LMFDB - Embedded newform 99.8.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,8,Mod(1,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("99.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	99.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:	$30.9261175229$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 510x^{2} - 1544x + 28880 $ x^4 - x^3 - 510x^2 - 1544x + 28880
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-17.6807$ of defining polynomial
Character	$\chi$	$=$	99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-21.6807 q^{2} +342.055 q^{4} +369.874 q^{5} +1000.53 q^{7} -4640.87 q^{8} +O(q^{10})$	\(q-21.6807 q^{2} +342.055 q^{4} +369.874 q^{5} +1000.53 q^{7} -4640.87 q^{8} -8019.14 q^{10} -1331.00 q^{11} -12773.6 q^{13} -21692.2 q^{14} +56834.4 q^{16} +3584.50 q^{17} -49986.6 q^{19} +126517. q^{20} +28857.1 q^{22} -9271.17 q^{23} +58681.8 q^{25} +276942. q^{26} +342236. q^{28} -107171. q^{29} -94316.2 q^{31} -638182. q^{32} -77714.5 q^{34} +370070. q^{35} -177984. q^{37} +1.08375e6 q^{38} -1.71654e6 q^{40} -385335. q^{41} -66987.9 q^{43} -455275. q^{44} +201006. q^{46} -407205. q^{47} +177518. q^{49} -1.27227e6 q^{50} -4.36929e6 q^{52} -418661. q^{53} -492302. q^{55} -4.64333e6 q^{56} +2.32355e6 q^{58} +817746. q^{59} +2.47483e6 q^{61} +2.04485e6 q^{62} +6.56146e6 q^{64} -4.72464e6 q^{65} -88685.6 q^{67} +1.22609e6 q^{68} -8.02340e6 q^{70} -2.96162e6 q^{71} +6.16122e6 q^{73} +3.85882e6 q^{74} -1.70982e7 q^{76} -1.33171e6 q^{77} -3.36849e6 q^{79} +2.10216e7 q^{80} +8.35434e6 q^{82} -2.92413e6 q^{83} +1.32581e6 q^{85} +1.45235e6 q^{86} +6.17699e6 q^{88} +5.54333e6 q^{89} -1.27804e7 q^{91} -3.17125e6 q^{92} +8.82850e6 q^{94} -1.84888e7 q^{95} -4.30094e6 q^{97} -3.84873e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 15 q^{2} + 565 q^{4} - 306 q^{5} + 890 q^{7} - 2457 q^{8}+O(q^{10}) $ 4 * q - 15 * q^2 + 565 * q^4 - 306 * q^5 + 890 * q^7 - 2457 * q^8	\( 4 q - 15 q^{2} + 565 q^{4} - 306 q^{5} + 890 q^{7} - 2457 q^{8} - 8946 q^{10} - 5324 q^{11} - 1822 q^{13} - 35340 q^{14} + 65041 q^{16} - 32856 q^{17} - 12784 q^{19} + 4002 q^{20} + 19965 q^{22} - 114858 q^{23} + 72856 q^{25} + 221466 q^{26} + 10112 q^{28} + 104952 q^{29} - 24976 q^{31} - 337761 q^{32} - 741690 q^{34} + 722856 q^{35} - 498856 q^{37} + 897156 q^{38} - 2676930 q^{40} - 734556 q^{41} - 201916 q^{43} - 752015 q^{44} - 3068508 q^{46} - 1995894 q^{47} - 771024 q^{49} - 1632129 q^{50} - 4412266 q^{52} - 929970 q^{53} + 407286 q^{55} - 7224888 q^{56} + 2864322 q^{58} - 1353156 q^{59} + 3998774 q^{61} + 3783264 q^{62} + 1480129 q^{64} - 6612108 q^{65} + 1722008 q^{67} - 1596906 q^{68} - 2751024 q^{70} - 5571858 q^{71} + 5600528 q^{73} + 10907838 q^{74} - 19634884 q^{76} - 1184590 q^{77} - 7710226 q^{79} + 24073794 q^{80} - 11230842 q^{82} - 3431856 q^{83} + 5909484 q^{85} + 25687140 q^{86} + 3270267 q^{88} - 4611528 q^{89} - 9032696 q^{91} - 13608576 q^{92} - 3497436 q^{94} - 21828000 q^{95} + 1401692 q^{97} + 7230081 q^{98}+O(q^{100}) \) 4 * q - 15 * q^2 + 565 * q^4 - 306 * q^5 + 890 * q^7 - 2457 * q^8 - 8946 * q^10 - 5324 * q^11 - 1822 * q^13 - 35340 * q^14 + 65041 * q^16 - 32856 * q^17 - 12784 * q^19 + 4002 * q^20 + 19965 * q^22 - 114858 * q^23 + 72856 * q^25 + 221466 * q^26 + 10112 * q^28 + 104952 * q^29 - 24976 * q^31 - 337761 * q^32 - 741690 * q^34 + 722856 * q^35 - 498856 * q^37 + 897156 * q^38 - 2676930 * q^40 - 734556 * q^41 - 201916 * q^43 - 752015 * q^44 - 3068508 * q^46 - 1995894 * q^47 - 771024 * q^49 - 1632129 * q^50 - 4412266 * q^52 - 929970 * q^53 + 407286 * q^55 - 7224888 * q^56 + 2864322 * q^58 - 1353156 * q^59 + 3998774 * q^61 + 3783264 * q^62 + 1480129 * q^64 - 6612108 * q^65 + 1722008 * q^67 - 1596906 * q^68 - 2751024 * q^70 - 5571858 * q^71 + 5600528 * q^73 + 10907838 * q^74 - 19634884 * q^76 - 1184590 * q^77 - 7710226 * q^79 + 24073794 * q^80 - 11230842 * q^82 - 3431856 * q^83 + 5909484 * q^85 + 25687140 * q^86 + 3270267 * q^88 - 4611528 * q^89 - 9032696 * q^91 - 13608576 * q^92 - 3497436 * q^94 - 21828000 * q^95 + 1401692 * q^97 + 7230081 * q^98

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 $

$2$	−21.6807	−1.91633	−0.958163	−	0.286224i	$-0.907600\pi$
$2$	−21.6807	−1.91633	−0.958163	+	0.286224i	$0.907600\pi$
$3$	0	0
$3$	0	0
$4$	342.055	2.67230
$5$	369.874	1.32330	0.661651	−	0.749812i	$-0.269856\pi$
$5$	369.874	1.32330	0.661651	+	0.749812i	$0.269856\pi$
$6$	0	0
$7$	1000.53	1.10252	0.551261	−	0.834333i	$-0.314147\pi$
$7$	1000.53	1.10252	0.551261	+	0.834333i	$0.314147\pi$
$8$	−4640.87	−3.20468
$9$	0	0
$10$	−8019.14	−2.53588
$11$	−1331.00	−0.301511
$11$	−1331.00	−0.301511
$12$	0	0
$13$	−12773.6	−1.61255	−0.806275	−	0.591541i	$-0.798520\pi$
$13$	−12773.6	−1.61255	−0.806275	+	0.591541i	$0.798520\pi$
$14$	−21692.2	−2.11279
$15$	0	0
$16$	56834.4	3.46890
$17$	3584.50	0.176953	0.0884763	−	0.996078i	$-0.471800\pi$
$17$	3584.50	0.176953	0.0884763	+	0.996078i	$0.471800\pi$
$18$	0	0
$19$	−49986.6	−1.67192	−0.835961	−	0.548788i	$-0.815089\pi$
$19$	−49986.6	−1.67192	−0.835961	+	0.548788i	$0.815089\pi$
$20$	126517.	3.53626
$21$	0	0
$22$	28857.1	0.577794
$23$	−9271.17	−0.158887	−0.0794433	−	0.996839i	$-0.525314\pi$
$23$	−9271.17	−0.158887	−0.0794433	+	0.996839i	$0.525314\pi$
$24$	0	0
$25$	58681.8	0.751127
$26$	276942.	3.09017
$27$	0	0
$28$	342236.	2.94627
$29$	−107171.	−0.815990	−0.407995	−	0.912984i	$-0.633772\pi$
$29$	−107171.	−0.815990	−0.407995	+	0.912984i	$0.633772\pi$
$30$	0	0
$31$	−94316.2	−0.568618	−0.284309	−	0.958733i	$-0.591764\pi$
$31$	−94316.2	−0.568618	−0.284309	+	0.958733i	$0.591764\pi$
$32$	−638182.	−3.44286
$33$	0	0
$34$	−77714.5	−0.339099
$35$	370070.	1.45897
$36$	0	0
$37$	−177984.	−0.577662	−0.288831	−	0.957380i	$-0.593267\pi$
$37$	−177984.	−0.577662	−0.288831	+	0.957380i	$0.593267\pi$
$38$	1.08375e6	3.20395
$39$	0	0
$40$	−1.71654e6	−4.24075
$41$	−385335.	−0.873162	−0.436581	−	0.899665i	$-0.643811\pi$
$41$	−385335.	−0.873162	−0.436581	+	0.899665i	$0.643811\pi$
$42$	0	0
$43$	−66987.9	−0.128486	−0.0642431	−	0.997934i	$-0.520463\pi$
$43$	−66987.9	−0.128486	−0.0642431	+	0.997934i	$0.520463\pi$
$44$	−455275.	−0.805730
$45$	0	0
$46$	201006.	0.304478
$47$	−407205.	−0.572098	−0.286049	−	0.958215i	$-0.592342\pi$
$47$	−407205.	−0.572098	−0.286049	+	0.958215i	$0.592342\pi$
$48$	0	0
$49$	177518.	0.215554
$50$	−1.27227e6	−1.43940
$51$	0	0
$52$	−4.36929e6	−4.30922
$53$	−418661.	−0.386275	−0.193138	−	0.981172i	$-0.561866\pi$
$53$	−418661.	−0.386275	−0.193138	+	0.981172i	$0.561866\pi$
$54$	0	0
$55$	−492302.	−0.398990
$56$	−4.64333e6	−3.53323
$57$	0	0
$58$	2.32355e6	1.56370
$59$	817746.	0.518366	0.259183	−	0.965828i	$-0.416547\pi$
$59$	817746.	0.518366	0.259183	+	0.965828i	$0.416547\pi$
$60$	0	0
$61$	2.47483e6	1.39602	0.698008	−	0.716090i	$-0.254070\pi$
$61$	2.47483e6	1.39602	0.698008	+	0.716090i	$0.254070\pi$
$62$	2.04485e6	1.08966
$63$	0	0
$64$	6.56146e6	3.12875
$65$	−4.72464e6	−2.13389
$66$	0	0
$67$	−88685.6	−0.0360240	−0.0180120	−	0.999838i	$-0.505734\pi$
$67$	−88685.6	−0.0360240	−0.0180120	+	0.999838i	$0.505734\pi$
$68$	1.22609e6	0.472871
$69$	0	0
$70$	−8.02340e6	−2.79586
$71$	−2.96162e6	−0.982032	−0.491016	−	0.871150i	$-0.663374\pi$
$71$	−2.96162e6	−0.982032	−0.491016	+	0.871150i	$0.663374\pi$
$72$	0	0
$73$	6.16122e6	1.85369	0.926844	−	0.375447i	$-0.122511\pi$
$73$	6.16122e6	1.85369	0.926844	+	0.375447i	$0.122511\pi$
$74$	3.85882e6	1.10699
$75$	0	0
$76$	−1.70982e7	−4.46788
$77$	−1.33171e6	−0.332423
$78$	0	0
$79$	−3.36849e6	−0.768671	−0.384335	−	0.923194i	$-0.625569\pi$
$79$	−3.36849e6	−0.768671	−0.384335	+	0.923194i	$0.625569\pi$
$80$	2.10216e7	4.59040
$81$	0	0
$82$	8.35434e6	1.67326
$83$	−2.92413e6	−0.561337	−0.280668	−	0.959805i	$-0.590556\pi$
$83$	−2.92413e6	−0.561337	−0.280668	+	0.959805i	$0.590556\pi$
$84$	0	0
$85$	1.32581e6	0.234162
$86$	1.45235e6	0.246221
$87$	0	0
$88$	6.17699e6	0.966246
$89$	5.54333e6	0.833501	0.416750	−	0.909021i	$-0.363169\pi$
$89$	5.54333e6	0.833501	0.416750	+	0.909021i	$0.363169\pi$
$90$	0	0
$91$	−1.27804e7	−1.77787
$92$	−3.17125e6	−0.424593
$93$	0	0
$94$	8.82850e6	1.09633
$95$	−1.84888e7	−2.21246
$96$	0	0
$97$	−4.30094e6	−0.478479	−0.239239	−	0.970961i	$-0.576898\pi$
$97$	−4.30094e6	−0.478479	−0.239239	+	0.970961i	$0.576898\pi$
$98$	−3.84873e6	−0.413072
$99$	0	0
$100$	2.00724e7	2.00724
$101$	−1.23262e7	−1.19044	−0.595218	−	0.803564i	$-0.702934\pi$
$101$	−1.23262e7	−1.19044	−0.595218	+	0.803564i	$0.702934\pi$
$102$	0	0
$103$	1.90939e7	1.72173	0.860863	−	0.508837i	$-0.169924\pi$
$103$	1.90939e7	1.72173	0.860863	+	0.508837i	$0.169924\pi$
$104$	5.92808e7	5.16770
$105$	0	0
$106$	9.07688e6	0.740229
$107$	1.51847e7	1.19829	0.599145	−	0.800641i	$-0.295507\pi$
$107$	1.51847e7	1.19829	0.599145	+	0.800641i	$0.295507\pi$
$108$	0	0
$109$	−2.42735e7	−1.79531	−0.897656	−	0.440697i	$-0.854731\pi$
$109$	−2.42735e7	−1.79531	−0.897656	+	0.440697i	$0.854731\pi$
$110$	1.06735e7	0.764595
$111$	0	0
$112$	5.68646e7	3.82454
$113$	6.53313e6	0.425939	0.212969	−	0.977059i	$-0.431687\pi$
$113$	6.53313e6	0.425939	0.212969	+	0.977059i	$0.431687\pi$
$114$	0	0
$115$	−3.42917e6	−0.210255
$116$	−3.66584e7	−2.18057
$117$	0	0
$118$	−1.77294e7	−0.993358
$119$	3.58640e6	0.195094
$120$	0	0
$121$	1.77156e6	0.0909091
$122$	−5.36561e7	−2.67522
$123$	0	0
$124$	−3.22613e7	−1.51952
$125$	−7.19154e6	−0.329334
$126$	0	0
$127$	−2.47318e7	−1.07138	−0.535689	−	0.844415i	$-0.679948\pi$
$127$	−2.47318e7	−1.07138	−0.535689	+	0.844415i	$0.679948\pi$
$128$	−6.05700e7	−2.55283
$129$	0	0
$130$	1.02434e8	4.08923
$131$	−5.44217e6	−0.211506	−0.105753	−	0.994392i	$-0.533725\pi$
$131$	−5.44217e6	−0.211506	−0.105753	+	0.994392i	$0.533725\pi$
$132$	0	0
$133$	−5.00131e7	−1.84333
$134$	1.92277e6	0.0690336
$135$	0	0
$136$	−1.66352e7	−0.567076
$137$	−1.63003e7	−0.541595	−0.270797	−	0.962636i	$-0.587287\pi$
$137$	−1.63003e7	−0.541595	−0.270797	+	0.962636i	$0.587287\pi$
$138$	0	0
$139$	−4.96266e7	−1.56734	−0.783669	−	0.621178i	$-0.786654\pi$
$139$	−4.96266e7	−1.56734	−0.783669	+	0.621178i	$0.786654\pi$
$140$	1.26584e8	3.89881
$141$	0	0
$142$	6.42102e7	1.88189
$143$	1.70017e7	0.486202
$144$	0	0
$145$	−3.96398e7	−1.07980
$146$	−1.33580e8	−3.55227
$147$	0	0
$148$	−6.08802e7	−1.54369
$149$	−6.43484e7	−1.59362	−0.796812	−	0.604228i	$-0.793482\pi$
$149$	−6.43484e7	−1.59362	−0.796812	+	0.604228i	$0.793482\pi$
$150$	0	0
$151$	5.20719e7	1.23079	0.615396	−	0.788218i	$-0.288996\pi$
$151$	5.20719e7	1.23079	0.615396	+	0.788218i	$0.288996\pi$
$152$	2.31981e8	5.35797
$153$	0	0
$154$	2.88724e7	0.637030
$155$	−3.48851e7	−0.752453
$156$	0	0
$157$	−1.23224e7	−0.254125	−0.127063	−	0.991895i	$-0.540555\pi$
$157$	−1.23224e7	−0.254125	−0.127063	+	0.991895i	$0.540555\pi$
$158$	7.30314e7	1.47302
$159$	0	0
$160$	−2.36047e8	−4.55595
$161$	−9.27609e6	−0.175176
$162$	0	0
$163$	1.93998e7	0.350866	0.175433	−	0.984491i	$-0.443867\pi$
$163$	1.93998e7	0.350866	0.175433	+	0.984491i	$0.443867\pi$
$164$	−1.31806e8	−2.33335
$165$	0	0
$166$	6.33973e7	1.07570
$167$	−2.62174e7	−0.435595	−0.217797	−	0.975994i	$-0.569887\pi$
$167$	−2.62174e7	−0.435595	−0.217797	+	0.975994i	$0.569887\pi$
$168$	0	0
$169$	1.00417e8	1.60032
$170$	−2.87446e7	−0.448730
$171$	0	0
$172$	−2.29135e7	−0.343354
$173$	9.92110e7	1.45680	0.728398	−	0.685155i	$-0.240265\pi$
$173$	9.92110e7	1.45680	0.728398	+	0.685155i	$0.240265\pi$
$174$	0	0
$175$	5.87129e7	0.828134
$176$	−7.56466e7	−1.04591
$177$	0	0
$178$	−1.20184e8	−1.59726
$179$	7.01768e7	0.914551	0.457276	−	0.889325i	$-0.348825\pi$
$179$	7.01768e7	0.914551	0.457276	+	0.889325i	$0.348825\pi$
$180$	0	0
$181$	−8.26398e7	−1.03589	−0.517945	−	0.855414i	$-0.673303\pi$
$181$	−8.26398e7	−1.03589	−0.517945	+	0.855414i	$0.673303\pi$
$182$	2.77089e8	3.40698
$183$	0	0
$184$	4.30263e7	0.509180
$185$	−6.58315e7	−0.764422
$186$	0	0
$187$	−4.77096e6	−0.0533532
$188$	−1.39286e8	−1.52882
$189$	0	0
$190$	4.00850e8	4.23979
$191$	9.57470e7	0.994280	0.497140	−	0.867670i	$-0.334384\pi$
$191$	9.57470e7	0.994280	0.497140	+	0.867670i	$0.334384\pi$
$192$	0	0
$193$	−618214.	−0.00618997	−0.00309499	−	0.999995i	$-0.500985\pi$
$193$	−618214.	−0.00618997	−0.00309499	+	0.999995i	$0.500985\pi$
$194$	9.32477e7	0.916921
$195$	0	0
$196$	6.07210e7	0.576026
$197$	1.20129e8	1.11948	0.559738	−	0.828669i	$-0.310902\pi$
$197$	1.20129e8	1.11948	0.559738	+	0.828669i	$0.310902\pi$
$198$	0	0
$199$	1.76191e8	1.58488	0.792442	−	0.609948i	$-0.208810\pi$
$199$	1.76191e8	1.58488	0.792442	+	0.609948i	$0.208810\pi$
$200$	−2.72334e8	−2.40712
$201$	0	0
$202$	2.67242e8	2.28126
$203$	−1.07228e8	−0.899647
$204$	0	0
$205$	−1.42525e8	−1.15546
$206$	−4.13970e8	−3.29939
$207$	0	0
$208$	−7.25983e8	−5.59377
$209$	6.65322e7	0.504104
$210$	0	0
$211$	−7.11007e7	−0.521057	−0.260528	−	0.965466i	$-0.583897\pi$
$211$	−7.11007e7	−0.521057	−0.260528	+	0.965466i	$0.583897\pi$
$212$	−1.43205e8	−1.03224
$213$	0	0
$214$	−3.29215e8	−2.29631
$215$	−2.47771e7	−0.170026
$216$	0	0
$217$	−9.43663e7	−0.626914
$218$	5.26268e8	3.44040
$219$	0	0
$220$	−1.68394e8	−1.06622
$221$	−4.57871e7	−0.285345
$222$	0	0
$223$	−1.99402e8	−1.20410	−0.602051	−	0.798458i	$-0.705650\pi$
$223$	−1.99402e8	−1.20410	−0.602051	+	0.798458i	$0.705650\pi$
$224$	−6.38521e8	−3.79583
$225$	0	0
$226$	−1.41643e8	−0.816237
$227$	−5.24061e7	−0.297366	−0.148683	−	0.988885i	$-0.547503\pi$
$227$	−5.24061e7	−0.297366	−0.148683	+	0.988885i	$0.547503\pi$
$228$	0	0
$229$	−3.63622e7	−0.200090	−0.100045	−	0.994983i	$-0.531899\pi$
$229$	−3.63622e7	−0.200090	−0.100045	+	0.994983i	$0.531899\pi$
$230$	7.43469e7	0.402917
$231$	0	0
$232$	4.97367e8	2.61498
$233$	1.77125e8	0.917350	0.458675	−	0.888604i	$-0.348324\pi$
$233$	1.77125e8	0.917350	0.458675	+	0.888604i	$0.348324\pi$
$234$	0	0
$235$	−1.50614e8	−0.757058
$236$	2.79714e8	1.38523
$237$	0	0
$238$	−7.77558e7	−0.373864
$239$	−2.22533e7	−0.105439	−0.0527195	−	0.998609i	$-0.516789\pi$
$239$	−2.22533e7	−0.105439	−0.0527195	+	0.998609i	$0.516789\pi$
$240$	0	0
$241$	−3.02283e7	−0.139109	−0.0695544	−	0.997578i	$-0.522158\pi$
$241$	−3.02283e7	−0.139109	−0.0695544	+	0.997578i	$0.522158\pi$
$242$	−3.84088e7	−0.174211
$243$	0	0
$244$	8.46527e8	3.73058
$245$	6.56594e7	0.285243
$246$	0	0
$247$	6.38511e8	2.69606
$248$	4.37709e8	1.82224
$249$	0	0
$250$	1.55918e8	0.631111
$251$	4.91732e7	0.196278	0.0981388	−	0.995173i	$-0.468711\pi$
$251$	4.91732e7	0.196278	0.0981388	+	0.995173i	$0.468711\pi$
$252$	0	0
$253$	1.23399e7	0.0479061
$254$	5.36204e8	2.05311
$255$	0	0
$256$	4.73336e8	1.76331
$257$	1.05842e8	0.388949	0.194475	−	0.980908i	$-0.437700\pi$
$257$	1.05842e8	0.388949	0.194475	+	0.980908i	$0.437700\pi$
$258$	0	0
$259$	−1.78078e8	−0.636885
$260$	−1.61609e9	−5.70240
$261$	0	0
$262$	1.17990e8	0.405315
$263$	1.19721e7	0.0405813	0.0202906	−	0.999794i	$-0.493541\pi$
$263$	1.19721e7	0.0405813	0.0202906	+	0.999794i	$0.493541\pi$
$264$	0	0
$265$	−1.54852e8	−0.511159
$266$	1.08432e9	3.53242
$267$	0	0
$268$	−3.03353e7	−0.0962669
$269$	−5.97932e8	−1.87292	−0.936460	−	0.350775i	$-0.885918\pi$
$269$	−5.97932e8	−1.87292	−0.936460	+	0.350775i	$0.885918\pi$
$270$	0	0
$271$	3.24130e8	0.989297	0.494649	−	0.869093i	$-0.335297\pi$
$271$	3.24130e8	0.989297	0.494649	+	0.869093i	$0.335297\pi$
$272$	2.03723e8	0.613831
$273$	0	0
$274$	3.53403e8	1.03787
$275$	−7.81055e7	−0.226473
$276$	0	0
$277$	−1.30171e8	−0.367989	−0.183994	−	0.982927i	$-0.558903\pi$
$277$	−1.30171e8	−0.367989	−0.183994	+	0.982927i	$0.558903\pi$
$278$	1.07594e9	3.00353
$279$	0	0
$280$	−1.71745e9	−4.67552
$281$	−8.00980e7	−0.215352	−0.107676	−	0.994186i	$-0.534341\pi$
$281$	−8.00980e7	−0.215352	−0.107676	+	0.994186i	$0.534341\pi$
$282$	0	0
$283$	2.18697e8	0.573576	0.286788	−	0.957994i	$-0.407412\pi$
$283$	2.18697e8	0.573576	0.286788	+	0.957994i	$0.407412\pi$
$284$	−1.01304e9	−2.62429
$285$	0	0
$286$	−3.68610e8	−0.931721
$287$	−3.85539e8	−0.962680
$288$	0	0
$289$	−3.97490e8	−0.968688
$290$	8.59421e8	2.06925
$291$	0	0
$292$	2.10747e9	4.95362
$293$	5.92558e8	1.37624	0.688120	−	0.725597i	$-0.258436\pi$
$293$	5.92558e8	1.37624	0.688120	+	0.725597i	$0.258436\pi$
$294$	0	0
$295$	3.02463e8	0.685955
$296$	8.25999e8	1.85122
$297$	0	0
$298$	1.39512e9	3.05390
$299$	1.18427e8	0.256212
$300$	0	0
$301$	−6.70234e7	−0.141659
$302$	−1.12896e9	−2.35860
$303$	0	0
$304$	−2.84096e9	−5.79973
$305$	9.15375e8	1.84735
$306$	0	0
$307$	8.98940e7	0.177315	0.0886577	−	0.996062i	$-0.471742\pi$
$307$	8.98940e7	0.177315	0.0886577	+	0.996062i	$0.471742\pi$
$308$	−4.55516e8	−0.888334
$309$	0	0
$310$	7.56336e8	1.44194
$311$	−8.84682e8	−1.66773	−0.833865	−	0.551969i	$-0.813877\pi$
$311$	−8.84682e8	−1.66773	−0.833865	+	0.551969i	$0.813877\pi$
$312$	0	0
$313$	−5.51109e8	−1.01586	−0.507929	−	0.861399i	$-0.669589\pi$
$313$	−5.51109e8	−1.01586	−0.507929	+	0.861399i	$0.669589\pi$
$314$	2.67160e8	0.486987
$315$	0	0
$316$	−1.15221e9	−2.05412
$317$	−1.00731e9	−1.77606	−0.888030	−	0.459786i	$-0.847926\pi$
$317$	−1.00731e9	−1.77606	−0.888030	+	0.459786i	$0.847926\pi$
$318$	0	0
$319$	1.42645e8	0.246030
$320$	2.42691e9	4.14028
$321$	0	0
$322$	2.01113e8	0.335694
$323$	−1.79177e8	−0.295851
$324$	0	0
$325$	−7.49580e8	−1.21123
$326$	−4.20603e8	−0.672373
$327$	0	0
$328$	1.78829e9	2.79820
$329$	−4.07421e8	−0.630750
$330$	0	0
$331$	5.97761e8	0.906003	0.453002	−	0.891510i	$-0.350353\pi$
$331$	5.97761e8	0.906003	0.453002	+	0.891510i	$0.350353\pi$
$332$	−1.00021e9	−1.50006
$333$	0	0
$334$	5.68414e8	0.834741
$335$	−3.28025e7	−0.0476706
$336$	0	0
$337$	−8.74411e8	−1.24455	−0.622273	−	0.782801i	$-0.713791\pi$
$337$	−8.74411e8	−1.24455	−0.622273	+	0.782801i	$0.713791\pi$
$338$	−2.17713e9	−3.06673
$339$	0	0
$340$	4.53500e8	0.625751
$341$	1.25535e8	0.171445
$342$	0	0
$343$	−6.46367e8	−0.864868
$344$	3.10882e8	0.411757
$345$	0	0
$346$	−2.15097e9	−2.79169
$347$	3.33399e8	0.428362	0.214181	−	0.976794i	$-0.431292\pi$
$347$	3.33399e8	0.428362	0.214181	+	0.976794i	$0.431292\pi$
$348$	0	0
$349$	4.76388e8	0.599891	0.299945	−	0.953956i	$-0.403032\pi$
$349$	4.76388e8	0.599891	0.299945	+	0.953956i	$0.403032\pi$
$350$	−1.27294e9	−1.58697
$351$	0	0
$352$	8.49421e8	1.03806
$353$	−5.52768e8	−0.668854	−0.334427	−	0.942422i	$-0.608543\pi$
$353$	−5.52768e8	−0.668854	−0.334427	+	0.942422i	$0.608543\pi$
$354$	0	0
$355$	−1.09543e9	−1.29953
$356$	1.89612e9	2.22737
$357$	0	0
$358$	−1.52149e9	−1.75258
$359$	−5.27376e8	−0.601575	−0.300787	−	0.953691i	$-0.597249\pi$
$359$	−5.27376e8	−0.601575	−0.300787	+	0.953691i	$0.597249\pi$
$360$	0	0
$361$	1.60479e9	1.79532
$362$	1.79169e9	1.98510
$363$	0	0
$364$	−4.37160e9	−4.75101
$365$	2.27887e9	2.45299
$366$	0	0
$367$	−1.51541e8	−0.160029	−0.0800144	−	0.996794i	$-0.525497\pi$
$367$	−1.51541e8	−0.160029	−0.0800144	+	0.996794i	$0.525497\pi$
$368$	−5.26922e8	−0.551161
$369$	0	0
$370$	1.42728e9	1.46488
$371$	−4.18883e8	−0.425877
$372$	0	0
$373$	1.07529e9	1.07287	0.536434	−	0.843942i	$-0.319771\pi$
$373$	1.07529e9	1.07287	0.536434	+	0.843942i	$0.319771\pi$
$374$	1.03438e8	0.102242
$375$	0	0
$376$	1.88978e9	1.83339
$377$	1.36897e9	1.31582
$378$	0	0
$379$	−9.53596e8	−0.899761	−0.449881	−	0.893089i	$-0.648534\pi$
$379$	−9.53596e8	−0.899761	−0.449881	+	0.893089i	$0.648534\pi$
$380$	−6.32417e9	−5.91236
$381$	0	0
$382$	−2.07587e9	−1.90536
$383$	1.16624e9	1.06070	0.530352	−	0.847778i	$-0.322060\pi$
$383$	1.16624e9	1.06070	0.530352	+	0.847778i	$0.322060\pi$
$384$	0	0
$385$	−4.92563e8	−0.439896
$386$	1.34033e7	0.0118620
$387$	0	0
$388$	−1.47116e9	−1.27864
$389$	−1.03668e9	−0.892940	−0.446470	−	0.894799i	$-0.647319\pi$
$389$	−1.03668e9	−0.892940	−0.446470	+	0.894799i	$0.647319\pi$
$390$	0	0
$391$	−3.32325e7	−0.0281154
$392$	−8.23839e8	−0.690782
$393$	0	0
$394$	−2.60448e9	−2.14528
$395$	−1.24592e9	−1.01718
$396$	0	0
$397$	1.00736e9	0.808012	0.404006	−	0.914756i	$-0.367617\pi$
$397$	1.00736e9	0.808012	0.404006	+	0.914756i	$0.367617\pi$
$398$	−3.81995e9	−3.03715
$399$	0	0
$400$	3.33515e9	2.60558
$401$	2.40582e8	0.186320	0.0931598	−	0.995651i	$-0.470303\pi$
$401$	2.40582e8	0.186320	0.0931598	+	0.995651i	$0.470303\pi$
$402$	0	0
$403$	1.20476e9	0.916925
$404$	−4.21625e9	−3.18120
$405$	0	0
$406$	2.32478e9	1.72402
$407$	2.36896e8	0.174172
$408$	0	0
$409$	−6.86188e8	−0.495920	−0.247960	−	0.968770i	$-0.579760\pi$
$409$	−6.86188e8	−0.495920	−0.247960	+	0.968770i	$0.579760\pi$
$410$	3.09005e9	2.21423
$411$	0	0
$412$	6.53115e9	4.60097
$413$	8.18180e8	0.571510
$414$	0	0
$415$	−1.08156e9	−0.742818
$416$	8.15191e9	5.55179
$417$	0	0
$418$	−1.44247e9	−0.966026
$419$	−5.29018e8	−0.351335	−0.175668	−	0.984450i	$-0.556208\pi$
$419$	−5.29018e8	−0.351335	−0.175668	+	0.984450i	$0.556208\pi$
$420$	0	0
$421$	−2.33887e8	−0.152763	−0.0763815	−	0.997079i	$-0.524337\pi$
$421$	−2.33887e8	−0.152763	−0.0763815	+	0.997079i	$0.524337\pi$
$422$	1.54152e9	0.998514
$423$	0	0
$424$	1.94295e9	1.23789
$425$	2.10345e8	0.132914
$426$	0	0
$427$	2.47614e9	1.53914
$428$	5.19398e9	3.20219
$429$	0	0
$430$	5.37186e8	0.325825
$431$	2.41695e9	1.45411	0.727056	−	0.686578i	$-0.240888\pi$
$431$	2.41695e9	1.45411	0.727056	+	0.686578i	$0.240888\pi$
$432$	0	0
$433$	1.22095e8	0.0722755	0.0361377	−	0.999347i	$-0.488494\pi$
$433$	1.22095e8	0.0722755	0.0361377	+	0.999347i	$0.488494\pi$
$434$	2.04593e9	1.20137
$435$	0	0
$436$	−8.30287e9	−4.79762
$437$	4.63434e8	0.265646
$438$	0	0
$439$	−1.85560e9	−1.04679	−0.523393	−	0.852092i	$-0.675334\pi$
$439$	−1.85560e9	−1.04679	−0.523393	+	0.852092i	$0.675334\pi$
$440$	2.28471e9	1.27864
$441$	0	0
$442$	9.92698e8	0.546813
$443$	−1.15786e9	−0.632763	−0.316382	−	0.948632i	$-0.602468\pi$
$443$	−1.15786e9	−0.632763	−0.316382	+	0.948632i	$0.602468\pi$
$444$	0	0
$445$	2.05033e9	1.10297
$446$	4.32319e9	2.30745
$447$	0	0
$448$	6.56494e9	3.44951
$449$	−5.80335e8	−0.302564	−0.151282	−	0.988491i	$-0.548340\pi$
$449$	−5.80335e8	−0.302564	−0.151282	+	0.988491i	$0.548340\pi$
$450$	0	0
$451$	5.12881e8	0.263268
$452$	2.23469e9	1.13824
$453$	0	0
$454$	1.13620e9	0.569850
$455$	−4.72715e9	−2.35266
$456$	0	0
$457$	8.26780e8	0.405213	0.202606	−	0.979260i	$-0.435059\pi$
$457$	8.26780e8	0.405213	0.202606	+	0.979260i	$0.435059\pi$
$458$	7.88359e8	0.383438
$459$	0	0
$460$	−1.17296e9	−0.561865
$461$	−3.29439e9	−1.56611	−0.783054	−	0.621954i	$-0.786339\pi$
$461$	−3.29439e9	−1.56611	−0.783054	+	0.621954i	$0.786339\pi$
$462$	0	0
$463$	3.02380e9	1.41586	0.707928	−	0.706285i	$-0.249630\pi$
$463$	3.02380e9	1.41586	0.707928	+	0.706285i	$0.249630\pi$
$464$	−6.09101e9	−2.83059
$465$	0	0
$466$	−3.84021e9	−1.75794
$467$	−1.33310e9	−0.605695	−0.302847	−	0.953039i	$-0.597937\pi$
$467$	−1.33310e9	−0.605695	−0.302847	+	0.953039i	$0.597937\pi$
$468$	0	0
$469$	−8.87327e7	−0.0397172
$470$	3.26543e9	1.45077
$471$	0	0
$472$	−3.79505e9	−1.66120
$473$	8.91609e7	0.0387401
$474$	0	0
$475$	−2.93330e9	−1.25583
$476$	1.22674e9	0.521350
$477$	0	0
$478$	4.82468e8	0.202055
$479$	3.39632e9	1.41200	0.705999	−	0.708213i	$-0.250498\pi$
$479$	3.39632e9	1.41200	0.705999	+	0.708213i	$0.250498\pi$
$480$	0	0
$481$	2.27350e9	0.931509
$482$	6.55373e8	0.266578
$483$	0	0
$484$	6.05971e8	0.242937
$485$	−1.59081e9	−0.633172
$486$	0	0
$487$	2.21807e9	0.870209	0.435104	−	0.900380i	$-0.356711\pi$
$487$	2.21807e9	0.870209	0.435104	+	0.900380i	$0.356711\pi$
$488$	−1.14853e10	−4.47378
$489$	0	0
$490$	−1.42354e9	−0.546619
$491$	−1.91361e9	−0.729570	−0.364785	−	0.931092i	$-0.618858\pi$
$491$	−1.91361e9	−0.729570	−0.364785	+	0.931092i	$0.618858\pi$
$492$	0	0
$493$	−3.84154e8	−0.144392
$494$	−1.38434e10	−5.16652
$495$	0	0
$496$	−5.36041e9	−1.97248
$497$	−2.96320e9	−1.08271
$498$	0	0
$499$	−1.61066e8	−0.0580298	−0.0290149	−	0.999579i	$-0.509237\pi$
$499$	−1.61066e8	−0.0580298	−0.0290149	+	0.999579i	$0.509237\pi$
$500$	−2.45990e9	−0.880080
$501$	0	0
$502$	−1.06611e9	−0.376132
$503$	4.64492e9	1.62739	0.813693	−	0.581295i	$-0.197454\pi$
$503$	4.64492e9	1.62739	0.813693	+	0.581295i	$0.197454\pi$
$504$	0	0
$505$	−4.55916e9	−1.57530
$506$	−2.67539e8	−0.0918037
$507$	0	0
$508$	−8.45963e9	−2.86305
$509$	4.63019e9	1.55628	0.778138	−	0.628093i	$-0.216164\pi$
$509$	4.63019e9	1.55628	0.778138	+	0.628093i	$0.216164\pi$
$510$	0	0
$511$	6.16449e9	2.04373
$512$	−2.50931e9	−0.826247
$513$	0	0
$514$	−2.29474e9	−0.745353
$515$	7.06233e9	2.27836
$516$	0	0
$517$	5.41990e8	0.172494
$518$	3.86087e9	1.22048
$519$	0	0
$520$	2.19264e10	6.83842
$521$	1.93785e9	0.600328	0.300164	−	0.953888i	$-0.402959\pi$
$521$	1.93785e9	0.600328	0.300164	+	0.953888i	$0.402959\pi$
$522$	0	0
$523$	3.70832e9	1.13350	0.566750	−	0.823890i	$-0.308200\pi$
$523$	3.70832e9	1.13350	0.566750	+	0.823890i	$0.308200\pi$
$524$	−1.86152e9	−0.565208
$525$	0	0
$526$	−2.59564e8	−0.0777670
$527$	−3.38076e8	−0.100618
$528$	0	0
$529$	−3.31887e9	−0.974755
$530$	3.35730e9	0.979546
$531$	0	0
$532$	−1.71072e10	−4.92594
$533$	4.92213e9	1.40802
$534$	0	0
$535$	5.61641e9	1.58570
$536$	4.11578e8	0.115445
$537$	0	0
$538$	1.29636e10	3.58912
$539$	−2.36277e8	−0.0649921
$540$	0	0
$541$	−2.58883e9	−0.702933	−0.351466	−	0.936200i	$-0.614317\pi$
$541$	−2.58883e9	−0.702933	−0.351466	+	0.936200i	$0.614317\pi$
$542$	−7.02738e9	−1.89582
$543$	0	0
$544$	−2.28756e9	−0.609223
$545$	−8.97814e9	−2.37574
$546$	0	0
$547$	9.24029e8	0.241396	0.120698	−	0.992689i	$-0.461487\pi$
$547$	9.24029e8	0.241396	0.120698	+	0.992689i	$0.461487\pi$
$548$	−5.57560e9	−1.44730
$549$	0	0
$550$	1.69338e9	0.433997
$551$	5.35712e9	1.36427
$552$	0	0
$553$	−3.37028e9	−0.847476
$554$	2.82220e9	0.705186
$555$	0	0
$556$	−1.69750e10	−4.18840
$557$	5.26554e9	1.29107	0.645535	−	0.763731i	$-0.276635\pi$
$557$	5.26554e9	1.29107	0.645535	+	0.763731i	$0.276635\pi$
$558$	0	0
$559$	8.55679e8	0.207190
$560$	2.10327e10	5.06102
$561$	0	0
$562$	1.73659e9	0.412685
$563$	6.92307e9	1.63500	0.817502	−	0.575925i	$-0.195358\pi$
$563$	6.92307e9	1.63500	0.817502	+	0.575925i	$0.195358\pi$
$564$	0	0
$565$	2.41644e9	0.563645
$566$	−4.74152e9	−1.09916
$567$	0	0
$568$	1.37445e10	3.14710
$569$	−5.11524e9	−1.16405	−0.582027	−	0.813169i	$-0.697740\pi$
$569$	−5.11524e9	−1.16405	−0.582027	+	0.813169i	$0.697740\pi$
$570$	0	0
$571$	−5.53148e9	−1.24341	−0.621706	−	0.783251i	$-0.713560\pi$
$571$	−5.53148e9	−1.24341	−0.621706	+	0.783251i	$0.713560\pi$
$572$	5.81552e9	1.29928
$573$	0	0
$574$	8.35878e9	1.84481
$575$	−5.44049e8	−0.119344
$576$	0	0
$577$	2.11390e9	0.458110	0.229055	−	0.973414i	$-0.426436\pi$
$577$	2.11390e9	0.458110	0.229055	+	0.973414i	$0.426436\pi$
$578$	8.61788e9	1.85632
$579$	0	0
$580$	−1.35590e10	−2.88555
$581$	−2.92568e9	−0.618886
$582$	0	0
$583$	5.57238e8	0.116466
$584$	−2.85934e10	−5.94047
$585$	0	0
$586$	−1.28471e10	−2.63732
$587$	6.37660e9	1.30124	0.650618	−	0.759405i	$-0.274510\pi$
$587$	6.37660e9	1.30124	0.650618	+	0.759405i	$0.274510\pi$
$588$	0	0
$589$	4.71455e9	0.950685
$590$	−6.55763e9	−1.31451
$591$	0	0
$592$	−1.01156e10	−2.00385
$593$	−3.35490e9	−0.660676	−0.330338	−	0.943863i	$-0.607163\pi$
$593$	−3.35490e9	−0.660676	−0.330338	+	0.943863i	$0.607163\pi$
$594$	0	0
$595$	1.32652e9	0.258168
$596$	−2.20107e10	−4.25864
$597$	0	0
$598$	−2.56758e9	−0.490986
$599$	1.01151e10	1.92299	0.961497	−	0.274817i	$-0.0886173\pi$
$599$	1.01151e10	1.92299	0.961497	+	0.274817i	$0.0886173\pi$
$600$	0	0
$601$	−4.39918e9	−0.826629	−0.413315	−	0.910588i	$-0.635629\pi$
$601$	−4.39918e9	−0.826629	−0.413315	+	0.910588i	$0.635629\pi$
$602$	1.45312e9	0.271465
$603$	0	0
$604$	1.78115e10	3.28905
$605$	6.55254e8	0.120300
$606$	0	0
$607$	−6.70282e9	−1.21646	−0.608229	−	0.793761i	$-0.708120\pi$
$607$	−6.70282e9	−1.21646	−0.608229	+	0.793761i	$0.708120\pi$
$608$	3.19006e10	5.75620
$609$	0	0
$610$	−1.98460e10	−3.54013
$611$	5.20149e9	0.922536
$612$	0	0
$613$	5.04966e9	0.885423	0.442711	−	0.896664i	$-0.354017\pi$
$613$	5.04966e9	0.885423	0.442711	+	0.896664i	$0.354017\pi$
$614$	−1.94897e9	−0.339794
$615$	0	0
$616$	6.18027e9	1.06531
$617$	−1.13969e10	−1.95338	−0.976692	−	0.214647i	$-0.931140\pi$
$617$	−1.13969e10	−1.95338	−0.976692	+	0.214647i	$0.931140\pi$
$618$	0	0
$619$	−9.95788e9	−1.68752	−0.843761	−	0.536719i	$-0.819663\pi$
$619$	−9.95788e9	−1.68752	−0.843761	+	0.536719i	$0.819663\pi$
$620$	−1.19326e10	−2.01078
$621$	0	0
$622$	1.91806e10	3.19591
$623$	5.54627e9	0.918953
$624$	0	0
$625$	−7.24448e9	−1.18694
$626$	1.19485e10	1.94671
$627$	0	0
$628$	−4.21495e9	−0.679100
$629$	−6.37982e8	−0.102219
$630$	0	0
$631$	9.44901e9	1.49721	0.748606	−	0.663015i	$-0.230723\pi$
$631$	9.44901e9	1.49721	0.748606	+	0.663015i	$0.230723\pi$
$632$	1.56327e10	2.46334
$633$	0	0
$634$	2.18393e10	3.40351
$635$	−9.14766e9	−1.41776
$636$	0	0
$637$	−2.26756e9	−0.347592
$638$	−3.09264e9	−0.471474
$639$	0	0
$640$	−2.24033e10	−3.37817
$641$	−3.14057e9	−0.470983	−0.235492	−	0.971876i	$-0.575670\pi$
$641$	−3.14057e9	−0.470983	−0.235492	+	0.971876i	$0.575670\pi$
$642$	0	0
$643$	−1.04904e10	−1.55616	−0.778079	−	0.628166i	$-0.783806\pi$
$643$	−1.04904e10	−1.55616	−0.778079	+	0.628166i	$0.783806\pi$
$644$	−3.17293e9	−0.468123
$645$	0	0
$646$	3.88469e9	0.566947
$647$	−7.66143e9	−1.11210	−0.556051	−	0.831148i	$-0.687684\pi$
$647$	−7.66143e9	−1.11210	−0.556051	+	0.831148i	$0.687684\pi$
$648$	0	0
$649$	−1.08842e9	−0.156293
$650$	1.62515e10	2.32111
$651$	0	0
$652$	6.63580e9	0.937620
$653$	−3.77500e9	−0.530544	−0.265272	−	0.964174i	$-0.585462\pi$
$653$	−3.77500e9	−0.530544	−0.265272	+	0.964174i	$0.585462\pi$
$654$	0	0
$655$	−2.01292e9	−0.279886
$656$	−2.19003e10	−3.02891
$657$	0	0
$658$	8.83319e9	1.20872
$659$	1.33044e10	1.81091	0.905457	−	0.424439i	$-0.139529\pi$
$659$	1.33044e10	1.81091	0.905457	+	0.424439i	$0.139529\pi$
$660$	0	0
$661$	−1.88734e9	−0.254182	−0.127091	−	0.991891i	$-0.540564\pi$
$661$	−1.88734e9	−0.254182	−0.127091	+	0.991891i	$0.540564\pi$
$662$	−1.29599e10	−1.73620
$663$	0	0
$664$	1.35705e10	1.79890
$665$	−1.84986e10	−2.43928
$666$	0	0
$667$	9.93602e8	0.129650
$668$	−8.96780e9	−1.16404
$669$	0	0
$670$	7.11183e8	0.0913523
$671$	−3.29400e9	−0.420915
$672$	0	0
$673$	3.67086e9	0.464211	0.232105	−	0.972691i	$-0.425439\pi$
$673$	3.67086e9	0.464211	0.232105	+	0.972691i	$0.425439\pi$
$674$	1.89579e10	2.38495
$675$	0	0
$676$	3.43483e10	4.27653
$677$	−9.61586e9	−1.19104	−0.595522	−	0.803339i	$-0.703055\pi$
$677$	−9.61586e9	−1.19104	−0.595522	+	0.803339i	$0.703055\pi$
$678$	0	0
$679$	−4.30323e9	−0.527533
$680$	−6.15292e9	−0.750412
$681$	0	0
$682$	−2.72169e9	−0.328544
$683$	−5.53540e9	−0.664778	−0.332389	−	0.943142i	$-0.607855\pi$
$683$	−5.53540e9	−0.664778	−0.332389	+	0.943142i	$0.607855\pi$
$684$	0	0
$685$	−6.02907e9	−0.716693
$686$	1.40137e10	1.65737
$687$	0	0
$688$	−3.80722e9	−0.445706
$689$	5.34783e9	0.622888
$690$	0	0
$691$	−2.33283e9	−0.268973	−0.134487	−	0.990915i	$-0.542939\pi$
$691$	−2.33283e9	−0.268973	−0.134487	+	0.990915i	$0.542939\pi$
$692$	3.39356e10	3.89300
$693$	0	0
$694$	−7.22834e9	−0.820882
$695$	−1.83556e10	−2.07406
$696$	0	0
$697$	−1.38123e9	−0.154508
$698$	−1.03285e10	−1.14959
$699$	0	0
$700$	2.00830e10	2.21302
$701$	3.70901e9	0.406673	0.203336	−	0.979109i	$-0.434822\pi$
$701$	3.70901e9	0.406673	0.203336	+	0.979109i	$0.434822\pi$
$702$	0	0
$703$	8.89680e9	0.965807
$704$	−8.73330e9	−0.943353
$705$	0	0
$706$	1.19844e10	1.28174
$707$	−1.23328e10	−1.31248
$708$	0	0
$709$	−1.38939e10	−1.46407	−0.732037	−	0.681264i	$-0.761430\pi$
$709$	−1.38939e10	−1.46407	−0.732037	+	0.681264i	$0.761430\pi$
$710$	2.37497e10	2.49031
$711$	0	0
$712$	−2.57259e10	−2.67110
$713$	8.74422e8	0.0903458
$714$	0	0
$715$	6.28849e9	0.643392
$716$	2.40043e10	2.44396
$717$	0	0
$718$	1.14339e10	1.15281
$719$	−9.01195e9	−0.904206	−0.452103	−	0.891966i	$-0.649326\pi$
$719$	−9.01195e9	−0.904206	−0.452103	+	0.891966i	$0.649326\pi$
$720$	0	0
$721$	1.91040e10	1.89824
$722$	−3.47930e10	−3.44043
$723$	0	0
$724$	−2.82673e10	−2.76821
$725$	−6.28899e9	−0.612912
$726$	0	0
$727$	−1.03734e9	−0.100127	−0.0500633	−	0.998746i	$-0.515942\pi$
$727$	−1.03734e9	−0.100127	−0.0500633	+	0.998746i	$0.515942\pi$
$728$	5.93122e10	5.69750
$729$	0	0
$730$	−4.94077e10	−4.70072
$731$	−2.40118e8	−0.0227360
$732$	0	0
$733$	−1.22466e10	−1.14856	−0.574278	−	0.818660i	$-0.694717\pi$
$733$	−1.22466e10	−1.14856	−0.574278	+	0.818660i	$0.694717\pi$
$734$	3.28552e9	0.306667
$735$	0	0
$736$	5.91670e9	0.547025
$737$	1.18041e8	0.0108616
$738$	0	0
$739$	1.16677e10	1.06348	0.531741	−	0.846907i	$-0.321538\pi$
$739$	1.16677e10	1.06348	0.531741	+	0.846907i	$0.321538\pi$
$740$	−2.25180e10	−2.04277
$741$	0	0
$742$	9.08170e9	0.816119
$743$	−6.73431e9	−0.602327	−0.301163	−	0.953573i	$-0.597375\pi$
$743$	−6.73431e9	−0.602327	−0.301163	+	0.953573i	$0.597375\pi$
$744$	0	0
$745$	−2.38008e10	−2.10884
$746$	−2.33132e10	−2.05596
$747$	0	0
$748$	−1.63193e9	−0.142576
$749$	1.51927e10	1.32114
$750$	0	0
$751$	1.54867e10	1.33419	0.667096	−	0.744972i	$-0.267537\pi$
$751$	1.54867e10	1.33419	0.667096	+	0.744972i	$0.267537\pi$
$752$	−2.31433e10	−1.98455
$753$	0	0
$754$	−2.96802e10	−2.52155
$755$	1.92601e10	1.62871
$756$	0	0
$757$	4.38064e9	0.367030	0.183515	−	0.983017i	$-0.441252\pi$
$757$	4.38064e9	0.367030	0.183515	+	0.983017i	$0.441252\pi$
$758$	2.06747e10	1.72424
$759$	0	0
$760$	8.58038e10	7.09021
$761$	2.03263e10	1.67191	0.835953	−	0.548801i	$-0.184916\pi$
$761$	2.03263e10	1.67191	0.835953	+	0.548801i	$0.184916\pi$
$762$	0	0
$763$	−2.42864e10	−1.97937
$764$	3.27507e10	2.65702
$765$	0	0
$766$	−2.52850e10	−2.03265
$767$	−1.04456e10	−0.835891
$768$	0	0
$769$	−7.96648e8	−0.0631720	−0.0315860	−	0.999501i	$-0.510056\pi$
$769$	−7.96648e8	−0.0631720	−0.0315860	+	0.999501i	$0.510056\pi$
$770$	1.06791e10	0.842983
$771$	0	0
$772$	−2.11463e8	−0.0165415
$773$	−6.97345e9	−0.543025	−0.271512	−	0.962435i	$-0.587524\pi$
$773$	−6.97345e9	−0.543025	−0.271512	+	0.962435i	$0.587524\pi$
$774$	0	0
$775$	−5.53465e9	−0.427104
$776$	1.99601e10	1.53337
$777$	0	0
$778$	2.24761e10	1.71116
$779$	1.92616e10	1.45986
$780$	0	0
$781$	3.94192e9	0.296094
$782$	7.20505e8	0.0538782
$783$	0	0
$784$	1.00892e10	0.747736
$785$	−4.55775e9	−0.336285
$786$	0	0
$787$	1.08404e10	0.792747	0.396374	−	0.918089i	$-0.370268\pi$
$787$	1.08404e10	0.792747	0.396374	+	0.918089i	$0.370268\pi$
$788$	4.10906e10	2.99158
$789$	0	0
$790$	2.70124e10	1.94925
$791$	6.53660e9	0.469606
$792$	0	0
$793$	−3.16126e10	−2.25115
$794$	−2.18403e10	−1.54841
$795$	0	0
$796$	6.02669e10	4.23529
$797$	−9.85652e9	−0.689635	−0.344818	−	0.938670i	$-0.612059\pi$
$797$	−9.85652e9	−0.689635	−0.344818	+	0.938670i	$0.612059\pi$
$798$	0	0
$799$	−1.45962e9	−0.101234
$800$	−3.74497e10	−2.58603
$801$	0	0
$802$	−5.21601e9	−0.357049
$803$	−8.20058e9	−0.558908
$804$	0	0
$805$	−3.43098e9	−0.231811
$806$	−2.61201e10	−1.75713
$807$	0	0
$808$	5.72044e10	3.81496
$809$	−7.96113e8	−0.0528634	−0.0264317	−	0.999651i	$-0.508414\pi$
$809$	−7.96113e8	−0.0528634	−0.0264317	+	0.999651i	$0.508414\pi$
$810$	0	0
$811$	−8.04789e8	−0.0529796	−0.0264898	−	0.999649i	$-0.508433\pi$
$811$	−8.04789e8	−0.0529796	−0.0264898	+	0.999649i	$0.508433\pi$
$812$	−3.66778e10	−2.40413
$813$	0	0
$814$	−5.13609e9	−0.333770
$815$	7.17549e9	0.464302
$816$	0	0
$817$	3.34850e9	0.214819
$818$	1.48771e10	0.950344
$819$	0	0
$820$	−4.87515e10	−3.08773
$821$	−4.67177e9	−0.294632	−0.147316	−	0.989089i	$-0.547063\pi$
$821$	−4.67177e9	−0.294632	−0.147316	+	0.989089i	$0.547063\pi$
$822$	0	0
$823$	1.73249e10	1.08335	0.541677	−	0.840587i	$-0.317790\pi$
$823$	1.73249e10	1.08335	0.541677	+	0.840587i	$0.317790\pi$
$824$	−8.86122e10	−5.51757
$825$	0	0
$826$	−1.77388e10	−1.09520
$827$	−6.40462e9	−0.393753	−0.196876	−	0.980428i	$-0.563080\pi$
$827$	−6.40462e9	−0.393753	−0.196876	+	0.980428i	$0.563080\pi$
$828$	0	0
$829$	1.69868e10	1.03555	0.517773	−	0.855518i	$-0.326761\pi$
$829$	1.69868e10	1.03555	0.517773	+	0.855518i	$0.326761\pi$
$830$	2.34490e10	1.42348
$831$	0	0
$832$	−8.38137e10	−5.04526
$833$	6.36313e8	0.0381429
$834$	0	0
$835$	−9.69715e9	−0.576423
$836$	2.27577e10	1.34712
$837$	0	0
$838$	1.14695e10	0.673272
$839$	−2.07072e10	−1.21047	−0.605237	−	0.796045i	$-0.706922\pi$
$839$	−2.07072e10	−1.21047	−0.605237	+	0.796045i	$0.706922\pi$
$840$	0	0
$841$	−5.76423e9	−0.334160
$842$	5.07084e9	0.292743
$843$	0	0
$844$	−2.43203e10	−1.39242
$845$	3.71418e10	2.11770
$846$	0	0
$847$	1.77250e9	0.100229
$848$	−2.37944e10	−1.33995
$849$	0	0
$850$	−4.56043e9	−0.254706
$851$	1.65012e9	0.0917828
$852$	0	0
$853$	6.26496e9	0.345619	0.172809	−	0.984955i	$-0.444716\pi$
$853$	6.26496e9	0.345619	0.172809	+	0.984955i	$0.444716\pi$
$854$	−5.36846e10	−2.94949
$855$	0	0
$856$	−7.04700e10	−3.84013
$857$	1.80433e10	0.979227	0.489613	−	0.871940i	$-0.337138\pi$
$857$	1.80433e10	0.979227	0.489613	+	0.871940i	$0.337138\pi$
$858$	0	0
$859$	2.29065e10	1.23306	0.616529	−	0.787332i	$-0.288538\pi$
$859$	2.29065e10	1.23306	0.616529	+	0.787332i	$0.288538\pi$
$860$	−8.47512e9	−0.454361
$861$	0	0
$862$	−5.24014e10	−2.78655
$863$	−1.94756e10	−1.03146	−0.515731	−	0.856751i	$-0.672480\pi$
$863$	−1.94756e10	−1.03146	−0.515731	+	0.856751i	$0.672480\pi$
$864$	0	0
$865$	3.66956e10	1.92778
$866$	−2.64711e9	−0.138503
$867$	0	0
$868$	−3.22784e10	−1.67530
$869$	4.48346e9	0.231763
$870$	0	0
$871$	1.13284e9	0.0580904
$872$	1.12650e11	5.75339
$873$	0	0
$874$	−1.00476e10	−0.509064
$875$	−7.19535e9	−0.363098
$876$	0	0
$877$	−1.05068e10	−0.525981	−0.262990	−	0.964798i	$-0.584709\pi$
$877$	−1.05068e10	−0.525981	−0.262990	+	0.964798i	$0.584709\pi$
$878$	4.02307e10	2.00598
$879$	0	0
$880$	−2.79797e10	−1.38406
$881$	−6.02366e9	−0.296787	−0.148393	−	0.988928i	$-0.547410\pi$
$881$	−6.02366e9	−0.296787	−0.148393	+	0.988928i	$0.547410\pi$
$882$	0	0
$883$	1.41279e10	0.690582	0.345291	−	0.938496i	$-0.387780\pi$
$883$	1.41279e10	0.690582	0.345291	+	0.938496i	$0.387780\pi$
$884$	−1.56617e10	−0.762528
$885$	0	0
$886$	2.51032e10	1.21258
$887$	−8.67025e9	−0.417156	−0.208578	−	0.978006i	$-0.566884\pi$
$887$	−8.67025e9	−0.417156	−0.208578	+	0.978006i	$0.566884\pi$
$888$	0	0
$889$	−2.47449e10	−1.18122
$890$	−4.44528e10	−2.11365
$891$	0	0
$892$	−6.82065e10	−3.21772
$893$	2.03548e10	0.956503
$894$	0	0
$895$	2.59566e10	1.21023
$896$	−6.06021e10	−2.81455
$897$	0	0
$898$	1.25821e10	0.579810
$899$	1.01080e10	0.463987
$900$	0	0
$901$	−1.50069e9	−0.0683524
$902$	−1.11196e10	−0.504507
$903$	0	0
$904$	−3.03194e10	−1.36499
$905$	−3.05663e10	−1.37080
$906$	0	0
$907$	−1.57873e10	−0.702557	−0.351279	−	0.936271i	$-0.614253\pi$
$907$	−1.57873e10	−0.702557	−0.351279	+	0.936271i	$0.614253\pi$
$908$	−1.79257e10	−0.794652
$909$	0	0
$910$	1.02488e11	4.50846
$911$	2.97837e10	1.30516	0.652581	−	0.757719i	$-0.273686\pi$
$911$	2.97837e10	1.30516	0.652581	+	0.757719i	$0.273686\pi$
$912$	0	0
$913$	3.89202e9	0.169249
$914$	−1.79252e10	−0.776519
$915$	0	0
$916$	−1.24378e10	−0.534701
$917$	−5.44506e9	−0.233190
$918$	0	0
$919$	2.15438e10	0.915625	0.457812	−	0.889049i	$-0.348633\pi$
$919$	2.15438e10	0.915625	0.457812	+	0.889049i	$0.348633\pi$
$920$	1.59143e10	0.673799
$921$	0	0
$922$	7.14248e10	3.00117
$923$	3.78307e10	1.58358
$924$	0	0
$925$	−1.04444e10	−0.433898
$926$	−6.55582e10	−2.71324
$927$	0	0
$928$	6.83947e10	2.80934
$929$	−3.18712e10	−1.30420	−0.652099	−	0.758134i	$-0.726111\pi$
$929$	−3.18712e10	−1.30420	−0.652099	+	0.758134i	$0.726111\pi$
$930$	0	0
$931$	−8.87354e9	−0.360390
$932$	6.05866e10	2.45144
$933$	0	0
$934$	2.89026e10	1.16071
$935$	−1.76466e9	−0.0706024
$936$	0	0
$937$	4.40711e10	1.75011	0.875055	−	0.484023i	$-0.160825\pi$
$937$	4.40711e10	1.75011	0.875055	+	0.484023i	$0.160825\pi$
$938$	1.92379e9	0.0761111
$939$	0	0
$940$	−5.15184e10	−2.02309
$941$	1.97672e10	0.773358	0.386679	−	0.922214i	$-0.373622\pi$
$941$	1.97672e10	0.773358	0.386679	+	0.922214i	$0.373622\pi$
$942$	0	0
$943$	3.57250e9	0.138734
$944$	4.64762e10	1.79816
$945$	0	0
$946$	−1.93307e9	−0.0742386
$947$	2.39422e10	0.916091	0.458045	−	0.888929i	$-0.348550\pi$
$947$	2.39422e10	0.916091	0.458045	+	0.888929i	$0.348550\pi$
$948$	0	0
$949$	−7.87012e10	−2.98916
$950$	6.35962e10	2.40657
$951$	0	0
$952$	−1.66440e10	−0.625213
$953$	4.61855e10	1.72854	0.864271	−	0.503026i	$-0.167780\pi$
$953$	4.61855e10	1.72854	0.864271	+	0.503026i	$0.167780\pi$
$954$	0	0
$955$	3.54143e10	1.31573
$956$	−7.61184e9	−0.281765
$957$	0	0
$958$	−7.36347e10	−2.70585
$959$	−1.63090e10	−0.597120
$960$	0	0
$961$	−1.86171e10	−0.676674
$962$	−4.92912e10	−1.78507
$963$	0	0
$964$	−1.03397e10	−0.371741
$965$	−2.28661e8	−0.00819120
$966$	0	0
$967$	−5.05460e9	−0.179760	−0.0898802	−	0.995953i	$-0.528648\pi$
$967$	−5.05460e9	−0.179760	−0.0898802	+	0.995953i	$0.528648\pi$
$968$	−8.22158e9	−0.291334
$969$	0	0
$970$	3.44899e10	1.21336
$971$	2.23310e10	0.782782	0.391391	−	0.920224i	$-0.371994\pi$
$971$	2.23310e10	0.782782	0.391391	+	0.920224i	$0.371994\pi$
$972$	0	0
$973$	−4.96529e10	−1.72802
$974$	−4.80894e10	−1.66760
$975$	0	0
$976$	1.40655e11	4.84264
$977$	−4.19940e9	−0.144064	−0.0720321	−	0.997402i	$-0.522948\pi$
$977$	−4.19940e9	−0.144064	−0.0720321	+	0.997402i	$0.522948\pi$
$978$	0	0
$979$	−7.37818e9	−0.251310
$980$	2.24591e10	0.762257
$981$	0	0
$982$	4.14884e10	1.39809
$983$	−4.36025e10	−1.46411	−0.732056	−	0.681244i	$-0.761439\pi$
$983$	−4.36025e10	−1.46411	−0.732056	+	0.681244i	$0.761439\pi$
$984$	0	0
$985$	4.44325e10	1.48140
$986$	8.32875e9	0.276701
$987$	0	0
$988$	2.18406e11	7.20468
$989$	6.21056e8	0.0204147
$990$	0	0
$991$	3.90622e10	1.27497	0.637484	−	0.770463i	$-0.279975\pi$
$991$	3.90622e10	1.27497	0.637484	+	0.770463i	$0.279975\pi$
$992$	6.01910e10	1.95767
$993$	0	0
$994$	6.42443e10	2.07483
$995$	6.51684e10	2.09728
$996$	0	0
$997$	9.58919e9	0.306442	0.153221	−	0.988192i	$-0.451035\pi$
$997$	9.58919e9	0.306442	0.153221	+	0.988192i	$0.451035\pi$
$998$	3.49202e9	0.111204
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.a.f.1.1		4
3.2	odd	2		33.8.a.e.1.4	✓	4
12.11	even	2		528.8.a.r.1.1		4
33.32	even	2		363.8.a.f.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.a.e.1.4	✓	4	3.2	odd	2
99.8.a.f.1.1		4	1.1	even	1	trivial
363.8.a.f.1.1		4	33.32	even	2
528.8.a.r.1.1		4	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	99.a (trivial)

\(f(q)\)	\(=\)	\(q-21.6807 q^{2} +342.055 q^{4} +369.874 q^{5} +1000.53 q^{7} -4640.87 q^{8} +O(q^{10})\)	\(q-21.6807 q^{2} +342.055 q^{4} +369.874 q^{5} +1000.53 q^{7} -4640.87 q^{8} -8019.14 q^{10} -1331.00 q^{11} -12773.6 q^{13} -21692.2 q^{14} +56834.4 q^{16} +3584.50 q^{17} -49986.6 q^{19} +126517. q^{20} +28857.1 q^{22} -9271.17 q^{23} +58681.8 q^{25} +276942. q^{26} +342236. q^{28} -107171. q^{29} -94316.2 q^{31} -638182. q^{32} -77714.5 q^{34} +370070. q^{35} -177984. q^{37} +1.08375e6 q^{38} -1.71654e6 q^{40} -385335. q^{41} -66987.9 q^{43} -455275. q^{44} +201006. q^{46} -407205. q^{47} +177518. q^{49} -1.27227e6 q^{50} -4.36929e6 q^{52} -418661. q^{53} -492302. q^{55} -4.64333e6 q^{56} +2.32355e6 q^{58} +817746. q^{59} +2.47483e6 q^{61} +2.04485e6 q^{62} +6.56146e6 q^{64} -4.72464e6 q^{65} -88685.6 q^{67} +1.22609e6 q^{68} -8.02340e6 q^{70} -2.96162e6 q^{71} +6.16122e6 q^{73} +3.85882e6 q^{74} -1.70982e7 q^{76} -1.33171e6 q^{77} -3.36849e6 q^{79} +2.10216e7 q^{80} +8.35434e6 q^{82} -2.92413e6 q^{83} +1.32581e6 q^{85} +1.45235e6 q^{86} +6.17699e6 q^{88} +5.54333e6 q^{89} -1.27804e7 q^{91} -3.17125e6 q^{92} +8.82850e6 q^{94} -1.84888e7 q^{95} -4.30094e6 q^{97} -3.84873e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 15 q^{2} + 565 q^{4} - 306 q^{5} + 890 q^{7} - 2457 q^{8}+O(q^{10}) \) 4 * q - 15 * q^2 + 565 * q^4 - 306 * q^5 + 890 * q^7 - 2457 * q^8	\( 4 q - 15 q^{2} + 565 q^{4} - 306 q^{5} + 890 q^{7} - 2457 q^{8} - 8946 q^{10} - 5324 q^{11} - 1822 q^{13} - 35340 q^{14} + 65041 q^{16} - 32856 q^{17} - 12784 q^{19} + 4002 q^{20} + 19965 q^{22} - 114858 q^{23} + 72856 q^{25} + 221466 q^{26} + 10112 q^{28} + 104952 q^{29} - 24976 q^{31} - 337761 q^{32} - 741690 q^{34} + 722856 q^{35} - 498856 q^{37} + 897156 q^{38} - 2676930 q^{40} - 734556 q^{41} - 201916 q^{43} - 752015 q^{44} - 3068508 q^{46} - 1995894 q^{47} - 771024 q^{49} - 1632129 q^{50} - 4412266 q^{52} - 929970 q^{53} + 407286 q^{55} - 7224888 q^{56} + 2864322 q^{58} - 1353156 q^{59} + 3998774 q^{61} + 3783264 q^{62} + 1480129 q^{64} - 6612108 q^{65} + 1722008 q^{67} - 1596906 q^{68} - 2751024 q^{70} - 5571858 q^{71} + 5600528 q^{73} + 10907838 q^{74} - 19634884 q^{76} - 1184590 q^{77} - 7710226 q^{79} + 24073794 q^{80} - 11230842 q^{82} - 3431856 q^{83} + 5909484 q^{85} + 25687140 q^{86} + 3270267 q^{88} - 4611528 q^{89} - 9032696 q^{91} - 13608576 q^{92} - 3497436 q^{94} - 21828000 q^{95} + 1401692 q^{97} + 7230081 q^{98}+O(q^{100}) \) 4 * q - 15 * q^2 + 565 * q^4 - 306 * q^5 + 890 * q^7 - 2457 * q^8 - 8946 * q^10 - 5324 * q^11 - 1822 * q^13 - 35340 * q^14 + 65041 * q^16 - 32856 * q^17 - 12784 * q^19 + 4002 * q^20 + 19965 * q^22 - 114858 * q^23 + 72856 * q^25 + 221466 * q^26 + 10112 * q^28 + 104952 * q^29 - 24976 * q^31 - 337761 * q^32 - 741690 * q^34 + 722856 * q^35 - 498856 * q^37 + 897156 * q^38 - 2676930 * q^40 - 734556 * q^41 - 201916 * q^43 - 752015 * q^44 - 3068508 * q^46 - 1995894 * q^47 - 771024 * q^49 - 1632129 * q^50 - 4412266 * q^52 - 929970 * q^53 + 407286 * q^55 - 7224888 * q^56 + 2864322 * q^58 - 1353156 * q^59 + 3998774 * q^61 + 3783264 * q^62 + 1480129 * q^64 - 6612108 * q^65 + 1722008 * q^67 - 1596906 * q^68 - 2751024 * q^70 - 5571858 * q^71 + 5600528 * q^73 + 10907838 * q^74 - 19634884 * q^76 - 1184590 * q^77 - 7710226 * q^79 + 24073794 * q^80 - 11230842 * q^82 - 3431856 * q^83 + 5909484 * q^85 + 25687140 * q^86 + 3270267 * q^88 - 4611528 * q^89 - 9032696 * q^91 - 13608576 * q^92 - 3497436 * q^94 - 21828000 * q^95 + 1401692 * q^97 + 7230081 * q^98

Introduction

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