LMFDB - Embedded newform 324.2.l.a.143.2

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			143.2
Character	$\chi$	$=$	324.143
Dual form			324.2.l.a.179.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32122 + 0.504364i) q^{2} +(1.49123 - 1.33275i) q^{4} +(3.39370 - 0.598401i) q^{5} +(1.88319 - 2.24430i) q^{7} +(-1.29805 + 2.51298i) q^{8} +O(q^{10})$	\(q+(-1.32122 + 0.504364i) q^{2} +(1.49123 - 1.33275i) q^{4} +(3.39370 - 0.598401i) q^{5} +(1.88319 - 2.24430i) q^{7} +(-1.29805 + 2.51298i) q^{8} +(-4.18200 + 2.50228i) q^{10} +(0.453915 - 2.57428i) q^{11} +(-5.09721 - 1.85523i) q^{13} +(-1.35616 + 3.91503i) q^{14} +(0.447553 - 3.97488i) q^{16} +(-1.15583 + 0.667320i) q^{17} +(0.0790760 + 0.0456546i) q^{19} +(4.26328 - 5.41531i) q^{20} +(0.698654 + 3.63012i) q^{22} +(-0.650322 + 0.545685i) q^{23} +(6.46065 - 2.35148i) q^{25} +(7.67024 - 0.119685i) q^{26} +(-0.182815 - 5.85661i) q^{28} +(0.171418 + 0.470966i) q^{29} +(4.28324 + 5.10457i) q^{31} +(1.41348 + 5.47742i) q^{32} +(1.19053 - 1.46464i) q^{34} +(5.04800 - 8.74340i) q^{35} +(2.75869 + 4.77819i) q^{37} +(-0.127503 - 0.0204365i) q^{38} +(-2.90143 + 9.30505i) q^{40} +(0.976880 - 2.68396i) q^{41} +(5.59737 + 0.986968i) q^{43} +(-2.75398 - 4.44381i) q^{44} +(0.583993 - 1.04897i) q^{46} +(-5.06200 - 4.24752i) q^{47} +(-0.274941 - 1.55927i) q^{49} +(-7.34992 + 6.36534i) q^{50} +(-10.0737 + 4.02673i) q^{52} +7.37249i q^{53} -9.00795i q^{55} +(3.19540 + 7.64565i) q^{56} +(-0.464019 - 0.535792i) q^{58} +(0.528787 + 2.99890i) q^{59} +(-1.85759 - 1.55871i) q^{61} +(-8.23365 - 4.58393i) q^{62} +(-4.63012 - 6.52395i) q^{64} +(-18.4086 - 3.24593i) q^{65} +(1.64904 - 4.53069i) q^{67} +(-0.834244 + 2.53557i) q^{68} +(-2.25965 + 14.0980i) q^{70} +(5.91940 + 10.2527i) q^{71} +(-5.83049 + 10.0987i) q^{73} +(-6.05478 - 4.92165i) q^{74} +(0.178767 - 0.0373070i) q^{76} +(-4.92266 - 5.86659i) q^{77} +(-0.576990 - 1.58527i) q^{79} +(-0.859714 - 13.7574i) q^{80} +(0.0630204 + 4.03879i) q^{82} +(-2.02940 + 0.738640i) q^{83} +(-3.52322 + 2.95633i) q^{85} +(-7.89314 + 1.51912i) q^{86} +(5.87990 + 4.48223i) q^{88} +(12.5801 + 7.26310i) q^{89} +(-13.7628 + 7.94593i) q^{91} +(-0.242520 + 1.68046i) q^{92} +(8.83031 + 3.05881i) q^{94} +(0.295680 + 0.107619i) q^{95} +(1.14607 - 6.49971i) q^{97} +(1.14969 + 1.92146i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.32122	+	0.504364i	−0.934242	+	0.356639i
$2$	−1.32122	+	0.504364i	−0.934242	+	0.356639i
$3$		0			0
$3$		0			0
$4$	1.49123	−	1.33275i	0.745617	−	0.666375i
$5$	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	−0.282024	−	0.959407i	$-0.591006\pi$
$7$	1.88319	−	2.24430i	0.711781	−	0.848267i	0.993805	+	0.111140i	$0.0354503\pi$
$8$	−1.29805	+	2.51298i	−0.458931	+	0.888472i
$9$		0			0
$10$	−4.18200	+	2.50228i	−1.32247	+	0.791290i
$11$	0.453915	−	2.57428i	0.136861	−	0.776174i	−0.836686	−	0.547684i	$-0.815510\pi$
$11$	0.453915	−	2.57428i	0.136861	−	0.776174i	0.973546	−	0.228491i	$-0.0733791\pi$
$12$		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	$0.882128\pi$
$14$	−1.35616	+	3.91503i	−0.362450	+	1.04634i
$15$		0			0
$16$	0.447553	−	3.97488i	0.111888	−	0.993721i
$17$	−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	0.509043	−	0.860741i	$-0.329999\pi$
$19$	0.0790760	+	0.0456546i	0.0181413	+	0.0104739i	−0.490902	+	0.871215i	$0.663333\pi$
$20$	4.26328	−	5.41531i	0.953298	−	1.21090i
$21$		0			0
$22$	0.698654	+	3.63012i	0.148954	+	0.773945i
$23$	−0.650322	+	0.545685i	−0.135602	+	0.113783i	−0.708066	−	0.706147i	$-0.750432\pi$
$23$	−0.650322	+	0.545685i	−0.135602	+	0.113783i	0.572464	+	0.819930i	$0.305988\pi$
$24$		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	0.998397	−	0.0565946i	$-0.0180243\pi$
$31$	4.28324	+	5.10457i	0.769293	+	0.916807i	−0.229105	+	0.973402i	$0.573580\pi$
$32$	1.41348	+	5.47742i	0.249869	+	0.968280i
$33$		0			0
$34$	1.19053	−	1.46464i	0.204175	−	0.251183i
$35$	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	$0.683499\pi$
$38$	−0.127503	−	0.0204365i	−0.0206838	−	0.00331524i
$39$		0			0
$40$	−2.90143	+	9.30505i	−0.458756	+	1.47126i
$41$	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	0.583289	−	0.812264i	$-0.301765\pi$
$43$	5.59737	+	0.986968i	0.853591	+	0.150511i	0.270302	+	0.962776i	$0.412876\pi$
$44$	−2.75398	−	4.44381i	−0.415178	−	0.669929i
$45$		0			0
$46$	0.583993	−	1.04897i	0.0861051	−	0.154662i
$47$	−5.06200	−	4.24752i	−0.738369	−	0.619565i	0.194030	−	0.980996i	$-0.437844\pi$
$47$	−5.06200	−	4.24752i	−0.738369	−	0.619565i	−0.932399	+	0.361430i	$0.882288\pi$
$48$		0			0
$49$	−0.274941	−	1.55927i	−0.0392772	−	0.222752i
$50$	−7.34992	+	6.36534i	−1.03944	+	0.900196i
$51$		0			0
$52$	−10.0737	+	4.02673i	−1.39697	+	0.558407i
$53$			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
$56$	3.19540	+	7.64565i	0.427004	+	1.02169i
$57$		0			0
$58$	−0.464019	−	0.535792i	−0.0609286	−	0.0703529i
$59$	0.528787	+	2.99890i	0.0688422	+	0.390423i	0.999687	+	0.0250093i	$0.00796152\pi$
$59$	0.528787	+	2.99890i	0.0688422	+	0.390423i	−0.930845	+	0.365414i	$0.880927\pi$
$60$		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	$0.771837\pi$
$62$	−8.23365	−	4.58393i	−1.04568	−	0.582160i
$63$		0			0
$64$	−4.63012	−	6.52395i	−0.578765	−	0.815494i
$65$	−18.4086	−	3.24593i	−2.28330	−	0.402608i
$66$		0			0
$67$	1.64904	−	4.53069i	0.201462	−	0.553512i	−0.797283	−	0.603606i	$-0.793730\pi$
$67$	1.64904	−	4.53069i	0.201462	−	0.553512i	0.998744	+	0.0500945i	$0.0159522\pi$
$68$	−0.834244	+	2.53557i	−0.101167	+	0.307482i
$69$		0			0
$70$	−2.25965	+	14.0980i	−0.270080	+	1.68503i
$71$	5.91940	+	10.2527i	0.702504	+	1.21677i	0.967585	+	0.252546i	$0.0812678\pi$
$71$	5.91940	+	10.2527i	0.702504	+	1.21677i	−0.265081	+	0.964226i	$0.585399\pi$
$72$		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	$0.927600\pi$
$74$	−6.05478	−	4.92165i	−0.703854	−	0.572130i
$75$		0			0
$76$	0.178767	−	0.0373070i	0.0205060	−	0.00427941i
$77$	−4.92266	−	5.86659i	−0.560989	−	0.668560i
$78$		0			0
$79$	−0.576990	−	1.58527i	−0.0649165	−	0.178357i	0.902993	−	0.429655i	$-0.141365\pi$
$79$	−0.576990	−	1.58527i	−0.0649165	−	0.178357i	−0.967910	+	0.251298i	$0.919143\pi$
$80$	−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	$-0.648928\pi$
$83$	−2.02940	+	0.738640i	−0.222755	+	0.0810763i	0.228232	+	0.973607i	$0.426706\pi$
$84$		0			0
$85$	−3.52322	+	2.95633i	−0.382147	+	0.320659i
$86$	−7.89314	+	1.51912i	−0.851139	+	0.163810i
$87$		0			0
$88$	5.87990	+	4.48223i	0.626800	+	0.477807i
$89$	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
$92$	−0.242520	+	1.68046i	−0.0252844	+	0.175200i
$93$		0			0
$94$	8.83031	+	3.05881i	0.910777	+	0.315492i
$95$	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	$-0.0532021\pi$
$98$	1.14969	+	1.92146i	0.116137	+	0.194097i
$99$		0			0
$100$	6.50039	−	12.1170i	0.650039	−	1.21170i
$101$	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	−0.886769	−	0.462214i	$-0.847055\pi$
$103$	−15.8523	+	2.79519i	−1.56197	+	0.275418i	−0.675203	+	0.737632i	$0.735944\pi$
$104$	11.2786	−	10.4010i	1.10596	−	1.01990i
$105$		0			0
$106$	−3.71842	−	9.74067i	−0.361165	−	0.946097i
$107$	−9.71808			−0.939482			−0.469741	−	0.882804i	$-0.655653\pi$
$107$	−9.71808			−0.939482			−0.469741	+	0.882804i	$0.655653\pi$
$108$		0			0
$109$	−4.69860			−0.450044			−0.225022	−	0.974354i	$-0.572245\pi$
$109$	−4.69860			−0.450044			−0.225022	+	0.974354i	$0.572245\pi$
$110$	4.54329	+	11.9015i	0.433186	+	1.13476i
$111$		0			0
$112$	−8.07802	−	8.48992i	−0.763301	−	0.802222i
$113$	−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
$116$	0.883304	+	0.473863i	0.0820127	+	0.0439971i
$117$		0			0
$118$	−2.21118	−	3.69550i	−0.203556	−	0.340198i
$119$	−0.678988	+	3.85073i	−0.0622427	+	0.352996i
$120$		0			0
$121$	3.91574	+	1.42521i	0.355977	+	0.129565i
$122$	3.24044	+	1.12249i	0.293376	+	0.101625i
$123$		0			0
$124$	13.1904	+	1.90361i	1.18453	+	0.170949i
$125$	5.59652	−	3.23116i	0.500568	−	0.289003i
$126$		0			0
$127$	9.63141	+	5.56070i	0.854649	+	0.493432i	0.862217	−	0.506539i	$-0.169076\pi$
$127$	9.63141	+	5.56070i	0.854649	+	0.493432i	−0.00756758	+	0.999971i	$0.502409\pi$
$128$	9.40785	+	6.28430i	0.831544	+	0.555458i
$129$		0			0
$130$	25.9589	−	4.99605i	2.27674	−	0.438183i
$131$	−2.37648	+	1.99411i	−0.207634	+	0.174226i	−0.740675	−	0.671864i	$-0.765494\pi$
$131$	−2.37648	+	1.99411i	−0.207634	+	0.174226i	0.533040	+	0.846090i	$0.321049\pi$
$132$		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	0.979332	−	0.202260i	$-0.0648286\pi$
$139$	7.19280	+	8.57205i	0.610085	+	0.727071i	−0.369246	+	0.929332i	$0.620384\pi$
$140$	−4.12502	−	19.7662i	−0.348628	−	1.67055i
$141$		0			0
$142$	−12.9919	−	10.5605i	−1.09026	−	0.886219i
$143$	−7.08959	+	12.2795i	−0.592862	+	1.02687i
$144$		0			0
$145$	0.863567	+	1.49574i	0.0717153	+	0.124215i
$146$	2.60992	−	16.2833i	0.215999	−	1.34762i
$147$		0			0
$148$	10.4820	+	3.44875i	0.861615	+	0.283486i
$149$	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	−0.663396	−	0.748269i	$-0.730885\pi$
$151$	−18.9571	−	3.34265i	−1.54271	−	0.272021i	−0.879311	+	0.476248i	$0.841996\pi$
$152$	−0.217374	+	0.139454i	−0.0176313	+	0.0113112i
$153$		0			0
$154$	9.46280	+	5.26823i	0.762534	+	0.424526i
$155$	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	$-0.290117\pi$
$158$	1.56188	+	1.80347i	0.124257	+	0.143476i
$159$		0			0
$160$	8.07460	+	17.7429i	0.638353	+	1.40270i
$161$			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	$0.898222\pi$
$164$	−2.12029	−	5.30434i	−0.165567	−	0.414199i
$165$		0			0
$166$	2.30873	−	1.99946i	0.179192	−	0.155188i
$167$	−0.226727	−	1.28583i	−0.0175447	−	0.0995008i	0.974778	−	0.223177i	$-0.0716427\pi$
$167$	−0.226727	−	1.28583i	−0.0175447	−	0.0995008i	−0.992323	+	0.123676i	$0.960532\pi$
$168$		0			0
$169$	12.5811	+	10.5568i	0.967779	+	0.812063i
$170$	3.16387	−	5.68295i	0.242658	−	0.435862i
$171$		0			0
$172$	9.66237	−	5.98810i	0.736749	−	0.456588i
$173$	−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
$176$	−10.0293	−	2.95638i	−0.755988	−	0.222846i
$177$		0			0
$178$	−20.2842	−	3.25120i	−1.52037	−	0.243688i
$179$	−10.7064	−	18.5441i	−0.800237	−	1.38605i	−0.919460	−	0.393184i	$-0.871373\pi$
$179$	−10.7064	−	18.5441i	−0.800237	−	1.38605i	0.119222	−	0.992868i	$-0.461960\pi$
$180$		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	$-0.0162941\pi$
$182$	14.1760	−	17.4397i	1.05079	−	1.29272i
$183$		0			0
$184$	−0.527143	−	2.34257i	−0.0388615	−	0.172697i
$185$	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	$-0.588960\pi$
$191$	1.80607	−	0.657357i	0.130683	−	0.0475647i	0.406534	+	0.913636i	$0.366737\pi$
$192$		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	$0.350132\pi$
$194$	1.76401	+	9.16557i	0.126648	+	0.658050i
$195$		0			0
$196$	−2.48811	−	1.95880i	−0.177722	−	0.139914i
$197$	−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	$-0.296054\pi$
$199$	22.4427	−	12.9573i	1.59092	−	0.918517i	0.993150	−	0.116849i	$-0.0372792\pi$
$200$	−2.47703	+	19.2878i	−0.175152	+	1.36385i
$201$		0			0
$202$	−3.81670	+	11.0182i	−0.268542	+	0.775240i
$203$	1.37980	+	0.502208i	0.0968433	+	0.0352481i
$204$		0			0
$205$	1.70916	−	9.69310i	0.119373	−	0.676996i
$206$	19.5345	−	11.6884i	1.36104	−	0.814368i
$207$		0			0
$208$	−9.65561	+	19.4305i	−0.669496	+	1.34726i
$209$	0.153421	−	0.182841i	0.0106124	−	0.0126473i
$210$		0			0
$211$	−17.1836	+	3.02993i	−1.18297	+	0.208589i	−0.730323	−	0.683102i	$-0.760631\pi$
$211$	−17.1836	+	3.02993i	−1.18297	+	0.208589i	−0.452645	+	0.891691i	$0.649519\pi$
$212$	9.82569	+	10.9941i	0.674831	+	0.755078i
$213$		0			0
$214$	12.8397	−	4.90145i	0.877704	−	0.335056i
$215$	19.5864			1.33578
$216$		0			0
$217$	19.5224			1.32526
$218$	6.20788	−	2.36981i	0.420450	−	0.160504i
$219$		0			0
$220$	−12.0054	−	13.4330i	−0.809401	−	0.905650i
$221$	7.12956	−	1.25713i	0.479586	−	0.0845639i
$222$		0			0
$223$	−11.3619	+	13.5406i	−0.760850	+	0.906746i	−0.997901	−	0.0647513i	$-0.979375\pi$
$223$	−11.3619	+	13.5406i	−0.760850	+	0.906746i	0.237051	+	0.971497i	$0.423819\pi$
$224$	14.9548	+	7.14277i	0.999212	+	0.477247i
$225$		0			0
$226$	0.685010	−	0.409872i	0.0455662	−	0.0272643i
$227$	−1.62005	+	9.18776i	−0.107527	+	0.609813i	0.882654	+	0.470022i	$0.155754\pi$
$227$	−1.62005	+	9.18776i	−0.107527	+	0.609813i	−0.990181	+	0.139791i	$0.955357\pi$
$228$		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	$0.798643\pi$
$230$	1.35419	−	3.90934i	0.0892929	−	0.257775i
$231$		0			0
$232$	−1.40604	−	0.180570i	−0.0923109	−	0.0118550i
$233$	−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
$236$	4.78533	+	3.76732i	0.311498	+	0.245231i
$237$		0			0
$238$	−1.04508	−	5.43011i	−0.0677425	−	0.351982i
$239$	7.05862	−	5.92289i	0.456584	−	0.383120i	−0.385288	−	0.922796i	$-0.625898\pi$
$239$	7.05862	−	5.92289i	0.456584	−	0.383120i	0.841872	+	0.539677i	$0.181453\pi$
$240$		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
$248$	−18.3875	+	4.13770i	−1.16761	+	0.262744i
$249$		0			0
$250$	−5.76455	+	7.09175i	−0.364582	+	0.448522i
$251$	−14.1765	+	24.5545i	−0.894814	+	1.54986i	−0.0607805	+	0.998151i	$0.519359\pi$
$251$	−14.1765	+	24.5545i	−0.894814	+	1.54986i	−0.834034	+	0.551713i	$0.813974\pi$
$252$		0			0
$253$	1.10955	+	1.92181i	0.0697571	+	0.120823i
$254$	−15.5298	−	2.48915i	−0.974427	−	0.156183i
$255$		0			0
$256$	−15.5994	−	3.55794i	−0.974962	−	0.222371i
$257$	−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
$260$	−31.7775	+	19.6936i	−1.97076	+	1.22135i
$261$		0			0
$262$	2.13410	−	3.83326i	0.131845	−	0.236820i
$263$	−18.5512	−	15.5663i	−1.14391	−	0.959859i	−0.144355	−	0.989526i	$-0.546111\pi$
$263$	−18.5512	−	15.5663i	−1.14391	−	0.959859i	−0.999560	+	0.0296674i	$0.990555\pi$
$264$		0			0
$265$	4.41171	+	25.0200i	0.271009	+	1.53697i
$266$	−0.285979	+	0.247670i	−0.0175345	+	0.0151856i
$267$		0			0
$268$	−3.57918	−	8.95406i	−0.218633	−	0.546956i
$269$		−	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	$0.274483\pi$
$271$			25.0009i			1.51870i	−0.650683	+	0.759349i	$0.725517\pi$
$272$	2.13522	+	4.89296i	0.129467	+	0.296679i
$273$		0			0
$274$	−15.9875	−	18.4604i	−0.965838	−	1.11523i
$275$	−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	$0.806770\pi$
$278$	−13.8267	−	7.69775i	−0.829270	−	0.461680i
$279$		0			0
$280$	15.4194	+	24.0349i	0.921485	+	1.43636i
$281$	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	$-0.536279\pi$
$283$	10.2956	−	28.2869i	0.612010	−	1.68148i	0.725737	−	0.687972i	$-0.241499\pi$
$284$	22.4915	+	7.40009i	1.33462	+	0.439114i
$285$		0			0
$286$	3.17354	−	19.7997i	0.187655	−	1.17078i
$287$	−4.18396	−	7.24682i	−0.246971	−	0.427766i
$288$		0			0
$289$	−7.60937	+	13.1798i	−0.447610	+	0.775283i
$290$	−1.89536	−	1.54065i	−0.111299	−	0.0904700i
$291$		0			0
$292$	4.76444	+	22.8301i	0.278818	+	1.33603i
$293$	−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
$302$	26.7324	−	5.14492i	1.53827	−	0.296057i
$303$		0			0
$304$	0.216862	−	0.293885i	0.0124379	−	0.0168555i
$305$	−7.23685	−	4.17820i	−0.414381	−	0.239243i
$306$		0			0
$307$	11.4064	−	6.58546i	0.650995	−	0.375852i	−0.137842	−	0.990454i	$-0.544017\pi$
$307$	11.4064	−	6.58546i	0.650995	−	0.375852i	0.788837	+	0.614602i	$0.210683\pi$
$308$	−15.1595	−	2.18779i	−0.863794	−	0.124661i
$309$		0			0
$310$	−30.6856	−	10.6295i	−1.74282	−	0.603713i
$311$	−5.80348	−	2.11230i	−0.329085	−	0.119777i	0.172193	−	0.985063i	$-0.444915\pi$
$311$	−5.80348	−	2.11230i	−0.329085	−	0.119777i	−0.501279	+	0.865286i	$0.667137\pi$
$312$		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	$0.848391\pi$
$314$	12.2281	+	20.4365i	0.690070	+	1.15330i
$315$		0			0
$316$	−2.97319	−	1.59502i	−0.167255	−	0.0897269i
$317$	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
$320$	−19.6172	−	19.3697i	−1.09663	−	1.08280i
$321$		0			0
$322$	−1.25443	−	3.28607i	−0.0699067	−	0.183125i
$323$	−0.121865			−0.00678074
$324$		0			0
$325$	−37.2939			−2.06869
$326$	−4.04806	−	10.6042i	−0.224201	−	0.587311i
$327$		0			0
$328$	5.47668	+	5.93879i	0.302399	+	0.327915i
$329$	−19.0655	+	3.36176i	−1.05111	+	0.185340i
$330$		0			0
$331$	17.0491	−	20.3184i	0.937106	−	1.11680i	−0.0558649	−	0.998438i	$-0.517792\pi$
$331$	17.0491	−	20.3184i	0.937106	−	1.11680i	0.992971	−	0.118361i	$-0.0377639\pi$
$332$	−2.04188	+	3.80616i	−0.112063	+	0.208890i
$333$		0			0
$334$	0.948085	+	1.58451i	0.0518769	+	0.0867007i
$335$	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	$0.473052\pi$
$338$	−21.9469	−	7.60238i	−1.19375	−	0.413515i
$339$		0			0
$340$	−1.31389	+	9.10416i	−0.0712557	+	0.493742i
$341$	15.0848	−	8.70922i	0.816888	−	0.471631i
$342$		0			0
$343$	13.7433	+	7.93471i	0.742069	+	0.428434i
$344$	−9.74591	+	12.7849i	−0.525464	+	0.689318i
$345$		0			0
$346$	15.9021	−	3.06052i	0.854903	−	0.164535i
$347$	16.4887	−	13.8357i	0.885162	−	0.742739i	−0.0820721	−	0.996626i	$-0.526154\pi$
$347$	16.4887	−	13.8357i	0.885162	−	0.742739i	0.967234	+	0.253888i	$0.0817093\pi$
$348$		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
$356$	28.4397	−	5.93510i	1.50730	−	0.314560i
$357$		0			0
$358$	23.4985	+	19.1009i	1.24194	+	1.00951i
$359$	16.1699	−	28.0070i	0.853413	−	1.47816i	−0.0246959	−	0.999695i	$-0.507862\pi$
$359$	16.1699	−	28.0070i	0.853413	−	1.47816i	0.878109	−	0.478460i	$-0.158805\pi$
$360$		0			0
$361$	−9.49583	−	16.4473i	−0.499781	−	0.865645i
$362$	−3.27406	+	20.4268i	−0.172081	+	1.07361i
$363$		0			0
$364$	−9.93353	+	30.1916i	−0.520659	+	1.58247i
$365$	−13.7439	+	37.7610i	−0.719387	+	1.97650i
$366$		0			0
$367$	0.656339	+	0.115730i	0.0342606	+	0.00604107i	0.190752	−	0.981638i	$-0.438907\pi$
$367$	0.656339	+	0.115730i	0.0342606	+	0.00604107i	−0.156492	+	0.987679i	$0.550018\pi$
$368$	1.87798	+	2.82918i	0.0978965	+	0.147481i
$369$		0			0
$370$	−23.4932	−	13.0794i	−1.22136	−	0.679966i
$371$	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	$0.763136\pi$
$374$	−3.22998	−	3.72959i	−0.167018	−	0.192852i
$375$		0			0
$376$	17.2447	−	7.20720i	0.889326	−	0.371683i
$377$		−	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	$-0.164053\pi$
$380$	0.584357	−	0.233583i	0.0299769	−	0.0119826i
$381$		0			0
$382$	−2.05467	+	1.77943i	−0.105126	+	0.0910436i
$383$	1.37744	+	7.81186i	0.0703840	+	0.399168i	0.999564	+	0.0295390i	$0.00940393\pi$
$383$	1.37744	+	7.81186i	0.0703840	+	0.399168i	−0.929180	+	0.369629i	$0.879485\pi$
$384$		0			0
$385$	−20.2166	−	16.9637i	−1.03033	−	0.864552i
$386$	4.30735	−	7.73685i	0.219238	−	0.393795i
$387$		0			0
$388$	−6.95343	−	11.2200i	−0.353007	−	0.569610i
$389$	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
$392$	4.27529	+	1.33309i	0.215935	+	0.0673311i
$393$		0			0
$394$	21.1262	+	3.38615i	1.06432	+	0.170592i
$395$	−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	$-0.0310558\pi$
$398$	−23.1165	+	28.4387i	−1.15872	+	1.42550i
$399$		0			0
$400$	−6.45539	−	26.7327i	−0.322770	−	1.33664i
$401$	−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	$0.129502\pi$
$410$	2.63069	+	13.6687i	0.129920	+	0.675051i
$411$		0			0
$412$	−19.9142	+	25.2954i	−0.981101	+	1.24622i
$413$	7.72625	+	4.46075i	0.380184	+	0.219499i
$414$		0			0
$415$	−6.44516	+	3.72111i	−0.316380	+	0.182662i
$416$	2.95711	−	30.5419i	0.144984	−	1.49744i
$417$		0			0
$418$	−0.110485	+	0.318952i	−0.00540399	+	0.0156005i
$419$	4.62462	+	1.68322i	0.225927	+	0.0822309i	0.452504	−	0.891763i	$-0.350531\pi$
$419$	4.62462	+	1.68322i	0.225927	+	0.0822309i	−0.226576	+	0.973993i	$0.572753\pi$
$420$		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	$0.962970\pi$
$422$	21.1751	−	12.6700i	1.03079	−	0.616766i
$423$		0			0
$424$	−18.5269	−	9.56988i	−0.899747	−	0.464754i
$425$	−5.89823	+	7.02924i	−0.286106	+	0.340968i
$426$		0			0
$427$	−6.99642	+	1.23366i	−0.338581	+	0.0597009i
$428$	−14.4919	+	12.9518i	−0.700494	+	0.626048i
$429$		0			0
$430$	−25.8779	+	9.87868i	−1.24794	+	0.476392i
$431$	−4.40894			−0.212371			−0.106186	−	0.994346i	$-0.533864\pi$
$431$	−4.40894			−0.212371			−0.106186	+	0.994346i	$0.533864\pi$
$432$		0			0
$433$	28.5232			1.37074			0.685369	−	0.728196i	$-0.259641\pi$
$433$	28.5232			1.37074			0.685369	+	0.728196i	$0.259641\pi$
$434$	−25.7933	+	9.84639i	−1.23812	+	0.472642i
$435$		0			0
$436$	−7.00671	+	6.26206i	−0.335561	+	0.299898i
$437$	−0.0763379	+	0.0134604i	−0.00365174	+	0.000643900i
$438$		0			0
$439$	−3.10907	+	3.70524i	−0.148388	+	0.176842i	−0.835118	−	0.550071i	$-0.814601\pi$
$439$	−3.10907	+	3.70524i	−0.148388	+	0.176842i	0.686730	+	0.726912i	$0.259045\pi$
$440$	22.6368	+	11.6928i	1.07917	+	0.557432i
$441$		0			0
$442$	−8.78565	+	5.25684i	−0.417891	+	0.250042i
$443$	1.26185	−	7.15628i	0.0599521	−	0.340005i	−0.940047	−	0.341044i	$-0.889220\pi$
$443$	1.26185	−	7.15628i	0.0599521	−	0.340005i	0.999999	+	0.00103872i	$0.000330635\pi$
$444$		0			0
$445$	47.0392	+	17.1209i	2.22987	+	0.811607i
$446$	8.18217	−	23.6206i	0.387437	−	1.11847i
$447$		0			0
$448$	−23.3612	−	1.89447i	−1.10371	−	0.0895054i
$449$	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
$452$	−0.698323	+	0.887025i	−0.0328463	+	0.0417222i
$453$		0			0
$454$	−2.49354	−	12.9561i	−0.117028	−	0.608062i
$455$	−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	0.745525	−	0.666478i	$-0.232199\pi$
$463$	−0.866856	−	1.03308i	−0.0402862	−	0.0480112i	−0.785811	+	0.618466i	$0.787754\pi$
$464$	1.94875	−	0.470583i	0.0904686	−	0.0218463i
$465$		0			0
$466$	15.7243	−	19.3445i	0.728412	−	0.896118i
$467$	9.81172	−	16.9944i	0.454032	−	0.786407i	−0.544600	−	0.838696i	$-0.683318\pi$
$467$	9.81172	−	16.9944i	0.454032	−	0.786407i	0.998632	+	0.0522890i	$0.0166517\pi$
$468$		0			0
$469$	−7.06278	−	12.2331i	−0.326129	−	0.564872i
$470$	31.7978	+	5.09662i	1.46672	+	0.235090i
$471$		0			0
$472$	−8.22256	−	2.56390i	−0.378474	−	0.118013i
$473$	5.08146	−	13.9612i	0.233646	−	0.641937i
$474$		0			0
$475$	0.618239	+	0.109012i	0.0283667	+	0.00500182i
$476$	4.11953	+	6.64726i	0.188819	+	0.304677i
$477$		0			0
$478$	−6.33869	+	11.3855i	−0.289925	+	0.520763i
$479$	−14.6017	−	12.2523i	−0.667170	−	0.559822i	0.245056	−	0.969509i	$-0.421194\pi$
$479$	−14.6017	−	12.2523i	−0.667170	−	0.559822i	−0.912226	+	0.409687i	$0.865638\pi$
$480$		0			0
$481$	−5.19697	−	29.4735i	−0.236962	−	1.34388i
$482$	6.65655	−	5.76486i	0.303198	−	0.262582i
$483$		0			0
$484$	7.73874	−	3.09338i	0.351761	−	0.140608i
$485$		−	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	$-0.0932373\pi$
$488$	6.32825	−	2.64481i	0.286466	−	0.119725i
$489$		0			0
$490$	5.05152	+	5.83288i	0.228204	+	0.263503i
$491$	4.29474	+	24.3567i	0.193819	+	1.09920i	0.914091	+	0.405510i	$0.132906\pi$
$491$	4.29474	+	24.3567i	0.193819	+	1.09920i	−0.720272	+	0.693692i	$0.755983\pi$
$492$		0			0
$493$	−0.512415	−	0.429967i	−0.0230780	−	0.0193648i
$494$	0.611997	+	0.340718i	0.0275350	+	0.0153296i
$495$		0			0
$496$	22.2070	−	14.7408i	0.997125	−	0.661882i
$497$	34.1576	+	6.02290i	1.53218	+	0.270164i
$498$		0			0
$499$	−13.5128	+	37.1262i	−0.604917	+	1.66199i	0.136251	+	0.990674i	$0.456495\pi$
$499$	−13.5128	+	37.1262i	−0.604917	+	1.66199i	−0.741167	+	0.671320i	$0.765727\pi$
$500$	4.03940	−	12.2772i	0.180647	−	0.549052i
$501$		0			0
$502$	6.34588	−	39.5919i	0.283231	−	1.76707i
$503$	18.2058	+	31.5334i	0.811757	+	1.40600i	0.911633	+	0.411005i	$0.134822\pi$
$503$	18.2058	+	31.5334i	0.811757	+	1.40600i	−0.0998757	+	0.995000i	$0.531845\pi$
$504$		0			0
$505$	14.2068	−	24.6069i	0.632194	−	1.09499i
$506$	−2.43525	−	1.97950i	−0.108260	−	0.0879997i
$507$		0			0
$508$	21.7737	−	4.54397i	0.966051	−	0.201606i
$509$	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
$518$	−22.4480	+	4.32035i	−0.986309	+	0.189825i
$519$		0			0
$520$	32.0523	−	42.0470i	1.40558	−	1.84388i
$521$	−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	−0.855296	−	0.518139i	$-0.826625\pi$
$523$	−19.0780	+	11.0147i	−0.834223	+	0.481639i	0.0210733	+	0.999778i	$0.493292\pi$
$524$	−0.886245	+	6.14094i	−0.0387158	+	0.268268i
$525$		0			0
$526$	32.3612	+	11.2099i	1.41102	+	0.488775i
$527$	−8.35708	−	3.04173i	−0.364040	−	0.132500i
$528$		0			0
$529$	−3.86876	+	21.9408i	−0.168207	+	0.953949i
$530$	−18.4480	−	30.8318i	−0.801331	−	1.33925i
$531$		0			0
$532$	0.252925	−	0.471464i	0.0109657	−	0.0204405i
$533$	−9.95873	+	11.8684i	−0.431361	+	0.514075i
$534$		0			0
$535$	−32.9802	+	5.81531i	−1.42586	+	0.251418i
$536$	9.24499	+	10.0251i	0.399323	+	0.433017i
$537$		0			0
$538$	6.15102	+	16.1130i	0.265189	+	0.694682i
$539$	−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	$0.592016\pi$
$542$	−12.6096	−	33.0317i	−0.541628	−	1.41883i
$543$		0			0
$544$	−5.28893	−	5.38773i	−0.226761	−	0.230997i
$545$	−15.9456	+	2.81165i	−0.683036	+	0.120438i
$546$		0			0
$547$	9.19354	−	10.9564i	0.393087	−	0.468463i	−0.532812	−	0.846234i	$-0.678865\pi$
$547$	9.19354	−	10.9564i	0.393087	−	0.468463i	0.925899	+	0.377770i	$0.123309\pi$
$548$	30.4337	+	16.3267i	1.30006	+	0.697440i
$549$		0			0
$550$	13.0499	+	21.8101i	0.556451	+	0.929985i
$551$	−0.00794673	+	0.0450681i	−0.000338542	+	0.00191997i
$552$		0			0
$553$	−4.64441	−	1.69043i	−0.197500	−	0.0718842i
$554$	11.6765	+	4.04472i	0.496086	+	0.171844i
$555$		0			0
$556$	22.1505	+	3.19671i	0.939392	+	0.135571i
$557$	−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
$560$	−32.4947	−	23.9784i	−1.37315	−	1.01327i
$561$		0			0
$562$	−30.3964	+	5.85009i	−1.28219	+	0.246771i
$563$	16.2270	−	13.6161i	0.683887	−	0.573850i	−0.233252	−	0.972416i	$-0.574937\pi$
$563$	16.2270	−	13.6161i	0.683887	−	0.573850i	0.917139	+	0.398567i	$0.130492\pi$
$564$		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	0.794194	−	0.607664i	$-0.207893\pi$
$571$	1.38240	+	1.64748i	0.0578516	+	0.0689449i	−0.736343	+	0.676609i	$0.763449\pi$
$572$	5.79332	+	27.7603i	0.242231	+	1.16072i
$573$		0			0
$574$	9.18296	+	7.46439i	0.383289	+	0.311558i
$575$	−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	$-0.399956\pi$
$578$	3.40621	−	21.2513i	0.141679	−	0.883937i
$579$		0			0
$580$	3.28123	+	1.07958i	0.136246	+	0.0448271i
$581$	−2.16402	+	5.94559i	−0.0897785	+	0.246664i
$582$		0			0
$583$	18.9789	+	3.34648i	0.786024	+	0.138597i
$584$	−17.8096	−	27.7606i	−0.736965	−	1.14874i
$585$		0			0
$586$	16.3584	+	9.10721i	0.675758	+	0.376215i
$587$	−27.6154	−	23.1721i	−1.13981	−	0.956414i	−0.140378	−	0.990098i	$-0.544832\pi$
$587$	−27.6154	−	23.1721i	−1.13981	−	0.956414i	−0.999433	+	0.0336838i	$0.989276\pi$
$588$		0			0
$589$	0.105655	+	0.599198i	0.00435343	+	0.0246895i
$590$	−9.71547	−	11.2182i	−0.399980	−	0.461848i
$591$		0			0
$592$	20.2274	−	8.82698i	0.831342	−	0.362787i
$593$		−	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
$596$	−13.5491	−	33.8960i	−0.554995	−	1.38844i
$597$		0			0
$598$	−4.92282	+	4.26337i	−0.201309	+	0.174342i
$599$	1.46823	+	8.32677i	0.0599904	+	0.340223i	1.00000		0.000926605i	$-0.000294948\pi$
$599$	1.46823	+	8.32677i	0.0599904	+	0.340223i	−0.940009	+	0.341149i	$0.889184\pi$
$600$		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	$0.519116\pi$
$602$	−11.4550	+	20.5754i	−0.466869	+	0.838590i
$603$		0			0
$604$	−32.7244	+	20.2804i	−1.33154	+	0.825198i
$605$	14.1417	+	2.49356i	0.574942	+	0.101378i
$606$		0			0
$607$	13.2715	−	36.4633i	0.538675	−	1.48000i	−0.309820	−	0.950795i	$-0.600269\pi$
$607$	13.2715	−	36.4633i	0.538675	−	1.48000i	0.848495	−	0.529203i	$-0.177509\pi$
$608$	−0.138297	+	0.497664i	−0.00560869	+	0.0201829i
$609$		0			0
$610$	11.6688	+	1.87030i	0.472455	+	0.0757262i
$611$	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	$0.175374\pi$
$614$	−11.7488	+	14.4538i	−0.474143	+	0.583307i
$615$		0			0
$616$	21.1325	−	4.75539i	0.851452	−	0.191600i
$617$	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	0.923546	−	0.383487i	$-0.125277\pi$
$619$	−0.757138	−	2.08022i	−0.0304320	−	0.0836111i	−0.953978	+	0.299876i	$0.903055\pi$
$620$	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
$626$	−5.72956	−	29.7701i	−0.228999	−	1.18985i
$627$		0			0
$628$	−26.4634	−	20.8337i	−1.05601	−	0.831355i
$629$	−6.37717	−	3.68186i	−0.254274	−	0.146805i
$630$		0			0
$631$	−10.3534	+	5.97752i	−0.412161	+	0.237961i	−0.691718	−	0.722168i	$-0.743146\pi$
$631$	−10.3534	+	5.97752i	−0.412161	+	0.237961i	0.279557	+	0.960129i	$0.409813\pi$
$632$	4.73271	+	0.607796i	0.188257	+	0.0241768i
$633$		0			0
$634$	−6.80576	+	19.6472i	−0.270291	+	0.780288i
$635$	36.0136	+	13.1079i	1.42916	+	0.520171i
$636$		0			0
$637$	−1.49137	+	8.45799i	−0.0590903	+	0.335118i
$638$	−1.58990	+	0.951310i	−0.0629449	+	0.0376627i
$639$		0			0
$640$	35.6879	+	15.6973i	1.41069	+	0.620492i
$641$	−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	0.390620	−	0.920552i	$-0.372261\pi$
$643$	27.1966	−	4.79550i	1.07253	−	0.189116i	0.681910	+	0.731436i	$0.261150\pi$
$644$	3.31475	+	3.70892i	0.130620	+	0.146152i
$645$		0			0
$646$	0.161010	−	0.0614643i	0.00633485	−	0.00241828i
$647$	15.2634			0.600064			0.300032	−	0.953929i	$-0.403003\pi$
$647$	15.2634			0.600064			0.300032	+	0.953929i	$0.403003\pi$
$648$		0			0
$649$	7.96003			0.312458
$650$	49.2733	−	18.8097i	1.93266	−	0.737777i
$651$		0			0
$652$	10.6967	+	11.9687i	0.418917	+	0.468732i
$653$	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
$656$	−10.2312	−	5.08419i	−0.399461	−	0.198504i
$657$		0			0
$658$	23.4941	−	14.0576i	0.915895	−	0.548021i
$659$	−7.25464	+	41.1431i	−0.282601	+	1.60271i	0.431132	+	0.902289i	$0.358114\pi$
$659$	−7.25464	+	41.1431i	−0.282601	+	1.60271i	−0.713732	+	0.700418i	$0.752997\pi$
$660$		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	$0.830632\pi$
$662$	−12.2778	+	35.4440i	−0.477189	+	1.37757i
$663$		0			0
$664$	0.778076	−	6.05862i	0.0301952	−	0.235120i
$665$	0.798352	−	0.460929i	0.0309588	−	0.0178741i
$666$		0			0
$667$	−0.368476	−	0.212740i	−0.0142674	−	0.00823731i
$668$	−2.05180	−	1.61531i	−0.0793865	−	0.0624981i
$669$		0			0
$670$	4.44077	+	23.0737i	0.171562	+	0.891415i
$671$	−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
$680$	−2.85588	−	12.6913i	−0.109518	−	0.486687i
$681$		0			0
$682$	−15.5377	+	19.1150i	−0.594969	+	0.731952i
$683$	2.35647	−	4.08153i	0.0901678	−	0.156175i	−0.817414	−	0.576051i	$-0.804593\pi$
$683$	2.35647	−	4.08153i	0.0901678	−	0.156175i	0.907582	+	0.419876i	$0.137926\pi$
$684$		0			0
$685$	29.7536	+	51.5348i	1.13683	+	1.96904i
$686$	−22.1599	−	3.55184i	−0.846069	−	0.135610i
$687$		0			0
$688$	6.42820	−	21.8072i	0.245073	−	0.831391i
$689$	13.6777	−	37.5792i	0.521079	−	1.43165i
$690$		0			0
$691$	−47.8656	−	8.44000i	−1.82089	−	0.321073i	−0.844251	−	0.535947i	$-0.819955\pi$
$691$	−47.8656	−	8.44000i	−1.82089	−	0.321073i	−0.976642	+	0.214875i	$0.931066\pi$
$692$	−19.4665	+	12.0641i	−0.740006	+	0.458607i
$693$		0			0
$694$	−14.8070	+	26.5963i	−0.562065	+	1.00958i
$695$	29.5397	+	24.7868i	1.12051	+	0.940216i
$696$		0			0
$697$	0.661948	+	3.75409i	0.0250731	+	0.142196i
$698$	13.5137	−	11.7035i	0.511502	−	0.442982i
$699$		0			0
$700$	−14.9528	−	37.4076i	−0.565164	−	1.41387i
$701$			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
$704$	−18.8962	+	8.95791i	−0.712176	+	0.337614i
$705$		0			0
$706$	10.3591	+	11.9615i	0.389871	+	0.450176i
$707$	−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	$0.777144\pi$
$710$	−50.4101	−	28.0649i	−1.89186	−	1.05326i
$711$		0			0
$712$	−34.5816	+	22.1855i	−1.29600	+	0.831438i
$713$	−5.57097	−	0.982312i	−0.208634	−	0.0367879i
$714$		0			0
$715$	−16.7119	+	45.9155i	−0.624988	+	1.71714i
$716$	−40.6805	−	13.3846i	−1.52030	−	0.500205i
$717$		0			0
$718$	−7.23817	+	45.1589i	−0.270126	+	1.68532i
$719$	−11.2528	−	19.4904i	−0.419658	−	0.726869i	0.576247	−	0.817276i	$-0.304517\pi$
$719$	−11.2528	−	19.4904i	−0.419658	−	0.726869i	−0.995905	+	0.0904064i	$0.971183\pi$
$720$		0			0
$721$	−23.5797	+	40.8412i	−0.878153	+	1.52101i
$722$	20.8415	+	16.9411i	0.775639	+	0.630481i
$723$		0			0
$724$	−5.97682	−	28.6396i	−0.222127	−	1.06438i
$725$	2.21494	+	2.63966i	0.0822608	+	0.0980346i
$726$		0			0
$727$	−5.99428	−	16.4691i	−0.222316	−	0.610807i	0.777522	−	0.628856i	$-0.216477\pi$
$727$	−5.99428	−	16.4691i	−0.222316	−	0.610807i	−0.999837	+	0.0180494i	$0.994254\pi$
$728$	−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	$0.414038\pi$
$734$	−0.925538	+	0.178129i	−0.0341622	+	0.00657487i
$735$		0			0
$736$	−3.90816	−	2.79077i	−0.144057	−	0.102869i
$737$	−10.9147	−	6.30162i	−0.402049	−	0.232123i
$738$		0			0
$739$	−7.76664	+	4.48407i	−0.285700	+	0.164949i	−0.636001	−	0.771688i	$-0.719413\pi$
$739$	−7.76664	+	4.48407i	−0.285700	+	0.164949i	0.350301	+	0.936637i	$0.386079\pi$
$740$	37.6365	+	5.43160i	1.38354	+	0.199670i
$741$		0			0
$742$	−28.8635	−	9.99830i	−1.05961	−	0.367049i
$743$	−44.6168	−	16.2392i	−1.63683	−	0.595758i	−0.650352	−	0.759633i	$-0.725378\pi$
$743$	−44.6168	−	16.2392i	−1.63683	−	0.595758i	−0.986481	+	0.163875i	$0.947601\pi$
$744$		0			0
$745$	10.9219	−	61.9413i	0.400148	−	2.26935i
$746$	−15.1259	−	25.2796i	−0.553800	−	0.925554i
$747$		0			0
$748$	6.14858	+	3.29851i	0.224814	+	0.120605i
$749$	−18.3010	+	21.8103i	−0.668705	+	0.796932i
$750$		0			0
$751$	13.7230	−	2.41974i	0.500761	−	0.0882976i	0.0824383	−	0.996596i	$-0.473729\pi$
$751$	13.7230	−	2.41974i	0.500761	−	0.0882976i	0.418323	+	0.908299i	$0.362618\pi$
$752$	−19.1489	+	18.2199i	−0.698289	+	0.664411i
$753$		0			0
$754$	1.37118	+	3.59191i	0.0499355	+	0.130810i
$755$	−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	$0.425214\pi$
$758$	9.67895	+	25.3547i	0.351555	+	0.920924i
$759$		0			0
$760$	−0.654252	+	0.603343i	−0.0237322	+	0.0218855i
$761$	−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
$764$	1.81718	−	3.38732i	0.0657434	−	0.122549i
$765$		0			0
$766$	−5.75993	−	9.62644i	−0.208115	−	0.347817i
$767$	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	$0.711007\pi$
$770$	35.2664	+	12.2163i	1.27091	+	0.440243i
$771$		0			0
$772$	−1.78875	+	12.3945i	−0.0643785	+	0.446089i
$773$	−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
$776$	14.8460	+	11.3170i	0.532939	+	0.406257i
$777$		0			0
$778$	−17.1453	+	3.29980i	−0.614690	+	0.118303i
$779$	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	$-0.188348\pi$
$787$	3.83079	+	4.56536i	0.136553	+	0.162737i	−0.693434	+	0.720520i	$0.743903\pi$
$788$	−29.6201	+	6.18145i	−1.05517	+	0.220205i
$789$		0			0
$790$	6.37976	+	5.18580i	0.226982	+	0.184503i
$791$	−0.826860	+	1.43216i	−0.0293998	+	0.0509219i
$792$		0			0
$793$	6.57679	+	11.3913i	0.233549	+	0.404518i
$794$	−5.19071	+	32.3848i	−0.184211	+	1.14929i
$795$		0			0
$796$	16.1984	−	49.2328i	0.574138	−	1.74501i
$797$	−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
$800$	22.0120	+	32.0639i	0.778243	+	1.13363i
$801$		0			0
$802$	8.39715	+	4.67495i	0.296514	+	0.165078i
$803$	23.3504	+	19.5933i	0.824016	+	0.691432i
$804$		0			0
$805$	1.48831	+	8.44064i	0.0524561	+	0.297494i
$806$	33.4644	+	38.6406i	1.17873	+	1.36106i
$807$		0			0
$808$	8.99295	+	21.5175i	0.316371	+	0.756982i
$809$			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	$-0.852675\pi$
$811$		−	25.4302i		−	0.892974i	0.894790	−	0.446487i	$-0.147325\pi$
$812$	2.72693	−	1.09003i	0.0956964	−	0.0382524i
$813$		0			0
$814$	−15.4181	+	13.3527i	−0.540403	+	0.468012i
$815$	4.80280	+	27.2380i	0.168235	+	0.954107i
$816$		0			0
$817$	0.397558	+	0.333591i	0.0139088	+	0.0116709i
$818$	−12.4975	+	22.4480i	−0.436965	+	0.784877i
$819$		0			0
$820$	−10.3697	−	16.7326i	−0.362127	−	0.584326i
$821$	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	−0.876428	−	0.481534i	$-0.840080\pi$
$823$	2.99728	−	8.23497i	0.104479	−	0.287053i	0.980906	+	0.194481i	$0.0623021\pi$
$824$	13.5528	−	43.4647i	0.472136	−	1.51417i
$825$		0			0
$826$	−12.4579	−	1.99678i	−0.433466	−	0.0694769i
$827$	−9.57006	−	16.5758i	−0.332784	−	0.576398i	0.650273	−	0.759701i	$-0.274655\pi$
$827$	−9.57006	−	16.5758i	−0.332784	−	0.576398i	−0.983057	+	0.183303i	$0.941321\pi$
$828$		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	$0.166952\pi$
$830$	6.63866	−	8.16711i	0.230431	−	0.283485i
$831$		0			0
$832$	11.4973	+	41.8440i	0.398596	+	1.45068i
$833$	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	$-0.670569\pi$
$839$	−10.1094	+	3.67952i	−0.349015	+	0.127031i	0.161563	+	0.986862i	$0.448346\pi$
$840$		0			0
$841$	22.0229	−	18.4794i	0.759409	−	0.637220i
$842$	−3.14544	−	16.3433i	−0.108399	−	0.563228i
$843$		0			0
$844$	−21.5866	+	27.4198i	−0.743042	+	0.943828i
$845$	49.0137	+	28.2981i	1.68612	+	0.973484i
$846$		0			0
$847$	10.5727	−	6.10416i	0.363283	−	0.209741i
$848$	29.3048	+	3.29958i	1.00633	+	0.113308i
$849$		0			0
$850$	4.24755	−	12.2620i	0.145690	−	0.420584i
$851$	−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	$-0.181229\pi$
$854$	8.62159	−	5.15868i	0.295025	−	0.176526i
$855$		0			0
$856$	12.6146	−	24.4213i	0.431157	−	0.834704i
$857$	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	−0.113780	−	0.993506i	$-0.536296\pi$
$859$	3.49071	−	0.615507i	0.119102	−	0.0210008i	0.232881	+	0.972505i	$0.425185\pi$
$860$	29.2079	−	26.1038i	0.995981	−	0.890132i
$861$		0			0
$862$	5.82517	−	2.22371i	0.198406	−	0.0757400i
$863$	6.36151			0.216548			0.108274	−	0.994121i	$-0.465468\pi$
$863$	6.36151			0.216548			0.108274	+	0.994121i	$0.465468\pi$
$864$		0			0
$865$	−39.4602			−1.34169
$866$	−37.6854	+	14.3861i	−1.28060	+	0.488860i
$867$		0			0
$868$	29.1124	−	26.0184i	0.988139	−	0.883124i
$869$	−4.34283	+	0.765757i	−0.147320	+	0.0259765i
$870$		0			0
$871$	−16.8110	+	20.0345i	−0.569618	+	0.678844i
$872$	6.09903	−	11.8075i	0.206539	−	0.399852i
$873$		0			0
$874$	0.0940700	−	0.0562863i	0.00318197	−	0.00190391i
$875$	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	$0.522198\pi$
$878$	2.23896	−	6.46354i	0.0755614	−	0.218134i
$879$		0			0
$880$	−35.8056	−	4.03153i	−1.20701	−	0.135903i
$881$	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	0.977901	−	0.209070i	$-0.0670437\pi$
$883$	38.2077	+	22.0592i	1.28579	+	0.742352i	0.307890	+	0.951422i	$0.400377\pi$
$884$	8.95639	−	11.3766i	0.301236	−	0.382636i
$885$		0			0
$886$	1.94220	+	10.0914i	0.0652495	+	0.339028i
$887$	−1.84120	+	1.54495i	−0.0618215	+	0.0518744i	−0.673175	−	0.739483i	$-0.735070\pi$
$887$	−1.84120	+	1.54495i	−0.0618215	+	0.0518744i	0.611353	+	0.791358i	$0.290625\pi$
$888$		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
$896$	31.8207	−	9.27952i	1.06305	−	0.310007i
$897$		0			0
$898$	−5.66967	+	6.97503i	−0.189199	+	0.232760i
$899$	−1.66986	+	2.89227i	−0.0556928	+	0.0964627i
$900$		0			0
$901$	−4.91981	−	8.52136i	−0.163903	−	0.283888i
$902$	10.4256	+	1.67104i	0.347134	+	0.0556394i
$903$		0			0
$904$	0.475253	−	1.52416i	0.0158067	−	0.0506929i
$905$	17.2412	−	47.3698i	0.573117	−	1.57463i
$906$		0			0
$907$	34.5531	+	6.09265i	1.14732	+	0.202303i	0.714804	−	0.699324i	$-0.246516\pi$
$907$	34.5531	+	6.09265i	1.14732	+	0.202303i	0.432513	+	0.901628i	$0.357627\pi$
$908$	9.82912	+	15.8602i	0.326191	+	0.526340i
$909$		0			0
$910$	37.6730	−	67.6682i	1.24885	−	2.24318i
$911$	−8.27443	−	6.94307i	−0.274144	−	0.230034i	0.495342	−	0.868698i	$-0.335043\pi$
$911$	−8.27443	−	6.94307i	−0.274144	−	0.230034i	−0.769486	+	0.638664i	$0.779487\pi$
$912$		0			0
$913$	0.980292	+	5.55951i	0.0324429	+	0.183993i
$914$	−0.955888	+	0.827840i	−0.0316180	+	0.0273825i
$915$		0			0
$916$	−31.2316	+	12.4841i	−1.03192	+	0.412486i
$917$			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	$-0.112203\pi$
$920$	−3.19076	−	7.63455i	−0.105196	−	0.251704i
$921$		0			0
$922$	−12.1299	−	14.0061i	−0.399477	−	0.461267i
$923$	−11.1513	−	63.2421i	−0.367049	−	2.08164i
$924$		0			0
$925$	29.0588	+	24.3832i	0.955447	+	0.801715i
$926$	1.66635	+	0.927710i	0.0547598	+	0.0304865i
$927$		0			0
$928$	−2.33738	+	1.60463i	−0.0767284	+	0.0526744i
$929$	−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
$932$	−11.0185	+	33.4891i	−0.360922	+	1.09697i
$933$		0			0
$934$	−4.39205	+	27.4020i	−0.143712	+	0.896621i
$935$	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	$0.301439\pi$
$938$	15.5014	+	12.6004i	0.506139	+	0.411417i
$939$		0			0
$940$	−44.5824	+	9.30393i	−1.45412	+	0.303461i
$941$	−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	0.728050	−	0.685524i	$-0.240427\pi$
$947$	53.1276	−	19.3369i	1.72642	−	0.628364i	0.998365	+	0.0571597i	$0.0182044\pi$
$948$		0			0
$949$	48.4548	−	40.6584i	1.57291	−	1.31983i
$950$	−0.871810	+	0.167789i	−0.0282852	+	0.00544378i
$951$		0			0
$952$	−8.79544	−	6.70473i	−0.285062	−	0.217302i
$953$	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
$956$	2.63232	−	18.2398i	0.0851354	−	0.589917i
$957$		0			0
$958$	25.4717	+	8.82338i	0.822953	+	0.285070i
$959$	47.5403	+	17.3032i	1.53516	+	0.558751i
$960$		0			0
$961$	−2.32736	+	13.1991i	−0.0750761	+	0.425778i
$962$	21.7317	+	36.3197i	0.700659	+	1.17100i
$963$		0			0
$964$	−5.88716	+	10.9740i	−0.189613	+	0.353447i
$965$	−13.8697	+	16.5292i	−0.446480	+	0.532094i
$966$		0			0
$967$	44.3616	−	7.82215i	1.42657	−	0.251543i	0.593557	−	0.804792i	$-0.297723\pi$
$967$	44.3616	−	7.82215i	1.42657	−	0.251543i	0.833016	+	0.553249i	$0.186612\pi$
$968$	−8.66437	+	7.99018i	−0.278483	+	0.256814i
$969$		0			0
$970$	11.4712	+	30.0496i	0.368318	+	0.964835i
$971$	40.1053			1.28704			0.643520	−	0.765429i	$-0.277473\pi$
$971$	40.1053			1.28704			0.643520	+	0.765429i	$0.277473\pi$
$972$		0			0
$973$	32.7837			1.05100
$974$	6.42762	+	16.8376i	0.205954	+	0.539512i
$975$		0			0
$976$	−7.02705	+	6.68612i	−0.224930	+	0.214017i
$977$	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
$980$	−9.61606	−	5.15870i	−0.307174	−	0.164788i
$981$		0			0
$982$	−17.9589	−	30.0144i	−0.573093	−	0.957797i
$983$	3.28853	−	18.6502i	0.104888	−	0.594848i	−0.886377	−	0.462963i	$-0.846786\pi$
$983$	3.28853	−	18.6502i	0.104888	−	0.594848i	0.991265	−	0.131884i	$-0.0421028\pi$
$984$		0			0
$985$	−48.9916	−	17.8315i	−1.56100	−	0.568158i
$986$	0.893872	+	0.309637i	0.0284667	+	0.00986084i
$987$		0			0
$988$	−0.980427	−	0.141493i	−0.0311915	−	0.00450148i
$989$	−4.17867	+	2.41256i	−0.132874	+	0.0767148i
$990$		0			0
$991$	30.3997	+	17.5513i	0.965680	+	0.557535i	0.897916	−	0.440166i	$-0.145080\pi$
$991$	30.3997	+	17.5513i	0.965680	+	0.557535i	0.0677633	+	0.997701i	$0.478414\pi$
$992$	−21.9056	+	30.6763i	−0.695503	+	0.973972i
$993$		0			0
$994$	−48.1673	+	9.27029i	−1.52777	+	0.294036i
$995$	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.143.2		96
3.2	odd	2		108.2.l.a.47.15	yes	96
4.3	odd	2	inner	324.2.l.a.143.15		96
9.2	odd	6		972.2.l.d.107.5		96
9.4	even	3		972.2.l.b.755.10		96
9.5	odd	6		972.2.l.c.755.7		96
9.7	even	3		972.2.l.a.107.12		96
12.11	even	2		108.2.l.a.47.2	yes	96
27.4	even	9		108.2.l.a.23.2	✓	96
27.5	odd	18		972.2.l.b.215.8		96
27.13	even	9		972.2.l.d.863.13		96
27.14	odd	18		972.2.l.a.863.4		96
27.22	even	9		972.2.l.c.215.9		96
27.23	odd	18	inner	324.2.l.a.179.15		96
36.7	odd	6		972.2.l.a.107.4		96
36.11	even	6		972.2.l.d.107.13		96
36.23	even	6		972.2.l.c.755.9		96
36.31	odd	6		972.2.l.b.755.8		96
108.23	even	18	inner	324.2.l.a.179.2		96
108.31	odd	18		108.2.l.a.23.15	yes	96
108.59	even	18		972.2.l.b.215.10		96
108.67	odd	18		972.2.l.d.863.5		96
108.95	even	18		972.2.l.a.863.12		96
108.103	odd	18		972.2.l.c.215.7		96

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

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)

\(f(q)\)	\(=\)	\(q+(-1.32122 + 0.504364i) q^{2} +(1.49123 - 1.33275i) q^{4} +(3.39370 - 0.598401i) q^{5} +(1.88319 - 2.24430i) q^{7} +(-1.29805 + 2.51298i) q^{8} +O(q^{10})\)	\(q+(-1.32122 + 0.504364i) q^{2} +(1.49123 - 1.33275i) q^{4} +(3.39370 - 0.598401i) q^{5} +(1.88319 - 2.24430i) q^{7} +(-1.29805 + 2.51298i) q^{8} +(-4.18200 + 2.50228i) q^{10} +(0.453915 - 2.57428i) q^{11} +(-5.09721 - 1.85523i) q^{13} +(-1.35616 + 3.91503i) q^{14} +(0.447553 - 3.97488i) q^{16} +(-1.15583 + 0.667320i) q^{17} +(0.0790760 + 0.0456546i) q^{19} +(4.26328 - 5.41531i) q^{20} +(0.698654 + 3.63012i) q^{22} +(-0.650322 + 0.545685i) q^{23} +(6.46065 - 2.35148i) q^{25} +(7.67024 - 0.119685i) q^{26} +(-0.182815 - 5.85661i) q^{28} +(0.171418 + 0.470966i) q^{29} +(4.28324 + 5.10457i) q^{31} +(1.41348 + 5.47742i) q^{32} +(1.19053 - 1.46464i) q^{34} +(5.04800 - 8.74340i) q^{35} +(2.75869 + 4.77819i) q^{37} +(-0.127503 - 0.0204365i) q^{38} +(-2.90143 + 9.30505i) q^{40} +(0.976880 - 2.68396i) q^{41} +(5.59737 + 0.986968i) q^{43} +(-2.75398 - 4.44381i) q^{44} +(0.583993 - 1.04897i) q^{46} +(-5.06200 - 4.24752i) q^{47} +(-0.274941 - 1.55927i) q^{49} +(-7.34992 + 6.36534i) q^{50} +(-10.0737 + 4.02673i) q^{52} +7.37249i q^{53} -9.00795i q^{55} +(3.19540 + 7.64565i) q^{56} +(-0.464019 - 0.535792i) q^{58} +(0.528787 + 2.99890i) q^{59} +(-1.85759 - 1.55871i) q^{61} +(-8.23365 - 4.58393i) q^{62} +(-4.63012 - 6.52395i) q^{64} +(-18.4086 - 3.24593i) q^{65} +(1.64904 - 4.53069i) q^{67} +(-0.834244 + 2.53557i) q^{68} +(-2.25965 + 14.0980i) q^{70} +(5.91940 + 10.2527i) q^{71} +(-5.83049 + 10.0987i) q^{73} +(-6.05478 - 4.92165i) q^{74} +(0.178767 - 0.0373070i) q^{76} +(-4.92266 - 5.86659i) q^{77} +(-0.576990 - 1.58527i) q^{79} +(-0.859714 - 13.7574i) q^{80} +(0.0630204 + 4.03879i) q^{82} +(-2.02940 + 0.738640i) q^{83} +(-3.52322 + 2.95633i) q^{85} +(-7.89314 + 1.51912i) q^{86} +(5.87990 + 4.48223i) q^{88} +(12.5801 + 7.26310i) q^{89} +(-13.7628 + 7.94593i) q^{91} +(-0.242520 + 1.68046i) q^{92} +(8.83031 + 3.05881i) q^{94} +(0.295680 + 0.107619i) q^{95} +(1.14607 - 6.49971i) q^{97} +(1.14969 + 1.92146i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 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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