LMFDB - Embedded newform 324.2.l.a.179.15

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			179.15
Character	$\chi$	$=$	324.179
Dual form			324.2.l.a.143.15

$q$-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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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	0.869532	−	0.493877i	$-0.164421\pi$
$5$	3.39370	+	0.598401i	1.51771	+	0.267613i	0.648177	+	0.761490i	$0.275532\pi$
$6$		0			0
$7$	−1.88319	−	2.24430i	−0.711781	−	0.848267i	0.282024	−	0.959407i	$-0.408994\pi$
$7$	−1.88319	−	2.24430i	−0.711781	−	0.848267i	−0.993805	+	0.111140i	$0.964550\pi$
$8$	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	−0.973546	−	0.228491i	$-0.926621\pi$
$11$	−0.453915	−	2.57428i	−0.136861	−	0.776174i	0.836686	−	0.547684i	$-0.184490\pi$
$12$		0			0
$13$	−5.09721	+	1.85523i	−1.41371	+	0.514549i	−0.932217	−	0.361899i	$-0.882128\pi$
$13$	−5.09721	+	1.85523i	−1.41371	+	0.514549i	−0.481496	+	0.876449i	$0.659906\pi$
$14$	−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	0.353243	−	0.935532i	$-0.385079\pi$
$17$	−1.15583	−	0.667320i	−0.280330	−	0.161849i	−0.633573	+	0.773683i	$0.718412\pi$
$18$		0			0
$19$	−0.0790760	+	0.0456546i	−0.0181413	+	0.0104739i	−0.509043	−	0.860741i	$-0.670001\pi$
$19$	−0.0790760	+	0.0456546i	−0.0181413	+	0.0104739i	0.490902	+	0.871215i	$0.336667\pi$
$20$	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	0.708066	−	0.706147i	$-0.249568\pi$
$23$	0.650322	+	0.545685i	0.135602	+	0.113783i	−0.572464	+	0.819930i	$0.694012\pi$
$24$		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	−0.922759	−	0.385378i	$-0.874071\pi$
$29$	0.171418	−	0.470966i	0.0318315	−	0.0874562i	0.954590	+	0.297922i	$0.0962934\pi$
$30$		0			0
$31$	−4.28324	+	5.10457i	−0.769293	+	0.916807i	−0.998397	−	0.0565946i	$-0.981976\pi$
$31$	−4.28324	+	5.10457i	−0.769293	+	0.916807i	0.229105	+	0.973402i	$0.426420\pi$
$32$	−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	−0.545076	−	0.838387i	$-0.683499\pi$
$37$	2.75869	−	4.77819i	0.453526	−	0.785530i	0.998602	+	0.0528563i	$0.0168325\pi$
$38$	−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	0.992304	−	0.123823i	$-0.0395156\pi$
$41$	0.976880	+	2.68396i	0.152563	+	0.419163i	−0.839741	+	0.542987i	$0.817293\pi$
$42$		0			0
$43$	−5.59737	+	0.986968i	−0.853591	+	0.150511i	−0.583289	−	0.812264i	$-0.698235\pi$
$43$	−5.59737	+	0.986968i	−0.853591	+	0.150511i	−0.270302	+	0.962776i	$0.587124\pi$
$44$	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	−0.194030	−	0.980996i	$-0.562156\pi$
$47$	5.06200	−	4.24752i	0.738369	−	0.619565i	0.932399	+	0.361430i	$0.117712\pi$
$48$		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	$-0.830996\pi$
$53$		−	7.37249i		−	1.01269i	0.862331	−	0.506345i	$-0.169004\pi$
$54$		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	0.930845	+	0.365414i	$0.119073\pi$
$59$	−0.528787	+	2.99890i	−0.0688422	+	0.390423i	−0.999687	+	0.0250093i	$0.992038\pi$
$60$		0			0
$61$	−1.85759	+	1.55871i	−0.237841	+	0.199572i	−0.753915	−	0.656972i	$-0.771837\pi$
$61$	−1.85759	+	1.55871i	−0.237841	+	0.199572i	0.516075	+	0.856544i	$0.327393\pi$
$62$	−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	0.797283	−	0.603606i	$-0.206270\pi$
$67$	−1.64904	−	4.53069i	−0.201462	−	0.553512i	−0.998744	+	0.0500945i	$0.984048\pi$
$68$	−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	0.265081	+	0.964226i	$0.414601\pi$
$71$	−5.91940	+	10.2527i	−0.702504	+	1.21677i	−0.967585	+	0.252546i	$0.918732\pi$
$72$		0			0
$73$	−5.83049	−	10.0987i	−0.682408	−	1.18197i	−0.974244	−	0.225497i	$-0.927600\pi$
$73$	−5.83049	−	10.0987i	−0.682408	−	1.18197i	0.291836	−	0.956468i	$-0.405734\pi$
$74$	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	−0.902993	−	0.429655i	$-0.858635\pi$
$79$	0.576990	−	1.58527i	0.0649165	−	0.178357i	0.967910	+	0.251298i	$0.0808575\pi$
$80$	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	0.450987	−	0.892531i	$-0.351072\pi$
$83$	2.02940	+	0.738640i	0.222755	+	0.0810763i	−0.228232	+	0.973607i	$0.573294\pi$
$84$		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	0.347652	−	0.937624i	$-0.386979\pi$
$89$	12.5801	−	7.26310i	1.33348	−	0.769887i	0.985832	+	0.167737i	$0.0536458\pi$
$90$		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	0.986065	+	0.166362i	$0.0532021\pi$
$97$	1.14607	+	6.49971i	0.116366	+	0.659946i	−0.869698	+	0.493583i	$0.835687\pi$
$98$	−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	0.962306	−	0.271970i	$-0.0876752\pi$
$101$	5.29995	+	6.31623i	0.527365	+	0.628489i	−0.434941	+	0.900459i	$0.643231\pi$
$102$		0			0
$103$	15.8523	+	2.79519i	1.56197	+	0.275418i	0.886769	−	0.462214i	$-0.152945\pi$
$103$	15.8523	+	2.79519i	1.56197	+	0.275418i	0.675203	+	0.737632i	$0.264056\pi$
$104$	−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	0.147440	−	0.989071i	$-0.452897\pi$
$113$	−0.555886	−	0.0980178i	−0.0522934	−	0.00922074i	−0.199734	+	0.979850i	$0.564008\pi$
$114$		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	−0.862217	−	0.506539i	$-0.830924\pi$
$127$	−9.63141	+	5.56070i	−0.854649	+	0.493432i	0.00756758	+	0.999971i	$0.497591\pi$
$128$	−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	0.740675	−	0.671864i	$-0.234506\pi$
$131$	2.37648	+	1.99411i	0.207634	+	0.174226i	−0.533040	+	0.846090i	$0.678951\pi$
$132$		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	−0.382156	−	0.924098i	$-0.624818\pi$
$137$	5.90609	−	16.2268i	0.504591	−	1.38635i	0.886747	−	0.462255i	$-0.152959\pi$
$138$		0			0
$139$	−7.19280	+	8.57205i	−0.610085	+	0.727071i	−0.979332	−	0.202260i	$-0.935171\pi$
$139$	−7.19280	+	8.57205i	−0.610085	+	0.727071i	0.369246	+	0.929332i	$0.379616\pi$
$140$	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	0.879773	+	0.475395i	$0.157695\pi$
$149$	6.24250	+	17.1511i	0.511406	+	1.40508i	−0.368367	+	0.929680i	$0.620083\pi$
$150$		0			0
$151$	18.9571	−	3.34265i	1.54271	−	0.272021i	0.663396	−	0.748269i	$-0.269115\pi$
$151$	18.9571	−	3.34265i	1.54271	−	0.272021i	0.879311	+	0.476248i	$0.158004\pi$
$152$	−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	0.612617	+	0.790380i	$0.290117\pi$
$157$	−2.92425	+	16.5843i	−0.233381	+	1.32357i	−0.845997	+	0.533187i	$0.820994\pi$
$158$	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	$0.101778\pi$
$163$			8.02606i			0.628650i	−0.949315	+	0.314325i	$0.898222\pi$
$164$	−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	−0.974778	−	0.223177i	$-0.928357\pi$
$167$	0.226727	−	1.28583i	0.0175447	−	0.0995008i	0.992323	+	0.123676i	$0.0394684\pi$
$168$		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	−0.585016	−	0.811022i	$-0.698912\pi$
$173$	−11.2769	+	1.98842i	−0.857366	+	0.151177i	−0.272350	+	0.962198i	$0.587801\pi$
$174$		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	−0.119222	−	0.992868i	$-0.538040\pi$
$179$	10.7064	−	18.5441i	0.800237	−	1.38605i	0.919460	−	0.393184i	$-0.128627\pi$
$180$		0			0
$181$	7.31416	+	12.6685i	0.543657	+	0.941641i	0.998690	+	0.0511670i	$0.0162941\pi$
$181$	7.31416	+	12.6685i	0.543657	+	0.941641i	−0.455033	+	0.890474i	$0.650373\pi$
$182$	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	0.275851	−	0.961200i	$-0.411040\pi$
$191$	−1.80607	−	0.657357i	−0.130683	−	0.0475647i	−0.406534	+	0.913636i	$0.633263\pi$
$192$		0			0
$193$	−4.79657	−	4.02480i	−0.345264	−	0.289711i	0.453621	−	0.891195i	$-0.350132\pi$
$193$	−4.79657	−	4.02480i	−0.345264	−	0.289711i	−0.798885	+	0.601484i	$0.794577\pi$
$194$	−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	−0.887915	−	0.460008i	$-0.847847\pi$
$197$	−13.1022	+	7.56456i	−0.933494	+	0.538953i	−0.0455788	+	0.998961i	$0.514513\pi$
$198$		0			0
$199$	−22.4427	−	12.9573i	−1.59092	−	0.918517i	−0.993150	−	0.116849i	$-0.962721\pi$
$199$	−22.4427	−	12.9573i	−1.59092	−	0.918517i	−0.597769	−	0.801669i	$-0.703946\pi$
$200$	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	0.730323	−	0.683102i	$-0.239369\pi$
$211$	17.1836	+	3.02993i	1.18297	+	0.208589i	0.452645	+	0.891691i	$0.350481\pi$
$212$	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	0.997901	−	0.0647513i	$-0.0206254\pi$
$223$	11.3619	+	13.5406i	0.760850	+	0.906746i	−0.237051	+	0.971497i	$0.576181\pi$
$224$	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	0.990181	+	0.139791i	$0.0446431\pi$
$227$	1.62005	+	9.18776i	0.107527	+	0.609813i	−0.882654	+	0.470022i	$0.844246\pi$
$228$		0			0
$229$	−15.8029	+	5.75180i	−1.04429	+	0.380090i	−0.806504	−	0.591228i	$-0.798643\pi$
$229$	−15.8029	+	5.75180i	−1.04429	+	0.380090i	−0.237784	+	0.971318i	$0.576421\pi$
$230$	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	−0.0918250	−	0.995775i	$-0.529270\pi$
$233$	−15.2659	−	8.81379i	−1.00010	−	0.577410i	−0.908279	+	0.418365i	$0.862603\pi$
$234$		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	0.385288	−	0.922796i	$-0.374102\pi$
$239$	−7.05862	−	5.92289i	−0.456584	−	0.383120i	−0.841872	+	0.539677i	$0.818547\pi$
$240$		0			0
$241$	−5.85117	−	2.12965i	−0.376907	−	0.137183i	0.146618	−	0.989193i	$-0.453161\pi$
$241$	−5.85117	−	2.12965i	−0.376907	−	0.137183i	−0.523525	+	0.852010i	$0.675383\pi$
$242$	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	0.834034	+	0.551713i	$0.186026\pi$
$251$	14.1765	+	24.5545i	0.894814	+	1.54986i	0.0607805	+	0.998151i	$0.480641\pi$
$252$		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	−0.981734	−	0.190261i	$-0.939067\pi$
$257$	−5.64266	−	15.5031i	−0.351979	−	0.967056i	0.629754	−	0.776795i	$-0.283156\pi$
$258$		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	0.144355	−	0.989526i	$-0.453889\pi$
$263$	18.5512	−	15.5663i	1.14391	−	0.959859i	0.999560	+	0.0296674i	$0.00944483\pi$
$264$		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	$0.121255\pi$
$269$			12.1956i			0.743578i	−0.928317	+	0.371789i	$0.878745\pi$
$270$		0			0
$271$			25.0009i			1.51870i	0.650683	+	0.759349i	$0.274483\pi$
$271$			25.0009i			1.51870i	−0.650683	+	0.759349i	$0.725517\pi$
$272$	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	−0.821335	−	0.570446i	$-0.806770\pi$
$277$	−6.69358	+	5.61658i	−0.402178	+	0.337468i	0.419157	+	0.907914i	$0.362326\pi$
$278$	−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	0.511409	−	0.859338i	$-0.329124\pi$
$281$	21.5554	−	3.80080i	1.28589	−	0.226737i	0.774478	+	0.632601i	$0.218013\pi$
$282$		0			0
$283$	−10.2956	−	28.2869i	−0.612010	−	1.68148i	−0.725737	−	0.687972i	$-0.758501\pi$
$283$	−10.2956	−	28.2869i	−0.612010	−	1.68148i	0.113727	−	0.993512i	$-0.463721\pi$
$284$	−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	−0.955021	−	0.296540i	$-0.904167\pi$
$293$	−8.50981	+	10.1416i	−0.497148	+	0.592478i	0.457872	+	0.889018i	$0.348612\pi$
$294$		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	0.137842	−	0.990454i	$-0.455983\pi$
$307$	−11.4064	−	6.58546i	−0.650995	−	0.375852i	−0.788837	+	0.614602i	$0.789317\pi$
$308$	−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	−0.172193	−	0.985063i	$-0.555085\pi$
$311$	5.80348	−	2.11230i	0.329085	−	0.119777i	0.501279	+	0.865286i	$0.332863\pi$
$312$		0			0
$313$	−3.72249	−	21.1113i	−0.210407	−	1.19328i	−0.888701	−	0.458488i	$-0.848391\pi$
$313$	−3.72249	−	21.1113i	−0.210407	−	1.19328i	0.678293	−	0.734791i	$-0.262720\pi$
$314$	−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	0.963099	−	0.269148i	$-0.0867422\pi$
$317$	9.45061	+	11.2628i	0.530799	+	0.632582i	−0.432300	+	0.901730i	$0.642298\pi$
$318$		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	−0.992971	−	0.118361i	$-0.962236\pi$
$331$	−17.0491	−	20.3184i	−0.937106	−	1.11680i	0.0558649	−	0.998438i	$-0.482208\pi$
$332$	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	0.0845588	−	0.996418i	$-0.473052\pi$
$337$	14.4992	−	5.27727i	0.789820	−	0.287471i	0.705261	+	0.708948i	$0.250830\pi$
$338$	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	0.0820721	−	0.996626i	$-0.473846\pi$
$347$	−16.4887	−	13.8357i	−0.885162	−	0.742739i	−0.967234	+	0.253888i	$0.918291\pi$
$348$		0			0
$349$	−11.8787	−	4.32349i	−0.635851	−	0.231431i	0.00392469	−	0.999992i	$-0.498751\pi$
$349$	−11.8787	−	4.32349i	−0.635851	−	0.231431i	−0.639776	+	0.768561i	$0.720973\pi$
$350$	−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	−0.998909	−	0.0466973i	$-0.985130\pi$
$353$	−3.82687	+	10.5142i	−0.203684	+	0.559617i	0.795225	+	0.606314i	$0.207353\pi$
$354$		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	−0.878109	−	0.478460i	$-0.841195\pi$
$359$	−16.1699	−	28.0070i	−0.853413	−	1.47816i	0.0246959	−	0.999695i	$-0.492138\pi$
$360$		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	−0.190752	−	0.981638i	$-0.561093\pi$
$367$	−0.656339	+	0.115730i	−0.0342606	+	0.00604107i	0.156492	+	0.987679i	$0.449982\pi$
$368$	−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	−0.735678	−	0.677331i	$-0.763136\pi$
$373$	3.61725	−	20.5144i	0.187294	−	1.06220i	0.922972	−	0.384867i	$-0.125753\pi$
$374$	−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	$-0.835947\pi$
$379$		−	19.1904i		−	0.985744i	0.870102	−	0.492872i	$-0.164053\pi$
$380$	−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	0.929180	+	0.369629i	$0.120515\pi$
$383$	−1.37744	+	7.81186i	−0.0703840	+	0.399168i	−0.999564	+	0.0295390i	$0.990596\pi$
$384$		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	0.143307	−	0.989678i	$-0.454226\pi$
$389$	12.1585	−	2.14387i	0.616461	−	0.108699i	0.473154	+	0.880980i	$0.343115\pi$
$390$		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	0.995244	+	0.0974099i	$0.0310558\pi$
$397$	11.5959	+	20.0847i	0.581982	+	1.00802i	−0.413263	+	0.910612i	$0.635611\pi$
$398$	−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	−0.864007	−	0.503480i	$-0.832053\pi$
$401$	−4.36829	+	5.20593i	−0.218142	+	0.259972i	0.645865	+	0.763452i	$0.276497\pi$
$402$		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	0.918375	−	0.395712i	$-0.129502\pi$
$409$	13.9170	+	11.6777i	0.688149	+	0.577426i	−0.230226	+	0.973137i	$0.573946\pi$
$410$	−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	−0.452504	−	0.891763i	$-0.649469\pi$
$419$	−4.62462	+	1.68322i	−0.225927	+	0.0822309i	0.226576	+	0.973993i	$0.427247\pi$
$420$		0			0
$421$	−2.04359	−	11.5898i	−0.0995984	−	0.564851i	−0.993241	−	0.116071i	$-0.962970\pi$
$421$	−2.04359	−	11.5898i	−0.0995984	−	0.564851i	0.893642	−	0.448780i	$-0.148141\pi$
$422$	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	0.835118	−	0.550071i	$-0.185399\pi$
$439$	3.10907	+	3.70524i	0.148388	+	0.176842i	−0.686730	+	0.726912i	$0.740955\pi$
$440$	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	0.940047	−	0.341044i	$-0.110780\pi$
$443$	−1.26185	−	7.15628i	−0.0599521	−	0.340005i	−0.999999	+	0.00103872i	$0.999669\pi$
$444$		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	0.624229	−	0.781241i	$-0.285413\pi$
$449$	5.50442	+	3.17798i	0.259769	+	0.149978i	−0.364460	+	0.931219i	$0.618746\pi$
$450$		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	0.361598	−	0.932334i	$-0.382231\pi$
$457$	0.840235	+	0.305821i	0.0393045	+	0.0143057i	−0.322293	+	0.946640i	$0.604454\pi$
$458$	−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	−0.790537	−	0.612415i	$-0.790198\pi$
$461$	4.48102	−	12.3115i	0.208702	−	0.573404i	0.999239	+	0.0390104i	$0.0124206\pi$
$462$		0			0
$463$	0.866856	−	1.03308i	0.0402862	−	0.0480112i	−0.745525	−	0.666478i	$-0.767801\pi$
$463$	0.866856	−	1.03308i	0.0402862	−	0.0480112i	0.785811	+	0.618466i	$0.212246\pi$
$464$	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	0.544600	−	0.838696i	$-0.316682\pi$
$467$	−9.81172	−	16.9944i	−0.454032	−	0.786407i	−0.998632	+	0.0522890i	$0.983348\pi$
$468$		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	−0.245056	−	0.969509i	$-0.578806\pi$
$479$	14.6017	−	12.2523i	0.667170	−	0.559822i	0.912226	+	0.409687i	$0.134362\pi$
$480$		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	$-0.906763\pi$
$487$		−	12.7440i		−	0.577486i	0.957407	−	0.288743i	$-0.0932373\pi$
$488$	−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	0.720272	+	0.693692i	$0.244017\pi$
$491$	−4.29474	+	24.3567i	−0.193819	+	1.09920i	−0.914091	+	0.405510i	$0.867094\pi$
$492$		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	0.741167	+	0.671320i	$0.234273\pi$
$499$	13.5128	+	37.1262i	0.604917	+	1.66199i	−0.136251	+	0.990674i	$0.543505\pi$
$500$	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	0.0998757	+	0.995000i	$0.468155\pi$
$503$	−18.2058	+	31.5334i	−0.811757	+	1.40600i	−0.911633	+	0.411005i	$0.865178\pi$
$504$		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	−0.711957	−	0.702223i	$-0.752191\pi$
$509$	2.32891	−	2.77549i	0.103227	−	0.123021i	0.815184	+	0.579201i	$0.196636\pi$
$510$		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	−0.840151	−	0.542353i	$-0.817534\pi$
$521$	−18.0443	+	10.4179i	−0.790534	+	0.456415i	0.0496162	+	0.998768i	$0.484200\pi$
$522$		0			0
$523$	19.0780	+	11.0147i	0.834223	+	0.481639i	0.855296	−	0.518139i	$-0.173375\pi$
$523$	19.0780	+	11.0147i	0.834223	+	0.481639i	−0.0210733	+	0.999778i	$0.506708\pi$
$524$	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	0.532812	−	0.846234i	$-0.321135\pi$
$547$	−9.19354	−	10.9564i	−0.393087	−	0.468463i	−0.925899	+	0.377770i	$0.876691\pi$
$548$	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	0.358147	−	0.933665i	$-0.383409\pi$
$557$	−6.40425	−	3.69750i	−0.271357	−	0.156668i	−0.629504	+	0.776997i	$0.716742\pi$
$558$		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	0.233252	−	0.972416i	$-0.425063\pi$
$563$	−16.2270	−	13.6161i	−0.683887	−	0.573850i	−0.917139	+	0.398567i	$0.869508\pi$
$564$		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	−0.903633	−	0.428308i	$-0.859110\pi$
$569$	1.52428	−	4.18793i	0.0639012	−	0.175567i	0.967534	+	0.252741i	$0.0813320\pi$
$570$		0			0
$571$	−1.38240	+	1.64748i	−0.0578516	+	0.0689449i	−0.794194	−	0.607664i	$-0.792107\pi$
$571$	−1.38240	+	1.64748i	−0.0578516	+	0.0689449i	0.736343	+	0.676609i	$0.236551\pi$
$572$	−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	0.309148	+	0.951014i	$0.399956\pi$
$577$	−16.0706	+	27.8351i	−0.669028	+	1.15879i	−0.978176	+	0.207777i	$0.933377\pi$
$578$	−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	0.140378	−	0.990098i	$-0.455168\pi$
$587$	27.6154	−	23.1721i	1.13981	−	0.956414i	0.999433	+	0.0336838i	$0.0107239\pi$
$588$		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	$0.0267880\pi$
$593$			4.09387i			0.168115i	−0.996461	+	0.0840576i	$0.973212\pi$
$594$		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	−1.00000		0.000926605i	$-0.999705\pi$
$599$	−1.46823	+	8.32677i	−0.0599904	+	0.340223i	0.940009	+	0.341149i	$0.110816\pi$
$600$		0			0
$601$	22.3724	−	18.7727i	0.912590	−	0.765754i	−0.0600202	−	0.998197i	$-0.519116\pi$
$601$	22.3724	−	18.7727i	0.912590	−	0.765754i	0.972610	+	0.232443i	$0.0746721\pi$
$602$	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	−0.848495	−	0.529203i	$-0.822491\pi$
$607$	−13.2715	−	36.4633i	−0.538675	−	1.48000i	0.309820	−	0.950795i	$-0.399731\pi$
$608$	−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	0.852025	−	0.523501i	$-0.175374\pi$
$613$	−0.677216	−	1.17297i	−0.0273525	−	0.0473759i	−0.879378	+	0.476125i	$0.842041\pi$
$614$	−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	−0.397909	−	0.917425i	$-0.630264\pi$
$617$	14.2746	−	17.0118i	0.574675	−	0.684871i	0.972583	+	0.232554i	$0.0747083\pi$
$618$		0			0
$619$	0.757138	−	2.08022i	0.0304320	−	0.0836111i	−0.923546	−	0.383487i	$-0.874723\pi$
$619$	0.757138	−	2.08022i	0.0304320	−	0.0836111i	0.953978	+	0.299876i	$0.0969453\pi$
$620$	−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	0.691718	−	0.722168i	$-0.256854\pi$
$631$	10.3534	+	5.97752i	0.412161	+	0.237961i	−0.279557	+	0.960129i	$0.590187\pi$
$632$	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	0.567250	−	0.823545i	$-0.308007\pi$
$641$	−8.66598	−	10.3277i	−0.342286	−	0.407920i	−0.909536	+	0.415625i	$0.863563\pi$
$642$		0			0
$643$	−27.1966	−	4.79550i	−1.07253	−	0.189116i	−0.390620	−	0.920552i	$-0.627739\pi$
$643$	−27.1966	−	4.79550i	−1.07253	−	0.189116i	−0.681910	+	0.731436i	$0.738850\pi$
$644$	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	0.728639	−	0.684898i	$-0.240153\pi$
$653$	30.1302	+	5.31277i	1.17909	+	0.207905i	0.450448	+	0.892803i	$0.351264\pi$
$654$		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	0.713732	+	0.700418i	$0.247003\pi$
$659$	7.25464	+	41.1431i	0.282601	+	1.60271i	−0.431132	+	0.902289i	$0.641886\pi$
$660$		0			0
$661$	−30.7435	+	11.1897i	−1.19578	+	0.435230i	−0.861751	−	0.507331i	$-0.830632\pi$
$661$	−30.7435	+	11.1897i	−1.19578	+	0.435230i	−0.334033	+	0.942561i	$0.608410\pi$
$662$	−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	−0.227166	−	0.973856i	$-0.572946\pi$
$673$	−26.6470	−	9.69872i	−1.02717	−	0.373858i	−0.800002	+	0.599998i	$0.795168\pi$
$674$	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	0.330453	+	0.943822i	$0.392799\pi$
$677$	−13.7737	+	37.8429i	−0.529366	+	1.45442i	−0.859819	+	0.510599i	$0.829424\pi$
$678$		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	0.817414	−	0.576051i	$-0.195407\pi$
$683$	−2.35647	−	4.08153i	−0.0901678	−	0.156175i	−0.907582	+	0.419876i	$0.862074\pi$
$684$		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	0.844251	−	0.535947i	$-0.180045\pi$
$691$	47.8656	−	8.44000i	1.82089	−	0.321073i	0.976642	+	0.214875i	$0.0689344\pi$
$692$	−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	$-0.969238\pi$
$701$		−	5.10945i		−	0.192981i	0.995334	−	0.0964906i	$-0.0307618\pi$
$702$		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	−0.764762	−	0.644313i	$-0.777144\pi$
$709$	−7.00392	+	5.87699i	−0.263038	+	0.220715i	0.501725	+	0.865027i	$0.332699\pi$
$710$	−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	−0.576247	−	0.817276i	$-0.695483\pi$
$719$	11.2528	−	19.4904i	0.419658	−	0.726869i	0.995905	+	0.0904064i	$0.0288166\pi$
$720$		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	−0.777522	−	0.628856i	$-0.783523\pi$
$727$	5.99428	−	16.4691i	0.222316	−	0.610807i	0.999837	+	0.0180494i	$0.00574560\pi$
$728$	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	0.266788	−	0.963755i	$-0.414038\pi$
$733$	−17.2190	−	14.4484i	−0.635998	−	0.533666i	−0.902786	+	0.430089i	$0.858482\pi$
$734$	−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	0.636001	−	0.771688i	$-0.280587\pi$
$739$	7.76664	+	4.48407i	0.285700	+	0.164949i	−0.350301	+	0.936637i	$0.613921\pi$
$740$	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	0.650352	−	0.759633i	$-0.274622\pi$
$743$	44.6168	−	16.2392i	1.63683	−	0.595758i	0.986481	+	0.163875i	$0.0523994\pi$
$744$		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	−0.0824383	−	0.996596i	$-0.526271\pi$
$751$	−13.7230	−	2.41974i	−0.500761	−	0.0882976i	−0.418323	+	0.908299i	$0.637382\pi$
$752$	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	−0.409508	−	0.912306i	$-0.634300\pi$
$761$	−30.5200	−	5.38149i	−1.10635	−	0.195079i	−0.696839	+	0.717227i	$0.745411\pi$
$762$		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	−0.615404	−	0.788211i	$-0.711007\pi$
$769$	−16.0889	+	5.85587i	−0.580179	+	0.211168i	0.0352254	+	0.999379i	$0.488785\pi$
$770$	−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	−0.349877	−	0.936795i	$-0.613777\pi$
$773$	−37.1476	−	21.4472i	−1.33610	−	0.771401i	−0.986227	+	0.165395i	$0.947110\pi$
$774$		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	−0.829987	−	0.557783i	$-0.811652\pi$
$787$	−3.83079	+	4.56536i	−0.136553	+	0.162737i	0.693434	+	0.720520i	$0.256097\pi$
$788$	−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	−0.890084	−	0.455797i	$-0.849354\pi$
$797$	−14.1501	−	38.8770i	−0.501221	−	1.37709i	0.388863	−	0.921296i	$-0.372868\pi$
$798$		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	$-0.701363\pi$
$809$		−	45.8780i		−	1.61298i	0.591245	−	0.806492i	$-0.298637\pi$
$810$		0			0
$811$		−	25.4302i		−	0.892974i	−0.894790	−	0.446487i	$-0.852675\pi$
$811$		−	25.4302i		−	0.892974i	0.894790	−	0.446487i	$-0.147325\pi$
$812$	−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	−0.0372556	−	0.999306i	$-0.511862\pi$
$821$	7.72253	−	1.36169i	0.269518	−	0.0475233i	0.306774	+	0.951782i	$0.400750\pi$
$822$		0			0
$823$	−2.99728	−	8.23497i	−0.104479	−	0.287053i	0.876428	−	0.481534i	$-0.159920\pi$
$823$	−2.99728	−	8.23497i	−0.104479	−	0.287053i	−0.980906	+	0.194481i	$0.937698\pi$
$824$	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	−0.650273	−	0.759701i	$-0.725345\pi$
$827$	9.57006	−	16.5758i	0.332784	−	0.576398i	0.983057	+	0.183303i	$0.0586788\pi$
$828$		0			0
$829$	−0.0258029	−	0.0446919i	−0.000896172	−	0.00155222i	0.865577	−	0.500776i	$-0.166952\pi$
$829$	−0.0258029	−	0.0446919i	−0.000896172	−	0.00155222i	−0.866473	+	0.499224i	$0.833619\pi$
$830$	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	0.510578	−	0.859831i	$-0.329431\pi$
$839$	10.1094	+	3.67952i	0.349015	+	0.127031i	−0.161563	+	0.986862i	$0.551654\pi$
$840$		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	0.842254	+	0.539082i	$0.181229\pi$
$853$	6.86844	+	38.9529i	0.235171	+	1.33372i	−0.607083	+	0.794639i	$0.707660\pi$
$854$	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	0.866820	−	0.498620i	$-0.166160\pi$
$857$	6.59420	+	7.85866i	0.225253	+	0.268447i	−0.641567	+	0.767067i	$0.721715\pi$
$858$		0			0
$859$	−3.49071	−	0.615507i	−0.119102	−	0.0210008i	0.113780	−	0.993506i	$-0.463704\pi$
$859$	−3.49071	−	0.615507i	−0.119102	−	0.0210008i	−0.232881	+	0.972505i	$0.574815\pi$
$860$	−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	−0.0696811	−	0.997569i	$-0.522198\pi$
$877$	15.3450	−	5.58514i	0.518165	−	0.188597i	0.587846	+	0.808973i	$0.299976\pi$
$878$	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	0.998709	−	0.0507963i	$-0.0161759\pi$
$881$	43.1593	+	24.9180i	1.45407	+	0.839509i	0.455364	+	0.890306i	$0.349509\pi$
$882$		0			0
$883$	−38.2077	+	22.0592i	−1.28579	+	0.742352i	−0.977901	−	0.209070i	$-0.932956\pi$
$883$	−38.2077	+	22.0592i	−1.28579	+	0.742352i	−0.307890	+	0.951422i	$0.599623\pi$
$884$	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	0.673175	−	0.739483i	$-0.264930\pi$
$887$	1.84120	+	1.54495i	0.0618215	+	0.0518744i	−0.611353	+	0.791358i	$0.709375\pi$
$888$		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	−0.714804	−	0.699324i	$-0.753484\pi$
$907$	−34.5531	+	6.09265i	−1.14732	+	0.202303i	−0.432513	+	0.901628i	$0.642373\pi$
$908$	−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	−0.495342	−	0.868698i	$-0.664957\pi$
$911$	8.27443	−	6.94307i	0.274144	−	0.230034i	0.769486	+	0.638664i	$0.220513\pi$
$912$		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	$-0.887797\pi$
$919$		−	20.9319i		−	0.690481i	0.938514	−	0.345241i	$-0.112203\pi$
$920$	−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	−0.688212	−	0.725510i	$-0.741604\pi$
$929$	−33.1245	+	5.84075i	−1.08678	+	0.191629i	−0.398568	+	0.917139i	$0.630493\pi$
$930$		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	0.584122	−	0.811666i	$-0.301439\pi$
$937$	−12.5767	−	21.7834i	−0.410862	−	0.711634i	−0.994984	+	0.100032i	$0.968106\pi$
$938$	−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	0.131175	+	0.991359i	$0.458125\pi$
$941$	−26.6235	+	31.7286i	−0.867901	+	1.03432i	−0.999077	+	0.0429652i	$0.986320\pi$
$942$		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	−0.728050	−	0.685524i	$-0.759573\pi$
$947$	−53.1276	−	19.3369i	−1.72642	−	0.628364i	−0.998365	+	0.0571597i	$0.981796\pi$
$948$		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	0.114405	−	0.993434i	$-0.463504\pi$
$953$	31.8569	−	18.3926i	1.03195	−	0.595795i	0.917542	+	0.397639i	$0.130170\pi$
$954$		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	−0.593557	−	0.804792i	$-0.702277\pi$
$967$	−44.3616	−	7.82215i	−1.42657	−	0.251543i	−0.833016	+	0.553249i	$0.813388\pi$
$968$	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	0.719157	−	0.694848i	$-0.244528\pi$
$977$	36.1734	+	6.37835i	1.15729	+	0.204062i	0.438134	+	0.898910i	$0.355639\pi$
$978$		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	−0.991265	−	0.131884i	$-0.957897\pi$
$983$	−3.28853	−	18.6502i	−0.104888	−	0.594848i	0.886377	−	0.462963i	$-0.153214\pi$
$984$		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	−0.897916	−	0.440166i	$-0.854920\pi$
$991$	−30.3997	+	17.5513i	−0.965680	+	0.557535i	−0.0677633	+	0.997701i	$0.521586\pi$
$992$	−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	−0.0409071	−	0.999163i	$-0.513025\pi$
$997$	−22.5603	−	8.21129i	−0.714493	−	0.260054i	−0.673586	+	0.739109i	$0.735247\pi$
$998$	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.179.15		96
3.2	odd	2		108.2.l.a.23.2	✓	96
4.3	odd	2	inner	324.2.l.a.179.2		96
9.2	odd	6		972.2.l.c.215.9		96
9.4	even	3		972.2.l.a.863.4		96
9.5	odd	6		972.2.l.d.863.13		96
9.7	even	3		972.2.l.b.215.8		96
12.11	even	2		108.2.l.a.23.15	yes	96
27.2	odd	18		972.2.l.a.107.12		96
27.7	even	9		108.2.l.a.47.15	yes	96
27.11	odd	18		972.2.l.b.755.10		96
27.16	even	9		972.2.l.c.755.7		96
27.20	odd	18	inner	324.2.l.a.143.2		96
27.25	even	9		972.2.l.d.107.5		96
36.7	odd	6		972.2.l.b.215.10		96
36.11	even	6		972.2.l.c.215.7		96
36.23	even	6		972.2.l.d.863.5		96
36.31	odd	6		972.2.l.a.863.12		96
108.7	odd	18		108.2.l.a.47.2	yes	96
108.11	even	18		972.2.l.b.755.8		96
108.43	odd	18		972.2.l.c.755.9		96
108.47	even	18	inner	324.2.l.a.143.15		96
108.79	odd	18		972.2.l.d.107.13		96
108.83	even	18		972.2.l.a.107.4		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.2	✓	96	3.2	odd	2
108.2.l.a.23.15	yes	96	12.11	even	2
108.2.l.a.47.2	yes	96	108.7	odd	18
108.2.l.a.47.15	yes	96	27.7	even	9
324.2.l.a.143.2		96	27.20	odd	18	inner
324.2.l.a.143.15		96	108.47	even	18	inner
324.2.l.a.179.2		96	4.3	odd	2	inner
324.2.l.a.179.15		96	1.1	even	1	trivial
972.2.l.a.107.4		96	108.83	even	18
972.2.l.a.107.12		96	27.2	odd	18
972.2.l.a.863.4		96	9.4	even	3
972.2.l.a.863.12		96	36.31	odd	6
972.2.l.b.215.8		96	9.7	even	3
972.2.l.b.215.10		96	36.7	odd	6
972.2.l.b.755.8		96	108.11	even	18
972.2.l.b.755.10		96	27.11	odd	18
972.2.l.c.215.7		96	36.11	even	6
972.2.l.c.215.9		96	9.2	odd	6
972.2.l.c.755.7		96	27.16	even	9
972.2.l.c.755.9		96	108.43	odd	18
972.2.l.d.107.5		96	27.25	even	9
972.2.l.d.107.13		96	108.79	odd	18
972.2.l.d.863.5		96	36.23	even	6
972.2.l.d.863.13		96	9.5	odd	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)

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