LMFDB - Embedded newform 504.2.cj.e.37.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(37,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("504.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cj (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.14
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.e.109.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31787 + 0.513056i) q^{2} +(1.47355 + 1.35228i) q^{4} +(0.0402223 + 0.0232224i) q^{5} +(-1.97032 + 1.76574i) q^{7} +(1.24814 + 2.53814i) q^{8} +O(q^{10})$	\(q+(1.31787 + 0.513056i) q^{2} +(1.47355 + 1.35228i) q^{4} +(0.0402223 + 0.0232224i) q^{5} +(-1.97032 + 1.76574i) q^{7} +(1.24814 + 2.53814i) q^{8} +(0.0410933 + 0.0512403i) q^{10} +(3.11586 - 1.79894i) q^{11} +6.29415i q^{13} +(-3.50254 + 1.31613i) q^{14} +(0.342679 + 3.98529i) q^{16} +(-0.258110 - 0.447060i) q^{17} +(2.80834 + 1.62140i) q^{19} +(0.0278663 + 0.0886110i) q^{20} +(5.02925 - 0.772156i) q^{22} +(3.47322 - 6.01578i) q^{23} +(-2.49892 - 4.32826i) q^{25} +(-3.22925 + 8.29485i) q^{26} +(-5.29113 - 0.0625230i) q^{28} +2.29579i q^{29} +(-1.05460 - 1.82662i) q^{31} +(-1.59308 + 5.42790i) q^{32} +(-0.110788 - 0.721591i) q^{34} +(-0.120255 + 0.0252667i) q^{35} +(1.12720 + 0.650790i) q^{37} +(2.86915 + 3.57762i) q^{38} +(-0.00873835 + 0.131074i) q^{40} -10.1883 q^{41} -9.12162i q^{43} +(7.02404 + 1.56269i) q^{44} +(7.66367 - 6.14605i) q^{46} +(2.32465 - 4.02641i) q^{47} +(0.764321 - 6.95815i) q^{49} +(-1.07261 - 6.98616i) q^{50} +(-8.51145 + 9.27472i) q^{52} +(4.91727 - 2.83899i) q^{53} +0.167103 q^{55} +(-6.94093 - 2.79705i) q^{56} +(-1.17787 + 3.02555i) q^{58} +(-1.42910 + 0.825090i) q^{59} +(1.10386 + 0.637312i) q^{61} +(-0.452663 - 2.94831i) q^{62} +(-4.88428 + 6.33591i) q^{64} +(-0.146165 + 0.253165i) q^{65} +(6.72366 - 3.88191i) q^{67} +(0.224213 - 1.00780i) q^{68} +(-0.171444 - 0.0283997i) q^{70} -11.8320 q^{71} +(5.57028 + 9.64802i) q^{73} +(1.15161 + 1.43597i) q^{74} +(1.94564 + 6.18687i) q^{76} +(-2.96278 + 9.04630i) q^{77} +(-2.75086 + 4.76463i) q^{79} +(-0.0787646 + 0.168255i) q^{80} +(-13.4269 - 5.22719i) q^{82} -8.25030i q^{83} -0.0239757i q^{85} +(4.67990 - 12.0211i) q^{86} +(8.45501 + 5.66315i) q^{88} +(7.38218 - 12.7863i) q^{89} +(-11.1138 - 12.4015i) q^{91} +(13.2530 - 4.16778i) q^{92} +(5.12936 - 4.11360i) q^{94} +(0.0753053 + 0.130433i) q^{95} -6.16464 q^{97} +(4.57719 - 8.77777i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8}+O(q^{10}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 6 q^{10} - 22 q^{14} - 10 q^{16} + 40 q^{20} - 12 q^{22} + 8 q^{23} + 16 q^{25} - 6 q^{26} - 26 q^{28} - 24 q^{31} + 8 q^{32} - 24 q^{34} + 26 q^{38} - 6 q^{40} - 20 q^{44} + 16 q^{46} + 24 q^{47} + 8 q^{49} - 52 q^{50} + 44 q^{52} - 64 q^{55} - 40 q^{56} + 34 q^{58} - 100 q^{62} - 20 q^{64} - 16 q^{68} + 38 q^{70} + 80 q^{71} + 8 q^{73} - 10 q^{74} - 32 q^{76} + 8 q^{79} + 56 q^{80} + 22 q^{86} + 50 q^{88} - 64 q^{92} - 48 q^{94} - 24 q^{95} - 48 q^{97} + 64 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 6 * q^10 - 22 * q^14 - 10 * q^16 + 40 * q^20 - 12 * q^22 + 8 * q^23 + 16 * q^25 - 6 * q^26 - 26 * q^28 - 24 * q^31 + 8 * q^32 - 24 * q^34 + 26 * q^38 - 6 * q^40 - 20 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^49 - 52 * q^50 + 44 * q^52 - 64 * q^55 - 40 * q^56 + 34 * q^58 - 100 * q^62 - 20 * q^64 - 16 * q^68 + 38 * q^70 + 80 * q^71 + 8 * q^73 - 10 * q^74 - 32 * q^76 + 8 * q^79 + 56 * q^80 + 22 * q^86 + 50 * q^88 - 64 * q^92 - 48 * q^94 - 24 * q^95 - 48 * q^97 + 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.31787	+	0.513056i	0.931873	+	0.362786i
$2$	1.31787	+	0.513056i	0.931873	+	0.362786i
$3$		0			0
$3$		0			0
$4$	1.47355	+	1.35228i	0.736773	+	0.676140i
$5$	0.0402223	+	0.0232224i	0.0179880	+	0.0103854i	0.508967	−	0.860786i	$-0.330028\pi$
$5$	0.0402223	+	0.0232224i	0.0179880	+	0.0103854i	−0.490979	+	0.871171i	$0.663361\pi$
$6$		0			0
$7$	−1.97032	+	1.76574i	−0.744711	+	0.667387i
$7$	−1.97032	+	1.76574i	−0.744711	+	0.667387i
$8$	1.24814	+	2.53814i	0.441285	+	0.897367i
$9$		0			0
$10$	0.0410933	+	0.0512403i	0.0129948	+	0.0162036i
$11$	3.11586	−	1.79894i	0.939468	−	0.542402i	0.0496743	−	0.998765i	$-0.484182\pi$
$11$	3.11586	−	1.79894i	0.939468	−	0.542402i	0.889793	+	0.456364i	$0.150848\pi$
$12$		0			0
$13$			6.29415i			1.74568i	0.488004	+	0.872842i	$0.337725\pi$
$13$			6.29415i			1.74568i	−0.488004	+	0.872842i	$0.662275\pi$
$14$	−3.50254	+	1.31613i	−0.936094	+	0.351749i
$15$		0			0
$16$	0.342679	+	3.98529i	0.0856697	+	0.996324i
$17$	−0.258110	−	0.447060i	−0.0626010	−	0.108428i	0.833026	−	0.553233i	$-0.186606\pi$
$17$	−0.258110	−	0.447060i	−0.0626010	−	0.108428i	−0.895627	+	0.444805i	$0.853273\pi$
$18$		0			0
$19$	2.80834	+	1.62140i	0.644278	+	0.371974i	0.786261	−	0.617895i	$-0.212014\pi$
$19$	2.80834	+	1.62140i	0.644278	+	0.371974i	−0.141983	+	0.989869i	$0.545348\pi$
$20$	0.0278663	+	0.0886110i	0.00623109	+	0.0198140i
$21$		0			0
$22$	5.02925	−	0.772156i	1.07224	−	0.164624i
$23$	3.47322	−	6.01578i	0.724215	−	1.25438i	−0.235081	−	0.971976i	$-0.575535\pi$
$23$	3.47322	−	6.01578i	0.724215	−	1.25438i	0.959296	−	0.282402i	$-0.0911312\pi$
$24$		0			0
$25$	−2.49892	−	4.32826i	−0.499784	−	0.865652i
$26$	−3.22925	+	8.29485i	−0.633309	+	1.62675i
$27$		0			0
$28$	−5.29113	−	0.0625230i	−0.999930	−	0.0118157i
$29$			2.29579i			0.426317i	0.977018	+	0.213159i	$0.0683751\pi$
$29$			2.29579i			0.426317i	−0.977018	+	0.213159i	$0.931625\pi$
$30$		0			0
$31$	−1.05460	−	1.82662i	−0.189411	−	0.328070i	0.755643	−	0.654984i	$-0.227325\pi$
$31$	−1.05460	−	1.82662i	−0.189411	−	0.328070i	−0.945054	+	0.326914i	$0.893991\pi$
$32$	−1.59308	+	5.42790i	−0.281619	+	0.959526i
$33$		0			0
$34$	−0.110788	−	0.721591i	−0.0190000	−	0.123752i
$35$	−0.120255	+	0.0252667i	−0.0203269	+	0.00427085i
$36$		0			0
$37$	1.12720	+	0.650790i	0.185311	+	0.106989i	0.589785	−	0.807560i	$-0.299212\pi$
$37$	1.12720	+	0.650790i	0.185311	+	0.106989i	−0.404475	+	0.914549i	$0.632546\pi$
$38$	2.86915	+	3.57762i	0.465438	+	0.580367i
$39$		0			0
$40$	−0.00873835	+	0.131074i	−0.00138165	+	0.0207247i
$41$	−10.1883			−1.59115			−0.795576	−	0.605854i	$-0.792832\pi$
$41$	−10.1883			−1.59115			−0.795576	+	0.605854i	$0.792832\pi$
$42$		0			0
$43$		−	9.12162i		−	1.39103i	−0.718510	−	0.695517i	$-0.755176\pi$
$43$		−	9.12162i		−	1.39103i	0.718510	−	0.695517i	$-0.244824\pi$
$44$	7.02404	+	1.56269i	1.05891	+	0.235584i
$45$		0			0
$46$	7.66367	−	6.14605i	1.12995	−	0.906186i
$47$	2.32465	−	4.02641i	0.339085	−	0.587313i	−0.645176	−	0.764034i	$-0.723216\pi$
$47$	2.32465	−	4.02641i	0.339085	−	0.587313i	0.984261	+	0.176722i	$0.0565492\pi$
$48$		0			0
$49$	0.764321	−	6.95815i	0.109189	−	0.994021i
$50$	−1.07261	−	6.98616i	−0.151689	−	0.987992i
$51$		0			0
$52$	−8.51145	+	9.27472i	−1.18033	+	1.28617i
$53$	4.91727	−	2.83899i	0.675439	−	0.389965i	−0.122696	−	0.992444i	$-0.539154\pi$
$53$	4.91727	−	2.83899i	0.675439	−	0.389965i	0.798134	+	0.602480i	$0.205821\pi$
$54$		0			0
$55$	0.167103			0.0225321
$56$	−6.94093	−	2.79705i	−0.927521	−	0.373771i
$57$		0			0
$58$	−1.17787	+	3.02555i	−0.154662	+	0.397274i
$59$	−1.42910	+	0.825090i	−0.186053	+	0.107418i	−0.590133	−	0.807306i	$-0.700925\pi$
$59$	−1.42910	+	0.825090i	−0.186053	+	0.107418i	0.404081	+	0.914723i	$0.367591\pi$
$60$		0			0
$61$	1.10386	+	0.637312i	0.141334	+	0.0815995i	0.569000	−	0.822338i	$-0.307331\pi$
$61$	1.10386	+	0.637312i	0.141334	+	0.0815995i	−0.427665	+	0.903937i	$0.640664\pi$
$62$	−0.452663	−	2.94831i	−0.0574882	−	0.374436i
$63$		0			0
$64$	−4.88428	+	6.33591i	−0.610535	+	0.791989i
$65$	−0.146165	+	0.253165i	−0.0181295	+	0.0314013i
$66$		0			0
$67$	6.72366	−	3.88191i	0.821426	−	0.474251i	−0.0294820	−	0.999565i	$-0.509386\pi$
$67$	6.72366	−	3.88191i	0.821426	−	0.474251i	0.850908	+	0.525315i	$0.176052\pi$
$68$	0.224213	−	1.00780i	0.0271898	−	0.122214i
$69$		0			0
$70$	−0.171444	−	0.0283997i	−0.0204915	−	0.00339441i
$71$	−11.8320			−1.40420			−0.702099	−	0.712080i	$-0.747753\pi$
$71$	−11.8320			−1.40420			−0.702099	+	0.712080i	$0.747753\pi$
$72$		0			0
$73$	5.57028	+	9.64802i	0.651953	+	1.12921i	0.982649	+	0.185478i	$0.0593832\pi$
$73$	5.57028	+	9.64802i	0.651953	+	1.12921i	−0.330696	+	0.943737i	$0.607283\pi$
$74$	1.15161	+	1.43597i	0.133872	+	0.166928i
$75$		0			0
$76$	1.94564	+	6.18687i	0.223180	+	0.709683i
$77$	−2.96278	+	9.04630i	−0.337640	+	1.03092i
$78$		0			0
$79$	−2.75086	+	4.76463i	−0.309496	+	0.536063i	−0.978252	−	0.207419i	$-0.933494\pi$
$79$	−2.75086	+	4.76463i	−0.309496	+	0.536063i	0.668756	+	0.743482i	$0.266827\pi$
$80$	−0.0787646	+	0.168255i	−0.00880615	+	0.0188115i
$81$		0			0
$82$	−13.4269	−	5.22719i	−1.48275	−	0.577247i
$83$		−	8.25030i		−	0.905588i	−0.891615	−	0.452794i	$-0.850427\pi$
$83$		−	8.25030i		−	0.905588i	0.891615	−	0.452794i	$-0.149573\pi$
$84$		0			0
$85$		−	0.0239757i		−	0.00260053i
$86$	4.67990	−	12.0211i	0.504647	−	1.29627i
$87$		0			0
$88$	8.45501	+	5.66315i	0.901307	+	0.603693i
$89$	7.38218	−	12.7863i	0.782510	−	1.35535i	−0.147966	−	0.988993i	$-0.547273\pi$
$89$	7.38218	−	12.7863i	0.782510	−	1.35535i	0.930475	−	0.366354i	$-0.119394\pi$
$90$		0			0
$91$	−11.1138	−	12.4015i	−1.16505	−	1.30003i
$92$	13.2530	−	4.16778i	1.38172	−	0.434521i
$93$		0			0
$94$	5.12936	−	4.11360i	0.529053	−	0.424285i
$95$	0.0753053	+	0.130433i	0.00772616	+	0.0133821i
$96$		0			0
$97$	−6.16464			−0.625925			−0.312962	−	0.949766i	$-0.601321\pi$
$97$	−6.16464			−0.625925			−0.312962	+	0.949766i	$0.601321\pi$
$98$	4.57719	−	8.77777i	0.462366	−	0.886689i
$99$		0			0
$100$	2.17074	−	9.75713i	0.217074	−	0.975713i
$101$	−6.93470	+	4.00375i	−0.690029	+	0.398388i	−0.803623	−	0.595139i	$-0.797097\pi$
$101$	−6.93470	+	4.00375i	−0.690029	+	0.398388i	0.113594	+	0.993527i	$0.463764\pi$
$102$		0			0
$103$	6.43821	−	11.1513i	0.634376	−	1.09877i	−0.352271	−	0.935898i	$-0.614591\pi$
$103$	6.43821	−	11.1513i	0.634376	−	1.09877i	0.986647	−	0.162873i	$-0.0520761\pi$
$104$	−15.9754	+	7.85600i	−1.56652	+	0.770344i
$105$		0			0
$106$	7.93686	−	1.21857i	0.770896	−	0.118358i
$107$	8.84815	+	5.10848i	0.855383	+	0.493856i	0.862463	−	0.506119i	$-0.168920\pi$
$107$	8.84815	+	5.10848i	0.855383	+	0.493856i	−0.00708048	+	0.999975i	$0.502254\pi$
$108$		0			0
$109$	−10.1275	+	5.84714i	−0.970043	+	0.560054i	−0.899249	−	0.437437i	$-0.855886\pi$
$109$	−10.1275	+	5.84714i	−0.970043	+	0.560054i	−0.0707935	+	0.997491i	$0.522553\pi$
$110$	0.220219	+	0.0857331i	0.0209971	+	0.00817433i
$111$		0			0
$112$	−7.71218	−	7.24722i	−0.728733	−	0.684798i
$113$	9.08476			0.854623			0.427311	−	0.904105i	$-0.359461\pi$
$113$	9.08476			0.854623			0.427311	+	0.904105i	$0.359461\pi$
$114$		0			0
$115$	0.279401	−	0.161312i	0.0260543	−	0.0150425i
$116$	−3.10455	+	3.38295i	−0.288250	+	0.314099i
$117$		0			0
$118$	−2.30668	+	0.354151i	−0.212347	+	0.0326023i
$119$	1.29795	+	0.425096i	0.118983	+	0.0389685i
$120$		0			0
$121$	0.972397	−	1.68424i	0.0883997	−	0.153113i
$122$	1.12776	+	1.40623i	0.102103	+	0.127314i
$123$		0			0
$124$	0.916099	−	4.11772i	0.0822681	−	0.369782i
$125$		−	0.464347i		−	0.0415324i
$126$		0			0
$127$	14.1059			1.25170			0.625849	−	0.779944i	$-0.284753\pi$
$127$	14.1059			1.25170			0.625849	+	0.779944i	$0.284753\pi$
$128$	−9.68751	+	5.84398i	−0.856263	+	0.516540i
$129$		0			0
$130$	−0.322514	+	0.258647i	−0.0282863	+	0.0226849i
$131$	−14.8183	−	8.55535i	−1.29468	−	0.747484i	−0.315200	−	0.949025i	$-0.602072\pi$
$131$	−14.8183	−	8.55535i	−1.29468	−	0.747484i	−0.979480	+	0.201541i	$0.935405\pi$
$132$		0			0
$133$	−8.39630	+	1.76413i	−0.728052	+	0.152970i
$134$	10.8525	−	1.66622i	0.937516	−	0.143940i
$135$		0			0
$136$	0.812542	−	1.21311i	0.0696749	−	0.104024i
$137$	−2.48594	−	4.30578i	−0.212388	−	0.367867i	0.740073	−	0.672526i	$-0.234791\pi$
$137$	−2.48594	−	4.30578i	−0.212388	−	0.367867i	−0.952462	+	0.304659i	$0.901458\pi$
$138$		0			0
$139$		−	5.20468i		−	0.441455i	−0.975335	−	0.220728i	$-0.929157\pi$
$139$		−	5.20468i		−	0.441455i	0.975335	−	0.220728i	$-0.0708432\pi$
$140$	−0.211370	−	0.125387i	−0.0178640	−	0.0105972i
$141$		0			0
$142$	−15.5930	−	6.07047i	−1.30853	−	0.509422i
$143$	11.3228	+	19.6117i	0.946862	+	1.64001i
$144$		0			0
$145$	−0.0533136	+	0.0923419i	−0.00442746	+	0.00766858i
$146$	2.39092	+	15.5727i	0.197874	+	1.28880i
$147$		0			0
$148$	0.780933	+	2.48326i	0.0641923	+	0.204123i
$149$	−0.725874	−	0.419084i	−0.0594659	−	0.0343327i	0.469972	−	0.882681i	$-0.344264\pi$
$149$	−0.725874	−	0.419084i	−0.0594659	−	0.0343327i	−0.529438	+	0.848349i	$0.677597\pi$
$150$		0			0
$151$	−3.21803	−	5.57379i	−0.261879	−	0.453588i	0.704862	−	0.709345i	$-0.251009\pi$
$151$	−3.21803	−	5.57379i	−0.261879	−	0.453588i	−0.966741	+	0.255756i	$0.917676\pi$
$152$	−0.610117	+	9.15169i	−0.0494870	+	0.742300i
$153$		0			0
$154$	−8.54581	+	10.4017i	−0.688641	+	0.838197i
$155$		−	0.0979610i		−	0.00786842i
$156$		0			0
$157$	4.73349	−	2.73288i	0.377774	−	0.218108i	−0.299075	−	0.954229i	$-0.596678\pi$
$157$	4.73349	−	2.73288i	0.377774	−	0.218108i	0.676849	+	0.736122i	$0.263345\pi$
$158$	−6.06979	+	4.86780i	−0.482887	+	0.387262i
$159$		0			0
$160$	−0.190126	+	0.181328i	−0.0150308	+	0.0143352i
$161$	3.77897	+	17.9858i	0.297825	+	1.41748i
$162$		0			0
$163$	13.2105	+	7.62708i	1.03473	+	0.597399i	0.918335	−	0.395805i	$-0.129534\pi$
$163$	13.2105	+	7.62708i	1.03473	+	0.597399i	0.116390	+	0.993204i	$0.462868\pi$
$164$	−15.0130	−	13.7775i	−1.17232	−	1.07584i
$165$		0			0
$166$	4.23287	−	10.8728i	0.328534	−	0.843893i
$167$	1.77463			0.137325			0.0686625	−	0.997640i	$-0.478127\pi$
$167$	1.77463			0.137325			0.0686625	+	0.997640i	$0.478127\pi$
$168$		0			0
$169$	−26.6163			−2.04741
$170$	0.0123009	−	0.0315968i	0.000943435	−	0.00242336i
$171$		0			0
$172$	12.3350	−	13.4411i	0.940533	−	1.02488i
$173$	−2.23631	−	1.29114i	−0.170024	−	0.0981633i	0.412573	−	0.910924i	$-0.364630\pi$
$173$	−2.23631	−	1.29114i	−0.170024	−	0.0981633i	−0.582597	+	0.812761i	$0.697963\pi$
$174$		0			0
$175$	12.5663	+	4.11561i	0.949920	+	0.311111i
$176$	8.23706	+	11.8012i	0.620892	+	0.889546i
$177$		0			0
$178$	16.2888	−	13.0632i	1.22090	−	0.979127i
$179$	17.0438	−	9.84027i	1.27392	−	0.735496i	0.298194	−	0.954505i	$-0.403616\pi$
$179$	17.0438	−	9.84027i	1.27392	−	0.735496i	0.975723	+	0.219009i	$0.0702824\pi$
$180$		0			0
$181$			25.5613i			1.89996i	0.312315	+	0.949979i	$0.398896\pi$
$181$			25.5613i			1.89996i	−0.312315	+	0.949979i	$0.601104\pi$
$182$	−8.28390	−	22.0455i	−0.614043	−	1.63412i
$183$		0			0
$184$	19.6040	+	1.30694i	1.44522	+	0.0963488i
$185$	0.0302257	+	0.0523525i	0.00222224	+	0.00384903i
$186$		0			0
$187$	−1.60847	−	0.928652i	−0.117623	−	0.0679098i
$188$	8.87032	−	2.78953i	0.646934	−	0.203447i
$189$		0			0
$190$	0.0323231	+	0.210529i	0.00234496	+	0.0152734i
$191$	−6.98804	+	12.1036i	−0.505637	+	0.875788i	0.494342	+	0.869267i	$0.335409\pi$
$191$	−6.98804	+	12.1036i	−0.505637	+	0.875788i	−0.999979	+	0.00652098i	$0.997924\pi$
$192$		0			0
$193$	9.00706	+	15.6007i	0.648342	+	1.12296i	0.983519	+	0.180806i	$0.0578707\pi$
$193$	9.00706	+	15.6007i	0.648342	+	1.12296i	−0.335176	+	0.942155i	$0.608796\pi$
$194$	−8.12418	−	3.16281i	−0.583282	−	0.227076i
$195$		0			0
$196$	10.5356	−	9.21958i	0.752545	−	0.658541i
$197$		−	3.70082i		−	0.263672i	−0.991272	−	0.131836i	$-0.957913\pi$
$197$		−	3.70082i		−	0.263672i	0.991272	−	0.131836i	$-0.0420873\pi$
$198$		0			0
$199$	0.882192	+	1.52800i	0.0625369	+	0.108317i	0.895599	−	0.444863i	$-0.146748\pi$
$199$	0.882192	+	1.52800i	0.0625369	+	0.108317i	−0.833062	+	0.553180i	$0.813414\pi$
$200$	7.86670	−	11.7449i	0.556260	−	0.830489i
$201$		0			0
$202$	−11.1932	+	1.71852i	−0.787549	+	0.120915i
$203$	−4.05377	−	4.52344i	−0.284519	−	0.317483i
$204$		0			0
$205$	−0.409799	−	0.236597i	−0.0286216	−	0.0165247i
$206$	14.2060	−	11.3928i	0.989776	−	0.793772i
$207$		0			0
$208$	−25.0840	+	2.15687i	−1.73927	+	0.149552i
$209$	11.6672			0.807038
$210$		0			0
$211$			10.6757i			0.734945i	0.930034	+	0.367473i	$0.119777\pi$
$211$			10.6757i			0.734945i	−0.930034	+	0.367473i	$0.880223\pi$
$212$	11.0849	+	2.46614i	0.761316	+	0.169375i
$213$		0			0
$214$	9.03975	+	11.2719i	0.617944	+	0.770531i
$215$	0.211825	−	0.366892i	0.0144464	−	0.0250218i
$216$		0			0
$217$	5.30323	+	1.73688i	0.360007	+	0.117907i
$218$	−16.3467	+	2.50975i	−1.10714	+	0.169982i
$219$		0			0
$220$	0.246234	+	0.225970i	0.0166011	+	0.0152349i
$221$	2.81386	−	1.62459i	0.189281	−	0.109281i
$222$		0			0
$223$	−22.2212			−1.48804			−0.744020	−	0.668158i	$-0.767083\pi$
$223$	−22.2212			−1.48804			−0.744020	+	0.668158i	$0.767083\pi$
$224$	−6.44540	−	13.5077i	−0.430651	−	0.902518i
$225$		0			0
$226$	11.9725	+	4.66099i	0.796400	+	0.310045i
$227$	−17.0728	+	9.85697i	−1.13316	+	0.654230i	−0.944728	−	0.327856i	$-0.893674\pi$
$227$	−17.0728	+	9.85697i	−1.13316	+	0.654230i	−0.188432	+	0.982086i	$0.560340\pi$
$228$		0			0
$229$	−6.06806	−	3.50340i	−0.400989	−	0.231511i	0.285922	−	0.958253i	$-0.407700\pi$
$229$	−6.06806	−	3.50340i	−0.400989	−	0.231511i	−0.686911	+	0.726742i	$0.741034\pi$
$230$	0.450976	−	0.0692397i	0.0297365	−	0.00456553i
$231$		0			0
$232$	−5.82703	+	2.86547i	−0.382563	+	0.188128i
$233$	−12.3717	+	21.4284i	−0.810495	+	1.40382i	0.102023	+	0.994782i	$0.467468\pi$
$233$	−12.3717	+	21.4284i	−0.810495	+	1.40382i	−0.912518	+	0.409036i	$0.865865\pi$
$234$		0			0
$235$	0.187006	−	0.107968i	0.0121989	−	0.00704303i
$236$	−3.22159	−	0.716731i	−0.209708	−	0.0466552i
$237$		0			0
$238$	1.49243	+	1.22614i	0.0967399	+	0.0794790i
$239$	−21.9503			−1.41985			−0.709924	−	0.704278i	$-0.751271\pi$
$239$	−21.9503			−1.41985			−0.709924	+	0.704278i	$0.751271\pi$
$240$		0			0
$241$	7.39162	+	12.8027i	0.476136	+	0.824692i	0.999626	−	0.0273397i	$-0.00870359\pi$
$241$	7.39162	+	12.8027i	0.476136	+	0.824692i	−0.523490	+	0.852032i	$0.675370\pi$
$242$	2.14560	−	1.72071i	0.137924	−	0.110612i
$243$		0			0
$244$	0.764761	+	2.43183i	0.0489588	+	0.155682i
$245$	0.192327	−	0.262123i	0.0122873	−	0.0167464i
$246$		0			0
$247$	−10.2053	+	17.6761i	−0.649349	+	1.12471i
$248$	3.31992	−	4.95660i	0.210815	−	0.314744i
$249$		0			0
$250$	0.238236	−	0.611947i	0.0150674	−	0.0387029i
$251$			14.4785i			0.913876i	0.889499	+	0.456938i	$0.151054\pi$
$251$			14.4785i			0.913876i	−0.889499	+	0.456938i	$0.848946\pi$
$252$		0			0
$253$		−	24.9925i		−	1.57126i
$254$	18.5897	+	7.23713i	1.16642	+	0.454098i
$255$		0			0
$256$	−15.7651	+	2.73135i	−0.985321	+	0.170710i
$257$	7.93731	−	13.7478i	0.495116	−	0.857566i	−0.504868	−	0.863196i	$-0.668459\pi$
$257$	7.93731	−	13.7478i	0.495116	−	0.857566i	0.999984	+	0.00563049i	$0.00179225\pi$
$258$		0			0
$259$	−3.37007	+	0.708080i	−0.209406	+	0.0439980i
$260$	−0.557731	+	0.175395i	−0.0345890	+	0.0108775i
$261$		0			0
$262$	−15.1392	−	18.8774i	−0.935301	−	1.16625i
$263$	0.162710	+	0.281822i	0.0100331	+	0.0173779i	0.870998	−	0.491286i	$-0.163473\pi$
$263$	0.162710	+	0.281822i	0.0100331	+	0.0173779i	−0.860965	+	0.508664i	$0.830140\pi$
$264$		0			0
$265$	0.263712			0.0161997
$266$	−11.9703	−	1.98288i	−0.733947	−	0.121578i
$267$		0			0
$268$	15.1571	+	3.37210i	0.925864	+	0.205984i
$269$	20.3761	−	11.7642i	1.24235	−	0.717273i	0.272780	−	0.962076i	$-0.412057\pi$
$269$	20.3761	−	11.7642i	1.24235	−	0.717273i	0.969573	+	0.244803i	$0.0787234\pi$
$270$		0			0
$271$	−0.751567	+	1.30175i	−0.0456544	+	0.0790758i	−0.887950	−	0.459941i	$-0.847871\pi$
$271$	−0.751567	+	1.30175i	−0.0456544	+	0.0790758i	0.842295	+	0.539017i	$0.181204\pi$
$272$	1.69322	−	1.18184i	0.102666	−	0.0716598i
$273$		0			0
$274$	−1.06703	−	6.94987i	−0.0644619	−	0.419857i
$275$	−15.5726	−	8.99084i	−0.939062	−	0.542168i
$276$		0			0
$277$	12.6685	−	7.31418i	0.761178	−	0.439466i	−0.0685405	−	0.997648i	$-0.521834\pi$
$277$	12.6685	−	7.31418i	0.761178	−	0.439466i	0.829719	+	0.558182i	$0.188501\pi$
$278$	2.67030	−	6.85908i	0.160154	−	0.411380i
$279$		0			0
$280$	−0.214226	−	0.273688i	−0.0128025	−	0.0163560i
$281$	−21.3285			−1.27235			−0.636175	−	0.771545i	$-0.719484\pi$
$281$	−21.3285			−1.27235			−0.636175	+	0.771545i	$0.719484\pi$
$282$		0			0
$283$	−15.0068	+	8.66416i	−0.892059	+	0.515031i	−0.874616	−	0.484817i	$-0.838886\pi$
$283$	−15.0068	+	8.66416i	−0.892059	+	0.515031i	−0.0174438	+	0.999848i	$0.505553\pi$
$284$	−17.4350	−	16.0001i	−1.03457	−	0.949434i
$285$		0			0
$286$	4.86007	+	31.6549i	0.287382	+	1.87179i
$287$	20.0743	−	17.9900i	1.18495	−	1.06191i
$288$		0			0
$289$	8.36676	−	14.4917i	0.492162	−	0.852450i
$290$	−0.117637	+	0.0943415i	−0.00690787	+	0.00553992i
$291$		0			0
$292$	−4.83874	+	21.7494i	−0.283166	+	1.27279i
$293$			29.6927i			1.73466i	0.497730	+	0.867332i	$0.334167\pi$
$293$			29.6927i			1.73466i	−0.497730	+	0.867332i	$0.665833\pi$
$294$		0			0
$295$	−0.0766421			−0.00446228
$296$	−0.244886	+	3.67327i	−0.0142337	+	0.213504i
$297$		0			0
$298$	−0.741592	−	0.924710i	−0.0429593	−	0.0535670i
$299$	37.8643	+	21.8609i	2.18975	+	1.26425i
$300$		0			0
$301$	16.1064	+	17.9725i	0.928358	+	1.03592i
$302$	−1.38127	−	8.99654i	−0.0794829	−	0.517693i
$303$		0			0
$304$	−5.49939	+	11.7477i	−0.315411	+	0.673776i
$305$	0.0295998	+	0.0512683i	0.00169488	+	0.00293562i
$306$		0			0
$307$			4.88243i			0.278655i	0.990246	+	0.139327i	$0.0444940\pi$
$307$			4.88243i			0.278655i	−0.990246	+	0.139327i	$0.955506\pi$
$308$	−16.5989	+	9.32364i	−0.945811	+	0.531264i
$309$		0			0
$310$	0.0502595	−	0.129100i	0.00285455	−	0.00733236i
$311$	9.08277	+	15.7318i	0.515036	+	0.892069i	0.999848	+	0.0174504i	$0.00555493\pi$
$311$	9.08277	+	15.7318i	0.515036	+	0.892069i	−0.484811	+	0.874619i	$0.661112\pi$
$312$		0			0
$313$	6.80533	−	11.7872i	0.384660	−	0.666251i	−0.607062	−	0.794655i	$-0.707652\pi$
$313$	6.80533	−	11.7872i	0.384660	−	0.666251i	0.991722	+	0.128404i	$0.0409853\pi$
$314$	7.64023	−	1.17303i	0.431163	−	0.0661978i
$315$		0			0
$316$	−10.4966	+	3.30097i	−0.590482	+	0.185694i
$317$	−21.6407	−	12.4943i	−1.21546	−	0.701749i	−0.251520	−	0.967852i	$-0.580930\pi$
$317$	−21.6407	−	12.4943i	−1.21546	−	0.701749i	−0.963944	+	0.266103i	$0.914264\pi$
$318$		0			0
$319$	4.13000	+	7.15336i	0.231235	+	0.400511i
$320$	−0.343592	+	0.141421i	−0.0192074	+	0.00790565i
$321$		0			0
$322$	−4.24756	+	25.6417i	−0.236707	+	1.42896i
$323$		−	1.67400i		−	0.0931437i
$324$		0			0
$325$	27.2427	−	15.7286i	1.51115	−	0.872465i
$326$	13.4965	+	16.8292i	0.747504	+	0.932083i
$327$		0			0
$328$	−12.7165	−	25.8594i	−0.702152	−	1.42785i
$329$	2.52929	+	12.0380i	0.139445	+	0.663679i
$330$		0			0
$331$	6.34783	+	3.66492i	0.348908	+	0.201442i	0.664204	−	0.747551i	$-0.268771\pi$
$331$	6.34783	+	3.66492i	0.348908	+	0.201442i	−0.315296	+	0.948993i	$0.602104\pi$
$332$	11.1567	−	12.1572i	0.612304	−	0.667213i
$333$		0			0
$334$	2.33873	+	0.910486i	0.127969	+	0.0498196i
$335$	0.360588			0.0197010
$336$		0			0
$337$	1.49107			0.0812237			0.0406118	−	0.999175i	$-0.487069\pi$
$337$	1.49107			0.0812237			0.0406118	+	0.999175i	$0.487069\pi$
$338$	−35.0768	−	13.6557i	−1.90793	−	0.742771i
$339$		0			0
$340$	0.0324219	−	0.0353293i	0.00175832	−	0.00191600i
$341$	−6.57197	−	3.79433i	−0.355892	−	0.205474i
$342$		0			0
$343$	10.7803	+	15.0594i	0.582083	+	0.813129i
$344$	23.1519	−	11.3851i	1.24827	−	0.613842i
$345$		0			0
$346$	−2.28474	−	2.84890i	−0.122828	−	0.153158i
$347$	−20.6494	+	11.9219i	−1.10852	+	0.640003i	−0.938445	−	0.345428i	$-0.887734\pi$
$347$	−20.6494	+	11.9219i	−1.10852	+	0.640003i	−0.170073	+	0.985431i	$0.554400\pi$
$348$		0			0
$349$		−	11.5733i		−	0.619504i	−0.950817	−	0.309752i	$-0.899754\pi$
$349$		−	11.5733i		−	0.619504i	0.950817	−	0.309752i	$-0.100246\pi$
$350$	14.4491	+	11.8710i	0.772338	+	0.634533i
$351$		0			0
$352$	4.80069	+	19.7784i	0.255877	+	1.05419i
$353$	5.01488	+	8.68603i	0.266915	+	0.462311i	0.968064	−	0.250705i	$-0.0806623\pi$
$353$	5.01488	+	8.68603i	0.266915	+	0.462311i	−0.701148	+	0.713015i	$0.747329\pi$
$354$		0			0
$355$	−0.475909	−	0.274766i	−0.0252586	−	0.0145831i
$356$	28.1687	−	8.85845i	1.49294	−	0.469497i
$357$		0			0
$358$	27.5101	−	4.22371i	1.45396	−	0.223230i
$359$	1.80639	−	3.12876i	0.0953375	−	0.165129i	−0.814412	−	0.580287i	$-0.802940\pi$
$359$	1.80639	−	3.12876i	0.0953375	−	0.165129i	0.909749	+	0.415158i	$0.136274\pi$
$360$		0			0
$361$	−4.24214	−	7.34760i	−0.223271	−	0.386716i
$362$	−13.1144	+	33.6864i	−0.689277	+	1.77052i
$363$		0			0
$364$	0.393529	−	33.3032i	0.0206265	−	1.74556i
$365$			0.517420i			0.0270830i
$366$		0			0
$367$	−11.0055	−	19.0620i	−0.574480	−	0.995029i	−0.996098	−	0.0882554i	$-0.971871\pi$
$367$	−11.0055	−	19.0620i	−0.574480	−	0.995029i	0.421617	−	0.906774i	$-0.361463\pi$
$368$	25.1649	+	11.7803i	1.31181	+	0.614091i
$369$		0			0
$370$	0.0129737	+	0.0845012i	0.000674471	+	0.00439301i
$371$	−4.67568	+	14.2763i	−0.242749	+	0.741190i
$372$		0			0
$373$	−27.9915	−	16.1609i	−1.44934	−	0.836780i	−0.450903	−	0.892573i	$-0.648898\pi$
$373$	−27.9915	−	16.1609i	−1.44934	−	0.836780i	−0.998442	+	0.0557935i	$0.982231\pi$
$374$	−1.64330	−	2.04908i	−0.0849731	−	0.105955i
$375$		0			0
$376$	13.1211	+	0.874744i	0.676668	+	0.0451115i
$377$	−14.4500			−0.744215
$378$		0			0
$379$			16.6668i			0.856115i	0.903751	+	0.428058i	$0.140802\pi$
$379$			16.6668i			0.856115i	−0.903751	+	0.428058i	$0.859198\pi$
$380$	−0.0654155	+	0.294032i	−0.00335575	+	0.0150835i
$381$		0			0
$382$	−15.4192	+	12.3657i	−0.788912	+	0.632686i
$383$	12.1998	−	21.1307i	0.623383	−	1.07973i	−0.365468	−	0.930824i	$-0.619091\pi$
$383$	12.1998	−	21.1307i	0.623383	−	1.07973i	0.988851	−	0.148907i	$-0.0475755\pi$
$384$		0			0
$385$	−0.329246	+	0.295060i	−0.0167799	+	0.0150377i
$386$	3.86608	+	25.1808i	0.196778	+	1.28167i
$387$		0			0
$388$	−9.08389	−	8.33632i	−0.461164	−	0.423213i
$389$	−7.38356	+	4.26290i	−0.374362	+	0.216138i	−0.675362	−	0.737486i	$-0.736013\pi$
$389$	−7.38356	+	4.26290i	−0.374362	+	0.216138i	0.301001	+	0.953624i	$0.402679\pi$
$390$		0			0
$391$	−3.58589			−0.181346
$392$	18.6147	−	6.74481i	0.940185	−	0.340664i
$393$		0			0
$394$	1.89873	−	4.87719i	0.0956565	−	0.245709i
$395$	−0.221292	+	0.127763i	−0.0111344	+	0.00642845i
$396$		0			0
$397$	−5.91805	−	3.41679i	−0.297019	−	0.171484i	0.344084	−	0.938939i	$-0.388189\pi$
$397$	−5.91805	−	3.41679i	−0.297019	−	0.171484i	−0.641103	+	0.767455i	$0.721523\pi$
$398$	0.378661	+	2.46632i	0.0189806	+	0.123625i
$399$		0			0
$400$	16.3931	−	11.4421i	0.819653	−	0.572107i
$401$	−5.24408	+	9.08301i	−0.261877	+	0.453584i	−0.966741	−	0.255759i	$-0.917675\pi$
$401$	−5.24408	+	9.08301i	−0.261877	+	0.453584i	0.704864	+	0.709343i	$0.251008\pi$
$402$		0			0
$403$	11.4970	−	6.63780i	0.572707	−	0.330652i
$404$	−15.6328	−	3.47794i	−0.777761	−	0.173034i
$405$		0			0
$406$	−3.02155	−	8.04110i	−0.149957	−	0.399073i
$407$	4.68294			0.232125
$408$		0			0
$409$	−4.01466	−	6.95360i	−0.198512	−	0.343833i	0.749534	−	0.661966i	$-0.230278\pi$
$409$	−4.01466	−	6.95360i	−0.198512	−	0.343833i	−0.948046	+	0.318133i	$0.896944\pi$
$410$	−0.418672	−	0.522054i	−0.0206768	−	0.0257824i
$411$		0			0
$412$	24.5667	−	7.72571i	1.21031	−	0.380618i
$413$	1.35888	−	4.14911i	0.0668663	−	0.204164i
$414$		0			0
$415$	0.191591	−	0.331846i	0.00940485	−	0.0162897i
$416$	−34.1640	−	10.0271i	−1.67503	−	0.491617i
$417$		0			0
$418$	15.3758	+	5.98594i	0.752057	+	0.292782i
$419$		−	16.7264i		−	0.817139i	−0.912727	−	0.408570i	$-0.866028\pi$
$419$		−	16.7264i		−	0.817139i	0.912727	−	0.408570i	$-0.133972\pi$
$420$		0			0
$421$		−	14.7157i		−	0.717199i	−0.933492	−	0.358599i	$-0.883254\pi$
$421$		−	14.7157i		−	0.717199i	0.933492	−	0.358599i	$-0.116746\pi$
$422$	−5.47723	+	14.0691i	−0.266627	+	0.684875i
$423$		0			0
$424$	13.3432	+	8.93724i	0.648003	+	0.434031i
$425$	−1.28999	+	2.23434i	−0.0625739	+	0.108381i
$426$		0			0
$427$	−3.30028	+	0.693416i	−0.159712	+	0.0335568i
$428$	6.13006	+	19.4928i	0.296308	+	0.942218i
$429$		0			0
$430$	0.467394	−	0.374837i	0.0225397	−	0.0180762i
$431$	−1.57036	−	2.71995i	−0.0756416	−	0.131015i	0.825723	−	0.564075i	$-0.190767\pi$
$431$	−1.57036	−	2.71995i	−0.0756416	−	0.131015i	−0.901365	+	0.433060i	$0.857434\pi$
$432$		0			0
$433$	33.6748			1.61831			0.809155	−	0.587595i	$-0.199925\pi$
$433$	33.6748			1.61831			0.809155	+	0.587595i	$0.199925\pi$
$434$	6.09784	+	5.00983i	0.292706	+	0.240479i
$435$		0			0
$436$	−22.8304	−	5.07924i	−1.09338	−	0.243251i
$437$	19.5080	−	11.2629i	0.933192	−	0.538779i
$438$		0			0
$439$	3.68016	−	6.37423i	0.175645	−	0.304225i	−0.764740	−	0.644340i	$-0.777132\pi$
$439$	3.68016	−	6.37423i	0.175645	−	0.304225i	0.940384	+	0.340114i	$0.110466\pi$
$440$	0.208568	+	0.424130i	0.00994310	+	0.0202196i
$441$		0			0
$442$	4.54180	−	0.697317i	0.216032	−	0.0331680i
$443$	22.3955	+	12.9300i	1.06404	+	0.614325i	0.926547	−	0.376178i	$-0.122762\pi$
$443$	22.3955	+	12.9300i	1.06404	+	0.614325i	0.137494	+	0.990503i	$0.456095\pi$
$444$		0			0
$445$	0.593857	−	0.342863i	0.0281515	−	0.0162533i
$446$	−29.2845	−	11.4007i	−1.38666	−	0.539839i
$447$		0			0
$448$	−1.56399	−	21.1081i	−0.0738914	−	0.997266i
$449$	19.7508			0.932096			0.466048	−	0.884759i	$-0.345677\pi$
$449$	19.7508			0.932096			0.466048	+	0.884759i	$0.345677\pi$
$450$		0			0
$451$	−31.7455	+	18.3283i	−1.49484	+	0.863044i
$452$	13.3868	+	12.2851i	0.629663	+	0.577844i
$453$		0			0
$454$	−27.5568	+	4.23088i	−1.29331	+	0.198565i
$455$	−0.159032	−	0.756906i	−0.00745555	−	0.0354843i
$456$		0			0
$457$	−1.28552	+	2.22658i	−0.0601339	+	0.104155i	−0.894525	−	0.447018i	$-0.852486\pi$
$457$	−1.28552	+	2.22658i	−0.0601339	+	0.104155i	0.834391	+	0.551173i	$0.185819\pi$
$458$	−6.19946	−	7.73027i	−0.289682	−	0.361212i
$459$		0			0
$460$	0.629850	+	0.140127i	0.0293669	+	0.00653347i
$461$		−	30.2081i		−	1.40693i	−0.710728	−	0.703467i	$-0.751634\pi$
$461$		−	30.2081i		−	1.40693i	0.710728	−	0.703467i	$-0.248366\pi$
$462$		0			0
$463$	−20.1707			−0.937412			−0.468706	−	0.883354i	$-0.655280\pi$
$463$	−20.1707			−0.937412			−0.468706	+	0.883354i	$0.655280\pi$
$464$	−9.14940	+	0.786718i	−0.424750	+	0.0365225i
$465$		0			0
$466$	−27.2982	+	21.8924i	−1.26456	+	1.01414i
$467$	−7.99333	−	4.61495i	−0.369887	−	0.213554i	0.303522	−	0.952824i	$-0.401837\pi$
$467$	−7.99333	−	4.61495i	−0.369887	−	0.213554i	−0.673409	+	0.739270i	$0.735171\pi$
$468$		0			0
$469$	−6.39332	+	19.5208i	−0.295216	+	0.901389i
$470$	0.301842	−	0.0463427i	0.0139229	−	0.00213763i
$471$		0			0
$472$	−3.87791	−	2.59742i	−0.178495	−	0.119556i
$473$	−16.4093	−	28.4217i	−0.754499	−	1.30683i
$474$		0			0
$475$		−	16.2070i		−	0.743627i
$476$	1.33774	+	2.38159i	0.0613154	+	0.109160i
$477$		0			0
$478$	−28.9276	−	11.2617i	−1.32312	−	0.515100i
$479$	−19.6055	−	33.9577i	−0.895797	−	1.55157i	−0.832815	−	0.553551i	$-0.813272\pi$
$479$	−19.6055	−	33.9577i	−0.895797	−	1.55157i	−0.0629820	−	0.998015i	$-0.520061\pi$
$480$		0			0
$481$	−4.09617	+	7.09477i	−0.186769	+	0.323494i
$482$	3.17269	+	20.6645i	0.144512	+	0.941243i
$483$		0			0
$484$	3.71044	−	1.16685i	0.168656	−	0.0530389i
$485$	−0.247956	−	0.143157i	−0.0112591	−	0.00650045i
$486$		0			0
$487$	−3.06454	−	5.30794i	−0.138868	−	0.240526i	0.788201	−	0.615418i	$-0.211013\pi$
$487$	−3.06454	−	5.30794i	−0.138868	−	0.240526i	−0.927068	+	0.374893i	$0.877680\pi$
$488$	−0.239815	+	3.59720i	−0.0108559	+	0.162838i
$489$		0			0
$490$	0.387946	−	0.246769i	0.0175256	−	0.0111479i
$491$		−	20.5291i		−	0.926463i	−0.886237	−	0.463232i	$-0.846690\pi$
$491$		−	20.5291i		−	0.926463i	0.886237	−	0.463232i	$-0.153310\pi$
$492$		0			0
$493$	1.02636	−	0.592567i	0.0462248	−	0.0266879i
$494$	−22.5181	+	18.0589i	−1.01314	+	0.812508i
$495$		0			0
$496$	6.91822	−	4.82883i	0.310637	−	0.216821i
$497$	23.3128	−	20.8922i	1.04572	−	0.937143i
$498$		0			0
$499$	9.57940	+	5.53067i	0.428833	+	0.247587i	0.698849	−	0.715269i	$-0.253696\pi$
$499$	9.57940	+	5.53067i	0.428833	+	0.247587i	−0.270016	+	0.962856i	$0.587029\pi$
$500$	0.627927	−	0.684237i	0.0280817	−	0.0306000i
$501$		0			0
$502$	−7.42829	+	19.0808i	−0.331541	+	0.851616i
$503$	−2.64242			−0.117820			−0.0589099	−	0.998263i	$-0.518762\pi$
$503$	−2.64242			−0.117820			−0.0589099	+	0.998263i	$0.518762\pi$
$504$		0			0
$505$	−0.371906			−0.0165496
$506$	12.8225	−	32.9368i	0.570032	−	1.46422i
$507$		0			0
$508$	20.7857	+	19.0751i	0.922218	+	0.846323i
$509$	28.9903	+	16.7376i	1.28497	+	0.741880i	0.977753	−	0.209758i	$-0.0672678\pi$
$509$	28.9903	+	16.7376i	1.28497	+	0.741880i	0.307220	+	0.951638i	$0.400601\pi$
$510$		0			0
$511$	−28.0111	−	9.17400i	−1.23914	−	0.405834i
$512$	−22.1777	−	4.48885i	−0.980125	−	0.198381i
$513$		0			0
$514$	17.5137	−	14.0455i	0.772498	−	0.619521i
$515$	0.517919	−	0.299021i	0.0228222	−	0.0131764i
$516$		0			0
$517$		−	16.7277i		−	0.735682i
$518$	−4.80459	−	0.795881i	−0.211102	−	0.0349690i
$519$		0			0
$520$	−0.825003	−	0.0550005i	−0.0361788	−	0.00241193i
$521$	−12.4133	−	21.5005i	−0.543837	−	0.941954i	−0.998679	−	0.0513815i	$-0.983638\pi$
$521$	−12.4133	−	21.5005i	−0.543837	−	0.941954i	0.454842	−	0.890572i	$-0.349696\pi$
$522$		0			0
$523$	4.00205	+	2.31058i	0.174997	+	0.101035i	0.584940	−	0.811076i	$-0.301118\pi$
$523$	4.00205	+	2.31058i	0.174997	+	0.101035i	−0.409943	+	0.912111i	$0.634451\pi$
$524$	−10.2662	−	32.6452i	−0.448482	−	1.42611i
$525$		0			0
$526$	0.0698396	+	0.454883i	0.00304515	+	0.0198338i
$527$	−0.544406	+	0.942938i	−0.0237147	+	0.0410750i
$528$		0			0
$529$	−12.6264	−	21.8696i	−0.548976	−	0.950854i
$530$	0.347537	+	0.135299i	0.0150960	+	0.00587701i
$531$		0			0
$532$	−14.7579	−	8.75462i	−0.639838	−	0.379561i
$533$		−	64.1270i		−	2.77765i
$534$		0			0
$535$	0.237262	+	0.410950i	0.0102577	+	0.0177669i
$536$	18.2449	+	12.2204i	0.788060	+	0.527841i
$537$		0			0
$538$	32.8887	−	5.04950i	1.41793	−	0.217699i
$539$	−10.1358	−	23.0556i	−0.436580	−	0.993075i
$540$		0			0
$541$	−21.7241	−	12.5424i	−0.933992	−	0.539241i	−0.0459203	−	0.998945i	$-0.514622\pi$
$541$	−21.7241	−	12.5424i	−0.933992	−	0.539241i	−0.888072	+	0.459704i	$0.847955\pi$
$542$	−1.65834	+	1.32994i	−0.0712317	+	0.0571258i
$543$		0			0
$544$	2.83779	−	0.688797i	0.121669	−	0.0295319i
$545$	−0.543137			−0.0232654
$546$		0			0
$547$			38.8014i			1.65903i	0.558487	+	0.829514i	$0.311382\pi$
$547$			38.8014i			1.65903i	−0.558487	+	0.829514i	$0.688618\pi$
$548$	2.15947	−	9.70645i	0.0922478	−	0.414639i
$549$		0			0
$550$	−15.9098	−	19.8383i	−0.678396	−	0.845910i
$551$	−3.72239	+	6.44736i	−0.158579	+	0.274667i
$552$		0			0
$553$	−2.99303	−	14.2452i	−0.127276	−	0.605766i
$554$	20.4480	−	3.13945i	0.868753	−	0.133382i
$555$		0			0
$556$	7.03819	−	7.66934i	0.298486	−	0.325253i
$557$	−27.2335	+	15.7233i	−1.15392	+	0.666217i	−0.949840	−	0.312737i	$-0.898754\pi$
$557$	−27.2335	+	15.7233i	−1.15392	+	0.666217i	−0.204082	+	0.978954i	$0.565421\pi$
$558$		0			0
$559$	57.4128			2.42830
$560$	−0.141904	−	0.470595i	−0.00599654	−	0.0198863i
$561$		0			0
$562$	−28.1081	−	10.9427i	−1.18567	−	0.461590i
$563$	−9.22107	+	5.32379i	−0.388622	+	0.224371i	−0.681563	−	0.731760i	$-0.738699\pi$
$563$	−9.22107	+	5.32379i	−0.388622	+	0.224371i	0.292941	+	0.956131i	$0.405366\pi$
$564$		0			0
$565$	0.365410	+	0.210970i	0.0153729	+	0.00887556i
$566$	−24.2221	+	3.71889i	−1.01813	+	0.156317i
$567$		0			0
$568$	−14.7680	−	30.0312i	−0.619651	−	1.26008i
$569$	13.1394	−	22.7581i	0.550832	−	0.954069i	−0.447383	−	0.894343i	$-0.647644\pi$
$569$	13.1394	−	22.7581i	0.550832	−	0.954069i	0.998215	−	0.0597265i	$-0.0190229\pi$
$570$		0			0
$571$	−6.37133	+	3.67849i	−0.266632	+	0.153940i	−0.627356	−	0.778733i	$-0.715863\pi$
$571$	−6.37133	+	3.67849i	−0.266632	+	0.153940i	0.360724	+	0.932673i	$0.382530\pi$
$572$	−9.83580	+	44.2104i	−0.411256	+	1.84853i
$573$		0			0
$574$	35.6851	−	13.4091i	1.48947	−	0.559687i
$575$	−34.7172			−1.44781
$576$		0			0
$577$	6.42935	+	11.1360i	0.267658	+	0.463596i	0.968256	−	0.249959i	$-0.0804171\pi$
$577$	6.42935	+	11.1360i	0.267658	+	0.463596i	−0.700599	+	0.713555i	$0.747084\pi$
$578$	18.4613	−	14.8054i	0.767889	−	0.615825i
$579$		0			0
$580$	−0.203432	+	0.0639752i	−0.00844706	+	0.00265642i
$581$	14.5679	+	16.2557i	0.604378	+	0.674402i
$582$		0			0
$583$	10.2144	−	17.6918i	0.423035	−	0.732719i
$584$	−17.5355	+	26.1802i	−0.725623	+	1.08335i
$585$		0			0
$586$	−15.2340	+	39.1310i	−0.629311	+	1.61649i
$587$			7.51402i			0.310137i	0.987904	+	0.155068i	$0.0495598\pi$
$587$			7.51402i			0.310137i	−0.987904	+	0.155068i	$0.950440\pi$
$588$		0			0
$589$		−	6.83969i		−	0.281825i
$590$	−0.101004	−	0.0393217i	−0.00415827	−	0.00161885i
$591$		0			0
$592$	−2.20732	+	4.71524i	−0.0907204	+	0.193795i
$593$	9.63761	−	16.6928i	0.395769	−	0.685492i	−0.597430	−	0.801921i	$-0.703811\pi$
$593$	9.63761	−	16.6928i	0.395769	−	0.685492i	0.993199	+	0.116429i	$0.0371448\pi$
$594$		0			0
$595$	0.0423349	+	0.0472398i	0.00173556	+	0.00193664i
$596$	−0.502891	−	1.59912i	−0.0205992	−	0.0655027i
$597$		0			0
$598$	38.6842	+	48.2363i	1.58191	+	1.97253i
$599$	−7.76773	−	13.4541i	−0.317381	−	0.549720i	0.662560	−	0.749009i	$-0.269470\pi$
$599$	−7.76773	−	13.4541i	−0.317381	−	0.549720i	−0.979941	+	0.199289i	$0.936137\pi$
$600$		0			0
$601$	−44.5011			−1.81524			−0.907620	−	0.419793i	$-0.862103\pi$
$601$	−44.5011			−1.81524			−0.907620	+	0.419793i	$0.862103\pi$
$602$	12.0052	+	31.9489i	0.489295	+	1.30214i
$603$		0			0
$604$	2.79541	−	12.5649i	0.113744	−	0.511259i
$605$	0.0782241	−	0.0451627i	0.00318026	−	0.00183612i
$606$		0			0
$607$	11.9183	−	20.6432i	0.483751	−	0.837881i	−0.516075	−	0.856543i	$-0.672607\pi$
$607$	11.9183	−	20.6432i	0.483751	−	0.837881i	0.999826	+	0.0186624i	$0.00594079\pi$
$608$	−13.2747	+	12.6604i	−0.538360	+	0.513447i
$609$		0			0
$610$	0.0127050	+	0.0827512i	0.000514412	+	0.00335050i
$611$	25.3428	+	14.6317i	1.02526	+	0.591935i
$612$		0			0
$613$	17.7261	−	10.2342i	0.715950	−	0.413354i	−0.0973099	−	0.995254i	$-0.531024\pi$
$613$	17.7261	−	10.2342i	0.715950	−	0.413354i	0.813260	+	0.581900i	$0.197690\pi$
$614$	−2.50496	+	6.43439i	−0.101092	+	0.259671i
$615$		0			0
$616$	−26.6587	+	3.77114i	−1.07411	+	0.151943i
$617$	−19.3039			−0.777146			−0.388573	−	0.921418i	$-0.627032\pi$
$617$	−19.3039			−0.777146			−0.388573	+	0.921418i	$0.627032\pi$
$618$		0			0
$619$	−21.1475	+	12.2095i	−0.849990	+	0.490742i	−0.860647	−	0.509201i	$-0.829941\pi$
$619$	−21.1475	+	12.2095i	−0.849990	+	0.490742i	0.0106577	+	0.999943i	$0.496607\pi$
$620$	0.132471	−	0.144350i	0.00532015	−	0.00579724i
$621$		0			0
$622$	3.89857	+	25.3924i	0.156319	+	1.01814i
$623$	8.03205	+	38.2282i	0.321797	+	1.53158i
$624$		0			0
$625$	−12.4838	+	21.6226i	−0.499353	+	0.864905i
$626$	15.0160	−	12.0424i	0.600161	−	0.481312i
$627$		0			0
$628$	10.6706	+	2.37398i	0.425805	+	0.0947319i
$629$		−	0.671902i		−	0.0267905i
$630$		0			0
$631$	−20.7613			−0.826494			−0.413247	−	0.910619i	$-0.635605\pi$
$631$	−20.7613			−0.826494			−0.413247	+	0.910619i	$0.635605\pi$
$632$	−15.5268	−	1.03512i	−0.617621	−	0.0411750i
$633$		0			0
$634$	−22.1093	−	27.5687i	−0.878074	−	1.09489i
$635$	0.567372	+	0.327573i	0.0225155	+	0.0129993i
$636$		0			0
$637$	43.7956	+	4.81075i	1.73525	+	0.190609i
$638$	1.77271	+	11.5461i	0.0701822	+	0.457115i
$639$		0			0
$640$	−0.525365	+	0.0100916i	−0.0207669	+	0.000398904i
$641$	11.0483	+	19.1363i	0.436383	+	0.755838i	0.997407	−	0.0719616i	$-0.0229259\pi$
$641$	11.0483	+	19.1363i	0.436383	+	0.755838i	−0.561024	+	0.827799i	$0.689593\pi$
$642$		0			0
$643$		−	31.9358i		−	1.25943i	−0.776828	−	0.629713i	$-0.783173\pi$
$643$		−	31.9358i		−	1.25943i	0.776828	−	0.629713i	$-0.216827\pi$
$644$	−18.7534	+	31.6132i	−0.738986	+	1.24573i
$645$		0			0
$646$	0.858855	−	2.20611i	0.0337912	−	0.0867981i
$647$	1.48741	+	2.57626i	0.0584760	+	0.101283i	0.893781	−	0.448503i	$-0.148043\pi$
$647$	1.48741	+	2.57626i	0.0584760	+	0.101283i	−0.835305	+	0.549786i	$0.814709\pi$
$648$		0			0
$649$	−2.96858	+	5.14173i	−0.116527	+	0.201831i
$650$	43.9719	−	6.75114i	1.72472	−	0.264802i
$651$		0			0
$652$	9.15232	+	29.1031i	0.358433	+	1.13977i
$653$	14.9217	+	8.61507i	0.583933	+	0.337134i	0.762695	−	0.646758i	$-0.223876\pi$
$653$	14.9217	+	8.61507i	0.583933	+	0.337134i	−0.178762	+	0.983892i	$0.557209\pi$
$654$		0			0
$655$	−0.397351	−	0.688231i	−0.0155258	−	0.0268914i
$656$	−3.49133	−	40.6036i	−0.136314	−	1.58530i
$657$		0			0
$658$	−2.84292	+	17.1622i	−0.110829	+	0.669053i
$659$			27.7588i			1.08133i	0.841238	+	0.540665i	$0.181827\pi$
$659$			27.7588i			1.08133i	−0.841238	+	0.540665i	$0.818173\pi$
$660$		0			0
$661$	28.3232	−	16.3524i	1.10164	−	0.636034i	0.164991	−	0.986295i	$-0.447241\pi$
$661$	28.3232	−	16.3524i	1.10164	−	0.636034i	0.936652	+	0.350261i	$0.113907\pi$
$662$	6.48528	+	8.08667i	0.252058	+	0.314297i
$663$		0			0
$664$	20.9404	−	10.2976i	0.812645	−	0.399623i
$665$	−0.378686	−	0.124024i	−0.0146848	−	0.00480946i
$666$		0			0
$667$	13.8110	+	7.97377i	0.534763	+	0.308746i
$668$	2.61500	+	2.39980i	0.101177	+	0.0928510i
$669$		0			0
$670$	0.475207	+	0.185002i	0.0183589	+	0.00714725i
$671$	4.58596			0.177039
$672$		0			0
$673$	12.9387			0.498752			0.249376	−	0.968407i	$-0.419775\pi$
$673$	12.9387			0.498752			0.249376	+	0.968407i	$0.419775\pi$
$674$	1.96503	+	0.765002i	0.0756901	+	0.0294668i
$675$		0			0
$676$	−39.2204	−	35.9927i	−1.50848	−	1.38434i
$677$	−1.12548	−	0.649798i	−0.0432558	−	0.0249738i	0.478216	−	0.878242i	$-0.341284\pi$
$677$	−1.12548	−	0.649798i	−0.0432558	−	0.0249738i	−0.521472	+	0.853268i	$0.674617\pi$
$678$		0			0
$679$	12.1463	−	10.8852i	0.466133	−	0.417734i
$680$	0.0608537	−	0.0299251i	0.00233363	−	0.00114758i
$681$		0			0
$682$	−6.71428	−	8.37221i	−0.257103	−	0.320588i
$683$	−16.8225	+	9.71249i	−0.643696	+	0.371638i	−0.786037	−	0.618179i	$-0.787870\pi$
$683$	−16.8225	+	9.71249i	−0.643696	+	0.371638i	0.142341	+	0.989818i	$0.454537\pi$
$684$		0			0
$685$		−	0.230918i		−	0.00882291i
$686$	6.48073	+	25.3772i	0.247435	+	0.968904i
$687$		0			0
$688$	36.3523	−	3.12578i	1.38592	−	0.119169i
$689$	17.8690	+	30.9500i	0.680755	+	1.17910i
$690$		0			0
$691$	11.1725	+	6.45042i	0.425020	+	0.245386i	0.697223	−	0.716854i	$-0.254419\pi$
$691$	11.1725	+	6.45042i	0.425020	+	0.245386i	−0.272203	+	0.962240i	$0.587752\pi$
$692$	−1.54933	−	4.92667i	−0.0588969	−	0.187284i
$693$		0			0
$694$	−33.3298	+	5.11722i	−1.26518	+	0.194247i
$695$	0.120865	−	0.209344i	0.00458467	−	0.00794088i
$696$		0			0
$697$	2.62972	+	4.55480i	0.0996076	+	0.172526i
$698$	5.93775	−	15.2520i	0.224747	−	0.577299i
$699$		0			0
$700$	12.9515	+	23.0576i	0.489521	+	0.871497i
$701$			34.3868i			1.29877i	0.760460	+	0.649385i	$0.224974\pi$
$701$			34.3868i			1.29877i	−0.760460	+	0.649385i	$0.775026\pi$
$702$		0			0
$703$	2.11038	+	3.65528i	0.0795944	+	0.137862i
$704$	−3.82079	+	28.5284i	−0.144001	+	1.07520i
$705$		0			0
$706$	2.15253	+	14.0200i	0.0810114	+	0.527648i
$707$	6.59400	−	20.1336i	0.247993	−	0.757201i
$708$		0			0
$709$	−19.7915	−	11.4266i	−0.743284	−	0.429135i	0.0799779	−	0.996797i	$-0.474515\pi$
$709$	−19.7915	−	11.4266i	−0.743284	−	0.429135i	−0.823262	+	0.567661i	$0.807848\pi$
$710$	−0.486214	−	0.606274i	−0.0182473	−	0.0227530i
$711$		0			0
$712$	41.6674	+	2.77785i	1.56155	+	0.104104i
$713$	−14.6514			−0.548699
$714$		0			0
$715$			1.05177i			0.0393340i
$716$	38.4217	+	8.54796i	1.43589	+	0.319452i
$717$		0			0
$718$	3.98581	−	3.19650i	0.148749	−	0.119293i
$719$	−5.21620	+	9.03472i	−0.194531	+	0.336938i	−0.946747	−	0.321979i	$-0.895652\pi$
$719$	−5.21620	+	9.03472i	−0.194531	+	0.336938i	0.752215	+	0.658917i	$0.228985\pi$
$720$		0			0
$721$	7.00498	+	33.3399i	0.260879	+	1.24164i
$722$	−1.82084	−	11.8596i	−0.0677648	−	0.441369i
$723$		0			0
$724$	−34.5660	+	37.6658i	−1.28464	+	1.39984i
$725$	9.93677	−	5.73700i	0.369042	−	0.213067i
$726$		0			0
$727$	−2.48753			−0.0922572			−0.0461286	−	0.998936i	$-0.514688\pi$
$727$	−2.48753			−0.0922572			−0.0461286	+	0.998936i	$0.514688\pi$
$728$	17.6050	−	43.6873i	0.652486	−	1.61916i
$729$		0			0
$730$	−0.265466	+	0.681891i	−0.00982533	+	0.0252379i
$731$	−4.07791	+	2.35438i	−0.150827	+	0.0870800i
$732$		0			0
$733$	−0.674033	−	0.389153i	−0.0248960	−	0.0143737i	0.487500	−	0.873123i	$-0.337909\pi$
$733$	−0.674033	−	0.389153i	−0.0248960	−	0.0143737i	−0.512396	+	0.858749i	$0.671242\pi$
$734$	−4.72385	−	30.7676i	−0.174360	−	1.13565i
$735$		0			0
$736$	27.1200	+	28.4359i	0.999656	+	1.04816i
$737$	13.9667	−	24.1910i	0.514469	−	0.891086i
$738$		0			0
$739$	22.4331	−	12.9518i	0.825215	−	0.476438i	−0.0269963	−	0.999636i	$-0.508594\pi$
$739$	22.4331	−	12.9518i	0.825215	−	0.476438i	0.852212	+	0.523197i	$0.175261\pi$
$740$	−0.0262562	+	0.118018i	−0.000965198	+	0.00433841i
$741$		0			0
$742$	−13.4865	+	16.4154i	−0.495104	+	0.602629i
$743$	27.7729			1.01889			0.509445	−	0.860503i	$-0.329851\pi$
$743$	27.7729			1.01889			0.509445	+	0.860503i	$0.329851\pi$
$744$		0			0
$745$	−0.0194642	−	0.0337130i	−0.000713113	−	0.00123515i
$746$	−28.5976	−	35.6591i	−1.04703	−	1.30557i
$747$		0			0
$748$	−1.11436	−	3.54352i	−0.0407451	−	0.129564i
$749$	−26.4539	+	5.55819i	−0.966606	+	0.203092i
$750$		0			0
$751$	−10.5549	+	18.2816i	−0.385153	+	0.667105i	−0.991790	−	0.127874i	$-0.959185\pi$
$751$	−10.5549	+	18.2816i	−0.385153	+	0.667105i	0.606637	+	0.794979i	$0.292518\pi$
$752$	16.8430	+	7.88465i	0.614203	+	0.287524i
$753$		0			0
$754$	−19.0432	−	7.41369i	−0.693514	−	0.269991i
$755$		−	0.298921i		−	0.0108788i
$756$		0			0
$757$			46.6419i			1.69523i	0.530612	+	0.847615i	$0.321962\pi$
$757$			46.6419i			1.69523i	−0.530612	+	0.847615i	$0.678038\pi$
$758$	−8.55100	+	21.9646i	−0.310586	+	0.797790i
$759$		0			0
$760$	−0.237064	+	0.353934i	−0.00859922	+	0.0128385i
$761$	−12.5114	+	21.6703i	−0.453537	+	0.785550i	−0.998603	−	0.0528439i	$-0.983171\pi$
$761$	−12.5114	+	21.6703i	−0.453537	+	0.785550i	0.545066	+	0.838393i	$0.316505\pi$
$762$		0			0
$763$	9.62997	−	29.4034i	0.348628	−	1.06447i
$764$	−26.6647	+	8.38549i	−0.964695	+	0.303376i
$765$		0			0
$766$	26.9190	−	21.5883i	0.972624	−	0.780017i
$767$	−5.19324	−	8.99495i	−0.187517	−	0.324789i
$768$		0			0
$769$	1.32800			0.0478891			0.0239445	−	0.999713i	$-0.492377\pi$
$769$	1.32800			0.0478891			0.0239445	+	0.999713i	$0.492377\pi$
$770$	−0.585285	+	0.219928i	−0.0210922	+	0.00792567i
$771$		0			0
$772$	−7.82417	+	35.1684i	−0.281598	+	1.26574i
$773$	−19.2488	+	11.1133i	−0.692332	+	0.399718i	−0.804485	−	0.593973i	$-0.797559\pi$
$773$	−19.2488	+	11.1133i	−0.692332	+	0.399718i	0.112153	+	0.993691i	$0.464225\pi$
$774$		0			0
$775$	−5.27072	+	9.12915i	−0.189330	+	0.327929i
$776$	−7.69435	−	15.6467i	−0.276211	−	0.561684i
$777$		0			0
$778$	−11.9177	+	1.82975i	−0.427269	+	0.0655999i
$779$	−28.6124	−	16.5194i	−1.02514	−	0.591867i
$780$		0			0
$781$	−36.8668	+	21.2851i	−1.31920	+	0.761639i
$782$	−4.72573	−	1.83976i	−0.168992	−	0.0657898i
$783$		0			0
$784$	27.9922	+	0.661635i	0.999721	+	0.0236298i
$785$	0.253856			0.00906050
$786$		0			0
$787$	−16.5930	+	9.57996i	−0.591476	+	0.341489i	−0.765681	−	0.643221i	$-0.777598\pi$
$787$	−16.5930	+	9.57996i	−0.591476	+	0.341489i	0.174205	+	0.984709i	$0.444264\pi$
$788$	5.00454	−	5.45333i	0.178279	−	0.194267i
$789$		0			0
$790$	−0.357183	+	0.0548394i	−0.0127080	+	0.00195110i
$791$	−17.8999	+	16.0413i	−0.636447	+	0.570364i
$792$		0			0
$793$	−4.01134	+	6.94784i	−0.142447	+	0.246725i
$794$	−6.04620	−	7.53917i	−0.214572	−	0.267555i
$795$		0			0
$796$	−0.766334	+	3.44455i	−0.0271620	+	0.122089i
$797$			35.9779i			1.27440i	0.770697	+	0.637201i	$0.219908\pi$
$797$			35.9779i			1.27440i	−0.770697	+	0.637201i	$0.780092\pi$
$798$		0			0
$799$	−2.40006			−0.0849082
$800$	27.4743	−	6.66866i	0.971364	−	0.235773i
$801$		0			0
$802$	−11.5711	+	9.27969i	−0.408589	+	0.327677i
$803$	34.7125	+	20.0413i	1.22498	+	0.707241i
$804$		0			0
$805$	−0.265674	+	0.811187i	−0.00936378	+	0.0285906i
$806$	18.5571	−	2.84913i	0.653646	−	0.100356i
$807$		0			0
$808$	−18.8176	−	12.6040i	−0.662000	−	0.443406i
$809$	−4.56264	−	7.90272i	−0.160414	−	0.277845i	0.774603	−	0.632447i	$-0.217950\pi$
$809$	−4.56264	−	7.90272i	−0.160414	−	0.277845i	−0.935017	+	0.354603i	$0.884616\pi$
$810$		0			0
$811$		−	9.64051i		−	0.338524i	−0.985571	−	0.169262i	$-0.945862\pi$
$811$		−	9.64051i		−	0.338524i	0.985571	−	0.169262i	$-0.0541384\pi$
$812$	0.143540	−	12.1473i	0.00503725	−	0.426288i
$813$		0			0
$814$	6.17149	+	2.40261i	0.216311	+	0.0842115i
$815$	0.354237	+	0.613557i	0.0124084	+	0.0214920i
$816$		0			0
$817$	14.7898	−	25.6166i	0.517428	−	0.896212i
$818$	−1.72320	−	11.2237i	−0.0602504	−	0.392426i
$819$		0			0
$820$	−0.283912	−	0.902800i	−0.00991462	−	0.0315271i
$821$	−16.6309	−	9.60187i	−0.580423	−	0.335107i	0.180878	−	0.983505i	$-0.442106\pi$
$821$	−16.6309	−	9.60187i	−0.580423	−	0.335107i	−0.761301	+	0.648398i	$0.775439\pi$
$822$		0			0
$823$	0.820157	+	1.42055i	0.0285889	+	0.0495174i	0.879966	−	0.475037i	$-0.157565\pi$
$823$	0.820157	+	1.42055i	0.0285889	+	0.0495174i	−0.851377	+	0.524554i	$0.824232\pi$
$824$	36.3394	+	2.42264i	1.26594	+	0.0843966i
$825$		0			0
$826$	3.91955	−	4.77079i	0.136379	−	0.165997i
$827$			27.3891i			0.952412i	0.879334	+	0.476206i	$0.157988\pi$
$827$			27.3891i			0.952412i	−0.879334	+	0.476206i	$0.842012\pi$
$828$		0			0
$829$	−15.4922	+	8.94441i	−0.538065	+	0.310652i	−0.744294	−	0.667852i	$-0.767214\pi$
$829$	−15.4922	+	8.94441i	−0.538065	+	0.310652i	0.206229	+	0.978504i	$0.433881\pi$
$830$	0.422748	−	0.339032i	0.0146738	−	0.0117680i
$831$		0			0
$832$	−39.8792	−	30.7424i	−1.38256	−	1.06580i
$833$	−3.30799	+	1.45427i	−0.114615	+	0.0503875i
$834$		0			0
$835$	0.0713797	+	0.0412111i	0.00247020	+	0.00142617i
$836$	17.1922	+	15.7773i	0.594604	+	0.545670i
$837$		0			0
$838$	8.58160	−	22.0432i	0.296446	−	0.761470i
$839$	−11.0644			−0.381986			−0.190993	−	0.981591i	$-0.561171\pi$
$839$	−11.0644			−0.381986			−0.190993	+	0.981591i	$0.561171\pi$
$840$		0			0
$841$	23.7294			0.818253
$842$	7.54997	−	19.3933i	0.260189	−	0.668338i
$843$		0			0
$844$	−14.4365	+	15.7311i	−0.496926	+	0.541488i
$845$	−1.07057	−	0.618094i	−0.0368287	−	0.0212631i
$846$		0			0
$847$	1.05800	+	5.03550i	0.0363533	+	0.173022i
$848$	12.9992	+	18.6239i	0.446396	+	0.639547i
$849$		0			0
$850$	−2.84638	+	2.28272i	−0.0976301	+	0.0782966i
$851$	7.83002	−	4.52067i	0.268410	−	0.154966i
$852$		0			0
$853$			29.4621i			1.00876i	0.863480	+	0.504382i	$0.168280\pi$
$853$			29.4621i			1.00876i	−0.863480	+	0.504382i	$0.831720\pi$
$854$	−4.70509	−	0.779399i	−0.161005	−	0.0266705i
$855$		0			0
$856$	−1.92227	+	28.8339i	−0.0657020	+	0.985524i
$857$	8.88103	+	15.3824i	0.303370	+	0.525453i	0.976897	−	0.213710i	$-0.0685548\pi$
$857$	8.88103	+	15.3824i	0.303370	+	0.525453i	−0.673527	+	0.739163i	$0.735221\pi$
$858$		0			0
$859$	31.7456	+	18.3283i	1.08314	+	0.625354i	0.931743	−	0.363118i	$-0.118288\pi$
$859$	31.7456	+	18.3283i	1.08314	+	0.625354i	0.151402	+	0.988472i	$0.451621\pi$
$860$	0.808276	−	0.254186i	0.0275620	−	0.00866766i
$861$		0			0
$862$	−0.674042	−	4.39021i	−0.0229580	−	0.149531i
$863$	−1.57129	+	2.72156i	−0.0534874	+	0.0926429i	−0.891529	−	0.452963i	$-0.850367\pi$
$863$	−1.57129	+	2.72156i	−0.0534874	+	0.0926429i	0.838042	+	0.545606i	$0.183700\pi$
$864$		0			0
$865$	−0.0599664	−	0.103865i	−0.00203892	−	0.00353151i
$866$	44.3790	+	17.2771i	1.50806	+	0.587099i
$867$		0			0
$868$	5.46582	+	9.73082i	0.185522	+	0.330285i
$869$			19.7946i			0.671485i
$870$		0			0
$871$	24.4333	+	42.3197i	0.827891	+	1.43395i
$872$	−27.4815	−	18.4070i	−0.930640	−	0.623341i
$873$		0			0
$874$	31.4874	−	4.83436i	1.06508	−	0.163525i
$875$	0.819916	+	0.914912i	0.0277182	+	0.0309297i
$876$		0			0
$877$	12.4428	+	7.18384i	0.420162	+	0.242581i	0.695147	−	0.718868i	$-0.255339\pi$
$877$	12.4428	+	7.18384i	0.420162	+	0.242581i	−0.274984	+	0.961449i	$0.588673\pi$
$878$	8.12031	−	6.51226i	0.274047	−	0.219778i
$879$		0			0
$880$	0.0572626	+	0.665954i	0.00193032	+	0.0224493i
$881$	21.4314			0.722043			0.361022	−	0.932557i	$-0.382428\pi$
$881$	21.4314			0.722043			0.361022	+	0.932557i	$0.382428\pi$
$882$		0			0
$883$		−	29.5761i		−	0.995316i	−0.867373	−	0.497658i	$-0.834194\pi$
$883$		−	29.5761i		−	0.995316i	0.867373	−	0.497658i	$-0.165806\pi$
$884$	6.34325	+	1.41123i	0.213347	+	0.0474648i
$885$		0			0
$886$	22.8804	+	28.5302i	0.768683	+	0.958491i
$887$	−1.90744	+	3.30379i	−0.0640456	+	0.110930i	−0.896270	−	0.443508i	$-0.853734\pi$
$887$	−1.90744	+	3.30379i	−0.0640456	+	0.110930i	0.832225	+	0.554439i	$0.187067\pi$
$888$		0			0
$889$	−27.7932	+	24.9074i	−0.932153	+	0.835367i
$890$	0.958532	−	0.147166i	0.0321301	−	0.00493303i
$891$		0			0
$892$	−32.7439	−	30.0492i	−1.09635	−	1.00612i
$893$	13.0568	−	7.53836i	0.436930	−	0.252262i
$894$		0			0
$895$	0.914057			0.0305536
$896$	8.76854	−	28.6201i	0.292936	−	0.956132i
$897$		0			0
$898$	26.0289	+	10.1333i	0.868595	+	0.338151i
$899$	4.19353	−	2.42114i	0.139862	−	0.0807494i
$900$		0			0
$901$	−2.53840	−	1.46554i	−0.0845662	−	0.0488243i
$902$	−51.2397	+	7.86699i	−1.70610	+	0.261942i
$903$		0			0
$904$	11.3391	+	23.0584i	0.377132	+	0.766910i
$905$	−0.593594	+	1.02813i	−0.0197317	+	0.0341763i
$906$		0			0
$907$	−4.23020	+	2.44231i	−0.140462	+	0.0810955i	−0.568584	−	0.822625i	$-0.692509\pi$
$907$	−4.23020	+	2.44231i	−0.140462	+	0.0810955i	0.428122	+	0.903721i	$0.359175\pi$
$908$	−38.4869	−	8.56246i	−1.27723	−	0.284155i
$909$		0			0
$910$	0.178752	−	1.07909i	0.00592557	−	0.0357716i
$911$	47.3325			1.56820			0.784098	−	0.620637i	$-0.213126\pi$
$911$	47.3325			1.56820			0.784098	+	0.620637i	$0.213126\pi$
$912$		0			0
$913$	−14.8418	−	25.7068i	−0.491193	−	0.850771i
$914$	−2.83650	+	2.27479i	−0.0938231	+	0.0752435i
$915$		0			0
$916$	−4.20400	−	13.3681i	−0.138904	−	0.441696i
$917$	44.3033	−	9.30849i	1.46302	−	0.307394i
$918$		0			0
$919$	15.5826	−	26.9898i	0.514022	−	0.890312i	−0.485846	−	0.874044i	$-0.661488\pi$
$919$	15.5826	−	26.9898i	0.514022	−	0.890312i	0.999868	−	0.0162672i	$-0.00517825\pi$
$920$	0.758166	+	0.507818i	0.0249960	+	0.0167423i
$921$		0			0
$922$	15.4985	−	39.8103i	0.510415	−	1.31108i
$923$		−	74.4722i		−	2.45128i
$924$		0			0
$925$		−	6.50509i		−	0.213886i
$926$	−26.5823	−	10.3487i	−0.873549	−	0.340080i
$927$		0			0
$928$	−12.4613	−	3.65737i	−0.409063	−	0.120059i
$929$	−14.3019	+	24.7717i	−0.469231	+	0.812733i	−0.999381	−	0.0351712i	$-0.988802\pi$
$929$	−14.3019	+	24.7717i	−0.469231	+	0.812733i	0.530150	+	0.847904i	$0.322136\pi$
$930$		0			0
$931$	13.4284	−	18.3016i	0.440098	−	0.599811i
$932$	−47.2074	+	14.8457i	−1.54633	+	0.486288i
$933$		0			0
$934$	−8.16641	−	10.1829i	−0.267213	−	0.333195i
$935$	−0.0431310	−	0.0747050i	−0.00141053	−	0.00244312i
$936$		0			0
$937$	5.62816			0.183864			0.0919320	−	0.995765i	$-0.470696\pi$
$937$	5.62816			0.183864			0.0919320	+	0.995765i	$0.470696\pi$
$938$	−18.4408	+	22.4457i	−0.602115	+	0.732879i
$939$		0			0
$940$	0.421564	+	0.0937884i	0.0137499	+	0.00305904i
$941$	29.2442	−	16.8842i	0.953334	−	0.550408i	0.0592190	−	0.998245i	$-0.481139\pi$
$941$	29.2442	−	16.8842i	0.953334	−	0.550408i	0.894115	+	0.447837i	$0.147806\pi$
$942$		0			0
$943$	−35.3863	+	61.2909i	−1.15234	+	1.99591i
$944$	−3.77795	−	5.41263i	−0.122962	−	0.176166i
$945$		0			0
$946$	−7.04331	−	45.8749i	−0.228998	−	1.49152i
$947$	10.1554	+	5.86321i	0.330005	+	0.190529i	0.655843	−	0.754897i	$-0.272313\pi$
$947$	10.1554	+	5.86321i	0.330005	+	0.190529i	−0.325838	+	0.945426i	$0.605646\pi$
$948$		0			0
$949$	−60.7261	+	35.0602i	−1.97125	+	1.13810i
$950$	8.31509	−	21.3586i	0.269777	−	0.692966i
$951$		0			0
$952$	0.541078	+	3.82496i	0.0175364	+	0.123968i
$953$	−37.7047			−1.22137			−0.610687	−	0.791872i	$-0.709107\pi$
$953$	−37.7047			−1.22137			−0.610687	+	0.791872i	$0.709107\pi$
$954$		0			0
$955$	−0.562150	+	0.324557i	−0.0181907	+	0.0105024i
$956$	−32.3448	−	29.6830i	−1.04611	−	0.960016i
$957$		0			0
$958$	−8.41521	−	54.8104i	−0.271883	−	1.77084i
$959$	12.5010	+	4.09423i	0.403678	+	0.132210i
$960$		0			0
$961$	13.2756	−	22.9941i	0.428247	−	0.741745i
$962$	−9.03822	+	7.24840i	−0.291404	+	0.233698i
$963$		0			0
$964$	−6.42089	+	28.8609i	−0.206803	+	0.929546i
$965$			0.836660i			0.0269330i
$966$		0			0
$967$	−8.89648			−0.286092			−0.143046	−	0.989716i	$-0.545690\pi$
$967$	−8.89648			−0.286092			−0.143046	+	0.989716i	$0.545690\pi$
$968$	5.48853	+	0.365904i	0.176408	+	0.0117606i
$969$		0			0
$970$	−0.253325	−	0.315878i	−0.00813378	−	0.0101422i
$971$	−52.8744	−	30.5270i	−1.69682	−	0.979659i	−0.948745	−	0.316044i	$-0.897645\pi$
$971$	−52.8744	−	30.5270i	−1.69682	−	0.979659i	−0.748074	−	0.663615i	$-0.769021\pi$
$972$		0			0
$973$	9.19012	+	10.2549i	0.294622	+	0.328757i
$974$	−1.31539	−	8.56744i	−0.0421477	−	0.274519i
$975$		0			0
$976$	−2.16161	+	4.61759i	−0.0691914	+	0.147805i
$977$	23.8132	+	41.2456i	0.761851	+	1.31956i	0.941896	+	0.335906i	$0.109042\pi$
$977$	23.8132	+	41.2456i	0.761851	+	1.31956i	−0.180045	+	0.983658i	$0.557624\pi$
$978$		0			0
$979$		−	53.1205i		−	1.69774i
$980$	0.637867	−	0.126171i	0.0203759	−	0.00403037i
$981$		0			0
$982$	10.5326	−	27.0546i	0.336107	−	0.863346i
$983$	6.89129	+	11.9361i	0.219798	+	0.380701i	0.954746	−	0.297422i	$-0.0961268\pi$
$983$	6.89129	+	11.9361i	0.219798	+	0.380701i	−0.734948	+	0.678123i	$0.762793\pi$
$984$		0			0
$985$	0.0859417	−	0.148855i	0.00273833	−	0.00474293i
$986$	1.65662	−	0.254346i	0.0527576	−	0.00810003i
$987$		0			0
$988$	−38.9411	+	12.2462i	−1.23888	+	0.389602i
$989$	−54.8737	−	31.6813i	−1.74488	−	1.00741i
$990$		0			0
$991$	−4.32034	−	7.48305i	−0.137240	−	0.237707i	0.789211	−	0.614122i	$-0.210490\pi$
$991$	−4.32034	−	7.48305i	−0.137240	−	0.237707i	−0.926451	+	0.376415i	$0.877157\pi$
$992$	11.5948	−	2.81432i	0.368134	−	0.0893546i
$993$		0			0
$994$	41.4420	−	15.5724i	1.31446	−	0.493926i
$995$			0.0819463i			0.00259787i
$996$		0			0
$997$	38.0017	−	21.9403i	1.20353	−	0.694856i	0.242188	−	0.970229i	$-0.422135\pi$
$997$	38.0017	−	21.9403i	1.20353	−	0.694856i	0.961337	+	0.275374i	$0.0888016\pi$
$998$	9.78683	+	12.2035i	0.309797	+	0.386294i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.e.37.14		32
3.2	odd	2		168.2.bc.a.37.3	✓	32
4.3	odd	2		2016.2.cr.e.1297.9		32
7.4	even	3	inner	504.2.cj.e.109.3		32
8.3	odd	2		2016.2.cr.e.1297.8		32
8.5	even	2	inner	504.2.cj.e.37.3		32
12.11	even	2		672.2.bk.a.625.13		32
21.2	odd	6		1176.2.c.e.589.10		16
21.5	even	6		1176.2.c.f.589.10		16
21.11	odd	6		168.2.bc.a.109.14	yes	32
24.5	odd	2		168.2.bc.a.37.14	yes	32
24.11	even	2		672.2.bk.a.625.4		32
28.11	odd	6		2016.2.cr.e.1873.8		32
56.11	odd	6		2016.2.cr.e.1873.9		32
56.53	even	6	inner	504.2.cj.e.109.14		32
84.11	even	6		672.2.bk.a.529.4		32
84.23	even	6		4704.2.c.e.2353.12		16
84.47	odd	6		4704.2.c.f.2353.5		16
168.5	even	6		1176.2.c.f.589.9		16
168.11	even	6		672.2.bk.a.529.13		32
168.53	odd	6		168.2.bc.a.109.3	yes	32
168.107	even	6		4704.2.c.e.2353.5		16
168.131	odd	6		4704.2.c.f.2353.12		16
168.149	odd	6		1176.2.c.e.589.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.3	✓	32	3.2	odd	2
168.2.bc.a.37.14	yes	32	24.5	odd	2
168.2.bc.a.109.3	yes	32	168.53	odd	6
168.2.bc.a.109.14	yes	32	21.11	odd	6
504.2.cj.e.37.3		32	8.5	even	2	inner
504.2.cj.e.37.14		32	1.1	even	1	trivial
504.2.cj.e.109.3		32	7.4	even	3	inner
504.2.cj.e.109.14		32	56.53	even	6	inner
672.2.bk.a.529.4		32	84.11	even	6
672.2.bk.a.529.13		32	168.11	even	6
672.2.bk.a.625.4		32	24.11	even	2
672.2.bk.a.625.13		32	12.11	even	2
1176.2.c.e.589.9		16	168.149	odd	6
1176.2.c.e.589.10		16	21.2	odd	6
1176.2.c.f.589.9		16	168.5	even	6
1176.2.c.f.589.10		16	21.5	even	6
2016.2.cr.e.1297.8		32	8.3	odd	2
2016.2.cr.e.1297.9		32	4.3	odd	2
2016.2.cr.e.1873.8		32	28.11	odd	6
2016.2.cr.e.1873.9		32	56.11	odd	6
4704.2.c.e.2353.5		16	168.107	even	6
4704.2.c.e.2353.12		16	84.23	even	6
4704.2.c.f.2353.5		16	84.47	odd	6
4704.2.c.f.2353.12		16	168.131	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31787 + 0.513056i) q^{2} +(1.47355 + 1.35228i) q^{4} +(0.0402223 + 0.0232224i) q^{5} +(-1.97032 + 1.76574i) q^{7} +(1.24814 + 2.53814i) q^{8} +O(q^{10})\)	\(q+(1.31787 + 0.513056i) q^{2} +(1.47355 + 1.35228i) q^{4} +(0.0402223 + 0.0232224i) q^{5} +(-1.97032 + 1.76574i) q^{7} +(1.24814 + 2.53814i) q^{8} +(0.0410933 + 0.0512403i) q^{10} +(3.11586 - 1.79894i) q^{11} +6.29415i q^{13} +(-3.50254 + 1.31613i) q^{14} +(0.342679 + 3.98529i) q^{16} +(-0.258110 - 0.447060i) q^{17} +(2.80834 + 1.62140i) q^{19} +(0.0278663 + 0.0886110i) q^{20} +(5.02925 - 0.772156i) q^{22} +(3.47322 - 6.01578i) q^{23} +(-2.49892 - 4.32826i) q^{25} +(-3.22925 + 8.29485i) q^{26} +(-5.29113 - 0.0625230i) q^{28} +2.29579i q^{29} +(-1.05460 - 1.82662i) q^{31} +(-1.59308 + 5.42790i) q^{32} +(-0.110788 - 0.721591i) q^{34} +(-0.120255 + 0.0252667i) q^{35} +(1.12720 + 0.650790i) q^{37} +(2.86915 + 3.57762i) q^{38} +(-0.00873835 + 0.131074i) q^{40} -10.1883 q^{41} -9.12162i q^{43} +(7.02404 + 1.56269i) q^{44} +(7.66367 - 6.14605i) q^{46} +(2.32465 - 4.02641i) q^{47} +(0.764321 - 6.95815i) q^{49} +(-1.07261 - 6.98616i) q^{50} +(-8.51145 + 9.27472i) q^{52} +(4.91727 - 2.83899i) q^{53} +0.167103 q^{55} +(-6.94093 - 2.79705i) q^{56} +(-1.17787 + 3.02555i) q^{58} +(-1.42910 + 0.825090i) q^{59} +(1.10386 + 0.637312i) q^{61} +(-0.452663 - 2.94831i) q^{62} +(-4.88428 + 6.33591i) q^{64} +(-0.146165 + 0.253165i) q^{65} +(6.72366 - 3.88191i) q^{67} +(0.224213 - 1.00780i) q^{68} +(-0.171444 - 0.0283997i) q^{70} -11.8320 q^{71} +(5.57028 + 9.64802i) q^{73} +(1.15161 + 1.43597i) q^{74} +(1.94564 + 6.18687i) q^{76} +(-2.96278 + 9.04630i) q^{77} +(-2.75086 + 4.76463i) q^{79} +(-0.0787646 + 0.168255i) q^{80} +(-13.4269 - 5.22719i) q^{82} -8.25030i q^{83} -0.0239757i q^{85} +(4.67990 - 12.0211i) q^{86} +(8.45501 + 5.66315i) q^{88} +(7.38218 - 12.7863i) q^{89} +(-11.1138 - 12.4015i) q^{91} +(13.2530 - 4.16778i) q^{92} +(5.12936 - 4.11360i) q^{94} +(0.0753053 + 0.130433i) q^{95} -6.16464 q^{97} +(4.57719 - 8.77777i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8}+O(q^{10}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 6 q^{10} - 22 q^{14} - 10 q^{16} + 40 q^{20} - 12 q^{22} + 8 q^{23} + 16 q^{25} - 6 q^{26} - 26 q^{28} - 24 q^{31} + 8 q^{32} - 24 q^{34} + 26 q^{38} - 6 q^{40} - 20 q^{44} + 16 q^{46} + 24 q^{47} + 8 q^{49} - 52 q^{50} + 44 q^{52} - 64 q^{55} - 40 q^{56} + 34 q^{58} - 100 q^{62} - 20 q^{64} - 16 q^{68} + 38 q^{70} + 80 q^{71} + 8 q^{73} - 10 q^{74} - 32 q^{76} + 8 q^{79} + 56 q^{80} + 22 q^{86} + 50 q^{88} - 64 q^{92} - 48 q^{94} - 24 q^{95} - 48 q^{97} + 64 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 6 * q^10 - 22 * q^14 - 10 * q^16 + 40 * q^20 - 12 * q^22 + 8 * q^23 + 16 * q^25 - 6 * q^26 - 26 * q^28 - 24 * q^31 + 8 * q^32 - 24 * q^34 + 26 * q^38 - 6 * q^40 - 20 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^49 - 52 * q^50 + 44 * q^52 - 64 * q^55 - 40 * q^56 + 34 * q^58 - 100 * q^62 - 20 * q^64 - 16 * q^68 + 38 * q^70 + 80 * q^71 + 8 * q^73 - 10 * q^74 - 32 * q^76 + 8 * q^79 + 56 * q^80 + 22 * q^86 + 50 * q^88 - 64 * q^92 - 48 * q^94 - 24 * q^95 - 48 * q^97 + 64 * q^98

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