LMFDB - Embedded newform 3024.2.t.i.1873.2

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1873.2
Root			$0.920620 + 1.59456i$ of defining polynomial
Character	$\chi$	$=$	3024.1873
Dual form			3024.2.t.i.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.33475 q^{5} +(2.54347 - 0.728536i) q^{7} +O(q^{10})$	$q-1.33475 q^{5} +(2.54347 - 0.728536i) q^{7} +1.51302 q^{11} +(-2.58800 + 4.48254i) q^{13} +(-0.774463 + 1.34141i) q^{17} +(1.25211 + 2.16872i) q^{19} -7.36079 q^{23} -3.21843 q^{25} +(0.0309713 + 0.0536439i) q^{29} +(-1.92388 - 3.33227i) q^{31} +(-3.39490 + 0.972416i) q^{35} +(-0.281608 - 0.487760i) q^{37} +(-4.51188 + 7.81481i) q^{41} +(-5.09988 - 8.83325i) q^{43} +(4.75925 - 8.24327i) q^{47} +(5.93847 - 3.70602i) q^{49} +(-0.755374 + 1.30835i) q^{53} -2.01950 q^{55} +(4.22166 + 7.31212i) q^{59} +(-1.61958 + 2.80520i) q^{61} +(3.45434 - 5.98309i) q^{65} +(3.46670 + 6.00449i) q^{67} -12.3304 q^{71} +(-1.37936 + 2.38912i) q^{73} +(3.84831 - 1.10229i) q^{77} +(-2.95969 + 5.12633i) q^{79} +(2.80111 + 4.85167i) q^{83} +(1.03372 - 1.79045i) q^{85} +(-0.703287 - 1.21813i) q^{89} +(-3.31680 + 13.2867i) q^{91} +(-1.67126 - 2.89470i) q^{95} +(-6.09713 - 10.5605i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 8 q^{5} + q^{7}+O(q^{10}) $ 10 * q + 8 * q^5 + q^7	$ 10 q + 8 q^{5} + q^{7} - 8 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} - 6 q^{23} + 2 q^{25} - 7 q^{29} + 3 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} + 27 q^{47} + 25 q^{49} + 21 q^{53} - 4 q^{55} + 30 q^{59} - 14 q^{61} + 11 q^{65} + 2 q^{67} - 6 q^{71} + 15 q^{73} + 31 q^{77} + 4 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} - 14 q^{95} - 12 q^{97}+O(q^{100}) $ 10 * q + 8 * q^5 + q^7 - 8 * q^11 - 8 * q^13 - 12 * q^17 - q^19 - 6 * q^23 + 2 * q^25 - 7 * q^29 + 3 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 + 27 * q^47 + 25 * q^49 + 21 * q^53 - 4 * q^55 + 30 * q^59 - 14 * q^61 + 11 * q^65 + 2 * q^67 - 6 * q^71 + 15 * q^73 + 31 * q^77 + 4 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 - 14 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−1.33475			−0.596920			−0.298460	−	0.954422i	$-0.596473\pi$
$5$	−1.33475			−0.596920			−0.298460	+	0.954422i	$0.596473\pi$
$6$		0			0
$7$	2.54347	−	0.728536i	0.961341	−	0.275361i
$7$	2.54347	−	0.728536i	0.961341	−	0.275361i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.51302			0.456192			0.228096	−	0.973639i	$-0.426750\pi$
$11$	1.51302			0.456192			0.228096	+	0.973639i	$0.426750\pi$
$12$		0			0
$13$	−2.58800	+	4.48254i	−0.717781	+	1.24323i	0.244096	+	0.969751i	$0.421509\pi$
$13$	−2.58800	+	4.48254i	−0.717781	+	1.24323i	−0.961877	+	0.273482i	$0.911824\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.774463	+	1.34141i	−0.187835	+	0.325340i	−0.944528	−	0.328430i	$-0.893480\pi$
$17$	−0.774463	+	1.34141i	−0.187835	+	0.325340i	0.756693	+	0.653770i	$0.226814\pi$
$18$		0			0
$19$	1.25211	+	2.16872i	0.287254	+	0.497538i	0.973153	−	0.230158i	$-0.0739244\pi$
$19$	1.25211	+	2.16872i	0.287254	+	0.497538i	−0.685900	+	0.727696i	$0.740591\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.36079			−1.53483			−0.767415	−	0.641151i	$-0.778457\pi$
$23$	−7.36079			−1.53483			−0.767415	+	0.641151i	$0.778457\pi$
$24$		0			0
$25$	−3.21843			−0.643687
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.0309713	+	0.0536439i	0.00575123	+	0.00996143i	0.868887	−	0.495011i	$-0.164836\pi$
$29$	0.0309713	+	0.0536439i	0.00575123	+	0.00996143i	−0.863135	+	0.504972i	$0.831503\pi$
$30$		0			0
$31$	−1.92388	−	3.33227i	−0.345540	−	0.598493i	0.639912	−	0.768448i	$-0.278971\pi$
$31$	−1.92388	−	3.33227i	−0.345540	−	0.598493i	−0.985452	+	0.169956i	$0.945638\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.39490	+	0.972416i	−0.573844	+	0.164368i
$36$		0			0
$37$	−0.281608	−	0.487760i	−0.0462961	−	0.0801872i	0.841949	−	0.539557i	$-0.181408\pi$
$37$	−0.281608	−	0.487760i	−0.0462961	−	0.0801872i	−0.888245	+	0.459370i	$0.848075\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.51188	+	7.81481i	−0.704638	+	1.22047i	0.262185	+	0.965018i	$0.415557\pi$
$41$	−4.51188	+	7.81481i	−0.704638	+	1.22047i	−0.966822	+	0.255450i	$0.917776\pi$
$42$		0			0
$43$	−5.09988	−	8.83325i	−0.777724	−	1.34706i	−0.933251	−	0.359226i	$-0.883041\pi$
$43$	−5.09988	−	8.83325i	−0.777724	−	1.34706i	0.155526	−	0.987832i	$-0.450293\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.75925	−	8.24327i	0.694209	−	1.20240i	−0.276238	−	0.961089i	$-0.589088\pi$
$47$	4.75925	−	8.24327i	0.694209	−	1.20240i	0.970447	−	0.241315i	$-0.0775788\pi$
$48$		0			0
$49$	5.93847	−	3.70602i	0.848353	−	0.529431i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.755374	+	1.30835i	−0.103759	+	0.179715i	−0.913230	−	0.407444i	$-0.866420\pi$
$53$	−0.755374	+	1.30835i	−0.103759	+	0.179715i	0.809472	+	0.587159i	$0.199754\pi$
$54$		0			0
$55$	−2.01950			−0.272310
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.22166	+	7.31212i	0.549613	+	0.951957i	0.998301	+	0.0582689i	$0.0185581\pi$
$59$	4.22166	+	7.31212i	0.549613	+	0.951957i	−0.448688	+	0.893688i	$0.648109\pi$
$60$		0			0
$61$	−1.61958	+	2.80520i	−0.207367	+	0.359169i	−0.950884	−	0.309547i	$-0.899823\pi$
$61$	−1.61958	+	2.80520i	−0.207367	+	0.359169i	0.743518	+	0.668716i	$0.233156\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.45434	−	5.98309i	0.428458	−	0.742111i
$66$		0			0
$67$	3.46670	+	6.00449i	0.423524	+	0.733566i	0.996281	−	0.0861595i	$-0.0274595\pi$
$67$	3.46670	+	6.00449i	0.423524	+	0.733566i	−0.572757	+	0.819725i	$0.694126\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−12.3304			−1.46335			−0.731673	−	0.681656i	$-0.761260\pi$
$71$	−12.3304			−1.46335			−0.731673	+	0.681656i	$0.761260\pi$
$72$		0			0
$73$	−1.37936	+	2.38912i	−0.161442	+	0.279625i	−0.935386	−	0.353629i	$-0.884948\pi$
$73$	−1.37936	+	2.38912i	−0.161442	+	0.279625i	0.773944	+	0.633254i	$0.218281\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.84831	−	1.10229i	0.438556	−	0.125617i
$78$		0			0
$79$	−2.95969	+	5.12633i	−0.332991	+	0.576758i	−0.983097	−	0.183086i	$-0.941391\pi$
$79$	−2.95969	+	5.12633i	−0.332991	+	0.576758i	0.650106	+	0.759844i	$0.274725\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.80111	+	4.85167i	0.307462	+	0.532540i	0.977806	−	0.209510i	$-0.0671870\pi$
$83$	2.80111	+	4.85167i	0.307462	+	0.532540i	−0.670344	+	0.742050i	$0.733854\pi$
$84$		0			0
$85$	1.03372	−	1.79045i	0.112122	−	0.194202i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.703287	−	1.21813i	−0.0745483	−	0.129121i	0.826341	−	0.563169i	$-0.190418\pi$
$89$	−0.703287	−	1.21813i	−0.0745483	−	0.129121i	−0.900890	+	0.434048i	$0.857085\pi$
$90$		0			0
$91$	−3.31680	+	13.2867i	−0.347695	+	1.39282i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.67126	−	2.89470i	−0.171467	−	0.296990i
$96$		0			0
$97$	−6.09713	−	10.5605i	−0.619070	−	1.07226i	−0.989656	−	0.143462i	$-0.954176\pi$
$97$	−6.09713	−	10.5605i	−0.619070	−	1.07226i	0.370586	−	0.928798i	$-0.379157\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.11867			−0.111312			−0.0556560	−	0.998450i	$-0.517725\pi$
$101$	−1.11867			−0.111312			−0.0556560	+	0.998450i	$0.517725\pi$
$102$		0			0
$103$	−1.93045			−0.190213			−0.0951063	−	0.995467i	$-0.530319\pi$
$103$	−1.93045			−0.190213			−0.0951063	+	0.995467i	$0.530319\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.88969	+	5.00509i	0.279357	+	0.483860i	0.971225	−	0.238163i	$-0.0765454\pi$
$107$	2.88969	+	5.00509i	0.279357	+	0.483860i	−0.691868	+	0.722024i	$0.743212\pi$
$108$		0			0
$109$	−4.12106	+	7.13788i	−0.394726	+	0.683685i	−0.993066	−	0.117557i	$-0.962494\pi$
$109$	−4.12106	+	7.13788i	−0.394726	+	0.683685i	0.598340	+	0.801242i	$0.295827\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.25105	+	12.5592i	−0.682121	+	1.18147i	0.292211	+	0.956354i	$0.405609\pi$
$113$	−7.25105	+	12.5592i	−0.682121	+	1.18147i	−0.974332	+	0.225115i	$0.927724\pi$
$114$		0			0
$115$	9.82483			0.916170
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.992558	+	3.97606i	−0.0909877	+	0.364485i
$120$		0			0
$121$	−8.71078			−0.791889
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.9696			0.981149
$126$		0			0
$127$	−8.50004			−0.754257			−0.377128	−	0.926161i	$-0.623088\pi$
$127$	−8.50004			−0.754257			−0.377128	+	0.926161i	$0.623088\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.01346			−0.175917			−0.0879585	−	0.996124i	$-0.528034\pi$
$131$	−2.01346			−0.175917			−0.0879585	+	0.996124i	$0.528034\pi$
$132$		0			0
$133$	4.76469	+	4.60386i	0.413151	+	0.399205i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.21740			−0.189445			−0.0947225	−	0.995504i	$-0.530196\pi$
$137$	−2.21740			−0.189445			−0.0947225	+	0.995504i	$0.530196\pi$
$138$		0			0
$139$	−0.377669	+	0.654143i	−0.0320335	+	0.0554836i	−0.881598	−	0.472002i	$-0.843532\pi$
$139$	−0.377669	+	0.654143i	−0.0320335	+	0.0554836i	0.849564	+	0.527485i	$0.176865\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.91568	+	6.78216i	−0.327446	+	0.567153i
$144$		0			0
$145$	−0.0413391	−	0.0716014i	−0.00343303	−	0.00594618i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.58499			−0.539463			−0.269732	−	0.962936i	$-0.586935\pi$
$149$	−6.58499			−0.539463			−0.269732	+	0.962936i	$0.586935\pi$
$150$		0			0
$151$	−12.6671			−1.03083			−0.515417	−	0.856939i	$-0.672363\pi$
$151$	−12.6671			−1.03083			−0.515417	+	0.856939i	$0.672363\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.56791	+	4.44775i	0.206260	+	0.357252i
$156$		0			0
$157$	8.65372	+	14.9887i	0.690642	+	1.19623i	0.971628	+	0.236515i	$0.0760052\pi$
$157$	8.65372	+	14.9887i	0.690642	+	1.19623i	−0.280986	+	0.959712i	$0.590662\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−18.7219	+	5.36260i	−1.47549	+	0.422632i
$162$		0			0
$163$	−6.10963	−	10.5822i	−0.478543	−	0.828861i	0.521154	−	0.853463i	$-0.325502\pi$
$163$	−6.10963	−	10.5822i	−0.478543	−	0.828861i	−0.999697	+	0.0246014i	$0.992168\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.76248	−	3.05270i	0.136385	−	0.236225i	−0.789741	−	0.613440i	$-0.789785\pi$
$167$	1.76248	−	3.05270i	0.136385	−	0.236225i	0.926126	+	0.377215i	$0.123118\pi$
$168$		0			0
$169$	−6.89546	−	11.9433i	−0.530420	−	0.918714i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.07046	−	8.78229i	0.385500	−	0.667705i	−0.606339	−	0.795206i	$-0.707362\pi$
$173$	5.07046	−	8.78229i	0.385500	−	0.667705i	0.991838	+	0.127502i	$0.0406958\pi$
$174$		0			0
$175$	−8.18599	+	2.34474i	−0.618802	+	0.177246i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.850579	−	1.47325i	0.0635752	−	0.110116i	−0.832486	−	0.554046i	$-0.813083\pi$
$179$	0.850579	−	1.47325i	0.0635752	−	0.110116i	0.896061	+	0.443931i	$0.146416\pi$
$180$		0			0
$181$	−16.9941			−1.26316			−0.631581	−	0.775310i	$-0.717594\pi$
$181$	−16.9941			−1.26316			−0.631581	+	0.775310i	$0.717594\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.375877	+	0.651039i	0.0276351	+	0.0478653i
$186$		0			0
$187$	−1.17178	+	2.02957i	−0.0856887	+	0.148417i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.3470	+	19.6535i	−0.821038	+	1.42208i	0.0838717	+	0.996477i	$0.473271\pi$
$191$	−11.3470	+	19.6535i	−0.821038	+	1.42208i	−0.904910	+	0.425603i	$0.860062\pi$
$192$		0			0
$193$	−3.09349	−	5.35808i	−0.222674	−	0.385683i	0.732945	−	0.680288i	$-0.238145\pi$
$193$	−3.09349	−	5.35808i	−0.222674	−	0.385683i	−0.955619	+	0.294605i	$0.904812\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−9.77010			−0.696091			−0.348045	−	0.937478i	$-0.613154\pi$
$197$	−9.77010			−0.696091			−0.348045	+	0.937478i	$0.613154\pi$
$198$		0			0
$199$	4.33973	−	7.51664i	0.307636	−	0.532840i	−0.670209	−	0.742172i	$-0.733796\pi$
$199$	4.33973	−	7.51664i	0.307636	−	0.532840i	0.977845	+	0.209332i	$0.0671289\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.117856	+	0.113878i	0.00827188	+	0.00799267i
$204$		0			0
$205$	6.02225	−	10.4308i	0.420612	−	0.728522i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.89446	+	3.28130i	0.131043	+	0.226973i
$210$		0			0
$211$	2.84219	−	4.92283i	0.195665	−	0.338901i	−0.751453	−	0.659786i	$-0.770647\pi$
$211$	2.84219	−	4.92283i	0.195665	−	0.338901i	0.947118	+	0.320885i	$0.103980\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.80708	+	11.7902i	0.464239	+	0.804086i
$216$		0			0
$217$	−7.32102	−	7.07390i	−0.496983	−	0.480207i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.00862	−	6.94313i	−0.269649	−	0.467045i
$222$		0			0
$223$	−5.86133	−	10.1521i	−0.392503	−	0.679836i	0.600276	−	0.799793i	$-0.295058\pi$
$223$	−5.86133	−	10.1521i	−0.392503	−	0.679836i	−0.992779	+	0.119957i	$0.961724\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.1831			0.742247			0.371123	−	0.928584i	$-0.378973\pi$
$227$	11.1831			0.742247			0.371123	+	0.928584i	$0.378973\pi$
$228$		0			0
$229$	−9.65647			−0.638118			−0.319059	−	0.947735i	$-0.603367\pi$
$229$	−9.65647			−0.638118			−0.319059	+	0.947735i	$0.603367\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.64492	+	16.7055i	0.631860	+	1.09441i	0.987171	+	0.159666i	$0.0510416\pi$
$233$	9.64492	+	16.7055i	0.631860	+	1.09441i	−0.355311	+	0.934748i	$0.615625\pi$
$234$		0			0
$235$	−6.35243	+	11.0027i	−0.414387	+	0.717739i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.194641	+	0.337128i	−0.0125903	+	0.0218070i	−0.872252	−	0.489057i	$-0.837341\pi$
$239$	−0.194641	+	0.337128i	−0.0125903	+	0.0218070i	0.859662	+	0.510864i	$0.170674\pi$
$240$		0			0
$241$	10.6361			0.685134			0.342567	−	0.939493i	$-0.388704\pi$
$241$	10.6361			0.685134			0.342567	+	0.939493i	$0.388704\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.92639	+	4.94662i	−0.506399	+	0.316028i
$246$		0			0
$247$	−12.9618			−0.824741
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−3.26628			−0.206166			−0.103083	−	0.994673i	$-0.532871\pi$
$251$	−3.26628			−0.206166			−0.103083	+	0.994673i	$0.532871\pi$
$252$		0			0
$253$	−11.1370			−0.700176
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.69573			0.292912			0.146456	−	0.989217i	$-0.453213\pi$
$257$	4.69573			0.292912			0.146456	+	0.989217i	$0.453213\pi$
$258$		0			0
$259$	−1.07161	−	1.03544i	−0.0665867	−	0.0643391i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	19.5498			1.20549			0.602747	−	0.797932i	$-0.294073\pi$
$263$	19.5498			1.20549			0.602747	+	0.797932i	$0.294073\pi$
$264$		0			0
$265$	1.00824	−	1.74632i	0.0619355	−	0.107276i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.88365	+	13.6549i	−0.480675	+	0.832553i	−0.999754	−	0.0221730i	$-0.992942\pi$
$269$	−7.88365	+	13.6549i	−0.480675	+	0.832553i	0.519079	+	0.854726i	$0.326275\pi$
$270$		0			0
$271$	−7.39882	−	12.8151i	−0.449446	−	0.778464i	0.548904	−	0.835886i	$-0.315045\pi$
$271$	−7.39882	−	12.8151i	−0.449446	−	0.778464i	−0.998350	+	0.0574218i	$0.981712\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.86954			−0.293644
$276$		0			0
$277$	−7.45122			−0.447701			−0.223850	−	0.974624i	$-0.571863\pi$
$277$	−7.45122			−0.447701			−0.223850	+	0.974624i	$0.571863\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	12.9938	+	22.5060i	0.775146	+	1.34259i	0.934712	+	0.355406i	$0.115657\pi$
$281$	12.9938	+	22.5060i	0.775146	+	1.34259i	−0.159566	+	0.987187i	$0.551009\pi$
$282$		0			0
$283$	9.37768	+	16.2426i	0.557445	+	0.965524i	0.997709	+	0.0676550i	$0.0215517\pi$
$283$	9.37768	+	16.2426i	0.557445	+	0.965524i	−0.440263	+	0.897869i	$0.645115\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.78246	+	23.1638i	−0.341328	+	1.36732i
$288$		0			0
$289$	7.30041	+	12.6447i	0.429436	+	0.743805i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.23089	−	2.13196i	0.0719093	−	0.124551i	−0.827829	−	0.560981i	$-0.810424\pi$
$293$	1.23089	−	2.13196i	0.0719093	−	0.124551i	0.899738	+	0.436430i	$0.143757\pi$
$294$		0			0
$295$	−5.63487	−	9.75988i	−0.328075	−	0.568242i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	19.0497	−	32.9950i	1.10167	−	1.90815i
$300$		0			0
$301$	−19.4067	−	18.7517i	−1.11858	−	1.08083i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.16175	−	3.74425i	0.123781	−	0.214395i
$306$		0			0
$307$	4.66277			0.266118			0.133059	−	0.991108i	$-0.457520\pi$
$307$	4.66277			0.266118			0.133059	+	0.991108i	$0.457520\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−13.7410	−	23.8002i	−0.779183	−	1.34958i	−0.932413	−	0.361393i	$-0.882301\pi$
$311$	−13.7410	−	23.8002i	−0.779183	−	1.34958i	0.153231	−	0.988190i	$-0.451032\pi$
$312$		0			0
$313$	−2.74666	+	4.75735i	−0.155250	+	0.268901i	−0.933150	−	0.359487i	$-0.882952\pi$
$313$	−2.74666	+	4.75735i	−0.155250	+	0.268901i	0.777900	+	0.628388i	$0.216285\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.93879	−	8.55424i	0.277390	−	0.480454i	−0.693345	−	0.720606i	$-0.743864\pi$
$317$	4.93879	−	8.55424i	0.277390	−	0.480454i	0.970735	+	0.240152i	$0.0771972\pi$
$318$		0			0
$319$	0.0468601	+	0.0811641i	0.00262366	+	0.00454432i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−3.87885			−0.215825
$324$		0			0
$325$	8.32930	−	14.4268i	0.462026	−	0.800253i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	6.09950	−	24.4338i	0.336276	−	1.34708i
$330$		0			0
$331$	−10.3471	+	17.9217i	−0.568729	+	0.985067i	0.427963	+	0.903796i	$0.359231\pi$
$331$	−10.3471	+	17.9217i	−0.568729	+	0.985067i	−0.996692	+	0.0812710i	$0.974102\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.62718	−	8.01452i	−0.252810	−	0.437880i
$336$		0			0
$337$	0.748747	−	1.29687i	0.0407869	−	0.0706449i	−0.844911	−	0.534906i	$-0.820347\pi$
$337$	0.748747	−	1.29687i	0.0407869	−	0.0706449i	0.885698	+	0.464261i	$0.153680\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.91087	−	5.04177i	−0.157632	−	0.273027i
$342$		0			0
$343$	12.4044	−	13.7525i	0.669772	−	0.742567i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	14.7694	+	25.5813i	0.792862	+	1.37328i	0.924188	+	0.381938i	$0.124743\pi$
$347$	14.7694	+	25.5813i	0.792862	+	1.37328i	−0.131326	+	0.991339i	$0.541923\pi$
$348$		0			0
$349$	18.0006	+	31.1780i	0.963551	+	1.66892i	0.713458	+	0.700698i	$0.247128\pi$
$349$	18.0006	+	31.1780i	0.963551	+	1.66892i	0.250094	+	0.968222i	$0.419539\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	29.4930			1.56975			0.784877	−	0.619652i	$-0.212726\pi$
$353$	29.4930			1.56975			0.784877	+	0.619652i	$0.212726\pi$
$354$		0			0
$355$	16.4580			0.873500
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.70535	+	4.68580i	0.142783	+	0.247307i	0.928544	−	0.371224i	$-0.121062\pi$
$359$	2.70535	+	4.68580i	0.142783	+	0.247307i	−0.785761	+	0.618531i	$0.787728\pi$
$360$		0			0
$361$	6.36444	−	11.0235i	0.334971	−	0.580186i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.84110	−	3.18888i	0.0963676	−	0.166914i
$366$		0			0
$367$	23.0843			1.20499			0.602496	−	0.798122i	$-0.294173\pi$
$367$	23.0843			1.20499			0.602496	+	0.798122i	$0.294173\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.968093	+	3.87805i	−0.0502609	+	0.201339i
$372$		0			0
$373$	21.5030			1.11338			0.556692	−	0.830719i	$-0.312070\pi$
$373$	21.5030			1.11338			0.556692	+	0.830719i	$0.312070\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.320615			−0.0165125
$378$		0			0
$379$	−5.72168			−0.293903			−0.146952	−	0.989144i	$-0.546946\pi$
$379$	−5.72168			−0.293903			−0.146952	+	0.989144i	$0.546946\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−34.9209			−1.78437			−0.892187	−	0.451666i	$-0.850830\pi$
$383$	−34.9209			−1.78437			−0.892187	+	0.451666i	$0.850830\pi$
$384$		0			0
$385$	−5.13654	+	1.47128i	−0.261783	+	0.0749834i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	28.8822			1.46438			0.732192	−	0.681098i	$-0.238497\pi$
$389$	28.8822			1.46438			0.732192	+	0.681098i	$0.238497\pi$
$390$		0			0
$391$	5.70066	−	9.87383i	0.288295	−	0.499341i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.95046	−	6.84239i	0.198769	−	0.344278i
$396$		0			0
$397$	5.59226	+	9.68607i	0.280667	+	0.486130i	0.971549	−	0.236838i	$-0.0761109\pi$
$397$	5.59226	+	9.68607i	0.280667	+	0.486130i	−0.690882	+	0.722968i	$0.742778\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.08212			0.0540386			0.0270193	−	0.999635i	$-0.491398\pi$
$401$	1.08212			0.0540386			0.0270193	+	0.999635i	$0.491398\pi$
$402$		0			0
$403$	19.9160			0.992088
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.426078	−	0.737988i	−0.0211199	−	0.0365807i
$408$		0			0
$409$	10.8674	+	18.8229i	0.537360	+	0.930735i	0.999045	+	0.0436908i	$0.0139116\pi$
$409$	10.8674	+	18.8229i	0.537360	+	0.930735i	−0.461685	+	0.887044i	$0.652755\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	16.0648	+	15.5225i	0.790497	+	0.763814i
$414$		0			0
$415$	−3.73879	−	6.47578i	−0.183530	−	0.317884i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.5906	−	21.8075i	0.615090	−	1.06537i	−0.375279	−	0.926912i	$-0.622453\pi$
$419$	12.5906	−	21.8075i	0.615090	−	1.06537i	0.990369	−	0.138455i	$-0.0442135\pi$
$420$		0			0
$421$	−14.8304	−	25.6869i	−0.722788	−	1.25191i	−0.959878	−	0.280418i	$-0.909527\pi$
$421$	−14.8304	−	25.6869i	−0.722788	−	1.25191i	0.237090	−	0.971488i	$-0.423806\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.49256	−	4.31724i	0.120907	−	0.209417i
$426$		0			0
$427$	−2.07567	+	8.31487i	−0.100449	+	0.402385i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.44517	−	4.23516i	0.117780	−	0.204000i	−0.801108	−	0.598520i	$-0.795756\pi$
$431$	2.44517	−	4.23516i	0.117780	−	0.204000i	0.918887	+	0.394520i	$0.129089\pi$
$432$		0			0
$433$	9.71430			0.466839			0.233420	−	0.972376i	$-0.425008\pi$
$433$	9.71430			0.466839			0.233420	+	0.972376i	$0.425008\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−9.21651	−	15.9635i	−0.440885	−	0.763636i
$438$		0			0
$439$	−7.41176	+	12.8375i	−0.353744	+	0.612703i	−0.986902	−	0.161320i	$-0.948425\pi$
$439$	−7.41176	+	12.8375i	−0.353744	+	0.612703i	0.633158	+	0.774022i	$0.281758\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.9510	−	18.9676i	0.520297	−	0.901180i	−0.479425	−	0.877583i	$-0.659155\pi$
$443$	10.9510	−	18.9676i	0.520297	−	0.901180i	0.999722	−	0.0235972i	$-0.00751192\pi$
$444$		0			0
$445$	0.938715	+	1.62590i	0.0444994	+	0.0770751i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−21.4952			−1.01442			−0.507212	−	0.861822i	$-0.669324\pi$
$449$	−21.4952			−1.01442			−0.507212	+	0.861822i	$0.669324\pi$
$450$		0			0
$451$	−6.82655	+	11.8239i	−0.321450	+	0.556767i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.42711	−	17.7344i	0.207546	−	0.831402i
$456$		0			0
$457$	−20.3128	+	35.1827i	−0.950190	+	1.64578i	−0.205181	+	0.978724i	$0.565778\pi$
$457$	−20.3128	+	35.1827i	−0.950190	+	1.64578i	−0.745009	+	0.667054i	$0.767555\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.41541	−	2.45155i	−0.0659220	−	0.114180i	0.831181	−	0.556003i	$-0.187666\pi$
$461$	−1.41541	−	2.45155i	−0.0659220	−	0.114180i	−0.897103	+	0.441822i	$0.854332\pi$
$462$		0			0
$463$	13.9324	−	24.1317i	0.647494	−	1.12149i	−0.336225	−	0.941782i	$-0.609150\pi$
$463$	13.9324	−	24.1317i	0.647494	−	1.12149i	0.983719	−	0.179711i	$-0.0575164\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.3219	−	23.0742i	−0.616464	−	1.06775i	−0.990126	−	0.140182i	$-0.955231\pi$
$467$	−13.3219	−	23.0742i	−0.616464	−	1.06775i	0.373661	−	0.927565i	$-0.378102\pi$
$468$		0			0
$469$	13.1919	+	12.7466i	0.609146	+	0.588585i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.71620	−	13.3648i	−0.354791	−	0.614516i
$474$		0			0
$475$	−4.02983	−	6.97987i	−0.184901	−	0.320258i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−31.5791			−1.44289			−0.721443	−	0.692474i	$-0.756521\pi$
$479$	−31.5791			−1.44289			−0.721443	+	0.692474i	$0.756521\pi$
$480$		0			0
$481$	2.91520			0.132922
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.13817	+	14.0957i	0.369535	+	0.640054i
$486$		0			0
$487$	0.153087	−	0.265154i	0.00693703	−	0.0120153i	−0.862536	−	0.505996i	$-0.831125\pi$
$487$	0.153087	−	0.265154i	0.00693703	−	0.0120153i	0.869473	+	0.493980i	$0.164459\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.06981	+	15.7094i	−0.409315	+	0.708954i	−0.994813	−	0.101720i	$-0.967566\pi$
$491$	−9.06981	+	15.7094i	−0.409315	+	0.708954i	0.585498	+	0.810674i	$0.300899\pi$
$492$		0			0
$493$	−0.0959447			−0.00432113
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−31.3619	+	8.98311i	−1.40677	+	0.402948i
$498$		0			0
$499$	21.3091			0.953928			0.476964	−	0.878923i	$-0.341737\pi$
$499$	21.3091			0.953928			0.476964	+	0.878923i	$0.341737\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−17.0738			−0.761285			−0.380642	−	0.924722i	$-0.624297\pi$
$503$	−17.0738			−0.761285			−0.380642	+	0.924722i	$0.624297\pi$
$504$		0			0
$505$	1.49315			0.0664443
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−36.7735			−1.62996			−0.814979	−	0.579490i	$-0.803252\pi$
$509$	−36.7735			−1.62996			−0.814979	+	0.579490i	$0.803252\pi$
$510$		0			0
$511$	−1.76780	+	7.08155i	−0.0782027	+	0.313270i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2.57667			0.113542
$516$		0			0
$517$	7.20083	−	12.4722i	0.316692	−	0.548527i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9.57535	−	16.5850i	0.419504	−	0.726602i	−0.576386	−	0.817178i	$-0.695537\pi$
$521$	9.57535	−	16.5850i	0.419504	−	0.726602i	0.995890	+	0.0905758i	$0.0288707\pi$
$522$		0			0
$523$	20.9715	+	36.3236i	0.917018	+	1.58832i	0.803920	+	0.594737i	$0.202744\pi$
$523$	20.9715	+	36.3236i	0.917018	+	1.58832i	0.113097	+	0.993584i	$0.463923\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.95991			0.259618
$528$		0			0
$529$	31.1812			1.35570
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−23.3535	−	40.4494i	−1.01155	−	1.75206i
$534$		0			0
$535$	−3.85702	−	6.68056i	−0.166754	−	0.288826i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	8.98500	−	5.60726i	0.387011	−	0.241522i
$540$		0			0
$541$	−1.44272	−	2.49886i	−0.0620273	−	0.107434i	0.833344	−	0.552754i	$-0.186423\pi$
$541$	−1.44272	−	2.49886i	−0.0620273	−	0.107434i	−0.895371	+	0.445320i	$0.853090\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.50059	−	9.52731i	0.235620	−	0.408105i
$546$		0			0
$547$	−1.38738	−	2.40301i	−0.0593201	−	0.102745i	0.834840	−	0.550492i	$-0.185560\pi$
$547$	−1.38738	−	2.40301i	−0.0593201	−	0.102745i	−0.894160	+	0.447747i	$0.852227\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.0775590	+	0.134336i	−0.00330413	+	0.00572291i
$552$		0			0
$553$	−3.79316	+	15.1949i	−0.161302	+	0.646154i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−15.5344	+	26.9064i	−0.658214	+	1.14006i	0.322864	+	0.946445i	$0.395354\pi$
$557$	−15.5344	+	26.9064i	−0.658214	+	1.14006i	−0.981078	+	0.193614i	$0.937979\pi$
$558$		0			0
$559$	52.7939			2.23294
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.144020	−	0.249451i	−0.00606973	−	0.0105131i	0.862975	−	0.505247i	$-0.168599\pi$
$563$	−0.144020	−	0.249451i	−0.00606973	−	0.0105131i	−0.869044	+	0.494734i	$0.835265\pi$
$564$		0			0
$565$	9.67836	−	16.7634i	0.407172	−	0.705242i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.04004	+	13.9258i	−0.337056	+	0.583798i	−0.983878	−	0.178843i	$-0.942765\pi$
$569$	−8.04004	+	13.9258i	−0.337056	+	0.583798i	0.646821	+	0.762641i	$0.276098\pi$
$570$		0			0
$571$	−7.64289	−	13.2379i	−0.319845	−	0.553988i	0.660610	−	0.750729i	$-0.270298\pi$
$571$	−7.64289	−	13.2379i	−0.319845	−	0.553988i	−0.980456	+	0.196741i	$0.936964\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	23.6902			0.987950
$576$		0			0
$577$	12.0812	−	20.9253i	0.502949	−	0.871133i	−0.497045	−	0.867725i	$-0.665582\pi$
$577$	12.0812	−	20.9253i	0.502949	−	0.871133i	0.999994	−	0.00340833i	$-0.00108491\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	10.6592	+	10.2994i	0.442216	+	0.427289i
$582$		0			0
$583$	−1.14289	+	1.97955i	−0.0473338	+	0.0819845i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.0145	+	31.2020i	0.743537	+	1.28784i	0.950875	+	0.309574i	$0.100186\pi$
$587$	18.0145	+	31.2020i	0.743537	+	1.28784i	−0.207339	+	0.978269i	$0.566480\pi$
$588$		0			0
$589$	4.81783	−	8.34472i	0.198515	−	0.343838i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−12.4668	−	21.5932i	−0.511951	−	0.886726i	−0.999904	−	0.0138558i	$-0.995589\pi$
$593$	−12.4668	−	21.5932i	−0.511951	−	0.886726i	0.487953	−	0.872870i	$-0.337744\pi$
$594$		0			0
$595$	1.32482	−	5.30706i	0.0543124	−	0.217568i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−19.7642	−	34.2325i	−0.807542	−	1.39870i	−0.914561	−	0.404447i	$-0.867464\pi$
$599$	−19.7642	−	34.2325i	−0.807542	−	1.39870i	0.107019	−	0.994257i	$-0.465869\pi$
$600$		0			0
$601$	1.86447	+	3.22936i	0.0760534	+	0.131728i	0.901544	−	0.432688i	$-0.142435\pi$
$601$	1.86447	+	3.22936i	0.0760534	+	0.131728i	−0.825490	+	0.564416i	$0.809101\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	11.6267			0.472694
$606$		0			0
$607$	−23.6528			−0.960036			−0.480018	−	0.877259i	$-0.659370\pi$
$607$	−23.6528			−0.960036			−0.480018	+	0.877259i	$0.659370\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	24.6339	+	42.6671i	0.996580	+	1.72613i
$612$		0			0
$613$	1.89952	−	3.29006i	0.0767208	−	0.132884i	−0.825113	−	0.564968i	$-0.808888\pi$
$613$	1.89952	−	3.29006i	0.0767208	−	0.132884i	0.901833	+	0.432084i	$0.142222\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	17.5615	−	30.4174i	0.706999	−	1.22456i	−0.258966	−	0.965886i	$-0.583382\pi$
$617$	17.5615	−	30.4174i	0.706999	−	1.22456i	0.965965	−	0.258672i	$-0.0832849\pi$
$618$		0			0
$619$	21.1632			0.850622			0.425311	−	0.905047i	$-0.360165\pi$
$619$	21.1632			0.850622			0.425311	+	0.905047i	$0.360165\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−2.67624	−	2.58590i	−0.107221	−	0.103602i
$624$		0			0
$625$	1.45048			0.0580192
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.872381			0.0347841
$630$		0			0
$631$	−4.74845			−0.189033			−0.0945164	−	0.995523i	$-0.530130\pi$
$631$	−4.74845			−0.189033			−0.0945164	+	0.995523i	$0.530130\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	11.3455			0.450231
$636$		0			0
$637$	1.24363	+	36.2106i	0.0492745	+	1.43472i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	9.87469			0.390027			0.195013	−	0.980801i	$-0.437525\pi$
$641$	9.87469			0.390027			0.195013	+	0.980801i	$0.437525\pi$
$642$		0			0
$643$	−21.9748	+	38.0615i	−0.866602	+	1.50100i	−0.00115462	+	0.999999i	$0.500368\pi$
$643$	−21.9748	+	38.0615i	−0.866602	+	1.50100i	−0.865448	+	0.501000i	$0.832966\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	22.1936	−	38.4404i	0.872521	−	1.51125i	0.0131398	−	0.999914i	$-0.495817\pi$
$647$	22.1936	−	38.4404i	0.872521	−	1.51125i	0.859381	−	0.511336i	$-0.170849\pi$
$648$		0			0
$649$	6.38743	+	11.0634i	0.250729	+	0.434275i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−41.9912			−1.64324			−0.821622	−	0.570033i	$-0.806930\pi$
$653$	−41.9912			−1.64324			−0.821622	+	0.570033i	$0.806930\pi$
$654$		0			0
$655$	2.68748			0.105008
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19.6365	−	34.0114i	−0.764928	−	1.32489i	−0.940284	−	0.340390i	$-0.889441\pi$
$659$	−19.6365	−	34.0114i	−0.764928	−	1.32489i	0.175356	−	0.984505i	$-0.443892\pi$
$660$		0			0
$661$	0.0933694	+	0.161721i	0.00363165	+	0.00629020i	0.867836	−	0.496852i	$-0.165511\pi$
$661$	0.0933694	+	0.161721i	0.00363165	+	0.00629020i	−0.864204	+	0.503142i	$0.832177\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6.35969	−	6.14502i	−0.246618	−	0.238293i
$666$		0			0
$667$	−0.227973	−	0.394862i	−0.00882717	−	0.0152891i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.45046	+	4.24432i	−0.0945989	+	0.163850i
$672$		0			0
$673$	−5.43382	−	9.41166i	−0.209458	−	0.362793i	0.742086	−	0.670305i	$-0.233837\pi$
$673$	−5.43382	−	9.41166i	−0.209458	−	0.362793i	−0.951544	+	0.307512i	$0.900503\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.1950	−	24.5865i	0.545560	−	0.944937i	−0.453012	−	0.891505i	$-0.649650\pi$
$677$	14.1950	−	24.5865i	0.545560	−	0.944937i	0.998571	−	0.0534326i	$-0.0170162\pi$
$678$		0			0
$679$	−23.2016	−	22.4184i	−0.890396	−	0.860341i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	5.92034	−	10.2543i	0.226536	−	0.392371i	−0.730243	−	0.683187i	$-0.760593\pi$
$683$	5.92034	−	10.2543i	0.226536	−	0.392371i	0.956779	+	0.290816i	$0.0939267\pi$
$684$		0			0
$685$	2.95968			0.113083
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.90981	−	6.77199i	−0.148952	−	0.257992i
$690$		0			0
$691$	5.95416	−	10.3129i	0.226507	−	0.392321i	−0.730264	−	0.683165i	$-0.760603\pi$
$691$	5.95416	−	10.3129i	0.226507	−	0.392321i	0.956770	+	0.290844i	$0.0939361\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.504096	−	0.873119i	0.0191214	−	0.0331193i
$696$		0			0
$697$	−6.98857	−	12.1046i	−0.264711	−	0.458493i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	31.3902			1.18559			0.592795	−	0.805353i	$-0.298024\pi$
$701$	31.3902			1.18559			0.592795	+	0.805353i	$0.298024\pi$
$702$		0			0
$703$	0.705208	−	1.22146i	0.0265974	−	0.0460681i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.84531	+	0.814992i	−0.107009	+	0.0306509i
$708$		0			0
$709$	−0.312609	+	0.541455i	−0.0117403	+	0.0203348i	−0.871836	−	0.489798i	$-0.837070\pi$
$709$	−0.312609	+	0.541455i	−0.0117403	+	0.0203348i	0.860096	+	0.510133i	$0.170404\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	14.1613	+	24.5281i	0.530345	+	0.918584i
$714$		0			0
$715$	5.22647	−	9.05251i	0.195459	−	0.338545i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	12.1969	+	21.1257i	0.454869	+	0.787857i	0.998681	−	0.0513506i	$-0.0163526\pi$
$719$	12.1969	+	21.1257i	0.454869	+	0.787857i	−0.543811	+	0.839208i	$0.683019\pi$
$720$		0			0
$721$	−4.91003	+	1.40640i	−0.182859	+	0.0523771i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.0996792	−	0.172649i	−0.00370199	−	0.00641204i
$726$		0			0
$727$	18.9253	+	32.7796i	0.701900	+	1.21573i	0.967799	+	0.251726i	$0.0809980\pi$
$727$	18.9253	+	32.7796i	0.701900	+	1.21573i	−0.265899	+	0.964001i	$0.585669\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	15.7987			0.584335
$732$		0			0
$733$	2.40155			0.0887033			0.0443516	−	0.999016i	$-0.485878\pi$
$733$	2.40155			0.0887033			0.0443516	+	0.999016i	$0.485878\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.24517	+	9.08490i	0.193208	+	0.334646i
$738$		0			0
$739$	15.1940	−	26.3167i	0.558920	−	0.968077i	−0.438667	−	0.898650i	$-0.644549\pi$
$739$	15.1940	−	26.3167i	0.558920	−	0.968077i	0.997587	−	0.0694277i	$-0.0221173\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−2.54785	+	4.41300i	−0.0934715	+	0.161897i	−0.908970	−	0.416862i	$-0.863130\pi$
$743$	−2.54785	+	4.41300i	−0.0934715	+	0.161897i	0.815498	+	0.578760i	$0.196463\pi$
$744$		0			0
$745$	8.78934			0.322016
$746$		0			0
$747$		0			0
$748$		0			0
$749$	10.9962	+	10.6251i	0.401793	+	0.388231i
$750$		0			0
$751$	0.975011			0.0355787			0.0177893	−	0.999842i	$-0.494337\pi$
$751$	0.975011			0.0355787			0.0177893	+	0.999842i	$0.494337\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	16.9075			0.615326
$756$		0			0
$757$	11.6346			0.422865			0.211433	−	0.977393i	$-0.432187\pi$
$757$	11.6346			0.422865			0.211433	+	0.977393i	$0.432187\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	54.1749			1.96384			0.981920	−	0.189298i	$-0.0606213\pi$
$761$	54.1749			1.96384			0.981920	+	0.189298i	$0.0606213\pi$
$762$		0			0
$763$	−5.28158	+	21.1573i	−0.191206	+	0.765946i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−43.7025			−1.57801
$768$		0			0
$769$	−10.4326	+	18.0698i	−0.376208	+	0.651612i	−0.990507	−	0.137462i	$-0.956106\pi$
$769$	−10.4326	+	18.0698i	−0.376208	+	0.651612i	0.614299	+	0.789074i	$0.289439\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	27.4972	−	47.6266i	0.989007	−	1.71301i	0.366447	−	0.930439i	$-0.380574\pi$
$773$	27.4972	−	47.6266i	0.989007	−	1.71301i	0.622561	−	0.782572i	$-0.286092\pi$
$774$		0			0
$775$	6.19189	+	10.7247i	0.222419	+	0.385242i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−22.5975			−0.809639
$780$		0			0
$781$	−18.6560			−0.667566
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−11.5506	−	20.0062i	−0.412258	−	0.714051i
$786$		0			0
$787$	4.59475	+	7.95833i	0.163785	+	0.283684i	0.936223	−	0.351406i	$-0.114296\pi$
$787$	4.59475	+	7.95833i	0.163785	+	0.283684i	−0.772438	+	0.635090i	$0.780963\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−9.29301	+	37.2266i	−0.330421	+	1.32362i
$792$		0			0
$793$	−8.38296	−	14.5197i	−0.297688	−	0.515610i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.53774	+	6.12754i	−0.125313	+	0.217049i	−0.921855	−	0.387534i	$-0.873327\pi$
$797$	−3.53774	+	6.12754i	−0.125313	+	0.217049i	0.796542	+	0.604583i	$0.206660\pi$
$798$		0			0
$799$	7.37174	+	12.7682i	0.260793	+	0.451707i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.08699	+	3.61477i	−0.0736483	+	0.127563i
$804$		0			0
$805$	24.9892	−	7.15774i	0.880752	−	0.252277i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	2.97060	−	5.14522i	0.104441	−	0.180896i	−0.809069	−	0.587714i	$-0.800028\pi$
$809$	2.97060	−	5.14522i	0.104441	−	0.180896i	0.913510	+	0.406817i	$0.133361\pi$
$810$		0			0
$811$	−44.4139			−1.55958			−0.779791	−	0.626039i	$-0.784675\pi$
$811$	−44.4139			−1.55958			−0.779791	+	0.626039i	$0.784675\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	8.15485	+	14.1246i	0.285652	+	0.494764i
$816$		0			0
$817$	12.7712	−	22.1204i	0.446808	−	0.773894i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.17761	−	5.50378i	0.110899	−	0.192083i	−0.805234	−	0.592958i	$-0.797960\pi$
$821$	3.17761	−	5.50378i	0.110899	−	0.192083i	0.916133	+	0.400874i	$0.131294\pi$
$822$		0			0
$823$	−4.73216	−	8.19635i	−0.164953	−	0.285707i	0.771686	−	0.636004i	$-0.219414\pi$
$823$	−4.73216	−	8.19635i	−0.164953	−	0.285707i	−0.936639	+	0.350297i	$0.886081\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.86261			−0.169090			−0.0845448	−	0.996420i	$-0.526944\pi$
$827$	−4.86261			−0.169090			−0.0845448	+	0.996420i	$0.526944\pi$
$828$		0			0
$829$	20.3926	−	35.3211i	0.708266	−	1.22675i	−0.257234	−	0.966349i	$-0.582811\pi$
$829$	20.3926	−	35.3211i	0.708266	−	1.22675i	0.965500	−	0.260403i	$-0.0838555\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.372159	+	10.8361i	0.0128946	+	0.375449i
$834$		0			0
$835$	−2.35247	+	4.07460i	−0.0814107	+	0.141007i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	9.60171	+	16.6307i	0.331488	+	0.574154i	0.982804	−	0.184653i	$-0.0591161\pi$
$839$	9.60171	+	16.6307i	0.331488	+	0.574154i	−0.651316	+	0.758807i	$0.725783\pi$
$840$		0			0
$841$	14.4981	−	25.1114i	0.499934	−	0.865911i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	9.20374	+	15.9413i	0.316618	+	0.548399i
$846$		0			0
$847$	−22.1556	+	6.34612i	−0.761276	+	0.218055i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.07286	+	3.59029i	0.0710566	+	0.123074i
$852$		0			0
$853$	−6.95055	−	12.0387i	−0.237982	−	0.412198i	0.722153	−	0.691734i	$-0.243153\pi$
$853$	−6.95055	−	12.0387i	−0.237982	−	0.412198i	−0.960135	+	0.279536i	$0.909819\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−56.9838			−1.94653			−0.973265	−	0.229686i	$-0.926230\pi$
$857$	−56.9838			−1.94653			−0.973265	+	0.229686i	$0.926230\pi$
$858$		0			0
$859$	20.1002			0.685810			0.342905	−	0.939370i	$-0.388589\pi$
$859$	20.1002			0.685810			0.342905	+	0.939370i	$0.388589\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−3.08893	−	5.35018i	−0.105148	−	0.182122i	0.808650	−	0.588289i	$-0.200198\pi$
$863$	−3.08893	−	5.35018i	−0.105148	−	0.182122i	−0.913799	+	0.406167i	$0.866865\pi$
$864$		0			0
$865$	−6.76781	+	11.7222i	−0.230112	+	0.398566i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.47806	+	7.75623i	−0.151908	+	0.263112i
$870$		0			0
$871$	−35.8872			−1.21599
$872$		0			0
$873$		0			0
$874$		0			0
$875$	27.9008	−	7.99173i	0.943219	−	0.270170i
$876$		0			0
$877$	−37.2574			−1.25809			−0.629046	−	0.777368i	$-0.716554\pi$
$877$	−37.2574			−1.25809			−0.629046	+	0.777368i	$0.716554\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	11.7848			0.397041			0.198520	−	0.980097i	$-0.436386\pi$
$881$	11.7848			0.397041			0.198520	+	0.980097i	$0.436386\pi$
$882$		0			0
$883$	29.2308			0.983693			0.491847	−	0.870682i	$-0.336322\pi$
$883$	29.2308			0.983693			0.491847	+	0.870682i	$0.336322\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	28.5161			0.957479			0.478739	−	0.877957i	$-0.341094\pi$
$887$	28.5161			0.957479			0.478739	+	0.877957i	$0.341094\pi$
$888$		0			0
$889$	−21.6196	+	6.19258i	−0.725098	+	0.207693i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	23.8364			0.797656
$894$		0			0
$895$	−1.13531	+	1.96642i	−0.0379493	+	0.0657301i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.119171	−	0.206410i	0.00397456	−	0.00688414i
$900$		0			0
$901$	−1.17002	−	2.02653i	−0.0389790	−	0.0675135i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	22.6829			0.754006
$906$		0			0
$907$	7.89155			0.262035			0.131017	−	0.991380i	$-0.458176\pi$
$907$	7.89155			0.262035			0.131017	+	0.991380i	$0.458176\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−14.2206	−	24.6308i	−0.471150	−	0.816055i	0.528306	−	0.849054i	$-0.322827\pi$
$911$	−14.2206	−	24.6308i	−0.471150	−	0.816055i	−0.999455	+	0.0329991i	$0.989494\pi$
$912$		0			0
$913$	4.23813	+	7.34065i	0.140262	+	0.242940i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.12118	+	1.46688i	−0.169116	+	0.0484406i
$918$		0			0
$919$	−3.99271	−	6.91558i	−0.131707	−	0.228124i	0.792627	−	0.609706i	$-0.208713\pi$
$919$	−3.99271	−	6.91558i	−0.131707	−	0.228124i	−0.924335	+	0.381582i	$0.875379\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	31.9110	−	55.2714i	1.05036	−	1.81928i
$924$		0			0
$925$	0.906337	+	1.56982i	0.0298002	+	0.0516154i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	9.40031	−	16.2818i	0.308414	−	0.534189i	−0.669601	−	0.742721i	$-0.733535\pi$
$929$	9.40031	−	16.2818i	0.308414	−	0.534189i	0.978016	+	0.208531i	$0.0668684\pi$
$930$		0			0
$931$	15.4729	+	8.23853i	0.507104	+	0.270007i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.56403	−	2.70898i	0.0511493	−	0.0885932i
$936$		0			0
$937$	48.5788			1.58700			0.793500	−	0.608570i	$-0.208256\pi$
$937$	48.5788			1.58700			0.793500	+	0.608570i	$0.208256\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.2425	+	17.7406i	0.333898	+	0.578328i	0.983272	−	0.182141i	$-0.0583027\pi$
$941$	10.2425	+	17.7406i	0.333898	+	0.578328i	−0.649375	+	0.760468i	$0.724969\pi$
$942$		0			0
$943$	33.2110	−	57.5231i	1.08150	−	1.87321i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.42524	−	12.8609i	0.241288	−	0.417923i	−0.719793	−	0.694188i	$-0.755764\pi$
$947$	7.42524	−	12.8609i	0.241288	−	0.417923i	0.961081	+	0.276265i	$0.0890969\pi$
$948$		0			0
$949$	−7.13954	−	12.3661i	−0.231759	−	0.401419i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−46.4678			−1.50524			−0.752620	−	0.658456i	$-0.771210\pi$
$953$	−46.4678			−1.50524			−0.752620	+	0.658456i	$0.771210\pi$
$954$		0			0
$955$	15.1454	−	26.2326i	0.490094	−	0.848868i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.63988	+	1.61545i	−0.182121	+	0.0521657i
$960$		0			0
$961$	8.09733	−	14.0250i	0.261204	−	0.452419i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	4.12905	+	7.15172i	0.132919	+	0.230222i
$966$		0			0
$967$	−0.863670	+	1.49592i	−0.0277738	+	0.0481056i	−0.879578	−	0.475754i	$-0.842175\pi$
$967$	−0.863670	+	1.49592i	−0.0277738	+	0.0481056i	0.851804	+	0.523860i	$0.175508\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−3.78085	−	6.54863i	−0.121333	−	0.210156i	0.798960	−	0.601384i	$-0.205384\pi$
$971$	−3.78085	−	6.54863i	−0.121333	−	0.210156i	−0.920294	+	0.391228i	$0.872050\pi$
$972$		0			0
$973$	−0.484024	+	1.93894i	−0.0155171	+	0.0621595i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−28.3101	−	49.0345i	−0.905721	−	1.56875i	−0.819947	−	0.572440i	$-0.805997\pi$
$977$	−28.3101	−	49.0345i	−0.905721	−	1.56875i	−0.0857737	−	0.996315i	$-0.527336\pi$
$978$		0			0
$979$	−1.06408	−	1.84305i	−0.0340083	−	0.0589041i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	32.2972			1.03012			0.515061	−	0.857154i	$-0.327769\pi$
$983$	32.2972			1.03012			0.515061	+	0.857154i	$0.327769\pi$
$984$		0			0
$985$	13.0407			0.415510
$986$		0			0
$987$		0			0
$988$		0			0
$989$	37.5391	+	65.0197i	1.19367	+	2.06750i
$990$		0			0
$991$	7.15502	−	12.3929i	0.227287	−	0.393672i	−0.729716	−	0.683750i	$-0.760348\pi$
$991$	7.15502	−	12.3929i	0.227287	−	0.393672i	0.957003	+	0.290078i	$0.0936812\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−5.79247	+	10.0329i	−0.183634	+	0.318063i
$996$		0			0
$997$	56.2524			1.78153			0.890765	−	0.454463i	$-0.150169\pi$
$997$	56.2524			1.78153			0.890765	+	0.454463i	$0.150169\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.i.1873.2		10
3.2	odd	2		1008.2.t.i.193.5		10
4.3	odd	2		189.2.g.b.172.2		10
7.2	even	3		3024.2.q.i.2305.4		10
9.2	odd	6		1008.2.q.i.529.2		10
9.7	even	3		3024.2.q.i.2881.4		10
12.11	even	2		63.2.g.b.4.4	✓	10
21.2	odd	6		1008.2.q.i.625.2		10
28.3	even	6		1323.2.f.f.442.2		10
28.11	odd	6		1323.2.f.e.442.2		10
28.19	even	6		1323.2.h.f.226.4		10
28.23	odd	6		189.2.h.b.37.4		10
28.27	even	2		1323.2.g.f.361.2		10
36.7	odd	6		189.2.h.b.46.4		10
36.11	even	6		63.2.h.b.25.2	yes	10
36.23	even	6		567.2.e.f.487.4		10
36.31	odd	6		567.2.e.e.487.2		10
63.2	odd	6		1008.2.t.i.961.5		10
63.16	even	3	inner	3024.2.t.i.289.2		10
84.11	even	6		441.2.f.e.148.4		10
84.23	even	6		63.2.h.b.58.2	yes	10
84.47	odd	6		441.2.h.f.373.2		10
84.59	odd	6		441.2.f.f.148.4		10
84.83	odd	2		441.2.g.f.67.4		10
252.11	even	6		441.2.f.e.295.4		10
252.23	even	6		567.2.e.f.163.4		10
252.31	even	6		3969.2.a.bb.1.4		5
252.47	odd	6		441.2.g.f.79.4		10
252.59	odd	6		3969.2.a.ba.1.2		5
252.67	odd	6		3969.2.a.bc.1.4		5
252.79	odd	6		189.2.g.b.100.2		10
252.83	odd	6		441.2.h.f.214.2		10
252.95	even	6		3969.2.a.z.1.2		5
252.115	even	6		1323.2.f.f.883.2		10
252.151	odd	6		1323.2.f.e.883.2		10
252.187	even	6		1323.2.g.f.667.2		10
252.191	even	6		63.2.g.b.16.4	yes	10
252.223	even	6		1323.2.h.f.802.4		10
252.227	odd	6		441.2.f.f.295.4		10
252.247	odd	6		567.2.e.e.163.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.4	✓	10	12.11	even	2
63.2.g.b.16.4	yes	10	252.191	even	6
63.2.h.b.25.2	yes	10	36.11	even	6
63.2.h.b.58.2	yes	10	84.23	even	6
189.2.g.b.100.2		10	252.79	odd	6
189.2.g.b.172.2		10	4.3	odd	2
189.2.h.b.37.4		10	28.23	odd	6
189.2.h.b.46.4		10	36.7	odd	6
441.2.f.e.148.4		10	84.11	even	6
441.2.f.e.295.4		10	252.11	even	6
441.2.f.f.148.4		10	84.59	odd	6
441.2.f.f.295.4		10	252.227	odd	6
441.2.g.f.67.4		10	84.83	odd	2
441.2.g.f.79.4		10	252.47	odd	6
441.2.h.f.214.2		10	252.83	odd	6
441.2.h.f.373.2		10	84.47	odd	6
567.2.e.e.163.2		10	252.247	odd	6
567.2.e.e.487.2		10	36.31	odd	6
567.2.e.f.163.4		10	252.23	even	6
567.2.e.f.487.4		10	36.23	even	6
1008.2.q.i.529.2		10	9.2	odd	6
1008.2.q.i.625.2		10	21.2	odd	6
1008.2.t.i.193.5		10	3.2	odd	2
1008.2.t.i.961.5		10	63.2	odd	6
1323.2.f.e.442.2		10	28.11	odd	6
1323.2.f.e.883.2		10	252.151	odd	6
1323.2.f.f.442.2		10	28.3	even	6
1323.2.f.f.883.2		10	252.115	even	6
1323.2.g.f.361.2		10	28.27	even	2
1323.2.g.f.667.2		10	252.187	even	6
1323.2.h.f.226.4		10	28.19	even	6
1323.2.h.f.802.4		10	252.223	even	6
3024.2.q.i.2305.4		10	7.2	even	3
3024.2.q.i.2881.4		10	9.7	even	3
3024.2.t.i.289.2		10	63.16	even	3	inner
3024.2.t.i.1873.2		10	1.1	even	1	trivial
3969.2.a.z.1.2		5	252.95	even	6
3969.2.a.ba.1.2		5	252.59	odd	6
3969.2.a.bb.1.4		5	252.31	even	6
3969.2.a.bc.1.4		5	252.67	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)

\(f(q)\)	\(=\)	\(q-1.33475 q^{5} +(2.54347 - 0.728536i) q^{7} +O(q^{10})\)	\(q-1.33475 q^{5} +(2.54347 - 0.728536i) q^{7} +1.51302 q^{11} +(-2.58800 + 4.48254i) q^{13} +(-0.774463 + 1.34141i) q^{17} +(1.25211 + 2.16872i) q^{19} -7.36079 q^{23} -3.21843 q^{25} +(0.0309713 + 0.0536439i) q^{29} +(-1.92388 - 3.33227i) q^{31} +(-3.39490 + 0.972416i) q^{35} +(-0.281608 - 0.487760i) q^{37} +(-4.51188 + 7.81481i) q^{41} +(-5.09988 - 8.83325i) q^{43} +(4.75925 - 8.24327i) q^{47} +(5.93847 - 3.70602i) q^{49} +(-0.755374 + 1.30835i) q^{53} -2.01950 q^{55} +(4.22166 + 7.31212i) q^{59} +(-1.61958 + 2.80520i) q^{61} +(3.45434 - 5.98309i) q^{65} +(3.46670 + 6.00449i) q^{67} -12.3304 q^{71} +(-1.37936 + 2.38912i) q^{73} +(3.84831 - 1.10229i) q^{77} +(-2.95969 + 5.12633i) q^{79} +(2.80111 + 4.85167i) q^{83} +(1.03372 - 1.79045i) q^{85} +(-0.703287 - 1.21813i) q^{89} +(-3.31680 + 13.2867i) q^{91} +(-1.67126 - 2.89470i) q^{95} +(-6.09713 - 10.5605i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 8 q^{5} + q^{7}+O(q^{10}) \) 10 * q + 8 * q^5 + q^7	\( 10 q + 8 q^{5} + q^{7} - 8 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} - 6 q^{23} + 2 q^{25} - 7 q^{29} + 3 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} + 27 q^{47} + 25 q^{49} + 21 q^{53} - 4 q^{55} + 30 q^{59} - 14 q^{61} + 11 q^{65} + 2 q^{67} - 6 q^{71} + 15 q^{73} + 31 q^{77} + 4 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} - 14 q^{95} - 12 q^{97}+O(q^{100}) \) 10 * q + 8 * q^5 + q^7 - 8 * q^11 - 8 * q^13 - 12 * q^17 - q^19 - 6 * q^23 + 2 * q^25 - 7 * q^29 + 3 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 + 27 * q^47 + 25 * q^49 + 21 * q^53 - 4 * q^55 + 30 * q^59 - 14 * q^61 + 11 * q^65 + 2 * q^67 - 6 * q^71 + 15 * q^73 + 31 * q^77 + 4 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 - 14 * q^95 - 12 * q^97

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