LMFDB - Embedded newform 99.8.a.f.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:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 510x^{2} - 1544x + 28880 $ x^4 - x^3 - 510x^2 - 1544x + 28880
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$6.33327$ 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)

$f(q)$	$=$	$q+2.33327 q^{2} -122.556 q^{4} +27.4165 q^{5} +860.612 q^{7} -584.614 q^{8} +O(q^{10})$	\(q+2.33327 q^{2} -122.556 q^{4} +27.4165 q^{5} +860.612 q^{7} -584.614 q^{8} +63.9699 q^{10} -1331.00 q^{11} +5372.32 q^{13} +2008.04 q^{14} +14323.1 q^{16} -20318.8 q^{17} +26353.8 q^{19} -3360.05 q^{20} -3105.58 q^{22} -71010.7 q^{23} -77373.3 q^{25} +12535.1 q^{26} -105473. q^{28} -39144.8 q^{29} -257799. q^{31} +108250. q^{32} -47409.2 q^{34} +23594.9 q^{35} +120353. q^{37} +61490.4 q^{38} -16028.0 q^{40} -431710. q^{41} -625909. q^{43} +163122. q^{44} -165687. q^{46} +568914. q^{47} -82889.3 q^{49} -180533. q^{50} -658409. q^{52} -453215. q^{53} -36491.3 q^{55} -503126. q^{56} -91335.3 q^{58} -2.91908e6 q^{59} +758185. q^{61} -601514. q^{62} -1.58078e6 q^{64} +147290. q^{65} -148420. q^{67} +2.49019e6 q^{68} +55053.3 q^{70} -2.01312e6 q^{71} -351135. q^{73} +280815. q^{74} -3.22981e6 q^{76} -1.14548e6 q^{77} +655295. q^{79} +392688. q^{80} -1.00729e6 q^{82} +7.86076e6 q^{83} -557069. q^{85} -1.46041e6 q^{86} +778121. q^{88} -5.32146e6 q^{89} +4.62348e6 q^{91} +8.70278e6 q^{92} +1.32743e6 q^{94} +722528. q^{95} -2.49765e6 q^{97} -193403. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 15 q^{2} + 565 q^{4} - 306 q^{5} + 890 q^{7} - 2457 q^{8}+O(q^{10}) $ 4 * q - 15 * q^2 + 565 * q^4 - 306 * q^5 + 890 * q^7 - 2457 * q^8	\( 4 q - 15 q^{2} + 565 q^{4} - 306 q^{5} + 890 q^{7} - 2457 q^{8} - 8946 q^{10} - 5324 q^{11} - 1822 q^{13} - 35340 q^{14} + 65041 q^{16} - 32856 q^{17} - 12784 q^{19} + 4002 q^{20} + 19965 q^{22} - 114858 q^{23} + 72856 q^{25} + 221466 q^{26} + 10112 q^{28} + 104952 q^{29} - 24976 q^{31} - 337761 q^{32} - 741690 q^{34} + 722856 q^{35} - 498856 q^{37} + 897156 q^{38} - 2676930 q^{40} - 734556 q^{41} - 201916 q^{43} - 752015 q^{44} - 3068508 q^{46} - 1995894 q^{47} - 771024 q^{49} - 1632129 q^{50} - 4412266 q^{52} - 929970 q^{53} + 407286 q^{55} - 7224888 q^{56} + 2864322 q^{58} - 1353156 q^{59} + 3998774 q^{61} + 3783264 q^{62} + 1480129 q^{64} - 6612108 q^{65} + 1722008 q^{67} - 1596906 q^{68} - 2751024 q^{70} - 5571858 q^{71} + 5600528 q^{73} + 10907838 q^{74} - 19634884 q^{76} - 1184590 q^{77} - 7710226 q^{79} + 24073794 q^{80} - 11230842 q^{82} - 3431856 q^{83} + 5909484 q^{85} + 25687140 q^{86} + 3270267 q^{88} - 4611528 q^{89} - 9032696 q^{91} - 13608576 q^{92} - 3497436 q^{94} - 21828000 q^{95} + 1401692 q^{97} + 7230081 q^{98}+O(q^{100}) \) 4 * q - 15 * q^2 + 565 * q^4 - 306 * q^5 + 890 * q^7 - 2457 * q^8 - 8946 * q^10 - 5324 * q^11 - 1822 * q^13 - 35340 * q^14 + 65041 * q^16 - 32856 * q^17 - 12784 * q^19 + 4002 * q^20 + 19965 * q^22 - 114858 * q^23 + 72856 * q^25 + 221466 * q^26 + 10112 * q^28 + 104952 * q^29 - 24976 * q^31 - 337761 * q^32 - 741690 * q^34 + 722856 * q^35 - 498856 * q^37 + 897156 * q^38 - 2676930 * q^40 - 734556 * q^41 - 201916 * q^43 - 752015 * q^44 - 3068508 * q^46 - 1995894 * q^47 - 771024 * q^49 - 1632129 * q^50 - 4412266 * q^52 - 929970 * q^53 + 407286 * q^55 - 7224888 * q^56 + 2864322 * q^58 - 1353156 * q^59 + 3998774 * q^61 + 3783264 * q^62 + 1480129 * q^64 - 6612108 * q^65 + 1722008 * q^67 - 1596906 * q^68 - 2751024 * q^70 - 5571858 * q^71 + 5600528 * q^73 + 10907838 * q^74 - 19634884 * q^76 - 1184590 * q^77 - 7710226 * q^79 + 24073794 * q^80 - 11230842 * q^82 - 3431856 * q^83 + 5909484 * q^85 + 25687140 * q^86 + 3270267 * q^88 - 4611528 * q^89 - 9032696 * q^91 - 13608576 * q^92 - 3497436 * q^94 - 21828000 * q^95 + 1401692 * q^97 + 7230081 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.33327	0.206234	0.103117	−	0.994669i	$-0.467118\pi$
$2$	2.33327	0.206234	0.103117	+	0.994669i	$0.467118\pi$
$3$	0	0
$3$	0	0
$4$	−122.556	−0.957468
$5$	27.4165	0.0980881	0.0490441	−	0.998797i	$-0.484383\pi$
$5$	27.4165	0.0980881	0.0490441	+	0.998797i	$0.484383\pi$
$6$	0	0
$7$	860.612	0.948341	0.474170	−	0.880433i	$-0.342748\pi$
$7$	860.612	0.948341	0.474170	+	0.880433i	$0.342748\pi$
$8$	−584.614	−0.403696
$9$	0	0
$10$	63.9699	0.0202291
$11$	−1331.00	−0.301511
$11$	−1331.00	−0.301511
$12$	0	0
$13$	5372.32	0.678203	0.339102	−	0.940750i	$-0.389877\pi$
$13$	5372.32	0.678203	0.339102	+	0.940750i	$0.389877\pi$
$14$	2008.04	0.195580
$15$	0	0
$16$	14323.1	0.874212
$17$	−20318.8	−1.00306	−0.501530	−	0.865140i	$-0.667229\pi$
$17$	−20318.8	−1.00306	−0.501530	+	0.865140i	$0.667229\pi$
$18$	0	0
$19$	26353.8	0.881466	0.440733	−	0.897638i	$-0.354719\pi$
$19$	26353.8	0.881466	0.440733	+	0.897638i	$0.354719\pi$
$20$	−3360.05	−0.0939162
$21$	0	0
$22$	−3105.58	−0.0621818
$23$	−71010.7	−1.21696	−0.608480	−	0.793569i	$-0.708221\pi$
$23$	−71010.7	−1.21696	−0.608480	+	0.793569i	$0.708221\pi$
$24$	0	0
$25$	−77373.3	−0.990379
$26$	12535.1	0.139868
$27$	0	0
$28$	−105473.	−0.908006
$29$	−39144.8	−0.298045	−0.149022	−	0.988834i	$-0.547613\pi$
$29$	−39144.8	−0.298045	−0.149022	+	0.988834i	$0.547613\pi$
$30$	0	0
$31$	−257799.	−1.55423	−0.777115	−	0.629358i	$-0.783318\pi$
$31$	−257799.	−1.55423	−0.777115	+	0.629358i	$0.783318\pi$
$32$	108250.	0.583988
$33$	0	0
$34$	−47409.2	−0.206865
$35$	23594.9	0.0930210
$36$	0	0
$37$	120353.	0.390616	0.195308	−	0.980742i	$-0.437429\pi$
$37$	120353.	0.390616	0.195308	+	0.980742i	$0.437429\pi$
$38$	61490.4	0.181788
$39$	0	0
$40$	−16028.0	−0.0395978
$41$	−431710.	−0.978247	−0.489123	−	0.872215i	$-0.662683\pi$
$41$	−431710.	−0.978247	−0.489123	+	0.872215i	$0.662683\pi$
$42$	0	0
$43$	−625909.	−1.20053	−0.600263	−	0.799803i	$-0.704937\pi$
$43$	−625909.	−1.20053	−0.600263	+	0.799803i	$0.704937\pi$
$44$	163122.	0.288687
$45$	0	0
$46$	−165687.	−0.250978
$47$	568914.	0.799290	0.399645	−	0.916670i	$-0.369133\pi$
$47$	568914.	0.799290	0.399645	+	0.916670i	$0.369133\pi$
$48$	0	0
$49$	−82889.3	−0.100650
$50$	−180533.	−0.204249
$51$	0	0
$52$	−658409.	−0.649358
$53$	−453215.	−0.418156	−0.209078	−	0.977899i	$-0.567046\pi$
$53$	−453215.	−0.418156	−0.209078	+	0.977899i	$0.567046\pi$
$54$	0	0
$55$	−36491.3	−0.0295747
$56$	−503126.	−0.382841
$57$	0	0
$58$	−91335.3	−0.0614668
$59$	−2.91908e6	−1.85039	−0.925195	−	0.379492i	$-0.876099\pi$
$59$	−2.91908e6	−1.85039	−0.925195	+	0.379492i	$0.876099\pi$
$60$	0	0
$61$	758185.	0.427682	0.213841	−	0.976868i	$-0.431403\pi$
$61$	758185.	0.427682	0.213841	+	0.976868i	$0.431403\pi$
$62$	−601514.	−0.320535
$63$	0	0
$64$	−1.58078e6	−0.753774
$65$	147290.	0.0665237
$66$	0	0
$67$	−148420.	−0.0602878	−0.0301439	−	0.999546i	$-0.509597\pi$
$67$	−148420.	−0.0602878	−0.0301439	+	0.999546i	$0.509597\pi$
$68$	2.49019e6	0.960397
$69$	0	0
$70$	55053.3	0.0191841
$71$	−2.01312e6	−0.667522	−0.333761	−	0.942658i	$-0.608318\pi$
$71$	−2.01312e6	−0.667522	−0.333761	+	0.942658i	$0.608318\pi$
$72$	0	0
$73$	−351135.	−0.105644	−0.0528219	−	0.998604i	$-0.516822\pi$
$73$	−351135.	−0.105644	−0.0528219	+	0.998604i	$0.516822\pi$
$74$	280815.	0.0805582
$75$	0	0
$76$	−3.22981e6	−0.843975
$77$	−1.14548e6	−0.285936
$78$	0	0
$79$	655295.	0.149535	0.0747674	−	0.997201i	$-0.476179\pi$
$79$	655295.	0.149535	0.0747674	+	0.997201i	$0.476179\pi$
$80$	392688.	0.0857498
$81$	0	0
$82$	−1.00729e6	−0.201747
$83$	7.86076e6	1.50901	0.754503	−	0.656297i	$-0.227878\pi$
$83$	7.86076e6	1.50901	0.754503	+	0.656297i	$0.227878\pi$
$84$	0	0
$85$	−557069.	−0.0983882
$86$	−1.46041e6	−0.247589
$87$	0	0
$88$	778121.	0.121719
$89$	−5.32146e6	−0.800140	−0.400070	−	0.916485i	$-0.631014\pi$
$89$	−5.32146e6	−0.800140	−0.400070	+	0.916485i	$0.631014\pi$
$90$	0	0
$91$	4.62348e6	0.643168
$92$	8.70278e6	1.16520
$93$	0	0
$94$	1.32743e6	0.164840
$95$	722528.	0.0864613
$96$	0	0
$97$	−2.49765e6	−0.277862	−0.138931	−	0.990302i	$-0.544367\pi$
$97$	−2.49765e6	−0.277862	−0.138931	+	0.990302i	$0.544367\pi$
$98$	−193403.	−0.0207573
$99$	0	0
$100$	9.48256e6	0.948256
$101$	1.22830e7	1.18626	0.593129	−	0.805107i	$-0.297892\pi$
$101$	1.22830e7	1.18626	0.593129	+	0.805107i	$0.297892\pi$
$102$	0	0
$103$	1.36936e6	0.123478	0.0617388	−	0.998092i	$-0.480335\pi$
$103$	1.36936e6	0.123478	0.0617388	+	0.998092i	$0.480335\pi$
$104$	−3.14073e6	−0.273788
$105$	0	0
$106$	−1.05747e6	−0.0862379
$107$	−3.46128e6	−0.273145	−0.136572	−	0.990630i	$-0.543609\pi$
$107$	−3.46128e6	−0.273145	−0.136572	+	0.990630i	$0.543609\pi$
$108$	0	0
$109$	1.60479e7	1.18693	0.593465	−	0.804860i	$-0.297759\pi$
$109$	1.60479e7	1.18693	0.593465	+	0.804860i	$0.297759\pi$
$110$	−85144.0	−0.00609929
$111$	0	0
$112$	1.23266e7	0.829051
$113$	−1.10371e7	−0.719584	−0.359792	−	0.933033i	$-0.617152\pi$
$113$	−1.10371e7	−0.719584	−0.359792	+	0.933033i	$0.617152\pi$
$114$	0	0
$115$	−1.94686e6	−0.119369
$116$	4.79743e6	0.285368
$117$	0	0
$118$	−6.81098e6	−0.381613
$119$	−1.74866e7	−0.951242
$120$	0	0
$121$	1.77156e6	0.0909091
$122$	1.76905e6	0.0882024
$123$	0	0
$124$	3.15948e7	1.48813
$125$	−4.26321e6	−0.195233
$126$	0	0
$127$	−3.44865e7	−1.49395	−0.746976	−	0.664851i	$-0.768495\pi$
$127$	−3.44865e7	−1.49395	−0.746976	+	0.664851i	$0.768495\pi$
$128$	−1.75444e7	−0.739441
$129$	0	0
$130$	343667.	0.0137194
$131$	4.16200e7	1.61753	0.808766	−	0.588130i	$-0.200136\pi$
$131$	4.16200e7	1.61753	0.808766	+	0.588130i	$0.200136\pi$
$132$	0	0
$133$	2.26804e7	0.835930
$134$	−346303.	−0.0124334
$135$	0	0
$136$	1.18786e7	0.404931
$137$	3.11128e7	1.03375	0.516877	−	0.856059i	$-0.327094\pi$
$137$	3.11128e7	1.03375	0.516877	+	0.856059i	$0.327094\pi$
$138$	0	0
$139$	4.10555e7	1.29664	0.648321	−	0.761367i	$-0.275472\pi$
$139$	4.10555e7	1.29664	0.648321	+	0.761367i	$0.275472\pi$
$140$	−2.89170e6	−0.0890646
$141$	0	0
$142$	−4.69715e6	−0.137665
$143$	−7.15055e6	−0.204486
$144$	0	0
$145$	−1.07321e6	−0.0292346
$146$	−819292.	−0.0217873
$147$	0	0
$148$	−1.47499e7	−0.374002
$149$	7.17630e7	1.77725	0.888626	−	0.458633i	$-0.151661\pi$
$149$	7.17630e7	1.77725	0.888626	+	0.458633i	$0.151661\pi$
$150$	0	0
$151$	−5.73789e7	−1.35623	−0.678114	−	0.734957i	$-0.737202\pi$
$151$	−5.73789e7	−1.35623	−0.678114	+	0.734957i	$0.737202\pi$
$152$	−1.54068e7	−0.355844
$153$	0	0
$154$	−2.67270e6	−0.0589695
$155$	−7.06794e6	−0.152452
$156$	0	0
$157$	−7.52927e7	−1.55276	−0.776379	−	0.630266i	$-0.782946\pi$
$157$	−7.52927e7	−1.55276	−0.776379	+	0.630266i	$0.782946\pi$
$158$	1.52898e6	0.0308391
$159$	0	0
$160$	2.96784e6	0.0572823
$161$	−6.11127e7	−1.15409
$162$	0	0
$163$	−5.73668e7	−1.03754	−0.518769	−	0.854914i	$-0.673610\pi$
$163$	−5.73668e7	−1.03754	−0.518769	+	0.854914i	$0.673610\pi$
$164$	5.29086e7	0.936640
$165$	0	0
$166$	1.83412e7	0.311208
$167$	−8.13503e7	−1.35161	−0.675805	−	0.737080i	$-0.736204\pi$
$167$	−8.13503e7	−1.35161	−0.675805	+	0.737080i	$0.736204\pi$
$168$	0	0
$169$	−3.38867e7	−0.540040
$170$	−1.29979e6	−0.0202910
$171$	0	0
$172$	7.67088e7	1.14946
$173$	−3.24507e7	−0.476499	−0.238250	−	0.971204i	$-0.576574\pi$
$173$	−3.24507e7	−0.476499	−0.238250	+	0.971204i	$0.576574\pi$
$174$	0	0
$175$	−6.65885e7	−0.939217
$176$	−1.90640e7	−0.263585
$177$	0	0
$178$	−1.24164e7	−0.165016
$179$	−7.37856e7	−0.961581	−0.480790	−	0.876836i	$-0.659650\pi$
$179$	−7.37856e7	−0.961581	−0.480790	+	0.876836i	$0.659650\pi$
$180$	0	0
$181$	−9.63645e7	−1.20793	−0.603965	−	0.797011i	$-0.706413\pi$
$181$	−9.63645e7	−1.20793	−0.603965	+	0.797011i	$0.706413\pi$
$182$	1.07878e7	0.132643
$183$	0	0
$184$	4.15139e7	0.491282
$185$	3.29965e6	0.0383148
$186$	0	0
$187$	2.70443e7	0.302434
$188$	−6.97238e7	−0.765294
$189$	0	0
$190$	1.68585e6	0.0178312
$191$	−8.78697e7	−0.912478	−0.456239	−	0.889857i	$-0.650804\pi$
$191$	−8.78697e7	−0.912478	−0.456239	+	0.889857i	$0.650804\pi$
$192$	0	0
$193$	−1.07431e8	−1.07567	−0.537834	−	0.843051i	$-0.680757\pi$
$193$	−1.07431e8	−1.07567	−0.537834	+	0.843051i	$0.680757\pi$
$194$	−5.82768e6	−0.0573046
$195$	0	0
$196$	1.01586e7	0.0963688
$197$	1.53098e8	1.42671	0.713357	−	0.700801i	$-0.247174\pi$
$197$	1.53098e8	1.42671	0.713357	+	0.700801i	$0.247174\pi$
$198$	0	0
$199$	1.86713e8	1.67954	0.839769	−	0.542944i	$-0.182690\pi$
$199$	1.86713e8	1.67954	0.839769	+	0.542944i	$0.182690\pi$
$200$	4.52335e7	0.399812
$201$	0	0
$202$	2.86595e7	0.244647
$203$	−3.36885e7	−0.282648
$204$	0	0
$205$	−1.18360e7	−0.0959544
$206$	3.19509e6	0.0254652
$207$	0	0
$208$	7.69482e7	0.592894
$209$	−3.50769e7	−0.265772
$210$	0	0
$211$	−7.77249e7	−0.569602	−0.284801	−	0.958587i	$-0.591928\pi$
$211$	−7.77249e7	−0.569602	−0.284801	+	0.958587i	$0.591928\pi$
$212$	5.55442e7	0.400371
$213$	0	0
$214$	−8.07608e6	−0.0563316
$215$	−1.71602e7	−0.117757
$216$	0	0
$217$	−2.21865e8	−1.47394
$218$	3.74440e7	0.244785
$219$	0	0
$220$	4.47222e6	0.0283168
$221$	−1.09159e8	−0.680278
$222$	0	0
$223$	2.57541e8	1.55517	0.777587	−	0.628776i	$-0.216444\pi$
$223$	2.57541e8	1.55517	0.777587	+	0.628776i	$0.216444\pi$
$224$	9.31614e7	0.553819
$225$	0	0
$226$	−2.57526e7	−0.148402
$227$	−1.92695e8	−1.09340	−0.546702	−	0.837328i	$-0.684117\pi$
$227$	−1.92695e8	−1.09340	−0.546702	+	0.837328i	$0.684117\pi$
$228$	0	0
$229$	−9.89335e6	−0.0544401	−0.0272201	−	0.999629i	$-0.508665\pi$
$229$	−9.89335e6	−0.0544401	−0.0272201	+	0.999629i	$0.508665\pi$
$230$	−4.54255e6	−0.0246180
$231$	0	0
$232$	2.28846e7	0.120319
$233$	7.06109e7	0.365701	0.182851	−	0.983141i	$-0.441468\pi$
$233$	7.06109e7	0.365701	0.182851	+	0.983141i	$0.441468\pi$
$234$	0	0
$235$	1.55976e7	0.0784009
$236$	3.57750e8	1.77169
$237$	0	0
$238$	−4.08009e7	−0.196178
$239$	3.57451e8	1.69365	0.846826	−	0.531870i	$-0.178510\pi$
$239$	3.57451e8	1.69365	0.846826	+	0.531870i	$0.178510\pi$
$240$	0	0
$241$	−1.69459e8	−0.779840	−0.389920	−	0.920849i	$-0.627497\pi$
$241$	−1.69459e8	−0.779840	−0.389920	+	0.920849i	$0.627497\pi$
$242$	4.13353e6	0.0187485
$243$	0	0
$244$	−9.29200e7	−0.409492
$245$	−2.27253e6	−0.00987254
$246$	0	0
$247$	1.41581e8	0.597813
$248$	1.50713e8	0.627436
$249$	0	0
$250$	−9.94722e6	−0.0402635
$251$	2.48090e7	0.0990266	0.0495133	−	0.998773i	$-0.484233\pi$
$251$	2.48090e7	0.0990266	0.0495133	+	0.998773i	$0.484233\pi$
$252$	0	0
$253$	9.45153e7	0.366927
$254$	−8.04663e7	−0.308103
$255$	0	0
$256$	1.61404e8	0.601276
$257$	−2.08682e8	−0.766866	−0.383433	−	0.923569i	$-0.625258\pi$
$257$	−2.08682e8	−0.766866	−0.383433	+	0.923569i	$0.625258\pi$
$258$	0	0
$259$	1.03577e8	0.370437
$260$	−1.80512e7	−0.0636943
$261$	0	0
$262$	9.71107e7	0.333590
$263$	−2.14839e8	−0.728230	−0.364115	−	0.931354i	$-0.618629\pi$
$263$	−2.14839e8	−0.728230	−0.364115	+	0.931354i	$0.618629\pi$
$264$	0	0
$265$	−1.24256e7	−0.0410162
$266$	5.29194e7	0.172397
$267$	0	0
$268$	1.81897e7	0.0577236
$269$	−1.27377e8	−0.398987	−0.199493	−	0.979899i	$-0.563930\pi$
$269$	−1.27377e8	−0.398987	−0.199493	+	0.979899i	$0.563930\pi$
$270$	0	0
$271$	3.03624e8	0.926710	0.463355	−	0.886173i	$-0.346645\pi$
$271$	3.03624e8	0.926710	0.463355	+	0.886173i	$0.346645\pi$
$272$	−2.91028e8	−0.876887
$273$	0	0
$274$	7.25945e7	0.213195
$275$	1.02984e8	0.298610
$276$	0	0
$277$	2.69926e8	0.763071	0.381535	−	0.924354i	$-0.375395\pi$
$277$	2.69926e8	0.763071	0.381535	+	0.924354i	$0.375395\pi$
$278$	9.57936e7	0.267411
$279$	0	0
$280$	−1.37939e7	−0.0375522
$281$	1.76671e8	0.475000	0.237500	−	0.971388i	$-0.423672\pi$
$281$	1.76671e8	0.475000	0.237500	+	0.971388i	$0.423672\pi$
$282$	0	0
$283$	3.43115e8	0.899886	0.449943	−	0.893057i	$-0.351444\pi$
$283$	3.43115e8	0.899886	0.449943	+	0.893057i	$0.351444\pi$
$284$	2.46720e8	0.639131
$285$	0	0
$286$	−1.66842e7	−0.0421719
$287$	−3.71535e8	−0.927712
$288$	0	0
$289$	2.51470e6	0.00612835
$290$	−2.50409e6	−0.00602917
$291$	0	0
$292$	4.30337e7	0.101151
$293$	9.79546e7	0.227504	0.113752	−	0.993509i	$-0.463713\pi$
$293$	9.79546e7	0.227504	0.113752	+	0.993509i	$0.463713\pi$
$294$	0	0
$295$	−8.00307e7	−0.181501
$296$	−7.03599e7	−0.157690
$297$	0	0
$298$	1.67442e8	0.366529
$299$	−3.81492e8	−0.825347
$300$	0	0
$301$	−5.38665e8	−1.13851
$302$	−1.33880e8	−0.279700
$303$	0	0
$304$	3.77468e8	0.770588
$305$	2.07868e7	0.0419505
$306$	0	0
$307$	−3.66102e7	−0.0722133	−0.0361067	−	0.999348i	$-0.511496\pi$
$307$	−3.66102e7	−0.0722133	−0.0361067	+	0.999348i	$0.511496\pi$
$308$	1.40385e8	0.273774
$309$	0	0
$310$	−1.64914e7	−0.0314406
$311$	9.96923e8	1.87932	0.939659	−	0.342112i	$-0.111142\pi$
$311$	9.96923e8	1.87932	0.939659	+	0.342112i	$0.111142\pi$
$312$	0	0
$313$	−3.62193e7	−0.0667629	−0.0333814	−	0.999443i	$-0.510628\pi$
$313$	−3.62193e7	−0.0667629	−0.0333814	+	0.999443i	$0.510628\pi$
$314$	−1.75678e8	−0.320231
$315$	0	0
$316$	−8.03103e7	−0.143175
$317$	2.85806e8	0.503922	0.251961	−	0.967737i	$-0.418924\pi$
$317$	2.85806e8	0.503922	0.251961	+	0.967737i	$0.418924\pi$
$318$	0	0
$319$	5.21018e7	0.0898638
$320$	−4.33394e7	−0.0739363
$321$	0	0
$322$	−1.42592e8	−0.238013
$323$	−5.35477e8	−0.884163
$324$	0	0
$325$	−4.15674e8	−0.671678
$326$	−1.33852e8	−0.213975
$327$	0	0
$328$	2.52384e8	0.394914
$329$	4.89615e8	0.757999
$330$	0	0
$331$	−1.29457e9	−1.96212	−0.981061	−	0.193698i	$-0.937952\pi$
$331$	−1.29457e9	−1.96212	−0.981061	+	0.193698i	$0.937952\pi$
$332$	−9.63382e8	−1.44482
$333$	0	0
$334$	−1.89812e8	−0.278748
$335$	−4.06914e6	−0.00591352
$336$	0	0
$337$	−1.37396e9	−1.95555	−0.977776	−	0.209652i	$-0.932767\pi$
$337$	−1.37396e9	−1.95555	−0.977776	+	0.209652i	$0.932767\pi$
$338$	−7.90668e7	−0.111374
$339$	0	0
$340$	6.82721e7	0.0942035
$341$	3.43131e8	0.468618
$342$	0	0
$343$	−7.80087e8	−1.04379
$344$	3.65915e8	0.484647
$345$	0	0
$346$	−7.57161e7	−0.0982702
$347$	−6.60159e8	−0.848195	−0.424097	−	0.905617i	$-0.639409\pi$
$347$	−6.60159e8	−0.848195	−0.424097	+	0.905617i	$0.639409\pi$
$348$	0	0
$349$	2.30224e8	0.289908	0.144954	−	0.989438i	$-0.453697\pi$
$349$	2.30224e8	0.289908	0.144954	+	0.989438i	$0.453697\pi$
$350$	−1.55369e8	−0.193698
$351$	0	0
$352$	−1.44081e8	−0.176079
$353$	1.21990e9	1.47610	0.738048	−	0.674749i	$-0.235748\pi$
$353$	1.21990e9	1.47610	0.738048	+	0.674749i	$0.235748\pi$
$354$	0	0
$355$	−5.51926e7	−0.0654760
$356$	6.52176e8	0.766108
$357$	0	0
$358$	−1.72161e8	−0.198310
$359$	−8.67372e8	−0.989406	−0.494703	−	0.869062i	$-0.664723\pi$
$359$	−8.67372e8	−0.989406	−0.494703	+	0.869062i	$0.664723\pi$
$360$	0	0
$361$	−1.99350e8	−0.223018
$362$	−2.24844e8	−0.249116
$363$	0	0
$364$	−5.66635e8	−0.615812
$365$	−9.62688e6	−0.0103624
$366$	0	0
$367$	8.70579e8	0.919342	0.459671	−	0.888089i	$-0.347967\pi$
$367$	8.70579e8	0.919342	0.459671	+	0.888089i	$0.347967\pi$
$368$	−1.01709e9	−1.06388
$369$	0	0
$370$	7.69896e6	0.00790180
$371$	−3.90043e8	−0.396555
$372$	0	0
$373$	1.48328e9	1.47993	0.739967	−	0.672643i	$-0.234841\pi$
$373$	1.48328e9	1.47993	0.739967	+	0.672643i	$0.234841\pi$
$374$	6.31016e7	0.0623720
$375$	0	0
$376$	−3.32595e8	−0.322670
$377$	−2.10298e8	−0.202135
$378$	0	0
$379$	1.45764e9	1.37535	0.687675	−	0.726019i	$-0.258631\pi$
$379$	1.45764e9	1.37535	0.687675	+	0.726019i	$0.258631\pi$
$380$	−8.85500e7	−0.0827839
$381$	0	0
$382$	−2.05024e8	−0.188184
$383$	9.81451e8	0.892633	0.446316	−	0.894875i	$-0.352736\pi$
$383$	9.81451e8	0.892633	0.446316	+	0.894875i	$0.352736\pi$
$384$	0	0
$385$	−3.14049e7	−0.0280469
$386$	−2.50665e8	−0.221839
$387$	0	0
$388$	3.06101e8	0.266044
$389$	−1.30140e9	−1.12095	−0.560477	−	0.828170i	$-0.689382\pi$
$389$	−1.30140e9	−1.12095	−0.560477	+	0.828170i	$0.689382\pi$
$390$	0	0
$391$	1.44285e9	1.22068
$392$	4.84583e7	0.0406318
$393$	0	0
$394$	3.57218e8	0.294236
$395$	1.79659e7	0.0146676
$396$	0	0
$397$	5.04630e7	0.0404768	0.0202384	−	0.999795i	$-0.493557\pi$
$397$	5.04630e7	0.0404768	0.0202384	+	0.999795i	$0.493557\pi$
$398$	4.35652e8	0.346377
$399$	0	0
$400$	−1.10823e9	−0.865801
$401$	1.10109e9	0.852742	0.426371	−	0.904548i	$-0.359792\pi$
$401$	1.10109e9	0.852742	0.426371	+	0.904548i	$0.359792\pi$
$402$	0	0
$403$	−1.38498e9	−1.05408
$404$	−1.50535e9	−1.13580
$405$	0	0
$406$	−7.86043e7	−0.0582915
$407$	−1.60190e8	−0.117775
$408$	0	0
$409$	3.48371e7	0.0251774	0.0125887	−	0.999921i	$-0.495993\pi$
$409$	3.48371e7	0.0251774	0.0125887	+	0.999921i	$0.495993\pi$
$410$	−2.76165e7	−0.0197890
$411$	0	0
$412$	−1.67824e8	−0.118226
$413$	−2.51219e9	−1.75480
$414$	0	0
$415$	2.15514e8	0.148016
$416$	5.81554e8	0.396062
$417$	0	0
$418$	−8.18438e7	−0.0548111
$419$	2.82026e9	1.87301	0.936504	−	0.350656i	$-0.114041\pi$
$419$	2.82026e9	1.87301	0.936504	+	0.350656i	$0.114041\pi$
$420$	0	0
$421$	8.60823e7	0.0562246	0.0281123	−	0.999605i	$-0.491050\pi$
$421$	8.60823e7	0.0562246	0.0281123	+	0.999605i	$0.491050\pi$
$422$	−1.81353e8	−0.117471
$423$	0	0
$424$	2.64956e8	0.168808
$425$	1.57213e9	0.993409
$426$	0	0
$427$	6.52503e8	0.405588
$428$	4.24200e8	0.261527
$429$	0	0
$430$	−4.00393e7	−0.0242855
$431$	−5.97749e8	−0.359624	−0.179812	−	0.983701i	$-0.557549\pi$
$431$	−5.97749e8	−0.359624	−0.179812	+	0.983701i	$0.557549\pi$
$432$	0	0
$433$	−7.92969e8	−0.469406	−0.234703	−	0.972067i	$-0.575412\pi$
$433$	−7.92969e8	−0.469406	−0.234703	+	0.972067i	$0.575412\pi$
$434$	−5.17671e8	−0.303976
$435$	0	0
$436$	−1.96676e9	−1.13645
$437$	−1.87140e9	−1.07271
$438$	0	0
$439$	2.01580e9	1.13716	0.568579	−	0.822629i	$-0.307493\pi$
$439$	2.01580e9	1.13716	0.568579	+	0.822629i	$0.307493\pi$
$440$	2.13333e7	0.0119392
$441$	0	0
$442$	−2.54697e8	−0.140296
$443$	3.28369e9	1.79452	0.897261	−	0.441500i	$-0.145553\pi$
$443$	3.28369e9	1.79452	0.897261	+	0.441500i	$0.145553\pi$
$444$	0	0
$445$	−1.45896e8	−0.0784842
$446$	6.00911e8	0.320729
$447$	0	0
$448$	−1.36044e9	−0.714835
$449$	−9.39633e8	−0.489887	−0.244944	−	0.969537i	$-0.578769\pi$
$449$	−9.39633e8	−0.489887	−0.244944	+	0.969537i	$0.578769\pi$
$450$	0	0
$451$	5.74606e8	0.294953
$452$	1.35267e9	0.688979
$453$	0	0
$454$	−4.49609e8	−0.225497
$455$	1.26760e8	0.0630871
$456$	0	0
$457$	3.12103e9	1.52965	0.764824	−	0.644239i	$-0.222826\pi$
$457$	3.12103e9	1.52965	0.764824	+	0.644239i	$0.222826\pi$
$458$	−2.30838e7	−0.0112274
$459$	0	0
$460$	2.38599e8	0.114292
$461$	4.01041e9	1.90649	0.953246	−	0.302195i	$-0.0977193\pi$
$461$	4.01041e9	1.90649	0.953246	+	0.302195i	$0.0977193\pi$
$462$	0	0
$463$	2.26220e9	1.05925	0.529623	−	0.848233i	$-0.322333\pi$
$463$	2.26220e9	1.05925	0.529623	+	0.848233i	$0.322333\pi$
$464$	−5.60675e8	−0.260554
$465$	0	0
$466$	1.64754e8	0.0754199
$467$	−2.56795e9	−1.16675	−0.583375	−	0.812203i	$-0.698268\pi$
$467$	−2.56795e9	−1.16675	−0.583375	+	0.812203i	$0.698268\pi$
$468$	0	0
$469$	−1.27732e8	−0.0571734
$470$	3.63934e7	0.0161689
$471$	0	0
$472$	1.70653e9	0.746994
$473$	8.33084e8	0.361972
$474$	0	0
$475$	−2.03908e9	−0.872985
$476$	2.14309e9	0.910784
$477$	0	0
$478$	8.34029e8	0.349288
$479$	4.74057e8	0.197086	0.0985431	−	0.995133i	$-0.468582\pi$
$479$	4.74057e8	0.197086	0.0985431	+	0.995133i	$0.468582\pi$
$480$	0	0
$481$	6.46573e8	0.264917
$482$	−3.95394e8	−0.160829
$483$	0	0
$484$	−2.17115e8	−0.0870425
$485$	−6.84766e7	−0.0272550
$486$	0	0
$487$	3.07593e9	1.20677	0.603386	−	0.797449i	$-0.293818\pi$
$487$	3.07593e9	1.20677	0.603386	+	0.797449i	$0.293818\pi$
$488$	−4.43245e8	−0.172653
$489$	0	0
$490$	−5.30243e6	−0.00203605
$491$	−2.15916e9	−0.823188	−0.411594	−	0.911367i	$-0.635028\pi$
$491$	−2.15916e9	−0.823188	−0.411594	+	0.911367i	$0.635028\pi$
$492$	0	0
$493$	7.95376e8	0.298957
$494$	3.30346e8	0.123289
$495$	0	0
$496$	−3.69248e9	−1.35873
$497$	−1.73252e9	−0.633038
$498$	0	0
$499$	7.32917e8	0.264060	0.132030	−	0.991246i	$-0.457850\pi$
$499$	7.32917e8	0.264060	0.132030	+	0.991246i	$0.457850\pi$
$500$	5.22482e8	0.186929
$501$	0	0
$502$	5.78861e7	0.0204226
$503$	−3.49969e9	−1.22614	−0.613071	−	0.790028i	$-0.710066\pi$
$503$	−3.49969e9	−1.22614	−0.613071	+	0.790028i	$0.710066\pi$
$504$	0	0
$505$	3.36756e8	0.116358
$506$	2.20529e8	0.0756728
$507$	0	0
$508$	4.22653e9	1.43041
$509$	3.79016e9	1.27393	0.636965	−	0.770893i	$-0.280190\pi$
$509$	3.79016e9	1.27393	0.636965	+	0.770893i	$0.280190\pi$
$510$	0	0
$511$	−3.02191e8	−0.100186
$512$	2.62228e9	0.863445
$513$	0	0
$514$	−4.86911e8	−0.158153
$515$	3.75431e7	0.0121117
$516$	0	0
$517$	−7.57225e8	−0.240995
$518$	2.41673e8	0.0763966
$519$	0	0
$520$	−8.61077e7	−0.0268553
$521$	−5.08070e9	−1.57395	−0.786975	−	0.616984i	$-0.788354\pi$
$521$	−5.08070e9	−1.57395	−0.786975	+	0.616984i	$0.788354\pi$
$522$	0	0
$523$	1.36705e9	0.417858	0.208929	−	0.977931i	$-0.433002\pi$
$523$	1.36705e9	0.417858	0.208929	+	0.977931i	$0.433002\pi$
$524$	−5.10078e9	−1.54873
$525$	0	0
$526$	−5.01278e8	−0.150186
$527$	5.23817e9	1.55899
$528$	0	0
$529$	1.63770e9	0.480993
$530$	−2.89921e7	−0.00845892
$531$	0	0
$532$	−2.77962e9	−0.800376
$533$	−2.31928e9	−0.663450
$534$	0	0
$535$	−9.48959e7	−0.0267923
$536$	8.67682e7	0.0243379
$537$	0	0
$538$	−2.97205e8	−0.0822845
$539$	1.10326e8	0.0303470
$540$	0	0
$541$	−1.14145e9	−0.309931	−0.154965	−	0.987920i	$-0.549527\pi$
$541$	−1.14145e9	−0.309931	−0.154965	+	0.987920i	$0.549527\pi$
$542$	7.08437e8	0.191119
$543$	0	0
$544$	−2.19951e9	−0.585774
$545$	4.39977e8	0.116424
$546$	0	0
$547$	−2.95139e9	−0.771029	−0.385514	−	0.922702i	$-0.625976\pi$
$547$	−2.95139e9	−0.771029	−0.385514	+	0.922702i	$0.625976\pi$
$548$	−3.81306e9	−0.989787
$549$	0	0
$550$	2.40289e8	0.0615835
$551$	−1.03161e9	−0.262716
$552$	0	0
$553$	5.63955e8	0.141810
$554$	6.29809e8	0.157371
$555$	0	0
$556$	−5.03160e9	−1.24149
$557$	−8.04857e9	−1.97345	−0.986724	−	0.162407i	$-0.948074\pi$
$557$	−8.04857e9	−1.97345	−0.986724	+	0.162407i	$0.948074\pi$
$558$	0	0
$559$	−3.36258e9	−0.814200
$560$	3.37953e8	0.0813201
$561$	0	0
$562$	4.12221e8	0.0979610
$563$	5.78188e9	1.36549	0.682747	−	0.730655i	$-0.260785\pi$
$563$	5.78188e9	1.36549	0.682747	+	0.730655i	$0.260785\pi$
$564$	0	0
$565$	−3.02599e8	−0.0705827
$566$	8.00580e8	0.185587
$567$	0	0
$568$	1.17690e9	0.269476
$569$	−3.25098e9	−0.739813	−0.369907	−	0.929069i	$-0.620610\pi$
$569$	−3.25098e9	−0.739813	−0.369907	+	0.929069i	$0.620610\pi$
$570$	0	0
$571$	−5.25242e9	−1.18068	−0.590341	−	0.807154i	$-0.701007\pi$
$571$	−5.25242e9	−1.18068	−0.590341	+	0.807154i	$0.701007\pi$
$572$	8.76342e8	0.195789
$573$	0	0
$574$	−8.66890e8	−0.191325
$575$	5.49434e9	1.20525
$576$	0	0
$577$	−4.00206e9	−0.867297	−0.433648	−	0.901082i	$-0.642774\pi$
$577$	−4.00206e9	−0.867297	−0.433648	+	0.901082i	$0.642774\pi$
$578$	5.86747e6	0.00126387
$579$	0	0
$580$	1.31529e8	0.0279912
$581$	6.76506e9	1.43105
$582$	0	0
$583$	6.03229e8	0.126079
$584$	2.05278e8	0.0426480
$585$	0	0
$586$	2.28554e8	0.0469189
$587$	1.67890e9	0.342603	0.171301	−	0.985219i	$-0.445203\pi$
$587$	1.67890e9	0.342603	0.171301	+	0.985219i	$0.445203\pi$
$588$	0	0
$589$	−6.79398e9	−1.37000
$590$	−1.86733e8	−0.0374317
$591$	0	0
$592$	1.72382e9	0.341481
$593$	−4.03630e8	−0.0794863	−0.0397432	−	0.999210i	$-0.512654\pi$
$593$	−4.03630e8	−0.0794863	−0.0397432	+	0.999210i	$0.512654\pi$
$594$	0	0
$595$	−4.79421e8	−0.0933056
$596$	−8.79498e9	−1.70166
$597$	0	0
$598$	−8.90123e8	−0.170214
$599$	1.33232e9	0.253289	0.126644	−	0.991948i	$-0.459579\pi$
$599$	1.33232e9	0.253289	0.126644	+	0.991948i	$0.459579\pi$
$600$	0	0
$601$	−8.79414e9	−1.65247	−0.826234	−	0.563328i	$-0.809521\pi$
$601$	−8.79414e9	−1.65247	−0.826234	+	0.563328i	$0.809521\pi$
$602$	−1.25685e9	−0.234799
$603$	0	0
$604$	7.03212e9	1.29854
$605$	4.85699e7	0.00891710
$606$	0	0
$607$	8.55029e8	0.155174	0.0775872	−	0.996986i	$-0.475278\pi$
$607$	8.55029e8	0.155174	0.0775872	+	0.996986i	$0.475278\pi$
$608$	2.85280e9	0.514765
$609$	0	0
$610$	4.85011e7	0.00865161
$611$	3.05639e9	0.542081
$612$	0	0
$613$	−4.29437e9	−0.752988	−0.376494	−	0.926419i	$-0.622871\pi$
$613$	−4.29437e9	−0.752988	−0.376494	+	0.926419i	$0.622871\pi$
$614$	−8.54213e7	−0.0148928
$615$	0	0
$616$	6.69661e8	0.115431
$617$	−7.06299e9	−1.21057	−0.605286	−	0.796008i	$-0.706941\pi$
$617$	−7.06299e9	−1.21057	−0.605286	+	0.796008i	$0.706941\pi$
$618$	0	0
$619$	8.78500e9	1.48876	0.744380	−	0.667756i	$-0.232745\pi$
$619$	8.78500e9	1.48876	0.744380	+	0.667756i	$0.232745\pi$
$620$	8.66218e8	0.145967
$621$	0	0
$622$	2.32609e9	0.387579
$623$	−4.57972e9	−0.758805
$624$	0	0
$625$	5.92791e9	0.971229
$626$	−8.45094e7	−0.0137688
$627$	0	0
$628$	9.22756e9	1.48672
$629$	−2.44542e9	−0.391811
$630$	0	0
$631$	6.55309e8	0.103835	0.0519175	−	0.998651i	$-0.483467\pi$
$631$	6.55309e8	0.103835	0.0519175	+	0.998651i	$0.483467\pi$
$632$	−3.83095e8	−0.0603665
$633$	0	0
$634$	6.66861e8	0.103926
$635$	−9.45499e8	−0.146539
$636$	0	0
$637$	−4.45308e8	−0.0682609
$638$	1.21567e8	0.0185329
$639$	0	0
$640$	−4.81005e8	−0.0725304
$641$	−4.53406e9	−0.679961	−0.339980	−	0.940432i	$-0.610420\pi$
$641$	−4.53406e9	−0.679961	−0.339980	+	0.940432i	$0.610420\pi$
$642$	0	0
$643$	−8.61045e9	−1.27728	−0.638642	−	0.769504i	$-0.720503\pi$
$643$	−8.61045e9	−1.27728	−0.638642	+	0.769504i	$0.720503\pi$
$644$	7.48972e9	1.10501
$645$	0	0
$646$	−1.24941e9	−0.182344
$647$	9.72467e9	1.41159	0.705797	−	0.708414i	$-0.250589\pi$
$647$	9.72467e9	1.41159	0.705797	+	0.708414i	$0.250589\pi$
$648$	0	0
$649$	3.88529e9	0.557914
$650$	−9.69879e8	−0.138523
$651$	0	0
$652$	7.03064e9	0.993409
$653$	−1.02091e10	−1.43479	−0.717397	−	0.696664i	$-0.754667\pi$
$653$	−1.02091e10	−1.43479	−0.717397	+	0.696664i	$0.754667\pi$
$654$	0	0
$655$	1.14107e9	0.158661
$656$	−6.18342e9	−0.855195
$657$	0	0
$658$	1.14240e9	0.156325
$659$	1.36813e10	1.86221	0.931104	−	0.364755i	$-0.118847\pi$
$659$	1.36813e10	1.86221	0.931104	+	0.364755i	$0.118847\pi$
$660$	0	0
$661$	6.17860e9	0.832119	0.416059	−	0.909337i	$-0.363411\pi$
$661$	6.17860e9	0.832119	0.416059	+	0.909337i	$0.363411\pi$
$662$	−3.02057e9	−0.404656
$663$	0	0
$664$	−4.59551e9	−0.609179
$665$	6.21816e8	0.0819948
$666$	0	0
$667$	2.77970e9	0.362709
$668$	9.96996e9	1.29412
$669$	0	0
$670$	−9.49440e6	−0.00121957
$671$	−1.00914e9	−0.128951
$672$	0	0
$673$	−1.07407e10	−1.35826	−0.679128	−	0.734020i	$-0.737642\pi$
$673$	−1.07407e10	−1.35826	−0.679128	+	0.734020i	$0.737642\pi$
$674$	−3.20582e9	−0.403301
$675$	0	0
$676$	4.15302e9	0.517071
$677$	−4.83727e9	−0.599157	−0.299578	−	0.954072i	$-0.596846\pi$
$677$	−4.83727e9	−0.599157	−0.299578	+	0.954072i	$0.596846\pi$
$678$	0	0
$679$	−2.14951e9	−0.263508
$680$	3.25671e8	0.0397189
$681$	0	0
$682$	8.00615e8	0.0966448
$683$	−1.00529e10	−1.20731	−0.603657	−	0.797244i	$-0.706290\pi$
$683$	−1.00529e10	−1.20731	−0.603657	+	0.797244i	$0.706290\pi$
$684$	0	0
$685$	8.53004e8	0.101399
$686$	−1.82015e9	−0.215265
$687$	0	0
$688$	−8.96495e9	−1.04951
$689$	−2.43482e9	−0.283595
$690$	0	0
$691$	3.37071e9	0.388641	0.194320	−	0.980938i	$-0.437750\pi$
$691$	3.37071e9	0.388641	0.194320	+	0.980938i	$0.437750\pi$
$692$	3.97702e9	0.456233
$693$	0	0
$694$	−1.54033e9	−0.174926
$695$	1.12560e9	0.127185
$696$	0	0
$697$	8.77182e9	0.981240
$698$	5.37173e8	0.0597889
$699$	0	0
$700$	8.16081e9	0.899270
$701$	4.63318e9	0.508002	0.254001	−	0.967204i	$-0.418253\pi$
$701$	4.63318e9	0.508002	0.254001	+	0.967204i	$0.418253\pi$
$702$	0	0
$703$	3.17175e9	0.344315
$704$	2.10402e9	0.227271
$705$	0	0
$706$	2.84636e9	0.304420
$707$	1.05709e10	1.12498
$708$	0	0
$709$	7.89618e8	0.0832061	0.0416031	−	0.999134i	$-0.486754\pi$
$709$	7.89618e8	0.0832061	0.0416031	+	0.999134i	$0.486754\pi$
$710$	−1.28779e8	−0.0135033
$711$	0	0
$712$	3.11100e9	0.323013
$713$	1.83065e10	1.89144
$714$	0	0
$715$	−1.96043e8	−0.0200576
$716$	9.04285e9	0.920682
$717$	0	0
$718$	−2.02381e9	−0.204049
$719$	−1.27467e10	−1.27893	−0.639464	−	0.768821i	$-0.720844\pi$
$719$	−1.27467e10	−1.27893	−0.639464	+	0.768821i	$0.720844\pi$
$720$	0	0
$721$	1.17849e9	0.117099
$722$	−4.65136e8	−0.0459938
$723$	0	0
$724$	1.18100e10	1.15655
$725$	3.02877e9	0.295177
$726$	0	0
$727$	5.87126e9	0.566710	0.283355	−	0.959015i	$-0.408553\pi$
$727$	5.87126e9	0.566710	0.283355	+	0.959015i	$0.408553\pi$
$728$	−2.70295e9	−0.259644
$729$	0	0
$730$	−2.24621e7	−0.00213708
$731$	1.27177e10	1.20420
$732$	0	0
$733$	−1.81404e9	−0.170131	−0.0850655	−	0.996375i	$-0.527110\pi$
$733$	−1.81404e9	−0.170131	−0.0850655	+	0.996375i	$0.527110\pi$
$734$	2.03129e9	0.189599
$735$	0	0
$736$	−7.68692e9	−0.710690
$737$	1.97547e8	0.0181775
$738$	0	0
$739$	−1.11652e10	−1.01768	−0.508842	−	0.860860i	$-0.669926\pi$
$739$	−1.11652e10	−1.01768	−0.508842	+	0.860860i	$0.669926\pi$
$740$	−4.04391e8	−0.0366852
$741$	0	0
$742$	−9.10074e8	−0.0817830
$743$	−2.57103e9	−0.229957	−0.114979	−	0.993368i	$-0.536680\pi$
$743$	−2.57103e9	−0.229957	−0.114979	+	0.993368i	$0.536680\pi$
$744$	0	0
$745$	1.96749e9	0.174327
$746$	3.46089e9	0.305212
$747$	0	0
$748$	−3.31444e9	−0.289571
$749$	−2.97882e9	−0.259034
$750$	0	0
$751$	7.11211e9	0.612716	0.306358	−	0.951916i	$-0.400890\pi$
$751$	7.11211e9	0.612716	0.306358	+	0.951916i	$0.400890\pi$
$752$	8.14861e9	0.698749
$753$	0	0
$754$	−4.90682e8	−0.0416870
$755$	−1.57313e9	−0.133030
$756$	0	0
$757$	−2.20614e10	−1.84841	−0.924203	−	0.381901i	$-0.875270\pi$
$757$	−2.20614e10	−1.84841	−0.924203	+	0.381901i	$0.875270\pi$
$758$	3.40106e9	0.283643
$759$	0	0
$760$	−4.22400e8	−0.0349041
$761$	−2.27373e10	−1.87022	−0.935108	−	0.354363i	$-0.884698\pi$
$761$	−2.27373e10	−1.87022	−0.935108	+	0.354363i	$0.884698\pi$
$762$	0	0
$763$	1.38110e10	1.12561
$764$	1.07689e10	0.873668
$765$	0	0
$766$	2.28999e9	0.184091
$767$	−1.56822e10	−1.25494
$768$	0	0
$769$	−9.90294e9	−0.785275	−0.392638	−	0.919693i	$-0.628437\pi$
$769$	−9.90294e9	−0.785275	−0.392638	+	0.919693i	$0.628437\pi$
$770$	−7.32760e7	−0.00578421
$771$	0	0
$772$	1.31663e10	1.02992
$773$	1.79846e10	1.40047	0.700234	−	0.713913i	$-0.253079\pi$
$773$	1.79846e10	1.40047	0.700234	+	0.713913i	$0.253079\pi$
$774$	0	0
$775$	1.99468e10	1.53928
$776$	1.46016e9	0.112172
$777$	0	0
$778$	−3.03652e9	−0.231179
$779$	−1.13772e10	−0.862291
$780$	0	0
$781$	2.67946e9	0.201265
$782$	3.36656e9	0.251746
$783$	0	0
$784$	−1.18723e9	−0.0879892
$785$	−2.06426e9	−0.152307
$786$	0	0
$787$	−6.74533e9	−0.493278	−0.246639	−	0.969107i	$-0.579326\pi$
$787$	−6.74533e9	−0.493278	−0.246639	+	0.969107i	$0.579326\pi$
$788$	−1.87630e10	−1.36603
$789$	0	0
$790$	4.19192e7	0.00302495
$791$	−9.49869e9	−0.682411
$792$	0	0
$793$	4.07321e9	0.290055
$794$	1.17744e8	0.00834768
$795$	0	0
$796$	−2.28828e10	−1.60810
$797$	−1.31332e10	−0.918895	−0.459448	−	0.888205i	$-0.651953\pi$
$797$	−1.31332e10	−0.918895	−0.459448	+	0.888205i	$0.651953\pi$
$798$	0	0
$799$	−1.15597e10	−0.801735
$800$	−8.37568e9	−0.578369
$801$	0	0
$802$	2.56914e9	0.175864
$803$	4.67361e8	0.0318528
$804$	0	0
$805$	−1.67549e9	−0.113203
$806$	−3.23153e9	−0.217388
$807$	0	0
$808$	−7.18081e9	−0.478888
$809$	−7.74432e9	−0.514237	−0.257119	−	0.966380i	$-0.582773\pi$
$809$	−7.74432e9	−0.514237	−0.257119	+	0.966380i	$0.582773\pi$
$810$	0	0
$811$	−2.53008e9	−0.166556	−0.0832781	−	0.996526i	$-0.526539\pi$
$811$	−2.53008e9	−0.166556	−0.0832781	+	0.996526i	$0.526539\pi$
$812$	4.12873e9	0.270626
$813$	0	0
$814$	−3.73765e8	−0.0242892
$815$	−1.57279e9	−0.101770
$816$	0	0
$817$	−1.64951e10	−1.05822
$818$	8.12843e7	0.00519243
$819$	0	0
$820$	1.45057e9	0.0918732
$821$	−5.07682e9	−0.320177	−0.160089	−	0.987103i	$-0.551178\pi$
$821$	−5.07682e9	−0.320177	−0.160089	+	0.987103i	$0.551178\pi$
$822$	0	0
$823$	2.53795e10	1.58703	0.793514	−	0.608552i	$-0.208249\pi$
$823$	2.53795e10	1.58703	0.793514	+	0.608552i	$0.208249\pi$
$824$	−8.00549e8	−0.0498474
$825$	0	0
$826$	−5.86162e9	−0.361899
$827$	1.25419e10	0.771073	0.385536	−	0.922693i	$-0.374016\pi$
$827$	1.25419e10	0.771073	0.385536	+	0.922693i	$0.374016\pi$
$828$	0	0
$829$	−1.47880e10	−0.901507	−0.450753	−	0.892649i	$-0.648845\pi$
$829$	−1.47880e10	−0.901507	−0.450753	+	0.892649i	$0.648845\pi$
$830$	5.02852e8	0.0305258
$831$	0	0
$832$	−8.49245e9	−0.511212
$833$	1.68421e9	0.100958
$834$	0	0
$835$	−2.23034e9	−0.132577
$836$	4.29888e9	0.254468
$837$	0	0
$838$	6.58042e9	0.386277
$839$	7.29515e9	0.426449	0.213225	−	0.977003i	$-0.431603\pi$
$839$	7.29515e9	0.426449	0.213225	+	0.977003i	$0.431603\pi$
$840$	0	0
$841$	−1.57176e10	−0.911169
$842$	2.00853e8	0.0115954
$843$	0	0
$844$	9.52564e9	0.545376
$845$	−9.29054e8	−0.0529715
$846$	0	0
$847$	1.52463e9	0.0862128
$848$	−6.49144e9	−0.365557
$849$	0	0
$850$	3.66821e9	0.204874
$851$	−8.54634e9	−0.475364
$852$	0	0
$853$	1.66031e10	0.915940	0.457970	−	0.888968i	$-0.348577\pi$
$853$	1.66031e10	0.915940	0.457970	+	0.888968i	$0.348577\pi$
$854$	1.52246e9	0.0836459
$855$	0	0
$856$	2.02351e9	0.110267
$857$	−2.29267e9	−0.124425	−0.0622126	−	0.998063i	$-0.519816\pi$
$857$	−2.29267e9	−0.124425	−0.0622126	+	0.998063i	$0.519816\pi$
$858$	0	0
$859$	−1.58052e10	−0.850794	−0.425397	−	0.905007i	$-0.639866\pi$
$859$	−1.58052e10	−0.850794	−0.425397	+	0.905007i	$0.639866\pi$
$860$	2.10308e9	0.112749
$861$	0	0
$862$	−1.39471e9	−0.0741665
$863$	−1.11057e10	−0.588177	−0.294089	−	0.955778i	$-0.595016\pi$
$863$	−1.11057e10	−0.588177	−0.294089	+	0.955778i	$0.595016\pi$
$864$	0	0
$865$	−8.89683e8	−0.0467389
$866$	−1.85021e9	−0.0968073
$867$	0	0
$868$	2.71909e10	1.41125
$869$	−8.72198e8	−0.0450864
$870$	0	0
$871$	−7.97357e8	−0.0408874
$872$	−9.38182e9	−0.479159
$873$	0	0
$874$	−4.36648e9	−0.221229
$875$	−3.66898e9	−0.185147
$876$	0	0
$877$	−2.70994e10	−1.35663	−0.678315	−	0.734771i	$-0.737289\pi$
$877$	−2.70994e10	−1.35663	−0.678315	+	0.734771i	$0.737289\pi$
$878$	4.70339e9	0.234520
$879$	0	0
$880$	−5.22668e8	−0.0258545
$881$	1.70163e10	0.838399	0.419199	−	0.907894i	$-0.362311\pi$
$881$	1.70163e10	0.838399	0.419199	+	0.907894i	$0.362311\pi$
$882$	0	0
$883$	6.08110e8	0.0297249	0.0148624	−	0.999890i	$-0.495269\pi$
$883$	6.08110e8	0.0297249	0.0148624	+	0.999890i	$0.495269\pi$
$884$	1.33781e10	0.651344
$885$	0	0
$886$	7.66172e9	0.370091
$887$	3.12792e10	1.50495	0.752477	−	0.658619i	$-0.228859\pi$
$887$	3.12792e10	1.50495	0.752477	+	0.658619i	$0.228859\pi$
$888$	0	0
$889$	−2.96795e10	−1.41678
$890$	−3.40414e8	−0.0161861
$891$	0	0
$892$	−3.15631e10	−1.48903
$893$	1.49930e10	0.704547
$894$	0	0
$895$	−2.02294e9	−0.0943197
$896$	−1.50989e10	−0.701242
$897$	0	0
$898$	−2.19241e9	−0.101031
$899$	1.00915e10	0.463230
$900$	0	0
$901$	9.20878e9	0.419436
$902$	1.34071e9	0.0608291
$903$	0	0
$904$	6.45246e9	0.290493
$905$	−2.64197e9	−0.118484
$906$	0	0
$907$	9.88633e9	0.439956	0.219978	−	0.975505i	$-0.429401\pi$
$907$	9.88633e9	0.439956	0.219978	+	0.975505i	$0.429401\pi$
$908$	2.36159e10	1.04690
$909$	0	0
$910$	2.95764e8	0.0130107
$911$	−3.32057e10	−1.45512	−0.727559	−	0.686045i	$-0.759345\pi$
$911$	−3.32057e10	−1.45512	−0.727559	+	0.686045i	$0.759345\pi$
$912$	0	0
$913$	−1.04627e10	−0.454982
$914$	7.28220e9	0.315465
$915$	0	0
$916$	1.21249e9	0.0521247
$917$	3.58187e10	1.53397
$918$	0	0
$919$	1.13328e10	0.481652	0.240826	−	0.970568i	$-0.422582\pi$
$919$	1.13328e10	0.481652	0.240826	+	0.970568i	$0.422582\pi$
$920$	1.13816e9	0.0481889
$921$	0	0
$922$	9.35735e9	0.393183
$923$	−1.08151e10	−0.452716
$924$	0	0
$925$	−9.31210e9	−0.386858
$926$	5.27831e9	0.218452
$927$	0	0
$928$	−4.23743e9	−0.174054
$929$	−2.47753e10	−1.01383	−0.506913	−	0.861997i	$-0.669214\pi$
$929$	−2.47753e10	−1.01383	−0.506913	+	0.861997i	$0.669214\pi$
$930$	0	0
$931$	−2.18445e9	−0.0887192
$932$	−8.65378e9	−0.350147
$933$	0	0
$934$	−5.99172e9	−0.240623
$935$	7.41459e8	0.0296652
$936$	0	0
$937$	−2.68892e10	−1.06780	−0.533899	−	0.845549i	$-0.679274\pi$
$937$	−2.68892e10	−1.06780	−0.533899	+	0.845549i	$0.679274\pi$
$938$	−2.98032e8	−0.0117911
$939$	0	0
$940$	−1.91158e9	−0.0750663
$941$	−3.87913e10	−1.51765	−0.758823	−	0.651297i	$-0.774225\pi$
$941$	−3.87913e10	−1.51765	−0.758823	+	0.651297i	$0.774225\pi$
$942$	0	0
$943$	3.06560e10	1.19049
$944$	−4.18102e10	−1.61763
$945$	0	0
$946$	1.94381e9	0.0746508
$947$	3.31566e10	1.26866	0.634330	−	0.773062i	$-0.281276\pi$
$947$	3.31566e10	1.26866	0.634330	+	0.773062i	$0.281276\pi$
$948$	0	0
$949$	−1.88641e9	−0.0716480
$950$	−4.75772e9	−0.180039
$951$	0	0
$952$	1.02229e10	0.384012
$953$	4.71659e10	1.76524	0.882619	−	0.470089i	$-0.155778\pi$
$953$	4.71659e10	1.76524	0.882619	+	0.470089i	$0.155778\pi$
$954$	0	0
$955$	−2.40908e9	−0.0895033
$956$	−4.38078e10	−1.62162
$957$	0	0
$958$	1.10610e9	0.0406458
$959$	2.67761e10	0.980352
$960$	0	0
$961$	3.89478e10	1.41563
$962$	1.50863e9	0.0546348
$963$	0	0
$964$	2.07682e10	0.746671
$965$	−2.94537e9	−0.105510
$966$	0	0
$967$	1.70372e10	0.605907	0.302954	−	0.953005i	$-0.402027\pi$
$967$	1.70372e10	0.605907	0.302954	+	0.953005i	$0.402027\pi$
$968$	−1.03568e9	−0.0366996
$969$	0	0
$970$	−1.59774e8	−0.00562090
$971$	6.82199e9	0.239135	0.119568	−	0.992826i	$-0.461849\pi$
$971$	6.82199e9	0.239135	0.119568	+	0.992826i	$0.461849\pi$
$972$	0	0
$973$	3.53329e10	1.22966
$974$	7.17698e9	0.248877
$975$	0	0
$976$	1.08596e10	0.373885
$977$	−2.60737e10	−0.894483	−0.447241	−	0.894413i	$-0.647594\pi$
$977$	−2.60737e10	−0.894483	−0.447241	+	0.894413i	$0.647594\pi$
$978$	0	0
$979$	7.08286e9	0.241251
$980$	2.78512e8	0.00945264
$981$	0	0
$982$	−5.03789e9	−0.169769
$983$	−3.10722e10	−1.04336	−0.521680	−	0.853141i	$-0.674694\pi$
$983$	−3.10722e10	−1.04336	−0.521680	+	0.853141i	$0.674694\pi$
$984$	0	0
$985$	4.19740e9	0.139944
$986$	1.85582e9	0.0616549
$987$	0	0
$988$	−1.73516e10	−0.572387
$989$	4.44462e10	1.46099
$990$	0	0
$991$	3.43972e10	1.12270	0.561352	−	0.827577i	$-0.310281\pi$
$991$	3.43972e10	1.12270	0.561352	+	0.827577i	$0.310281\pi$
$992$	−2.79068e10	−0.907652
$993$	0	0
$994$	−4.04242e9	−0.130554
$995$	5.11902e9	0.164743
$996$	0	0
$997$	−3.23954e10	−1.03526	−0.517631	−	0.855604i	$-0.673186\pi$
$997$	−3.23954e10	−1.03526	−0.517631	+	0.855604i	$0.673186\pi$
$998$	1.71009e9	0.0544581
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.a.f.1.3		4
3.2	odd	2		33.8.a.e.1.2	✓	4
12.11	even	2		528.8.a.r.1.2		4
33.32	even	2		363.8.a.f.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.a.e.1.2	✓	4	3.2	odd	2
99.8.a.f.1.3		4	1.1	even	1	trivial
363.8.a.f.1.3		4	33.32	even	2
528.8.a.r.1.2		4	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.33327 q^{2} -122.556 q^{4} +27.4165 q^{5} +860.612 q^{7} -584.614 q^{8} +O(q^{10})\)	\(q+2.33327 q^{2} -122.556 q^{4} +27.4165 q^{5} +860.612 q^{7} -584.614 q^{8} +63.9699 q^{10} -1331.00 q^{11} +5372.32 q^{13} +2008.04 q^{14} +14323.1 q^{16} -20318.8 q^{17} +26353.8 q^{19} -3360.05 q^{20} -3105.58 q^{22} -71010.7 q^{23} -77373.3 q^{25} +12535.1 q^{26} -105473. q^{28} -39144.8 q^{29} -257799. q^{31} +108250. q^{32} -47409.2 q^{34} +23594.9 q^{35} +120353. q^{37} +61490.4 q^{38} -16028.0 q^{40} -431710. q^{41} -625909. q^{43} +163122. q^{44} -165687. q^{46} +568914. q^{47} -82889.3 q^{49} -180533. q^{50} -658409. q^{52} -453215. q^{53} -36491.3 q^{55} -503126. q^{56} -91335.3 q^{58} -2.91908e6 q^{59} +758185. q^{61} -601514. q^{62} -1.58078e6 q^{64} +147290. q^{65} -148420. q^{67} +2.49019e6 q^{68} +55053.3 q^{70} -2.01312e6 q^{71} -351135. q^{73} +280815. q^{74} -3.22981e6 q^{76} -1.14548e6 q^{77} +655295. q^{79} +392688. q^{80} -1.00729e6 q^{82} +7.86076e6 q^{83} -557069. q^{85} -1.46041e6 q^{86} +778121. q^{88} -5.32146e6 q^{89} +4.62348e6 q^{91} +8.70278e6 q^{92} +1.32743e6 q^{94} +722528. q^{95} -2.49765e6 q^{97} -193403. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 15 q^{2} + 565 q^{4} - 306 q^{5} + 890 q^{7} - 2457 q^{8}+O(q^{10}) \) 4 * q - 15 * q^2 + 565 * q^4 - 306 * q^5 + 890 * q^7 - 2457 * q^8	\( 4 q - 15 q^{2} + 565 q^{4} - 306 q^{5} + 890 q^{7} - 2457 q^{8} - 8946 q^{10} - 5324 q^{11} - 1822 q^{13} - 35340 q^{14} + 65041 q^{16} - 32856 q^{17} - 12784 q^{19} + 4002 q^{20} + 19965 q^{22} - 114858 q^{23} + 72856 q^{25} + 221466 q^{26} + 10112 q^{28} + 104952 q^{29} - 24976 q^{31} - 337761 q^{32} - 741690 q^{34} + 722856 q^{35} - 498856 q^{37} + 897156 q^{38} - 2676930 q^{40} - 734556 q^{41} - 201916 q^{43} - 752015 q^{44} - 3068508 q^{46} - 1995894 q^{47} - 771024 q^{49} - 1632129 q^{50} - 4412266 q^{52} - 929970 q^{53} + 407286 q^{55} - 7224888 q^{56} + 2864322 q^{58} - 1353156 q^{59} + 3998774 q^{61} + 3783264 q^{62} + 1480129 q^{64} - 6612108 q^{65} + 1722008 q^{67} - 1596906 q^{68} - 2751024 q^{70} - 5571858 q^{71} + 5600528 q^{73} + 10907838 q^{74} - 19634884 q^{76} - 1184590 q^{77} - 7710226 q^{79} + 24073794 q^{80} - 11230842 q^{82} - 3431856 q^{83} + 5909484 q^{85} + 25687140 q^{86} + 3270267 q^{88} - 4611528 q^{89} - 9032696 q^{91} - 13608576 q^{92} - 3497436 q^{94} - 21828000 q^{95} + 1401692 q^{97} + 7230081 q^{98}+O(q^{100}) \) 4 * q - 15 * q^2 + 565 * q^4 - 306 * q^5 + 890 * q^7 - 2457 * q^8 - 8946 * q^10 - 5324 * q^11 - 1822 * q^13 - 35340 * q^14 + 65041 * q^16 - 32856 * q^17 - 12784 * q^19 + 4002 * q^20 + 19965 * q^22 - 114858 * q^23 + 72856 * q^25 + 221466 * q^26 + 10112 * q^28 + 104952 * q^29 - 24976 * q^31 - 337761 * q^32 - 741690 * q^34 + 722856 * q^35 - 498856 * q^37 + 897156 * q^38 - 2676930 * q^40 - 734556 * q^41 - 201916 * q^43 - 752015 * q^44 - 3068508 * q^46 - 1995894 * q^47 - 771024 * q^49 - 1632129 * q^50 - 4412266 * q^52 - 929970 * q^53 + 407286 * q^55 - 7224888 * q^56 + 2864322 * q^58 - 1353156 * q^59 + 3998774 * q^61 + 3783264 * q^62 + 1480129 * q^64 - 6612108 * q^65 + 1722008 * q^67 - 1596906 * q^68 - 2751024 * q^70 - 5571858 * q^71 + 5600528 * q^73 + 10907838 * q^74 - 19634884 * q^76 - 1184590 * q^77 - 7710226 * q^79 + 24073794 * q^80 - 11230842 * q^82 - 3431856 * q^83 + 5909484 * q^85 + 25687140 * q^86 + 3270267 * q^88 - 4611528 * q^89 - 9032696 * q^91 - 13608576 * q^92 - 3497436 * q^94 - 21828000 * q^95 + 1401692 * q^97 + 7230081 * q^98

Introduction

L-functions

Modular forms

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Database

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