LMFDB - Embedded newform 99.8.a.e.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:	$0$
Dimension:	$3$
Coefficient field:	3.3.115512.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 70x - 194 $ x^3 - x^2 - 70*x - 194
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-5.30133$ 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)

$f(q)$	$=$	$q-17.9120 q^{2} +192.840 q^{4} -84.6717 q^{5} +1679.06 q^{7} -1161.42 q^{8} +O(q^{10})$	\(q-17.9120 q^{2} +192.840 q^{4} -84.6717 q^{5} +1679.06 q^{7} -1161.42 q^{8} +1516.64 q^{10} +1331.00 q^{11} +14614.0 q^{13} -30075.3 q^{14} -3880.24 q^{16} +28806.7 q^{17} -20668.0 q^{19} -16328.1 q^{20} -23840.9 q^{22} -24408.1 q^{23} -70955.7 q^{25} -261766. q^{26} +323790. q^{28} -44808.9 q^{29} -79797.2 q^{31} +218164. q^{32} -515985. q^{34} -142169. q^{35} +114809. q^{37} +370205. q^{38} +98339.1 q^{40} +124871. q^{41} -182014. q^{43} +256670. q^{44} +437198. q^{46} +1.17849e6 q^{47} +1.99569e6 q^{49} +1.27096e6 q^{50} +2.81817e6 q^{52} +1.08629e6 q^{53} -112698. q^{55} -1.95008e6 q^{56} +802617. q^{58} -1.64390e6 q^{59} +470621. q^{61} +1.42933e6 q^{62} -3.41109e6 q^{64} -1.23739e6 q^{65} +2.85835e6 q^{67} +5.55508e6 q^{68} +2.54653e6 q^{70} -5.01261e6 q^{71} -2.89295e6 q^{73} -2.05646e6 q^{74} -3.98561e6 q^{76} +2.23483e6 q^{77} -530006. q^{79} +328547. q^{80} -2.23670e6 q^{82} +3.43217e6 q^{83} -2.43911e6 q^{85} +3.26023e6 q^{86} -1.54584e6 q^{88} +1.84475e6 q^{89} +2.45378e7 q^{91} -4.70686e6 q^{92} -2.11091e7 q^{94} +1.74999e6 q^{95} +1.81707e6 q^{97} -3.57469e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 9 q^{2} - 15 q^{4} + 444 q^{5} + 1614 q^{7} - 3153 q^{8}+O(q^{10}) $ 3 * q - 9 * q^2 - 15 * q^4 + 444 * q^5 + 1614 * q^7 - 3153 * q^8	\( 3 q - 9 q^{2} - 15 q^{4} + 444 q^{5} + 1614 q^{7} - 3153 q^{8} + 2880 q^{10} + 3993 q^{11} + 20772 q^{13} - 36258 q^{14} + 12225 q^{16} + 14538 q^{17} + 24492 q^{19} - 80112 q^{20} - 11979 q^{22} - 35094 q^{23} + 29121 q^{25} - 203832 q^{26} + 278034 q^{28} + 179862 q^{29} + 288888 q^{31} + 519567 q^{32} - 491586 q^{34} + 532872 q^{35} + 107562 q^{37} + 686328 q^{38} - 237360 q^{40} + 135198 q^{41} + 193536 q^{43} - 19965 q^{44} + 16422 q^{46} + 591486 q^{47} + 4461159 q^{49} + 1192245 q^{50} + 2449992 q^{52} - 79044 q^{53} + 590964 q^{55} - 752658 q^{56} + 2289930 q^{58} - 2532768 q^{59} + 6678792 q^{61} + 2660808 q^{62} - 3966303 q^{64} - 3191832 q^{65} + 7150356 q^{67} + 7821954 q^{68} + 4029120 q^{70} - 1390398 q^{71} - 6429114 q^{73} - 2507478 q^{74} - 7654728 q^{76} + 2148234 q^{77} + 6873186 q^{79} + 7556016 q^{80} - 1774590 q^{82} - 6505596 q^{83} - 16546032 q^{85} + 6519468 q^{86} - 4196643 q^{88} + 8842962 q^{89} + 3066648 q^{91} - 6921990 q^{92} - 24038238 q^{94} + 190968 q^{95} - 1764774 q^{97} - 24377397 q^{98}+O(q^{100}) \) 3 * q - 9 * q^2 - 15 * q^4 + 444 * q^5 + 1614 * q^7 - 3153 * q^8 + 2880 * q^10 + 3993 * q^11 + 20772 * q^13 - 36258 * q^14 + 12225 * q^16 + 14538 * q^17 + 24492 * q^19 - 80112 * q^20 - 11979 * q^22 - 35094 * q^23 + 29121 * q^25 - 203832 * q^26 + 278034 * q^28 + 179862 * q^29 + 288888 * q^31 + 519567 * q^32 - 491586 * q^34 + 532872 * q^35 + 107562 * q^37 + 686328 * q^38 - 237360 * q^40 + 135198 * q^41 + 193536 * q^43 - 19965 * q^44 + 16422 * q^46 + 591486 * q^47 + 4461159 * q^49 + 1192245 * q^50 + 2449992 * q^52 - 79044 * q^53 + 590964 * q^55 - 752658 * q^56 + 2289930 * q^58 - 2532768 * q^59 + 6678792 * q^61 + 2660808 * q^62 - 3966303 * q^64 - 3191832 * q^65 + 7150356 * q^67 + 7821954 * q^68 + 4029120 * q^70 - 1390398 * q^71 - 6429114 * q^73 - 2507478 * q^74 - 7654728 * q^76 + 2148234 * q^77 + 6873186 * q^79 + 7556016 * q^80 - 1774590 * q^82 - 6505596 * q^83 - 16546032 * q^85 + 6519468 * q^86 - 4196643 * q^88 + 8842962 * q^89 + 3066648 * q^91 - 6921990 * q^92 - 24038238 * q^94 + 190968 * q^95 - 1764774 * q^97 - 24377397 * 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 $

$2$	−17.9120	−1.58321	−0.791606	−	0.611031i	$-0.790755\pi$
$2$	−17.9120	−1.58321	−0.791606	+	0.611031i	$0.790755\pi$
$3$	0	0
$3$	0	0
$4$	192.840	1.50656
$5$	−84.6717	−0.302931	−0.151465	−	0.988463i	$-0.548399\pi$
$5$	−84.6717	−0.302931	−0.151465	+	0.988463i	$0.548399\pi$
$6$	0	0
$7$	1679.06	1.85022	0.925109	−	0.379703i	$-0.123974\pi$
$7$	1679.06	1.85022	0.925109	+	0.379703i	$0.123974\pi$
$8$	−1161.42	−0.801997
$9$	0	0
$10$	1516.64	0.479604
$11$	1331.00	0.301511
$11$	1331.00	0.301511
$12$	0	0
$13$	14614.0	1.84488	0.922439	−	0.386143i	$-0.126193\pi$
$13$	14614.0	1.84488	0.922439	+	0.386143i	$0.126193\pi$
$14$	−30075.3	−2.92929
$15$	0	0
$16$	−3880.24	−0.236831
$17$	28806.7	1.42207	0.711036	−	0.703156i	$-0.248226\pi$
$17$	28806.7	1.42207	0.711036	+	0.703156i	$0.248226\pi$
$18$	0	0
$19$	−20668.0	−0.691289	−0.345645	−	0.938365i	$-0.612340\pi$
$19$	−20668.0	−0.691289	−0.345645	+	0.938365i	$0.612340\pi$
$20$	−16328.1	−0.456384
$21$	0	0
$22$	−23840.9	−0.477357
$23$	−24408.1	−0.418299	−0.209149	−	0.977884i	$-0.567070\pi$
$23$	−24408.1	−0.418299	−0.209149	+	0.977884i	$0.567070\pi$
$24$	0	0
$25$	−70955.7	−0.908233
$26$	−261766.	−2.92083
$27$	0	0
$28$	323790.	2.78747
$29$	−44808.9	−0.341170	−0.170585	−	0.985343i	$-0.554566\pi$
$29$	−44808.9	−0.341170	−0.170585	+	0.985343i	$0.554566\pi$
$30$	0	0
$31$	−79797.2	−0.481085	−0.240543	−	0.970639i	$-0.577325\pi$
$31$	−79797.2	−0.481085	−0.240543	+	0.970639i	$0.577325\pi$
$32$	218164.	1.17695
$33$	0	0
$34$	−515985.	−2.25144
$35$	−142169.	−0.560488
$36$	0	0
$37$	114809.	0.372624	0.186312	−	0.982491i	$-0.440346\pi$
$37$	114809.	0.372624	0.186312	+	0.982491i	$0.440346\pi$
$38$	370205.	1.09446
$39$	0	0
$40$	98339.1	0.242950
$41$	124871.	0.282956	0.141478	−	0.989941i	$-0.454814\pi$
$41$	124871.	0.282956	0.141478	+	0.989941i	$0.454814\pi$
$42$	0	0
$43$	−182014.	−0.349112	−0.174556	−	0.984647i	$-0.555849\pi$
$43$	−182014.	−0.349112	−0.174556	+	0.984647i	$0.555849\pi$
$44$	256670.	0.454246
$45$	0	0
$46$	437198.	0.662256
$47$	1.17849e6	1.65570	0.827851	−	0.560948i	$-0.189563\pi$
$47$	1.17849e6	1.65570	0.827851	+	0.560948i	$0.189563\pi$
$48$	0	0
$49$	1.99569e6	2.42330
$50$	1.27096e6	1.43793
$51$	0	0
$52$	2.81817e6	2.77942
$53$	1.08629e6	1.00226	0.501131	−	0.865371i	$-0.332918\pi$
$53$	1.08629e6	1.00226	0.501131	+	0.865371i	$0.332918\pi$
$54$	0	0
$55$	−112698.	−0.0913371
$56$	−1.95008e6	−1.48387
$57$	0	0
$58$	802617.	0.540145
$59$	−1.64390e6	−1.04206	−0.521031	−	0.853538i	$-0.674452\pi$
$59$	−1.64390e6	−1.04206	−0.521031	+	0.853538i	$0.674452\pi$
$60$	0	0
$61$	470621.	0.265471	0.132735	−	0.991151i	$-0.457624\pi$
$61$	470621.	0.265471	0.132735	+	0.991151i	$0.457624\pi$
$62$	1.42933e6	0.761660
$63$	0	0
$64$	−3.41109e6	−1.62653
$65$	−1.23739e6	−0.558870
$66$	0	0
$67$	2.85835e6	1.16106	0.580528	−	0.814240i	$-0.302846\pi$
$67$	2.85835e6	1.16106	0.580528	+	0.814240i	$0.302846\pi$
$68$	5.55508e6	2.14244
$69$	0	0
$70$	2.54653e6	0.887371
$71$	−5.01261e6	−1.66211	−0.831056	−	0.556189i	$-0.812263\pi$
$71$	−5.01261e6	−1.66211	−0.831056	+	0.556189i	$0.812263\pi$
$72$	0	0
$73$	−2.89295e6	−0.870384	−0.435192	−	0.900338i	$-0.643320\pi$
$73$	−2.89295e6	−0.870384	−0.435192	+	0.900338i	$0.643320\pi$
$74$	−2.05646e6	−0.589943
$75$	0	0
$76$	−3.98561e6	−1.04147
$77$	2.23483e6	0.557861
$78$	0	0
$79$	−530006.	−0.120944	−0.0604722	−	0.998170i	$-0.519261\pi$
$79$	−530006.	−0.120944	−0.0604722	+	0.998170i	$0.519261\pi$
$80$	328547.	0.0717435
$81$	0	0
$82$	−2.23670e6	−0.447980
$83$	3.43217e6	0.658864	0.329432	−	0.944179i	$-0.393143\pi$
$83$	3.43217e6	0.658864	0.329432	+	0.944179i	$0.393143\pi$
$84$	0	0
$85$	−2.43911e6	−0.430789
$86$	3.26023e6	0.552719
$87$	0	0
$88$	−1.54584e6	−0.241811
$89$	1.84475e6	0.277378	0.138689	−	0.990336i	$-0.455711\pi$
$89$	1.84475e6	0.277378	0.138689	+	0.990336i	$0.455711\pi$
$90$	0	0
$91$	2.45378e7	3.41342
$92$	−4.70686e6	−0.630194
$93$	0	0
$94$	−2.11091e7	−2.62133
$95$	1.74999e6	0.209413
$96$	0	0
$97$	1.81707e6	0.202148	0.101074	−	0.994879i	$-0.467772\pi$
$97$	1.81707e6	0.202148	0.101074	+	0.994879i	$0.467772\pi$
$98$	−3.57469e7	−3.83660
$99$	0	0
$100$	−1.36831e7	−1.36831
$101$	6.54808e6	0.632396	0.316198	−	0.948693i	$-0.397594\pi$
$101$	6.54808e6	0.632396	0.316198	+	0.948693i	$0.397594\pi$
$102$	0	0
$103$	1.65984e6	0.149670	0.0748350	−	0.997196i	$-0.476157\pi$
$103$	1.65984e6	0.149670	0.0748350	+	0.997196i	$0.476157\pi$
$104$	−1.69729e7	−1.47959
$105$	0	0
$106$	−1.94577e7	−1.58679
$107$	1.21374e7	0.957819	0.478909	−	0.877864i	$-0.341032\pi$
$107$	1.21374e7	0.957819	0.478909	+	0.877864i	$0.341032\pi$
$108$	0	0
$109$	−1.55927e7	−1.15326	−0.576632	−	0.817004i	$-0.695633\pi$
$109$	−1.55927e7	−1.15326	−0.576632	+	0.817004i	$0.695633\pi$
$110$	2.01865e6	0.144606
$111$	0	0
$112$	−6.51515e6	−0.438189
$113$	−1.90097e7	−1.23937	−0.619684	−	0.784851i	$-0.712739\pi$
$113$	−1.90097e7	−1.23937	−0.619684	+	0.784851i	$0.712739\pi$
$114$	0	0
$115$	2.06668e6	0.126716
$116$	−8.64094e6	−0.513994
$117$	0	0
$118$	2.94455e7	1.64980
$119$	4.83681e7	2.63114
$120$	0	0
$121$	1.77156e6	0.0909091
$122$	−8.42977e6	−0.420297
$123$	0	0
$124$	−1.53881e7	−0.724785
$125$	1.26229e7	0.578063
$126$	0	0
$127$	3.78164e7	1.63820	0.819101	−	0.573649i	$-0.194473\pi$
$127$	3.78164e7	1.63820	0.819101	+	0.573649i	$0.194473\pi$
$128$	3.31744e7	1.39820
$129$	0	0
$130$	2.21642e7	0.884811
$131$	−3.18728e6	−0.123871	−0.0619356	−	0.998080i	$-0.519727\pi$
$131$	−3.18728e6	−0.123871	−0.0619356	+	0.998080i	$0.519727\pi$
$132$	0	0
$133$	−3.47027e7	−1.27904
$134$	−5.11988e7	−1.83820
$135$	0	0
$136$	−3.34565e7	−1.14050
$137$	1.19898e7	0.398374	0.199187	−	0.979962i	$-0.436170\pi$
$137$	1.19898e7	0.398374	0.199187	+	0.979962i	$0.436170\pi$
$138$	0	0
$139$	−3.72434e7	−1.17625	−0.588123	−	0.808772i	$-0.700133\pi$
$139$	−3.72434e7	−1.17625	−0.588123	+	0.808772i	$0.700133\pi$
$140$	−2.74158e7	−0.844410
$141$	0	0
$142$	8.97860e7	2.63148
$143$	1.94512e7	0.556252
$144$	0	0
$145$	3.79404e6	0.103351
$146$	5.18186e7	1.37800
$147$	0	0
$148$	2.21398e7	0.561381
$149$	2.57274e7	0.637153	0.318577	−	0.947897i	$-0.396795\pi$
$149$	2.57274e7	0.637153	0.318577	+	0.947897i	$0.396795\pi$
$150$	0	0
$151$	6.21116e7	1.46809	0.734046	−	0.679100i	$-0.237630\pi$
$151$	6.21116e7	1.46809	0.734046	+	0.679100i	$0.237630\pi$
$152$	2.40041e7	0.554412
$153$	0	0
$154$	−4.00302e7	−0.883213
$155$	6.75657e6	0.145736
$156$	0	0
$157$	−9.21174e7	−1.89973	−0.949867	−	0.312655i	$-0.898782\pi$
$157$	−9.21174e7	−1.89973	−0.949867	+	0.312655i	$0.898782\pi$
$158$	9.49347e6	0.191481
$159$	0	0
$160$	−1.84723e7	−0.356535
$161$	−4.09827e7	−0.773944
$162$	0	0
$163$	4.45131e7	0.805066	0.402533	−	0.915405i	$-0.368130\pi$
$163$	4.45131e7	0.805066	0.402533	+	0.915405i	$0.368130\pi$
$164$	2.40802e7	0.426292
$165$	0	0
$166$	−6.14771e7	−1.04312
$167$	−9.92107e7	−1.64835	−0.824177	−	0.566332i	$-0.808362\pi$
$167$	−9.92107e7	−1.64835	−0.824177	+	0.566332i	$0.808362\pi$
$168$	0	0
$169$	1.50821e8	2.40357
$170$	4.36893e7	0.682031
$171$	0	0
$172$	−3.50996e7	−0.525959
$173$	1.10605e8	1.62411	0.812053	−	0.583584i	$-0.198350\pi$
$173$	1.10605e8	1.62411	0.812053	+	0.583584i	$0.198350\pi$
$174$	0	0
$175$	−1.19139e8	−1.68043
$176$	−5.16460e6	−0.0714073
$177$	0	0
$178$	−3.30431e7	−0.439148
$179$	1.72547e7	0.224866	0.112433	−	0.993659i	$-0.464136\pi$
$179$	1.72547e7	0.224866	0.112433	+	0.993659i	$0.464136\pi$
$180$	0	0
$181$	−6.38371e6	−0.0800199	−0.0400100	−	0.999199i	$-0.512739\pi$
$181$	−6.38371e6	−0.0800199	−0.0400100	+	0.999199i	$0.512739\pi$
$182$	−4.39521e8	−5.40418
$183$	0	0
$184$	2.83480e7	0.335474
$185$	−9.72110e6	−0.112879
$186$	0	0
$187$	3.83417e7	0.428771
$188$	2.27260e8	2.49442
$189$	0	0
$190$	−3.13459e7	−0.331545
$191$	−5.28928e7	−0.549263	−0.274631	−	0.961550i	$-0.588556\pi$
$191$	−5.28928e7	−0.549263	−0.274631	+	0.961550i	$0.588556\pi$
$192$	0	0
$193$	7.37840e7	0.738774	0.369387	−	0.929276i	$-0.379568\pi$
$193$	7.37840e7	0.738774	0.369387	+	0.929276i	$0.379568\pi$
$194$	−3.25474e7	−0.320044
$195$	0	0
$196$	3.84850e8	3.65086
$197$	−1.54444e8	−1.43926	−0.719632	−	0.694355i	$-0.755690\pi$
$197$	−1.54444e8	−1.43926	−0.719632	+	0.694355i	$0.755690\pi$
$198$	0	0
$199$	1.71708e8	1.54456	0.772282	−	0.635280i	$-0.219115\pi$
$199$	1.71708e8	1.54456	0.772282	+	0.635280i	$0.219115\pi$
$200$	8.24090e7	0.728400
$201$	0	0
$202$	−1.17289e8	−1.00122
$203$	−7.52367e7	−0.631239
$204$	0	0
$205$	−1.05731e7	−0.0857162
$206$	−2.97310e7	−0.236960
$207$	0	0
$208$	−5.67059e7	−0.436925
$209$	−2.75090e7	−0.208432
$210$	0	0
$211$	1.74167e8	1.27638	0.638188	−	0.769881i	$-0.279684\pi$
$211$	1.74167e8	1.27638	0.638188	+	0.769881i	$0.279684\pi$
$212$	2.09481e8	1.50997
$213$	0	0
$214$	−2.17406e8	−1.51643
$215$	1.54114e7	0.105757
$216$	0	0
$217$	−1.33984e8	−0.890112
$218$	2.79297e8	1.82586
$219$	0	0
$220$	−2.17327e7	−0.137605
$221$	4.20981e8	2.62355
$222$	0	0
$223$	−3.30551e7	−0.199605	−0.0998024	−	0.995007i	$-0.531821\pi$
$223$	−3.30551e7	−0.199605	−0.0998024	+	0.995007i	$0.531821\pi$
$224$	3.66310e8	2.17761
$225$	0	0
$226$	3.40502e8	1.96218
$227$	2.39768e7	0.136051	0.0680254	−	0.997684i	$-0.478330\pi$
$227$	2.39768e7	0.136051	0.0680254	+	0.997684i	$0.478330\pi$
$228$	0	0
$229$	5.27005e7	0.289995	0.144997	−	0.989432i	$-0.453683\pi$
$229$	5.27005e7	0.289995	0.144997	+	0.989432i	$0.453683\pi$
$230$	−3.70183e7	−0.200618
$231$	0	0
$232$	5.20417e7	0.273617
$233$	1.28749e8	0.666805	0.333403	−	0.942785i	$-0.391803\pi$
$233$	1.28749e8	0.666805	0.333403	+	0.942785i	$0.391803\pi$
$234$	0	0
$235$	−9.97846e7	−0.501563
$236$	−3.17010e8	−1.56993
$237$	0	0
$238$	−8.66369e8	−4.16566
$239$	−2.07063e8	−0.981093	−0.490547	−	0.871415i	$-0.663203\pi$
$239$	−2.07063e8	−0.981093	−0.490547	+	0.871415i	$0.663203\pi$
$240$	0	0
$241$	1.42333e8	0.655005	0.327503	−	0.944850i	$-0.393793\pi$
$241$	1.42333e8	0.655005	0.327503	+	0.944850i	$0.393793\pi$
$242$	−3.17322e7	−0.143928
$243$	0	0
$244$	9.07546e7	0.399949
$245$	−1.68979e8	−0.734093
$246$	0	0
$247$	−3.02042e8	−1.27534
$248$	9.26777e7	0.385829
$249$	0	0
$250$	−2.26102e8	−0.915196
$251$	−1.95278e8	−0.779464	−0.389732	−	0.920928i	$-0.627432\pi$
$251$	−1.95278e8	−0.779464	−0.389732	+	0.920928i	$0.627432\pi$
$252$	0	0
$253$	−3.24872e7	−0.126122
$254$	−6.77368e8	−2.59362
$255$	0	0
$256$	−1.57601e8	−0.587110
$257$	−1.26071e8	−0.463285	−0.231643	−	0.972801i	$-0.574410\pi$
$257$	−1.26071e8	−0.463285	−0.231643	+	0.972801i	$0.574410\pi$
$258$	0	0
$259$	1.92771e8	0.689435
$260$	−2.38619e8	−0.841973
$261$	0	0
$262$	5.70905e7	0.196114
$263$	−3.01855e7	−0.102318	−0.0511592	−	0.998691i	$-0.516292\pi$
$263$	−3.01855e7	−0.102318	−0.0511592	+	0.998691i	$0.516292\pi$
$264$	0	0
$265$	−9.19783e7	−0.303616
$266$	6.21595e8	2.02499
$267$	0	0
$268$	5.51204e8	1.74920
$269$	1.24498e8	0.389967	0.194984	−	0.980807i	$-0.437535\pi$
$269$	1.24498e8	0.389967	0.194984	+	0.980807i	$0.437535\pi$
$270$	0	0
$271$	−6.31118e8	−1.92627	−0.963136	−	0.269014i	$-0.913302\pi$
$271$	−6.31118e8	−1.92627	−0.963136	+	0.269014i	$0.913302\pi$
$272$	−1.11777e8	−0.336791
$273$	0	0
$274$	−2.14762e8	−0.630710
$275$	−9.44420e7	−0.273843
$276$	0	0
$277$	4.21993e8	1.19296	0.596480	−	0.802628i	$-0.296566\pi$
$277$	4.21993e8	1.19296	0.596480	+	0.802628i	$0.296566\pi$
$278$	6.67105e8	1.86225
$279$	0	0
$280$	1.65117e8	0.449509
$281$	−8.82276e7	−0.237210	−0.118605	−	0.992942i	$-0.537842\pi$
$281$	−8.82276e7	−0.237210	−0.118605	+	0.992942i	$0.537842\pi$
$282$	0	0
$283$	5.13265e8	1.34614	0.673069	−	0.739580i	$-0.264976\pi$
$283$	5.13265e8	1.34614	0.673069	+	0.739580i	$0.264976\pi$
$284$	−9.66633e8	−2.50408
$285$	0	0
$286$	−3.48411e8	−0.880665
$287$	2.09666e8	0.523531
$288$	0	0
$289$	4.19484e8	1.02229
$290$	−6.79590e7	−0.163627
$291$	0	0
$292$	−5.57877e8	−1.31129
$293$	−5.48004e8	−1.27276	−0.636381	−	0.771375i	$-0.719569\pi$
$293$	−5.48004e8	−1.27276	−0.636381	+	0.771375i	$0.719569\pi$
$294$	0	0
$295$	1.39192e8	0.315672
$296$	−1.33341e8	−0.298843
$297$	0	0
$298$	−4.60829e8	−1.00875
$299$	−3.56700e8	−0.771711
$300$	0	0
$301$	−3.05612e8	−0.645933
$302$	−1.11254e9	−2.32430
$303$	0	0
$304$	8.01967e7	0.163719
$305$	−3.98483e7	−0.0804193
$306$	0	0
$307$	2.02567e8	0.399562	0.199781	−	0.979841i	$-0.435977\pi$
$307$	2.02567e8	0.399562	0.199781	+	0.979841i	$0.435977\pi$
$308$	4.30964e8	0.840453
$309$	0	0
$310$	−1.21024e8	−0.230730
$311$	−3.03524e8	−0.572179	−0.286089	−	0.958203i	$-0.592355\pi$
$311$	−3.03524e8	−0.572179	−0.286089	+	0.958203i	$0.592355\pi$
$312$	0	0
$313$	5.20257e6	0.00958987	0.00479494	−	0.999989i	$-0.498474\pi$
$313$	5.20257e6	0.00958987	0.00479494	+	0.999989i	$0.498474\pi$
$314$	1.65001e9	3.00768
$315$	0	0
$316$	−1.02206e8	−0.182210
$317$	1.00853e9	1.77821	0.889104	−	0.457705i	$-0.151328\pi$
$317$	1.00853e9	1.77821	0.889104	+	0.457705i	$0.151328\pi$
$318$	0	0
$319$	−5.96406e7	−0.102867
$320$	2.88823e8	0.492727
$321$	0	0
$322$	7.34082e8	1.22532
$323$	−5.95375e8	−0.983063
$324$	0	0
$325$	−1.03695e9	−1.67558
$326$	−7.97320e8	−1.27459
$327$	0	0
$328$	−1.45028e8	−0.226930
$329$	1.97875e9	3.06341
$330$	0	0
$331$	4.78969e8	0.725954	0.362977	−	0.931798i	$-0.381760\pi$
$331$	4.78969e8	0.725954	0.362977	+	0.931798i	$0.381760\pi$
$332$	6.61860e8	0.992619
$333$	0	0
$334$	1.77706e9	2.60970
$335$	−2.42021e8	−0.351720
$336$	0	0
$337$	−2.29982e8	−0.327333	−0.163667	−	0.986516i	$-0.552332\pi$
$337$	−2.29982e8	−0.327333	−0.163667	+	0.986516i	$0.552332\pi$
$338$	−2.70150e9	−3.80537
$339$	0	0
$340$	−4.70358e8	−0.649011
$341$	−1.06210e8	−0.145053
$342$	0	0
$343$	1.96811e9	2.63342
$344$	2.11394e8	0.279987
$345$	0	0
$346$	−1.98116e9	−2.57130
$347$	6.33227e8	0.813591	0.406796	−	0.913519i	$-0.366646\pi$
$347$	6.33227e8	0.813591	0.406796	+	0.913519i	$0.366646\pi$
$348$	0	0
$349$	−5.37194e8	−0.676460	−0.338230	−	0.941063i	$-0.609828\pi$
$349$	−5.37194e8	−0.676460	−0.338230	+	0.941063i	$0.609828\pi$
$350$	2.13401e9	2.66048
$351$	0	0
$352$	2.90376e8	0.354864
$353$	1.56430e9	1.89282	0.946408	−	0.322975i	$-0.104683\pi$
$353$	1.56430e9	1.89282	0.946408	+	0.322975i	$0.104683\pi$
$354$	0	0
$355$	4.24427e8	0.503505
$356$	3.55741e8	0.417887
$357$	0	0
$358$	−3.09067e8	−0.356010
$359$	3.09660e8	0.353227	0.176613	−	0.984280i	$-0.443486\pi$
$359$	3.09660e8	0.353227	0.176613	+	0.984280i	$0.443486\pi$
$360$	0	0
$361$	−4.66707e8	−0.522119
$362$	1.14345e8	0.126689
$363$	0	0
$364$	4.73187e9	5.14254
$365$	2.44951e8	0.263666
$366$	0	0
$367$	−2.61453e8	−0.276098	−0.138049	−	0.990425i	$-0.544083\pi$
$367$	−2.61453e8	−0.276098	−0.138049	+	0.990425i	$0.544083\pi$
$368$	9.47094e7	0.0990662
$369$	0	0
$370$	1.74124e8	0.178712
$371$	1.82395e9	1.85440
$372$	0	0
$373$	1.64951e8	0.164579	0.0822897	−	0.996608i	$-0.473777\pi$
$373$	1.64951e8	0.164579	0.0822897	+	0.996608i	$0.473777\pi$
$374$	−6.86776e8	−0.678835
$375$	0	0
$376$	−1.36871e9	−1.32787
$377$	−6.54837e8	−0.629417
$378$	0	0
$379$	−1.26692e9	−1.19540	−0.597699	−	0.801721i	$-0.703918\pi$
$379$	−1.26692e9	−1.19540	−0.597699	+	0.801721i	$0.703918\pi$
$380$	3.37468e8	0.315494
$381$	0	0
$382$	9.47417e8	0.869600
$383$	−1.71179e9	−1.55688	−0.778441	−	0.627718i	$-0.783989\pi$
$383$	−1.71179e9	−1.55688	−0.778441	+	0.627718i	$0.783989\pi$
$384$	0	0
$385$	−1.89227e8	−0.168993
$386$	−1.32162e9	−1.16964
$387$	0	0
$388$	3.50404e8	0.304549
$389$	1.32730e9	1.14326	0.571630	−	0.820512i	$-0.306311\pi$
$389$	1.32730e9	1.14326	0.571630	+	0.820512i	$0.306311\pi$
$390$	0	0
$391$	−7.03116e8	−0.594851
$392$	−2.31783e9	−1.94348
$393$	0	0
$394$	2.76641e9	2.27866
$395$	4.48765e7	0.0366378
$396$	0	0
$397$	−1.24222e9	−0.996397	−0.498199	−	0.867063i	$-0.666005\pi$
$397$	−1.24222e9	−0.996397	−0.498199	+	0.867063i	$0.666005\pi$
$398$	−3.07564e9	−2.44537
$399$	0	0
$400$	2.75325e8	0.215098
$401$	−9.25894e8	−0.717061	−0.358530	−	0.933518i	$-0.616722\pi$
$401$	−9.25894e8	−0.717061	−0.358530	+	0.933518i	$0.616722\pi$
$402$	0	0
$403$	−1.16616e9	−0.887543
$404$	1.26273e9	0.952744
$405$	0	0
$406$	1.34764e9	0.999385
$407$	1.52811e8	0.112350
$408$	0	0
$409$	5.85741e8	0.423325	0.211663	−	0.977343i	$-0.432112\pi$
$409$	5.85741e8	0.423325	0.211663	+	0.977343i	$0.432112\pi$
$410$	1.89385e8	0.135707
$411$	0	0
$412$	3.20083e8	0.225487
$413$	−2.76020e9	−1.92804
$414$	0	0
$415$	−2.90608e8	−0.199590
$416$	3.18825e9	2.17133
$417$	0	0
$418$	4.92742e8	0.329992
$419$	2.56026e8	0.170033	0.0850167	−	0.996380i	$-0.472906\pi$
$419$	2.56026e8	0.170033	0.0850167	+	0.996380i	$0.472906\pi$
$420$	0	0
$421$	6.64580e8	0.434070	0.217035	−	0.976164i	$-0.430361\pi$
$421$	6.64580e8	0.434070	0.217035	+	0.976164i	$0.430361\pi$
$422$	−3.11969e9	−2.02077
$423$	0	0
$424$	−1.26164e9	−0.803811
$425$	−2.04400e9	−1.29157
$426$	0	0
$427$	7.90200e8	0.491179
$428$	2.34058e9	1.44301
$429$	0	0
$430$	−2.76050e8	−0.167436
$431$	3.54271e8	0.213140	0.106570	−	0.994305i	$-0.466013\pi$
$431$	3.54271e8	0.213140	0.106570	+	0.994305i	$0.466013\pi$
$432$	0	0
$433$	−1.77346e9	−1.04981	−0.524907	−	0.851159i	$-0.675900\pi$
$433$	−1.77346e9	−1.04981	−0.524907	+	0.851159i	$0.675900\pi$
$434$	2.39993e9	1.40924
$435$	0	0
$436$	−3.00690e9	−1.73746
$437$	5.04466e8	0.289166
$438$	0	0
$439$	−2.65420e9	−1.49729	−0.748647	−	0.662969i	$-0.769296\pi$
$439$	−2.65420e9	−1.49729	−0.748647	+	0.662969i	$0.769296\pi$
$440$	1.30889e8	0.0732521
$441$	0	0
$442$	−7.54061e9	−4.15364
$443$	−1.94908e9	−1.06517	−0.532583	−	0.846378i	$-0.678779\pi$
$443$	−1.94908e9	−1.06517	−0.532583	+	0.846378i	$0.678779\pi$
$444$	0	0
$445$	−1.56198e8	−0.0840263
$446$	5.92083e8	0.316017
$447$	0	0
$448$	−5.72741e9	−3.00944
$449$	9.24726e8	0.482115	0.241058	−	0.970511i	$-0.422506\pi$
$449$	9.24726e8	0.482115	0.241058	+	0.970511i	$0.422506\pi$
$450$	0	0
$451$	1.66204e8	0.0853146
$452$	−3.66583e9	−1.86719
$453$	0	0
$454$	−4.29473e8	−0.215397
$455$	−2.07766e9	−1.03403
$456$	0	0
$457$	3.00088e9	1.47076	0.735379	−	0.677656i	$-0.237004\pi$
$457$	3.00088e9	1.47076	0.735379	+	0.677656i	$0.237004\pi$
$458$	−9.43971e8	−0.459124
$459$	0	0
$460$	3.98538e8	0.190905
$461$	−1.87779e9	−0.892678	−0.446339	−	0.894864i	$-0.647272\pi$
$461$	−1.87779e9	−0.892678	−0.446339	+	0.894864i	$0.647272\pi$
$462$	0	0
$463$	−1.16774e9	−0.546778	−0.273389	−	0.961904i	$-0.588145\pi$
$463$	−1.16774e9	−0.546778	−0.273389	+	0.961904i	$0.588145\pi$
$464$	1.73869e8	0.0807997
$465$	0	0
$466$	−2.30616e9	−1.05569
$467$	4.01912e9	1.82609	0.913043	−	0.407863i	$-0.133726\pi$
$467$	4.01912e9	1.82609	0.913043	+	0.407863i	$0.133726\pi$
$468$	0	0
$469$	4.79933e9	2.14821
$470$	1.78734e9	0.794082
$471$	0	0
$472$	1.90925e9	0.835730
$473$	−2.42260e8	−0.105261
$474$	0	0
$475$	1.46651e9	0.627852
$476$	9.32730e9	3.96398
$477$	0	0
$478$	3.70892e9	1.55328
$479$	−3.87806e8	−0.161228	−0.0806139	−	0.996745i	$-0.525688\pi$
$479$	−3.87806e8	−0.161228	−0.0806139	+	0.996745i	$0.525688\pi$
$480$	0	0
$481$	1.67782e9	0.687446
$482$	−2.54946e9	−1.03701
$483$	0	0
$484$	3.41628e8	0.136960
$485$	−1.53854e8	−0.0612370
$486$	0	0
$487$	−2.76181e8	−0.108353	−0.0541766	−	0.998531i	$-0.517253\pi$
$487$	−2.76181e8	−0.108353	−0.0541766	+	0.998531i	$0.517253\pi$
$488$	−5.46587e8	−0.212907
$489$	0	0
$490$	3.02675e9	1.16223
$491$	−1.75761e9	−0.670098	−0.335049	−	0.942201i	$-0.608753\pi$
$491$	−1.75761e9	−0.670098	−0.335049	+	0.942201i	$0.608753\pi$
$492$	0	0
$493$	−1.29079e9	−0.485168
$494$	5.41017e9	2.01914
$495$	0	0
$496$	3.09633e8	0.113936
$497$	−8.41647e9	−3.07527
$498$	0	0
$499$	−5.78797e8	−0.208533	−0.104266	−	0.994549i	$-0.533249\pi$
$499$	−5.78797e8	−0.208533	−0.104266	+	0.994549i	$0.533249\pi$
$500$	2.43420e9	0.870888
$501$	0	0
$502$	3.49783e9	1.23406
$503$	−1.78609e9	−0.625772	−0.312886	−	0.949791i	$-0.601296\pi$
$503$	−1.78609e9	−0.625772	−0.312886	+	0.949791i	$0.601296\pi$
$504$	0	0
$505$	−5.54437e8	−0.191572
$506$	5.81911e8	0.199678
$507$	0	0
$508$	7.29252e9	2.46805
$509$	1.97986e9	0.665459	0.332730	−	0.943022i	$-0.392030\pi$
$509$	1.97986e9	0.665459	0.332730	+	0.943022i	$0.392030\pi$
$510$	0	0
$511$	−4.85743e9	−1.61040
$512$	−1.42337e9	−0.468677
$513$	0	0
$514$	2.25818e9	0.733479
$515$	−1.40541e8	−0.0453397
$516$	0	0
$517$	1.56857e9	0.499213
$518$	−3.45292e9	−1.09152
$519$	0	0
$520$	1.43713e9	0.448212
$521$	3.74479e9	1.16010	0.580051	−	0.814580i	$-0.303033\pi$
$521$	3.74479e9	1.16010	0.580051	+	0.814580i	$0.303033\pi$
$522$	0	0
$523$	3.97812e8	0.121597	0.0607984	−	0.998150i	$-0.480635\pi$
$523$	3.97812e8	0.121597	0.0607984	+	0.998150i	$0.480635\pi$
$524$	−6.14634e8	−0.186620
$525$	0	0
$526$	5.40683e8	0.161992
$527$	−2.29869e9	−0.684138
$528$	0	0
$529$	−2.80907e9	−0.825026
$530$	1.64752e9	0.480689
$531$	0	0
$532$	−6.69207e9	−1.92695
$533$	1.82487e9	0.522020
$534$	0	0
$535$	−1.02770e9	−0.290153
$536$	−3.31973e9	−0.931164
$537$	0	0
$538$	−2.23000e9	−0.617401
$539$	2.65627e9	0.730653
$540$	0	0
$541$	−3.75208e9	−1.01878	−0.509391	−	0.860535i	$-0.670129\pi$
$541$	−3.75208e9	−1.01878	−0.509391	+	0.860535i	$0.670129\pi$
$542$	1.13046e10	3.04970
$543$	0	0
$544$	6.28458e9	1.67371
$545$	1.32026e9	0.349359
$546$	0	0
$547$	−1.88842e9	−0.493335	−0.246667	−	0.969100i	$-0.579336\pi$
$547$	−1.88842e9	−0.493335	−0.246667	+	0.969100i	$0.579336\pi$
$548$	2.31212e9	0.600175
$549$	0	0
$550$	1.69165e9	0.433551
$551$	9.26108e8	0.235847
$552$	0	0
$553$	−8.89911e8	−0.223774
$554$	−7.55874e9	−1.88871
$555$	0	0
$556$	−7.18203e9	−1.77209
$557$	5.58269e8	0.136883	0.0684416	−	0.997655i	$-0.478197\pi$
$557$	5.58269e8	0.136883	0.0684416	+	0.997655i	$0.478197\pi$
$558$	0	0
$559$	−2.65995e9	−0.644069
$560$	5.51649e8	0.132741
$561$	0	0
$562$	1.58033e9	0.375553
$563$	−2.10337e9	−0.496747	−0.248374	−	0.968664i	$-0.579896\pi$
$563$	−2.10337e9	−0.496747	−0.248374	+	0.968664i	$0.579896\pi$
$564$	0	0
$565$	1.60958e9	0.375443
$566$	−9.19361e9	−2.13122
$567$	0	0
$568$	5.82173e9	1.33301
$569$	−5.17228e9	−1.17704	−0.588518	−	0.808484i	$-0.700288\pi$
$569$	−5.17228e9	−1.17704	−0.588518	+	0.808484i	$0.700288\pi$
$570$	0	0
$571$	−2.45037e9	−0.550814	−0.275407	−	0.961328i	$-0.588813\pi$
$571$	−2.45037e9	−0.550814	−0.275407	+	0.961328i	$0.588813\pi$
$572$	3.75098e9	0.838028
$573$	0	0
$574$	−3.75555e9	−0.828861
$575$	1.73189e9	0.379913
$576$	0	0
$577$	4.18992e9	0.908011	0.454005	−	0.890999i	$-0.349995\pi$
$577$	4.18992e9	0.908011	0.454005	+	0.890999i	$0.349995\pi$
$578$	−7.51381e9	−1.61850
$579$	0	0
$580$	7.31644e8	0.155705
$581$	5.76281e9	1.21904
$582$	0	0
$583$	1.44586e9	0.302193
$584$	3.35992e9	0.698045
$585$	0	0
$586$	9.81585e9	2.01505
$587$	−3.46463e9	−0.707007	−0.353503	−	0.935433i	$-0.615010\pi$
$587$	−3.46463e9	−0.707007	−0.353503	+	0.935433i	$0.615010\pi$
$588$	0	0
$589$	1.64925e9	0.332569
$590$	−2.49321e9	−0.499777
$591$	0	0
$592$	−4.45488e8	−0.0882490
$593$	−1.28200e9	−0.252462	−0.126231	−	0.992001i	$-0.540288\pi$
$593$	−1.28200e9	−0.252462	−0.126231	+	0.992001i	$0.540288\pi$
$594$	0	0
$595$	−4.09541e9	−0.797054
$596$	4.96127e9	0.959911
$597$	0	0
$598$	6.38922e9	1.22178
$599$	−6.40800e9	−1.21823	−0.609114	−	0.793083i	$-0.708475\pi$
$599$	−6.40800e9	−1.21823	−0.609114	+	0.793083i	$0.708475\pi$
$600$	0	0
$601$	3.72569e9	0.700077	0.350039	−	0.936735i	$-0.386168\pi$
$601$	3.72569e9	0.700077	0.350039	+	0.936735i	$0.386168\pi$
$602$	5.47412e9	1.02265
$603$	0	0
$604$	1.19776e10	2.21177
$605$	−1.50001e8	−0.0275392
$606$	0	0
$607$	−5.51998e9	−1.00179	−0.500895	−	0.865508i	$-0.666996\pi$
$607$	−5.51998e9	−1.00179	−0.500895	+	0.865508i	$0.666996\pi$
$608$	−4.50901e9	−0.813614
$609$	0	0
$610$	7.13763e8	0.127321
$611$	1.72224e10	3.05457
$612$	0	0
$613$	−7.49019e9	−1.31335	−0.656676	−	0.754173i	$-0.728038\pi$
$613$	−7.49019e9	−1.31335	−0.656676	+	0.754173i	$0.728038\pi$
$614$	−3.62838e9	−0.632592
$615$	0	0
$616$	−2.59556e9	−0.447403
$617$	−2.10268e9	−0.360392	−0.180196	−	0.983631i	$-0.557673\pi$
$617$	−2.10268e9	−0.360392	−0.180196	+	0.983631i	$0.557673\pi$
$618$	0	0
$619$	−9.42831e8	−0.159778	−0.0798889	−	0.996804i	$-0.525457\pi$
$619$	−9.42831e8	−0.159778	−0.0798889	+	0.996804i	$0.525457\pi$
$620$	1.30294e9	0.219560
$621$	0	0
$622$	5.43672e9	0.905880
$623$	3.09744e9	0.513209
$624$	0	0
$625$	4.47461e9	0.733120
$626$	−9.31885e7	−0.0151828
$627$	0	0
$628$	−1.77639e10	−2.86207
$629$	3.30727e9	0.529898
$630$	0	0
$631$	−1.11126e10	−1.76081	−0.880405	−	0.474223i	$-0.842729\pi$
$631$	−1.11126e10	−1.76081	−0.880405	+	0.474223i	$0.842729\pi$
$632$	6.15557e8	0.0969971
$633$	0	0
$634$	−1.80648e10	−2.81528
$635$	−3.20198e9	−0.496262
$636$	0	0
$637$	2.91651e10	4.47070
$638$	1.06828e9	0.162860
$639$	0	0
$640$	−2.80893e9	−0.423557
$641$	−8.00380e9	−1.20031	−0.600154	−	0.799884i	$-0.704894\pi$
$641$	−8.00380e9	−1.20031	−0.600154	+	0.799884i	$0.704894\pi$
$642$	0	0
$643$	2.72761e9	0.404617	0.202308	−	0.979322i	$-0.435156\pi$
$643$	2.72761e9	0.404617	0.202308	+	0.979322i	$0.435156\pi$
$644$	−7.90310e9	−1.16600
$645$	0	0
$646$	1.06644e10	1.55640
$647$	−8.76207e9	−1.27187	−0.635934	−	0.771744i	$-0.719385\pi$
$647$	−8.76207e9	−1.27187	−0.635934	+	0.771744i	$0.719385\pi$
$648$	0	0
$649$	−2.18803e9	−0.314193
$650$	1.85738e10	2.65280
$651$	0	0
$652$	8.58392e9	1.21288
$653$	6.26088e9	0.879912	0.439956	−	0.898019i	$-0.354994\pi$
$653$	6.26088e9	0.879912	0.439956	+	0.898019i	$0.354994\pi$
$654$	0	0
$655$	2.69872e8	0.0375244
$656$	−4.84531e8	−0.0670129
$657$	0	0
$658$	−3.54434e10	−4.85003
$659$	1.06118e10	1.44441	0.722205	−	0.691679i	$-0.243129\pi$
$659$	1.06118e10	1.44441	0.722205	+	0.691679i	$0.243129\pi$
$660$	0	0
$661$	5.77805e9	0.778173	0.389087	−	0.921201i	$-0.372791\pi$
$661$	5.77805e9	0.778173	0.389087	+	0.921201i	$0.372791\pi$
$662$	−8.57929e9	−1.14934
$663$	0	0
$664$	−3.98618e9	−0.528407
$665$	2.93834e9	0.387459
$666$	0	0
$667$	1.09370e9	0.142711
$668$	−1.91318e10	−2.48335
$669$	0	0
$670$	4.33509e9	0.556847
$671$	6.26397e8	0.0800425
$672$	0	0
$673$	4.20986e9	0.532371	0.266186	−	0.963922i	$-0.414237\pi$
$673$	4.20986e9	0.532371	0.266186	+	0.963922i	$0.414237\pi$
$674$	4.11945e9	0.518238
$675$	0	0
$676$	2.90843e10	3.62114
$677$	4.91057e9	0.608235	0.304118	−	0.952634i	$-0.401638\pi$
$677$	4.91057e9	0.608235	0.304118	+	0.952634i	$0.401638\pi$
$678$	0	0
$679$	3.05097e9	0.374019
$680$	2.83282e9	0.345492
$681$	0	0
$682$	1.90244e9	0.229649
$683$	−9.00588e9	−1.08157	−0.540784	−	0.841162i	$-0.681872\pi$
$683$	−9.00588e9	−1.08157	−0.540784	+	0.841162i	$0.681872\pi$
$684$	0	0
$685$	−1.01520e9	−0.120680
$686$	−3.52528e10	−4.16926
$687$	0	0
$688$	7.06258e8	0.0826806
$689$	1.58751e10	1.84905
$690$	0	0
$691$	2.67573e9	0.308510	0.154255	−	0.988031i	$-0.450702\pi$
$691$	2.67573e9	0.308510	0.154255	+	0.988031i	$0.450702\pi$
$692$	2.13291e10	2.44682
$693$	0	0
$694$	−1.13424e10	−1.28809
$695$	3.15347e9	0.356321
$696$	0	0
$697$	3.59713e9	0.402384
$698$	9.62222e9	1.07098
$699$	0	0
$700$	−2.29747e10	−2.53167
$701$	−1.46686e10	−1.60833	−0.804166	−	0.594405i	$-0.797387\pi$
$701$	−1.46686e10	−1.60833	−0.804166	+	0.594405i	$0.797387\pi$
$702$	0	0
$703$	−2.37287e9	−0.257591
$704$	−4.54016e9	−0.490418
$705$	0	0
$706$	−2.80197e10	−2.99673
$707$	1.09946e10	1.17007
$708$	0	0
$709$	4.70273e9	0.495551	0.247775	−	0.968817i	$-0.420300\pi$
$709$	4.70273e9	0.495551	0.247775	+	0.968817i	$0.420300\pi$
$710$	−7.60234e9	−0.797155
$711$	0	0
$712$	−2.14252e9	−0.222456
$713$	1.94770e9	0.201237
$714$	0	0
$715$	−1.64697e9	−0.168506
$716$	3.32741e9	0.338774
$717$	0	0
$718$	−5.54662e9	−0.559234
$719$	1.44754e10	1.45238	0.726190	−	0.687494i	$-0.241289\pi$
$719$	1.44754e10	1.45238	0.726190	+	0.687494i	$0.241289\pi$
$720$	0	0
$721$	2.78696e9	0.276922
$722$	8.35967e9	0.826625
$723$	0	0
$724$	−1.23103e9	−0.120555
$725$	3.17944e9	0.309862
$726$	0	0
$727$	8.12115e9	0.783875	0.391938	−	0.919992i	$-0.371805\pi$
$727$	8.12115e9	0.783875	0.391938	+	0.919992i	$0.371805\pi$
$728$	−2.84986e10	−2.73756
$729$	0	0
$730$	−4.38757e9	−0.417440
$731$	−5.24321e9	−0.496462
$732$	0	0
$733$	1.58815e10	1.48945	0.744726	−	0.667370i	$-0.232580\pi$
$733$	1.58815e10	1.48945	0.744726	+	0.667370i	$0.232580\pi$
$734$	4.68316e9	0.437122
$735$	0	0
$736$	−5.32497e9	−0.492317
$737$	3.80446e9	0.350072
$738$	0	0
$739$	1.54228e9	0.140575	0.0702874	−	0.997527i	$-0.477608\pi$
$739$	1.54228e9	0.140575	0.0702874	+	0.997527i	$0.477608\pi$
$740$	−1.87462e9	−0.170060
$741$	0	0
$742$	−3.26706e10	−2.93591
$743$	8.45656e8	0.0756367	0.0378184	−	0.999285i	$-0.487959\pi$
$743$	8.45656e8	0.0756367	0.0378184	+	0.999285i	$0.487959\pi$
$744$	0	0
$745$	−2.17838e9	−0.193013
$746$	−2.95461e9	−0.260564
$747$	0	0
$748$	7.39381e9	0.645970
$749$	2.03794e10	1.77217
$750$	0	0
$751$	−1.19584e10	−1.03023	−0.515115	−	0.857121i	$-0.672251\pi$
$751$	−1.19584e10	−1.03023	−0.515115	+	0.857121i	$0.672251\pi$
$752$	−4.57282e9	−0.392122
$753$	0	0
$754$	1.17294e10	0.996501
$755$	−5.25909e9	−0.444730
$756$	0	0
$757$	1.64003e10	1.37409	0.687045	−	0.726615i	$-0.258908\pi$
$757$	1.64003e10	1.37409	0.687045	+	0.726615i	$0.258908\pi$
$758$	2.26931e10	1.89257
$759$	0	0
$760$	−2.03247e9	−0.167948
$761$	−1.45875e10	−1.19987	−0.599937	−	0.800047i	$-0.704808\pi$
$761$	−1.45875e10	−1.19987	−0.599937	+	0.800047i	$0.704808\pi$
$762$	0	0
$763$	−2.61811e10	−2.13379
$764$	−1.01999e10	−0.827499
$765$	0	0
$766$	3.06617e10	2.46487
$767$	−2.40240e10	−1.92248
$768$	0	0
$769$	−2.48714e10	−1.97223	−0.986117	−	0.166054i	$-0.946897\pi$
$769$	−2.48714e10	−1.97223	−0.986117	+	0.166054i	$0.946897\pi$
$770$	3.38943e9	0.267553
$771$	0	0
$772$	1.42285e10	1.11301
$773$	−2.94099e9	−0.229015	−0.114508	−	0.993422i	$-0.536529\pi$
$773$	−2.94099e9	−0.229015	−0.114508	+	0.993422i	$0.536529\pi$
$774$	0	0
$775$	5.66207e9	0.436937
$776$	−2.11037e9	−0.162122
$777$	0	0
$778$	−2.37746e10	−1.81002
$779$	−2.58084e9	−0.195605
$780$	0	0
$781$	−6.67179e9	−0.501145
$782$	1.25942e10	0.941776
$783$	0	0
$784$	−7.74378e9	−0.573914
$785$	7.79974e9	0.575488
$786$	0	0
$787$	3.41977e9	0.250084	0.125042	−	0.992151i	$-0.460093\pi$
$787$	3.41977e9	0.250084	0.125042	+	0.992151i	$0.460093\pi$
$788$	−2.97831e10	−2.16834
$789$	0	0
$790$	−8.03829e8	−0.0580055
$791$	−3.19184e10	−2.29310
$792$	0	0
$793$	6.87766e9	0.489762
$794$	2.22507e10	1.57751
$795$	0	0
$796$	3.31123e10	2.32698
$797$	−1.09396e10	−0.765419	−0.382709	−	0.923869i	$-0.625009\pi$
$797$	−1.09396e10	−0.765419	−0.382709	+	0.923869i	$0.625009\pi$
$798$	0	0
$799$	3.39483e10	2.35453
$800$	−1.54800e10	−1.06895
$801$	0	0
$802$	1.65846e10	1.13526
$803$	−3.85052e9	−0.262431
$804$	0	0
$805$	3.47007e9	0.234451
$806$	2.08882e10	1.40517
$807$	0	0
$808$	−7.60504e9	−0.507180
$809$	−9.62137e9	−0.638877	−0.319438	−	0.947607i	$-0.603494\pi$
$809$	−9.62137e9	−0.638877	−0.319438	+	0.947607i	$0.603494\pi$
$810$	0	0
$811$	−2.08135e10	−1.37016	−0.685080	−	0.728468i	$-0.740233\pi$
$811$	−2.08135e10	−1.37016	−0.685080	+	0.728468i	$0.740233\pi$
$812$	−1.45086e10	−0.951001
$813$	0	0
$814$	−2.73715e9	−0.177875
$815$	−3.76901e9	−0.243879
$816$	0	0
$817$	3.76185e9	0.241337
$818$	−1.04918e10	−0.670214
$819$	0	0
$820$	−2.03891e9	−0.129137
$821$	−1.07357e10	−0.677064	−0.338532	−	0.940955i	$-0.609930\pi$
$821$	−1.07357e10	−0.677064	−0.338532	+	0.940955i	$0.609930\pi$
$822$	0	0
$823$	1.39671e10	0.873388	0.436694	−	0.899610i	$-0.356149\pi$
$823$	1.39671e10	0.873388	0.436694	+	0.899610i	$0.356149\pi$
$824$	−1.92776e9	−0.120035
$825$	0	0
$826$	4.94408e10	3.05250
$827$	3.06795e10	1.88616	0.943081	−	0.332564i	$-0.107914\pi$
$827$	3.06795e10	1.88616	0.943081	+	0.332564i	$0.107914\pi$
$828$	0	0
$829$	−1.51733e9	−0.0924995	−0.0462497	−	0.998930i	$-0.514727\pi$
$829$	−1.51733e9	−0.0924995	−0.0462497	+	0.998930i	$0.514727\pi$
$830$	5.20537e9	0.315994
$831$	0	0
$832$	−4.98496e10	−3.00075
$833$	5.74893e10	3.44611
$834$	0	0
$835$	8.40034e9	0.499338
$836$	−5.30485e9	−0.314015
$837$	0	0
$838$	−4.58593e9	−0.269199
$839$	3.27713e10	1.91570	0.957848	−	0.287276i	$-0.0927498\pi$
$839$	3.27713e10	1.91570	0.957848	+	0.287276i	$0.0927498\pi$
$840$	0	0
$841$	−1.52420e10	−0.883603
$842$	−1.19040e10	−0.687226
$843$	0	0
$844$	3.35865e10	1.92294
$845$	−1.27703e10	−0.728117
$846$	0	0
$847$	2.97455e9	0.168202
$848$	−4.21508e9	−0.237367
$849$	0	0
$850$	3.66121e10	2.04483
$851$	−2.80228e9	−0.155868
$852$	0	0
$853$	−9.71082e9	−0.535716	−0.267858	−	0.963458i	$-0.586316\pi$
$853$	−9.71082e9	−0.535716	−0.267858	+	0.963458i	$0.586316\pi$
$854$	−1.41541e10	−0.777641
$855$	0	0
$856$	−1.40966e10	−0.768168
$857$	2.20307e10	1.19562	0.597812	−	0.801636i	$-0.296037\pi$
$857$	2.20307e10	1.19562	0.597812	+	0.801636i	$0.296037\pi$
$858$	0	0
$859$	−2.00371e10	−1.07860	−0.539298	−	0.842115i	$-0.681310\pi$
$859$	−2.00371e10	−1.07860	−0.539298	+	0.842115i	$0.681310\pi$
$860$	2.97194e9	0.159329
$861$	0	0
$862$	−6.34570e9	−0.337446
$863$	2.67107e9	0.141465	0.0707323	−	0.997495i	$-0.477466\pi$
$863$	2.67107e9	0.141465	0.0707323	+	0.997495i	$0.477466\pi$
$864$	0	0
$865$	−9.36513e9	−0.491991
$866$	3.17662e10	1.66208
$867$	0	0
$868$	−2.58375e10	−1.34101
$869$	−7.05438e8	−0.0364661
$870$	0	0
$871$	4.17719e10	2.14201
$872$	1.81096e10	0.924914
$873$	0	0
$874$	−9.03600e9	−0.457811
$875$	2.11946e10	1.06954
$876$	0	0
$877$	−1.74553e10	−0.873832	−0.436916	−	0.899502i	$-0.643929\pi$
$877$	−1.74553e10	−0.873832	−0.436916	+	0.899502i	$0.643929\pi$
$878$	4.75420e10	2.37054
$879$	0	0
$880$	4.37296e8	0.0216315
$881$	−3.48759e10	−1.71834	−0.859171	−	0.511689i	$-0.829020\pi$
$881$	−3.48759e10	−1.71834	−0.859171	+	0.511689i	$0.829020\pi$
$882$	0	0
$883$	−1.18476e10	−0.579121	−0.289561	−	0.957160i	$-0.593509\pi$
$883$	−1.18476e10	−0.579121	−0.289561	+	0.957160i	$0.593509\pi$
$884$	8.11819e10	3.95254
$885$	0	0
$886$	3.49120e10	1.68639
$887$	−2.64987e10	−1.27494	−0.637472	−	0.770473i	$-0.720020\pi$
$887$	−2.64987e10	−1.27494	−0.637472	+	0.770473i	$0.720020\pi$
$888$	0	0
$889$	6.34960e10	3.03103
$890$	2.79782e9	0.133031
$891$	0	0
$892$	−6.37434e9	−0.300717
$893$	−2.43569e10	−1.14457
$894$	0	0
$895$	−1.46099e9	−0.0681187
$896$	5.57018e10	2.58697
$897$	0	0
$898$	−1.65637e10	−0.763291
$899$	3.57562e9	0.164132
$900$	0	0
$901$	3.12924e10	1.42529
$902$	−2.97704e9	−0.135071
$903$	0	0
$904$	2.20782e10	0.993970
$905$	5.40520e8	0.0242405
$906$	0	0
$907$	−4.98476e9	−0.221829	−0.110915	−	0.993830i	$-0.535378\pi$
$907$	−4.98476e9	−0.221829	−0.110915	+	0.993830i	$0.535378\pi$
$908$	4.62369e9	0.204969
$909$	0	0
$910$	3.72150e10	1.63709
$911$	−1.45013e10	−0.635465	−0.317733	−	0.948180i	$-0.602921\pi$
$911$	−1.45013e10	−0.635465	−0.317733	+	0.948180i	$0.602921\pi$
$912$	0	0
$913$	4.56822e9	0.198655
$914$	−5.37517e10	−2.32852
$915$	0	0
$916$	1.01628e10	0.436896
$917$	−5.35162e9	−0.229189
$918$	0	0
$919$	−2.19450e10	−0.932678	−0.466339	−	0.884606i	$-0.654427\pi$
$919$	−2.19450e10	−0.932678	−0.466339	+	0.884606i	$0.654427\pi$
$920$	−2.40027e9	−0.101626
$921$	0	0
$922$	3.36351e10	1.41330
$923$	−7.32544e10	−3.06639
$924$	0	0
$925$	−8.14637e9	−0.338429
$926$	2.09165e10	0.865666
$927$	0	0
$928$	−9.77569e9	−0.401540
$929$	−1.43781e10	−0.588365	−0.294182	−	0.955749i	$-0.595047\pi$
$929$	−1.43781e10	−0.588365	−0.294182	+	0.955749i	$0.595047\pi$
$930$	0	0
$931$	−4.12469e10	−1.67520
$932$	2.48280e10	1.00458
$933$	0	0
$934$	−7.19904e10	−2.89108
$935$	−3.24645e9	−0.129888
$936$	0	0
$937$	−1.51530e10	−0.601741	−0.300871	−	0.953665i	$-0.597277\pi$
$937$	−1.51530e10	−0.601741	−0.300871	+	0.953665i	$0.597277\pi$
$938$	−8.59657e10	−3.40107
$939$	0	0
$940$	−1.92425e10	−0.755637
$941$	2.22919e10	0.872134	0.436067	−	0.899914i	$-0.356371\pi$
$941$	2.22919e10	0.872134	0.436067	+	0.899914i	$0.356371\pi$
$942$	0	0
$943$	−3.04788e9	−0.118360
$944$	6.37873e9	0.246793
$945$	0	0
$946$	4.33937e9	0.166651
$947$	−1.63897e9	−0.0627115	−0.0313557	−	0.999508i	$-0.509982\pi$
$947$	−1.63897e9	−0.0627115	−0.0313557	+	0.999508i	$0.509982\pi$
$948$	0	0
$949$	−4.22776e10	−1.60575
$950$	−2.62681e10	−0.994023
$951$	0	0
$952$	−5.61754e10	−2.11017
$953$	2.30180e10	0.861475	0.430738	−	0.902477i	$-0.358253\pi$
$953$	2.30180e10	0.861475	0.430738	+	0.902477i	$0.358253\pi$
$954$	0	0
$955$	4.47853e9	0.166389
$956$	−3.99301e10	−1.47808
$957$	0	0
$958$	6.94638e9	0.255258
$959$	2.01316e10	0.737078
$960$	0	0
$961$	−2.11450e10	−0.768557
$962$	−3.00532e10	−1.08837
$963$	0	0
$964$	2.74474e10	0.986806
$965$	−6.24742e9	−0.223797
$966$	0	0
$967$	−1.59030e10	−0.565571	−0.282785	−	0.959183i	$-0.591258\pi$
$967$	−1.59030e10	−0.565571	−0.282785	+	0.959183i	$0.591258\pi$
$968$	−2.05752e9	−0.0729088
$969$	0	0
$970$	2.75584e9	0.0969512
$971$	−2.99324e10	−1.04924	−0.524619	−	0.851337i	$-0.675792\pi$
$971$	−2.99324e10	−1.04924	−0.524619	+	0.851337i	$0.675792\pi$
$972$	0	0
$973$	−6.25339e10	−2.17631
$974$	4.94695e9	0.171546
$975$	0	0
$976$	−1.82612e9	−0.0628718
$977$	3.39606e10	1.16505	0.582524	−	0.812813i	$-0.302065\pi$
$977$	3.39606e10	1.16505	0.582524	+	0.812813i	$0.302065\pi$
$978$	0	0
$979$	2.45536e9	0.0836325
$980$	−3.25859e10	−1.10596
$981$	0	0
$982$	3.14824e10	1.06091
$983$	−3.34888e10	−1.12451	−0.562254	−	0.826965i	$-0.690066\pi$
$983$	−3.34888e10	−1.12451	−0.562254	+	0.826965i	$0.690066\pi$
$984$	0	0
$985$	1.30771e10	0.435998
$986$	2.31207e10	0.768125
$987$	0	0
$988$	−5.82457e10	−1.92139
$989$	4.44262e9	0.146033
$990$	0	0
$991$	−1.14251e10	−0.372907	−0.186453	−	0.982464i	$-0.559699\pi$
$991$	−1.14251e10	−0.372907	−0.186453	+	0.982464i	$0.559699\pi$
$992$	−1.74089e10	−0.566214
$993$	0	0
$994$	1.50756e11	4.86880
$995$	−1.45389e10	−0.467896
$996$	0	0
$997$	−2.07985e10	−0.664659	−0.332329	−	0.943163i	$-0.607835\pi$
$997$	−2.07985e10	−0.664659	−0.332329	+	0.943163i	$0.607835\pi$
$998$	1.03674e10	0.330152
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.a.e.1.1		3
3.2	odd	2		33.8.a.d.1.3	✓	3
12.11	even	2		528.8.a.o.1.3		3
33.32	even	2		363.8.a.e.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.a.d.1.3	✓	3	3.2	odd	2
99.8.a.e.1.1		3	1.1	even	1	trivial
363.8.a.e.1.1		3	33.32	even	2
528.8.a.o.1.3		3	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)

\(f(q)\)	\(=\)	\(q-17.9120 q^{2} +192.840 q^{4} -84.6717 q^{5} +1679.06 q^{7} -1161.42 q^{8} +O(q^{10})\)	\(q-17.9120 q^{2} +192.840 q^{4} -84.6717 q^{5} +1679.06 q^{7} -1161.42 q^{8} +1516.64 q^{10} +1331.00 q^{11} +14614.0 q^{13} -30075.3 q^{14} -3880.24 q^{16} +28806.7 q^{17} -20668.0 q^{19} -16328.1 q^{20} -23840.9 q^{22} -24408.1 q^{23} -70955.7 q^{25} -261766. q^{26} +323790. q^{28} -44808.9 q^{29} -79797.2 q^{31} +218164. q^{32} -515985. q^{34} -142169. q^{35} +114809. q^{37} +370205. q^{38} +98339.1 q^{40} +124871. q^{41} -182014. q^{43} +256670. q^{44} +437198. q^{46} +1.17849e6 q^{47} +1.99569e6 q^{49} +1.27096e6 q^{50} +2.81817e6 q^{52} +1.08629e6 q^{53} -112698. q^{55} -1.95008e6 q^{56} +802617. q^{58} -1.64390e6 q^{59} +470621. q^{61} +1.42933e6 q^{62} -3.41109e6 q^{64} -1.23739e6 q^{65} +2.85835e6 q^{67} +5.55508e6 q^{68} +2.54653e6 q^{70} -5.01261e6 q^{71} -2.89295e6 q^{73} -2.05646e6 q^{74} -3.98561e6 q^{76} +2.23483e6 q^{77} -530006. q^{79} +328547. q^{80} -2.23670e6 q^{82} +3.43217e6 q^{83} -2.43911e6 q^{85} +3.26023e6 q^{86} -1.54584e6 q^{88} +1.84475e6 q^{89} +2.45378e7 q^{91} -4.70686e6 q^{92} -2.11091e7 q^{94} +1.74999e6 q^{95} +1.81707e6 q^{97} -3.57469e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 9 q^{2} - 15 q^{4} + 444 q^{5} + 1614 q^{7} - 3153 q^{8}+O(q^{10}) \) 3 * q - 9 * q^2 - 15 * q^4 + 444 * q^5 + 1614 * q^7 - 3153 * q^8	\( 3 q - 9 q^{2} - 15 q^{4} + 444 q^{5} + 1614 q^{7} - 3153 q^{8} + 2880 q^{10} + 3993 q^{11} + 20772 q^{13} - 36258 q^{14} + 12225 q^{16} + 14538 q^{17} + 24492 q^{19} - 80112 q^{20} - 11979 q^{22} - 35094 q^{23} + 29121 q^{25} - 203832 q^{26} + 278034 q^{28} + 179862 q^{29} + 288888 q^{31} + 519567 q^{32} - 491586 q^{34} + 532872 q^{35} + 107562 q^{37} + 686328 q^{38} - 237360 q^{40} + 135198 q^{41} + 193536 q^{43} - 19965 q^{44} + 16422 q^{46} + 591486 q^{47} + 4461159 q^{49} + 1192245 q^{50} + 2449992 q^{52} - 79044 q^{53} + 590964 q^{55} - 752658 q^{56} + 2289930 q^{58} - 2532768 q^{59} + 6678792 q^{61} + 2660808 q^{62} - 3966303 q^{64} - 3191832 q^{65} + 7150356 q^{67} + 7821954 q^{68} + 4029120 q^{70} - 1390398 q^{71} - 6429114 q^{73} - 2507478 q^{74} - 7654728 q^{76} + 2148234 q^{77} + 6873186 q^{79} + 7556016 q^{80} - 1774590 q^{82} - 6505596 q^{83} - 16546032 q^{85} + 6519468 q^{86} - 4196643 q^{88} + 8842962 q^{89} + 3066648 q^{91} - 6921990 q^{92} - 24038238 q^{94} + 190968 q^{95} - 1764774 q^{97} - 24377397 q^{98}+O(q^{100}) \) 3 * q - 9 * q^2 - 15 * q^4 + 444 * q^5 + 1614 * q^7 - 3153 * q^8 + 2880 * q^10 + 3993 * q^11 + 20772 * q^13 - 36258 * q^14 + 12225 * q^16 + 14538 * q^17 + 24492 * q^19 - 80112 * q^20 - 11979 * q^22 - 35094 * q^23 + 29121 * q^25 - 203832 * q^26 + 278034 * q^28 + 179862 * q^29 + 288888 * q^31 + 519567 * q^32 - 491586 * q^34 + 532872 * q^35 + 107562 * q^37 + 686328 * q^38 - 237360 * q^40 + 135198 * q^41 + 193536 * q^43 - 19965 * q^44 + 16422 * q^46 + 591486 * q^47 + 4461159 * q^49 + 1192245 * q^50 + 2449992 * q^52 - 79044 * q^53 + 590964 * q^55 - 752658 * q^56 + 2289930 * q^58 - 2532768 * q^59 + 6678792 * q^61 + 2660808 * q^62 - 3966303 * q^64 - 3191832 * q^65 + 7150356 * q^67 + 7821954 * q^68 + 4029120 * q^70 - 1390398 * q^71 - 6429114 * q^73 - 2507478 * q^74 - 7654728 * q^76 + 2148234 * q^77 + 6873186 * q^79 + 7556016 * q^80 - 1774590 * q^82 - 6505596 * q^83 - 16546032 * q^85 + 6519468 * q^86 - 4196643 * q^88 + 8842962 * q^89 + 3066648 * q^91 - 6921990 * q^92 - 24038238 * q^94 + 190968 * q^95 - 1764774 * q^97 - 24377397 * q^98

Introduction

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