LMFDB - Embedded newform 729.2.k.a.4.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(4,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(486))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.k (of order $243$, degree $162$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12960$
Relative dimension:	$80$ over $\Q(\zeta_{243})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{243}]$

Embedding invariants

Embedding label			4.15
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93424 - 0.0250080i) q^{2} +(1.62140 + 0.609150i) q^{3} +(1.74134 + 0.0450353i) q^{4} +(0.582227 + 0.178416i) q^{5} +(-3.12095 - 1.21879i) q^{6} +(-1.25911 + 3.13976i) q^{7} +(0.498860 + 0.0193580i) q^{8} +(2.25787 + 1.97535i) q^{9} +O(q^{10})$	\(q+(-1.93424 - 0.0250080i) q^{2} +(1.62140 + 0.609150i) q^{3} +(1.74134 + 0.0450353i) q^{4} +(0.582227 + 0.178416i) q^{5} +(-3.12095 - 1.21879i) q^{6} +(-1.25911 + 3.13976i) q^{7} +(0.498860 + 0.0193580i) q^{8} +(2.25787 + 1.97535i) q^{9} +(-1.12171 - 0.359660i) q^{10} +(1.10197 + 0.626758i) q^{11} +(2.79597 + 1.13375i) q^{12} +(-0.0673362 - 0.150715i) q^{13} +(2.51394 - 6.04157i) q^{14} +(0.835340 + 0.643947i) q^{15} +(-4.44361 - 0.230000i) q^{16} +(5.00315 + 2.27421i) q^{17} +(-4.31787 - 3.87727i) q^{18} +(-2.16207 - 3.15237i) q^{19} +(1.00582 + 0.336903i) q^{20} +(-3.95411 + 4.32382i) q^{21} +(-2.11580 - 1.23986i) q^{22} +(-2.08370 + 6.35698i) q^{23} +(0.797059 + 0.335268i) q^{24} +(-3.83441 - 2.59356i) q^{25} +(0.126475 + 0.293203i) q^{26} +(2.45763 + 4.57821i) q^{27} +(-2.33393 + 5.41067i) q^{28} +(-0.844715 + 0.540064i) q^{29} +(-1.59965 - 1.26644i) q^{30} +(-0.347508 - 1.28035i) q^{31} +(7.59288 + 0.491502i) q^{32} +(1.40494 + 1.68749i) q^{33} +(-9.62043 - 4.52399i) q^{34} +(-1.29327 + 1.60341i) q^{35} +(3.84275 + 3.54143i) q^{36} +(4.58208 + 0.899892i) q^{37} +(4.10313 + 6.15152i) q^{38} +(-0.0173710 - 0.285387i) q^{39} +(0.286996 + 0.100275i) q^{40} +(-0.155747 + 0.0589785i) q^{41} +(7.75633 - 8.26442i) q^{42} +(-6.18902 + 2.71727i) q^{43} +(1.89067 + 1.14102i) q^{44} +(0.962160 + 1.55294i) q^{45} +(4.18935 - 12.2438i) q^{46} +(0.450856 - 1.66112i) q^{47} +(-7.06476 - 3.07974i) q^{48} +(-3.21227 - 3.07011i) q^{49} +(7.35183 + 5.11247i) q^{50} +(6.72677 + 6.73507i) q^{51} +(-0.110467 - 0.265478i) q^{52} +(-0.285476 + 0.302587i) q^{53} +(-4.63916 - 8.91684i) q^{54} +(0.529770 + 0.561524i) q^{55} +(-0.688900 + 1.54193i) q^{56} +(-1.58531 - 6.42828i) q^{57} +(1.64739 - 1.02349i) q^{58} +(2.32325 - 0.394185i) q^{59} +(1.42561 + 1.15895i) q^{60} +(0.376654 - 0.693176i) q^{61} +(0.640146 + 2.48520i) q^{62} +(-9.04504 + 4.60199i) q^{63} +(-5.80182 - 0.450953i) q^{64} +(-0.0123150 - 0.0997641i) q^{65} +(-2.67529 - 3.29914i) q^{66} +(0.488074 - 0.253073i) q^{67} +(8.60974 + 4.18548i) q^{68} +(-7.25086 + 9.03792i) q^{69} +(2.54160 - 3.06903i) q^{70} +(-0.358270 - 0.277680i) q^{71} +(1.08812 + 1.02913i) q^{72} +(0.379435 - 0.121661i) q^{73} +(-8.84036 - 1.85520i) q^{74} +(-4.63725 - 6.54094i) q^{75} +(-3.62292 - 5.58671i) q^{76} +(-3.35537 + 2.67075i) q^{77} +(0.0264627 + 0.552442i) q^{78} +(-2.90592 + 15.3195i) q^{79} +(-2.54615 - 0.926724i) q^{80} +(1.19598 + 8.92018i) q^{81} +(0.302727 - 0.110184i) q^{82} +(1.16079 + 7.12027i) q^{83} +(-7.08015 + 7.35114i) q^{84} +(2.50721 + 2.21675i) q^{85} +(12.0390 - 5.10108i) q^{86} +(-1.69860 + 0.361101i) q^{87} +(0.537594 + 0.333996i) q^{88} +(7.22157 + 2.95034i) q^{89} +(-1.82221 - 3.02783i) q^{90} +(0.557992 - 0.0216526i) q^{91} +(-3.91470 + 10.9758i) q^{92} +(0.216476 - 2.28765i) q^{93} +(-0.913605 + 3.20174i) q^{94} +(-0.696380 - 2.22114i) q^{95} +(12.0117 + 5.42212i) q^{96} +(-2.10889 + 9.16163i) q^{97} +(6.13652 + 6.01866i) q^{98} +(1.25003 + 3.59191i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) $ 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{243}\right)$

Coefficient data

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

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

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

$2$	−1.93424	−	0.0250080i	−1.36772	−	0.0176833i	−0.674426	−	0.738342i	$-0.735609\pi$
$2$	−1.93424	−	0.0250080i	−1.36772	−	0.0176833i	−0.693290	+	0.720659i	$0.743839\pi$
$3$	1.62140	+	0.609150i	0.936115	+	0.351693i
$3$	1.62140	+	0.609150i	0.936115	+	0.351693i
$4$	1.74134	+	0.0450353i	0.870668	+	0.0225176i
$5$	0.582227	+	0.178416i	0.260380	+	0.0797901i	0.420451	−	0.907315i	$-0.361872\pi$
$5$	0.582227	+	0.178416i	0.260380	+	0.0797901i	−0.160071	+	0.987105i	$0.551172\pi$
$6$	−3.12095	−	1.21879i	−1.27412	−	0.497569i
$7$	−1.25911	+	3.13976i	−0.475899	+	1.18672i	0.475764	+	0.879573i	$0.342172\pi$
$7$	−1.25911	+	3.13976i	−0.475899	+	1.18672i	−0.951663	+	0.307144i	$0.900627\pi$
$8$	0.498860	+	0.0193580i	0.176374	+	0.00684410i
$9$	2.25787	+	1.97535i	0.752624	+	0.658450i
$10$	−1.12171	−	0.359660i	−0.354714	−	0.113735i
$11$	1.10197	+	0.626758i	0.332255	+	0.188975i	0.651406	−	0.758729i	$-0.274179\pi$
$11$	1.10197	+	0.626758i	0.332255	+	0.188975i	−0.319151	+	0.947704i	$0.603398\pi$
$12$	2.79597	+	1.13375i	0.807126	+	0.327287i
$13$	−0.0673362	−	0.150715i	−0.0186757	−	0.0418008i	0.903442	−	0.428711i	$-0.141032\pi$
$13$	−0.0673362	−	0.150715i	−0.0186757	−	0.0418008i	−0.922117	+	0.386910i	$0.873542\pi$
$14$	2.51394	−	6.04157i	0.671880	−	1.61468i
$15$	0.835340	+	0.643947i	0.215684	+	0.166266i
$16$	−4.44361	−	0.230000i	−1.11090	−	0.0574999i
$17$	5.00315	+	2.27421i	1.21344	+	0.551577i	0.915234	−	0.402924i	$-0.132006\pi$
$17$	5.00315	+	2.27421i	1.21344	+	0.551577i	0.298208	+	0.954501i	$0.403611\pi$
$18$	−4.31787	−	3.87727i	−1.01773	−	0.913881i
$19$	−2.16207	−	3.15237i	−0.496013	−	0.723204i	0.493164	−	0.869937i	$-0.335840\pi$
$19$	−2.16207	−	3.15237i	−0.496013	−	0.723204i	−0.989176	+	0.146733i	$0.953124\pi$
$20$	1.00582	+	0.336903i	0.224908	+	0.0753338i
$21$	−3.95411	+	4.32382i	−0.862857	+	0.943534i
$22$	−2.11580	−	1.23986i	−0.451089	−	0.264339i
$23$	−2.08370	+	6.35698i	−0.434481	+	1.32552i	0.463738	+	0.885972i	$0.346508\pi$
$23$	−2.08370	+	6.35698i	−0.434481	+	1.32552i	−0.898218	+	0.439549i	$0.855138\pi$
$24$	0.797059	+	0.335268i	0.162699	+	0.0684362i
$25$	−3.83441	−	2.59356i	−0.766883	−	0.518713i
$26$	0.126475	+	0.293203i	0.0248039	+	0.0575019i
$27$	2.45763	+	4.57821i	0.472971	+	0.881078i
$28$	−2.33393	+	5.41067i	−0.441072	+	1.02252i
$29$	−0.844715	+	0.540064i	−0.156860	+	0.100287i	−0.614753	−	0.788720i	$-0.710744\pi$
$29$	−0.844715	+	0.540064i	−0.156860	+	0.100287i	0.457893	+	0.889007i	$0.348604\pi$
$30$	−1.59965	−	1.26644i	−0.292054	−	0.231219i
$31$	−0.347508	−	1.28035i	−0.0624143	−	0.229958i	0.927003	−	0.375053i	$-0.122375\pi$
$31$	−0.347508	−	1.28035i	−0.0624143	−	0.229958i	−0.989418	+	0.145095i	$0.953651\pi$
$32$	7.59288	+	0.491502i	1.34224	+	0.0868862i
$33$	1.40494	+	1.68749i	0.244568	+	0.293754i
$34$	−9.62043	−	4.52399i	−1.64989	−	0.775858i
$35$	−1.29327	+	1.60341i	−0.218603	+	0.271025i
$36$	3.84275	+	3.54143i	0.640459	+	0.590239i
$37$	4.58208	+	0.899892i	0.753290	+	0.147941i	0.554595	−	0.832120i	$-0.312873\pi$
$37$	4.58208	+	0.899892i	0.753290	+	0.147941i	0.198695	+	0.980061i	$0.436330\pi$
$38$	4.10313	+	6.15152i	0.665615	+	0.997909i
$39$	−0.0173710	−	0.285387i	−0.00278158	−	0.0456985i
$40$	0.286996	+	0.100275i	0.0453780	+	0.0158549i
$41$	−0.155747	+	0.0589785i	−0.0243236	+	0.00921089i	−0.366272	−	0.930508i	$-0.619366\pi$
$41$	−0.155747	+	0.0589785i	−0.0243236	+	0.00921089i	0.341948	+	0.939719i	$0.388913\pi$
$42$	7.75633	−	8.26442i	1.19683	−	1.27523i
$43$	−6.18902	+	2.71727i	−0.943816	+	0.414379i	−0.816411	−	0.577472i	$-0.804039\pi$
$43$	−6.18902	+	2.71727i	−0.943816	+	0.414379i	−0.127406	+	0.991851i	$0.540665\pi$
$44$	1.89067	+	1.14102i	0.285029	+	0.172016i
$45$	0.962160	+	1.55294i	0.143430	+	0.231499i
$46$	4.18935	−	12.2438i	0.617685	−	1.80525i
$47$	0.450856	−	1.66112i	0.0657641	−	0.242300i	−0.924568	−	0.381017i	$-0.875574\pi$
$47$	0.450856	−	1.66112i	0.0657641	−	0.242300i	0.990332	+	0.138718i	$0.0442981\pi$
$48$	−7.06476	−	3.07974i	−1.01971	−	0.444523i
$49$	−3.21227	−	3.07011i	−0.458895	−	0.438587i
$50$	7.35183	+	5.11247i	1.03971	+	0.723013i
$51$	6.72677	+	6.73507i	0.941936	+	0.943099i
$52$	−0.110467	−	0.265478i	−0.0153191	−	0.0368151i
$53$	−0.285476	+	0.302587i	−0.0392132	+	0.0415635i	−0.746683	−	0.665180i	$-0.768355\pi$
$53$	−0.285476	+	0.302587i	−0.0392132	+	0.0415635i	0.707470	+	0.706743i	$0.249836\pi$
$54$	−4.63916	−	8.91684i	−0.631310	−	1.21343i
$55$	0.529770	+	0.561524i	0.0714342	+	0.0757158i
$56$	−0.688900	+	1.54193i	−0.0920581	+	0.206049i
$57$	−1.58531	−	6.42828i	−0.209979	−	0.851446i
$58$	1.64739	−	1.02349i	0.216313	−	0.134391i
$59$	2.32325	−	0.394185i	0.302462	−	0.0513185i	−0.0140680	−	0.999901i	$-0.504478\pi$
$59$	2.32325	−	0.394185i	0.302462	−	0.0513185i	0.316530	+	0.948583i	$0.397482\pi$
$60$	1.42561	+	1.15895i	0.184045	+	0.149620i
$61$	0.376654	−	0.693176i	0.0482256	−	0.0887521i	−0.853429	−	0.521210i	$-0.825481\pi$
$61$	0.376654	−	0.693176i	0.0482256	−	0.0887521i	0.901654	+	0.432457i	$0.142353\pi$
$62$	0.640146	+	2.48520i	0.0812987	+	0.315621i
$63$	−9.04504	+	4.60199i	−1.13957	+	0.579796i
$64$	−5.80182	−	0.450953i	−0.725227	−	0.0563691i
$65$	−0.0123150	−	0.0997641i	−0.00152748	−	0.0123742i
$66$	−2.67529	−	3.29914i	−0.329305	−	0.406097i
$67$	0.488074	−	0.253073i	0.0596277	−	0.0309178i	−0.430241	−	0.902714i	$-0.641571\pi$
$67$	0.488074	−	0.253073i	0.0596277	−	0.0309178i	0.489869	+	0.871796i	$0.337045\pi$
$68$	8.60974	+	4.18548i	1.04408	+	0.507564i
$69$	−7.25086	+	9.03792i	−0.872900	+	1.08804i
$70$	2.54160	−	3.06903i	0.303779	−	0.366820i
$71$	−0.358270	−	0.277680i	−0.0425188	−	0.0329545i	0.591120	−	0.806584i	$-0.298686\pi$
$71$	−0.358270	−	0.277680i	−0.0425188	−	0.0329545i	−0.633638	+	0.773629i	$0.718439\pi$
$72$	1.08812	+	1.02913i	0.128237	+	0.121284i
$73$	0.379435	−	0.121661i	0.0444095	−	0.0142393i	−0.283038	−	0.959109i	$-0.591342\pi$
$73$	0.379435	−	0.121661i	0.0444095	−	0.0142393i	0.327448	+	0.944869i	$0.393811\pi$
$74$	−8.84036	−	1.85520i	−1.02767	−	0.215662i
$75$	−4.63725	−	6.54094i	−0.535463	−	0.755282i
$76$	−3.62292	−	5.58671i	−0.415577	−	0.640839i
$77$	−3.35537	+	2.67075i	−0.382379	+	0.304360i
$78$	0.0264627	+	0.552442i	0.00299631	+	0.0625517i
$79$	−2.90592	+	15.3195i	−0.326942	+	1.72357i	0.308325	+	0.951281i	$0.400232\pi$
$79$	−2.90592	+	15.3195i	−0.326942	+	1.72357i	−0.635267	+	0.772292i	$0.719110\pi$
$80$	−2.54615	−	0.926724i	−0.284669	−	0.103611i
$81$	1.19598	+	8.92018i	0.132887	+	0.991131i
$82$	0.302727	−	0.110184i	0.0334306	−	0.0121678i
$83$	1.16079	+	7.12027i	0.127413	+	0.781551i	0.970021	+	0.243023i	$0.0781389\pi$
$83$	1.16079	+	7.12027i	0.127413	+	0.781551i	−0.842607	+	0.538529i	$0.818980\pi$
$84$	−7.08015	+	7.35114i	−0.772507	+	0.802075i
$85$	2.50721	+	2.21675i	0.271945	+	0.240440i
$86$	12.0390	−	5.10108i	1.29820	−	0.550063i
$87$	−1.69860	+	0.361101i	−0.182109	+	0.0387141i
$88$	0.537594	+	0.333996i	0.0573077	+	0.0356041i
$89$	7.22157	+	2.95034i	0.765485	+	0.312735i	0.727103	−	0.686528i	$-0.240866\pi$
$89$	7.22157	+	2.95034i	0.765485	+	0.312735i	0.0383816	+	0.999263i	$0.487780\pi$
$90$	−1.82221	−	3.02783i	−0.192078	−	0.319161i
$91$	0.557992	−	0.0216526i	0.0584935	−	0.00226981i
$92$	−3.91470	+	10.9758i	−0.408136	+	1.14431i
$93$	0.216476	−	2.28765i	0.0224475	−	0.237218i
$94$	−0.913605	+	3.20174i	−0.0942312	+	0.330234i
$95$	−0.696380	−	2.22114i	−0.0714470	−	0.227885i
$96$	12.0117	+	5.42212i	1.22594	+	0.553393i
$97$	−2.10889	+	9.16163i	−0.214126	+	0.930223i	0.749297	+	0.662234i	$0.230392\pi$
$97$	−2.10889	+	9.16163i	−0.214126	+	0.930223i	−0.963422	+	0.267988i	$0.913641\pi$
$98$	6.13652	+	6.01866i	0.619883	+	0.607977i
$99$	1.25003	+	3.59191i	0.125633	+	0.361000i
$100$	−6.56020	−	4.68895i	−0.656020	−	0.468895i
$101$	0.220299	−	1.47080i	0.0219205	−	0.146350i	−0.975297	−	0.220898i	$-0.929101\pi$
$101$	0.220299	−	1.47080i	0.0219205	−	0.146350i	0.997217	+	0.0745480i	$0.0237514\pi$
$102$	−12.8428	−	13.1955i	−1.27162	−	1.30655i
$103$	2.29489	+	6.43427i	0.226122	+	0.633987i	1.00000		0.000651928i	$0.000207515\pi$
$103$	2.29489	+	6.43427i	0.226122	+	0.633987i	−0.773878	+	0.633335i	$0.781685\pi$
$104$	−0.0306738	−	0.0764892i	−0.00300781	−	0.00750038i
$105$	−3.07362	+	1.81196i	−0.299955	+	0.176830i
$106$	0.559747	−	0.578137i	0.0543674	−	0.0561537i
$107$	−0.643585	−	11.0499i	−0.0622177	−	1.06824i	−0.874517	−	0.484995i	$-0.838821\pi$
$107$	−0.643585	−	11.0499i	−0.0622177	−	1.06824i	0.812299	−	0.583241i	$-0.198216\pi$
$108$	4.07338	+	8.08289i	0.391961	+	0.777776i
$109$	−0.947292	+	16.2644i	−0.0907341	+	1.55784i	0.579052	+	0.815290i	$0.303423\pi$
$109$	−0.947292	+	16.2644i	−0.0907341	+	1.55784i	−0.669786	+	0.742554i	$0.733614\pi$
$110$	−1.01066	−	1.09937i	−0.0963628	−	0.104821i
$111$	6.88122	+	4.25026i	0.653137	+	0.403417i
$112$	6.31714	−	13.6623i	0.596914	−	1.29096i
$113$	12.2610	−	9.00540i	1.15342	−	0.847157i	0.163190	−	0.986595i	$-0.447822\pi$
$113$	12.2610	−	9.00540i	1.15342	−	0.847157i	0.990231	+	0.139438i	$0.0445296\pi$
$114$	2.90561	+	12.4735i	0.272136	+	1.16825i
$115$	−2.34737	+	3.32944i	−0.218893	+	0.310472i
$116$	−1.49525	+	0.902390i	−0.138831	+	0.0837848i
$117$	0.145678	−	0.473308i	0.0134680	−	0.0437573i
$118$	−4.50359	+	0.704349i	−0.414589	+	0.0648406i
$119$	−13.4400	+	12.8452i	−1.23204	+	1.17752i
$120$	0.404252	+	0.337410i	0.0369030	+	0.0308012i
$121$	−4.80119	−	8.07305i	−0.436472	−	0.733913i
$122$	−0.745875	+	1.33135i	−0.0675284	+	0.120535i
$123$	−0.288455		0.000754438i	−0.0260091		6.80254e-5i
$124$	−0.547468	−	2.24517i	−0.0491640	−	0.201622i
$125$	−3.68130	−	4.56409i	−0.329265	−	0.408225i
$126$	17.6104	−	8.67517i	1.56886	−	0.772845i
$127$	−0.139007	−	7.16719i	−0.0123349	−	0.635985i	−0.954062	−	0.299608i	$-0.903144\pi$
$127$	−0.139007	−	7.16719i	−0.0123349	−	0.635985i	0.941727	−	0.336377i	$-0.109202\pi$
$128$	−3.94442	−	0.357942i	−0.348641	−	0.0316379i
$129$	−11.6901	+	0.635736i	−1.02926	+	0.0559734i
$130$	0.0213252	+	0.193276i	0.00187035	+	0.0169514i
$131$	4.33009	−	0.392941i	0.378322	−	0.0343314i	0.100431	−	0.994944i	$-0.467978\pi$
$131$	4.33009	−	0.392941i	0.378322	−	0.0343314i	0.277891	+	0.960613i	$0.410365\pi$
$132$	2.37047	+	3.00175i	0.206323	+	0.261269i
$133$	12.6200	−	2.81919i	1.09429	−	0.244454i
$134$	−0.950381	+	0.477299i	−0.0821004	+	0.0412324i
$135$	0.614070	+	3.10404i	0.0528508	+	0.267153i
$136$	2.45185	+	1.23136i	0.210244	+	0.105589i
$137$	18.9087	+	4.74045i	1.61548	+	0.405004i	0.942380	−	0.334544i	$-0.108582\pi$
$137$	18.9087	+	4.74045i	1.61548	+	0.405004i	0.673103	+	0.739549i	$0.264961\pi$
$138$	14.2509	−	17.3002i	1.21312	−	1.47269i
$139$	−23.1972	−	3.32134i	−1.96756	−	0.281712i	−0.999522	−	0.0309115i	$-0.990159\pi$
$139$	−23.1972	−	3.32134i	−1.96756	−	0.281712i	−0.968039	−	0.250801i	$-0.919306\pi$
$140$	−2.32423	+	2.73382i	−0.196433	+	0.231050i
$141$	1.74289	−	2.41870i	0.146778	−	0.203692i
$142$	0.686036	+	0.546060i	0.0575709	+	0.0458243i
$143$	0.0202595	−	0.208286i	0.00169419	−	0.0174178i
$144$	−9.57878	−	9.29700i	−0.798232	−	0.774750i
$145$	−0.588172	+	0.163729i	−0.0488450	+	0.0135969i
$146$	−0.736961	+	0.225833i	−0.0609913	+	0.0186900i
$147$	−3.33821	−	6.93462i	−0.275331	−	0.571958i
$148$	7.93842	+	1.77337i	0.652534	+	0.145770i
$149$	2.55587	−	0.640760i	0.209385	−	0.0524931i	−0.137063	−	0.990562i	$-0.543766\pi$
$149$	2.55587	−	0.640760i	0.209385	−	0.0524931i	0.346448	+	0.938069i	$0.387388\pi$
$150$	8.80599	+	12.7677i	0.719006	+	1.04248i
$151$	−0.591659	−	0.695926i	−0.0481485	−	0.0566337i	0.737273	−	0.675595i	$-0.236113\pi$
$151$	−0.591659	−	0.695926i	−0.0481485	−	0.0566337i	−0.785421	+	0.618962i	$0.787554\pi$
$152$	−1.01755	−	1.61445i	−0.0825339	−	0.130949i
$153$	6.80411	+	15.0179i	0.550080	+	1.21412i
$154$	6.55688	−	5.08197i	0.528369	−	0.409516i
$155$	0.0261068	−	0.807456i	0.00209695	−	0.0648564i
$156$	−0.0173962	−	0.497737i	−0.00139281	−	0.0398508i
$157$	2.65729	−	21.5268i	0.212074	−	1.71803i	−0.391042	−	0.920373i	$-0.627885\pi$
$157$	2.65729	−	21.5268i	0.212074	−	1.71803i	0.603116	−	0.797653i	$-0.293925\pi$
$158$	6.00387	−	29.5589i	0.477642	−	2.35158i
$159$	−0.647192	+	0.316717i	−0.0513256	+	0.0251173i
$160$	4.33309	+	1.64086i	0.342560	+	0.129721i
$161$	−17.3358	−	14.5464i	−1.36625	−	1.14642i
$162$	−2.09024	−	17.2837i	−0.164225	−	1.35794i
$163$	3.87610	−	3.25244i	0.303600	−	0.254751i	−0.478241	−	0.878229i	$-0.658725\pi$
$163$	3.87610	−	3.25244i	0.303600	−	0.254751i	0.781841	+	0.623478i	$0.214281\pi$
$164$	−0.273864	+	0.0956872i	−0.0213852	+	0.00747191i
$165$	0.516917	+	1.23316i	0.0402420	+	0.0960017i
$166$	−2.06719	−	13.8014i	−0.160445	−	1.07119i
$167$	−1.25678	+	2.46263i	−0.0972525	+	0.190564i	−0.934228	−	0.356676i	$-0.883910\pi$
$167$	−1.25678	+	2.46263i	−0.0972525	+	0.190564i	0.836976	+	0.547240i	$0.184322\pi$
$168$	−2.05625	+	2.08044i	−0.158643	+	0.160509i
$169$	8.65551	−	9.66305i	0.665808	−	0.743311i
$170$	−4.79412	−	4.35043i	−0.367692	−	0.333663i
$171$	1.34536	−	11.3885i	0.102883	−	0.870900i
$172$	−10.8995	+	4.45295i	−0.831081	+	0.339534i
$173$	−16.1404	−	2.73854i	−1.22714	−	0.208207i	−0.482630	−	0.875824i	$-0.660319\pi$
$173$	−16.1404	−	2.73854i	−1.22714	−	0.208207i	−0.744505	+	0.667617i	$0.767314\pi$
$174$	3.29453	−	0.655979i	0.249758	−	0.0497296i
$175$	12.9711	−	8.77355i	0.980524	−	0.663218i
$176$	−4.75255	−	3.03852i	−0.358237	−	0.229037i
$177$	4.00704	+	0.776078i	0.301188	+	0.0583336i
$178$	−13.8945	−	5.88726i	−1.04144	−	0.441269i
$179$	−5.27595	−	11.0337i	−0.394343	−	0.824698i	−0.999589	−	0.0286597i	$-0.990876\pi$
$179$	−5.27595	−	11.0337i	−0.394343	−	0.824698i	0.605247	−	0.796038i	$-0.293075\pi$
$180$	1.60551	+	2.74753i	0.119667	+	0.204788i
$181$	−0.265021	−	0.0737735i	−0.0196988	−	0.00548354i	0.258309	−	0.966062i	$-0.416835\pi$
$181$	−0.265021	−	0.0737735i	−0.0196988	−	0.00548354i	−0.278008	+	0.960579i	$0.589674\pi$
$182$	−1.07983	+	0.0279272i	−0.0800426	+	0.00207010i
$183$	1.03296	−	0.894477i	0.0763582	−	0.0661216i
$184$	−1.16253	+	3.13091i	−0.0857029	+	0.230813i
$185$	2.50726	+	1.34146i	0.184337	+	0.0986260i
$186$	−0.475926	+	4.41945i	−0.0348966	+	0.324050i
$187$	4.08792	+	5.64187i	0.298938	+	0.412574i
$188$	0.859900	−	2.87227i	0.0627147	−	0.209482i
$189$	−17.4689	+	1.95189i	−1.27068	+	0.141979i
$190$	1.29142	+	4.31364i	0.0936895	+	0.312945i
$191$	13.7065	−	17.9226i	0.991767	−	1.29683i	0.0370510	−	0.999313i	$-0.488204\pi$
$191$	13.7065	−	17.9226i	0.991767	−	1.29683i	0.954716	−	0.297517i	$-0.0961585\pi$
$192$	−9.13237	−	4.26535i	−0.659072	−	0.307825i
$193$	20.9558	−	9.85445i	1.50843	−	0.709339i	0.519060	−	0.854738i	$-0.326282\pi$
$193$	20.9558	−	9.85445i	1.50843	−	0.709339i	0.989373	+	0.145399i	$0.0464466\pi$
$194$	4.30822	−	17.6681i	0.309312	−	1.26849i
$195$	0.0408038	−	0.169259i	0.00292202	−	0.0121209i
$196$	−5.45537	−	5.49075i	−0.389669	−	0.392196i
$197$	6.91584	−	1.35823i	0.492733	−	0.0967697i	0.0598274	−	0.998209i	$-0.480945\pi$
$197$	6.91584	−	1.35823i	0.492733	−	0.0967697i	0.432906	+	0.901439i	$0.357488\pi$
$198$	−2.32804	−	6.97888i	−0.165447	−	0.495968i
$199$	15.2030	−	8.38868i	1.07772	−	0.594658i	0.158078	−	0.987427i	$-0.449470\pi$
$199$	15.2030	−	8.38868i	1.07772	−	0.594658i	0.919637	+	0.392769i	$0.128483\pi$
$200$	−1.86263	−	1.36805i	−0.131708	−	0.0967359i
$201$	0.945522	−	0.113023i	0.0666920	−	0.00797204i
$202$	−0.462892	+	2.83937i	−0.0325690	+	0.199778i
$203$	−0.632080	−	3.33220i	−0.0443633	−	0.233875i
$204$	11.4102	+	12.0310i	0.798877	+	0.842336i
$205$	−0.101203	+	0.00655106i	−0.00706831	+	0.000457546i
$206$	−4.27796	−	12.5028i	−0.298060	−	0.871113i
$207$	−17.2620	+	10.2372i	−1.19979	+	0.711536i
$208$	0.264552	+	0.685206i	0.0183434	+	0.0475105i
$209$	−0.406752	−	4.82890i	−0.0281356	−	0.334022i
$210$	5.99045	−	3.42791i	0.413380	−	0.236549i
$211$	9.65264	−	14.4715i	0.664515	−	0.996258i	−0.334042	−	0.942558i	$-0.608413\pi$
$211$	9.65264	−	14.4715i	0.664515	−	0.996258i	0.998557	−	0.0537003i	$-0.0171016\pi$
$212$	−0.510737	+	0.514049i	−0.0350775	+	0.0353050i
$213$	−0.411750	−	0.668470i	−0.0282126	−	0.0458028i
$214$	0.968512	+	21.3893i	0.0662061	+	1.46214i
$215$	−4.08822	+	0.477844i	−0.278814	+	0.0325887i
$216$	1.13739	+	2.33146i	0.0773895	+	0.158636i
$217$	4.45755	+	0.521012i	0.302598	+	0.0353686i
$218$	2.23903	−	31.4355i	0.151646	−	2.12908i
$219$	0.689325	+	0.0338717i	0.0465802	+	0.00228884i
$220$	0.897219	+	1.00166i	0.0604905	+	0.0675319i
$221$	0.00586430	−	0.907186i	0.000394475	−	0.0610239i
$222$	−13.2037	−	8.39312i	−0.886171	−	0.563309i
$223$	−8.58329	+	7.58891i	−0.574780	+	0.508191i	−0.899092	−	0.437759i	$-0.855772\pi$
$223$	−8.58329	+	7.58891i	−0.574780	+	0.508191i	0.324313	+	0.945950i	$0.394867\pi$
$224$	−11.1035	+	23.2210i	−0.741882	+	1.55152i
$225$	−3.53442	−	13.4302i	−0.235628	−	0.895350i
$226$	−23.9410	+	17.1120i	−1.59253	+	1.13827i
$227$	−9.81704	−	19.2363i	−0.651580	−	1.27676i	−0.946952	−	0.321374i	$-0.895855\pi$
$227$	−9.81704	−	19.2363i	−0.651580	−	1.27676i	0.295373	−	0.955382i	$-0.404556\pi$
$228$	−2.47106	−	11.2652i	−0.163650	−	0.746055i
$229$	−1.42999	−	1.86985i	−0.0944966	−	0.123563i	0.744682	−	0.667420i	$-0.232601\pi$
$229$	−1.42999	−	1.86985i	−0.0944966	−	0.123563i	−0.839178	+	0.543857i	$0.816964\pi$
$230$	4.62365	−	6.38124i	0.304874	−	0.420766i
$231$	−7.06728	+	2.28643i	−0.464993	+	0.150436i
$232$	−0.431849	+	0.253064i	−0.0283523	+	0.0166145i
$233$	−0.303708	−	1.40207i	−0.0198966	−	0.0918528i	0.966306	−	0.257396i	$-0.0828646\pi$
$233$	−0.303708	−	1.40207i	−0.0198966	−	0.0918528i	−0.986202	+	0.165544i	$0.947062\pi$
$234$	−0.293613	+	0.911849i	−0.0191941	+	0.0596094i
$235$	0.558871	−	0.886710i	0.0364567	−	0.0578426i
$236$	4.06332	−	0.581780i	0.264499	−	0.0378706i
$237$	−14.0435	+	23.0688i	−0.912224	+	1.49848i
$238$	26.3174	−	24.5096i	1.70591	−	1.58872i
$239$	11.4162	+	21.0098i	0.738451	+	1.35901i	0.926291	+	0.376810i	$0.122979\pi$
$239$	11.4162	+	21.0098i	0.738451	+	1.35901i	−0.187840	+	0.982200i	$0.560148\pi$
$240$	−3.56382	−	3.05358i	−0.230043	−	0.197108i
$241$	6.26238	−	10.5300i	0.403395	−	0.678296i	−0.588049	−	0.808825i	$-0.700104\pi$
$241$	6.26238	−	10.5300i	0.403395	−	0.678296i	0.991444	+	0.130529i	$0.0416677\pi$
$242$	9.08478	+	15.7353i	0.583992	+	1.01150i
$243$	−3.49456	+	15.1917i	−0.224176	+	0.974549i
$244$	0.687099	−	1.19009i	0.0439870	−	0.0761877i
$245$	−1.32251	−	2.36062i	−0.0844921	−	0.150814i
$246$	0.557960	+	0.00575440i	0.0355742	+	0.000366887i
$247$	−0.329524	+	0.538125i	−0.0209671	+	0.0342401i
$248$	−0.148573	−	0.645443i	−0.00943439	−	0.0409857i
$249$	−2.45521	+	12.2519i	−0.155592	+	0.776433i
$250$	7.00638	+	8.92012i	0.443122	+	0.564158i
$251$	−4.69231	−	8.90813i	−0.296176	−	0.562276i	0.690819	−	0.723028i	$-0.257250\pi$
$251$	−4.69231	−	8.90813i	−0.296176	−	0.562276i	−0.986995	+	0.160751i	$0.948608\pi$
$252$	−15.9577	+	7.60627i	−1.00524	+	0.479150i
$253$	−6.28045	+	5.69920i	−0.394848	+	0.358306i
$254$	0.0896371	+	13.8665i	0.00562433	+	0.870065i
$255$	2.71486	+	5.12150i	0.170011	+	0.320721i
$256$	19.1970	+	1.99259i	1.19981	+	0.124537i
$257$	24.2720	−	3.15558i	1.51405	−	0.196839i	0.673748	−	0.738962i	$-0.264684\pi$
$257$	24.2720	−	3.15558i	1.51405	−	0.196839i	0.840300	+	0.542122i	$0.182379\pi$
$258$	22.6274	−	0.937321i	1.40872	−	0.0583550i
$259$	−8.59480	+	13.2536i	−0.534055	+	0.823537i
$260$	−0.0169516	−	0.174277i	−0.00105129	−	0.0108082i
$261$	−2.97407	−	0.449212i	−0.184091	−	0.0278055i
$262$	−8.38528	+	0.651755i	−0.518044	+	0.0402656i
$263$	−0.284414	−	1.40026i	−0.0175377	−	0.0863435i	0.970269	−	0.242030i	$-0.0778131\pi$
$263$	−0.284414	−	1.40026i	−0.0175377	−	0.0863435i	−0.987807	+	0.155686i	$0.950241\pi$
$264$	0.668201	+	0.869017i	0.0411249	+	0.0534843i
$265$	−0.220198	+	0.125241i	−0.0135267	+	0.00769347i
$266$	−24.4806	+	5.13739i	−1.50100	+	0.314993i
$267$	9.91185	+	9.18269i	0.606595	+	0.561971i
$268$	0.861297	−	0.418705i	0.0526121	−	0.0255765i
$269$	0.0427987	−	0.0574887i	0.00260949	−	0.00350515i	−0.800817	−	0.598910i	$-0.795601\pi$
$269$	0.0427987	−	0.0574887i	0.00260949	−	0.00350515i	0.803426	+	0.595405i	$0.203008\pi$
$270$	−1.11014	−	6.01932i	−0.0675607	−	0.366324i
$271$	10.2344	+	13.7472i	0.621694	+	0.835080i	0.995728	−	0.0923348i	$-0.0294330\pi$
$271$	10.2344	+	13.7472i	0.621694	+	0.835080i	−0.374034	+	0.927415i	$0.622026\pi$
$272$	−21.7090	−	11.2564i	−1.31630	−	0.682521i
$273$	0.917918	+	0.304793i	0.0555549	+	0.0184469i
$274$	−36.4555	−	9.64205i	−2.20236	−	0.582498i
$275$	−2.59986	−	5.26127i	−0.156777	−	0.317266i
$276$	−13.0332	+	15.4115i	−0.784506	+	0.927664i
$277$	2.62628	−	1.82632i	0.157798	−	0.109733i	−0.489384	−	0.872068i	$-0.662778\pi$
$277$	2.62628	−	1.82632i	0.157798	−	0.109733i	0.647182	+	0.762335i	$0.275947\pi$
$278$	44.7859	+	7.00439i	2.68608	+	0.420096i
$279$	1.74451	−	3.57732i	0.104441	−	0.214169i
$280$	−0.676200	+	0.774840i	−0.0404107	+	0.0463055i
$281$	−13.9275	+	28.1847i	−0.830843	+	1.68136i	−0.103974	+	0.994580i	$0.533156\pi$
$281$	−13.9275	+	28.1847i	−0.830843	+	1.68136i	−0.726869	+	0.686776i	$0.759025\pi$
$282$	−3.43166	+	4.63477i	−0.204352	+	0.275997i
$283$	−0.123527	+	0.106402i	−0.00734289	+	0.00632497i	−0.656301	−	0.754499i	$-0.727880\pi$
$283$	−0.123527	+	0.106402i	−0.00734289	+	0.00632497i	0.648958	+	0.760824i	$0.275205\pi$
$284$	−0.611362	−	0.499669i	−0.0362777	−	0.0296499i
$285$	0.223899	−	4.02556i	0.0132627	−	0.238454i
$286$	−0.0443957	+	0.402369i	−0.00262517	+	0.0237926i
$287$	0.0109246	−	0.563268i	0.000644857	−	0.0332487i
$288$	16.1729	+	16.1083i	0.952996	+	0.949193i
$289$	8.68161	+	9.94802i	0.510683	+	0.585177i
$290$	1.14176	−	0.301982i	0.0670465	−	0.0177330i
$291$	−9.00016	+	13.5700i	−0.527599	+	0.795489i
$292$	0.666202	−	0.194764i	0.0389865	−	0.0113977i
$293$	−2.78434	+	33.0553i	−0.162663	+	1.93111i	0.164953	+	0.986301i	$0.447253\pi$
$293$	−2.78434	+	33.0553i	−0.162663	+	1.93111i	−0.327616	+	0.944811i	$0.606245\pi$
$294$	6.28349	+	13.4967i	0.366461	+	0.787145i
$295$	1.42299	+	0.185001i	0.0828496	+	0.0107712i
$296$	2.26840	+	0.537620i	0.131848	+	0.0312485i
$297$	−0.161207	+	6.58538i	−0.00935416	+	0.382122i
$298$	−4.95969	+	1.17547i	−0.287307	+	0.0680930i
$299$	1.09840	−	0.114011i	0.0635221	−	0.00659342i
$300$	−7.78043	−	11.5988i	−0.449203	−	0.669657i
$301$	−0.738899	−	22.8534i	−0.0425894	−	1.31725i
$302$	1.12701	+	1.36089i	0.0648521	+	0.0783102i
$303$	1.25313	−	2.25056i	0.0719904	−	0.129291i
$304$	8.88234	+	14.5052i	0.509437	+	0.831930i
$305$	0.342972	−	0.336385i	0.0196385	−	0.0192613i
$306$	−12.7852	−	29.2183i	−0.730883	−	1.67030i
$307$	13.8330	−	20.1690i	0.789491	−	1.15111i	−0.195870	−	0.980630i	$-0.562753\pi$
$307$	13.8330	−	20.1690i	0.789491	−	1.15111i	0.985362	−	0.170477i	$-0.0545308\pi$
$308$	−5.96310	+	4.49956i	−0.339779	+	0.256386i
$309$	−0.198499	+	11.8304i	−0.0112922	+	0.673011i
$310$	−0.0706897	+	1.56116i	−0.00401491	+	0.0886681i
$311$	−1.02607	−	14.4059i	−0.0581833	−	0.816881i	−0.939107	−	0.343624i	$-0.888346\pi$
$311$	−1.02607	−	14.4059i	−0.0581833	−	0.816881i	0.880924	−	0.473257i	$-0.156922\pi$
$312$	−0.00314114	−	0.142704i	−0.000177832	−	0.00807905i
$313$	−11.1770	−	30.1016i	−0.631760	−	1.70144i	−0.709716	−	0.704487i	$-0.751177\pi$
$313$	−11.1770	−	30.1016i	−0.631760	−	1.70144i	0.0779563	−	0.996957i	$-0.475161\pi$
$314$	−5.67818	+	41.5716i	−0.320438	+	2.34602i
$315$	−6.08733	+	1.06562i	−0.342982	+	0.0600410i
$316$	−5.75011	+	26.5454i	−0.323469	+	1.49330i
$317$	3.74018	+	11.4106i	0.210069	+	0.640884i	0.999630	+	0.0272107i	$0.00866251\pi$
$317$	3.74018	+	11.4106i	0.210069	+	0.640884i	−0.789560	+	0.613673i	$0.789691\pi$
$318$	1.25975	−	0.596422i	0.0706430	−	0.0334457i
$319$	−1.26934	+	0.0657003i	−0.0710692	+	0.00367851i
$320$	−3.29752	−	1.29770i	−0.184337	−	0.0725434i
$321$	5.68755	−	18.3084i	0.317448	−	1.02187i
$322$	33.1678	+	28.5699i	1.84837	+	1.59214i
$323$	−3.64799	−	20.6888i	−0.202980	−	1.15116i
$324$	1.68088	+	15.5869i	0.0933825	+	0.865938i
$325$	−0.132694	+	0.752544i	−0.00736053	+	0.0417437i
$326$	−7.57866	+	6.19407i	−0.419743	+	0.343058i
$327$	−11.4434	+	25.7940i	−0.632820	+	1.42641i
$328$	−0.0788376	+	0.0264070i	−0.00435308	+	0.00145808i
$329$	4.64784	+	3.50712i	0.256244	+	0.193354i
$330$	−0.969004	−	2.39816i	−0.0533419	−	0.132015i
$331$	22.2208	−	11.8888i	1.22137	−	0.653469i	0.270397	−	0.962749i	$-0.412845\pi$
$331$	22.2208	−	11.8888i	1.22137	−	0.653469i	0.950971	+	0.309279i	$0.100088\pi$
$332$	1.70066	+	12.4511i	0.0933360	+	0.683340i
$333$	8.56816	+	11.0831i	0.469532	+	0.607348i
$334$	2.49250	−	4.73190i	0.136384	−	0.258918i
$335$	0.329322	−	0.0602658i	0.0179928	−	0.00329268i
$336$	18.5650	−	18.3039i	1.01280	−	0.998560i
$337$	−0.579347	−	0.598382i	−0.0315591	−	0.0325959i	0.702477	−	0.711707i	$-0.252078\pi$
$337$	−0.579347	−	0.598382i	−0.0315591	−	0.0325959i	−0.734036	+	0.679111i	$0.762366\pi$
$338$	−16.9835	+	18.4742i	−0.923781	+	1.00486i
$339$	25.3657	−	7.13255i	1.37767	−	0.387387i
$340$	4.26606	+	3.97302i	0.231360	+	0.215467i
$341$	0.419528	−	1.62871i	0.0227187	−	0.0881995i
$342$	−2.88706	+	21.9945i	−0.156115	+	1.18932i
$343$	−7.87314	+	3.57878i	−0.425110	+	0.193236i
$344$	−3.14005	+	1.23573i	−0.169300	+	0.0666260i
$345$	−5.83415	+	3.96845i	−0.314100	+	0.213654i
$346$	31.1510	+	5.70064i	1.67469	+	0.306468i
$347$	−0.947956	+	1.20688i	−0.0508889	+	0.0647889i	−0.811193	−	0.584778i	$-0.801182\pi$
$347$	−0.947956	+	1.20688i	−0.0508889	+	0.0647889i	0.760304	+	0.649567i	$0.225050\pi$
$348$	−2.97409	+	0.552302i	−0.159428	+	0.0296065i
$349$	−2.98698	−	10.4679i	−0.159889	−	0.560334i	−0.999844	−	0.0176765i	$-0.994373\pi$
$349$	−2.98698	−	10.4679i	−0.159889	−	0.560334i	0.839954	−	0.542657i	$-0.182582\pi$
$350$	−25.3087	+	16.6458i	−1.35281	+	0.889755i
$351$	0.524518	−	0.678681i	0.0279967	−	0.0362253i
$352$	8.05904	+	5.30052i	0.429548	+	0.282518i
$353$	8.46992	−	27.0153i	0.450808	−	1.43788i	−0.401992	−	0.915643i	$-0.631682\pi$
$353$	8.46992	−	27.0153i	0.450808	−	1.43788i	0.852800	−	0.522237i	$-0.174902\pi$
$354$	−7.73118	−	1.60133i	−0.410907	−	0.0851098i
$355$	−0.159052	−	0.225594i	−0.00844158	−	0.0119733i
$356$	12.4423	+	5.46275i	0.659441	+	0.289525i
$357$	−29.6162	+	12.6402i	−1.56746	+	0.668992i
$358$	9.92902	+	21.4738i	0.524765	+	1.13493i
$359$	−6.63175	−	3.65924i	−0.350010	−	0.193128i	0.298359	−	0.954454i	$-0.403561\pi$
$359$	−6.63175	−	3.65924i	−0.350010	−	0.193128i	−0.648369	+	0.761326i	$0.724549\pi$
$360$	0.449921	+	0.793327i	0.0237129	+	0.0418120i
$361$	1.58046	−	4.09350i	0.0831822	−	0.215447i
$362$	0.510769	+	0.149323i	0.0268454	+	0.00784827i
$363$	−2.86696	−	16.0143i	−0.150476	−	0.840532i
$364$	0.972627	−	0.0125752i	0.0509795	−	0.000659118i
$365$	0.242623	−	0.00313690i	0.0126995	−	0.000164193i
$366$	−2.02035	+	1.70430i	−0.105606	+	0.0890853i
$367$	15.8927	+	4.64623i	0.829591	+	0.242531i	0.667844	−	0.744301i	$-0.267217\pi$
$367$	15.8927	+	4.64623i	0.829591	+	0.242531i	0.161747	+	0.986832i	$0.448287\pi$
$368$	10.7212	−	27.7687i	0.558883	−	1.44754i
$369$	−0.468160	−	0.174489i	−0.0243714	−	0.00908353i
$370$	−4.81609	−	2.65741i	−0.250377	−	0.138152i
$371$	−0.590604	−	1.27732i	−0.0306626	−	0.0663150i
$372$	0.479982	−	3.97381i	0.0248859	−	0.206032i
$373$	−7.18718	−	3.15550i	−0.372138	−	0.163386i	0.207550	−	0.978224i	$-0.433451\pi$
$373$	−7.18718	−	3.15550i	−0.372138	−	0.163386i	−0.579688	+	0.814839i	$0.696826\pi$
$374$	−7.76594	−	11.0150i	−0.401567	−	0.569570i
$375$	−3.18864	−	9.64268i	−0.164661	−	0.497946i
$376$	0.257070	−	0.819940i	0.0132574	−	0.0422852i
$377$	0.138276	+	0.0909453i	0.00712155	+	0.00468392i
$378$	33.8379	−	3.33856i	1.74044	−	0.171717i
$379$	−26.9948	+	17.7548i	−1.38663	+	0.912002i	−0.999948	−	0.0102105i	$-0.996750\pi$
$379$	−26.9948	+	17.7548i	−1.38663	+	0.912002i	−0.386684	+	0.922212i	$0.626379\pi$
$380$	−1.11260	−	3.89912i	−0.0570752	−	0.200021i
$381$	4.14050	−	11.7055i	0.212124	−	0.599693i
$382$	−26.9599	+	34.3238i	−1.37939	+	1.75616i
$383$	17.2060	+	3.14869i	0.879183	+	0.160890i	0.600627	−	0.799529i	$-0.294918\pi$
$383$	17.2060	+	3.14869i	0.879183	+	0.160890i	0.278556	+	0.960420i	$0.410144\pi$
$384$	−6.17745	−	2.98311i	−0.315241	−	0.152231i
$385$	−2.43009	+	0.956330i	−0.123849	+	0.0487391i
$386$	−40.7801	+	18.5368i	−2.07565	+	0.943499i
$387$	−19.3416	−	6.09024i	−0.983187	−	0.309584i
$388$	−4.08488	+	15.8585i	−0.207379	+	0.805093i
$389$	−2.03790	−	1.89791i	−0.103326	−	0.0962280i	0.628162	−	0.778083i	$-0.283807\pi$
$389$	−2.03790	−	1.89791i	−0.103326	−	0.0962280i	−0.731488	+	0.681854i	$0.761174\pi$
$390$	−0.0831573	+	0.326368i	−0.00421083	+	0.0165263i
$391$	−24.8821	+	27.0662i	−1.25834	+	1.36879i
$392$	−1.54304	−	1.59374i	−0.0779353	−	0.0804958i
$393$	7.26017	+	2.00056i	0.366227	+	0.100915i
$394$	−13.4109	+	2.45419i	−0.675630	+	0.123640i
$395$	−4.42515	+	8.40093i	−0.222653	+	0.422697i
$396$	2.01496	+	6.31101i	0.101256	+	0.317140i
$397$	−2.92537	−	21.4175i	−0.146820	−	1.07491i	−0.905771	−	0.423767i	$-0.860708\pi$
$397$	−2.92537	−	21.4175i	−0.146820	−	1.07491i	0.758951	−	0.651148i	$-0.225712\pi$
$398$	−29.6161	+	15.8455i	−1.48452	+	0.794266i
$399$	22.1793	+	3.11643i	1.11036	+	0.156017i
$400$	16.4421	+	12.4067i	0.822106	+	0.620335i
$401$	16.3508	−	5.47678i	0.816520	−	0.273497i	0.121595	−	0.992580i	$-0.461199\pi$
$401$	16.3508	−	5.47678i	0.816520	−	0.273497i	0.694925	+	0.719083i	$0.255438\pi$
$402$	−1.83169	+	0.194969i	−0.0913566	+	0.00972415i
$403$	−0.169568	+	0.138589i	−0.00844680	+	0.00690360i
$404$	0.449851	−	2.55123i	0.0223809	−	0.126929i
$405$	−0.895172	+	5.40695i	−0.0444814	+	0.268674i
$406$	1.13926	+	6.46109i	0.0565407	+	0.320658i
$407$	4.48529	+	3.86351i	0.222327	+	0.191507i
$408$	3.22534	+	3.49007i	0.159678	+	0.172784i
$409$	−29.0295	−	11.4242i	−1.43542	−	0.564890i	−0.484625	−	0.874722i	$-0.661044\pi$
$409$	−29.0295	−	11.4242i	−1.43542	−	0.564890i	−0.950791	+	0.309832i	$0.899727\pi$
$410$	0.195914	−	0.0101405i	0.00967552	−	0.000500801i
$411$	27.7710	+	19.2044i	1.36984	+	0.947285i
$412$	3.70640	+	11.3076i	0.182601	+	0.557084i
$413$	−1.68759	+	7.79078i	−0.0830408	+	0.383359i
$414$	33.6449	−	19.3696i	1.65355	−	0.951963i
$415$	−0.594528	+	4.35272i	−0.0291842	+	0.213666i
$416$	−0.437199	−	1.17746i	−0.0214355	−	0.0577296i
$417$	−35.5887	−	19.5158i	−1.74279	−	0.955692i
$418$	0.665995	+	9.35044i	0.0325749	+	0.457345i
$419$	−1.35167	+	29.8513i	−0.0660336	+	1.45833i	0.649822	+	0.760086i	$0.274843\pi$
$419$	−1.35167	+	29.8513i	−0.0660336	+	1.45833i	−0.715856	+	0.698248i	$0.753963\pi$
$420$	−5.43381	+	3.01682i	−0.265143	+	0.147206i
$421$	−9.33698	+	7.04539i	−0.455057	+	0.343371i	−0.804873	−	0.593447i	$-0.797767\pi$
$421$	−9.33698	+	7.04539i	−0.455057	+	0.343371i	0.349816	+	0.936818i	$0.386244\pi$
$422$	−19.0324	+	27.7500i	−0.926484	+	1.35085i
$423$	4.29927	−	2.86000i	0.209038	−	0.139058i
$424$	−0.148270	+	0.145422i	−0.00720063	+	0.00706233i
$425$	−13.2858	−	21.6963i	−0.644458	−	1.05242i
$426$	0.779706	+	1.30328i	0.0377769	+	0.0631441i
$427$	1.70216	+	2.05539i	0.0823731	+	0.0994673i
$428$	−0.623060	−	19.2706i	−0.0301168	−	0.931480i
$429$	0.159726	−	0.325374i	0.00771166	−	0.0157092i
$430$	7.91955	−	0.822028i	0.381915	−	0.0396417i
$431$	−30.8952	+	7.32229i	−1.48817	+	0.352702i	−0.892691	−	0.450670i	$-0.851185\pi$
$431$	−30.8952	+	7.32229i	−1.48817	+	0.352702i	−0.595477	+	0.803372i	$0.703037\pi$
$432$	−9.86776	−	20.9091i	−0.474763	−	1.00599i
$433$	−14.2063	−	3.36695i	−0.682710	−	0.161805i	−0.125395	−	0.992107i	$-0.540020\pi$
$433$	−14.2063	−	3.36695i	−0.682710	−	0.161805i	−0.557314	+	0.830302i	$0.688168\pi$
$434$	−8.60894	−	1.11924i	−0.413243	−	0.0537252i
$435$	−1.05340	−	0.0928148i	−0.0505065	−	0.00445013i
$436$	−2.38202	+	28.2791i	−0.114078	+	1.35432i
$437$	24.5447	−	7.17564i	1.17413	−	0.343257i
$438$	−1.33247	−	0.0827547i	−0.0636681	−	0.00395417i
$439$	−2.87154	+	0.759488i	−0.137051	+	0.0362484i	−0.323578	−	0.946201i	$-0.604886\pi$
$439$	−2.87154	+	0.759488i	−0.137051	+	0.0362484i	0.186527	+	0.982450i	$0.440277\pi$
$440$	0.253411	+	0.290377i	0.0120809	+	0.0138432i
$441$	−1.18836	−	13.2773i	−0.0565884	−	0.632251i
$442$	−0.0340299	+	1.75457i	−0.00161864	+	0.0834564i
$443$	−0.407250	+	3.69101i	−0.0193490	+	0.175365i	−0.999768	−	0.0215598i	$-0.993137\pi$
$443$	−0.407250	+	3.69101i	−0.0193490	+	0.175365i	0.980419	+	0.196925i	$0.0630956\pi$
$444$	11.7911	+	7.71103i	0.559581	+	0.365949i
$445$	3.67820	+	3.00621i	0.174364	+	0.142508i
$446$	16.7919	−	14.4641i	0.795122	−	0.684897i
$447$	4.53440	+	0.517977i	0.214470	+	0.0244995i
$448$	8.72102	−	17.6485i	0.412029	−	0.833814i
$449$	−4.53556	+	5.19718i	−0.214046	+	0.245270i	−0.850412	−	0.526118i	$-0.823647\pi$
$449$	−4.53556	+	5.19718i	−0.214046	+	0.245270i	0.636365	+	0.771388i	$0.280437\pi$
$450$	6.50057	+	26.0657i	0.306440	+	1.22875i
$451$	−0.208593	−	0.0326234i	−0.00982226	−	0.00153617i
$452$	21.7561	−	15.1292i	1.02332	−	0.711620i
$453$	−0.535393	−	1.48878i	−0.0251550	−	0.0699491i
$454$	18.5075	+	37.4531i	0.868599	+	1.75776i
$455$	0.328741	+	0.0869481i	0.0154116	+	0.00407619i
$456$	−0.666409	−	3.23750i	−0.0312074	−	0.151610i
$457$	31.7828	+	16.4799i	1.48674	+	0.770895i	0.995003	−	0.0998499i	$-0.0318363\pi$
$457$	31.7828	+	16.4799i	1.48674	+	0.770895i	0.491735	+	0.870745i	$0.336363\pi$
$458$	2.71919	+	3.65251i	0.127059	+	0.170670i
$459$	1.88407	+	28.4947i	0.0879408	+	1.33002i
$460$	−4.23750	+	5.69195i	−0.197575	+	0.265389i
$461$	19.9584	−	9.70245i	0.929557	−	0.451888i	0.0904779	−	0.995898i	$-0.471161\pi$
$461$	19.9584	−	9.70245i	0.929557	−	0.451888i	0.839079	+	0.544010i	$0.183095\pi$
$462$	13.7270	−	4.24578i	0.638638	−	0.197531i
$463$	32.9530	−	6.91537i	1.53146	−	0.321385i	0.637823	−	0.770183i	$-0.279835\pi$
$463$	32.9530	−	6.91537i	1.53146	−	0.321385i	0.893633	+	0.448798i	$0.148148\pi$
$464$	3.87780	−	2.20555i	0.180022	−	0.102390i
$465$	0.534191	−	1.29331i	0.0247725	−	0.0599756i
$466$	0.552382	+	2.71954i	0.0255886	+	0.125980i
$467$	30.8651	−	2.39902i	1.42826	−	0.111013i	0.660057	−	0.751215i	$-0.270532\pi$
$467$	30.8651	−	2.39902i	1.42826	−	0.111013i	0.768207	+	0.640202i	$0.221149\pi$
$468$	0.274990	−	0.817627i	0.0127114	−	0.0377948i
$469$	0.180050	+	1.85108i	0.00831396	+	0.0854750i
$470$	−1.10317	+	1.70113i	−0.0508853	+	0.0784675i
$471$	17.4216	−	33.2849i	0.802744	−	1.53369i
$472$	1.16661	−	0.151669i	0.0536975	−	0.00698115i
$473$	−8.52316	−	0.884681i	−0.391895	−	0.0406777i
$474$	27.7404	−	44.2695i	1.27416	−	2.03336i
$475$	0.114385	+	17.6950i	0.00524835	+	0.811901i
$476$	−23.9820	+	21.7625i	−1.09921	+	0.997484i
$477$	−1.24228	+	0.119288i	−0.0568803	+	0.00546181i
$478$	−21.5562	−	40.9235i	−0.985959	−	1.87180i
$479$	8.54375	+	10.8774i	0.390374	+	0.497002i	0.941309	−	0.337547i	$-0.109597\pi$
$479$	8.54375	+	10.8774i	0.390374	+	0.497002i	−0.550935	+	0.834548i	$0.685729\pi$
$480$	6.02613	+	5.29998i	0.275054	+	0.241910i
$481$	−0.172913	−	0.751184i	−0.00788416	−	0.0342510i
$482$	−12.3763	+	20.2109i	−0.563724	+	0.920583i
$483$	−19.2473	−	34.1457i	−0.875781	−	1.55368i
$484$	−7.99691	−	14.2741i	−0.363496	−	0.648823i
$485$	−2.86244	+	4.95788i	−0.129977	+	0.225126i
$486$	7.13924	−	29.2971i	0.323842	−	1.32894i
$487$	7.72054	+	13.3724i	0.349851	+	0.605960i	0.986223	−	0.165423i	$-0.0528989\pi$
$487$	7.72054	+	13.3724i	0.349851	+	0.605960i	−0.636372	+	0.771383i	$0.719566\pi$
$488$	0.201316	−	0.338507i	0.00911316	−	0.0153235i
$489$	8.26594	−	2.91237i	0.373799	−	0.131702i
$490$	2.49902	+	4.59908i	0.112894	+	0.207765i
$491$	−13.0628	+	12.1655i	−0.589517	+	0.549021i	−0.918554	−	0.395296i	$-0.870642\pi$
$491$	−13.0628	+	12.1655i	−0.589517	+	0.549021i	0.329037	+	0.944317i	$0.393276\pi$
$492$	−0.502330	−	0.0116769i	−0.0226468	−	0.000526436i
$493$	−5.45445	+	0.780960i	−0.245656	+	0.0351727i
$494$	0.650837	−	1.03262i	0.0292825	−	0.0464599i
$495$	0.0869482	+	2.31433i	0.00390803	+	0.104021i
$496$	1.24971	+	5.76931i	0.0561137	+	0.259050i
$497$	1.32295	−	0.775250i	0.0593424	−	0.0347747i
$498$	5.05536	−	23.6367i	0.226536	−	1.05919i
$499$	−18.0157	+	24.8640i	−0.806493	+	1.11307i	0.184978	+	0.982743i	$0.440779\pi$
$499$	−18.0157	+	24.8640i	−0.806493	+	1.11307i	−0.991472	+	0.130324i	$0.958398\pi$
$500$	−6.20483	−	8.11340i	−0.277488	−	0.362842i
$501$	−3.53785	+	3.22734i	−0.158060	+	0.144187i
$502$	8.85329	+	17.3478i	0.395142	+	0.774272i
$503$	−9.15749	+	6.54538i	−0.408312	+	0.291844i	−0.767041	−	0.641598i	$-0.778272\pi$
$503$	−9.15749	+	6.54538i	−0.408312	+	0.291844i	0.358729	+	0.933442i	$0.383210\pi$
$504$	−4.60129	+	2.12066i	−0.204958	+	0.0944615i
$505$	0.390678	−	0.817034i	0.0173849	−	0.0363575i
$506$	12.2904	−	10.8666i	0.546376	−	0.483078i
$507$	19.9203	−	10.3952i	0.884691	−	0.461665i
$508$	0.0807177	−	12.4867i	0.00358127	−	0.554009i
$509$	−14.1238	−	15.7678i	−0.626026	−	0.698898i	0.344802	−	0.938675i	$-0.387946\pi$
$509$	−14.1238	−	15.7678i	−0.626026	−	0.698898i	−0.970828	+	0.239778i	$0.922925\pi$
$510$	−5.12312	−	9.97412i	−0.226855	−	0.441661i
$511$	−0.0957647	+	1.34452i	−0.00423638	+	0.0594779i
$512$	−29.2140	−	3.41463i	−1.29109	−	0.150907i
$513$	9.11868	−	17.6458i	0.402599	−	0.779080i
$514$	−47.0269	+	5.49665i	−2.07427	+	0.242447i
$515$	0.188168	+	4.15565i	0.00829169	+	0.183120i
$516$	−20.3850	+	0.580562i	−0.897400	+	0.0255578i
$517$	1.53795	−	1.54792i	0.0676389	−	0.0680776i
$518$	16.9559	−	25.4207i	0.744998	−	1.11692i
$519$	−24.5019	−	14.2722i	−1.07552	−	0.626481i
$520$	−0.00421220	−	0.0500067i	−0.000184717	−	0.00219294i
$521$	4.17914	+	10.8242i	0.183091	+	0.474218i	0.993794	−	0.111240i	$-0.0354823\pi$
$521$	4.17914	+	10.8242i	0.183091	+	0.474218i	−0.810702	+	0.585459i	$0.800914\pi$
$522$	5.74134	+	0.943260i	0.251292	+	0.0412854i
$523$	−11.4037	−	33.3287i	−0.498651	−	1.45736i	−0.852832	−	0.522185i	$-0.825117\pi$
$523$	−11.4037	−	33.3287i	−0.498651	−	1.45736i	0.354182	−	0.935177i	$-0.384759\pi$
$524$	7.55784	−	0.489234i	0.330166	−	0.0213723i
$525$	26.3758	−	6.32408i	1.15113	−	0.276005i
$526$	0.515108	+	2.71555i	0.0224598	+	0.118403i
$527$	1.17315	−	7.19610i	0.0511033	−	0.313467i
$528$	−5.85488	−	7.82167i	−0.254801	−	0.340395i
$529$	−17.5322	−	12.8769i	−0.762268	−	0.559866i
$530$	0.429049	−	0.236739i	0.0186367	−	0.0102833i
$531$	6.02427	+	3.69922i	0.261431	+	0.160532i
$532$	22.1026	−	4.34080i	0.958268	−	0.188198i
$533$	0.0193763	+	0.0195020i	0.000839283	+	0.000844726i
$534$	−18.9423	−	18.0094i	−0.819713	−	0.779344i
$535$	1.59677	−	6.54839i	0.0690345	−	0.283111i
$536$	0.248379	−	0.116800i	0.0107284	−	0.00504499i
$537$	−1.83324	−	21.1039i	−0.0791101	−	0.910700i
$538$	−0.0842208	+	0.110127i	−0.00363102	+	0.00474790i
$539$	−1.61560	−	5.39647i	−0.0695887	−	0.232442i
$540$	0.929511	+	5.43283i	0.0399998	+	0.233792i
$541$	−8.53475	+	28.5080i	−0.366937	+	1.22566i	0.552864	+	0.833272i	$0.313535\pi$
$541$	−8.53475	+	28.5080i	−0.366937	+	1.22566i	−0.919801	+	0.392385i	$0.871650\pi$
$542$	−19.4520	−	26.8463i	−0.835534	−	1.15315i
$543$	−0.384765	−	0.281054i	−0.0165118	−	0.0120612i
$544$	36.8705	+	19.7269i	1.58081	+	0.845782i
$545$	−3.45337	+	9.30054i	−0.147926	+	0.398391i
$546$	−1.76785	−	0.612499i	−0.0756572	−	0.0262126i
$547$	−7.80753	+	0.201922i	−0.333826	+	0.00863357i	−0.192404	−	0.981316i	$-0.561628\pi$
$547$	−7.80753	+	0.201922i	−0.333826	+	0.00863357i	−0.141422	+	0.989949i	$0.545167\pi$
$548$	32.7130	+	9.10628i	1.39743	+	0.389001i
$549$	2.21970	−	0.821080i	0.0947346	−	0.0350429i
$550$	4.89718	+	10.2416i	0.208816	+	0.436703i
$551$	3.52881	+	1.49520i	0.150333	+	0.0636977i
$552$	−3.79212	+	4.36829i	−0.161403	+	0.185927i
$553$	−44.4405	−	28.4128i	−1.88980	−	1.20824i
$554$	−5.12554	+	3.46687i	−0.217763	+	0.147293i
$555$	3.24812	+	3.70234i	0.137875	+	0.157155i
$556$	−40.2445	−	6.82826i	−1.70675	−	0.289583i
$557$	24.8897	−	10.1686i	1.05461	−	0.430856i	0.216458	−	0.976292i	$-0.430550\pi$
$557$	24.8897	−	10.1686i	1.05461	−	0.430856i	0.838152	+	0.545436i	$0.183636\pi$
$558$	−3.46377	+	6.87578i	−0.146633	+	0.291075i
$559$	0.826278	+	0.749807i	0.0349478	+	0.0317135i
$560$	6.11558	−	6.82746i	0.258430	−	0.288513i
$561$	3.19141	+	11.6379i	0.134742	+	0.491351i
$562$	27.6439	−	54.1677i	1.16609	−	2.28493i
$563$	3.58268	+	23.9194i	0.150992	+	1.00808i	0.926378	+	0.376594i	$0.122905\pi$
$563$	3.58268	+	23.9194i	0.150992	+	1.00808i	−0.775387	+	0.631487i	$0.782445\pi$
$564$	3.14388	−	4.13328i	0.132381	−	0.174043i
$565$	8.74541	−	3.05562i	0.367922	−	0.128551i
$566$	0.241591	−	0.202719i	0.0101548	−	0.00852092i
$567$	−29.5131	−	7.47640i	−1.23943	−	0.313979i
$568$	−0.173351	−	0.145459i	−0.00727365	−	0.00610332i
$569$	−29.0041	−	10.9833i	−1.21592	−	0.460445i	−0.338862	−	0.940836i	$-0.610042\pi$
$569$	−29.0041	−	10.9833i	−1.21592	−	0.460445i	−0.877054	+	0.480392i	$0.840495\pi$
$570$	−0.533747	+	7.78081i	−0.0223562	+	0.325902i
$571$	−6.08460	+	29.9563i	−0.254632	+	1.25363i	0.625996	+	0.779826i	$0.284692\pi$
$571$	−6.08460	+	29.9563i	−0.254632	+	1.25363i	−0.880629	+	0.473807i	$0.842880\pi$
$572$	0.0446589	−	0.361784i	0.00186728	−	0.0151269i
$573$	33.1412	−	20.7103i	1.38449	−	0.865186i
$574$	−0.0352170	+	1.08922i	−0.00146993	+	0.0454633i
$575$	24.4770	−	18.9711i	1.02076	−	0.791149i
$576$	−12.2090	−	12.4788i	−0.508708	−	0.519951i
$577$	3.02524	+	4.79988i	0.125943	+	0.199822i	0.903037	−	0.429562i	$-0.141332\pi$
$577$	3.02524	+	4.79988i	0.125943	+	0.199822i	−0.777095	+	0.629384i	$0.783307\pi$
$578$	−16.5435	−	19.4590i	−0.688121	−	0.809387i
$579$	39.9806	−	3.21276i	1.66154	−	0.133518i
$580$	−1.03158	+	0.258618i	−0.0428339	+	0.0107385i
$581$	−23.8175	−	5.32061i	−0.988116	−	0.220736i
$582$	17.7478	−	26.0226i	0.735672	−	1.07867i
$583$	−0.504234	+	0.154516i	−0.0208832	+	0.00639941i
$584$	0.191640	−	0.0533466i	0.00793011	−	0.00220750i
$585$	0.169264	−	0.249581i	0.00699818	−	0.0103189i
$586$	6.21223	−	63.8674i	0.256625	−	2.63834i
$587$	−29.7178	−	23.6543i	−1.22659	−	0.976318i	−0.999997	−	0.00232806i	$-0.999259\pi$
$587$	−29.7178	−	23.6543i	−1.22659	−	0.976318i	−0.226589	−	0.973990i	$-0.572758\pi$
$588$	−5.50065	−	12.2258i	−0.226843	−	0.504185i
$589$	−3.28481	+	3.86368i	−0.135348	+	0.159200i
$590$	−2.74778	−	0.393423i	−0.113124	−	0.0161970i
$591$	12.0407	+	2.01056i	0.495289	+	0.0827032i
$592$	−20.1540	−	5.05265i	−0.828325	−	0.207662i
$593$	6.39224	+	3.21031i	0.262498	+	0.131831i	0.575181	−	0.818026i	$-0.304932\pi$
$593$	6.39224	+	3.21031i	0.262498	+	0.131831i	−0.312683	+	0.949857i	$0.601228\pi$
$594$	0.476500	−	12.7337i	0.0195510	−	0.522469i
$595$	−10.1169	+	5.08090i	−0.414753	+	0.208297i
$596$	4.47948	−	1.00067i	0.183487	−	0.0409892i
$597$	29.7602	−	4.34048i	1.21800	−	0.177644i
$598$	−2.12742	+	0.193056i	−0.0869968	+	0.00789465i
$599$	−1.87259	−	16.9717i	−0.0765118	−	0.693446i	−0.969790	−	0.243942i	$-0.921559\pi$
$599$	−1.87259	−	16.9717i	−0.0765118	−	0.693446i	0.893278	−	0.449504i	$-0.148399\pi$
$600$	−2.18672	−	3.35278i	−0.0892724	−	0.136877i
$601$	3.46490	+	0.314427i	0.141336	+	0.0128258i	0.160815	−	0.986985i	$-0.448588\pi$
$601$	3.46490	+	0.314427i	0.141336	+	0.0128258i	−0.0194791	+	0.999810i	$0.506201\pi$
$602$	0.857693	+	44.2224i	0.0349569	+	1.80237i
$603$	1.60192	+	0.392709i	0.0652351	+	0.0159923i
$604$	−0.998936	−	1.23849i	−0.0406461	−	0.0503933i
$605$	−1.35502	−	5.55695i	−0.0550894	−	0.225922i
$606$	−2.48014	+	4.32179i	−0.100749	+	0.175561i
$607$	11.3073	−	20.1830i	0.458949	−	0.819201i	−0.540811	−	0.841144i	$-0.681882\pi$
$607$	11.3073	−	20.1830i	0.458949	−	0.819201i	0.999759	+	0.0219432i	$0.00698531\pi$
$608$	−14.8669	−	24.9983i	−0.602934	−	1.01381i
$609$	1.00495	−	5.78786i	0.0407228	−	0.234536i
$610$	−0.671803	+	0.642072i	−0.0272005	+	0.0259967i
$611$	−0.280715	+	0.0439030i	−0.0113565	+	0.00177613i
$612$	11.1719	+	26.4575i	0.451598	+	1.06948i
$613$	35.1482	−	21.2121i	1.41962	−	0.856748i	0.420893	−	0.907110i	$-0.361717\pi$
$613$	35.1482	−	21.2121i	1.41962	−	0.856748i	0.998731	+	0.0503625i	$0.0160377\pi$
$614$	−27.2608	+	38.6658i	−1.10016	+	1.56043i
$615$	−0.168081	−	0.0510257i	−0.00677767	−	0.00205756i
$616$	−1.72556	+	1.26738i	−0.0695247	+	0.0510641i
$617$	11.2478	−	24.3260i	0.452821	−	0.979330i	−0.537848	−	0.843042i	$-0.680763\pi$
$617$	11.2478	−	24.3260i	0.452821	−	0.979330i	0.990669	−	0.136288i	$-0.0435172\pi$
$618$	0.679801	−	22.8780i	0.0273456	−	0.920287i
$619$	20.7340	+	22.5539i	0.833369	+	0.906517i	0.996792	−	0.0800387i	$-0.0255044\pi$
$619$	20.7340	+	22.5539i	0.833369	+	0.906517i	−0.163422	+	0.986556i	$0.552253\pi$
$620$	0.0818247	−	1.40488i	0.00328616	−	0.0564212i
$621$	−34.2246	+	6.08350i	−1.37338	+	0.244122i
$622$	1.62441	+	27.8901i	0.0651330	+	1.11829i
$623$	−18.3561	+	18.9592i	−0.735422	+	0.759584i
$624$	0.0115509	+	1.27214i	0.000462406	+	0.0509265i
$625$	7.28605	+	18.1687i	0.291442	+	0.726749i
$626$	20.8662	+	58.5033i	0.833981	+	2.33826i
$627$	2.28202	−	8.07735i	0.0911350	−	0.322578i
$628$	5.59669	−	37.3657i	0.223332	−	1.49105i
$629$	20.8783	+	14.9229i	0.832473	+	0.595016i
$630$	11.8010	−	1.90894i	0.470164	−	0.0760539i
$631$	1.45527	+	1.42732i	0.0579334	+	0.0568206i	0.728607	−	0.684932i	$-0.240168\pi$
$631$	1.45527	+	1.42732i	0.0579334	+	0.0568206i	−0.670674	+	0.741752i	$0.733995\pi$
$632$	−1.74620	+	7.58601i	−0.0694603	+	0.301755i
$633$	24.4661	−	17.5842i	0.972439	−	0.698908i
$634$	−6.94905	−	22.1644i	−0.275982	−	0.880261i
$635$	1.19781	−	4.19773i	0.0475336	−	0.166582i
$636$	−1.14124	+	0.522364i	−0.0452532	+	0.0207131i
$637$	−0.246409	+	0.690866i	−0.00976308	+	0.0273731i
$638$	2.45685	−	0.0953368i	0.0972675	−	0.00377442i
$639$	−0.260412	−	1.33467i	−0.0103018	−	0.0527989i
$640$	−2.23269	−	0.912153i	−0.0882547	−	0.0360560i
$641$	40.6837	+	25.2760i	1.60691	+	0.998342i	0.974692	+	0.223552i	$0.0717653\pi$
$641$	40.6837	+	25.2760i	1.60691	+	0.998342i	0.632219	+	0.774789i	$0.282144\pi$
$642$	−11.4590	+	35.2706i	−0.452249	+	1.39202i
$643$	−10.8840	+	4.61167i	−0.429222	+	0.181867i	−0.594002	−	0.804464i	$-0.702453\pi$
$643$	−10.8840	+	4.61167i	−0.429222	+	0.181867i	0.164780	+	0.986330i	$0.447309\pi$
$644$	−29.5323	−	26.1110i	−1.16374	−	1.02892i
$645$	−6.91971	−	1.71556i	−0.272463	−	0.0675501i
$646$	6.53871	+	40.1084i	0.257262	+	1.57804i
$647$	−22.9872	+	8.36667i	−0.903721	+	0.328928i	−0.751743	−	0.659456i	$-0.770787\pi$
$647$	−22.9872	+	8.36667i	−0.903721	+	0.328928i	−0.151978	+	0.988384i	$0.548564\pi$
$648$	0.423951	+	4.47307i	0.0166544	+	0.175719i
$649$	2.80721	+	1.02174i	0.110192	+	0.0401068i
$650$	0.275482	−	1.45228i	0.0108053	−	0.0569633i
$651$	6.91009	+	3.56008i	0.270828	+	0.139531i
$652$	6.89607	−	5.48902i	0.270071	−	0.214967i
$653$	10.6990	+	16.4984i	0.418686	+	0.645633i	0.983777	−	0.179395i	$-0.0574141\pi$
$653$	10.6990	+	16.4984i	0.418686	+	0.645633i	−0.565091	+	0.825029i	$0.691159\pi$
$654$	22.7793	−	49.6057i	0.890742	−	1.93974i
$655$	2.59120	+	0.543779i	0.101247	+	0.0212472i
$656$	0.705644	−	0.226256i	0.0275508	−	0.00883379i
$657$	1.09704	+	0.474821i	0.0427995	+	0.0185246i
$658$	−8.90235	−	6.89984i	−0.347050	−	0.268984i
$659$	19.8469	−	23.9656i	0.773127	−	0.933566i	−0.226051	−	0.974115i	$-0.572582\pi$
$659$	19.8469	−	23.9656i	0.773127	−	0.933566i	0.999178	+	0.0405494i	$0.0129108\pi$
$660$	0.844591	+	2.17063i	0.0328756	+	0.0844917i
$661$	−12.3464	−	6.00198i	−0.480218	−	0.233450i	0.181230	−	0.983441i	$-0.441992\pi$
$661$	−12.3464	−	6.00198i	−0.480218	−	0.233450i	−0.661448	+	0.749991i	$0.730058\pi$
$662$	−43.2778	+	22.4402i	−1.68204	+	0.872163i
$663$	0.562121	−	1.46734i	0.0218310	−	0.0569867i
$664$	0.441238	+	3.57449i	0.0171233	+	0.138717i
$665$	7.85068	+	0.610203i	0.304436	+	0.0236626i
$666$	−16.2957	−	21.6516i	−0.631447	−	0.838983i
$667$	−1.67305	−	6.49516i	−0.0647806	−	0.251494i
$668$	−2.29938	+	4.23167i	−0.0889657	+	0.163728i
$669$	−18.5397	+	7.07615i	−0.716787	+	0.273580i
$670$	−0.638495	+	0.108333i	−0.0246672	+	0.00418527i
$671$	0.849514	−	0.527786i	0.0327951	−	0.0203749i
$672$	−32.1482	+	30.8868i	−1.24014	+	1.19148i
$673$	10.2658	−	22.9773i	0.395717	−	0.885711i	−0.600566	−	0.799575i	$-0.705058\pi$
$673$	10.2658	−	22.9773i	0.395717	−	0.885711i	0.996283	−	0.0861364i	$-0.0274521\pi$
$674$	1.10563	+	1.17190i	0.0425874	+	0.0451400i
$675$	2.45032	−	23.9288i	0.0943128	−	0.921020i
$676$	15.5073	−	16.4368i	0.596435	−	0.632185i
$677$	1.84951	+	4.44478i	0.0710823	+	0.170827i	0.954842	−	0.297115i	$-0.0960245\pi$
$677$	1.84951	+	4.44478i	0.0710823	+	0.170827i	−0.883759	+	0.467942i	$0.844996\pi$
$678$	−49.2417	+	13.1617i	−1.89112	+	0.505473i
$679$	−26.1100	−	18.1569i	−1.00201	−	0.696799i
$680$	1.20784	+	1.15438i	0.0463184	+	0.0442685i
$681$	−4.19957	−	37.1697i	−0.160928	−	1.42435i
$682$	−0.852199	+	3.13982i	−0.0326324	+	0.120230i
$683$	−7.82744	+	22.8765i	−0.299508	+	0.875347i	0.689077	+	0.724688i	$0.258016\pi$
$683$	−7.82744	+	22.8765i	−0.299508	+	0.875347i	−0.988586	+	0.150659i	$0.951861\pi$
$684$	2.85561	−	19.7706i	0.109187	−	0.755948i
$685$	10.1634	+	6.13364i	0.388324	+	0.234355i
$686$	15.3181	−	6.72534i	0.584846	−	0.256775i
$687$	−1.17957	−	3.90286i	−0.0450034	−	0.148903i
$688$	28.1266	−	10.6510i	1.07231	−	0.406066i
$689$	0.0648273	+	0.0226505i	0.00246972	+	0.000862914i
$690$	11.3839	−	7.53004i	0.433378	−	0.286664i
$691$	−2.50385	−	3.75384i	−0.0952510	−	0.142803i	0.781223	−	0.624252i	$-0.214596\pi$
$691$	−2.50385	−	3.75384i	−0.0952510	−	0.142803i	−0.876474	+	0.481449i	$0.840111\pi$
$692$	−27.9826	−	5.49560i	−1.06374	−	0.208911i
$693$	−12.8517	−	0.597809i	−0.488194	−	0.0227089i
$694$	1.86376	−	2.31070i	0.0707473	−	0.0877129i
$695$	−12.9134	−	6.07253i	−0.489835	−	0.230344i
$696$	−0.854354	+	0.147257i	−0.0323842	+	0.00558178i
$697$	−0.913355	−	0.0591233i	−0.0345958	−	0.00223945i
$698$	5.51576	+	20.3221i	0.208775	+	0.769204i
$699$	0.361640	−	2.45832i	0.0136785	−	0.0929823i
$700$	22.9822	−	14.6935i	0.868645	−	0.555363i
$701$	15.9438	−	36.9619i	0.602189	−	1.39603i	−0.295475	−	0.955350i	$-0.595478\pi$
$701$	15.9438	−	36.9619i	0.602189	−	1.39603i	0.897664	−	0.440681i	$-0.145263\pi$
$702$	−1.03152	+	1.29962i	−0.0389321	+	0.0490509i
$703$	−7.06999	−	16.3901i	−0.266650	−	0.618163i
$704$	−6.11077	−	4.13327i	−0.230308	−	0.155779i
$705$	1.44629	−	1.09727i	0.0544705	−	0.0413257i
$706$	−17.0585	+	52.0423i	−0.642004	+	1.95864i
$707$	4.34058	+	2.54358i	0.163244	+	0.0956613i
$708$	6.94265	+	1.53187i	0.260921	+	0.0575712i
$709$	−17.5998	−	5.89513i	−0.660974	−	0.221396i	−0.0327910	−	0.999462i	$-0.510440\pi$
$709$	−17.5998	−	5.89513i	−0.660974	−	0.221396i	−0.628183	+	0.778066i	$0.716201\pi$
$710$	0.302003	+	0.440330i	0.0113340	+	0.0165253i
$711$	−36.8225	+	28.8492i	−1.38095	+	1.08193i
$712$	3.54544	+	1.61160i	0.132871	+	0.0603973i
$713$	8.86327	+	0.458759i	0.331932	+	0.0171807i
$714$	57.6011	−	23.7086i	2.15567	−	0.887273i
$715$	0.0489573	−	0.117655i	0.00183090	−	0.00440006i
$716$	−8.69028	−	19.4510i	−0.324771	−	0.726917i
$717$	5.71208	+	41.0194i	0.213321	+	1.53190i
$718$	12.7359	+	7.24371i	0.475299	+	0.270333i
$719$	35.0654	+	11.2433i	1.30772	+	0.419304i	0.875829	−	0.482622i	$-0.160316\pi$
$719$	35.0654	+	11.2433i	1.30772	+	0.419304i	0.431891	+	0.901926i	$0.357846\pi$
$720$	−3.91829	−	7.12197i	−0.146026	−	0.265420i
$721$	−23.0916	−	0.896058i	−0.859975	−	0.0333709i
$722$	−3.15936	+	7.87829i	−0.117579	+	0.293200i
$723$	16.5682	−	13.2586i	0.616176	−	0.493092i
$724$	−0.458167	−	0.140400i	−0.0170276	−	0.00521791i
$725$	4.63968	+	0.119994i	0.172313	+	0.00445645i
$726$	5.14490	+	31.0472i	0.190945	+	1.15227i
$727$	−4.22562	−	0.0546334i	−0.156720	−	0.00202624i	−0.0654716	−	0.997854i	$-0.520855\pi$
$727$	−4.22562	−	0.0546334i	−0.156720	−	0.00202624i	−0.0912481	+	0.995828i	$0.529086\pi$
$728$	0.278779			0.0103322
$729$	−14.9201	+	22.5031i	−0.552596	+	0.833449i
$730$	−0.469370			−0.0173722
$731$	−37.1442	−	0.480241i	−1.37383	−	0.0177623i
$732$	1.83900	−	1.51107i	0.0679716	−	0.0558506i
$733$	32.6641	+	0.844775i	1.20648	+	0.0312025i	0.623854	−	0.781541i	$-0.285566\pi$
$733$	32.6641	+	0.844775i	1.20648	+	0.0312025i	0.582622	+	0.812743i	$0.302027\pi$
$734$	−30.6241	−	9.38437i	−1.13036	−	0.346383i
$735$	−0.706349	−	4.63311i	−0.0260541	−	0.170895i
$736$	−18.9457	+	47.2436i	−0.698348	+	1.74142i
$737$	0.696456	+	0.0270257i	0.0256543	+	0.000995504i
$738$	0.901171	+	0.349211i	0.0331726	+	0.0128547i
$739$	21.0489	+	6.74906i	0.774296	+	0.248268i	0.666101	−	0.745862i	$-0.267962\pi$
$739$	21.0489	+	6.74906i	0.774296	+	0.248268i	0.108195	+	0.994130i	$0.465493\pi$
$740$	4.30556	+	2.44885i	0.158276	+	0.0900214i
$741$	−0.862089	+	0.671786i	−0.0316696	+	0.0246787i
$742$	1.11043	+	2.48541i	0.0407651	+	0.0912423i
$743$	−12.9008	+	31.0035i	−0.473284	+	1.13741i	0.490671	+	0.871345i	$0.336752\pi$
$743$	−12.9008	+	31.0035i	−0.473284	+	1.13741i	−0.963956	+	0.266063i	$0.914277\pi$
$744$	0.152276	−	1.13702i	0.00558269	−	0.0416853i
$745$	1.60242	+	0.0829404i	0.0587080	+	0.00303870i
$746$	13.8228	+	6.28324i	0.506090	+	0.230046i
$747$	−11.4441	+	18.3696i	−0.418718	+	0.672110i
$748$	6.86436	+	10.0085i	0.250986	+	0.365946i
$749$	35.5044	+	11.8924i	1.29730	+	0.434538i
$750$	5.92645	+	18.7310i	0.216403	+	0.683960i
$751$	20.1346	+	11.7989i	0.734722	+	0.430548i	0.824828	−	0.565384i	$-0.191272\pi$
$751$	20.1346	+	11.7989i	0.734722	+	0.430548i	−0.0901057	+	0.995932i	$0.528720\pi$
$752$	−2.38548	+	7.27768i	−0.0869896	+	0.265390i
$753$	−2.18172	−	17.3020i	−0.0795065	−	0.630519i
$754$	−0.265184	−	0.179368i	−0.00965744	−	0.00653220i
$755$	−0.220315	−	0.510748i	−0.00801810	−	0.0185880i
$756$	−30.5072	+	2.61217i	−1.10953	+	0.0950037i
$757$	−4.68670	+	10.8650i	−0.170341	+	0.394895i	−0.981906	−	0.189366i	$-0.939357\pi$
$757$	−4.68670	+	10.8650i	−0.170341	+	0.394895i	0.811565	+	0.584262i	$0.198616\pi$
$758$	52.6586	−	33.6670i	1.91264	−	1.22284i
$759$	−13.6548	+	5.41495i	−0.495637	+	0.196550i
$760$	−0.304399	−	1.12152i	−0.0110417	−	0.0406818i
$761$	9.22008	+	0.596834i	0.334228	+	0.0216352i	0.230798	−	0.973002i	$-0.425866\pi$
$761$	9.22008	+	0.596834i	0.334228	+	0.0216352i	0.103429	+	0.994637i	$0.467018\pi$
$762$	−8.30147	+	22.5378i	−0.300730	+	0.816459i
$763$	−49.8735	−	23.4529i	−1.80554	−	0.849053i
$764$	24.6748	−	30.5919i	0.892701	−	1.10678i
$765$	1.28211	+	9.95776i	0.0463548	+	0.360023i
$766$	−33.2017	−	6.52061i	−1.19963	−	0.235599i
$767$	−0.215849	−	0.323606i	−0.00779384

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.k (of order \(243\), degree \(162\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.93424 - 0.0250080i) q^{2} +(1.62140 + 0.609150i) q^{3} +(1.74134 + 0.0450353i) q^{4} +(0.582227 + 0.178416i) q^{5} +(-3.12095 - 1.21879i) q^{6} +(-1.25911 + 3.13976i) q^{7} +(0.498860 + 0.0193580i) q^{8} +(2.25787 + 1.97535i) q^{9} +O(q^{10})\)	\(q+(-1.93424 - 0.0250080i) q^{2} +(1.62140 + 0.609150i) q^{3} +(1.74134 + 0.0450353i) q^{4} +(0.582227 + 0.178416i) q^{5} +(-3.12095 - 1.21879i) q^{6} +(-1.25911 + 3.13976i) q^{7} +(0.498860 + 0.0193580i) q^{8} +(2.25787 + 1.97535i) q^{9} +(-1.12171 - 0.359660i) q^{10} +(1.10197 + 0.626758i) q^{11} +(2.79597 + 1.13375i) q^{12} +(-0.0673362 - 0.150715i) q^{13} +(2.51394 - 6.04157i) q^{14} +(0.835340 + 0.643947i) q^{15} +(-4.44361 - 0.230000i) q^{16} +(5.00315 + 2.27421i) q^{17} +(-4.31787 - 3.87727i) q^{18} +(-2.16207 - 3.15237i) q^{19} +(1.00582 + 0.336903i) q^{20} +(-3.95411 + 4.32382i) q^{21} +(-2.11580 - 1.23986i) q^{22} +(-2.08370 + 6.35698i) q^{23} +(0.797059 + 0.335268i) q^{24} +(-3.83441 - 2.59356i) q^{25} +(0.126475 + 0.293203i) q^{26} +(2.45763 + 4.57821i) q^{27} +(-2.33393 + 5.41067i) q^{28} +(-0.844715 + 0.540064i) q^{29} +(-1.59965 - 1.26644i) q^{30} +(-0.347508 - 1.28035i) q^{31} +(7.59288 + 0.491502i) q^{32} +(1.40494 + 1.68749i) q^{33} +(-9.62043 - 4.52399i) q^{34} +(-1.29327 + 1.60341i) q^{35} +(3.84275 + 3.54143i) q^{36} +(4.58208 + 0.899892i) q^{37} +(4.10313 + 6.15152i) q^{38} +(-0.0173710 - 0.285387i) q^{39} +(0.286996 + 0.100275i) q^{40} +(-0.155747 + 0.0589785i) q^{41} +(7.75633 - 8.26442i) q^{42} +(-6.18902 + 2.71727i) q^{43} +(1.89067 + 1.14102i) q^{44} +(0.962160 + 1.55294i) q^{45} +(4.18935 - 12.2438i) q^{46} +(0.450856 - 1.66112i) q^{47} +(-7.06476 - 3.07974i) q^{48} +(-3.21227 - 3.07011i) q^{49} +(7.35183 + 5.11247i) q^{50} +(6.72677 + 6.73507i) q^{51} +(-0.110467 - 0.265478i) q^{52} +(-0.285476 + 0.302587i) q^{53} +(-4.63916 - 8.91684i) q^{54} +(0.529770 + 0.561524i) q^{55} +(-0.688900 + 1.54193i) q^{56} +(-1.58531 - 6.42828i) q^{57} +(1.64739 - 1.02349i) q^{58} +(2.32325 - 0.394185i) q^{59} +(1.42561 + 1.15895i) q^{60} +(0.376654 - 0.693176i) q^{61} +(0.640146 + 2.48520i) q^{62} +(-9.04504 + 4.60199i) q^{63} +(-5.80182 - 0.450953i) q^{64} +(-0.0123150 - 0.0997641i) q^{65} +(-2.67529 - 3.29914i) q^{66} +(0.488074 - 0.253073i) q^{67} +(8.60974 + 4.18548i) q^{68} +(-7.25086 + 9.03792i) q^{69} +(2.54160 - 3.06903i) q^{70} +(-0.358270 - 0.277680i) q^{71} +(1.08812 + 1.02913i) q^{72} +(0.379435 - 0.121661i) q^{73} +(-8.84036 - 1.85520i) q^{74} +(-4.63725 - 6.54094i) q^{75} +(-3.62292 - 5.58671i) q^{76} +(-3.35537 + 2.67075i) q^{77} +(0.0264627 + 0.552442i) q^{78} +(-2.90592 + 15.3195i) q^{79} +(-2.54615 - 0.926724i) q^{80} +(1.19598 + 8.92018i) q^{81} +(0.302727 - 0.110184i) q^{82} +(1.16079 + 7.12027i) q^{83} +(-7.08015 + 7.35114i) q^{84} +(2.50721 + 2.21675i) q^{85} +(12.0390 - 5.10108i) q^{86} +(-1.69860 + 0.361101i) q^{87} +(0.537594 + 0.333996i) q^{88} +(7.22157 + 2.95034i) q^{89} +(-1.82221 - 3.02783i) q^{90} +(0.557992 - 0.0216526i) q^{91} +(-3.91470 + 10.9758i) q^{92} +(0.216476 - 2.28765i) q^{93} +(-0.913605 + 3.20174i) q^{94} +(-0.696380 - 2.22114i) q^{95} +(12.0117 + 5.42212i) q^{96} +(-2.10889 + 9.16163i) q^{97} +(6.13652 + 6.01866i) q^{98} +(1.25003 + 3.59191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Introduction

L-functions

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