LMFDB - Embedded newform 507.2.q.b.16.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.10
Character	$\chi$	$=$	507.16
Dual form			507.2.q.b.412.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.655764 + 0.0529387i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-1.54688 - 0.251392i) q^{4} +(-1.61643 - 1.43203i) q^{5} +(-0.525951 - 0.395227i) q^{6} +(1.45558 - 1.51542i) q^{7} +(-2.27864 - 0.561634i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-0.984187 - 1.02465i) q^{10} +(-2.14574 + 4.52204i) q^{11} +(1.17304 + 1.03923i) q^{12} +(0.547978 + 3.56367i) q^{13} +(1.03474 - 0.916700i) q^{14} +(0.600819 + 2.07427i) q^{15} +(1.50852 + 0.503619i) q^{16} +(-1.62333 + 1.69006i) q^{17} +(0.233294 + 0.615144i) q^{18} +(-1.40954 + 2.44140i) q^{19} +(2.14042 + 2.62154i) q^{20} +(-2.04018 + 0.502859i) q^{21} +(-1.64649 + 2.85180i) q^{22} +(0.954346 + 1.65298i) q^{23} +(1.62571 + 1.69254i) q^{24} +(-0.0405526 - 0.333981i) q^{25} +(0.170688 + 2.36593i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-2.63257 + 1.97824i) q^{28} +(-5.71698 - 0.461522i) q^{29} +(0.284186 + 1.39204i) q^{30} +(0.304449 - 2.50736i) q^{31} +(5.28065 + 2.24987i) q^{32} +(4.23043 - 2.67516i) q^{33} +(-1.15399 + 1.02234i) q^{34} +(-4.52297 + 0.365132i) q^{35} +(-0.436014 - 1.50530i) q^{36} +(-4.18034 + 1.78108i) q^{37} +(-1.05357 + 1.52636i) q^{38} +(1.44151 - 3.30485i) q^{39} +(2.87898 + 4.17092i) q^{40} +(-2.30738 - 1.45910i) q^{41} +(-1.36450 + 0.221752i) q^{42} +(-9.34268 - 3.98054i) q^{43} +(4.45600 - 6.45563i) q^{44} +(0.600819 - 2.07427i) q^{45} +(0.538319 + 1.13448i) q^{46} +(-3.00003 + 7.91042i) q^{47} +(-1.00582 - 1.23191i) q^{48} +(0.104079 + 2.58270i) q^{49} +(-0.00891242 - 0.221159i) q^{50} +(2.27530 - 0.560811i) q^{51} +(0.0482220 - 5.65031i) q^{52} +(-0.675275 - 0.166440i) q^{53} +(0.131596 - 0.644601i) q^{54} +(9.94415 - 4.23681i) q^{55} +(-4.16785 + 2.63559i) q^{56} +(2.49618 - 1.31009i) q^{57} +(-3.72455 - 0.605299i) q^{58} +(-0.625402 + 0.208790i) q^{59} +(-0.407939 - 3.35968i) q^{60} +(-0.421437 + 1.45497i) q^{61} +(0.332383 - 1.62812i) q^{62} +(1.99310 + 0.665395i) q^{63} +(0.527347 + 0.276773i) q^{64} +(4.21752 - 6.54514i) q^{65} +(2.91578 - 1.53032i) q^{66} +(13.9417 - 2.26574i) q^{67} +(2.93595 - 2.20622i) q^{68} +(0.0768553 - 1.90714i) q^{69} -2.98533 q^{70} +(0.0728044 - 1.80662i) q^{71} +(-0.469427 - 2.29940i) q^{72} +(4.28470 + 6.20747i) q^{73} +(-2.83560 + 0.946664i) q^{74} +(-0.144227 + 0.303951i) q^{75} +(2.79414 - 3.42220i) q^{76} +(3.72950 + 9.83388i) q^{77} +(1.12025 - 2.09089i) q^{78} +(3.77399 - 9.95118i) q^{79} +(-1.71722 - 2.97432i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-1.43585 - 1.07897i) q^{82} +(-14.5951 - 7.66010i) q^{83} +(3.28232 - 0.264976i) q^{84} +(5.04421 - 0.407211i) q^{85} +(-5.91586 - 3.10488i) q^{86} +(4.58526 + 3.44560i) q^{87} +(7.42909 - 9.09898i) q^{88} +(-3.92591 - 6.79987i) q^{89} +(0.503804 - 1.32842i) q^{90} +(6.19807 + 4.35678i) q^{91} +(-1.06071 - 2.79687i) q^{92} +(-1.59741 + 1.95648i) q^{93} +(-2.38608 + 5.02855i) q^{94} +(5.77459 - 1.92784i) q^{95} +(-3.26067 - 4.72390i) q^{96} +(-0.144348 - 0.707065i) q^{97} +(-0.0684735 + 1.69915i) q^{98} -5.00530 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

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 $

$2$	0.655764	+	0.0529387i	0.463695	+	0.0374333i	0.310107	−	0.950702i	$-0.399635\pi$
$2$	0.655764	+	0.0529387i	0.463695	+	0.0374333i	0.153588	+	0.988135i	$0.450917\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	−1.54688	−	0.251392i	−0.773439	−	0.125696i
$5$	−1.61643	−	1.43203i	−0.722890	−	0.640424i	0.219241	−	0.975671i	$-0.429642\pi$
$5$	−1.61643	−	1.43203i	−0.722890	−	0.640424i	−0.942131	+	0.335246i	$0.891180\pi$
$6$	−0.525951	−	0.395227i	−0.214719	−	0.161351i
$7$	1.45558	−	1.51542i	0.550157	−	0.572774i	−0.386824	−	0.922153i	$-0.626428\pi$
$7$	1.45558	−	1.51542i	0.550157	−	0.572774i	0.936981	+	0.349379i	$0.113608\pi$
$8$	−2.27864	−	0.561634i	−0.805620	−	0.198567i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	−0.984187	−	1.02465i	−0.311227	−	0.324022i
$11$	−2.14574	+	4.52204i	−0.646964	+	1.36345i	0.269372	+	0.963036i	$0.413184\pi$
$11$	−2.14574	+	4.52204i	−0.646964	+	1.36345i	−0.916336	+	0.400411i	$0.868867\pi$
$12$	1.17304	+	1.03923i	0.338629	+	0.299999i
$13$	0.547978	+	3.56367i	0.151982	+	0.988383i
$13$	0.547978	+	3.56367i	0.151982	+	0.988383i
$14$	1.03474	−	0.916700i	0.276546	−	0.244998i
$15$	0.600819	+	2.07427i	0.155131	+	0.535573i
$16$	1.50852	+	0.503619i	0.377131	+	0.125905i
$17$	−1.62333	+	1.69006i	−0.393714	+	0.409900i	−0.888325	−	0.459214i	$-0.848131\pi$
$17$	−1.62333	+	1.69006i	−0.393714	+	0.409900i	0.494611	+	0.869114i	$0.335310\pi$
$18$	0.233294	+	0.615144i	0.0549878	+	0.144991i
$19$	−1.40954	+	2.44140i	−0.323371	+	0.560096i	−0.981181	−	0.193088i	$-0.938150\pi$
$19$	−1.40954	+	2.44140i	−0.323371	+	0.560096i	0.657810	+	0.753184i	$0.271483\pi$
$20$	2.14042	+	2.62154i	0.478612	+	0.586193i
$21$	−2.04018	+	0.502859i	−0.445204	+	0.109733i
$22$	−1.64649	+	2.85180i	−0.351032	+	0.608006i
$23$	0.954346	+	1.65298i	0.198995	+	0.344669i	0.948203	−	0.317666i	$-0.102899\pi$
$23$	0.954346	+	1.65298i	0.198995	+	0.344669i	−0.749208	+	0.662335i	$0.769566\pi$
$24$	1.62571	+	1.69254i	0.331846	+	0.345488i
$25$	−0.0405526	−	0.333981i	−0.00811053	−	0.0667962i
$26$	0.170688	+	2.36593i	0.0334747	+	0.463998i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	−2.63257	+	1.97824i	−0.497508	+	0.373853i
$29$	−5.71698	−	0.461522i	−1.06162	−	0.0857025i	−0.462700	−	0.886515i	$-0.653119\pi$
$29$	−5.71698	−	0.461522i	−1.06162	−	0.0857025i	−0.598916	+	0.800812i	$0.704402\pi$
$30$	0.284186	+	1.39204i	0.0518850	+	0.254150i
$31$	0.304449	−	2.50736i	0.0546806	−	0.450335i	−0.939495	−	0.342563i	$-0.888705\pi$
$31$	0.304449	−	2.50736i	0.0546806	−	0.450335i	0.994176	−	0.107772i	$-0.0343718\pi$
$32$	5.28065	+	2.24987i	0.933495	+	0.397725i
$33$	4.23043	−	2.67516i	0.736424	−	0.465686i
$34$	−1.15399	+	1.02234i	−0.197907	+	0.175330i
$35$	−4.52297	+	0.365132i	−0.764522	+	0.0617186i
$36$	−0.436014	−	1.50530i	−0.0726691	−	0.250883i
$37$	−4.18034	+	1.78108i	−0.687244	+	0.292807i	−0.707220	−	0.706993i	$-0.750051\pi$
$37$	−4.18034	+	1.78108i	−0.687244	+	0.292807i	0.0199763	+	0.999800i	$0.493641\pi$
$38$	−1.05357	+	1.52636i	−0.170912	+	0.247609i
$39$	1.44151	−	3.30485i	0.230827	−	0.529200i
$40$	2.87898	+	4.17092i	0.455207	+	0.659481i
$41$	−2.30738	−	1.45910i	−0.360352	−	0.227873i	0.342004	−	0.939698i	$-0.388894\pi$
$41$	−2.30738	−	1.45910i	−0.360352	−	0.227873i	−0.702356	+	0.711825i	$0.747869\pi$
$42$	−1.36450	+	0.221752i	−0.210546	+	0.0342171i
$43$	−9.34268	−	3.98054i	−1.42474	−	0.607027i	−0.464345	−	0.885654i	$-0.653710\pi$
$43$	−9.34268	−	3.98054i	−1.42474	−	0.607027i	−0.960399	+	0.278627i	$0.910121\pi$
$44$	4.45600	−	6.45563i	0.671767	−	0.973222i
$45$	0.600819	−	2.07427i	0.0895648	−	0.309213i
$46$	0.538319	+	1.13448i	0.0793708	+	0.167270i
$47$	−3.00003	+	7.91042i	−0.437599	+	1.15385i	0.517007	+	0.855981i	$0.327046\pi$
$47$	−3.00003	+	7.91042i	−0.437599	+	1.15385i	−0.954606	+	0.297872i	$0.903723\pi$
$48$	−1.00582	−	1.23191i	−0.145178	−	0.177811i
$49$	0.104079	+	2.58270i	0.0148685	+	0.368957i
$50$	−0.00891242	−	0.221159i	−0.00126041	−	0.0312767i
$51$	2.27530	−	0.560811i	0.318605	−	0.0785292i
$52$	0.0482220	−	5.65031i	0.00668720	−	0.783557i
$53$	−0.675275	−	0.166440i	−0.0927562	−	0.0228624i	0.192664	−	0.981265i	$-0.438287\pi$
$53$	−0.675275	−	0.166440i	−0.0927562	−	0.0228624i	−0.285421	+	0.958402i	$0.592133\pi$
$54$	0.131596	−	0.644601i	0.0179080	−	0.0877191i
$55$	9.94415	−	4.23681i	1.34087	−	0.571291i
$56$	−4.16785	+	2.63559i	−0.556952	+	0.352195i
$57$	2.49618	−	1.31009i	0.330627	−	0.173526i
$58$	−3.72455	−	0.605299i	−0.489058	−	0.0794796i
$59$	−0.625402	+	0.208790i	−0.0814204	+	0.0271821i	−0.357086	−	0.934071i	$-0.616230\pi$
$59$	−0.625402	+	0.208790i	−0.0814204	+	0.0271821i	0.275666	+	0.961253i	$0.411102\pi$
$60$	−0.407939	−	3.35968i	−0.0526646	−	0.433732i
$61$	−0.421437	+	1.45497i	−0.0539595	+	0.186290i	−0.982971	−	0.183761i	$-0.941173\pi$
$61$	−0.421437	+	1.45497i	−0.0539595	+	0.186290i	0.929011	+	0.370051i	$0.120660\pi$
$62$	0.332383	−	1.62812i	0.0422126	−	0.206771i
$63$	1.99310	+	0.665395i	0.251107	+	0.0838319i
$64$	0.527347	+	0.276773i	0.0659184	+	0.0345966i
$65$	4.21752	−	6.54514i	0.523119	−	0.811825i
$66$	2.91578	−	1.53032i	0.358908	−	0.188370i
$67$	13.9417	−	2.26574i	1.70325	−	0.276805i	0.770527	−	0.637407i	$-0.219993\pi$
$67$	13.9417	−	2.26574i	1.70325	−	0.276805i	0.932720	+	0.360602i	$0.117429\pi$
$68$	2.93595	−	2.20622i	0.356036	−	0.267544i
$69$	0.0768553	−	1.90714i	0.00925229	−	0.229593i
$70$	−2.98533			−0.356815
$71$	0.0728044	−	1.80662i	0.00864029	−	0.214407i	−0.989101	−	0.147237i	$-0.952962\pi$
$71$	0.0728044	−	1.80662i	0.00864029	−	0.214407i	0.997742	−	0.0671698i	$-0.0213969\pi$
$72$	−0.469427	−	2.29940i	−0.0553225	−	0.270987i
$73$	4.28470	+	6.20747i	0.501487	+	0.726529i	0.989216	−	0.146466i	$-0.0467900\pi$
$73$	4.28470	+	6.20747i	0.501487	+	0.726529i	−0.487729	+	0.872995i	$0.662175\pi$
$74$	−2.83560	+	0.946664i	−0.329632	+	0.110047i
$75$	−0.144227	+	0.303951i	−0.0166539	+	0.0350973i
$76$	2.79414	−	3.42220i	0.320510	−	0.392553i
$77$	3.72950	+	9.83388i	0.425016	+	1.12067i
$78$	1.12025	−	2.09089i	0.126843	−	0.236747i
$79$	3.77399	−	9.95118i	0.424607	−	1.11960i	−0.536617	−	0.843826i	$-0.680298\pi$
$79$	3.77399	−	9.95118i	0.424607	−	1.11960i	0.961224	−	0.275770i	$-0.0889328\pi$
$80$	−1.71722	−	2.97432i	−0.191992	−	0.332539i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	−1.43585	−	1.07897i	−0.158563	−	0.119153i
$83$	−14.5951	−	7.66010i	−1.60202	−	0.840805i	−0.999074	−	0.0430226i	$-0.986301\pi$
$83$	−14.5951	−	7.66010i	−1.60202	−	0.840805i	−0.602946	−	0.797782i	$-0.706006\pi$
$84$	3.28232	−	0.264976i	0.358131	−	0.0289113i
$85$	5.04421	−	0.407211i	0.547122	−	0.0441682i
$86$	−5.91586	−	3.10488i	−0.637924	−	0.334808i
$87$	4.58526	+	3.44560i	0.491592	+	0.369407i
$88$	7.42909	−	9.09898i	0.791943	−	0.969954i
$89$	−3.92591	−	6.79987i	−0.416145	−	0.720785i	0.579402	−	0.815042i	$-0.303286\pi$
$89$	−3.92591	−	6.79987i	−0.416145	−	0.720785i	−0.995548	+	0.0942565i	$0.969953\pi$
$90$	0.503804	−	1.32842i	0.0531056	−	0.140028i
$91$	6.19807	+	4.35678i	0.649734	+	0.456715i
$92$	−1.06071	−	2.79687i	−0.110587	−	0.291593i
$93$	−1.59741	+	1.95648i	−0.165644	+	0.202877i
$94$	−2.38608	+	5.02855i	−0.246105	+	0.518655i
$95$	5.77459	−	1.92784i	0.592461	−	0.197793i
$96$	−3.26067	−	4.72390i	−0.332791	−	0.482131i
$97$	−0.144348	−	0.707065i	−0.0146564	−	0.0717916i	0.971805	−	0.235787i	$-0.0757668\pi$
$97$	−0.144348	−	0.707065i	−0.0146564	−	0.0717916i	−0.986461	+	0.163996i	$0.947562\pi$
$98$	−0.0684735	+	1.69915i	−0.00691687	+	0.171640i
$99$	−5.00530			−0.503052
$100$	−0.0212302	+	0.526822i	−0.00212302	+	0.0526822i
$101$	−8.59588	+	6.45938i	−0.855322	+	0.642733i	−0.935219	−	0.354071i	$-0.884797\pi$
$101$	−8.59588	+	6.45938i	−0.855322	+	0.642733i	0.0798971	+	0.996803i	$0.474541\pi$
$102$	1.52175	−	0.247308i	0.150675	−	0.0244871i
$103$	−11.4523	+	6.01061i	−1.12843	+	0.592243i	−0.922374	−	0.386298i	$-0.873754\pi$
$103$	−11.4523	+	6.01061i	−1.12843	+	0.592243i	−0.206051	+	0.978541i	$0.566061\pi$
$104$	0.752831	−	8.42807i	0.0738211	−	0.826440i
$105$	4.01792	+	2.10877i	0.392109	+	0.205795i
$106$	−0.434010	−	0.144894i	−0.0421548	−	0.0140733i
$107$	−3.18245	+	15.5887i	−0.307659	+	1.50701i	0.472443	+	0.881361i	$0.343372\pi$
$107$	−3.18245	+	15.5887i	−0.307659	+	1.50701i	−0.780102	+	0.625652i	$0.784833\pi$
$108$	−0.436014	+	1.50530i	−0.0419555	+	0.144847i
$109$	−0.362017	−	2.98148i	−0.0346750	−	0.285574i	−0.999724	−	0.0235037i	$-0.992518\pi$
$109$	−0.362017	−	2.98148i	−0.0346750	−	0.285574i	0.965049	−	0.262070i	$-0.0844052\pi$
$110$	6.74530	−	2.25191i	0.643139	−	0.214711i
$111$	4.48511	+	0.728901i	0.425708	+	0.0691842i
$112$	2.95897	−	1.55299i	0.279596	−	0.146743i
$113$	−7.85835	+	4.96932i	−0.739251	+	0.467474i	−0.850272	−	0.526344i	$-0.823562\pi$
$113$	−7.85835	+	4.96932i	−0.739251	+	0.467474i	0.111020	+	0.993818i	$0.464588\pi$
$114$	1.70626	−	0.726968i	0.159806	−	0.0680868i
$115$	0.824481	−	4.03858i	0.0768833	−	0.376599i
$116$	8.72744	+	2.15112i	0.810322	+	0.199727i
$117$	−2.98468	+	2.02279i	−0.275934	+	0.187007i
$118$	−0.421169	+	0.103809i	−0.0387717	+	0.00955638i
$119$	0.198271	+	4.92003i	0.0181754	+	0.451019i
$120$	−0.204070	−	5.06394i	−0.0186289	−	0.462272i
$121$	−8.88780	−	10.8856i	−0.807982	−	0.989598i
$122$	−0.353387	+	0.931806i	−0.0319942	+	0.0843617i
$123$	1.17034	+	2.46643i	0.105526	+	0.222391i
$124$	−1.10127	+	3.80204i	−0.0988974	+	0.341433i
$125$	−6.54648	+	9.48422i	−0.585535	+	0.848294i
$126$	1.27178	+	0.541854i	0.113299	+	0.0482722i
$127$	18.1293	−	2.94630i	1.60872	−	0.261442i	0.711387	−	0.702800i	$-0.248067\pi$
$127$	18.1293	−	2.94630i	1.60872	−	0.261442i	0.897331	+	0.441358i	$0.145503\pi$
$128$	−9.37156	−	5.92621i	−0.828336	−	0.523808i
$129$	5.76887	+	8.35766i	0.507921	+	0.735851i
$130$	3.11219	−	4.06880i	0.272957	−	0.356857i
$131$	3.38450	−	4.90329i	0.295705	−	0.428403i	−0.646767	−	0.762688i	$-0.723879\pi$
$131$	3.38450	−	4.90329i	0.295705	−	0.428403i	0.942472	+	0.334285i	$0.108495\pi$
$132$	−7.21647	+	3.07465i	−0.628114	+	0.267614i
$133$	1.64804	+	5.68970i	0.142903	+	0.493359i
$134$	9.26239	−	0.747737i	0.800149	−	0.0645947i
$135$	−1.61643	+	1.43203i	−0.139120	+	0.123250i
$136$	4.64816	−	2.93932i	0.398577	−	0.252045i
$137$	−6.85938	−	2.92251i	−0.586036	−	0.249687i	0.0785354	−	0.996911i	$-0.474976\pi$
$137$	−6.85938	−	2.92251i	−0.586036	−	0.249687i	−0.664571	+	0.747225i	$0.731386\pi$
$138$	0.151361	−	1.24657i	0.0128847	−	0.106115i
$139$	−3.43400	−	16.8208i	−0.291268	−	1.42673i	−0.817276	−	0.576246i	$-0.804517\pi$
$139$	−3.43400	−	16.8208i	−0.291268	−	1.42673i	0.526008	−	0.850479i	$-0.323688\pi$
$140$	7.08827	+	0.572224i	0.599068	+	0.0483618i
$141$	6.76344	−	5.08240i	0.569585	−	0.428015i
$142$	0.143383	−	1.18086i	0.0120324	−	0.0990958i
$143$	−17.2909	−	5.16871i	−1.44594	−	0.432229i
$144$	0.191698	+	1.57877i	0.0159748	+	0.131564i
$145$	8.58018	+	8.93292i	0.712545	+	0.741838i
$146$	2.48114	+	4.29746i	0.205340	+	0.355660i
$147$	1.29240	−	2.23850i	0.106595	−	0.184628i
$148$	6.91422	−	1.70420i	0.568346	−	0.140085i
$149$	5.78924	+	7.09053i	0.474273	+	0.580879i	0.955230	−	0.295865i	$-0.0956080\pi$
$149$	5.78924	+	7.09053i	0.474273	+	0.580879i	−0.480957	+	0.876744i	$0.659711\pi$
$150$	−0.110669	+	0.191685i	−0.00903612	+	0.0156510i
$151$	2.24713	+	5.92520i	0.182869	+	0.482186i	0.994833	−	0.101521i	$-0.0323710\pi$
$151$	2.24713	+	5.92520i	0.182869	+	0.482186i	−0.811964	+	0.583707i	$0.801602\pi$
$152$	4.58301	−	4.77142i	0.371731	−	0.387013i
$153$	−2.22279	−	0.742077i	−0.179702	−	0.0599934i
$154$	1.92508	+	6.64614i	0.155127	+	0.535561i
$155$	−4.08274	+	3.61699i	−0.327934	+	0.290524i
$156$	−3.06066	+	4.74981i	−0.245049	+	0.380289i
$157$	−5.14338	−	4.55663i	−0.410486	−	0.363659i	0.432463	−	0.901651i	$-0.357644\pi$
$157$	−5.14338	−	4.55663i	−0.410486	−	0.363659i	−0.842950	+	0.537992i	$0.819183\pi$
$158$	3.00165	−	6.32584i	0.238798	−	0.503256i
$159$	0.481779	+	0.501585i	0.0382076	+	0.0397783i
$160$	−5.31391	−	11.1988i	−0.420101	−	0.885345i
$161$	3.89408	+	0.959803i	0.306896	+	0.0756431i
$162$	−0.455741	+	0.474477i	−0.0358064	+	0.0372784i
$163$	−13.1609	−	9.88980i	−1.03084	−	0.774629i	−0.0562062	−	0.998419i	$-0.517900\pi$
$163$	−13.1609	−	9.88980i	−1.03084	−	0.774629i	−0.974637	+	0.223791i	$0.928157\pi$
$164$	3.20243	+	2.83710i	0.250068	+	0.221541i
$165$	−10.6691	−	1.73390i	−0.830590	−	0.134984i
$166$	−9.16542	−	5.79586i	−0.711374	−	0.449846i
$167$	3.77683	+	0.304897i	0.292260	+	0.0235936i	0.225727	−	0.974191i	$-0.427524\pi$
$167$	3.77683	+	0.304897i	0.292260	+	0.0235936i	0.0665328	+	0.997784i	$0.478806\pi$
$168$	4.93125			0.380454
$169$	−12.3994	+	3.90562i	−0.953803	+	0.300433i
$170$	3.32937			0.255351
$171$	−2.80995	−	0.226842i	−0.214882	−	0.0173471i
$172$	13.4513	+	8.50608i	1.02565	+	0.648583i
$173$	−11.5536	−	1.87764i	−0.878404	−	0.142755i	−0.295546	−	0.955328i	$-0.595502\pi$
$173$	−11.5536	−	1.87764i	−0.878404	−	0.142755i	−0.582858	+	0.812574i	$0.698066\pi$
$174$	2.82444	+	2.50224i	0.214121	+	0.189694i
$175$	−0.565148	−	0.424682i	−0.0427212	−	0.0321029i
$176$	−5.51428	+	5.74098i	−0.415655	+	0.432742i
$177$	0.640174	+	0.157789i	0.0481185	+	0.0118601i
$178$	−2.21449	−	4.66694i	−0.165983	−	0.349802i
$179$	10.3381	+	10.7631i	0.772705	+	0.804471i	0.984967	−	0.172742i	$-0.0552627\pi$
$179$	10.3381	+	10.7631i	0.772705	+	0.804471i	−0.212262	+	0.977213i	$0.568083\pi$
$180$	−1.45085	+	3.05759i	−0.108140	+	0.227900i
$181$	1.93466	+	1.71396i	0.143802	+	0.127398i	0.731957	−	0.681350i	$-0.238607\pi$
$181$	1.93466	+	1.71396i	0.143802	+	0.127398i	−0.588155	+	0.808748i	$0.700145\pi$
$182$	3.83383	+	3.18514i	0.284182	+	0.236098i
$183$	1.13383	−	1.00448i	0.0838148	−	0.0742535i
$184$	−1.24624	−	4.30253i	−0.0918742	−	0.317186i
$185$	9.30780	+	3.10740i	0.684323	+	0.228461i
$186$	−1.15110	+	1.19842i	−0.0844027	+	0.0878726i
$187$	−4.15930	−	10.9672i	−0.304158	−	0.801999i
$188$	6.62929	−	11.4823i	0.483491	−	0.837430i
$189$	−1.32892	−	1.62763i	−0.0966646	−	0.118393i
$190$	3.88883	−	0.958510i	0.282125	−	0.0695376i
$191$	8.09248	−	14.0166i	0.585551	−	1.01420i	−0.409255	−	0.912420i	$-0.634211\pi$
$191$	8.09248	−	14.0166i	0.585551	−	1.01420i	0.994806	−	0.101785i	$-0.0324553\pi$
$192$	−0.297783	−	0.515775i	−0.0214906	−	0.0372228i
$193$	14.0719	+	14.6504i	1.01291	+	1.05456i	0.998505	+	0.0546597i	$0.0174074\pi$
$193$	14.0719	+	14.6504i	1.01291	+	1.05456i	0.0144096	+	0.999896i	$0.495413\pi$
$194$	−0.0572273	−	0.471309i	−0.00410868	−	0.0338380i
$195$	−7.06276	+	3.27777i	−0.505775	+	0.234726i
$196$	0.488273	−	4.02129i	0.0348766	−	0.287235i
$197$	13.9065	−	10.4501i	0.990798	−	0.744536i	0.0239038	−	0.999714i	$-0.492390\pi$
$197$	13.9065	−	10.4501i	0.990798	−	0.744536i	0.966894	+	0.255178i	$0.0821341\pi$
$198$	−3.28230	−	0.264974i	−0.233263	−	0.0188309i
$199$	2.45664	+	12.0334i	0.174147	+	0.853027i	0.969160	+	0.246434i	$0.0792589\pi$
$199$	2.45664	+	12.0334i	0.174147	+	0.853027i	−0.795013	+	0.606593i	$0.792536\pi$
$200$	−0.0951702	+	0.783797i	−0.00672955	+	0.0554228i
$201$	−12.9943	−	5.53637i	−0.916549	−	0.390505i
$202$	−5.97881	+	3.78077i	−0.420668	+	0.266014i
$203$	−9.02091	+	7.99183i	−0.633144	+	0.560916i
$204$	−3.66059	+	0.295513i	−0.256293	+	0.0206901i
$205$	1.64024	+	5.66278i	0.114560	+	0.395506i
$206$	−7.82817	+	3.33527i	−0.545415	+	0.232380i
$207$	−1.08426	+	1.57082i	−0.0753613	+	0.109180i
$208$	−0.968092	+	5.65185i	−0.0671251	+	0.391885i
$209$	−8.01561	−	11.6126i	−0.554451	−	0.803262i
$210$	2.52317	+	1.59556i	0.174115	+	0.110104i
$211$	−4.99281	+	0.811411i	−0.343719	+	0.0558598i	−0.329821	−	0.944044i	$-0.606988\pi$
$211$	−4.99281	+	0.811411i	−0.343719	+	0.0558598i	−0.0138986	+	0.999903i	$0.504424\pi$
$212$	1.00273	+	0.427222i	0.0688675	+	0.0293417i
$213$	−1.02711	+	1.48803i	−0.0703765	+	0.101958i
$214$	−2.91218	+	10.0540i	−0.199072	+	0.687278i
$215$	9.40152	+	19.8133i	0.641178	+	1.35125i
$216$	−0.832198	+	2.19433i	−0.0566239	+	0.149305i
$217$	−3.35655	−	4.11103i	−0.227857	−	0.279075i
$218$	−0.0795620	−	1.97431i	−0.00538862	−	0.133717i
$219$	−0.303711	−	7.53652i	−0.0205229	−	0.509271i
$220$	−16.4475	+	4.05394i	−1.10889	+	0.273316i
$221$	−6.91236	−	4.85887i	−0.464976	−	0.326843i
$222$	2.90258	+	0.715423i	0.194809	+	0.0480160i
$223$	−2.27738	+	11.1554i	−0.152505	+	0.747018i	0.829552	+	0.558430i	$0.188596\pi$
$223$	−2.27738	+	11.1554i	−0.152505	+	0.747018i	−0.982056	+	0.188588i	$0.939609\pi$
$224$	11.0959	−	4.72752i	0.741376	−	0.315871i
$225$	0.284351	−	0.179812i	0.0189567	−	0.0119875i
$226$	−5.41629	+	2.84269i	−0.360286	+	0.189093i
$227$	20.8234	+	3.38413i	1.38210	+	0.224613i	0.805587	−	0.592478i	$-0.201850\pi$
$227$	20.8234	+	3.38413i	1.38210	+	0.224613i	0.576510	+	0.817090i	$0.304414\pi$
$228$	−4.19063	+	1.39904i	−0.277531	+	0.0926535i
$229$	2.26657	+	18.6669i	0.149779	+	1.23354i	0.852747	+	0.522323i	$0.174935\pi$
$229$	2.26657	+	18.6669i	0.149779	+	1.23354i	−0.702968	+	0.711221i	$0.748142\pi$
$230$	0.754462	−	2.60470i	0.0497477	−	0.171749i
$231$	2.10374	−	10.3048i	0.138416	−	0.678005i
$232$	12.7677	+	4.26249i	0.838241	+	0.279846i
$233$	−11.3858	−	5.97573i	−0.745908	−	0.391483i	0.0485347	−	0.998821i	$-0.484545\pi$
$233$	−11.3858	−	5.97573i	−0.745908	−	0.391483i	−0.794443	+	0.607339i	$0.792237\pi$
$234$	−2.06433	+	1.16847i	−0.134949	+	0.0763850i
$235$	16.1773	−	8.49051i	1.05529	−	0.553860i
$236$	1.01991	−	0.165751i	0.0663903	−	0.0107895i
$237$	−8.50830	+	6.39358i	−0.552674	+	0.415307i
$238$	−0.130442	+	3.23687i	−0.00845527	+	0.209815i
$239$	6.67572			0.431817			0.215908	−	0.976414i	$-0.430729\pi$
$239$	6.67572			0.431817			0.215908	+	0.976414i	$0.430729\pi$
$240$	−0.138291	+	3.43166i	−0.00892667	+	0.221513i
$241$	−2.57397	−	12.6081i	−0.165804	−	0.812162i	−0.974579	−	0.224044i	$-0.928074\pi$
$241$	−2.57397	−	12.6081i	−0.165804	−	0.812162i	0.808775	−	0.588118i	$-0.200131\pi$
$242$	−5.25203	−	7.60887i	−0.337613	−	0.489117i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	1.01768	−	2.14471i	0.0651502	−	0.137301i
$245$	3.53028	−	4.32380i	0.225541	−	0.276238i
$246$	0.636894	+	1.67935i	0.0406069	+	0.107072i
$247$	−9.47274	−	3.68531i	−0.602736	−	0.234490i
$248$	−2.10194	+	5.54237i	−0.133474	+	0.351941i
$249$	8.24157	+	14.2748i	0.522288	+	0.904630i
$250$	−4.79503	+	5.87284i	−0.303264	+	0.371431i
$251$	−8.89069	−	6.68092i	−0.561175	−	0.421696i	0.281938	−	0.959433i	$-0.409023\pi$
$251$	−8.89069	−	6.68092i	−0.561175	−	0.421696i	−0.843113	+	0.537737i	$0.819279\pi$
$252$	−2.91581	−	1.53033i	−0.183679	−	0.0964020i
$253$	−9.52261	+	0.768744i	−0.598681	+	0.0483305i
$254$	12.0445	−	0.972335i	0.755741	−	0.0610097i
$255$	−4.48096	−	2.35179i	−0.280609	−	0.147275i
$256$	−6.78404	−	5.09788i	−0.424003	−	0.318617i
$257$	−2.40651	+	2.94743i	−0.150114	+	0.183856i	−0.844188	−	0.536048i	$-0.819917\pi$
$257$	−2.40651	+	2.94743i	−0.150114	+	0.183856i	0.694074	+	0.719904i	$0.255814\pi$
$258$	3.34057	+	5.78604i	0.207975	+	0.360223i
$259$	−3.38574	+	8.92747i	−0.210380	+	0.554726i
$260$	−8.16938	+	9.06428i	−0.506643	+	0.562143i
$261$	−2.03386	−	5.36286i	−0.125893	−	0.331953i
$262$	2.47900	−	3.03623i	0.153153	−	0.187579i
$263$	13.1550	−	27.7235i	0.811169	−	1.70950i	0.112971	−	0.993598i	$-0.463963\pi$
$263$	13.1550	−	27.7235i	0.811169	−	1.70950i	0.698198	−	0.715905i	$-0.253985\pi$
$264$	−11.1421	+	3.71977i	−0.685748	+	0.228936i
$265$	0.853188	+	1.23606i	0.0524109	+	0.0759303i
$266$	0.779520	+	3.81834i	0.0477954	+	0.234118i
$267$	−0.316161	+	7.84545i	−0.0193487	+	0.480134i
$268$	−22.1356			−1.35215
$269$	−0.122967	+	3.05140i	−0.00749744	+	0.186047i	0.991101	+	0.133115i	$0.0424978\pi$
$269$	−0.122967	+	3.05140i	−0.00749744	+	0.186047i	−0.998598	+	0.0529325i	$0.983143\pi$
$270$	−1.13581	+	0.853503i	−0.0691230	+	0.0519426i
$271$	15.6646	−	2.54575i	0.951557	−	0.154643i	0.335233	−	0.942135i	$-0.391185\pi$
$271$	15.6646	−	2.54575i	0.951557	−	0.154643i	0.616325	+	0.787492i	$0.288621\pi$
$272$	−3.29997	+	1.73196i	−0.200090	+	0.105015i
$273$	−2.91000	−	6.99496i	−0.176121	−	0.423355i
$274$	−4.34342	−	2.27960i	−0.262395	−	0.137716i
$275$	1.59729	+	0.533255i	0.0963203	+	0.0321565i
$276$	−0.598327	+	2.93080i	−0.0360150	+	0.176413i
$277$	−8.78267	+	30.3213i	−0.527699	+	1.82183i	0.0408290	+	0.999166i	$0.487000\pi$
$277$	−8.78267	+	30.3213i	−0.527699	+	1.82183i	−0.568528	+	0.822664i	$0.692487\pi$
$278$	−1.36142	−	11.2123i	−0.0816524	−	0.672468i
$279$	2.39579	−	0.799832i	0.143432	−	0.0478847i
$280$	10.5113	+	1.70825i	0.628169	+	0.102087i
$281$	−14.5284	+	7.62508i	−0.866690	+	0.454874i	−0.838610	−	0.544732i	$-0.816631\pi$
$281$	−14.5284	+	7.62508i	−0.866690	+	0.454874i	−0.0280795	+	0.999606i	$0.508939\pi$
$282$	4.70427	−	2.97480i	0.280135	−	0.177147i
$283$	19.2022	−	8.18131i	1.14145	−	0.486328i	0.263304	−	0.964713i	$-0.415188\pi$
$283$	19.2022	−	8.18131i	1.14145	−	0.486328i	0.878150	+	0.478385i	$0.158778\pi$
$284$	−0.566790	+	2.77632i	−0.0336328	+	0.164744i
$285$	−5.91100	−	1.45693i	−0.350137	−	0.0863011i
$286$	−11.0651	−	4.30481i	−0.654293	−	0.254549i
$287$	−5.56972	+	1.37281i	−0.328770	+	0.0810346i
$288$	0.231125	+	5.73531i	0.0136192	+	0.337956i
$289$	0.463401	+	11.4992i	0.0272589	+	0.676422i
$290$	5.15368	+	6.31211i	0.302634	+	0.370660i
$291$	−0.255900	+	0.674753i	−0.0150011	+	0.0395547i
$292$	−5.06740	−	10.6793i	−0.296547	−	0.624960i
$293$	−7.84198	+	27.0736i	−0.458133	+	1.58166i	0.316079	+	0.948733i	$0.397634\pi$
$293$	−7.84198	+	27.0736i	−0.458133	+	1.58166i	−0.774212	+	0.632926i	$0.781854\pi$
$294$	0.966012	−	1.39951i	0.0563390	−	0.0816211i
$295$	1.30991	+	0.558102i	0.0762661	+	0.0324939i
$296$	10.5258	−	1.71061i	0.611799	−	0.0994271i
$297$	4.23043	+	2.67516i	0.245475	+	0.155229i
$298$	3.42101	+	4.95619i	0.198174	+	0.287104i
$299$	−5.36769	+	4.30677i	−0.310422	+	0.249067i
$300$	0.299512	−	0.433918i	0.0172923	−	0.0250523i
$301$	−19.6312	+	8.36407i	−1.13152	+	0.482097i
$302$	1.15991	+	4.00449i	0.0667456	+	0.230432i
$303$	10.7175	−	0.865203i	0.615702	−	0.0497046i
$304$	−3.35586	+	2.97304i	−0.192472	+	0.170515i
$305$	2.76479	−	1.74835i	0.158311	−	0.100110i
$306$	−1.41834	−	0.604299i	−0.0810812	−	0.0345455i
$307$	2.33587	−	19.2376i	0.133315	−	1.09795i	−0.760444	−	0.649404i	$-0.775019\pi$
$307$	2.33587	−	19.2376i	0.133315	−	1.09795i	0.893759	−	0.448547i	$-0.148058\pi$
$308$	−3.29692	−	16.1494i	−0.187859	−	0.920196i
$309$	12.8918	+	1.04073i	0.733389	+	0.0592053i
$310$	−2.86879	+	2.15576i	−0.162936	+	0.122439i
$311$	0.449944	−	3.70563i	0.0255140	−	0.210127i	−0.974377	−	0.224923i	$-0.927787\pi$
$311$	0.449944	−	3.70563i	0.0255140	−	0.210127i	0.999891	+	0.0147963i	$0.00470999\pi$
$312$	−5.14080	+	6.72095i	−0.291040	+	0.380499i
$313$	−2.11460	−	17.4153i	−0.119524	−	0.984372i	−0.921866	−	0.387508i	$-0.873336\pi$
$313$	−2.11460	−	17.4153i	−0.119524	−	0.984372i	0.802342	−	0.596865i	$-0.203587\pi$
$314$	−3.13162	−	3.26036i	−0.176727	−	0.183993i
$315$	−2.26884	−	3.92975i	−0.127835	−	0.221416i
$316$	−8.33954	+	14.4445i	−0.469136	+	0.812567i
$317$	21.3781	−	5.26923i	1.20071	−	0.295949i	0.412273	−	0.911060i	$-0.364735\pi$
$317$	21.3781	−	5.26923i	1.20071	−	0.295949i	0.788441	+	0.615111i	$0.210889\pi$
$318$	0.289380	+	0.354426i	0.0162276	+	0.0198752i
$319$	14.3542	−	24.8621i	0.803678	−	1.39201i
$320$	−0.456072	−	1.20256i	−0.0254952	−	0.0672253i
$321$	11.0214	−	11.4745i	0.615154	−	0.640443i
$322$	2.50278	+	0.835552i	0.139475	+	0.0465635i
$323$	−1.83797	−	6.34540i	−0.102267	−	0.353068i
$324$	1.17304	−	1.03923i	0.0651692	−	0.0577348i
$325$	1.16798	−	0.327530i	0.0647876	−	0.0181681i
$326$	−8.10691	−	7.18209i	−0.449000	−	0.397779i
$327$	−1.28753	+	2.71340i	−0.0712003	+	0.150052i
$328$	4.43820	+	4.62066i	0.245059	+	0.255133i
$329$	7.62082	+	16.0605i	0.420149	+	0.885446i
$330$	−6.90463	−	1.70184i	−0.380088	−	0.0936832i
$331$	0.264072	−	0.274928i	0.0145147	−	0.0151114i	−0.713906	−	0.700242i	$-0.753075\pi$
$331$	0.264072	−	0.274928i	0.0145147	−	0.0151114i	0.728420	+	0.685131i	$0.240255\pi$
$332$	20.6511	+	15.5183i	1.13338	+	0.851678i
$333$	−3.40120	−	3.01320i	−0.186384	−	0.165122i
$334$	2.46057	+	0.399881i	0.134636	+	0.0218805i
$335$	−25.7804	−	16.3025i	−1.40853	−	0.890702i
$336$	−3.33091	−	0.268899i	−0.181716	−	0.0146696i
$337$	−18.9384			−1.03164			−0.515820	−	0.856697i	$-0.672513\pi$
$337$	−18.9384			−1.03164			−0.515820	+	0.856697i	$0.672513\pi$
$338$	−8.33786	+	1.90476i	−0.453520	+	0.103605i
$339$	9.29773			0.504983
$340$	−7.90515	−	0.638170i	−0.428717	−	0.0346096i
$341$	10.6851	+	6.75686i	0.578632	+	0.365905i
$342$	−1.83065	−	0.297510i	−0.0989903	−	0.0160875i
$343$	15.0750	+	13.3553i	0.813972	+	0.721116i
$344$	19.0530	+	14.3174i	1.02727	+	0.771941i
$345$	−2.85532	+	2.97271i	−0.153725	+	0.160045i
$346$	−7.47704	−	1.84292i	−0.401968	−	0.0990762i
$347$	0.456854	+	0.962799i	0.0245252	+	0.0516857i	0.915343	−	0.402674i	$-0.131919\pi$
$347$	0.456854	+	0.962799i	0.0245252	+	0.0516857i	−0.890818	+	0.454360i	$0.849868\pi$
$348$	−6.22664	−	6.48262i	−0.333783	−	0.347505i
$349$	−14.5242	+	30.6091i	−0.777462	+	1.63847i	−0.00783822	+	0.999969i	$0.502495\pi$
$349$	−14.5242	+	30.6091i	−0.777462	+	1.63847i	−0.769624	+	0.638497i	$0.779556\pi$
$350$	−0.348122	−	0.308409i	−0.0186079	−	0.0164852i
$351$	3.60373	−	0.114430i	0.192353	−	0.00610785i
$352$	−21.5049	+	19.0517i	−1.14622	+	1.01546i
$353$	−0.855517	−	2.95359i	−0.0455346	−	0.157204i	0.934529	−	0.355886i	$-0.115821\pi$
$353$	−0.855517	−	2.95359i	−0.0455346	−	0.157204i	−0.980064	+	0.198683i	$0.936334\pi$
$354$	0.411450	+	0.137362i	0.0218683	+	0.00730072i
$355$	−2.70483	+	2.81602i	−0.143557	+	0.149459i
$356$	4.36346	+	11.5055i	0.231263	+	0.609791i
$357$	2.46201	−	4.26433i	0.130304	−	0.225692i
$358$	6.20956	+	7.60533i	0.328185	+	0.401954i
$359$	15.7601	−	3.88452i	0.831787	−	0.205017i	0.199644	−	0.979869i	$-0.436022\pi$
$359$	15.7601	−	3.88452i	0.831787	−	0.205017i	0.632143	+	0.774851i	$0.282175\pi$
$360$	−2.53403	+	4.38906i	−0.133555	+	0.231324i
$361$	5.52638	+	9.57196i	0.290862	+	0.503788i
$362$	1.17795	+	1.22637i	0.0619115	+	0.0644567i
$363$	1.69391	+	13.9506i	0.0889072	+	0.732217i
$364$	−8.49239	−	8.29755i	−0.445122	−	0.434910i
$365$	1.96337	−	16.1698i	0.102767	−	0.846365i
$366$	0.796698	−	0.598680i	0.0416441	−	0.0312935i
$367$	−29.6792	−	2.39595i	−1.54924	−	0.125068i	−0.723981	−	0.689820i	$-0.757690\pi$
$367$	−29.6792	−	2.39595i	−1.54924	−	0.125068i	−0.825260	+	0.564752i	$0.808972\pi$
$368$	0.607183	+	2.97418i	0.0316516	+	0.155040i
$369$	0.329067	−	2.71011i	0.0171305	−	0.141083i
$370$	5.93921	+	2.53046i	0.308765	+	0.131552i
$371$	−1.23514	+	0.781057i	−0.0641255	+	0.0405505i
$372$	2.96285	−	2.62485i	0.153616	−	0.136092i
$373$	−25.1155	+	2.02753i	−1.30043	+	0.104982i	−0.711205	−	0.702985i	$-0.751850\pi$
$373$	−25.1155	+	2.02753i	−1.30043	+	0.104982i	−0.589228	+	0.807967i	$0.700568\pi$
$374$	−2.14693	−	7.41206i	−0.111015	−	0.383269i
$375$	10.6020	−	4.51710i	0.547486	−	0.233262i
$376$	11.2787	−	16.3401i	0.581656	−	0.842674i
$377$	−1.48807	−	20.6263i	−0.0766395	−	1.06231i
$378$	−0.785292	−	1.13769i	−0.0403910	−	0.0585165i
$379$	23.3800	+	14.7846i	1.20095	+	0.759434i	0.976598	−	0.215075i	$-0.0689996\pi$
$379$	23.3800	+	14.7846i	1.20095	+	0.759434i	0.224351	+	0.974508i	$0.427974\pi$
$380$	−9.41723	+	1.53045i	−0.483094	+	0.0785104i
$381$	−16.8974	−	7.19932i	−0.865682	−	0.368832i
$382$	6.04878	−	8.76317i	0.309482	−	0.448363i
$383$	−2.18405	+	7.54021i	−0.111600	+	0.385287i	−0.996801	−	0.0799211i	$-0.974533\pi$
$383$	−2.18405	+	7.54021i	−0.111600	+	0.385287i	0.885202	+	0.465208i	$0.154020\pi$
$384$	4.75339	+	10.0176i	0.242570	+	0.511206i
$385$	8.05396	−	21.2365i	0.410468	−	1.08231i
$386$	8.45224	+	10.3521i	0.430208	+	0.526909i
$387$	−0.408913	−	10.1471i	−0.0207862	−	0.515805i
$388$	0.0455387	+	1.13003i	0.00231188	+	0.0573686i
$389$	−25.1704	+	6.20396i	−1.27619	+	0.314553i	−0.818474	−	0.574544i	$-0.805179\pi$
$389$	−25.1704	+	6.20396i	−1.27619	+	0.314553i	−0.457719	+	0.889097i	$0.651333\pi$
$390$	−4.80502	+	1.77555i	−0.243312	+	0.0899085i
$391$	−4.34284	−	1.07041i	−0.219627	−	0.0541332i
$392$	1.21337	−	5.94350i	0.0612846	−	0.300192i
$393$	−5.48119	+	2.33532i	−0.276489	+	0.117801i
$394$	9.67260	−	6.11658i	0.487298	−	0.308149i
$395$	−20.3508	+	10.6809i	−1.02396	+	0.537416i
$396$	7.74259	+	1.25829i	0.389080	+	0.0632316i
$397$	7.70940	−	2.57378i	0.386924	−	0.129174i	−0.116550	−	0.993185i	$-0.537183\pi$
$397$	7.70940	−	2.57378i	0.386924	−	0.129174i	0.503473	+	0.864011i	$0.332055\pi$
$398$	0.973942	+	8.02113i	0.0488193	+	0.402063i
$399$	1.64804	−	5.68970i	0.0825053	−	0.284841i
$400$	0.107025	−	0.524241i	0.00535123	−	0.0262121i
$401$	32.1465	+	10.7321i	1.60532	+	0.535935i	0.971397	−	0.237460i	$-0.0763149\pi$
$401$	32.1465	+	10.7321i	1.60532	+	0.535935i	0.633924	+	0.773395i	$0.281443\pi$
$402$	−8.22812	−	4.31845i	−0.410381	−	0.215385i
$403$	9.10222	−	0.289026i	0.453414	−	0.0143974i
$404$	14.9206	−	7.83094i	0.742328	−	0.389604i
$405$	2.13156	−	0.346413i	0.105918	−	0.0172134i
$406$	−6.33866	+	4.76320i	−0.314583	+	0.236393i
$407$	0.915803	−	22.7254i	0.0453947	−	1.12646i
$408$	−5.49955			−0.272268
$409$	0.272032	−	6.75040i	0.0134511	−	0.333786i	−0.978427	−	0.206593i	$-0.933762\pi$
$409$	0.272032	−	6.75040i	0.0134511	−	0.333786i	0.991878	−	0.127193i	$-0.0405966\pi$
$410$	0.775832	+	3.80028i	0.0383156	+	0.187682i
$411$	4.23550	+	6.13618i	0.208922	+	0.302675i
$412$	19.2263	−	6.41867i	0.947210	−	0.316225i
$413$	−0.593918	+	1.25166i	−0.0292248	+	0.0615899i
$414$	−0.794176	+	0.972689i	−0.0390316	+	0.0478051i
$415$	12.6225	+	33.2827i	0.619612	+	1.63378i
$416$	−5.12412	+	20.0513i	−0.251231	+	0.983098i
$417$	−6.08778	+	16.0522i	−0.298120	+	0.786078i
$418$	−4.64159	−	8.03947i	−0.227028	−	0.393223i
$419$	12.0002	−	14.6976i	0.586249	−	0.718025i	−0.393259	−	0.919428i	$-0.628653\pi$
$419$	12.0002	−	14.6976i	0.586249	−	0.718025i	0.979509	+	0.201403i	$0.0645500\pi$
$420$	−5.68510	−	4.27208i	−0.277405	−	0.208456i
$421$	−3.66136	−	1.92163i	−0.178444	−	0.0936545i	0.373136	−	0.927777i	$-0.378282\pi$
$421$	−3.66136	−	1.92163i	−0.178444	−	0.0936545i	−0.551580	+	0.834122i	$0.685975\pi$
$422$	−3.31706	+	0.267781i	−0.161472	+	0.0130354i
$423$	−8.43276	+	0.680763i	−0.410015	+	0.0330998i
$424$	1.44523	+	0.758515i	0.0701865	+	0.0368367i
$425$	0.630278	+	0.473623i	0.0305730	+	0.0229741i
$426$	−0.752317	+	0.921421i	−0.0364499	+	0.0446430i
$427$	1.59145	+	2.75648i	0.0770158	+	0.133395i
$428$	8.84172	−	23.3137i	0.427381	−	1.12691i
$429$	11.8516	+	13.6099i	0.572200	+	0.657093i
$430$	5.11629	+	13.4905i	0.246729	+	0.650572i
$431$	17.0683	−	20.9048i	0.822150	−	1.00695i	−0.177589	−	0.984105i	$-0.556830\pi$
$431$	17.0683	−	20.9048i	0.822150	−	1.00695i	0.999739	−	0.0228460i	$-0.00727275\pi$
$432$	0.681780	−	1.43682i	0.0328021	−	0.0691290i
$433$	−24.3605	+	8.13272i	−1.17069	+	0.390834i	−0.834525	−	0.550970i	$-0.814258\pi$
$433$	−24.3605	+	8.13272i	−1.17069	+	0.390834i	−0.336164	+	0.941803i	$0.609130\pi$
$434$	−1.98347	−	2.87355i	−0.0952096	−	0.137935i
$435$	−2.47755	−	12.1358i	−0.118789	−	0.581868i
$436$	−0.189524	+	4.70299i	−0.00907656	+	0.225232i
$437$	−5.38077			−0.257397
$438$	0.199811	−	4.95825i	0.00954733	−	0.236914i
$439$	5.72992	−	4.30575i	0.273474	−	0.205502i	−0.455153	−	0.890413i	$-0.650415\pi$
$439$	5.72992	−	4.30575i	0.273474	−	0.205502i	0.728627	+	0.684911i	$0.240159\pi$
$440$	−25.0386	+	4.06917i	−1.19367	+	0.193990i
$441$	−2.28873	+	1.20122i	−0.108987	+	0.0572008i
$442$	−4.27565	−	3.55220i	−0.203372	−	0.168961i
$443$	3.77499	+	1.98127i	0.179355	+	0.0941330i	0.552011	−	0.833837i	$-0.313861\pi$
$443$	3.77499	+	1.98127i	0.179355	+	0.0941330i	−0.372656	+	0.927970i	$0.621553\pi$
$444$	−6.75467	−	2.25504i	−0.320563	−	0.107020i
$445$	−3.39168	+	16.6136i	−0.160781	+	0.787558i
$446$	−2.08397	+	7.19471i	−0.0986790	+	0.340679i
$447$	−1.10336	−	9.08700i	−0.0521872	−	0.429800i
$448$	1.18702	−	0.396286i	0.0560815	−	0.0187228i
$449$	16.1820	+	2.62983i	0.763675	+	0.124109i	0.529760	−	0.848148i	$-0.322282\pi$
$449$	16.1820	+	2.62983i	0.763675	+	0.124109i	0.233915	+	0.972257i	$0.424846\pi$
$450$	0.195986	−	0.102861i	0.00923886	−	0.00484893i
$451$	11.5491	−	7.30323i	0.543828	−	0.343896i
$452$	13.4051	−	5.71140i	0.630525	−	0.268642i
$453$	1.26756	−	6.20893i	0.0595553	−	0.291721i
$454$	13.4761	+	3.32155i	0.632463	+	0.155888i
$455$	−3.77970	−	15.9183i	−0.177195	−	0.746260i
$456$	−6.42367	+	1.58329i	−0.300816	+	0.0741445i
$457$	−1.47790	−	36.6738i	−0.0691334	−	1.71553i	−0.547032	−	0.837112i	$-0.684242\pi$
$457$	−1.47790	−	36.6738i	−0.0691334	−	1.71553i	0.477899	−	0.878415i	$-0.341399\pi$
$458$	0.498134	+	12.3611i	0.0232763	+	0.577595i
$459$	1.48207	+	1.81520i	0.0691770	+	0.0847264i
$460$	−2.29064	+	6.03991i	−0.106801	+	0.281612i
$461$	4.43049	+	9.33706i	0.206349	+	0.434870i	0.980069	−	0.198657i	$-0.0636578\pi$
$461$	4.43049	+	9.33706i	0.206349	+	0.434870i	−0.773721	+	0.633527i	$0.781607\pi$
$462$	1.92508	−	6.64614i	0.0895627	−	0.309206i
$463$	8.61903	−	12.4868i	0.400560	−	0.580311i	−0.569858	−	0.821743i	$-0.693002\pi$
$463$	8.61903	−	12.4868i	0.400560	−	0.580311i	0.970418	+	0.241432i	$0.0776171\pi$
$464$	−8.39176	−	3.57540i	−0.389578	−	0.165984i
$465$	5.38385	−	0.874961i	0.249670	−	0.0405753i
$466$	−7.15005	−	4.52141i	−0.331219	−	0.209450i
$467$	−3.53714	−	5.12443i	−0.163679	−	0.237130i	0.732559	−	0.680704i	$-0.238326\pi$
$467$	−3.53714	−	5.12443i	−0.163679	−	0.237130i	−0.896238	+	0.443573i	$0.853711\pi$
$468$	5.12545	−	2.37868i	0.236924	−	0.109955i
$469$	16.8597	−	24.4254i	0.778507	−	1.12786i
$470$	11.0580	−	4.71136i	0.510066	−	0.217319i
$471$	1.91177	+	6.60018i	0.0880895	+	0.304120i
$472$	1.54233	−	0.124510i	0.0709914	−	0.00573102i
$473$	38.0471	−	33.7068i	1.74941	−	1.54984i
$474$	−5.91790	+	3.74226i	−0.271818	+	0.171888i
$475$	0.872542	+	0.371755i	0.0400350	+	0.0170573i
$476$	0.930157	−	7.66053i	0.0426337	−	0.351120i
$477$	−0.139115	−	0.681430i	−0.00636963	−	0.0312005i
$478$	4.37770	+	0.353404i	0.200231	+	0.0161643i
$479$	15.4936	−	11.6427i	0.707920	−	0.531967i	−0.184690	−	0.982797i	$-0.559128\pi$
$479$	15.4936	−	11.6427i	0.707920	−	0.531967i	0.892610	+	0.450830i	$0.148872\pi$
$480$	−1.49413	+	12.3052i	−0.0681972	+	0.561655i
$481$	−8.63790	−	13.9214i	−0.393855	−	0.634759i
$482$	−1.02046	−	8.40422i	−0.0464806	−	0.382802i
$483$	−2.77825	−	2.89247i	−0.126415	−	0.131612i
$484$	11.0118	+	19.0730i	0.500536	+	0.866953i
$485$	−0.779211	+	1.34963i	−0.0353821	+	0.0612837i
$486$	0.638780	−	0.157445i	0.0289756	−	0.00714185i
$487$	−11.5198	−	14.1092i	−0.522011	−	0.639347i	0.444559	−	0.895749i	$-0.353360\pi$
$487$	−11.5198	−	14.1092i	−0.522011	−	0.639347i	−0.966570	+	0.256402i	$0.917463\pi$
$488$	1.77746	−	3.07865i	0.0804619	−	0.139364i
$489$	5.83773	+	15.3928i	0.263991	+	0.696088i
$490$	2.54392	−	2.64851i	0.114923	−	0.119647i
$491$	−8.21642	−	2.74304i	−0.370802	−	0.123792i	0.125159	−	0.992137i	$-0.460056\pi$
$491$	−8.21642	−	2.74304i	−0.370802	−	0.123792i	−0.495961	+	0.868345i	$0.665184\pi$
$492$	−1.19033	−	4.10948i	−0.0536640	−	0.185270i
$493$	10.0605	−	8.91284i	0.453103	−	0.401414i
$494$	−6.01678	−	2.91817i	−0.270708	−	0.131294i
$495$	8.09073	+	7.16776i	0.363651	+	0.322167i
$496$	1.72202	−	3.62908i	0.0773211	−	0.162951i
$497$	−2.63182	−	2.74001i	−0.118053	−	0.122906i
$498$	4.64883	+	9.79720i	0.208319	+	0.439023i
$499$	−29.8209	−	7.35018i	−1.33496	−	0.329039i	−0.493686	−	0.869640i	$-0.664351\pi$
$499$	−29.8209	−	7.35018i	−1.33496	−	0.329039i	−0.841279	+	0.540601i	$0.818197\pi$
$500$	12.5109	−	13.0252i	0.559503	−	0.582504i
$501$	−3.02918	−	2.27628i	−0.135334	−	0.101697i
$502$	−5.47651	−	4.85176i	−0.244429	−	0.216545i
$503$	−35.9002	−	5.83435i	−1.60071	−	0.260141i	−0.706476	−	0.707737i	$-0.749716\pi$
$503$	−35.9002	−	5.83435i	−1.60071	−	0.260141i	−0.894236	+	0.447596i	$0.852280\pi$
$504$	−4.16785	−	2.63559i	−0.185651	−	0.117398i
$505$	23.1447	+	1.86843i	1.02992	+	0.0831441i
$506$	−6.28528			−0.279415
$507$	12.5673	+	3.32608i	0.558134	+	0.147716i
$508$	−28.7845			−1.27711
$509$	−3.39550	−	0.274113i	−0.150503	−	0.0121498i	0.00498555	−	0.999988i	$-0.498413\pi$
$509$	−3.39550	−	0.274113i	−0.150503	−	0.0121498i	−0.155488	+	0.987838i	$0.549695\pi$
$510$	−2.81395	−	1.77943i	−0.124604	−	0.0787947i
$511$	15.6436	+	2.54234i	0.692033	+	0.112466i
$512$	12.4203	+	11.0034i	0.548904	+	0.486286i
$513$	2.25370	+	1.69354i	0.0995032	+	0.0747718i
$514$	−1.73413	+	1.80542i	−0.0764893	+	0.0796338i
$515$	27.1192	+	6.68428i	1.19501	+	0.294545i
$516$	−6.82269	−	14.3785i	−0.300352	−	0.632979i
$517$	−29.3340	−	30.5399i	−1.29011	−	1.34314i
$518$	−2.69285	+	5.67507i	−0.118317	+	0.249348i
$519$	8.76146	+	7.76197i	0.384585	+	0.340713i
$520$	−13.2862	+	12.5453i	−0.582637	+	0.550148i
$521$	6.38439	−	5.65607i	0.279705	−	0.247797i	−0.511593	−	0.859228i	$-0.670944\pi$
$521$	6.38439	−	5.65607i	0.279705	−	0.247797i	0.791298	+	0.611431i	$0.209406\pi$
$522$	−1.04983	−	3.62444i	−0.0459499	−	0.158637i
$523$	−34.2108	−	11.4212i	−1.49593	−	0.499416i	−0.553225	−	0.833032i	$-0.686603\pi$
$523$	−34.2108	−	11.4212i	−1.49593	−	0.499416i	−0.942709	+	0.333616i	$0.891731\pi$
$524$	−6.46805	+	6.73395i	−0.282558	+	0.294174i
$525$	0.250680	+	0.660989i	0.0109406	+	0.0288479i
$526$	10.0942	−	17.4836i	0.440127	−	0.762323i
$527$	3.74337	+	4.58480i	0.163064	+	0.199717i
$528$	7.72897	−	1.90502i	0.336360	−	0.0829054i
$529$	9.67845	−	16.7636i	0.420802	−	0.728850i
$530$	0.494054	+	0.855727i	0.0214604	+	0.0371704i
$531$	−0.456736	−	0.475513i	−0.0198207	−	0.0206355i
$532$	−1.11897	−	9.21557i	−0.0485136	−	0.399546i
$533$	3.93535	−	9.02229i	0.170459	−	0.390799i
$534$	−0.622655	+	5.12802i	−0.0269449	+	0.221911i
$535$	27.4677	−	20.6406i	1.18753	−	0.892372i
$536$	−33.0405	−	2.66731i	−1.42713	−	0.115210i
$537$	−2.98514	−	14.6222i	−0.128818	−	0.630995i
$538$	−0.242175	+	1.99449i	−0.0104409	+	0.0859884i
$539$	−11.9024	−	5.07115i	−0.512674	−	0.218430i
$540$	2.86042	−	1.80882i	0.123093	−	0.0778393i
$541$	−14.8333	+	13.1412i	−0.637733	+	0.564982i	−0.918809	−	0.394703i	$-0.870847\pi$
$541$	−14.8333	+	13.1412i	−0.637733	+	0.564982i	0.281075	+	0.959686i	$0.409309\pi$
$542$	10.4071	−	0.840144i	0.447021	−	0.0360873i
$543$	−0.719104	−	2.48264i	−0.0308597	−	0.106540i
$544$	−12.3746	+	5.27234i	−0.530558	+	0.226050i
$545$	−3.68440	+	5.33778i	−0.157822	+	0.228645i
$546$	−1.53797	−	4.74110i	−0.0658189	−	0.202900i
$547$	11.5408	+	16.7197i	0.493448	+	0.714882i	0.988032	−	0.154247i	$-0.0492952\pi$
$547$	11.5408	+	16.7197i	0.493448	+	0.714882i	−0.494585	+	0.869130i	$0.664680\pi$
$548$	9.87592	+	6.24515i	0.421878	+	0.266780i
$549$	−1.49516	+	0.242987i	−0.0638119	+	0.0103704i
$550$	1.01922	+	0.434248i	0.0434595	+	0.0185164i
$551$	9.18509	−	13.3069i	0.391298	−	0.566893i
$552$	−1.24624	+	4.30253i	−0.0530436	+	0.183128i
$553$	−9.58687	−	20.2039i	−0.407675	−	0.859157i
$554$	−7.36453	+	19.4187i	−0.312889	+	0.825020i
$555$	−6.20606	−	7.60104i	−0.263433	−	0.322646i
$556$	1.08335	+	26.8831i	0.0459443	+	1.14010i
$557$	1.25087	+	31.0401i	0.0530012	+	1.31521i	0.778786	+	0.627289i	$0.215836\pi$
$557$	1.25087	+	31.0401i	0.0530012	+	1.31521i	−0.725785	+	0.687921i	$0.758523\pi$
$558$	1.61341	−	0.397671i	0.0683013	−	0.0168347i
$559$	9.06574	−	35.4754i	0.383440	−	1.50045i
$560$	−7.00689	−	1.72704i	−0.296095	−	0.0729809i
$561$	−2.34618	+	11.4923i	−0.0990558	+	0.485207i
$562$	−9.93084	+	4.23113i	−0.418907	+	0.178480i
$563$	24.3465	−	15.3958i	1.02608	−	0.648856i	0.0883066	−	0.996093i	$-0.471854\pi$
$563$	24.3465	−	15.3958i	1.02608	−	0.648856i	0.937777	+	0.347237i	$0.112880\pi$
$564$	−11.7399	+	6.16157i	−0.494338	+	0.259449i
$565$	19.8187	+	3.22085i	0.833779	+	0.135502i
$566$	13.0252	−	4.34846i	0.547491	−	0.182779i
$567$	0.253276	+	2.08592i	0.0106366	+	0.0876003i
$568$	−1.18055	+	4.07575i	−0.0495350	+	0.171015i
$569$	0.280606	−	1.37450i	0.0117636	−	0.0576220i	−0.973485	−	0.228750i	$-0.926536\pi$
$569$	0.280606	−	1.37450i	0.0117636	−	0.0576220i	0.985249	+	0.171128i	$0.0547412\pi$
$570$	−3.79909	−	1.26832i	−0.159126	−	0.0531242i
$571$	32.7876	+	17.2083i	1.37212	+	0.720144i	0.979855	−	0.199708i	$-0.0639995\pi$
$571$	32.7876	+	17.2083i	1.37212	+	0.720144i	0.392265	+	0.919852i	$0.371692\pi$
$572$	25.4475	+	12.3421i	1.06401	+	0.516051i
$573$	−14.3311	+	7.52153i	−0.598689	+	0.314216i
$574$	−3.72509	+	0.605387i	−0.155482	+	0.0252684i
$575$	0.513361	−	0.385766i	0.0214087	−	0.0160876i
$576$	−0.0239810	+	0.595082i	−0.000999208	+	0.0247951i
$577$	−4.80380			−0.199985			−0.0999925	−	0.994988i	$-0.531882\pi$
$577$	−4.80380			−0.199985			−0.0999925	+	0.994988i	$0.531882\pi$
$578$	−0.304870	+	7.56527i	−0.0126809	+	0.314674i
$579$	−4.06328	−	19.9033i	−0.168864	−	0.827152i
$580$	−11.0268	−	15.9751i	−0.457864	−	0.663330i
$581$	−32.8526	+	10.9678i	−1.36295	+	0.455021i
$582$	−0.203531	+	0.428932i	−0.00843662	+	0.0177798i
$583$	2.20161	−	2.69649i	0.0911815	−	0.111677i
$584$	−6.27696	−	16.5510i	−0.259743	−	0.684885i
$585$	7.72123	+	1.00446i	0.319234	+	0.0415295i
$586$	−6.57573	+	17.3388i	−0.271641	+	0.716258i
$587$	15.8614	+	27.4728i	0.654671	+	1.13392i	0.981976	+	0.189004i	$0.0605260\pi$
$587$	15.8614	+	27.4728i	0.654671	+	1.13392i	−0.327306	+	0.944918i	$0.606141\pi$
$588$	−2.56192	+	3.13779i	−0.105652	+	0.129400i
$589$	5.69233	+	4.27751i	0.234549	+	0.176252i
$590$	0.829448	+	0.435328i	0.0341478	+	0.0179222i
$591$	−17.3388	+	1.39974i	−0.713225	+	0.0575775i
$592$	−7.20313	+	0.581497i	−0.296047	+	0.0238994i
$593$	−4.82428	−	2.53198i	−0.198109	−	0.103976i	0.362751	−	0.931886i	$-0.381837\pi$
$593$	−4.82428	−	2.53198i	−0.198109	−	0.103976i	−0.560861	+	0.827910i	$0.689530\pi$
$594$	2.63254	+	1.97823i	0.108015	+	0.0811677i
$595$	6.72516	−	8.23682i	0.275705	−	0.337677i
$596$	−7.17274	−	12.4236i	−0.293807	−	0.508888i
$597$	4.35513	−	11.4835i	0.178243	−	0.469989i
$598$	−3.74793	+	2.54006i	−0.153264	+	0.103871i
$599$	7.59869	+	20.0361i	0.310474	+	0.818653i	0.995896	+	0.0905064i	$0.0288486\pi$
$599$	7.59869	+	20.0361i	0.310474	+	0.818653i	−0.685422	+	0.728146i	$0.740382\pi$
$600$	0.499350	−	0.611592i	0.0203859	−	0.0249682i
$601$	−2.70555	+	5.70183i	−0.110362	+	0.232582i	−0.951116	−	0.308835i	$-0.900061\pi$
$601$	−2.70555	+	5.70183i	−0.110362	+	0.232582i	0.840754	+	0.541418i	$0.182112\pi$
$602$	−13.3162	+	4.44560i	−0.542728	+	0.181189i
$603$	8.02368	+	11.6243i	0.326749	+	0.473378i
$604$	−1.98649	−	9.73046i	−0.0808290	−	0.395927i
$605$	−1.22199	+	30.3234i	−0.0496810	+	1.23282i
$606$	7.07393			0.287359
$607$	−1.25056	+	31.0324i	−0.0507587	+	1.25956i	0.750348	+	0.661043i	$0.229886\pi$
$607$	−1.25056	+	31.0324i	−0.0507587	+	1.25956i	−0.801107	+	0.598522i	$0.795755\pi$
$608$	−12.9361	+	9.72088i	−0.524630	+	0.394234i
$609$	11.8957	−	1.93325i	0.482040	−	0.0783391i
$610$	1.90560	−	1.00014i	0.0771556	−	0.0404944i
$611$	−29.8340	−	6.35636i	−1.20696	−	0.257151i
$612$	3.25184	+	1.70670i	0.131448	+	0.0689891i
$613$	18.0624	+	6.03011i	0.729533	+	0.243554i	0.657083	−	0.753818i	$-0.271790\pi$
$613$	18.0624	+	6.03011i	0.729533	+	0.243554i	0.0724496	+	0.997372i	$0.476918\pi$
$614$	2.55020	−	12.4917i	0.102918	−	0.504124i
$615$	1.64024	−	5.66278i	0.0661410	−	0.228345i
$616$	−2.97514	−	24.5025i	−0.119872	−	0.987232i
$617$	34.2282	−	11.4271i	1.37798	−	0.460036i	0.471341	−	0.881951i	$-0.343770\pi$
$617$	34.2282	−	11.4271i	1.37798	−	0.460036i	0.906635	+	0.421915i	$0.138642\pi$
$618$	8.39889	+	1.36495i	0.337853	+	0.0549064i
$619$	24.5294	−	12.8740i	0.985919	−	0.517450i	0.106917	−	0.994268i	$-0.465902\pi$
$619$	24.5294	−	12.8740i	0.985919	−	0.517450i	0.879002	+	0.476818i	$0.158210\pi$
$620$	7.22478	−	4.56867i	0.290154	−	0.183482i
$621$	1.75596	−	0.748144i	0.0704642	−	0.0300220i
$622$	0.491228	−	2.40620i	0.0196965	−	0.0964797i
$623$	−16.0191	−	3.94836i	−0.641792	−	0.158188i
$624$	3.83894	−	4.25947i	0.153681	−	0.170515i
$625$	22.5304	−	5.55323i	0.901214	−	0.222129i
$626$	−0.464735	−	11.5323i	−0.0185745	−	0.460923i
$627$	0.568168	+	14.0989i	0.0226904	+	0.563057i
$628$	6.81067	+	8.34156i	0.271775	+	0.332864i
$629$	3.77593	−	9.95630i	0.150556	−	0.396984i
$630$	−1.27979	−	2.69710i	−0.0509880	−	0.107455i
$631$	−12.3094	+	42.4969i	−0.490029	+	1.69178i	0.210034	+	0.977694i	$0.432643\pi$
$631$	−12.3094	+	42.4969i	−0.490029	+	1.69178i	−0.700062	+	0.714082i	$0.746845\pi$
$632$	−14.1885	+	20.5555i	−0.564387	+	0.817655i
$633$	4.65355	+	1.98269i	0.184962	+	0.0788049i
$634$	14.2979	−	2.32364i	0.567843	−	0.0922835i
$635$	−33.5240	−	21.1993i	−1.33036	−	0.841269i
$636$	−0.619159	−	0.897007i	−0.0245512	−	0.0355686i
$637$	−9.14686	+	1.78617i	−0.362412	+	0.0707706i
$638$	10.7291	−	15.5438i	0.424769	−	0.615384i
$639$	1.66340	−	0.708710i	0.0658033	−	0.0280361i
$640$	6.66194	+	22.9997i	0.263336	+	0.909142i
$641$	45.0463	−	3.63651i	1.77922	−	0.143633i	0.853316	−	0.521393i	$-0.174588\pi$
$641$	45.0463	−	3.63651i	1.77922	−	0.143633i	0.925904	+	0.377760i	$0.123306\pi$
$642$	7.83487	−	6.94109i	0.309218	−	0.273943i
$643$	11.5513	−	7.30458i	0.455537	−	0.288064i	−0.286924	−	0.957953i	$-0.592633\pi$
$643$	11.5513	−	7.30458i	0.455537	−	0.288064i	0.742461	+	0.669889i	$0.233658\pi$
$644$	−5.78237	−	2.46364i	−0.227857	−	0.0970809i
$645$	2.64345	−	21.7708i	0.104086	−	0.857224i
$646$	−0.869355	−	4.25838i	−0.0342043	−	0.167544i
$647$	−23.9101	−	1.93022i	−0.940004	−	0.0758849i	−0.399042	−	0.916932i	$-0.630657\pi$
$647$	−23.9101	−	1.93022i	−0.940004	−	0.0758849i	−0.540961	+	0.841048i	$0.681939\pi$
$648$	1.87616	−	1.40984i	0.0737024	−	0.0553838i
$649$	0.397791	−	3.27610i	0.0156147	−	0.128598i
$650$	0.783255	−	0.152951i	0.0307218	−	0.00599925i
$651$	0.639719	+	5.26856i	0.0250726	+	0.206491i
$652$	17.8721	+	18.6069i	0.699926	+	0.728701i
$653$	−1.62784	−	2.81950i	−0.0637022	−	0.110336i	0.832415	−	0.554152i	$-0.186957\pi$
$653$	−1.62784	−	2.81950i	−0.0637022	−	0.110336i	−0.896118	+	0.443817i	$0.853624\pi$
$654$	−0.987957	+	1.71119i	−0.0386322	+	0.0669129i
$655$	−12.4925	+	3.07912i	−0.488122	+	0.120311i
$656$	−2.74591	−	3.36313i	−0.107210	−	0.131308i
$657$	−3.77132	+	6.53211i	−0.147133	+	0.254842i
$658$	4.14723	+	10.9354i	0.161676	+	0.426304i
$659$	−4.00776	+	4.17252i	−0.156120	+	0.162538i	−0.794669	−	0.607043i	$-0.792356\pi$
$659$	−4.00776	+	4.17252i	−0.156120	+	0.162538i	0.638549	+	0.769581i	$0.279535\pi$
$660$	16.0679	+	5.36426i	0.625444	+	0.208804i
$661$	−2.61551	−	9.02978i	−0.101731	−	0.351218i	0.893463	−	0.449137i	$-0.148268\pi$
$661$	−2.61551	−	9.02978i	−0.101731	−	0.351218i	−0.995194	+	0.0979193i	$0.968781\pi$
$662$	0.187723	−	0.166308i	0.00729607	−	0.00646376i
$663$	3.24536	+	7.80109i	0.126039	+	0.302969i
$664$	28.9548	+	25.6517i	1.12366	+	0.995478i
$665$	5.48389	−	11.5571i	0.212656	−	0.448163i
$666$	−2.07087	−	2.15600i	−0.0802445	−	0.0835433i
$667$	−4.69309	−	9.89048i	−0.181717	−	0.382961i
$668$	−5.76564	−	1.42110i	−0.223079	−	0.0549841i
$669$	7.88697	−	8.21121i	0.304928	−	0.317464i
$670$	−16.0428	−	12.0554i	−0.619787	−	0.465740i
$671$	−5.67514	−	5.02774i	−0.219087	−	0.194094i
$672$	−11.9048	−	1.93472i	−0.459239	−	0.0746336i
$673$	−19.7015	−	12.4585i	−0.759438	−	0.480240i	0.0977703	−	0.995209i	$-0.468829\pi$
$673$	−19.7015	−	12.4585i	−0.759438	−	0.480240i	−0.857209	+	0.514969i	$0.827803\pi$
$674$	−12.4191	−	1.00257i	−0.478366	−	0.0386177i
$675$	−0.336434			−0.0129494
$676$	20.1623	−	2.92440i	0.775471	−	0.112477i
$677$	−31.0559			−1.19358			−0.596788	−	0.802399i	$-0.703557\pi$
$677$	−31.0559			−1.19358			−0.596788	+	0.802399i	$0.703557\pi$
$678$	6.09711	+	0.492210i	0.234158	+	0.0189032i
$679$	−1.28161	−	0.810441i	−0.0491836	−	0.0311019i
$680$	−11.7226	−	1.90511i	−0.449543	−	0.0730578i
$681$	−15.7910	−	13.9896i	−0.605113	−	0.536083i
$682$	6.64922	+	4.99656i	0.254612	+	0.191328i
$683$	−27.5659	+	28.6992i	−1.05478	+	1.09814i	−0.0597875	+	0.998211i	$0.519042\pi$
$683$	−27.5659	+	28.6992i	−1.05478	+	1.09814i	−0.994994	+	0.0999330i	$0.968137\pi$
$684$	4.28961	+	1.05729i	0.164017	+	0.0404267i
$685$	6.90258	+	14.5469i	0.263734	+	0.555808i
$686$	9.17860	+	9.55594i	0.350441	+	0.364847i
$687$	8.06114	−	16.9885i	0.307552	−	0.648152i
$688$	−12.0890	−	10.7099i	−0.460888	−	0.408311i
$689$	0.223102	−	2.49766i	0.00849951	−	0.0951534i
$690$	−2.02979	+	1.79824i	−0.0772728	+	0.0684577i
$691$	9.84011	+	33.9720i	0.374335	+	1.29236i	0.897836	+	0.440330i	$0.145139\pi$
$691$	9.84011	+	33.9720i	0.374335	+	1.29236i	−0.523500	+	0.852025i	$0.675374\pi$
$692$	17.4000	+	5.80897i	0.661448	+	0.220824i
$693$	−7.28561	+	7.58513i	−0.276758	+	0.288135i
$694$	0.248619	+	0.655554i	0.00943744	+	0.0248845i
$695$	−18.5372	+	32.1073i	−0.703155	+	1.21790i
$696$	−8.51299	−	10.4265i	−0.322684	−	0.395216i
$697$	6.21159	−	1.53102i	0.235281	−	0.0579915i
$698$	−11.1448	+	19.3034i	−0.421839	+	0.730646i
$699$	6.42934	+	11.1359i	0.243180	+	0.421200i
$700$	0.767454	+	0.799004i	0.0290070	+	0.0301995i
$701$	−0.690930	−	5.69032i	−0.0260961	−	0.214921i	0.973827	−	0.227289i	$-0.0729861\pi$
$701$	−0.690930	−	5.69032i	−0.0260961	−	0.214921i	−0.999924	+	0.0123681i	$0.996063\pi$
$702$	2.36926	+	0.115738i	0.0894218	+	0.00436824i
$703$	1.54405	−	12.7164i	0.0582350	−	0.479608i
$704$	−2.38313	+	1.79080i	−0.0898175	+	0.0674935i
$705$	−18.2108	−	1.47013i	−0.685858	−	0.0553682i
$706$	−0.404658	−	1.98214i	−0.0152295	−	0.0745990i
$707$	−2.72331	+	22.4285i	−0.102421	+	0.843510i
$708$	−0.950604	−	0.405015i	−0.0357259	−	0.0152214i
$709$	−1.08703	+	0.687399i	−0.0408244	+	0.0258158i	−0.554722	−	0.832036i	$-0.687175\pi$
$709$	−1.08703	+	0.687399i	−0.0408244	+	0.0258158i	0.513898	+	0.857851i	$0.328201\pi$
$710$	−1.92280	+	1.70345i	−0.0721615	+	0.0639295i
$711$	10.6083	−	0.856389i	0.397842	−	0.0321171i
$712$	5.12668	+	17.6994i	0.192131	+	0.663312i
$713$	4.43515	−	1.88964i	0.166098	−	0.0707677i
$714$	1.84025	−	2.66606i	0.0688695	−	0.0997747i
$715$	20.5477	+	33.1160i	0.768442	+	1.23847i
$716$	−13.2860	−	19.2481i	−0.496521	−	0.719335i
$717$	−5.64226	−	3.56795i	−0.210714	−	0.133247i
$718$	10.5406	−	1.71301i	0.393370	−	0.0639288i
$719$	−48.7095	−	20.7532i	−1.81656	−	0.773964i	−0.970593	−	0.240728i	$-0.922614\pi$
$719$	−48.7095	−	20.7532i	−1.81656	−	0.773964i	−0.845967	−	0.533236i	$-0.820976\pi$
$720$	1.95099	−	2.82650i	0.0727091	−	0.105337i
$721$	−7.56108	+	26.1039i	−0.281589	+	0.972160i
$722$	3.11727	+	6.56951i	0.116013	+	0.244492i
$723$	−4.56313	+	12.0320i	−0.169705	+	0.447474i
$724$	−2.56181	−	3.13765i	−0.0952090	−	0.116610i
$725$	0.0776989	+	1.92808i	0.00288566	+	0.0716070i
$726$	0.372278	+	9.23797i	0.0138165	+	0.342853i
$727$	−37.0467	+	9.13120i	−1.37399	+	0.338657i	−0.856108	−	0.516797i	$-0.827124\pi$
$727$	−37.0467	+	9.13120i	−1.37399	+	0.338657i	−0.517879	+	0.855454i	$0.673278\pi$
$728$	−11.6762	−	13.4086i	−0.432750	−	0.496955i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	2.14351	−	10.4996i	0.0793349	−	0.388608i
$731$	21.8936	−	9.32797i	0.809762	−	0.345008i
$732$	−2.00641	+	1.26878i	−0.0741590	+	0.0468953i
$733$	−6.91716	+	3.63040i	−0.255491	+	0.134092i	−0.587607	−	0.809147i	$-0.699930\pi$
$733$	−6.91716	+	3.63040i	−0.255491	+	0.134092i	0.332116	+	0.943239i	$0.392238\pi$
$734$	−19.3357	−	3.14236i	−0.713694	−	0.115986i
$735$	−5.29468	+	1.76762i	−0.195297	+	0.0651998i
$736$	1.32058	+	10.8759i	0.0486772	+	0.400893i
$737$	−19.6694	+	67.9066i	−0.724531	+	2.50137i
$738$	0.359260	−	1.75977i	0.0132245	−	0.0647781i
$739$	18.3549	+	6.12776i	0.675195	+	0.225413i	0.633530	−	0.773718i	$-0.281605\pi$
$739$	18.3549	+	6.12776i	0.675195	+	0.225413i	0.0416654	+	0.999132i	$0.486734\pi$
$740$	−13.6168	−	7.14667i	−0.500565	−	0.262717i
$741$	6.03659	+	8.17764i	0.221760	+	0.300413i
$742$	−0.851310	+	0.446802i	−0.0312526	+	0.0164026i
$743$	−41.2739	+	6.70766i	−1.51419	+	0.246080i	−0.860018	−	0.510264i	$-0.829548\pi$
$743$	−41.2739	+	6.70766i	−1.51419	+	0.246080i	−0.654174	+	0.756344i	$0.726984\pi$
$744$	4.73875	−	3.56094i	0.173731	−	0.130550i
$745$	0.795968	−	19.7517i	0.0291620	−	0.723648i
$746$	−16.5772			−0.606934
$747$	0.663709	−	16.4698i	0.0242838	−	0.602597i
$748$	3.67687	+	18.0105i	0.134440	+	0.658528i
$749$	18.9910	+	27.5133i	0.693918	+	1.00531i
$750$	7.19154	−	2.40089i	0.262598	−	0.0876681i
$751$	1.79779	−	3.78875i	0.0656021	−	0.138254i	−0.868001	−	0.496563i	$-0.834595\pi$
$751$	1.79779	−	3.78875i	0.0656021	−	0.138254i	0.933603	+	0.358309i	$0.116647\pi$
$752$	−8.50945	+	10.4222i	−0.310308	+	0.380058i
$753$	3.94360	+	10.3984i	0.143713	+	0.378939i
$754$	0.116109	−	13.6048i	0.00422842	−	0.495456i
$755$	4.85274	−	12.7956i	0.176609	−	0.465681i
$756$	1.64650	+	2.85182i	0.0598826	+	0.103720i
$757$	−5.46726	+	6.69617i	−0.198711	+	0.243377i	−0.864342	−	0.502904i	$-0.832265\pi$
$757$	−5.46726	+	6.69617i	−0.198711	+	0.243377i	0.665631	+	0.746281i	$0.268162\pi$
$758$	14.5491	+	10.9329i	0.528445	+	0.397101i
$759$	8.45928	+	4.43977i	0.307052	+	0.161154i
$760$	−14.2409	+	1.14965i	−0.516573	+	0.0417021i
$761$	22.6218	−	1.82622i	0.820041	−	0.0662005i	0.336677	−	0.941620i	$-0.390697\pi$
$761$	22.6218	−	1.82622i	0.820041	−	0.0662005i	0.483364	+	0.875420i	$0.339415\pi$
$762$	−10.6996	−	5.61558i	−0.387606	−	0.203431i
$763$	−5.04513	−	3.79117i	−0.182646	−	0.137250i
$764$	−16.0417	+	19.6476i	−0.580370	+	0.710824i
$765$	2.53031	+	4.38263i	0.0914836	+	0.158454i
$766$	−1.83139	+	4.82897i	−0.0661707	+	0.174478i
$767$	−1.08676	−	2.11431i	−0.0392408	−	0.0763434i
$768$	3.00916	+	7.93451i	0.108584	+	0.286312i
$769$	−29.4294	+	36.0445i

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.655764 + 0.0529387i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-1.54688 - 0.251392i) q^{4} +(-1.61643 - 1.43203i) q^{5} +(-0.525951 - 0.395227i) q^{6} +(1.45558 - 1.51542i) q^{7} +(-2.27864 - 0.561634i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-0.984187 - 1.02465i) q^{10} +(-2.14574 + 4.52204i) q^{11} +(1.17304 + 1.03923i) q^{12} +(0.547978 + 3.56367i) q^{13} +(1.03474 - 0.916700i) q^{14} +(0.600819 + 2.07427i) q^{15} +(1.50852 + 0.503619i) q^{16} +(-1.62333 + 1.69006i) q^{17} +(0.233294 + 0.615144i) q^{18} +(-1.40954 + 2.44140i) q^{19} +(2.14042 + 2.62154i) q^{20} +(-2.04018 + 0.502859i) q^{21} +(-1.64649 + 2.85180i) q^{22} +(0.954346 + 1.65298i) q^{23} +(1.62571 + 1.69254i) q^{24} +(-0.0405526 - 0.333981i) q^{25} +(0.170688 + 2.36593i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-2.63257 + 1.97824i) q^{28} +(-5.71698 - 0.461522i) q^{29} +(0.284186 + 1.39204i) q^{30} +(0.304449 - 2.50736i) q^{31} +(5.28065 + 2.24987i) q^{32} +(4.23043 - 2.67516i) q^{33} +(-1.15399 + 1.02234i) q^{34} +(-4.52297 + 0.365132i) q^{35} +(-0.436014 - 1.50530i) q^{36} +(-4.18034 + 1.78108i) q^{37} +(-1.05357 + 1.52636i) q^{38} +(1.44151 - 3.30485i) q^{39} +(2.87898 + 4.17092i) q^{40} +(-2.30738 - 1.45910i) q^{41} +(-1.36450 + 0.221752i) q^{42} +(-9.34268 - 3.98054i) q^{43} +(4.45600 - 6.45563i) q^{44} +(0.600819 - 2.07427i) q^{45} +(0.538319 + 1.13448i) q^{46} +(-3.00003 + 7.91042i) q^{47} +(-1.00582 - 1.23191i) q^{48} +(0.104079 + 2.58270i) q^{49} +(-0.00891242 - 0.221159i) q^{50} +(2.27530 - 0.560811i) q^{51} +(0.0482220 - 5.65031i) q^{52} +(-0.675275 - 0.166440i) q^{53} +(0.131596 - 0.644601i) q^{54} +(9.94415 - 4.23681i) q^{55} +(-4.16785 + 2.63559i) q^{56} +(2.49618 - 1.31009i) q^{57} +(-3.72455 - 0.605299i) q^{58} +(-0.625402 + 0.208790i) q^{59} +(-0.407939 - 3.35968i) q^{60} +(-0.421437 + 1.45497i) q^{61} +(0.332383 - 1.62812i) q^{62} +(1.99310 + 0.665395i) q^{63} +(0.527347 + 0.276773i) q^{64} +(4.21752 - 6.54514i) q^{65} +(2.91578 - 1.53032i) q^{66} +(13.9417 - 2.26574i) q^{67} +(2.93595 - 2.20622i) q^{68} +(0.0768553 - 1.90714i) q^{69} -2.98533 q^{70} +(0.0728044 - 1.80662i) q^{71} +(-0.469427 - 2.29940i) q^{72} +(4.28470 + 6.20747i) q^{73} +(-2.83560 + 0.946664i) q^{74} +(-0.144227 + 0.303951i) q^{75} +(2.79414 - 3.42220i) q^{76} +(3.72950 + 9.83388i) q^{77} +(1.12025 - 2.09089i) q^{78} +(3.77399 - 9.95118i) q^{79} +(-1.71722 - 2.97432i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-1.43585 - 1.07897i) q^{82} +(-14.5951 - 7.66010i) q^{83} +(3.28232 - 0.264976i) q^{84} +(5.04421 - 0.407211i) q^{85} +(-5.91586 - 3.10488i) q^{86} +(4.58526 + 3.44560i) q^{87} +(7.42909 - 9.09898i) q^{88} +(-3.92591 - 6.79987i) q^{89} +(0.503804 - 1.32842i) q^{90} +(6.19807 + 4.35678i) q^{91} +(-1.06071 - 2.79687i) q^{92} +(-1.59741 + 1.95648i) q^{93} +(-2.38608 + 5.02855i) q^{94} +(5.77459 - 1.92784i) q^{95} +(-3.26067 - 4.72390i) q^{96} +(-0.144348 - 0.707065i) q^{97} +(-0.0684735 + 1.69915i) q^{98} -5.00530 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

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