LMFDB - Embedded newform 585.2.j.f.406.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(406,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("585.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.j (of order $3$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1714608.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 30x^2 - 21*x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.2
Root			$0.500000 + 1.75780i$ of defining polynomial
Character	$\chi$	$=$	585.406
Dual form			585.2.j.f.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.169938 - 0.294342i) q^{2} +(0.942242 - 1.63201i) q^{4} -1.00000 q^{5} +(-0.330062 + 0.571683i) q^{7} -1.32025 q^{8} +O(q^{10})$	\(q+(-0.169938 - 0.294342i) q^{2} +(0.942242 - 1.63201i) q^{4} -1.00000 q^{5} +(-0.330062 + 0.571683i) q^{7} -1.32025 q^{8} +(0.169938 + 0.294342i) q^{10} +(0.339877 + 0.588684i) q^{11} +(1.93243 - 3.04397i) q^{13} +0.224361 q^{14} +(-1.66012 - 2.87542i) q^{16} +(3.71455 - 6.43378i) q^{17} +(-0.0577581 + 0.100040i) q^{19} +(-0.942242 + 1.63201i) q^{20} +(0.115516 - 0.200080i) q^{22} +(-3.88448 - 6.72812i) q^{23} +1.00000 q^{25} +(-1.22436 - 0.0515075i) q^{26} +(0.621996 + 1.07733i) q^{28} +(2.77230 + 4.80177i) q^{29} -9.97370 q^{31} +(-1.88448 + 3.26402i) q^{32} -2.52498 q^{34} +(0.330062 - 0.571683i) q^{35} +(-4.88448 - 8.46017i) q^{37} +0.0392613 q^{38} +1.32025 q^{40} +(2.11218 + 3.65840i) q^{41} +(0.272303 - 0.471643i) q^{43} +1.28098 q^{44} +(-1.32025 + 2.28673i) q^{46} +5.01963 q^{47} +(3.28212 + 5.68480i) q^{49} +(-0.169938 - 0.294342i) q^{50} +(-3.14697 - 6.02189i) q^{52} -0.679754 q^{53} +(-0.339877 - 0.588684i) q^{55} +(0.435763 - 0.754763i) q^{56} +(0.942242 - 1.63201i) q^{58} +(1.11218 - 1.92635i) q^{59} +(2.10236 - 3.64140i) q^{61} +(1.69491 + 2.93568i) q^{62} -5.35951 q^{64} +(-1.93243 + 3.04397i) q^{65} +(3.81691 + 6.61108i) q^{67} +(-7.00000 - 12.1244i) q^{68} -0.224361 q^{70} +(3.65679 - 6.33374i) q^{71} +8.01963 q^{73} +(-1.66012 + 2.87542i) q^{74} +(0.108844 + 0.188524i) q^{76} -0.448721 q^{77} +9.97370 q^{79} +(1.66012 + 2.87542i) q^{80} +(0.717881 - 1.24341i) q^{82} -1.76897 q^{83} +(-3.71455 + 6.43378i) q^{85} -0.185099 q^{86} +(-0.448721 - 0.777208i) q^{88} +(6.77230 + 11.7300i) q^{89} +(1.10236 + 2.10943i) q^{91} -14.6405 q^{92} +(-0.853028 - 1.47749i) q^{94} +(0.0577581 - 0.100040i) q^{95} +(-4.95206 + 8.57721i) q^{97} +(1.11552 - 1.93213i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{5} - 3 q^{7} - 12 q^{8}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^5 - 3 * q^7 - 12 * q^8	$ 6 q - 6 q^{4} - 6 q^{5} - 3 q^{7} - 12 q^{8} + 3 q^{13} - 24 q^{14} - 12 q^{16} - 12 q^{19} + 6 q^{20} + 24 q^{22} + 6 q^{25} + 18 q^{26} - 12 q^{28} + 6 q^{29} + 6 q^{31} + 12 q^{32} + 3 q^{35} - 6 q^{37} - 12 q^{38} + 12 q^{40} - 9 q^{43} + 24 q^{44} - 12 q^{46} + 24 q^{47} + 6 q^{49} + 12 q^{52} + 30 q^{56} - 6 q^{58} - 6 q^{59} + 3 q^{61} - 6 q^{62} - 24 q^{64} - 3 q^{65} - 9 q^{67} - 42 q^{68} + 24 q^{70} - 12 q^{71} + 42 q^{73} - 12 q^{74} - 48 q^{76} + 48 q^{77} - 6 q^{79} + 12 q^{80} + 18 q^{82} + 36 q^{83} + 12 q^{86} + 48 q^{88} + 30 q^{89} - 3 q^{91} - 96 q^{92} - 36 q^{94} + 12 q^{95} - 15 q^{97} + 30 q^{98}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^5 - 3 * q^7 - 12 * q^8 + 3 * q^13 - 24 * q^14 - 12 * q^16 - 12 * q^19 + 6 * q^20 + 24 * q^22 + 6 * q^25 + 18 * q^26 - 12 * q^28 + 6 * q^29 + 6 * q^31 + 12 * q^32 + 3 * q^35 - 6 * q^37 - 12 * q^38 + 12 * q^40 - 9 * q^43 + 24 * q^44 - 12 * q^46 + 24 * q^47 + 6 * q^49 + 12 * q^52 + 30 * q^56 - 6 * q^58 - 6 * q^59 + 3 * q^61 - 6 * q^62 - 24 * q^64 - 3 * q^65 - 9 * q^67 - 42 * q^68 + 24 * q^70 - 12 * q^71 + 42 * q^73 - 12 * q^74 - 48 * q^76 + 48 * q^77 - 6 * q^79 + 12 * q^80 + 18 * q^82 + 36 * q^83 + 12 * q^86 + 48 * q^88 + 30 * q^89 - 3 * q^91 - 96 * q^92 - 36 * q^94 + 12 * q^95 - 15 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.169938	−	0.294342i	−0.120165	−	0.208131i	0.799668	−	0.600443i	$-0.205009\pi$
$2$	−0.169938	−	0.294342i	−0.120165	−	0.208131i	−0.919832	+	0.392311i	$0.871676\pi$
$3$		0			0
$3$		0			0
$4$	0.942242	−	1.63201i	0.471121	−	0.816005i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−0.330062	+	0.571683i	−0.124752	+	0.216076i	−0.921636	−	0.388056i	$-0.873147\pi$
$7$	−0.330062	+	0.571683i	−0.124752	+	0.216076i	0.796884	+	0.604132i	$0.206480\pi$
$8$	−1.32025			−0.466778
$9$		0			0
$10$	0.169938	+	0.294342i	0.0537393	+	0.0930791i
$11$	0.339877	+	0.588684i	0.102477	+	0.177495i	0.912704	−	0.408620i	$-0.133990\pi$
$11$	0.339877	+	0.588684i	0.102477	+	0.177495i	−0.810228	+	0.586115i	$0.800657\pi$
$12$		0			0
$13$	1.93243	−	3.04397i	0.535959	−	0.844244i
$13$	1.93243	−	3.04397i	0.535959	−	0.844244i
$14$	0.224361			0.0599629
$15$		0			0
$16$	−1.66012	−	2.87542i	−0.415031	−	0.718854i
$17$	3.71455	−	6.43378i	0.900910	−	1.56042i	0.0745938	−	0.997214i	$-0.476234\pi$
$17$	3.71455	−	6.43378i	0.900910	−	1.56042i	0.826316	−	0.563207i	$-0.190433\pi$
$18$		0			0
$19$	−0.0577581	+	0.100040i	−0.0132506	+	0.0229508i	−0.872575	−	0.488481i	$-0.837551\pi$
$19$	−0.0577581	+	0.100040i	−0.0132506	+	0.0229508i	0.859324	+	0.511431i	$0.170885\pi$
$20$	−0.942242	+	1.63201i	−0.210692	+	0.364929i
$21$		0			0
$22$	0.115516	−	0.200080i	0.0246282	−	0.0426572i
$23$	−3.88448	−	6.72812i	−0.809971	−	1.40291i	−0.912883	−	0.408220i	$-0.866150\pi$
$23$	−3.88448	−	6.72812i	−0.809971	−	1.40291i	0.102913	−	0.994690i	$-0.467184\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−1.22436	−	0.0515075i	−0.240117	−	0.0101015i
$27$		0			0
$28$	0.621996	+	1.07733i	0.117546	+	0.203596i
$29$	2.77230	+	4.80177i	0.514804	+	0.891666i	0.999852	+	0.0171792i	$0.00546857\pi$
$29$	2.77230	+	4.80177i	0.514804	+	0.891666i	−0.485049	+	0.874487i	$0.661198\pi$
$30$		0			0
$31$	−9.97370			−1.79133			−0.895664	−	0.444730i	$-0.853299\pi$
$31$	−9.97370			−1.79133			−0.895664	+	0.444730i	$0.853299\pi$
$32$	−1.88448	+	3.26402i	−0.333133	+	0.577003i
$33$		0			0
$34$	−2.52498			−0.433030
$35$	0.330062	−	0.571683i	0.0557906	−	0.0966321i
$36$		0			0
$37$	−4.88448	−	8.46017i	−0.803004	−	1.39084i	−0.917630	−	0.397435i	$-0.869900\pi$
$37$	−4.88448	−	8.46017i	−0.803004	−	1.39084i	0.114626	−	0.993409i	$-0.463433\pi$
$38$	0.0392613			0.00636903
$39$		0			0
$40$	1.32025			0.208749
$41$	2.11218	+	3.65840i	0.329867	+	0.571347i	0.982485	−	0.186340i	$-0.0596627\pi$
$41$	2.11218	+	3.65840i	0.329867	+	0.571347i	−0.652618	+	0.757687i	$0.726329\pi$
$42$		0			0
$43$	0.272303	−	0.471643i	0.0415259	−	0.0719249i	−0.844515	−	0.535531i	$-0.820111\pi$
$43$	0.272303	−	0.471643i	0.0415259	−	0.0719249i	0.886041	+	0.463606i	$0.153445\pi$
$44$	1.28098			0.193116
$45$		0			0
$46$	−1.32025	+	2.28673i	−0.194660	+	0.337160i
$47$	5.01963			0.732188			0.366094	−	0.930578i	$-0.380695\pi$
$47$	5.01963			0.732188			0.366094	+	0.930578i	$0.380695\pi$
$48$		0			0
$49$	3.28212	+	5.68480i	0.468874	+	0.812114i
$50$	−0.169938	−	0.294342i	−0.0240329	−	0.0416262i
$51$		0			0
$52$	−3.14697	−	6.02189i	−0.436406	−	0.835086i
$53$	−0.679754			−0.0933714			−0.0466857	−	0.998910i	$-0.514866\pi$
$53$	−0.679754			−0.0933714			−0.0466857	+	0.998910i	$0.514866\pi$
$54$		0			0
$55$	−0.339877	−	0.588684i	−0.0458290	−	0.0793781i
$56$	0.435763	−	0.754763i	0.0582312	−	0.100859i
$57$		0			0
$58$	0.942242	−	1.63201i	0.123722	−	0.214294i
$59$	1.11218	−	1.92635i	0.144794	−	0.250790i	−0.784502	−	0.620126i	$-0.787082\pi$
$59$	1.11218	−	1.92635i	0.144794	−	0.250790i	0.929296	+	0.369336i	$0.120415\pi$
$60$		0			0
$61$	2.10236	−	3.64140i	0.269180	−	0.466234i	−0.699470	−	0.714662i	$-0.746581\pi$
$61$	2.10236	−	3.64140i	0.269180	−	0.466234i	0.968650	+	0.248428i	$0.0799139\pi$
$62$	1.69491	+	2.93568i	0.215254	+	0.372832i
$63$		0			0
$64$	−5.35951			−0.669938
$65$	−1.93243	+	3.04397i	−0.239688	+	0.377557i
$66$		0			0
$67$	3.81691	+	6.61108i	0.466310	+	0.807672i	0.999260	−	0.0384746i	$-0.0122499\pi$
$67$	3.81691	+	6.61108i	0.466310	+	0.807672i	−0.532950	+	0.846147i	$0.678917\pi$
$68$	−7.00000	−	12.1244i	−0.848875	−	1.47029i
$69$		0			0
$70$	−0.224361			−0.0268162
$71$	3.65679	−	6.33374i	0.433981	−	0.751677i	−0.563231	−	0.826299i	$-0.690442\pi$
$71$	3.65679	−	6.33374i	0.433981	−	0.751677i	0.997212	+	0.0746227i	$0.0237752\pi$
$72$		0			0
$73$	8.01963			0.938627			0.469313	−	0.883032i	$-0.344501\pi$
$73$	8.01963			0.938627			0.469313	+	0.883032i	$0.344501\pi$
$74$	−1.66012	+	2.87542i	−0.192985	+	0.334261i
$75$		0			0
$76$	0.108844	+	0.188524i	0.0124853	+	0.0216252i
$77$	−0.448721			−0.0511365
$78$		0			0
$79$	9.97370			1.12213			0.561064	−	0.827772i	$-0.310392\pi$
$79$	9.97370			1.12213			0.561064	+	0.827772i	$0.310392\pi$
$80$	1.66012	+	2.87542i	0.185607	+	0.321481i
$81$		0			0
$82$	0.717881	−	1.24341i	0.0792767	−	0.137311i
$83$	−1.76897			−0.194169			−0.0970847	−	0.995276i	$-0.530952\pi$
$83$	−1.76897			−0.194169			−0.0970847	+	0.995276i	$0.530952\pi$
$84$		0			0
$85$	−3.71455	+	6.43378i	−0.402899	+	0.697842i
$86$	−0.185099			−0.0199598
$87$		0			0
$88$	−0.448721	−	0.777208i	−0.0478338	−	0.0828506i
$89$	6.77230	+	11.7300i	0.717863	+	1.24337i	0.961845	+	0.273595i	$0.0882128\pi$
$89$	6.77230	+	11.7300i	0.717863	+	1.24337i	−0.243982	+	0.969780i	$0.578454\pi$
$90$		0			0
$91$	1.10236	+	2.10943i	0.115559	+	0.221129i
$92$	−14.6405			−1.52638
$93$		0			0
$94$	−0.853028	−	1.47749i	−0.0879831	−	0.152391i
$95$	0.0577581	−	0.100040i	0.00592586	−	0.0102639i
$96$		0			0
$97$	−4.95206	+	8.57721i	−0.502805	+	0.870884i	0.497190	+	0.867642i	$0.334365\pi$
$97$	−4.95206	+	8.57721i	−0.502805	+	0.870884i	−0.999995	+	0.00324223i	$0.998968\pi$
$98$	1.11552	−	1.93213i	0.112684	−	0.195175i
$99$		0			0
$100$	0.942242	−	1.63201i	0.0942242	−	0.163201i
$101$	−4.67975	−	8.10557i	−0.465653	−	0.806534i	0.533578	−	0.845751i	$-0.320847\pi$
$101$	−4.67975	−	8.10557i	−0.465653	−	0.806534i	−0.999231	+	0.0392165i	$0.987514\pi$
$102$		0			0
$103$	4.50535			0.443925			0.221962	−	0.975055i	$-0.428754\pi$
$103$	4.50535			0.443925			0.221962	+	0.975055i	$0.428754\pi$
$104$	−2.55128	+	4.01878i	−0.250173	+	0.394074i
$105$		0			0
$106$	0.115516	+	0.200080i	0.0112199	+	0.0194335i
$107$	0.285455	+	0.494422i	0.0275960	+	0.0477976i	0.879494	−	0.475911i	$-0.157881\pi$
$107$	0.285455	+	0.494422i	0.0275960	+	0.0477976i	−0.851898	+	0.523708i	$0.824548\pi$
$108$		0			0
$109$	15.4095			1.47596			0.737979	−	0.674823i	$-0.235780\pi$
$109$	15.4095			1.47596			0.737979	+	0.674823i	$0.235780\pi$
$110$	−0.115516	+	0.200080i	−0.0110140	+	0.0190769i
$111$		0			0
$112$	2.19177			0.207103
$113$	−2.66012	+	4.60747i	−0.250243	+	0.433434i	−0.963593	−	0.267374i	$-0.913844\pi$
$113$	−2.66012	+	4.60747i	−0.250243	+	0.433434i	0.713349	+	0.700809i	$0.247177\pi$
$114$		0			0
$115$	3.88448	+	6.72812i	0.362230	+	0.627401i
$116$	10.4487			0.970139
$117$		0			0
$118$	−0.756009			−0.0695962
$119$	2.45206	+	4.24709i	0.224780	+	0.389330i
$120$		0			0
$121$	5.26897	−	9.12612i	0.478997	−	0.829647i
$122$	−1.42909			−0.129384
$123$		0			0
$124$	−9.39764	+	16.2772i	−0.843933	+	1.46173i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	6.00982	+	10.4093i	0.533285	+	0.923676i	0.999244	+	0.0388704i	$0.0123759\pi$
$127$	6.00982	+	10.4093i	0.533285	+	0.923676i	−0.465959	+	0.884806i	$0.654291\pi$
$128$	4.67975	+	8.10557i	0.413636	+	0.716438i
$129$		0			0
$130$	1.22436	+	0.0515075i	0.107384	+	0.00451751i
$131$	−10.9041			−0.952697			−0.476348	−	0.879257i	$-0.658040\pi$
$131$	−10.9041			−0.952697			−0.476348	+	0.879257i	$0.658040\pi$
$132$		0			0
$133$	−0.0381275	−	0.0660387i	−0.00330607	−	0.00572629i
$134$	1.29728	−	2.24695i	0.112068	−	0.194107i
$135$		0			0
$136$	−4.90411	+	8.49418i	−0.420524	+	0.728370i
$137$	1.69491	−	2.93568i	0.144806	−	0.250812i	−0.784494	−	0.620136i	$-0.787077\pi$
$137$	1.69491	−	2.93568i	0.144806	−	0.250812i	0.929301	+	0.369324i	$0.120411\pi$
$138$		0			0
$139$	−7.40411	+	12.8243i	−0.628009	+	1.08774i	0.359942	+	0.932975i	$0.382796\pi$
$139$	−7.40411	+	12.8243i	−0.628009	+	1.08774i	−0.987951	+	0.154768i	$0.950537\pi$
$140$	−0.621996	−	1.07733i	−0.0525682	−	0.0910508i
$141$		0			0
$142$	−2.48571			−0.208597
$143$	2.44872	+	0.103015i	0.204772	+	0.00861455i
$144$		0			0
$145$	−2.77230	−	4.80177i	−0.230227	−	0.398765i
$146$	−1.36284	−	2.36051i	−0.112790	−	0.195358i
$147$		0			0
$148$	−18.4095			−1.51325
$149$	−8.54461	+	14.7997i	−0.700001	+	1.21244i	0.268464	+	0.963290i	$0.413484\pi$
$149$	−8.54461	+	14.7997i	−0.700001	+	1.21244i	−0.968465	+	0.249148i	$0.919849\pi$
$150$		0			0
$151$	13.0130			1.05898			0.529490	−	0.848316i	$-0.322383\pi$
$151$	13.0130			1.05898			0.529490	+	0.848316i	$0.322383\pi$
$152$	0.0762550	−	0.132077i	0.00618510	−	0.0107129i
$153$		0			0
$154$	0.0762550	+	0.132077i	0.00614480	+	0.0106431i
$155$	9.97370			0.801107
$156$		0			0
$157$	−0.775639			−0.0619028			−0.0309514	−	0.999521i	$-0.509854\pi$
$157$	−0.775639			−0.0619028			−0.0309514	+	0.999521i	$0.509854\pi$
$158$	−1.69491	−	2.93568i	−0.134840	−	0.233550i
$159$		0			0
$160$	1.88448	−	3.26402i	0.148982	−	0.258044i
$161$	5.12847			0.404180
$162$		0			0
$163$	−6.09903	+	10.5638i	−0.477713	+	0.827423i	−0.999674	−	0.0255466i	$-0.991867\pi$
$163$	−6.09903	+	10.5638i	−0.477713	+	0.827423i	0.521961	+	0.852969i	$0.325201\pi$
$164$	7.96074			0.621629
$165$		0			0
$166$	0.300616	+	0.520681i	0.0233323	+	0.0404127i
$167$	−0.795270	−	1.37745i	−0.0615398	−	0.106590i	0.833614	−	0.552347i	$-0.186268\pi$
$167$	−0.795270	−	1.37745i	−0.0615398	−	0.106590i	−0.895154	+	0.445757i	$0.852934\pi$
$168$		0			0
$169$	−5.53146	−	11.7645i	−0.425497	−	0.904960i
$170$	2.52498			0.193657
$171$		0			0
$172$	−0.513151	−	0.888804i	−0.0391274	−	0.0677707i
$173$	6.37467	−	11.0412i	0.484657	−	0.839451i	−0.515188	−	0.857077i	$-0.672278\pi$
$173$	6.37467	−	11.0412i	0.484657	−	0.839451i	0.999845	+	0.0176268i	$0.00561108\pi$
$174$		0			0
$175$	−0.330062	+	0.571683i	−0.0249503	+	0.0432152i
$176$	1.12847	−	1.95458i	0.0850620	−	0.147332i
$177$		0			0
$178$	2.30175	−	3.98675i	0.172523	−	0.298819i
$179$	8.88115	+	15.3826i	0.663808	+	1.14975i	0.979607	+	0.200923i	$0.0643942\pi$
$179$	8.88115	+	15.3826i	0.663808	+	1.14975i	−0.315799	+	0.948826i	$0.602272\pi$
$180$		0			0
$181$	7.02630			0.522261			0.261130	−	0.965304i	$-0.415905\pi$
$181$	7.02630			0.522261			0.261130	+	0.965304i	$0.415905\pi$
$182$	0.433560	−	0.682946i	0.0321376	−	0.0506233i
$183$		0			0
$184$	5.12847	+	8.88278i	0.378076	+	0.654847i
$185$	4.88448	+	8.46017i	0.359114	+	0.622004i
$186$		0			0
$187$	5.04995			0.369289
$188$	4.72971	−	8.19209i	0.344949	−	0.597470i
$189$		0			0
$190$	−0.0392613			−0.00284832
$191$	−6.97703	+	12.0846i	−0.504840	+	0.874409i	0.495144	+	0.868811i	$0.335115\pi$
$191$	−6.97703	+	12.0846i	−0.504840	+	0.874409i	−0.999984	+	0.00559828i	$0.998218\pi$
$192$		0			0
$193$	−11.8747	−	20.5675i	−0.854757	−	1.48048i	−0.876870	−	0.480728i	$-0.840373\pi$
$193$	−11.8747	−	20.5675i	−0.854757	−	1.48048i	0.0221126	−	0.999755i	$-0.492961\pi$
$194$	3.36618			0.241678
$195$		0			0
$196$	12.3702			0.883586
$197$	7.90411	+	13.6903i	0.563145	+	0.975395i	0.997220	+	0.0745186i	$0.0237420\pi$
$197$	7.90411	+	13.6903i	0.563145	+	0.975395i	−0.434075	+	0.900877i	$0.642925\pi$
$198$		0			0
$199$	−4.38448	+	7.59415i	−0.310808	+	0.538335i	−0.978537	−	0.206069i	$-0.933933\pi$
$199$	−4.38448	+	7.59415i	−0.310808	+	0.538335i	0.667730	+	0.744404i	$0.267266\pi$
$200$	−1.32025			−0.0933555
$201$		0			0
$202$	−1.59054	+	2.75490i	−0.111910	+	0.193834i
$203$	−3.66012			−0.256890
$204$		0			0
$205$	−2.11218	−	3.65840i	−0.147521	−	0.255514i
$206$	−0.765631	−	1.32611i	−0.0533441	−	0.0923946i
$207$		0			0
$208$	−11.9607	−	0.503175i	−0.829328	−	0.0348889i
$209$	−0.0785226			−0.00543152
$210$		0			0
$211$	−4.40411	−	7.62815i	−0.303192	−	0.525143i	0.673665	−	0.739037i	$-0.264719\pi$
$211$	−4.40411	−	7.62815i	−0.303192	−	0.525143i	−0.976857	+	0.213893i	$0.931386\pi$
$212$	−0.640492	+	1.10937i	−0.0439892	+	0.0761915i
$213$		0			0
$214$	0.0970195	−	0.168043i	0.00663211	−	0.0114872i
$215$	−0.272303	+	0.471643i	−0.0185709	+	0.0321658i
$216$		0			0
$217$	3.29193	−	5.70180i	0.223471	−	0.387063i
$218$	−2.61866	−	4.53565i	−0.177358	−	0.307193i
$219$		0			0
$220$	−1.28098			−0.0863640
$221$	−12.4061	−	23.7398i	−0.834526	−	1.59691i
$222$		0			0
$223$	−5.01963	−	8.69426i	−0.336139	−	0.582210i	0.647564	−	0.762011i	$-0.275788\pi$
$223$	−5.01963	−	8.69426i	−0.336139	−	0.582210i	−0.983703	+	0.179801i	$0.942455\pi$
$224$	−1.24399	−	2.15466i	−0.0831177	−	0.143964i
$225$		0			0
$226$	1.80823			0.120282
$227$	0.605701	−	1.04910i	0.0402018	−	0.0696315i	−0.845224	−	0.534412i	$-0.820533\pi$
$227$	0.605701	−	1.04910i	0.0402018	−	0.0696315i	0.885426	+	0.464780i	$0.153867\pi$
$228$		0			0
$229$	19.2440			1.27168			0.635839	−	0.771821i	$-0.280654\pi$
$229$	19.2440			1.27168			0.635839	+	0.771821i	$0.280654\pi$
$230$	1.32025	−	2.28673i	0.0870545	−	0.150783i
$231$		0			0
$232$	−3.66012	−	6.33952i	−0.240299	−	0.416210i
$233$	23.9081			1.56627			0.783137	−	0.621849i	$-0.213618\pi$
$233$	23.9081			1.56627			0.783137	+	0.621849i	$0.213618\pi$
$234$		0			0
$235$	−5.01963			−0.327445
$236$	−2.09589	−	3.63018i	−0.136431	−	0.236305i
$237$		0			0
$238$	0.833398	−	1.44349i	0.0540211	−	0.0935674i
$239$	−18.6798			−1.20829			−0.604146	−	0.796873i	$-0.706486\pi$
$239$	−18.6798			−1.20829			−0.604146	+	0.796873i	$0.706486\pi$
$240$		0			0
$241$	−3.05776	+	5.29619i	−0.196968	+	0.341158i	−0.947544	−	0.319626i	$-0.896443\pi$
$241$	−3.05776	+	5.29619i	−0.196968	+	0.341158i	0.750576	+	0.660784i	$0.229776\pi$
$242$	−3.58160			−0.230234
$243$		0			0
$244$	−3.96187	−	6.86216i	−0.253633	−	0.439305i
$245$	−3.28212	−	5.68480i	−0.209687	−	0.363188i
$246$		0			0
$247$	0.192905	+	0.369134i	0.0122743	+	0.0234874i
$248$	13.1677			0.836152
$249$		0			0
$250$	0.169938	+	0.294342i	0.0107479	+	0.0186158i
$251$	1.67975	−	2.90942i	0.106025	−	0.183641i	−0.808131	−	0.589002i	$-0.799521\pi$
$251$	1.67975	−	2.90942i	0.106025	−	0.183641i	0.914157	+	0.405361i	$0.132854\pi$
$252$		0			0
$253$	2.64049	−	4.57347i	0.166006	−	0.287531i
$254$	2.04260	−	3.53788i	0.128164	−	0.221986i
$255$		0			0
$256$	−3.76897	+	6.52804i	−0.235560	+	0.408003i
$257$	−5.05442	−	8.75452i	−0.315286	−	0.546092i	0.664212	−	0.747544i	$-0.268767\pi$
$257$	−5.05442	−	8.75452i	−0.315286	−	0.546092i	−0.979498	+	0.201452i	$0.935434\pi$
$258$		0			0
$259$	6.44872			0.400704
$260$	3.14697	+	6.02189i	0.195167	+	0.373462i
$261$		0			0
$262$	1.85303	+	3.20954i	0.114480	+	0.198286i
$263$	−11.2592	−	19.5014i	−0.694269	−	1.20251i	−0.970426	−	0.241397i	$-0.922394\pi$
$263$	−11.2592	−	19.5014i	−0.694269	−	1.20251i	0.276157	−	0.961112i	$-0.410939\pi$
$264$		0			0
$265$	0.679754			0.0417569
$266$	−0.0129587	+	0.0224450i	−0.000794546	+	0.00137619i
$267$		0			0
$268$	14.3858			0.878753
$269$	4.24733	−	7.35659i	0.258964	−	0.448539i	−0.707001	−	0.707213i	$-0.749952\pi$
$269$	4.24733	−	7.35659i	0.258964	−	0.448539i	0.965965	+	0.258674i	$0.0832855\pi$
$270$		0			0
$271$	−4.68510	−	8.11483i	−0.284600	−	0.492941i	0.687912	−	0.725794i	$-0.258527\pi$
$271$	−4.68510	−	8.11483i	−0.284600	−	0.492941i	−0.972512	+	0.232853i	$0.925194\pi$
$272$	−24.6664			−1.49562
$273$		0			0
$274$	−1.15212			−0.0696024
$275$	0.339877	+	0.588684i	0.0204953	+	0.0354990i
$276$		0			0
$277$	−0.359508	+	0.622685i	−0.0216007	+	0.0374135i	−0.876624	−	0.481177i	$-0.840210\pi$
$277$	−0.359508	+	0.622685i	−0.0216007	+	0.0374135i	0.855023	+	0.518590i	$0.173543\pi$
$278$	5.03297			0.301858
$279$		0			0
$280$	−0.435763	+	0.754763i	−0.0260418	+	0.0451057i
$281$	−1.54461			−0.0921435			−0.0460718	−	0.998938i	$-0.514670\pi$
$281$	−1.54461			−0.0921435			−0.0460718	+	0.998938i	$0.514670\pi$
$282$		0			0
$283$	9.05977	+	15.6920i	0.538547	+	0.932791i	0.998983	+	0.0450980i	$0.0143600\pi$
$283$	9.05977	+	15.6920i	0.538547	+	0.932791i	−0.460435	+	0.887693i	$0.652307\pi$
$284$	−6.89116	−	11.9358i	−0.408915	−	0.708261i
$285$		0			0
$286$	−0.385810	−	0.738268i	−0.0228134	−	0.0436547i
$287$	−2.78860			−0.164606
$288$		0			0
$289$	−19.0957	−	33.0747i	−1.12328	−	1.94557i
$290$	−0.942242	+	1.63201i	−0.0553303	+	0.0958350i
$291$		0			0
$292$	7.55643	−	13.0881i	0.442207	−	0.765924i
$293$	−15.2525	+	26.4181i	−0.891059	+	1.54336i	−0.0524523	+	0.998623i	$0.516704\pi$
$293$	−15.2525	+	26.4181i	−0.891059	+	1.54336i	−0.838607	+	0.544737i	$0.816630\pi$
$294$		0			0
$295$	−1.11218	+	1.92635i	−0.0647536	+	0.112157i
$296$	6.44872	+	11.1695i	0.374824	+	0.649215i
$297$		0			0
$298$	5.80823			0.336462
$299$	−27.9867	−	1.17737i	−1.61851	−	0.0680890i
$300$		0			0
$301$	0.179754	+	0.311343i	0.0103608	+	0.0179455i
$302$	−2.21140	−	3.83026i	−0.127252	−	0.220407i
$303$		0			0
$304$	0.383543			0.0219977
$305$	−2.10236	+	3.64140i	−0.120381	+	0.208506i
$306$		0			0
$307$	−4.77564			−0.272560			−0.136280	−	0.990670i	$-0.543515\pi$
$307$	−4.77564			−0.272560			−0.136280	+	0.990670i	$0.543515\pi$
$308$	−0.422804	+	0.732318i	−0.0240915	+	0.0417277i
$309$		0			0
$310$	−1.69491	−	2.93568i	−0.0962647	−	0.166735i
$311$	−30.5812			−1.73410			−0.867051	−	0.498220i	$-0.833987\pi$
$311$	−30.5812			−1.73410			−0.867051	+	0.498220i	$0.833987\pi$
$312$		0			0
$313$	−26.7230			−1.51048			−0.755238	−	0.655451i	$-0.772479\pi$
$313$	−26.7230			−1.51048			−0.755238	+	0.655451i	$0.772479\pi$
$314$	0.131811	+	0.228303i	0.00743852	+	0.0128839i
$315$		0			0
$316$	9.39764	−	16.2772i	0.528658	−	0.915663i
$317$	20.6271			1.15854			0.579268	−	0.815137i	$-0.303338\pi$
$317$	20.6271			1.15854			0.579268	+	0.815137i	$0.303338\pi$
$318$		0			0
$319$	−1.88448	+	3.26402i	−0.105511	+	0.182750i
$320$	5.35951			0.299606
$321$		0			0
$322$	−0.871525	−	1.50953i	−0.0485682	−	0.0841226i
$323$	0.429091	+	0.743207i	0.0238752	+	0.0413531i
$324$		0			0
$325$	1.93243	−	3.04397i	0.107192	−	0.168849i
$326$	4.14584			0.229617
$327$		0			0
$328$	−2.78860	−	4.82999i	−0.153975	−	0.266692i
$329$	−1.65679	+	2.86964i	−0.0913416	+	0.158208i
$330$		0			0
$331$	−2.68510	+	4.65073i	−0.147586	+	0.255627i	−0.930335	−	0.366711i	$-0.880484\pi$
$331$	−2.68510	+	4.65073i	−0.147586	+	0.255627i	0.782749	+	0.622338i	$0.213817\pi$
$332$	−1.66680	+	2.88697i	−0.0914773	+	0.158443i
$333$		0			0
$334$	−0.270294	+	0.468163i	−0.0147898	+	0.0256167i
$335$	−3.81691	−	6.61108i	−0.208540	−	0.361202i
$336$		0			0
$337$	28.7623			1.56678			0.783391	−	0.621529i	$-0.213488\pi$
$337$	28.7623			1.56678			0.783391	+	0.621529i	$0.213488\pi$
$338$	−2.52277	+	3.62738i	−0.137221	+	0.197303i
$339$		0			0
$340$	7.00000	+	12.1244i	0.379628	+	0.657536i
$341$	−3.38983	−	5.87136i	−0.183570	−	0.317952i
$342$		0			0
$343$	−8.95407			−0.483474
$344$	−0.359508	+	0.622685i	−0.0193833	+	0.0335729i
$345$		0			0
$346$	−4.33320			−0.232955
$347$	11.1981	−	19.3956i	0.601143	−	1.04121i	−0.391505	−	0.920176i	$-0.628045\pi$
$347$	11.1981	−	19.3956i	0.601143	−	1.04121i	0.992648	−	0.121035i	$-0.0386212\pi$
$348$		0			0
$349$	5.98685	+	10.3695i	0.320469	+	0.555068i	0.980585	−	0.196096i	$-0.0628263\pi$
$349$	5.98685	+	10.3695i	0.320469	+	0.555068i	−0.660116	+	0.751164i	$0.729493\pi$
$350$	0.224361			0.0119926
$351$		0			0
$352$	−2.56197			−0.136553
$353$	−8.51830	−	14.7541i	−0.453384	−	0.785283i	0.545210	−	0.838299i	$-0.316450\pi$
$353$	−8.51830	−	14.7541i	−0.453384	−	0.785283i	−0.998594	+	0.0530161i	$0.983117\pi$
$354$		0			0
$355$	−3.65679	+	6.33374i	−0.194082	+	0.336160i
$356$	25.5246			1.35280
$357$		0			0
$358$	3.01850	−	5.22819i	0.159533	−	0.276318i
$359$	35.0825			1.85159			0.925793	−	0.378031i	$-0.123399\pi$
$359$	35.0825			1.85159			0.925793	+	0.378031i	$0.123399\pi$
$360$		0			0
$361$	9.49333	+	16.4429i	0.499649	+	0.865417i
$362$	−1.19404	−	2.06814i	−0.0627573	−	0.108699i
$363$		0			0
$364$	4.48131	+	0.188524i	0.234884	+	0.00988133i
$365$	−8.01963			−0.419767
$366$		0			0
$367$	−10.0413	−	17.3920i	−0.524150	−	0.907855i	−0.999605	−	0.0281143i	$-0.991050\pi$
$367$	−10.0413	−	17.3920i	−0.524150	−	0.907855i	0.475455	−	0.879740i	$-0.342284\pi$
$368$	−12.8974	+	22.3390i	−0.672326	+	1.16450i
$369$		0			0
$370$	1.66012	−	2.87542i	0.0863057	−	0.149486i
$371$	0.224361	−	0.388604i	0.0116482	−	0.0201753i
$372$		0			0
$373$	11.7395	−	20.3334i	0.607849	−	1.05283i	−0.383745	−	0.923439i	$-0.625366\pi$
$373$	11.7395	−	20.3334i	0.607849	−	1.05283i	0.991594	−	0.129387i	$-0.0413009\pi$
$374$	−0.858181	−	1.48641i	−0.0443755	−	0.0768606i
$375$		0			0
$376$	−6.62715			−0.341769
$377$	19.9737	+	0.840272i	1.02870	+	0.0432762i
$378$		0			0
$379$	−10.5707	−	18.3090i	−0.542981	−	0.940471i	−0.998731	−	0.0503631i	$-0.983962\pi$
$379$	−10.5707	−	18.3090i	−0.542981	−	0.940471i	0.455750	−	0.890108i	$-0.349371\pi$
$380$	−0.108844	−	0.188524i	−0.00558359	−	0.00967107i
$381$		0			0
$382$	4.74266			0.242656
$383$	0.869323	−	1.50571i	0.0444203	−	0.0769383i	−0.842960	−	0.537976i	$-0.819189\pi$
$383$	0.869323	−	1.50571i	0.0444203	−	0.0769383i	0.887381	+	0.461037i	$0.152523\pi$
$384$		0			0
$385$	0.448721			0.0228689
$386$	−4.03593	+	6.99043i	−0.205423	+	0.355803i
$387$		0			0
$388$	9.33207	+	16.1636i	0.473764	+	0.820584i
$389$	26.6664			1.35204			0.676020	−	0.736883i	$-0.263703\pi$
$389$	26.6664			1.35204			0.676020	+	0.736883i	$0.263703\pi$
$390$		0			0
$391$	−57.7164			−2.91884
$392$	−4.33320	−	7.50533i	−0.218860	−	0.379076i
$393$		0			0
$394$	2.68643	−	4.65303i	0.135340	−	0.234416i
$395$	−9.97370			−0.501831
$396$		0			0
$397$	−7.27230	+	12.5960i	−0.364986	+	0.632175i	−0.988774	−	0.149419i	$-0.952260\pi$
$397$	−7.27230	+	12.5960i	−0.364986	+	0.632175i	0.623788	+	0.781594i	$0.285593\pi$
$398$	2.98037			0.149392
$399$		0			0
$400$	−1.66012	−	2.87542i	−0.0830062	−	0.143771i
$401$	−4.18510	−	7.24880i	−0.208994	−	0.361988i	0.742404	−	0.669952i	$-0.233686\pi$
$401$	−4.18510	−	7.24880i	−0.208994	−	0.361988i	−0.951398	+	0.307964i	$0.900352\pi$
$402$		0			0
$403$	−19.2734	+	30.3596i	−0.960078	+	1.51232i
$404$	−17.6378			−0.877515
$405$		0			0
$406$	0.621996	+	1.07733i	0.0308691	+	0.0534669i
$407$	3.32025	−	5.75084i	0.164578	−	0.285058i
$408$		0			0
$409$	−8.62734	+	14.9430i	−0.426595	+	0.738883i	−0.996568	−	0.0827798i	$-0.973620\pi$
$409$	−8.62734	+	14.9430i	−0.426595	+	0.738883i	0.569973	+	0.821663i	$0.306954\pi$
$410$	−0.717881	+	1.24341i	−0.0354536	+	0.0614075i
$411$		0			0
$412$	4.24513	−	7.35277i	0.209142	−	0.362245i
$413$	0.734176	+	1.27163i	0.0361264	+	0.0625728i
$414$		0			0
$415$	1.76897			0.0868352
$416$	6.29394	+	12.0438i	0.308586	+	0.590495i
$417$		0			0
$418$	0.0133440	+	0.0231125i	0.000652677	+	0.00113047i
$419$	6.43243	+	11.1413i	0.314245	+	0.544288i	0.979277	−	0.202527i	$-0.0649155\pi$
$419$	6.43243	+	11.1413i	0.314245	+	0.544288i	−0.665032	+	0.746815i	$0.731582\pi$
$420$		0			0
$421$	24.5616			1.19706			0.598529	−	0.801101i	$-0.295752\pi$
$421$	24.5616			1.19706			0.598529	+	0.801101i	$0.295752\pi$
$422$	−1.49686	+	2.59263i	−0.0728658	+	0.126207i
$423$		0			0
$424$	0.897442			0.0435837
$425$	3.71455	−	6.43378i	0.180182	−	0.312084i
$426$		0			0
$427$	1.38782	+	2.40377i	0.0671613	+	0.116327i
$428$	1.07587			0.0520041
$429$		0			0
$430$	0.185099			0.00892628
$431$	12.3898	+	21.4598i	0.596797	+	1.03368i	0.993291	+	0.115645i	$0.0368936\pi$
$431$	12.3898	+	21.4598i	0.596797	+	1.03368i	−0.396493	+	0.918038i	$0.629773\pi$
$432$		0			0
$433$	7.02945	−	12.1754i	0.337814	−	0.585110i	−0.646208	−	0.763162i	$-0.723646\pi$
$433$	7.02945	−	12.1754i	0.337814	−	0.585110i	0.984021	+	0.178051i	$0.0569793\pi$
$434$	−2.23770			−0.107413
$435$		0			0
$436$	14.5194	−	25.1484i	0.695355	−	1.20439i
$437$	0.897442			0.0429305
$438$		0			0
$439$	−10.4226	−	18.0525i	−0.497444	−	0.861598i	0.502552	−	0.864547i	$-0.332395\pi$
$439$	−10.4226	−	18.0525i	−0.497444	−	0.861598i	−0.999996	+	0.00294880i	$0.999061\pi$
$440$	0.448721	+	0.777208i	0.0213919	+	0.0370519i
$441$		0			0
$442$	−4.87933	+	7.68594i	−0.232086	+	0.365583i
$443$	11.4291			0.543012			0.271506	−	0.962437i	$-0.412478\pi$
$443$	11.4291			0.543012			0.271506	+	0.962437i	$0.412478\pi$
$444$		0			0
$445$	−6.77230	−	11.7300i	−0.321038	−	0.556054i
$446$	−1.70606	+	2.95498i	−0.0807841	+	0.139922i
$447$		0			0
$448$	1.76897	−	3.06394i	0.0835759	−	0.144758i
$449$	12.9541	−	22.4371i	0.611340	−	1.05887i	−0.379675	−	0.925120i	$-0.623964\pi$
$449$	12.9541	−	22.4371i	0.611340	−	1.05887i	0.991015	−	0.133752i	$-0.0427026\pi$
$450$		0			0
$451$	−1.43576	+	2.48681i	−0.0676074	+	0.117099i
$452$	5.01296	+	8.68270i	0.235790	+	0.408400i
$453$		0			0
$454$	−0.411728			−0.0193233
$455$	−1.10236	−	2.10943i	−0.0516797	−	0.0988917i
$456$		0			0
$457$	−2.95206	−	5.11311i	−0.138091	−	0.239181i	0.788683	−	0.614800i	$-0.210763\pi$
$457$	−2.95206	−	5.11311i	−0.138091	−	0.239181i	−0.926774	+	0.375619i	$0.877430\pi$
$458$	−3.27029	−	5.66432i	−0.152811	−	0.264676i
$459$		0			0
$460$	14.6405			0.682616
$461$	−7.74600	+	13.4165i	−0.360767	+	0.624867i	−0.988087	−	0.153894i	$-0.950818\pi$
$461$	−7.74600	+	13.4165i	−0.360767	+	0.624867i	0.627320	+	0.778762i	$0.284152\pi$
$462$		0			0
$463$	17.4420			0.810601			0.405300	−	0.914184i	$-0.367167\pi$
$463$	17.4420			0.810601			0.405300	+	0.914184i	$0.367167\pi$
$464$	9.20473	−	15.9431i	0.427319	−	0.740138i
$465$		0			0
$466$	−4.06291	−	7.03717i	−0.188211	−	0.325991i
$467$	20.4790			0.947657			0.473829	−	0.880617i	$-0.342872\pi$
$467$	20.4790			0.947657			0.473829	+	0.880617i	$0.342872\pi$
$468$		0			0
$469$	−5.03926			−0.232691
$470$	0.853028	+	1.47749i	0.0393473	+	0.0681514i
$471$		0			0
$472$	−1.46835	+	2.54326i	−0.0675864	+	0.117063i
$473$	0.370199			0.0170217
$474$		0			0
$475$	−0.0577581	+	0.100040i	−0.00265013	+	0.00459015i
$476$	9.24172			0.423594
$477$		0			0
$478$	3.17441	+	5.49824i	0.145194	+	0.251483i
$479$	−20.4953	−	35.4990i	−0.936456	−	1.62199i	−0.772017	−	0.635602i	$-0.780752\pi$
$479$	−20.4953	−	35.4990i	−0.936456	−	1.62199i	−0.164439	−	0.986387i	$-0.552581\pi$
$480$		0			0
$481$	−35.1914	−	1.48046i	−1.60459	−	0.0675033i
$482$	2.07852			0.0946741
$483$		0			0
$484$	−9.92928	−	17.1980i	−0.451331	−	0.781728i
$485$	4.95206	−	8.57721i	0.224861	−	0.389471i
$486$		0			0
$487$	−12.0315	+	20.8391i	−0.545197	+	0.944309i	0.453397	+	0.891309i	$0.350212\pi$
$487$	−12.0315	+	20.8391i	−0.545197	+	0.944309i	−0.998594	+	0.0530008i	$0.983121\pi$
$488$	−2.77564	+	4.80755i	−0.125647	+	0.217627i
$489$		0			0
$490$	−1.11552	+	1.93213i	−0.0503939	+	0.0872848i
$491$	18.3865	+	31.8463i	0.829771	+	1.43721i	0.898218	+	0.439550i	$0.144862\pi$
$491$	18.3865	+	31.8463i	0.829771	+	1.43721i	−0.0684471	+	0.997655i	$0.521804\pi$
$492$		0			0
$493$	41.1914			1.85517
$494$	0.0758696	−	0.119510i	0.00341354	−	0.00537701i
$495$		0			0
$496$	16.5576	+	28.6785i	0.743457	+	1.28770i
$497$	2.41393	+	4.18105i	0.108280	+	0.187546i
$498$		0			0
$499$	34.8212			1.55881			0.779405	−	0.626520i	$-0.215521\pi$
$499$	34.8212			1.55881			0.779405	+	0.626520i	$0.215521\pi$
$500$	−0.942242	+	1.63201i	−0.0421383	+	0.0729857i
$501$		0			0
$502$	−1.14182			−0.0509619
$503$	−16.0130	+	27.7353i	−0.713983	+	1.23665i	0.249368	+	0.968409i	$0.419777\pi$
$503$	−16.0130	+	27.7353i	−0.713983	+	1.23665i	−0.963351	+	0.268245i	$0.913556\pi$
$504$		0			0
$505$	4.67975	+	8.10557i	0.208246	+	0.360693i
$506$	−1.79488			−0.0797924
$507$		0			0
$508$	22.6508			1.00497
$509$	−20.6731	−	35.8068i	−0.916318	−	1.58711i	−0.804960	−	0.593329i	$-0.797813\pi$
$509$	−20.6731	−	35.8068i	−0.916318	−	1.58711i	−0.111359	−	0.993780i	$-0.535520\pi$
$510$		0			0
$511$	−2.64697	+	4.58469i	−0.117095	+	0.202815i
$512$	21.2810			0.940496
$513$		0			0
$514$	−1.71788	+	2.97546i	−0.0757725	+	0.131242i
$515$	−4.50535			−0.198529
$516$		0			0
$517$	1.70606	+	2.95498i	0.0750323	+	0.129960i
$518$	−1.09589	−	1.89813i	−0.0481505	−	0.0833990i
$519$		0			0
$520$	2.55128	−	4.01878i	0.111881	−	0.176235i
$521$	−4.40279			−0.192890			−0.0964448	−	0.995338i	$-0.530747\pi$
$521$	−4.40279			−0.192890			−0.0964448	+	0.995338i	$0.530747\pi$
$522$		0			0
$523$	16.2244	+	28.1014i	0.709442	+	1.22879i	0.965064	+	0.262013i	$0.0843862\pi$
$523$	16.2244	+	28.1014i	0.709442	+	1.22879i	−0.255623	+	0.966777i	$0.582280\pi$
$524$	−10.2743	+	17.7956i	−0.448835	+	0.777406i
$525$		0			0
$526$	−3.82673	+	6.62808i	−0.166853	+	0.288998i
$527$	−37.0478	+	64.1686i	−1.61383	+	2.79523i
$528$		0			0
$529$	−18.6784	+	32.3520i	−0.812106	+	1.40661i
$530$	−0.115516	−	0.200080i	−0.00501771	−	0.00869092i
$531$		0			0
$532$	−0.143701			−0.00623024
$533$	15.2177	+	0.640192i	0.659151	+	0.0277298i
$534$		0			0
$535$	−0.285455	−	0.494422i	−0.0123413	−	0.0213757i
$536$	−5.03926	−	8.72826i	−0.217663	−	0.377003i
$537$		0			0
$538$	−2.88714			−0.124473
$539$	−2.23103	+	3.86426i	−0.0960974	+	0.166446i
$540$		0			0
$541$	−8.57720			−0.368762			−0.184381	−	0.982855i	$-0.559028\pi$
$541$	−8.57720			−0.368762			−0.184381	+	0.982855i	$0.559028\pi$
$542$	−1.59236	+	2.75804i	−0.0683976	+	0.118468i
$543$		0			0
$544$	14.0000	+	24.2487i	0.600245	+	1.03965i
$545$	−15.4095			−0.660069
$546$		0			0
$547$	−32.4920			−1.38926			−0.694629	−	0.719368i	$-0.744431\pi$
$547$	−32.4920			−1.38926			−0.694629	+	0.719368i	$0.744431\pi$
$548$	−3.19404	−	5.53224i	−0.136443	−	0.236325i
$549$		0			0
$550$	0.115516	−	0.200080i	0.00492563	−	0.00853144i
$551$	−0.640492			−0.0272859
$552$		0			0
$553$	−3.29193	+	5.70180i	−0.139987	+	0.242465i
$554$	0.244377			0.0103826
$555$		0			0
$556$	13.9529	+	24.1672i	0.591736	+	1.02492i
$557$	−20.6075	−	35.6933i	−0.873169	−	1.51237i	−0.858701	−	0.512477i	$-0.828728\pi$
$557$	−20.6075	−	35.6933i	−0.873169	−	1.51237i	−0.0144676	−	0.999895i	$-0.504605\pi$
$558$		0			0
$559$	−0.909460	−	1.74030i	−0.0384661	−	0.0736068i
$560$	−2.19177			−0.0926192
$561$		0			0
$562$	0.262488	+	0.454643i	0.0110724	+	0.0191779i
$563$	−6.08921	+	10.5468i	−0.256630	+	0.444496i	−0.965337	−	0.261007i	$-0.915945\pi$
$563$	−6.08921	+	10.5468i	−0.256630	+	0.444496i	0.708707	+	0.705503i	$0.249279\pi$
$564$		0			0
$565$	2.66012	−	4.60747i	0.111912	−	0.193838i
$566$	3.07921	−	5.33334i	0.129429	−	0.224177i
$567$		0			0
$568$	−4.82786	+	8.36210i	−0.202572	+	0.350866i
$569$	3.47169	+	6.01314i	0.145541	+	0.252084i	0.929575	−	0.368634i	$-0.120174\pi$
$569$	3.47169	+	6.01314i	0.145541	+	0.252084i	−0.784034	+	0.620718i	$0.786841\pi$
$570$		0			0
$571$	3.51429			0.147068			0.0735341	−	0.997293i	$-0.476572\pi$
$571$	3.51429			0.147068			0.0735341	+	0.997293i	$0.476572\pi$
$572$	2.47541	−	3.89927i	0.103502	−	0.163037i
$573$		0			0
$574$	0.473890	+	0.820802i	0.0197798	+	0.0342596i
$575$	−3.88448	−	6.72812i	−0.161994	−	0.280582i
$576$		0			0
$577$	3.14182			0.130796			0.0653978	−	0.997859i	$-0.479168\pi$
$577$	3.14182			0.130796			0.0653978	+	0.997859i	$0.479168\pi$
$578$	−6.49018	+	11.2413i	−0.269956	+	0.467578i
$579$		0			0
$580$	−10.4487			−0.433860
$581$	0.583868	−	1.01129i	0.0242229	−	0.0419553i
$582$		0			0
$583$	−0.231033	−	0.400160i	−0.00956839	−	0.0165729i
$584$	−10.5879			−0.438130
$585$		0			0
$586$	10.3679			0.428295
$587$	18.9889	+	32.8897i	0.783754	+	1.35750i	0.929741	+	0.368215i	$0.120031\pi$
$587$	18.9889	+	32.8897i	0.783754	+	1.35750i	−0.145987	+	0.989287i	$0.546636\pi$
$588$		0			0
$589$	0.576062	−	0.997769i	0.0237362	−	0.0411124i
$590$	0.756009			0.0311244
$591$		0			0
$592$	−16.2177	+	28.0899i	−0.666543	+	1.15449i
$593$	−10.4487			−0.429078			−0.214539	−	0.976715i	$-0.568825\pi$
$593$	−10.4487			−0.429078			−0.214539	+	0.976715i	$0.568825\pi$
$594$		0			0
$595$	−2.45206	−	4.24709i	−0.100525	−	0.174114i
$596$	16.1022	+	27.8898i	0.659571	+	1.14241i
$597$		0			0
$598$	4.40946	+	8.43773i	0.180316	+	0.345044i
$599$	45.5705			1.86196			0.930981	−	0.365069i	$-0.118955\pi$
$599$	45.5705			1.86196			0.930981	+	0.365069i	$0.118955\pi$
$600$		0			0
$601$	7.39096	+	12.8015i	0.301484	+	0.522185i	0.976472	−	0.215643i	$-0.0691848\pi$
$601$	7.39096	+	12.8015i	0.301484	+	0.522185i	−0.674989	+	0.737828i	$0.735851\pi$
$602$	0.0610942	−	0.105818i	0.00249001	−	0.00431283i
$603$		0			0
$604$	12.2614	−	21.2373i	0.498907	−	0.864133i
$605$	−5.26897	+	9.12612i	−0.214214	+	0.371030i
$606$		0			0
$607$	9.46722	−	16.3977i	0.384263	−	0.665562i	−0.607404	−	0.794393i	$-0.707789\pi$
$607$	9.46722	−	16.3977i	0.384263	−	0.665562i	0.991667	+	0.128831i	$0.0411224\pi$
$608$	−0.217689	−	0.377048i	−0.00882844	−	0.0152913i
$609$		0			0
$610$	1.42909			0.0578622
$611$	9.70007	−	15.2796i	0.392423	−	0.618146i
$612$		0			0
$613$	1.29193	+	2.23770i	0.0521807	+	0.0903797i	0.890936	−	0.454129i	$-0.150049\pi$
$613$	1.29193	+	2.23770i	0.0521807	+	0.0903797i	−0.838755	+	0.544509i	$0.816716\pi$
$614$	0.811565	+	1.40567i	0.0327521	+	0.0567283i
$615$		0			0
$616$	0.592422			0.0238694
$617$	7.01963	−	12.1584i	0.282600	−	0.489477i	−0.689425	−	0.724357i	$-0.742137\pi$
$617$	7.01963	−	12.1584i	0.282600	−	0.489477i	0.972024	+	0.234880i	$0.0754699\pi$
$618$		0			0
$619$	−17.8582			−0.717781			−0.358890	−	0.933380i	$-0.616845\pi$
$619$	−17.8582			−0.717781			−0.358890	+	0.933380i	$0.616845\pi$
$620$	9.39764	−	16.2772i	0.377418	−	0.653707i
$621$		0			0
$622$	5.19692	+	9.00134i	0.208378	+	0.360921i
$623$	−8.94111			−0.358218
$624$		0			0
$625$	1.00000			0.0400000
$626$	4.54127	+	7.86571i	0.181506	+	0.314377i
$627$		0			0
$628$	−0.730840	+	1.26585i	−0.0291637	+	0.0505130i
$629$	−72.5745			−2.89374
$630$		0			0
$631$	12.4815	−	21.6186i	0.496881	−	0.860623i	−0.503113	−	0.864221i	$-0.667812\pi$
$631$	12.4815	−	21.6186i	0.496881	−	0.860623i	0.999994	+	0.00359801i	$0.00114528\pi$
$632$	−13.1677			−0.523784
$633$		0			0
$634$	−3.50535	−	6.07144i	−0.139215	−	0.241128i
$635$	−6.00982	−	10.4093i	−0.238492	−	0.413081i
$636$		0			0
$637$	23.6468	+	0.994794i	0.936920	+	0.0394152i
$638$	1.28098			0.0507147
$639$		0			0
$640$	−4.67975	−	8.10557i	−0.184984	−	0.320401i
$641$	11.6535	−	20.1844i	0.460284	−	0.797235i	−0.538691	−	0.842503i	$-0.681081\pi$
$641$	11.6535	−	20.1844i	0.460284	−	0.797235i	0.998975	+	0.0452686i	$0.0144144\pi$
$642$		0			0
$643$	−22.7395	+	39.3860i	−0.896759	+	1.55323i	−0.0651470	+	0.997876i	$0.520752\pi$
$643$	−22.7395	+	39.3860i	−0.896759	+	1.55323i	−0.831612	+	0.555357i	$0.812582\pi$
$644$	4.83226	−	8.36973i	0.190418	−	0.329813i
$645$		0			0
$646$	0.145838	−	0.252599i	0.00573792	−	0.00993836i
$647$	3.20473	+	5.55076i	0.125991	+	0.218223i	0.922120	−	0.386904i	$-0.126456\pi$
$647$	3.20473	+	5.55076i	0.125991	+	0.218223i	−0.796129	+	0.605127i	$0.793122\pi$
$648$		0			0
$649$	1.51202			0.0593519
$650$	−1.22436	−	0.0515075i	−0.0480234	−	0.00202029i
$651$		0			0
$652$	11.4935	+	19.9074i	0.450121	+	0.779632i
$653$	0.740848	+	1.28319i	0.0289916	+	0.0502150i	0.880157	−	0.474682i	$-0.157437\pi$
$653$	0.740848	+	1.28319i	0.0289916	+	0.0502150i	−0.851166	+	0.524897i	$0.824104\pi$
$654$		0			0
$655$	10.9041			0.426059
$656$	7.01296	−	12.1468i	0.273810	−	0.474253i
$657$		0			0
$658$	1.12621			0.0439041
$659$	−3.54461	+	6.13944i	−0.138078	+	0.239159i	−0.926769	−	0.375631i	$-0.877426\pi$
$659$	−3.54461	+	6.13944i	−0.138078	+	0.239159i	0.788691	+	0.614790i	$0.210759\pi$
$660$		0			0
$661$	−0.589214	−	1.02055i	−0.0229178	−	0.0396947i	0.854339	−	0.519716i	$-0.173962\pi$
$661$	−0.589214	−	1.02055i	−0.0229178	−	0.0396947i	−0.877257	+	0.480021i	$0.840629\pi$
$662$	1.82521			0.0709387
$663$		0			0
$664$	2.33547			0.0906339
$665$	0.0381275	+	0.0660387i	0.00147852	+	0.00256087i
$666$		0			0
$667$	21.5379	−	37.3048i	0.833952	−	1.44445i
$668$	−2.99735			−0.115971
$669$		0			0
$670$	−1.29728	+	2.24695i	−0.0501183	+	0.0868074i
$671$	2.85818			0.110339
$672$		0			0
$673$	−6.77878	−	11.7412i	−0.261303	−	0.452590i	0.705286	−	0.708923i	$-0.250819\pi$
$673$	−6.77878	−	11.7412i	−0.261303	−	0.452590i	−0.966588	+	0.256334i	$0.917485\pi$
$674$	−4.88782	−	8.46595i	−0.188272	−	0.326096i
$675$		0			0
$676$	−24.4117	−	2.05759i	−0.938913	−	0.0791381i
$677$	−9.53793			−0.366573			−0.183286	−	0.983060i	$-0.558674\pi$
$677$	−9.53793			−0.366573			−0.183286	+	0.983060i	$0.558674\pi$
$678$		0			0
$679$	−3.26897	−	5.66202i	−0.125451	−	0.217288i
$680$	4.90411	−	8.49418i	0.188064	−	0.325737i
$681$		0			0
$682$	−1.15212	+	1.99554i	−0.0441171	+	0.0764131i
$683$	−22.2592	+	38.5540i	−0.851723	+	1.47523i	0.0279296	+	0.999610i	$0.491109\pi$
$683$	−22.2592	+	38.5540i	−0.851723	+	1.47523i	−0.879652	+	0.475617i	$0.842225\pi$
$684$		0			0
$685$	−1.69491	+	2.93568i	−0.0647594	+	0.112166i
$686$	1.52164	+	2.63556i	0.0580965	+	0.100626i
$687$		0			0
$688$	−1.80823			−0.0689381
$689$	−1.31357	+	2.06915i	−0.0500432	+	0.0788282i
$690$		0			0
$691$	2.64030	+	4.57313i	0.100442	+	0.173970i	0.911867	−	0.410486i	$-0.134641\pi$
$691$	2.64030	+	4.57313i	0.100442	+	0.173970i	−0.811425	+	0.584457i	$0.801308\pi$
$692$	−12.0130	−	20.8071i	−0.456664	−	0.790966i
$693$		0			0
$694$	−7.61192			−0.288945
$695$	7.40411	−	12.8243i	0.280854	−	0.486454i
$696$		0			0
$697$	31.3832			1.18872
$698$	2.03479	−	3.52436i	0.0770180	−	0.133399i
$699$		0			0
$700$	0.621996	+	1.07733i	0.0235092	+	0.0407192i
$701$	−20.1392			−0.760646			−0.380323	−	0.924854i	$-0.624187\pi$
$701$	−20.1392			−0.760646			−0.380323	+	0.924854i	$0.624187\pi$
$702$		0			0
$703$	1.12847			0.0425612
$704$	−1.82157	−	3.15506i	−0.0686531	−	0.118911i
$705$		0			0
$706$	−2.89517	+	5.01459i	−0.108961	+	0.188727i
$707$	6.17843			0.232364
$708$		0			0
$709$	−0.770294	+	1.33419i	−0.0289290	+	0.0501065i	−0.880127	−	0.474737i	$-0.842543\pi$
$709$	−0.770294	+	1.33419i	−0.0289290	+	0.0501065i	0.851198	+	0.524844i	$0.175876\pi$
$710$	2.48571			0.0932872
$711$		0			0
$712$	−8.94111	−	15.4865i	−0.335082	−	0.580379i
$713$	38.7427	+	67.1043i	1.45092	+	2.51307i
$714$		0			0
$715$	−2.44872	−	0.103015i	−0.0915770	−	0.00385254i
$716$	33.4728			1.25094
$717$		0			0
$718$	−5.96187	−	10.3263i	−0.222495	−	0.385373i
$719$	18.5020	−	32.0464i	0.690009	−	1.19513i	−0.281826	−	0.959466i	$-0.590940\pi$
$719$	18.5020	−	32.0464i	0.690009	−	1.19513i	0.971835	−	0.235664i	$-0.0757266\pi$
$720$		0			0
$721$	−1.48704	+	2.57563i	−0.0553803	+	0.0959215i
$722$	3.22656	−	5.58857i	0.120080	−	0.207985i
$723$		0			0
$724$	6.62048	−	11.4670i	0.246048	−	0.426168i
$725$	2.77230	+	4.80177i	0.102961	+	0.178333i
$726$		0			0
$727$	−44.9015			−1.66530			−0.832652	−	0.553797i	$-0.813178\pi$
$727$	−44.9015			−1.66530			−0.832652	+	0.553797i	$0.813178\pi$
$728$	−1.45539	−	2.78497i	−0.0539405	−	0.103218i
$729$		0			0
$730$	1.36284	+	2.36051i	0.0504411	+	0.0873666i
$731$	−2.02297	−	3.50388i	−0.0748221	−	0.129596i
$732$		0			0
$733$	−4.94072			−0.182490			−0.0912449	−	0.995828i	$-0.529085\pi$
$733$	−4.94072			−0.182490			−0.0912449	+	0.995828i	$0.529085\pi$
$734$	−3.41280	+	5.91114i	−0.125969	+	0.218184i
$735$		0			0
$736$	29.2810			1.07931
$737$	−2.59456	+	4.49391i	−0.0955718	+	0.165535i
$738$		0			0
$739$	−3.01963	−	5.23015i	−0.111079	−	0.192394i	0.805127	−	0.593103i	$-0.202097\pi$
$739$	−3.01963	−	5.23015i	−0.111079	−	0.192394i	−0.916206	+	0.400709i	$0.868764\pi$
$740$	18.4095			0.676745
$741$		0			0
$742$	−0.152510			−0.00559882
$743$	−6.52945	−	11.3093i	−0.239542	−	0.414899i	0.721041	−	0.692893i	$-0.243664\pi$
$743$	−6.52945	−	11.3093i	−0.239542	−	0.414899i	−0.960583	+	0.277993i	$0.910331\pi$
$744$		0			0
$745$	8.54461	−	14.7997i	0.313050	−	0.542219i
$746$	−7.97998			−0.292168
$747$		0			0
$748$	4.75828	−	8.24158i	0.173980	−	0.301342i
$749$	−0.376871			−0.0137706
$750$		0			0
$751$	−24.0118	−	41.5897i	−0.876204	−	1.51763i	−0.855475	−	0.517845i	$-0.826735\pi$
$751$	−24.0118	−	41.5897i	−0.876204	−	1.51763i	−0.0207292	−	0.999785i	$-0.506599\pi$
$752$	−8.33320	−	14.4335i	−0.303881	−	0.526337i
$753$		0			0
$754$	−3.14697	−	6.02189i	−0.114606	−	0.219304i
$755$	−13.0130			−0.473590
$756$		0			0
$757$	2.28212	+	3.95275i	0.0829450	+	0.143665i	0.904514	−	0.426445i	$-0.140234\pi$
$757$	2.28212	+	3.95275i	0.0829450	+	0.143665i	−0.821569	+	0.570110i	$0.806901\pi$
$758$	−3.59274	+	6.22281i	−0.130494	+	0.226023i
$759$		0			0
$760$	−0.0762550	+	0.132077i	−0.00276606	+	0.00479095i
$761$	10.5446	−	18.2638i	0.382242	−	0.662062i	−0.609141	−	0.793062i	$-0.708486\pi$
$761$	10.5446	−	18.2638i	0.382242	−	0.662062i	0.991382	+	0.131000i	$0.0418188\pi$
$762$		0			0
$763$	−5.08607	+	8.80933i	−0.184128	+	0.318919i
$764$	13.1481	+	22.7732i	0.475682	+	0.823905i
$765$		0			0
$766$	−0.590926			−0.0213510
$767$	−3.71455	−	7.10797i	−0.134124	−	0.256654i
$768$		0			0
$769$	−21.1666	−	36.6616i	−0.763287	−	1.32205i	−0.941147	−	0.337996i	$-0.890251\pi$
$769$	−21.1666	−	36.6616i	−0.763287	−	1.32205i	0.177860	−	0.984056i	$-0.443083\pi$
$770$	−0.0762550	−	0.132077i	−0.00274804	−	0.00475974i
$771$		0			0
$772$	−44.7552			−1.61078
$773$	25.1218	−	43.5122i	0.903568	−	1.56503i	0.0807410	−	0.996735i	$-0.474271\pi$
$773$	25.1218	−	43.5122i	0.903568	−	1.56503i	0.822827	−	0.568291i	$-0.192395\pi$
$774$		0			0
$775$	−9.97370			−0.358266
$776$	6.53793	−	11.3240i	0.234698	−	0.406509i
$777$		0			0
$778$	−4.53165	−	7.84904i	−0.162467	−	0.281402i
$779$	−0.487982			−0.0174838
$780$		0			0
$781$	4.97143			0.177892
$782$	9.80823	+	16.9884i	0.350742	+	0.607502i

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.169938 - 0.294342i) q^{2} +(0.942242 - 1.63201i) q^{4} -1.00000 q^{5} +(-0.330062 + 0.571683i) q^{7} -1.32025 q^{8} +O(q^{10})\)	\(q+(-0.169938 - 0.294342i) q^{2} +(0.942242 - 1.63201i) q^{4} -1.00000 q^{5} +(-0.330062 + 0.571683i) q^{7} -1.32025 q^{8} +(0.169938 + 0.294342i) q^{10} +(0.339877 + 0.588684i) q^{11} +(1.93243 - 3.04397i) q^{13} +0.224361 q^{14} +(-1.66012 - 2.87542i) q^{16} +(3.71455 - 6.43378i) q^{17} +(-0.0577581 + 0.100040i) q^{19} +(-0.942242 + 1.63201i) q^{20} +(0.115516 - 0.200080i) q^{22} +(-3.88448 - 6.72812i) q^{23} +1.00000 q^{25} +(-1.22436 - 0.0515075i) q^{26} +(0.621996 + 1.07733i) q^{28} +(2.77230 + 4.80177i) q^{29} -9.97370 q^{31} +(-1.88448 + 3.26402i) q^{32} -2.52498 q^{34} +(0.330062 - 0.571683i) q^{35} +(-4.88448 - 8.46017i) q^{37} +0.0392613 q^{38} +1.32025 q^{40} +(2.11218 + 3.65840i) q^{41} +(0.272303 - 0.471643i) q^{43} +1.28098 q^{44} +(-1.32025 + 2.28673i) q^{46} +5.01963 q^{47} +(3.28212 + 5.68480i) q^{49} +(-0.169938 - 0.294342i) q^{50} +(-3.14697 - 6.02189i) q^{52} -0.679754 q^{53} +(-0.339877 - 0.588684i) q^{55} +(0.435763 - 0.754763i) q^{56} +(0.942242 - 1.63201i) q^{58} +(1.11218 - 1.92635i) q^{59} +(2.10236 - 3.64140i) q^{61} +(1.69491 + 2.93568i) q^{62} -5.35951 q^{64} +(-1.93243 + 3.04397i) q^{65} +(3.81691 + 6.61108i) q^{67} +(-7.00000 - 12.1244i) q^{68} -0.224361 q^{70} +(3.65679 - 6.33374i) q^{71} +8.01963 q^{73} +(-1.66012 + 2.87542i) q^{74} +(0.108844 + 0.188524i) q^{76} -0.448721 q^{77} +9.97370 q^{79} +(1.66012 + 2.87542i) q^{80} +(0.717881 - 1.24341i) q^{82} -1.76897 q^{83} +(-3.71455 + 6.43378i) q^{85} -0.185099 q^{86} +(-0.448721 - 0.777208i) q^{88} +(6.77230 + 11.7300i) q^{89} +(1.10236 + 2.10943i) q^{91} -14.6405 q^{92} +(-0.853028 - 1.47749i) q^{94} +(0.0577581 - 0.100040i) q^{95} +(-4.95206 + 8.57721i) q^{97} +(1.11552 - 1.93213i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{5} - 3 q^{7} - 12 q^{8}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^5 - 3 * q^7 - 12 * q^8	\( 6 q - 6 q^{4} - 6 q^{5} - 3 q^{7} - 12 q^{8} + 3 q^{13} - 24 q^{14} - 12 q^{16} - 12 q^{19} + 6 q^{20} + 24 q^{22} + 6 q^{25} + 18 q^{26} - 12 q^{28} + 6 q^{29} + 6 q^{31} + 12 q^{32} + 3 q^{35} - 6 q^{37} - 12 q^{38} + 12 q^{40} - 9 q^{43} + 24 q^{44} - 12 q^{46} + 24 q^{47} + 6 q^{49} + 12 q^{52} + 30 q^{56} - 6 q^{58} - 6 q^{59} + 3 q^{61} - 6 q^{62} - 24 q^{64} - 3 q^{65} - 9 q^{67} - 42 q^{68} + 24 q^{70} - 12 q^{71} + 42 q^{73} - 12 q^{74} - 48 q^{76} + 48 q^{77} - 6 q^{79} + 12 q^{80} + 18 q^{82} + 36 q^{83} + 12 q^{86} + 48 q^{88} + 30 q^{89} - 3 q^{91} - 96 q^{92} - 36 q^{94} + 12 q^{95} - 15 q^{97} + 30 q^{98}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^5 - 3 * q^7 - 12 * q^8 + 3 * q^13 - 24 * q^14 - 12 * q^16 - 12 * q^19 + 6 * q^20 + 24 * q^22 + 6 * q^25 + 18 * q^26 - 12 * q^28 + 6 * q^29 + 6 * q^31 + 12 * q^32 + 3 * q^35 - 6 * q^37 - 12 * q^38 + 12 * q^40 - 9 * q^43 + 24 * q^44 - 12 * q^46 + 24 * q^47 + 6 * q^49 + 12 * q^52 + 30 * q^56 - 6 * q^58 - 6 * q^59 + 3 * q^61 - 6 * q^62 - 24 * q^64 - 3 * q^65 - 9 * q^67 - 42 * q^68 + 24 * q^70 - 12 * q^71 + 42 * q^73 - 12 * q^74 - 48 * q^76 + 48 * q^77 - 6 * q^79 + 12 * q^80 + 18 * q^82 + 36 * q^83 + 12 * q^86 + 48 * q^88 + 30 * q^89 - 3 * q^91 - 96 * q^92 - 36 * q^94 + 12 * q^95 - 15 * q^97 + 30 * q^98

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