LMFDB - Embedded newform 260.3.be.b.63.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,3,Mod(63,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("260.63");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	260.be (of order $12$, degree $4$, 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:	$7.08448687337$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{12}]$

Embedding invariants

Embedding label			63.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	260.63
Dual form			260.3.be.b.227.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-4.96410 + 0.598076i) q^{5} -8.00000 q^{8} +(-7.79423 - 4.50000i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-4.96410 + 0.598076i) q^{5} -8.00000 q^{8} +(-7.79423 - 4.50000i) q^{9} +(-6.00000 - 8.00000i) q^{10} +(7.89230 - 10.3301i) q^{13} +(-8.00000 - 13.8564i) q^{16} +(-23.9904 + 6.42820i) q^{17} -18.0000i q^{18} +(7.85641 - 18.3923i) q^{20} +(24.2846 - 5.93782i) q^{25} +(25.7846 + 3.33975i) q^{26} +(-48.1865 + 27.8205i) q^{29} +(16.0000 - 27.7128i) q^{32} +(-35.1244 - 35.1244i) q^{34} +(31.1769 - 18.0000i) q^{36} +(-48.3109 + 27.8923i) q^{37} +(39.7128 - 4.78461i) q^{40} +(0.858984 - 3.20577i) q^{41} +(41.3827 + 17.6769i) q^{45} +(24.5000 + 42.4352i) q^{49} +(34.5692 + 36.1244i) q^{50} +(20.0000 + 48.0000i) q^{52} +(21.7776 + 21.7776i) q^{53} +(-96.3731 - 55.6410i) q^{58} +(20.4737 - 35.4615i) q^{61} +64.0000 q^{64} +(-33.0000 + 56.0000i) q^{65} +(25.7128 - 95.9615i) q^{68} +(62.3538 + 36.0000i) q^{72} -143.263 q^{73} +(-96.6218 - 55.7846i) q^{74} +(48.0000 + 64.0000i) q^{80} +(40.5000 + 70.1481i) q^{81} +(6.41154 - 1.71797i) q^{82} +(115.246 - 46.2583i) q^{85} +(-15.0070 + 56.0070i) q^{89} +(10.7654 + 89.3538i) q^{90} +(-65.0000 + 112.583i) q^{97} +(-49.0000 + 84.8705i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} - 6 q^{5} - 32 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^4 - 6 * q^5 - 32 * q^8	$ 4 q + 4 q^{2} - 8 q^{4} - 6 q^{5} - 32 q^{8} - 24 q^{10} - 10 q^{13} - 32 q^{16} - 44 q^{17} - 24 q^{20} + 14 q^{25} + 20 q^{26} - 120 q^{29} + 64 q^{32} - 92 q^{34} - 72 q^{37} + 48 q^{40} + 142 q^{41} + 72 q^{45} + 98 q^{49} - 28 q^{50} + 80 q^{52} + 146 q^{53} - 240 q^{58} + 120 q^{61} + 256 q^{64} - 132 q^{65} - 8 q^{68} - 192 q^{73} - 144 q^{74} + 192 q^{80} + 162 q^{81} + 88 q^{82} + 170 q^{85} + 82 q^{89} - 144 q^{90} - 260 q^{97} - 196 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 - 6 * q^5 - 32 * q^8 - 24 * q^10 - 10 * q^13 - 32 * q^16 - 44 * q^17 - 24 * q^20 + 14 * q^25 + 20 * q^26 - 120 * q^29 + 64 * q^32 - 92 * q^34 - 72 * q^37 + 48 * q^40 + 142 * q^41 + 72 * q^45 + 98 * q^49 - 28 * q^50 + 80 * q^52 + 146 * q^53 - 240 * q^58 + 120 * q^61 + 256 * q^64 - 132 * q^65 - 8 * q^68 - 192 * q^73 - 144 * q^74 + 192 * q^80 + 162 * q^81 + 88 * q^82 + 170 * q^85 + 82 * q^89 - 144 * q^90 - 260 * q^97 - 196 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.00000	+	1.73205i	0.500000	+	0.866025i
$2$	1.00000	+	1.73205i	0.500000	+	0.866025i
$3$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$3$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$4$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$5$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$5$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$6$		0			0
$7$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$7$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$8$	−8.00000			−1.00000
$9$	−7.79423	−	4.50000i	−0.866025	−	0.500000i
$10$	−6.00000	−	8.00000i	−0.600000	−	0.800000i
$11$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$11$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$12$		0			0
$13$	7.89230	−	10.3301i	0.607100	−	0.794625i
$13$	7.89230	−	10.3301i	0.607100	−	0.794625i
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$17$	−23.9904	+	6.42820i	−1.41120	+	0.378130i	−0.882353	−	0.470588i	$-0.844042\pi$
$17$	−23.9904	+	6.42820i	−1.41120	+	0.378130i	−0.528846	+	0.848718i	$0.677375\pi$
$18$		−	18.0000i		−	1.00000i
$19$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$19$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$20$	7.85641	−	18.3923i	0.392820	−	0.919615i
$21$		0			0
$22$		0			0
$23$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$23$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$24$		0			0
$25$	24.2846	−	5.93782i	0.971384	−	0.237513i
$26$	25.7846	+	3.33975i	0.991716	+	0.128452i
$27$		0			0
$28$		0			0
$29$	−48.1865	+	27.8205i	−1.66160	+	0.959328i	−0.689655	+	0.724138i	$0.742238\pi$
$29$	−48.1865	+	27.8205i	−1.66160	+	0.959328i	−0.971949	+	0.235190i	$0.924429\pi$
$30$		0			0
$31$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$31$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$32$	16.0000	−	27.7128i	0.500000	−	0.866025i
$33$		0			0
$34$	−35.1244	−	35.1244i	−1.03307	−	1.03307i
$35$		0			0
$36$	31.1769	−	18.0000i	0.866025	−	0.500000i
$37$	−48.3109	+	27.8923i	−1.30570	+	0.753846i	−0.981375	−	0.192100i	$-0.938470\pi$
$37$	−48.3109	+	27.8923i	−1.30570	+	0.753846i	−0.324324	+	0.945946i	$0.605137\pi$
$38$		0			0
$39$		0			0
$40$	39.7128	−	4.78461i	0.992820	−	0.119615i
$41$	0.858984	−	3.20577i	0.0209508	−	0.0781895i	−0.954659	−	0.297702i	$-0.903780\pi$
$41$	0.858984	−	3.20577i	0.0209508	−	0.0781895i	0.975610	+	0.219512i	$0.0704466\pi$
$42$		0			0
$43$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$43$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$44$		0			0
$45$	41.3827	+	17.6769i	0.919615	+	0.392820i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	24.5000	+	42.4352i	0.500000	+	0.866025i
$50$	34.5692	+	36.1244i	0.691384	+	0.722487i
$51$		0			0
$52$	20.0000	+	48.0000i	0.384615	+	0.923077i
$53$	21.7776	+	21.7776i	0.410898	+	0.410898i	0.882051	−	0.471154i	$-0.156162\pi$
$53$	21.7776	+	21.7776i	0.410898	+	0.410898i	−0.471154	+	0.882051i	$0.656162\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−96.3731	−	55.6410i	−1.66160	−	0.959328i
$59$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$59$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$60$		0			0
$61$	20.4737	−	35.4615i	0.335635	−	0.581336i	−0.647972	−	0.761664i	$-0.724383\pi$
$61$	20.4737	−	35.4615i	0.335635	−	0.581336i	0.983607	+	0.180328i	$0.0577159\pi$
$62$		0			0
$63$		0			0
$64$	64.0000			1.00000
$65$	−33.0000	+	56.0000i	−0.507692	+	0.861538i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	25.7128	−	95.9615i	0.378130	−	1.41120i
$69$		0			0
$70$		0			0
$71$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$71$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$72$	62.3538	+	36.0000i	0.866025	+	0.500000i
$73$	−143.263			−1.96250			−0.981252	−	0.192729i	$-0.938266\pi$
$73$	−143.263			−1.96250			−0.981252	+	0.192729i	$0.938266\pi$
$74$	−96.6218	−	55.7846i	−1.30570	−	0.753846i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	48.0000	+	64.0000i	0.600000	+	0.800000i
$81$	40.5000	+	70.1481i	0.500000	+	0.866025i
$82$	6.41154	−	1.71797i	0.0781895	−	0.0209508i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	115.246	−	46.2583i	1.35584	−	0.544216i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−15.0070	+	56.0070i	−0.168618	+	0.629293i	0.828932	+	0.559349i	$0.188949\pi$
$89$	−15.0070	+	56.0070i	−0.168618	+	0.629293i	−0.997551	+	0.0699439i	$0.977718\pi$
$90$	10.7654	+	89.3538i	0.119615	+	0.992820i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−65.0000	+	112.583i	−0.670103	+	1.16065i	0.307771	+	0.951460i	$0.400417\pi$
$97$	−65.0000	+	112.583i	−0.670103	+	1.16065i	−0.977875	+	0.209192i	$0.932917\pi$
$98$	−49.0000	+	84.8705i	−0.500000	+	0.866025i
$99$		0			0
$100$	−28.0000	+	96.0000i	−0.280000	+	0.960000i
$101$	131.179	−	75.7365i	1.29881	−	0.749866i	0.318609	−	0.947886i	$-0.396784\pi$
$101$	131.179	−	75.7365i	1.29881	−	0.749866i	0.980198	+	0.198020i	$0.0634510\pi$
$102$		0			0
$103$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$103$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$104$	−63.1384	+	82.6410i	−0.607100	+	0.794625i
$105$		0			0
$106$	−15.9423	+	59.4974i	−0.150399	+	0.561296i
$107$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$107$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$108$		0			0
$109$	151.000	−	151.000i	1.38532	−	1.38532i	0.550459	−	0.834862i	$-0.314453\pi$
$109$	151.000	−	151.000i	1.38532	−	1.38532i	0.834862	−	0.550459i	$-0.185547\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−216.495	+	58.0096i	−1.91588	+	0.513359i	−0.924733	+	0.380616i	$0.875712\pi$
$113$	−216.495	+	58.0096i	−1.91588	+	0.513359i	−0.991150	+	0.132743i	$0.957621\pi$
$114$		0			0
$115$		0			0
$116$		−	222.564i		−	1.91866i
$117$	−108.000	+	45.0000i	−0.923077	+	0.384615i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	104.789	+	60.5000i	0.866025	+	0.500000i
$122$	81.8949			0.671270
$123$		0			0
$124$		0			0
$125$	−117.000	+	44.0000i	−0.936000	+	0.352000i
$126$		0			0
$127$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$127$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$128$	64.0000	+	110.851i	0.500000	+	0.866025i
$129$		0			0
$130$	−129.995	−	1.15768i	−0.999960	−	0.00890520i
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	191.923	−	51.4256i	1.41120	−	0.378130i
$137$	−81.2898	−	46.9327i	−0.593356	−	0.342574i	0.173067	−	0.984910i	$-0.444632\pi$
$137$	−81.2898	−	46.9327i	−0.593356	−	0.342574i	−0.766423	+	0.642336i	$0.777965\pi$
$138$		0			0
$139$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$139$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$			144.000i			1.00000i
$145$	222.564	−	166.923i	1.53492	−	1.15119i
$146$	−143.263	−	248.138i	−0.981252	−	1.69958i
$147$		0			0
$148$		−	223.138i		−	1.50769i
$149$	−76.8327	−	286.744i	−0.515656	−	1.92445i	−0.342282	−	0.939597i	$-0.611200\pi$
$149$	−76.8327	−	286.744i	−0.515656	−	1.92445i	−0.173374	−	0.984856i	$-0.555467\pi$
$150$		0			0
$151$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$151$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$152$		0			0
$153$	215.913	+	57.8538i	1.41120	+	0.378130i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	211.428	−	211.428i	1.34667	−	1.34667i	0.457423	−	0.889249i	$-0.348773\pi$
$157$	211.428	−	211.428i	1.34667	−	1.34667i	0.889249	−	0.457423i	$-0.151227\pi$
$158$		0			0
$159$		0			0
$160$	−62.8513	+	147.138i	−0.392820	+	0.919615i
$161$		0			0
$162$	−81.0000	+	140.296i	−0.500000	+	0.866025i
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$	9.38715	+	9.38715i	0.0572387	+	0.0572387i
$165$		0			0
$166$		0			0
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$		0			0
$169$	−44.4230	−	163.057i	−0.262858	−	0.964834i
$170$	195.368	+	153.354i	1.14922	+	0.902081i
$171$		0			0
$172$		0			0
$173$	79.4275	+	296.428i	0.459119	+	1.71345i	0.675689	+	0.737187i	$0.263846\pi$
$173$	79.4275	+	296.428i	0.459119	+	1.71345i	−0.216570	+	0.976267i	$0.569487\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−112.014	+	30.0141i	−0.629293	+	0.168618i
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$	−144.000	+	108.000i	−0.800000	+	0.600000i
$181$		−	292.769i		−	1.61751i	−0.588146	−	0.808755i	$-0.700142\pi$
$181$		−	292.769i		−	1.61751i	0.588146	−	0.808755i	$-0.299858\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	223.138	−	167.354i	1.20615	−	0.904615i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$		0			0
$193$	−97.9923	−	169.728i	−0.507732	−	0.879418i	−0.999960	−	0.00895123i	$-0.997151\pi$
$193$	−97.9923	−	169.728i	−0.507732	−	0.879418i	0.492228	−	0.870466i	$-0.336183\pi$
$194$	−260.000			−1.34021
$195$		0			0
$196$	−196.000			−1.00000
$197$	−195.000	−	337.750i	−0.989848	−	1.71447i	−0.618014	−	0.786167i	$-0.712062\pi$
$197$	−195.000	−	337.750i	−0.989848	−	1.71447i	−0.371834	−	0.928299i	$-0.621271\pi$
$198$		0			0
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	−194.277	+	47.5026i	−0.971384	+	0.237513i
$201$		0			0
$202$	262.359	+	151.473i	1.29881	+	0.749866i
$203$		0			0
$204$		0			0
$205$	−2.34679	+	16.4275i	−0.0114477	+	0.0801342i
$206$		0			0
$207$		0			0
$208$	−206.277	−	26.7180i	−0.991716	−	0.128452i
$209$		0			0
$210$		0			0
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$	−118.995	+	31.8846i	−0.561296	+	0.150399i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	412.540	+	110.540i	1.89238	+	0.507063i
$219$		0			0
$220$		0			0
$221$	−122.935	+	298.557i	−0.556268	+	1.35094i
$222$		0			0
$223$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$223$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$224$		0			0
$225$	−216.000	−	63.0000i	−0.960000	−	0.280000i
$226$	−316.970	−	316.970i	−1.40252	−	1.40252i
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$		0			0
$229$	−161.000	−	161.000i	−0.703057	−	0.703057i	0.262009	−	0.965066i	$-0.415615\pi$
$229$	−161.000	−	161.000i	−0.703057	−	0.703057i	−0.965066	+	0.262009i	$0.915615\pi$
$230$		0			0
$231$		0			0
$232$	385.492	−	222.564i	1.66160	−	0.959328i
$233$	−103.000	+	103.000i	−0.442060	+	0.442060i	−0.892704	−	0.450644i	$-0.851194\pi$
$233$	−103.000	+	103.000i	−0.442060	+	0.442060i	0.450644	+	0.892704i	$0.351194\pi$
$234$	−185.942	−	142.061i	−0.794625	−	0.607100i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$239$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$240$		0			0
$241$	88.0007	+	328.423i	0.365148	+	1.36275i	0.867220	+	0.497925i	$0.165905\pi$
$241$	88.0007	+	328.423i	0.365148	+	1.36275i	−0.502072	+	0.864826i	$0.667429\pi$
$242$			242.000i			1.00000i
$243$		0			0
$244$	81.8949	+	141.846i	0.335635	+	0.581336i
$245$	−147.000	−	196.000i	−0.600000	−	0.800000i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−193.210	−	158.650i	−0.772841	−	0.634600i
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−128.000	+	221.703i	−0.500000	+	0.866025i
$257$	−123.213	+	459.836i	−0.479427	+	1.78925i	0.124514	+	0.992218i	$0.460263\pi$
$257$	−123.213	+	459.836i	−0.479427	+	1.78925i	−0.603941	+	0.797029i	$0.706404\pi$
$258$		0			0
$259$		0			0
$260$	−127.990	−	226.315i	−0.492268	−	0.870444i
$261$	500.769			1.91866
$262$		0			0
$263$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$263$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$264$		0			0
$265$	−121.131	−	95.0814i	−0.457097	−	0.358798i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	450.333	+	260.000i	1.67410	+	0.966543i	0.965303	+	0.261131i	$0.0840955\pi$
$269$	450.333	+	260.000i	1.67410	+	0.966543i	0.708798	+	0.705412i	$0.249238\pi$
$270$		0			0
$271$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$271$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$272$	280.995	+	280.995i	1.03307	+	1.03307i
$273$		0			0
$274$		−	187.731i		−	0.685148i
$275$		0			0
$276$		0			0
$277$	−88.5929	+	23.7384i	−0.319830	+	0.0856982i	−0.415162	−	0.909747i	$-0.636275\pi$
$277$	−88.5929	+	23.7384i	−0.319830	+	0.0856982i	0.0953324	+	0.995445i	$0.469609\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−303.116	+	303.116i	−1.07870	+	1.07870i	−0.0820785	+	0.996626i	$0.526156\pi$
$281$	−303.116	+	303.116i	−1.07870	+	1.07870i	−0.996626	+	0.0820785i	$0.973844\pi$
$282$		0			0
$283$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$283$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−249.415	+	144.000i	−0.866025	+	0.500000i
$289$	283.935	−	163.930i	0.982475	−	0.567232i
$290$	511.683	+	218.569i	1.76443	+	0.753687i
$291$		0			0
$292$	286.526	−	496.277i	0.981252	−	1.69958i
$293$	−212.817	+	368.610i	−0.726339	+	1.25806i	0.232082	+	0.972696i	$0.425446\pi$
$293$	−212.817	+	368.610i	−0.726339	+	1.25806i	−0.958421	+	0.285359i	$0.907887\pi$
$294$		0			0
$295$		0			0
$296$	386.487	−	223.138i	1.30570	−	0.753846i
$297$		0			0
$298$	419.822	−	419.822i	1.40880	−	1.40880i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−80.4249	+	188.279i	−0.263688	+	0.617310i
$306$	115.708	+	431.827i	0.378130	+	1.41120i
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	337.000	+	337.000i	1.07668	+	1.07668i	0.996805	+	0.0798722i	$0.0254512\pi$
$313$	337.000	+	337.000i	1.07668	+	1.07668i	0.0798722	+	0.996805i	$0.474549\pi$
$314$	577.631	+	154.776i	1.83959	+	0.492916i
$315$		0			0
$316$		0			0
$317$	−178.096			−0.561818			−0.280909	−	0.959734i	$-0.590636\pi$
$317$	−178.096			−0.561818			−0.280909	+	0.959734i	$0.590636\pi$
$318$		0			0
$319$		0			0
$320$	−317.703	+	38.2769i	−0.992820	+	0.119615i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−324.000			−1.00000
$325$	130.323	−	297.726i	0.400994	−	0.916081i
$326$		0			0
$327$		0			0
$328$	−6.87187	+	25.6462i	−0.0209508	+	0.0781895i
$329$		0			0
$330$		0			0
$331$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$331$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$332$		0			0
$333$	502.061			1.50769
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−329.361	−	329.361i	−0.977332	−	0.977332i	0.0224168	−	0.999749i	$-0.492864\pi$
$337$	−329.361	−	329.361i	−0.977332	−	0.977332i	−0.999749	+	0.0224168i	$0.992864\pi$
$338$	238.000	−	240.000i	0.704142	−	0.710059i
$339$		0			0
$340$	−70.2487	+	491.741i	−0.206614	+	1.44630i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−434.000	+	434.000i	−1.25434	+	1.25434i
$347$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$347$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$348$		0			0
$349$	−175.326	+	654.326i	−0.502367	+	1.87486i	−0.0182939	+	0.999833i	$0.505823\pi$
$349$	−175.326	+	654.326i	−0.502367	+	1.87486i	−0.484073	+	0.875027i	$0.660843\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	213.144	−	123.059i	0.603808	−	0.348609i	−0.166730	−	0.986003i	$-0.553321\pi$
$353$	213.144	−	123.059i	0.603808	−	0.348609i	0.770538	+	0.637394i	$0.219988\pi$
$354$		0			0
$355$		0			0
$356$	−164.000	−	164.000i	−0.460674	−	0.460674i
$357$		0			0
$358$		0			0
$359$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$359$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$360$	−331.061	−	141.415i	−0.919615	−	0.392820i
$361$	−312.635	+	180.500i	−0.866025	+	0.500000i
$362$	507.091	−	292.769i	1.40080	−	0.808755i
$363$		0			0
$364$		0			0
$365$	711.171	−	85.6821i	1.94841	−	0.234745i
$366$		0			0
$367$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$367$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$368$		0			0
$369$	−21.1211	+	21.1211i	−0.0572387	+	0.0572387i
$370$	513.004	+	219.133i	1.38650	+	0.592252i
$371$		0			0
$372$		0			0
$373$	−639.157	+	171.262i	−1.71356	+	0.459146i	−0.976292	−	0.216457i	$-0.930550\pi$
$373$	−639.157	+	171.262i	−1.71356	+	0.459146i	−0.737265	+	0.675603i	$0.763883\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−92.9134	+	717.341i	−0.246455	+	1.90276i
$378$		0			0
$379$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$379$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		0			0
$385$		0			0
$386$	195.985	−	339.455i	0.507732	−	0.879418i
$387$		0			0
$388$	−260.000	−	450.333i	−0.670103	−	1.16065i
$389$	399.897			1.02801			0.514007	−	0.857786i	$-0.328161\pi$
$389$	399.897			1.02801			0.514007	+	0.857786i	$0.328161\pi$
$390$		0			0
$391$		0			0
$392$	−196.000	−	339.482i	−0.500000	−	0.866025i
$393$		0			0
$394$	390.000	−	675.500i	0.989848	−	1.71447i
$395$		0			0
$396$		0			0
$397$	−562.917	−	325.000i	−1.41793	−	0.818640i	−0.421809	−	0.906685i	$-0.638605\pi$
$397$	−562.917	−	325.000i	−1.41793	−	0.818640i	−0.996117	+	0.0880448i	$0.971938\pi$
$398$		0			0
$399$		0			0
$400$	−276.554	−	288.995i	−0.691384	−	0.722487i
$401$	−274.141	−	73.4559i	−0.683643	−	0.183182i	−0.0997506	−	0.995012i	$-0.531805\pi$
$401$	−274.141	−	73.4559i	−0.683643	−	0.183182i	−0.583893	+	0.811831i	$0.698471\pi$
$402$		0			0
$403$		0			0
$404$			605.892i			1.49973i
$405$	−243.000	−	324.000i	−0.600000	−	0.800000i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	179.423	+	669.616i	0.438687	+	1.63720i	0.732086	+	0.681213i	$0.238547\pi$
$409$	179.423	+	669.616i	0.438687	+	1.63720i	−0.293399	+	0.955990i	$0.594786\pi$
$410$	−30.8001	+	12.3628i	−0.0751221	+	0.0301531i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−160.000	−	384.000i	−0.384615	−	0.923077i
$417$		0			0
$418$		0			0
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$	193.345	+	193.345i	0.459253	+	0.459253i	0.898410	−	0.439157i	$-0.144723\pi$
$421$	193.345	+	193.345i	0.459253	+	0.459253i	−0.439157	+	0.898410i	$0.644723\pi$
$422$		0			0
$423$		0			0
$424$	−174.221	−	174.221i	−0.410898	−	0.410898i
$425$	−544.428	+	298.557i	−1.28101	+	0.702487i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$431$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$432$		0			0
$433$	−127.162	−	474.574i	−0.293676	−	1.09601i	−0.942263	−	0.334873i	$-0.891307\pi$
$433$	−127.162	−	474.574i	−0.293676	−	1.09601i	0.648587	−	0.761140i	$-0.275360\pi$
$434$		0			0
$435$		0			0
$436$	221.079	+	825.079i	0.507063	+	1.89238i
$437$		0			0
$438$		0			0
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$		0			0
$441$		−	441.000i		−	1.00000i
$442$	−640.051	+	85.6269i	−1.44808	+	0.193726i
$443$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$443$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$444$		0			0
$445$	41.0000	−	287.000i	0.0921348	−	0.644944i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−96.9878	+	25.9878i	−0.216008	+	0.0578793i	−0.365200	−	0.930929i	$-0.618999\pi$
$449$	−96.9878	+	25.9878i	−0.216008	+	0.0578793i	0.149192	+	0.988808i	$0.452333\pi$
$450$	−106.881	−	437.123i	−0.237513	−	0.971384i
$451$		0			0
$452$	232.038	−	865.979i	0.513359	−	1.91588i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−357.992	−	620.061i	−0.783353	−	1.35681i	−0.929978	−	0.367615i	$-0.880174\pi$
$457$	−357.992	−	620.061i	−0.783353	−	1.35681i	0.146625	−	0.989192i	$-0.453159\pi$
$458$	117.860	−	439.860i	0.257337	−	0.960393i
$459$		0			0
$460$		0			0
$461$	−839.590	+	224.967i	−1.82124	+	0.487999i	−0.996941	−	0.0781619i	$-0.975095\pi$
$461$	−839.590	+	224.967i	−1.82124	+	0.487999i	−0.824295	+	0.566161i	$0.808428\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$	770.985	+	445.128i	1.66160	+	0.959328i
$465$		0			0
$466$	−281.401	−	75.4012i	−0.603865	−	0.161805i
$467$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$467$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$468$	60.1154	−	464.123i	0.128452	−	0.991716i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−71.7403	−	267.738i	−0.150399	−	0.561296i
$478$		0			0
$479$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$479$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$480$		0			0
$481$	−93.1532	+	719.192i	−0.193666	+	1.49520i
$482$	−480.845	+	480.845i	−0.997603	+	0.997603i
$483$		0			0
$484$	−419.156	+	242.000i	−0.866025	+	0.500000i
$485$	255.333	−	597.750i	0.526460	−	1.23247i
$486$		0			0
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$	−163.790	+	283.692i	−0.335635	+	0.581336i
$489$		0			0
$490$	192.482	−	450.611i	0.392820	−	0.919615i
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$		0			0
$493$	977.177	−	977.177i	1.98210	−	1.98210i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$499$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$500$	81.5795	−	493.300i	0.163159	−	0.986600i
$501$		0			0
$502$		0			0
$503$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$503$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$504$		0			0
$505$	−605.892	+	454.419i	−1.19979	+	0.899840i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−746.506	−	200.026i	−1.46661	−	0.392978i	−0.564844	−	0.825198i	$-0.691064\pi$
$509$	−746.506	−	200.026i	−1.46661	−	0.392978i	−0.901768	+	0.432220i	$0.857730\pi$
$510$		0			0
$511$		0			0
$512$	−512.000			−1.00000
$513$		0			0
$514$	−919.673	+	246.426i	−1.78925	+	0.479427i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	264.000	−	448.000i	0.507692	−	0.861538i
$521$	923.242			1.77206			0.886029	−	0.463630i	$-0.153453\pi$
$521$	923.242			1.77206			0.886029	+	0.463630i	$0.153453\pi$
$522$	500.769	+	867.358i	0.959328	+	1.66160i
$523$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$523$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	458.127	+	264.500i	0.866025	+	0.500000i
$530$	43.5551	−	304.886i	0.0821795	−	0.575257i
$531$		0			0
$532$		0			0
$533$	−26.3367	−	34.1743i	−0.0494121	−	0.0641170i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$			1040.00i			1.93309i
$539$		0			0
$540$		0			0
$541$	619.545	−	619.545i	1.14519	−	1.14519i	0.157698	−	0.987487i	$-0.449593\pi$
$541$	619.545	−	619.545i	1.14519	−	1.14519i	0.987487	−	0.157698i	$-0.0504073\pi$
$542$		0			0
$543$		0			0
$544$	−205.703	+	767.692i	−0.378130	+	1.41120i
$545$	−659.270	+	839.889i	−1.20967	+	1.54108i
$546$		0			0
$547$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$547$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$548$	325.159	−	187.731i	0.593356	−	0.342574i
$549$	−319.154	+	184.263i	−0.581336	+	0.335635i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−129.709	−	129.709i	−0.234132	−	0.234132i
$555$		0			0
$556$		0			0
$557$	940.894	−	543.226i	1.68922	−	0.975270i	0.734101	−	0.679040i	$-0.237604\pi$
$557$	940.894	−	543.226i	1.68922	−	0.975270i	0.955117	−	0.296230i	$-0.0957294\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−828.128	−	221.896i	−1.47354	−	0.394833i
$563$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$563$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$564$		0			0
$565$	1040.01	−	417.446i	1.84072	−	0.738843i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−520.000	−	900.666i	−0.913884	−	1.58289i	−0.808527	−	0.588459i	$-0.799735\pi$
$569$	−520.000	−	900.666i	−0.913884	−	1.58289i	−0.105357	−	0.994434i	$-0.533599\pi$
$570$		0			0
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−498.831	−	288.000i	−0.866025	−	0.500000i
$577$	1043.93			1.80924			0.904618	−	0.426223i	$-0.140156\pi$
$577$	1043.93			1.80924			0.904618	+	0.426223i	$0.140156\pi$
$578$	567.870	+	327.860i	0.982475	+	0.567232i
$579$		0			0
$580$	133.110	+	1104.83i	0.229500	+	1.90488i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	1146.10			1.96250
$585$	509.210	−	287.977i	0.870444	−	0.492268i
$586$	−851.269			−1.45268
$587$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$587$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	772.974	+	446.277i	1.30570	+	0.753846i
$593$	−172.395			−0.290716			−0.145358	−	0.989379i	$-0.546433\pi$
$593$	−172.395			−0.290716			−0.145358	+	0.989379i	$0.546433\pi$
$594$		0			0
$595$		0			0
$596$	1146.97	+	307.331i	1.92445	+	0.515656i
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	483.346	+	837.180i	0.804236	+	1.39298i	0.916805	+	0.399334i	$0.130759\pi$
$601$	483.346	+	837.180i	0.804236	+	1.39298i	−0.112569	+	0.993644i	$0.535908\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−556.367	−	237.656i	−0.919615	−	0.392820i
$606$		0			0
$607$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$607$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$608$		0			0
$609$		0			0
$610$	−406.535	+	48.9794i	−0.666450	+	0.0802941i
$611$		0			0
$612$	−632.238	+	632.238i	−1.03307	+	1.03307i
$613$	582.508	−	336.311i	0.950257	−	0.548631i	0.0570962	−	0.998369i	$-0.481816\pi$
$613$	582.508	−	336.311i	0.950257	−	0.548631i	0.893161	+	0.449738i	$0.148482\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−579.043	+	1002.93i	−0.938482	+	1.62550i	−0.170178	+	0.985413i	$0.554434\pi$
$617$	−579.043	+	1002.93i	−0.938482	+	1.62550i	−0.768304	+	0.640085i	$0.778899\pi$
$618$		0			0
$619$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$619$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	554.485	−	288.395i	0.887175	−	0.461433i
$626$	−246.701	+	920.701i	−0.394091	+	1.47077i
$627$		0			0
$628$	309.551	+	1155.26i	0.492916	+	1.83959i
$629$	979.699	−	979.699i	1.55755	−	1.55755i
$630$		0			0
$631$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$631$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$632$		0			0
$633$		0			0
$634$	−178.096	−	308.472i	−0.280909	−	0.486548i
$635$		0			0
$636$		0			0
$637$	631.723	+	81.8238i	0.991716	+	0.128452i
$638$		0			0
$639$		0			0
$640$	−384.000	−	512.000i	−0.600000	−	0.800000i
$641$	−1086.71	−	627.409i	−1.69533	−	0.978798i	−0.950078	−	0.312012i	$-0.898997\pi$
$641$	−1086.71	−	627.409i	−1.69533	−	0.978798i	−0.745250	−	0.666785i	$-0.767670\pi$
$642$		0			0
$643$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$643$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$647$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$648$	−324.000	−	561.184i	−0.500000	−	0.866025i
$649$		0			0
$650$	646.000	−	72.0000i	0.993846	−	0.110769i
$651$		0			0
$652$		0			0
$653$	−94.0685	+	351.069i	−0.144056	+	0.537624i	0.855740	+	0.517407i	$0.173103\pi$
$653$	−94.0685	+	351.069i	−0.144056	+	0.537624i	−0.999796	+	0.0202175i	$0.993564\pi$
$654$		0			0
$655$		0			0
$656$	−51.2923	+	13.7437i	−0.0781895	+	0.0209508i
$657$	1116.62	+	644.683i	1.69958	+	0.981252i
$658$		0			0
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$		0			0
$661$	−1249.09	−	334.692i	−1.88970	−	0.506342i	−0.998622	−	0.0524847i	$-0.983286\pi$
$661$	−1249.09	−	334.692i	−1.88970	−	0.506342i	−0.891074	−	0.453858i	$-0.850047\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	502.061	+	869.596i	0.753846	+	1.30570i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1222.55	−	327.580i	−1.81656	−	0.486746i	−0.820208	−	0.572065i	$-0.806142\pi$
$673$	−1222.55	−	327.580i	−1.81656	−	0.486746i	−0.996354	+	0.0853191i	$0.972809\pi$
$674$	241.109	−	899.831i	0.357728	−	1.33506i
$675$		0			0
$676$	653.692	+	172.228i	0.967000	+	0.254775i
$677$	623.000	−	623.000i	0.920236	−	0.920236i	−0.0768095	−	0.997046i	$-0.524473\pi$
$677$	623.000	−	623.000i	0.920236	−	0.920236i	0.997046	+	0.0768095i	$0.0244733\pi$
$678$		0			0
$679$		0			0
$680$	−921.969	+	370.067i	−1.35584	+	0.544216i
$681$		0			0
$682$		0			0
$683$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$683$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$684$		0			0
$685$	431.600	+	184.361i	0.630073	+	0.269140i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	396.840	−	53.0898i	0.575966	−	0.0770535i
$690$		0			0
$691$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$691$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$692$	−1185.71	−	317.710i	−1.71345	−	0.459119i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$			82.4294i			0.118263i
$698$	−1308.65	+	350.652i	−1.87486	+	0.502367i
$699$		0			0
$700$		0			0
$701$			520.000i			0.741797i	0.928673	+	0.370899i	$0.120950\pi$
$701$			520.000i			0.741797i	−0.928673	+	0.370899i	$0.879050\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	426.289	+	246.118i	0.603808	+	0.348609i
$707$		0			0
$708$		0			0
$709$	−1361.08	+	364.699i	−1.91971	+	0.514386i	−0.930889	+	0.365303i	$0.880965\pi$
$709$	−1361.08	+	364.699i	−1.91971	+	0.514386i	−0.988825	+	0.149082i	$0.952368\pi$
$710$		0			0
$711$		0			0
$712$	120.056	−	448.056i	0.168618	−	0.629293i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$	−86.1230	−	714.831i	−0.119615	−	0.992820i
$721$		0			0
$722$	−625.270	−	361.000i	−0.866025	−	0.500000i
$723$		0			0
$724$	1014.18	+	585.538i	1.40080	+	0.808755i
$725$	−1005.00	+	961.733i	−1.38620	+	1.32653i
$726$		0			0
$727$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$727$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$728$		0			0
$729$		−	729.000i		−	1.00000i
$730$	859.577	+	1146.10i	1.17750	+	1.57000i
$731$		0			0
$732$		0			0
$733$			1363.74i			1.86049i	0.366943	+	0.930243i	$0.380404\pi$
$733$			1363.74i			1.86049i	−0.366943	+	0.930243i	$0.619596\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−57.7039	−	15.4617i	−0.0781895	−	0.0209508i
$739$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$739$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$740$	133.454	+	1107.68i	0.180343	+	1.49687i
$741$		0			0
$742$		0			0
$743$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$743$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$744$		0			0
$745$	552.900	+	1377.47i	0.742147	+	1.84896i
$746$	−935.791	−	935.791i	−1.25441	−	1.25441i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$751$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$752$		0			0
$753$		0			0
$754$	−1335.38	+	556.410i	−1.77107	+	0.737945i
$755$		0			0
$756$		0			0
$757$	1452.09	+	389.085i	1.91821	+	0.513983i	0.989809	+	0.142404i	$0.0454832\pi$
$757$	1452.09	+	389.085i	1.91821	+	0.513983i	0.928401	+	0.371579i	$0.121183\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−292.454	−	1091.45i	−0.384303	−	1.43424i	−0.839263	−	0.543725i	$-0.817013\pi$
$761$	−292.454	−	1091.45i	−0.384303	−	1.43424i	0.454961	−	0.890512i	$-0.349653\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1106.42	−	158.060i	−1.44630	−	0.206614i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	162.557	+	43.5570i	0.211388	+	0.0566411i	0.362959	−	0.931805i	$-0.381767\pi$
$769$	162.557	+	43.5570i	0.211388	+	0.0566411i	−0.151571	+	0.988446i	$0.548433\pi$
$770$		0			0
$771$		0			0
$772$	783.938			1.01546
$773$	−337.750	−	195.000i	−0.436934	−	0.252264i	0.265362	−	0.964149i	$-0.414508\pi$
$773$	−337.750	−	195.000i	−0.436934	−	0.252264i	−0.702296	+	0.711885i	$0.747842\pi$
$774$		0			0
$775$		0			0
$776$	520.000	−	900.666i	0.670103	−	1.16065i
$777$		0			0
$778$	399.897	+	692.642i	0.514007	+	0.890286i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	392.000	−	678.964i	0.500000	−	0.866025i
$785$	−923.098	+	1176.00i	−1.17592	+	1.49809i
$786$		0			0
$787$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$787$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$788$	1560.00			1.97970
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−204.737	−	491.369i	−0.258181	−	0.619633i
$794$		−	1300.00i		−	1.63728i
$795$		0			0
$796$		0			0
$797$	−23.2224	+	6.22243i	−0.0291373	+	0.00780732i	−0.273358	−	0.961912i	$-0.588134\pi$
$797$	−23.2224	+	6.22243i	−0.0291373	+	0.00780732i	0.244221	+	0.969720i	$0.421468\pi$
$798$		0			0
$799$		0			0
$800$	224.000	−	768.000i	0.280000	−	0.960000i
$801$	369.000	−	369.000i	0.460674	−	0.460674i
$802$	−146.912	−	548.282i	−0.183182	−	0.683643i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−1049.44	+	605.892i	−1.29881	+	0.749866i
$809$	−237.313	+	137.013i	−0.293342	+	0.169361i	−0.639448	−	0.768835i	$-0.720837\pi$
$809$	−237.313	+	137.013i	−0.293342	+	0.169361i	0.346106	+	0.938195i	$0.387504\pi$
$810$	318.184	−	744.888i	0.392820	−	0.919615i
$811$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$811$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−980.386	+	980.386i	−1.19852	+	1.19852i
$819$		0			0
$820$	−52.2130	−	40.9845i	−0.0636744	−	0.0499811i
$821$	413.243	−	1542.24i	0.503341	−	1.87849i	0.0262179	−	0.999656i	$-0.491654\pi$
$821$	413.243	−	1542.24i	0.503341	−	1.87849i	0.477123	−	0.878837i	$-0.341680\pi$
$822$		0			0
$823$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$823$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$		0			0
$829$	814.730	+	1411.15i	0.982786	+	1.70224i	0.651387	+	0.758745i	$0.274187\pi$
$829$	814.730	+	1411.15i	0.982786	+	1.70224i	0.331399	+	0.943491i	$0.392479\pi$
$830$		0			0
$831$		0			0
$832$	505.108	−	661.128i	0.607100	−	0.794625i
$833$	−860.547	−	860.547i	−1.03307	−	1.03307i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$839$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$840$		0			0
$841$	1127.46	−	1952.82i	1.34062	−	2.32202i
$842$	−141.539	+	528.229i	−0.168098	+	0.627351i
$843$		0			0
$844$		0			0
$845$	318.041	+	782.863i	0.376380	+	0.926465i
$846$		0			0
$847$		0			0
$848$	127.538	−	475.979i	0.150399	−	0.561296i
$849$		0			0
$850$	−1061.54	−	644.419i	−1.24887	−	0.758140i
$851$		0			0
$852$		0			0
$853$	472.930			0.554431			0.277215	−	0.960808i	$-0.410588\pi$
$853$	472.930			0.554431			0.277215	+	0.960808i	$0.410588\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−618.889	−	618.889i	−0.722157	−	0.722157i	0.246887	−	0.969044i	$-0.420592\pi$
$857$	−618.889	−	618.889i	−0.722157	−	0.722157i	−0.969044	+	0.246887i	$0.920592\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	−571.572	−	1423.99i	−0.660777	−	1.64623i
$866$	694.824	−	694.824i	0.802337	−	0.802337i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−1208.00	+	1208.00i	−1.38532	+	1.38532i
$873$	1013.25	−	585.000i	1.16065	−	0.670103i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−101.123	+	175.150i	−0.115306	+	0.199715i	−0.917902	−	0.396807i	$-0.870118\pi$
$877$	−101.123	+	175.150i	−0.115306	+	0.199715i	0.802596	+	0.596523i	$0.203451\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	880.437	−	508.320i	0.999361	−	0.576981i	0.0913015	−	0.995823i	$-0.470897\pi$
$881$	880.437	−	508.320i	0.999361	−	0.576981i	0.908059	+	0.418842i	$0.137564\pi$
$882$	763.834	−	441.000i	0.866025	−	0.500000i
$883$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$883$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$884$	−788.361	−	1022.97i	−0.891812	−	1.15721i
$885$		0			0
$886$		0			0
$887$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$887$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$888$		0			0
$889$		0			0
$890$	538.099	−	215.986i	0.604605	−	0.242681i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−142.000	−	142.000i	−0.158129	−	0.158129i
$899$		0			0
$900$	650.238	−	622.246i	0.722487	−	0.691384i
$901$	−662.443	−	382.462i	−0.735231	−	0.424486i
$902$		0			0
$903$		0			0
$904$	1731.96	−	464.077i	1.91588	−	0.513359i
$905$	175.098	+	1453.34i	0.193479	+	1.60590i
$906$		0			0
$907$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$907$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$908$		0			0
$909$	−1363.26			−1.49973
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$	715.985	−	1240.12i	0.783353	−	1.35681i
$915$		0			0
$916$	879.720	−	235.720i	0.960393	−	0.257337i
$917$		0			0
$918$		0			0
$919$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$919$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$920$		0			0
$921$		0			0
$922$	−1229.24	−	1229.24i	−1.33324	−	1.33324i
$923$		0			0
$924$		0			0
$925$	−1007.59	+	964.215i	−1.08929	+	1.04239i
$926$		0			0
$927$		0			0
$928$			1780.51i			1.91866i
$929$	−58.7566	−	219.283i	−0.0632472	−	0.236042i	0.927065	−	0.374901i	$-0.122323\pi$
$929$	−58.7566	−	219.283i	−0.0632472	−	0.236042i	−0.990312	+	0.138859i	$0.955657\pi$
$930$		0			0
$931$		0			0
$932$	−150.802	−	562.802i	−0.161805	−	0.603865i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	864.000	−	360.000i	0.923077	−	0.384615i
$937$	−1324.51	+	1324.51i	−1.41357	+	1.41357i	−0.685374	+	0.728191i	$0.740361\pi$
$937$	−1324.51	+	1324.51i	−1.41357	+	1.41357i	−0.728191	+	0.685374i	$0.759639\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−161.000	−	161.000i	−0.171095	−	0.171095i	0.616366	−	0.787460i	$-0.288604\pi$
$941$	−161.000	−	161.000i	−0.171095	−	0.171095i	−0.787460	+	0.616366i	$0.788604\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$		0			0
$949$	−1130.67	+	1479.92i	−1.19144	+	1.55946i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	491.572	+	1834.57i	0.515815	+	1.92505i	0.338895	+	0.940824i	$0.389947\pi$
$953$	491.572	+	1834.57i	0.515815	+	1.92505i	0.176921	+	0.984225i	$0.443386\pi$
$954$	391.996	−	391.996i	0.410898	−	0.410898i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$			961.000i			1.00000i
$962$	−1338.83	+	557.846i	−1.39172	+	0.579882i
$963$		0			0
$964$	−1313.69	−	352.003i	−1.36275	−	0.365148i
$965$	587.954	+	783.938i	0.609278	+	0.812371i
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	−838.313	−	484.000i	−0.866025	−	0.500000i
$969$		0			0
$970$	1290.67	−	155.500i	1.33058	−	0.160309i
$971$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$971$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−655.159			−0.671270
$977$	−942.394	−	1632.27i	−0.964579	−	1.67070i	−0.710741	−	0.703454i	$-0.751640\pi$
$977$	−942.394	−	1632.27i	−0.964579	−	1.67070i	−0.253838	−	0.967247i	$-0.581693\pi$
$978$		0			0
$979$		0			0
$980$	972.964	−	117.223i	0.992820	−	0.119615i
$981$	−1856.43	+	497.429i	−1.89238	+	0.507063i
$982$		0			0
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$		0			0
$985$	1170.00	+	1560.00i	1.18782	+	1.58376i
$986$	2669.70	+	715.344i	2.70760	+	0.725501i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$991$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	412.661	+	1540.07i	0.413903	+	1.54471i	0.787023	+	0.616924i	$0.211622\pi$
$997$	412.661	+	1540.07i	0.413903	+	1.54471i	−0.373119	+	0.927783i	$0.621712\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.3.be.b.63.1	✓	4
4.3	odd	2	CM	260.3.be.b.63.1	✓	4
5.2	odd	4		260.3.bl.a.167.1	yes	4
13.6	odd	12		260.3.bl.a.123.1	yes	4
20.7	even	4		260.3.bl.a.167.1	yes	4
52.19	even	12		260.3.bl.a.123.1	yes	4
65.32	even	12	inner	260.3.be.b.227.1	yes	4
260.227	odd	12	inner	260.3.be.b.227.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.3.be.b.63.1	✓	4	1.1	even	1	trivial
260.3.be.b.63.1	✓	4	4.3	odd	2	CM
260.3.be.b.227.1	yes	4	65.32	even	12	inner
260.3.be.b.227.1	yes	4	260.227	odd	12	inner
260.3.bl.a.123.1	yes	4	13.6	odd	12
260.3.bl.a.123.1	yes	4	52.19	even	12
260.3.bl.a.167.1	yes	4	5.2	odd	4
260.3.bl.a.167.1	yes	4	20.7	even	4

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	260.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-4.96410 + 0.598076i) q^{5} -8.00000 q^{8} +(-7.79423 - 4.50000i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-4.96410 + 0.598076i) q^{5} -8.00000 q^{8} +(-7.79423 - 4.50000i) q^{9} +(-6.00000 - 8.00000i) q^{10} +(7.89230 - 10.3301i) q^{13} +(-8.00000 - 13.8564i) q^{16} +(-23.9904 + 6.42820i) q^{17} -18.0000i q^{18} +(7.85641 - 18.3923i) q^{20} +(24.2846 - 5.93782i) q^{25} +(25.7846 + 3.33975i) q^{26} +(-48.1865 + 27.8205i) q^{29} +(16.0000 - 27.7128i) q^{32} +(-35.1244 - 35.1244i) q^{34} +(31.1769 - 18.0000i) q^{36} +(-48.3109 + 27.8923i) q^{37} +(39.7128 - 4.78461i) q^{40} +(0.858984 - 3.20577i) q^{41} +(41.3827 + 17.6769i) q^{45} +(24.5000 + 42.4352i) q^{49} +(34.5692 + 36.1244i) q^{50} +(20.0000 + 48.0000i) q^{52} +(21.7776 + 21.7776i) q^{53} +(-96.3731 - 55.6410i) q^{58} +(20.4737 - 35.4615i) q^{61} +64.0000 q^{64} +(-33.0000 + 56.0000i) q^{65} +(25.7128 - 95.9615i) q^{68} +(62.3538 + 36.0000i) q^{72} -143.263 q^{73} +(-96.6218 - 55.7846i) q^{74} +(48.0000 + 64.0000i) q^{80} +(40.5000 + 70.1481i) q^{81} +(6.41154 - 1.71797i) q^{82} +(115.246 - 46.2583i) q^{85} +(-15.0070 + 56.0070i) q^{89} +(10.7654 + 89.3538i) q^{90} +(-65.0000 + 112.583i) q^{97} +(-49.0000 + 84.8705i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} - 6 q^{5} - 32 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^4 - 6 * q^5 - 32 * q^8	\( 4 q + 4 q^{2} - 8 q^{4} - 6 q^{5} - 32 q^{8} - 24 q^{10} - 10 q^{13} - 32 q^{16} - 44 q^{17} - 24 q^{20} + 14 q^{25} + 20 q^{26} - 120 q^{29} + 64 q^{32} - 92 q^{34} - 72 q^{37} + 48 q^{40} + 142 q^{41} + 72 q^{45} + 98 q^{49} - 28 q^{50} + 80 q^{52} + 146 q^{53} - 240 q^{58} + 120 q^{61} + 256 q^{64} - 132 q^{65} - 8 q^{68} - 192 q^{73} - 144 q^{74} + 192 q^{80} + 162 q^{81} + 88 q^{82} + 170 q^{85} + 82 q^{89} - 144 q^{90} - 260 q^{97} - 196 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 - 6 * q^5 - 32 * q^8 - 24 * q^10 - 10 * q^13 - 32 * q^16 - 44 * q^17 - 24 * q^20 + 14 * q^25 + 20 * q^26 - 120 * q^29 + 64 * q^32 - 92 * q^34 - 72 * q^37 + 48 * q^40 + 142 * q^41 + 72 * q^45 + 98 * q^49 - 28 * q^50 + 80 * q^52 + 146 * q^53 - 240 * q^58 + 120 * q^61 + 256 * q^64 - 132 * q^65 - 8 * q^68 - 192 * q^73 - 144 * q^74 + 192 * q^80 + 162 * q^81 + 88 * q^82 + 170 * q^85 + 82 * q^89 - 144 * q^90 - 260 * q^97 - 196 * q^98

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