LMFDB - Embedded newform 3024.2.cc.a.881.4

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:	$12$
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			881.4
Root			$-1.29589 - 0.748185i$ of defining polynomial
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.a.2897.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.717144 - 1.24213i) q^{5} +(2.40147 - 1.11037i) q^{7} +(2.80150 - 1.61745i) q^{11} +(4.43334 + 2.55959i) q^{13} -1.09132 q^{17} +4.48911i q^{19} +(3.47141 + 2.00422i) q^{23} +(1.47141 + 2.54856i) q^{25} +(-1.02859 + 0.593857i) q^{29} +(3.24275 + 1.87220i) q^{31} +(0.342971 - 3.77924i) q^{35} -0.239123 q^{37} +(-3.71620 + 6.43664i) q^{41} +(3.82326 + 6.62208i) q^{43} +(-2.11042 - 3.65536i) q^{47} +(4.53414 - 5.33307i) q^{49} -7.01414i q^{53} -4.63977i q^{55} +(-4.73531 + 8.20179i) q^{59} +(-2.82757 + 1.63250i) q^{61} +(6.35868 - 3.67119i) q^{65} +(0.330095 - 0.571741i) q^{67} +3.82347i q^{71} -7.31073i q^{73} +(4.93176 - 6.99498i) q^{77} +(1.83009 + 3.16982i) q^{79} +(-5.45245 - 9.44392i) q^{83} +(-0.782630 + 1.35556i) q^{85} -13.6915 q^{89} +(13.4887 + 1.22412i) q^{91} +(5.57605 + 3.21934i) q^{95} +(2.69709 - 1.55716i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.659920	−	0.751336i	$-0.729410\pi$
$5$	0.717144	−	1.24213i	0.320716	−	0.555497i	0.980636	+	0.195839i	$0.0627430\pi$
$6$		0			0
$7$	2.40147	−	1.11037i	0.907671	−	0.419682i
$7$	2.40147	−	1.11037i	0.907671	−	0.419682i
$8$		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	0.966944	−	0.254990i	$-0.0820722\pi$
$13$	4.43334	+	2.55959i	1.22959	+	0.709903i	0.262644	+	0.964893i	$0.415406\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.09132			−0.264683			−0.132341	−	0.991204i	$-0.542250\pi$
$17$	−1.09132			−0.264683			−0.132341	+	0.991204i	$0.542250\pi$
$18$		0			0
$19$			4.48911i			1.02987i	0.857228	+	0.514936i	$0.172184\pi$
$19$			4.48911i			1.02987i	−0.857228	+	0.514936i	$0.827816\pi$
$20$		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	0.762092	−	0.647468i	$-0.224172\pi$
$31$	3.24275	+	1.87220i	0.582414	+	0.336257i	−0.179678	+	0.983726i	$0.557506\pi$
$32$		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	$0.363760\pi$
$41$	−3.71620	+	6.43664i	−0.580373	+	1.00523i	−0.995435	+	0.0954418i	$0.969574\pi$
$42$		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	0.670052	−	0.742314i	$-0.266272\pi$
$47$	−2.11042	−	3.65536i	−0.307837	−	0.533189i	−0.977889	+	0.209125i	$0.932939\pi$
$48$		0			0
$49$	4.53414	−	5.33307i	0.647734	−	0.761867i
$50$		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	$0.378110\pi$
$59$	−4.73531	+	8.20179i	−0.616484	+	1.06778i	−0.990122	+	0.140208i	$0.955223\pi$
$60$		0			0
$61$	−2.82757	+	1.63250i	−0.362033	+	0.209020i	−0.669972	−	0.742386i	$-0.733694\pi$
$61$	−2.82757	+	1.63250i	−0.362033	+	0.209020i	0.307939	+	0.951406i	$0.400361\pi$
$62$		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	$-0.859279\pi$
$73$		−	7.31073i		−	0.855656i	0.903860	−	0.427828i	$-0.140721\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.93176	−	6.99498i	0.562026	−	0.797152i
$78$		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	$-0.962437\pi$
$83$	−5.45245	−	9.44392i	−0.598484	−	1.03660i	0.394561	−	0.918870i	$-0.370897\pi$
$84$		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	$-0.758459\pi$
$89$	−13.6915			−1.45129			−0.725646	+	0.688068i	$0.758459\pi$
$90$		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	−0.356787	−	0.934186i	$-0.616128\pi$
$97$	2.69709	−	1.55716i	0.273848	−	0.158106i	0.630635	+	0.776080i	$0.282795\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.54471	−	6.13962i	−0.352712	−	0.610915i	0.634012	−	0.773324i	$-0.281407\pi$
$101$	−3.54471	−	6.13962i	−0.352712	−	0.610915i	−0.986724	+	0.162408i	$0.948074\pi$
$102$		0			0
$103$	−1.47529	−	0.851761i	−0.145365	−	0.0839265i	0.425553	−	0.904933i	$-0.360079\pi$
$103$	−1.47529	−	0.851761i	−0.145365	−	0.0839265i	−0.570918	+	0.821007i	$0.693413\pi$
$104$		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
$119$	−2.62076	+	1.21177i	−0.240245	+	0.111083i
$120$		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	−0.627159	−	0.778891i	$-0.715782\pi$
$131$	4.13138	−	7.15575i	0.360960	−	0.625201i	0.988119	+	0.153690i	$0.0491158\pi$
$132$		0			0
$133$	4.98459	+	10.7805i	0.432219	+	0.934786i
$134$		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	−0.328912	−	0.944361i	$-0.606682\pi$
$139$	−15.4589	−	8.92521i	−1.31121	−	0.757026i	−0.982296	+	0.187334i	$0.940015\pi$
$140$		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	0.123277	−	0.992372i	$-0.460660\pi$
$157$	−8.45150	−	4.87948i	−0.674503	−	0.389425i	−0.797781	+	0.602947i	$0.793993\pi$
$158$		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	$0.400236\pi$
$167$	−8.65419	+	14.9895i	−0.669681	+	1.15992i	−0.977993	+	0.208637i	$0.933097\pi$
$168$		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	0.826446	−	0.563017i	$-0.190359\pi$
$173$	−0.978103	−	1.69412i	−0.0743638	−	0.128802i	−0.900809	+	0.434215i	$0.857026\pi$
$174$		0			0
$175$	6.36340	+	4.48647i	0.481028	+	0.339145i
$176$		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	$0.124711\pi$
$181$			10.2744i			0.763689i	−0.924226	+	0.381845i	$0.875289\pi$
$182$		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	$-0.934263\pi$
$199$		−	5.78528i		−	0.410108i	0.978751	−	0.205054i	$-0.0657369\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.81073	+	2.56825i	−0.127088	+	0.180256i
$204$		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	−0.918924	−	0.394435i	$-0.870940\pi$
$223$	−15.4827	+	8.93892i	−1.03680	+	0.598594i	−0.117871	+	0.993029i	$0.537607\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.48365	−	9.49796i	−0.363963	−	0.630402i	0.624646	−	0.780908i	$-0.285243\pi$
$227$	−5.48365	−	9.49796i	−0.363963	−	0.630402i	−0.988609	+	0.150506i	$0.951910\pi$
$228$		0			0
$229$	−16.8349	−	9.71965i	−1.11248	−	0.642293i	−0.173012	−	0.984920i	$-0.555350\pi$
$229$	−16.8349	−	9.71965i	−1.11248	−	0.642293i	−0.939471	+	0.342627i	$0.888683\pi$
$230$		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	−0.0735896	−	0.997289i	$-0.523445\pi$
$241$	11.6943	−	6.75168i	0.753293	−	0.434914i	0.826882	+	0.562375i	$0.190112\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.37273	−	9.45656i	−0.215476	−	0.604157i
$246$		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	$-0.423786\pi$
$251$	7.51441			0.474305			0.237153	+	0.971472i	$0.423786\pi$
$252$		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	−0.961254	−	0.275664i	$-0.911102\pi$
$257$	−3.87788	+	6.71668i	−0.241895	+	0.418975i	0.719359	+	0.694639i	$0.244436\pi$
$258$		0			0
$259$	−0.574248	+	0.265516i	−0.0356820	+	0.0164984i
$260$		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	$-0.211372\pi$
$269$	25.8321			1.57501			0.787505	+	0.616308i	$0.211372\pi$
$270$		0			0
$271$			16.6537i			1.01164i	0.862639	+	0.505821i	$0.168810\pi$
$271$			16.6537i			1.01164i	−0.862639	+	0.505821i	$0.831190\pi$
$272$		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	0.847656	−	0.530546i	$-0.178013\pi$
$283$	13.6603	+	7.88676i	0.812018	+	0.468819i	−0.0356380	+	0.999365i	$0.511346\pi$
$284$		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	$0.425331\pi$
$293$	−12.4287	+	21.5271i	−0.726090	+	1.25762i	−0.958524	+	0.285013i	$0.908002\pi$
$294$		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
$301$	16.5344	+	11.6575i	0.953029	+	0.671926i
$302$		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	$-0.818805\pi$
$307$		−	18.8878i		−	1.07799i	0.842310	−	0.538993i	$-0.181195\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.97716	−	6.88864i	0.225524	−	0.390619i	−0.730953	−	0.682428i	$-0.760924\pi$
$311$	3.97716	−	6.88864i	0.225524	−	0.390619i	0.956476	+	0.291809i	$0.0942573\pi$
$312$		0			0
$313$	9.64210	−	5.56687i	0.545004	−	0.314658i	−0.202101	−	0.979365i	$-0.564777\pi$
$313$	9.64210	−	5.56687i	0.545004	−	0.314658i	0.747104	+	0.664707i	$0.231444\pi$
$314$		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
$329$	−9.12695	−	6.43489i	−0.503185	−	0.354767i
$330$		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	−0.971498	−	0.237048i	$-0.923820\pi$
$349$	−23.3885	+	13.5034i	−1.25196	+	0.722818i	−0.280460	+	0.959866i	$0.590487\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.8238	−	25.6755i	−0.788990	−	1.36657i	−0.926586	−	0.376083i	$-0.877271\pi$
$353$	−14.8238	−	25.6755i	−0.788990	−	1.36657i	0.137596	−	0.990488i	$-0.456063\pi$
$354$		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	−0.367877	−	0.929875i	$-0.619915\pi$
$367$	4.85598	−	2.80360i	0.253480	−	0.146347i	0.621357	+	0.783528i	$0.286582\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.78832	−	16.8443i	−0.404349	−	0.874510i
$372$		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	−0.997209	−	0.0746601i	$-0.976213\pi$
$383$	−8.49251	+	14.7095i	−0.433947	+	0.751618i	0.563262	+	0.826278i	$0.309546\pi$
$384$		0			0
$385$	−5.15189	−	11.1423i	−0.262565	−	0.567864i
$386$		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	$-0.810920\pi$
$397$		−	22.3035i		−	1.11938i	0.828702	−	0.559690i	$-0.189080\pi$
$398$		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	0.943515	−	0.331330i	$-0.107497\pi$
$409$	22.8191	+	13.1746i	1.12833	+	0.651443i	0.184817	+	0.982773i	$0.440831\pi$
$410$		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	$0.456717\pi$
$419$	−16.1761	+	28.0178i	−0.790252	+	1.36876i	−0.925811	+	0.377988i	$0.876616\pi$
$420$		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
$427$	−4.97764	+	7.06006i	−0.240885	+	0.341660i
$428$		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	$-0.902606\pi$
$433$		−	12.5359i		−	0.602438i	0.953555	−	0.301219i	$-0.0973936\pi$
$434$		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	−0.0630496	−	0.998010i	$-0.520083\pi$
$439$	16.1276	−	9.31127i	0.769728	−	0.444403i	0.832778	+	0.553608i	$0.186749\pi$
$440$		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
$455$	11.1938	−	15.8768i	0.524774	−	0.744315i
$456$		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	$-0.846497\pi$
$461$	−18.1346	−	31.4101i	−0.844613	−	1.46291i	0.0413440	−	0.999145i	$-0.486836\pi$
$462$		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	$-0.480529\pi$
$467$	2.64215			0.122264			0.0611320	+	0.998130i	$0.480529\pi$
$468$		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	$-0.915324\pi$
$479$	−15.5409	−	26.9177i	−0.710083	−	1.22990i	0.254742	−	0.967009i	$-0.418009\pi$
$480$		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
$497$	4.24548	+	9.18195i	0.190436	+	0.411867i
$498$		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	$-0.819673\pi$
$503$	−37.8479			−1.68756			−0.843778	+	0.536693i	$0.819673\pi$
$504$		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	$0.453593\pi$
$509$	−17.6924	+	30.6441i	−0.784200	+	1.35827i	−0.929476	+	0.368883i	$0.879740\pi$
$510$		0			0
$511$	−8.11764	−	17.5565i	−0.359103	−	0.776654i
$512$		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	$-0.483825\pi$
$521$	2.31879			0.101588			0.0507940	+	0.998709i	$0.483825\pi$
$522$		0			0
$523$		−	20.1840i		−	0.882585i	−0.897363	−	0.441293i	$-0.854520\pi$
$523$		−	20.1840i		−	0.882585i	0.897363	−	0.441293i	$-0.145480\pi$
$524$		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
$553$	7.91461	+	5.58014i	0.336563	+	0.237292i
$554$		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	$-0.637830\pi$
$563$	13.6742	−	23.6844i	0.576299	−	0.998179i	0.995899	−	0.0904697i	$-0.0288368\pi$
$564$		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	$0.0148080\pi$
$577$			2.23413i			0.0930079i	−0.998918	+	0.0465039i	$0.985192\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−23.5802	−	16.6250i	−0.978271	−	0.689723i
$582$		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	$0.0134298\pi$
$587$	12.9883	+	22.4963i	0.536083	+	0.928522i	−0.463028	+	0.886344i	$0.653237\pi$
$588$		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	$-0.462545\pi$
$593$	5.71754			0.234791			0.117396	+	0.993085i	$0.462545\pi$
$594$		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	$0.730252\pi$
$601$	−40.2546	+	23.2410i	−1.64202	+	0.948021i	−0.980114	+	0.198435i	$0.936414\pi$
$602$		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	0.371200	−	0.928553i	$-0.378946\pi$
$607$	−6.09405	−	3.51840i	−0.247350	−	0.142808i	−0.618550	+	0.785745i	$0.712280\pi$
$608$		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	−0.174412	−	0.984673i	$-0.555802\pi$
$619$	14.7072	−	8.49123i	0.591134	−	0.341291i	0.765546	+	0.643381i	$0.222469\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−32.8797	+	15.2027i	−1.31730	+	0.609081i
$624$		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
$637$	33.7518	−	12.0378i	1.33730	−	0.476954i
$638$		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	0.771060	−	0.636763i	$-0.219727\pi$
$643$	15.3447	+	8.85928i	0.605136	+	0.349376i	−0.165923	+	0.986139i	$0.553060\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.7902			0.856661			0.428330	−	0.903622i	$-0.359102\pi$
$647$	21.7902			0.856661			0.428330	+	0.903622i	$0.359102\pi$
$648$		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	0.999518	−	0.0310314i	$-0.00987918\pi$
$661$	37.8554	+	21.8558i	1.47240	+	0.850093i	0.472885	+	0.881124i	$0.343213\pi$
$662$		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	0.558722	−	0.829355i	$-0.311292\pi$
$677$	−11.4194	−	19.7789i	−0.438882	−	0.760165i	−0.997604	+	0.0691899i	$0.977959\pi$
$678$		0			0
$679$	4.74795	−	6.73427i	0.182209	−	0.258437i
$680$		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	−0.504256	−	0.863554i	$-0.668233\pi$
$691$	−0.224082	+	0.129374i	−0.00852446	+	0.00492160i	0.495732	+	0.868476i	$0.334900\pi$
$692$		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
$707$	−15.3298	−	10.8082i	−0.576537	−	0.406483i
$708$		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	$-0.439350\pi$
$719$	10.1566			0.378776			0.189388	+	0.981902i	$0.439350\pi$
$720$		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	−0.602802	−	0.797891i	$-0.705949\pi$
$727$	−5.74874	+	3.31904i	−0.213209	+	0.123096i	0.389593	+	0.920987i	$0.372616\pi$
$728$		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	0.400858	−	0.916140i	$-0.368712\pi$
$733$	−5.20130	−	3.00297i	−0.192114	−	0.110917i	−0.592972	+	0.805223i	$0.702046\pi$
$734$		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
$749$	−5.48062	−	11.8532i	−0.200257	−	0.433108i
$750$		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	−0.808000	−	0.589183i	$-0.799450\pi$
$761$	2.93098	−	5.07660i	0.106248	−	0.184027i	0.914247	+	0.405157i	$0.132783\pi$
$762$		0			0
$763$	19.5442	−	9.03671i	0.707549	−	0.327151i
$764$		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	−0.0876307	−	0.996153i	$-0.527930\pi$
$769$	−27.5683	−	15.9166i	−0.994140	−	0.573967i	−0.906509	+	0.422186i	$0.861263\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	19.0382			0.684755			0.342378	−	0.939562i	$-0.388768\pi$
$773$	19.0382			0.684755			0.342378	+	0.939562i	$0.388768\pi$
$774$		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	0.178097	−	0.984013i	$-0.443006\pi$
$787$	−16.4123	−	9.47564i	−0.585035	−	0.337770i	−0.763132	+	0.646243i	$0.776339\pi$
$788$		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	$0.562071\pi$
$797$	−26.7207	+	46.2816i	−0.946497	+	1.63938i	−0.752727	+	0.658333i	$0.771262\pi$
$798$		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
$805$	8.76501	−	12.4319i	0.308926	−	0.438167i
$806$		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	$-0.966016\pi$
$811$		−	6.06938i		−	0.213125i	0.994306	−	0.106562i	$-0.0339844\pi$
$812$		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	$-0.969841\pi$
$829$		−	5.44792i		−	0.189214i	0.995515	−	0.0946071i	$-0.0301595\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.94817	+	5.82006i	−0.171444	+	0.201653i
$834$		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	$0.149492\pi$
$839$	24.2673	+	42.0322i	0.837801	+	1.45111i	−0.0539281	+	0.998545i	$0.517174\pi$
$840$		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	−0.304152	−	0.952623i	$-0.598373\pi$
$853$	10.7703	−	6.21823i	0.368768	−	0.212908i	0.672920	+	0.739715i	$0.265040\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.29077	+	9.16388i	0.180729	+	0.313032i	0.942129	−	0.335250i	$-0.108821\pi$
$857$	5.29077	+	9.16388i	0.180729	+	0.313032i	−0.761400	+	0.648283i	$0.775488\pi$
$858$		0			0
$859$	−28.1452	−	16.2496i	−0.960302	−	0.554431i	−0.0640360	−	0.997948i	$-0.520397\pi$
$859$	−28.1452	−	16.2496i	−0.960302	−	0.554431i	−0.896266	+	0.443517i	$0.853731\pi$
$860$		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
$875$	27.3583	−	12.6497i	0.924878	−	0.427638i
$876$		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	$-0.710434\pi$
$881$	−36.4482			−1.22797			−0.613985	+	0.789318i	$0.710434\pi$
$882$		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	$0.474552\pi$
$887$	−24.5208	+	42.4713i	−0.823329	+	1.42605i	−0.903190	+	0.429241i	$0.858781\pi$
$888$		0			0
$889$	−14.8129	+	6.84909i	−0.496810	+	0.229711i
$890$		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	0.999904	−	0.0138670i	$-0.00441415\pi$
$929$	14.8723	+	25.7595i	0.487943	+	0.845142i	−0.511961	+	0.859009i	$0.671081\pi$
$930$		0			0
$931$	23.9407	+	20.3542i	0.784626	+	0.667083i
$932$		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	$0.0210057\pi$
$937$			4.03712i			0.131887i	−0.997823	+	0.0659434i	$0.978994\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7.20264	−	12.4753i	0.234799	−	0.406684i	−0.724415	−	0.689364i	$-0.757890\pi$
$941$	7.20264	−	12.4753i	0.234799	−	0.406684i	0.959214	+	0.282680i	$0.0912234\pi$
$942$		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
$959$	15.7761	−	22.3761i	0.509438	−	0.722563i
$960$		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	$-0.679051\pi$
$971$	−33.2366			−1.06661			−0.533307	+	0.845922i	$0.679051\pi$
$972$		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	0.991982	−	0.126379i	$-0.0403356\pi$
$983$	12.1192	+	20.9911i	0.386544	+	0.669513i	−0.605438	+	0.795892i	$0.707002\pi$
$984$		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	−0.633110	−	0.774062i	$-0.718222\pi$
$997$	−8.81920	+	5.09177i	−0.279307	+	0.161258i	0.353803	+	0.935320i	$0.384888\pi$
$998$		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.881.4		12
3.2	odd	2		1008.2.cc.a.545.2		12
4.3	odd	2		189.2.o.a.125.6		12
7.6	odd	2	inner	3024.2.cc.a.881.3		12
9.2	odd	6	inner	3024.2.cc.a.2897.3		12
9.7	even	3		1008.2.cc.a.209.5		12
12.11	even	2		63.2.o.a.41.2	yes	12
21.20	even	2		1008.2.cc.a.545.5		12
28.3	even	6		1323.2.i.c.1097.5		12
28.11	odd	6		1323.2.i.c.1097.6		12
28.19	even	6		1323.2.s.c.962.2		12
28.23	odd	6		1323.2.s.c.962.1		12
28.27	even	2		189.2.o.a.125.5		12
36.7	odd	6		63.2.o.a.20.1	✓	12
36.11	even	6		189.2.o.a.62.5		12
36.23	even	6		567.2.c.c.566.2		12
36.31	odd	6		567.2.c.c.566.11		12
63.20	even	6	inner	3024.2.cc.a.2897.4		12
63.34	odd	6		1008.2.cc.a.209.2		12
84.11	even	6		441.2.i.c.68.2		12
84.23	even	6		441.2.s.c.374.5		12
84.47	odd	6		441.2.s.c.374.6		12
84.59	odd	6		441.2.i.c.68.1		12
84.83	odd	2		63.2.o.a.41.1	yes	12
252.11	even	6		1323.2.s.c.656.2		12
252.47	odd	6		1323.2.i.c.521.2		12
252.79	odd	6		441.2.i.c.227.5		12
252.83	odd	6		189.2.o.a.62.6		12
252.115	even	6		441.2.s.c.362.5		12
252.139	even	6		567.2.c.c.566.12		12
252.151	odd	6		441.2.s.c.362.6		12
252.167	odd	6		567.2.c.c.566.1		12
252.187	even	6		441.2.i.c.227.6		12
252.191	even	6		1323.2.i.c.521.1		12
252.223	even	6		63.2.o.a.20.2	yes	12
252.227	odd	6		1323.2.s.c.656.1		12

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

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)

\(f(q)\)	\(=\)	\(q+(0.717144 - 1.24213i) q^{5} +(2.40147 - 1.11037i) q^{7} +(2.80150 - 1.61745i) q^{11} +(4.43334 + 2.55959i) q^{13} -1.09132 q^{17} +4.48911i q^{19} +(3.47141 + 2.00422i) q^{23} +(1.47141 + 2.54856i) q^{25} +(-1.02859 + 0.593857i) q^{29} +(3.24275 + 1.87220i) q^{31} +(0.342971 - 3.77924i) q^{35} -0.239123 q^{37} +(-3.71620 + 6.43664i) q^{41} +(3.82326 + 6.62208i) q^{43} +(-2.11042 - 3.65536i) q^{47} +(4.53414 - 5.33307i) q^{49} -7.01414i q^{53} -4.63977i q^{55} +(-4.73531 + 8.20179i) q^{59} +(-2.82757 + 1.63250i) q^{61} +(6.35868 - 3.67119i) q^{65} +(0.330095 - 0.571741i) q^{67} +3.82347i q^{71} -7.31073i q^{73} +(4.93176 - 6.99498i) q^{77} +(1.83009 + 3.16982i) q^{79} +(-5.45245 - 9.44392i) q^{83} +(-0.782630 + 1.35556i) q^{85} -13.6915 q^{89} +(13.4887 + 1.22412i) q^{91} +(5.57605 + 3.21934i) q^{95} +(2.69709 - 1.55716i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{7} + 24 q^{23} - 30 q^{29} - 4 q^{37} + 10 q^{43} + 6 q^{49} + 78 q^{65} - 12 q^{67} + 24 q^{77} + 6 q^{79} - 6 q^{85} + 24 q^{91} + 72 q^{95}+O(q^{100}) \) 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

Groups

Database

Properties

Related objects

Downloads

Learn more