LMFDB - Embedded newform 96.11.e.a.65.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [96,11,Mod(65,96)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(96, 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("96.65");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	96.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:	$60.9942962567$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 10188 x^{18} + 45921062 x^{16} + 120525675724 x^{14} + 203898078666673 x^{12} + \cdots + 53\!\cdots\!00 $ x^20 + 10188x^18 + 45921062x^16 + 120525675724x^14 + 203898078666673x^12 + 232245025861282784x^10 + 180340506376759114096x^8 + 94263173180849529156160x^6 + 31744131361978925137656320x^4 + 6220793838503133099948518400*x^2 + 538885657771587042410102809600
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{176}\cdot 3^{47} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			65.15
Root			$-26.0163i$ of defining polynomial
Character	$\chi$	$=$	96.65
Dual form			96.11.e.a.65.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(168.749 - 174.851i) q^{3} -5349.27i q^{5} -28157.9 q^{7} +(-2096.84 - 59011.8i) q^{9} +O(q^{10})$	\(q+(168.749 - 174.851i) q^{3} -5349.27i q^{5} -28157.9 q^{7} +(-2096.84 - 59011.8i) q^{9} -178116. i q^{11} +450204. q^{13} +(-935326. - 902681. i) q^{15} -1.63099e6i q^{17} -1.37708e6 q^{19} +(-4.75161e6 + 4.92344e6i) q^{21} -1.19808e6i q^{23} -1.88490e7 q^{25} +(-1.06721e7 - 9.59152e6i) q^{27} +7.50212e6i q^{29} +3.53697e7 q^{31} +(-3.11438e7 - 3.00569e7i) q^{33} +1.50624e8i q^{35} +4.95516e7 q^{37} +(7.59713e7 - 7.87187e7i) q^{39} -3.90414e7i q^{41} -1.40453e8 q^{43} +(-3.15670e8 + 1.12165e7i) q^{45} +75336.3i q^{47} +5.10393e8 q^{49} +(-2.85180e8 - 2.75226e8i) q^{51} +4.45933e8i q^{53} -9.52791e8 q^{55} +(-2.32381e8 + 2.40784e8i) q^{57} +1.38477e8i q^{59} +1.60888e9 q^{61} +(5.90425e7 + 1.66165e9i) q^{63} -2.40826e9i q^{65} +1.71653e9 q^{67} +(-2.09486e8 - 2.02175e8i) q^{69} +2.26776e9i q^{71} +2.96508e8 q^{73} +(-3.18075e9 + 3.29578e9i) q^{75} +5.01538e9i q^{77} -5.23007e9 q^{79} +(-3.47799e9 + 2.47476e8i) q^{81} -7.44213e8i q^{83} -8.72458e9 q^{85} +(1.31175e9 + 1.26597e9i) q^{87} -1.07832e9i q^{89} -1.26768e10 q^{91} +(5.96859e9 - 6.18444e9i) q^{93} +7.36638e9i q^{95} -7.33891e9 q^{97} +(-1.05109e10 + 3.73480e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 100284 q^{9}+O(q^{10}) $ 20 * q - 100284 * q^9	$ 20 q - 100284 q^{9} + 527880 q^{13} - 11589912 q^{21} - 56425772 q^{25} - 55706832 q^{33} - 148642168 q^{37} - 377224224 q^{45} + 1363854748 q^{49} + 1399004568 q^{57} + 1635155656 q^{61} - 435726432 q^{69} + 654515880 q^{73} - 9447541740 q^{81} - 19066455296 q^{85} + 2169686088 q^{93} - 15378184440 q^{97}+O(q^{100}) $ 20 * q - 100284 * q^9 + 527880 * q^13 - 11589912 * q^21 - 56425772 * q^25 - 55706832 * q^33 - 148642168 * q^37 - 377224224 * q^45 + 1363854748 * q^49 + 1399004568 * q^57 + 1635155656 * q^61 - 435726432 * q^69 + 654515880 * q^73 - 9447541740 * q^81 - 19066455296 * q^85 + 2169686088 * q^93 - 15378184440 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$1$	$1$	$-1$

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
$3$	168.749	−	174.851i	0.694439	−	0.719552i
$3$	168.749	−	174.851i	0.694439	−	0.719552i
$4$		0			0
$5$		−	5349.27i		−	1.71177i	−0.517170	−	0.855883i	$-0.673014\pi$
$5$		−	5349.27i		−	1.71177i	0.517170	−	0.855883i	$-0.326986\pi$
$6$		0			0
$7$	−28157.9			−1.67537			−0.837684	−	0.546155i	$-0.816091\pi$
$7$	−28157.9			−1.67537			−0.837684	+	0.546155i	$0.816091\pi$
$8$		0			0
$9$	−2096.84	−	59011.8i	−0.0355101	−	0.999369i
$10$		0			0
$11$		−	178116.i		−	1.10596i	−0.833194	−	0.552981i	$-0.813490\pi$
$11$		−	178116.i		−	1.10596i	0.833194	−	0.552981i	$-0.186510\pi$
$12$		0			0
$13$	450204.			1.21253			0.606265	−	0.795262i	$-0.292667\pi$
$13$	450204.			1.21253			0.606265	+	0.795262i	$0.292667\pi$
$14$		0			0
$15$	−935326.	−	902681.i	−1.23170	−	1.18872i
$16$		0			0
$17$		−	1.63099e6i		−	1.14870i	−0.818611	−	0.574348i	$-0.805255\pi$
$17$		−	1.63099e6i		−	1.14870i	0.818611	−	0.574348i	$-0.194745\pi$
$18$		0			0
$19$	−1.37708e6			−0.556150			−0.278075	−	0.960559i	$-0.589696\pi$
$19$	−1.37708e6			−0.556150			−0.278075	+	0.960559i	$0.589696\pi$
$20$		0			0
$21$	−4.75161e6	+	4.92344e6i	−1.16344	+	1.20551i
$22$		0			0
$23$		−	1.19808e6i		−	0.186143i	−0.995659	−	0.0930717i	$-0.970331\pi$
$23$		−	1.19808e6i		−	0.186143i	0.995659	−	0.0930717i	$-0.0296686\pi$
$24$		0			0
$25$	−1.88490e7			−1.93014
$26$		0			0
$27$	−1.06721e7	−	9.59152e6i	−0.743758	−	0.668449i
$28$		0			0
$29$			7.50212e6i			0.365758i	0.983135	+	0.182879i	$0.0585417\pi$
$29$			7.50212e6i			0.365758i	−0.983135	+	0.182879i	$0.941458\pi$
$30$		0			0
$31$	3.53697e7			1.23544			0.617722	−	0.786396i	$-0.288056\pi$
$31$	3.53697e7			1.23544			0.617722	+	0.786396i	$0.288056\pi$
$32$		0			0
$33$	−3.11438e7	−	3.00569e7i	−0.795797	−	0.768022i
$34$		0			0
$35$			1.50624e8i			2.86784i
$36$		0			0
$37$	4.95516e7			0.714578			0.357289	−	0.933994i	$-0.383701\pi$
$37$	4.95516e7			0.714578			0.357289	+	0.933994i	$0.383701\pi$
$38$		0			0
$39$	7.59713e7	−	7.87187e7i	0.842028	−	0.872479i
$40$		0			0
$41$		−	3.90414e7i		−	0.336981i	−0.985703	−	0.168491i	$-0.946111\pi$
$41$		−	3.90414e7i		−	0.336981i	0.985703	−	0.168491i	$-0.0538893\pi$
$42$		0			0
$43$	−1.40453e8			−0.955409			−0.477705	−	0.878521i	$-0.658531\pi$
$43$	−1.40453e8			−0.955409			−0.477705	+	0.878521i	$0.658531\pi$
$44$		0			0
$45$	−3.15670e8	+	1.12165e7i	−1.71069	+	0.0607850i
$46$		0			0
$47$			75336.3i			0.000328485i	1.00000		0.000164242i	$5.22800e-5\pi$
$47$			75336.3i			0.000328485i	−1.00000		0.000164242i	$0.999948\pi$
$48$		0			0
$49$	5.10393e8			1.80686
$50$		0			0
$51$	−2.85180e8	−	2.75226e8i	−0.826547	−	0.797700i
$52$		0			0
$53$			4.45933e8i			1.06633i	0.846012	+	0.533164i	$0.178997\pi$
$53$			4.45933e8i			1.06633i	−0.846012	+	0.533164i	$0.821003\pi$
$54$		0			0
$55$	−9.52791e8			−1.89315
$56$		0			0
$57$	−2.32381e8	+	2.40784e8i	−0.386212	+	0.400179i
$58$		0			0
$59$			1.38477e8i			0.193694i	0.995299	+	0.0968471i	$0.0308758\pi$
$59$			1.38477e8i			0.193694i	−0.995299	+	0.0968471i	$0.969124\pi$
$60$		0			0
$61$	1.60888e9			1.90491			0.952454	−	0.304682i	$-0.0985501\pi$
$61$	1.60888e9			1.90491			0.952454	+	0.304682i	$0.0985501\pi$
$62$		0			0
$63$	5.90425e7	+	1.66165e9i	0.0594925	+	1.67431i
$64$		0			0
$65$		−	2.40826e9i		−	2.07557i
$66$		0			0
$67$	1.71653e9			1.27139			0.635694	−	0.771941i	$-0.280714\pi$
$67$	1.71653e9			1.27139			0.635694	+	0.771941i	$0.280714\pi$
$68$		0			0
$69$	−2.09486e8	−	2.02175e8i	−0.133940	−	0.129265i
$70$		0			0
$71$			2.26776e9i			1.25691i	0.777844	+	0.628457i	$0.216313\pi$
$71$			2.26776e9i			1.25691i	−0.777844	+	0.628457i	$0.783687\pi$
$72$		0			0
$73$	2.96508e8			0.143028			0.0715141	−	0.997440i	$-0.477217\pi$
$73$	2.96508e8			0.143028			0.0715141	+	0.997440i	$0.477217\pi$
$74$		0			0
$75$	−3.18075e9	+	3.29578e9i	−1.34036	+	1.38884i
$76$		0			0
$77$			5.01538e9i			1.85289i
$78$		0			0
$79$	−5.23007e9			−1.69970			−0.849849	−	0.527026i	$-0.823307\pi$
$79$	−5.23007e9			−1.69970			−0.849849	+	0.527026i	$0.823307\pi$
$80$		0			0
$81$	−3.47799e9	+	2.47476e8i	−0.997478	+	0.0709754i
$82$		0			0
$83$		−	7.44213e8i		−	0.188932i	−0.995528	−	0.0944662i	$-0.969886\pi$
$83$		−	7.44213e8i		−	0.188932i	0.995528	−	0.0944662i	$-0.0301144\pi$
$84$		0			0
$85$	−8.72458e9			−1.96630
$86$		0			0
$87$	1.31175e9	+	1.26597e9i	0.263182	+	0.253997i
$88$		0			0
$89$		−	1.07832e9i		−	0.193106i	−0.995328	−	0.0965531i	$-0.969218\pi$
$89$		−	1.07832e9i		−	0.193106i	0.995328	−	0.0965531i	$-0.0307818\pi$
$90$		0			0
$91$	−1.26768e10			−2.03144
$92$		0			0
$93$	5.96859e9	−	6.18444e9i	0.857940	−	0.888966i
$94$		0			0
$95$			7.36638e9i			0.951998i
$96$		0			0
$97$	−7.33891e9			−0.854619			−0.427310	−	0.904105i	$-0.640539\pi$
$97$	−7.33891e9			−0.854619			−0.427310	+	0.904105i	$0.640539\pi$
$98$		0			0
$99$	−1.05109e10	+	3.73480e8i	−1.10526	+	0.0392728i
$100$		0			0
$101$		−	1.20616e10i		−	1.14762i	−0.818987	−	0.573812i	$-0.805464\pi$
$101$		−	1.20616e10i		−	1.14762i	0.818987	−	0.573812i	$-0.194536\pi$
$102$		0			0
$103$	−7.94813e9			−0.685613			−0.342806	−	0.939406i	$-0.611377\pi$
$103$	−7.94813e9			−0.685613			−0.342806	+	0.939406i	$0.611377\pi$
$104$		0			0
$105$	2.63368e10	+	2.54176e10i	2.06356	+	1.99154i
$106$		0			0
$107$			2.62129e10i			1.86895i	0.356033	+	0.934473i	$0.384129\pi$
$107$			2.62129e10i			1.86895i	−0.356033	+	0.934473i	$0.615871\pi$
$108$		0			0
$109$	4.12947e9			0.268387			0.134194	−	0.990955i	$-0.457156\pi$
$109$	4.12947e9			0.268387			0.134194	+	0.990955i	$0.457156\pi$
$110$		0			0
$111$	8.36177e9	−	8.66416e9i	0.496230	−	0.514176i
$112$		0			0
$113$		−	6.12310e9i		−	0.332337i	−0.986097	−	0.166169i	$-0.946860\pi$
$113$		−	6.12310e9i		−	0.332337i	0.986097	−	0.166169i	$-0.0531396\pi$
$114$		0			0
$115$	−6.40887e9			−0.318634
$116$		0			0
$117$	−9.44004e8	−	2.65673e10i	−0.0430571	−	1.21177i
$118$		0			0
$119$			4.59251e10i			1.92449i
$120$		0			0
$121$	−5.78795e9			−0.223151
$122$		0			0
$123$	−6.82642e9	−	6.58817e9i	−0.242475	−	0.234013i
$124$		0			0
$125$			4.85896e10i			1.59218i
$126$		0			0
$127$	5.47457e10			1.65704			0.828518	−	0.559963i	$-0.189185\pi$
$127$	5.47457e10			1.65704			0.828518	+	0.559963i	$0.189185\pi$
$128$		0			0
$129$	−2.37013e10	+	2.45584e10i	−0.663473	+	0.687466i
$130$		0			0
$131$		−	5.62381e10i		−	1.45772i	−0.684662	−	0.728861i	$-0.740050\pi$
$131$		−	5.62381e10i		−	1.45772i	0.684662	−	0.728861i	$-0.259950\pi$
$132$		0			0
$133$	3.87757e10			0.931756
$134$		0			0
$135$	−5.13076e10	+	5.70880e10i	−1.14423	+	1.27314i
$136$		0			0
$137$		−	6.26992e10i		−	1.29915i	−0.760298	−	0.649575i	$-0.774947\pi$
$137$		−	6.26992e10i		−	1.29915i	0.760298	−	0.649575i	$-0.225053\pi$
$138$		0			0
$139$	−6.97029e10			−1.34331			−0.671656	−	0.740863i	$-0.734417\pi$
$139$	−6.97029e10			−1.34331			−0.671656	+	0.740863i	$0.734417\pi$
$140$		0			0
$141$	1.31726e7	+	1.27129e7i	0.000236362	+	0.000228112i
$142$		0			0
$143$		−	8.01886e10i		−	1.34101i
$144$		0			0
$145$	4.01309e10			0.626093
$146$		0			0
$147$	8.61281e10	−	8.92428e10i	1.25475	−	1.30013i
$148$		0			0
$149$		−	6.56743e10i		−	0.894260i	−0.894469	−	0.447130i	$-0.852446\pi$
$149$		−	6.56743e10i		−	0.894260i	0.894469	−	0.447130i	$-0.147554\pi$
$150$		0			0
$151$	3.21530e10			0.409578			0.204789	−	0.978806i	$-0.434349\pi$
$151$	3.21530e10			0.409578			0.204789	+	0.978806i	$0.434349\pi$
$152$		0			0
$153$	−9.62473e10	+	3.41991e9i	−1.14797	+	0.0407904i
$154$		0			0
$155$		−	1.89202e11i		−	2.11479i
$156$		0			0
$157$	−9.67081e10			−1.01383			−0.506914	−	0.861997i	$-0.669214\pi$
$157$	−9.67081e10			−1.01383			−0.506914	+	0.861997i	$0.669214\pi$
$158$		0			0
$159$	7.79720e10	+	7.52506e10i	0.767278	+	0.740499i
$160$		0			0
$161$			3.37355e10i			0.311859i
$162$		0			0
$163$	5.50185e10			0.478157			0.239079	−	0.971000i	$-0.423155\pi$
$163$	5.50185e10			0.478157			0.239079	+	0.971000i	$0.423155\pi$
$164$		0			0
$165$	−1.60782e11	+	1.66597e11i	−1.31467	+	1.36222i
$166$		0			0
$167$			1.35753e11i			1.04512i	0.852602	+	0.522561i	$0.175023\pi$
$167$			1.35753e11i			1.04512i	−0.852602	+	0.522561i	$0.824977\pi$
$168$		0			0
$169$	6.48252e10			0.470230
$170$		0			0
$171$	2.88752e9	+	8.12640e10i	0.0197489	+	0.555799i
$172$		0			0
$173$		−	5.42251e10i		−	0.349921i	−0.984575	−	0.174961i	$-0.944020\pi$
$173$		−	5.42251e10i		−	0.349921i	0.984575	−	0.174961i	$-0.0559798\pi$
$174$		0			0
$175$	5.30750e11			3.23370
$176$		0			0
$177$	2.42128e10	+	2.33677e10i	0.139373	+	0.134509i
$178$		0			0
$179$		−	9.73734e10i		−	0.529877i	−0.964265	−	0.264939i	$-0.914648\pi$
$179$		−	9.73734e10i		−	0.529877i	0.964265	−	0.264939i	$-0.0853517\pi$
$180$		0			0
$181$	1.86408e11			0.959561			0.479781	−	0.877389i	$-0.340716\pi$
$181$	1.86408e11			0.959561			0.479781	+	0.877389i	$0.340716\pi$
$182$		0			0
$183$	2.71496e11	−	2.81314e11i	1.32284	−	1.37068i
$184$		0			0
$185$		−	2.65065e11i		−	1.22319i
$186$		0			0
$187$	−2.90505e11			−1.27041
$188$		0			0
$189$	3.00504e11	+	2.70077e11i	1.24607	+	1.11990i
$190$		0			0
$191$		−	1.04353e11i		−	0.410525i	−0.978707	−	0.205263i	$-0.934195\pi$
$191$		−	1.04353e11i		−	0.410525i	0.978707	−	0.205263i	$-0.0658048\pi$
$192$		0			0
$193$	1.12618e11			0.420555			0.210278	−	0.977642i	$-0.432563\pi$
$193$	1.12618e11			0.420555			0.210278	+	0.977642i	$0.432563\pi$
$194$		0			0
$195$	−4.21087e11	−	4.06391e11i	−1.49348	−	1.44135i
$196$		0			0
$197$		−	2.09320e11i		−	0.705472i	−0.935723	−	0.352736i	$-0.885251\pi$
$197$		−	2.09320e11i		−	0.705472i	0.935723	−	0.352736i	$-0.114749\pi$
$198$		0			0
$199$	1.51611e10			0.0485808			0.0242904	−	0.999705i	$-0.492267\pi$
$199$	1.51611e10			0.0485808			0.0242904	+	0.999705i	$0.492267\pi$
$200$		0			0
$201$	2.89663e11	−	3.00138e11i	0.882901	−	0.914830i
$202$		0			0
$203$		−	2.11244e11i		−	0.612780i
$204$		0			0
$205$	−2.08843e11			−0.576833
$206$		0			0
$207$	−7.07010e10	+	2.51218e9i	−0.186026	+	0.00660997i
$208$		0			0
$209$			2.45281e11i			0.615080i
$210$		0			0
$211$	2.66929e11			0.638238			0.319119	−	0.947715i	$-0.396613\pi$
$211$	2.66929e11			0.638238			0.319119	+	0.947715i	$0.396613\pi$
$212$		0			0
$213$	3.96521e11	+	3.82681e11i	0.904415	+	0.872849i
$214$		0			0
$215$			7.51322e11i			1.63544i
$216$		0			0
$217$	−9.95938e11			−2.06982
$218$		0			0
$219$	5.00352e10	−	5.18447e10i	0.0993243	−	0.102916i
$220$		0			0
$221$		−	7.34276e11i		−	1.39283i
$222$		0			0
$223$	−6.57318e11			−1.19193			−0.595966	−	0.803010i	$-0.703231\pi$
$223$	−6.57318e11			−1.19193			−0.595966	+	0.803010i	$0.703231\pi$
$224$		0			0
$225$	3.95234e10	+	1.11232e12i	0.0685395	+	1.92892i
$226$		0			0
$227$		−	3.05930e11i		−	0.507566i	−0.967261	−	0.253783i	$-0.918325\pi$
$227$		−	3.05930e11i		−	0.507566i	0.967261	−	0.253783i	$-0.0816750\pi$
$228$		0			0
$229$	−4.20549e11			−0.667789			−0.333895	−	0.942610i	$-0.608363\pi$
$229$	−4.20549e11			−0.667789			−0.333895	+	0.942610i	$0.608363\pi$
$230$		0			0
$231$	8.76945e11	+	8.46338e11i	1.33325	+	1.28672i
$232$		0			0
$233$		−	9.41814e10i		−	0.137147i	−0.997646	−	0.0685734i	$-0.978155\pi$
$233$		−	9.41814e10i		−	0.137147i	0.997646	−	0.0685734i	$-0.0218447\pi$
$234$		0			0
$235$	4.02994e8			0.000562289
$236$		0			0
$237$	−8.82567e11	+	9.14483e11i	−1.18034	+	1.22302i
$238$		0			0
$239$			1.04683e12i			1.34241i	0.741270	+	0.671207i	$0.234224\pi$
$239$			1.04683e12i			1.34241i	−0.741270	+	0.671207i	$0.765776\pi$
$240$		0			0
$241$	4.83352e11			0.594536			0.297268	−	0.954794i	$-0.403925\pi$
$241$	4.83352e11			0.594536			0.297268	+	0.954794i	$0.403925\pi$
$242$		0			0
$243$	−5.43635e11	+	6.49892e11i	−0.641617	+	0.767025i
$244$		0			0
$245$		−	2.73023e12i		−	3.09292i
$246$		0			0
$247$	−6.19968e11			−0.674348
$248$		0			0
$249$	−1.30126e11	−	1.25585e11i	−0.135947	−	0.131202i
$250$		0			0
$251$			1.46442e10i			0.0146993i	0.999973	+	0.00734967i	$0.00233949\pi$
$251$			1.46442e10i			0.0146993i	−0.999973	+	0.00734967i	$0.997661\pi$
$252$		0			0
$253$	−2.13398e11			−0.205867
$254$		0			0
$255$	−1.47226e12	+	1.52550e12i	−1.36547	+	1.41486i
$256$		0			0
$257$		−	1.85667e11i		−	0.165604i	−0.996566	−	0.0828018i	$-0.973613\pi$
$257$		−	1.85667e11i		−	0.165604i	0.996566	−	0.0828018i	$-0.0263869\pi$
$258$		0			0
$259$	−1.39527e12			−1.19718
$260$		0			0
$261$	4.42714e11	−	1.57307e10i	0.365528	−	0.0129881i
$262$		0			0
$263$		−	2.37088e12i		−	1.88422i	−0.335311	−	0.942108i	$-0.608841\pi$
$263$		−	2.37088e12i		−	1.88422i	0.335311	−	0.942108i	$-0.391159\pi$
$264$		0			0
$265$	2.38542e12			1.82530
$266$		0			0
$267$	−1.88545e11	−	1.81964e11i	−0.138950	−	0.134100i
$268$		0			0
$269$			2.10863e12i			1.49706i	0.663103	+	0.748528i	$0.269239\pi$
$269$			2.10863e12i			1.49706i	−0.663103	+	0.748528i	$0.730761\pi$
$270$		0			0
$271$	7.03984e9			0.00481633			0.00240817	−	0.999997i	$-0.499233\pi$
$271$	7.03984e9			0.00481633			0.00240817	+	0.999997i	$0.499233\pi$
$272$		0			0
$273$	−2.13919e12	+	2.21655e12i	−1.41071	+	1.46172i
$274$		0			0
$275$			3.35732e12i			2.13466i
$276$		0			0
$277$	5.66329e11			0.347272			0.173636	−	0.984810i	$-0.444448\pi$
$277$	5.66329e11			0.347272			0.173636	+	0.984810i	$0.444448\pi$
$278$		0			0
$279$	−7.41645e10	−	2.08723e12i	−0.0438708	−	1.23467i
$280$		0			0
$281$		−	2.59975e12i		−	1.48388i	−0.670465	−	0.741942i	$-0.733905\pi$
$281$		−	2.59975e12i		−	1.48388i	0.670465	−	0.741942i	$-0.266095\pi$
$282$		0			0
$283$	−1.69836e12			−0.935617			−0.467808	−	0.883830i	$-0.654956\pi$
$283$	−1.69836e12			−0.935617			−0.467808	+	0.883830i	$0.654956\pi$
$284$		0			0
$285$	1.28802e12	+	1.24307e12i	0.685012	+	0.661104i
$286$		0			0
$287$			1.09932e12i			0.564568i
$288$		0			0
$289$	−6.44120e11			−0.319505
$290$		0			0
$291$	−1.23843e12	+	1.28322e12i	−0.593481	+	0.614943i
$292$		0			0
$293$		−	5.67611e11i		−	0.262853i	−0.991326	−	0.131426i	$-0.958044\pi$
$293$		−	5.67611e11i		−	0.262853i	0.991326	−	0.131426i	$-0.0419557\pi$
$294$		0			0
$295$	7.40749e11			0.331559
$296$		0			0
$297$	−1.70840e12	+	1.90088e12i	−0.739279	+	0.822567i
$298$		0			0
$299$		−	5.39382e11i		−	0.225705i
$300$		0			0
$301$	3.95487e12			1.60066
$302$		0			0
$303$	−2.10899e12	−	2.03538e12i	−0.825775	−	0.796954i
$304$		0			0
$305$		−	8.60632e12i		−	3.26076i
$306$		0			0
$307$	2.77370e12			1.01711			0.508555	−	0.861030i	$-0.330180\pi$
$307$	2.77370e12			1.01711			0.508555	+	0.861030i	$0.330180\pi$
$308$		0			0
$309$	−1.34124e12	+	1.38974e12i	−0.476116	+	0.493334i
$310$		0			0
$311$			3.17799e12i			1.09232i	0.837681	+	0.546161i	$0.183911\pi$
$311$			3.17799e12i			1.09232i	−0.837681	+	0.546161i	$0.816089\pi$
$312$		0			0
$313$	3.55843e12			1.18450			0.592252	−	0.805752i	$-0.298239\pi$
$313$	3.55843e12			1.18450			0.592252	+	0.805752i	$0.298239\pi$
$314$		0			0
$315$	8.88860e12	−	3.15834e11i	2.86603	−	0.101837i
$316$		0			0
$317$			3.35804e12i			1.04904i	0.851400	+	0.524518i	$0.175754\pi$
$317$			3.35804e12i			1.04904i	−0.851400	+	0.524518i	$0.824246\pi$
$318$		0			0
$319$	1.33625e12			0.404515
$320$		0			0
$321$	4.58336e12	+	4.42340e12i	1.34480	+	1.29787i
$322$		0			0
$323$			2.24600e12i			0.638847i
$324$		0			0
$325$	−8.48591e12			−2.34036
$326$		0			0
$327$	6.96842e11	−	7.22043e11i	0.186378	−	0.193119i
$328$		0			0
$329$		−	2.12131e9i		−	0.000550333i
$330$		0			0
$331$	1.34093e12			0.337493			0.168747	−	0.985659i	$-0.446028\pi$
$331$	1.34093e12			0.337493			0.168747	+	0.985659i	$0.446028\pi$
$332$		0			0
$333$	−1.03902e11	−	2.92413e12i	−0.0253747	−	0.714127i
$334$		0			0
$335$		−	9.18220e12i		−	2.17632i
$336$		0			0
$337$	−7.61536e12			−1.75203			−0.876014	−	0.482285i	$-0.839807\pi$
$337$	−7.61536e12			−1.75203			−0.876014	+	0.482285i	$0.839807\pi$
$338$		0			0
$339$	−1.07063e12	−	1.03326e12i	−0.239134	−	0.230788i
$340$		0			0
$341$		−	6.29992e12i		−	1.36635i
$342$		0			0
$343$	−6.41769e12			−1.35179
$344$		0			0
$345$	−1.08149e12	+	1.12060e12i	−0.221272	+	0.229274i
$346$		0			0
$347$		−	4.04512e12i		−	0.804052i	−0.915628	−	0.402026i	$-0.868306\pi$
$347$		−	4.04512e12i		−	0.804052i	0.915628	−	0.402026i	$-0.131694\pi$
$348$		0			0
$349$	−7.58213e12			−1.46441			−0.732207	−	0.681082i	$-0.761510\pi$
$349$	−7.58213e12			−1.46441			−0.732207	+	0.681082i	$0.761510\pi$
$350$		0			0
$351$	−4.80463e12	−	4.31814e12i	−0.901829	−	0.810515i
$352$		0			0
$353$			3.96340e12i			0.723093i	0.932354	+	0.361547i	$0.117751\pi$
$353$			3.96340e12i			0.723093i	−0.932354	+	0.361547i	$0.882249\pi$
$354$		0			0
$355$	1.21309e13			2.15154
$356$		0			0
$357$	8.03006e12	+	7.74980e12i	1.38477	+	1.33644i
$358$		0			0
$359$		−	9.40340e12i		−	1.57693i	−0.615079	−	0.788465i	$-0.710876\pi$
$359$		−	9.40340e12i		−	1.57693i	0.615079	−	0.788465i	$-0.289124\pi$
$360$		0			0
$361$	−4.23471e12			−0.690698
$362$		0			0
$363$	−9.76708e11	+	1.01203e12i	−0.154964	+	0.160568i
$364$		0			0
$365$		−	1.58610e12i		−	0.244831i
$366$		0			0
$367$	2.67351e12			0.401562			0.200781	−	0.979636i	$-0.435652\pi$
$367$	2.67351e12			0.401562			0.200781	+	0.979636i	$0.435652\pi$
$368$		0			0
$369$	−2.30390e12	+	8.18633e10i	−0.336769	+	0.0119662i
$370$		0			0
$371$		−	1.25566e13i		−	1.78649i
$372$		0			0
$373$	7.52230e12			1.04185			0.520927	−	0.853602i	$-0.325587\pi$
$373$	7.52230e12			1.04185			0.520927	+	0.853602i	$0.325587\pi$
$374$		0			0
$375$	8.49595e12	+	8.19943e12i	1.14566	+	1.10567i
$376$		0			0
$377$			3.37749e12i			0.443493i
$378$		0			0
$379$	4.82171e12			0.616602			0.308301	−	0.951289i	$-0.400240\pi$
$379$	4.82171e12			0.616602			0.308301	+	0.951289i	$0.400240\pi$
$380$		0			0
$381$	9.23827e12	−	9.57236e12i	1.15071	−	1.19232i
$382$		0			0
$383$			2.52117e11i			0.0305920i	0.999883	+	0.0152960i	$0.00486906\pi$
$383$			2.52117e11i			0.0305920i	−0.999883	+	0.0152960i	$0.995131\pi$
$384$		0			0
$385$	2.68286e13			3.17172
$386$		0			0
$387$	2.94507e11	+	8.28839e12i	0.0339267	+	0.954806i
$388$		0			0
$389$		−	5.39301e12i		−	0.605457i	−0.953077	−	0.302729i	$-0.902102\pi$
$389$		−	5.39301e12i		−	0.605457i	0.953077	−	0.302729i	$-0.0978976\pi$
$390$		0			0
$391$	−1.95406e12			−0.213822
$392$		0			0
$393$	−9.83330e12	−	9.49010e12i	−1.04891	−	1.01230i
$394$		0			0
$395$			2.79770e13i			2.90949i
$396$		0			0
$397$	−8.66288e12			−0.878435			−0.439218	−	0.898381i	$-0.644744\pi$
$397$	−8.66288e12			−0.878435			−0.439218	+	0.898381i	$0.644744\pi$
$398$		0			0
$399$	6.54335e12	−	6.77998e12i	0.647047	−	0.670447i
$400$		0			0
$401$		−	5.59724e12i		−	0.539824i	−0.962885	−	0.269912i	$-0.913005\pi$
$401$		−	5.59724e12i		−	0.539824i	0.962885	−	0.269912i	$-0.0869947\pi$
$402$		0			0
$403$	1.59236e13			1.49801
$404$		0			0
$405$	1.32382e12	+	1.86047e13i	0.121493	+	1.70745i
$406$		0			0
$407$		−	8.82595e12i		−	0.790295i
$408$		0			0
$409$	2.38459e12			0.208352			0.104176	−	0.994559i	$-0.466779\pi$
$409$	2.38459e12			0.208352			0.104176	+	0.994559i	$0.466779\pi$
$410$		0			0
$411$	−1.09630e13	−	1.05804e13i	−0.934805	−	0.902179i
$412$		0			0
$413$		−	3.89921e12i		−	0.324509i
$414$		0			0
$415$	−3.98099e12			−0.323408
$416$		0			0
$417$	−1.17623e13	+	1.21876e13i	−0.932848	+	0.966583i
$418$		0			0
$419$			9.44038e12i			0.731004i	0.930811	+	0.365502i	$0.119103\pi$
$419$			9.44038e12i			0.731004i	−0.930811	+	0.365502i	$0.880897\pi$
$420$		0			0
$421$	6.89623e12			0.521436			0.260718	−	0.965415i	$-0.416041\pi$
$421$	6.89623e12			0.521436			0.260718	+	0.965415i	$0.416041\pi$
$422$		0			0
$423$	4.44573e9	−	1.57968e8i	0.000328278	−	1.16645e-5i
$424$		0			0
$425$			3.07425e13i			2.21715i
$426$		0			0
$427$	−4.53027e13			−3.19142
$428$		0			0
$429$	−1.40211e13	−	1.35317e13i	−0.964928	−	0.931250i
$430$		0			0
$431$			1.36918e12i			0.0920604i	0.998940	+	0.0460302i	$0.0146570\pi$
$431$			1.36918e12i			0.0920604i	−0.998940	+	0.0460302i	$0.985343\pi$
$432$		0			0
$433$	−6.62027e12			−0.434947			−0.217474	−	0.976066i	$-0.569782\pi$
$433$	−6.62027e12			−0.434947			−0.217474	+	0.976066i	$0.569782\pi$
$434$		0			0
$435$	6.77203e12	−	7.01693e12i	0.434783	−	0.450506i
$436$		0			0
$437$			1.64986e12i			0.103524i
$438$		0			0
$439$	−1.25660e13			−0.770679			−0.385339	−	0.922775i	$-0.625916\pi$
$439$	−1.25660e13			−0.770679			−0.385339	+	0.922775i	$0.625916\pi$
$440$		0			0
$441$	−1.07021e12	−	3.01192e13i	−0.0641618	−	1.80572i
$442$		0			0
$443$		−	1.42122e13i		−	0.832997i	−0.909136	−	0.416499i	$-0.863257\pi$
$443$		−	1.42122e13i		−	0.832997i	0.909136	−	0.416499i	$-0.136743\pi$
$444$		0			0
$445$	−5.76820e12			−0.330553
$446$		0			0
$447$	−1.14832e13	−	1.10824e13i	−0.643467	−	0.621009i
$448$		0			0
$449$			2.33640e12i			0.128031i	0.997949	+	0.0640154i	$0.0203907\pi$
$449$			2.33640e12i			0.128031i	−0.997949	+	0.0640154i	$0.979609\pi$
$450$		0			0
$451$	−6.95390e12			−0.372688
$452$		0			0
$453$	5.42577e12	−	5.62199e12i	0.284427	−	0.294713i
$454$		0			0
$455$			6.78116e13i			3.47734i
$456$		0			0
$457$	3.00514e13			1.50759			0.753797	−	0.657108i	$-0.228220\pi$
$457$	3.00514e13			1.50759			0.753797	+	0.657108i	$0.228220\pi$
$458$		0			0
$459$	−1.56436e13	+	1.74061e13i	−0.767846	+	0.854352i
$460$		0			0
$461$			3.81933e12i			0.183435i	0.995785	+	0.0917176i	$0.0292357\pi$
$461$			3.81933e12i			0.183435i	−0.995785	+	0.0917176i	$0.970764\pi$
$462$		0			0
$463$	4.23279e11			0.0198940			0.00994700	−	0.999951i	$-0.496834\pi$
$463$	4.23279e11			0.0198940			0.00994700	+	0.999951i	$0.496834\pi$
$464$		0			0
$465$	−3.30822e13	−	3.19276e13i	−1.52170	−	1.46859i
$466$		0			0
$467$		−	3.30173e12i		−	0.148647i	−0.997234	−	0.0743236i	$-0.976320\pi$
$467$		−	3.30173e12i		−	0.148647i	0.997234	−	0.0743236i	$-0.0236798\pi$
$468$		0			0
$469$	−4.83340e13			−2.13004
$470$		0			0
$471$	−1.63193e13	+	1.69095e13i	−0.704041	+	0.729502i
$472$		0			0
$473$			2.50170e13i			1.05665i
$474$		0			0
$475$	2.59567e13			1.07345
$476$		0			0
$477$	2.63153e13	−	9.35049e11i	1.06566	−	0.0378654i
$478$		0			0
$479$			9.64798e12i			0.382612i	0.981530	+	0.191306i	$0.0612723\pi$
$479$			9.64798e12i			0.382612i	−0.981530	+	0.191306i	$0.938728\pi$
$480$		0			0
$481$	2.23084e13			0.866447
$482$		0			0
$483$	5.89869e12	+	5.69282e12i	0.224399	+	0.216567i
$484$		0			0
$485$			3.92578e13i			1.46291i
$486$		0			0
$487$	2.19673e13			0.801923			0.400962	−	0.916095i	$-0.368676\pi$
$487$	2.19673e13			0.801923			0.400962	+	0.916095i	$0.368676\pi$
$488$		0			0
$489$	9.28429e12	−	9.62005e12i	0.332051	−	0.344059i
$490$		0			0
$491$		−	4.28264e13i		−	1.50074i	−0.661021	−	0.750368i	$-0.729877\pi$
$491$		−	4.28264e13i		−	1.50074i	0.661021	−	0.750368i	$-0.270123\pi$
$492$		0			0
$493$	1.22359e13			0.420146
$494$		0			0
$495$	1.99785e12	+	5.62259e13i	0.0672258	+	1.89195i
$496$		0			0
$497$		−	6.38554e13i		−	2.10579i
$498$		0			0
$499$	−4.94645e13			−1.59879			−0.799394	−	0.600808i	$-0.794846\pi$
$499$	−4.94645e13			−1.59879			−0.799394	+	0.600808i	$0.794846\pi$
$500$		0			0
$501$	2.37366e13	+	2.29081e13i	0.752020	+	0.725773i
$502$		0			0
$503$			8.19508e12i			0.254515i	0.991870	+	0.127257i	$0.0406174\pi$
$503$			8.19508e12i			0.254515i	−0.991870	+	0.127257i	$0.959383\pi$
$504$		0			0
$505$	−6.45210e13			−1.96446
$506$		0			0
$507$	1.09392e13	−	1.13348e13i	0.326546	−	0.338355i
$508$		0			0
$509$			6.27293e13i			1.83604i	0.396538	+	0.918018i	$0.370211\pi$
$509$			6.27293e13i			1.83604i	−0.396538	+	0.918018i	$0.629789\pi$
$510$		0			0
$511$	−8.34904e12			−0.239625
$512$		0			0
$513$	1.46964e13	+	1.32083e13i	0.413641	+	0.371758i
$514$		0			0
$515$			4.25167e13i			1.17361i
$516$		0			0
$517$	1.34186e10			0.000363291
$518$		0			0
$519$	−9.48132e12	−	9.15041e12i	−0.251786	−	0.242999i
$520$		0			0
$521$			6.82197e13i			1.77714i	0.458742	+	0.888570i	$0.348300\pi$
$521$			6.82197e13i			1.77714i	−0.458742	+	0.888570i	$0.651700\pi$
$522$		0			0
$523$	−5.20501e13			−1.33019			−0.665094	−	0.746760i	$-0.731608\pi$
$523$	−5.20501e13			−1.33019			−0.665094	+	0.746760i	$0.731608\pi$
$524$		0			0
$525$	8.95632e13	−	9.28022e13i	2.24560	−	2.32681i
$526$		0			0
$527$		−	5.76875e13i		−	1.41915i
$528$		0			0
$529$	3.99911e13			0.965351
$530$		0			0
$531$	8.17175e12	−	2.90363e11i	0.193572	−	0.00687810i
$532$		0			0
$533$		−	1.75766e13i		−	0.408600i
$534$		0			0
$535$	1.40220e14			3.19920
$536$		0			0
$537$	−1.70258e13	−	1.64316e13i	−0.381274	−	0.367967i
$538$		0			0
$539$		−	9.09092e13i		−	1.99832i
$540$		0			0
$541$	−8.97274e13			−1.93615			−0.968074	−	0.250664i	$-0.919351\pi$
$541$	−8.97274e13			−1.93615			−0.968074	+	0.250664i	$0.919351\pi$
$542$		0			0
$543$	3.14562e13	−	3.25937e13i	0.666356	−	0.690454i
$544$		0			0
$545$		−	2.20896e13i		−	0.459416i
$546$		0			0
$547$	−7.14970e13			−1.45999			−0.729997	−	0.683450i	$-0.760479\pi$
$547$	−7.14970e13			−1.45999			−0.729997	+	0.683450i	$0.760479\pi$
$548$		0			0
$549$	−3.37356e12	−	9.49428e13i	−0.0676435	−	1.90371i
$550$		0			0
$551$		−	1.03310e13i		−	0.203416i
$552$		0			0
$553$	1.47268e14			2.84762
$554$		0			0
$555$	−4.63469e13	−	4.47293e13i	−0.880148	−	0.849430i
$556$		0			0
$557$			3.15650e13i			0.588748i	0.955690	+	0.294374i	$0.0951112\pi$
$557$			3.15650e13i			0.588748i	−0.955690	+	0.294374i	$0.904889\pi$
$558$		0			0
$559$	−6.32326e13			−1.15846
$560$		0			0
$561$	−4.90223e13	+	5.07951e13i	−0.882225	+	0.914129i
$562$		0			0
$563$			2.62866e13i			0.464721i	0.972630	+	0.232360i	$0.0746449\pi$
$563$			2.62866e13i			0.464721i	−0.972630	+	0.232360i	$0.925355\pi$
$564$		0			0
$565$	−3.27541e13			−0.568883
$566$		0			0
$567$	9.79330e13	−	6.96841e12i	1.67114	−	0.118910i
$568$		0			0
$569$			7.15953e13i			1.20039i	0.799853	+	0.600196i	$0.204911\pi$
$569$			7.15953e13i			1.20039i	−0.799853	+	0.600196i	$0.795089\pi$
$570$		0			0
$571$	8.82970e13			1.45467			0.727337	−	0.686281i	$-0.240758\pi$
$571$	8.82970e13			1.45467			0.727337	+	0.686281i	$0.240758\pi$
$572$		0			0
$573$	−1.82463e13	−	1.76095e13i	−0.295394	−	0.285085i
$574$		0			0
$575$			2.25827e13i			0.359283i
$576$		0			0
$577$	−5.49027e13			−0.858449			−0.429225	−	0.903198i	$-0.641213\pi$
$577$	−5.49027e13			−0.858449			−0.429225	+	0.903198i	$0.641213\pi$
$578$		0			0
$579$	1.90042e13	−	1.96915e13i	0.292050	−	0.302611i
$580$		0			0
$581$			2.09555e13i			0.316531i
$582$		0			0
$583$	7.94280e13			1.17932
$584$		0			0
$585$	−1.42116e14	+	5.04973e12i	−2.07426	+	0.0737036i
$586$		0			0
$587$			3.24821e13i			0.466073i	0.972468	+	0.233037i	$0.0748662\pi$
$587$			3.24821e13i			0.466073i	−0.972468	+	0.233037i	$0.925134\pi$
$588$		0			0
$589$	−4.87070e13			−0.687092
$590$		0			0
$591$	−3.65999e13	−	3.53225e13i	−0.507624	−	0.489907i
$592$		0			0
$593$			5.39408e13i			0.735603i	0.929904	+	0.367802i	$0.119889\pi$
$593$			5.39408e13i			0.735603i	−0.929904	+	0.367802i	$0.880111\pi$
$594$		0			0
$595$	2.45666e14			3.29428
$596$		0			0
$597$	2.55841e12	−	2.65093e12i	0.0337364	−	0.0349564i
$598$		0			0
$599$			3.22481e13i			0.418186i	0.977896	+	0.209093i	$0.0670512\pi$
$599$			3.22481e13i			0.418186i	−0.977896	+	0.209093i	$0.932949\pi$
$600$		0			0
$601$	3.59568e13			0.458573			0.229286	−	0.973359i	$-0.426361\pi$
$601$	3.59568e13			0.458573			0.229286	+	0.973359i	$0.426361\pi$
$602$		0			0
$603$	−3.59929e12	−	1.01296e14i	−0.0451471	−	1.27059i
$604$		0			0
$605$			3.09613e13i			0.381981i
$606$		0			0
$607$	−5.98176e13			−0.725915			−0.362957	−	0.931806i	$-0.618233\pi$
$607$	−5.98176e13			−0.725915			−0.362957	+	0.931806i	$0.618233\pi$
$608$		0			0
$609$	−3.69363e13	−	3.56472e13i	−0.440927	−	0.425538i
$610$		0			0
$611$			3.39167e10i			0.000398298i
$612$		0			0
$613$	5.00692e12			0.0578454			0.0289227	−	0.999582i	$-0.490792\pi$
$613$	5.00692e12			0.0578454			0.0289227	+	0.999582i	$0.490792\pi$
$614$		0			0
$615$	−3.52419e13	+	3.65164e13i	−0.400575	+	0.415061i
$616$		0			0
$617$		−	1.77476e14i		−	1.98479i	−0.123095	−	0.992395i	$-0.539282\pi$
$617$		−	1.77476e14i		−	1.98479i	0.123095	−	0.992395i	$-0.460718\pi$
$618$		0			0
$619$	1.46484e13			0.161189			0.0805946	−	0.996747i	$-0.474318\pi$
$619$	1.46484e13			0.161189			0.0805946	+	0.996747i	$0.474318\pi$
$620$		0			0
$621$	−1.14914e13	+	1.27861e13i	−0.124427	+	0.138446i
$622$		0			0
$623$			3.03631e13i			0.323524i
$624$		0			0
$625$	7.58462e13			0.795305
$626$		0			0
$627$	4.28876e13	+	4.13907e13i	0.442582	+	0.427135i
$628$		0			0
$629$		−	8.08180e13i		−	0.820833i
$630$		0			0
$631$	−5.18554e13			−0.518379			−0.259189	−	0.965827i	$-0.583455\pi$
$631$	−5.18554e13			−0.518379			−0.259189	+	0.965827i	$0.583455\pi$
$632$		0			0
$633$	4.50438e13	−	4.66728e13i	0.443217	−	0.459246i
$634$		0			0
$635$		−	2.92850e14i		−	2.83646i
$636$		0			0
$637$	2.29781e14			2.19087
$638$		0			0
$639$	1.33825e14	−	4.75512e12i	1.25612	−	0.0446331i
$640$		0			0
$641$			1.58207e14i			1.46196i	0.682396	+	0.730982i	$0.260938\pi$
$641$			1.58207e14i			1.46196i	−0.682396	+	0.730982i	$0.739062\pi$
$642$		0			0
$643$	−1.36125e14			−1.23846			−0.619231	−	0.785209i	$-0.712556\pi$
$643$	−1.36125e14			−1.23846			−0.619231	+	0.785209i	$0.712556\pi$
$644$		0			0
$645$	1.31369e14	+	1.26784e14i	1.17678	+	1.13571i
$646$		0			0
$647$		−	9.00820e13i		−	0.794541i	−0.917702	−	0.397271i	$-0.869957\pi$
$647$		−	9.00820e13i		−	0.794541i	0.917702	−	0.397271i	$-0.130043\pi$
$648$		0			0
$649$	2.46649e13			0.214218
$650$		0			0
$651$	−1.68063e14	+	1.74141e14i	−1.43737	+	1.48935i
$652$		0			0
$653$			3.05209e13i			0.257059i	0.991706	+	0.128529i	$0.0410256\pi$
$653$			3.05209e13i			0.257059i	−0.991706	+	0.128529i	$0.958974\pi$
$654$		0			0
$655$	−3.00833e14			−2.49528
$656$		0			0
$657$	−6.21728e11	−	1.74974e13i	−0.00507895	−	0.142938i
$658$		0			0
$659$			1.37676e14i			1.10773i	0.832608	+	0.553863i	$0.186847\pi$
$659$			1.37676e14i			1.10773i	−0.832608	+	0.553863i	$0.813153\pi$
$660$		0			0
$661$	−5.75218e13			−0.455854			−0.227927	−	0.973678i	$-0.573195\pi$
$661$	−5.75218e13			−0.455854			−0.227927	+	0.973678i	$0.573195\pi$
$662$		0			0
$663$	−1.28389e14	−	1.23908e14i	−1.00221	−	0.967235i
$664$		0			0
$665$		−	2.07422e14i		−	1.59495i
$666$		0			0
$667$	8.98817e12			0.0680835
$668$		0			0
$669$	−1.10922e14	+	1.14933e14i	−0.827723	+	0.857657i
$670$		0			0
$671$		−	2.86567e14i		−	2.10676i
$672$		0			0
$673$	8.10871e13			0.587322			0.293661	−	0.955910i	$-0.405126\pi$
$673$	8.10871e13			0.587322			0.293661	+	0.955910i	$0.405126\pi$
$674$		0			0
$675$	2.01159e14	+	1.80791e14i	1.43556	+	1.29020i
$676$		0			0
$677$		−	4.40518e13i		−	0.309756i	−0.987934	−	0.154878i	$-0.950501\pi$
$677$		−	4.40518e13i		−	0.309756i	0.987934	−	0.154878i	$-0.0494985\pi$
$678$		0			0
$679$	2.06648e14			1.43180
$680$		0			0
$681$	−5.34922e13	−	5.16253e13i	−0.365220	−	0.352474i
$682$		0			0
$683$			2.80952e14i			1.89029i	0.326654	+	0.945144i	$0.394079\pi$
$683$			2.80952e14i			1.89029i	−0.326654	+	0.945144i	$0.605921\pi$
$684$		0			0
$685$	−3.35395e14			−2.22384
$686$		0			0
$687$	−7.09671e13	+	7.35335e13i	−0.463739	+	0.480509i
$688$		0			0
$689$			2.00761e14i			1.29295i
$690$		0			0
$691$	1.40745e14			0.893393			0.446697	−	0.894686i	$-0.352600\pi$
$691$	1.40745e14			0.893393			0.446697	+	0.894686i	$0.352600\pi$
$692$		0			0
$693$	2.95966e14	−	1.05164e13i	1.85172	−	0.0657964i
$694$		0			0
$695$			3.72860e14i			2.29944i
$696$		0			0
$697$	−6.36759e13			−0.387089
$698$		0			0
$699$	−1.64677e13	−	1.58930e13i	−0.0986842	−	0.0952400i
$700$		0			0
$701$		−	3.11816e13i		−	0.184208i	−0.995749	−	0.0921040i	$-0.970641\pi$
$701$		−	3.11816e13i		−	0.184208i	0.995749	−	0.0921040i	$-0.0293592\pi$
$702$		0			0
$703$	−6.82367e13			−0.397412
$704$		0			0
$705$	6.80047e10	−	7.04640e10i	0.000390475	−	0.000404596i
$706$		0			0
$707$			3.39631e14i			1.92269i
$708$		0			0
$709$	−3.26220e14			−1.82087			−0.910436	−	0.413651i	$-0.864253\pi$
$709$	−3.26220e14			−1.82087			−0.910436	+	0.413651i	$0.864253\pi$
$710$		0			0
$711$	1.09666e13	+	3.08636e14i	0.0603565	+	1.69863i
$712$		0			0
$713$		−	4.23759e13i		−	0.229970i
$714$		0			0
$715$	−4.28950e14			−2.29550
$716$		0			0
$717$	1.83039e14	+	1.76651e14i	0.965936	+	0.932224i
$718$		0			0
$719$		−	2.80158e14i		−	1.45801i	−0.684511	−	0.729003i	$-0.739984\pi$
$719$		−	2.80158e14i		−	1.45801i	0.684511	−	0.729003i	$-0.260016\pi$
$720$		0			0
$721$	2.23803e14			1.14865
$722$		0			0
$723$	8.15649e13	−	8.45146e13i	0.412869	−	0.427799i
$724$		0			0
$725$		−	1.41408e14i		−	0.705965i
$726$		0			0
$727$	−1.09502e14			−0.539202			−0.269601	−	0.962972i	$-0.586892\pi$
$727$	−1.09502e14			−0.539202			−0.269601	+	0.962972i	$0.586892\pi$
$728$		0			0
$729$	2.18968e13	+	2.04723e14i	0.106351	+	0.994329i
$730$		0			0
$731$			2.29077e14i			1.09748i
$732$		0			0
$733$	−1.14955e14			−0.543262			−0.271631	−	0.962401i	$-0.587563\pi$
$733$	−1.14955e14			−0.543262			−0.271631	+	0.962401i	$0.587563\pi$
$734$		0			0
$735$	−4.77383e14	−	4.60722e14i	−2.22552	−	2.14784i
$736$		0			0
$737$		−	3.05742e14i		−	1.40611i
$738$		0			0
$739$	1.62362e14			0.736651			0.368325	−	0.929697i	$-0.379931\pi$
$739$	1.62362e14			0.736651			0.368325	+	0.929697i	$0.379931\pi$
$740$		0			0
$741$	−1.04619e14	+	1.08402e14i	−0.468294	+	0.485229i
$742$		0			0
$743$			7.87172e13i			0.347636i	0.984778	+	0.173818i	$0.0556105\pi$
$743$			7.87172e13i			0.347636i	−0.984778	+	0.173818i	$0.944389\pi$
$744$		0			0
$745$	−3.51309e14			−1.53076
$746$		0			0
$747$	−4.39173e13	+	1.56049e12i	−0.188813	+	0.00670901i
$748$		0			0
$749$		−	7.38102e14i		−	3.13117i
$750$		0			0
$751$	2.16911e14			0.907990			0.453995	−	0.891004i	$-0.349998\pi$
$751$	2.16911e14			0.907990			0.453995	+	0.891004i	$0.349998\pi$
$752$		0			0
$753$	2.56056e12	+	2.47119e12i	0.0105769	+	0.0102078i
$754$		0			0
$755$		−	1.71995e14i		−	0.701102i
$756$		0			0
$757$	3.18882e14			1.28277			0.641387	−	0.767217i	$-0.278359\pi$
$757$	3.18882e14			1.28277			0.641387	+	0.767217i	$0.278359\pi$
$758$		0			0
$759$	−3.60106e13	+	3.73129e13i	−0.142962	+	0.148132i
$760$		0			0
$761$		−	1.03295e14i		−	0.404720i	−0.979311	−	0.202360i	$-0.935139\pi$
$761$		−	1.03295e14i		−	0.404720i	0.979311	−	0.202360i	$-0.0648610\pi$
$762$		0			0
$763$	−1.16277e14			−0.449648
$764$		0			0
$765$	1.82940e13	+	5.14853e14i	0.0698235	+	1.96506i
$766$		0			0
$767$			6.23428e13i			0.234860i
$768$		0			0
$769$	−4.32731e14			−1.60911			−0.804556	−	0.593877i	$-0.797597\pi$
$769$	−4.32731e14			−1.60911			−0.804556	+	0.593877i	$0.797597\pi$
$770$		0			0
$771$	−3.24642e13	−	3.13311e13i	−0.119160	−	0.115002i
$772$		0			0
$773$			1.82569e14i			0.661499i	0.943719	+	0.330749i	$0.107301\pi$
$773$			1.82569e14i			0.661499i	−0.943719	+	0.330749i	$0.892699\pi$
$774$		0			0
$775$	−6.66685e14			−2.38458
$776$		0			0
$777$	−2.35450e14	+	2.43965e14i	−0.831368	+	0.861434i
$778$		0			0
$779$			5.37631e13i			0.187412i
$780$		0			0
$781$	4.03925e14			1.39010
$782$		0			0
$783$	7.19567e13	−	8.00635e13i	0.244491	−	0.272036i
$784$		0			0
$785$			5.17317e14i			1.73544i
$786$		0			0
$787$	2.59519e14			0.859599			0.429799	−	0.902924i	$-0.358584\pi$
$787$	2.59519e14			0.859599			0.429799	+	0.902924i	$0.358584\pi$
$788$		0			0
$789$	−4.14551e14	−	4.00082e14i	−1.35579	−	1.30847i
$790$		0			0
$791$			1.72414e14i			0.556787i
$792$		0			0
$793$	7.24324e14			2.30976
$794$		0			0
$795$	4.02536e14	−	4.17093e14i	1.26756	−	1.31340i
$796$		0			0
$797$			4.01181e14i			1.24752i	0.781615	+	0.623762i	$0.214396\pi$
$797$			4.01181e14i			1.24752i	−0.781615	+	0.623762i	$0.785604\pi$
$798$		0			0
$799$	1.22872e11			0.000377329
$800$		0			0
$801$	−6.36334e13	+	2.26105e12i	−0.192984	+	0.00685722i
$802$		0			0
$803$		−	5.28128e13i		−	0.158184i
$804$		0			0
$805$	1.80460e14			0.533829
$806$		0			0
$807$	3.68696e14	+	3.55828e14i	1.07721	+	1.03961i
$808$		0			0
$809$		−	3.58715e14i		−	1.03516i	−0.855635	−	0.517580i	$-0.826833\pi$
$809$		−	3.58715e14i		−	1.03516i	0.855635	−	0.517580i	$-0.173167\pi$
$810$		0			0
$811$	1.70575e14			0.486197			0.243099	−	0.970002i	$-0.421836\pi$
$811$	1.70575e14			0.486197			0.243099	+	0.970002i	$0.421836\pi$
$812$		0			0
$813$	1.18796e12	−	1.23092e12i	0.00334465	−	0.00346560i
$814$		0			0
$815$		−	2.94309e14i		−	0.818493i
$816$		0			0
$817$	1.93416e14			0.531350
$818$		0			0
$819$	2.65812e13	+	7.48081e14i	0.0721365	+	2.03015i
$820$		0			0
$821$		−	5.41602e14i		−	1.45199i	−0.687699	−	0.725996i	$-0.741379\pi$
$821$		−	5.41602e14i		−	1.45199i	0.687699	−	0.725996i	$-0.258621\pi$
$822$		0			0
$823$	6.00889e14			1.59146			0.795728	−	0.605654i	$-0.207088\pi$
$823$	6.00889e14			1.59146			0.795728	+	0.605654i	$0.207088\pi$
$824$		0			0
$825$	5.87031e14	+	5.66543e14i	1.53600	+	1.48239i
$826$		0			0
$827$		−	6.42677e14i		−	1.66137i	−0.556746	−	0.830683i	$-0.687950\pi$
$827$		−	6.42677e14i		−	1.66137i	0.556746	−	0.830683i	$-0.312050\pi$
$828$		0			0
$829$	2.94214e14			0.751433			0.375716	−	0.926735i	$-0.377397\pi$
$829$	2.94214e14			0.751433			0.375716	+	0.926735i	$0.377397\pi$
$830$		0			0
$831$	9.55673e13	−	9.90233e13i	0.241159	−	0.249881i
$832$		0			0
$833$		−	8.32443e14i		−	2.07553i
$834$		0			0
$835$	7.26179e14			1.78900
$836$		0			0
$837$	−3.77470e14	−	3.39249e14i	−0.918871	−	0.825832i
$838$		0			0
$839$		−	3.32908e14i		−	0.800783i	−0.916344	−	0.400391i	$-0.868874\pi$
$839$		−	3.32908e14i		−	0.800783i	0.916344	−	0.400391i	$-0.131126\pi$
$840$		0			0
$841$	3.64425e14			0.866221
$842$		0			0
$843$	−4.54569e14	−	4.38704e14i	−1.06773	−	1.03047i
$844$		0			0
$845$		−	3.46768e14i		−	0.804924i
$846$		0			0
$847$	1.62977e14			0.373859
$848$		0			0
$849$	−2.86596e14	+	2.96960e14i	−0.649728	+	0.673225i
$850$		0			0
$851$		−	5.93670e13i		−	0.133014i
$852$		0			0
$853$	−3.59443e14			−0.795948			−0.397974	−	0.917397i	$-0.630287\pi$
$853$	−3.59443e14			−0.795948			−0.397974	+	0.917397i	$0.630287\pi$
$854$		0			0
$855$	4.34703e14	−	1.54461e13i	0.951398	−	0.0338056i
$856$		0			0
$857$			2.64547e14i			0.572267i	0.958190	+	0.286133i	$0.0923700\pi$
$857$			2.64547e14i			0.572267i	−0.958190	+	0.286133i	$0.907630\pi$
$858$		0			0
$859$	−8.74692e14			−1.87021			−0.935103	−	0.354376i	$-0.884693\pi$
$859$	−8.74692e14			−1.87021			−0.935103	+	0.354376i	$0.884693\pi$
$860$		0			0
$861$	1.92218e14	+	1.85509e14i	0.406236	+	0.392057i
$862$		0			0
$863$			4.64635e14i			0.970639i	0.874337	+	0.485320i	$0.161297\pi$
$863$			4.64635e14i			0.970639i	−0.874337	+	0.485320i	$0.838703\pi$
$864$		0			0
$865$	−2.90065e14			−0.598983
$866$		0			0
$867$	−1.08694e14	+	1.12625e14i	−0.221876	+	0.229900i
$868$		0			0
$869$			9.31560e14i			1.87980i
$870$		0			0
$871$	7.72790e14			1.54160
$872$		0			0
$873$	1.53885e13	+	4.33082e14i	0.0303476	+	0.854080i
$874$		0			0
$875$		−	1.36818e15i		−	2.66750i
$876$		0			0
$877$	−3.09510e14			−0.596591			−0.298295	−	0.954474i	$-0.596418\pi$
$877$	−3.09510e14			−0.596591			−0.298295	+	0.954474i	$0.596418\pi$
$878$		0			0
$879$	−9.92474e13	−	9.57835e13i	−0.189136	−	0.182535i
$880$		0			0
$881$		−	3.87713e14i		−	0.730518i	−0.930906	−	0.365259i	$-0.880980\pi$
$881$		−	3.87713e14i		−	0.730518i	0.930906	−	0.365259i	$-0.119020\pi$
$882$		0			0
$883$	3.34305e14			0.622786			0.311393	−	0.950281i	$-0.399204\pi$
$883$	3.34305e14			0.622786			0.311393	+	0.950281i	$0.399204\pi$
$884$		0			0
$885$	1.25000e14	−	1.29521e14i	0.230247	−	0.238574i
$886$		0			0
$887$		−	4.02259e14i		−	0.732636i	−0.930490	−	0.366318i	$-0.880618\pi$
$887$		−	4.02259e14i		−	0.732636i	0.930490	−	0.366318i	$-0.119382\pi$
$888$		0			0
$889$	−1.54153e15			−2.77614
$890$		0			0
$891$	4.40795e13	+	6.19486e14i	0.0784961	+	1.10317i
$892$		0			0
$893$		−	1.03744e11i		−	0.000182687i
$894$		0			0
$895$	−5.20876e14			−0.907025
$896$		0			0
$897$	−9.43115e13	−	9.10199e13i	−0.162406	−	0.156738i
$898$		0			0
$899$			2.65348e14i			0.451874i
$900$		0			0
$901$	7.27311e14			1.22489
$902$		0			0
$903$	6.67379e14	−	6.91513e14i	1.11156	−	1.15176i
$904$		0			0
$905$		−	9.97148e14i		−	1.64254i
$906$		0			0
$907$	1.22073e14			0.198877			0.0994383	−	0.995044i	$-0.468295\pi$
$907$	1.22073e14			0.198877			0.0994383	+	0.995044i	$0.468295\pi$
$908$		0			0
$909$	−7.11779e14	+	2.52913e13i	−1.14690	+	0.0407522i
$910$		0			0
$911$		−	8.78434e14i		−	1.39997i	−0.714160	−	0.699983i	$-0.753191\pi$
$911$		−	8.78434e14i		−	1.39997i	0.714160	−	0.699983i	$-0.246809\pi$
$912$		0			0
$913$	−1.32556e14			−0.208952
$914$		0			0
$915$	−1.50483e15	−	1.45230e15i	−2.34628	−	2.26440i
$916$		0			0
$917$			1.58355e15i			2.44222i
$918$		0			0
$919$	6.50552e14			0.992440			0.496220	−	0.868197i	$-0.334721\pi$
$919$	6.50552e14			0.992440			0.496220	+	0.868197i	$0.334721\pi$
$920$		0			0
$921$	4.68058e14	−	4.84985e14i	0.706320	−	0.731863i
$922$		0			0
$923$			1.02096e15i			1.52405i
$924$		0			0
$925$	−9.34001e14			−1.37924
$926$		0			0
$927$	1.66659e13	+	4.69033e14i	0.0243462	+	0.685180i
$928$		0			0
$929$			3.32678e14i			0.480779i	0.970676	+	0.240390i	$0.0772752\pi$
$929$			3.32678e14i			0.480779i	−0.970676	+	0.240390i	$0.922725\pi$
$930$		0			0
$931$	−7.02853e14			−1.00488
$932$		0			0
$933$	5.55675e14	+	5.36281e14i	0.785982	+	0.758550i
$934$		0			0
$935$			1.55399e15i			2.17465i
$936$		0			0
$937$	−3.20052e14			−0.443121			−0.221561	−	0.975147i	$-0.571115\pi$
$937$	−3.20052e14			−0.443121			−0.221561	+	0.975147i	$0.571115\pi$
$938$		0			0
$939$	6.00480e14	−	6.22196e14i	0.822566	−	0.852313i
$940$		0			0
$941$		−	9.14134e14i		−	1.23897i	−0.785007	−	0.619487i	$-0.787341\pi$
$941$		−	9.14134e14i		−	1.23897i	0.785007	−	0.619487i	$-0.212659\pi$
$942$		0			0
$943$	−4.67748e13			−0.0627268
$944$		0			0
$945$	1.44471e15	−	1.60748e15i	1.91700	−	2.13298i
$946$		0			0
$947$			6.50116e14i			0.853573i	0.904352	+	0.426787i	$0.140354\pi$
$947$			6.50116e14i			0.853573i	−0.904352	+	0.426787i	$0.859646\pi$
$948$		0			0
$949$	1.33489e14			0.173426
$950$		0			0
$951$	5.87158e14	+	5.66665e14i	0.754835	+	0.728490i
$952$		0			0
$953$			2.90513e14i			0.369574i	0.982779	+	0.184787i	$0.0591595\pi$
$953$			2.90513e14i			0.369574i	−0.982779	+	0.184787i	$0.940840\pi$
$954$		0			0
$955$	−5.58214e14			−0.702723
$956$		0			0
$957$	2.25490e14	−	2.33645e14i	0.280911	−	0.291069i
$958$		0			0
$959$			1.76548e15i			2.17655i
$960$		0			0
$961$	4.31389e14			0.526322
$962$		0			0
$963$	1.54687e15	−	5.49643e13i	1.86777	−	0.0663665i
$964$		0			0
$965$		−	6.02426e14i		−	0.719892i
$966$		0			0
$967$	−6.49279e13			−0.0767890			−0.0383945	−	0.999263i	$-0.512224\pi$
$967$	−6.49279e13			−0.0767890			−0.0383945	+	0.999263i	$0.512224\pi$
$968$		0			0
$969$	3.92716e14	+	3.79009e14i	0.459684	+	0.443640i
$970$		0			0
$971$		−	1.14450e15i		−	1.32593i	−0.748652	−	0.662963i	$-0.769298\pi$
$971$		−	1.14450e15i		−	1.32593i	0.748652	−	0.662963i	$-0.230702\pi$
$972$		0			0
$973$	1.96269e15			2.25054
$974$		0			0
$975$	−1.43199e15	+	1.48377e15i	−1.62523	+	1.68401i
$976$		0			0
$977$			1.42540e15i			1.60127i	0.599151	+	0.800636i	$0.295505\pi$
$977$			1.42540e15i			1.60127i	−0.599151	+	0.800636i	$0.704495\pi$
$978$		0			0
$979$	−1.92066e14			−0.213568
$980$		0			0
$981$	−8.65882e12	−	2.43687e14i	−0.00953046	−	0.268218i
$982$		0			0
$983$			8.80673e14i			0.959504i	0.877404	+	0.479752i	$0.159273\pi$
$983$			8.80673e14i			0.959504i	−0.877404	+	0.479752i	$0.840727\pi$
$984$		0			0
$985$	−1.11971e15			−1.20760
$986$		0			0
$987$	−3.70914e11	−	3.57969e11i	−0.000395993	−	0.000382172i
$988$		0			0
$989$			1.68275e14i			0.177843i
$990$		0			0
$991$	−3.31440e14			−0.346766			−0.173383	−	0.984854i	$-0.555470\pi$
$991$	−3.31440e14			−0.346766			−0.173383	+	0.984854i	$0.555470\pi$
$992$		0			0
$993$	2.26279e14	−	2.34462e14i	0.234368	−	0.242844i
$994$		0			0
$995$		−	8.11007e13i		−	0.0831590i
$996$		0			0
$997$	−4.53229e14			−0.460089			−0.230044	−	0.973180i	$-0.573887\pi$
$997$	−4.53229e14			−0.460089			−0.230044	+	0.973180i	$0.573887\pi$
$998$		0			0
$999$	−5.28821e14	−	4.75275e14i	−0.531473	−	0.477659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.11.e.a.65.15	yes	20
3.2	odd	2	inner	96.11.e.a.65.16	yes	20
4.3	odd	2	inner	96.11.e.a.65.6	yes	20
8.3	odd	2		192.11.e.k.65.15		20
8.5	even	2		192.11.e.k.65.6		20
12.11	even	2	inner	96.11.e.a.65.5	✓	20
24.5	odd	2		192.11.e.k.65.5		20
24.11	even	2		192.11.e.k.65.16		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.11.e.a.65.5	✓	20	12.11	even	2	inner
96.11.e.a.65.6	yes	20	4.3	odd	2	inner
96.11.e.a.65.15	yes	20	1.1	even	1	trivial
96.11.e.a.65.16	yes	20	3.2	odd	2	inner
192.11.e.k.65.5		20	24.5	odd	2
192.11.e.k.65.6		20	8.5	even	2
192.11.e.k.65.15		20	8.3	odd	2
192.11.e.k.65.16		20	24.11	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:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	96.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(168.749 - 174.851i) q^{3} -5349.27i q^{5} -28157.9 q^{7} +(-2096.84 - 59011.8i) q^{9} +O(q^{10})\)	\(q+(168.749 - 174.851i) q^{3} -5349.27i q^{5} -28157.9 q^{7} +(-2096.84 - 59011.8i) q^{9} -178116. i q^{11} +450204. q^{13} +(-935326. - 902681. i) q^{15} -1.63099e6i q^{17} -1.37708e6 q^{19} +(-4.75161e6 + 4.92344e6i) q^{21} -1.19808e6i q^{23} -1.88490e7 q^{25} +(-1.06721e7 - 9.59152e6i) q^{27} +7.50212e6i q^{29} +3.53697e7 q^{31} +(-3.11438e7 - 3.00569e7i) q^{33} +1.50624e8i q^{35} +4.95516e7 q^{37} +(7.59713e7 - 7.87187e7i) q^{39} -3.90414e7i q^{41} -1.40453e8 q^{43} +(-3.15670e8 + 1.12165e7i) q^{45} +75336.3i q^{47} +5.10393e8 q^{49} +(-2.85180e8 - 2.75226e8i) q^{51} +4.45933e8i q^{53} -9.52791e8 q^{55} +(-2.32381e8 + 2.40784e8i) q^{57} +1.38477e8i q^{59} +1.60888e9 q^{61} +(5.90425e7 + 1.66165e9i) q^{63} -2.40826e9i q^{65} +1.71653e9 q^{67} +(-2.09486e8 - 2.02175e8i) q^{69} +2.26776e9i q^{71} +2.96508e8 q^{73} +(-3.18075e9 + 3.29578e9i) q^{75} +5.01538e9i q^{77} -5.23007e9 q^{79} +(-3.47799e9 + 2.47476e8i) q^{81} -7.44213e8i q^{83} -8.72458e9 q^{85} +(1.31175e9 + 1.26597e9i) q^{87} -1.07832e9i q^{89} -1.26768e10 q^{91} +(5.96859e9 - 6.18444e9i) q^{93} +7.36638e9i q^{95} -7.33891e9 q^{97} +(-1.05109e10 + 3.73480e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 100284 q^{9}+O(q^{10}) \) 20 * q - 100284 * q^9	\( 20 q - 100284 q^{9} + 527880 q^{13} - 11589912 q^{21} - 56425772 q^{25} - 55706832 q^{33} - 148642168 q^{37} - 377224224 q^{45} + 1363854748 q^{49} + 1399004568 q^{57} + 1635155656 q^{61} - 435726432 q^{69} + 654515880 q^{73} - 9447541740 q^{81} - 19066455296 q^{85} + 2169686088 q^{93} - 15378184440 q^{97}+O(q^{100}) \) 20 * q - 100284 * q^9 + 527880 * q^13 - 11589912 * q^21 - 56425772 * q^25 - 55706832 * q^33 - 148642168 * q^37 - 377224224 * q^45 + 1363854748 * q^49 + 1399004568 * q^57 + 1635155656 * q^61 - 435726432 * q^69 + 654515880 * q^73 - 9447541740 * q^81 - 19066455296 * q^85 + 2169686088 * q^93 - 15378184440 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more