LMFDB - Embedded newform 3024.2.ca.b.2609.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2033,3024)]

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, 1, 1]))

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

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

chi := DirichletCharacter("3024.2033");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.ca (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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2609.4
Root			$0.187540 - 0.324828i$ of defining polynomial
Character	$\chi$	$=$	3024.2609
Dual form			3024.2.ca.b.2033.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.723774 + 1.25361i) q^{5} +(-0.182786 - 2.63943i) q^{7} +O(q^{10})$	$q+(0.723774 + 1.25361i) q^{5} +(-0.182786 - 2.63943i) q^{7} +(-1.55933 - 0.900281i) q^{11} +(-1.88867 - 1.09042i) q^{13} +(-1.95230 - 3.38149i) q^{17} +(3.47456 + 2.00604i) q^{19} +(-4.91522 + 2.83781i) q^{23} +(1.45230 - 2.51546i) q^{25} +(-8.49418 + 4.90412i) q^{29} -2.83050i q^{31} +(3.17653 - 2.13949i) q^{35} +(-0.411767 + 0.713202i) q^{37} +(-5.90617 + 10.2298i) q^{41} +(3.76766 + 6.52578i) q^{43} +2.33839 q^{47} +(-6.93318 + 0.964903i) q^{49} +(-0.996713 + 0.575453i) q^{53} -2.60640i q^{55} -9.79110 q^{59} +2.35536i q^{61} -3.15688i q^{65} +0.312805 q^{67} +1.94933i q^{71} +(2.42847 - 1.40208i) q^{73} +(-2.09120 + 4.28031i) q^{77} -12.4317 q^{79} +(3.60916 + 6.25124i) q^{83} +(2.82605 - 4.89486i) q^{85} +(5.28999 - 9.16253i) q^{89} +(-2.53287 + 5.18433i) q^{91} +5.80767i q^{95} +(-13.4322 + 7.75510i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 6 q^{7}+O(q^{10}) $ 10 * q + 6 * q^7	$ 10 q + 6 q^{7} - 12 q^{11} - 6 q^{13} - 12 q^{17} - 3 q^{19} - 15 q^{23} + 7 q^{25} + 15 q^{29} + 15 q^{35} + 6 q^{37} - 9 q^{41} - 3 q^{43} + 30 q^{47} + 4 q^{49} - 9 q^{53} - 36 q^{59} - 20 q^{67} + 3 q^{73} - 39 q^{77} + 40 q^{79} + 15 q^{83} + 18 q^{85} + 24 q^{89} + 24 q^{91} - 6 q^{97}+O(q^{100}) $ 10 * q + 6 * q^7 - 12 * q^11 - 6 * q^13 - 12 * q^17 - 3 * q^19 - 15 * q^23 + 7 * q^25 + 15 * q^29 + 15 * q^35 + 6 * q^37 - 9 * q^41 - 3 * q^43 + 30 * q^47 + 4 * q^49 - 9 * q^53 - 36 * q^59 - 20 * q^67 + 3 * q^73 - 39 * q^77 + 40 * q^79 + 15 * q^83 + 18 * q^85 + 24 * q^89 + 24 * q^91 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.723774	+	1.25361i	0.323682	+	0.560633i	0.981245	−	0.192766i	$-0.0617460\pi$
$5$	0.723774	+	1.25361i	0.323682	+	0.560633i	−0.657563	+	0.753400i	$0.728413\pi$
$6$		0			0
$7$	−0.182786	−	2.63943i	−0.0690867	−	0.997611i
$7$	−0.182786	−	2.63943i	−0.0690867	−	0.997611i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.55933	−	0.900281i	−0.470156	−	0.271445i	0.246149	−	0.969232i	$-0.420835\pi$
$11$	−1.55933	−	0.900281i	−0.470156	−	0.271445i	−0.716305	+	0.697787i	$0.754168\pi$
$12$		0			0
$13$	−1.88867	−	1.09042i	−0.523823	−	0.302429i	0.214675	−	0.976686i	$-0.431131\pi$
$13$	−1.88867	−	1.09042i	−0.523823	−	0.302429i	−0.738497	+	0.674256i	$0.764464\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.95230	−	3.38149i	−0.473503	−	0.820131i	0.526037	−	0.850462i	$-0.323677\pi$
$17$	−1.95230	−	3.38149i	−0.473503	−	0.820131i	−0.999540	+	0.0303308i	$0.990344\pi$
$18$		0			0
$19$	3.47456	+	2.00604i	0.797118	+	0.460216i	0.842462	−	0.538755i	$-0.181105\pi$
$19$	3.47456	+	2.00604i	0.797118	+	0.460216i	−0.0453446	+	0.998971i	$0.514439\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.91522	+	2.83781i	−1.02490	+	0.591723i	−0.915518	−	0.402277i	$-0.868219\pi$
$23$	−4.91522	+	2.83781i	−1.02490	+	0.591723i	−0.109377	+	0.994000i	$0.534886\pi$
$24$		0			0
$25$	1.45230	−	2.51546i	0.290460	−	0.503092i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−8.49418	+	4.90412i	−1.57733	+	0.910672i	−0.582100	+	0.813117i	$0.697769\pi$
$29$	−8.49418	+	4.90412i	−1.57733	+	0.910672i	−0.995230	+	0.0975551i	$0.968898\pi$
$30$		0			0
$31$		−	2.83050i		−	0.508374i	−0.967155	−	0.254187i	$-0.918192\pi$
$31$		−	2.83050i		−	0.508374i	0.967155	−	0.254187i	$-0.0818078\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.17653	−	2.13949i	0.536931	−	0.361641i
$36$		0			0
$37$	−0.411767	+	0.713202i	−0.0676941	+	0.117250i	−0.897886	−	0.440228i	$-0.854898\pi$
$37$	−0.411767	+	0.713202i	−0.0676941	+	0.117250i	0.830192	+	0.557478i	$0.188231\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.90617	+	10.2298i	−0.922389	+	1.59762i	−0.126681	+	0.991943i	$0.540433\pi$
$41$	−5.90617	+	10.2298i	−0.922389	+	1.59762i	−0.795708	+	0.605681i	$0.792901\pi$
$42$		0			0
$43$	3.76766	+	6.52578i	0.574563	+	0.995172i	0.996089	+	0.0883555i	$0.0281612\pi$
$43$	3.76766	+	6.52578i	0.574563	+	0.995172i	−0.421526	+	0.906816i	$0.638506\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.33839			0.341089			0.170545	−	0.985350i	$-0.445447\pi$
$47$	2.33839			0.341089			0.170545	+	0.985350i	$0.445447\pi$
$48$		0			0
$49$	−6.93318	+	0.964903i	−0.990454	+	0.137843i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.996713	+	0.575453i	−0.136909	+	0.0790445i	−0.566890	−	0.823793i	$-0.691854\pi$
$53$	−0.996713	+	0.575453i	−0.136909	+	0.0790445i	0.429981	+	0.902838i	$0.358520\pi$
$54$		0			0
$55$		−	2.60640i		−	0.351447i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−9.79110			−1.27469			−0.637346	−	0.770577i	$-0.719968\pi$
$59$	−9.79110			−1.27469			−0.637346	+	0.770577i	$0.719968\pi$
$60$		0			0
$61$			2.35536i			0.301573i	0.988566	+	0.150786i	$0.0481806\pi$
$61$			2.35536i			0.301573i	−0.988566	+	0.150786i	$0.951819\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	3.15688i		−	0.391563i
$66$		0			0
$67$	0.312805			0.0382152			0.0191076	−	0.999817i	$-0.493917\pi$
$67$	0.312805			0.0382152			0.0191076	+	0.999817i	$0.493917\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			1.94933i			0.231343i	0.993288	+	0.115671i	$0.0369019\pi$
$71$			1.94933i			0.231343i	−0.993288	+	0.115671i	$0.963098\pi$
$72$		0			0
$73$	2.42847	−	1.40208i	0.284231	−	0.164101i	−0.351106	−	0.936336i	$-0.614194\pi$
$73$	2.42847	−	1.40208i	0.284231	−	0.164101i	0.635337	+	0.772235i	$0.280861\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.09120	+	4.28031i	−0.238315	+	0.487786i
$78$		0			0
$79$	−12.4317			−1.39867			−0.699336	−	0.714793i	$-0.746521\pi$
$79$	−12.4317			−1.39867			−0.699336	+	0.714793i	$0.746521\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.60916	+	6.25124i	0.396157	+	0.686163i	0.993248	−	0.116010i	$-0.0370104\pi$
$83$	3.60916	+	6.25124i	0.396157	+	0.686163i	−0.597092	+	0.802173i	$0.703677\pi$
$84$		0			0
$85$	2.82605	−	4.89486i	0.306528	−	0.530923i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.28999	−	9.16253i	0.560737	−	0.971226i	−0.436695	−	0.899610i	$-0.643851\pi$
$89$	5.28999	−	9.16253i	0.560737	−	0.971226i	0.997432	−	0.0716161i	$-0.0228156\pi$
$90$		0			0
$91$	−2.53287	+	5.18433i	−0.265517	+	0.543465i
$92$		0			0
$93$		0			0
$94$		0			0
$95$			5.80767i			0.595854i
$96$		0			0
$97$	−13.4322	+	7.75510i	−1.36384	+	0.787411i	−0.990132	−	0.140137i	$-0.955246\pi$
$97$	−13.4322	+	7.75510i	−1.36384	+	0.787411i	−0.373704	+	0.927548i	$0.621912\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.97309	−	3.41749i	0.196330	−	0.340053i	−0.751006	−	0.660295i	$-0.770431\pi$
$101$	1.97309	−	3.41749i	0.196330	−	0.340053i	0.947336	+	0.320242i	$0.103764\pi$
$102$		0			0
$103$	−3.59853	+	2.07761i	−0.354573	+	0.204713i	−0.666698	−	0.745328i	$-0.732293\pi$
$103$	−3.59853	+	2.07761i	−0.354573	+	0.204713i	0.312124	+	0.950041i	$0.398959\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.91092	−	2.83532i	−0.474757	−	0.274101i	0.243472	−	0.969908i	$-0.421714\pi$
$107$	−4.91092	−	2.83532i	−0.474757	−	0.274101i	−0.718229	+	0.695807i	$0.755047\pi$
$108$		0			0
$109$	5.99916	+	10.3908i	0.574615	+	0.995262i	0.996083	+	0.0884193i	$0.0281815\pi$
$109$	5.99916	+	10.3908i	0.574615	+	0.995262i	−0.421468	+	0.906843i	$0.638485\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.27800	−	3.62461i	−0.590585	−	0.340974i	0.174744	−	0.984614i	$-0.444090\pi$
$113$	−6.27800	−	3.62461i	−0.590585	−	0.340974i	−0.765329	+	0.643640i	$0.777424\pi$
$114$		0			0
$115$	−7.11502	−	4.10786i	−0.663479	−	0.383060i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.56834	+	5.77105i	−0.785458	+	0.529032i
$120$		0			0
$121$	−3.87899	−	6.71861i	−0.352635	−	0.610782i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.4423			1.02343
$126$		0			0
$127$	0.881336			0.0782059			0.0391030	−	0.999235i	$-0.487550\pi$
$127$	0.881336			0.0782059			0.0391030	+	0.999235i	$0.487550\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.48721	−	2.57592i	−0.129938	−	0.225059i	0.793714	−	0.608291i	$-0.208144\pi$
$131$	−1.48721	−	2.57592i	−0.129938	−	0.225059i	−0.923652	+	0.383232i	$0.874811\pi$
$132$		0			0
$133$	4.65969	−	9.53752i	0.404046	−	0.827008i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.3045	+	5.94930i	0.880372	+	0.508283i	0.870781	−	0.491671i	$-0.163614\pi$
$137$	10.3045	+	5.94930i	0.880372	+	0.508283i	0.00959114	+	0.999954i	$0.496947\pi$
$138$		0			0
$139$	−10.4143	−	6.01268i	−0.883327	−	0.509989i	−0.0115731	−	0.999933i	$-0.503684\pi$
$139$	−10.4143	−	6.01268i	−0.883327	−	0.509989i	−0.871754	+	0.489944i	$0.837017\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.96338	+	3.40067i	0.164186	+	0.284378i
$144$		0			0
$145$	−12.2957	−	7.09895i	−1.02111	−	0.589536i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.13061	+	3.53951i	−0.502239	+	0.289968i	−0.729638	−	0.683834i	$-0.760311\pi$
$149$	−6.13061	+	3.53951i	−0.502239	+	0.289968i	0.227399	+	0.973802i	$0.426978\pi$
$150$		0			0
$151$	7.79093	−	13.4943i	0.634017	−	1.09815i	−0.352706	−	0.935734i	$-0.614738\pi$
$151$	7.79093	−	13.4943i	0.634017	−	1.09815i	0.986723	−	0.162415i	$-0.0519283\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.54836	−	2.04865i	0.285011	−	0.164551i
$156$		0			0
$157$		−	2.08628i		−	0.166503i	−0.996529	−	0.0832517i	$-0.973469\pi$
$157$		−	2.08628i		−	0.166503i	0.996529	−	0.0832517i	$-0.0265305\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.38862	+	12.4547i	0.661116	+	0.981566i
$162$		0			0
$163$	5.58983	−	9.68188i	0.437830	−	0.758343i	−0.559692	−	0.828700i	$-0.689081\pi$
$163$	5.58983	−	9.68188i	0.437830	−	0.758343i	0.997522	+	0.0703575i	$0.0224140\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.960750	+	1.66407i	−0.0743450	+	0.128769i	−0.900801	−	0.434232i	$-0.857020\pi$
$167$	−0.960750	+	1.66407i	−0.0743450	+	0.128769i	0.826456	+	0.563001i	$0.190353\pi$
$168$		0			0
$169$	−4.12195	−	7.13943i	−0.317073	−	0.549187i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−15.2258			−1.15760			−0.578798	−	0.815471i	$-0.696478\pi$
$173$	−15.2258			−1.15760			−0.578798	+	0.815471i	$0.696478\pi$
$174$		0			0
$175$	−6.90484	−	3.37346i	−0.521957	−	0.255009i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.299401	−	0.172859i	0.0223783	−	0.0129201i	−0.488769	−	0.872413i	$-0.662554\pi$
$179$	0.299401	−	0.172859i	0.0223783	−	0.0129201i	0.511147	+	0.859493i	$0.329221\pi$
$180$		0			0
$181$			3.27661i			0.243548i	0.992558	+	0.121774i	$0.0388583\pi$
$181$			3.27661i			0.243548i	−0.992558	+	0.121774i	$0.961142\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.19211			−0.0876454
$186$		0			0
$187$			7.03048i			0.514120i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	7.39120i		−	0.534808i	−0.963584	−	0.267404i	$-0.913834\pi$
$191$		−	7.39120i		−	0.534808i	0.963584	−	0.267404i	$-0.0861659\pi$
$192$		0			0
$193$	13.0285			0.937812			0.468906	−	0.883248i	$-0.344648\pi$
$193$	13.0285			0.937812			0.468906	+	0.883248i	$0.344648\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			4.03035i			0.287151i	0.989639	+	0.143575i	$0.0458599\pi$
$197$			4.03035i			0.287151i	−0.989639	+	0.143575i	$0.954140\pi$
$198$		0			0
$199$	−14.2096	+	8.20390i	−1.00729	+	0.581559i	−0.910397	−	0.413736i	$-0.864224\pi$
$199$	−14.2096	+	8.20390i	−1.00729	+	0.581559i	−0.0968925	+	0.995295i	$0.530890\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	14.4967	+	21.5234i	1.01747	+	1.51065i
$204$		0			0
$205$	−17.0989			−1.19424
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.61199	−	6.25615i	−0.249847	−	0.432747i
$210$		0			0
$211$	6.00827	−	10.4066i	0.413627	−	0.716422i	−0.581657	−	0.813434i	$-0.697595\pi$
$211$	6.00827	−	10.4066i	0.413627	−	0.716422i	0.995283	+	0.0970121i	$0.0309286\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.45387	+	9.44638i	−0.371951	+	0.644238i
$216$		0			0
$217$	−7.47092	+	0.517377i	−0.507159	+	0.0351219i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			8.51535i			0.572804i
$222$		0			0
$223$	−22.7932	+	13.1597i	−1.52635	+	0.881237i	−0.526836	+	0.849967i	$0.676622\pi$
$223$	−22.7932	+	13.1597i	−1.52635	+	0.881237i	−0.999511	+	0.0312693i	$0.990045\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.40410	−	9.36018i	0.358683	−	0.621257i	−0.629058	−	0.777358i	$-0.716559\pi$
$227$	5.40410	−	9.36018i	0.358683	−	0.621257i	0.987741	+	0.156101i	$0.0498926\pi$
$228$		0			0
$229$	−8.39777	+	4.84846i	−0.554941	+	0.320395i	−0.751112	−	0.660174i	$-0.770482\pi$
$229$	−8.39777	+	4.84846i	−0.554941	+	0.320395i	0.196172	+	0.980570i	$0.437149\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.92897	−	1.11369i	−0.126371	−	0.0729605i	0.435482	−	0.900198i	$-0.356578\pi$
$233$	−1.92897	−	1.11369i	−0.126371	−	0.0729605i	−0.561853	+	0.827237i	$0.689911\pi$
$234$		0			0
$235$	1.69247	+	2.93144i	0.110404	+	0.191226i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−15.9697	−	9.22008i	−1.03299	−	0.596398i	−0.115151	−	0.993348i	$-0.536735\pi$
$239$	−15.9697	−	9.22008i	−1.03299	−	0.596398i	−0.917840	+	0.396950i	$0.870068\pi$
$240$		0			0
$241$	5.60475	+	3.23591i	0.361034	+	0.208443i	0.669534	−	0.742781i	$-0.266494\pi$
$241$	5.60475	+	3.23591i	0.361034	+	0.208443i	−0.308500	+	0.951224i	$0.599827\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.22767	−	7.99316i	−0.397871	−	0.510664i
$246$		0			0
$247$	−4.37486	−	7.57748i	−0.278366	−	0.482143i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.416679			−0.0263005			−0.0131503	−	0.999914i	$-0.504186\pi$
$251$	−0.416679			−0.0263005			−0.0131503	+	0.999914i	$0.504186\pi$
$252$		0			0
$253$	10.2193			0.642481
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.5642	+	18.2977i	0.658976	+	1.14138i	0.980881	+	0.194607i	$0.0623433\pi$
$257$	10.5642	+	18.2977i	0.658976	+	1.14138i	−0.321906	+	0.946772i	$0.604323\pi$
$258$		0			0
$259$	1.95771	+	0.956467i	0.121646	+	0.0594320i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−19.2653	−	11.1228i	−1.18795	−	0.685862i	−0.230108	−	0.973165i	$-0.573908\pi$
$263$	−19.2653	−	11.1228i	−1.18795	−	0.685862i	−0.957840	+	0.287304i	$0.907241\pi$
$264$		0			0
$265$	−1.44279	−	0.832996i	−0.0886299	−	0.0511705i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−14.5164	−	25.1432i	−0.885083	−	1.53301i	−0.845619	−	0.533788i	$-0.820768\pi$
$269$	−14.5164	−	25.1432i	−0.885083	−	1.53301i	−0.0394642	−	0.999221i	$-0.512565\pi$
$270$		0			0
$271$	−20.8174	−	12.0189i	−1.26456	−	0.730097i	−0.290610	−	0.956842i	$-0.593858\pi$
$271$	−20.8174	−	12.0189i	−1.26456	−	0.730097i	−0.973954	+	0.226745i	$0.927192\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.52924	+	2.61496i	−0.273124	+	0.157688i
$276$		0			0
$277$	−4.03243	+	6.98437i	−0.242285	+	0.419650i	−0.961365	−	0.275278i	$-0.911230\pi$
$277$	−4.03243	+	6.98437i	−0.242285	+	0.419650i	0.719080	+	0.694928i	$0.244564\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	12.0876	−	6.97879i	0.721087	−	0.416320i	−0.0940658	−	0.995566i	$-0.529986\pi$
$281$	12.0876	−	6.97879i	0.721087	−	0.416320i	0.815153	+	0.579246i	$0.196653\pi$
$282$		0			0
$283$			15.5375i			0.923609i	0.886982	+	0.461805i	$0.152798\pi$
$283$			15.5375i			0.923609i	−0.886982	+	0.461805i	$0.847202\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	28.0804	+	13.7191i	1.65753	+	0.809810i
$288$		0			0
$289$	0.877036	−	1.51907i	0.0515904	−	0.0893571i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	6.73712	−	11.6690i	0.393587	−	0.681712i	−0.599333	−	0.800500i	$-0.704567\pi$
$293$	6.73712	−	11.6690i	0.393587	−	0.681712i	0.992920	+	0.118788i	$0.0379008\pi$
$294$		0			0
$295$	−7.08655	−	12.2743i	−0.412595	−	0.714635i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	12.3776			0.715818
$300$		0			0
$301$	16.5357	−	11.1373i	0.953099	−	0.641943i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.95271	+	1.70475i	−0.169072	+	0.0976136i
$306$		0			0
$307$			8.62791i			0.492421i	0.969216	+	0.246210i	$0.0791854\pi$
$307$			8.62791i			0.492421i	−0.969216	+	0.246210i	$0.920815\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−16.2440			−0.921113			−0.460556	−	0.887630i	$-0.652350\pi$
$311$	−16.2440			−0.921113			−0.460556	+	0.887630i	$0.652350\pi$
$312$		0			0
$313$			6.77692i			0.383054i	0.981487	+	0.191527i	$0.0613440\pi$
$313$			6.77692i			0.383054i	−0.981487	+	0.191527i	$0.938656\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			21.9676i			1.23382i	0.787033	+	0.616911i	$0.211616\pi$
$317$			21.9676i			1.23382i	−0.787033	+	0.616911i	$0.788384\pi$
$318$		0			0
$319$	17.6603			0.988789
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	15.6655i		−	0.871654i
$324$		0			0
$325$	−5.48584	+	3.16725i	−0.304299	+	0.175687i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.427426	−	6.17202i	−0.0235648	−	0.340274i
$330$		0			0
$331$	14.6036			0.802685			0.401342	−	0.915928i	$-0.368544\pi$
$331$	14.6036			0.802685			0.401342	+	0.915928i	$0.368544\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.226400	+	0.392137i	0.0123696	+	0.0214247i
$336$		0			0
$337$	−16.2629	+	28.1681i	−0.885894	+	1.53441i	−0.0412090	+	0.999151i	$0.513121\pi$
$337$	−16.2629	+	28.1681i	−0.885894	+	1.53441i	−0.844685	+	0.535263i	$0.820212\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.54825	+	4.41370i	−0.137995	+	0.239015i
$342$		0			0
$343$	3.81408	+	18.1233i	0.205941	+	0.978564i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			3.18703i			0.171089i	0.996334	+	0.0855444i	$0.0272630\pi$
$347$			3.18703i			0.171089i	−0.996334	+	0.0855444i	$0.972737\pi$
$348$		0			0
$349$	6.48224	−	3.74252i	0.346986	−	0.200333i	−0.316371	−	0.948636i	$-0.602464\pi$
$349$	6.48224	−	3.74252i	0.346986	−	0.200333i	0.663357	+	0.748303i	$0.269131\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.69040	−	9.85606i	0.302869	−	0.524585i	−0.673915	−	0.738809i	$-0.735389\pi$
$353$	5.69040	−	9.85606i	0.302869	−	0.524585i	0.976785	+	0.214223i	$0.0687220\pi$
$354$		0			0
$355$	−2.44370	+	1.41087i	−0.129698	+	0.0748814i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.77569	+	2.75725i	0.252051	+	0.145522i	0.620703	−	0.784046i	$-0.286847\pi$
$359$	4.77569	+	2.75725i	0.252051	+	0.145522i	−0.368652	+	0.929568i	$0.620181\pi$
$360$		0			0
$361$	−1.45164	−	2.51432i	−0.0764022	−	0.132332i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.51533	+	2.02958i	0.184001	+	0.106233i
$366$		0			0
$367$	18.2753	+	10.5512i	0.953962	+	0.550770i	0.894309	−	0.447449i	$-0.147667\pi$
$367$	18.2753	+	10.5512i	0.953962	+	0.550770i	0.0596526	+	0.998219i	$0.481001\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.70105	+	2.52557i	0.0883143	+	0.131121i
$372$		0			0
$373$	−7.68498	−	13.3108i	−0.397913	−	0.689206i	0.595555	−	0.803314i	$-0.296932\pi$
$373$	−7.68498	−	13.3108i	−0.397913	−	0.689206i	−0.993468	+	0.114109i	$0.963599\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	21.3903			1.10166
$378$		0			0
$379$	32.3630			1.66238			0.831188	−	0.555991i	$-0.187661\pi$
$379$	32.3630			1.66238			0.831188	+	0.555991i	$0.187661\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.91730	+	17.1773i	0.506750	+	0.877718i	0.999969	+	0.00781236i	$0.00248678\pi$
$383$	9.91730	+	17.1773i	0.506750	+	0.877718i	−0.493219	+	0.869905i	$0.664180\pi$
$384$		0			0
$385$	−6.87941	+	0.476414i	−0.350607	+	0.0242803i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.41918	−	2.55141i	−0.224061	−	0.129362i	0.383768	−	0.923429i	$-0.374626\pi$
$389$	−4.41918	−	2.55141i	−0.224061	−	0.129362i	−0.607829	+	0.794068i	$0.707960\pi$
$390$		0			0
$391$	19.1920	+	11.0805i	0.970581	+	0.560365i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.99772	−	15.5845i	−0.452724	−	0.784141i
$396$		0			0
$397$	−11.5288	−	6.65615i	−0.578613	−	0.334062i	0.181969	−	0.983304i	$-0.441753\pi$
$397$	−11.5288	−	6.65615i	−0.578613	−	0.334062i	−0.760582	+	0.649242i	$0.775086\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.1750	+	8.18392i	−0.707864	+	0.408685i	−0.810270	−	0.586057i	$-0.800679\pi$
$401$	−14.1750	+	8.18392i	−0.707864	+	0.408685i	0.102406	+	0.994743i	$0.467346\pi$
$402$		0			0
$403$	−3.08645	+	5.34589i	−0.153747	+	0.266298i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.28416	−	0.741412i	0.0636536	−	0.0367504i
$408$		0			0
$409$		−	4.33710i		−	0.214456i	−0.994234	−	0.107228i	$-0.965803\pi$
$409$		−	4.33710i		−	0.214456i	0.994234	−	0.107228i	$-0.0341975\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.78968	+	25.8429i	0.0880644	+	1.27165i
$414$		0			0
$415$	−5.22443	+	9.04898i	−0.256457	+	0.444197i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	9.41294	−	16.3037i	0.459852	−	0.796487i	−0.539100	−	0.842241i	$-0.681236\pi$
$419$	9.41294	−	16.3037i	0.459852	−	0.796487i	0.998953	+	0.0457540i	$0.0145690\pi$
$420$		0			0
$421$	0.913453	+	1.58215i	0.0445190	+	0.0771092i	0.887426	−	0.460950i	$-0.152491\pi$
$421$	0.913453	+	1.58215i	0.0445190	+	0.0771092i	−0.842907	+	0.538059i	$0.819158\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−11.3413			−0.550135
$426$		0			0
$427$	6.21680	−	0.430527i	0.300852	−	0.0208347i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	12.4526	−	7.18954i	0.599823	−	0.346308i	−0.169149	−	0.985590i	$-0.554102\pi$
$431$	12.4526	−	7.18954i	0.599823	−	0.346308i	0.768972	+	0.639283i	$0.220769\pi$
$432$		0			0
$433$			2.22130i			0.106749i	0.998575	+	0.0533745i	$0.0169977\pi$
$433$			2.22130i			0.106749i	−0.998575	+	0.0533745i	$0.983002\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−22.7710			−1.08928
$438$		0			0
$439$		−	10.0448i		−	0.479413i	−0.970845	−	0.239706i	$-0.922949\pi$
$439$		−	10.0448i		−	0.479413i	0.970845	−	0.239706i	$-0.0770512\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	13.8934i		−	0.660097i	−0.943964	−	0.330049i	$-0.892935\pi$
$443$		−	13.8934i		−	0.660097i	0.943964	−	0.330049i	$-0.107065\pi$
$444$		0			0
$445$	15.3150			0.726002
$446$		0			0
$447$		0			0
$448$		0			0
$449$			10.5630i			0.498498i	0.968439	+	0.249249i	$0.0801837\pi$
$449$			10.5630i			0.498498i	−0.968439	+	0.249249i	$0.919816\pi$
$450$		0			0
$451$	18.4194	−	10.6344i	0.867334	−	0.500755i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−8.33237	+	0.577035i	−0.390628	+	0.0270518i
$456$		0			0
$457$	5.11307			0.239179			0.119590	−	0.992823i	$-0.461842\pi$
$457$	5.11307			0.239179			0.119590	+	0.992823i	$0.461842\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.16691	−	7.21730i	−0.194072	−	0.336143i	0.752524	−	0.658565i	$-0.228836\pi$
$461$	−4.16691	−	7.21730i	−0.194072	−	0.336143i	−0.946596	+	0.322422i	$0.895503\pi$
$462$		0			0
$463$	−10.0143	+	17.3452i	−0.465403	+	0.806102i	−0.999220	−	0.0394986i	$-0.987424\pi$
$463$	−10.0143	+	17.3452i	−0.465403	+	0.806102i	0.533817	+	0.845600i	$0.320757\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.3896	−	17.9953i	0.480773	−	0.832723i	−0.518984	−	0.854784i	$-0.673690\pi$
$467$	10.3896	−	17.9953i	0.480773	−	0.832723i	0.999757	+	0.0220611i	$0.00702284\pi$
$468$		0			0
$469$	−0.0571765	−	0.825627i	−0.00264016	−	0.0381239i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	13.5678i		−	0.623848i
$474$		0			0
$475$	10.0922	−	5.82674i	0.463062	−	0.267349i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−16.0308	+	27.7662i	−0.732468	+	1.26867i	0.223357	+	0.974737i	$0.428298\pi$
$479$	−16.0308	+	27.7662i	−0.732468	+	1.26867i	−0.955825	+	0.293935i	$0.905035\pi$
$480$		0			0
$481$	1.55538	−	0.898002i	0.0709194	−	0.0409454i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−19.4438	−	11.2259i	−0.882897	−	0.509741i
$486$		0			0
$487$	−11.8375	−	20.5032i	−0.536408	−	0.929087i	−0.999094	−	0.0425641i	$-0.986447\pi$
$487$	−11.8375	−	20.5032i	−0.536408	−	0.929087i	0.462685	−	0.886523i	$-0.346886\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	15.4664	+	8.92951i	0.697987	+	0.402983i	0.806597	−	0.591101i	$-0.201307\pi$
$491$	15.4664	+	8.92951i	0.697987	+	0.402983i	−0.108610	+	0.994084i	$0.534640\pi$
$492$		0			0
$493$	33.1664	+	19.1486i	1.49374	+	0.862411i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	5.14511	−	0.356310i	0.230790	−	0.0159827i
$498$		0			0
$499$	−11.5602	−	20.0229i	−0.517506	−	0.896346i	−0.999793	−	0.0203330i	$-0.993527\pi$
$499$	−11.5602	−	20.0229i	−0.517506	−	0.896346i	0.482288	−	0.876013i	$-0.339806\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	13.9995			0.624206			0.312103	−	0.950048i	$-0.398967\pi$
$503$	13.9995			0.624206			0.312103	+	0.950048i	$0.398967\pi$
$504$		0			0
$505$	5.71228			0.254193
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.79171	+	11.7636i	0.301037	+	0.521411i	0.976371	−	0.216100i	$-0.0693339\pi$
$509$	6.79171	+	11.7636i	0.301037	+	0.521411i	−0.675334	+	0.737512i	$0.736001\pi$
$510$		0			0
$511$	−4.14458	−	6.15350i	−0.183345	−	0.272215i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−5.20904	−	3.00744i	−0.229538	−	0.132524i
$516$		0			0
$517$	−3.64633	−	2.10521i	−0.160365	−	0.0925870i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	15.9477	+	27.6222i	0.698682	+	1.21015i	0.968924	+	0.247360i	$0.0795630\pi$
$521$	15.9477	+	27.6222i	0.698682	+	1.21015i	−0.270242	+	0.962792i	$0.587104\pi$
$522$		0			0
$523$	1.20531	+	0.695886i	0.0527046	+	0.0304290i	0.526121	−	0.850410i	$-0.323646\pi$
$523$	1.20531	+	0.695886i	0.0527046	+	0.0304290i	−0.473416	+	0.880839i	$0.656979\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−9.57131	+	5.52600i	−0.416933	+	0.240716i
$528$		0			0
$529$	4.60628	−	7.97832i	0.200273	−	0.346883i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	22.3096	−	12.8805i	0.966337	−	0.557915i
$534$		0			0
$535$		−	8.20854i		−	0.354886i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	11.6798	+	4.73720i	0.503085	+	0.204046i
$540$		0			0
$541$	12.9736	−	22.4709i	0.557779	−	0.966101i	−0.439903	−	0.898045i	$-0.644987\pi$
$541$	12.9736	−	22.4709i	0.557779	−	0.966101i	0.997682	−	0.0680555i	$-0.0216795\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−8.68407	+	15.0413i	−0.371985	+	0.644296i
$546$		0			0
$547$	9.32438	+	16.1503i	0.398682	+	0.690537i	0.993564	−	0.113276i	$-0.0361345\pi$
$547$	9.32438	+	16.1503i	0.398682	+	0.690537i	−0.594882	+	0.803813i	$0.702801\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−39.3514			−1.67642
$552$		0			0
$553$	2.27234	+	32.8125i	0.0966296	+	1.39533i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	36.3567	−	20.9905i	1.54048	−	0.889398i	0.541674	−	0.840589i	$-0.317791\pi$
$557$	36.3567	−	20.9905i	1.54048	−	0.889398i	0.998808	−	0.0488092i	$-0.0155426\pi$
$558$		0			0
$559$		−	16.4334i		−	0.695058i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	38.6011			1.62684			0.813422	−	0.581675i	$-0.197602\pi$
$563$	38.6011			1.62684			0.813422	+	0.581675i	$0.197602\pi$
$564$		0			0
$565$		−	10.4936i		−	0.441468i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	35.1560i		−	1.47382i	−0.675993	−	0.736908i	$-0.736285\pi$
$569$		−	35.1560i		−	1.47382i	0.675993	−	0.736908i	$-0.263715\pi$
$570$		0			0
$571$	35.3532			1.47948			0.739742	−	0.672891i	$-0.234948\pi$
$571$	35.3532			1.47948			0.739742	+	0.672891i	$0.234948\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			16.4854i			0.687489i
$576$		0			0
$577$	23.2557	−	13.4267i	0.968147	−	0.558960i	0.0694761	−	0.997584i	$-0.477867\pi$
$577$	23.2557	−	13.4267i	0.968147	−	0.558960i	0.898671	+	0.438624i	$0.144534\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	15.8400	−	10.6688i	0.657155	−	0.442615i
$582$		0			0
$583$	2.07228			0.0858249
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−15.6788	−	27.1565i	−0.647134	−	1.12087i	−0.983804	−	0.179246i	$-0.942634\pi$
$587$	−15.6788	−	27.1565i	−0.647134	−	1.12087i	0.336671	−	0.941622i	$-0.390699\pi$
$588$		0			0
$589$	5.67809	−	9.83474i	0.233962	−	0.405234i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−4.56131	+	7.90043i	−0.187311	+	0.324432i	−0.944353	−	0.328935i	$-0.893310\pi$
$593$	−4.56131	+	7.90043i	−0.187311	+	0.324432i	0.757042	+	0.653366i	$0.226644\pi$
$594$		0			0
$595$	−13.4362	−	6.56445i	−0.550831	−	0.269116i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			1.28537i			0.0525186i	0.999655	+	0.0262593i	$0.00835956\pi$
$599$			1.28537i			0.0525186i	−0.999655	+	0.0262593i	$0.991640\pi$
$600$		0			0
$601$	16.7126	−	9.64903i	0.681721	−	0.393592i	−0.118782	−	0.992920i	$-0.537899\pi$
$601$	16.7126	−	9.64903i	0.681721	−	0.393592i	0.800503	+	0.599328i	$0.204566\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.61502	−	9.72551i	0.228283	−	0.395398i
$606$		0			0
$607$	−33.7319	+	19.4751i	−1.36913	+	0.790470i	−0.990817	−	0.135206i	$-0.956830\pi$
$607$	−33.7319	+	19.4751i	−1.36913	+	0.790470i	−0.378317	+	0.925676i	$0.623497\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.41645	−	2.54984i	−0.178670	−	0.103155i
$612$		0			0
$613$	−3.65018	−	6.32229i	−0.147429	−	0.255355i	0.782847	−	0.622214i	$-0.213767\pi$
$613$	−3.65018	−	6.32229i	−0.147429	−	0.255355i	−0.930277	+	0.366859i	$0.880433\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−38.3641	−	22.1495i	−1.54448	−	0.891706i	−0.998548	−	0.0538763i	$-0.982842\pi$
$617$	−38.3641	−	22.1495i	−1.54448	−	0.891706i	−0.545932	−	0.837829i	$-0.683824\pi$
$618$		0			0
$619$	0.408449	+	0.235818i	0.0164169	+	0.00947832i	0.508186	−	0.861247i	$-0.330316\pi$
$619$	0.408449	+	0.235818i	0.0164169	+	0.00947832i	−0.491769	+	0.870726i	$0.663650\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−25.1508	−	12.2878i	−1.00764	−	0.492299i
$624$		0			0
$625$	1.02013	+	1.76692i	0.0408052	+	0.0706768i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	3.21558			0.128213
$630$		0			0
$631$	−10.2247			−0.407038			−0.203519	−	0.979071i	$-0.565238\pi$
$631$	−10.2247			−0.407038			−0.203519	+	0.979071i	$0.565238\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.637888	+	1.10485i	0.0253138	+	0.0438448i
$636$		0			0
$637$	14.1466	+	5.73772i	0.560510	+	0.227337i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−43.4584	−	25.0907i	−1.71651	−	0.991025i	−0.925091	−	0.379745i	$-0.876012\pi$
$641$	−43.4584	−	25.0907i	−1.71651	−	0.991025i	−0.791414	−	0.611280i	$-0.790655\pi$
$642$		0			0
$643$	9.18633	+	5.30373i	0.362274	+	0.209159i	0.670078	−	0.742291i	$-0.266261\pi$
$643$	9.18633	+	5.30373i	0.362274	+	0.209159i	−0.307804	+	0.951450i	$0.599594\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−14.9203	−	25.8427i	−0.586577	−	1.01598i	−0.994677	−	0.103044i	$-0.967142\pi$
$647$	−14.9203	−	25.8427i	−0.586577	−	1.01598i	0.408100	−	0.912937i	$-0.366191\pi$
$648$		0			0
$649$	15.2676	+	8.81474i	0.599305	+	0.346009i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	30.5327	−	17.6281i	1.19484	−	0.689839i	0.235437	−	0.971890i	$-0.424348\pi$
$653$	30.5327	−	17.6281i	1.19484	−	0.689839i	0.959400	+	0.282050i	$0.0910144\pi$
$654$		0			0
$655$	2.15280	−	3.72877i	0.0841170	−	0.145695i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	29.3751	−	16.9597i	1.14429	−	0.660656i	0.196801	−	0.980443i	$-0.436945\pi$
$659$	29.3751	−	16.9597i	1.14429	−	0.660656i	0.947489	+	0.319787i	$0.103611\pi$
$660$		0			0
$661$			15.7674i			0.613281i	0.951825	+	0.306641i	$0.0992050\pi$
$661$			15.7674i			0.613281i	−0.951825	+	0.306641i	$0.900795\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	15.3289	−	1.06156i	0.594430	−	0.0411656i
$666$		0			0
$667$	27.8339	−	48.2097i	1.07773	−	1.86669i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.12048	−	3.67279i	0.0818604	−	0.141786i
$672$		0			0
$673$	−7.35627	−	12.7414i	−0.283563	−	0.491146i	0.688696	−	0.725050i	$-0.258183\pi$
$673$	−7.35627	−	12.7414i	−0.283563	−	0.491146i	−0.972260	+	0.233904i	$0.924850\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.98434			−0.153131			−0.0765654	−	0.997065i	$-0.524395\pi$
$677$	−3.98434			−0.153131			−0.0765654	+	0.997065i	$0.524395\pi$
$678$		0			0
$679$	22.9243	+	34.0359i	0.879753	+	1.30618i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	19.2812	−	11.1320i	0.737774	−	0.425954i	−0.0834856	−	0.996509i	$-0.526605\pi$
$683$	19.2812	−	11.1320i	0.737774	−	0.425954i	0.821259	+	0.570555i	$0.193272\pi$
$684$		0			0
$685$			17.2238i			0.658088i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.50995			0.0956215
$690$		0			0
$691$			48.3823i			1.84055i	0.391271	+	0.920275i	$0.372035\pi$
$691$			48.3823i			1.84055i	−0.391271	+	0.920275i	$0.627965\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	17.4073i		−	0.660297i
$696$		0			0
$697$	46.1225			1.74701
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	23.3129i		−	0.880514i	−0.897872	−	0.440257i	$-0.854887\pi$
$701$		−	23.3129i		−	0.880514i	0.897872	−	0.440257i	$-0.145113\pi$
$702$		0			0
$703$	−2.86142	+	1.65204i	−0.107920	+	0.0623079i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.38088	−	4.58316i	−0.352804	−	0.172367i
$708$		0			0
$709$	17.6777			0.663899			0.331949	−	0.943297i	$-0.392294\pi$
$709$	17.6777			0.663899			0.331949	+	0.943297i	$0.392294\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	8.03242	+	13.9126i	0.300817	+	0.521030i
$714$		0			0
$715$	−2.84208	+	4.92263i	−0.106288	+	0.184096i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−15.2102	+	26.3449i	−0.567246	+	0.982498i	0.429591	+	0.903024i	$0.358658\pi$
$719$	−15.2102	+	26.3449i	−0.567246	+	0.982498i	−0.996837	+	0.0794749i	$0.974676\pi$
$720$		0			0
$721$	6.14147	+	9.11830i	0.228720	+	0.339583i
$722$		0			0
$723$		0			0
$724$		0			0
$725$			28.4890i			1.05806i
$726$		0			0
$727$	38.5219	−	22.2406i	1.42870	−	0.824859i	0.431680	−	0.902027i	$-0.357921\pi$
$727$	38.5219	−	22.2406i	1.42870	−	0.824859i	0.997018	+	0.0771674i	$0.0245876\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	14.7112	−	25.4806i	0.544114	−	0.942433i
$732$		0			0
$733$	−39.2270	+	22.6477i	−1.44888	+	0.836512i	−0.998415	−	0.0562818i	$-0.982075\pi$
$733$	−39.2270	+	22.6477i	−1.44888	+	0.836512i	−0.450466	+	0.892794i	$0.648742\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.487767	−	0.281612i	−0.0179671	−	0.0103733i
$738$		0			0
$739$	10.3086	+	17.8550i	0.379208	+	0.656808i	0.990947	−	0.134252i	$-0.0428631\pi$
$739$	10.3086	+	17.8550i	0.379208	+	0.656808i	−0.611739	+	0.791060i	$0.709530\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	7.69885	+	4.44493i	0.282443	+	0.163069i	0.634529	−	0.772899i	$-0.281194\pi$
$743$	7.69885	+	4.44493i	0.282443	+	0.163069i	−0.352086	+	0.935968i	$0.614527\pi$
$744$		0			0
$745$	−8.87435	−	5.12361i	−0.325131	−	0.187714i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−6.58599	+	13.4803i	−0.240647	+	0.492559i
$750$		0			0
$751$	−12.5008	−	21.6521i	−0.456162	−	0.790095i	0.542592	−	0.839996i	$-0.317443\pi$
$751$	−12.5008	−	21.6521i	−0.456162	−	0.790095i	−0.998754	+	0.0499007i	$0.984110\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	22.5555			0.820878
$756$		0			0
$757$	−27.1262			−0.985919			−0.492959	−	0.870052i	$-0.664085\pi$
$757$	−27.1262			−0.985919			−0.492959	+	0.870052i	$0.664085\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.58366	+	2.74298i	0.0574075	+	0.0994328i	0.893301	−	0.449459i	$-0.148383\pi$
$761$	1.58366	+	2.74298i	0.0574075	+	0.0994328i	−0.835893	+	0.548892i	$0.815050\pi$
$762$		0			0
$763$	26.3293	−	17.7337i	0.953186	−	0.642002i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	18.4922	+	10.6765i	0.667713	+	0.385504i
$768$		0			0
$769$	−2.48873	−	1.43687i	−0.0897460	−	0.0518149i	0.454455	−	0.890770i	$-0.349834\pi$
$769$	−2.48873	−	1.43687i	−0.0897460	−	0.0518149i	−0.544201	+	0.838955i	$0.683167\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	6.15679	+	10.6639i	0.221444	+	0.383553i	0.955247	−	0.295810i	$-0.0955895\pi$
$773$	6.15679	+	10.6639i	0.221444	+	0.383553i	−0.733802	+	0.679363i	$0.762256\pi$
$774$		0			0
$775$	−7.12002	−	4.11075i	−0.255759	−	0.147662i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−41.0426	+	23.6960i	−1.47051	+	0.848997i
$780$		0			0
$781$	1.75494	−	3.03965i	0.0627968	−	0.108767i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.61539	−	1.51000i	0.0933473	−	0.0538941i
$786$		0			0
$787$		−	3.81570i		−	0.136015i	−0.997685	−	0.0680076i	$-0.978336\pi$
$787$		−	3.81570i		−	0.136015i	0.997685	−	0.0680076i	$-0.0216642\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−8.41936	+	17.2329i	−0.299358	+	0.612730i
$792$		0			0
$793$	2.56834	−	4.44849i	0.0912044	−	0.157971i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	24.5682	−	42.5535i	0.870252	−	1.50732i	0.00851609	−	0.999964i	$-0.497289\pi$
$797$	24.5682	−	42.5535i	0.870252	−	1.50732i	0.861736	−	0.507357i	$-0.169377\pi$
$798$		0			0
$799$	−4.56524	−	7.90724i	−0.161507	−	0.279738i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.04906			−0.178177
$804$		0			0
$805$	−9.54188	+	19.5305i	−0.336307	+	0.688359i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	39.4929	−	22.8012i	1.38850	−	0.801648i	0.395350	−	0.918531i	$-0.370623\pi$
$809$	39.4929	−	22.8012i	1.38850	−	0.801648i	0.993146	+	0.116882i	$0.0372900\pi$
$810$		0			0
$811$			39.1391i			1.37436i	0.726488	+	0.687180i	$0.241151\pi$
$811$			39.1391i			1.37436i	−0.726488	+	0.687180i	$0.758849\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	16.1831			0.566870
$816$		0			0
$817$			30.2322i			1.05769i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			11.8906i			0.414985i	0.978237	+	0.207492i	$0.0665302\pi$
$821$			11.8906i			0.414985i	−0.978237	+	0.207492i	$0.933470\pi$
$822$		0			0
$823$	−3.02389			−0.105406			−0.0527031	−	0.998610i	$-0.516784\pi$
$823$	−3.02389			−0.105406			−0.0527031	+	0.998610i	$0.516784\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	15.2436i		−	0.530071i	−0.964239	−	0.265035i	$-0.914616\pi$
$827$		−	15.2436i		−	0.530071i	0.964239	−	0.265035i	$-0.0853836\pi$
$828$		0			0
$829$	−29.7306	+	17.1649i	−1.03259	+	0.596163i	−0.917724	−	0.397218i	$-0.869976\pi$
$829$	−29.7306	+	17.1649i	−1.03259	+	0.596163i	−0.114861	+	0.993382i	$0.536642\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	16.7985	+	21.5607i	0.582032	+	0.747033i
$834$		0			0
$835$	−2.78146			−0.0962565
$836$		0			0
$837$		0			0
$838$		0			0
$839$	6.16024	+	10.6698i	0.212675	+	0.368364i	0.952551	−	0.304379i	$-0.0984491\pi$
$839$	6.16024	+	10.6698i	0.212675	+	0.368364i	−0.739876	+	0.672744i	$0.765116\pi$
$840$		0			0
$841$	33.6008	−	58.1983i	1.15865	−	2.00684i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.96672	−	10.3347i	0.205262	−	0.355523i
$846$		0			0
$847$	−17.0243	+	11.4664i	−0.584961	+	0.393990i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	4.67406i		−	0.160225i
$852$		0			0
$853$	3.92537	−	2.26631i	0.134402	−	0.0775971i	−0.431291	−	0.902213i	$-0.641942\pi$
$853$	3.92537	−	2.26631i	0.134402	−	0.0775971i	0.565693	+	0.824616i	$0.308609\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	16.1307	−	27.9392i	0.551014	−	0.954384i	−0.447188	−	0.894440i	$-0.647574\pi$
$857$	16.1307	−	27.9392i	0.551014	−	0.954384i	0.998202	−	0.0599442i	$-0.0190923\pi$
$858$		0			0
$859$	−15.2711	+	8.81675i	−0.521042	+	0.300824i	−0.737361	−	0.675499i	$-0.763928\pi$
$859$	−15.2711	+	8.81675i	−0.521042	+	0.300824i	0.216319	+	0.976323i	$0.430595\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	26.4091	+	15.2473i	0.898975	+	0.519023i	0.876867	−	0.480732i	$-0.159629\pi$
$863$	26.4091	+	15.2473i	0.898975	+	0.519023i	0.0221074	+	0.999756i	$0.492962\pi$
$864$		0			0
$865$	−11.0200	−	19.0873i	−0.374693	−	0.648987i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	19.3851	+	11.1920i	0.657594	+	0.379662i
$870$		0			0
$871$	−0.590785	−	0.341090i	−0.0200180	−	0.0115574i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.09150	−	30.2011i	−0.0707055	−	1.02098i
$876$		0			0
$877$	−4.40363	−	7.62730i	−0.148700	−	0.257556i	0.782047	−	0.623219i	$-0.214176\pi$
$877$	−4.40363	−	7.62730i	−0.148700	−	0.257556i	−0.930747	+	0.365663i	$0.880842\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−38.6776			−1.30308			−0.651540	−	0.758614i	$-0.725877\pi$
$881$	−38.6776			−1.30308			−0.651540	+	0.758614i	$0.725877\pi$
$882$		0			0
$883$	−37.4489			−1.26026			−0.630128	−	0.776491i	$-0.716998\pi$
$883$	−37.4489			−1.26026			−0.630128	+	0.776491i	$0.716998\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	13.7025	+	23.7335i	0.460086	+	0.796892i	0.998965	−	0.0454915i	$-0.0144854\pi$
$887$	13.7025	+	23.7335i	0.460086	+	0.796892i	−0.538879	+	0.842383i	$0.681152\pi$
$888$		0			0
$889$	−0.161096	−	2.32622i	−0.00540299	−	0.0780191i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.12487	+	4.69090i	0.271888	+	0.156975i
$894$		0			0
$895$	0.433397	+	0.250222i	0.0144869	+	0.00836400i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	13.8811	+	24.0428i	0.462962	+	0.801873i
$900$		0			0
$901$	3.89177	+	2.24691i	0.129654	+	0.0748556i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.10760	+	2.37152i	−0.136541	+	0.0788321i
$906$		0			0
$907$	−11.8216	+	20.4757i	−0.392531	+	0.679883i	−0.992783	−	0.119928i	$-0.961734\pi$
$907$	−11.8216	+	20.4757i	−0.392531	+	0.679883i	0.600252	+	0.799811i	$0.295067\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−3.92249	+	2.26465i	−0.129958	+	0.0750313i	−0.563570	−	0.826069i	$-0.690572\pi$
$911$	−3.92249	+	2.26465i	−0.129958	+	0.0750313i	0.433612	+	0.901100i	$0.357239\pi$
$912$		0			0
$913$		−	12.9970i		−	0.430139i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−6.52711	+	4.39622i	−0.215544	+	0.145176i
$918$		0			0
$919$	−16.9149	+	29.2975i	−0.557971	+	0.966434i	0.439695	+	0.898147i	$0.355087\pi$
$919$	−16.9149	+	29.2975i	−0.557971	+	0.966434i	−0.997666	+	0.0682866i	$0.978247\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.12559	−	3.68164i	0.0699648	−	0.121183i
$924$		0			0
$925$	1.19602	+	2.07157i	0.0393249	+	0.0681127i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−32.9164			−1.07995			−0.539976	−	0.841680i	$-0.681567\pi$
$929$	−32.9164			−1.07995			−0.539976	+	0.841680i	$0.681567\pi$
$930$		0			0
$931$	−26.0253	−	10.5556i	−0.852946	−	0.345946i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−8.81350	+	5.08848i	−0.288232	+	0.166411i
$936$		0			0
$937$			38.1057i			1.24486i	0.782676	+	0.622430i	$0.213854\pi$
$937$			38.1057i			1.24486i	−0.782676	+	0.622430i	$0.786146\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	19.8771			0.647975			0.323987	−	0.946061i	$-0.394976\pi$
$941$	19.8771			0.647975			0.323987	+	0.946061i	$0.394976\pi$
$942$		0			0
$943$		−	67.0423i		−	2.18320i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	20.7495i		−	0.674267i	−0.941457	−	0.337134i	$-0.890543\pi$
$947$		−	20.7495i		−	0.674267i	0.941457	−	0.337134i	$-0.109457\pi$
$948$		0			0
$949$	−6.11544			−0.198516
$950$		0			0
$951$		0			0
$952$		0			0
$953$			12.8345i			0.415751i	0.978155	+	0.207876i	$0.0666549\pi$
$953$			12.8345i			0.415751i	−0.978155	+	0.207876i	$0.933345\pi$
$954$		0			0
$955$	9.26571	−	5.34956i	0.299831	−	0.173108i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	13.8192	−	28.2854i	0.446247	−	0.913384i
$960$		0			0
$961$	22.9882			0.741556
$962$		0			0
$963$		0			0
$964$		0			0
$965$	9.42969	+	16.3327i	0.303552	+	0.525768i
$966$		0			0
$967$	17.8941	−	30.9936i	0.575437	−	0.996685i	−0.420557	−	0.907266i	$-0.638165\pi$
$967$	17.8941	−	30.9936i	0.575437	−	0.996685i	0.995994	−	0.0894195i	$-0.0285012\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−14.5129	+	25.1370i	−0.465740	+	0.806686i	−0.999235	−	0.0391177i	$-0.987545\pi$
$971$	−14.5129	+	25.1370i	−0.465740	+	0.806686i	0.533494	+	0.845804i	$0.320879\pi$
$972$		0			0
$973$	−13.9665	+	28.5868i	−0.447744	+	0.916450i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	8.93090i		−	0.285725i	−0.989743	−	0.142862i	$-0.954369\pi$
$977$		−	8.93090i		−	0.285725i	0.989743	−	0.142862i	$-0.0456306\pi$
$978$		0			0
$979$	−16.4977	+	9.52495i	−0.527268	+	0.304419i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−26.1346	+	45.2665i	−0.833566	+	1.44378i	0.0616269	+	0.998099i	$0.480371\pi$
$983$	−26.1346	+	45.2665i	−0.833566	+	1.44378i	−0.895193	+	0.445679i	$0.852962\pi$
$984$		0			0
$985$	−5.05250	+	2.91707i	−0.160986	+	0.0929454i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−37.0378	−	21.3838i	−1.17773	−	0.679964i
$990$		0			0
$991$	21.9151	+	37.9581i	0.696158	+	1.20578i	0.969789	+	0.243946i	$0.0784418\pi$
$991$	21.9151	+	37.9581i	0.696158	+	1.20578i	−0.273631	+	0.961835i	$0.588225\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−20.5690	−	11.8755i	−0.652082	−	0.376480i
$996$		0			0
$997$	−38.9689	−	22.4987i	−1.23416	−	0.712542i	−0.266264	−	0.963900i	$-0.585789\pi$
$997$	−38.9689	−	22.4987i	−1.23416	−	0.712542i	−0.967894	+	0.251358i	$0.919123\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.ca.b.2609.4		10
3.2	odd	2		1008.2.ca.b.257.3		10
4.3	odd	2		189.2.i.b.152.2		10
7.3	odd	6		3024.2.df.b.17.4		10
9.2	odd	6		3024.2.df.b.1601.4		10
9.7	even	3		1008.2.df.b.929.2		10
12.11	even	2		63.2.i.b.5.4	✓	10
21.17	even	6		1008.2.df.b.689.2		10
28.3	even	6		189.2.s.b.17.4		10
28.11	odd	6		1323.2.s.b.962.4		10
28.19	even	6		1323.2.o.d.881.2		10
28.23	odd	6		1323.2.o.c.881.2		10
28.27	even	2		1323.2.i.b.1097.2		10
36.7	odd	6		63.2.s.b.47.2	yes	10
36.11	even	6		189.2.s.b.89.4		10
36.23	even	6		567.2.p.d.404.2		10
36.31	odd	6		567.2.p.c.404.4		10
63.38	even	6	inner	3024.2.ca.b.2033.4		10
63.52	odd	6		1008.2.ca.b.353.3		10
84.11	even	6		441.2.s.b.374.2		10
84.23	even	6		441.2.o.d.293.4		10
84.47	odd	6		441.2.o.c.293.4		10
84.59	odd	6		63.2.s.b.59.2	yes	10
84.83	odd	2		441.2.i.b.68.4		10
252.11	even	6		1323.2.i.b.521.4		10
252.31	even	6		567.2.p.d.80.2		10
252.47	odd	6		1323.2.o.c.440.2		10
252.59	odd	6		567.2.p.c.80.4		10
252.79	odd	6		441.2.o.c.146.4		10
252.83	odd	6		1323.2.s.b.656.4		10
252.115	even	6		63.2.i.b.38.2	yes	10
252.151	odd	6		441.2.i.b.227.2		10
252.187	even	6		441.2.o.d.146.4		10
252.191	even	6		1323.2.o.d.440.2		10
252.223	even	6		441.2.s.b.362.2		10
252.227	odd	6		189.2.i.b.143.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.4	✓	10	12.11	even	2
63.2.i.b.38.2	yes	10	252.115	even	6
63.2.s.b.47.2	yes	10	36.7	odd	6
63.2.s.b.59.2	yes	10	84.59	odd	6
189.2.i.b.143.4		10	252.227	odd	6
189.2.i.b.152.2		10	4.3	odd	2
189.2.s.b.17.4		10	28.3	even	6
189.2.s.b.89.4		10	36.11	even	6
441.2.i.b.68.4		10	84.83	odd	2
441.2.i.b.227.2		10	252.151	odd	6
441.2.o.c.146.4		10	252.79	odd	6
441.2.o.c.293.4		10	84.47	odd	6
441.2.o.d.146.4		10	252.187	even	6
441.2.o.d.293.4		10	84.23	even	6
441.2.s.b.362.2		10	252.223	even	6
441.2.s.b.374.2		10	84.11	even	6
567.2.p.c.80.4		10	252.59	odd	6
567.2.p.c.404.4		10	36.31	odd	6
567.2.p.d.80.2		10	252.31	even	6
567.2.p.d.404.2		10	36.23	even	6
1008.2.ca.b.257.3		10	3.2	odd	2
1008.2.ca.b.353.3		10	63.52	odd	6
1008.2.df.b.689.2		10	21.17	even	6
1008.2.df.b.929.2		10	9.7	even	3
1323.2.i.b.521.4		10	252.11	even	6
1323.2.i.b.1097.2		10	28.27	even	2
1323.2.o.c.440.2		10	252.47	odd	6
1323.2.o.c.881.2		10	28.23	odd	6
1323.2.o.d.440.2		10	252.191	even	6
1323.2.o.d.881.2		10	28.19	even	6
1323.2.s.b.656.4		10	252.83	odd	6
1323.2.s.b.962.4		10	28.11	odd	6
3024.2.ca.b.2033.4		10	63.38	even	6	inner
3024.2.ca.b.2609.4		10	1.1	even	1	trivial
3024.2.df.b.17.4		10	7.3	odd	6
3024.2.df.b.1601.4		10	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.723774 + 1.25361i) q^{5} +(-0.182786 - 2.63943i) q^{7} +O(q^{10})\)	\(q+(0.723774 + 1.25361i) q^{5} +(-0.182786 - 2.63943i) q^{7} +(-1.55933 - 0.900281i) q^{11} +(-1.88867 - 1.09042i) q^{13} +(-1.95230 - 3.38149i) q^{17} +(3.47456 + 2.00604i) q^{19} +(-4.91522 + 2.83781i) q^{23} +(1.45230 - 2.51546i) q^{25} +(-8.49418 + 4.90412i) q^{29} -2.83050i q^{31} +(3.17653 - 2.13949i) q^{35} +(-0.411767 + 0.713202i) q^{37} +(-5.90617 + 10.2298i) q^{41} +(3.76766 + 6.52578i) q^{43} +2.33839 q^{47} +(-6.93318 + 0.964903i) q^{49} +(-0.996713 + 0.575453i) q^{53} -2.60640i q^{55} -9.79110 q^{59} +2.35536i q^{61} -3.15688i q^{65} +0.312805 q^{67} +1.94933i q^{71} +(2.42847 - 1.40208i) q^{73} +(-2.09120 + 4.28031i) q^{77} -12.4317 q^{79} +(3.60916 + 6.25124i) q^{83} +(2.82605 - 4.89486i) q^{85} +(5.28999 - 9.16253i) q^{89} +(-2.53287 + 5.18433i) q^{91} +5.80767i q^{95} +(-13.4322 + 7.75510i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 6 q^{7}+O(q^{10}) \) 10 * q + 6 * q^7	\( 10 q + 6 q^{7} - 12 q^{11} - 6 q^{13} - 12 q^{17} - 3 q^{19} - 15 q^{23} + 7 q^{25} + 15 q^{29} + 15 q^{35} + 6 q^{37} - 9 q^{41} - 3 q^{43} + 30 q^{47} + 4 q^{49} - 9 q^{53} - 36 q^{59} - 20 q^{67} + 3 q^{73} - 39 q^{77} + 40 q^{79} + 15 q^{83} + 18 q^{85} + 24 q^{89} + 24 q^{91} - 6 q^{97}+O(q^{100}) \) 10 * q + 6 * q^7 - 12 * q^11 - 6 * q^13 - 12 * q^17 - 3 * q^19 - 15 * q^23 + 7 * q^25 + 15 * q^29 + 15 * q^35 + 6 * q^37 - 9 * q^41 - 3 * q^43 + 30 * q^47 + 4 * q^49 - 9 * q^53 - 36 * q^59 - 20 * q^67 + 3 * q^73 - 39 * q^77 + 40 * q^79 + 15 * q^83 + 18 * q^85 + 24 * q^89 + 24 * q^91 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more