LMFDB - Embedded newform 24.11.e.a.17.4

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			17.4
Root			$-11.0996 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	24.17
Dual form			24.11.e.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-126.767 + 207.314i) q^{3} -1673.71i q^{5} -12918.9 q^{7} +(-26909.2 - 52561.2i) q^{9} +O(q^{10})$	\(q+(-126.767 + 207.314i) q^{3} -1673.71i q^{5} -12918.9 q^{7} +(-26909.2 - 52561.2i) q^{9} +51725.9i q^{11} +609886. q^{13} +(346982. + 212171. i) q^{15} -1.57218e6i q^{17} +2.24801e6 q^{19} +(1.63769e6 - 2.67826e6i) q^{21} -5.09279e6i q^{23} +6.96434e6 q^{25} +(1.43079e7 + 1.08439e6i) q^{27} -6.16692e6i q^{29} +2.42426e7 q^{31} +(-1.07235e7 - 6.55715e6i) q^{33} +2.16224e7i q^{35} -1.00883e8 q^{37} +(-7.73136e7 + 1.26438e8i) q^{39} -1.55786e8i q^{41} -4.90309e7 q^{43} +(-8.79720e7 + 4.50380e7i) q^{45} +3.76080e8i q^{47} -1.15578e8 q^{49} +(3.25934e8 + 1.99300e8i) q^{51} -5.66224e8i q^{53} +8.65740e7 q^{55} +(-2.84973e8 + 4.66043e8i) q^{57} -1.38894e9i q^{59} +3.24607e8 q^{61} +(3.47636e8 + 6.79032e8i) q^{63} -1.02077e9i q^{65} +1.43065e9 q^{67} +(1.05581e9 + 6.45598e8i) q^{69} -9.32563e8i q^{71} +2.35147e9 q^{73} +(-8.82849e8 + 1.44380e9i) q^{75} -6.68241e8i q^{77} -5.12199e9 q^{79} +(-2.03858e9 + 2.82876e9i) q^{81} -4.15152e9i q^{83} -2.63136e9 q^{85} +(1.27849e9 + 7.81763e8i) q^{87} +7.29413e9i q^{89} -7.87904e9 q^{91} +(-3.07316e9 + 5.02582e9i) q^{93} -3.76250e9i q^{95} +7.42633e9 q^{97} +(2.71878e9 - 1.39190e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−126.767	+	207.314i	−0.521676	+	0.853144i
$3$	−126.767	+	207.314i	−0.521676	+	0.853144i
$4$		0			0
$5$		−	1673.71i		−	0.535586i	−0.963477	−	0.267793i	$-0.913706\pi$
$5$		−	1673.71i		−	0.535586i	0.963477	−	0.267793i	$-0.0862943\pi$
$6$		0			0
$7$	−12918.9			−0.768660			−0.384330	−	0.923196i	$-0.625568\pi$
$7$	−12918.9			−0.768660			−0.384330	+	0.923196i	$0.625568\pi$
$8$		0			0
$9$	−26909.2	−	52561.2i	−0.455709	−	0.890129i
$10$		0			0
$11$			51725.9i			0.321177i	0.987021	+	0.160589i	$0.0513393\pi$
$11$			51725.9i			0.321177i	−0.987021	+	0.160589i	$0.948661\pi$
$12$		0			0
$13$	609886.			1.64260			0.821301	−	0.570496i	$-0.193249\pi$
$13$	609886.			1.64260			0.821301	+	0.570496i	$0.193249\pi$
$14$		0			0
$15$	346982.	+	212171.i	0.456932	+	0.279402i
$16$		0			0
$17$		−	1.57218e6i		−	1.10728i	−0.832757	−	0.553639i	$-0.813239\pi$
$17$		−	1.57218e6i		−	1.10728i	0.832757	−	0.553639i	$-0.186761\pi$
$18$		0			0
$19$	2.24801e6			0.907883			0.453941	−	0.891032i	$-0.350018\pi$
$19$	2.24801e6			0.907883			0.453941	+	0.891032i	$0.350018\pi$
$20$		0			0
$21$	1.63769e6	−	2.67826e6i	0.400991	−	0.655778i
$22$		0			0
$23$		−	5.09279e6i		−	0.791255i	−0.918411	−	0.395628i	$-0.870527\pi$
$23$		−	5.09279e6i		−	0.791255i	0.918411	−	0.395628i	$-0.129473\pi$
$24$		0			0
$25$	6.96434e6			0.713148
$26$		0			0
$27$	1.43079e7	+	1.08439e6i	0.997140	+	0.0755729i
$28$		0			0
$29$		−	6.16692e6i		−	0.300662i	−0.988636	−	0.150331i	$-0.951966\pi$
$29$		−	6.16692e6i		−	0.300662i	0.988636	−	0.150331i	$-0.0480339\pi$
$30$		0			0
$31$	2.42426e7			0.846779			0.423390	−	0.905948i	$-0.360840\pi$
$31$	2.42426e7			0.846779			0.423390	+	0.905948i	$0.360840\pi$
$32$		0			0
$33$	−1.07235e7	−	6.55715e6i	−0.274011	−	0.167550i
$34$		0			0
$35$			2.16224e7i			0.411683i
$36$		0			0
$37$	−1.00883e8			−1.45482			−0.727411	−	0.686202i	$-0.759277\pi$
$37$	−1.00883e8			−1.45482			−0.727411	+	0.686202i	$0.759277\pi$
$38$		0			0
$39$	−7.73136e7	+	1.26438e8i	−0.856905	+	1.40138i
$40$		0			0
$41$		−	1.55786e8i		−	1.34465i	−0.740255	−	0.672327i	$-0.765295\pi$
$41$		−	1.55786e8i		−	1.34465i	0.740255	−	0.672327i	$-0.234705\pi$
$42$		0			0
$43$	−4.90309e7			−0.333524			−0.166762	−	0.985997i	$-0.553331\pi$
$43$	−4.90309e7			−0.333524			−0.166762	+	0.985997i	$0.553331\pi$
$44$		0			0
$45$	−8.79720e7	+	4.50380e7i	−0.476740	+	0.244071i
$46$		0			0
$47$			3.76080e8i			1.63980i	0.572507	+	0.819900i	$0.305971\pi$
$47$			3.76080e8i			1.63980i	−0.572507	+	0.819900i	$0.694029\pi$
$48$		0			0
$49$	−1.15578e8			−0.409162
$50$		0			0
$51$	3.25934e8	+	1.99300e8i	0.944668	+	0.577640i
$52$		0			0
$53$		−	5.66224e8i		−	1.35397i	−0.735996	−	0.676985i	$-0.763286\pi$
$53$		−	5.66224e8i		−	1.35397i	0.735996	−	0.676985i	$-0.236714\pi$
$54$		0			0
$55$	8.65740e7			0.172018
$56$		0			0
$57$	−2.84973e8	+	4.66043e8i	−0.473620	+	0.774554i
$58$		0			0
$59$		−	1.38894e9i		−	1.94277i	−0.237506	−	0.971386i	$-0.576330\pi$
$59$		−	1.38894e9i		−	1.94277i	0.237506	−	0.971386i	$-0.423670\pi$
$60$		0			0
$61$	3.24607e8			0.384334			0.192167	−	0.981362i	$-0.438448\pi$
$61$	3.24607e8			0.384334			0.192167	+	0.981362i	$0.438448\pi$
$62$		0			0
$63$	3.47636e8	+	6.79032e8i	0.350285	+	0.684206i
$64$		0			0
$65$		−	1.02077e9i		−	0.879754i
$66$		0			0
$67$	1.43065e9			1.05964			0.529822	−	0.848109i	$-0.322259\pi$
$67$	1.43065e9			1.05964			0.529822	+	0.848109i	$0.322259\pi$
$68$		0			0
$69$	1.05581e9	+	6.45598e8i	0.675054	+	0.412778i
$70$		0			0
$71$		−	9.32563e8i		−	0.516876i	−0.966028	−	0.258438i	$-0.916792\pi$
$71$		−	9.32563e8i		−	0.516876i	0.966028	−	0.258438i	$-0.0832078\pi$
$72$		0			0
$73$	2.35147e9			1.13429			0.567145	−	0.823618i	$-0.308048\pi$
$73$	2.35147e9			1.13429			0.567145	+	0.823618i	$0.308048\pi$
$74$		0			0
$75$	−8.82849e8	+	1.44380e9i	−0.372032	+	0.608418i
$76$		0			0
$77$		−	6.68241e8i		−	0.246876i
$78$		0			0
$79$	−5.12199e9			−1.66458			−0.832288	−	0.554344i	$-0.812969\pi$
$79$	−5.12199e9			−1.66458			−0.832288	+	0.554344i	$0.812969\pi$
$80$		0			0
$81$	−2.03858e9	+	2.82876e9i	−0.584658	+	0.811280i
$82$		0			0
$83$		−	4.15152e9i		−	1.05394i	−0.849883	−	0.526971i	$-0.823327\pi$
$83$		−	4.15152e9i		−	1.05394i	0.849883	−	0.526971i	$-0.176673\pi$
$84$		0			0
$85$	−2.63136e9			−0.593042
$86$		0			0
$87$	1.27849e9	+	7.81763e8i	0.256508	+	0.156848i
$88$		0			0
$89$			7.29413e9i			1.30624i	0.757254	+	0.653121i	$0.226541\pi$
$89$			7.29413e9i			1.30624i	−0.757254	+	0.653121i	$0.773459\pi$
$90$		0			0
$91$	−7.87904e9			−1.26260
$92$		0			0
$93$	−3.07316e9	+	5.02582e9i	−0.441744	+	0.722424i
$94$		0			0
$95$		−	3.76250e9i		−	0.486249i
$96$		0			0
$97$	7.42633e9			0.864800			0.432400	−	0.901682i	$-0.357667\pi$
$97$	7.42633e9			0.864800			0.432400	+	0.901682i	$0.357667\pi$
$98$		0			0
$99$	2.71878e9	−	1.39190e9i	0.285889	−	0.146363i
$100$		0			0
$101$		−	5.58679e8i		−	0.0531564i	−0.999647	−	0.0265782i	$-0.991539\pi$
$101$		−	5.58679e8i		−	0.0531564i	0.999647	−	0.0265782i	$-0.00846111\pi$
$102$		0			0
$103$	3.99633e9			0.344727			0.172363	−	0.985033i	$-0.444860\pi$
$103$	3.99633e9			0.344727			0.172363	+	0.985033i	$0.444860\pi$
$104$		0			0
$105$	−4.48262e9	−	2.74101e9i	−0.351225	−	0.214765i
$106$		0			0
$107$			9.48329e9i			0.676146i	0.941120	+	0.338073i	$0.109775\pi$
$107$			9.48329e9i			0.676146i	−0.941120	+	0.338073i	$0.890225\pi$
$108$		0			0
$109$	1.26428e10			0.821697			0.410848	−	0.911704i	$-0.365233\pi$
$109$	1.26428e10			0.821697			0.410848	+	0.911704i	$0.365233\pi$
$110$		0			0
$111$	1.27887e10	−	2.09145e10i	0.758945	−	1.24117i
$112$		0			0
$113$		−	5.47299e9i		−	0.297052i	−0.988909	−	0.148526i	$-0.952547\pi$
$113$		−	5.47299e9i		−	0.297052i	0.988909	−	0.148526i	$-0.0474529\pi$
$114$		0			0
$115$	−8.52383e9			−0.423785
$116$		0			0
$117$	−1.64115e10	−	3.20564e10i	−0.748548	−	1.46213i
$118$		0			0
$119$			2.03107e10i			0.851121i
$120$		0			0
$121$	2.32619e10			0.896845
$122$		0			0
$123$	3.22967e10	+	1.97486e10i	1.14718	+	0.701473i
$124$		0			0
$125$		−	2.80010e10i		−	0.917537i
$126$		0			0
$127$	1.32783e10			0.401905			0.200952	−	0.979601i	$-0.435596\pi$
$127$	1.32783e10			0.401905			0.200952	+	0.979601i	$0.435596\pi$
$128$		0			0
$129$	6.21551e9	−	1.01648e10i	0.173992	−	0.284544i
$130$		0			0
$131$			4.13418e10i			1.07160i	0.844345	+	0.535800i	$0.179990\pi$
$131$			4.13418e10i			1.07160i	−0.844345	+	0.535800i	$0.820010\pi$
$132$		0			0
$133$	−2.90417e10			−0.697853
$134$		0			0
$135$	1.81495e9	−	2.39472e10i	0.0404758	−	0.534054i
$136$		0			0
$137$			8.53738e10i			1.76898i	0.466564	+	0.884488i	$0.345492\pi$
$137$			8.53738e10i			1.76898i	−0.466564	+	0.884488i	$0.654508\pi$
$138$		0			0
$139$	−3.98817e10			−0.768599			−0.384300	−	0.923208i	$-0.625557\pi$
$139$	−3.98817e10			−0.768599			−0.384300	+	0.923208i	$0.625557\pi$
$140$		0			0
$141$	−7.79666e10	−	4.76746e10i	−1.39899	−	0.855444i
$142$		0			0
$143$			3.15469e10i			0.527566i
$144$		0			0
$145$	−1.03216e10			−0.161030
$146$		0			0
$147$	1.46515e10	−	2.39609e10i	0.213450	−	0.349074i
$148$		0			0
$149$		−	6.59483e9i		−	0.0897991i	−0.998992	−	0.0448996i	$-0.985703\pi$
$149$		−	6.59483e9i		−	0.0897991i	0.998992	−	0.0448996i	$-0.0142968\pi$
$150$		0			0
$151$	−1.25469e11			−1.59828			−0.799140	−	0.601145i	$-0.794711\pi$
$151$	−1.25469e11			−1.59828			−0.799140	+	0.601145i	$0.794711\pi$
$152$		0			0
$153$	−8.26355e10	+	4.23060e10i	−0.985620	+	0.504597i
$154$		0			0
$155$		−	4.05749e10i		−	0.453523i
$156$		0			0
$157$	9.59143e10			1.00551			0.502753	−	0.864430i	$-0.332320\pi$
$157$	9.59143e10			1.00551			0.502753	+	0.864430i	$0.332320\pi$
$158$		0			0
$159$	1.17386e11	+	7.17787e10i	1.15513	+	0.706333i
$160$		0			0
$161$			6.57931e10i			0.608206i
$162$		0			0
$163$	3.48974e10			0.303288			0.151644	−	0.988435i	$-0.451543\pi$
$163$	3.48974e10			0.303288			0.151644	+	0.988435i	$0.451543\pi$
$164$		0			0
$165$	−1.09747e10	+	1.79480e10i	−0.0897376	+	0.146756i
$166$		0			0
$167$			2.45080e9i			0.0188680i	0.999955	+	0.00943398i	$0.00300297\pi$
$167$			2.45080e9i			0.0188680i	−0.999955	+	0.00943398i	$0.996997\pi$
$168$		0			0
$169$	2.34103e11			1.69814
$170$		0			0
$171$	−6.04920e10	−	1.18158e11i	−0.413730	−	0.808132i
$172$		0			0
$173$		−	2.71438e11i		−	1.75162i	−0.482656	−	0.875810i	$-0.660328\pi$
$173$		−	2.71438e11i		−	1.75162i	0.482656	−	0.875810i	$-0.339672\pi$
$174$		0			0
$175$	−8.99714e10			−0.548168
$176$		0			0
$177$	2.87946e11	+	1.76071e11i	1.65746	+	1.01350i
$178$		0			0
$179$		−	2.78660e11i		−	1.51639i	−0.652031	−	0.758193i	$-0.726083\pi$
$179$		−	2.78660e11i		−	1.51639i	0.652031	−	0.758193i	$-0.273917\pi$
$180$		0			0
$181$	−1.49482e11			−0.769480			−0.384740	−	0.923025i	$-0.625709\pi$
$181$	−1.49482e11			−0.769480			−0.384740	+	0.923025i	$0.625709\pi$
$182$		0			0
$183$	−4.11495e10	+	6.72956e10i	−0.200498	+	0.327892i
$184$		0			0
$185$			1.68849e11i			0.779182i
$186$		0			0
$187$	8.13223e10			0.355633
$188$		0			0
$189$	−1.84842e11	−	1.40091e10i	−0.766462	−	0.0580899i
$190$		0			0
$191$		−	2.99762e11i		−	1.17926i	−0.807674	−	0.589630i	$-0.799274\pi$
$191$		−	2.99762e11i		−	1.17926i	0.807674	−	0.589630i	$-0.200726\pi$
$192$		0			0
$193$	2.30280e11			0.859942			0.429971	−	0.902843i	$-0.358524\pi$
$193$	2.30280e11			0.859942			0.429971	+	0.902843i	$0.358524\pi$
$194$		0			0
$195$	2.11620e11	+	1.29400e11i	0.750557	+	0.458946i
$196$		0			0
$197$		−	4.24747e10i		−	0.143153i	−0.997435	−	0.0715763i	$-0.977197\pi$
$197$		−	4.24747e10i		−	0.143153i	0.997435	−	0.0715763i	$-0.0228030\pi$
$198$		0			0
$199$	1.32171e11			0.423518			0.211759	−	0.977322i	$-0.432081\pi$
$199$	1.32171e11			0.423518			0.211759	+	0.977322i	$0.432081\pi$
$200$		0			0
$201$	−1.81360e11	+	2.96594e11i	−0.552790	+	0.904029i
$202$		0			0
$203$			7.96697e10i			0.231107i
$204$		0			0
$205$	−2.60741e11			−0.720177
$206$		0			0
$207$	−2.67683e11	+	1.37043e11i	−0.704319	+	0.360582i
$208$		0			0
$209$			1.16280e11i			0.291591i
$210$		0			0
$211$	−3.91651e11			−0.936454			−0.468227	−	0.883608i	$-0.655107\pi$
$211$	−3.91651e11			−0.936454			−0.468227	+	0.883608i	$0.655107\pi$
$212$		0			0
$213$	1.93333e11	+	1.18218e11i	0.440970	+	0.269642i
$214$		0			0
$215$			8.20633e10i			0.178631i
$216$		0			0
$217$	−3.13187e11			−0.650885
$218$		0			0
$219$	−2.98089e11	+	4.87492e11i	−0.591732	+	0.967713i
$220$		0			0
$221$		−	9.58849e11i		−	1.81882i
$222$		0			0
$223$	1.38592e11			0.251312			0.125656	−	0.992074i	$-0.459896\pi$
$223$	1.38592e11			0.251312			0.125656	+	0.992074i	$0.459896\pi$
$224$		0			0
$225$	−1.87404e11	−	3.66054e11i	−0.324988	−	0.634794i
$226$		0			0
$227$			9.04124e11i			1.50003i	0.661424	+	0.750013i	$0.269953\pi$
$227$			9.04124e11i			1.50003i	−0.661424	+	0.750013i	$0.730047\pi$
$228$		0			0
$229$	−8.96357e11			−1.42332			−0.711662	−	0.702522i	$-0.752057\pi$
$229$	−8.96357e11			−1.42332			−0.711662	+	0.702522i	$0.752057\pi$
$230$		0			0
$231$	1.38536e11	+	8.47110e10i	0.210621	+	0.128789i
$232$		0			0
$233$			4.16745e11i			0.606863i	0.952853	+	0.303432i	$0.0981324\pi$
$233$			4.16745e11i			0.606863i	−0.952853	+	0.303432i	$0.901868\pi$
$234$		0			0
$235$	6.29447e11			0.878253
$236$		0			0
$237$	6.49300e11	−	1.06186e12i	0.868368	−	1.42012i
$238$		0			0
$239$			2.18359e10i			0.0280016i	0.999902	+	0.0140008i	$0.00445673\pi$
$239$			2.18359e10i			0.0280016i	−0.999902	+	0.0140008i	$0.995543\pi$
$240$		0			0
$241$	2.81917e11			0.346765			0.173383	−	0.984855i	$-0.444530\pi$
$241$	2.81917e11			0.346765			0.173383	+	0.984855i	$0.444530\pi$
$242$		0			0
$243$	−3.28016e11	−	7.81219e11i	−0.387136	−	0.922022i
$244$		0			0
$245$			1.93444e11i			0.219141i
$246$		0			0
$247$	1.37103e12			1.49129
$248$		0			0
$249$	8.60669e11	+	5.26277e11i	0.899165	+	0.549816i
$250$		0			0
$251$			2.12158e11i			0.212956i	0.994315	+	0.106478i	$0.0339574\pi$
$251$			2.12158e11i			0.212956i	−0.994315	+	0.106478i	$0.966043\pi$
$252$		0			0
$253$	2.63429e11			0.254133
$254$		0			0
$255$	3.33570e11	−	5.45518e11i	0.309376	−	0.505950i
$256$		0			0
$257$		−	5.86148e11i		−	0.522807i	−0.965230	−	0.261404i	$-0.915815\pi$
$257$		−	5.86148e11i		−	0.522807i	0.965230	−	0.261404i	$-0.0841853\pi$
$258$		0			0
$259$	1.30330e12			1.11826
$260$		0			0
$261$	−3.24141e11	+	1.65947e11i	−0.267628	+	0.137014i
$262$		0			0
$263$		−	4.31510e11i		−	0.342935i	−0.985190	−	0.171468i	$-0.945149\pi$
$263$		−	4.31510e11i		−	0.342935i	0.985190	−	0.171468i	$-0.0548509\pi$
$264$		0			0
$265$	−9.47693e11			−0.725167
$266$		0			0
$267$	−1.51218e12	−	9.24656e11i	−1.11441	−	0.681434i
$268$		0			0
$269$			1.44619e12i			1.02675i	0.858165	+	0.513373i	$0.171604\pi$
$269$			1.44619e12i			1.02675i	−0.858165	+	0.513373i	$0.828396\pi$
$270$		0			0
$271$	−1.48128e12			−1.01342			−0.506711	−	0.862116i	$-0.669139\pi$
$271$	−1.48128e12			−1.01342			−0.506711	+	0.862116i	$0.669139\pi$
$272$		0			0
$273$	9.98804e11	−	1.63344e12i	0.658669	−	1.07718i
$274$		0			0
$275$			3.60237e11i			0.229047i
$276$		0			0
$277$	−1.11993e11			−0.0686738			−0.0343369	−	0.999410i	$-0.510932\pi$
$277$	−1.11993e11			−0.0686738			−0.0343369	+	0.999410i	$0.510932\pi$
$278$		0			0
$279$	−6.52347e11	−	1.27422e12i	−0.385885	−	0.753742i
$280$		0			0
$281$			1.29433e12i			0.738777i	0.929275	+	0.369389i	$0.120433\pi$
$281$			1.29433e12i			0.738777i	−0.929275	+	0.369389i	$0.879567\pi$
$282$		0			0
$283$	5.20223e11			0.286587			0.143294	−	0.989680i	$-0.454231\pi$
$283$	5.20223e11			0.286587			0.143294	+	0.989680i	$0.454231\pi$
$284$		0			0
$285$	7.80019e11	+	4.76962e11i	0.414840	+	0.253664i
$286$		0			0
$287$			2.01258e12i			1.03358i
$288$		0			0
$289$	−4.55746e11			−0.226065
$290$		0			0
$291$	−9.41415e11	+	1.53958e12i	−0.451145	+	0.737799i
$292$		0			0
$293$			2.83940e12i			1.31488i	0.753505	+	0.657442i	$0.228362\pi$
$293$			2.83940e12i			1.31488i	−0.753505	+	0.657442i	$0.771638\pi$
$294$		0			0
$295$	−2.32467e12			−1.04052
$296$		0			0
$297$	−5.60910e10	+	7.40088e11i	−0.0242723	+	0.320259i
$298$		0			0
$299$		−	3.10602e12i		−	1.29972i
$300$		0			0
$301$	6.33424e11			0.256367
$302$		0			0
$303$	1.15822e11	+	7.08222e10i	0.0453501	+	0.0277304i
$304$		0			0
$305$		−	5.43297e11i		−	0.205844i
$306$		0			0
$307$	−1.59206e12			−0.583804			−0.291902	−	0.956448i	$-0.594288\pi$
$307$	−1.59206e12			−0.583804			−0.291902	+	0.956448i	$0.594288\pi$
$308$		0			0
$309$	−5.06603e11	+	8.28495e11i	−0.179836	+	0.294102i
$310$		0			0
$311$			8.93981e11i			0.307274i	0.988127	+	0.153637i	$0.0490987\pi$
$311$			8.93981e11i			0.307274i	−0.988127	+	0.153637i	$0.950901\pi$
$312$		0			0
$313$	−2.61303e12			−0.869806			−0.434903	−	0.900477i	$-0.643217\pi$
$313$	−2.61303e12			−0.869806			−0.434903	+	0.900477i	$0.643217\pi$
$314$		0			0
$315$	1.13650e12	−	5.81840e11i	0.366451	−	0.187608i
$316$		0			0
$317$		−	9.69816e11i		−	0.302966i	−0.988460	−	0.151483i	$-0.951595\pi$
$317$		−	9.69816e11i		−	0.302966i	0.988460	−	0.151483i	$-0.0484048\pi$
$318$		0			0
$319$	3.18990e11			0.0965658
$320$		0			0
$321$	−1.96602e12	−	1.20217e12i	−0.576850	−	0.352729i
$322$		0			0
$323$		−	3.53426e12i		−	1.00528i
$324$		0			0
$325$	4.24745e12			1.17142
$326$		0			0
$327$	−1.60269e12	+	2.62103e12i	−0.428659	+	0.701026i
$328$		0			0
$329$		−	4.85853e12i		−	1.26045i
$330$		0			0
$331$	5.23315e12			1.31711			0.658557	−	0.752531i	$-0.271167\pi$
$331$	5.23315e12			1.31711			0.658557	+	0.752531i	$0.271167\pi$
$332$		0			0
$333$	2.71468e12	+	5.30254e12i	0.662976	+	1.29498i
$334$		0			0
$335$		−	2.39449e12i		−	0.567530i
$336$		0			0
$337$	1.29717e11			0.0298434			0.0149217	−	0.999889i	$-0.495250\pi$
$337$	1.29717e11			0.0298434			0.0149217	+	0.999889i	$0.495250\pi$
$338$		0			0
$339$	1.13463e12	+	6.93795e11i	0.253428	+	0.154965i
$340$		0			0
$341$			1.25397e12i			0.271966i
$342$		0			0
$343$	5.14240e12			1.08317
$344$		0			0
$345$	1.08054e12	−	1.76711e12i	0.221078	−	0.361549i
$346$		0			0
$347$			1.29573e12i			0.257554i	0.991674	+	0.128777i	$0.0411052\pi$
$347$			1.29573e12i			0.257554i	−0.991674	+	0.128777i	$0.958895\pi$
$348$		0			0
$349$	4.56845e11			0.0882351			0.0441176	−	0.999026i	$-0.485952\pi$
$349$	4.56845e11			0.0882351			0.0441176	+	0.999026i	$0.485952\pi$
$350$		0			0
$351$	8.72618e12	+	6.61354e11i	1.63790	+	0.124136i
$352$		0			0
$353$		−	1.07717e13i		−	1.96521i	−0.185710	−	0.982605i	$-0.559458\pi$
$353$		−	1.07717e13i		−	1.96521i	0.185710	−	0.982605i	$-0.440542\pi$
$354$		0			0
$355$	−1.56084e12			−0.276831
$356$		0			0
$357$	−4.21070e12	−	2.57474e12i	−0.726128	−	0.444009i
$358$		0			0
$359$			3.47769e12i			0.583202i	0.956540	+	0.291601i	$0.0941880\pi$
$359$			3.47769e12i			0.583202i	−0.956540	+	0.291601i	$0.905812\pi$
$360$		0			0
$361$	−1.07753e12			−0.175749
$362$		0			0
$363$	−2.94884e12	+	4.82251e12i	−0.467862	+	0.765138i
$364$		0			0
$365$		−	3.93566e12i		−	0.607510i
$366$		0			0
$367$	−1.25892e13			−1.89090			−0.945448	−	0.325773i	$-0.894376\pi$
$367$	−1.25892e13			−1.89090			−0.945448	+	0.325773i	$0.894376\pi$
$368$		0			0
$369$	−8.18832e12	+	4.19208e12i	−1.19691	+	0.612771i
$370$		0			0
$371$			7.31498e12i			1.04074i
$372$		0			0
$373$	5.81519e12			0.805415			0.402708	−	0.915329i	$-0.368069\pi$
$373$	5.81519e12			0.805415			0.402708	+	0.915329i	$0.368069\pi$
$374$		0			0
$375$	5.80500e12	+	3.54961e12i	0.782792	+	0.478657i
$376$		0			0
$377$		−	3.76112e12i		−	0.493868i
$378$		0			0
$379$	−6.13477e12			−0.784517			−0.392259	−	0.919855i	$-0.628306\pi$
$379$	−6.13477e12			−0.784517			−0.392259	+	0.919855i	$0.628306\pi$
$380$		0			0
$381$	−1.68325e12	+	2.75277e12i	−0.209664	+	0.342883i
$382$		0			0
$383$		−	9.99194e12i		−	1.21243i	−0.795301	−	0.606214i	$-0.792687\pi$
$383$		−	9.99194e12i		−	1.21243i	0.795301	−	0.606214i	$-0.207313\pi$
$384$		0			0
$385$	−1.11844e12			−0.132223
$386$		0			0
$387$	1.31938e12	+	2.57712e12i	0.151990	+	0.296880i
$388$		0			0
$389$			9.19594e12i			1.03240i	0.856468	+	0.516200i	$0.172654\pi$
$389$			9.19594e12i			1.03240i	−0.856468	+	0.516200i	$0.827346\pi$
$390$		0			0
$391$	−8.00676e12			−0.876139
$392$		0			0
$393$	−8.57073e12	−	5.24078e12i	−0.914229	−	0.559028i
$394$		0			0
$395$			8.57270e12i			0.891522i
$396$		0			0
$397$	−3.12151e12			−0.316528			−0.158264	−	0.987397i	$-0.550590\pi$
$397$	−3.12151e12			−0.316528			−0.158264	+	0.987397i	$0.550590\pi$
$398$		0			0
$399$	3.68154e12	−	6.02075e12i	0.364053	−	0.595369i
$400$		0			0
$401$			1.54221e13i			1.48737i	0.668528	+	0.743687i	$0.266925\pi$
$401$			1.54221e13i			1.48737i	−0.668528	+	0.743687i	$0.733075\pi$
$402$		0			0
$403$	1.47852e13			1.39092
$404$		0			0
$405$	4.73451e12	+	3.41198e12i	0.434510	+	0.313135i
$406$		0			0
$407$		−	5.21827e12i		−	0.467256i
$408$		0			0
$409$	7.31834e12			0.639434			0.319717	−	0.947513i	$-0.396412\pi$
$409$	7.31834e12			0.639434			0.319717	+	0.947513i	$0.396412\pi$
$410$		0			0
$411$	−1.76992e13	−	1.08226e13i	−1.50919	−	0.922831i
$412$		0			0
$413$			1.79435e13i			1.49333i
$414$		0			0
$415$	−6.94843e12			−0.564477
$416$		0			0
$417$	5.05569e12	−	8.26804e12i	0.400960	−	0.655726i
$418$		0			0
$419$		−	8.13569e12i		−	0.629976i	−0.949096	−	0.314988i	$-0.897999\pi$
$419$		−	8.13569e12i		−	0.629976i	0.949096	−	0.314988i	$-0.102001\pi$
$420$		0			0
$421$	3.14838e11			0.0238055			0.0119027	−	0.999929i	$-0.496211\pi$
$421$	3.14838e11			0.0238055			0.0119027	+	0.999929i	$0.496211\pi$
$422$		0			0
$423$	1.97672e13	−	1.01200e13i	1.45963	−	0.747272i
$424$		0			0
$425$		−	1.09492e13i		−	0.789653i
$426$		0			0
$427$	−4.19356e12			−0.295422
$428$		0			0
$429$	−6.54012e12	−	3.99912e12i	−0.450090	−	0.275218i
$430$		0			0
$431$			8.49355e12i			0.571088i	0.958366	+	0.285544i	$0.0921742\pi$
$431$			8.49355e12i			0.571088i	−0.958366	+	0.285544i	$0.907826\pi$
$432$		0			0
$433$	1.67769e13			1.10223			0.551113	−	0.834430i	$-0.314203\pi$
$433$	1.67769e13			1.10223			0.551113	+	0.834430i	$0.314203\pi$
$434$		0			0
$435$	1.30844e12	−	2.13981e12i	0.0840056	−	0.137382i
$436$		0			0
$437$		−	1.14486e13i		−	0.718367i
$438$		0			0
$439$	−1.17035e13			−0.717781			−0.358891	−	0.933380i	$-0.616845\pi$
$439$	−1.17035e13			−0.717781			−0.358891	+	0.933380i	$0.616845\pi$
$440$		0			0
$441$	3.11011e12	+	6.07492e12i	0.186459	+	0.364206i
$442$		0			0
$443$		−	1.76231e13i		−	1.03291i	−0.856314	−	0.516456i	$-0.827251\pi$
$443$		−	1.76231e13i		−	1.03291i	0.856314	−	0.516456i	$-0.172749\pi$
$444$		0			0
$445$	1.22082e13			0.699604
$446$		0			0
$447$	1.36720e12	+	8.36008e11i	0.0766116	+	0.0468460i
$448$		0			0
$449$			3.38101e13i			1.85274i	0.376611	+	0.926372i	$0.377089\pi$
$449$			3.38101e13i			1.85274i	−0.376611	+	0.926372i	$0.622911\pi$
$450$		0			0
$451$	8.05820e12			0.431872
$452$		0			0
$453$	1.59054e13	−	2.60115e13i	0.833783	−	1.36356i
$454$		0			0
$455$			1.31872e13i			0.676232i
$456$		0			0
$457$	1.60342e13			0.804391			0.402195	−	0.915554i	$-0.368247\pi$
$457$	1.60342e13			0.804391			0.402195	+	0.915554i	$0.368247\pi$
$458$		0			0
$459$	1.70485e12	−	2.24945e13i	0.0836803	−	1.10411i
$460$		0			0
$461$		−	1.24098e13i		−	0.596017i	−0.954563	−	0.298008i	$-0.903678\pi$
$461$		−	1.24098e13i		−	0.596017i	0.954563	−	0.298008i	$-0.0963224\pi$
$462$		0			0
$463$	4.50331e12			0.211654			0.105827	−	0.994385i	$-0.466251\pi$
$463$	4.50331e12			0.211654			0.105827	+	0.994385i	$0.466251\pi$
$464$		0			0
$465$	8.41175e12	+	5.14357e12i	0.386920	+	0.236592i
$466$		0			0
$467$			3.90046e13i			1.75603i	0.478635	+	0.878014i	$0.341132\pi$
$467$			3.90046e13i			1.75603i	−0.478635	+	0.878014i	$0.658868\pi$
$468$		0			0
$469$	−1.84824e13			−0.814506
$470$		0			0
$471$	−1.21588e13	+	1.98844e13i	−0.524548	+	0.857842i
$472$		0			0
$473$		−	2.53617e12i		−	0.107121i
$474$		0			0
$475$	1.56559e13			0.647455
$476$		0			0
$477$	−2.97614e13	+	1.52366e13i	−1.20521	+	0.617017i
$478$		0			0
$479$		−	8.66274e12i		−	0.343540i	−0.985137	−	0.171770i	$-0.945051\pi$
$479$		−	8.66274e12i		−	0.343540i	0.985137	−	0.171770i	$-0.0549486\pi$
$480$		0			0
$481$	−6.15272e13			−2.38969
$482$		0			0
$483$	−1.36398e13	−	8.34040e12i	−0.518887	−	0.317286i
$484$		0			0
$485$		−	1.24295e13i		−	0.463174i
$486$		0			0
$487$	−1.48741e13			−0.542981			−0.271490	−	0.962441i	$-0.587517\pi$
$487$	−1.48741e13			−0.542981			−0.271490	+	0.962441i	$0.587517\pi$
$488$		0			0
$489$	−4.42384e12	+	7.23471e12i	−0.158218	+	0.258748i
$490$		0			0
$491$		−	2.41461e13i		−	0.846133i	−0.906099	−	0.423067i	$-0.860954\pi$
$491$		−	2.41461e13i		−	0.846133i	0.906099	−	0.423067i	$-0.139046\pi$
$492$		0			0
$493$	−9.69549e12			−0.332916
$494$		0			0
$495$	−2.32963e12	−	4.55043e12i	−0.0783902	−	0.153118i
$496$		0			0
$497$			1.20477e13i			0.397302i
$498$		0			0
$499$	2.84689e13			0.920171			0.460085	−	0.887875i	$-0.347819\pi$
$499$	2.84689e13			0.920171			0.460085	+	0.887875i	$0.347819\pi$
$500$		0			0
$501$	−5.08085e11	−	3.10681e11i	−0.0160971	−	0.00984296i
$502$		0			0
$503$			3.73576e13i			1.16022i	0.814540	+	0.580108i	$0.196990\pi$
$503$			3.73576e13i			1.16022i	−0.814540	+	0.580108i	$0.803010\pi$
$504$		0			0
$505$	−9.35065e11			−0.0284698
$506$		0			0
$507$	−2.96766e13	+	4.85328e13i	−0.885878	+	1.44876i
$508$		0			0
$509$		−	2.75970e13i		−	0.807743i	−0.914816	−	0.403872i	$-0.867664\pi$
$509$		−	2.75970e13i		−	0.807743i	0.914816	−	0.403872i	$-0.132336\pi$
$510$		0			0
$511$	−3.03783e13			−0.871884
$512$		0			0
$513$	3.21642e13	+	2.43771e12i	0.905286	+	0.0686114i
$514$		0			0
$515$		−	6.68868e12i		−	0.184631i
$516$		0			0
$517$	−1.94531e13			−0.526667
$518$		0			0
$519$	5.62729e13	+	3.44094e13i	1.49438	+	0.913777i
$520$		0			0
$521$			6.66935e12i			0.173738i	0.996220	+	0.0868690i	$0.0276861\pi$
$521$			6.66935e12i			0.173738i	−0.996220	+	0.0868690i	$0.972314\pi$
$522$		0			0
$523$	6.59796e13			1.68617			0.843085	−	0.537781i	$-0.180737\pi$
$523$	6.59796e13			1.68617			0.843085	+	0.537781i	$0.180737\pi$
$524$		0			0
$525$	1.14054e13	−	1.86523e13i	0.285966	−	0.467667i
$526$		0			0
$527$		−	3.81136e13i		−	0.937620i
$528$		0			0
$529$	1.54900e13			0.373916
$530$		0			0
$531$	−7.30041e13	+	3.73751e13i	−1.72932	+	0.885339i
$532$		0			0
$533$		−	9.50120e13i		−	2.20873i
$534$		0			0
$535$	1.58722e13			0.362134
$536$		0			0
$537$	5.77701e13	+	3.53249e13i	1.29369	+	0.791061i
$538$		0			0
$539$		−	5.97838e12i		−	0.131413i
$540$		0			0
$541$	−6.40927e13			−1.38300			−0.691500	−	0.722377i	$-0.743050\pi$
$541$	−6.40927e13			−1.38300			−0.691500	+	0.722377i	$0.743050\pi$
$542$		0			0
$543$	1.89495e13	−	3.09898e13i	0.401419	−	0.656477i
$544$		0			0
$545$		−	2.11604e13i		−	0.440089i
$546$		0			0
$547$	6.77315e13			1.38310			0.691551	−	0.722327i	$-0.256928\pi$
$547$	6.77315e13			1.38310			0.691551	+	0.722327i	$0.256928\pi$
$548$		0			0
$549$	−8.73491e12	−	1.70618e13i	−0.175145	−	0.342107i
$550$		0			0
$551$		−	1.38633e13i		−	0.272966i
$552$		0			0
$553$	6.61703e13			1.27949
$554$		0			0
$555$	−3.50047e13	−	2.14045e13i	−0.664754	−	0.406480i
$556$		0			0
$557$			4.17173e13i			0.778109i	0.921215	+	0.389054i	$0.127198\pi$
$557$			4.17173e13i			0.778109i	−0.921215	+	0.389054i	$0.872802\pi$
$558$		0			0
$559$	−2.99033e13			−0.547848
$560$		0			0
$561$	−1.03090e13	+	1.68593e13i	−0.185525	+	0.303406i
$562$		0			0
$563$		−	2.15796e13i		−	0.381506i	−0.981638	−	0.190753i	$-0.938907\pi$
$563$		−	2.15796e13i		−	0.381506i	0.981638	−	0.190753i	$-0.0610930\pi$
$564$		0			0
$565$	−9.16017e12			−0.159097
$566$		0			0
$567$	2.63361e13	−	3.65443e13i	0.449404	−	0.623598i
$568$		0			0
$569$		−	3.78967e12i		−	0.0635390i	−0.999495	−	0.0317695i	$-0.989886\pi$
$569$		−	3.78967e12i		−	0.0635390i	0.999495	−	0.0317695i	$-0.0101143\pi$
$570$		0			0
$571$	−5.09794e13			−0.839874			−0.419937	−	0.907553i	$-0.637948\pi$
$571$	−5.09794e13			−0.839874			−0.419937	+	0.907553i	$0.637948\pi$
$572$		0			0
$573$	6.21448e13	+	3.80000e13i	1.00608	+	0.615191i
$574$		0			0
$575$		−	3.54679e13i		−	0.564282i
$576$		0			0
$577$	3.65713e13			0.571823			0.285912	−	0.958256i	$-0.407704\pi$
$577$	3.65713e13			0.571823			0.285912	+	0.958256i	$0.407704\pi$
$578$		0			0
$579$	−2.91919e13	+	4.77402e13i	−0.448611	+	0.733654i
$580$		0			0
$581$			5.36330e13i			0.810124i
$582$		0			0
$583$	2.92885e13			0.434865
$584$		0			0
$585$	−5.36529e13	+	2.74681e13i	−0.783094	+	0.400912i
$586$		0			0
$587$		−	9.13079e13i		−	1.31014i	−0.755568	−	0.655070i	$-0.772639\pi$
$587$		−	9.13079e13i		−	1.31014i	0.755568	−	0.655070i	$-0.227361\pi$
$588$		0			0
$589$	5.44975e13			0.768776
$590$		0			0
$591$	8.80560e12	+	5.38440e12i	0.122130	+	0.0746793i
$592$		0			0
$593$			9.04777e13i			1.23387i	0.787016	+	0.616933i	$0.211625\pi$
$593$			9.04777e13i			1.23387i	−0.787016	+	0.616933i	$0.788375\pi$
$594$		0			0
$595$	3.39942e13			0.455848
$596$		0			0
$597$	−1.67550e13	+	2.74009e13i	−0.220939	+	0.361322i
$598$		0			0
$599$			2.97596e13i			0.385917i	0.981207	+	0.192958i	$0.0618082\pi$
$599$			2.97596e13i			0.385917i	−0.981207	+	0.192958i	$0.938192\pi$
$600$		0			0
$601$	−1.42916e14			−1.82267			−0.911334	−	0.411668i	$-0.864946\pi$
$601$	−1.42916e14			−1.82267			−0.911334	+	0.411668i	$0.864946\pi$
$602$		0			0
$603$	−3.84977e13	−	7.51968e13i	−0.482889	−	0.943219i
$604$		0			0
$605$		−	3.89335e13i		−	0.480337i
$606$		0			0
$607$	−1.50770e14			−1.82967			−0.914835	−	0.403828i	$-0.867680\pi$
$607$	−1.50770e14			−1.82967			−0.914835	+	0.403828i	$0.867680\pi$
$608$		0			0
$609$	−1.65166e13	−	1.00995e13i	−0.197167	−	0.120563i
$610$		0			0
$611$			2.29366e14i			2.69354i
$612$		0			0
$613$	1.41065e13			0.162974			0.0814869	−	0.996674i	$-0.474033\pi$
$613$	1.41065e13			0.162974			0.0814869	+	0.996674i	$0.474033\pi$
$614$		0			0
$615$	3.30533e13	−	5.40552e13i	0.375699	−	0.614415i
$616$		0			0
$617$			6.10903e13i			0.683198i	0.939846	+	0.341599i	$0.110968\pi$
$617$			6.10903e13i			0.683198i	−0.939846	+	0.341599i	$0.889032\pi$
$618$		0			0
$619$	−8.28130e13			−0.911266			−0.455633	−	0.890168i	$-0.650587\pi$
$619$	−8.28130e13			−0.911266			−0.455633	+	0.890168i	$0.650587\pi$
$620$		0			0
$621$	5.52256e12	−	7.28670e13i	0.0597975	−	0.788992i
$622$		0			0
$623$		−	9.42319e13i		−	1.00406i
$624$		0			0
$625$	2.11456e13			0.221728
$626$		0			0
$627$	−2.41065e13	−	1.47405e13i	−0.248769	−	0.152116i
$628$		0			0
$629$			1.58606e14i			1.61089i
$630$		0			0
$631$	−4.71407e13			−0.471247			−0.235624	−	0.971844i	$-0.575713\pi$
$631$	−4.71407e13			−0.471247			−0.235624	+	0.971844i	$0.575713\pi$
$632$		0			0
$633$	4.96484e13	−	8.11946e13i	0.488525	−	0.798930i
$634$		0			0
$635$		−	2.22239e13i		−	0.215254i
$636$		0			0
$637$	−7.04895e13			−0.672089
$638$		0			0
$639$	−4.90166e13	+	2.50945e13i	−0.460086	+	0.235545i
$640$		0			0
$641$		−	1.11826e14i		−	1.03336i	−0.856178	−	0.516681i	$-0.827167\pi$
$641$		−	1.11826e14i		−	1.03336i	0.856178	−	0.516681i	$-0.172833\pi$
$642$		0			0
$643$	1.97100e14			1.79321			0.896606	−	0.442829i	$-0.146025\pi$
$643$	1.97100e14			1.79321			0.896606	+	0.442829i	$0.146025\pi$
$644$		0			0
$645$	−1.70129e13	−	1.04029e13i	−0.152398	−	0.0931874i
$646$		0			0
$647$			2.13218e14i			1.88062i	0.340314	+	0.940312i	$0.389467\pi$
$647$			2.13218e14i			1.88062i	−0.340314	+	0.940312i	$0.610533\pi$
$648$		0			0
$649$	7.18440e13			0.623974
$650$		0			0
$651$	3.97018e13	−	6.49280e13i	0.339551	−	0.555299i
$652$		0			0
$653$		−	1.54717e14i		−	1.30308i	−0.758613	−	0.651541i	$-0.774123\pi$
$653$		−	1.54717e14i		−	1.30308i	0.758613	−	0.651541i	$-0.225877\pi$
$654$		0			0
$655$	6.91940e13			0.573934
$656$		0			0
$657$	−6.32760e13	−	1.23596e14i	−0.516907	−	1.00966i
$658$		0			0
$659$		−	1.66486e13i		−	0.133952i	−0.997755	−	0.0669760i	$-0.978665\pi$
$659$		−	1.66486e13i		−	0.133952i	0.997755	−	0.0669760i	$-0.0213351\pi$
$660$		0			0
$661$	1.38186e14			1.09511			0.547553	−	0.836771i	$-0.315559\pi$
$661$	1.38186e14			1.09511			0.547553	+	0.836771i	$0.315559\pi$
$662$		0			0
$663$	1.98783e14	+	1.21551e14i	1.55171	+	0.948832i
$664$		0			0
$665$			4.86073e13i			0.373760i
$666$		0			0
$667$	−3.14068e13			−0.237900
$668$		0			0
$669$	−1.75689e13	+	2.87320e13i	−0.131103	+	0.214405i
$670$		0			0
$671$			1.67906e13i			0.123439i
$672$		0			0
$673$	1.35116e14			0.978657			0.489328	−	0.872100i	$-0.337242\pi$
$673$	1.35116e14			0.978657			0.489328	+	0.872100i	$0.337242\pi$
$674$		0			0
$675$	9.96448e13	+	7.55205e12i	0.711109	+	0.0538947i
$676$		0			0
$677$			1.65956e14i			1.16694i	0.812134	+	0.583470i	$0.198306\pi$
$677$			1.65956e14i			1.16694i	−0.812134	+	0.583470i	$0.801694\pi$
$678$		0			0
$679$	−9.59398e13			−0.664737
$680$		0			0
$681$	−1.87437e14	−	1.14613e14i	−1.27974	−	0.782526i
$682$		0			0
$683$		−	1.31523e14i		−	0.884910i	−0.896791	−	0.442455i	$-0.854108\pi$
$683$		−	1.31523e14i		−	0.884910i	0.896791	−	0.442455i	$-0.145892\pi$
$684$		0			0
$685$	1.42891e14			0.947438
$686$		0			0
$687$	1.13629e14	−	1.85827e14i	0.742513	−	1.21430i
$688$		0			0
$689$		−	3.45333e14i		−	2.22403i
$690$		0			0
$691$	9.95292e13			0.631772			0.315886	−	0.948797i	$-0.397698\pi$
$691$	9.95292e13			0.631772			0.315886	+	0.948797i	$0.397698\pi$
$692$		0			0
$693$	−3.51235e13	+	1.79818e13i	−0.219752	+	0.112504i
$694$		0			0
$695$			6.67503e13i			0.411651i
$696$		0			0
$697$	−2.44924e14			−1.48891
$698$		0			0
$699$	−8.63971e13	−	5.28296e13i	−0.517742	−	0.316586i
$700$		0			0
$701$			2.04464e14i			1.20789i	0.797028	+	0.603943i	$0.206404\pi$
$701$			2.04464e14i			1.20789i	−0.797028	+	0.603943i	$0.793596\pi$
$702$		0			0
$703$	−2.26786e14			−1.32081
$704$		0			0
$705$	−7.97932e13	+	1.30493e14i	−0.458163	+	0.749277i
$706$		0			0
$707$			7.21751e12i			0.0408592i
$708$		0			0
$709$	−5.99663e13			−0.334716			−0.167358	−	0.985896i	$-0.553523\pi$
$709$	−5.99663e13			−0.334716			−0.167358	+	0.985896i	$0.553523\pi$
$710$		0			0
$711$	1.37829e14	+	2.69218e14i	0.758562	+	1.48169i
$712$		0			0
$713$		−	1.23462e14i		−	0.670018i
$714$		0			0
$715$	5.28003e13			0.282557
$716$		0			0
$717$	−4.52690e12	−	2.76808e12i	−0.0238894	−	0.0146077i
$718$		0			0
$719$			2.65469e13i			0.138156i	0.997611	+	0.0690779i	$0.0220057\pi$
$719$			2.65469e13i			0.138156i	−0.997611	+	0.0690779i	$0.977994\pi$
$720$		0			0
$721$	−5.16281e13			−0.264978
$722$		0			0
$723$	−3.57378e13	+	5.84453e13i	−0.180899	+	0.295841i
$724$		0			0
$725$		−	4.29485e13i		−	0.214416i
$726$		0			0
$727$	−1.72410e13			−0.0848965			−0.0424483	−	0.999099i	$-0.513516\pi$
$727$	−1.72410e13			−0.0848965			−0.0424483	+	0.999099i	$0.513516\pi$
$728$		0			0
$729$	2.03539e14	+	3.10306e13i	0.988577	+	0.150714i
$730$		0			0
$731$			7.70853e13i			0.369304i
$732$		0			0
$733$	1.57140e14			0.742621			0.371310	−	0.928509i	$-0.378909\pi$
$733$	1.57140e14			0.742621			0.371310	+	0.928509i	$0.378909\pi$
$734$		0			0
$735$	−4.01035e13	−	2.45223e13i	−0.186959	−	0.114321i
$736$		0			0
$737$			7.40018e13i			0.340334i
$738$		0			0
$739$	−1.47886e14			−0.670971			−0.335486	−	0.942045i	$-0.608900\pi$
$739$	−1.47886e14			−0.670971			−0.335486	+	0.942045i	$0.608900\pi$
$740$		0			0
$741$	−1.73801e14	+	2.84233e14i	−0.777969	+	1.27228i
$742$		0			0
$743$		−	3.41362e13i		−	0.150755i	−0.997155	−	0.0753774i	$-0.975984\pi$
$743$		−	3.41362e13i		−	0.150755i	0.997155	−	0.0753774i	$-0.0240162\pi$
$744$		0			0
$745$	−1.10378e13			−0.0480951
$746$		0			0
$747$	−2.18209e14	+	1.11714e14i	−0.938145	+	0.480291i
$748$		0			0
$749$		−	1.22513e14i		−	0.519726i
$750$		0			0
$751$	−2.76329e14			−1.15672			−0.578358	−	0.815783i	$-0.696306\pi$
$751$	−2.76329e14			−1.15672			−0.578358	+	0.815783i	$0.696306\pi$
$752$		0			0
$753$	−4.39832e13	−	2.68946e13i	−0.181682	−	0.111094i
$754$		0			0
$755$			2.09999e14i			0.856016i
$756$		0			0
$757$	1.84901e14			0.743808			0.371904	−	0.928271i	$-0.378705\pi$
$757$	1.84901e14			0.743808			0.371904	+	0.928271i	$0.378705\pi$
$758$		0			0
$759$	−3.33942e13	+	5.46126e13i	−0.132575	+	0.216812i
$760$		0			0
$761$		−	6.09364e13i		−	0.238755i	−0.992849	−	0.119378i	$-0.961910\pi$
$761$		−	6.09364e13i		−	0.238755i	0.992849	−	0.119378i	$-0.0380900\pi$
$762$		0			0
$763$	−1.63331e14			−0.631606
$764$		0			0
$765$	7.08077e13	+	1.38307e14i	0.270255	+	0.527884i
$766$		0			0
$767$		−	8.47093e14i		−	3.19120i
$768$		0			0
$769$	−1.38187e14			−0.513850			−0.256925	−	0.966431i	$-0.582709\pi$
$769$	−1.38187e14			−0.513850			−0.256925	+	0.966431i	$0.582709\pi$
$770$		0			0
$771$	1.21517e14	+	7.43043e13i	0.446030	+	0.272736i
$772$		0			0
$773$			9.61124e13i			0.348243i	0.984724	+	0.174121i	$0.0557085\pi$
$773$			9.61124e13i			0.348243i	−0.984724	+	0.174121i	$0.944292\pi$
$774$		0			0
$775$	1.68833e14			0.603879
$776$		0			0
$777$	−1.65215e14	+	2.70191e14i	−0.583371	+	0.954040i
$778$		0			0
$779$		−	3.50209e14i		−	1.22079i
$780$		0			0
$781$	4.82377e13			0.166009
$782$		0			0
$783$	6.68734e12	−	8.82356e13i	0.0227219	−	0.299802i
$784$		0			0
$785$		−	1.60532e14i		−	0.538535i
$786$		0			0
$787$	3.87548e13			0.128367			0.0641833	−	0.997938i	$-0.479556\pi$
$787$	3.87548e13			0.128367			0.0641833	+	0.997938i	$0.479556\pi$
$788$		0			0
$789$	8.94581e13	+	5.47013e13i	0.292573	+	0.178901i
$790$		0			0
$791$			7.07048e13i			0.228332i
$792$		0			0
$793$	1.97974e14			0.631308
$794$		0			0
$795$	1.20136e14	−	1.96470e14i	0.378302	−	0.618672i
$796$		0			0
$797$			4.89299e14i			1.52154i	0.649022	+	0.760770i	$0.275178\pi$
$797$			4.89299e14i			1.52154i	−0.649022	+	0.760770i	$0.724822\pi$
$798$		0			0
$799$	5.91264e14			1.81571
$800$		0			0
$801$	3.83388e14	−	1.96279e14i	1.16272	−	0.595266i
$802$		0			0
$803$			1.21632e14i			0.364308i
$804$		0			0
$805$	1.10118e14			0.325747
$806$		0			0
$807$	−2.99815e14	−	1.83329e14i	−0.875963	−	0.535629i
$808$		0			0
$809$			2.19619e14i			0.633764i	0.948465	+	0.316882i	$0.102636\pi$
$809$			2.19619e14i			0.633764i	−0.948465	+	0.316882i	$0.897364\pi$
$810$		0			0
$811$	1.94199e13			0.0553533			0.0276766	−	0.999617i	$-0.491189\pi$
$811$	1.94199e13			0.0553533			0.0276766	+	0.999617i	$0.491189\pi$
$812$		0			0
$813$	1.87777e14	−	3.07090e14i	0.528677	−	0.864595i
$814$		0			0
$815$		−	5.84079e13i		−	0.162437i
$816$		0			0
$817$	−1.10222e14			−0.302801
$818$		0			0
$819$	2.12019e14	+	4.14132e14i	0.575379	+	1.12388i
$820$		0			0
$821$		−	5.29303e14i		−	1.41902i	−0.704696	−	0.709509i	$-0.748917\pi$
$821$		−	5.29303e14i		−	1.41902i	0.704696	−	0.709509i	$-0.251083\pi$
$822$		0			0
$823$	1.79384e14			0.475098			0.237549	−	0.971376i	$-0.423656\pi$
$823$	1.79384e14			0.475098			0.237549	+	0.971376i	$0.423656\pi$
$824$		0			0
$825$	−7.46821e13	−	4.56662e13i	−0.195410	−	0.119488i
$826$		0			0
$827$		−	4.43305e14i		−	1.14597i	−0.819564	−	0.572987i	$-0.805784\pi$
$827$		−	4.43305e14i		−	1.14597i	0.819564	−	0.572987i	$-0.194216\pi$
$828$		0			0
$829$	−2.71887e14			−0.694410			−0.347205	−	0.937789i	$-0.612869\pi$
$829$	−2.71887e14			−0.694410			−0.347205	+	0.937789i	$0.612869\pi$
$830$		0			0
$831$	1.41970e13	−	2.32176e13i	0.0358254	−	0.0585886i
$832$		0			0
$833$			1.81709e14i			0.453056i
$834$		0			0
$835$	4.10191e12			0.0101054
$836$		0			0
$837$	3.46860e14	+	2.62884e13i	0.844358	+	0.0639936i
$838$		0			0
$839$			4.34596e14i			1.04539i	0.852521	+	0.522693i	$0.175072\pi$
$839$			4.34596e14i			1.04539i	−0.852521	+	0.522693i	$0.824928\pi$
$840$		0			0
$841$	3.82676e14			0.909602
$842$		0			0
$843$	−2.68333e14	−	1.64079e14i	−0.630283	−	0.385402i
$844$		0			0
$845$		−	3.91819e14i		−	0.909499i
$846$		0			0
$847$	−3.00517e14			−0.689369
$848$		0			0
$849$	−6.59472e13	+	1.07849e14i	−0.149506	+	0.244500i
$850$		0			0
$851$			5.13776e14i			1.15114i
$852$		0			0
$853$	−8.28539e14			−1.83471			−0.917356	−	0.398069i	$-0.869681\pi$
$853$	−8.28539e14			−1.83471			−0.917356	+	0.398069i	$0.869681\pi$
$854$		0			0
$855$	−1.97762e14	+	1.01246e14i	−0.432824	+	0.221588i
$856$		0			0
$857$			9.09174e13i			0.196672i	0.995153	+	0.0983361i	$0.0313520\pi$
$857$			9.09174e13i			0.196672i	−0.995153	+	0.0983361i	$0.968648\pi$
$858$		0			0
$859$	−4.89435e14			−1.04648			−0.523238	−	0.852187i	$-0.675276\pi$
$859$	−4.89435e14			−1.04648			−0.523238	+	0.852187i	$0.675276\pi$
$860$		0			0
$861$	−4.17237e14	−	2.55130e14i	−0.881794	−	0.539194i
$862$		0			0
$863$			8.96710e14i			1.87326i	0.350321	+	0.936630i	$0.386073\pi$
$863$			8.96710e14i			1.87326i	−0.350321	+	0.936630i	$0.613927\pi$
$864$		0			0
$865$	−4.54307e14			−0.938142
$866$		0			0
$867$	5.77736e13	−	9.44824e13i	0.117933	−	0.192866i
$868$		0			0
$869$		−	2.64940e14i		−	0.534624i
$870$		0			0
$871$	8.72535e14			1.74057
$872$		0			0
$873$	−1.99836e14	−	3.90337e14i	−0.394097	−	0.769783i
$874$		0			0
$875$			3.61742e14i			0.705275i
$876$		0			0
$877$	−5.74839e13			−0.110802			−0.0554011	−	0.998464i	$-0.517644\pi$
$877$	−5.74839e13			−0.110802			−0.0554011	+	0.998464i	$0.517644\pi$
$878$		0			0
$879$	−5.88646e14	−	3.59942e14i	−1.12179	−	0.685943i
$880$		0			0
$881$			1.83558e14i			0.345854i	0.984935	+	0.172927i	$0.0553225\pi$
$881$			1.83558e14i			0.345854i	−0.984935	+	0.172927i	$0.944677\pi$
$882$		0			0
$883$	6.64761e14			1.23840			0.619202	−	0.785232i	$-0.287456\pi$
$883$	6.64761e14			1.23840			0.619202	+	0.785232i	$0.287456\pi$
$884$		0			0
$885$	2.94692e14	−	4.81936e14i	0.542814	−	0.887714i
$886$		0			0
$887$			6.08142e14i			1.10761i	0.832646	+	0.553805i	$0.186825\pi$
$887$			6.08142e14i			1.10761i	−0.832646	+	0.553805i	$0.813175\pi$
$888$		0			0
$889$	−1.71540e14			−0.308928
$890$		0			0
$891$	−1.46320e14	−	1.05447e14i	−0.260565	−	0.187779i
$892$		0			0
$893$			8.45430e14i			1.48875i
$894$		0			0
$895$	−4.66395e14			−0.812154
$896$		0			0
$897$	6.43922e14	+	3.93742e14i	1.10885	+	0.678030i
$898$		0			0
$899$		−	1.49502e14i		−	0.254594i
$900$		0			0
$901$	−8.90205e14			−1.49922
$902$		0			0
$903$	−8.02974e13	+	1.31318e14i	−0.133740	+	0.218718i
$904$		0			0
$905$			2.50190e14i			0.412123i
$906$		0			0
$907$	6.12741e14			0.998252			0.499126	−	0.866529i	$-0.333654\pi$
$907$	6.12741e14			0.998252			0.499126	+	0.866529i	$0.333654\pi$
$908$		0			0
$909$	−2.93649e13	+	1.50336e13i	−0.0473161	+	0.0242239i
$910$		0			0
$911$		−	1.79609e14i		−	0.286243i	−0.989705	−	0.143122i	$-0.954286\pi$
$911$		−	1.79609e14i		−	0.286243i	0.989705	−	0.143122i	$-0.0457140\pi$
$912$		0			0
$913$	2.14741e14			0.338503
$914$		0			0
$915$	1.12633e14	+	6.88722e13i	0.175614	+	0.107384i
$916$		0			0
$917$		−	5.34089e14i		−	0.823697i
$918$		0			0
$919$	5.43513e14			0.829148			0.414574	−	0.910016i	$-0.363931\pi$
$919$	5.43513e14			0.829148			0.414574	+	0.910016i	$0.363931\pi$
$920$		0			0
$921$	2.01821e14	−	3.30056e14i	0.304556	−	0.498069i
$922$		0			0
$923$		−	5.68757e14i		−	0.849021i
$924$		0			0
$925$	−7.02584e14			−1.03750
$926$		0			0
$927$	−1.07538e14	−	2.10052e14i	−0.157095	−	0.306851i
$928$		0			0
$929$			8.27070e14i			1.19526i	0.801771	+	0.597632i	$0.203892\pi$
$929$			8.27070e14i			1.19526i	−0.801771	+	0.597632i	$0.796108\pi$
$930$		0			0
$931$	−2.59820e14			−0.371471
$932$		0			0
$933$	−1.85335e14	−	1.13327e14i	−0.262149	−	0.160297i
$934$		0			0
$935$		−	1.36110e14i		−	0.190472i
$936$		0			0
$937$	1.02363e15			1.41725			0.708625	−	0.705585i	$-0.249316\pi$
$937$	1.02363e15			1.41725			0.708625	+	0.705585i	$0.249316\pi$
$938$		0			0
$939$	3.31246e14	−	5.41717e14i	0.453756	−	0.742069i
$940$		0			0
$941$		−	1.06687e15i		−	1.44598i	−0.690856	−	0.722992i	$-0.742766\pi$
$941$		−	1.06687e15i		−	1.44598i	0.690856	−	0.722992i	$-0.257234\pi$
$942$		0			0
$943$	−7.93387e14			−1.06396
$944$		0			0
$945$	−2.34471e13	+	3.09370e14i	−0.0311121	+	0.410506i
$946$		0			0
$947$			1.68712e14i			0.221511i	0.993848	+	0.110756i	$0.0353271\pi$
$947$			1.68712e14i			0.221511i	−0.993848	+	0.110756i	$0.964673\pi$
$948$		0			0
$949$	1.43413e15			1.86319
$950$		0			0
$951$	2.01056e14	+	1.22941e14i	0.258473	+	0.158050i
$952$		0			0
$953$		−	1.27096e14i		−	0.161684i	−0.996727	−	0.0808419i	$-0.974239\pi$
$953$		−	1.27096e14i		−	0.161684i	0.996727	−	0.0808419i	$-0.0257609\pi$
$954$		0			0
$955$	−5.01713e14			−0.631595
$956$		0			0
$957$	−4.04374e13	+	6.61311e13i	−0.0503760	+	0.0823845i
$958$		0			0
$959$		−	1.10293e15i		−	1.35974i
$960$		0			0
$961$	−2.31926e14			−0.282965
$962$		0			0
$963$	4.98453e14	−	2.55188e14i	0.601857	−	0.308126i
$964$		0			0
$965$		−	3.85420e14i		−	0.460573i
$966$		0			0
$967$	9.05976e14			1.07148			0.535741	−	0.844383i	$-0.320033\pi$
$967$	9.05976e14			1.07148			0.535741	+	0.844383i	$0.320033\pi$
$968$		0			0
$969$	7.32702e14	+	4.48029e14i	0.857647	+	0.524429i
$970$		0			0
$971$		−	1.01655e14i		−	0.117770i	−0.998265	−	0.0588848i	$-0.981246\pi$
$971$		−	1.01655e14i		−	0.117770i	0.998265	−	0.0588848i	$-0.0187545\pi$
$972$		0			0
$973$	5.15227e14			0.590792
$974$		0			0
$975$	−5.38438e14	+	8.80557e14i	−0.611100	+	0.999388i
$976$		0			0
$977$			8.93599e14i			1.00385i	0.864911	+	0.501926i	$0.167375\pi$
$977$			8.93599e14i			1.00385i	−0.864911	+	0.501926i	$0.832625\pi$
$978$		0			0
$979$	−3.77296e14			−0.419535
$980$		0			0
$981$	−3.40208e14	−	6.64522e14i	−0.374455	−	0.731416i
$982$		0			0
$983$		−	1.85315e14i		−	0.201903i	−0.994891	−	0.100952i	$-0.967811\pi$
$983$		−	1.85315e14i		−	0.201903i	0.994891	−	0.100952i	$-0.0321887\pi$
$984$		0			0
$985$	−7.10902e13			−0.0766705
$986$		0			0
$987$	1.00724e15	+	6.15902e14i	1.07534	+	0.657545i
$988$		0			0
$989$			2.49704e14i			0.263903i
$990$		0			0
$991$	1.26183e15			1.32018			0.660088	−	0.751188i	$-0.270519\pi$
$991$	1.26183e15			1.32018			0.660088	+	0.751188i	$0.270519\pi$
$992$		0			0
$993$	−6.63392e14	+	1.08491e15i	−0.687106	+	1.12369i
$994$		0			0
$995$		−	2.21216e14i		−	0.226830i
$996$		0			0
$997$	8.85043e14			0.898439			0.449220	−	0.893421i	$-0.351702\pi$
$997$	8.85043e14			0.898439			0.449220	+	0.893421i	$0.351702\pi$
$998$		0			0
$999$	−1.44342e15	−	1.09397e14i	−1.45066	−	0.109945i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-126.767 + 207.314i) q^{3} -1673.71i q^{5} -12918.9 q^{7} +(-26909.2 - 52561.2i) q^{9} +O(q^{10})\)	\(q+(-126.767 + 207.314i) q^{3} -1673.71i q^{5} -12918.9 q^{7} +(-26909.2 - 52561.2i) q^{9} +51725.9i q^{11} +609886. q^{13} +(346982. + 212171. i) q^{15} -1.57218e6i q^{17} +2.24801e6 q^{19} +(1.63769e6 - 2.67826e6i) q^{21} -5.09279e6i q^{23} +6.96434e6 q^{25} +(1.43079e7 + 1.08439e6i) q^{27} -6.16692e6i q^{29} +2.42426e7 q^{31} +(-1.07235e7 - 6.55715e6i) q^{33} +2.16224e7i q^{35} -1.00883e8 q^{37} +(-7.73136e7 + 1.26438e8i) q^{39} -1.55786e8i q^{41} -4.90309e7 q^{43} +(-8.79720e7 + 4.50380e7i) q^{45} +3.76080e8i q^{47} -1.15578e8 q^{49} +(3.25934e8 + 1.99300e8i) q^{51} -5.66224e8i q^{53} +8.65740e7 q^{55} +(-2.84973e8 + 4.66043e8i) q^{57} -1.38894e9i q^{59} +3.24607e8 q^{61} +(3.47636e8 + 6.79032e8i) q^{63} -1.02077e9i q^{65} +1.43065e9 q^{67} +(1.05581e9 + 6.45598e8i) q^{69} -9.32563e8i q^{71} +2.35147e9 q^{73} +(-8.82849e8 + 1.44380e9i) q^{75} -6.68241e8i q^{77} -5.12199e9 q^{79} +(-2.03858e9 + 2.82876e9i) q^{81} -4.15152e9i q^{83} -2.63136e9 q^{85} +(1.27849e9 + 7.81763e8i) q^{87} +7.29413e9i q^{89} -7.87904e9 q^{91} +(-3.07316e9 + 5.02582e9i) q^{93} -3.76250e9i q^{95} +7.42633e9 q^{97} +(2.71878e9 - 1.39190e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 22 q^{3} - 5436 q^{7} - 28934 q^{9}+O(q^{10}) \) 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

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