LMFDB - Embedded newform 24.11.e.a.17.5

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			17.5
Root			$-8.61800 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	24.17
Dual form			24.11.e.a.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-27.8503 - 241.399i) q^{3} -5802.43i q^{5} +13554.8 q^{7} +(-57497.7 + 13446.0i) q^{9} +O(q^{10})$	\(q+(-27.8503 - 241.399i) q^{3} -5802.43i q^{5} +13554.8 q^{7} +(-57497.7 + 13446.0i) q^{9} -75531.2i q^{11} +168776. q^{13} +(-1.40070e6 + 161599. i) q^{15} +1.11250e6i q^{17} -3.06013e6 q^{19} +(-377505. - 3.27211e6i) q^{21} -9.92894e6i q^{23} -2.39026e7 q^{25} +(4.84719e6 + 1.35054e7i) q^{27} +2.45882e7i q^{29} -5.62973e6 q^{31} +(-1.82331e7 + 2.10356e6i) q^{33} -7.86507e7i q^{35} +1.33143e8 q^{37} +(-4.70047e6 - 4.07424e7i) q^{39} +7.43102e7i q^{41} +1.78023e8 q^{43} +(7.80197e7 + 3.33626e8i) q^{45} -2.03433e8i q^{47} -9.87428e7 q^{49} +(2.68556e8 - 3.09834e7i) q^{51} -2.79648e8i q^{53} -4.38264e8 q^{55} +(8.52253e7 + 7.38710e8i) q^{57} -6.72037e8i q^{59} -8.46127e8 q^{61} +(-7.79370e8 + 1.82258e8i) q^{63} -9.79314e8i q^{65} +1.62203e8 q^{67} +(-2.39683e9 + 2.76524e8i) q^{69} -9.65442e8i q^{71} +1.62313e9 q^{73} +(6.65693e8 + 5.77005e9i) q^{75} -1.02381e9i q^{77} -3.45342e9 q^{79} +(3.12519e9 - 1.54623e9i) q^{81} -3.33228e9i q^{83} +6.45519e9 q^{85} +(5.93556e9 - 6.84788e8i) q^{87} -6.75131e9i q^{89} +2.28773e9 q^{91} +(1.56789e8 + 1.35901e9i) q^{93} +1.77562e10i q^{95} -6.36953e9 q^{97} +(1.01560e9 + 4.34287e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−27.8503	−	241.399i	−0.114610	−	0.993411i
$3$	−27.8503	−	241.399i	−0.114610	−	0.993411i
$4$		0			0
$5$		−	5802.43i		−	1.85678i	−0.371611	−	0.928389i	$-0.621194\pi$
$5$		−	5802.43i		−	1.85678i	0.371611	−	0.928389i	$-0.378806\pi$
$6$		0			0
$7$	13554.8			0.806497			0.403248	−	0.915091i	$-0.367881\pi$
$7$	13554.8			0.806497			0.403248	+	0.915091i	$0.367881\pi$
$8$		0			0
$9$	−57497.7	+	13446.0i	−0.973729	+	0.227710i
$10$		0			0
$11$		−	75531.2i		−	0.468989i	−0.972117	−	0.234495i	$-0.924656\pi$
$11$		−	75531.2i		−	0.468989i	0.972117	−	0.234495i	$-0.0753435\pi$
$12$		0			0
$13$	168776.			0.454564			0.227282	−	0.973829i	$-0.427016\pi$
$13$	168776.			0.454564			0.227282	+	0.973829i	$0.427016\pi$
$14$		0			0
$15$	−1.40070e6	+	161599.i	−1.84454	+	0.212806i
$16$		0			0
$17$			1.11250e6i			0.783528i	0.920066	+	0.391764i	$0.128135\pi$
$17$			1.11250e6i			0.783528i	−0.920066	+	0.391764i	$0.871865\pi$
$18$		0			0
$19$	−3.06013e6			−1.23587			−0.617933	−	0.786231i	$-0.712030\pi$
$19$	−3.06013e6			−1.23587			−0.617933	+	0.786231i	$0.712030\pi$
$20$		0			0
$21$	−377505.	−	3.27211e6i	−0.0924328	−	0.801182i
$22$		0			0
$23$		−	9.92894e6i		−	1.54264i	−0.636449	−	0.771319i	$-0.719598\pi$
$23$		−	9.92894e6i		−	1.54264i	0.636449	−	0.771319i	$-0.280402\pi$
$24$		0			0
$25$	−2.39026e7			−2.44762
$26$		0			0
$27$	4.84719e6	+	1.35054e7i	0.337809	+	0.941215i
$28$		0			0
$29$			2.45882e7i			1.19877i	0.800460	+	0.599386i	$0.204589\pi$
$29$			2.45882e7i			1.19877i	−0.800460	+	0.599386i	$0.795411\pi$
$30$		0			0
$31$	−5.62973e6			−0.196643			−0.0983216	−	0.995155i	$-0.531347\pi$
$31$	−5.62973e6			−0.196643			−0.0983216	+	0.995155i	$0.531347\pi$
$32$		0			0
$33$	−1.82331e7	+	2.10356e6i	−0.465899	+	0.0537509i
$34$		0			0
$35$		−	7.86507e7i		−	1.49748i
$36$		0			0
$37$	1.33143e8			1.92004			0.960021	−	0.279929i	$-0.0903110\pi$
$37$	1.33143e8			1.92004			0.960021	+	0.279929i	$0.0903110\pi$
$38$		0			0
$39$	−4.70047e6	−	4.07424e7i	−0.0520977	−	0.451569i
$40$		0			0
$41$			7.43102e7i			0.641400i	0.947181	+	0.320700i	$0.103918\pi$
$41$			7.43102e7i			0.641400i	−0.947181	+	0.320700i	$0.896082\pi$
$42$		0			0
$43$	1.78023e8			1.21097			0.605486	−	0.795856i	$-0.292979\pi$
$43$	1.78023e8			1.21097			0.605486	+	0.795856i	$0.292979\pi$
$44$		0			0
$45$	7.80197e7	+	3.33626e8i	0.422807	+	1.80800i
$46$		0			0
$47$		−	2.03433e8i		−	0.887018i	−0.896270	−	0.443509i	$-0.853733\pi$
$47$		−	2.03433e8i		−	0.887018i	0.896270	−	0.443509i	$-0.146267\pi$
$48$		0			0
$49$	−9.87428e7			−0.349563
$50$		0			0
$51$	2.68556e8	−	3.09834e7i	0.778365	−	0.0898003i
$52$		0			0
$53$		−	2.79648e8i		−	0.668701i	−0.942449	−	0.334351i	$-0.891483\pi$
$53$		−	2.79648e8i		−	0.668701i	0.942449	−	0.334351i	$-0.108517\pi$
$54$		0			0
$55$	−4.38264e8			−0.870808
$56$		0			0
$57$	8.52253e7	+	7.38710e8i	0.141643	+	1.22772i
$58$		0			0
$59$		−	6.72037e8i		−	0.940011i	−0.882664	−	0.470005i	$-0.844252\pi$
$59$		−	6.72037e8i		−	0.940011i	0.882664	−	0.470005i	$-0.155748\pi$
$60$		0			0
$61$	−8.46127e8			−1.00181			−0.500906	−	0.865502i	$-0.667000\pi$
$61$	−8.46127e8			−1.00181			−0.500906	+	0.865502i	$0.667000\pi$
$62$		0			0
$63$	−7.79370e8	+	1.82258e8i	−0.785309	+	0.183647i
$64$		0			0
$65$		−	9.79314e8i		−	0.844024i
$66$		0			0
$67$	1.62203e8			0.120140			0.0600698	−	0.998194i	$-0.480868\pi$
$67$	1.62203e8			0.120140			0.0600698	+	0.998194i	$0.480868\pi$
$68$		0			0
$69$	−2.39683e9	+	2.76524e8i	−1.53247	+	0.176802i
$70$		0			0
$71$		−	9.65442e8i		−	0.535100i	−0.963544	−	0.267550i	$-0.913786\pi$
$71$		−	9.65442e8i		−	0.535100i	0.963544	−	0.267550i	$-0.0862140\pi$
$72$		0			0
$73$	1.62313e9			0.782957			0.391478	−	0.920187i	$-0.371964\pi$
$73$	1.62313e9			0.782957			0.391478	+	0.920187i	$0.371964\pi$
$74$		0			0
$75$	6.65693e8	+	5.77005e9i	0.280522	+	2.43149i
$76$		0			0
$77$		−	1.02381e9i		−	0.378238i
$78$		0			0
$79$	−3.45342e9			−1.12231			−0.561157	−	0.827709i	$-0.689644\pi$
$79$	−3.45342e9			−1.12231			−0.561157	+	0.827709i	$0.689644\pi$
$80$		0			0
$81$	3.12519e9	−	1.54623e9i	0.896296	−	0.443456i
$82$		0			0
$83$		−	3.33228e9i		−	0.845962i	−0.906138	−	0.422981i	$-0.860984\pi$
$83$		−	3.33228e9i		−	0.845962i	0.906138	−	0.422981i	$-0.139016\pi$
$84$		0			0
$85$	6.45519e9			1.45484
$86$		0			0
$87$	5.93556e9	−	6.84788e8i	1.19087	−	0.137392i
$88$		0			0
$89$		−	6.75131e9i		−	1.20903i	−0.796593	−	0.604516i	$-0.793366\pi$
$89$		−	6.75131e9i		−	1.20903i	0.796593	−	0.604516i	$-0.206634\pi$
$90$		0			0
$91$	2.28773e9			0.366605
$92$		0			0
$93$	1.56789e8	+	1.35901e9i	0.0225373	+	0.195347i
$94$		0			0
$95$			1.77562e10i			2.29473i
$96$		0			0
$97$	−6.36953e9			−0.741735			−0.370867	−	0.928686i	$-0.620940\pi$
$97$	−6.36953e9			−0.741735			−0.370867	+	0.928686i	$0.620940\pi$
$98$		0			0
$99$	1.01560e9	+	4.34287e9i	0.106794	+	0.456668i
$100$		0			0
$101$		−	9.15770e8i		−	0.0871324i	−0.999051	−	0.0435662i	$-0.986128\pi$
$101$		−	9.15770e8i		−	0.0871324i	0.999051	−	0.0435662i	$-0.0138719\pi$
$102$		0			0
$103$	9.62257e9			0.830051			0.415026	−	0.909810i	$-0.363773\pi$
$103$	9.62257e9			0.830051			0.415026	+	0.909810i	$0.363773\pi$
$104$		0			0
$105$	−1.89862e10	+	2.19044e9i	−1.48762	+	0.171627i
$106$		0			0
$107$		−	1.12129e10i		−	0.799466i	−0.916632	−	0.399733i	$-0.869103\pi$
$107$		−	1.12129e10i		−	0.799466i	0.916632	−	0.399733i	$-0.130897\pi$
$108$		0			0
$109$	1.29020e10			0.838541			0.419270	−	0.907861i	$-0.362286\pi$
$109$	1.29020e10			0.838541			0.419270	+	0.907861i	$0.362286\pi$
$110$		0			0
$111$	−3.70808e9	−	3.21406e10i	−0.220056	−	1.90739i
$112$		0			0
$113$		−	3.96001e9i		−	0.214933i	−0.994209	−	0.107467i	$-0.965726\pi$
$113$		−	3.96001e9i		−	0.214933i	0.994209	−	0.107467i	$-0.0342739\pi$
$114$		0			0
$115$	−5.76120e10			−2.86433
$116$		0			0
$117$	−9.70426e9	+	2.26938e9i	−0.442622	+	0.103509i
$118$		0			0
$119$			1.50797e10i			0.631913i
$120$		0			0
$121$	2.02325e10			0.780049
$122$		0			0
$123$	1.79384e10	−	2.06956e9i	0.637174	−	0.0735110i
$124$		0			0
$125$			8.20285e10i			2.68791i
$126$		0			0
$127$	−2.59488e10			−0.785414			−0.392707	−	0.919664i	$-0.628461\pi$
$127$	−2.59488e10			−0.785414			−0.392707	+	0.919664i	$0.628461\pi$
$128$		0			0
$129$	−4.95800e9	−	4.29746e10i	−0.138790	−	1.20299i
$130$		0			0
$131$		−	2.86988e10i		−	0.743887i	−0.928255	−	0.371943i	$-0.878692\pi$
$131$		−	2.86988e10i		−	0.743887i	0.928255	−	0.371943i	$-0.121308\pi$
$132$		0			0
$133$	−4.14794e10			−0.996722
$134$		0			0
$135$	7.83641e10	−	2.81255e10i	1.74763	−	0.627236i
$136$		0			0
$137$			2.42874e10i			0.503244i	0.967826	+	0.251622i	$0.0809639\pi$
$137$			2.42874e10i			0.503244i	−0.967826	+	0.251622i	$0.919036\pi$
$138$		0			0
$139$	6.99218e10			1.34753			0.673765	−	0.738946i	$-0.264676\pi$
$139$	6.99218e10			1.34753			0.673765	+	0.738946i	$0.264676\pi$
$140$		0			0
$141$	−4.91085e10	+	5.66567e9i	−0.881173	+	0.101661i
$142$		0			0
$143$		−	1.27479e10i		−	0.213186i
$144$		0			0
$145$	1.42671e11			2.22585
$146$		0			0
$147$	2.75002e9	+	2.38364e10i	0.0400635	+	0.347259i
$148$		0			0
$149$			4.24001e10i			0.577345i	0.957428	+	0.288673i	$0.0932139\pi$
$149$			4.24001e10i			0.577345i	−0.957428	+	0.288673i	$0.906786\pi$
$150$		0			0
$151$	1.08822e9			0.0138622			0.00693108	−	0.999976i	$-0.497794\pi$
$151$	1.08822e9			0.0138622			0.00693108	+	0.999976i	$0.497794\pi$
$152$		0			0
$153$	−1.49587e10	−	6.39661e10i	−0.178417	−	0.762944i
$154$		0			0
$155$			3.26661e10i			0.365123i
$156$		0			0
$157$	7.92026e10			0.830312			0.415156	−	0.909750i	$-0.363727\pi$
$157$	7.92026e10			0.830312			0.415156	+	0.909750i	$0.363727\pi$
$158$		0			0
$159$	−6.75066e10	+	7.78827e9i	−0.664295	+	0.0766400i
$160$		0			0
$161$		−	1.34585e11i		−	1.24413i
$162$		0			0
$163$	−1.01444e11			−0.881632			−0.440816	−	0.897598i	$-0.645311\pi$
$163$	−1.01444e11			−0.881632			−0.440816	+	0.897598i	$0.645311\pi$
$164$		0			0
$165$	1.22058e10	+	1.05796e11i	0.0998035	+	0.865070i
$166$		0			0
$167$			1.09882e11i			0.845946i	0.906142	+	0.422973i	$0.139014\pi$
$167$			1.09882e11i			0.845946i	−0.906142	+	0.422973i	$0.860986\pi$
$168$		0			0
$169$	−1.09373e11			−0.793371
$170$		0			0
$171$	1.75950e11	−	4.11466e10i	1.20340	−	0.281419i
$172$		0			0
$173$		−	1.87002e10i		−	0.120674i	−0.998178	−	0.0603372i	$-0.980782\pi$
$173$		−	1.87002e10i		−	0.120674i	0.998178	−	0.0603372i	$-0.0192176\pi$
$174$		0			0
$175$	−3.23994e11			−1.97400
$176$		0			0
$177$	−1.62229e11	+	1.87164e10i	−0.933817	+	0.107735i
$178$		0			0
$179$			1.06101e11i			0.577370i	0.957424	+	0.288685i	$0.0932181\pi$
$179$			1.06101e11i			0.577370i	−0.957424	+	0.288685i	$0.906782\pi$
$180$		0			0
$181$	−8.00379e10			−0.412005			−0.206003	−	0.978551i	$-0.566046\pi$
$181$	−8.00379e10			−0.412005			−0.206003	+	0.978551i	$0.566046\pi$
$182$		0			0
$183$	2.35649e10	+	2.04254e11i	0.114818	+	0.995211i
$184$		0			0
$185$		−	7.72554e11i		−	3.56509i
$186$		0			0
$187$	8.40283e10			0.367466
$188$		0			0
$189$	6.57026e10	+	1.83063e11i	0.272442	+	0.759087i
$190$		0			0
$191$		−	3.48609e11i		−	1.37142i	−0.727873	−	0.685712i	$-0.759491\pi$
$191$		−	3.48609e11i		−	1.37142i	0.727873	−	0.685712i	$-0.240509\pi$
$192$		0			0
$193$	−3.50886e9			−0.0131032			−0.00655162	−	0.999979i	$-0.502085\pi$
$193$	−3.50886e9			−0.0131032			−0.00655162	+	0.999979i	$0.502085\pi$
$194$		0			0
$195$	−2.36405e11	+	2.72742e10i	−0.838463	+	0.0967338i
$196$		0			0
$197$			4.57379e11i			1.54151i	0.637134	+	0.770753i	$0.280120\pi$
$197$			4.57379e11i			1.54151i	−0.637134	+	0.770753i	$0.719880\pi$
$198$		0			0
$199$	1.79850e11			0.576296			0.288148	−	0.957586i	$-0.406960\pi$
$199$	1.79850e11			0.576296			0.288148	+	0.957586i	$0.406960\pi$
$200$		0			0
$201$	−4.51741e9	−	3.91557e10i	−0.0137692	−	0.119348i
$202$		0			0
$203$			3.33288e11i			0.966806i
$204$		0			0
$205$	4.31180e11			1.19094
$206$		0			0
$207$	1.33505e11	+	5.70892e11i	0.351274	+	1.50211i
$208$		0			0
$209$			2.31135e11i			0.579607i
$210$		0			0
$211$	4.17655e11			0.998631			0.499316	−	0.866420i	$-0.333585\pi$
$211$	4.17655e11			0.998631			0.499316	+	0.866420i	$0.333585\pi$
$212$		0			0
$213$	−2.33057e11	+	2.68878e10i	−0.531574	+	0.0613279i
$214$		0			0
$215$		−	1.03297e12i		−	2.24851i
$216$		0			0
$217$	−7.63098e10			−0.158592
$218$		0			0
$219$	−4.52045e10	−	3.91821e11i	−0.0897349	−	0.777798i
$220$		0			0
$221$			1.87764e11i			0.356164i
$222$		0			0
$223$	8.42169e11			1.52713			0.763564	−	0.645733i	$-0.223448\pi$
$223$	8.42169e11			1.52713			0.763564	+	0.645733i	$0.223448\pi$
$224$		0			0
$225$	1.37434e12	−	3.21395e11i	2.38332	−	0.557348i
$226$		0			0
$227$		−	5.83167e11i		−	0.967529i	−0.875198	−	0.483764i	$-0.839269\pi$
$227$		−	5.83167e11i		−	0.967529i	0.875198	−	0.483764i	$-0.160731\pi$
$228$		0			0
$229$	−9.51372e11			−1.51068			−0.755341	−	0.655332i	$-0.772529\pi$
$229$	−9.51372e11			−1.51068			−0.755341	+	0.655332i	$0.772529\pi$
$230$		0			0
$231$	−2.47146e11	+	2.85134e10i	−0.375746	+	0.0433500i
$232$		0			0
$233$			4.14607e11i			0.603749i	0.953348	+	0.301875i	$0.0976124\pi$
$233$			4.14607e11i			0.603749i	−0.953348	+	0.301875i	$0.902388\pi$
$234$		0			0
$235$	−1.18041e12			−1.64700
$236$		0			0
$237$	9.61788e10	+	8.33652e11i	0.128629	+	1.11492i
$238$		0			0
$239$			1.06637e12i			1.36747i	0.729731	+	0.683735i	$0.239645\pi$
$239$			1.06637e12i			1.36747i	−0.729731	+	0.683735i	$0.760355\pi$
$240$		0			0
$241$	1.40854e11			0.173254			0.0866270	−	0.996241i	$-0.472391\pi$
$241$	1.40854e11			0.173254			0.0866270	+	0.996241i	$0.472391\pi$
$242$		0			0
$243$	−4.60296e11	−	7.11354e11i	−0.543258	−	0.839566i
$244$		0			0
$245$			5.72948e11i			0.649060i
$246$		0			0
$247$	−5.16477e11			−0.561780
$248$		0			0
$249$	−8.04408e11	+	9.28049e10i	−0.840388	+	0.0969559i
$250$		0			0
$251$			1.69195e11i			0.169832i	0.996388	+	0.0849160i	$0.0270622\pi$
$251$			1.69195e11i			0.169832i	−0.996388	+	0.0849160i	$0.972938\pi$
$252$		0			0
$253$	−7.49945e11			−0.723480
$254$		0			0
$255$	−1.79779e11	−	1.55827e12i	−0.166739	−	1.44525i
$256$		0			0
$257$		−	7.00335e11i		−	0.624655i	−0.949974	−	0.312328i	$-0.898891\pi$
$257$		−	7.00335e11i		−	0.624655i	0.949974	−	0.312328i	$-0.101109\pi$
$258$		0			0
$259$	1.80473e12			1.54851
$260$		0			0
$261$	−3.30614e11	−	1.41377e12i	−0.272972	−	1.16728i
$262$		0			0
$263$			9.23544e11i			0.733971i	0.930227	+	0.366986i	$0.119610\pi$
$263$			9.23544e11i			0.733971i	−0.930227	+	0.366986i	$0.880390\pi$
$264$		0			0
$265$	−1.62264e12			−1.24163
$266$		0			0
$267$	−1.62976e12	+	1.88026e11i	−1.20107	+	0.138567i
$268$		0			0
$269$			1.49097e11i			0.105854i	0.998598	+	0.0529270i	$0.0168551\pi$
$269$			1.49097e11i			0.105854i	−0.998598	+	0.0529270i	$0.983145\pi$
$270$		0			0
$271$	1.43290e12			0.980321			0.490160	−	0.871632i	$-0.336938\pi$
$271$	1.43290e12			0.980321			0.490160	+	0.871632i	$0.336938\pi$
$272$		0			0
$273$	−6.37139e10	−	5.52255e11i	−0.0420166	−	0.364189i
$274$		0			0
$275$			1.80539e12i			1.14791i
$276$		0			0
$277$	5.47781e11			0.335899			0.167949	−	0.985796i	$-0.446285\pi$
$277$	5.47781e11			0.335899			0.167949	+	0.985796i	$0.446285\pi$
$278$		0			0
$279$	3.23696e11	−	7.56976e10i	0.191477	−	0.0447776i
$280$		0			0
$281$			2.04493e11i			0.116720i	0.998296	+	0.0583601i	$0.0185872\pi$
$281$			2.04493e11i			0.116720i	−0.998296	+	0.0583601i	$0.981413\pi$
$282$		0			0
$283$	5.78598e11			0.318746			0.159373	−	0.987218i	$-0.449053\pi$
$283$	5.78598e11			0.318746			0.159373	+	0.987218i	$0.449053\pi$
$284$		0			0
$285$	4.28631e12	−	4.94514e11i	2.27961	−	0.262999i
$286$		0			0
$287$			1.00726e12i			0.517287i
$288$		0			0
$289$	7.78342e11			0.386084
$290$		0			0
$291$	1.77393e11	+	1.53760e12i	0.0850104	+	0.736847i
$292$		0			0
$293$		−	1.99797e12i		−	0.925233i	−0.886558	−	0.462617i	$-0.846911\pi$
$293$		−	1.99797e12i		−	0.925233i	0.886558	−	0.462617i	$-0.153089\pi$
$294$		0			0
$295$	−3.89944e12			−1.74539
$296$		0			0
$297$	1.02008e12	−	3.66114e11i	0.441419	−	0.158429i
$298$		0			0
$299$		−	1.67577e12i		−	0.701228i
$300$		0			0
$301$	2.41307e12			0.976646
$302$		0			0
$303$	−2.21066e11	+	2.55044e10i	−0.0865582	+	0.00998626i
$304$		0			0
$305$			4.90959e12i			1.86014i
$306$		0			0
$307$	4.11891e12			1.51040			0.755198	−	0.655497i	$-0.227541\pi$
$307$	4.11891e12			1.51040			0.755198	+	0.655497i	$0.227541\pi$
$308$		0			0
$309$	−2.67991e11	−	2.32288e12i	−0.0951323	−	0.824582i
$310$		0			0
$311$			1.12194e12i			0.385628i	0.981235	+	0.192814i	$0.0617614\pi$
$311$			1.12194e12i			0.385628i	−0.981235	+	0.192814i	$0.938239\pi$
$312$		0			0
$313$	−1.83833e12			−0.611931			−0.305966	−	0.952043i	$-0.598979\pi$
$313$	−1.83833e12			−0.611931			−0.305966	+	0.952043i	$0.598979\pi$
$314$		0			0
$315$	1.05754e12	+	4.52224e12i	0.340992	+	1.45814i
$316$		0			0
$317$		−	4.43300e12i		−	1.38485i	−0.721492	−	0.692423i	$-0.756543\pi$
$317$		−	4.43300e12i		−	1.38485i	0.721492	−	0.692423i	$-0.243457\pi$
$318$		0			0
$319$	1.85717e12			0.562211
$320$		0			0
$321$	−2.70679e12	+	3.12283e11i	−0.794198	+	0.0916270i
$322$		0			0
$323$		−	3.40438e12i		−	0.968335i
$324$		0			0
$325$	−4.03419e12			−1.11260
$326$		0			0
$327$	−3.59324e11	−	3.11452e12i	−0.0961053	−	0.833015i
$328$		0			0
$329$		−	2.75749e12i		−	0.715377i
$330$		0			0
$331$	−1.84805e12			−0.465129			−0.232565	−	0.972581i	$-0.574712\pi$
$331$	−1.84805e12			−0.465129			−0.232565	+	0.972581i	$0.574712\pi$
$332$		0			0
$333$	−7.65543e12	+	1.79025e12i	−1.86960	+	0.437213i
$334$		0			0
$335$		−	9.41174e11i		−	0.223072i
$336$		0			0
$337$	4.79911e12			1.10411			0.552053	−	0.833809i	$-0.313844\pi$
$337$	4.79911e12			1.10411			0.552053	+	0.833809i	$0.313844\pi$
$338$		0			0
$339$	−9.55941e11	+	1.10287e11i	−0.213517	+	0.0246336i
$340$		0			0
$341$			4.25220e11i			0.0922235i
$342$		0			0
$343$	−5.16733e12			−1.08842
$344$		0			0
$345$	1.60451e12	+	1.39075e13i	0.328282	+	2.84546i
$346$		0			0
$347$		−	4.81984e12i		−	0.958043i	−0.877803	−	0.479022i	$-0.840992\pi$
$347$		−	4.81984e12i		−	0.958043i	0.877803	−	0.479022i	$-0.159008\pi$
$348$		0			0
$349$	−3.34142e12			−0.645363			−0.322681	−	0.946508i	$-0.604584\pi$
$349$	−3.34142e12			−0.645363			−0.322681	+	0.946508i	$0.604584\pi$
$350$		0			0
$351$	8.18091e11	+	2.27939e12i	0.153556	+	0.427843i
$352$		0			0
$353$			4.44359e12i			0.810700i	0.914162	+	0.405350i	$0.132850\pi$
$353$			4.44359e12i			0.810700i	−0.914162	+	0.405350i	$0.867150\pi$
$354$		0			0
$355$	−5.60191e12			−0.993561
$356$		0			0
$357$	3.64022e12	−	4.19973e11i	0.627749	−	0.0724237i
$358$		0			0
$359$		−	1.66501e11i		−	0.0279219i	−0.999903	−	0.0139610i	$-0.995556\pi$
$359$		−	1.66501e11i		−	0.0279219i	0.999903	−	0.0139610i	$-0.00444406\pi$
$360$		0			0
$361$	3.23330e12			0.527363
$362$		0			0
$363$	−5.63480e11	−	4.88409e12i	−0.0894016	−	0.774909i
$364$		0			0
$365$		−	9.41807e12i		−	1.45378i
$366$		0			0
$367$	−6.53227e12			−0.981146			−0.490573	−	0.871400i	$-0.663213\pi$
$367$	−6.53227e12			−0.981146			−0.490573	+	0.871400i	$0.663213\pi$
$368$		0			0
$369$	−9.99179e11	−	4.27267e12i	−0.146053	−	0.624550i
$370$		0			0
$371$		−	3.79057e12i		−	0.539305i
$372$		0			0
$373$	7.67738e12			1.06333			0.531666	−	0.846954i	$-0.321566\pi$
$373$	7.67738e12			1.06333			0.531666	+	0.846954i	$0.321566\pi$
$374$		0			0
$375$	1.98016e13	−	2.28452e12i	2.67020	−	0.308062i
$376$		0			0
$377$			4.14991e12i			0.544919i
$378$		0			0
$379$	9.65973e12			1.23529			0.617645	−	0.786457i	$-0.288087\pi$
$379$	9.65973e12			1.23529			0.617645	+	0.786457i	$0.288087\pi$
$380$		0			0
$381$	7.22681e11	+	6.26401e12i	0.0900165	+	0.780239i
$382$		0			0
$383$		−	6.63412e12i		−	0.804988i	−0.915423	−	0.402494i	$-0.868143\pi$
$383$		−	6.63412e12i		−	0.804988i	0.915423	−	0.402494i	$-0.131857\pi$
$384$		0			0
$385$	−5.94058e12			−0.702304
$386$		0			0
$387$	−1.02359e13	+	2.39371e12i	−1.17916	+	0.275751i
$388$		0			0
$389$			1.62626e12i			0.182575i	0.995825	+	0.0912876i	$0.0290983\pi$
$389$			1.62626e12i			0.182575i	−0.995825	+	0.0912876i	$0.970902\pi$
$390$		0			0
$391$	1.10459e13			1.20870
$392$		0			0
$393$	−6.92785e12	+	7.99269e11i	−0.738985	+	0.0852570i
$394$		0			0
$395$			2.00382e13i			2.08389i
$396$		0			0
$397$	1.70094e13			1.72479			0.862395	−	0.506236i	$-0.168964\pi$
$397$	1.70094e13			1.72479			0.862395	+	0.506236i	$0.168964\pi$
$398$		0			0
$399$	1.15521e12	+	1.00131e13i	0.114234	+	0.990154i
$400$		0			0
$401$			1.87795e13i			1.81118i	0.424149	+	0.905592i	$0.360573\pi$
$401$			1.87795e13i			1.81118i	−0.424149	+	0.905592i	$0.639427\pi$
$402$		0			0
$403$	−9.50166e11			−0.0893869
$404$		0			0
$405$	−8.97191e12	−	1.81337e13i	−0.823398	−	1.66422i
$406$		0			0
$407$		−	1.00565e13i		−	0.900478i
$408$		0			0
$409$	2.11117e12			0.184462			0.0922311	−	0.995738i	$-0.470600\pi$
$409$	2.11117e12			0.184462			0.0922311	+	0.995738i	$0.470600\pi$
$410$		0			0
$411$	5.86295e12	−	6.76411e11i	0.499928	−	0.0576769i
$412$		0			0
$413$		−	9.10932e12i		−	0.758116i
$414$		0			0
$415$	−1.93353e13			−1.57076
$416$		0			0
$417$	−1.94734e12	−	1.68790e13i	−0.154441	−	1.33865i
$418$		0			0
$419$		−	3.33240e12i		−	0.258040i	−0.991642	−	0.129020i	$-0.958817\pi$
$419$		−	3.33240e12i		−	0.258040i	0.991642	−	0.129020i	$-0.0411831\pi$
$420$		0			0
$421$	1.43061e13			1.08171			0.540856	−	0.841115i	$-0.318100\pi$
$421$	1.43061e13			1.08171			0.540856	+	0.841115i	$0.318100\pi$
$422$		0			0
$423$	2.73537e12	+	1.16969e13i	0.201983	+	0.863715i
$424$		0			0
$425$		−	2.65915e13i		−	1.91778i
$426$		0			0
$427$	−1.14691e13			−0.807959
$428$		0			0
$429$	−3.07732e12	+	3.55032e11i	−0.211781	+	0.0244333i
$430$		0			0
$431$			2.60032e13i			1.74840i	0.485569	+	0.874199i	$0.338613\pi$
$431$			2.60032e13i			1.74840i	−0.485569	+	0.874199i	$0.661387\pi$
$432$		0			0
$433$	−2.18163e13			−1.43332			−0.716659	−	0.697424i	$-0.754329\pi$
$433$	−2.18163e13			−1.43332			−0.716659	+	0.697424i	$0.754329\pi$
$434$		0			0
$435$	−3.97343e12	−	3.44407e13i	−0.255105	−	2.21119i
$436$		0			0
$437$			3.03838e13i			1.90649i
$438$		0			0
$439$	−9.20776e12			−0.564717			−0.282359	−	0.959309i	$-0.591117\pi$
$439$	−9.20776e12			−0.564717			−0.282359	+	0.959309i	$0.591117\pi$
$440$		0			0
$441$	5.67749e12	−	1.32770e12i	0.340379	−	0.0795989i
$442$		0			0
$443$			2.63275e13i			1.54309i	0.636176	+	0.771544i	$0.280515\pi$
$443$			2.63275e13i			1.54309i	−0.636176	+	0.771544i	$0.719485\pi$
$444$		0			0
$445$	−3.91740e13			−2.24490
$446$		0			0
$447$	1.02353e13	−	1.18085e12i	0.573541	−	0.0661697i
$448$		0			0
$449$		−	8.75875e11i		−	0.0479966i	−0.999712	−	0.0239983i	$-0.992360\pi$
$449$		−	8.75875e11i		−	0.0479966i	0.999712	−	0.0239983i	$-0.00763963\pi$
$450$		0			0
$451$	5.61274e12			0.300810
$452$		0			0
$453$	−3.03072e10	−	2.62694e11i	−0.00158875	−	0.0137708i
$454$		0			0
$455$		−	1.32744e13i		−	0.680703i
$456$		0			0
$457$	3.47862e13			1.74512			0.872562	−	0.488503i	$-0.162457\pi$
$457$	3.47862e13			1.74512			0.872562	+	0.488503i	$0.162457\pi$
$458$		0			0
$459$	−1.50247e13	+	5.39249e12i	−0.737468	+	0.264683i
$460$		0			0
$461$		−	1.65995e13i		−	0.797244i	−0.917115	−	0.398622i	$-0.869489\pi$
$461$		−	1.65995e13i		−	0.797244i	0.917115	−	0.398622i	$-0.130511\pi$
$462$		0			0
$463$	−3.42406e13			−1.60930			−0.804648	−	0.593752i	$-0.797646\pi$
$463$	−3.42406e13			−1.60930			−0.804648	+	0.593752i	$0.797646\pi$
$464$		0			0
$465$	7.88555e12	−	9.09760e11i	0.362717	−	0.0418468i
$466$		0			0
$467$			2.33990e13i			1.05345i	0.850036	+	0.526724i	$0.176580\pi$
$467$			2.33990e13i			1.05345i	−0.850036	+	0.526724i	$0.823420\pi$
$468$		0			0
$469$	2.19863e12			0.0968922
$470$		0			0
$471$	−2.20581e12	−	1.91194e13i	−0.0951622	−	0.824840i
$472$		0			0
$473$		−	1.34463e13i		−	0.567933i
$474$		0			0
$475$	7.31448e13			3.02493
$476$		0			0
$477$	3.76016e12	+	1.60791e13i	0.152270	+	0.651134i
$478$		0			0
$479$		−	1.04694e13i		−	0.415186i	−0.978215	−	0.207593i	$-0.933437\pi$
$479$		−	1.04694e13i		−	0.415186i	0.978215	−	0.207593i	$-0.0665630\pi$
$480$		0			0
$481$	2.24715e13			0.872782
$482$		0			0
$483$	−3.24886e13	+	3.74822e12i	−1.23593	+	0.142590i
$484$		0			0
$485$			3.69587e13i			1.37724i
$486$		0			0
$487$	5.06527e12			0.184909			0.0924545	−	0.995717i	$-0.470529\pi$
$487$	5.06527e12			0.184909			0.0924545	+	0.995717i	$0.470529\pi$
$488$		0			0
$489$	2.82524e12	+	2.44884e13i	0.101044	+	0.875822i
$490$		0			0
$491$		−	4.41773e13i		−	1.54808i	−0.633139	−	0.774038i	$-0.718234\pi$
$491$		−	4.41773e13i		−	1.54808i	0.633139	−	0.774038i	$-0.281766\pi$
$492$		0			0
$493$	−2.73543e13			−0.939272
$494$		0			0
$495$	2.51992e13	−	5.89292e12i	0.847931	−	0.198292i
$496$		0			0
$497$		−	1.30864e13i		−	0.431556i
$498$		0			0
$499$	5.73554e13			1.85384			0.926918	−	0.375264i	$-0.122448\pi$
$499$	5.73554e13			1.85384			0.926918	+	0.375264i	$0.122448\pi$
$500$		0			0
$501$	2.65253e13	−	3.06024e12i	0.840372	−	0.0969541i
$502$		0			0
$503$			3.29790e11i			0.0102423i	0.999987	+	0.00512115i	$0.00163012\pi$
$503$			3.29790e11i			0.0102423i	−0.999987	+	0.00512115i	$0.998370\pi$
$504$		0			0
$505$	−5.31369e12			−0.161785
$506$		0			0
$507$	3.04607e12	+	2.64025e13i	0.0909285	+	0.788144i
$508$		0			0
$509$			2.77743e13i			0.812931i	0.913666	+	0.406465i	$0.133239\pi$
$509$			2.77743e13i			0.812931i	−0.913666	+	0.406465i	$0.866761\pi$
$510$		0			0
$511$	2.20011e13			0.631452
$512$		0			0
$513$	−1.48330e13	−	4.13282e13i	−0.417486	−	1.16321i
$514$		0			0
$515$		−	5.58343e13i		−	1.54122i
$516$		0			0
$517$	−1.53655e13			−0.416002
$518$		0			0
$519$	−4.51420e12	+	5.20805e11i	−0.119879	+	0.0138305i
$520$		0			0
$521$			1.40266e13i			0.365397i	0.983169	+	0.182699i	$0.0584832\pi$
$521$			1.40266e13i			0.365397i	−0.983169	+	0.182699i	$0.941517\pi$
$522$		0			0
$523$	−6.59922e13			−1.68649			−0.843246	−	0.537528i	$-0.819358\pi$
$523$	−6.59922e13			−1.68649			−0.843246	+	0.537528i	$0.819358\pi$
$524$		0			0
$525$	9.02333e12	+	7.82118e13i	0.226240	+	1.96099i
$526$		0			0
$527$		−	6.26306e12i		−	0.154075i
$528$		0			0
$529$	−5.71574e13			−1.37973
$530$		0			0
$531$	9.03624e12	+	3.86406e13i	0.214050	+	0.915316i
$532$		0			0
$533$			1.25418e13i			0.291558i
$534$		0			0
$535$	−6.50622e13			−1.48443
$536$		0			0
$537$	2.56127e13	−	2.95494e12i	0.573566	−	0.0661725i
$538$		0			0
$539$			7.45816e12i			0.163941i
$540$		0			0
$541$	3.99428e13			0.861891			0.430945	−	0.902378i	$-0.358180\pi$
$541$	3.99428e13			0.861891			0.430945	+	0.902378i	$0.358180\pi$
$542$		0			0
$543$	2.22908e12	+	1.93211e13i	0.0472200	+	0.409290i
$544$		0			0
$545$		−	7.48629e13i		−	1.55698i
$546$		0			0
$547$	9.47227e12			0.193427			0.0967136	−	0.995312i	$-0.469167\pi$
$547$	9.47227e12			0.193427			0.0967136	+	0.995312i	$0.469167\pi$
$548$		0			0
$549$	4.86504e13	−	1.13771e13i	0.975494	−	0.228123i
$550$		0			0
$551$		−	7.52429e13i		−	1.48152i
$552$		0			0
$553$	−4.68104e13			−0.905143
$554$		0			0
$555$	−1.86494e14	+	2.15159e13i	−3.54160	+	0.408596i
$556$		0			0
$557$			2.28578e13i			0.426342i	0.977015	+	0.213171i	$0.0683791\pi$
$557$			2.28578e13i			0.426342i	−0.977015	+	0.213171i	$0.931621\pi$
$558$		0			0
$559$	3.00461e13			0.550465
$560$		0			0
$561$	−2.34021e12	−	2.02843e13i	−0.0421154	−	0.365045i
$562$		0			0
$563$		−	9.59613e13i		−	1.69650i	−0.529595	−	0.848251i	$-0.677656\pi$
$563$		−	9.59613e13i		−	1.69650i	0.529595	−	0.848251i	$-0.322344\pi$
$564$		0			0
$565$	−2.29777e13			−0.399083
$566$		0			0
$567$	4.23613e13	−	2.09589e13i	0.722860	−	0.357646i
$568$		0			0
$569$		−	9.52826e13i		−	1.59754i	−0.601635	−	0.798771i	$-0.705484\pi$
$569$		−	9.52826e13i		−	1.59754i	0.601635	−	0.798771i	$-0.294516\pi$
$570$		0			0
$571$	1.06283e14			1.75098			0.875490	−	0.483235i	$-0.160538\pi$
$571$	1.06283e14			1.75098			0.875490	+	0.483235i	$0.160538\pi$
$572$		0			0
$573$	−8.41538e13	+	9.70887e12i	−1.36239	+	0.157179i
$574$		0			0
$575$			2.37327e14i			3.77579i
$576$		0			0
$577$	−6.28962e12			−0.0983434			−0.0491717	−	0.998790i	$-0.515658\pi$
$577$	−6.28962e12			−0.0983434			−0.0491717	+	0.998790i	$0.515658\pi$
$578$		0			0
$579$	9.77226e10	+	8.47033e11i	0.00150177	+	0.0130169i
$580$		0			0
$581$		−	4.51684e13i		−	0.682266i
$582$		0			0
$583$	−2.11221e13			−0.313614
$584$		0			0
$585$	1.31679e13	+	5.63083e13i	0.192193	+	0.821851i
$586$		0			0
$587$			1.13706e14i			1.63152i	0.578391	+	0.815759i	$0.303681\pi$
$587$			1.13706e14i			1.63152i	−0.578391	+	0.815759i	$0.696319\pi$
$588$		0			0
$589$	1.72277e13			0.243024
$590$		0			0
$591$	1.10411e14	−	1.27381e13i	1.53135	−	0.176672i
$592$		0			0
$593$			8.46377e13i			1.15423i	0.816665	+	0.577113i	$0.195821\pi$
$593$			8.46377e13i			1.15423i	−0.816665	+	0.577113i	$0.804179\pi$
$594$		0			0
$595$	8.74988e13			1.17332
$596$		0			0
$597$	−5.00888e12	−	4.34157e13i	−0.0660495	−	0.572499i
$598$		0			0
$599$			4.18247e13i			0.542374i	0.962527	+	0.271187i	$0.0874162\pi$
$599$			4.18247e13i			0.542374i	−0.962527	+	0.271187i	$0.912584\pi$
$600$		0			0
$601$	7.04526e12			0.0898513			0.0449257	−	0.998990i	$-0.485695\pi$
$601$	7.04526e12			0.0898513			0.0449257	+	0.998990i	$0.485695\pi$
$602$		0			0
$603$	−9.32633e12	+	2.18100e12i	−0.116983	+	0.0273570i
$604$		0			0
$605$		−	1.17397e14i		−	1.44838i
$606$		0			0
$607$	−1.63194e13			−0.198044			−0.0990221	−	0.995085i	$-0.531571\pi$
$607$	−1.63194e13			−0.198044			−0.0990221	+	0.995085i	$0.531571\pi$
$608$		0			0
$609$	8.04553e13	−	9.28216e12i	0.960435	−	0.110806i
$610$		0			0
$611$		−	3.43347e13i		−	0.403207i
$612$		0			0
$613$	−2.93389e13			−0.338954			−0.169477	−	0.985534i	$-0.554208\pi$
$613$	−2.93389e13			−0.338954			−0.169477	+	0.985534i	$0.554208\pi$
$614$		0			0
$615$	−1.20085e13	−	1.04086e14i	−0.136494	−	1.18309i
$616$		0			0
$617$		−	5.24889e13i		−	0.587005i	−0.955958	−	0.293502i	$-0.905179\pi$
$617$		−	5.24889e13i		−	0.587005i	0.955958	−	0.293502i	$-0.0948208\pi$
$618$		0			0
$619$	−1.14532e14			−1.26030			−0.630152	−	0.776472i	$-0.717007\pi$
$619$	−1.14532e14			−1.26030			−0.630152	+	0.776472i	$0.717007\pi$
$620$		0			0
$621$	1.34094e14	−	4.81274e13i	1.45195	−	0.521116i
$622$		0			0
$623$		−	9.15126e13i		−	0.975081i
$624$		0			0
$625$	2.42541e14			2.54323
$626$		0			0
$627$	5.57957e13	−	6.43717e12i	0.575788	−	0.0664289i
$628$		0			0
$629$			1.48122e14i			1.50441i
$630$		0			0
$631$	−3.29558e13			−0.329446			−0.164723	−	0.986340i	$-0.552673\pi$
$631$	−3.29558e13			−0.329446			−0.164723	+	0.986340i	$0.552673\pi$
$632$		0			0
$633$	−1.16318e13	−	1.00821e14i	−0.114453	−	0.992051i
$634$		0			0
$635$			1.50566e14i			1.45834i
$636$		0			0
$637$	−1.66655e13			−0.158899
$638$		0			0
$639$	1.29814e13	+	5.55107e13i	0.121848	+	0.521042i
$640$		0			0
$641$			1.82367e14i			1.68522i	0.538528	+	0.842608i	$0.318981\pi$
$641$			1.82367e14i			1.68522i	−0.538528	+	0.842608i	$0.681019\pi$
$642$		0			0
$643$	−5.57836e13			−0.507518			−0.253759	−	0.967267i	$-0.581667\pi$
$643$	−5.57836e13			−0.507518			−0.253759	+	0.967267i	$0.581667\pi$
$644$		0			0
$645$	−2.49357e14	+	2.87684e13i	−2.23369	+	0.257702i
$646$		0			0
$647$		−	1.12500e14i		−	0.992276i	−0.868244	−	0.496138i	$-0.834751\pi$
$647$		−	1.12500e14i		−	0.992276i	0.868244	−	0.496138i	$-0.165249\pi$
$648$		0			0
$649$	−5.07597e13			−0.440855
$650$		0			0
$651$	2.12525e12	+	1.84211e13i	0.0181763	+	0.157547i
$652$		0			0
$653$			3.56208e13i			0.300011i	0.988685	+	0.150006i	$0.0479292\pi$
$653$			3.56208e13i			0.300011i	−0.988685	+	0.150006i	$0.952071\pi$
$654$		0			0
$655$	−1.66523e14			−1.38123
$656$		0			0
$657$	−9.33260e13	+	2.18246e13i	−0.762388	+	0.178287i
$658$		0			0
$659$		−	1.04508e14i		−	0.840861i	−0.907325	−	0.420430i	$-0.861879\pi$
$659$		−	1.04508e14i		−	0.840861i	0.907325	−	0.420430i	$-0.138121\pi$
$660$		0			0
$661$	3.32358e13			0.263390			0.131695	−	0.991290i	$-0.457958\pi$
$661$	3.32358e13			0.263390			0.131695	+	0.991290i	$0.457958\pi$
$662$		0			0
$663$	4.53259e13	−	5.22927e12i	0.353817	−	0.0408200i
$664$		0			0
$665$			2.40681e14i			1.85069i
$666$		0			0
$667$	2.44135e14			1.84927
$668$		0			0
$669$	−2.34547e13	−	2.03299e14i	−0.175024	−	1.51706i
$670$		0			0
$671$			6.39090e13i			0.469839i
$672$		0			0
$673$	−2.26496e14			−1.64053			−0.820267	−	0.571981i	$-0.806175\pi$
$673$	−2.26496e14			−1.64053			−0.820267	+	0.571981i	$0.806175\pi$
$674$		0			0
$675$	−1.15860e14	−	3.22814e14i	−0.826828	−	2.30374i
$676$		0			0
$677$		−	1.33273e14i		−	0.937129i	−0.883429	−	0.468564i	$-0.844771\pi$
$677$		−	1.33273e14i		−	0.937129i	0.883429	−	0.468564i	$-0.155229\pi$
$678$		0			0
$679$	−8.63376e13			−0.598207
$680$		0			0
$681$	−1.40776e14	+	1.62414e13i	−0.961153	+	0.110889i
$682$		0			0
$683$			9.92433e13i			0.667725i	0.942622	+	0.333863i	$0.108352\pi$
$683$			9.92433e13i			0.667725i	−0.942622	+	0.333863i	$0.891648\pi$
$684$		0			0
$685$	1.40926e14			0.934412
$686$		0			0
$687$	2.64960e13	+	2.29660e14i	0.173140	+	1.50073i
$688$		0			0
$689$		−	4.71980e13i		−	0.303968i
$690$		0			0
$691$	1.01015e14			0.641204			0.320602	−	0.947214i	$-0.396115\pi$
$691$	1.01015e14			0.641204			0.320602	+	0.947214i	$0.396115\pi$
$692$		0			0
$693$	1.37662e13	+	5.88667e13i	0.0861286	+	0.368302i
$694$		0			0
$695$		−	4.05716e14i		−	2.50206i
$696$		0			0
$697$	−8.26700e13			−0.502555
$698$		0			0
$699$	1.00086e14	−	1.15469e13i	0.599771	−	0.0691958i
$700$		0			0
$701$			1.80568e14i			1.06672i	0.845889	+	0.533360i	$0.179071\pi$
$701$			1.80568e14i			1.06672i	−0.845889	+	0.533360i	$0.820929\pi$
$702$		0			0
$703$	−4.07435e14			−2.37291
$704$		0			0
$705$	3.28747e13	+	2.84949e14i	0.188762	+	1.63614i
$706$		0			0
$707$		−	1.24131e13i		−	0.0702720i
$708$		0			0
$709$	1.62634e14			0.907776			0.453888	−	0.891059i	$-0.350037\pi$
$709$	1.62634e14			0.907776			0.453888	+	0.891059i	$0.350037\pi$
$710$		0			0
$711$	1.98564e14	−	4.64349e13i	1.09283	−	0.255562i
$712$		0			0
$713$			5.58972e13i			0.303349i
$714$		0			0
$715$	−7.39687e13			−0.395838
$716$		0			0
$717$	2.57420e14	−	2.96986e13i	1.35846	−	0.156726i
$718$		0			0
$719$			1.68986e14i			0.879438i	0.898135	+	0.439719i	$0.144922\pi$
$719$			1.68986e14i			0.879438i	−0.898135	+	0.439719i	$0.855078\pi$
$720$		0			0
$721$	1.30432e14			0.669434
$722$		0			0
$723$	−3.92282e12	−	3.40019e13i	−0.0198567	−	0.172112i
$724$		0			0
$725$		−	5.87721e14i		−	2.93414i
$726$		0			0
$727$	3.06554e14			1.50951			0.754754	−	0.656008i	$-0.227756\pi$
$727$	3.06554e14			1.50951			0.754754	+	0.656008i	$0.227756\pi$
$728$		0			0
$729$	−1.58901e14	+	1.30926e14i	−0.771770	+	0.635901i
$730$		0			0
$731$			1.98051e14i			0.948831i
$732$		0			0
$733$	2.64601e13			0.125047			0.0625233	−	0.998044i	$-0.480085\pi$
$733$	2.64601e13			0.125047			0.0625233	+	0.998044i	$0.480085\pi$
$734$		0			0
$735$	1.38309e14	−	1.59568e13i	0.644783	−	0.0743889i
$736$		0			0
$737$		−	1.22514e13i		−	0.0563442i
$738$		0			0
$739$	−1.43782e14			−0.652352			−0.326176	−	0.945309i	$-0.605760\pi$
$739$	−1.43782e14			−0.652352			−0.326176	+	0.945309i	$0.605760\pi$
$740$		0			0
$741$	1.43840e13	+	1.24677e14i	0.0643857	+	0.558078i
$742$		0			0
$743$			7.09223e13i			0.313212i	0.987661	+	0.156606i	$0.0500553\pi$
$743$			7.09223e13i			0.313212i	−0.987661	+	0.156606i	$0.949945\pi$
$744$		0			0
$745$	2.46024e14			1.07200
$746$		0			0
$747$	4.48060e13	+	1.91599e14i	0.192634	+	0.823738i
$748$		0			0
$749$		−	1.51989e14i		−	0.644767i
$750$		0			0
$751$	3.84369e13			0.160897			0.0804486	−	0.996759i	$-0.474365\pi$
$751$	3.84369e13			0.160897			0.0804486	+	0.996759i	$0.474365\pi$
$752$		0			0
$753$	4.08435e13	−	4.71213e12i	0.168713	−	0.0194645i
$754$		0			0
$755$		−	6.31431e12i		−	0.0257390i
$756$		0			0
$757$	−9.91882e13			−0.399007			−0.199504	−	0.979897i	$-0.563933\pi$
$757$	−9.91882e13			−0.399007			−0.199504	+	0.979897i	$0.563933\pi$
$758$		0			0
$759$	2.08862e13	+	1.81036e14i	0.0829182	+	0.718713i
$760$		0			0
$761$			1.75204e14i			0.686470i	0.939249	+	0.343235i	$0.111523\pi$
$761$			1.75204e14i			0.686470i	−0.939249	+	0.343235i	$0.888477\pi$
$762$		0			0
$763$	1.74884e14			0.676281
$764$		0			0
$765$	−3.71159e14	+	8.67968e13i	−1.41662	+	0.331281i
$766$		0			0
$767$		−	1.13424e14i		−	0.427295i
$768$		0			0
$769$	3.86666e14			1.43782			0.718910	−	0.695103i	$-0.244641\pi$
$769$	3.86666e14			1.43782			0.718910	+	0.695103i	$0.244641\pi$
$770$		0			0
$771$	−1.69060e14	+	1.95045e13i	−0.620539	+	0.0715919i
$772$		0			0
$773$		−	1.90846e14i		−	0.691490i	−0.938328	−	0.345745i	$-0.887626\pi$
$773$		−	1.90846e14i		−	0.691490i	0.938328	−	0.345745i	$-0.112374\pi$
$774$		0			0
$775$	1.34565e14			0.481308
$776$		0			0
$777$	−5.02622e13	−	4.35659e14i	−0.177475	−	1.53830i
$778$		0			0
$779$		−	2.27399e14i		−	0.792685i
$780$		0			0
$781$	−7.29210e13			−0.250956
$782$		0			0
$783$	−3.32073e14	+	1.19184e14i	−1.12830	+	0.404956i
$784$		0			0
$785$		−	4.59567e14i		−	1.54170i
$786$		0			0
$787$	−4.67690e14			−1.54912			−0.774560	−	0.632501i	$-0.782028\pi$
$787$	−4.67690e14			−1.54912			−0.774560	+	0.632501i	$0.782028\pi$
$788$		0			0
$789$	2.22942e14	−	2.57210e13i	0.729135	−	0.0841206i
$790$		0			0
$791$		−	5.36771e13i		−	0.173343i
$792$		0			0
$793$	−1.42806e14			−0.455388
$794$		0			0
$795$	4.51909e13	+	3.91702e14i	0.142303	+	1.23345i
$796$		0			0
$797$		−	1.16859e14i		−	0.363388i	−0.983355	−	0.181694i	$-0.941842\pi$
$797$		−	1.16859e14i		−	0.363388i	0.983355	−	0.181694i	$-0.0581581\pi$
$798$		0			0
$799$	2.26319e14			0.695004
$800$		0			0
$801$	9.07784e13	+	3.88185e14i	0.275309	+	1.17727i
$802$		0			0
$803$		−	1.22597e14i		−	0.367198i
$804$		0			0
$805$	−7.80918e14			−2.31008
$806$		0			0
$807$	3.59918e13	−	4.15239e12i	0.105156	−	0.0121319i
$808$		0			0
$809$			2.68008e14i			0.773402i	0.922205	+	0.386701i	$0.126386\pi$
$809$			2.68008e14i			0.773402i	−0.922205	+	0.386701i	$0.873614\pi$
$810$		0			0
$811$	−3.24321e14			−0.924422			−0.462211	−	0.886770i	$-0.652944\pi$
$811$	−3.24321e14			−0.924422			−0.462211	+	0.886770i	$0.652944\pi$
$812$		0			0
$813$	−3.99066e13	−	3.45899e14i	−0.112355	−	0.973861i
$814$		0			0
$815$			5.88620e14i			1.63699i
$816$		0			0
$817$	−5.44773e14			−1.49660
$818$		0			0
$819$	−1.31539e14	+	3.07609e13i	−0.356974	+	0.0834795i
$820$		0			0
$821$			4.36324e14i			1.16975i	0.811123	+	0.584876i	$0.198857\pi$
$821$			4.36324e14i			1.16975i	−0.811123	+	0.584876i	$0.801143\pi$
$822$		0			0
$823$	−1.15987e14			−0.307191			−0.153596	−	0.988134i	$-0.549085\pi$
$823$	−1.15987e14			−0.307191			−0.153596	+	0.988134i	$0.549085\pi$
$824$		0			0
$825$	4.35818e14	−	5.02806e13i	1.14034	−	0.131562i
$826$		0			0
$827$			1.63492e14i			0.422640i	0.977417	+	0.211320i	$0.0677761\pi$
$827$			1.63492e14i			0.422640i	−0.977417	+	0.211320i	$0.932224\pi$
$828$		0			0
$829$	−2.55982e13			−0.0653788			−0.0326894	−	0.999466i	$-0.510407\pi$
$829$	−2.55982e13			−0.0653788			−0.0326894	+	0.999466i	$0.510407\pi$
$830$		0			0
$831$	−1.52559e13	−	1.32234e14i	−0.0384974	−	0.333685i
$832$		0			0
$833$		−	1.09851e14i		−	0.273892i
$834$		0			0
$835$	6.37580e14			1.57073
$836$		0			0
$837$	−2.72883e13	−	7.60317e13i	−0.0664278	−	0.185083i
$838$		0			0
$839$		−	4.12389e14i		−	0.991968i	−0.868332	−	0.495984i	$-0.834807\pi$
$839$		−	4.12389e14i		−	0.991968i	0.868332	−	0.495984i	$-0.165193\pi$
$840$		0			0
$841$	−1.83872e14			−0.437054
$842$		0			0
$843$	4.93643e13	−	5.69518e12i	0.115951	−	0.0133773i
$844$		0			0
$845$			6.34629e14i			1.47311i
$846$		0			0
$847$	2.74247e14			0.629107
$848$		0			0
$849$	−1.61141e13	−	1.39673e14i	−0.0365316	−	0.316646i
$850$		0			0
$851$		−	1.32197e15i		−	2.96193i
$852$		0			0
$853$	7.64373e14			1.69262			0.846311	−	0.532689i	$-0.178818\pi$
$853$	7.64373e14			1.69262			0.846311	+	0.532689i	$0.178818\pi$
$854$		0			0
$855$	−2.38750e14	−	1.02094e15i	−0.522532	−	2.23444i
$856$		0			0
$857$		−	4.35169e13i		−	0.0941357i	−0.998892	−	0.0470678i	$-0.985012\pi$
$857$		−	4.35169e13i		−	0.0941357i	0.998892	−	0.0470678i	$-0.0149877\pi$
$858$		0			0
$859$	−7.80673e13			−0.166918			−0.0834591	−	0.996511i	$-0.526597\pi$
$859$	−7.80673e13			−0.166918			−0.0834591	+	0.996511i	$0.526597\pi$
$860$		0			0
$861$	2.43151e14	−	2.80525e13i	0.513879	−	0.0592864i
$862$		0			0
$863$			7.35863e14i			1.53724i	0.639703	+	0.768622i	$0.279057\pi$
$863$			7.35863e14i			1.53724i	−0.639703	+	0.768622i	$0.720943\pi$
$864$		0			0
$865$	−1.08506e14			−0.224065
$866$		0			0
$867$	−2.16770e13	−	1.87891e14i	−0.0442491	−	0.383539i
$868$		0			0
$869$			2.60841e14i			0.526353i
$870$		0			0
$871$	2.73761e13			0.0546112
$872$		0			0
$873$	3.66233e14	−	8.56450e13i	0.722249	−	0.168900i
$874$		0			0
$875$			1.11188e15i			2.16779i
$876$		0			0
$877$	9.76225e14			1.88171			0.940854	−	0.338813i	$-0.110025\pi$
$877$	9.76225e14			1.88171			0.940854	+	0.338813i	$0.110025\pi$
$878$		0			0
$879$	−4.82308e14	+	5.56441e13i	−0.919137	+	0.106041i
$880$		0			0
$881$		−	2.34624e14i		−	0.442073i	−0.975266	−	0.221036i	$-0.929056\pi$
$881$		−	2.34624e14i		−	0.442073i	0.975266	−	0.221036i	$-0.0709439\pi$
$882$		0			0
$883$	5.46354e14			1.01782			0.508909	−	0.860820i	$-0.330049\pi$
$883$	5.46354e14			1.01782			0.508909	+	0.860820i	$0.330049\pi$
$884$		0			0
$885$	1.08601e14	+	9.41321e14i	0.200040	+	1.73389i
$886$		0			0
$887$			3.88094e14i			0.706837i	0.935465	+	0.353418i	$0.114981\pi$
$887$			3.88094e14i			0.706837i	−0.935465	+	0.353418i	$0.885019\pi$
$888$		0			0
$889$	−3.51731e14			−0.633434
$890$		0			0
$891$	−1.16789e14	−	2.36049e14i	−0.207976	−	0.420353i
$892$		0			0
$893$			6.22531e14i			1.09624i
$894$		0			0
$895$	6.15644e14			1.07205
$896$		0			0
$897$	−4.04529e14	+	4.66707e13i	−0.696607	+	0.0803678i
$898$		0			0
$899$		−	1.38425e14i		−	0.235730i
$900$		0			0
$901$	3.11108e14			0.523946
$902$		0			0
$903$	−6.72046e13	−	5.82512e14i	−0.111934	−	0.970210i
$904$		0			0
$905$			4.64414e14i			0.765002i
$906$		0			0
$907$	−3.16289e13			−0.0515286			−0.0257643	−	0.999668i	$-0.508202\pi$
$907$	−3.16289e13			−0.0515286			−0.0257643	+	0.999668i	$0.508202\pi$
$908$		0			0
$909$	1.23135e13	+	5.26547e13i	0.0198409	+	0.0848433i
$910$		0			0
$911$		−	4.61691e14i		−	0.735799i	−0.929866	−	0.367899i	$-0.880077\pi$
$911$		−	4.61691e14i		−	0.735799i	0.929866	−	0.367899i	$-0.119923\pi$
$912$		0			0
$913$	−2.51691e14			−0.396747
$914$		0			0
$915$	1.18517e15	−	1.36734e14i	1.84789	−	0.213191i
$916$		0			0
$917$		−	3.89006e14i		−	0.599942i
$918$		0			0
$919$	−2.34832e14			−0.358245			−0.179123	−	0.983827i	$-0.557326\pi$
$919$	−2.34832e14			−0.358245			−0.179123	+	0.983827i	$0.557326\pi$
$920$		0			0
$921$	−1.14713e14	−	9.94300e14i	−0.173107	−	1.50044i
$922$		0			0
$923$		−	1.62944e14i		−	0.243237i
$924$		0			0
$925$	−3.18246e15			−4.69953
$926$		0			0
$927$	−5.53276e14	+	1.29385e14i	−0.808245	+	0.189011i
$928$		0			0
$929$		−	9.97961e14i		−	1.44223i	−0.692815	−	0.721116i	$-0.743630\pi$
$929$		−	9.97961e14i		−	1.44223i	0.692815	−	0.721116i	$-0.256370\pi$
$930$		0			0
$931$	3.02165e14			0.432013
$932$		0			0
$933$	2.70835e14	−	3.12464e13i	0.383087	−	0.0441969i
$934$		0			0
$935$		−	4.87568e14i		−	0.682303i
$936$		0			0
$937$	7.06091e14			0.977603			0.488802	−	0.872395i	$-0.337434\pi$
$937$	7.06091e14			0.977603			0.488802	+	0.872395i	$0.337434\pi$
$938$		0			0
$939$	5.11981e13	+	4.43771e14i	0.0701336	+	0.607899i
$940$		0			0
$941$			1.34662e15i			1.82514i	0.408917	+	0.912572i	$0.365907\pi$
$941$			1.34662e15i			1.82514i	−0.408917	+	0.912572i	$0.634093\pi$
$942$		0			0
$943$	7.37822e14			0.989448
$944$		0			0
$945$	1.06221e15	−	3.81235e14i	1.40945	−	0.505864i
$946$		0			0
$947$			1.27023e15i			1.66775i	0.551952	+	0.833876i	$0.313883\pi$
$947$			1.27023e15i			1.66775i	−0.551952	+	0.833876i	$0.686117\pi$
$948$		0			0
$949$	2.73945e14			0.355904
$950$		0			0
$951$	−1.07012e15	+	1.23460e14i	−1.37572	+	0.158717i
$952$		0			0
$953$		−	8.40169e14i		−	1.06881i	−0.845227	−	0.534407i	$-0.820535\pi$
$953$		−	8.40169e14i		−	1.06881i	0.845227	−	0.534407i	$-0.179465\pi$
$954$		0			0
$955$	−2.02278e15			−2.54643
$956$		0			0
$957$	−5.17228e13	−	4.48320e14i	−0.0644351	−	0.558506i
$958$		0			0
$959$			3.29211e14i			0.405865i
$960$		0			0
$961$	−7.87934e14			−0.961331
$962$		0			0
$963$	1.50770e14	+	6.44718e14i	0.182046	+	0.778463i
$964$		0			0
$965$			2.03599e13i			0.0243298i
$966$		0			0
$967$	−1.27345e15			−1.50609			−0.753044	−	0.657970i	$-0.771416\pi$
$967$	−1.27345e15			−1.50609			−0.753044	+	0.657970i	$0.771416\pi$
$968$		0			0
$969$	−8.21814e14	+	9.48130e13i	−0.961955	+	0.110981i
$970$		0			0
$971$		−	9.81893e14i		−	1.13754i	−0.822495	−	0.568772i	$-0.807419\pi$
$971$		−	9.81893e14i		−	1.13754i	0.822495	−	0.568772i	$-0.192581\pi$
$972$		0			0
$973$	9.47775e14			1.08678
$974$		0			0
$975$	1.12353e14	+	9.73848e14i	0.127515	+	1.10527i
$976$		0			0
$977$			4.60114e14i			0.516883i	0.966027	+	0.258442i	$0.0832089\pi$
$977$			4.60114e14i			0.516883i	−0.966027	+	0.258442i	$0.916791\pi$
$978$		0			0
$979$	−5.09934e14			−0.567023
$980$		0			0
$981$	−7.41835e14	+	1.73481e14i	−0.816512	+	0.190944i
$982$		0			0
$983$		−	6.41354e14i		−	0.698763i	−0.936980	−	0.349382i	$-0.886392\pi$
$983$		−	6.41354e14i		−	0.698763i	0.936980	−	0.349382i	$-0.113608\pi$
$984$		0			0
$985$	2.65391e15			2.86223
$986$		0			0
$987$	−6.65656e14	+	7.67970e13i	−0.710663	+	0.0819896i
$988$		0			0
$989$		−	1.76758e15i		−	1.86809i
$990$		0			0
$991$	8.54702e14			0.894224			0.447112	−	0.894478i	$-0.352453\pi$
$991$	8.54702e14			0.894224			0.447112	+	0.894478i	$0.352453\pi$
$992$		0			0
$993$	5.14687e13	+	4.46117e14i	0.0533086	+	0.462064i
$994$		0			0
$995$		−	1.04357e15i		−	1.07005i
$996$		0			0
$997$	−1.69409e14			−0.171974			−0.0859868	−	0.996296i	$-0.527404\pi$
$997$	−1.69409e14			−0.171974			−0.0859868	+	0.996296i	$0.527404\pi$
$998$		0			0
$999$	6.45370e14	+	1.79815e15i	0.648607	+	1.80717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.11.e.a.17.5	✓	10
3.2	odd	2	inner	24.11.e.a.17.6	yes	10
4.3	odd	2		48.11.e.e.17.6		10
8.3	odd	2		192.11.e.i.65.5		10
8.5	even	2		192.11.e.j.65.6		10
12.11	even	2		48.11.e.e.17.5		10
24.5	odd	2		192.11.e.j.65.5		10
24.11	even	2		192.11.e.i.65.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.11.e.a.17.5	✓	10	1.1	even	1	trivial
24.11.e.a.17.6	yes	10	3.2	odd	2	inner
48.11.e.e.17.5		10	12.11	even	2
48.11.e.e.17.6		10	4.3	odd	2
192.11.e.i.65.5		10	8.3	odd	2
192.11.e.i.65.6		10	24.11	even	2
192.11.e.j.65.5		10	24.5	odd	2
192.11.e.j.65.6		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)

\(f(q)\)	\(=\)	\(q+(-27.8503 - 241.399i) q^{3} -5802.43i q^{5} +13554.8 q^{7} +(-57497.7 + 13446.0i) q^{9} +O(q^{10})\)	\(q+(-27.8503 - 241.399i) q^{3} -5802.43i q^{5} +13554.8 q^{7} +(-57497.7 + 13446.0i) q^{9} -75531.2i q^{11} +168776. q^{13} +(-1.40070e6 + 161599. i) q^{15} +1.11250e6i q^{17} -3.06013e6 q^{19} +(-377505. - 3.27211e6i) q^{21} -9.92894e6i q^{23} -2.39026e7 q^{25} +(4.84719e6 + 1.35054e7i) q^{27} +2.45882e7i q^{29} -5.62973e6 q^{31} +(-1.82331e7 + 2.10356e6i) q^{33} -7.86507e7i q^{35} +1.33143e8 q^{37} +(-4.70047e6 - 4.07424e7i) q^{39} +7.43102e7i q^{41} +1.78023e8 q^{43} +(7.80197e7 + 3.33626e8i) q^{45} -2.03433e8i q^{47} -9.87428e7 q^{49} +(2.68556e8 - 3.09834e7i) q^{51} -2.79648e8i q^{53} -4.38264e8 q^{55} +(8.52253e7 + 7.38710e8i) q^{57} -6.72037e8i q^{59} -8.46127e8 q^{61} +(-7.79370e8 + 1.82258e8i) q^{63} -9.79314e8i q^{65} +1.62203e8 q^{67} +(-2.39683e9 + 2.76524e8i) q^{69} -9.65442e8i q^{71} +1.62313e9 q^{73} +(6.65693e8 + 5.77005e9i) q^{75} -1.02381e9i q^{77} -3.45342e9 q^{79} +(3.12519e9 - 1.54623e9i) q^{81} -3.33228e9i q^{83} +6.45519e9 q^{85} +(5.93556e9 - 6.84788e8i) q^{87} -6.75131e9i q^{89} +2.28773e9 q^{91} +(1.56789e8 + 1.35901e9i) q^{93} +1.77562e10i q^{95} -6.36953e9 q^{97} +(1.01560e9 + 4.34287e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 22 q^{3} - 5436 q^{7} - 28934 q^{9}+O(q^{10}) \) 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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