LMFDB - Embedded newform 99.8.a.e.1.3

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			1.3
Root			$-3.66999$ 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)

$f(q)$	$=$	$q+6.51124 q^{2} -85.6037 q^{4} +22.9029 q^{5} -1466.13 q^{7} -1390.83 q^{8} +O(q^{10})$	\(q+6.51124 q^{2} -85.6037 q^{4} +22.9029 q^{5} -1466.13 q^{7} -1390.83 q^{8} +149.126 q^{10} +1331.00 q^{11} +10497.7 q^{13} -9546.34 q^{14} +1901.28 q^{16} +14269.6 q^{17} +50530.6 q^{19} -1960.57 q^{20} +8666.46 q^{22} -96125.6 q^{23} -77600.5 q^{25} +68352.7 q^{26} +125506. q^{28} +230613. q^{29} +84260.8 q^{31} +190405. q^{32} +92912.5 q^{34} -33578.6 q^{35} -105490. q^{37} +329017. q^{38} -31853.9 q^{40} +106391. q^{41} +573565. q^{43} -113939. q^{44} -625897. q^{46} -369766. q^{47} +1.32600e6 q^{49} -505275. q^{50} -898638. q^{52} -321116. q^{53} +30483.7 q^{55} +2.03913e6 q^{56} +1.50158e6 q^{58} -2.03704e6 q^{59} +3.00081e6 q^{61} +548643. q^{62} +996412. q^{64} +240426. q^{65} +2.19360e6 q^{67} -1.22153e6 q^{68} -218639. q^{70} +4.26371e6 q^{71} -278806. q^{73} -686872. q^{74} -4.32561e6 q^{76} -1.95142e6 q^{77} -283782. q^{79} +43544.7 q^{80} +692735. q^{82} -5.87262e6 q^{83} +326814. q^{85} +3.73462e6 q^{86} -1.85119e6 q^{88} +8.64670e6 q^{89} -1.53909e7 q^{91} +8.22871e6 q^{92} -2.40764e6 q^{94} +1.15730e6 q^{95} +37857.4 q^{97} +8.63391e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	6.51124	0.575518	0.287759	−	0.957703i	$-0.407090\pi$
$2$	6.51124	0.575518	0.287759	+	0.957703i	$0.407090\pi$
$3$	0	0
$3$	0	0
$4$	−85.6037	−0.668779
$5$	22.9029	0.0819398	0.0409699	−	0.999160i	$-0.486955\pi$
$5$	22.9029	0.0819398	0.0409699	+	0.999160i	$0.486955\pi$
$6$	0	0
$7$	−1466.13	−1.61559	−0.807793	−	0.589467i	$-0.799338\pi$
$7$	−1466.13	−1.61559	−0.807793	+	0.589467i	$0.799338\pi$
$8$	−1390.83	−0.960412
$9$	0	0
$10$	149.126	0.0471578
$11$	1331.00	0.301511
$11$	1331.00	0.301511
$12$	0	0
$13$	10497.7	1.32523	0.662614	−	0.748961i	$-0.269447\pi$
$13$	10497.7	1.32523	0.662614	+	0.748961i	$0.269447\pi$
$14$	−9546.34	−0.929798
$15$	0	0
$16$	1901.28	0.116045
$17$	14269.6	0.704432	0.352216	−	0.935919i	$-0.385428\pi$
$17$	14269.6	0.704432	0.352216	+	0.935919i	$0.385428\pi$
$18$	0	0
$19$	50530.6	1.69012	0.845059	−	0.534673i	$-0.179565\pi$
$19$	50530.6	1.69012	0.845059	+	0.534673i	$0.179565\pi$
$20$	−1960.57	−0.0547996
$21$	0	0
$22$	8666.46	0.173525
$23$	−96125.6	−1.64737	−0.823686	−	0.567046i	$-0.808086\pi$
$23$	−96125.6	−1.64737	−0.823686	+	0.567046i	$0.808086\pi$
$24$	0	0
$25$	−77600.5	−0.993286
$26$	68352.7	0.762692
$27$	0	0
$28$	125506.	1.08047
$29$	230613.	1.75587	0.877934	−	0.478782i	$-0.158922\pi$
$29$	230613.	1.75587	0.877934	+	0.478782i	$0.158922\pi$
$30$	0	0
$31$	84260.8	0.507995	0.253998	−	0.967205i	$-0.418254\pi$
$31$	84260.8	0.507995	0.253998	+	0.967205i	$0.418254\pi$
$32$	190405.	1.02720
$33$	0	0
$34$	92912.5	0.405413
$35$	−33578.6	−0.132381
$36$	0	0
$37$	−105490.	−0.342378	−0.171189	−	0.985238i	$-0.554761\pi$
$37$	−105490.	−0.342378	−0.171189	+	0.985238i	$0.554761\pi$
$38$	329017.	0.972693
$39$	0	0
$40$	−31853.9	−0.0786960
$41$	106391.	0.241079	0.120540	−	0.992709i	$-0.461537\pi$
$41$	106391.	0.241079	0.120540	+	0.992709i	$0.461537\pi$
$42$	0	0
$43$	573565.	1.10013	0.550064	−	0.835122i	$-0.314603\pi$
$43$	573565.	1.10013	0.550064	+	0.835122i	$0.314603\pi$
$44$	−113939.	−0.201644
$45$	0	0
$46$	−625897.	−0.948092
$47$	−369766.	−0.519499	−0.259749	−	0.965676i	$-0.583640\pi$
$47$	−369766.	−0.519499	−0.259749	+	0.965676i	$0.583640\pi$
$48$	0	0
$49$	1.32600e6	1.61012
$50$	−505275.	−0.571654
$51$	0	0
$52$	−898638.	−0.886284
$53$	−321116.	−0.296276	−0.148138	−	0.988967i	$-0.547328\pi$
$53$	−321116.	−0.296276	−0.148138	+	0.988967i	$0.547328\pi$
$54$	0	0
$55$	30483.7	0.0247058
$56$	2.03913e6	1.55163
$57$	0	0
$58$	1.50158e6	1.01053
$59$	−2.03704e6	−1.29127	−0.645636	−	0.763646i	$-0.723408\pi$
$59$	−2.03704e6	−1.29127	−0.645636	+	0.763646i	$0.723408\pi$
$60$	0	0
$61$	3.00081e6	1.69271	0.846357	−	0.532616i	$-0.178791\pi$
$61$	3.00081e6	1.69271	0.846357	+	0.532616i	$0.178791\pi$
$62$	548643.	0.292361
$63$	0	0
$64$	996412.	0.475126
$65$	240426.	0.108589
$66$	0	0
$67$	2.19360e6	0.891036	0.445518	−	0.895273i	$-0.353019\pi$
$67$	2.19360e6	0.891036	0.445518	+	0.895273i	$0.353019\pi$
$68$	−1.22153e6	−0.471110
$69$	0	0
$70$	−218639.	−0.0761875
$71$	4.26371e6	1.41379	0.706893	−	0.707321i	$-0.250096\pi$
$71$	4.26371e6	1.41379	0.706893	+	0.707321i	$0.250096\pi$
$72$	0	0
$73$	−278806.	−0.0838825	−0.0419413	−	0.999120i	$-0.513354\pi$
$73$	−278806.	−0.0838825	−0.0419413	+	0.999120i	$0.513354\pi$
$74$	−686872.	−0.197045
$75$	0	0
$76$	−4.32561e6	−1.13032
$77$	−1.95142e6	−0.487117
$78$	0	0
$79$	−283782.	−0.0647575	−0.0323788	−	0.999476i	$-0.510308\pi$
$79$	−283782.	−0.0647575	−0.0323788	+	0.999476i	$0.510308\pi$
$80$	43544.7	0.00950867
$81$	0	0
$82$	692735.	0.138745
$83$	−5.87262e6	−1.12735	−0.563675	−	0.825997i	$-0.690613\pi$
$83$	−5.87262e6	−1.12735	−0.563675	+	0.825997i	$0.690613\pi$
$84$	0	0
$85$	326814.	0.0577210
$86$	3.73462e6	0.633144
$87$	0	0
$88$	−1.85119e6	−0.289575
$89$	8.64670e6	1.30013	0.650063	−	0.759880i	$-0.274743\pi$
$89$	8.64670e6	1.30013	0.650063	+	0.759880i	$0.274743\pi$
$90$	0	0
$91$	−1.53909e7	−2.14102
$92$	8.22871e6	1.10173
$93$	0	0
$94$	−2.40764e6	−0.298981
$95$	1.15730e6	0.138488
$96$	0	0
$97$	37857.4	0.00421162	0.00210581	−	0.999998i	$-0.499330\pi$
$97$	37857.4	0.00421162	0.00210581	+	0.999998i	$0.499330\pi$
$98$	8.63391e6	0.926651
$99$	0	0
$100$	6.64289e6	0.664289
$101$	−9.01395e6	−0.870543	−0.435272	−	0.900299i	$-0.643348\pi$
$101$	−9.01395e6	−0.870543	−0.435272	+	0.900299i	$0.643348\pi$
$102$	0	0
$103$	−5.26940e6	−0.475150	−0.237575	−	0.971369i	$-0.576353\pi$
$103$	−5.26940e6	−0.475150	−0.237575	+	0.971369i	$0.576353\pi$
$104$	−1.46004e7	−1.27276
$105$	0	0
$106$	−2.09087e6	−0.170512
$107$	−1.56526e7	−1.23522	−0.617608	−	0.786486i	$-0.711898\pi$
$107$	−1.56526e7	−1.23522	−0.617608	+	0.786486i	$0.711898\pi$
$108$	0	0
$109$	1.44413e7	1.06811	0.534054	−	0.845451i	$-0.320668\pi$
$109$	1.44413e7	1.06811	0.534054	+	0.845451i	$0.320668\pi$
$110$	198487.	0.0142186
$111$	0	0
$112$	−2.78752e6	−0.187480
$113$	6.12092e6	0.399064	0.199532	−	0.979891i	$-0.436058\pi$
$113$	6.12092e6	0.399064	0.199532	+	0.979891i	$0.436058\pi$
$114$	0	0
$115$	−2.20155e6	−0.134985
$116$	−1.97414e7	−1.17429
$117$	0	0
$118$	−1.32637e7	−0.743150
$119$	−2.09211e7	−1.13807
$120$	0	0
$121$	1.77156e6	0.0909091
$122$	1.95390e7	0.974187
$123$	0	0
$124$	−7.21304e6	−0.339737
$125$	−3.56656e6	−0.163329
$126$	0	0
$127$	3.21582e7	1.39309	0.696545	−	0.717513i	$-0.254720\pi$
$127$	3.21582e7	1.39309	0.696545	+	0.717513i	$0.254720\pi$
$128$	−1.78840e7	−0.753754
$129$	0	0
$130$	1.56547e6	0.0624948
$131$	−8.62966e6	−0.335385	−0.167693	−	0.985839i	$-0.553632\pi$
$131$	−8.62966e6	−0.335385	−0.167693	+	0.985839i	$0.553632\pi$
$132$	0	0
$133$	−7.40846e7	−2.73053
$134$	1.42831e7	0.512807
$135$	0	0
$136$	−1.98465e7	−0.676545
$137$	−1.01093e6	−0.0335891	−0.0167946	−	0.999859i	$-0.505346\pi$
$137$	−1.01093e6	−0.0335891	−0.0167946	+	0.999859i	$0.505346\pi$
$138$	0	0
$139$	−8.19986e6	−0.258973	−0.129486	−	0.991581i	$-0.541333\pi$
$139$	−8.19986e6	−0.258973	−0.129486	+	0.991581i	$0.541333\pi$
$140$	2.87446e6	0.0885335
$141$	0	0
$142$	2.77620e7	0.813659
$143$	1.39724e7	0.399571
$144$	0	0
$145$	5.28171e6	0.143875
$146$	−1.81537e6	−0.0482759
$147$	0	0
$148$	9.03035e6	0.228975
$149$	5.18686e7	1.28455	0.642277	−	0.766473i	$-0.277990\pi$
$149$	5.18686e7	1.28455	0.642277	+	0.766473i	$0.277990\pi$
$150$	0	0
$151$	1.99247e7	0.470947	0.235473	−	0.971881i	$-0.424336\pi$
$151$	1.99247e7	0.470947	0.235473	+	0.971881i	$0.424336\pi$
$152$	−7.02793e7	−1.62321
$153$	0	0
$154$	−1.27062e7	−0.280345
$155$	1.92981e6	0.0416250
$156$	0	0
$157$	1.99000e7	0.410397	0.205199	−	0.978720i	$-0.434216\pi$
$157$	1.99000e7	0.410397	0.205199	+	0.978720i	$0.434216\pi$
$158$	−1.84777e6	−0.0372691
$159$	0	0
$160$	4.36083e6	0.0841684
$161$	1.40933e8	2.66147
$162$	0	0
$163$	−2.85113e7	−0.515657	−0.257829	−	0.966191i	$-0.583007\pi$
$163$	−2.85113e7	−0.515657	−0.257829	+	0.966191i	$0.583007\pi$
$164$	−9.10744e6	−0.161229
$165$	0	0
$166$	−3.82381e7	−0.648810
$167$	3.46095e7	0.575027	0.287513	−	0.957777i	$-0.407171\pi$
$167$	3.46095e7	0.575027	0.287513	+	0.957777i	$0.407171\pi$
$168$	0	0
$169$	4.74522e7	0.756228
$170$	2.12796e6	0.0332195
$171$	0	0
$172$	−4.90993e7	−0.735743
$173$	−7.55804e7	−1.10981	−0.554904	−	0.831915i	$-0.687245\pi$
$173$	−7.55804e7	−1.10981	−0.554904	+	0.831915i	$0.687245\pi$
$174$	0	0
$175$	1.13773e8	1.60474
$176$	2.53060e6	0.0349888
$177$	0	0
$178$	5.63008e7	0.748246
$179$	1.10056e8	1.43426	0.717131	−	0.696938i	$-0.245455\pi$
$179$	1.10056e8	1.43426	0.717131	+	0.696938i	$0.245455\pi$
$180$	0	0
$181$	1.15485e8	1.44761	0.723806	−	0.690004i	$-0.242391\pi$
$181$	1.15485e8	1.44761	0.723806	+	0.690004i	$0.242391\pi$
$182$	−1.00214e8	−1.23219
$183$	0	0
$184$	1.33694e8	1.58216
$185$	−2.41603e6	−0.0280544
$186$	0	0
$187$	1.89928e7	0.212394
$188$	3.16534e7	0.347430
$189$	0	0
$190$	7.53544e6	0.0797023
$191$	1.04151e8	1.08155	0.540775	−	0.841167i	$-0.318131\pi$
$191$	1.04151e8	1.08155	0.540775	+	0.841167i	$0.318131\pi$
$192$	0	0
$193$	1.05802e8	1.05936	0.529678	−	0.848199i	$-0.322313\pi$
$193$	1.05802e8	1.05936	0.529678	+	0.848199i	$0.322313\pi$
$194$	246498.	0.00242386
$195$	0	0
$196$	−1.13511e8	−1.07681
$197$	−3.92196e7	−0.365486	−0.182743	−	0.983161i	$-0.558498\pi$
$197$	−3.92196e7	−0.365486	−0.182743	+	0.983161i	$0.558498\pi$
$198$	0	0
$199$	1.74839e7	0.157272	0.0786361	−	0.996903i	$-0.474943\pi$
$199$	1.74839e7	0.157272	0.0786361	+	0.996903i	$0.474943\pi$
$200$	1.07929e8	0.953964
$201$	0	0
$202$	−5.86920e7	−0.501013
$203$	−3.38110e8	−2.83675
$204$	0	0
$205$	2.43665e6	0.0197540
$206$	−3.43103e7	−0.273457
$207$	0	0
$208$	1.99589e7	0.153786
$209$	6.72563e7	0.509590
$210$	0	0
$211$	−8.52190e7	−0.624522	−0.312261	−	0.949996i	$-0.601086\pi$
$211$	−8.52190e7	−0.624522	−0.312261	+	0.949996i	$0.601086\pi$
$212$	2.74888e7	0.198143
$213$	0	0
$214$	−1.01918e8	−0.710889
$215$	1.31363e7	0.0901443
$216$	0	0
$217$	−1.23538e8	−0.820710
$218$	9.40311e7	0.614715
$219$	0	0
$220$	−2.60952e6	−0.0165227
$221$	1.49797e8	0.933533
$222$	0	0
$223$	8.83128e7	0.533282	0.266641	−	0.963796i	$-0.414086\pi$
$223$	8.83128e7	0.533282	0.266641	+	0.963796i	$0.414086\pi$
$224$	−2.79159e8	−1.65953
$225$	0	0
$226$	3.98548e7	0.229668
$227$	1.76040e7	0.0998896	0.0499448	−	0.998752i	$-0.484095\pi$
$227$	1.76040e7	0.0998896	0.0499448	+	0.998752i	$0.484095\pi$
$228$	0	0
$229$	4.87412e7	0.268208	0.134104	−	0.990967i	$-0.457184\pi$
$229$	4.87412e7	0.268208	0.134104	+	0.990967i	$0.457184\pi$
$230$	−1.43348e7	−0.0776865
$231$	0	0
$232$	−3.20743e8	−1.68636
$233$	−4.83355e7	−0.250334	−0.125167	−	0.992136i	$-0.539947\pi$
$233$	−4.83355e7	−0.250334	−0.125167	+	0.992136i	$0.539947\pi$
$234$	0	0
$235$	−8.46870e6	−0.0425676
$236$	1.74378e8	0.863575
$237$	0	0
$238$	−1.36222e8	−0.654980
$239$	−1.90542e8	−0.902815	−0.451407	−	0.892318i	$-0.649078\pi$
$239$	−1.90542e8	−0.902815	−0.451407	+	0.892318i	$0.649078\pi$
$240$	0	0
$241$	−1.61022e8	−0.741014	−0.370507	−	0.928830i	$-0.620816\pi$
$241$	−1.61022e8	−0.741014	−0.370507	+	0.928830i	$0.620816\pi$
$242$	1.15351e7	0.0523198
$243$	0	0
$244$	−2.56880e8	−1.13205
$245$	3.03692e7	0.131933
$246$	0	0
$247$	5.30453e8	2.23979
$248$	−1.17192e8	−0.487885
$249$	0	0
$250$	−2.32227e7	−0.0939990
$251$	1.96074e8	0.782640	0.391320	−	0.920255i	$-0.372019\pi$
$251$	1.96074e8	0.782640	0.391320	+	0.920255i	$0.372019\pi$
$252$	0	0
$253$	−1.27943e8	−0.496701
$254$	2.09390e8	0.801748
$255$	0	0
$256$	−2.43988e8	−0.908925
$257$	−2.41346e8	−0.886900	−0.443450	−	0.896299i	$-0.646246\pi$
$257$	−2.41346e8	−0.886900	−0.443450	+	0.896299i	$0.646246\pi$
$258$	0	0
$259$	1.54663e8	0.553141
$260$	−2.05814e7	−0.0726220
$261$	0	0
$262$	−5.61898e7	−0.193020
$263$	3.44355e7	0.116724	0.0583621	−	0.998295i	$-0.481412\pi$
$263$	3.44355e7	0.116724	0.0583621	+	0.998295i	$0.481412\pi$
$264$	0	0
$265$	−7.35449e6	−0.0242768
$266$	−4.82383e8	−1.57147
$267$	0	0
$268$	−1.87780e8	−0.595906
$269$	5.11883e8	1.60338	0.801692	−	0.597737i	$-0.203933\pi$
$269$	5.11883e8	1.60338	0.801692	+	0.597737i	$0.203933\pi$
$270$	0	0
$271$	1.26396e8	0.385782	0.192891	−	0.981220i	$-0.438214\pi$
$271$	1.26396e8	0.385782	0.192891	+	0.981220i	$0.438214\pi$
$272$	2.71304e7	0.0817456
$273$	0	0
$274$	−6.58240e6	−0.0193311
$275$	−1.03286e8	−0.299487
$276$	0	0
$277$	−1.36972e8	−0.387216	−0.193608	−	0.981079i	$-0.562019\pi$
$277$	−1.36972e8	−0.387216	−0.193608	+	0.981079i	$0.562019\pi$
$278$	−5.33912e7	−0.149044
$279$	0	0
$280$	4.67020e7	0.127140
$281$	−2.62615e8	−0.706070	−0.353035	−	0.935610i	$-0.614850\pi$
$281$	−2.62615e8	−0.706070	−0.353035	+	0.935610i	$0.614850\pi$
$282$	0	0
$283$	1.77203e8	0.464749	0.232375	−	0.972626i	$-0.425350\pi$
$283$	1.77203e8	0.464749	0.232375	+	0.972626i	$0.425350\pi$
$284$	−3.64989e8	−0.945510
$285$	0	0
$286$	9.09775e7	0.229960
$287$	−1.55983e8	−0.389484
$288$	0	0
$289$	−2.06718e8	−0.503775
$290$	3.43905e7	0.0828029
$291$	0	0
$292$	2.38668e7	0.0560989
$293$	2.63396e8	0.611748	0.305874	−	0.952072i	$-0.401051\pi$
$293$	2.63396e8	0.611748	0.305874	+	0.952072i	$0.401051\pi$
$294$	0	0
$295$	−4.66541e7	−0.105807
$296$	1.46718e8	0.328824
$297$	0	0
$298$	3.37729e8	0.739284
$299$	−1.00909e9	−2.18314
$300$	0	0
$301$	−8.40923e8	−1.77735
$302$	1.29734e8	0.271038
$303$	0	0
$304$	9.60726e7	0.196129
$305$	6.87271e7	0.138701
$306$	0	0
$307$	8.90623e8	1.75675	0.878374	−	0.477974i	$-0.158629\pi$
$307$	8.90623e8	1.75675	0.878374	+	0.477974i	$0.158629\pi$
$308$	1.67049e8	0.325774
$309$	0	0
$310$	1.25655e7	0.0239560
$311$	5.94300e8	1.12033	0.560163	−	0.828383i	$-0.310739\pi$
$311$	5.94300e8	1.12033	0.560163	+	0.828383i	$0.310739\pi$
$312$	0	0
$313$	4.92264e7	0.0907388	0.0453694	−	0.998970i	$-0.485554\pi$
$313$	4.92264e7	0.0907388	0.0453694	+	0.998970i	$0.485554\pi$
$314$	1.29574e8	0.236191
$315$	0	0
$316$	2.42928e7	0.0433085
$317$	4.18014e8	0.737027	0.368513	−	0.929622i	$-0.379867\pi$
$317$	4.18014e8	0.737027	0.368513	+	0.929622i	$0.379867\pi$
$318$	0	0
$319$	3.06947e8	0.529414
$320$	2.28207e7	0.0389317
$321$	0	0
$322$	9.17648e8	1.53172
$323$	7.21050e8	1.19057
$324$	0	0
$325$	−8.14623e8	−1.31633
$326$	−1.85644e8	−0.296770
$327$	0	0
$328$	−1.47971e8	−0.231536
$329$	5.42126e8	0.839295
$330$	0	0
$331$	−7.83135e8	−1.18697	−0.593484	−	0.804846i	$-0.702248\pi$
$331$	−7.83135e8	−1.18697	−0.593484	+	0.804846i	$0.702248\pi$
$332$	5.02718e8	0.753948
$333$	0	0
$334$	2.25351e8	0.330938
$335$	5.02397e7	0.0730113
$336$	0	0
$337$	1.03792e9	1.47726	0.738631	−	0.674109i	$-0.235472\pi$
$337$	1.03792e9	1.47726	0.738631	+	0.674109i	$0.235472\pi$
$338$	3.08973e8	0.435223
$339$	0	0
$340$	−2.79765e7	−0.0386026
$341$	1.12151e8	0.153166
$342$	0	0
$343$	−7.36669e8	−0.985696
$344$	−7.97729e8	−1.05658
$345$	0	0
$346$	−4.92122e8	−0.638714
$347$	6.64048e7	0.0853191	0.0426596	−	0.999090i	$-0.486417\pi$
$347$	6.64048e7	0.0853191	0.0426596	+	0.999090i	$0.486417\pi$
$348$	0	0
$349$	−1.46818e9	−1.84880	−0.924400	−	0.381424i	$-0.875434\pi$
$349$	−1.46818e9	−1.84880	−0.924400	+	0.381424i	$0.875434\pi$
$350$	7.40800e8	0.923556
$351$	0	0
$352$	2.53430e8	0.309712
$353$	−1.42534e9	−1.72468	−0.862338	−	0.506334i	$-0.831000\pi$
$353$	−1.42534e9	−1.72468	−0.862338	+	0.506334i	$0.831000\pi$
$354$	0	0
$355$	9.76512e7	0.115845
$356$	−7.40190e8	−0.869497
$357$	0	0
$358$	7.16602e8	0.825443
$359$	−1.35677e9	−1.54766	−0.773830	−	0.633394i	$-0.781661\pi$
$359$	−1.35677e9	−1.54766	−0.773830	+	0.633394i	$0.781661\pi$
$360$	0	0
$361$	1.65947e9	1.85650
$362$	7.51953e8	0.833126
$363$	0	0
$364$	1.31752e9	1.43187
$365$	−6.38545e6	−0.00687332
$366$	0	0
$367$	8.30382e8	0.876893	0.438446	−	0.898757i	$-0.355529\pi$
$367$	8.30382e8	0.876893	0.438446	+	0.898757i	$0.355529\pi$
$368$	−1.82761e8	−0.191169
$369$	0	0
$370$	−1.57313e7	−0.0161458
$371$	4.70799e8	0.478660
$372$	0	0
$373$	5.28884e8	0.527691	0.263845	−	0.964565i	$-0.415009\pi$
$373$	5.28884e8	0.527691	0.263845	+	0.964565i	$0.415009\pi$
$374$	1.23667e8	0.122237
$375$	0	0
$376$	5.14280e8	0.498933
$377$	2.42090e9	2.32692
$378$	0	0
$379$	−1.11808e9	−1.05496	−0.527480	−	0.849567i	$-0.676863\pi$
$379$	−1.11808e9	−1.05496	−0.527480	+	0.849567i	$0.676863\pi$
$380$	−9.90689e7	−0.0926178
$381$	0	0
$382$	6.78153e8	0.622452
$383$	−1.68891e9	−1.53607	−0.768034	−	0.640409i	$-0.778765\pi$
$383$	−1.68891e9	−1.53607	−0.768034	+	0.640409i	$0.778765\pi$
$384$	0	0
$385$	−4.46932e7	−0.0399143
$386$	6.88900e8	0.609678
$387$	0	0
$388$	−3.24073e6	−0.00281664
$389$	−1.20012e9	−1.03372	−0.516858	−	0.856071i	$-0.672898\pi$
$389$	−1.20012e9	−1.03372	−0.516858	+	0.856071i	$0.672898\pi$
$390$	0	0
$391$	−1.37167e9	−1.16046
$392$	−1.84424e9	−1.54638
$393$	0	0
$394$	−2.55368e8	−0.210344
$395$	−6.49942e6	−0.00530622
$396$	0	0
$397$	6.39914e8	0.513281	0.256640	−	0.966507i	$-0.417384\pi$
$397$	6.39914e8	0.513281	0.256640	+	0.966507i	$0.417384\pi$
$398$	1.13842e8	0.0905130
$399$	0	0
$400$	−1.47540e8	−0.115265
$401$	6.93705e8	0.537241	0.268621	−	0.963246i	$-0.413432\pi$
$401$	6.93705e8	0.537241	0.268621	+	0.963246i	$0.413432\pi$
$402$	0	0
$403$	8.84541e8	0.673210
$404$	7.71628e8	0.582201
$405$	0	0
$406$	−2.20151e9	−1.63260
$407$	−1.40407e8	−0.103231
$408$	0	0
$409$	6.30962e8	0.456007	0.228004	−	0.973660i	$-0.426780\pi$
$409$	6.30962e8	0.456007	0.228004	+	0.973660i	$0.426780\pi$
$410$	1.58656e7	0.0113688
$411$	0	0
$412$	4.51080e8	0.317771
$413$	2.98657e9	2.08616
$414$	0	0
$415$	−1.34500e8	−0.0923748
$416$	1.99881e9	1.36127
$417$	0	0
$418$	4.37922e8	0.293278
$419$	−2.67057e9	−1.77360	−0.886799	−	0.462156i	$-0.847076\pi$
$419$	−2.67057e9	−1.77360	−0.886799	+	0.462156i	$0.847076\pi$
$420$	0	0
$421$	1.82965e9	1.19503	0.597517	−	0.801857i	$-0.296154\pi$
$421$	1.82965e9	1.19503	0.597517	+	0.801857i	$0.296154\pi$
$422$	−5.54882e8	−0.359424
$423$	0	0
$424$	4.46617e8	0.284547
$425$	−1.10732e9	−0.699703
$426$	0	0
$427$	−4.39958e9	−2.73472
$428$	1.33992e9	0.826087
$429$	0	0
$430$	8.55336e7	0.0518797
$431$	1.18514e9	0.713015	0.356508	−	0.934292i	$-0.383967\pi$
$431$	1.18514e9	0.713015	0.356508	+	0.934292i	$0.383967\pi$
$432$	0	0
$433$	−3.02434e8	−0.179029	−0.0895143	−	0.995986i	$-0.528531\pi$
$433$	−3.02434e8	−0.179029	−0.0895143	+	0.995986i	$0.528531\pi$
$434$	−8.04383e8	−0.472333
$435$	0	0
$436$	−1.23623e9	−0.714328
$437$	−4.85729e9	−2.78425
$438$	0	0
$439$	−7.56157e8	−0.426566	−0.213283	−	0.976990i	$-0.568416\pi$
$439$	−7.56157e8	−0.426566	−0.213283	+	0.976990i	$0.568416\pi$
$440$	−4.23975e7	−0.0237277
$441$	0	0
$442$	9.75363e8	0.537265
$443$	2.13366e9	1.16604	0.583018	−	0.812459i	$-0.301872\pi$
$443$	2.13366e9	1.16604	0.583018	+	0.812459i	$0.301872\pi$
$444$	0	0
$445$	1.98034e8	0.106532
$446$	5.75026e8	0.306913
$447$	0	0
$448$	−1.46087e9	−0.767607
$449$	9.63080e8	0.502112	0.251056	−	0.967973i	$-0.419222\pi$
$449$	9.63080e8	0.502112	0.251056	+	0.967973i	$0.419222\pi$
$450$	0	0
$451$	1.41606e8	0.0726882
$452$	−5.23974e8	−0.266885
$453$	0	0
$454$	1.14624e8	0.0574883
$455$	−3.52497e8	−0.175435
$456$	0	0
$457$	−1.40297e9	−0.687609	−0.343805	−	0.939041i	$-0.611716\pi$
$457$	−1.40297e9	−0.687609	−0.343805	+	0.939041i	$0.611716\pi$
$458$	3.17366e8	0.154359
$459$	0	0
$460$	1.88461e8	0.0902754
$461$	2.52827e9	1.20191	0.600953	−	0.799284i	$-0.294788\pi$
$461$	2.52827e9	1.20191	0.600953	+	0.799284i	$0.294788\pi$
$462$	0	0
$463$	2.99988e8	0.140466	0.0702329	−	0.997531i	$-0.477626\pi$
$463$	2.99988e8	0.140466	0.0702329	+	0.997531i	$0.477626\pi$
$464$	4.38460e8	0.203759
$465$	0	0
$466$	−3.14724e8	−0.144072
$467$	−9.43831e8	−0.428830	−0.214415	−	0.976743i	$-0.568784\pi$
$467$	−9.43831e8	−0.428830	−0.214415	+	0.976743i	$0.568784\pi$
$468$	0	0
$469$	−3.21611e9	−1.43955
$470$	−5.51418e7	−0.0244984
$471$	0	0
$472$	2.83317e9	1.24015
$473$	7.63416e8	0.331701
$474$	0	0
$475$	−3.92120e9	−1.67877
$476$	1.79092e9	0.761118
$477$	0	0
$478$	−1.24067e9	−0.519586
$479$	2.70997e6	0.00112665	0.000563326	−	1.00000i	$-0.499821\pi$
$479$	2.70997e6	0.00112665	0.000563326		1.00000i	$0.499821\pi$
$480$	0	0
$481$	−1.10740e9	−0.453729
$482$	−1.04845e9	−0.426467
$483$	0	0
$484$	−1.51652e8	−0.0607981
$485$	867042.	0.000345099 0
$486$	0	0
$487$	4.14451e9	1.62600	0.813002	−	0.582261i	$-0.197832\pi$
$487$	4.14451e9	1.62600	0.813002	+	0.582261i	$0.197832\pi$
$488$	−4.17360e9	−1.62570
$489$	0	0
$490$	1.97741e8	0.0759296
$491$	−5.05782e9	−1.92831	−0.964157	−	0.265332i	$-0.914518\pi$
$491$	−5.05782e9	−1.92831	−0.964157	+	0.265332i	$0.914518\pi$
$492$	0	0
$493$	3.29075e9	1.23689
$494$	3.45391e9	1.28904
$495$	0	0
$496$	1.60203e8	0.0589501
$497$	−6.25116e9	−2.28409
$498$	0	0
$499$	−5.07724e9	−1.82926	−0.914631	−	0.404290i	$-0.867519\pi$
$499$	−5.07724e9	−1.82926	−0.914631	+	0.404290i	$0.867519\pi$
$500$	3.05311e8	0.109231
$501$	0	0
$502$	1.27668e9	0.450423
$503$	1.20032e9	0.420542	0.210271	−	0.977643i	$-0.432565\pi$
$503$	1.20032e9	0.420542	0.210271	+	0.977643i	$0.432565\pi$
$504$	0	0
$505$	−2.06445e8	−0.0713321
$506$	−8.33069e8	−0.285861
$507$	0	0
$508$	−2.75286e9	−0.931669
$509$	−3.95700e9	−1.33001	−0.665003	−	0.746841i	$-0.731570\pi$
$509$	−3.95700e9	−1.33001	−0.665003	+	0.746841i	$0.731570\pi$
$510$	0	0
$511$	4.08766e8	0.135519
$512$	7.00489e8	0.230651
$513$	0	0
$514$	−1.57146e9	−0.510427
$515$	−1.20684e8	−0.0389337
$516$	0	0
$517$	−4.92159e8	−0.156635
$518$	1.00705e9	0.318343
$519$	0	0
$520$	−3.34391e8	−0.104290
$521$	5.64143e8	0.174766	0.0873830	−	0.996175i	$-0.472150\pi$
$521$	5.64143e8	0.174766	0.0873830	+	0.996175i	$0.472150\pi$
$522$	0	0
$523$	−1.78145e9	−0.544526	−0.272263	−	0.962223i	$-0.587772\pi$
$523$	−1.78145e9	−0.544526	−0.272263	+	0.962223i	$0.587772\pi$
$524$	7.38731e8	0.224299
$525$	0	0
$526$	2.24218e8	0.0671768
$527$	1.20236e9	0.357848
$528$	0	0
$529$	5.83531e9	1.71384
$530$	−4.78868e7	−0.0139717
$531$	0	0
$532$	6.34192e9	1.82612
$533$	1.11685e9	0.319485
$534$	0	0
$535$	−3.58489e8	−0.101213
$536$	−3.05091e9	−0.855762
$537$	0	0
$538$	3.33299e9	0.922777
$539$	1.76491e9	0.485468
$540$	0	0
$541$	6.13363e9	1.66543	0.832717	−	0.553699i	$-0.186784\pi$
$541$	6.13363e9	1.66543	0.832717	+	0.553699i	$0.186784\pi$
$542$	8.22998e8	0.222025
$543$	0	0
$544$	2.71700e9	0.723591
$545$	3.30748e8	0.0875205
$546$	0	0
$547$	−1.02383e9	−0.267467	−0.133734	−	0.991017i	$-0.542697\pi$
$547$	−1.02383e9	−0.267467	−0.133734	+	0.991017i	$0.542697\pi$
$548$	8.65393e7	0.0224637
$549$	0	0
$550$	−6.72522e8	−0.172360
$551$	1.16530e10	2.96762
$552$	0	0
$553$	4.16062e8	0.104621
$554$	−8.91859e8	−0.222850
$555$	0	0
$556$	7.01938e8	0.173196
$557$	−8.68740e8	−0.213008	−0.106504	−	0.994312i	$-0.533966\pi$
$557$	−8.68740e8	−0.213008	−0.106504	+	0.994312i	$0.533966\pi$
$558$	0	0
$559$	6.02109e9	1.45792
$560$	−6.38422e7	−0.0153621
$561$	0	0
$562$	−1.70995e9	−0.406356
$563$	7.92129e8	0.187075	0.0935376	−	0.995616i	$-0.470182\pi$
$563$	7.92129e8	0.187075	0.0935376	+	0.995616i	$0.470182\pi$
$564$	0	0
$565$	1.40187e8	0.0326992
$566$	1.15381e9	0.267471
$567$	0	0
$568$	−5.93008e9	−1.35782
$569$	−3.06956e9	−0.698526	−0.349263	−	0.937025i	$-0.613568\pi$
$569$	−3.06956e9	−0.698526	−0.349263	+	0.937025i	$0.613568\pi$
$570$	0	0
$571$	1.36993e9	0.307943	0.153972	−	0.988075i	$-0.450794\pi$
$571$	1.36993e9	0.307943	0.153972	+	0.988075i	$0.450794\pi$
$572$	−1.19609e9	−0.267225
$573$	0	0
$574$	−1.01564e9	−0.224155
$575$	7.45939e9	1.63631
$576$	0	0
$577$	−7.02749e9	−1.52295	−0.761473	−	0.648196i	$-0.775524\pi$
$577$	−7.02749e9	−1.52295	−0.761473	+	0.648196i	$0.775524\pi$
$578$	−1.34599e9	−0.289932
$579$	0	0
$580$	−4.52134e8	−0.0962209
$581$	8.61004e9	1.82133
$582$	0	0
$583$	−4.27406e8	−0.0893307
$584$	3.87770e8	0.0805618
$585$	0	0
$586$	1.71504e9	0.352072
$587$	5.15208e9	1.05135	0.525677	−	0.850684i	$-0.323812\pi$
$587$	5.15208e9	1.05135	0.525677	+	0.850684i	$0.323812\pi$
$588$	0	0
$589$	4.25775e9	0.858572
$590$	−3.03776e8	−0.0608935
$591$	0	0
$592$	−2.00566e8	−0.0397311
$593$	2.10968e9	0.415457	0.207728	−	0.978187i	$-0.433393\pi$
$593$	2.10968e9	0.415457	0.207728	+	0.978187i	$0.433393\pi$
$594$	0	0
$595$	−4.79152e8	−0.0932533
$596$	−4.44014e9	−0.859083
$597$	0	0
$598$	−6.57045e9	−1.25644
$599$	−9.31625e9	−1.77112	−0.885558	−	0.464529i	$-0.846224\pi$
$599$	−9.31625e9	−1.77112	−0.885558	+	0.464529i	$0.846224\pi$
$600$	0	0
$601$	−3.64612e9	−0.685127	−0.342563	−	0.939495i	$-0.611295\pi$
$601$	−3.64612e9	−0.685127	−0.342563	+	0.939495i	$0.611295\pi$
$602$	−5.47545e9	−1.02290
$603$	0	0
$604$	−1.70563e9	−0.314959
$605$	4.05738e7	0.00744907
$606$	0	0
$607$	1.09624e9	0.198951	0.0994755	−	0.995040i	$-0.468284\pi$
$607$	1.09624e9	0.198951	0.0994755	+	0.995040i	$0.468284\pi$
$608$	9.62130e9	1.73609
$609$	0	0
$610$	4.47499e8	0.0798247
$611$	−3.88167e9	−0.688454
$612$	0	0
$613$	6.44955e9	1.13088	0.565442	−	0.824788i	$-0.308706\pi$
$613$	6.44955e9	1.13088	0.565442	+	0.824788i	$0.308706\pi$
$614$	5.79906e9	1.01104
$615$	0	0
$616$	2.71409e9	0.467834
$617$	7.65657e9	1.31231	0.656155	−	0.754626i	$-0.272182\pi$
$617$	7.65657e9	1.31231	0.656155	+	0.754626i	$0.272182\pi$
$618$	0	0
$619$	−6.11175e9	−1.03573	−0.517867	−	0.855461i	$-0.673274\pi$
$619$	−6.11175e9	−1.03573	−0.517867	+	0.855461i	$0.673274\pi$
$620$	−1.65199e8	−0.0278380
$621$	0	0
$622$	3.86963e9	0.644767
$623$	−1.26772e10	−2.10046
$624$	0	0
$625$	5.98085e9	0.979903
$626$	3.20525e8	0.0522218
$627$	0	0
$628$	−1.70351e9	−0.274465
$629$	−1.50530e9	−0.241182
$630$	0	0
$631$	−1.23495e9	−0.195680	−0.0978399	−	0.995202i	$-0.531193\pi$
$631$	−1.23495e9	−0.195680	−0.0978399	+	0.995202i	$0.531193\pi$
$632$	3.94691e8	0.0621939
$633$	0	0
$634$	2.72179e9	0.424172
$635$	7.36516e8	0.114149
$636$	0	0
$637$	1.39199e10	2.13377
$638$	1.99860e9	0.304687
$639$	0	0
$640$	−4.09595e8	−0.0617625
$641$	3.11269e9	0.466802	0.233401	−	0.972381i	$-0.425015\pi$
$641$	3.11269e9	0.466802	0.233401	+	0.972381i	$0.425015\pi$
$642$	0	0
$643$	2.24869e9	0.333574	0.166787	−	0.985993i	$-0.446661\pi$
$643$	2.24869e9	0.333574	0.166787	+	0.985993i	$0.446661\pi$
$644$	−1.20644e10	−1.77994
$645$	0	0
$646$	4.69493e9	0.685197
$647$	−3.45334e9	−0.501274	−0.250637	−	0.968081i	$-0.580640\pi$
$647$	−3.45334e9	−0.501274	−0.250637	+	0.968081i	$0.580640\pi$
$648$	0	0
$649$	−2.71130e9	−0.389333
$650$	−5.30420e9	−0.757571
$651$	0	0
$652$	2.44068e9	0.344861
$653$	−4.81658e9	−0.676929	−0.338464	−	0.940979i	$-0.609907\pi$
$653$	−4.81658e9	−0.676929	−0.338464	+	0.940979i	$0.609907\pi$
$654$	0	0
$655$	−1.97644e8	−0.0274814
$656$	2.02278e8	0.0279760
$657$	0	0
$658$	3.52991e9	0.483029
$659$	5.84569e9	0.795677	0.397838	−	0.917456i	$-0.369761\pi$
$659$	5.84569e9	0.795677	0.397838	+	0.917456i	$0.369761\pi$
$660$	0	0
$661$	−1.39642e10	−1.88067	−0.940334	−	0.340252i	$-0.889488\pi$
$661$	−1.39642e10	−1.88067	−0.940334	+	0.340252i	$0.889488\pi$
$662$	−5.09918e9	−0.683121
$663$	0	0
$664$	8.16780e9	1.08272
$665$	−1.69675e9	−0.223739
$666$	0	0
$667$	−2.21679e10	−2.89257
$668$	−2.96270e9	−0.384566
$669$	0	0
$670$	3.27123e8	0.0420193
$671$	3.99407e9	0.510372
$672$	0	0
$673$	−6.23105e9	−0.787967	−0.393984	−	0.919117i	$-0.628903\pi$
$673$	−6.23105e9	−0.787967	−0.393984	+	0.919117i	$0.628903\pi$
$674$	6.75813e9	0.850191
$675$	0	0
$676$	−4.06208e9	−0.505749
$677$	−3.65484e9	−0.452698	−0.226349	−	0.974046i	$-0.572679\pi$
$677$	−3.65484e9	−0.452698	−0.226349	+	0.974046i	$0.572679\pi$
$678$	0	0
$679$	−5.55039e7	−0.00680423
$680$	−4.54541e8	−0.0554360
$681$	0	0
$682$	7.30243e8	0.0881500
$683$	−7.30759e9	−0.877611	−0.438805	−	0.898582i	$-0.644598\pi$
$683$	−7.30759e9	−0.877611	−0.438805	+	0.898582i	$0.644598\pi$
$684$	0	0
$685$	−2.31532e7	−0.00275228
$686$	−4.79663e9	−0.567286
$687$	0	0
$688$	1.09051e9	0.127664
$689$	−3.37097e9	−0.392633
$690$	0	0
$691$	1.66378e9	0.191833	0.0959163	−	0.995389i	$-0.469422\pi$
$691$	1.66378e9	0.191833	0.0959163	+	0.995389i	$0.469422\pi$
$692$	6.46996e9	0.742216
$693$	0	0
$694$	4.32378e8	0.0491027
$695$	−1.87800e8	−0.0212202
$696$	0	0
$697$	1.51815e9	0.169824
$698$	−9.55967e9	−1.06402
$699$	0	0
$700$	−9.73935e9	−1.07322
$701$	7.01449e9	0.769100	0.384550	−	0.923104i	$-0.374357\pi$
$701$	7.01449e9	0.769100	0.384550	+	0.923104i	$0.374357\pi$
$702$	0	0
$703$	−5.33049e9	−0.578660
$704$	1.32622e9	0.143256
$705$	0	0
$706$	−9.28074e9	−0.992582
$707$	1.32156e10	1.40644
$708$	0	0
$709$	5.76802e8	0.0607806	0.0303903	−	0.999538i	$-0.490325\pi$
$709$	5.76802e8	0.0607806	0.0303903	+	0.999538i	$0.490325\pi$
$710$	6.35830e8	0.0666710
$711$	0	0
$712$	−1.20261e10	−1.24866
$713$	−8.09963e9	−0.836858
$714$	0	0
$715$	3.20007e8	0.0327408
$716$	−9.42121e9	−0.959204
$717$	0	0
$718$	−8.83425e9	−0.890706
$719$	−9.27391e9	−0.930490	−0.465245	−	0.885182i	$-0.654034\pi$
$719$	−9.27391e9	−0.930490	−0.465245	+	0.885182i	$0.654034\pi$
$720$	0	0
$721$	7.72564e9	0.767646
$722$	1.08052e10	1.06845
$723$	0	0
$724$	−9.88598e9	−0.968132
$725$	−1.78957e10	−1.74408
$726$	0	0
$727$	−1.35691e10	−1.30972	−0.654862	−	0.755749i	$-0.727273\pi$
$727$	−1.35691e10	−1.30972	−0.654862	+	0.755749i	$0.727273\pi$
$728$	2.14061e10	2.05626
$729$	0	0
$730$	−4.15772e7	−0.00395572
$731$	8.18452e9	0.774966
$732$	0	0
$733$	1.86948e10	1.75330	0.876651	−	0.481126i	$-0.159772\pi$
$733$	1.86948e10	1.75330	0.876651	+	0.481126i	$0.159772\pi$
$734$	5.40682e9	0.504668
$735$	0	0
$736$	−1.83028e10	−1.69218
$737$	2.91968e9	0.268658
$738$	0	0
$739$	2.11872e10	1.93116	0.965578	−	0.260115i	$-0.0837605\pi$
$739$	2.11872e10	1.93116	0.965578	+	0.260115i	$0.0837605\pi$
$740$	2.06821e8	0.0187622
$741$	0	0
$742$	3.06549e9	0.275477
$743$	4.13191e9	0.369565	0.184782	−	0.982779i	$-0.440842\pi$
$743$	4.13191e9	0.369565	0.184782	+	0.982779i	$0.440842\pi$
$744$	0	0
$745$	1.18794e9	0.105256
$746$	3.44369e9	0.303695
$747$	0	0
$748$	−1.62585e9	−0.142045
$749$	2.29488e10	1.99560
$750$	0	0
$751$	1.78743e10	1.53989	0.769946	−	0.638109i	$-0.220283\pi$
$751$	1.78743e10	1.53989	0.769946	+	0.638109i	$0.220283\pi$
$752$	−7.03027e8	−0.0602850
$753$	0	0
$754$	1.57631e10	1.33919
$755$	4.56332e8	0.0385893
$756$	0	0
$757$	7.62595e9	0.638938	0.319469	−	0.947597i	$-0.396496\pi$
$757$	7.62595e9	0.638938	0.319469	+	0.947597i	$0.396496\pi$
$758$	−7.28010e9	−0.607148
$759$	0	0
$760$	−1.60960e9	−0.133006
$761$	−1.24031e10	−1.02020	−0.510099	−	0.860116i	$-0.670391\pi$
$761$	−1.24031e10	−1.02020	−0.510099	+	0.860116i	$0.670391\pi$
$762$	0	0
$763$	−2.11729e10	−1.72562
$764$	−8.91572e9	−0.723319
$765$	0	0
$766$	−1.09969e10	−0.884035
$767$	−2.13841e10	−1.71123
$768$	0	0
$769$	1.10128e10	0.873283	0.436641	−	0.899636i	$-0.356168\pi$
$769$	1.10128e10	0.873283	0.436641	+	0.899636i	$0.356168\pi$
$770$	−2.91008e8	−0.0229714
$771$	0	0
$772$	−9.05701e9	−0.708475
$773$	8.73173e9	0.679942	0.339971	−	0.940436i	$-0.389583\pi$
$773$	8.73173e9	0.679942	0.339971	+	0.940436i	$0.389583\pi$
$774$	0	0
$775$	−6.53868e9	−0.504585
$776$	−5.26530e7	−0.00404489
$777$	0	0
$778$	−7.81427e9	−0.594922
$779$	5.37599e9	0.407453
$780$	0	0
$781$	5.67500e9	0.426272
$782$	−8.93128e9	−0.667867
$783$	0	0
$784$	2.52109e9	0.186845
$785$	4.55767e8	0.0336279
$786$	0	0
$787$	−2.15808e10	−1.57818	−0.789089	−	0.614278i	$-0.789447\pi$
$787$	−2.15808e10	−1.57818	−0.789089	+	0.614278i	$0.789447\pi$
$788$	3.35734e9	0.244430
$789$	0	0
$790$	−4.23193e7	−0.00305382
$791$	−8.97408e9	−0.644721
$792$	0	0
$793$	3.15014e10	2.24323
$794$	4.16664e9	0.295402
$795$	0	0
$796$	−1.49669e9	−0.105180
$797$	1.43410e10	1.00340	0.501702	−	0.865040i	$-0.332707\pi$
$797$	1.43410e10	1.00340	0.501702	+	0.865040i	$0.332707\pi$
$798$	0	0
$799$	−5.27640e9	−0.365952
$800$	−1.47755e10	−1.02030
$801$	0	0
$802$	4.51688e9	0.309192
$803$	−3.71090e8	−0.0252915
$804$	0	0
$805$	3.22777e9	0.218080
$806$	5.75946e9	0.387444
$807$	0	0
$808$	1.25368e10	0.836080
$809$	7.87747e9	0.523079	0.261539	−	0.965193i	$-0.415770\pi$
$809$	7.87747e9	0.523079	0.261539	+	0.965193i	$0.415770\pi$
$810$	0	0
$811$	1.79798e10	1.18362	0.591810	−	0.806077i	$-0.298413\pi$
$811$	1.79798e10	1.18362	0.591810	+	0.806077i	$0.298413\pi$
$812$	2.89435e10	1.89716
$813$	0	0
$814$	−9.14227e8	−0.0594112
$815$	−6.52992e8	−0.0422528
$816$	0	0
$817$	2.89826e10	1.85935
$818$	4.10835e9	0.262440
$819$	0	0
$820$	−2.08586e8	−0.0132111
$821$	−1.51047e10	−0.952603	−0.476302	−	0.879282i	$-0.658023\pi$
$821$	−1.51047e10	−0.952603	−0.476302	+	0.879282i	$0.658023\pi$
$822$	0	0
$823$	−2.28969e9	−0.143178	−0.0715891	−	0.997434i	$-0.522807\pi$
$823$	−2.28969e9	−0.143178	−0.0715891	+	0.997434i	$0.522807\pi$
$824$	7.32882e9	0.456340
$825$	0	0
$826$	1.94463e10	1.20062
$827$	−1.65291e10	−1.01620	−0.508100	−	0.861298i	$-0.669652\pi$
$827$	−1.65291e10	−1.01620	−0.508100	+	0.861298i	$0.669652\pi$
$828$	0	0
$829$	6.28590e8	0.0383201	0.0191600	−	0.999816i	$-0.493901\pi$
$829$	6.28590e8	0.0383201	0.0191600	+	0.999816i	$0.493901\pi$
$830$	−8.75762e8	−0.0531634
$831$	0	0
$832$	1.04600e10	0.629650
$833$	1.89214e10	1.13422
$834$	0	0
$835$	7.92657e8	0.0471176
$836$	−5.75739e9	−0.340803
$837$	0	0
$838$	−1.73887e10	−1.02074
$839$	−2.41206e10	−1.41001	−0.705005	−	0.709202i	$-0.749055\pi$
$839$	−2.41206e10	−1.41001	−0.705005	+	0.709202i	$0.749055\pi$
$840$	0	0
$841$	3.59327e10	2.08307
$842$	1.19133e10	0.687763
$843$	0	0
$844$	7.29507e9	0.417667
$845$	1.08679e9	0.0619651
$846$	0	0
$847$	−2.59734e9	−0.146871
$848$	−6.10531e8	−0.0343813
$849$	0	0
$850$	−7.21006e9	−0.402691
$851$	1.01403e10	0.564024
$852$	0	0
$853$	−2.75650e10	−1.52067	−0.760337	−	0.649529i	$-0.774966\pi$
$853$	−2.75650e10	−1.52067	−0.760337	+	0.649529i	$0.774966\pi$
$854$	−2.86467e10	−1.57388
$855$	0	0
$856$	2.17700e10	1.18632
$857$	3.29561e10	1.78856	0.894280	−	0.447508i	$-0.147688\pi$
$857$	3.29561e10	1.78856	0.894280	+	0.447508i	$0.147688\pi$
$858$	0	0
$859$	−1.74671e10	−0.940251	−0.470126	−	0.882599i	$-0.655791\pi$
$859$	−1.74671e10	−0.940251	−0.470126	+	0.882599i	$0.655791\pi$
$860$	−1.12452e9	−0.0602866
$861$	0	0
$862$	7.71672e9	0.410353
$863$	−1.33149e10	−0.705179	−0.352589	−	0.935778i	$-0.614699\pi$
$863$	−1.33149e10	−0.705179	−0.352589	+	0.935778i	$0.614699\pi$
$864$	0	0
$865$	−1.73101e9	−0.0909374
$866$	−1.96922e9	−0.103034
$867$	0	0
$868$	1.05753e10	0.548874
$869$	−3.77714e8	−0.0195251
$870$	0	0
$871$	2.30276e10	1.18083
$872$	−2.00854e10	−1.02582
$873$	0	0
$874$	−3.16270e10	−1.60239
$875$	5.22905e9	0.263873
$876$	0	0
$877$	−2.16552e10	−1.08409	−0.542043	−	0.840351i	$-0.682349\pi$
$877$	−2.16552e10	−1.08409	−0.542043	+	0.840351i	$0.682349\pi$
$878$	−4.92352e9	−0.245496
$879$	0	0
$880$	5.79579e7	0.00286697
$881$	1.89906e10	0.935670	0.467835	−	0.883816i	$-0.345034\pi$
$881$	1.89906e10	0.935670	0.467835	+	0.883816i	$0.345034\pi$
$882$	0	0
$883$	−1.59282e10	−0.778580	−0.389290	−	0.921115i	$-0.627280\pi$
$883$	−1.59282e10	−0.778580	−0.389290	+	0.921115i	$0.627280\pi$
$884$	−1.28232e10	−0.624327
$885$	0	0
$886$	1.38928e10	0.671074
$887$	1.80968e10	0.870703	0.435352	−	0.900260i	$-0.356624\pi$
$887$	1.80968e10	0.870703	0.435352	+	0.900260i	$0.356624\pi$
$888$	0	0
$889$	−4.71482e10	−2.25066
$890$	1.28945e9	0.0613111
$891$	0	0
$892$	−7.55990e9	−0.356648
$893$	−1.86845e10	−0.878014
$894$	0	0
$895$	2.52060e9	0.117523
$896$	2.62203e10	1.21775
$897$	0	0
$898$	6.27085e9	0.288974
$899$	1.94317e10	0.891973
$900$	0	0
$901$	−4.58219e9	−0.208707
$902$	9.22031e8	0.0418333
$903$	0	0
$904$	−8.51313e9	−0.383266
$905$	2.64495e9	0.118617
$906$	0	0
$907$	−1.96520e10	−0.874544	−0.437272	−	0.899329i	$-0.644055\pi$
$907$	−1.96520e10	−0.874544	−0.437272	+	0.899329i	$0.644055\pi$
$908$	−1.50697e9	−0.0668041
$909$	0	0
$910$	−2.29519e9	−0.100966
$911$	−3.74053e10	−1.63915	−0.819576	−	0.572971i	$-0.805791\pi$
$911$	−3.74053e10	−1.63915	−0.819576	+	0.572971i	$0.805791\pi$
$912$	0	0
$913$	−7.81646e9	−0.339909
$914$	−9.13508e9	−0.395731
$915$	0	0
$916$	−4.17243e9	−0.179372
$917$	1.26522e10	0.541844
$918$	0	0
$919$	−4.10744e10	−1.74569	−0.872845	−	0.487998i	$-0.837727\pi$
$919$	−4.10744e10	−1.74569	−0.872845	+	0.487998i	$0.837727\pi$
$920$	3.06198e9	0.129642
$921$	0	0
$922$	1.64622e10	0.691719
$923$	4.47589e10	1.87359
$924$	0	0
$925$	8.18609e9	0.340079
$926$	1.95329e9	0.0808405
$927$	0	0
$928$	4.39100e10	1.80362
$929$	1.49524e10	0.611864	0.305932	−	0.952053i	$-0.401032\pi$
$929$	1.49524e10	0.611864	0.305932	+	0.952053i	$0.401032\pi$
$930$	0	0
$931$	6.70036e10	2.72129
$932$	4.13770e9	0.167418
$933$	0	0
$934$	−6.14551e9	−0.246799
$935$	4.34989e8	0.0174035
$936$	0	0
$937$	−1.06439e10	−0.422679	−0.211339	−	0.977413i	$-0.567783\pi$
$937$	−1.06439e10	−0.422679	−0.211339	+	0.977413i	$0.567783\pi$
$938$	−2.09408e10	−0.828484
$939$	0	0
$940$	7.24952e8	0.0284683
$941$	1.23064e10	0.481468	0.240734	−	0.970591i	$-0.422612\pi$
$941$	1.23064e10	0.481468	0.240734	+	0.970591i	$0.422612\pi$
$942$	0	0
$943$	−1.02269e10	−0.397147
$944$	−3.87297e9	−0.149845
$945$	0	0
$946$	4.97078e9	0.190900
$947$	−3.69429e10	−1.41353	−0.706766	−	0.707447i	$-0.749847\pi$
$947$	−3.69429e10	−1.41353	−0.706766	+	0.707447i	$0.749847\pi$
$948$	0	0
$949$	−2.92680e9	−0.111163
$950$	−2.55319e10	−0.966163
$951$	0	0
$952$	2.90975e10	1.09302
$953$	−8.91918e9	−0.333810	−0.166905	−	0.985973i	$-0.553377\pi$
$953$	−8.91918e9	−0.333810	−0.166905	+	0.985973i	$0.553377\pi$
$954$	0	0
$955$	2.38536e9	0.0886220
$956$	1.63111e10	0.603784
$957$	0	0
$958$	1.76453e7	0.000648409 0
$959$	1.48216e9	0.0542661
$960$	0	0
$961$	−2.04127e10	−0.741941
$962$	−7.21054e9	−0.261129
$963$	0	0
$964$	1.37841e10	0.495574
$965$	2.42316e9	0.0868034
$966$	0	0
$967$	9.73150e9	0.346088	0.173044	−	0.984914i	$-0.444640\pi$
$967$	9.73150e9	0.346088	0.173044	+	0.984914i	$0.444640\pi$
$968$	−2.46393e9	−0.0873102
$969$	0	0
$970$	5.64552e6	0.000198611 0
$971$	−2.82145e10	−0.989021	−0.494510	−	0.869172i	$-0.664653\pi$
$971$	−2.82145e10	−0.989021	−0.494510	+	0.869172i	$0.664653\pi$
$972$	0	0
$973$	1.20221e10	0.418393
$974$	2.69859e10	0.935794
$975$	0	0
$976$	5.70536e9	0.196430
$977$	1.91767e10	0.657873	0.328936	−	0.944352i	$-0.393310\pi$
$977$	1.91767e10	0.657873	0.328936	+	0.944352i	$0.393310\pi$
$978$	0	0
$979$	1.15088e10	0.392003
$980$	−2.59972e9	−0.0882338
$981$	0	0
$982$	−3.29327e10	−1.10978
$983$	1.90138e10	0.638457	0.319228	−	0.947678i	$-0.396576\pi$
$983$	1.90138e10	0.638457	0.319228	+	0.947678i	$0.396576\pi$
$984$	0	0
$985$	−8.98241e8	−0.0299479
$986$	2.14269e10	0.711852
$987$	0	0
$988$	−4.54087e10	−1.49793
$989$	−5.51343e10	−1.81232
$990$	0	0
$991$	2.54270e10	0.829922	0.414961	−	0.909839i	$-0.363795\pi$
$991$	2.54270e10	0.829922	0.414961	+	0.909839i	$0.363795\pi$
$992$	1.60437e10	0.521812
$993$	0	0
$994$	−4.07028e10	−1.31454
$995$	4.00431e8	0.0128869
$996$	0	0
$997$	1.76129e10	0.562858	0.281429	−	0.959582i	$-0.409192\pi$
$997$	1.76129e10	0.562858	0.281429	+	0.959582i	$0.409192\pi$
$998$	−3.30591e10	−1.05277
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.a.e.1.3		3
3.2	odd	2		33.8.a.d.1.1	✓	3
12.11	even	2		528.8.a.o.1.2		3
33.32	even	2		363.8.a.e.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.a.d.1.1	✓	3	3.2	odd	2
99.8.a.e.1.3		3	1.1	even	1	trivial
363.8.a.e.1.3		3	33.32	even	2
528.8.a.o.1.2		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)

\(f(q)\)	\(=\)	\(q+6.51124 q^{2} -85.6037 q^{4} +22.9029 q^{5} -1466.13 q^{7} -1390.83 q^{8} +O(q^{10})\)	\(q+6.51124 q^{2} -85.6037 q^{4} +22.9029 q^{5} -1466.13 q^{7} -1390.83 q^{8} +149.126 q^{10} +1331.00 q^{11} +10497.7 q^{13} -9546.34 q^{14} +1901.28 q^{16} +14269.6 q^{17} +50530.6 q^{19} -1960.57 q^{20} +8666.46 q^{22} -96125.6 q^{23} -77600.5 q^{25} +68352.7 q^{26} +125506. q^{28} +230613. q^{29} +84260.8 q^{31} +190405. q^{32} +92912.5 q^{34} -33578.6 q^{35} -105490. q^{37} +329017. q^{38} -31853.9 q^{40} +106391. q^{41} +573565. q^{43} -113939. q^{44} -625897. q^{46} -369766. q^{47} +1.32600e6 q^{49} -505275. q^{50} -898638. q^{52} -321116. q^{53} +30483.7 q^{55} +2.03913e6 q^{56} +1.50158e6 q^{58} -2.03704e6 q^{59} +3.00081e6 q^{61} +548643. q^{62} +996412. q^{64} +240426. q^{65} +2.19360e6 q^{67} -1.22153e6 q^{68} -218639. q^{70} +4.26371e6 q^{71} -278806. q^{73} -686872. q^{74} -4.32561e6 q^{76} -1.95142e6 q^{77} -283782. q^{79} +43544.7 q^{80} +692735. q^{82} -5.87262e6 q^{83} +326814. q^{85} +3.73462e6 q^{86} -1.85119e6 q^{88} +8.64670e6 q^{89} -1.53909e7 q^{91} +8.22871e6 q^{92} -2.40764e6 q^{94} +1.15730e6 q^{95} +37857.4 q^{97} +8.63391e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 9 q^{2} - 15 q^{4} + 444 q^{5} + 1614 q^{7} - 3153 q^{8}+O(q^{10}) \) 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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