LMFDB - Embedded newform 3024.2.q.i.2881.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.q (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:	$\Z[a_1, \ldots, a_{7}]$
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			2881.4
Root			$0.920620 - 1.59456i$ of defining polynomial
Character	$\chi$	$=$	3024.2881
Dual form			3024.2.q.i.2305.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.667377 - 1.15593i) q^{5} +(-1.90267 - 1.83844i) q^{7} +O(q^{10})$	$q+(0.667377 - 1.15593i) q^{5} +(-1.90267 - 1.83844i) q^{7} +(-0.756508 - 1.31031i) q^{11} +(-2.58800 - 4.48254i) q^{13} +(-0.774463 + 1.34141i) q^{17} +(1.25211 + 2.16872i) q^{19} +(3.68039 - 6.37463i) q^{23} +(1.60922 + 2.78725i) q^{25} +(0.0309713 - 0.0536439i) q^{29} +3.84777 q^{31} +(-3.39490 + 0.972416i) q^{35} +(-0.281608 - 0.487760i) q^{37} +(-4.51188 - 7.81481i) q^{41} +(-5.09988 + 8.83325i) q^{43} -9.51851 q^{47} +(0.240269 + 6.99588i) q^{49} +(-0.755374 + 1.30835i) q^{53} -2.01950 q^{55} -8.44331 q^{59} +3.23917 q^{61} -6.90868 q^{65} -6.93339 q^{67} -12.3304 q^{71} +(-1.37936 + 2.38912i) q^{73} +(-0.969547 + 3.88388i) q^{77} +5.91938 q^{79} +(2.80111 - 4.85167i) q^{83} +(1.03372 + 1.79045i) q^{85} +(-0.703287 - 1.21813i) q^{89} +(-3.31680 + 13.2867i) q^{91} +3.34251 q^{95} +(-6.09713 + 10.5605i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{5} + 4 q^{7}+O(q^{10}) $ 10 * q - 4 * q^5 + 4 * q^7	$ 10 q - 4 q^{5} + 4 q^{7} + 4 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} + 3 q^{23} - q^{25} - 7 q^{29} - 6 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} - 54 q^{47} - 8 q^{49} + 21 q^{53} - 4 q^{55} - 60 q^{59} + 28 q^{61} - 22 q^{65} - 4 q^{67} - 6 q^{71} + 15 q^{73} - 11 q^{77} - 8 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} + 28 q^{95} - 12 q^{97}+O(q^{100}) $ 10 * q - 4 * q^5 + 4 * q^7 + 4 * q^11 - 8 * q^13 - 12 * q^17 - q^19 + 3 * q^23 - q^25 - 7 * q^29 - 6 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 - 54 * q^47 - 8 * q^49 + 21 * q^53 - 4 * q^55 - 60 * q^59 + 28 * q^61 - 22 * q^65 - 4 * q^67 - 6 * q^71 + 15 * q^73 - 11 * q^77 - 8 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 + 28 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	0.667377	−	1.15593i	0.298460	−	0.516948i	−0.677324	−	0.735685i	$-0.736860\pi$
$5$	0.667377	−	1.15593i	0.298460	−	0.516948i	0.975784	+	0.218737i	$0.0701937\pi$
$6$		0			0
$7$	−1.90267	−	1.83844i	−0.719140	−	0.694865i
$7$	−1.90267	−	1.83844i	−0.719140	−	0.694865i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.756508	−	1.31031i	−0.228096	−	0.395073i	0.729148	−	0.684356i	$-0.239917\pi$
$11$	−0.756508	−	1.31031i	−0.228096	−	0.395073i	−0.957244	+	0.289283i	$0.906583\pi$
$12$		0			0
$13$	−2.58800	−	4.48254i	−0.717781	−	1.24323i	−0.961877	−	0.273482i	$-0.911824\pi$
$13$	−2.58800	−	4.48254i	−0.717781	−	1.24323i	0.244096	−	0.969751i	$-0.421509\pi$
$14$		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
$23$	3.68039	−	6.37463i	0.767415	−	1.32920i	−0.171545	−	0.985176i	$-0.554876\pi$
$23$	3.68039	−	6.37463i	0.767415	−	1.32920i	0.938960	−	0.344025i	$-0.111791\pi$
$24$		0			0
$25$	1.60922	+	2.78725i	0.321843	+	0.557449i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.0309713	−	0.0536439i	0.00575123	−	0.00996143i	−0.863135	−	0.504972i	$-0.831503\pi$
$29$	0.0309713	−	0.0536439i	0.00575123	−	0.00996143i	0.868887	+	0.495011i	$0.164836\pi$
$30$		0			0
$31$	3.84777			0.691080			0.345540	−	0.938404i	$-0.387696\pi$
$31$	3.84777			0.691080			0.345540	+	0.938404i	$0.387696\pi$
$32$		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	−0.966822	−	0.255450i	$-0.917776\pi$
$41$	−4.51188	−	7.81481i	−0.704638	−	1.22047i	0.262185	−	0.965018i	$-0.415557\pi$
$42$		0			0
$43$	−5.09988	+	8.83325i	−0.777724	+	1.34706i	0.155526	+	0.987832i	$0.450293\pi$
$43$	−5.09988	+	8.83325i	−0.777724	+	1.34706i	−0.933251	+	0.359226i	$0.883041\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−9.51851			−1.38842			−0.694209	−	0.719774i	$-0.744245\pi$
$47$	−9.51851			−1.38842			−0.694209	+	0.719774i	$0.744245\pi$
$48$		0			0
$49$	0.240269	+	6.99588i	0.0343242	+	0.999411i
$50$		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
$59$	−8.44331			−1.09923			−0.549613	−	0.835419i	$-0.685225\pi$
$59$	−8.44331			−1.09923			−0.549613	+	0.835419i	$0.685225\pi$
$60$		0			0
$61$	3.23917			0.414733			0.207367	−	0.978263i	$-0.433511\pi$
$61$	3.23917			0.414733			0.207367	+	0.978263i	$0.433511\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.90868			−0.856916
$66$		0			0
$67$	−6.93339			−0.847049			−0.423524	−	0.905885i	$-0.639207\pi$
$67$	−6.93339			−0.847049			−0.423524	+	0.905885i	$0.639207\pi$
$68$		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
$77$	−0.969547	+	3.88388i	−0.110490	+	0.442609i
$78$		0			0
$79$	5.91938			0.665982			0.332991	−	0.942930i	$-0.391942\pi$
$79$	5.91938			0.665982			0.332991	+	0.942930i	$0.391942\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.80111	−	4.85167i	0.307462	−	0.532540i	−0.670344	−	0.742050i	$-0.733854\pi$
$83$	2.80111	−	4.85167i	0.307462	−	0.532540i	0.977806	+	0.209510i	$0.0671870\pi$
$84$		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
$95$	3.34251			0.342935
$96$		0			0
$97$	−6.09713	+	10.5605i	−0.619070	+	1.07226i	0.370586	+	0.928798i	$0.379157\pi$
$97$	−6.09713	+	10.5605i	−0.619070	+	1.07226i	−0.989656	+	0.143462i	$0.954176\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.559336	+	0.968798i	0.0556560	+	0.0963990i	0.892511	−	0.451025i	$-0.148942\pi$
$101$	0.559336	+	0.968798i	0.0556560	+	0.0963990i	−0.836855	+	0.547425i	$0.815608\pi$
$102$		0			0
$103$	0.965224	−	1.67182i	0.0951063	−	0.164729i	−0.814547	−	0.580098i	$-0.803014\pi$
$103$	0.965224	−	1.67182i	0.0951063	−	0.164729i	0.909653	+	0.415369i	$0.136348\pi$
$104$		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	−0.974332	−	0.225115i	$-0.927724\pi$
$113$	−7.25105	−	12.5592i	−0.682121	−	1.18147i	0.292211	−	0.956354i	$-0.405609\pi$
$114$		0			0
$115$	−4.91242	−	8.50856i	−0.458085	−	0.793427i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.93965	−	1.12845i	0.361147	−	0.103445i
$120$		0			0
$121$	4.35539	−	7.54376i	0.395945	−	0.685796i
$122$		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
$131$	1.00673	−	1.74371i	0.0879585	−	0.152349i	−0.818690	−	0.574236i	$-0.805299\pi$
$131$	1.00673	−	1.74371i	0.0879585	−	0.152349i	0.906648	+	0.421888i	$0.138632\pi$
$132$		0			0
$133$	1.60471	−	6.42827i	0.139146	−	0.557402i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.10870	+	1.92032i	0.0947225	+	0.164064i	0.909493	−	0.415720i	$-0.136470\pi$
$137$	1.10870	+	1.92032i	0.0947225	+	0.164064i	−0.814770	+	0.579784i	$0.803137\pi$
$138$		0			0
$139$	−0.377669	−	0.654143i	−0.0320335	−	0.0554836i	0.849564	−	0.527485i	$-0.176865\pi$
$139$	−0.377669	−	0.654143i	−0.0320335	−	0.0554836i	−0.881598	+	0.472002i	$0.843532\pi$
$140$		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
$149$	3.29249	−	5.70277i	0.269732	−	0.467189i	−0.699061	−	0.715062i	$-0.746398\pi$
$149$	3.29249	−	5.70277i	0.269732	−	0.467189i	0.968792	+	0.247873i	$0.0797317\pi$
$150$		0			0
$151$	6.33356	+	10.9700i	0.515417	+	0.892729i	0.999840	+	0.0178950i	$0.00569645\pi$
$151$	6.33356	+	10.9700i	0.515417	+	0.892729i	−0.484422	+	0.874834i	$0.660970\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.56791	−	4.44775i	0.206260	−	0.357252i
$156$		0			0
$157$	−17.3074			−1.38128			−0.690642	−	0.723197i	$-0.742672\pi$
$157$	−17.3074			−1.38128			−0.690642	+	0.723197i	$0.742672\pi$
$158$		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	0.926126	−	0.377215i	$-0.123118\pi$
$167$	1.76248	+	3.05270i	0.136385	+	0.236225i	−0.789741	+	0.613440i	$0.789785\pi$
$168$		0			0
$169$	−6.89546	+	11.9433i	−0.530420	+	0.918714i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−10.1409			−0.770999			−0.385500	−	0.922708i	$-0.625971\pi$
$173$	−10.1409			−0.770999			−0.385500	+	0.922708i	$0.625971\pi$
$174$		0			0
$175$	2.06239	−	8.26164i	0.155902	−	0.624522i
$176$		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
$185$	−0.751755			−0.0552701
$186$		0			0
$187$	2.34355			0.171377
$188$		0			0
$189$		0			0
$190$		0			0
$191$	22.6939			1.64208			0.821038	−	0.570873i	$-0.193395\pi$
$191$	22.6939			1.64208			0.821038	+	0.570873i	$0.193395\pi$
$192$		0			0
$193$	6.18698			0.445348			0.222674	−	0.974893i	$-0.428521\pi$
$193$	6.18698			0.445348			0.222674	+	0.974893i	$0.428521\pi$
$194$		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
$203$	−0.157549	+	0.0451275i	−0.0110578	+	0.00316733i
$204$		0			0
$205$	−12.0445			−0.841224
$206$		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	0.947118	−	0.320885i	$-0.103980\pi$
$211$	2.84219	+	4.92283i	0.195665	+	0.338901i	−0.751453	+	0.659786i	$0.770647\pi$
$212$		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
$221$	8.01723			0.539298
$222$		0			0
$223$	−5.86133	+	10.1521i	−0.392503	+	0.679836i	−0.992779	−	0.119957i	$-0.961724\pi$
$223$	−5.86133	+	10.1521i	−0.392503	+	0.679836i	0.600276	+	0.799793i	$0.295058\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.59154	−	9.68482i	−0.371123	−	0.642804i	0.618615	−	0.785694i	$-0.287694\pi$
$227$	−5.59154	−	9.68482i	−0.371123	−	0.642804i	−0.989739	+	0.142890i	$0.954361\pi$
$228$		0			0
$229$	4.82824	−	8.36275i	0.319059	−	0.552626i	−0.661233	−	0.750181i	$-0.729967\pi$
$229$	4.82824	−	8.36275i	0.319059	−	0.552626i	0.980292	+	0.197554i	$0.0632999\pi$
$230$		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	0.859662	−	0.510864i	$-0.170674\pi$
$239$	−0.194641	−	0.337128i	−0.0125903	−	0.0218070i	−0.872252	+	0.489057i	$0.837341\pi$
$240$		0			0
$241$	−5.31807	−	9.21117i	−0.342567	−	0.593344i	0.642342	−	0.766419i	$-0.277963\pi$
$241$	−5.31807	−	9.21117i	−0.342567	−	0.593344i	−0.984909	+	0.173075i	$0.944630\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.24709	+	4.39115i	0.526888	+	0.280540i
$246$		0			0
$247$	6.48091	−	11.2253i	0.412370	−	0.714247i
$248$		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
$257$	−2.34787	+	4.06663i	−0.146456	+	0.253669i	−0.929915	−	0.367774i	$-0.880120\pi$
$257$	−2.34787	+	4.06663i	−0.146456	+	0.253669i	0.783459	+	0.621443i	$0.213453\pi$
$258$		0			0
$259$	−0.360911	+	1.44576i	−0.0224259	+	0.0898354i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−9.77491	−	16.9306i	−0.602747	−	1.04399i	−0.992403	−	0.123028i	$-0.960740\pi$
$263$	−9.77491	−	16.9306i	−0.602747	−	1.04399i	0.389656	−	0.920960i	$-0.372594\pi$
$264$		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
$275$	2.43477	−	4.21715i	0.146822	−	0.254304i
$276$		0			0
$277$	3.72561	+	6.45295i	0.223850	+	0.387720i	0.955974	−	0.293452i	$-0.0948040\pi$
$277$	3.72561	+	6.45295i	0.223850	+	0.387720i	−0.732124	+	0.681172i	$0.761471\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	12.9938	−	22.5060i	0.775146	−	1.34259i	−0.159566	−	0.987187i	$-0.551009\pi$
$281$	12.9938	−	22.5060i	0.775146	−	1.34259i	0.934712	−	0.355406i	$-0.115657\pi$
$282$		0			0
$283$	−18.7554			−1.11489			−0.557445	−	0.830214i	$-0.688218\pi$
$283$	−18.7554			−1.11489			−0.557445	+	0.830214i	$0.688218\pi$
$284$		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	0.899738	−	0.436430i	$-0.143757\pi$
$293$	1.23089	+	2.13196i	0.0719093	+	0.124551i	−0.827829	+	0.560981i	$0.810424\pi$
$294$		0			0
$295$	−5.63487	+	9.75988i	−0.328075	+	0.568242i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−38.0994			−2.20334
$300$		0			0
$301$	25.9428	−	7.43089i	1.49532	−	0.428309i
$302$		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
$311$	27.4821			1.55837			0.779183	−	0.626797i	$-0.215634\pi$
$311$	27.4821			1.55837			0.779183	+	0.626797i	$0.215634\pi$
$312$		0			0
$313$	5.49332			0.310501			0.155250	−	0.987875i	$-0.450382\pi$
$313$	5.49332			0.310501			0.155250	+	0.987875i	$0.450382\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.87758			−0.554780			−0.277390	−	0.960757i	$-0.589469\pi$
$317$	−9.87758			−0.554780			−0.277390	+	0.960757i	$0.589469\pi$
$318$		0			0
$319$	−0.0937203			−0.00524733
$320$		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
$329$	18.1105	+	17.4992i	0.998466	+	0.964763i
$330$		0			0
$331$	20.6942			1.13746			0.568729	−	0.822525i	$-0.307435\pi$
$331$	20.6942			1.13746			0.568729	+	0.822525i	$0.307435\pi$
$332$		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	0.885698	−	0.464261i	$-0.153680\pi$
$337$	0.748747	+	1.29687i	0.0407869	+	0.0706449i	−0.844911	+	0.534906i	$0.820347\pi$
$338$		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
$347$	−29.5388			−1.58572			−0.792862	−	0.609401i	$-0.791410\pi$
$347$	−29.5388			−1.58572			−0.792862	+	0.609401i	$0.791410\pi$
$348$		0			0
$349$	18.0006	−	31.1780i	0.963551	−	1.66892i	0.250094	−	0.968222i	$-0.419539\pi$
$349$	18.0006	−	31.1780i	0.963551	−	1.66892i	0.713458	−	0.700698i	$-0.247128\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.7465	−	25.5417i	−0.784877	−	1.35945i	−0.929073	−	0.369897i	$-0.879393\pi$
$353$	−14.7465	−	25.5417i	−0.784877	−	1.35945i	0.144196	−	0.989549i	$-0.453940\pi$
$354$		0			0
$355$	−8.22900	+	14.2530i	−0.436750	+	0.756473i
$356$		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
$367$	−11.5422	−	19.9916i	−0.602496	−	1.04355i	−0.992442	−	0.122715i	$-0.960840\pi$
$367$	−11.5422	−	19.9916i	−0.602496	−	1.04355i	0.389946	−	0.920838i	$-0.372494\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.84254	−	1.10063i	0.199495	−	0.0571421i
$372$		0			0
$373$	−10.7515	+	18.6222i	−0.556692	+	0.964219i	0.441078	+	0.897469i	$0.354596\pi$
$373$	−10.7515	+	18.6222i	−0.556692	+	0.964219i	−0.997770	+	0.0667498i	$0.978737\pi$
$374$		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
$383$	17.4604	−	30.2424i	0.892187	−	1.54531i	0.0549390	−	0.998490i	$-0.482504\pi$
$383$	17.4604	−	30.2424i	0.892187	−	1.54531i	0.837248	−	0.546823i	$-0.184163\pi$
$384$		0			0
$385$	3.84244	+	3.71274i	0.195829	+	0.189219i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−14.4411	−	25.0127i	−0.732192	−	1.26819i	−0.955944	−	0.293548i	$-0.905164\pi$
$389$	−14.4411	−	25.0127i	−0.732192	−	1.26819i	0.223752	−	0.974646i	$-0.428169\pi$
$390$		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
$401$	−0.541061	+	0.937146i	−0.0270193	+	0.0467988i	−0.879219	−	0.476418i	$-0.841935\pi$
$401$	−0.541061	+	0.937146i	−0.0270193	+	0.0467988i	0.852200	+	0.523217i	$0.175268\pi$
$402$		0			0
$403$	−9.95802	−	17.2478i	−0.496044	−	0.859174i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.426078	+	0.737988i	−0.0211199	+	0.0365807i
$408$		0			0
$409$	−21.7349			−1.07472			−0.537360	−	0.843353i	$-0.680578\pi$
$409$	−21.7349			−1.07472			−0.537360	+	0.843353i	$0.680578\pi$
$410$		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	0.990369	+	0.138455i	$0.0442135\pi$
$419$	12.5906	+	21.8075i	0.615090	+	1.06537i	−0.375279	+	0.926912i	$0.622453\pi$
$420$		0			0
$421$	−14.8304	+	25.6869i	−0.722788	+	1.25191i	0.237090	+	0.971488i	$0.423806\pi$
$421$	−14.8304	+	25.6869i	−0.722788	+	1.25191i	−0.959878	+	0.280418i	$0.909527\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.98512			−0.241814
$426$		0			0
$427$	−6.16305	−	5.95502i	−0.298251	−	0.288184i
$428$		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
$437$	18.4330			0.881771
$438$		0			0
$439$	14.8235			0.707488			0.353744	−	0.935342i	$-0.384908\pi$
$439$	14.8235			0.707488			0.353744	+	0.935342i	$0.384908\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−21.9020			−1.04059			−0.520297	−	0.853986i	$-0.674179\pi$
$443$	−21.9020			−1.04059			−0.520297	+	0.853986i	$0.674179\pi$
$444$		0			0
$445$	−1.87743			−0.0889987
$446$		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
$455$	13.1449	+	12.7012i	0.616242	+	0.595441i
$456$		0			0
$457$	40.6255			1.90038			0.950190	−	0.311670i	$-0.100888\pi$
$457$	40.6255			1.90038			0.950190	+	0.311670i	$0.100888\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.41541	+	2.45155i	−0.0659220	+	0.114180i	−0.897103	−	0.441822i	$-0.854332\pi$
$461$	−1.41541	+	2.45155i	−0.0659220	+	0.114180i	0.831181	+	0.556003i	$0.187666\pi$
$462$		0			0
$463$	13.9324	+	24.1317i	0.647494	+	1.12149i	0.983719	+	0.179711i	$0.0575164\pi$
$463$	13.9324	+	24.1317i	0.647494	+	1.12149i	−0.336225	+	0.941782i	$0.609150\pi$
$464$		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
$473$	15.4324			0.709582
$474$		0			0
$475$	−4.02983	+	6.97987i	−0.184901	+	0.320258i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	15.7895	+	27.3483i	0.721443	+	1.24958i	0.960422	+	0.278551i	$0.0898540\pi$
$479$	15.7895	+	27.3483i	0.721443	+	1.24958i	−0.238979	+	0.971025i	$0.576813\pi$
$480$		0			0
$481$	−1.45760	+	2.52464i	−0.0664609	+	0.115114i
$482$		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	0.585498	−	0.810674i	$-0.300899\pi$
$491$	−9.06981	−	15.7094i	−0.409315	−	0.708954i	−0.994813	+	0.101720i	$0.967566\pi$
$492$		0			0
$493$	0.0479723	+	0.0830905i	0.00216057	+	0.00374221i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	23.4606	+	22.6687i	1.05235	+	1.01683i
$498$		0			0
$499$	−10.6546	+	18.4543i	−0.476964	+	0.826126i	−0.999652	−	0.0263983i	$-0.991596\pi$
$499$	−10.6546	+	18.4543i	−0.476964	+	0.826126i	0.522687	+	0.852524i	$0.324930\pi$
$500$		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
$509$	18.3868	−	31.8468i	0.814979	−	1.41159i	−0.0943635	−	0.995538i	$-0.530082\pi$
$509$	18.3868	−	31.8468i	0.814979	−	1.41159i	0.909343	−	0.416048i	$-0.136585\pi$
$510$		0			0
$511$	7.01670	−	2.00982i	0.310401	−	0.0889093i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.28834	−	2.23146i	−0.0567709	−	0.0983300i
$516$		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
$527$	−2.97996	+	5.16144i	−0.129809	+	0.224836i
$528$		0			0
$529$	−15.5906	−	27.0037i	−0.677851	−	1.17407i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−23.3535	+	40.4494i	−1.01155	+	1.75206i
$534$		0			0
$535$	7.71405			0.333507
$536$		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	−0.894160	−	0.447747i	$-0.852227\pi$
$547$	−1.38738	+	2.40301i	−0.0593201	+	0.102745i	0.834840	+	0.550492i	$0.185560\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.155118			0.00660825
$552$		0			0
$553$	−11.2626	−	10.8824i	−0.478935	−	0.462768i
$554$		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
$563$	0.288041			0.0121395			0.00606973	−	0.999982i	$-0.498068\pi$
$563$	0.288041			0.0121395			0.00606973	+	0.999982i	$0.498068\pi$
$564$		0			0
$565$	−19.3567			−0.814344
$566$		0			0
$567$		0			0
$568$		0			0
$569$	16.0801			0.674112			0.337056	−	0.941485i	$-0.390569\pi$
$569$	16.0801			0.674112			0.337056	+	0.941485i	$0.390569\pi$
$570$		0			0
$571$	15.2858			0.639690			0.319845	−	0.947470i	$-0.396369\pi$
$571$	15.2858			0.639690			0.319845	+	0.947470i	$0.396369\pi$
$572$		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
$581$	−14.2491	+	4.08142i	−0.591152	+	0.169326i
$582$		0			0
$583$	2.28579			0.0946676
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.0145	−	31.2020i	0.743537	−	1.28784i	−0.207339	−	0.978269i	$-0.566480\pi$
$587$	18.0145	−	31.2020i	0.743537	−	1.28784i	0.950875	−	0.309574i	$-0.100186\pi$
$588$		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
$599$	39.5283			1.61508			0.807542	−	0.589810i	$-0.200797\pi$
$599$	39.5283			1.61508			0.807542	+	0.589810i	$0.200797\pi$
$600$		0			0
$601$	1.86447	−	3.22936i	0.0760534	−	0.131728i	−0.825490	−	0.564416i	$-0.809101\pi$
$601$	1.86447	−	3.22936i	0.0760534	−	0.131728i	0.901544	+	0.432688i	$0.142435\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.81337	−	10.0691i	−0.236347	−	0.409365i
$606$		0			0
$607$	11.8264	−	20.4839i	0.480018	−	0.831415i	−0.519719	−	0.854337i	$-0.673964\pi$
$607$	11.8264	−	20.4839i	0.480018	−	0.831415i	0.999737	+	0.0229218i	$0.00729686\pi$
$608$		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	0.965965	+	0.258672i	$0.0832849\pi$
$617$	17.5615	+	30.4174i	0.706999	+	1.22456i	−0.258966	+	0.965886i	$0.583382\pi$
$618$		0			0
$619$	−10.5816	−	18.3279i	−0.425311	−	0.736660i	0.571138	−	0.820854i	$-0.306502\pi$
$619$	−10.5816	−	18.3279i	−0.425311	−	0.736660i	−0.996449	+	0.0841934i	$0.973169\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.901339	+	3.61064i	−0.0361114	+	0.144657i
$624$		0			0
$625$	−0.725240	+	1.25615i	−0.0290096	+	0.0502461i
$626$		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
$635$	−5.67273	+	9.82546i	−0.225115	+	0.389911i
$636$		0			0
$637$	30.7375	−	19.1823i	1.21786	−	0.760031i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−4.93735	−	8.55174i	−0.195013	−	0.337773i	0.751891	−	0.659287i	$-0.229142\pi$
$641$	−4.93735	−	8.55174i	−0.195013	−	0.337773i	−0.946905	+	0.321514i	$0.895808\pi$
$642$		0			0
$643$	−21.9748	−	38.0615i	−0.866602	−	1.50100i	−0.865448	−	0.501000i	$-0.832966\pi$
$643$	−21.9748	−	38.0615i	−0.866602	−	1.50100i	−0.00115462	−	0.999999i	$-0.500368\pi$
$644$		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
$653$	20.9956	−	36.3655i	0.821622	−	1.42309i	−0.0828523	−	0.996562i	$-0.526403\pi$
$653$	20.9956	−	36.3655i	0.821622	−	1.42309i	0.904474	−	0.426529i	$-0.140264\pi$
$654$		0			0
$655$	−1.34374	−	2.32742i	−0.0525042	−	0.0909399i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19.6365	+	34.0114i	−0.764928	+	1.32489i	0.175356	+	0.984505i	$0.443892\pi$
$659$	−19.6365	+	34.0114i	−0.764928	+	1.32489i	−0.940284	+	0.340390i	$0.889441\pi$
$660$		0			0
$661$	−0.186739			−0.00726330			−0.00363165	−	0.999993i	$-0.501156\pi$
$661$	−0.186739			−0.00726330			−0.00363165	+	0.999993i	$0.501156\pi$
$662$		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	−0.951544	−	0.307512i	$-0.900503\pi$
$673$	−5.43382	+	9.41166i	−0.209458	+	0.362793i	0.742086	+	0.670305i	$0.233837\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−28.3901			−1.09112			−0.545560	−	0.838072i	$-0.683683\pi$
$677$	−28.3901			−1.09112			−0.545560	+	0.838072i	$0.683683\pi$
$678$		0			0
$679$	31.0157	−	8.88396i	1.19027	−	0.340935i
$680$		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
$689$	7.81962			0.297904
$690$		0			0
$691$	−11.9083			−0.453014			−0.226507	−	0.974010i	$-0.572731\pi$
$691$	−11.9083			−0.453014			−0.226507	+	0.974010i	$0.572731\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.00819			−0.0382429
$696$		0			0
$697$	13.9771			0.529422
$698$		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
$707$	0.716849	−	2.87160i	0.0269599	−	0.107998i
$708$		0			0
$709$	0.625218			0.0234806			0.0117403	−	0.999931i	$-0.496263\pi$
$709$	0.625218			0.0234806			0.0117403	+	0.999931i	$0.496263\pi$
$710$		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
$725$	0.199358			0.00740399
$726$		0			0
$727$	18.9253	−	32.7796i	0.701900	−	1.21573i	−0.265899	−	0.964001i	$-0.585669\pi$
$727$	18.9253	−	32.7796i	0.701900	−	1.21573i	0.967799	−	0.251726i	$-0.0809980\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−7.89934	−	13.6821i	−0.292168	−	0.506049i
$732$		0			0
$733$	−1.20077	+	2.07980i	−0.0443516	+	0.0768193i	−0.887349	−	0.461098i	$-0.847456\pi$
$733$	−1.20077	+	2.07980i	−0.0443516	+	0.0768193i	0.842997	+	0.537918i	$0.180789\pi$
$734$		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	0.815498	−	0.578760i	$-0.196463\pi$
$743$	−2.54785	−	4.41300i	−0.0934715	−	0.161897i	−0.908970	+	0.416862i	$0.863130\pi$
$744$		0			0
$745$	−4.39467	−	7.61179i	−0.161008	−	0.278874i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.70345	−	14.8355i	0.135321	−	0.542079i
$750$		0			0
$751$	−0.487506	+	0.844384i	−0.0177893	+	0.0308120i	−0.874783	−	0.484515i	$-0.838996\pi$
$751$	−0.487506	+	0.844384i	−0.0177893	+	0.0308120i	0.856994	+	0.515327i	$0.172329\pi$
$752$		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
$761$	−27.0875	+	46.9169i	−0.981920	+	1.70073i	−0.327023	+	0.945016i	$0.606045\pi$
$761$	−27.0875	+	46.9169i	−0.981920	+	1.70073i	−0.654897	+	0.755718i	$0.727288\pi$
$762$		0			0
$763$	20.9636	−	6.00468i	0.758932	−	0.217384i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	21.8513	+	37.8475i	0.789004	+	1.36659i
$768$		0			0
$769$	−10.4326	−	18.0698i	−0.376208	−	0.651612i	0.614299	−	0.789074i	$-0.289439\pi$
$769$	−10.4326	−	18.0698i	−0.376208	−	0.651612i	−0.990507	+	0.137462i	$0.956106\pi$
$770$		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
$779$	11.2987	−	19.5700i	0.404819	−	0.701168i
$780$		0			0
$781$	9.32802	+	16.1566i	0.333783	+	0.578129i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−11.5506	+	20.0062i	−0.412258	+	0.714051i
$786$		0			0
$787$	−9.18949			−0.327570			−0.163785	−	0.986496i	$-0.552370\pi$
$787$	−9.18949			−0.327570			−0.163785	+	0.986496i	$0.552370\pi$
$788$		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	0.796542	−	0.604583i	$-0.206660\pi$
$797$	−3.53774	−	6.12754i	−0.125313	−	0.217049i	−0.921855	+	0.387534i	$0.873327\pi$
$798$		0			0
$799$	7.37174	−	12.7682i	0.260793	−	0.451707i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.17398			0.147297
$804$		0			0
$805$	−6.29579	+	25.2201i	−0.221898	+	0.888892i
$806$		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
$815$	−16.3097			−0.571304
$816$		0			0
$817$	−25.5424			−0.893616
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6.35522			−0.221799			−0.110899	−	0.993832i	$-0.535373\pi$
$821$	−6.35522			−0.221799			−0.110899	+	0.993832i	$0.535373\pi$
$822$		0			0
$823$	9.46433			0.329906			0.164953	−	0.986301i	$-0.447253\pi$
$823$	9.46433			0.329906			0.164953	+	0.986301i	$0.447253\pi$
$824$		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
$833$	−9.57041	−	5.09575i	−0.331595	−	0.176557i
$834$		0			0
$835$	4.70494			0.162821
$836$		0			0
$837$		0			0
$838$		0			0
$839$	9.60171	−	16.6307i	0.331488	−	0.574154i	−0.651316	−	0.758807i	$-0.725783\pi$
$839$	9.60171	−	16.6307i	0.331488	−	0.574154i	0.982804	+	0.184653i	$0.0591161\pi$
$840$		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
$851$	−4.14571			−0.142113
$852$		0			0
$853$	−6.95055	+	12.0387i	−0.237982	+	0.412198i	−0.960135	−	0.279536i	$-0.909819\pi$
$853$	−6.95055	+	12.0387i	−0.237982	+	0.412198i	0.722153	+	0.691734i	$0.243153\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	28.4919	+	49.3494i	0.973265	+	1.68574i	0.685547	+	0.728029i	$0.259563\pi$
$857$	28.4919	+	49.3494i	0.973265	+	1.68574i	0.287718	+	0.957715i	$0.407103\pi$
$858$		0			0
$859$	−10.0501	+	17.4073i	−0.342905	+	0.593929i	−0.984971	−	0.172721i	$-0.944744\pi$
$859$	−10.0501	+	17.4073i	−0.342905	+	0.593929i	0.642066	+	0.766650i	$0.278078\pi$
$860$		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
$871$	17.9436	+	31.0792i	0.607996	+	1.05308i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−20.8714	−	20.1669i	−0.705583	−	0.681767i
$876$		0			0
$877$	18.6287	−	32.2658i	0.629046	−	1.08954i	−0.358697	−	0.933454i	$-0.616779\pi$
$877$	18.6287	−	32.2658i	0.629046	−	1.08954i	0.987743	−	0.156086i	$-0.0498877\pi$
$878$		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
$887$	−14.2581	+	24.6957i	−0.478739	+	0.829201i	−0.999703	−	0.0243782i	$-0.992239\pi$
$887$	−14.2581	+	24.6957i	−0.478739	+	0.829201i	0.520964	+	0.853579i	$0.325573\pi$
$888$		0			0
$889$	16.1727	+	15.6268i	0.542416	+	0.524107i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−11.9182	−	20.6430i	−0.398828	−	0.690790i
$894$		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
$905$	−11.3415	+	19.6440i	−0.377003	+	0.652989i
$906$		0			0
$907$	−3.94577	−	6.83428i	−0.131017	−	0.226929i	0.793052	−	0.609154i	$-0.208491\pi$
$907$	−3.94577	−	6.83428i	−0.131017	−	0.226929i	−0.924069	+	0.382226i	$0.875158\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−14.2206	+	24.6308i	−0.471150	+	0.816055i	−0.999455	−	0.0329991i	$-0.989494\pi$
$911$	−14.2206	+	24.6308i	−0.471150	+	0.816055i	0.528306	+	0.849054i	$0.322827\pi$
$912$		0			0
$913$	−8.47625			−0.280523
$914$		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
$929$	−18.8006			−0.616829			−0.308414	−	0.951252i	$-0.599798\pi$
$929$	−18.8006			−0.616829			−0.308414	+	0.951252i	$0.599798\pi$
$930$		0			0
$931$	−14.8712	+	9.28068i	−0.487385	+	0.304162i
$932$		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
$941$	−20.4851			−0.667795			−0.333898	−	0.942609i	$-0.608364\pi$
$941$	−20.4851			−0.667795			−0.333898	+	0.942609i	$0.608364\pi$
$942$		0			0
$943$	−66.4220			−2.16300
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.8505			−0.482576			−0.241288	−	0.970454i	$-0.577570\pi$
$947$	−14.8505			−0.482576			−0.241288	+	0.970454i	$0.577570\pi$
$948$		0			0
$949$	14.2791			0.463519
$950$		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
$959$	1.42092	−	5.69201i	0.0458838	−	0.183804i
$960$		0			0
$961$	−16.1947			−0.522409
$962$		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	0.851804	−	0.523860i	$-0.175508\pi$
$967$	−0.863670	−	1.49592i	−0.0277738	−	0.0481056i	−0.879578	+	0.475754i	$0.842175\pi$
$968$		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
$977$	56.6202			1.81144			0.905721	−	0.423875i	$-0.139330\pi$
$977$	56.6202			1.81144			0.905721	+	0.423875i	$0.139330\pi$
$978$		0			0
$979$	−1.06408	+	1.84305i	−0.0340083	+	0.0589041i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−16.1486	−	27.9702i	−0.515061	−	0.892112i	−0.999847	−	0.0174790i	$-0.994436\pi$
$983$	−16.1486	−	27.9702i	−0.515061	−	0.892112i	0.484786	−	0.874633i	$-0.338897\pi$
$984$		0			0
$985$	−6.52033	+	11.2936i	−0.207755	+	0.359842i
$986$		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
$997$	−28.1262	−	48.7160i	−0.890765	−	1.54285i	−0.838960	−	0.544194i	$-0.816836\pi$
$997$	−28.1262	−	48.7160i	−0.890765	−	1.54285i	−0.0518058	−	0.998657i	$-0.516498\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.4	✓	10	36.23	even	6
63.2.g.b.16.4	yes	10	84.23	even	6
63.2.h.b.25.2	yes	10	12.11	even	2
63.2.h.b.58.2	yes	10	252.23	even	6
189.2.g.b.100.2		10	28.23	odd	6
189.2.g.b.172.2		10	36.31	odd	6
189.2.h.b.37.4		10	252.247	odd	6
189.2.h.b.46.4		10	4.3	odd	2
441.2.f.e.148.4		10	252.95	even	6
441.2.f.e.295.4		10	84.11	even	6
441.2.f.f.148.4		10	252.59	odd	6
441.2.f.f.295.4		10	84.59	odd	6
441.2.g.f.67.4		10	252.167	odd	6
441.2.g.f.79.4		10	84.47	odd	6
441.2.h.f.214.2		10	84.83	odd	2
441.2.h.f.373.2		10	252.131	odd	6
567.2.e.e.163.2		10	252.79	odd	6
567.2.e.e.487.2		10	36.7	odd	6
567.2.e.f.163.4		10	252.191	even	6
567.2.e.f.487.4		10	36.11	even	6
1008.2.q.i.529.2		10	3.2	odd	2
1008.2.q.i.625.2		10	63.23	odd	6
1008.2.t.i.193.5		10	9.5	odd	6
1008.2.t.i.961.5		10	21.2	odd	6
1323.2.f.e.442.2		10	252.67	odd	6
1323.2.f.e.883.2		10	28.11	odd	6
1323.2.f.f.442.2		10	252.31	even	6
1323.2.f.f.883.2		10	28.3	even	6
1323.2.g.f.361.2		10	252.139	even	6
1323.2.g.f.667.2		10	28.19	even	6
1323.2.h.f.226.4		10	252.103	even	6
1323.2.h.f.802.4		10	28.27	even	2
3024.2.q.i.2305.4		10	63.58	even	3	inner
3024.2.q.i.2881.4		10	1.1	even	1	trivial
3024.2.t.i.289.2		10	7.2	even	3
3024.2.t.i.1873.2		10	9.4	even	3
3969.2.a.z.1.2		5	252.11	even	6
3969.2.a.ba.1.2		5	252.227	odd	6
3969.2.a.bb.1.4		5	252.115	even	6
3969.2.a.bc.1.4		5	252.151	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.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.667377 - 1.15593i) q^{5} +(-1.90267 - 1.83844i) q^{7} +O(q^{10})\)	\(q+(0.667377 - 1.15593i) q^{5} +(-1.90267 - 1.83844i) q^{7} +(-0.756508 - 1.31031i) q^{11} +(-2.58800 - 4.48254i) q^{13} +(-0.774463 + 1.34141i) q^{17} +(1.25211 + 2.16872i) q^{19} +(3.68039 - 6.37463i) q^{23} +(1.60922 + 2.78725i) q^{25} +(0.0309713 - 0.0536439i) q^{29} +3.84777 q^{31} +(-3.39490 + 0.972416i) q^{35} +(-0.281608 - 0.487760i) q^{37} +(-4.51188 - 7.81481i) q^{41} +(-5.09988 + 8.83325i) q^{43} -9.51851 q^{47} +(0.240269 + 6.99588i) q^{49} +(-0.755374 + 1.30835i) q^{53} -2.01950 q^{55} -8.44331 q^{59} +3.23917 q^{61} -6.90868 q^{65} -6.93339 q^{67} -12.3304 q^{71} +(-1.37936 + 2.38912i) q^{73} +(-0.969547 + 3.88388i) q^{77} +5.91938 q^{79} +(2.80111 - 4.85167i) q^{83} +(1.03372 + 1.79045i) q^{85} +(-0.703287 - 1.21813i) q^{89} +(-3.31680 + 13.2867i) q^{91} +3.34251 q^{95} +(-6.09713 + 10.5605i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{5} + 4 q^{7}+O(q^{10}) \) 10 * q - 4 * q^5 + 4 * q^7	\( 10 q - 4 q^{5} + 4 q^{7} + 4 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} + 3 q^{23} - q^{25} - 7 q^{29} - 6 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} - 54 q^{47} - 8 q^{49} + 21 q^{53} - 4 q^{55} - 60 q^{59} + 28 q^{61} - 22 q^{65} - 4 q^{67} - 6 q^{71} + 15 q^{73} - 11 q^{77} - 8 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} + 28 q^{95} - 12 q^{97}+O(q^{100}) \) 10 * q - 4 * q^5 + 4 * q^7 + 4 * q^11 - 8 * q^13 - 12 * q^17 - q^19 + 3 * q^23 - q^25 - 7 * q^29 - 6 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 - 54 * q^47 - 8 * q^49 + 21 * q^53 - 4 * q^55 - 60 * q^59 + 28 * q^61 - 22 * q^65 - 4 * q^67 - 6 * q^71 + 15 * q^73 - 11 * q^77 - 8 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 + 28 * q^95 - 12 * q^97

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