LMFDB - Embedded newform 8281.2.a.cu.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8281,2,Mod(1,8281)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8281, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8281.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8281 = 7^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8281.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:	$66.1241179138$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 1183)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.94710 q^{2} -1.73455 q^{3} +1.79121 q^{4} +3.71933 q^{5} +3.37734 q^{6} +0.406541 q^{8} +0.00865975 q^{9} +O(q^{10})$	\(q-1.94710 q^{2} -1.73455 q^{3} +1.79121 q^{4} +3.71933 q^{5} +3.37734 q^{6} +0.406541 q^{8} +0.00865975 q^{9} -7.24191 q^{10} -3.56402 q^{11} -3.10694 q^{12} -6.45135 q^{15} -4.37399 q^{16} +1.69473 q^{17} -0.0168614 q^{18} +5.49624 q^{19} +6.66208 q^{20} +6.93951 q^{22} +6.19919 q^{23} -0.705165 q^{24} +8.83339 q^{25} +5.18863 q^{27} -1.39237 q^{29} +12.5614 q^{30} -7.04774 q^{31} +7.70353 q^{32} +6.18196 q^{33} -3.29981 q^{34} +0.0155114 q^{36} +1.81477 q^{37} -10.7017 q^{38} +1.51206 q^{40} -0.877683 q^{41} +11.5399 q^{43} -6.38389 q^{44} +0.0322084 q^{45} -12.0705 q^{46} +2.72895 q^{47} +7.58690 q^{48} -17.1995 q^{50} -2.93959 q^{51} +4.04770 q^{53} -10.1028 q^{54} -13.2557 q^{55} -9.53350 q^{57} +2.71109 q^{58} -3.21359 q^{59} -11.5557 q^{60} -14.4840 q^{61} +13.7227 q^{62} -6.25157 q^{64} -12.0369 q^{66} +8.33306 q^{67} +3.03561 q^{68} -10.7528 q^{69} -2.11396 q^{71} +0.00352054 q^{72} -3.06402 q^{73} -3.53354 q^{74} -15.3219 q^{75} +9.84490 q^{76} -1.68683 q^{79} -16.2683 q^{80} -9.02590 q^{81} +1.70894 q^{82} -1.44516 q^{83} +6.30324 q^{85} -22.4693 q^{86} +2.41514 q^{87} -1.44892 q^{88} +4.46715 q^{89} -0.0627131 q^{90} +11.1040 q^{92} +12.2246 q^{93} -5.31354 q^{94} +20.4423 q^{95} -13.3621 q^{96} +12.8868 q^{97} -0.0308635 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} + 23 q^{4} + 13 q^{5} + 14 q^{6} + 26 q^{9}+O(q^{10}) $ 24 * q - q^2 + 23 * q^4 + 13 * q^5 + 14 * q^6 + 26 * q^9	$ 24 q - q^{2} + 23 q^{4} + 13 q^{5} + 14 q^{6} + 26 q^{9} + 5 q^{10} - q^{11} + 5 q^{12} + 5 q^{15} + 17 q^{16} - 5 q^{17} + 24 q^{19} + 34 q^{20} - 14 q^{22} + 11 q^{23} + 32 q^{24} + 33 q^{25} - 21 q^{27} + 4 q^{29} - 22 q^{30} + 40 q^{31} - 6 q^{32} + 24 q^{33} + 36 q^{34} - 15 q^{36} - 4 q^{37} - 29 q^{38} - 4 q^{40} + 49 q^{41} + 13 q^{43} + 10 q^{44} + 58 q^{45} - 10 q^{46} + 62 q^{47} + 89 q^{48} - 23 q^{50} - 21 q^{51} - 18 q^{53} + 12 q^{54} - 14 q^{55} - 13 q^{57} + 56 q^{58} + 79 q^{59} + 22 q^{60} + 13 q^{61} + 12 q^{62} + 18 q^{64} - 38 q^{66} - 2 q^{67} - 12 q^{68} - 28 q^{69} - 19 q^{71} + 81 q^{72} + 17 q^{73} + 17 q^{74} + 24 q^{75} + 58 q^{76} - 9 q^{79} + 63 q^{80} + 16 q^{81} - 22 q^{82} + 81 q^{83} - 34 q^{85} + 22 q^{86} + 70 q^{87} - 33 q^{88} + 72 q^{89} + q^{90} - 4 q^{92} + 19 q^{93} - 30 q^{94} + 13 q^{95} + 11 q^{96} + 45 q^{97} - 39 q^{99}+O(q^{100}) $ 24 * q - q^2 + 23 * q^4 + 13 * q^5 + 14 * q^6 + 26 * q^9 + 5 * q^10 - q^11 + 5 * q^12 + 5 * q^15 + 17 * q^16 - 5 * q^17 + 24 * q^19 + 34 * q^20 - 14 * q^22 + 11 * q^23 + 32 * q^24 + 33 * q^25 - 21 * q^27 + 4 * q^29 - 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 + 36 * q^34 - 15 * q^36 - 4 * q^37 - 29 * q^38 - 4 * q^40 + 49 * q^41 + 13 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 89 * q^48 - 23 * q^50 - 21 * q^51 - 18 * q^53 + 12 * q^54 - 14 * q^55 - 13 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 + 13 * q^61 + 12 * q^62 + 18 * q^64 - 38 * q^66 - 2 * q^67 - 12 * q^68 - 28 * q^69 - 19 * q^71 + 81 * q^72 + 17 * q^73 + 17 * q^74 + 24 * q^75 + 58 * q^76 - 9 * q^79 + 63 * q^80 + 16 * q^81 - 22 * q^82 + 81 * q^83 - 34 * q^85 + 22 * q^86 + 70 * q^87 - 33 * q^88 + 72 * q^89 + q^90 - 4 * q^92 + 19 * q^93 - 30 * q^94 + 13 * q^95 + 11 * q^96 + 45 * q^97 - 39 * 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 $

$2$	−1.94710	−1.37681	−0.688405	−	0.725327i	$-0.741689\pi$
$2$	−1.94710	−1.37681	−0.688405	+	0.725327i	$0.741689\pi$
$3$	−1.73455	−1.00144	−0.500721	−	0.865609i	$-0.666932\pi$
$3$	−1.73455	−1.00144	−0.500721	+	0.865609i	$0.666932\pi$
$4$	1.79121	0.895604
$5$	3.71933	1.66333	0.831667	−	0.555275i	$-0.187387\pi$
$5$	3.71933	1.66333	0.831667	+	0.555275i	$0.187387\pi$
$6$	3.37734	1.37879
$7$	0	0
$7$	0	0
$8$	0.406541	0.143734
$9$	0.00865975	0.00288658
$10$	−7.24191	−2.29009
$11$	−3.56402	−1.07459	−0.537296	−	0.843394i	$-0.680554\pi$
$11$	−3.56402	−1.07459	−0.537296	+	0.843394i	$0.680554\pi$
$12$	−3.10694	−0.896895
$13$	0	0
$13$	0	0
$14$	0	0
$15$	−6.45135	−1.66573
$16$	−4.37399	−1.09350
$17$	1.69473	0.411032	0.205516	−	0.978654i	$-0.434113\pi$
$17$	1.69473	0.411032	0.205516	+	0.978654i	$0.434113\pi$
$18$	−0.0168614	−0.00397427
$19$	5.49624	1.26092	0.630462	−	0.776220i	$-0.282865\pi$
$19$	5.49624	1.26092	0.630462	+	0.776220i	$0.282865\pi$
$20$	6.66208	1.48969
$21$	0	0
$22$	6.93951	1.47951
$23$	6.19919	1.29262	0.646310	−	0.763075i	$-0.276311\pi$
$23$	6.19919	1.29262	0.646310	+	0.763075i	$0.276311\pi$
$24$	−0.705165	−0.143941
$25$	8.83339	1.76668
$26$	0	0
$27$	5.18863	0.998552
$28$	0	0
$29$	−1.39237	−0.258557	−0.129279	−	0.991608i	$-0.541266\pi$
$29$	−1.39237	−0.258557	−0.129279	+	0.991608i	$0.541266\pi$
$30$	12.5614	2.29340
$31$	−7.04774	−1.26581	−0.632905	−	0.774229i	$-0.718138\pi$
$31$	−7.04774	−1.26581	−0.632905	+	0.774229i	$0.718138\pi$
$32$	7.70353	1.36180
$33$	6.18196	1.07614
$34$	−3.29981	−0.565912
$35$	0	0
$36$	0.0155114	0.00258523
$37$	1.81477	0.298346	0.149173	−	0.988811i	$-0.452339\pi$
$37$	1.81477	0.298346	0.149173	+	0.988811i	$0.452339\pi$
$38$	−10.7017	−1.73605
$39$	0	0
$40$	1.51206	0.239077
$41$	−0.877683	−0.137071	−0.0685355	−	0.997649i	$-0.521833\pi$
$41$	−0.877683	−0.137071	−0.0685355	+	0.997649i	$0.521833\pi$
$42$	0	0
$43$	11.5399	1.75981	0.879906	−	0.475148i	$-0.157606\pi$
$43$	11.5399	1.75981	0.879906	+	0.475148i	$0.157606\pi$
$44$	−6.38389	−0.962408
$45$	0.0322084	0.00480135
$46$	−12.0705	−1.77969
$47$	2.72895	0.398058	0.199029	−	0.979994i	$-0.436221\pi$
$47$	2.72895	0.398058	0.199029	+	0.979994i	$0.436221\pi$
$48$	7.58690	1.09507
$49$	0	0
$50$	−17.1995	−2.43238
$51$	−2.93959	−0.411625
$52$	0	0
$53$	4.04770	0.555995	0.277997	−	0.960582i	$-0.410329\pi$
$53$	4.04770	0.555995	0.277997	+	0.960582i	$0.410329\pi$
$54$	−10.1028	−1.37481
$55$	−13.2557	−1.78740
$56$	0	0
$57$	−9.53350	−1.26274
$58$	2.71109	0.355984
$59$	−3.21359	−0.418374	−0.209187	−	0.977876i	$-0.567082\pi$
$59$	−3.21359	−0.418374	−0.209187	+	0.977876i	$0.567082\pi$
$60$	−11.5557	−1.49184
$61$	−14.4840	−1.85449	−0.927243	−	0.374460i	$-0.877828\pi$
$61$	−14.4840	−1.85449	−0.927243	+	0.374460i	$0.877828\pi$
$62$	13.7227	1.74278
$63$	0	0
$64$	−6.25157	−0.781446
$65$	0	0
$66$	−12.0369	−1.48164
$67$	8.33306	1.01805	0.509023	−	0.860753i	$-0.330007\pi$
$67$	8.33306	1.01805	0.509023	+	0.860753i	$0.330007\pi$
$68$	3.03561	0.368121
$69$	−10.7528	−1.29448
$70$	0	0
$71$	−2.11396	−0.250881	−0.125441	−	0.992101i	$-0.540034\pi$
$71$	−2.11396	−0.250881	−0.125441	+	0.992101i	$0.540034\pi$
$72$	0.00352054	0.000414900 0
$73$	−3.06402	−0.358617	−0.179308	−	0.983793i	$-0.557386\pi$
$73$	−3.06402	−0.358617	−0.179308	+	0.983793i	$0.557386\pi$
$74$	−3.53354	−0.410766
$75$	−15.3219	−1.76923
$76$	9.84490	1.12929
$77$	0	0
$78$	0	0
$79$	−1.68683	−0.189783	−0.0948915	−	0.995488i	$-0.530250\pi$
$79$	−1.68683	−0.189783	−0.0948915	+	0.995488i	$0.530250\pi$
$80$	−16.2683	−1.81885
$81$	−9.02590	−1.00288
$82$	1.70894	0.188721
$83$	−1.44516	−0.158627	−0.0793135	−	0.996850i	$-0.525273\pi$
$83$	−1.44516	−0.158627	−0.0793135	+	0.996850i	$0.525273\pi$
$84$	0	0
$85$	6.30324	0.683683
$86$	−22.4693	−2.42292
$87$	2.41514	0.258930
$88$	−1.44892	−0.154455
$89$	4.46715	0.473517	0.236759	−	0.971568i	$-0.423915\pi$
$89$	4.46715	0.473517	0.236759	+	0.971568i	$0.423915\pi$
$90$	−0.0627131	−0.00661054
$91$	0	0
$92$	11.1040	1.15768
$93$	12.2246	1.26764
$94$	−5.31354	−0.548050
$95$	20.4423	2.09734
$96$	−13.3621	−1.36377
$97$	12.8868	1.30845	0.654226	−	0.756299i	$-0.272995\pi$
$97$	12.8868	1.30845	0.654226	+	0.756299i	$0.272995\pi$
$98$	0	0
$99$	−0.0308635	−0.00310190
$100$	15.8224	1.58224
$101$	0.473153	0.0470804	0.0235402	−	0.999723i	$-0.492506\pi$
$101$	0.473153	0.0470804	0.0235402	+	0.999723i	$0.492506\pi$
$102$	5.72368	0.566728
$103$	−0.211769	−0.0208662	−0.0104331	−	0.999946i	$-0.503321\pi$
$103$	−0.211769	−0.0208662	−0.0104331	+	0.999946i	$0.503321\pi$
$104$	0	0
$105$	0	0
$106$	−7.88129	−0.765499
$107$	4.63166	0.447759	0.223880	−	0.974617i	$-0.428128\pi$
$107$	4.63166	0.447759	0.223880	+	0.974617i	$0.428128\pi$
$108$	9.29390	0.894306
$109$	10.8624	1.04043	0.520215	−	0.854035i	$-0.325852\pi$
$109$	10.8624	1.04043	0.520215	+	0.854035i	$0.325852\pi$
$110$	25.8103	2.46091
$111$	−3.14781	−0.298777
$112$	0	0
$113$	−17.3707	−1.63410	−0.817051	−	0.576565i	$-0.804393\pi$
$113$	−17.3707	−1.63410	−0.817051	+	0.576565i	$0.804393\pi$
$114$	18.5627	1.73856
$115$	23.0568	2.15006
$116$	−2.49403	−0.231565
$117$	0	0
$118$	6.25719	0.576021
$119$	0	0
$120$	−2.62274	−0.239422
$121$	1.70222	0.154747
$122$	28.2018	2.55327
$123$	1.52238	0.137269
$124$	−12.6240	−1.13366
$125$	14.2576	1.27524
$126$	0	0
$127$	−17.3981	−1.54383	−0.771916	−	0.635725i	$-0.780701\pi$
$127$	−17.3981	−1.54383	−0.771916	+	0.635725i	$0.780701\pi$
$128$	−3.23461	−0.285901
$129$	−20.0164	−1.76235
$130$	0	0
$131$	12.5064	1.09269	0.546343	−	0.837562i	$-0.316020\pi$
$131$	12.5064	1.09269	0.546343	+	0.837562i	$0.316020\pi$
$132$	11.0732	0.963796
$133$	0	0
$134$	−16.2253	−1.40165
$135$	19.2982	1.66092
$136$	0.688976	0.0590792
$137$	7.36806	0.629496	0.314748	−	0.949175i	$-0.398080\pi$
$137$	7.36806	0.629496	0.314748	+	0.949175i	$0.398080\pi$
$138$	20.9368	1.78226
$139$	15.8286	1.34256	0.671281	−	0.741203i	$-0.265744\pi$
$139$	15.8286	1.34256	0.671281	+	0.741203i	$0.265744\pi$
$140$	0	0
$141$	−4.73349	−0.398632
$142$	4.11610	0.345415
$143$	0	0
$144$	−0.0378777	−0.00315647
$145$	−5.17869	−0.430067
$146$	5.96597	0.493747
$147$	0	0
$148$	3.25063	0.267200
$149$	−21.2772	−1.74310	−0.871549	−	0.490308i	$-0.836884\pi$
$149$	−21.2772	−1.74310	−0.871549	+	0.490308i	$0.836884\pi$
$150$	29.8334	2.43589
$151$	12.6878	1.03252	0.516259	−	0.856432i	$-0.327324\pi$
$151$	12.6878	1.03252	0.516259	+	0.856432i	$0.327324\pi$
$152$	2.23445	0.181238
$153$	0.0146759	0.00118648
$154$	0	0
$155$	−26.2128	−2.10547
$156$	0	0
$157$	16.3251	1.30289	0.651443	−	0.758697i	$-0.274164\pi$
$157$	16.3251	1.30289	0.651443	+	0.758697i	$0.274164\pi$
$158$	3.28443	0.261295
$159$	−7.02094	−0.556797
$160$	28.6519	2.26513
$161$	0	0
$162$	17.5744	1.38077
$163$	2.24523	0.175860	0.0879299	−	0.996127i	$-0.471975\pi$
$163$	2.24523	0.175860	0.0879299	+	0.996127i	$0.471975\pi$
$164$	−1.57211	−0.122761
$165$	22.9927	1.78998
$166$	2.81388	0.218399
$167$	2.18075	0.168751	0.0843757	−	0.996434i	$-0.473110\pi$
$167$	2.18075	0.168751	0.0843757	+	0.996434i	$0.473110\pi$
$168$	0	0
$169$	0	0
$170$	−12.2731	−0.941301
$171$	0.0475961	0.00363976
$172$	20.6703	1.57609
$173$	−9.75571	−0.741713	−0.370857	−	0.928690i	$-0.620936\pi$
$173$	−9.75571	−0.741713	−0.370857	+	0.928690i	$0.620936\pi$
$174$	−4.70252	−0.356497
$175$	0	0
$176$	15.5890	1.17506
$177$	5.57413	0.418977
$178$	−8.69801	−0.651943
$179$	19.8446	1.48325	0.741627	−	0.670813i	$-0.234055\pi$
$179$	19.8446	1.48325	0.741627	+	0.670813i	$0.234055\pi$
$180$	0.0576920	0.00430011
$181$	−14.4120	−1.07124	−0.535618	−	0.844460i	$-0.679921\pi$
$181$	−14.4120	−1.07124	−0.535618	+	0.844460i	$0.679921\pi$
$182$	0	0
$183$	25.1232	1.85716
$184$	2.52023	0.185793
$185$	6.74972	0.496249
$186$	−23.8026	−1.74529
$187$	−6.04004	−0.441691
$188$	4.88811	0.356502
$189$	0	0
$190$	−39.8033	−2.88763
$191$	−11.5992	−0.839287	−0.419643	−	0.907689i	$-0.637845\pi$
$191$	−11.5992	−0.839287	−0.419643	+	0.907689i	$0.637845\pi$
$192$	10.8437	0.782573
$193$	−8.43654	−0.607275	−0.303638	−	0.952788i	$-0.598201\pi$
$193$	−8.43654	−0.607275	−0.303638	+	0.952788i	$0.598201\pi$
$194$	−25.0918	−1.80149
$195$	0	0
$196$	0	0
$197$	18.3858	1.30994	0.654969	−	0.755656i	$-0.272682\pi$
$197$	18.3858	1.30994	0.654969	+	0.755656i	$0.272682\pi$
$198$	0.0600944	0.00427072
$199$	−1.23412	−0.0874847	−0.0437424	−	0.999043i	$-0.513928\pi$
$199$	−1.23412	−0.0874847	−0.0437424	+	0.999043i	$0.513928\pi$
$200$	3.59113	0.253932
$201$	−14.4541	−1.01951
$202$	−0.921276	−0.0648208
$203$	0	0
$204$	−5.26541	−0.368652
$205$	−3.26439	−0.227995
$206$	0.412336	0.0287288
$207$	0.0536834	0.00373126
$208$	0	0
$209$	−19.5887	−1.35498
$210$	0	0
$211$	17.7041	1.21880	0.609401	−	0.792862i	$-0.291410\pi$
$211$	17.7041	1.21880	0.609401	+	0.792862i	$0.291410\pi$
$212$	7.25027	0.497951
$213$	3.66677	0.251243
$214$	−9.01831	−0.616479
$215$	42.9205	2.92715
$216$	2.10939	0.143526
$217$	0	0
$218$	−21.1502	−1.43247
$219$	5.31470	0.359134
$220$	−23.7438	−1.60081
$221$	0	0
$222$	6.12910	0.411358
$223$	−14.3068	−0.958055	−0.479028	−	0.877800i	$-0.659011\pi$
$223$	−14.3068	−0.958055	−0.479028	+	0.877800i	$0.659011\pi$
$224$	0	0
$225$	0.0764949	0.00509966
$226$	33.8226	2.24985
$227$	15.7476	1.04520	0.522602	−	0.852577i	$-0.324961\pi$
$227$	15.7476	1.04520	0.522602	+	0.852577i	$0.324961\pi$
$228$	−17.0765	−1.13092
$229$	0.349161	0.0230732	0.0115366	−	0.999933i	$-0.496328\pi$
$229$	0.349161	0.0230732	0.0115366	+	0.999933i	$0.496328\pi$
$230$	−44.8940	−2.96022
$231$	0	0
$232$	−0.566057	−0.0371634
$233$	−15.6502	−1.02528	−0.512639	−	0.858604i	$-0.671332\pi$
$233$	−15.6502	−1.02528	−0.512639	+	0.858604i	$0.671332\pi$
$234$	0	0
$235$	10.1498	0.662103
$236$	−5.75620	−0.374697
$237$	2.92589	0.190057
$238$	0	0
$239$	3.71354	0.240209	0.120104	−	0.992761i	$-0.461677\pi$
$239$	3.71354	0.240209	0.120104	+	0.992761i	$0.461677\pi$
$240$	28.2182	1.82147
$241$	22.1505	1.42684	0.713420	−	0.700737i	$-0.247145\pi$
$241$	22.1505	1.42684	0.713420	+	0.700737i	$0.247145\pi$
$242$	−3.31439	−0.213057
$243$	0.0899945	0.00577315
$244$	−25.9438	−1.66088
$245$	0	0
$246$	−2.96424	−0.188993
$247$	0	0
$248$	−2.86519	−0.181940
$249$	2.50670	0.158856
$250$	−27.7610	−1.75576
$251$	6.17932	0.390035	0.195018	−	0.980800i	$-0.437524\pi$
$251$	6.17932	0.390035	0.195018	+	0.980800i	$0.437524\pi$
$252$	0	0
$253$	−22.0940	−1.38904
$254$	33.8759	2.12556
$255$	−10.9333	−0.684669
$256$	18.8012	1.17508
$257$	0.0226628	0.00141367	0.000706833	−	1.00000i	$-0.499775\pi$
$257$	0.0226628	0.00141367	0.000706833		1.00000i	$0.499775\pi$
$258$	38.9741	2.42642
$259$	0	0
$260$	0	0
$261$	−0.0120576	−0.000746347 0
$262$	−24.3512	−1.50442
$263$	−7.03576	−0.433843	−0.216922	−	0.976189i	$-0.569602\pi$
$263$	−7.03576	−0.433843	−0.216922	+	0.976189i	$0.569602\pi$
$264$	2.51322	0.154678
$265$	15.0547	0.924804
$266$	0	0
$267$	−7.74850	−0.474200
$268$	14.9262	0.911765
$269$	10.4776	0.638833	0.319416	−	0.947614i	$-0.396513\pi$
$269$	10.4776	0.638833	0.319416	+	0.947614i	$0.396513\pi$
$270$	−37.5756	−2.28678
$271$	−4.23151	−0.257046	−0.128523	−	0.991707i	$-0.541024\pi$
$271$	−4.23151	−0.257046	−0.128523	+	0.991707i	$0.541024\pi$
$272$	−7.41272	−0.449462
$273$	0	0
$274$	−14.3464	−0.866695
$275$	−31.4823	−1.89846
$276$	−19.2605	−1.15935
$277$	−28.3546	−1.70366	−0.851830	−	0.523818i	$-0.824507\pi$
$277$	−28.3546	−1.70366	−0.851830	+	0.523818i	$0.824507\pi$
$278$	−30.8199	−1.84845
$279$	−0.0610316	−0.00365387
$280$	0	0
$281$	17.3688	1.03614	0.518068	−	0.855340i	$-0.326652\pi$
$281$	17.3688	1.03614	0.518068	+	0.855340i	$0.326652\pi$
$282$	9.21660	0.548840
$283$	6.41971	0.381612	0.190806	−	0.981628i	$-0.438890\pi$
$283$	6.41971	0.381612	0.190806	+	0.981628i	$0.438890\pi$
$284$	−3.78654	−0.224690
$285$	−35.4582	−2.10036
$286$	0	0
$287$	0	0
$288$	0.0667106	0.00393096
$289$	−14.1279	−0.831053
$290$	10.0834	0.592120
$291$	−22.3527	−1.31034
$292$	−5.48830	−0.321178
$293$	4.96836	0.290255	0.145127	−	0.989413i	$-0.453641\pi$
$293$	4.96836	0.290255	0.145127	+	0.989413i	$0.453641\pi$
$294$	0	0
$295$	−11.9524	−0.695895
$296$	0.737778	0.0428825
$297$	−18.4924	−1.07304
$298$	41.4289	2.39991
$299$	0	0
$300$	−27.4448	−1.58452
$301$	0	0
$302$	−24.7044	−1.42158
$303$	−0.820706	−0.0471483
$304$	−24.0405	−1.37882
$305$	−53.8707	−3.08463
$306$	−0.0285755	−0.00163355
$307$	−10.0306	−0.572478	−0.286239	−	0.958158i	$-0.592405\pi$
$307$	−10.0306	−0.572478	−0.286239	+	0.958158i	$0.592405\pi$
$308$	0	0
$309$	0.367323	0.0208963
$310$	51.0391	2.89882
$311$	−18.3165	−1.03863	−0.519316	−	0.854582i	$-0.673813\pi$
$311$	−18.3165	−1.03863	−0.519316	+	0.854582i	$0.673813\pi$
$312$	0	0
$313$	−14.4659	−0.817662	−0.408831	−	0.912610i	$-0.634063\pi$
$313$	−14.4659	−0.817662	−0.408831	+	0.912610i	$0.634063\pi$
$314$	−31.7867	−1.79383
$315$	0	0
$316$	−3.02146	−0.169970
$317$	−5.20218	−0.292183	−0.146092	−	0.989271i	$-0.546669\pi$
$317$	−5.20218	−0.292183	−0.146092	+	0.989271i	$0.546669\pi$
$318$	13.6705	0.766603
$319$	4.96244	0.277843
$320$	−23.2516	−1.29981
$321$	−8.03383	−0.448405
$322$	0	0
$323$	9.31463	0.518280
$324$	−16.1673	−0.898181
$325$	0	0
$326$	−4.37169	−0.242125
$327$	−18.8414	−1.04193
$328$	−0.356814	−0.0197018
$329$	0	0
$330$	−44.7692	−2.46446
$331$	−15.5814	−0.856429	−0.428215	−	0.903677i	$-0.640857\pi$
$331$	−15.5814	−0.856429	−0.428215	+	0.903677i	$0.640857\pi$
$332$	−2.58858	−0.142067
$333$	0.0157154	0.000861201 0
$334$	−4.24614	−0.232338
$335$	30.9934	1.69335
$336$	0	0
$337$	0.259486	0.0141351	0.00706756	−	0.999975i	$-0.497750\pi$
$337$	0.259486	0.0141351	0.00706756	+	0.999975i	$0.497750\pi$
$338$	0	0
$339$	30.1304	1.63646
$340$	11.2904	0.612309
$341$	25.1183	1.36023
$342$	−0.0926744	−0.00501126
$343$	0	0
$344$	4.69143	0.252945
$345$	−39.9932	−2.15316
$346$	18.9954	1.02120
$347$	−34.6344	−1.85927	−0.929636	−	0.368478i	$-0.879879\pi$
$347$	−34.6344	−1.85927	−0.929636	+	0.368478i	$0.879879\pi$
$348$	4.32601	0.231899
$349$	−19.6011	−1.04922	−0.524611	−	0.851342i	$-0.675789\pi$
$349$	−19.6011	−1.04922	−0.524611	+	0.851342i	$0.675789\pi$
$350$	0	0
$351$	0	0
$352$	−27.4555	−1.46338
$353$	−11.9849	−0.637891	−0.318945	−	0.947773i	$-0.603329\pi$
$353$	−11.9849	−0.637891	−0.318945	+	0.947773i	$0.603329\pi$
$354$	−10.8534	−0.576852
$355$	−7.86251	−0.417299
$356$	8.00160	0.424084
$357$	0	0
$358$	−38.6394	−2.04216
$359$	17.2052	0.908057	0.454029	−	0.890987i	$-0.349986\pi$
$359$	17.2052	0.908057	0.454029	+	0.890987i	$0.349986\pi$
$360$	0.0130940	0.000690117 0
$361$	11.2087	0.589929
$362$	28.0616	1.47489
$363$	−2.95258	−0.154970
$364$	0	0
$365$	−11.3961	−0.596499
$366$	−48.9175	−2.55696
$367$	0.702048	0.0366466	0.0183233	−	0.999832i	$-0.494167\pi$
$367$	0.702048	0.0366466	0.0183233	+	0.999832i	$0.494167\pi$
$368$	−27.1152	−1.41348
$369$	−0.00760051	−0.000395667 0
$370$	−13.1424	−0.683240
$371$	0	0
$372$	21.8969	1.13530
$373$	10.8819	0.563443	0.281722	−	0.959496i	$-0.409095\pi$
$373$	10.8819	0.563443	0.281722	+	0.959496i	$0.409095\pi$
$374$	11.7606	0.608125
$375$	−24.7305	−1.27708
$376$	1.10943	0.0572145
$377$	0	0
$378$	0	0
$379$	2.13763	0.109803	0.0549014	−	0.998492i	$-0.482516\pi$
$379$	2.13763	0.109803	0.0549014	+	0.998492i	$0.482516\pi$
$380$	36.6164	1.87838
$381$	30.1779	1.54606
$382$	22.5848	1.15554
$383$	30.0085	1.53336	0.766681	−	0.642028i	$-0.221907\pi$
$383$	30.0085	1.53336	0.766681	+	0.642028i	$0.221907\pi$
$384$	5.61058	0.286314
$385$	0	0
$386$	16.4268	0.836102
$387$	0.0999323	0.00507984
$388$	23.0828	1.17185
$389$	−5.78040	−0.293078	−0.146539	−	0.989205i	$-0.546813\pi$
$389$	−5.78040	−0.293078	−0.146539	+	0.989205i	$0.546813\pi$
$390$	0	0
$391$	10.5059	0.531308
$392$	0	0
$393$	−21.6929	−1.09426
$394$	−35.7991	−1.80353
$395$	−6.27387	−0.315672
$396$	−0.0552829	−0.00277807
$397$	10.2576	0.514817	0.257408	−	0.966303i	$-0.417131\pi$
$397$	10.2576	0.514817	0.257408	+	0.966303i	$0.417131\pi$
$398$	2.40296	0.120450
$399$	0	0
$400$	−38.6372	−1.93186
$401$	22.6917	1.13317	0.566584	−	0.824004i	$-0.308265\pi$
$401$	22.6917	1.13317	0.566584	+	0.824004i	$0.308265\pi$
$402$	28.1436	1.40368
$403$	0	0
$404$	0.847514	0.0421654
$405$	−33.5703	−1.66812
$406$	0	0
$407$	−6.46787	−0.320600
$408$	−1.19506	−0.0591644
$409$	6.06529	0.299909	0.149955	−	0.988693i	$-0.452087\pi$
$409$	6.06529	0.299909	0.149955	+	0.988693i	$0.452087\pi$
$410$	6.35610	0.313905
$411$	−12.7803	−0.630404
$412$	−0.379322	−0.0186879
$413$	0	0
$414$	−0.104527	−0.00513723
$415$	−5.37502	−0.263850
$416$	0	0
$417$	−27.4554	−1.34450
$418$	38.1412	1.86555
$419$	5.55842	0.271547	0.135773	−	0.990740i	$-0.456648\pi$
$419$	5.55842	0.271547	0.135773	+	0.990740i	$0.456648\pi$
$420$	0	0
$421$	1.55303	0.0756901	0.0378450	−	0.999284i	$-0.487951\pi$
$421$	1.55303	0.0756901	0.0378450	+	0.999284i	$0.487951\pi$
$422$	−34.4717	−1.67806
$423$	0.0236320	0.00114903
$424$	1.64556	0.0799153
$425$	14.9702	0.726160
$426$	−7.13958	−0.345914
$427$	0	0
$428$	8.29625	0.401015
$429$	0	0
$430$	−83.5706	−4.03013
$431$	−16.6594	−0.802455	−0.401228	−	0.915978i	$-0.631416\pi$
$431$	−16.6594	−0.802455	−0.401228	+	0.915978i	$0.631416\pi$
$432$	−22.6950	−1.09191
$433$	−31.9913	−1.53740	−0.768702	−	0.639607i	$-0.779097\pi$
$433$	−31.9913	−1.53740	−0.768702	+	0.639607i	$0.779097\pi$
$434$	0	0
$435$	8.98269	0.430687
$436$	19.4568	0.931813
$437$	34.0722	1.62990
$438$	−10.3483	−0.494459
$439$	28.8063	1.37485	0.687424	−	0.726257i	$-0.258742\pi$
$439$	28.8063	1.37485	0.687424	+	0.726257i	$0.258742\pi$
$440$	−5.38900	−0.256911
$441$	0	0
$442$	0	0
$443$	−37.6089	−1.78685	−0.893426	−	0.449210i	$-0.851705\pi$
$443$	−37.6089	−1.78685	−0.893426	+	0.449210i	$0.851705\pi$
$444$	−5.63837	−0.267585
$445$	16.6148	0.787617
$446$	27.8568	1.31906
$447$	36.9064	1.74561
$448$	0	0
$449$	−4.01209	−0.189342	−0.0946711	−	0.995509i	$-0.530180\pi$
$449$	−4.01209	−0.189342	−0.0946711	+	0.995509i	$0.530180\pi$
$450$	−0.148943	−0.00702126
$451$	3.12808	0.147295
$452$	−31.1146	−1.46351
$453$	−22.0076	−1.03401
$454$	−30.6622	−1.43905
$455$	0	0
$456$	−3.87576	−0.181499
$457$	22.8634	1.06950	0.534752	−	0.845009i	$-0.320405\pi$
$457$	22.8634	1.06950	0.534752	+	0.845009i	$0.320405\pi$
$458$	−0.679851	−0.0317674
$459$	8.79331	0.410436
$460$	41.2995	1.92560
$461$	−20.2952	−0.945241	−0.472621	−	0.881266i	$-0.656692\pi$
$461$	−20.2952	−0.945241	−0.472621	+	0.881266i	$0.656692\pi$
$462$	0	0
$463$	24.0017	1.11546	0.557728	−	0.830024i	$-0.311673\pi$
$463$	24.0017	1.11546	0.557728	+	0.830024i	$0.311673\pi$
$464$	6.09023	0.282732
$465$	45.4674	2.10850
$466$	30.4725	1.41161
$467$	31.1400	1.44099	0.720494	−	0.693462i	$-0.243915\pi$
$467$	31.1400	1.44099	0.720494	+	0.693462i	$0.243915\pi$
$468$	0	0
$469$	0	0
$470$	−19.7628	−0.911590
$471$	−28.3167	−1.30477
$472$	−1.30646	−0.0601345
$473$	−41.1282	−1.89108
$474$	−5.69700	−0.261672
$475$	48.5504	2.22765
$476$	0	0
$477$	0.0350521	0.00160492
$478$	−7.23064	−0.330722
$479$	17.2802	0.789552	0.394776	−	0.918777i	$-0.370822\pi$
$479$	17.2802	0.789552	0.394776	+	0.918777i	$0.370822\pi$
$480$	−49.6982	−2.26840
$481$	0	0
$482$	−43.1293	−1.96449
$483$	0	0
$484$	3.04903	0.138592
$485$	47.9300	2.17639
$486$	−0.175228	−0.00794852
$487$	6.47481	0.293402	0.146701	−	0.989181i	$-0.453135\pi$
$487$	6.47481	0.293402	0.146701	+	0.989181i	$0.453135\pi$
$488$	−5.88834	−0.266553
$489$	−3.89446	−0.176114
$490$	0	0
$491$	25.6959	1.15964	0.579821	−	0.814744i	$-0.303123\pi$
$491$	25.6959	1.15964	0.579821	+	0.814744i	$0.303123\pi$
$492$	2.72690	0.122938
$493$	−2.35969	−0.106275
$494$	0	0
$495$	−0.114791	−0.00515949
$496$	30.8267	1.38416
$497$	0	0
$498$	−4.88081	−0.218714
$499$	−1.25448	−0.0561581	−0.0280790	−	0.999606i	$-0.508939\pi$
$499$	−1.25448	−0.0561581	−0.0280790	+	0.999606i	$0.508939\pi$
$500$	25.5383	1.14211
$501$	−3.78261	−0.168995
$502$	−12.0318	−0.537004
$503$	7.58143	0.338039	0.169020	−	0.985613i	$-0.445940\pi$
$503$	7.58143	0.338039	0.169020	+	0.985613i	$0.445940\pi$
$504$	0	0
$505$	1.75981	0.0783104
$506$	43.0193	1.91244
$507$	0	0
$508$	−31.1636	−1.38266
$509$	15.9816	0.708372	0.354186	−	0.935175i	$-0.384758\pi$
$509$	15.9816	0.708372	0.354186	+	0.935175i	$0.384758\pi$
$510$	21.2882	0.942658
$511$	0	0
$512$	−30.1387	−1.33196
$513$	28.5179	1.25910
$514$	−0.0441267	−0.00194635
$515$	−0.787638	−0.0347075
$516$	−35.8536	−1.57837
$517$	−9.72602	−0.427750
$518$	0	0
$519$	16.9218	0.742783
$520$	0	0
$521$	−24.6896	−1.08167	−0.540837	−	0.841128i	$-0.681892\pi$
$521$	−24.6896	−1.08167	−0.540837	+	0.841128i	$0.681892\pi$
$522$	0.0234774	0.00102758
$523$	31.1105	1.36037	0.680183	−	0.733042i	$-0.261900\pi$
$523$	31.1105	1.36037	0.680183	+	0.733042i	$0.261900\pi$
$524$	22.4015	0.978613
$525$	0	0
$526$	13.6993	0.597320
$527$	−11.9440	−0.520288
$528$	−27.0398	−1.17676
$529$	15.4300	0.670868
$530$	−29.3131	−1.27328
$531$	−0.0278289	−0.00120767
$532$	0	0
$533$	0	0
$534$	15.0871	0.652883
$535$	17.2266	0.744772
$536$	3.38773	0.146328
$537$	−34.4214	−1.48539
$538$	−20.4010	−0.879551
$539$	0	0
$540$	34.5671	1.48753
$541$	38.0332	1.63518	0.817588	−	0.575804i	$-0.195311\pi$
$541$	38.0332	1.63518	0.817588	+	0.575804i	$0.195311\pi$
$542$	8.23918	0.353903
$543$	24.9983	1.07278
$544$	13.0554	0.559745
$545$	40.4008	1.73058
$546$	0	0
$547$	28.4782	1.21764	0.608819	−	0.793309i	$-0.291643\pi$
$547$	28.4782	1.21764	0.608819	+	0.793309i	$0.291643\pi$
$548$	13.1977	0.563779
$549$	−0.125428	−0.00535313
$550$	61.2993	2.61381
$551$	−7.65281	−0.326021
$552$	−4.37145	−0.186061
$553$	0	0
$554$	55.2092	2.34562
$555$	−11.7077	−0.496965
$556$	28.3523	1.20240
$557$	−14.4383	−0.611768	−0.305884	−	0.952069i	$-0.598952\pi$
$557$	−14.4383	−0.611768	−0.305884	+	0.952069i	$0.598952\pi$
$558$	0.118835	0.00503068
$559$	0	0
$560$	0	0
$561$	10.4767	0.442328
$562$	−33.8188	−1.42656
$563$	4.13941	0.174456	0.0872278	−	0.996188i	$-0.472199\pi$
$563$	4.13941	0.174456	0.0872278	+	0.996188i	$0.472199\pi$
$564$	−8.47867	−0.357016
$565$	−64.6075	−2.71806
$566$	−12.4998	−0.525407
$567$	0	0
$568$	−0.859412	−0.0360601
$569$	−12.5871	−0.527678	−0.263839	−	0.964567i	$-0.584989\pi$
$569$	−12.5871	−0.527678	−0.263839	+	0.964567i	$0.584989\pi$
$570$	69.0407	2.89180
$571$	4.80303	0.201001	0.100500	−	0.994937i	$-0.467956\pi$
$571$	4.80303	0.201001	0.100500	+	0.994937i	$0.467956\pi$
$572$	0	0
$573$	20.1193	0.840497
$574$	0	0
$575$	54.7598	2.28364
$576$	−0.0541370	−0.00225571
$577$	33.0122	1.37432	0.687159	−	0.726507i	$-0.258858\pi$
$577$	33.0122	1.37432	0.687159	+	0.726507i	$0.258858\pi$
$578$	27.5085	1.14420
$579$	14.6336	0.608151
$580$	−9.27610	−0.385169
$581$	0	0
$582$	43.5230	1.80409
$583$	−14.4261	−0.597467
$584$	−1.24565	−0.0515454
$585$	0	0
$586$	−9.67391	−0.399626
$587$	42.2403	1.74344	0.871721	−	0.490002i	$-0.163004\pi$
$587$	42.2403	1.74344	0.871721	+	0.490002i	$0.163004\pi$
$588$	0	0
$589$	−38.7361	−1.59609
$590$	23.2725	0.958114
$591$	−31.8911	−1.31183
$592$	−7.93778	−0.326241
$593$	25.5577	1.04953	0.524764	−	0.851248i	$-0.324153\pi$
$593$	25.5577	1.04953	0.524764	+	0.851248i	$0.324153\pi$
$594$	36.0065	1.47736
$595$	0	0
$596$	−38.1119	−1.56112
$597$	2.14065	0.0876109
$598$	0	0
$599$	13.9420	0.569654	0.284827	−	0.958579i	$-0.408064\pi$
$599$	13.9420	0.569654	0.284827	+	0.958579i	$0.408064\pi$
$600$	−6.22900	−0.254298
$601$	10.8658	0.443227	0.221614	−	0.975135i	$-0.428868\pi$
$601$	10.8658	0.443227	0.221614	+	0.975135i	$0.428868\pi$
$602$	0	0
$603$	0.0721622	0.00293867
$604$	22.7265	0.924727
$605$	6.33110	0.257396
$606$	1.59800	0.0649143
$607$	3.48580	0.141484	0.0707421	−	0.997495i	$-0.477463\pi$
$607$	3.48580	0.141484	0.0707421	+	0.997495i	$0.477463\pi$
$608$	42.3404	1.71713
$609$	0	0
$610$	104.892	4.24694
$611$	0	0
$612$	0.0262876	0.00106261
$613$	−16.1945	−0.654092	−0.327046	−	0.945008i	$-0.606053\pi$
$613$	−16.1945	−0.654092	−0.327046	+	0.945008i	$0.606053\pi$
$614$	19.5307	0.788193
$615$	5.66224	0.228324
$616$	0	0
$617$	−7.73498	−0.311398	−0.155699	−	0.987805i	$-0.549763\pi$
$617$	−7.73498	−0.311398	−0.155699	+	0.987805i	$0.549763\pi$
$618$	−0.715216	−0.0287702
$619$	−0.341092	−0.0137097	−0.00685483	−	0.999977i	$-0.502182\pi$
$619$	−0.341092	−0.0137097	−0.00685483	+	0.999977i	$0.502182\pi$
$620$	−46.9526	−1.88566
$621$	32.1653	1.29075
$622$	35.6641	1.43000
$623$	0	0
$624$	0	0
$625$	8.86177	0.354471
$626$	28.1666	1.12576
$627$	33.9775	1.35693
$628$	29.2417	1.16687
$629$	3.07554	0.122630
$630$	0	0
$631$	−6.93421	−0.276047	−0.138023	−	0.990429i	$-0.544075\pi$
$631$	−6.93421	−0.276047	−0.138023	+	0.990429i	$0.544075\pi$
$632$	−0.685765	−0.0272783
$633$	−30.7087	−1.22056
$634$	10.1292	0.402281
$635$	−64.7092	−2.56791
$636$	−12.5760	−0.498669
$637$	0	0
$638$	−9.66238	−0.382537
$639$	−0.0183064	−0.000724189 0
$640$	−12.0306	−0.475549
$641$	−33.1154	−1.30798	−0.653990	−	0.756503i	$-0.726906\pi$
$641$	−33.1154	−1.30798	−0.653990	+	0.756503i	$0.726906\pi$
$642$	15.6427	0.617368
$643$	−27.6136	−1.08897	−0.544486	−	0.838770i	$-0.683275\pi$
$643$	−27.6136	−1.08897	−0.544486	+	0.838770i	$0.683275\pi$
$644$	0	0
$645$	−74.4477	−2.93137
$646$	−18.1365	−0.713572
$647$	−8.36197	−0.328743	−0.164371	−	0.986399i	$-0.552560\pi$
$647$	−8.36197	−0.328743	−0.164371	+	0.986399i	$0.552560\pi$
$648$	−3.66940	−0.144148
$649$	11.4533	0.449581
$650$	0	0
$651$	0	0
$652$	4.02167	0.157501
$653$	42.0521	1.64563	0.822813	−	0.568312i	$-0.192403\pi$
$653$	42.0521	1.64563	0.822813	+	0.568312i	$0.192403\pi$
$654$	36.6861	1.43454
$655$	46.5152	1.81750
$656$	3.83898	0.149887
$657$	−0.0265337	−0.00103518
$658$	0	0
$659$	−4.79514	−0.186792	−0.0933961	−	0.995629i	$-0.529772\pi$
$659$	−4.79514	−0.186792	−0.0933961	+	0.995629i	$0.529772\pi$
$660$	41.1847	1.60311
$661$	47.9111	1.86353	0.931763	−	0.363066i	$-0.118270\pi$
$661$	47.9111	1.86353	0.931763	+	0.363066i	$0.118270\pi$
$662$	30.3385	1.17914
$663$	0	0
$664$	−0.587517	−0.0228001
$665$	0	0
$666$	−0.0305996	−0.00118571
$667$	−8.63158	−0.334216
$668$	3.90617	0.151134
$669$	24.8159	0.959437
$670$	−60.3473	−2.33142
$671$	51.6212	1.99282
$672$	0	0
$673$	29.8549	1.15082	0.575410	−	0.817865i	$-0.304842\pi$
$673$	29.8549	1.15082	0.575410	+	0.817865i	$0.304842\pi$
$674$	−0.505246	−0.0194614
$675$	45.8331	1.76412
$676$	0	0
$677$	15.8550	0.609355	0.304678	−	0.952456i	$-0.401451\pi$
$677$	15.8550	0.609355	0.304678	+	0.952456i	$0.401451\pi$
$678$	−58.6670	−2.25309
$679$	0	0
$680$	2.56253	0.0982684
$681$	−27.3150	−1.04671
$682$	−48.9078	−1.87278
$683$	18.4614	0.706404	0.353202	−	0.935547i	$-0.385093\pi$
$683$	18.4614	0.706404	0.353202	+	0.935547i	$0.385093\pi$
$684$	0.0852544	0.00325978
$685$	27.4042	1.04706
$686$	0	0
$687$	−0.605636	−0.0231065
$688$	−50.4752	−1.92435
$689$	0	0
$690$	77.8708	2.96449
$691$	−31.2898	−1.19032	−0.595160	−	0.803607i	$-0.702911\pi$
$691$	−31.2898	−1.19032	−0.595160	+	0.803607i	$0.702911\pi$
$692$	−17.4745	−0.664281
$693$	0	0
$694$	67.4367	2.55986
$695$	58.8716	2.23313
$696$	0.981853	0.0372170
$697$	−1.48743	−0.0563405
$698$	38.1653	1.44458
$699$	27.1460	1.02676
$700$	0	0
$701$	−22.4859	−0.849279	−0.424640	−	0.905362i	$-0.639599\pi$
$701$	−22.4859	−0.849279	−0.424640	+	0.905362i	$0.639599\pi$
$702$	0	0
$703$	9.97441	0.376192
$704$	22.2807	0.839736
$705$	−17.6054	−0.663058
$706$	23.3358	0.878254
$707$	0	0
$708$	9.98442	0.375237
$709$	16.7526	0.629157	0.314578	−	0.949232i	$-0.398137\pi$
$709$	16.7526	0.629157	0.314578	+	0.949232i	$0.398137\pi$
$710$	15.3091	0.574541
$711$	−0.0146075	−0.000547825 0
$712$	1.81608	0.0680605
$713$	−43.6903	−1.63621
$714$	0	0
$715$	0	0
$716$	35.5457	1.32841
$717$	−6.44132	−0.240555
$718$	−33.5003	−1.25022
$719$	22.9919	0.857455	0.428727	−	0.903434i	$-0.358962\pi$
$719$	22.9919	0.857455	0.428727	+	0.903434i	$0.358962\pi$
$720$	−0.140879	−0.00525027
$721$	0	0
$722$	−21.8244	−0.812220
$723$	−38.4211	−1.42890
$724$	−25.8149	−0.959403
$725$	−12.2994	−0.456787
$726$	5.74898	0.213365
$727$	−21.9814	−0.815246	−0.407623	−	0.913150i	$-0.633642\pi$
$727$	−21.9814	−0.815246	−0.407623	+	0.913150i	$0.633642\pi$
$728$	0	0
$729$	26.9216	0.997097
$730$	22.1894	0.821266
$731$	19.5569	0.723338
$732$	45.0009	1.66328
$733$	22.8415	0.843668	0.421834	−	0.906673i	$-0.361386\pi$
$733$	22.8415	0.843668	0.421834	+	0.906673i	$0.361386\pi$
$734$	−1.36696	−0.0504554
$735$	0	0
$736$	47.7556	1.76030
$737$	−29.6992	−1.09398
$738$	0.0147990	0.000544758 0
$739$	−34.7941	−1.27992	−0.639960	−	0.768408i	$-0.721049\pi$
$739$	−34.7941	−1.27992	−0.639960	+	0.768408i	$0.721049\pi$
$740$	12.0901	0.444443
$741$	0	0
$742$	0	0
$743$	10.9822	0.402899	0.201449	−	0.979499i	$-0.435435\pi$
$743$	10.9822	0.402899	0.201449	+	0.979499i	$0.435435\pi$
$744$	4.96982	0.182202
$745$	−79.1369	−2.89935
$746$	−21.1882	−0.775754
$747$	−0.0125147	−0.000457890 0
$748$	−10.8190	−0.395580
$749$	0	0
$750$	48.1529	1.75829
$751$	30.9219	1.12836	0.564178	−	0.825653i	$-0.309193\pi$
$751$	30.9219	1.12836	0.564178	+	0.825653i	$0.309193\pi$
$752$	−11.9364	−0.435276
$753$	−10.7183	−0.390598
$754$	0	0
$755$	47.1901	1.71742
$756$	0	0
$757$	12.3709	0.449627	0.224813	−	0.974402i	$-0.427823\pi$
$757$	12.3709	0.449627	0.224813	+	0.974402i	$0.427823\pi$
$758$	−4.16219	−0.151177
$759$	38.3232	1.39104
$760$	8.31064	0.301458
$761$	−52.1340	−1.88986	−0.944928	−	0.327278i	$-0.893869\pi$
$761$	−52.1340	−1.88986	−0.944928	+	0.327278i	$0.893869\pi$
$762$	−58.7594	−2.12863
$763$	0	0
$764$	−20.7765	−0.751668
$765$	0.0545845	0.00197351
$766$	−58.4296	−2.11115
$767$	0	0
$768$	−32.6117	−1.17677
$769$	−25.6383	−0.924540	−0.462270	−	0.886739i	$-0.652965\pi$
$769$	−25.6383	−0.924540	−0.462270	+	0.886739i	$0.652965\pi$
$770$	0	0
$771$	−0.0393097	−0.00141570
$772$	−15.1116	−0.543878
$773$	32.5754	1.17165	0.585827	−	0.810436i	$-0.300770\pi$
$773$	32.5754	1.17165	0.585827	+	0.810436i	$0.300770\pi$
$774$	−0.194578	−0.00699397
$775$	−62.2554	−2.23628
$776$	5.23899	0.188069
$777$	0	0
$778$	11.2550	0.403512
$779$	−4.82395	−0.172836
$780$	0	0
$781$	7.53420	0.269595
$782$	−20.4561	−0.731510
$783$	−7.22450	−0.258183
$784$	0	0
$785$	60.7184	2.16713
$786$	42.2383	1.50659
$787$	−2.15241	−0.0767252	−0.0383626	−	0.999264i	$-0.512214\pi$
$787$	−2.15241	−0.0767252	−0.0383626	+	0.999264i	$0.512214\pi$
$788$	32.9329	1.17318
$789$	12.2039	0.434469
$790$	12.2159	0.434621
$791$	0	0
$792$	−0.0125473	−0.000445848 0
$793$	0	0
$794$	−19.9727	−0.708804
$795$	−26.1132	−0.926138
$796$	−2.21057	−0.0783516
$797$	8.95220	0.317103	0.158552	−	0.987351i	$-0.449318\pi$
$797$	8.95220	0.317103	0.158552	+	0.987351i	$0.449318\pi$
$798$	0	0
$799$	4.62482	0.163614
$800$	68.0482	2.40587
$801$	0.0386844	0.00136685
$802$	−44.1830	−1.56016
$803$	10.9202	0.385367
$804$	−25.8903	−0.913080
$805$	0	0
$806$	0	0
$807$	−18.1740	−0.639754
$808$	0.192356	0.00676706
$809$	16.8065	0.590886	0.295443	−	0.955360i	$-0.404533\pi$
$809$	16.8065	0.590886	0.295443	+	0.955360i	$0.404533\pi$
$810$	65.3648	2.29668
$811$	−43.5400	−1.52890	−0.764448	−	0.644685i	$-0.776989\pi$
$811$	−43.5400	−1.52890	−0.764448	+	0.644685i	$0.776989\pi$
$812$	0	0
$813$	7.33976	0.257417
$814$	12.5936	0.441405
$815$	8.35074	0.292514
$816$	12.8577	0.450111
$817$	63.4258	2.21899
$818$	−11.8097	−0.412918
$819$	0	0
$820$	−5.84720	−0.204193
$821$	−18.6453	−0.650727	−0.325364	−	0.945589i	$-0.605487\pi$
$821$	−18.6453	−0.650727	−0.325364	+	0.945589i	$0.605487\pi$
$822$	24.8845	0.867945
$823$	42.4676	1.48033	0.740164	−	0.672427i	$-0.234748\pi$
$823$	42.4676	1.48033	0.740164	+	0.672427i	$0.234748\pi$
$824$	−0.0860927	−0.00299918
$825$	54.6077	1.90119
$826$	0	0
$827$	−22.4566	−0.780893	−0.390447	−	0.920626i	$-0.627679\pi$
$827$	−22.4566	−0.780893	−0.390447	+	0.920626i	$0.627679\pi$
$828$	0.0961582	0.00334173
$829$	−45.8532	−1.59255	−0.796274	−	0.604936i	$-0.793199\pi$
$829$	−45.8532	−1.59255	−0.796274	+	0.604936i	$0.793199\pi$
$830$	10.4657	0.363271
$831$	49.1824	1.70612
$832$	0	0
$833$	0	0
$834$	53.4586	1.85112
$835$	8.11091	0.280690
$836$	−35.0874	−1.21352
$837$	−36.5681	−1.26398
$838$	−10.8228	−0.373868
$839$	31.9075	1.10157	0.550785	−	0.834647i	$-0.314329\pi$
$839$	31.9075	1.10157	0.550785	+	0.834647i	$0.314329\pi$
$840$	0	0
$841$	−27.0613	−0.933148
$842$	−3.02391	−0.104211
$843$	−30.1270	−1.03763
$844$	31.7117	1.09156
$845$	0	0
$846$	−0.0460139	−0.00158199
$847$	0	0
$848$	−17.7046	−0.607979
$849$	−11.1353	−0.382162
$850$	−29.1485	−0.999784
$851$	11.2501	0.385648
$852$	6.56795	0.225014
$853$	−11.1783	−0.382736	−0.191368	−	0.981518i	$-0.561292\pi$
$853$	−11.1783	−0.382736	−0.191368	+	0.981518i	$0.561292\pi$
$854$	0	0
$855$	0.177025	0.00605414
$856$	1.88296	0.0643582
$857$	43.9664	1.50186	0.750932	−	0.660379i	$-0.229604\pi$
$857$	43.9664	1.50186	0.750932	+	0.660379i	$0.229604\pi$
$858$	0	0
$859$	−11.4413	−0.390373	−0.195187	−	0.980766i	$-0.562531\pi$
$859$	−11.4413	−0.390373	−0.195187	+	0.980766i	$0.562531\pi$
$860$	76.8795	2.62157
$861$	0	0
$862$	32.4376	1.10483
$863$	−9.33887	−0.317899	−0.158949	−	0.987287i	$-0.550811\pi$
$863$	−9.33887	−0.317899	−0.158949	+	0.987287i	$0.550811\pi$
$864$	39.9707	1.35983
$865$	−36.2847	−1.23372
$866$	62.2903	2.11671
$867$	24.5055	0.832252
$868$	0	0
$869$	6.01189	0.203939
$870$	−17.4902	−0.592974
$871$	0	0
$872$	4.41601	0.149545
$873$	0.111596	0.00377695
$874$	−66.3421	−2.24406
$875$	0	0
$876$	9.51973	0.321642
$877$	−45.0983	−1.52286	−0.761431	−	0.648246i	$-0.775503\pi$
$877$	−45.0983	−1.52286	−0.761431	+	0.648246i	$0.775503\pi$
$878$	−56.0887	−1.89290
$879$	−8.61787	−0.290674
$880$	57.9805	1.95452
$881$	−13.4579	−0.453407	−0.226704	−	0.973964i	$-0.572795\pi$
$881$	−13.4579	−0.453407	−0.226704	+	0.973964i	$0.572795\pi$
$882$	0	0
$883$	46.1531	1.55317	0.776587	−	0.630010i	$-0.216949\pi$
$883$	46.1531	1.55317	0.776587	+	0.630010i	$0.216949\pi$
$884$	0	0
$885$	20.7320	0.696899
$886$	73.2284	2.46015
$887$	23.6131	0.792849	0.396424	−	0.918067i	$-0.370251\pi$
$887$	23.6131	0.792849	0.396424	+	0.918067i	$0.370251\pi$
$888$	−1.27971	−0.0429443
$889$	0	0
$890$	−32.3507	−1.08440
$891$	32.1685	1.07768
$892$	−25.6265	−0.858038
$893$	14.9990	0.501921
$894$	−71.8605	−2.40337
$895$	73.8084	2.46714
$896$	0	0
$897$	0	0
$898$	7.81194	0.260688
$899$	9.81308	0.327284
$900$	0.137018	0.00456727
$901$	6.85975	0.228531
$902$	−6.09068	−0.202798
$903$	0	0
$904$	−7.06192	−0.234876
$905$	−53.6029	−1.78182
$906$	42.8511	1.42363
$907$	−16.4932	−0.547649	−0.273825	−	0.961780i	$-0.588289\pi$
$907$	−16.4932	−0.547649	−0.273825	+	0.961780i	$0.588289\pi$
$908$	28.2072	0.936089
$909$	0.00409738	0.000135902 0
$910$	0	0
$911$	−52.7129	−1.74646	−0.873229	−	0.487311i	$-0.837978\pi$
$911$	−52.7129	−1.74646	−0.873229	+	0.487311i	$0.837978\pi$
$912$	41.6994	1.38081
$913$	5.15058	0.170459
$914$	−44.5173	−1.47250
$915$	93.4414	3.08908
$916$	0.625419	0.0206644
$917$	0	0
$918$	−17.1215	−0.565093
$919$	7.69403	0.253803	0.126901	−	0.991915i	$-0.459497\pi$
$919$	7.69403	0.253803	0.126901	+	0.991915i	$0.459497\pi$
$920$	9.37354	0.309036
$921$	17.3986	0.573304
$922$	39.5168	1.30142
$923$	0	0
$924$	0	0
$925$	16.0306	0.527081
$926$	−46.7338	−1.53577
$927$	−0.00183387	−6.02320e−5 0
$928$	−10.7262	−0.352104
$929$	16.9630	0.556538	0.278269	−	0.960503i	$-0.410239\pi$
$929$	16.9630	0.556538	0.278269	+	0.960503i	$0.410239\pi$
$930$	−88.5297	−2.90300
$931$	0	0
$932$	−28.0327	−0.918243
$933$	31.7708	1.04013
$934$	−60.6328	−1.98396
$935$	−22.4649	−0.734680
$936$	0	0
$937$	−10.1305	−0.330949	−0.165474	−	0.986214i	$-0.552916\pi$
$937$	−10.1305	−0.330949	−0.165474	+	0.986214i	$0.552916\pi$
$938$	0	0
$939$	25.0918	0.818841
$940$	18.1805	0.592982
$941$	54.5020	1.77672	0.888358	−	0.459152i	$-0.151847\pi$
$941$	54.5020	1.77672	0.888358	+	0.459152i	$0.151847\pi$
$942$	55.1355	1.79641
$943$	−5.44092	−0.177181
$944$	14.0562	0.457491
$945$	0	0
$946$	80.0809	2.60365
$947$	54.3205	1.76518	0.882590	−	0.470143i	$-0.155798\pi$
$947$	54.3205	1.76518	0.882590	+	0.470143i	$0.155798\pi$
$948$	5.24087	0.170216
$949$	0	0
$950$	−94.5326	−3.06704
$951$	9.02343	0.292605
$952$	0	0
$953$	−5.70885	−0.184928	−0.0924640	−	0.995716i	$-0.529474\pi$
$953$	−5.70885	−0.184928	−0.0924640	+	0.995716i	$0.529474\pi$
$954$	−0.0682500	−0.00220968
$955$	−43.1411	−1.39601
$956$	6.65172	0.215132
$957$	−8.60760	−0.278244
$958$	−33.6463	−1.08706
$959$	0	0
$960$	40.3311	1.30168
$961$	18.6706	0.602277
$962$	0	0
$963$	0.0401090	0.00129249
$964$	39.6762	1.27788
$965$	−31.3782	−1.01010
$966$	0	0
$967$	−2.15318	−0.0692416	−0.0346208	−	0.999401i	$-0.511022\pi$
$967$	−2.15318	−0.0692416	−0.0346208	+	0.999401i	$0.511022\pi$
$968$	0.692022	0.0222424
$969$	−16.1567	−0.519027
$970$	−93.3247	−2.99647
$971$	−24.0968	−0.773303	−0.386652	−	0.922226i	$-0.626368\pi$
$971$	−24.0968	−0.773303	−0.386652	+	0.922226i	$0.626368\pi$
$972$	0.161199	0.00517045
$973$	0	0
$974$	−12.6071	−0.403958
$975$	0	0
$976$	63.3529	2.02788
$977$	−15.7686	−0.504482	−0.252241	−	0.967664i	$-0.581168\pi$
$977$	−15.7686	−0.504482	−0.252241	+	0.967664i	$0.581168\pi$
$978$	7.58291	0.242475
$979$	−15.9210	−0.508838
$980$	0	0
$981$	0.0940657	0.00300329
$982$	−50.0326	−1.59661
$983$	11.4651	0.365679	0.182840	−	0.983143i	$-0.441471\pi$
$983$	11.4651	0.365679	0.182840	+	0.983143i	$0.441471\pi$
$984$	0.618911	0.0197302
$985$	68.3829	2.17886
$986$	4.59456	0.146321
$987$	0	0
$988$	0	0
$989$	71.5378	2.27477
$990$	0.223511	0.00710363
$991$	−19.3101	−0.613405	−0.306702	−	0.951805i	$-0.599226\pi$
$991$	−19.3101	−0.613405	−0.306702	+	0.951805i	$0.599226\pi$
$992$	−54.2924	−1.72379
$993$	27.0266	0.857664
$994$	0	0
$995$	−4.59011	−0.145516
$996$	4.49002	0.142272
$997$	19.0134	0.602162	0.301081	−	0.953599i	$-0.402653\pi$
$997$	19.0134	0.602162	0.301081	+	0.953599i	$0.402653\pi$
$998$	2.44259	0.0773189
$999$	9.41616	0.297914

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8281.2.a.cu.1.5		24
7.2	even	3		1183.2.e.l.508.20	yes	48
7.4	even	3		1183.2.e.l.170.20	yes	48
7.6	odd	2		8281.2.a.ct.1.5		24
13.12	even	2		8281.2.a.cv.1.20		24
91.25	even	6		1183.2.e.k.170.5	✓	48
91.51	even	6		1183.2.e.k.508.5	yes	48
91.90	odd	2		8281.2.a.cw.1.20		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.e.k.170.5	✓	48	91.25	even	6
1183.2.e.k.508.5	yes	48	91.51	even	6
1183.2.e.l.170.20	yes	48	7.4	even	3
1183.2.e.l.508.20	yes	48	7.2	even	3
8281.2.a.ct.1.5		24	7.6	odd	2
8281.2.a.cu.1.5		24	1.1	even	1	trivial
8281.2.a.cv.1.20		24	13.12	even	2
8281.2.a.cw.1.20		24	91.90	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8281.a (trivial)

\(f(q)\)	\(=\)	\(q-1.94710 q^{2} -1.73455 q^{3} +1.79121 q^{4} +3.71933 q^{5} +3.37734 q^{6} +0.406541 q^{8} +0.00865975 q^{9} +O(q^{10})\)	\(q-1.94710 q^{2} -1.73455 q^{3} +1.79121 q^{4} +3.71933 q^{5} +3.37734 q^{6} +0.406541 q^{8} +0.00865975 q^{9} -7.24191 q^{10} -3.56402 q^{11} -3.10694 q^{12} -6.45135 q^{15} -4.37399 q^{16} +1.69473 q^{17} -0.0168614 q^{18} +5.49624 q^{19} +6.66208 q^{20} +6.93951 q^{22} +6.19919 q^{23} -0.705165 q^{24} +8.83339 q^{25} +5.18863 q^{27} -1.39237 q^{29} +12.5614 q^{30} -7.04774 q^{31} +7.70353 q^{32} +6.18196 q^{33} -3.29981 q^{34} +0.0155114 q^{36} +1.81477 q^{37} -10.7017 q^{38} +1.51206 q^{40} -0.877683 q^{41} +11.5399 q^{43} -6.38389 q^{44} +0.0322084 q^{45} -12.0705 q^{46} +2.72895 q^{47} +7.58690 q^{48} -17.1995 q^{50} -2.93959 q^{51} +4.04770 q^{53} -10.1028 q^{54} -13.2557 q^{55} -9.53350 q^{57} +2.71109 q^{58} -3.21359 q^{59} -11.5557 q^{60} -14.4840 q^{61} +13.7227 q^{62} -6.25157 q^{64} -12.0369 q^{66} +8.33306 q^{67} +3.03561 q^{68} -10.7528 q^{69} -2.11396 q^{71} +0.00352054 q^{72} -3.06402 q^{73} -3.53354 q^{74} -15.3219 q^{75} +9.84490 q^{76} -1.68683 q^{79} -16.2683 q^{80} -9.02590 q^{81} +1.70894 q^{82} -1.44516 q^{83} +6.30324 q^{85} -22.4693 q^{86} +2.41514 q^{87} -1.44892 q^{88} +4.46715 q^{89} -0.0627131 q^{90} +11.1040 q^{92} +12.2246 q^{93} -5.31354 q^{94} +20.4423 q^{95} -13.3621 q^{96} +12.8868 q^{97} -0.0308635 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} + 23 q^{4} + 13 q^{5} + 14 q^{6} + 26 q^{9}+O(q^{10}) \) 24 * q - q^2 + 23 * q^4 + 13 * q^5 + 14 * q^6 + 26 * q^9	\( 24 q - q^{2} + 23 q^{4} + 13 q^{5} + 14 q^{6} + 26 q^{9} + 5 q^{10} - q^{11} + 5 q^{12} + 5 q^{15} + 17 q^{16} - 5 q^{17} + 24 q^{19} + 34 q^{20} - 14 q^{22} + 11 q^{23} + 32 q^{24} + 33 q^{25} - 21 q^{27} + 4 q^{29} - 22 q^{30} + 40 q^{31} - 6 q^{32} + 24 q^{33} + 36 q^{34} - 15 q^{36} - 4 q^{37} - 29 q^{38} - 4 q^{40} + 49 q^{41} + 13 q^{43} + 10 q^{44} + 58 q^{45} - 10 q^{46} + 62 q^{47} + 89 q^{48} - 23 q^{50} - 21 q^{51} - 18 q^{53} + 12 q^{54} - 14 q^{55} - 13 q^{57} + 56 q^{58} + 79 q^{59} + 22 q^{60} + 13 q^{61} + 12 q^{62} + 18 q^{64} - 38 q^{66} - 2 q^{67} - 12 q^{68} - 28 q^{69} - 19 q^{71} + 81 q^{72} + 17 q^{73} + 17 q^{74} + 24 q^{75} + 58 q^{76} - 9 q^{79} + 63 q^{80} + 16 q^{81} - 22 q^{82} + 81 q^{83} - 34 q^{85} + 22 q^{86} + 70 q^{87} - 33 q^{88} + 72 q^{89} + q^{90} - 4 q^{92} + 19 q^{93} - 30 q^{94} + 13 q^{95} + 11 q^{96} + 45 q^{97} - 39 q^{99}+O(q^{100}) \) 24 * q - q^2 + 23 * q^4 + 13 * q^5 + 14 * q^6 + 26 * q^9 + 5 * q^10 - q^11 + 5 * q^12 + 5 * q^15 + 17 * q^16 - 5 * q^17 + 24 * q^19 + 34 * q^20 - 14 * q^22 + 11 * q^23 + 32 * q^24 + 33 * q^25 - 21 * q^27 + 4 * q^29 - 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 + 36 * q^34 - 15 * q^36 - 4 * q^37 - 29 * q^38 - 4 * q^40 + 49 * q^41 + 13 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 89 * q^48 - 23 * q^50 - 21 * q^51 - 18 * q^53 + 12 * q^54 - 14 * q^55 - 13 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 + 13 * q^61 + 12 * q^62 + 18 * q^64 - 38 * q^66 - 2 * q^67 - 12 * q^68 - 28 * q^69 - 19 * q^71 + 81 * q^72 + 17 * q^73 + 17 * q^74 + 24 * q^75 + 58 * q^76 - 9 * q^79 + 63 * q^80 + 16 * q^81 - 22 * q^82 + 81 * q^83 - 34 * q^85 + 22 * q^86 + 70 * q^87 - 33 * q^88 + 72 * q^89 + q^90 - 4 * q^92 + 19 * q^93 - 30 * q^94 + 13 * q^95 + 11 * q^96 + 45 * q^97 - 39 * q^99

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