LMFDB - Embedded newform 3024.2.cc.a.881.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(881,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [12,0,0,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.3
Root			$1.29589 + 0.748185i$ of defining polynomial
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.a.2897.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.717144 + 1.24213i) q^{5} +(-2.16235 + 1.52455i) q^{7} +(2.80150 - 1.61745i) q^{11} +(-4.43334 - 2.55959i) q^{13} +1.09132 q^{17} -4.48911i q^{19} +(3.47141 + 2.00422i) q^{23} +(1.47141 + 2.54856i) q^{25} +(-1.02859 + 0.593857i) q^{29} +(-3.24275 - 1.87220i) q^{31} +(-0.342971 - 3.77924i) q^{35} -0.239123 q^{37} +(3.71620 - 6.43664i) q^{41} +(3.82326 + 6.62208i) q^{43} +(2.11042 + 3.65536i) q^{47} +(2.35150 - 6.59321i) q^{49} -7.01414i q^{53} +4.63977i q^{55} +(4.73531 - 8.20179i) q^{59} +(2.82757 - 1.63250i) q^{61} +(6.35868 - 3.67119i) q^{65} +(0.330095 - 0.571741i) q^{67} +3.82347i q^{71} +7.31073i q^{73} +(-3.59195 + 7.76852i) q^{77} +(1.83009 + 3.16982i) q^{79} +(5.45245 + 9.44392i) q^{83} +(-0.782630 + 1.35556i) q^{85} +13.6915 q^{89} +(13.4887 - 1.22412i) q^{91} +(5.57605 + 3.21934i) q^{95} +(-2.69709 + 1.55716i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{7} + 24 q^{23} - 30 q^{29} - 4 q^{37} + 10 q^{43} + 6 q^{49} + 78 q^{65} - 12 q^{67} + 24 q^{77} + 6 q^{79} - 6 q^{85} + 24 q^{91} + 72 q^{95}+O(q^{100}) $ 12 * q + 2 * q^7 + 24 * q^23 - 30 * q^29 - 4 * q^37 + 10 * q^43 + 6 * q^49 + 78 * q^65 - 12 * q^67 + 24 * q^77 + 6 * q^79 - 6 * q^85 + 24 * q^91 + 72 * q^95

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
$5$	−0.717144	+	1.24213i	−0.320716	+	0.555497i	−0.980636	−	0.195839i	$-0.937257\pi$
$5$	−0.717144	+	1.24213i	−0.320716	+	0.555497i	0.659920	+	0.751336i	$0.270590\pi$
$6$		0			0
$7$	−2.16235	+	1.52455i	−0.817291	+	0.576225i
$7$	−2.16235	+	1.52455i	−0.817291	+	0.576225i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.80150	−	1.61745i	0.844686	−	0.487679i	−0.0141686	−	0.999900i	$-0.504510\pi$
$11$	2.80150	−	1.61745i	0.844686	−	0.487679i	0.858854	+	0.512220i	$0.171177\pi$
$12$		0			0
$13$	−4.43334	−	2.55959i	−1.22959	−	0.709903i	−0.262644	−	0.964893i	$-0.584594\pi$
$13$	−4.43334	−	2.55959i	−1.22959	−	0.709903i	−0.966944	+	0.254990i	$0.917928\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.09132			0.264683			0.132341	−	0.991204i	$-0.457750\pi$
$17$	1.09132			0.264683			0.132341	+	0.991204i	$0.457750\pi$
$18$		0			0
$19$		−	4.48911i		−	1.02987i	−0.857228	−	0.514936i	$-0.827816\pi$
$19$		−	4.48911i		−	1.02987i	0.857228	−	0.514936i	$-0.172184\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.47141	+	2.00422i	0.723839	+	0.417909i	0.816164	−	0.577820i	$-0.196097\pi$
$23$	3.47141	+	2.00422i	0.723839	+	0.417909i	−0.0923250	+	0.995729i	$0.529430\pi$
$24$		0			0
$25$	1.47141	+	2.54856i	0.294282	+	0.509711i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.02859	+	0.593857i	−0.191004	+	0.110276i	−0.592453	−	0.805605i	$-0.701840\pi$
$29$	−1.02859	+	0.593857i	−0.191004	+	0.110276i	0.401448	+	0.915882i	$0.368507\pi$
$30$		0			0
$31$	−3.24275	−	1.87220i	−0.582414	−	0.336257i	0.179678	−	0.983726i	$-0.442494\pi$
$31$	−3.24275	−	1.87220i	−0.582414	−	0.336257i	−0.762092	+	0.647468i	$0.775828\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.342971	−	3.77924i	−0.0579728	−	0.638808i
$36$		0			0
$37$	−0.239123			−0.0393116			−0.0196558	−	0.999807i	$-0.506257\pi$
$37$	−0.239123			−0.0393116			−0.0196558	+	0.999807i	$0.506257\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.71620	−	6.43664i	0.580373	−	1.00523i	−0.415062	−	0.909793i	$-0.636240\pi$
$41$	3.71620	−	6.43664i	0.580373	−	1.00523i	0.995435	−	0.0954418i	$-0.0304264\pi$
$42$		0			0
$43$	3.82326	+	6.62208i	0.583041	+	1.00986i	0.995116	+	0.0987075i	$0.0314708\pi$
$43$	3.82326	+	6.62208i	0.583041	+	1.00986i	−0.412075	+	0.911150i	$0.635196\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.11042	+	3.65536i	0.307837	+	0.533189i	0.977889	−	0.209125i	$-0.0670615\pi$
$47$	2.11042	+	3.65536i	0.307837	+	0.533189i	−0.670052	+	0.742314i	$0.733728\pi$
$48$		0			0
$49$	2.35150	−	6.59321i	0.335929	−	0.941887i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	7.01414i		−	0.963466i	−0.876318	−	0.481733i	$-0.840008\pi$
$53$		−	7.01414i		−	0.963466i	0.876318	−	0.481733i	$-0.159992\pi$
$54$		0			0
$55$			4.63977i			0.625627i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.73531	−	8.20179i	0.616484	−	1.06778i	−0.373638	−	0.927575i	$-0.621890\pi$
$59$	4.73531	−	8.20179i	0.616484	−	1.06778i	0.990122	−	0.140208i	$-0.0447770\pi$
$60$		0			0
$61$	2.82757	−	1.63250i	0.362033	−	0.209020i	−0.307939	−	0.951406i	$-0.599639\pi$
$61$	2.82757	−	1.63250i	0.362033	−	0.209020i	0.669972	+	0.742386i	$0.266306\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.35868	−	3.67119i	0.788698	−	0.455355i
$66$		0			0
$67$	0.330095	−	0.571741i	0.0403275	−	0.0698493i	−0.845157	−	0.534518i	$-0.820493\pi$
$67$	0.330095	−	0.571741i	0.0403275	−	0.0698493i	0.885485	+	0.464669i	$0.153827\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			3.82347i			0.453762i	0.973922	+	0.226881i	$0.0728529\pi$
$71$			3.82347i			0.453762i	−0.973922	+	0.226881i	$0.927147\pi$
$72$		0			0
$73$			7.31073i			0.855656i	0.903860	+	0.427828i	$0.140721\pi$
$73$			7.31073i			0.855656i	−0.903860	+	0.427828i	$0.859279\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.59195	+	7.76852i	−0.409341	+	0.885305i
$78$		0			0
$79$	1.83009	+	3.16982i	0.205902	+	0.356632i	0.950420	−	0.310970i	$-0.100654\pi$
$79$	1.83009	+	3.16982i	0.205902	+	0.356632i	−0.744518	+	0.667602i	$0.767321\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.45245	+	9.44392i	0.598484	+	1.03660i	0.993045	+	0.117735i	$0.0375634\pi$
$83$	5.45245	+	9.44392i	0.598484	+	1.03660i	−0.394561	+	0.918870i	$0.629103\pi$
$84$		0			0
$85$	−0.782630	+	1.35556i	−0.0848882	+	0.147031i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	13.6915			1.45129			0.725646	−	0.688068i	$-0.241541\pi$
$89$	13.6915			1.45129			0.725646	+	0.688068i	$0.241541\pi$
$90$		0			0
$91$	13.4887	−	1.22412i	1.41399	−	0.128322i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.57605	+	3.21934i	0.572091	+	0.330297i
$96$		0			0
$97$	−2.69709	+	1.55716i	−0.273848	+	0.158106i	−0.630635	−	0.776080i	$-0.717205\pi$
$97$	−2.69709	+	1.55716i	−0.273848	+	0.158106i	0.356787	+	0.934186i	$0.383872\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.54471	+	6.13962i	0.352712	+	0.610915i	0.986724	−	0.162408i	$-0.0519262\pi$
$101$	3.54471	+	6.13962i	0.352712	+	0.610915i	−0.634012	+	0.773324i	$0.718593\pi$
$102$		0			0
$103$	1.47529	+	0.851761i	0.145365	+	0.0839265i	0.570918	−	0.821007i	$-0.306587\pi$
$103$	1.47529	+	0.851761i	0.145365	+	0.0839265i	−0.425553	+	0.904933i	$0.639921\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	4.93582i		−	0.477164i	−0.971122	−	0.238582i	$-0.923317\pi$
$107$		−	4.93582i		−	0.477164i	0.971122	−	0.238582i	$-0.0766826\pi$
$108$		0			0
$109$	8.13844			0.779521			0.389760	−	0.920916i	$-0.372558\pi$
$109$	8.13844			0.779521			0.389760	+	0.920916i	$0.372558\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.39699	+	1.96125i	0.319562	+	0.184499i	0.651197	−	0.758908i	$-0.274267\pi$
$113$	3.39699	+	1.96125i	0.319562	+	0.184499i	−0.331635	+	0.943408i	$0.607600\pi$
$114$		0			0
$115$	−4.97900	+	2.87463i	−0.464294	+	0.268060i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.35981	+	1.66376i	−0.216323	+	0.152517i
$120$		0			0
$121$	−0.267713	+	0.463693i	−0.0243376	+	0.0421539i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.3923			−1.01896
$126$		0			0
$127$	−6.16827			−0.547345			−0.273673	−	0.961823i	$-0.588239\pi$
$127$	−6.16827			−0.547345			−0.273673	+	0.961823i	$0.588239\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.13138	+	7.15575i	−0.360960	+	0.625201i	−0.988119	−	0.153690i	$-0.950884\pi$
$131$	−4.13138	+	7.15575i	−0.360960	+	0.625201i	0.627159	+	0.778891i	$0.284218\pi$
$132$		0			0
$133$	6.84387	+	9.70702i	0.593438	+	0.841706i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.96169	−	5.17404i	0.765649	−	0.442048i	−0.0656711	−	0.997841i	$-0.520919\pi$
$137$	8.96169	−	5.17404i	0.765649	−	0.442048i	0.831320	+	0.555794i	$0.187585\pi$
$138$		0			0
$139$	15.4589	+	8.92521i	1.31121	+	0.757026i	0.982296	−	0.187334i	$-0.0599848\pi$
$139$	15.4589	+	8.92521i	1.31121	+	0.757026i	0.328912	+	0.944361i	$0.393318\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−16.5600			−1.38482
$144$		0			0
$145$		−	1.70352i		−	0.141470i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	15.1758	+	8.76175i	1.24325	+	0.717790i	0.969754	−	0.244083i	$-0.0784869\pi$
$149$	15.1758	+	8.76175i	1.24325	+	0.717790i	0.273495	+	0.961873i	$0.411820\pi$
$150$		0			0
$151$	0.550343	+	0.953223i	0.0447863	+	0.0775722i	0.887550	−	0.460712i	$-0.152406\pi$
$151$	0.550343	+	0.953223i	0.0447863	+	0.0775722i	−0.842763	+	0.538284i	$0.819073\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.65103	−	2.68527i	0.373580	−	0.215686i
$156$		0			0
$157$	8.45150	+	4.87948i	0.674503	+	0.389425i	0.797781	−	0.602947i	$-0.206007\pi$
$157$	8.45150	+	4.87948i	0.674503	+	0.389425i	−0.123277	+	0.992372i	$0.539340\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−10.5619	+	0.958511i	−0.832397	+	0.0755413i
$162$		0			0
$163$	7.22545			0.565941			0.282970	−	0.959129i	$-0.408680\pi$
$163$	7.22545			0.565941			0.282970	+	0.959129i	$0.408680\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.65419	−	14.9895i	0.669681	−	1.15992i	−0.308312	−	0.951285i	$-0.599764\pi$
$167$	8.65419	−	14.9895i	0.669681	−	1.15992i	0.977993	−	0.208637i	$-0.0669027\pi$
$168$		0			0
$169$	6.60301	+	11.4367i	0.507924	+	0.879750i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.978103	+	1.69412i	0.0743638	+	0.128802i	0.900809	−	0.434215i	$-0.142974\pi$
$173$	0.978103	+	1.69412i	0.0743638	+	0.128802i	−0.826446	+	0.563017i	$0.809641\pi$
$174$		0			0
$175$	−7.06710	−	3.26763i	−0.534223	−	0.247010i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	23.2017i		−	1.73418i	−0.498152	−	0.867090i	$-0.665988\pi$
$179$		−	23.2017i		−	1.73418i	0.498152	−	0.867090i	$-0.334012\pi$
$180$		0			0
$181$		−	10.2744i		−	0.763689i	−0.924226	−	0.381845i	$-0.875289\pi$
$181$		−	10.2744i		−	0.763689i	0.924226	−	0.381845i	$-0.124711\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.171486	−	0.297022i	0.0126079	−	0.0218375i
$186$		0			0
$187$	3.05733	−	1.76515i	0.223574	−	0.129080i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	19.6758	−	11.3598i	1.42369	−	0.821968i	0.427079	−	0.904215i	$-0.359543\pi$
$191$	19.6758	−	11.3598i	1.42369	−	0.821968i	0.996612	+	0.0822464i	$0.0262094\pi$
$192$		0			0
$193$	−8.43598	+	14.6116i	−0.607235	+	1.05176i	0.384459	+	0.923142i	$0.374388\pi$
$193$	−8.43598	+	14.6116i	−0.607235	+	1.05176i	−0.991694	+	0.128620i	$0.958945\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	8.94426i		−	0.637252i	−0.947880	−	0.318626i	$-0.896779\pi$
$197$		−	8.94426i		−	0.637252i	0.947880	−	0.318626i	$-0.103221\pi$
$198$		0			0
$199$			5.78528i			0.410108i	0.978751	+	0.205054i	$0.0657369\pi$
$199$			5.78528i			0.410108i	−0.978751	+	0.205054i	$0.934263\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.31881	−	2.85226i	0.0925621	−	0.200189i
$204$		0			0
$205$	5.33009	+	9.23200i	0.372270	+	0.644791i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−7.26091	−	12.5763i	−0.502248	−	0.869918i
$210$		0			0
$211$	12.9451	−	22.4216i	0.891180	−	1.54357i	0.0527186	−	0.998609i	$-0.483211\pi$
$211$	12.9451	−	22.4216i	0.891180	−	1.54357i	0.838462	−	0.544960i	$-0.183455\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−10.9673			−0.747964
$216$		0			0
$217$	9.86621	−	0.895374i	0.669762	−	0.0607819i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.83818	−	2.79332i	−0.325451	−	0.187899i
$222$		0			0
$223$	15.4827	−	8.93892i	1.03680	−	0.598594i	0.117871	−	0.993029i	$-0.462393\pi$
$223$	15.4827	−	8.93892i	1.03680	−	0.598594i	0.918924	+	0.394435i	$0.129060\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.48365	+	9.49796i	0.363963	+	0.630402i	0.988609	−	0.150506i	$-0.0480902\pi$
$227$	5.48365	+	9.49796i	0.363963	+	0.630402i	−0.624646	+	0.780908i	$0.714757\pi$
$228$		0			0
$229$	16.8349	+	9.71965i	1.11248	+	0.642293i	0.939471	−	0.342627i	$-0.111317\pi$
$229$	16.8349	+	9.71965i	1.11248	+	0.642293i	0.173012	+	0.984920i	$0.444650\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			2.94031i			0.192626i	0.995351	+	0.0963131i	$0.0307050\pi$
$233$			2.94031i			0.192626i	−0.995351	+	0.0963131i	$0.969295\pi$
$234$		0			0
$235$	−6.05391			−0.394914
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−10.7255	−	6.19234i	−0.693772	−	0.400549i	0.111252	−	0.993792i	$-0.464514\pi$
$239$	−10.7255	−	6.19234i	−0.693772	−	0.400549i	−0.805023	+	0.593243i	$0.797847\pi$
$240$		0			0
$241$	−11.6943	+	6.75168i	−0.753293	+	0.434914i	−0.826882	−	0.562375i	$-0.809888\pi$
$241$	−11.6943	+	6.75168i	−0.753293	+	0.434914i	0.0735896	+	0.997289i	$0.476555\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.50325	+	7.64915i	0.415478	+	0.488686i
$246$		0			0
$247$	−11.4903	+	19.9018i	−0.731109	+	1.26632i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7.51441			−0.474305			−0.237153	−	0.971472i	$-0.576214\pi$
$251$	−7.51441			−0.474305			−0.237153	+	0.971472i	$0.576214\pi$
$252$		0			0
$253$	12.9669			0.815222
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.87788	−	6.71668i	0.241895	−	0.418975i	−0.719359	−	0.694639i	$-0.755564\pi$
$257$	3.87788	−	6.71668i	0.241895	−	0.418975i	0.961254	+	0.275664i	$0.0888976\pi$
$258$		0			0
$259$	0.517068	−	0.364555i	0.0321290	−	0.0226523i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−12.1127	+	6.99329i	−0.746903	+	0.431224i	−0.824574	−	0.565755i	$-0.808585\pi$
$263$	−12.1127	+	6.99329i	−0.746903	+	0.431224i	0.0776710	+	0.996979i	$0.475252\pi$
$264$		0			0
$265$	8.71246	+	5.03014i	0.535202	+	0.308999i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−25.8321			−1.57501			−0.787505	−	0.616308i	$-0.788628\pi$
$269$	−25.8321			−1.57501			−0.787505	+	0.616308i	$0.788628\pi$
$270$		0			0
$271$		−	16.6537i		−	1.01164i	−0.862639	−	0.505821i	$-0.831190\pi$
$271$		−	16.6537i		−	1.01164i	0.862639	−	0.505821i	$-0.168810\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.24433	+	4.75986i	0.497152	+	0.287031i
$276$		0			0
$277$	−15.7044	−	27.2008i	−0.943585	−	1.63434i	−0.758560	−	0.651603i	$-0.774097\pi$
$277$	−15.7044	−	27.2008i	−0.943585	−	1.63434i	−0.185025	−	0.982734i	$-0.559237\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−8.10464	+	4.67922i	−0.483483	+	0.279139i	−0.721867	−	0.692032i	$-0.756716\pi$
$281$	−8.10464	+	4.67922i	−0.483483	+	0.279139i	0.238384	+	0.971171i	$0.423382\pi$
$282$		0			0
$283$	−13.6603	−	7.88676i	−0.812018	−	0.468819i	0.0356380	−	0.999365i	$-0.488654\pi$
$283$	−13.6603	−	7.88676i	−0.812018	−	0.468819i	−0.847656	+	0.530546i	$0.821987\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.77726	+	19.5838i	0.104908	+	1.15599i
$288$		0			0
$289$	−15.8090			−0.929943
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.4287	−	21.5271i	0.726090	−	1.25762i	−0.232434	−	0.972612i	$-0.574669\pi$
$293$	12.4287	−	21.5271i	0.726090	−	1.25762i	0.958524	−	0.285013i	$-0.0919978\pi$
$294$		0			0
$295$	6.79179	+	11.7637i	0.395433	+	0.684911i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−10.2600	−	17.7708i	−0.593349	−	1.02771i
$300$		0			0
$301$	−18.3629	−	8.49050i	−1.05842	−	0.489384i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			4.68294i			0.268144i
$306$		0			0
$307$			18.8878i			1.07799i	0.842310	+	0.538993i	$0.181195\pi$
$307$			18.8878i			1.07799i	−0.842310	+	0.538993i	$0.818805\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.97716	+	6.88864i	−0.225524	+	0.390619i	−0.956476	−	0.291809i	$-0.905743\pi$
$311$	−3.97716	+	6.88864i	−0.225524	+	0.390619i	0.730953	+	0.682428i	$0.239076\pi$
$312$		0			0
$313$	−9.64210	+	5.56687i	−0.545004	+	0.314658i	−0.747104	−	0.664707i	$-0.768556\pi$
$313$	−9.64210	+	5.56687i	−0.545004	+	0.314658i	0.202101	+	0.979365i	$0.435223\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	20.1380	−	11.6267i	1.13107	−	0.653021i	0.186863	−	0.982386i	$-0.440168\pi$
$317$	20.1380	−	11.6267i	1.13107	−	0.653021i	0.944203	+	0.329365i	$0.106835\pi$
$318$		0			0
$319$	−1.92107	+	3.32738i	−0.107559	+	0.186298i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	4.89904i		−	0.272590i
$324$		0			0
$325$		−	15.0648i		−	0.835646i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−10.1363	−	4.68672i	−0.558830	−	0.258387i
$330$		0			0
$331$	−9.57962	−	16.5924i	−0.526544	−	0.912000i	−0.999522	−	0.0309261i	$-0.990154\pi$
$331$	−9.57962	−	16.5924i	−0.526544	−	0.912000i	0.472978	−	0.881074i	$-0.343179\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.473451	+	0.820041i	0.0258674	+	0.0448036i
$336$		0			0
$337$	14.2781	−	24.7304i	0.777779	−	1.34715i	−0.155441	−	0.987845i	$-0.549680\pi$
$337$	14.2781	−	24.7304i	0.777779	−	1.34715i	0.933219	−	0.359307i	$-0.116987\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−12.1128			−0.655943
$342$		0			0
$343$	4.96690	+	17.8418i	0.268187	+	0.963367i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.56690	+	1.48200i	0.137798	+	0.0795578i	0.567314	−	0.823501i	$-0.307983\pi$
$347$	2.56690	+	1.48200i	0.137798	+	0.0795578i	−0.429516	+	0.903059i	$0.641316\pi$
$348$		0			0
$349$	23.3885	−	13.5034i	1.25196	−	0.722818i	0.280460	−	0.959866i	$-0.409513\pi$
$349$	23.3885	−	13.5034i	1.25196	−	0.722818i	0.971498	+	0.237048i	$0.0761797\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	14.8238	+	25.6755i	0.788990	+	1.36657i	0.926586	+	0.376083i	$0.122729\pi$
$353$	14.8238	+	25.6755i	0.788990	+	1.36657i	−0.137596	+	0.990488i	$0.543937\pi$
$354$		0			0
$355$	−4.74924	−	2.74198i	−0.252064	−	0.145529i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			24.6261i			1.29972i	0.760056	+	0.649858i	$0.225172\pi$
$359$			24.6261i			1.29972i	−0.760056	+	0.649858i	$0.774828\pi$
$360$		0			0
$361$	−1.15211			−0.0606373
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−9.08087	−	5.24284i	−0.475314	−	0.274423i
$366$		0			0
$367$	−4.85598	+	2.80360i	−0.253480	+	0.146347i	−0.621357	−	0.783528i	$-0.713418\pi$
$367$	−4.85598	+	2.80360i	−0.253480	+	0.146347i	0.367877	+	0.929875i	$0.380085\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	10.6934	+	15.1670i	0.555173	+	0.787432i
$372$		0			0
$373$	1.86677	−	3.23333i	0.0966574	−	0.167416i	−0.813642	−	0.581367i	$-0.802518\pi$
$373$	1.86677	−	3.23333i	0.0966574	−	0.167416i	0.910299	+	0.413951i	$0.135852\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.08012			0.313142
$378$		0			0
$379$	30.4419			1.56369			0.781847	−	0.623470i	$-0.214278\pi$
$379$	30.4419			1.56369			0.781847	+	0.623470i	$0.214278\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.49251	−	14.7095i	0.433947	−	0.751618i	−0.563262	−	0.826278i	$-0.690454\pi$
$383$	8.49251	−	14.7095i	0.433947	−	0.751618i	0.997209	+	0.0746601i	$0.0237872\pi$
$384$		0			0
$385$	−7.07356	−	10.0328i	−0.360502	−	0.511319i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.43310	+	5.44621i	−0.478277	+	0.276134i	−0.719698	−	0.694287i	$-0.755720\pi$
$389$	−9.43310	+	5.44621i	−0.478277	+	0.276134i	0.241421	+	0.970420i	$0.422387\pi$
$390$		0			0
$391$	3.78840	+	2.18724i	0.191588	+	0.110613i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−5.24976			−0.264144
$396$		0			0
$397$			22.3035i			1.11938i	0.828702	+	0.559690i	$0.189080\pi$
$397$			22.3035i			1.11938i	−0.828702	+	0.559690i	$0.810920\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−20.8554	−	12.0409i	−1.04147	−	0.601293i	−0.121221	−	0.992626i	$-0.538681\pi$
$401$	−20.8554	−	12.0409i	−1.04147	−	0.601293i	−0.920249	+	0.391333i	$0.872014\pi$
$402$		0			0
$403$	9.58414	+	16.6002i	0.477420	+	0.826915i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.669905	+	0.386770i	−0.0332060	+	0.0191715i
$408$		0			0
$409$	−22.8191	−	13.1746i	−1.12833	−	0.651443i	−0.184817	−	0.982773i	$-0.559169\pi$
$409$	−22.8191	−	13.1746i	−1.12833	−	0.651443i	−0.943515	+	0.331330i	$0.892503\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	2.26464	+	24.9543i	0.111436	+	1.22792i
$414$		0			0
$415$	−15.6408			−0.767775
$416$		0			0
$417$		0			0
$418$		0			0
$419$	16.1761	−	28.0178i	0.790252	−	1.36876i	−0.135558	−	0.990769i	$-0.543283\pi$
$419$	16.1761	−	28.0178i	0.790252	−	1.36876i	0.925811	−	0.377988i	$-0.123384\pi$
$420$		0			0
$421$	−5.54746	−	9.60849i	−0.270367	−	0.468289i	0.698589	−	0.715523i	$-0.253812\pi$
$421$	−5.54746	−	9.60849i	−0.270367	−	0.468289i	−0.968956	+	0.247234i	$0.920478\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.60577	+	2.78128i	0.0778914	+	0.134912i
$426$		0			0
$427$	−3.62537	+	7.84079i	−0.175444	+	0.379443i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			16.3047i			0.785368i	0.919673	+	0.392684i	$0.128453\pi$
$431$			16.3047i			0.785368i	−0.919673	+	0.392684i	$0.871547\pi$
$432$		0			0
$433$			12.5359i			0.602438i	0.953555	+	0.301219i	$0.0973936\pi$
$433$			12.5359i			0.602438i	−0.953555	+	0.301219i	$0.902606\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	8.99716	−	15.5835i	0.430393	−	0.745462i
$438$		0			0
$439$	−16.1276	+	9.31127i	−0.769728	+	0.444403i	−0.832778	−	0.553608i	$-0.813251\pi$
$439$	−16.1276	+	9.31127i	−0.769728	+	0.444403i	0.0630496	+	0.998010i	$0.479917\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4.11436	−	2.37543i	0.195479	−	0.112860i	−0.399066	−	0.916922i	$-0.630666\pi$
$443$	4.11436	−	2.37543i	0.195479	−	0.112860i	0.594545	+	0.804062i	$0.297332\pi$
$444$		0			0
$445$	−9.81875	+	17.0066i	−0.465453	+	0.806189i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	16.2393i		−	0.766379i	−0.923670	−	0.383189i	$-0.874826\pi$
$449$		−	16.2393i		−	0.766379i	0.923670	−	0.383189i	$-0.125174\pi$
$450$		0			0
$451$		−	24.0431i		−	1.13214i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−8.15279	+	17.6325i	−0.382209	+	0.826625i
$456$		0			0
$457$	2.87360	+	4.97722i	0.134421	+	0.232825i	0.925376	−	0.379050i	$-0.123749\pi$
$457$	2.87360	+	4.97722i	0.134421	+	0.232825i	−0.790955	+	0.611874i	$0.790416\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	18.1346	+	31.4101i	0.844613	+	1.46291i	0.885957	+	0.463768i	$0.153503\pi$
$461$	18.1346	+	31.4101i	0.844613	+	1.46291i	−0.0413440	+	0.999145i	$0.513164\pi$
$462$		0			0
$463$	−14.6202	+	25.3230i	−0.679461	+	1.17686i	0.295683	+	0.955286i	$0.404453\pi$
$463$	−14.6202	+	25.3230i	−0.679461	+	1.17686i	−0.975144	+	0.221574i	$0.928881\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.64215			−0.122264			−0.0611320	−	0.998130i	$-0.519471\pi$
$467$	−2.64215			−0.122264			−0.0611320	+	0.998130i	$0.519471\pi$
$468$		0			0
$469$	0.157867	+	1.73955i	0.00728961	+	0.0803249i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	21.4218	+	12.3679i	0.984973	+	0.568675i
$474$		0			0
$475$	11.4408	−	6.60532i	0.524938	−	0.303073i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	15.5409	+	26.9177i	0.710083	+	1.22990i	0.964826	+	0.262891i	$0.0846760\pi$
$479$	15.5409	+	26.9177i	0.710083	+	1.22990i	−0.254742	+	0.967009i	$0.581991\pi$
$480$		0			0
$481$	1.06012	+	0.612058i	0.0483371	+	0.0279074i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	4.46684i		−	0.202829i
$486$		0			0
$487$	−34.8720			−1.58020			−0.790100	−	0.612978i	$-0.789971\pi$
$487$	−34.8720			−1.58020			−0.790100	+	0.612978i	$0.789971\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−22.6758	−	13.0919i	−1.02334	−	0.590828i	−0.108273	−	0.994121i	$-0.534532\pi$
$491$	−22.6758	−	13.0919i	−1.02334	−	0.590828i	−0.915071	+	0.403293i	$0.867866\pi$
$492$		0			0
$493$	−1.12252	+	0.648085i	−0.0505556	+	0.0291883i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.82906	−	8.26767i	−0.261469	−	0.370856i
$498$		0			0
$499$	6.23912	−	10.8065i	0.279302	−	0.483764i	−0.691910	−	0.721984i	$-0.743230\pi$
$499$	6.23912	−	10.8065i	0.279302	−	0.483764i	0.971211	+	0.238220i	$0.0765638\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	37.8479			1.68756			0.843778	−	0.536693i	$-0.180327\pi$
$503$	37.8479			1.68756			0.843778	+	0.536693i	$0.180327\pi$
$504$		0			0
$505$	−10.1683			−0.452482
$506$		0			0
$507$		0			0
$508$		0			0
$509$	17.6924	−	30.6441i	0.784200	−	1.35827i	−0.145276	−	0.989391i	$-0.546407\pi$
$509$	17.6924	−	30.6441i	0.784200	−	1.35827i	0.929476	−	0.368883i	$-0.120260\pi$
$510$		0			0
$511$	−11.1456	−	15.8083i	−0.493050	−	0.699320i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.11599	+	1.22167i	−0.0932419	+	0.0538332i
$516$		0			0
$517$	11.8247	+	6.82701i	0.520051	+	0.300252i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.31879			−0.101588			−0.0507940	−	0.998709i	$-0.516175\pi$
$521$	−2.31879			−0.101588			−0.0507940	+	0.998709i	$0.516175\pi$
$522$		0			0
$523$			20.1840i			0.882585i	0.897363	+	0.441293i	$0.145480\pi$
$523$			20.1840i			0.882585i	−0.897363	+	0.441293i	$0.854520\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.53886	−	2.04316i	−0.154155	−	0.0890015i
$528$		0			0
$529$	−3.46621	−	6.00365i	−0.150705	−	0.261028i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−32.9503	+	19.0239i	−1.42724	+	0.824016i
$534$		0			0
$535$	6.13093	+	3.53970i	0.265063	+	0.153034i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−4.07644	−	22.2744i	−0.175585	−	0.959424i
$540$		0			0
$541$	−22.7713			−0.979014			−0.489507	−	0.871999i	$-0.662823\pi$
$541$	−22.7713			−0.979014			−0.489507	+	0.871999i	$0.662823\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−5.83643	+	10.1090i	−0.250005	+	0.433022i
$546$		0			0
$547$	−14.7918	−	25.6201i	−0.632451	−	1.09544i	−0.987049	−	0.160419i	$-0.948716\pi$
$547$	−14.7918	−	25.6201i	−0.632451	−	1.09544i	0.354598	−	0.935019i	$-0.384618\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.66589	+	4.61745i	0.113571	+	0.196710i
$552$		0			0
$553$	−8.78984	−	4.06418i	−0.373782	−	0.172827i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			4.71407i			0.199741i	0.995000	+	0.0998707i	$0.0318429\pi$
$557$			4.71407i			0.199741i	−0.995000	+	0.0998707i	$0.968157\pi$
$558$		0			0
$559$		−	39.1439i		−	1.65561i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−13.6742	+	23.6844i	−0.576299	+	0.998179i	0.419601	+	0.907709i	$0.362170\pi$
$563$	−13.6742	+	23.6844i	−0.576299	+	0.998179i	−0.995899	+	0.0904697i	$0.971163\pi$
$564$		0			0
$565$	−4.87226	+	2.81300i	−0.204977	+	0.118344i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−20.4018	+	11.7790i	−0.855288	+	0.493801i	−0.862432	−	0.506174i	$-0.831059\pi$
$569$	−20.4018	+	11.7790i	−0.855288	+	0.493801i	0.00714355	+	0.999974i	$0.497726\pi$
$570$		0			0
$571$	9.59385	−	16.6170i	0.401490	−	0.695401i	−0.592416	−	0.805632i	$-0.701826\pi$
$571$	9.59385	−	16.6170i	0.401490	−	0.695401i	0.993906	+	0.110231i	$0.0351591\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			11.7961i			0.491932i
$576$		0			0
$577$		−	2.23413i		−	0.0930079i	−0.998918	−	0.0465039i	$-0.985192\pi$
$577$		−	2.23413i		−	0.0930079i	0.998918	−	0.0465039i	$-0.0148080\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−26.1878	−	12.1085i	−1.08645	−	0.502346i
$582$		0			0
$583$	−11.3450	−	19.6501i	−0.469862	−	0.813826i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.9883	−	22.4963i	−0.536083	−	0.928522i	−0.999110	−	0.0421784i	$-0.986570\pi$
$587$	−12.9883	−	22.4963i	−0.536083	−	0.928522i	0.463028	−	0.886344i	$-0.346763\pi$
$588$		0			0
$589$	−8.40451	+	14.5570i	−0.346302	+	0.599813i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−5.71754			−0.234791			−0.117396	−	0.993085i	$-0.537455\pi$
$593$	−5.71754			−0.234791			−0.117396	+	0.993085i	$0.537455\pi$
$594$		0			0
$595$	−0.374290	−	4.12434i	−0.0153444	−	0.169081i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	21.8662	+	12.6245i	0.893429	+	0.515822i	0.875063	−	0.484010i	$-0.160820\pi$
$599$	21.8662	+	12.6245i	0.893429	+	0.515822i	0.0183665	+	0.999831i	$0.494153\pi$
$600$		0			0
$601$	40.2546	−	23.2410i	1.64202	−	0.948021i	0.661907	−	0.749586i	$-0.269748\pi$
$601$	40.2546	−	23.2410i	1.64202	−	0.948021i	0.980114	−	0.198435i	$-0.0635858\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.383978	−	0.665069i	−0.0156109	−	0.0270389i
$606$		0			0
$607$	6.09405	+	3.51840i	0.247350	+	0.142808i	0.618550	−	0.785745i	$-0.287720\pi$
$607$	6.09405	+	3.51840i	0.247350	+	0.142808i	−0.371200	+	0.928553i	$0.621054\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	21.6073i		−	0.874138i
$612$		0			0
$613$	6.54256			0.264252			0.132126	−	0.991233i	$-0.457820\pi$
$613$	6.54256			0.264252			0.132126	+	0.991233i	$0.457820\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	30.0043	+	17.3230i	1.20793	+	0.697396i	0.962306	−	0.271970i	$-0.0876751\pi$
$617$	30.0043	+	17.3230i	1.20793	+	0.697396i	0.245620	+	0.969366i	$0.421008\pi$
$618$		0			0
$619$	−14.7072	+	8.49123i	−0.591134	+	0.341291i	−0.765546	−	0.643381i	$-0.777531\pi$
$619$	−14.7072	+	8.49123i	−0.591134	+	0.341291i	0.174412	+	0.984673i	$0.444198\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−29.6057	+	20.8733i	−1.18613	+	0.836271i
$624$		0			0
$625$	0.812855	−	1.40791i	0.0325142	−	0.0563162i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−0.260959			−0.0104051
$630$		0			0
$631$	−26.2438			−1.04475			−0.522374	−	0.852716i	$-0.674953\pi$
$631$	−26.2438			−1.04475			−0.522374	+	0.852716i	$0.674953\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.42354	−	7.66179i	0.175543	−	0.304049i
$636$		0			0
$637$	−27.3009	+	23.2111i	−1.08170	+	0.919656i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.5092	+	9.53157i	−0.652073	+	0.376474i	−0.789250	−	0.614072i	$-0.789530\pi$
$641$	−16.5092	+	9.53157i	−0.652073	+	0.376474i	0.137177	+	0.990547i	$0.456197\pi$
$642$		0			0
$643$	−15.3447	−	8.85928i	−0.605136	−	0.349376i	0.165923	−	0.986139i	$-0.446940\pi$
$643$	−15.3447	−	8.85928i	−0.605136	−	0.349376i	−0.771060	+	0.636763i	$0.780273\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−21.7902			−0.856661			−0.428330	−	0.903622i	$-0.640898\pi$
$647$	−21.7902			−0.856661			−0.428330	+	0.903622i	$0.640898\pi$
$648$		0			0
$649$		−	30.6365i		−	1.20259i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.0852	+	7.55475i	0.512064	+	0.295640i	0.733682	−	0.679493i	$-0.237800\pi$
$653$	13.0852	+	7.55475i	0.512064	+	0.295640i	−0.221618	+	0.975134i	$0.571134\pi$
$654$		0			0
$655$	−5.92558	−	10.2634i	−0.231532	−	0.401024i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−27.1850	+	15.6952i	−1.05898	+	0.611400i	−0.925149	−	0.379605i	$-0.876060\pi$
$659$	−27.1850	+	15.6952i	−1.05898	+	0.611400i	−0.133827	+	0.991005i	$0.542727\pi$
$660$		0			0
$661$	−37.8554	−	21.8558i	−1.47240	−	0.850093i	−0.472885	−	0.881124i	$-0.656787\pi$
$661$	−37.8554	−	21.8558i	−1.47240	−	0.850093i	−0.999518	+	0.0310314i	$0.990121\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−16.9654	+	1.53964i	−0.657890	+	0.0597046i
$666$		0			0
$667$	−4.76088			−0.184342
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.28096	−	9.14690i	0.203869	−	0.353112i
$672$		0			0
$673$	−4.60589	−	7.97763i	−0.177544	−	0.307515i	0.763495	−	0.645814i	$-0.223482\pi$
$673$	−4.60589	−	7.97763i	−0.177544	−	0.307515i	−0.941039	+	0.338299i	$0.890149\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.4194	+	19.7789i	0.438882	+	0.760165i	0.997604	−	0.0691899i	$-0.0220414\pi$
$677$	11.4194	+	19.7789i	0.438882	+	0.760165i	−0.558722	+	0.829355i	$0.688708\pi$
$678$		0			0
$679$	3.45807	−	7.47898i	0.132709	−	0.287017i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	34.1826i		−	1.30796i	−0.756511	−	0.653981i	$-0.773098\pi$
$683$		−	34.1826i		−	1.30796i	0.756511	−	0.653981i	$-0.226902\pi$
$684$		0			0
$685$			14.8421i			0.567088i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−17.9533	+	31.0961i	−0.683967	+	1.18467i
$690$		0			0
$691$	0.224082	−	0.129374i	0.00852446	−	0.00492160i	−0.495732	−	0.868476i	$-0.665100\pi$
$691$	0.224082	−	0.129374i	0.00852446	−	0.00492160i	0.504256	+	0.863554i	$0.331767\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−22.1725	+	12.8013i	−0.841052	+	0.485582i
$696$		0			0
$697$	4.05555	−	7.02441i	0.153615	−	0.266069i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			5.16189i			0.194962i	0.995237	+	0.0974810i	$0.0310785\pi$
$701$			5.16189i			0.194962i	−0.995237	+	0.0974810i	$0.968921\pi$
$702$		0			0
$703$			1.07345i			0.0404860i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−17.0251	−	7.87192i	−0.640293	−	0.296054i
$708$		0			0
$709$	−11.7472	−	20.3468i	−0.441175	−	0.764138i	0.556602	−	0.830780i	$-0.312105\pi$
$709$	−11.7472	−	20.3468i	−0.441175	−	0.764138i	−0.997777	+	0.0666412i	$0.978772\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−7.50460	−	12.9984i	−0.281050	−	0.486792i
$714$		0			0
$715$	11.8759	−	20.5697i	0.444134	−	0.769263i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−10.1566			−0.378776			−0.189388	−	0.981902i	$-0.560650\pi$
$719$	−10.1566			−0.378776			−0.189388	+	0.981902i	$0.560650\pi$
$720$		0			0
$721$	−4.48865	+	0.407352i	−0.167166	+	0.0151706i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.02696	−	1.74761i	−0.112418	−	0.0649047i
$726$		0			0
$727$	5.74874	−	3.31904i	0.213209	−	0.123096i	−0.389593	−	0.920987i	$-0.627384\pi$
$727$	5.74874	−	3.31904i	0.213209	−	0.123096i	0.602802	+	0.797891i	$0.294051\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.17238	+	7.22678i	0.154321	+	0.267292i
$732$		0			0
$733$	5.20130	+	3.00297i	0.192114	+	0.110917i	0.592972	−	0.805223i	$-0.297954\pi$
$733$	5.20130	+	3.00297i	0.192114	+	0.110917i	−0.400858	+	0.916140i	$0.631288\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	2.13565i		−	0.0786676i
$738$		0			0
$739$	15.6386			0.575275			0.287638	−	0.957739i	$-0.407130\pi$
$739$	15.6386			0.575275			0.287638	+	0.957739i	$0.407130\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	27.3807	+	15.8083i	1.00450	+	0.579949i	0.909577	−	0.415535i	$-0.136406\pi$
$743$	27.3807	+	15.8083i	1.00450	+	0.579949i	0.0949246	+	0.995484i	$0.469739\pi$
$744$		0			0
$745$	−21.7664	+	12.5669i	−0.797461	+	0.460414i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	7.52490	+	10.6730i	0.274954	+	0.389982i
$750$		0			0
$751$	−7.13680	+	12.3613i	−0.260426	+	0.451070i	−0.966355	−	0.257212i	$-0.917196\pi$
$751$	−7.13680	+	12.3613i	−0.260426	+	0.451070i	0.705929	+	0.708282i	$0.250530\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−1.57870			−0.0574548
$756$		0			0
$757$	−10.8227			−0.393358			−0.196679	−	0.980468i	$-0.563016\pi$
$757$	−10.8227			−0.393358			−0.196679	+	0.980468i	$0.563016\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.93098	+	5.07660i	−0.106248	+	0.184027i	−0.914247	−	0.405157i	$-0.867217\pi$
$761$	−2.93098	+	5.07660i	−0.106248	+	0.184027i	0.808000	+	0.589183i	$0.200550\pi$
$762$		0			0
$763$	−17.5981	+	12.4074i	−0.637095	+	0.449180i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−41.9865	+	24.2409i	−1.51604	+	0.875288i
$768$		0			0
$769$	27.5683	+	15.9166i	0.994140	+	0.573967i	0.906509	−	0.422186i	$-0.138737\pi$
$769$	27.5683	+	15.9166i	0.994140	+	0.573967i	0.0876307	+	0.996153i	$0.472070\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−19.0382			−0.684755			−0.342378	−	0.939562i	$-0.611232\pi$
$773$	−19.0382			−0.684755			−0.342378	+	0.939562i	$0.611232\pi$
$774$		0			0
$775$		−	11.0191i		−	0.395818i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−28.8948	−	16.6824i	−1.03526	−	0.597710i
$780$		0			0
$781$	6.18427	+	10.7115i	0.221290	+	0.383286i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−12.1219	+	6.99857i	−0.432649	+	0.249790i
$786$		0			0
$787$	16.4123	+	9.47564i	0.585035	+	0.337770i	0.763132	−	0.646243i	$-0.223661\pi$
$787$	16.4123	+	9.47564i	0.585035	+	0.337770i	−0.178097	+	0.984013i	$0.556994\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−10.3355	+	0.937963i	−0.367488	+	0.0333501i
$792$		0			0
$793$	−16.7141			−0.593535
$794$		0			0
$795$		0			0
$796$		0			0
$797$	26.7207	−	46.2816i	0.946497	−	1.63938i	0.193770	−	0.981047i	$-0.437929\pi$
$797$	26.7207	−	46.2816i	0.946497	−	1.63938i	0.752727	−	0.658333i	$-0.228738\pi$
$798$		0			0
$799$	2.30314	+	3.98916i	0.0814792	+	0.141126i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	11.8247	+	20.4810i	0.417286	+	0.722760i
$804$		0			0
$805$	6.38383	−	13.8067i	0.225000	−	0.486621i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	2.58095i		−	0.0907413i	−0.998970	−	0.0453706i	$-0.985553\pi$
$809$		−	2.58095i		−	0.0907413i	0.998970	−	0.0453706i	$-0.0144469\pi$
$810$		0			0
$811$			6.06938i			0.213125i	0.994306	+	0.106562i	$0.0339844\pi$
$811$			6.06938i			0.213125i	−0.994306	+	0.106562i	$0.966016\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.18169	+	8.97494i	−0.181507	+	0.314379i
$816$		0			0
$817$	29.7272	−	17.1630i	1.04002	−	0.600458i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.03938	+	4.64154i	−0.280576	+	0.161991i	−0.633684	−	0.773592i	$-0.718458\pi$
$821$	−8.03938	+	4.64154i	−0.280576	+	0.161991i	0.353108	+	0.935583i	$0.385125\pi$
$822$		0			0
$823$	9.03448	−	15.6482i	0.314922	−	0.545461i	−0.664499	−	0.747289i	$-0.731355\pi$
$823$	9.03448	−	15.6482i	0.314922	−	0.545461i	0.979421	+	0.201828i	$0.0646882\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			48.5440i			1.68804i	0.536310	+	0.844021i	$0.319818\pi$
$827$			48.5440i			1.68804i	−0.536310	+	0.844021i	$0.680182\pi$
$828$		0			0
$829$			5.44792i			0.189214i	0.995515	+	0.0946071i	$0.0301595\pi$
$829$			5.44792i			0.189214i	−0.995515	+	0.0946071i	$0.969841\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	2.56623	−	7.19527i	0.0889147	−	0.249302i
$834$		0			0
$835$	12.4126	+	21.4992i	0.429556	+	0.744012i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−24.2673	−	42.0322i	−0.837801	−	1.45111i	−0.891729	−	0.452569i	$-0.850508\pi$
$839$	−24.2673	−	42.0322i	−0.837801	−	1.45111i	0.0539281	−	0.998545i	$-0.482826\pi$
$840$		0			0
$841$	−13.7947	+	23.8931i	−0.475678	+	0.823899i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−18.9412			−0.651598
$846$		0			0
$847$	−0.128033	−	1.41081i	−0.00439926	−	0.0484759i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.830095	−	0.479256i	−0.0284553	−	0.0164287i
$852$		0			0
$853$	−10.7703	+	6.21823i	−0.368768	+	0.212908i	−0.672920	−	0.739715i	$-0.734960\pi$
$853$	−10.7703	+	6.21823i	−0.368768	+	0.212908i	0.304152	+	0.952623i	$0.401627\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.29077	−	9.16388i	−0.180729	−	0.313032i	0.761400	−	0.648283i	$-0.224512\pi$
$857$	−5.29077	−	9.16388i	−0.180729	−	0.313032i	−0.942129	+	0.335250i	$0.891179\pi$
$858$		0			0
$859$	28.1452	+	16.2496i	0.960302	+	0.554431i	0.896266	−	0.443517i	$-0.146269\pi$
$859$	28.1452	+	16.2496i	0.960302	+	0.554431i	0.0640360	+	0.997948i	$0.479603\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			25.2203i			0.858510i	0.903183	+	0.429255i	$0.141224\pi$
$863$			25.2203i			0.858510i	−0.903183	+	0.429255i	$0.858776\pi$
$864$		0			0
$865$	−2.80576			−0.0953987
$866$		0			0
$867$		0			0
$868$		0			0
$869$	10.2540	+	5.92017i	0.347844	+	0.200828i
$870$		0			0
$871$	−2.92685	+	1.68982i	−0.0991724	+	0.0572572i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	24.6341	−	17.3681i	0.832784	−	0.587149i
$876$		0			0
$877$	7.47893	−	12.9539i	0.252546	−	0.437422i	−0.711680	−	0.702503i	$-0.752066\pi$
$877$	7.47893	−	12.9539i	0.252546	−	0.437422i	0.964226	+	0.265082i	$0.0853989\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	36.4482			1.22797			0.613985	−	0.789318i	$-0.289566\pi$
$881$	36.4482			1.22797			0.613985	+	0.789318i	$0.289566\pi$
$882$		0			0
$883$	−15.9831			−0.537873			−0.268936	−	0.963158i	$-0.586672\pi$
$883$	−15.9831			−0.537873			−0.268936	+	0.963158i	$0.586672\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	24.5208	−	42.4713i	0.823329	−	1.42605i	−0.0798613	−	0.996806i	$-0.525448\pi$
$887$	24.5208	−	42.4713i	0.823329	−	1.42605i	0.903190	−	0.429241i	$-0.141219\pi$
$888$		0			0
$889$	13.3380	−	9.40383i	0.447341	−	0.315394i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	16.4093	−	9.47393i	0.549117	−	0.317033i
$894$		0			0
$895$	28.8196	+	16.6390i	0.963332	+	0.556180i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	4.44728			0.148325
$900$		0			0
$901$		−	7.65464i		−	0.255013i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	12.7621	+	7.36821i	0.424227	+	0.244928i
$906$		0			0
$907$	−2.42915	−	4.20741i	−0.0806585	−	0.139705i	0.822874	−	0.568223i	$-0.192369\pi$
$907$	−2.42915	−	4.20741i	−0.0806585	−	0.139705i	−0.903533	+	0.428519i	$0.859036\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	14.4945	−	8.36843i	0.480226	−	0.277258i	−0.240285	−	0.970702i	$-0.577241\pi$
$911$	14.4945	−	8.36843i	0.480226	−	0.277258i	0.720510	+	0.693444i	$0.243908\pi$
$912$		0			0
$913$	30.5501	+	17.6381i	1.01106	+	0.583737i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.97582	−	21.7717i	−0.0652472	−	0.718965i
$918$		0			0
$919$	−30.6400			−1.01072			−0.505360	−	0.862909i	$-0.668640\pi$
$919$	−30.6400			−1.01072			−0.505360	+	0.862909i	$0.668640\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	9.78651	−	16.9507i	0.322127	−	0.557940i
$924$		0			0
$925$	−0.351848	−	0.609419i	−0.0115687	−	0.0200376i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−14.8723	−	25.7595i	−0.487943	−	0.845142i	0.511961	−	0.859009i	$-0.328919\pi$
$929$	−14.8723	−	25.7595i	−0.487943	−	0.845142i	−0.999904	+	0.0138670i	$0.995586\pi$
$930$		0			0
$931$	−29.5976	−	10.5562i	−0.970024	−	0.345964i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			5.06346i			0.165593i
$936$		0			0
$937$		−	4.03712i		−	0.131887i	−0.997823	−	0.0659434i	$-0.978994\pi$
$937$		−	4.03712i		−	0.131887i	0.997823	−	0.0659434i	$-0.0210057\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−7.20264	+	12.4753i	−0.234799	+	0.406684i	−0.959214	−	0.282680i	$-0.908777\pi$
$941$	−7.20264	+	12.4753i	−0.234799	+	0.406684i	0.724415	+	0.689364i	$0.242110\pi$
$942$		0			0
$943$	25.8009	−	14.8962i	0.840193	−	0.485085i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	27.0334	−	15.6077i	0.878467	−	0.507183i	0.00831468	−	0.999965i	$-0.497353\pi$
$947$	27.0334	−	15.6077i	0.878467	−	0.507183i	0.870153	+	0.492782i	$0.164020\pi$
$948$		0			0
$949$	18.7125	−	32.4109i	0.607432	−	1.05210i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			8.55869i			0.277243i	0.990345	+	0.138622i	$0.0442672\pi$
$953$			8.55869i			0.277243i	−0.990345	+	0.138622i	$0.955733\pi$
$954$		0			0
$955$			32.5865i			1.05447i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−11.4902	+	24.8506i	−0.371039	+	0.802468i
$960$		0			0
$961$	−8.48973	−	14.7046i	−0.273862	−	0.474343i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.0996	−	20.9572i	−0.389501	−	0.674635i
$966$		0			0
$967$	−16.0280	+	27.7614i	−0.515427	+	0.892745i	0.484413	+	0.874840i	$0.339033\pi$
$967$	−16.0280	+	27.7614i	−0.515427	+	0.892745i	−0.999840	+	0.0179059i	$0.994300\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	33.2366			1.06661			0.533307	−	0.845922i	$-0.320949\pi$
$971$	33.2366			1.06661			0.533307	+	0.845922i	$0.320949\pi$
$972$		0			0
$973$	−47.0345	+	4.26845i	−1.50786	+	0.136840i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−45.1558	−	26.0707i	−1.44466	−	0.834076i	−0.446507	−	0.894780i	$-0.647332\pi$
$977$	−45.1558	−	26.0707i	−1.44466	−	0.834076i	−0.998156	+	0.0607042i	$0.980665\pi$
$978$		0			0
$979$	38.3567	−	22.1453i	1.22589	−	0.707765i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−12.1192	−	20.9911i	−0.386544	−	0.669513i	0.605438	−	0.795892i	$-0.292998\pi$
$983$	−12.1192	−	20.9911i	−0.386544	−	0.669513i	−0.991982	+	0.126379i	$0.959664\pi$
$984$		0			0
$985$	11.1099	+	6.41432i	0.353992	+	0.204377i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			30.6506i			0.974632i
$990$		0			0
$991$	24.1981			0.768678			0.384339	−	0.923192i	$-0.374429\pi$
$991$	24.1981			0.768678			0.384339	+	0.923192i	$0.374429\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.18607	−	4.14888i	−0.227814	−	0.131528i
$996$		0			0
$997$	8.81920	−	5.09177i	0.279307	−	0.161258i	−0.353803	−	0.935320i	$-0.615112\pi$
$997$	8.81920	−	5.09177i	0.279307	−	0.161258i	0.633110	+	0.774062i	$0.281778\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cc.a.881.3		12
3.2	odd	2		1008.2.cc.a.545.5		12
4.3	odd	2		189.2.o.a.125.5		12
7.6	odd	2	inner	3024.2.cc.a.881.4		12
9.2	odd	6	inner	3024.2.cc.a.2897.4		12
9.7	even	3		1008.2.cc.a.209.2		12
12.11	even	2		63.2.o.a.41.1	yes	12
21.20	even	2		1008.2.cc.a.545.2		12
28.3	even	6		1323.2.i.c.1097.6		12
28.11	odd	6		1323.2.i.c.1097.5		12
28.19	even	6		1323.2.s.c.962.1		12
28.23	odd	6		1323.2.s.c.962.2		12
28.27	even	2		189.2.o.a.125.6		12
36.7	odd	6		63.2.o.a.20.2	yes	12
36.11	even	6		189.2.o.a.62.6		12
36.23	even	6		567.2.c.c.566.1		12
36.31	odd	6		567.2.c.c.566.12		12
63.20	even	6	inner	3024.2.cc.a.2897.3		12
63.34	odd	6		1008.2.cc.a.209.5		12
84.11	even	6		441.2.i.c.68.1		12
84.23	even	6		441.2.s.c.374.6		12
84.47	odd	6		441.2.s.c.374.5		12
84.59	odd	6		441.2.i.c.68.2		12
84.83	odd	2		63.2.o.a.41.2	yes	12
252.11	even	6		1323.2.s.c.656.1		12
252.47	odd	6		1323.2.i.c.521.1		12
252.79	odd	6		441.2.i.c.227.6		12
252.83	odd	6		189.2.o.a.62.5		12
252.115	even	6		441.2.s.c.362.6		12
252.139	even	6		567.2.c.c.566.11		12
252.151	odd	6		441.2.s.c.362.5		12
252.167	odd	6		567.2.c.c.566.2		12
252.187	even	6		441.2.i.c.227.5		12
252.191	even	6		1323.2.i.c.521.2		12
252.223	even	6		63.2.o.a.20.1	✓	12
252.227	odd	6		1323.2.s.c.656.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.1	✓	12	252.223	even	6
63.2.o.a.20.2	yes	12	36.7	odd	6
63.2.o.a.41.1	yes	12	12.11	even	2
63.2.o.a.41.2	yes	12	84.83	odd	2
189.2.o.a.62.5		12	252.83	odd	6
189.2.o.a.62.6		12	36.11	even	6
189.2.o.a.125.5		12	4.3	odd	2
189.2.o.a.125.6		12	28.27	even	2
441.2.i.c.68.1		12	84.11	even	6
441.2.i.c.68.2		12	84.59	odd	6
441.2.i.c.227.5		12	252.187	even	6
441.2.i.c.227.6		12	252.79	odd	6
441.2.s.c.362.5		12	252.151	odd	6
441.2.s.c.362.6		12	252.115	even	6
441.2.s.c.374.5		12	84.47	odd	6
441.2.s.c.374.6		12	84.23	even	6
567.2.c.c.566.1		12	36.23	even	6
567.2.c.c.566.2		12	252.167	odd	6
567.2.c.c.566.11		12	252.139	even	6
567.2.c.c.566.12		12	36.31	odd	6
1008.2.cc.a.209.2		12	9.7	even	3
1008.2.cc.a.209.5		12	63.34	odd	6
1008.2.cc.a.545.2		12	21.20	even	2
1008.2.cc.a.545.5		12	3.2	odd	2
1323.2.i.c.521.1		12	252.47	odd	6
1323.2.i.c.521.2		12	252.191	even	6
1323.2.i.c.1097.5		12	28.11	odd	6
1323.2.i.c.1097.6		12	28.3	even	6
1323.2.s.c.656.1		12	252.11	even	6
1323.2.s.c.656.2		12	252.227	odd	6
1323.2.s.c.962.1		12	28.19	even	6
1323.2.s.c.962.2		12	28.23	odd	6
3024.2.cc.a.881.3		12	1.1	even	1	trivial
3024.2.cc.a.881.4		12	7.6	odd	2	inner
3024.2.cc.a.2897.3		12	63.20	even	6	inner
3024.2.cc.a.2897.4		12	9.2	odd	6	inner

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 $\F_{q}$
Belyi maps

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)

\(f(q)\)	\(=\)	\(q+(-0.717144 + 1.24213i) q^{5} +(-2.16235 + 1.52455i) q^{7} +(2.80150 - 1.61745i) q^{11} +(-4.43334 - 2.55959i) q^{13} +1.09132 q^{17} -4.48911i q^{19} +(3.47141 + 2.00422i) q^{23} +(1.47141 + 2.54856i) q^{25} +(-1.02859 + 0.593857i) q^{29} +(-3.24275 - 1.87220i) q^{31} +(-0.342971 - 3.77924i) q^{35} -0.239123 q^{37} +(3.71620 - 6.43664i) q^{41} +(3.82326 + 6.62208i) q^{43} +(2.11042 + 3.65536i) q^{47} +(2.35150 - 6.59321i) q^{49} -7.01414i q^{53} +4.63977i q^{55} +(4.73531 - 8.20179i) q^{59} +(2.82757 - 1.63250i) q^{61} +(6.35868 - 3.67119i) q^{65} +(0.330095 - 0.571741i) q^{67} +3.82347i q^{71} +7.31073i q^{73} +(-3.59195 + 7.76852i) q^{77} +(1.83009 + 3.16982i) q^{79} +(5.45245 + 9.44392i) q^{83} +(-0.782630 + 1.35556i) q^{85} +13.6915 q^{89} +(13.4887 - 1.22412i) q^{91} +(5.57605 + 3.21934i) q^{95} +(-2.69709 + 1.55716i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{7} + 24 q^{23} - 30 q^{29} - 4 q^{37} + 10 q^{43} + 6 q^{49} + 78 q^{65} - 12 q^{67} + 24 q^{77} + 6 q^{79} - 6 q^{85} + 24 q^{91} + 72 q^{95}+O(q^{100}) \) 12 * q + 2 * q^7 + 24 * q^23 - 30 * q^29 - 4 * q^37 + 10 * q^43 + 6 * q^49 + 78 * q^65 - 12 * q^67 + 24 * q^77 + 6 * q^79 - 6 * q^85 + 24 * q^91 + 72 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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