LMFDB - Embedded newform 99.8.a.f.1.2

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			1.2
Root			$-11.0316$ 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)

$f(q)$	$=$	$q-15.0316 q^{2} +97.9505 q^{4} -367.278 q^{5} -91.9512 q^{7} +451.694 q^{8} +O(q^{10})$	\(q-15.0316 q^{2} +97.9505 q^{4} -367.278 q^{5} -91.9512 q^{7} +451.694 q^{8} +5520.80 q^{10} -1331.00 q^{11} +5118.56 q^{13} +1382.18 q^{14} -19327.4 q^{16} +8838.56 q^{17} +13319.2 q^{19} -35975.1 q^{20} +20007.1 q^{22} +70727.0 q^{23} +56768.3 q^{25} -76940.4 q^{26} -9006.66 q^{28} +123137. q^{29} +116235. q^{31} +232705. q^{32} -132858. q^{34} +33771.7 q^{35} -445173. q^{37} -200209. q^{38} -165897. q^{40} +586341. q^{41} -470214. q^{43} -130372. q^{44} -1.06314e6 q^{46} -818322. q^{47} -815088. q^{49} -853322. q^{50} +501366. q^{52} -2.08896e6 q^{53} +488847. q^{55} -41533.8 q^{56} -1.85096e6 q^{58} -1.96982e6 q^{59} +1.31411e6 q^{61} -1.74721e6 q^{62} -1.02404e6 q^{64} -1.87994e6 q^{65} +2.43094e6 q^{67} +865741. q^{68} -507644. q^{70} +2.63282e6 q^{71} -576963. q^{73} +6.69169e6 q^{74} +1.30462e6 q^{76} +122387. q^{77} -1.00612e6 q^{79} +7.09852e6 q^{80} -8.81367e6 q^{82} -8.42647e6 q^{83} -3.24621e6 q^{85} +7.06809e6 q^{86} -601204. q^{88} -3.80212e6 q^{89} -470658. q^{91} +6.92775e6 q^{92} +1.23007e7 q^{94} -4.89184e6 q^{95} +1.53023e7 q^{97} +1.22521e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−15.0316	−1.32862	−0.664311	−	0.747456i	$-0.731275\pi$
$2$	−15.0316	−1.32862	−0.664311	+	0.747456i	$0.731275\pi$
$3$	0	0
$3$	0	0
$4$	97.9505	0.765238
$5$	−367.278	−1.31401	−0.657007	−	0.753884i	$-0.728178\pi$
$5$	−367.278	−1.31401	−0.657007	+	0.753884i	$0.728178\pi$
$6$	0	0
$7$	−91.9512	−0.101324	−0.0506622	−	0.998716i	$-0.516133\pi$
$7$	−91.9512	−0.101324	−0.0506622	+	0.998716i	$0.516133\pi$
$8$	451.694	0.311910
$9$	0	0
$10$	5520.80	1.74583
$11$	−1331.00	−0.301511
$11$	−1331.00	−0.301511
$12$	0	0
$13$	5118.56	0.646169	0.323084	−	0.946370i	$-0.395280\pi$
$13$	5118.56	0.646169	0.323084	+	0.946370i	$0.395280\pi$
$14$	1382.18	0.134622
$15$	0	0
$16$	−19327.4	−1.17965
$17$	8838.56	0.436325	0.218163	−	0.975912i	$-0.429994\pi$
$17$	8838.56	0.436325	0.218163	+	0.975912i	$0.429994\pi$
$18$	0	0
$19$	13319.2	0.445491	0.222746	−	0.974877i	$-0.428498\pi$
$19$	13319.2	0.445491	0.222746	+	0.974877i	$0.428498\pi$
$20$	−35975.1	−1.00553
$21$	0	0
$22$	20007.1	0.400595
$23$	70727.0	1.21210	0.606049	−	0.795427i	$-0.292753\pi$
$23$	70727.0	1.21210	0.606049	+	0.795427i	$0.292753\pi$
$24$	0	0
$25$	56768.3	0.726635
$26$	−76940.4	−0.858515
$27$	0	0
$28$	−9006.66	−0.0775373
$29$	123137.	0.937554	0.468777	−	0.883317i	$-0.344695\pi$
$29$	123137.	0.937554	0.468777	+	0.883317i	$0.344695\pi$
$30$	0	0
$31$	116235.	0.700764	0.350382	−	0.936607i	$-0.386052\pi$
$31$	116235.	0.700764	0.350382	+	0.936607i	$0.386052\pi$
$32$	232705.	1.25540
$33$	0	0
$34$	−132858.	−0.579712
$35$	33771.7	0.133142
$36$	0	0
$37$	−445173.	−1.44485	−0.722426	−	0.691449i	$-0.756973\pi$
$37$	−445173.	−1.44485	−0.722426	+	0.691449i	$0.756973\pi$
$38$	−200209.	−0.591890
$39$	0	0
$40$	−165897.	−0.409854
$41$	586341.	1.32864	0.664319	−	0.747449i	$-0.268722\pi$
$41$	586341.	1.32864	0.664319	+	0.747449i	$0.268722\pi$
$42$	0	0
$43$	−470214.	−0.901895	−0.450947	−	0.892550i	$-0.648914\pi$
$43$	−470214.	−0.901895	−0.450947	+	0.892550i	$0.648914\pi$
$44$	−130372.	−0.230728
$45$	0	0
$46$	−1.06314e6	−1.61042
$47$	−818322.	−1.14969	−0.574846	−	0.818261i	$-0.694938\pi$
$47$	−818322.	−1.14969	−0.574846	+	0.818261i	$0.694938\pi$
$48$	0	0
$49$	−815088.	−0.989733
$50$	−853322.	−0.965423
$51$	0	0
$52$	501366.	0.494473
$53$	−2.08896e6	−1.92737	−0.963684	−	0.267046i	$-0.913952\pi$
$53$	−2.08896e6	−1.92737	−0.963684	+	0.267046i	$0.913952\pi$
$54$	0	0
$55$	488847.	0.396190
$56$	−41533.8	−0.0316041
$57$	0	0
$58$	−1.85096e6	−1.24566
$59$	−1.96982e6	−1.24866	−0.624331	−	0.781160i	$-0.714628\pi$
$59$	−1.96982e6	−1.24866	−0.624331	+	0.781160i	$0.714628\pi$
$60$	0	0
$61$	1.31411e6	0.741270	0.370635	−	0.928779i	$-0.379140\pi$
$61$	1.31411e6	0.741270	0.370635	+	0.928779i	$0.379140\pi$
$62$	−1.74721e6	−0.931051
$63$	0	0
$64$	−1.02404e6	−0.488302
$65$	−1.87994e6	−0.849076
$66$	0	0
$67$	2.43094e6	0.987445	0.493723	−	0.869619i	$-0.335636\pi$
$67$	2.43094e6	0.987445	0.493723	+	0.869619i	$0.335636\pi$
$68$	865741.	0.333893
$69$	0	0
$70$	−507644.	−0.176895
$71$	2.63282e6	0.873006	0.436503	−	0.899703i	$-0.356217\pi$
$71$	2.63282e6	0.873006	0.436503	+	0.899703i	$0.356217\pi$
$72$	0	0
$73$	−576963.	−0.173587	−0.0867937	−	0.996226i	$-0.527662\pi$
$73$	−576963.	−0.173587	−0.0867937	+	0.996226i	$0.527662\pi$
$74$	6.69169e6	1.91966
$75$	0	0
$76$	1.30462e6	0.340907
$77$	122387.	0.0305505
$78$	0	0
$79$	−1.00612e6	−0.229590	−0.114795	−	0.993389i	$-0.536621\pi$
$79$	−1.00612e6	−0.229590	−0.114795	+	0.993389i	$0.536621\pi$
$80$	7.09852e6	1.55008
$81$	0	0
$82$	−8.81367e6	−1.76526
$83$	−8.42647e6	−1.61760	−0.808802	−	0.588081i	$-0.799884\pi$
$83$	−8.42647e6	−1.61760	−0.808802	+	0.588081i	$0.799884\pi$
$84$	0	0
$85$	−3.24621e6	−0.573338
$86$	7.06809e6	1.19828
$87$	0	0
$88$	−601204.	−0.0940443
$89$	−3.80212e6	−0.571691	−0.285845	−	0.958276i	$-0.592274\pi$
$89$	−3.80212e6	−0.571691	−0.285845	+	0.958276i	$0.592274\pi$
$90$	0	0
$91$	−470658.	−0.0654727
$92$	6.92775e6	0.927544
$93$	0	0
$94$	1.23007e7	1.52751
$95$	−4.89184e6	−0.585382
$96$	0	0
$97$	1.53023e7	1.70238	0.851191	−	0.524856i	$-0.175881\pi$
$97$	1.53023e7	1.70238	0.851191	+	0.524856i	$0.175881\pi$
$98$	1.22521e7	1.31498
$99$	0	0
$100$	5.56049e6	0.556049
$101$	−1.30361e7	−1.25899	−0.629494	−	0.777005i	$-0.716738\pi$
$101$	−1.30361e7	−1.25899	−0.629494	+	0.777005i	$0.716738\pi$
$102$	0	0
$103$	−4.86462e6	−0.438650	−0.219325	−	0.975652i	$-0.570386\pi$
$103$	−4.86462e6	−0.438650	−0.219325	+	0.975652i	$0.570386\pi$
$104$	2.31202e6	0.201546
$105$	0	0
$106$	3.14005e7	2.56074
$107$	1.22653e7	0.967909	0.483954	−	0.875093i	$-0.339200\pi$
$107$	1.22653e7	0.967909	0.483954	+	0.875093i	$0.339200\pi$
$108$	0	0
$109$	−1.54745e7	−1.14452	−0.572262	−	0.820071i	$-0.693934\pi$
$109$	−1.54745e7	−1.14452	−0.572262	+	0.820071i	$0.693934\pi$
$110$	−7.34818e6	−0.526387
$111$	0	0
$112$	1.77717e6	0.119527
$113$	1.56100e7	1.01772	0.508861	−	0.860849i	$-0.330067\pi$
$113$	1.56100e7	1.01772	0.508861	+	0.860849i	$0.330067\pi$
$114$	0	0
$115$	−2.59765e7	−1.59272
$116$	1.20613e7	0.717452
$117$	0	0
$118$	2.96097e7	1.65900
$119$	−812716.	−0.0442104
$120$	0	0
$121$	1.77156e6	0.0909091
$122$	−1.97532e7	−0.984868
$123$	0	0
$124$	1.13853e7	0.536251
$125$	7.84384e6	0.359206
$126$	0	0
$127$	−873608.	−0.0378446	−0.0189223	−	0.999821i	$-0.506024\pi$
$127$	−873608.	−0.0378446	−0.0189223	+	0.999821i	$0.506024\pi$
$128$	−1.43932e7	−0.606629
$129$	0	0
$130$	2.82585e7	1.12810
$131$	−3.74565e7	−1.45572	−0.727861	−	0.685725i	$-0.759485\pi$
$131$	−3.74565e7	−1.45572	−0.727861	+	0.685725i	$0.759485\pi$
$132$	0	0
$133$	−1.22471e6	−0.0451391
$134$	−3.65411e7	−1.31194
$135$	0	0
$136$	3.99232e6	0.136094
$137$	−3.94359e6	−0.131030	−0.0655149	−	0.997852i	$-0.520869\pi$
$137$	−3.94359e6	−0.131030	−0.0655149	+	0.997852i	$0.520869\pi$
$138$	0	0
$139$	1.38786e6	0.0438321	0.0219161	−	0.999760i	$-0.493023\pi$
$139$	1.38786e6	0.0438321	0.0219161	+	0.999760i	$0.493023\pi$
$140$	3.30795e6	0.101885
$141$	0	0
$142$	−3.95756e7	−1.15989
$143$	−6.81280e6	−0.194827
$144$	0	0
$145$	−4.52256e7	−1.23196
$146$	8.67271e6	0.230632
$147$	0	0
$148$	−4.36050e7	−1.10566
$149$	4.82972e7	1.19611	0.598053	−	0.801457i	$-0.295941\pi$
$149$	4.82972e7	1.19611	0.598053	+	0.801457i	$0.295941\pi$
$150$	0	0
$151$	−5.21333e7	−1.23224	−0.616121	−	0.787652i	$-0.711297\pi$
$151$	−5.21333e7	−1.23224	−0.616121	+	0.787652i	$0.711297\pi$
$152$	6.01618e6	0.138953
$153$	0	0
$154$	−1.83968e6	−0.0405900
$155$	−4.26907e7	−0.920814
$156$	0	0
$157$	6.04356e7	1.24636	0.623181	−	0.782078i	$-0.285840\pi$
$157$	6.04356e7	1.24636	0.623181	+	0.782078i	$0.285840\pi$
$158$	1.51236e7	0.305039
$159$	0	0
$160$	−8.54676e7	−1.64961
$161$	−6.50343e6	−0.122815
$162$	0	0
$163$	1.19287e7	0.215743	0.107872	−	0.994165i	$-0.465596\pi$
$163$	1.19287e7	0.215743	0.107872	+	0.994165i	$0.465596\pi$
$164$	5.74324e7	1.01672
$165$	0	0
$166$	1.26664e8	2.14919
$167$	5.74301e7	0.954183	0.477091	−	0.878854i	$-0.341691\pi$
$167$	5.74301e7	0.954183	0.477091	+	0.878854i	$0.341691\pi$
$168$	0	0
$169$	−3.65489e7	−0.582466
$170$	4.87959e7	0.761750
$171$	0	0
$172$	−4.60577e7	−0.690164
$173$	8.60605e7	1.26369	0.631847	−	0.775093i	$-0.282297\pi$
$173$	8.60605e7	1.26369	0.631847	+	0.775093i	$0.282297\pi$
$174$	0	0
$175$	−5.21992e6	−0.0736258
$176$	2.57247e7	0.355677
$177$	0	0
$178$	5.71522e7	0.759561
$179$	−1.27863e8	−1.66632	−0.833161	−	0.553031i	$-0.813471\pi$
$179$	−1.27863e8	−1.66632	−0.833161	+	0.553031i	$0.813471\pi$
$180$	0	0
$181$	6.33489e6	0.0794080	0.0397040	−	0.999211i	$-0.487358\pi$
$181$	6.33489e6	0.0794080	0.0397040	+	0.999211i	$0.487358\pi$
$182$	7.07476e6	0.0869885
$183$	0	0
$184$	3.19469e7	0.378065
$185$	1.63503e8	1.89856
$186$	0	0
$187$	−1.17641e7	−0.131557
$188$	−8.01551e7	−0.879789
$189$	0	0
$190$	7.35324e7	0.777752
$191$	−1.68610e8	−1.75092	−0.875460	−	0.483291i	$-0.839441\pi$
$191$	−1.68610e8	−1.75092	−0.875460	+	0.483291i	$0.839441\pi$
$192$	0	0
$193$	−1.62754e8	−1.62960	−0.814800	−	0.579742i	$-0.803153\pi$
$193$	−1.62754e8	−1.62960	−0.814800	+	0.579742i	$0.803153\pi$
$194$	−2.30020e8	−2.26182
$195$	0	0
$196$	−7.98383e7	−0.757382
$197$	−1.64384e8	−1.53189	−0.765944	−	0.642908i	$-0.777728\pi$
$197$	−1.64384e8	−1.53189	−0.765944	+	0.642908i	$0.777728\pi$
$198$	0	0
$199$	8.15883e7	0.733909	0.366955	−	0.930239i	$-0.380400\pi$
$199$	8.15883e7	0.733909	0.366955	+	0.930239i	$0.380400\pi$
$200$	2.56419e7	0.226645
$201$	0	0
$202$	1.95954e8	1.67272
$203$	−1.13226e7	−0.0949971
$204$	0	0
$205$	−2.15350e8	−1.74585
$206$	7.31233e7	0.582801
$207$	0	0
$208$	−9.89283e7	−0.762252
$209$	−1.77278e7	−0.134321
$210$	0	0
$211$	1.73181e8	1.26914	0.634571	−	0.772864i	$-0.281177\pi$
$211$	1.73181e8	1.26914	0.634571	+	0.772864i	$0.281177\pi$
$212$	−2.04615e8	−1.47490
$213$	0	0
$214$	−1.84367e8	−1.28599
$215$	1.72699e8	1.18510
$216$	0	0
$217$	−1.06880e7	−0.0710045
$218$	2.32608e8	1.52064
$219$	0	0
$220$	4.78828e7	0.303180
$221$	4.52407e7	0.281940
$222$	0	0
$223$	−1.55928e8	−0.941582	−0.470791	−	0.882245i	$-0.656031\pi$
$223$	−1.55928e8	−0.941582	−0.470791	+	0.882245i	$0.656031\pi$
$224$	−2.13975e7	−0.127202
$225$	0	0
$226$	−2.34644e8	−1.35217
$227$	−1.35680e8	−0.769882	−0.384941	−	0.922941i	$-0.625778\pi$
$227$	−1.35680e8	−0.769882	−0.384941	+	0.922941i	$0.625778\pi$
$228$	0	0
$229$	5.12748e7	0.282150	0.141075	−	0.989999i	$-0.454944\pi$
$229$	5.12748e7	0.282150	0.141075	+	0.989999i	$0.454944\pi$
$230$	3.90470e8	2.11612
$231$	0	0
$232$	5.56203e7	0.292432
$233$	1.22312e8	0.633465	0.316733	−	0.948515i	$-0.397414\pi$
$233$	1.22312e8	0.633465	0.316733	+	0.948515i	$0.397414\pi$
$234$	0	0
$235$	3.00552e8	1.51071
$236$	−1.92945e8	−0.955524
$237$	0	0
$238$	1.22165e7	0.0587389
$239$	−2.92687e8	−1.38679	−0.693396	−	0.720557i	$-0.743886\pi$
$239$	−2.92687e8	−1.38679	−0.693396	+	0.720557i	$0.743886\pi$
$240$	0	0
$241$	−2.62795e8	−1.20937	−0.604684	−	0.796466i	$-0.706700\pi$
$241$	−2.62795e8	−1.20937	−0.604684	+	0.796466i	$0.706700\pi$
$242$	−2.66295e7	−0.120784
$243$	0	0
$244$	1.28717e8	0.567248
$245$	2.99364e8	1.30052
$246$	0	0
$247$	6.81749e7	0.287863
$248$	5.25027e7	0.218575
$249$	0	0
$250$	−1.17906e8	−0.477249
$251$	−1.48087e8	−0.591096	−0.295548	−	0.955328i	$-0.595502\pi$
$251$	−1.48087e8	−0.591096	−0.295548	+	0.955328i	$0.595502\pi$
$252$	0	0
$253$	−9.41377e7	−0.365462
$254$	1.31318e7	0.0502812
$255$	0	0
$256$	3.47432e8	1.29428
$257$	1.32655e8	0.487480	0.243740	−	0.969841i	$-0.421626\pi$
$257$	1.32655e8	0.487480	0.243740	+	0.969841i	$0.421626\pi$
$258$	0	0
$259$	4.09342e7	0.146399
$260$	−1.84141e8	−0.649745
$261$	0	0
$262$	5.63034e8	1.93410
$263$	2.18061e8	0.739149	0.369575	−	0.929201i	$-0.379503\pi$
$263$	2.18061e8	0.739149	0.369575	+	0.929201i	$0.379503\pi$
$264$	0	0
$265$	7.67230e8	2.53259
$266$	1.84094e7	0.0599729
$267$	0	0
$268$	2.38112e8	0.755631
$269$	−1.38257e8	−0.433065	−0.216532	−	0.976275i	$-0.569475\pi$
$269$	−1.38257e8	−0.433065	−0.216532	+	0.976275i	$0.569475\pi$
$270$	0	0
$271$	−4.82337e8	−1.47217	−0.736086	−	0.676888i	$-0.763328\pi$
$271$	−4.82337e8	−1.47217	−0.736086	+	0.676888i	$0.763328\pi$
$272$	−1.70826e8	−0.514710
$273$	0	0
$274$	5.92787e7	0.174089
$275$	−7.55587e7	−0.219089
$276$	0	0
$277$	1.12004e8	0.316631	0.158316	−	0.987389i	$-0.449394\pi$
$277$	1.12004e8	0.316631	0.158316	+	0.987389i	$0.449394\pi$
$278$	−2.08618e7	−0.0582364
$279$	0	0
$280$	1.52544e7	0.0415282
$281$	2.64955e8	0.712360	0.356180	−	0.934417i	$-0.384079\pi$
$281$	2.64955e8	0.712360	0.356180	+	0.934417i	$0.384079\pi$
$282$	0	0
$283$	−3.02507e8	−0.793384	−0.396692	−	0.917952i	$-0.629842\pi$
$283$	−3.02507e8	−0.793384	−0.396692	+	0.917952i	$0.629842\pi$
$284$	2.57886e8	0.668057
$285$	0	0
$286$	1.02408e8	0.258852
$287$	−5.39147e7	−0.134623
$288$	0	0
$289$	−3.32219e8	−0.809620
$290$	6.79816e8	1.63681
$291$	0	0
$292$	−5.65138e7	−0.132836
$293$	−3.85014e8	−0.894210	−0.447105	−	0.894481i	$-0.647545\pi$
$293$	−3.85014e8	−0.894210	−0.447105	+	0.894481i	$0.647545\pi$
$294$	0	0
$295$	7.23473e8	1.64076
$296$	−2.01082e8	−0.450663
$297$	0	0
$298$	−7.25986e8	−1.58917
$299$	3.62021e8	0.783221
$300$	0	0
$301$	4.32367e7	0.0913840
$302$	7.83649e8	1.63718
$303$	0	0
$304$	−2.57424e8	−0.525523
$305$	−4.82643e8	−0.974040
$306$	0	0
$307$	6.36045e8	1.25460	0.627298	−	0.778780i	$-0.284161\pi$
$307$	6.36045e8	1.25460	0.627298	+	0.778780i	$0.284161\pi$
$308$	1.19879e7	0.0233784
$309$	0	0
$310$	6.41711e8	1.22341
$311$	1.01932e9	1.92153	0.960766	−	0.277360i	$-0.0894595\pi$
$311$	1.01932e9	1.92153	0.960766	+	0.277360i	$0.0894595\pi$
$312$	0	0
$313$	−9.69295e8	−1.78670	−0.893348	−	0.449365i	$-0.851650\pi$
$313$	−9.69295e8	−1.78670	−0.893348	+	0.449365i	$0.851650\pi$
$314$	−9.08447e8	−1.65594
$315$	0	0
$316$	−9.85497e7	−0.175691
$317$	−4.71892e8	−0.832023	−0.416012	−	0.909359i	$-0.636572\pi$
$317$	−4.71892e8	−0.832023	−0.416012	+	0.909359i	$0.636572\pi$
$318$	0	0
$319$	−1.63896e8	−0.282683
$320$	3.76109e8	0.641636
$321$	0	0
$322$	9.77573e7	0.163175
$323$	1.17722e8	0.194379
$324$	0	0
$325$	2.90572e8	0.469529
$326$	−1.79308e8	−0.286641
$327$	0	0
$328$	2.64846e8	0.414415
$329$	7.52457e7	0.116492
$330$	0	0
$331$	3.19142e8	0.483711	0.241856	−	0.970312i	$-0.422244\pi$
$331$	3.19142e8	0.483711	0.241856	+	0.970312i	$0.422244\pi$
$332$	−8.25377e8	−1.23785
$333$	0	0
$334$	−8.63268e8	−1.26775
$335$	−8.92833e8	−1.29752
$336$	0	0
$337$	−4.45647e8	−0.634287	−0.317144	−	0.948378i	$-0.602724\pi$
$337$	−4.45647e8	−0.634287	−0.317144	+	0.948378i	$0.602724\pi$
$338$	5.49390e8	0.773877
$339$	0	0
$340$	−3.17968e8	−0.438740
$341$	−1.54709e8	−0.211288
$342$	0	0
$343$	1.50674e8	0.201609
$344$	−2.12393e8	−0.281310
$345$	0	0
$346$	−1.29363e9	−1.67897
$347$	−6.40262e8	−0.822630	−0.411315	−	0.911493i	$-0.634930\pi$
$347$	−6.40262e8	−0.822630	−0.411315	+	0.911493i	$0.634930\pi$
$348$	0	0
$349$	−1.44158e9	−1.81530	−0.907651	−	0.419725i	$-0.862127\pi$
$349$	−1.44158e9	−1.81530	−0.907651	+	0.419725i	$0.862127\pi$
$350$	7.84639e7	0.0978210
$351$	0	0
$352$	−3.09731e8	−0.378517
$353$	5.37426e8	0.650290	0.325145	−	0.945664i	$-0.394587\pi$
$353$	5.37426e8	0.650290	0.325145	+	0.945664i	$0.394587\pi$
$354$	0	0
$355$	−9.66978e8	−1.14714
$356$	−3.72420e8	−0.437479
$357$	0	0
$358$	1.92199e9	2.21391
$359$	−1.03148e9	−1.17660	−0.588302	−	0.808641i	$-0.700203\pi$
$359$	−1.03148e9	−1.17660	−0.588302	+	0.808641i	$0.700203\pi$
$360$	0	0
$361$	−7.16472e8	−0.801538
$362$	−9.52239e7	−0.105503
$363$	0	0
$364$	−4.61011e7	−0.0501022
$365$	2.11906e8	0.228096
$366$	0	0
$367$	−2.80377e8	−0.296082	−0.148041	−	0.988981i	$-0.547297\pi$
$367$	−2.80377e8	−0.296082	−0.148041	+	0.988981i	$0.547297\pi$
$368$	−1.36697e9	−1.42985
$369$	0	0
$370$	−2.45771e9	−2.52246
$371$	1.92082e8	0.195289
$372$	0	0
$373$	−2.55292e8	−0.254716	−0.127358	−	0.991857i	$-0.540650\pi$
$373$	−2.55292e8	−0.254716	−0.127358	+	0.991857i	$0.540650\pi$
$374$	1.76834e8	0.174790
$375$	0	0
$376$	−3.69631e8	−0.358601
$377$	6.30285e8	0.605818
$378$	0	0
$379$	9.45832e7	0.0892435	0.0446218	−	0.999004i	$-0.485792\pi$
$379$	9.45832e7	0.0892435	0.0446218	+	0.999004i	$0.485792\pi$
$380$	−4.79158e8	−0.447957
$381$	0	0
$382$	2.53448e9	2.32631
$383$	−3.60129e8	−0.327538	−0.163769	−	0.986499i	$-0.552365\pi$
$383$	−3.60129e8	−0.327538	−0.163769	+	0.986499i	$0.552365\pi$
$384$	0	0
$385$	−4.49501e7	−0.0401438
$386$	2.44646e9	2.16512
$387$	0	0
$388$	1.49887e9	1.30273
$389$	−9.18457e8	−0.791107	−0.395553	−	0.918443i	$-0.629447\pi$
$389$	−9.18457e8	−0.791107	−0.395553	+	0.918443i	$0.629447\pi$
$390$	0	0
$391$	6.25125e8	0.528869
$392$	−3.68170e8	−0.308708
$393$	0	0
$394$	2.47096e9	2.03530
$395$	3.69525e8	0.301685
$396$	0	0
$397$	8.33128e8	0.668259	0.334130	−	0.942527i	$-0.391558\pi$
$397$	8.33128e8	0.668259	0.334130	+	0.942527i	$0.391558\pi$
$398$	−1.22641e9	−0.975088
$399$	0	0
$400$	−1.09718e9	−0.857174
$401$	−1.29459e9	−1.00260	−0.501301	−	0.865273i	$-0.667145\pi$
$401$	−1.29459e9	−1.00260	−0.501301	+	0.865273i	$0.667145\pi$
$402$	0	0
$403$	5.94957e8	0.452812
$404$	−1.27689e9	−0.963426
$405$	0	0
$406$	1.70197e8	0.126215
$407$	5.92526e8	0.435639
$408$	0	0
$409$	−2.18443e9	−1.57873	−0.789364	−	0.613925i	$-0.789590\pi$
$409$	−2.18443e9	−1.57873	−0.789364	+	0.613925i	$0.789590\pi$
$410$	3.23707e9	2.31958
$411$	0	0
$412$	−4.76492e8	−0.335672
$413$	1.81128e8	0.126520
$414$	0	0
$415$	3.09486e9	2.12556
$416$	1.19112e9	0.811199
$417$	0	0
$418$	2.66478e8	0.178461
$419$	4.94882e8	0.328664	0.164332	−	0.986405i	$-0.447453\pi$
$419$	4.94882e8	0.328664	0.164332	+	0.986405i	$0.447453\pi$
$420$	0	0
$421$	−3.37073e8	−0.220159	−0.110079	−	0.993923i	$-0.535111\pi$
$421$	−3.37073e8	−0.220159	−0.110079	+	0.993923i	$0.535111\pi$
$422$	−2.60319e9	−1.68621
$423$	0	0
$424$	−9.43570e8	−0.601165
$425$	5.01750e8	0.317049
$426$	0	0
$427$	−1.20834e8	−0.0751087
$428$	1.20139e9	0.740681
$429$	0	0
$430$	−2.59596e9	−1.57456
$431$	2.13731e9	1.28587	0.642934	−	0.765922i	$-0.277717\pi$
$431$	2.13731e9	1.28587	0.642934	+	0.765922i	$0.277717\pi$
$432$	0	0
$433$	3.01414e9	1.78425	0.892125	−	0.451789i	$-0.149214\pi$
$433$	3.01414e9	1.78425	0.892125	+	0.451789i	$0.149214\pi$
$434$	1.60658e8	0.0943382
$435$	0	0
$436$	−1.51574e9	−0.875834
$437$	9.42024e8	0.539979
$438$	0	0
$439$	2.34406e9	1.32234	0.661170	−	0.750236i	$-0.270060\pi$
$439$	2.34406e9	1.32234	0.661170	+	0.750236i	$0.270060\pi$
$440$	2.20809e8	0.123576
$441$	0	0
$442$	−6.80042e8	−0.374592
$443$	1.66669e9	0.910837	0.455418	−	0.890278i	$-0.349490\pi$
$443$	1.66669e9	0.910837	0.455418	+	0.890278i	$0.349490\pi$
$444$	0	0
$445$	1.39644e9	0.751210
$446$	2.34386e9	1.25101
$447$	0	0
$448$	9.41620e7	0.0494769
$449$	1.67459e9	0.873067	0.436533	−	0.899688i	$-0.356206\pi$
$449$	1.67459e9	0.873067	0.436533	+	0.899688i	$0.356206\pi$
$450$	0	0
$451$	−7.80420e8	−0.400599
$452$	1.52901e9	0.778799
$453$	0	0
$454$	2.03949e9	1.02288
$455$	1.72862e8	0.0860321
$456$	0	0
$457$	1.90338e9	0.932866	0.466433	−	0.884556i	$-0.345539\pi$
$457$	1.90338e9	0.932866	0.466433	+	0.884556i	$0.345539\pi$
$458$	−7.70744e8	−0.374870
$459$	0	0
$460$	−2.54441e9	−1.21881
$461$	9.64789e8	0.458647	0.229324	−	0.973350i	$-0.426349\pi$
$461$	9.64789e8	0.458647	0.229324	+	0.973350i	$0.426349\pi$
$462$	0	0
$463$	−2.59795e8	−0.121646	−0.0608229	−	0.998149i	$-0.519372\pi$
$463$	−2.59795e8	−0.121646	−0.0608229	+	0.998149i	$0.519372\pi$
$464$	−2.37992e9	−1.10598
$465$	0	0
$466$	−1.83855e9	−0.841637
$467$	−1.25810e9	−0.571620	−0.285810	−	0.958286i	$-0.592263\pi$
$467$	−1.25810e9	−0.571620	−0.285810	+	0.958286i	$0.592263\pi$
$468$	0	0
$469$	−2.23528e8	−0.100052
$470$	−4.51779e9	−2.00717
$471$	0	0
$472$	−8.89756e8	−0.389470
$473$	6.25855e8	0.271932
$474$	0	0
$475$	7.56106e8	0.323709
$476$	−7.96059e7	−0.0338315
$477$	0	0
$478$	4.39957e9	1.84252
$479$	−2.45751e9	−1.02169	−0.510847	−	0.859672i	$-0.670668\pi$
$479$	−2.45751e9	−1.02169	−0.510847	+	0.859672i	$0.670668\pi$
$480$	0	0
$481$	−2.27865e9	−0.933618
$482$	3.95025e9	1.60679
$483$	0	0
$484$	1.73525e8	0.0695671
$485$	−5.62022e9	−2.23695
$486$	0	0
$487$	4.00331e9	1.57061	0.785305	−	0.619109i	$-0.212506\pi$
$487$	4.00331e9	1.57061	0.785305	+	0.619109i	$0.212506\pi$
$488$	5.93574e8	0.231209
$489$	0	0
$490$	−4.49994e9	−1.72791
$491$	4.80277e9	1.83108	0.915539	−	0.402230i	$-0.131765\pi$
$491$	4.80277e9	1.83108	0.915539	+	0.402230i	$0.131765\pi$
$492$	0	0
$493$	1.08836e9	0.409078
$494$	−1.02478e9	−0.382461
$495$	0	0
$496$	−2.24652e9	−0.826655
$497$	−2.42091e8	−0.0884568
$498$	0	0
$499$	1.56779e8	0.0564855	0.0282427	−	0.999601i	$-0.491009\pi$
$499$	1.56779e8	0.0564855	0.0282427	+	0.999601i	$0.491009\pi$
$500$	7.68308e8	0.274878
$501$	0	0
$502$	2.22599e9	0.785343
$503$	−3.38644e9	−1.18647	−0.593233	−	0.805031i	$-0.702149\pi$
$503$	−3.38644e9	−1.18647	−0.593233	+	0.805031i	$0.702149\pi$
$504$	0	0
$505$	4.78787e9	1.65433
$506$	1.41504e9	0.485560
$507$	0	0
$508$	−8.55704e7	−0.0289601
$509$	−3.74614e9	−1.25913	−0.629567	−	0.776946i	$-0.716768\pi$
$509$	−3.74614e9	−1.25913	−0.629567	+	0.776946i	$0.716768\pi$
$510$	0	0
$511$	5.30524e7	0.0175886
$512$	−3.38014e9	−1.11298
$513$	0	0
$514$	−1.99402e9	−0.647677
$515$	1.78667e9	0.576393
$516$	0	0
$517$	1.08919e9	0.346645
$518$	−6.15309e8	−0.194509
$519$	0	0
$520$	−8.49155e8	−0.264835
$521$	−1.73449e9	−0.537328	−0.268664	−	0.963234i	$-0.586582\pi$
$521$	−1.73449e9	−0.537328	−0.268664	+	0.963234i	$0.586582\pi$
$522$	0	0
$523$	−4.28089e7	−0.0130851	−0.00654256	−	0.999979i	$-0.502083\pi$
$523$	−4.28089e7	−0.0130851	−0.00654256	+	0.999979i	$0.502083\pi$
$524$	−3.66889e9	−1.11397
$525$	0	0
$526$	−3.27781e9	−0.982050
$527$	1.02735e9	0.305761
$528$	0	0
$529$	1.59749e9	0.469183
$530$	−1.15327e10	−3.36486
$531$	0	0
$532$	−1.19961e8	−0.0345422
$533$	3.00122e9	0.858525
$534$	0	0
$535$	−4.50477e9	−1.27185
$536$	1.09804e9	0.307994
$537$	0	0
$538$	2.07822e9	0.575379
$539$	1.08488e9	0.298416
$540$	0	0
$541$	−4.18440e9	−1.13617	−0.568085	−	0.822970i	$-0.692315\pi$
$541$	−4.18440e9	−1.13617	−0.568085	+	0.822970i	$0.692315\pi$
$542$	7.25033e9	1.95596
$543$	0	0
$544$	2.05678e9	0.547762
$545$	5.68346e9	1.50392
$546$	0	0
$547$	−3.60517e9	−0.941825	−0.470913	−	0.882180i	$-0.656075\pi$
$547$	−3.60517e9	−0.941825	−0.470913	+	0.882180i	$0.656075\pi$
$548$	−3.86277e8	−0.100269
$549$	0	0
$550$	1.13577e9	0.291086
$551$	1.64008e9	0.417672
$552$	0	0
$553$	9.25137e7	0.0232631
$554$	−1.68360e9	−0.420683
$555$	0	0
$556$	1.35941e8	0.0335420
$557$	−3.16535e9	−0.776120	−0.388060	−	0.921634i	$-0.626855\pi$
$557$	−3.16535e9	−0.776120	−0.388060	+	0.921634i	$0.626855\pi$
$558$	0	0
$559$	−2.40682e9	−0.582777
$560$	−6.52717e8	−0.157061
$561$	0	0
$562$	−3.98270e9	−0.946457
$563$	3.44458e9	0.813499	0.406750	−	0.913540i	$-0.366662\pi$
$563$	3.44458e9	0.813499	0.406750	+	0.913540i	$0.366662\pi$
$564$	0	0
$565$	−5.73322e9	−1.33730
$566$	4.54719e9	1.05411
$567$	0	0
$568$	1.18923e9	0.272299
$569$	2.13767e8	0.0486460	0.0243230	−	0.999704i	$-0.492257\pi$
$569$	2.13767e8	0.0486460	0.0243230	+	0.999704i	$0.492257\pi$
$570$	0	0
$571$	1.69649e9	0.381350	0.190675	−	0.981653i	$-0.438932\pi$
$571$	1.69649e9	0.381350	0.190675	+	0.981653i	$0.438932\pi$
$572$	−6.67318e8	−0.149089
$573$	0	0
$574$	8.10427e8	0.178864
$575$	4.01506e9	0.880753
$576$	0	0
$577$	−1.59938e9	−0.346607	−0.173304	−	0.984868i	$-0.555444\pi$
$577$	−1.59938e9	−0.346607	−0.173304	+	0.984868i	$0.555444\pi$
$578$	4.99379e9	1.07568
$579$	0	0
$580$	−4.42987e9	−0.942743
$581$	7.74824e8	0.163903
$582$	0	0
$583$	2.78041e9	0.581123
$584$	−2.60611e8	−0.0541436
$585$	0	0
$586$	5.78739e9	1.18807
$587$	−2.17523e9	−0.443886	−0.221943	−	0.975060i	$-0.571240\pi$
$587$	−2.17523e9	−0.443886	−0.221943	+	0.975060i	$0.571240\pi$
$588$	0	0
$589$	1.54815e9	0.312184
$590$	−1.08750e10	−2.17995
$591$	0	0
$592$	8.60403e9	1.70442
$593$	8.69992e9	1.71326	0.856632	−	0.515929i	$-0.172553\pi$
$593$	8.69992e9	1.71326	0.856632	+	0.515929i	$0.172553\pi$
$594$	0	0
$595$	2.98493e8	0.0580931
$596$	4.73073e9	0.915306
$597$	0	0
$598$	−5.44177e9	−1.04060
$599$	1.16124e9	0.220764	0.110382	−	0.993889i	$-0.464793\pi$
$599$	1.16124e9	0.220764	0.110382	+	0.993889i	$0.464793\pi$
$600$	0	0
$601$	8.37192e9	1.57313	0.786564	−	0.617508i	$-0.211858\pi$
$601$	8.37192e9	1.57313	0.786564	+	0.617508i	$0.211858\pi$
$602$	−6.49919e8	−0.121415
$603$	0	0
$604$	−5.10648e9	−0.942958
$605$	−6.50656e8	−0.119456
$606$	0	0
$607$	−4.65984e9	−0.845688	−0.422844	−	0.906202i	$-0.638968\pi$
$607$	−4.65984e9	−0.845688	−0.422844	+	0.906202i	$0.638968\pi$
$608$	3.09944e9	0.559269
$609$	0	0
$610$	7.25492e9	1.29413
$611$	−4.18863e9	−0.742896
$612$	0	0
$613$	−3.82596e9	−0.670855	−0.335428	−	0.942066i	$-0.608881\pi$
$613$	−3.82596e9	−0.670855	−0.335428	+	0.942066i	$0.608881\pi$
$614$	−9.56081e9	−1.66688
$615$	0	0
$616$	5.52814e7	0.00952899
$617$	−3.15185e9	−0.540216	−0.270108	−	0.962830i	$-0.587059\pi$
$617$	−3.15185e9	−0.540216	−0.270108	+	0.962830i	$0.587059\pi$
$618$	0	0
$619$	−1.11183e10	−1.88417	−0.942086	−	0.335372i	$-0.891138\pi$
$619$	−1.11183e10	−1.88417	−0.942086	+	0.335372i	$0.891138\pi$
$620$	−4.18157e9	−0.704642
$621$	0	0
$622$	−1.53220e10	−2.55299
$623$	3.49610e8	0.0579262
$624$	0	0
$625$	−7.31590e9	−1.19864
$626$	1.45701e10	2.37385
$627$	0	0
$628$	5.91970e9	0.953764
$629$	−3.93469e9	−0.630425
$630$	0	0
$631$	−3.74087e9	−0.592748	−0.296374	−	0.955072i	$-0.595778\pi$
$631$	−3.74087e9	−0.592748	−0.296374	+	0.955072i	$0.595778\pi$
$632$	−4.54457e8	−0.0716115
$633$	0	0
$634$	7.09332e9	1.10545
$635$	3.20857e8	0.0497283
$636$	0	0
$637$	−4.17208e9	−0.639535
$638$	2.46362e9	0.375579
$639$	0	0
$640$	5.28632e9	0.797120
$641$	1.30668e9	0.195959	0.0979796	−	0.995188i	$-0.468762\pi$
$641$	1.30668e9	0.195959	0.0979796	+	0.995188i	$0.468762\pi$
$642$	0	0
$643$	5.01887e9	0.744504	0.372252	−	0.928132i	$-0.378586\pi$
$643$	5.01887e9	0.744504	0.372252	+	0.928132i	$0.378586\pi$
$644$	−6.37014e8	−0.0939829
$645$	0	0
$646$	−1.76956e9	−0.258256
$647$	−6.91469e9	−1.00371	−0.501855	−	0.864952i	$-0.667349\pi$
$647$	−6.91469e9	−1.00371	−0.501855	+	0.864952i	$0.667349\pi$
$648$	0	0
$649$	2.62183e9	0.376486
$650$	−4.36778e9	−0.623827
$651$	0	0
$652$	1.16842e9	0.165095
$653$	−7.49431e9	−1.05326	−0.526630	−	0.850094i	$-0.676545\pi$
$653$	−7.49431e9	−1.05326	−0.526630	+	0.850094i	$0.676545\pi$
$654$	0	0
$655$	1.37570e10	1.91284
$656$	−1.13324e10	−1.56733
$657$	0	0
$658$	−1.13107e9	−0.154774
$659$	4.01111e9	0.545966	0.272983	−	0.962019i	$-0.411990\pi$
$659$	4.01111e9	0.545966	0.272983	+	0.962019i	$0.411990\pi$
$660$	0	0
$661$	4.43123e9	0.596786	0.298393	−	0.954443i	$-0.403549\pi$
$661$	4.43123e9	0.596786	0.298393	+	0.954443i	$0.403549\pi$
$662$	−4.79723e9	−0.642670
$663$	0	0
$664$	−3.80618e9	−0.504547
$665$	4.49810e8	0.0593135
$666$	0	0
$667$	8.70913e9	1.13641
$668$	5.62530e9	0.730177
$669$	0	0
$670$	1.34208e10	1.72391
$671$	−1.74908e9	−0.223501
$672$	0	0
$673$	−1.09178e9	−0.138064	−0.0690322	−	0.997614i	$-0.521991\pi$
$673$	−1.09178e9	−0.138064	−0.0690322	+	0.997614i	$0.521991\pi$
$674$	6.69880e9	0.842728
$675$	0	0
$676$	−3.57998e9	−0.445725
$677$	−1.13823e10	−1.40984	−0.704919	−	0.709288i	$-0.749017\pi$
$677$	−1.13823e10	−1.40984	−0.704919	+	0.709288i	$0.749017\pi$
$678$	0	0
$679$	−1.40707e9	−0.172493
$680$	−1.46629e9	−0.178830
$681$	0	0
$682$	2.32553e9	0.280722
$683$	7.14821e9	0.858470	0.429235	−	0.903193i	$-0.358783\pi$
$683$	7.14821e9	0.858470	0.429235	+	0.903193i	$0.358783\pi$
$684$	0	0
$685$	1.44840e9	0.172175
$686$	−2.26488e9	−0.267862
$687$	0	0
$688$	9.08800e9	1.06392
$689$	−1.06925e10	−1.24541
$690$	0	0
$691$	−7.94882e9	−0.916494	−0.458247	−	0.888825i	$-0.651522\pi$
$691$	−7.94882e9	−0.916494	−0.458247	+	0.888825i	$0.651522\pi$
$692$	8.42966e9	0.967028
$693$	0	0
$694$	9.62419e9	1.09296
$695$	−5.09729e8	−0.0575961
$696$	0	0
$697$	5.18241e9	0.579718
$698$	2.16693e10	2.41185
$699$	0	0
$700$	−5.11293e8	−0.0563413
$701$	−1.42083e10	−1.55786	−0.778932	−	0.627109i	$-0.784238\pi$
$701$	−1.42083e10	−1.55786	−0.778932	+	0.627109i	$0.784238\pi$
$702$	0	0
$703$	−5.92933e9	−0.643668
$704$	1.36300e9	0.147229
$705$	0	0
$706$	−8.07839e9	−0.863990
$707$	1.19868e9	0.127566
$708$	0	0
$709$	−1.72520e10	−1.81793	−0.908967	−	0.416868i	$-0.863128\pi$
$709$	−1.72520e10	−1.81793	−0.908967	+	0.416868i	$0.863128\pi$
$710$	1.45353e10	1.52412
$711$	0	0
$712$	−1.71739e9	−0.178316
$713$	8.22097e9	0.849395
$714$	0	0
$715$	2.50219e9	0.256006
$716$	−1.25242e10	−1.27513
$717$	0	0
$718$	1.55049e10	1.56326
$719$	−6.01848e9	−0.603859	−0.301929	−	0.953330i	$-0.597631\pi$
$719$	−6.01848e9	−0.603859	−0.301929	+	0.953330i	$0.597631\pi$
$720$	0	0
$721$	4.47307e8	0.0444460
$722$	1.07698e10	1.06494
$723$	0	0
$724$	6.20506e8	0.0607661
$725$	6.99029e9	0.681259
$726$	0	0
$727$	−6.27113e9	−0.605306	−0.302653	−	0.953101i	$-0.597872\pi$
$727$	−6.27113e9	−0.605306	−0.302653	+	0.953101i	$0.597872\pi$
$728$	−2.12593e8	−0.0204216
$729$	0	0
$730$	−3.18530e9	−0.303054
$731$	−4.15601e9	−0.393519
$732$	0	0
$733$	1.07976e9	0.101266	0.0506328	−	0.998717i	$-0.483876\pi$
$733$	1.07976e9	0.101266	0.0506328	+	0.998717i	$0.483876\pi$
$734$	4.21453e9	0.393381
$735$	0	0
$736$	1.64586e10	1.52167
$737$	−3.23559e9	−0.297726
$738$	0	0
$739$	−2.74991e9	−0.250647	−0.125324	−	0.992116i	$-0.539997\pi$
$739$	−2.74991e9	−0.250647	−0.125324	+	0.992116i	$0.539997\pi$
$740$	1.60152e10	1.45285
$741$	0	0
$742$	−2.88731e9	−0.259466
$743$	1.45368e10	1.30019	0.650096	−	0.759852i	$-0.274729\pi$
$743$	1.45368e10	1.30019	0.650096	+	0.759852i	$0.274729\pi$
$744$	0	0
$745$	−1.77385e10	−1.57170
$746$	3.83746e9	0.338422
$747$	0	0
$748$	−1.15230e9	−0.100672
$749$	−1.12781e9	−0.0980728
$750$	0	0
$751$	1.24242e10	1.07035	0.535177	−	0.844740i	$-0.320245\pi$
$751$	1.24242e10	1.07035	0.535177	+	0.844740i	$0.320245\pi$
$752$	1.58160e10	1.35623
$753$	0	0
$754$	−9.47423e9	−0.804904
$755$	1.91474e10	1.61918
$756$	0	0
$757$	−6.60390e9	−0.553305	−0.276653	−	0.960970i	$-0.589225\pi$
$757$	−6.60390e9	−0.553305	−0.276653	+	0.960970i	$0.589225\pi$
$758$	−1.42174e9	−0.118571
$759$	0	0
$760$	−2.20961e9	−0.182586
$761$	−7.65346e9	−0.629523	−0.314762	−	0.949171i	$-0.601925\pi$
$761$	−7.65346e9	−0.629523	−0.314762	+	0.949171i	$0.601925\pi$
$762$	0	0
$763$	1.42290e9	0.115968
$764$	−1.65154e10	−1.33987
$765$	0	0
$766$	5.41333e9	0.435175
$767$	−1.00827e10	−0.806847
$768$	0	0
$769$	−7.34905e9	−0.582759	−0.291380	−	0.956607i	$-0.594114\pi$
$769$	−7.34905e9	−0.582759	−0.291380	+	0.956607i	$0.594114\pi$
$770$	6.75674e8	0.0533359
$771$	0	0
$772$	−1.59418e10	−1.24703
$773$	−2.99068e9	−0.232885	−0.116443	−	0.993197i	$-0.537149\pi$
$773$	−2.99068e9	−0.232885	−0.116443	+	0.993197i	$0.537149\pi$
$774$	0	0
$775$	6.59848e9	0.509199
$776$	6.91197e9	0.530990
$777$	0	0
$778$	1.38059e10	1.05108
$779$	7.80957e9	0.591896
$780$	0	0
$781$	−3.50428e9	−0.263221
$782$	−9.39666e9	−0.702668
$783$	0	0
$784$	1.57535e10	1.16754
$785$	−2.21967e10	−1.63774
$786$	0	0
$787$	2.40705e10	1.76025	0.880125	−	0.474742i	$-0.157459\pi$
$787$	2.40705e10	1.76025	0.880125	+	0.474742i	$0.157459\pi$
$788$	−1.61015e10	−1.17226
$789$	0	0
$790$	−5.55457e9	−0.400826
$791$	−1.43536e9	−0.103120
$792$	0	0
$793$	6.72634e9	0.478986
$794$	−1.25233e10	−0.887865
$795$	0	0
$796$	7.99162e9	0.561615
$797$	−4.33730e9	−0.303470	−0.151735	−	0.988421i	$-0.548486\pi$
$797$	−4.33730e9	−0.303470	−0.151735	+	0.988421i	$0.548486\pi$
$798$	0	0
$799$	−7.23279e9	−0.501640
$800$	1.32103e10	0.912216
$801$	0	0
$802$	1.94599e10	1.33208
$803$	7.67938e8	0.0523386
$804$	0	0
$805$	2.38857e9	0.161381
$806$	−8.94319e9	−0.601616
$807$	0	0
$808$	−5.88831e9	−0.392691
$809$	7.50051e7	0.00498048	0.00249024	−	0.999997i	$-0.499207\pi$
$809$	7.50051e7	0.00498048	0.00249024	+	0.999997i	$0.499207\pi$
$810$	0	0
$811$	1.60048e10	1.05361	0.526803	−	0.849988i	$-0.323391\pi$
$811$	1.60048e10	1.05361	0.526803	+	0.849988i	$0.323391\pi$
$812$	−1.10906e9	−0.0726954
$813$	0	0
$814$	−8.90664e9	−0.578800
$815$	−4.38115e9	−0.283490
$816$	0	0
$817$	−6.26285e9	−0.401786
$818$	3.28356e10	2.09753
$819$	0	0
$820$	−2.10937e10	−1.33599
$821$	9.00415e9	0.567860	0.283930	−	0.958845i	$-0.408362\pi$
$821$	9.00415e9	0.567860	0.283930	+	0.958845i	$0.408362\pi$
$822$	0	0
$823$	1.74879e10	1.09355	0.546776	−	0.837279i	$-0.315855\pi$
$823$	1.74879e10	1.09355	0.546776	+	0.837279i	$0.315855\pi$
$824$	−2.19732e9	−0.136819
$825$	0	0
$826$	−2.72265e9	−0.168097
$827$	9.24503e9	0.568381	0.284190	−	0.958768i	$-0.408275\pi$
$827$	9.24503e9	0.568381	0.284190	+	0.958768i	$0.408275\pi$
$828$	0	0
$829$	−8.34392e9	−0.508662	−0.254331	−	0.967117i	$-0.581855\pi$
$829$	−8.34392e9	−0.508662	−0.254331	+	0.967117i	$0.581855\pi$
$830$	−4.65208e10	−2.82406
$831$	0	0
$832$	−5.24163e9	−0.315525
$833$	−7.20420e9	−0.431846
$834$	0	0
$835$	−2.10928e10	−1.25381
$836$	−1.73645e9	−0.102787
$837$	0	0
$838$	−7.43889e9	−0.436671
$839$	−3.52733e9	−0.206195	−0.103098	−	0.994671i	$-0.532875\pi$
$839$	−3.52733e9	−0.206195	−0.103098	+	0.994671i	$0.532875\pi$
$840$	0	0
$841$	−2.08711e9	−0.120993
$842$	5.06676e9	0.292508
$843$	0	0
$844$	1.69631e10	0.971197
$845$	1.34236e10	0.765368
$846$	0	0
$847$	−1.62897e8	−0.00921131
$848$	4.03741e10	2.27362
$849$	0	0
$850$	−7.54214e9	−0.421239
$851$	−3.14858e10	−1.75130
$852$	0	0
$853$	−3.29500e10	−1.81775	−0.908875	−	0.417069i	$-0.863057\pi$
$853$	−3.29500e10	−1.81775	−0.908875	+	0.417069i	$0.863057\pi$
$854$	1.81633e9	0.0997912
$855$	0	0
$856$	5.54015e9	0.301900
$857$	−1.15453e10	−0.626576	−0.313288	−	0.949658i	$-0.601430\pi$
$857$	−1.15453e10	−0.626576	−0.313288	+	0.949658i	$0.601430\pi$
$858$	0	0
$859$	−1.10119e10	−0.592773	−0.296386	−	0.955068i	$-0.595782\pi$
$859$	−1.10119e10	−0.592773	−0.296386	+	0.955068i	$0.595782\pi$
$860$	1.69160e10	0.906886
$861$	0	0
$862$	−3.21272e10	−1.70843
$863$	4.86919e9	0.257881	0.128940	−	0.991652i	$-0.458842\pi$
$863$	4.86919e9	0.257881	0.128940	+	0.991652i	$0.458842\pi$
$864$	0	0
$865$	−3.16081e10	−1.66051
$866$	−4.53075e10	−2.37060
$867$	0	0
$868$	−1.04689e9	−0.0543354
$869$	1.33914e9	0.0692241
$870$	0	0
$871$	1.24429e10	0.638057
$872$	−6.98975e9	−0.356988
$873$	0	0
$874$	−1.41602e10	−0.717429
$875$	−7.21250e8	−0.0363963
$876$	0	0
$877$	2.78944e9	0.139643	0.0698214	−	0.997560i	$-0.477757\pi$
$877$	2.78944e9	0.139643	0.0698214	+	0.997560i	$0.477757\pi$
$878$	−3.52351e10	−1.75689
$879$	0	0
$880$	−9.44813e9	−0.467365
$881$	2.69844e10	1.32953	0.664763	−	0.747054i	$-0.268533\pi$
$881$	2.69844e10	1.32953	0.664763	+	0.747054i	$0.268533\pi$
$882$	0	0
$883$	−8.92756e9	−0.436386	−0.218193	−	0.975906i	$-0.570016\pi$
$883$	−8.92756e9	−0.436386	−0.218193	+	0.975906i	$0.570016\pi$
$884$	4.43135e9	0.215751
$885$	0	0
$886$	−2.50530e10	−1.21016
$887$	−2.24812e10	−1.08165	−0.540824	−	0.841136i	$-0.681888\pi$
$887$	−2.24812e10	−1.08165	−0.540824	+	0.841136i	$0.681888\pi$
$888$	0	0
$889$	8.03293e7	0.00383458
$890$	−2.09908e10	−0.998074
$891$	0	0
$892$	−1.52733e10	−0.720534
$893$	−1.08994e10	−0.512178
$894$	0	0
$895$	4.69613e10	2.18957
$896$	1.32347e9	0.0614664
$897$	0	0
$898$	−2.51719e10	−1.15998
$899$	1.43129e10	0.657004
$900$	0	0
$901$	−1.84634e10	−0.840959
$902$	1.17310e10	0.532246
$903$	0	0
$904$	7.05095e9	0.317437
$905$	−2.32667e9	−0.104343
$906$	0	0
$907$	3.82511e9	0.170223	0.0851115	−	0.996371i	$-0.472875\pi$
$907$	3.82511e9	0.170223	0.0851115	+	0.996371i	$0.472875\pi$
$908$	−1.32899e10	−0.589144
$909$	0	0
$910$	−2.59841e9	−0.114304
$911$	2.83658e10	1.24303	0.621514	−	0.783403i	$-0.286518\pi$
$911$	2.83658e10	1.24303	0.621514	+	0.783403i	$0.286518\pi$
$912$	0	0
$913$	1.12156e10	0.487726
$914$	−2.86110e10	−1.23943
$915$	0	0
$916$	5.02239e9	0.215912
$917$	3.44417e9	0.147500
$918$	0	0
$919$	4.26088e10	1.81090	0.905450	−	0.424452i	$-0.139533\pi$
$919$	4.26088e10	1.81090	0.905450	+	0.424452i	$0.139533\pi$
$920$	−1.17334e10	−0.496784
$921$	0	0
$922$	−1.45024e10	−0.609369
$923$	1.34762e10	0.564109
$924$	0	0
$925$	−2.52718e10	−1.04988
$926$	3.90514e9	0.161621
$927$	0	0
$928$	2.86547e10	1.17700
$929$	1.62785e10	0.666131	0.333065	−	0.942904i	$-0.391917\pi$
$929$	1.62785e10	0.666131	0.333065	+	0.942904i	$0.391917\pi$
$930$	0	0
$931$	−1.08563e10	−0.440917
$932$	1.19805e10	0.484752
$933$	0	0
$934$	1.89114e10	0.759467
$935$	4.32071e9	0.172868
$936$	0	0
$937$	1.42832e10	0.567202	0.283601	−	0.958942i	$-0.408471\pi$
$937$	1.42832e10	0.567202	0.283601	+	0.958942i	$0.408471\pi$
$938$	3.36000e9	0.132932
$939$	0	0
$940$	2.94392e10	1.15606
$941$	−2.28343e10	−0.893356	−0.446678	−	0.894695i	$-0.647393\pi$
$941$	−2.28343e10	−0.893356	−0.446678	+	0.894695i	$0.647393\pi$
$942$	0	0
$943$	4.14702e10	1.61044
$944$	3.80715e10	1.47298
$945$	0	0
$946$	−9.40763e9	−0.361294
$947$	3.56818e10	1.36528	0.682641	−	0.730754i	$-0.260831\pi$
$947$	3.56818e10	1.36528	0.682641	+	0.730754i	$0.260831\pi$
$948$	0	0
$949$	−2.95322e9	−0.112167
$950$	−1.13655e10	−0.430088
$951$	0	0
$952$	−3.67099e8	−0.0137897
$953$	3.09703e10	1.15910	0.579549	−	0.814937i	$-0.303229\pi$
$953$	3.09703e10	1.15910	0.579549	+	0.814937i	$0.303229\pi$
$954$	0	0
$955$	6.19267e10	2.30073
$956$	−2.86689e10	−1.06123
$957$	0	0
$958$	3.69404e10	1.35744
$959$	3.62618e8	0.0132765
$960$	0	0
$961$	−1.40020e10	−0.508930
$962$	3.42518e10	1.24043
$963$	0	0
$964$	−2.57409e10	−0.925454
$965$	5.97760e10	2.14132
$966$	0	0
$967$	−2.33295e10	−0.829683	−0.414841	−	0.909894i	$-0.636163\pi$
$967$	−2.33295e10	−0.829683	−0.414841	+	0.909894i	$0.636163\pi$
$968$	8.00203e8	0.0283554
$969$	0	0
$970$	8.44812e10	2.97207
$971$	−3.59204e9	−0.125914	−0.0629571	−	0.998016i	$-0.520053\pi$
$971$	−3.59204e9	−0.125914	−0.0629571	+	0.998016i	$0.520053\pi$
$972$	0	0
$973$	−1.27615e8	−0.00444127
$974$	−6.01764e10	−2.08675
$975$	0	0
$976$	−2.53982e10	−0.874438
$977$	4.27678e10	1.46719	0.733594	−	0.679588i	$-0.237842\pi$
$977$	4.27678e10	1.46719	0.733594	+	0.679588i	$0.237842\pi$
$978$	0	0
$979$	5.06062e9	0.172371
$980$	2.93229e10	0.995211
$981$	0	0
$982$	−7.21936e10	−2.43281
$983$	5.36514e10	1.80154	0.900769	−	0.434298i	$-0.143003\pi$
$983$	5.36514e10	1.80154	0.900769	+	0.434298i	$0.143003\pi$
$984$	0	0
$985$	6.03745e10	2.01292
$986$	−1.63598e10	−0.543511
$987$	0	0
$988$	6.67776e9	0.220283
$989$	−3.32568e10	−1.09319
$990$	0	0
$991$	2.06830e10	0.675081	0.337541	−	0.941311i	$-0.390405\pi$
$991$	2.06830e10	0.675081	0.337541	+	0.941311i	$0.390405\pi$
$992$	2.70486e10	0.879738
$993$	0	0
$994$	3.63903e9	0.117526
$995$	−2.99656e10	−0.964367
$996$	0	0
$997$	−2.42215e10	−0.774049	−0.387025	−	0.922069i	$-0.626497\pi$
$997$	−2.42215e10	−0.774049	−0.387025	+	0.922069i	$0.626497\pi$
$998$	−2.35665e9	−0.0750479
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.a.f.1.2		4
3.2	odd	2		33.8.a.e.1.3	✓	4
12.11	even	2		528.8.a.r.1.4		4
33.32	even	2		363.8.a.f.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.a.e.1.3	✓	4	3.2	odd	2
99.8.a.f.1.2		4	1.1	even	1	trivial
363.8.a.f.1.2		4	33.32	even	2
528.8.a.r.1.4		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)

\(f(q)\)	\(=\)	\(q-15.0316 q^{2} +97.9505 q^{4} -367.278 q^{5} -91.9512 q^{7} +451.694 q^{8} +O(q^{10})\)	\(q-15.0316 q^{2} +97.9505 q^{4} -367.278 q^{5} -91.9512 q^{7} +451.694 q^{8} +5520.80 q^{10} -1331.00 q^{11} +5118.56 q^{13} +1382.18 q^{14} -19327.4 q^{16} +8838.56 q^{17} +13319.2 q^{19} -35975.1 q^{20} +20007.1 q^{22} +70727.0 q^{23} +56768.3 q^{25} -76940.4 q^{26} -9006.66 q^{28} +123137. q^{29} +116235. q^{31} +232705. q^{32} -132858. q^{34} +33771.7 q^{35} -445173. q^{37} -200209. q^{38} -165897. q^{40} +586341. q^{41} -470214. q^{43} -130372. q^{44} -1.06314e6 q^{46} -818322. q^{47} -815088. q^{49} -853322. q^{50} +501366. q^{52} -2.08896e6 q^{53} +488847. q^{55} -41533.8 q^{56} -1.85096e6 q^{58} -1.96982e6 q^{59} +1.31411e6 q^{61} -1.74721e6 q^{62} -1.02404e6 q^{64} -1.87994e6 q^{65} +2.43094e6 q^{67} +865741. q^{68} -507644. q^{70} +2.63282e6 q^{71} -576963. q^{73} +6.69169e6 q^{74} +1.30462e6 q^{76} +122387. q^{77} -1.00612e6 q^{79} +7.09852e6 q^{80} -8.81367e6 q^{82} -8.42647e6 q^{83} -3.24621e6 q^{85} +7.06809e6 q^{86} -601204. q^{88} -3.80212e6 q^{89} -470658. q^{91} +6.92775e6 q^{92} +1.23007e7 q^{94} -4.89184e6 q^{95} +1.53023e7 q^{97} +1.22521e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 15 q^{2} + 565 q^{4} - 306 q^{5} + 890 q^{7} - 2457 q^{8}+O(q^{10}) \) 4 * q - 15 * q^2 + 565 * q^4 - 306 * q^5 + 890 * q^7 - 2457 * q^8	\( 4 q - 15 q^{2} + 565 q^{4} - 306 q^{5} + 890 q^{7} - 2457 q^{8} - 8946 q^{10} - 5324 q^{11} - 1822 q^{13} - 35340 q^{14} + 65041 q^{16} - 32856 q^{17} - 12784 q^{19} + 4002 q^{20} + 19965 q^{22} - 114858 q^{23} + 72856 q^{25} + 221466 q^{26} + 10112 q^{28} + 104952 q^{29} - 24976 q^{31} - 337761 q^{32} - 741690 q^{34} + 722856 q^{35} - 498856 q^{37} + 897156 q^{38} - 2676930 q^{40} - 734556 q^{41} - 201916 q^{43} - 752015 q^{44} - 3068508 q^{46} - 1995894 q^{47} - 771024 q^{49} - 1632129 q^{50} - 4412266 q^{52} - 929970 q^{53} + 407286 q^{55} - 7224888 q^{56} + 2864322 q^{58} - 1353156 q^{59} + 3998774 q^{61} + 3783264 q^{62} + 1480129 q^{64} - 6612108 q^{65} + 1722008 q^{67} - 1596906 q^{68} - 2751024 q^{70} - 5571858 q^{71} + 5600528 q^{73} + 10907838 q^{74} - 19634884 q^{76} - 1184590 q^{77} - 7710226 q^{79} + 24073794 q^{80} - 11230842 q^{82} - 3431856 q^{83} + 5909484 q^{85} + 25687140 q^{86} + 3270267 q^{88} - 4611528 q^{89} - 9032696 q^{91} - 13608576 q^{92} - 3497436 q^{94} - 21828000 q^{95} + 1401692 q^{97} + 7230081 q^{98}+O(q^{100}) \) 4 * q - 15 * q^2 + 565 * q^4 - 306 * q^5 + 890 * q^7 - 2457 * q^8 - 8946 * q^10 - 5324 * q^11 - 1822 * q^13 - 35340 * q^14 + 65041 * q^16 - 32856 * q^17 - 12784 * q^19 + 4002 * q^20 + 19965 * q^22 - 114858 * q^23 + 72856 * q^25 + 221466 * q^26 + 10112 * q^28 + 104952 * q^29 - 24976 * q^31 - 337761 * q^32 - 741690 * q^34 + 722856 * q^35 - 498856 * q^37 + 897156 * q^38 - 2676930 * q^40 - 734556 * q^41 - 201916 * q^43 - 752015 * q^44 - 3068508 * q^46 - 1995894 * q^47 - 771024 * q^49 - 1632129 * q^50 - 4412266 * q^52 - 929970 * q^53 + 407286 * q^55 - 7224888 * q^56 + 2864322 * q^58 - 1353156 * q^59 + 3998774 * q^61 + 3783264 * q^62 + 1480129 * q^64 - 6612108 * q^65 + 1722008 * q^67 - 1596906 * q^68 - 2751024 * q^70 - 5571858 * q^71 + 5600528 * q^73 + 10907838 * q^74 - 19634884 * q^76 - 1184590 * q^77 - 7710226 * q^79 + 24073794 * q^80 - 11230842 * q^82 - 3431856 * q^83 + 5909484 * q^85 + 25687140 * q^86 + 3270267 * q^88 - 4611528 * q^89 - 9032696 * q^91 - 13608576 * q^92 - 3497436 * q^94 - 21828000 * q^95 + 1401692 * q^97 + 7230081 * q^98

Introduction

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