LMFDB - Embedded newform 288.2.v.d.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (of order $8$, degree $4$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			181.2
Character	$\chi$	$=$	288.181
Dual form			288.2.v.d.253.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.890433 - 1.09869i) q^{2} +(-0.414259 + 1.95663i) q^{4} +(0.00259461 - 0.00626394i) q^{5} +(-2.41880 - 2.41880i) q^{7} +(2.51860 - 1.28710i) q^{8} +O(q^{10})$	\(q+(-0.890433 - 1.09869i) q^{2} +(-0.414259 + 1.95663i) q^{4} +(0.00259461 - 0.00626394i) q^{5} +(-2.41880 - 2.41880i) q^{7} +(2.51860 - 1.28710i) q^{8} +(-0.00919248 + 0.00272694i) q^{10} +(-1.29952 - 0.538278i) q^{11} +(-0.559497 - 1.35074i) q^{13} +(-0.503742 + 4.81130i) q^{14} +(-3.65678 - 1.62110i) q^{16} -5.82199i q^{17} +(-2.67819 - 6.46573i) q^{19} +(0.0111814 + 0.00767157i) q^{20} +(0.565730 + 1.90707i) q^{22} +(-0.178878 + 0.178878i) q^{23} +(3.53550 + 3.53550i) q^{25} +(-0.985861 + 1.81746i) q^{26} +(5.73469 - 3.73068i) q^{28} +(-5.72901 + 2.37303i) q^{29} -6.19719 q^{31} +(1.47502 + 5.46116i) q^{32} +(-6.39659 + 5.18409i) q^{34} +(-0.0214270 + 0.00887537i) q^{35} +(-2.02932 + 4.89922i) q^{37} +(-4.71911 + 8.69981i) q^{38} +(-0.00152753 - 0.0191159i) q^{40} +(3.36712 - 3.36712i) q^{41} +(9.37558 + 3.88349i) q^{43} +(1.59154 - 2.31968i) q^{44} +(0.355812 + 0.0372534i) q^{46} -12.5050i q^{47} +4.70117i q^{49} +(0.736309 - 7.03256i) q^{50} +(2.87468 - 0.535169i) q^{52} +(8.36811 + 3.46618i) q^{53} +(-0.00674348 + 0.00674348i) q^{55} +(-9.20523 - 2.97876i) q^{56} +(7.70854 + 4.18140i) q^{58} +(-1.59507 + 3.85084i) q^{59} +(7.27395 - 3.01297i) q^{61} +(5.51818 + 6.80881i) q^{62} +(4.68674 - 6.48340i) q^{64} -0.00991266 q^{65} +(-4.38775 + 1.81747i) q^{67} +(11.3915 + 2.41181i) q^{68} +(0.0288307 + 0.0156388i) q^{70} +(-5.95188 - 5.95188i) q^{71} +(7.85539 - 7.85539i) q^{73} +(7.18972 - 2.13282i) q^{74} +(13.7605 - 2.56174i) q^{76} +(1.84128 + 4.44525i) q^{77} -1.42456i q^{79} +(-0.0196424 + 0.0186997i) q^{80} +(-6.69763 - 0.701242i) q^{82} +(3.03596 + 7.32946i) q^{83} +(-0.0364686 - 0.0151058i) q^{85} +(-4.08155 - 13.7589i) q^{86} +(-3.96579 + 0.316902i) q^{88} +(9.96127 + 9.96127i) q^{89} +(-1.91387 + 4.62049i) q^{91} +(-0.275896 - 0.424100i) q^{92} +(-13.7392 + 11.1349i) q^{94} -0.0474498 q^{95} -1.24058 q^{97} +(5.16515 - 4.18607i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) $ 32 * q - 8 * q^10 + 32 * q^14 - 8 * q^16 + 32 * q^20 - 8 * q^22 + 16 * q^23 - 40 * q^26 + 40 * q^28 - 48 * q^31 - 40 * q^32 + 40 * q^34 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 16 * q^43 - 8 * q^44 - 32 * q^46 - 24 * q^50 - 8 * q^52 + 32 * q^53 + 32 * q^55 - 56 * q^56 - 32 * q^58 - 64 * q^59 - 32 * q^61 - 48 * q^62 + 24 * q^64 + 16 * q^67 + 8 * q^68 - 24 * q^70 - 64 * q^71 + 32 * q^74 - 56 * q^76 + 32 * q^77 + 56 * q^80 - 40 * q^82 + 64 * q^86 - 48 * q^88 - 48 * q^91 + 80 * q^92 - 32 * q^94 + 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$1$

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 $

$2$	−0.890433	−	1.09869i	−0.629631	−	0.776894i
$2$	−0.890433	−	1.09869i	−0.629631	−	0.776894i
$3$		0			0
$3$		0			0
$4$	−0.414259	+	1.95663i	−0.207129	+	0.978314i
$5$	0.00259461	−	0.00626394i	0.00116034	−	0.00280132i	−0.923298	−	0.384084i	$-0.874517\pi$
$5$	0.00259461	−	0.00626394i	0.00116034	−	0.00280132i	0.924459	+	0.381282i	$0.124517\pi$
$6$		0			0
$7$	−2.41880	−	2.41880i	−0.914220	−	0.914220i	0.0823812	−	0.996601i	$-0.473747\pi$
$7$	−2.41880	−	2.41880i	−0.914220	−	0.914220i	−0.996601	+	0.0823812i	$0.973747\pi$
$8$	2.51860	−	1.28710i	0.890461	−	0.455059i
$9$		0			0
$10$	−0.00919248	+	0.00272694i	−0.00290692	+	0.000862333i
$11$	−1.29952	−	0.538278i	−0.391819	−	0.162297i	0.178071	−	0.984018i	$-0.443014\pi$
$11$	−1.29952	−	0.538278i	−0.391819	−	0.162297i	−0.569890	+	0.821721i	$0.693014\pi$
$12$		0			0
$13$	−0.559497	−	1.35074i	−0.155176	−	0.374629i	0.827103	−	0.562050i	$-0.189987\pi$
$13$	−0.559497	−	1.35074i	−0.155176	−	0.374629i	−0.982280	+	0.187421i	$0.939987\pi$
$14$	−0.503742	+	4.81130i	−0.134631	+	1.28587i
$15$		0			0
$16$	−3.65678	−	1.62110i	−0.914195	−	0.405275i
$17$		−	5.82199i		−	1.41204i	−0.708192	−	0.706020i	$-0.750489\pi$
$17$		−	5.82199i		−	1.41204i	0.708192	−	0.706020i	$-0.249511\pi$
$18$		0			0
$19$	−2.67819	−	6.46573i	−0.614420	−	1.48334i	−0.858099	−	0.513484i	$-0.828354\pi$
$19$	−2.67819	−	6.46573i	−0.614420	−	1.48334i	0.243679	−	0.969856i	$-0.421646\pi$
$20$	0.0111814	+	0.00767157i	0.00250023	+	0.00171542i
$21$		0			0
$22$	0.565730	+	1.90707i	0.120614	+	0.406589i
$23$	−0.178878	+	0.178878i	−0.0372987	+	0.0372987i	−0.725510	−	0.688211i	$-0.758396\pi$
$23$	−0.178878	+	0.178878i	−0.0372987	+	0.0372987i	0.688211	+	0.725510i	$0.258396\pi$
$24$		0			0
$25$	3.53550	+	3.53550i	0.707100	+	0.707100i
$26$	−0.985861	+	1.81746i	−0.193343	+	0.356434i
$27$		0			0
$28$	5.73469	−	3.73068i	1.08376	−	0.705032i
$29$	−5.72901	+	2.37303i	−1.06385	+	0.440661i	−0.844817	−	0.535056i	$-0.820290\pi$
$29$	−5.72901	+	2.37303i	−1.06385	+	0.440661i	−0.219034	+	0.975717i	$0.570290\pi$
$30$		0			0
$31$	−6.19719			−1.11305			−0.556524	−	0.830832i	$-0.687865\pi$
$31$	−6.19719			−1.11305			−0.556524	+	0.830832i	$0.687865\pi$
$32$	1.47502	+	5.46116i	0.260750	+	0.965406i
$33$		0			0
$34$	−6.39659	+	5.18409i	−1.09701	+	0.889064i
$35$	−0.0214270	+	0.00887537i	−0.00362183	+	0.00150021i
$36$		0			0
$37$	−2.02932	+	4.89922i	−0.333619	+	0.805427i	0.664680	+	0.747128i	$0.268568\pi$
$37$	−2.02932	+	4.89922i	−0.333619	+	0.805427i	−0.998299	+	0.0582992i	$0.981432\pi$
$38$	−4.71911	+	8.69981i	−0.765541	+	1.41130i
$39$		0			0
$40$	−0.00152753	−	0.0191159i	−0.000241524	−	0.00302249i
$41$	3.36712	−	3.36712i	0.525856	−	0.525856i	−0.393478	−	0.919334i	$-0.628728\pi$
$41$	3.36712	−	3.36712i	0.525856	−	0.525856i	0.919334	+	0.393478i	$0.128728\pi$
$42$		0			0
$43$	9.37558	+	3.88349i	1.42976	+	0.592227i	0.957293	−	0.289120i	$-0.0933625\pi$
$43$	9.37558	+	3.88349i	1.42976	+	0.592227i	0.472470	+	0.881347i	$0.343363\pi$
$44$	1.59154	−	2.31968i	0.239934	−	0.349706i
$45$		0			0
$46$	0.355812	+	0.0372534i	0.0524616	+	0.00549272i
$47$		−	12.5050i		−	1.82405i	−0.410137	−	0.912024i	$-0.634519\pi$
$47$		−	12.5050i		−	1.82405i	0.410137	−	0.912024i	$-0.365481\pi$
$48$		0			0
$49$			4.70117i			0.671595i
$50$	0.736309	−	7.03256i	0.104130	−	0.994554i
$51$		0			0
$52$	2.87468	−	0.535169i	0.398646	−	0.0742146i
$53$	8.36811	+	3.46618i	1.14945	+	0.476117i	0.874348	−	0.485299i	$-0.161289\pi$
$53$	8.36811	+	3.46618i	1.14945	+	0.476117i	0.275100	+	0.961416i	$0.411289\pi$
$54$		0			0
$55$	−0.00674348	+	0.00674348i	−0.000909291	+	0.000909291i
$56$	−9.20523	−	2.97876i	−1.23010	−	0.398053i
$57$		0			0
$58$	7.70854	+	4.18140i	1.01218	+	0.549045i
$59$	−1.59507	+	3.85084i	−0.207661	+	0.501337i	−0.993054	−	0.117660i	$-0.962461\pi$
$59$	−1.59507	+	3.85084i	−0.207661	+	0.501337i	0.785393	+	0.618997i	$0.212461\pi$
$60$		0			0
$61$	7.27395	−	3.01297i	0.931333	−	0.385771i	0.135149	−	0.990825i	$-0.456849\pi$
$61$	7.27395	−	3.01297i	0.931333	−	0.385771i	0.796184	+	0.605054i	$0.206849\pi$
$62$	5.51818	+	6.80881i	0.700809	+	0.864720i
$63$		0			0
$64$	4.68674	−	6.48340i	0.585842	−	0.810425i
$65$	−0.00991266			−0.00122951
$66$		0			0
$67$	−4.38775	+	1.81747i	−0.536049	+	0.222039i	−0.634250	−	0.773128i	$-0.718691\pi$
$67$	−4.38775	+	1.81747i	−0.536049	+	0.222039i	0.0982011	+	0.995167i	$0.468691\pi$
$68$	11.3915	+	2.41181i	1.38142	+	0.292475i
$69$		0			0
$70$	0.0288307	+	0.0156388i	0.00344592	+	0.00186920i
$71$	−5.95188	−	5.95188i	−0.706358	−	0.706358i	0.259409	−	0.965768i	$-0.416472\pi$
$71$	−5.95188	−	5.95188i	−0.706358	−	0.706358i	−0.965768	+	0.259409i	$0.916472\pi$
$72$		0			0
$73$	7.85539	−	7.85539i	0.919404	−	0.919404i	−0.0775823	−	0.996986i	$-0.524720\pi$
$73$	7.85539	−	7.85539i	0.919404	−	0.919404i	0.996986	+	0.0775823i	$0.0247201\pi$
$74$	7.18972	−	2.13282i	0.835788	−	0.247935i
$75$		0			0
$76$	13.7605	−	2.56174i	1.57844	−	0.293852i
$77$	1.84128	+	4.44525i	0.209834	+	0.506584i
$78$		0			0
$79$		−	1.42456i		−	0.160276i	−0.996784	−	0.0801378i	$-0.974464\pi$
$79$		−	1.42456i		−	0.160276i	0.996784	−	0.0801378i	$-0.0255360\pi$
$80$	−0.0196424	+	0.0186997i	−0.00219609	+	0.00209069i
$81$		0			0
$82$	−6.69763	−	0.701242i	−0.739630	−	0.0774392i
$83$	3.03596	+	7.32946i	0.333240	+	0.804513i	0.998331	+	0.0577507i	$0.0183929\pi$
$83$	3.03596	+	7.32946i	0.333240	+	0.804513i	−0.665091	+	0.746763i	$0.731607\pi$
$84$		0			0
$85$	−0.0364686	−	0.0151058i	−0.00395557	−	0.00163845i
$86$	−4.08155	−	13.7589i	−0.440125	−	1.48366i
$87$		0			0
$88$	−3.96579	+	0.316902i	−0.422754	+	0.0337819i
$89$	9.96127	+	9.96127i	1.05589	+	1.05589i	0.998343	+	0.0575498i	$0.0183288\pi$
$89$	9.96127	+	9.96127i	1.05589	+	1.05589i	0.0575498	+	0.998343i	$0.481671\pi$
$90$		0			0
$91$	−1.91387	+	4.62049i	−0.200628	+	0.484359i
$92$	−0.275896	−	0.424100i	−0.0287642	−	0.0442155i
$93$		0			0
$94$	−13.7392	+	11.1349i	−1.41709	+	1.14848i
$95$	−0.0474498			−0.00486825
$96$		0			0
$97$	−1.24058			−0.125961			−0.0629807	−	0.998015i	$-0.520061\pi$
$97$	−1.24058			−0.125961			−0.0629807	+	0.998015i	$0.520061\pi$
$98$	5.16515	−	4.18607i	0.521758	−	0.422857i
$99$		0			0
$100$	−8.38227	+	5.45305i	−0.838227	+	0.545305i
$101$	−6.15953	+	14.8704i	−0.612896	+	1.47966i	0.246908	+	0.969039i	$0.420585\pi$
$101$	−6.15953	+	14.8704i	−0.612896	+	1.47966i	−0.859804	+	0.510624i	$0.829415\pi$
$102$		0			0
$103$	−5.60558	−	5.60558i	−0.552334	−	0.552334i	0.374779	−	0.927114i	$-0.377718\pi$
$103$	−5.60558	−	5.60558i	−0.552334	−	0.552334i	−0.927114	+	0.374779i	$0.877718\pi$
$104$	−3.14770	−	2.68186i	−0.308657	−	0.262978i
$105$		0			0
$106$	−3.64296	−	12.2804i	−0.353836	−	1.19278i
$107$	5.46375	+	2.26316i	0.528201	+	0.218788i	0.630815	−	0.775933i	$-0.282721\pi$
$107$	5.46375	+	2.26316i	0.528201	+	0.218788i	−0.102614	+	0.994721i	$0.532721\pi$
$108$		0			0
$109$	−0.982918	−	2.37297i	−0.0941464	−	0.227290i	0.869790	−	0.493422i	$-0.164254\pi$
$109$	−0.982918	−	2.37297i	−0.0941464	−	0.227290i	−0.963936	+	0.266132i	$0.914254\pi$
$110$	0.0134136	+	0.00140441i	0.00127894	+	0.000133905i
$111$		0			0
$112$	4.92390	+	12.7661i	0.465265	+	1.20629i
$113$		−	4.42809i		−	0.416560i	−0.978069	−	0.208280i	$-0.933213\pi$
$113$		−	4.42809i		−	0.416560i	0.978069	−	0.208280i	$-0.0667865\pi$
$114$		0			0
$115$	0.000656364		0.00158460i	6.12062e−5		0.000147765i
$116$	−2.26985	−	12.1926i	−0.210750	−	1.13205i
$117$		0			0
$118$	5.65121	−	1.67642i	0.520236	−	0.154327i
$119$	−14.0822	+	14.0822i	−1.29091	+	1.29091i
$120$		0			0
$121$	−6.37917	−	6.37917i	−0.579925	−	0.579925i
$122$	−9.78729	−	5.30900i	−0.886100	−	0.480654i
$123$		0			0
$124$	2.56724	−	12.1256i	0.230545	−	1.08891i
$125$	0.0626391	−	0.0259460i	0.00560261	−	0.00232068i
$126$		0			0
$127$	14.5930			1.29492			0.647458	−	0.762101i	$-0.275832\pi$
$127$	14.5930			1.29492			0.647458	+	0.762101i	$0.275832\pi$
$128$	−11.2965	+	0.623739i	−0.998479	+	0.0551313i
$129$		0			0
$130$	0.00882656	+	0.0108910i	0.000774140	+	0.000955202i
$131$	8.62727	−	3.57353i	0.753768	−	0.312221i	0.0274902	−	0.999622i	$-0.491248\pi$
$131$	8.62727	−	3.57353i	0.753768	−	0.312221i	0.726278	+	0.687401i	$0.241248\pi$
$132$		0			0
$133$	−9.16129	+	22.1173i	−0.794384	+	1.91781i
$134$	5.90384	+	3.20247i	0.510014	+	0.276651i
$135$		0			0
$136$	−7.49349	−	14.6633i	−0.642561	−	1.25737i
$137$	0.109126	−	0.109126i	0.00932323	−	0.00932323i	−0.702430	−	0.711753i	$-0.747902\pi$
$137$	0.109126	−	0.109126i	0.00932323	−	0.00932323i	0.711753	+	0.702430i	$0.247902\pi$
$138$		0			0
$139$	5.80724	+	2.40544i	0.492564	+	0.204027i	0.615118	−	0.788435i	$-0.289108\pi$
$139$	5.80724	+	2.40544i	0.492564	+	0.204027i	−0.122554	+	0.992462i	$0.539108\pi$
$140$	−0.00848946	−	0.0456014i	−0.000717490	−	0.00385402i
$141$		0			0
$142$	−1.23955	+	11.8391i	−0.104021	+	0.993511i
$143$			2.05648i			0.171971i
$144$		0			0
$145$			0.0420433i			0.00349150i
$146$	−15.6254	−	1.63597i	−1.29316	−	0.135394i
$147$		0			0
$148$	−8.74529	−	6.00018i	−0.718858	−	0.493211i
$149$	−15.4722	−	6.40879i	−1.26753	−	0.525028i	−0.355318	−	0.934745i	$-0.615627\pi$
$149$	−15.4722	−	6.40879i	−1.26753	−	0.525028i	−0.912213	+	0.409717i	$0.865627\pi$
$150$		0			0
$151$	−9.38822	+	9.38822i	−0.764003	+	0.764003i	−0.977043	−	0.213041i	$-0.931663\pi$
$151$	−9.38822	+	9.38822i	−0.764003	+	0.764003i	0.213041	+	0.977043i	$0.431663\pi$
$152$	−15.0674	−	12.8375i	−1.22212	−	1.04126i
$153$		0			0
$154$	3.24444	−	5.98121i	0.261444	−	0.481980i
$155$	−0.0160793	+	0.0388188i	−0.00129152	+	0.00311800i
$156$		0			0
$157$	−0.959615	+	0.397486i	−0.0765856	+	0.0317228i	−0.420647	−	0.907224i	$-0.638197\pi$
$157$	−0.959615	+	0.397486i	−0.0765856	+	0.0317228i	0.344062	+	0.938947i	$0.388197\pi$
$158$	−1.56516	+	1.26848i	−0.124517	+	0.100915i
$159$		0			0
$160$	0.0380355	+	0.00493012i	0.00300697	+	0.000389760i
$161$	0.865341			0.0681984
$162$		0			0
$163$	−7.39543	+	3.06329i	−0.579255	+	0.239935i	−0.653020	−	0.757340i	$-0.726498\pi$
$163$	−7.39543	+	3.06329i	−0.579255	+	0.239935i	0.0737655	+	0.997276i	$0.476498\pi$
$164$	5.19334	+	7.98306i	0.405532	+	0.623372i
$165$		0			0
$166$	5.34952	−	9.86199i	0.415203	−	0.765439i
$167$	−0.697073	−	0.697073i	−0.0539412	−	0.0539412i	0.679622	−	0.733563i	$-0.262144\pi$
$167$	−0.697073	−	0.697073i	−0.0539412	−	0.0539412i	−0.733563	+	0.679622i	$0.762144\pi$
$168$		0			0
$169$	7.68091	−	7.68091i	0.590840	−	0.590840i
$170$	0.0158762	+	0.0535185i	0.00121765	+	0.00410468i
$171$		0			0
$172$	−11.4825	+	16.7357i	−0.875530	+	1.27609i
$173$	−6.61178	−	15.9623i	−0.502685	−	1.21359i	−0.948016	−	0.318222i	$-0.896914\pi$
$173$	−6.61178	−	15.9623i	−0.502685	−	1.21359i	0.445331	−	0.895366i	$-0.353086\pi$
$174$		0			0
$175$		−	17.1033i		−	1.29289i
$176$	3.87945	+	4.07501i	0.292424	+	0.307165i
$177$		0			0
$178$	2.07455	−	19.8142i	0.155494	−	1.48514i
$179$	−1.14101	−	2.75465i	−0.0852832	−	0.205892i	0.875484	−	0.483246i	$-0.160542\pi$
$179$	−1.14101	−	2.75465i	−0.0852832	−	0.205892i	−0.960768	+	0.277354i	$0.910542\pi$
$180$		0			0
$181$	−6.23325	−	2.58190i	−0.463314	−	0.191911i	0.138801	−	0.990320i	$-0.455675\pi$
$181$	−6.23325	−	2.58190i	−0.463314	−	0.191911i	−0.602115	+	0.798409i	$0.705675\pi$
$182$	6.78067	−	2.01148i	0.502617	−	0.149101i
$183$		0			0
$184$	−0.220289	+	0.680758i	−0.0162399	+	0.0501861i
$185$	0.0254231	+	0.0254231i	0.00186915	+	0.00186915i
$186$		0			0
$187$	−3.13385	+	7.56577i	−0.229170	+	0.553264i
$188$	24.4677	+	5.18032i	1.78449	+	0.377814i
$189$		0			0
$190$	0.0422509	+	0.0521328i	0.00306520	+	0.00378211i
$191$	5.12197			0.370613			0.185306	−	0.982681i	$-0.440672\pi$
$191$	5.12197			0.370613			0.185306	+	0.982681i	$0.440672\pi$
$192$		0			0
$193$	−20.7951			−1.49686			−0.748431	−	0.663213i	$-0.769192\pi$
$193$	−20.7951			−1.49686			−0.748431	+	0.663213i	$0.769192\pi$
$194$	1.10465	+	1.36301i	0.0793093	+	0.0978588i
$195$		0			0
$196$	−9.19843	−	1.94750i	−0.657031	−	0.139107i
$197$	3.47339	−	8.38550i	0.247469	−	0.597442i	−0.750519	−	0.660849i	$-0.770196\pi$
$197$	3.47339	−	8.38550i	0.247469	−	0.597442i	0.997988	+	0.0634065i	$0.0201965\pi$
$198$		0			0
$199$	9.79652	+	9.79652i	0.694457	+	0.694457i	0.963209	−	0.268753i	$-0.0866114\pi$
$199$	9.79652	+	9.79652i	0.694457	+	0.694457i	−0.268753	+	0.963209i	$0.586611\pi$
$200$	13.4551	+	4.35398i	0.951418	+	0.307873i
$201$		0			0
$202$	21.8227	−	6.47367i	1.53544	−	0.455486i
$203$	19.5972	+	8.11743i	1.37545	+	0.569732i
$204$		0			0
$205$	−0.0123551	−	0.0298278i	−0.000862917	−	0.00208326i
$206$	−1.16743	+	11.1502i	−0.0813385	+	0.776872i
$207$		0			0
$208$	−0.143735	+	5.84637i	−0.00996620	+	0.405373i
$209$			9.84394i			0.680919i
$210$		0			0
$211$	−2.59646	−	6.26841i	−0.178748	−	0.431535i	0.808957	−	0.587868i	$-0.200033\pi$
$211$	−2.59646	−	6.26841i	−0.178748	−	0.431535i	−0.987704	+	0.156333i	$0.950033\pi$
$212$	−10.2486	+	14.9374i	−0.703876	+	1.02590i
$213$		0			0
$214$	−2.37858	−	8.01818i	−0.162597	−	0.548112i
$215$	0.0486519	−	0.0486519i	0.00331804	−	0.00331804i
$216$		0			0
$217$	14.9897	+	14.9897i	1.01757	+	1.01757i
$218$	−1.73195	+	3.19290i	−0.117302	+	0.216250i
$219$		0			0
$220$	−0.0104009	−	0.0159880i	−0.000701231	−	0.00107791i
$221$	−7.86402	+	3.25738i	−0.528991	+	0.219115i
$222$		0			0
$223$	14.6051			0.978032			0.489016	−	0.872275i	$-0.337356\pi$
$223$	14.6051			0.978032			0.489016	+	0.872275i	$0.337356\pi$
$224$	9.64166	−	16.7772i	0.644211	−	1.12098i
$225$		0			0
$226$	−4.86512	+	3.94292i	−0.323623	+	0.262279i
$227$	3.75119	−	1.55379i	0.248975	−	0.103129i	−0.254706	−	0.967019i	$-0.581979\pi$
$227$	3.75119	−	1.55379i	0.248975	−	0.103129i	0.503681	+	0.863890i	$0.331979\pi$
$228$		0			0
$229$	2.06540	−	4.98631i	0.136485	−	0.329505i	−0.840828	−	0.541302i	$-0.817932\pi$
$229$	2.06540	−	4.98631i	0.136485	−	0.329505i	0.977314	+	0.211797i	$0.0679316\pi$
$230$	0.00115655	−	0.00213212i	7.62603e−5	−	0.000140588i
$231$		0			0
$232$	−11.3748	+	13.3506i	−0.746791	+	0.876507i
$233$	20.5003	−	20.5003i	1.34302	−	1.34302i	0.449987	−	0.893035i	$-0.351428\pi$
$233$	20.5003	−	20.5003i	1.34302	−	1.34302i	0.893035	−	0.449987i	$-0.148572\pi$
$234$		0			0
$235$	−0.0783308	−	0.0324457i	−0.00510974	−	0.00211652i
$236$	−6.87389	−	4.71621i	−0.447452	−	0.306999i
$237$		0			0
$238$	28.0113	+	2.93278i	1.81570	+	0.190104i
$239$			2.23671i			0.144680i	0.997380	+	0.0723402i	$0.0230467\pi$
$239$			2.23671i			0.144680i	−0.997380	+	0.0723402i	$0.976953\pi$
$240$		0			0
$241$		−	19.6755i		−	1.26741i	−0.773575	−	0.633704i	$-0.781534\pi$
$241$		−	19.6755i		−	1.26741i	0.773575	−	0.633704i	$-0.218466\pi$
$242$	−1.32854	+	12.6890i	−0.0854015	+	0.815679i
$243$		0			0
$244$	2.88196	+	15.4805i	0.184498	+	0.991040i
$245$	0.0294478	+	0.0121977i	0.00188135	+	0.000779282i
$246$		0			0
$247$	−7.23511	+	7.23511i	−0.460359	+	0.460359i
$248$	−15.6083	+	7.97641i	−0.991126	+	0.506502i
$249$		0			0
$250$	−0.0842826	−	0.0457181i	−0.00533050	−	0.00289147i
$251$	−2.41942	+	5.84100i	−0.152712	+	0.368680i	−0.981658	−	0.190648i	$-0.938941\pi$
$251$	−2.41942	+	5.84100i	−0.152712	+	0.368680i	0.828946	+	0.559329i	$0.188941\pi$
$252$		0			0
$253$	0.328742	−	0.136169i	0.0206678	−	0.00856088i
$254$	−12.9940	−	16.0332i	−0.815319	−	1.00601i
$255$		0			0
$256$	10.7441	+	11.8560i	0.671505	+	0.741000i
$257$	−9.46013			−0.590106			−0.295053	−	0.955481i	$-0.595337\pi$
$257$	−9.46013			−0.590106			−0.295053	+	0.955481i	$0.595337\pi$
$258$		0			0
$259$	16.7588	−	6.94170i	1.04134	−	0.431336i
$260$	0.00410640	−	0.0193954i	0.000254668	−	0.00120285i
$261$		0			0
$262$	−11.6082	−	6.29674i	−0.717159	−	0.389014i
$263$	7.01762	+	7.01762i	0.432725	+	0.432725i	0.889554	−	0.456829i	$-0.151015\pi$
$263$	7.01762	+	7.01762i	0.432725	+	0.432725i	−0.456829	+	0.889554i	$0.651015\pi$
$264$		0			0
$265$	0.0434239	−	0.0434239i	0.00266751	−	0.00266751i
$266$	32.4577	−	9.62852i	1.99011	−	0.590362i
$267$		0			0
$268$	−1.73844	−	9.33810i	−0.106192	−	0.570415i
$269$	−0.579856	−	1.39990i	−0.0353545	−	0.0853532i	0.905216	−	0.424952i	$-0.139709\pi$
$269$	−0.579856	−	1.39990i	−0.0353545	−	0.0853532i	−0.940571	+	0.339598i	$0.889709\pi$
$270$		0			0
$271$		−	2.19594i		−	0.133394i	−0.997773	−	0.0666969i	$-0.978754\pi$
$271$		−	2.19594i		−	0.133394i	0.997773	−	0.0666969i	$-0.0212460\pi$
$272$	−9.43802	+	21.2897i	−0.572264	+	1.29088i
$273$		0			0
$274$	−0.217065	−	0.0227267i	−0.0131134	−	0.00137297i
$275$	−2.69136	−	6.49753i	−0.162295	−	0.391816i
$276$		0			0
$277$	24.0612	+	9.96649i	1.44570	+	0.598829i	0.961173	−	0.275948i	$-0.0889916\pi$
$277$	24.0612	+	9.96649i	1.44570	+	0.598829i	0.484527	+	0.874776i	$0.338992\pi$
$278$	−2.52812	−	8.52226i	−0.151626	−	0.511131i
$279$		0			0
$280$	−0.0425427	+	0.0499323i	−0.00254242	+	0.00298403i
$281$	−18.0180	−	18.0180i	−1.07487	−	1.07487i	−0.996961	−	0.0779048i	$-0.975177\pi$
$281$	−18.0180	−	18.0180i	−1.07487	−	1.07487i	−0.0779048	−	0.996961i	$-0.524823\pi$
$282$		0			0
$283$	−1.15856	+	2.79702i	−0.0688695	+	0.166266i	−0.954566	−	0.297998i	$-0.903681\pi$
$283$	−1.15856	+	2.79702i	−0.0688695	+	0.166266i	0.885697	+	0.464264i	$0.153681\pi$
$284$	14.1112	−	9.18000i	0.837348	−	0.544733i
$285$		0			0
$286$	2.25944	−	1.83116i	0.133604	−	0.108279i
$287$	−16.2888			−0.961496
$288$		0			0
$289$	−16.8955			−0.993855
$290$	0.0461927	−	0.0374367i	0.00271253	−	0.00219836i
$291$		0			0
$292$	12.1159	+	18.6242i	0.709030	+	1.08990i
$293$	−3.52001	+	8.49805i	−0.205641	+	0.496461i	−0.992728	−	0.120381i	$-0.961588\pi$
$293$	−3.52001	+	8.49805i	−0.205641	+	0.496461i	0.787087	+	0.616842i	$0.211588\pi$
$294$		0			0
$295$	0.0199829	+	0.0199829i	0.00116345	+	0.00116345i
$296$	1.19473	+	14.9511i	0.0694423	+	0.869018i
$297$		0			0
$298$	6.73564	+	22.7058i	0.390185	+	1.31531i
$299$	0.341700	+	0.141537i	0.0197610	+	0.00818529i
$300$		0			0
$301$	−13.2843	−	32.0710i	−0.765692	−	1.84854i
$302$	18.6744	+	1.95520i	1.07459	+	0.112509i
$303$		0			0
$304$	−0.688028	+	27.9854i	−0.0394611	+	1.60507i
$305$		−	0.0533810i		−	0.00305659i
$306$		0			0
$307$	−1.41754	−	3.42224i	−0.0809032	−	0.195318i	0.878252	−	0.478198i	$-0.158710\pi$
$307$	−1.41754	−	3.42224i	−0.0809032	−	0.195318i	−0.959155	+	0.282881i	$0.908710\pi$
$308$	−9.46047	+	1.76122i	−0.539061	+	0.100355i
$309$		0			0
$310$	0.0569675	−	0.0168993i	0.00323554	−	0.000959818i
$311$	22.4396	−	22.4396i	1.27243	−	1.27243i	0.327622	−	0.944809i	$-0.393753\pi$
$311$	22.4396	−	22.4396i	1.27243	−	1.27243i	0.944809	−	0.327622i	$-0.106247\pi$
$312$		0			0
$313$	−2.24961	−	2.24961i	−0.127155	−	0.127155i	0.640665	−	0.767821i	$-0.278659\pi$
$313$	−2.24961	−	2.24961i	−0.127155	−	0.127155i	−0.767821	+	0.640665i	$0.778659\pi$
$314$	1.29119	+	0.700390i	0.0728660	+	0.0395253i
$315$		0			0
$316$	2.78733	+	0.590137i	0.156800	+	0.0331978i
$317$	31.4340	−	13.0204i	1.76551	−	0.731298i	0.769852	−	0.638223i	$-0.220330\pi$
$317$	31.4340	−	13.0204i	1.76551	−	0.731298i	0.995659	−	0.0930756i	$-0.0296698\pi$
$318$		0			0
$319$	8.72230			0.488355
$320$	−0.0284514	−	0.0461793i	−0.00159048	−	0.00258150i
$321$		0			0
$322$	−0.770528	−	0.950745i	−0.0429398	−	0.0529829i
$323$	−37.6434	+	15.5924i	−2.09453	+	0.867585i
$324$		0			0
$325$	2.79746	−	6.75366i	0.155175	−	0.374626i
$326$	9.95075	+	5.39767i	0.551121	+	0.298949i
$327$		0			0
$328$	4.14662	−	12.8143i	0.228959	−	0.707550i
$329$	−30.2472	+	30.2472i	−1.66758	+	1.66758i
$330$		0			0
$331$	24.6043	+	10.1914i	1.35237	+	0.560172i	0.936952	−	0.349457i	$-0.113634\pi$
$331$	24.6043	+	10.1914i	1.35237	+	0.560172i	0.415422	+	0.909629i	$0.363634\pi$
$332$	−15.5987	+	2.90396i	−0.856090	+	0.159375i
$333$		0			0
$334$	−0.145174	+	1.38657i	−0.00794354	+	0.0758696i
$335$			0.0322002i			0.00175929i
$336$		0			0
$337$		−	20.1009i		−	1.09497i	−0.836817	−	0.547483i	$-0.815586\pi$
$337$		−	20.1009i		−	1.09497i	0.836817	−	0.547483i	$-0.184414\pi$
$338$	−15.2783	−	1.59964i	−0.831031	−	0.0870089i
$339$		0			0
$340$	0.0446638	−	0.0650977i	0.00242224	−	0.00353042i
$341$	8.05335	+	3.33581i	0.436113	+	0.180644i
$342$		0			0
$343$	−5.56041	+	5.56041i	−0.300234	+	0.300234i
$344$	28.6118	−	2.28634i	1.54265	−	0.123271i
$345$		0			0
$346$	−11.6503	+	21.4777i	−0.626324	+	1.15465i
$347$	5.23707	−	12.6434i	0.281141	−	0.678734i	−0.718722	−	0.695297i	$-0.755273\pi$
$347$	5.23707	−	12.6434i	0.281141	−	0.678734i	0.999863	+	0.0165638i	$0.00527266\pi$
$348$		0			0
$349$	−16.5877	+	6.87085i	−0.887920	+	0.367788i	−0.779563	−	0.626324i	$-0.784559\pi$
$349$	−16.5877	+	6.87085i	−0.887920	+	0.367788i	−0.108357	+	0.994112i	$0.534559\pi$
$350$	−18.7913	+	15.2294i	−1.00444	+	0.814044i
$351$		0			0
$352$	1.02280	−	7.89085i	0.0545156	−	0.420584i
$353$	−10.8817			−0.579174			−0.289587	−	0.957152i	$-0.593518\pi$
$353$	−10.8817			−0.579174			−0.289587	+	0.957152i	$0.593518\pi$
$354$		0			0
$355$	−0.0527250	+	0.0218394i	−0.00279835	+	0.00115912i
$356$	−23.6170	+	15.3639i	−1.25170	+	0.814288i
$357$		0			0
$358$	−2.01052	+	3.70645i	−0.106259	+	0.195892i
$359$	−5.54201	−	5.54201i	−0.292496	−	0.292496i	0.545570	−	0.838066i	$-0.316313\pi$
$359$	−5.54201	−	5.54201i	−0.292496	−	0.292496i	−0.838066	+	0.545570i	$0.816313\pi$
$360$		0			0
$361$	−21.1979	+	21.1979i	−1.11568	+	1.11568i
$362$	2.71357	+	9.14744i	0.142622	+	0.480779i
$363$		0			0
$364$	−8.24773	−	5.65880i	−0.432299	−	0.296602i
$365$	−0.0288240	−	0.0695874i	−0.00150872	−	0.00364237i
$366$		0			0
$367$			2.99994i			0.156596i	0.996930	+	0.0782979i	$0.0249485\pi$
$367$			2.99994i			0.156596i	−0.996930	+	0.0782979i	$0.975051\pi$
$368$	0.944098	−	0.364139i	0.0492145	−	0.0189821i
$369$		0			0
$370$	0.00529466	−	0.0505698i	0.000275256	−	0.00262900i
$371$	−11.8568	−	28.6248i	−0.615572	−	1.48612i
$372$		0			0
$373$	−15.3503	−	6.35832i	−0.794811	−	0.329221i	−0.0519347	−	0.998650i	$-0.516539\pi$
$373$	−15.3503	−	6.35832i	−0.794811	−	0.329221i	−0.742876	+	0.669429i	$0.766539\pi$
$374$	11.1030	−	3.29367i	0.574120	−	0.170312i
$375$		0			0
$376$	−16.0953	−	31.4953i	−0.830050	−	1.62424i
$377$	6.41072	+	6.41072i	0.330169	+	0.330169i
$378$		0			0
$379$	−2.50517	+	6.04801i	−0.128682	+	0.310665i	−0.975069	−	0.221903i	$-0.928773\pi$
$379$	−2.50517	+	6.04801i	−0.128682	+	0.310665i	0.846387	+	0.532568i	$0.178773\pi$
$380$	0.0196565	−	0.0928416i	0.00100836	−	0.00476267i
$381$		0			0
$382$	−4.56077	−	5.62748i	−0.233349	−	0.287927i
$383$	32.1450			1.64253			0.821266	−	0.570545i	$-0.193268\pi$
$383$	32.1450			1.64253			0.821266	+	0.570545i	$0.193268\pi$
$384$		0			0
$385$	0.0326222			0.00166258
$386$	18.5166	+	22.8474i	0.942471	+	1.16290i
$387$		0			0
$388$	0.513920	−	2.42735i	0.0260903	−	0.123230i
$389$	−2.48310	+	5.99473i	−0.125898	+	0.303945i	−0.974244	−	0.225498i	$-0.927599\pi$
$389$	−2.48310	+	5.99473i	−0.125898	+	0.303945i	0.848346	+	0.529443i	$0.177599\pi$
$390$		0			0
$391$	1.04143	+	1.04143i	0.0526672	+	0.0526672i
$392$	6.05088	+	11.8404i	0.305616	+	0.598029i
$393$		0			0
$394$	−12.3059	+	3.65053i	−0.619963	+	0.183911i
$395$	−0.00892336	−	0.00369618i	−0.000448983	−	0.000185975i
$396$		0			0
$397$	−9.62118	−	23.2276i	−0.482873	−	1.16576i	−0.958238	−	0.285970i	$-0.907684\pi$
$397$	−9.62118	−	23.2276i	−0.482873	−	1.16576i	0.475365	−	0.879788i	$-0.342316\pi$
$398$	2.04024	−	19.4865i	0.102268	−	0.976771i
$399$		0			0
$400$	−7.19715	−	18.6599i	−0.359858	−	0.932997i
$401$		−	4.48158i		−	0.223800i	−0.993719	−	0.111900i	$-0.964306\pi$
$401$		−	4.48158i		−	0.223800i	0.993719	−	0.111900i	$-0.0356936\pi$
$402$		0			0
$403$	3.46730	+	8.37081i	0.172719	+	0.416980i
$404$	−26.5442	−	18.2121i	−1.32063	−	0.906086i
$405$		0			0
$406$	−8.53142	−	28.7594i	−0.423407	−	1.42730i
$407$	5.27428	−	5.27428i	0.261437	−	0.261437i
$408$		0			0
$409$	22.1171	+	22.1171i	1.09362	+	1.09362i	0.995139	+	0.0984792i	$0.0313978\pi$
$409$	22.1171	+	22.1171i	1.09362	+	1.09362i	0.0984792	+	0.995139i	$0.468602\pi$
$410$	−0.0217703	+	0.0401341i	−0.00107516	+	0.00198208i
$411$		0			0
$412$	13.2902	−	8.64587i	0.654761	−	0.425952i
$413$	13.1726	−	5.45626i	0.648180	−	0.268485i
$414$		0			0
$415$	0.0537885			0.00264037
$416$	6.55136	−	5.04788i	0.321207	−	0.247493i
$417$		0			0
$418$	10.8155	−	8.76537i	0.529002	−	0.428728i
$419$	8.59414	−	3.55981i	0.419851	−	0.173908i	−0.162748	−	0.986668i	$-0.552036\pi$
$419$	8.59414	−	3.55981i	0.419851	−	0.173908i	0.582599	+	0.812760i	$0.302036\pi$
$420$		0			0
$421$	7.82429	−	18.8895i	0.381333	−	0.920619i	−0.610376	−	0.792112i	$-0.708982\pi$
$421$	7.82429	−	18.8895i	0.381333	−	0.920619i	0.991709	−	0.128507i	$-0.0410184\pi$
$422$	−4.57509	+	8.43432i	−0.222712	+	0.410576i
$423$		0			0
$424$	25.5373	−	2.04066i	1.24020	−	0.0991031i
$425$	20.5836	−	20.5836i	0.998453	−	0.998453i
$426$		0			0
$427$	−24.8820	−	10.3064i	−1.20412	−	0.498764i
$428$	−6.69156	+	9.75299i	−0.323449	+	0.471428i
$429$		0			0
$430$	−0.0967749	−	0.0101323i	−0.00466690	−	0.000488624i
$431$			17.2386i			0.830353i	0.909741	+	0.415177i	$0.136280\pi$
$431$			17.2386i			0.830353i	−0.909741	+	0.415177i	$0.863720\pi$
$432$		0			0
$433$			20.8456i			1.00177i	0.865513	+	0.500887i	$0.166993\pi$
$433$			20.8456i			1.00177i	−0.865513	+	0.500887i	$0.833007\pi$
$434$	3.12179	−	29.8165i	0.149851	−	1.43124i
$435$		0			0
$436$	5.05021	−	0.940179i	0.241861	−	0.0450264i
$437$	1.63565	+	0.677508i	0.0782437	+	0.0324096i
$438$		0			0
$439$	−11.5583	+	11.5583i	−0.551648	+	0.551648i	−0.926916	−	0.375269i	$-0.877550\pi$
$439$	−11.5583	+	11.5583i	−0.551648	+	0.551648i	0.375269	+	0.926916i	$0.377550\pi$
$440$	−0.00830462	+	0.0256637i	−0.000395907	+	0.00122347i
$441$		0			0
$442$	10.5812	+	5.73967i	0.503299	+	0.273008i
$443$	−7.86432	+	18.9861i	−0.373645	+	0.902059i	0.619481	+	0.785011i	$0.287343\pi$
$443$	−7.86432	+	18.9861i	−0.373645	+	0.902059i	−0.993126	+	0.117047i	$0.962657\pi$
$444$		0			0
$445$	0.0882424	−	0.0365512i	0.00418309	−	0.00173269i
$446$	−13.0049	−	16.0466i	−0.615799	−	0.759827i
$447$		0			0
$448$	−27.0183	+	4.34576i	−1.27650	+	0.205318i
$449$	2.11825			0.0999665			0.0499832	−	0.998750i	$-0.484083\pi$
$449$	2.11825			0.0999665			0.0499832	+	0.998750i	$0.484083\pi$
$450$		0			0
$451$	−6.18808	+	2.56319i	−0.291385	+	0.120696i
$452$	8.66413	+	1.83438i	0.407526	+	0.0862818i
$453$		0			0
$454$	−5.04733	−	2.73786i	−0.236883	−	0.128494i
$455$	0.0239767	+	0.0239767i	0.00112405	+	0.00112405i
$456$		0			0
$457$	7.54089	−	7.54089i	0.352748	−	0.352748i	−0.508383	−	0.861131i	$-0.669757\pi$
$457$	7.54089	−	7.54089i	0.352748	−	0.352748i	0.861131	+	0.508383i	$0.169757\pi$
$458$	−7.31753	+	2.17073i	−0.341926	+	0.101432i
$459$		0			0
$460$	−0.00337238		0.000627824i	−0.000157238		2.92724e-5i
$461$	1.56851	+	3.78672i	0.0730529	+	0.176365i	0.956188	−	0.292754i	$-0.0945716\pi$
$461$	1.56851	+	3.78672i	0.0730529	+	0.176365i	−0.883135	+	0.469119i	$0.844572\pi$
$462$		0			0
$463$			8.35374i			0.388231i	0.980979	+	0.194116i	$0.0621837\pi$
$463$			8.35374i			0.388231i	−0.980979	+	0.194116i	$0.937816\pi$
$464$	24.7966	+	0.609632i	1.15116	+	0.0283015i
$465$		0			0
$466$	−40.7778	−	4.26943i	−1.88899	−	0.197778i
$467$	−11.8505	−	28.6097i	−0.548377	−	1.32390i	−0.918685	−	0.394990i	$-0.870748\pi$
$467$	−11.8505	−	28.6097i	−0.548377	−	1.32390i	0.370308	−	0.928909i	$-0.379252\pi$
$468$		0			0
$469$	15.0092	+	6.21700i	0.693059	+	0.287075i
$470$	0.0341005	+	0.114952i	0.00157294	+	0.00530236i
$471$		0			0
$472$	0.939072	+	11.7518i	0.0432243	+	0.540919i
$473$	−10.0933	−	10.0933i	−0.464092	−	0.464092i
$474$		0			0
$475$	13.3908	−	32.3283i	0.614414	−	1.48333i
$476$	−21.7200	−	33.3873i	−0.995533	−	1.53031i
$477$		0			0
$478$	2.45746	−	1.99164i	0.112401	−	0.0910953i
$479$	4.36086			0.199253			0.0996264	−	0.995025i	$-0.468235\pi$
$479$	4.36086			0.199253			0.0996264	+	0.995025i	$0.468235\pi$
$480$		0			0
$481$	7.75299			0.353506
$482$	−21.6173	+	17.5197i	−0.984643	+	0.798000i
$483$		0			0
$484$	15.1243	−	9.83903i	0.687468	−	0.447229i
$485$	−0.00321881	+	0.00777090i	−0.000146159	+	0.000352858i
$486$		0			0
$487$	7.91861	+	7.91861i	0.358827	+	0.358827i	0.863380	−	0.504554i	$-0.168343\pi$
$487$	7.91861	+	7.91861i	0.358827	+	0.358827i	−0.504554	+	0.863380i	$0.668343\pi$
$488$	14.4422	−	16.9508i	0.653768	−	0.767326i
$489$		0			0
$490$	−0.0128198	−	0.0432154i	−0.000579139	−	0.00195227i
$491$	−37.8921	−	15.6954i	−1.71005	−	0.708324i	−0.999991	−	0.00417652i	$-0.998671\pi$
$491$	−37.8921	−	15.6954i	−1.71005	−	0.708324i	−0.710054	−	0.704147i	$-0.751329\pi$
$492$		0			0
$493$	13.8158	+	33.3542i	0.622231	+	1.50220i
$494$	14.3915	+	1.50679i	0.647506	+	0.0677939i
$495$		0			0
$496$	22.6617	+	10.0463i	1.01754	+	0.451090i
$497$			28.7928i			1.29153i
$498$		0			0
$499$	−9.18191	−	22.1671i	−0.411039	−	0.992336i	−0.984859	−	0.173355i	$-0.944539\pi$
$499$	−9.18191	−	22.1671i	−0.411039	−	0.992336i	0.573821	−	0.818981i	$-0.305461\pi$
$500$	0.0248178	+	0.133310i	0.00110989	+	0.00596179i
$501$		0			0
$502$	8.57180	−	2.54281i	0.382578	−	0.113491i
$503$	−16.5963	+	16.5963i	−0.739995	+	0.739995i	−0.972577	−	0.232582i	$-0.925283\pi$
$503$	−16.5963	+	16.5963i	−0.739995	+	0.739995i	0.232582	+	0.972577i	$0.425283\pi$
$504$		0			0
$505$	0.0771659	+	0.0771659i	0.00343384	+	0.00343384i
$506$	−0.442331	−	0.239937i	−0.0196640	−	0.0106665i
$507$		0			0
$508$	−6.04526	+	28.5530i	−0.268215	+	1.26683i
$509$	−5.26058	+	2.17900i	−0.233171	+	0.0965826i	−0.496210	−	0.868203i	$-0.665275\pi$
$509$	−5.26058	+	2.17900i	−0.233171	+	0.0965826i	0.263039	+	0.964785i	$0.415275\pi$
$510$		0			0
$511$	−38.0012			−1.68107
$512$	3.45925	−	22.3614i	0.152879	−	0.988245i
$513$		0			0
$514$	8.42361	+	10.3938i	0.371549	+	0.458450i
$515$	−0.0496573	+	0.0205687i	−0.00218816	+	0.000906367i
$516$		0			0
$517$	−6.73118	+	16.2505i	−0.296037	+	0.714697i
$518$	−22.5494	−	12.2316i	−0.990762	−	0.537427i
$519$		0			0
$520$	−0.0249661	+	0.0127586i	−0.00109483	+	0.000559501i
$521$	−13.8290	+	13.8290i	−0.605861	+	0.605861i	−0.941862	−	0.336001i	$-0.890926\pi$
$521$	−13.8290	+	13.8290i	−0.605861	+	0.605861i	0.336001	+	0.941862i	$0.390926\pi$
$522$		0			0
$523$	−20.8657	−	8.64286i	−0.912393	−	0.377926i	−0.123421	−	0.992354i	$-0.539387\pi$
$523$	−20.8657	−	8.64286i	−0.912393	−	0.377926i	−0.788972	+	0.614429i	$0.789387\pi$
$524$	3.41815	+	18.3607i	0.149323	+	0.802092i
$525$		0			0
$526$	1.46150	−	13.9589i	0.0637244	−	0.608639i
$527$			36.0799i			1.57167i
$528$		0			0
$529$			22.9360i			0.997218i
$530$	−0.0863757	−	0.00904353i	−0.00375192	−	0.000392826i
$531$		0			0
$532$	−39.4802	−	27.0875i	−1.71168	−	1.17439i
$533$	−6.43201	−	2.66423i	−0.278601	−	0.115400i
$534$		0			0
$535$	0.0283526	−	0.0283526i	0.00122579	−	0.00122579i
$536$	−8.71175	+	10.2250i	−0.376290	+	0.441651i
$537$		0			0
$538$	−1.02174	+	1.88360i	−0.0440502	+	0.0812077i
$539$	2.53053	−	6.10925i	0.108998	−	0.263144i
$540$		0			0
$541$	24.5863	−	10.1840i	1.05705	−	0.437843i	0.214645	−	0.976692i	$-0.431141\pi$
$541$	24.5863	−	10.1840i	1.05705	−	0.437843i	0.842402	+	0.538849i	$0.181141\pi$
$542$	−2.41267	+	1.95534i	−0.103633	+	0.0839889i
$543$		0			0
$544$	31.7948	−	8.58757i	1.36319	−	0.368189i
$545$	−0.0174145			−0.000745953
$546$		0			0
$547$	9.15022	−	3.79015i	0.391235	−	0.162055i	−0.178389	−	0.983960i	$-0.557089\pi$
$547$	9.15022	−	3.79015i	0.391235	−	0.162055i	0.569625	+	0.821905i	$0.307089\pi$
$548$	0.168312	+	0.258724i	0.00718993	+	0.0110522i
$549$		0			0
$550$	−4.74232	+	8.74260i	−0.202213	+	0.372786i
$551$	30.6868	+	30.6868i	1.30730	+	1.30730i
$552$		0			0
$553$	−3.44572	+	3.44572i	−0.146527	+	0.146527i
$554$	−10.4748	−	35.3104i	−0.445031	−	1.50020i
$555$		0			0
$556$	−7.11224	+	10.3661i	−0.301626	+	0.439622i
$557$	2.57099	+	6.20693i	0.108936	+	0.262996i	0.968942	−	0.247289i	$-0.0795398\pi$
$557$	2.57099	+	6.20693i	0.108936	+	0.262996i	−0.860005	+	0.510285i	$0.829540\pi$
$558$		0			0
$559$		−	14.8368i		−	0.627530i
$560$	0.0927418	+	0.00228008i	0.00391906	+	9.63511e-5i
$561$		0			0
$562$	−3.75246	+	35.8402i	−0.158288	+	1.51183i
$563$	16.2626	+	39.2615i	0.685388	+	1.65467i	0.753872	+	0.657021i	$0.228184\pi$
$563$	16.2626	+	39.2615i	0.685388	+	1.65467i	−0.0684842	+	0.997652i	$0.521816\pi$
$564$		0			0
$565$	−0.0277373	−	0.0114892i	−0.00116692	−	0.000483353i
$566$	4.10469	−	1.21765i	0.172533	−	0.0511817i
$567$		0			0
$568$	−22.6511	−	7.32976i	−0.950420	−	0.307550i
$569$	23.1230	+	23.1230i	0.969368	+	0.969368i	0.999545	−	0.0301764i	$-0.00960691\pi$
$569$	23.1230	+	23.1230i	0.969368	+	0.969368i	−0.0301764	+	0.999545i	$0.509607\pi$
$570$		0			0
$571$	−3.47053	+	8.37861i	−0.145237	+	0.350634i	−0.979711	−	0.200413i	$-0.935772\pi$
$571$	−3.47053	+	8.37861i	−0.145237	+	0.350634i	0.834474	+	0.551047i	$0.185772\pi$
$572$	−4.02376	−	0.851914i	−0.168242	−	0.0356203i
$573$		0			0
$574$	14.5041	+	17.8964i	0.605388	+	0.746981i
$575$	−1.26485			−0.0527478
$576$		0			0
$577$	18.7910			0.782278			0.391139	−	0.920332i	$-0.372081\pi$
$577$	18.7910			0.782278			0.391139	+	0.920332i	$0.372081\pi$
$578$	15.0443	+	18.5630i	0.625762	+	0.772120i
$579$		0			0
$580$	−0.0822630	−	0.0174168i	−0.00341579	−	0.000723193i
$581$	10.3851	−	25.0719i	0.430847	−	1.04016i
$582$		0			0
$583$	−9.00873	−	9.00873i	−0.373104	−	0.373104i
$584$	9.67393	−	29.8953i	0.400310	−	1.23708i
$585$		0			0
$586$	12.4711	−	3.69953i	0.515176	−	0.152826i
$587$	28.1601	+	11.6643i	1.16229	+	0.481436i	0.878637	−	0.477490i	$-0.158453\pi$
$587$	28.1601	+	11.6643i	1.16229	+	0.481436i	0.283653	+	0.958927i	$0.408453\pi$
$588$		0			0
$589$	16.5973	+	40.0693i	0.683878	+	1.65103i
$590$	0.00416166	−	0.0397485i	0.000171333	−	0.00163642i
$591$		0			0
$592$	15.3629	−	14.6256i	0.631412	−	0.601110i
$593$			12.2535i			0.503189i	0.967833	+	0.251594i	$0.0809549\pi$
$593$			12.2535i			0.503189i	−0.967833	+	0.251594i	$0.919045\pi$
$594$		0			0
$595$	0.0516723	+	0.124748i	0.00211836	+	0.00511417i
$596$	18.9491	−	27.6184i	0.776185	−	1.13129i
$597$		0			0
$598$	−0.148755	−	0.501454i	−0.00608306	−	0.0205060i
$599$	−8.63937	+	8.63937i	−0.352995	+	0.352995i	−0.861223	−	0.508228i	$-0.830301\pi$
$599$	−8.63937	+	8.63937i	−0.352995	+	0.352995i	0.508228	+	0.861223i	$0.330301\pi$
$600$		0			0
$601$	−14.3695	−	14.3695i	−0.586143	−	0.586143i	0.350441	−	0.936585i	$-0.386032\pi$
$601$	−14.3695	−	14.3695i	−0.586143	−	0.586143i	−0.936585	+	0.350441i	$0.886032\pi$
$602$	−23.4075	+	43.1524i	−0.954019	+	1.75876i
$603$		0			0
$604$	−14.4801	−	22.2584i	−0.589187	−	0.905681i
$605$	−0.0565102	+	0.0234073i	−0.00229747	+	0.000951642i
$606$		0			0
$607$	21.4916			0.872319			0.436159	−	0.899869i	$-0.356338\pi$
$607$	21.4916			0.872319			0.436159	+	0.899869i	$0.356338\pi$
$608$	31.3600	−	24.1632i	1.27182	−	0.979945i
$609$		0			0
$610$	−0.0586494	+	0.0475322i	−0.00237465	+	0.00192452i
$611$	−16.8911	+	6.99653i	−0.683341	+	0.283049i
$612$		0			0
$613$	12.3921	−	29.9172i	0.500513	−	1.20834i	−0.448693	−	0.893686i	$-0.648110\pi$
$613$	12.3921	−	29.9172i	0.500513	−	1.20834i	0.949205	−	0.314658i	$-0.101890\pi$
$614$	−2.49777	+	4.60472i	−0.100802	+	0.185831i
$615$		0			0
$616$	10.3590	+	8.82592i	0.417374	+	0.355606i
$617$	−17.5651	+	17.5651i	−0.707143	+	0.707143i	−0.965933	−	0.258790i	$-0.916676\pi$
$617$	−17.5651	+	17.5651i	−0.707143	+	0.707143i	0.258790	+	0.965933i	$0.416676\pi$
$618$		0			0
$619$	−16.3569	−	6.77526i	−0.657440	−	0.272321i	0.0289208	−	0.999582i	$-0.490793\pi$
$619$	−16.3569	−	6.77526i	−0.657440	−	0.272321i	−0.686361	+	0.727261i	$0.740793\pi$
$620$	−0.0692930	−	0.0475422i	−0.00278287	−	0.00190934i
$621$		0			0
$622$	−44.6351	−	4.67330i	−1.78971	−	0.187382i
$623$		−	48.1886i		−	1.93064i
$624$		0			0
$625$			24.9993i			0.999972i
$626$	−0.468507	+	4.47476i	−0.0187253	+	0.178847i
$627$		0			0
$628$	−0.380202	−	2.04227i	−0.0151717	−	0.0814955i
$629$	28.5232	+	11.8147i	1.13729	+	0.471083i
$630$		0			0
$631$	23.6874	−	23.6874i	0.942982	−	0.942982i	−0.0554784	−	0.998460i	$-0.517668\pi$
$631$	23.6874	−	23.6874i	0.942982	−	0.942982i	0.998460	+	0.0554784i	$0.0176684\pi$
$632$	−1.83355	−	3.58791i	−0.0729349	−	0.142719i
$633$		0			0
$634$	−42.2953	−	22.9426i	−1.67976	−	0.911167i
$635$	0.0378630	−	0.0914094i	0.00150255	−	0.00362747i
$636$		0			0
$637$	6.35007	−	2.63029i	0.251599	−	0.104216i
$638$	−7.76662	−	9.58314i	−0.307483	−	0.379400i
$639$		0			0
$640$	−0.0254029	+	0.0723790i	−0.00100414	+	0.00286103i
$641$	−6.79529			−0.268398			−0.134199	−	0.990954i	$-0.542846\pi$
$641$	−6.79529			−0.268398			−0.134199	+	0.990954i	$0.542846\pi$
$642$		0			0
$643$	−18.4729	+	7.65173i	−0.728500	+	0.301755i	−0.715935	−	0.698166i	$-0.754000\pi$
$643$	−18.4729	+	7.65173i	−0.728500	+	0.301755i	−0.0125646	+	0.999921i	$0.504000\pi$
$644$	−0.358475	+	1.69315i	−0.0141259	+	0.0667194i
$645$		0			0
$646$	50.6502	+	27.4746i	1.99281	+	1.08097i
$647$	5.34732	+	5.34732i	0.210225	+	0.210225i	0.804363	−	0.594138i	$-0.202507\pi$
$647$	5.34732	+	5.34732i	0.210225	+	0.210225i	−0.594138	+	0.804363i	$0.702507\pi$
$648$		0			0
$649$	4.14565	−	4.14565i	0.162731	−	0.162731i
$650$	−9.91115	+	2.94013i	−0.388747	+	0.115321i
$651$		0			0
$652$	−2.93009	−	15.7391i	−0.114751	−	0.616390i
$653$	1.51225	+	3.65091i	0.0591791	+	0.142871i	0.950703	−	0.310102i	$-0.100363\pi$
$653$	1.51225	+	3.65091i	0.0591791	+	0.142871i	−0.891524	+	0.452973i	$0.850363\pi$
$654$		0			0
$655$		−	0.0633126i		−	0.00247383i
$656$	−17.7713	+	6.85438i	−0.693851	+	0.267619i
$657$		0			0
$658$	60.1655	+	6.29932i	2.34549	+	0.245573i
$659$	7.07771	+	17.0871i	0.275708	+	0.665619i	0.999708	−	0.0241818i	$-0.00769807\pi$
$659$	7.07771	+	17.0871i	0.275708	+	0.665619i	−0.723999	+	0.689801i	$0.757698\pi$
$660$		0			0
$661$	15.2261	+	6.30685i	0.592226	+	0.245308i	0.658608	−	0.752486i	$-0.271146\pi$
$661$	15.2261	+	6.30685i	0.592226	+	0.245308i	−0.0663821	+	0.997794i	$0.521146\pi$
$662$	−10.7112	−	36.1074i	−0.416303	−	1.40335i
$663$		0			0
$664$	17.0802	+	14.5524i	0.662839	+	0.564744i
$665$	0.114772	+	0.114772i	0.00445065	+	0.00445065i
$666$		0			0
$667$	0.600311	−	1.44928i	0.0232441	−	0.0561163i
$668$	1.65268	−	1.07514i	0.0639442	−	0.0415986i
$669$		0			0
$670$	0.0353782	−	0.0286722i	0.00136678	−	0.00110770i
$671$	−11.0744			−0.427524
$672$		0			0
$673$	5.46222			0.210553			0.105276	−	0.994443i	$-0.466427\pi$
$673$	5.46222			0.210553			0.105276	+	0.994443i	$0.466427\pi$
$674$	−22.0848	+	17.8985i	−0.850673	+	0.689425i
$675$		0			0
$676$	11.8468	+	18.2106i	0.455646	+	0.700407i
$677$	4.02477	−	9.71665i	0.154684	−	0.373441i	−0.827472	−	0.561507i	$-0.810222\pi$
$677$	4.02477	−	9.71665i	0.154684	−	0.373441i	0.982156	+	0.188066i	$0.0602218\pi$
$678$		0			0
$679$	3.00070	+	3.00070i	0.115156	+	0.115156i
$680$	−0.111293	+	0.00889328i	−0.00426788	+	0.000341042i
$681$		0			0
$682$	−3.50594	−	11.8185i	−0.134249	−	0.452553i
$683$	−39.7212	−	16.4530i	−1.51989	−	0.629558i	−0.542319	−	0.840173i	$-0.682453\pi$
$683$	−39.7212	−	16.4530i	−1.51989	−	0.629558i	−0.977569	+	0.210615i	$0.932453\pi$
$684$		0			0
$685$	−0.000400418	0	0.000966695i	−1.52992e−5	0	3.69355e-5i
$686$	11.0604	+	1.15802i	0.422287	+	0.0442134i
$687$		0			0
$688$	−27.9889	−	29.3998i	−1.06707	−	1.12086i
$689$		−	13.2425i		−	0.504499i
$690$		0			0
$691$	7.36888	+	17.7900i	0.280325	+	0.676765i	0.999843	−	0.0177088i	$-0.00563718\pi$
$691$	7.36888	+	17.7900i	0.280325	+	0.676765i	−0.719518	+	0.694474i	$0.755637\pi$
$692$	33.9712	−	6.32429i	1.29139	−	0.240414i
$693$		0			0
$694$	−18.5545	+	5.50416i	−0.704319	+	0.208935i
$695$	0.0301350	−	0.0301350i	0.00114309	−	0.00114309i
$696$		0			0
$697$	−19.6033	−	19.6033i	−0.742529	−	0.742529i
$698$	22.3192	+	12.1068i	0.844795	+	0.458249i
$699$		0			0
$700$	33.4648	+	7.08520i	1.26485	+	0.267795i
$701$	−0.759834	+	0.314734i	−0.0286985	+	0.0118873i	−0.396987	−	0.917824i	$-0.629944\pi$
$701$	−0.759834	+	0.314734i	−0.0286985	+	0.0118873i	0.368288	+	0.929712i	$0.379944\pi$
$702$		0			0
$703$	37.1120			1.39970
$704$	−9.58037	+	5.90252i	−0.361074	+	0.222460i
$705$		0			0
$706$	9.68941	+	11.9556i	0.364666	+	0.449957i
$707$	50.8672	−	21.0699i	1.91306	−	0.792415i
$708$		0			0
$709$	−18.3991	+	44.4194i	−0.690994	+	1.66821i	0.0517745	+	0.998659i	$0.483512\pi$
$709$	−18.3991	+	44.4194i	−0.690994	+	1.66821i	−0.742768	+	0.669548i	$0.766488\pi$
$710$	0.0709430	+	0.0384822i	0.00266244	+	0.00144421i
$711$		0			0
$712$	37.9097	+	12.2673i	1.42072	+	0.459738i
$713$	1.10854	−	1.10854i	0.0415152	−	0.0415152i
$714$		0			0
$715$	0.0128817	+	0.00533576i	0.000481747	+	0.000199546i
$716$	5.86249	−	1.09140i	0.219092	−	0.0407875i
$717$		0			0
$718$	−1.15419	+	11.0238i	−0.0430739	+	0.411403i
$719$		−	0.494401i		−	0.0184380i	−0.999958	−	0.00921901i	$-0.997065\pi$
$719$		−	0.494401i		−	0.0184380i	0.999958	−	0.00921901i	$-0.00293455\pi$
$720$		0			0
$721$			27.1175i			1.00991i
$722$	42.1653	+	4.41471i	1.56923	+	0.164298i
$723$		0			0
$724$	7.63398	−	11.1266i	0.283715	−	0.413516i
$725$	−28.6448	−	11.8651i	−1.06384	−	0.440657i
$726$		0			0
$727$	13.9621	−	13.9621i	0.517826	−	0.517826i	−0.399087	−	0.916913i	$-0.630673\pi$
$727$	13.9621	−	13.9621i	0.517826	−	0.517826i	0.916913	+	0.399087i	$0.130673\pi$
$728$	1.12676	+	14.1005i	0.0417604	+	0.522600i
$729$		0			0
$730$	−0.0507894	+	0.0936317i	−0.00187980	+	0.00346546i
$731$	22.6097	−	54.5845i	0.836248	−	2.01888i
$732$		0			0
$733$	21.0117	−	8.70335i	0.776087	−	0.321466i	0.0407515	−	0.999169i	$-0.487025\pi$
$733$	21.0117	−	8.70335i	0.776087	−	0.321466i	0.735335	+	0.677704i	$0.237025\pi$
$734$	3.29602	−	2.67125i	0.121658	−	0.0985976i
$735$		0			0
$736$	−1.24073	−	0.713033i	−0.0457340	−	0.0262828i
$737$	6.68026			0.246071
$738$		0			0
$739$	−23.9176	+	9.90698i	−0.879822	+	0.364434i	−0.776428	−	0.630206i	$-0.782970\pi$
$739$	−23.9176	+	9.90698i	−0.879822	+	0.364434i	−0.103394	+	0.994640i	$0.532970\pi$
$740$	−0.0602753	+	0.0392118i	−0.00221577	+	0.00144146i
$741$		0			0
$742$	−20.8922	+	38.5154i	−0.766977	+	1.41394i
$743$	−22.7644	−	22.7644i	−0.835144	−	0.835144i	0.153071	−	0.988215i	$-0.451084\pi$
$743$	−22.7644	−	22.7644i	−0.835144	−	0.835144i	−0.988215	+	0.153071i	$0.951084\pi$
$744$		0			0
$745$	−0.0802886	+	0.0802886i	−0.00294155	+	0.00294155i
$746$	6.68260	+	22.5270i	0.244667	+	0.824772i
$747$		0			0
$748$	−13.5052	−	9.26595i	−0.493798	−	0.338797i
$749$	−7.74158	−	18.6898i	−0.282871	−	0.682912i
$750$		0			0
$751$			31.4436i			1.14739i	0.819068	+	0.573697i	$0.194491\pi$
$751$			31.4436i			1.14739i	−0.819068	+	0.573697i	$0.805509\pi$
$752$	−20.2719	+	45.7282i	−0.739241	+	1.66754i
$753$		0			0
$754$	1.33511	−	12.7517i	0.0486217	−	0.464391i
$755$	0.0344485	+	0.0831660i	0.00125371	+	0.00302672i
$756$		0			0
$757$	−23.6692	−	9.80412i	−0.860273	−	0.356337i	−0.0914586	−	0.995809i	$-0.529153\pi$
$757$	−23.6692	−	9.80412i	−0.860273	−	0.356337i	−0.768814	+	0.639472i	$0.779153\pi$
$758$	8.87560	−	2.63293i	0.322376	−	0.0956324i
$759$		0			0
$760$	−0.119507	+	0.0610727i	−0.00433499	+	0.00221534i
$761$	5.35154	+	5.35154i	0.193993	+	0.193993i	0.797419	−	0.603426i	$-0.206198\pi$
$761$	5.35154	+	5.35154i	0.193993	+	0.193993i	−0.603426	+	0.797419i	$0.706198\pi$
$762$		0			0
$763$	−3.36226	+	8.11722i	−0.121722	+	0.293863i
$764$	−2.12182	+	10.0218i	−0.0767647	+	0.362575i
$765$		0			0
$766$	−28.6230	−	35.3175i	−1.03419	−	1.27607i
$767$	6.09394			0.220040
$768$		0			0
$769$	16.9993			0.613011			0.306505	−	0.951869i	$-0.400840\pi$
$769$	16.9993			0.613011			0.306505	+	0.951869i	$0.400840\pi$
$770$	−0.0290479	−	0.0358419i	−0.00104681	−	0.00129165i
$771$		0			0
$772$	8.61453	−	40.6882i	0.310044	−	1.46440i
$773$	16.2444	−	39.2174i	0.584269	−	1.41055i	−0.304640	−	0.952467i	$-0.598536\pi$
$773$	16.2444	−	39.2174i	0.584269	−	1.41055i	0.888910	−	0.458083i	$-0.151464\pi$
$774$		0			0
$775$	−21.9102	−	21.9102i	−0.787036	−	0.787036i
$776$	−3.12452	+	1.59675i	−0.112164	+	0.0573199i
$777$		0			0
$778$	8.79740	−	2.60974i	0.315402	−	0.0935636i
$779$	−30.7887	−	12.7531i	−1.10312	−	0.456927i
$780$		0			0
$781$	4.53081	+	10.9383i	0.162125	+	0.391405i
$782$	0.216889	−	2.07153i	0.00775594	−	0.0740778i
$783$		0			0
$784$	7.62106	−	17.1911i	0.272181	−	0.613969i
$785$			0.00704229i			0.000251350i
$786$		0			0
$787$	1.91880	+	4.63239i	0.0683978	+	0.165127i	0.954382	−	0.298589i	$-0.0965159\pi$
$787$	1.91880	+	4.63239i	0.0683978	+	0.165127i	−0.885984	+	0.463716i	$0.846516\pi$
$788$	14.9684	+	10.2699i	0.533228	+	0.365850i
$789$		0			0
$790$	0.00388469	+	0.0130952i	0.000138211	+	0.000465908i
$791$	−10.7107	+	10.7107i	−0.380827	+	0.380827i
$792$		0			0
$793$	−8.13949	−	8.13949i	−0.289042	−	0.289042i
$794$	−16.9530	+	31.2533i	−0.601639	+	1.10914i
$795$		0			0
$796$	−23.2264	+	15.1098i	−0.823239	+	0.535554i
$797$	8.85578	−	3.66818i	0.313688	−	0.129934i	−0.220285	−	0.975436i	$-0.570699\pi$
$797$	8.85578	−	3.66818i	0.313688	−	0.129934i	0.533972	+	0.845502i	$0.320699\pi$
$798$		0			0
$799$	−72.8042			−2.57563
$800$	−14.0930	+	24.5229i	−0.498263	+	0.867015i
$801$		0			0
$802$	−4.92389	+	3.99055i	−0.173869	+	0.140911i
$803$	−14.4366	+	5.97983i	−0.509456	+	0.211024i
$804$		0			0
$805$	0.00224522	−	0.00542044i	7.91336e−5	−	0.000191045i
$806$	6.10956	−	11.2632i	0.215200	−	0.396728i
$807$		0			0
$808$	3.62632	+	45.3807i	0.127574	+	1.59649i
$809$	−13.2208	+	13.2208i	−0.464819	+	0.464819i	−0.900231	−	0.435412i	$-0.856603\pi$
$809$	−13.2208	+	13.2208i	−0.464819	+	0.464819i	0.435412	+	0.900231i	$0.356603\pi$
$810$		0			0
$811$	−9.46797	−	3.92176i	−0.332465	−	0.137712i	0.210205	−	0.977657i	$-0.432587\pi$
$811$	−9.46797	−	3.92176i	−0.332465	−	0.137712i	−0.542671	+	0.839946i	$0.682587\pi$
$812$	−24.0011	+	34.9817i	−0.842273	+	1.22762i
$813$		0			0
$814$	−10.4912	−	1.09843i	−0.367717	−	0.0385000i
$815$			0.0542726i			0.00190109i
$816$		0			0
$817$		−	71.0207i		−	2.48470i
$818$	4.60613	−	43.9937i	0.161050	−	1.53820i
$819$		0			0
$820$	0.0634801	−	0.0118179i	0.00221682	−	0.000412698i
$821$	47.1649	+	19.5363i	1.64607	+	0.681823i	0.996889	−	0.0788144i	$-0.0251134\pi$
$821$	47.1649	+	19.5363i	1.64607	+	0.681823i	0.649177	+	0.760637i	$0.275113\pi$
$822$		0			0
$823$	17.1355	−	17.1355i	0.597306	−	0.597306i	−0.342289	−	0.939595i	$-0.611202\pi$
$823$	17.1355	−	17.1355i	0.597306	−	0.597306i	0.939595	+	0.342289i	$0.111202\pi$
$824$	−21.3332	−	6.90329i	−0.743177	−	0.240488i
$825$		0			0
$826$	−17.7241	−	9.61420i	−0.616699	−	0.334521i
$827$	−7.74891	+	18.7075i	−0.269456	+	0.650524i	−0.999458	−	0.0329210i	$-0.989519\pi$
$827$	−7.74891	+	18.7075i	−0.269456	+	0.650524i	0.730002	+	0.683445i	$0.239519\pi$
$828$		0			0
$829$	2.18250	−	0.904020i	0.0758013	−	0.0313979i	−0.344461	−	0.938801i	$-0.611938\pi$
$829$	2.18250	−	0.904020i	0.0758013	−	0.0313979i	0.420262	+	0.907403i	$0.361938\pi$
$830$	−0.0478950	−	0.0590971i	−0.00166246	−	0.00205129i
$831$		0			0
$832$	−11.3796	−	2.70315i	−0.394518	−	0.0937147i
$833$	27.3701			0.948319
$834$		0			0
$835$	−0.00617506	+	0.00255779i	−0.000213697	+	8.85161e-5i
$836$	−19.2609	−	4.07794i	−0.666153	−	0.141038i
$837$		0			0
$838$	−11.5636	−	6.27256i	−0.399460	−	0.216682i
$839$	−19.2057	−	19.2057i	−0.663056	−	0.663056i	0.293043	−	0.956099i	$-0.405332\pi$
$839$	−19.2057	−	19.2057i	−0.663056	−	0.663056i	−0.956099	+	0.293043i	$0.905332\pi$
$840$		0			0
$841$	6.68416	−	6.68416i	0.230488	−	0.230488i
$842$	−27.7208	+	8.22334i	−0.955322	+	0.283395i
$843$		0			0
$844$	13.3405	−	2.48356i	0.459201	−	0.0854877i
$845$	−0.0281838	−	0.0680418i	−0.000969553	−	0.00234071i
$846$		0			0
$847$			30.8599i			1.06036i
$848$	−24.9813	−	26.2406i	−0.857861	−	0.901106i
$849$		0			0
$850$	−40.9435	−	4.28678i	−1.40435	−	0.147035i
$851$	−0.513362	−	1.23937i	−0.0175978	−	0.0424849i
$852$		0			0
$853$	−35.6393	−	14.7623i	−1.22026	−	0.505450i	−0.322771	−	0.946477i	$-0.604614\pi$
$853$	−35.6393	−	14.7623i	−1.22026	−	0.505450i	−0.897494	+	0.441027i	$0.854614\pi$
$854$	10.8321	+	36.5149i	0.370666	+	1.24951i
$855$		0			0
$856$	16.6739	−	1.33240i	0.569904	−	0.0455404i
$857$	−8.16918	−	8.16918i	−0.279054	−	0.279054i	0.553677	−	0.832731i	$-0.313224\pi$
$857$	−8.16918	−	8.16918i	−0.279054	−	0.279054i	−0.832731	+	0.553677i	$0.813224\pi$
$858$		0			0
$859$	2.26963	−	5.47938i	0.0774389	−	0.186954i	−0.880419	−	0.474197i	$-0.842739\pi$
$859$	2.26963	−	5.47938i	0.0774389	−	0.186954i	0.957858	+	0.287243i	$0.0927386\pi$
$860$	0.0750392	+	0.115348i	0.00255882	+	0.00393334i
$861$		0			0
$862$	18.9399	−	15.3498i	0.645097	−	0.522816i
$863$	−40.5672			−1.38092			−0.690462	−	0.723369i	$-0.742593\pi$
$863$	−40.5672			−1.38092			−0.690462	+	0.723369i	$0.742593\pi$
$864$		0			0
$865$	−0.117142			−0.00398294
$866$	22.9029	−	18.5616i	0.778273	−	0.630748i
$867$		0			0
$868$	−35.5390	+	23.1197i	−1.20627	+	0.784734i
$869$	−0.766809	+	1.85124i	−0.0260122	+	0.0627991i
$870$		0			0
$871$	4.90987	+	4.90987i	0.166364	+	0.166364i
$872$	−5.52984	−	4.71147i	−0.187264	−	0.159550i
$873$		0			0
$874$	−0.712061	−	2.40035i	−0.0240858	−	0.0811932i
$875$	−0.214269	−	0.0887533i	−0.00724363	−	0.00300041i
$876$		0			0
$877$	0.389401	+	0.940098i	0.0131491	+	0.0317449i	0.930318	−	0.366755i	$-0.119531\pi$
$877$	0.389401	+	0.940098i	0.0131491	+	0.0317449i	−0.917169	+	0.398499i	$0.869531\pi$
$878$	22.9909	+	2.40715i	0.775906	+	0.0812373i
$879$		0			0
$880$	0.0355913	−	0.0137276i	0.00119978	−	0.000462756i
$881$		−	19.7730i		−	0.666169i	−0.942897	−	0.333085i	$-0.891910\pi$
$881$		−	19.7730i		−	0.666169i	0.942897	−	0.333085i	$-0.108090\pi$
$882$		0			0
$883$	1.09620	+	2.64647i	0.0368902	+	0.0890608i	0.941251	−	0.337708i	$-0.109652\pi$
$883$	1.09620	+	2.64647i	0.0368902	+	0.0890608i	−0.904361	+	0.426769i	$0.859652\pi$
$884$	−3.11575	−	16.7363i	−0.104794	−	0.562904i
$885$		0			0
$886$	27.8626	−	8.26540i	0.936063	−	0.277682i
$887$	24.5575	−	24.5575i	0.824561	−	0.824561i	−0.162198	−	0.986758i	$-0.551858\pi$
$887$	24.5575	−	24.5575i	0.824561	−	0.824561i	0.986758	+	0.162198i	$0.0518582\pi$
$888$		0			0
$889$	−35.2974	−	35.2974i	−1.18384	−	1.18384i
$890$	−0.118733	−	0.0644050i	−0.00397992	−	0.00215886i
$891$		0			0
$892$	−6.05030	+	28.5768i	−0.202579	+	0.956822i
$893$	−80.8542	+	33.4909i	−2.70568	+	1.12073i
$894$		0			0
$895$	−0.0202154			−0.000675727
$896$	28.8327	+	25.8153i	0.963231	+	0.862427i
$897$		0			0
$898$	−1.88616	−	2.32731i	−0.0629420	−	0.0776634i
$899$	35.5037	−	14.7061i	1.18412	−	0.490477i
$900$		0			0
$901$	20.1801	−	48.7190i	0.672296	−	1.62307i
$902$	8.32623	+	4.51646i	0.277233	+	0.150382i
$903$		0			0
$904$	−5.69941	−	11.1526i	−0.189559	−	0.370931i
$905$	−0.0323457	+	0.0323457i	−0.00107521	+	0.00107521i
$906$		0			0
$907$	20.3745	+	8.43938i	0.676523	+	0.280225i	0.694373	−	0.719616i	$-0.255682\pi$
$907$	20.3745	+	8.43938i	0.676523	+	0.280225i	−0.0178494	+	0.999841i	$0.505682\pi$
$908$	1.48623	+	7.98336i	0.0493224	+	0.264937i
$909$		0			0
$910$	0.00499343	−	0.0476927i	0.000165530	−	0.00158100i
$911$			15.6069i			0.517081i	0.966000	+	0.258540i	$0.0832415\pi$
$911$			15.6069i			0.517081i	−0.966000	+	0.258540i	$0.916758\pi$
$912$		0			0
$913$		−	11.1590i		−	0.369308i
$914$	−14.9998	−	1.57048i	−0.496149	−	0.0519467i
$915$		0			0
$916$	8.90074	+	6.10684i	0.294089	+	0.201776i
$917$	−29.5113	−	12.2240i	−0.974548	−	0.403671i
$918$		0			0
$919$	37.7928	−	37.7928i	1.24667	−	1.24667i	0.289489	−	0.957181i	$-0.406515\pi$
$919$	37.7928	−	37.7928i	1.24667	−	1.24667i	0.957181	−	0.289489i	$-0.0934854\pi$
$920$	0.00369266	+	0.00314618i	0.000121744	+	0.000103726i
$921$		0			0
$922$	2.76380	−	5.09514i	0.0910207	−	0.167799i
$923$	−4.70941	+	11.3695i	−0.155012	+	0.374233i
$924$		0			0
$925$	−24.4959	+	10.1465i	−0.805420	+	0.333616i
$926$	9.17821	−	7.43845i	0.301615	−	0.244443i
$927$		0			0
$928$	−21.4100	−	27.7868i	−0.702816	−	0.912146i
$929$	−8.36281			−0.274375			−0.137187	−	0.990545i	$-0.543806\pi$
$929$	−8.36281			−0.274375			−0.137187	+	0.990545i	$0.543806\pi$
$930$		0			0
$931$	30.3965	−	12.5906i	0.996204	−	0.412641i
$932$	31.6191	+	48.6040i	1.03572	+	1.59208i
$933$		0			0
$934$	−20.8812	+	38.4951i	−0.683255	+	1.25960i
$935$	0.0392605	+	0.0392605i	0.00128395	+	0.00128395i
$936$		0			0
$937$	−37.8809	+	37.8809i	−1.23752	+	1.23752i	−0.276502	+	0.961013i	$0.589175\pi$
$937$	−37.8809	+	37.8809i	−1.23752	+	1.23752i	−0.961013	+	0.276502i	$0.910825\pi$
$938$	−6.53407	−	22.0263i	−0.213345	−	0.719185i
$939$		0			0
$940$	0.0959334	−	0.139823i	0.00312900	−	0.00456053i
$941$	19.7558	+	47.6947i	0.644020	+	1.55480i	0.821211	+	0.570625i	$0.193299\pi$
$941$	19.7558	+	47.6947i	0.644020	+	1.55480i	−0.177191	+	0.984176i	$0.556701\pi$
$942$		0			0
$943$			1.20461i			0.0392275i
$944$	12.0754	−	11.4959i	0.393022	−	0.374160i
$945$		0			0
$946$	−2.10205	+	20.0769i	−0.0683436	+	0.652757i
$947$	−2.05678	−	4.96550i	−0.0668363	−	0.161357i	0.886932	−	0.461900i	$-0.152832\pi$
$947$	−2.05678	−	4.96550i	−0.0668363	−	0.161357i	−0.953768	+	0.300543i	$0.902832\pi$
$948$		0			0
$949$	−15.0057	−	6.21556i	−0.487105	−	0.201766i
$950$	−47.4426	+	14.0738i	−1.53924	+	0.456614i
$951$		0			0
$952$	−17.3423	+	53.5928i	−0.562067	+	1.73695i
$953$	4.72605	+	4.72605i	0.153092	+	0.153092i	0.779497	−	0.626406i	$-0.215475\pi$
$953$	4.72605	+	4.72605i	0.153092	+	0.153092i	−0.626406	+	0.779497i	$0.715475\pi$
$954$		0			0
$955$	0.0132895	−	0.0320837i	0.000430038	−	0.00103820i
$956$	−4.37640	−	0.926574i	−0.141543	−	0.0299676i
$957$		0			0
$958$	−3.88305	−	4.79125i	−0.125456	−	0.154798i
$959$	−0.527906			−0.0170470
$960$		0			0
$961$	7.40512			0.238875
$962$	−6.90352	−	8.51817i	−0.222578	−	0.274637i
$963$		0			0
$964$	38.4976	+	8.15073i	1.23992	+	0.262517i
$965$	−0.0539551	+	0.130259i	−0.00173688	+	0.00419319i
$966$		0			0
$967$	29.3805	+	29.3805i	0.944812	+	0.944812i	0.998555	−	0.0537426i	$-0.0171150\pi$
$967$	29.3805	+	29.3805i	0.944812	+	0.944812i	−0.0537426	+	0.998555i	$0.517115\pi$
$968$	−24.2773	−	7.85597i	−0.780301	−	0.252500i
$969$		0			0
$970$	0.0114040	−	0.00338297i	0.000366160	−	0.000108621i
$971$	22.4822	+	9.31244i	0.721489	+	0.298850i	0.713049	−	0.701114i	$-0.247314\pi$
$971$	22.4822	+	9.31244i	0.721489	+	0.298850i	0.00843940	+	0.999964i	$0.497314\pi$
$972$		0			0
$973$	−8.22827	−	19.8648i	−0.263786	−	0.636836i
$974$	1.64914	−	15.7511i	0.0528419	−	0.504699i
$975$		0			0
$976$	−31.4835	−	0.774031i	−1.00776	−	0.0247761i
$977$		−	30.9704i		−	0.990831i	−0.868656	−	0.495415i	$-0.835016\pi$
$977$		−	30.9704i		−	0.990831i	0.868656	−	0.495415i	$-0.164984\pi$
$978$		0			0
$979$	−7.58291	−	18.3068i	−0.242351	−	0.585087i
$980$	−0.0360653	+	0.0525654i	−0.00115207	+	0.00167914i
$981$		0			0
$982$	16.4959	+	55.6075i	0.526405	+	1.77451i
$983$	−8.78738	+	8.78738i	−0.280274	+	0.280274i	−0.833218	−	0.552944i	$-0.813504\pi$
$983$	−8.78738	+	8.78738i	−0.280274	+	0.280274i	0.552944	+	0.833218i	$0.313504\pi$
$984$		0			0
$985$	−0.0435142	−	0.0435142i	−0.00138648	−	0.00138648i
$986$	24.3441	−	44.8790i	0.775273	−	1.42924i
$987$		0			0
$988$	−11.1592	−	17.1536i	−0.355021	−	0.545729i
$989$	−2.37176	+	0.982415i	−0.0754176	+	0.0312390i
$990$		0			0
$991$	−43.3371			−1.37665			−0.688324	−	0.725403i	$-0.741653\pi$
$991$	−43.3371			−1.37665			−0.688324	+	0.725403i	$0.741653\pi$
$992$	−9.14100	−	33.8438i	−0.290227	−	1.07454i
$993$		0			0
$994$	31.6345	−	25.6381i	1.00338	−	0.813190i
$995$	0.0867829	−	0.0359467i	0.00275120	−	0.00113959i
$996$		0			0
$997$	4.40977	−	10.6461i	0.139659	−	0.337166i	−0.838539	−	0.544842i	$-0.816590\pi$
$997$	4.40977	−	10.6461i	0.139659	−	0.337166i	0.978198	+	0.207675i	$0.0665897\pi$
$998$	−16.1790	+	29.8264i	−0.512137	+	0.944139i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.d.181.2		32
3.2	odd	2		96.2.n.a.85.7	yes	32
4.3	odd	2		1152.2.v.c.433.5		32
12.11	even	2		384.2.n.a.49.3		32
24.5	odd	2		768.2.n.a.97.2		32
24.11	even	2		768.2.n.b.97.6		32
32.3	odd	8		1152.2.v.c.721.5		32
32.29	even	8	inner	288.2.v.d.253.2		32
96.29	odd	8		96.2.n.a.61.7	✓	32
96.35	even	8		384.2.n.a.337.3		32
96.77	odd	8		768.2.n.a.673.2		32
96.83	even	8		768.2.n.b.673.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.7	✓	32	96.29	odd	8
96.2.n.a.85.7	yes	32	3.2	odd	2
288.2.v.d.181.2		32	1.1	even	1	trivial
288.2.v.d.253.2		32	32.29	even	8	inner
384.2.n.a.49.3		32	12.11	even	2
384.2.n.a.337.3		32	96.35	even	8
768.2.n.a.97.2		32	24.5	odd	2
768.2.n.a.673.2		32	96.77	odd	8
768.2.n.b.97.6		32	24.11	even	2
768.2.n.b.673.6		32	96.83	even	8
1152.2.v.c.433.5		32	4.3	odd	2
1152.2.v.c.721.5		32	32.3	odd	8

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.890433 - 1.09869i) q^{2} +(-0.414259 + 1.95663i) q^{4} +(0.00259461 - 0.00626394i) q^{5} +(-2.41880 - 2.41880i) q^{7} +(2.51860 - 1.28710i) q^{8} +O(q^{10})\)	\(q+(-0.890433 - 1.09869i) q^{2} +(-0.414259 + 1.95663i) q^{4} +(0.00259461 - 0.00626394i) q^{5} +(-2.41880 - 2.41880i) q^{7} +(2.51860 - 1.28710i) q^{8} +(-0.00919248 + 0.00272694i) q^{10} +(-1.29952 - 0.538278i) q^{11} +(-0.559497 - 1.35074i) q^{13} +(-0.503742 + 4.81130i) q^{14} +(-3.65678 - 1.62110i) q^{16} -5.82199i q^{17} +(-2.67819 - 6.46573i) q^{19} +(0.0111814 + 0.00767157i) q^{20} +(0.565730 + 1.90707i) q^{22} +(-0.178878 + 0.178878i) q^{23} +(3.53550 + 3.53550i) q^{25} +(-0.985861 + 1.81746i) q^{26} +(5.73469 - 3.73068i) q^{28} +(-5.72901 + 2.37303i) q^{29} -6.19719 q^{31} +(1.47502 + 5.46116i) q^{32} +(-6.39659 + 5.18409i) q^{34} +(-0.0214270 + 0.00887537i) q^{35} +(-2.02932 + 4.89922i) q^{37} +(-4.71911 + 8.69981i) q^{38} +(-0.00152753 - 0.0191159i) q^{40} +(3.36712 - 3.36712i) q^{41} +(9.37558 + 3.88349i) q^{43} +(1.59154 - 2.31968i) q^{44} +(0.355812 + 0.0372534i) q^{46} -12.5050i q^{47} +4.70117i q^{49} +(0.736309 - 7.03256i) q^{50} +(2.87468 - 0.535169i) q^{52} +(8.36811 + 3.46618i) q^{53} +(-0.00674348 + 0.00674348i) q^{55} +(-9.20523 - 2.97876i) q^{56} +(7.70854 + 4.18140i) q^{58} +(-1.59507 + 3.85084i) q^{59} +(7.27395 - 3.01297i) q^{61} +(5.51818 + 6.80881i) q^{62} +(4.68674 - 6.48340i) q^{64} -0.00991266 q^{65} +(-4.38775 + 1.81747i) q^{67} +(11.3915 + 2.41181i) q^{68} +(0.0288307 + 0.0156388i) q^{70} +(-5.95188 - 5.95188i) q^{71} +(7.85539 - 7.85539i) q^{73} +(7.18972 - 2.13282i) q^{74} +(13.7605 - 2.56174i) q^{76} +(1.84128 + 4.44525i) q^{77} -1.42456i q^{79} +(-0.0196424 + 0.0186997i) q^{80} +(-6.69763 - 0.701242i) q^{82} +(3.03596 + 7.32946i) q^{83} +(-0.0364686 - 0.0151058i) q^{85} +(-4.08155 - 13.7589i) q^{86} +(-3.96579 + 0.316902i) q^{88} +(9.96127 + 9.96127i) q^{89} +(-1.91387 + 4.62049i) q^{91} +(-0.275896 - 0.424100i) q^{92} +(-13.7392 + 11.1349i) q^{94} -0.0474498 q^{95} -1.24058 q^{97} +(5.16515 - 4.18607i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) \) 32 * q - 8 * q^10 + 32 * q^14 - 8 * q^16 + 32 * q^20 - 8 * q^22 + 16 * q^23 - 40 * q^26 + 40 * q^28 - 48 * q^31 - 40 * q^32 + 40 * q^34 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 16 * q^43 - 8 * q^44 - 32 * q^46 - 24 * q^50 - 8 * q^52 + 32 * q^53 + 32 * q^55 - 56 * q^56 - 32 * q^58 - 64 * q^59 - 32 * q^61 - 48 * q^62 + 24 * q^64 + 16 * q^67 + 8 * q^68 - 24 * q^70 - 64 * q^71 + 32 * q^74 - 56 * q^76 + 32 * q^77 + 56 * q^80 - 40 * q^82 + 64 * q^86 - 48 * q^88 - 48 * q^91 + 80 * q^92 - 32 * q^94 + 80 * q^98

Introduction

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