LMFDB - Embedded newform 930.2.e.a.929.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(929,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("930.929");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.e (of order $2$, degree $1$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			929.15
Character	$\chi$	$=$	930.929
Dual form			930.2.e.a.929.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.230519 - 1.71664i) q^{3} +1.00000 q^{4} +(-0.286520 - 2.21764i) q^{5} +(0.230519 + 1.71664i) q^{6} +4.09004i q^{7} -1.00000 q^{8} +(-2.89372 + 0.791438i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.230519 - 1.71664i) q^{3} +1.00000 q^{4} +(-0.286520 - 2.21764i) q^{5} +(0.230519 + 1.71664i) q^{6} +4.09004i q^{7} -1.00000 q^{8} +(-2.89372 + 0.791438i) q^{9} +(0.286520 + 2.21764i) q^{10} +2.91858 q^{11} +(-0.230519 - 1.71664i) q^{12} +2.84883 q^{13} -4.09004i q^{14} +(-3.74084 + 1.00306i) q^{15} +1.00000 q^{16} +3.40740i q^{17} +(2.89372 - 0.791438i) q^{18} +2.22746 q^{19} +(-0.286520 - 2.21764i) q^{20} +(7.02114 - 0.942833i) q^{21} -2.91858 q^{22} +3.74121i q^{23} +(0.230519 + 1.71664i) q^{24} +(-4.83581 + 1.27079i) q^{25} -2.84883 q^{26} +(2.02567 + 4.78504i) q^{27} +4.09004i q^{28} +5.67587 q^{29} +(3.74084 - 1.00306i) q^{30} +(4.53321 + 3.23264i) q^{31} -1.00000 q^{32} +(-0.672789 - 5.01016i) q^{33} -3.40740i q^{34} +(9.07022 - 1.17188i) q^{35} +(-2.89372 + 0.791438i) q^{36} -1.51417 q^{37} -2.22746 q^{38} +(-0.656709 - 4.89042i) q^{39} +(0.286520 + 2.21764i) q^{40} +0.438141i q^{41} +(-7.02114 + 0.942833i) q^{42} +8.29665 q^{43} +2.91858 q^{44} +(2.58423 + 6.19046i) q^{45} -3.74121i q^{46} -7.81439 q^{47} +(-0.230519 - 1.71664i) q^{48} -9.72844 q^{49} +(4.83581 - 1.27079i) q^{50} +(5.84929 - 0.785471i) q^{51} +2.84883 q^{52} -10.9500i q^{53} +(-2.02567 - 4.78504i) q^{54} +(-0.836232 - 6.47235i) q^{55} -4.09004i q^{56} +(-0.513473 - 3.82376i) q^{57} -5.67587 q^{58} +2.26138i q^{59} +(-3.74084 + 1.00306i) q^{60} +3.00611i q^{61} +(-4.53321 - 3.23264i) q^{62} +(-3.23701 - 11.8354i) q^{63} +1.00000 q^{64} +(-0.816246 - 6.31766i) q^{65} +(0.672789 + 5.01016i) q^{66} -9.68140i q^{67} +3.40740i q^{68} +(6.42233 - 0.862421i) q^{69} +(-9.07022 + 1.17188i) q^{70} -11.2189i q^{71} +(2.89372 - 0.791438i) q^{72} +2.62078 q^{73} +1.51417 q^{74} +(3.29625 + 8.00842i) q^{75} +2.22746 q^{76} +11.9371i q^{77} +(0.656709 + 4.89042i) q^{78} +15.1711i q^{79} +(-0.286520 - 2.21764i) q^{80} +(7.74725 - 4.58040i) q^{81} -0.438141i q^{82} -8.73047i q^{83} +(7.02114 - 0.942833i) q^{84} +(7.55637 - 0.976288i) q^{85} -8.29665 q^{86} +(-1.30840 - 9.74344i) q^{87} -2.91858 q^{88} +13.2216 q^{89} +(-2.58423 - 6.19046i) q^{90} +11.6518i q^{91} +3.74121i q^{92} +(4.50430 - 8.52709i) q^{93} +7.81439 q^{94} +(-0.638213 - 4.93970i) q^{95} +(0.230519 + 1.71664i) q^{96} -3.32455i q^{97} +9.72844 q^{98} +(-8.44557 + 2.30988i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 + 32 * q^4 + 2 * q^5 - 32 * q^8 + 4 * q^9	$ 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9} - 2 q^{10} + 32 q^{16} - 4 q^{18} + 8 q^{19} + 2 q^{20} + 10 q^{25} - 12 q^{31} - 32 q^{32} - 8 q^{33} + 16 q^{35} + 4 q^{36} - 8 q^{38} - 4 q^{39} - 2 q^{40} + 10 q^{45} - 4 q^{47} - 36 q^{49} - 10 q^{50} - 4 q^{51} + 12 q^{62} - 24 q^{63} + 32 q^{64} + 8 q^{66} - 8 q^{69} - 16 q^{70} - 4 q^{72} + 8 q^{76} + 4 q^{78} + 2 q^{80} + 24 q^{81} - 4 q^{87} - 10 q^{90} + 24 q^{93} + 4 q^{94} - 26 q^{95} + 36 q^{98}+O(q^{100}) $ 32 * q - 32 * q^2 + 32 * q^4 + 2 * q^5 - 32 * q^8 + 4 * q^9 - 2 * q^10 + 32 * q^16 - 4 * q^18 + 8 * q^19 + 2 * q^20 + 10 * q^25 - 12 * q^31 - 32 * q^32 - 8 * q^33 + 16 * q^35 + 4 * q^36 - 8 * q^38 - 4 * q^39 - 2 * q^40 + 10 * q^45 - 4 * q^47 - 36 * q^49 - 10 * q^50 - 4 * q^51 + 12 * q^62 - 24 * q^63 + 32 * q^64 + 8 * q^66 - 8 * q^69 - 16 * q^70 - 4 * q^72 + 8 * q^76 + 4 * q^78 + 2 * q^80 + 24 * q^81 - 4 * q^87 - 10 * q^90 + 24 * q^93 + 4 * q^94 - 26 * q^95 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.230519	−	1.71664i	−0.133090	−	0.991104i
$3$	−0.230519	−	1.71664i	−0.133090	−	0.991104i
$4$	1.00000			0.500000
$5$	−0.286520	−	2.21764i	−0.128136	−	0.991757i
$5$	−0.286520	−	2.21764i	−0.128136	−	0.991757i
$6$	0.230519	+	1.71664i	0.0941090	+	0.700816i
$7$			4.09004i			1.54589i	0.634473	+	0.772945i	$0.281217\pi$
$7$			4.09004i			1.54589i	−0.634473	+	0.772945i	$0.718783\pi$
$8$	−1.00000			−0.353553
$9$	−2.89372	+	0.791438i	−0.964574	+	0.263813i
$10$	0.286520	+	2.21764i	0.0906056	+	0.701278i
$11$	2.91858			0.879986			0.439993	−	0.898001i	$-0.354981\pi$
$11$	2.91858			0.879986			0.439993	+	0.898001i	$0.354981\pi$
$12$	−0.230519	−	1.71664i	−0.0665451	−	0.495552i
$13$	2.84883			0.790123			0.395061	−	0.918655i	$-0.370723\pi$
$13$	2.84883			0.790123			0.395061	+	0.918655i	$0.370723\pi$
$14$		−	4.09004i		−	1.09311i
$15$	−3.74084	+	1.00306i	−0.965880	+	0.258989i
$16$	1.00000			0.250000
$17$			3.40740i			0.826416i	0.910637	+	0.413208i	$0.135592\pi$
$17$			3.40740i			0.826416i	−0.910637	+	0.413208i	$0.864408\pi$
$18$	2.89372	−	0.791438i	0.682057	−	0.186544i
$19$	2.22746			0.511015			0.255508	−	0.966807i	$-0.417757\pi$
$19$	2.22746			0.511015			0.255508	+	0.966807i	$0.417757\pi$
$20$	−0.286520	−	2.21764i	−0.0640678	−	0.495878i
$21$	7.02114	−	0.942833i	1.53214	−	0.205743i
$22$	−2.91858			−0.622244
$23$			3.74121i			0.780097i	0.920794	+	0.390049i	$0.127542\pi$
$23$			3.74121i			0.780097i	−0.920794	+	0.390049i	$0.872458\pi$
$24$	0.230519	+	1.71664i	0.0470545	+	0.350408i
$25$	−4.83581	+	1.27079i	−0.967163	+	0.254159i
$26$	−2.84883			−0.558701
$27$	2.02567	+	4.78504i	0.389841	+	0.920882i
$28$			4.09004i			0.772945i
$29$	5.67587			1.05398			0.526991	−	0.849871i	$-0.323320\pi$
$29$	5.67587			1.05398			0.526991	+	0.849871i	$0.323320\pi$
$30$	3.74084	−	1.00306i	0.682981	−	0.183133i
$31$	4.53321	+	3.23264i	0.814189	+	0.580600i
$31$	4.53321	+	3.23264i	0.814189	+	0.580600i
$32$	−1.00000			−0.176777
$33$	−0.672789	−	5.01016i	−0.117118	−	0.872157i
$34$		−	3.40740i		−	0.584364i
$35$	9.07022	−	1.17188i	1.53315	−	0.198084i
$36$	−2.89372	+	0.791438i	−0.482287	+	0.131906i
$37$	−1.51417			−0.248928			−0.124464	−	0.992224i	$-0.539721\pi$
$37$	−1.51417			−0.248928			−0.124464	+	0.992224i	$0.539721\pi$
$38$	−2.22746			−0.361342
$39$	−0.656709	−	4.89042i	−0.105158	−	0.783094i
$40$	0.286520	+	2.21764i	0.0453028	+	0.350639i
$41$			0.438141i			0.0684261i	0.999415	+	0.0342131i	$0.0108925\pi$
$41$			0.438141i			0.0684261i	−0.999415	+	0.0342131i	$0.989108\pi$
$42$	−7.02114	+	0.942833i	−1.08339	+	0.145482i
$43$	8.29665			1.26523			0.632614	−	0.774468i	$-0.281982\pi$
$43$	8.29665			1.26523			0.632614	+	0.774468i	$0.281982\pi$
$44$	2.91858			0.439993
$45$	2.58423	+	6.19046i	0.385234	+	0.922819i
$46$		−	3.74121i		−	0.551612i
$47$	−7.81439			−1.13985			−0.569923	−	0.821698i	$-0.693027\pi$
$47$	−7.81439			−1.13985			−0.569923	+	0.821698i	$0.693027\pi$
$48$	−0.230519	−	1.71664i	−0.0332726	−	0.247776i
$49$	−9.72844			−1.38978
$50$	4.83581	−	1.27079i	0.683887	−	0.179717i
$51$	5.84929	−	0.785471i	0.819064	−	0.109988i
$52$	2.84883			0.395061
$53$		−	10.9500i		−	1.50409i	−0.659111	−	0.752046i	$-0.729067\pi$
$53$		−	10.9500i		−	1.50409i	0.659111	−	0.752046i	$-0.270933\pi$
$54$	−2.02567	−	4.78504i	−0.275659	−	0.651162i
$55$	−0.836232	−	6.47235i	−0.112758	−	0.872732i
$56$		−	4.09004i		−	0.546555i
$57$	−0.513473	−	3.82376i	−0.0680111	−	0.506469i
$58$	−5.67587			−0.745279
$59$			2.26138i			0.294406i	0.989106	+	0.147203i	$0.0470271\pi$
$59$			2.26138i			0.294406i	−0.989106	+	0.147203i	$0.952973\pi$
$60$	−3.74084	+	1.00306i	−0.482940	+	0.129494i
$61$			3.00611i			0.384893i	0.981307	+	0.192447i	$0.0616422\pi$
$61$			3.00611i			0.384893i	−0.981307	+	0.192447i	$0.938358\pi$
$62$	−4.53321	−	3.23264i	−0.575719	−	0.410546i
$63$	−3.23701	−	11.8354i	−0.407825	−	1.49113i
$64$	1.00000			0.125000
$65$	−0.816246	−	6.31766i	−0.101243	−	0.783609i
$66$	0.672789	+	5.01016i	0.0828146	+	0.616708i
$67$		−	9.68140i		−	1.18277i	−0.806389	−	0.591385i	$-0.798581\pi$
$67$		−	9.68140i		−	1.18277i	0.806389	−	0.591385i	$-0.201419\pi$
$68$			3.40740i			0.413208i
$69$	6.42233	−	0.862421i	0.773157	−	0.103823i
$70$	−9.07022	+	1.17188i	−1.08410	+	0.140066i
$71$		−	11.2189i		−	1.33144i	−0.746200	−	0.665722i	$-0.768124\pi$
$71$		−	11.2189i		−	1.33144i	0.746200	−	0.665722i	$-0.231876\pi$
$72$	2.89372	−	0.791438i	0.341028	−	0.0932718i
$73$	2.62078			0.306739			0.153369	−	0.988169i	$-0.450988\pi$
$73$	2.62078			0.306739			0.153369	+	0.988169i	$0.450988\pi$
$74$	1.51417			0.176019
$75$	3.29625	+	8.00842i	0.380618	+	0.924732i
$76$	2.22746			0.255508
$77$			11.9371i			1.36036i
$78$	0.656709	+	4.89042i	0.0743577	+	0.553731i
$79$			15.1711i			1.70688i	0.521191	+	0.853440i	$0.325488\pi$
$79$			15.1711i			1.70688i	−0.521191	+	0.853440i	$0.674512\pi$
$80$	−0.286520	−	2.21764i	−0.0320339	−	0.247939i
$81$	7.74725	−	4.58040i	0.860806	−	0.508933i
$82$		−	0.438141i		−	0.0483846i
$83$		−	8.73047i		−	0.958294i	−0.877735	−	0.479147i	$-0.840946\pi$
$83$		−	8.73047i		−	0.958294i	0.877735	−	0.479147i	$-0.159054\pi$
$84$	7.02114	−	0.942833i	0.766069	−	0.102871i
$85$	7.55637	−	0.976288i	0.819603	−	0.105893i
$86$	−8.29665			−0.894651
$87$	−1.30840	−	9.74344i	−0.140275	−	1.04461i
$88$	−2.91858			−0.311122
$89$	13.2216			1.40149			0.700746	−	0.713411i	$-0.252851\pi$
$89$	13.2216			1.40149			0.700746	+	0.713411i	$0.252851\pi$
$90$	−2.58423	−	6.19046i	−0.272402	−	0.652531i
$91$			11.6518i			1.22144i
$92$			3.74121i			0.390049i
$93$	4.50430	−	8.52709i	0.467074	−	0.884218i
$94$	7.81439			0.805993
$95$	−0.638213	−	4.93970i	−0.0654793	−	0.506803i
$96$	0.230519	+	1.71664i	0.0235273	+	0.175204i
$97$		−	3.32455i		−	0.337557i	−0.985654	−	0.168778i	$-0.946018\pi$
$97$		−	3.32455i		−	0.337557i	0.985654	−	0.168778i	$-0.0539822\pi$
$98$	9.72844			0.982721
$99$	−8.44557	+	2.30988i	−0.848811	+	0.232151i
$100$	−4.83581	+	1.27079i	−0.483581	+	0.127079i
$101$			0.426790i			0.0424671i	0.999775	+	0.0212336i	$0.00675936\pi$
$101$			0.426790i			0.0424671i	−0.999775	+	0.0212336i	$0.993241\pi$
$102$	−5.84929	+	0.785471i	−0.579166	+	0.0777732i
$103$			11.7899i			1.16169i	0.814013	+	0.580846i	$0.197278\pi$
$103$			11.7899i			1.16169i	−0.814013	+	0.580846i	$0.802722\pi$
$104$	−2.84883			−0.279351
$105$	−4.10256	−	15.3002i	−0.400368	−	1.49315i
$106$			10.9500i			1.06355i
$107$	16.4991			1.59503			0.797513	−	0.603302i	$-0.206149\pi$
$107$	16.4991			1.59503			0.797513	+	0.603302i	$0.206149\pi$
$108$	2.02567	+	4.78504i	0.194921	+	0.460441i
$109$	4.44187			0.425454			0.212727	−	0.977112i	$-0.431766\pi$
$109$	4.44187			0.425454			0.212727	+	0.977112i	$0.431766\pi$
$110$	0.836232	+	6.47235i	0.0797316	+	0.617115i
$111$	0.349045	+	2.59929i	0.0331299	+	0.246713i
$112$			4.09004i			0.386473i
$113$	−15.2316			−1.43287			−0.716434	−	0.697654i	$-0.754227\pi$
$113$	−15.2316			−1.43287			−0.716434	+	0.697654i	$0.754227\pi$
$114$	0.513473	+	3.82376i	0.0480911	+	0.358128i
$115$	8.29665	−	1.07193i	0.773667	−	0.0999583i
$116$	5.67587			0.526991
$117$	−8.24371	+	2.25467i	−0.762132	+	0.208444i
$118$		−	2.26138i		−	0.208176i
$119$	−13.9364			−1.27755
$120$	3.74084	−	1.00306i	0.341490	−	0.0915664i
$121$	−2.48188			−0.225625
$122$		−	3.00611i		−	0.272161i
$123$	0.752131	−	0.101000i	0.0678174	−	0.00910685i
$124$	4.53321	+	3.23264i	0.407095	+	0.290300i
$125$	4.20371	+	10.3600i	0.375992	+	0.926623i
$126$	3.23701	+	11.8354i	0.288376	+	1.05439i
$127$	21.0528			1.86814			0.934069	−	0.357094i	$-0.116232\pi$
$127$	21.0528			1.86814			0.934069	+	0.357094i	$0.116232\pi$
$128$	−1.00000			−0.0883883
$129$	−1.91254	−	14.2424i	−0.168389	−	1.25397i
$130$	0.816246	+	6.31766i	0.0715895	+	0.554095i
$131$			6.73650i			0.588571i	0.955718	+	0.294285i	$0.0950816\pi$
$131$			6.73650i			0.588571i	−0.955718	+	0.294285i	$0.904918\pi$
$132$	−0.672789	−	5.01016i	−0.0585588	−	0.436079i
$133$			9.11042i			0.789974i
$134$			9.68140i			0.836345i
$135$	10.0311	−	5.86322i	0.863338	−	0.504625i
$136$		−	3.40740i		−	0.292182i
$137$			18.8237i			1.60821i	0.594485	+	0.804107i	$0.297356\pi$
$137$			18.8237i			1.60821i	−0.594485	+	0.804107i	$0.702644\pi$
$138$	−6.42233	+	0.862421i	−0.546705	+	0.0734142i
$139$		−	20.8428i		−	1.76787i	−0.467613	−	0.883933i	$-0.654886\pi$
$139$		−	20.8428i		−	1.76787i	0.467613	−	0.883933i	$-0.345114\pi$
$140$	9.07022	−	1.17188i	0.766574	−	0.0990418i
$141$	1.80137	+	13.4145i	0.151702	+	1.12971i
$142$			11.2189i			0.941473i
$143$	8.31454			0.695297
$144$	−2.89372	+	0.791438i	−0.241143	+	0.0659531i
$145$	−1.62625	−	12.5870i	−0.135053	−	1.04529i
$146$	−2.62078			−0.216897
$147$	2.24259	+	16.7002i	0.184966	+	1.37741i
$148$	−1.51417			−0.124464
$149$			15.1166i			1.23840i	0.785232	+	0.619201i	$0.212544\pi$
$149$			15.1166i			1.23840i	−0.785232	+	0.619201i	$0.787456\pi$
$150$	−3.29625	−	8.00842i	−0.269137	−	0.653885i
$151$		−	2.58653i		−	0.210488i	−0.994446	−	0.105244i	$-0.966438\pi$
$151$		−	2.58653i		−	0.210488i	0.994446	−	0.105244i	$-0.0335624\pi$
$152$	−2.22746			−0.180671
$153$	−2.69674	−	9.86007i	−0.218019	−	0.797139i
$154$		−	11.9371i		−	0.961921i
$155$	5.86997	−	10.9792i	0.471487	−	0.881873i
$156$	−0.656709	−	4.89042i	−0.0525788	−	0.391547i
$157$			1.88558i			0.150485i	0.997165	+	0.0752427i	$0.0239731\pi$
$157$			1.88558i			0.150485i	−0.997165	+	0.0752427i	$0.976027\pi$
$158$		−	15.1711i		−	1.20695i
$159$	−18.7971	+	2.52417i	−1.49071	+	0.200180i
$160$	0.286520	+	2.21764i	0.0226514	+	0.175319i
$161$	−15.3017			−1.20594
$162$	−7.74725	+	4.58040i	−0.608682	+	0.359870i
$163$		−	6.96572i		−	0.545597i	−0.962071	−	0.272799i	$-0.912051\pi$
$163$		−	6.96572i		−	0.545597i	0.962071	−	0.272799i	$-0.0879493\pi$
$164$			0.438141i			0.0342131i
$165$	−10.9179	+	2.92751i	−0.849961	+	0.227907i
$166$			8.73047i			0.677616i
$167$		−	9.29213i		−	0.719047i	−0.933136	−	0.359523i	$-0.882939\pi$
$167$		−	9.29213i		−	0.719047i	0.933136	−	0.359523i	$-0.117061\pi$
$168$	−7.02114	+	0.942833i	−0.541693	+	0.0727411i
$169$	−4.88418			−0.375706
$170$	−7.55637	+	0.976288i	−0.579547	+	0.0748779i
$171$	−6.44566	+	1.76290i	−0.492912	+	0.134812i
$172$	8.29665			0.632614
$173$	−16.6921			−1.26908			−0.634539	−	0.772891i	$-0.718810\pi$
$173$	−16.6921			−1.26908			−0.634539	+	0.772891i	$0.718810\pi$
$174$	1.30840	+	9.74344i	0.0991893	+	0.738648i
$175$	−5.19760	−	19.7787i	−0.392902	−	1.49513i
$176$	2.91858			0.219996
$177$	3.88197	−	0.521290i	0.291787	−	0.0391826i
$178$	−13.2216			−0.991004
$179$	−23.2724			−1.73946			−0.869730	−	0.493527i	$-0.835707\pi$
$179$	−23.2724			−1.73946			−0.869730	+	0.493527i	$0.835707\pi$
$180$	2.58423	+	6.19046i	0.192617	+	0.461409i
$181$			8.84237i			0.657248i	0.944461	+	0.328624i	$0.106585\pi$
$181$			8.84237i			0.657248i	−0.944461	+	0.328624i	$0.893415\pi$
$182$		−	11.6518i		−	0.863691i
$183$	5.16042	−	0.692966i	0.381469	−	0.0512255i
$184$		−	3.74121i		−	0.275806i
$185$	0.433840	+	3.35788i	0.0318965	+	0.246876i
$186$	−4.50430	+	8.52709i	−0.330271	+	0.625237i
$187$			9.94478i			0.727234i
$188$	−7.81439			−0.569923
$189$	−19.5710	+	8.28509i	−1.42358	+	0.602652i
$190$	0.638213	+	4.93970i	0.0463008	+	0.358364i
$191$			15.0585i			1.08960i	0.838567	+	0.544799i	$0.183394\pi$
$191$			15.0585i			1.08960i	−0.838567	+	0.544799i	$0.816606\pi$
$192$	−0.230519	−	1.71664i	−0.0166363	−	0.123888i
$193$			13.9665i			1.00533i	0.864481	+	0.502665i	$0.167647\pi$
$193$			13.9665i			1.00533i	−0.864481	+	0.502665i	$0.832353\pi$
$194$			3.32455i			0.238689i
$195$	−10.6570	+	2.85754i	−0.763164	+	0.204633i
$196$	−9.72844			−0.694888
$197$		−	5.51824i		−	0.393159i	−0.980488	−	0.196579i	$-0.937017\pi$
$197$		−	5.51824i		−	0.393159i	0.980488	−	0.196579i	$-0.0629833\pi$
$198$	8.44557	−	2.30988i	0.600200	−	0.164156i
$199$		−	18.3955i		−	1.30402i	−0.758209	−	0.652012i	$-0.773925\pi$
$199$		−	18.3955i		−	1.30402i	0.758209	−	0.652012i	$-0.226075\pi$
$200$	4.83581	−	1.27079i	0.341944	−	0.0898587i
$201$	−16.6195	+	2.23175i	−1.17225	+	0.157415i
$202$		−	0.426790i		−	0.0300288i
$203$			23.2146i			1.62934i
$204$	5.84929	−	0.785471i	0.409532	−	0.0549940i
$205$	0.971637	−	0.125536i	0.0678621	−	0.00876783i
$206$		−	11.7899i		−	0.821441i
$207$	−2.96094	−	10.8260i	−0.205799	−	0.752461i
$208$	2.84883			0.197531
$209$	6.50104			0.449686
$210$	4.10256	+	15.3002i	0.283103	+	1.05581i
$211$	24.3355			1.67532			0.837662	−	0.546189i	$-0.183922\pi$
$211$	24.3355			1.67532			0.837662	+	0.546189i	$0.183922\pi$
$212$		−	10.9500i		−	0.752046i
$213$	−19.2589	+	2.58618i	−1.31960	+	0.177202i
$214$	−16.4991			−1.12785
$215$	−2.37716	−	18.3989i	−0.162121	−	1.25480i
$216$	−2.02567	−	4.78504i	−0.137830	−	0.325581i
$217$	−13.2216	+	18.5410i	−0.897544	+	1.25865i
$218$	−4.44187			−0.300841
$219$	−0.604139	−	4.49894i	−0.0408239	−	0.304010i
$220$	−0.836232	−	6.47235i	−0.0563788	−	0.436366i
$221$			9.70710i			0.652970i
$222$	−0.349045	−	2.59929i	−0.0234264	−	0.174453i
$223$	13.5432			0.906920			0.453460	−	0.891277i	$-0.350189\pi$
$223$	13.5432			0.906920			0.453460	+	0.891277i	$0.350189\pi$
$224$		−	4.09004i		−	0.273277i
$225$	12.9877	−	7.50457i	0.865850	−	0.500305i
$226$	15.2316			1.01319
$227$	−4.08250			−0.270965			−0.135483	−	0.990780i	$-0.543259\pi$
$227$	−4.08250			−0.270965			−0.135483	+	0.990780i	$0.543259\pi$
$228$	−0.513473	−	3.82376i	−0.0340056	−	0.253235i
$229$		−	7.25882i		−	0.479676i	−0.970813	−	0.239838i	$-0.922906\pi$
$229$		−	7.25882i		−	0.479676i	0.970813	−	0.239838i	$-0.0770944\pi$
$230$	−8.29665	+	1.07193i	−0.547065	+	0.0706812i
$231$	20.4918	−	2.75173i	1.34826	−	0.181051i
$232$	−5.67587			−0.372639
$233$	−4.27441			−0.280026			−0.140013	−	0.990150i	$-0.544714\pi$
$233$	−4.27441			−0.280026			−0.140013	+	0.990150i	$0.544714\pi$
$234$	8.24371	−	2.25467i	0.538908	−	0.147392i
$235$	2.23898	+	17.3295i	0.146055	+	1.13045i
$236$			2.26138i			0.147203i
$237$	26.0433	−	3.49722i	1.69170	−	0.227169i
$238$	13.9364			0.903363
$239$	17.2289			1.11444			0.557222	−	0.830364i	$-0.311867\pi$
$239$	17.2289			1.11444			0.557222	+	0.830364i	$0.311867\pi$
$240$	−3.74084	+	1.00306i	−0.241470	+	0.0647472i
$241$			12.1407i			0.782050i	0.920380	+	0.391025i	$0.127879\pi$
$241$			12.1407i			0.782050i	−0.920380	+	0.391025i	$0.872121\pi$
$242$	2.48188			0.159541
$243$	−9.64880	−	12.2434i	−0.618971	−	0.785414i
$244$			3.00611i			0.192447i
$245$	2.78739	+	21.5741i	0.178080	+	1.37832i
$246$	−0.752131	+	0.101000i	−0.0479541	+	0.00643952i
$247$	6.34566			0.403765
$248$	−4.53321	−	3.23264i	−0.287859	−	0.205273i
$249$	−14.9871	+	2.01254i	−0.949769	+	0.127540i
$250$	−4.20371	−	10.3600i	−0.265866	−	0.655221i
$251$	−8.17847			−0.516220			−0.258110	−	0.966116i	$-0.583100\pi$
$251$	−8.17847			−0.516220			−0.258110	+	0.966116i	$0.583100\pi$
$252$	−3.23701	−	11.8354i	−0.203913	−	0.745563i
$253$			10.9190i			0.686474i
$254$	−21.0528			−1.32097
$255$	−3.41783	−	12.7465i	−0.214033	−	0.798219i
$256$	1.00000			0.0625000
$257$	−1.43812			−0.0897076			−0.0448538	−	0.998994i	$-0.514282\pi$
$257$	−1.43812			−0.0897076			−0.0448538	+	0.998994i	$0.514282\pi$
$258$	1.91254	+	14.2424i	0.119069	+	0.886692i
$259$		−	6.19302i		−	0.384815i
$260$	−0.816246	−	6.31766i	−0.0506214	−	0.391805i
$261$	−16.4244	+	4.49210i	−1.01664	+	0.278054i
$262$		−	6.73650i		−	0.416182i
$263$			4.53066i			0.279372i	0.990196	+	0.139686i	$0.0446093\pi$
$263$			4.53066i			0.279372i	−0.990196	+	0.139686i	$0.955391\pi$
$264$	0.672789	+	5.01016i	0.0414073	+	0.308354i
$265$	−24.2830	+	3.13738i	−1.49169	+	0.192728i
$266$		−	9.11042i		−	0.558596i
$267$	−3.04784	−	22.6968i	−0.186525	−	1.38902i
$268$		−	9.68140i		−	0.591385i
$269$	15.0129			0.915350			0.457675	−	0.889120i	$-0.348682\pi$
$269$	15.0129			0.915350			0.457675	+	0.889120i	$0.348682\pi$
$270$	−10.0311	+	5.86322i	−0.610472	+	0.356824i
$271$			18.1048i			1.09979i	0.835234	+	0.549895i	$0.185332\pi$
$271$			18.1048i			1.09979i	−0.835234	+	0.549895i	$0.814668\pi$
$272$			3.40740i			0.206604i
$273$	20.0020	−	2.68597i	1.21058	−	0.162562i
$274$		−	18.8237i		−	1.13718i
$275$	−14.1137	+	3.70892i	−0.851089	+	0.223656i
$276$	6.42233	−	0.862421i	0.386579	−	0.0519117i
$277$	−20.2172			−1.21474			−0.607368	−	0.794421i	$-0.707774\pi$
$277$	−20.2172			−1.21474			−0.607368	+	0.794421i	$0.707774\pi$
$278$			20.8428i			1.25007i
$279$	−15.6763	−	5.76662i	−0.938515	−	0.345238i
$280$	−9.07022	+	1.17188i	−0.542049	+	0.0700332i
$281$			31.7271i			1.89268i	0.323172	+	0.946340i	$0.395251\pi$
$281$			31.7271i			1.89268i	−0.323172	+	0.946340i	$0.604749\pi$
$282$	−1.80137	−	13.4145i	−0.107270	−	0.798823i
$283$		−	27.7595i		−	1.65013i	−0.565036	−	0.825066i	$-0.691138\pi$
$283$		−	27.7595i		−	1.65013i	0.565036	−	0.825066i	$-0.308862\pi$
$284$		−	11.2189i		−	0.665722i
$285$	−8.33258	+	2.23428i	−0.493580	+	0.132347i
$286$	−8.31454			−0.491649
$287$	−1.79201			−0.105779
$288$	2.89372	−	0.791438i	0.170514	−	0.0466359i
$289$	5.38962			0.317037
$290$	1.62625	+	12.5870i	0.0954968	+	0.739135i
$291$	−5.70706	+	0.766372i	−0.334554	+	0.0449255i
$292$	2.62078			0.153369
$293$	−19.6074			−1.14548			−0.572739	−	0.819738i	$-0.694119\pi$
$293$	−19.6074			−1.14548			−0.572739	+	0.819738i	$0.694119\pi$
$294$	−2.24259	−	16.7002i	−0.130791	−	0.973978i
$295$	5.01491	−	0.647929i	0.291979	−	0.0377239i
$296$	1.51417			0.0880093
$297$	5.91210	+	13.9655i	0.343055	+	0.810363i
$298$		−	15.1166i		−	0.875683i
$299$			10.6581i			0.616372i
$300$	3.29625	+	8.00842i	0.190309	+	0.462366i
$301$			33.9336i			1.95590i
$302$			2.58653i			0.148838i
$303$	0.732645	−	0.0983831i	0.0420894	−	0.00565196i
$304$	2.22746			0.127754
$305$	6.66646	−	0.861311i	0.381720	−	0.0493185i
$306$	2.69674	+	9.86007i	0.154163	+	0.563663i
$307$			9.74769i			0.556330i	0.960533	+	0.278165i	$0.0897262\pi$
$307$			9.74769i			0.556330i	−0.960533	+	0.278165i	$0.910274\pi$
$308$			11.9371i			0.680181i
$309$	20.2390	−	2.71780i	1.15136	−	0.154610i
$310$	−5.86997	+	10.9792i	−0.333392	+	0.623578i
$311$		−	6.19303i		−	0.351175i	−0.984464	−	0.175587i	$-0.943818\pi$
$311$		−	6.19303i		−	0.351175i	0.984464	−	0.175587i	$-0.0561824\pi$
$312$	0.656709	+	4.89042i	0.0371788	+	0.276865i
$313$	−21.4203			−1.21074			−0.605372	−	0.795943i	$-0.706976\pi$
$313$	−21.4203			−1.21074			−0.605372	+	0.795943i	$0.706976\pi$
$314$		−	1.88558i		−	0.106409i
$315$	−25.3192	+	10.5696i	−1.42658	+	0.595530i
$316$			15.1711i			0.853440i
$317$	20.7870			1.16751			0.583757	−	0.811928i	$-0.301582\pi$
$317$	20.7870			1.16751			0.583757	+	0.811928i	$0.301582\pi$
$318$	18.7971	−	2.52417i	1.05409	−	0.141549i
$319$	16.5655			0.927490
$320$	−0.286520	−	2.21764i	−0.0160170	−	0.123970i
$321$	−3.80335	−	28.3230i	−0.212282	−	1.58084i
$322$	15.3017			0.852732
$323$			7.58986i			0.422311i
$324$	7.74725	−	4.58040i	0.430403	−	0.254467i
$325$	−13.7764	+	3.62027i	−0.764177	+	0.200817i
$326$			6.96572i			0.385796i
$327$	−1.02393	−	7.62509i	−0.0566237	−	0.421669i
$328$		−	0.438141i		−	0.0241923i
$329$		−	31.9612i		−	1.76208i
$330$	10.9179	−	2.92751i	0.601013	−	0.161154i
$331$		−	24.7544i		−	1.36063i	−0.732921	−	0.680314i	$-0.761844\pi$
$331$		−	24.7544i		−	1.36063i	0.732921	−	0.680314i	$-0.238156\pi$
$332$		−	8.73047i		−	0.479147i
$333$	4.38159	−	1.19837i	0.240109	−	0.0656703i
$334$			9.29213i			0.508443i
$335$	−21.4698	+	2.77391i	−1.17302	+	0.151555i
$336$	7.02114	−	0.942833i	0.383034	−	0.0514357i
$337$	−11.4622			−0.624385			−0.312192	−	0.950019i	$-0.601063\pi$
$337$	−11.4622			−0.624385			−0.312192	+	0.950019i	$0.601063\pi$
$338$	4.88418			0.265664
$339$	3.51118	+	26.1472i	0.190701	+	1.42012i
$340$	7.55637	−	0.976288i	0.409802	−	0.0529467i
$341$	13.2306	+	9.43474i	0.716475	+	0.510920i
$342$	6.44566	−	1.76290i	0.348541	−	0.0953266i
$343$		−	11.1594i		−	0.602552i
$344$	−8.29665			−0.447325
$345$	−3.75266	−	13.9953i	−0.202037	−	0.753480i
$346$	16.6921			0.897373
$347$		−	11.5962i		−	0.622515i	−0.950326	−	0.311257i	$-0.899250\pi$
$347$		−	11.5962i		−	0.622515i	0.950326	−	0.311257i	$-0.100750\pi$
$348$	−1.30840	−	9.74344i	−0.0701374	−	0.522303i
$349$	−7.63161			−0.408511			−0.204255	−	0.978918i	$-0.565477\pi$
$349$	−7.63161			−0.408511			−0.204255	+	0.978918i	$0.565477\pi$
$350$	5.19760	+	19.7787i	0.277823	+	1.05721i
$351$	5.77079	+	13.6318i	0.308022	+	0.727610i
$352$	−2.91858			−0.155561
$353$		−	1.21958i		−	0.0649118i	−0.999473	−	0.0324559i	$-0.989667\pi$
$353$		−	1.21958i		−	0.0649118i	0.999473	−	0.0324559i	$-0.0103329\pi$
$354$	−3.88197	+	0.521290i	−0.206325	+	0.0277063i
$355$	−24.8795	+	3.21445i	−1.32047	+	0.170605i
$356$	13.2216			0.700746
$357$	3.21261	+	23.9238i	0.170029	+	1.26618i
$358$	23.2724			1.22998
$359$			18.5454i			0.978789i	0.872062	+	0.489395i	$0.162782\pi$
$359$			18.5454i			0.978789i	−0.872062	+	0.489395i	$0.837218\pi$
$360$	−2.58423	−	6.19046i	−0.136201	−	0.326266i
$361$	−14.0384			−0.738863
$362$		−	8.84237i		−	0.464745i
$363$	0.572120	+	4.26049i	0.0300285	+	0.223618i
$364$			11.6518i			0.610721i
$365$	−0.750905	−	5.81193i	−0.0393042	−	0.304210i
$366$	−5.16042	+	0.692966i	−0.269739	+	0.0362219i
$367$	1.68634			0.0880263			0.0440131	−	0.999031i	$-0.485986\pi$
$367$	1.68634			0.0880263			0.0440131	+	0.999031i	$0.485986\pi$
$368$			3.74121i			0.195024i
$369$	−0.346761	−	1.26786i	−0.0180517	−	0.0660021i
$370$	−0.433840	−	3.35788i	−0.0225543	−	0.174568i
$371$	44.7858			2.32516
$372$	4.50430	−	8.52709i	0.233537	−	0.442109i
$373$		−	0.208485i		−	0.0107950i	−0.999985	−	0.00539748i	$-0.998282\pi$
$373$		−	0.208485i		−	0.0107950i	0.999985	−	0.00539748i	$-0.00171808\pi$
$374$		−	9.94478i		−	0.514232i
$375$	16.8153	−	9.60444i	0.868339	−	0.495971i
$376$	7.81439			0.402997
$377$	16.1696			0.832776
$378$	19.5710	−	8.28509i	1.00663	−	0.426139i
$379$	−26.6546			−1.36915			−0.684577	−	0.728940i	$-0.740013\pi$
$379$	−26.6546			−1.36915			−0.684577	+	0.728940i	$0.740013\pi$
$380$	−0.638213	−	4.93970i	−0.0327396	−	0.253401i
$381$	−4.85308	−	36.1402i	−0.248631	−	1.85152i
$382$		−	15.0585i		−	0.770462i
$383$			1.48850i			0.0760590i	0.999277	+	0.0380295i	$0.0121081\pi$
$383$			1.48850i			0.0760590i	−0.999277	+	0.0380295i	$0.987892\pi$
$384$	0.230519	+	1.71664i	0.0117636	+	0.0876020i
$385$	26.4722	−	3.42023i	1.34915	−	0.174311i
$386$		−	13.9665i		−	0.710876i
$387$	−24.0082	+	6.56628i	−1.22041	+	0.333783i
$388$		−	3.32455i		−	0.168778i
$389$	15.3464			0.778091			0.389046	−	0.921218i	$-0.372805\pi$
$389$	15.3464			0.778091			0.389046	+	0.921218i	$0.372805\pi$
$390$	10.6570	−	2.85754i	0.539638	−	0.144697i
$391$	−12.7478			−0.644685
$392$	9.72844			0.491360
$393$	11.5642	−	1.55289i	0.583335	−	0.0783330i
$394$			5.51824i			0.278005i
$395$	33.6439	−	4.34682i	1.69281	−	0.218712i
$396$	−8.44557	+	2.30988i	−0.424406	+	0.116076i
$397$		−	18.8139i		−	0.944245i	−0.881533	−	0.472122i	$-0.843488\pi$
$397$		−	18.8139i		−	0.944245i	0.881533	−	0.472122i	$-0.156512\pi$
$398$			18.3955i			0.922084i
$399$	15.6393	−	2.10013i	0.782946	−	0.105138i
$400$	−4.83581	+	1.27079i	−0.241791	+	0.0635397i
$401$	−24.5289			−1.22491			−0.612457	−	0.790504i	$-0.709819\pi$
$401$	−24.5289			−1.22491			−0.612457	+	0.790504i	$0.709819\pi$
$402$	16.6195	−	2.23175i	0.828905	−	0.111309i
$403$	12.9143	+	9.20924i	0.643309	+	0.458745i
$404$			0.426790i			0.0212336i
$405$	−12.3774	−	15.8682i	−0.615038	−	0.788497i
$406$		−	23.2146i		−	1.15212i
$407$	−4.41923			−0.219053
$408$	−5.84929	+	0.785471i	−0.289583	+	0.0388866i
$409$		−	22.5622i		−	1.11563i	−0.829966	−	0.557815i	$-0.811640\pi$
$409$		−	22.5622i		−	1.11563i	0.829966	−	0.557815i	$-0.188360\pi$
$410$	−0.971637	+	0.125536i	−0.0479857	+	0.00619979i
$411$	32.3135	−	4.33921i	1.59391	−	0.214038i
$412$			11.7899i			0.580846i
$413$	−9.24912			−0.455119
$414$	2.96094	+	10.8260i	0.145522	+	0.532071i
$415$	−19.3610	+	2.50145i	−0.950394	+	0.122792i
$416$	−2.84883			−0.139675
$417$	−35.7797	+	4.80467i	−1.75214	+	0.235286i
$418$	−6.50104			−0.317976
$419$		−	14.8743i		−	0.726657i	−0.931661	−	0.363329i	$-0.881640\pi$
$419$		−	14.8743i		−	0.726657i	0.931661	−	0.363329i	$-0.118360\pi$
$420$	−4.10256	−	15.3002i	−0.200184	−	0.746573i
$421$	0.454924			0.0221716			0.0110858	−	0.999939i	$-0.496471\pi$
$421$	0.454924			0.0221716			0.0110858	+	0.999939i	$0.496471\pi$
$422$	−24.3355			−1.18463
$423$	22.6127	−	6.18461i	1.09947	−	0.300706i
$424$			10.9500i			0.531777i
$425$	−4.33010	−	16.4775i	−0.210041	−	0.799278i
$426$	19.2589	−	2.58618i	0.933097	−	0.125301i
$427$	−12.2951			−0.595003
$428$	16.4991			0.797513
$429$	−1.91666	−	14.2731i	−0.0925372	−	0.689111i
$430$	2.37716	+	18.3989i	0.114637	+	0.887276i
$431$		−	18.4340i		−	0.887935i	−0.896043	−	0.443967i	$-0.853571\pi$
$431$		−	18.4340i		−	0.887935i	0.896043	−	0.443967i	$-0.146429\pi$
$432$	2.02567	+	4.78504i	0.0974603	+	0.230221i
$433$	32.5252			1.56306			0.781530	−	0.623867i	$-0.214439\pi$
$433$	32.5252			1.56306			0.781530	+	0.623867i	$0.214439\pi$
$434$	13.2216	−	18.5410i	0.634659	−	0.889998i
$435$	−21.2325	+	5.69324i	−1.01802	+	0.272970i
$436$	4.44187			0.212727
$437$			8.33342i			0.398642i
$438$	0.604139	+	4.49894i	0.0288669	+	0.214968i
$439$	12.8991			0.615640			0.307820	−	0.951445i	$-0.400401\pi$
$439$	12.8991			0.615640			0.307820	+	0.951445i	$0.400401\pi$
$440$	0.836232	+	6.47235i	0.0398658	+	0.308557i
$441$	28.1514	−	7.69945i	1.34054	−	0.366641i
$442$		−	9.70710i		−	0.461719i
$443$	−13.0784			−0.621374			−0.310687	−	0.950512i	$-0.600559\pi$
$443$	−13.0784			−0.621374			−0.310687	+	0.950512i	$0.600559\pi$
$444$	0.349045	+	2.59929i	0.0165649	+	0.123357i
$445$	−3.78827	−	29.3208i	−0.179581	−	1.38994i
$446$	−13.5432			−0.641289
$447$	25.9498	−	3.48467i	1.22739	−	0.164819i
$448$			4.09004i			0.193236i
$449$	−5.97465			−0.281961			−0.140980	−	0.990012i	$-0.545025\pi$
$449$	−5.97465			−0.281961			−0.140980	+	0.990012i	$0.545025\pi$
$450$	−12.9877	+	7.50457i	−0.612248	+	0.353769i
$451$			1.27875i			0.0602140i
$452$	−15.2316			−0.716434
$453$	−4.44014	+	0.596243i	−0.208616	+	0.0280140i
$454$	4.08250			0.191601
$455$	25.8395	−	3.33848i	1.21137	−	0.156510i
$456$	0.513473	+	3.82376i	0.0240456	+	0.179064i
$457$	11.2528			0.526383			0.263191	−	0.964744i	$-0.415225\pi$
$457$	11.2528			0.526383			0.263191	+	0.964744i	$0.415225\pi$
$458$			7.25882i			0.339182i
$459$	−16.3046	+	6.90228i	−0.761032	+	0.322171i
$460$	8.29665	−	1.07193i	0.386833	−	0.0499791i
$461$	18.7636			0.873907			0.436953	−	0.899484i	$-0.356057\pi$
$461$	18.7636			0.873907			0.436953	+	0.899484i	$0.356057\pi$
$462$	−20.4918	+	2.75173i	−0.953364	+	0.128022i
$463$	16.0690			0.746792			0.373396	−	0.927672i	$-0.378193\pi$
$463$	16.0690			0.746792			0.373396	+	0.927672i	$0.378193\pi$
$464$	5.67587			0.263496
$465$	−20.2005	−	7.54571i	−0.936778	−	0.349924i
$466$	4.27441			0.198008
$467$	36.1871			1.67454			0.837269	−	0.546791i	$-0.184151\pi$
$467$	36.1871			1.67454			0.837269	+	0.546791i	$0.184151\pi$
$468$	−8.24371	+	2.25467i	−0.381066	+	0.104222i
$469$	39.5973			1.82843
$470$	−2.23898	−	17.3295i	−0.103276	−	0.799349i
$471$	3.23686	−	0.434661i	0.149147	−	0.0200281i
$472$		−	2.26138i		−	0.104088i
$473$	24.2145			1.11338
$474$	−26.0433	+	3.49722i	−1.19621	+	0.160633i
$475$	−10.7716	+	2.83065i	−0.494235	+	0.129879i
$476$	−13.9364			−0.638774
$477$	8.66620	+	31.6861i	0.396798	+	1.45081i
$478$	−17.2289			−0.788031
$479$			12.6657i			0.578711i	0.957222	+	0.289356i	$0.0934410\pi$
$479$			12.6657i			0.578711i	−0.957222	+	0.289356i	$0.906559\pi$
$480$	3.74084	−	1.00306i	0.170745	−	0.0457832i
$481$	−4.31361			−0.196684
$482$		−	12.1407i		−	0.552993i
$483$	3.52734	+	26.2676i	0.160499	+	1.19522i
$484$	−2.48188			−0.112813
$485$	−7.37264	+	0.952550i	−0.334774	+	0.0432531i
$486$	9.64880	+	12.2434i	0.437678	+	0.555372i
$487$	29.5112			1.33728			0.668640	−	0.743586i	$-0.266877\pi$
$487$	29.5112			1.33728			0.668640	+	0.743586i	$0.266877\pi$
$488$		−	3.00611i		−	0.136080i
$489$	−11.9577	+	1.60573i	−0.540744	+	0.0726137i
$490$	−2.78739	−	21.5741i	−0.125922	−	0.974620i
$491$	−24.9330			−1.12521			−0.562604	−	0.826726i	$-0.690201\pi$
$491$	−24.9330			−1.12521			−0.562604	+	0.826726i	$0.690201\pi$
$492$	0.752131	−	0.101000i	0.0339087	−	0.00455343i
$493$			19.3400i			0.871028i
$494$	−6.34566			−0.285505
$495$	7.54229	+	18.0674i	0.339001	+	0.812067i
$496$	4.53321	+	3.23264i	0.203547	+	0.145150i
$497$	45.8859			2.05827
$498$	14.9871	−	2.01254i	0.671588	−	0.0901841i
$499$			38.9920i			1.74552i	0.488147	+	0.872761i	$0.337673\pi$
$499$			38.9920i			1.74552i	−0.488147	+	0.872761i	$0.662327\pi$
$500$	4.20371	+	10.3600i	0.187996	+	0.463312i
$501$	−15.9513	+	2.14201i	−0.712650	+	0.0956981i
$502$	8.17847			0.365023
$503$	−30.1111			−1.34259			−0.671295	−	0.741190i	$-0.734262\pi$
$503$	−30.1111			−1.34259			−0.671295	+	0.741190i	$0.734262\pi$
$504$	3.23701	+	11.8354i	0.144188	+	0.527193i
$505$	0.946463	−	0.122284i	0.0421171	−	0.00544156i
$506$		−	10.9190i		−	0.485411i
$507$	1.12590	+	8.38439i	0.0500028	+	0.372364i
$508$	21.0528			0.934069
$509$	−5.10170			−0.226129			−0.113064	−	0.993588i	$-0.536067\pi$
$509$	−5.10170			−0.226129			−0.113064	+	0.993588i	$0.536067\pi$
$510$	3.41783	+	12.7465i	0.151344	+	0.564426i
$511$			10.7191i			0.474185i
$512$	−1.00000			−0.0441942
$513$	4.51211	+	10.6585i	0.199215	+	0.470585i
$514$	1.43812			0.0634328
$515$	26.1457	−	3.37804i	1.15212	−	0.148854i
$516$	−1.91254	−	14.2424i	−0.0841947	−	0.626986i
$517$	−22.8070			−1.00305
$518$			6.19302i			0.272106i
$519$	3.84785	+	28.6544i	0.168902	+	1.25779i
$520$	0.816246	+	6.31766i	0.0357948	+	0.277048i
$521$		−	35.0124i		−	1.53392i	−0.641694	−	0.766960i	$-0.721768\pi$
$521$		−	35.0124i		−	1.53392i	0.641694	−	0.766960i	$-0.278232\pi$
$522$	16.4244	−	4.49210i	0.718876	−	0.196614i
$523$	−43.7355			−1.91242			−0.956210	−	0.292680i	$-0.905453\pi$
$523$	−43.7355			−1.91242			−0.956210	+	0.292680i	$0.905453\pi$
$524$			6.73650i			0.294285i
$525$	−32.7548	+	13.4818i	−1.42954	+	0.588393i
$526$		−	4.53066i		−	0.197546i
$527$	−11.0149	+	15.4465i	−0.479817	+	0.672859i
$528$	−0.672789	−	5.01016i	−0.0292794	−	0.218039i
$529$	9.00331			0.391448
$530$	24.2830	−	3.13738i	1.05479	−	0.136279i
$531$	−1.78974	−	6.54379i	−0.0776680	−	0.283976i
$532$			9.11042i			0.394987i
$533$			1.24819i			0.0540650i
$534$	3.04784	+	22.6968i	0.131893	+	0.982188i
$535$	−4.72732	−	36.5889i	−0.204380	−	1.58188i
$536$			9.68140i			0.418173i
$537$	5.36473	+	39.9504i	0.231505	+	1.72399i
$538$	−15.0129			−0.647250
$539$	−28.3933			−1.22298
$540$	10.0311	−	5.86322i	0.431669	−	0.252313i
$541$	−20.8818			−0.897780			−0.448890	−	0.893587i	$-0.648180\pi$
$541$	−20.8818			−0.897780			−0.448890	+	0.893587i	$0.648180\pi$
$542$		−	18.1048i		−	0.777670i
$543$	15.1792	−	2.03833i	0.651401	−	0.0874733i
$544$		−	3.40740i		−	0.146091i
$545$	−1.27268	−	9.85044i	−0.0545158	−	0.421946i
$546$	−20.0020	+	2.68597i	−0.856007	+	0.114949i
$547$			9.87086i			0.422047i	0.977481	+	0.211024i	$0.0676797\pi$
$547$			9.87086i			0.422047i	−0.977481	+	0.211024i	$0.932320\pi$
$548$			18.8237i			0.804107i
$549$	−2.37915	−	8.69885i	−0.101540	−	0.371258i
$550$	14.1137	−	3.70892i	0.601811	−	0.158149i
$551$	12.6428			0.538601
$552$	−6.42233	+	0.862421i	−0.273352	+	0.0367071i
$553$	−62.0504			−2.63865
$554$	20.2172			0.858947
$555$	5.66426	−	1.51880i	0.240435	−	0.0644696i
$556$		−	20.8428i		−	0.883933i
$557$		−	2.15940i		−	0.0914965i	−0.998953	−	0.0457483i	$-0.985433\pi$
$557$		−	2.15940i		−	0.0914965i	0.998953	−	0.0457483i	$-0.0145672\pi$
$558$	15.6763	+	5.76662i	0.663630	+	0.244120i
$559$	23.6357			0.999685
$560$	9.07022	−	1.17188i	0.383287	−	0.0495209i
$561$	17.0716	−	2.29246i	0.720765	−	0.0967878i
$562$		−	31.7271i		−	1.33833i
$563$	10.3014			0.434152			0.217076	−	0.976155i	$-0.430348\pi$
$563$	10.3014			0.434152			0.217076	+	0.976155i	$0.430348\pi$
$564$	1.80137	+	13.4145i	0.0758512	+	0.564853i
$565$	4.36416	+	33.7781i	0.183602	+	1.42106i
$566$			27.7595i			1.16682i
$567$	18.7340	+	31.6866i	0.786755	+	1.33071i
$568$			11.2189i			0.470736i
$569$	−2.46545			−0.103357			−0.0516786	−	0.998664i	$-0.516457\pi$
$569$	−2.46545			−0.103357			−0.0516786	+	0.998664i	$0.516457\pi$
$570$	8.33258	−	2.23428i	0.349013	−	0.0935837i
$571$		−	19.3834i		−	0.811171i	−0.914057	−	0.405585i	$-0.867068\pi$
$571$		−	19.3834i		−	0.811171i	0.914057	−	0.405585i	$-0.132932\pi$
$572$	8.31454			0.347648
$573$	25.8501	−	3.47128i	1.07991	−	0.145015i
$574$	1.79201			0.0747972
$575$	−4.75431	−	18.0918i	−0.198269	−	0.754481i
$576$	−2.89372	+	0.791438i	−0.120572	+	0.0329766i
$577$		−	33.5306i		−	1.39590i	−0.716147	−	0.697949i	$-0.754096\pi$
$577$		−	33.5306i		−	1.39590i	0.716147	−	0.697949i	$-0.245904\pi$
$578$	−5.38962			−0.224179
$579$	23.9755	−	3.21954i	0.996386	−	0.133800i
$580$	−1.62625	−	12.5870i	−0.0675264	−	0.522647i
$581$	35.7080			1.48142
$582$	5.70706	−	0.766372i	0.236565	−	0.0317671i
$583$		−	31.9583i		−	1.32358i
$584$	−2.62078			−0.108449
$585$	7.36202	+	17.6355i	0.304382	+	0.729140i
$586$	19.6074			0.809975
$587$		−	0.734237i		−	0.0303052i	−0.999885	−	0.0151526i	$-0.995177\pi$
$587$		−	0.734237i		−	0.0303052i	0.999885	−	0.0151526i	$-0.00482341\pi$
$588$	2.24259	+	16.7002i	0.0924829	+	0.688707i
$589$	10.0976	+	7.20060i	0.416063	+	0.296695i
$590$	−5.01491	+	0.647929i	−0.206460	+	0.0266748i
$591$	−9.47285	+	1.27206i	−0.389661	+	0.0523256i
$592$	−1.51417			−0.0622320
$593$	−22.1696			−0.910396			−0.455198	−	0.890390i	$-0.650431\pi$
$593$	−22.1696			−0.910396			−0.455198	+	0.890390i	$0.650431\pi$
$594$	−5.91210	−	13.9655i	−0.242576	−	0.573013i
$595$	3.99306	+	30.9059i	0.163699	+	1.26702i
$596$			15.1166i			0.619201i
$597$	−31.5785	+	4.24052i	−1.29242	+	0.173553i
$598$		−	10.6581i		−	0.435841i
$599$		−	14.7023i		−	0.600718i	−0.953826	−	0.300359i	$-0.902894\pi$
$599$		−	14.7023i		−	0.600718i	0.953826	−	0.300359i	$-0.0971065\pi$
$600$	−3.29625	−	8.00842i	−0.134569	−	0.326942i
$601$		−	4.14184i		−	0.168949i	−0.996426	−	0.0844746i	$-0.973079\pi$
$601$		−	4.14184i		−	0.168949i	0.996426	−	0.0844746i	$-0.0269212\pi$
$602$		−	33.9336i		−	1.38303i
$603$	7.66222	+	28.0153i	0.312030	+	1.14087i
$604$		−	2.58653i		−	0.105244i
$605$	0.711107	+	5.50389i	0.0289106	+	0.223765i
$606$	−0.732645	+	0.0983831i	−0.0297617	+	0.00399654i
$607$		−	27.5963i		−	1.12010i	−0.828460	−	0.560049i	$-0.810782\pi$
$607$		−	27.5963i		−	1.12010i	0.828460	−	0.560049i	$-0.189218\pi$
$608$	−2.22746			−0.0903356
$609$	39.8511	−	5.35140i	1.61485	−	0.216850i
$610$	−6.66646	+	0.861311i	−0.269917	+	0.0348735i
$611$	−22.2619			−0.900618
$612$	−2.69674	−	9.86007i	−0.109009	−	0.398570i
$613$	−32.6944			−1.32052			−0.660258	−	0.751039i	$-0.729553\pi$
$613$	−32.6944			−1.32052			−0.660258	+	0.751039i	$0.729553\pi$
$614$		−	9.74769i		−	0.393385i
$615$	−0.439482	−	1.63901i	−0.0177216	−	0.0660914i
$616$		−	11.9371i		−	0.480960i
$617$	−27.8024			−1.11928			−0.559641	−	0.828735i	$-0.689061\pi$
$617$	−27.8024			−1.11928			−0.559641	+	0.828735i	$0.689061\pi$
$618$	−20.2390	+	2.71780i	−0.814133	+	0.109326i
$619$		−	13.9590i		−	0.561059i	−0.959845	−	0.280529i	$-0.909490\pi$
$619$		−	13.9590i		−	0.561059i	0.959845	−	0.280529i	$-0.0905100\pi$
$620$	5.86997	−	10.9792i	0.235744	−	0.440936i
$621$	−17.9019	+	7.57848i	−0.718378	+	0.304114i
$622$			6.19303i			0.248318i
$623$			54.0771i			2.16655i
$624$	−0.656709	−	4.89042i	−0.0262894	−	0.195773i
$625$	21.7702	−	12.2906i	0.870807	−	0.491626i
$626$	21.4203			0.856126
$627$	−1.49861	−	11.1600i	−0.0598488	−	0.445686i
$628$			1.88558i			0.0752427i
$629$		−	5.15938i		−	0.205718i
$630$	25.3192	−	10.5696i	1.00874	−	0.421103i
$631$			17.4643i			0.695243i	0.937635	+	0.347622i	$0.113011\pi$
$631$			17.4643i			0.695243i	−0.937635	+	0.347622i	$0.886989\pi$
$632$		−	15.1711i		−	0.603473i
$633$	−5.60979	−	41.7753i	−0.222969	−	1.66042i
$634$	−20.7870			−0.825557
$635$	−6.03206	−	46.6875i	−0.239375	−	1.85274i
$636$	−18.7971	+	2.52417i	−0.745355	+	0.100090i
$637$	−27.7146			−1.09809
$638$	−16.5655			−0.655835
$639$	8.87909	+	32.4645i	0.351251	+	1.28428i
$640$	0.286520	+	2.21764i	0.0113257	+	0.0876597i
$641$	17.9988			0.710910			0.355455	−	0.934693i	$-0.384326\pi$
$641$	17.9988			0.710910			0.355455	+	0.934693i	$0.384326\pi$
$642$	3.80335	+	28.3230i	0.150106	+	1.11782i
$643$	−30.6135			−1.20728			−0.603640	−	0.797257i	$-0.706283\pi$
$643$	−30.6135			−1.20728			−0.603640	+	0.797257i	$0.706283\pi$
$644$	−15.3017			−0.602972
$645$	−31.0364	+	8.32203i	−1.22206	+	0.327680i
$646$		−	7.58986i		−	0.298619i
$647$			23.1577i			0.910424i	0.890383	+	0.455212i	$0.150436\pi$
$647$			23.1577i			0.910424i	−0.890383	+	0.455212i	$0.849564\pi$
$648$	−7.74725	+	4.58040i	−0.304341	+	0.179935i
$649$			6.60001i			0.259073i
$650$	13.7764	−	3.62027i	0.540355	−	0.141999i
$651$	34.8762	+	18.4228i	1.36690	+	0.722045i
$652$		−	6.96572i		−	0.272799i
$653$	−9.05857			−0.354489			−0.177245	−	0.984167i	$-0.556718\pi$
$653$	−9.05857			−0.354489			−0.177245	+	0.984167i	$0.556718\pi$
$654$	1.02393	+	7.62509i	0.0400390	+	0.298165i
$655$	14.9391	−	1.93014i	0.583719	−	0.0754169i
$656$			0.438141i			0.0171065i
$657$	−7.58380	+	2.07418i	−0.295872	+	0.0809215i
$658$			31.9612i			1.24598i
$659$		−	40.2254i		−	1.56696i	−0.621417	−	0.783480i	$-0.713443\pi$
$659$		−	40.2254i		−	1.56696i	0.621417	−	0.783480i	$-0.286557\pi$
$660$	−10.9179	+	2.92751i	−0.424980	+	0.113953i
$661$	−34.7878			−1.35309			−0.676545	−	0.736401i	$-0.736523\pi$
$661$	−34.7878			−1.35309			−0.676545	+	0.736401i	$0.736523\pi$
$662$			24.7544i			0.962109i
$663$	16.6636	−	2.23767i	0.647161	−	0.0869039i
$664$			8.73047i			0.338808i
$665$	20.2036	−	2.61032i	0.783461	−	0.101224i
$666$	−4.38159	+	1.19837i	−0.169783	+	0.0464359i
$667$			21.2347i			0.822209i
$668$		−	9.29213i		−	0.359523i
$669$	−3.12197	−	23.2488i	−0.120702	−	0.898852i
$670$	21.4698	−	2.77391i	0.829451	−	0.107166i
$671$			8.77359i			0.338700i
$672$	−7.02114	+	0.942833i	−0.270846	+	0.0363706i
$673$	−0.138935			−0.00535554			−0.00267777	−	0.999996i	$-0.500852\pi$
$673$	−0.138935			−0.00535554			−0.00267777	+	0.999996i	$0.500852\pi$
$674$	11.4622			0.441507
$675$	−15.8766	−	20.5654i	−0.611090	−	0.791561i
$676$	−4.88418			−0.187853
$677$		−	30.4756i		−	1.17127i	−0.810574	−	0.585637i	$-0.800845\pi$
$677$		−	30.4756i		−	1.17127i	0.810574	−	0.585637i	$-0.199155\pi$
$678$	−3.51118	−	26.1472i	−0.134846	−	1.00418i
$679$	13.5975			0.521826
$680$	−7.55637	+	0.976288i	−0.289774	+	0.0374390i
$681$	0.941095	+	7.00820i	0.0360628	+	0.268555i
$682$	−13.2306	−	9.43474i	−0.506624	−	0.361275i
$683$	1.84243			0.0704985			0.0352492	−	0.999379i	$-0.488777\pi$
$683$	1.84243			0.0704985			0.0352492	+	0.999379i	$0.488777\pi$
$684$	−6.44566	+	1.76290i	−0.246456	+	0.0674061i
$685$	41.7440	−	5.39335i	1.59496	−	0.206069i
$686$			11.1594i			0.426069i
$687$	−12.4608	+	1.67330i	−0.475409	+	0.0638402i
$688$	8.29665			0.316307
$689$		−	31.1945i		−	1.18842i
$690$	3.75266	+	13.9953i	0.142861	+	0.532791i
$691$	27.3382			1.03999			0.519996	−	0.854169i	$-0.325933\pi$
$691$	27.3382			1.03999			0.519996	+	0.854169i	$0.325933\pi$
$692$	−16.6921			−0.634539
$693$	−9.44749	−	34.5427i	−0.358880	−	1.31217i
$694$			11.5962i			0.440184i
$695$	−46.2218	+	5.97189i	−1.75329	+	0.226527i
$696$	1.30840	+	9.74344i	0.0495947	+	0.369324i
$697$	−1.49292			−0.0565484
$698$	7.63161			0.288861
$699$	0.985333	+	7.33763i	0.0372687	+	0.277535i
$700$	−5.19760	−	19.7787i	−0.196451	−	0.747564i
$701$		−	17.1268i		−	0.646871i	−0.946250	−	0.323435i	$-0.895162\pi$
$701$		−	17.1268i		−	0.646871i	0.946250	−	0.323435i	$-0.104838\pi$
$702$	−5.77079	−	13.6318i	−0.217805	−	0.514498i
$703$	−3.37276			−0.127206
$704$	2.91858			0.109998
$705$	29.2324	−	7.83830i	1.10096	−	0.295208i
$706$			1.21958i			0.0458996i
$707$	−1.74559			−0.0656495
$708$	3.88197	−	0.521290i	0.145893	−	0.0195913i
$709$		−	48.3391i		−	1.81541i	−0.419605	−	0.907707i	$-0.637831\pi$
$709$		−	48.3391i		−	1.81541i	0.419605	−	0.907707i	$-0.362169\pi$
$710$	24.8795	−	3.21445i	0.933712	−	0.120636i
$711$	−12.0070	−	43.9009i	−0.450296	−	1.64641i
$712$	−13.2216			−0.495502
$713$	−12.0940	+	16.9597i	−0.452924	+	0.635147i
$714$	−3.21261	−	23.9238i	−0.120229	−	0.895327i
$715$	−2.38228	−	18.4386i	−0.0890923	−	0.689565i
$716$	−23.2724			−0.869730
$717$	−3.97159	−	29.5758i	−0.148322	−	1.10453i
$718$		−	18.5454i		−	0.692109i
$719$	−0.950880			−0.0354618			−0.0177309	−	0.999843i	$-0.505644\pi$
$719$	−0.950880			−0.0354618			−0.0177309	+	0.999843i	$0.505644\pi$
$720$	2.58423	+	6.19046i	0.0963085	+	0.230705i
$721$	−48.2212			−1.79585
$722$	14.0384			0.522455
$723$	20.8412	−	2.79866i	0.775093	−	0.104083i
$724$			8.84237i			0.328624i
$725$	−27.4475	+	7.21286i	−1.01937	+	0.267879i
$726$	−0.572120	−	4.26049i	−0.0212334	−	0.158122i
$727$		−	27.5020i		−	1.01999i	−0.860177	−	0.509996i	$-0.829647\pi$
$727$		−	27.5020i		−	1.01999i	0.860177	−	0.509996i	$-0.170353\pi$
$728$		−	11.6518i		−	0.431845i
$729$	−18.7933	+	19.3859i	−0.696048	+	0.717995i
$730$	0.750905	+	5.81193i	0.0277922	+	0.215109i
$731$			28.2700i			1.04560i
$732$	5.16042	−	0.692966i	0.190735	−	0.0256128i
$733$		−	41.5605i		−	1.53507i	−0.641006	−	0.767536i	$-0.721483\pi$
$733$		−	41.5605i		−	1.53507i	0.641006	−	0.767536i	$-0.278517\pi$
$734$	−1.68634			−0.0622440
$735$	36.3925	−	9.75820i	1.34236	−	0.359937i
$736$		−	3.74121i		−	0.137903i
$737$		−	28.2560i		−	1.04082i
$738$	0.346761	+	1.26786i	0.0127645	+	0.0466705i
$739$			6.19512i			0.227891i	0.993487	+	0.113946i	$0.0363490\pi$
$739$			6.19512i			0.227891i	−0.993487	+	0.113946i	$0.963651\pi$
$740$	0.433840	+	3.35788i	0.0159483	+	0.123438i
$741$	−1.46280	−	10.8932i	−0.0537371	−	0.400173i
$742$	−44.7858			−1.64414
$743$		−	0.553173i		−	0.0202939i	−0.999949	−	0.0101470i	$-0.996770\pi$
$743$		−	0.553173i		−	0.0202939i	0.999949	−	0.0101470i	$-0.00322993\pi$
$744$	−4.50430	+	8.52709i	−0.165136	+	0.312618i
$745$	33.5232	−	4.33122i	1.22819	−	0.158684i
$746$			0.208485i			0.00763319i
$747$	6.90962	+	25.2636i	0.252810	+	0.924345i
$748$			9.94478i			0.363617i
$749$			67.4819i			2.46574i
$750$	−16.8153	+	9.60444i	−0.614008	+	0.350705i
$751$	−5.01637			−0.183050			−0.0915250	−	0.995803i	$-0.529174\pi$
$751$	−5.01637			−0.183050			−0.0915250	+	0.995803i	$0.529174\pi$
$752$	−7.81439			−0.284962
$753$	1.88529	+	14.0395i	0.0687039	+	0.511628i
$754$	−16.1696			−0.588861
$755$	−5.73597	+	0.741091i	−0.208753	+	0.0269711i
$756$	−19.5710	+	8.28509i	−0.711791	+	0.301326i
$757$	25.6984			0.934026			0.467013	−	0.884251i	$-0.345330\pi$
$757$	25.6984			0.934026			0.467013	+	0.884251i	$0.345330\pi$
$758$	26.6546			0.968139
$759$	18.7441	−	2.51705i	0.680367	−	0.0913631i
$760$	0.638213	+	4.93970i	0.0231504	+	0.179182i
$761$	−12.3377			−0.447240			−0.223620	−	0.974676i	$-0.571787\pi$
$761$	−12.3377			−0.447240			−0.223620	+	0.974676i	$0.571787\pi$
$762$	4.85308	+	36.1402i	0.175809	+	1.30922i
$763$			18.1674i			0.657705i
$764$			15.0585i			0.544799i
$765$	−21.0934	+	8.80550i	−0.762632	+	0.318364i
$766$		−	1.48850i		−	0.0537818i
$767$			6.44227i			0.232617i
$768$	−0.230519	−	1.71664i	−0.00831814	−	0.0619440i
$769$	−9.50315			−0.342692			−0.171346	−	0.985211i	$-0.554812\pi$
$769$	−9.50315			−0.342692			−0.171346	+	0.985211i	$0.554812\pi$
$770$	−26.4722	+	3.42023i	−0.953991	+	0.123256i
$771$	0.331514	+	2.46874i	0.0119392	+	0.0889095i
$772$			13.9665i			0.502665i
$773$		−	8.90886i		−	0.320429i	−0.987082	−	0.160215i	$-0.948781\pi$
$773$		−	8.90886i		−	0.320429i	0.987082	−	0.160215i	$-0.0512187\pi$
$774$	24.0082	−	6.56628i	0.862957	−	0.236020i
$775$	−26.0298	−	9.87168i	−0.935018	−	0.354601i
$776$			3.32455i			0.119344i
$777$	−10.6312	+	1.42761i	−0.381392	+	0.0512152i
$778$	−15.3464			−0.550194
$779$			0.975943i			0.0349668i
$780$	−10.6570	+	2.85754i	−0.381582	+	0.102316i
$781$		−	32.7434i		−	1.17165i
$782$	12.7478			0.455861
$783$	11.4975	+	27.1593i	0.410886	+	0.970594i
$784$	−9.72844			−0.347444
$785$	4.18152	−	0.540255i	0.149245	−	0.0192825i
$786$	−11.5642	+	1.55289i	−0.412480	+	0.0553898i
$787$	−43.8373			−1.56263			−0.781315	−	0.624136i	$-0.785451\pi$
$787$	−43.8373			−1.56263			−0.781315	+	0.624136i	$0.785451\pi$
$788$		−	5.51824i		−	0.196579i
$789$	7.77752	−	1.04440i	0.276887	−	0.0371817i
$790$	−33.6439	+	4.34682i	−1.19700	+	0.154653i
$791$		−	62.2979i		−	2.21506i
$792$	8.44557	−	2.30988i	0.300100	−	0.0820779i
$793$			8.56389i			0.304113i
$794$			18.8139i			0.667682i
$795$	10.9835	+	40.9620i	0.389543	+	1.45277i
$796$		−	18.3955i		−	0.652012i
$797$			33.1072i			1.17272i	0.810052	+	0.586358i	$0.199439\pi$
$797$			33.1072i			1.17272i	−0.810052	+	0.586358i	$0.800561\pi$
$798$	−15.6393	+	2.10013i	−0.553626	+	0.0743436i
$799$		−	26.6268i		−	0.941987i
$800$	4.83581	−	1.27079i	0.170972	−	0.0449293i
$801$	−38.2598	+	10.4641i	−1.35184	+	0.369731i
$802$	24.5289			0.866145
$803$	7.64896			0.269926
$804$	−16.6195	+	2.23175i	−0.586124	+	0.0787076i
$805$	4.38425	+	33.9336i	0.154525	+	1.19600i
$806$	−12.9143	−	9.20924i	−0.454888	−	0.324382i
$807$	−3.46075	−	25.7717i	−0.121824	−	0.907207i
$808$		−	0.426790i		−	0.0150144i
$809$	−36.6028			−1.28688			−0.643442	−	0.765495i	$-0.722494\pi$
$809$	−36.6028			−1.28688			−0.643442	+	0.765495i	$0.722494\pi$
$810$	12.3774	+	15.8682i	0.434898	+	0.557552i
$811$	−43.9576			−1.54356			−0.771780	−	0.635890i	$-0.780633\pi$
$811$	−43.9576			−1.54356			−0.771780	+	0.635890i	$0.780633\pi$
$812$			23.2146i			0.814671i
$813$	31.0795	−	4.17351i	1.09001	−	0.146371i
$814$	4.41923			0.154894
$815$	−15.4474	+	1.99582i	−0.541100	+	0.0699105i
$816$	5.84929	−	0.785471i	0.204766	−	0.0274970i
$817$	18.4805			0.646550
$818$			22.5622i			0.788869i
$819$	−9.22169	−	33.7171i	−0.322232	−	1.17817i
$820$	0.971637	−	0.125536i	0.0339310	−	0.00438391i
$821$	−6.09440			−0.212696			−0.106348	−	0.994329i	$-0.533916\pi$
$821$	−6.09440			−0.212696			−0.106348	+	0.994329i	$0.533916\pi$
$822$	−32.3135	+	4.33921i	−1.12706	+	0.151347i
$823$	46.0283			1.60445			0.802223	−	0.597024i	$-0.203650\pi$
$823$	46.0283			1.60445			0.802223	+	0.597024i	$0.203650\pi$
$824$		−	11.7899i		−	0.410720i
$825$	9.62037	+	23.3732i	0.334938	+	0.813751i
$826$	9.24912			0.321818
$827$			41.7520i			1.45186i	0.687769	+	0.725930i	$0.258590\pi$
$827$			41.7520i			1.45186i	−0.687769	+	0.725930i	$0.741410\pi$
$828$	−2.96094	−	10.8260i	−0.102900	−	0.376231i
$829$		−	7.29517i		−	0.253372i	−0.991943	−	0.126686i	$-0.959566\pi$
$829$		−	7.29517i		−	0.253372i	0.991943	−	0.126686i	$-0.0404340\pi$
$830$	19.3610	−	2.50145i	0.672030	−	0.0868268i
$831$	4.66046	+	34.7057i	0.161669	+	1.20393i
$832$	2.84883			0.0987653
$833$		−	33.1487i		−	1.14853i
$834$	35.7797	−	4.80467i	1.23895	−	0.166372i
$835$	−20.6066	+	2.66238i	−0.713120	+	0.0921355i
$836$	6.50104			0.224843
$837$	−6.28553	+	28.2399i	−0.217260	+	0.976114i
$838$			14.8743i			0.513824i
$839$		−	11.1406i		−	0.384616i	−0.981335	−	0.192308i	$-0.938403\pi$
$839$		−	11.1406i		−	0.384616i	0.981335	−	0.192308i	$-0.0615972\pi$
$840$	4.10256	+	15.3002i	0.141552	+	0.527906i
$841$	3.21552			0.110880
$842$	−0.454924			−0.0156777
$843$	54.4641	−	7.31370i	1.87584	−	0.251897i
$844$	24.3355			0.837662
$845$	1.39942	+	10.8313i	0.0481414	+	0.372609i
$846$	−22.6127	+	6.18461i	−0.777440	+	0.212631i
$847$		−	10.1510i		−	0.348792i
$848$		−	10.9500i		−	0.376023i
$849$	−47.6532	+	6.39910i	−1.63545	+	0.219617i
$850$	4.33010	+	16.4775i	0.148521	+	0.565175i
$851$		−	5.66483i		−	0.194188i
$852$	−19.2589	+	2.58618i	−0.659799	+	0.0886011i
$853$		−	9.91130i		−	0.339356i	−0.985500	−	0.169678i	$-0.945727\pi$
$853$		−	9.91130i		−	0.339356i	0.985500	−	0.169678i	$-0.0542728\pi$
$854$	12.2951			0.420730
$855$	5.75628	+	13.7890i	0.196861	+	0.471574i
$856$	−16.4991			−0.563927
$857$	8.31059			0.283884			0.141942	−	0.989875i	$-0.454665\pi$
$857$	8.31059			0.283884			0.141942	+	0.989875i	$0.454665\pi$
$858$	1.91666	+	14.2731i	0.0654337	+	0.487275i
$859$		−	10.7888i		−	0.368110i	−0.982916	−	0.184055i	$-0.941078\pi$
$859$		−	10.7888i		−	0.368110i	0.982916	−	0.184055i	$-0.0589224\pi$
$860$	−2.37716	−	18.3989i	−0.0810604	−	0.627399i
$861$	0.413094	+	3.07625i	0.0140782	+	0.104838i
$862$			18.4340i			0.627865i
$863$			37.9404i			1.29151i	0.763546	+	0.645754i	$0.223457\pi$
$863$			37.9404i			1.29151i	−0.763546	+	0.645754i	$0.776543\pi$
$864$	−2.02567	−	4.78504i	−0.0689148	−	0.162791i
$865$	4.78262	+	37.0170i	0.162614	+	1.25862i
$866$	−32.5252			−1.10525
$867$	−1.24241	−	9.25206i	−0.0421945	−	0.314216i
$868$	−13.2216	+	18.5410i	−0.448772	+	0.629323i
$869$			44.2781i			1.50203i
$870$	21.2325	−	5.69324i	0.719850	−	0.193019i
$871$		−	27.5806i		−	0.934534i
$872$	−4.44187			−0.150421
$873$	2.63117	+	9.62032i	0.0890517	+	0.325599i
$874$		−	8.33342i		−	0.281882i
$875$	−42.3727	+	17.1934i	−1.43246	+	0.581242i
$876$	−0.604139	−	4.49894i	−0.0204120	−	0.152005i
$877$		−	21.9885i		−	0.742498i	−0.928533	−	0.371249i	$-0.878930\pi$
$877$		−	21.9885i		−	0.742498i	0.928533	−	0.371249i	$-0.121070\pi$
$878$	−12.8991			−0.435323
$879$	4.51988	+	33.6589i	0.152452	+	1.13529i
$880$	−0.836232	−	6.47235i	−0.0281894	−	0.218183i
$881$	−56.3949			−1.89999			−0.949996	−	0.312262i	$-0.898913\pi$
$881$	−56.3949			−1.89999			−0.949996	+	0.312262i	$0.898913\pi$
$882$	−28.1514	+	7.69945i	−0.947907	+	0.259254i
$883$	30.8908			1.03956			0.519780	−	0.854300i	$-0.326014\pi$
$883$	30.8908			1.03956			0.519780	+	0.854300i	$0.326014\pi$
$884$			9.70710i			0.326485i
$885$	−2.26829	−	8.45944i	−0.0762479	−	0.284361i
$886$	13.0784			0.439378
$887$	−11.8004			−0.396219			−0.198109	−	0.980180i	$-0.563480\pi$
$887$	−11.8004			−0.396219			−0.198109	+	0.980180i	$0.563480\pi$
$888$	−0.349045	−	2.59929i	−0.0117132	−	0.0872264i
$889$			86.1070i			2.88794i
$890$	3.78827	+	29.3208i	0.126983	+	0.982835i
$891$	22.6110	−	13.3683i	0.757497	−	0.447854i
$892$	13.5432			0.453460
$893$	−17.4063			−0.582479
$894$	−25.9498	+	3.48467i	−0.867893	+	0.116545i
$895$	6.66801	+	51.6097i	0.222887	+	1.72512i
$896$		−	4.09004i		−	0.136639i
$897$	18.2961	−	2.45689i	0.610889	−	0.0820332i
$898$	5.97465			0.199377
$899$	25.7299	+	18.3481i	0.858141	+	0.611942i
$900$	12.9877	−	7.50457i	0.432925	−	0.250152i
$901$	37.3109			1.24301
$902$		−	1.27875i		−	0.0425777i
$903$	58.2519	−	7.82235i	1.93850	−	0.260312i
$904$	15.2316			0.506596
$905$	19.6091	−	2.53352i	0.651830	−	0.0842169i
$906$	4.44014	−	0.596243i	0.147514	−	0.0198089i
$907$			18.7685i			0.623199i	0.950214	+	0.311599i	$0.100865\pi$
$907$			18.7685i			0.623199i	−0.950214	+	0.311599i	$0.899135\pi$
$908$	−4.08250			−0.135483
$909$	−0.337777	−	1.23501i	−0.0112034	−	0.0409627i
$910$	−25.8395	+	3.33848i	−0.856571	+	0.110670i
$911$	−25.8413			−0.856161			−0.428081	−	0.903741i	$-0.640810\pi$
$911$	−25.8413			−0.856161			−0.428081	+	0.903741i	$0.640810\pi$
$912$	−0.513473	−	3.82376i	−0.0170028	−	0.126617i
$913$		−	25.4806i		−	0.843285i
$914$	−11.2528			−0.372209
$915$	−3.01531	−	11.2454i	−0.0996831	−	0.371761i
$916$		−	7.25882i		−	0.239838i
$917$	−27.5526			−0.909866
$918$	16.3046	−	6.90228i	0.538131	−	0.227809i
$919$	−54.9584			−1.81291			−0.906455	−	0.422303i	$-0.861222\pi$
$919$	−54.9584			−1.81291			−0.906455	+	0.422303i	$0.861222\pi$
$920$	−8.29665	+	1.07193i	−0.273532	+	0.0353406i
$921$	16.7333	−	2.24703i	0.551381	−	0.0740421i
$922$	−18.7636			−0.617945
$923$		−	31.9608i		−	1.05200i
$924$	20.4918	−	2.75173i	0.674130	−	0.0905254i
$925$	7.32224	−	1.92420i	0.240754	−	0.0632672i
$926$	−16.0690			−0.528062
$927$	−9.33097	−	34.1167i	−0.306469	−	1.12054i
$928$	−5.67587			−0.186320
$929$	48.5580			1.59314			0.796568	−	0.604549i	$-0.206647\pi$
$929$	48.5580			1.59314			0.796568	+	0.604549i	$0.206647\pi$
$930$	20.2005	+	7.54571i	0.662402	+	0.247434i
$931$	−21.6697			−0.710197
$932$	−4.27441			−0.140013
$933$	−10.6312	+	1.42761i	−0.348051	+	0.0467379i
$934$	−36.1871			−1.18408
$935$	22.0539	−	2.84938i	0.721239	−	0.0931846i
$936$	8.24371	−	2.25467i	0.269454	−	0.0736962i
$937$			16.8277i			0.549737i	0.961482	+	0.274868i	$0.0886343\pi$
$937$			16.8277i			0.549737i	−0.961482	+	0.274868i	$0.911366\pi$
$938$	−39.5973			−1.29290
$939$	4.93778	+	36.7709i	0.161138	+	1.19997i
$940$	2.23898	+	17.3295i	0.0730275	+	0.565225i
$941$	34.0449			1.10983			0.554916	−	0.831907i	$-0.312750\pi$
$941$	34.0449			1.10983			0.554916	+	0.831907i	$0.312750\pi$
$942$	−3.23686	+	0.434661i	−0.105463	+	0.0141620i
$943$	−1.63918			−0.0533790
$944$			2.26138i			0.0736015i
$945$	23.9808	+	41.0276i	0.780095	+	1.33463i
$946$	−24.2145			−0.787280
$947$		−	37.7618i		−	1.22709i	−0.789659	−	0.613547i	$-0.789742\pi$
$947$		−	37.7618i		−	1.22709i	0.789659	−	0.613547i	$-0.210258\pi$
$948$	26.0433	−	3.49722i	0.845848	−	0.113585i
$949$	7.46614			0.242361
$950$	10.7716	−	2.83065i	0.349477	−	0.0918383i
$951$	−4.79180	−	35.6838i	−0.155385	−	1.15713i
$952$	13.9364			0.451682
$953$		−	31.3086i		−	1.01418i	−0.861892	−	0.507092i	$-0.830720\pi$
$953$		−	31.3086i		−	1.01418i	0.861892	−	0.507092i	$-0.169280\pi$
$954$	−8.66620	−	31.6861i	−0.280579	−	1.02588i
$955$	33.3944	−	4.31458i	1.08062	−	0.139616i
$956$	17.2289			0.557222
$957$	−3.81866	−	28.4370i	−0.123440	−	0.919239i
$958$		−	12.6657i		−	0.409211i
$959$	−76.9895			−2.48612
$960$	−3.74084	+	1.00306i	−0.120735	+	0.0323736i
$961$	10.1000	+	29.3085i	0.325808	+	0.945436i
$962$	4.31361			0.139076
$963$	−47.7437	+	13.0580i	−1.53852	+	0.420788i
$964$			12.1407i			0.391025i
$965$	30.9726	−	4.00168i	0.997043	−	0.128819i
$966$	−3.52734	−	26.2676i	−0.113490	−	0.845146i
$967$	37.5527			1.20761			0.603806	−	0.797131i	$-0.293650\pi$
$967$	37.5527			1.20761			0.603806	+	0.797131i	$0.293650\pi$
$968$	2.48188			0.0797705
$969$	13.0291	−	1.74961i	0.418554	−	0.0562055i
$970$	7.37264	−	0.952550i	0.236721	−	0.0305845i
$971$		−	23.0698i		−	0.740344i	−0.928963	−	0.370172i	$-0.879299\pi$
$971$		−	23.0698i		−	0.740344i	0.928963	−	0.370172i	$-0.120701\pi$
$972$	−9.64880	−	12.2434i	−0.309485	−	0.392707i
$973$	85.2481			2.73293
$974$	−29.5112			−0.945600
$975$	9.39044	+	22.8146i	0.300735	+	0.730652i
$976$			3.00611i			0.0962233i
$977$	−10.3277			−0.330411			−0.165205	−	0.986259i	$-0.552829\pi$
$977$	−10.3277			−0.330411			−0.165205	+	0.986259i	$0.552829\pi$
$978$	11.9577	−	1.60573i	0.382364	−	0.0513456i
$979$	38.5885			1.23329
$980$	2.78739	+	21.5741i	0.0890400	+	0.689160i
$981$	−12.8535	+	3.51546i	−0.410381	+	0.112240i
$982$	24.9330			0.795643
$983$			47.3825i			1.51127i	0.654995	+	0.755633i	$0.272671\pi$
$983$			47.3825i			1.51127i	−0.654995	+	0.755633i	$0.727329\pi$
$984$	−0.752131	+	0.101000i	−0.0239771	+	0.00321976i
$985$	−12.2375	+	1.58109i	−0.389918	+	0.0503776i
$986$		−	19.3400i		−	0.615910i
$987$	−54.8659	+	7.36766i	−1.74640	+	0.234515i
$988$	6.34566			0.201882
$989$			31.0395i			0.987000i
$990$	−7.54229	−	18.0674i	−0.239710	−	0.574218i
$991$			30.0174i			0.953535i	0.879029	+	0.476768i	$0.158192\pi$
$991$			30.0174i			0.953535i	−0.879029	+	0.476768i	$0.841808\pi$
$992$	−4.53321	−	3.23264i	−0.143930	−	0.102637i
$993$	−42.4945	+	5.70637i	−1.34852	+	0.181086i
$994$	−45.8859			−1.45541
$995$	−40.7945	+	5.27068i	−1.29327	+	0.167092i
$996$	−14.9871	+	2.01254i	−0.474884	+	0.0637698i
$997$		−	15.6584i		−	0.495905i	−0.968772	−	0.247953i	$-0.920242\pi$
$997$		−	15.6584i		−	0.495905i	0.968772	−	0.247953i	$-0.0797577\pi$
$998$		−	38.9920i		−	1.23427i
$999$	−3.06721	−	7.24537i	−0.0970423	−	0.229233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.e.a.929.15	✓	32
3.2	odd	2		930.2.e.b.929.16	yes	32
5.4	even	2		930.2.e.b.929.18	yes	32
15.14	odd	2	inner	930.2.e.a.929.17	yes	32
31.30	odd	2	inner	930.2.e.a.929.18	yes	32
93.92	even	2		930.2.e.b.929.17	yes	32
155.154	odd	2		930.2.e.b.929.15	yes	32
465.464	even	2	inner	930.2.e.a.929.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.e.a.929.15	✓	32	1.1	even	1	trivial
930.2.e.a.929.16	yes	32	465.464	even	2	inner
930.2.e.a.929.17	yes	32	15.14	odd	2	inner
930.2.e.a.929.18	yes	32	31.30	odd	2	inner
930.2.e.b.929.15	yes	32	155.154	odd	2
930.2.e.b.929.16	yes	32	3.2	odd	2
930.2.e.b.929.17	yes	32	93.92	even	2
930.2.e.b.929.18	yes	32	5.4	even	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.230519 - 1.71664i) q^{3} +1.00000 q^{4} +(-0.286520 - 2.21764i) q^{5} +(0.230519 + 1.71664i) q^{6} +4.09004i q^{7} -1.00000 q^{8} +(-2.89372 + 0.791438i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.230519 - 1.71664i) q^{3} +1.00000 q^{4} +(-0.286520 - 2.21764i) q^{5} +(0.230519 + 1.71664i) q^{6} +4.09004i q^{7} -1.00000 q^{8} +(-2.89372 + 0.791438i) q^{9} +(0.286520 + 2.21764i) q^{10} +2.91858 q^{11} +(-0.230519 - 1.71664i) q^{12} +2.84883 q^{13} -4.09004i q^{14} +(-3.74084 + 1.00306i) q^{15} +1.00000 q^{16} +3.40740i q^{17} +(2.89372 - 0.791438i) q^{18} +2.22746 q^{19} +(-0.286520 - 2.21764i) q^{20} +(7.02114 - 0.942833i) q^{21} -2.91858 q^{22} +3.74121i q^{23} +(0.230519 + 1.71664i) q^{24} +(-4.83581 + 1.27079i) q^{25} -2.84883 q^{26} +(2.02567 + 4.78504i) q^{27} +4.09004i q^{28} +5.67587 q^{29} +(3.74084 - 1.00306i) q^{30} +(4.53321 + 3.23264i) q^{31} -1.00000 q^{32} +(-0.672789 - 5.01016i) q^{33} -3.40740i q^{34} +(9.07022 - 1.17188i) q^{35} +(-2.89372 + 0.791438i) q^{36} -1.51417 q^{37} -2.22746 q^{38} +(-0.656709 - 4.89042i) q^{39} +(0.286520 + 2.21764i) q^{40} +0.438141i q^{41} +(-7.02114 + 0.942833i) q^{42} +8.29665 q^{43} +2.91858 q^{44} +(2.58423 + 6.19046i) q^{45} -3.74121i q^{46} -7.81439 q^{47} +(-0.230519 - 1.71664i) q^{48} -9.72844 q^{49} +(4.83581 - 1.27079i) q^{50} +(5.84929 - 0.785471i) q^{51} +2.84883 q^{52} -10.9500i q^{53} +(-2.02567 - 4.78504i) q^{54} +(-0.836232 - 6.47235i) q^{55} -4.09004i q^{56} +(-0.513473 - 3.82376i) q^{57} -5.67587 q^{58} +2.26138i q^{59} +(-3.74084 + 1.00306i) q^{60} +3.00611i q^{61} +(-4.53321 - 3.23264i) q^{62} +(-3.23701 - 11.8354i) q^{63} +1.00000 q^{64} +(-0.816246 - 6.31766i) q^{65} +(0.672789 + 5.01016i) q^{66} -9.68140i q^{67} +3.40740i q^{68} +(6.42233 - 0.862421i) q^{69} +(-9.07022 + 1.17188i) q^{70} -11.2189i q^{71} +(2.89372 - 0.791438i) q^{72} +2.62078 q^{73} +1.51417 q^{74} +(3.29625 + 8.00842i) q^{75} +2.22746 q^{76} +11.9371i q^{77} +(0.656709 + 4.89042i) q^{78} +15.1711i q^{79} +(-0.286520 - 2.21764i) q^{80} +(7.74725 - 4.58040i) q^{81} -0.438141i q^{82} -8.73047i q^{83} +(7.02114 - 0.942833i) q^{84} +(7.55637 - 0.976288i) q^{85} -8.29665 q^{86} +(-1.30840 - 9.74344i) q^{87} -2.91858 q^{88} +13.2216 q^{89} +(-2.58423 - 6.19046i) q^{90} +11.6518i q^{91} +3.74121i q^{92} +(4.50430 - 8.52709i) q^{93} +7.81439 q^{94} +(-0.638213 - 4.93970i) q^{95} +(0.230519 + 1.71664i) q^{96} -3.32455i q^{97} +9.72844 q^{98} +(-8.44557 + 2.30988i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 + 32 * q^4 + 2 * q^5 - 32 * q^8 + 4 * q^9	\( 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9} - 2 q^{10} + 32 q^{16} - 4 q^{18} + 8 q^{19} + 2 q^{20} + 10 q^{25} - 12 q^{31} - 32 q^{32} - 8 q^{33} + 16 q^{35} + 4 q^{36} - 8 q^{38} - 4 q^{39} - 2 q^{40} + 10 q^{45} - 4 q^{47} - 36 q^{49} - 10 q^{50} - 4 q^{51} + 12 q^{62} - 24 q^{63} + 32 q^{64} + 8 q^{66} - 8 q^{69} - 16 q^{70} - 4 q^{72} + 8 q^{76} + 4 q^{78} + 2 q^{80} + 24 q^{81} - 4 q^{87} - 10 q^{90} + 24 q^{93} + 4 q^{94} - 26 q^{95} + 36 q^{98}+O(q^{100}) \) 32 * q - 32 * q^2 + 32 * q^4 + 2 * q^5 - 32 * q^8 + 4 * q^9 - 2 * q^10 + 32 * q^16 - 4 * q^18 + 8 * q^19 + 2 * q^20 + 10 * q^25 - 12 * q^31 - 32 * q^32 - 8 * q^33 + 16 * q^35 + 4 * q^36 - 8 * q^38 - 4 * q^39 - 2 * q^40 + 10 * q^45 - 4 * q^47 - 36 * q^49 - 10 * q^50 - 4 * q^51 + 12 * q^62 - 24 * q^63 + 32 * q^64 + 8 * q^66 - 8 * q^69 - 16 * q^70 - 4 * q^72 + 8 * q^76 + 4 * q^78 + 2 * q^80 + 24 * q^81 - 4 * q^87 - 10 * q^90 + 24 * q^93 + 4 * q^94 - 26 * q^95 + 36 * q^98

Introduction

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