LMFDB - Embedded newform 5390.2.a.bt.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5390,2,Mod(1,5390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5390, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("5390.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5390.a (trivial)

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:	yes
Analytic conductor:	$43.0393666895$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	5390.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.82843 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.82843 q^{6} +1.00000 q^{8} +5.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.82843 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.82843 q^{6} +1.00000 q^{8} +5.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.82843 q^{12} -2.00000 q^{13} -2.82843 q^{15} +1.00000 q^{16} -7.65685 q^{17} +5.00000 q^{18} +2.82843 q^{19} +1.00000 q^{20} -1.00000 q^{22} -2.82843 q^{23} -2.82843 q^{24} +1.00000 q^{25} -2.00000 q^{26} -5.65685 q^{27} +3.17157 q^{29} -2.82843 q^{30} +5.65685 q^{31} +1.00000 q^{32} +2.82843 q^{33} -7.65685 q^{34} +5.00000 q^{36} +3.17157 q^{37} +2.82843 q^{38} +5.65685 q^{39} +1.00000 q^{40} +0.828427 q^{41} -9.65685 q^{43} -1.00000 q^{44} +5.00000 q^{45} -2.82843 q^{46} +8.00000 q^{47} -2.82843 q^{48} +1.00000 q^{50} +21.6569 q^{51} -2.00000 q^{52} -10.4853 q^{53} -5.65685 q^{54} -1.00000 q^{55} -8.00000 q^{57} +3.17157 q^{58} +8.00000 q^{59} -2.82843 q^{60} +9.31371 q^{61} +5.65685 q^{62} +1.00000 q^{64} -2.00000 q^{65} +2.82843 q^{66} +15.3137 q^{67} -7.65685 q^{68} +8.00000 q^{69} -5.65685 q^{71} +5.00000 q^{72} -7.65685 q^{73} +3.17157 q^{74} -2.82843 q^{75} +2.82843 q^{76} +5.65685 q^{78} -5.17157 q^{79} +1.00000 q^{80} +1.00000 q^{81} +0.828427 q^{82} +2.34315 q^{83} -7.65685 q^{85} -9.65685 q^{86} -8.97056 q^{87} -1.00000 q^{88} +11.6569 q^{89} +5.00000 q^{90} -2.82843 q^{92} -16.0000 q^{93} +8.00000 q^{94} +2.82843 q^{95} -2.82843 q^{96} +0.828427 q^{97} -5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{8} + 10 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^8 + 10 * q^9	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{8} + 10 q^{9} + 2 q^{10} - 2 q^{11} - 4 q^{13} + 2 q^{16} - 4 q^{17} + 10 q^{18} + 2 q^{20} - 2 q^{22} + 2 q^{25} - 4 q^{26} + 12 q^{29} + 2 q^{32} - 4 q^{34} + 10 q^{36} + 12 q^{37} + 2 q^{40} - 4 q^{41} - 8 q^{43} - 2 q^{44} + 10 q^{45} + 16 q^{47} + 2 q^{50} + 32 q^{51} - 4 q^{52} - 4 q^{53} - 2 q^{55} - 16 q^{57} + 12 q^{58} + 16 q^{59} - 4 q^{61} + 2 q^{64} - 4 q^{65} + 8 q^{67} - 4 q^{68} + 16 q^{69} + 10 q^{72} - 4 q^{73} + 12 q^{74} - 16 q^{79} + 2 q^{80} + 2 q^{81} - 4 q^{82} + 16 q^{83} - 4 q^{85} - 8 q^{86} + 16 q^{87} - 2 q^{88} + 12 q^{89} + 10 q^{90} - 32 q^{93} + 16 q^{94} - 4 q^{97} - 10 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^8 + 10 * q^9 + 2 * q^10 - 2 * q^11 - 4 * q^13 + 2 * q^16 - 4 * q^17 + 10 * q^18 + 2 * q^20 - 2 * q^22 + 2 * q^25 - 4 * q^26 + 12 * q^29 + 2 * q^32 - 4 * q^34 + 10 * q^36 + 12 * q^37 + 2 * q^40 - 4 * q^41 - 8 * q^43 - 2 * q^44 + 10 * q^45 + 16 * q^47 + 2 * q^50 + 32 * q^51 - 4 * q^52 - 4 * q^53 - 2 * q^55 - 16 * q^57 + 12 * q^58 + 16 * q^59 - 4 * q^61 + 2 * q^64 - 4 * q^65 + 8 * q^67 - 4 * q^68 + 16 * q^69 + 10 * q^72 - 4 * q^73 + 12 * q^74 - 16 * q^79 + 2 * q^80 + 2 * q^81 - 4 * q^82 + 16 * q^83 - 4 * q^85 - 8 * q^86 + 16 * q^87 - 2 * q^88 + 12 * q^89 + 10 * q^90 - 32 * q^93 + 16 * q^94 - 4 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

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	0.707107
$2$	1.00000	0.707107
$3$	−2.82843	−1.63299	−0.816497	−	0.577350i	$-0.804087\pi$
$3$	−2.82843	−1.63299	−0.816497	+	0.577350i	$0.804087\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.82843	−1.15470
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	5.00000	1.66667
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.82843	−0.816497
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	−2.82843	−0.730297
$16$	1.00000	0.250000
$17$	−7.65685	−1.85706	−0.928530	−	0.371257i	$-0.878927\pi$
$17$	−7.65685	−1.85706	−0.928530	+	0.371257i	$0.878927\pi$
$18$	5.00000	1.17851
$19$	2.82843	0.648886	0.324443	−	0.945905i	$-0.394823\pi$
$19$	2.82843	0.648886	0.324443	+	0.945905i	$0.394823\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−1.00000	−0.213201
$23$	−2.82843	−0.589768	−0.294884	−	0.955533i	$-0.595281\pi$
$23$	−2.82843	−0.589768	−0.294884	+	0.955533i	$0.595281\pi$
$24$	−2.82843	−0.577350
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	−5.65685	−1.08866
$28$	0	0
$29$	3.17157	0.588946	0.294473	−	0.955660i	$-0.404856\pi$
$29$	3.17157	0.588946	0.294473	+	0.955660i	$0.404856\pi$
$30$	−2.82843	−0.516398
$31$	5.65685	1.01600	0.508001	−	0.861357i	$-0.330385\pi$
$31$	5.65685	1.01600	0.508001	+	0.861357i	$0.330385\pi$
$32$	1.00000	0.176777
$33$	2.82843	0.492366
$34$	−7.65685	−1.31314
$35$	0	0
$36$	5.00000	0.833333
$37$	3.17157	0.521403	0.260702	−	0.965419i	$-0.416046\pi$
$37$	3.17157	0.521403	0.260702	+	0.965419i	$0.416046\pi$
$38$	2.82843	0.458831
$39$	5.65685	0.905822
$40$	1.00000	0.158114
$41$	0.828427	0.129379	0.0646893	−	0.997905i	$-0.479394\pi$
$41$	0.828427	0.129379	0.0646893	+	0.997905i	$0.479394\pi$
$42$	0	0
$43$	−9.65685	−1.47266	−0.736328	−	0.676625i	$-0.763442\pi$
$43$	−9.65685	−1.47266	−0.736328	+	0.676625i	$0.763442\pi$
$44$	−1.00000	−0.150756
$45$	5.00000	0.745356
$46$	−2.82843	−0.417029
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	−2.82843	−0.408248
$49$	0	0
$50$	1.00000	0.141421
$51$	21.6569	3.03257
$52$	−2.00000	−0.277350
$53$	−10.4853	−1.44026	−0.720132	−	0.693837i	$-0.755919\pi$
$53$	−10.4853	−1.44026	−0.720132	+	0.693837i	$0.755919\pi$
$54$	−5.65685	−0.769800
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−8.00000	−1.05963
$58$	3.17157	0.416448
$59$	8.00000	1.04151	0.520756	−	0.853706i	$-0.325650\pi$
$59$	8.00000	1.04151	0.520756	+	0.853706i	$0.325650\pi$
$60$	−2.82843	−0.365148
$61$	9.31371	1.19250	0.596249	−	0.802799i	$-0.296657\pi$
$61$	9.31371	1.19250	0.596249	+	0.802799i	$0.296657\pi$
$62$	5.65685	0.718421
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.00000	−0.248069
$66$	2.82843	0.348155
$67$	15.3137	1.87087	0.935434	−	0.353502i	$-0.115009\pi$
$67$	15.3137	1.87087	0.935434	+	0.353502i	$0.115009\pi$
$68$	−7.65685	−0.928530
$69$	8.00000	0.963087
$70$	0	0
$71$	−5.65685	−0.671345	−0.335673	−	0.941979i	$-0.608964\pi$
$71$	−5.65685	−0.671345	−0.335673	+	0.941979i	$0.608964\pi$
$72$	5.00000	0.589256
$73$	−7.65685	−0.896167	−0.448084	−	0.893992i	$-0.647893\pi$
$73$	−7.65685	−0.896167	−0.448084	+	0.893992i	$0.647893\pi$
$74$	3.17157	0.368688
$75$	−2.82843	−0.326599
$76$	2.82843	0.324443
$77$	0	0
$78$	5.65685	0.640513
$79$	−5.17157	−0.581847	−0.290924	−	0.956746i	$-0.593963\pi$
$79$	−5.17157	−0.581847	−0.290924	+	0.956746i	$0.593963\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	0.828427	0.0914845
$83$	2.34315	0.257194	0.128597	−	0.991697i	$-0.458953\pi$
$83$	2.34315	0.257194	0.128597	+	0.991697i	$0.458953\pi$
$84$	0	0
$85$	−7.65685	−0.830502
$86$	−9.65685	−1.04133
$87$	−8.97056	−0.961745
$88$	−1.00000	−0.106600
$89$	11.6569	1.23562	0.617812	−	0.786326i	$-0.288019\pi$
$89$	11.6569	1.23562	0.617812	+	0.786326i	$0.288019\pi$
$90$	5.00000	0.527046
$91$	0	0
$92$	−2.82843	−0.294884
$93$	−16.0000	−1.65912
$94$	8.00000	0.825137
$95$	2.82843	0.290191
$96$	−2.82843	−0.288675
$97$	0.828427	0.0841140	0.0420570	−	0.999115i	$-0.486609\pi$
$97$	0.828427	0.0841140	0.0420570	+	0.999115i	$0.486609\pi$
$98$	0	0
$99$	−5.00000	−0.502519
$100$	1.00000	0.100000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	21.6569	2.14435
$103$	5.65685	0.557386	0.278693	−	0.960380i	$-0.410099\pi$
$103$	5.65685	0.557386	0.278693	+	0.960380i	$0.410099\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	−10.4853	−1.01842
$107$	−1.65685	−0.160174	−0.0800871	−	0.996788i	$-0.525520\pi$
$107$	−1.65685	−0.160174	−0.0800871	+	0.996788i	$0.525520\pi$
$108$	−5.65685	−0.544331
$109$	14.4853	1.38744	0.693719	−	0.720246i	$-0.255971\pi$
$109$	14.4853	1.38744	0.693719	+	0.720246i	$0.255971\pi$
$110$	−1.00000	−0.0953463
$111$	−8.97056	−0.851448
$112$	0	0
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	−8.00000	−0.749269
$115$	−2.82843	−0.263752
$116$	3.17157	0.294473
$117$	−10.0000	−0.924500
$118$	8.00000	0.736460
$119$	0	0
$120$	−2.82843	−0.258199
$121$	1.00000	0.0909091
$122$	9.31371	0.843224
$123$	−2.34315	−0.211274
$124$	5.65685	0.508001
$125$	1.00000	0.0894427
$126$	0	0
$127$	19.3137	1.71381	0.856907	−	0.515471i	$-0.172383\pi$
$127$	19.3137	1.71381	0.856907	+	0.515471i	$0.172383\pi$
$128$	1.00000	0.0883883
$129$	27.3137	2.40484
$130$	−2.00000	−0.175412
$131$	−18.8284	−1.64505	−0.822524	−	0.568731i	$-0.807435\pi$
$131$	−18.8284	−1.64505	−0.822524	+	0.568731i	$0.807435\pi$
$132$	2.82843	0.246183
$133$	0	0
$134$	15.3137	1.32290
$135$	−5.65685	−0.486864
$136$	−7.65685	−0.656570
$137$	5.31371	0.453981	0.226990	−	0.973897i	$-0.427111\pi$
$137$	5.31371	0.453981	0.226990	+	0.973897i	$0.427111\pi$
$138$	8.00000	0.681005
$139$	−18.8284	−1.59701	−0.798503	−	0.601991i	$-0.794374\pi$
$139$	−18.8284	−1.59701	−0.798503	+	0.601991i	$0.794374\pi$
$140$	0	0
$141$	−22.6274	−1.90557
$142$	−5.65685	−0.474713
$143$	2.00000	0.167248
$144$	5.00000	0.416667
$145$	3.17157	0.263385
$146$	−7.65685	−0.633686
$147$	0	0
$148$	3.17157	0.260702
$149$	−1.51472	−0.124091	−0.0620453	−	0.998073i	$-0.519762\pi$
$149$	−1.51472	−0.124091	−0.0620453	+	0.998073i	$0.519762\pi$
$150$	−2.82843	−0.230940
$151$	10.8284	0.881205	0.440602	−	0.897702i	$-0.354765\pi$
$151$	10.8284	0.881205	0.440602	+	0.897702i	$0.354765\pi$
$152$	2.82843	0.229416
$153$	−38.2843	−3.09510
$154$	0	0
$155$	5.65685	0.454369
$156$	5.65685	0.452911
$157$	−15.6569	−1.24955	−0.624777	−	0.780804i	$-0.714810\pi$
$157$	−15.6569	−1.24955	−0.624777	+	0.780804i	$0.714810\pi$
$158$	−5.17157	−0.411428
$159$	29.6569	2.35194
$160$	1.00000	0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	12.0000	0.939913	0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000	0.939913	0.469956	+	0.882690i	$0.344270\pi$
$164$	0.828427	0.0646893
$165$	2.82843	0.220193
$166$	2.34315	0.181863
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−7.65685	−0.587254
$171$	14.1421	1.08148
$172$	−9.65685	−0.736328
$173$	1.31371	0.0998794	0.0499397	−	0.998752i	$-0.484097\pi$
$173$	1.31371	0.0998794	0.0499397	+	0.998752i	$0.484097\pi$
$174$	−8.97056	−0.680057
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	−22.6274	−1.70078
$178$	11.6569	0.873718
$179$	6.34315	0.474109	0.237054	−	0.971496i	$-0.423818\pi$
$179$	6.34315	0.474109	0.237054	+	0.971496i	$0.423818\pi$
$180$	5.00000	0.372678
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	0	0
$183$	−26.3431	−1.94734
$184$	−2.82843	−0.208514
$185$	3.17157	0.233179
$186$	−16.0000	−1.17318
$187$	7.65685	0.559925
$188$	8.00000	0.583460
$189$	0	0
$190$	2.82843	0.205196
$191$	19.3137	1.39749	0.698745	−	0.715370i	$-0.253742\pi$
$191$	19.3137	1.39749	0.698745	+	0.715370i	$0.253742\pi$
$192$	−2.82843	−0.204124
$193$	21.3137	1.53419	0.767097	−	0.641531i	$-0.221700\pi$
$193$	21.3137	1.53419	0.767097	+	0.641531i	$0.221700\pi$
$194$	0.828427	0.0594776
$195$	5.65685	0.405096
$196$	0	0
$197$	−12.3431	−0.879413	−0.439706	−	0.898142i	$-0.644917\pi$
$197$	−12.3431	−0.879413	−0.439706	+	0.898142i	$0.644917\pi$
$198$	−5.00000	−0.355335
$199$	11.3137	0.802008	0.401004	−	0.916076i	$-0.368661\pi$
$199$	11.3137	0.802008	0.401004	+	0.916076i	$0.368661\pi$
$200$	1.00000	0.0707107
$201$	−43.3137	−3.05511
$202$	−10.0000	−0.703598
$203$	0	0
$204$	21.6569	1.51628
$205$	0.828427	0.0578599
$206$	5.65685	0.394132
$207$	−14.1421	−0.982946
$208$	−2.00000	−0.138675
$209$	−2.82843	−0.195646
$210$	0	0
$211$	15.3137	1.05424	0.527120	−	0.849791i	$-0.323272\pi$
$211$	15.3137	1.05424	0.527120	+	0.849791i	$0.323272\pi$
$212$	−10.4853	−0.720132
$213$	16.0000	1.09630
$214$	−1.65685	−0.113260
$215$	−9.65685	−0.658592
$216$	−5.65685	−0.384900
$217$	0	0
$218$	14.4853	0.981067
$219$	21.6569	1.46343
$220$	−1.00000	−0.0674200
$221$	15.3137	1.03011
$222$	−8.97056	−0.602065
$223$	28.2843	1.89405	0.947027	−	0.321153i	$-0.104070\pi$
$223$	28.2843	1.89405	0.947027	+	0.321153i	$0.104070\pi$
$224$	0	0
$225$	5.00000	0.333333
$226$	2.00000	0.133038
$227$	24.0000	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$228$	−8.00000	−0.529813
$229$	1.31371	0.0868123	0.0434062	−	0.999058i	$-0.486179\pi$
$229$	1.31371	0.0868123	0.0434062	+	0.999058i	$0.486179\pi$
$230$	−2.82843	−0.186501
$231$	0	0
$232$	3.17157	0.208224
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	−10.0000	−0.653720
$235$	8.00000	0.521862
$236$	8.00000	0.520756
$237$	14.6274	0.950153
$238$	0	0
$239$	−7.51472	−0.486087	−0.243043	−	0.970015i	$-0.578146\pi$
$239$	−7.51472	−0.486087	−0.243043	+	0.970015i	$0.578146\pi$
$240$	−2.82843	−0.182574
$241$	8.82843	0.568689	0.284344	−	0.958722i	$-0.408224\pi$
$241$	8.82843	0.568689	0.284344	+	0.958722i	$0.408224\pi$
$242$	1.00000	0.0642824
$243$	14.1421	0.907218
$244$	9.31371	0.596249
$245$	0	0
$246$	−2.34315	−0.149394
$247$	−5.65685	−0.359937
$248$	5.65685	0.359211
$249$	−6.62742	−0.419995
$250$	1.00000	0.0632456
$251$	11.3137	0.714115	0.357057	−	0.934082i	$-0.383780\pi$
$251$	11.3137	0.714115	0.357057	+	0.934082i	$0.383780\pi$
$252$	0	0
$253$	2.82843	0.177822
$254$	19.3137	1.21185
$255$	21.6569	1.35620
$256$	1.00000	0.0625000
$257$	−23.1716	−1.44540	−0.722702	−	0.691160i	$-0.757100\pi$
$257$	−23.1716	−1.44540	−0.722702	+	0.691160i	$0.757100\pi$
$258$	27.3137	1.70048
$259$	0	0
$260$	−2.00000	−0.124035
$261$	15.8579	0.981577
$262$	−18.8284	−1.16322
$263$	−14.6274	−0.901965	−0.450983	−	0.892533i	$-0.648926\pi$
$263$	−14.6274	−0.901965	−0.450983	+	0.892533i	$0.648926\pi$
$264$	2.82843	0.174078
$265$	−10.4853	−0.644106
$266$	0	0
$267$	−32.9706	−2.01777
$268$	15.3137	0.935434
$269$	−2.00000	−0.121942	−0.0609711	−	0.998140i	$-0.519420\pi$
$269$	−2.00000	−0.121942	−0.0609711	+	0.998140i	$0.519420\pi$
$270$	−5.65685	−0.344265
$271$	−16.9706	−1.03089	−0.515444	−	0.856923i	$-0.672373\pi$
$271$	−16.9706	−1.03089	−0.515444	+	0.856923i	$0.672373\pi$
$272$	−7.65685	−0.464265
$273$	0	0
$274$	5.31371	0.321013
$275$	−1.00000	−0.0603023
$276$	8.00000	0.481543
$277$	−13.3137	−0.799943	−0.399972	−	0.916528i	$-0.630980\pi$
$277$	−13.3137	−0.799943	−0.399972	+	0.916528i	$0.630980\pi$
$278$	−18.8284	−1.12925
$279$	28.2843	1.69334
$280$	0	0
$281$	−6.97056	−0.415829	−0.207914	−	0.978147i	$-0.566668\pi$
$281$	−6.97056	−0.415829	−0.207914	+	0.978147i	$0.566668\pi$
$282$	−22.6274	−1.34744
$283$	22.6274	1.34506	0.672530	−	0.740070i	$-0.265208\pi$
$283$	22.6274	1.34506	0.672530	+	0.740070i	$0.265208\pi$
$284$	−5.65685	−0.335673
$285$	−8.00000	−0.473879
$286$	2.00000	0.118262
$287$	0	0
$288$	5.00000	0.294628
$289$	41.6274	2.44867
$290$	3.17157	0.186241
$291$	−2.34315	−0.137358
$292$	−7.65685	−0.448084
$293$	−2.00000	−0.116841	−0.0584206	−	0.998292i	$-0.518606\pi$
$293$	−2.00000	−0.116841	−0.0584206	+	0.998292i	$0.518606\pi$
$294$	0	0
$295$	8.00000	0.465778
$296$	3.17157	0.184344
$297$	5.65685	0.328244
$298$	−1.51472	−0.0877453
$299$	5.65685	0.327144
$300$	−2.82843	−0.163299
$301$	0	0
$302$	10.8284	0.623106
$303$	28.2843	1.62489
$304$	2.82843	0.162221
$305$	9.31371	0.533301
$306$	−38.2843	−2.18857
$307$	8.97056	0.511977	0.255989	−	0.966680i	$-0.417599\pi$
$307$	8.97056	0.511977	0.255989	+	0.966680i	$0.417599\pi$
$308$	0	0
$309$	−16.0000	−0.910208
$310$	5.65685	0.321288
$311$	−0.970563	−0.0550356	−0.0275178	−	0.999621i	$-0.508760\pi$
$311$	−0.970563	−0.0550356	−0.0275178	+	0.999621i	$0.508760\pi$
$312$	5.65685	0.320256
$313$	8.82843	0.499012	0.249506	−	0.968373i	$-0.419732\pi$
$313$	8.82843	0.499012	0.249506	+	0.968373i	$0.419732\pi$
$314$	−15.6569	−0.883567
$315$	0	0
$316$	−5.17157	−0.290924
$317$	3.17157	0.178133	0.0890666	−	0.996026i	$-0.471612\pi$
$317$	3.17157	0.178133	0.0890666	+	0.996026i	$0.471612\pi$
$318$	29.6569	1.66307
$319$	−3.17157	−0.177574
$320$	1.00000	0.0559017
$321$	4.68629	0.261563
$322$	0	0
$323$	−21.6569	−1.20502
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	12.0000	0.664619
$327$	−40.9706	−2.26568
$328$	0.828427	0.0457422
$329$	0	0
$330$	2.82843	0.155700
$331$	28.9706	1.59237	0.796183	−	0.605056i	$-0.206849\pi$
$331$	28.9706	1.59237	0.796183	+	0.605056i	$0.206849\pi$
$332$	2.34315	0.128597
$333$	15.8579	0.869006
$334$	16.0000	0.875481
$335$	15.3137	0.836677
$336$	0	0
$337$	29.3137	1.59682	0.798410	−	0.602115i	$-0.205675\pi$
$337$	29.3137	1.59682	0.798410	+	0.602115i	$0.205675\pi$
$338$	−9.00000	−0.489535
$339$	−5.65685	−0.307238
$340$	−7.65685	−0.415251
$341$	−5.65685	−0.306336
$342$	14.1421	0.764719
$343$	0	0
$344$	−9.65685	−0.520663
$345$	8.00000	0.430706
$346$	1.31371	0.0706254
$347$	28.9706	1.55522	0.777611	−	0.628746i	$-0.216432\pi$
$347$	28.9706	1.55522	0.777611	+	0.628746i	$0.216432\pi$
$348$	−8.97056	−0.480873
$349$	−26.9706	−1.44370	−0.721851	−	0.692049i	$-0.756708\pi$
$349$	−26.9706	−1.44370	−0.721851	+	0.692049i	$0.756708\pi$
$350$	0	0
$351$	11.3137	0.603881
$352$	−1.00000	−0.0533002
$353$	24.8284	1.32148	0.660742	−	0.750613i	$-0.270242\pi$
$353$	24.8284	1.32148	0.660742	+	0.750613i	$0.270242\pi$
$354$	−22.6274	−1.20263
$355$	−5.65685	−0.300235
$356$	11.6569	0.617812
$357$	0	0
$358$	6.34315	0.335246
$359$	33.4558	1.76573	0.882866	−	0.469625i	$-0.155611\pi$
$359$	33.4558	1.76573	0.882866	+	0.469625i	$0.155611\pi$
$360$	5.00000	0.263523
$361$	−11.0000	−0.578947
$362$	14.0000	0.735824
$363$	−2.82843	−0.148454
$364$	0	0
$365$	−7.65685	−0.400778
$366$	−26.3431	−1.37698
$367$	−28.2843	−1.47643	−0.738213	−	0.674567i	$-0.764330\pi$
$367$	−28.2843	−1.47643	−0.738213	+	0.674567i	$0.764330\pi$
$368$	−2.82843	−0.147442
$369$	4.14214	0.215631
$370$	3.17157	0.164882
$371$	0	0
$372$	−16.0000	−0.829561
$373$	3.65685	0.189345	0.0946724	−	0.995508i	$-0.469820\pi$
$373$	3.65685	0.189345	0.0946724	+	0.995508i	$0.469820\pi$
$374$	7.65685	0.395927
$375$	−2.82843	−0.146059
$376$	8.00000	0.412568
$377$	−6.34315	−0.326689
$378$	0	0
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	2.82843	0.145095
$381$	−54.6274	−2.79865
$382$	19.3137	0.988175
$383$	29.6569	1.51539	0.757697	−	0.652606i	$-0.226324\pi$
$383$	29.6569	1.51539	0.757697	+	0.652606i	$0.226324\pi$
$384$	−2.82843	−0.144338
$385$	0	0
$386$	21.3137	1.08484
$387$	−48.2843	−2.45443
$388$	0.828427	0.0420570
$389$	30.9706	1.57027	0.785135	−	0.619325i	$-0.212594\pi$
$389$	30.9706	1.57027	0.785135	+	0.619325i	$0.212594\pi$
$390$	5.65685	0.286446
$391$	21.6569	1.09523
$392$	0	0
$393$	53.2548	2.68635
$394$	−12.3431	−0.621839
$395$	−5.17157	−0.260210
$396$	−5.00000	−0.251259
$397$	22.9706	1.15286	0.576430	−	0.817147i	$-0.304445\pi$
$397$	22.9706	1.15286	0.576430	+	0.817147i	$0.304445\pi$
$398$	11.3137	0.567105
$399$	0	0
$400$	1.00000	0.0500000
$401$	10.0000	0.499376	0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000	0.499376	0.249688	+	0.968326i	$0.419672\pi$
$402$	−43.3137	−2.16029
$403$	−11.3137	−0.563576
$404$	−10.0000	−0.497519
$405$	1.00000	0.0496904
$406$	0	0
$407$	−3.17157	−0.157209
$408$	21.6569	1.07217
$409$	12.1421	0.600390	0.300195	−	0.953878i	$-0.402948\pi$
$409$	12.1421	0.600390	0.300195	+	0.953878i	$0.402948\pi$
$410$	0.828427	0.0409131
$411$	−15.0294	−0.741347
$412$	5.65685	0.278693
$413$	0	0
$414$	−14.1421	−0.695048
$415$	2.34315	0.115021
$416$	−2.00000	−0.0980581
$417$	53.2548	2.60790
$418$	−2.82843	−0.138343
$419$	30.6274	1.49625	0.748124	−	0.663559i	$-0.230955\pi$
$419$	30.6274	1.49625	0.748124	+	0.663559i	$0.230955\pi$
$420$	0	0
$421$	28.6274	1.39521	0.697607	−	0.716480i	$-0.254248\pi$
$421$	28.6274	1.39521	0.697607	+	0.716480i	$0.254248\pi$
$422$	15.3137	0.745460
$423$	40.0000	1.94487
$424$	−10.4853	−0.509210
$425$	−7.65685	−0.371412
$426$	16.0000	0.775203
$427$	0	0
$428$	−1.65685	−0.0800871
$429$	−5.65685	−0.273115
$430$	−9.65685	−0.465695
$431$	−19.7990	−0.953684	−0.476842	−	0.878989i	$-0.658219\pi$
$431$	−19.7990	−0.953684	−0.476842	+	0.878989i	$0.658219\pi$
$432$	−5.65685	−0.272166
$433$	−20.8284	−1.00095	−0.500475	−	0.865751i	$-0.666841\pi$
$433$	−20.8284	−1.00095	−0.500475	+	0.865751i	$0.666841\pi$
$434$	0	0
$435$	−8.97056	−0.430106
$436$	14.4853	0.693719
$437$	−8.00000	−0.382692
$438$	21.6569	1.03480
$439$	−24.9706	−1.19178	−0.595890	−	0.803066i	$-0.703201\pi$
$439$	−24.9706	−1.19178	−0.595890	+	0.803066i	$0.703201\pi$
$440$	−1.00000	−0.0476731
$441$	0	0
$442$	15.3137	0.728399
$443$	−8.68629	−0.412698	−0.206349	−	0.978478i	$-0.566158\pi$
$443$	−8.68629	−0.412698	−0.206349	+	0.978478i	$0.566158\pi$
$444$	−8.97056	−0.425724
$445$	11.6569	0.552588
$446$	28.2843	1.33930
$447$	4.28427	0.202639
$448$	0	0
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	5.00000	0.235702
$451$	−0.828427	−0.0390091
$452$	2.00000	0.0940721
$453$	−30.6274	−1.43900
$454$	24.0000	1.12638
$455$	0	0
$456$	−8.00000	−0.374634
$457$	−22.0000	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	1.31371	0.0613856
$459$	43.3137	2.02171
$460$	−2.82843	−0.131876
$461$	11.6569	0.542914	0.271457	−	0.962451i	$-0.412495\pi$
$461$	11.6569	0.542914	0.271457	+	0.962451i	$0.412495\pi$
$462$	0	0
$463$	−9.45584	−0.439450	−0.219725	−	0.975562i	$-0.570516\pi$
$463$	−9.45584	−0.439450	−0.219725	+	0.975562i	$0.570516\pi$
$464$	3.17157	0.147237
$465$	−16.0000	−0.741982
$466$	−6.00000	−0.277945
$467$	−11.7990	−0.545992	−0.272996	−	0.962015i	$-0.588015\pi$
$467$	−11.7990	−0.545992	−0.272996	+	0.962015i	$0.588015\pi$
$468$	−10.0000	−0.462250
$469$	0	0
$470$	8.00000	0.369012
$471$	44.2843	2.04051
$472$	8.00000	0.368230
$473$	9.65685	0.444023
$474$	14.6274	0.671860
$475$	2.82843	0.129777
$476$	0	0
$477$	−52.4264	−2.40044
$478$	−7.51472	−0.343715
$479$	−35.3137	−1.61352	−0.806762	−	0.590876i	$-0.798782\pi$
$479$	−35.3137	−1.61352	−0.806762	+	0.590876i	$0.798782\pi$
$480$	−2.82843	−0.129099
$481$	−6.34315	−0.289223
$482$	8.82843	0.402124
$483$	0	0
$484$	1.00000	0.0454545
$485$	0.828427	0.0376169
$486$	14.1421	0.641500
$487$	−36.7696	−1.66619	−0.833094	−	0.553132i	$-0.813433\pi$
$487$	−36.7696	−1.66619	−0.833094	+	0.553132i	$0.813433\pi$
$488$	9.31371	0.421612
$489$	−33.9411	−1.53487
$490$	0	0
$491$	−8.68629	−0.392007	−0.196003	−	0.980603i	$-0.562796\pi$
$491$	−8.68629	−0.392007	−0.196003	+	0.980603i	$0.562796\pi$
$492$	−2.34315	−0.105637
$493$	−24.2843	−1.09371
$494$	−5.65685	−0.254514
$495$	−5.00000	−0.224733
$496$	5.65685	0.254000
$497$	0	0
$498$	−6.62742	−0.296982
$499$	28.9706	1.29690	0.648450	−	0.761257i	$-0.275417\pi$
$499$	28.9706	1.29690	0.648450	+	0.761257i	$0.275417\pi$
$500$	1.00000	0.0447214
$501$	−45.2548	−2.02184
$502$	11.3137	0.504956
$503$	3.31371	0.147751	0.0738755	−	0.997267i	$-0.476463\pi$
$503$	3.31371	0.147751	0.0738755	+	0.997267i	$0.476463\pi$
$504$	0	0
$505$	−10.0000	−0.444994
$506$	2.82843	0.125739
$507$	25.4558	1.13053
$508$	19.3137	0.856907
$509$	10.6863	0.473662	0.236831	−	0.971551i	$-0.423891\pi$
$509$	10.6863	0.473662	0.236831	+	0.971551i	$0.423891\pi$
$510$	21.6569	0.958982
$511$	0	0
$512$	1.00000	0.0441942
$513$	−16.0000	−0.706417
$514$	−23.1716	−1.02205
$515$	5.65685	0.249271
$516$	27.3137	1.20242
$517$	−8.00000	−0.351840
$518$	0	0
$519$	−3.71573	−0.163102
$520$	−2.00000	−0.0877058
$521$	−41.5980	−1.82244	−0.911220	−	0.411919i	$-0.864859\pi$
$521$	−41.5980	−1.82244	−0.911220	+	0.411919i	$0.864859\pi$
$522$	15.8579	0.694080
$523$	10.3431	0.452274	0.226137	−	0.974095i	$-0.427390\pi$
$523$	10.3431	0.452274	0.226137	+	0.974095i	$0.427390\pi$
$524$	−18.8284	−0.822524
$525$	0	0
$526$	−14.6274	−0.637786
$527$	−43.3137	−1.88677
$528$	2.82843	0.123091
$529$	−15.0000	−0.652174
$530$	−10.4853	−0.455452
$531$	40.0000	1.73585
$532$	0	0
$533$	−1.65685	−0.0717663
$534$	−32.9706	−1.42678
$535$	−1.65685	−0.0716321
$536$	15.3137	0.661451
$537$	−17.9411	−0.774217
$538$	−2.00000	−0.0862261
$539$	0	0
$540$	−5.65685	−0.243432
$541$	−33.1127	−1.42363	−0.711813	−	0.702369i	$-0.752126\pi$
$541$	−33.1127	−1.42363	−0.711813	+	0.702369i	$0.752126\pi$
$542$	−16.9706	−0.728948
$543$	−39.5980	−1.69931
$544$	−7.65685	−0.328285
$545$	14.4853	0.620481
$546$	0	0
$547$	23.3137	0.996822	0.498411	−	0.866941i	$-0.333917\pi$
$547$	23.3137	0.996822	0.498411	+	0.866941i	$0.333917\pi$
$548$	5.31371	0.226990
$549$	46.5685	1.98750
$550$	−1.00000	−0.0426401
$551$	8.97056	0.382159
$552$	8.00000	0.340503
$553$	0	0
$554$	−13.3137	−0.565645
$555$	−8.97056	−0.380779
$556$	−18.8284	−0.798503
$557$	−26.9706	−1.14278	−0.571390	−	0.820679i	$-0.693596\pi$
$557$	−26.9706	−1.14278	−0.571390	+	0.820679i	$0.693596\pi$
$558$	28.2843	1.19737
$559$	19.3137	0.816883
$560$	0	0
$561$	−21.6569	−0.914353
$562$	−6.97056	−0.294035
$563$	22.6274	0.953632	0.476816	−	0.879003i	$-0.341791\pi$
$563$	22.6274	0.953632	0.476816	+	0.879003i	$0.341791\pi$
$564$	−22.6274	−0.952786
$565$	2.00000	0.0841406
$566$	22.6274	0.951101
$567$	0	0
$568$	−5.65685	−0.237356
$569$	16.6274	0.697058	0.348529	−	0.937298i	$-0.386681\pi$
$569$	16.6274	0.697058	0.348529	+	0.937298i	$0.386681\pi$
$570$	−8.00000	−0.335083
$571$	−35.5980	−1.48973	−0.744865	−	0.667216i	$-0.767486\pi$
$571$	−35.5980	−1.48973	−0.744865	+	0.667216i	$0.767486\pi$
$572$	2.00000	0.0836242
$573$	−54.6274	−2.28209
$574$	0	0
$575$	−2.82843	−0.117954
$576$	5.00000	0.208333
$577$	−25.1127	−1.04546	−0.522728	−	0.852500i	$-0.675086\pi$
$577$	−25.1127	−1.04546	−0.522728	+	0.852500i	$0.675086\pi$
$578$	41.6274	1.73147
$579$	−60.2843	−2.50533
$580$	3.17157	0.131692
$581$	0	0
$582$	−2.34315	−0.0971265
$583$	10.4853	0.434256
$584$	−7.65685	−0.316843
$585$	−10.0000	−0.413449
$586$	−2.00000	−0.0826192
$587$	38.1421	1.57429	0.787147	−	0.616765i	$-0.211557\pi$
$587$	38.1421	1.57429	0.787147	+	0.616765i	$0.211557\pi$
$588$	0	0
$589$	16.0000	0.659269
$590$	8.00000	0.329355
$591$	34.9117	1.43607
$592$	3.17157	0.130351
$593$	−20.3431	−0.835393	−0.417696	−	0.908587i	$-0.637162\pi$
$593$	−20.3431	−0.835393	−0.417696	+	0.908587i	$0.637162\pi$
$594$	5.65685	0.232104
$595$	0	0
$596$	−1.51472	−0.0620453
$597$	−32.0000	−1.30967
$598$	5.65685	0.231326
$599$	21.6569	0.884875	0.442438	−	0.896799i	$-0.354114\pi$
$599$	21.6569	0.884875	0.442438	+	0.896799i	$0.354114\pi$
$600$	−2.82843	−0.115470
$601$	−12.8284	−0.523282	−0.261641	−	0.965165i	$-0.584264\pi$
$601$	−12.8284	−0.523282	−0.261641	+	0.965165i	$0.584264\pi$
$602$	0	0
$603$	76.5685	3.11811
$604$	10.8284	0.440602
$605$	1.00000	0.0406558
$606$	28.2843	1.14897
$607$	−29.6569	−1.20373	−0.601867	−	0.798596i	$-0.705576\pi$
$607$	−29.6569	−1.20373	−0.601867	+	0.798596i	$0.705576\pi$
$608$	2.82843	0.114708
$609$	0	0
$610$	9.31371	0.377101
$611$	−16.0000	−0.647291
$612$	−38.2843	−1.54755
$613$	22.9706	0.927772	0.463886	−	0.885895i	$-0.346455\pi$
$613$	22.9706	0.927772	0.463886	+	0.885895i	$0.346455\pi$
$614$	8.97056	0.362022
$615$	−2.34315	−0.0944848
$616$	0	0
$617$	−32.3431	−1.30209	−0.651043	−	0.759041i	$-0.725668\pi$
$617$	−32.3431	−1.30209	−0.651043	+	0.759041i	$0.725668\pi$
$618$	−16.0000	−0.643614
$619$	−40.0000	−1.60774	−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000	−1.60774	−0.803868	+	0.594808i	$0.797228\pi$
$620$	5.65685	0.227185
$621$	16.0000	0.642058
$622$	−0.970563	−0.0389160
$623$	0	0
$624$	5.65685	0.226455
$625$	1.00000	0.0400000
$626$	8.82843	0.352855
$627$	8.00000	0.319489
$628$	−15.6569	−0.624777
$629$	−24.2843	−0.968277
$630$	0	0
$631$	−22.6274	−0.900783	−0.450392	−	0.892831i	$-0.648716\pi$
$631$	−22.6274	−0.900783	−0.450392	+	0.892831i	$0.648716\pi$
$632$	−5.17157	−0.205714
$633$	−43.3137	−1.72157
$634$	3.17157	0.125959
$635$	19.3137	0.766441
$636$	29.6569	1.17597
$637$	0	0
$638$	−3.17157	−0.125564
$639$	−28.2843	−1.11891
$640$	1.00000	0.0395285
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	4.68629	0.184953
$643$	−14.1421	−0.557711	−0.278856	−	0.960333i	$-0.589955\pi$
$643$	−14.1421	−0.557711	−0.278856	+	0.960333i	$0.589955\pi$
$644$	0	0
$645$	27.3137	1.07548
$646$	−21.6569	−0.852078
$647$	−12.2843	−0.482945	−0.241472	−	0.970408i	$-0.577630\pi$
$647$	−12.2843	−0.482945	−0.241472	+	0.970408i	$0.577630\pi$
$648$	1.00000	0.0392837
$649$	−8.00000	−0.314027
$650$	−2.00000	−0.0784465
$651$	0	0
$652$	12.0000	0.469956
$653$	7.45584	0.291770	0.145885	−	0.989302i	$-0.453397\pi$
$653$	7.45584	0.291770	0.145885	+	0.989302i	$0.453397\pi$
$654$	−40.9706	−1.60208
$655$	−18.8284	−0.735688
$656$	0.828427	0.0323446
$657$	−38.2843	−1.49361
$658$	0	0
$659$	−9.65685	−0.376178	−0.188089	−	0.982152i	$-0.560229\pi$
$659$	−9.65685	−0.376178	−0.188089	+	0.982152i	$0.560229\pi$
$660$	2.82843	0.110096
$661$	6.00000	0.233373	0.116686	−	0.993169i	$-0.462773\pi$
$661$	6.00000	0.233373	0.116686	+	0.993169i	$0.462773\pi$
$662$	28.9706	1.12597
$663$	−43.3137	−1.68217
$664$	2.34315	0.0909317
$665$	0	0
$666$	15.8579	0.614480
$667$	−8.97056	−0.347342
$668$	16.0000	0.619059
$669$	−80.0000	−3.09298
$670$	15.3137	0.591620
$671$	−9.31371	−0.359552
$672$	0	0
$673$	−36.6274	−1.41188	−0.705942	−	0.708270i	$-0.749476\pi$
$673$	−36.6274	−1.41188	−0.705942	+	0.708270i	$0.749476\pi$
$674$	29.3137	1.12912
$675$	−5.65685	−0.217732
$676$	−9.00000	−0.346154
$677$	14.0000	0.538064	0.269032	−	0.963131i	$-0.413296\pi$
$677$	14.0000	0.538064	0.269032	+	0.963131i	$0.413296\pi$
$678$	−5.65685	−0.217250
$679$	0	0
$680$	−7.65685	−0.293627
$681$	−67.8823	−2.60125
$682$	−5.65685	−0.216612
$683$	22.3431	0.854937	0.427468	−	0.904030i	$-0.359406\pi$
$683$	22.3431	0.854937	0.427468	+	0.904030i	$0.359406\pi$
$684$	14.1421	0.540738
$685$	5.31371	0.203026
$686$	0	0
$687$	−3.71573	−0.141764
$688$	−9.65685	−0.368164
$689$	20.9706	0.798915
$690$	8.00000	0.304555
$691$	−0.970563	−0.0369219	−0.0184610	−	0.999830i	$-0.505877\pi$
$691$	−0.970563	−0.0369219	−0.0184610	+	0.999830i	$0.505877\pi$
$692$	1.31371	0.0499397
$693$	0	0
$694$	28.9706	1.09971
$695$	−18.8284	−0.714203
$696$	−8.97056	−0.340028
$697$	−6.34315	−0.240264
$698$	−26.9706	−1.02085
$699$	16.9706	0.641886
$700$	0	0
$701$	40.8284	1.54207	0.771034	−	0.636794i	$-0.219740\pi$
$701$	40.8284	1.54207	0.771034	+	0.636794i	$0.219740\pi$
$702$	11.3137	0.427008
$703$	8.97056	0.338331
$704$	−1.00000	−0.0376889
$705$	−22.6274	−0.852198
$706$	24.8284	0.934430
$707$	0	0
$708$	−22.6274	−0.850390
$709$	26.2843	0.987127	0.493563	−	0.869710i	$-0.335694\pi$
$709$	26.2843	0.987127	0.493563	+	0.869710i	$0.335694\pi$
$710$	−5.65685	−0.212298
$711$	−25.8579	−0.969746
$712$	11.6569	0.436859
$713$	−16.0000	−0.599205
$714$	0	0
$715$	2.00000	0.0747958
$716$	6.34315	0.237054
$717$	21.2548	0.793776
$718$	33.4558	1.24856
$719$	8.00000	0.298350	0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000	0.298350	0.149175	+	0.988811i	$0.452338\pi$
$720$	5.00000	0.186339
$721$	0	0
$722$	−11.0000	−0.409378
$723$	−24.9706	−0.928665
$724$	14.0000	0.520306
$725$	3.17157	0.117789
$726$	−2.82843	−0.104973
$727$	−4.68629	−0.173805	−0.0869025	−	0.996217i	$-0.527697\pi$
$727$	−4.68629	−0.173805	−0.0869025	+	0.996217i	$0.527697\pi$
$728$	0	0
$729$	−43.0000	−1.59259
$730$	−7.65685	−0.283393
$731$	73.9411	2.73481
$732$	−26.3431	−0.973671
$733$	46.0000	1.69905	0.849524	−	0.527549i	$-0.176889\pi$
$733$	46.0000	1.69905	0.849524	+	0.527549i	$0.176889\pi$
$734$	−28.2843	−1.04399
$735$	0	0
$736$	−2.82843	−0.104257
$737$	−15.3137	−0.564088
$738$	4.14214	0.152474
$739$	41.2548	1.51758	0.758792	−	0.651333i	$-0.225790\pi$
$739$	41.2548	1.51758	0.758792	+	0.651333i	$0.225790\pi$
$740$	3.17157	0.116589
$741$	16.0000	0.587775
$742$	0	0
$743$	−16.0000	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$744$	−16.0000	−0.586588
$745$	−1.51472	−0.0554950
$746$	3.65685	0.133887
$747$	11.7157	0.428656
$748$	7.65685	0.279962
$749$	0	0
$750$	−2.82843	−0.103280
$751$	39.5980	1.44495	0.722475	−	0.691397i	$-0.243004\pi$
$751$	39.5980	1.44495	0.722475	+	0.691397i	$0.243004\pi$
$752$	8.00000	0.291730
$753$	−32.0000	−1.16614
$754$	−6.34315	−0.231004
$755$	10.8284	0.394087
$756$	0	0
$757$	−25.1127	−0.912737	−0.456368	−	0.889791i	$-0.650850\pi$
$757$	−25.1127	−0.912737	−0.456368	+	0.889791i	$0.650850\pi$
$758$	4.00000	0.145287
$759$	−8.00000	−0.290382
$760$	2.82843	0.102598
$761$	7.45584	0.270274	0.135137	−	0.990827i	$-0.456853\pi$
$761$	7.45584	0.270274	0.135137	+	0.990827i	$0.456853\pi$
$762$	−54.6274	−1.97894
$763$	0	0
$764$	19.3137	0.698745
$765$	−38.2843	−1.38417
$766$	29.6569	1.07155
$767$	−16.0000	−0.577727
$768$	−2.82843	−0.102062
$769$	14.4853	0.522353	0.261176	−	0.965291i	$-0.415890\pi$
$769$	14.4853	0.522353	0.261176	+	0.965291i	$0.415890\pi$
$770$	0	0
$771$	65.5391	2.36033
$772$	21.3137	0.767097
$773$	10.6863	0.384359	0.192180	−	0.981360i	$-0.438444\pi$
$773$	10.6863	0.384359	0.192180	+	0.981360i	$0.438444\pi$
$774$	−48.2843	−1.73554
$775$	5.65685	0.203200
$776$	0.828427	0.0297388
$777$	0	0
$778$	30.9706	1.11035
$779$	2.34315	0.0839519
$780$	5.65685	0.202548
$781$	5.65685	0.202418
$782$	21.6569	0.774448
$783$	−17.9411	−0.641164
$784$	0	0
$785$	−15.6569	−0.558817
$786$	53.2548	1.89954
$787$	−30.6274	−1.09175	−0.545875	−	0.837867i	$-0.683803\pi$
$787$	−30.6274	−1.09175	−0.545875	+	0.837867i	$0.683803\pi$
$788$	−12.3431	−0.439706
$789$	41.3726	1.47290
$790$	−5.17157	−0.183996
$791$	0	0
$792$	−5.00000	−0.177667
$793$	−18.6274	−0.661479
$794$	22.9706	0.815195
$795$	29.6569	1.05182
$796$	11.3137	0.401004
$797$	−6.28427	−0.222600	−0.111300	−	0.993787i	$-0.535501\pi$
$797$	−6.28427	−0.222600	−0.111300	+	0.993787i	$0.535501\pi$
$798$	0	0
$799$	−61.2548	−2.16704
$800$	1.00000	0.0353553
$801$	58.2843	2.05937
$802$	10.0000	0.353112
$803$	7.65685	0.270205
$804$	−43.3137	−1.52756
$805$	0	0
$806$	−11.3137	−0.398508
$807$	5.65685	0.199131
$808$	−10.0000	−0.351799
$809$	22.2843	0.783473	0.391737	−	0.920077i	$-0.371874\pi$
$809$	22.2843	0.783473	0.391737	+	0.920077i	$0.371874\pi$
$810$	1.00000	0.0351364
$811$	−22.1421	−0.777516	−0.388758	−	0.921340i	$-0.627096\pi$
$811$	−22.1421	−0.777516	−0.388758	+	0.921340i	$0.627096\pi$
$812$	0	0
$813$	48.0000	1.68343
$814$	−3.17157	−0.111164
$815$	12.0000	0.420342
$816$	21.6569	0.758142
$817$	−27.3137	−0.955586
$818$	12.1421	0.424540
$819$	0	0
$820$	0.828427	0.0289299
$821$	−29.7990	−1.03999	−0.519996	−	0.854169i	$-0.674067\pi$
$821$	−29.7990	−1.03999	−0.519996	+	0.854169i	$0.674067\pi$
$822$	−15.0294	−0.524212
$823$	21.1716	0.737995	0.368997	−	0.929430i	$-0.379701\pi$
$823$	21.1716	0.737995	0.368997	+	0.929430i	$0.379701\pi$
$824$	5.65685	0.197066
$825$	2.82843	0.0984732
$826$	0	0
$827$	−49.2548	−1.71276	−0.856379	−	0.516347i	$-0.827291\pi$
$827$	−49.2548	−1.71276	−0.856379	+	0.516347i	$0.827291\pi$
$828$	−14.1421	−0.491473
$829$	−39.2548	−1.36338	−0.681688	−	0.731643i	$-0.738754\pi$
$829$	−39.2548	−1.36338	−0.681688	+	0.731643i	$0.738754\pi$
$830$	2.34315	0.0813318
$831$	37.6569	1.30630
$832$	−2.00000	−0.0693375
$833$	0	0
$834$	53.2548	1.84406
$835$	16.0000	0.553703
$836$	−2.82843	−0.0978232
$837$	−32.0000	−1.10608
$838$	30.6274	1.05801
$839$	34.3431	1.18566	0.592829	−	0.805329i	$-0.298011\pi$
$839$	34.3431	1.18566	0.592829	+	0.805329i	$0.298011\pi$
$840$	0	0
$841$	−18.9411	−0.653142
$842$	28.6274	0.986566
$843$	19.7157	0.679046
$844$	15.3137	0.527120
$845$	−9.00000	−0.309609
$846$	40.0000	1.37523
$847$	0	0
$848$	−10.4853	−0.360066
$849$	−64.0000	−2.19647
$850$	−7.65685	−0.262628
$851$	−8.97056	−0.307507
$852$	16.0000	0.548151
$853$	25.3137	0.866725	0.433362	−	0.901220i	$-0.357327\pi$
$853$	25.3137	0.866725	0.433362	+	0.901220i	$0.357327\pi$
$854$	0	0
$855$	14.1421	0.483651
$856$	−1.65685	−0.0566301
$857$	6.97056	0.238110	0.119055	−	0.992888i	$-0.462014\pi$
$857$	6.97056	0.238110	0.119055	+	0.992888i	$0.462014\pi$
$858$	−5.65685	−0.193122
$859$	−4.68629	−0.159894	−0.0799471	−	0.996799i	$-0.525475\pi$
$859$	−4.68629	−0.159894	−0.0799471	+	0.996799i	$0.525475\pi$
$860$	−9.65685	−0.329296
$861$	0	0
$862$	−19.7990	−0.674356
$863$	−36.7696	−1.25165	−0.625825	−	0.779963i	$-0.715238\pi$
$863$	−36.7696	−1.25165	−0.625825	+	0.779963i	$0.715238\pi$
$864$	−5.65685	−0.192450
$865$	1.31371	0.0446674
$866$	−20.8284	−0.707779
$867$	−117.740	−3.99866
$868$	0	0
$869$	5.17157	0.175434
$870$	−8.97056	−0.304131
$871$	−30.6274	−1.03777
$872$	14.4853	0.490534
$873$	4.14214	0.140190
$874$	−8.00000	−0.270604
$875$	0	0
$876$	21.6569	0.731717
$877$	−2.97056	−0.100309	−0.0501544	−	0.998741i	$-0.515971\pi$
$877$	−2.97056	−0.100309	−0.0501544	+	0.998741i	$0.515971\pi$
$878$	−24.9706	−0.842716
$879$	5.65685	0.190801
$880$	−1.00000	−0.0337100
$881$	2.68629	0.0905035	0.0452517	−	0.998976i	$-0.485591\pi$
$881$	2.68629	0.0905035	0.0452517	+	0.998976i	$0.485591\pi$
$882$	0	0
$883$	41.6569	1.40186	0.700932	−	0.713228i	$-0.252767\pi$
$883$	41.6569	1.40186	0.700932	+	0.713228i	$0.252767\pi$
$884$	15.3137	0.515056
$885$	−22.6274	−0.760612
$886$	−8.68629	−0.291822
$887$	22.6274	0.759754	0.379877	−	0.925037i	$-0.375966\pi$
$887$	22.6274	0.759754	0.379877	+	0.925037i	$0.375966\pi$
$888$	−8.97056	−0.301032
$889$	0	0
$890$	11.6569	0.390739
$891$	−1.00000	−0.0335013
$892$	28.2843	0.947027
$893$	22.6274	0.757198
$894$	4.28427	0.143287
$895$	6.34315	0.212028
$896$	0	0
$897$	−16.0000	−0.534224
$898$	−6.00000	−0.200223
$899$	17.9411	0.598370
$900$	5.00000	0.166667
$901$	80.2843	2.67466
$902$	−0.828427	−0.0275836
$903$	0	0
$904$	2.00000	0.0665190
$905$	14.0000	0.465376
$906$	−30.6274	−1.01753
$907$	17.6569	0.586286	0.293143	−	0.956069i	$-0.405299\pi$
$907$	17.6569	0.586286	0.293143	+	0.956069i	$0.405299\pi$
$908$	24.0000	0.796468
$909$	−50.0000	−1.65840
$910$	0	0
$911$	−21.6569	−0.717524	−0.358762	−	0.933429i	$-0.616801\pi$
$911$	−21.6569	−0.717524	−0.358762	+	0.933429i	$0.616801\pi$
$912$	−8.00000	−0.264906
$913$	−2.34315	−0.0775468
$914$	−22.0000	−0.727695
$915$	−26.3431	−0.870878
$916$	1.31371	0.0434062
$917$	0	0
$918$	43.3137	1.42957
$919$	20.7696	0.685124	0.342562	−	0.939495i	$-0.388705\pi$
$919$	20.7696	0.685124	0.342562	+	0.939495i	$0.388705\pi$
$920$	−2.82843	−0.0932505
$921$	−25.3726	−0.836055
$922$	11.6569	0.383898
$923$	11.3137	0.372395
$924$	0	0
$925$	3.17157	0.104281
$926$	−9.45584	−0.310738
$927$	28.2843	0.928977
$928$	3.17157	0.104112
$929$	38.9706	1.27858	0.639291	−	0.768965i	$-0.279228\pi$
$929$	38.9706	1.27858	0.639291	+	0.768965i	$0.279228\pi$
$930$	−16.0000	−0.524661
$931$	0	0
$932$	−6.00000	−0.196537
$933$	2.74517	0.0898727
$934$	−11.7990	−0.386075
$935$	7.65685	0.250406
$936$	−10.0000	−0.326860
$937$	−24.6274	−0.804543	−0.402271	−	0.915520i	$-0.631779\pi$
$937$	−24.6274	−0.804543	−0.402271	+	0.915520i	$0.631779\pi$
$938$	0	0
$939$	−24.9706	−0.814884
$940$	8.00000	0.260931
$941$	−13.3137	−0.434014	−0.217007	−	0.976170i	$-0.569630\pi$
$941$	−13.3137	−0.434014	−0.217007	+	0.976170i	$0.569630\pi$
$942$	44.2843	1.44286
$943$	−2.34315	−0.0763033
$944$	8.00000	0.260378
$945$	0	0
$946$	9.65685	0.313971
$947$	35.5980	1.15678	0.578389	−	0.815761i	$-0.303681\pi$
$947$	35.5980	1.15678	0.578389	+	0.815761i	$0.303681\pi$
$948$	14.6274	0.475076
$949$	15.3137	0.497104
$950$	2.82843	0.0917663
$951$	−8.97056	−0.290890
$952$	0	0
$953$	−43.2548	−1.40116	−0.700581	−	0.713573i	$-0.747076\pi$
$953$	−43.2548	−1.40116	−0.700581	+	0.713573i	$0.747076\pi$
$954$	−52.4264	−1.69737
$955$	19.3137	0.624977
$956$	−7.51472	−0.243043
$957$	8.97056	0.289977
$958$	−35.3137	−1.14093
$959$	0	0
$960$	−2.82843	−0.0912871
$961$	1.00000	0.0322581
$962$	−6.34315	−0.204511
$963$	−8.28427	−0.266957
$964$	8.82843	0.284344
$965$	21.3137	0.686113
$966$	0	0
$967$	59.3137	1.90740	0.953700	−	0.300759i	$-0.0972400\pi$
$967$	59.3137	1.90740	0.953700	+	0.300759i	$0.0972400\pi$
$968$	1.00000	0.0321412
$969$	61.2548	1.96779
$970$	0.828427	0.0265992
$971$	41.9411	1.34595	0.672977	−	0.739663i	$-0.265015\pi$
$971$	41.9411	1.34595	0.672977	+	0.739663i	$0.265015\pi$
$972$	14.1421	0.453609
$973$	0	0
$974$	−36.7696	−1.17817
$975$	5.65685	0.181164
$976$	9.31371	0.298125
$977$	−20.6274	−0.659930	−0.329965	−	0.943993i	$-0.607037\pi$
$977$	−20.6274	−0.659930	−0.329965	+	0.943993i	$0.607037\pi$
$978$	−33.9411	−1.08532
$979$	−11.6569	−0.372555
$980$	0	0
$981$	72.4264	2.31240
$982$	−8.68629	−0.277191
$983$	−39.5980	−1.26298	−0.631490	−	0.775384i	$-0.717556\pi$
$983$	−39.5980	−1.26298	−0.631490	+	0.775384i	$0.717556\pi$
$984$	−2.34315	−0.0746968
$985$	−12.3431	−0.393285
$986$	−24.2843	−0.773369
$987$	0	0
$988$	−5.65685	−0.179969
$989$	27.3137	0.868525
$990$	−5.00000	−0.158910
$991$	−40.0000	−1.27064	−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000	−1.27064	−0.635321	+	0.772248i	$0.719132\pi$
$992$	5.65685	0.179605
$993$	−81.9411	−2.60032
$994$	0	0
$995$	11.3137	0.358669
$996$	−6.62742	−0.209998
$997$	−42.0000	−1.33015	−0.665077	−	0.746775i	$-0.731601\pi$
$997$	−42.0000	−1.33015	−0.665077	+	0.746775i	$0.731601\pi$
$998$	28.9706	0.917047
$999$	−17.9411	−0.567632

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5390.2.a.bt.1.1		2
7.6	odd	2		770.2.a.i.1.2	✓	2
21.20	even	2		6930.2.a.br.1.1		2
28.27	even	2		6160.2.a.ba.1.1		2
35.13	even	4		3850.2.c.u.1849.2		4
35.27	even	4		3850.2.c.u.1849.3		4
35.34	odd	2		3850.2.a.bi.1.1		2
77.76	even	2		8470.2.a.bo.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.i.1.2	✓	2	7.6	odd	2
3850.2.a.bi.1.1		2	35.34	odd	2
3850.2.c.u.1849.2		4	35.13	even	4
3850.2.c.u.1849.3		4	35.27	even	4
5390.2.a.bt.1.1		2	1.1	even	1	trivial
6160.2.a.ba.1.1		2	28.27	even	2
6930.2.a.br.1.1		2	21.20	even	2
8470.2.a.bo.1.2		2	77.76	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:	\( N \)	\(=\)	\( 5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5390.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.82843 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.82843 q^{6} +1.00000 q^{8} +5.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.82843 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.82843 q^{6} +1.00000 q^{8} +5.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.82843 q^{12} -2.00000 q^{13} -2.82843 q^{15} +1.00000 q^{16} -7.65685 q^{17} +5.00000 q^{18} +2.82843 q^{19} +1.00000 q^{20} -1.00000 q^{22} -2.82843 q^{23} -2.82843 q^{24} +1.00000 q^{25} -2.00000 q^{26} -5.65685 q^{27} +3.17157 q^{29} -2.82843 q^{30} +5.65685 q^{31} +1.00000 q^{32} +2.82843 q^{33} -7.65685 q^{34} +5.00000 q^{36} +3.17157 q^{37} +2.82843 q^{38} +5.65685 q^{39} +1.00000 q^{40} +0.828427 q^{41} -9.65685 q^{43} -1.00000 q^{44} +5.00000 q^{45} -2.82843 q^{46} +8.00000 q^{47} -2.82843 q^{48} +1.00000 q^{50} +21.6569 q^{51} -2.00000 q^{52} -10.4853 q^{53} -5.65685 q^{54} -1.00000 q^{55} -8.00000 q^{57} +3.17157 q^{58} +8.00000 q^{59} -2.82843 q^{60} +9.31371 q^{61} +5.65685 q^{62} +1.00000 q^{64} -2.00000 q^{65} +2.82843 q^{66} +15.3137 q^{67} -7.65685 q^{68} +8.00000 q^{69} -5.65685 q^{71} +5.00000 q^{72} -7.65685 q^{73} +3.17157 q^{74} -2.82843 q^{75} +2.82843 q^{76} +5.65685 q^{78} -5.17157 q^{79} +1.00000 q^{80} +1.00000 q^{81} +0.828427 q^{82} +2.34315 q^{83} -7.65685 q^{85} -9.65685 q^{86} -8.97056 q^{87} -1.00000 q^{88} +11.6569 q^{89} +5.00000 q^{90} -2.82843 q^{92} -16.0000 q^{93} +8.00000 q^{94} +2.82843 q^{95} -2.82843 q^{96} +0.828427 q^{97} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{8} + 10 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^8 + 10 * q^9	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{8} + 10 q^{9} + 2 q^{10} - 2 q^{11} - 4 q^{13} + 2 q^{16} - 4 q^{17} + 10 q^{18} + 2 q^{20} - 2 q^{22} + 2 q^{25} - 4 q^{26} + 12 q^{29} + 2 q^{32} - 4 q^{34} + 10 q^{36} + 12 q^{37} + 2 q^{40} - 4 q^{41} - 8 q^{43} - 2 q^{44} + 10 q^{45} + 16 q^{47} + 2 q^{50} + 32 q^{51} - 4 q^{52} - 4 q^{53} - 2 q^{55} - 16 q^{57} + 12 q^{58} + 16 q^{59} - 4 q^{61} + 2 q^{64} - 4 q^{65} + 8 q^{67} - 4 q^{68} + 16 q^{69} + 10 q^{72} - 4 q^{73} + 12 q^{74} - 16 q^{79} + 2 q^{80} + 2 q^{81} - 4 q^{82} + 16 q^{83} - 4 q^{85} - 8 q^{86} + 16 q^{87} - 2 q^{88} + 12 q^{89} + 10 q^{90} - 32 q^{93} + 16 q^{94} - 4 q^{97} - 10 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^8 + 10 * q^9 + 2 * q^10 - 2 * q^11 - 4 * q^13 + 2 * q^16 - 4 * q^17 + 10 * q^18 + 2 * q^20 - 2 * q^22 + 2 * q^25 - 4 * q^26 + 12 * q^29 + 2 * q^32 - 4 * q^34 + 10 * q^36 + 12 * q^37 + 2 * q^40 - 4 * q^41 - 8 * q^43 - 2 * q^44 + 10 * q^45 + 16 * q^47 + 2 * q^50 + 32 * q^51 - 4 * q^52 - 4 * q^53 - 2 * q^55 - 16 * q^57 + 12 * q^58 + 16 * q^59 - 4 * q^61 + 2 * q^64 - 4 * q^65 + 8 * q^67 - 4 * q^68 + 16 * q^69 + 10 * q^72 - 4 * q^73 + 12 * q^74 - 16 * q^79 + 2 * q^80 + 2 * q^81 - 4 * q^82 + 16 * q^83 - 4 * q^85 - 8 * q^86 + 16 * q^87 - 2 * q^88 + 12 * q^89 + 10 * q^90 - 32 * q^93 + 16 * q^94 - 4 * q^97 - 10 * q^99

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