LMFDB - Embedded newform 324.2.l.a.35.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(35,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("324.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, degree $6$, not 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.8
Character	$\chi$	$=$	324.35
Dual form			324.2.l.a.287.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0793838 + 1.41198i) q^{2} +(-1.98740 - 0.224177i) q^{4} +(-0.470103 + 1.29160i) q^{5} +(-1.57428 - 0.277589i) q^{7} +(0.474302 - 2.78838i) q^{8} +O(q^{10})$	\(q+(-0.0793838 + 1.41198i) q^{2} +(-1.98740 - 0.224177i) q^{4} +(-0.470103 + 1.29160i) q^{5} +(-1.57428 - 0.277589i) q^{7} +(0.474302 - 2.78838i) q^{8} +(-1.78640 - 0.766310i) q^{10} +(-3.66920 + 1.33548i) q^{11} +(-5.10894 + 4.28691i) q^{13} +(0.516924 - 2.20083i) q^{14} +(3.89949 + 0.891059i) q^{16} +(2.32950 - 1.34494i) q^{17} +(-3.15841 - 1.82351i) q^{19} +(1.22383 - 2.46153i) q^{20} +(-1.59440 - 5.28687i) q^{22} +(-0.644252 - 3.65373i) q^{23} +(2.38300 + 1.99957i) q^{25} +(-5.64747 - 7.55405i) q^{26} +(3.06650 + 0.904598i) q^{28} +(-1.98152 + 2.36148i) q^{29} +(-1.45019 + 0.255708i) q^{31} +(-1.56772 + 5.43528i) q^{32} +(1.71411 + 3.39599i) q^{34} +(1.09861 - 1.90285i) q^{35} +(1.27577 + 2.20970i) q^{37} +(2.82549 - 4.31487i) q^{38} +(3.37849 + 1.92343i) q^{40} +(6.30271 + 7.51128i) q^{41} +(-1.27388 - 3.49995i) q^{43} +(7.59155 - 1.83158i) q^{44} +(5.21016 - 0.619626i) q^{46} +(-0.901707 + 5.11384i) q^{47} +(-4.17653 - 1.52013i) q^{49} +(-3.01253 + 3.20602i) q^{50} +(11.1145 - 7.37447i) q^{52} +3.96045i q^{53} -5.36695i q^{55} +(-1.52071 + 4.25804i) q^{56} +(-3.17707 - 2.98534i) q^{58} +(-0.666798 - 0.242695i) q^{59} +(0.969119 - 5.49615i) q^{61} +(-0.245933 - 2.06794i) q^{62} +(-7.55008 - 2.64506i) q^{64} +(-3.13523 - 8.61397i) q^{65} +(10.4714 + 12.4793i) q^{67} +(-4.93115 + 2.15071i) q^{68} +(2.59958 + 1.70227i) q^{70} +(7.76079 + 13.4421i) q^{71} +(4.04282 - 7.00237i) q^{73} +(-3.22134 + 1.62595i) q^{74} +(5.86823 + 4.33208i) q^{76} +(6.14709 - 1.08390i) q^{77} +(-8.37729 + 9.98366i) q^{79} +(-2.98405 + 4.61768i) q^{80} +(-11.1061 + 8.30305i) q^{82} +(0.344982 + 0.289474i) q^{83} +(0.642014 + 3.64104i) q^{85} +(5.04300 - 1.52086i) q^{86} +(1.98351 + 10.8645i) q^{88} +(-0.994859 - 0.574382i) q^{89} +(9.23292 - 5.33063i) q^{91} +(0.461299 + 7.40584i) q^{92} +(-7.14907 - 1.67915i) q^{94} +(3.84002 - 3.22216i) q^{95} +(-9.00157 + 3.27630i) q^{97} +(2.47795 - 5.77652i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−0.0793838	+	1.41198i	−0.0561329	+	0.998423i
$2$	−0.0793838	+	1.41198i	−0.0561329	+	0.998423i
$3$		0			0
$3$		0			0
$4$	−1.98740	−	0.224177i	−0.993698	−	0.112089i
$5$	−0.470103	+	1.29160i	−0.210236	+	0.577620i	−0.999328	−	0.0366558i	$-0.988329\pi$
$5$	−0.470103	+	1.29160i	−0.210236	+	0.577620i	0.789092	+	0.614276i	$0.210552\pi$
$6$		0			0
$7$	−1.57428	−	0.277589i	−0.595024	−	0.104919i	−0.131977	−	0.991253i	$-0.542133\pi$
$7$	−1.57428	−	0.277589i	−0.595024	−	0.104919i	−0.463046	+	0.886334i	$0.653244\pi$
$8$	0.474302	−	2.78838i	0.167691	−	0.985840i
$9$		0			0
$10$	−1.78640	−	0.766310i	−0.564908	−	0.242328i
$11$	−3.66920	+	1.33548i	−1.10631	+	0.402663i	−0.829637	−	0.558303i	$-0.811453\pi$
$11$	−3.66920	+	1.33548i	−1.10631	+	0.402663i	−0.276669	+	0.960965i	$0.589231\pi$
$12$		0			0
$13$	−5.10894	+	4.28691i	−1.41696	+	1.18897i	−0.464021	+	0.885824i	$0.653594\pi$
$13$	−5.10894	+	4.28691i	−1.41696	+	1.18897i	−0.952943	+	0.303149i	$0.901962\pi$
$14$	0.516924	−	2.20083i	0.138154	−	0.588196i
$15$		0			0
$16$	3.89949	+	0.891059i	0.974872	+	0.222765i
$17$	2.32950	−	1.34494i	0.564988	−	0.326196i	−0.190157	−	0.981754i	$-0.560900\pi$
$17$	2.32950	−	1.34494i	0.564988	−	0.326196i	0.755145	+	0.655558i	$0.227566\pi$
$18$		0			0
$19$	−3.15841	−	1.82351i	−0.724590	−	0.418342i	0.0918500	−	0.995773i	$-0.470722\pi$
$19$	−3.15841	−	1.82351i	−0.724590	−	0.418342i	−0.816440	+	0.577431i	$0.804055\pi$
$20$	1.22383	−	2.46153i	0.273656	−	0.550415i
$21$		0			0
$22$	−1.59440	−	5.28687i	−0.339928	−	1.12716i
$23$	−0.644252	−	3.65373i	−0.134336	−	0.761856i	−0.975320	−	0.220796i	$-0.929134\pi$
$23$	−0.644252	−	3.65373i	−0.134336	−	0.761856i	0.840984	−	0.541060i	$-0.181977\pi$
$24$		0			0
$25$	2.38300	+	1.99957i	0.476599	+	0.399914i
$26$	−5.64747	−	7.55405i	−1.10756	−	1.48147i
$27$		0			0
$28$	3.06650	+	0.904598i	0.579514	+	0.170953i
$29$	−1.98152	+	2.36148i	−0.367959	+	0.438516i	−0.917975	−	0.396638i	$-0.870177\pi$
$29$	−1.98152	+	2.36148i	−0.367959	+	0.438516i	0.550016	+	0.835154i	$0.314621\pi$
$30$		0			0
$31$	−1.45019	+	0.255708i	−0.260462	+	0.0459264i	−0.302354	−	0.953196i	$-0.597772\pi$
$31$	−1.45019	+	0.255708i	−0.260462	+	0.0459264i	0.0418922	+	0.999122i	$0.486661\pi$
$32$	−1.56772	+	5.43528i	−0.277136	+	0.960831i
$33$		0			0
$34$	1.71411	+	3.39599i	0.293967	+	0.582407i
$35$	1.09861	−	1.90285i	0.185699	−	0.321640i
$36$		0			0
$37$	1.27577	+	2.20970i	0.209736	+	0.363273i	0.951631	−	0.307243i	$-0.0994063\pi$
$37$	1.27577	+	2.20970i	0.209736	+	0.363273i	−0.741896	+	0.670515i	$0.766073\pi$
$38$	2.82549	−	4.31487i	0.458356	−	0.699964i
$39$		0			0
$40$	3.37849	+	1.92343i	0.534186	+	0.304121i
$41$	6.30271	+	7.51128i	0.984318	+	1.17306i	0.984910	+	0.173065i	$0.0553671\pi$
$41$	6.30271	+	7.51128i	0.984318	+	1.17306i	−0.000592131		1.00000i	$0.500188\pi$
$42$		0			0
$43$	−1.27388	−	3.49995i	−0.194265	−	0.533738i	0.803869	−	0.594807i	$-0.202771\pi$
$43$	−1.27388	−	3.49995i	−0.194265	−	0.533738i	−0.998134	+	0.0610687i	$0.980549\pi$
$44$	7.59155	−	1.83158i	1.14447	−	0.276121i
$45$		0			0
$46$	5.21016	−	0.619626i	0.768196	−	0.0913588i
$47$	−0.901707	+	5.11384i	−0.131528	+	0.745930i	0.845688	+	0.533678i	$0.179191\pi$
$47$	−0.901707	+	5.11384i	−0.131528	+	0.745930i	−0.977215	+	0.212251i	$0.931920\pi$
$48$		0			0
$49$	−4.17653	−	1.52013i	−0.596647	−	0.217162i
$50$	−3.01253	+	3.20602i	−0.426036	+	0.453399i
$51$		0			0
$52$	11.1145	−	7.37447i	1.54130	−	1.02266i
$53$			3.96045i			0.544009i	0.962296	+	0.272005i	$0.0876866\pi$
$53$			3.96045i			0.544009i	−0.962296	+	0.272005i	$0.912313\pi$
$54$		0			0
$55$		−	5.36695i		−	0.723679i
$56$	−1.52071	+	4.25804i	−0.203213	+	0.569004i
$57$		0			0
$58$	−3.17707	−	2.98534i	−0.417170	−	0.391994i
$59$	−0.666798	−	0.242695i	−0.0868098	−	0.0315962i	0.298250	−	0.954488i	$-0.403597\pi$
$59$	−0.666798	−	0.242695i	−0.0868098	−	0.0315962i	−0.385060	+	0.922892i	$0.625819\pi$
$60$		0			0
$61$	0.969119	−	5.49615i	0.124083	−	0.703709i	−0.857765	−	0.514041i	$-0.828148\pi$
$61$	0.969119	−	5.49615i	0.124083	−	0.703709i	0.981848	−	0.189668i	$-0.0607411\pi$
$62$	−0.245933	−	2.06794i	−0.0312336	−	0.262629i
$63$		0			0
$64$	−7.55008	−	2.64506i	−0.943759	−	0.330633i
$65$	−3.13523	−	8.61397i	−0.388877	−	1.06843i
$66$		0			0
$67$	10.4714	+	12.4793i	1.27928	+	1.52459i	0.715344	+	0.698773i	$0.246270\pi$
$67$	10.4714	+	12.4793i	1.27928	+	1.52459i	0.563939	+	0.825817i	$0.309285\pi$
$68$	−4.93115	+	2.15071i	−0.597990	+	0.260812i
$69$		0			0
$70$	2.59958	+	1.70227i	0.310709	+	0.203461i
$71$	7.76079	+	13.4421i	0.921036	+	1.59528i	0.797815	+	0.602903i	$0.205989\pi$
$71$	7.76079	+	13.4421i	0.921036	+	1.59528i	0.123222	+	0.992379i	$0.460677\pi$
$72$		0			0
$73$	4.04282	−	7.00237i	0.473176	−	0.819565i	−0.526352	−	0.850266i	$-0.676441\pi$
$73$	4.04282	−	7.00237i	0.473176	−	0.819565i	0.999529	+	0.0307013i	$0.00977408\pi$
$74$	−3.22134	+	1.62595i	−0.374473	+	0.189013i
$75$		0			0
$76$	5.86823	+	4.33208i	0.673132	+	0.496924i
$77$	6.14709	−	1.08390i	0.700525	−	0.123522i
$78$		0			0
$79$	−8.37729	+	9.98366i	−0.942518	+	1.12325i	0.0497030	+	0.998764i	$0.484173\pi$
$79$	−8.37729	+	9.98366i	−0.942518	+	1.12325i	−0.992221	+	0.124486i	$0.960272\pi$
$80$	−2.98405	+	4.61768i	−0.333627	+	0.516272i
$81$		0			0
$82$	−11.1061	+	8.30305i	−1.22647	+	0.916919i
$83$	0.344982	+	0.289474i	0.0378667	+	0.0317739i	0.661525	−	0.749923i	$-0.269910\pi$
$83$	0.344982	+	0.289474i	0.0378667	+	0.0317739i	−0.623658	+	0.781697i	$0.714354\pi$
$84$		0			0
$85$	0.642014	+	3.64104i	0.0696362	+	0.394927i
$86$	5.04300	−	1.52086i	0.543801	−	0.163998i
$87$		0			0
$88$	1.98351	+	10.8645i	0.211443	+	1.15816i
$89$	−0.994859	−	0.574382i	−0.105455	−	0.0608844i	0.446345	−	0.894861i	$-0.352725\pi$
$89$	−0.994859	−	0.574382i	−0.105455	−	0.0608844i	−0.551800	+	0.833977i	$0.686059\pi$
$90$		0			0
$91$	9.23292	−	5.33063i	0.967873	−	0.558802i
$92$	0.461299	+	7.40584i	0.0480938	+	0.772113i
$93$		0			0
$94$	−7.14907	−	1.67915i	−0.737370	−	0.173191i
$95$	3.84002	−	3.22216i	0.393978	−	0.330587i
$96$		0			0
$97$	−9.00157	+	3.27630i	−0.913971	+	0.332658i	−0.755837	−	0.654760i	$-0.772770\pi$
$97$	−9.00157	+	3.27630i	−0.913971	+	0.332658i	−0.158134	+	0.987418i	$0.550548\pi$
$98$	2.47795	−	5.77652i	0.250311	−	0.583517i
$99$		0			0
$100$	−4.28770	−	4.50815i	−0.428770	−	0.450815i
$101$	−12.4723	−	2.19921i	−1.24104	−	0.218830i	−0.485681	−	0.874136i	$-0.661428\pi$
$101$	−12.4723	−	2.19921i	−1.24104	−	0.218830i	−0.755363	+	0.655306i	$0.772540\pi$
$102$		0			0
$103$	1.92687	−	5.29404i	0.189860	−	0.521637i	−0.807841	−	0.589400i	$-0.799364\pi$
$103$	1.92687	−	5.29404i	0.189860	−	0.521637i	0.997701	+	0.0677632i	$0.0215862\pi$
$104$	9.53032	+	16.2789i	0.934525	+	1.59628i
$105$		0			0
$106$	−5.59209	−	0.314396i	−0.543152	−	0.0305368i
$107$	−8.38143			−0.810264			−0.405132	−	0.914258i	$-0.632774\pi$
$107$	−8.38143			−0.810264			−0.405132	+	0.914258i	$0.632774\pi$
$108$		0			0
$109$	6.18810			0.592713			0.296356	−	0.955077i	$-0.404228\pi$
$109$	6.18810			0.592713			0.296356	+	0.955077i	$0.404228\pi$
$110$	7.57804	+	0.426049i	0.722538	+	0.0406222i
$111$		0			0
$112$	−5.89156	−	2.48524i	−0.556700	−	0.234833i
$113$	4.37086	−	12.0088i	0.411176	−	1.12970i	−0.545390	−	0.838182i	$-0.683618\pi$
$113$	4.37086	−	12.0088i	0.411176	−	1.12970i	0.956566	−	0.291515i	$-0.0941593\pi$
$114$		0			0
$115$	5.02202	+	0.885517i	0.468305	+	0.0825749i
$116$	4.46745	−	4.24899i	0.414793	−	0.394509i
$117$		0			0
$118$	0.395614	−	0.922243i	0.0364192	−	0.0848993i
$119$	−4.04064	+	1.47067i	−0.370405	+	0.134816i
$120$		0			0
$121$	3.25306	−	2.72964i	0.295732	−	0.248149i
$122$	7.68354	+	1.80469i	0.695635	+	0.163389i
$123$		0			0
$124$	2.93943	−	0.183093i	0.263968	−	0.0164422i
$125$	−9.65461	+	5.57409i	−0.863534	+	0.498562i
$126$		0			0
$127$	6.61685	+	3.82024i	0.587151	+	0.338992i	0.763970	−	0.645252i	$-0.223247\pi$
$127$	6.61685	+	3.82024i	0.587151	+	0.338992i	−0.176819	+	0.984243i	$0.556581\pi$
$128$	4.33414	−	10.4506i	0.383088	−	0.923712i
$129$		0			0
$130$	12.4117	−	3.74308i	1.08858	−	0.328290i
$131$	−1.87334	−	10.6242i	−0.163674	−	0.928243i	−0.950421	−	0.310967i	$-0.899347\pi$
$131$	−1.87334	−	10.6242i	−0.163674	−	0.928243i	0.786746	−	0.617276i	$-0.211764\pi$
$132$		0			0
$133$	4.46606	+	3.74747i	0.387256	+	0.324946i
$134$	−18.4518	+	13.7948i	−1.59400	+	1.19169i
$135$		0			0
$136$	−2.64531	−	7.13344i	−0.226833	−	0.611688i
$137$	6.79690	−	8.10023i	0.580699	−	0.692050i	−0.393091	−	0.919499i	$-0.628594\pi$
$137$	6.79690	−	8.10023i	0.580699	−	0.692050i	0.973790	+	0.227450i	$0.0730388\pi$
$138$		0			0
$139$	−1.59536	+	0.281305i	−0.135317	+	0.0238600i	−0.240896	−	0.970551i	$-0.577441\pi$
$139$	−1.59536	+	0.281305i	−0.135317	+	0.0238600i	0.105580	+	0.994411i	$0.466330\pi$
$140$	−2.60995	+	3.53543i	−0.220581	+	0.298798i
$141$		0			0
$142$	−19.5961	+	9.89103i	−1.64447	+	0.830037i
$143$	13.0206	−	22.5524i	1.08884	−	1.88593i
$144$		0			0
$145$	−2.11857	−	3.66946i	−0.175937	−	0.304732i
$146$	9.56630	+	6.26427i	0.791712	+	0.518435i
$147$		0			0
$148$	−2.04010	−	4.67755i	−0.167695	−	0.384493i
$149$	−9.08882	−	10.8316i	−0.744585	−	0.887362i	0.252185	−	0.967679i	$-0.418851\pi$
$149$	−9.08882	−	10.8316i	−0.744585	−	0.887362i	−0.996769	+	0.0803176i	$0.974407\pi$
$150$		0			0
$151$	−3.73181	−	10.2531i	−0.303691	−	0.834384i	−0.993851	−	0.110727i	$-0.964682\pi$
$151$	−3.73181	−	10.2531i	−0.303691	−	0.834384i	0.690160	−	0.723657i	$-0.257540\pi$
$152$	−6.58267	+	7.94195i	−0.533925	+	0.644177i
$153$		0			0
$154$	1.04247	+	8.76563i	0.0840043	+	0.706355i
$155$	0.351467	−	1.99327i	0.0282305	−	0.160103i
$156$		0			0
$157$	9.66944	+	3.51939i	0.771705	+	0.280878i	0.697709	−	0.716381i	$-0.254203\pi$
$157$	9.66944	+	3.51939i	0.771705	+	0.280878i	0.0739957	+	0.997259i	$0.476425\pi$
$158$	−13.4317	−	12.6211i	−1.06857	−	1.00408i
$159$		0			0
$160$	−6.28320	−	4.58000i	−0.496731	−	0.362081i
$161$			5.93085i			0.467417i
$162$		0			0
$163$		−	6.18193i		−	0.484206i	−0.970251	−	0.242103i	$-0.922163\pi$
$163$		−	6.18193i		−	0.484206i	0.970251	−	0.242103i	$-0.0778372\pi$
$164$	−10.8421	−	16.3408i	−0.846628	−	1.27600i
$165$		0			0
$166$	−0.436119	+	0.464129i	−0.0338494	+	0.0360234i
$167$	−0.411580	−	0.149803i	−0.0318490	−	0.0115921i	0.326047	−	0.945354i	$-0.394283\pi$
$167$	−0.411580	−	0.149803i	−0.0318490	−	0.0115921i	−0.357896	+	0.933762i	$0.616506\pi$
$168$		0			0
$169$	5.46623	−	31.0006i	0.420480	−	2.38466i
$170$	−5.19206	+	0.617473i	−0.398213	+	0.0473581i
$171$		0			0
$172$	1.74709	+	7.24137i	0.133214	+	0.552149i
$173$	2.70503	+	7.43201i	0.205660	+	0.565045i	0.999046	−	0.0436734i	$-0.0139061\pi$
$173$	2.70503	+	7.43201i	0.205660	+	0.565045i	−0.793386	+	0.608719i	$0.791684\pi$
$174$		0			0
$175$	−3.19646	−	3.80939i	−0.241629	−	0.287963i
$176$	−15.4980	+	1.93822i	−1.16821	+	0.146099i
$177$		0			0
$178$	0.889994	−	1.35913i	0.0667079	−	0.101871i
$179$	5.74464	+	9.95001i	0.429374	+	0.743698i	0.996818	−	0.0797141i	$-0.0254007\pi$
$179$	5.74464	+	9.95001i	0.429374	+	0.743698i	−0.567443	+	0.823412i	$0.692067\pi$
$180$		0			0
$181$	−7.34496	+	12.7218i	−0.545946	+	0.945607i	0.452600	+	0.891714i	$0.350496\pi$
$181$	−7.34496	+	12.7218i	−0.545946	+	0.945607i	−0.998547	+	0.0538935i	$0.982837\pi$
$182$	6.79381	+	13.4599i	0.503591	+	0.997714i
$183$		0			0
$184$	−10.4936	+	0.0634427i	−0.773595	+	0.00467706i
$185$	−3.45379	+	0.608996i	−0.253928	+	0.0447743i
$186$		0			0
$187$	−6.75129	+	8.04587i	−0.493703	+	0.588372i
$188$	2.93846	−	9.96108i	0.214309	−	0.726486i
$189$		0			0
$190$	4.24480	+	5.67783i	0.307950	+	0.411913i
$191$	−10.5145	−	8.82269i	−0.760800	−	0.638387i	0.177535	−	0.984115i	$-0.443188\pi$
$191$	−10.5145	−	8.82269i	−0.760800	−	0.638387i	−0.938335	+	0.345727i	$0.887632\pi$
$192$		0			0
$193$	−1.42837	−	8.10071i	−0.102817	−	0.583102i	−0.992070	−	0.125687i	$-0.959887\pi$
$193$	−1.42837	−	8.10071i	−0.102817	−	0.583102i	0.889253	−	0.457415i	$-0.151225\pi$
$194$	−3.91151	−	12.9702i	−0.280830	−	0.931203i
$195$		0			0
$196$	7.95964	+	3.95739i	0.568546	+	0.282671i
$197$	−8.28713	−	4.78458i	−0.590434	−	0.340887i	0.174835	−	0.984598i	$-0.444061\pi$
$197$	−8.28713	−	4.78458i	−0.590434	−	0.340887i	−0.765269	+	0.643711i	$0.777394\pi$
$198$		0			0
$199$	−12.3825	+	7.14906i	−0.877774	+	0.506783i	−0.869924	−	0.493186i	$-0.835832\pi$
$199$	−12.3825	+	7.14906i	−0.877774	+	0.506783i	−0.00785032	+	0.999969i	$0.502499\pi$
$200$	6.70581	−	5.69629i	0.474173	−	0.402788i
$201$		0			0
$202$	4.09535	−	17.4362i	0.288148	−	1.22680i
$203$	3.77500	−	3.16760i	0.264953	−	0.222322i
$204$		0			0
$205$	−12.6645	+	4.60949i	−0.884525	+	0.321941i
$206$	7.32214	+	3.14097i	0.510157	+	0.218842i
$207$		0			0
$208$	−23.7421	+	12.1644i	−1.64622	+	0.843448i
$209$	14.0241	+	2.47283i	0.970069	+	0.171049i
$210$		0			0
$211$	−5.92941	+	16.2909i	−0.408197	+	1.12151i	0.549940	+	0.835204i	$0.314651\pi$
$211$	−5.92941	+	16.2909i	−0.408197	+	1.12151i	−0.958137	+	0.286309i	$0.907572\pi$
$212$	0.887843	−	7.87098i	0.0609773	−	0.540581i
$213$		0			0
$214$	0.665350	−	11.8344i	0.0454824	−	0.808986i
$215$	5.11938			0.349139
$216$		0			0
$217$	2.35399			0.159800
$218$	−0.491235	+	8.73750i	−0.0332706	+	0.591778i
$219$		0			0
$220$	−1.20315	+	10.6663i	−0.0811162	+	0.719118i
$221$	−6.13566	+	16.8576i	−0.412729	+	1.13396i
$222$		0			0
$223$	6.25203	+	1.10240i	0.418667	+	0.0738223i	0.379013	−	0.925391i	$-0.376263\pi$
$223$	6.25203	+	1.10240i	0.418667	+	0.0738223i	0.0396537	+	0.999213i	$0.487375\pi$
$224$	3.97681	−	8.12150i	0.265712	−	0.542640i
$225$		0			0
$226$	16.6093	+	7.12490i	1.10484	+	0.473941i
$227$	14.5711	−	5.30345i	0.967119	−	0.352002i	0.190299	−	0.981726i	$-0.439054\pi$
$227$	14.5711	−	5.30345i	0.967119	−	0.352002i	0.776819	+	0.629724i	$0.216832\pi$
$228$		0			0
$229$	0.780733	−	0.655113i	0.0515923	−	0.0432911i	−0.616627	−	0.787256i	$-0.711501\pi$
$229$	0.780733	−	0.655113i	0.0515923	−	0.0432911i	0.668219	+	0.743964i	$0.267057\pi$
$230$	−1.64900	+	7.02071i	−0.108732	+	0.462932i
$231$		0			0
$232$	5.64486	+	6.64527i	0.370603	+	0.436284i
$233$	8.68625	−	5.01501i	0.569055	−	0.328544i	−0.187717	−	0.982223i	$-0.560109\pi$
$233$	8.68625	−	5.01501i	0.569055	−	0.328544i	0.756772	+	0.653679i	$0.226775\pi$
$234$		0			0
$235$	−6.18112	−	3.56867i	−0.403212	−	0.232794i
$236$	1.27079	+	0.631812i	0.0827211	+	0.0411275i
$237$		0			0
$238$	−1.75581	−	5.82207i	−0.113812	−	0.377389i
$239$	3.33468	+	18.9119i	0.215702	+	1.22331i	0.879684	+	0.475560i	$0.157754\pi$
$239$	3.33468	+	18.9119i	0.215702	+	1.22331i	−0.663981	+	0.747749i	$0.731134\pi$
$240$		0			0
$241$	0.880417	+	0.738758i	0.0567127	+	0.0475876i	0.670703	−	0.741726i	$-0.265992\pi$
$241$	0.880417	+	0.738758i	0.0567127	+	0.0475876i	−0.613991	+	0.789313i	$0.710437\pi$
$242$	3.59596	+	4.80995i	0.231157	+	0.309195i
$243$		0			0
$244$	−3.15813	+	10.7058i	−0.202179	+	0.685366i
$245$	3.92680	−	4.67978i	0.250874	−	0.298980i
$246$		0			0
$247$	23.9533	−	4.22362i	1.52411	−	0.268743i
$248$	0.0251808	+	4.16496i	0.00159898	+	0.264475i
$249$		0			0
$250$	−7.10410	−	14.0746i	−0.449303	−	0.890158i
$251$	−11.3633	+	19.6818i	−0.717243	+	1.24230i	0.244845	+	0.969562i	$0.421263\pi$
$251$	−11.3633	+	19.6818i	−0.717243	+	1.24230i	−0.962088	+	0.272739i	$0.912070\pi$
$252$		0			0
$253$	7.24338	+	12.5459i	0.455388	+	0.788754i
$254$	−5.91939	+	9.03962i	−0.371416	+	0.567196i
$255$		0			0
$256$	14.4120	+	6.94935i	0.900752	+	0.434334i
$257$	−7.00172	−	8.34433i	−0.436755	−	0.520505i	0.502103	−	0.864808i	$-0.332560\pi$
$257$	−7.00172	−	8.34433i	−0.436755	−	0.520505i	−0.938859	+	0.344303i	$0.888115\pi$
$258$		0			0
$259$	−1.39504	−	3.83284i	−0.0866836	−	0.238161i
$260$	4.29989	+	17.8222i	0.266668	+	1.10529i
$261$		0			0
$262$	15.1500	−	1.80173i	0.935967	−	0.111311i
$263$	0.0454458	−	0.257736i	0.00280231	−	0.0158927i	−0.983375	−	0.181589i	$-0.941876\pi$
$263$	0.0454458	−	0.257736i	0.00280231	−	0.0158927i	0.986177	+	0.165696i	$0.0529871\pi$
$264$		0			0
$265$	−5.11531	−	1.86182i	−0.314231	−	0.114371i
$266$	−5.64589	+	6.00851i	−0.346172	+	0.368405i
$267$		0			0
$268$	−18.0132	−	27.1488i	−1.10033	−	1.65837i
$269$			7.47642i			0.455845i	0.973679	+	0.227923i	$0.0731933\pi$
$269$			7.47642i			0.455845i	−0.973679	+	0.227923i	$0.926807\pi$
$270$		0			0
$271$			14.5903i			0.886299i	0.896448	+	0.443150i	$0.146139\pi$
$271$			14.5903i			0.886299i	−0.896448	+	0.443150i	$0.853861\pi$
$272$	10.2823	−	3.16885i	0.623456	−	0.192140i
$273$		0			0
$274$	10.8978	+	10.2401i	0.658362	+	0.618630i
$275$	−11.4141	−	4.15439i	−0.688295	−	0.250519i
$276$		0			0
$277$	−0.964532	+	5.47013i	−0.0579531	+	0.328668i	−0.999976	−	0.00687933i	$-0.997810\pi$
$277$	−0.964532	+	5.47013i	−0.0579531	+	0.328668i	0.942023	+	0.335548i	$0.108921\pi$
$278$	−0.270552	−	2.27495i	−0.0162266	−	0.136443i
$279$		0			0
$280$	−4.78478	−	3.96586i	−0.285945	−	0.237005i
$281$	2.82619	+	7.76489i	0.168596	+	0.463214i	0.995001	−	0.0998617i	$-0.0318400\pi$
$281$	2.82619	+	7.76489i	0.168596	+	0.463214i	−0.826405	+	0.563076i	$0.809618\pi$
$282$		0			0
$283$	−20.8899	−	24.8956i	−1.24178	−	1.47989i	−0.819143	−	0.573590i	$-0.805550\pi$
$283$	−20.8899	−	24.8956i	−1.24178	−	1.47989i	−0.422633	−	0.906301i	$-0.638894\pi$
$284$	−12.4104	−	28.4545i	−0.736419	−	1.68847i
$285$		0			0
$286$	30.8100	+	20.1752i	1.82183	+	1.19299i
$287$	−7.83722	−	13.5745i	−0.462616	−	0.801275i
$288$		0			0
$289$	−4.88227	+	8.45634i	−0.287192	+	0.497432i
$290$	5.34940	−	2.70009i	0.314128	−	0.158554i
$291$		0			0
$292$	−9.60446	+	13.0102i	−0.562058	+	0.761363i
$293$	−3.37269	+	0.594697i	−0.197035	+	0.0347426i	−0.271295	−	0.962496i	$-0.587452\pi$
$293$	−3.37269	+	0.594697i	−0.197035	+	0.0347426i	0.0742597	+	0.997239i	$0.476341\pi$
$294$		0			0
$295$	0.626928	−	0.747144i	0.0365012	−	0.0435004i
$296$	6.76658	−	2.50927i	0.393299	−	0.145848i
$297$		0			0
$298$	16.0156	−	11.9734i	0.927758	−	0.693601i
$299$	18.9547	+	15.9048i	1.09618	+	0.919801i
$300$		0			0
$301$	1.03390	+	5.86354i	0.0595930	+	0.337969i
$302$	14.7734	−	4.45533i	0.850115	−	0.256376i
$303$		0			0
$304$	−10.6913	−	9.92509i	−0.613191	−	0.569243i
$305$	6.64322	+	3.83547i	0.380390	+	0.219618i
$306$		0			0
$307$	3.67167	−	2.11984i	0.209553	−	0.120986i	−0.391550	−	0.920157i	$-0.628061\pi$
$307$	3.67167	−	2.11984i	0.209553	−	0.120986i	0.601104	+	0.799171i	$0.294728\pi$
$308$	−12.4597	+	0.776095i	−0.709956	+	0.0442221i
$309$		0			0
$310$	2.78656	+	0.654500i	0.158266	+	0.0371731i
$311$	−17.8431	+	14.9722i	−1.01179	+	0.848994i	−0.988574	−	0.150737i	$-0.951835\pi$
$311$	−17.8431	+	14.9722i	−1.01179	+	0.848994i	−0.0232172	+	0.999730i	$0.507391\pi$
$312$		0			0
$313$	−7.63152	+	2.77765i	−0.431359	+	0.157002i	−0.548569	−	0.836105i	$-0.684827\pi$
$313$	−7.63152	+	2.77765i	−0.431359	+	0.157002i	0.117210	+	0.993107i	$0.462605\pi$
$314$	−5.73691	+	13.3737i	−0.323753	+	0.754722i
$315$		0			0
$316$	18.8871	−	17.9635i	1.06248	−	1.01053i
$317$	17.9863	+	3.17148i	1.01021	+	0.178128i	0.654175	−	0.756343i	$-0.273016\pi$
$317$	17.9863	+	3.17148i	1.01021	+	0.178128i	0.356039	+	0.934471i	$0.384127\pi$
$318$		0			0
$319$	4.11688	−	11.3110i	0.230501	−	0.633297i
$320$	6.96567	−	8.50820i	0.389393	−	0.475623i
$321$		0			0
$322$	−8.37427	−	0.470814i	−0.466680	−	0.0262374i
$323$	−9.81005			−0.545846
$324$		0			0
$325$	−20.7465			−1.15081
$326$	8.72878	+	0.490745i	0.483443	+	0.0271799i
$327$		0			0
$328$	23.9337	−	14.0117i	1.32152	−	0.773667i
$329$	2.83909	−	7.80033i	0.156524	−	0.430046i
$330$		0			0
$331$	27.7857	+	4.89938i	1.52724	+	0.269294i	0.873275	−	0.487228i	$-0.161992\pi$
$331$	27.7857	+	4.89938i	1.52724	+	0.269294i	0.653968	+	0.756522i	$0.273103\pi$
$332$	−0.620722	−	0.652637i	−0.0340666	−	0.0358181i
$333$		0			0
$334$	0.244192	−	0.569253i	0.0133616	−	0.0311481i
$335$	−21.0409	+	7.65825i	−1.14958	+	0.418415i
$336$		0			0
$337$	9.31991	−	7.82033i	0.507688	−	0.426001i	−0.352627	−	0.935764i	$-0.614712\pi$
$337$	9.31991	−	7.82033i	0.507688	−	0.426001i	0.860315	+	0.509763i	$0.170267\pi$
$338$	43.3383	+	10.1792i	2.35730	+	0.553674i
$339$		0			0
$340$	−0.459697	−	7.38012i	−0.0249306	−	0.400243i
$341$	4.97955	−	2.87494i	0.269658	−	0.155687i
$342$		0			0
$343$	15.8439	+	9.14748i	0.855490	+	0.493917i
$344$	−10.3634	+	1.89202i	−0.558756	+	0.102011i
$345$		0			0
$346$	−10.7086	+	3.22948i	−0.575698	+	0.173618i
$347$	1.12983	+	6.40758i	0.0606524	+	0.343977i	0.999999	+	0.00100899i	$0.000321173\pi$
$347$	1.12983	+	6.40758i	0.0606524	+	0.343977i	−0.939347	+	0.342968i	$0.888568\pi$
$348$		0			0
$349$	23.5937	+	19.7975i	1.26294	+	1.05974i	0.995362	+	0.0962012i	$0.0306692\pi$
$349$	23.5937	+	19.7975i	1.26294	+	1.05974i	0.267582	+	0.963535i	$0.413775\pi$
$350$	5.63254	−	4.21094i	0.301072	−	0.225084i
$351$		0			0
$352$	−1.50644	−	22.0368i	−0.0802935	−	1.17457i
$353$	−18.3162	+	21.8284i	−0.974873	+	1.16181i	0.0119377	+	0.999929i	$0.496200\pi$
$353$	−18.3162	+	21.8284i	−0.974873	+	1.16181i	−0.986811	+	0.161879i	$0.948244\pi$
$354$		0			0
$355$	−21.0101	+	3.70465i	−1.11510	+	0.196623i
$356$	1.84842	+	1.36455i	0.0979659	+	0.0723210i
$357$		0			0
$358$	−14.5053	+	7.32147i	−0.766628	+	0.386952i
$359$	−1.50638	+	2.60913i	−0.0795039	+	0.137705i	−0.903036	−	0.429565i	$-0.858667\pi$
$359$	−1.50638	+	2.60913i	−0.0795039	+	0.137705i	0.823532	+	0.567270i	$0.192000\pi$
$360$		0			0
$361$	−2.84962	−	4.93568i	−0.149980	−	0.259773i
$362$	−17.3800	−	11.3809i	−0.913471	−	0.598165i
$363$		0			0
$364$	−19.5445	+	8.52426i	−1.02441	+	0.446793i
$365$	7.14370	+	8.51353i	0.373918	+	0.445618i
$366$		0			0
$367$	−1.08161	−	2.97170i	−0.0564595	−	0.155121i	0.908257	−	0.418414i	$-0.137414\pi$
$367$	−1.08161	−	2.97170i	−0.0564595	−	0.155121i	−0.964716	+	0.263292i	$0.915192\pi$
$368$	0.743438	−	14.8218i	0.0387544	−	0.772638i
$369$		0			0
$370$	−0.585718	−	4.92504i	−0.0304500	−	0.256041i
$371$	1.09938	−	6.23487i	0.0570768	−	0.323699i
$372$		0			0
$373$	2.76041	+	1.00471i	0.142928	+	0.0520217i	0.412494	−	0.910960i	$-0.364658\pi$
$373$	2.76041	+	1.00471i	0.142928	+	0.0520217i	−0.269565	+	0.962982i	$0.586880\pi$
$374$	−10.8247	−	10.1714i	−0.559732	−	0.525951i
$375$		0			0
$376$	13.8316	+	4.93980i	0.713311	+	0.254751i
$377$		−	20.5592i		−	1.05886i
$378$		0			0
$379$			1.91457i			0.0983448i	0.998790	+	0.0491724i	$0.0156584\pi$
$379$			1.91457i			0.0983448i	−0.998790	+	0.0491724i	$0.984342\pi$
$380$	−8.35398	+	5.54286i	−0.428550	+	0.284343i
$381$		0			0
$382$	13.2922	−	14.1459i	0.680087	−	0.723766i
$383$	17.6014	+	6.40639i	0.899390	+	0.327351i	0.750008	−	0.661428i	$-0.230049\pi$
$383$	17.6014	+	6.40639i	0.899390	+	0.327351i	0.149382	+	0.988780i	$0.452272\pi$
$384$		0			0
$385$	−1.48980	+	8.44910i	−0.0759275	+	0.430606i
$386$	11.5515	−	1.37377i	0.587954	−	0.0699233i
$387$		0			0
$388$	18.6242	−	4.49336i	0.945498	−	0.228116i
$389$	3.55765	+	9.77456i	0.180380	+	0.495590i	0.996622	−	0.0821196i	$-0.0261689\pi$
$389$	3.55765	+	9.77456i	0.180380	+	0.495590i	−0.816243	+	0.577709i	$0.803947\pi$
$390$		0			0
$391$	−6.41484	−	7.64491i	−0.324412	−	0.386620i
$392$	−6.21964	+	10.9247i	−0.314139	+	0.551782i
$393$		0			0
$394$	7.41361	−	11.3215i	0.373492	−	0.570368i
$395$	−8.95668	−	15.5134i	−0.450660	−	0.780565i
$396$		0			0
$397$	7.93455	−	13.7430i	0.398224	−	0.689744i	−0.595283	−	0.803516i	$-0.702960\pi$
$397$	7.93455	−	13.7430i	0.398224	−	0.689744i	0.993507	+	0.113772i	$0.0362934\pi$
$398$	−9.11138	−	18.0514i	−0.456712	−	0.904837i
$399$		0			0
$400$	7.51073	+	9.92069i	0.375536	+	0.496035i
$401$	5.87809	−	1.03647i	0.293538	−	0.0517586i	−0.0249400	−	0.999689i	$-0.507939\pi$
$401$	5.87809	−	1.03647i	0.293538	−	0.0517586i	0.318478	+	0.947930i	$0.396828\pi$
$402$		0			0
$403$	6.31273	−	7.52322i	0.314460	−	0.374758i
$404$	24.2945	+	7.16672i	1.20870	+	0.356558i
$405$		0			0
$406$	4.17292	+	5.58169i	0.207099	+	0.277015i
$407$	−7.63208	−	6.40408i	−0.378308	−	0.317438i
$408$		0			0
$409$	2.36345	+	13.4038i	0.116865	+	0.662775i	0.985810	+	0.167866i	$0.0536875\pi$
$409$	2.36345	+	13.4038i	0.116865	+	0.662775i	−0.868945	+	0.494909i	$0.835201\pi$
$410$	−5.50317	−	18.2479i	−0.271782	−	0.901202i
$411$		0			0
$412$	−5.01626	+	10.0894i	−0.247134	+	0.497069i
$413$	0.982361	+	0.567167i	0.0483388	+	0.0279084i
$414$		0			0
$415$	−0.536061	+	0.309495i	−0.0263142	+	0.0151925i
$416$	−15.2912	−	34.4891i	−0.749711	−	1.69097i
$417$		0			0
$418$	−4.60489	+	19.6055i	−0.225232	+	0.958938i
$419$	7.77815	−	6.52664i	0.379988	−	0.318847i	−0.432710	−	0.901533i	$-0.642443\pi$
$419$	7.77815	−	6.52664i	0.379988	−	0.318847i	0.812698	+	0.582686i	$0.197998\pi$
$420$		0			0
$421$	−22.4900	+	8.18570i	−1.09610	+	0.398947i	−0.825876	−	0.563852i	$-0.809319\pi$
$421$	−22.4900	+	8.18570i	−1.09610	+	0.398947i	−0.270221	+	0.962798i	$0.587097\pi$
$422$	−22.5318	−	9.66547i	−1.09683	−	0.470508i
$423$		0			0
$424$	11.0432	+	1.87845i	0.536306	+	0.0912255i
$425$	8.24050	+	1.45302i	0.399723	+	0.0704820i
$426$		0			0
$427$	−3.05134	+	8.38348i	−0.147665	+	0.405705i
$428$	16.6572	+	1.87893i	0.805158	+	0.0908214i
$429$		0			0
$430$	−0.406396	+	7.22849i	−0.0195982	+	0.348589i
$431$	−19.6478			−0.946399			−0.473199	−	0.880955i	$-0.656901\pi$
$431$	−19.6478			−0.946399			−0.473199	+	0.880955i	$0.656901\pi$
$432$		0			0
$433$	−11.5738			−0.556202			−0.278101	−	0.960552i	$-0.589705\pi$
$433$	−11.5738			−0.556202			−0.278101	+	0.960552i	$0.589705\pi$
$434$	−0.186869	+	3.32380i	−0.00897000	+	0.159548i
$435$		0			0
$436$	−12.2982	−	1.38723i	−0.588977	−	0.0664364i
$437$	−4.62781	+	12.7148i	−0.221378	+	0.608231i
$438$		0			0
$439$	−11.0923	−	1.95588i	−0.529408	−	0.0933490i	−0.0974464	−	0.995241i	$-0.531067\pi$
$439$	−11.0923	−	1.95588i	−0.529408	−	0.0933490i	−0.431962	+	0.901892i	$0.642179\pi$
$440$	−14.9651	−	2.54555i	−0.713431	−	0.121355i
$441$		0			0
$442$	−23.3156	−	10.0017i	−1.10901	−	0.475731i
$443$	34.5395	−	12.5713i	1.64102	−	0.597282i	0.653802	−	0.756666i	$-0.273173\pi$
$443$	34.5395	−	12.5713i	1.64102	−	0.597282i	0.987217	+	0.159383i	$0.0509506\pi$
$444$		0			0
$445$	1.20956	−	1.01494i	0.0573385	−	0.0481127i
$446$	−2.05288	+	8.74026i	−0.0972069	+	0.413863i
$447$		0			0
$448$	11.1517	+	6.25990i	0.526870	+	0.295753i
$449$	2.77399	−	1.60156i	0.130913	−	0.0755824i	−0.433114	−	0.901339i	$-0.642585\pi$
$449$	2.77399	−	1.60156i	0.130913	−	0.0755824i	0.564026	+	0.825757i	$0.309252\pi$
$450$		0			0
$451$	−33.1571	−	19.1433i	−1.56131	−	0.901421i
$452$	−11.3787	+	22.8865i	−0.535211	+	1.07649i
$453$		0			0
$454$	6.33168	+	20.9952i	0.297160	+	0.985353i
$455$	2.54460	+	14.4312i	0.119293	+	0.676543i
$456$		0			0
$457$	14.8332	+	12.4465i	0.693868	+	0.582224i	0.920022	−	0.391867i	$-0.128171\pi$
$457$	14.8332	+	12.4465i	0.693868	+	0.582224i	−0.226154	+	0.974092i	$0.572615\pi$
$458$	0.863031	+	1.15439i	0.0403268	+	0.0539410i
$459$		0			0
$460$	−9.78223	−	2.88570i	−0.456099	−	0.134546i
$461$	−1.37982	+	1.64440i	−0.0642645	+	0.0765874i	−0.797219	−	0.603690i	$-0.793696\pi$
$461$	−1.37982	+	1.64440i	−0.0642645	+	0.0765874i	0.732954	+	0.680278i	$0.238141\pi$
$462$		0			0
$463$	−19.6343	+	3.46206i	−0.912483	+	0.160895i	−0.610131	−	0.792301i	$-0.708883\pi$
$463$	−19.6343	+	3.46206i	−0.912483	+	0.160895i	−0.302352	+	0.953196i	$0.597772\pi$
$464$	−9.83113	+	7.44292i	−0.456399	+	0.345529i
$465$		0			0
$466$	6.39156	+	12.6630i	0.296083	+	0.586600i
$467$	−4.94711	+	8.56864i	−0.228925	+	0.396509i	−0.957490	−	0.288467i	$-0.906854\pi$
$467$	−4.94711	+	8.56864i	−0.228925	+	0.396509i	0.728565	+	0.684977i	$0.240188\pi$
$468$		0			0
$469$	−13.0208	−	22.5527i	−0.601245	−	1.04139i
$470$	5.52959	−	8.44435i	0.255061	−	0.389509i
$471$		0			0
$472$	−0.992988	+	1.74417i	−0.0457060	+	0.0802821i
$473$	9.34824	+	11.1408i	0.429833	+	0.512254i
$474$		0			0
$475$	−3.88025	−	10.6609i	−0.178038	−	0.489155i
$476$	8.36005	−	2.01699i	0.383182	−	0.0924487i
$477$		0			0
$478$	−26.9680	+	3.20721i	−1.23349	+	0.146694i
$479$	4.47267	−	25.3658i	0.204362	−	1.15899i	−0.694079	−	0.719898i	$-0.744188\pi$
$479$	4.47267	−	25.3658i	0.204362	−	1.15899i	0.898441	−	0.439094i	$-0.144701\pi$
$480$		0			0
$481$	−15.9906	−	5.82011i	−0.729110	−	0.265374i
$482$	−1.11301	+	1.18449i	−0.0506960	+	0.0539520i
$483$		0			0
$484$	−7.07704	+	4.69561i	−0.321683	+	0.213437i
$485$		−	13.1666i		−	0.597865i
$486$		0			0
$487$			25.1669i			1.14042i	0.821498	+	0.570212i	$0.193139\pi$
$487$			25.1669i			1.14042i	−0.821498	+	0.570212i	$0.806861\pi$
$488$	−14.8657	−	5.30910i	−0.672937	−	0.240332i
$489$		0			0
$490$	6.29605	+	5.91608i	0.284426	+	0.267261i
$491$	4.40319	+	1.60263i	0.198713	+	0.0723257i	0.439460	−	0.898262i	$-0.355170\pi$
$491$	4.40319	+	1.60263i	0.198713	+	0.0723257i	−0.240746	+	0.970588i	$0.577392\pi$
$492$		0			0
$493$	−1.43991	+	8.16611i	−0.0648501	+	0.367783i
$494$	4.06218	+	34.1570i	0.182766	+	1.53680i
$495$		0			0
$496$	−5.88285	−	0.295075i	−0.264148	−	0.0132493i
$497$	−8.48632	−	23.3160i	−0.380664	−	1.04586i
$498$		0			0
$499$	6.36794	+	7.58902i	0.285068	+	0.339731i	0.889508	−	0.456920i	$-0.151047\pi$
$499$	6.36794	+	7.58902i	0.285068	+	0.339731i	−0.604440	+	0.796651i	$0.706603\pi$
$500$	20.4371	−	8.91358i	0.913976	−	0.398627i
$501$		0			0
$502$	−26.8883	−	17.6072i	−1.20008	−	0.785846i
$503$	−6.96764	−	12.0683i	−0.310672	−	0.538099i	0.667836	−	0.744308i	$-0.267221\pi$
$503$	−6.96764	−	12.0683i	−0.310672	−	0.538099i	−0.978508	+	0.206209i	$0.933887\pi$
$504$		0			0
$505$	8.70378	−	15.0754i	0.387313	−	0.670846i
$506$	−18.2896	+	9.23160i	−0.813073	+	0.410394i
$507$		0			0
$508$	−12.2939	−	9.07568i	−0.545454	−	0.402668i
$509$	−29.7725	+	5.24969i	−1.31964	+	0.232688i	−0.788730	−	0.614740i	$-0.789261\pi$
$509$	−29.7725	+	5.24969i	−1.31964	+	0.232688i	−0.530911	+	0.847428i	$0.678150\pi$
$510$		0			0
$511$	−8.30833	+	9.90148i	−0.367539	+	0.438016i
$512$	−10.9564	+	19.7979i	−0.484211	+	0.874951i
$513$		0			0
$514$	12.3379	−	9.22391i	0.544201	−	0.406849i
$515$	5.93194	+	4.97749i	0.261392	+	0.219334i
$516$		0			0
$517$	−3.52088	−	19.9679i	−0.154848	−	0.878188i
$518$	5.52265	−	1.66551i	0.242651	−	0.0731782i
$519$		0			0
$520$	−25.5060	+	4.65657i	−1.11851	+	0.204204i
$521$	16.1661	+	9.33349i	0.708249	+	0.408908i	0.810412	−	0.585860i	$-0.199243\pi$
$521$	16.1661	+	9.33349i	0.708249	+	0.408908i	−0.102164	+	0.994768i	$0.532577\pi$
$522$		0			0
$523$	−31.7939	+	18.3562i	−1.39025	+	0.802662i	−0.993343	−	0.115196i	$-0.963250\pi$
$523$	−31.7939	+	18.3562i	−1.39025	+	0.802662i	−0.396909	+	0.917858i	$0.629917\pi$
$524$	1.34135	+	21.5345i	0.0585973	+	0.940740i
$525$		0			0
$526$	0.360311	+	0.0846288i	0.0157103	+	0.00368999i
$527$	−3.03431	+	2.54609i	−0.132177	+	0.110909i
$528$		0			0
$529$	8.67822	−	3.15861i	0.377314	−	0.137331i
$530$	3.03493	−	7.07493i	0.131829	−	0.307315i
$531$		0			0
$532$	−8.03573	−	8.44889i	−0.348393	−	0.366306i
$533$	−64.4003	−	11.3555i	−2.78949	−	0.491862i
$534$		0			0
$535$	3.94014	−	10.8254i	0.170347	−	0.468024i
$536$	39.7636	−	23.2792i	1.71752	−	1.00551i
$537$		0			0
$538$	−10.5566	−	0.593507i	−0.455126	−	0.0255879i
$539$	17.3547			0.747518
$540$		0			0
$541$	12.0288			0.517156			0.258578	−	0.965990i	$-0.416746\pi$
$541$	12.0288			0.517156			0.258578	+	0.965990i	$0.416746\pi$
$542$	−20.6013	−	1.15824i	−0.884902	−	0.0497505i
$543$		0			0
$544$	3.65812	+	14.7700i	0.156841	+	0.633258i
$545$	−2.90904	+	7.99253i	−0.124610	+	0.342363i
$546$		0			0
$547$	28.2762	+	4.98585i	1.20900	+	0.213180i	0.741586	−	0.670858i	$-0.234074\pi$
$547$	28.2762	+	4.98585i	1.20900	+	0.213180i	0.467416	+	0.884038i	$0.345185\pi$
$548$	−15.3240	+	14.5747i	−0.654610	+	0.622599i
$549$		0			0
$550$	6.77202	−	15.7867i	0.288760	−	0.673148i
$551$	10.5646	−	3.84522i	0.450069	−	0.163812i
$552$		0			0
$553$	15.9596	−	13.3917i	0.678671	−	0.569472i
$554$	−7.64717	−	1.79614i	−0.324897	−	0.0763108i
$555$		0			0
$556$	3.23367	−	0.201421i	0.137138	−	0.00854214i
$557$	6.08867	−	3.51530i	0.257985	−	0.148948i	−0.365430	−	0.930839i	$-0.619078\pi$
$557$	6.08867	−	3.51530i	0.257985	−	0.148948i	0.623415	+	0.781891i	$0.285745\pi$
$558$		0			0
$559$	21.5121	+	12.4200i	0.909866	+	0.525312i
$560$	5.97956	−	6.44120i	0.252683	−	0.272191i
$561$		0			0
$562$	−11.1882	+	3.37412i	−0.471948	+	0.142329i
$563$	−3.67394	−	20.8360i	−0.154838	−	0.878132i	−0.958933	−	0.283631i	$-0.908461\pi$
$563$	−3.67394	−	20.8360i	−0.154838	−	0.878132i	0.804095	−	0.594501i	$-0.202650\pi$
$564$		0			0
$565$	13.4558	+	11.2908i	0.566091	+	0.475007i
$566$	36.8105	−	27.5199i	1.54726	−	1.15675i
$567$		0			0
$568$	41.1625	−	15.2644i	1.72714	−	0.640480i
$569$	1.16629	−	1.38993i	0.0488934	−	0.0582688i	−0.741044	−	0.671457i	$-0.765669\pi$
$569$	1.16629	−	1.38993i	0.0488934	−	0.0582688i	0.789937	+	0.613188i	$0.210113\pi$
$570$		0			0
$571$	20.8305	−	3.67297i	0.871728	−	0.153709i	0.280149	−	0.959956i	$-0.409616\pi$
$571$	20.8305	−	3.67297i	0.871728	−	0.153709i	0.591579	+	0.806247i	$0.298505\pi$
$572$	−30.9329	+	41.9017i	−1.29337	+	1.75200i
$573$		0			0
$574$	19.7891	−	9.98843i	0.825979	−	0.416909i
$575$	5.77065	−	9.99506i	0.240653	−	0.416823i
$576$		0			0
$577$	−9.92984	−	17.1990i	−0.413385	−	0.716003i	0.581873	−	0.813280i	$-0.302320\pi$
$577$	−9.92984	−	17.1990i	−0.413385	−	0.716003i	−0.995257	+	0.0972766i	$0.968987\pi$
$578$	−11.5526	−	7.56498i	−0.480527	−	0.314662i
$579$		0			0
$580$	3.38782	+	7.76762i	0.140672	+	0.322533i
$581$	−0.462745	−	0.551478i	−0.0191979	−	0.0228792i
$582$		0			0
$583$	−5.28910	−	14.5317i	−0.219052	−	0.601841i
$584$	−17.6077	−	14.5941i	−0.728612	−	0.603910i
$585$		0			0
$586$	−0.571965	−	4.80940i	−0.0236277	−	0.198674i
$587$	−3.45020	+	19.5670i	−0.142405	+	0.807618i	0.827009	+	0.562188i	$0.190040\pi$
$587$	−3.45020	+	19.5670i	−0.142405	+	0.807618i	−0.969414	+	0.245430i	$0.921071\pi$
$588$		0			0
$589$	5.04659	+	1.83681i	0.207941	+	0.0756843i
$590$	1.00519	+	0.944523i	0.0413829	+	0.0388854i
$591$		0			0
$592$	3.00588	+	9.75350i	0.123541	+	0.400866i
$593$		−	25.8771i		−	1.06265i	−0.847169	−	0.531323i	$-0.821695\pi$
$593$		−	25.8771i		−	1.06265i	0.847169	−	0.531323i	$-0.178305\pi$
$594$		0			0
$595$		−	5.91025i		−	0.242297i
$596$	15.6349	+	23.5642i	0.640429	+	0.965229i
$597$		0			0
$598$	−23.9621	+	25.5011i	−0.979882	+	1.04282i
$599$	0.696001	+	0.253324i	0.0284378	+	0.0103505i	0.356200	−	0.934410i	$-0.384072\pi$
$599$	0.696001	+	0.253324i	0.0284378	+	0.0103505i	−0.327762	+	0.944760i	$0.606294\pi$
$600$		0			0
$601$	−1.05648	+	5.99159i	−0.0430947	+	0.244402i	−0.998744	−	0.0501051i	$-0.984044\pi$
$601$	−1.05648	+	5.99159i	−0.0430947	+	0.244402i	0.955649	+	0.294507i	$0.0951555\pi$
$602$	−8.36129	+	0.994380i	−0.340781	+	0.0405279i
$603$		0			0
$604$	5.11809	+	21.2135i	0.208252	+	0.863166i
$605$	1.99632	+	5.48485i	0.0811620	+	0.222991i
$606$		0			0
$607$	2.46703	+	2.94009i	0.100134	+	0.119335i	0.813784	−	0.581167i	$-0.197404\pi$
$607$	2.46703	+	2.94009i	0.100134	+	0.119335i	−0.713650	+	0.700502i	$0.752959\pi$
$608$	14.8628	−	14.3081i	0.602766	−	0.580270i
$609$		0			0
$610$	−5.94298	+	9.07565i	−0.240624	+	0.367462i
$611$	−17.3158	−	29.9918i	−0.700521	−	1.21334i
$612$		0			0
$613$	−0.245022	+	0.424390i	−0.00989633	+	0.0171409i	−0.870931	−	0.491405i	$-0.836483\pi$
$613$	−0.245022	+	0.424390i	−0.00989633	+	0.0171409i	0.861035	+	0.508546i	$0.169817\pi$
$614$	2.70171	+	5.35262i	0.109032	+	0.216014i
$615$		0			0
$616$	−0.106737	−	17.6545i	−0.00430054	−	0.711319i
$617$	13.7119	−	2.41778i	0.552020	−	0.0973360i	0.109321	−	0.994006i	$-0.465132\pi$
$617$	13.7119	−	2.41778i	0.552020	−	0.0973360i	0.442699	+	0.896671i	$0.354021\pi$
$618$		0			0
$619$	26.8642	−	32.0155i	1.07976	−	1.28681i	0.124124	−	0.992267i	$-0.460388\pi$
$619$	26.8642	−	32.0155i	1.07976	−	1.28681i	0.955638	−	0.294543i	$-0.0951676\pi$
$620$	−1.14535	+	3.88263i	−0.0459984	+	0.155930i
$621$		0			0
$622$	−19.7240	−	26.3828i	−0.790860	−	1.05785i
$623$	1.40675	+	1.18040i	0.0563602	+	0.0472919i
$624$		0			0
$625$	0.0400863	+	0.227341i	0.00160345	+	0.00909364i
$626$	−3.31617	−	10.9961i	−0.132541	−	0.439492i
$627$		0			0
$628$	−18.4280	−	9.16209i	−0.735359	−	0.365607i
$629$	5.94383	+	3.43167i	0.236996	+	0.136830i
$630$		0			0
$631$	34.7995	−	20.0915i	1.38535	−	0.799831i	0.392562	−	0.919726i	$-0.371589\pi$
$631$	34.7995	−	20.0915i	1.38535	−	0.799831i	0.992787	+	0.119895i	$0.0382557\pi$
$632$	23.8648	+	28.0943i	0.949292	+	1.11753i
$633$		0			0
$634$	−5.90590	+	25.1447i	−0.234553	+	0.998622i
$635$	−8.04482	+	6.75040i	−0.319249	+	0.267882i
$636$		0			0
$637$	27.8543	−	10.1381i	1.10363	−	0.401688i
$638$	15.6442	+	6.71088i	0.619359	+	0.265686i
$639$		0			0
$640$	11.4605	+	10.5108i	0.453015	+	0.415477i
$641$	27.8087	+	4.90343i	1.09838	+	0.193674i	0.693330	−	0.720621i	$-0.256143\pi$
$641$	27.8087	+	4.90343i	1.09838	+	0.193674i	0.405050	+	0.914295i	$0.367254\pi$
$642$		0			0
$643$	−3.39235	+	9.32039i	−0.133781	+	0.367560i	−0.988437	−	0.151635i	$-0.951546\pi$
$643$	−3.39235	+	9.32039i	−0.133781	+	0.367560i	0.854655	+	0.519196i	$0.173768\pi$
$644$	1.32956	−	11.7870i	0.0523921	−	0.464471i
$645$		0			0
$646$	0.778760	−	13.8516i	0.0306399	−	0.544985i
$647$	35.8829			1.41070			0.705352	−	0.708857i	$-0.250789\pi$
$647$	35.8829			1.41070			0.705352	+	0.708857i	$0.250789\pi$
$648$		0			0
$649$	2.77073			0.108761
$650$	1.64694	−	29.2938i	0.0645983	−	1.14900i
$651$		0			0
$652$	−1.38585	+	12.2859i	−0.0542740	+	0.481155i
$653$	13.2180	−	36.3162i	0.517261	−	1.42116i	−0.356264	−	0.934385i	$-0.615950\pi$
$653$	13.2180	−	36.3162i	0.517261	−	1.42116i	0.873525	−	0.486779i	$-0.161828\pi$
$654$		0			0
$655$	14.6029	+	2.57488i	0.570582	+	0.100609i
$656$	17.8844	+	34.9062i	0.698267	+	1.36286i
$657$		0			0
$658$	10.7886	+	4.62797i	0.420582	+	0.180417i
$659$	−25.4346	+	9.25743i	−0.990791	+	0.360618i	−0.786026	−	0.618193i	$-0.787865\pi$
$659$	−25.4346	+	9.25743i	−0.990791	+	0.360618i	−0.204764	+	0.978811i	$0.565643\pi$
$660$		0			0
$661$	−31.8188	+	26.6991i	−1.23761	+	1.03848i	−0.239901	+	0.970797i	$0.577115\pi$
$661$	−31.8188	+	26.6991i	−1.23761	+	1.03848i	−0.997707	+	0.0676787i	$0.978441\pi$
$662$	−9.12358	+	38.8441i	−0.354598	+	1.50972i
$663$		0			0
$664$	0.970788	−	0.824641i	0.0376739	−	0.0320023i
$665$	−6.93972	+	4.00665i	−0.269111	+	0.155371i
$666$		0			0
$667$	9.90482	+	5.71855i	0.383516	+	0.221423i
$668$	0.784391	+	0.389985i	0.0303490	+	0.0150890i
$669$		0			0
$670$	−9.14302	−	30.3173i	−0.353225	−	1.17126i
$671$	3.78410	+	21.4607i	0.146084	+	0.828482i
$672$		0			0
$673$	−12.2531	−	10.2816i	−0.472323	−	0.396326i	0.375318	−	0.926896i	$-0.377533\pi$
$673$	−12.2531	−	10.2816i	−0.472323	−	0.396326i	−0.847641	+	0.530570i	$0.821978\pi$
$674$	10.3023	+	13.7804i	0.396831	+	0.530800i
$675$		0			0
$676$	−17.8132	+	60.3850i	−0.685123	+	2.32250i
$677$	20.2335	−	24.1133i	0.777635	−	0.926750i	−0.221189	−	0.975231i	$-0.570994\pi$
$677$	20.2335	−	24.1133i	0.777635	−	0.926750i	0.998824	+	0.0484812i	$0.0154381\pi$
$678$		0			0
$679$	15.0805	−	2.65910i	0.578736	−	0.102047i
$680$	10.4571	−	0.0632223i	0.401012	−	0.00242446i
$681$		0			0
$682$	3.66408	+	7.25927i	0.140305	+	0.277972i
$683$	−19.8352	+	34.3556i	−0.758973	+	1.31458i	0.184402	+	0.982851i	$0.440965\pi$
$683$	−19.8352	+	34.3556i	−0.758973	+	1.31458i	−0.943375	+	0.331729i	$0.892368\pi$
$684$		0			0
$685$	7.26700	+	12.5868i	0.277658	+	0.480917i
$686$	−14.1738	+	21.6452i	−0.541160	+	0.826416i
$687$		0			0
$688$	−1.84881	−	14.7831i	−0.0704853	−	0.563602i
$689$	−16.9781	−	20.2337i	−0.646813	−	0.770842i
$690$		0			0
$691$	13.5569	+	37.2473i	0.515729	+	1.41695i	0.875184	+	0.483790i	$0.160740\pi$
$691$	13.5569	+	37.2473i	0.515729	+	1.41695i	−0.359455	+	0.933162i	$0.617038\pi$
$692$	−3.70988	−	15.3768i	−0.141028	−	0.584536i
$693$		0			0
$694$	−9.13709	+	1.08664i	−0.346839	+	0.0412484i
$695$	0.386650	−	2.19280i	0.0146665	−	0.0831778i
$696$		0			0
$697$	24.7844	+	9.02079i	0.938777	+	0.341687i
$698$	−29.8267	+	31.7424i	−1.12896	+	1.20147i
$699$		0			0
$700$	5.49864	+	8.28733i	0.207829	+	0.313232i
$701$		−	14.6338i		−	0.552710i	−0.961056	−	0.276355i	$-0.910873\pi$
$701$		−	14.6338i		−	0.552710i	0.961056	−	0.276355i	$-0.0891265\pi$
$702$		0			0
$703$		−	9.30554i		−	0.350965i
$704$	31.2352	−	0.377702i	1.17722	−	0.0142352i
$705$		0			0
$706$	−29.3673	−	27.5950i	−1.10525	−	1.03855i
$707$	19.0245	+	6.92437i	0.715491	+	0.260418i
$708$		0			0
$709$	6.05391	−	34.3334i	0.227359	−	1.28942i	−0.630764	−	0.775975i	$-0.717258\pi$
$709$	6.05391	−	34.3334i	0.227359	−	1.28942i	0.858123	−	0.513444i	$-0.171630\pi$
$710$	−3.56304	−	29.9601i	−0.133719	−	1.12438i
$711$		0			0
$712$	−2.07346	+	2.50161i	−0.0777061	+	0.0937518i
$713$	1.86858	+	5.13387i	0.0699787	+	0.192265i
$714$		0			0
$715$	23.0076	+	27.4194i	0.860435	+	1.02543i
$716$	−9.18631	−	21.0624i	−0.343308	−	0.787140i
$717$		0			0
$718$	−3.56447	−	2.33411i	−0.133025	−	0.0871083i
$719$	−3.63844	−	6.30196i	−0.135691	−	0.235024i	0.790170	−	0.612887i	$-0.209992\pi$
$719$	−3.63844	−	6.30196i	−0.135691	−	0.235024i	−0.925861	+	0.377864i	$0.876659\pi$
$720$		0			0
$721$	−4.50301	+	7.79945i	−0.167701	+	0.290467i
$722$	7.19532	−	3.63180i	0.267782	−	0.135162i
$723$		0			0
$724$	17.4493	−	23.6368i	0.648498	−	0.878454i
$725$	−9.44390	+	1.66521i	−0.350738	+	0.0618445i
$726$		0			0
$727$	−25.9765	+	30.9576i	−0.963414	+	1.14815i	0.0255013	+	0.999675i	$0.491882\pi$
$727$	−25.9765	+	30.9576i	−0.963414	+	1.14815i	−0.988916	+	0.148478i	$0.952563\pi$
$728$	−10.4846	−	28.2732i	−0.388585	−	1.04787i
$729$		0			0
$730$	−12.5881	+	9.41095i	−0.465905	+	0.348315i
$731$	−7.67473	−	6.43987i	−0.283860	−	0.238187i
$732$		0			0
$733$	−7.32008	−	41.5142i	−0.270373	−	1.53336i	−0.753285	−	0.657694i	$-0.771532\pi$
$733$	−7.32008	−	41.5142i	−0.270373	−	1.53336i	0.482912	−	0.875669i	$-0.339579\pi$
$734$	4.28185	−	1.29131i	0.158046	−	0.0476631i
$735$		0			0
$736$	20.8691	+	2.22633i	0.769244	+	0.0820637i
$737$	−55.0875	−	31.8048i	−2.02917	−	1.17154i
$738$		0			0
$739$	−7.93929	+	4.58375i	−0.292052	+	0.168616i	−0.638867	−	0.769317i	$-0.720596\pi$
$739$	−7.93929	+	4.58375i	−0.292052	+	0.168616i	0.346815	+	0.937934i	$0.387263\pi$
$740$	7.00057	−	0.436055i	0.257346	−	0.0160297i
$741$		0			0
$742$	8.71627	+	2.04725i	0.319984	+	0.0751569i
$743$	10.4100	−	8.73505i	0.381907	−	0.320458i	−0.431544	−	0.902092i	$-0.642031\pi$
$743$	10.4100	−	8.73505i	0.381907	−	0.320458i	0.813450	+	0.581634i	$0.197586\pi$
$744$		0			0
$745$	18.2628	−	6.64711i	0.669097	−	0.243531i
$746$	−1.63776	+	3.81789i	−0.0599627	+	0.139783i
$747$		0			0
$748$	15.2212	−	14.4768i	0.556542	−	0.529326i
$749$	13.1948	+	2.32659i	0.482126	+	0.0850118i
$750$		0			0
$751$	12.3201	−	33.8492i	0.449567	−	1.23518i	−0.483459	−	0.875367i	$-0.660620\pi$
$751$	12.3201	−	33.8492i	0.449567	−	1.23518i	0.933026	−	0.359809i	$-0.117158\pi$
$752$	−8.07292	+	19.1379i	−0.294389	+	0.697886i
$753$		0			0
$754$	29.0293	+	1.63207i	1.05719	+	0.0594366i
$755$	14.9972			0.545803
$756$		0			0
$757$	20.5853			0.748185			0.374093	−	0.927391i	$-0.377954\pi$
$757$	20.5853			0.748185			0.374093	+	0.927391i	$0.377954\pi$
$758$	−2.70334	−	0.151986i	−0.0981898	−	0.00552038i
$759$		0			0
$760$	−7.16326	−	12.2357i	−0.259839	−	0.443835i
$761$	−15.1391	+	41.5945i	−0.548793	+	1.50780i	0.286548	+	0.958066i	$0.407492\pi$
$761$	−15.1391	+	41.5945i	−0.548793	+	1.50780i	−0.835341	+	0.549732i	$0.814730\pi$
$762$		0			0
$763$	−9.74183	−	1.71775i	−0.352678	−	0.0621866i
$764$	18.9186	+	19.8913i	0.684450	+	0.719641i
$765$		0			0
$766$	−10.4430	+	24.3443i	−0.377320	+	0.879597i
$767$	4.44704	−	1.61859i	0.160573	−	0.0584439i
$768$		0			0
$769$	−22.3866	+	18.7846i	−0.807281	+	0.677389i	−0.949957	−	0.312381i	$-0.898874\pi$
$769$	−22.3866	+	18.7846i	−0.807281	+	0.677389i	0.142677	+	0.989769i	$0.454429\pi$
$770$	−11.8117	−	2.77430i	−0.425665	−	0.0999789i
$771$		0			0
$772$	1.02275	+	16.4195i	0.0368095	+	0.590952i
$773$	2.91631	−	1.68373i	0.104892	−	0.0605596i	−0.446636	−	0.894716i	$-0.647378\pi$
$773$	2.91631	−	1.68373i	0.104892	−	0.0605596i	0.551528	+	0.834156i	$0.314045\pi$
$774$		0			0
$775$	−3.96710	−	2.29041i	−0.142503	−	0.0822739i
$776$	4.86610	+	26.6537i	0.174683	+	0.956812i
$777$		0			0
$778$	−14.0839	+	4.24740i	−0.504934	+	0.152277i
$779$	−6.20967	−	35.2168i	−0.222485	−	1.26177i
$780$		0			0
$781$	−46.4276	−	38.9574i	−1.66131	−	1.39400i
$782$	11.3037	−	8.45077i	0.404220	−	0.302199i
$783$		0			0
$784$	−14.9318	−	9.64928i	−0.533279	−	0.344617i
$785$	−9.09126	+	10.8345i	−0.324481	+	0.386701i
$786$		0			0
$787$	−38.7602	+	6.83447i	−1.38165	+	0.243622i	−0.814582	−	0.580048i	$-0.803034\pi$
$787$	−38.7602	+	6.83447i	−1.38165	+	0.243622i	−0.567069	+	0.823670i	$0.691923\pi$
$788$	15.3972	+	11.3666i	0.548503	+	0.404920i
$789$		0			0
$790$	22.6157	−	11.4152i	0.804632	−	0.406134i
$791$	−10.2145	+	17.6920i	−0.363186	+	0.629057i
$792$		0			0
$793$	18.6103	+	32.2340i	0.660871	+	1.14466i
$794$	18.7751	+	12.2944i	0.666303	+	0.436313i
$795$		0			0
$796$	26.2117	−	11.4321i	0.929047	−	0.405201i
$797$	16.5914	+	19.7729i	0.587699	+	0.700392i	0.975162	−	0.221493i	$-0.0710931\pi$
$797$	16.5914	+	19.7729i	0.587699	+	0.700392i	−0.387463	+	0.921885i	$0.626649\pi$
$798$		0			0
$799$	4.77727	+	13.1254i	0.169008	+	0.464345i
$800$	−14.6041	+	9.81749i	−0.516332	+	0.347101i
$801$		0			0
$802$	0.996847	+	8.38204i	0.0351999	+	0.295980i
$803$	−5.48240	+	31.0922i	−0.193470	+	1.09722i
$804$		0			0
$805$	−7.66028	−	2.78811i	−0.269989	−	0.0982680i
$806$	10.1215	+	9.51070i	0.356516	+	0.335000i
$807$		0			0
$808$	−12.0479	+	33.7345i	−0.423843	+	1.18677i
$809$			54.1748i			1.90469i	0.305029	+	0.952343i	$0.401334\pi$
$809$			54.1748i			1.90469i	−0.305029	+	0.952343i	$0.598666\pi$
$810$		0			0
$811$		−	25.4797i		−	0.894714i	−0.894356	−	0.447357i	$-0.852365\pi$
$811$		−	25.4797i		−	0.894714i	0.894356	−	0.447357i	$-0.147635\pi$
$812$	−8.21252	+	5.44900i	−0.288203	+	0.191223i
$813$		0			0
$814$	9.64832	−	10.2680i	0.338173	−	0.359893i
$815$	7.98456	+	2.90614i	0.279687	+	0.101798i
$816$		0			0
$817$	−2.35877	+	13.3772i	−0.0825228	+	0.468010i
$818$	−19.1135	+	2.27311i	−0.668290	+	0.0794774i
$819$		0			0
$820$	26.2027	−	6.32180i	0.915037	−	0.220767i
$821$	15.2379	+	41.8658i	0.531807	+	1.46113i	0.856919	+	0.515451i	$0.172376\pi$
$821$	15.2379	+	41.8658i	0.531807	+	1.46113i	−0.325112	+	0.945675i	$0.605402\pi$
$822$		0			0
$823$	−8.99956	−	10.7253i	−0.313705	−	0.373859i	0.586035	−	0.810286i	$-0.300688\pi$
$823$	−8.99956	−	10.7253i	−0.313705	−	0.373859i	−0.899740	+	0.436427i	$0.856244\pi$
$824$	−13.8479	−	7.88382i	−0.482413	−	0.274646i
$825$		0			0
$826$	−0.878814	+	1.34205i	−0.0305778	+	0.0466960i
$827$	21.2656	+	36.8331i	0.739478	+	1.28081i	0.952730	+	0.303817i	$0.0982611\pi$
$827$	21.2656	+	36.8331i	0.739478	+	1.28081i	−0.213252	+	0.976997i	$0.568406\pi$
$828$		0			0
$829$	−2.02999	+	3.51605i	−0.0705046	+	0.122118i	−0.899123	−	0.437697i	$-0.855794\pi$
$829$	−2.02999	+	3.51605i	−0.0705046	+	0.122118i	0.828618	+	0.559815i	$0.189128\pi$
$830$	−0.394447	−	0.781479i	−0.0136915	−	0.0271255i
$831$		0			0
$832$	49.9120	−	18.8530i	1.73039	−	0.653610i
$833$	−11.7737	+	2.07603i	−0.407936	+	0.0719301i
$834$		0			0
$835$	0.386970	−	0.461173i	0.0133917	−	0.0159596i
$836$	−27.3171	−	8.05839i	−0.944783	−	0.278705i
$837$		0			0
$838$	8.59806	+	11.5007i	0.297015	+	0.397286i
$839$	−7.46280	−	6.26203i	−0.257644	−	0.216189i	0.504811	−	0.863230i	$-0.331562\pi$
$839$	−7.46280	−	6.26203i	−0.257644	−	0.216189i	−0.762456	+	0.647040i	$0.776007\pi$
$840$		0			0
$841$	3.38562	+	19.2008i	0.116745	+	0.662096i
$842$	−9.77273	−	32.4054i	−0.336791	−	1.11676i
$843$		0			0
$844$	15.4361	−	31.0473i	0.531334	−	1.06869i
$845$	37.4705	+	21.6336i	1.28903	+	0.744219i
$846$		0			0
$847$	−5.87895	+	3.39422i	−0.202003	+	0.116627i
$848$	−3.52899	+	15.4437i	−0.121186	+	0.530340i
$849$		0			0
$850$	−2.70581	+	11.5201i	−0.0928084	+	0.395136i
$851$	7.25174	−	6.08494i	0.248587	−	0.208589i
$852$		0			0
$853$	−15.2217	+	5.54023i	−0.521179	+	0.189694i	−0.589196	−	0.807990i	$-0.700555\pi$
$853$	−15.2217	+	5.54023i	−0.521179	+	0.189694i	0.0680162	+	0.997684i	$0.478333\pi$
$854$	−11.5951	−	4.97395i	−0.396777	−	0.170205i
$855$		0			0
$856$	−3.97533	+	23.3706i	−0.135874	+	0.798790i
$857$	1.64050	+	0.289264i	0.0560383	+	0.00988106i	0.201597	−	0.979469i	$-0.435387\pi$
$857$	1.64050	+	0.289264i	0.0560383	+	0.00988106i	−0.145559	+	0.989350i	$0.546498\pi$
$858$		0			0
$859$	−1.29836	+	3.56720i	−0.0442993	+	0.121711i	−0.959870	−	0.280446i	$-0.909517\pi$
$859$	−1.29836	+	3.56720i	−0.0442993	+	0.121711i	0.915570	+	0.402158i	$0.131740\pi$
$860$	−10.1742	−	1.14765i	−0.346939	−	0.0391345i
$861$		0			0
$862$	1.55971	−	27.7423i	0.0531241	−	0.944907i
$863$	50.6239			1.72326			0.861629	−	0.507538i	$-0.169444\pi$
$863$	50.6239			1.72326			0.861629	+	0.507538i	$0.169444\pi$
$864$		0			0
$865$	−10.8708			−0.369618
$866$	0.918773	−	16.3420i	0.0312212	−	0.555325i
$867$		0			0
$868$	−4.67832	−	0.527712i	−0.158792	−	0.0179117i
$869$	17.4050	−	47.8198i	0.590424	−	1.62218i
$870$		0			0
$871$	−106.995	−	18.8661i	−3.62539	−	0.639255i
$872$	2.93503	−	17.2547i	0.0993926	−	0.584319i
$873$		0			0
$874$	−17.5857	−	7.54374i	−0.594846	−	0.255171i
$875$	16.7464	−	6.09519i	0.566132	−	0.206055i
$876$		0			0
$877$	28.4064	−	23.8358i	0.959217	−	0.804879i	−0.0216083	−	0.999767i	$-0.506879\pi$
$877$	28.4064	−	23.8358i	0.959217	−	0.804879i	0.980826	+	0.194888i	$0.0624342\pi$
$878$	3.64222	−	15.5069i	0.122919	−	0.523334i
$879$		0			0
$880$	4.78226	−	20.9283i	0.161210	−	0.705495i
$881$	−32.9375	+	19.0165i	−1.10969	+	0.640682i	−0.938750	−	0.344599i	$-0.888015\pi$
$881$	−32.9375	+	19.0165i	−1.10969	+	0.640682i	−0.170944	+	0.985281i	$0.554682\pi$
$882$		0			0
$883$	19.2734	+	11.1275i	0.648603	+	0.374471i	0.787921	−	0.615777i	$-0.211158\pi$
$883$	19.2734	+	11.1275i	0.648603	+	0.374471i	−0.139318	+	0.990248i	$0.544491\pi$
$884$	15.9731	−	32.1272i	0.537233	−	1.08056i
$885$		0			0
$886$	15.0086	+	49.7671i	0.504225	+	1.67196i
$887$	−2.07379	−	11.7610i	−0.0696309	−	0.394897i	−0.999627	−	0.0273261i	$-0.991301\pi$
$887$	−2.07379	−	11.7610i	−0.0696309	−	0.394897i	0.929996	−	0.367571i	$-0.119810\pi$
$888$		0			0
$889$	−9.35636	−	7.85091i	−0.313802	−	0.263311i
$890$	1.33706	+	1.78844i	0.0448183	+	0.0599488i
$891$		0			0
$892$	−12.1781	−	3.59247i	−0.407754	−	0.120285i
$893$	12.1731	−	14.5073i	0.407357	−	0.485469i
$894$		0			0
$895$	−15.5520	+	2.74223i	−0.519845	+	0.0916627i
$896$	−9.72415	+	15.2491i	−0.324861	+	0.509437i
$897$		0			0
$898$	2.04117	+	4.04396i	0.0681147	+	0.134949i
$899$	2.26973	−	3.93129i	0.0756997	−	0.131116i
$900$		0			0
$901$	5.32657	+	9.22589i	0.177454	+	0.307359i
$902$	29.6621	−	45.2976i	0.987640	−	1.50825i
$903$		0			0
$904$	−31.4121	−	17.8834i	−1.04475	−	0.594794i
$905$	−12.9786	−	15.4673i	−0.431424	−	0.514151i
$906$		0			0
$907$	−2.47672	−	6.80473i	−0.0822381	−	0.225947i	0.891758	−	0.452513i	$-0.149472\pi$
$907$	−2.47672	−	6.80473i	−0.0822381	−	0.225947i	−0.973996	+	0.226566i	$0.927250\pi$
$908$	−30.1475	+	7.27355i	−1.00048	+	0.241381i
$909$		0			0
$910$	−20.5786	+	2.44734i	−0.682173	+	0.0811284i
$911$	−2.01998	+	11.4559i	−0.0669251	+	0.379551i	0.932887	+	0.360169i	$0.117281\pi$
$911$	−2.01998	+	11.4559i	−0.0669251	+	0.379551i	−0.999812	+	0.0193820i	$0.993830\pi$
$912$		0			0
$913$	−1.65240	−	0.601423i	−0.0546863	−	0.0199042i
$914$	−18.7518	+	19.9562i	−0.620255	+	0.660092i
$915$		0			0
$916$	−1.69849	+	1.12695i	−0.0561196	+	0.0372353i
$917$			17.2456i			0.569499i
$918$		0			0
$919$			21.8452i			0.720605i	0.932835	+	0.360303i	$0.117327\pi$
$919$			21.8452i			0.720605i	−0.932835	+	0.360303i	$0.882673\pi$
$920$	4.85111	−	13.5833i	0.159936	−	0.447827i
$921$		0			0
$922$	−2.21233	−	2.07882i	−0.0728593	−	0.0684622i
$923$	−97.2743	−	35.4050i	−3.20182	−	1.16537i
$924$		0			0
$925$	−1.37830	+	7.81671i	−0.0453181	+	0.257012i
$926$	−3.32972	−	27.9981i	−0.109421	−	0.920076i
$927$		0			0
$928$	−9.72886	−	14.4722i	−0.319365	−	0.475075i
$929$	−18.5670	−	51.0125i	−0.609164	−	1.67366i	−0.732056	−	0.681244i	$-0.761439\pi$
$929$	−18.5670	−	51.0125i	−0.609164	−	1.67366i	0.122892	−	0.992420i	$-0.460783\pi$
$930$		0			0
$931$	10.4192	+	12.4172i	0.341477	+	0.406956i
$932$	−18.3873	+	8.01955i	−0.602295	+	0.262689i
$933$		0			0
$934$	−11.7061	−	7.66545i	−0.383034	−	0.250821i
$935$	−7.21822	−	12.5023i	−0.236061	−	0.408870i
$936$		0			0
$937$	−16.0875	+	27.8643i	−0.525555	+	0.910288i	0.474002	+	0.880524i	$0.342809\pi$
$937$	−16.0875	+	27.8643i	−0.525555	+	0.910288i	−0.999557	+	0.0297643i	$0.990524\pi$
$938$	32.8777	−	16.5949i	1.07350	−	0.541841i
$939$		0			0
$940$	11.4843	+	8.47803i	0.374577	+	0.276523i
$941$	41.3860	−	7.29746i	1.34914	−	0.237891i	0.548058	−	0.836440i	$-0.315367\pi$
$941$	41.3860	−	7.29746i	1.34914	−	0.237891i	0.801086	+	0.598550i	$0.204256\pi$
$942$		0			0
$943$	23.3837	−	27.8676i	0.761477	−	0.907493i
$944$	−2.38392	−	1.54054i	−0.0775899	−	0.0501404i
$945$		0			0
$946$	−16.4727	+	12.3152i	−0.535575	+	0.400401i
$947$	−0.0104289	−	0.00875091i	−0.000338895	−	0.000284366i	0.642618	−	0.766187i	$-0.277848\pi$
$947$	−0.0104289	−	0.00875091i	−0.000338895	−	0.000284366i	−0.642957	+	0.765902i	$0.722293\pi$
$948$		0			0
$949$	9.36399	+	53.1058i	0.303968	+	1.72389i
$950$	15.3610	−	4.63254i	0.498378	−	0.150299i
$951$		0			0
$952$	2.18431	+	11.9644i	0.0707938	+	0.387768i
$953$	41.1680	+	23.7683i	1.33356	+	0.769932i	0.985844	−	0.167667i	$-0.0536235\pi$
$953$	41.1680	+	23.7683i	1.33356	+	0.769932i	0.347718	+	0.937599i	$0.386957\pi$
$954$		0			0
$955$	16.3382	−	9.43289i	0.528693	−	0.305241i
$956$	−2.38771	−	38.3330i	−0.0772239	−	1.23978i
$957$		0			0
$958$	35.4610	+	8.32898i	1.14569	+	0.269097i
$959$	−12.9488	+	10.8653i	−0.418138	+	0.350860i
$960$		0			0
$961$	−27.0928	+	9.86098i	−0.873961	+	0.318096i
$962$	9.48730	−	22.1165i	0.305883	−	0.713064i
$963$		0			0
$964$	−1.58413	−	1.66557i	−0.0510212	−	0.0536445i
$965$	11.1343	+	1.96328i	0.358427	+	0.0632003i
$966$		0			0
$967$	−1.45894	+	4.00841i	−0.0469164	+	0.128902i	−0.960938	−	0.276764i	$-0.910738\pi$
$967$	−1.45894	+	4.00841i	−0.0469164	+	0.128902i	0.914022	+	0.405666i	$0.132960\pi$
$968$	−6.06833	−	10.3654i	−0.195043	−	0.333157i
$969$		0			0
$970$	18.5910	+	1.04522i	0.596922	+	0.0335598i
$971$	−40.5152			−1.30019			−0.650097	−	0.759851i	$-0.725272\pi$
$971$	−40.5152			−1.30019			−0.650097	+	0.759851i	$0.725272\pi$
$972$		0			0
$973$	2.58964			0.0830199
$974$	−35.5353	−	1.99785i	−1.13863	−	0.0640152i
$975$		0			0
$976$	8.67646	−	20.5686i	0.277727	−	0.658385i
$977$	0.197548	−	0.542760i	0.00632013	−	0.0173644i	−0.936492	−	0.350688i	$-0.885948\pi$
$977$	0.197548	−	0.542760i	0.00632013	−	0.0173644i	0.942813	+	0.333323i	$0.108170\pi$
$978$		0			0
$979$	4.41742	+	0.778910i	0.141181	+	0.0248941i
$980$	−8.85321	+	8.42027i	−0.282805	+	0.268976i
$981$		0			0
$982$	−2.61243	+	6.09001i	−0.0833660	+	0.194340i
$983$	−48.7103	+	17.7291i	−1.55362	+	0.565471i	−0.969263	−	0.246028i	$-0.920875\pi$
$983$	−48.7103	+	17.7291i	−1.55362	+	0.565471i	−0.584355	+	0.811498i	$0.698652\pi$
$984$		0			0
$985$	10.0756	−	8.45440i	0.321034	−	0.269379i
$986$	−11.4161	−	2.68138i	−0.363563	−	0.0853925i
$987$		0			0
$988$	−48.5516	+	3.02421i	−1.54463	+	0.0962130i
$989$	−11.9672	+	6.90926i	−0.380535	+	0.219702i
$990$		0			0
$991$	−45.4196	−	26.2230i	−1.44280	−	0.833002i	−0.444766	−	0.895647i	$-0.646713\pi$
$991$	−45.4196	−	26.2230i	−1.44280	−	0.833002i	−0.998036	+	0.0626443i	$0.980047\pi$
$992$	0.883645	−	8.28307i	0.0280558	−	0.262988i
$993$		0			0
$994$	33.5955	−	10.1316i	1.06558	−	0.321356i
$995$	−3.41264	−	19.3540i	−0.108188	−	0.613564i
$996$		0			0
$997$	−30.7742	−	25.8226i	−0.974627	−	0.817809i	0.00864294	−	0.999963i	$-0.497249\pi$
$997$	−30.7742	−	25.8226i	−0.974627	−	0.817809i	−0.983270	+	0.182153i	$0.941693\pi$
$998$	−11.2211	+	8.38899i	−0.355197	+	0.265549i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.35.8		96
3.2	odd	2		108.2.l.a.11.9	✓	96
4.3	odd	2	inner	324.2.l.a.35.2		96
9.2	odd	6		972.2.l.d.755.2		96
9.4	even	3		972.2.l.b.431.3		96
9.5	odd	6		972.2.l.c.431.14		96
9.7	even	3		972.2.l.a.755.15		96
12.11	even	2		108.2.l.a.11.15	yes	96
27.4	even	9		972.2.l.d.215.4		96
27.5	odd	18	inner	324.2.l.a.287.2		96
27.13	even	9		972.2.l.c.539.7		96
27.14	odd	18		972.2.l.b.539.10		96
27.22	even	9		108.2.l.a.59.15	yes	96
27.23	odd	18		972.2.l.a.215.13		96
36.7	odd	6		972.2.l.a.755.13		96
36.11	even	6		972.2.l.d.755.4		96
36.23	even	6		972.2.l.c.431.7		96
36.31	odd	6		972.2.l.b.431.10		96
108.23	even	18		972.2.l.a.215.15		96
108.31	odd	18		972.2.l.d.215.2		96
108.59	even	18	inner	324.2.l.a.287.8		96
108.67	odd	18		972.2.l.c.539.14		96
108.95	even	18		972.2.l.b.539.3		96
108.103	odd	18		108.2.l.a.59.9	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.9	✓	96	3.2	odd	2
108.2.l.a.11.15	yes	96	12.11	even	2
108.2.l.a.59.9	yes	96	108.103	odd	18
108.2.l.a.59.15	yes	96	27.22	even	9
324.2.l.a.35.2		96	4.3	odd	2	inner
324.2.l.a.35.8		96	1.1	even	1	trivial
324.2.l.a.287.2		96	27.5	odd	18	inner
324.2.l.a.287.8		96	108.59	even	18	inner
972.2.l.a.215.13		96	27.23	odd	18
972.2.l.a.215.15		96	108.23	even	18
972.2.l.a.755.13		96	36.7	odd	6
972.2.l.a.755.15		96	9.7	even	3
972.2.l.b.431.3		96	9.4	even	3
972.2.l.b.431.10		96	36.31	odd	6
972.2.l.b.539.3		96	108.95	even	18
972.2.l.b.539.10		96	27.14	odd	18
972.2.l.c.431.7		96	36.23	even	6
972.2.l.c.431.14		96	9.5	odd	6
972.2.l.c.539.7		96	27.13	even	9
972.2.l.c.539.14		96	108.67	odd	18
972.2.l.d.215.2		96	108.31	odd	18
972.2.l.d.215.4		96	27.4	even	9
972.2.l.d.755.2		96	9.2	odd	6
972.2.l.d.755.4		96	36.11	even	6

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0793838 + 1.41198i) q^{2} +(-1.98740 - 0.224177i) q^{4} +(-0.470103 + 1.29160i) q^{5} +(-1.57428 - 0.277589i) q^{7} +(0.474302 - 2.78838i) q^{8} +O(q^{10})\)	\(q+(-0.0793838 + 1.41198i) q^{2} +(-1.98740 - 0.224177i) q^{4} +(-0.470103 + 1.29160i) q^{5} +(-1.57428 - 0.277589i) q^{7} +(0.474302 - 2.78838i) q^{8} +(-1.78640 - 0.766310i) q^{10} +(-3.66920 + 1.33548i) q^{11} +(-5.10894 + 4.28691i) q^{13} +(0.516924 - 2.20083i) q^{14} +(3.89949 + 0.891059i) q^{16} +(2.32950 - 1.34494i) q^{17} +(-3.15841 - 1.82351i) q^{19} +(1.22383 - 2.46153i) q^{20} +(-1.59440 - 5.28687i) q^{22} +(-0.644252 - 3.65373i) q^{23} +(2.38300 + 1.99957i) q^{25} +(-5.64747 - 7.55405i) q^{26} +(3.06650 + 0.904598i) q^{28} +(-1.98152 + 2.36148i) q^{29} +(-1.45019 + 0.255708i) q^{31} +(-1.56772 + 5.43528i) q^{32} +(1.71411 + 3.39599i) q^{34} +(1.09861 - 1.90285i) q^{35} +(1.27577 + 2.20970i) q^{37} +(2.82549 - 4.31487i) q^{38} +(3.37849 + 1.92343i) q^{40} +(6.30271 + 7.51128i) q^{41} +(-1.27388 - 3.49995i) q^{43} +(7.59155 - 1.83158i) q^{44} +(5.21016 - 0.619626i) q^{46} +(-0.901707 + 5.11384i) q^{47} +(-4.17653 - 1.52013i) q^{49} +(-3.01253 + 3.20602i) q^{50} +(11.1145 - 7.37447i) q^{52} +3.96045i q^{53} -5.36695i q^{55} +(-1.52071 + 4.25804i) q^{56} +(-3.17707 - 2.98534i) q^{58} +(-0.666798 - 0.242695i) q^{59} +(0.969119 - 5.49615i) q^{61} +(-0.245933 - 2.06794i) q^{62} +(-7.55008 - 2.64506i) q^{64} +(-3.13523 - 8.61397i) q^{65} +(10.4714 + 12.4793i) q^{67} +(-4.93115 + 2.15071i) q^{68} +(2.59958 + 1.70227i) q^{70} +(7.76079 + 13.4421i) q^{71} +(4.04282 - 7.00237i) q^{73} +(-3.22134 + 1.62595i) q^{74} +(5.86823 + 4.33208i) q^{76} +(6.14709 - 1.08390i) q^{77} +(-8.37729 + 9.98366i) q^{79} +(-2.98405 + 4.61768i) q^{80} +(-11.1061 + 8.30305i) q^{82} +(0.344982 + 0.289474i) q^{83} +(0.642014 + 3.64104i) q^{85} +(5.04300 - 1.52086i) q^{86} +(1.98351 + 10.8645i) q^{88} +(-0.994859 - 0.574382i) q^{89} +(9.23292 - 5.33063i) q^{91} +(0.461299 + 7.40584i) q^{92} +(-7.14907 - 1.67915i) q^{94} +(3.84002 - 3.22216i) q^{95} +(-9.00157 + 3.27630i) q^{97} +(2.47795 - 5.77652i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more