LMFDB - Embedded newform 162.2.g.b.13.5

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			13.5
Character	$\chi$	$=$	162.13
Dual form			162.2.g.b.25.5

$q$-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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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	−0.999955	−	0.00951452i	$-0.996971\pi$
$5$	−0.379535	−	1.26773i	−0.169733	−	0.566948i	0.830222	−	0.557433i	$-0.188214\pi$
$6$	0.971622	+	1.43386i	0.396663	+	0.585370i
$7$	−0.768169	−	1.78082i	−0.290341	−	0.673085i	0.709148	−	0.705060i	$-0.249080\pi$
$7$	−0.768169	−	1.78082i	−0.290341	−	0.673085i	−0.999489	+	0.0319744i	$0.989821\pi$
$8$	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	−0.535916	−	0.844271i	$-0.680034\pi$
$11$	−2.10911	+	0.499867i	−0.635919	+	0.150716i	−0.100004	+	0.994987i	$0.531885\pi$
$12$	0.224758	+	1.71741i	0.0648821	+	0.495772i
$13$	−1.69934	−	1.11767i	−0.471312	−	0.309987i	0.291541	−	0.956558i	$-0.405832\pi$
$13$	−1.69934	−	1.11767i	−0.471312	−	0.309987i	−0.762854	+	0.646571i	$0.776202\pi$
$14$	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	−0.996165	−	0.0874893i	$-0.972116\pi$
$17$	−7.02180	+	2.55572i	−1.70304	+	0.619854i	−0.706870	+	0.707343i	$0.749893\pi$
$18$	0.256873	+	2.98898i	0.0605456	+	0.704510i
$19$	2.13356	+	0.776551i	0.489471	+	0.178153i	0.574952	−	0.818187i	$-0.305021\pi$
$19$	2.13356	+	0.776551i	0.489471	+	0.178153i	−0.0854813	+	0.996340i	$0.527243\pi$
$20$	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	−0.717661	−	0.696393i	$-0.754787\pi$
$23$	1.34938	−	3.12822i	0.281366	−	0.652279i	0.999027	+	0.0441139i	$0.0140465\pi$
$24$	−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	−0.917193	−	0.398444i	$-0.869550\pi$
$29$	−0.282496	−	4.85027i	−0.0524582	−	0.900673i	0.864735	−	0.502229i	$-0.167487\pi$
$30$	1.44899	−	1.77596i	0.264548	−	0.324244i
$31$	5.07563	−	0.593256i	0.911610	−	0.106552i	0.352658	−	0.935752i	$-0.385278\pi$
$31$	5.07563	−	0.593256i	0.911610	−	0.106552i	0.558952	+	0.829200i	$0.311204\pi$
$32$	−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	0.941733	−	0.336360i	$-0.109196\pi$
$37$	4.70814	+	3.95060i	0.774013	+	0.649474i	−0.167720	+	0.985835i	$0.553640\pi$
$38$	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	−0.901006	−	0.433807i	$-0.857170\pi$
$41$	−6.98634	+	3.50867i	−1.09108	+	0.547962i	−0.190077	+	0.981769i	$0.560874\pi$
$42$	1.80707	−	2.83173i	0.278837	−	0.436945i
$43$	−4.77609	−	5.06236i	−0.728347	−	0.772003i	0.252329	−	0.967641i	$-0.418803\pi$
$43$	−4.77609	−	5.06236i	−0.728347	−	0.772003i	−0.980676	+	0.195639i	$0.937322\pi$
$44$	−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	0.415741	−	0.909483i	$-0.363522\pi$
$47$	4.18562	+	0.489229i	0.610535	+	0.0713614i	0.194794	+	0.980844i	$0.437596\pi$
$48$	−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	0.210316	+	0.977633i	$0.432551\pi$
$53$	−5.39818	+	9.34993i	−0.741497	+	1.28431i	−0.951813	+	0.306678i	$0.900783\pi$
$54$	−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	0.643469	−	0.765472i	$-0.277495\pi$
$59$	6.72062	+	1.59282i	0.874950	+	0.207367i	0.231481	+	0.972839i	$0.425643\pi$
$60$	2.09191	−	0.936749i	0.270065	−	0.120934i
$61$	−5.37986	+	7.22641i	−0.688820	+	0.925246i	−0.999682	−	0.0252087i	$-0.991975\pi$
$61$	−5.37986	+	7.22641i	−0.688820	+	0.925246i	0.310862	+	0.950455i	$0.399382\pi$
$62$	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	−0.676994	−	0.735988i	$-0.736718\pi$
$67$	0.661912	−	11.3646i	0.0808654	−	1.38841i	0.757860	−	0.652417i	$-0.226245\pi$
$68$	−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	−0.938479	−	0.345336i	$-0.887765\pi$
$71$	0.518333	−	2.93961i	0.0615148	−	0.348868i	0.999994	−	0.00353124i	$-0.00112403\pi$
$72$	−2.24414	+	1.99094i	−0.264474	+	0.234635i
$73$	1.80390	+	10.2304i	0.211131	+	1.19738i	0.887496	+	0.460816i	$0.152443\pi$
$73$	1.80390	+	10.2304i	0.211131	+	1.19738i	−0.676365	+	0.736567i	$0.736446\pi$
$74$	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	0.882131	−	0.471005i	$-0.156108\pi$
$79$	9.16461	+	4.60264i	1.03110	+	0.517837i	0.148968	+	0.988842i	$0.452405\pi$
$80$	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	0.617912	−	0.786247i	$-0.287979\pi$
$83$	3.24547	+	1.62994i	0.356237	+	0.178909i	−0.261675	+	0.965156i	$0.584275\pi$
$84$	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	0.961915	+	0.273350i	$0.0881319\pi$
$89$	1.42927	+	8.10577i	0.151502	+	0.859210i	−0.810413	+	0.585860i	$0.800757\pi$
$90$	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	0.757274	+	0.653098i	$0.226531\pi$
$97$	−2.30761	+	7.70796i	−0.234302	+	0.782624i	−0.991576	+	0.129527i	$0.958654\pi$
$98$	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	0.250357	−	0.968153i	$-0.419452\pi$
$101$	11.1155	−	14.9307i	1.10603	−	1.48566i	0.855678	−	0.517509i	$-0.173141\pi$
$102$	−10.4871	−	7.58507i	−1.03838	−	0.751033i
$103$	−17.5969	−	4.17055i	−1.73388	−	0.410937i	−0.762218	−	0.647320i	$-0.775890\pi$
$103$	−17.5969	−	4.17055i	−1.73388	−	0.410937i	−0.971660	+	0.236383i	$0.924038\pi$
$104$	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	0.947730	−	0.319075i	$-0.103372\pi$
$107$	2.04335	+	3.53919i	0.197538	+	0.342146i	−0.750192	+	0.661221i	$0.770039\pi$
$108$	−4.03620	+	3.27248i	−0.388383	+	0.314895i
$109$	−6.16219	+	10.6732i	−0.590231	+	1.02231i	0.403970	+	0.914772i	$0.367630\pi$
$109$	−6.16219	+	10.6732i	−0.590231	+	1.02231i	−0.994201	+	0.107538i	$0.965703\pi$
$110$	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	0.00348030	−	0.999994i	$-0.498892\pi$
$113$	10.6469	−	11.2851i	1.00158	−	1.06161i	0.998100	−	0.0616189i	$-0.0196263\pi$
$114$	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	0.196121	−	0.980580i	$-0.437165\pi$
$127$	13.4767	−	11.3083i	1.19586	−	1.00345i	0.999739	−	0.0228661i	$-0.00727913\pi$
$128$	−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	−0.322413	−	0.946599i	$-0.604494\pi$
$131$	−4.78234	+	0.558975i	−0.417835	+	0.0488379i	−0.0954217	+	0.995437i	$0.530420\pi$
$132$	−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	−0.527127	−	0.849786i	$-0.676731\pi$
$137$	0.519408	−	0.341620i	0.0443760	−	0.0291866i	0.571503	+	0.820600i	$0.306360\pi$
$138$	5.79651	−	1.10462i	0.493432	−	0.0940317i
$139$	1.16974	−	2.71177i	0.0992164	−	0.230010i	−0.861377	−	0.507966i	$-0.830398\pi$
$139$	1.16974	−	2.71177i	0.0992164	−	0.230010i	0.960594	+	0.277956i	$0.0896570\pi$
$140$	−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	0.503512	−	0.863988i	$-0.332041\pi$
$149$	−1.10328	−	0.725642i	−0.0903846	−	0.0594469i	−0.593897	+	0.804541i	$0.702411\pi$
$150$	5.19710	+	2.15739i	0.424341	+	0.176150i
$151$	−1.68015	+	0.398202i	−0.136728	+	0.0324052i	−0.298410	−	0.954438i	$-0.596456\pi$
$151$	−1.68015	+	0.398202i	−0.136728	+	0.0324052i	0.161682	+	0.986843i	$0.448308\pi$
$152$	−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	−0.986707	−	0.162509i	$-0.948041\pi$
$157$	−3.15286	−	10.5313i	−0.251625	−	0.840487i	0.735082	−	0.677979i	$-0.237144\pi$
$158$	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	−0.993554	−	0.113357i	$-0.963839\pi$
$167$	−2.91724	−	9.74426i	−0.225743	−	0.754033i	0.767812	−	0.640676i	$-0.221346\pi$
$168$	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	−0.853957	−	0.520344i	$-0.825804\pi$
$173$	−18.1978	+	4.31295i	−1.38355	+	0.327908i	−0.529594	+	0.848251i	$0.677656\pi$
$174$	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	0.341338	−	0.939941i	$-0.389120\pi$
$179$	16.1486	−	5.87760i	1.20700	−	0.439312i	0.865662	+	0.500628i	$0.166898\pi$
$180$	3.95434	+	0.352085i	0.294739	+	0.0262429i
$181$	−21.3524	−	7.77164i	−1.58711	−	0.577661i	−0.610376	−	0.792112i	$-0.708982\pi$
$181$	−21.3524	−	7.77164i	−1.58711	−	0.577661i	−0.976735	+	0.214450i	$0.931204\pi$
$182$	−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	−0.987903	−	0.155073i	$-0.950439\pi$
$191$	−0.341122	−	5.85684i	−0.0246827	−	0.423786i	0.963220	−	0.268713i	$-0.0865984\pi$
$192$	−1.70972	−	0.277242i	−0.123388	−	0.0200082i
$193$	11.7776	−	1.37661i	0.847771	−	0.0990903i	0.318896	−	0.947790i	$-0.396688\pi$
$193$	11.7776	−	1.37661i	0.847771	−	0.0990903i	0.528875	+	0.848699i	$0.322614\pi$
$194$	−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	−0.557315	−	0.830301i	$-0.688168\pi$
$197$	2.29618	−	1.92672i	0.163596	−	0.137273i	0.720911	+	0.693028i	$0.243724\pi$
$198$	−2.03587	−	6.17568i	−0.144683	−	0.438886i
$199$	15.4208	+	12.9396i	1.09315	+	0.917261i	0.996945	−	0.0781009i	$-0.0248856\pi$
$199$	15.4208	+	12.9396i	1.09315	+	0.917261i	0.0962034	+	0.995362i	$0.469330\pi$
$200$	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	−0.971498	−	0.237046i	$-0.923821\pi$
$211$	−9.85383	+	10.4445i	−0.678366	+	0.719026i	0.293133	+	0.956072i	$0.405302\pi$
$212$	−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	−0.519843	−	0.854262i	$-0.674010\pi$
$223$	6.68444	−	8.97876i	0.447623	−	0.601262i	0.967466	+	0.252999i	$0.0814171\pi$
$224$	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	0.661980	+	0.749522i	$0.269717\pi$
$227$	−4.56463	+	15.2469i	−0.302965	+	1.01197i	−0.964945	+	0.262453i	$0.915469\pi$
$228$	−0.854119	+	3.83872i	−0.0565654	+	0.254225i
$229$	0.625990	−	10.7478i	0.0413666	−	0.710236i	−0.912328	−	0.409460i	$-0.865717\pi$
$229$	0.625990	−	10.7478i	0.0413666	−	0.710236i	0.953695	−	0.300776i	$-0.0972458\pi$
$230$	−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	−0.713746	−	0.700405i	$-0.753003\pi$
$233$	2.99957	−	17.0114i	0.196508	−	1.11445i	0.910254	−	0.414050i	$-0.135886\pi$
$234$	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	0.963896	+	0.266279i	$0.0857942\pi$
$239$	14.5713	+	19.5727i	0.942540	+	1.26605i	−0.0213560	+	0.999772i	$0.506798\pi$
$240$	2.00059	+	1.11858i	0.129138	+	0.0722042i
$241$	24.9082	+	12.5094i	1.60448	+	0.805800i	0.999958	+	0.00921168i	$0.00293221\pi$
$241$	24.9082	+	12.5094i	1.60448	+	0.805800i	0.604522	+	0.796588i	$0.293364\pi$
$242$	−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	−0.955129	−	0.296191i	$-0.904284\pi$
$251$	−2.51752	−	14.2776i	−0.158904	−	0.901192i	0.796224	−	0.605001i	$-0.206827\pi$
$252$	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	0.735832	+	0.677165i	$0.236792\pi$
$257$	−1.18052	+	20.2687i	−0.0736386	+	1.26433i	−0.809470	+	0.587161i	$0.800246\pi$
$258$	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	−0.607894	−	0.794018i	$-0.707985\pi$
$263$	5.30489	−	7.12570i	0.327114	−	0.439390i	0.935007	+	0.354629i	$0.115393\pi$
$264$	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	0.889347	−	0.457232i	$-0.151159\pi$
$269$	0.798719	+	1.38342i	0.0486987	+	0.0843487i	−0.840649	+	0.541581i	$0.817826\pi$
$270$	6.81530	+	0.913242i	0.414766	+	0.0555781i
$271$	10.0971	−	17.4887i	0.613355	−	1.06236i	−0.377316	−	0.926084i	$-0.623153\pi$
$271$	10.0971	−	17.4887i	0.613355	−	1.06236i	0.990671	−	0.136277i	$-0.0435137\pi$
$272$	−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	0.165547	−	0.986202i	$-0.447061\pi$
$277$	1.65097	+	0.192970i	0.0991970	+	0.0115945i	−0.0663496	+	0.997796i	$0.521135\pi$
$278$	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	0.429722	−	0.902961i	$-0.358612\pi$
$281$	−8.32617	−	8.82522i	−0.496698	−	0.526469i	−0.926420	+	0.376492i	$0.877130\pi$
$282$	3.36535	+	6.47693i	0.200404	+	0.385696i
$283$	−12.6764	+	6.36632i	−0.753533	+	0.378439i	−0.783727	−	0.621105i	$-0.786684\pi$
$283$	−12.6764	+	6.36632i	−0.753533	+	0.378439i	0.0301938	+	0.999544i	$0.490388\pi$
$284$	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	−0.676573	−	0.736375i	$-0.736536\pi$
$293$	−19.9431	+	2.33102i	−1.16509	+	0.136179i	−0.488517	+	0.872555i	$0.662462\pi$
$294$	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	−0.919142	−	0.393926i	$-0.871117\pi$
$307$	−24.0050	+	8.73709i	−1.37004	+	0.498652i	−0.450893	+	0.892578i	$0.648894\pi$
$308$	−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	0.769695	−	0.638412i	$-0.220408\pi$
$311$	8.61224	+	5.66436i	0.488355	+	0.321196i	−0.281340	+	0.959608i	$0.590779\pi$
$312$	2.79655	−	2.14246i	0.158324	−	0.121293i
$313$	−11.2681	+	2.67060i	−0.636913	+	0.150951i	−0.536372	−	0.843982i	$-0.680205\pi$
$313$	−11.2681	+	2.67060i	−0.636913	+	0.150951i	−0.100541	+	0.994933i	$0.532057\pi$
$314$	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	−0.952095	−	0.305802i	$-0.901075\pi$
$317$	−9.27900	−	21.5111i	−0.521160	−	1.20819i	0.430935	−	0.902383i	$-0.358184\pi$
$318$	−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	0.920817	−	0.389994i	$-0.127523\pi$
$331$	0.0953783	+	0.221112i	0.00524246	+	0.0121534i	−0.915575	+	0.402148i	$0.868264\pi$
$332$	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	0.352026	−	0.935990i	$-0.385493\pi$
$337$	−6.75532	−	4.44304i	−0.367986	−	0.242028i	−0.720011	+	0.693962i	$0.755863\pi$
$338$	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	−0.988404	−	0.151849i	$-0.951477\pi$
$347$	−3.71942	+	8.62258i	−0.199669	+	0.462884i	0.788735	+	0.614733i	$0.210736\pi$
$348$	8.26639	−	1.57530i	0.443125	−	0.0844449i
$349$	−2.98629	+	1.96411i	−0.159853	+	0.105137i	−0.626915	−	0.779088i	$-0.715683\pi$
$349$	−2.98629	+	1.96411i	−0.159853	+	0.105137i	0.467062	+	0.884224i	$0.345312\pi$
$350$	−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	−0.998844	−	0.0480749i	$-0.984691\pi$
$353$	−0.231753	−	3.97905i	−0.0123350	−	0.211783i	0.986509	−	0.163709i	$-0.0523457\pi$
$354$	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	−0.0716159	−	0.997432i	$-0.522816\pi$
$359$	17.0190	−	14.2806i	0.898227	−	0.753702i	0.969843	+	0.243730i	$0.0783711\pi$
$360$	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	0.460877	−	0.887464i	$-0.347535\pi$
$367$	−8.65683	−	9.17571i	−0.451883	−	0.478968i	−0.912760	+	0.408496i	$0.866053\pi$
$368$	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	−0.795193	−	0.606356i	$-0.792631\pi$
$373$	−2.77388	+	2.94015i	−0.143626	+	0.152235i	0.651567	+	0.758591i	$0.274112\pi$
$374$	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	0.771402	+	0.636348i	$0.219556\pi$
$379$	18.2374	+	31.5882i	0.936795	+	1.62258i	0.165392	+	0.986228i	$0.447111\pi$
$380$	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	0.132905	−	0.991129i	$-0.457570\pi$
$383$	−3.77992	−	0.895858i	−0.193145	−	0.0457762i	−0.326050	+	0.945353i	$0.605718\pi$
$384$	−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	−0.484235	−	0.874938i	$-0.660902\pi$
$389$	7.91140	−	26.4259i	0.401124	−	1.33985i	0.885359	−	0.464909i	$-0.153913\pi$
$390$	−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	0.992220	−	0.124493i	$-0.0397305\pi$
$397$	0.343883	+	1.95026i	0.0172590	+	0.0978806i	−0.974961	+	0.222374i	$0.928619\pi$
$398$	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	0.999231	+	0.0392012i	$0.0124813\pi$
$401$	15.0228	+	20.1791i	0.750203	+	1.00770i	−0.249028	+	0.968496i	$0.580111\pi$
$402$	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	0.966410	+	0.257006i	$0.0827361\pi$
$409$	18.9183	+	25.4117i	0.935450	+	1.25653i	−0.0309600	+	0.999521i	$0.509856\pi$
$410$	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	−0.994953	−	0.100345i	$-0.968005\pi$
$419$	0.100748	−	1.72977i	0.00492185	−	0.0845049i	0.999875	+	0.0158403i	$0.00504233\pi$
$420$	−3.27512	−	3.00573i	−0.159809	−	0.146664i
$421$	−8.06168	+	26.9279i	−0.392902	+	1.31238i	0.501514	+	0.865149i	$0.332777\pi$
$421$	−8.06168	+	26.9279i	−0.392902	+	1.31238i	−0.894416	+	0.447235i	$0.852409\pi$
$422$	−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	0.852037	−	0.523482i	$-0.175367\pi$
$431$	−0.567396	−	0.982759i	−0.0273305	−	0.0473378i	−0.879367	+	0.476144i	$0.842034\pi$
$432$	−5.03518	−	1.28334i	−0.242255	−	0.0617445i
$433$	8.75124	−	15.1576i	0.420558	−	0.728427i	−0.575436	−	0.817846i	$-0.695168\pi$
$433$	8.75124	−	15.1576i	0.420558	−	0.728427i	0.995994	+	0.0894194i	$0.0285011\pi$
$434$	−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	−0.287878	−	0.957667i	$-0.592950\pi$
$439$	−16.5282	−	1.93187i	−0.788849	−	0.0922032i	−0.500971	+	0.865464i	$0.667024\pi$
$440$	−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	0.998194	−	0.0600754i	$-0.0191341\pi$
$443$	18.5257	+	19.6360i	0.880180	+	0.932937i	−0.118014	+	0.993012i	$0.537653\pi$
$444$	−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	0.918765	−	0.394806i	$-0.129188\pi$
$449$	14.6102	+	12.2594i	0.689499	+	0.578558i	−0.229266	+	0.973364i	$0.573633\pi$
$450$	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	−0.985033	−	0.172368i	$-0.944858\pi$
$457$	−0.570163	−	9.78932i	−0.0266711	−	0.457925i	0.958362	−	0.285558i	$-0.0921788\pi$
$458$	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	−0.802111	−	0.597175i	$-0.796290\pi$
$461$	−12.2701	+	8.07018i	−0.571476	+	0.375866i	0.230635	+	0.973040i	$0.425920\pi$
$462$	−2.39581	+	6.87570i	−0.111463	+	0.319887i
$463$	−12.0622	+	27.9633i	−0.560577	+	1.29956i	0.368482	+	0.929635i	$0.379877\pi$
$463$	−12.0622	+	27.9633i	−0.560577	+	1.29956i	−0.929060	+	0.369930i	$0.879382\pi$
$464$	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	0.235462	−	0.971884i	$-0.424340\pi$
$467$	−4.51390	−	1.64293i	−0.208879	−	0.0760256i	−0.444340	+	0.895858i	$0.646562\pi$
$468$	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	0.892668	−	0.450714i	$-0.148831\pi$
$479$	−1.04518	−	2.42300i	−0.0477555	−	0.110710i	−0.940424	+	0.340005i	$0.889571\pi$
$480$	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	−0.982689	−	0.185263i	$-0.940686\pi$
$491$	−5.83806	−	19.5005i	−0.263468	−	0.880045i	0.719221	−	0.694782i	$-0.244499\pi$
$492$	−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	0.527331	−	0.849660i	$-0.323193\pi$
$499$	−0.982338	−	0.646094i	−0.0439755	−	0.0289231i	−0.571306	+	0.820737i	$0.693563\pi$
$500$	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	0.407705	−	0.913114i	$-0.366329\pi$
$503$	29.3121	−	10.6687i	1.30696	−	0.475696i	0.899258	+	0.437418i	$0.144107\pi$
$504$	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	−0.896756	−	0.442525i	$-0.854083\pi$
$509$	0.914081	−	2.11908i	0.0405159	−	0.0939265i	0.937272	+	0.348598i	$0.113342\pi$
$510$	−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	−0.972967	−	0.230944i	$-0.925818\pi$
$521$	−20.8735	+	17.5150i	−0.914485	+	0.767344i	0.0584819	+	0.998288i	$0.481374\pi$
$522$	14.4248	−	2.09028i	0.631357	−	0.0914891i
$523$	20.3758	+	17.0974i	0.890973	+	0.747615i	0.968405	−	0.249382i	$-0.0802276\pi$
$523$	20.3758	+	17.0974i	0.890973	+	0.747615i	−0.0774318	+	0.996998i	$0.524672\pi$
$524$	−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	0.888399	−	0.459071i	$-0.151818\pi$
$541$	1.08463	+	1.87864i	0.0466321	+	0.0807692i	−0.841767	+	0.539841i	$0.818484\pi$
$542$	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	−0.994110	−	0.108378i	$-0.965434\pi$
$547$	−14.1538	+	19.0118i	−0.605171	+	0.812886i	0.388939	+	0.921264i	$0.372842\pi$
$548$	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	0.904692	+	0.426065i	$0.140101\pi$
$557$	−2.15153	+	12.2019i	−0.0911633	+	0.517013i	−0.995856	+	0.0909475i	$0.971010\pi$
$558$	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	−0.745366	−	0.666655i	$-0.767725\pi$
$563$	−27.7670	−	37.2976i	−1.17024	−	1.57191i	−0.424875	−	0.905252i	$-0.639682\pi$
$564$	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	0.827411	−	0.561596i	$-0.189813\pi$
$569$	20.7775	+	10.4349i	0.871038	+	0.437452i	0.0436265	+	0.999048i	$0.486109\pi$
$570$	4.47062	−	2.66389i	0.187253	−	0.111578i
$571$	−9.27277	−	12.4555i	−0.388053	−	0.521246i	0.564575	−	0.825381i	$-0.309040\pi$
$571$	−9.27277	−	12.4555i	−0.388053	−	0.521246i	−0.952629	+	0.304135i	$0.901633\pi$
$572$	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	−0.617374	−	0.786670i	$-0.711803\pi$
$577$	5.56862	−	31.5812i	0.231825	−	1.31474i	0.849199	−	0.528074i	$-0.177086\pi$
$578$	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	0.147719	+	0.989029i	$0.452807\pi$
$587$	−20.4031	+	27.4061i	−0.842127	+	1.13117i	−0.989846	+	0.142143i	$0.954601\pi$
$588$	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	0.960019	−	0.279936i	$-0.0903134\pi$
$593$	5.78538	+	10.0206i	0.237577	+	0.411496i	−0.722441	+	0.691432i	$0.756980\pi$
$594$	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	−0.963009	−	0.269470i	$-0.913151\pi$
$599$	−15.6147	+	16.5506i	−0.638000	+	0.676241i	0.325008	+	0.945711i	$0.394633\pi$
$600$	1.37300	+	5.45702i	0.0560525	+	0.222782i
$601$	4.24750	+	0.496462i	0.173259	+	0.0202511i	0.202280	−	0.979328i	$-0.435165\pi$
$601$	4.24750	+	0.496462i	0.173259	+	0.0202511i	−0.0290209	+	0.999579i	$0.509239\pi$
$602$	−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	−0.244523	−	0.969643i	$-0.578631\pi$
$607$	9.54035	−	4.79135i	0.387231	−	0.194475i	0.631754	+	0.775169i	$0.282335\pi$
$608$	−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	−0.471226	−	0.882012i	$-0.656188\pi$
$613$	7.81287	−	6.55577i	0.315559	−	0.264785i	0.786785	+	0.617227i	$0.211744\pi$
$614$	−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	−0.760845	−	0.648934i	$-0.775215\pi$
$617$	−33.5712	+	3.92391i	−1.35153	+	0.157971i	−0.590682	+	0.806905i	$0.701141\pi$
$618$	−11.1176	−	29.2837i	−0.447215	−	1.17796i
$619$	1.53303	+	26.3211i	0.0616177	+	1.05793i	0.877457	+	0.479656i	$0.159238\pi$
$619$	1.53303	+	26.3211i	0.0616177	+	1.05793i	−0.815839	+	0.578279i	$0.803725\pi$
$620$	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	−0.653105	−	0.757267i	$-0.726534\pi$
$631$	−16.7461	+	6.09507i	−0.666650	+	0.242641i	−0.0135452	+	0.999908i	$0.504312\pi$
$632$	−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	0.999778	+	0.0210581i	$0.00670349\pi$
$641$	8.32976	+	19.3106i	0.329006	+	0.762721i	−0.670772	+	0.741663i	$0.734037\pi$
$642$	−3.08933	+	6.36862i	−0.121926	+	0.251350i
$643$	−0.298435	−	0.996842i	−0.0117691	−	0.0393116i	0.951903	−	0.306399i	$-0.0991241\pi$
$643$	−0.298435	−	0.996842i	−0.0117691	−	0.0393116i	−0.963672	+	0.267087i	$0.913939\pi$
$644$	−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	−0.999604	−	0.0281555i	$-0.991037\pi$
$653$	−4.59762	−	15.3571i	−0.179919	−	0.600970i	0.819685	−	0.572815i	$-0.194149\pi$
$654$	−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	−0.330480	−	0.943813i	$-0.607211\pi$
$659$	−5.19134	+	1.23037i	−0.202226	+	0.0479284i	0.128254	+	0.991741i	$0.459063\pi$
$660$	−3.94381	+	3.02138i	−0.153513	+	0.117607i
$661$	5.47643	+	3.60191i	0.213009	+	0.140098i	0.651530	−	0.758623i	$-0.274127\pi$
$661$	5.47643	+	3.60191i	0.213009	+	0.140098i	−0.438522	+	0.898721i	$0.644498\pi$
$662$	−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	−0.806918	−	0.590663i	$-0.798866\pi$
$673$	−15.1546	+	9.96731i	−0.584165	+	0.384212i	0.222753	+	0.974875i	$0.428496\pi$
$674$	−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	0.957380	+	0.288830i	$0.0932664\pi$
$677$	1.04089	+	17.8714i	0.0400046	+	0.686853i	−0.917376	+	0.398023i	$0.869697\pi$
$678$	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	−0.191770	−	0.981440i	$-0.561423\pi$
$683$	19.3775	−	16.2596i	0.741459	−	0.622158i	0.933229	+	0.359282i	$0.116978\pi$
$684$	−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	0.648297	−	0.761388i	$-0.275482\pi$
$691$	−3.92984	−	4.16539i	−0.149498	−	0.158459i	−0.797795	+	0.602929i	$0.794000\pi$
$692$	−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	−0.310543	−	0.950559i	$-0.600511\pi$
$701$	17.6846	−	30.6306i	0.667937	−	1.15690i	0.978480	−	0.206342i	$-0.0661559\pi$
$702$	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	−0.869906	−	0.493217i	$-0.835821\pi$
$709$	−3.93861	+	5.29048i	−0.147918	+	0.198688i	0.721989	+	0.691905i	$0.243228\pi$
$710$	−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	0.235845	+	0.971791i	$0.424214\pi$
$719$	−8.53090	+	48.3811i	−0.318149	+	1.80431i	−0.553993	+	0.832521i	$0.686897\pi$
$720$	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	−0.270590	−	0.962695i	$-0.587219\pi$
$727$	−32.4735	−	16.3088i	−1.20438	−	0.604860i	−0.933785	+	0.357835i	$0.883515\pi$
$728$	−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	0.690337	−	0.723488i	$-0.257462\pi$
$733$	−5.43505	−	7.30054i	−0.200748	−	0.269652i	−0.891085	+	0.453837i	$0.850055\pi$
$734$	−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	0.932273	+	0.361756i	$0.117823\pi$
$739$	−1.83509	+	10.4073i	−0.0675048	+	0.382839i	−0.999778	+	0.0210830i	$0.993289\pi$
$740$	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	−0.828333	−	0.560235i	$-0.810711\pi$
$743$	1.62018	−	27.8173i	0.0594385	−	1.02052i	0.887772	−	0.460284i	$-0.152252\pi$
$744$	−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	0.277402	−	0.960754i	$-0.410527\pi$
$751$	2.57908	+	0.611252i	0.0941118	+	0.0223049i	−0.183290	+	0.983059i	$0.558675\pi$
$752$	−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	−0.964813	−	0.262936i	$-0.915309\pi$
$757$	−7.00766	+	12.1376i	−0.254698	+	0.441149i	0.710116	+	0.704085i	$0.248643\pi$
$758$	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	−0.470810	−	0.882235i	$-0.656038\pi$
$761$	12.0637	−	12.7867i	0.437308	−	0.463519i	0.908117	+	0.418716i	$0.137520\pi$
$762$	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
$768$	−0.798591	−	1.53696i	−0.0288167	−	0.0554603i
$769$	−7.88360	+	3.95929i	−0.284290	+	0.142776i	−0.585230	−	0.810867i	$-0.698996\pi$
$769$	−7.88360	+	3.95929i	−0.284290	+	0.142776i	0.300940	+	0.953643i	$0.402699\pi$
$770$	4.97126	−	2.49666i	0.179152	−	0.0899733i
$771$	−18.9174	+	29.6441i	−0.681294	+	1.06761i
$772$	8.13731	+	8.62505i	0.292868	+	0.310422i
$773$	3.30370	+	2.77213i	0.118826	+	0.0997066i	0.700264	−	0.713884i	$-0.253065\pi$
$773$	3.30370	+	2.77213i	0.118826	+	0.0997066i	−0.581439	+	0.813590i	$0.697510\pi$
$774$	13.9045	−	15.5760i	0.499785	−	0.559869i
$775$	12.7179	−	10.6715i	0.456839	−	0.383333i
$776$	−7.99157	−	0.934080i	−0.286881	−	0.0335315i
$777$	14.8206	−	14.3735i	0.531685	−	0.515646i
$778$	18.9298	−	20.0644i	0.678666	−	0.719344i
$779$	−17.6304	+	2.06070i	−0.631675	+	0.0738322i
$780$	−4.60185	−	0.746219i	−0.164773	−	0.0267189i
$781$	0.376197	+	6.45905i	0.0134614	+	0.231123i
$782$	−12.7287	+	22.0468i	−0.455178	+	0.788391i
$783$	25.1206	−	2.50791i	0.897737	−	0.0896255i
$784$	1.61931	+	2.80472i	0.0578323	+	0.100169i
$785$	−12.1542	+	7.99397i	−0.433803	+	0.285317i
$786$	−5.44811	−	6.31409i	−0.194328	−	0.225216i
$787$	19.1364	−	44.3631i	0.682138	−	1.58137i	−0.125767	−	0.992060i	$-0.540139\pi$
$787$	19.1364	−	44.3631i	0.682138	−	1.58137i	0.807905	−	0.589313i	$-0.200602\pi$
$788$	2.91665	+	0.691259i	0.103901	+	0.0246251i
$789$	14.0431	−	6.28843i	0.499947	−	0.223874i
$790$	8.10423	−	10.8859i	0.288336	−	0.387302i
$791$	−28.2753	−	10.2914i	−1.00536	−	0.365919i
$792$	3.73792	−	5.32088i	0.132821	−	0.189069i
$793$	17.2190	−	6.26719i	0.611464	−	0.222555i
$794$	−0.567969	+	1.89715i	−0.0201565	+	0.0673273i
$795$	18.2318	+	16.7322i	0.646617	+	0.593430i
$796$	−1.17048	+	20.0963i	−0.0414865	+	0.712295i
$797$	21.2718	+	13.9907i	0.753484	+	0.495574i	0.867213	−	0.497938i	$-0.165909\pi$
$797$	21.2718	+	13.9907i	0.753484	+	0.495574i	−0.113729	+	0.993512i	$0.536280\pi$
$798$	6.05446	−	4.63836i	0.214326	−	0.164196i
$799$	−30.6409	+	7.26203i	−1.08400	+	0.256912i
$800$	−0.564149	+	3.19945i	−0.0199457	+	0.113118i
$801$	−18.4711	+	16.3871i	−0.652644	+	0.579008i
$802$	4.36849	+	24.7749i	0.154257	+	0.874834i
$803$	−8.91848	−	20.6754i	−0.314726	−	0.729618i
$804$	19.6664	−	1.41751i	0.693580	−	0.0499918i
$805$	2.50771	+	8.37635i	0.0883853	+	0.295227i
$806$	−6.20678	−	8.33715i	−0.218624	−	0.293664i
$807$	0.0381145	+	2.76658i	0.00134169	+	0.0973883i
$808$	16.6341	+	8.35395i	0.585185	+	0.293891i
$809$	17.8042			0.625963			0.312982	−	0.949759i	$-0.398672\pi$
$809$	17.8042			0.625963			0.312982	+	0.949759i	$0.398672\pi$
$810$	9.53134	+	7.14146i	0.334897	+	0.250925i
$811$	17.6535			0.619898			0.309949	−	0.950753i	$-0.399688\pi$
$811$	17.6535			0.619898			0.309949	+	0.950753i	$0.399688\pi$
$812$	−8.42044	−	4.22890i	−0.295499	−	0.148405i
$813$	30.0475	−	17.9043i	1.05381	−	0.627931i
$814$	−7.95519	−	10.6857i	−0.278829	−	0.374533i
$815$	7.15759	+	23.9080i	0.250719	+	0.837461i
$816$	5.64877	−	11.6449i	0.197747	−	0.407653i
$817$	−6.25887	−	14.5097i	−0.218970	−	0.507630i
$818$	5.50127	+	31.1992i	0.192347	+	1.09086i
$819$	−11.0047	+	4.35232i	−0.384535	+	0.152082i
$820$	−1.79650	+	10.1885i	−0.0627367	+	0.355797i
$821$	−11.3701	+	2.69476i	−0.396819	+	0.0940478i	−0.424180	−	0.905578i	$-0.639438\pi$
$821$	−11.3701	+	2.69476i	−0.396819	+	0.0940478i	0.0273612	+	0.999626i	$0.491290\pi$
$822$	0.994503	+	0.412833i	0.0346873	+	0.0143992i
$823$	8.74128	+	5.74923i	0.304702	+	0.200406i	0.692647	−	0.721277i	$-0.256445\pi$
$823$	8.74128	+	5.74923i	0.304702	+	0.200406i	−0.387945	+	0.921683i	$0.626815\pi$
$824$	1.05151	−	18.0538i	0.0366313	−	0.628934i
$825$	−11.6352	+	3.65874i	−0.405086	+	0.127381i
$826$	3.84180	−	12.8325i	0.133673	−	0.446500i
$827$	36.5997	−	13.3212i	1.27270	−	0.463224i	0.384687	−	0.923047i	$-0.374310\pi$
$827$	36.5997	−	13.3212i	1.27270	−	0.463224i	0.888010	+	0.459823i	$0.152087\pi$
$828$	7.21589	+	7.23811i	0.250770	+	0.251542i
$829$	−9.00820	−	3.27872i	−0.312868	−	0.113875i	0.180814	−	0.983517i	$-0.442127\pi$
$829$	−9.00820	−	3.27872i	−0.312868	−	0.113875i	−0.493681	+	0.869643i	$0.664349\pi$
$830$	2.86996	−	3.85503i	0.0996178	−	0.133810i
$831$	2.33280	+	1.68726i	0.0809239	+	0.0585304i
$832$	1.97912	+	0.469061i	0.0686138	+	0.0162618i
$833$	−9.58526	+	22.2211i	−0.332109	+	0.769916i
$834$	5.02485	−	0.957568i	0.173996	−	0.0331579i
$835$	−11.2459	+	7.39657i	−0.389182	+	0.255969i
$836$	−2.46067	−	4.26201i	−0.0851041	−	0.147405i
$837$	4.16967	+	26.2239i	0.144125	+	0.906429i
$838$	0.866352	−	1.50057i	0.0299276	−	0.0518362i
$839$	−1.25711	−	21.5837i	−0.0434001	−	0.745151i	−0.947879	−	0.318632i	$-0.896777\pi$
$839$	−1.25711	−	21.5837i	−0.0434001	−	0.745151i	0.904479	−	0.426519i	$-0.140260\pi$
$840$	−1.57778	−	4.15589i	−0.0544387	−	0.143392i
$841$	5.35857	−	0.626327i	0.184778	−	0.0215975i
$842$	−19.2894	+	20.4456i	−0.664756	+	0.704601i
$843$	−5.12761	−	20.3798i	−0.176604	−	0.701918i
$844$	−14.2620	−	1.66699i	−0.490920	−	0.0573803i
$845$	−8.98472	+	7.53908i	−0.309084	+	0.259352i
$846$	−0.387123	+	12.6364i	−0.0133095	+	0.434449i
$847$	9.36253	+	7.85609i	0.321700	+	0.269939i
$848$	−7.40892	−	7.85299i	−0.254423	−	0.269673i
$849$	−24.5453	−	1.09057i	−0.842394	−	0.0374284i
$850$	−21.6943	+	10.8953i	−0.744107	+	0.373705i
$851$	18.7114	−	9.39723i	0.641419	−	0.322133i
$852$	5.16500	+	0.229486i	0.176950	+	0.00786207i
$853$	−33.9735	−	36.0098i	−1.16323	−	1.23295i	−0.967659	−	0.252261i	$-0.918826\pi$
$853$	−33.9735	−	36.0098i	−1.16323	−	1.23295i	−0.195570	−	0.980690i	$-0.562656\pi$
$854$	13.3847	+	11.2311i	0.458016	+	0.384321i
$855$	7.94050	−	4.26574i	0.271559	−	0.145885i
$856$	−3.13059	+	2.62688i	−0.107001	+	0.0897849i
$857$	32.9963	+	3.85671i	1.12713	+	0.131743i	0.659162	−	0.752001i	$-0.270911\pi$
$857$	32.9963	+	3.85671i	1.12713	+	0.131743i	0.467970	+	0.883744i	$0.344985\pi$
$858$	1.86317	+	7.40521i	0.0636076	+	0.252810i
$859$	−4.73995	+	5.02406i	−0.161725	+	0.171419i	−0.803169	−	0.595752i	$-0.796854\pi$
$859$	−4.73995	+	5.02406i	−0.161725	+	0.171419i	0.641444	+	0.767170i	$0.278336\pi$
$860$	−9.14779	+	1.06922i	−0.311937	+	0.0364602i
$861$	9.32118	+	24.5520i	0.317665	+	0.836730i
$862$	−0.0659823	−	1.13287i	−0.00224737	−	0.0385858i
$863$	6.07200	−	10.5170i	0.206693	−	0.358003i	−0.743978	−	0.668205i	$-0.767063\pi$
$863$	6.07200	−	10.5170i	0.206693	−	0.358003i	0.950671	+	0.310201i	$0.100396\pi$
$864$	−3.92364	−	3.40662i	−0.133485	−	0.115895i
$865$	12.3744	+	21.4330i	0.420741	+	0.728744i
$866$	14.6231	−	9.61777i	0.496913	−	0.326825i
$867$	66.0791	−	12.5925i	2.24416	−	0.427663i
$868$	3.92548	−	9.10030i	0.133240	−	0.308884i
$869$	−21.6298	−	5.12637i	−0.733742	−	0.173900i
$870$	−9.02321	−	6.52628i	−0.305915	−	0.221262i
$871$	−13.8267	+	18.5725i	−0.468500	+	0.629305i
$872$	−11.5811	−	4.21519i	−0.392187	−	0.142744i
$873$	−23.3250	+	6.21151i	−0.789432	+	0.210228i
$874$	7.26869	−	2.64559i	0.245867	−	0.0894883i
$875$	−6.07179	+	20.2812i	−0.205264	+	0.685629i
$876$	−17.1644	+	5.39741i	−0.579931	+	0.182362i
$877$	−0.965302	+	16.5736i	−0.0325959	+	0.559651i	0.941991	+	0.335639i	$0.108952\pi$
$877$	−0.965302	+	16.5736i	−0.0325959	+	0.559651i	−0.974587	+	0.224011i	$0.928085\pi$
$878$	−13.9031	−	9.14424i	−0.469208	−	0.308603i
$879$	−32.1201	−	13.3335i	−1.08339	−	0.449729i
$880$	−2.79104	+	0.661488i	−0.0940859	+	0.0222988i
$881$	−1.14695	+	6.50466i	−0.0386416	+	0.219147i	−0.998014	−	0.0629963i	$-0.979934\pi$
$881$	−1.14695	+	6.50466i	−0.0386416	+	0.219147i	0.959372	+	0.282144i	$0.0910455\pi$
$882$	7.61198	+	6.03781i	0.256309	+	0.203304i
$883$	8.02198	+	45.4949i	0.269961	+	1.53103i	0.754526	+	0.656270i	$0.227867\pi$
$883$	8.02198	+	45.4949i	0.269961	+	1.53103i	−0.484565	+	0.874755i	$0.661022\pi$
$884$	6.01984	+	13.9556i	0.202469	+	0.469376i
$885$	6.90932	−	14.2435i	0.232254	−	0.478790i
$886$	7.74249	+	25.8617i	0.260114	+	0.868841i
$887$	−27.1247	−	36.4348i	−0.910758	−	1.22336i	−0.974271	−	0.225379i	$-0.927638\pi$
$887$	−27.1247	−	36.4348i	−0.910758	−	1.22336i	0.0635135	−	0.997981i	$-0.479769\pi$
$888$	−9.14486	+	5.44912i	−0.306882	+	0.182860i
$889$	−30.4903	−	15.3128i	−1.02261	−	0.513575i
$890$	10.8921			0.365103
$891$	4.55714	−	18.9680i	0.152670	−	0.635453i
$892$	11.1937			0.374794
$893$	8.55034	+	4.29414i	0.286126	+	0.143698i
$894$	−0.0315075	−	2.28700i	−0.00105377	−	0.0764889i
$895$	−13.5802	−	18.2413i	−0.453935	−	0.609740i
$896$	0.556235	+	1.85795i	0.0185825	+	0.0620699i
$897$	−11.9709	+	0.862840i	−0.399698	+	0.0288094i
$898$	7.55415	+	17.5125i	0.252085	+	0.584399i
$899$	−4.31130	−	24.4506i	−0.143790	−	0.815473i
$900$	1.95622	+	9.54807i	0.0652074	+	0.318269i
$901$	14.0091	−	79.4495i	0.466711	−	2.64685i
$902$	16.4888	−	3.90792i	0.549017	−	0.130119i
$903$	−18.5589	+	14.2181i	−0.617602	+	0.473149i
$904$	12.9625	+	8.52555i	0.431126	+	0.283556i
$905$	−1.74839	+	30.0188i	−0.0581186	+	0.997857i
$906$	−2.20343	−	2.02219i	−0.0732042	−	0.0671829i
$907$	10.2417	−	34.2095i	0.340069	−	1.13591i	−0.601439	−	0.798919i	$-0.705406\pi$
$907$	10.2417	−	34.2095i	0.340069	−	1.13591i	0.941508	−	0.336991i	$-0.109409\pi$
$908$	−14.9557	+	5.44344i	−0.496323	+	0.180647i
$909$	55.6220	+	4.95245i	1.84486	+	0.164263i
$910$	4.90532	+	1.78539i	0.162610	+	0.0591851i
$911$	−23.6477	+	31.7643i	−0.783483	+	1.05240i	0.213664	+	0.976907i	$0.431460\pi$
$911$	−23.6477	+	31.7643i	−0.783483	+	1.05240i	−0.997146	+	0.0754926i	$0.975947\pi$
$912$	−3.58917	+	1.60721i	−0.118849	+	0.0532202i
$913$	−7.65980	−	1.81540i	−0.253502	−	0.0600811i
$914$	3.88392	−	9.00395i	0.128469	−	0.297824i
$915$	13.4899	+	15.6341i	0.445962	+	0.516847i
$916$	8.99490	−	5.91604i	0.297200	−	0.195471i
$917$	4.66908	+	8.08708i	0.154186	+	0.267059i
$918$	2.91044	−	38.7187i	0.0960587	−	1.27791i
$919$	10.6420	−	18.4325i	0.351047	−	0.608031i	−0.635386	−	0.772194i	$-0.719159\pi$
$919$	10.6420	−	18.4325i	0.351047	−	0.608031i	0.986433	+	0.164163i	$0.0524924\pi$
$920$	−0.262138	−	4.50074i	−0.00864245	−	0.148385i
$921$	−43.6757	−	7.08229i	−1.43916	−	0.233369i
$922$	−14.5869	+	1.70496i	−0.480392	+	0.0561498i
$923$	−4.16635	+	4.41607i	−0.137137	+	0.145357i
$924$	−5.22679	+	5.06911i	−0.171949	+	0.166762i
$925$	19.8323	+	2.31806i	0.652081	+	0.0762173i
$926$	−23.3291	+	19.5754i	−0.766641	+	0.643288i
$927$	−16.9859	−	51.5256i	−0.557890	−	1.69232i
$928$	3.72182	+	3.12298i	0.122175	+	0.102517i
$929$	14.9295	+	15.8243i	0.489820	+	0.519179i	0.924385	−	0.381462i	$-0.124579\pi$
$929$	14.9295	+	15.8243i	0.489820	+	0.519179i	−0.434565	+	0.900641i	$0.643098\pi$
$930$	6.30093	−	9.87372i	0.206616	−	0.323772i
$931$	6.57107	−	3.30011i	0.215358	−	0.108157i
$932$	15.4365	−	7.75249i	0.505638	−	0.253941i
$933$	8.23190	+	15.8431i	0.269500	+	0.518678i
$934$	−3.29643	−	3.49401i	−0.107862	−	0.114327i
$935$	−16.4191	−	13.7773i	−0.536962	−	0.450564i
$936$	6.03877	−	0.875071i	0.197384	−	0.0286026i
$937$	−15.1205	+	12.6876i	−0.493965	+	0.414485i	−0.855445	−	0.517894i	$-0.826716\pi$
$937$	−15.1205	+	12.6876i	−0.493965	+	0.414485i	0.361480	+	0.932380i	$0.382272\pi$
$938$	−21.9289	−	2.56312i	−0.716004	−	0.0836888i
$939$	−19.2924	−	5.48736i	−0.629585	−	0.179073i
$940$	3.82693	−	4.05631i	0.124821	−	0.132302i
$941$	30.4590	−	3.56014i	0.992933	−	0.116057i	0.395917	−	0.918286i	$-0.370427\pi$
$941$	30.4590	−	3.56014i	0.992933	−	0.116057i	0.597016	+	0.802229i	$0.296353\pi$
$942$	12.0370	−	14.7532i	0.392186	−	0.480684i
$943$	1.54865	+	26.5893i	0.0504311	+	0.865868i
$944$	−3.45340	+	5.98146i	−0.112398	+	0.194680i
$945$	−8.98693	−	9.85303i	−0.292345	−	0.320519i
$946$	7.54277	+	13.0645i	0.245237	+	0.424762i
$947$	33.4232	−	21.9828i	1.08611	−	0.714345i	0.125457	−	0.992099i	$-0.459960\pi$
$947$	33.4232	−	21.9828i	1.08611	−	0.714345i	0.960652	+	0.277754i	$0.0895901\pi$
$948$	−5.84478	+	16.7738i	−0.189830	+	0.544789i
$949$	8.36885	−	19.4012i	0.271664	−	0.629789i
$950$	7.17752	+	1.70110i	0.232869	+	0.0551911i
$951$	4.15506	−	40.3636i	0.134737	−	1.30888i
$952$	−8.65419	+	11.6246i	−0.280484	+	0.376755i
$953$	36.9499	+	13.4487i	1.19692	+	0.435645i	0.862150	−	0.506654i	$-0.169118\pi$
$953$	36.9499	+	13.4487i	1.19692	+	0.435645i	0.334774	+	0.942298i	$0.391340\pi$
$954$	−29.3334	−	13.7333i	−0.949704	−	0.444633i
$955$	−7.29545	+	2.65533i	−0.236075	+	0.0859244i
$956$	−6.99831	+	23.3760i	−0.226341	+	0.756033i
$957$	−3.96157	+	17.8047i	−0.128059	+	0.575545i
$958$	0.153433	−	2.63435i	0.00495720	−	0.0851119i
$959$	−1.00736	−	0.662548i	−0.0325292	−	0.0213948i
$960$	0.297429	+	2.27269i	0.00959947	+	0.0733508i
$961$	−4.75432	+	1.12680i	−0.153365	+	0.0363482i
$962$	2.17073	−	12.3108i	0.0699871	−	0.396917i
$963$	−5.83523	+	10.7824i	−0.188038	+	0.347458i
$964$	4.84010	+	27.4495i	0.155889	+	0.884090i
$965$	−6.21518	−	14.4084i	−0.200074	−	0.463823i
$966$	−6.41983	−	9.47399i	−0.206555	−	0.304821i
$967$	5.19840	+	17.3639i	0.167169	+	0.558384i	0.999988	+	0.00483874i	$0.00154022\pi$
$967$	5.19840	+	17.3639i	0.167169	+	0.558384i	−0.832819	+	0.553545i	$0.813275\pi$
$968$	−3.76318	−	5.05482i	−0.120953	−	0.162468i
$969$	−25.6490	−	14.3411i	−0.823966	−	0.460701i
$970$	9.51492	+	4.77857i	0.305506	+	0.153431i
$971$	4.40089			0.141231			0.0706156	−	0.997504i	$-0.477504\pi$
$971$	4.40089			0.141231			0.0706156	+	0.997504i	$0.477504\pi$
$972$	−14.7046	−	5.17450i	−0.471649	−	0.165972i
$973$	−5.72773			−0.183623
$974$	27.1619	+	13.6412i	0.870323	+	0.437092i
$975$	−9.98975	−	5.58553i	−0.319928	−	0.178880i
$976$	−5.37986	−	7.22641i	−0.172205	−	0.231312i
$977$	8.04738	+	26.8801i	0.257458	+	0.859971i	0.984800	+	0.173695i	$0.0555707\pi$
$977$	8.04738	+	26.8801i	0.257458	+	0.859971i	−0.727341	+	0.686276i	$0.759244\pi$
$978$	−18.3237	−	27.0409i	−0.585926	−	0.864674i
$979$	−7.06628	−	16.3815i	−0.225839	−	0.523555i
$980$	−0.744211	−	4.22063i	−0.0237730	−	0.134823i
$981$	−36.9591	+	1.01855i	−1.18001	+	0.0325197i
$982$	3.53472	−	20.0464i	0.112797	−	0.639706i
$983$	0.938898	−	0.222523i	0.0299462	−	0.00709738i	−0.215615	−	0.976478i	$-0.569176\pi$
$983$	0.938898	−	0.222523i	0.0299462	−	0.00709738i	0.245562	+	0.969381i	$0.421028\pi$
$984$	−1.75714	−	13.4265i	−0.0560156	−	0.428022i
$985$	−3.31405	−	2.17968i	−0.105594	−	0.0694505i
$986$	−2.11094	+	36.2434i	−0.0672259	+	1.15422i
$987$	3.07454	−	13.8181i	0.0978638	−	0.439835i
$988$	1.32447	−	4.42404i	0.0421370	−	0.140747i
$989$	−22.2809	+	8.10960i	−0.708493	+	0.257870i
$990$	−7.05644	+	4.92482i	−0.224268	+	0.156521i
$991$	−50.9827	−	18.5562i	−1.61952	−	0.589457i	−0.636229	−	0.771500i	$-0.719507\pi$
$991$	−50.9827	−	18.5562i	−1.61952	−	0.589457i	−0.983291	+	0.182043i	$0.941729\pi$
$992$	−3.05159	+	4.09900i	−0.0968881	+	0.130143i
$993$	−0.0427096	+	0.414895i	−0.00135535	+	0.0131663i
$994$	−5.63307	−	1.33506i	−0.178670	−	0.0423456i
$995$	10.5512	−	24.4604i	0.334496	−	0.775448i
$996$	−2.06982	+	5.94013i	−0.0655847	+	0.188220i
$997$	−12.5945	+	8.28354i	−0.398872	+	0.262342i	−0.733060	−	0.680164i	$-0.761908\pi$
$997$	−12.5945	+	8.28354i	−0.398872	+	0.262342i	0.334188	+	0.942507i	$0.391538\pi$
$998$	−0.587883	−	1.01824i	−0.0186091	−	0.0322319i
$999$	−19.4996	+	25.2914i	−0.616941	+	0.800186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.b.13.5	✓	90
3.2	odd	2		486.2.g.b.253.3		90
81.25	even	27	inner	162.2.g.b.25.5	yes	90
81.56	odd	54		486.2.g.b.73.3		90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.13.5	✓	90	1.1	even	1	trivial
162.2.g.b.25.5	yes	90	81.25	even	27	inner
486.2.g.b.73.3		90	81.56	odd	54
486.2.g.b.253.3		90	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

Introduction

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