LMFDB - Embedded newform 81.2.g.a.76.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,2,Mod(4,81)] 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("81.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			76.6
Character	$\chi$	$=$	81.76
Dual form			81.2.g.a.16.6

$q$-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} +(1.15662 - 1.28928i) q^{3} +(-1.37812 + 0.692120i) q^{4} +(0.563225 + 0.756542i) q^{5} +(0.560332 - 1.02934i) q^{6} +(1.22035 - 0.802640i) q^{7} +(-1.83603 + 1.54061i) q^{8} +(-0.324478 - 2.98240i) q^{9} +(0.488880 + 0.410219i) q^{10} +(-6.07936 - 0.710575i) q^{11} +(-0.701626 + 2.57730i) q^{12} +(1.50478 + 5.02631i) q^{13} +(0.678234 - 0.718886i) q^{14} +(1.62683 + 0.148875i) q^{15} +(0.873392 - 1.17317i) q^{16} +(-0.00536485 + 0.0304256i) q^{17} +(-0.679021 - 1.91298i) q^{18} +(0.634963 + 3.60105i) q^{19} +(-1.29981 - 0.652790i) q^{20} +(0.376655 - 2.50172i) q^{21} +(-4.11353 + 0.480802i) q^{22} +(-0.0873480 - 0.0574497i) q^{23} +(-0.137304 + 4.14904i) q^{24} +(1.17888 - 3.93774i) q^{25} +(1.77507 + 3.07451i) q^{26} +(-4.22044 - 3.03115i) q^{27} +(-1.12628 + 1.95077i) q^{28} +(-0.351839 - 0.372928i) q^{29} +(1.09433 - 0.155837i) q^{30} +(0.475004 - 8.15551i) q^{31} +(2.29059 - 5.31019i) q^{32} +(-7.94761 + 7.01612i) q^{33} +(0.00121550 + 0.0208694i) q^{34} +(1.29456 + 0.471183i) q^{35} +(2.51135 + 3.88554i) q^{36} +(5.42328 - 1.97391i) q^{37} +(0.979980 + 2.27185i) q^{38} +(8.22077 + 3.87344i) q^{39} +(-2.19963 - 0.521322i) q^{40} +(4.26774 + 1.01147i) q^{41} +(-0.142388 - 1.70591i) q^{42} +(0.545274 + 1.26409i) q^{43} +(8.86991 - 3.22838i) q^{44} +(2.07356 - 1.92524i) q^{45} +(-0.0664745 - 0.0241947i) q^{46} +(-0.326176 - 5.60023i) q^{47} +(-0.502362 - 2.48295i) q^{48} +(-1.92752 + 4.46850i) q^{49} +(0.161716 - 2.77656i) q^{50} +(0.0330220 + 0.0421075i) q^{51} +(-5.55259 - 5.88540i) q^{52} +(-4.89106 + 8.47157i) q^{53} +(-3.25173 - 1.33714i) q^{54} +(-2.88646 - 4.99950i) q^{55} +(-1.00405 + 3.35376i) q^{56} +(5.37717 + 3.34639i) q^{57} +(-0.289844 - 0.190633i) q^{58} +(5.61120 - 0.655856i) q^{59} +(-2.34501 + 0.920792i) q^{60} +(1.53507 + 0.770942i) q^{61} +(-0.959872 - 5.44370i) q^{62} +(-2.78977 - 3.37915i) q^{63} +(0.171556 - 0.972942i) q^{64} +(-2.95509 + 3.96937i) q^{65} +(-4.13788 + 5.85958i) q^{66} +(-1.87870 + 1.99130i) q^{67} +(-0.0136647 - 0.0456434i) q^{68} +(-0.175097 + 0.0461687i) q^{69} +(0.925866 + 0.108218i) q^{70} +(1.66448 + 1.39666i) q^{71} +(5.19046 + 4.97587i) q^{72} +(-6.38204 + 5.35517i) q^{73} +(3.26267 - 2.14589i) q^{74} +(-3.71333 - 6.07436i) q^{75} +(-3.36742 - 4.52323i) q^{76} +(-7.98930 + 4.01238i) q^{77} +(6.01698 + 1.26747i) q^{78} +(-12.2728 + 2.90871i) q^{79} +1.37947 q^{80} +(-8.78943 + 1.93545i) q^{81} +2.96771 q^{82} +(17.3440 - 4.11059i) q^{83} +(1.21241 + 3.70838i) q^{84} +(-0.0260399 + 0.0130777i) q^{85} +(0.556260 + 0.747187i) q^{86} +(-0.887750 + 0.0222844i) q^{87} +(12.2566 - 8.06128i) q^{88} +(-10.6853 + 8.96604i) q^{89} +(1.06481 - 1.59114i) q^{90} +(5.87068 + 4.92609i) q^{91} +(0.160139 + 0.0187175i) q^{92} +(-9.96532 - 10.0452i) q^{93} +(-1.08863 - 3.63629i) q^{94} +(-2.36672 + 2.50858i) q^{95} +(-4.19698 - 9.09507i) q^{96} +(-4.18690 + 5.62398i) q^{97} +(-0.571800 + 3.24284i) q^{98} +(-0.146600 + 18.3616i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{25}{27}\right)$

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	$-0.497180\pi$
$2$	0.658400	−	0.156044i	0.465559	−	0.110339i	0.456699	+	0.889621i	$0.349032\pi$
$3$	1.15662	−	1.28928i	0.667773	−	0.744365i
$3$	1.15662	−	1.28928i	0.667773	−	0.744365i
$4$	−1.37812	+	0.692120i	−0.689062	+	0.346060i
$5$	0.563225	+	0.756542i	0.251882	+	0.338336i	0.910022	−	0.414559i	$-0.136064\pi$
$5$	0.563225	+	0.756542i	0.251882	+	0.338336i	−0.658141	+	0.752895i	$0.728657\pi$
$6$	0.560332	−	1.02934i	0.228755	−	0.420228i
$7$	1.22035	−	0.802640i	0.461251	−	0.303369i	−0.297534	−	0.954711i	$-0.596164\pi$
$7$	1.22035	−	0.802640i	0.461251	−	0.303369i	0.758784	+	0.651342i	$0.225794\pi$
$8$	−1.83603	+	1.54061i	−0.649133	+	0.544688i
$9$	−0.324478	−	2.98240i	−0.108159	−	0.994134i
$10$	0.488880	+	0.410219i	0.154598	+	0.129723i
$11$	−6.07936	−	0.710575i	−1.83299	−	0.214246i	−0.871751	−	0.489948i	$-0.837016\pi$
$11$	−6.07936	−	0.710575i	−1.83299	−	0.214246i	−0.961243	+	0.275702i	$0.911090\pi$
$12$	−0.701626	+	2.57730i	−0.202542	+	0.744004i
$13$	1.50478	+	5.02631i	0.417351	+	1.39405i	0.865867	+	0.500274i	$0.166767\pi$
$13$	1.50478	+	5.02631i	0.417351	+	1.39405i	−0.448516	+	0.893775i	$0.648047\pi$
$14$	0.678234	−	0.718886i	0.181266	−	0.192130i
$15$	1.62683	+	0.148875i	0.420045	+	0.0384394i
$16$	0.873392	−	1.17317i	0.218348	−	0.293292i
$17$	−0.00536485	+	0.0304256i	−0.00130117	+	0.00737929i	−0.985451	−	0.169957i	$-0.945637\pi$
$17$	−0.00536485	+	0.0304256i	−0.00130117	+	0.00737929i	0.984150	+	0.177337i	$0.0567481\pi$
$18$	−0.679021	−	1.91298i	−0.160047	−	0.450893i
$19$	0.634963	+	3.60105i	0.145670	+	0.826138i	0.966826	+	0.255434i	$0.0822184\pi$
$19$	0.634963	+	3.60105i	0.145670	+	0.826138i	−0.821156	+	0.570704i	$0.806670\pi$
$20$	−1.29981	−	0.652790i	−0.290647	−	0.145968i
$21$	0.376655	−	2.50172i	0.0821930	−	0.545921i
$22$	−4.11353	+	0.480802i	−0.877007	+	0.102507i
$23$	−0.0873480	−	0.0574497i	−0.0182133	−	0.0119791i	0.540370	−	0.841428i	$-0.318284\pi$
$23$	−0.0873480	−	0.0574497i	−0.0182133	−	0.0119791i	−0.558583	+	0.829449i	$0.688655\pi$
$24$	−0.137304	+	4.14904i	−0.0280270	+	0.846920i
$25$	1.17888	−	3.93774i	0.235776	−	0.787548i
$26$	1.77507	+	3.07451i	0.348120	+	0.602961i
$27$	−4.22044	−	3.03115i	−0.812224	−	0.583345i
$28$	−1.12628	+	1.95077i	−0.212846	+	0.368661i
$29$	−0.351839	−	0.372928i	−0.0653349	−	0.0692509i	0.693882	−	0.720089i	$-0.255899\pi$
$29$	−0.351839	−	0.372928i	−0.0653349	−	0.0692509i	−0.759216	+	0.650838i	$0.774418\pi$
$30$	1.09433	−	0.155837i	0.199797	−	0.0284517i
$31$	0.475004	−	8.15551i	0.0853133	−	1.46477i	−0.635746	−	0.771898i	$-0.719307\pi$
$31$	0.475004	−	8.15551i	0.0853133	−	1.46477i	0.721059	−	0.692874i	$-0.243656\pi$
$32$	2.29059	−	5.31019i	0.404924	−	0.938718i
$33$	−7.94761	+	7.01612i	−1.38350	+	1.22135i
$34$	0.00121550	+	0.0208694i	0.000208457	+	0.00357906i
$35$	1.29456	+	0.471183i	0.218821	+	0.0796444i
$36$	2.51135	+	3.88554i	0.418559	+	0.647590i
$37$	5.42328	−	1.97391i	0.891581	−	0.324509i	0.144707	−	0.989475i	$-0.453776\pi$
$37$	5.42328	−	1.97391i	0.891581	−	0.324509i	0.746874	+	0.664965i	$0.231554\pi$
$38$	0.979980	+	2.27185i	0.158974	+	0.368543i
$39$	8.22077	+	3.87344i	1.31638	+	0.620246i
$40$	−2.19963	−	0.521322i	−0.347792	−	0.0824282i
$41$	4.26774	+	1.01147i	0.666509	+	0.157966i	0.549924	−	0.835215i	$-0.314657\pi$
$41$	4.26774	+	1.01147i	0.666509	+	0.157966i	0.116586	+	0.993181i	$0.462805\pi$
$42$	−0.142388	−	1.70591i	−0.0219709	−	0.263227i
$43$	0.545274	+	1.26409i	0.0831534	+	0.192771i	0.954720	−	0.297506i	$-0.0961548\pi$
$43$	0.545274	+	1.26409i	0.0831534	+	0.192771i	−0.871567	+	0.490277i	$0.836896\pi$
$44$	8.86991	−	3.22838i	1.33719	−	0.486697i
$45$	2.07356	−	1.92524i	0.309108	−	0.286998i
$46$	−0.0664745	−	0.0241947i	−0.00980113	−	0.00356732i
$47$	−0.326176	−	5.60023i	−0.0475777	−	0.816877i	−0.934721	−	0.355383i	$-0.884351\pi$
$47$	−0.326176	−	5.60023i	−0.0475777	−	0.816877i	0.887143	−	0.461494i	$-0.152687\pi$
$48$	−0.502362	−	2.48295i	−0.0725097	−	0.358383i
$49$	−1.92752	+	4.46850i	−0.275361	+	0.638358i
$50$	0.161716	−	2.77656i	0.0228702	−	0.392666i
$51$	0.0330220	+	0.0421075i	0.00462400	+	0.00589623i
$52$	−5.55259	−	5.88540i	−0.770005	−	0.816158i
$53$	−4.89106	+	8.47157i	−0.671839	+	1.16366i	0.305543	+	0.952178i	$0.401162\pi$
$53$	−4.89106	+	8.47157i	−0.671839	+	1.16366i	−0.977382	+	0.211481i	$0.932171\pi$
$54$	−3.25173	−	1.33714i	−0.442504	−	0.181961i
$55$	−2.88646	−	4.99950i	−0.389211	−	0.674132i
$56$	−1.00405	+	3.35376i	−0.134172	+	0.448165i
$57$	5.37717	+	3.34639i	0.712223	+	0.443240i
$58$	−0.289844	−	0.190633i	−0.0380583	−	0.0250314i
$59$	5.61120	−	0.655856i	0.730517	−	0.0853851i	0.257300	−	0.966331i	$-0.417167\pi$
$59$	5.61120	−	0.655856i	0.730517	−	0.0853851i	0.473216	+	0.880946i	$0.343093\pi$
$60$	−2.34501	+	0.920792i	−0.302740	+	0.118874i
$61$	1.53507	+	0.770942i	0.196546	+	0.0987090i	0.544350	−	0.838858i	$-0.316776\pi$
$61$	1.53507	+	0.770942i	0.196546	+	0.0987090i	−0.347804	+	0.937567i	$0.613073\pi$
$62$	−0.959872	−	5.44370i	−0.121904	−	0.691351i
$63$	−2.78977	−	3.37915i	−0.351478	−	0.425732i
$64$	0.171556	−	0.972942i	0.0214445	−	0.121618i
$65$	−2.95509	+	3.96937i	−0.366534	+	0.492340i
$66$	−4.13788	+	5.85958i	−0.509338	+	0.721265i
$67$	−1.87870	+	1.99130i	−0.229520	+	0.243277i	−0.831891	−	0.554940i	$-0.812741\pi$
$67$	−1.87870	+	1.99130i	−0.229520	+	0.243277i	0.602371	+	0.798216i	$0.294223\pi$
$68$	−0.0136647	−	0.0456434i	−0.00165709	−	0.00553508i
$69$	−0.175097	+	0.0461687i	−0.0210792	+	0.00555805i
$70$	0.925866	+	0.108218i	0.110662	+	0.0129345i
$71$	1.66448	+	1.39666i	0.197537	+	0.165753i	0.736191	−	0.676774i	$-0.236623\pi$
$71$	1.66448	+	1.39666i	0.197537	+	0.165753i	−0.538654	+	0.842527i	$0.681067\pi$
$72$	5.19046	+	4.97587i	0.611702	+	0.586412i
$73$	−6.38204	+	5.35517i	−0.746961	+	0.626775i	−0.934697	−	0.355445i	$-0.884329\pi$
$73$	−6.38204	+	5.35517i	−0.746961	+	0.626775i	0.187736	+	0.982219i	$0.439885\pi$
$74$	3.26267	−	2.14589i	0.379277	−	0.249455i
$75$	−3.71333	−	6.07436i	−0.428779	−	0.701407i
$76$	−3.36742	−	4.52323i	−0.386269	−	0.518850i
$77$	−7.98930	+	4.01238i	−0.910466	+	0.457253i
$78$	6.01698	+	1.26747i	0.681289	+	0.143513i
$79$	−12.2728	+	2.90871i	−1.38080	+	0.327256i	−0.852911	−	0.522056i	$-0.825165\pi$
$79$	−12.2728	+	2.90871i	−1.38080	+	0.327256i	−0.527891	+	0.849312i	$0.677017\pi$
$80$	1.37947			0.154229
$81$	−8.78943	+	1.93545i	−0.976603	+	0.215050i
$82$	2.96771			0.327729
$83$	17.3440	−	4.11059i	1.90375	−	0.451196i	0.904029	−	0.427471i	$-0.140596\pi$
$83$	17.3440	−	4.11059i	1.90375	−	0.451196i	0.999719	−	0.0237250i	$-0.00755260\pi$
$84$	1.21241	+	3.70838i	0.132285	+	0.404617i
$85$	−0.0260399	+	0.0130777i	−0.00282442	+	0.00141848i
$86$	0.556260	+	0.747187i	0.0599831	+	0.0805713i
$87$	−0.887750	+	0.0222844i	−0.0951768	+	0.00238914i
$88$	12.2566	−	8.06128i	1.30656	−	0.859335i
$89$	−10.6853	+	8.96604i	−1.13264	+	0.950399i	−0.999173	−	0.0406545i	$-0.987056\pi$
$89$	−10.6853	+	8.96604i	−1.13264	+	0.950399i	−0.133468	+	0.991053i	$0.542611\pi$
$90$	1.06481	−	1.59114i	0.112241	−	0.167721i
$91$	5.87068	+	4.92609i	0.615415	+	0.516394i
$92$	0.160139	+	0.0187175i	0.0166956	+	0.00195143i
$93$	−9.96532	−	10.0452i	−1.03336	−	1.04164i
$94$	−1.08863	−	3.63629i	−0.112284	−	0.375055i
$95$	−2.36672	+	2.50858i	−0.242820	+	0.257375i
$96$	−4.19698	−	9.09507i	−0.428352	−	0.928261i
$97$	−4.18690	+	5.62398i	−0.425115	+	0.571029i	−0.962146	−	0.272534i	$-0.912138\pi$
$97$	−4.18690	+	5.62398i	−0.425115	+	0.571029i	0.537031	+	0.843562i	$0.319546\pi$
$98$	−0.571800	+	3.24284i	−0.0577605	+	0.327576i
$99$	−0.146600	+	18.3616i	−0.0147339	+	1.84541i
$100$	1.10074	+	6.24263i	0.110074	+	0.624263i
$101$	−7.76637	−	3.90042i	−0.772782	−	0.388106i	0.0182867	−	0.999833i	$-0.494179\pi$
$101$	−7.76637	−	3.90042i	−0.772782	−	0.388106i	−0.791069	+	0.611727i	$0.790475\pi$
$102$	0.0283123	+	0.0225707i	0.00280333	+	0.00223483i
$103$	5.09302	−	0.595289i	0.501830	−	0.0586556i	0.138588	−	0.990350i	$-0.455744\pi$
$103$	5.09302	−	0.595289i	0.501830	−	0.0586556i	0.363243	+	0.931695i	$0.381670\pi$
$104$	−10.5064	−	6.91017i	−1.03024	−	0.677598i
$105$	2.10480	−	1.12408i	0.205407	−	0.109699i
$106$	−1.89834	+	6.34090i	−0.184383	+	0.615882i
$107$	−4.97642	−	8.61941i	−0.481089	−	0.833270i	0.518676	−	0.854971i	$-0.326425\pi$
$107$	−4.97642	−	8.61941i	−0.481089	−	0.833270i	−0.999765	+	0.0217011i	$0.993092\pi$
$108$	7.91422	+	1.25625i	0.761546	+	0.120883i
$109$	6.36856	−	11.0307i	0.609997	−	1.05655i	−0.381243	−	0.924475i	$-0.624504\pi$
$109$	6.36856	−	11.0307i	0.609997	−	1.05655i	0.991240	−	0.132071i	$-0.0421627\pi$
$110$	−2.68059	−	2.84126i	−0.255584	−	0.270903i
$111$	3.72773	−	9.27517i	0.353820	−	0.880361i
$112$	0.124216	−	2.13270i	0.0117373	−	0.201521i
$113$	2.27623	−	5.27688i	0.214129	−	0.496408i	−0.776969	−	0.629539i	$-0.783244\pi$
$113$	2.27623	−	5.27688i	0.214129	−	0.496408i	0.991098	+	0.133131i	$0.0425032\pi$
$114$	4.06251	+	1.36419i	0.380489	+	0.127768i
$115$	−0.00573345	−	0.0984395i	−0.000534647	−	0.00917953i
$116$	0.742989	+	0.270426i	0.0689848	+	0.0251084i
$117$	14.5022	−	6.11879i	1.34073	−	0.565682i
$118$	3.59207	−	1.30741i	0.330677	−	0.120357i
$119$	0.0178738	+	0.0414361i	0.00163849	+	0.00379844i
$120$	−3.21626	+	2.23297i	−0.293603	+	0.203841i
$121$	25.7502	+	6.10290i	2.34092	+	0.554809i
$122$	1.13099	+	0.268050i	0.102395	+	0.0242681i
$123$	6.24021	−	4.33242i	0.562661	−	0.390641i
$124$	4.98998	+	11.5681i	0.448113	+	1.03884i
$125$	8.07451	−	2.93888i	0.722206	−	0.262862i
$126$	−2.36408	−	1.78950i	−0.210609	−	0.159422i
$127$	−9.96192	−	3.62584i	−0.883977	−	0.321741i	−0.140163	−	0.990128i	$-0.544763\pi$
$127$	−9.96192	−	3.62584i	−0.883977	−	0.321741i	−0.743814	+	0.668387i	$0.766985\pi$
$128$	0.633653	+	10.8794i	0.0560075	+	0.961612i
$129$	2.26043	+	0.759053i	0.199020	+	0.0668309i
$130$	−1.32623	+	3.07456i	−0.116318	+	0.269656i
$131$	−0.829365	+	14.2396i	−0.0724619	+	1.24412i	0.744575	+	0.667538i	$0.232652\pi$
$131$	−0.829365	+	14.2396i	−0.0724619	+	1.24412i	−0.817037	+	0.576585i	$0.804385\pi$
$132$	6.09680	−	15.1698i	0.530658	−	1.32036i
$133$	3.66523	+	3.88491i	0.317815	+	0.336865i
$134$	−0.926205	+	1.60423i	−0.0800119	+	0.138585i
$135$	−0.0838645	−	4.90016i	−0.00721791	−	0.421739i
$136$	−0.0370239	−	0.0641273i	−0.00317478	−	0.00549887i
$137$	−1.53043	+	5.11200i	−0.130754	+	0.436748i	−0.998145	−	0.0608786i	$-0.980610\pi$
$137$	−1.53043	+	5.11200i	−0.130754	+	0.436748i	0.867391	+	0.497626i	$0.165795\pi$
$138$	−0.108079	+	0.0577201i	−0.00920032	+	0.00491346i
$139$	3.42061	+	2.24977i	0.290133	+	0.190823i	0.686229	−	0.727386i	$-0.259265\pi$
$139$	3.42061	+	2.24977i	0.290133	+	0.190823i	−0.396096	+	0.918209i	$0.629635\pi$
$140$	−2.11019	+	0.246645i	−0.178343	+	0.0208453i
$141$	−7.59751	−	6.05678i	−0.639826	−	0.510073i
$142$	1.31383	+	0.659830i	0.110254	+	0.0553717i
$143$	−5.57652	−	31.6260i	−0.466332	−	2.64470i
$144$	−3.78226	−	2.22414i	−0.315188	−	0.185345i
$145$	0.0839709	−	0.476223i	0.00697341	−	0.0395482i
$146$	−3.36629	+	4.52172i	−0.278596	+	0.374220i
$147$	3.53174	+	7.65346i	0.291293	+	0.631247i
$148$	−6.10777	+	6.47386i	−0.502056	+	0.532148i
$149$	5.41385	+	18.0835i	0.443520	+	1.48146i	0.829266	+	0.558855i	$0.188759\pi$
$149$	5.41385	+	18.0835i	0.443520	+	1.48146i	−0.385746	+	0.922605i	$0.626056\pi$
$150$	−3.39272	−	3.41992i	−0.277015	−	0.279235i
$151$	3.05960	+	0.357617i	0.248987	+	0.0291024i	0.239671	−	0.970854i	$-0.422960\pi$
$151$	3.05960	+	0.357617i	0.248987	+	0.0291024i	0.00931618	+	0.999957i	$0.497035\pi$
$152$	−6.71362	−	5.63340i	−0.544547	−	0.456929i
$153$	0.0924821	+	0.00612770i	0.00747674	+	0.000495395i
$154$	−4.63405	+	3.88843i	−0.373422	+	0.313338i
$155$	6.43752	−	4.23402i	0.517074	−	0.340085i
$156$	−14.0101	+	0.351684i	−1.12171	+	0.0281573i
$157$	−2.04742	−	2.75017i	−0.163402	−	0.219487i	0.712879	−	0.701287i	$-0.247391\pi$
$157$	−2.04742	−	2.75017i	−0.163402	−	0.219487i	−0.876281	+	0.481800i	$0.839983\pi$
$158$	−7.62654	+	3.83019i	−0.606735	+	0.304714i
$159$	5.26513	+	16.1043i	0.417552	+	1.27715i
$160$	5.30750	−	1.25790i	0.419595	−	0.0994458i
$161$	−0.152707			−0.0120350
$162$	−5.48494	+	2.64583i	−0.430938	+	0.207876i
$163$	−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
$165$	−9.78428	−	2.06105i	−0.761705	−	0.160452i
$166$	10.7778	−	5.41283i	0.836522	−	0.420117i
$167$	−11.5505	−	15.5151i	−0.893808	−	1.20059i	−0.978925	−	0.204222i	$-0.934534\pi$
$167$	−11.5505	−	15.5151i	−0.893808	−	1.20059i	0.0851164	−	0.996371i	$-0.472874\pi$
$168$	3.16263	+	5.17351i	0.244002	+	0.399145i
$169$	−12.1381	+	7.98337i	−0.933702	+	0.614106i
$170$	−0.0151039	+	0.0126737i	−0.00115842	+	0.000972029i
$171$	10.5337	−	3.06218i	0.805536	−	0.234170i
$172$	−1.62635	−	1.36467i	−0.124008	−	0.104055i
$173$	6.12562	+	0.715983i	0.465723	+	0.0544352i	0.345719	−	0.938338i	$-0.387635\pi$
$173$	6.12562	+	0.715983i	0.465723	+	0.0544352i	0.120004	+	0.992773i	$0.461709\pi$
$174$	−0.581017	+	0.153200i	−0.0440468	+	0.0116140i
$175$	−1.72193	−	5.75166i	−0.130166	−	0.434784i
$176$	−6.14328	+	6.51150i	−0.463067	+	0.490823i
$177$	5.64443	−	7.99298i	0.424261	−	0.600789i
$178$	−5.63611	+	7.57061i	−0.422445	+	0.567441i
$179$	−0.601129	+	3.40917i	−0.0449305	+	0.254814i	−0.998997	−	0.0447821i	$-0.985741\pi$
$179$	−0.601129	+	3.40917i	−0.0449305	+	0.254814i	0.954066	+	0.299596i	$0.0968518\pi$
$180$	−1.52512	+	4.08838i	−0.113676	+	0.304730i
$181$	−3.31327	−	18.7905i	−0.246273	−	1.39668i	−0.817517	−	0.575904i	$-0.804650\pi$
$181$	−3.31327	−	18.7905i	−0.246273	−	1.39668i	0.571244	−	0.820780i	$-0.306461\pi$
$182$	4.63394	+	2.32725i	0.343490	+	0.172507i
$183$	2.76945	−	1.08745i	0.204723	−	0.0803867i
$184$	0.248881	−	0.0290900i	0.0183477	−	0.00214454i
$185$	4.54787	+	2.99118i	0.334366	+	0.219916i
$186$	−8.12865	−	5.05873i	−0.596022	−	0.370924i
$187$	0.0542345	−	0.181156i	0.00396602	−	0.0132474i
$188$	4.32554	+	7.49206i	0.315473	+	0.546415i
$189$	−7.58336	−	0.311583i	−0.551608	−	0.0226643i
$190$	−1.16680	+	2.02096i	−0.0846486	+	0.146616i
$191$	13.6753	+	14.4949i	0.989508	+	1.04882i	0.998806	+	0.0488602i	$0.0155589\pi$
$191$	13.6753	+	14.4949i	0.989508	+	1.04882i	−0.00929782	+	0.999957i	$0.502960\pi$
$192$	−1.05597	−	1.34650i	−0.0762080	−	0.0971755i
$193$	0.623160	−	10.6992i	0.0448561	−	0.770149i	−0.898624	−	0.438720i	$-0.855432\pi$
$193$	0.623160	−	10.6992i	0.0448561	−	0.770149i	0.943480	−	0.331429i	$-0.107531\pi$
$194$	−1.87907	+	4.35616i	−0.134909	+	0.312754i
$195$	1.69972	+	8.40097i	0.121720	+	0.601606i
$196$	−0.436373	−	7.49223i	−0.0311695	−	0.535160i
$197$	22.2725	+	8.10651i	1.58685	+	0.577565i	0.976679	−	0.214707i	$-0.0688795\pi$
$197$	22.2725	+	8.10651i	1.58685	+	0.577565i	0.610169	+	0.792272i	$0.291102\pi$
$198$	2.76869	+	12.1122i	0.196763	+	0.860775i
$199$	−8.20833	+	2.98759i	−0.581873	+	0.211785i	−0.616151	−	0.787628i	$-0.711309\pi$
$199$	−8.20833	+	2.98759i	−0.581873	+	0.211785i	0.0342781	+	0.999412i	$0.489087\pi$
$200$	3.90206	+	9.04599i	0.275917	+	0.639648i
$201$	0.394413	+	4.72534i	0.0278197	+	0.333300i
$202$	−5.72201	−	1.35614i	−0.402599	−	0.0954177i
$203$	−0.728695	−	0.172704i	−0.0511443	−	0.0121214i
$204$	−0.0746519	−	0.0351742i	−0.00522668	−	0.00246269i
$205$	1.63848	+	3.79841i	0.114436	+	0.265293i
$206$	3.26035	−	1.18667i	0.227160	−	0.0826793i
$207$	−0.142995	+	0.279148i	−0.00993887	+	0.0194021i
$208$	7.21098	+	2.62458i	0.499991	+	0.181982i
$209$	−1.30135	−	22.3433i	−0.0900161	−	1.54552i
$210$	1.21039	−	1.06853i	0.0835251	−	0.0737357i
$211$	−2.88269	+	6.68284i	−0.198453	+	0.460065i	−0.988162	−	0.153416i	$-0.950972\pi$
$211$	−2.88269	+	6.68284i	−0.198453	+	0.460065i	0.789709	+	0.613482i	$0.210232\pi$
$212$	0.877150	−	15.0601i	0.0602429	−	1.03433i
$213$	3.72584	−	0.530572i	0.255291	−	0.0363542i
$214$	−4.62148	−	4.89848i	−0.315918	−	0.334853i
$215$	−0.649223	+	1.12449i	−0.0442766	+	0.0766894i
$216$	12.4187	−	0.936779i	0.844983	−	0.0637398i
$217$	−5.96626	−	10.3339i	−0.405016	−	0.701508i
$218$	2.47179	−	8.25636i	0.167411	−	0.559191i
$219$	−0.477268	+	14.4221i	−0.0322508	+	0.974555i
$220$	7.43816	+	4.89216i	0.501481	+	0.329829i
$221$	−0.161002	+	0.0188184i	−0.0108301	+	0.00126586i
$222$	1.00700	−	6.68846i	0.0675857	−	0.448900i
$223$	0.668861	+	0.335914i	0.0447902	+	0.0224945i	0.471053	−	0.882105i	$-0.343874\pi$
$223$	0.668861	+	0.335914i	0.0447902	+	0.0224945i	−0.426263	+	0.904599i	$0.640170\pi$
$224$	−1.46684	−	8.31884i	−0.0980071	−	0.555826i
$225$	−12.1264	−	2.23819i	−0.808430	−	0.149213i
$226$	0.675242	−	3.82949i	0.0449164	−	0.254734i
$227$	4.54197	−	6.10092i	0.301461	−	0.404932i	−0.625420	−	0.780288i	$-0.715072\pi$
$227$	4.54197	−	6.10092i	0.301461	−	0.404932i	0.926881	+	0.375356i	$0.122480\pi$
$228$	−9.72651	−	0.890098i	−0.644154	−	0.0589482i
$229$	10.7066	−	11.3484i	0.707514	−	0.749921i	−0.269522	−	0.962994i	$-0.586866\pi$
$229$	10.7066	−	11.3484i	0.707514	−	0.749921i	0.977036	+	0.213073i	$0.0683472\pi$
$230$	−0.0191357	−	0.0639178i	−0.00126177	−	0.00421462i
$231$	−4.06748	+	14.9412i	−0.267621	+	0.983060i
$232$	1.22052	+	0.142658i	0.0801311	+	0.00936599i
$233$	−12.6227	−	10.5917i	−0.826940	−	0.693885i	0.127647	−	0.991820i	$-0.459258\pi$
$233$	−12.6227	−	10.5917i	−0.826940	−	0.693885i	−0.954586	+	0.297935i	$0.903702\pi$
$234$	8.59346	−	6.29158i	0.561772	−	0.411294i
$235$	4.05310	−	3.40095i	0.264395	−	0.221854i
$236$	−7.27901	+	4.78748i	−0.473823	+	0.311638i
$237$	−10.4448	+	19.1874i	−0.678464	+	1.24635i
$238$	0.0182339	+	0.0244924i	0.00118193	+	0.00158761i
$239$	17.2890	−	8.68288i	1.11834	−	0.561649i	0.209084	−	0.977898i	$-0.432952\pi$
$239$	17.2890	−	8.68288i	1.11834	−	0.561649i	0.909251	+	0.416249i	$0.136655\pi$
$240$	1.59551	−	1.77852i	0.102990	−	0.114803i
$241$	5.60951	−	1.32948i	0.361340	−	0.0856392i	−0.0459358	−	0.998944i	$-0.514627\pi$
$241$	5.60951	−	1.32948i	0.361340	−	0.0856392i	0.407276	+	0.913305i	$0.366479\pi$
$242$	17.9062			1.15105
$243$	−7.67066	+	13.5706i	−0.492073	+	0.870554i
$244$	−2.64910			−0.169591
$245$	−4.46624	+	1.05852i	−0.285338	+	0.0676262i
$246$	3.43251	−	3.82621i	0.218849	−	0.243950i
$247$	−17.1445	+	8.61031i	−1.09088	+	0.547861i
$248$	11.6923	+	15.7055i	0.742463	+	0.997301i
$249$	14.7606	−	27.1156i	0.935415	−	1.71838i
$250$	4.85766	−	3.19493i	0.307225	−	0.202065i
$251$	−14.4752	+	12.1462i	−0.913668	+	0.766659i	−0.972813	−	0.231591i	$-0.925607\pi$
$251$	−14.4752	+	12.1462i	−0.913668	+	0.766659i	0.0591449	+	0.998249i	$0.481163\pi$
$252$	6.18343	+	2.72603i	0.389519	+	0.171724i
$253$	0.490197	+	0.411324i	0.0308184	+	0.0258597i
$254$	−7.12471	−	0.832759i	−0.447044	−	0.0522520i
$255$	−0.0132573	+	0.0486985i	−0.000830205	+	0.00304962i
$256$	2.68155	+	8.95701i	0.167597	+	0.559813i
$257$	12.4352	−	13.1805i	0.775685	−	0.822178i	−0.212222	−	0.977221i	$-0.568070\pi$
$257$	12.4352	−	13.1805i	0.775685	−	0.822178i	0.987908	+	0.155043i	$0.0495516\pi$
$258$	1.60671	+	0.147034i	0.100030	+	0.00915396i
$259$	5.03398	−	6.76181i	0.312796	−	0.420158i
$260$	1.32520	−	7.51557i	0.0821853	−	0.466096i
$261$	−0.998055	+	1.17033i	−0.0617781	+	0.0724417i
$262$	1.67595	+	9.50479i	0.103541	+	0.587208i
$263$	7.74703	+	3.89071i	0.477703	+	0.239911i	0.671323	−	0.741165i	$-0.265727\pi$
$263$	7.74703	+	3.89071i	0.477703	+	0.239911i	−0.193620	+	0.981077i	$0.562023\pi$
$264$	3.78292	−	25.1259i	0.232823	−	1.54639i
$265$	−9.16387	+	1.07110i	−0.562932	+	0.0657973i
$266$	3.01940	+	1.98589i	0.185131	+	0.121763i
$267$	−0.799080	+	24.1466i	−0.0489029	+	1.47775i
$268$	1.21086	−	4.04455i	0.0739650	−	0.247060i
$269$	−5.59305	−	9.68745i	−0.341014	−	0.590654i	0.643607	−	0.765356i	$-0.277437\pi$
$269$	−5.59305	−	9.68745i	−0.341014	−	0.590654i	−0.984621	+	0.174702i	$0.944104\pi$
$270$	−0.819855	−	3.21318i	−0.0498948	−	0.195548i
$271$	5.08705	−	8.81103i	0.309016	−	0.535232i	−0.669131	−	0.743144i	$-0.733334\pi$
$271$	5.08705	−	8.81103i	0.309016	−	0.535232i	0.978147	+	0.207912i	$0.0666669\pi$
$272$	0.0310087	+	0.0328673i	0.00188018	+	0.00199288i
$273$	13.1412	−	1.87135i	0.795343	−	0.113259i
$274$	−0.209941	+	3.60456i	−0.0126830	+	0.217759i
$275$	−9.96490	+	23.1012i	−0.600906	+	1.39306i
$276$	0.209351	−	0.184814i	0.0126014	−	0.0111245i
$277$	0.0757068	+	1.29984i	0.00454878	+	0.0780996i	0.999819	−	0.0190505i	$-0.00606434\pi$
$277$	0.0757068	+	1.29984i	0.00454878	+	0.0780996i	−0.995270	+	0.0971501i	$0.969027\pi$
$278$	2.60319	+	0.947485i	0.156129	+	0.0568264i
$279$	−24.4771	+	1.22963i	−1.46541	+	0.0736161i
$280$	−3.10276	+	1.12931i	−0.185425	+	0.0674894i
$281$	−2.53880	−	5.88560i	−0.151452	−	0.351105i	0.825552	−	0.564326i	$-0.190864\pi$
$281$	−2.53880	−	5.88560i	−0.151452	−	0.351105i	−0.977004	+	0.213221i	$0.931605\pi$
$282$	−5.94732	−	2.80224i	−0.354158	−	0.166871i
$283$	−18.6018	−	4.40871i	−1.10576	−	0.262071i	−0.363110	−	0.931746i	$-0.618285\pi$
$283$	−18.6018	−	4.40871i	−1.10576	−	0.262071i	−0.742654	+	0.669675i	$0.766433\pi$
$284$	−3.26051	−	0.772756i	−0.193476	−	0.0458546i
$285$	0.496867	+	5.95282i	0.0294319	+	0.352615i
$286$	−8.60661	−	19.9524i	−0.508920	−	1.17981i
$287$	6.02001	−	2.19110i	0.355350	−	0.129337i
$288$	−16.5804	−	5.10843i	−0.977008	−	0.301017i
$289$	15.9739	+	5.81402i	0.939640	+	0.342001i
$290$	−0.0190251	−	0.326648i	−0.00111719	−	0.0191814i
$291$	2.40824	+	11.9029i	0.141174	+	0.697758i
$292$	5.08883	−	11.7972i	0.297801	−	0.690380i
$293$	0.106176	−	1.82297i	0.00620287	−	0.106499i	−0.993786	−	0.111312i	$-0.964495\pi$
$293$	0.106176	−	1.82297i	0.00620287	−	0.106499i	0.999988	+	0.00481246i	$0.00153186\pi$
$294$	3.51957	+	4.48793i	0.205265	+	0.261741i
$295$	3.65655	+	3.87572i	0.212893	+	0.225653i
$296$	−6.91625	+	11.9793i	−0.401999	+	0.696283i
$297$	23.5037	+	21.4264i	1.36382	+	1.24328i
$298$	6.38629	+	11.0614i	0.369948	+	0.640769i
$299$	0.157321	−	0.525488i	0.00909809	−	0.0303897i
$300$	9.32162	+	5.80116i	0.538184	+	0.334930i
$301$	1.68003	+	1.10497i	0.0968355	+	0.0636897i
$302$	2.07025	−	0.241977i	0.119129	−	0.0139242i
$303$	−14.0114	+	5.50173i	−0.804935	+	0.316066i
$304$	4.77921	+	2.40021i	0.274107	+	0.137662i
$305$	0.281340	+	1.59556i	0.0161095	+	0.0913614i
$306$	0.0618464	−	0.0103968i	0.00353552	−	0.000594343i
$307$	−2.60207	+	14.7571i	−0.148508	+	0.842232i	0.815975	+	0.578087i	$0.196201\pi$
$307$	−2.60207	+	14.7571i	−0.148508	+	0.842232i	−0.964483	+	0.264145i	$0.914910\pi$
$308$	8.23321	−	11.0591i	0.469131	−	0.630152i
$309$	5.12318	−	7.25485i	0.291447	−	0.412714i
$310$	3.57777	−	3.79221i	0.203203	−	0.215383i
$311$	−5.92528	−	19.7918i	−0.335992	−	1.12229i	−0.944436	−	0.328695i	$-0.893391\pi$
$311$	−5.92528	−	19.7918i	−0.335992	−	1.12229i	0.608444	−	0.793597i	$-0.291794\pi$
$312$	−21.0610	+	5.55326i	−1.19234	+	0.314392i
$313$	−22.1725	−	2.59159i	−1.25326	−	0.146486i	−0.536559	−	0.843863i	$-0.680276\pi$
$313$	−22.1725	−	2.59159i	−1.25326	−	0.146486i	−0.716704	+	0.697377i	$0.754350\pi$
$314$	−1.77717	−	1.49122i	−0.100291	−	0.0841545i
$315$	0.985198	−	4.01380i	0.0555096	−	0.226152i
$316$	14.9003	−	12.5028i	0.838208	−	0.703340i
$317$	−9.49125	+	6.24250i	−0.533082	+	0.350614i	−0.787336	−	0.616524i	$-0.788540\pi$
$317$	−9.49125	+	6.24250i	−0.533082	+	0.350614i	0.254254	+	0.967137i	$0.418170\pi$
$318$	5.97953	+	9.78147i	0.335316	+	0.548518i
$319$	1.87396	+	2.51717i	0.104922	+	0.140934i
$320$	0.832696	−	0.418196i	0.0465491	−	0.0233778i
$321$	−16.8686	−	3.55336i	−0.941515	−	0.198329i
$322$	−0.100542	+	0.0238289i	−0.00560299	+	0.00132793i
$323$	−0.112971			−0.00628586
$324$	10.7734	−	8.75063i	0.598520	−	0.486146i
$325$	21.5663			1.19628
$326$	−12.9804	+	3.07641i	−0.718917	+	0.170386i
$327$	−6.85562	−	20.9691i	−0.379117	−	1.15959i
$328$	−9.39397	+	4.71783i	−0.518695	+	0.260499i
$329$	−4.89302	−	6.57246i	−0.269761	−	0.362351i
$330$	−6.76358	+	0.169780i	−0.372323	+	0.00934610i
$331$	−12.0371	+	7.91690i	−0.661617	+	0.435152i	−0.835408	−	0.549630i	$-0.814769\pi$
$331$	−12.0371	+	7.91690i	−0.661617	+	0.435152i	0.173791	+	0.984783i	$0.444398\pi$
$332$	−21.0571	+	17.6690i	−1.15566	+	0.969714i
$333$	−7.64673	−	15.5339i	−0.419038	−	0.851252i
$334$	−10.0259	−	8.41273i	−0.548593	−	0.460324i
$335$	−2.56464	−	0.299763i	−0.140121	−	0.0163778i
$336$	−2.60597	−	2.62686i	−0.142168	−	0.143307i
$337$	2.84153	+	9.49138i	0.154788	+	0.517029i	0.999844	−	0.0176492i	$-0.00561820\pi$
$337$	2.84153	+	9.49138i	0.154788	+	0.517029i	−0.845056	+	0.534678i	$0.820433\pi$
$338$	−6.74599	+	7.15033i	−0.366933	+	0.388927i
$339$	−4.17065	−	9.03802i	−0.226519	−	0.490878i
$340$	0.0268348	−	0.0360454i	0.00145532	−	0.00195484i
$341$	−8.68281	+	49.2427i	−0.470201	+	2.66664i
$342$	6.45758	−	3.65986i	0.349186	−	0.197903i
$343$	3.00981	+	17.0695i	0.162514	+	0.921665i
$344$	−2.94860	−	1.48084i	−0.158978	−	0.0798417i
$345$	−0.133547	−	0.106465i	−0.00718994	−	0.00573187i
$346$	4.14483	−	0.484462i	0.222828	−	0.0260448i
$347$	2.82247	+	1.85637i	0.151518	+	0.0996552i	0.623004	−	0.782218i	$-0.285912\pi$
$347$	2.82247	+	1.85637i	0.151518	+	0.0996552i	−0.471486	+	0.881874i	$0.656282\pi$
$348$	1.20801	−	0.645141i	0.0647560	−	0.0345832i
$349$	0.381429	−	1.27406i	0.0204174	−	0.0681990i	−0.947174	−	0.320721i	$-0.896075\pi$
$349$	0.381429	−	1.27406i	0.0204174	−	0.0681990i	0.967591	+	0.252522i	$0.0812600\pi$
$350$	−2.03123	−	3.51819i	−0.108574	−	0.188055i
$351$	8.88468	−	25.7745i	0.474229	−	1.37574i
$352$	−17.6986	+	30.6549i	−0.943340	+	1.63391i
$353$	−8.09324	−	8.57833i	−0.430760	−	0.456579i	0.475240	−	0.879856i	$-0.342361\pi$
$353$	−8.09324	−	8.57833i	−0.430760	−	0.456579i	−0.906000	+	0.423277i	$0.860880\pi$
$354$	2.46904	−	6.14335i	0.131228	−	0.326515i
$355$	−0.119159	+	2.04588i	−0.00632430	+	0.108584i
$356$	8.52012	−	19.7518i	0.451565	−	1.04685i
$357$	0.0740957	+	0.0248813i	0.00392156	+	0.00131686i
$358$	0.136196	+	2.33840i	0.00719820	+	0.123588i
$359$	27.9195	+	10.1619i	1.47353	+	0.536323i	0.949058	−	0.315102i	$-0.102039\pi$
$359$	27.9195	+	10.1619i	1.47353	+	0.536323i	0.524477	+	0.851425i	$0.324261\pi$
$360$	−0.841059	+	6.72934i	−0.0443277	+	0.354667i
$361$	5.28976	−	1.92531i	0.278408	−	0.101332i
$362$	−5.11358	−	11.8546i	−0.268764	−	0.623065i
$363$	37.6514	−	26.1404i	1.97618	−	1.37202i
$364$	−11.5000	−	2.72555i	−0.602763	−	0.142857i
$365$	−7.64593	−	1.81212i	−0.400206	−	0.0948506i
$366$	1.65371	−	1.14813i	0.0864410	−	0.0600138i
$367$	−3.17934	−	7.37053i	−0.165960	−	0.384738i	0.814859	−	0.579659i	$-0.196814\pi$
$367$	−3.17934	−	7.37053i	−0.165960	−	0.384738i	−0.980819	+	0.194921i	$0.937555\pi$
$368$	−0.143687	+	0.0522978i	−0.00749021	+	0.00272621i
$369$	1.63183	−	13.0563i	0.0849497	−	0.679685i
$370$	3.46107	+	1.25973i	0.179933	+	0.0654901i
$371$	0.830788	+	14.2641i	0.0431324	+	0.740554i
$372$	20.6859	+	6.94634i	1.07252	+	0.360151i
$373$	−1.18579	+	2.74898i	−0.0613980	+	0.142337i	−0.946153	−	0.323720i	$-0.895066\pi$
$373$	−1.18579	+	2.74898i	−0.0613980	+	0.142337i	0.884755	+	0.466057i	$0.154326\pi$
$374$	0.00743977	−	0.127736i	0.000384701	−	0.00660507i
$375$	5.55007	−	13.8095i	0.286605	−	0.713117i
$376$	9.22663	+	9.77966i	0.475827	+	0.504347i
$377$	1.34501	−	2.32963i	0.0692716	−	0.119982i
$378$	−5.04150	+	0.978188i	−0.259307	+	0.0503125i
$379$	11.0537	+	19.1456i	0.567792	+	0.983444i	0.996784	+	0.0801362i	$0.0255355\pi$
$379$	11.0537	+	19.1456i	0.567792	+	0.983444i	−0.428992	+	0.903308i	$0.641131\pi$
$380$	1.52540	−	5.09519i	0.0782513	−	0.261378i
$381$	−16.1968	+	8.64998i	−0.829789	+	0.443152i
$382$	11.2656	+	7.40952i	0.576400	+	0.379104i
$383$	−14.2605	+	1.66682i	−0.728680	+	0.0851705i	−0.472340	−	0.881416i	$-0.656591\pi$
$383$	−14.2605	+	1.66682i	−0.728680	+	0.0851705i	−0.256340	+	0.966587i	$0.582517\pi$
$384$	14.7595	+	11.7663i	0.753191	+	0.600448i
$385$	−7.53530	−	3.78437i	−0.384035	−	0.192869i
$386$	−1.25926	−	7.14162i	−0.0640947	−	0.363499i
$387$	3.59308	−	2.03639i	0.182647	−	0.103516i
$388$	1.87760	−	10.6484i	0.0953206	−	0.540590i
$389$	−10.8862	+	14.6227i	−0.551953	+	0.741401i	−0.987301	−	0.158861i	$-0.949218\pi$
$389$	−10.8862	+	14.6227i	−0.551953	+	0.741401i	0.435348	+	0.900262i	$0.356625\pi$
$390$	2.43002	+	5.26597i	0.123049	+	0.266653i
$391$	0.00221655	−	0.00234941i	0.000112096	−	0.000118815i
$392$	−3.34523	−	11.1739i	−0.168960	−	0.564365i
$393$	17.3996	+	17.5391i	0.877694	+	0.884729i
$394$	15.9291	+	1.86185i	0.802499	+	0.0937987i
$395$	−9.11293	−	7.64665i	−0.458521	−	0.384745i
$396$	−12.5064	−	25.4061i	−0.628472	−	1.27670i
$397$	1.06250	−	0.891545i	0.0533255	−	0.0447454i	−0.615735	−	0.787953i	$-0.711141\pi$
$397$	1.06250	−	0.891545i	0.0533255	−	0.0447454i	0.669061	+	0.743208i	$0.266697\pi$
$398$	−4.93817	+	3.24788i	−0.247528	+	0.162802i
$399$	9.24800	−	0.232145i	0.462979	−	0.0116218i
$400$	−3.59001	−	4.82222i	−0.179500	−	0.241111i
$401$	19.7370	−	9.91231i	0.985620	−	0.494997i	0.118424	−	0.992963i	$-0.462216\pi$
$401$	19.7370	−	9.91231i	0.985620	−	0.494997i	0.867197	+	0.497966i	$0.165920\pi$
$402$	0.997040	+	3.04962i	0.0497279	+	0.152101i
$403$	41.7069	−	9.88472i	2.07757	−	0.492393i
$404$	13.4026			0.666803
$405$	−6.41467	−	5.55948i	−0.318747	−	0.276253i
$406$	−0.506722			−0.0251482
$407$	−34.3726	+	8.14647i	−1.70379	+	0.403805i
$408$	−0.125500	−	0.0264366i	−0.00621320	−	0.00130880i
$409$	0.515967	−	0.259128i	0.0255129	−	0.0128131i	−0.435997	−	0.899948i	$-0.643604\pi$
$409$	0.515967	−	0.259128i	0.0255129	−	0.0128131i	0.461510	+	0.887135i	$0.347308\pi$
$410$	1.67149	+	2.24520i	0.0825490	+	0.110883i
$411$	4.82067	+	7.88578i	0.237786	+	0.388977i
$412$	−6.60681	+	4.34537i	−0.325494	+	0.214081i
$413$	6.32124	−	5.30415i	0.311048	−	0.261000i
$414$	−0.0505889	+	0.206104i	−0.00248631	+	0.0101295i
$415$	12.8784	+	10.8062i	0.632175	+	0.530458i
$416$	30.1375	+	3.52257i	1.47761	+	0.172708i
$417$	6.85692	−	1.80800i	0.335785	−	0.0885381i
$418$	−4.34333	−	14.5077i	−0.212439	−	0.709596i
$419$	8.66829	−	9.18785i	0.423474	−	0.448856i	−0.480148	−	0.877187i	$-0.659417\pi$
$419$	8.66829	−	9.18785i	0.423474	−	0.448856i	0.903622	+	0.428332i	$0.140899\pi$
$420$	−2.12268	+	3.00589i	−0.103576	+	0.146672i
$421$	12.7947	−	17.1863i	0.623577	−	0.837610i	−0.372319	−	0.928105i	$-0.621437\pi$
$421$	12.7947	−	17.1863i	0.623577	−	0.837610i	0.995897	+	0.0904947i	$0.0288448\pi$
$422$	−0.855151	+	4.84980i	−0.0416281	+	0.236085i
$423$	−16.5963	+	2.78994i	−0.806939	+	0.135652i
$424$	−4.07126	−	23.0892i	−0.197718	−	1.12131i
$425$	0.113484	+	0.0569936i	0.00550476	+	0.00276460i
$426$	2.37030	−	0.930723i	0.114842	−	0.0450937i
$427$	2.49212	−	0.291287i	0.120602	−	0.0140964i
$428$	12.8238	+	8.43434i	0.619862	+	0.407689i
$429$	−47.2246	−	29.3895i	−2.28003	−	1.41894i
$430$	−0.251979	+	0.841669i	−0.0121515	+	0.0405889i
$431$	−2.23566	−	3.87227i	−0.107688	−	0.186521i	0.807145	−	0.590353i	$-0.201011\pi$
$431$	−2.23566	−	3.87227i	−0.107688	−	0.186521i	−0.914833	+	0.403832i	$0.867678\pi$
$432$	−7.24215	+	2.30391i	−0.348438	+	0.110847i
$433$	−4.56671	+	7.90977i	−0.219462	+	0.380119i	−0.954644	−	0.297751i	$-0.903763\pi$
$433$	−4.56671	+	7.90977i	−0.219462	+	0.380119i	0.735182	+	0.677870i	$0.237097\pi$
$434$	−5.54072	−	5.87281i	−0.265963	−	0.281904i
$435$	−0.516862	−	0.659069i	−0.0247816	−	0.0315999i
$436$	−1.14212	+	19.6094i	−0.0546976	+	0.939122i
$437$	0.151417	−	0.351023i	0.00724324	−	0.0167917i
$438$	1.93624	+	9.56998i	0.0925172	+	0.457271i
$439$	−0.165633	−	2.84382i	−0.00790525	−	0.135728i	−0.999951	−	0.00985365i	$-0.996863\pi$
$439$	−0.165633	−	2.84382i	−0.00790525	−	0.135728i	0.992046	−	0.125874i	$-0.0401736\pi$
$440$	13.0019	+	4.73230i	0.619841	+	0.225604i
$441$	13.9523	+	4.29872i	0.664396	+	0.204701i
$442$	−0.103067	+	0.0375133i	−0.00490239	+	0.00178432i
$443$	−4.90013	−	11.3598i	−0.232812	−	0.539719i	0.761260	−	0.648447i	$-0.224581\pi$
$443$	−4.90013	−	11.3598i	−0.232812	−	0.539719i	−0.994071	+	0.108729i	$0.965322\pi$
$444$	1.28226	+	15.3624i	0.0608534	+	0.729066i
$445$	−12.8014	−	3.03399i	−0.606845	−	0.143825i
$446$	0.492795	+	0.116795i	0.0233345	+	0.00553038i
$447$	29.5764	+	13.9357i	1.39892	+	0.659137i
$448$	−0.571563	−	1.32503i	−0.0270038	−	0.0626019i
$449$	−16.1389	+	5.87407i	−0.761640	+	0.277214i	−0.693495	−	0.720461i	$-0.743930\pi$
$449$	−16.1389	+	5.87407i	−0.761640	+	0.277214i	−0.0681449	+	0.997675i	$0.521708\pi$
$450$	−8.33330	+	0.418631i	−0.392836	+	0.0197345i
$451$	−25.2264	−	9.18166i	−1.18786	−	0.432347i
$452$	0.515316	+	8.84763i	0.0242384	+	0.416157i
$453$	3.99986	−	3.53106i	0.187930	−	0.165904i
$454$	2.03842	−	4.72559i	0.0956678	−	0.221783i
$455$	−0.420279	+	7.21591i	−0.0197030	+	0.338287i
$456$	−15.0281	+	2.14005i	−0.703755	+	0.100217i
$457$	−0.607162	−	0.643554i	−0.0284018	−	0.0301042i	0.713017	−	0.701147i	$-0.247328\pi$
$457$	−0.607162	−	0.643554i	−0.0284018	−	0.0301042i	−0.741419	+	0.671043i	$0.765847\pi$
$458$	5.27840	−	9.14246i	0.246644	−	0.427199i
$459$	0.114867	−	0.112148i	0.00536151	−	0.00523461i
$460$	0.0760334	+	0.131694i	0.00354507	+	0.00614025i
$461$	4.36853	−	14.5919i	0.203463	−	0.679614i	−0.793967	−	0.607961i	$-0.791988\pi$
$461$	4.36853	−	14.5919i	0.203463	−	0.679614i	0.997430	−	0.0716523i	$-0.0228272\pi$
$462$	−0.346548	+	10.4720i	−0.0161229	+	0.487201i
$463$	−28.1033	−	18.4838i	−1.30607	−	0.859016i	−0.310277	−	0.950646i	$-0.600422\pi$
$463$	−28.1033	−	18.4838i	−1.30607	−	0.859016i	−0.995793	+	0.0916304i	$0.970792\pi$
$464$	−0.744800	+	0.0870547i	−0.0345765	+	0.00404141i
$465$	1.98690	−	13.1969i	0.0921404	−	0.611991i
$466$	−9.96354	−	5.00388i	−0.461552	−	0.231800i
$467$	1.91520	+	10.8616i	0.0886249	+	0.502617i	0.996515	+	0.0834093i	$0.0265809\pi$
$467$	1.91520	+	10.8616i	0.0886249	+	0.502617i	−0.907890	+	0.419207i	$0.862308\pi$
$468$	−15.7509	+	18.4697i	−0.728087	+	0.853763i
$469$	−0.694378	+	3.93802i	−0.0320634	+	0.181841i
$470$	2.13786	−	2.87165i	0.0986122	−	0.132459i
$471$	−5.91381	−	0.541188i	−0.272494	−	0.0249366i
$472$	−9.29190	+	9.84884i	−0.427694	+	0.453330i
$473$	−2.41668	−	8.07229i	−0.111119	−	0.371164i
$474$	−3.88280	+	14.2628i	−0.178343	+	0.655112i
$475$	14.9286	+	1.74490i	0.684969	+	0.0800614i
$476$	−0.0533110	−	0.0447333i	−0.00244351	−	0.00205035i
$477$	26.8527	+	11.8383i	1.22950	+	0.542037i
$478$	10.0282	−	8.41465i	0.458679	−	0.384877i
$479$	9.96137	−	6.55170i	0.455147	−	0.299355i	−0.301158	−	0.953574i	$-0.597373\pi$
$479$	9.96137	−	6.55170i	0.455147	−	0.299355i	0.756305	+	0.654220i	$0.227003\pi$
$480$	4.51696	−	8.29776i	0.206170	−	0.378739i
$481$	18.0823	+	24.2888i	0.824484	+	1.10747i
$482$	3.48584	−	1.75065i	0.158776	−	0.0797401i
$483$	−0.176623	+	0.196882i	−0.00803663	+	0.00895843i
$484$	−39.7109	+	9.41165i	−1.80504	+	0.427802i
$485$	−6.61294			−0.300278
$486$	−2.93276	+	10.1318i	−0.133033	+	0.459589i
$487$	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
$489$	−22.8027	+	25.4182i	−1.03118	+	1.14945i
$490$	−2.77540	+	1.39386i	−0.125380	+	0.0629680i
$491$	2.53169	+	3.40065i	0.114254	+	0.153469i	0.855571	−	0.517685i	$-0.173206\pi$
$491$	2.53169	+	3.40065i	0.114254	+	0.153469i	−0.741318	+	0.671154i	$0.765799\pi$
$492$	−5.60123	+	10.2896i	−0.252523	+	0.463891i
$493$	0.0132341	−	0.00870421i	0.000596034	−	0.000392018i
$494$	−9.94438	+	8.34432i	−0.447419	+	0.375429i
$495$	−13.9739	+	10.2308i	−0.628081	+	0.459841i
$496$	−9.15292	−	7.68021i	−0.410978	−	0.344852i
$497$	3.15227	+	0.368447i	0.141398	+	0.0165271i
$498$	5.48717	−	20.1562i	0.245886	−	0.903220i
$499$	−10.7276	−	35.8326i	−0.480232	−	1.60409i	−0.764014	−	0.645199i	$-0.776774\pi$
$499$	−10.7276	−	35.8326i	−0.480232	−	1.60409i	0.283782	−	0.958889i	$-0.408411\pi$
$500$	−9.09362	+	9.63868i	−0.406679	+	0.431055i
$501$	−33.3628	−	3.05312i	−1.49054	−	0.136403i
$502$	−7.63516	+	10.2558i	−0.340774	+	0.457738i
$503$	0.0594062	−	0.336909i	0.00264879	−	0.0150220i	−0.983455	−	0.181154i	$-0.942017\pi$
$503$	0.0594062	−	0.336909i	0.00264879	−	0.0150220i	0.986104	+	0.166132i	$0.0531278\pi$
$504$	10.3280	+	1.90625i	0.460047	+	0.0849113i
$505$	−1.42338	−	8.07239i	−0.0633396	−	0.359217i
$506$	0.386930	+	0.194324i	0.0172011	+	0.00863874i
$507$	−3.74637	+	24.8831i	−0.166382	+	1.10510i
$508$	16.2383	−	1.89798i	0.720457	−	0.0842094i
$509$	5.22506	+	3.43658i	0.231597	+	0.152324i	0.660004	−	0.751262i	$-0.270555\pi$
$509$	5.22506	+	3.43658i	0.231597	+	0.152324i	−0.428407	+	0.903586i	$0.640925\pi$
$510$	−0.00112952	+	0.0341318i	−5.00159e−5	+	0.00151138i
$511$	−3.49008	+	11.6577i	−0.154392	+	0.515705i
$512$	−7.73462	−	13.3968i	−0.341825	−	0.592059i
$513$	8.23551	−	17.1227i	0.363607	−	0.755986i
$514$	6.13058	−	10.6185i	0.270408	−	0.468361i
$515$	3.31888	+	3.51780i	0.146247	+	0.155013i
$516$	−3.64051	+	0.518421i	−0.160265	+	0.0228222i
$517$	−1.99644	+	34.2775i	−0.0878033	+	1.50752i
$518$	2.25923	−	5.23749i	0.0992650	−	0.230122i
$519$	8.00810	−	7.06952i	0.351516	−	0.310317i
$520$	−0.689631	−	11.8405i	−0.0302423	−	0.519241i
$521$	29.5418	+	10.7523i	1.29425	+	0.471068i	0.895119	−	0.445827i	$-0.147090\pi$
$521$	29.5418	+	10.7523i	1.29425	+	0.471068i	0.399129	+	0.916895i	$0.369313\pi$
$522$	−0.474496	+	0.926286i	−0.0207681	+	0.0405424i
$523$	−20.1279	+	7.32597i	−0.880134	+	0.320342i	−0.742264	−	0.670108i	$-0.766248\pi$
$523$	−20.1279	+	7.32597i	−0.880134	+	0.320342i	−0.137870	+	0.990450i	$0.544026\pi$
$524$	−8.71258	−	20.1980i	−0.380611	−	0.882355i
$525$	−9.40710	−	4.43241i	−0.410560	−	0.193446i
$526$	5.70776	+	1.35276i	0.248870	+	0.0589834i
$527$	0.245588	+	0.0582054i	0.0106980	+	0.00253547i
$528$	1.28972	+	15.4517i	0.0561277	+	0.672449i
$529$	−9.10551	−	21.1089i	−0.395892	−	0.917780i
$530$	−5.86635	+	2.13518i	−0.254818	+	0.0927461i
$531$	−3.77674	−	16.5220i	−0.163896	−	0.716996i
$532$	−7.73997	−	2.81712i	−0.335570	−	0.122138i
$533$	1.33803	+	22.9731i	0.0579564	+	0.995074i
$534$	3.24181	+	16.0228i	0.140287	+	0.693375i
$535$	3.71810	−	8.61953i	0.160748	−	0.372655i
$536$	0.381519	−	6.55043i	0.0164791	−	0.282935i
$537$	3.70010	+	4.71813i	0.159671	+	0.203602i
$538$	−5.19413	−	5.50545i	−0.223935	−	0.237357i
$539$	14.8933	−	25.7960i	0.641500	−	1.11111i
$540$	3.50708	+	6.69499i	0.150921	+	0.288106i
$541$	0.188033	+	0.325682i	0.00808416	+	0.0140022i	0.870039	−	0.492983i	$-0.164093\pi$
$541$	0.188033	+	0.325682i	0.00808416	+	0.0140022i	−0.861955	+	0.506985i	$0.830760\pi$
$542$	1.97441	−	6.59498i	0.0848081	−	0.283279i
$543$	−28.0583	−	17.4616i	−1.20410	−	0.749350i
$544$	0.149277	+	0.0981811i	0.00640020	+	0.00420948i
$545$	11.9321	−	1.39466i	0.511114	−	0.0597407i
$546$	8.36017	−	3.28270i	0.357782	−	0.140487i
$547$	−5.96696	−	2.99672i	−0.255129	−	0.128131i	0.316639	−	0.948546i	$-0.397446\pi$
$547$	−5.96696	−	2.99672i	−0.255129	−	0.128131i	−0.571767	+	0.820416i	$0.693742\pi$
$548$	−1.42899	−	8.10422i	−0.0610436	−	0.346195i
$549$	1.80116	−	4.82835i	0.0768716	−	0.206069i
$550$	−2.95609	+	16.7648i	−0.126048	+	0.714854i
$551$	1.11953	−	1.50379i	0.0476935	−	0.0640634i
$552$	0.250354	−	0.354522i	0.0106558	−	0.0150895i
$553$	−12.6426	+	13.4003i	−0.537616	+	0.569840i
$554$	0.252676	+	0.843998i	0.0107352	+	0.0358580i
$555$	9.11661	−	2.40382i	0.386978	−	0.102037i
$556$	−6.27115	−	0.732992i	−0.265956	−	0.0310858i
$557$	2.30382	+	1.93313i	0.0976160	+	0.0819095i	0.690290	−	0.723533i	$-0.257483\pi$
$557$	2.30382	+	1.93313i	0.0976160	+	0.0819095i	−0.592674	+	0.805443i	$0.701928\pi$
$558$	−15.9238	+	4.62908i	−0.674110	+	0.195965i
$559$	−5.53318	+	4.64289i	−0.234028	+	0.196373i
$560$	1.68344	−	1.10721i	0.0711383	−	0.0467884i
$561$	−0.170832	−	0.279451i	−0.00721253	−	0.0117984i
$562$	−2.58995	−	3.47891i	−0.109251	−	0.146749i
$563$	−29.3209	+	14.7255i	−1.23573	+	0.620607i	−0.942106	−	0.335315i	$-0.891157\pi$
$563$	−29.3209	+	14.7255i	−1.23573	+	0.620607i	−0.293623	+	0.955921i	$0.594861\pi$
$564$	14.6623	+	3.08861i	0.617396	+	0.130054i
$565$	5.27421	−	1.25001i	0.221888	−	0.0525884i
$566$	−12.9354			−0.543715
$567$	−9.17275	+	9.41668i	−0.385219	+	0.395463i
$568$	−5.20773			−0.218511
$569$	25.4422	−	6.02992i	1.06659	−	0.252787i	0.340402	−	0.940280i	$-0.389437\pi$
$569$	25.4422	−	6.02992i	1.06659	−	0.252787i	0.726191	+	0.687493i	$0.241289\pi$
$570$	1.25604	+	3.84180i	0.0526096	+	0.160915i
$571$	−0.715579	+	0.359377i	−0.0299461	+	0.0150395i	−0.463709	−	0.885987i	$-0.653482\pi$
$571$	−0.715579	+	0.359377i	−0.0299461	+	0.0150395i	0.433763	+	0.901027i	$0.357185\pi$
$572$	29.5741	+	39.7250i	1.23656	+	1.66098i
$573$	34.5051	−	0.866151i	1.44147	−	0.0361840i
$574$	3.62166	−	2.38200i	0.151165	−	0.0994230i
$575$	−0.329195	+	0.276227i	−0.0137284	+	0.0115195i
$576$	−2.95737	−	0.195950i	−0.123224	−	0.00816459i
$577$	−32.3968	−	27.1841i	−1.34869	−	1.13169i	−0.979300	−	0.202416i	$-0.935121\pi$
$577$	−32.3968	−	27.1841i	−1.34869	−	1.13169i	−0.369395	−	0.929273i	$-0.620435\pi$
$578$	11.4244	+	1.33532i	0.475194	+	0.0555422i
$579$	−13.0736	−	13.1783i	−0.543318	−	0.547674i
$580$	0.213881	+	0.714413i	0.00888093	+	0.0296644i
$581$	17.8665	−	18.9373i	0.741225	−	0.785653i
$582$	3.44295	+	7.46105i	0.142715	+	0.309270i
$583$	35.7542	−	48.0262i	1.48079	−	1.98904i
$584$	3.46737	−	19.6644i	0.143481	−	0.813721i
$585$	12.7971	+	7.52528i	0.529096	+	0.311132i
$586$	−0.214557	−	1.21681i	−0.00886326	−	0.0502661i
$587$	11.9254	+	5.98914i	0.492212	+	0.247198i	0.677550	−	0.735476i	$-0.263042\pi$
$587$	11.9254	+	5.98914i	0.492212	+	0.247198i	−0.185338	+	0.982675i	$0.559338\pi$
$588$	−10.1643	−	8.10303i	−0.419168	−	0.334163i
$589$	29.6700	−	3.46793i	1.22253	−	0.142893i
$590$	3.01225	+	1.98119i	0.124012	+	0.0815643i
$591$	36.2122	−	19.3393i	1.48957	−	0.795512i
$592$	2.42091	−	8.08642i	0.0994990	−	0.332350i
$593$	−17.2045	−	29.7990i	−0.706503	−	1.22370i	−0.966147	−	0.257994i	$-0.916939\pi$
$593$	−17.2045	−	29.7990i	−0.706503	−	1.22370i	0.259644	−	0.965704i	$-0.416395\pi$
$594$	18.8183	+	10.4395i	0.772123	+	0.428339i
$595$	−0.0212812	+	0.0368601i	−0.000872443	+	0.00151112i
$596$	−19.9769	−	21.1743i	−0.818287	−	0.867334i
$597$	−5.64206	+	14.0383i	−0.230914	+	0.574550i
$598$	0.0215809	−	0.370530i	0.000882508	−	0.0151521i
$599$	−15.8671	+	36.7842i	−0.648314	+	1.50296i	0.203478	+	0.979080i	$0.434776\pi$
$599$	−15.8671	+	36.7842i	−0.648314	+	1.50296i	−0.851792	+	0.523881i	$0.824484\pi$
$600$	16.1760	+	5.43190i	0.660382	+	0.221756i
$601$	2.51105	+	43.1130i	0.102428	+	1.75862i	0.523905	+	0.851777i	$0.324475\pi$
$601$	2.51105	+	43.1130i	0.102428	+	1.75862i	−0.421477	+	0.906839i	$0.638488\pi$
$602$	1.27856	+	0.465357i	0.0521101	+	0.0189665i
$603$	6.54847	+	4.95690i	0.266674	+	0.201861i
$604$	−4.46403	+	1.62477i	−0.181639	+	0.0661111i
$605$	9.88602	+	22.9184i	0.401924	+	0.931764i
$606$	−8.36661	+	5.80873i	−0.339870	+	0.235963i
$607$	17.1451	+	4.06345i	0.695896	+	0.164930i	0.563316	−	0.826242i	$-0.309526\pi$
$607$	17.1451	+	4.06345i	0.695896	+	0.164930i	0.132581	+	0.991172i	$0.457674\pi$
$608$	20.5767	+	4.87677i	0.834496	+	0.197779i
$609$	−1.06548	+	0.739738i	−0.0431756	+	0.0299757i
$610$	0.434211	+	1.00661i	0.0175807	+	0.0407566i
$611$	27.6577	−	10.0666i	1.11891	−	0.407250i
$612$	−0.131693	+	0.0555640i	−0.00532337	+	0.00224604i
$613$	25.9691	+	9.45198i	1.04888	+	0.381762i	0.808241	−	0.588852i	$-0.200420\pi$
$613$	25.9691	+	9.45198i	1.04888	+	0.381762i	0.240641	+	0.970614i	$0.422642\pi$
$614$	0.589545	+	10.1221i	0.0237921	+	0.408495i
$615$	6.79230	+	2.28085i	0.273892	+	0.0919729i
$616$	8.48706	−	19.6752i	0.341954	−	0.792737i
$617$	−0.256394	+	4.40211i	−0.0103220	+	0.177222i	0.989207	+	0.146526i	$0.0468094\pi$
$617$	−0.256394	+	4.40211i	−0.0103220	+	0.177222i	−0.999529	+	0.0306958i	$0.990228\pi$
$618$	2.24103	−	5.57603i	0.0901473	−	0.224301i
$619$	17.1670	+	18.1960i	0.690001	+	0.731358i	0.973770	−	0.227535i	$-0.0730665\pi$
$619$	17.1670	+	18.1960i	0.690001	+	0.731358i	−0.283769	+	0.958893i	$0.591585\pi$
$620$	−5.94125	+	10.2905i	−0.238606	+	0.413278i
$621$	0.194508	+	0.507228i	0.00780536	+	0.0203544i
$622$	−6.98959	−	12.1063i	−0.280257	−	0.485420i
$623$	−5.84337	+	19.5182i	−0.234110	+	0.781980i
$624$	11.7241	−	6.26132i	0.469342	−	0.250654i
$625$	−10.3999	−	6.84011i	−0.415996	−	0.273605i
$626$	−15.0028	+	1.75357i	−0.599631	+	0.0700868i
$627$	−30.3119	−	24.1648i	−1.21054	−	0.965048i
$628$	4.72505	+	2.37301i	0.188550	+	0.0946934i
$629$	0.0309624	+	0.175596i	0.00123455	+	0.00700148i
$630$	0.0223268	−	2.79642i	0.000889519	−	0.111412i
$631$	2.45133	−	13.9022i	0.0975857	−	0.553436i	−0.896339	−	0.443370i	$-0.853783\pi$
$631$	2.45133	−	13.9022i	0.0975857	−	0.553436i	0.993924	−	0.110066i	$-0.0351062\pi$
$632$	18.0521	−	24.2481i	0.718072	−	0.964538i
$633$	5.28187	+	11.4461i	0.209935	+	0.454941i
$634$	−5.27494	+	5.59111i	−0.209495	+	0.222051i
$635$	−2.86770	−	9.57877i	−0.113801	−	0.380122i
$636$	−18.4021	−	18.5496i	−0.729692	−	0.735541i
$637$	−25.3606	−	2.96423i	−1.00482	−	0.117447i
$638$	1.62660	+	1.36488i	0.0643978	+	0.0540362i
$639$	3.62532	−	5.41732i	0.143415	−	0.214306i
$640$	−7.87383	+	6.60693i	−0.311241	+	0.261162i
$641$	−28.5813	+	18.7982i	−1.12889	+	0.742484i	−0.969587	−	0.244746i	$-0.921296\pi$
$641$	−28.5813	+	18.7982i	−1.12889	+	0.742484i	−0.159304	+	0.987230i	$0.550925\pi$
$642$	−11.6608	+	0.292711i	−0.460214	+	0.0115524i
$643$	−8.05359	−	10.8178i	−0.317603	−	0.426614i	0.614440	−	0.788964i	$-0.289382\pi$
$643$	−8.05359	−	10.8178i	−0.317603	−	0.426614i	−0.932042	+	0.362349i	$0.881975\pi$
$644$	0.210449	−	0.105692i	0.00829286	−	0.00416483i
$645$	0.698875	+	2.13763i	0.0275182	+	0.0841690i
$646$	−0.0743798	+	0.0176283i	−0.00292644	+	0.000693578i
$647$	3.19249			0.125510			0.0627548	−	0.998029i	$-0.480011\pi$
$647$	3.19249			0.125510			0.0627548	+	0.998029i	$0.480011\pi$
$648$	13.1559	−	17.0946i	0.516811	−	0.671539i
$649$	−34.5785			−1.35733
$650$	14.1992	−	3.36528i	0.556940	−	0.131997i
$651$	−20.2239	−	4.26014i	−0.792637	−	0.166968i
$652$	27.1698	−	13.6452i	1.06405	−	0.534387i
$653$	−19.2091	−	25.8023i	−0.751710	−	1.00972i	−0.999166	−	0.0408223i	$-0.987002\pi$
$653$	−19.2091	−	25.8023i	−0.751710	−	1.00972i	0.247457	−	0.968899i	$-0.420405\pi$
$654$	−7.78583	−	12.7363i	−0.304450	−	0.498027i
$655$	−11.2400	+	7.39267i	−0.439183	+	0.288855i
$656$	4.91404	−	4.12337i	0.191861	−	0.160991i
$657$	18.0421	+	17.2962i	0.703889	+	0.674787i
$658$	−4.24715	−	3.56378i	−0.165571	−	0.138931i
$659$	−14.4955	−	1.69428i	−0.564666	−	0.0659999i	−0.171029	−	0.985266i	$-0.554709\pi$
$659$	−14.4955	−	1.69428i	−0.564666	−	0.0659999i	−0.393637	+	0.919266i	$0.628783\pi$
$660$	14.9104	−	3.93152i	0.580388	−	0.153034i
$661$	2.23469	+	7.46440i	0.0869195	+	0.290331i	0.990387	−	0.138326i	$-0.0441721\pi$
$661$	2.23469	+	7.46440i	0.0869195	+	0.290331i	−0.903467	+	0.428657i	$0.858987\pi$
$662$	−6.68982	+	7.09079i	−0.260007	+	0.275592i
$663$	−0.161955	+	0.229342i	−0.00628981	+	0.00890689i
$664$	−25.5112	+	34.2674i	−0.990025	+	1.32983i
$665$	−0.874754	+	4.96098i	−0.0339215	+	0.192378i
$666$	−7.45857	−	9.03429i	−0.289014	−	0.350072i
$667$	0.00930786	+	0.0527875i	0.000360402	+	0.00204394i
$668$	26.6564	+	13.3873i	1.03137	+	0.517972i
$669$	1.20670	−	0.473824i	0.0466538	−	0.0183191i
$670$	−1.73533	+	0.202831i	−0.0670417	+	0.00783605i
$671$	−8.78443	−	5.77761i	−0.339119	−	0.223042i
$672$	−12.4219	−	7.73054i	−0.479184	−	0.298212i
$673$	−2.29949	+	7.68083i	−0.0886388	+	0.296074i	−0.990802	−	0.135321i	$-0.956793\pi$
$673$	−2.29949	+	7.68083i	−0.0886388	+	0.296074i	0.902163	+	0.431395i	$0.141979\pi$
$674$	3.35193	+	5.80572i	0.129112	+	0.223628i
$675$	−16.9113	+	13.0456i	−0.650916	+	0.502127i
$676$	11.2024	−	19.4031i	0.430862	−	0.746274i
$677$	−5.84612	−	6.19652i	−0.224685	−	0.238152i	0.605218	−	0.796059i	$-0.293086\pi$
$677$	−5.84612	−	6.19652i	−0.224685	−	0.238152i	−0.829903	+	0.557908i	$0.811604\pi$
$678$	−4.15628	−	5.29982i	−0.159621	−	0.203539i
$679$	−0.595470	+	10.2238i	−0.0228520	+	0.392354i
$680$	0.0276622	−	0.0641283i	0.00106080	−	0.00245921i
$681$	−2.61247	−	12.9123i	−0.100110	−	0.494800i
$682$	1.96724	+	33.7763i	0.0753296	+	1.29336i
$683$	−13.5460	−	4.93034i	−0.518323	−	0.188654i	0.0695940	−	0.997575i	$-0.477830\pi$
$683$	−13.5460	−	4.93034i	−0.518323	−	0.188654i	−0.587917	+	0.808921i	$0.700052\pi$
$684$	−12.3974	+	11.5107i	−0.474027	+	0.440122i
$685$	−4.72942	+	1.72137i	−0.180702	+	0.0657701i
$686$	4.64524	+	10.7689i	0.177356	+	0.411157i
$687$	−2.24774	−	26.9295i	−0.0857567	−	1.02743i
$688$	1.95922	+	0.464345i	0.0746947	+	0.0177030i
$689$	−49.9408	−	11.8362i	−1.90259	−	0.450922i
$690$	−0.104541	−	0.0492571i	−0.00397979	−	0.00187519i
$691$	14.4448	+	33.4868i	0.549506	+	1.27390i	0.936128	+	0.351659i	$0.114382\pi$
$691$	14.4448	+	33.4868i	0.549506	+	1.27390i	−0.386622	+	0.922238i	$0.626358\pi$
$692$	−8.93742	+	3.25296i	−0.339750	+	0.123659i
$693$	14.5589	+	22.5254i	0.553046	+	0.855668i
$694$	2.14799	+	0.781805i	0.0815366	+	0.0296769i
$695$	0.224526	+	3.85496i	0.00851676	+	0.146227i
$696$	1.59560	−	1.40859i	0.0604811	−	0.0533925i
$697$	−0.0536705	+	0.124422i	−0.00203292	+	0.00471283i
$698$	0.0523236	−	0.898362i	0.00198048	−	0.0340035i
$699$	−28.2552	+	4.02364i	−1.06871	+	0.152188i
$700$	6.35388	+	6.73472i	0.240154	+	0.254548i
$701$	−4.76010	+	8.24474i	−0.179787	+	0.311399i	−0.941807	−	0.336153i	$-0.890874\pi$
$701$	−4.76010	+	8.24474i	−0.179787	+	0.311399i	0.762021	+	0.647553i	$0.224207\pi$
$702$	1.82773	−	18.3563i	0.0689831	−	0.692814i
$703$	10.5517	+	18.2761i	0.397966	+	0.689298i
$704$	−1.73430	+	5.79296i	−0.0653638	+	0.218330i
$705$	0.303103	−	9.15917i	0.0114155	−	0.344954i
$706$	−6.66718	−	4.38507i	−0.250923	−	0.165034i
$707$	−12.6083	+	1.47370i	−0.474186	+	0.0554244i
$708$	−2.24662	+	14.9219i	−0.0844333	+	0.560801i
$709$	10.6876	+	5.36752i	0.401382	+	0.201581i	0.638026	−	0.770015i	$-0.279751\pi$
$709$	10.6876	+	5.36752i	0.401382	+	0.201581i	−0.236644	+	0.971596i	$0.576048\pi$
$710$	0.240792	+	1.36560i	0.00903677	+	0.0512501i
$711$	12.6572	+	35.6587i	0.474683	+	1.33731i
$712$	5.80535	−	32.9238i	0.217565	−	1.23387i
$713$	−0.510022	+	0.685078i	−0.0191005	+	0.0256564i
$714$	0.0526672	+	0.00481971i	0.00197102	+	0.000180373i
$715$	20.7856	−	22.0314i	0.777336	−	0.823928i
$716$	−1.53113	−	5.11432i	−0.0572209	−	0.191131i
$717$	8.80213	−	32.3332i	0.328722	−	1.20750i
$718$	19.9679	+	2.33391i	0.745195	+	0.0871008i
$719$	−16.3766	−	13.7416i	−0.610743	−	0.512474i	0.284135	−	0.958784i	$-0.408294\pi$
$719$	−16.3766	−	13.7416i	−0.610743	−	0.512474i	−0.894879	+	0.446310i	$0.852738\pi$
$720$	−0.447607	−	4.11412i	−0.0166813	−	0.153324i
$721$	5.73749	−	4.81433i	0.213675	−	0.179295i
$722$	3.18234	−	2.09306i	0.118435	−	0.0778956i
$723$	4.77398	−	8.76991i	0.177546	−	0.326156i
$724$	17.5714	+	23.6024i	0.653034	+	0.877177i
$725$	−1.88327	+	0.945813i	−0.0699429	+	0.0351266i
$726$	20.7106	−	23.0861i	0.768643	−	0.856805i
$727$	−7.66871	+	1.81752i	−0.284417	+	0.0674080i	−0.370348	−	0.928893i	$-0.620762\pi$
$727$	−7.66871	+	1.81752i	−0.284417	+	0.0674080i	0.0859313	+	0.996301i	$0.472613\pi$
$728$	−18.3679			−0.680760
$729$	8.62426	+	25.5856i	0.319417	+	0.947614i
$730$	−5.31685			−0.196785
$731$	−0.0413859	+	0.00980864i	−0.00153071	+	0.000362786i
$732$	−3.06400	+	3.41543i	−0.113249	+	0.126238i
$733$	31.1192	−	15.6287i	1.14942	−	0.577258i	0.231030	−	0.972947i	$-0.425790\pi$
$733$	31.1192	−	15.6287i	1.14942	−	0.577258i	0.918385	+	0.395689i	$0.129494\pi$
$734$	−3.24340	−	4.35664i	−0.119716	−	0.160806i
$735$	−3.80100	+	6.98253i	−0.140202	+	0.257554i
$736$	−0.505147	+	0.332241i	−0.0186200	+	0.0122466i
$737$	12.8363	−	10.7709i	0.472829	−	0.396751i
$738$	−0.962958	−	8.85091i	−0.0354470	−	0.325807i
$739$	33.5899	+	28.1853i	1.23563	+	1.03681i	0.997853	+	0.0654916i	$0.0208615\pi$
$739$	33.5899	+	28.1853i	1.23563	+	1.03681i	0.237772	+	0.971321i	$0.423583\pi$
$740$	−8.33779	−	0.974548i	−0.306503	−	0.0358251i
$741$	−8.72856	+	32.0629i	−0.320652	+	1.17786i
$742$	2.77281	+	9.26183i	0.101793	+	0.340012i
$743$	−14.6529	+	15.5312i	−0.537563	+	0.569784i	−0.938042	−	0.346522i	$-0.887362\pi$
$743$	−14.6529	+	15.5312i	−0.537563	+	0.569784i	0.400478	+	0.916306i	$0.368844\pi$
$744$	33.7723	+	3.09059i	1.23815	+	0.113307i
$745$	−10.6317	+	14.2809i	−0.389516	+	0.523211i
$746$	−0.351765	+	1.99496i	−0.0128790	+	0.0730407i
$747$	−17.8872	−	50.3929i	−0.654458	−	1.84378i
$748$	0.0506397	+	0.287192i	0.00185157	+	0.0105008i
$749$	−12.9913	−	6.52446i	−0.474691	−	0.238399i
$750$	1.49929	−	9.95819i	0.0547463	−	0.363622i
$751$	−4.49756	+	0.525689i	−0.164118	+	0.0191827i	−0.197755	−	0.980251i	$-0.563365\pi$
$751$	−4.49756	+	0.525689i	−0.164118	+	0.0191827i	0.0336369	+	0.999434i	$0.489291\pi$
$752$	−6.85489	−	4.50853i	−0.249972	−	0.164409i
$753$	−1.08250	+	32.7110i	−0.0394485	+	1.19206i
$754$	0.522031	−	1.74371i	0.0190113	−	0.0635020i
$755$	1.45269	+	2.51614i	0.0528689	+	0.0915716i
$756$	10.6665	−	4.81919i	0.387936	−	0.175272i
$757$	−15.3969	+	26.6682i	−0.559610	+	0.969273i	0.437919	+	0.899014i	$0.355716\pi$
$757$	−15.3969	+	26.6682i	−0.559610	+	0.969273i	−0.997529	+	0.0702583i	$0.977618\pi$
$758$	10.2653	+	10.8806i	0.372853	+	0.395201i
$759$	1.09728	−	0.156256i	0.0398288	−	0.00567175i
$760$	0.480625	−	8.25200i	0.0174341	−	0.299332i
$761$	−1.41749	+	3.28612i	−0.0513841	+	0.119122i	−0.941974	−	0.335685i	$-0.891032\pi$
$761$	−1.41749	+	3.28612i	−0.0513841	+	0.119122i	0.890590	+	0.454806i	$0.150292\pi$
$762$	−9.31421	+	8.22255i	−0.337418	+	0.297872i
$763$	−1.08175	−	18.5730i	−0.0391621	−	0.672387i
$764$	−28.8785	−	10.5109i	−1.04479	−	0.380271i
$765$	0.0474523	+	0.0734179i	0.00171564	+	0.00265443i
$766$	−9.12904	+	3.32270i	−0.329846	+	0.120054i
$767$	11.7402	+	27.2168i	0.423913	+	0.982740i
$768$	14.6496	+	6.90255i	0.528622	+	0.249074i
$769$	−14.2113	−	3.36814i	−0.512473	−	0.121458i	−0.0337603	−	0.999430i	$-0.510748\pi$
$769$	−14.2113	−	3.36814i	−0.512473	−	0.121458i	−0.478713	+	0.877972i	$0.658896\pi$
$770$	−5.55177	−	1.31579i	−0.200072	−	0.0474179i
$771$	−2.61063	−	31.2772i	−0.0940196	−	1.12642i
$772$	6.54637	+	15.1762i	0.235609	+	0.546203i
$773$	−18.7983	+	6.84203i	−0.676129	+	0.246091i	−0.657184	−	0.753730i	$-0.728253\pi$
$773$	−18.7983	+	6.84203i	−0.676129	+	0.246091i	−0.0189442	+	0.999821i	$0.506030\pi$
$774$	2.04792	−	1.90144i	0.0736109	−	0.0683458i
$775$	−31.5543	−	11.4848i	−1.13346	−	0.412547i
$776$	−0.977099	−	16.7761i	−0.0350758	−	0.602229i
$777$	−2.89547	−	14.3110i	−0.103874	−	0.513405i
$778$	−4.88570	+	11.3263i	−0.175161	+	0.406068i
$779$	−0.932512	+	16.0106i	−0.0334107	+	0.573640i
$780$	−8.15692	−	10.4012i	−0.292064	−	0.372422i
$781$	−9.12651	−	9.67353i	−0.326572	−	0.346146i
$782$	0.00109277	−	0.00189273i	3.90772e−5	−	6.76838e-5i
$783$	0.354517	+	2.64040i	0.0126694	+	0.0943600i
$784$	3.55882	+	6.16407i	0.127101	+	0.220145i
$785$	0.927457	−	3.09792i	0.0331024	−	0.110570i
$786$	14.1928	+	8.83263i	0.506239	+	0.315049i
$787$	11.3167	+	7.44313i	0.403398	+	0.265319i	0.734955	−	0.678116i	$-0.237203\pi$
$787$	11.3167	+	7.44313i	0.403398	+	0.265319i	−0.331557	+	0.943435i	$0.607574\pi$
$788$	−36.3049	+	4.24344i	−1.29331	+	0.151166i
$789$	13.9765	−	5.48803i	0.497578	−	0.195379i
$790$	−7.19316	−	3.61254i	−0.255921	−	0.128528i
$791$	−1.45763	−	8.26666i	−0.0518275	−	0.293929i
$792$	−28.0189	−	33.9383i	−0.995610	−	1.20595i
$793$	−1.56505	+	8.87585i	−0.0555766	+	0.315191i
$794$	0.560431	−	0.752790i	0.0198890	−	0.0267155i
$795$	−9.21813	+	13.0536i	−0.326933	+	0.462965i
$796$	9.24434	−	9.79842i	0.327657	−	0.347296i
$797$	8.60409	+	28.7397i	0.304772	+	1.01801i	0.963963	+	0.266035i	$0.0857137\pi$
$797$	8.60409	+	28.7397i	0.304772	+	1.01801i	−0.659191	+	0.751976i	$0.729101\pi$
$798$	6.05265	−	1.59593i	0.214262	−	0.0564955i
$799$	0.172140	+	0.0201203i	0.00608988	+	0.000711805i
$800$	−18.2098	−	15.2799i	−0.643814	−	0.540225i
$801$	30.2075	+	28.9586i	1.06733	+	1.02320i
$802$	11.4481	−	9.60610i	0.404247	−	0.339203i
$803$	42.6039	−	28.0210i	1.50346	−	0.988841i
$804$	−3.81405	−	6.23913i	−0.134511	−	0.220037i
$805$	−0.0860083	−	0.115529i	−0.00303139	−	0.00407187i
$806$	25.9174	−	13.0162i	0.912900	−	0.458476i
$807$	−18.9588	−	3.99366i	−0.667382	−	0.140583i
$808$	20.2683	−	4.80367i	0.713035	−	0.168992i
$809$	48.8577			1.71774			0.858872	−	0.512190i	$-0.171166\pi$
$809$	48.8577			1.71774			0.858872	+	0.512190i	$0.171166\pi$
$810$	−5.09094	−	2.65939i	−0.178877	−	0.0934415i
$811$	−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
$813$	−5.47611	−	16.7496i	−0.192055	−	0.587434i
$814$	−21.3597	+	10.7273i	−0.748658	+	0.375990i
$815$	−11.1040	−	14.9153i	−0.388956	−	0.522459i
$816$	0.0782404	−	0.00196400i	0.00273896	−	6.87538e-5i
$817$	−4.20581	+	2.76621i	−0.147143	+	0.0967773i
$818$	0.299277	−	0.251123i	0.0104640	−	0.00878032i
$819$	12.7867	−	19.1071i	0.446802	−	0.667657i
$820$	−4.88698	−	4.10067i	−0.170661	−	0.143201i
$821$	−32.0276	−	3.74348i	−1.11777	−	0.130648i	−0.462914	−	0.886403i	$-0.653196\pi$
$821$	−32.0276	−	3.74348i	−1.11777	−	0.130648i	−0.654855	+	0.755755i	$0.727270\pi$
$822$	4.40445	+	4.43976i	0.153623	+	0.154854i
$823$	9.48786	+	31.6917i	0.330726	+	1.10470i	0.948084	+	0.318020i	$0.103018\pi$
$823$	9.48786	+	31.6917i	0.330726	+	1.10470i	−0.617358	+	0.786682i	$0.711797\pi$
$824$	−8.43382	+	8.93932i	−0.293806	+	0.311416i
$825$	18.2584	+	39.5668i	0.635675	+	1.37754i
$826$	3.33422	−	4.47864i	0.116012	−	0.155832i
$827$	6.93056	−	39.3051i	0.240999	−	1.36677i	−0.588605	−	0.808421i	$-0.700323\pi$
$827$	6.93056	−	39.3051i	0.240999	−	1.36677i	0.829604	−	0.558352i	$-0.188566\pi$
$828$	0.00386166	−	0.483671i	0.000134202	−	0.0168087i
$829$	−3.03189	−	17.1947i	−0.105302	−	0.597198i	−0.991099	−	0.133125i	$-0.957499\pi$
$829$	−3.03189	−	17.1947i	−0.105302	−	0.597198i	0.885797	−	0.464073i	$-0.153612\pi$
$830$	10.1654	+	5.10524i	0.352845	+	0.177205i
$831$	1.76341	+	1.40580i	0.0611722	+	0.0487668i
$832$	5.14847	−	0.601769i	0.178491	−	0.0208626i
$833$	−0.125616	−	0.0826190i	−0.00435234	−	0.00286258i
$834$	4.23247	−	2.26036i	0.146558	−	0.0782700i
$835$	5.23225	−	17.4769i	0.181070	−	0.604815i
$836$	17.2576	+	29.8911i	0.596868	+	1.03381i
$837$	−26.7253	+	32.9800i	−0.923761	+	1.13996i
$838$	4.27349	−	7.40191i	0.147625	−	0.255695i
$839$	27.0966	+	28.7207i	0.935478	+	0.991549i	0.999980	−	0.00636894i	$-0.00202731\pi$
$839$	27.0966	+	28.7207i	0.935478	+	0.991549i	−0.0645018	+	0.997918i	$0.520546\pi$
$840$	−2.13271	+	5.30651i	−0.0735853	+	0.183092i
$841$	1.67092	−	28.6885i	0.0576178	−	0.989259i
$842$	5.74224	−	13.3120i	0.197891	−	0.458762i
$843$	−10.5246	−	3.53416i	−0.362486	−	0.121723i
$844$	−0.652614	−	11.2050i	−0.0224639	−	0.385690i
$845$	−12.8763	−	4.68657i	−0.442957	−	0.161223i
$846$	−10.4916	+	4.42664i	−0.360710	+	0.152191i
$847$	36.3227	−	13.2204i	1.24806	−	0.454258i
$848$	5.66677	+	13.1370i	0.194598	+	0.451128i
$849$	−27.1992	+	18.8837i	−0.933475	+	0.648089i
$850$	0.0836111	+	0.0198162i	0.00286784	+	0.000679690i
$851$	−0.587113	−	0.139148i	−0.0201260	−	0.00476994i
$852$	−4.76746	+	3.30993i	−0.163330	+	0.113396i
$853$	−12.4048	−	28.7576i	−0.424733	−	0.984643i	−0.987441	−	0.157987i	$-0.949500\pi$
$853$	−12.4048	−	28.7576i	−0.424733	−	0.984643i	0.562708	−	0.826656i	$-0.309760\pi$
$854$	1.59536	−	0.580662i	0.0545920	−	0.0198699i
$855$	8.24953	+	6.24453i	0.282128	+	0.213558i
$856$	22.4160	+	8.15875i	0.766162	+	0.278860i
$857$	−2.05526	−	35.2874i	−0.0702062	−	1.20539i	−0.830952	−	0.556344i	$-0.812204\pi$
$857$	−2.05526	−	35.2874i	−0.0702062	−	1.20539i	0.760746	−	0.649050i	$-0.224833\pi$
$858$	−35.6787	−	11.9809i	−1.21805	−	0.409022i
$859$	11.1903	−	25.9420i	0.381808	−	0.885131i	−0.613619	−	0.789603i	$-0.710287\pi$
$859$	11.1903	−	25.9420i	0.381808	−	0.885131i	0.995427	−	0.0955282i	$-0.0304540\pi$
$860$	0.116430	−	1.99902i	0.00397022	−	0.0681661i
$861$	4.13789	−	10.2957i	0.141019	−	0.350878i
$862$	−2.07620	−	2.20064i	−0.0707156	−	0.0749542i
$863$	−1.91089	+	3.30976i	−0.0650475	+	0.112666i	−0.896715	−	0.442608i	$-0.854053\pi$
$863$	−1.91089	+	3.30976i	−0.0650475	+	0.112666i	0.831668	+	0.555274i	$0.187387\pi$
$864$	−25.7633	+	15.4682i	−0.876485	+	0.526240i
$865$	2.90843	+	5.03755i	0.0988896	+	0.171282i
$866$	−1.77245	+	5.92039i	−0.0602303	+	0.201183i
$867$	25.9715	−	13.8702i	0.882039	−	0.471056i
$868$	15.3745	+	10.1120i	0.521845	+	0.343223i
$869$	76.6778	−	8.96235i	2.60112	−	0.304027i
$870$	−0.443145	−	0.353278i	−0.0150240	−	0.0119772i
$871$	−12.8360	−	6.44646i	−0.434930	−	0.218430i
$872$	5.30110	+	30.0640i	0.179518	+	1.01810i
$873$	18.1315	+	10.6621i	0.613659	+	0.360859i
$874$	0.0449177	−	0.254741i	0.00151936	−	0.00861674i
$875$	7.49490	−	10.0674i	0.253374	−	0.340340i
$876$	−9.32409	−	20.2058i	−0.315032	−	0.682690i
$877$	23.5311	−	24.9415i	0.794588	−	0.842214i	−0.195784	−	0.980647i	$-0.562725\pi$
$877$	23.5311	−	24.9415i	0.794588	−	0.842214i	0.990372	+	0.138433i	$0.0442065\pi$
$878$	−0.552812	−	1.84652i	−0.0186565	−	0.0623171i
$879$	−2.22751	−	2.24537i	−0.0751322	−	0.0757344i
$880$	−8.38627	−	0.980214i	−0.282701	−	0.0330430i
$881$	39.1151	+	32.8215i	1.31782	+	1.10578i	0.986762	+	0.162173i	$0.0518502\pi$
$881$	39.1151	+	32.8215i	1.31782	+	1.10578i	0.331059	+	0.943610i	$0.392594\pi$
$882$	9.85698	+	0.653106i	0.331902	+	0.0219912i
$883$	−30.6669	+	25.7326i	−1.03202	+	0.865972i	−0.991091	−	0.133190i	$-0.957478\pi$
$883$	−30.6669	+	25.7326i	−1.03202	+	0.865972i	−0.0409344	+	0.999162i	$0.513033\pi$
$884$	0.208856	−	0.137367i	0.00702458	−	0.00462014i
$885$	9.22610	−	0.231595i	0.310132	−	0.00778498i
$886$	−4.99886	−	6.71463i	−0.167940	−	0.225583i
$887$	20.4630	−	10.2769i	0.687079	−	0.345064i	−0.0707713	−	0.997493i	$-0.522546\pi$
$887$	20.4630	−	10.2769i	0.687079	−	0.345064i	0.757850	+	0.652429i	$0.226250\pi$
$888$	7.44521	+	22.7724i	0.249845	+	0.764193i
$889$	−15.0673	+	3.57102i	−0.505341	+	0.119768i
$890$	−8.90188			−0.298392
$891$	54.8093	−	5.52073i	1.83618	−	0.184951i
$892$	−1.15427			−0.0386477
$893$	19.9596	−	4.73051i	0.667923	−	0.158301i
$894$	21.6477	+	4.56007i	0.724007	+	0.152511i
$895$	−2.91775	+	1.46535i	−0.0975297	+	0.0489813i
$896$	9.50552	+	12.7681i	0.317557	+	0.426553i
$897$	−0.495540	−	0.810617i	−0.0165456	−	0.0270657i
$898$	−9.70921	+	6.38585i	−0.324001	+	0.213099i
$899$	−3.20854	+	2.69228i	−0.107011	+	0.0897927i
$900$	18.2609	−	5.30846i	0.608695	−	0.176949i
$901$	−0.231513	−	0.194262i	−0.00771281	−	0.00647182i
$902$	−18.0418	−	2.10878i	−0.600726	−	0.0702148i
$903$	3.36777	−	0.887998i	0.112072	−	0.0295507i
$904$	3.95041	+	13.1953i	0.131389	+	0.438868i
$905$	12.3497	−	13.0899i	0.410517	−	0.435122i
$906$	2.08250	−	2.94900i	0.0691866	−	0.0979739i
$907$	−14.2978	+	19.2053i	−0.474752	+	0.637702i	−0.973403	−	0.229100i	$-0.926422\pi$
$907$	−14.2978	+	19.2053i	−0.474752	+	0.637702i	0.498651	+	0.866803i	$0.333829\pi$
$908$	−2.03683	+	11.5514i	−0.0675944	+	0.383347i
$909$	−9.11259	+	24.4280i	−0.302245	+	0.810226i
$910$	0.849285	+	4.81654i	0.0281535	+	0.159667i
$911$	−27.5089	−	13.8155i	−0.911411	−	0.457728i	−0.0696462	−	0.997572i	$-0.522187\pi$
$911$	−27.5089	−	13.8155i	−0.911411	−	0.457728i	−0.841765	+	0.539844i	$0.818483\pi$
$912$	8.62226	−	3.38561i	0.285511	−	0.112109i
$913$	−108.361	+	12.6656i	−3.58623	+	0.419170i
$914$	−0.500177	−	0.328972i	−0.0165444	−	0.0108814i
$915$	2.38252	+	1.48272i	0.0787638	+	0.0490173i
$916$	−6.90064	+	23.0497i	−0.228004	+	0.761585i
$917$	10.4172	+	18.0431i	0.344006	+	0.595835i
$918$	0.0581282	−	0.0917623i	0.00191852	−	0.00302861i
$919$	21.9894	−	38.0868i	0.725365	−	1.25637i	−0.233459	−	0.972367i	$-0.575004\pi$
$919$	21.9894	−	38.0868i	0.725365	−	1.25637i	0.958824	−	0.284002i	$-0.0916623\pi$
$920$	0.162183	+	0.171904i	0.00534703	+	0.00566752i
$921$	16.0164	+	20.4231i	0.527759	+	0.672964i
$922$	0.599266	−	10.2890i	0.0197358	−	0.338850i
$923$	−4.51539	+	10.4678i	−0.148626	+	0.344553i
$924$	−4.73562	−	23.4061i	−0.155790	−	0.770003i
$925$	−1.37935	−	23.6825i	−0.0453527	−	0.778675i
$926$	−21.3875	−	7.78440i	−0.702836	−	0.255811i
$927$	−3.42797	−	14.9963i	−0.112589	−	0.492542i
$928$	−2.78624	+	1.01411i	−0.0914627	+	0.0332897i
$929$	−11.2233	−	26.0185i	−0.368224	−	0.853640i	−0.997098	−	0.0761324i	$-0.975743\pi$
$929$	−11.2233	−	26.0185i	−0.368224	−	0.853640i	0.628873	−	0.777508i	$-0.283516\pi$
$930$	−0.751113	−	8.99887i	−0.0246300	−	0.295085i
$931$	−17.3152	−	4.10378i	−0.567483	−	0.134496i
$932$	24.7264	+	5.86025i	0.809939	+	0.191959i
$933$	−32.3705	−	15.2522i	−1.05976	−	0.499335i
$934$	2.95586	+	6.85245i	0.0967186	+	0.224219i
$935$	0.167598	−	0.0610008i	0.00548105	−	0.00199494i
$936$	−17.1998	+	33.5765i	−0.562193	+	1.09748i
$937$	12.4825	+	4.54327i	0.407787	+	0.148422i	0.537765	−	0.843095i	$-0.319269\pi$
$937$	12.4825	+	4.54327i	0.407787	+	0.148422i	−0.129979	+	0.991517i	$0.541491\pi$
$938$	0.157324	+	2.70114i	0.00513680	+	0.0881954i
$939$	−28.9864	+	25.5891i	−0.945934	+	0.835067i
$940$	−3.23181	+	7.49217i	−0.105410	+	0.244368i
$941$	0.819975	−	14.0784i	0.0267304	−	0.458944i	−0.958212	−	0.286060i	$-0.907654\pi$
$941$	0.819975	−	14.0784i	0.0267304	−	0.458944i	0.984942	−	0.172884i	$-0.0553086\pi$
$942$	−3.97810	+	0.566494i	−0.129614	+	0.0184574i
$943$	−0.314670	−	0.333531i	−0.0102471	−	0.0108613i
$944$	4.13135	−	7.15571i	0.134464	−	0.232898i
$945$	−4.03541	−	5.91262i	−0.131272	−	0.192337i
$946$	−2.85077	−	4.93768i	−0.0926866	−	0.160538i
$947$	−6.94085	+	23.1841i	−0.225547	+	0.753381i	0.768049	+	0.640391i	$0.221228\pi$
$947$	−6.94085	+	23.1841i	−0.225547	+	0.753381i	−0.993596	+	0.112990i	$0.963957\pi$
$948$	1.11429	−	33.6717i	0.0361905	−	1.09360i
$949$	−36.5203	−	24.0198i	−1.18550	−	0.779715i
$950$	10.1012	−	1.18067i	0.327727	−	0.0383058i
$951$	−2.92942	+	19.4570i	−0.0949930	+	0.630938i
$952$	−0.0966535	−	0.0485412i	−0.00313256	−	0.00157323i
$953$	−0.315523	−	1.78942i	−0.0102208	−	0.0579650i	0.979271	−	0.202555i	$-0.0649246\pi$
$953$	−0.315523	−	1.78942i	−0.0102208	−	0.0579650i	−0.989492	+	0.144590i	$0.953814\pi$
$954$	19.5271	+	3.60413i	0.632212	+	0.116688i
$955$	−3.26378	+	18.5098i	−0.105613	+	0.598964i
$956$	−17.8169	+	23.9322i	−0.576238	+	0.774022i
$957$	5.41278	+	0.495338i	0.174970	+	0.0160120i
$958$	5.53621	−	5.86804i	0.178867	−	0.189588i
$959$	2.23543	+	7.46684i	0.0721857	+	0.241117i
$960$	0.423939	−	1.55727i	0.0136826	−	0.0502606i
$961$	−35.4962	−	4.14892i	−1.14504	−	0.133836i
$962$	15.6955	+	13.1701i	0.506044	+	0.424621i
$963$	−24.0918	+	17.6385i	−0.776347	+	0.568392i
$964$	−6.81044	+	5.71464i	−0.219350	+	0.184056i
$965$	8.44541	−	5.55463i	0.271867	−	0.178810i
$966$	−0.0855665	+	0.157188i	−0.00275306	+	0.00505743i
$967$	−1.13266	−	1.52143i	−0.0364240	−	0.0489259i	0.783538	−	0.621344i	$-0.213413\pi$
$967$	−1.13266	−	1.52143i	−0.0364240	−	0.0489259i	−0.819962	+	0.572418i	$0.806006\pi$
$968$	−56.6801	+	28.4658i	−1.82177	+	0.914926i
$969$	−0.130664	+	0.145651i	−0.00419752	+	0.00467897i
$970$	−4.35396	+	1.03191i	−0.139797	+	0.0331325i
$971$	−27.1629			−0.871698			−0.435849	−	0.900020i	$-0.643552\pi$
$971$	−27.1629			−0.871698			−0.435849	+	0.900020i	$0.643552\pi$
$972$	1.17865	−	24.0110i	0.0378052	−	0.770153i
$973$	5.98012			0.191714
$974$	25.1795	−	5.96765i	0.806803	−	0.191216i
$975$	24.9439	−	27.8049i	0.798845	−	0.890471i
$976$	2.24516	−	1.12756i	0.0718659	−	0.0360924i
$977$	−15.2926	−	20.5416i	−0.489255	−	0.657183i	0.487103	−	0.873345i	$-0.338054\pi$
$977$	−15.2926	−	20.5416i	−0.489255	−	0.657183i	−0.976358	+	0.216162i	$0.930646\pi$
$978$	−11.0470	+	20.2936i	−0.353243	+	0.648916i
$979$	71.3309	−	46.9150i	2.27974	−	1.49941i
$980$	5.42241	−	4.54994i	0.173213	−	0.145343i
$981$	−34.9643	−	15.4144i	−1.11632	−	0.492143i
$982$	2.19751	+	1.84393i	0.0701255	+	0.0588423i
$983$	28.8465	+	3.37167i	0.920061	+	0.107540i	0.562921	−	0.826511i	$-0.309678\pi$
$983$	28.8465	+	3.37167i	0.920061	+	0.107540i	0.357140	+	0.934051i	$0.383752\pi$
$984$	−4.78262	+	17.5682i	−0.152464	+	0.560053i
$985$	6.41148	+	21.4158i	0.204287	+	0.682365i
$986$	0.00735510	−	0.00779595i	0.000234234	−	0.000248274i
$987$	−14.1331	−	1.29335i	−0.449861	−	0.0411679i
$988$	17.6679	−	23.7322i	0.562092	−	0.755021i
$989$	0.0249928	−	0.141741i	0.000794725	−	0.00450711i
$990$	−7.60397	+	8.91651i	−0.241670	+	0.283385i
$991$	6.28903	+	35.6669i	0.199778	+	1.13300i	0.905449	+	0.424456i	$0.139534\pi$
$991$	6.28903	+	35.6669i	0.199778	+	1.13300i	−0.705671	+	0.708539i	$0.749354\pi$
$992$	−42.2193	−	21.2033i	−1.34046	−	0.673206i
$993$	−3.71517	+	24.6760i	−0.117897	+	0.783068i
$994$	2.13294	−	0.249305i	0.0676529	−	0.00790749i
$995$	−6.88337	−	4.52726i	−0.218218	−	0.143524i
$996$	−1.57472	+	47.5848i	−0.0498968	+	1.50778i
$997$	4.35195	−	14.5365i	0.137828	−	0.460376i	−0.861009	−	0.508589i	$-0.830167\pi$
$997$	4.35195	−	14.5365i	0.137828	−	0.460376i	0.998837	+	0.0482126i	$0.0153525\pi$
$998$	−12.6545	−	21.9182i	−0.400571	−	0.693809i
$999$	−28.8719	−	8.10799i	−0.913465	−	0.256525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.76.6	yes	144
3.2	odd	2		243.2.g.a.118.3		144
9.2	odd	6		729.2.g.a.109.6		144
9.4	even	3		729.2.g.c.352.3		144
9.5	odd	6		729.2.g.b.352.6		144
9.7	even	3		729.2.g.d.109.3		144
81.4	even	27		6561.2.a.c.1.46		72
81.11	odd	54		729.2.g.b.379.6		144
81.16	even	27	inner	81.2.g.a.16.6	✓	144
81.38	odd	54		729.2.g.a.622.6		144
81.43	even	27		729.2.g.d.622.3		144
81.65	odd	54		243.2.g.a.208.3		144
81.70	even	27		729.2.g.c.379.3		144
81.77	odd	54		6561.2.a.d.1.27		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.6	✓	144	81.16	even	27	inner
81.2.g.a.76.6	yes	144	1.1	even	1	trivial
243.2.g.a.118.3		144	3.2	odd	2
243.2.g.a.208.3		144	81.65	odd	54
729.2.g.a.109.6		144	9.2	odd	6
729.2.g.a.622.6		144	81.38	odd	54
729.2.g.b.352.6		144	9.5	odd	6
729.2.g.b.379.6		144	81.11	odd	54
729.2.g.c.352.3		144	9.4	even	3
729.2.g.c.379.3		144	81.70	even	27
729.2.g.d.109.3		144	9.7	even	3
729.2.g.d.622.3		144	81.43	even	27
6561.2.a.c.1.46		72	81.4	even	27
6561.2.a.d.1.27		72	81.77	odd	54

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.658400 - 0.156044i) q^{2} +(1.15662 - 1.28928i) q^{3} +(-1.37812 + 0.692120i) q^{4} +(0.563225 + 0.756542i) q^{5} +(0.560332 - 1.02934i) q^{6} +(1.22035 - 0.802640i) q^{7} +(-1.83603 + 1.54061i) q^{8} +(-0.324478 - 2.98240i) q^{9} +(0.488880 + 0.410219i) q^{10} +(-6.07936 - 0.710575i) q^{11} +(-0.701626 + 2.57730i) q^{12} +(1.50478 + 5.02631i) q^{13} +(0.678234 - 0.718886i) q^{14} +(1.62683 + 0.148875i) q^{15} +(0.873392 - 1.17317i) q^{16} +(-0.00536485 + 0.0304256i) q^{17} +(-0.679021 - 1.91298i) q^{18} +(0.634963 + 3.60105i) q^{19} +(-1.29981 - 0.652790i) q^{20} +(0.376655 - 2.50172i) q^{21} +(-4.11353 + 0.480802i) q^{22} +(-0.0873480 - 0.0574497i) q^{23} +(-0.137304 + 4.14904i) q^{24} +(1.17888 - 3.93774i) q^{25} +(1.77507 + 3.07451i) q^{26} +(-4.22044 - 3.03115i) q^{27} +(-1.12628 + 1.95077i) q^{28} +(-0.351839 - 0.372928i) q^{29} +(1.09433 - 0.155837i) q^{30} +(0.475004 - 8.15551i) q^{31} +(2.29059 - 5.31019i) q^{32} +(-7.94761 + 7.01612i) q^{33} +(0.00121550 + 0.0208694i) q^{34} +(1.29456 + 0.471183i) q^{35} +(2.51135 + 3.88554i) q^{36} +(5.42328 - 1.97391i) q^{37} +(0.979980 + 2.27185i) q^{38} +(8.22077 + 3.87344i) q^{39} +(-2.19963 - 0.521322i) q^{40} +(4.26774 + 1.01147i) q^{41} +(-0.142388 - 1.70591i) q^{42} +(0.545274 + 1.26409i) q^{43} +(8.86991 - 3.22838i) q^{44} +(2.07356 - 1.92524i) q^{45} +(-0.0664745 - 0.0241947i) q^{46} +(-0.326176 - 5.60023i) q^{47} +(-0.502362 - 2.48295i) q^{48} +(-1.92752 + 4.46850i) q^{49} +(0.161716 - 2.77656i) q^{50} +(0.0330220 + 0.0421075i) q^{51} +(-5.55259 - 5.88540i) q^{52} +(-4.89106 + 8.47157i) q^{53} +(-3.25173 - 1.33714i) q^{54} +(-2.88646 - 4.99950i) q^{55} +(-1.00405 + 3.35376i) q^{56} +(5.37717 + 3.34639i) q^{57} +(-0.289844 - 0.190633i) q^{58} +(5.61120 - 0.655856i) q^{59} +(-2.34501 + 0.920792i) q^{60} +(1.53507 + 0.770942i) q^{61} +(-0.959872 - 5.44370i) q^{62} +(-2.78977 - 3.37915i) q^{63} +(0.171556 - 0.972942i) q^{64} +(-2.95509 + 3.96937i) q^{65} +(-4.13788 + 5.85958i) q^{66} +(-1.87870 + 1.99130i) q^{67} +(-0.0136647 - 0.0456434i) q^{68} +(-0.175097 + 0.0461687i) q^{69} +(0.925866 + 0.108218i) q^{70} +(1.66448 + 1.39666i) q^{71} +(5.19046 + 4.97587i) q^{72} +(-6.38204 + 5.35517i) q^{73} +(3.26267 - 2.14589i) q^{74} +(-3.71333 - 6.07436i) q^{75} +(-3.36742 - 4.52323i) q^{76} +(-7.98930 + 4.01238i) q^{77} +(6.01698 + 1.26747i) q^{78} +(-12.2728 + 2.90871i) q^{79} +1.37947 q^{80} +(-8.78943 + 1.93545i) q^{81} +2.96771 q^{82} +(17.3440 - 4.11059i) q^{83} +(1.21241 + 3.70838i) q^{84} +(-0.0260399 + 0.0130777i) q^{85} +(0.556260 + 0.747187i) q^{86} +(-0.887750 + 0.0222844i) q^{87} +(12.2566 - 8.06128i) q^{88} +(-10.6853 + 8.96604i) q^{89} +(1.06481 - 1.59114i) q^{90} +(5.87068 + 4.92609i) q^{91} +(0.160139 + 0.0187175i) q^{92} +(-9.96532 - 10.0452i) q^{93} +(-1.08863 - 3.63629i) q^{94} +(-2.36672 + 2.50858i) q^{95} +(-4.19698 - 9.09507i) q^{96} +(-4.18690 + 5.62398i) q^{97} +(-0.571800 + 3.24284i) q^{98} +(-0.146600 + 18.3616i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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