LMFDB - Embedded newform 324.2.l.a.143.15

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			143.15
Character	$\chi$	$=$	324.143
Dual form			324.2.l.a.179.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33631 - 0.462897i) q^{2} +(1.57145 - 1.23715i) q^{4} +(3.39370 - 0.598401i) q^{5} +(-1.88319 + 2.24430i) q^{7} +(1.52728 - 2.38064i) q^{8} +O(q^{10})$	\(q+(1.33631 - 0.462897i) q^{2} +(1.57145 - 1.23715i) q^{4} +(3.39370 - 0.598401i) q^{5} +(-1.88319 + 2.24430i) q^{7} +(1.52728 - 2.38064i) q^{8} +(4.25804 - 2.37058i) q^{10} +(-0.453915 + 2.57428i) q^{11} +(-5.09721 - 1.85523i) q^{13} +(-1.47765 + 3.87081i) q^{14} +(0.938928 - 3.88824i) q^{16} +(-1.15583 + 0.667320i) q^{17} +(-0.0790760 - 0.0456546i) q^{19} +(4.59273 - 5.13887i) q^{20} +(0.585055 + 3.65015i) q^{22} +(0.650322 - 0.545685i) q^{23} +(6.46065 - 2.35148i) q^{25} +(-7.67024 - 0.119685i) q^{26} +(-0.182815 + 5.85661i) q^{28} +(0.171418 + 0.470966i) q^{29} +(-4.28324 - 5.10457i) q^{31} +(-0.545155 - 5.63052i) q^{32} +(-1.23565 + 1.42678i) q^{34} +(-5.04800 + 8.74340i) q^{35} +(2.75869 + 4.77819i) q^{37} +(-0.126804 - 0.0244046i) q^{38} +(3.75855 - 8.99308i) q^{40} +(0.976880 - 2.68396i) q^{41} +(-5.59737 - 0.986968i) q^{43} +(2.47146 + 4.60692i) q^{44} +(0.616436 - 1.03024i) q^{46} +(5.06200 + 4.24752i) q^{47} +(-0.274941 - 1.55927i) q^{49} +(7.54494 - 6.13293i) q^{50} +(-10.3052 + 3.39060i) q^{52} +7.37249i q^{53} +9.00795i q^{55} +(2.46671 + 7.91087i) q^{56} +(0.447076 + 0.550009i) q^{58} +(-0.528787 - 2.99890i) q^{59} +(-1.85759 - 1.55871i) q^{61} +(-8.08663 - 4.83859i) q^{62} +(-3.33485 - 7.27178i) q^{64} +(-18.4086 - 3.24593i) q^{65} +(-1.64904 + 4.53069i) q^{67} +(-0.990762 + 2.47860i) q^{68} +(-2.69841 + 14.0206i) q^{70} +(-5.91940 - 10.2527i) q^{71} +(-5.83049 + 10.0987i) q^{73} +(5.89828 + 5.10816i) q^{74} +(-0.180746 + 0.0260848i) q^{76} +(-4.92266 - 5.86659i) q^{77} +(0.576990 + 1.58527i) q^{79} +(0.859714 - 13.7574i) q^{80} +(0.0630204 - 4.03879i) q^{82} +(2.02940 - 0.738640i) q^{83} +(-3.52322 + 2.95633i) q^{85} +(-7.93669 + 1.27211i) q^{86} +(5.43517 + 5.01224i) q^{88} +(12.5801 + 7.26310i) q^{89} +(13.7628 - 7.94593i) q^{91} +(0.346857 - 1.66206i) q^{92} +(8.73057 + 3.33283i) q^{94} +(-0.295680 - 0.107619i) q^{95} +(1.14607 - 6.49971i) q^{97} +(-1.08919 - 1.95639i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	1.33631	−	0.462897i	0.944914	−	0.327318i
$2$	1.33631	−	0.462897i	0.944914	−	0.327318i
$3$		0			0
$3$		0			0
$4$	1.57145	−	1.23715i	0.785726	−	0.618574i
$5$	3.39370	−	0.598401i	1.51771	−	0.267613i	0.648177	−	0.761490i	$-0.275532\pi$
$5$	3.39370	−	0.598401i	1.51771	−	0.267613i	0.869532	+	0.493877i	$0.164421\pi$
$6$		0			0
$7$	−1.88319	+	2.24430i	−0.711781	+	0.848267i	−0.993805	−	0.111140i	$-0.964550\pi$
$7$	−1.88319	+	2.24430i	−0.711781	+	0.848267i	0.282024	+	0.959407i	$0.408994\pi$
$8$	1.52728	−	2.38064i	0.539974	−	0.841682i
$9$		0			0
$10$	4.25804	−	2.37058i	1.34651	−	0.749644i
$11$	−0.453915	+	2.57428i	−0.136861	+	0.776174i	0.836686	+	0.547684i	$0.184490\pi$
$11$	−0.453915	+	2.57428i	−0.136861	+	0.776174i	−0.973546	+	0.228491i	$0.926621\pi$
$12$		0			0
$13$	−5.09721	−	1.85523i	−1.41371	−	0.514549i	−0.481496	−	0.876449i	$-0.659906\pi$
$13$	−5.09721	−	1.85523i	−1.41371	−	0.514549i	−0.932217	+	0.361899i	$0.882128\pi$
$14$	−1.47765	+	3.87081i	−0.394919	+	1.03452i
$15$		0			0
$16$	0.938928	−	3.88824i	0.234732	−	0.972060i
$17$	−1.15583	+	0.667320i	−0.280330	+	0.161849i	−0.633573	−	0.773683i	$-0.718412\pi$
$17$	−1.15583	+	0.667320i	−0.280330	+	0.161849i	0.353243	+	0.935532i	$0.385079\pi$
$18$		0			0
$19$	−0.0790760	−	0.0456546i	−0.0181413	−	0.0104739i	0.490902	−	0.871215i	$-0.336667\pi$
$19$	−0.0790760	−	0.0456546i	−0.0181413	−	0.0104739i	−0.509043	+	0.860741i	$0.670001\pi$
$20$	4.59273	−	5.13887i	1.02697	−	1.14909i
$21$		0			0
$22$	0.585055	+	3.65015i	0.124734	+	0.778215i
$23$	0.650322	−	0.545685i	0.135602	−	0.113783i	−0.572464	−	0.819930i	$-0.694012\pi$
$23$	0.650322	−	0.545685i	0.135602	−	0.113783i	0.708066	+	0.706147i	$0.249568\pi$
$24$		0			0
$25$	6.46065	−	2.35148i	1.29213	−	0.470297i
$26$	−7.67024	−	0.119685i	−1.50426	−	0.0234721i
$27$		0			0
$28$	−0.182815	+	5.85661i	−0.0345487	+	1.10679i
$29$	0.171418	+	0.470966i	0.0318315	+	0.0874562i	0.954590	−	0.297922i	$-0.0962934\pi$
$29$	0.171418	+	0.470966i	0.0318315	+	0.0874562i	−0.922759	+	0.385378i	$0.874071\pi$
$30$		0			0
$31$	−4.28324	−	5.10457i	−0.769293	−	0.916807i	0.229105	−	0.973402i	$-0.426420\pi$
$31$	−4.28324	−	5.10457i	−0.769293	−	0.916807i	−0.998397	+	0.0565946i	$0.981976\pi$
$32$	−0.545155	−	5.63052i	−0.0963706	−	0.995346i
$33$		0			0
$34$	−1.23565	+	1.42678i	−0.211912	+	0.244690i
$35$	−5.04800	+	8.74340i	−0.853268	+	1.47790i
$36$		0			0
$37$	2.75869	+	4.77819i	0.453526	+	0.785530i	0.998602	−	0.0528563i	$-0.0168325\pi$
$37$	2.75869	+	4.77819i	0.453526	+	0.785530i	−0.545076	+	0.838387i	$0.683499\pi$
$38$	−0.126804	−	0.0244046i	−0.0205702	−	0.00395896i
$39$		0			0
$40$	3.75855	−	8.99308i	0.594278	−	1.42193i
$41$	0.976880	−	2.68396i	0.152563	−	0.419163i	−0.839741	−	0.542987i	$-0.817293\pi$
$41$	0.976880	−	2.68396i	0.152563	−	0.419163i	0.992304	+	0.123823i	$0.0395156\pi$
$42$		0			0
$43$	−5.59737	−	0.986968i	−0.853591	−	0.150511i	−0.270302	−	0.962776i	$-0.587124\pi$
$43$	−5.59737	−	0.986968i	−0.853591	−	0.150511i	−0.583289	+	0.812264i	$0.698235\pi$
$44$	2.47146	+	4.60692i	0.372587	+	0.694519i
$45$		0			0
$46$	0.616436	−	1.03024i	0.0908886	−	0.151900i
$47$	5.06200	+	4.24752i	0.738369	+	0.619565i	0.932399	−	0.361430i	$-0.117712\pi$
$47$	5.06200	+	4.24752i	0.738369	+	0.619565i	−0.194030	+	0.980996i	$0.562156\pi$
$48$		0			0
$49$	−0.274941	−	1.55927i	−0.0392772	−	0.222752i
$50$	7.54494	−	6.13293i	1.06702	−	0.867327i
$51$		0			0
$52$	−10.3052	+	3.39060i	−1.42908	+	0.470191i
$53$			7.37249i			1.01269i	0.862331	+	0.506345i	$0.169004\pi$
$53$			7.37249i			1.01269i	−0.862331	+	0.506345i	$0.830996\pi$
$54$		0			0
$55$			9.00795i			1.21463i
$56$	2.46671	+	7.91087i	0.329628	+	1.05713i
$57$		0			0
$58$	0.447076	+	0.550009i	0.0587040	+	0.0722197i
$59$	−0.528787	−	2.99890i	−0.0688422	−	0.390423i	−0.999687	−	0.0250093i	$-0.992038\pi$
$59$	−0.528787	−	2.99890i	−0.0688422	−	0.390423i	0.930845	−	0.365414i	$-0.119073\pi$
$60$		0			0
$61$	−1.85759	−	1.55871i	−0.237841	−	0.199572i	0.516075	−	0.856544i	$-0.327393\pi$
$61$	−1.85759	−	1.55871i	−0.237841	−	0.199572i	−0.753915	+	0.656972i	$0.771837\pi$
$62$	−8.08663	−	4.83859i	−1.02700	−	0.614501i
$63$		0			0
$64$	−3.33485	−	7.27178i	−0.416856	−	0.908973i
$65$	−18.4086	−	3.24593i	−2.28330	−	0.402608i
$66$		0			0
$67$	−1.64904	+	4.53069i	−0.201462	+	0.553512i	−0.998744	−	0.0500945i	$-0.984048\pi$
$67$	−1.64904	+	4.53069i	−0.201462	+	0.553512i	0.797283	+	0.603606i	$0.206270\pi$
$68$	−0.990762	+	2.47860i	−0.120148	+	0.300574i
$69$		0			0
$70$	−2.69841	+	14.0206i	−0.322522	+	1.67578i
$71$	−5.91940	−	10.2527i	−0.702504	−	1.21677i	−0.967585	−	0.252546i	$-0.918732\pi$
$71$	−5.91940	−	10.2527i	−0.702504	−	1.21677i	0.265081	−	0.964226i	$-0.414601\pi$
$72$		0			0
$73$	−5.83049	+	10.0987i	−0.682408	+	1.18197i	0.291836	+	0.956468i	$0.405734\pi$
$73$	−5.83049	+	10.0987i	−0.682408	+	1.18197i	−0.974244	+	0.225497i	$0.927600\pi$
$74$	5.89828	+	5.10816i	0.685661	+	0.593812i
$75$		0			0
$76$	−0.180746	+	0.0260848i	−0.0207330	+	0.00299213i
$77$	−4.92266	−	5.86659i	−0.560989	−	0.668560i
$78$		0			0
$79$	0.576990	+	1.58527i	0.0649165	+	0.178357i	0.967910	−	0.251298i	$-0.0808575\pi$
$79$	0.576990	+	1.58527i	0.0649165	+	0.178357i	−0.902993	+	0.429655i	$0.858635\pi$
$80$	0.859714	−	13.7574i	0.0961190	−	1.53812i
$81$		0			0
$82$	0.0630204	−	4.03879i	0.00695944	−	0.446010i
$83$	2.02940	−	0.738640i	0.222755	−	0.0810763i	−0.228232	−	0.973607i	$-0.573294\pi$
$83$	2.02940	−	0.738640i	0.222755	−	0.0810763i	0.450987	+	0.892531i	$0.351072\pi$
$84$		0			0
$85$	−3.52322	+	2.95633i	−0.382147	+	0.320659i
$86$	−7.93669	+	1.27211i	−0.855836	+	0.137175i
$87$		0			0
$88$	5.43517	+	5.01224i	0.579391	+	0.534307i
$89$	12.5801	+	7.26310i	1.33348	+	0.769887i	0.985832	−	0.167737i	$-0.0536458\pi$
$89$	12.5801	+	7.26310i	1.33348	+	0.769887i	0.347652	+	0.937624i	$0.386979\pi$
$90$		0			0
$91$	13.7628	−	7.94593i	1.44273	−	0.832960i
$92$	0.346857	−	1.66206i	0.0361624	−	0.173282i
$93$		0			0
$94$	8.73057	+	3.33283i	0.900490	+	0.343755i
$95$	−0.295680	−	0.107619i	−0.0303361	−	0.0110414i
$96$		0			0
$97$	1.14607	−	6.49971i	0.116366	−	0.659946i	−0.869698	−	0.493583i	$-0.835687\pi$
$97$	1.14607	−	6.49971i	0.116366	−	0.659946i	0.986065	−	0.166362i	$-0.0532021\pi$
$98$	−1.08919	−	1.95639i	−0.110024	−	0.197626i
$99$		0			0
$100$	7.24347	−	11.6880i	0.724347	−	1.16880i
$101$	5.29995	−	6.31623i	0.527365	−	0.628489i	−0.434941	−	0.900459i	$-0.643231\pi$
$101$	5.29995	−	6.31623i	0.527365	−	0.628489i	0.962306	+	0.271970i	$0.0876752\pi$
$102$		0			0
$103$	15.8523	−	2.79519i	1.56197	−	0.275418i	0.675203	−	0.737632i	$-0.264056\pi$
$103$	15.8523	−	2.79519i	1.56197	−	0.275418i	0.886769	+	0.462214i	$0.152945\pi$
$104$	−12.2015	+	9.30115i	−1.19646	+	0.912053i
$105$		0			0
$106$	3.41270	+	9.85194i	0.331471	+	0.956905i
$107$	9.71808			0.939482			0.469741	−	0.882804i	$-0.344347\pi$
$107$	9.71808			0.939482			0.469741	+	0.882804i	$0.344347\pi$
$108$		0			0
$109$	−4.69860			−0.450044			−0.225022	−	0.974354i	$-0.572245\pi$
$109$	−4.69860			−0.450044			−0.225022	+	0.974354i	$0.572245\pi$
$110$	4.16975	+	12.0374i	0.397570	+	1.14772i
$111$		0			0
$112$	6.95821	+	9.42955i	0.657489	+	0.891009i
$113$	−0.555886	+	0.0980178i	−0.0522934	+	0.00922074i	−0.199734	−	0.979850i	$-0.564008\pi$
$113$	−0.555886	+	0.0980178i	−0.0522934	+	0.00922074i	0.147440	+	0.989071i	$0.452897\pi$
$114$		0			0
$115$	1.88046	−	2.24104i	0.175354	−	0.208978i
$116$	0.852030	+	0.528032i	0.0791090	+	0.0490266i
$117$		0			0
$118$	−2.09480	−	3.76269i	−0.192842	−	0.346383i
$119$	0.678988	−	3.85073i	0.0622427	−	0.352996i
$120$		0			0
$121$	3.91574	+	1.42521i	0.355977	+	0.129565i
$122$	−3.20384	−	1.22304i	−0.290062	−	0.110729i
$123$		0			0
$124$	−13.0460	−	2.72258i	−1.17157	−	0.244495i
$125$	5.59652	−	3.23116i	0.500568	−	0.289003i
$126$		0			0
$127$	−9.63141	−	5.56070i	−0.854649	−	0.493432i	0.00756758	−	0.999971i	$-0.497591\pi$
$127$	−9.63141	−	5.56070i	−0.854649	−	0.493432i	−0.862217	+	0.506539i	$0.830924\pi$
$128$	−7.82248	−	8.17367i	−0.691416	−	0.722457i
$129$		0			0
$130$	−26.1021	+	4.18371i	−2.28931	+	0.366935i
$131$	2.37648	−	1.99411i	0.207634	−	0.174226i	−0.533040	−	0.846090i	$-0.678951\pi$
$131$	2.37648	−	1.99411i	0.207634	−	0.174226i	0.740675	+	0.671864i	$0.234506\pi$
$132$		0			0
$133$	0.251378	−	0.0914942i	0.0217973	−	0.00793355i
$134$	−0.106382	+	6.81774i	−0.00919004	+	0.588963i
$135$		0			0
$136$	−0.176631	+	3.77080i	−0.0151459	+	0.323343i
$137$	5.90609	+	16.2268i	0.504591	+	1.38635i	0.886747	+	0.462255i	$0.152959\pi$
$137$	5.90609	+	16.2268i	0.504591	+	1.38635i	−0.382156	+	0.924098i	$0.624818\pi$
$138$		0			0
$139$	−7.19280	−	8.57205i	−0.610085	−	0.727071i	0.369246	−	0.929332i	$-0.379616\pi$
$139$	−7.19280	−	8.57205i	−0.610085	−	0.727071i	−0.979332	+	0.202260i	$0.935171\pi$
$140$	2.88418	+	19.9850i	0.243758	+	1.68904i
$141$		0			0
$142$	−12.6561	−	10.9607i	−1.06208	−	0.919803i
$143$	7.08959	−	12.2795i	0.592862	−	1.02687i
$144$		0			0
$145$	0.863567	+	1.49574i	0.0717153	+	0.124215i
$146$	−3.11669	+	16.1939i	−0.257939	+	1.34022i
$147$		0			0
$148$	10.2465	+	4.09580i	0.842256	+	0.336672i
$149$	6.24250	−	17.1511i	0.511406	−	1.40508i	−0.368367	−	0.929680i	$-0.620083\pi$
$149$	6.24250	−	17.1511i	0.511406	−	1.40508i	0.879773	−	0.475395i	$-0.157695\pi$
$150$		0			0
$151$	18.9571	+	3.34265i	1.54271	+	0.272021i	0.879311	−	0.476248i	$-0.158004\pi$
$151$	18.9571	+	3.34265i	1.54271	+	0.272021i	0.663396	+	0.748269i	$0.269115\pi$
$152$	−0.229458	+	0.118524i	−0.0186115	+	0.00961357i
$153$		0			0
$154$	−9.29382	−	5.56091i	−0.748918	−	0.448111i
$155$	−17.5906	−	14.7603i	−1.41291	−	1.18557i
$156$		0			0
$157$	−2.92425	−	16.5843i	−0.233381	−	1.32357i	−0.845997	−	0.533187i	$-0.820994\pi$
$157$	−2.92425	−	16.5843i	−0.233381	−	1.32357i	0.612617	−	0.790380i	$-0.290117\pi$
$158$	1.50485	+	1.85132i	0.119720	+	0.147283i
$159$		0			0
$160$	−5.21940	−	18.7821i	−0.412630	−	1.48485i
$161$			2.48715i			0.196015i
$162$		0			0
$163$		−	8.02606i		−	0.628650i	−0.949315	−	0.314325i	$-0.898222\pi$
$163$		−	8.02606i		−	0.628650i	0.949315	−	0.314325i	$-0.101778\pi$
$164$	−1.78533	−	5.42625i	−0.139411	−	0.423719i
$165$		0			0
$166$	2.36999	−	1.92645i	0.183947	−	0.149522i
$167$	0.226727	+	1.28583i	0.0175447	+	0.0995008i	0.992323	−	0.123676i	$-0.0394684\pi$
$167$	0.226727	+	1.28583i	0.0175447	+	0.0995008i	−0.974778	+	0.223177i	$0.928357\pi$
$168$		0			0
$169$	12.5811	+	10.5568i	0.967779	+	0.812063i
$170$	−3.33964	+	5.58147i	−0.256139	+	0.428079i
$171$		0			0
$172$	−10.0170	+	5.37381i	−0.763792	+	0.409749i
$173$	−11.2769	−	1.98842i	−0.857366	−	0.151177i	−0.272350	−	0.962198i	$-0.587801\pi$
$173$	−11.2769	−	1.98842i	−0.857366	−	0.151177i	−0.585016	+	0.811022i	$0.698912\pi$
$174$		0			0
$175$	−6.88921	+	18.9280i	−0.520776	+	1.43082i
$176$	9.58322	+	4.18199i	0.722363	+	0.315230i
$177$		0			0
$178$	20.1729	+	3.88249i	1.51203	+	0.291005i
$179$	10.7064	+	18.5441i	0.800237	+	1.38605i	0.919460	+	0.393184i	$0.128627\pi$
$179$	10.7064	+	18.5441i	0.800237	+	1.38605i	−0.119222	+	0.992868i	$0.538040\pi$
$180$		0			0
$181$	7.31416	−	12.6685i	0.543657	−	0.941641i	−0.455033	−	0.890474i	$-0.650373\pi$
$181$	7.31416	−	12.6685i	0.543657	−	0.941641i	0.998690	−	0.0511670i	$-0.0162941\pi$
$182$	14.7132	−	16.9890i	1.09061	−	1.25931i
$183$		0			0
$184$	−0.305855	−	2.38159i	−0.0225479	−	0.175573i
$185$	12.2214	+	14.5650i	0.898539	+	1.07084i
$186$		0			0
$187$	−1.19322	−	3.27834i	−0.0872568	−	0.239736i
$188$	13.2095	+	0.412337i	0.963403	+	0.0300728i
$189$		0			0
$190$	−0.444937	−	0.00694269i	−0.0322791	−	0.000503676i
$191$	−1.80607	+	0.657357i	−0.130683	+	0.0475647i	−0.406534	−	0.913636i	$-0.633263\pi$
$191$	−1.80607	+	0.657357i	−0.130683	+	0.0475647i	0.275851	+	0.961200i	$0.411040\pi$
$192$		0			0
$193$	−4.79657	+	4.02480i	−0.345264	+	0.289711i	−0.798885	−	0.601484i	$-0.794577\pi$
$193$	−4.79657	+	4.02480i	−0.345264	+	0.289711i	0.453621	+	0.891195i	$0.350132\pi$
$194$	−1.47718	−	9.21615i	−0.106056	−	0.661681i
$195$		0			0
$196$	−2.36110	−	2.11017i	−0.168650	−	0.150726i
$197$	−13.1022	−	7.56456i	−0.933494	−	0.538953i	−0.0455788	−	0.998961i	$-0.514513\pi$
$197$	−13.1022	−	7.56456i	−0.933494	−	0.538953i	−0.887915	+	0.460008i	$0.847847\pi$
$198$		0			0
$199$	−22.4427	+	12.9573i	−1.59092	+	0.918517i	−0.597769	+	0.801669i	$0.703946\pi$
$199$	−22.4427	+	12.9573i	−1.59092	+	0.918517i	−0.993150	+	0.116849i	$0.962721\pi$
$200$	4.26918	−	18.9718i	0.301876	−	1.34151i
$201$		0			0
$202$	4.15861	−	10.8938i	0.292599	−	0.766484i
$203$	−1.37980	−	0.502208i	−0.0968433	−	0.0352481i
$204$		0			0
$205$	1.70916	−	9.69310i	0.119373	−	0.676996i
$206$	19.8897	−	11.0732i	1.38578	−	0.771507i
$207$		0			0
$208$	−11.9995	+	18.0773i	−0.832017	+	1.25343i
$209$	0.153421	−	0.182841i	0.0106124	−	0.0126473i
$210$		0			0
$211$	17.1836	−	3.02993i	1.18297	−	0.208589i	0.452645	−	0.891691i	$-0.350481\pi$
$211$	17.1836	−	3.02993i	1.18297	−	0.208589i	0.730323	+	0.683102i	$0.239369\pi$
$212$	9.12087	+	11.5855i	0.626424	+	0.795697i
$213$		0			0
$214$	12.9864	−	4.49847i	0.887730	−	0.307509i
$215$	−19.5864			−1.33578
$216$		0			0
$217$	19.5224			1.32526
$218$	−6.27879	+	2.17497i	−0.425253	+	0.147307i
$219$		0			0
$220$	11.1442	+	14.1556i	0.751340	+	0.954369i
$221$	7.12956	−	1.25713i	0.479586	−	0.0845639i
$222$		0			0
$223$	11.3619	−	13.5406i	0.760850	−	0.906746i	−0.237051	−	0.971497i	$-0.576181\pi$
$223$	11.3619	−	13.5406i	0.760850	−	0.906746i	0.997901	+	0.0647513i	$0.0206254\pi$
$224$	13.6632	+	9.37988i	0.912914	+	0.626720i
$225$		0			0
$226$	−0.697465	+	0.388300i	−0.0463947	+	0.0258294i
$227$	1.62005	−	9.18776i	0.107527	−	0.609813i	−0.882654	−	0.470022i	$-0.844246\pi$
$227$	1.62005	−	9.18776i	0.107527	−	0.609813i	0.990181	−	0.139791i	$-0.0446431\pi$
$228$		0			0
$229$	−15.8029	−	5.75180i	−1.04429	−	0.380090i	−0.237784	−	0.971318i	$-0.576421\pi$
$229$	−15.8029	−	5.75180i	−1.04429	−	0.380090i	−0.806504	+	0.591228i	$0.798643\pi$
$230$	1.47551	−	3.86519i	0.0972920	−	0.254863i
$231$		0			0
$232$	1.38300	+	0.311213i	0.0907985	+	0.0204321i
$233$	−15.2659	+	8.81379i	−1.00010	+	0.577410i	−0.908279	−	0.418365i	$-0.862603\pi$
$233$	−15.2659	+	8.81379i	−1.00010	+	0.577410i	−0.0918250	+	0.995775i	$0.529270\pi$
$234$		0			0
$235$	19.7206	+	11.3857i	1.28643	+	0.742722i
$236$	−4.54105	−	4.05844i	−0.295597	−	0.264182i
$237$		0			0
$238$	−0.875153	−	5.46007i	−0.0567277	−	0.353924i
$239$	−7.05862	+	5.92289i	−0.456584	+	0.383120i	−0.841872	−	0.539677i	$-0.818547\pi$
$239$	−7.05862	+	5.92289i	−0.456584	+	0.383120i	0.385288	+	0.922796i	$0.374102\pi$
$240$		0			0
$241$	−5.85117	+	2.12965i	−0.376907	+	0.137183i	−0.523525	−	0.852010i	$-0.675383\pi$
$241$	−5.85117	+	2.12965i	−0.376907	+	0.137183i	0.146618	+	0.989193i	$0.453161\pi$
$242$	5.89238	+	0.0919433i	0.378776	+	0.00591034i
$243$		0			0
$244$	−4.84747	−	0.151315i	−0.310328	−	0.00968692i
$245$	−1.86613	−	5.12716i	−0.119223	−	0.327562i
$246$		0			0
$247$	0.318368	+	0.379416i	0.0202572	+	0.0241416i
$248$	−18.6938	+	2.40074i	−1.18706	+	0.152447i
$249$		0			0
$250$	5.98300	−	6.90844i	0.378398	−	0.436928i
$251$	14.1765	−	24.5545i	0.894814	−	1.54986i	0.0607805	−	0.998151i	$-0.480641\pi$
$251$	14.1765	−	24.5545i	0.894814	−	1.54986i	0.834034	−	0.551713i	$-0.186026\pi$
$252$		0			0
$253$	1.10955	+	1.92181i	0.0697571	+	0.120823i
$254$	−15.4446	−	2.97247i	−0.969079	−	0.186509i
$255$		0			0
$256$	−14.2368	−	7.30156i	−0.889802	−	0.456347i
$257$	−5.64266	+	15.5031i	−0.351979	+	0.967056i	0.629754	+	0.776795i	$0.283156\pi$
$257$	−5.64266	+	15.5031i	−0.351979	+	0.967056i	−0.981734	+	0.190261i	$0.939067\pi$
$258$		0			0
$259$	−15.9189	−	2.80693i	−0.989151	−	0.174414i
$260$	−32.9439	+	17.6733i	−2.04310	+	1.09605i
$261$		0			0
$262$	2.25266	−	3.76481i	0.139170	−	0.232591i
$263$	18.5512	+	15.5663i	1.14391	+	0.959859i	0.999560	−	0.0296674i	$-0.00944483\pi$
$263$	18.5512	+	15.5663i	1.14391	+	0.959859i	0.144355	+	0.989526i	$0.453889\pi$
$264$		0			0
$265$	4.41171	+	25.0200i	0.271009	+	1.53697i
$266$	0.293567	−	0.238627i	0.0179998	−	0.0146312i
$267$		0			0
$268$	3.01375	+	9.15986i	0.184094	+	0.559528i
$269$		−	12.1956i		−	0.743578i	−0.928317	−	0.371789i	$-0.878745\pi$
$269$		−	12.1956i		−	0.743578i	0.928317	−	0.371789i	$-0.121255\pi$
$270$		0			0
$271$		−	25.0009i		−	1.51870i	−0.650683	−	0.759349i	$-0.725517\pi$
$271$		−	25.0009i		−	1.51870i	0.650683	−	0.759349i	$-0.274483\pi$
$272$	1.50946	+	5.12072i	0.0915243	+	0.310489i
$273$		0			0
$274$	15.4037	+	18.9502i	0.930573	+	1.14482i
$275$	3.12079	+	17.6989i	0.188191	+	1.06728i
$276$		0			0
$277$	−6.69358	−	5.61658i	−0.402178	−	0.337468i	0.419157	−	0.907914i	$-0.362326\pi$
$277$	−6.69358	−	5.61658i	−0.402178	−	0.337468i	−0.821335	+	0.570446i	$0.806770\pi$
$278$	−13.5798	−	8.12539i	−0.814462	−	0.487329i
$279$		0			0
$280$	13.1051	+	25.3710i	0.783182	+	1.51621i
$281$	21.5554	+	3.80080i	1.28589	+	0.226737i	0.774478	−	0.632601i	$-0.218013\pi$
$281$	21.5554	+	3.80080i	1.28589	+	0.226737i	0.511409	+	0.859338i	$0.329124\pi$
$282$		0			0
$283$	−10.2956	+	28.2869i	−0.612010	+	1.68148i	0.113727	+	0.993512i	$0.463721\pi$
$283$	−10.2956	+	28.2869i	−0.612010	+	1.68148i	−0.725737	+	0.687972i	$0.758501\pi$
$284$	−21.9862	−	8.78846i	−1.30464	−	0.521499i
$285$		0			0
$286$	3.78974	−	19.6910i	0.224092	−	1.16435i
$287$	4.18396	+	7.24682i	0.246971	+	0.427766i
$288$		0			0
$289$	−7.60937	+	13.1798i	−0.447610	+	0.775283i
$290$	1.84637	+	1.59903i	0.108422	+	0.0938984i
$291$		0			0
$292$	3.33126	+	23.0828i	0.194947	+	1.35082i
$293$	−8.50981	−	10.1416i	−0.497148	−	0.592478i	0.457872	−	0.889018i	$-0.348612\pi$
$293$	−8.50981	−	10.1416i	−0.497148	−	0.592478i	−0.955021	+	0.296540i	$0.904167\pi$
$294$		0			0
$295$	−3.58909	−	9.86094i	−0.208965	−	0.574126i
$296$	15.5884	+	0.730189i	0.906059	+	0.0424413i
$297$		0			0
$298$	0.402716	−	25.8089i	0.0233287	−	1.49507i
$299$	−4.32720	+	1.57497i	−0.250249	+	0.0910831i
$300$		0			0
$301$	12.7560	−	10.7036i	0.735243	−	0.616942i
$302$	26.8799	−	4.30837i	1.54676	−	0.247919i
$303$		0			0
$304$	−0.251763	+	0.264600i	−0.0144396	+	0.0151759i
$305$	−7.23685	−	4.17820i	−0.414381	−	0.239243i
$306$		0			0
$307$	−11.4064	+	6.58546i	−0.650995	+	0.375852i	−0.788837	−	0.614602i	$-0.789317\pi$
$307$	−11.4064	+	6.58546i	−0.650995	+	0.375852i	0.137842	+	0.990454i	$0.455983\pi$
$308$	−14.9936	−	3.12902i	−0.854338	−	0.178292i
$309$		0			0
$310$	−30.3390	−	11.5817i	−1.72314	−	0.657795i
$311$	5.80348	+	2.11230i	0.329085	+	0.119777i	0.501279	−	0.865286i	$-0.332863\pi$
$311$	5.80348	+	2.11230i	0.329085	+	0.119777i	−0.172193	+	0.985063i	$0.555085\pi$
$312$		0			0
$313$	−3.72249	+	21.1113i	−0.210407	+	1.19328i	0.678293	+	0.734791i	$0.262720\pi$
$313$	−3.72249	+	21.1113i	−0.210407	+	1.19328i	−0.888701	+	0.458488i	$0.848391\pi$
$314$	−11.5845	−	20.8081i	−0.653752	−	1.17427i
$315$		0			0
$316$	2.86792	+	1.77735i	0.161333	+	0.0999838i
$317$	9.45061	−	11.2628i	0.530799	−	0.632582i	−0.432300	−	0.901730i	$-0.642298\pi$
$317$	9.45061	−	11.2628i	0.530799	−	0.632582i	0.963099	+	0.269148i	$0.0867422\pi$
$318$		0			0
$319$	−1.29021	+	0.227498i	−0.0722378	+	0.0127375i
$320$	−15.6689	−	22.6827i	−0.875919	−	1.26800i
$321$		0			0
$322$	1.15129	+	3.32361i	0.0641591	+	0.185217i
$323$	0.121865			0.00678074
$324$		0			0
$325$	−37.2939			−2.06869
$326$	−3.71524	−	10.7253i	−0.205768	−	0.594020i
$327$		0			0
$328$	−4.89755	−	6.42474i	−0.270422	−	0.354747i
$329$	−19.0655	+	3.36176i	−1.05111	+	0.185340i
$330$		0			0
$331$	−17.0491	+	20.3184i	−0.937106	+	1.11680i	0.0558649	+	0.998438i	$0.482208\pi$
$331$	−17.0491	+	20.3184i	−0.937106	+	1.11680i	−0.992971	+	0.118361i	$0.962236\pi$
$332$	2.27529	−	3.67140i	0.124873	−	0.201494i
$333$		0			0
$334$	0.898186	+	1.61332i	0.0491466	+	0.0882770i
$335$	−2.88516	+	16.3626i	−0.157633	+	0.893983i
$336$		0			0
$337$	14.4992	+	5.27727i	0.789820	+	0.287471i	0.705261	−	0.708948i	$-0.250830\pi$
$337$	14.4992	+	5.27727i	0.789820	+	0.287471i	0.0845588	+	0.996418i	$0.473052\pi$
$338$	21.6990	+	8.28342i	1.18027	+	0.450559i
$339$		0			0
$340$	−1.87915	+	9.00449i	−0.101911	+	0.488337i
$341$	15.0848	−	8.70922i	0.816888	−	0.471631i
$342$		0			0
$343$	−13.7433	−	7.93471i	−0.742069	−	0.428434i
$344$	−10.8983	+	11.8179i	−0.587600	+	0.637180i
$345$		0			0
$346$	−15.9899	+	2.56289i	−0.859620	+	0.137782i
$347$	−16.4887	+	13.8357i	−0.885162	+	0.742739i	−0.967234	−	0.253888i	$-0.918291\pi$
$347$	−16.4887	+	13.8357i	−0.885162	+	0.742739i	0.0820721	+	0.996626i	$0.473846\pi$
$348$		0			0
$349$	−11.8787	+	4.32349i	−0.635851	+	0.231431i	−0.639776	−	0.768561i	$-0.720973\pi$
$349$	−11.8787	+	4.32349i	−0.635851	+	0.231431i	0.00392469	+	0.999992i	$0.498751\pi$
$350$	−0.444436	+	28.4826i	−0.0237561	+	1.52246i
$351$		0			0
$352$	14.7420	+	1.15240i	0.785751	+	0.0614231i
$353$	−3.82687	−	10.5142i	−0.203684	−	0.559617i	0.795225	−	0.606314i	$-0.207353\pi$
$353$	−3.82687	−	10.5142i	−0.203684	−	0.559617i	−0.998909	+	0.0466973i	$0.985130\pi$
$354$		0			0
$355$	−26.2239	−	31.2524i	−1.39182	−	1.65871i
$356$	28.7545	−	4.14978i	1.52399	−	0.219938i
$357$		0			0
$358$	22.8912	+	19.8247i	1.20983	+	1.04777i
$359$	−16.1699	+	28.0070i	−0.853413	+	1.47816i	0.0246959	+	0.999695i	$0.492138\pi$
$359$	−16.1699	+	28.0070i	−0.853413	+	1.47816i	−0.878109	+	0.478460i	$0.841195\pi$
$360$		0			0
$361$	−9.49583	−	16.4473i	−0.499781	−	0.865645i
$362$	3.90978	−	20.3147i	0.205494	−	1.06772i
$363$		0			0
$364$	11.7972	−	29.5132i	0.618343	−	1.54691i
$365$	−13.7439	+	37.7610i	−0.719387	+	1.97650i
$366$		0			0
$367$	−0.656339	−	0.115730i	−0.0342606	−	0.00604107i	0.156492	−	0.987679i	$-0.449982\pi$
$367$	−0.656339	−	0.115730i	−0.0342606	−	0.00604107i	−0.190752	+	0.981638i	$0.561093\pi$
$368$	−1.51115	−	3.04097i	−0.0787741	−	0.158521i
$369$		0			0
$370$	23.0737	+	13.8060i	1.19955	+	0.717741i
$371$	−16.5461	−	13.8838i	−0.859031	−	0.720813i
$372$		0			0
$373$	3.61725	+	20.5144i	0.187294	+	1.06220i	0.922972	+	0.384867i	$0.125753\pi$
$373$	3.61725	+	20.5144i	0.187294	+	1.06220i	−0.735678	+	0.677331i	$0.763136\pi$
$374$	−3.11204	−	3.82855i	−0.160920	−	0.197969i
$375$		0			0
$376$	17.8429	−	5.56363i	0.920177	−	0.286923i
$377$		−	2.71864i		−	0.140017i
$378$		0			0
$379$			19.1904i			0.985744i	0.870102	+	0.492872i	$0.164053\pi$
$379$			19.1904i			0.985744i	−0.870102	+	0.492872i	$0.835947\pi$
$380$	−0.597788	+	0.196682i	−0.0306659	+	0.0100896i
$381$		0			0
$382$	−2.10919	+	1.71446i	−0.107915	+	0.0877194i
$383$	−1.37744	−	7.81186i	−0.0703840	−	0.399168i	−0.999564	−	0.0295390i	$-0.990596\pi$
$383$	−1.37744	−	7.81186i	−0.0703840	−	0.399168i	0.929180	−	0.369629i	$-0.120515\pi$
$384$		0			0
$385$	−20.2166	−	16.9637i	−1.03033	−	0.864552i
$386$	−4.54664	+	7.59870i	−0.231418	+	0.386763i
$387$		0			0
$388$	−6.24010	−	11.6319i	−0.316793	−	0.590518i
$389$	12.1585	+	2.14387i	0.616461	+	0.108699i	0.473154	−	0.880980i	$-0.343115\pi$
$389$	12.1585	+	2.14387i	0.616461	+	0.108699i	0.143307	+	0.989678i	$0.454226\pi$
$390$		0			0
$391$	−0.387517	+	1.06469i	−0.0195976	+	0.0538438i
$392$	−4.13195	−	1.72690i	−0.208695	−	0.0872215i
$393$		0			0
$394$	−21.0102	−	4.04364i	−1.05848	−	0.203715i
$395$	2.90676	+	5.03465i	0.146255	+	0.253321i
$396$		0			0
$397$	11.5959	−	20.0847i	0.581982	−	1.00802i	−0.413263	−	0.910612i	$-0.635611\pi$
$397$	11.5959	−	20.0847i	0.581982	−	1.00802i	0.995244	−	0.0974099i	$-0.0310558\pi$
$398$	−23.9925	+	27.7036i	−1.20263	+	1.38866i
$399$		0			0
$400$	−3.07705	−	27.3284i	−0.153852	−	1.36642i
$401$	−4.36829	−	5.20593i	−0.218142	−	0.259972i	0.645865	−	0.763452i	$-0.276497\pi$
$401$	−4.36829	−	5.20593i	−0.218142	−	0.259972i	−0.864007	+	0.503480i	$0.832053\pi$
$402$		0			0
$403$	12.3624	+	33.9655i	0.615816	+	1.69194i
$404$	0.514503	−	16.4825i	0.0255975	−	0.820034i
$405$		0			0
$406$	−2.07632	−	0.0323984i	−0.103046	−	0.00160790i
$407$	−13.5526	+	4.93275i	−0.671778	+	0.244507i
$408$		0			0
$409$	13.9170	−	11.6777i	0.688149	−	0.577426i	−0.230226	−	0.973137i	$-0.573946\pi$
$409$	13.9170	−	11.6777i	0.688149	−	0.577426i	0.918375	+	0.395712i	$0.129502\pi$
$410$	−2.20294	−	13.7442i	−0.108796	−	0.678776i
$411$		0			0
$412$	21.4531	−	24.0041i	1.05692	−	1.18260i
$413$	7.72625	+	4.46075i	0.380184	+	0.219499i
$414$		0			0
$415$	6.44516	−	3.72111i	0.316380	−	0.182662i
$416$	−7.66717	+	29.7114i	−0.375914	+	1.45672i
$417$		0			0
$418$	0.120382	−	0.315350i	0.00588809	−	0.0154243i
$419$	−4.62462	−	1.68322i	−0.225927	−	0.0822309i	0.226576	−	0.973993i	$-0.427247\pi$
$419$	−4.62462	−	1.68322i	−0.225927	−	0.0822309i	−0.452504	+	0.891763i	$0.649469\pi$
$420$		0			0
$421$	−2.04359	+	11.5898i	−0.0995984	+	0.564851i	0.893642	+	0.448780i	$0.148141\pi$
$421$	−2.04359	+	11.5898i	−0.0995984	+	0.564851i	−0.993241	+	0.116071i	$0.962970\pi$
$422$	21.5601	−	12.0032i	1.04953	−	0.584305i
$423$		0			0
$424$	17.5512	+	11.2598i	0.852362	+	0.546826i
$425$	−5.89823	+	7.02924i	−0.286106	+	0.340968i
$426$		0			0
$427$	6.99642	−	1.23366i	0.338581	−	0.0597009i
$428$	15.2715	−	12.0227i	0.738176	−	0.581139i
$429$		0			0
$430$	−26.1735	+	9.06649i	−1.26220	+	0.437225i
$431$	4.40894			0.212371			0.106186	−	0.994346i	$-0.466136\pi$
$431$	4.40894			0.212371			0.106186	+	0.994346i	$0.466136\pi$
$432$		0			0
$433$	28.5232			1.37074			0.685369	−	0.728196i	$-0.259641\pi$
$433$	28.5232			1.37074			0.685369	+	0.728196i	$0.259641\pi$
$434$	26.0880	−	9.03684i	1.25226	−	0.433782i
$435$		0			0
$436$	−7.38363	+	5.81287i	−0.353612	+	0.278386i
$437$	−0.0763379	+	0.0134604i	−0.00365174	+	0.000643900i
$438$		0			0
$439$	3.10907	−	3.70524i	0.148388	−	0.176842i	−0.686730	−	0.726912i	$-0.740955\pi$
$439$	3.10907	−	3.70524i	0.148388	−	0.176842i	0.835118	+	0.550071i	$0.185399\pi$
$440$	21.4447	+	13.7576i	1.02233	+	0.655870i
$441$		0			0
$442$	8.94538	−	4.98017i	0.425488	−	0.236883i
$443$	−1.26185	+	7.15628i	−0.0599521	+	0.340005i	−0.999999	−	0.00103872i	$-0.999669\pi$
$443$	−1.26185	+	7.15628i	−0.0599521	+	0.340005i	0.940047	+	0.341044i	$0.110780\pi$
$444$		0			0
$445$	47.0392	+	17.1209i	2.22987	+	0.811607i
$446$	8.91515	−	23.3538i	0.422144	−	1.10584i
$447$		0			0
$448$	22.6003	+	6.20976i	1.06776	+	0.293384i
$449$	5.50442	−	3.17798i	0.259769	−	0.149978i	−0.364460	−	0.931219i	$-0.618746\pi$
$449$	5.50442	−	3.17798i	0.259769	−	0.149978i	0.624229	+	0.781241i	$0.285413\pi$
$450$		0			0
$451$	6.46583	+	3.73305i	0.304464	+	0.175782i
$452$	−0.752287	+	0.841744i	−0.0353846	+	0.0395923i
$453$		0			0
$454$	−2.08810	−	13.0276i	−0.0979992	−	0.611417i
$455$	41.9518	−	35.2017i	1.96673	−	1.65028i
$456$		0			0
$457$	0.840235	−	0.305821i	0.0393045	−	0.0143057i	−0.322293	−	0.946640i	$-0.604454\pi$
$457$	0.840235	−	0.305821i	0.0393045	−	0.0143057i	0.361598	+	0.932334i	$0.382231\pi$
$458$	−23.7801	−	0.371060i	−1.11117	−	0.0173385i
$459$		0			0
$460$	0.182549	−	5.84810i	0.00851140	−	0.272669i
$461$	4.48102	+	12.3115i	0.208702	+	0.573404i	0.999239	−	0.0390104i	$-0.0124206\pi$
$461$	4.48102	+	12.3115i	0.208702	+	0.573404i	−0.790537	+	0.612415i	$0.790198\pi$
$462$		0			0
$463$	0.866856	+	1.03308i	0.0402862	+	0.0480112i	0.785811	−	0.618466i	$-0.212246\pi$
$463$	0.866856	+	1.03308i	0.0402862	+	0.0480112i	−0.745525	+	0.666478i	$0.767801\pi$
$464$	1.99218	−	0.224310i	0.0924846	−	0.0104133i
$465$		0			0
$466$	−16.3201	+	18.8445i	−0.756016	+	0.872955i
$467$	−9.81172	+	16.9944i	−0.454032	+	0.786407i	−0.998632	−	0.0522890i	$-0.983348\pi$
$467$	−9.81172	+	16.9944i	−0.454032	+	0.786407i	0.544600	+	0.838696i	$0.316682\pi$
$468$		0			0
$469$	−7.06278	−	12.2331i	−0.326129	−	0.564872i
$470$	31.6233	+	6.08623i	1.45867	+	0.280737i
$471$		0			0
$472$	−7.94689	−	3.32130i	−0.365785	−	0.152875i
$473$	5.08146	−	13.9612i	0.233646	−	0.641937i
$474$		0			0
$475$	−0.618239	−	0.109012i	−0.0283667	−	0.00500182i
$476$	−3.69693	−	6.89125i	−0.169448	−	0.315860i
$477$		0			0
$478$	−6.69083	+	11.1822i	−0.306031	+	0.511464i
$479$	14.6017	+	12.2523i	0.667170	+	0.559822i	0.912226	−	0.409687i	$-0.134362\pi$
$479$	14.6017	+	12.2523i	0.667170	+	0.559822i	−0.245056	+	0.969509i	$0.578806\pi$
$480$		0			0
$481$	−5.19697	−	29.4735i	−0.236962	−	1.34388i
$482$	−6.83317	+	5.55437i	−0.311242	+	0.252994i
$483$		0			0
$484$	7.91661	−	2.60470i	0.359846	−	0.118395i
$485$		−	22.7439i		−	1.03275i
$486$		0			0
$487$			12.7440i			0.577486i	0.957407	+	0.288743i	$0.0932373\pi$
$487$			12.7440i			0.577486i	−0.957407	+	0.288743i	$0.906763\pi$
$488$	−6.54777	+	2.04168i	−0.296404	+	0.0924224i
$489$		0			0
$490$	−4.86708	−	5.98765i	−0.219872	−	0.270494i
$491$	−4.29474	−	24.3567i	−0.193819	−	1.09920i	−0.914091	−	0.405510i	$-0.867094\pi$
$491$	−4.29474	−	24.3567i	−0.193819	−	1.09920i	0.720272	−	0.693692i	$-0.244017\pi$
$492$		0			0
$493$	−0.512415	−	0.429967i	−0.0230780	−	0.0193648i
$494$	0.601068	+	0.359646i	0.0270433	+	0.0161812i
$495$		0			0
$496$	−23.8694	+	11.8614i	−1.07177	+	0.532595i
$497$	34.1576	+	6.02290i	1.53218	+	0.270164i
$498$		0			0
$499$	13.5128	−	37.1262i	0.604917	−	1.66199i	−0.136251	−	0.990674i	$-0.543505\pi$
$499$	13.5128	−	37.1262i	0.604917	−	1.66199i	0.741167	−	0.671320i	$-0.234273\pi$
$500$	4.79726	−	12.0013i	0.214540	−	0.536716i
$501$		0			0
$502$	7.57806	−	39.3747i	0.338225	−	1.75738i
$503$	−18.2058	−	31.5334i	−0.811757	−	1.40600i	−0.911633	−	0.411005i	$-0.865178\pi$
$503$	−18.2058	−	31.5334i	−0.811757	−	1.40600i	0.0998757	−	0.995000i	$-0.468155\pi$
$504$		0			0
$505$	14.2068	−	24.6069i	0.632194	−	1.09499i
$506$	2.37231	+	2.05452i	0.105462	+	0.0913345i
$507$		0			0
$508$	−22.0147	+	3.17711i	−0.976745	+	0.140961i
$509$	2.32891	+	2.77549i	0.103227	+	0.123021i	0.815184	−	0.579201i	$-0.196636\pi$
$509$	2.32891	+	2.77549i	0.103227	+	0.123021i	−0.711957	+	0.702223i	$0.752191\pi$
$510$		0			0
$511$	−11.6846	−	32.1032i	−0.516897	−	1.42016i
$512$	−22.4047	−	3.16697i	−0.990157	−	0.139961i
$513$		0			0
$514$	−0.364019	+	23.3289i	−0.0160562	+	1.02899i
$515$	52.1252	−	18.9720i	2.29691	−	0.836008i
$516$		0			0
$517$	−13.2320	+	11.1030i	−0.581944	+	0.488309i
$518$	−22.5719	+	3.61787i	−0.991751	+	0.158960i
$519$		0			0
$520$	−35.8424	+	38.8667i	−1.57179	+	1.70442i
$521$	−18.0443	−	10.4179i	−0.790534	−	0.456415i	0.0496162	−	0.998768i	$-0.484200\pi$
$521$	−18.0443	−	10.4179i	−0.790534	−	0.456415i	−0.840151	+	0.542353i	$0.817534\pi$
$522$		0			0
$523$	19.0780	−	11.0147i	0.834223	−	0.481639i	−0.0210733	−	0.999778i	$-0.506708\pi$
$523$	19.0780	−	11.0147i	0.834223	−	0.481639i	0.855296	+	0.518139i	$0.173375\pi$
$524$	1.26753	−	6.07371i	0.0553722	−	0.265331i
$525$		0			0
$526$	31.9957	+	12.2141i	1.39508	+	0.532561i
$527$	8.35708	+	3.04173i	0.364040	+	0.132500i
$528$		0			0
$529$	−3.86876	+	21.9408i	−0.168207	+	0.953949i
$530$	17.4771	+	31.3924i	0.759157	+	1.36360i
$531$		0			0
$532$	0.281837	−	0.454771i	0.0122192	−	0.0197168i
$533$	−9.95873	+	11.8684i	−0.431361	+	0.514075i
$534$		0			0
$535$	32.9802	−	5.81531i	1.42586	−	0.251418i
$536$	8.26738	+	10.8454i	0.357096	+	0.468449i
$537$		0			0
$538$	−5.64530	−	16.2971i	−0.243386	−	0.702617i
$539$	4.13879			0.178270
$540$		0			0
$541$	−13.2610			−0.570135			−0.285067	−	0.958507i	$-0.592016\pi$
$541$	−13.2610			−0.570135			−0.285067	+	0.958507i	$0.592016\pi$
$542$	−11.5729	−	33.4090i	−0.497097	−	1.43504i
$543$		0			0
$544$	4.38747	+	6.14415i	0.188111	+	0.263428i
$545$	−15.9456	+	2.81165i	−0.683036	+	0.120438i
$546$		0			0
$547$	−9.19354	+	10.9564i	−0.393087	+	0.468463i	−0.925899	−	0.377770i	$-0.876691\pi$
$547$	−9.19354	+	10.9564i	−0.393087	+	0.468463i	0.532812	+	0.846234i	$0.321135\pi$
$548$	29.3561	+	18.1930i	1.25403	+	0.777167i
$549$		0			0
$550$	12.3631	+	22.2066i	0.527165	+	0.946893i
$551$	0.00794673	−	0.0450681i	0.000338542	−	0.00191997i
$552$		0			0
$553$	−4.64441	−	1.69043i	−0.197500	−	0.0718842i
$554$	−11.5446	−	4.40706i	−0.490483	−	0.187238i
$555$		0			0
$556$	−21.9080	−	4.57201i	−0.929108	−	0.193896i
$557$	−6.40425	+	3.69750i	−0.271357	+	0.156668i	−0.629504	−	0.776997i	$-0.716742\pi$
$557$	−6.40425	+	3.69750i	−0.271357	+	0.156668i	0.358147	+	0.933665i	$0.383409\pi$
$558$		0			0
$559$	26.6999	+	15.4152i	1.12929	+	0.651994i
$560$	29.2567	+	27.8373i	1.23632	+	1.17634i
$561$		0			0
$562$	30.5641	−	4.89888i	1.28927	−	0.206647i
$563$	−16.2270	+	13.6161i	−0.683887	+	0.573850i	−0.917139	−	0.398567i	$-0.869508\pi$
$563$	−16.2270	+	13.6161i	−0.683887	+	0.573850i	0.233252	+	0.972416i	$0.425063\pi$
$564$		0			0
$565$	−1.82786	+	0.665286i	−0.0768985	+	0.0279888i
$566$	−0.664189	+	42.5660i	−0.0279180	+	1.78918i
$567$		0			0
$568$	−33.4485	−	1.56679i	−1.40347	−	0.0657409i
$569$	1.52428	+	4.18793i	0.0639012	+	0.175567i	0.967534	−	0.252741i	$-0.0813320\pi$
$569$	1.52428	+	4.18793i	0.0639012	+	0.175567i	−0.903633	+	0.428308i	$0.859110\pi$
$570$		0			0
$571$	−1.38240	−	1.64748i	−0.0578516	−	0.0689449i	0.736343	−	0.676609i	$-0.236551\pi$
$571$	−1.38240	−	1.64748i	−0.0578516	−	0.0689449i	−0.794194	+	0.607664i	$0.792107\pi$
$572$	−4.05064	−	28.0676i	−0.169366	−	1.17356i
$573$		0			0
$574$	8.94560	+	7.74727i	0.373382	+	0.323365i
$575$	2.91833	−	5.05470i	0.121703	−	0.210796i
$576$		0			0
$577$	−16.0706	−	27.8351i	−0.669028	−	1.15879i	−0.978176	−	0.207777i	$-0.933377\pi$
$577$	−16.0706	−	27.8351i	−0.669028	−	1.15879i	0.309148	−	0.951014i	$-0.399956\pi$
$578$	−4.06759	+	21.1347i	−0.169189	+	0.879087i
$579$		0			0
$580$	3.20751	+	1.28213i	0.133185	+	0.0532374i
$581$	−2.16402	+	5.94559i	−0.0897785	+	0.246664i
$582$		0			0
$583$	−18.9789	−	3.34648i	−0.786024	−	0.138597i
$584$	15.1366	+	29.3038i	0.626356	+	1.21260i
$585$		0			0
$586$	−16.0663	−	9.61316i	−0.663691	−	0.397116i
$587$	27.6154	+	23.1721i	1.13981	+	0.956414i	0.999433	−	0.0336838i	$-0.0107239\pi$
$587$	27.6154	+	23.1721i	1.13981	+	0.956414i	0.140378	+	0.990098i	$0.455168\pi$
$588$		0			0
$589$	0.105655	+	0.599198i	0.00435343	+	0.0246895i
$590$	−9.36073	−	11.5159i	−0.385375	−	0.474102i
$591$		0			0
$592$	21.1690	−	6.24008i	0.870040	−	0.256466i
$593$		−	4.09387i		−	0.168115i	−0.996461	−	0.0840576i	$-0.973212\pi$
$593$		−	4.09387i		−	0.168115i	0.996461	−	0.0840576i	$-0.0267880\pi$
$594$		0			0
$595$		−	13.4745i		−	0.552402i
$596$	−11.4087	−	34.6751i	−0.467318	−	1.42035i
$597$		0			0
$598$	−5.05344	+	4.10770i	−0.206651	+	0.167977i
$599$	−1.46823	−	8.32677i	−0.0599904	−	0.340223i	0.940009	−	0.341149i	$-0.110816\pi$
$599$	−1.46823	−	8.32677i	−0.0599904	−	0.340223i	−1.00000		0.000926605i	$0.999705\pi$
$600$		0			0
$601$	22.3724	+	18.7727i	0.912590	+	0.765754i	0.972610	−	0.232443i	$-0.0746721\pi$
$601$	22.3724	+	18.7727i	0.912590	+	0.765754i	−0.0600202	+	0.998197i	$0.519116\pi$
$602$	12.0913	−	20.2080i	0.492806	−	0.823616i
$603$		0			0
$604$	33.9255	−	18.1999i	1.38041	−	0.740544i
$605$	14.1417	+	2.49356i	0.574942	+	0.101378i
$606$		0			0
$607$	−13.2715	+	36.4633i	−0.538675	+	1.48000i	0.309820	+	0.950795i	$0.399731\pi$
$607$	−13.2715	+	36.4633i	−0.538675	+	1.48000i	−0.848495	+	0.529203i	$0.822491\pi$
$608$	−0.213951	+	0.470128i	−0.00867684	+	0.0190662i
$609$		0			0
$610$	−11.6048	−	2.23345i	−0.469863	−	0.0904299i
$611$	−17.9220	−	31.0417i	−0.725045	−	1.25581i
$612$		0			0
$613$	−0.677216	+	1.17297i	−0.0273525	+	0.0473759i	−0.879378	−	0.476125i	$-0.842041\pi$
$613$	−0.677216	+	1.17297i	−0.0273525	+	0.0473759i	0.852025	+	0.523501i	$0.175374\pi$
$614$	−12.1940	+	14.0802i	−0.492111	+	0.568230i
$615$		0			0
$616$	−21.4845	+	2.75913i	−0.865634	+	0.111169i
$617$	14.2746	+	17.0118i	0.574675	+	0.684871i	0.972583	−	0.232554i	$-0.0747083\pi$
$617$	14.2746	+	17.0118i	0.574675	+	0.684871i	−0.397909	+	0.917425i	$0.630264\pi$
$618$		0			0
$619$	0.757138	+	2.08022i	0.0304320	+	0.0836111i	0.953978	−	0.299876i	$-0.0969453\pi$
$619$	0.757138	+	2.08022i	0.0304320	+	0.0836111i	−0.923546	+	0.383487i	$0.874723\pi$
$620$	−45.9034	−	1.43288i	−1.84353	−	0.0575459i
$621$		0			0
$622$	8.73303	+	0.136268i	0.350163	+	0.00546386i
$623$	−39.9913	+	14.5556i	−1.60222	+	0.583160i
$624$		0			0
$625$	−9.27445	+	7.78219i	−0.370978	+	0.311287i
$626$	4.79794	+	29.9343i	0.191764	+	1.19642i
$627$		0			0
$628$	−25.1125	−	22.4436i	−1.00210	−	0.895599i
$629$	−6.37717	−	3.68186i	−0.254274	−	0.146805i
$630$		0			0
$631$	10.3534	−	5.97752i	0.412161	−	0.237961i	−0.279557	−	0.960129i	$-0.590187\pi$
$631$	10.3534	−	5.97752i	0.412161	−	0.237961i	0.691718	+	0.722168i	$0.256854\pi$
$632$	4.65517	+	1.04754i	0.185173	+	0.0416689i
$633$		0			0
$634$	7.41544	−	19.4253i	0.294505	−	0.771475i
$635$	−36.0136	−	13.1079i	−1.42916	−	0.520171i
$636$		0			0
$637$	−1.49137	+	8.45799i	−0.0590903	+	0.335118i
$638$	−1.61881	+	0.901242i	−0.0640893	+	0.0356805i
$639$		0			0
$640$	−31.4383	−	23.0580i	−1.24271	−	0.911447i
$641$	−8.66598	+	10.3277i	−0.342286	+	0.407920i	−0.909536	−	0.415625i	$-0.863563\pi$
$641$	−8.66598	+	10.3277i	−0.342286	+	0.407920i	0.567250	+	0.823545i	$0.308007\pi$
$642$		0			0
$643$	−27.1966	+	4.79550i	−1.07253	+	0.189116i	−0.681910	−	0.731436i	$-0.738850\pi$
$643$	−27.1966	+	4.79550i	−1.07253	+	0.189116i	−0.390620	+	0.920552i	$0.627739\pi$
$644$	3.07697	+	3.90844i	0.121250	+	0.154014i
$645$		0			0
$646$	0.162849	−	0.0564109i	0.00640722	−	0.00221946i
$647$	−15.2634			−0.600064			−0.300032	−	0.953929i	$-0.596997\pi$
$647$	−15.2634			−0.600064			−0.300032	+	0.953929i	$0.596997\pi$
$648$		0			0
$649$	7.96003			0.312458
$650$	−49.8362	+	17.2632i	−1.95474	+	0.677119i
$651$		0			0
$652$	−9.92943	−	12.6126i	−0.388866	−	0.493947i
$653$	30.1302	−	5.31277i	1.17909	−	0.207905i	0.450448	−	0.892803i	$-0.351264\pi$
$653$	30.1302	−	5.31277i	1.17909	−	0.207905i	0.728639	+	0.684898i	$0.240153\pi$
$654$		0			0
$655$	6.87180	−	8.18949i	0.268503	−	0.319990i
$656$	−9.51864	−	6.31838i	−0.371641	−	0.246691i
$657$		0			0
$658$	−23.9212	+	13.3177i	−0.932547	+	0.519178i
$659$	7.25464	−	41.1431i	0.282601	−	1.60271i	−0.431132	−	0.902289i	$-0.641886\pi$
$659$	7.25464	−	41.1431i	0.282601	−	1.60271i	0.713732	−	0.700418i	$-0.247003\pi$
$660$		0			0
$661$	−30.7435	−	11.1897i	−1.19578	−	0.435230i	−0.334033	−	0.942561i	$-0.608410\pi$
$661$	−30.7435	−	11.1897i	−1.19578	−	0.435230i	−0.861751	+	0.507331i	$0.830632\pi$
$662$	−13.3776	+	35.0437i	−0.519937	+	1.36201i
$663$		0			0
$664$	1.34102	−	5.95936i	0.0520416	−	0.231268i
$665$	0.798352	−	0.460929i	0.0309588	−	0.0178741i
$666$		0			0
$667$	0.368476	+	0.212740i	0.0142674	+	0.00823731i
$668$	1.94706	+	1.74013i	0.0753339	+	0.0673277i
$669$		0			0
$670$	3.71871	+	23.2010i	0.143666	+	0.896334i
$671$	4.85574	−	4.07445i	0.187454	−	0.157292i
$672$		0			0
$673$	−26.6470	+	9.69872i	−1.02717	+	0.373858i	−0.800002	−	0.599998i	$-0.795168\pi$
$673$	−26.6470	+	9.69872i	−1.02717	+	0.373858i	−0.227166	+	0.973856i	$0.572946\pi$
$674$	21.8182	+	0.340446i	0.840407	+	0.0131135i
$675$		0			0
$676$	32.8310	+	1.02482i	1.26273	+	0.0394163i
$677$	−13.7737	−	37.8429i	−0.529366	−	1.45442i	−0.859819	−	0.510599i	$-0.829424\pi$
$677$	−13.7737	−	37.8429i	−0.529366	−	1.45442i	0.330453	−	0.943822i	$-0.392799\pi$
$678$		0			0
$679$	12.4290	+	14.8124i	0.476983	+	0.568446i
$680$	1.65702	+	12.9026i	0.0635437	+	0.494794i
$681$		0			0
$682$	16.1265	−	18.6209i	0.617516	−	0.713032i
$683$	−2.35647	+	4.08153i	−0.0901678	+	0.156175i	−0.907582	−	0.419876i	$-0.862074\pi$
$683$	−2.35647	+	4.08153i	−0.0901678	+	0.156175i	0.817414	+	0.576051i	$0.195407\pi$
$684$		0			0
$685$	29.7536	+	51.5348i	1.13683	+	1.96904i
$686$	−22.0383	−	4.24150i	−0.841426	−	0.161941i
$687$		0			0
$688$	−9.09310	+	20.8372i	−0.346671	+	0.794412i
$689$	13.6777	−	37.5792i	0.521079	−	1.43165i
$690$		0			0
$691$	47.8656	+	8.44000i	1.82089	+	0.321073i	0.976642	−	0.214875i	$-0.0689344\pi$
$691$	47.8656	+	8.44000i	1.82089	+	0.321073i	0.844251	+	0.535947i	$0.180045\pi$
$692$	−20.1811	+	10.8265i	−0.767169	+	0.411561i
$693$		0			0
$694$	−15.6296	+	26.1214i	−0.593291	+	0.991553i
$695$	−29.5397	−	24.7868i	−1.12051	−	0.940216i
$696$		0			0
$697$	0.661948	+	3.75409i	0.0250731	+	0.142196i
$698$	−13.8723	+	11.2761i	−0.525074	+	0.426808i
$699$		0			0
$700$	12.5906	+	38.2674i	0.475881	+	1.44637i
$701$			5.10945i			0.192981i	0.995334	+	0.0964906i	$0.0307618\pi$
$701$			5.10945i			0.192981i	−0.995334	+	0.0964906i	$0.969238\pi$
$702$		0			0
$703$		−	0.503788i		−	0.0190007i
$704$	20.2333	−	5.28406i	0.762572	−	0.199151i
$705$		0			0
$706$	−9.98090	−	12.2789i	−0.375636	−	0.462121i
$707$	4.19471	+	23.7894i	0.157758	+	0.894692i
$708$		0			0
$709$	−7.00392	−	5.87699i	−0.263038	−	0.220715i	0.501725	−	0.865027i	$-0.332699\pi$
$709$	−7.00392	−	5.87699i	−0.263038	−	0.220715i	−0.764762	+	0.644313i	$0.777144\pi$
$710$	−49.5099	−	29.6240i	−1.85807	−	1.11177i
$711$		0			0
$712$	36.5040	−	18.8558i	1.36805	−	0.706650i
$713$	−5.57097	−	0.982312i	−0.208634	−	0.0367879i
$714$		0			0
$715$	16.7119	−	45.9155i	0.624988	−	1.71714i
$716$	39.7665	+	15.8957i	1.48614	+	0.594051i
$717$		0			0
$718$	−8.64360	+	44.9111i	−0.322576	+	1.67607i
$719$	11.2528	+	19.4904i	0.419658	+	0.726869i	0.995905	−	0.0904064i	$-0.0288166\pi$
$719$	11.2528	+	19.4904i	0.419658	+	0.726869i	−0.576247	+	0.817276i	$0.695483\pi$
$720$		0			0
$721$	−23.5797	+	40.8412i	−0.878153	+	1.52101i
$722$	−20.3028	−	17.5831i	−0.755591	−	0.654374i
$723$		0			0
$724$	−4.17895	−	28.9566i	−0.155309	−	1.07616i
$725$	2.21494	+	2.63966i	0.0822608	+	0.0980346i
$726$		0			0
$727$	5.99428	+	16.4691i	0.222316	+	0.610807i	0.999837	−	0.0180494i	$-0.00574560\pi$
$727$	5.99428	+	16.4691i	0.222316	+	0.610807i	−0.777522	+	0.628856i	$0.783523\pi$
$728$	2.10318	−	44.8997i	0.0779491	−	1.66409i
$729$		0			0
$730$	−0.886643	+	56.8224i	−0.0328161	+	2.10309i
$731$	7.12825	−	2.59447i	0.263648	−	0.0959599i
$732$		0			0
$733$	−17.2190	+	14.4484i	−0.635998	+	0.533666i	−0.902786	−	0.430089i	$-0.858482\pi$
$733$	−17.2190	+	14.4484i	−0.635998	+	0.533666i	0.266788	+	0.963755i	$0.414038\pi$
$734$	−0.930645	+	0.149166i	−0.0343507	+	0.00550581i
$735$		0			0
$736$	−3.42702	−	3.36417i	−0.126322	−	0.124005i
$737$	−10.9147	−	6.30162i	−0.402049	−	0.232123i
$738$		0			0
$739$	7.76664	−	4.48407i	0.285700	−	0.164949i	−0.350301	−	0.936637i	$-0.613921\pi$
$739$	7.76664	−	4.48407i	0.285700	−	0.164949i	0.636001	+	0.771688i	$0.280587\pi$
$740$	37.2244	+	7.76839i	1.36840	+	0.285572i
$741$		0			0
$742$	−28.5375	−	10.8940i	−1.04765	−	0.399930i
$743$	44.6168	+	16.2392i	1.63683	+	0.595758i	0.986481	−	0.163875i	$-0.0523994\pi$
$743$	44.6168	+	16.2392i	1.63683	+	0.595758i	0.650352	+	0.759633i	$0.274622\pi$
$744$		0			0
$745$	10.9219	−	61.9413i	0.400148	−	2.26935i
$746$	14.3298	+	25.7393i	0.524653	+	0.942381i
$747$		0			0
$748$	−5.93088	−	3.67557i	−0.216854	−	0.134392i
$749$	−18.3010	+	21.8103i	−0.668705	+	0.796932i
$750$		0			0
$751$	−13.7230	+	2.41974i	−0.500761	+	0.0882976i	−0.418323	−	0.908299i	$-0.637382\pi$
$751$	−13.7230	+	2.41974i	−0.500761	+	0.0882976i	−0.0824383	+	0.996596i	$0.526271\pi$
$752$	21.2683	−	15.6942i	0.775573	−	0.572307i
$753$		0			0
$754$	−1.25845	−	3.63294i	−0.0458300	−	0.132304i
$755$	66.3349			2.41418
$756$		0			0
$757$	12.8098			0.465582			0.232791	−	0.972527i	$-0.425214\pi$
$757$	12.8098			0.465582			0.232791	+	0.972527i	$0.425214\pi$
$758$	8.88317	+	25.6443i	0.322651	+	0.931444i
$759$		0			0
$760$	−0.707786	+	0.539543i	−0.0256741	+	0.0195713i
$761$	−30.5200	+	5.38149i	−1.10635	+	0.195079i	−0.696839	−	0.717227i	$-0.745411\pi$
$761$	−30.5200	+	5.38149i	−1.10635	+	0.195079i	−0.409508	+	0.912306i	$0.634300\pi$
$762$		0			0
$763$	8.84838	−	10.5451i	0.320333	−	0.381758i
$764$	−2.02491	+	3.26739i	−0.0732587	+	0.118210i
$765$		0			0
$766$	−5.45678	−	9.80146i	−0.197161	−	0.354141i
$767$	−2.86832	+	16.2671i	−0.103569	+	0.587369i
$768$		0			0
$769$	−16.0889	−	5.85587i	−0.580179	−	0.211168i	0.0352254	−	0.999379i	$-0.488785\pi$
$769$	−16.0889	−	5.85587i	−0.580179	−	0.211168i	−0.615404	+	0.788211i	$0.711007\pi$
$770$	−34.8681	−	13.3106i	−1.25656	−	0.479681i
$771$		0			0
$772$	−2.55831	+	12.2588i	−0.0920755	+	0.441205i
$773$	−37.1476	+	21.4472i	−1.33610	+	0.771401i	−0.986227	−	0.165395i	$-0.947110\pi$
$773$	−37.1476	+	21.4472i	−1.33610	+	0.771401i	−0.349877	+	0.936795i	$0.613777\pi$
$774$		0			0
$775$	−39.6758	−	22.9068i	−1.42520	−	0.822838i
$776$	−13.7231	−	12.6552i	−0.492629	−	0.454297i
$777$		0			0
$778$	17.2399	−	2.76326i	0.618082	−	0.0990676i
$779$	−0.199783	+	0.167638i	−0.00715795	+	0.00600624i
$780$		0			0
$781$	29.0802	−	10.5843i	1.04057	−	0.378737i
$782$	−0.0249994	+	1.60214i	−0.000893978	+	0.0572924i
$783$		0			0
$784$	−6.32095	−	0.395004i	−0.225748	−	0.0141073i
$785$	−19.8481	−	54.5321i	−0.708408	−	1.94633i
$786$		0			0
$787$	−3.83079	−	4.56536i	−0.136553	−	0.162737i	0.693434	−	0.720520i	$-0.256097\pi$
$787$	−3.83079	−	4.56536i	−0.136553	−	0.162737i	−0.829987	+	0.557783i	$0.811652\pi$
$788$	−29.9480	+	4.32202i	−1.06685	+	0.153966i
$789$		0			0
$790$	6.21485	+	5.38233i	0.221115	+	0.191495i
$791$	0.826860	−	1.43216i	0.0293998	−	0.0509219i
$792$		0			0
$793$	6.57679	+	11.3913i	0.233549	+	0.404518i
$794$	6.19859	−	32.2071i	0.219980	−	1.14299i
$795$		0			0
$796$	−19.2375	+	48.1267i	−0.681856	+	1.70580i
$797$	−14.1501	+	38.8770i	−0.501221	+	1.37709i	0.388863	+	0.921296i	$0.372868\pi$
$797$	−14.1501	+	38.8770i	−0.501221	+	1.37709i	−0.890084	+	0.455797i	$0.849354\pi$
$798$		0			0
$799$	−8.68528	−	1.53145i	−0.307263	−	0.0541788i
$800$	−16.7621	−	35.0949i	−0.592631	−	1.24079i
$801$		0			0
$802$	−8.24720	−	4.93467i	−0.291219	−	0.174249i
$803$	−23.3504	−	19.5933i	−0.824016	−	0.691432i
$804$		0			0
$805$	1.48831	+	8.44064i	0.0524561	+	0.297494i
$806$	32.2426	+	39.6659i	1.13570	+	1.39717i
$807$		0			0
$808$	−6.94216	−	22.2639i	−0.244224	−	0.783241i
$809$			45.8780i			1.61298i	0.591245	+	0.806492i	$0.298637\pi$
$809$			45.8780i			1.61298i	−0.591245	+	0.806492i	$0.701363\pi$
$810$		0			0
$811$			25.4302i			0.892974i	0.894790	+	0.446487i	$0.147325\pi$
$811$			25.4302i			0.892974i	−0.894790	+	0.446487i	$0.852675\pi$
$812$	−2.78960	+	0.917827i	−0.0978959	+	0.0322094i
$813$		0			0
$814$	−15.8272	+	12.8652i	−0.554742	+	0.450923i
$815$	−4.80280	−	27.2380i	−0.168235	−	0.954107i
$816$		0			0
$817$	0.397558	+	0.333591i	0.0139088	+	0.0116709i
$818$	13.1918	−	22.0472i	0.461241	−	0.770861i
$819$		0			0
$820$	−9.30595	−	17.3467i	−0.324978	−	0.605774i
$821$	7.72253	+	1.36169i	0.269518	+	0.0475233i	0.306774	−	0.951782i	$-0.400750\pi$
$821$	7.72253	+	1.36169i	0.269518	+	0.0475233i	−0.0372556	+	0.999306i	$0.511862\pi$
$822$		0			0
$823$	−2.99728	+	8.23497i	−0.104479	+	0.287053i	−0.980906	−	0.194481i	$-0.937698\pi$
$823$	−2.99728	+	8.23497i	−0.104479	+	0.287053i	0.876428	+	0.481534i	$0.159920\pi$
$824$	17.5565	−	42.0075i	0.611610	−	1.46340i
$825$		0			0
$826$	12.3895	+	2.38449i	0.431087	+	0.0829672i
$827$	9.57006	+	16.5758i	0.332784	+	0.576398i	0.983057	−	0.183303i	$-0.0586788\pi$
$827$	9.57006	+	16.5758i	0.332784	+	0.576398i	−0.650273	+	0.759701i	$0.725345\pi$
$828$		0			0
$829$	−0.0258029	+	0.0446919i	−0.000896172	+	0.00155222i	−0.866473	−	0.499224i	$-0.833619\pi$
$829$	−0.0258029	+	0.0446919i	−0.000896172	+	0.00155222i	0.865577	+	0.500776i	$0.166952\pi$
$830$	6.89024	−	7.95601i	0.239164	−	0.276157i
$831$		0			0
$832$	3.50758	+	43.2527i	0.121604	+	1.49952i
$833$	1.35831	+	1.61878i	0.0470628	+	0.0560873i
$834$		0			0
$835$	1.53889	+	4.22806i	0.0532554	+	0.146318i
$836$	0.0148937	−	0.477130i	0.000515109	−	0.0165019i
$837$		0			0
$838$	−6.95909	−	0.108588i	−0.240398	−	0.00375111i
$839$	10.1094	−	3.67952i	0.349015	−	0.127031i	−0.161563	−	0.986862i	$-0.551654\pi$
$839$	10.1094	−	3.67952i	0.349015	−	0.127031i	0.510578	+	0.859831i	$0.329431\pi$
$840$		0			0
$841$	22.0229	−	18.4794i	0.759409	−	0.637220i
$842$	2.63400	+	16.4335i	0.0907736	+	0.566336i
$843$		0			0
$844$	23.2547	−	26.0201i	0.800461	−	0.895647i
$845$	49.0137	+	28.2981i	1.68612	+	0.973484i
$846$		0			0
$847$	−10.5727	+	6.10416i	−0.363283	+	0.209741i
$848$	28.6660	+	6.92224i	0.984395	+	0.237711i
$849$		0			0
$850$	−4.62806	+	12.1235i	−0.158741	+	0.415833i
$851$	4.40143	+	1.60199i	0.150879	+	0.0549155i
$852$		0			0
$853$	6.86844	−	38.9529i	0.235171	−	1.33372i	−0.607083	−	0.794639i	$-0.707660\pi$
$853$	6.86844	−	38.9529i	0.235171	−	1.33372i	0.842254	−	0.539082i	$-0.181229\pi$
$854$	8.77834	−	4.88717i	0.300389	−	0.167236i
$855$		0			0
$856$	14.8422	−	23.1352i	0.507296	−	0.790745i
$857$	6.59420	−	7.85866i	0.225253	−	0.268447i	−0.641567	−	0.767067i	$-0.721715\pi$
$857$	6.59420	−	7.85866i	0.225253	−	0.268447i	0.866820	+	0.498620i	$0.166160\pi$
$858$		0			0
$859$	−3.49071	+	0.615507i	−0.119102	+	0.0210008i	−0.232881	−	0.972505i	$-0.574815\pi$
$859$	−3.49071	+	0.615507i	−0.119102	+	0.0210008i	0.113780	+	0.993506i	$0.463704\pi$
$860$	−30.7791	+	24.2313i	−1.04956	+	0.826280i
$861$		0			0
$862$	5.89172	−	2.04089i	0.200673	−	0.0695129i
$863$	−6.36151			−0.216548			−0.108274	−	0.994121i	$-0.534532\pi$
$863$	−6.36151			−0.216548			−0.108274	+	0.994121i	$0.534532\pi$
$864$		0			0
$865$	−39.4602			−1.34169
$866$	38.1159	−	13.2033i	1.29523	−	0.448667i
$867$		0			0
$868$	30.6785	−	24.1521i	1.04130	−	0.819775i
$869$	−4.34283	+	0.765757i	−0.147320	+	0.0259765i
$870$		0			0
$871$	16.8110	−	20.0345i	0.569618	−	0.678844i
$872$	−7.17607	+	11.1857i	−0.243012	+	0.378794i
$873$		0			0
$874$	−0.0957804	+	0.0533239i	−0.00323982	+	0.00180371i
$875$	−3.28765	+	18.6452i	−0.111143	+	0.630323i
$876$		0			0
$877$	15.3450	+	5.58514i	0.518165	+	0.188597i	0.587846	−	0.808973i	$-0.299976\pi$
$877$	15.3450	+	5.58514i	0.518165	+	0.188597i	−0.0696811	+	0.997569i	$0.522198\pi$
$878$	2.43954	−	6.39054i	0.0823303	−	0.215670i
$879$		0			0
$880$	35.0251	+	8.45782i	1.18070	+	0.285113i
$881$	43.1593	−	24.9180i	1.45407	−	0.839509i	0.455364	−	0.890306i	$-0.349509\pi$
$881$	43.1593	−	24.9180i	1.45407	−	0.839509i	0.998709	+	0.0507963i	$0.0161759\pi$
$882$		0			0
$883$	−38.2077	−	22.0592i	−1.28579	−	0.742352i	−0.307890	−	0.951422i	$-0.599623\pi$
$883$	−38.2077	−	22.0592i	−1.28579	−	0.742352i	−0.977901	+	0.209070i	$0.932956\pi$
$884$	9.64850	−	10.7958i	0.324514	−	0.363104i
$885$		0			0
$886$	1.62640	+	10.1471i	0.0546401	+	0.340899i
$887$	1.84120	−	1.54495i	0.0618215	−	0.0518744i	−0.611353	−	0.791358i	$-0.709375\pi$
$887$	1.84120	−	1.54495i	0.0618215	−	0.0518744i	0.673175	+	0.739483i	$0.264930\pi$
$888$		0			0
$889$	30.6177	−	11.1439i	1.02688	−	0.373756i
$890$	70.7842	+	1.10450i	2.37269	+	0.0370229i
$891$		0			0
$892$	1.10298	−	35.3348i	0.0369305	−	1.18310i
$893$	−0.206364	−	0.566981i	−0.00690571	−	0.0189733i
$894$		0			0
$895$	47.4313	+	56.5264i	1.58545	+	1.88947i
$896$	33.0754	−	2.16341i	1.10497	−	0.0722746i
$897$		0			0
$898$	5.88453	−	6.79474i	0.196369	−	0.226743i
$899$	1.66986	−	2.89227i	0.0556928	−	0.0964627i
$900$		0			0
$901$	−4.91981	−	8.52136i	−0.163903	−	0.283888i
$902$	10.3684	+	1.99550i	0.345229	+	0.0664429i
$903$		0			0
$904$	−0.615648	+	1.47306i	−0.0204761	+	0.0489933i
$905$	17.2412	−	47.3698i	0.573117	−	1.57463i
$906$		0			0
$907$	−34.5531	−	6.09265i	−1.14732	−	0.202303i	−0.432513	−	0.901628i	$-0.642373\pi$
$907$	−34.5531	−	6.09265i	−1.14732	−	0.202303i	−0.714804	+	0.699324i	$0.753484\pi$
$908$	−8.82079	−	16.4424i	−0.292728	−	0.545660i
$909$		0			0
$910$	39.7659	−	66.4598i	1.31823	−	2.20312i
$911$	8.27443	+	6.94307i	0.274144	+	0.230034i	0.769486	−	0.638664i	$-0.220513\pi$
$911$	8.27443	+	6.94307i	0.274144	+	0.230034i	−0.495342	+	0.868698i	$0.664957\pi$
$912$		0			0
$913$	0.980292	+	5.55951i	0.0324429	+	0.183993i
$914$	0.981252	−	0.797613i	0.0324569	−	0.0263827i
$915$		0			0
$916$	−31.9494	+	10.5119i	−1.05564	+	0.347323i
$917$			9.08884i			0.300140i
$918$		0			0
$919$			20.9319i			0.690481i	0.938514	+	0.345241i	$0.112203\pi$
$919$			20.9319i			0.690481i	−0.938514	+	0.345241i	$0.887797\pi$
$920$	−2.46313	−	7.89938i	−0.0812069	−	0.260435i
$921$		0			0
$922$	11.6870	+	14.3778i	0.384891	+	0.473506i
$923$	11.1513	+	63.2421i	0.367049	+	2.08164i
$924$		0			0
$925$	29.0588	+	24.3832i	0.955447	+	0.801715i
$926$	1.63660	+	0.979249i	0.0537819	+	0.0321801i
$927$		0			0
$928$	2.55834	−	1.22192i	0.0839816	−	0.0401115i
$929$	−33.1245	−	5.84075i	−1.08678	−	0.191629i	−0.398568	−	0.917139i	$-0.630493\pi$
$929$	−33.1245	−	5.84075i	−1.08678	−	0.191629i	−0.688212	+	0.725510i	$0.741604\pi$
$930$		0			0
$931$	−0.0494464	+	0.135853i	−0.00162054	+	0.00445240i
$932$	−13.0857	+	32.7367i	−0.428637	+	1.07233i
$933$		0			0
$934$	−5.24485	+	27.2516i	−0.171617	+	0.891700i
$935$	−6.01119	−	10.4117i	−0.196587	−	0.340498i
$936$		0			0
$937$	−12.5767	+	21.7834i	−0.410862	+	0.711634i	−0.994984	−	0.100032i	$-0.968106\pi$
$937$	−12.5767	+	21.7834i	−0.410862	+	0.711634i	0.584122	+	0.811666i	$0.301439\pi$
$938$	−15.1007	−	13.0779i	−0.493057	−	0.427008i
$939$		0			0
$940$	45.0759	−	6.50524i	1.47021	−	0.212177i
$941$	−26.6235	−	31.7286i	−0.867901	−	1.03432i	−0.999077	−	0.0429652i	$-0.986320\pi$
$941$	−26.6235	−	31.7286i	−0.867901	−	1.03432i	0.131175	−	0.991359i	$-0.458125\pi$
$942$		0			0
$943$	−0.829308	−	2.27850i	−0.0270060	−	0.0741983i
$944$	−12.1569	−	0.759701i	−0.395675	−	0.0247262i
$945$		0			0
$946$	0.327815	−	21.0087i	0.0106582	−	0.683052i
$947$	−53.1276	+	19.3369i	−1.72642	+	0.628364i	−0.998365	−	0.0571597i	$-0.981796\pi$
$947$	−53.1276	+	19.3369i	−1.72642	+	0.628364i	−0.728050	+	0.685524i	$0.759573\pi$
$948$		0			0
$949$	48.4548	−	40.6584i	1.57291	−	1.31983i
$950$	−0.876620	+	0.140507i	−0.0284413	+	0.00455864i
$951$		0			0
$952$	−8.13018	−	7.49756i	−0.263501	−	0.242997i
$953$	31.8569	+	18.3926i	1.03195	+	0.595795i	0.917542	−	0.397639i	$-0.130170\pi$
$953$	31.8569	+	18.3926i	1.03195	+	0.595795i	0.114405	+	0.993434i	$0.463504\pi$
$954$		0			0
$955$	−5.73591	+	3.31163i	−0.185610	+	0.107162i
$956$	−3.76480	+	18.0401i	−0.121762	+	0.583459i
$957$		0			0
$958$	25.1840	+	9.61380i	0.813658	+	0.310608i
$959$	−47.5403	−	17.3032i	−1.53516	−	0.558751i
$960$		0			0
$961$	−2.32736	+	13.1991i	−0.0750761	+	0.425778i
$962$	−20.5880	−	36.9801i	−0.663783	−	1.19229i
$963$		0			0
$964$	−6.56014	+	10.5854i	−0.211288	+	0.340933i
$965$	−13.8697	+	16.5292i	−0.446480	+	0.532094i
$966$		0			0
$967$	−44.3616	+	7.82215i	−1.42657	+	0.251543i	−0.833016	−	0.553249i	$-0.813388\pi$
$967$	−44.3616	+	7.82215i	−1.42657	+	0.251543i	−0.593557	+	0.804792i	$0.702277\pi$
$968$	9.37334	−	7.14526i	0.301271	−	0.229657i
$969$		0			0
$970$	−10.5281	−	30.3929i	−0.338036	−	0.975857i
$971$	−40.1053			−1.28704			−0.643520	−	0.765429i	$-0.722527\pi$
$971$	−40.1053			−1.28704			−0.643520	+	0.765429i	$0.722527\pi$
$972$		0			0
$973$	32.7837			1.05100
$974$	5.89916	+	17.0300i	0.189021	+	0.545675i
$975$		0			0
$976$	−7.80477	+	5.75926i	−0.249825	+	0.184349i
$977$	36.1734	−	6.37835i	1.15729	−	0.204062i	0.438134	−	0.898910i	$-0.355639\pi$
$977$	36.1734	−	6.37835i	1.15729	−	0.204062i	0.719157	+	0.694848i	$0.244528\pi$
$978$		0			0
$979$	−24.4075	+	29.0878i	−0.780068	+	0.929649i
$980$	−9.27559	−	5.74840i	−0.296298	−	0.183626i
$981$		0			0
$982$	−17.0137	−	30.5601i	−0.542930	−	0.975211i
$983$	−3.28853	+	18.6502i	−0.104888	+	0.594848i	0.886377	+	0.462963i	$0.153214\pi$
$983$	−3.28853	+	18.6502i	−0.104888	+	0.594848i	−0.991265	+	0.131884i	$0.957897\pi$
$984$		0			0
$985$	−48.9916	−	17.8315i	−1.56100	−	0.568158i
$986$	−0.883777	−	0.337375i	−0.0281452	−	0.0107442i
$987$		0			0
$988$	0.969693	+	0.202366i	0.0308500	+	0.00643812i
$989$	−4.17867	+	2.41256i	−0.132874	+	0.0767148i
$990$		0			0
$991$	−30.3997	−	17.5513i	−0.965680	−	0.557535i	−0.0677633	−	0.997701i	$-0.521586\pi$
$991$	−30.3997	−	17.5513i	−0.965680	−	0.557535i	−0.897916	+	0.440166i	$0.854920\pi$
$992$	−26.4064	+	26.8997i	−0.838403	+	0.854065i
$993$		0			0
$994$	48.4331	−	7.76296i	1.53620	−	0.246226i
$995$	−68.4100	+	57.4028i	−2.16874	+	1.81979i
$996$		0			0
$997$	−22.5603	+	8.21129i	−0.714493	+	0.260054i	−0.673586	−	0.739109i	$-0.735247\pi$
$997$	−22.5603	+	8.21129i	−0.714493	+	0.260054i	−0.0409071	+	0.999163i	$0.513025\pi$
$998$	0.871737	−	55.8671i	0.0275944	−	1.76844i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.143.15		96
3.2	odd	2		108.2.l.a.47.2	yes	96
4.3	odd	2	inner	324.2.l.a.143.2		96
9.2	odd	6		972.2.l.d.107.13		96
9.4	even	3		972.2.l.b.755.8		96
9.5	odd	6		972.2.l.c.755.9		96
9.7	even	3		972.2.l.a.107.4		96
12.11	even	2		108.2.l.a.47.15	yes	96
27.4	even	9		108.2.l.a.23.15	yes	96
27.5	odd	18		972.2.l.b.215.10		96
27.13	even	9		972.2.l.d.863.5		96
27.14	odd	18		972.2.l.a.863.12		96
27.22	even	9		972.2.l.c.215.7		96
27.23	odd	18	inner	324.2.l.a.179.2		96
36.7	odd	6		972.2.l.a.107.12		96
36.11	even	6		972.2.l.d.107.5		96
36.23	even	6		972.2.l.c.755.7		96
36.31	odd	6		972.2.l.b.755.10		96
108.23	even	18	inner	324.2.l.a.179.15		96
108.31	odd	18		108.2.l.a.23.2	✓	96
108.59	even	18		972.2.l.b.215.8		96
108.67	odd	18		972.2.l.d.863.13		96
108.95	even	18		972.2.l.a.863.4		96
108.103	odd	18		972.2.l.c.215.9		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.2	✓	96	108.31	odd	18
108.2.l.a.23.15	yes	96	27.4	even	9
108.2.l.a.47.2	yes	96	3.2	odd	2
108.2.l.a.47.15	yes	96	12.11	even	2
324.2.l.a.143.2		96	4.3	odd	2	inner
324.2.l.a.143.15		96	1.1	even	1	trivial
324.2.l.a.179.2		96	27.23	odd	18	inner
324.2.l.a.179.15		96	108.23	even	18	inner
972.2.l.a.107.4		96	9.7	even	3
972.2.l.a.107.12		96	36.7	odd	6
972.2.l.a.863.4		96	108.95	even	18
972.2.l.a.863.12		96	27.14	odd	18
972.2.l.b.215.8		96	108.59	even	18
972.2.l.b.215.10		96	27.5	odd	18
972.2.l.b.755.8		96	9.4	even	3
972.2.l.b.755.10		96	36.31	odd	6
972.2.l.c.215.7		96	27.22	even	9
972.2.l.c.215.9		96	108.103	odd	18
972.2.l.c.755.7		96	36.23	even	6
972.2.l.c.755.9		96	9.5	odd	6
972.2.l.d.107.5		96	36.11	even	6
972.2.l.d.107.13		96	9.2	odd	6
972.2.l.d.863.5		96	27.13	even	9
972.2.l.d.863.13		96	108.67	odd	18

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)

\(f(q)\)	\(=\)	\(q+(1.33631 - 0.462897i) q^{2} +(1.57145 - 1.23715i) q^{4} +(3.39370 - 0.598401i) q^{5} +(-1.88319 + 2.24430i) q^{7} +(1.52728 - 2.38064i) q^{8} +O(q^{10})\)	\(q+(1.33631 - 0.462897i) q^{2} +(1.57145 - 1.23715i) q^{4} +(3.39370 - 0.598401i) q^{5} +(-1.88319 + 2.24430i) q^{7} +(1.52728 - 2.38064i) q^{8} +(4.25804 - 2.37058i) q^{10} +(-0.453915 + 2.57428i) q^{11} +(-5.09721 - 1.85523i) q^{13} +(-1.47765 + 3.87081i) q^{14} +(0.938928 - 3.88824i) q^{16} +(-1.15583 + 0.667320i) q^{17} +(-0.0790760 - 0.0456546i) q^{19} +(4.59273 - 5.13887i) q^{20} +(0.585055 + 3.65015i) q^{22} +(0.650322 - 0.545685i) q^{23} +(6.46065 - 2.35148i) q^{25} +(-7.67024 - 0.119685i) q^{26} +(-0.182815 + 5.85661i) q^{28} +(0.171418 + 0.470966i) q^{29} +(-4.28324 - 5.10457i) q^{31} +(-0.545155 - 5.63052i) q^{32} +(-1.23565 + 1.42678i) q^{34} +(-5.04800 + 8.74340i) q^{35} +(2.75869 + 4.77819i) q^{37} +(-0.126804 - 0.0244046i) q^{38} +(3.75855 - 8.99308i) q^{40} +(0.976880 - 2.68396i) q^{41} +(-5.59737 - 0.986968i) q^{43} +(2.47146 + 4.60692i) q^{44} +(0.616436 - 1.03024i) q^{46} +(5.06200 + 4.24752i) q^{47} +(-0.274941 - 1.55927i) q^{49} +(7.54494 - 6.13293i) q^{50} +(-10.3052 + 3.39060i) q^{52} +7.37249i q^{53} +9.00795i q^{55} +(2.46671 + 7.91087i) q^{56} +(0.447076 + 0.550009i) q^{58} +(-0.528787 - 2.99890i) q^{59} +(-1.85759 - 1.55871i) q^{61} +(-8.08663 - 4.83859i) q^{62} +(-3.33485 - 7.27178i) q^{64} +(-18.4086 - 3.24593i) q^{65} +(-1.64904 + 4.53069i) q^{67} +(-0.990762 + 2.47860i) q^{68} +(-2.69841 + 14.0206i) q^{70} +(-5.91940 - 10.2527i) q^{71} +(-5.83049 + 10.0987i) q^{73} +(5.89828 + 5.10816i) q^{74} +(-0.180746 + 0.0260848i) q^{76} +(-4.92266 - 5.86659i) q^{77} +(0.576990 + 1.58527i) q^{79} +(0.859714 - 13.7574i) q^{80} +(0.0630204 - 4.03879i) q^{82} +(2.02940 - 0.738640i) q^{83} +(-3.52322 + 2.95633i) q^{85} +(-7.93669 + 1.27211i) q^{86} +(5.43517 + 5.01224i) q^{88} +(12.5801 + 7.26310i) q^{89} +(13.7628 - 7.94593i) q^{91} +(0.346857 - 1.66206i) q^{92} +(8.73057 + 3.33283i) q^{94} +(-0.295680 - 0.107619i) q^{95} +(1.14607 - 6.49971i) q^{97} +(-1.08919 - 1.95639i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 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

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