89848i	−0.315918	+	0.334853i
$215$	0.649223	+	1.12449i	0.0442766	+	0.0766894i
$216$		0			0
$217$	−5.96626	+	10.3339i	−0.405016	+	0.701508i
$218$	−2.47179	−	8.25636i	−0.167411	−	0.559191i
$219$		0			0
$220$	7.43816	−	4.89216i	0.501481	−	0.329829i
$221$	0.161002	+	0.0188184i	0.0108301	+	0.00126586i
$222$		0			0
$223$	0.668861	−	0.335914i	0.0447902	−	0.0224945i	−0.426263	−	0.904599i	$-0.640170\pi$
$223$	0.668861	−	0.335914i	0.0447902	−	0.0224945i	0.471053	+	0.882105i	$0.343874\pi$
$224$	1.46684	−	8.31884i	0.0980071	−	0.555826i
$225$		0			0
$226$	0.675242	+	3.82949i	0.0449164	+	0.254734i
$227$	−4.54197	−	6.10092i	−0.301461	−	0.404932i	0.625420	−	0.780288i	$-0.284928\pi$
$227$	−4.54197	−	6.10092i	−0.301461	−	0.404932i	−0.926881	+	0.375356i	$0.877520\pi$
$228$		0			0
$229$	10.7066	+	11.3484i	0.707514	+	0.749921i	0.977036	−	0.213073i	$-0.0683472\pi$
$229$	10.7066	+	11.3484i	0.707514	+	0.749921i	−0.269522	+	0.962994i	$0.586866\pi$
$230$	0.0191357	−	0.0639178i	0.00126177	−	0.00421462i
$231$		0			0
$232$	1.22052	−	0.142658i	0.0801311	−	0.00936599i
$233$	12.6227	−	10.5917i	0.826940	−	0.693885i	−0.127647	−	0.991820i	$-0.540742\pi$
$233$	12.6227	−	10.5917i	0.826940	−	0.693885i	0.954586	+	0.297935i	$0.0962979\pi$
$234$		0			0
$235$	4.05310	+	3.40095i	0.264395	+	0.221854i
$236$	7.27901	+	4.78748i	0.473823	+	0.311638i
$237$		0			0
$238$	0.0182339	−	0.0244924i	0.00118193	−	0.00158761i
$239$	−17.2890	−	8.68288i	−1.11834	−	0.561649i	−0.209084	−	0.977898i	$-0.567048\pi$
$239$	−17.2890	−	8.68288i	−1.11834	−	0.561649i	−0.909251	+	0.416249i	$0.863345\pi$
$240$		0			0
$241$	5.60951	+	1.32948i	0.361340	+	0.0856392i	0.407276	−	0.913305i	$-0.366479\pi$
$241$	5.60951	+	1.32948i	0.361340	+	0.0856392i	−0.0459358	+	0.998944i	$0.514627\pi$
$242$	−17.9062			−1.15105
$243$		0			0
$244$	−2.64910			−0.169591
$245$	4.46624	+	1.05852i	0.285338	+	0.0676262i
$246$		0			0
$247$	−17.1445	−	8.61031i	−1.09088	−	0.547861i
$248$	−11.6923	+	15.7055i	−0.742463	+	0.997301i
$249$		0			0
$250$	4.85766	+	3.19493i	0.307225	+	0.202065i
$251$	14.4752	+	12.1462i	0.913668	+	0.766659i	0.972813	−	0.231591i	$-0.0743930\pi$
$251$	14.4752	+	12.1462i	0.913668	+	0.766659i	−0.0591449	+	0.998249i	$0.518837\pi$
$252$		0			0
$253$	0.490197	−	0.411324i	0.0308184	−	0.0258597i
$254$	7.12471	−	0.832759i	0.447044	−	0.0522520i
$255$		0			0
$256$	2.68155	−	8.95701i	0.167597	−	0.559813i
$257$	−12.4352	−	13.1805i	−0.775685	−	0.822178i	0.212222	−	0.977221i	$-0.431930\pi$
$257$	−12.4352	−	13.1805i	−0.775685	−	0.822178i	−0.987908	+	0.155043i	$0.950448\pi$
$258$		0			0
$259$	5.03398	+	6.76181i	0.312796	+	0.420158i
$260$	−1.32520	−	7.51557i	−0.0821853	−	0.466096i
$261$		0			0
$262$	1.67595	−	9.50479i	0.103541	−	0.587208i
$263$	−7.74703	+	3.89071i	−0.477703	+	0.239911i	−0.671323	−	0.741165i	$-0.734273\pi$
$263$	−7.74703	+	3.89071i	−0.477703	+	0.239911i	0.193620	+	0.981077i	$0.437977\pi$
$264$		0			0
$265$	−9.16387	−	1.07110i	−0.562932	−	0.0657973i
$266$	−3.01940	+	1.98589i	−0.185131	+	0.121763i
$267$		0			0
$268$	1.21086	+	4.04455i	0.0739650	+	0.247060i
$269$	5.59305	−	9.68745i	0.341014	−	0.590654i	−0.643607	−	0.765356i	$-0.722563\pi$
$269$	5.59305	−	9.68745i	0.341014	−	0.590654i	0.984621	+	0.174702i	$0.0558962\pi$
$270$		0			0
$271$	5.08705	+	8.81103i	0.309016	+	0.535232i	0.978147	−	0.207912i	$-0.0666669\pi$
$271$	5.08705	+	8.81103i	0.309016	+	0.535232i	−0.669131	+	0.743144i	$0.733334\pi$
$272$	−0.0310087	+	0.0328673i	−0.00188018	+	0.00199288i
$273$		0			0
$274$	−0.209941	−	3.60456i	−0.0126830	−	0.217759i
$275$	9.96490	+	23.1012i	0.600906	+	1.39306i
$276$		0			0
$277$	0.0757068	−	1.29984i	0.00454878	−	0.0780996i	−0.995270	−	0.0971501i	$-0.969027\pi$
$277$	0.0757068	−	1.29984i	0.00454878	−	0.0780996i	0.999819	+	0.0190505i	$0.00606434\pi$
$278$	−2.60319	+	0.947485i	−0.156129	+	0.0568264i
$279$		0			0
$280$	−3.10276	−	1.12931i	−0.185425	−	0.0674894i
$281$	2.53880	−	5.88560i	0.151452	−	0.351105i	−0.825552	−	0.564326i	$-0.809136\pi$
$281$	2.53880	−	5.88560i	0.151452	−	0.351105i	0.977004	+	0.213221i	$0.0683953\pi$
$282$		0			0
$283$	−18.6018	+	4.40871i	−1.10576	+	0.262071i	−0.742654	−	0.669675i	$-0.766433\pi$
$283$	−18.6018	+	4.40871i	−1.10576	+	0.262071i	−0.363110	+	0.931746i	$0.618285\pi$
$284$	3.26051	−	0.772756i	0.193476	−	0.0458546i
$285$		0			0
$286$	−8.60661	+	19.9524i	−0.508920	+	1.17981i
$287$	−6.02001	−	2.19110i	−0.355350	−	0.129337i
$288$		0			0
$289$	15.9739	−	5.81402i	0.939640	−	0.342001i
$290$	0.0190251	−	0.326648i	0.00111719	−	0.0191814i
$291$		0			0
$292$	5.08883	+	11.7972i	0.297801	+	0.690380i
$293$	−0.106176	−	1.82297i	−0.00620287	−	0.106499i	0.993786	−	0.111312i	$-0.0355052\pi$
$293$	−0.106176	−	1.82297i	−0.00620287	−	0.106499i	−0.999988	+	0.00481246i	$0.998468\pi$
$294$		0			0
$295$	3.65655	−	3.87572i	0.212893	−	0.225653i
$296$	6.91625	+	11.9793i	0.401999	+	0.696283i
$297$		0			0
$298$	6.38629	−	11.0614i	0.369948	−	0.640769i
$299$	−0.157321	−	0.525488i	−0.00909809	−	0.0303897i
$300$		0			0
$301$	1.68003	−	1.10497i	0.0968355	−	0.0636897i
$302$	−2.07025	−	0.241977i	−0.119129	−	0.0139242i
$303$		0			0
$304$	4.77921	−	2.40021i	0.274107	−	0.137662i
$305$	−0.281340	+	1.59556i	−0.0161095	+	0.0913614i
$306$		0			0
$307$	−2.60207	−	14.7571i	−0.148508	−	0.842232i	−0.964483	−	0.264145i	$-0.914910\pi$
$307$	−2.60207	−	14.7571i	−0.148508	−	0.842232i	0.815975	−	0.578087i	$-0.196201\pi$
$308$	−8.23321	−	11.0591i	−0.469131	−	0.630152i
$309$		0			0
$310$	3.57777	+	3.79221i	0.203203	+	0.215383i
$311$	5.92528	−	19.7918i	0.335992	−	1.12229i	−0.608444	−	0.793597i	$-0.708206\pi$
$311$	5.92528	−	19.7918i	0.335992	−	1.12229i	0.944436	−	0.328695i	$-0.106609\pi$
$312$		0			0
$313$	−22.1725	+	2.59159i	−1.25326	+	0.146486i	−0.716704	−	0.697377i	$-0.754350\pi$
$313$	−22.1725	+	2.59159i	−1.25326	+	0.146486i	−0.536559	+	0.843863i	$0.680276\pi$
$314$	1.77717	−	1.49122i	0.100291	−	0.0841545i
$315$		0			0
$316$	14.9003	+	12.5028i	0.838208	+	0.703340i
$317$	9.49125	+	6.24250i	0.533082	+	0.350614i	0.787336	−	0.616524i	$-0.211460\pi$
$317$	9.49125	+	6.24250i	0.533082	+	0.350614i	−0.254254	+	0.967137i	$0.581830\pi$
$318$		0			0
$319$	1.87396	−	2.51717i	0.104922	−	0.140934i
$320$	−0.832696	−	0.418196i	−0.0465491	−	0.0233778i
$321$		0			0
$322$	−0.100542	−	0.0238289i	−0.00560299	−	0.00132793i
$323$	0.112971			0.00628586
$324$		0			0
$325$	21.5663			1.19628
$326$	12.9804	+	3.07641i	0.718917	+	0.170386i
$327$		0			0
$328$	−9.39397	−	4.71783i	−0.518695	−	0.260499i
$329$	4.89302	−	6.57246i	0.269761	−	0.362351i
$330$		0			0
$331$	−12.0371	−	7.91690i	−0.661617	−	0.435152i	0.173791	−	0.984783i	$-0.444398\pi$
$331$	−12.0371	−	7.91690i	−0.661617	−	0.435152i	−0.835408	+	0.549630i	$0.814769\pi$
$332$	21.0571	+	17.6690i	1.15566	+	0.969714i
$333$		0			0
$334$	−10.0259	+	8.41273i	−0.548593	+	0.460324i
$335$	2.56464	−	0.299763i	0.140121	−	0.0163778i
$336$		0			0
$337$	2.84153	−	9.49138i	0.154788	−	0.517029i	−0.845056	−	0.534678i	$-0.820433\pi$
$337$	2.84153	−	9.49138i	0.154788	−	0.517029i	0.999844	+	0.0176492i	$0.00561820\pi$
$338$	6.74599	+	7.15033i	0.366933	+	0.388927i
$339$		0			0
$340$	0.0268348	+	0.0360454i	0.00145532	+	0.00195484i
$341$	8.68281	+	49.2427i	0.470201	+	2.66664i
$342$		0			0
$343$	3.00981	−	17.0695i	0.162514	−	0.921665i
$344$	2.94860	−	1.48084i	0.158978	−	0.0798417i
$345$		0			0
$346$	4.14483	+	0.484462i	0.222828	+	0.0260448i
$347$	−2.82247	+	1.85637i	−0.151518	+	0.0996552i	−0.623004	−	0.782218i	$-0.714088\pi$
$347$	−2.82247	+	1.85637i	−0.151518	+	0.0996552i	0.471486	+	0.881874i	$0.343718\pi$
$348$		0			0
$349$	0.381429	+	1.27406i	0.0204174	+	0.0681990i	0.967591	−	0.252522i	$-0.0812600\pi$
$349$	0.381429	+	1.27406i	0.0204174	+	0.0681990i	−0.947174	+	0.320721i	$0.896075\pi$
$350$	2.03123	−	3.51819i	0.108574	−	0.188055i
$351$		0			0
$352$	−17.6986	−	30.6549i	−0.943340	−	1.63391i
$353$	8.09324	−	8.57833i	0.430760	−	0.456579i	−0.475240	−	0.879856i	$-0.657639\pi$
$353$	8.09324	−	8.57833i	0.430760	−	0.456579i	0.906000	+	0.423277i	$0.139120\pi$
$354$		0			0
$355$	−0.119159	−	2.04588i	−0.00632430	−	0.108584i
$356$	−8.52012	−	19.7518i	−0.451565	−	1.04685i
$357$		0			0
$358$	0.136196	−	2.33840i	0.00719820	−	0.123588i
$359$	−27.9195	+	10.1619i	−1.47353	+	0.536323i	−0.949058	−	0.315102i	$-0.897961\pi$
$359$	−27.9195	+	10.1619i	−1.47353	+	0.536323i	−0.524477	+	0.851425i	$0.675739\pi$
$360$		0			0
$361$	5.28976	+	1.92531i	0.278408	+	0.101332i
$362$	5.11358	−	11.8546i	0.268764	−	0.623065i
$363$		0			0
$364$	−11.5000	+	2.72555i	−0.602763	+	0.142857i
$365$	7.64593	−	1.81212i	0.400206	−	0.0948506i
$366$		0			0
$367$	−3.17934	+	7.37053i	−0.165960	+	0.384738i	−0.980819	−	0.194921i	$-0.937555\pi$
$367$	−3.17934	+	7.37053i	−0.165960	+	0.384738i	0.814859	+	0.579659i	$0.196814\pi$
$368$	0.143687	+	0.0522978i	0.00749021	+	0.00272621i
$369$		0			0
$370$	3.46107	−	1.25973i	0.179933	−	0.0654901i
$371$	−0.830788	+	14.2641i	−0.0431324	+	0.740554i
$372$		0			0
$373$	−1.18579	−	2.74898i	−0.0613980	−	0.142337i	0.884755	−	0.466057i	$-0.154326\pi$
$373$	−1.18579	−	2.74898i	−0.0613980	−	0.142337i	−0.946153	+	0.323720i	$0.895066\pi$
$374$	−0.00743977	−	0.127736i	−0.000384701	−	0.00660507i
$375$		0			0
$376$	9.22663	−	9.77966i	0.475827	−	0.504347i
$377$	−1.34501	−	2.32963i	−0.0692716	−	0.119982i
$378$		0			0
$379$	11.0537	−	19.1456i	0.567792	−	0.983444i	−0.428992	−	0.903308i	$-0.641131\pi$
$379$	11.0537	−	19.1456i	0.567792	−	0.983444i	0.996784	−	0.0801362i	$-0.0255355\pi$
$380$	−1.52540	−	5.09519i	−0.0782513	−	0.261378i
$381$		0			0
$382$	11.2656	−	7.40952i	0.576400	−	0.379104i
$383$	14.2605	+	1.66682i	0.728680	+	0.0851705i	0.472340	−	0.881416i	$-0.343409\pi$
$383$	14.2605	+	1.66682i	0.728680	+	0.0851705i	0.256340	+	0.966587i	$0.417483\pi$
$384$		0			0
$385$	−7.53530	+	3.78437i	−0.384035	+	0.192869i
$386$	1.25926	−	7.14162i	0.0640947	−	0.363499i
$387$		0			0
$388$	1.87760	+	10.6484i	0.0953206	+	0.540590i
$389$	10.8862	+	14.6227i	0.551953	+	0.741401i	0.987301	−	0.158861i	$-0.0507821\pi$
$389$	10.8862	+	14.6227i	0.551953	+	0.741401i	−0.435348	+	0.900262i	$0.643375\pi$
$390$		0			0
$391$	0.00221655	+	0.00234941i	0.000112096	+	0.000118815i
$392$	3.34523	−	11.1739i	0.168960	−	0.564365i
$393$		0			0
$394$	15.9291	−	1.86185i	0.802499	−	0.0937987i
$395$	9.11293	−	7.64665i	0.458521	−	0.384745i
$396$		0			0
$397$	1.06250	+	0.891545i	0.0533255	+	0.0447454i	0.669061	−	0.743208i	$-0.266697\pi$
$397$	1.06250	+	0.891545i	0.0533255	+	0.0447454i	−0.615735	+	0.787953i	$0.711141\pi$
$398$	4.93817	+	3.24788i	0.247528	+	0.162802i
$399$		0			0
$400$	−3.59001	+	4.82222i	−0.179500	+	0.241111i
$401$	−19.7370	−	9.91231i	−0.985620	−	0.494997i	−0.118424	−	0.992963i	$-0.537784\pi$
$401$	−19.7370	−	9.91231i	−0.985620	−	0.494997i	−0.867197	+	0.497966i	$0.834080\pi$
$402$		0			0
$403$	41.7069	+	9.88472i	2.07757	+	0.492393i
$404$	−13.4026			−0.666803
$405$		0			0
$406$	−0.506722			−0.0251482
$407$	34.3726	+	8.14647i	1.70379	+	0.403805i
$408$		0			0
$409$	0.515967	+	0.259128i	0.0255129	+	0.0128131i	0.461510	−	0.887135i	$-0.347308\pi$
$409$	0.515967	+	0.259128i	0.0255129	+	0.0128131i	−0.435997	+	0.899948i	$0.643604\pi$
$410$	−1.67149	+	2.24520i	−0.0825490	+	0.110883i
$411$		0			0
$412$	−6.60681	−	4.34537i	−0.325494	−	0.214081i
$413$	−6.32124	−	5.30415i	−0.311048	−	0.261000i
$414$		0			0
$415$	12.8784	−	10.8062i	0.632175	−	0.530458i
$416$	−30.1375	+	3.52257i	−1.47761	+	0.172708i
$417$		0			0
$418$	−4.34333	+	14.5077i	−0.212439	+	0.709596i
$419$	−8.66829	−	9.18785i	−0.423474	−	0.448856i	0.480148	−	0.877187i	$-0.340583\pi$
$419$	−8.66829	−	9.18785i	−0.423474	−	0.448856i	−0.903622	+	0.428332i	$0.859101\pi$
$420$		0			0
$421$	12.7947	+	17.1863i	0.623577	+	0.837610i	0.995897	−	0.0904947i	$-0.0288448\pi$
$421$	12.7947	+	17.1863i	0.623577	+	0.837610i	−0.372319	+	0.928105i	$0.621437\pi$
$422$	0.855151	+	4.84980i	0.0416281	+	0.236085i
$423$		0			0
$424$	−4.07126	+	23.0892i	−0.197718	+	1.12131i
$425$	−0.113484	+	0.0569936i	−0.00550476	+	0.00276460i
$426$		0			0
$427$	2.49212	+	0.291287i	0.120602	+	0.0140964i
$428$	−12.8238	+	8.43434i	−0.619862	+	0.407689i
$429$		0			0
$430$	−0.251979	−	0.841669i	−0.0121515	−	0.0405889i
$431$	2.23566	−	3.87227i	0.107688	−	0.186521i	−0.807145	−	0.590353i	$-0.798989\pi$
$431$	2.23566	−	3.87227i	0.107688	−	0.186521i	0.914833	+	0.403832i	$0.132322\pi$
$432$		0			0
$433$	−4.56671	−	7.90977i	−0.219462	−	0.380119i	0.735182	−	0.677870i	$-0.237097\pi$
$433$	−4.56671	−	7.90977i	−0.219462	−	0.380119i	−0.954644	+	0.297751i	$0.903763\pi$
$434$	5.54072	−	5.87281i	0.265963	−	0.281904i
$435$		0			0
$436$	−1.14212	−	19.6094i	−0.0546976	−	0.939122i
$437$	−0.151417	−	0.351023i	−0.00724324	−	0.0167917i
$438$		0			0
$439$	−0.165633	+	2.84382i	−0.00790525	+	0.135728i	0.992046	+	0.125874i	$0.0401736\pi$
$439$	−0.165633	+	2.84382i	−0.00790525	+	0.135728i	−0.999951	+	0.00985365i	$0.996863\pi$
$440$	−13.0019	+	4.73230i	−0.619841	+	0.225604i
$441$		0			0
$442$	−0.103067	−	0.0375133i	−0.00490239	−	0.00178432i
$443$	4.90013	−	11.3598i	0.232812	−	0.539719i	−0.761260	−	0.648447i	$-0.775419\pi$
$443$	4.90013	−	11.3598i	0.232812	−	0.539719i	0.994071	+	0.108729i	$0.0346779\pi$
$444$		0			0
$445$	−12.8014	+	3.03399i	−0.606845	+	0.143825i
$446$	−0.492795	+	0.116795i	−0.0233345	+	0.00553038i
$447$		0			0
$448$	−0.571563	+	1.32503i	−0.0270038	+	0.0626019i
$449$	16.1389	+	5.87407i	0.761640	+	0.277214i	0.693495	−	0.720461i	$-0.256070\pi$
$449$	16.1389	+	5.87407i	0.761640	+	0.277214i	0.0681449	+	0.997675i	$0.478292\pi$
$450$		0			0
$451$	−25.2264	+	9.18166i	−1.18786	+	0.432347i
$452$	−0.515316	+	8.84763i	−0.0242384	+	0.416157i
$453$		0			0
$454$	2.03842	+	4.72559i	0.0956678	+	0.221783i
$455$	0.420279	+	7.21591i	0.0197030	+	0.338287i
$456$		0			0
$457$	−0.607162	+	0.643554i	−0.0284018	+	0.0301042i	−0.741419	−	0.671043i	$-0.765847\pi$
$457$	−0.607162	+	0.643554i	−0.0284018	+	0.0301042i	0.713017	+	0.701147i	$0.247328\pi$
$458$	−5.27840	−	9.14246i	−0.246644	−	0.427199i
$459$		0			0
$460$	0.0760334	−	0.131694i	0.00354507	−	0.00614025i
$461$	−4.36853	−	14.5919i	−0.203463	−	0.679614i	−0.997430	−	0.0716523i	$-0.977173\pi$
$461$	−4.36853	−	14.5919i	−0.203463	−	0.679614i	0.793967	−	0.607961i	$-0.208012\pi$
$462$		0			0
$463$	−28.1033	+	18.4838i	−1.30607	+	0.859016i	−0.995793	−	0.0916304i	$-0.970792\pi$
$463$	−28.1033	+	18.4838i	−1.30607	+	0.859016i	−0.310277	+	0.950646i	$0.600422\pi$
$464$	0.744800	+	0.0870547i	0.0345765	+	0.00404141i
$465$		0			0
$466$	−9.96354	+	5.00388i	−0.461552	+	0.231800i
$467$	−1.91520	+	10.8616i	−0.0886249	+	0.502617i	0.907890	+	0.419207i	$0.137692\pi$
$467$	−1.91520	+	10.8616i	−0.0886249	+	0.502617i	−0.996515	+	0.0834093i	$0.973419\pi$
$468$		0			0
$469$	−0.694378	−	3.93802i	−0.0320634	−	0.181841i
$470$	−2.13786	−	2.87165i	−0.0986122	−	0.132459i
$471$		0			0
$472$	−9.29190	−	9.84884i	−0.427694	−	0.453330i
$473$	2.41668	−	8.07229i	0.111119	−	0.371164i
$474$		0			0
$475$	14.9286	−	1.74490i	0.684969	−	0.0800614i
$476$	0.0533110	−	0.0447333i	0.00244351	−	0.00205035i
$477$		0			0
$478$	10.0282	+	8.41465i	0.458679	+	0.384877i
$479$	−9.96137	−	6.55170i	−0.455147	−	0.299355i	0.301158	−	0.953574i	$-0.402627\pi$
$479$	−9.96137	−	6.55170i	−0.455147	−	0.299355i	−0.756305	+	0.654220i	$0.772997\pi$
$480$		0			0
$481$	18.0823	−	24.2888i	0.824484	−	1.10747i
$482$	−3.48584	−	1.75065i	−0.158776	−	0.0797401i
$483$		0			0
$484$	−39.7109	−	9.41165i	−1.80504	−	0.427802i
$485$	6.61294			0.300278
$486$		0			0
$487$	38.2435			1.73298			0.866489	−	0.499196i	$-0.166371\pi$
$487$	38.2435			1.73298			0.866489	+	0.499196i	$0.166371\pi$
$488$	4.00615	+	0.949475i	0.181350	+	0.0429807i
$489$		0			0
$490$	−2.77540	−	1.39386i	−0.125380	−	0.0629680i
$491$	−2.53169	+	3.40065i	−0.114254	+	0.153469i	−0.855571	−	0.517685i	$-0.826794\pi$
$491$	−2.53169	+	3.40065i	−0.114254	+	0.153469i	0.741318	+	0.671154i	$0.234201\pi$
$492$		0			0
$493$	0.0132341	+	0.00870421i	0.000596034	+	0.000392018i
$494$	9.94438	+	8.34432i	0.447419	+	0.375429i
$495$		0			0
$496$	−9.15292	+	7.68021i	−0.410978	+	0.344852i
$497$	−3.15227	+	0.368447i	−0.141398	+	0.0165271i
$498$		0			0
$499$	−10.7276	+	35.8326i	−0.480232	+	1.60409i	0.283782	+	0.958889i	$0.408411\pi$
$499$	−10.7276	+	35.8326i	−0.480232	+	1.60409i	−0.764014	+	0.645199i	$0.776774\pi$
$500$	9.09362	+	9.63868i	0.406679	+	0.431055i
$501$		0			0
$502$	−7.63516	−	10.2558i	−0.340774	−	0.457738i
$503$	−0.0594062	−	0.336909i	−0.00264879	−	0.0150220i	0.983455	−	0.181154i	$-0.0579833\pi$
$503$	−0.0594062	−	0.336909i	−0.00264879	−	0.0150220i	−0.986104	+	0.166132i	$0.946872\pi$
$504$		0			0
$505$	−1.42338	+	8.07239i	−0.0633396	+	0.359217i
$506$	−0.386930	+	0.194324i	−0.0172011	+	0.00863874i
$507$		0			0
$508$	16.2383	+	1.89798i	0.720457	+	0.0842094i
$509$	−5.22506	+	3.43658i	−0.231597	+	0.152324i	−0.660004	−	0.751262i	$-0.729445\pi$
$509$	−5.22506	+	3.43658i	−0.231597	+	0.152324i	0.428407	+	0.903586i	$0.359075\pi$
$510$		0			0
$511$	−3.49008	−	11.6577i	−0.154392	−	0.515705i
$512$	7.73462	−	13.3968i	0.341825	−	0.592059i
$513$		0			0
$514$	6.13058	+	10.6185i	0.270408	+	0.468361i
$515$	−3.31888	+	3.51780i	−0.146247	+	0.155013i
$516$		0			0
$517$	−1.99644	−	34.2775i	−0.0878033	−	1.50752i
$518$	−2.25923	−	5.23749i	−0.0992650	−	0.230122i
$519$		0			0
$520$	−0.689631	+	11.8405i	−0.0302423	+	0.519241i
$521$	−29.5418	+	10.7523i	−1.29425	+	0.471068i	−0.895119	−	0.445827i	$-0.852910\pi$
$521$	−29.5418	+	10.7523i	−1.29425	+	0.471068i	−0.399129	+	0.916895i	$0.630687\pi$
$522$		0			0
$523$	−20.1279	−	7.32597i	−0.880134	−	0.320342i	−0.137870	−	0.990450i	$-0.544026\pi$
$523$	−20.1279	−	7.32597i	−0.880134	−	0.320342i	−0.742264	+	0.670108i	$0.766248\pi$
$524$	8.71258	−	20.1980i	0.380611	−	0.882355i
$525$		0			0
$526$	5.70776	−	1.35276i	0.248870	−	0.0589834i
$527$	−0.245588	+	0.0582054i	−0.0106980	+	0.00253547i
$528$		0			0
$529$	−9.10551	+	21.1089i	−0.395892	+	0.917780i
$530$	5.86635	+	2.13518i	0.254818	+	0.0927461i
$531$		0			0
$532$	−7.73997	+	2.81712i	−0.335570	+	0.122138i
$533$	−1.33803	+	22.9731i	−0.0579564	+	0.995074i
$534$		0			0
$535$	3.71810	+	8.61953i	0.160748	+	0.372655i
$536$	−0.381519	−	6.55043i	−0.0164791	−	0.282935i
$537$		0			0
$538$	−5.19413	+	5.50545i	−0.223935	+	0.237357i
$539$	−14.8933	−	25.7960i	−0.641500	−	1.11111i
$540$		0			0
$541$	0.188033	−	0.325682i	0.00808416	−	0.0140022i	−0.861955	−	0.506985i	$-0.830760\pi$
$541$	0.188033	−	0.325682i	0.00808416	−	0.0140022i	0.870039	+	0.492983i	$0.164093\pi$
$542$	−1.97441	−	6.59498i	−0.0848081	−	0.283279i
$543$		0			0
$544$	0.149277	−	0.0981811i	0.00640020	−	0.00420948i
$545$	−11.9321	−	1.39466i	−0.511114	−	0.0597407i
$546$		0			0
$547$	−5.96696	+	2.99672i	−0.255129	+	0.128131i	−0.571767	−	0.820416i	$-0.693742\pi$
$547$	−5.96696	+	2.99672i	−0.255129	+	0.128131i	0.316639	+	0.948546i	$0.397446\pi$
$548$	1.42899	−	8.10422i	0.0610436	−	0.346195i
$549$		0			0
$550$	−2.95609	−	16.7648i	−0.126048	−	0.714854i
$551$	−1.11953	−	1.50379i	−0.0476935	−	0.0640634i
$552$		0			0
$553$	−12.6426	−	13.4003i	−0.537616	−	0.569840i
$554$	−0.252676	+	0.843998i	−0.0107352	+	0.0358580i
$555$		0			0
$556$	−6.27115	+	0.732992i	−0.265956	+	0.0310858i
$557$	−2.30382	+	1.93313i	−0.0976160	+	0.0819095i	−0.690290	−	0.723533i	$-0.742517\pi$
$557$	−2.30382	+	1.93313i	−0.0976160	+	0.0819095i	0.592674	+	0.805443i	$0.298072\pi$
$558$		0			0
$559$	−5.53318	−	4.64289i	−0.234028	−	0.196373i
$560$	−1.68344	−	1.10721i	−0.0711383	−	0.0467884i
$561$		0			0
$562$	−2.58995	+	3.47891i	−0.109251	+	0.146749i
$563$	29.3209	+	14.7255i	1.23573	+	0.620607i	0.942106	−	0.335315i	$-0.108843\pi$
$563$	29.3209	+	14.7255i	1.23573	+	0.620607i	0.293623	+	0.955921i	$0.405139\pi$
$564$		0			0
$565$	5.27421	+	1.25001i	0.221888	+	0.0525884i
$566$	12.9354			0.543715
$567$		0			0
$568$	−5.20773			−0.218511
$569$	−25.4422	−	6.02992i	−1.06659	−	0.252787i	−0.340402	−	0.940280i	$-0.610563\pi$
$569$	−25.4422	−	6.02992i	−1.06659	−	0.252787i	−0.726191	+	0.687493i	$0.758711\pi$
$570$		0			0
$571$	−0.715579	−	0.359377i	−0.0299461	−	0.0150395i	0.433763	−	0.901027i	$-0.357185\pi$
$571$	−0.715579	−	0.359377i	−0.0299461	−	0.0150395i	−0.463709	+	0.885987i	$0.653482\pi$
$572$	−29.5741	+	39.7250i	−1.23656	+	1.66098i
$573$		0			0
$574$	3.62166	+	2.38200i	0.151165	+	0.0994230i
$575$	0.329195	+	0.276227i	0.0137284	+	0.0115195i
$576$		0			0
$577$	−32.3968	+	27.1841i	−1.34869	+	1.13169i	−0.369395	+	0.929273i	$0.620435\pi$
$577$	−32.3968	+	27.1841i	−1.34869	+	1.13169i	−0.979300	+	0.202416i	$0.935121\pi$
$578$	−11.4244	+	1.33532i	−0.475194	+	0.0555422i
$579$		0			0
$580$	0.213881	−	0.714413i	0.00888093	−	0.0296644i
$581$	−17.8665	−	18.9373i	−0.741225	−	0.785653i
$582$		0			0
$583$	35.7542	+	48.0262i	1.48079	+	1.98904i
$584$	−3.46737	−	19.6644i	−0.143481	−	0.813721i
$585$		0			0
$586$	−0.214557	+	1.21681i	−0.00886326	+	0.0502661i
$587$	−11.9254	+	5.98914i	−0.492212	+	0.247198i	−0.677550	−	0.735476i	$-0.736958\pi$
$587$	−11.9254	+	5.98914i	−0.492212	+	0.247198i	0.185338	+	0.982675i	$0.440662\pi$
$588$		0			0
$589$	29.6700	+	3.46793i	1.22253	+	0.142893i
$590$	−3.01225	+	1.98119i	−0.124012	+	0.0815643i
$591$		0			0
$592$	2.42091	+	8.08642i	0.0994990	+	0.332350i
$593$	17.2045	−	29.7990i	0.706503	−	1.22370i	−0.259644	−	0.965704i	$-0.583605\pi$
$593$	17.2045	−	29.7990i	0.706503	−	1.22370i	0.966147	−	0.257994i	$-0.0830615\pi$
$594$		0			0
$595$	−0.0212812	−	0.0368601i	−0.000872443	−	0.00151112i
$596$	19.9769	−	21.1743i	0.818287	−	0.867334i
$597$		0			0
$598$	0.0215809	+	0.370530i	0.000882508	+	0.0151521i
$599$	15.8671	+	36.7842i	0.648314	+	1.50296i	0.851792	+	0.523881i	$0.175516\pi$
$599$	15.8671	+	36.7842i	0.648314	+	1.50296i	−0.203478	+	0.979080i	$0.565224\pi$
$600$		0			0
$601$	2.51105	−	43.1130i	0.102428	−	1.75862i	−0.421477	−	0.906839i	$-0.638488\pi$
$601$	2.51105	−	43.1130i	0.102428	−	1.75862i	0.523905	−	0.851777i	$-0.324475\pi$
$602$	−1.27856	+	0.465357i	−0.0521101	+	0.0189665i
$603$		0			0
$604$	−4.46403	−	1.62477i	−0.181639	−	0.0661111i
$605$	−9.88602	+	22.9184i	−0.401924	+	0.931764i
$606$		0			0
$607$	17.1451	−	4.06345i	0.695896	−	0.164930i	0.132581	−	0.991172i	$-0.457674\pi$
$607$	17.1451	−	4.06345i	0.695896	−	0.164930i	0.563316	+	0.826242i	$0.309526\pi$
$608$	−20.5767	+	4.87677i	−0.834496	+	0.197779i
$609$		0			0
$610$	0.434211	−	1.00661i	0.0175807	−	0.0407566i
$611$	−27.6577	−	10.0666i	−1.11891	−	0.407250i
$612$		0			0
$613$	25.9691	−	9.45198i	1.04888	−	0.381762i	0.240641	−	0.970614i	$-0.422642\pi$
$613$	25.9691	−	9.45198i	1.04888	−	0.381762i	0.808241	+	0.588852i	$0.200420\pi$
$614$	−0.589545	+	10.1221i	−0.0237921	+	0.408495i
$615$		0			0
$616$	8.48706	+	19.6752i	0.341954	+	0.792737i
$617$	0.256394	+	4.40211i	0.0103220	+	0.177222i	0.999529	+	0.0306958i	$0.00977232\pi$
$617$	0.256394	+	4.40211i	0.0103220	+	0.177222i	−0.989207	+	0.146526i	$0.953191\pi$
$618$		0			0
$619$	17.1670	−	18.1960i	0.690001	−	0.731358i	−0.283769	−	0.958893i	$-0.591585\pi$
$619$	17.1670	−	18.1960i	0.690001	−	0.731358i	0.973770	+	0.227535i	$0.0730665\pi$
$620$	5.94125	+	10.2905i	0.238606	+	0.413278i
$621$		0			0
$622$	−6.98959	+	12.1063i	−0.280257	+	0.485420i
$623$	5.84337	+	19.5182i	0.234110	+	0.781980i
$624$		0			0
$625$	−10.3999	+	6.84011i	−0.415996	+	0.273605i
$626$	15.0028	+	1.75357i	0.599631	+	0.0700868i
$627$		0			0
$628$	4.72505	−	2.37301i	0.188550	−	0.0946934i
$629$	−0.0309624	+	0.175596i	−0.00123455	+	0.00700148i
$630$		0			0
$631$	2.45133	+	13.9022i	0.0975857	+	0.553436i	0.993924	+	0.110066i	$0.0351062\pi$
$631$	2.45133	+	13.9022i	0.0975857	+	0.553436i	−0.896339	+	0.443370i	$0.853783\pi$
$632$	−18.0521	−	24.2481i	−0.718072	−	0.964538i
$633$		0			0
$634$	−5.27494	−	5.59111i	−0.209495	−	0.222051i
$635$	2.86770	−	9.57877i	0.113801	−	0.380122i
$636$		0			0
$637$	−25.3606	+	2.96423i	−1.00482	+	0.117447i
$638$	−1.62660	+	1.36488i	−0.0643978	+	0.0540362i
$639$		0			0
$640$	−7.87383	−	6.60693i	−0.311241	−	0.261162i
$641$	28.5813	+	18.7982i	1.12889	+	0.742484i	0.969587	−	0.244746i	$-0.0787045\pi$
$641$	28.5813	+	18.7982i	1.12889	+	0.742484i	0.159304	+	0.987230i	$0.449075\pi$
$642$		0			0
$643$	−8.05359	+	10.8178i	−0.317603	+	0.426614i	−0.932042	−	0.362349i	$-0.881975\pi$
$643$	−8.05359	+	10.8178i	−0.317603	+	0.426614i	0.614440	+	0.788964i	$0.289382\pi$
$644$	−0.210449	−	0.105692i	−0.00829286	−	0.00416483i
$645$		0			0
$646$	−0.0743798	−	0.0176283i	−0.00292644	−	0.000693578i
$647$	−3.19249			−0.125510			−0.0627548	−	0.998029i	$-0.519989\pi$
$647$	−3.19249			−0.125510			−0.0627548	+	0.998029i	$0.519989\pi$
$648$		0			0
$649$	−34.5785			−1.35733
$650$	−14.1992	−	3.36528i	−0.556940	−	0.131997i
$651$		0			0
$652$	27.1698	+	13.6452i	1.06405	+	0.534387i
$653$	19.2091	−	25.8023i	0.751710	−	1.00972i	−0.247457	−	0.968899i	$-0.579595\pi$
$653$	19.2091	−	25.8023i	0.751710	−	1.00972i	0.999166	−	0.0408223i	$-0.0129978\pi$
$654$		0			0
$655$	−11.2400	−	7.39267i	−0.439183	−	0.288855i
$656$	−4.91404	−	4.12337i	−0.191861	−	0.160991i
$657$		0			0
$658$	−4.24715	+	3.56378i	−0.165571	+	0.138931i
$659$	14.4955	−	1.69428i	0.564666	−	0.0659999i	0.171029	−	0.985266i	$-0.445291\pi$
$659$	14.4955	−	1.69428i	0.564666	−	0.0659999i	0.393637	+	0.919266i	$0.371217\pi$
$660$		0			0
$661$	2.23469	−	7.46440i	0.0869195	−	0.290331i	−0.903467	−	0.428657i	$-0.858987\pi$
$661$	2.23469	−	7.46440i	0.0869195	−	0.290331i	0.990387	+	0.138326i	$0.0441721\pi$
$662$	6.68982	+	7.09079i	0.260007	+	0.275592i
$663$		0			0
$664$	−25.5112	−	34.2674i	−0.990025	−	1.32983i
$665$	0.874754	+	4.96098i	0.0339215	+	0.192378i
$666$		0			0
$667$	0.00930786	−	0.0527875i	0.000360402	−	0.00204394i
$668$	−26.6564	+	13.3873i	−1.03137	+	0.517972i
$669$		0			0
$670$	−1.73533	−	0.202831i	−0.0670417	−	0.00783605i
$671$	8.78443	−	5.77761i	0.339119	−	0.223042i
$672$		0			0
$673$	−2.29949	−	7.68083i	−0.0886388	−	0.296074i	0.902163	−	0.431395i	$-0.141979\pi$
$673$	−2.29949	−	7.68083i	−0.0886388	−	0.296074i	−0.990802	+	0.135321i	$0.956793\pi$
$674$	−3.35193	+	5.80572i	−0.129112	+	0.223628i
$675$		0			0
$676$	11.2024	+	19.4031i	0.430862	+	0.746274i
$677$	5.84612	−	6.19652i	0.224685	−	0.238152i	−0.605218	−	0.796059i	$-0.706914\pi$
$677$	5.84612	−	6.19652i	0.224685	−	0.238152i	0.829903	+	0.557908i	$0.188396\pi$
$678$		0			0
$679$	−0.595470	−	10.2238i	−0.0228520	−	0.392354i
$680$	−0.0276622	−	0.0641283i	−0.00106080	−	0.00245921i
$681$		0			0
$682$	1.96724	−	33.7763i	0.0753296	−	1.29336i
$683$	13.5460	−	4.93034i	0.518323	−	0.188654i	−0.0695940	−	0.997575i	$-0.522170\pi$
$683$	13.5460	−	4.93034i	0.518323	−	0.188654i	0.587917	+	0.808921i	$0.299948\pi$
$684$		0			0
$685$	−4.72942	−	1.72137i	−0.180702	−	0.0657701i
$686$	−4.64524	+	10.7689i	−0.177356	+	0.411157i
$687$		0			0
$688$	1.95922	−	0.464345i	0.0746947	−	0.0177030i
$689$	49.9408	−	11.8362i	1.90259	−	0.450922i
$690$		0			0
$691$	14.4448	−	33.4868i	0.549506	−	1.27390i	−0.386622	−	0.922238i	$-0.626358\pi$
$691$	14.4448	−	33.4868i	0.549506	−	1.27390i	0.936128	−	0.351659i	$-0.114382\pi$
$692$	8.93742	+	3.25296i	0.339750	+	0.123659i
$693$		0			0
$694$	2.14799	−	0.781805i	0.0815366	−	0.0296769i
$695$	−0.224526	+	3.85496i	−0.00851676	+	0.146227i
$696$		0			0
$697$	−0.0536705	−	0.124422i	−0.00203292	−	0.00471283i
$698$	−0.0523236	−	0.898362i	−0.00198048	−	0.0340035i
$699$		0			0
$700$	6.35388	−	6.73472i	0.240154	−	0.254548i
$701$	4.76010	+	8.24474i	0.179787	+	0.311399i	0.941807	−	0.336153i	$-0.109126\pi$
$701$	4.76010	+	8.24474i	0.179787	+	0.311399i	−0.762021	+	0.647553i	$0.775793\pi$
$702$		0			0
$703$	10.5517	−	18.2761i	0.397966	−	0.689298i
$704$	1.73430	+	5.79296i	0.0653638	+	0.218330i
$705$		0			0
$706$	−6.66718	+	4.38507i	−0.250923	+	0.165034i
$707$	12.6083	+	1.47370i	0.474186	+	0.0554244i
$708$		0			0
$709$	10.6876	−	5.36752i	0.401382	−	0.201581i	−0.236644	−	0.971596i	$-0.576048\pi$
$709$	10.6876	−	5.36752i	0.401382	−	0.201581i	0.638026	+	0.770015i	$0.279751\pi$
$710$	−0.240792	+	1.36560i	−0.00903677	+	0.0512501i
$711$		0			0
$712$	5.80535	+	32.9238i	0.217565	+	1.23387i
$713$	0.510022	+	0.685078i	0.0191005	+	0.0256564i
$714$		0			0
$715$	20.7856	+	22.0314i	0.777336	+	0.823928i
$716$	1.53113	−	5.11432i	0.0572209	−	0.191131i
$717$		0			0
$718$	19.9679	−	2.33391i	0.745195	−	0.0871008i
$719$	16.3766	−	13.7416i	0.610743	−	0.512474i	−0.284135	−	0.958784i	$-0.591706\pi$
$719$	16.3766	−	13.7416i	0.610743	−	0.512474i	0.894879	+	0.446310i	$0.147262\pi$
$720$		0			0
$721$	5.73749	+	4.81433i	0.213675	+	0.179295i
$722$	−3.18234	−	2.09306i	−0.118435	−	0.0778956i
$723$		0			0
$724$	17.5714	−	23.6024i	0.653034	−	0.877177i
$725$	1.88327	+	0.945813i	0.0699429	+	0.0351266i
$726$		0			0
$727$	−7.66871	−	1.81752i	−0.284417	−	0.0674080i	0.0859313	−	0.996301i	$-0.472613\pi$
$727$	−7.66871	−	1.81752i	−0.284417	−	0.0674080i	−0.370348	+	0.928893i	$0.620762\pi$
$728$	18.3679			0.680760
$729$		0			0
$730$	−5.31685			−0.196785
$731$	0.0413859	+	0.00980864i	0.00153071	+	0.000362786i
$732$		0			0
$733$	31.1192	+	15.6287i	1.14942	+	0.577258i	0.918385	−	0.395689i	$-0.129494\pi$
$733$	31.1192	+	15.6287i	1.14942	+	0.577258i	0.231030	+	0.972947i	$0.425790\pi$
$734$	3.24340	−	4.35664i	0.119716	−	0.160806i
$735$		0			0
$736$	−0.505147	−	0.332241i	−0.0186200	−	0.0122466i
$737$	−12.8363	−	10.7709i	−0.472829	−	0.396751i
$738$		0			0
$739$	33.5899	−	28.1853i	1.23563	−	1.03681i	0.237772	−	0.971321i	$-0.423583\pi$
$739$	33.5899	−	28.1853i	1.23563	−	1.03681i	0.997853	−	0.0654916i	$-0.0208615\pi$
$740$	8.33779	−	0.974548i	0.306503	−	0.0358251i
$741$		0			0
$742$	2.77281	−	9.26183i	0.101793	−	0.340012i
$743$	14.6529	+	15.5312i	0.537563	+	0.569784i	0.938042	−	0.346522i	$-0.112638\pi$
$743$	14.6529	+	15.5312i	0.537563	+	0.569784i	−0.400478	+	0.916306i	$0.631156\pi$
$744$		0			0
$745$	−10.6317	−	14.2809i	−0.389516	−	0.523211i
$746$	0.351765	+	1.99496i	0.0128790	+	0.0730407i
$747$		0			0
$748$	0.0506397	−	0.287192i	0.00185157	−	0.0105008i
$749$	12.9913	−	6.52446i	0.474691	−	0.238399i
$750$		0			0
$751$	−4.49756	−	0.525689i	−0.164118	−	0.0191827i	0.0336369	−	0.999434i	$-0.489291\pi$
$751$	−4.49756	−	0.525689i	−0.164118	−	0.0191827i	−0.197755	+	0.980251i	$0.563365\pi$
$752$	6.85489	−	4.50853i	0.249972	−	0.164409i
$753$		0			0
$754$	0.522031	+	1.74371i	0.0190113	+	0.0635020i
$755$	−1.45269	+	2.51614i	−0.0528689	+	0.0915716i
$756$		0			0
$757$	−15.3969	−	26.6682i	−0.559610	−	0.969273i	−0.997529	−	0.0702583i	$-0.977618\pi$
$757$	−15.3969	−	26.6682i	−0.559610	−	0.969273i	0.437919	−	0.899014i	$-0.355716\pi$
$758$	−10.2653	+	10.8806i	−0.372853	+	0.395201i
$759$		0			0
$760$	0.480625	+	8.25200i	0.0174341	+	0.299332i
$761$	1.41749	+	3.28612i	0.0513841	+	0.119122i	0.941974	−	0.335685i	$-0.108968\pi$
$761$	1.41749	+	3.28612i	0.0513841	+	0.119122i	−0.890590	+	0.454806i	$0.849708\pi$
$762$		0			0
$763$	−1.08175	+	18.5730i	−0.0391621	+	0.672387i
$764$	28.8785	−	10.5109i	1.04479	−	0.380271i
$765$		0			0
$766$	−9.12904	−	3.32270i	−0.329846	−	0.120054i
$767$	−11.7402	+	27.2168i	−0.423913	+	0.982740i
$768$		0			0
$769$	−14.2113	+	3.36814i	−0.512473	+	0.121458i	−0.478713	−	0.877972i	$-0.658896\pi$
$769$	−14.2113	+	3.36814i	−0.512473	+	0.121458i	−0.0337603	+	0.999430i	$0.510748\pi$
$770$	5.55177	−	1.31579i	0.200072	−	0.0474179i
$771$		0			0
$772$	6.54637	−	15.1762i	0.235609	−	0.546203i
$773$	18.7983	+	6.84203i	0.676129	+	0.246091i	0.657184	−	0.753730i	$-0.271747\pi$
$773$	18.7983	+	6.84203i	0.676129	+	0.246091i	0.0189442	+	0.999821i	$0.493970\pi$
$774$		0			0
$775$	−31.5543	+	11.4848i	−1.13346	+	0.412547i
$776$	0.977099	−	16.7761i	0.0350758	−	0.602229i
$777$		0			0
$778$	−4.88570	−	11.3263i	−0.175161	−	0.406068i
$779$	0.932512	+	16.0106i	0.0334107	+	0.573640i
$780$		0			0
$781$	−9.12651	+	9.67353i	−0.326572	+	0.346146i
$782$	−0.00109277	−	0.00189273i	−3.90772e−5	−	6.76838e-5i
$783$		0			0
$784$	3.55882	−	6.16407i	0.127101	−	0.220145i
$785$	−0.927457	−	3.09792i	−0.0331024	−	0.110570i
$786$		0			0
$787$	11.3167	−	7.44313i	0.403398	−	0.265319i	−0.331557	−	0.943435i	$-0.607574\pi$
$787$	11.3167	−	7.44313i	0.403398	−	0.265319i	0.734955	+	0.678116i	$0.237203\pi$
$788$	36.3049	+	4.24344i	1.29331	+	0.151166i
$789$		0			0
$790$	−7.19316	+	3.61254i	−0.255921	+	0.128528i
$791$	1.45763	−	8.26666i	0.0518275	−	0.293929i
$792$		0			0
$793$	−1.56505	−	8.87585i	−0.0555766	−	0.315191i
$794$	−0.560431	−	0.752790i	−0.0198890	−	0.0267155i
$795$		0			0
$796$	9.24434	+	9.79842i	0.327657	+	0.347296i
$797$	−8.60409	+	28.7397i	−0.304772	+	1.01801i	0.659191	+	0.751976i	$0.270899\pi$
$797$	−8.60409	+	28.7397i	−0.304772	+	1.01801i	−0.963963	+	0.266035i	$0.914286\pi$
$798$		0			0
$799$	0.172140	−	0.0201203i	0.00608988	−	0.000711805i
$800$	18.2098	−	15.2799i	0.643814	−	0.540225i
$801$		0			0
$802$	11.4481	+	9.60610i	0.404247	+	0.339203i
$803$	−42.6039	−	28.0210i	−1.50346	−	0.988841i
$804$		0			0
$805$	−0.0860083	+	0.115529i	−0.00303139	+	0.00407187i
$806$	−25.9174	−	13.0162i	−0.912900	−	0.458476i
$807$		0			0
$808$	20.2683	+	4.80367i	0.713035	+	0.168992i
$809$	−48.8577			−1.71774			−0.858872	−	0.512190i	$-0.828834\pi$
$809$	−48.8577			−1.71774			−0.858872	+	0.512190i	$0.828834\pi$
$810$		0			0
$811$	−14.0558			−0.493566			−0.246783	−	0.969071i	$-0.579373\pi$
$811$	−14.0558			−0.493566			−0.246783	+	0.969071i	$0.579373\pi$
$812$	−1.12376	−	0.266337i	−0.0394364	−	0.00934659i
$813$		0			0
$814$	−21.3597	−	10.7273i	−0.748658	−	0.375990i
$815$	11.1040	−	14.9153i	0.388956	−	0.522459i
$816$		0			0
$817$	−4.20581	−	2.76621i	−0.147143	−	0.0967773i
$818$	−0.299277	−	0.251123i	−0.0104640	−	0.00878032i
$819$		0			0
$820$	−4.88698	+	4.10067i	−0.170661	+	0.143201i
$821$	32.0276	−	3.74348i	1.11777	−	0.130648i	0.462914	−	0.886403i	$-0.346804\pi$
$821$	32.0276	−	3.74348i	1.11777	−	0.130648i	0.654855	+	0.755755i	$0.272730\pi$
$822$		0			0
$823$	9.48786	−	31.6917i	0.330726	−	1.10470i	−0.617358	−	0.786682i	$-0.711797\pi$
$823$	9.48786	−	31.6917i	0.330726	−	1.10470i	0.948084	−	0.318020i	$-0.103018\pi$
$824$	8.43382	+	8.93932i	0.293806	+	0.311416i
$825$		0			0
$826$	3.33422	+	4.47864i	0.116012	+	0.155832i
$827$	−6.93056	−	39.3051i	−0.240999	−	1.36677i	−0.829604	−	0.558352i	$-0.811434\pi$
$827$	−6.93056	−	39.3051i	−0.240999	−	1.36677i	0.588605	−	0.808421i	$-0.299677\pi$
$828$		0			0
$829$	−3.03189	+	17.1947i	−0.105302	+	0.597198i	0.885797	+	0.464073i	$0.153612\pi$
$829$	−3.03189	+	17.1947i	−0.105302	+	0.597198i	−0.991099	+	0.133125i	$0.957499\pi$
$830$	−10.1654	+	5.10524i	−0.352845	+	0.177205i
$831$		0			0
$832$	5.14847	+	0.601769i	0.178491	+	0.0208626i
$833$	0.125616	−	0.0826190i	0.00435234	−	0.00286258i
$834$		0			0
$835$	5.23225	+	17.4769i	0.181070	+	0.604815i
$836$	−17.2576	+	29.8911i	−0.596868	+	1.03381i
$837$		0			0
$838$	4.27349	+	7.40191i	0.147625	+	0.255695i
$839$	−27.0966	+	28.7207i	−0.935478	+	0.991549i	−0.999980	−	0.00636894i	$-0.997973\pi$
$839$	−27.0966	+	28.7207i	−0.935478	+	0.991549i	0.0645018	+	0.997918i	$0.479454\pi$
$840$		0			0
$841$	1.67092	+	28.6885i	0.0576178	+	0.989259i
$842$	−5.74224	−	13.3120i	−0.197891	−	0.458762i
$843$		0			0
$844$	−0.652614	+	11.2050i	−0.0224639	+	0.385690i
$845$	12.8763	−	4.68657i	0.442957	−	0.161223i
$846$		0			0
$847$	36.3227	+	13.2204i	1.24806	+	0.454258i
$848$	−5.66677	+	13.1370i	−0.194598	+	0.451128i
$849$		0			0
$850$	0.0836111	−	0.0198162i	0.00286784	−	0.000679690i
$851$	0.587113	−	0.139148i	0.0201260	−	0.00476994i
$852$		0			0
$853$	−12.4048	+	28.7576i	−0.424733	+	0.984643i	0.562708	+	0.826656i	$0.309760\pi$
$853$	−12.4048	+	28.7576i	−0.424733	+	0.984643i	−0.987441	+	0.157987i	$0.949500\pi$
$854$	−1.59536	−	0.580662i	−0.0545920	−	0.0198699i
$855$		0			0
$856$	22.4160	−	8.15875i	0.766162	−	0.278860i
$857$	2.05526	−	35.2874i	0.0702062	−	1.20539i	−0.760746	−	0.649050i	$-0.775167\pi$
$857$	2.05526	−	35.2874i	0.0702062	−	1.20539i	0.830952	−	0.556344i	$-0.187796\pi$
$858$		0			0
$859$	11.1903	+	25.9420i	0.381808	+	0.885131i	0.995427	+	0.0955282i	$0.0304540\pi$
$859$	11.1903	+	25.9420i	0.381808	+	0.885131i	−0.613619	+	0.789603i	$0.710287\pi$
$860$	−0.116430	−	1.99902i	−0.00397022	−	0.0681661i
$861$		0			0
$862$	−2.07620	+	2.20064i	−0.0707156	+	0.0749542i
$863$	1.91089	+	3.30976i	0.0650475	+	0.112666i	0.896715	−	0.442608i	$-0.145947\pi$
$863$	1.91089	+	3.30976i	0.0650475	+	0.112666i	−0.831668	+	0.555274i	$0.812613\pi$
$864$		0			0
$865$	2.90843	−	5.03755i	0.0988896	−	0.171282i
$866$	1.77245	+	5.92039i	0.0602303	+	0.201183i
$867$		0			0
$868$	15.3745	−	10.1120i	0.521845	−	0.343223i
$869$	−76.6778	−	8.96235i	−2.60112	−	0.304027i
$870$		0			0
$871$	−12.8360	+	6.44646i	−0.434930	+	0.218430i
$872$	−5.30110	+	30.0640i	−0.179518	+	1.01810i
$873$		0			0
$874$	0.0449177	+	0.254741i	0.00151936	+	0.00861674i
$875$	−7.49490	−	10.0674i	−0.253374	−	0.340340i
$876$		0			0
$877$	23.5311	+	24.9415i	0.794588	+	0.842214i	0.990372	−	0.138433i	$-0.0442065\pi$
$877$	23.5311	+	24.9415i	0.794588	+	0.842214i	−0.195784	+	0.980647i	$0.562725\pi$
$878$	0.552812	−	1.84652i	0.0186565	−	0.0623171i
$879$		0			0
$880$	−8.38627	+	0.980214i	−0.282701	+	0.0330430i
$881$	−39.1151	+	32.8215i	−1.31782	+	1.10578i	−0.331059	+	0.943610i	$0.607406\pi$
$881$	−39.1151	+	32.8215i	−1.31782	+	1.10578i	−0.986762	+	0.162173i	$0.948150\pi$
$882$		0			0
$883$	−30.6669	−	25.7326i	−1.03202	−	0.865972i	−0.0409344	−	0.999162i	$-0.513033\pi$
$883$	−30.6669	−	25.7326i	−1.03202	−	0.865972i	−0.991091	+	0.133190i	$0.957478\pi$
$884$	−0.208856	−	0.137367i	−0.00702458	−	0.00462014i
$885$		0			0
$886$	−4.99886	+	6.71463i	−0.167940	+	0.225583i
$887$	−20.4630	−	10.2769i	−0.687079	−	0.345064i	0.0707713	−	0.997493i	$-0.477454\pi$
$887$	−20.4630	−	10.2769i	−0.687079	−	0.345064i	−0.757850	+	0.652429i	$0.773750\pi$
$888$		0			0
$889$	−15.0673	−	3.57102i	−0.505341	−	0.119768i
$890$	8.90188			0.298392
$891$		0			0
$892$	−1.15427			−0.0386477
$893$	−19.9596	−	4.73051i	−0.667923	−	0.158301i
$894$		0			0
$895$	−2.91775	−	1.46535i	−0.0975297	−	0.0489813i
$896$	−9.50552	+	12.7681i	−0.317557	+	0.426553i
$897$		0			0
$898$	−9.70921	−	6.38585i	−0.324001	−	0.213099i
$899$	3.20854	+	2.69228i	0.107011	+	0.0897927i
$900$		0			0
$901$	−0.231513	+	0.194262i	−0.00771281	+	0.00647182i
$902$	18.0418	−	2.10878i	0.600726	−	0.0702148i
$903$		0			0
$904$	3.95041	−	13.1953i	0.131389	−	0.438868i
$905$	−12.3497	−	13.0899i	−0.410517	−	0.435122i
$906$		0			0
$907$	−14.2978	−	19.2053i	−0.474752	−	0.637702i	0.498651	−	0.866803i	$-0.333829\pi$
$907$	−14.2978	−	19.2053i	−0.474752	−	0.637702i	−0.973403	+	0.229100i	$0.926422\pi$
$908$	2.03683	+	11.5514i	0.0675944	+	0.383347i
$909$		0			0
$910$	0.849285	−	4.81654i	0.0281535	−	0.159667i
$911$	27.5089	−	13.8155i	0.911411	−	0.457728i	0.0696462	−	0.997572i	$-0.477813\pi$
$911$	27.5089	−	13.8155i	0.911411	−	0.457728i	0.841765	+	0.539844i	$0.181517\pi$
$912$		0			0
$913$	−108.361	−	12.6656i	−3.58623	−	0.419170i
$914$	0.500177	−	0.328972i	0.0165444	−	0.0108814i
$915$		0			0
$916$	−6.90064	−	23.0497i	−0.228004	−	0.761585i
$917$	−10.4172	+	18.0431i	−0.344006	+	0.595835i
$918$		0			0
$919$	21.9894	+	38.0868i	0.725365	+	1.25637i	0.958824	+	0.284002i	$0.0916623\pi$
$919$	21.9894	+	38.0868i	0.725365	+	1.25637i	−0.233459	+	0.972367i	$0.575004\pi$
$920$	−0.162183	+	0.171904i	−0.00534703	+	0.00566752i
$921$		0			0
$922$	0.599266	+	10.2890i	0.0197358	+	0.338850i
$923$	4.51539	+	10.4678i	0.148626	+	0.344553i
$924$		0			0
$925$	−1.37935	+	23.6825i	−0.0453527	+	0.778675i
$926$	21.3875	−	7.78440i	0.702836	−	0.255811i
$927$		0			0
$928$	−2.78624	−	1.01411i	−0.0914627	−	0.0332897i
$929$	11.2233	−	26.0185i	0.368224	−	0.853640i	−0.628873	−	0.777508i	$-0.716484\pi$
$929$	11.2233	−	26.0185i	0.368224	−	0.853640i	0.997098	−	0.0761324i	$-0.0242572\pi$
$930$		0			0
$931$	−17.3152	+	4.10378i	−0.567483	+	0.134496i
$932$	−24.7264	+	5.86025i	−0.809939	+	0.191959i
$933$		0			0
$934$	2.95586	−	6.85245i	0.0967186	−	0.224219i
$935$	−0.167598	−	0.0610008i	−0.00548105	−	0.00199494i
$936$		0			0
$937$	12.4825	−	4.54327i	0.407787	−	0.148422i	−0.129979	−	0.991517i	$-0.541491\pi$
$937$	12.4825	−	4.54327i	0.407787	−	0.148422i	0.537765	+	0.843095i	$0.319269\pi$
$938$	−0.157324	+	2.70114i	−0.00513680	+	0.0881954i
$939$		0			0
$940$	−3.23181	−	7.49217i	−0.105410	−	0.244368i
$941$	−0.819975	−	14.0784i	−0.0267304	−	0.458944i	−0.984942	−	0.172884i	$-0.944691\pi$
$941$	−0.819975	−	14.0784i	−0.0267304	−	0.458944i	0.958212	−	0.286060i	$-0.0923456\pi$
$942$		0			0
$943$	−0.314670	+	0.333531i	−0.0102471	+	0.0108613i
$944$	−4.13135	−	7.15571i	−0.134464	−	0.232898i
$945$		0			0
$946$	−2.85077	+	4.93768i	−0.0926866	+	0.160538i
$947$	6.94085	+	23.1841i	0.225547	+	0.753381i	0.993596	+	0.112990i	$0.0360427\pi$
$947$	6.94085	+	23.1841i	0.225547	+	0.753381i	−0.768049	+	0.640391i	$0.778772\pi$
$948$		0			0
$949$	−36.5203	+	24.0198i	−1.18550	+	0.779715i
$950$	−10.1012	−	1.18067i	−0.327727	−	0.0383058i
$951$		0			0
$952$	−0.0966535	+	0.0485412i	−0.00313256	+	0.00157323i
$953$	0.315523	−	1.78942i	0.0102208	−	0.0579650i	−0.979271	−	0.202555i	$-0.935075\pi$
$953$	0.315523	−	1.78942i	0.0102208	−	0.0579650i	0.989492	+	0.144590i	$0.0461865\pi$
$954$		0			0
$955$	−3.26378	−	18.5098i	−0.105613	−	0.598964i
$956$	17.8169	+	23.9322i	0.576238	+	0.774022i
$957$		0			0
$958$	5.53621	+	5.86804i	0.178867	+	0.189588i
$959$	−2.23543	+	7.46684i	−0.0721857	+	0.241117i
$960$		0			0
$961$	−35.4962	+	4.14892i	−1.14504	+	0.133836i
$962$	−15.6955	+	13.1701i	−0.506044	+	0.424621i
$963$		0			0
$964$	−6.81044	−	5.71464i	−0.219350	−	0.184056i
$965$	−8.44541	−	5.55463i	−0.271867	−	0.178810i
$966$		0			0
$967$	−1.13266	+	1.52143i	−0.0364240	+	0.0489259i	−0.819962	−	0.572418i	$-0.806006\pi$
$967$	−1.13266	+	1.52143i	−0.0364240	+	0.0489259i	0.783538	+	0.621344i	$0.213413\pi$
$968$	56.6801	+	28.4658i	1.82177	+	0.914926i
$969$		0			0
$970$	−4.35396	−	1.03191i	−0.139797	−	0.0331325i
$971$	27.1629			0.871698			0.435849	−	0.900020i	$-0.356448\pi$
$971$	27.1629			0.871698			0.435849	+	0.900020i	$0.356448\pi$
$972$		0			0
$973$	5.98012			0.191714
$974$	−25.1795	−	5.96765i	−0.806803	−	0.191216i
$975$		0			0
$976$	2.24516	+	1.12756i	0.0718659	+	0.0360924i
$977$	15.2926	−	20.5416i	0.489255	−	0.657183i	−0.487103	−	0.873345i	$-0.661946\pi$
$977$	15.2926	−	20.5416i	0.489255	−	0.657183i	0.976358	+	0.216162i	$0.0693538\pi$
$978$		0			0
$979$	71.3309	+	46.9150i	2.27974	+	1.49941i
$980$	−5.42241	−	4.54994i	−0.173213	−	0.145343i
$981$		0			0
$982$	2.19751	−	1.84393i	0.0701255	−	0.0588423i
$983$	−28.8465	+	3.37167i	−0.920061	+	0.107540i	−0.562921	−	0.826511i	$-0.690322\pi$
$983$	−28.8465	+	3.37167i	−0.920061	+	0.107540i	−0.357140	+	0.934051i	$0.616248\pi$
$984$		0			0
$985$	6.41148	−	21.4158i	0.204287	−	0.682365i
$986$	−0.00735510	−	0.00779595i	−0.000234234	−	0.000248274i
$987$		0			0
$988$	17.6679	+	23.7322i	0.562092	+	0.755021i
$989$	−0.0249928	−	0.141741i	−0.000794725	−	0.00450711i
$990$		0			0
$991$	6.28903	−	35.6669i	0.199778	−	1.13300i	−0.705671	−	0.708539i	$-0.749354\pi$
$991$	6.28903	−	35.6669i	0.199778	−	1.13300i	0.905449	−	0.424456i	$-0.139534\pi$
$992$	42.2193	−	21.2033i	1.34046	−	0.673206i
$993$		0			0
$994$	2.13294	+	0.249305i	0.0676529	+	0.00790749i
$995$	6.88337	−	4.52726i	0.218218	−	0.143524i
$996$		0			0
$997$	4.35195	+	14.5365i	0.137828	+	0.460376i	0.998837	−	0.0482126i	$-0.0153525\pi$
$997$	4.35195	+	14.5365i	0.137828	+	0.460376i	−0.861009	+	0.508589i	$0.830167\pi$
$998$	12.6545	−	21.9182i	0.400571	−	0.693809i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.208.3		144
3.2	odd	2		81.2.g.a.16.6	✓	144
9.2	odd	6		729.2.g.c.379.3		144
9.4	even	3		729.2.g.a.622.6		144
9.5	odd	6		729.2.g.d.622.3		144
9.7	even	3		729.2.g.b.379.6		144
81.5	odd	54		81.2.g.a.76.6	yes	144
81.20	odd	54		6561.2.a.c.1.46		72
81.22	even	27		729.2.g.b.352.6		144
81.32	odd	54		729.2.g.d.109.3		144
81.49	even	27		729.2.g.a.109.6		144
81.59	odd	54		729.2.g.c.352.3		144
81.61	even	27		6561.2.a.d.1.27		72
81.76	even	27	inner	243.2.g.a.118.3		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.6	✓	144	3.2	odd	2
81.2.g.a.76.6	yes	144	81.5	odd	54
243.2.g.a.118.3		144	81.76	even	27	inner
243.2.g.a.208.3		144	1.1	even	1	trivial
729.2.g.a.109.6		144	81.49	even	27
729.2.g.a.622.6		144	9.4	even	3
729.2.g.b.352.6		144	81.22	even	27
729.2.g.b.379.6		144	9.7	even	3
729.2.g.c.352.3		144	81.59	odd	54
729.2.g.c.379.3		144	9.2	odd	6
729.2.g.d.109.3		144	81.32	odd	54
729.2.g.d.622.3		144	9.5	odd	6
6561.2.a.c.1.46		72	81.20	odd	54
6561.2.a.d.1.27		72	81.61	even	27

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.658400 - 0.156044i) q^{2} +(-1.37812 - 0.692120i) q^{4} +(-0.563225 + 0.756542i) q^{5} +(1.22035 + 0.802640i) q^{7} +(1.83603 + 1.54061i) q^{8} +(0.488880 - 0.410219i) q^{10} +(6.07936 - 0.710575i) q^{11} +(1.50478 - 5.02631i) q^{13} +(-0.678234 - 0.718886i) q^{14} +(0.873392 + 1.17317i) q^{16} +(0.00536485 + 0.0304256i) q^{17} +(0.634963 - 3.60105i) q^{19} +(1.29981 - 0.652790i) q^{20} +(-4.11353 - 0.480802i) q^{22} +(0.0873480 - 0.0574497i) q^{23} +(1.17888 + 3.93774i) q^{25} +(-1.77507 + 3.07451i) q^{26} +(-1.12628 - 1.95077i) q^{28} +(0.351839 - 0.372928i) q^{29} +(0.475004 + 8.15551i) q^{31} +(-2.29059 - 5.31019i) q^{32} +(0.00121550 - 0.0208694i) q^{34} +(-1.29456 + 0.471183i) q^{35} +(5.42328 + 1.97391i) q^{37} +(-0.979980 + 2.27185i) q^{38} +(-2.19963 + 0.521322i) q^{40} +(-4.26774 + 1.01147i) q^{41} +(0.545274 - 1.26409i) q^{43} +(-8.86991 - 3.22838i) q^{44} +(-0.0664745 + 0.0241947i) q^{46} +(0.326176 - 5.60023i) q^{47} +(-1.92752 - 4.46850i) q^{49} +(-0.161716 - 2.77656i) q^{50} +(-5.55259 + 5.88540i) q^{52} +(4.89106 + 8.47157i) q^{53} +(-2.88646 + 4.99950i) q^{55} +(1.00405 + 3.35376i) q^{56} +(-0.289844 + 0.190633i) q^{58} +(-5.61120 - 0.655856i) q^{59} +(1.53507 - 0.770942i) q^{61} +(0.959872 - 5.44370i) q^{62} +(0.171556 + 0.972942i) q^{64} +(2.95509 + 3.96937i) q^{65} +(-1.87870 - 1.99130i) q^{67} +(0.0136647 - 0.0456434i) q^{68} +(0.925866 - 0.108218i) q^{70} +(-1.66448 + 1.39666i) q^{71} +(-6.38204 - 5.35517i) q^{73} +(-3.26267 - 2.14589i) q^{74} +(-3.36742 + 4.52323i) q^{76} +(7.98930 + 4.01238i) q^{77} +(-12.2728 - 2.90871i) q^{79} -1.37947 q^{80} +2.96771 q^{82} +(-17.3440 - 4.11059i) q^{83} +(-0.0260399 - 0.0130777i) q^{85} +(-0.556260 + 0.747187i) q^{86} +(12.2566 + 8.06128i) q^{88} +(10.6853 + 8.96604i) q^{89} +(5.87068 - 4.92609i) q^{91} +(-0.160139 + 0.0187175i) q^{92} +(-1.08863 + 3.63629i) q^{94} +(2.36672 + 2.50858i) q^{95} +(-4.18690 - 5.62398i) q^{97} +(0.571800 + 3.24284i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

L-functions

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