LMFDB - Embedded newform 24.11.e.a.17.10

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			17.10
Root			$14.5165 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	24.17
Dual form			24.11.e.a.17.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(202.837 + 133.814i) q^{3} +265.153i q^{5} +17613.7 q^{7} +(23236.7 + 54284.8i) q^{9} +O(q^{10})$	\(q+(202.837 + 133.814i) q^{3} +265.153i q^{5} +17613.7 q^{7} +(23236.7 + 54284.8i) q^{9} -32032.5i q^{11} -91137.3 q^{13} +(-35481.1 + 53782.8i) q^{15} +2.04721e6i q^{17} +2.78892e6 q^{19} +(3.57271e6 + 2.35695e6i) q^{21} +9.08885e6i q^{23} +9.69532e6 q^{25} +(-2.55079e6 + 1.41204e7i) q^{27} -1.14961e7i q^{29} -2.46721e7 q^{31} +(4.28639e6 - 6.49737e6i) q^{33} +4.67032e6i q^{35} +5.71187e7 q^{37} +(-1.84860e7 - 1.21954e7i) q^{39} -1.65218e8i q^{41} -2.32317e8 q^{43} +(-1.43938e7 + 6.16129e6i) q^{45} -3.07360e8i q^{47} +2.77665e7 q^{49} +(-2.73944e8 + 4.15249e8i) q^{51} -5.26036e8i q^{53} +8.49350e6 q^{55} +(5.65697e8 + 3.73196e8i) q^{57} +8.42358e8i q^{59} +1.05677e9 q^{61} +(4.09284e8 + 9.56155e8i) q^{63} -2.41653e7i q^{65} +5.01986e7 q^{67} +(-1.21621e9 + 1.84355e9i) q^{69} -2.68594e9i q^{71} -1.27936e9 q^{73} +(1.96657e9 + 1.29737e9i) q^{75} -5.64210e8i q^{77} +7.20112e8 q^{79} +(-2.40689e9 + 2.52280e9i) q^{81} -5.92964e9i q^{83} -5.42823e8 q^{85} +(1.53834e9 - 2.33183e9i) q^{87} -3.18929e9i q^{89} -1.60526e9 q^{91} +(-5.00442e9 - 3.30147e9i) q^{93} +7.39491e8i q^{95} -7.26620e9 q^{97} +(1.73888e9 - 7.44330e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	202.837	+	133.814i	0.834720	+	0.550674i
$3$	202.837	+	133.814i	0.834720	+	0.550674i
$4$		0			0
$5$			265.153i			0.0848489i	0.999100	+	0.0424245i	$0.0135082\pi$
$5$			265.153i			0.0848489i	−0.999100	+	0.0424245i	$0.986492\pi$
$6$		0			0
$7$	17613.7			1.04800			0.523998	−	0.851719i	$-0.324440\pi$
$7$	17613.7			1.04800			0.523998	+	0.851719i	$0.324440\pi$
$8$		0			0
$9$	23236.7	+	54284.8i	0.393516	+	0.919318i
$10$		0			0
$11$		−	32032.5i		−	0.198896i	−0.995043	−	0.0994482i	$-0.968292\pi$
$11$		−	32032.5i		−	0.198896i	0.995043	−	0.0994482i	$-0.0317078\pi$
$12$		0			0
$13$	−91137.3			−0.245459			−0.122730	−	0.992440i	$-0.539165\pi$
$13$	−91137.3			−0.245459			−0.122730	+	0.992440i	$0.539165\pi$
$14$		0			0
$15$	−35481.1	+	53782.8i	−0.0467241	+	0.0708251i
$16$		0			0
$17$			2.04721e6i			1.44184i	0.693018	+	0.720920i	$0.256280\pi$
$17$			2.04721e6i			1.44184i	−0.693018	+	0.720920i	$0.743720\pi$
$18$		0			0
$19$	2.78892e6			1.12634			0.563169	−	0.826342i	$-0.309582\pi$
$19$	2.78892e6			1.12634			0.563169	+	0.826342i	$0.309582\pi$
$20$		0			0
$21$	3.57271e6	+	2.35695e6i	0.874784	+	0.577105i
$22$		0			0
$23$			9.08885e6i			1.41211i	0.708155	+	0.706057i	$0.249528\pi$
$23$			9.08885e6i			1.41211i	−0.708155	+	0.706057i	$0.750472\pi$
$24$		0			0
$25$	9.69532e6			0.992801
$26$		0			0
$27$	−2.55079e6	+	1.41204e7i	−0.177769	+	0.984072i
$28$		0			0
$29$		−	1.14961e7i		−	0.560480i	−0.959930	−	0.280240i	$-0.909586\pi$
$29$		−	1.14961e7i		−	0.560480i	0.959930	−	0.280240i	$-0.0904140\pi$
$30$		0			0
$31$	−2.46721e7			−0.861783			−0.430891	−	0.902404i	$-0.641801\pi$
$31$	−2.46721e7			−0.861783			−0.430891	+	0.902404i	$0.641801\pi$
$32$		0			0
$33$	4.28639e6	−	6.49737e6i	0.109527	−	0.166023i
$34$		0			0
$35$			4.67032e6i			0.0889214i
$36$		0			0
$37$	5.71187e7			0.823701			0.411851	−	0.911251i	$-0.364883\pi$
$37$	5.71187e7			0.823701			0.411851	+	0.911251i	$0.364883\pi$
$38$		0			0
$39$	−1.84860e7	−	1.21954e7i	−0.204890	−	0.135168i
$40$		0			0
$41$		−	1.65218e8i		−	1.42606i	−0.701133	−	0.713031i	$-0.747322\pi$
$41$		−	1.65218e8i		−	1.42606i	0.701133	−	0.713031i	$-0.252678\pi$
$42$		0			0
$43$	−2.32317e8			−1.58029			−0.790147	−	0.612917i	$-0.789996\pi$
$43$	−2.32317e8			−1.58029			−0.790147	+	0.612917i	$0.789996\pi$
$44$		0			0
$45$	−1.43938e7	+	6.16129e6i	−0.0780031	+	0.0333894i
$46$		0			0
$47$		−	3.07360e8i		−	1.34017i	−0.742287	−	0.670083i	$-0.766259\pi$
$47$		−	3.07360e8i		−	1.34017i	0.742287	−	0.670083i	$-0.233741\pi$
$48$		0			0
$49$	2.77665e7			0.0982971
$50$		0			0
$51$	−2.73944e8	+	4.15249e8i	−0.793984	+	1.20353i
$52$		0			0
$53$		−	5.26036e8i		−	1.25787i	−0.777458	−	0.628935i	$-0.783491\pi$
$53$		−	5.26036e8i		−	1.25787i	0.777458	−	0.628935i	$-0.216509\pi$
$54$		0			0
$55$	8.49350e6			0.0168761
$56$		0			0
$57$	5.65697e8	+	3.73196e8i	0.940177	+	0.620245i
$58$		0			0
$59$			8.42358e8i			1.17825i	0.808043	+	0.589124i	$0.200527\pi$
$59$			8.42358e8i			1.17825i	−0.808043	+	0.589124i	$0.799473\pi$
$60$		0			0
$61$	1.05677e9			1.25121			0.625606	−	0.780139i	$-0.284852\pi$
$61$	1.05677e9			1.25121			0.625606	+	0.780139i	$0.284852\pi$
$62$		0			0
$63$	4.09284e8	+	9.56155e8i	0.412404	+	0.963442i
$64$		0			0
$65$		−	2.41653e7i		−	0.0208269i
$66$		0			0
$67$	5.01986e7			0.0371807			0.0185904	−	0.999827i	$-0.494082\pi$
$67$	5.01986e7			0.0371807			0.0185904	+	0.999827i	$0.494082\pi$
$68$		0			0
$69$	−1.21621e9	+	1.84355e9i	−0.777614	+	1.17872i
$70$		0			0
$71$		−	2.68594e9i		−	1.48869i	−0.667796	−	0.744344i	$-0.732762\pi$
$71$		−	2.68594e9i		−	1.48869i	0.667796	−	0.744344i	$-0.267238\pi$
$72$		0			0
$73$	−1.27936e9			−0.617132			−0.308566	−	0.951203i	$-0.599849\pi$
$73$	−1.27936e9			−0.617132			−0.308566	+	0.951203i	$0.599849\pi$
$74$		0			0
$75$	1.96657e9	+	1.29737e9i	0.828711	+	0.546710i
$76$		0			0
$77$		−	5.64210e8i		−	0.208443i
$78$		0			0
$79$	7.20112e8			0.234026			0.117013	−	0.993130i	$-0.462668\pi$
$79$	7.20112e8			0.234026			0.117013	+	0.993130i	$0.462668\pi$
$80$		0			0
$81$	−2.40689e9	+	2.52280e9i	−0.690290	+	0.723533i
$82$		0			0
$83$		−	5.92964e9i		−	1.50535i	−0.658391	−	0.752676i	$-0.728763\pi$
$83$		−	5.92964e9i		−	1.50535i	0.658391	−	0.752676i	$-0.271237\pi$
$84$		0			0
$85$	−5.42823e8			−0.122339
$86$		0			0
$87$	1.53834e9	−	2.33183e9i	0.308642	−	0.467844i
$88$		0			0
$89$		−	3.18929e9i		−	0.571142i	−0.958358	−	0.285571i	$-0.907817\pi$
$89$		−	3.18929e9i		−	0.571142i	0.958358	−	0.285571i	$-0.0921832\pi$
$90$		0			0
$91$	−1.60526e9			−0.257240
$92$		0			0
$93$	−5.00442e9	−	3.30147e9i	−0.719348	−	0.474561i
$94$		0			0
$95$			7.39491e8i			0.0955685i
$96$		0			0
$97$	−7.26620e9			−0.846152			−0.423076	−	0.906094i	$-0.639050\pi$
$97$	−7.26620e9			−0.846152			−0.423076	+	0.906094i	$0.639050\pi$
$98$		0			0
$99$	1.73888e9	−	7.44330e8i	0.182849	−	0.0782689i
$100$		0			0
$101$		−	1.58748e9i		−	0.151043i	−0.997144	−	0.0755216i	$-0.975938\pi$
$101$		−	1.58748e9i		−	0.151043i	0.997144	−	0.0755216i	$-0.0240622\pi$
$102$		0			0
$103$	−3.60275e9			−0.310777			−0.155388	−	0.987853i	$-0.549663\pi$
$103$	−3.60275e9			−0.310777			−0.155388	+	0.987853i	$0.549663\pi$
$104$		0			0
$105$	−6.24953e8	+	9.47314e8i	−0.0489667	+	0.0742245i
$106$		0			0
$107$			4.98827e9i			0.355657i	0.984062	+	0.177828i	$0.0569072\pi$
$107$			4.98827e9i			0.355657i	−0.984062	+	0.177828i	$0.943093\pi$
$108$		0			0
$109$	2.76855e10			1.79937			0.899684	−	0.436541i	$-0.143797\pi$
$109$	2.76855e10			1.79937			0.899684	+	0.436541i	$0.143797\pi$
$110$		0			0
$111$	1.15858e10	+	7.64327e9i	0.687560	+	0.453591i
$112$		0			0
$113$			2.97771e10i			1.61618i	0.589057	+	0.808091i	$0.299499\pi$
$113$			2.97771e10i			1.61618i	−0.589057	+	0.808091i	$0.700501\pi$
$114$		0			0
$115$	−2.40993e9			−0.119816
$116$		0			0
$117$	−2.11773e9	−	4.94737e9i	−0.0965921	−	0.225655i
$118$		0			0
$119$			3.60588e10i			1.51104i
$120$		0			0
$121$	2.49113e10			0.960440
$122$		0			0
$123$	2.21085e10	−	3.35123e10i	0.785295	−	1.19036i
$124$		0			0
$125$			5.16013e9i			0.169087i
$126$		0			0
$127$	−5.91407e10			−1.79006			−0.895031	−	0.446004i	$-0.852847\pi$
$127$	−5.91407e10			−1.79006			−0.895031	+	0.446004i	$0.852847\pi$
$128$		0			0
$129$	−4.71224e10	−	3.10872e10i	−1.31910	−	0.870227i
$130$		0			0
$131$			2.15069e10i			0.557471i	0.960368	+	0.278735i	$0.0899153\pi$
$131$			2.15069e10i			0.557471i	−0.960368	+	0.278735i	$0.910085\pi$
$132$		0			0
$133$	4.91232e10			1.18040
$134$		0			0
$135$	−3.74406e9	−	6.76348e8i	−0.0834975	−	0.0150835i
$136$		0			0
$137$		−	1.48676e10i		−	0.308062i	−0.988066	−	0.154031i	$-0.950774\pi$
$137$		−	1.48676e10i		−	0.308062i	0.988066	−	0.154031i	$-0.0492255\pi$
$138$		0			0
$139$	−5.88102e10			−1.13339			−0.566694	−	0.823928i	$-0.691778\pi$
$139$	−5.88102e10			−1.13339			−0.566694	+	0.823928i	$0.691778\pi$
$140$		0			0
$141$	4.11290e10	−	6.23440e10i	0.737994	−	1.11866i
$142$		0			0
$143$			2.91935e9i			0.0488209i
$144$		0			0
$145$	3.04822e9			0.0475561
$146$		0			0
$147$	5.63207e9	+	3.71554e9i	0.0820506	+	0.0541296i
$148$		0			0
$149$		−	9.39891e10i		−	1.27981i	−0.768453	−	0.639906i	$-0.778973\pi$
$149$		−	9.39891e10i		−	1.27981i	0.768453	−	0.639906i	$-0.221027\pi$
$150$		0			0
$151$	−1.87685e9			−0.0239081			−0.0119541	−	0.999929i	$-0.503805\pi$
$151$	−1.87685e9			−0.0239081			−0.0119541	+	0.999929i	$0.503805\pi$
$152$		0			0
$153$	−1.11132e11	+	4.75704e10i	−1.32551	+	0.567387i
$154$		0			0
$155$		−	6.54188e9i		−	0.0731213i
$156$		0			0
$157$	8.88866e9			0.0931833			0.0465916	−	0.998914i	$-0.485164\pi$
$157$	8.88866e9			0.0931833			0.0465916	+	0.998914i	$0.485164\pi$
$158$		0			0
$159$	7.03908e10	−	1.06700e11i	0.692676	−	1.04997i
$160$		0			0
$161$			1.60088e11i			1.47989i
$162$		0			0
$163$	−2.07571e10			−0.180396			−0.0901982	−	0.995924i	$-0.528750\pi$
$163$	−2.07571e10			−0.180396			−0.0901982	+	0.995924i	$0.528750\pi$
$164$		0			0
$165$	1.72280e9	+	1.13655e9i	0.0140869	+	0.00929326i
$166$		0			0
$167$		−	1.35601e11i		−	1.04395i	−0.852960	−	0.521975i	$-0.825195\pi$
$167$		−	1.35601e11i		−	1.04395i	0.852960	−	0.521975i	$-0.174805\pi$
$168$		0			0
$169$	−1.29552e11			−0.939750
$170$		0			0
$171$	6.48055e10	+	1.51396e11i	0.443232	+	1.03546i
$172$		0			0
$173$			6.88686e10i			0.444417i	0.974999	+	0.222208i	$0.0713266\pi$
$173$			6.88686e10i			0.444417i	−0.974999	+	0.222208i	$0.928673\pi$
$174$		0			0
$175$	1.70770e11			1.04045
$176$		0			0
$177$	−1.12719e11	+	1.70861e11i	−0.648831	+	0.983508i
$178$		0			0
$179$			4.21842e10i			0.229554i	0.993391	+	0.114777i	$0.0366153\pi$
$179$			4.21842e10i			0.229554i	−0.993391	+	0.114777i	$0.963385\pi$
$180$		0			0
$181$	3.61460e11			1.86066			0.930331	−	0.366721i	$-0.119519\pi$
$181$	3.61460e11			1.86066			0.930331	+	0.366721i	$0.119519\pi$
$182$		0			0
$183$	2.14352e11	+	1.41410e11i	1.04441	+	0.689010i
$184$		0			0
$185$			1.51452e10i			0.0698902i
$186$		0			0
$187$	6.55771e10			0.286777
$188$		0			0
$189$	−4.49287e10	+	2.48712e11i	−0.186301	+	1.03130i
$190$		0			0
$191$		−	1.29874e11i		−	0.510922i	−0.966819	−	0.255461i	$-0.917773\pi$
$191$		−	1.29874e11i		−	0.510922i	0.966819	−	0.255461i	$-0.0822272\pi$
$192$		0			0
$193$	−3.40860e11			−1.27289			−0.636443	−	0.771324i	$-0.719595\pi$
$193$	−3.40860e11			−1.27289			−0.636443	+	0.771324i	$0.719595\pi$
$194$		0			0
$195$	3.23365e9	−	4.90162e9i	0.0114689	−	0.0173847i
$196$		0			0
$197$		−	5.07832e11i		−	1.71155i	−0.517350	−	0.855774i	$-0.673081\pi$
$197$		−	5.07832e11i		−	1.71155i	0.517350	−	0.855774i	$-0.326919\pi$
$198$		0			0
$199$	−2.86709e11			−0.918704			−0.459352	−	0.888254i	$-0.651918\pi$
$199$	−2.86709e11			−0.918704			−0.459352	+	0.888254i	$0.651918\pi$
$200$		0			0
$201$	1.01821e10	+	6.71727e9i	0.0310355	+	0.0204745i
$202$		0			0
$203$		−	2.02488e11i		−	0.587381i
$204$		0			0
$205$	4.38080e10			0.121000
$206$		0			0
$207$	−4.93386e11	+	2.11195e11i	−1.29818	+	0.555689i
$208$		0			0
$209$		−	8.93361e10i		−	0.224024i
$210$		0			0
$211$	9.59137e10			0.229334			0.114667	−	0.993404i	$-0.463420\pi$
$211$	9.59137e10			0.229334			0.114667	+	0.993404i	$0.463420\pi$
$212$		0			0
$213$	3.59415e11	−	5.44807e11i	0.819782	−	1.24264i
$214$		0			0
$215$		−	6.15994e10i		−	0.134086i
$216$		0			0
$217$	−4.34567e11			−0.903145
$218$		0			0
$219$	−2.59501e11	−	1.71196e11i	−0.515133	−	0.339839i
$220$		0			0
$221$		−	1.86577e11i		−	0.353913i
$222$		0			0
$223$	4.61392e10			0.0836654			0.0418327	−	0.999125i	$-0.486680\pi$
$223$	4.61392e10			0.0836654			0.0418327	+	0.999125i	$0.486680\pi$
$224$		0			0
$225$	2.25288e11	+	5.26308e11i	0.390683	+	0.912699i
$226$		0			0
$227$		−	3.83757e11i		−	0.636688i	−0.947975	−	0.318344i	$-0.896873\pi$
$227$		−	3.83757e11i		−	0.636688i	0.947975	−	0.318344i	$-0.103127\pi$
$228$		0			0
$229$	4.93640e11			0.783850			0.391925	−	0.919997i	$-0.371809\pi$
$229$	4.93640e11			0.783850			0.391925	+	0.919997i	$0.371809\pi$
$230$		0			0
$231$	7.54990e10	−	1.14443e11i	0.114784	−	0.173991i
$232$		0			0
$233$			9.12174e10i			0.132831i	0.997792	+	0.0664153i	$0.0211562\pi$
$233$			9.12174e10i			0.132831i	−0.997792	+	0.0664153i	$0.978844\pi$
$234$		0			0
$235$	8.14974e10			0.113712
$236$		0			0
$237$	1.46065e11	+	9.63609e10i	0.195346	+	0.128872i
$238$		0			0
$239$			1.13207e12i			1.45173i	0.687839	+	0.725863i	$0.258559\pi$
$239$			1.13207e12i			1.45173i	−0.687839	+	0.725863i	$0.741441\pi$
$240$		0			0
$241$	−2.27807e11			−0.280209			−0.140105	−	0.990137i	$-0.544744\pi$
$241$	−2.27807e11			−0.280209			−0.140105	+	0.990137i	$0.544744\pi$
$242$		0			0
$243$	−8.25793e11	+	1.89642e11i	−0.974630	+	0.223822i
$244$		0			0
$245$			7.36236e9i			0.00834040i
$246$		0			0
$247$	−2.54175e11			−0.276470
$248$		0			0
$249$	7.93468e11	−	1.20275e12i	0.828958	−	1.25655i
$250$		0			0
$251$			1.01242e12i			1.01623i	0.861289	+	0.508115i	$0.169657\pi$
$251$			1.01242e12i			1.01623i	−0.861289	+	0.508115i	$0.830343\pi$
$252$		0			0
$253$	2.91138e11			0.280864
$254$		0			0
$255$	−1.10105e11	−	7.26372e10i	−0.102118	−	0.0673687i
$256$		0			0
$257$			1.40019e12i			1.24888i	0.781073	+	0.624440i	$0.214673\pi$
$257$			1.40019e12i			1.24888i	−0.781073	+	0.624440i	$0.785327\pi$
$258$		0			0
$259$	1.00607e12			0.863236
$260$		0			0
$261$	6.24063e11	−	2.67131e11i	0.515259	−	0.220558i
$262$		0			0
$263$			1.17657e12i			0.935057i	0.883978	+	0.467529i	$0.154856\pi$
$263$			1.17657e12i			0.935057i	−0.883978	+	0.467529i	$0.845144\pi$
$264$		0			0
$265$	1.39480e11			0.106729
$266$		0			0
$267$	4.26771e11	−	6.46906e11i	0.314513	−	0.476744i
$268$		0			0
$269$			1.49503e12i			1.06142i	0.847552	+	0.530712i	$0.178076\pi$
$269$			1.49503e12i			1.06142i	−0.847552	+	0.530712i	$0.821924\pi$
$270$		0			0
$271$	1.46282e12			1.00079			0.500397	−	0.865796i	$-0.333187\pi$
$271$	1.46282e12			1.00079			0.500397	+	0.865796i	$0.333187\pi$
$272$		0			0
$273$	−3.25607e11	−	2.14806e11i	−0.214724	−	0.141656i
$274$		0			0
$275$		−	3.10565e11i		−	0.197464i
$276$		0			0
$277$	−2.42833e12			−1.48905			−0.744525	−	0.667595i	$-0.767324\pi$
$277$	−2.42833e12			−1.48905			−0.744525	+	0.667595i	$0.767324\pi$
$278$		0			0
$279$	−5.73299e11	−	1.33932e12i	−0.339125	−	0.792252i
$280$		0			0
$281$		−	1.11264e12i		−	0.635074i	−0.948246	−	0.317537i	$-0.897144\pi$
$281$		−	1.11264e12i		−	0.635074i	0.948246	−	0.317537i	$-0.102856\pi$
$282$		0			0
$283$	7.72550e11			0.425593			0.212797	−	0.977097i	$-0.431743\pi$
$283$	7.72550e11			0.425593			0.212797	+	0.977097i	$0.431743\pi$
$284$		0			0
$285$	−9.89541e10	+	1.49996e11i	−0.0526271	+	0.0797730i
$286$		0			0
$287$		−	2.91010e12i		−	1.49451i
$288$		0			0
$289$	−2.17506e12			−1.07890
$290$		0			0
$291$	−1.47385e12	−	9.72318e11i	−0.706300	−	0.465954i
$292$		0			0
$293$			2.43385e11i			0.112708i	0.998411	+	0.0563542i	$0.0179476\pi$
$293$			2.43385e11i			0.112708i	−0.998411	+	0.0563542i	$0.982052\pi$
$294$		0			0
$295$	−2.23354e11			−0.0999731
$296$		0			0
$297$	4.52310e11	+	8.17079e10i	0.195728	+	0.0353575i
$298$		0			0
$299$		−	8.28333e11i		−	0.346616i
$300$		0			0
$301$	−4.09195e12			−1.65614
$302$		0			0
$303$	2.12427e11	−	3.21999e11i	0.0831755	−	0.126079i
$304$		0			0
$305$			2.80205e11i			0.106164i
$306$		0			0
$307$	2.26967e12			0.832284			0.416142	−	0.909300i	$-0.363382\pi$
$307$	2.26967e12			0.832284			0.416142	+	0.909300i	$0.363382\pi$
$308$		0			0
$309$	−7.30772e11	−	4.82098e11i	−0.259412	−	0.171137i
$310$		0			0
$311$		−	2.21995e12i		−	0.763028i	−0.924363	−	0.381514i	$-0.875403\pi$
$311$		−	2.21995e12i		−	0.763028i	0.924363	−	0.381514i	$-0.124597\pi$
$312$		0			0
$313$	5.19862e12			1.73048			0.865239	−	0.501359i	$-0.167167\pi$
$313$	5.19862e12			1.73048			0.865239	+	0.501359i	$0.167167\pi$
$314$		0			0
$315$	−2.53527e11	+	1.08523e11i	−0.0817470	+	0.0349920i
$316$		0			0
$317$			1.04125e12i			0.325281i	0.986685	+	0.162640i	$0.0520011\pi$
$317$			1.04125e12i			0.325281i	−0.986685	+	0.162640i	$0.947999\pi$
$318$		0			0
$319$	−3.68248e11			−0.111477
$320$		0			0
$321$	−6.67500e11	+	1.01181e12i	−0.195851	+	0.296874i
$322$		0			0
$323$			5.70950e12i			1.62400i
$324$		0			0
$325$	−8.83605e11			−0.243692
$326$		0			0
$327$	5.61565e12	+	3.70470e12i	1.50197	+	0.990866i
$328$		0			0
$329$		−	5.41374e12i		−	1.40449i
$330$		0			0
$331$	−3.51657e12			−0.885074			−0.442537	−	0.896750i	$-0.645921\pi$
$331$	−3.51657e12			−0.885074			−0.442537	+	0.896750i	$0.645921\pi$
$332$		0			0
$333$	1.32725e12	+	3.10068e12i	0.324140	+	0.757243i
$334$		0			0
$335$			1.33103e10i			0.00315474i
$336$		0			0
$337$	7.68031e12			1.76697			0.883485	−	0.468460i	$-0.155191\pi$
$337$	7.68031e12			1.76697			0.883485	+	0.468460i	$0.155191\pi$
$338$		0			0
$339$	−3.98459e12	+	6.03990e12i	−0.889990	+	1.34906i
$340$		0			0
$341$			7.90308e11i			0.171405i
$342$		0			0
$343$	−4.48636e12			−0.944982
$344$		0			0
$345$	−4.88824e11	−	3.22482e11i	−0.100013	−	0.0659797i
$346$		0			0
$347$		−	4.45731e12i		−	0.885983i	−0.896526	−	0.442992i	$-0.853917\pi$
$347$		−	4.45731e12i		−	0.885983i	0.896526	−	0.442992i	$-0.146083\pi$
$348$		0			0
$349$	2.21699e12			0.428190			0.214095	−	0.976813i	$-0.431320\pi$
$349$	2.21699e12			0.428190			0.214095	+	0.976813i	$0.431320\pi$
$350$		0			0
$351$	2.32472e11	−	1.28689e12i	0.0436349	−	0.241550i
$352$		0			0
$353$		−	3.43394e12i		−	0.626496i	−0.949671	−	0.313248i	$-0.898583\pi$
$353$		−	3.43394e12i		−	0.626496i	0.949671	−	0.313248i	$-0.101417\pi$
$354$		0			0
$355$	7.12184e11			0.126314
$356$		0			0
$357$	−4.82517e12	+	7.31407e12i	−0.832092	+	1.26130i
$358$		0			0
$359$			4.26774e12i			0.715691i	0.933781	+	0.357845i	$0.116488\pi$
$359$			4.26774e12i			0.715691i	−0.933781	+	0.357845i	$0.883512\pi$
$360$		0			0
$361$	1.64703e12			0.268637
$362$		0			0
$363$	5.05294e12	+	3.33348e12i	0.801699	+	0.528890i
$364$		0			0
$365$		−	3.39226e11i		−	0.0523630i
$366$		0			0
$367$	−3.69275e12			−0.554651			−0.277326	−	0.960776i	$-0.589448\pi$
$367$	−3.69275e12			−0.554651			−0.277326	+	0.960776i	$0.589448\pi$
$368$		0			0
$369$	8.96883e12	−	3.83913e12i	1.31100	−	0.561178i
$370$		0			0
$371$		−	9.26542e12i		−	1.31824i
$372$		0			0
$373$	1.38125e12			0.191306			0.0956531	−	0.995415i	$-0.469506\pi$
$373$	1.38125e12			0.191306			0.0956531	+	0.995415i	$0.469506\pi$
$374$		0			0
$375$	−6.90496e11	+	1.04666e12i	−0.0931118	+	0.141140i
$376$		0			0
$377$			1.04772e12i			0.137575i
$378$		0			0
$379$	2.18457e12			0.279364			0.139682	−	0.990196i	$-0.455392\pi$
$379$	2.18457e12			0.279364			0.139682	+	0.990196i	$0.455392\pi$
$380$		0			0
$381$	−1.19959e13	−	7.91385e12i	−1.49420	−	0.985741i
$382$		0			0
$383$			2.13683e12i			0.259284i	0.991561	+	0.129642i	$0.0413828\pi$
$383$			2.13683e12i			0.259284i	−0.991561	+	0.129642i	$0.958617\pi$
$384$		0			0
$385$	1.49602e11			0.0176861
$386$		0			0
$387$	−5.39828e12	−	1.26113e13i	−0.621871	−	1.45279i
$388$		0			0
$389$		−	6.99501e12i		−	0.785309i	−0.919686	−	0.392654i	$-0.871557\pi$
$389$		−	6.99501e12i		−	0.785309i	0.919686	−	0.392654i	$-0.128443\pi$
$390$		0			0
$391$	−1.86067e13			−2.03604
$392$		0			0
$393$	−2.87793e12	+	4.36240e12i	−0.306985	+	0.465332i
$394$		0			0
$395$			1.90940e11i			0.0198569i
$396$		0			0
$397$	−1.18993e11			−0.0120661			−0.00603306	−	0.999982i	$-0.501920\pi$
$397$	−1.18993e11			−0.0120661			−0.00603306	+	0.999982i	$0.501920\pi$
$398$		0			0
$399$	9.96401e12	+	6.57336e12i	0.985302	+	0.650015i
$400$		0			0
$401$		−	1.05537e13i		−	1.01785i	−0.860810	−	0.508926i	$-0.830043\pi$
$401$		−	1.05537e13i		−	1.01785i	0.860810	−	0.508926i	$-0.169957\pi$
$402$		0			0
$403$	2.24855e12			0.211532
$404$		0			0
$405$	−6.68928e11	−	6.38195e11i	−0.0613910	−	0.0585704i
$406$		0			0
$407$		−	1.82965e12i		−	0.163831i
$408$		0			0
$409$	−1.30772e12			−0.114261			−0.0571303	−	0.998367i	$-0.518195\pi$
$409$	−1.30772e12			−0.114261			−0.0571303	+	0.998367i	$0.518195\pi$
$410$		0			0
$411$	1.98949e12	−	3.01570e12i	0.169642	−	0.257145i
$412$		0			0
$413$			1.48370e13i			1.23480i
$414$		0			0
$415$	1.57226e12			0.127728
$416$		0			0
$417$	−1.19289e13	−	7.86961e12i	−0.946062	−	0.624127i
$418$		0			0
$419$			8.40683e12i			0.650972i	0.945547	+	0.325486i	$0.105528\pi$
$419$			8.40683e12i			0.650972i	−0.945547	+	0.325486i	$0.894472\pi$
$420$		0			0
$421$	2.33262e12			0.176374			0.0881869	−	0.996104i	$-0.471893\pi$
$421$	2.33262e12			0.176374			0.0881869	+	0.996104i	$0.471893\pi$
$422$		0			0
$423$	1.66850e13	−	7.14204e12i	1.23204	−	0.527376i
$424$		0			0
$425$			1.98483e13i			1.43146i
$426$		0			0
$427$	1.86136e13			1.31127
$428$		0			0
$429$	−3.90649e11	+	5.92153e11i	−0.0268844	+	0.0407518i
$430$		0			0
$431$			6.78801e12i			0.456411i	0.973613	+	0.228206i	$0.0732858\pi$
$431$			6.78801e12i			0.456411i	−0.973613	+	0.228206i	$0.926714\pi$
$432$		0			0
$433$	1.02617e13			0.674186			0.337093	−	0.941471i	$-0.390556\pi$
$433$	1.02617e13			0.674186			0.337093	+	0.941471i	$0.390556\pi$
$434$		0			0
$435$	6.18292e11	+	4.07894e11i	0.0396961	+	0.0261879i
$436$		0			0
$437$			2.53481e13i			1.59052i
$438$		0			0
$439$	3.19707e12			0.196078			0.0980390	−	0.995183i	$-0.468743\pi$
$439$	3.19707e12			0.196078			0.0980390	+	0.995183i	$0.468743\pi$
$440$		0			0
$441$	6.45202e11	+	1.50730e12i	0.0386815	+	0.0903662i
$442$		0			0
$443$			8.04995e12i			0.471818i	0.971775	+	0.235909i	$0.0758068\pi$
$443$			8.04995e12i			0.471818i	−0.971775	+	0.235909i	$0.924193\pi$
$444$		0			0
$445$	8.45649e11			0.0484608
$446$		0			0
$447$	1.25770e13	−	1.90645e13i	0.704759	−	1.06828i
$448$		0			0
$449$			1.84655e13i			1.01188i	0.862569	+	0.505940i	$0.168854\pi$
$449$			1.84655e13i			1.01188i	−0.862569	+	0.505940i	$0.831146\pi$
$450$		0			0
$451$	−5.29234e12			−0.283638
$452$		0			0
$453$	−3.80695e11	−	2.51149e11i	−0.0199566	−	0.0131656i
$454$		0			0
$455$		−	4.25640e11i		−	0.0218266i
$456$		0			0
$457$	−2.99666e13			−1.50334			−0.751668	−	0.659541i	$-0.770751\pi$
$457$	−2.99666e13			−1.50334			−0.751668	+	0.659541i	$0.770751\pi$
$458$		0			0
$459$	−2.89073e13	−	5.22198e12i	−1.41887	−	0.256314i
$460$		0			0
$461$		−	3.62367e13i		−	1.74038i	−0.492717	−	0.870189i	$-0.663996\pi$
$461$		−	3.62367e13i		−	1.74038i	0.492717	−	0.870189i	$-0.336004\pi$
$462$		0			0
$463$	6.09056e12			0.286255			0.143127	−	0.989704i	$-0.454284\pi$
$463$	6.09056e12			0.286255			0.143127	+	0.989704i	$0.454284\pi$
$464$		0			0
$465$	8.75394e11	−	1.32694e12i	0.0402660	−	0.0610359i
$466$		0			0
$467$			1.41726e13i			0.638064i	0.947744	+	0.319032i	$0.103358\pi$
$467$			1.41726e13i			0.638064i	−0.947744	+	0.319032i	$0.896642\pi$
$468$		0			0
$469$	8.84183e11			0.0389653
$470$		0			0
$471$	1.80295e12	+	1.18943e12i	0.0777820	+	0.0513136i
$472$		0			0
$473$			7.44167e12i			0.314315i
$474$		0			0
$475$	2.70395e13			1.11823
$476$		0			0
$477$	2.85557e13	−	1.22233e13i	1.15638	−	0.494992i
$478$		0			0
$479$		−	3.35462e13i		−	1.33035i	−0.746688	−	0.665175i	$-0.768357\pi$
$479$		−	3.35462e13i		−	1.33035i	0.746688	−	0.665175i	$-0.231643\pi$
$480$		0			0
$481$	−5.20564e12			−0.202185
$482$		0			0
$483$	−2.14220e13	+	3.24718e13i	−0.814937	+	1.23529i
$484$		0			0
$485$		−	1.92665e12i		−	0.0717951i
$486$		0			0
$487$	−4.58960e13			−1.67544			−0.837721	−	0.546098i	$-0.816113\pi$
$487$	−4.58960e13			−1.67544			−0.837721	+	0.546098i	$0.816113\pi$
$488$		0			0
$489$	−4.21030e12	−	2.77758e12i	−0.150581	−	0.0993396i
$490$		0			0
$491$		−	1.91047e13i		−	0.669474i	−0.942312	−	0.334737i	$-0.891353\pi$
$491$		−	1.91047e13i		−	0.669474i	0.942312	−	0.334737i	$-0.108647\pi$
$492$		0			0
$493$	2.35349e13			0.808122
$494$		0			0
$495$	1.97361e11	+	4.61068e11i	0.00664103	+	0.0155145i
$496$		0			0
$497$		−	4.73092e13i		−	1.56014i
$498$		0			0
$499$	−1.15091e13			−0.371997			−0.185999	−	0.982550i	$-0.559552\pi$
$499$	−1.15091e13			−0.371997			−0.185999	+	0.982550i	$0.559552\pi$
$500$		0			0
$501$	1.81453e13	−	2.75049e13i	0.574877	−	0.871407i
$502$		0			0
$503$			5.31745e13i			1.65144i	0.564078	+	0.825722i	$0.309232\pi$
$503$			5.31745e13i			1.65144i	−0.564078	+	0.825722i	$0.690768\pi$
$504$		0			0
$505$	4.20925e11			0.0128158
$506$		0			0
$507$	−2.62780e13	−	1.73359e13i	−0.784428	−	0.517496i
$508$		0			0
$509$		−	6.42368e13i		−	1.88016i	−0.340952	−	0.940081i	$-0.610749\pi$
$509$		−	6.42368e13i		−	1.88016i	0.340952	−	0.940081i	$-0.389251\pi$
$510$		0			0
$511$	−2.25342e13			−0.646752
$512$		0			0
$513$	−7.11395e12	+	3.93806e13i	−0.200227	+	1.10840i
$514$		0			0
$515$		−	9.55281e11i		−	0.0263691i
$516$		0			0
$517$	−9.84550e12			−0.266554
$518$		0			0
$519$	−9.21557e12	+	1.39691e13i	−0.244729	+	0.370964i
$520$		0			0
$521$			3.62516e13i			0.944363i	0.881501	+	0.472181i	$0.156533\pi$
$521$			3.62516e13i			0.944363i	−0.881501	+	0.472181i	$0.843467\pi$
$522$		0			0
$523$	5.41875e13			1.38481			0.692406	−	0.721508i	$-0.256551\pi$
$523$	5.41875e13			1.38481			0.692406	+	0.721508i	$0.256551\pi$
$524$		0			0
$525$	3.46385e13	+	2.28514e13i	0.868486	+	0.572950i
$526$		0			0
$527$		−	5.05089e13i		−	1.24255i
$528$		0			0
$529$	−4.11806e13			−0.994065
$530$		0			0
$531$	−4.57272e13	+	1.95737e13i	−1.08318	+	0.463660i
$532$		0			0
$533$			1.50575e13i			0.350040i
$534$		0			0
$535$	−1.32265e12			−0.0301771
$536$		0			0
$537$	−5.64483e12	+	8.55652e12i	−0.126409	+	0.191613i
$538$		0			0
$539$		−	8.89429e11i		−	0.0195509i
$540$		0			0
$541$	3.40248e13			0.734192			0.367096	−	0.930183i	$-0.380352\pi$
$541$	3.40248e13			0.734192			0.367096	+	0.930183i	$0.380352\pi$
$542$		0			0
$543$	7.33175e13	+	4.83684e13i	1.55313	+	1.02462i
$544$		0			0
$545$			7.34089e12i			0.152674i
$546$		0			0
$547$	4.37136e13			0.892647			0.446324	−	0.894872i	$-0.352733\pi$
$547$	4.37136e13			0.892647			0.446324	+	0.894872i	$0.352733\pi$
$548$		0			0
$549$	2.45558e13	+	5.73665e13i	0.492372	+	1.15026i
$550$		0			0
$551$		−	3.20617e13i		−	0.631290i
$552$		0			0
$553$	1.26838e13			0.245259
$554$		0			0
$555$	−2.02664e12	+	3.07201e12i	−0.0384867	+	0.0583387i
$556$		0			0
$557$			4.36690e13i			0.814512i	0.913314	+	0.407256i	$0.133514\pi$
$557$			4.36690e13i			0.814512i	−0.913314	+	0.407256i	$0.866486\pi$
$558$		0			0
$559$	2.11727e13			0.387898
$560$		0			0
$561$	1.33015e13	+	8.77512e12i	0.239378	+	0.157921i
$562$		0			0
$563$			1.18145e13i			0.208868i	0.994532	+	0.104434i	$0.0333031\pi$
$563$			1.18145e13i			0.208868i	−0.994532	+	0.104434i	$0.966697\pi$
$564$		0			0
$565$	−7.89549e12			−0.137131
$566$		0			0
$567$	−4.23942e13	+	4.44358e13i	−0.723422	+	0.758260i
$568$		0			0
$569$		−	2.34550e13i		−	0.393255i	−0.980478	−	0.196627i	$-0.937001\pi$
$569$		−	2.34550e13i		−	0.393255i	0.980478	−	0.196627i	$-0.0629989\pi$
$570$		0			0
$571$	7.70201e13			1.26889			0.634444	−	0.772969i	$-0.281229\pi$
$571$	7.70201e13			1.26889			0.634444	+	0.772969i	$0.281229\pi$
$572$		0			0
$573$	1.73789e13	−	2.63432e13i	0.281351	−	0.426477i
$574$		0			0
$575$			8.81193e13i			1.40195i
$576$		0			0
$577$	−1.00094e14			−1.56505			−0.782523	−	0.622621i	$-0.786068\pi$
$577$	−1.00094e14			−1.56505			−0.782523	+	0.622621i	$0.786068\pi$
$578$		0			0
$579$	−6.91390e13	−	4.56118e13i	−1.06250	−	0.700945i
$580$		0			0
$581$		−	1.04443e14i		−	1.57760i
$582$		0			0
$583$	−1.68502e13			−0.250186
$584$		0			0
$585$	1.31181e12	−	5.61523e11i	0.0191466	−	0.00819574i
$586$		0			0
$587$		−	1.13166e14i		−	1.62377i	−0.583817	−	0.811886i	$-0.698441\pi$
$587$		−	1.13166e14i		−	1.62377i	0.583817	−	0.811886i	$-0.301559\pi$
$588$		0			0
$589$	−6.88086e13			−0.970658
$590$		0			0
$591$	6.79550e13	−	1.03007e14i	0.942505	−	1.42866i
$592$		0			0
$593$			1.23335e14i			1.68195i	0.541071	+	0.840977i	$0.318019\pi$
$593$			1.23335e14i			1.68195i	−0.541071	+	0.840977i	$0.681981\pi$
$594$		0			0
$595$	−9.56111e12			−0.128210
$596$		0			0
$597$	−5.81551e13	−	3.83656e13i	−0.766861	−	0.505906i
$598$		0			0
$599$		−	1.49572e13i		−	0.193962i	−0.995286	−	0.0969810i	$-0.969081\pi$
$599$		−	1.49572e13i		−	0.193962i	0.995286	−	0.0969810i	$-0.0309186\pi$
$600$		0			0
$601$	−6.19721e13			−0.790358			−0.395179	−	0.918604i	$-0.629317\pi$
$601$	−6.19721e13			−0.790358			−0.395179	+	0.918604i	$0.629317\pi$
$602$		0			0
$603$	1.16645e12	+	2.72502e12i	0.0146312	+	0.0341809i
$604$		0			0
$605$			6.60532e12i			0.0814923i
$606$		0			0
$607$	−5.61495e13			−0.681400			−0.340700	−	0.940172i	$-0.610664\pi$
$607$	−5.61495e13			−0.681400			−0.340700	+	0.940172i	$0.610664\pi$
$608$		0			0
$609$	2.70957e13	−	4.10721e13i	0.323456	−	0.490299i
$610$		0			0
$611$			2.80120e13i			0.328956i
$612$		0			0
$613$	7.67438e13			0.886627			0.443314	−	0.896367i	$-0.353803\pi$
$613$	7.67438e13			0.886627			0.443314	+	0.896367i	$0.353803\pi$
$614$		0			0
$615$	8.88589e12	+	5.86212e12i	0.101001	+	0.0666314i
$616$		0			0
$617$		−	6.45577e13i		−	0.721975i	−0.932571	−	0.360988i	$-0.882440\pi$
$617$		−	6.45577e13i		−	0.721975i	0.932571	−	0.360988i	$-0.117560\pi$
$618$		0			0
$619$	1.30770e14			1.43898			0.719488	−	0.694505i	$-0.244377\pi$
$619$	1.30770e14			1.43898			0.719488	+	0.694505i	$0.244377\pi$
$620$		0			0
$621$	−1.28338e14	−	2.31837e13i	−1.38962	−	0.251029i
$622$		0			0
$623$		−	5.61751e13i		−	0.598555i
$624$		0			0
$625$	9.33126e13			0.978454
$626$		0			0
$627$	1.19544e13	−	1.81207e13i	0.123364	−	0.186998i
$628$		0			0
$629$			1.16934e14i			1.18765i
$630$		0			0
$631$	−1.52517e14			−1.52465			−0.762325	−	0.647194i	$-0.775942\pi$
$631$	−1.52517e14			−1.52465			−0.762325	+	0.647194i	$0.775942\pi$
$632$		0			0
$633$	1.94549e13	+	1.28346e13i	0.191430	+	0.126288i
$634$		0			0
$635$		−	1.56813e13i		−	0.151885i
$636$		0			0
$637$	−2.53056e12			−0.0241279
$638$		0			0
$639$	1.45805e14	−	6.24124e13i	1.36858	−	0.585823i
$640$		0			0
$641$		−	7.73137e13i		−	0.714441i	−0.934020	−	0.357221i	$-0.883724\pi$
$641$		−	7.73137e13i		−	0.714441i	0.934020	−	0.357221i	$-0.116276\pi$
$642$		0			0
$643$	−1.04038e14			−0.946539			−0.473270	−	0.880918i	$-0.656926\pi$
$643$	−1.04038e14			−0.946539			−0.473270	+	0.880918i	$0.656926\pi$
$644$		0			0
$645$	8.24285e12	−	1.24946e13i	0.0738378	−	0.111925i
$646$		0			0
$647$			1.48687e14i			1.31145i	0.755001	+	0.655724i	$0.227636\pi$
$647$			1.48687e14i			1.31145i	−0.755001	+	0.655724i	$0.772364\pi$
$648$		0			0
$649$	2.69828e13			0.234349
$650$		0			0
$651$	−8.81462e13	−	5.81510e13i	−0.753874	−	0.497339i
$652$		0			0
$653$			2.34795e14i			1.97753i	0.149489	+	0.988763i	$0.452237\pi$
$653$			2.34795e14i			1.97753i	−0.149489	+	0.988763i	$0.547763\pi$
$654$		0			0
$655$	−5.70263e12			−0.0473008
$656$		0			0
$657$	−2.97281e13	−	6.94497e13i	−0.242851	−	0.567340i
$658$		0			0
$659$			1.68129e14i			1.35274i	0.736560	+	0.676372i	$0.236449\pi$
$659$			1.68129e14i			1.35274i	−0.736560	+	0.676372i	$0.763551\pi$
$660$		0			0
$661$	2.59191e13			0.205405			0.102703	−	0.994712i	$-0.467251\pi$
$661$	2.59191e13			0.205405			0.102703	+	0.994712i	$0.467251\pi$
$662$		0			0
$663$	2.49666e13	−	3.78447e13i	0.194891	−	0.295418i
$664$		0			0
$665$			1.30252e13i			0.100156i
$666$		0			0
$667$	1.04486e14			0.791461
$668$		0			0
$669$	9.35874e12	+	6.17406e12i	0.0698372	+	0.0460724i
$670$		0			0
$671$		−	3.38509e13i		−	0.248861i
$672$		0			0
$673$	2.27840e14			1.65027			0.825133	−	0.564939i	$-0.191100\pi$
$673$	2.27840e14			1.65027			0.825133	+	0.564939i	$0.191100\pi$
$674$		0			0
$675$	−2.47307e13	+	1.36901e14i	−0.176489	+	0.976988i
$676$		0			0
$677$		−	1.70427e14i		−	1.19838i	−0.800608	−	0.599189i	$-0.795490\pi$
$677$		−	1.70427e14i		−	1.19838i	0.800608	−	0.599189i	$-0.204510\pi$
$678$		0			0
$679$	−1.27984e14			−0.886765
$680$		0			0
$681$	5.13519e13	−	7.78401e13i	0.350608	−	0.531456i
$682$		0			0
$683$			2.93785e14i			1.97663i	0.152418	+	0.988316i	$0.451294\pi$
$683$			2.93785e14i			1.97663i	−0.152418	+	0.988316i	$0.548706\pi$
$684$		0			0
$685$	3.94218e12			0.0261387
$686$		0			0
$687$	1.00128e14	+	6.60558e13i	0.654295	+	0.431646i
$688$		0			0
$689$			4.79414e13i			0.308756i
$690$		0			0
$691$	−2.70936e14			−1.71979			−0.859897	−	0.510468i	$-0.829472\pi$
$691$	−2.70936e14			−1.71979			−0.859897	+	0.510468i	$0.829472\pi$
$692$		0			0
$693$	3.06280e13	−	1.31104e13i	0.191625	−	0.0820256i
$694$		0			0
$695$		−	1.55937e13i		−	0.0961667i
$696$		0			0
$697$	3.38235e14			2.05615
$698$		0			0
$699$	−1.22061e13	+	1.85023e13i	−0.0731463	+	0.110876i
$700$		0			0
$701$			1.88080e13i			0.111110i	0.998456	+	0.0555550i	$0.0176928\pi$
$701$			1.88080e13i			0.111110i	−0.998456	+	0.0555550i	$0.982307\pi$
$702$		0			0
$703$	1.59300e14			0.927766
$704$		0			0
$705$	1.65307e13	+	1.09055e13i	0.0949174	+	0.0626180i
$706$		0			0
$707$		−	2.79613e13i		−	0.158293i
$708$		0			0
$709$	−1.31971e14			−0.736629			−0.368314	−	0.929701i	$-0.620065\pi$
$709$	−1.31971e14			−0.736629			−0.368314	+	0.929701i	$0.620065\pi$
$710$		0			0
$711$	1.67330e13	+	3.90911e13i	0.0920931	+	0.215144i
$712$		0			0
$713$		−	2.24241e14i		−	1.21693i
$714$		0			0
$715$	−7.74074e11			−0.00414240
$716$		0			0
$717$	−1.51487e14	+	2.29626e14i	−0.799428	+	1.21178i
$718$		0			0
$719$		−	2.87193e14i		−	1.49462i	−0.664477	−	0.747309i	$-0.731346\pi$
$719$		−	2.87193e14i		−	1.49462i	0.664477	−	0.747309i	$-0.268654\pi$
$720$		0			0
$721$	−6.34577e13			−0.325693
$722$		0			0
$723$	−4.62078e13	−	3.04838e13i	−0.233896	−	0.154304i
$724$		0			0
$725$		−	1.11458e14i		−	0.556445i
$726$		0			0
$727$	−2.19922e14			−1.08292			−0.541461	−	0.840726i	$-0.682129\pi$
$727$	−2.19922e14			−1.08292			−0.541461	+	0.840726i	$0.682129\pi$
$728$		0			0
$729$	−1.92878e14	−	7.20360e13i	−0.936797	−	0.349874i
$730$		0			0
$731$		−	4.75600e14i		−	2.27853i
$732$		0			0
$733$	−2.67129e14			−1.26241			−0.631205	−	0.775616i	$-0.717439\pi$
$733$	−2.67129e14			−1.26241			−0.631205	+	0.775616i	$0.717439\pi$
$734$		0			0
$735$	−9.85186e11	+	1.49336e12i	−0.00459284	+	0.00696190i
$736$		0			0
$737$		−	1.60799e12i		−	0.00739511i
$738$		0			0
$739$	−6.45317e13			−0.292787			−0.146393	−	0.989226i	$-0.546766\pi$
$739$	−6.45317e13			−0.292787			−0.146393	+	0.989226i	$0.546766\pi$
$740$		0			0
$741$	−5.15561e13	−	3.40121e13i	−0.230775	−	0.152245i
$742$		0			0
$743$			7.48325e13i			0.330481i	0.986253	+	0.165240i	$0.0528400\pi$
$743$			7.48325e13i			0.330481i	−0.986253	+	0.165240i	$0.947160\pi$
$744$		0			0
$745$	2.49215e13			0.108591
$746$		0			0
$747$	3.21889e14	−	1.37786e14i	1.38390	−	0.592380i
$748$		0			0
$749$			8.78618e13i			0.372727i
$750$		0			0
$751$	−6.89793e13			−0.288748			−0.144374	−	0.989523i	$-0.546117\pi$
$751$	−6.89793e13			−0.288748			−0.144374	+	0.989523i	$0.546117\pi$
$752$		0			0
$753$	−1.35476e14	+	2.05356e14i	−0.559611	+	0.848267i
$754$		0			0
$755$		−	4.97653e11i		−	0.00202858i
$756$		0			0
$757$	−1.86189e13			−0.0748988			−0.0374494	−	0.999299i	$-0.511923\pi$
$757$	−1.86189e13			−0.0748988			−0.0374494	+	0.999299i	$0.511923\pi$
$758$		0			0
$759$	5.90536e13	+	3.89583e13i	0.234443	+	0.154665i
$760$		0			0
$761$		−	2.55433e14i		−	1.00081i	−0.865790	−	0.500407i	$-0.833184\pi$
$761$		−	2.55433e14i		−	1.00081i	0.865790	−	0.500407i	$-0.166816\pi$
$762$		0			0
$763$	4.87644e14			1.88573
$764$		0			0
$765$	−1.26134e13	−	2.94670e13i	−0.0481422	−	0.112468i
$766$		0			0
$767$		−	7.67702e13i		−	0.289212i
$768$		0			0
$769$	1.58663e14			0.589990			0.294995	−	0.955499i	$-0.404682\pi$
$769$	1.58663e14			0.589990			0.294995	+	0.955499i	$0.404682\pi$
$770$		0			0
$771$	−1.87364e14	+	2.84010e14i	−0.687726	+	1.04247i
$772$		0			0
$773$			3.33005e14i			1.20657i	0.797525	+	0.603286i	$0.206142\pi$
$773$			3.33005e14i			1.20657i	−0.797525	+	0.603286i	$0.793858\pi$
$774$		0			0
$775$	−2.39204e14			−0.855578
$776$		0			0
$777$	2.04068e14	+	1.34626e14i	0.720561	+	0.475362i
$778$		0			0
$779$		−	4.60780e14i		−	1.60623i
$780$		0			0
$781$	−8.60371e13			−0.296095
$782$		0			0
$783$	1.62329e14	+	2.93241e13i	0.551553	+	0.0996357i
$784$		0			0
$785$			2.35685e12i			0.00790650i
$786$		0			0
$787$	1.29978e14			0.430524			0.215262	−	0.976556i	$-0.430939\pi$
$787$	1.29978e14			0.430524			0.215262	+	0.976556i	$0.430939\pi$
$788$		0			0
$789$	−1.57441e14	+	2.38652e14i	−0.514912	+	0.780511i
$790$		0			0
$791$			5.24485e14i			1.69375i
$792$		0			0
$793$	−9.63110e13			−0.307121
$794$		0			0
$795$	2.82917e13	+	1.86643e13i	0.0890888	+	0.0587729i
$796$		0			0
$797$		−	2.85887e14i		−	0.889001i	−0.895778	−	0.444501i	$-0.853381\pi$
$797$		−	2.85887e14i		−	0.889001i	0.895778	−	0.444501i	$-0.146619\pi$
$798$		0			0
$799$	6.29230e14			1.93230
$800$		0			0
$801$	1.73130e14	−	7.41087e13i	0.525061	−	0.224753i
$802$		0			0
$803$			4.09810e13i			0.122745i
$804$		0			0
$805$	−4.24478e13			−0.125567
$806$		0			0
$807$	−2.00056e14	+	3.03248e14i	−0.584499	+	0.885993i
$808$		0			0
$809$			2.38584e14i			0.688490i	0.938880	+	0.344245i	$0.111865\pi$
$809$			2.38584e14i			0.688490i	−0.938880	+	0.344245i	$0.888135\pi$
$810$		0			0
$811$	−9.61918e13			−0.274179			−0.137089	−	0.990559i	$-0.543775\pi$
$811$	−9.61918e13			−0.274179			−0.137089	+	0.990559i	$0.543775\pi$
$812$		0			0
$813$	2.96714e14	+	1.95746e14i	0.835383	+	0.551111i
$814$		0			0
$815$		−	5.50380e12i		−	0.0153064i
$816$		0			0
$817$	−6.47913e14			−1.77994
$818$		0			0
$819$	−3.73011e13	−	8.71414e13i	−0.101228	−	0.236486i
$820$		0			0
$821$			3.47839e13i			0.0932528i	0.998912	+	0.0466264i	$0.0148470\pi$
$821$			3.47839e13i			0.0932528i	−0.998912	+	0.0466264i	$0.985153\pi$
$822$		0			0
$823$	−7.53533e13			−0.199574			−0.0997869	−	0.995009i	$-0.531816\pi$
$823$	−7.53533e13			−0.199574			−0.0997869	+	0.995009i	$0.531816\pi$
$824$		0			0
$825$	4.15579e13	−	6.29941e13i	0.108739	−	0.164828i
$826$		0			0
$827$			3.13573e14i			0.810608i	0.914182	+	0.405304i	$0.132834\pi$
$827$			3.13573e14i			0.810608i	−0.914182	+	0.405304i	$0.867166\pi$
$828$		0			0
$829$	4.23153e14			1.08075			0.540375	−	0.841424i	$-0.318282\pi$
$829$	4.23153e14			1.08075			0.540375	+	0.841424i	$0.318282\pi$
$830$		0			0
$831$	−4.92556e14	−	3.24944e14i	−1.24294	−	0.819981i
$832$		0			0
$833$			5.68437e13i			0.141729i
$834$		0			0
$835$	3.59550e13			0.0885781
$836$		0			0
$837$	6.29333e13	−	3.48379e14i	0.153198	−	0.848056i
$838$		0			0
$839$		−	9.35881e13i		−	0.225118i	−0.993645	−	0.112559i	$-0.964095\pi$
$839$		−	9.35881e13i		−	0.225118i	0.993645	−	0.112559i	$-0.0359048\pi$
$840$		0			0
$841$	2.88547e14			0.685862
$842$		0			0
$843$	1.48887e14	−	2.25685e14i	0.349719	−	0.530109i
$844$		0			0
$845$		−	3.43512e13i		−	0.0797368i
$846$		0			0
$847$	4.38780e14			1.00654
$848$		0			0
$849$	1.56702e14	+	1.03378e14i	0.355251	+	0.234363i
$850$		0			0
$851$			5.19143e14i			1.16316i
$852$		0			0
$853$	−2.32176e14			−0.514129			−0.257064	−	0.966394i	$-0.582755\pi$
$853$	−2.32176e14			−0.514129			−0.257064	+	0.966394i	$0.582755\pi$
$854$		0			0
$855$	−4.01431e13	+	1.71834e13i	−0.0878579	+	0.0376078i
$856$		0			0
$857$			6.13116e14i			1.32629i	0.748491	+	0.663145i	$0.230779\pi$
$857$			6.13116e14i			1.32629i	−0.748491	+	0.663145i	$0.769221\pi$
$858$		0			0
$859$	−3.86538e14			−0.826468			−0.413234	−	0.910625i	$-0.635601\pi$
$859$	−3.86538e14			−0.826468			−0.413234	+	0.910625i	$0.635601\pi$
$860$		0			0
$861$	3.89411e14	−	5.90276e14i	0.822986	−	1.24750i
$862$		0			0
$863$		−	5.49299e14i		−	1.14751i	−0.819029	−	0.573753i	$-0.805487\pi$
$863$		−	5.49299e14i		−	1.14751i	0.819029	−	0.573753i	$-0.194513\pi$
$864$		0			0
$865$	−1.82607e13			−0.0377083
$866$		0			0
$867$	−4.41183e14	−	2.91053e14i	−0.900582	−	0.594124i
$868$		0			0
$869$		−	2.30670e13i		−	0.0465470i
$870$		0			0
$871$	−4.57497e12			−0.00912635
$872$		0			0
$873$	−1.68843e14	−	3.94444e14i	−0.332974	−	0.777883i
$874$		0			0
$875$			9.08888e13i			0.177203i
$876$		0			0
$877$	−5.59563e13			−0.107858			−0.0539288	−	0.998545i	$-0.517174\pi$
$877$	−5.59563e13			−0.107858			−0.0539288	+	0.998545i	$0.517174\pi$
$878$		0			0
$879$	−3.25683e13	+	4.93675e13i	−0.0620656	+	0.0940799i
$880$		0			0
$881$		−	4.46766e14i		−	0.841783i	−0.907111	−	0.420892i	$-0.861717\pi$
$881$		−	4.46766e14i		−	0.841783i	0.907111	−	0.420892i	$-0.138283\pi$
$882$		0			0
$883$	−8.02409e14			−1.49483			−0.747416	−	0.664356i	$-0.768706\pi$
$883$	−8.02409e14			−1.49483			−0.747416	+	0.664356i	$0.768706\pi$
$884$		0			0
$885$	−4.53044e13	−	2.98878e13i	−0.0834496	−	0.0550526i
$886$		0			0
$887$		−	2.35117e14i		−	0.428219i	−0.976810	−	0.214109i	$-0.931315\pi$
$887$		−	2.35117e14i		−	0.428219i	0.976810	−	0.214109i	$-0.0686849\pi$
$888$		0			0
$889$	−1.04169e15			−1.87598
$890$		0			0
$891$	8.08116e13	+	7.70987e13i	0.143908	+	0.137296i
$892$		0			0
$893$		−	8.57204e14i		−	1.50948i
$894$		0			0
$895$	−1.11853e13			−0.0194774
$896$		0			0
$897$	1.10842e14	−	1.68017e14i	0.190873	−	0.289328i
$898$		0			0
$899$			2.83633e14i			0.483012i
$900$		0			0
$901$	1.07690e15			1.81365
$902$		0			0
$903$	−8.29999e14	−	5.47559e14i	−1.38242	−	0.911995i
$904$		0			0
$905$			9.58422e13i			0.157875i
$906$		0			0
$907$	4.31138e14			0.702392			0.351196	−	0.936302i	$-0.385775\pi$
$907$	4.31138e14			0.702392			0.351196	+	0.936302i	$0.385775\pi$
$908$		0			0
$909$	8.61759e13	−	3.68878e13i	0.138857	−	0.0594379i
$910$		0			0
$911$			1.14927e15i			1.83160i	0.401640	+	0.915798i	$0.368440\pi$
$911$			1.14927e15i			1.83160i	−0.401640	+	0.915798i	$0.631560\pi$
$912$		0			0
$913$	−1.89941e14			−0.299409
$914$		0			0
$915$	−3.74953e13	+	5.68360e13i	−0.0584617	+	0.0886172i
$916$		0			0
$917$			3.78816e14i			0.584228i
$918$		0			0
$919$	−2.48242e14			−0.378702			−0.189351	−	0.981909i	$-0.560638\pi$
$919$	−2.48242e14			−0.378702			−0.189351	+	0.981909i	$0.560638\pi$
$920$		0			0
$921$	4.60374e14	+	3.03714e14i	0.694724	+	0.458317i
$922$		0			0
$923$			2.44789e14i			0.365412i
$924$		0			0
$925$	5.53784e14			0.817771
$926$		0			0
$927$	−8.37162e13	−	1.95575e14i	−0.122296	−	0.285703i
$928$		0			0
$929$			7.72359e13i			0.111620i	0.998441	+	0.0558098i	$0.0177740\pi$
$929$			7.72359e13i			0.111620i	−0.998441	+	0.0558098i	$0.982226\pi$
$930$		0			0
$931$	7.74386e13			0.110716
$932$		0			0
$933$	2.97059e14	−	4.50287e14i	0.420180	−	0.636915i
$934$		0			0
$935$			1.73879e13i			0.0243327i
$936$		0			0
$937$	−6.10923e14			−0.845841			−0.422920	−	0.906167i	$-0.638995\pi$
$937$	−6.10923e14			−0.845841			−0.422920	+	0.906167i	$0.638995\pi$
$938$		0			0
$939$	1.05447e15	+	6.95647e14i	1.44447	+	0.952930i
$940$		0			0
$941$			9.13159e14i			1.23765i	0.785529	+	0.618825i	$0.212391\pi$
$941$			9.13159e14i			1.23765i	−0.785529	+	0.618825i	$0.787609\pi$
$942$		0			0
$943$	1.50164e15			2.01376
$944$		0			0
$945$	−6.59466e13	−	1.19130e13i	−0.0875051	−	0.0158074i
$946$		0			0
$947$		−	1.45213e14i		−	0.190658i	−0.995446	−	0.0953291i	$-0.969610\pi$
$947$		−	1.45213e14i		−	0.190658i	0.995446	−	0.0953291i	$-0.0303904\pi$
$948$		0			0
$949$	1.16597e14			0.151481
$950$		0			0
$951$	−1.39334e14	+	2.11204e14i	−0.179124	+	0.271519i
$952$		0			0
$953$			7.20639e14i			0.916755i	0.888758	+	0.458377i	$0.151569\pi$
$953$			7.20639e14i			0.916755i	−0.888758	+	0.458377i	$0.848431\pi$
$954$		0			0
$955$	3.44364e13			0.0433512
$956$		0			0
$957$	−7.46943e13	−	4.92767e13i	−0.0930525	−	0.0613877i
$958$		0			0
$959$		−	2.61873e14i		−	0.322848i
$960$		0			0
$961$	−2.10915e14			−0.257331
$962$		0			0
$963$	−2.70787e14	+	1.15911e14i	−0.326962	+	0.139957i
$964$		0			0
$965$		−	9.03800e13i		−	0.108003i
$966$		0			0
$967$	9.53278e14			1.12742			0.563712	−	0.825971i	$-0.309373\pi$
$967$	9.53278e14			1.12742			0.563712	+	0.825971i	$0.309373\pi$
$968$		0			0
$969$	−7.64010e14	+	1.15810e15i	−0.894294	+	1.35558i
$970$		0			0
$971$		−	8.74672e14i		−	1.01333i	−0.862144	−	0.506663i	$-0.830879\pi$
$971$		−	8.74672e14i		−	1.01333i	0.862144	−	0.506663i	$-0.169121\pi$
$972$		0			0
$973$	−1.03586e15			−1.18779
$974$		0			0
$975$	−1.79228e14	−	1.18239e14i	−0.203415	−	0.134195i
$976$		0			0
$977$			1.10619e15i			1.24267i	0.783545	+	0.621335i	$0.213409\pi$
$977$			1.10619e15i			1.24267i	−0.783545	+	0.621335i	$0.786591\pi$
$978$		0			0
$979$	−1.02161e14			−0.113598
$980$		0			0
$981$	6.43321e14	+	1.50290e15i	0.708080	+	1.65419i
$982$		0			0
$983$		−	5.20911e14i		−	0.567539i	−0.958893	−	0.283770i	$-0.908415\pi$
$983$		−	5.20911e14i		−	0.567539i	0.958893	−	0.283770i	$-0.0915851\pi$
$984$		0			0
$985$	1.34653e14			0.145223
$986$		0			0
$987$	7.24434e14	−	1.09811e15i	0.773415	−	1.17236i
$988$		0			0
$989$		−	2.11149e15i		−	2.23155i
$990$		0			0
$991$	6.21243e12			0.00649970			0.00324985	−	0.999995i	$-0.498966\pi$
$991$	6.21243e12			0.00649970			0.00324985	+	0.999995i	$0.498966\pi$
$992$		0			0
$993$	−7.13291e14	−	4.70566e14i	−0.738789	−	0.487387i
$994$		0			0
$995$		−	7.60216e13i		−	0.0779510i
$996$		0			0
$997$	−1.08662e15			−1.10307			−0.551534	−	0.834152i	$-0.685957\pi$
$997$	−1.08662e15			−1.10307			−0.551534	+	0.834152i	$0.685957\pi$
$998$		0			0
$999$	−1.45698e14	+	8.06537e14i	−0.146428	+	0.810581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.11.e.a.17.10	yes	10
3.2	odd	2	inner	24.11.e.a.17.9	✓	10
4.3	odd	2		48.11.e.e.17.1		10
8.3	odd	2		192.11.e.i.65.10		10
8.5	even	2		192.11.e.j.65.1		10
12.11	even	2		48.11.e.e.17.2		10
24.5	odd	2		192.11.e.j.65.2		10
24.11	even	2		192.11.e.i.65.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.11.e.a.17.9	✓	10	3.2	odd	2	inner
24.11.e.a.17.10	yes	10	1.1	even	1	trivial
48.11.e.e.17.1		10	4.3	odd	2
48.11.e.e.17.2		10	12.11	even	2
192.11.e.i.65.9		10	24.11	even	2
192.11.e.i.65.10		10	8.3	odd	2
192.11.e.j.65.1		10	8.5	even	2
192.11.e.j.65.2		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)

\(f(q)\)	\(=\)	\(q+(202.837 + 133.814i) q^{3} +265.153i q^{5} +17613.7 q^{7} +(23236.7 + 54284.8i) q^{9} +O(q^{10})\)	\(q+(202.837 + 133.814i) q^{3} +265.153i q^{5} +17613.7 q^{7} +(23236.7 + 54284.8i) q^{9} -32032.5i q^{11} -91137.3 q^{13} +(-35481.1 + 53782.8i) q^{15} +2.04721e6i q^{17} +2.78892e6 q^{19} +(3.57271e6 + 2.35695e6i) q^{21} +9.08885e6i q^{23} +9.69532e6 q^{25} +(-2.55079e6 + 1.41204e7i) q^{27} -1.14961e7i q^{29} -2.46721e7 q^{31} +(4.28639e6 - 6.49737e6i) q^{33} +4.67032e6i q^{35} +5.71187e7 q^{37} +(-1.84860e7 - 1.21954e7i) q^{39} -1.65218e8i q^{41} -2.32317e8 q^{43} +(-1.43938e7 + 6.16129e6i) q^{45} -3.07360e8i q^{47} +2.77665e7 q^{49} +(-2.73944e8 + 4.15249e8i) q^{51} -5.26036e8i q^{53} +8.49350e6 q^{55} +(5.65697e8 + 3.73196e8i) q^{57} +8.42358e8i q^{59} +1.05677e9 q^{61} +(4.09284e8 + 9.56155e8i) q^{63} -2.41653e7i q^{65} +5.01986e7 q^{67} +(-1.21621e9 + 1.84355e9i) q^{69} -2.68594e9i q^{71} -1.27936e9 q^{73} +(1.96657e9 + 1.29737e9i) q^{75} -5.64210e8i q^{77} +7.20112e8 q^{79} +(-2.40689e9 + 2.52280e9i) q^{81} -5.92964e9i q^{83} -5.42823e8 q^{85} +(1.53834e9 - 2.33183e9i) q^{87} -3.18929e9i q^{89} -1.60526e9 q^{91} +(-5.00442e9 - 3.30147e9i) q^{93} +7.39491e8i q^{95} -7.26620e9 q^{97} +(1.73888e9 - 7.44330e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 22 q^{3} - 5436 q^{7} - 28934 q^{9}+O(q^{10}) \) 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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