LMFDB - Embedded newform 3024.2.cc.c.881.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(881,3024)]

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, 5, 3]))

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

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

chi := DirichletCharacter("3024.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 $ x^16 - 3x^14 - 9x^12 - 9x^10 + 225x^8 - 81x^6 - 729x^4 - 2187*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.3
Root			$-0.744857 + 1.56371i$ of defining polynomial
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.c.2897.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.276914 + 0.479629i) q^{5} +(1.98718 + 1.74675i) q^{7} +O(q^{10})$	$q+(-0.276914 + 0.479629i) q^{5} +(1.98718 + 1.74675i) q^{7} +(4.03478 - 2.32948i) q^{11} +(3.58265 + 2.06844i) q^{13} +7.24527 q^{17} -6.71715i q^{19} +(-4.85295 - 2.80185i) q^{23} +(2.34664 + 4.06450i) q^{25} +(-1.16599 + 0.673187i) q^{29} +(0.830741 + 0.479629i) q^{31} +(-1.38807 + 0.469409i) q^{35} -7.06956 q^{37} +(2.39152 - 4.14224i) q^{41} +(1.02846 + 1.78135i) q^{43} +(-4.90301 - 8.49226i) q^{47} +(0.897752 + 6.94219i) q^{49} -8.43202i q^{53} +2.58026i q^{55} +(3.89955 - 6.75422i) q^{59} +(-5.37336 + 3.10231i) q^{61} +(-1.98417 + 1.14556i) q^{65} +(-1.68814 + 2.92394i) q^{67} +0.407556i q^{71} +8.63566i q^{73} +(12.0868 + 2.41864i) q^{77} +(0.318176 + 0.551097i) q^{79} +(2.78840 + 4.82965i) q^{83} +(-2.00632 + 3.47504i) q^{85} +6.93137 q^{89} +(3.50632 + 10.3683i) q^{91} +(3.22174 + 1.86007i) q^{95} +(7.48798 - 4.32318i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{7}+O(q^{10}) $ 16 * q + q^7	$ 16 q + q^{7} + 6 q^{11} + 6 q^{23} - 8 q^{25} + 12 q^{29} + 4 q^{37} - 4 q^{43} - 5 q^{49} + 24 q^{65} - 14 q^{67} + 21 q^{77} - 20 q^{79} + 6 q^{85} + 18 q^{91} - 60 q^{95}+O(q^{100}) $ 16 * q + q^7 + 6 * q^11 + 6 * q^23 - 8 * q^25 + 12 * q^29 + 4 * q^37 - 4 * q^43 - 5 * q^49 + 24 * q^65 - 14 * q^67 + 21 * q^77 - 20 * q^79 + 6 * q^85 + 18 * q^91 - 60 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.276914	+	0.479629i	−0.123840	+	0.214496i	−0.921279	−	0.388903i	$-0.872854\pi$
$5$	−0.276914	+	0.479629i	−0.123840	+	0.214496i	0.797439	+	0.603399i	$0.206187\pi$
$6$		0			0
$7$	1.98718	+	1.74675i	0.751083	+	0.660208i
$7$	1.98718	+	1.74675i	0.751083	+	0.660208i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.03478	−	2.32948i	1.21653	−	0.702365i	0.252357	−	0.967634i	$-0.418794\pi$
$11$	4.03478	−	2.32948i	1.21653	−	0.702365i	0.964174	+	0.265270i	$0.0854610\pi$
$12$		0			0
$13$	3.58265	+	2.06844i	0.993648	+	0.573683i	0.906363	−	0.422500i	$-0.138847\pi$
$13$	3.58265	+	2.06844i	0.993648	+	0.573683i	0.0872856	+	0.996183i	$0.472181\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	7.24527			1.75724			0.878619	−	0.477524i	$-0.158466\pi$
$17$	7.24527			1.75724			0.878619	+	0.477524i	$0.158466\pi$
$18$		0			0
$19$		−	6.71715i		−	1.54102i	−0.637428	−	0.770510i	$-0.720002\pi$
$19$		−	6.71715i		−	1.54102i	0.637428	−	0.770510i	$-0.279998\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.85295	−	2.80185i	−1.01191	−	0.584227i	−0.100160	−	0.994971i	$-0.531936\pi$
$23$	−4.85295	−	2.80185i	−1.01191	−	0.584227i	−0.911751	+	0.410744i	$0.865269\pi$
$24$		0			0
$25$	2.34664	+	4.06450i	0.469328	+	0.812899i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.16599	+	0.673187i	−0.216520	+	0.125008i	−0.604338	−	0.796728i	$-0.706562\pi$
$29$	−1.16599	+	0.673187i	−0.216520	+	0.125008i	0.387818	+	0.921736i	$0.373229\pi$
$30$		0			0
$31$	0.830741	+	0.479629i	0.149206	+	0.0861438i	0.572744	−	0.819734i	$-0.305879\pi$
$31$	0.830741	+	0.479629i	0.149206	+	0.0861438i	−0.423539	+	0.905878i	$0.639212\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.38807	+	0.469409i	−0.234626	+	0.0793447i
$36$		0			0
$37$	−7.06956			−1.16223			−0.581114	−	0.813822i	$-0.697383\pi$
$37$	−7.06956			−1.16223			−0.581114	+	0.813822i	$0.697383\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.39152	−	4.14224i	0.373493	−	0.646909i	−0.616607	−	0.787271i	$-0.711493\pi$
$41$	2.39152	−	4.14224i	0.373493	−	0.646909i	0.990100	+	0.140362i	$0.0448265\pi$
$42$		0			0
$43$	1.02846	+	1.78135i	0.156839	+	0.271653i	0.933727	−	0.357986i	$-0.116536\pi$
$43$	1.02846	+	1.78135i	0.156839	+	0.271653i	−0.776888	+	0.629639i	$0.783203\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.90301	−	8.49226i	−0.715177	−	1.23872i	−0.962891	−	0.269890i	$-0.913013\pi$
$47$	−4.90301	−	8.49226i	−0.715177	−	1.23872i	0.247714	−	0.968833i	$-0.420321\pi$
$48$		0			0
$49$	0.897752	+	6.94219i	0.128250	+	0.991742i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	8.43202i		−	1.15823i	−0.815247	−	0.579114i	$-0.803399\pi$
$53$		−	8.43202i		−	1.15823i	0.815247	−	0.579114i	$-0.196601\pi$
$54$		0			0
$55$			2.58026i			0.347922i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.89955	−	6.75422i	0.507678	−	0.879325i	−0.492282	−	0.870436i	$-0.663837\pi$
$59$	3.89955	−	6.75422i	0.507678	−	0.879325i	0.999960	−	0.00888893i	$-0.00282947\pi$
$60$		0			0
$61$	−5.37336	+	3.10231i	−0.687989	+	0.397211i	−0.802858	−	0.596170i	$-0.796688\pi$
$61$	−5.37336	+	3.10231i	−0.687989	+	0.397211i	0.114869	+	0.993381i	$0.463355\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.98417	+	1.14556i	−0.246106	+	0.142089i
$66$		0			0
$67$	−1.68814	+	2.92394i	−0.206239	+	0.357217i	−0.950527	−	0.310642i	$-0.899456\pi$
$67$	−1.68814	+	2.92394i	−0.206239	+	0.357217i	0.744288	+	0.667859i	$0.232789\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			0.407556i			0.0483680i	0.999708	+	0.0241840i	$0.00769875\pi$
$71$			0.407556i			0.0483680i	−0.999708	+	0.0241840i	$0.992301\pi$
$72$		0			0
$73$			8.63566i			1.01073i	0.862906	+	0.505364i	$0.168642\pi$
$73$			8.63566i			1.01073i	−0.862906	+	0.505364i	$0.831358\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	12.0868	+	2.41864i	1.37742	+	0.275630i
$78$		0			0
$79$	0.318176	+	0.551097i	0.0357976	+	0.0620032i	0.883369	−	0.468678i	$-0.155270\pi$
$79$	0.318176	+	0.551097i	0.0357976	+	0.0620032i	−0.847572	+	0.530681i	$0.821936\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.78840	+	4.82965i	0.306066	+	0.530123i	0.977498	−	0.210944i	$-0.0676537\pi$
$83$	2.78840	+	4.82965i	0.306066	+	0.530123i	−0.671432	+	0.741066i	$0.734320\pi$
$84$		0			0
$85$	−2.00632	+	3.47504i	−0.217616	+	0.376921i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.93137			0.734723			0.367362	−	0.930078i	$-0.380261\pi$
$89$	6.93137			0.734723			0.367362	+	0.930078i	$0.380261\pi$
$90$		0			0
$91$	3.50632	+	10.3683i	0.367562	+	1.08690i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.22174	+	1.86007i	0.330543	+	0.190839i
$96$		0			0
$97$	7.48798	−	4.32318i	0.760289	−	0.438953i	−0.0691107	−	0.997609i	$-0.522016\pi$
$97$	7.48798	−	4.32318i	0.760289	−	0.438953i	0.829399	+	0.558656i	$0.188683\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.34227	−	4.05692i	−0.233064	−	0.403679i	0.725644	−	0.688070i	$-0.241542\pi$
$101$	−2.34227	−	4.05692i	−0.233064	−	0.403679i	−0.958708	+	0.284391i	$0.908209\pi$
$102$		0			0
$103$	6.40804	+	3.69969i	0.631403	+	0.364541i	0.781295	−	0.624162i	$-0.214559\pi$
$103$	6.40804	+	3.69969i	0.631403	+	0.364541i	−0.149892	+	0.988702i	$0.547893\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			5.06059i			0.489225i	0.969621	+	0.244613i	$0.0786608\pi$
$107$			5.06059i			0.489225i	−0.969621	+	0.244613i	$0.921339\pi$
$108$		0			0
$109$	11.7628			1.12667			0.563337	−	0.826227i	$-0.309517\pi$
$109$	11.7628			1.12667			0.563337	+	0.826227i	$0.309517\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.51895	+	0.876965i	0.142891	+	0.0824979i	0.569741	−	0.821824i	$-0.307044\pi$
$113$	1.51895	+	0.876965i	0.142891	+	0.0824979i	−0.426850	+	0.904322i	$0.640377\pi$
$114$		0			0
$115$	2.68770	−	1.55174i	0.250629	−	0.144701i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	14.3976	+	12.6557i	1.31983	+	1.16014i
$120$		0			0
$121$	5.35295	−	9.27159i	0.486632	−	0.842872i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−5.36840			−0.480164
$126$		0			0
$127$	−11.0822			−0.983385			−0.491693	−	0.870769i	$-0.663622\pi$
$127$	−11.0822			−0.983385			−0.491693	+	0.870769i	$0.663622\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.23643	−	15.9980i	0.806990	−	1.39775i	−0.107949	−	0.994156i	$-0.534428\pi$
$131$	9.23643	−	15.9980i	0.806990	−	1.39775i	0.914939	−	0.403592i	$-0.132238\pi$
$132$		0			0
$133$	11.7332	−	13.3482i	1.01739	−	1.15743i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−19.0537	+	11.0007i	−1.62787	+	0.939851i	−0.643142	+	0.765747i	$0.722370\pi$
$137$	−19.0537	+	11.0007i	−1.62787	+	0.939851i	−0.984727	+	0.174104i	$0.944297\pi$
$138$		0			0
$139$	8.55986	+	4.94204i	0.726038	+	0.419178i	0.816971	−	0.576679i	$-0.195652\pi$
$139$	8.55986	+	4.94204i	0.726038	+	0.419178i	−0.0909332	+	0.995857i	$0.528985\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	19.2736			1.61174
$144$		0			0
$145$		−	0.745659i		−	0.0619236i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.36677	+	3.67585i	0.521586	+	0.301138i	0.737583	−	0.675256i	$-0.235967\pi$
$149$	6.36677	+	3.67585i	0.521586	+	0.301138i	−0.215997	+	0.976394i	$0.569300\pi$
$150$		0			0
$151$	−2.16599	−	3.75161i	−0.176266	−	0.305302i	0.764333	−	0.644822i	$-0.223069\pi$
$151$	−2.16599	−	3.75161i	−0.176266	−	0.305302i	−0.940599	+	0.339520i	$0.889735\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.460087	+	0.265632i	−0.0369551	+	0.0213360i
$156$		0			0
$157$	−1.54152	−	0.889998i	−0.123027	−	0.0710296i	0.437224	−	0.899353i	$-0.355962\pi$
$157$	−1.54152	−	0.889998i	−0.123027	−	0.0710296i	−0.560251	+	0.828323i	$0.689295\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−4.74955	−	14.0447i	−0.374317	−	1.10687i
$162$		0			0
$163$	5.63635			0.441473			0.220737	−	0.975333i	$-0.429154\pi$
$163$	5.63635			0.441473			0.220737	+	0.975333i	$0.429154\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.38803	+	4.13618i	−0.184791	+	0.320067i	−0.943506	−	0.331355i	$-0.892494\pi$
$167$	−2.38803	+	4.13618i	−0.184791	+	0.320067i	0.758715	+	0.651423i	$0.225827\pi$
$168$		0			0
$169$	2.05692	+	3.56270i	0.158225	+	0.274054i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.83766	+	4.91497i	0.215743	+	0.373678i	0.953502	−	0.301386i	$-0.0974493\pi$
$173$	2.83766	+	4.91497i	0.215743	+	0.373678i	−0.737759	+	0.675064i	$0.764116\pi$
$174$		0			0
$175$	−2.43646	+	12.1759i	−0.184179	+	0.920408i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			12.6305i			0.944048i	0.881586	+	0.472024i	$0.156476\pi$
$179$			12.6305i			0.944048i	−0.881586	+	0.472024i	$0.843524\pi$
$180$		0			0
$181$		−	22.7424i		−	1.69043i	−0.534426	−	0.845215i	$-0.679472\pi$
$181$		−	22.7424i		−	1.69043i	0.534426	−	0.845215i	$-0.320528\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.95766	−	3.39076i	0.143930	−	0.249294i
$186$		0			0
$187$	29.2331	−	16.8777i	2.13773	−	1.23422i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.0537	+	5.80452i	−0.727462	+	0.420000i	−0.817493	−	0.575939i	$-0.804637\pi$
$191$	−10.0537	+	5.80452i	−0.727462	+	0.420000i	0.0900309	+	0.995939i	$0.471303\pi$
$192$		0			0
$193$	−3.16599	+	5.48366i	−0.227893	+	0.394723i	−0.957184	−	0.289482i	$-0.906517\pi$
$193$	−3.16599	+	5.48366i	−0.227893	+	0.394723i	0.729290	+	0.684204i	$0.239850\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	3.10030i		−	0.220888i	−0.993882	−	0.110444i	$-0.964773\pi$
$197$		−	3.10030i		−	0.220888i	0.993882	−	0.110444i	$-0.0352272\pi$
$198$		0			0
$199$			15.7268i			1.11484i	0.830229	+	0.557422i	$0.188210\pi$
$199$			15.7268i			1.11484i	−0.830229	+	0.557422i	$0.811790\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.49293	−	0.698954i	−0.245155	−	0.0490570i
$204$		0			0
$205$	1.32449	+	2.29409i	0.0925065	+	0.160226i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−15.6475	−	27.1022i	−1.08236	−	1.87470i
$210$		0			0
$211$	−3.51263	+	6.08406i	−0.241820	+	0.418844i	−0.961233	−	0.275739i	$-0.911078\pi$
$211$	−3.51263	+	6.08406i	−0.241820	+	0.418844i	0.719413	+	0.694582i	$0.244411\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.13918			−0.0776915
$216$		0			0
$217$	0.813041	+	2.40420i	0.0551928	+	0.163208i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	25.9573	+	14.9864i	1.74608	+	1.00810i
$222$		0			0
$223$	−21.3477	+	12.3251i	−1.42955	+	0.825350i	−0.997085	−	0.0763008i	$-0.975689\pi$
$223$	−21.3477	+	12.3251i	−1.42955	+	0.825350i	−0.432464	+	0.901651i	$0.642356\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.0372	−	17.3849i	−0.666190	−	1.15388i	−0.978961	−	0.204047i	$-0.934590\pi$
$227$	−10.0372	−	17.3849i	−0.666190	−	1.15388i	0.312771	−	0.949829i	$-0.398743\pi$
$228$		0			0
$229$	6.75865	+	3.90211i	0.446624	+	0.257859i	0.706403	−	0.707809i	$-0.250316\pi$
$229$	6.75865	+	3.90211i	0.446624	+	0.257859i	−0.259779	+	0.965668i	$0.583650\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			7.96562i			0.521845i	0.965360	+	0.260922i	$0.0840267\pi$
$233$			7.96562i			0.521845i	−0.965360	+	0.260922i	$0.915973\pi$
$234$		0			0
$235$	5.43084			0.354269
$236$		0			0
$237$		0			0
$238$		0			0
$239$	23.2059	+	13.3979i	1.50107	+	0.866640i	0.999999	+	0.00123146i	$0.000391987\pi$
$239$	23.2059	+	13.3979i	1.50107	+	0.866640i	0.501066	+	0.865409i	$0.332941\pi$
$240$		0			0
$241$	0.757259	−	0.437203i	0.0487793	−	0.0281628i	−0.475412	−	0.879763i	$-0.657701\pi$
$241$	0.757259	−	0.437203i	0.0487793	−	0.0281628i	0.524191	+	0.851601i	$0.324368\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.57827	−	1.49180i	−0.228608	−	0.0953077i
$246$		0			0
$247$	13.8940	−	24.0652i	0.884057	−	1.53123i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.32082			−0.146489			−0.0732445	−	0.997314i	$-0.523335\pi$
$251$	−2.32082			−0.146489			−0.0732445	+	0.997314i	$0.523335\pi$
$252$		0			0
$253$	−26.1075			−1.64136
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−12.3017	+	21.3072i	−0.767361	+	1.32911i	0.171628	+	0.985162i	$0.445097\pi$
$257$	−12.3017	+	21.3072i	−0.767361	+	1.32911i	−0.938989	+	0.343947i	$0.888236\pi$
$258$		0			0
$259$	−14.0485	−	12.3487i	−0.872929	−	0.767312i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−20.5268	+	11.8512i	−1.26574	+	0.730775i	−0.974179	−	0.225778i	$-0.927508\pi$
$263$	−20.5268	+	11.8512i	−1.26574	+	0.730775i	−0.291560	+	0.956552i	$0.594174\pi$
$264$		0			0
$265$	4.04424	+	2.33494i	0.248436	+	0.143434i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	20.6212			1.25730			0.628648	−	0.777690i	$-0.283609\pi$
$269$	20.6212			1.25730			0.628648	+	0.777690i	$0.283609\pi$
$270$		0			0
$271$		−	13.9454i		−	0.847123i	−0.905867	−	0.423562i	$-0.860780\pi$
$271$		−	13.9454i		−	0.847123i	0.905867	−	0.423562i	$-0.139220\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	18.9363	+	10.9329i	1.14190	+	0.659278i
$276$		0			0
$277$	−10.3940	−	18.0030i	−0.624518	−	1.08170i	−0.988634	−	0.150343i	$-0.951962\pi$
$277$	−10.3940	−	18.0030i	−0.624518	−	1.08170i	0.364116	−	0.931354i	$-0.381371\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	20.3371	−	11.7416i	1.21321	−	0.700448i	0.249754	−	0.968309i	$-0.419650\pi$
$281$	20.3371	−	11.7416i	1.21321	−	0.700448i	0.963457	+	0.267862i	$0.0863170\pi$
$282$		0			0
$283$	11.1906	+	6.46089i	0.665211	+	0.384060i	0.794260	−	0.607578i	$-0.207859\pi$
$283$	11.1906	+	6.46089i	0.665211	+	0.384060i	−0.129048	+	0.991638i	$0.541192\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	11.9878	−	4.05398i	0.707619	−	0.239299i
$288$		0			0
$289$	35.4940			2.08788
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.99115	−	3.44878i	0.116324	−	0.201480i	−0.801984	−	0.597346i	$-0.796222\pi$
$293$	1.99115	−	3.44878i	0.116324	−	0.201480i	0.918308	+	0.395866i	$0.129555\pi$
$294$		0			0
$295$	2.15968	+	3.74067i	0.125741	+	0.217790i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−11.5910	−	20.0761i	−0.670322	−	1.16103i
$300$		0			0
$301$	−1.06783	+	5.33632i	−0.0615485	+	0.307580i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	3.43629i		−	0.196762i
$306$		0			0
$307$		−	22.3162i		−	1.27365i	−0.771008	−	0.636825i	$-0.780247\pi$
$307$		−	22.3162i		−	1.27365i	0.771008	−	0.636825i	$-0.219753\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−8.18371	+	14.1746i	−0.464056	+	0.803768i	−0.999158	−	0.0410190i	$-0.986940\pi$
$311$	−8.18371	+	14.1746i	−0.464056	+	0.803768i	0.535103	+	0.844787i	$0.320273\pi$
$312$		0			0
$313$	−16.5547	+	9.55785i	−0.935726	+	0.540242i	−0.888618	−	0.458648i	$-0.848334\pi$
$313$	−16.5547	+	9.55785i	−0.935726	+	0.540242i	−0.0471079	+	0.998890i	$0.515000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.8798	+	12.0550i	−1.17273	+	0.677074i	−0.954321	−	0.298784i	$-0.903419\pi$
$317$	−20.8798	+	12.0550i	−1.17273	+	0.677074i	−0.218405	+	0.975858i	$0.570086\pi$
$318$		0			0
$319$	−3.13635	+	5.43232i	−0.175602	+	0.304152i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	48.6676i		−	2.70794i
$324$		0			0
$325$			19.4156i			1.07698i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	5.09068	−	25.4399i	0.280658	−	1.40255i
$330$		0			0
$331$	5.70077	+	9.87403i	0.313343	+	0.542726i	0.979084	−	0.203457i	$-0.0652178\pi$
$331$	5.70077	+	9.87403i	0.313343	+	0.542726i	−0.665741	+	0.746183i	$0.731884\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.934938	−	1.61936i	−0.0510811	−	0.0884751i
$336$		0			0
$337$	2.16599	−	3.75161i	0.117989	−	0.204363i	−0.800981	−	0.598689i	$-0.795689\pi$
$337$	2.16599	−	3.75161i	0.117989	−	0.204363i	0.918971	+	0.394326i	$0.129022\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	4.46914			0.242018
$342$		0			0
$343$	−10.3423	+	15.3635i	−0.558429	+	0.829552i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.62254	−	2.66882i	−0.248151	−	0.143270i	0.370766	−	0.928726i	$-0.379095\pi$
$347$	−4.62254	−	2.66882i	−0.248151	−	0.143270i	−0.618917	+	0.785456i	$0.712428\pi$
$348$		0			0
$349$	8.78031	−	5.06931i	0.469999	−	0.271354i	−0.246240	−	0.969209i	$-0.579195\pi$
$349$	8.78031	−	5.06931i	0.469999	−	0.271354i	0.716239	+	0.697855i	$0.245862\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.67564	+	13.2946i	0.408533	+	0.707600i	0.994726	−	0.102571i	$-0.0327070\pi$
$353$	7.67564	+	13.2946i	0.408533	+	0.707600i	−0.586192	+	0.810172i	$0.699374\pi$
$354$		0			0
$355$	−0.195475	−	0.112858i	−0.0103748	−	0.00598987i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	1.74800i		−	0.0922559i	−0.998936	−	0.0461280i	$-0.985312\pi$
$359$		−	1.74800i		−	0.0922559i	0.998936	−	0.0461280i	$-0.0146882\pi$
$360$		0			0
$361$	−26.1201			−1.37474
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.14191	−	2.39133i	−0.216798	−	0.125168i
$366$		0			0
$367$	11.1720	−	6.45018i	0.583176	−	0.336697i	−0.179219	−	0.983809i	$-0.557357\pi$
$367$	11.1720	−	6.45018i	0.583176	−	0.336697i	0.762394	+	0.647113i	$0.224024\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	14.7286	−	16.7559i	0.764671	−	0.869925i
$372$		0			0
$373$	5.34782	−	9.26269i	0.276900	−	0.479604i	−0.693713	−	0.720251i	$-0.744026\pi$
$373$	5.34782	−	9.26269i	0.276900	−	0.479604i	0.970613	+	0.240647i	$0.0773597\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.56980			−0.286859
$378$		0			0
$379$	−0.566797			−0.0291144			−0.0145572	−	0.999894i	$-0.504634\pi$
$379$	−0.566797			−0.0291144			−0.0145572	+	0.999894i	$0.504634\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−9.43059	+	16.3343i	−0.481880	+	0.834641i	−0.999784	−	0.0207978i	$-0.993379\pi$
$383$	−9.43059	+	16.3343i	−0.481880	+	0.834641i	0.517903	+	0.855439i	$0.326713\pi$
$384$		0			0
$385$	−4.50706	+	5.12744i	−0.229701	+	0.261318i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−14.3182	+	8.26660i	−0.725960	+	0.419133i	−0.816943	−	0.576719i	$-0.804333\pi$
$389$	−14.3182	+	8.26660i	−0.725960	+	0.419133i	0.0909822	+	0.995853i	$0.470999\pi$
$390$		0			0
$391$	−35.1610	−	20.3002i	−1.77817	−	1.02663i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.352429			−0.0177326
$396$		0			0
$397$			34.1080i			1.71183i	0.517114	+	0.855917i	$0.327006\pi$
$397$			34.1080i			1.71183i	−0.517114	+	0.855917i	$0.672994\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−18.6395	−	10.7615i	−0.930811	−	0.537404i	−0.0437428	−	0.999043i	$-0.513928\pi$
$401$	−18.6395	−	10.7615i	−0.930811	−	0.537404i	−0.887068	+	0.461639i	$0.847262\pi$
$402$		0			0
$403$	1.98417	+	3.43668i	0.0988386	+	0.171193i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−28.5241	+	16.4684i	−1.41389	+	0.816308i
$408$		0			0
$409$	19.2516	+	11.1149i	0.951933	+	0.549599i	0.893681	−	0.448703i	$-0.148114\pi$
$409$	19.2516	+	11.1149i	0.951933	+	0.549599i	0.0582520	+	0.998302i	$0.481447\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	19.5470	−	6.61031i	0.961846	−	0.325272i
$414$		0			0
$415$	−3.08858			−0.151613
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.81490	+	11.8038i	−0.332930	+	0.576651i	−0.983085	−	0.183150i	$-0.941371\pi$
$419$	−6.81490	+	11.8038i	−0.332930	+	0.576651i	0.650155	+	0.759802i	$0.274704\pi$
$420$		0			0
$421$	13.7071	+	23.7414i	0.668043	+	1.15708i	0.978451	+	0.206480i	$0.0662009\pi$
$421$	13.7071	+	23.7414i	0.668043	+	1.15708i	−0.310408	+	0.950603i	$0.600466\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	17.0020	+	29.4484i	0.824720	+	1.42846i
$426$		0			0
$427$	−16.0968	−	3.22106i	−0.778978	−	0.155878i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	34.8331i		−	1.67785i	−0.544248	−	0.838925i	$-0.683185\pi$
$431$		−	34.8331i		−	1.67785i	0.544248	−	0.838925i	$-0.316815\pi$
$432$		0			0
$433$		−	19.5648i		−	0.940223i	−0.882607	−	0.470112i	$-0.844214\pi$
$433$		−	19.5648i		−	0.940223i	0.882607	−	0.470112i	$-0.155786\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−18.8205	+	32.5980i	−0.900305	+	1.55937i
$438$		0			0
$439$	−24.7361	+	14.2814i	−1.18059	+	0.681614i	−0.956151	−	0.292874i	$-0.905388\pi$
$439$	−24.7361	+	14.2814i	−1.18059	+	0.681614i	−0.224439	+	0.974488i	$0.572055\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−21.8612	+	12.6216i	−1.03866	+	0.599669i	−0.919453	−	0.393201i	$-0.871368\pi$
$443$	−21.8612	+	12.6216i	−1.03866	+	0.599669i	−0.119205	+	0.992870i	$0.538034\pi$
$444$		0			0
$445$	−1.91939	+	3.32448i	−0.0909878	+	0.157596i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			15.1042i			0.712811i	0.934331	+	0.356405i	$0.115998\pi$
$449$			15.1042i			0.712811i	−0.934331	+	0.356405i	$0.884002\pi$
$450$		0			0
$451$		−	22.2840i		−	1.04931i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−5.94390	−	1.18941i	−0.278655	−	0.0557603i
$456$		0			0
$457$	−1.75138	−	3.03348i	−0.0819261	−	0.141900i	0.822151	−	0.569269i	$-0.192774\pi$
$457$	−1.75138	−	3.03348i	−0.0819261	−	0.141900i	−0.904077	+	0.427369i	$0.859440\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.98765	−	3.44272i	−0.0925743	−	0.160343i	0.816019	−	0.578025i	$-0.196176\pi$
$461$	−1.98765	−	3.44272i	−0.0925743	−	0.160343i	−0.908594	+	0.417681i	$0.862843\pi$
$462$		0			0
$463$	5.18494	−	8.98058i	0.240965	−	0.417363i	−0.720025	−	0.693948i	$-0.755870\pi$
$463$	5.18494	−	8.98058i	0.240965	−	0.417363i	0.960989	+	0.276585i	$0.0892029\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.6190			−0.907860			−0.453930	−	0.891037i	$-0.649978\pi$
$467$	−19.6190			−0.907860			−0.453930	+	0.891037i	$0.649978\pi$
$468$		0			0
$469$	−8.46202	+	2.86164i	−0.390740	+	0.132138i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	8.29923	+	4.79156i	0.381599	+	0.220316i
$474$		0			0
$475$	27.3018	−	15.7627i	1.25269	−	0.723243i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	15.8237	+	27.4074i	0.723002	+	1.25228i	0.959791	+	0.280715i	$0.0905717\pi$
$479$	15.8237	+	27.4074i	0.723002	+	1.25228i	−0.236789	+	0.971561i	$0.576095\pi$
$480$		0			0
$481$	−25.3277	−	14.6230i	−1.15485	−	0.666751i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			4.78860i			0.217439i
$486$		0			0
$487$	19.4585			0.881747			0.440874	−	0.897569i	$-0.354669\pi$
$487$	19.4585			0.881747			0.440874	+	0.897569i	$0.354669\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	23.9525	+	13.8290i	1.08096	+	0.624094i	0.931156	−	0.364622i	$-0.118802\pi$
$491$	23.9525	+	13.8290i	1.08096	+	0.624094i	0.149806	+	0.988715i	$0.452135\pi$
$492$		0			0
$493$	−8.44795	+	4.87743i	−0.380476	+	0.219668i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.711896	+	0.809886i	−0.0319329	+	0.0363283i
$498$		0			0
$499$	−4.50632	+	7.80517i	−0.201730	+	0.349407i	−0.949086	−	0.315017i	$-0.897990\pi$
$499$	−4.50632	+	7.80517i	−0.201730	+	0.349407i	0.747356	+	0.664424i	$0.231323\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−27.1572			−1.21088			−0.605440	−	0.795891i	$-0.707003\pi$
$503$	−27.1572			−1.21088			−0.605440	+	0.795891i	$0.707003\pi$
$504$		0			0
$505$	2.59442			0.115450
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.56799	−	11.3761i	0.291121	−	0.504236i	−0.682954	−	0.730461i	$-0.739305\pi$
$509$	6.56799	−	11.3761i	0.291121	−	0.504236i	0.974075	+	0.226225i	$0.0726384\pi$
$510$		0			0
$511$	−15.0843	+	17.1606i	−0.667291	+	0.759140i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.54895	+	2.04899i	−0.156385	+	0.0902892i
$516$		0			0
$517$	−39.5651	−	22.8429i	−1.74007	−	1.00463i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−4.03219			−0.176653			−0.0883266	−	0.996092i	$-0.528152\pi$
$521$	−4.03219			−0.176653			−0.0883266	+	0.996092i	$0.528152\pi$
$522$		0			0
$523$		−	0.595961i		−	0.0260595i	−0.999915	−	0.0130298i	$-0.995852\pi$
$523$		−	0.595961i		−	0.0260595i	0.999915	−	0.0130298i	$-0.00414762\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.01895	+	3.47504i	0.262189	+	0.151375i
$528$		0			0
$529$	4.20077	+	7.27595i	0.182642	+	0.316346i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	17.1360	−	9.89347i	0.742242	−	0.428534i
$534$		0			0
$535$	−2.42720	−	1.40135i	−0.104937	−	0.0605855i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	19.7939	+	25.9189i	0.852585	+	1.11641i
$540$		0			0
$541$	−14.1012			−0.606259			−0.303129	−	0.952949i	$-0.598031\pi$
$541$	−14.1012			−0.606259			−0.303129	+	0.952949i	$0.598031\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.25729	+	5.64179i	−0.139527	+	0.241668i
$546$		0			0
$547$	18.9921	+	32.8952i	0.812042	+	1.40650i	0.911433	+	0.411450i	$0.134977\pi$
$547$	18.9921	+	32.8952i	0.812042	+	1.40650i	−0.0993905	+	0.995049i	$0.531689\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.52190	+	7.83216i	0.192639	+	0.333661i
$552$		0			0
$553$	−0.330354	+	1.65090i	−0.0140481	+	0.0702034i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	41.7056i		−	1.76712i	−0.468313	−	0.883562i	$-0.655138\pi$
$557$		−	41.7056i		−	1.76712i	0.468313	−	0.883562i	$-0.344862\pi$
$558$		0			0
$559$			8.50926i			0.359903i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.938436	+	1.62542i	−0.0395504	+	0.0685033i	−0.885123	−	0.465357i	$-0.845926\pi$
$563$	−0.938436	+	1.62542i	−0.0395504	+	0.0685033i	0.845573	+	0.533860i	$0.179259\pi$
$564$		0			0
$565$	−0.841235	+	0.485687i	−0.0353910	+	0.0204330i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	20.6391	−	11.9160i	0.865237	−	0.499545i	−0.000525844	−	1.00000i	$-0.500167\pi$
$569$	20.6391	−	11.9160i	0.865237	−	0.499545i	0.865762	+	0.500455i	$0.166834\pi$
$570$		0			0
$571$	14.8719	−	25.7589i	0.622370	−	1.07798i	−0.366674	−	0.930350i	$-0.619503\pi$
$571$	14.8719	−	25.7589i	0.622370	−	1.07798i	0.989043	−	0.147626i	$-0.0471633\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	26.2997i		−	1.09678i
$576$		0			0
$577$		−	14.6589i		−	0.610260i	−0.952311	−	0.305130i	$-0.901300\pi$
$577$		−	14.6589i		−	0.610260i	0.952311	−	0.305130i	$-0.0986999\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.89513	+	14.4680i	−0.120110	+	0.600233i
$582$		0			0
$583$	−19.6422	−	34.0213i	−0.813498	−	1.40902i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−22.2189	−	38.4843i	−0.917074	−	1.58842i	−0.803836	−	0.594851i	$-0.797211\pi$
$587$	−22.2189	−	38.4843i	−0.917074	−	1.58842i	−0.113238	−	0.993568i	$-0.536122\pi$
$588$		0			0
$589$	3.22174	−	5.58021i	0.132749	−	0.229929i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−37.1186			−1.52428			−0.762140	−	0.647412i	$-0.775851\pi$
$593$	−37.1186			−1.52428			−0.762140	+	0.647412i	$0.775851\pi$
$594$		0			0
$595$	−10.0569	+	3.40100i	−0.412294	+	0.139427i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−12.0534	−	6.95901i	−0.492487	−	0.284338i	0.233119	−	0.972448i	$-0.425107\pi$
$599$	−12.0534	−	6.95901i	−0.492487	−	0.284338i	−0.725606	+	0.688111i	$0.758440\pi$
$600$		0			0
$601$	0.377613	−	0.218015i	0.0154032	−	0.00889301i	−0.492279	−	0.870438i	$-0.663836\pi$
$601$	0.377613	−	0.218015i	0.0154032	−	0.00889301i	0.507682	+	0.861545i	$0.330503\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.96461	+	5.13486i	0.120529	+	0.208762i
$606$		0			0
$607$	−1.92117	−	1.10919i	−0.0779778	−	0.0450205i	0.460504	−	0.887658i	$-0.347669\pi$
$607$	−1.92117	−	1.10919i	−0.0779778	−	0.0450205i	−0.538482	+	0.842637i	$0.681002\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	40.5664i		−	1.64114i
$612$		0			0
$613$	38.2023			1.54298			0.771488	−	0.636244i	$-0.219513\pi$
$613$	38.2023			1.54298			0.771488	+	0.636244i	$0.219513\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−21.1043	−	12.1846i	−0.849628	−	0.490533i	0.0108970	−	0.999941i	$-0.496531\pi$
$617$	−21.1043	−	12.1846i	−0.849628	−	0.490533i	−0.860525	+	0.509407i	$0.829865\pi$
$618$		0			0
$619$	−25.4477	+	14.6922i	−1.02283	+	0.590531i	−0.914922	−	0.403630i	$-0.867748\pi$
$619$	−25.4477	+	14.6922i	−1.02283	+	0.590531i	−0.107907	+	0.994161i	$0.534415\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	13.7739	+	12.1073i	0.551838	+	0.485070i
$624$		0			0
$625$	−10.2466	+	17.7476i	−0.409864	+	0.709906i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−51.2209			−2.04231
$630$		0			0
$631$	−5.17077			−0.205845			−0.102923	−	0.994689i	$-0.532819\pi$
$631$	−5.17077			−0.205845			−0.102923	+	0.994689i	$0.532819\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.06881	−	5.31533i	0.121782	−	0.210933i
$636$		0			0
$637$	−11.1432	+	26.7284i	−0.441510	+	1.05902i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	5.32405	−	3.07384i	0.210287	−	0.121410i	−0.391158	−	0.920324i	$-0.627925\pi$
$641$	5.32405	−	3.07384i	0.210287	−	0.121410i	0.601445	+	0.798914i	$0.294592\pi$
$642$		0			0
$643$	−23.9599	−	13.8333i	−0.944886	−	0.545530i	−0.0533976	−	0.998573i	$-0.517005\pi$
$643$	−23.9599	−	13.8333i	−0.944886	−	0.545530i	−0.891489	+	0.453043i	$0.850338\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.81457			0.189280			0.0946402	−	0.995512i	$-0.469830\pi$
$647$	4.81457			0.189280			0.0946402	+	0.995512i	$0.469830\pi$
$648$		0			0
$649$		−	36.3357i		−	1.42630i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.1759	−	12.2259i	−0.828677	−	0.478437i	0.0247223	−	0.999694i	$-0.492130\pi$
$653$	−21.1759	−	12.2259i	−0.828677	−	0.478437i	−0.853400	+	0.521257i	$0.825463\pi$
$654$		0			0
$655$	5.11539	+	8.86011i	0.199875	+	0.346193i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−20.7514	+	11.9808i	−0.808359	+	0.466706i	−0.846386	−	0.532570i	$-0.821226\pi$
$659$	−20.7514	+	11.9808i	−0.808359	+	0.466706i	0.0380267	+	0.999277i	$0.487893\pi$
$660$		0			0
$661$	−6.73275	−	3.88715i	−0.261874	−	0.151193i	0.363315	−	0.931666i	$-0.381645\pi$
$661$	−6.73275	−	3.88715i	−0.261874	−	0.151193i	−0.625189	+	0.780473i	$0.714978\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3.15309	+	9.32385i	0.122272	+	0.361563i
$666$		0			0
$667$	7.54469			0.292131
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−14.4536	+	25.0343i	−0.557973	+	0.966438i
$672$		0			0
$673$	−14.7281	−	25.5097i	−0.567725	−	0.983328i	−0.996790	−	0.0800548i	$-0.974490\pi$
$673$	−14.7281	−	25.5097i	−0.567725	−	0.983328i	0.429066	−	0.903273i	$-0.358843\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−17.8293	−	30.8812i	−0.685235	−	1.18686i	−0.973363	−	0.229270i	$-0.926366\pi$
$677$	−17.8293	−	30.8812i	−0.685235	−	1.18686i	0.288128	−	0.957592i	$-0.406967\pi$
$678$		0			0
$679$	22.4314	+	4.48866i	0.860840	+	0.172259i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			13.0969i			0.501139i	0.968099	+	0.250570i	$0.0806179\pi$
$683$			13.0969i			0.501139i	−0.968099	+	0.250570i	$0.919382\pi$
$684$		0			0
$685$		−	12.1850i		−	0.465563i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	17.4412	−	30.2090i	0.664456	−	1.15087i
$690$		0			0
$691$	−7.81992	+	4.51483i	−0.297484	+	0.171752i	−0.641312	−	0.767280i	$-0.721610\pi$
$691$	−7.81992	+	4.51483i	−0.297484	+	0.171752i	0.343828	+	0.939033i	$0.388276\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.74068	+	2.73704i	−0.179824	+	0.103822i
$696$		0			0
$697$	17.3273	−	30.0117i	0.656316	−	1.13677i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			0.259274i			0.00979264i	0.999988	+	0.00489632i	$0.00155855\pi$
$701$			0.259274i			0.00979264i	−0.999988	+	0.00489632i	$0.998441\pi$
$702$		0			0
$703$			47.4873i			1.79102i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.43192	−	12.1532i	0.0914617	−	0.457067i
$708$		0			0
$709$	−3.08574	−	5.34467i	−0.115888	−	0.200723i	0.802247	−	0.596993i	$-0.203638\pi$
$709$	−3.08574	−	5.34467i	−0.115888	−	0.200723i	−0.918134	+	0.396270i	$0.870305\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2.68770	−	4.65523i	−0.100655	−	0.174340i
$714$		0			0
$715$	−5.33712	+	9.24417i	−0.199597	+	0.345712i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	19.5275			0.728253			0.364127	−	0.931349i	$-0.381368\pi$
$719$	19.5275			0.728253			0.364127	+	0.931349i	$0.381368\pi$
$720$		0			0
$721$	6.27151	+	18.5452i	0.233563	+	0.690658i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5.47233	−	3.15945i	−0.203237	−	0.117339i
$726$		0			0
$727$	−0.425312	+	0.245554i	−0.0157740	+	0.00910710i	−0.507866	−	0.861436i	$-0.669566\pi$
$727$	−0.425312	+	0.245554i	−0.0157740	+	0.00910710i	0.492092	+	0.870543i	$0.336232\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	7.45149	+	12.9064i	0.275603	+	0.477359i
$732$		0			0
$733$	6.68424	+	3.85915i	0.246888	+	0.142541i	0.618338	−	0.785912i	$-0.287806\pi$
$733$	6.68424	+	3.85915i	0.246888	+	0.142541i	−0.371450	+	0.928453i	$0.621139\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			15.7300i			0.579420i
$738$		0			0
$739$	−10.9083			−0.401270			−0.200635	−	0.979666i	$-0.564300\pi$
$739$	−10.9083			−0.401270			−0.200635	+	0.979666i	$0.564300\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	27.0051	+	15.5914i	0.990722	+	0.571994i	0.905490	−	0.424367i	$-0.139503\pi$
$743$	27.0051	+	15.5914i	0.990722	+	0.571994i	0.0852322	+	0.996361i	$0.472837\pi$
$744$		0			0
$745$	−3.52609	+	2.03579i	−0.129186	+	0.0745855i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−8.83956	+	10.0563i	−0.322991	+	0.367449i
$750$		0			0
$751$	−23.0367	+	39.9008i	−0.840622	+	1.45600i	0.0487482	+	0.998811i	$0.484477\pi$
$751$	−23.0367	+	39.9008i	−0.840622	+	1.45600i	−0.889370	+	0.457188i	$0.848857\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.39917			0.0873149
$756$		0			0
$757$	40.6419			1.47715			0.738577	−	0.674169i	$-0.235498\pi$
$757$	40.6419			1.47715			0.738577	+	0.674169i	$0.235498\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.64190	+	6.30795i	−0.132019	+	0.228663i	−0.924455	−	0.381292i	$-0.875479\pi$
$761$	−3.64190	+	6.30795i	−0.132019	+	0.228663i	0.792436	+	0.609955i	$0.208813\pi$
$762$		0			0
$763$	23.3748	+	20.5467i	0.846226	+	0.743840i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	27.9415	−	16.1320i	1.00891	−	0.582493i
$768$		0			0
$769$	−35.8261	−	20.6842i	−1.29192	−	0.745892i	−0.312927	−	0.949777i	$-0.601310\pi$
$769$	−35.8261	−	20.6842i	−1.29192	−	0.745892i	−0.978995	+	0.203886i	$0.934643\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−17.1183			−0.615702			−0.307851	−	0.951435i	$-0.599610\pi$
$773$	−17.1183			−0.615702			−0.307851	+	0.951435i	$0.599610\pi$
$774$		0			0
$775$			4.50206i			0.161719i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−27.8241	−	16.0642i	−0.996900	−	0.575561i
$780$		0			0
$781$	0.949393	+	1.64440i	0.0339719	+	0.0588411i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.853737	−	0.492906i	0.0304712	−	0.0175926i
$786$		0			0
$787$	25.7426	+	14.8625i	0.917623	+	0.529790i	0.882876	−	0.469606i	$-0.155604\pi$
$787$	25.7426	+	14.8625i	0.917623	+	0.529790i	0.0347472	+	0.999396i	$0.488937\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.48658	+	4.39590i	0.0528568	+	0.156300i
$792$		0			0
$793$	−25.6679			−0.911492
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−20.6019	+	35.6836i	−0.729757	+	1.26398i	0.227229	+	0.973841i	$0.427034\pi$
$797$	−20.6019	+	35.6836i	−0.729757	+	1.26398i	−0.956986	+	0.290135i	$0.906300\pi$
$798$		0			0
$799$	−35.5236	−	61.5288i	−1.25674	−	2.17673i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	20.1166	+	34.8430i	0.709900	+	1.22958i
$804$		0			0
$805$	8.05144	+	1.61114i	0.283776	+	0.0567852i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	12.4233i		−	0.436780i	−0.975862	−	0.218390i	$-0.929920\pi$
$809$		−	12.4233i		−	0.436780i	0.975862	−	0.218390i	$-0.0700805\pi$
$810$		0			0
$811$		−	32.8713i		−	1.15427i	−0.816650	−	0.577133i	$-0.804171\pi$
$811$		−	32.8713i		−	1.15427i	0.816650	−	0.577133i	$-0.195829\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.56078	+	2.70336i	−0.0546719	+	0.0946944i
$816$		0			0
$817$	11.9656	−	6.90833i	0.418623	−	0.241692i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	11.7411	−	6.77873i	0.409768	−	0.236579i	−0.280922	−	0.959731i	$-0.590640\pi$
$821$	11.7411	−	6.77873i	0.409768	−	0.236579i	0.690690	+	0.723151i	$0.257307\pi$
$822$		0			0
$823$	−12.2565	+	21.2289i	−0.427235	+	0.739993i	−0.996626	−	0.0820737i	$-0.973846\pi$
$823$	−12.2565	+	21.2289i	−0.427235	+	0.739993i	0.569391	+	0.822067i	$0.307179\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	14.7323i		−	0.512292i	−0.966638	−	0.256146i	$-0.917547\pi$
$827$		−	14.7323i		−	0.512292i	0.966638	−	0.256146i	$-0.0824527\pi$
$828$		0			0
$829$		−	13.5191i		−	0.469539i	−0.972051	−	0.234770i	$-0.924566\pi$
$829$		−	13.5191i		−	0.469539i	0.972051	−	0.234770i	$-0.0754336\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	6.50446	+	50.2981i	0.225366	+	1.74273i
$834$		0			0
$835$	−1.32255	−	2.29073i	−0.0457689	−	0.0792740i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.511154	−	0.885345i	−0.0176470	−	0.0305655i	0.857067	−	0.515205i	$-0.172284\pi$
$839$	−0.511154	−	0.885345i	−0.0176470	−	0.0305655i	−0.874714	+	0.484639i	$0.838951\pi$
$840$		0			0
$841$	−13.5936	+	23.5449i	−0.468746	+	0.811892i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.27836			−0.0783780
$846$		0			0
$847$	26.8324	−	9.07404i	0.921972	−	0.311788i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	34.3082	+	19.8079i	1.17607	+	0.679005i
$852$		0			0
$853$	8.70682	−	5.02689i	0.298116	−	0.172117i	−0.343480	−	0.939160i	$-0.611606\pi$
$853$	8.70682	−	5.02689i	0.298116	−	0.172117i	0.641596	+	0.767043i	$0.278273\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.1272	+	24.4690i	0.482575	+	0.835844i	0.999800	−	0.0200052i	$-0.00636826\pi$
$857$	14.1272	+	24.4690i	0.482575	+	0.835844i	−0.517225	+	0.855850i	$0.673035\pi$
$858$		0			0
$859$	−26.9800	−	15.5769i	−0.920544	−	0.531476i	−0.0367356	−	0.999325i	$-0.511696\pi$
$859$	−26.9800	−	15.5769i	−0.920544	−	0.531476i	−0.883809	+	0.467849i	$0.845029\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			57.1234i			1.94450i	0.233938	+	0.972252i	$0.424839\pi$
$863$			57.1234i			1.94450i	−0.233938	+	0.972252i	$0.575161\pi$
$864$		0			0
$865$	−3.14314			−0.106870
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.56754	+	1.48237i	0.0870978	+	0.0502859i
$870$		0			0
$871$	−12.0960	+	6.98365i	−0.409858	+	0.236632i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−10.6680	−	9.37724i	−0.360643	−	0.317009i
$876$		0			0
$877$	15.6691	−	27.1397i	0.529108	−	0.916443i	−0.470315	−	0.882498i	$-0.655860\pi$
$877$	15.6691	−	27.1397i	0.529108	−	0.916443i	0.999424	−	0.0339441i	$-0.0108068\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−12.2822			−0.413799			−0.206900	−	0.978362i	$-0.566337\pi$
$881$	−12.2822			−0.413799			−0.206900	+	0.978362i	$0.566337\pi$
$882$		0			0
$883$	−3.61496			−0.121653			−0.0608266	−	0.998148i	$-0.519374\pi$
$883$	−3.61496			−0.121653			−0.0608266	+	0.998148i	$0.519374\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.44264	+	16.3551i	−0.317053	+	0.549152i	−0.979872	−	0.199628i	$-0.936027\pi$
$887$	−9.44264	+	16.3551i	−0.317053	+	0.549152i	0.662819	+	0.748780i	$0.269360\pi$
$888$		0			0
$889$	−22.0223	−	19.3578i	−0.738603	−	0.649239i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−57.0438	+	32.9342i	−1.90890	+	1.10210i
$894$		0			0
$895$	−6.05795	−	3.49756i	−0.202495	−	0.116911i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.29152			−0.0430746
$900$		0			0
$901$		−	61.0923i		−	2.03528i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	10.9079	+	6.29769i	0.362591	+	0.209342i
$906$		0			0
$907$	−28.8802	−	50.0219i	−0.958950	−	1.66095i	−0.725059	−	0.688687i	$-0.758187\pi$
$907$	−28.8802	−	50.0219i	−0.958950	−	1.66095i	−0.233891	−	0.972263i	$-0.575146\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−33.7810	+	19.5034i	−1.11921	+	0.646178i	−0.941200	−	0.337850i	$-0.890300\pi$
$911$	−33.7810	+	19.5034i	−1.11921	+	0.646178i	−0.178013	+	0.984028i	$0.556967\pi$
$912$		0			0
$913$	22.5011	+	12.9910i	0.744679	+	0.429940i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	46.2988	−	15.6571i	1.52892	−	0.517043i
$918$		0			0
$919$	31.8095			1.04930			0.524649	−	0.851319i	$-0.324197\pi$
$919$	31.8095			1.04930			0.524649	+	0.851319i	$0.324197\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.843006	+	1.46013i	−0.0277479	+	0.0480607i
$924$		0			0
$925$	−16.5897	−	28.7342i	−0.545465	−	0.944774i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−19.0424	−	32.9825i	−0.624762	−	1.08212i	−0.988587	−	0.150653i	$-0.951863\pi$
$929$	−19.0424	−	32.9825i	−0.624762	−	1.08212i	0.363824	−	0.931468i	$-0.381471\pi$
$930$		0			0
$931$	46.6317	−	6.03033i	1.52829	−	0.197636i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			18.6947i			0.611382i
$936$		0			0
$937$			37.6261i			1.22919i	0.788842	+	0.614596i	$0.210681\pi$
$937$			37.6261i			1.22919i	−0.788842	+	0.614596i	$0.789319\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.837737	−	1.45100i	0.0273094	−	0.0473014i	−0.852048	−	0.523464i	$-0.824639\pi$
$941$	0.837737	−	1.45100i	0.0273094	−	0.0473014i	0.879357	+	0.476163i	$0.157973\pi$
$942$		0			0
$943$	−23.2119	+	13.4014i	−0.755884	+	0.436410i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	19.2331	−	11.1042i	0.624992	−	0.360839i	−0.153818	−	0.988099i	$-0.549157\pi$
$947$	19.2331	−	11.1042i	0.624992	−	0.360839i	0.778810	+	0.627260i	$0.215824\pi$
$948$		0			0
$949$	−17.8624	+	30.9386i	−0.579838	+	1.00431i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			27.1505i			0.879491i	0.898122	+	0.439746i	$0.144931\pi$
$953$			27.1505i			0.879491i	−0.898122	+	0.439746i	$0.855069\pi$
$954$		0			0
$955$		−	6.42941i		−	0.208051i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−57.0785	−	11.4217i	−1.84316	−	0.368827i
$960$		0			0
$961$	−15.0399	−	26.0499i	−0.485158	−	0.840319i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.75341	−	3.03700i	−0.0564444	−	0.0977646i
$966$		0			0
$967$	16.7553	−	29.0211i	0.538815	−	0.933255i	−0.460153	−	0.887840i	$-0.652205\pi$
$967$	16.7553	−	29.0211i	0.538815	−	0.933255i	0.998968	−	0.0454157i	$-0.0144612\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−35.7465			−1.14716			−0.573580	−	0.819149i	$-0.694446\pi$
$971$	−35.7465			−1.14716			−0.573580	+	0.819149i	$0.694446\pi$
$972$		0			0
$973$	8.37748	+	24.7726i	0.268570	+	0.794173i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	39.5696	+	22.8455i	1.26594	+	0.730892i	0.974218	−	0.225610i	$-0.0724376\pi$
$977$	39.5696	+	22.8455i	1.26594	+	0.730892i	0.291725	+	0.956502i	$0.405771\pi$
$978$		0			0
$979$	27.9665	−	16.1465i	0.893814	−	0.516044i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.33713	+	16.1724i	0.297808	+	0.515819i	0.975634	−	0.219404i	$-0.0704111\pi$
$983$	9.33713	+	16.1724i	0.297808	+	0.515819i	−0.677826	+	0.735222i	$0.737078\pi$
$984$		0			0
$985$	1.48699	+	0.858517i	0.0473796	+	0.0273546i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	11.5264i		−	0.366518i
$990$		0			0
$991$	−48.5612			−1.54260			−0.771299	−	0.636473i	$-0.780392\pi$
$991$	−48.5612			−1.54260			−0.771299	+	0.636473i	$0.780392\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.54303	−	4.35497i	−0.239130	−	0.138062i
$996$		0			0
$997$	−45.1982	+	26.0952i	−1.43144	+	0.826442i	−0.997231	−	0.0743700i	$-0.976305\pi$
$997$	−45.1982	+	26.0952i	−1.43144	+	0.826442i	−0.434209	+	0.900812i	$0.642972\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cc.c.881.3		16
3.2	odd	2		1008.2.cc.c.545.1		16
4.3	odd	2		756.2.x.a.125.3		16
7.6	odd	2	inner	3024.2.cc.c.881.6		16
9.2	odd	6	inner	3024.2.cc.c.2897.6		16
9.7	even	3		1008.2.cc.c.209.8		16
12.11	even	2		252.2.x.a.41.8	yes	16
21.20	even	2		1008.2.cc.c.545.8		16
28.3	even	6		5292.2.w.a.1097.6		16
28.11	odd	6		5292.2.w.a.1097.3		16
28.19	even	6		5292.2.bm.b.2285.3		16
28.23	odd	6		5292.2.bm.b.2285.6		16
28.27	even	2		756.2.x.a.125.6		16
36.7	odd	6		252.2.x.a.209.1	yes	16
36.11	even	6		756.2.x.a.629.6		16
36.23	even	6		2268.2.f.b.1133.5		16
36.31	odd	6		2268.2.f.b.1133.11		16
63.20	even	6	inner	3024.2.cc.c.2897.3		16
63.34	odd	6		1008.2.cc.c.209.1		16
84.11	even	6		1764.2.w.a.509.3		16
84.23	even	6		1764.2.bm.b.1697.3		16
84.47	odd	6		1764.2.bm.b.1697.6		16
84.59	odd	6		1764.2.w.a.509.6		16
84.83	odd	2		252.2.x.a.41.1	✓	16
252.11	even	6		5292.2.bm.b.4625.3		16
252.47	odd	6		5292.2.w.a.521.3		16
252.79	odd	6		1764.2.w.a.1109.6		16
252.83	odd	6		756.2.x.a.629.3		16
252.115	even	6		1764.2.bm.b.1685.3		16
252.139	even	6		2268.2.f.b.1133.6		16
252.151	odd	6		1764.2.bm.b.1685.6		16
252.167	odd	6		2268.2.f.b.1133.12		16
252.187	even	6		1764.2.w.a.1109.3		16
252.191	even	6		5292.2.w.a.521.6		16
252.223	even	6		252.2.x.a.209.8	yes	16
252.227	odd	6		5292.2.bm.b.4625.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.1	✓	16	84.83	odd	2
252.2.x.a.41.8	yes	16	12.11	even	2
252.2.x.a.209.1	yes	16	36.7	odd	6
252.2.x.a.209.8	yes	16	252.223	even	6
756.2.x.a.125.3		16	4.3	odd	2
756.2.x.a.125.6		16	28.27	even	2
756.2.x.a.629.3		16	252.83	odd	6
756.2.x.a.629.6		16	36.11	even	6
1008.2.cc.c.209.1		16	63.34	odd	6
1008.2.cc.c.209.8		16	9.7	even	3
1008.2.cc.c.545.1		16	3.2	odd	2
1008.2.cc.c.545.8		16	21.20	even	2
1764.2.w.a.509.3		16	84.11	even	6
1764.2.w.a.509.6		16	84.59	odd	6
1764.2.w.a.1109.3		16	252.187	even	6
1764.2.w.a.1109.6		16	252.79	odd	6
1764.2.bm.b.1685.3		16	252.115	even	6
1764.2.bm.b.1685.6		16	252.151	odd	6
1764.2.bm.b.1697.3		16	84.23	even	6
1764.2.bm.b.1697.6		16	84.47	odd	6
2268.2.f.b.1133.5		16	36.23	even	6
2268.2.f.b.1133.6		16	252.139	even	6
2268.2.f.b.1133.11		16	36.31	odd	6
2268.2.f.b.1133.12		16	252.167	odd	6
3024.2.cc.c.881.3		16	1.1	even	1	trivial
3024.2.cc.c.881.6		16	7.6	odd	2	inner
3024.2.cc.c.2897.3		16	63.20	even	6	inner
3024.2.cc.c.2897.6		16	9.2	odd	6	inner
5292.2.w.a.521.3		16	252.47	odd	6
5292.2.w.a.521.6		16	252.191	even	6
5292.2.w.a.1097.3		16	28.11	odd	6
5292.2.w.a.1097.6		16	28.3	even	6
5292.2.bm.b.2285.3		16	28.19	even	6
5292.2.bm.b.2285.6		16	28.23	odd	6
5292.2.bm.b.4625.3		16	252.11	even	6
5292.2.bm.b.4625.6		16	252.227	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.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.276914 + 0.479629i) q^{5} +(1.98718 + 1.74675i) q^{7} +O(q^{10})\)	\(q+(-0.276914 + 0.479629i) q^{5} +(1.98718 + 1.74675i) q^{7} +(4.03478 - 2.32948i) q^{11} +(3.58265 + 2.06844i) q^{13} +7.24527 q^{17} -6.71715i q^{19} +(-4.85295 - 2.80185i) q^{23} +(2.34664 + 4.06450i) q^{25} +(-1.16599 + 0.673187i) q^{29} +(0.830741 + 0.479629i) q^{31} +(-1.38807 + 0.469409i) q^{35} -7.06956 q^{37} +(2.39152 - 4.14224i) q^{41} +(1.02846 + 1.78135i) q^{43} +(-4.90301 - 8.49226i) q^{47} +(0.897752 + 6.94219i) q^{49} -8.43202i q^{53} +2.58026i q^{55} +(3.89955 - 6.75422i) q^{59} +(-5.37336 + 3.10231i) q^{61} +(-1.98417 + 1.14556i) q^{65} +(-1.68814 + 2.92394i) q^{67} +0.407556i q^{71} +8.63566i q^{73} +(12.0868 + 2.41864i) q^{77} +(0.318176 + 0.551097i) q^{79} +(2.78840 + 4.82965i) q^{83} +(-2.00632 + 3.47504i) q^{85} +6.93137 q^{89} +(3.50632 + 10.3683i) q^{91} +(3.22174 + 1.86007i) q^{95} +(7.48798 - 4.32318i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{7}+O(q^{10}) \) 16 * q + q^7	\( 16 q + q^{7} + 6 q^{11} + 6 q^{23} - 8 q^{25} + 12 q^{29} + 4 q^{37} - 4 q^{43} - 5 q^{49} + 24 q^{65} - 14 q^{67} + 21 q^{77} - 20 q^{79} + 6 q^{85} + 18 q^{91} - 60 q^{95}+O(q^{100}) \) 16 * q + q^7 + 6 * q^11 + 6 * q^23 - 8 * q^25 + 12 * q^29 + 4 * q^37 - 4 * q^43 - 5 * q^49 + 24 * q^65 - 14 * q^67 + 21 * q^77 - 20 * q^79 + 6 * q^85 + 18 * q^91 - 60 * q^95

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