LMFDB - Embedded newform 99.8.a.h.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:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 382x^{3} + 558x^{2} + 23640x + 53488 $ x^5 - x^4 - 382x^3 + 558x^2 + 23640*x + 53488
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-18.2221$ 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)

$f(q)$	$=$	$q-3.32273 q^{2} -116.959 q^{4} +363.595 q^{5} -794.809 q^{7} +813.934 q^{8} +O(q^{10})$	\(q-3.32273 q^{2} -116.959 q^{4} +363.595 q^{5} -794.809 q^{7} +813.934 q^{8} -1208.13 q^{10} +1331.00 q^{11} -5608.93 q^{13} +2640.93 q^{14} +12266.3 q^{16} +9204.61 q^{17} +22370.7 q^{19} -42525.9 q^{20} -4422.55 q^{22} -9815.63 q^{23} +54076.3 q^{25} +18636.9 q^{26} +92960.4 q^{28} -135837. q^{29} -115429. q^{31} -144941. q^{32} -30584.4 q^{34} -288989. q^{35} -330903. q^{37} -74331.8 q^{38} +295942. q^{40} -107046. q^{41} -170860. q^{43} -155673. q^{44} +32614.7 q^{46} -142534. q^{47} -191822. q^{49} -179681. q^{50} +656017. q^{52} -579622. q^{53} +483945. q^{55} -646922. q^{56} +451349. q^{58} -3.06499e6 q^{59} -382006. q^{61} +383539. q^{62} -1.08849e6 q^{64} -2.03938e6 q^{65} -2.73570e6 q^{67} -1.07657e6 q^{68} +960230. q^{70} -3.54119e6 q^{71} -2.61462e6 q^{73} +1.09950e6 q^{74} -2.61647e6 q^{76} -1.05789e6 q^{77} +5.83248e6 q^{79} +4.45998e6 q^{80} +355685. q^{82} +6.59532e6 q^{83} +3.34675e6 q^{85} +567723. q^{86} +1.08335e6 q^{88} +7.10746e6 q^{89} +4.45803e6 q^{91} +1.14803e6 q^{92} +473603. q^{94} +8.13388e6 q^{95} +1.25999e7 q^{97} +637372. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 8 q^{2} + 166 q^{4} - 500 q^{5} + 446 q^{7} - 2754 q^{8}+O(q^{10}) $ 5 * q - 8 * q^2 + 166 * q^4 - 500 * q^5 + 446 * q^7 - 2754 * q^8	\( 5 q - 8 q^{2} + 166 q^{4} - 500 q^{5} + 446 q^{7} - 2754 q^{8} + 11516 q^{10} + 6655 q^{11} - 16666 q^{13} - 20516 q^{14} + 15010 q^{16} + 1906 q^{17} - 10446 q^{19} - 155572 q^{20} - 10648 q^{22} + 35468 q^{23} + 104239 q^{25} + 136396 q^{26} + 118456 q^{28} - 259062 q^{29} - 44932 q^{31} - 609010 q^{32} - 592888 q^{34} - 963800 q^{35} + 393978 q^{37} - 1319448 q^{38} + 1650684 q^{40} - 1554074 q^{41} + 263118 q^{43} + 220946 q^{44} - 1948268 q^{46} - 2481904 q^{47} + 498177 q^{49} - 5560984 q^{50} - 4530056 q^{52} - 2325840 q^{53} - 665500 q^{55} - 5221992 q^{56} + 2479968 q^{58} - 4613452 q^{59} + 529362 q^{61} - 3077192 q^{62} + 1437674 q^{64} + 2187496 q^{65} - 4612664 q^{67} + 2362916 q^{68} + 7327832 q^{70} - 5583864 q^{71} + 980054 q^{73} - 3387480 q^{74} + 1023396 q^{76} + 593626 q^{77} + 2804758 q^{79} - 10053364 q^{80} - 110080 q^{82} + 2451324 q^{83} - 4240456 q^{85} + 5937408 q^{86} - 3665574 q^{88} - 4025472 q^{89} - 12525436 q^{91} + 44606548 q^{92} + 1592764 q^{94} - 4273320 q^{95} - 234806 q^{97} + 26686536 q^{98}+O(q^{100}) \) 5 * q - 8 * q^2 + 166 * q^4 - 500 * q^5 + 446 * q^7 - 2754 * q^8 + 11516 * q^10 + 6655 * q^11 - 16666 * q^13 - 20516 * q^14 + 15010 * q^16 + 1906 * q^17 - 10446 * q^19 - 155572 * q^20 - 10648 * q^22 + 35468 * q^23 + 104239 * q^25 + 136396 * q^26 + 118456 * q^28 - 259062 * q^29 - 44932 * q^31 - 609010 * q^32 - 592888 * q^34 - 963800 * q^35 + 393978 * q^37 - 1319448 * q^38 + 1650684 * q^40 - 1554074 * q^41 + 263118 * q^43 + 220946 * q^44 - 1948268 * q^46 - 2481904 * q^47 + 498177 * q^49 - 5560984 * q^50 - 4530056 * q^52 - 2325840 * q^53 - 665500 * q^55 - 5221992 * q^56 + 2479968 * q^58 - 4613452 * q^59 + 529362 * q^61 - 3077192 * q^62 + 1437674 * q^64 + 2187496 * q^65 - 4612664 * q^67 + 2362916 * q^68 + 7327832 * q^70 - 5583864 * q^71 + 980054 * q^73 - 3387480 * q^74 + 1023396 * q^76 + 593626 * q^77 + 2804758 * q^79 - 10053364 * q^80 - 110080 * q^82 + 2451324 * q^83 - 4240456 * q^85 + 5937408 * q^86 - 3665574 * q^88 - 4025472 * q^89 - 12525436 * q^91 + 44606548 * q^92 + 1592764 * q^94 - 4273320 * q^95 - 234806 * q^97 + 26686536 * 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 $

$2$	−3.32273	−0.293690	−0.146845	−	0.989159i	$-0.546912\pi$
$2$	−3.32273	−0.293690	−0.146845	+	0.989159i	$0.546912\pi$
$3$	0	0
$3$	0	0
$4$	−116.959	−0.913746
$5$	363.595	1.30084	0.650419	−	0.759576i	$-0.274594\pi$
$5$	363.595	1.30084	0.650419	+	0.759576i	$0.274594\pi$
$6$	0	0
$7$	−794.809	−0.875829	−0.437915	−	0.899017i	$-0.644283\pi$
$7$	−794.809	−0.875829	−0.437915	+	0.899017i	$0.644283\pi$
$8$	813.934	0.562049
$9$	0	0
$10$	−1208.13	−0.382043
$11$	1331.00	0.301511
$11$	1331.00	0.301511
$12$	0	0
$13$	−5608.93	−0.708073	−0.354037	−	0.935232i	$-0.615191\pi$
$13$	−5608.93	−0.708073	−0.354037	+	0.935232i	$0.615191\pi$
$14$	2640.93	0.257223
$15$	0	0
$16$	12266.3	0.748678
$17$	9204.61	0.454396	0.227198	−	0.973849i	$-0.427044\pi$
$17$	9204.61	0.454396	0.227198	+	0.973849i	$0.427044\pi$
$18$	0	0
$19$	22370.7	0.748243	0.374121	−	0.927380i	$-0.377944\pi$
$19$	22370.7	0.748243	0.374121	+	0.927380i	$0.377944\pi$
$20$	−42525.9	−1.18863
$21$	0	0
$22$	−4422.55	−0.0885510
$23$	−9815.63	−0.168217	−0.0841086	−	0.996457i	$-0.526804\pi$
$23$	−9815.63	−0.168217	−0.0841086	+	0.996457i	$0.526804\pi$
$24$	0	0
$25$	54076.3	0.692177
$26$	18636.9	0.207954
$27$	0	0
$28$	92960.4	0.800286
$29$	−135837.	−1.03425	−0.517124	−	0.855911i	$-0.672997\pi$
$29$	−135837.	−1.03425	−0.517124	+	0.855911i	$0.672997\pi$
$30$	0	0
$31$	−115429.	−0.695904	−0.347952	−	0.937512i	$-0.613123\pi$
$31$	−115429.	−0.695904	−0.347952	+	0.937512i	$0.613123\pi$
$32$	−144941.	−0.781928
$33$	0	0
$34$	−30584.4	−0.133452
$35$	−288989.	−1.13931
$36$	0	0
$37$	−330903.	−1.07398	−0.536988	−	0.843590i	$-0.680438\pi$
$37$	−330903.	−1.07398	−0.536988	+	0.843590i	$0.680438\pi$
$38$	−74331.8	−0.219752
$39$	0	0
$40$	295942.	0.731134
$41$	−107046.	−0.242565	−0.121282	−	0.992618i	$-0.538701\pi$
$41$	−107046.	−0.242565	−0.121282	+	0.992618i	$0.538701\pi$
$42$	0	0
$43$	−170860.	−0.327719	−0.163860	−	0.986484i	$-0.552394\pi$
$43$	−170860.	−0.327719	−0.163860	+	0.986484i	$0.552394\pi$
$44$	−155673.	−0.275505
$45$	0	0
$46$	32614.7	0.0494038
$47$	−142534.	−0.200252	−0.100126	−	0.994975i	$-0.531925\pi$
$47$	−142534.	−0.200252	−0.100126	+	0.994975i	$0.531925\pi$
$48$	0	0
$49$	−191822.	−0.232923
$50$	−179681.	−0.203286
$51$	0	0
$52$	656017.	0.646999
$53$	−579622.	−0.534785	−0.267393	−	0.963588i	$-0.586162\pi$
$53$	−579622.	−0.534785	−0.267393	+	0.963588i	$0.586162\pi$
$54$	0	0
$55$	483945.	0.392217
$56$	−646922.	−0.492259
$57$	0	0
$58$	451349.	0.303749
$59$	−3.06499e6	−1.94288	−0.971441	−	0.237282i	$-0.923744\pi$
$59$	−3.06499e6	−1.94288	−0.971441	+	0.237282i	$0.923744\pi$
$60$	0	0
$61$	−382006.	−0.215484	−0.107742	−	0.994179i	$-0.534362\pi$
$61$	−382006.	−0.215484	−0.107742	+	0.994179i	$0.534362\pi$
$62$	383539.	0.204380
$63$	0	0
$64$	−1.08849e6	−0.519033
$65$	−2.03938e6	−0.921088
$66$	0	0
$67$	−2.73570e6	−1.11124	−0.555618	−	0.831437i	$-0.687518\pi$
$67$	−2.73570e6	−1.11124	−0.555618	+	0.831437i	$0.687518\pi$
$68$	−1.07657e6	−0.415202
$69$	0	0
$70$	960230.	0.334605
$71$	−3.54119e6	−1.17421	−0.587104	−	0.809512i	$-0.699732\pi$
$71$	−3.54119e6	−1.17421	−0.587104	+	0.809512i	$0.699732\pi$
$72$	0	0
$73$	−2.61462e6	−0.786643	−0.393322	−	0.919401i	$-0.628674\pi$
$73$	−2.61462e6	−0.786643	−0.393322	+	0.919401i	$0.628674\pi$
$74$	1.09950e6	0.315417
$75$	0	0
$76$	−2.61647e6	−0.683704
$77$	−1.05789e6	−0.264073
$78$	0	0
$79$	5.83248e6	1.33094	0.665470	−	0.746425i	$-0.268231\pi$
$79$	5.83248e6	1.33094	0.665470	+	0.746425i	$0.268231\pi$
$80$	4.45998e6	0.973908
$81$	0	0
$82$	355685.	0.0712389
$83$	6.59532e6	1.26608	0.633042	−	0.774118i	$-0.281806\pi$
$83$	6.59532e6	1.26608	0.633042	+	0.774118i	$0.281806\pi$
$84$	0	0
$85$	3.34675e6	0.591095
$86$	567723.	0.0962480
$87$	0	0
$88$	1.08335e6	0.169464
$89$	7.10746e6	1.06868	0.534342	−	0.845268i	$-0.320559\pi$
$89$	7.10746e6	1.06868	0.534342	+	0.845268i	$0.320559\pi$
$90$	0	0
$91$	4.45803e6	0.620151
$92$	1.14803e6	0.153708
$93$	0	0
$94$	473603.	0.0588121
$95$	8.13388e6	0.973342
$96$	0	0
$97$	1.25999e7	1.40173	0.700866	−	0.713293i	$-0.252797\pi$
$97$	1.25999e7	1.40173	0.700866	+	0.713293i	$0.252797\pi$
$98$	637372.	0.0684072
$99$	0	0
$100$	−6.32474e6	−0.632474
$101$	−1.66883e7	−1.61171	−0.805857	−	0.592110i	$-0.798295\pi$
$101$	−1.66883e7	−1.61171	−0.805857	+	0.592110i	$0.798295\pi$
$102$	0	0
$103$	−2.36597e6	−0.213343	−0.106672	−	0.994294i	$-0.534019\pi$
$103$	−2.36597e6	−0.213343	−0.106672	+	0.994294i	$0.534019\pi$
$104$	−4.56530e6	−0.397972
$105$	0	0
$106$	1.92593e6	0.157061
$107$	2.33715e7	1.84435	0.922175	−	0.386772i	$-0.126410\pi$
$107$	2.33715e7	1.84435	0.922175	+	0.386772i	$0.126410\pi$
$108$	0	0
$109$	−2.56100e7	−1.89416	−0.947081	−	0.320996i	$-0.895983\pi$
$109$	−2.56100e7	−1.89416	−0.947081	+	0.320996i	$0.895983\pi$
$110$	−1.60802e6	−0.115190
$111$	0	0
$112$	−9.74939e6	−0.655714
$113$	1.77975e7	1.16034	0.580170	−	0.814495i	$-0.302986\pi$
$113$	1.77975e7	1.16034	0.580170	+	0.814495i	$0.302986\pi$
$114$	0	0
$115$	−3.56891e6	−0.218823
$116$	1.58874e7	0.945040
$117$	0	0
$118$	1.01841e7	0.570606
$119$	−7.31591e6	−0.397973
$120$	0	0
$121$	1.77156e6	0.0909091
$122$	1.26930e6	0.0632857
$123$	0	0
$124$	1.35005e7	0.635879
$125$	−8.74398e6	−0.400428
$126$	0	0
$127$	−8.86928e6	−0.384216	−0.192108	−	0.981374i	$-0.561532\pi$
$127$	−8.86928e6	−0.384216	−0.192108	+	0.981374i	$0.561532\pi$
$128$	2.21692e7	0.934363
$129$	0	0
$130$	6.77630e6	0.270515
$131$	1.82538e7	0.709419	0.354710	−	0.934976i	$-0.384580\pi$
$131$	1.82538e7	0.709419	0.354710	+	0.934976i	$0.384580\pi$
$132$	0	0
$133$	−1.77804e7	−0.655333
$134$	9.08999e6	0.326360
$135$	0	0
$136$	7.49194e6	0.255393
$137$	−4.62840e7	−1.53783	−0.768915	−	0.639351i	$-0.779203\pi$
$137$	−4.62840e7	−1.53783	−0.768915	+	0.639351i	$0.779203\pi$
$138$	0	0
$139$	1.68328e7	0.531625	0.265812	−	0.964025i	$-0.414360\pi$
$139$	1.68328e7	0.531625	0.265812	+	0.964025i	$0.414360\pi$
$140$	3.37999e7	1.04104
$141$	0	0
$142$	1.17664e7	0.344854
$143$	−7.46548e6	−0.213492
$144$	0	0
$145$	−4.93896e7	−1.34539
$146$	8.68766e6	0.231030
$147$	0	0
$148$	3.87023e7	0.981342
$149$	−8.76235e6	−0.217004	−0.108502	−	0.994096i	$-0.534605\pi$
$149$	−8.76235e6	−0.217004	−0.108502	+	0.994096i	$0.534605\pi$
$150$	0	0
$151$	4.35131e7	1.02849	0.514246	−	0.857643i	$-0.328072\pi$
$151$	4.35131e7	1.02849	0.514246	+	0.857643i	$0.328072\pi$
$152$	1.82083e7	0.420549
$153$	0	0
$154$	3.51508e6	0.0775556
$155$	−4.19694e7	−0.905258
$156$	0	0
$157$	−5.90648e7	−1.21809	−0.609046	−	0.793135i	$-0.708447\pi$
$157$	−5.90648e7	−1.21809	−0.609046	+	0.793135i	$0.708447\pi$
$158$	−1.93797e7	−0.390884
$159$	0	0
$160$	−5.26999e7	−1.01716
$161$	7.80155e6	0.147330
$162$	0	0
$163$	8.21926e7	1.48654	0.743269	−	0.668993i	$-0.233274\pi$
$163$	8.21926e7	1.48654	0.743269	+	0.668993i	$0.233274\pi$
$164$	1.25201e7	0.221642
$165$	0	0
$166$	−2.19144e7	−0.371837
$167$	−9.09254e7	−1.51070	−0.755349	−	0.655323i	$-0.772533\pi$
$167$	−9.09254e7	−1.51070	−0.755349	+	0.655323i	$0.772533\pi$
$168$	0	0
$169$	−3.12884e7	−0.498632
$170$	−1.11203e7	−0.173599
$171$	0	0
$172$	1.99837e7	0.299452
$173$	−7.51067e7	−1.10285	−0.551426	−	0.834224i	$-0.685916\pi$
$173$	−7.51067e7	−1.10285	−0.551426	+	0.834224i	$0.685916\pi$
$174$	0	0
$175$	−4.29803e7	−0.606229
$176$	1.63265e7	0.225735
$177$	0	0
$178$	−2.36162e7	−0.313862
$179$	−9.81065e7	−1.27853	−0.639267	−	0.768985i	$-0.720762\pi$
$179$	−9.81065e7	−1.27853	−0.639267	+	0.768985i	$0.720762\pi$
$180$	0	0
$181$	8.06735e7	1.01124	0.505622	−	0.862755i	$-0.331263\pi$
$181$	8.06735e7	1.01124	0.505622	+	0.862755i	$0.331263\pi$
$182$	−1.48128e7	−0.182132
$183$	0	0
$184$	−7.98927e6	−0.0945463
$185$	−1.20315e8	−1.39707
$186$	0	0
$187$	1.22513e7	0.137005
$188$	1.66707e7	0.182979
$189$	0	0
$190$	−2.70267e7	−0.285861
$191$	−4.86364e6	−0.0505061	−0.0252531	−	0.999681i	$-0.508039\pi$
$191$	−4.86364e6	−0.0505061	−0.0252531	+	0.999681i	$0.508039\pi$
$192$	0	0
$193$	5.35710e6	0.0536388	0.0268194	−	0.999640i	$-0.491462\pi$
$193$	5.35710e6	0.0536388	0.0268194	+	0.999640i	$0.491462\pi$
$194$	−4.18659e7	−0.411675
$195$	0	0
$196$	2.24354e7	0.212832
$197$	−6.75521e7	−0.629517	−0.314758	−	0.949172i	$-0.601923\pi$
$197$	−6.75521e7	−0.629517	−0.314758	+	0.949172i	$0.601923\pi$
$198$	0	0
$199$	1.54778e8	1.39227	0.696137	−	0.717909i	$-0.254901\pi$
$199$	1.54778e8	1.39227	0.696137	+	0.717909i	$0.254901\pi$
$200$	4.40145e7	0.389037
$201$	0	0
$202$	5.54508e7	0.473345
$203$	1.07964e8	0.905825
$204$	0	0
$205$	−3.89214e7	−0.315537
$206$	7.86148e6	0.0626569
$207$	0	0
$208$	−6.88010e7	−0.530118
$209$	2.97754e7	0.225604
$210$	0	0
$211$	3.37502e7	0.247336	0.123668	−	0.992324i	$-0.460534\pi$
$211$	3.37502e7	0.247336	0.123668	+	0.992324i	$0.460534\pi$
$212$	6.77923e7	0.488658
$213$	0	0
$214$	−7.76572e7	−0.541668
$215$	−6.21240e7	−0.426309
$216$	0	0
$217$	9.17440e7	0.609493
$218$	8.50951e7	0.556297
$219$	0	0
$220$	−5.66020e7	−0.358387
$221$	−5.16280e7	−0.321745
$222$	0	0
$223$	−6.71608e7	−0.405554	−0.202777	−	0.979225i	$-0.564997\pi$
$223$	−6.71608e7	−0.405554	−0.202777	+	0.979225i	$0.564997\pi$
$224$	1.15201e8	0.684836
$225$	0	0
$226$	−5.91364e7	−0.340781
$227$	−2.65102e7	−0.150426	−0.0752130	−	0.997167i	$-0.523964\pi$
$227$	−2.65102e7	−0.150426	−0.0752130	+	0.997167i	$0.523964\pi$
$228$	0	0
$229$	−1.26371e8	−0.695381	−0.347690	−	0.937609i	$-0.613034\pi$
$229$	−1.26371e8	−0.695381	−0.347690	+	0.937609i	$0.613034\pi$
$230$	1.18585e7	0.0642663
$231$	0	0
$232$	−1.10562e8	−0.581298
$233$	2.92316e8	1.51394	0.756968	−	0.653452i	$-0.226680\pi$
$233$	2.92316e8	1.51394	0.756968	+	0.653452i	$0.226680\pi$
$234$	0	0
$235$	−5.18247e7	−0.260495
$236$	3.58479e8	1.77530
$237$	0	0
$238$	2.43088e7	0.116881
$239$	−3.50366e8	−1.66008	−0.830040	−	0.557704i	$-0.811682\pi$
$239$	−3.50366e8	−1.66008	−0.830040	+	0.557704i	$0.811682\pi$
$240$	0	0
$241$	−2.60449e7	−0.119857	−0.0599285	−	0.998203i	$-0.519087\pi$
$241$	−2.60449e7	−0.119857	−0.0599285	+	0.998203i	$0.519087\pi$
$242$	−5.88641e6	−0.0266991
$243$	0	0
$244$	4.46792e7	0.196898
$245$	−6.97455e7	−0.302995
$246$	0	0
$247$	−1.25476e8	−0.529810
$248$	−9.39516e7	−0.391132
$249$	0	0
$250$	2.90539e7	0.117602
$251$	−9.86114e7	−0.393613	−0.196806	−	0.980442i	$-0.563057\pi$
$251$	−9.86114e7	−0.393613	−0.196806	+	0.980442i	$0.563057\pi$
$252$	0	0
$253$	−1.30646e7	−0.0507194
$254$	2.94702e7	0.112840
$255$	0	0
$256$	6.56645e7	0.244619
$257$	−2.03862e8	−0.749153	−0.374576	−	0.927196i	$-0.622212\pi$
$257$	−2.03862e8	−0.749153	−0.374576	+	0.927196i	$0.622212\pi$
$258$	0	0
$259$	2.63005e8	0.940620
$260$	2.38525e8	0.841640
$261$	0	0
$262$	−6.06523e7	−0.208350
$263$	3.08006e8	1.04403	0.522017	−	0.852935i	$-0.325180\pi$
$263$	3.08006e8	1.04403	0.522017	+	0.852935i	$0.325180\pi$
$264$	0	0
$265$	−2.10748e8	−0.695668
$266$	5.90796e7	0.192465
$267$	0	0
$268$	3.19966e8	1.01539
$269$	5.87468e8	1.84014	0.920071	−	0.391751i	$-0.128130\pi$
$269$	5.87468e8	1.84014	0.920071	+	0.391751i	$0.128130\pi$
$270$	0	0
$271$	3.40801e8	1.04018	0.520090	−	0.854112i	$-0.325899\pi$
$271$	3.40801e8	1.04018	0.520090	+	0.854112i	$0.325899\pi$
$272$	1.12907e8	0.340196
$273$	0	0
$274$	1.53789e8	0.451646
$275$	7.19756e7	0.208699
$276$	0	0
$277$	6.23932e8	1.76384	0.881918	−	0.471404i	$-0.156252\pi$
$277$	6.23932e8	1.76384	0.881918	+	0.471404i	$0.156252\pi$
$278$	−5.59309e7	−0.156133
$279$	0	0
$280$	−2.35217e8	−0.640349
$281$	1.49890e8	0.402995	0.201497	−	0.979489i	$-0.435419\pi$
$281$	1.49890e8	0.402995	0.201497	+	0.979489i	$0.435419\pi$
$282$	0	0
$283$	−1.77375e8	−0.465200	−0.232600	−	0.972572i	$-0.574723\pi$
$283$	−1.77375e8	−0.465200	−0.232600	+	0.972572i	$0.574723\pi$
$284$	4.14176e8	1.07293
$285$	0	0
$286$	2.48058e7	0.0627006
$287$	8.50812e7	0.212445
$288$	0	0
$289$	−3.25614e8	−0.793524
$290$	1.64108e8	0.395128
$291$	0	0
$292$	3.05804e8	0.718792
$293$	−9.22209e7	−0.214187	−0.107093	−	0.994249i	$-0.534154\pi$
$293$	−9.22209e7	−0.214187	−0.107093	+	0.994249i	$0.534154\pi$
$294$	0	0
$295$	−1.11441e9	−2.52737
$296$	−2.69333e8	−0.603627
$297$	0	0
$298$	2.91149e7	0.0637321
$299$	5.50551e7	0.119110
$300$	0	0
$301$	1.35801e8	0.287026
$302$	−1.44582e8	−0.302058
$303$	0	0
$304$	2.74407e8	0.560192
$305$	−1.38895e8	−0.280310
$306$	0	0
$307$	−2.24607e8	−0.443037	−0.221518	−	0.975156i	$-0.571101\pi$
$307$	−2.24607e8	−0.443037	−0.221518	+	0.975156i	$0.571101\pi$
$308$	1.23730e8	0.241295
$309$	0	0
$310$	1.39453e8	0.265865
$311$	−8.40990e7	−0.158537	−0.0792683	−	0.996853i	$-0.525258\pi$
$311$	−8.40990e7	−0.158537	−0.0792683	+	0.996853i	$0.525258\pi$
$312$	0	0
$313$	3.65347e8	0.673442	0.336721	−	0.941604i	$-0.390682\pi$
$313$	3.65347e8	0.673442	0.336721	+	0.941604i	$0.390682\pi$
$314$	1.96256e8	0.357742
$315$	0	0
$316$	−6.82164e8	−1.21614
$317$	−1.03643e9	−1.82740	−0.913699	−	0.406391i	$-0.866787\pi$
$317$	−1.03643e9	−1.82740	−0.913699	+	0.406391i	$0.866787\pi$
$318$	0	0
$319$	−1.80799e8	−0.311837
$320$	−3.95770e8	−0.675177
$321$	0	0
$322$	−2.59224e7	−0.0432693
$323$	2.05914e8	0.339998
$324$	0	0
$325$	−3.03310e8	−0.490112
$326$	−2.73104e8	−0.436582
$327$	0	0
$328$	−8.71285e7	−0.136333
$329$	1.13287e8	0.175387
$330$	0	0
$331$	4.40845e8	0.668172	0.334086	−	0.942543i	$-0.391572\pi$
$331$	4.40845e8	0.668172	0.334086	+	0.942543i	$0.391572\pi$
$332$	−7.71385e8	−1.15688
$333$	0	0
$334$	3.02120e8	0.443677
$335$	−9.94687e8	−1.44554
$336$	0	0
$337$	3.15315e8	0.448787	0.224393	−	0.974499i	$-0.427960\pi$
$337$	3.15315e8	0.448787	0.224393	+	0.974499i	$0.427960\pi$
$338$	1.03963e8	0.146444
$339$	0	0
$340$	−3.91434e8	−0.540111
$341$	−1.53636e8	−0.209823
$342$	0	0
$343$	8.07021e8	1.07983
$344$	−1.39069e8	−0.184194
$345$	0	0
$346$	2.49559e8	0.323897
$347$	−2.95419e8	−0.379565	−0.189782	−	0.981826i	$-0.560778\pi$
$347$	−2.95419e8	−0.379565	−0.189782	+	0.981826i	$0.560778\pi$
$348$	0	0
$349$	1.14965e9	1.44769	0.723844	−	0.689964i	$-0.242373\pi$
$349$	1.14965e9	1.44769	0.723844	+	0.689964i	$0.242373\pi$
$350$	1.42812e8	0.178044
$351$	0	0
$352$	−1.92917e8	−0.235760
$353$	−3.68889e8	−0.446359	−0.223180	−	0.974777i	$-0.571644\pi$
$353$	−3.68889e8	−0.446359	−0.223180	+	0.974777i	$0.571644\pi$
$354$	0	0
$355$	−1.28756e9	−1.52745
$356$	−8.31285e8	−0.976506
$357$	0	0
$358$	3.25981e8	0.375493
$359$	1.45600e9	1.66085	0.830425	−	0.557131i	$-0.188098\pi$
$359$	1.45600e9	1.66085	0.830425	+	0.557131i	$0.188098\pi$
$360$	0	0
$361$	−3.93423e8	−0.440133
$362$	−2.68056e8	−0.296993
$363$	0	0
$364$	−5.21408e8	−0.566661
$365$	−9.50661e8	−1.02329
$366$	0	0
$367$	8.92778e7	0.0942784	0.0471392	−	0.998888i	$-0.484990\pi$
$367$	8.92778e7	0.0942784	0.0471392	+	0.998888i	$0.484990\pi$
$368$	−1.20402e8	−0.125941
$369$	0	0
$370$	3.99773e8	0.410306
$371$	4.60689e8	0.468381
$372$	0	0
$373$	−1.57006e8	−0.156652	−0.0783260	−	0.996928i	$-0.524958\pi$
$373$	−1.57006e8	−0.156652	−0.0783260	+	0.996928i	$0.524958\pi$
$374$	−4.07079e7	−0.0402372
$375$	0	0
$376$	−1.16013e8	−0.112551
$377$	7.61899e8	0.732323
$378$	0	0
$379$	−1.08200e9	−1.02092	−0.510458	−	0.859902i	$-0.670524\pi$
$379$	−1.08200e9	−1.02092	−0.510458	+	0.859902i	$0.670524\pi$
$380$	−9.51335e8	−0.889387
$381$	0	0
$382$	1.61605e7	0.0148332
$383$	−7.14031e8	−0.649413	−0.324707	−	0.945815i	$-0.605266\pi$
$383$	−7.14031e8	−0.649413	−0.324707	+	0.945815i	$0.605266\pi$
$384$	0	0
$385$	−3.84644e8	−0.343515
$386$	−1.78002e7	−0.0157532
$387$	0	0
$388$	−1.47367e9	−1.28083
$389$	−8.01111e8	−0.690032	−0.345016	−	0.938597i	$-0.612127\pi$
$389$	−8.01111e8	−0.690032	−0.345016	+	0.938597i	$0.612127\pi$
$390$	0	0
$391$	−9.03490e7	−0.0764372
$392$	−1.56130e8	−0.130914
$393$	0	0
$394$	2.24457e8	0.184883
$395$	2.12066e9	1.73134
$396$	0	0
$397$	1.57410e9	1.26260	0.631300	−	0.775539i	$-0.282522\pi$
$397$	1.57410e9	1.26260	0.631300	+	0.775539i	$0.282522\pi$
$398$	−5.14287e8	−0.408897
$399$	0	0
$400$	6.63318e8	0.518217
$401$	−1.76966e9	−1.37052	−0.685259	−	0.728300i	$-0.740311\pi$
$401$	−1.76966e9	−1.37052	−0.685259	+	0.728300i	$0.740311\pi$
$402$	0	0
$403$	6.47433e8	0.492751
$404$	1.95186e9	1.47270
$405$	0	0
$406$	−3.58736e8	−0.266032
$407$	−4.40432e8	−0.323816
$408$	0	0
$409$	−6.07845e8	−0.439300	−0.219650	−	0.975579i	$-0.570492\pi$
$409$	−6.07845e8	−0.439300	−0.219650	+	0.975579i	$0.570492\pi$
$410$	1.29325e8	0.0926702
$411$	0	0
$412$	2.76723e8	0.194942
$413$	2.43608e9	1.70163
$414$	0	0
$415$	2.39802e9	1.64697
$416$	8.12965e8	0.553662
$417$	0	0
$418$	−9.89356e7	−0.0662576
$419$	1.34553e9	0.893602	0.446801	−	0.894633i	$-0.352563\pi$
$419$	1.34553e9	0.893602	0.446801	+	0.894633i	$0.352563\pi$
$420$	0	0
$421$	−2.74604e9	−1.79357	−0.896787	−	0.442462i	$-0.854105\pi$
$421$	−2.74604e9	−1.79357	−0.896787	+	0.442462i	$0.854105\pi$
$422$	−1.12143e8	−0.0726404
$423$	0	0
$424$	−4.71774e8	−0.300575
$425$	4.97752e8	0.314522
$426$	0	0
$427$	3.03622e8	0.188727
$428$	−2.73352e9	−1.68527
$429$	0	0
$430$	2.06421e8	0.125203
$431$	8.80296e8	0.529613	0.264806	−	0.964302i	$-0.414692\pi$
$431$	8.80296e8	0.529613	0.264806	+	0.964302i	$0.414692\pi$
$432$	0	0
$433$	2.33636e9	1.38303	0.691517	−	0.722360i	$-0.256943\pi$
$433$	2.33636e9	1.38303	0.691517	+	0.722360i	$0.256943\pi$
$434$	−3.04840e8	−0.179002
$435$	0	0
$436$	2.99533e9	1.73078
$437$	−2.19583e8	−0.125867
$438$	0	0
$439$	−2.96425e9	−1.67220	−0.836102	−	0.548574i	$-0.815171\pi$
$439$	−2.96425e9	−1.67220	−0.836102	+	0.548574i	$0.815171\pi$
$440$	3.93899e8	0.220445
$441$	0	0
$442$	1.71546e8	0.0944936
$443$	1.34705e9	0.736155	0.368078	−	0.929795i	$-0.380016\pi$
$443$	1.34705e9	0.736155	0.368078	+	0.929795i	$0.380016\pi$
$444$	0	0
$445$	2.58424e9	1.39018
$446$	2.23157e8	0.119107
$447$	0	0
$448$	8.65142e8	0.454584
$449$	4.13954e8	0.215819	0.107909	−	0.994161i	$-0.465584\pi$
$449$	4.13954e8	0.215819	0.107909	+	0.994161i	$0.465584\pi$
$450$	0	0
$451$	−1.42478e8	−0.0731360
$452$	−2.08159e9	−1.06026
$453$	0	0
$454$	8.80863e7	0.0441787
$455$	1.62092e9	0.806716
$456$	0	0
$457$	−2.61565e9	−1.28196	−0.640978	−	0.767559i	$-0.721471\pi$
$457$	−2.61565e9	−1.28196	−0.640978	+	0.767559i	$0.721471\pi$
$458$	4.19896e8	0.204227
$459$	0	0
$460$	4.17418e8	0.199949
$461$	8.26588e8	0.392949	0.196474	−	0.980509i	$-0.437051\pi$
$461$	8.26588e8	0.392949	0.196474	+	0.980509i	$0.437051\pi$
$462$	0	0
$463$	−3.31462e9	−1.55203	−0.776014	−	0.630715i	$-0.782762\pi$
$463$	−3.31462e9	−1.55203	−0.776014	+	0.630715i	$0.782762\pi$
$464$	−1.66622e9	−0.774318
$465$	0	0
$466$	−9.71287e8	−0.444628
$467$	2.64652e9	1.20245	0.601223	−	0.799081i	$-0.294680\pi$
$467$	2.64652e9	1.20245	0.601223	+	0.799081i	$0.294680\pi$
$468$	0	0
$469$	2.17436e9	0.973254
$470$	1.72200e8	0.0765049
$471$	0	0
$472$	−2.49469e9	−1.09199
$473$	−2.27415e8	−0.0988110
$474$	0	0
$475$	1.20973e9	0.517916
$476$	8.55665e8	0.363646
$477$	0	0
$478$	1.16417e9	0.487550
$479$	3.58620e9	1.49094	0.745471	−	0.666538i	$-0.232225\pi$
$479$	3.58620e9	1.49094	0.745471	+	0.666538i	$0.232225\pi$
$480$	0	0
$481$	1.85601e9	0.760454
$482$	8.65402e7	0.0352009
$483$	0	0
$484$	−2.07201e8	−0.0830678
$485$	4.58125e9	1.82342
$486$	0	0
$487$	−3.81449e9	−1.49653	−0.748265	−	0.663400i	$-0.769113\pi$
$487$	−3.81449e9	−1.49653	−0.748265	+	0.663400i	$0.769113\pi$
$488$	−3.10927e8	−0.121113
$489$	0	0
$490$	2.31745e8	0.0889866
$491$	−1.16025e8	−0.0442352	−0.0221176	−	0.999755i	$-0.507041\pi$
$491$	−1.16025e8	−0.0442352	−0.0221176	+	0.999755i	$0.507041\pi$
$492$	0	0
$493$	−1.25033e9	−0.469958
$494$	4.16922e8	0.155600
$495$	0	0
$496$	−1.41589e9	−0.521008
$497$	2.81457e9	1.02841
$498$	0	0
$499$	1.62837e9	0.586681	0.293341	−	0.956008i	$-0.405233\pi$
$499$	1.62837e9	0.586681	0.293341	+	0.956008i	$0.405233\pi$
$500$	1.02269e9	0.365889
$501$	0	0
$502$	3.27659e8	0.115600
$503$	−1.27065e9	−0.445181	−0.222590	−	0.974912i	$-0.571451\pi$
$503$	−1.27065e9	−0.445181	−0.222590	+	0.974912i	$0.571451\pi$
$504$	0	0
$505$	−6.06779e9	−2.09658
$506$	4.34101e7	0.0148958
$507$	0	0
$508$	1.03735e9	0.351076
$509$	−2.97698e9	−1.00061	−0.500304	−	0.865850i	$-0.666778\pi$
$509$	−2.97698e9	−1.00061	−0.500304	+	0.865850i	$0.666778\pi$
$510$	0	0
$511$	2.07812e9	0.688965
$512$	−3.05585e9	−1.00621
$513$	0	0
$514$	6.77378e8	0.220019
$515$	−8.60255e8	−0.277525
$516$	0	0
$517$	−1.89713e8	−0.0603782
$518$	−8.73893e8	−0.276251
$519$	0	0
$520$	−1.65992e9	−0.517696
$521$	3.33012e8	0.103164	0.0515820	−	0.998669i	$-0.483574\pi$
$521$	3.33012e8	0.103164	0.0515820	+	0.998669i	$0.483574\pi$
$522$	0	0
$523$	3.42136e9	1.04579	0.522894	−	0.852398i	$-0.324852\pi$
$523$	3.42136e9	1.04579	0.522894	+	0.852398i	$0.324852\pi$
$524$	−2.13495e9	−0.648229
$525$	0	0
$526$	−1.02342e9	−0.306623
$527$	−1.06248e9	−0.316216
$528$	0	0
$529$	−3.30848e9	−0.971703
$530$	7.00257e8	0.204311
$531$	0	0
$532$	2.07959e9	0.598808
$533$	6.00414e8	0.171754
$534$	0	0
$535$	8.49776e9	2.39920
$536$	−2.22668e9	−0.624569
$537$	0	0
$538$	−1.95200e9	−0.540432
$539$	−2.55315e8	−0.0702289
$540$	0	0
$541$	4.19654e9	1.13947	0.569733	−	0.821830i	$-0.307047\pi$
$541$	4.19654e9	1.13947	0.569733	+	0.821830i	$0.307047\pi$
$542$	−1.13239e9	−0.305491
$543$	0	0
$544$	−1.33413e9	−0.355305
$545$	−9.31167e9	−2.46400
$546$	0	0
$547$	5.71370e9	1.49266	0.746331	−	0.665575i	$-0.231813\pi$
$547$	5.71370e9	1.49266	0.746331	+	0.665575i	$0.231813\pi$
$548$	5.41335e9	1.40519
$549$	0	0
$550$	−2.39155e8	−0.0612930
$551$	−3.03877e9	−0.773868
$552$	0	0
$553$	−4.63570e9	−1.16568
$554$	−2.07316e9	−0.518021
$555$	0	0
$556$	−1.96876e9	−0.485770
$557$	−7.31630e9	−1.79390	−0.896950	−	0.442133i	$-0.854222\pi$
$557$	−7.31630e9	−1.79390	−0.896950	+	0.442133i	$0.854222\pi$
$558$	0	0
$559$	9.58344e8	0.232049
$560$	−3.54483e9	−0.852977
$561$	0	0
$562$	−4.98043e8	−0.118356
$563$	5.51362e9	1.30214	0.651069	−	0.759018i	$-0.274321\pi$
$563$	5.51362e9	1.30214	0.651069	+	0.759018i	$0.274321\pi$
$564$	0	0
$565$	6.47109e9	1.50941
$566$	5.89369e8	0.136625
$567$	0	0
$568$	−2.88229e9	−0.659962
$569$	−5.25806e9	−1.19655	−0.598277	−	0.801289i	$-0.704148\pi$
$569$	−5.25806e9	−1.19655	−0.598277	+	0.801289i	$0.704148\pi$
$570$	0	0
$571$	−6.47973e9	−1.45657	−0.728283	−	0.685276i	$-0.759682\pi$
$571$	−6.47973e9	−1.45657	−0.728283	+	0.685276i	$0.759682\pi$
$572$	8.73159e8	0.195078
$573$	0	0
$574$	−2.82702e8	−0.0623931
$575$	−5.30793e8	−0.116436
$576$	0	0
$577$	−5.81347e9	−1.25985	−0.629927	−	0.776654i	$-0.716915\pi$
$577$	−5.81347e9	−1.25985	−0.629927	+	0.776654i	$0.716915\pi$
$578$	1.08193e9	0.233051
$579$	0	0
$580$	5.77658e9	1.22934
$581$	−5.24202e9	−1.10887
$582$	0	0
$583$	−7.71477e8	−0.161244
$584$	−2.12812e9	−0.442132
$585$	0	0
$586$	3.06425e8	0.0629046
$587$	4.35821e9	0.889355	0.444678	−	0.895691i	$-0.353318\pi$
$587$	4.35821e9	0.889355	0.444678	+	0.895691i	$0.353318\pi$
$588$	0	0
$589$	−2.58223e9	−0.520705
$590$	3.70289e9	0.742265
$591$	0	0
$592$	−4.05897e9	−0.804062
$593$	3.81931e9	0.752132	0.376066	−	0.926593i	$-0.377277\pi$
$593$	3.81931e9	0.752132	0.376066	+	0.926593i	$0.377277\pi$
$594$	0	0
$595$	−2.66003e9	−0.517698
$596$	1.02484e9	0.198287
$597$	0	0
$598$	−1.82933e8	−0.0349815
$599$	−1.51991e9	−0.288950	−0.144475	−	0.989508i	$-0.546149\pi$
$599$	−1.51991e9	−0.288950	−0.144475	+	0.989508i	$0.546149\pi$
$600$	0	0
$601$	7.82880e9	1.47107	0.735537	−	0.677484i	$-0.236930\pi$
$601$	7.82880e9	1.47107	0.735537	+	0.677484i	$0.236930\pi$
$602$	−4.51231e8	−0.0842968
$603$	0	0
$604$	−5.08927e9	−0.939780
$605$	6.44131e8	0.118258
$606$	0	0
$607$	7.80571e9	1.41662	0.708308	−	0.705904i	$-0.249459\pi$
$607$	7.80571e9	1.41662	0.708308	+	0.705904i	$0.249459\pi$
$608$	−3.24244e9	−0.585072
$609$	0	0
$610$	4.61512e8	0.0823243
$611$	7.99464e8	0.141793
$612$	0	0
$613$	3.15017e9	0.552360	0.276180	−	0.961106i	$-0.410931\pi$
$613$	3.15017e9	0.552360	0.276180	+	0.961106i	$0.410931\pi$
$614$	7.46309e8	0.130116
$615$	0	0
$616$	−8.61053e8	−0.148422
$617$	1.07359e9	0.184009	0.0920044	−	0.995759i	$-0.470673\pi$
$617$	1.07359e9	0.184009	0.0920044	+	0.995759i	$0.470673\pi$
$618$	0	0
$619$	−7.48615e9	−1.26865	−0.634324	−	0.773067i	$-0.718722\pi$
$619$	−7.48615e9	−1.26865	−0.634324	+	0.773067i	$0.718722\pi$
$620$	4.90872e9	0.827175
$621$	0	0
$622$	2.79438e8	0.0465607
$623$	−5.64907e9	−0.935985
$624$	0	0
$625$	−7.40398e9	−1.21307
$626$	−1.21395e9	−0.197783
$627$	0	0
$628$	6.90819e9	1.11303
$629$	−3.04583e9	−0.488010
$630$	0	0
$631$	1.61146e9	0.255339	0.127670	−	0.991817i	$-0.459250\pi$
$631$	1.61146e9	0.255339	0.127670	+	0.991817i	$0.459250\pi$
$632$	4.74725e9	0.748053
$633$	0	0
$634$	3.44378e9	0.536689
$635$	−3.22482e9	−0.499802
$636$	0	0
$637$	1.07592e9	0.164926
$638$	6.00745e8	0.0915837
$639$	0	0
$640$	8.06062e9	1.21545
$641$	−5.08539e9	−0.762643	−0.381322	−	0.924442i	$-0.624531\pi$
$641$	−5.08539e9	−0.762643	−0.381322	+	0.924442i	$0.624531\pi$
$642$	0	0
$643$	4.14213e9	0.614448	0.307224	−	0.951637i	$-0.400600\pi$
$643$	4.14213e9	0.614448	0.307224	+	0.951637i	$0.400600\pi$
$644$	−9.12465e8	−0.134622
$645$	0	0
$646$	−6.84196e8	−0.0998542
$647$	5.45536e9	0.791879	0.395939	−	0.918277i	$-0.370419\pi$
$647$	5.45536e9	0.791879	0.395939	+	0.918277i	$0.370419\pi$
$648$	0	0
$649$	−4.07950e9	−0.585801
$650$	1.00782e9	0.143941
$651$	0	0
$652$	−9.61320e9	−1.35832
$653$	3.48691e9	0.490054	0.245027	−	0.969516i	$-0.421203\pi$
$653$	3.48691e9	0.490054	0.245027	+	0.969516i	$0.421203\pi$
$654$	0	0
$655$	6.63698e9	0.922839
$656$	−1.31306e9	−0.181603
$657$	0	0
$658$	−3.76423e8	−0.0515093
$659$	−1.73924e8	−0.0236733	−0.0118367	−	0.999930i	$-0.503768\pi$
$659$	−1.73924e8	−0.0236733	−0.0118367	+	0.999930i	$0.503768\pi$
$660$	0	0
$661$	1.82919e9	0.246351	0.123175	−	0.992385i	$-0.460692\pi$
$661$	1.82919e9	0.246351	0.123175	+	0.992385i	$0.460692\pi$
$662$	−1.46481e9	−0.196236
$663$	0	0
$664$	5.36815e9	0.711601
$665$	−6.46488e9	−0.852481
$666$	0	0
$667$	1.33332e9	0.173978
$668$	1.06346e10	1.38039
$669$	0	0
$670$	3.30507e9	0.424541
$671$	−5.08450e8	−0.0649710
$672$	0	0
$673$	−5.78179e9	−0.731156	−0.365578	−	0.930781i	$-0.619129\pi$
$673$	−5.78179e9	−0.731156	−0.365578	+	0.930781i	$0.619129\pi$
$674$	−1.04771e9	−0.131804
$675$	0	0
$676$	3.65948e9	0.455623
$677$	5.04957e9	0.625452	0.312726	−	0.949843i	$-0.398758\pi$
$677$	5.04957e9	0.625452	0.312726	+	0.949843i	$0.398758\pi$
$678$	0	0
$679$	−1.00145e10	−1.22768
$680$	2.72403e9	0.332224
$681$	0	0
$682$	5.10491e8	0.0616230
$683$	3.95420e9	0.474883	0.237441	−	0.971402i	$-0.423691\pi$
$683$	3.95420e9	0.474883	0.237441	+	0.971402i	$0.423691\pi$
$684$	0	0
$685$	−1.68286e10	−2.00047
$686$	−2.68151e9	−0.317136
$687$	0	0
$688$	−2.09583e9	−0.245356
$689$	3.25106e9	0.378667
$690$	0	0
$691$	−9.10443e9	−1.04973	−0.524867	−	0.851184i	$-0.675885\pi$
$691$	−9.10443e9	−1.04973	−0.524867	+	0.851184i	$0.675885\pi$
$692$	8.78445e9	1.00773
$693$	0	0
$694$	9.81598e8	0.111474
$695$	6.12033e9	0.691557
$696$	0	0
$697$	−9.85318e8	−0.110220
$698$	−3.81996e9	−0.425172
$699$	0	0
$700$	5.02696e9	0.553939
$701$	4.44249e9	0.487094	0.243547	−	0.969889i	$-0.421689\pi$
$701$	4.44249e9	0.487094	0.243547	+	0.969889i	$0.421689\pi$
$702$	0	0
$703$	−7.40254e9	−0.803595
$704$	−1.44878e9	−0.156494
$705$	0	0
$706$	1.22572e9	0.131091
$707$	1.32640e10	1.41159
$708$	0	0
$709$	5.68144e9	0.598682	0.299341	−	0.954146i	$-0.403233\pi$
$709$	5.68144e9	0.598682	0.299341	+	0.954146i	$0.403233\pi$
$710$	4.27821e9	0.448598
$711$	0	0
$712$	5.78500e9	0.600653
$713$	1.13301e9	0.117063
$714$	0	0
$715$	−2.71441e9	−0.277718
$716$	1.14745e10	1.16826
$717$	0	0
$718$	−4.83789e9	−0.487776
$719$	−1.74161e9	−0.174743	−0.0873714	−	0.996176i	$-0.527847\pi$
$719$	−1.74161e9	−0.174743	−0.0873714	+	0.996176i	$0.527847\pi$
$720$	0	0
$721$	1.88049e9	0.186852
$722$	1.30724e9	0.129263
$723$	0	0
$724$	−9.43553e9	−0.924020
$725$	−7.34556e9	−0.715883
$726$	0	0
$727$	1.63948e9	0.158247	0.0791234	−	0.996865i	$-0.474788\pi$
$727$	1.63948e9	0.158247	0.0791234	+	0.996865i	$0.474788\pi$
$728$	3.62854e9	0.348555
$729$	0	0
$730$	3.15879e9	0.300532
$731$	−1.57270e9	−0.148914
$732$	0	0
$733$	1.84574e10	1.73104	0.865518	−	0.500877i	$-0.166989\pi$
$733$	1.84574e10	1.73104	0.865518	+	0.500877i	$0.166989\pi$
$734$	−2.96646e8	−0.0276887
$735$	0	0
$736$	1.42269e9	0.131534
$737$	−3.64122e9	−0.335051
$738$	0	0
$739$	5.69446e9	0.519035	0.259518	−	0.965738i	$-0.416436\pi$
$739$	5.69446e9	0.519035	0.259518	+	0.965738i	$0.416436\pi$
$740$	1.40719e10	1.27657
$741$	0	0
$742$	−1.53074e9	−0.137559
$743$	−1.59748e9	−0.142881	−0.0714404	−	0.997445i	$-0.522760\pi$
$743$	−1.59748e9	−0.142881	−0.0714404	+	0.997445i	$0.522760\pi$
$744$	0	0
$745$	−3.18595e9	−0.282287
$746$	5.21689e8	0.0460072
$747$	0	0
$748$	−1.43291e9	−0.125188
$749$	−1.85759e10	−1.61534
$750$	0	0
$751$	−1.40723e8	−0.0121234	−0.00606170	−	0.999982i	$-0.501930\pi$
$751$	−1.40723e8	−0.0121234	−0.00606170	+	0.999982i	$0.501930\pi$
$752$	−1.74837e9	−0.149924
$753$	0	0
$754$	−2.53158e9	−0.215076
$755$	1.58211e10	1.33790
$756$	0	0
$757$	3.16126e9	0.264865	0.132433	−	0.991192i	$-0.457721\pi$
$757$	3.16126e9	0.264865	0.132433	+	0.991192i	$0.457721\pi$
$758$	3.59519e9	0.299833
$759$	0	0
$760$	6.62044e9	0.547066
$761$	−1.50756e10	−1.24002	−0.620008	−	0.784596i	$-0.712871\pi$
$761$	−1.50756e10	−1.24002	−0.620008	+	0.784596i	$0.712871\pi$
$762$	0	0
$763$	2.03551e10	1.65896
$764$	5.68848e8	0.0461498
$765$	0	0
$766$	2.37253e9	0.190726
$767$	1.71913e10	1.37570
$768$	0	0
$769$	1.33189e10	1.05615	0.528075	−	0.849198i	$-0.322914\pi$
$769$	1.33189e10	1.05615	0.528075	+	0.849198i	$0.322914\pi$
$770$	1.27807e9	0.100887
$771$	0	0
$772$	−6.26563e8	−0.0490122
$773$	1.78676e9	0.139135	0.0695676	−	0.997577i	$-0.477838\pi$
$773$	1.78676e9	0.139135	0.0695676	+	0.997577i	$0.477838\pi$
$774$	0	0
$775$	−6.24198e9	−0.481689
$776$	1.02555e10	0.787842
$777$	0	0
$778$	2.66187e9	0.202656
$779$	−2.39470e9	−0.181497
$780$	0	0
$781$	−4.71332e9	−0.354037
$782$	3.00205e8	0.0224489
$783$	0	0
$784$	−2.35295e9	−0.174384
$785$	−2.14757e10	−1.58454
$786$	0	0
$787$	−5.38510e9	−0.393806	−0.196903	−	0.980423i	$-0.563088\pi$
$787$	−5.38510e9	−0.393806	−0.196903	+	0.980423i	$0.563088\pi$
$788$	7.90086e9	0.575218
$789$	0	0
$790$	−7.04638e9	−0.508477
$791$	−1.41456e10	−1.01626
$792$	0	0
$793$	2.14264e9	0.152579
$794$	−5.23030e9	−0.370813
$795$	0	0
$796$	−1.81028e10	−1.27218
$797$	−2.05802e10	−1.43994	−0.719971	−	0.694004i	$-0.755845\pi$
$797$	−2.05802e10	−1.43994	−0.719971	+	0.694004i	$0.755845\pi$
$798$	0	0
$799$	−1.31197e9	−0.0909936
$800$	−7.83789e9	−0.541233
$801$	0	0
$802$	5.88010e9	0.402508
$803$	−3.48005e9	−0.237182
$804$	0	0
$805$	2.83660e9	0.191652
$806$	−2.15124e9	−0.144716
$807$	0	0
$808$	−1.35832e10	−0.905862
$809$	−7.42304e9	−0.492904	−0.246452	−	0.969155i	$-0.579265\pi$
$809$	−7.42304e9	−0.492904	−0.246452	+	0.969155i	$0.579265\pi$
$810$	0	0
$811$	3.18690e9	0.209795	0.104898	−	0.994483i	$-0.466548\pi$
$811$	3.18690e9	0.209795	0.104898	+	0.994483i	$0.466548\pi$
$812$	−1.26275e10	−0.827694
$813$	0	0
$814$	1.46344e9	0.0951017
$815$	2.98848e10	1.93374
$816$	0	0
$817$	−3.82227e9	−0.245213
$818$	2.01970e9	0.129018
$819$	0	0
$820$	4.55223e9	0.288321
$821$	−2.75485e10	−1.73739	−0.868695	−	0.495347i	$-0.835041\pi$
$821$	−2.75485e10	−1.73739	−0.868695	+	0.495347i	$0.835041\pi$
$822$	0	0
$823$	−4.39773e9	−0.274998	−0.137499	−	0.990502i	$-0.543906\pi$
$823$	−4.39773e9	−0.274998	−0.137499	+	0.990502i	$0.543906\pi$
$824$	−1.92574e9	−0.119909
$825$	0	0
$826$	−8.09442e9	−0.499753
$827$	−2.40157e10	−1.47648	−0.738239	−	0.674540i	$-0.764342\pi$
$827$	−2.40157e10	−1.47648	−0.738239	+	0.674540i	$0.764342\pi$
$828$	0	0
$829$	2.07059e10	1.26227	0.631135	−	0.775673i	$-0.282589\pi$
$829$	2.07059e10	1.26227	0.631135	+	0.775673i	$0.282589\pi$
$830$	−7.96798e9	−0.483699
$831$	0	0
$832$	6.10527e9	0.367513
$833$	−1.76565e9	−0.105839
$834$	0	0
$835$	−3.30600e10	−1.96517
$836$	−3.48252e9	−0.206144
$837$	0	0
$838$	−4.47083e9	−0.262442
$839$	−8.93746e9	−0.522453	−0.261227	−	0.965277i	$-0.584127\pi$
$839$	−8.93746e9	−0.522453	−0.261227	+	0.965277i	$0.584127\pi$
$840$	0	0
$841$	1.20178e9	0.0696687
$842$	9.12434e9	0.526756
$843$	0	0
$844$	−3.94741e9	−0.226003
$845$	−1.13763e10	−0.648640
$846$	0	0
$847$	−1.40805e9	−0.0796209
$848$	−7.10984e9	−0.400382
$849$	0	0
$850$	−1.65389e9	−0.0923722
$851$	3.24802e9	0.180661
$852$	0	0
$853$	1.98705e10	1.09619	0.548096	−	0.836415i	$-0.315353\pi$
$853$	1.98705e10	1.09619	0.548096	+	0.836415i	$0.315353\pi$
$854$	−1.00885e9	−0.0554275
$855$	0	0
$856$	1.90229e10	1.03662
$857$	−2.36533e9	−0.128368	−0.0641842	−	0.997938i	$-0.520445\pi$
$857$	−2.36533e9	−0.128368	−0.0641842	+	0.997938i	$0.520445\pi$
$858$	0	0
$859$	−1.62974e10	−0.877289	−0.438644	−	0.898661i	$-0.644541\pi$
$859$	−1.62974e10	−0.877289	−0.438644	+	0.898661i	$0.644541\pi$
$860$	7.26599e9	0.389538
$861$	0	0
$862$	−2.92498e9	−0.155542
$863$	2.04265e10	1.08182	0.540912	−	0.841079i	$-0.318079\pi$
$863$	2.04265e10	1.08182	0.540912	+	0.841079i	$0.318079\pi$
$864$	0	0
$865$	−2.73084e10	−1.43463
$866$	−7.76310e9	−0.406184
$867$	0	0
$868$	−1.07303e10	−0.556922
$869$	7.76303e9	0.401293
$870$	0	0
$871$	1.53443e10	0.786837
$872$	−2.08448e10	−1.06461
$873$	0	0
$874$	7.29613e8	0.0369660
$875$	6.94979e9	0.350706
$876$	0	0
$877$	2.27339e10	1.13808	0.569042	−	0.822308i	$-0.307314\pi$
$877$	2.27339e10	1.13808	0.569042	+	0.822308i	$0.307314\pi$
$878$	9.84940e9	0.491110
$879$	0	0
$880$	5.93623e9	0.293644
$881$	−3.21809e10	−1.58556	−0.792780	−	0.609507i	$-0.791367\pi$
$881$	−3.21809e10	−1.58556	−0.792780	+	0.609507i	$0.791367\pi$
$882$	0	0
$883$	1.63414e10	0.798780	0.399390	−	0.916781i	$-0.369222\pi$
$883$	1.63414e10	0.798780	0.399390	+	0.916781i	$0.369222\pi$
$884$	6.03838e9	0.293994
$885$	0	0
$886$	−4.47587e9	−0.216202
$887$	2.41932e10	1.16402	0.582010	−	0.813181i	$-0.302266\pi$
$887$	2.41932e10	1.16402	0.582010	+	0.813181i	$0.302266\pi$
$888$	0	0
$889$	7.04938e9	0.336507
$890$	−8.58672e9	−0.408284
$891$	0	0
$892$	7.85509e9	0.370573
$893$	−3.18859e9	−0.149837
$894$	0	0
$895$	−3.56710e10	−1.66316
$896$	−1.76203e10	−0.818343
$897$	0	0
$898$	−1.37546e9	−0.0633839
$899$	1.56795e10	0.719737
$900$	0	0
$901$	−5.33520e9	−0.243004
$902$	4.73417e8	0.0214793
$903$	0	0
$904$	1.44860e10	0.652168
$905$	2.93325e10	1.31546
$906$	0	0
$907$	2.12335e10	0.944921	0.472460	−	0.881352i	$-0.343366\pi$
$907$	2.12335e10	0.944921	0.472460	+	0.881352i	$0.343366\pi$
$908$	3.10062e9	0.137451
$909$	0	0
$910$	−5.38586e9	−0.236925
$911$	1.27480e10	0.558635	0.279317	−	0.960199i	$-0.409892\pi$
$911$	1.27480e10	0.558635	0.279317	+	0.960199i	$0.409892\pi$
$912$	0	0
$913$	8.77837e9	0.381739
$914$	8.69110e9	0.376498
$915$	0	0
$916$	1.47803e10	0.635401
$917$	−1.45083e10	−0.621330
$918$	0	0
$919$	−2.13856e10	−0.908900	−0.454450	−	0.890772i	$-0.650164\pi$
$919$	−2.13856e10	−0.908900	−0.454450	+	0.890772i	$0.650164\pi$
$920$	−2.90486e9	−0.122989
$921$	0	0
$922$	−2.74653e9	−0.115405
$923$	1.98623e10	0.831425
$924$	0	0
$925$	−1.78940e10	−0.743382
$926$	1.10136e10	0.455816
$927$	0	0
$928$	1.96884e10	0.808708
$929$	3.88471e10	1.58966	0.794829	−	0.606833i	$-0.207560\pi$
$929$	3.88471e10	1.58966	0.794829	+	0.606833i	$0.207560\pi$
$930$	0	0
$931$	−4.29120e9	−0.174283
$932$	−3.41892e10	−1.38335
$933$	0	0
$934$	−8.79366e9	−0.353147
$935$	4.45453e9	0.178222
$936$	0	0
$937$	−1.21269e10	−0.481571	−0.240785	−	0.970578i	$-0.577405\pi$
$937$	−1.21269e10	−0.481571	−0.240785	+	0.970578i	$0.577405\pi$
$938$	−7.22480e9	−0.285835
$939$	0	0
$940$	6.06139e9	0.238026
$941$	−4.90877e10	−1.92048	−0.960239	−	0.279179i	$-0.909938\pi$
$941$	−4.90877e10	−1.92048	−0.960239	+	0.279179i	$0.909938\pi$
$942$	0	0
$943$	1.05073e9	0.0408036
$944$	−3.75961e10	−1.45459
$945$	0	0
$946$	7.55639e8	0.0290199
$947$	−3.57028e10	−1.36608	−0.683042	−	0.730379i	$-0.739343\pi$
$947$	−3.57028e10	−1.36608	−0.683042	+	0.730379i	$0.739343\pi$
$948$	0	0
$949$	1.46652e10	0.557001
$950$	−4.01959e9	−0.152107
$951$	0	0
$952$	−5.95466e9	−0.223680
$953$	−2.38859e9	−0.0893959	−0.0446979	−	0.999001i	$-0.514233\pi$
$953$	−2.38859e9	−0.0893959	−0.0446979	+	0.999001i	$0.514233\pi$
$954$	0	0
$955$	−1.76839e9	−0.0657003
$956$	4.09786e10	1.51689
$957$	0	0
$958$	−1.19160e10	−0.437875
$959$	3.67869e10	1.34688
$960$	0	0
$961$	−1.41887e10	−0.515718
$962$	−6.16702e9	−0.223338
$963$	0	0
$964$	3.04620e9	0.109519
$965$	1.94781e9	0.0697753
$966$	0	0
$967$	3.05875e10	1.08780	0.543902	−	0.839149i	$-0.316946\pi$
$967$	3.05875e10	1.08780	0.543902	+	0.839149i	$0.316946\pi$
$968$	1.44193e9	0.0510953
$969$	0	0
$970$	−1.52222e10	−0.535522
$971$	−3.15942e10	−1.10749	−0.553746	−	0.832686i	$-0.686802\pi$
$971$	−3.15942e10	−1.10749	−0.553746	+	0.832686i	$0.686802\pi$
$972$	0	0
$973$	−1.33789e10	−0.465613
$974$	1.26745e10	0.439516
$975$	0	0
$976$	−4.68581e9	−0.161328
$977$	2.87270e10	0.985505	0.492752	−	0.870170i	$-0.335991\pi$
$977$	2.87270e10	0.985505	0.492752	+	0.870170i	$0.335991\pi$
$978$	0	0
$979$	9.46003e9	0.322220
$980$	8.15740e9	0.276860
$981$	0	0
$982$	3.85521e8	0.0129914
$983$	5.25872e10	1.76580	0.882902	−	0.469557i	$-0.155586\pi$
$983$	5.25872e10	1.76580	0.882902	+	0.469557i	$0.155586\pi$
$984$	0	0
$985$	−2.45616e10	−0.818899
$986$	4.15449e9	0.138022
$987$	0	0
$988$	1.46756e10	0.484112
$989$	1.67710e9	0.0551280
$990$	0	0
$991$	1.23209e10	0.402146	0.201073	−	0.979576i	$-0.435557\pi$
$991$	1.23209e10	0.402146	0.201073	+	0.979576i	$0.435557\pi$
$992$	1.67304e10	0.544147
$993$	0	0
$994$	−9.35205e9	−0.302033
$995$	5.62767e10	1.81112
$996$	0	0
$997$	−8.77582e9	−0.280450	−0.140225	−	0.990120i	$-0.544783\pi$
$997$	−8.77582e9	−0.280450	−0.140225	+	0.990120i	$0.544783\pi$
$998$	−5.41064e9	−0.172303
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.a.h.1.3	✓	5
3.2	odd	2		99.8.a.i.1.3	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.8.a.h.1.3	✓	5	1.1	even	1	trivial
99.8.a.i.1.3	yes	5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-3.32273 q^{2} -116.959 q^{4} +363.595 q^{5} -794.809 q^{7} +813.934 q^{8} +O(q^{10})\)	\(q-3.32273 q^{2} -116.959 q^{4} +363.595 q^{5} -794.809 q^{7} +813.934 q^{8} -1208.13 q^{10} +1331.00 q^{11} -5608.93 q^{13} +2640.93 q^{14} +12266.3 q^{16} +9204.61 q^{17} +22370.7 q^{19} -42525.9 q^{20} -4422.55 q^{22} -9815.63 q^{23} +54076.3 q^{25} +18636.9 q^{26} +92960.4 q^{28} -135837. q^{29} -115429. q^{31} -144941. q^{32} -30584.4 q^{34} -288989. q^{35} -330903. q^{37} -74331.8 q^{38} +295942. q^{40} -107046. q^{41} -170860. q^{43} -155673. q^{44} +32614.7 q^{46} -142534. q^{47} -191822. q^{49} -179681. q^{50} +656017. q^{52} -579622. q^{53} +483945. q^{55} -646922. q^{56} +451349. q^{58} -3.06499e6 q^{59} -382006. q^{61} +383539. q^{62} -1.08849e6 q^{64} -2.03938e6 q^{65} -2.73570e6 q^{67} -1.07657e6 q^{68} +960230. q^{70} -3.54119e6 q^{71} -2.61462e6 q^{73} +1.09950e6 q^{74} -2.61647e6 q^{76} -1.05789e6 q^{77} +5.83248e6 q^{79} +4.45998e6 q^{80} +355685. q^{82} +6.59532e6 q^{83} +3.34675e6 q^{85} +567723. q^{86} +1.08335e6 q^{88} +7.10746e6 q^{89} +4.45803e6 q^{91} +1.14803e6 q^{92} +473603. q^{94} +8.13388e6 q^{95} +1.25999e7 q^{97} +637372. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 8 q^{2} + 166 q^{4} - 500 q^{5} + 446 q^{7} - 2754 q^{8}+O(q^{10}) \) 5 * q - 8 * q^2 + 166 * q^4 - 500 * q^5 + 446 * q^7 - 2754 * q^8	\( 5 q - 8 q^{2} + 166 q^{4} - 500 q^{5} + 446 q^{7} - 2754 q^{8} + 11516 q^{10} + 6655 q^{11} - 16666 q^{13} - 20516 q^{14} + 15010 q^{16} + 1906 q^{17} - 10446 q^{19} - 155572 q^{20} - 10648 q^{22} + 35468 q^{23} + 104239 q^{25} + 136396 q^{26} + 118456 q^{28} - 259062 q^{29} - 44932 q^{31} - 609010 q^{32} - 592888 q^{34} - 963800 q^{35} + 393978 q^{37} - 1319448 q^{38} + 1650684 q^{40} - 1554074 q^{41} + 263118 q^{43} + 220946 q^{44} - 1948268 q^{46} - 2481904 q^{47} + 498177 q^{49} - 5560984 q^{50} - 4530056 q^{52} - 2325840 q^{53} - 665500 q^{55} - 5221992 q^{56} + 2479968 q^{58} - 4613452 q^{59} + 529362 q^{61} - 3077192 q^{62} + 1437674 q^{64} + 2187496 q^{65} - 4612664 q^{67} + 2362916 q^{68} + 7327832 q^{70} - 5583864 q^{71} + 980054 q^{73} - 3387480 q^{74} + 1023396 q^{76} + 593626 q^{77} + 2804758 q^{79} - 10053364 q^{80} - 110080 q^{82} + 2451324 q^{83} - 4240456 q^{85} + 5937408 q^{86} - 3665574 q^{88} - 4025472 q^{89} - 12525436 q^{91} + 44606548 q^{92} + 1592764 q^{94} - 4273320 q^{95} - 234806 q^{97} + 26686536 q^{98}+O(q^{100}) \) 5 * q - 8 * q^2 + 166 * q^4 - 500 * q^5 + 446 * q^7 - 2754 * q^8 + 11516 * q^10 + 6655 * q^11 - 16666 * q^13 - 20516 * q^14 + 15010 * q^16 + 1906 * q^17 - 10446 * q^19 - 155572 * q^20 - 10648 * q^22 + 35468 * q^23 + 104239 * q^25 + 136396 * q^26 + 118456 * q^28 - 259062 * q^29 - 44932 * q^31 - 609010 * q^32 - 592888 * q^34 - 963800 * q^35 + 393978 * q^37 - 1319448 * q^38 + 1650684 * q^40 - 1554074 * q^41 + 263118 * q^43 + 220946 * q^44 - 1948268 * q^46 - 2481904 * q^47 + 498177 * q^49 - 5560984 * q^50 - 4530056 * q^52 - 2325840 * q^53 - 665500 * q^55 - 5221992 * q^56 + 2479968 * q^58 - 4613452 * q^59 + 529362 * q^61 - 3077192 * q^62 + 1437674 * q^64 + 2187496 * q^65 - 4612664 * q^67 + 2362916 * q^68 + 7327832 * q^70 - 5583864 * q^71 + 980054 * q^73 - 3387480 * q^74 + 1023396 * q^76 + 593626 * q^77 + 2804758 * q^79 - 10053364 * q^80 - 110080 * q^82 + 2451324 * q^83 - 4240456 * q^85 + 5937408 * q^86 - 3665574 * q^88 - 4025472 * q^89 - 12525436 * q^91 + 44606548 * q^92 + 1592764 * q^94 - 4273320 * q^95 - 234806 * q^97 + 26686536 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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