LMFDB - Embedded newform 24.11.e.a.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,11,Mod(17,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("24.17");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	24.e (of order $2$, degree $1$, 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:	$15.2485740642$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 532 x^{8} - 1350 x^{7} + 106101 x^{6} + 516780 x^{5} - 8879077 x^{4} - 65126430 x^{3} + \cdots + 6338653425 $ x^10 - 532x^8 - 1350x^7 + 106101x^6 + 516780x^5 - 8879077x^4 - 65126430x^3 + 204512770x^2 + 2776831200x + 6338653425
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{72}\cdot 3^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			17.7
Root			$10.3554 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	24.17
Dual form			24.11.e.a.17.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(171.197 - 172.454i) q^{3} +2896.26i q^{5} -28955.7 q^{7} +(-431.864 - 59047.4i) q^{9} +O(q^{10})$	\(q+(171.197 - 172.454i) q^{3} +2896.26i q^{5} -28955.7 q^{7} +(-431.864 - 59047.4i) q^{9} +194676. i q^{11} -114481. q^{13} +(499472. + 495833. i) q^{15} +39710.7i q^{17} -4.65684e6 q^{19} +(-4.95715e6 + 4.99354e6i) q^{21} +7.57809e6i q^{23} +1.37729e6 q^{25} +(-1.02569e7 - 1.00343e7i) q^{27} +2.03229e7i q^{29} -8.24006e6 q^{31} +(3.35727e7 + 3.33281e7i) q^{33} -8.38634e7i q^{35} +1.91039e7 q^{37} +(-1.95989e7 + 1.97428e7i) q^{39} -1.15568e8i q^{41} -4.08453e6 q^{43} +(1.71017e8 - 1.25079e6i) q^{45} -2.81165e8i q^{47} +5.55960e8 q^{49} +(6.84827e6 + 6.79836e6i) q^{51} +3.33283e8i q^{53} -5.63833e8 q^{55} +(-7.97239e8 + 8.03091e8i) q^{57} -1.23488e9i q^{59} -5.77494e8 q^{61} +(1.25049e7 + 1.70976e9i) q^{63} -3.31568e8i q^{65} -8.61148e8 q^{67} +(1.30687e9 + 1.29735e9i) q^{69} +1.70435e9i q^{71} -8.23189e8 q^{73} +(2.35789e8 - 2.37520e8i) q^{75} -5.63699e9i q^{77} +3.61377e9 q^{79} +(-3.48641e9 + 5.10009e7i) q^{81} +7.05763e8i q^{83} -1.15012e8 q^{85} +(3.50477e9 + 3.47923e9i) q^{87} -6.89745e9i q^{89} +3.31489e9 q^{91} +(-1.41068e9 + 1.42103e9i) q^{93} -1.34874e10i q^{95} +1.18738e10 q^{97} +(1.14951e10 - 8.40736e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 22 q^{3} - 5436 q^{7} - 28934 q^{9}+O(q^{10}) $ 10 * q - 22 * q^3 - 5436 * q^7 - 28934 * q^9	$ 10 q - 22 q^{3} - 5436 q^{7} - 28934 q^{9} - 124508 q^{13} - 627808 q^{15} - 4893484 q^{19} - 3929724 q^{21} - 17742214 q^{25} - 3536326 q^{27} - 4251484 q^{31} - 2965600 q^{33} + 89985156 q^{37} + 52569188 q^{39} + 159987316 q^{43} + 39125824 q^{45} + 301480958 q^{49} + 387377536 q^{51} - 852340544 q^{55} - 970086764 q^{57} - 101460764 q^{61} + 733153572 q^{63} - 3014528044 q^{67} - 3501669184 q^{69} + 4920922036 q^{73} + 5355440986 q^{75} - 7631690012 q^{79} - 7700105942 q^{81} + 18713636096 q^{85} + 19781179104 q^{87} - 17913072600 q^{91} - 24272938652 q^{93} + 37861379156 q^{97} + 43508497216 q^{99}+O(q^{100}) $ 10 * q - 22 * q^3 - 5436 * q^7 - 28934 * q^9 - 124508 * q^13 - 627808 * q^15 - 4893484 * q^19 - 3929724 * q^21 - 17742214 * q^25 - 3536326 * q^27 - 4251484 * q^31 - 2965600 * q^33 + 89985156 * q^37 + 52569188 * q^39 + 159987316 * q^43 + 39125824 * q^45 + 301480958 * q^49 + 387377536 * q^51 - 852340544 * q^55 - 970086764 * q^57 - 101460764 * q^61 + 733153572 * q^63 - 3014528044 * q^67 - 3501669184 * q^69 + 4920922036 * q^73 + 5355440986 * q^75 - 7631690012 * q^79 - 7700105942 * q^81 + 18713636096 * q^85 + 19781179104 * q^87 - 17913072600 * q^91 - 24272938652 * q^93 + 37861379156 * q^97 + 43508497216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$1$	$1$	$-1$

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
$3$	171.197	−	172.454i	0.704516	−	0.709688i
$3$	171.197	−	172.454i	0.704516	−	0.709688i
$4$		0			0
$5$			2896.26i			0.926804i	0.886148	+	0.463402i	$0.153371\pi$
$5$			2896.26i			0.926804i	−0.886148	+	0.463402i	$0.846629\pi$
$6$		0			0
$7$	−28955.7			−1.72284			−0.861419	−	0.507895i	$-0.830424\pi$
$7$	−28955.7			−1.72284			−0.861419	+	0.507895i	$0.830424\pi$
$8$		0			0
$9$	−431.864	−	59047.4i	−0.00731365	−	0.999973i
$10$		0			0
$11$			194676.i			1.20879i	0.796687	+	0.604393i	$0.206584\pi$
$11$			194676.i			1.20879i	−0.796687	+	0.604393i	$0.793416\pi$
$12$		0			0
$13$	−114481.			−0.308331			−0.154166	−	0.988045i	$-0.549269\pi$
$13$	−114481.			−0.308331			−0.154166	+	0.988045i	$0.549269\pi$
$14$		0			0
$15$	499472.	+	495833.i	0.657741	+	0.652948i
$16$		0			0
$17$			39710.7i			0.0279681i	0.999902	+	0.0139840i	$0.00445140\pi$
$17$			39710.7i			0.0279681i	−0.999902	+	0.0139840i	$0.995549\pi$
$18$		0			0
$19$	−4.65684e6			−1.88071			−0.940357	−	0.340188i	$-0.889509\pi$
$19$	−4.65684e6			−1.88071			−0.940357	+	0.340188i	$0.889509\pi$
$20$		0			0
$21$	−4.95715e6	+	4.99354e6i	−1.21377	+	1.22268i
$22$		0			0
$23$			7.57809e6i			1.17739i	0.808355	+	0.588695i	$0.200358\pi$
$23$			7.57809e6i			1.17739i	−0.808355	+	0.588695i	$0.799642\pi$
$24$		0			0
$25$	1.37729e6			0.141035
$26$		0			0
$27$	−1.02569e7	−	1.00343e7i	−0.714821	−	0.699307i
$28$		0			0
$29$			2.03229e7i			0.990824i	0.868658	+	0.495412i	$0.164983\pi$
$29$			2.03229e7i			0.990824i	−0.868658	+	0.495412i	$0.835017\pi$
$30$		0			0
$31$	−8.24006e6			−0.287821			−0.143910	−	0.989591i	$-0.545968\pi$
$31$	−8.24006e6			−0.287821			−0.143910	+	0.989591i	$0.545968\pi$
$32$		0			0
$33$	3.35727e7	+	3.33281e7i	0.857860	+	0.851609i
$34$		0			0
$35$		−	8.38634e7i		−	1.59673i
$36$		0			0
$37$	1.91039e7			0.275496			0.137748	−	0.990467i	$-0.456014\pi$
$37$	1.91039e7			0.275496			0.137748	+	0.990467i	$0.456014\pi$
$38$		0			0
$39$	−1.95989e7	+	1.97428e7i	−0.217225	+	0.218819i
$40$		0			0
$41$		−	1.15568e8i		−	0.997516i	−0.866741	−	0.498758i	$-0.833790\pi$
$41$		−	1.15568e8i		−	0.997516i	0.866741	−	0.498758i	$-0.166210\pi$
$42$		0			0
$43$	−4.08453e6			−0.0277843			−0.0138922	−	0.999903i	$-0.504422\pi$
$43$	−4.08453e6			−0.0277843			−0.0138922	+	0.999903i	$0.504422\pi$
$44$		0			0
$45$	1.71017e8	−	1.25079e6i	0.926779	−	0.00677832i
$46$		0			0
$47$		−	2.81165e8i		−	1.22595i	−0.790104	−	0.612973i	$-0.789973\pi$
$47$		−	2.81165e8i		−	1.22595i	0.790104	−	0.612973i	$-0.210027\pi$
$48$		0			0
$49$	5.55960e8			1.96817
$50$		0			0
$51$	6.84827e6	+	6.79836e6i	0.0198486	+	0.0197040i
$52$		0			0
$53$			3.33283e8i			0.796954i	0.917178	+	0.398477i	$0.130461\pi$
$53$			3.33283e8i			0.796954i	−0.917178	+	0.398477i	$0.869539\pi$
$54$		0			0
$55$	−5.63833e8			−1.12031
$56$		0			0
$57$	−7.97239e8	+	8.03091e8i	−1.32499	+	1.33472i
$58$		0			0
$59$		−	1.23488e9i		−	1.72729i	−0.504102	−	0.863644i	$-0.668176\pi$
$59$		−	1.23488e9i		−	1.72729i	0.504102	−	0.863644i	$-0.331824\pi$
$60$		0			0
$61$	−5.77494e8			−0.683751			−0.341876	−	0.939745i	$-0.611062\pi$
$61$	−5.77494e8			−0.683751			−0.341876	+	0.939745i	$0.611062\pi$
$62$		0			0
$63$	1.25049e7	+	1.70976e9i	0.0126002	+	1.72279i
$64$		0			0
$65$		−	3.31568e8i		−	0.285763i
$66$		0			0
$67$	−8.61148e8			−0.637828			−0.318914	−	0.947784i	$-0.603318\pi$
$67$	−8.61148e8			−0.637828			−0.318914	+	0.947784i	$0.603318\pi$
$68$		0			0
$69$	1.30687e9	+	1.29735e9i	0.835579	+	0.829490i
$70$		0			0
$71$			1.70435e9i			0.944641i	0.881427	+	0.472320i	$0.156583\pi$
$71$			1.70435e9i			0.944641i	−0.881427	+	0.472320i	$0.843417\pi$
$72$		0			0
$73$	−8.23189e8			−0.397087			−0.198543	−	0.980092i	$-0.563621\pi$
$73$	−8.23189e8			−0.397087			−0.198543	+	0.980092i	$0.563621\pi$
$74$		0			0
$75$	2.35789e8	−	2.37520e8i	0.0993612	−	0.100091i
$76$		0			0
$77$		−	5.63699e9i		−	2.08254i
$78$		0			0
$79$	3.61377e9			1.17442			0.587212	−	0.809433i	$-0.300225\pi$
$79$	3.61377e9			1.17442			0.587212	+	0.809433i	$0.300225\pi$
$80$		0			0
$81$	−3.48641e9	+	5.10009e7i	−0.999893	+	0.0146269i
$82$		0			0
$83$			7.05763e8i			0.179171i	0.995979	+	0.0895856i	$0.0285543\pi$
$83$			7.05763e8i			0.179171i	−0.995979	+	0.0895856i	$0.971446\pi$
$84$		0			0
$85$	−1.15012e8			−0.0259209
$86$		0			0
$87$	3.50477e9	+	3.47923e9i	0.703176	+	0.698052i
$88$		0			0
$89$		−	6.89745e9i		−	1.23520i	−0.786491	−	0.617602i	$-0.788104\pi$
$89$		−	6.89745e9i		−	1.23520i	0.786491	−	0.617602i	$-0.211896\pi$
$90$		0			0
$91$	3.31489e9			0.531205
$92$		0			0
$93$	−1.41068e9	+	1.42103e9i	−0.202774	+	0.204263i
$94$		0			0
$95$		−	1.34874e10i		−	1.74305i
$96$		0			0
$97$	1.18738e10			1.38271			0.691353	−	0.722517i	$-0.257015\pi$
$97$	1.18738e10			1.38271			0.691353	+	0.722517i	$0.257015\pi$
$98$		0			0
$99$	1.14951e10	−	8.40736e7i	1.20875	−	0.00884063i
$100$		0			0
$101$			1.31279e10i			1.24907i	0.780995	+	0.624537i	$0.214712\pi$
$101$			1.31279e10i			1.24907i	−0.780995	+	0.624537i	$0.785288\pi$
$102$		0			0
$103$	−1.80950e10			−1.56089			−0.780445	−	0.625225i	$-0.785007\pi$
$103$	−1.80950e10			−1.56089			−0.780445	+	0.625225i	$0.785007\pi$
$104$		0			0
$105$	−1.44626e10	−	1.43572e10i	−1.13318	−	1.12492i
$106$		0			0
$107$			2.72427e10i			1.94237i	0.238334	+	0.971183i	$0.423399\pi$
$107$			2.72427e10i			1.94237i	−0.238334	+	0.971183i	$0.576601\pi$
$108$		0			0
$109$	−3.20673e9			−0.208416			−0.104208	−	0.994556i	$-0.533231\pi$
$109$	−3.20673e9			−0.208416			−0.104208	+	0.994556i	$0.533231\pi$
$110$		0			0
$111$	3.27055e9	−	3.29456e9i	0.194091	−	0.195516i
$112$		0			0
$113$			1.35851e10i			0.737342i	0.929560	+	0.368671i	$0.120187\pi$
$113$			1.35851e10i			0.737342i	−0.929560	+	0.368671i	$0.879813\pi$
$114$		0			0
$115$	−2.19481e10			−1.09121
$116$		0			0
$117$	4.94403e7	+	6.75983e9i	0.00225503	+	0.308323i
$118$		0			0
$119$		−	1.14985e9i		−	0.0481844i
$120$		0			0
$121$	−1.19614e10			−0.461162
$122$		0			0
$123$	−1.99303e10	−	1.97850e10i	−0.707925	−	0.702766i
$124$		0			0
$125$			3.22728e10i			1.05752i
$126$		0			0
$127$	−2.49525e9			−0.0755259			−0.0377629	−	0.999287i	$-0.512023\pi$
$127$	−2.49525e9			−0.0755259			−0.0377629	+	0.999287i	$0.512023\pi$
$128$		0			0
$129$	−6.99261e8	+	7.04394e8i	−0.0195745	+	0.0197182i
$130$		0			0
$131$			7.63293e9i			0.197849i	0.995095	+	0.0989247i	$0.0315403\pi$
$131$			7.63293e9i			0.197849i	−0.995095	+	0.0989247i	$0.968460\pi$
$132$		0			0
$133$	1.34842e11			3.24017
$134$		0			0
$135$	2.90619e10	−	2.97067e10i	0.648120	−	0.662499i
$136$		0			0
$137$		−	8.02271e9i		−	0.166233i	−0.996540	−	0.0831167i	$-0.973513\pi$
$137$		−	8.02271e9i		−	0.166233i	0.996540	−	0.0831167i	$-0.0264874\pi$
$138$		0			0
$139$	−4.71352e10			−0.908389			−0.454194	−	0.890903i	$-0.650073\pi$
$139$	−4.71352e10			−0.908389			−0.454194	+	0.890903i	$0.650073\pi$
$140$		0			0
$141$	−4.84880e10	−	4.81347e10i	−0.870039	−	0.863699i
$142$		0			0
$143$		−	2.22868e10i		−	0.372707i
$144$		0			0
$145$	−5.88605e10			−0.918299
$146$		0			0
$147$	9.51789e10	−	9.58776e10i	1.38661	−	1.39679i
$148$		0			0
$149$			9.14868e10i			1.24574i	0.782325	+	0.622870i	$0.214033\pi$
$149$			9.14868e10i			1.24574i	−0.782325	+	0.622870i	$0.785967\pi$
$150$		0			0
$151$	−5.96294e10			−0.759583			−0.379792	−	0.925072i	$-0.624004\pi$
$151$	−5.96294e10			−0.759583			−0.379792	+	0.925072i	$0.624004\pi$
$152$		0			0
$153$	2.34481e9	−	1.71496e7i	0.0279673	−	0.000204549i
$154$		0			0
$155$		−	2.38654e10i		−	0.266753i
$156$		0			0
$157$	1.63632e11			1.71542			0.857711	−	0.514133i	$-0.171886\pi$
$157$	1.63632e11			1.71542			0.857711	+	0.514133i	$0.171886\pi$
$158$		0			0
$159$	5.74760e10	+	5.70571e10i	0.565589	+	0.561467i
$160$		0			0
$161$		−	2.19429e11i		−	2.02845i
$162$		0			0
$163$	5.15923e10			0.448380			0.224190	−	0.974545i	$-0.428026\pi$
$163$	5.15923e10			0.448380			0.224190	+	0.974545i	$0.428026\pi$
$164$		0			0
$165$	−9.65268e10	+	9.72353e10i	−0.789275	+	0.795068i
$166$		0			0
$167$			1.56828e11i			1.20737i	0.797222	+	0.603686i	$0.206302\pi$
$167$			1.56828e11i			1.20737i	−0.797222	+	0.603686i	$0.793698\pi$
$168$		0			0
$169$	−1.24753e11			−0.904932
$170$		0			0
$171$	2.01112e9	+	2.74974e11i	0.0137549	+	1.88066i
$172$		0			0
$173$		−	6.19891e9i		−	0.0400023i	−0.999800	−	0.0200012i	$-0.993633\pi$
$173$		−	6.19891e9i		−	0.0400023i	0.999800	−	0.0200012i	$-0.00636699\pi$
$174$		0			0
$175$	−3.98805e10			−0.242980
$176$		0			0
$177$	−2.12960e11	−	2.11408e11i	−1.22584	−	1.21690i
$178$		0			0
$179$		−	6.16221e10i		−	0.335329i	−0.985844	−	0.167665i	$-0.946377\pi$
$179$		−	6.16221e10i		−	0.335329i	0.985844	−	0.167665i	$-0.0536226\pi$
$180$		0			0
$181$	−2.01755e11			−1.03856			−0.519280	−	0.854604i	$-0.673800\pi$
$181$	−2.01755e11			−1.03856			−0.519280	+	0.854604i	$0.673800\pi$
$182$		0			0
$183$	−9.88655e10	+	9.95912e10i	−0.481714	+	0.485250i
$184$		0			0
$185$			5.53300e10i			0.255330i
$186$		0			0
$187$	−7.73072e9			−0.0338074
$188$		0			0
$189$	2.96996e11	+	2.90550e11i	1.23152	+	1.20479i
$190$		0			0
$191$			8.09166e9i			0.0318325i	0.999873	+	0.0159163i	$0.00506651\pi$
$191$			8.09166e9i			0.0318325i	−0.999873	+	0.0159163i	$0.994933\pi$
$192$		0			0
$193$	−1.16879e11			−0.436465			−0.218232	−	0.975897i	$-0.570029\pi$
$193$	−1.16879e11			−0.436465			−0.218232	+	0.975897i	$0.570029\pi$
$194$		0			0
$195$	−5.71802e10	−	5.67636e10i	−0.202802	−	0.201325i
$196$		0			0
$197$			4.95881e10i			0.167127i	0.996502	+	0.0835634i	$0.0266301\pi$
$197$			4.95881e10i			0.167127i	−0.996502	+	0.0835634i	$0.973370\pi$
$198$		0			0
$199$	3.11416e11			0.997872			0.498936	−	0.866639i	$-0.333724\pi$
$199$	3.11416e11			0.997872			0.498936	+	0.866639i	$0.333724\pi$
$200$		0			0
$201$	−1.47426e11	+	1.48509e11i	−0.449360	+	0.452659i
$202$		0			0
$203$		−	5.88466e11i		−	1.70703i
$204$		0			0
$205$	3.34716e11			0.924502
$206$		0			0
$207$	4.47466e11	−	3.27270e9i	1.17736	−	0.00861102i
$208$		0			0
$209$		−	9.06575e11i		−	2.27338i
$210$		0			0
$211$	−1.14486e11			−0.273740			−0.136870	−	0.990589i	$-0.543704\pi$
$211$	−1.14486e11			−0.273740			−0.136870	+	0.990589i	$0.543704\pi$
$212$		0			0
$213$	2.93922e11	+	2.91780e11i	0.670400	+	0.665515i
$214$		0			0
$215$		−	1.18299e10i		−	0.0257506i
$216$		0			0
$217$	2.38597e11			0.495869
$218$		0			0
$219$	−1.40928e11	+	1.41962e11i	−0.279754	+	0.281808i
$220$		0			0
$221$		−	4.54613e9i		−	0.00862343i
$222$		0			0
$223$	−5.84007e11			−1.05899			−0.529497	−	0.848312i	$-0.677619\pi$
$223$	−5.84007e11			−1.05899			−0.529497	+	0.848312i	$0.677619\pi$
$224$		0			0
$225$	−5.94802e8	−	8.13255e10i	−0.00103148	−	0.141031i
$226$		0			0
$227$			4.76098e11i			0.789891i	0.918705	+	0.394946i	$0.129237\pi$
$227$			4.76098e11i			0.789891i	−0.918705	+	0.394946i	$0.870763\pi$
$228$		0			0
$229$	3.81466e11			0.605729			0.302864	−	0.953034i	$-0.402057\pi$
$229$	3.81466e11			0.605729			0.302864	+	0.953034i	$0.402057\pi$
$230$		0			0
$231$	−9.72123e11	−	9.65039e11i	−1.47795	−	1.46718i
$232$		0			0
$233$			8.06247e11i			1.17405i	0.809567	+	0.587027i	$0.199702\pi$
$233$			8.06247e11i			1.17405i	−0.809567	+	0.587027i	$0.800298\pi$
$234$		0			0
$235$	8.14326e11			1.13621
$236$		0			0
$237$	6.18668e11	−	6.23210e11i	0.827401	−	0.833475i
$238$		0			0
$239$		−	8.67498e11i		−	1.11245i	−0.831033	−	0.556223i	$-0.812250\pi$
$239$		−	8.67498e11i		−	1.11245i	0.831033	−	0.556223i	$-0.187750\pi$
$240$		0			0
$241$	−7.44941e11			−0.916298			−0.458149	−	0.888875i	$-0.651487\pi$
$241$	−7.44941e11			−0.916298			−0.458149	+	0.888875i	$0.651487\pi$
$242$		0			0
$243$	−5.88069e11	+	6.09977e11i	−0.694060	+	0.719917i
$244$		0			0
$245$			1.61021e12i			1.82411i
$246$		0			0
$247$	5.33121e11			0.579884
$248$		0			0
$249$	1.21712e11	+	1.20825e11i	0.127156	+	0.126229i
$250$		0			0
$251$			9.82693e11i			0.986391i	0.869919	+	0.493195i	$0.164171\pi$
$251$			9.82693e11i			0.986391i	−0.869919	+	0.493195i	$0.835829\pi$
$252$		0			0
$253$	−1.47527e12			−1.42321
$254$		0			0
$255$	−1.96898e10	+	1.98344e10i	−0.0182617	+	0.0183958i
$256$		0			0
$257$			5.47313e11i			0.488169i	0.969754	+	0.244084i	$0.0784874\pi$
$257$			5.47313e11i			0.488169i	−0.969754	+	0.244084i	$0.921513\pi$
$258$		0			0
$259$	−5.53169e11			−0.474634
$260$		0			0
$261$	1.20002e12	−	8.77674e9i	0.990797	−	0.00724654i
$262$		0			0
$263$			3.74576e11i			0.297688i	0.988861	+	0.148844i	$0.0475552\pi$
$263$			3.74576e11i			0.297688i	−0.988861	+	0.148844i	$0.952445\pi$
$264$		0			0
$265$	−9.65274e11			−0.738620
$266$		0			0
$267$	−1.18949e12	−	1.18083e12i	−0.876609	−	0.870221i
$268$		0			0
$269$		−	3.13820e11i		−	0.222802i	−0.993776	−	0.111401i	$-0.964466\pi$
$269$		−	3.13820e11i		−	0.222802i	0.993776	−	0.111401i	$-0.0355338\pi$
$270$		0			0
$271$	−3.64330e11			−0.249257			−0.124629	−	0.992203i	$-0.539774\pi$
$271$	−3.64330e11			−0.249257			−0.124629	+	0.992203i	$0.539774\pi$
$272$		0			0
$273$	5.67501e11	−	5.71667e11i	0.374243	−	0.376990i
$274$		0			0
$275$			2.68126e11i			0.170481i
$276$		0			0
$277$	−6.46521e11			−0.396446			−0.198223	−	0.980157i	$-0.563517\pi$
$277$	−6.46521e11			−0.396446			−0.198223	+	0.980157i	$0.563517\pi$
$278$		0			0
$279$	3.55858e9	+	4.86554e11i	0.00210502	+	0.287813i
$280$		0			0
$281$		−	5.02357e11i		−	0.286735i	−0.989670	−	0.143367i	$-0.954207\pi$
$281$		−	5.02357e11i		−	0.286735i	0.989670	−	0.143367i	$-0.0457931\pi$
$282$		0			0
$283$	3.08013e12			1.69682			0.848412	−	0.529337i	$-0.177559\pi$
$283$	3.08013e12			1.69682			0.848412	+	0.529337i	$0.177559\pi$
$284$		0			0
$285$	−2.32596e12	−	2.30901e12i	−1.23702	−	1.22801i
$286$		0			0
$287$			3.34637e12i			1.71856i
$288$		0			0
$289$	2.01442e12			0.999218
$290$		0			0
$291$	2.03276e12	−	2.04768e12i	0.974139	−	0.981290i
$292$		0			0
$293$		−	1.63922e12i		−	0.759102i	−0.925171	−	0.379551i	$-0.876078\pi$
$293$		−	1.63922e12i		−	0.759102i	0.925171	−	0.379551i	$-0.123922\pi$
$294$		0			0
$295$	3.57654e12			1.60086
$296$		0			0
$297$	1.95344e12	−	1.99677e12i	0.845312	−	0.864066i
$298$		0			0
$299$		−	8.67549e11i		−	0.363026i
$300$		0			0
$301$	1.18271e11			0.0478679
$302$		0			0
$303$	2.26396e12	+	2.24746e12i	0.886453	+	0.879993i
$304$		0			0
$305$		−	1.67257e12i		−	0.633703i
$306$		0			0
$307$	−1.92793e12			−0.706968			−0.353484	−	0.935441i	$-0.615003\pi$
$307$	−1.92793e12			−0.706968			−0.353484	+	0.935441i	$0.615003\pi$
$308$		0			0
$309$	−3.09781e12	+	3.12055e12i	−1.09967	+	1.10774i
$310$		0			0
$311$		−	2.19382e12i		−	0.754048i	−0.926203	−	0.377024i	$-0.876947\pi$
$311$		−	2.19382e12i		−	0.754048i	0.926203	−	0.377024i	$-0.123053\pi$
$312$		0			0
$313$	−2.54264e12			−0.846377			−0.423189	−	0.906042i	$-0.639089\pi$
$313$	−2.54264e12			−0.846377			−0.423189	+	0.906042i	$0.639089\pi$
$314$		0			0
$315$	−4.95192e12	+	3.62176e10i	−1.59669	+	0.0116779i
$316$		0			0
$317$		−	4.30864e12i		−	1.34600i	−0.739645	−	0.672998i	$-0.765006\pi$
$317$		−	4.30864e12i		−	1.34600i	0.739645	−	0.672998i	$-0.234994\pi$
$318$		0			0
$319$	−3.95639e12			−1.19769
$320$		0			0
$321$	4.69812e12	+	4.66388e12i	1.37847	+	1.36843i
$322$		0			0
$323$		−	1.84926e11i		−	0.0526000i
$324$		0			0
$325$	−1.57674e11			−0.0434854
$326$		0			0
$327$	−5.48984e11	+	5.53014e11i	−0.146832	+	0.147910i
$328$		0			0
$329$			8.14133e12i			2.11211i
$330$		0			0
$331$	5.00163e12			1.25884			0.629422	−	0.777064i	$-0.283292\pi$
$331$	5.00163e12			1.25884			0.629422	+	0.777064i	$0.283292\pi$
$332$		0			0
$333$	−8.25030e9	−	1.12804e12i	−0.00201488	−	0.275488i
$334$		0			0
$335$		−	2.49411e12i		−	0.591142i
$336$		0			0
$337$	−1.46058e12			−0.336028			−0.168014	−	0.985785i	$-0.553735\pi$
$337$	−1.46058e12			−0.336028			−0.168014	+	0.985785i	$0.553735\pi$
$338$		0			0
$339$	2.34280e12	+	2.32573e12i	0.523283	+	0.519470i
$340$		0			0
$341$		−	1.60414e12i		−	0.347914i
$342$		0			0
$343$	−7.91895e12			−1.66800
$344$		0			0
$345$	−3.75746e12	+	3.78504e12i	−0.768775	+	0.774418i
$346$		0			0
$347$			1.30574e12i			0.259543i	0.991544	+	0.129772i	$0.0414244\pi$
$347$			1.30574e12i			0.259543i	−0.991544	+	0.129772i	$0.958576\pi$
$348$		0			0
$349$	1.59463e11			0.0307987			0.0153993	−	0.999881i	$-0.495098\pi$
$349$	1.59463e11			0.0307987			0.0153993	+	0.999881i	$0.495098\pi$
$350$		0			0
$351$	1.17422e12	+	1.14874e12i	0.220402	+	0.215618i
$352$		0			0
$353$			3.32899e12i			0.607350i	0.952776	+	0.303675i	$0.0982138\pi$
$353$			3.32899e12i			0.607350i	−0.952776	+	0.303675i	$0.901786\pi$
$354$		0			0
$355$	−4.93624e12			−0.875497
$356$		0			0
$357$	−1.98297e11	−	1.96852e11i	−0.0341959	−	0.0339467i
$358$		0			0
$359$		−	6.56753e12i		−	1.10136i	−0.834716	−	0.550681i	$-0.814368\pi$
$359$		−	6.56753e12i		−	1.10136i	0.834716	−	0.550681i	$-0.185632\pi$
$360$		0			0
$361$	1.55551e13			2.53709
$362$		0			0
$363$	−2.04776e12	+	2.06279e12i	−0.324896	+	0.327281i
$364$		0			0
$365$		−	2.38417e12i		−	0.368021i
$366$		0			0
$367$	−2.57363e12			−0.386559			−0.193279	−	0.981144i	$-0.561912\pi$
$367$	−2.57363e12			−0.386559			−0.193279	+	0.981144i	$0.561912\pi$
$368$		0			0
$369$	−6.82402e12	+	4.99098e10i	−0.997489	+	0.00729548i
$370$		0			0
$371$		−	9.65045e12i		−	1.37302i
$372$		0			0
$373$	−2.63844e12			−0.365428			−0.182714	−	0.983166i	$-0.558488\pi$
$373$	−2.63844e12			−0.365428			−0.182714	+	0.983166i	$0.558488\pi$
$374$		0			0
$375$	5.56558e12	+	5.52502e12i	0.750506	+	0.745037i
$376$		0			0
$377$		−	2.32660e12i		−	0.305502i
$378$		0			0
$379$	−1.18638e12			−0.151715			−0.0758573	−	0.997119i	$-0.524169\pi$
$379$	−1.18638e12			−0.151715			−0.0758573	+	0.997119i	$0.524169\pi$
$380$		0			0
$381$	−4.27181e11	+	4.30317e11i	−0.0532092	+	0.0535998i
$382$		0			0
$383$			2.81521e11i			0.0341599i	0.999854	+	0.0170799i	$0.00543698\pi$
$383$			2.81521e11i			0.0341599i	−0.999854	+	0.0170799i	$0.994563\pi$
$384$		0			0
$385$	1.63262e13			1.93011
$386$		0			0
$387$	1.76396e9	+	2.41181e11i	0.000203205	+	0.0277836i
$388$		0			0
$389$		−	9.28352e12i		−	1.04223i	−0.853486	−	0.521117i	$-0.825516\pi$
$389$		−	9.28352e12i		−	1.04223i	0.853486	−	0.521117i	$-0.174484\pi$
$390$		0			0
$391$	−3.00931e11			−0.0329293
$392$		0			0
$393$	1.31633e12	+	1.30674e12i	0.140411	+	0.139388i
$394$		0			0
$395$			1.04664e13i			1.08846i
$396$		0			0
$397$	−6.05417e12			−0.613907			−0.306953	−	0.951725i	$-0.599310\pi$
$397$	−6.05417e12			−0.613907			−0.306953	+	0.951725i	$0.599310\pi$
$398$		0			0
$399$	2.30846e13	−	2.32541e13i	2.28275	−	2.29951i
$400$		0			0
$401$		−	1.02940e13i		−	0.992803i	−0.868093	−	0.496401i	$-0.834654\pi$
$401$		−	1.02940e13i		−	0.992803i	0.868093	−	0.496401i	$-0.165346\pi$
$402$		0			0
$403$	9.43333e11			0.0887442
$404$		0			0
$405$	−1.47712e11	−	1.00976e13i	−0.0135563	−	0.926705i
$406$		0			0
$407$			3.71908e12i			0.333015i
$408$		0			0
$409$	4.30585e11			0.0376220			0.0188110	−	0.999823i	$-0.494012\pi$
$409$	4.30585e11			0.0376220			0.0188110	+	0.999823i	$0.494012\pi$
$410$		0			0
$411$	−1.38355e12	−	1.37347e12i	−0.117974	−	0.117114i
$412$		0			0
$413$			3.57569e13i			2.97584i
$414$		0			0
$415$	−2.04407e12			−0.166057
$416$		0			0
$417$	−8.06943e12	+	8.12867e12i	−0.639974	+	0.644672i
$418$		0			0
$419$			3.34433e12i			0.258964i	0.991582	+	0.129482i	$0.0413315\pi$
$419$			3.34433e12i			0.258964i	−0.991582	+	0.129482i	$0.958669\pi$
$420$		0			0
$421$	−1.21958e13			−0.922145			−0.461073	−	0.887362i	$-0.652535\pi$
$421$	−1.21958e13			−0.922145			−0.461073	+	0.887362i	$0.652535\pi$
$422$		0			0
$423$	−1.66020e13	+	1.21425e11i	−1.22591	+	0.00896614i
$424$		0			0
$425$			5.46931e10i			0.00394446i
$426$		0			0
$427$	1.67218e13			1.17799
$428$		0			0
$429$	−3.84345e12	−	3.81544e12i	−0.264505	−	0.262578i
$430$		0			0
$431$			2.44756e13i			1.64568i	0.568270	+	0.822842i	$0.307613\pi$
$431$			2.44756e13i			1.64568i	−0.568270	+	0.822842i	$0.692387\pi$
$432$		0			0
$433$	−2.53458e13			−1.66520			−0.832601	−	0.553873i	$-0.813149\pi$
$433$	−2.53458e13			−1.66520			−0.832601	+	0.553873i	$0.813149\pi$
$434$		0			0
$435$	−1.00768e13	+	1.01507e13i	−0.646957	+	0.651706i
$436$		0			0
$437$		−	3.52899e13i		−	2.21433i
$438$		0			0
$439$	−2.40755e13			−1.47656			−0.738282	−	0.674492i	$-0.764363\pi$
$439$	−2.40755e13			−1.47656			−0.738282	+	0.674492i	$0.764363\pi$
$440$		0			0
$441$	−2.40099e11	−	3.28280e13i	−0.0143945	−	1.96812i
$442$		0			0
$443$			1.24137e13i			0.727585i	0.931480	+	0.363792i	$0.118518\pi$
$443$			1.24137e13i			0.727585i	−0.931480	+	0.363792i	$0.881482\pi$
$444$		0			0
$445$	1.99768e13			1.14479
$446$		0			0
$447$	1.57773e13	+	1.56623e13i	0.884086	+	0.877644i
$448$		0			0
$449$			2.90273e13i			1.59065i	0.606181	+	0.795327i	$0.292701\pi$
$449$			2.90273e13i			1.59065i	−0.606181	+	0.795327i	$0.707299\pi$
$450$		0			0
$451$	2.24984e13			1.20578
$452$		0			0
$453$	−1.02084e13	+	1.02833e13i	−0.535139	+	0.539067i
$454$		0			0
$455$			9.60079e12i			0.492323i
$456$		0			0
$457$	−6.83053e12			−0.342668			−0.171334	−	0.985213i	$-0.554808\pi$
$457$	−6.83053e12			−0.342668			−0.171334	+	0.985213i	$0.554808\pi$
$458$		0			0
$459$	3.98468e11	−	4.07308e11i	0.0195583	−	0.0199922i
$460$		0			0
$461$			8.98477e12i			0.431522i	0.976446	+	0.215761i	$0.0692231\pi$
$461$			8.98477e12i			0.431522i	−0.976446	+	0.215761i	$0.930777\pi$
$462$		0			0
$463$	−1.37787e13			−0.647595			−0.323797	−	0.946126i	$-0.604960\pi$
$463$	−1.37787e13			−0.647595			−0.323797	+	0.946126i	$0.604960\pi$
$464$		0			0
$465$	−4.11568e12	−	4.08569e12i	−0.189312	−	0.187932i
$466$		0			0
$467$		−	1.44791e13i		−	0.651866i	−0.945393	−	0.325933i	$-0.894322\pi$
$467$		−	1.44791e13i		−	0.651866i	0.945393	−	0.325933i	$-0.105678\pi$
$468$		0			0
$469$	2.49352e13			1.09887
$470$		0			0
$471$	2.80134e13	−	2.82191e13i	1.20854	−	1.21741i
$472$		0			0
$473$		−	7.95161e11i		−	0.0335853i
$474$		0			0
$475$	−6.41382e12			−0.265246
$476$		0			0
$477$	1.96795e13	−	1.43933e11i	0.796933	−	0.00582864i
$478$		0			0
$479$		−	1.56308e13i		−	0.619876i	−0.950757	−	0.309938i	$-0.899692\pi$
$479$		−	1.56308e13i		−	0.619876i	0.950757	−	0.309938i	$-0.100308\pi$
$480$		0			0
$481$	−2.18704e12			−0.0849439
$482$		0			0
$483$	−3.78415e13	−	3.75657e13i	−1.43957	−	1.42908i
$484$		0			0
$485$			3.43896e13i			1.28150i
$486$		0			0
$487$	3.42315e12			0.124963			0.0624815	−	0.998046i	$-0.480099\pi$
$487$	3.42315e12			0.124963			0.0624815	+	0.998046i	$0.480099\pi$
$488$		0			0
$489$	8.83246e12	−	8.89730e12i	0.315891	−	0.318210i
$490$		0			0
$491$		−	4.18001e13i		−	1.46477i	−0.680891	−	0.732385i	$-0.738407\pi$
$491$		−	4.18001e13i		−	1.46477i	0.680891	−	0.732385i	$-0.261593\pi$
$492$		0			0
$493$	−8.07037e11			−0.0277114
$494$		0			0
$495$	2.43499e11	+	3.32929e13i	0.00819353	+	1.12028i
$496$		0			0
$497$		−	4.93507e13i		−	1.62746i
$498$		0			0
$499$	9.50002e12			0.307059			0.153529	−	0.988144i	$-0.450936\pi$
$499$	9.50002e12			0.307059			0.153529	+	0.988144i	$0.450936\pi$
$500$		0			0
$501$	2.70456e13	+	2.68485e13i	0.856857	+	0.850613i
$502$		0			0
$503$		−	1.27832e12i		−	0.0397007i	−0.999803	−	0.0198504i	$-0.993681\pi$
$503$		−	1.27832e12i		−	0.0397007i	0.999803	−	0.0198504i	$-0.00631898\pi$
$504$		0			0
$505$	−3.80218e13			−1.15765
$506$		0			0
$507$	−2.13573e13	+	2.15141e13i	−0.637539	+	0.642219i
$508$		0			0
$509$			9.67555e11i			0.0283196i	0.999900	+	0.0141598i	$0.00450735\pi$
$509$			9.67555e11i			0.0283196i	−0.999900	+	0.0141598i	$0.995493\pi$
$510$		0			0
$511$	2.38361e13			0.684116
$512$		0			0
$513$	4.77647e13	+	4.67281e13i	1.34438	+	1.31520i
$514$		0			0
$515$		−	5.24078e13i		−	1.44664i
$516$		0			0
$517$	5.47360e13			1.48191
$518$		0			0
$519$	−1.06903e12	−	1.06124e12i	−0.0283891	−	0.0281823i
$520$		0			0
$521$		−	2.98648e13i		−	0.777985i	−0.921241	−	0.388992i	$-0.872823\pi$
$521$		−	2.98648e13i		−	0.777985i	0.921241	−	0.388992i	$-0.127177\pi$
$522$		0			0
$523$	5.68489e13			1.45283			0.726413	−	0.687259i	$-0.241186\pi$
$523$	5.68489e13			1.45283			0.726413	+	0.687259i	$0.241186\pi$
$524$		0			0
$525$	−6.82744e12	+	6.87755e12i	−0.171183	+	0.172440i
$526$		0			0
$527$		−	3.27218e11i		−	0.00804979i
$528$		0			0
$529$	−1.60009e13			−0.386247
$530$		0			0
$531$	−7.29165e13	+	5.33300e11i	−1.72724	+	0.0126328i
$532$		0			0
$533$			1.32304e13i			0.307566i
$534$		0			0
$535$	−7.89020e13			−1.80019
$536$		0			0
$537$	−1.06270e13	−	1.05496e13i	−0.237979	−	0.236245i
$538$		0			0
$539$			1.08232e14i			2.37910i
$540$		0			0
$541$	−3.15417e13			−0.680610			−0.340305	−	0.940315i	$-0.610530\pi$
$541$	−3.15417e13			−0.680610			−0.340305	+	0.940315i	$0.610530\pi$
$542$		0			0
$543$	−3.45400e13	+	3.47935e13i	−0.731683	+	0.737054i
$544$		0			0
$545$		−	9.28754e12i		−	0.193160i
$546$		0			0
$547$	2.80363e13			0.572511			0.286256	−	0.958153i	$-0.407589\pi$
$547$	2.80363e13			0.572511			0.286256	+	0.958153i	$0.407589\pi$
$548$		0			0
$549$	2.49399e11	+	3.40995e13i	0.00500072	+	0.683733i
$550$		0			0
$551$		−	9.46406e13i		−	1.86346i
$552$		0			0
$553$	−1.04639e14			−2.02334
$554$		0			0
$555$	9.54190e12	+	9.47236e12i	0.181205	+	0.179884i
$556$		0			0
$557$			3.80012e13i			0.708796i	0.935095	+	0.354398i	$0.115314\pi$
$557$			3.80012e13i			0.708796i	−0.935095	+	0.354398i	$0.884686\pi$
$558$		0			0
$559$	4.67602e11			0.00856678
$560$		0			0
$561$	−1.32348e12	+	1.33319e12i	−0.0238179	+	0.0239927i
$562$		0			0
$563$			8.97052e13i			1.58590i	0.609287	+	0.792950i	$0.291456\pi$
$563$			8.97052e13i			1.58590i	−0.609287	+	0.792950i	$0.708544\pi$
$564$		0			0
$565$	−3.93459e13			−0.683372
$566$		0			0
$567$	1.00952e14	−	1.47677e12i	1.72265	−	0.0251998i
$568$		0			0
$569$		−	7.70896e13i		−	1.29251i	−0.763121	−	0.646256i	$-0.776334\pi$
$569$		−	7.70896e13i		−	1.29251i	0.763121	−	0.646256i	$-0.223666\pi$
$570$		0			0
$571$	5.45952e13			0.899444			0.449722	−	0.893169i	$-0.351523\pi$
$571$	5.45952e13			0.899444			0.449722	+	0.893169i	$0.351523\pi$
$572$		0			0
$573$	1.39544e12	+	1.38527e12i	0.0225911	+	0.0224265i
$574$		0			0
$575$			1.04372e13i			0.166053i
$576$		0			0
$577$	4.32936e13			0.676932			0.338466	−	0.940979i	$-0.390092\pi$
$577$	4.32936e13			0.676932			0.338466	+	0.940979i	$0.390092\pi$
$578$		0			0
$579$	−2.00093e13	+	2.01562e13i	−0.307496	+	0.309754i
$580$		0			0
$581$		−	2.04359e13i		−	0.308683i
$582$		0			0
$583$	−6.48822e13			−0.963347
$584$		0			0
$585$	−1.95782e13	+	1.43192e11i	−0.285755	+	0.00208997i
$586$		0			0
$587$		−	6.69167e13i		−	0.960161i	−0.877224	−	0.480080i	$-0.840607\pi$
$587$		−	6.69167e13i		−	0.960161i	0.877224	−	0.480080i	$-0.159393\pi$
$588$		0			0
$589$	3.83726e13			0.541309
$590$		0			0
$591$	8.55167e12	+	8.48935e12i	0.118608	+	0.117744i
$592$		0			0
$593$			3.42544e13i			0.467136i	0.972340	+	0.233568i	$0.0750401\pi$
$593$			3.42544e13i			0.467136i	−0.972340	+	0.233568i	$0.924960\pi$
$594$		0			0
$595$	3.33027e12			0.0446575
$596$		0			0
$597$	5.33136e13	−	5.37049e13i	0.703017	−	0.708178i
$598$		0			0
$599$		−	1.09769e14i		−	1.42346i	−0.702455	−	0.711728i	$-0.747913\pi$
$599$		−	1.09769e14i		−	1.42346i	0.702455	−	0.711728i	$-0.252087\pi$
$600$		0			0
$601$	1.21221e14			1.54598			0.772990	−	0.634418i	$-0.218760\pi$
$601$	1.21221e14			1.54598			0.772990	+	0.634418i	$0.218760\pi$
$602$		0			0
$603$	3.71899e11	+	5.08486e13i	0.00466485	+	0.637811i
$604$		0			0
$605$		−	3.46432e13i		−	0.427407i
$606$		0			0
$607$	1.42306e14			1.72695			0.863473	−	0.504394i	$-0.168284\pi$
$607$	1.42306e14			1.72695			0.863473	+	0.504394i	$0.168284\pi$
$608$		0			0
$609$	−1.01483e14	−	1.00744e14i	−1.21146	−	1.20263i
$610$		0			0
$611$			3.21881e13i			0.377998i
$612$		0			0
$613$	−1.15590e14			−1.33542			−0.667711	−	0.744421i	$-0.732726\pi$
$613$	−1.15590e14			−1.33542			−0.667711	+	0.744421i	$0.732726\pi$
$614$		0			0
$615$	5.73026e13	−	5.77232e13i	0.651326	−	0.656108i
$616$		0			0
$617$			8.06571e13i			0.902021i	0.892519	+	0.451011i	$0.148936\pi$
$617$			8.06571e13i			0.902021i	−0.892519	+	0.451011i	$0.851064\pi$
$618$		0			0
$619$	1.74323e14			1.91823			0.959115	−	0.283015i	$-0.0913347\pi$
$619$	1.74323e14			1.91823			0.959115	+	0.283015i	$0.0913347\pi$
$620$		0			0
$621$	7.60407e13	−	7.77277e13i	0.823357	−	0.841624i
$622$		0			0
$623$			1.99721e14i			2.12806i
$624$		0			0
$625$	−8.00204e13			−0.839075
$626$		0			0
$627$	−1.56343e14	−	1.55203e14i	−1.61339	−	1.60163i
$628$		0			0
$629$			7.58630e11i			0.00770508i
$630$		0			0
$631$	−1.66535e14			−1.66479			−0.832393	−	0.554185i	$-0.813030\pi$
$631$	−1.66535e14			−1.66479			−0.832393	+	0.554185i	$0.813030\pi$
$632$		0			0
$633$	−1.95996e13	+	1.97435e13i	−0.192854	+	0.194270i
$634$		0			0
$635$		−	7.22690e12i		−	0.0699977i
$636$		0			0
$637$	−6.36470e13			−0.606849
$638$		0			0
$639$	1.00637e14	−	7.36046e11i	0.944616	−	0.00690877i
$640$		0			0
$641$		−	3.87340e13i		−	0.357933i	−0.983855	−	0.178967i	$-0.942725\pi$
$641$		−	3.87340e13i		−	0.357933i	0.983855	−	0.178967i	$-0.0572754\pi$
$642$		0			0
$643$	−9.69076e13			−0.881664			−0.440832	−	0.897590i	$-0.645316\pi$
$643$	−9.69076e13			−0.881664			−0.440832	+	0.897590i	$0.645316\pi$
$644$		0			0
$645$	−2.04011e12	−	2.02524e12i	−0.0182749	−	0.0181417i
$646$		0			0
$647$			2.22038e14i			1.95842i	0.202856	+	0.979209i	$0.434978\pi$
$647$			2.22038e14i			1.95842i	−0.202856	+	0.979209i	$0.565022\pi$
$648$		0			0
$649$	2.40402e14			2.08792
$650$		0			0
$651$	4.08472e13	−	4.11471e13i	0.349347	−	0.351912i
$652$		0			0
$653$		−	1.00663e14i		−	0.847823i	−0.905704	−	0.423912i	$-0.860657\pi$
$653$		−	1.00663e14i		−	0.847823i	0.905704	−	0.423912i	$-0.139343\pi$
$654$		0			0
$655$	−2.21070e13			−0.183368
$656$		0			0
$657$	3.55506e11	+	4.86072e13i	0.00290415	+	0.397076i
$658$		0			0
$659$		−	1.49486e14i		−	1.20274i	−0.798970	−	0.601371i	$-0.794621\pi$
$659$		−	1.49486e14i		−	1.20274i	0.798970	−	0.601371i	$-0.205379\pi$
$660$		0			0
$661$	1.32290e14			1.04838			0.524191	−	0.851601i	$-0.324368\pi$
$661$	1.32290e14			1.04838			0.524191	+	0.851601i	$0.324368\pi$
$662$		0			0
$663$	−7.83998e11	−	7.78285e11i	−0.00611995	−	0.00607535i
$664$		0			0
$665$			3.90538e14i			3.00300i
$666$		0			0
$667$	−1.54009e14			−1.16659
$668$		0			0
$669$	−9.99805e13	+	1.00714e14i	−0.746079	+	0.751556i
$670$		0			0
$671$		−	1.12424e14i		−	0.826509i
$672$		0			0
$673$	−5.71199e13			−0.413726			−0.206863	−	0.978370i	$-0.566325\pi$
$673$	−5.71199e13			−0.413726			−0.206863	+	0.978370i	$0.566325\pi$
$674$		0			0
$675$	−1.41267e13	−	1.38201e13i	−0.100815	−	0.0986265i
$676$		0			0
$677$			2.69430e13i			0.189454i	0.995503	+	0.0947269i	$0.0301978\pi$
$677$			2.69430e13i			0.189454i	−0.995503	+	0.0947269i	$0.969802\pi$
$678$		0			0
$679$	−3.43814e14			−2.38218
$680$		0			0
$681$	8.21051e13	+	8.15068e13i	0.560576	+	0.556491i
$682$		0			0
$683$			2.11908e14i			1.42575i	0.701289	+	0.712877i	$0.252608\pi$
$683$			2.11908e14i			1.42575i	−0.701289	+	0.712877i	$0.747392\pi$
$684$		0			0
$685$	2.32359e13			0.154066
$686$		0			0
$687$	6.53060e13	−	6.57854e13i	0.426746	−	0.429878i
$688$		0			0
$689$		−	3.81546e13i		−	0.245726i
$690$		0			0
$691$	7.02683e13			0.446035			0.223018	−	0.974814i	$-0.428409\pi$
$691$	7.02683e13			0.446035			0.223018	+	0.974814i	$0.428409\pi$
$692$		0			0
$693$	−3.32850e14	+	2.43441e12i	−2.08249	+	0.0152310i
$694$		0			0
$695$		−	1.36516e14i		−	0.841898i
$696$		0			0
$697$	4.58930e12			0.0278986
$698$		0			0
$699$	1.39041e14	+	1.38027e14i	0.833212	+	0.827141i
$700$		0			0
$701$			1.48408e14i			0.876734i	0.898796	+	0.438367i	$0.144443\pi$
$701$			1.48408e14i			0.876734i	−0.898796	+	0.438367i	$0.855557\pi$
$702$		0			0
$703$	−8.89640e13			−0.518129
$704$		0			0
$705$	1.39411e14	−	1.40434e14i	0.800479	−	0.806355i
$706$		0			0
$707$		−	3.80128e14i		−	2.15195i
$708$		0			0
$709$	−7.47672e13			−0.417330			−0.208665	−	0.977987i	$-0.566912\pi$
$709$	−7.47672e13			−0.417330			−0.208665	+	0.977987i	$0.566912\pi$
$710$		0			0
$711$	−1.56066e12	−	2.13384e14i	−0.00858933	−	1.17439i
$712$		0			0
$713$		−	6.24439e13i		−	0.338877i
$714$		0			0
$715$	6.45483e13			0.345426
$716$		0			0
$717$	−1.49604e14	−	1.48514e14i	−0.789490	−	0.783737i
$718$		0			0
$719$			2.07074e14i			1.07766i	0.842415	+	0.538829i	$0.181133\pi$
$719$			2.07074e14i			1.07766i	−0.842415	+	0.538829i	$0.818867\pi$
$720$		0			0
$721$	5.23954e14			2.68916
$722$		0			0
$723$	−1.27532e14	+	1.28468e14i	−0.645547	+	0.650286i
$724$		0			0
$725$			2.79906e13i			0.139740i
$726$		0			0
$727$	1.67871e14			0.826615			0.413307	−	0.910592i	$-0.364374\pi$
$727$	1.67871e14			0.826615			0.413307	+	0.910592i	$0.364374\pi$
$728$		0			0
$729$	4.51713e12	+	2.05842e14i	0.0219394	+	0.999759i
$730$		0			0
$731$		−	1.62199e11i		−	0.000777074i
$732$		0			0
$733$	2.75732e14			1.30307			0.651535	−	0.758618i	$-0.274125\pi$
$733$	2.75732e14			1.30307			0.651535	+	0.758618i	$0.274125\pi$
$734$		0			0
$735$	2.77687e14	+	2.75663e14i	1.29455	+	1.28511i
$736$		0			0
$737$		−	1.67645e14i		−	0.770998i
$738$		0			0
$739$	1.56316e13			0.0709220			0.0354610	−	0.999371i	$-0.488710\pi$
$739$	1.56316e13			0.0709220			0.0354610	+	0.999371i	$0.488710\pi$
$740$		0			0
$741$	9.12689e13	−	9.19389e13i	0.408537	−	0.411536i
$742$		0			0
$743$		−	2.10001e14i		−	0.927420i	−0.885987	−	0.463710i	$-0.846518\pi$
$743$		−	2.10001e14i		−	0.927420i	0.885987	−	0.463710i	$-0.153482\pi$
$744$		0			0
$745$	−2.64970e14			−1.15456
$746$		0			0
$747$	4.16735e13	−	3.04793e11i	0.179166	−	0.00131040i
$748$		0			0
$749$		−	7.88832e14i		−	3.34638i
$750$		0			0
$751$	1.85250e14			0.775457			0.387729	−	0.921774i	$-0.373260\pi$
$751$	1.85250e14			0.775457			0.387729	+	0.921774i	$0.373260\pi$
$752$		0			0
$753$	1.69469e14	+	1.68234e14i	0.700030	+	0.694928i
$754$		0			0
$755$		−	1.72702e14i		−	0.703985i
$756$		0			0
$757$	−3.17483e14			−1.27715			−0.638574	−	0.769561i	$-0.720475\pi$
$757$	−3.17483e14			−1.27715			−0.638574	+	0.769561i	$0.720475\pi$
$758$		0			0
$759$	−2.52563e14	+	2.54417e14i	−1.00268	+	1.01004i
$760$		0			0
$761$		−	2.60646e14i		−	1.02124i	−0.859807	−	0.510620i	$-0.829416\pi$
$761$		−	2.60646e14i		−	1.02124i	0.859807	−	0.510620i	$-0.170584\pi$
$762$		0			0
$763$	9.28533e13			0.359066
$764$		0			0
$765$	4.96697e10	+	6.79119e12i	0.000189576	+	0.0259202i
$766$		0			0
$767$			1.41371e14i			0.532577i
$768$		0			0
$769$	−3.97900e14			−1.47959			−0.739797	−	0.672830i	$-0.765079\pi$
$769$	−3.97900e14			−1.47959			−0.739797	+	0.672830i	$0.765079\pi$
$770$		0			0
$771$	9.43864e13	+	9.36986e13i	0.346448	+	0.343923i
$772$		0			0
$773$			9.65561e13i			0.349850i	0.984582	+	0.174925i	$0.0559683\pi$
$773$			9.65561e13i			0.349850i	−0.984582	+	0.174925i	$0.944032\pi$
$774$		0			0
$775$	−1.13490e13			−0.0405927
$776$		0			0
$777$	−9.47011e13	+	9.53963e13i	−0.334388	+	0.336842i
$778$		0			0
$779$			5.38183e14i			1.87604i
$780$		0			0
$781$	−3.31796e14			−1.14187
$782$		0			0
$783$	2.03926e14	−	2.08450e14i	0.692890	−	0.708262i
$784$		0			0
$785$			4.73922e14i			1.58986i
$786$		0			0
$787$	−1.67204e14			−0.553826			−0.276913	−	0.960895i	$-0.589311\pi$
$787$	−1.67204e14			−0.553826			−0.276913	+	0.960895i	$0.589311\pi$
$788$		0			0
$789$	6.45972e13	+	6.41265e13i	0.211266	+	0.209726i
$790$		0			0
$791$		−	3.93365e14i		−	1.27032i
$792$		0			0
$793$	6.61122e13			0.210822
$794$		0			0
$795$	−1.65252e14	+	1.66465e14i	−0.520370	+	0.524190i
$796$		0			0
$797$			2.24257e14i			0.697355i	0.937243	+	0.348678i	$0.113369\pi$
$797$			2.24257e14i			0.697355i	−0.937243	+	0.348678i	$0.886631\pi$
$798$		0			0
$799$	1.11652e13			0.0342873
$800$		0			0
$801$	−4.07277e14	+	2.97876e12i	−1.23517	+	0.00903385i
$802$		0			0
$803$		−	1.60255e14i		−	0.479993i
$804$		0			0
$805$	6.35524e14			1.87998
$806$		0			0
$807$	−5.41196e13	−	5.37252e13i	−0.158120	−	0.156968i
$808$		0			0
$809$		−	5.61446e13i		−	0.162019i	−0.996713	−	0.0810094i	$-0.974186\pi$
$809$		−	5.61446e13i		−	0.162019i	0.996713	−	0.0810094i	$-0.0258144\pi$
$810$		0			0
$811$	2.29094e14			0.652994			0.326497	−	0.945198i	$-0.394132\pi$
$811$	2.29094e14			0.652994			0.326497	+	0.945198i	$0.394132\pi$
$812$		0			0
$813$	−6.23723e13	+	6.28302e13i	−0.175606	+	0.176895i
$814$		0			0
$815$			1.49425e14i			0.415561i
$816$		0			0
$817$	1.90210e13			0.0522544
$818$		0			0
$819$	−1.43158e12	−	1.95736e14i	−0.00388505	−	0.531191i
$820$		0			0
$821$			1.07005e13i			0.0286872i	0.999897	+	0.0143436i	$0.00456586\pi$
$821$			1.07005e13i			0.0286872i	−0.999897	+	0.0143436i	$0.995434\pi$
$822$		0			0
$823$	−1.45374e14			−0.385023			−0.192511	−	0.981295i	$-0.561663\pi$
$823$	−1.45374e14			−0.385023			−0.192511	+	0.981295i	$0.561663\pi$
$824$		0			0
$825$	4.62394e13	+	4.59024e13i	0.120988	+	0.120106i
$826$		0			0
$827$			7.18994e14i			1.85865i	0.369263	+	0.929325i	$0.379610\pi$
$827$			7.18994e14i			1.85865i	−0.369263	+	0.929325i	$0.620390\pi$
$828$		0			0
$829$	−5.70290e14			−1.45654			−0.728272	−	0.685288i	$-0.759676\pi$
$829$	−5.70290e14			−1.45654			−0.728272	+	0.685288i	$0.759676\pi$
$830$		0			0
$831$	−1.10683e14	+	1.11495e14i	−0.279302	+	0.281353i
$832$		0			0
$833$			2.20775e13i			0.0550459i
$834$		0			0
$835$	−4.54215e14			−1.11900
$836$		0			0
$837$	8.45176e13	+	8.26832e13i	0.205740	+	0.201275i
$838$		0			0
$839$		−	2.29884e14i		−	0.552967i	−0.961019	−	0.276483i	$-0.910831\pi$
$839$		−	2.29884e14i		−	0.552967i	0.961019	−	0.276483i	$-0.0891690\pi$
$840$		0			0
$841$	7.68552e12			0.0182681
$842$		0			0
$843$	−8.66335e13	−	8.60022e13i	−0.203492	−	0.202009i
$844$		0			0
$845$		−	3.61316e14i		−	0.838694i
$846$		0			0
$847$	3.46350e14			0.794508
$848$		0			0
$849$	5.27310e14	−	5.31181e14i	1.19544	−	1.20421i
$850$		0			0
$851$			1.44771e14i			0.324366i
$852$		0			0
$853$	−4.32069e13			−0.0956772			−0.0478386	−	0.998855i	$-0.515233\pi$
$853$	−4.32069e13			−0.0956772			−0.0478386	+	0.998855i	$0.515233\pi$
$854$		0			0
$855$	−7.96397e14	+	5.82473e12i	−1.74301	+	0.0127481i
$856$		0			0
$857$		−	4.26827e14i		−	0.923311i	−0.887059	−	0.461656i	$-0.847256\pi$
$857$		−	4.26827e14i		−	0.923311i	0.887059	−	0.461656i	$-0.152744\pi$
$858$		0			0
$859$	6.71870e14			1.43655			0.718273	−	0.695761i	$-0.244933\pi$
$859$	6.71870e14			1.43655			0.718273	+	0.695761i	$0.244933\pi$
$860$		0			0
$861$	5.77095e14	+	5.72890e14i	1.21964	+	1.21075i
$862$		0			0
$863$		−	4.48581e13i		−	0.0937102i	−0.998902	−	0.0468551i	$-0.985080\pi$
$863$		−	4.48581e13i		−	0.0937102i	0.998902	−	0.0468551i	$-0.0149199\pi$
$864$		0			0
$865$	1.79537e13			0.0370743
$866$		0			0
$867$	3.44863e14	−	3.47395e14i	0.703965	−	0.709133i
$868$		0			0
$869$			7.03515e14i			1.41963i
$870$		0			0
$871$	9.85853e13			0.196662
$872$		0			0
$873$	−5.12785e12	−	7.01116e14i	−0.0101126	−	1.38267i
$874$		0			0
$875$		−	9.34483e14i		−	1.82193i
$876$		0			0
$877$	1.48985e14			0.287174			0.143587	−	0.989638i	$-0.454136\pi$
$877$	1.48985e14			0.287174			0.143587	+	0.989638i	$0.454136\pi$
$878$		0			0
$879$	−2.82691e14	−	2.80631e14i	−0.538726	−	0.534800i
$880$		0			0
$881$			7.70640e14i			1.45202i	0.687685	+	0.726009i	$0.258627\pi$
$881$			7.70640e14i			1.45202i	−0.687685	+	0.726009i	$0.741373\pi$
$882$		0			0
$883$	−3.72274e14			−0.693521			−0.346761	−	0.937954i	$-0.612718\pi$
$883$	−3.72274e14			−0.693521			−0.346761	+	0.937954i	$0.612718\pi$
$884$		0			0
$885$	6.12294e14	−	6.16789e14i	1.12783	−	1.13611i
$886$		0			0
$887$		−	1.00591e14i		−	0.183207i	−0.995796	−	0.0916034i	$-0.970801\pi$
$887$		−	1.00591e14i		−	0.183207i	0.995796	−	0.0916034i	$-0.0291992\pi$
$888$		0			0
$889$	7.22519e13			0.130119
$890$		0			0
$891$	−9.92865e12	−	6.78721e14i	−0.0176808	−	1.20866i
$892$		0			0
$893$			1.30934e15i			2.30565i
$894$		0			0
$895$	1.78474e14			0.310785
$896$		0			0
$897$	−1.49612e14	−	1.48522e14i	−0.257635	−	0.255758i
$898$		0			0
$899$		−	1.67462e14i		−	0.285180i
$900$		0			0
$901$	−1.32349e13			−0.0222893
$902$		0			0
$903$	2.02476e13	−	2.03963e13i	0.0337237	−	0.0339713i
$904$		0			0
$905$		−	5.84336e14i		−	0.962542i
$906$		0			0
$907$	7.35465e14			1.19819			0.599095	−	0.800678i	$-0.295527\pi$
$907$	7.35465e14			1.19819			0.599095	+	0.800678i	$0.295527\pi$
$908$		0			0
$909$	7.75168e14	−	5.66946e12i	1.24904	−	0.00913529i
$910$		0			0
$911$			9.08632e14i			1.44809i	0.689751	+	0.724046i	$0.257720\pi$
$911$			9.08632e14i			1.44809i	−0.689751	+	0.724046i	$0.742280\pi$
$912$		0			0
$913$	−1.37395e14			−0.216580
$914$		0			0
$915$	−2.88442e14	−	2.86340e14i	−0.449732	−	0.446454i
$916$		0			0
$917$		−	2.21017e14i		−	0.340863i
$918$		0			0
$919$	8.54977e14			1.30430			0.652149	−	0.758091i	$-0.273868\pi$
$919$	8.54977e14			1.30430			0.652149	+	0.758091i	$0.273868\pi$
$920$		0			0
$921$	−3.30057e14	+	3.32480e14i	−0.498071	+	0.501727i
$922$		0			0
$923$		−	1.95116e14i		−	0.291262i
$924$		0			0
$925$	2.63117e13			0.0388544
$926$		0			0
$927$	7.81457e12	+	1.06846e15i	0.0114158	+	1.56085i
$928$		0			0
$929$		−	7.98341e13i		−	0.115375i	−0.998335	−	0.0576873i	$-0.981627\pi$
$929$		−	7.98341e13i		−	0.115375i	0.998335	−	0.0576873i	$-0.0183726\pi$
$930$		0			0
$931$	−2.58901e15			−3.70157
$932$		0			0
$933$	−3.78333e14	−	3.75576e14i	−0.535139	−	0.531239i
$934$		0			0
$935$		−	2.23902e13i		−	0.0313328i
$936$		0			0
$937$	−7.34741e14			−1.01727			−0.508635	−	0.860982i	$-0.669850\pi$
$937$	−7.34741e14			−1.01727			−0.508635	+	0.860982i	$0.669850\pi$
$938$		0			0
$939$	−4.35294e14	+	4.38489e14i	−0.596286	+	0.600663i
$940$		0			0
$941$			4.61320e14i			0.625251i	0.949876	+	0.312626i	$0.101209\pi$
$941$			4.61320e14i			0.625251i	−0.949876	+	0.312626i	$0.898791\pi$
$942$		0			0
$943$	8.75787e14			1.17447
$944$		0			0
$945$	−8.41510e14	+	8.60179e14i	−1.11661	+	1.14138i
$946$		0			0
$947$			5.37004e14i			0.705063i	0.935800	+	0.352531i	$0.114679\pi$
$947$			5.37004e14i			0.705063i	−0.935800	+	0.352531i	$0.885321\pi$
$948$		0			0
$949$	9.42398e13			0.122434
$950$		0			0
$951$	−7.43042e14	−	7.37627e14i	−0.955236	−	0.948275i
$952$		0			0
$953$		−	5.35229e14i		−	0.680887i	−0.940265	−	0.340443i	$-0.889423\pi$
$953$		−	5.35229e14i		−	0.680887i	0.940265	−	0.340443i	$-0.110577\pi$
$954$		0			0
$955$	−2.34356e13			−0.0295025
$956$		0			0
$957$	−6.77324e14	+	6.82296e14i	−0.843795	+	0.849989i
$958$		0			0
$959$			2.32304e14i			0.286393i
$960$		0			0
$961$	−7.51730e14			−0.917159
$962$		0			0
$963$	1.60861e15	−	1.17651e13i	1.94231	−	0.0142058i
$964$		0			0
$965$		−	3.38511e14i		−	0.404517i
$966$		0			0
$967$	−4.03515e14			−0.477229			−0.238614	−	0.971114i	$-0.576693\pi$
$967$	−4.03515e14			−0.477229			−0.238614	+	0.971114i	$0.576693\pi$
$968$		0			0
$969$	−3.18913e13	−	3.16589e13i	−0.0373295	−	0.0370575i
$970$		0			0
$971$			2.59080e14i			0.300149i	0.988675	+	0.150075i	$0.0479514\pi$
$971$			2.59080e14i			0.300149i	−0.988675	+	0.150075i	$0.952049\pi$
$972$		0			0
$973$	1.36484e15			1.56501
$974$		0			0
$975$	−2.69934e13	+	2.71915e13i	−0.0306362	+	0.0308611i
$976$		0			0
$977$		−	1.64717e15i		−	1.85040i	−0.379476	−	0.925202i	$-0.623896\pi$
$977$		−	1.64717e15i		−	1.85040i	0.379476	−	0.925202i	$-0.376104\pi$
$978$		0			0
$979$	1.34277e15			1.49310
$980$		0			0
$981$	1.38487e12	+	1.89349e14i	0.00152428	+	0.208410i
$982$		0			0
$983$			1.13285e15i			1.23425i	0.786863	+	0.617127i	$0.211704\pi$
$983$			1.13285e15i			1.23425i	−0.786863	+	0.617127i	$0.788296\pi$
$984$		0			0
$985$	−1.43620e14			−0.154894
$986$		0			0
$987$	1.40401e15	+	1.39377e15i	1.49894	+	1.48801i
$988$		0			0
$989$		−	3.09529e13i		−	0.0327130i
$990$		0			0
$991$	−1.14488e15			−1.19782			−0.598910	−	0.800816i	$-0.704399\pi$
$991$	−1.14488e15			−1.19782			−0.598910	+	0.800816i	$0.704399\pi$
$992$		0			0
$993$	8.56267e14	−	8.62552e14i	0.886876	−	0.893386i
$994$		0			0
$995$			9.01941e14i			0.924832i
$996$		0			0
$997$	−9.48757e14			−0.963118			−0.481559	−	0.876414i	$-0.659929\pi$
$997$	−9.48757e14			−0.963118			−0.481559	+	0.876414i	$0.659929\pi$
$998$		0			0
$999$	−1.95947e14	−	1.91695e14i	−0.196930	−	0.192656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.11.e.a.17.7	✓	10
3.2	odd	2	inner	24.11.e.a.17.8	yes	10
4.3	odd	2		48.11.e.e.17.4		10
8.3	odd	2		192.11.e.i.65.7		10
8.5	even	2		192.11.e.j.65.4		10
12.11	even	2		48.11.e.e.17.3		10
24.5	odd	2		192.11.e.j.65.3		10
24.11	even	2		192.11.e.i.65.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.11.e.a.17.7	✓	10	1.1	even	1	trivial
24.11.e.a.17.8	yes	10	3.2	odd	2	inner
48.11.e.e.17.3		10	12.11	even	2
48.11.e.e.17.4		10	4.3	odd	2
192.11.e.i.65.7		10	8.3	odd	2
192.11.e.i.65.8		10	24.11	even	2
192.11.e.j.65.3		10	24.5	odd	2
192.11.e.j.65.4		10	8.5	even	2

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:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	24.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(171.197 - 172.454i) q^{3} +2896.26i q^{5} -28955.7 q^{7} +(-431.864 - 59047.4i) q^{9} +O(q^{10})\)	\(q+(171.197 - 172.454i) q^{3} +2896.26i q^{5} -28955.7 q^{7} +(-431.864 - 59047.4i) q^{9} +194676. i q^{11} -114481. q^{13} +(499472. + 495833. i) q^{15} +39710.7i q^{17} -4.65684e6 q^{19} +(-4.95715e6 + 4.99354e6i) q^{21} +7.57809e6i q^{23} +1.37729e6 q^{25} +(-1.02569e7 - 1.00343e7i) q^{27} +2.03229e7i q^{29} -8.24006e6 q^{31} +(3.35727e7 + 3.33281e7i) q^{33} -8.38634e7i q^{35} +1.91039e7 q^{37} +(-1.95989e7 + 1.97428e7i) q^{39} -1.15568e8i q^{41} -4.08453e6 q^{43} +(1.71017e8 - 1.25079e6i) q^{45} -2.81165e8i q^{47} +5.55960e8 q^{49} +(6.84827e6 + 6.79836e6i) q^{51} +3.33283e8i q^{53} -5.63833e8 q^{55} +(-7.97239e8 + 8.03091e8i) q^{57} -1.23488e9i q^{59} -5.77494e8 q^{61} +(1.25049e7 + 1.70976e9i) q^{63} -3.31568e8i q^{65} -8.61148e8 q^{67} +(1.30687e9 + 1.29735e9i) q^{69} +1.70435e9i q^{71} -8.23189e8 q^{73} +(2.35789e8 - 2.37520e8i) q^{75} -5.63699e9i q^{77} +3.61377e9 q^{79} +(-3.48641e9 + 5.10009e7i) q^{81} +7.05763e8i q^{83} -1.15012e8 q^{85} +(3.50477e9 + 3.47923e9i) q^{87} -6.89745e9i q^{89} +3.31489e9 q^{91} +(-1.41068e9 + 1.42103e9i) q^{93} -1.34874e10i q^{95} +1.18738e10 q^{97} +(1.14951e10 - 8.40736e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 22 q^{3} - 5436 q^{7} - 28934 q^{9}+O(q^{10}) \) 10 * q - 22 * q^3 - 5436 * q^7 - 28934 * q^9	\( 10 q - 22 q^{3} - 5436 q^{7} - 28934 q^{9} - 124508 q^{13} - 627808 q^{15} - 4893484 q^{19} - 3929724 q^{21} - 17742214 q^{25} - 3536326 q^{27} - 4251484 q^{31} - 2965600 q^{33} + 89985156 q^{37} + 52569188 q^{39} + 159987316 q^{43} + 39125824 q^{45} + 301480958 q^{49} + 387377536 q^{51} - 852340544 q^{55} - 970086764 q^{57} - 101460764 q^{61} + 733153572 q^{63} - 3014528044 q^{67} - 3501669184 q^{69} + 4920922036 q^{73} + 5355440986 q^{75} - 7631690012 q^{79} - 7700105942 q^{81} + 18713636096 q^{85} + 19781179104 q^{87} - 17913072600 q^{91} - 24272938652 q^{93} + 37861379156 q^{97} + 43508497216 q^{99}+O(q^{100}) \) 10 * q - 22 * q^3 - 5436 * q^7 - 28934 * q^9 - 124508 * q^13 - 627808 * q^15 - 4893484 * q^19 - 3929724 * q^21 - 17742214 * q^25 - 3536326 * q^27 - 4251484 * q^31 - 2965600 * q^33 + 89985156 * q^37 + 52569188 * q^39 + 159987316 * q^43 + 39125824 * q^45 + 301480958 * q^49 + 387377536 * q^51 - 852340544 * q^55 - 970086764 * q^57 - 101460764 * q^61 + 733153572 * q^63 - 3014528044 * q^67 - 3501669184 * q^69 + 4920922036 * q^73 + 5355440986 * q^75 - 7631690012 * q^79 - 7700105942 * q^81 + 18713636096 * q^85 + 19781179104 * q^87 - 17913072600 * q^91 - 24272938652 * q^93 + 37861379156 * q^97 + 43508497216 * q^99

Introduction

L-functions

Modular forms

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Database

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