LMFDB - Embedded newform 3024.2.t.h.289.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(289,3024)]

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, 4, 2]))

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

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

chi := DirichletCharacter("3024.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.t (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:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.3
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	3024.289
Dual form			3024.2.t.h.1873.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.18194 q^{5} +(-0.710533 - 2.54856i) q^{7} +O(q^{10})$	$q+3.18194 q^{5} +(-0.710533 - 2.54856i) q^{7} +3.18194 q^{11} +(2.85185 + 4.93955i) q^{13} +(0.760877 + 1.31788i) q^{17} +(0.641315 - 1.11079i) q^{19} +2.23912 q^{23} +5.12476 q^{25} +(3.54063 - 6.13255i) q^{29} +(-4.71053 + 8.15888i) q^{31} +(-2.26088 - 8.10936i) q^{35} +(0.500000 - 0.866025i) q^{37} +(2.80150 + 4.85235i) q^{41} +(-3.41423 + 5.91362i) q^{43} +(2.91423 + 5.04759i) q^{47} +(-5.99028 + 3.62167i) q^{49} +(-1.02859 - 1.78157i) q^{53} +10.1248 q^{55} +(0.562382 - 0.974074i) q^{59} +(-1.56238 - 2.70612i) q^{61} +(9.07442 + 15.7174i) q^{65} +(5.48345 - 9.49761i) q^{67} +8.69002 q^{71} +(-2.48345 - 4.30146i) q^{73} +(-2.26088 - 8.10936i) q^{77} +(-2.06922 - 3.58399i) q^{79} +(-4.03379 + 6.98673i) q^{83} +(2.42107 + 4.19341i) q^{85} +(-0.112725 + 0.195246i) q^{89} +(10.5624 - 10.7778i) q^{91} +(2.04063 - 3.53447i) q^{95} +(7.42107 - 12.8537i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{5} + 4 q^{7}+O(q^{10}) $ 6 * q + 2 * q^5 + 4 * q^7	$ 6 q + 2 q^{5} + 4 q^{7} + 2 q^{11} + 8 q^{13} + 4 q^{17} + 3 q^{19} + 14 q^{23} - 4 q^{25} + 5 q^{29} - 20 q^{31} - 13 q^{35} + 3 q^{37} + 6 q^{43} - 9 q^{47} - 12 q^{49} - 15 q^{53} + 26 q^{55} - 14 q^{59} + 8 q^{61} + 12 q^{65} - q^{67} + 14 q^{71} + 19 q^{73} - 13 q^{77} - 5 q^{79} + 2 q^{83} - 2 q^{85} + 9 q^{89} + 46 q^{91} - 4 q^{95} + 28 q^{97}+O(q^{100}) $ 6 * q + 2 * q^5 + 4 * q^7 + 2 * q^11 + 8 * q^13 + 4 * q^17 + 3 * q^19 + 14 * q^23 - 4 * q^25 + 5 * q^29 - 20 * q^31 - 13 * q^35 + 3 * q^37 + 6 * q^43 - 9 * q^47 - 12 * q^49 - 15 * q^53 + 26 * q^55 - 14 * q^59 + 8 * q^61 + 12 * q^65 - q^67 + 14 * q^71 + 19 * q^73 - 13 * q^77 - 5 * q^79 + 2 * q^83 - 2 * q^85 + 9 * q^89 + 46 * q^91 - 4 * q^95 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	3.18194			1.42301			0.711504	−	0.702682i	$-0.248014\pi$
$5$	3.18194			1.42301			0.711504	+	0.702682i	$0.248014\pi$
$6$		0			0
$7$	−0.710533	−	2.54856i	−0.268556	−	0.963264i
$7$	−0.710533	−	2.54856i	−0.268556	−	0.963264i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.18194			0.959392			0.479696	−	0.877435i	$-0.340747\pi$
$11$	3.18194			0.959392			0.479696	+	0.877435i	$0.340747\pi$
$12$		0			0
$13$	2.85185	+	4.93955i	0.790960	+	1.36998i	0.925373	+	0.379058i	$0.123752\pi$
$13$	2.85185	+	4.93955i	0.790960	+	1.36998i	−0.134412	+	0.990925i	$0.542915\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.760877	+	1.31788i	0.184540	+	0.319632i	0.943421	−	0.331596i	$-0.107587\pi$
$17$	0.760877	+	1.31788i	0.184540	+	0.319632i	−0.758882	+	0.651229i	$0.774254\pi$
$18$		0			0
$19$	0.641315	−	1.11079i	0.147128	−	0.254833i	−0.783037	−	0.621975i	$-0.786330\pi$
$19$	0.641315	−	1.11079i	0.147128	−	0.254833i	0.930165	+	0.367142i	$0.119664\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.23912			0.466889			0.233445	−	0.972370i	$-0.425000\pi$
$23$	2.23912			0.466889			0.233445	+	0.972370i	$0.425000\pi$
$24$		0			0
$25$	5.12476			1.02495
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.54063	−	6.13255i	0.657478	−	1.13879i	−0.323788	−	0.946130i	$-0.604957\pi$
$29$	3.54063	−	6.13255i	0.657478	−	1.13879i	0.981266	−	0.192656i	$-0.0617101\pi$
$30$		0			0
$31$	−4.71053	+	8.15888i	−0.846037	+	1.46538i	0.0386810	+	0.999252i	$0.487684\pi$
$31$	−4.71053	+	8.15888i	−0.846037	+	1.46538i	−0.884718	+	0.466127i	$0.845649\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.26088	−	8.10936i	−0.382158	−	1.37073i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.80150	+	4.85235i	0.437522	+	0.757810i	0.997498	−	0.0706992i	$-0.0225230\pi$
$41$	2.80150	+	4.85235i	0.437522	+	0.757810i	−0.559976	+	0.828509i	$0.689190\pi$
$42$		0			0
$43$	−3.41423	+	5.91362i	−0.520665	+	0.901819i	0.479046	+	0.877790i	$0.340983\pi$
$43$	−3.41423	+	5.91362i	−0.520665	+	0.901819i	−0.999711	+	0.0240288i	$0.992351\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.91423	+	5.04759i	0.425084	+	0.736267i	0.996428	−	0.0844432i	$-0.0269112\pi$
$47$	2.91423	+	5.04759i	0.425084	+	0.736267i	−0.571344	+	0.820711i	$0.693578\pi$
$48$		0			0
$49$	−5.99028	+	3.62167i	−0.855755	+	0.517381i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.02859	−	1.78157i	−0.141288	−	0.244717i	0.786694	−	0.617343i	$-0.211791\pi$
$53$	−1.02859	−	1.78157i	−0.141288	−	0.244717i	−0.927982	+	0.372626i	$0.878458\pi$
$54$		0			0
$55$	10.1248			1.36522
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.562382	−	0.974074i	0.0732159	−	0.126814i	−0.827093	−	0.562065i	$-0.810007\pi$
$59$	0.562382	−	0.974074i	0.0732159	−	0.126814i	0.900309	+	0.435251i	$0.143340\pi$
$60$		0			0
$61$	−1.56238	−	2.70612i	−0.200042	−	0.346484i	0.748499	−	0.663135i	$-0.230775\pi$
$61$	−1.56238	−	2.70612i	−0.200042	−	0.346484i	−0.948542	+	0.316652i	$0.897441\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.07442	+	15.7174i	1.12554	+	1.94950i
$66$		0			0
$67$	5.48345	−	9.49761i	0.669910	−	1.16032i	−0.308019	−	0.951380i	$-0.599666\pi$
$67$	5.48345	−	9.49761i	0.669910	−	1.16032i	0.977929	−	0.208938i	$-0.0670006\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.69002			1.03132			0.515658	−	0.856794i	$-0.327548\pi$
$71$	8.69002			1.03132			0.515658	+	0.856794i	$0.327548\pi$
$72$		0			0
$73$	−2.48345	−	4.30146i	−0.290666	−	0.503448i	0.683302	−	0.730136i	$-0.260543\pi$
$73$	−2.48345	−	4.30146i	−0.290666	−	0.503448i	−0.973967	+	0.226689i	$0.927210\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.26088	−	8.10936i	−0.257651	−	0.924148i
$78$		0			0
$79$	−2.06922	−	3.58399i	−0.232805	−	0.403231i	0.725827	−	0.687877i	$-0.241457\pi$
$79$	−2.06922	−	3.58399i	−0.232805	−	0.403231i	−0.958633	+	0.284646i	$0.908124\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.03379	+	6.98673i	−0.442766	+	0.766893i	−0.997894	−	0.0648718i	$-0.979336\pi$
$83$	−4.03379	+	6.98673i	−0.442766	+	0.766893i	0.555127	+	0.831765i	$0.312669\pi$
$84$		0			0
$85$	2.42107	+	4.19341i	0.262602	+	0.454839i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.112725	+	0.195246i	−0.0119488	+	0.0206960i	−0.871938	−	0.489616i	$-0.837137\pi$
$89$	−0.112725	+	0.195246i	−0.0119488	+	0.0206960i	0.859989	+	0.510312i	$0.170470\pi$
$90$		0			0
$91$	10.5624	−	10.7778i	1.10724	−	1.12982i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.04063	−	3.53447i	0.209364	−	0.362629i
$96$		0			0
$97$	7.42107	−	12.8537i	0.753495	−	1.30509i	−0.192624	−	0.981273i	$-0.561700\pi$
$97$	7.42107	−	12.8537i	0.753495	−	1.30509i	0.946119	−	0.323819i	$-0.104967\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−18.5893			−1.84971			−0.924854	−	0.380322i	$-0.875813\pi$
$101$	−18.5893			−1.84971			−0.924854	+	0.380322i	$0.875813\pi$
$102$		0			0
$103$	0.282630			0.0278484			0.0139242	−	0.999903i	$-0.495568\pi$
$103$	0.282630			0.0278484			0.0139242	+	0.999903i	$0.495568\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.68878	−	9.85326i	0.549955	−	0.952550i	−0.448322	−	0.893872i	$-0.647978\pi$
$107$	5.68878	−	9.85326i	0.549955	−	0.952550i	0.998277	−	0.0586780i	$-0.0186885\pi$
$108$		0			0
$109$	−2.21053	−	3.82876i	−0.211731	−	0.366728i	0.740526	−	0.672028i	$-0.234577\pi$
$109$	−2.21053	−	3.82876i	−0.211731	−	0.366728i	−0.952256	+	0.305300i	$0.901243\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.60752	+	2.78431i	0.151223	+	0.261926i	0.931677	−	0.363287i	$-0.118345\pi$
$113$	1.60752	+	2.78431i	0.151223	+	0.261926i	−0.780454	+	0.625213i	$0.785012\pi$
$114$		0			0
$115$	7.12476			0.664388
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.81806	−	2.87553i	0.258331	−	0.263600i
$120$		0			0
$121$	−0.875237			−0.0795670
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.396990			0.0355079
$126$		0			0
$127$	−20.1053			−1.78406			−0.892030	−	0.451976i	$-0.850719\pi$
$127$	−20.1053			−1.78406			−0.892030	+	0.451976i	$0.850719\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.36389			0.556015			0.278008	−	0.960579i	$-0.410326\pi$
$131$	6.36389			0.556015			0.278008	+	0.960579i	$0.410326\pi$
$132$		0			0
$133$	−3.28659	−	0.845174i	−0.284983	−	0.0732859i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.74145			−0.234218			−0.117109	−	0.993119i	$-0.537363\pi$
$137$	−2.74145			−0.234218			−0.117109	+	0.993119i	$0.537363\pi$
$138$		0			0
$139$	3.98345	+	6.89953i	0.337872	+	0.585211i	0.984032	−	0.177991i	$-0.0569597\pi$
$139$	3.98345	+	6.89953i	0.337872	+	0.585211i	−0.646161	+	0.763202i	$0.723626\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.07442	+	15.7174i	0.758841	+	1.31435i
$144$		0			0
$145$	11.2661	−	19.5134i	0.935597	−	1.62050i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	23.2599			1.90553			0.952764	−	0.303712i	$-0.0982261\pi$
$149$	23.2599			1.90553			0.952764	+	0.303712i	$0.0982261\pi$
$150$		0			0
$151$	8.12476			0.661184			0.330592	−	0.943774i	$-0.392752\pi$
$151$	8.12476			0.661184			0.330592	+	0.943774i	$0.392752\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−14.9887	+	25.9611i	−1.20392	+	2.08525i
$156$		0			0
$157$	5.63160	−	9.75422i	0.449451	−	0.778471i	−0.548900	−	0.835888i	$-0.684953\pi$
$157$	5.63160	−	9.75422i	0.449451	−	0.778471i	0.998350	+	0.0574170i	$0.0182864\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.59097	−	5.70653i	−0.125386	−	0.449738i
$162$		0			0
$163$	1.99028	−	3.44727i	0.155891	−	0.270011i	−0.777492	−	0.628893i	$-0.783508\pi$
$163$	1.99028	−	3.44727i	0.155891	−	0.270011i	0.933383	+	0.358881i	$0.116842\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.61956	+	4.53721i	0.202708	+	0.351100i	0.949400	−	0.314070i	$-0.101693\pi$
$167$	2.61956	+	4.53721i	0.202708	+	0.351100i	−0.746692	+	0.665170i	$0.768359\pi$
$168$		0			0
$169$	−9.76608	+	16.9153i	−0.751237	+	1.30118i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.27579	+	2.20974i	0.0969968	+	0.168003i	0.910440	−	0.413641i	$-0.135743\pi$
$173$	1.27579	+	2.20974i	0.0969968	+	0.168003i	−0.813443	+	0.581644i	$0.802410\pi$
$174$		0			0
$175$	−3.64132	−	13.0608i	−0.275258	−	0.987300i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.51887	+	6.09487i	0.263013	+	0.455552i	0.967041	−	0.254620i	$-0.0819504\pi$
$179$	3.51887	+	6.09487i	0.263013	+	0.455552i	−0.704028	+	0.710172i	$0.748617\pi$
$180$		0			0
$181$	−12.9669			−0.963822			−0.481911	−	0.876220i	$-0.660057\pi$
$181$	−12.9669			−0.963822			−0.481911	+	0.876220i	$0.660057\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.59097	−	2.75564i	0.116971	−	0.202599i
$186$		0			0
$187$	2.42107	+	4.19341i	0.177046	+	0.306653i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.990285	−	1.71522i	−0.0716545	−	0.124109i	0.827972	−	0.560769i	$-0.189495\pi$
$191$	−0.990285	−	1.71522i	−0.0716545	−	0.124109i	−0.899627	+	0.436660i	$0.856161\pi$
$192$		0			0
$193$	2.27292	−	3.93680i	0.163608	−	0.283377i	−0.772552	−	0.634951i	$-0.781020\pi$
$193$	2.27292	−	3.93680i	0.163608	−	0.283377i	0.936160	+	0.351574i	$0.114353\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	21.8148			1.55424			0.777120	−	0.629353i	$-0.216680\pi$
$197$	21.8148			1.55424			0.777120	+	0.629353i	$0.216680\pi$
$198$		0			0
$199$	−6.14132	−	10.6371i	−0.435346	−	0.754042i	0.561978	−	0.827152i	$-0.310041\pi$
$199$	−6.14132	−	10.6371i	−0.435346	−	0.754042i	−0.997324	+	0.0731106i	$0.976707\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−18.1449	−	4.66611i	−1.27352	−	0.327497i
$204$		0			0
$205$	8.91423	+	15.4399i	0.622597	+	1.07837i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.04063	−	3.53447i	0.141153	−	0.244485i
$210$		0			0
$211$	8.32846	+	14.4253i	0.573355	+	0.993080i	0.996218	+	0.0868863i	$0.0276917\pi$
$211$	8.32846	+	14.4253i	0.573355	+	0.993080i	−0.422863	+	0.906193i	$0.638975\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−10.8639	+	18.8168i	−0.740911	+	1.28330i
$216$		0			0
$217$	24.1404	+	6.20790i	1.63876	+	0.421420i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.33981	+	7.51677i	−0.291927	+	0.505633i
$222$		0			0
$223$	5.32846	−	9.22916i	0.356820	−	0.618031i	−0.630608	−	0.776102i	$-0.717194\pi$
$223$	5.32846	−	9.22916i	0.356820	−	0.618031i	0.987428	+	0.158071i	$0.0505276\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−14.5081			−0.962935			−0.481468	−	0.876464i	$-0.659896\pi$
$227$	−14.5081			−0.962935			−0.481468	+	0.876464i	$0.659896\pi$
$228$		0			0
$229$	10.2495			0.677308			0.338654	−	0.940911i	$-0.390028\pi$
$229$	10.2495			0.677308			0.338654	+	0.940911i	$0.390028\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.540628	+	0.936396i	−0.0354177	+	0.0613453i	−0.883191	−	0.469014i	$-0.844610\pi$
$233$	−0.540628	+	0.936396i	−0.0354177	+	0.0613453i	0.847773	+	0.530359i	$0.177943\pi$
$234$		0			0
$235$	9.27292	+	16.0612i	0.604898	+	1.04771i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.16019	−	10.6698i	−0.398470	−	0.690170i	0.595068	−	0.803676i	$-0.297125\pi$
$239$	−6.16019	−	10.6698i	−0.398470	−	0.690170i	−0.993537	+	0.113506i	$0.963792\pi$
$240$		0			0
$241$	−13.0000			−0.837404			−0.418702	−	0.908124i	$-0.637515\pi$
$241$	−13.0000			−0.837404			−0.418702	+	0.908124i	$0.637515\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−19.0607	+	11.5239i	−1.21775	+	0.736238i
$246$		0			0
$247$	7.31573			0.465489
$248$		0			0
$249$		0			0
$250$		0			0
$251$	5.11109			0.322609			0.161305	−	0.986905i	$-0.448430\pi$
$251$	5.11109			0.322609			0.161305	+	0.986905i	$0.448430\pi$
$252$		0			0
$253$	7.12476			0.447930
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.66019			−0.477830			−0.238915	−	0.971041i	$-0.576792\pi$
$257$	−7.66019			−0.477830			−0.238915	+	0.971041i	$0.576792\pi$
$258$		0			0
$259$	−2.56238	−	0.658939i	−0.159219	−	0.0409445i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.09493			−0.190842			−0.0954208	−	0.995437i	$-0.530420\pi$
$263$	−3.09493			−0.190842			−0.0954208	+	0.995437i	$0.530420\pi$
$264$		0			0
$265$	−3.27292	−	5.66886i	−0.201054	−	0.348235i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	13.4451	+	23.2877i	0.819765	+	1.41987i	0.905855	+	0.423587i	$0.139229\pi$
$269$	13.4451	+	23.2877i	0.819765	+	1.41987i	−0.0860906	+	0.996287i	$0.527437\pi$
$270$		0			0
$271$	11.1082	−	19.2400i	0.674776	−	1.16875i	−0.301759	−	0.953384i	$-0.597574\pi$
$271$	11.1082	−	19.2400i	0.674776	−	1.16875i	0.976534	−	0.215362i	$-0.0690930\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	16.3067			0.983331
$276$		0			0
$277$	−14.6375			−0.879482			−0.439741	−	0.898125i	$-0.644930\pi$
$277$	−14.6375			−0.879482			−0.439741	+	0.898125i	$0.644930\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−11.6992	+	20.2636i	−0.697915	+	1.20882i	0.271273	+	0.962502i	$0.412555\pi$
$281$	−11.6992	+	20.2636i	−0.697915	+	1.20882i	−0.969188	+	0.246322i	$0.920778\pi$
$282$		0			0
$283$	−13.0624	+	22.6247i	−0.776478	+	1.34490i	0.157482	+	0.987522i	$0.449662\pi$
$283$	−13.0624	+	22.6247i	−0.776478	+	1.34490i	−0.933960	+	0.357377i	$0.883671\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	10.3759	−	10.5876i	0.612471	−	0.624963i
$288$		0			0
$289$	7.34213	−	12.7169i	0.431890	−	0.748056i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−12.9315	−	22.3980i	−0.755465	−	1.30850i	−0.945143	−	0.326657i	$-0.894078\pi$
$293$	−12.9315	−	22.3980i	−0.755465	−	1.30850i	0.189678	−	0.981846i	$-0.439255\pi$
$294$		0			0
$295$	1.78947	−	3.09945i	0.104187	−	0.180457i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.38564	+	11.0603i	0.369291	+	0.639631i
$300$		0			0
$301$	17.4971	+	4.49954i	1.00852	+	0.259349i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.97141	−	8.61073i	−0.284662	−	0.493049i
$306$		0			0
$307$	−3.53216			−0.201591			−0.100795	−	0.994907i	$-0.532139\pi$
$307$	−3.53216			−0.201591			−0.100795	+	0.994907i	$0.532139\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.851848	+	1.47544i	−0.0483039	+	0.0836648i	−0.889166	−	0.457584i	$-0.848715\pi$
$311$	−0.851848	+	1.47544i	−0.0483039	+	0.0836648i	0.840863	+	0.541249i	$0.182048\pi$
$312$		0			0
$313$	1.42107	+	2.46136i	0.0803234	+	0.139124i	0.903389	−	0.428822i	$-0.141071\pi$
$313$	1.42107	+	2.46136i	0.0803234	+	0.139124i	−0.823065	+	0.567947i	$0.807738\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−12.4601	−	21.5815i	−0.699827	−	1.21214i	−0.968526	−	0.248911i	$-0.919927\pi$
$317$	−12.4601	−	21.5815i	−0.699827	−	1.21214i	0.268700	−	0.963224i	$-0.413406\pi$
$318$		0			0
$319$	11.2661	−	19.5134i	0.630779	−	1.09254i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.95185			0.108604
$324$		0			0
$325$	14.6150	+	25.3140i	0.810697	+	1.40417i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	10.7934	−	11.0136i	0.595061	−	0.607198i
$330$		0			0
$331$	−3.58577	−	6.21074i	−0.197092	−	0.341373i	0.750492	−	0.660879i	$-0.229816\pi$
$331$	−3.58577	−	6.21074i	−0.197092	−	0.341373i	−0.947584	+	0.319506i	$0.896483\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	17.4480	−	30.2209i	0.953287	−	1.65114i
$336$		0			0
$337$	−10.9211	−	18.9158i	−0.594908	−	1.03041i	−0.993560	−	0.113309i	$-0.963855\pi$
$337$	−10.9211	−	18.9158i	−0.594908	−	1.03041i	0.398651	−	0.917103i	$-0.369478\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−14.9887	+	25.9611i	−0.811681	+	1.40587i
$342$		0			0
$343$	13.4863	+	12.6933i	0.728193	+	0.685372i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.05555	−	1.82826i	0.0566646	−	0.0981460i	−0.836302	−	0.548270i	$-0.815287\pi$
$347$	1.05555	−	1.82826i	0.0566646	−	0.0981460i	0.892966	+	0.450124i	$0.148620\pi$
$348$		0			0
$349$	18.1082	−	31.3643i	0.969310	−	1.67889i	0.271751	−	0.962368i	$-0.412397\pi$
$349$	18.1082	−	31.3643i	0.969310	−	1.67889i	0.697559	−	0.716527i	$-0.254269\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	10.4887			0.558255			0.279127	−	0.960254i	$-0.409955\pi$
$353$	10.4887			0.558255			0.279127	+	0.960254i	$0.409955\pi$
$354$		0			0
$355$	27.6512			1.46757
$356$		0			0
$357$		0			0
$358$		0			0
$359$	16.2209	−	28.0955i	0.856108	−	1.48282i	−0.0195047	−	0.999810i	$-0.506209\pi$
$359$	16.2209	−	28.0955i	0.856108	−	1.48282i	0.875613	−	0.483013i	$-0.160458\pi$
$360$		0			0
$361$	8.67743	+	15.0297i	0.456707	+	0.791039i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−7.90219	−	13.6870i	−0.413620	−	0.716410i
$366$		0			0
$367$	18.1111			0.945391			0.472696	−	0.881226i	$-0.343281\pi$
$367$	18.1111			0.945391			0.472696	+	0.881226i	$0.343281\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.80959	+	3.88728i	−0.197784	+	0.201818i
$372$		0			0
$373$	−11.6706			−0.604280			−0.302140	−	0.953263i	$-0.597701\pi$
$373$	−11.6706			−0.604280			−0.302140	+	0.953263i	$0.597701\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	40.3893			2.08016
$378$		0			0
$379$	−14.2690			−0.732947			−0.366474	−	0.930428i	$-0.619435\pi$
$379$	−14.2690			−0.732947			−0.366474	+	0.930428i	$0.619435\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.64979			−0.0843001			−0.0421501	−	0.999111i	$-0.513421\pi$
$383$	−1.64979			−0.0843001			−0.0421501	+	0.999111i	$0.513421\pi$
$384$		0			0
$385$	−7.19398	−	25.8035i	−0.366639	−	1.31507i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	32.0676			1.62589			0.812946	−	0.582340i	$-0.197863\pi$
$389$	32.0676			1.62589			0.812946	+	0.582340i	$0.197863\pi$
$390$		0			0
$391$	1.70370	+	2.95089i	0.0861596	+	0.149233i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−6.58414	−	11.4041i	−0.331284	−	0.573800i
$396$		0			0
$397$	−18.9669	+	32.8516i	−0.951921	+	1.64878i	−0.210660	+	0.977559i	$0.567561\pi$
$397$	−18.9669	+	32.8516i	−0.951921	+	1.64878i	−0.741261	+	0.671217i	$0.765772\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.6192			−0.530296			−0.265148	−	0.964208i	$-0.585421\pi$
$401$	−10.6192			−0.530296			−0.265148	+	0.964208i	$0.585421\pi$
$402$		0			0
$403$	−53.7349			−2.67673
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.59097	−	2.75564i	0.0788615	−	0.136592i
$408$		0			0
$409$	−2.77292	+	4.80283i	−0.137112	+	0.237485i	−0.926402	−	0.376535i	$-0.877115\pi$
$409$	−2.77292	+	4.80283i	−0.137112	+	0.237485i	0.789290	+	0.614020i	$0.210449\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.88207	−	0.741150i	−0.141818	−	0.0364696i
$414$		0			0
$415$	−12.8353	+	22.2314i	−0.630060	+	1.09130i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2.77455	+	4.80566i	0.135546	+	0.234772i	0.925806	−	0.378000i	$-0.123388\pi$
$419$	2.77455	+	4.80566i	0.135546	+	0.234772i	−0.790260	+	0.612772i	$0.790055\pi$
$420$		0			0
$421$	−3.42107	+	5.92546i	−0.166733	+	0.288789i	−0.937269	−	0.348606i	$-0.886655\pi$
$421$	−3.42107	+	5.92546i	−0.166733	+	0.288789i	0.770537	+	0.637396i	$0.219988\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.89931	+	6.75381i	0.189144	+	0.327608i
$426$		0			0
$427$	−5.78659	+	5.90461i	−0.280033	+	0.285744i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	16.5539	+	28.6722i	0.797374	+	1.38109i	0.921321	+	0.388803i	$0.127111\pi$
$431$	16.5539	+	28.6722i	0.797374	+	1.38109i	−0.123947	+	0.992289i	$0.539555\pi$
$432$		0			0
$433$	−12.1111			−0.582022			−0.291011	−	0.956720i	$-0.593992\pi$
$433$	−12.1111			−0.582022			−0.291011	+	0.956720i	$0.593992\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.43598	−	2.48720i	0.0686924	−	0.118979i
$438$		0			0
$439$	−4.41711	−	7.65066i	−0.210817	−	0.365146i	0.741153	−	0.671336i	$-0.234279\pi$
$439$	−4.41711	−	7.65066i	−0.210817	−	0.365146i	−0.951970	+	0.306190i	$0.900946\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8.75924	−	15.1715i	−0.416164	−	0.720817i	0.579386	−	0.815053i	$-0.303292\pi$
$443$	−8.75924	−	15.1715i	−0.416164	−	0.720817i	−0.995550	+	0.0942360i	$0.969959\pi$
$444$		0			0
$445$	−0.358685	+	0.621261i	−0.0170033	+	0.0294506i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−31.2301			−1.47384			−0.736920	−	0.675980i	$-0.763720\pi$
$449$	−31.2301			−1.47384			−0.736920	+	0.675980i	$0.763720\pi$
$450$		0			0
$451$	8.91423	+	15.4399i	0.419755	+	0.727036i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	33.6089	−	34.2944i	1.57561	−	1.60775i
$456$		0			0
$457$	16.0624	+	27.8209i	0.751367	+	1.30140i	0.947161	+	0.320760i	$0.103938\pi$
$457$	16.0624	+	27.8209i	0.751367	+	1.30140i	−0.195794	+	0.980645i	$0.562728\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.23229	+	2.13438i	−0.0573933	+	0.0994081i	−0.893295	−	0.449472i	$-0.851612\pi$
$461$	−1.23229	+	2.13438i	−0.0573933	+	0.0994081i	0.835901	+	0.548880i	$0.184946\pi$
$462$		0			0
$463$	−15.1735	−	26.2812i	−0.705171	−	1.22139i	−0.966630	−	0.256177i	$-0.917537\pi$
$463$	−15.1735	−	26.2812i	−0.705171	−	1.22139i	0.261459	−	0.965215i	$-0.415796\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.98181	+	13.8249i	−0.369354	+	0.639740i	−0.989465	−	0.144774i	$-0.953754\pi$
$467$	−7.98181	+	13.8249i	−0.369354	+	0.639740i	0.620110	+	0.784515i	$0.287088\pi$
$468$		0			0
$469$	−28.1014	−	7.22651i	−1.29760	−	0.333689i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.8639	+	18.8168i	−0.499522	+	0.865198i
$474$		0			0
$475$	3.28659	−	5.69254i	0.150799	−	0.261192i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−23.1729			−1.05880			−0.529399	−	0.848373i	$-0.677582\pi$
$479$	−23.1729			−1.05880			−0.529399	+	0.848373i	$0.677582\pi$
$480$		0			0
$481$	5.70370			0.260066
$482$		0			0
$483$		0			0
$484$		0			0
$485$	23.6134	−	40.8996i	1.07223	−	1.85716i
$486$		0			0
$487$	−1.70658	−	2.95588i	−0.0773323	−	0.133943i	0.824766	−	0.565474i	$-0.191307\pi$
$487$	−1.70658	−	2.95588i	−0.0773323	−	0.133943i	−0.902098	+	0.431531i	$0.857974\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.58414	−	16.6002i	−0.432526	−	0.749157i	0.564564	−	0.825389i	$-0.309044\pi$
$491$	−9.58414	−	16.6002i	−0.432526	−	0.749157i	−0.997090	+	0.0762323i	$0.975711\pi$
$492$		0			0
$493$	10.7759			0.485323
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.17455	−	22.1470i	−0.276966	−	0.993430i
$498$		0			0
$499$	−41.1696			−1.84301			−0.921503	−	0.388371i	$-0.873038\pi$
$499$	−41.1696			−1.84301			−0.921503	+	0.388371i	$0.873038\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−26.4542			−1.17953			−0.589767	−	0.807574i	$-0.700780\pi$
$503$	−26.4542			−1.17953			−0.589767	+	0.807574i	$0.700780\pi$
$504$		0			0
$505$	−59.1502			−2.63215
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−12.7713			−0.566077			−0.283039	−	0.959109i	$-0.591342\pi$
$509$	−12.7713			−0.566077			−0.283039	+	0.959109i	$0.591342\pi$
$510$		0			0
$511$	−9.19794	+	9.38554i	−0.406893	+	0.415192i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.899313			0.0396285
$516$		0			0
$517$	9.27292	+	16.0612i	0.407822	+	0.706369i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.40615	+	5.89962i	0.149226	+	0.258467i	0.930942	−	0.365168i	$-0.118988\pi$
$521$	3.40615	+	5.89962i	0.149226	+	0.258467i	−0.781716	+	0.623635i	$0.785655\pi$
$522$		0			0
$523$	−14.7535	+	25.5538i	−0.645125	+	1.11739i	0.339148	+	0.940733i	$0.389861\pi$
$523$	−14.7535	+	25.5538i	−0.645125	+	1.11739i	−0.984273	+	0.176656i	$0.943472\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−14.3365			−0.624510
$528$		0			0
$529$	−17.9863			−0.782014
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−15.9789	+	27.6763i	−0.692125	+	1.19879i
$534$		0			0
$535$	18.1014	−	31.3525i	0.782591	−	1.35549i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−19.0607	+	11.5239i	−0.821004	+	0.496371i
$540$		0			0
$541$	14.7008	−	25.4626i	0.632038	−	1.09472i	−0.355097	−	0.934829i	$-0.615552\pi$
$541$	14.7008	−	25.4626i	0.632038	−	1.09472i	0.987135	−	0.159892i	$-0.0511145\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.03379	−	12.1829i	−0.301295	−	0.521857i
$546$		0			0
$547$	−17.6150	+	30.5102i	−0.753165	+	1.30452i	0.193116	+	0.981176i	$0.438141\pi$
$547$	−17.6150	+	30.5102i	−0.753165	+	1.30452i	−0.946281	+	0.323344i	$0.895193\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−4.54132	−	7.86579i	−0.193467	−	0.335094i
$552$		0			0
$553$	−7.66376	+	7.82007i	−0.325896	+	0.332543i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.36909	+	5.83543i	0.142753	+	0.247255i	0.928532	−	0.371252i	$-0.121071\pi$
$557$	3.36909	+	5.83543i	0.142753	+	0.247255i	−0.785779	+	0.618507i	$0.787738\pi$
$558$		0			0
$559$	−38.9475			−1.64730
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.729964	−	1.26433i	0.0307643	−	0.0532853i	−0.850233	−	0.526406i	$-0.823539\pi$
$563$	0.729964	−	1.26433i	0.0307643	−	0.0532853i	0.880998	+	0.473121i	$0.156873\pi$
$564$		0			0
$565$	5.11505	+	8.85952i	0.215192	+	0.372723i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.78263	+	16.9440i	0.410109	+	0.710330i	0.994901	−	0.100853i	$-0.0321573\pi$
$569$	9.78263	+	16.9440i	0.410109	+	0.710330i	−0.584792	+	0.811183i	$0.698824\pi$
$570$		0			0
$571$	−10.9629	+	18.9884i	−0.458785	+	0.794638i	−0.998897	−	0.0469545i	$-0.985048\pi$
$571$	−10.9629	+	18.9884i	−0.458785	+	0.794638i	0.540112	+	0.841593i	$0.318382\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	11.4750			0.478540
$576$		0			0
$577$	12.3655	+	21.4177i	0.514783	+	0.891631i	0.999853	+	0.0171554i	$0.00546099\pi$
$577$	12.3655	+	21.4177i	0.514783	+	0.891631i	−0.485069	+	0.874476i	$0.661206\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	20.6722	+	5.31604i	0.857629	+	0.220547i
$582$		0			0
$583$	−3.27292	−	5.66886i	−0.135550	−	0.234780i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−18.0796	+	31.3148i	−0.746226	+	1.29250i	0.203394	+	0.979097i	$0.434803\pi$
$587$	−18.0796	+	31.3148i	−0.746226	+	1.29250i	−0.949620	+	0.313404i	$0.898531\pi$
$588$		0			0
$589$	6.04187	+	10.4648i	0.248951	+	0.431196i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.55391	−	13.0838i	0.310202	−	0.537285i	−0.668204	−	0.743978i	$-0.732937\pi$
$593$	7.55391	−	13.0838i	0.310202	−	0.537285i	0.978406	+	0.206693i	$0.0662700\pi$
$594$		0			0
$595$	8.96690	−	9.14978i	0.367607	−	0.375105i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.72708	−	4.72345i	0.111426	−	0.192995i	−0.804920	−	0.593384i	$-0.797792\pi$
$599$	2.72708	−	4.72345i	0.111426	−	0.192995i	0.916345	+	0.400389i	$0.131125\pi$
$600$		0			0
$601$	−3.36840	+	5.83424i	−0.137400	+	0.237984i	−0.926512	−	0.376266i	$-0.877208\pi$
$601$	−3.36840	+	5.83424i	−0.137400	+	0.237984i	0.789112	+	0.614250i	$0.210541\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.78495			−0.113224
$606$		0			0
$607$	−6.67059			−0.270751			−0.135376	−	0.990794i	$-0.543224\pi$
$607$	−6.67059			−0.270751			−0.135376	+	0.990794i	$0.543224\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−16.6219	+	28.7899i	−0.672449	+	1.16472i
$612$		0			0
$613$	0.654988	+	1.13447i	0.0264547	+	0.0458209i	0.878950	−	0.476915i	$-0.158245\pi$
$613$	0.654988	+	1.13447i	0.0264547	+	0.0458209i	−0.852495	+	0.522735i	$0.824912\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−17.2483	−	29.8749i	−0.694390	−	1.20272i	−0.970386	−	0.241560i	$-0.922341\pi$
$617$	−17.2483	−	29.8749i	−0.694390	−	1.20272i	0.275996	−	0.961159i	$-0.410992\pi$
$618$		0			0
$619$	16.4484			0.661118			0.330559	−	0.943785i	$-0.392763\pi$
$619$	16.4484			0.661118			0.330559	+	0.943785i	$0.392763\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.577690	+	0.148558i	0.0231446	+	0.00595184i
$624$		0			0
$625$	−24.3606			−0.974425
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.52175			0.0606763
$630$		0			0
$631$	30.0118			1.19475			0.597375	−	0.801962i	$-0.296210\pi$
$631$	30.0118			1.19475			0.597375	+	0.801962i	$0.296210\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−63.9740			−2.53873
$636$		0			0
$637$	−34.9728	−	19.2608i	−1.38567	−	0.763142i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−27.8993			−1.10196			−0.550978	−	0.834520i	$-0.685745\pi$
$641$	−27.8993			−1.10196			−0.550978	+	0.834520i	$0.685745\pi$
$642$		0			0
$643$	−14.2524	−	24.6859i	−0.562060	−	0.973516i	−0.997317	−	0.0732100i	$-0.976676\pi$
$643$	−14.2524	−	24.6859i	−0.562060	−	0.973516i	0.435257	−	0.900306i	$-0.356658\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.35705	+	14.4748i	0.328550	+	0.569065i	0.982224	−	0.187711i	$-0.0601069\pi$
$647$	8.35705	+	14.4748i	0.328550	+	0.569065i	−0.653675	+	0.756776i	$0.726774\pi$
$648$		0			0
$649$	1.78947	−	3.09945i	0.0702427	−	0.121664i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−38.1650			−1.49351			−0.746756	−	0.665098i	$-0.768390\pi$
$653$	−38.1650			−1.49351			−0.746756	+	0.665098i	$0.768390\pi$
$654$		0			0
$655$	20.2495			0.791214
$656$		0			0
$657$		0			0
$658$		0			0
$659$	4.37072	−	7.57031i	0.170259	−	0.294898i	−0.768251	−	0.640148i	$-0.778873\pi$
$659$	4.37072	−	7.57031i	0.170259	−	0.294898i	0.938510	+	0.345251i	$0.112206\pi$
$660$		0			0
$661$	10.0419	−	17.3930i	0.390584	−	0.676511i	−0.601943	−	0.798539i	$-0.705607\pi$
$661$	10.0419	−	17.3930i	0.390584	−	0.676511i	0.992527	+	0.122028i	$0.0389399\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−10.4577	−	2.68930i	−0.405534	−	0.104286i
$666$		0			0
$667$	7.92790	−	13.7315i	0.306970	−	0.531687i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.97141	−	8.61073i	−0.191919	−	0.332414i
$672$		0			0
$673$	−17.0264	+	29.4906i	−0.656319	+	1.13678i	0.325242	+	0.945631i	$0.394554\pi$
$673$	−17.0264	+	29.4906i	−0.656319	+	1.13678i	−0.981561	+	0.191148i	$0.938779\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−0.358685	−	0.621261i	−0.0137854	−	0.0238770i	0.859050	−	0.511891i	$-0.171055\pi$
$677$	−0.358685	−	0.621261i	−0.0137854	−	0.0238770i	−0.872836	+	0.488014i	$0.837721\pi$
$678$		0			0
$679$	−38.0312	−	9.78005i	−1.45950	−	0.375324i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−10.5270	−	18.2332i	−0.402803	−	0.697675i	0.591260	−	0.806481i	$-0.298631\pi$
$683$	−10.5270	−	18.2332i	−0.402803	−	0.697675i	−0.994063	+	0.108806i	$0.965297\pi$
$684$		0			0
$685$	−8.72313			−0.333294
$686$		0			0
$687$		0			0
$688$		0			0
$689$	5.86677	−	10.1615i	0.223506	−	0.387124i
$690$		0			0
$691$	2.92395	+	5.06442i	0.111232	+	0.192660i	0.916267	−	0.400567i	$-0.131187\pi$
$691$	2.92395	+	5.06442i	0.111232	+	0.192660i	−0.805035	+	0.593227i	$0.797854\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.6751	+	21.9539i	0.480794	+	0.832760i
$696$		0			0
$697$	−4.26320	+	7.38408i	−0.161480	+	0.279692i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−10.2711			−0.387935			−0.193967	−	0.981008i	$-0.562136\pi$
$701$	−10.2711			−0.387935			−0.193967	+	0.981008i	$0.562136\pi$
$702$		0			0
$703$	−0.641315	−	1.11079i	−0.0241877	−	0.0418942i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	13.2083	+	47.3760i	0.496751	+	1.78176i
$708$		0			0
$709$	−21.7427	−	37.6594i	−0.816564	−	1.41433i	−0.908200	−	0.418538i	$-0.862543\pi$
$709$	−21.7427	−	37.6594i	−0.816564	−	1.41433i	0.0916356	−	0.995793i	$-0.470790\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−10.5475	+	18.2687i	−0.395006	+	0.684170i
$714$		0			0
$715$	28.8743	+	50.0117i	1.07984	+	1.87033i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	25.4412	−	44.0654i	0.948796	−	1.64336i	0.200830	−	0.979626i	$-0.435636\pi$
$719$	25.4412	−	44.0654i	0.948796	−	1.64336i	0.747966	−	0.663737i	$-0.231031\pi$
$720$		0			0
$721$	−0.200818	−	0.720299i	−0.00747886	−	0.0268253i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	18.1449	−	31.4279i	0.673884	−	1.16720i
$726$		0			0
$727$	−6.07210	+	10.5172i	−0.225202	+	0.390061i	−0.956380	−	0.292126i	$-0.905637\pi$
$727$	−6.07210	+	10.5172i	−0.225202	+	0.390061i	0.731178	+	0.682186i	$0.238971\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−10.3912			−0.384334
$732$		0			0
$733$	−46.1696			−1.70531			−0.852657	−	0.522470i	$-0.825011\pi$
$733$	−46.1696			−1.70531			−0.852657	+	0.522470i	$0.825011\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	17.4480	−	30.2209i	0.642706	−	1.11320i
$738$		0			0
$739$	2.49604	+	4.32327i	0.0918184	+	0.159034i	0.908276	−	0.418371i	$-0.137399\pi$
$739$	2.49604	+	4.32327i	0.0918184	+	0.159034i	−0.816458	+	0.577405i	$0.804065\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−15.7060	−	27.2036i	−0.576198	−	0.998004i	−0.995910	−	0.0903470i	$-0.971202\pi$
$743$	−15.7060	−	27.2036i	−0.576198	−	0.998004i	0.419712	−	0.907657i	$-0.362131\pi$
$744$		0			0
$745$	74.0118			2.71158
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−29.1537	−	7.49711i	−1.06525	−	0.273939i
$750$		0			0
$751$	−3.29630			−0.120284			−0.0601419	−	0.998190i	$-0.519155\pi$
$751$	−3.29630			−0.120284			−0.0601419	+	0.998190i	$0.519155\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	25.8525			0.940870
$756$		0			0
$757$	−10.1384			−0.368488			−0.184244	−	0.982881i	$-0.558984\pi$
$757$	−10.1384			−0.368488			−0.184244	+	0.982881i	$0.558984\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−14.0676			−0.509950			−0.254975	−	0.966948i	$-0.582067\pi$
$761$	−14.0676			−0.509950			−0.254975	+	0.966948i	$0.582067\pi$
$762$		0			0
$763$	−8.18715	+	8.35413i	−0.296395	+	0.302440i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.41531			0.231643
$768$		0			0
$769$	11.3461	+	19.6520i	0.409151	+	0.708669i	0.994795	−	0.101899i	$-0.0324918\pi$
$769$	11.3461	+	19.6520i	0.409151	+	0.708669i	−0.585644	+	0.810568i	$0.699158\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−0.327772	−	0.567717i	−0.0117891	−	0.0204194i	0.860071	−	0.510175i	$-0.170419\pi$
$773$	−0.327772	−	0.567717i	−0.0117891	−	0.0204194i	−0.871860	+	0.489756i	$0.837086\pi$
$774$		0			0
$775$	−24.1404	+	41.8123i	−0.867148	+	1.50194i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	7.18659			0.257486
$780$		0			0
$781$	27.6512			0.989436
$782$		0			0
$783$		0			0
$784$		0			0
$785$	17.9194	−	31.0374i	0.639572	−	1.10777i
$786$		0			0
$787$	0.270036	−	0.467717i	0.00962576	−	0.0166723i	−0.861172	−	0.508313i	$-0.830269\pi$
$787$	0.270036	−	0.467717i	0.00962576	−	0.0166723i	0.870798	+	0.491641i	$0.163603\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	5.95378	−	6.07521i	0.211692	−	0.216010i
$792$		0			0
$793$	8.91135	−	15.4349i	0.316451	−	0.548110i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	12.5550	+	21.7459i	0.444721	+	0.770279i	0.998033	−	0.0626954i	$-0.0199697\pi$
$797$	12.5550	+	21.7459i	0.444721	+	0.770279i	−0.553312	+	0.832974i	$0.686636\pi$
$798$		0			0
$799$	−4.43474	+	7.68119i	−0.156890	+	0.271741i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.90219	−	13.6870i	−0.278862	−	0.483004i
$804$		0			0
$805$	−5.06238	−	18.1579i	−0.178426	−	0.639981i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	14.5865	+	25.2645i	0.512833	+	0.888252i	0.999889	+	0.0148817i	$0.00473717\pi$
$809$	14.5865	+	25.2645i	0.512833	+	0.888252i	−0.487057	+	0.873370i	$0.661929\pi$
$810$		0			0
$811$	15.4290			0.541785			0.270892	−	0.962610i	$-0.412681\pi$
$811$	15.4290			0.541785			0.270892	+	0.962610i	$0.412681\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.33297	−	10.9690i	0.221834	−	0.384228i
$816$		0			0
$817$	4.37919	+	7.58499i	0.153209	+	0.265365i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	4.24364	+	7.35019i	0.148104	+	0.256524i	0.930527	−	0.366224i	$-0.119350\pi$
$821$	4.24364	+	7.35019i	0.148104	+	0.256524i	−0.782423	+	0.622748i	$0.786016\pi$
$822$		0			0
$823$	14.5487	−	25.1991i	0.507136	−	0.878385i	−0.492830	−	0.870126i	$-0.664037\pi$
$823$	14.5487	−	25.1991i	0.507136	−	0.878385i	0.999966	−	0.00825976i	$-0.00262919\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−25.9396			−0.902007			−0.451003	−	0.892522i	$-0.648934\pi$
$827$	−25.9396			−0.902007			−0.451003	+	0.892522i	$0.648934\pi$
$828$		0			0
$829$	3.10821	+	5.38358i	0.107953	+	0.186979i	0.914941	−	0.403588i	$-0.132237\pi$
$829$	3.10821	+	5.38358i	0.107953	+	0.186979i	−0.806988	+	0.590568i	$0.798904\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−9.33078	−	5.13882i	−0.323292	−	0.178049i
$834$		0			0
$835$	8.33530	+	14.4372i	0.288455	+	0.499618i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	21.2947	−	36.8834i	0.735174	−	1.27336i	−0.219474	−	0.975618i	$-0.570434\pi$
$839$	21.2947	−	36.8834i	0.735174	−	1.27336i	0.954647	−	0.297740i	$-0.0962327\pi$
$840$		0			0
$841$	−10.5721	−	18.3114i	−0.364555	−	0.631428i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−31.0751	+	53.8237i	−1.06902	+	1.85159i
$846$		0			0
$847$	0.621885	+	2.23059i	0.0213682	+	0.0766440i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.11956	−	1.93914i	0.0383781	−	0.0664728i
$852$		0			0
$853$	−10.6969	+	18.5275i	−0.366254	+	0.634370i	−0.988976	−	0.148073i	$-0.952693\pi$
$853$	−10.6969	+	18.5275i	−0.366254	+	0.634370i	0.622723	+	0.782442i	$0.286026\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	36.8435			1.25855			0.629275	−	0.777183i	$-0.283352\pi$
$857$	36.8435			1.25855			0.629275	+	0.777183i	$0.283352\pi$
$858$		0			0
$859$	17.6375			0.601783			0.300892	−	0.953658i	$-0.402716\pi$
$859$	17.6375			0.601783			0.300892	+	0.953658i	$0.402716\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.380438	+	0.658939i	−0.0129503	+	0.0224305i	−0.872428	−	0.488743i	$-0.837456\pi$
$863$	−0.380438	+	0.658939i	−0.0129503	+	0.0224305i	0.859478	+	0.511173i	$0.170789\pi$
$864$		0			0
$865$	4.05950	+	7.03127i	0.138027	+	0.239070i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−6.58414	−	11.4041i	−0.223351	−	0.386856i
$870$		0			0
$871$	62.5519			2.11949
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.282075	−	1.01175i	−0.00953586	−	0.0342035i
$876$		0			0
$877$	−41.4991			−1.40132			−0.700662	−	0.713494i	$-0.747112\pi$
$877$	−41.4991			−1.40132			−0.700662	+	0.713494i	$0.747112\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−8.35486			−0.281482			−0.140741	−	0.990046i	$-0.544949\pi$
$881$	−8.35486			−0.281482			−0.140741	+	0.990046i	$0.544949\pi$
$882$		0			0
$883$	−35.6181			−1.19864			−0.599322	−	0.800508i	$-0.704563\pi$
$883$	−35.6181			−1.19864			−0.599322	+	0.800508i	$0.704563\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−37.1100			−1.24603			−0.623016	−	0.782209i	$-0.714093\pi$
$887$	−37.1100			−1.24603			−0.623016	+	0.782209i	$0.714093\pi$
$888$		0			0
$889$	14.2855	+	51.2396i	0.479121	+	1.71852i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	7.47576			0.250167
$894$		0			0
$895$	11.1969	+	19.3935i	0.374270	+	0.648254i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	33.3565	+	57.7751i	1.11250	+	1.92691i
$900$		0			0
$901$	1.56526	−	2.71111i	0.0521464	−	0.0903202i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−41.2599			−1.37153
$906$		0			0
$907$	48.1502			1.59880			0.799401	−	0.600798i	$-0.205150\pi$
$907$	48.1502			1.59880			0.799401	+	0.600798i	$0.205150\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	17.4428	−	30.2119i	0.577906	−	1.00096i	−0.417813	−	0.908533i	$-0.637203\pi$
$911$	17.4428	−	30.2119i	0.577906	−	1.00096i	0.995719	−	0.0924301i	$-0.0294635\pi$
$912$		0			0
$913$	−12.8353	+	22.2314i	−0.424786	+	0.735751i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.52175	−	16.2187i	−0.149321	−	0.535590i
$918$		0			0
$919$	25.8675	−	44.8037i	0.853289	−	1.47794i	−0.0249351	−	0.999689i	$-0.507938\pi$
$919$	25.8675	−	44.8037i	0.853289	−	1.47794i	0.878224	−	0.478250i	$-0.158729\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	24.7826	+	42.9248i	0.815730	+	1.41289i
$924$		0			0
$925$	2.56238	−	4.43818i	0.0842506	−	0.145926i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−25.4142	−	44.0187i	−0.833814	−	1.44421i	−0.894993	−	0.446081i	$-0.852819\pi$
$929$	−25.4142	−	44.0187i	−0.833814	−	1.44421i	0.0611787	−	0.998127i	$-0.480514\pi$
$930$		0			0
$931$	0.181255	+	8.97658i	0.00594039	+	0.294196i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	7.70370	+	13.3432i	0.251938	+	0.436369i
$936$		0			0
$937$	2.54583			0.0831686			0.0415843	−	0.999135i	$-0.486759\pi$
$937$	2.54583			0.0831686			0.0415843	+	0.999135i	$0.486759\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.578933	−	1.00274i	0.0188727	−	0.0326885i	−0.856435	−	0.516255i	$-0.827326\pi$
$941$	0.578933	−	1.00274i	0.0188727	−	0.0326885i	0.875308	+	0.483567i	$0.160659\pi$
$942$		0			0
$943$	6.27292	+	10.8650i	0.204274	+	0.353813i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.90739	−	8.49985i	−0.159469	−	0.276208i	0.775208	−	0.631706i	$-0.217645\pi$
$947$	−4.90739	−	8.49985i	−0.159469	−	0.276208i	−0.934677	+	0.355497i	$0.884311\pi$
$948$		0			0
$949$	14.1648	−	24.5342i	0.459810	−	0.796414i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.53791			−0.211784			−0.105892	−	0.994378i	$-0.533770\pi$
$953$	−6.53791			−0.211784			−0.105892	+	0.994378i	$0.533770\pi$
$954$		0			0
$955$	−3.15103	−	5.45774i	−0.101965	−	0.176608i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.94789	+	6.98673i	0.0629006	+	0.225613i
$960$		0			0
$961$	−28.8782	−	50.0186i	−0.931556	−	1.61350i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	7.23229	−	12.5267i	0.232816	−	0.403248i
$966$		0			0
$967$	−14.4445	−	25.0185i	−0.464502	−	0.804542i	0.534677	−	0.845057i	$-0.320433\pi$
$967$	−14.4445	−	25.0185i	−0.464502	−	0.804542i	−0.999179	+	0.0405151i	$0.987100\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	2.66827	−	4.62158i	0.0856289	−	0.148314i	−0.820030	−	0.572320i	$-0.806043\pi$
$971$	2.66827	−	4.62158i	0.0856289	−	0.148314i	0.905659	+	0.424007i	$0.139377\pi$
$972$		0			0
$973$	14.7535	−	15.0544i	0.472975	−	0.482622i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−24.0361	+	41.6318i	−0.768983	+	1.33192i	0.169131	+	0.985594i	$0.445904\pi$
$977$	−24.0361	+	41.6318i	−0.768983	+	1.33192i	−0.938115	+	0.346325i	$0.887429\pi$
$978$		0			0
$979$	−0.358685	+	0.621261i	−0.0114636	+	0.0198556i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	29.4627			0.939714			0.469857	−	0.882743i	$-0.344306\pi$
$983$	29.4627			0.939714			0.469857	+	0.882743i	$0.344306\pi$
$984$		0			0
$985$	69.4134			2.21170
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−7.64488	+	13.2413i	−0.243093	+	0.421050i
$990$		0			0
$991$	−15.4142	−	26.6982i	−0.489649	−	0.848097i	0.510280	−	0.860008i	$-0.329542\pi$
$991$	−15.4142	−	26.6982i	−0.489649	−	0.848097i	−0.999929	+	0.0119112i	$0.996208\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−19.5413	−	33.8466i	−0.619501	−	1.07301i
$996$		0			0
$997$	5.54583			0.175638			0.0878191	−	0.996136i	$-0.472010\pi$
$997$	5.54583			0.175638			0.0878191	+	0.996136i	$0.472010\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.h.289.3		6
3.2	odd	2		1008.2.t.h.961.3		6
4.3	odd	2		378.2.h.c.289.3		6
7.4	even	3		3024.2.q.g.2881.1		6
9.4	even	3		3024.2.q.g.2305.1		6
9.5	odd	6		1008.2.q.g.625.1		6
12.11	even	2		126.2.h.d.79.1	yes	6
21.11	odd	6		1008.2.q.g.529.1		6
28.3	even	6		2646.2.e.p.2125.3		6
28.11	odd	6		378.2.e.d.235.1		6
28.19	even	6		2646.2.f.m.883.3		6
28.23	odd	6		2646.2.f.l.883.1		6
28.27	even	2		2646.2.h.o.667.1		6
36.7	odd	6		1134.2.g.l.163.1		6
36.11	even	6		1134.2.g.m.163.3		6
36.23	even	6		126.2.e.c.121.3	yes	6
36.31	odd	6		378.2.e.d.37.1		6
63.4	even	3	inner	3024.2.t.h.1873.3		6
63.32	odd	6		1008.2.t.h.193.3		6
84.11	even	6		126.2.e.c.25.3	✓	6
84.23	even	6		882.2.f.n.295.2		6
84.47	odd	6		882.2.f.o.295.2		6
84.59	odd	6		882.2.e.o.655.1		6
84.83	odd	2		882.2.h.p.79.3		6
252.11	even	6		1134.2.g.m.487.3		6
252.23	even	6		882.2.f.n.589.2		6
252.31	even	6		2646.2.h.o.361.1		6
252.47	odd	6		7938.2.a.bw.1.3		3
252.59	odd	6		882.2.h.p.67.3		6
252.67	odd	6		378.2.h.c.361.3		6
252.79	odd	6		7938.2.a.ca.1.3		3
252.95	even	6		126.2.h.d.67.1	yes	6
252.103	even	6		2646.2.f.m.1765.3		6
252.131	odd	6		882.2.f.o.589.2		6
252.139	even	6		2646.2.e.p.1549.3		6
252.151	odd	6		1134.2.g.l.487.1		6
252.167	odd	6		882.2.e.o.373.1		6
252.187	even	6		7938.2.a.bz.1.1		3
252.191	even	6		7938.2.a.bv.1.1		3
252.247	odd	6		2646.2.f.l.1765.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.3	✓	6	84.11	even	6
126.2.e.c.121.3	yes	6	36.23	even	6
126.2.h.d.67.1	yes	6	252.95	even	6
126.2.h.d.79.1	yes	6	12.11	even	2
378.2.e.d.37.1		6	36.31	odd	6
378.2.e.d.235.1		6	28.11	odd	6
378.2.h.c.289.3		6	4.3	odd	2
378.2.h.c.361.3		6	252.67	odd	6
882.2.e.o.373.1		6	252.167	odd	6
882.2.e.o.655.1		6	84.59	odd	6
882.2.f.n.295.2		6	84.23	even	6
882.2.f.n.589.2		6	252.23	even	6
882.2.f.o.295.2		6	84.47	odd	6
882.2.f.o.589.2		6	252.131	odd	6
882.2.h.p.67.3		6	252.59	odd	6
882.2.h.p.79.3		6	84.83	odd	2
1008.2.q.g.529.1		6	21.11	odd	6
1008.2.q.g.625.1		6	9.5	odd	6
1008.2.t.h.193.3		6	63.32	odd	6
1008.2.t.h.961.3		6	3.2	odd	2
1134.2.g.l.163.1		6	36.7	odd	6
1134.2.g.l.487.1		6	252.151	odd	6
1134.2.g.m.163.3		6	36.11	even	6
1134.2.g.m.487.3		6	252.11	even	6
2646.2.e.p.1549.3		6	252.139	even	6
2646.2.e.p.2125.3		6	28.3	even	6
2646.2.f.l.883.1		6	28.23	odd	6
2646.2.f.l.1765.1		6	252.247	odd	6
2646.2.f.m.883.3		6	28.19	even	6
2646.2.f.m.1765.3		6	252.103	even	6
2646.2.h.o.361.1		6	252.31	even	6
2646.2.h.o.667.1		6	28.27	even	2
3024.2.q.g.2305.1		6	9.4	even	3
3024.2.q.g.2881.1		6	7.4	even	3
3024.2.t.h.289.3		6	1.1	even	1	trivial
3024.2.t.h.1873.3		6	63.4	even	3	inner
7938.2.a.bv.1.1		3	252.191	even	6
7938.2.a.bw.1.3		3	252.47	odd	6
7938.2.a.bz.1.1		3	252.187	even	6
7938.2.a.ca.1.3		3	252.79	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.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+3.18194 q^{5} +(-0.710533 - 2.54856i) q^{7} +O(q^{10})\)	\(q+3.18194 q^{5} +(-0.710533 - 2.54856i) q^{7} +3.18194 q^{11} +(2.85185 + 4.93955i) q^{13} +(0.760877 + 1.31788i) q^{17} +(0.641315 - 1.11079i) q^{19} +2.23912 q^{23} +5.12476 q^{25} +(3.54063 - 6.13255i) q^{29} +(-4.71053 + 8.15888i) q^{31} +(-2.26088 - 8.10936i) q^{35} +(0.500000 - 0.866025i) q^{37} +(2.80150 + 4.85235i) q^{41} +(-3.41423 + 5.91362i) q^{43} +(2.91423 + 5.04759i) q^{47} +(-5.99028 + 3.62167i) q^{49} +(-1.02859 - 1.78157i) q^{53} +10.1248 q^{55} +(0.562382 - 0.974074i) q^{59} +(-1.56238 - 2.70612i) q^{61} +(9.07442 + 15.7174i) q^{65} +(5.48345 - 9.49761i) q^{67} +8.69002 q^{71} +(-2.48345 - 4.30146i) q^{73} +(-2.26088 - 8.10936i) q^{77} +(-2.06922 - 3.58399i) q^{79} +(-4.03379 + 6.98673i) q^{83} +(2.42107 + 4.19341i) q^{85} +(-0.112725 + 0.195246i) q^{89} +(10.5624 - 10.7778i) q^{91} +(2.04063 - 3.53447i) q^{95} +(7.42107 - 12.8537i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{5} + 4 q^{7}+O(q^{10}) \) 6 * q + 2 * q^5 + 4 * q^7	\( 6 q + 2 q^{5} + 4 q^{7} + 2 q^{11} + 8 q^{13} + 4 q^{17} + 3 q^{19} + 14 q^{23} - 4 q^{25} + 5 q^{29} - 20 q^{31} - 13 q^{35} + 3 q^{37} + 6 q^{43} - 9 q^{47} - 12 q^{49} - 15 q^{53} + 26 q^{55} - 14 q^{59} + 8 q^{61} + 12 q^{65} - q^{67} + 14 q^{71} + 19 q^{73} - 13 q^{77} - 5 q^{79} + 2 q^{83} - 2 q^{85} + 9 q^{89} + 46 q^{91} - 4 q^{95} + 28 q^{97}+O(q^{100}) \) 6 * q + 2 * q^5 + 4 * q^7 + 2 * q^11 + 8 * q^13 + 4 * q^17 + 3 * q^19 + 14 * q^23 - 4 * q^25 + 5 * q^29 - 20 * q^31 - 13 * q^35 + 3 * q^37 + 6 * q^43 - 9 * q^47 - 12 * q^49 - 15 * q^53 + 26 * q^55 - 14 * q^59 + 8 * q^61 + 12 * q^65 - q^67 + 14 * q^71 + 19 * q^73 - 13 * q^77 - 5 * q^79 + 2 * q^83 - 2 * q^85 + 9 * q^89 + 46 * q^91 - 4 * q^95 + 28 * q^97

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