LMFDB - Embedded newform 165.2.c.b.34.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.c (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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.2
Root			$0.403032 - 0.403032i$ of defining polynomial
Character	$\chi$	$=$	165.34
Dual form			165.2.c.b.34.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.48119i q^{2} -1.00000i q^{3} -0.193937 q^{4} +(-1.48119 - 1.67513i) q^{5} -1.48119 q^{6} +1.19394i q^{7} -2.67513i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.48119i q^{2} -1.00000i q^{3} -0.193937 q^{4} +(-1.48119 - 1.67513i) q^{5} -1.48119 q^{6} +1.19394i q^{7} -2.67513i q^{8} -1.00000 q^{9} +(-2.48119 + 2.19394i) q^{10} +1.00000 q^{11} +0.193937i q^{12} -0.806063i q^{13} +1.76845 q^{14} +(-1.67513 + 1.48119i) q^{15} -4.35026 q^{16} +3.76845i q^{17} +1.48119i q^{18} +5.35026 q^{19} +(0.287258 + 0.324869i) q^{20} +1.19394 q^{21} -1.48119i q^{22} -4.00000i q^{23} -2.67513 q^{24} +(-0.612127 + 4.96239i) q^{25} -1.19394 q^{26} +1.00000i q^{27} -0.231548i q^{28} +4.31265 q^{29} +(2.19394 + 2.48119i) q^{30} +0.962389 q^{31} +1.09332i q^{32} -1.00000i q^{33} +5.58181 q^{34} +(2.00000 - 1.76845i) q^{35} +0.193937 q^{36} +1.61213i q^{37} -7.92478i q^{38} -0.806063 q^{39} +(-4.48119 + 3.96239i) q^{40} +9.08840 q^{41} -1.76845i q^{42} -4.41819i q^{43} -0.193937 q^{44} +(1.48119 + 1.67513i) q^{45} -5.92478 q^{46} +12.3127i q^{47} +4.35026i q^{48} +5.57452 q^{49} +(7.35026 + 0.906679i) q^{50} +3.76845 q^{51} +0.156325i q^{52} -1.42548i q^{53} +1.48119 q^{54} +(-1.48119 - 1.67513i) q^{55} +3.19394 q^{56} -5.35026i q^{57} -6.38787i q^{58} -13.2750 q^{59} +(0.324869 - 0.287258i) q^{60} -0.0752228 q^{61} -1.42548i q^{62} -1.19394i q^{63} -7.08110 q^{64} +(-1.35026 + 1.19394i) q^{65} -1.48119 q^{66} -2.70052i q^{67} -0.730841i q^{68} -4.00000 q^{69} +(-2.61942 - 2.96239i) q^{70} -14.0508 q^{71} +2.67513i q^{72} +10.7308i q^{73} +2.38787 q^{74} +(4.96239 + 0.612127i) q^{75} -1.03761 q^{76} +1.19394i q^{77} +1.19394i q^{78} -13.9756 q^{79} +(6.44358 + 7.28726i) q^{80} +1.00000 q^{81} -13.4617i q^{82} +9.89446i q^{83} -0.231548 q^{84} +(6.31265 - 5.58181i) q^{85} -6.54420 q^{86} -4.31265i q^{87} -2.67513i q^{88} -16.8872 q^{89} +(2.48119 - 2.19394i) q^{90} +0.962389 q^{91} +0.775746i q^{92} -0.962389i q^{93} +18.2374 q^{94} +(-7.92478 - 8.96239i) q^{95} +1.09332 q^{96} +11.4763i q^{97} -8.25694i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^9	$ 6 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{9} - 4 q^{10} + 6 q^{11} - 12 q^{14} - 6 q^{16} + 12 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{24} - 2 q^{25} - 8 q^{26} - 16 q^{29} + 14 q^{30} - 16 q^{31} + 36 q^{34} + 12 q^{35} + 2 q^{36} - 4 q^{39} - 16 q^{40} + 16 q^{41} - 2 q^{44} - 2 q^{45} + 8 q^{46} + 10 q^{49} + 24 q^{50} - 2 q^{54} + 2 q^{55} + 20 q^{56} - 16 q^{59} + 12 q^{60} - 44 q^{61} + 22 q^{64} + 12 q^{65} + 2 q^{66} - 24 q^{69} - 40 q^{70} - 24 q^{71} + 16 q^{74} + 8 q^{75} - 28 q^{76} + 20 q^{79} + 6 q^{80} + 6 q^{81} - 24 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} + 4 q^{90} - 16 q^{91} + 24 q^{94} - 4 q^{95} - 6 q^{96} - 6 q^{99}+O(q^{100}) $ 6 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^9 - 4 * q^10 + 6 * q^11 - 12 * q^14 - 6 * q^16 + 12 * q^19 - 10 * q^20 + 8 * q^21 - 6 * q^24 - 2 * q^25 - 8 * q^26 - 16 * q^29 + 14 * q^30 - 16 * q^31 + 36 * q^34 + 12 * q^35 + 2 * q^36 - 4 * q^39 - 16 * q^40 + 16 * q^41 - 2 * q^44 - 2 * q^45 + 8 * q^46 + 10 * q^49 + 24 * q^50 - 2 * q^54 + 2 * q^55 + 20 * q^56 - 16 * q^59 + 12 * q^60 - 44 * q^61 + 22 * q^64 + 12 * q^65 + 2 * q^66 - 24 * q^69 - 40 * q^70 - 24 * q^71 + 16 * q^74 + 8 * q^75 - 28 * q^76 + 20 * q^79 + 6 * q^80 + 6 * q^81 - 24 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 + 4 * q^90 - 16 * q^91 + 24 * q^94 - 4 * q^95 - 6 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	1.48119i		−	1.04736i	−0.851914	−	0.523681i	$-0.824558\pi$
$2$		−	1.48119i		−	1.04736i	0.851914	−	0.523681i	$-0.175442\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−0.193937			−0.0969683
$5$	−1.48119	−	1.67513i	−0.662410	−	0.749141i
$5$	−1.48119	−	1.67513i	−0.662410	−	0.749141i
$6$	−1.48119			−0.604695
$7$			1.19394i			0.451266i	0.974212	+	0.225633i	$0.0724450\pi$
$7$			1.19394i			0.451266i	−0.974212	+	0.225633i	$0.927555\pi$
$8$		−	2.67513i		−	0.945802i
$9$	−1.00000			−0.333333
$10$	−2.48119	+	2.19394i	−0.784623	+	0.693784i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$			0.193937i			0.0559847i
$13$		−	0.806063i		−	0.223562i	−0.993733	−	0.111781i	$-0.964345\pi$
$13$		−	0.806063i		−	0.223562i	0.993733	−	0.111781i	$-0.0356555\pi$
$14$	1.76845			0.472639
$15$	−1.67513	+	1.48119i	−0.432517	+	0.382443i
$16$	−4.35026			−1.08757
$17$			3.76845i			0.913984i	0.889471	+	0.456992i	$0.151073\pi$
$17$			3.76845i			0.913984i	−0.889471	+	0.456992i	$0.848927\pi$
$18$			1.48119i			0.349121i
$19$	5.35026			1.22743			0.613717	−	0.789526i	$-0.289674\pi$
$19$	5.35026			1.22743			0.613717	+	0.789526i	$0.289674\pi$
$20$	0.287258	+	0.324869i	0.0642328	+	0.0726429i
$21$	1.19394			0.260538
$22$		−	1.48119i		−	0.315792i
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$	−2.67513			−0.546059
$25$	−0.612127	+	4.96239i	−0.122425	+	0.992478i
$26$	−1.19394			−0.234150
$27$			1.00000i			0.192450i
$28$		−	0.231548i		−	0.0437585i
$29$	4.31265			0.800839			0.400420	−	0.916332i	$-0.368864\pi$
$29$	4.31265			0.800839			0.400420	+	0.916332i	$0.368864\pi$
$30$	2.19394	+	2.48119i	0.400556	+	0.453002i
$31$	0.962389			0.172850			0.0864250	−	0.996258i	$-0.472456\pi$
$31$	0.962389			0.172850			0.0864250	+	0.996258i	$0.472456\pi$
$32$			1.09332i			0.193274i
$33$		−	1.00000i		−	0.174078i
$34$	5.58181			0.957272
$35$	2.00000	−	1.76845i	0.338062	−	0.298923i
$36$	0.193937			0.0323228
$37$			1.61213i			0.265032i	0.991181	+	0.132516i	$0.0423056\pi$
$37$			1.61213i			0.265032i	−0.991181	+	0.132516i	$0.957694\pi$
$38$		−	7.92478i		−	1.28557i
$39$	−0.806063			−0.129073
$40$	−4.48119	+	3.96239i	−0.708539	+	0.626509i
$41$	9.08840			1.41937			0.709685	−	0.704520i	$-0.248837\pi$
$41$	9.08840			1.41937			0.709685	+	0.704520i	$0.248837\pi$
$42$		−	1.76845i		−	0.272878i
$43$		−	4.41819i		−	0.673768i	−0.941546	−	0.336884i	$-0.890627\pi$
$43$		−	4.41819i		−	0.673768i	0.941546	−	0.336884i	$-0.109373\pi$
$44$	−0.193937			−0.0292370
$45$	1.48119	+	1.67513i	0.220803	+	0.249714i
$46$	−5.92478			−0.873561
$47$			12.3127i			1.79598i	0.440011	+	0.897992i	$0.354974\pi$
$47$			12.3127i			1.79598i	−0.440011	+	0.897992i	$0.645026\pi$
$48$			4.35026i			0.627906i
$49$	5.57452			0.796359
$50$	7.35026	+	0.906679i	1.03948	+	0.128224i
$51$	3.76845			0.527689
$52$			0.156325i			0.0216784i
$53$		−	1.42548i		−	0.195805i	−0.995196	−	0.0979027i	$-0.968787\pi$
$53$		−	1.42548i		−	0.195805i	0.995196	−	0.0979027i	$-0.0312134\pi$
$54$	1.48119			0.201565
$55$	−1.48119	−	1.67513i	−0.199724	−	0.225875i
$56$	3.19394			0.426808
$57$		−	5.35026i		−	0.708659i
$58$		−	6.38787i		−	0.838769i
$59$	−13.2750			−1.72826			−0.864131	−	0.503266i	$-0.832132\pi$
$59$	−13.2750			−1.72826			−0.864131	+	0.503266i	$0.832132\pi$
$60$	0.324869	−	0.287258i	0.0419404	−	0.0370848i
$61$	−0.0752228			−0.00963129			−0.00481565	−	0.999988i	$-0.501533\pi$
$61$	−0.0752228			−0.00963129			−0.00481565	+	0.999988i	$0.501533\pi$
$62$		−	1.42548i		−	0.181037i
$63$		−	1.19394i		−	0.150422i
$64$	−7.08110			−0.885138
$65$	−1.35026	+	1.19394i	−0.167479	+	0.148090i
$66$	−1.48119			−0.182322
$67$		−	2.70052i		−	0.329921i	−0.986300	−	0.164961i	$-0.947250\pi$
$67$		−	2.70052i		−	0.329921i	0.986300	−	0.164961i	$-0.0527497\pi$
$68$		−	0.730841i		−	0.0886274i
$69$	−4.00000			−0.481543
$70$	−2.61942	−	2.96239i	−0.313081	−	0.354073i
$71$	−14.0508			−1.66752			−0.833761	−	0.552126i	$-0.813817\pi$
$71$	−14.0508			−1.66752			−0.833761	+	0.552126i	$0.813817\pi$
$72$			2.67513i			0.315267i
$73$			10.7308i			1.25595i	0.778234	+	0.627975i	$0.216116\pi$
$73$			10.7308i			1.25595i	−0.778234	+	0.627975i	$0.783884\pi$
$74$	2.38787			0.277585
$75$	4.96239	+	0.612127i	0.573007	+	0.0706823i
$76$	−1.03761			−0.119022
$77$			1.19394i			0.136062i
$78$			1.19394i			0.135187i
$79$	−13.9756			−1.57237			−0.786187	−	0.617989i	$-0.787948\pi$
$79$	−13.9756			−1.57237			−0.786187	+	0.617989i	$0.787948\pi$
$80$	6.44358	+	7.28726i	0.720414	+	0.814740i
$81$	1.00000			0.111111
$82$		−	13.4617i		−	1.48659i
$83$			9.89446i			1.08606i	0.839714	+	0.543029i	$0.182723\pi$
$83$			9.89446i			1.08606i	−0.839714	+	0.543029i	$0.817277\pi$
$84$	−0.231548			−0.0252640
$85$	6.31265	−	5.58181i	0.684703	−	0.605432i
$86$	−6.54420			−0.705679
$87$		−	4.31265i		−	0.462365i
$88$		−	2.67513i		−	0.285170i
$89$	−16.8872			−1.79004			−0.895018	−	0.446030i	$-0.852837\pi$
$89$	−16.8872			−1.79004			−0.895018	+	0.446030i	$0.852837\pi$
$90$	2.48119	−	2.19394i	0.261541	−	0.231261i
$91$	0.962389			0.100886
$92$			0.775746i			0.0808771i
$93$		−	0.962389i		−	0.0997950i
$94$	18.2374			1.88105
$95$	−7.92478	−	8.96239i	−0.813065	−	0.919522i
$96$	1.09332			0.111587
$97$			11.4763i			1.16524i	0.812745	+	0.582619i	$0.197972\pi$
$97$			11.4763i			1.16524i	−0.812745	+	0.582619i	$0.802028\pi$
$98$		−	8.25694i		−	0.834077i
$99$	−1.00000			−0.100504
$100$	0.118714	−	0.962389i	0.0118714	−	0.0962389i
$101$	10.7612			1.07078			0.535388	−	0.844606i	$-0.320166\pi$
$101$	10.7612			1.07078			0.535388	+	0.844606i	$0.320166\pi$
$102$		−	5.58181i		−	0.552682i
$103$		−	16.9380i		−	1.66895i	−0.551049	−	0.834473i	$-0.685772\pi$
$103$		−	16.9380i		−	1.66895i	0.551049	−	0.834473i	$-0.314228\pi$
$104$	−2.15633			−0.211445
$105$	−1.76845	−	2.00000i	−0.172583	−	0.195180i
$106$	−2.11142			−0.205079
$107$			8.28233i			0.800683i	0.916366	+	0.400342i	$0.131109\pi$
$107$			8.28233i			0.800683i	−0.916366	+	0.400342i	$0.868891\pi$
$108$		−	0.193937i		−	0.0186616i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$	−2.48119	+	2.19394i	−0.236573	+	0.209184i
$111$	1.61213			0.153016
$112$		−	5.19394i		−	0.490781i
$113$		−	2.26187i		−	0.212778i	−0.994325	−	0.106389i	$-0.966071\pi$
$113$		−	2.26187i		−	0.212778i	0.994325	−	0.106389i	$-0.0339289\pi$
$114$	−7.92478			−0.742223
$115$	−6.70052	+	5.92478i	−0.624827	+	0.552488i
$116$	−0.836381			−0.0776560
$117$			0.806063i			0.0745206i
$118$			19.6629i			1.81012i
$119$	−4.49929			−0.412449
$120$	3.96239	+	4.48119i	0.361715	+	0.409075i
$121$	1.00000			0.0909091
$122$			0.111420i			0.0100875i
$123$		−	9.08840i		−	0.819473i
$124$	−0.186642			−0.0167610
$125$	9.21933	−	6.32487i	0.824602	−	0.565713i
$126$	−1.76845			−0.157546
$127$		−	13.8192i		−	1.22626i	−0.789982	−	0.613130i	$-0.789910\pi$
$127$		−	13.8192i		−	1.22626i	0.789982	−	0.613130i	$-0.210090\pi$
$128$			12.6751i			1.12033i
$129$	−4.41819			−0.389000
$130$	1.76845	+	2.00000i	0.155104	+	0.175412i
$131$	−5.92478			−0.517650			−0.258825	−	0.965924i	$-0.583335\pi$
$131$	−5.92478			−0.517650			−0.258825	+	0.965924i	$0.583335\pi$
$132$			0.193937i			0.0168800i
$133$			6.38787i			0.553899i
$134$	−4.00000			−0.345547
$135$	1.67513	−	1.48119i	0.144172	−	0.127481i
$136$	10.0811			0.864447
$137$			3.35026i			0.286232i	0.989706	+	0.143116i	$0.0457122\pi$
$137$			3.35026i			0.286232i	−0.989706	+	0.143116i	$0.954288\pi$
$138$			5.92478i			0.504351i
$139$	21.1998			1.79814			0.899072	−	0.437800i	$-0.144242\pi$
$139$	21.1998			1.79814			0.899072	+	0.437800i	$0.144242\pi$
$140$	−0.387873	+	0.342968i	−0.0327813	+	0.0289860i
$141$	12.3127			1.03691
$142$			20.8119i			1.74650i
$143$		−	0.806063i		−	0.0674064i
$144$	4.35026			0.362522
$145$	−6.38787	−	7.22425i	−0.530484	−	0.599942i
$146$	15.8945			1.31543
$147$		−	5.57452i		−	0.459778i
$148$		−	0.312650i		−	0.0256997i
$149$	−6.38787			−0.523315			−0.261657	−	0.965161i	$-0.584269\pi$
$149$	−6.38787			−0.523315			−0.261657	+	0.965161i	$0.584269\pi$
$150$	0.906679	−	7.35026i	0.0740300	−	0.600146i
$151$	−2.64974			−0.215633			−0.107816	−	0.994171i	$-0.534386\pi$
$151$	−2.64974			−0.215633			−0.107816	+	0.994171i	$0.534386\pi$
$152$		−	14.3127i		−	1.16091i
$153$		−	3.76845i		−	0.304661i
$154$	1.76845			0.142506
$155$	−1.42548	−	1.61213i	−0.114498	−	0.129489i
$156$	0.156325			0.0125160
$157$			1.61213i			0.128662i	0.997929	+	0.0643309i	$0.0204913\pi$
$157$			1.61213i			0.128662i	−0.997929	+	0.0643309i	$0.979509\pi$
$158$			20.7005i			1.64685i
$159$	−1.42548			−0.113048
$160$	1.83146	−	1.61942i	0.144789	−	0.128026i
$161$	4.77575			0.376382
$162$		−	1.48119i		−	0.116374i
$163$			0.312650i			0.0244887i	0.999925	+	0.0122443i	$0.00389759\pi$
$163$			0.312650i			0.0244887i	−0.999925	+	0.0122443i	$0.996102\pi$
$164$	−1.76257			−0.137634
$165$	−1.67513	+	1.48119i	−0.130409	+	0.115311i
$166$	14.6556			1.13750
$167$			0.493413i			0.0381815i	0.999818	+	0.0190907i	$0.00607714\pi$
$167$			0.493413i			0.0381815i	−0.999818	+	0.0190907i	$0.993923\pi$
$168$		−	3.19394i		−	0.246418i
$169$	12.3503			0.950020
$170$	−8.26774	−	9.35026i	−0.634107	−	0.717132i
$171$	−5.35026			−0.409145
$172$			0.856849i			0.0653341i
$173$			23.3054i			1.77187i	0.463806	+	0.885937i	$0.346483\pi$
$173$			23.3054i			1.77187i	−0.463806	+	0.885937i	$0.653517\pi$
$174$	−6.38787			−0.484263
$175$	−5.92478	−	0.730841i	−0.447871	−	0.0552464i
$176$	−4.35026			−0.327913
$177$			13.2750i			0.997813i
$178$			25.0132i			1.87482i
$179$	10.7005			0.799795			0.399897	−	0.916560i	$-0.369046\pi$
$179$	10.7005			0.799795			0.399897	+	0.916560i	$0.369046\pi$
$180$	−0.287258	−	0.324869i	−0.0214109	−	0.0242143i
$181$	−7.79877			−0.579678			−0.289839	−	0.957075i	$-0.593602\pi$
$181$	−7.79877			−0.579678			−0.289839	+	0.957075i	$0.593602\pi$
$182$		−	1.42548i		−	0.105664i
$183$			0.0752228i			0.00556063i
$184$	−10.7005			−0.788853
$185$	2.70052	−	2.38787i	0.198546	−	0.175560i
$186$	−1.42548			−0.104522
$187$			3.76845i			0.275577i
$188$		−	2.38787i		−	0.174154i
$189$	−1.19394			−0.0868461
$190$	−13.2750	+	11.7381i	−0.963073	+	0.851574i
$191$	1.29948			0.0940268			0.0470134	−	0.998894i	$-0.485030\pi$
$191$	1.29948			0.0940268			0.0470134	+	0.998894i	$0.485030\pi$
$192$			7.08110i			0.511035i
$193$		−	8.59498i		−	0.618680i	−0.950951	−	0.309340i	$-0.899892\pi$
$193$		−	8.59498i		−	0.618680i	0.950951	−	0.309340i	$-0.100108\pi$
$194$	16.9986			1.22043
$195$	1.19394	+	1.35026i	0.0854996	+	0.0966943i
$196$	−1.08110			−0.0772216
$197$		−	20.7064i		−	1.47527i	−0.675200	−	0.737635i	$-0.735943\pi$
$197$		−	20.7064i		−	1.47527i	0.675200	−	0.737635i	$-0.264057\pi$
$198$			1.48119i			0.105264i
$199$	−5.55149			−0.393535			−0.196767	−	0.980450i	$-0.563044\pi$
$199$	−5.55149			−0.393535			−0.196767	+	0.980450i	$0.563044\pi$
$200$	13.2750	+	1.63752i	0.938687	+	0.115790i
$201$	−2.70052			−0.190480
$202$		−	15.9394i		−	1.12149i
$203$			5.14903i			0.361391i
$204$	−0.730841			−0.0511691
$205$	−13.4617	−	15.2243i	−0.940205	−	1.06331i
$206$	−25.0884			−1.74799
$207$			4.00000i			0.278019i
$208$			3.50659i			0.243138i
$209$	5.35026			0.370085
$210$	−2.96239	+	2.61942i	−0.204424	+	0.180757i
$211$	−18.4993			−1.27354			−0.636772	−	0.771052i	$-0.719731\pi$
$211$	−18.4993			−1.27354			−0.636772	+	0.771052i	$0.719731\pi$
$212$			0.276454i			0.0189869i
$213$			14.0508i			0.962744i
$214$	12.2677			0.838606
$215$	−7.40105	+	6.54420i	−0.504747	+	0.446311i
$216$	2.67513			0.182020
$217$			1.14903i			0.0780013i
$218$		−	14.8119i		−	1.00319i
$219$	10.7308			0.725123
$220$	0.287258	+	0.324869i	0.0193669	+	0.0219027i
$221$	3.03761			0.204332
$222$		−	2.38787i		−	0.160264i
$223$		−	17.6121i		−	1.17940i	−0.807624	−	0.589698i	$-0.799247\pi$
$223$		−	17.6121i		−	1.17940i	0.807624	−	0.589698i	$-0.200753\pi$
$224$	−1.30536			−0.0872178
$225$	0.612127	−	4.96239i	0.0408085	−	0.330826i
$226$	−3.35026			−0.222856
$227$		−	17.4314i		−	1.15696i	−0.815696	−	0.578480i	$-0.803646\pi$
$227$		−	17.4314i		−	1.15696i	0.815696	−	0.578480i	$-0.196354\pi$
$228$			1.03761i			0.0687175i
$229$	−13.0738			−0.863942			−0.431971	−	0.901888i	$-0.642182\pi$
$229$	−13.0738			−0.863942			−0.431971	+	0.901888i	$0.642182\pi$
$230$	8.77575	+	9.92478i	0.578656	+	0.654420i
$231$	1.19394			0.0785553
$232$		−	11.5369i		−	0.757435i
$233$			13.8437i			0.906929i	0.891274	+	0.453465i	$0.149812\pi$
$233$			13.8437i			0.906929i	−0.891274	+	0.453465i	$0.850188\pi$
$234$	1.19394			0.0780501
$235$	20.6253	−	18.2374i	1.34545	−	1.18968i
$236$	2.57452			0.167587
$237$			13.9756i			0.907810i
$238$			6.66433i			0.431984i
$239$	12.3733			0.800361			0.400181	−	0.916436i	$-0.368947\pi$
$239$	12.3733			0.800361			0.400181	+	0.916436i	$0.368947\pi$
$240$	7.28726	−	6.44358i	0.470390	−	0.415931i
$241$	−24.5501			−1.58141			−0.790705	−	0.612198i	$-0.790286\pi$
$241$	−24.5501			−1.58141			−0.790705	+	0.612198i	$0.790286\pi$
$242$		−	1.48119i		−	0.0952148i
$243$		−	1.00000i		−	0.0641500i
$244$	0.0145884			0.000933930
$245$	−8.25694	−	9.33804i	−0.527517	−	0.596586i
$246$	−13.4617			−0.858285
$247$		−	4.31265i		−	0.274407i
$248$		−	2.57452i		−	0.163482i
$249$	9.89446			0.627036
$250$	−9.36836	−	13.6556i	−0.592507	−	0.863657i
$251$	13.9003			0.877382			0.438691	−	0.898638i	$-0.355442\pi$
$251$	13.9003			0.877382			0.438691	+	0.898638i	$0.355442\pi$
$252$			0.231548i			0.0145862i
$253$		−	4.00000i		−	0.251478i
$254$	−20.4690			−1.28434
$255$	−5.58181	−	6.31265i	−0.349546	−	0.395313i
$256$	4.61213			0.288258
$257$		−	18.8872i		−	1.17815i	−0.808079	−	0.589075i	$-0.799492\pi$
$257$		−	18.8872i		−	1.17815i	0.808079	−	0.589075i	$-0.200508\pi$
$258$			6.54420i			0.407424i
$259$	−1.92478			−0.119600
$260$	0.261865	−	0.231548i	0.0162402	−	0.0143600i
$261$	−4.31265			−0.266946
$262$			8.77575i			0.542167i
$263$		−	20.8061i		−	1.28296i	−0.767141	−	0.641478i	$-0.778321\pi$
$263$		−	20.8061i		−	1.28296i	0.767141	−	0.641478i	$-0.221679\pi$
$264$	−2.67513			−0.164643
$265$	−2.38787	+	2.11142i	−0.146686	+	0.129703i
$266$	9.46168			0.580133
$267$			16.8872i			1.03348i
$268$			0.523730i			0.0319919i
$269$	32.3996			1.97544			0.987720	−	0.156233i	$-0.0499351\pi$
$269$	32.3996			1.97544			0.987720	+	0.156233i	$0.0499351\pi$
$270$	−2.19394	−	2.48119i	−0.133519	−	0.151001i
$271$	−16.8265			−1.02214			−0.511069	−	0.859539i	$-0.670751\pi$
$271$	−16.8265			−1.02214			−0.511069	+	0.859539i	$0.670751\pi$
$272$		−	16.3938i		−	0.994017i
$273$		−	0.962389i		−	0.0582464i
$274$	4.96239			0.299789
$275$	−0.612127	+	4.96239i	−0.0369126	+	0.299243i
$276$	0.775746			0.0466944
$277$			16.9076i			1.01588i	0.861392	+	0.507941i	$0.169593\pi$
$277$			16.9076i			1.01588i	−0.861392	+	0.507941i	$0.830407\pi$
$278$		−	31.4010i		−	1.88331i
$279$	−0.962389			−0.0576167
$280$	−4.73084	−	5.35026i	−0.282722	−	0.319739i
$281$	5.61213			0.334791			0.167396	−	0.985890i	$-0.446464\pi$
$281$	5.61213			0.334791			0.167396	+	0.985890i	$0.446464\pi$
$282$		−	18.2374i		−	1.08602i
$283$		−	5.81924i		−	0.345918i	−0.984929	−	0.172959i	$-0.944667\pi$
$283$		−	5.81924i		−	0.345918i	0.984929	−	0.172959i	$-0.0553328\pi$
$284$	2.72496			0.161697
$285$	−8.96239	+	7.92478i	−0.530886	+	0.469423i
$286$	−1.19394			−0.0705989
$287$			10.8510i			0.640512i
$288$		−	1.09332i		−	0.0644246i
$289$	2.79877			0.164633
$290$	−10.7005	+	9.46168i	−0.628356	+	0.555609i
$291$	11.4763			0.672751
$292$		−	2.08110i		−	0.121787i
$293$			8.29218i			0.484434i	0.970222	+	0.242217i	$0.0778747\pi$
$293$			8.29218i			0.484434i	−0.970222	+	0.242217i	$0.922125\pi$
$294$	−8.25694			−0.481555
$295$	19.6629	+	22.2374i	1.14482	+	1.29471i
$296$	4.31265			0.250668
$297$			1.00000i			0.0580259i
$298$			9.46168i			0.548100i
$299$	−3.22425			−0.186463
$300$	−0.962389	−	0.118714i	−0.0555635	−	0.00685394i
$301$	5.27504			0.304048
$302$			3.92478i			0.225846i
$303$		−	10.7612i		−	0.618212i
$304$	−23.2750			−1.33492
$305$	0.111420	+	0.126008i	0.00637987	+	0.00721520i
$306$	−5.58181			−0.319091
$307$			25.6688i			1.46500i	0.680770	+	0.732498i	$0.261646\pi$
$307$			25.6688i			1.46500i	−0.680770	+	0.732498i	$0.738354\pi$
$308$		−	0.231548i		−	0.0131937i
$309$	−16.9380			−0.963566
$310$	−2.38787	+	2.11142i	−0.135622	+	0.119921i
$311$	−15.7235			−0.891601			−0.445800	−	0.895132i	$-0.647081\pi$
$311$	−15.7235			−0.891601			−0.445800	+	0.895132i	$0.647081\pi$
$312$			2.15633i			0.122078i
$313$			26.8627i			1.51837i	0.650874	+	0.759186i	$0.274403\pi$
$313$			26.8627i			1.51837i	−0.650874	+	0.759186i	$0.725597\pi$
$314$	2.38787			0.134755
$315$	−2.00000	+	1.76845i	−0.112687	+	0.0996410i
$316$	2.71037			0.152470
$317$			0.710373i			0.0398985i	0.999801	+	0.0199492i	$0.00635046\pi$
$317$			0.710373i			0.0398985i	−0.999801	+	0.0199492i	$0.993650\pi$
$318$			2.11142i			0.118403i
$319$	4.31265			0.241462
$320$	10.4885	+	11.8618i	0.586324	+	0.663093i
$321$	8.28233			0.462275
$322$		−	7.07381i		−	0.394208i
$323$			20.1622i			1.12186i
$324$	−0.193937			−0.0107743
$325$	4.00000	+	0.493413i	0.221880	+	0.0273696i
$326$	0.463096			0.0256485
$327$		−	10.0000i		−	0.553001i
$328$		−	24.3127i		−	1.34244i
$329$	−14.7005			−0.810466
$330$	2.19394	+	2.48119i	0.120772	+	0.136585i
$331$	0.962389			0.0528977			0.0264488	−	0.999650i	$-0.491580\pi$
$331$	0.962389			0.0528977			0.0264488	+	0.999650i	$0.491580\pi$
$332$		−	1.91890i		−	0.105313i
$333$		−	1.61213i		−	0.0883440i
$334$	0.730841			0.0399898
$335$	−4.52373	+	4.00000i	−0.247158	+	0.218543i
$336$	−5.19394			−0.283352
$337$			19.8192i			1.07962i	0.841786	+	0.539811i	$0.181504\pi$
$337$			19.8192i			1.07962i	−0.841786	+	0.539811i	$0.818496\pi$
$338$		−	18.2931i		−	0.995015i
$339$	−2.26187			−0.122848
$340$	−1.22425	+	1.08252i	−0.0663945	+	0.0587077i
$341$	0.962389			0.0521163
$342$			7.92478i			0.428523i
$343$			15.0132i			0.810635i
$344$	−11.8192			−0.637251
$345$	5.92478	+	6.70052i	0.318979	+	0.360744i
$346$	34.5198			1.85579
$347$			6.20711i			0.333215i	0.986023	+	0.166608i	$0.0532813\pi$
$347$			6.20711i			0.333215i	−0.986023	+	0.166608i	$0.946719\pi$
$348$			0.836381i			0.0448347i
$349$	−4.44851			−0.238123			−0.119062	−	0.992887i	$-0.537989\pi$
$349$	−4.44851			−0.238123			−0.119062	+	0.992887i	$0.537989\pi$
$350$	−1.08252	+	8.77575i	−0.0578630	+	0.469083i
$351$	0.806063			0.0430245
$352$			1.09332i			0.0582742i
$353$		−	6.57452i		−	0.349926i	−0.984575	−	0.174963i	$-0.944019\pi$
$353$		−	6.57452i		−	0.349926i	0.984575	−	0.174963i	$-0.0559806\pi$
$354$	19.6629			1.04507
$355$	20.8119	+	23.5369i	1.10458	+	1.24921i
$356$	3.27504			0.173577
$357$			4.49929i			0.238128i
$358$		−	15.8496i		−	0.837675i
$359$	−8.62530			−0.455226			−0.227613	−	0.973752i	$-0.573092\pi$
$359$	−8.62530			−0.455226			−0.227613	+	0.973752i	$0.573092\pi$
$360$	4.48119	−	3.96239i	0.236180	−	0.208836i
$361$	9.62530			0.506595
$362$			11.5515i			0.607133i
$363$		−	1.00000i		−	0.0524864i
$364$	−0.186642			−0.00978272
$365$	17.9756	−	15.8945i	0.940884	−	0.831954i
$366$	0.111420			0.00582399
$367$			23.0132i			1.20128i	0.799520	+	0.600639i	$0.205087\pi$
$367$			23.0132i			1.20128i	−0.799520	+	0.600639i	$0.794913\pi$
$368$			17.4010i			0.907092i
$369$	−9.08840			−0.473123
$370$	−3.53690	−	4.00000i	−0.183875	−	0.207950i
$371$	1.70194			0.0883602
$372$			0.186642i			0.00967695i
$373$		−	28.1925i		−	1.45975i	−0.683579	−	0.729877i	$-0.739577\pi$
$373$		−	28.1925i		−	1.45975i	0.683579	−	0.729877i	$-0.260423\pi$
$374$	5.58181			0.288629
$375$	−6.32487	−	9.21933i	−0.326615	−	0.476084i
$376$	32.9380			1.69865
$377$		−	3.47627i		−	0.179037i
$378$			1.76845i			0.0909594i
$379$	−3.74798			−0.192521			−0.0962605	−	0.995356i	$-0.530688\pi$
$379$	−3.74798			−0.192521			−0.0962605	+	0.995356i	$0.530688\pi$
$380$	1.53690	+	1.73813i	0.0788415	+	0.0891644i
$381$	−13.8192			−0.707981
$382$		−	1.92478i		−	0.0984802i
$383$		−	1.76257i		−	0.0900632i	−0.998986	−	0.0450316i	$-0.985661\pi$
$383$		−	1.76257i		−	0.0900632i	0.998986	−	0.0450316i	$-0.0143389\pi$
$384$	12.6751			0.646825
$385$	2.00000	−	1.76845i	0.101929	−	0.0901287i
$386$	−12.7308			−0.647983
$387$			4.41819i			0.224589i
$388$		−	2.22567i		−	0.112991i
$389$	−6.52373			−0.330766			−0.165383	−	0.986229i	$-0.552886\pi$
$389$	−6.52373			−0.330766			−0.165383	+	0.986229i	$0.552886\pi$
$390$	2.00000	−	1.76845i	0.101274	−	0.0895491i
$391$	15.0738			0.762315
$392$		−	14.9126i		−	0.753198i
$393$			5.92478i			0.298865i
$394$	−30.6702			−1.54514
$395$	20.7005	+	23.4109i	1.04156	+	1.17793i
$396$	0.193937			0.00974568
$397$		−	23.6991i		−	1.18942i	−0.803939	−	0.594712i	$-0.797266\pi$
$397$		−	23.6991i		−	1.18942i	0.803939	−	0.594712i	$-0.202734\pi$
$398$			8.22284i			0.412174i
$399$	6.38787			0.319794
$400$	2.66291	−	21.5877i	0.133146	−	1.07938i
$401$	8.88717			0.443804			0.221902	−	0.975069i	$-0.428774\pi$
$401$	8.88717			0.443804			0.221902	+	0.975069i	$0.428774\pi$
$402$			4.00000i			0.199502i
$403$		−	0.775746i		−	0.0386427i
$404$	−2.08698			−0.103831
$405$	−1.48119	−	1.67513i	−0.0736011	−	0.0832379i
$406$	7.62672			0.378508
$407$			1.61213i			0.0799102i
$408$		−	10.0811i		−	0.499089i
$409$	4.85097			0.239865			0.119932	−	0.992782i	$-0.461732\pi$
$409$	4.85097			0.239865			0.119932	+	0.992782i	$0.461732\pi$
$410$	−22.5501	+	19.9394i	−1.11367	+	0.984735i
$411$	3.35026			0.165256
$412$			3.28489i			0.161835i
$413$		−	15.8496i		−	0.779906i
$414$	5.92478			0.291187
$415$	16.5745	−	14.6556i	0.813611	−	0.719416i
$416$	0.881286			0.0432086
$417$		−	21.1998i		−	1.03816i
$418$		−	7.92478i		−	0.387614i
$419$	10.7005			0.522755			0.261377	−	0.965237i	$-0.415823\pi$
$419$	10.7005			0.522755			0.261377	+	0.965237i	$0.415823\pi$
$420$	0.342968	+	0.387873i	0.0167351	+	0.0189263i
$421$	−30.6009			−1.49139			−0.745697	−	0.666285i	$-0.767884\pi$
$421$	−30.6009			−1.49139			−0.745697	+	0.666285i	$0.767884\pi$
$422$			27.4010i			1.33386i
$423$		−	12.3127i		−	0.598662i
$424$	−3.81336			−0.185193
$425$	−18.7005	−	2.30677i	−0.907109	−	0.111895i
$426$	20.8119			1.00834
$427$		−	0.0898112i		−	0.00434627i
$428$		−	1.60625i		−	0.0776409i
$429$	−0.806063			−0.0389171
$430$	9.69323	+	10.9624i	0.467449	+	0.528653i
$431$	−5.92478			−0.285386			−0.142693	−	0.989767i	$-0.545576\pi$
$431$	−5.92478			−0.285386			−0.142693	+	0.989767i	$0.545576\pi$
$432$		−	4.35026i		−	0.209302i
$433$			16.0000i			0.768911i	0.923144	+	0.384455i	$0.125611\pi$
$433$			16.0000i			0.768911i	−0.923144	+	0.384455i	$0.874389\pi$
$434$	1.70194			0.0816956
$435$	−7.22425	+	6.38787i	−0.346376	+	0.306275i
$436$	−1.93937			−0.0928788
$437$		−	21.4010i		−	1.02375i
$438$		−	15.8945i		−	0.759467i
$439$	−5.35026			−0.255354			−0.127677	−	0.991816i	$-0.540752\pi$
$439$	−5.35026			−0.255354			−0.127677	+	0.991816i	$0.540752\pi$
$440$	−4.48119	+	3.96239i	−0.213633	+	0.188899i
$441$	−5.57452			−0.265453
$442$		−	4.49929i		−	0.214010i
$443$		−	19.6873i		−	0.935374i	−0.883894	−	0.467687i	$-0.845087\pi$
$443$		−	19.6873i		−	0.935374i	0.883894	−	0.467687i	$-0.154913\pi$
$444$	−0.312650			−0.0148377
$445$	25.0132	+	28.2882i	1.18574	+	1.34099i
$446$	−26.0870			−1.23525
$447$			6.38787i			0.302136i
$448$		−	8.45439i		−	0.399432i
$449$	31.3357			1.47882			0.739411	−	0.673254i	$-0.235104\pi$
$449$	31.3357			1.47882			0.739411	+	0.673254i	$0.235104\pi$
$450$	−7.35026	−	0.906679i	−0.346495	−	0.0427412i
$451$	9.08840			0.427956
$452$			0.438658i			0.0206328i
$453$			2.64974i			0.124496i
$454$	−25.8192			−1.21176
$455$	−1.42548	−	1.61213i	−0.0668277	−	0.0755777i
$456$	−14.3127			−0.670251
$457$		−	37.5936i		−	1.75855i	−0.476312	−	0.879276i	$-0.658027\pi$
$457$		−	37.5936i		−	1.75855i	0.476312	−	0.879276i	$-0.341973\pi$
$458$			19.3649i			0.904860i
$459$	−3.76845			−0.175896
$460$	1.29948	−	1.14903i	0.0605884	−	0.0535738i
$461$	17.9854			0.837664			0.418832	−	0.908064i	$-0.362440\pi$
$461$	17.9854			0.837664			0.418832	+	0.908064i	$0.362440\pi$
$462$		−	1.76845i		−	0.0822758i
$463$		−	39.0132i		−	1.81310i	−0.422103	−	0.906548i	$-0.638708\pi$
$463$		−	39.0132i		−	1.81310i	0.422103	−	0.906548i	$-0.361292\pi$
$464$	−18.7612			−0.870965
$465$	−1.61213	+	1.42548i	−0.0747606	+	0.0661053i
$466$	20.5052			0.949884
$467$			14.5501i			0.673297i	0.941630	+	0.336649i	$0.109293\pi$
$467$			14.5501i			0.673297i	−0.941630	+	0.336649i	$0.890707\pi$
$468$		−	0.156325i		−	0.00722613i
$469$	3.22425			0.148882
$470$	−27.0132	−	30.5501i	−1.24602	−	1.40917i
$471$	1.61213			0.0742829
$472$			35.5125i			1.63459i
$473$		−	4.41819i		−	0.203149i
$474$	20.7005			0.950807
$475$	−3.27504	+	26.5501i	−0.150269	+	1.21820i
$476$	0.872577			0.0399945
$477$			1.42548i			0.0652685i
$478$		−	18.3272i		−	0.838268i
$479$	−28.6253			−1.30792			−0.653962	−	0.756528i	$-0.726894\pi$
$479$	−28.6253			−1.30792			−0.653962	+	0.756528i	$0.726894\pi$
$480$	−1.61942	−	1.83146i	−0.0739161	−	0.0835941i
$481$	1.29948			0.0592510
$482$			36.3634i			1.65631i
$483$		−	4.77575i		−	0.217304i
$484$	−0.193937			−0.00881530
$485$	19.2243	−	16.9986i	0.872928	−	0.771866i
$486$	−1.48119			−0.0671883
$487$			1.44992i			0.0657022i	0.999460	+	0.0328511i	$0.0104587\pi$
$487$			1.44992i			0.0657022i	−0.999460	+	0.0328511i	$0.989541\pi$
$488$			0.201231i			0.00910929i
$489$	0.312650			0.0141385
$490$	−13.8315	+	12.2301i	−0.624841	+	0.552501i
$491$	−8.00000			−0.361035			−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000			−0.361035			−0.180517	+	0.983572i	$0.557777\pi$
$492$			1.76257i			0.0794629i
$493$			16.2520i			0.731954i
$494$	−6.38787			−0.287404
$495$	1.48119	+	1.67513i	0.0665747	+	0.0752915i
$496$	−4.18664			−0.187986
$497$		−	16.7757i		−	0.752495i
$498$		−	14.6556i		−	0.656734i
$499$	−30.7005			−1.37434			−0.687172	−	0.726495i	$-0.741148\pi$
$499$	−30.7005			−1.37434			−0.687172	+	0.726495i	$0.741148\pi$
$500$	−1.78797	+	1.22662i	−0.0799602	+	0.0548563i
$501$	0.493413			0.0220441
$502$		−	20.5891i		−	0.918937i
$503$			19.7586i			0.880993i	0.897754	+	0.440496i	$0.145198\pi$
$503$			19.7586i			0.880993i	−0.897754	+	0.440496i	$0.854802\pi$
$504$	−3.19394			−0.142269
$505$	−15.9394	−	18.0263i	−0.709292	−	0.802162i
$506$	−5.92478			−0.263388
$507$		−	12.3503i		−	0.548494i
$508$			2.68006i			0.118908i
$509$	−22.1016			−0.979635			−0.489817	−	0.871825i	$-0.662937\pi$
$509$	−22.1016			−0.979635			−0.489817	+	0.871825i	$0.662937\pi$
$510$	−9.35026	+	8.26774i	−0.414037	+	0.366102i
$511$	−12.8119			−0.566767
$512$			18.5188i			0.818423i
$513$			5.35026i			0.236220i
$514$	−27.9756			−1.23395
$515$	−28.3733	+	25.0884i	−1.25028	+	1.10553i
$516$	0.856849			0.0377207
$517$			12.3127i			0.541510i
$518$			2.85097i			0.125264i
$519$	23.3054			1.02299
$520$	3.19394	+	3.61213i	0.140063	+	0.158402i
$521$	−22.8119			−0.999409			−0.499705	−	0.866196i	$-0.666558\pi$
$521$	−22.8119			−0.999409			−0.499705	+	0.866196i	$0.666558\pi$
$522$			6.38787i			0.279590i
$523$			12.2677i			0.536431i	0.963359	+	0.268216i	$0.0864339\pi$
$523$			12.2677i			0.536431i	−0.963359	+	0.268216i	$0.913566\pi$
$524$	1.14903			0.0501957
$525$	−0.730841	+	5.92478i	−0.0318965	+	0.258578i
$526$	−30.8178			−1.34372
$527$			3.62672i			0.157982i
$528$			4.35026i			0.189321i
$529$	7.00000			0.304348
$530$	3.12742	+	3.53690i	0.135847	+	0.153633i
$531$	13.2750			0.576088
$532$		−	1.23884i		−	0.0537106i
$533$		−	7.32582i		−	0.317317i
$534$	25.0132			1.08243
$535$	13.8740	−	12.2677i	0.599825	−	0.530381i
$536$	−7.22425			−0.312040
$537$		−	10.7005i		−	0.461762i
$538$		−	47.9902i		−	2.06900i
$539$	5.57452			0.240111
$540$	−0.324869	+	0.287258i	−0.0139801	+	0.0123616i
$541$	−5.22425			−0.224608			−0.112304	−	0.993674i	$-0.535823\pi$
$541$	−5.22425			−0.224608			−0.112304	+	0.993674i	$0.535823\pi$
$542$			24.9234i			1.07055i
$543$			7.79877i			0.334677i
$544$	−4.12013			−0.176649
$545$	−14.8119	−	16.7513i	−0.634474	−	0.717547i
$546$	−1.42548			−0.0610051
$547$		−	17.9697i		−	0.768328i	−0.923265	−	0.384164i	$-0.874490\pi$
$547$		−	17.9697i		−	0.768328i	0.923265	−	0.384164i	$-0.125510\pi$
$548$		−	0.649738i		−	0.0277554i
$549$	0.0752228			0.00321043
$550$	7.35026	+	0.906679i	0.313416	+	0.0386609i
$551$	23.0738			0.982977
$552$			10.7005i			0.455445i
$553$		−	16.6859i		−	0.709558i
$554$	25.0435			1.06400
$555$	−2.38787	−	2.70052i	−0.101360	−	0.114631i
$556$	−4.11142			−0.174363
$557$			15.8700i			0.672434i	0.941784	+	0.336217i	$0.109148\pi$
$557$			15.8700i			0.672434i	−0.941784	+	0.336217i	$0.890852\pi$
$558$			1.42548i			0.0603456i
$559$	−3.56134			−0.150629
$560$	−8.70052	+	7.69323i	−0.367664	+	0.325098i
$561$	3.76845			0.159104
$562$		−	8.31265i		−	0.350648i
$563$		−	31.6688i		−	1.33468i	−0.744753	−	0.667340i	$-0.767433\pi$
$563$		−	31.6688i		−	1.33468i	0.744753	−	0.667340i	$-0.232567\pi$
$564$	−2.38787			−0.100548
$565$	−3.78892	+	3.35026i	−0.159401	+	0.140947i
$566$	−8.61942			−0.362301
$567$			1.19394i			0.0501406i
$568$			37.5877i			1.57714i
$569$	24.3127			1.01924			0.509620	−	0.860400i	$-0.329786\pi$
$569$	24.3127			1.01924			0.509620	+	0.860400i	$0.329786\pi$
$570$	11.7381	+	13.2750i	0.491656	+	0.556030i
$571$	8.05079			0.336915			0.168457	−	0.985709i	$-0.446121\pi$
$571$	8.05079			0.336915			0.168457	+	0.985709i	$0.446121\pi$
$572$			0.156325i			0.00653628i
$573$		−	1.29948i		−	0.0542864i
$574$	16.0724			0.670849
$575$	19.8496	+	2.44851i	0.827784	+	0.102110i
$576$	7.08110			0.295046
$577$		−	44.5355i		−	1.85404i	−0.375016	−	0.927018i	$-0.622363\pi$
$577$		−	44.5355i		−	1.85404i	0.375016	−	0.927018i	$-0.377637\pi$
$578$		−	4.14552i		−	0.172431i
$579$	−8.59498			−0.357195
$580$	1.23884	+	1.40105i	0.0514401	+	0.0581753i
$581$	−11.8134			−0.490101
$582$		−	16.9986i		−	0.704614i
$583$		−	1.42548i		−	0.0590375i
$584$	28.7064			1.18788
$585$	1.35026	−	1.19394i	0.0558265	−	0.0493632i
$586$	12.2823			0.507379
$587$		−	15.4763i		−	0.638774i	−0.947624	−	0.319387i	$-0.896523\pi$
$587$		−	15.4763i		−	0.638774i	0.947624	−	0.319387i	$-0.103477\pi$
$588$			1.08110i			0.0445839i
$589$	5.14903			0.212162
$590$	32.9380	−	29.1246i	1.35603	−	1.19904i
$591$	−20.7064			−0.851748
$592$		−	7.01317i		−	0.288240i
$593$			9.53102i			0.391392i	0.980665	+	0.195696i	$0.0626966\pi$
$593$			9.53102i			0.391392i	−0.980665	+	0.195696i	$0.937303\pi$
$594$	1.48119			0.0607741
$595$	6.66433	+	7.53690i	0.273211	+	0.308983i
$596$	1.23884			0.0507450
$597$			5.55149i			0.227207i
$598$			4.77575i			0.195295i
$599$	25.5515			1.04401			0.522003	−	0.852944i	$-0.325185\pi$
$599$	25.5515			1.04401			0.522003	+	0.852944i	$0.325185\pi$
$600$	1.63752	−	13.2750i	0.0668515	−	0.541951i
$601$	12.0263			0.490565			0.245282	−	0.969452i	$-0.421119\pi$
$601$	12.0263			0.490565			0.245282	+	0.969452i	$0.421119\pi$
$602$		−	7.81336i		−	0.318449i
$603$			2.70052i			0.109974i
$604$	0.513881			0.0209095
$605$	−1.48119	−	1.67513i	−0.0602191	−	0.0681038i
$606$	−15.9394			−0.647492
$607$		−	6.86670i		−	0.278711i	−0.990242	−	0.139355i	$-0.955497\pi$
$607$		−	6.86670i		−	0.278711i	0.990242	−	0.139355i	$-0.0445030\pi$
$608$			5.84955i			0.237231i
$609$	5.14903			0.208649
$610$	0.186642	−	0.165034i	0.00755693	−	0.00668203i
$611$	9.92478			0.401514
$612$			0.730841i			0.0295425i
$613$			7.25457i			0.293009i	0.989210	+	0.146505i	$0.0468023\pi$
$613$			7.25457i			0.293009i	−0.989210	+	0.146505i	$0.953198\pi$
$614$	38.0205			1.53438
$615$	−15.2243	+	13.4617i	−0.613901	+	0.542827i
$616$	3.19394			0.128687
$617$			38.3634i			1.54445i	0.635347	+	0.772227i	$0.280857\pi$
$617$			38.3634i			1.54445i	−0.635347	+	0.772227i	$0.719143\pi$
$618$			25.0884i			1.00920i
$619$	29.6893			1.19331			0.596656	−	0.802497i	$-0.296496\pi$
$619$	29.6893			1.19331			0.596656	+	0.802497i	$0.296496\pi$
$620$	0.276454	+	0.312650i	0.0111026	+	0.0125563i
$621$	4.00000			0.160514
$622$			23.2896i			0.933829i
$623$		−	20.1622i		−	0.807782i
$624$	3.50659			0.140376
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$	39.7889			1.59029
$627$		−	5.35026i		−	0.213669i
$628$		−	0.312650i		−	0.0124761i
$629$	−6.07522			−0.242235
$630$	2.61942	+	2.96239i	0.104360	+	0.118024i
$631$	−19.6991			−0.784209			−0.392105	−	0.919921i	$-0.628253\pi$
$631$	−19.6991			−0.784209			−0.392105	+	0.919921i	$0.628253\pi$
$632$			37.3865i			1.48715i
$633$			18.4993i			0.735281i
$634$	1.05220			0.0417882
$635$	−23.1490	+	20.4690i	−0.918641	+	0.812287i
$636$	0.276454			0.0109621
$637$		−	4.49341i		−	0.178036i
$638$		−	6.38787i		−	0.252898i
$639$	14.0508			0.555840
$640$	21.2325	−	18.7743i	0.839288	−	0.742121i
$641$	−31.4372			−1.24170			−0.620848	−	0.783931i	$-0.713212\pi$
$641$	−31.4372			−1.24170			−0.620848	+	0.783931i	$0.713212\pi$
$642$		−	12.2677i		−	0.484169i
$643$			34.4894i			1.36013i	0.733151	+	0.680065i	$0.238049\pi$
$643$			34.4894i			1.36013i	−0.733151	+	0.680065i	$0.761951\pi$
$644$	−0.926192			−0.0364971
$645$	6.54420	+	7.40105i	0.257678	+	0.291416i
$646$	29.8641			1.17499
$647$		−	5.61213i		−	0.220635i	−0.993896	−	0.110318i	$-0.964813\pi$
$647$		−	5.61213i		−	0.220635i	0.993896	−	0.110318i	$-0.0351868\pi$
$648$		−	2.67513i		−	0.105089i
$649$	−13.2750			−0.521091
$650$	0.730841	−	5.92478i	0.0286659	−	0.232389i
$651$	1.14903			0.0450341
$652$		−	0.0606343i		−	0.00237462i
$653$		−	4.06537i		−	0.159090i	−0.996831	−	0.0795452i	$-0.974653\pi$
$653$		−	4.06537i		−	0.159090i	0.996831	−	0.0795452i	$-0.0253468\pi$
$654$	−14.8119			−0.579193
$655$	8.77575	+	9.92478i	0.342897	+	0.387793i
$656$	−39.5369			−1.54366
$657$		−	10.7308i		−	0.418650i
$658$			21.7743i			0.848852i
$659$	−11.3747			−0.443095			−0.221548	−	0.975150i	$-0.571111\pi$
$659$	−11.3747			−0.443095			−0.221548	+	0.975150i	$0.571111\pi$
$660$	0.324869	−	0.287258i	0.0126455	−	0.0111815i
$661$	−42.4749			−1.65208			−0.826040	−	0.563611i	$-0.809412\pi$
$661$	−42.4749			−1.65208			−0.826040	+	0.563611i	$0.809412\pi$
$662$		−	1.42548i		−	0.0554030i
$663$		−	3.03761i		−	0.117971i
$664$	26.4690			1.02720
$665$	10.7005	−	9.46168i	0.414949	−	0.366908i
$666$	−2.38787			−0.0925282
$667$		−	17.2506i		−	0.667946i
$668$		−	0.0956908i		−	0.00370239i
$669$	−17.6121			−0.680924
$670$	5.92478	+	6.70052i	0.228894	+	0.258864i
$671$	−0.0752228			−0.00290394
$672$			1.30536i			0.0503552i
$673$			14.8813i			0.573631i	0.957986	+	0.286816i	$0.0925967\pi$
$673$			14.8813i			0.573631i	−0.957986	+	0.286816i	$0.907403\pi$
$674$	29.3561			1.13076
$675$	−4.96239	−	0.612127i	−0.191002	−	0.0235608i
$676$	−2.39517			−0.0921218
$677$		−	27.7685i		−	1.06723i	−0.845728	−	0.533614i	$-0.820833\pi$
$677$		−	27.7685i		−	1.06723i	0.845728	−	0.533614i	$-0.179167\pi$
$678$			3.35026i			0.128666i
$679$	−13.7019			−0.525832
$680$	−14.9321	−	16.8872i	−0.572619	−	0.647593i
$681$	−17.4314			−0.667971
$682$		−	1.42548i		−	0.0545846i
$683$			25.4617i			0.974264i	0.873328	+	0.487132i	$0.161957\pi$
$683$			25.4617i			0.974264i	−0.873328	+	0.487132i	$0.838043\pi$
$684$	1.03761			0.0396741
$685$	5.61213	−	4.96239i	0.214428	−	0.189603i
$686$	22.2374			0.849029
$687$			13.0738i			0.498797i
$688$			19.2203i			0.732766i
$689$	−1.14903			−0.0437746
$690$	9.92478	−	8.77575i	0.377830	−	0.334087i
$691$	43.6991			1.66239			0.831196	−	0.555979i	$-0.187657\pi$
$691$	43.6991			1.66239			0.831196	+	0.555979i	$0.187657\pi$
$692$		−	4.51976i		−	0.171816i
$693$		−	1.19394i		−	0.0453539i
$694$	9.19394			0.348997
$695$	−31.4010	−	35.5125i	−1.19111	−	1.34706i
$696$	−11.5369			−0.437305
$697$			34.2492i			1.29728i
$698$			6.58910i			0.249401i
$699$	13.8437			0.523616
$700$	1.14903	+	0.141737i	0.0434293	+	0.00535714i
$701$	7.01317			0.264884			0.132442	−	0.991191i	$-0.457718\pi$
$701$	7.01317			0.264884			0.132442	+	0.991191i	$0.457718\pi$
$702$		−	1.19394i		−	0.0450622i
$703$			8.62530i			0.325309i
$704$	−7.08110			−0.266879
$705$	−18.2374	−	20.6253i	−0.686861	−	0.776794i
$706$	−9.73813			−0.366500
$707$			12.8481i			0.483204i
$708$		−	2.57452i		−	0.0967562i
$709$	−45.6747			−1.71535			−0.857674	−	0.514194i	$-0.828091\pi$
$709$	−45.6747			−1.71535			−0.857674	+	0.514194i	$0.828091\pi$
$710$	34.8627	−	30.8265i	1.30837	−	1.15690i
$711$	13.9756			0.524125
$712$			45.1754i			1.69302i
$713$		−	3.84955i		−	0.144167i
$714$	6.66433			0.249406
$715$	−1.35026	+	1.19394i	−0.0504969	+	0.0446507i
$716$	−2.07522			−0.0775547
$717$		−	12.3733i		−	0.462089i
$718$			12.7757i			0.476787i
$719$	−16.2520			−0.606098			−0.303049	−	0.952975i	$-0.598005\pi$
$719$	−16.2520			−0.606098			−0.303049	+	0.952975i	$0.598005\pi$
$720$	−6.44358	−	7.28726i	−0.240138	−	0.271580i
$721$	20.2228			0.753138
$722$		−	14.2569i		−	0.530588i
$723$			24.5501i			0.913027i
$724$	1.51247			0.0562104
$725$	−2.63989	+	21.4010i	−0.0980430	+	0.794815i
$726$	−1.48119			−0.0549723
$727$			15.2243i			0.564636i	0.959321	+	0.282318i	$0.0911034\pi$
$727$			15.2243i			0.564636i	−0.959321	+	0.282318i	$0.908897\pi$
$728$		−	2.57452i		−	0.0954179i
$729$	−1.00000			−0.0370370
$730$	−23.5428	−	26.6253i	−0.871358	−	0.985447i
$731$	16.6497			0.615813
$732$		−	0.0145884i		−	0.000539205i
$733$			43.5066i			1.60695i	0.595337	+	0.803476i	$0.297019\pi$
$733$			43.5066i			1.60695i	−0.595337	+	0.803476i	$0.702981\pi$
$734$	34.0870			1.25817
$735$	−9.33804	+	8.25694i	−0.344439	+	0.304562i
$736$	4.37328			0.161201
$737$		−	2.70052i		−	0.0994751i
$738$			13.4617i			0.495531i
$739$	7.02302			0.258346			0.129173	−	0.991622i	$-0.458768\pi$
$739$	7.02302			0.258346			0.129173	+	0.991622i	$0.458768\pi$
$740$	−0.523730	+	0.463096i	−0.0192527	+	0.0170237i
$741$	−4.31265			−0.158429
$742$		−	2.52090i		−	0.0925452i
$743$			2.94192i			0.107929i	0.998543	+	0.0539643i	$0.0171857\pi$
$743$			2.94192i			0.107929i	−0.998543	+	0.0539643i	$0.982814\pi$
$744$	−2.57452			−0.0943863
$745$	9.46168	+	10.7005i	0.346649	+	0.392037i
$746$	−41.7586			−1.52889
$747$		−	9.89446i		−	0.362019i
$748$		−	0.730841i		−	0.0267222i
$749$	−9.88858			−0.361321
$750$	−13.6556	+	9.36836i	−0.498633	+	0.342084i
$751$	24.1016			0.879479			0.439739	−	0.898125i	$-0.355071\pi$
$751$	24.1016			0.879479			0.439739	+	0.898125i	$0.355071\pi$
$752$		−	53.5633i		−	1.95325i
$753$		−	13.9003i		−	0.506557i
$754$	−5.14903			−0.187517
$755$	3.92478	+	4.43866i	0.142837	+	0.161539i
$756$	0.231548			0.00842132
$757$		−	16.3127i		−	0.592893i	−0.955049	−	0.296447i	$-0.904198\pi$
$757$		−	16.3127i		−	0.592893i	0.955049	−	0.296447i	$-0.0958017\pi$
$758$			5.55149i			0.201639i
$759$	−4.00000			−0.145191
$760$	−23.9756	+	21.1998i	−0.869685	+	0.768998i
$761$	−5.08840			−0.184454			−0.0922271	−	0.995738i	$-0.529399\pi$
$761$	−5.08840			−0.184454			−0.0922271	+	0.995738i	$0.529399\pi$
$762$			20.4690i			0.741513i
$763$			11.9394i			0.432234i
$764$	−0.252016			−0.00911762
$765$	−6.31265	+	5.58181i	−0.228234	+	0.201811i
$766$	−2.61071			−0.0943289
$767$			10.7005i			0.386374i
$768$		−	4.61213i		−	0.166426i
$769$	−2.10157			−0.0757846			−0.0378923	−	0.999282i	$-0.512064\pi$
$769$	−2.10157			−0.0757846			−0.0378923	+	0.999282i	$0.512064\pi$
$770$	−2.61942	−	2.96239i	−0.0943974	−	0.106757i
$771$	−18.8872			−0.680205
$772$			1.66688i			0.0599924i
$773$		−	46.0625i		−	1.65675i	−0.560171	−	0.828377i	$-0.689264\pi$
$773$		−	46.0625i		−	1.65675i	0.560171	−	0.828377i	$-0.310736\pi$
$774$	6.54420			0.235226
$775$	−0.589104	+	4.77575i	−0.0211612	+	0.171550i
$776$	30.7005			1.10208
$777$			1.92478i			0.0690510i
$778$			9.66291i			0.346432i
$779$	48.6253			1.74218
$780$	−0.231548	−	0.261865i	−0.00829075	−	0.00937628i
$781$	−14.0508			−0.502777
$782$

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.48119i q^{2} -1.00000i q^{3} -0.193937 q^{4} +(-1.48119 - 1.67513i) q^{5} -1.48119 q^{6} +1.19394i q^{7} -2.67513i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.48119i q^{2} -1.00000i q^{3} -0.193937 q^{4} +(-1.48119 - 1.67513i) q^{5} -1.48119 q^{6} +1.19394i q^{7} -2.67513i q^{8} -1.00000 q^{9} +(-2.48119 + 2.19394i) q^{10} +1.00000 q^{11} +0.193937i q^{12} -0.806063i q^{13} +1.76845 q^{14} +(-1.67513 + 1.48119i) q^{15} -4.35026 q^{16} +3.76845i q^{17} +1.48119i q^{18} +5.35026 q^{19} +(0.287258 + 0.324869i) q^{20} +1.19394 q^{21} -1.48119i q^{22} -4.00000i q^{23} -2.67513 q^{24} +(-0.612127 + 4.96239i) q^{25} -1.19394 q^{26} +1.00000i q^{27} -0.231548i q^{28} +4.31265 q^{29} +(2.19394 + 2.48119i) q^{30} +0.962389 q^{31} +1.09332i q^{32} -1.00000i q^{33} +5.58181 q^{34} +(2.00000 - 1.76845i) q^{35} +0.193937 q^{36} +1.61213i q^{37} -7.92478i q^{38} -0.806063 q^{39} +(-4.48119 + 3.96239i) q^{40} +9.08840 q^{41} -1.76845i q^{42} -4.41819i q^{43} -0.193937 q^{44} +(1.48119 + 1.67513i) q^{45} -5.92478 q^{46} +12.3127i q^{47} +4.35026i q^{48} +5.57452 q^{49} +(7.35026 + 0.906679i) q^{50} +3.76845 q^{51} +0.156325i q^{52} -1.42548i q^{53} +1.48119 q^{54} +(-1.48119 - 1.67513i) q^{55} +3.19394 q^{56} -5.35026i q^{57} -6.38787i q^{58} -13.2750 q^{59} +(0.324869 - 0.287258i) q^{60} -0.0752228 q^{61} -1.42548i q^{62} -1.19394i q^{63} -7.08110 q^{64} +(-1.35026 + 1.19394i) q^{65} -1.48119 q^{66} -2.70052i q^{67} -0.730841i q^{68} -4.00000 q^{69} +(-2.61942 - 2.96239i) q^{70} -14.0508 q^{71} +2.67513i q^{72} +10.7308i q^{73} +2.38787 q^{74} +(4.96239 + 0.612127i) q^{75} -1.03761 q^{76} +1.19394i q^{77} +1.19394i q^{78} -13.9756 q^{79} +(6.44358 + 7.28726i) q^{80} +1.00000 q^{81} -13.4617i q^{82} +9.89446i q^{83} -0.231548 q^{84} +(6.31265 - 5.58181i) q^{85} -6.54420 q^{86} -4.31265i q^{87} -2.67513i q^{88} -16.8872 q^{89} +(2.48119 - 2.19394i) q^{90} +0.962389 q^{91} +0.775746i q^{92} -0.962389i q^{93} +18.2374 q^{94} +(-7.92478 - 8.96239i) q^{95} +1.09332 q^{96} +11.4763i q^{97} -8.25694i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^9	\( 6 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{9} - 4 q^{10} + 6 q^{11} - 12 q^{14} - 6 q^{16} + 12 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{24} - 2 q^{25} - 8 q^{26} - 16 q^{29} + 14 q^{30} - 16 q^{31} + 36 q^{34} + 12 q^{35} + 2 q^{36} - 4 q^{39} - 16 q^{40} + 16 q^{41} - 2 q^{44} - 2 q^{45} + 8 q^{46} + 10 q^{49} + 24 q^{50} - 2 q^{54} + 2 q^{55} + 20 q^{56} - 16 q^{59} + 12 q^{60} - 44 q^{61} + 22 q^{64} + 12 q^{65} + 2 q^{66} - 24 q^{69} - 40 q^{70} - 24 q^{71} + 16 q^{74} + 8 q^{75} - 28 q^{76} + 20 q^{79} + 6 q^{80} + 6 q^{81} - 24 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} + 4 q^{90} - 16 q^{91} + 24 q^{94} - 4 q^{95} - 6 q^{96} - 6 q^{99}+O(q^{100}) \) 6 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^9 - 4 * q^10 + 6 * q^11 - 12 * q^14 - 6 * q^16 + 12 * q^19 - 10 * q^20 + 8 * q^21 - 6 * q^24 - 2 * q^25 - 8 * q^26 - 16 * q^29 + 14 * q^30 - 16 * q^31 + 36 * q^34 + 12 * q^35 + 2 * q^36 - 4 * q^39 - 16 * q^40 + 16 * q^41 - 2 * q^44 - 2 * q^45 + 8 * q^46 + 10 * q^49 + 24 * q^50 - 2 * q^54 + 2 * q^55 + 20 * q^56 - 16 * q^59 + 12 * q^60 - 44 * q^61 + 22 * q^64 + 12 * q^65 + 2 * q^66 - 24 * q^69 - 40 * q^70 - 24 * q^71 + 16 * q^74 + 8 * q^75 - 28 * q^76 + 20 * q^79 + 6 * q^80 + 6 * q^81 - 24 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 + 4 * q^90 - 16 * q^91 + 24 * q^94 - 4 * q^95 - 6 * q^96 - 6 * q^99

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