LMFDB - Embedded newform 3024.2.r.k.2017.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1009,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3024.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2017.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	3024.2017
Dual form			3024.2.r.k.1009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.439693 - 0.761570i) q^{5} +(0.500000 - 0.866025i) q^{7} +O(q^{10})$	$q+(-0.439693 - 0.761570i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-1.93969 + 3.35965i) q^{11} +(2.72668 + 4.72275i) q^{13} -1.65270 q^{17} -2.41147 q^{19} +(-1.58125 - 2.73881i) q^{23} +(2.11334 - 3.66041i) q^{25} +(-3.02481 + 5.23913i) q^{29} +(-2.27719 - 3.94421i) q^{31} -0.879385 q^{35} -4.55438 q^{37} +(-0.592396 - 1.02606i) q^{41} +(0.0923963 - 0.160035i) q^{43} +(0.511144 - 0.885328i) q^{47} +(-0.500000 - 0.866025i) q^{49} -7.29086 q^{53} +3.41147 q^{55} +(-3.33022 - 5.76811i) q^{59} +(1.29813 - 2.24843i) q^{61} +(2.39780 - 4.15312i) q^{65} +(-1.47906 - 2.56180i) q^{67} -3.68004 q^{71} -12.7811 q^{73} +(1.93969 + 3.35965i) q^{77} +(-2.97906 + 5.15988i) q^{79} +(0.109470 - 0.189608i) q^{83} +(0.726682 + 1.25865i) q^{85} -11.0273 q^{89} +5.45336 q^{91} +(1.06031 + 1.83651i) q^{95} +(-6.25150 + 10.8279i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 3 q^{7}+O(q^{10}) $ 6 * q + 3 * q^5 + 3 * q^7	$ 6 q + 3 q^{5} + 3 q^{7} - 6 q^{11} + 3 q^{13} - 12 q^{17} + 6 q^{19} - 12 q^{23} + 6 q^{25} + 9 q^{29} - 3 q^{31} + 6 q^{35} - 6 q^{37} - 3 q^{43} - 3 q^{47} - 3 q^{49} - 12 q^{53} + 3 q^{59} - 6 q^{61} + 15 q^{65} - 12 q^{67} + 18 q^{71} - 42 q^{73} + 6 q^{77} - 21 q^{79} + 18 q^{83} - 9 q^{85} - 24 q^{89} + 6 q^{91} + 12 q^{95} + 3 q^{97}+O(q^{100}) $ 6 * q + 3 * q^5 + 3 * q^7 - 6 * q^11 + 3 * q^13 - 12 * q^17 + 6 * q^19 - 12 * q^23 + 6 * q^25 + 9 * q^29 - 3 * q^31 + 6 * q^35 - 6 * q^37 - 3 * q^43 - 3 * q^47 - 3 * q^49 - 12 * q^53 + 3 * q^59 - 6 * q^61 + 15 * q^65 - 12 * q^67 + 18 * q^71 - 42 * q^73 + 6 * q^77 - 21 * q^79 + 18 * q^83 - 9 * q^85 - 24 * q^89 + 6 * q^91 + 12 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.439693	−	0.761570i	−0.196637	−	0.340584i	0.750799	−	0.660530i	$-0.229669\pi$
$5$	−0.439693	−	0.761570i	−0.196637	−	0.340584i	−0.947436	+	0.319946i	$0.896335\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.93969	+	3.35965i	−0.584839	+	1.01297i	0.410056	+	0.912060i	$0.365509\pi$
$11$	−1.93969	+	3.35965i	−0.584839	+	1.01297i	−0.994895	+	0.100911i	$0.967824\pi$
$12$		0			0
$13$	2.72668	+	4.72275i	0.756245	+	1.30986i	0.944753	+	0.327784i	$0.106302\pi$
$13$	2.72668	+	4.72275i	0.756245	+	1.30986i	−0.188507	+	0.982072i	$0.560365\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.65270			−0.400840			−0.200420	−	0.979710i	$-0.564231\pi$
$17$	−1.65270			−0.400840			−0.200420	+	0.979710i	$0.564231\pi$
$18$		0			0
$19$	−2.41147			−0.553230			−0.276615	−	0.960981i	$-0.589213\pi$
$19$	−2.41147			−0.553230			−0.276615	+	0.960981i	$0.589213\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.58125	−	2.73881i	−0.329714	−	0.571081i	0.652741	−	0.757581i	$-0.273619\pi$
$23$	−1.58125	−	2.73881i	−0.329714	−	0.571081i	−0.982455	+	0.186500i	$0.940286\pi$
$24$		0			0
$25$	2.11334	−	3.66041i	0.422668	−	0.732083i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.02481	+	5.23913i	−0.561694	+	0.972883i	0.435655	+	0.900114i	$0.356517\pi$
$29$	−3.02481	+	5.23913i	−0.561694	+	0.972883i	−0.997349	+	0.0727688i	$0.976816\pi$
$30$		0			0
$31$	−2.27719	−	3.94421i	−0.408995	−	0.708400i	0.585782	−	0.810468i	$-0.300787\pi$
$31$	−2.27719	−	3.94421i	−0.408995	−	0.708400i	−0.994777	+	0.102068i	$0.967454\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.879385			−0.148643
$36$		0			0
$37$	−4.55438			−0.748735			−0.374368	−	0.927280i	$-0.622140\pi$
$37$	−4.55438			−0.748735			−0.374368	+	0.927280i	$0.622140\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.592396	−	1.02606i	−0.0925168	−	0.160244i	0.816053	−	0.577977i	$-0.196158\pi$
$41$	−0.592396	−	1.02606i	−0.0925168	−	0.160244i	−0.908570	+	0.417734i	$0.862825\pi$
$42$		0			0
$43$	0.0923963	−	0.160035i	0.0140903	−	0.0244051i	−0.858894	−	0.512153i	$-0.828848\pi$
$43$	0.0923963	−	0.160035i	0.0140903	−	0.0244051i	0.872985	+	0.487748i	$0.162181\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.511144	−	0.885328i	0.0745581	−	0.129138i	−0.826336	−	0.563178i	$-0.809579\pi$
$47$	0.511144	−	0.885328i	0.0745581	−	0.129138i	0.900894	+	0.434039i	$0.142912\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−7.29086			−1.00148			−0.500738	−	0.865599i	$-0.666938\pi$
$53$	−7.29086			−1.00148			−0.500738	+	0.865599i	$0.666938\pi$
$54$		0			0
$55$	3.41147			0.460003
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.33022	−	5.76811i	−0.433558	−	0.750944i	0.563619	−	0.826035i	$-0.309409\pi$
$59$	−3.33022	−	5.76811i	−0.433558	−	0.750944i	−0.997177	+	0.0750906i	$0.976075\pi$
$60$		0			0
$61$	1.29813	−	2.24843i	0.166209	−	0.287882i	−0.770875	−	0.636986i	$-0.780181\pi$
$61$	1.29813	−	2.24843i	0.166209	−	0.287882i	0.937084	+	0.349104i	$0.113514\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.39780	−	4.15312i	0.297411	−	0.515131i
$66$		0			0
$67$	−1.47906	−	2.56180i	−0.180695	−	0.312974i	0.761422	−	0.648256i	$-0.224501\pi$
$67$	−1.47906	−	2.56180i	−0.180695	−	0.312974i	−0.942118	+	0.335283i	$0.891168\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.68004			−0.436741			−0.218370	−	0.975866i	$-0.570074\pi$
$71$	−3.68004			−0.436741			−0.218370	+	0.975866i	$0.570074\pi$
$72$		0			0
$73$	−12.7811			−1.49591			−0.747955	−	0.663750i	$-0.768964\pi$
$73$	−12.7811			−1.49591			−0.747955	+	0.663750i	$0.768964\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.93969	+	3.35965i	0.221048	+	0.382867i
$78$		0			0
$79$	−2.97906	+	5.15988i	−0.335170	+	0.580531i	−0.983517	−	0.180813i	$-0.942127\pi$
$79$	−2.97906	+	5.15988i	−0.335170	+	0.580531i	0.648348	+	0.761345i	$0.275460\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.109470	−	0.189608i	0.0120159	−	0.0208122i	−0.859955	−	0.510370i	$-0.829508\pi$
$83$	0.109470	−	0.189608i	0.0120159	−	0.0208122i	0.871971	+	0.489558i	$0.162842\pi$
$84$		0			0
$85$	0.726682	+	1.25865i	0.0788197	+	0.136520i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−11.0273			−1.16890			−0.584448	−	0.811431i	$-0.698689\pi$
$89$	−11.0273			−1.16890			−0.584448	+	0.811431i	$0.698689\pi$
$90$		0			0
$91$	5.45336			0.571668
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.06031	+	1.83651i	0.108785	+	0.188422i
$96$		0			0
$97$	−6.25150	+	10.8279i	−0.634743	+	1.09941i	0.351826	+	0.936065i	$0.385561\pi$
$97$	−6.25150	+	10.8279i	−0.634743	+	1.09941i	−0.986569	+	0.163342i	$0.947773\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.85844	+	8.41507i	−0.483433	+	0.837330i	−0.999819	−	0.0190255i	$-0.993944\pi$
$101$	−4.85844	+	8.41507i	−0.483433	+	0.837330i	0.516386	+	0.856356i	$0.327277\pi$
$102$		0			0
$103$	3.29813	+	5.71253i	0.324975	+	0.562873i	0.981507	−	0.191425i	$-0.0613109\pi$
$103$	3.29813	+	5.71253i	0.324975	+	0.562873i	−0.656533	+	0.754298i	$0.727978\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.38919			0.230971			0.115486	−	0.993309i	$-0.463158\pi$
$107$	2.38919			0.230971			0.115486	+	0.993309i	$0.463158\pi$
$108$		0			0
$109$	3.95811			0.379118			0.189559	−	0.981869i	$-0.439294\pi$
$109$	3.95811			0.379118			0.189559	+	0.981869i	$0.439294\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.22668	+	14.2490i	0.773901	+	1.34044i	0.935410	+	0.353565i	$0.115031\pi$
$113$	8.22668	+	14.2490i	0.773901	+	1.34044i	−0.161509	+	0.986871i	$0.551636\pi$
$114$		0			0
$115$	−1.39053	+	2.40847i	−0.129668	+	0.224591i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.826352	+	1.43128i	−0.0757515	+	0.131206i
$120$		0			0
$121$	−2.02481	−	3.50708i	−0.184074	−	0.318826i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−8.11381			−0.725721
$126$		0			0
$127$	−17.6536			−1.56651			−0.783253	−	0.621702i	$-0.786441\pi$
$127$	−17.6536			−1.56651			−0.783253	+	0.621702i	$0.786441\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.59879	+	16.6256i	0.838650	+	1.45259i	0.891023	+	0.453958i	$0.149988\pi$
$131$	9.59879	+	16.6256i	0.838650	+	1.45259i	−0.0523729	+	0.998628i	$0.516678\pi$
$132$		0			0
$133$	−1.20574	+	2.08840i	−0.104551	+	0.181087i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.07785	−	15.7233i	0.775573	−	1.34333i	−0.158899	−	0.987295i	$-0.550794\pi$
$137$	9.07785	−	15.7233i	0.775573	−	1.34333i	0.934472	−	0.356037i	$-0.115872\pi$
$138$		0			0
$139$	11.0287	+	19.1022i	0.935441	+	1.62023i	0.773846	+	0.633374i	$0.218330\pi$
$139$	11.0287	+	19.1022i	0.935441	+	1.62023i	0.161595	+	0.986857i	$0.448336\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−21.1557			−1.76913
$144$		0			0
$145$	5.31996			0.441798
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.57785	−	13.1252i	−0.620802	−	1.07526i	−0.989337	−	0.145646i	$-0.953474\pi$
$149$	−7.57785	−	13.1252i	−0.620802	−	1.07526i	0.368535	−	0.929614i	$-0.379859\pi$
$150$		0			0
$151$	−9.47818	+	16.4167i	−0.771323	+	1.33597i	0.165515	+	0.986207i	$0.447071\pi$
$151$	−9.47818	+	16.4167i	−0.771323	+	1.33597i	−0.936838	+	0.349764i	$0.886262\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.00253	+	3.46848i	−0.160847	+	0.278595i
$156$		0			0
$157$	9.02869	+	15.6381i	0.720568	+	1.24806i	0.960773	+	0.277337i	$0.0894520\pi$
$157$	9.02869	+	15.6381i	0.720568	+	1.24806i	−0.240205	+	0.970722i	$0.577215\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.16250			−0.249240
$162$		0			0
$163$	−0.958111			−0.0750450			−0.0375225	−	0.999296i	$-0.511947\pi$
$163$	−0.958111			−0.0750450			−0.0375225	+	0.999296i	$0.511947\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.91921	−	17.1806i	−0.767572	−	1.32947i	−0.938876	−	0.344255i	$-0.888131\pi$
$167$	−9.91921	−	17.1806i	−0.767572	−	1.32947i	0.171304	−	0.985218i	$-0.445202\pi$
$168$		0			0
$169$	−8.36959	+	14.4965i	−0.643814	+	1.11512i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.3414	−	19.6438i	0.862268	−	1.49349i	−0.00746626	−	0.999972i	$-0.502377\pi$
$173$	11.3414	−	19.6438i	0.862268	−	1.49349i	0.869734	−	0.493520i	$-0.164290\pi$
$174$		0			0
$175$	−2.11334	−	3.66041i	−0.159754	−	0.276701i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−7.34730			−0.549163			−0.274581	−	0.961564i	$-0.588539\pi$
$179$	−7.34730			−0.549163			−0.274581	+	0.961564i	$0.588539\pi$
$180$		0			0
$181$	−3.44562			−0.256111			−0.128056	−	0.991767i	$-0.540874\pi$
$181$	−3.44562			−0.256111			−0.128056	+	0.991767i	$0.540874\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.00253	+	3.46848i	0.147229	+	0.255008i
$186$		0			0
$187$	3.20574	−	5.55250i	0.234427	−	0.406039i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.82888	+	4.89976i	−0.204690	+	0.354534i	−0.950034	−	0.312146i	$-0.898952\pi$
$191$	−2.82888	+	4.89976i	−0.204690	+	0.354534i	0.745344	+	0.666680i	$0.232285\pi$
$192$		0			0
$193$	−4.79813	−	8.31061i	−0.345377	−	0.598211i	0.640045	−	0.768337i	$-0.278916\pi$
$193$	−4.79813	−	8.31061i	−0.345377	−	0.598211i	−0.985422	+	0.170127i	$0.945582\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.31996			−0.592772			−0.296386	−	0.955068i	$-0.595782\pi$
$197$	−8.31996			−0.592772			−0.296386	+	0.955068i	$0.595782\pi$
$198$		0			0
$199$	−6.59627			−0.467597			−0.233798	−	0.972285i	$-0.575116\pi$
$199$	−6.59627			−0.467597			−0.233798	+	0.972285i	$0.575116\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.02481	+	5.23913i	0.212300	+	0.367715i
$204$		0			0
$205$	−0.520945	+	0.902302i	−0.0363843	+	0.0630195i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.67752	−	8.10170i	0.323551	−	0.560406i
$210$		0			0
$211$	−1.68479	−	2.91815i	−0.115986	−	0.200893i	0.802188	−	0.597072i	$-0.203669\pi$
$211$	−1.68479	−	2.91815i	−0.115986	−	0.200893i	−0.918173	+	0.396179i	$0.870336\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.162504			−0.0110827
$216$		0			0
$217$	−4.55438			−0.309171
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.50640	−	7.80531i	−0.303133	−	0.525042i
$222$		0			0
$223$	−3.13816	+	5.43545i	−0.210146	+	0.363984i	−0.951760	−	0.306843i	$-0.900727\pi$
$223$	−3.13816	+	5.43545i	−0.210146	+	0.363984i	0.741614	+	0.670827i	$0.234061\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.08125	−	5.33688i	0.204510	−	0.354221i	−0.745467	−	0.666543i	$-0.767773\pi$
$227$	3.08125	−	5.33688i	0.204510	−	0.354221i	0.949976	+	0.312322i	$0.101107\pi$
$228$		0			0
$229$	−11.6925	−	20.2521i	−0.772664	−	1.33829i	−0.936098	−	0.351740i	$-0.885590\pi$
$229$	−11.6925	−	20.2521i	−0.772664	−	1.33829i	0.163434	−	0.986554i	$-0.447743\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.52528			0.558510			0.279255	−	0.960217i	$-0.409913\pi$
$233$	8.52528			0.558510			0.279255	+	0.960217i	$0.409913\pi$
$234$		0			0
$235$	−0.898986			−0.0586434
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.28106	−	12.6112i	−0.470973	−	0.815748i	0.528476	−	0.848948i	$-0.322764\pi$
$239$	−7.28106	−	12.6112i	−0.470973	−	0.815748i	−0.999449	+	0.0331997i	$0.989430\pi$
$240$		0			0
$241$	2.70187	−	4.67977i	0.174043	−	0.301451i	−0.765787	−	0.643094i	$-0.777650\pi$
$241$	2.70187	−	4.67977i	0.174043	−	0.301451i	0.939830	+	0.341644i	$0.110984\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.439693	+	0.761570i	−0.0280909	+	0.0486549i
$246$		0			0
$247$	−6.57532	−	11.3888i	−0.418378	−	0.724651i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.0669			−0.761654			−0.380827	−	0.924646i	$-0.624361\pi$
$251$	−12.0669			−0.761654			−0.380827	+	0.924646i	$0.624361\pi$
$252$		0			0
$253$	12.2686			0.771318
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.28312	+	9.15063i	0.329552	+	0.570801i	0.982423	−	0.186668i	$-0.0597690\pi$
$257$	5.28312	+	9.15063i	0.329552	+	0.570801i	−0.652871	+	0.757469i	$0.726436\pi$
$258$		0			0
$259$	−2.27719	+	3.94421i	−0.141498	+	0.245081i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	14.1766	−	24.5547i	0.874169	−	1.51411i	0.0165240	−	0.999863i	$-0.494740\pi$
$263$	14.1766	−	24.5547i	0.874169	−	1.51411i	0.857645	−	0.514242i	$-0.171927\pi$
$264$		0			0
$265$	3.20574	+	5.55250i	0.196927	+	0.341087i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.48339			−0.456271			−0.228135	−	0.973629i	$-0.573263\pi$
$269$	−7.48339			−0.456271			−0.228135	+	0.973629i	$0.573263\pi$
$270$		0			0
$271$	−13.6382			−0.828459			−0.414229	−	0.910172i	$-0.635949\pi$
$271$	−13.6382			−0.828459			−0.414229	+	0.910172i	$0.635949\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.19846	+	14.2002i	0.494386	+	0.856302i
$276$		0			0
$277$	3.07532	−	5.32661i	0.184778	−	0.320045i	−0.758724	−	0.651413i	$-0.774177\pi$
$277$	3.07532	−	5.32661i	0.184778	−	0.320045i	0.943502	+	0.331368i	$0.107510\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.65611	−	2.86846i	0.0987951	−	0.171118i	−0.812391	−	0.583113i	$-0.801835\pi$
$281$	1.65611	−	2.86846i	0.0987951	−	0.171118i	0.911186	+	0.411995i	$0.135168\pi$
$282$		0			0
$283$	14.5116	+	25.1348i	0.862626	+	1.49411i	0.869385	+	0.494134i	$0.164515\pi$
$283$	14.5116	+	25.1348i	0.862626	+	1.49411i	−0.00675974	+	0.999977i	$0.502152\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.18479			−0.0699361
$288$		0			0
$289$	−14.2686			−0.839328
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.20961	−	7.29125i	−0.245928	−	0.425960i	0.716464	−	0.697624i	$-0.245759\pi$
$293$	−4.20961	−	7.29125i	−0.245928	−	0.425960i	−0.962392	+	0.271664i	$0.912426\pi$
$294$		0			0
$295$	−2.92855	+	5.07239i	−0.170507	+	0.295326i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	8.62314	−	14.9357i	0.498689	−	0.863755i
$300$		0			0
$301$	−0.0923963	−	0.160035i	−0.00532563	−	0.00922427i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.28312			−0.130731
$306$		0			0
$307$	12.6878			0.724130			0.362065	−	0.932153i	$-0.382072\pi$
$307$	12.6878			0.724130			0.362065	+	0.932153i	$0.382072\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.24510	+	14.2809i	0.467537	+	0.809797i	0.999312	−	0.0370881i	$-0.0118082\pi$
$311$	8.24510	+	14.2809i	0.467537	+	0.809797i	−0.531775	+	0.846886i	$0.678475\pi$
$312$		0			0
$313$	−14.2592	+	24.6977i	−0.805980	+	1.39600i	0.109648	+	0.993970i	$0.465028\pi$
$313$	−14.2592	+	24.6977i	−0.805980	+	1.39600i	−0.915628	+	0.402027i	$0.868306\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−12.9474	+	22.4256i	−0.727200	+	1.25955i	0.230862	+	0.972987i	$0.425846\pi$
$317$	−12.9474	+	22.4256i	−0.727200	+	1.25955i	−0.958062	+	0.286561i	$0.907488\pi$
$318$		0			0
$319$	−11.7344	−	20.3246i	−0.657002	−	1.13796i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.98545			0.221756
$324$		0			0
$325$	23.0496			1.27856
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.511144	−	0.885328i	−0.0281803	−	0.0488097i
$330$		0			0
$331$	4.10947	−	7.11781i	0.225877	−	0.391230i	−0.730705	−	0.682693i	$-0.760809\pi$
$331$	4.10947	−	7.11781i	0.225877	−	0.391230i	0.956582	+	0.291463i	$0.0941419\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.30066	+	2.25281i	−0.0710626	+	0.123084i
$336$		0			0
$337$	−2.28564	−	3.95885i	−0.124507	−	0.215652i	0.797033	−	0.603936i	$-0.206402\pi$
$337$	−2.28564	−	3.95885i	−0.124507	−	0.215652i	−0.921540	+	0.388283i	$0.873068\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	17.6682			0.956786
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−11.2331	−	19.4563i	−0.603023	−	1.04447i	−0.992361	−	0.123372i	$-0.960629\pi$
$347$	−11.2331	−	19.4563i	−0.603023	−	1.04447i	0.389337	−	0.921095i	$-0.372704\pi$
$348$		0			0
$349$	−13.0496	+	22.6026i	−0.698531	+	1.20989i	0.270445	+	0.962735i	$0.412829\pi$
$349$	−13.0496	+	22.6026i	−0.698531	+	1.20989i	−0.968976	+	0.247155i	$0.920504\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.177519	+	0.307471i	−0.00944836	+	0.0163650i	−0.870711	−	0.491795i	$-0.836341\pi$
$353$	−0.177519	+	0.307471i	−0.00944836	+	0.0163650i	0.861263	+	0.508160i	$0.169674\pi$
$354$		0			0
$355$	1.61809	+	2.80261i	0.0858792	+	0.148747i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.45605			0.287959			0.143980	−	0.989581i	$-0.454010\pi$
$359$	5.45605			0.287959			0.143980	+	0.989581i	$0.454010\pi$
$360$		0			0
$361$	−13.1848			−0.693936
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.61974	+	9.73367i	0.294150	+	0.509484i
$366$		0			0
$367$	5.46198	−	9.46043i	0.285113	−	0.493830i	−0.687523	−	0.726162i	$-0.741302\pi$
$367$	5.46198	−	9.46043i	0.285113	−	0.493830i	0.972637	+	0.232332i	$0.0746355\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.64543	+	6.31407i	−0.189261	+	0.327810i
$372$		0			0
$373$	−0.865715	−	1.49946i	−0.0448250	−	0.0776392i	0.842742	−	0.538317i	$-0.180940\pi$
$373$	−0.865715	−	1.49946i	−0.0448250	−	0.0776392i	−0.887567	+	0.460678i	$0.847606\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−32.9908			−1.69911
$378$		0			0
$379$	12.1334			0.623251			0.311626	−	0.950205i	$-0.399127\pi$
$379$	12.1334			0.623251			0.311626	+	0.950205i	$0.399127\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.35591	+	7.54467i	0.222577	+	0.385514i	0.955590	−	0.294700i	$-0.0952198\pi$
$383$	4.35591	+	7.54467i	0.222577	+	0.385514i	−0.733013	+	0.680215i	$0.761887\pi$
$384$		0			0
$385$	1.70574	−	2.95442i	0.0869324	−	0.150571i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.82160	−	3.15511i	0.0923590	−	0.159970i	−0.816144	−	0.577848i	$-0.803893\pi$
$389$	1.82160	−	3.15511i	0.0923590	−	0.159970i	0.908503	+	0.417878i	$0.137226\pi$
$390$		0			0
$391$	2.61334	+	4.52644i	0.132162	+	0.228912i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.23947			0.263627
$396$		0			0
$397$	−15.4456			−0.775194			−0.387597	−	0.921829i	$-0.626695\pi$
$397$	−15.4456			−0.775194			−0.387597	+	0.921829i	$0.626695\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9.21095	+	15.9538i	0.459973	+	0.796697i	0.998959	−	0.0456182i	$-0.0145258\pi$
$401$	9.21095	+	15.9538i	0.459973	+	0.796697i	−0.538986	+	0.842315i	$0.681192\pi$
$402$		0			0
$403$	12.4183	−	21.5092i	0.618601	−	1.07145i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	8.83409	−	15.3011i	0.437890	−	0.758447i
$408$		0			0
$409$	14.3182	+	24.7999i	0.707989	+	1.22627i	0.965602	+	0.260025i	$0.0837309\pi$
$409$	14.3182	+	24.7999i	0.707989	+	1.22627i	−0.257612	+	0.966248i	$0.582936\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−6.66044			−0.327739
$414$		0			0
$415$	−0.192533			−0.00945109
$416$		0			0
$417$		0			0
$418$		0			0
$419$	17.3478	+	30.0472i	0.847494	+	1.46790i	0.883438	+	0.468548i	$0.155223\pi$
$419$	17.3478	+	30.0472i	0.847494	+	1.46790i	−0.0359442	+	0.999354i	$0.511444\pi$
$420$		0			0
$421$	13.7010	−	23.7308i	0.667745	−	1.15657i	−0.310788	−	0.950479i	$-0.600593\pi$
$421$	13.7010	−	23.7308i	0.667745	−	1.15657i	0.978533	−	0.206090i	$-0.0660738\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.49273	+	6.04958i	−0.169422	+	0.293448i
$426$		0			0
$427$	−1.29813	−	2.24843i	−0.0628211	−	0.108809i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	26.5921			1.28090			0.640449	−	0.768000i	$-0.278748\pi$
$431$	26.5921			1.28090			0.640449	+	0.768000i	$0.278748\pi$
$432$		0			0
$433$	37.1830			1.78690			0.893451	−	0.449160i	$-0.148277\pi$
$433$	37.1830			1.78690			0.893451	+	0.449160i	$0.148277\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.81315	+	6.60457i	0.182408	+	0.315939i
$438$		0			0
$439$	12.5373	−	21.7152i	0.598373	−	1.03641i	−0.394689	−	0.918815i	$-0.629147\pi$
$439$	12.5373	−	21.7152i	0.598373	−	1.03641i	0.993061	−	0.117597i	$-0.0375192\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.02229	+	1.77066i	−0.0485704	+	0.0841264i	−0.889288	−	0.457347i	$-0.848800\pi$
$443$	−1.02229	+	1.77066i	−0.0485704	+	0.0841264i	0.840718	+	0.541473i	$0.182133\pi$
$444$		0			0
$445$	4.84864	+	8.39809i	0.229848	+	0.398108i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	10.2344			0.482992			0.241496	−	0.970402i	$-0.422362\pi$
$449$	10.2344			0.482992			0.241496	+	0.970402i	$0.422362\pi$
$450$		0			0
$451$	4.59627			0.216430
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.39780	−	4.15312i	−0.112411	−	0.194701i
$456$		0			0
$457$	21.2973	−	36.8879i	0.996244	−	1.72554i	0.423129	−	0.906070i	$-0.360932\pi$
$457$	21.2973	−	36.8879i	0.996244	−	1.72554i	0.573115	−	0.819475i	$-0.305735\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.252374	−	0.437124i	0.0117542	−	0.0203589i	−0.860088	−	0.510145i	$-0.829592\pi$
$461$	0.252374	−	0.437124i	0.0117542	−	0.0203589i	0.871843	+	0.489786i	$0.162925\pi$
$462$		0			0
$463$	1.34002	+	2.32099i	0.0622761	+	0.107865i	0.895482	−	0.445097i	$-0.146831\pi$
$463$	1.34002	+	2.32099i	0.0622761	+	0.107865i	−0.833206	+	0.552962i	$0.813497\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−31.4165			−1.45378			−0.726892	−	0.686752i	$-0.759036\pi$
$467$	−31.4165			−1.45378			−0.726892	+	0.686752i	$0.759036\pi$
$468$		0			0
$469$	−2.95811			−0.136593
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.358441	+	0.620838i	0.0164811	+	0.0285461i
$474$		0			0
$475$	−5.09627	+	8.82699i	−0.233833	+	0.405010i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8.22028	−	14.2380i	0.375594	−	0.650549i	−0.614821	−	0.788666i	$-0.710772\pi$
$479$	8.22028	−	14.2380i	0.375594	−	0.650549i	0.990416	+	0.138118i	$0.0441052\pi$
$480$		0			0
$481$	−12.4183	−	21.5092i	−0.566227	−	0.980735i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	10.9949			0.499255
$486$		0			0
$487$	2.97535			0.134826			0.0674129	−	0.997725i	$-0.478526\pi$
$487$	2.97535			0.134826			0.0674129	+	0.997725i	$0.478526\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13.2430	+	22.9376i	0.597650	+	1.03516i	0.993167	+	0.116702i	$0.0372321\pi$
$491$	13.2430	+	22.9376i	0.597650	+	1.03516i	−0.395517	+	0.918459i	$0.629435\pi$
$492$		0			0
$493$	4.99912	−	8.65873i	0.225149	−	0.389970i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.84002	+	3.18701i	−0.0825363	+	0.142957i
$498$		0			0
$499$	−6.72193	−	11.6427i	−0.300915	−	0.521200i	0.675428	−	0.737426i	$-0.263959\pi$
$499$	−6.72193	−	11.6427i	−0.300915	−	0.521200i	−0.976343	+	0.216225i	$0.930625\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−22.6631			−1.01050			−0.505250	−	0.862973i	$-0.668600\pi$
$503$	−22.6631			−1.01050			−0.505250	+	0.862973i	$0.668600\pi$
$504$		0			0
$505$	8.54488			0.380242
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.77379	+	8.26844i	0.211594	+	0.366492i	0.952214	−	0.305433i	$-0.0988011\pi$
$509$	4.77379	+	8.26844i	0.211594	+	0.366492i	−0.740619	+	0.671925i	$0.765468\pi$
$510$		0			0
$511$	−6.39053	+	11.0687i	−0.282700	+	0.489651i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2.90033	−	5.02352i	0.127804	−	0.221363i
$516$		0			0
$517$	1.98293	+	3.43453i	0.0872090	+	0.151050i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.11287			0.136377			0.0681887	−	0.997672i	$-0.478278\pi$
$521$	3.11287			0.136377			0.0681887	+	0.997672i	$0.478278\pi$
$522$		0			0
$523$	16.1489			0.706142			0.353071	−	0.935597i	$-0.385137\pi$
$523$	16.1489			0.706142			0.353071	+	0.935597i	$0.385137\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.76352	+	6.51860i	0.163941	+	0.283955i
$528$		0			0
$529$	6.49928	−	11.2571i	0.282578	−	0.489439i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.23055	−	5.59548i	0.139931	−	0.242367i
$534$		0			0
$535$	−1.05051	−	1.81953i	−0.0454174	−	0.0786652i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.87939			0.167097
$540$		0			0
$541$	−5.01548			−0.215632			−0.107816	−	0.994171i	$-0.534386\pi$
$541$	−5.01548			−0.215632			−0.107816	+	0.994171i	$0.534386\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.74035	−	3.01438i	−0.0745485	−	0.129122i
$546$		0			0
$547$	8.23901	−	14.2704i	0.352275	−	0.610157i	−0.634373	−	0.773027i	$-0.718742\pi$
$547$	8.23901	−	14.2704i	0.352275	−	0.610157i	0.986648	+	0.162870i	$0.0520750\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.29426	−	12.6340i	0.310746	−	0.538228i
$552$		0			0
$553$	2.97906	+	5.15988i	0.126682	+	0.219420i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	34.5631			1.46448			0.732242	−	0.681045i	$-0.238474\pi$
$557$	34.5631			1.46448			0.732242	+	0.681045i	$0.238474\pi$
$558$		0			0
$559$	1.00774			0.0426229
$560$		0			0
$561$		0			0
$562$		0			0
$563$	18.6052	+	32.2251i	0.784115	+	1.35813i	0.929526	+	0.368756i	$0.120216\pi$
$563$	18.6052	+	32.2251i	0.784115	+	1.35813i	−0.145411	+	0.989371i	$0.546450\pi$
$564$		0			0
$565$	7.23442	−	12.5304i	0.304354	−	0.527157i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.202333	−	0.350452i	0.00848226	−	0.0146917i	−0.861753	−	0.507328i	$-0.830633\pi$
$569$	0.202333	−	0.350452i	0.00848226	−	0.0146917i	0.870235	+	0.492636i	$0.163967\pi$
$570$		0			0
$571$	−18.8897	−	32.7178i	−0.790507	−	1.36920i	−0.925653	−	0.378373i	$-0.876484\pi$
$571$	−18.8897	−	32.7178i	−0.790507	−	1.36920i	0.135146	−	0.990826i	$-0.456850\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−13.3669			−0.557438
$576$		0			0
$577$	−2.21120			−0.0920535			−0.0460267	−	0.998940i	$-0.514656\pi$
$577$	−2.21120			−0.0920535			−0.0460267	+	0.998940i	$0.514656\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.109470	−	0.189608i	−0.00454160	−	0.00786628i
$582$		0			0
$583$	14.1420	−	24.4947i	0.585703	−	1.01447i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.1049	+	20.9663i	−0.499622	+	0.865371i	−1.00000		0.000436347i	$-0.999861\pi$
$587$	−12.1049	+	20.9663i	−0.499622	+	0.865371i	0.500378	+	0.865807i	$0.333194\pi$
$588$		0			0
$589$	5.49138	+	9.51135i	0.226268	+	0.391908i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−12.2385			−0.502577			−0.251288	−	0.967912i	$-0.580854\pi$
$593$	−12.2385			−0.502577			−0.251288	+	0.967912i	$0.580854\pi$
$594$		0			0
$595$	1.45336			0.0595821
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−19.8084	−	34.3092i	−0.809349	−	1.40183i	−0.913315	−	0.407253i	$-0.866487\pi$
$599$	−19.8084	−	34.3092i	−0.809349	−	1.40183i	0.103966	−	0.994581i	$-0.466847\pi$
$600$		0			0
$601$	15.0039	−	25.9875i	0.612021	−	1.06005i	−0.378879	−	0.925446i	$-0.623690\pi$
$601$	15.0039	−	25.9875i	0.612021	−	1.06005i	0.990899	−	0.134605i	$-0.0429764\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.78059	+	3.08408i	−0.0723914	+	0.125386i
$606$		0			0
$607$	−9.74216	−	16.8739i	−0.395422	−	0.684891i	0.597733	−	0.801695i	$-0.296068\pi$
$607$	−9.74216	−	16.8739i	−0.395422	−	0.684891i	−0.993155	+	0.116804i	$0.962735\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.57491			0.225537
$612$		0			0
$613$	−18.5276			−0.748325			−0.374162	−	0.927363i	$-0.622070\pi$
$613$	−18.5276			−0.748325			−0.374162	+	0.927363i	$0.622070\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.9201	+	24.1103i	0.560402	+	0.970644i	0.997461	+	0.0712118i	$0.0226866\pi$
$617$	13.9201	+	24.1103i	0.560402	+	0.970644i	−0.437059	+	0.899433i	$0.643980\pi$
$618$		0			0
$619$	−22.4907	+	38.9550i	−0.903976	+	1.56573i	−0.0816906	+	0.996658i	$0.526032\pi$
$619$	−22.4907	+	38.9550i	−0.903976	+	1.56573i	−0.822286	+	0.569075i	$0.807301\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−5.51367	+	9.54996i	−0.220901	+	0.382611i
$624$		0			0
$625$	−6.99912	−	12.1228i	−0.279965	−	0.484913i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	7.52704			0.300123
$630$		0			0
$631$	−9.43613			−0.375646			−0.187823	−	0.982203i	$-0.560143\pi$
$631$	−9.43613			−0.375646			−0.187823	+	0.982203i	$0.560143\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	7.76217	+	13.4445i	0.308032	+	0.533528i
$636$		0			0
$637$	2.72668	−	4.72275i	0.108035	−	0.187122i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	18.6951	−	32.3808i	0.738410	−	1.27896i	−0.214800	−	0.976658i	$-0.568910\pi$
$641$	18.6951	−	32.3808i	0.738410	−	1.27896i	0.953211	−	0.302306i	$-0.0977566\pi$
$642$		0			0
$643$	0.805874	+	1.39581i	0.0317806	+	0.0550456i	0.881478	−	0.472225i	$-0.156549\pi$
$643$	0.805874	+	1.39581i	0.0317806	+	0.0550456i	−0.849698	+	0.527270i	$0.823216\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−41.1762			−1.61880			−0.809402	−	0.587255i	$-0.800209\pi$
$647$	−41.1762			−1.61880			−0.809402	+	0.587255i	$0.800209\pi$
$648$		0			0
$649$	25.8384			1.01425
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.52600	+	2.64310i	0.0597169	+	0.103433i	0.894338	−	0.447391i	$-0.147647\pi$
$653$	1.52600	+	2.64310i	0.0597169	+	0.103433i	−0.834621	+	0.550824i	$0.814314\pi$
$654$		0			0
$655$	8.44104	−	14.6203i	0.329819	−	0.571263i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−20.8175	+	36.0569i	−0.810934	+	1.40458i	0.101277	+	0.994858i	$0.467707\pi$
$659$	−20.8175	+	36.0569i	−0.810934	+	1.40458i	−0.912211	+	0.409721i	$0.865626\pi$
$660$		0			0
$661$	−10.1505	−	17.5812i	−0.394808	−	0.683828i	0.598269	−	0.801296i	$-0.295856\pi$
$661$	−10.1505	−	17.5812i	−0.394808	−	0.683828i	−0.993077	+	0.117468i	$0.962522\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.12061			0.0822339
$666$		0			0
$667$	19.1320			0.740793
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.03596	+	8.72254i	0.194411	+	0.336730i
$672$		0			0
$673$	0.415345	−	0.719398i	0.0160104	−	0.0277307i	−0.857909	−	0.513801i	$-0.828237\pi$
$673$	0.415345	−	0.719398i	0.0160104	−	0.0277307i	0.873920	+	0.486071i	$0.161570\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	5.43360	−	9.41127i	0.208830	−	0.361705i	−0.742516	−	0.669828i	$-0.766368\pi$
$677$	5.43360	−	9.41127i	0.208830	−	0.361705i	0.951346	+	0.308124i	$0.0997011\pi$
$678$		0			0
$679$	6.25150	+	10.8279i	0.239910	+	0.415537i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	32.6946			1.25102			0.625512	−	0.780215i	$-0.284890\pi$
$683$	32.6946			1.25102			0.625512	+	0.780215i	$0.284890\pi$
$684$		0			0
$685$	−15.9659			−0.610024
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−19.8799	−	34.4329i	−0.757362	−	1.31179i
$690$		0			0
$691$	7.49912	−	12.9889i	0.285280	−	0.494120i	−0.687397	−	0.726282i	$-0.741247\pi$
$691$	7.49912	−	12.9889i	0.285280	−	0.494120i	0.972677	+	0.232162i	$0.0745801\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	9.69846	−	16.7982i	0.367884	−	0.637193i
$696$		0			0
$697$	0.979055	+	1.69577i	0.0370844	+	0.0642320i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−26.4688			−0.999714			−0.499857	−	0.866108i	$-0.666614\pi$
$701$	−26.4688			−0.999714			−0.499857	+	0.866108i	$0.666614\pi$
$702$		0			0
$703$	10.9828			0.414223
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.85844	+	8.41507i	0.182720	+	0.316481i
$708$		0			0
$709$	−7.68004	+	13.3022i	−0.288430	+	0.499576i	−0.973435	−	0.228963i	$-0.926467\pi$
$709$	−7.68004	+	13.3022i	−0.288430	+	0.499576i	0.685005	+	0.728538i	$0.259800\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−7.20162	+	12.4736i	−0.269703	+	0.467139i
$714$		0			0
$715$	9.30200	+	16.1115i	0.347875	+	0.602538i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	26.7306			0.996883			0.498442	−	0.866923i	$-0.333906\pi$
$719$	26.7306			0.996883			0.498442	+	0.866923i	$0.333906\pi$
$720$		0			0
$721$	6.59627			0.245658
$722$		0			0
$723$		0			0
$724$		0			0
$725$	12.7849	+	22.1441i	0.474820	+	0.822413i
$726$		0			0
$727$	−22.8221	+	39.5290i	−0.846424	+	1.46605i	0.0379552	+	0.999279i	$0.487916\pi$
$727$	−22.8221	+	39.5290i	−0.846424	+	1.46605i	−0.884379	+	0.466770i	$0.845418\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.152704	+	0.264490i	−0.00564795	+	0.00978253i
$732$		0			0
$733$	−2.98751	−	5.17452i	−0.110346	−	0.191125i	0.805564	−	0.592509i	$-0.201863\pi$
$733$	−2.98751	−	5.17452i	−0.110346	−	0.191125i	−0.915910	+	0.401384i	$0.868529\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	11.4757			0.422711
$738$		0			0
$739$	35.5963			1.30943			0.654715	−	0.755876i	$-0.272789\pi$
$739$	35.5963			1.30943			0.654715	+	0.755876i	$0.272789\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	14.6544	+	25.3821i	0.537616	+	0.931178i	0.999032	+	0.0439943i	$0.0140083\pi$
$743$	14.6544	+	25.3821i	0.537616	+	0.931178i	−0.461416	+	0.887184i	$0.652658\pi$
$744$		0			0
$745$	−6.66385	+	11.5421i	−0.244145	+	0.422871i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.19459	−	2.06910i	0.0436495	−	0.0756031i
$750$		0			0
$751$	−8.66684	−	15.0114i	−0.316258	−	0.547774i	0.663446	−	0.748224i	$-0.269093\pi$
$751$	−8.66684	−	15.0114i	−0.316258	−	0.547774i	−0.979704	+	0.200450i	$0.935760\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	16.6699			0.606681
$756$		0			0
$757$	−2.77156			−0.100734			−0.0503671	−	0.998731i	$-0.516039\pi$
$757$	−2.77156			−0.100734			−0.0503671	+	0.998731i	$0.516039\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.75372	+	6.50163i	0.136072	+	0.235684i	0.926007	−	0.377508i	$-0.123219\pi$
$761$	3.75372	+	6.50163i	0.136072	+	0.235684i	−0.789934	+	0.613191i	$0.789885\pi$
$762$		0			0
$763$	1.97906	−	3.42782i	0.0716466	−	0.124096i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	18.1609	−	31.4556i	0.655752	−	1.13580i
$768$		0			0
$769$	−1.02182	−	1.76985i	−0.0368478	−	0.0638223i	0.847013	−	0.531572i	$-0.178398\pi$
$769$	−1.02182	−	1.76985i	−0.0368478	−	0.0638223i	−0.883861	+	0.467749i	$0.845065\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	24.9418			0.897094			0.448547	−	0.893759i	$-0.351942\pi$
$773$	24.9418			0.897094			0.448547	+	0.893759i	$0.351942\pi$
$774$		0			0
$775$	−19.2499			−0.691477
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.42855	+	2.47432i	0.0511831	+	0.0886516i
$780$		0			0
$781$	7.13816	−	12.3636i	0.255423	−	0.442406i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	7.93969	−	13.7520i	0.283380	−	0.490828i
$786$		0			0
$787$	3.55350	+	6.15484i	0.126669	+	0.219396i	0.922384	−	0.386274i	$-0.126238\pi$
$787$	3.55350	+	6.15484i	0.126669	+	0.219396i	−0.795715	+	0.605671i	$0.792905\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	16.4534			0.585014
$792$		0			0
$793$	14.1584			0.502779
$794$		0			0
$795$		0			0
$796$		0			0
$797$	16.8314	+	29.1528i	0.596199	+	1.03265i	0.993376	+	0.114905i	$0.0366564\pi$
$797$	16.8314	+	29.1528i	0.596199	+	1.03265i	−0.397178	+	0.917742i	$0.630010\pi$
$798$		0			0
$799$	−0.844770	+	1.46318i	−0.0298858	+	0.0517638i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	24.7913	−	42.9398i	0.874867	−	1.51531i
$804$		0			0
$805$	1.39053	+	2.40847i	0.0490097	+	0.0848873i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	12.8161			0.450592			0.225296	−	0.974290i	$-0.427665\pi$
$809$	12.8161			0.450592			0.225296	+	0.974290i	$0.427665\pi$
$810$		0			0
$811$	26.1239			0.917335			0.458667	−	0.888608i	$-0.348327\pi$
$811$	26.1239			0.917335			0.458667	+	0.888608i	$0.348327\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.421274	+	0.729669i	0.0147566	+	0.0255592i
$816$		0			0
$817$	−0.222811	+	0.385920i	−0.00779518	+	0.0135016i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	13.8320	−	23.9578i	0.482741	−	0.836132i	−0.517062	−	0.855948i	$-0.672974\pi$
$821$	13.8320	−	23.9578i	0.482741	−	0.836132i	0.999804	+	0.0198153i	$0.00630781\pi$
$822$		0			0
$823$	13.9162	+	24.1036i	0.485089	+	0.840199i	0.999853	−	0.0171330i	$-0.00545387\pi$
$823$	13.9162	+	24.1036i	0.485089	+	0.840199i	−0.514764	+	0.857332i	$0.672121\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	4.65507			0.161873			0.0809363	−	0.996719i	$-0.474209\pi$
$827$	4.65507			0.161873			0.0809363	+	0.996719i	$0.474209\pi$
$828$		0			0
$829$	−9.97359			−0.346397			−0.173199	−	0.984887i	$-0.555410\pi$
$829$	−9.97359			−0.346397			−0.173199	+	0.984887i	$0.555410\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.826352	+	1.43128i	0.0286314	+	0.0495910i
$834$		0			0
$835$	−8.72281	+	15.1084i	−0.301865	+	0.522846i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	3.36484	−	5.82807i	0.116167	−	0.201207i	−0.802079	−	0.597218i	$-0.796273\pi$
$839$	3.36484	−	5.82807i	0.116167	−	0.201207i	0.918246	+	0.396011i	$0.129606\pi$
$840$		0			0
$841$	−3.79901	−	6.58008i	−0.131000	−	0.226899i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	14.7202			0.506390
$846$		0			0
$847$	−4.04963			−0.139147
$848$		0			0
$849$		0			0
$850$		0			0
$851$	7.20162	+	12.4736i	0.246868	+	0.427588i
$852$		0			0
$853$	−2.89528	+	5.01477i	−0.0991324	+	0.171702i	−0.911326	−	0.411686i	$-0.864940\pi$
$853$	−2.89528	+	5.01477i	−0.0991324	+	0.171702i	0.812193	+	0.583388i	$0.198273\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−17.4538	+	30.2309i	−0.596211	+	1.03267i	0.397163	+	0.917748i	$0.369995\pi$
$857$	−17.4538	+	30.2309i	−0.596211	+	1.03267i	−0.993375	+	0.114921i	$0.963339\pi$
$858$		0			0
$859$	−6.30747	−	10.9249i	−0.215208	−	0.372751i	0.738129	−	0.674660i	$-0.235710\pi$
$859$	−6.30747	−	10.9249i	−0.215208	−	0.372751i	−0.953337	+	0.301909i	$0.902376\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−24.2053			−0.823959			−0.411979	−	0.911193i	$-0.635162\pi$
$863$	−24.2053			−0.823959			−0.411979	+	0.911193i	$0.635162\pi$
$864$		0			0
$865$	−19.9469			−0.678214
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−11.5569	−	20.0171i	−0.392041	−	0.679035i
$870$		0			0
$871$	8.06583	−	13.9704i	0.273300	−	0.473370i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.05690	+	7.02676i	−0.137148	+	0.237548i
$876$		0			0
$877$	0.562834	+	0.974856i	0.0190055	+	0.0329186i	0.875372	−	0.483450i	$-0.160617\pi$
$877$	0.562834	+	0.974856i	0.0190055	+	0.0329186i	−0.856366	+	0.516369i	$0.827283\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	4.38331			0.147678			0.0738388	−	0.997270i	$-0.476475\pi$
$881$	4.38331			0.147678			0.0738388	+	0.997270i	$0.476475\pi$
$882$		0			0
$883$	6.88949			0.231850			0.115925	−	0.993258i	$-0.463017\pi$
$883$	6.88949			0.231850			0.115925	+	0.993258i	$0.463017\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−19.5376	−	33.8401i	−0.656009	−	1.13624i	−0.981640	−	0.190744i	$-0.938910\pi$
$887$	−19.5376	−	33.8401i	−0.656009	−	1.13624i	0.325631	−	0.945497i	$-0.394423\pi$
$888$		0			0
$889$	−8.82682	+	15.2885i	−0.296042	+	0.512760i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.23261	+	2.13495i	−0.0412478	+	0.0714432i
$894$		0			0
$895$	3.23055	+	5.59548i	0.107985	+	0.187036i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	27.5523			0.918921
$900$		0			0
$901$	12.0496			0.401431
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.51501	+	2.62408i	0.0503608	+	0.0872275i
$906$		0			0
$907$	21.2469	−	36.8007i	0.705492	−	1.22195i	−0.261022	−	0.965333i	$-0.584059\pi$
$907$	21.2469	−	36.8007i	0.705492	−	1.22195i	0.966514	−	0.256615i	$-0.0826073\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	7.74675	−	13.4178i	0.256661	−	0.444550i	−0.708684	−	0.705526i	$-0.750711\pi$
$911$	7.74675	−	13.4178i	0.256661	−	0.444550i	0.965345	+	0.260976i	$0.0840442\pi$
$912$		0			0
$913$	0.424678	+	0.735564i	0.0140548	+	0.0243436i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	19.1976			0.633960
$918$		0			0
$919$	−6.52940			−0.215385			−0.107693	−	0.994184i	$-0.534346\pi$
$919$	−6.52940			−0.215385			−0.107693	+	0.994184i	$0.534346\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−10.0343	−	17.3799i	−0.330283	−	0.572068i
$924$		0			0
$925$	−9.62495	+	16.6709i	−0.316466	+	0.548136i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	29.1386	−	50.4696i	0.956007	−	1.65585i	0.223961	−	0.974598i	$-0.428101\pi$
$929$	29.1386	−	50.4696i	0.956007	−	1.65585i	0.732046	−	0.681255i	$-0.238565\pi$
$930$		0			0
$931$	1.20574	+	2.08840i	0.0395164	+	0.0684445i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−5.63816			−0.184387
$936$		0			0
$937$	32.4175			1.05903			0.529516	−	0.848300i	$-0.322374\pi$
$937$	32.4175			1.05903			0.529516	+	0.848300i	$0.322374\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.6613	−	23.6621i	−0.445346	−	0.771363i	0.552730	−	0.833360i	$-0.313586\pi$
$941$	−13.6613	−	23.6621i	−0.445346	−	0.771363i	−0.998076	+	0.0619979i	$0.980253\pi$
$942$		0			0
$943$	−1.87346	+	3.24492i	−0.0610081	+	0.105669i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	19.1065	−	33.0935i	0.620879	−	1.07539i	−0.368443	−	0.929650i	$-0.620109\pi$
$947$	19.1065	−	33.0935i	0.620879	−	1.07539i	0.989322	−	0.145744i	$-0.0465575\pi$
$948$		0			0
$949$	−34.8499	−	60.3618i	−1.13127	−	1.95943i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−58.9377			−1.90918			−0.954590	−	0.297924i	$-0.903706\pi$
$953$	−58.9377			−1.90918			−0.954590	+	0.297924i	$0.903706\pi$
$954$		0			0
$955$	4.97535			0.160998
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−9.07785	−	15.7233i	−0.293139	−	0.507732i
$960$		0			0
$961$	5.12882	−	8.88338i	0.165446	−	0.286561i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−4.21941	+	7.30823i	−0.135828	+	0.235260i
$966$		0			0
$967$	12.3594	+	21.4071i	0.397451	+	0.688405i	0.993411	−	0.114609i	$-0.0365616\pi$
$967$	12.3594	+	21.4071i	0.397451	+	0.688405i	−0.595960	+	0.803014i	$0.703228\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	8.17623			0.262388			0.131194	−	0.991357i	$-0.458119\pi$
$971$	8.17623			0.262388			0.131194	+	0.991357i	$0.458119\pi$
$972$		0			0
$973$	22.0574			0.707127
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.92427	−	13.7252i	−0.253520	−	0.439109i	0.710973	−	0.703220i	$-0.248255\pi$
$977$	−7.92427	−	13.7252i	−0.253520	−	0.439109i	−0.964492	+	0.264111i	$0.914922\pi$
$978$		0			0
$979$	21.3897	−	37.0480i	0.683616	−	1.18406i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−26.6532	+	46.1646i	−0.850104	+	1.47242i	0.0310096	+	0.999519i	$0.490128\pi$
$983$	−26.6532	+	46.1646i	−0.850104	+	1.47242i	−0.881114	+	0.472904i	$0.843206\pi$
$984$		0			0
$985$	3.65822	+	6.33623i	0.116561	+	0.201889i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.584407			−0.0185831
$990$		0			0
$991$	−40.2094			−1.27730			−0.638648	−	0.769499i	$-0.720506\pi$
$991$	−40.2094			−1.27730			−0.638648	+	0.769499i	$0.720506\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.90033	+	5.02352i	0.0919466	+	0.159256i
$996$		0			0
$997$	−14.3601	+	24.8724i	−0.454789	+	0.787717i	−0.998676	−	0.0514412i	$-0.983619\pi$
$997$	−14.3601	+	24.8724i	−0.454789	+	0.787717i	0.543887	+	0.839158i	$0.316952\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.r.k.2017.1		6
3.2	odd	2		1008.2.r.h.673.3		6
4.3	odd	2		189.2.f.b.127.3		6
9.2	odd	6		9072.2.a.ca.1.1		3
9.4	even	3	inner	3024.2.r.k.1009.1		6
9.5	odd	6		1008.2.r.h.337.3		6
9.7	even	3		9072.2.a.bs.1.3		3
12.11	even	2		63.2.f.a.43.1	yes	6
28.3	even	6		1323.2.g.e.667.3		6
28.11	odd	6		1323.2.g.d.667.3		6
28.19	even	6		1323.2.h.b.802.1		6
28.23	odd	6		1323.2.h.c.802.1		6
28.27	even	2		1323.2.f.d.883.3		6
36.7	odd	6		567.2.a.c.1.1		3
36.11	even	6		567.2.a.h.1.3		3
36.23	even	6		63.2.f.a.22.1	✓	6
36.31	odd	6		189.2.f.b.64.3		6
84.11	even	6		441.2.g.c.79.1		6
84.23	even	6		441.2.h.d.214.3		6
84.47	odd	6		441.2.h.e.214.3		6
84.59	odd	6		441.2.g.b.79.1		6
84.83	odd	2		441.2.f.c.295.1		6
252.23	even	6		441.2.g.c.67.1		6
252.31	even	6		1323.2.h.b.226.1		6
252.59	odd	6		441.2.h.e.373.3		6
252.67	odd	6		1323.2.h.c.226.1		6
252.83	odd	6		3969.2.a.q.1.3		3
252.95	even	6		441.2.h.d.373.3		6
252.103	even	6		1323.2.g.e.361.3		6
252.131	odd	6		441.2.g.b.67.1		6
252.139	even	6		1323.2.f.d.442.3		6
252.167	odd	6		441.2.f.c.148.1		6
252.223	even	6		3969.2.a.l.1.1		3
252.247	odd	6		1323.2.g.d.361.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.1	✓	6	36.23	even	6
63.2.f.a.43.1	yes	6	12.11	even	2
189.2.f.b.64.3		6	36.31	odd	6
189.2.f.b.127.3		6	4.3	odd	2
441.2.f.c.148.1		6	252.167	odd	6
441.2.f.c.295.1		6	84.83	odd	2
441.2.g.b.67.1		6	252.131	odd	6
441.2.g.b.79.1		6	84.59	odd	6
441.2.g.c.67.1		6	252.23	even	6
441.2.g.c.79.1		6	84.11	even	6
441.2.h.d.214.3		6	84.23	even	6
441.2.h.d.373.3		6	252.95	even	6
441.2.h.e.214.3		6	84.47	odd	6
441.2.h.e.373.3		6	252.59	odd	6
567.2.a.c.1.1		3	36.7	odd	6
567.2.a.h.1.3		3	36.11	even	6
1008.2.r.h.337.3		6	9.5	odd	6
1008.2.r.h.673.3		6	3.2	odd	2
1323.2.f.d.442.3		6	252.139	even	6
1323.2.f.d.883.3		6	28.27	even	2
1323.2.g.d.361.3		6	252.247	odd	6
1323.2.g.d.667.3		6	28.11	odd	6
1323.2.g.e.361.3		6	252.103	even	6
1323.2.g.e.667.3		6	28.3	even	6
1323.2.h.b.226.1		6	252.31	even	6
1323.2.h.b.802.1		6	28.19	even	6
1323.2.h.c.226.1		6	252.67	odd	6
1323.2.h.c.802.1		6	28.23	odd	6
3024.2.r.k.1009.1		6	9.4	even	3	inner
3024.2.r.k.2017.1		6	1.1	even	1	trivial
3969.2.a.l.1.1		3	252.223	even	6
3969.2.a.q.1.3		3	252.83	odd	6
9072.2.a.bs.1.3		3	9.7	even	3
9072.2.a.ca.1.1		3	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.439693 - 0.761570i) q^{5} +(0.500000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(-0.439693 - 0.761570i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-1.93969 + 3.35965i) q^{11} +(2.72668 + 4.72275i) q^{13} -1.65270 q^{17} -2.41147 q^{19} +(-1.58125 - 2.73881i) q^{23} +(2.11334 - 3.66041i) q^{25} +(-3.02481 + 5.23913i) q^{29} +(-2.27719 - 3.94421i) q^{31} -0.879385 q^{35} -4.55438 q^{37} +(-0.592396 - 1.02606i) q^{41} +(0.0923963 - 0.160035i) q^{43} +(0.511144 - 0.885328i) q^{47} +(-0.500000 - 0.866025i) q^{49} -7.29086 q^{53} +3.41147 q^{55} +(-3.33022 - 5.76811i) q^{59} +(1.29813 - 2.24843i) q^{61} +(2.39780 - 4.15312i) q^{65} +(-1.47906 - 2.56180i) q^{67} -3.68004 q^{71} -12.7811 q^{73} +(1.93969 + 3.35965i) q^{77} +(-2.97906 + 5.15988i) q^{79} +(0.109470 - 0.189608i) q^{83} +(0.726682 + 1.25865i) q^{85} -11.0273 q^{89} +5.45336 q^{91} +(1.06031 + 1.83651i) q^{95} +(-6.25150 + 10.8279i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7}+O(q^{10}) \) 6 * q + 3 * q^5 + 3 * q^7	\( 6 q + 3 q^{5} + 3 q^{7} - 6 q^{11} + 3 q^{13} - 12 q^{17} + 6 q^{19} - 12 q^{23} + 6 q^{25} + 9 q^{29} - 3 q^{31} + 6 q^{35} - 6 q^{37} - 3 q^{43} - 3 q^{47} - 3 q^{49} - 12 q^{53} + 3 q^{59} - 6 q^{61} + 15 q^{65} - 12 q^{67} + 18 q^{71} - 42 q^{73} + 6 q^{77} - 21 q^{79} + 18 q^{83} - 9 q^{85} - 24 q^{89} + 6 q^{91} + 12 q^{95} + 3 q^{97}+O(q^{100}) \) 6 * q + 3 * q^5 + 3 * q^7 - 6 * q^11 + 3 * q^13 - 12 * q^17 + 6 * q^19 - 12 * q^23 + 6 * q^25 + 9 * q^29 - 3 * q^31 + 6 * q^35 - 6 * q^37 - 3 * q^43 - 3 * q^47 - 3 * q^49 - 12 * q^53 + 3 * q^59 - 6 * q^61 + 15 * q^65 - 12 * q^67 + 18 * q^71 - 42 * q^73 + 6 * q^77 - 21 * q^79 + 18 * q^83 - 9 * q^85 - 24 * q^89 + 6 * q^91 + 12 * q^95 + 3 * q^97

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