LMFDB - Embedded newform 3024.2.ca.c.2033.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2033,3024)]

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, 1, 1]))

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

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

chi := DirichletCharacter("3024.2033");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.ca (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2033.3
Root			$-1.68301 + 0.409224i$ of defining polynomial
Character	$\chi$	$=$	3024.2033
Dual form			3024.2.ca.c.2609.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.714925 + 1.23829i) q^{5} +(-0.327442 - 2.62541i) q^{7} +(2.96133 - 1.70972i) q^{11} +(-5.48813 + 3.16857i) q^{13} +(1.14201 - 1.97802i) q^{17} +(1.87673 - 1.08353i) q^{19} +(-6.97507 - 4.02706i) q^{23} +(1.47776 + 2.55956i) q^{25} +(0.298879 + 0.172558i) q^{29} +4.34228i q^{31} +(3.48511 + 1.47150i) q^{35} +(1.07786 + 1.86690i) q^{37} +(-0.202180 - 0.350186i) q^{41} +(-2.90883 + 5.03824i) q^{43} -5.51829 q^{47} +(-6.78556 + 1.71934i) q^{49} +(-8.56310 - 4.94391i) q^{53} +4.88930i q^{55} +11.0296 q^{59} +11.4797i q^{61} -9.06117i q^{65} -4.25366 q^{67} -3.55393i q^{71} +(-0.201057 - 0.116080i) q^{73} +(-5.45839 - 7.21486i) q^{77} -14.5620 q^{79} +(0.811624 - 1.40577i) q^{83} +(1.63290 + 2.82827i) q^{85} +(2.02974 + 3.51562i) q^{89} +(10.1159 + 13.3711i) q^{91} +3.09858i q^{95} +(-9.18719 - 5.30423i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7} + 12 q^{11} + 6 q^{13} + 18 q^{17} - 6 q^{23} - 8 q^{25} - 6 q^{29} + 30 q^{35} - 2 q^{37} + 6 q^{41} + 2 q^{43} - 36 q^{47} - 8 q^{49} + 36 q^{53} + 60 q^{59} + 28 q^{67} + 42 q^{77} - 32 q^{79}+ \cdots + 6 q^{97}+O(q^{100}) $ 16 * q - 2 * q^7 + 12 * q^11 + 6 * q^13 + 18 * q^17 - 6 * q^23 - 8 * q^25 - 6 * q^29 + 30 * q^35 - 2 * q^37 + 6 * q^41 + 2 * q^43 - 36 * q^47 - 8 * q^49 + 36 * q^53 + 60 * q^59 + 28 * q^67 + 42 * q^77 - 32 * q^79 - 12 * q^85 + 24 * q^89 + 12 * q^91 + 6 * q^97

Character values

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

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.714925	+	1.23829i	−0.319724	+	0.553779i	−0.980430	−	0.196866i	$-0.936924\pi$
$5$	−0.714925	+	1.23829i	−0.319724	+	0.553779i	0.660706	+	0.750645i	$0.270257\pi$
$6$		0			0
$7$	−0.327442	−	2.62541i	−0.123762	−	0.992312i
$7$	−0.327442	−	2.62541i	−0.123762	−	0.992312i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.96133	−	1.70972i	0.892874	−	0.515501i	0.0179923	−	0.999838i	$-0.494273\pi$
$11$	2.96133	−	1.70972i	0.892874	−	0.515501i	0.874881	+	0.484337i	$0.160939\pi$
$12$		0			0
$13$	−5.48813	+	3.16857i	−1.52213	+	0.878804i	−0.522476	+	0.852654i	$0.674991\pi$
$13$	−5.48813	+	3.16857i	−1.52213	+	0.878804i	−0.999658	+	0.0261501i	$0.991675\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.14201	−	1.97802i	0.276978	−	0.479739i	−0.693655	−	0.720308i	$-0.744001\pi$
$17$	1.14201	−	1.97802i	0.276978	−	0.479739i	0.970632	+	0.240569i	$0.0773339\pi$
$18$		0			0
$19$	1.87673	−	1.08353i	0.430553	−	0.248580i	−0.269029	−	0.963132i	$-0.586703\pi$
$19$	1.87673	−	1.08353i	0.430553	−	0.248580i	0.699582	+	0.714552i	$0.253370\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.97507	−	4.02706i	−1.45440	−	0.839699i	−0.455675	−	0.890146i	$-0.650602\pi$
$23$	−6.97507	−	4.02706i	−1.45440	−	0.839699i	−0.998727	+	0.0504469i	$0.983935\pi$
$24$		0			0
$25$	1.47776	+	2.55956i	0.295553	+	0.511912i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.298879	+	0.172558i	0.0555003	+	0.0320431i	0.527493	−	0.849559i	$-0.323132\pi$
$29$	0.298879	+	0.172558i	0.0555003	+	0.0320431i	−0.471993	+	0.881602i	$0.656465\pi$
$30$		0			0
$31$			4.34228i			0.779896i	0.920837	+	0.389948i	$0.127507\pi$
$31$			4.34228i			0.779896i	−0.920837	+	0.389948i	$0.872493\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.48511	+	1.47150i	0.589091	+	0.248730i
$36$		0			0
$37$	1.07786	+	1.86690i	0.177199	+	0.306917i	0.940920	−	0.338629i	$-0.109963\pi$
$37$	1.07786	+	1.86690i	0.177199	+	0.306917i	−0.763721	+	0.645546i	$0.776630\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.202180	−	0.350186i	−0.0315752	−	0.0546898i	0.849806	−	0.527096i	$-0.176719\pi$
$41$	−0.202180	−	0.350186i	−0.0315752	−	0.0546898i	−0.881381	+	0.472406i	$0.843386\pi$
$42$		0			0
$43$	−2.90883	+	5.03824i	−0.443592	+	0.768325i	−0.997953	−	0.0639521i	$-0.979630\pi$
$43$	−2.90883	+	5.03824i	−0.443592	+	0.768325i	0.554361	+	0.832277i	$0.312963\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.51829			−0.804926			−0.402463	−	0.915436i	$-0.631846\pi$
$47$	−5.51829			−0.804926			−0.402463	+	0.915436i	$0.631846\pi$
$48$		0			0
$49$	−6.78556	+	1.71934i	−0.969366	+	0.245620i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−8.56310	−	4.94391i	−1.17623	−	0.679098i	−0.221093	−	0.975253i	$-0.570962\pi$
$53$	−8.56310	−	4.94391i	−1.17623	−	0.679098i	−0.955140	+	0.296155i	$0.904296\pi$
$54$		0			0
$55$			4.88930i			0.659273i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	11.0296			1.43593			0.717966	−	0.696079i	$-0.245074\pi$
$59$	11.0296			1.43593			0.717966	+	0.696079i	$0.245074\pi$
$60$		0			0
$61$			11.4797i			1.46983i	0.678159	+	0.734915i	$0.262778\pi$
$61$			11.4797i			1.46983i	−0.678159	+	0.734915i	$0.737222\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	9.06117i		−	1.12390i
$66$		0			0
$67$	−4.25366			−0.519667			−0.259833	−	0.965653i	$-0.583668\pi$
$67$	−4.25366			−0.519667			−0.259833	+	0.965653i	$0.583668\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	3.55393i		−	0.421773i	−0.977511	−	0.210887i	$-0.932365\pi$
$71$		−	3.55393i		−	0.421773i	0.977511	−	0.210887i	$-0.0676351\pi$
$72$		0			0
$73$	−0.201057	−	0.116080i	−0.0235320	−	0.0135862i	0.488188	−	0.872739i	$-0.337658\pi$
$73$	−0.201057	−	0.116080i	−0.0235320	−	0.0135862i	−0.511720	+	0.859152i	$0.670991\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.45839	−	7.21486i	−0.622041	−	0.822210i
$78$		0			0
$79$	−14.5620			−1.63835			−0.819177	−	0.573541i	$-0.805569\pi$
$79$	−14.5620			−1.63835			−0.819177	+	0.573541i	$0.805569\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.811624	−	1.40577i	0.0890873	−	0.154304i	−0.818038	−	0.575164i	$-0.804938\pi$
$83$	0.811624	−	1.40577i	0.0890873	−	0.154304i	0.907126	+	0.420860i	$0.138272\pi$
$84$		0			0
$85$	1.63290	+	2.82827i	0.177113	+	0.306769i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.02974	+	3.51562i	0.215152	+	0.372655i	0.953320	−	0.301963i	$-0.0976419\pi$
$89$	2.02974	+	3.51562i	0.215152	+	0.372655i	−0.738167	+	0.674618i	$0.764309\pi$
$90$		0			0
$91$	10.1159	+	13.3711i	1.06043	+	1.40167i
$92$		0			0
$93$		0			0
$94$		0			0
$95$			3.09858i			0.317908i
$96$		0			0
$97$	−9.18719	−	5.30423i	−0.932818	−	0.538563i	−0.0451164	−	0.998982i	$-0.514366\pi$
$97$	−9.18719	−	5.30423i	−0.932818	−	0.538563i	−0.887702	+	0.460419i	$0.847699\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.02443	+	6.97052i	0.400446	+	0.693593i	0.993780	−	0.111364i	$-0.0355219\pi$
$101$	4.02443	+	6.97052i	0.400446	+	0.693593i	−0.593334	+	0.804957i	$0.702189\pi$
$102$		0			0
$103$	2.43692	+	1.40695i	0.240117	+	0.138631i	0.615230	−	0.788347i	$-0.289063\pi$
$103$	2.43692	+	1.40695i	0.240117	+	0.138631i	−0.375114	+	0.926979i	$0.622396\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.7019	+	7.91078i	−1.32461	+	0.764764i	−0.984460	−	0.175607i	$-0.943811\pi$
$107$	−13.7019	+	7.91078i	−1.32461	+	0.764764i	−0.340150	+	0.940371i	$0.610478\pi$
$108$		0			0
$109$	5.10675	−	8.84514i	0.489138	−	0.847211i	−0.510784	−	0.859709i	$-0.670645\pi$
$109$	5.10675	−	8.84514i	0.489138	−	0.847211i	0.999922	+	0.0124977i	$0.00397826\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.28808	+	4.20778i	−0.685605	+	0.395834i	−0.801963	−	0.597373i	$-0.796211\pi$
$113$	−7.28808	+	4.20778i	−0.685605	+	0.395834i	0.116359	+	0.993207i	$0.462878\pi$
$114$		0			0
$115$	9.97330	−	5.75809i	0.930015	−	0.536945i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−5.56705	−	2.35055i	−0.510330	−	0.215475i
$120$		0			0
$121$	0.346305	−	0.599818i	0.0314823	−	0.0545289i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.3752			−1.01743
$126$		0			0
$127$	−5.77773			−0.512691			−0.256345	−	0.966585i	$-0.582518\pi$
$127$	−5.77773			−0.512691			−0.256345	+	0.966585i	$0.582518\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.22833	−	3.85959i	0.194690	−	0.337214i	−0.752109	−	0.659039i	$-0.770963\pi$
$131$	2.22833	−	3.85959i	0.194690	−	0.337214i	0.946799	+	0.321825i	$0.104296\pi$
$132$		0			0
$133$	−3.45924	−	4.57241i	−0.299954	−	0.396478i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.36293	+	4.82834i	−0.714493	+	0.412513i	−0.812723	−	0.582651i	$-0.802016\pi$
$137$	−8.36293	+	4.82834i	−0.714493	+	0.412513i	0.0982292	+	0.995164i	$0.468682\pi$
$138$		0			0
$139$	−16.0680	+	9.27686i	−1.36287	+	0.786853i	−0.990005	−	0.141033i	$-0.954958\pi$
$139$	−16.0680	+	9.27686i	−1.36287	+	0.786853i	−0.372864	+	0.927886i	$0.621624\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−10.8348	+	18.7664i	−0.906049	+	1.56932i
$144$		0			0
$145$	−0.427352	+	0.246732i	−0.0354896	+	0.0204899i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.63517	+	3.25347i	0.461651	+	0.266535i	0.712738	−	0.701430i	$-0.247455\pi$
$149$	5.63517	+	3.25347i	0.461651	+	0.266535i	−0.251087	+	0.967965i	$0.580788\pi$
$150$		0			0
$151$	2.87950	+	4.98745i	0.234331	+	0.405873i	0.959078	−	0.283142i	$-0.0913768\pi$
$151$	2.87950	+	4.98745i	0.234331	+	0.405873i	−0.724747	+	0.689015i	$0.758044\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.37699	−	3.10441i	−0.431890	−	0.249352i
$156$		0			0
$157$			7.96361i			0.635565i	0.948164	+	0.317783i	$0.102938\pi$
$157$			7.96361i			0.635565i	−0.948164	+	0.317783i	$0.897062\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−8.28874	+	19.6310i	−0.653245	+	1.54714i
$162$		0			0
$163$	−5.69256	−	9.85980i	−0.445876	−	0.772279i	0.552237	−	0.833687i	$-0.313774\pi$
$163$	−5.69256	−	9.85980i	−0.445876	−	0.772279i	−0.998113	+	0.0614080i	$0.980441\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.66418	−	9.81065i	−0.438308	−	0.759171i	0.559252	−	0.828998i	$-0.311089\pi$
$167$	−5.66418	−	9.81065i	−0.438308	−	0.759171i	−0.997559	+	0.0698271i	$0.977755\pi$
$168$		0			0
$169$	13.5797	−	23.5208i	1.04459	−	1.80929i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	21.6914			1.64917			0.824584	−	0.565739i	$-0.191409\pi$
$173$	21.6914			1.64917			0.824584	+	0.565739i	$0.191409\pi$
$174$		0			0
$175$	6.23602	−	4.71785i	0.471399	−	0.356636i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−18.0057	−	10.3956i	−1.34581	−	0.777002i	−0.358155	−	0.933662i	$-0.616594\pi$
$179$	−18.0057	−	10.3956i	−1.34581	−	0.777002i	−0.987653	+	0.156660i	$0.949927\pi$
$180$		0			0
$181$			21.5301i			1.60032i	0.599788	+	0.800159i	$0.295252\pi$
$181$			21.5301i			1.60032i	−0.599788	+	0.800159i	$0.704748\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.08235			−0.226619
$186$		0			0
$187$		−	7.81007i		−	0.571129i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	7.36938i		−	0.533230i	−0.963803	−	0.266615i	$-0.914095\pi$
$191$		−	7.36938i		−	0.533230i	0.963803	−	0.266615i	$-0.0859052\pi$
$192$		0			0
$193$	−2.82559			−0.203390			−0.101695	−	0.994816i	$-0.532427\pi$
$193$	−2.82559			−0.203390			−0.101695	+	0.994816i	$0.532427\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	26.0883i		−	1.85871i	−0.369183	−	0.929357i	$-0.620363\pi$
$197$		−	26.0883i		−	1.85871i	0.369183	−	0.929357i	$-0.379637\pi$
$198$		0			0
$199$	−13.3511	−	7.70826i	−0.946434	−	0.546424i	−0.0544625	−	0.998516i	$-0.517345\pi$
$199$	−13.3511	−	7.70826i	−0.946434	−	0.546424i	−0.891971	+	0.452092i	$0.850678\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.355169	−	0.841182i	0.0249280	−	0.0590394i
$204$		0			0
$205$	0.578174			0.0403814
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.70508	−	6.41739i	0.256286	−	0.443900i
$210$		0			0
$211$	−4.42465	−	7.66371i	−0.304605	−	0.527592i	0.672568	−	0.740035i	$-0.265191\pi$
$211$	−4.42465	−	7.66371i	−0.304605	−	0.527592i	−0.977173	+	0.212443i	$0.931858\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.15919	−	7.20393i	−0.283655	−	0.491304i
$216$		0			0
$217$	11.4003	−	1.42185i	0.773901	−	0.0965212i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			14.4741i			0.973637i
$222$		0			0
$223$	6.88961	+	3.97772i	0.461363	+	0.266368i	0.712617	−	0.701553i	$-0.247510\pi$
$223$	6.88961	+	3.97772i	0.461363	+	0.266368i	−0.251254	+	0.967921i	$0.580843\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.61984	+	8.00180i	0.306630	+	0.531098i	0.977623	−	0.210365i	$-0.0674654\pi$
$227$	4.61984	+	8.00180i	0.306630	+	0.531098i	−0.670993	+	0.741464i	$0.734132\pi$
$228$		0			0
$229$	−7.31319	−	4.22227i	−0.483269	−	0.279016i	0.238509	−	0.971140i	$-0.423341\pi$
$229$	−7.31319	−	4.22227i	−0.483269	−	0.279016i	−0.721778	+	0.692125i	$0.756675\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14.4176	+	8.32399i	−0.944526	+	0.545323i	−0.891376	−	0.453264i	$-0.850259\pi$
$233$	−14.4176	+	8.32399i	−0.944526	+	0.545323i	−0.0531500	+	0.998587i	$0.516926\pi$
$234$		0			0
$235$	3.94517	−	6.83323i	0.257354	−	0.445751i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−23.6325	+	13.6442i	−1.52866	+	0.882572i	−0.529242	+	0.848471i	$0.677524\pi$
$239$	−23.6325	+	13.6442i	−1.52866	+	0.882572i	−0.999418	+	0.0341012i	$0.989143\pi$
$240$		0			0
$241$	−21.9018	+	12.6450i	−1.41082	+	0.814537i	−0.995466	−	0.0951223i	$-0.969676\pi$
$241$	−21.9018	+	12.6450i	−1.41082	+	0.814537i	−0.415354	+	0.909660i	$0.636342\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.72213	−	9.63167i	0.173911	−	0.615345i
$246$		0			0
$247$	−6.86651	+	11.8931i	−0.436906	+	0.756743i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−8.19337			−0.517161			−0.258581	−	0.965990i	$-0.583255\pi$
$251$	−8.19337			−0.517161			−0.258581	+	0.965990i	$0.583255\pi$
$252$		0			0
$253$	−27.5406			−1.73146
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.31723	−	5.74560i	0.206923	−	0.358401i	−0.743821	−	0.668379i	$-0.766988\pi$
$257$	3.31723	−	5.74560i	0.206923	−	0.358401i	0.950744	+	0.309978i	$0.100322\pi$
$258$		0			0
$259$	4.54845	−	3.44112i	0.282627	−	0.213821i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.23590	−	3.02295i	0.322860	−	0.186403i	−0.329807	−	0.944048i	$-0.606984\pi$
$263$	5.23590	−	3.02295i	0.322860	−	0.186403i	0.652666	+	0.757645i	$0.273650\pi$
$264$		0			0
$265$	12.2440	−	7.06905i	0.752140	−	0.434248i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.41069	+	5.90750i	−0.207954	+	0.360186i	−0.951070	−	0.308976i	$-0.900014\pi$
$269$	−3.41069	+	5.90750i	−0.207954	+	0.360186i	0.743116	+	0.669163i	$0.233347\pi$
$270$		0			0
$271$	4.39780	−	2.53907i	0.267148	−	0.154238i	−0.360443	−	0.932781i	$-0.617375\pi$
$271$	4.39780	−	2.53907i	0.267148	−	0.154238i	0.627591	+	0.778543i	$0.284041\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.75228	+	5.05313i	0.527783	+	0.304715i
$276$		0			0
$277$	0.989567	+	1.71398i	0.0594573	+	0.102983i	0.894222	−	0.447624i	$-0.147730\pi$
$277$	0.989567	+	1.71398i	0.0594573	+	0.102983i	−0.834765	+	0.550607i	$0.814396\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	15.2703	+	8.81631i	0.910950	+	0.525937i	0.880737	−	0.473606i	$-0.157048\pi$
$281$	15.2703	+	8.81631i	0.910950	+	0.525937i	0.0302131	+	0.999543i	$0.490381\pi$
$282$		0			0
$283$		−	5.15385i		−	0.306365i	−0.988198	−	0.153182i	$-0.951048\pi$
$283$		−	5.15385i		−	0.306365i	0.988198	−	0.153182i	$-0.0489522\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.853179	+	0.645471i	−0.0503616	+	0.0381009i
$288$		0			0
$289$	5.89164	+	10.2046i	0.346567	+	0.600271i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.03248	−	1.78831i	−0.0603183	−	0.104474i	0.834289	−	0.551327i	$-0.185878\pi$
$293$	−1.03248	−	1.78831i	−0.0603183	−	0.104474i	−0.894608	+	0.446852i	$0.852545\pi$
$294$		0			0
$295$	−7.88534	+	13.6578i	−0.459102	+	0.795188i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	51.0401			2.95173
$300$		0			0
$301$	14.1799	+	5.98714i	0.817317	+	0.345093i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−14.2152	−	8.20716i	−0.813961	−	0.469941i
$306$		0			0
$307$			1.09119i			0.0622772i	0.999515	+	0.0311386i	$0.00991333\pi$
$307$			1.09119i			0.0622772i	−0.999515	+	0.0311386i	$0.990087\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	15.2220			0.863161			0.431580	−	0.902075i	$-0.357956\pi$
$311$	15.2220			0.863161			0.431580	+	0.902075i	$0.357956\pi$
$312$		0			0
$313$		−	11.5704i		−	0.653996i	−0.945025	−	0.326998i	$-0.893963\pi$
$313$		−	11.5704i		−	0.653996i	0.945025	−	0.326998i	$-0.106037\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	17.1604i		−	0.963824i	−0.876220	−	0.481912i	$-0.839942\pi$
$317$		−	17.1604i		−	0.963824i	0.876220	−	0.481912i	$-0.160058\pi$
$318$		0			0
$319$	1.18010			0.0660731
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	4.94962i		−	0.275404i
$324$		0			0
$325$	−16.2203	−	9.36481i	−0.899742	−	0.519466i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.80692	+	14.4878i	0.0996189	+	0.798738i
$330$		0			0
$331$	26.4931			1.45619			0.728096	−	0.685475i	$-0.240405\pi$
$331$	26.4931			1.45619			0.728096	+	0.685475i	$0.240405\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3.04105	−	5.26725i	0.166150	−	0.287780i
$336$		0			0
$337$	4.06451	+	7.03993i	0.221408	+	0.383490i	0.955236	−	0.295846i	$-0.0956015\pi$
$337$	4.06451	+	7.03993i	0.221408	+	0.383490i	−0.733828	+	0.679335i	$0.762268\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	7.42410	+	12.8589i	0.402037	+	0.696349i
$342$		0			0
$343$	6.73586	+	17.2519i	0.363702	+	0.931515i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			25.6171i			1.37520i	0.726090	+	0.687599i	$0.241335\pi$
$347$			25.6171i			1.37520i	−0.726090	+	0.687599i	$0.758665\pi$
$348$		0			0
$349$	9.11932	+	5.26504i	0.488146	+	0.281831i	0.723805	−	0.690005i	$-0.242391\pi$
$349$	9.11932	+	5.26504i	0.488146	+	0.281831i	−0.235659	+	0.971836i	$0.575725\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.42186	−	11.1230i	−0.341801	−	0.592017i	0.642966	−	0.765895i	$-0.277704\pi$
$353$	−6.42186	−	11.1230i	−0.341801	−	0.592017i	−0.984767	+	0.173878i	$0.944370\pi$
$354$		0			0
$355$	4.40078	+	2.54079i	0.233569	+	0.134851i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	25.6881	−	14.8311i	1.35577	−	0.782753i	0.366718	−	0.930332i	$-0.380482\pi$
$359$	25.6881	−	14.8311i	1.35577	−	0.782753i	0.989050	+	0.147579i	$0.0471482\pi$
$360$		0			0
$361$	−7.15191	+	12.3875i	−0.376416	+	0.651972i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.287482	−	0.165978i	0.0150475	−	0.00868767i
$366$		0			0
$367$	−20.7828	+	11.9989i	−1.08485	+	0.626340i	−0.932201	−	0.361940i	$-0.882115\pi$
$367$	−20.7828	+	11.9989i	−1.08485	+	0.626340i	−0.152651	+	0.988280i	$0.548781\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−10.1759	+	24.1005i	−0.528305	+	1.25124i
$372$		0			0
$373$	5.91948	−	10.2528i	0.306499	−	0.530872i	−0.671095	−	0.741371i	$-0.734176\pi$
$373$	5.91948	−	10.2528i	0.306499	−	0.530872i	0.977594	+	0.210500i	$0.0675091\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.18705			−0.112639
$378$		0			0
$379$	13.1379			0.674850			0.337425	−	0.941352i	$-0.390444\pi$
$379$	13.1379			0.674850			0.337425	+	0.941352i	$0.390444\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−8.77603	+	15.2005i	−0.448434	+	0.776711i	−0.998284	−	0.0585527i	$-0.981351\pi$
$383$	−8.77603	+	15.2005i	−0.448434	+	0.776711i	0.549850	+	0.835263i	$0.314685\pi$
$384$		0			0
$385$	12.8364	−	1.60096i	0.654204	−	0.0815926i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−18.9148	+	10.9205i	−0.959020	+	0.553691i	−0.895871	−	0.444313i	$-0.853448\pi$
$389$	−18.9148	+	10.9205i	−0.959020	+	0.553691i	−0.0631489	+	0.998004i	$0.520114\pi$
$390$		0			0
$391$	−15.9312	+	9.19786i	−0.805674	+	0.465156i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	10.4107	−	18.0319i	0.523821	−	0.907285i
$396$		0			0
$397$	33.7636	−	19.4935i	1.69455	−	0.978348i	0.743792	−	0.668411i	$-0.233025\pi$
$397$	33.7636	−	19.4935i	1.69455	−	0.978348i	0.950757	−	0.309937i	$-0.100308\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	20.0899	+	11.5989i	1.00324	+	0.579223i	0.909206	−	0.416346i	$-0.136689\pi$
$401$	20.0899	+	11.5989i	1.00324	+	0.579223i	0.0940373	+	0.995569i	$0.470023\pi$
$402$		0			0
$403$	−13.7588	−	23.8310i	−0.685376	−	1.18711i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.38377	+	3.68567i	0.316432	+	0.182692i
$408$		0			0
$409$		−	24.6187i		−	1.21732i	−0.793432	−	0.608659i	$-0.791708\pi$
$409$		−	24.6187i		−	1.21732i	0.793432	−	0.608659i	$-0.208292\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.61156	−	28.9572i	−0.177713	−	1.42489i
$414$		0			0
$415$	1.16050	+	2.01005i	0.0569667	+	0.0986693i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.53996	+	14.7916i	0.417204	+	0.722619i	0.995657	−	0.0930969i	$-0.0296766\pi$
$419$	8.53996	+	14.7916i	0.417204	+	0.722619i	−0.578453	+	0.815716i	$0.696343\pi$
$420$		0			0
$421$	−7.35652	+	12.7419i	−0.358535	+	0.621000i	−0.987716	−	0.156258i	$-0.950057\pi$
$421$	−7.35652	+	12.7419i	−0.358535	+	0.621000i	0.629182	+	0.777258i	$0.283390\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.75047			0.327446
$426$		0			0
$427$	30.1391	−	3.75896i	1.45853	−	0.181909i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8.32286	−	4.80521i	−0.400898	−	0.231459i	0.285973	−	0.958238i	$-0.407683\pi$
$431$	−8.32286	−	4.80521i	−0.400898	−	0.231459i	−0.686871	+	0.726779i	$0.741016\pi$
$432$		0			0
$433$			9.04314i			0.434585i	0.976106	+	0.217293i	$0.0697226\pi$
$433$			9.04314i			0.434585i	−0.976106	+	0.217293i	$0.930277\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−17.4538			−0.834929
$438$		0			0
$439$			0.913795i			0.0436131i	0.999762	+	0.0218065i	$0.00694178\pi$
$439$			0.913795i			0.0436131i	−0.999762	+	0.0218065i	$0.993058\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	29.3616i		−	1.39501i	−0.716578	−	0.697507i	$-0.754293\pi$
$443$		−	29.3616i		−	1.39501i	0.716578	−	0.697507i	$-0.245707\pi$
$444$		0			0
$445$	−5.80446			−0.275158
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	3.36736i		−	0.158915i	−0.996838	−	0.0794577i	$-0.974681\pi$
$449$		−	3.36736i		−	0.158915i	0.996838	−	0.0794577i	$-0.0253189\pi$
$450$		0			0
$451$	−1.19744	−	0.691343i	−0.0563853	−	0.0325541i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−23.7893	+	2.96701i	−1.11526	+	0.139096i
$456$		0			0
$457$	−15.1139			−0.706996			−0.353498	−	0.935435i	$-0.615008\pi$
$457$	−15.1139			−0.706996			−0.353498	+	0.935435i	$0.615008\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−5.19445	+	8.99706i	−0.241930	+	0.419035i	−0.961264	−	0.275629i	$-0.911114\pi$
$461$	−5.19445	+	8.99706i	−0.241930	+	0.419035i	0.719334	+	0.694664i	$0.244447\pi$
$462$		0			0
$463$	2.65722	+	4.60244i	0.123492	+	0.213894i	0.921142	−	0.389226i	$-0.127257\pi$
$463$	2.65722	+	4.60244i	0.123492	+	0.213894i	−0.797651	+	0.603120i	$0.793924\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.74994	+	16.8874i	0.451173	+	0.781455i	0.998459	−	0.0554907i	$-0.0176723\pi$
$467$	9.74994	+	16.8874i	0.451173	+	0.781455i	−0.547286	+	0.836946i	$0.684339\pi$
$468$		0			0
$469$	1.39283	+	11.1676i	0.0643148	+	0.515672i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			19.8932i			0.914689i
$474$		0			0
$475$	5.54674	+	3.20241i	0.254502	+	0.146937i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−13.9012	−	24.0776i	−0.635163	−	1.10013i	−0.986481	−	0.163878i	$-0.947600\pi$
$479$	−13.9012	−	24.0776i	−0.635163	−	1.10013i	0.351318	−	0.936256i	$-0.385734\pi$
$480$		0			0
$481$	−11.8308	−	6.83054i	−0.539440	−	0.311446i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	13.1363	−	7.58425i	0.596489	−	0.344383i
$486$		0			0
$487$	−3.73838	+	6.47506i	−0.169402	+	0.293413i	−0.938210	−	0.346067i	$-0.887517\pi$
$487$	−3.73838	+	6.47506i	−0.169402	+	0.293413i	0.768808	+	0.639480i	$0.220850\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	19.1466	−	11.0543i	0.864073	−	0.498873i	−0.00130103	−	0.999999i	$-0.500414\pi$
$491$	19.1466	−	11.0543i	0.864073	−	0.498873i	0.865374	+	0.501126i	$0.167081\pi$
$492$		0			0
$493$	0.682643	−	0.394124i	0.0307447	−	0.0177505i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.33052	+	1.16371i	−0.418531	+	0.0521994i
$498$		0			0
$499$	16.4521	−	28.4959i	0.736498	−	1.27565i	−0.217565	−	0.976046i	$-0.569811\pi$
$499$	16.4521	−	28.4959i	0.736498	−	1.27565i	0.954063	−	0.299606i	$-0.0968554\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−25.6142			−1.14208			−0.571039	−	0.820923i	$-0.693460\pi$
$503$	−25.6142			−1.14208			−0.571039	+	0.820923i	$0.693460\pi$
$504$		0			0
$505$	−11.5087			−0.512129
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10.7358	−	18.5950i	0.475857	−	0.824209i	−0.523760	−	0.851866i	$-0.675471\pi$
$509$	10.7358	−	18.5950i	0.475857	−	0.824209i	0.999617	+	0.0276567i	$0.00880451\pi$
$510$		0			0
$511$	−0.238924	+	0.565868i	−0.0105694	+	0.0250325i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.48443	+	2.01173i	−0.153542	+	0.0886476i
$516$		0			0
$517$	−16.3415	+	9.43475i	−0.718697	+	0.414940i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.23087	−	5.59604i	0.141547	−	0.245167i	−0.786532	−	0.617549i	$-0.788126\pi$
$521$	3.23087	−	5.59604i	0.141547	−	0.245167i	0.928079	+	0.372382i	$0.121459\pi$
$522$		0			0
$523$	−11.7830	+	6.80291i	−0.515234	+	0.297470i	−0.734982	−	0.678086i	$-0.762810\pi$
$523$	−11.7830	+	6.80291i	−0.515234	+	0.297470i	0.219749	+	0.975557i	$0.429476\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.58910	+	4.95892i	0.374147	+	0.216014i
$528$		0			0
$529$	20.9344	+	36.2594i	0.910190	+	1.57649i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.21918	+	1.28124i	0.0961233	+	0.0554968i
$534$		0			0
$535$		−	22.6225i		−	0.978055i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−17.1547	+	16.6930i	−0.738904	+	0.719017i
$540$		0			0
$541$	−14.9288	−	25.8574i	−0.641838	−	1.11170i	−0.985022	−	0.172428i	$-0.944839\pi$
$541$	−14.9288	−	25.8574i	−0.641838	−	1.11170i	0.343184	−	0.939268i	$-0.388494\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	7.30188	+	12.6472i	0.312778	+	0.541748i
$546$		0			0
$547$	9.07207	−	15.7133i	0.387894	−	0.671852i	−0.604272	−	0.796778i	$-0.706536\pi$
$547$	9.07207	−	15.7133i	0.387894	−	0.671852i	0.992166	+	0.124926i	$0.0398694\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.747888			0.0318611
$552$		0			0
$553$	4.76822	+	38.2312i	0.202765	+	1.62576i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	32.5079	+	18.7684i	1.37740	+	0.795245i	0.991846	−	0.127439i	$-0.0406757\pi$
$557$	32.5079	+	18.7684i	1.37740	+	0.795245i	0.385558	+	0.922684i	$0.374009\pi$
$558$		0			0
$559$		−	36.8674i		−	1.55932i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.10681			0.299516			0.149758	−	0.988723i	$-0.452150\pi$
$563$	7.10681			0.299516			0.149758	+	0.988723i	$0.452150\pi$
$564$		0			0
$565$		−	12.0330i		−	0.506231i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	41.1650i		−	1.72572i	−0.505439	−	0.862862i	$-0.668669\pi$
$569$		−	41.1650i		−	1.72572i	0.505439	−	0.862862i	$-0.331331\pi$
$570$		0			0
$571$	−4.42585			−0.185216			−0.0926080	−	0.995703i	$-0.529520\pi$
$571$	−4.42585			−0.185216			−0.0926080	+	0.995703i	$0.529520\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	23.8042i		−	0.992702i
$576$		0			0
$577$	2.37542	+	1.37145i	0.0988900	+	0.0570941i	0.548629	−	0.836066i	$-0.315150\pi$
$577$	2.37542	+	1.37145i	0.0988900	+	0.0570941i	−0.449739	+	0.893160i	$0.648483\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.95649	−	1.67054i	−0.164143	−	0.0693055i
$582$		0			0
$583$	−33.8109			−1.40030
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.90248	−	17.1516i	0.408719	−	0.707922i	−0.586027	−	0.810291i	$-0.699309\pi$
$587$	9.90248	−	17.1516i	0.408719	−	0.707922i	0.994747	+	0.102369i	$0.0326422\pi$
$588$		0			0
$589$	4.70501	+	8.14931i	0.193866	+	0.335786i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.434850	−	0.753183i	−0.0178572	−	0.0309295i	0.856959	−	0.515385i	$-0.172351\pi$
$593$	−0.434850	−	0.753183i	−0.0178572	−	0.0309295i	−0.874816	+	0.484456i	$0.839018\pi$
$594$		0			0
$595$	6.89068	−	5.21313i	0.282490	−	0.213717i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	2.69365i		−	0.110059i	−0.998485	−	0.0550297i	$-0.982475\pi$
$599$		−	2.69365i		−	0.110059i	0.998485	−	0.0550297i	$-0.0175254\pi$
$600$		0			0
$601$	0.115325	+	0.0665827i	0.00470419	+	0.00271596i	0.502350	−	0.864664i	$-0.332469\pi$
$601$	0.115325	+	0.0665827i	0.00470419	+	0.00271596i	−0.497646	+	0.867380i	$0.665802\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.495165	+	0.857650i	0.0201313	+	0.0348684i
$606$		0			0
$607$	38.3860	+	22.1622i	1.55804	+	0.899534i	0.997445	+	0.0714432i	$0.0227605\pi$
$607$	38.3860	+	22.1622i	1.55804	+	0.899534i	0.560594	+	0.828091i	$0.310573\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	30.2851	−	17.4851i	1.22520	−	0.707372i
$612$		0			0
$613$	3.29901	−	5.71406i	0.133246	−	0.230789i	−0.791680	−	0.610936i	$-0.790793\pi$
$613$	3.29901	−	5.71406i	0.133246	−	0.230789i	0.924926	+	0.380147i	$0.124127\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.99450	−	4.61563i	0.321846	−	0.185818i	−0.330369	−	0.943852i	$-0.607173\pi$
$617$	7.99450	−	4.61563i	0.321846	−	0.185818i	0.652215	+	0.758034i	$0.273840\pi$
$618$		0			0
$619$	5.66289	−	3.26947i	0.227611	−	0.131411i	−0.381859	−	0.924221i	$-0.624716\pi$
$619$	5.66289	−	3.26947i	0.227611	−	0.131411i	0.609469	+	0.792810i	$0.291383\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8.56532	−	6.48007i	0.343162	−	0.259619i
$624$		0			0
$625$	0.743610	−	1.28797i	0.0297444	−	0.0515188i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	4.92368			0.196320
$630$		0			0
$631$	−13.8837			−0.552699			−0.276350	−	0.961057i	$-0.589125\pi$
$631$	−13.8837			−0.552699			−0.276350	+	0.961057i	$0.589125\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.13064	−	7.15449i	0.163920	−	0.283917i
$636$		0			0
$637$	31.7922	−	30.9365i	1.25965	−	1.22575i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	13.1940	−	7.61757i	0.521133	−	0.300876i	−0.216265	−	0.976335i	$-0.569388\pi$
$641$	13.1940	−	7.61757i	0.521133	−	0.300876i	0.737398	+	0.675459i	$0.236054\pi$
$642$		0			0
$643$	16.5813	−	9.57324i	0.653904	−	0.377532i	−0.136046	−	0.990702i	$-0.543440\pi$
$643$	16.5813	−	9.57324i	0.653904	−	0.377532i	0.789950	+	0.613171i	$0.210106\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.793991	−	1.37523i	0.0312150	−	0.0540660i	−0.849996	−	0.526789i	$-0.823396\pi$
$647$	0.793991	−	1.37523i	0.0312150	−	0.0540660i	0.881211	+	0.472723i	$0.156729\pi$
$648$		0			0
$649$	32.6622	−	18.8576i	1.28211	−	0.740224i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	15.5572	+	8.98197i	0.608802	+	0.351492i	0.772496	−	0.635019i	$-0.219008\pi$
$653$	15.5572	+	8.98197i	0.608802	+	0.351492i	−0.163695	+	0.986511i	$0.552341\pi$
$654$		0			0
$655$	3.18619	+	5.51863i	0.124495	+	0.215631i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	10.0955	+	5.82866i	0.393266	+	0.227052i	0.683574	−	0.729881i	$-0.260424\pi$
$659$	10.0955	+	5.82866i	0.393266	+	0.227052i	−0.290308	+	0.956933i	$0.593758\pi$
$660$		0			0
$661$		−	18.2195i		−	0.708657i	−0.935121	−	0.354328i	$-0.884710\pi$
$661$		−	18.2195i		−	0.708657i	0.935121	−	0.354328i	$-0.115290\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	8.13505	−	1.01461i	0.315464	−	0.0393448i
$666$		0			0
$667$	−1.38980	−	2.40720i	−0.0538132	−	0.0932072i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	19.6272	+	33.9953i	0.757699	+	1.31237i
$672$		0			0
$673$	2.41106	−	4.17608i	0.0929395	−	0.160976i	−0.815807	−	0.578324i	$-0.803707\pi$
$673$	2.41106	−	4.17608i	0.0929395	−	0.160976i	0.908747	+	0.417348i	$0.137040\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−23.1290			−0.888920			−0.444460	−	0.895799i	$-0.646604\pi$
$677$	−23.1290			−0.888920			−0.444460	+	0.895799i	$0.646604\pi$
$678$		0			0
$679$	−10.9175	+	25.8570i	−0.418975	+	0.992300i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−6.80041	−	3.92622i	−0.260210	−	0.150233i	0.364220	−	0.931313i	$-0.381336\pi$
$683$	−6.80041	−	3.92622i	−0.260210	−	0.150233i	−0.624431	+	0.781080i	$0.714669\pi$
$684$		0			0
$685$		−	13.8076i		−	0.527562i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	62.6606			2.38718
$690$		0			0
$691$		−	17.1676i		−	0.653085i	−0.945182	−	0.326543i	$-0.894116\pi$
$691$		−	17.1676i		−	0.653085i	0.945182	−	0.326543i	$-0.105884\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	26.5290i		−	1.00630i
$696$		0			0
$697$	−0.923564			−0.0349825
$698$		0			0
$699$		0			0
$700$		0			0
$701$			34.9404i			1.31968i	0.751406	+	0.659840i	$0.229376\pi$
$701$			34.9404i			1.31968i	−0.751406	+	0.659840i	$0.770624\pi$
$702$		0			0
$703$	4.04570	+	2.33579i	0.152587	+	0.0880959i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	16.9827	−	12.8482i	0.638701	−	0.483207i
$708$		0			0
$709$	−24.3336			−0.913867			−0.456933	−	0.889501i	$-0.651052\pi$
$709$	−24.3336			−0.913867			−0.456933	+	0.889501i	$0.651052\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	17.4866	−	30.2877i	0.654879	−	1.13428i
$714$		0			0
$715$	−15.4921	−	26.8331i	−0.579372	−	1.00350i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	8.76887	+	15.1881i	0.327024	+	0.566422i	0.981920	−	0.189297i	$-0.0606210\pi$
$719$	8.76887	+	15.1881i	0.327024	+	0.566422i	−0.654896	+	0.755719i	$0.727288\pi$
$720$		0			0
$721$	2.89588	−	6.85860i	0.107848	−	0.255428i
$722$		0			0
$723$		0			0
$724$		0			0
$725$			1.02000i			0.0378818i
$726$		0			0
$727$	33.8627	+	19.5507i	1.25590	+	0.725094i	0.972275	−	0.233841i	$-0.0751296\pi$
$727$	33.8627	+	19.5507i	1.25590	+	0.725094i	0.283625	+	0.958935i	$0.408463\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	6.64381	+	11.5074i	0.245730	+	0.425617i
$732$		0			0
$733$	20.3073	+	11.7245i	0.750069	+	0.433053i	0.825719	−	0.564082i	$-0.190770\pi$
$733$	20.3073	+	11.7245i	0.750069	+	0.433053i	−0.0756499	+	0.997134i	$0.524103\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.5965	+	7.27257i	−0.463997	+	0.267889i
$738$		0			0
$739$	−13.3662	+	23.1509i	−0.491682	+	0.851618i	−0.999954	−	0.00957820i	$-0.996951\pi$
$739$	−13.3662	+	23.1509i	−0.491682	+	0.851618i	0.508272	+	0.861197i	$0.330284\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−11.0914	+	6.40360i	−0.406903	+	0.234925i	−0.689458	−	0.724326i	$-0.742151\pi$
$743$	−11.0914	+	6.40360i	−0.406903	+	0.234925i	0.282555	+	0.959251i	$0.408818\pi$
$744$		0			0
$745$	−8.05745	+	4.65197i	−0.295202	+	0.170435i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	25.2556	+	33.3827i	0.922821	+	1.21978i
$750$		0			0
$751$	−5.12417	+	8.87532i	−0.186984	+	0.323865i	−0.944243	−	0.329249i	$-0.893204\pi$
$751$	−5.12417	+	8.87532i	−0.186984	+	0.323865i	0.757260	+	0.653114i	$0.226538\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−8.23452			−0.299685
$756$		0			0
$757$	11.0844			0.402868			0.201434	−	0.979502i	$-0.435440\pi$
$757$	11.0844			0.402868			0.201434	+	0.979502i	$0.435440\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	8.14993	−	14.1161i	0.295435	−	0.511708i	−0.679651	−	0.733536i	$-0.737869\pi$
$761$	8.14993	−	14.1161i	0.295435	−	0.511708i	0.975086	+	0.221827i	$0.0712022\pi$
$762$		0			0
$763$	−24.8943	−	10.5110i	−0.901234	−	0.380525i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−60.5319	+	34.9481i	−2.18568	+	1.26190i
$768$		0			0
$769$	41.4043	−	23.9048i	1.49308	−	0.862029i	0.493110	−	0.869967i	$-0.335860\pi$
$769$	41.4043	−	23.9048i	1.49308	−	0.862029i	0.999968	+	0.00793771i	$0.00252668\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	6.25441	−	10.8330i	0.224956	−	0.389635i	−0.731350	−	0.682002i	$-0.761110\pi$
$773$	6.25441	−	10.8330i	0.224956	−	0.389635i	0.956306	+	0.292367i	$0.0944429\pi$
$774$		0			0
$775$	−11.1143	+	6.41686i	−0.399239	+	0.230501i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.758876	−	0.438137i	−0.0271896	−	0.0156979i
$780$		0			0
$781$	−6.07623	−	10.5243i	−0.217425	−	0.376590i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−9.86123	−	5.69338i	−0.351962	−	0.203206i
$786$		0			0
$787$		−	0.261017i		−	0.00930426i	−0.999989	−	0.00465213i	$-0.998519\pi$
$787$		−	0.261017i		−	0.00930426i	0.999989	−	0.00465213i	$-0.00148082\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	13.4336	+	17.7564i	0.477643	+	0.631345i
$792$		0			0
$793$	−36.3744	−	63.0024i	−1.29169	−	2.23728i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.85220	−	3.20810i	−0.0656083	−	0.113637i	0.831355	−	0.555741i	$-0.187565\pi$
$797$	−1.85220	−	3.20810i	−0.0656083	−	0.113637i	−0.896964	+	0.442104i	$0.854232\pi$
$798$		0			0
$799$	−6.30194	+	10.9153i	−0.222946	+	0.386155i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.793862			−0.0280148
$804$		0			0
$805$	−18.3830	−	24.2986i	−0.647917	−	0.856412i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−5.94276	−	3.43105i	−0.208936	−	0.120629i	0.391881	−	0.920016i	$-0.371825\pi$
$809$	−5.94276	−	3.43105i	−0.208936	−	0.120629i	−0.600817	+	0.799387i	$0.705158\pi$
$810$		0			0
$811$			23.1945i			0.814470i	0.913323	+	0.407235i	$0.133507\pi$
$811$			23.1945i			0.814470i	−0.913323	+	0.407235i	$0.866493\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	16.2790			0.570229
$816$		0			0
$817$			12.6073i			0.441072i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			3.79377i			0.132403i	0.997806	+	0.0662017i	$0.0210881\pi$
$821$			3.79377i			0.132403i	−0.997806	+	0.0662017i	$0.978912\pi$
$822$		0			0
$823$	14.9079			0.519656			0.259828	−	0.965655i	$-0.416334\pi$
$823$	14.9079			0.519656			0.259828	+	0.965655i	$0.416334\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	21.9819i		−	0.764384i	−0.924083	−	0.382192i	$-0.875169\pi$
$827$		−	21.9819i		−	0.764384i	0.924083	−	0.382192i	$-0.124831\pi$
$828$		0			0
$829$	12.2406	+	7.06713i	0.425135	+	0.245452i	0.697272	−	0.716807i	$-0.254397\pi$
$829$	12.2406	+	7.06713i	0.425135	+	0.245452i	−0.272137	+	0.962259i	$0.587730\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.34828	+	15.3855i	−0.150659	+	0.533074i
$834$		0			0
$835$	16.1979			0.560550
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.92488	−	15.4583i	0.308121	−	0.533681i	−0.669830	−	0.742514i	$-0.733633\pi$
$839$	8.92488	−	15.4583i	0.308121	−	0.533681i	0.977951	+	0.208833i	$0.0669665\pi$
$840$		0			0
$841$	−14.4404	−	25.0116i	−0.497946	−	0.862469i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	19.4170	+	33.6312i	0.667964	+	1.15695i
$846$		0			0
$847$	−1.68816	−	0.712787i	−0.0580060	−	0.0244917i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	17.3624i		−	0.595174i
$852$		0			0
$853$	35.2392	+	20.3454i	1.20657	+	0.696612i	0.962008	−	0.273022i	$-0.0880233\pi$
$853$	35.2392	+	20.3454i	1.20657	+	0.696612i	0.244559	+	0.969634i	$0.421357\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.72896	−	4.72669i	−0.0932194	−	0.161461i	0.815645	−	0.578553i	$-0.196382\pi$
$857$	−2.72896	−	4.72669i	−0.0932194	−	0.161461i	−0.908864	+	0.417092i	$0.863049\pi$
$858$		0			0
$859$	−38.8822	−	22.4487i	−1.32664	−	0.765938i	−0.341865	−	0.939749i	$-0.611059\pi$
$859$	−38.8822	−	22.4487i	−1.32664	−	0.765938i	−0.984779	+	0.173810i	$0.944392\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	19.6689	−	11.3559i	0.669539	−	0.386558i	−0.126363	−	0.991984i	$-0.540330\pi$
$863$	19.6689	−	11.3559i	0.669539	−	0.386558i	0.795902	+	0.605426i	$0.206997\pi$
$864$		0			0
$865$	−15.5077	+	26.8602i	−0.527279	+	0.913274i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−43.1229	+	24.8970i	−1.46284	+	0.844573i
$870$		0			0
$871$	23.3446	−	13.4780i	0.791002	−	0.456685i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	3.72473	+	29.8646i	0.125919	+	1.00961i
$876$		0			0
$877$	15.2445	−	26.4043i	0.514771	−	0.891610i	−0.485082	−	0.874469i	$-0.661210\pi$
$877$	15.2445	−	26.4043i	0.514771	−	0.891610i	0.999853	−	0.0171413i	$-0.00545653\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−29.3810			−0.989871			−0.494935	−	0.868930i	$-0.664808\pi$
$881$	−29.3810			−0.989871			−0.494935	+	0.868930i	$0.664808\pi$
$882$		0			0
$883$	−14.1682			−0.476798			−0.238399	−	0.971167i	$-0.576623\pi$
$883$	−14.1682			−0.476798			−0.238399	+	0.971167i	$0.576623\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.3537	+	28.3254i	−0.549103	+	0.951074i	0.449234	+	0.893414i	$0.351697\pi$
$887$	−16.3537	+	28.3254i	−0.549103	+	0.951074i	−0.998336	+	0.0576593i	$0.981636\pi$
$888$		0			0
$889$	1.89187	+	15.1689i	0.0634514	+	0.508749i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−10.3564	+	5.97926i	−0.346563	+	0.200088i
$894$		0			0
$895$	25.7454	−	14.8641i	0.860575	−	0.496853i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.749293	+	1.29781i	−0.0249903	+	0.0432845i
$900$		0			0
$901$	−19.5583	+	11.2920i	−0.651580	+	0.376190i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−26.6604	−	15.3924i	−0.886222	−	0.511661i
$906$		0			0
$907$	28.3467	+	49.0980i	0.941238	+	1.63027i	0.763115	+	0.646263i	$0.223669\pi$
$907$	28.3467	+	49.0980i	0.941238	+	1.63027i	0.178123	+	0.984008i	$0.442998\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.621795	+	0.358994i	0.0206010	+	0.0118940i	0.510265	−	0.860017i	$-0.329547\pi$
$911$	0.621795	+	0.358994i	0.0206010	+	0.0118940i	−0.489664	+	0.871911i	$0.662881\pi$
$912$		0			0
$913$		−	5.55061i		−	0.183698i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−10.8627	−	4.58650i	−0.358717	−	0.151460i
$918$		0			0
$919$	−18.9720	−	32.8605i	−0.625829	−	1.08397i	−0.988380	−	0.152004i	$-0.951427\pi$
$919$	−18.9720	−	32.8605i	−0.625829	−	1.08397i	0.362550	−	0.931964i	$-0.381906\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	11.2609	+	19.5044i	0.370656	+	0.641996i
$924$		0			0
$925$	−3.18563	+	5.51768i	−0.104743	+	0.181420i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−42.8700			−1.40652			−0.703259	−	0.710934i	$-0.748273\pi$
$929$	−42.8700			−1.40652			−0.703259	+	0.710934i	$0.748273\pi$
$930$		0			0
$931$	−10.8717	+	10.5791i	−0.356307	+	0.346717i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	9.67111	+	5.58362i	0.316279	+	0.182604i
$936$		0			0
$937$			8.64637i			0.282464i	0.989976	+	0.141232i	$0.0451064\pi$
$937$			8.64637i			0.282464i	−0.989976	+	0.141232i	$0.954894\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−10.0921			−0.328991			−0.164496	−	0.986378i	$-0.552600\pi$
$941$	−10.0921			−0.328991			−0.164496	+	0.986378i	$0.552600\pi$
$942$		0			0
$943$			3.25676i			0.106055i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			58.2693i			1.89350i	0.321973	+	0.946749i	$0.395654\pi$
$947$			58.2693i			1.89350i	−0.321973	+	0.946749i	$0.604346\pi$
$948$		0			0
$949$	1.47124			0.0477584
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	46.9356i		−	1.52039i	−0.649694	−	0.760196i	$-0.725103\pi$
$953$		−	46.9356i		−	1.52039i	0.649694	−	0.760196i	$-0.274897\pi$
$954$		0			0
$955$	9.12541	+	5.26856i	0.295291	+	0.170487i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	15.4148	+	20.3751i	0.497768	+	0.657947i
$960$		0			0
$961$	12.1446			0.391761
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.02008	−	3.49889i	0.0650288	−	0.112633i
$966$		0			0
$967$	−6.43145	−	11.1396i	−0.206822	−	0.358226i	0.743890	−	0.668302i	$-0.232979\pi$
$967$	−6.43145	−	11.1396i	−0.206822	−	0.358226i	−0.950712	+	0.310077i	$0.899645\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	17.3742	+	30.0930i	0.557565	+	0.965731i	0.997699	+	0.0677990i	$0.0215977\pi$
$971$	17.3742	+	30.0930i	0.557565	+	0.965731i	−0.440134	+	0.897932i	$0.645069\pi$
$972$		0			0
$973$	29.6169	+	39.1474i	0.949474	+	1.25501i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	20.3667i		−	0.651590i	−0.945441	−	0.325795i	$-0.894368\pi$
$977$		−	20.3667i		−	0.651590i	0.945441	−	0.325795i	$-0.105632\pi$
$978$		0			0
$979$	12.0215	+	6.94060i	0.384208	+	0.221822i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−14.6682	−	25.4061i	−0.467843	−	0.810328i	0.531482	−	0.847070i	$-0.321635\pi$
$983$	−14.6682	−	25.4061i	−0.467843	−	0.810328i	−0.999325	+	0.0367416i	$0.988302\pi$
$984$		0			0
$985$	32.3048	+	18.6512i	1.02932	+	0.594276i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	40.5786	−	23.4280i	1.29032	−	0.744968i
$990$		0			0
$991$	14.8114	−	25.6540i	0.470498	−	0.814927i	−0.528933	−	0.848664i	$-0.677408\pi$
$991$	14.8114	−	25.6540i	0.470498	−	0.814927i	0.999431	+	0.0337371i	$0.0107409\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	19.0901	−	11.0217i	0.605196	−	0.349410i
$996$		0			0
$997$	23.4011	−	13.5106i	0.741120	−	0.427886i	−0.0813562	−	0.996685i	$-0.525925\pi$
$997$	23.4011	−	13.5106i	0.741120	−	0.427886i	0.822477	+	0.568799i	$0.192592\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.ca.c.2033.3		16
3.2	odd	2		1008.2.ca.c.353.3		16
4.3	odd	2		378.2.l.a.143.2		16
7.5	odd	6		3024.2.df.c.1601.3		16
9.4	even	3		1008.2.df.c.689.6		16
9.5	odd	6		3024.2.df.c.17.3		16
12.11	even	2		126.2.l.a.101.7	yes	16
21.5	even	6		1008.2.df.c.929.6		16
28.3	even	6		2646.2.m.a.1763.7		16
28.11	odd	6		2646.2.m.b.1763.6		16
28.19	even	6		378.2.t.a.89.2		16
28.23	odd	6		2646.2.t.b.1979.3		16
28.27	even	2		2646.2.l.a.521.3		16
36.7	odd	6		1134.2.k.b.647.2		16
36.11	even	6		1134.2.k.a.647.7		16
36.23	even	6		378.2.t.a.17.2		16
36.31	odd	6		126.2.t.a.59.6	yes	16
63.5	even	6	inner	3024.2.ca.c.2609.3		16
63.40	odd	6		1008.2.ca.c.257.3		16
84.11	even	6		882.2.m.b.587.1		16
84.23	even	6		882.2.t.a.803.7		16
84.47	odd	6		126.2.t.a.47.6	yes	16
84.59	odd	6		882.2.m.a.587.4		16
84.83	odd	2		882.2.l.b.227.6		16
252.23	even	6		2646.2.l.a.1097.7		16
252.31	even	6		882.2.m.b.293.1		16
252.47	odd	6		1134.2.k.b.971.2		16
252.59	odd	6		2646.2.m.b.881.6		16
252.67	odd	6		882.2.m.a.293.4		16
252.95	even	6		2646.2.m.a.881.7		16
252.103	even	6		126.2.l.a.5.3	✓	16
252.131	odd	6		378.2.l.a.341.6		16
252.139	even	6		882.2.t.a.815.7		16
252.167	odd	6		2646.2.t.b.2285.3		16
252.187	even	6		1134.2.k.a.971.7		16
252.247	odd	6		882.2.l.b.509.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.3	✓	16	252.103	even	6
126.2.l.a.101.7	yes	16	12.11	even	2
126.2.t.a.47.6	yes	16	84.47	odd	6
126.2.t.a.59.6	yes	16	36.31	odd	6
378.2.l.a.143.2		16	4.3	odd	2
378.2.l.a.341.6		16	252.131	odd	6
378.2.t.a.17.2		16	36.23	even	6
378.2.t.a.89.2		16	28.19	even	6
882.2.l.b.227.6		16	84.83	odd	2
882.2.l.b.509.2		16	252.247	odd	6
882.2.m.a.293.4		16	252.67	odd	6
882.2.m.a.587.4		16	84.59	odd	6
882.2.m.b.293.1		16	252.31	even	6
882.2.m.b.587.1		16	84.11	even	6
882.2.t.a.803.7		16	84.23	even	6
882.2.t.a.815.7		16	252.139	even	6
1008.2.ca.c.257.3		16	63.40	odd	6
1008.2.ca.c.353.3		16	3.2	odd	2
1008.2.df.c.689.6		16	9.4	even	3
1008.2.df.c.929.6		16	21.5	even	6
1134.2.k.a.647.7		16	36.11	even	6
1134.2.k.a.971.7		16	252.187	even	6
1134.2.k.b.647.2		16	36.7	odd	6
1134.2.k.b.971.2		16	252.47	odd	6
2646.2.l.a.521.3		16	28.27	even	2
2646.2.l.a.1097.7		16	252.23	even	6
2646.2.m.a.881.7		16	252.95	even	6
2646.2.m.a.1763.7		16	28.3	even	6
2646.2.m.b.881.6		16	252.59	odd	6
2646.2.m.b.1763.6		16	28.11	odd	6
2646.2.t.b.1979.3		16	28.23	odd	6
2646.2.t.b.2285.3		16	252.167	odd	6
3024.2.ca.c.2033.3		16	1.1	even	1	trivial
3024.2.ca.c.2609.3		16	63.5	even	6	inner
3024.2.df.c.17.3		16	9.5	odd	6
3024.2.df.c.1601.3		16	7.5	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.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.714925 + 1.23829i) q^{5} +(-0.327442 - 2.62541i) q^{7} +(2.96133 - 1.70972i) q^{11} +(-5.48813 + 3.16857i) q^{13} +(1.14201 - 1.97802i) q^{17} +(1.87673 - 1.08353i) q^{19} +(-6.97507 - 4.02706i) q^{23} +(1.47776 + 2.55956i) q^{25} +(0.298879 + 0.172558i) q^{29} +4.34228i q^{31} +(3.48511 + 1.47150i) q^{35} +(1.07786 + 1.86690i) q^{37} +(-0.202180 - 0.350186i) q^{41} +(-2.90883 + 5.03824i) q^{43} -5.51829 q^{47} +(-6.78556 + 1.71934i) q^{49} +(-8.56310 - 4.94391i) q^{53} +4.88930i q^{55} +11.0296 q^{59} +11.4797i q^{61} -9.06117i q^{65} -4.25366 q^{67} -3.55393i q^{71} +(-0.201057 - 0.116080i) q^{73} +(-5.45839 - 7.21486i) q^{77} -14.5620 q^{79} +(0.811624 - 1.40577i) q^{83} +(1.63290 + 2.82827i) q^{85} +(2.02974 + 3.51562i) q^{89} +(10.1159 + 13.3711i) q^{91} +3.09858i q^{95} +(-9.18719 - 5.30423i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7} + 12 q^{11} + 6 q^{13} + 18 q^{17} - 6 q^{23} - 8 q^{25} - 6 q^{29} + 30 q^{35} - 2 q^{37} + 6 q^{41} + 2 q^{43} - 36 q^{47} - 8 q^{49} + 36 q^{53} + 60 q^{59} + 28 q^{67} + 42 q^{77} - 32 q^{79}+ \cdots + 6 q^{97}+O(q^{100}) \) 16 * q - 2 * q^7 + 12 * q^11 + 6 * q^13 + 18 * q^17 - 6 * q^23 - 8 * q^25 - 6 * q^29 + 30 * q^35 - 2 * q^37 + 6 * q^41 + 2 * q^43 - 36 * q^47 - 8 * q^49 + 36 * q^53 + 60 * q^59 + 28 * q^67 + 42 * q^77 - 32 * q^79 - 12 * q^85 + 24 * q^89 + 12 * q^91 + 6 * q^97

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