LMFDB - Embedded newform 162.2.g.b.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			25.5
Character	$\chi$	$=$	162.25
Dual form			162.2.g.b.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.893633 - 0.448799i) q^{2} +(1.51179 - 0.845280i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-0.379535 + 1.26773i) q^{5} +(0.971622 - 1.43386i) q^{6} +(-0.768169 + 1.78082i) q^{7} +(0.173648 - 0.984808i) q^{8} +(1.57100 - 2.55577i) q^{9} +O(q^{10})$	\(q+(0.893633 - 0.448799i) q^{2} +(1.51179 - 0.845280i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-0.379535 + 1.26773i) q^{5} +(0.971622 - 1.43386i) q^{6} +(-0.768169 + 1.78082i) q^{7} +(0.173648 - 0.984808i) q^{8} +(1.57100 - 2.55577i) q^{9} +(0.229793 + 1.30322i) q^{10} +(-2.10911 - 0.499867i) q^{11} +(0.224758 - 1.71741i) q^{12} +(-1.69934 + 1.11767i) q^{13} +(0.112768 + 1.93615i) q^{14} +(0.497815 + 2.23736i) q^{15} +(-0.286803 - 0.957990i) q^{16} +(-7.02180 - 2.55572i) q^{17} +(0.256873 - 2.98898i) q^{18} +(2.13356 - 0.776551i) q^{19} +(0.790236 + 1.06147i) q^{20} +(0.343980 + 3.34153i) q^{21} +(-2.10911 + 0.499867i) q^{22} +(1.34938 + 3.12822i) q^{23} +(-0.569919 - 1.63560i) q^{24} +(2.71434 + 1.78525i) q^{25} +(-1.01697 + 1.76145i) q^{26} +(0.214683 - 5.19172i) q^{27} +(0.969715 + 1.67960i) q^{28} +(-0.282496 + 4.85027i) q^{29} +(1.44899 + 1.77596i) q^{30} +(5.07563 + 0.593256i) q^{31} +(-0.686242 - 0.727374i) q^{32} +(-3.61105 + 1.02709i) q^{33} +(-7.42191 + 0.867497i) q^{34} +(-1.96605 - 1.64972i) q^{35} +(-1.11190 - 2.78634i) q^{36} +(4.70814 - 3.95060i) q^{37} +(1.55810 - 1.65149i) q^{38} +(-1.62429 + 3.12610i) q^{39} +(1.18257 + 0.593908i) q^{40} +(-6.98634 - 3.50867i) q^{41} +(1.80707 + 2.83173i) q^{42} +(-4.77609 + 5.06236i) q^{43} +(-1.66043 + 1.39326i) q^{44} +(2.64378 + 2.96162i) q^{45} +(2.60979 + 2.18988i) q^{46} +(4.18562 - 0.489229i) q^{47} +(-1.24336 - 1.20585i) q^{48} +(2.22247 + 2.35568i) q^{49} +(3.22684 + 0.377163i) q^{50} +(-12.7758 + 2.07167i) q^{51} +(-0.118264 + 2.03051i) q^{52} +(-5.39818 - 9.34993i) q^{53} +(-2.13819 - 4.73584i) q^{54} +(1.43418 - 2.48407i) q^{55} +(1.62037 + 1.06573i) q^{56} +(2.56908 - 2.97743i) q^{57} +(1.92435 + 4.46115i) q^{58} +(6.72062 - 1.59282i) q^{59} +(2.09191 + 0.936749i) q^{60} +(-5.37986 - 7.22641i) q^{61} +(4.80200 - 1.74779i) q^{62} +(3.34456 + 4.76093i) q^{63} +(-0.939693 - 0.342020i) q^{64} +(-0.771954 - 2.57851i) q^{65} +(-2.76599 + 2.53848i) q^{66} +(0.661912 + 11.3646i) q^{67} +(-6.24313 + 4.10617i) q^{68} +(4.68420 + 3.58860i) q^{69} +(-2.49732 - 0.591876i) q^{70} +(0.518333 + 2.93961i) q^{71} +(-2.24414 - 1.99094i) q^{72} +(1.80390 - 10.2304i) q^{73} +(2.43432 - 5.64339i) q^{74} +(5.61253 + 0.404540i) q^{75} +(0.651182 - 2.17510i) q^{76} +(2.51032 - 3.37195i) q^{77} +(-0.0485295 + 3.52257i) q^{78} +(9.16461 - 4.60264i) q^{79} +1.32333 q^{80} +(-4.06390 - 8.03024i) q^{81} -7.81791 q^{82} +(3.24547 - 1.62994i) q^{83} +(2.88573 + 1.71951i) q^{84} +(5.90499 - 7.93178i) q^{85} +(-1.99609 + 6.66740i) q^{86} +(3.67276 + 7.57137i) q^{87} +(-0.858516 + 1.99026i) q^{88} +(1.42927 - 8.10577i) q^{89} +(3.69174 + 1.46007i) q^{90} +(-0.684990 - 3.88477i) q^{91} +(3.31501 + 0.785672i) q^{92} +(8.17474 - 3.39345i) q^{93} +(3.52084 - 2.31569i) q^{94} +(0.174701 + 2.99951i) q^{95} +(-1.65229 - 0.519568i) q^{96} +(-2.30761 - 7.70796i) q^{97} +(3.04330 + 1.10767i) q^{98} +(-4.59096 + 4.60509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

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 $

$2$	0.893633	−	0.448799i	0.631894	−	0.317349i
$2$	0.893633	−	0.448799i	0.631894	−	0.317349i
$3$	1.51179	−	0.845280i	0.872831	−	0.488023i
$3$	1.51179	−	0.845280i	0.872831	−	0.488023i
$4$	0.597159	−	0.802123i	0.298579	−	0.401062i
$5$	−0.379535	+	1.26773i	−0.169733	+	0.566948i	0.830222	+	0.557433i	$0.188214\pi$
$5$	−0.379535	+	1.26773i	−0.169733	+	0.566948i	−0.999955	+	0.00951452i	$0.996971\pi$
$6$	0.971622	−	1.43386i	0.396663	−	0.585370i
$7$	−0.768169	+	1.78082i	−0.290341	+	0.673085i	−0.999489	−	0.0319744i	$-0.989821\pi$
$7$	−0.768169	+	1.78082i	−0.290341	+	0.673085i	0.709148	+	0.705060i	$0.249080\pi$
$8$	0.173648	−	0.984808i	0.0613939	−	0.348182i
$9$	1.57100	−	2.55577i	0.523668	−	0.851923i
$10$	0.229793	+	1.30322i	0.0726671	+	0.412115i
$11$	−2.10911	−	0.499867i	−0.635919	−	0.150716i	−0.100004	−	0.994987i	$-0.531885\pi$
$11$	−2.10911	−	0.499867i	−0.635919	−	0.150716i	−0.535916	+	0.844271i	$0.680034\pi$
$12$	0.224758	−	1.71741i	0.0648821	−	0.495772i
$13$	−1.69934	+	1.11767i	−0.471312	+	0.309987i	−0.762854	−	0.646571i	$-0.776202\pi$
$13$	−1.69934	+	1.11767i	−0.471312	+	0.309987i	0.291541	+	0.956558i	$0.405832\pi$
$14$	0.112768	+	1.93615i	0.0301385	+	0.517458i
$15$	0.497815	+	2.23736i	0.128535	+	0.577683i
$16$	−0.286803	−	0.957990i	−0.0717008	−	0.239497i
$17$	−7.02180	−	2.55572i	−1.70304	−	0.619854i	−0.706870	−	0.707343i	$-0.749893\pi$
$17$	−7.02180	−	2.55572i	−1.70304	−	0.619854i	−0.996165	+	0.0874893i	$0.972116\pi$
$18$	0.256873	−	2.98898i	0.0605456	−	0.704510i
$19$	2.13356	−	0.776551i	0.489471	−	0.178153i	−0.0854813	−	0.996340i	$-0.527243\pi$
$19$	2.13356	−	0.776551i	0.489471	−	0.178153i	0.574952	+	0.818187i	$0.305021\pi$
$20$	0.790236	+	1.06147i	0.176702	+	0.237352i
$21$	0.343980	+	3.34153i	0.0750626	+	0.729182i
$22$	−2.10911	+	0.499867i	−0.449663	+	0.106572i
$23$	1.34938	+	3.12822i	0.281366	+	0.652279i	0.999027	−	0.0441139i	$-0.0140465\pi$
$23$	1.34938	+	3.12822i	0.281366	+	0.652279i	−0.717661	+	0.696393i	$0.754787\pi$
$24$	−0.569919	−	1.63560i	−0.116334	−	0.333866i
$25$	2.71434	+	1.78525i	0.542867	+	0.357049i
$26$	−1.01697	+	1.76145i	−0.199445	+	0.345449i
$27$	0.214683	−	5.19172i	0.0413159	−	0.999146i
$28$	0.969715	+	1.67960i	0.183259	+	0.317414i
$29$	−0.282496	+	4.85027i	−0.0524582	+	0.900673i	0.864735	+	0.502229i	$0.167487\pi$
$29$	−0.282496	+	4.85027i	−0.0524582	+	0.900673i	−0.917193	+	0.398444i	$0.869550\pi$
$30$	1.44899	+	1.77596i	0.264548	+	0.324244i
$31$	5.07563	+	0.593256i	0.911610	+	0.106552i	0.558952	−	0.829200i	$-0.311204\pi$
$31$	5.07563	+	0.593256i	0.911610	+	0.106552i	0.352658	+	0.935752i	$0.385278\pi$
$32$	−0.686242	−	0.727374i	−0.121312	−	0.128583i
$33$	−3.61105	+	1.02709i	−0.628603	+	0.178794i
$34$	−7.42191	+	0.867497i	−1.27285	+	0.148775i
$35$	−1.96605	−	1.64972i	−0.332324	−	0.278853i
$36$	−1.11190	−	2.78634i	−0.185317	−	0.464389i
$37$	4.70814	−	3.95060i	0.774013	−	0.649474i	−0.167720	−	0.985835i	$-0.553640\pi$
$37$	4.70814	−	3.95060i	0.774013	−	0.649474i	0.941733	+	0.336360i	$0.109196\pi$
$38$	1.55810	−	1.65149i	0.252757	−	0.267907i
$39$	−1.62429	+	3.12610i	−0.260095	+	0.500577i
$40$	1.18257	+	0.593908i	0.186981	+	0.0939052i
$41$	−6.98634	−	3.50867i	−1.09108	−	0.547962i	−0.190077	−	0.981769i	$-0.560874\pi$
$41$	−6.98634	−	3.50867i	−1.09108	−	0.547962i	−0.901006	+	0.433807i	$0.857170\pi$
$42$	1.80707	+	2.83173i	0.278837	+	0.436945i
$43$	−4.77609	+	5.06236i	−0.728347	+	0.772003i	−0.980676	−	0.195639i	$-0.937322\pi$
$43$	−4.77609	+	5.06236i	−0.728347	+	0.772003i	0.252329	+	0.967641i	$0.418803\pi$
$44$	−1.66043	+	1.39326i	−0.250319	+	0.210042i
$45$	2.64378	+	2.96162i	0.394112	+	0.441492i
$46$	2.60979	+	2.18988i	0.384793	+	0.322880i
$47$	4.18562	−	0.489229i	0.610535	−	0.0713614i	0.194794	−	0.980844i	$-0.437596\pi$
$47$	4.18562	−	0.489229i	0.610535	−	0.0713614i	0.415741	+	0.909483i	$0.363522\pi$
$48$	−1.24336	−	1.20585i	−0.179463	−	0.174049i
$49$	2.22247	+	2.35568i	0.317496	+	0.336526i
$50$	3.22684	+	0.377163i	0.456344	+	0.0533389i
$51$	−12.7758	+	2.07167i	−1.78896	+	0.290092i
$52$	−0.118264	+	2.03051i	−0.0164002	+	0.281581i
$53$	−5.39818	−	9.34993i	−0.741497	−	1.28431i	−0.951813	−	0.306678i	$-0.900783\pi$
$53$	−5.39818	−	9.34993i	−0.741497	−	1.28431i	0.210316	−	0.977633i	$-0.432551\pi$
$54$	−2.13819	−	4.73584i	−0.290971	−	0.644466i
$55$	1.43418	−	2.48407i	0.193384	−	0.334952i
$56$	1.62037	+	1.06573i	0.216531	+	0.142415i
$57$	2.56908	−	2.97743i	0.340283	−	0.394370i
$58$	1.92435	+	4.46115i	0.252680	+	0.585777i
$59$	6.72062	−	1.59282i	0.874950	−	0.207367i	0.231481	−	0.972839i	$-0.425643\pi$
$59$	6.72062	−	1.59282i	0.874950	−	0.207367i	0.643469	+	0.765472i	$0.277495\pi$
$60$	2.09191	+	0.936749i	0.270065	+	0.120934i
$61$	−5.37986	−	7.22641i	−0.688820	−	0.925246i	0.310862	−	0.950455i	$-0.399382\pi$
$61$	−5.37986	−	7.22641i	−0.688820	−	0.925246i	−0.999682	+	0.0252087i	$0.991975\pi$
$62$	4.80200	−	1.74779i	0.609855	−	0.221969i
$63$	3.34456	+	4.76093i	0.421374	+	0.599821i
$64$	−0.939693	−	0.342020i	−0.117462	−	0.0427525i
$65$	−0.771954	−	2.57851i	−0.0957491	−	0.319824i
$66$	−2.76599	+	2.53848i	−0.340470	+	0.312465i
$67$	0.661912	+	11.3646i	0.0808654	+	1.38841i	0.757860	+	0.652417i	$0.226245\pi$
$67$	0.661912	+	11.3646i	0.0808654	+	1.38841i	−0.676994	+	0.735988i	$0.736718\pi$
$68$	−6.24313	+	4.10617i	−0.757091	+	0.497946i
$69$	4.68420	+	3.58860i	0.563911	+	0.432016i
$70$	−2.49732	−	0.591876i	−0.298487	−	0.0707427i
$71$	0.518333	+	2.93961i	0.0615148	+	0.348868i	0.999994	+	0.00353124i	$0.00112403\pi$
$71$	0.518333	+	2.93961i	0.0615148	+	0.348868i	−0.938479	+	0.345336i	$0.887765\pi$
$72$	−2.24414	−	1.99094i	−0.264474	−	0.234635i
$73$	1.80390	−	10.2304i	0.211131	−	1.19738i	−0.676365	−	0.736567i	$-0.736446\pi$
$73$	1.80390	−	10.2304i	0.211131	−	1.19738i	0.887496	−	0.460816i	$-0.152443\pi$
$74$	2.43432	−	5.64339i	0.282984	−	0.656031i
$75$	5.61253	+	0.404540i	0.648079	+	0.0467122i
$76$	0.651182	−	2.17510i	0.0746956	−	0.249501i
$77$	2.51032	−	3.37195i	0.286078	−	0.384269i
$78$	−0.0485295	+	3.52257i	−0.00549489	+	0.398852i
$79$	9.16461	−	4.60264i	1.03110	−	0.517837i	0.148968	−	0.988842i	$-0.452405\pi$
$79$	9.16461	−	4.60264i	1.03110	−	0.517837i	0.882131	+	0.471005i	$0.156108\pi$
$80$	1.32333			0.147953
$81$	−4.06390	−	8.03024i	−0.451544	−	0.892249i
$82$	−7.81791			−0.863344
$83$	3.24547	−	1.62994i	0.356237	−	0.178909i	−0.261675	−	0.965156i	$-0.584275\pi$
$83$	3.24547	−	1.62994i	0.356237	−	0.178909i	0.617912	+	0.786247i	$0.287979\pi$
$84$	2.88573	+	1.71951i	0.314859	+	0.187614i
$85$	5.90499	−	7.93178i	0.640486	−	0.860323i
$86$	−1.99609	+	6.66740i	−0.215244	+	0.718964i
$87$	3.67276	+	7.57137i	0.393762	+	0.811736i
$88$	−0.858516	+	1.99026i	−0.0915181	+	0.212163i
$89$	1.42927	−	8.10577i	0.151502	−	0.859210i	−0.810413	−	0.585860i	$-0.800757\pi$
$89$	1.42927	−	8.10577i	0.151502	−	0.859210i	0.961915	−	0.273350i	$-0.0881319\pi$
$90$	3.69174	+	1.46007i	0.389144	+	0.153905i
$91$	−0.684990	−	3.88477i	−0.0718065	−	0.407235i
$92$	3.31501	+	0.785672i	0.345614	+	0.0819120i
$93$	8.17474	−	3.39345i	0.847681	−	0.351885i
$94$	3.52084	−	2.31569i	0.363147	−	0.238846i
$95$	0.174701	+	2.99951i	0.0179240	+	0.307743i
$96$	−1.65229	−	0.519568i	−0.168636	−	0.0530282i
$97$	−2.30761	−	7.70796i	−0.234302	−	0.782624i	−0.991576	−	0.129527i	$-0.958654\pi$
$97$	−2.30761	−	7.70796i	−0.234302	−	0.782624i	0.757274	−	0.653098i	$-0.226531\pi$
$98$	3.04330	+	1.10767i	0.307420	+	0.111892i
$99$	−4.59096	+	4.60509i	−0.461409	+	0.462829i
$100$	3.05288	−	1.11116i	0.305288	−	0.111116i
$101$	11.1155	+	14.9307i	1.10603	+	1.48566i	0.855678	+	0.517509i	$0.173141\pi$
$101$	11.1155	+	14.9307i	1.10603	+	1.48566i	0.250357	+	0.968153i	$0.419452\pi$
$102$	−10.4871	+	7.58507i	−1.03838	+	0.751033i
$103$	−17.5969	+	4.17055i	−1.73388	+	0.410937i	−0.971660	−	0.236383i	$-0.924038\pi$
$103$	−17.5969	+	4.17055i	−1.73388	+	0.410937i	−0.762218	+	0.647320i	$0.775890\pi$
$104$	0.805606	+	1.86761i	0.0789962	+	0.183134i
$105$	−4.36673	−	0.832153i	−0.426149	−	0.0812098i
$106$	−9.02023	−	5.93270i	−0.876122	−	0.576235i
$107$	2.04335	−	3.53919i	0.197538	−	0.342146i	−0.750192	−	0.661221i	$-0.770039\pi$
$107$	2.04335	−	3.53919i	0.197538	−	0.342146i	0.947730	+	0.319075i	$0.103372\pi$
$108$	−4.03620	−	3.27248i	−0.388383	−	0.314895i
$109$	−6.16219	−	10.6732i	−0.590231	−	1.02231i	−0.994201	−	0.107538i	$-0.965703\pi$
$109$	−6.16219	−	10.6732i	−0.590231	−	1.02231i	0.403970	−	0.914772i	$-0.367630\pi$
$110$	0.166780	−	2.86350i	0.0159019	−	0.273024i
$111$	3.77834	−	9.95216i	0.358625	−	0.944617i
$112$	1.92632	+	0.225154i	0.182020	+	0.0212751i
$113$	10.6469	+	11.2851i	1.00158	+	1.06161i	0.998100	+	0.0616189i	$0.0196263\pi$
$113$	10.6469	+	11.2851i	1.00158	+	1.06161i	0.00348030	+	0.999994i	$0.498892\pi$
$114$	0.959545	−	3.81373i	0.0898696	−	0.357189i
$115$	−4.47789	+	0.523390i	−0.417565	+	0.0488064i
$116$	3.72182	+	3.12298i	0.345562	+	0.289961i
$117$	0.186845	+	6.09899i	0.0172739	+	0.563852i
$118$	5.29091	−	4.43960i	0.487068	−	0.408698i
$119$	9.94520	−	10.5413i	0.911675	−	0.966319i
$120$	2.28981	−	0.101739i	0.209030	−	0.00928742i
$121$	−5.63150	−	2.82824i	−0.511954	−	0.257113i
$122$	−8.05082	−	4.04328i	−0.728887	−	0.366061i
$123$	−13.5277	+	0.601048i	−1.21975	+	0.0541946i
$124$	3.50682	−	3.71701i	0.314922	−	0.333798i
$125$	−8.36204	+	7.01659i	−0.747924	+	0.627583i
$126$	5.12551	+	2.75349i	0.456616	+	0.245300i
$127$	13.4767	+	11.3083i	1.19586	+	1.00345i	0.999739	+	0.0228661i	$0.00727913\pi$
$127$	13.4767	+	11.3083i	1.19586	+	1.00345i	0.196121	+	0.980580i	$0.437165\pi$
$128$	−0.993238	+	0.116093i	−0.0877907	+	0.0102613i
$129$	−2.94132	+	11.6903i	−0.258969	+	1.02928i
$130$	−1.84708	−	1.95779i	−0.161999	−	0.171709i
$131$	−4.78234	−	0.558975i	−0.417835	−	0.0488379i	−0.0954217	−	0.995437i	$-0.530420\pi$
$131$	−4.78234	−	0.558975i	−0.417835	−	0.0488379i	−0.322413	+	0.946599i	$0.604494\pi$
$132$	−1.33251	+	3.50984i	−0.115980	+	0.305493i
$133$	−0.256037	+	4.39599i	−0.0222013	+	0.381181i
$134$	5.69192	+	9.85870i	0.491707	+	0.851662i
$135$	6.50023	+	2.24260i	0.559451	+	0.193012i
$136$	−3.73622	+	6.47132i	−0.320378	+	0.554911i
$137$	0.519408	+	0.341620i	0.0443760	+	0.0291866i	0.571503	−	0.820600i	$-0.306360\pi$
$137$	0.519408	+	0.341620i	0.0443760	+	0.0291866i	−0.527127	+	0.849786i	$0.676731\pi$
$138$	5.79651	+	1.10462i	0.493432	+	0.0940317i
$139$	1.16974	+	2.71177i	0.0992164	+	0.230010i	0.960594	−	0.277956i	$-0.0896570\pi$
$139$	1.16974	+	2.71177i	0.0992164	+	0.230010i	−0.861377	+	0.507966i	$0.830398\pi$
$140$	−2.49732	+	0.591876i	−0.211062	+	0.0500227i
$141$	5.91423	−	4.27763i	0.498068	−	0.360242i
$142$	1.78249	+	2.39430i	0.149584	+	0.200926i
$143$	4.14278	−	1.50785i	0.346436	−	0.126093i
$144$	−2.89897	−	0.772002i	−0.241581	−	0.0643335i
$145$	−6.04164	−	2.19898i	−0.501731	−	0.182615i
$146$	−2.97939	−	9.95185i	−0.246576	−	0.823621i
$147$	5.35111	+	1.68268i	0.441352	+	0.138785i
$148$	−0.357360	−	6.13564i	−0.0293748	−	0.504347i
$149$	−1.10328	+	0.725642i	−0.0903846	+	0.0594469i	−0.593897	−	0.804541i	$-0.702411\pi$
$149$	−1.10328	+	0.725642i	−0.0903846	+	0.0594469i	0.503512	+	0.863988i	$0.332041\pi$
$150$	5.19710	−	2.15739i	0.424341	−	0.176150i
$151$	−1.68015	−	0.398202i	−0.136728	−	0.0324052i	0.161682	−	0.986843i	$-0.448308\pi$
$151$	−1.68015	−	0.398202i	−0.136728	−	0.0324052i	−0.298410	+	0.954438i	$0.596456\pi$
$152$	−0.394265	−	2.23599i	−0.0319791	−	0.181363i
$153$	−17.5631	+	13.9310i	−1.41989	+	1.12626i
$154$	0.729978	−	4.13991i	0.0588233	−	0.333604i
$155$	−2.67847	+	6.20939i	−0.215140	+	0.498750i
$156$	1.53756	+	3.16966i	0.123103	+	0.253776i
$157$	−3.15286	+	10.5313i	−0.251625	+	0.840487i	0.735082	+	0.677979i	$0.237144\pi$
$157$	−3.15286	+	10.5313i	−0.251625	+	0.840487i	−0.986707	+	0.162509i	$0.948041\pi$
$158$	6.12413	−	8.22614i	0.487210	−	0.654436i
$159$	−16.0642	−	9.57213i	−1.27397	−	0.759119i
$160$	1.18257	−	0.593908i	0.0934903	−	0.0469526i
$161$	−6.60734			−0.520731
$162$	−7.23560	−	5.35221i	−0.568482	−	0.420509i
$163$	−18.8589			−1.47714			−0.738570	−	0.674177i	$-0.764498\pi$
$163$	−18.8589			−1.47714			−0.738570	+	0.674177i	$0.764498\pi$
$164$	−6.98634	+	3.50867i	−0.545541	+	0.273981i
$165$	0.0684383	−	4.96767i	0.00532791	−	0.386732i
$166$	2.16874	−	2.91313i	0.168327	−	0.226103i
$167$	−2.91724	+	9.74426i	−0.225743	+	0.754033i	0.767812	+	0.640676i	$0.221346\pi$
$167$	−2.91724	+	9.74426i	−0.225743	+	0.754033i	−0.993554	+	0.113357i	$0.963839\pi$
$168$	3.35050	+	0.241497i	0.258497	+	0.0186319i
$169$	−3.51047	+	8.13820i	−0.270037	+	0.626015i
$170$	1.71712	−	9.73826i	0.131697	−	0.746890i
$171$	1.36714	−	6.67283i	0.104548	−	0.510284i
$172$	1.20855	+	6.85404i	0.0921513	+	0.522616i
$173$	−18.1978	−	4.31295i	−1.38355	−	0.327908i	−0.529594	−	0.848251i	$-0.677656\pi$
$173$	−18.1978	−	4.31295i	−1.38355	−	0.327908i	−0.853957	+	0.520344i	$0.825804\pi$
$174$	6.68013	+	5.11769i	0.506419	+	0.387971i
$175$	−5.26427	+	3.46236i	−0.397941	+	0.261730i
$176$	0.126031	+	2.16386i	0.00949993	+	0.163107i
$177$	8.81377	−	8.08881i	0.662484	−	0.607992i
$178$	−2.36062	−	7.88504i	−0.176936	−	0.591008i
$179$	16.1486	+	5.87760i	1.20700	+	0.439312i	0.865662	−	0.500628i	$-0.166898\pi$
$179$	16.1486	+	5.87760i	1.20700	+	0.439312i	0.341338	+	0.939941i	$0.389120\pi$
$180$	3.95434	−	0.352085i	0.294739	−	0.0262429i
$181$	−21.3524	+	7.77164i	−1.58711	+	0.577661i	−0.976735	−	0.214450i	$-0.931204\pi$
$181$	−21.3524	+	7.77164i	−1.58711	+	0.577661i	−0.610376	+	0.792112i	$0.708982\pi$
$182$	−2.35561	−	3.16414i	−0.174610	−	0.234541i
$183$	−14.2415	−	6.37730i	−1.05276	−	0.471424i
$184$	3.31501	−	0.785672i	0.244386	−	0.0579205i
$185$	3.22141	+	7.46806i	0.236842	+	0.549062i
$186$	5.78224	−	6.70132i	0.423974	−	0.491364i
$187$	13.5322	+	8.90026i	0.989571	+	0.650851i
$188$	2.10706	−	3.64953i	0.153673	−	0.266169i
$189$	9.08058	+	4.37043i	0.660515	+	0.317902i
$190$	1.50230	+	2.60205i	0.108988	+	0.188773i
$191$	−0.341122	+	5.85684i	−0.0246827	+	0.423786i	0.963220	+	0.268713i	$0.0865984\pi$
$191$	−0.341122	+	5.85684i	−0.0246827	+	0.423786i	−0.987903	+	0.155073i	$0.950439\pi$
$192$	−1.70972	+	0.277242i	−0.123388	+	0.0200082i
$193$	11.7776	+	1.37661i	0.847771	+	0.0990903i	0.528875	−	0.848699i	$-0.322614\pi$
$193$	11.7776	+	1.37661i	0.847771	+	0.0990903i	0.318896	+	0.947790i	$0.396688\pi$
$194$	−5.52148	−	5.85243i	−0.396419	−	0.420180i
$195$	−3.34659	−	3.24564i	−0.239654	−	0.232425i
$196$	3.21671	−	0.375980i	0.229765	−	0.0268557i
$197$	2.29618	+	1.92672i	0.163596	+	0.137273i	0.720911	−	0.693028i	$-0.243724\pi$
$197$	2.29618	+	1.92672i	0.163596	+	0.137273i	−0.557315	+	0.830301i	$0.688168\pi$
$198$	−2.03587	+	6.17568i	−0.144683	+	0.438886i
$199$	15.4208	−	12.9396i	1.09315	−	0.917261i	0.0962034	−	0.995362i	$-0.469330\pi$
$199$	15.4208	−	12.9396i	1.09315	−	0.917261i	0.996945	+	0.0781009i	$0.0248856\pi$
$200$	2.22946	−	2.36309i	0.157647	−	0.167096i
$201$	10.6069	+	16.6213i	0.748155	+	1.17238i
$202$	16.6341	+	8.35395i	1.17037	+	0.587782i
$203$	−8.42044	−	4.22890i	−0.590999	−	0.296811i
$204$	−5.96742	+	11.4849i	−0.417803	+	0.804101i
$205$	7.09962	−	7.52516i	0.495859	−	0.525580i
$206$	−13.8535	+	11.6244i	−0.965216	+	0.809913i
$207$	10.1149	+	1.46574i	0.703033	+	0.101876i
$208$	1.55810	+	1.30740i	0.108034	+	0.0906517i
$209$	−4.88807	+	0.571333i	−0.338115	+	0.0395199i
$210$	−4.27572	+	1.21615i	−0.295053	+	0.0839220i
$211$	−9.85383	−	10.4445i	−0.678366	−	0.719026i	0.293133	−	0.956072i	$-0.405302\pi$
$211$	−9.85383	−	10.4445i	−0.678366	−	0.719026i	−0.971498	+	0.237046i	$0.923821\pi$
$212$	−10.7234	−	1.25338i	−0.736484	−	0.0860826i
$213$	3.26840	+	4.00593i	0.223947	+	0.274482i
$214$	0.237620	−	4.07979i	0.0162434	−	0.278888i
$215$	−4.60503	−	7.97615i	−0.314061	−	0.543969i
$216$	−5.07556	−	1.11295i	−0.345348	−	0.0757269i
$217$	−4.95542	+	8.58304i	−0.336396	+	0.582655i
$218$	−10.2969	−	6.77236i	−0.697392	−	0.458682i
$219$	−5.92047	−	16.9911i	−0.400068	−	1.14815i
$220$	−1.13610	−	2.63377i	−0.0765957	−	0.177569i
$221$	14.7889	−	3.50503i	0.994808	−	0.235774i
$222$	−1.09007	−	10.5893i	−0.0731607	−	0.710707i
$223$	6.68444	+	8.97876i	0.447623	+	0.601262i	0.967466	−	0.252999i	$-0.0814171\pi$
$223$	6.68444	+	8.97876i	0.447623	+	0.601262i	−0.519843	+	0.854262i	$0.674010\pi$
$224$	1.82247	−	0.663324i	0.121769	−	0.0443202i
$225$	8.82691	−	4.13258i	0.588460	−	0.275506i
$226$	14.5792	+	5.30639i	0.969794	+	0.352976i
$227$	−4.56463	−	15.2469i	−0.302965	−	1.01197i	−0.964945	−	0.262453i	$-0.915469\pi$
$227$	−4.56463	−	15.2469i	−0.302965	−	1.01197i	0.661980	−	0.749522i	$-0.269717\pi$
$228$	−0.854119	−	3.83872i	−0.0565654	−	0.254225i
$229$	0.625990	+	10.7478i	0.0413666	+	0.710236i	0.953695	+	0.300776i	$0.0972458\pi$
$229$	0.625990	+	10.7478i	0.0413666	+	0.710236i	−0.912328	+	0.409460i	$0.865717\pi$
$230$	−3.76669	+	2.47739i	−0.248368	+	0.163354i
$231$	0.944833	−	7.21959i	0.0621655	−	0.475014i
$232$	4.72753	+	1.12045i	0.310378	+	0.0735608i
$233$	2.99957	+	17.0114i	0.196508	+	1.11445i	0.910254	+	0.414050i	$0.135886\pi$
$233$	2.99957	+	17.0114i	0.196508	+	1.11445i	−0.713746	+	0.700405i	$0.753003\pi$
$234$	2.90419	+	5.36640i	0.189853	+	0.350812i
$235$	−0.968376	+	5.49193i	−0.0631699	+	0.358254i
$236$	2.73564	−	6.34193i	0.178075	−	0.412824i
$237$	9.96442	−	14.7049i	0.647259	−	0.955184i
$238$	4.15643	−	13.8834i	0.269421	−	0.899930i
$239$	14.5713	−	19.5727i	0.942540	−	1.26605i	−0.0213560	−	0.999772i	$-0.506798\pi$
$239$	14.5713	−	19.5727i	0.942540	−	1.26605i	0.963896	−	0.266279i	$-0.0857942\pi$
$240$	2.00059	−	1.11858i	0.129138	−	0.0722042i
$241$	24.9082	−	12.5094i	1.60448	−	0.805800i	0.604522	−	0.796588i	$-0.293364\pi$
$241$	24.9082	−	12.5094i	1.60448	−	0.805800i	0.999958	−	0.00921168i	$-0.00293221\pi$
$242$	−6.30180			−0.405095
$243$	−12.9316	−	8.70488i	−0.829559	−	0.558418i
$244$	−9.00910			−0.576748
$245$	−3.82988	+	1.92344i	−0.244682	+	0.122884i
$246$	−11.8190	+	6.60832i	−0.753553	+	0.421331i
$247$	−2.75771	+	3.70424i	−0.175469	+	0.235695i
$248$	1.46562	−	4.89550i	0.0930668	−	0.310865i
$249$	3.52871	−	5.20745i	0.223623	−	0.330009i
$250$	−4.32356	+	10.0231i	−0.273446	+	0.633918i
$251$	−2.51752	+	14.2776i	−0.158904	+	0.901192i	0.796224	+	0.605001i	$0.206827\pi$
$251$	−2.51752	+	14.2776i	−0.158904	+	0.901192i	−0.955129	+	0.296191i	$0.904284\pi$
$252$	5.81608	+	0.160284i	0.366379	+	0.0100969i
$253$	−1.28230	−	7.27226i	−0.0806172	−	0.457203i
$254$	17.1183	+	4.05712i	1.07410	+	0.254566i
$255$	2.22252	−	16.9825i	0.139179	−	1.06349i
$256$	−0.835488	+	0.549509i	−0.0522180	+	0.0343443i
$257$	−1.18052	−	20.2687i	−0.0736386	−	1.26433i	−0.809470	−	0.587161i	$-0.800246\pi$
$257$	−1.18052	−	20.2687i	−0.0736386	−	1.26433i	0.735832	−	0.677165i	$-0.236792\pi$
$258$	2.61816	+	11.7669i	0.162999	+	0.732578i
$259$	3.41864	+	11.4191i	0.212424	+	0.709546i
$260$	−2.52926	−	0.920575i	−0.156858	−	0.0570916i
$261$	11.9524	+	8.34179i	0.739833	+	0.516344i
$262$	−4.52452	+	1.64679i	−0.279526	+	0.101739i
$263$	5.30489	+	7.12570i	0.327114	+	0.439390i	0.935007	−	0.354629i	$-0.115393\pi$
$263$	5.30489	+	7.12570i	0.327114	+	0.439390i	−0.607894	+	0.794018i	$0.707985\pi$
$264$	0.384436	+	3.73454i	0.0236604	+	0.229845i
$265$	13.9020	−	3.29484i	0.853994	−	0.202400i
$266$	1.74411	+	4.04331i	0.106938	+	0.247911i
$267$	−4.69090	−	13.4623i	−0.287078	−	0.823881i
$268$	9.51107	+	6.25553i	0.580981	+	0.382117i
$269$	0.798719	−	1.38342i	0.0486987	−	0.0843487i	−0.840649	−	0.541581i	$-0.817826\pi$
$269$	0.798719	−	1.38342i	0.0486987	−	0.0843487i	0.889347	+	0.457232i	$0.151159\pi$
$270$	6.81530	−	0.913242i	0.414766	−	0.0555781i
$271$	10.0971	+	17.4887i	0.613355	+	1.06236i	0.990671	+	0.136277i	$0.0435137\pi$
$271$	10.0971	+	17.4887i	0.613355	+	1.06236i	−0.377316	+	0.926084i	$0.623153\pi$
$272$	−0.434484	+	7.45980i	−0.0263444	+	0.452317i
$273$	−4.31928	−	5.29394i	−0.261415	−	0.320404i
$274$	0.617479	+	0.0721729i	0.0373033	+	0.00436013i
$275$	−4.83244	−	5.12208i	−0.291407	−	0.308873i
$276$	5.67571	−	1.61434i	0.341637	−	0.0971721i
$277$	1.65097	−	0.192970i	0.0991970	−	0.0115945i	−0.0663496	−	0.997796i	$-0.521135\pi$
$277$	1.65097	−	0.192970i	0.0991970	−	0.0115945i	0.165547	+	0.986202i	$0.447061\pi$
$278$	2.26236	+	1.89835i	0.135688	+	0.113855i
$279$	9.49006	−	12.0401i	0.568155	−	0.720823i
$280$	−1.96605	+	1.64972i	−0.117494	+	0.0985894i
$281$	−8.32617	+	8.82522i	−0.496698	+	0.526469i	−0.926420	−	0.376492i	$-0.877130\pi$
$281$	−8.32617	+	8.82522i	−0.496698	+	0.526469i	0.429722	+	0.902961i	$0.358612\pi$
$282$	3.36535	−	6.47693i	0.200404	−	0.385696i
$283$	−12.6764	−	6.36632i	−0.753533	−	0.378439i	0.0301938	−	0.999544i	$-0.490388\pi$
$283$	−12.6764	−	6.36632i	−0.753533	−	0.378439i	−0.783727	+	0.621105i	$0.786684\pi$
$284$	2.66746	+	1.33965i	0.158284	+	0.0794934i
$285$	2.79954	+	4.38695i	0.165830	+	0.259860i
$286$	3.02540	−	3.20674i	0.178896	−	0.189618i
$287$	11.6150	−	9.74613i	0.685611	−	0.575296i
$288$	−2.93709	+	0.611168i	−0.173069	+	0.0360134i
$289$	29.7511	+	24.9642i	1.75007	+	1.46848i
$290$	−6.38590	+	0.746405i	−0.374993	+	0.0438304i
$291$	−10.0040	−	9.70222i	−0.586445	−	0.568754i
$292$	−7.12886	−	7.55615i	−0.417185	−	0.442190i
$293$	−19.9431	−	2.33102i	−1.16509	−	0.136179i	−0.488517	−	0.872555i	$-0.662462\pi$
$293$	−19.9431	−	2.33102i	−1.16509	−	0.136179i	−0.676573	+	0.736375i	$0.736536\pi$
$294$	5.53711	−	0.897878i	0.322931	−	0.0523653i
$295$	−0.531441	+	9.12449i	−0.0309417	+	0.531248i
$296$	−3.07302	−	5.32263i	−0.178616	−	0.309371i
$297$	−3.04796	+	10.8426i	−0.176861	+	0.629149i
$298$	−0.660264	+	1.14361i	−0.0382481	+	0.0662476i
$299$	−5.78939	−	3.80774i	−0.334809	−	0.220207i
$300$	3.67606	−	4.26037i	0.212238	−	0.245972i
$301$	−5.34629	−	12.3941i	−0.308155	−	0.714383i
$302$	−1.68015	+	0.398202i	−0.0966816	+	0.0229140i
$303$	29.4249	+	13.1764i	1.69042	+	0.756962i
$304$	−1.35584	−	1.82121i	−0.0777626	−	0.104453i
$305$	11.2030	−	4.07756i	0.641482	−	0.233480i
$306$	−9.44273	+	20.3315i	−0.539805	+	1.16228i
$307$	−24.0050	−	8.73709i	−1.37004	−	0.498652i	−0.450893	−	0.892578i	$-0.648894\pi$
$307$	−24.0050	−	8.73709i	−1.37004	−	0.498652i	−0.919142	+	0.393926i	$0.871117\pi$
$308$	−1.20566	−	4.02717i	−0.0686987	−	0.229470i
$309$	−23.0776	+	21.1793i	−1.31284	+	1.20485i
$310$	0.393201	+	6.75101i	0.0223323	+	0.383431i
$311$	8.61224	−	5.66436i	0.488355	−	0.321196i	−0.281340	−	0.959608i	$-0.590779\pi$
$311$	8.61224	−	5.66436i	0.488355	−	0.321196i	0.769695	+	0.638412i	$0.220408\pi$
$312$	2.79655	+	2.14246i	0.158324	+	0.121293i
$313$	−11.2681	−	2.67060i	−0.636913	−	0.150951i	−0.100541	−	0.994933i	$-0.532057\pi$
$313$	−11.2681	−	2.67060i	−0.636913	−	0.150951i	−0.536372	+	0.843982i	$0.680205\pi$
$314$	1.90893	+	10.8261i	0.107727	+	0.610952i
$315$	−7.30497	+	2.43307i	−0.411588	+	0.137088i
$316$	1.78084	−	10.0997i	0.100180	−	0.568150i
$317$	−9.27900	+	21.5111i	−0.521160	+	1.20819i	0.430935	+	0.902383i	$0.358184\pi$
$317$	−9.27900	+	21.5111i	−0.521160	+	1.20819i	−0.952095	+	0.305802i	$0.901075\pi$
$318$	−18.6515	−	1.34436i	−1.04592	−	0.0753879i
$319$	3.02031	−	10.0885i	0.169105	−	0.564849i
$320$	0.790236	−	1.06147i	0.0441756	−	0.0593381i
$321$	0.0975076	−	7.07770i	0.00544235	−	0.395039i
$322$	−5.90453	+	2.96537i	−0.329047	+	0.165253i
$323$	−16.9660			−0.944015
$324$	−8.86803	−	1.53558i	−0.492668	−	0.0853100i
$325$	−6.60790			−0.366540
$326$	−16.8529	+	8.46384i	−0.933395	+	0.468769i
$327$	−18.3378	−	10.9269i	−1.01408	−	0.604258i
$328$	−4.66853	+	6.27093i	−0.257777	+	0.346254i
$329$	−2.34404	+	7.82963i	−0.129231	+	0.431661i
$330$	−2.16833	−	4.46998i	−0.119362	−	0.246064i
$331$	0.0953783	−	0.221112i	0.00524246	−	0.0121534i	−0.915575	−	0.402148i	$-0.868264\pi$
$331$	0.0953783	−	0.221112i	0.00524246	−	0.0121534i	0.920817	+	0.389994i	$0.127523\pi$
$332$	0.630651	−	3.57660i	0.0346115	−	0.196291i
$333$	−2.70031	−	18.2393i	−0.147976	−	0.999508i
$334$	1.76627	+	10.0170i	0.0966462	+	0.548108i
$335$	−14.6585	−	3.47413i	−0.800879	−	0.189812i
$336$	3.10250	−	1.28789i	0.169255	−	0.0702603i
$337$	−6.75532	+	4.44304i	−0.367986	+	0.242028i	−0.720011	−	0.693962i	$-0.755863\pi$
$337$	−6.75532	+	4.44304i	−0.367986	+	0.242028i	0.352026	+	0.935990i	$0.385493\pi$
$338$	0.515341	+	8.84805i	0.0280308	+	0.481271i
$339$	25.6350	+	8.06102i	1.39230	+	0.437815i
$340$	−2.83605	−	9.47306i	−0.153806	−	0.513749i
$341$	−10.4085	−	3.78838i	−0.563651	−	0.205152i
$342$	−1.77304	−	6.57663i	−0.0958752	−	0.355624i
$343$	−18.6595	+	6.79152i	−1.00752	+	0.366708i
$344$	4.15609	+	5.58260i	0.224081	+	0.300994i
$345$	−6.32720	+	4.57632i	−0.340645	+	0.246381i
$346$	−18.1978	+	4.31295i	−0.978318	+	0.231866i
$347$	−3.71942	−	8.62258i	−0.199669	−	0.462884i	0.788735	−	0.614733i	$-0.210736\pi$
$347$	−3.71942	−	8.62258i	−0.199669	−	0.462884i	−0.988404	+	0.151849i	$0.951477\pi$
$348$	8.26639	+	1.57530i	0.443125	+	0.0844449i
$349$	−2.98629	−	1.96411i	−0.159853	−	0.105137i	0.467062	−	0.884224i	$-0.345312\pi$
$349$	−2.98629	−	1.96411i	−0.159853	−	0.105137i	−0.626915	+	0.779088i	$0.715683\pi$
$350$	−3.15041	+	5.45668i	−0.168397	+	0.291672i
$351$	5.43782	+	9.06244i	0.290249	+	0.483717i
$352$	1.08377	+	1.87714i	0.0577649	+	0.100052i
$353$	−0.231753	+	3.97905i	−0.0123350	+	0.211783i	0.986509	+	0.163709i	$0.0523457\pi$
$353$	−0.231753	+	3.97905i	−0.0123350	+	0.211783i	−0.998844	+	0.0480749i	$0.984691\pi$
$354$	4.24603	−	11.1840i	0.225674	−	0.594425i
$355$	−3.92337	−	0.458576i	−0.208231	−	0.0243387i
$356$	−5.64833	−	5.98688i	−0.299361	−	0.317304i
$357$	6.12468	−	24.3427i	0.324153	−	1.28835i
$358$	17.0687	−	1.99505i	0.902111	−	0.105442i
$359$	17.0190	+	14.2806i	0.898227	+	0.753702i	0.969843	−	0.243730i	$-0.0783711\pi$
$359$	17.0190	+	14.2806i	0.898227	+	0.753702i	−0.0716159	+	0.997432i	$0.522816\pi$
$360$	3.37571	−	2.08934i	0.177916	−	0.110118i
$361$	−10.6058	+	8.89934i	−0.558201	+	0.468386i
$362$	−15.5933	+	16.5279i	−0.819565	+	0.868688i
$363$	−10.9043	+	0.484488i	−0.572327	+	0.0254290i
$364$	−3.52512	−	1.77038i	−0.184766	−	0.0927931i
$365$	12.2848	+	6.16968i	0.643018	+	0.322936i
$366$	−15.5888	+	0.692627i	−0.814841	+	0.0362042i
$367$	−8.65683	+	9.17571i	−0.451883	+	0.478968i	−0.912760	−	0.408496i	$-0.866053\pi$
$367$	−8.65683	+	9.17571i	−0.451883	+	0.478968i	0.460877	+	0.887464i	$0.347535\pi$
$368$	2.60979	−	2.18988i	0.136045	−	0.114155i
$369$	−19.9429	+	12.3433i	−1.03819	+	0.642568i
$370$	6.23041	+	5.22794i	0.323904	+	0.271787i
$371$	20.7972	−	2.43085i	1.07974	−	0.126203i
$372$	2.15965	−	8.58358i	0.111973	−	0.445038i
$373$	−2.77388	−	2.94015i	−0.143626	−	0.152235i	0.651567	−	0.758591i	$-0.274112\pi$
$373$	−2.77388	−	2.94015i	−0.143626	−	0.152235i	−0.795193	+	0.606356i	$0.792631\pi$
$374$	16.0872	+	1.88033i	0.831851	+	0.0972294i
$375$	−6.71065	+	17.6759i	−0.346536	+	0.912777i
$376$	0.245029	−	4.20698i	0.0126364	−	0.216959i
$377$	−4.94096	−	8.55800i	−0.254473	−	0.440759i
$378$	10.0761	−	0.169799i	0.518261	−	0.00873354i
$379$	18.2374	−	31.5882i	0.936795	−	1.62258i	0.165392	−	0.986228i	$-0.447111\pi$
$379$	18.2374	−	31.5882i	0.936795	−	1.62258i	0.771402	−	0.636348i	$-0.219556\pi$
$380$	2.51030	+	1.65105i	0.128776	+	0.0846971i
$381$	29.9325	+	5.70413i	1.53349	+	0.292232i
$382$	2.32371	+	5.38696i	0.118891	+	0.275621i
$383$	−3.77992	+	0.895858i	−0.193145	+	0.0457762i	−0.326050	−	0.945353i	$-0.605718\pi$
$383$	−3.77992	+	0.895858i	−0.193145	+	0.0457762i	0.132905	+	0.991129i	$0.457570\pi$
$384$	−1.40343	+	1.01507i	−0.0716187	+	0.0518002i
$385$	3.32198	+	4.46219i	0.169304	+	0.227414i
$386$	11.1427	−	4.05560i	0.567148	−	0.206425i
$387$	5.43496	+	20.1596i	0.276275	+	1.02477i
$388$	−7.56074	−	2.75188i	−0.383838	−	0.139706i
$389$	7.91140	+	26.4259i	0.401124	+	1.33985i	0.885359	+	0.464909i	$0.153913\pi$
$389$	7.91140	+	26.4259i	0.401124	+	1.33985i	−0.484235	+	0.874938i	$0.660902\pi$
$390$	−4.44726	−	1.39846i	−0.225196	−	0.0708138i
$391$	−1.48022	−	25.4144i	−0.0748578	−	1.28526i
$392$	2.70582	−	1.77965i	0.136665	−	0.0898857i
$393$	−7.70237	+	3.19736i	−0.388533	+	0.161286i
$394$	2.91665	+	0.691259i	0.146939	+	0.0348251i
$395$	2.35664	+	13.3651i	0.118575	+	0.672474i
$396$	0.952322	+	6.43248i	0.0478560	+	0.323244i
$397$	0.343883	−	1.95026i	0.0172590	−	0.0978806i	−0.974961	−	0.222374i	$-0.928619\pi$
$397$	0.343883	−	1.95026i	0.0172590	−	0.0978806i	0.992220	+	0.124493i	$0.0397305\pi$
$398$	7.97323	−	18.4840i	0.399662	−	0.926521i
$399$	3.32877	+	6.86223i	0.166647	+	0.343541i
$400$	0.931767	−	3.11232i	0.0465884	−	0.155616i
$401$	15.0228	−	20.1791i	0.750203	−	1.00770i	−0.249028	−	0.968496i	$-0.580111\pi$
$401$	15.0228	−	20.1791i	0.750203	−	1.00770i	0.999231	−	0.0392012i	$-0.0124813\pi$
$402$	16.9383	+	10.0930i	0.844808	+	0.503393i
$403$	−9.28829	+	4.66475i	−0.462683	+	0.232368i
$404$	18.6140			0.926081
$405$	11.7226	−	2.10419i	0.582501	−	0.104558i
$406$	−9.42271			−0.467641
$407$	−11.9047	+	5.97878i	−0.590096	+	0.296357i
$408$	−0.178291	+	12.9414i	−0.00882670	+	0.640695i
$409$	18.9183	−	25.4117i	0.935450	−	1.25653i	−0.0309600	−	0.999521i	$-0.509856\pi$
$409$	18.9183	−	25.4117i	0.935450	−	1.25653i	0.966410	−	0.257006i	$-0.0827361\pi$
$410$	2.96717	−	9.91103i	0.146538	−	0.489471i
$411$	1.07400	+	0.0774117i	0.0529765	+	0.00381844i
$412$	−7.16287	+	16.6054i	−0.352889	+	0.818089i
$413$	−2.32606	+	13.1917i	−0.114458	+	0.649123i
$414$	9.69681	−	3.22972i	0.476572	−	0.158732i
$415$	0.834558	+	4.73301i	0.0409668	+	0.232334i
$416$	1.97912	+	0.469061i	0.0970345	+	0.0229976i
$417$	4.06061	+	3.11086i	0.198849	+	0.152340i
$418$	−4.11172	+	2.70432i	−0.201111	+	0.132273i
$419$	0.100748	+	1.72977i	0.00492185	+	0.0845049i	0.999875	−	0.0158403i	$-0.00504233\pi$
$419$	0.100748	+	1.72977i	0.00492185	+	0.0845049i	−0.994953	+	0.100345i	$0.968005\pi$
$420$	−3.27512	+	3.00573i	−0.159809	+	0.146664i
$421$	−8.06168	−	26.9279i	−0.392902	−	1.31238i	−0.894416	−	0.447235i	$-0.852409\pi$
$421$	−8.06168	−	26.9279i	−0.392902	−	1.31238i	0.501514	−	0.865149i	$-0.332777\pi$
$422$	−13.4932	−	4.91111i	−0.656837	−	0.239069i
$423$	5.32527	−	11.4661i	0.258923	−	0.557499i
$424$	−10.1453	+	3.69257i	−0.492698	+	0.179327i
$425$	−14.4969	−	19.4727i	−0.703204	−	0.944566i
$426$	4.71861	+	2.11297i	0.228617	+	0.102374i
$427$	17.0015	−	4.02944i	0.822762	−	0.194998i
$428$	−1.61866	−	3.75247i	−0.0782408	−	0.181383i
$429$	4.98844	−	5.78135i	0.240844	−	0.279126i
$430$	−7.69490	−	5.06102i	−0.371081	−	0.244064i
$431$	−0.567396	+	0.982759i	−0.0273305	+	0.0473378i	−0.879367	−	0.476144i	$-0.842034\pi$
$431$	−0.567396	+	0.982759i	−0.0273305	+	0.0473378i	0.852037	+	0.523482i	$0.175367\pi$
$432$	−5.03518	+	1.28334i	−0.242255	+	0.0617445i
$433$	8.75124	+	15.1576i	0.420558	+	0.728427i	0.995994	−	0.0894194i	$-0.0285011\pi$
$433$	8.75124	+	15.1576i	0.420558	+	0.728427i	−0.575436	+	0.817846i	$0.695168\pi$
$434$	−0.576264	+	9.89408i	−0.0276616	+	0.474931i
$435$	−10.9924	+	1.78249i	−0.527046	+	0.0854639i
$436$	−12.2410	−	1.43077i	−0.586240	−	0.0685216i
$437$	5.30820	+	5.62636i	0.253926	+	0.269146i
$438$	−12.9163	−	12.5267i	−0.617165	−	0.598547i
$439$	−16.5282	+	1.93187i	−0.788849	+	0.0922032i	−0.500971	−	0.865464i	$-0.667024\pi$
$439$	−16.5282	+	1.93187i	−0.788849	+	0.0922032i	−0.287878	+	0.957667i	$0.592950\pi$
$440$	−2.19729	−	1.84374i	−0.104752	−	0.0878970i
$441$	9.51208	−	1.97933i	0.452956	−	0.0942540i
$442$	11.6428	−	9.76945i	0.553790	−	0.464685i
$443$	18.5257	−	19.6360i	0.880180	−	0.932937i	−0.118014	−	0.993012i	$-0.537653\pi$
$443$	18.5257	−	19.6360i	0.880180	−	0.932937i	0.998194	+	0.0600754i	$0.0191341\pi$
$444$	−5.72659	−	8.97372i	−0.271772	−	0.425874i
$445$	9.73351	+	4.88835i	0.461412	+	0.231730i
$446$	10.0031	+	5.02374i	0.473660	+	0.237881i
$447$	−1.05456	+	2.02960i	−0.0498791	+	0.0959968i
$448$	1.33092	−	1.41069i	0.0628800	−	0.0666489i
$449$	14.6102	−	12.2594i	0.689499	−	0.578558i	−0.229266	−	0.973364i	$-0.573633\pi$
$449$	14.6102	−	12.2594i	0.689499	−	0.578558i	0.918765	+	0.394806i	$0.129188\pi$
$450$	6.03331	−	7.65452i	0.284413	−	0.360838i
$451$	12.9811	+	10.8924i	0.611254	+	0.512903i
$452$	15.4100	−	1.80117i	0.724823	−	0.0847197i
$453$	−2.87662	+	0.818198i	−0.135155	+	0.0384423i
$454$	−10.9219	−	11.5766i	−0.512591	−	0.543315i
$455$	5.18484	+	0.606021i	0.243069	+	0.0284107i
$456$	−2.48608	−	3.04707i	−0.116421	−	0.142692i
$457$	−0.570163	+	9.78932i	−0.0266711	+	0.457925i	0.958362	+	0.285558i	$0.0921788\pi$
$457$	−0.570163	+	9.78932i	−0.0266711	+	0.457925i	−0.985033	+	0.172368i	$0.944858\pi$
$458$	5.38302	+	9.32367i	0.251532	+	0.435666i
$459$	−14.7761	+	35.9065i	−0.689687	+	1.67597i
$460$	−2.25419	+	3.90436i	−0.105102	+	0.182042i
$461$	−12.2701	−	8.07018i	−0.571476	−	0.375866i	0.230635	−	0.973040i	$-0.425920\pi$
$461$	−12.2701	−	8.07018i	−0.571476	−	0.375866i	−0.802111	+	0.597175i	$0.796290\pi$
$462$	−2.39581	−	6.87570i	−0.111463	−	0.319887i
$463$	−12.0622	−	27.9633i	−0.560577	−	1.29956i	−0.929060	−	0.369930i	$-0.879382\pi$
$463$	−12.0622	−	27.9633i	−0.560577	−	1.29956i	0.368482	−	0.929635i	$-0.379877\pi$
$464$	4.72753	−	1.12045i	0.219470	−	0.0520154i
$465$	1.19940	+	11.6513i	0.0556207	+	0.540318i
$466$	10.3152	+	13.8558i	0.477844	+	0.641855i
$467$	−4.51390	+	1.64293i	−0.208879	+	0.0760256i	−0.444340	−	0.895858i	$-0.646562\pi$
$467$	−4.51390	+	1.64293i	−0.208879	+	0.0760256i	0.235462	+	0.971884i	$0.424340\pi$
$468$	5.00372	+	3.49219i	0.231297	+	0.161427i
$469$	−20.7467	−	7.55118i	−0.957994	−	0.348681i
$470$	1.59940	+	5.34238i	0.0737749	+	0.246425i
$471$	4.13543	+	18.5861i	0.190550	+	0.856402i
$472$	−0.401594	−	6.89511i	−0.0184849	−	0.317373i
$473$	12.6038	−	8.28964i	0.579523	−	0.381158i
$474$	2.30500	−	17.6128i	0.105872	−	0.808982i
$475$	7.17752	+	1.70110i	0.329327	+	0.0780520i
$476$	−2.51656	−	14.2721i	−0.115346	−	0.654161i
$477$	−32.3768	−	0.892263i	−1.48243	−	0.0408539i
$478$	4.23720	−	24.0304i	0.193805	−	1.09912i
$479$	−1.04518	+	2.42300i	−0.0477555	+	0.110710i	−0.940424	−	0.340005i	$-0.889571\pi$
$479$	−1.04518	+	2.42300i	−0.0477555	+	0.110710i	0.892668	+	0.450714i	$0.148831\pi$
$480$	1.28577	−	1.89747i	0.0586873	−	0.0866070i
$481$	−3.58525	+	11.9756i	−0.163473	+	0.546039i
$482$	16.6446	−	22.3576i	0.758141	−	1.01836i
$483$	−9.98889	+	5.58505i	−0.454510	+	0.254129i
$484$	−5.63150	+	2.82824i	−0.255977	+	0.128557i
$485$	10.6475			0.483476
$486$	−15.4628	−	1.97530i	−0.701407	−	0.0896013i
$487$	30.3949			1.37732			0.688662	−	0.725082i	$-0.258198\pi$
$487$	30.3949			1.37732			0.688662	+	0.725082i	$0.258198\pi$
$488$	−8.05082	+	4.04328i	−0.364444	+	0.183030i
$489$	−28.5106	+	15.9410i	−1.28929	+	0.720877i
$490$	−2.55927	+	3.43769i	−0.115616	+	0.155299i
$491$	−5.83806	+	19.5005i	−0.263468	+	0.880045i	0.719221	+	0.694782i	$0.244499\pi$
$491$	−5.83806	+	19.5005i	−0.263468	+	0.880045i	−0.982689	+	0.185263i	$0.940686\pi$
$492$	−7.59605	+	11.2098i	−0.342456	+	0.505376i
$493$	14.3796	−	33.3356i	0.647624	−	1.50136i
$494$	−0.801915	+	4.54789i	−0.0360799	+	0.204619i
$495$	−4.09560	−	7.56790i	−0.184084	−	0.340152i
$496$	−0.887374	−	5.03255i	−0.0398443	−	0.225968i
$497$	−5.63307	−	1.33506i	−0.252678	−	0.0598857i
$498$	0.816271	−	6.23723i	0.0365780	−	0.279497i
$499$	−0.982338	+	0.646094i	−0.0439755	+	0.0289231i	−0.571306	−	0.820737i	$-0.693563\pi$
$499$	−0.982338	+	0.646094i	−0.0439755	+	0.0289231i	0.527331	+	0.849660i	$0.323193\pi$
$500$	0.634701	+	10.8974i	0.0283847	+	0.487347i
$501$	3.82638	+	17.1971i	0.170950	+	0.768311i
$502$	4.15802	+	13.8888i	0.185582	+	0.619886i
$503$	29.3121	+	10.6687i	1.30696	+	0.475696i	0.899258	−	0.437418i	$-0.144107\pi$
$503$	29.3121	+	10.6687i	1.30696	+	0.475696i	0.407705	+	0.913114i	$0.366329\pi$
$504$	5.26938	−	2.46702i	0.234717	−	0.109890i
$505$	−23.1469	+	8.42479i	−1.03002	+	0.374898i
$506$	−4.40968	−	5.92323i	−0.196034	−	0.263320i
$507$	1.57196	+	15.2706i	0.0698133	+	0.678189i
$508$	17.1183	−	4.05712i	0.759503	−	0.180005i
$509$	0.914081	+	2.11908i	0.0405159	+	0.0939265i	0.937272	−	0.348598i	$-0.113342\pi$
$509$	0.914081	+	2.11908i	0.0405159	+	0.0939265i	−0.896756	+	0.442525i	$0.854083\pi$
$510$	−5.63564	−	16.1736i	−0.249550	−	0.716180i
$511$	16.8328	+	11.0711i	0.744641	+	0.489758i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	−3.57359	−	11.2435i	−0.157778	−	0.496414i
$514$	−10.1515	−	17.5829i	−0.447764	−	0.775550i
$515$	1.39150	−	23.8911i	0.0613168	−	1.05277i
$516$	7.62066	+	9.34029i	0.335481	+	0.411184i
$517$	−9.07246	−	1.06042i	−0.399007	−	0.0466372i
$518$	8.17987	+	8.67016i	0.359403	+	0.380945i
$519$	−31.1568	+	8.86195i	−1.36763	+	0.388996i
$520$	−2.67338	+	0.312474i	−0.117236	+	0.0137029i
$521$	−20.8735	−	17.5150i	−0.914485	−	0.767344i	0.0584819	−	0.998288i	$-0.481374\pi$
$521$	−20.8735	−	17.5150i	−0.914485	−	0.767344i	−0.972967	+	0.230944i	$0.925818\pi$
$522$	14.4248	+	2.09028i	0.631357	+	0.0914891i
$523$	20.3758	−	17.0974i	0.890973	−	0.747615i	−0.0774318	−	0.996998i	$-0.524672\pi$
$523$	20.3758	−	17.0974i	0.890973	−	0.747615i	0.968405	+	0.249382i	$0.0802276\pi$
$524$	−3.30418	+	3.50223i	−0.144344	+	0.152996i
$525$	−5.03179	+	9.68413i	−0.219605	+	0.422650i
$526$	7.93863	+	3.98693i	0.346141	+	0.173838i
$527$	−34.1238	−	17.1376i	−1.48646	−	0.746527i
$528$	2.01960	+	3.16477i	0.0878920	+	0.137729i
$529$	7.81863	−	8.28727i	0.339941	−	0.360316i
$530$	10.9446	−	9.18359i	0.475402	−	0.398910i
$531$	6.48725	−	19.6787i	0.281523	−	0.853981i
$532$	3.37323	+	2.83048i	0.146248	+	0.122717i
$533$	15.7937	−	1.84602i	0.684102	−	0.0799600i
$534$	−10.2338	−	9.92511i	−0.442861	−	0.429501i
$535$	3.71122	+	3.93367i	0.160450	+	0.170067i
$536$	11.3069	+	1.32158i	0.488383	+	0.0570837i
$537$	29.3814	−	4.76438i	1.26790	−	0.205598i
$538$	0.0928827	−	1.59474i	0.00400446	−	0.0687539i
$539$	−3.50990	−	6.07932i	−0.151182	−	0.261855i
$540$	5.68051	−	3.87480i	0.244450	−	0.166745i
$541$	1.08463	−	1.87864i	0.0466321	−	0.0807692i	−0.841767	−	0.539841i	$-0.818484\pi$
$541$	1.08463	−	1.87864i	0.0466321	−	0.0807692i	0.888399	+	0.459071i	$0.151818\pi$
$542$	16.8720	+	11.0969i	0.724714	+	0.476652i
$543$	−25.7111	+	29.7978i	−1.10337	+	1.27875i
$544$	2.95968	+	6.86131i	0.126895	+	0.294176i
$545$	15.8696	−	3.76116i	0.679778	−	0.161110i
$546$	−6.23577	−	2.79235i	−0.266866	−	0.119502i
$547$	−14.1538	−	19.0118i	−0.605171	−	0.812886i	0.388939	−	0.921264i	$-0.372842\pi$
$547$	−14.1538	−	19.0118i	−0.605171	−	0.812886i	−0.994110	+	0.108378i	$0.965434\pi$
$548$	0.584191	−	0.212628i	0.0249554	−	0.00908302i
$549$	−26.9208	+	2.39697i	−1.14895	+	0.102300i
$550$	−6.61721	−	2.40847i	−0.282159	−	0.102697i
$551$	3.16376	+	10.5677i	0.134781	+	0.450199i
$552$	4.34748	−	3.98988i	0.185041	−	0.169821i
$553$	1.15649	+	19.8561i	0.0491788	+	0.844367i
$554$	1.38875	−	0.913398i	0.0590025	−	0.0388065i
$555$	11.1827	+	8.56713i	0.474678	+	0.363654i
$556$	2.87370	+	0.681079i	0.121872	+	0.0288842i
$557$	−2.15153	−	12.2019i	−0.0911633	−	0.517013i	−0.995856	−	0.0909475i	$-0.971010\pi$
$557$	−2.15153	−	12.2019i	−0.0911633	−	0.517013i	0.904692	−	0.426065i	$-0.140101\pi$
$558$	3.07703	−	15.0186i	0.130261	−	0.635787i
$559$	2.45814	−	13.9408i	0.103968	−	0.589632i
$560$	−1.01654	+	2.35660i	−0.0429566	+	0.0995847i
$561$	27.9810	+	2.01681i	1.18136	+	0.0851499i
$562$	−3.47978	+	11.6233i	−0.146786	+	0.490299i
$563$	−27.7670	+	37.2976i	−1.17024	+	1.57191i	−0.424875	+	0.905252i	$0.639682\pi$
$563$	−27.7670	+	37.2976i	−1.17024	+	1.57191i	−0.745366	+	0.666655i	$0.767725\pi$
$564$	0.100548	−	7.29837i	0.00423382	−	0.307317i
$565$	−18.3474	+	9.21440i	−0.771880	+	0.387653i
$566$	−14.1852			−0.596250
$567$	17.4221	−	1.06847i	0.731661	−	0.0448717i
$568$	2.98496			0.125246
$569$	20.7775	−	10.4349i	0.871038	−	0.437452i	0.0436265	−	0.999048i	$-0.486109\pi$
$569$	20.7775	−	10.4349i	0.871038	−	0.437452i	0.827411	+	0.561596i	$0.189813\pi$
$570$	4.47062	+	2.66389i	0.187253	+	0.111578i
$571$	−9.27277	+	12.4555i	−0.388053	+	0.521246i	−0.952629	−	0.304135i	$-0.901633\pi$
$571$	−9.27277	+	12.4555i	−0.388053	+	0.521246i	0.564575	+	0.825381i	$0.309040\pi$
$572$	1.26442	−	4.22344i	0.0528679	−	0.176591i
$573$	4.43497	+	9.14265i	0.185273	+	0.381940i
$574$	6.00548	−	13.9223i	0.250664	−	0.581104i
$575$	−1.92197	+	10.9000i	−0.0801516	+	0.454562i
$576$	−2.35038	+	1.86432i	−0.0979327	+	0.0776801i
$577$	5.56862	+	31.5812i	0.231825	+	1.31474i	0.849199	+	0.528074i	$0.177086\pi$
$577$	5.56862	+	31.5812i	0.231825	+	1.31474i	−0.617374	+	0.786670i	$0.711803\pi$
$578$	37.7905	+	8.95651i	1.57188	+	0.372542i
$579$	18.9689	−	7.87425i	0.788319	−	0.327243i
$580$	−5.37167	+	3.53300i	−0.223046	+	0.146700i
$581$	0.409547	+	7.03166i	0.0169909	+	0.291722i
$582$	−13.2942	−	4.18043i	−0.551064	−	0.173284i
$583$	6.71162	+	22.4184i	0.277967	+	0.928474i
$584$	−9.76177	−	3.55299i	−0.403945	−	0.147024i
$585$	−7.80281	−	2.07791i	−0.322606	−	0.0859109i
$586$	−18.8680	+	6.86739i	−0.779429	+	0.283689i
$587$	−20.4031	−	27.4061i	−0.842127	−	1.13117i	−0.989846	−	0.142143i	$-0.954601\pi$
$587$	−20.4031	−	27.4061i	−0.842127	−	1.13117i	0.147719	−	0.989029i	$-0.452807\pi$
$588$	4.54518	−	3.28742i	0.187440	−	0.135571i
$589$	11.2898	−	2.67574i	0.465189	−	0.110252i
$590$	3.62015	+	8.39245i	0.149039	+	0.345512i
$591$	5.09995	+	0.971881i	0.209784	+	0.0399778i
$592$	−5.13494	−	3.37730i	−0.211045	−	0.138806i
$593$	5.78538	−	10.0206i	0.237577	−	0.411496i	−0.722441	−	0.691432i	$-0.756980\pi$
$593$	5.78538	−	10.0206i	0.237577	−	0.411496i	0.960019	+	0.279936i	$0.0903134\pi$
$594$	2.14238	+	11.0572i	0.0879029	+	0.453682i
$595$	9.58901	+	16.6087i	0.393111	+	0.680889i
$596$	−0.0767819	+	1.31829i	−0.00314511	+	0.0539994i
$597$	12.3754	−	32.5967i	0.506490	−	1.33410i
$598$	−6.88250	−	0.804448i	−0.281446	−	0.0328963i
$599$	−15.6147	−	16.5506i	−0.638000	−	0.676241i	0.325008	−	0.945711i	$-0.394633\pi$
$599$	−15.6147	−	16.5506i	−0.638000	−	0.676241i	−0.963009	+	0.269470i	$0.913151\pi$
$600$	1.37300	−	5.45702i	0.0560525	−	0.222782i
$601$	4.24750	−	0.496462i	0.173259	−	0.0202511i	−0.0290209	−	0.999579i	$-0.509239\pi$
$601$	4.24750	−	0.496462i	0.173259	−	0.0202511i	0.202280	+	0.979328i	$0.435165\pi$
$602$	−10.3401	−	8.67635i	−0.421430	−	0.353622i
$603$	30.0851	+	16.1621i	1.22516	+	0.658172i
$604$	−1.32272	+	1.10990i	−0.0538208	+	0.0451610i
$605$	5.72281	−	6.06583i	0.232665	−	0.246611i
$606$	32.2086	−	1.43106i	1.30839	−	0.0581329i
$607$	9.54035	+	4.79135i	0.387231	+	0.194475i	0.631754	−	0.775169i	$-0.282335\pi$
$607$	9.54035	+	4.79135i	0.387231	+	0.194475i	−0.244523	+	0.969643i	$0.578631\pi$
$608$	−2.02898	−	1.01899i	−0.0822859	−	0.0413255i
$609$	−16.3045	+	0.724426i	−0.660693	+	0.0293552i
$610$	8.18136	−	8.67174i	0.331254	−	0.351108i
$611$	−6.56599	+	5.50952i	−0.265632	+	0.222891i
$612$	0.686443	+	22.4068i	0.0277478	+	0.905741i
$613$	7.81287	+	6.55577i	0.315559	+	0.264785i	0.786785	−	0.617227i	$-0.211744\pi$
$613$	7.81287	+	6.55577i	0.315559	+	0.264785i	−0.471226	+	0.882012i	$0.656188\pi$
$614$	−25.3728	+	2.96566i	−1.02396	+	0.119684i
$615$	4.37225	−	17.3776i	0.176306	−	0.700733i
$616$	−2.88481	−	3.05772i	−0.116232	−	0.123199i
$617$	−33.5712	−	3.92391i	−1.35153	−	0.157971i	−0.590682	−	0.806905i	$-0.701141\pi$
$617$	−33.5712	−	3.92391i	−1.35153	−	0.157971i	−0.760845	+	0.648934i	$0.775215\pi$
$618$	−11.1176	+	29.2837i	−0.447215	+	1.17796i
$619$	1.53303	−	26.3211i	0.0616177	−	1.05793i	−0.815839	−	0.578279i	$-0.803725\pi$
$619$	1.53303	−	26.3211i	0.0616177	−	1.05793i	0.877457	−	0.479656i	$-0.159238\pi$
$620$	3.38122	+	5.85645i	0.135793	+	0.235201i
$621$	16.5305	−	6.33403i	0.663347	−	0.254176i
$622$	5.15402	−	8.92702i	0.206657	−	0.357941i
$623$	13.3370	+	8.77186i	0.534334	+	0.351437i
$624$	3.46063	+	0.659480i	0.138536	+	0.0264003i
$625$	0.712447	+	1.65164i	0.0284979	+	0.0660655i
$626$	−11.2681	+	2.67060i	−0.450365	+	0.106739i
$627$	−6.90678	+	4.99552i	−0.275830	+	0.199502i
$628$	6.56463	+	8.81782i	0.261957	+	0.351869i
$629$	−43.1562	+	15.7076i	−1.72075	+	0.626302i
$630$	−5.43600	+	5.45273i	−0.216575	+	0.217242i
$631$	−16.7461	−	6.09507i	−0.666650	−	0.242641i	−0.0135452	−	0.999908i	$-0.504312\pi$
$631$	−16.7461	−	6.09507i	−0.666650	−	0.242641i	−0.653105	+	0.757267i	$0.726534\pi$
$632$	−2.94130	−	9.82462i	−0.116999	−	0.390802i
$633$	−23.7254	−	7.46054i	−0.942999	−	0.296530i
$634$	1.36216	+	23.3875i	0.0540984	+	0.928834i
$635$	−19.4507	+	12.7929i	−0.771878	+	0.507672i
$636$	−17.2709	+	7.16940i	−0.684836	+	0.284285i
$637$	−6.40961	−	1.51911i	−0.253958	−	0.0601892i
$638$	−1.82868	−	10.3709i	−0.0723981	−	0.410590i
$639$	8.32726	+	3.29340i	0.329421	+	0.130285i
$640$	0.229793	−	1.30322i	0.00908338	−	0.0515144i
$641$	8.32976	−	19.3106i	0.329006	−	0.762721i	−0.670772	−	0.741663i	$-0.734037\pi$
$641$	8.32976	−	19.3106i	0.329006	−	0.762721i	0.999778	−	0.0210581i	$-0.00670349\pi$
$642$	−3.08933	−	6.36862i	−0.121926	−	0.251350i
$643$	−0.298435	+	0.996842i	−0.0117691	+	0.0393116i	−0.963672	−	0.267087i	$-0.913939\pi$
$643$	−0.298435	+	0.996842i	−0.0117691	+	0.0393116i	0.951903	+	0.306399i	$0.0991241\pi$
$644$	−3.94563	+	5.29990i	−0.155480	+	0.208845i
$645$	−13.7039	−	8.16571i	−0.539591	−	0.321524i
$646$	−15.1614	+	7.61434i	−0.596517	+	0.299582i
$647$	−3.98241			−0.156565			−0.0782823	−	0.996931i	$-0.524944\pi$
$647$	−3.98241			−0.156565			−0.0782823	+	0.996931i	$0.524944\pi$
$648$	−8.61393	+	2.60772i	−0.338387	+	0.102441i
$649$	−14.9707			−0.587651
$650$	−5.90504	+	2.96562i	−0.231615	+	0.116321i
$651$	−0.236470	+	17.1645i	−0.00926800	+	0.672728i
$652$	−11.2617	+	15.1271i	−0.441043	+	0.592424i
$653$	−4.59762	+	15.3571i	−0.179919	+	0.600970i	0.819685	+	0.572815i	$0.194149\pi$
$653$	−4.59762	+	15.3571i	−0.179919	+	0.600970i	−0.999604	+	0.0281555i	$0.991037\pi$
$654$	−21.2912	−	1.53463i	−0.832553	−	0.0600087i
$655$	2.52369	−	5.85058i	0.0986089	−	0.228601i
$656$	−1.35757	+	7.69914i	−0.0530040	+	0.300601i
$657$	−23.3127	−	20.6824i	−0.909515	−	0.806898i
$658$	1.41922	+	8.04881i	0.0553271	+	0.313775i
$659$	−5.19134	−	1.23037i	−0.202226	−	0.0479284i	0.128254	−	0.991741i	$-0.459063\pi$
$659$	−5.19134	−	1.23037i	−0.202226	−	0.0479284i	−0.330480	+	0.943813i	$0.607211\pi$
$660$	−3.94381	−	3.02138i	−0.153513	−	0.117607i
$661$	5.47643	−	3.60191i	0.213009	−	0.140098i	−0.438522	−	0.898721i	$-0.644498\pi$
$661$	5.47643	−	3.60191i	0.213009	−	0.140098i	0.651530	+	0.758623i	$0.274127\pi$
$662$	−0.0140016	−	0.240398i	−0.000544188	−	0.00934334i
$663$	19.3949	−	17.7996i	0.753236	−	0.691279i
$664$	−1.04160	−	3.47920i	−0.0404221	−	0.135019i
$665$	−5.47577	−	1.99302i	−0.212341	−	0.0772859i
$666$	−10.5989	−	15.0873i	−0.410698	−	0.584623i
$667$	−15.5539	+	5.66116i	−0.602250	+	0.219201i
$668$	6.07404	+	8.15885i	0.235012	+	0.315675i
$669$	17.6950	+	7.92375i	0.684129	+	0.306350i
$670$	−14.6585	+	3.47413i	−0.566307	+	0.134217i
$671$	7.73445	+	17.9305i	0.298585	+	0.692198i
$672$	2.19449	−	2.54330i	0.0846543	−	0.0981100i
$673$	−15.1546	−	9.96731i	−0.584165	−	0.384212i	0.222753	−	0.974875i	$-0.428496\pi$
$673$	−15.1546	−	9.96731i	−0.584165	−	0.384212i	−0.806918	+	0.590663i	$0.798866\pi$
$674$	−4.04274	+	7.00223i	−0.155720	+	0.269716i
$675$	9.85122	−	13.7088i	0.379174	−	0.527652i
$676$	4.43152	+	7.67563i	0.170443	+	0.295216i
$677$	1.04089	−	17.8714i	0.0400046	−	0.686853i	−0.917376	−	0.398023i	$-0.869697\pi$
$677$	1.04089	−	17.8714i	0.0400046	−	0.686853i	0.957380	−	0.288830i	$-0.0932664\pi$
$678$	26.5260	−	4.30137i	1.01873	−	0.165193i
$679$	15.4991	+	1.81158i	0.594800	+	0.0695222i
$680$	−6.78589	−	7.19262i	−0.260227	−	0.275824i
$681$	−19.7887	−	19.1917i	−0.758304	−	0.735429i
$682$	−11.0016	+	1.28590i	−0.421273	+	0.0492397i
$683$	19.3775	+	16.2596i	0.741459	+	0.622158i	0.933229	−	0.359282i	$-0.116978\pi$
$683$	19.3775	+	16.2596i	0.741459	+	0.622158i	−0.191770	+	0.981440i	$0.561423\pi$
$684$	−4.53604	−	5.08135i	−0.173440	−	0.194290i
$685$	−0.630217	+	0.528815i	−0.0240793	+	0.0202050i
$686$	−13.6267	+	14.4435i	−0.520272	+	0.551456i
$687$	10.0313	+	15.7193i	0.382717	+	0.599729i
$688$	6.21949	+	3.12354i	0.237116	+	0.119084i
$689$	19.6235	+	9.85530i	0.747596	+	0.375457i
$690$	−3.60035	+	6.92920i	−0.137063	+	0.263790i
$691$	−3.92984	+	4.16539i	−0.149498	+	0.158459i	−0.797795	−	0.602929i	$-0.794000\pi$
$691$	−3.92984	+	4.16539i	−0.149498	+	0.158459i	0.648297	+	0.761388i	$0.275482\pi$
$692$	−14.3265	+	12.0213i	−0.544611	+	0.456983i
$693$	−4.67419	−	11.7131i	−0.177558	−	0.444945i
$694$	−7.19360	−	6.03614i	−0.273065	−	0.229129i
$695$	−3.88176	+	0.453713i	−0.147244	+	0.0172103i
$696$	8.09411	−	2.30221i	0.306807	−	0.0872651i
$697$	40.0894	+	42.4923i	1.51850	+	1.60951i
$698$	−3.55014	−	0.414952i	−0.134375	−	0.0157062i
$699$	18.9141	+	23.1822i	0.715398	+	0.876830i
$700$	−0.366361	+	6.29017i	−0.0138471	+	0.237746i
$701$	17.6846	+	30.6306i	0.667937	+	1.15690i	0.978480	+	0.206342i	$0.0661559\pi$
$701$	17.6846	+	30.6306i	0.667937	+	1.15690i	−0.310543	+	0.950559i	$0.600511\pi$
$702$	8.92663	+	5.65800i	0.336914	+	0.213547i
$703$	6.97724	−	12.0849i	0.263151	−	0.455792i
$704$	1.81095	+	1.19108i	0.0682526	+	0.0448905i
$705$	3.17824	+	9.12118i	0.119700	+	0.343524i
$706$	1.57869	+	3.65982i	0.0594148	+	0.137739i
$707$	−35.1275	+	8.32536i	−1.32110	+	0.313108i
$708$	−1.22500	−	11.9000i	−0.0460382	−	0.447231i
$709$	−3.93861	−	5.29048i	−0.147918	−	0.198688i	0.721989	−	0.691905i	$-0.243228\pi$
$709$	−3.93861	−	5.29048i	−0.147918	−	0.198688i	−0.869906	+	0.493217i	$0.835821\pi$
$710$	−3.71186	+	1.35101i	−0.139304	+	0.0507024i
$711$	2.63435	−	30.6534i	0.0987959	−	1.14959i
$712$	−7.73444	−	2.81510i	−0.289860	−	0.105501i
$713$	4.99313	+	16.6782i	0.186994	+	0.624604i
$714$	−5.45176	−	24.5022i	−0.204027	−	0.916971i
$715$	0.339222	+	5.82422i	0.0126862	+	0.217813i
$716$	14.3578	−	9.44328i	0.536577	−	0.352912i
$717$	5.48434	−	41.9066i	0.204817	−	1.56503i
$718$	21.6178	+	5.12352i	0.806771	+	0.191208i
$719$	−8.53090	−	48.3811i	−0.318149	−	1.80431i	−0.553993	−	0.832521i	$-0.686897\pi$
$719$	−8.53090	−	48.3811i	−0.318149	−	1.80431i	0.235845	−	0.971791i	$-0.424214\pi$
$720$	2.07895	−	3.38212i	0.0774780	−	0.126044i
$721$	6.09044	−	34.5406i	0.226820	−	1.28636i
$722$	−5.48369	+	12.7126i	−0.204082	+	0.473115i
$723$	27.0820	−	39.9660i	1.00719	−	1.48635i
$724$	−6.51696	+	21.7682i	−0.242201	+	0.809007i
$725$	−9.42572	+	12.6609i	−0.350063	+	0.470216i
$726$	−9.52699	+	5.32679i	−0.353580	+	0.197696i
$727$	−32.4735	+	16.3088i	−1.20438	+	0.604860i	−0.933785	−	0.357835i	$-0.883515\pi$
$727$	−32.4735	+	16.3088i	−1.20438	+	0.604860i	−0.270590	+	0.962695i	$0.587219\pi$
$728$	−3.94470			−0.146200
$729$	−26.9078	−	2.22915i	−0.996586	−	0.0825612i
$730$	13.7471			0.508802
$731$	46.4747	−	23.3405i	1.71893	−	0.863279i
$732$	−13.6198	+	7.61521i	−0.503404	+	0.281466i
$733$	−5.43505	+	7.30054i	−0.200748	+	0.269652i	−0.891085	−	0.453837i	$-0.850055\pi$
$733$	−5.43505	+	7.30054i	−0.200748	+	0.269652i	0.690337	+	0.723488i	$0.257462\pi$
$734$	−3.61798	+	12.0849i	−0.133542	+	0.446062i
$735$	−4.16412	+	6.14515i	−0.153596	+	0.226667i
$736$	1.34938	−	3.12822i	0.0497389	−	0.115308i
$737$	4.28474	−	24.3000i	0.157831	−	0.895102i
$738$	−12.2820	+	19.9808i	−0.452105	+	0.735502i
$739$	−1.83509	−	10.4073i	−0.0675048	−	0.382839i	−0.999778	−	0.0210830i	$-0.993289\pi$
$739$	−1.83509	−	10.4073i	−0.0675048	−	0.382839i	0.932273	−	0.361756i	$-0.117823\pi$
$740$	7.91399	+	1.87565i	0.290924	+	0.0689503i
$741$	−1.03794	+	7.93106i	−0.0381298	+	0.291355i
$742$	17.4941	−	11.5061i	0.642229	−	0.422401i
$743$	1.62018	+	27.8173i	0.0594385	+	1.02052i	0.887772	+	0.460284i	$0.152252\pi$
$743$	1.62018	+	27.8173i	0.0594385	+	1.02052i	−0.828333	+	0.560235i	$0.810711\pi$
$744$	−1.92237	−	8.63982i	−0.0704775	−	0.316751i
$745$	−0.501186	−	1.67408i	−0.0183620	−	0.0613335i
$746$	−3.79837	−	1.38249i	−0.139068	−	0.0506167i
$747$	0.932906	−	10.8553i	0.0341332	−	0.397175i
$748$	15.2200	−	5.53961i	0.556497	−	0.202548i
$749$	4.73300	+	6.35752i	0.172940	+	0.232299i
$750$	1.93605	+	18.8075i	0.0706947	+	0.686751i
$751$	2.57908	−	0.611252i	0.0941118	−	0.0223049i	−0.183290	−	0.983059i	$-0.558675\pi$
$751$	2.57908	−	0.611252i	0.0941118	−	0.0223049i	0.277402	+	0.960754i	$0.410527\pi$
$752$	−1.66913	−	3.86947i	−0.0608667	−	0.141105i
$753$	8.26259	+	23.7127i	0.301105	+	0.864137i
$754$	−8.25623	−	5.43021i	−0.300674	−	0.197757i
$755$	1.14249	−	1.97885i	0.0415794	−	0.0720177i
$756$	8.92817	−	4.67390i	0.324714	−	0.169988i
$757$	−7.00766	−	12.1376i	−0.254698	−	0.441149i	0.710116	−	0.704085i	$-0.248643\pi$
$757$	−7.00766	−	12.1376i	−0.254698	−	0.441149i	−0.964813	+	0.262936i	$0.915309\pi$
$758$	2.12083	−	36.4132i	0.0770319	−	1.32259i
$759$	−8.08565	−	9.91021i	−0.293491	−	0.359718i
$760$	2.98428	+	0.348812i	0.108251	+	0.0126527i
$761$	12.0637	+	12.7867i	0.437308	+	0.463519i	0.908117	−	0.418716i	$-0.137520\pi$
$761$	12.0637	+	12.7867i	0.437308	+	0.463519i	−0.470810	+	0.882235i	$0.656038\pi$
$762$	29.3087	−	8.33628i	1.06174	−	0.301991i
$763$	23.7407	−	2.77489i	0.859470	−	0.100458i
$764$	4.49421	+	3.77109i	0.162595	+	0.136433i
$765$	−10.9950	−	27.5526i	−0.397526	−	0.996168i
$766$	−2.97580	+	2.49699i	−0.107520	+	0.0902200i
$767$	−9.64037	+	10.2182i	−0.348094	+	0.368958i

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.893633 - 0.448799i) q^{2} +(1.51179 - 0.845280i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-0.379535 + 1.26773i) q^{5} +(0.971622 - 1.43386i) q^{6} +(-0.768169 + 1.78082i) q^{7} +(0.173648 - 0.984808i) q^{8} +(1.57100 - 2.55577i) q^{9} +O(q^{10})\)	\(q+(0.893633 - 0.448799i) q^{2} +(1.51179 - 0.845280i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-0.379535 + 1.26773i) q^{5} +(0.971622 - 1.43386i) q^{6} +(-0.768169 + 1.78082i) q^{7} +(0.173648 - 0.984808i) q^{8} +(1.57100 - 2.55577i) q^{9} +(0.229793 + 1.30322i) q^{10} +(-2.10911 - 0.499867i) q^{11} +(0.224758 - 1.71741i) q^{12} +(-1.69934 + 1.11767i) q^{13} +(0.112768 + 1.93615i) q^{14} +(0.497815 + 2.23736i) q^{15} +(-0.286803 - 0.957990i) q^{16} +(-7.02180 - 2.55572i) q^{17} +(0.256873 - 2.98898i) q^{18} +(2.13356 - 0.776551i) q^{19} +(0.790236 + 1.06147i) q^{20} +(0.343980 + 3.34153i) q^{21} +(-2.10911 + 0.499867i) q^{22} +(1.34938 + 3.12822i) q^{23} +(-0.569919 - 1.63560i) q^{24} +(2.71434 + 1.78525i) q^{25} +(-1.01697 + 1.76145i) q^{26} +(0.214683 - 5.19172i) q^{27} +(0.969715 + 1.67960i) q^{28} +(-0.282496 + 4.85027i) q^{29} +(1.44899 + 1.77596i) q^{30} +(5.07563 + 0.593256i) q^{31} +(-0.686242 - 0.727374i) q^{32} +(-3.61105 + 1.02709i) q^{33} +(-7.42191 + 0.867497i) q^{34} +(-1.96605 - 1.64972i) q^{35} +(-1.11190 - 2.78634i) q^{36} +(4.70814 - 3.95060i) q^{37} +(1.55810 - 1.65149i) q^{38} +(-1.62429 + 3.12610i) q^{39} +(1.18257 + 0.593908i) q^{40} +(-6.98634 - 3.50867i) q^{41} +(1.80707 + 2.83173i) q^{42} +(-4.77609 + 5.06236i) q^{43} +(-1.66043 + 1.39326i) q^{44} +(2.64378 + 2.96162i) q^{45} +(2.60979 + 2.18988i) q^{46} +(4.18562 - 0.489229i) q^{47} +(-1.24336 - 1.20585i) q^{48} +(2.22247 + 2.35568i) q^{49} +(3.22684 + 0.377163i) q^{50} +(-12.7758 + 2.07167i) q^{51} +(-0.118264 + 2.03051i) q^{52} +(-5.39818 - 9.34993i) q^{53} +(-2.13819 - 4.73584i) q^{54} +(1.43418 - 2.48407i) q^{55} +(1.62037 + 1.06573i) q^{56} +(2.56908 - 2.97743i) q^{57} +(1.92435 + 4.46115i) q^{58} +(6.72062 - 1.59282i) q^{59} +(2.09191 + 0.936749i) q^{60} +(-5.37986 - 7.22641i) q^{61} +(4.80200 - 1.74779i) q^{62} +(3.34456 + 4.76093i) q^{63} +(-0.939693 - 0.342020i) q^{64} +(-0.771954 - 2.57851i) q^{65} +(-2.76599 + 2.53848i) q^{66} +(0.661912 + 11.3646i) q^{67} +(-6.24313 + 4.10617i) q^{68} +(4.68420 + 3.58860i) q^{69} +(-2.49732 - 0.591876i) q^{70} +(0.518333 + 2.93961i) q^{71} +(-2.24414 - 1.99094i) q^{72} +(1.80390 - 10.2304i) q^{73} +(2.43432 - 5.64339i) q^{74} +(5.61253 + 0.404540i) q^{75} +(0.651182 - 2.17510i) q^{76} +(2.51032 - 3.37195i) q^{77} +(-0.0485295 + 3.52257i) q^{78} +(9.16461 - 4.60264i) q^{79} +1.32333 q^{80} +(-4.06390 - 8.03024i) q^{81} -7.81791 q^{82} +(3.24547 - 1.62994i) q^{83} +(2.88573 + 1.71951i) q^{84} +(5.90499 - 7.93178i) q^{85} +(-1.99609 + 6.66740i) q^{86} +(3.67276 + 7.57137i) q^{87} +(-0.858516 + 1.99026i) q^{88} +(1.42927 - 8.10577i) q^{89} +(3.69174 + 1.46007i) q^{90} +(-0.684990 - 3.88477i) q^{91} +(3.31501 + 0.785672i) q^{92} +(8.17474 - 3.39345i) q^{93} +(3.52084 - 2.31569i) q^{94} +(0.174701 + 2.99951i) q^{95} +(-1.65229 - 0.519568i) q^{96} +(-2.30761 - 7.70796i) q^{97} +(3.04330 + 1.10767i) q^{98} +(-4.59096 + 4.60509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

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