LMFDB - Embedded newform 387.10.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,10,Mod(1,387)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("387.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	387.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:	$199.318868595$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} + \cdots + 52\!\cdots\!00 $ x^15 - 2x^14 - 5425x^13 + 14888x^12 + 11288030x^11 - 37600244x^10 - 11474166224x^9 + 47465836576x^8 + 5986976782464x^7 - 32493903147264x^6 - 1516975415483904x^5 + 10892588268404224x^4 + 139803541742443008x^3 - 1349125586394823680x^2 + 2103623681144094720x + 529838441422848000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-25.8680$ of defining polynomial
Character	$\chi$	$=$	387.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-23.8680 q^{2} +57.6838 q^{4} +578.837 q^{5} -413.035 q^{7} +10843.6 q^{8} +O(q^{10})$	\(q-23.8680 q^{2} +57.6838 q^{4} +578.837 q^{5} -413.035 q^{7} +10843.6 q^{8} -13815.7 q^{10} -40989.1 q^{11} -154895. q^{13} +9858.34 q^{14} -288351. q^{16} +37046.5 q^{17} -572136. q^{19} +33389.5 q^{20} +978329. q^{22} -1.53076e6 q^{23} -1.61807e6 q^{25} +3.69704e6 q^{26} -23825.4 q^{28} -5.10452e6 q^{29} -6.63330e6 q^{31} +1.33042e6 q^{32} -884227. q^{34} -239080. q^{35} +1.17863e7 q^{37} +1.36558e7 q^{38} +6.27670e6 q^{40} +1.86693e7 q^{41} -3.41880e6 q^{43} -2.36440e6 q^{44} +3.65362e7 q^{46} +4.17423e7 q^{47} -4.01830e7 q^{49} +3.86202e7 q^{50} -8.93492e6 q^{52} -1.09354e8 q^{53} -2.37260e7 q^{55} -4.47880e6 q^{56} +1.21835e8 q^{58} -1.08726e8 q^{59} +8.96497e7 q^{61} +1.58324e8 q^{62} +1.15881e8 q^{64} -8.96588e7 q^{65} -2.02489e8 q^{67} +2.13698e6 q^{68} +5.70637e6 q^{70} -1.86518e8 q^{71} +2.88219e8 q^{73} -2.81315e8 q^{74} -3.30030e7 q^{76} +1.69299e7 q^{77} +1.54282e8 q^{79} -1.66908e8 q^{80} -4.45599e8 q^{82} -1.44177e8 q^{83} +2.14439e7 q^{85} +8.16001e7 q^{86} -4.44471e8 q^{88} +5.50623e8 q^{89} +6.39770e7 q^{91} -8.82999e7 q^{92} -9.96306e8 q^{94} -3.31174e8 q^{95} -1.15464e9 q^{97} +9.59090e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) $ 15 * q + 32 * q^2 + 3242 * q^4 + 4717 * q^5 - 9680 * q^7 + 20394 * q^8	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8} - 36237 q^{10} + 104484 q^{11} - 116174 q^{13} - 416064 q^{14} + 996762 q^{16} + 884265 q^{17} - 689535 q^{19} + 3077879 q^{20} - 7276218 q^{22} + 2504077 q^{23} + 1315350 q^{25} + 13343414 q^{26} - 28059568 q^{28} + 18406221 q^{29} - 12033699 q^{31} + 18952630 q^{32} - 30383125 q^{34} + 27855546 q^{35} - 8722847 q^{37} + 63941843 q^{38} - 39665611 q^{40} + 18689389 q^{41} - 51282015 q^{43} + 68723220 q^{44} - 2067521 q^{46} + 104960741 q^{47} + 92663095 q^{49} + 42446347 q^{50} + 149226080 q^{52} + 215907800 q^{53} + 384379852 q^{55} - 430441344 q^{56} + 295963139 q^{58} - 185924544 q^{59} + 247538102 q^{61} - 139798853 q^{62} + 848556290 q^{64} - 94294394 q^{65} + 467904656 q^{67} + 88234341 q^{68} + 647526126 q^{70} + 8252944 q^{71} - 715627902 q^{73} - 725122989 q^{74} + 346300359 q^{76} + 1236779964 q^{77} + 560681783 q^{79} + 1157214179 q^{80} + 941346367 q^{82} + 1442854698 q^{83} + 699302088 q^{85} - 109401632 q^{86} - 1464507256 q^{88} + 396710008 q^{89} - 3278076852 q^{91} - 155864647 q^{92} + 4666638949 q^{94} + 3854114395 q^{95} - 3063837815 q^{97} + 6161086984 q^{98}+O(q^{100}) \) 15 * q + 32 * q^2 + 3242 * q^4 + 4717 * q^5 - 9680 * q^7 + 20394 * q^8 - 36237 * q^10 + 104484 * q^11 - 116174 * q^13 - 416064 * q^14 + 996762 * q^16 + 884265 * q^17 - 689535 * q^19 + 3077879 * q^20 - 7276218 * q^22 + 2504077 * q^23 + 1315350 * q^25 + 13343414 * q^26 - 28059568 * q^28 + 18406221 * q^29 - 12033699 * q^31 + 18952630 * q^32 - 30383125 * q^34 + 27855546 * q^35 - 8722847 * q^37 + 63941843 * q^38 - 39665611 * q^40 + 18689389 * q^41 - 51282015 * q^43 + 68723220 * q^44 - 2067521 * q^46 + 104960741 * q^47 + 92663095 * q^49 + 42446347 * q^50 + 149226080 * q^52 + 215907800 * q^53 + 384379852 * q^55 - 430441344 * q^56 + 295963139 * q^58 - 185924544 * q^59 + 247538102 * q^61 - 139798853 * q^62 + 848556290 * q^64 - 94294394 * q^65 + 467904656 * q^67 + 88234341 * q^68 + 647526126 * q^70 + 8252944 * q^71 - 715627902 * q^73 - 725122989 * q^74 + 346300359 * q^76 + 1236779964 * q^77 + 560681783 * q^79 + 1157214179 * q^80 + 941346367 * q^82 + 1442854698 * q^83 + 699302088 * q^85 - 109401632 * q^86 - 1464507256 * q^88 + 396710008 * q^89 - 3278076852 * q^91 - 155864647 * q^92 + 4666638949 * q^94 + 3854114395 * q^95 - 3063837815 * q^97 + 6161086984 * 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 $

$2$	−23.8680	−1.05483	−0.527414	−	0.849608i	$-0.676838\pi$
$2$	−23.8680	−1.05483	−0.527414	+	0.849608i	$0.676838\pi$
$3$	0	0
$3$	0	0
$4$	57.6838	0.112664
$5$	578.837	0.414182	0.207091	−	0.978322i	$-0.433600\pi$
$5$	578.837	0.414182	0.207091	+	0.978322i	$0.433600\pi$
$6$	0	0
$7$	−413.035	−0.0650198	−0.0325099	−	0.999471i	$-0.510350\pi$
$7$	−413.035	−0.0650198	−0.0325099	+	0.999471i	$0.510350\pi$
$8$	10843.6	0.935988
$9$	0	0
$10$	−13815.7	−0.436891
$11$	−40989.1	−0.844114	−0.422057	−	0.906569i	$-0.638692\pi$
$11$	−40989.1	−0.844114	−0.422057	+	0.906569i	$0.638692\pi$
$12$	0	0
$13$	−154895.	−1.50415	−0.752076	−	0.659076i	$-0.770947\pi$
$13$	−154895.	−1.50415	−0.752076	+	0.659076i	$0.770947\pi$
$14$	9858.34	0.0685848
$15$	0	0
$16$	−288351.	−1.09997
$17$	37046.5	0.107579	0.0537894	−	0.998552i	$-0.482870\pi$
$17$	37046.5	0.107579	0.0537894	+	0.998552i	$0.482870\pi$
$18$	0	0
$19$	−572136.	−1.00718	−0.503591	−	0.863942i	$-0.667988\pi$
$19$	−572136.	−1.00718	−0.503591	+	0.863942i	$0.667988\pi$
$20$	33389.5	0.0466632
$21$	0	0
$22$	978329.	0.890395
$23$	−1.53076e6	−1.14059	−0.570297	−	0.821439i	$-0.693172\pi$
$23$	−1.53076e6	−1.14059	−0.570297	+	0.821439i	$0.693172\pi$
$24$	0	0
$25$	−1.61807e6	−0.828453
$26$	3.69704e6	1.58662
$27$	0	0
$28$	−23825.4	−0.00732537
$29$	−5.10452e6	−1.34018	−0.670091	−	0.742279i	$-0.733745\pi$
$29$	−5.10452e6	−1.34018	−0.670091	+	0.742279i	$0.733745\pi$
$30$	0	0
$31$	−6.63330e6	−1.29004	−0.645018	−	0.764167i	$-0.723150\pi$
$31$	−6.63330e6	−1.29004	−0.645018	+	0.764167i	$0.723150\pi$
$32$	1.33042e6	0.224293
$33$	0	0
$34$	−884227.	−0.113477
$35$	−239080.	−0.0269300
$36$	0	0
$37$	1.17863e7	1.03387	0.516937	−	0.856023i	$-0.327072\pi$
$37$	1.17863e7	1.03387	0.516937	+	0.856023i	$0.327072\pi$
$38$	1.36558e7	1.06241
$39$	0	0
$40$	6.27670e6	0.387669
$41$	1.86693e7	1.03181	0.515905	−	0.856646i	$-0.327456\pi$
$41$	1.86693e7	1.03181	0.515905	+	0.856646i	$0.327456\pi$
$42$	0	0
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	−2.36440e6	−0.0951009
$45$	0	0
$46$	3.65362e7	1.20313
$47$	4.17423e7	1.24777	0.623886	−	0.781515i	$-0.285553\pi$
$47$	4.17423e7	1.24777	0.623886	+	0.781515i	$0.285553\pi$
$48$	0	0
$49$	−4.01830e7	−0.995772
$50$	3.86202e7	0.873876
$51$	0	0
$52$	−8.93492e6	−0.169463
$53$	−1.09354e8	−1.90368	−0.951842	−	0.306590i	$-0.900812\pi$
$53$	−1.09354e8	−1.90368	−0.951842	+	0.306590i	$0.900812\pi$
$54$	0	0
$55$	−2.37260e7	−0.349617
$56$	−4.47880e6	−0.0608578
$57$	0	0
$58$	1.21835e8	1.41366
$59$	−1.08726e8	−1.16815	−0.584075	−	0.811699i	$-0.698543\pi$
$59$	−1.08726e8	−1.16815	−0.584075	+	0.811699i	$0.698543\pi$
$60$	0	0
$61$	8.96497e7	0.829019	0.414510	−	0.910045i	$-0.363953\pi$
$61$	8.96497e7	0.829019	0.414510	+	0.910045i	$0.363953\pi$
$62$	1.58324e8	1.36077
$63$	0	0
$64$	1.15881e8	0.863380
$65$	−8.96588e7	−0.622993
$66$	0	0
$67$	−2.02489e8	−1.22762	−0.613810	−	0.789454i	$-0.710364\pi$
$67$	−2.02489e8	−1.22762	−0.613810	+	0.789454i	$0.710364\pi$
$68$	2.13698e6	0.0121202
$69$	0	0
$70$	5.70637e6	0.0284066
$71$	−1.86518e8	−0.871081	−0.435541	−	0.900169i	$-0.643443\pi$
$71$	−1.86518e8	−0.871081	−0.435541	+	0.900169i	$0.643443\pi$
$72$	0	0
$73$	2.88219e8	1.18787	0.593937	−	0.804512i	$-0.297573\pi$
$73$	2.88219e8	1.18787	0.593937	+	0.804512i	$0.297573\pi$
$74$	−2.81315e8	−1.09056
$75$	0	0
$76$	−3.30030e7	−0.113473
$77$	1.69299e7	0.0548841
$78$	0	0
$79$	1.54282e8	0.445650	0.222825	−	0.974858i	$-0.428472\pi$
$79$	1.54282e8	0.445650	0.222825	+	0.974858i	$0.428472\pi$
$80$	−1.66908e8	−0.455588
$81$	0	0
$82$	−4.45599e8	−1.08838
$83$	−1.44177e8	−0.333461	−0.166730	−	0.986003i	$-0.553321\pi$
$83$	−1.44177e8	−0.333461	−0.166730	+	0.986003i	$0.553321\pi$
$84$	0	0
$85$	2.14439e7	0.0445572
$86$	8.16001e7	0.160860
$87$	0	0
$88$	−4.44471e8	−0.790080
$89$	5.50623e8	0.930248	0.465124	−	0.885245i	$-0.346010\pi$
$89$	5.50623e8	0.930248	0.465124	+	0.885245i	$0.346010\pi$
$90$	0	0
$91$	6.39770e7	0.0977997
$92$	−8.82999e7	−0.128503
$93$	0	0
$94$	−9.96306e8	−1.31619
$95$	−3.31174e8	−0.417157
$96$	0	0
$97$	−1.15464e9	−1.32427	−0.662133	−	0.749387i	$-0.730348\pi$
$97$	−1.15464e9	−1.32427	−0.662133	+	0.749387i	$0.730348\pi$
$98$	9.59090e8	1.05037
$99$	0	0
$100$	−9.33366e7	−0.0933366
$101$	1.66204e9	1.58926	0.794630	−	0.607094i	$-0.207665\pi$
$101$	1.66204e9	1.58926	0.794630	+	0.607094i	$0.207665\pi$
$102$	0	0
$103$	−2.01491e8	−0.176396	−0.0881979	−	0.996103i	$-0.528111\pi$
$103$	−2.01491e8	−0.176396	−0.0881979	+	0.996103i	$0.528111\pi$
$104$	−1.67962e9	−1.40787
$105$	0	0
$106$	2.61008e9	2.00806
$107$	2.22025e9	1.63748	0.818738	−	0.574168i	$-0.194674\pi$
$107$	2.22025e9	1.63748	0.818738	+	0.574168i	$0.194674\pi$
$108$	0	0
$109$	−1.44526e9	−0.980679	−0.490340	−	0.871531i	$-0.663127\pi$
$109$	−1.44526e9	−0.980679	−0.490340	+	0.871531i	$0.663127\pi$
$110$	5.66293e8	0.368786
$111$	0	0
$112$	1.19099e8	0.0715199
$113$	−1.98255e9	−1.14385	−0.571927	−	0.820304i	$-0.693804\pi$
$113$	−1.98255e9	−1.14385	−0.571927	+	0.820304i	$0.693804\pi$
$114$	0	0
$115$	−8.86059e8	−0.472413
$116$	−2.94448e8	−0.150990
$117$	0	0
$118$	2.59507e9	1.23220
$119$	−1.53015e7	−0.00699476
$120$	0	0
$121$	−6.77844e8	−0.287472
$122$	−2.13976e9	−0.874473
$123$	0	0
$124$	−3.82634e8	−0.145340
$125$	−2.06714e9	−0.757312
$126$	0	0
$127$	−5.25769e9	−1.79340	−0.896702	−	0.442635i	$-0.854044\pi$
$127$	−5.25769e9	−1.79340	−0.896702	+	0.442635i	$0.854044\pi$
$128$	−3.44703e9	−1.13501
$129$	0	0
$130$	2.13998e9	0.657150
$131$	−4.26420e8	−0.126508	−0.0632538	−	0.997997i	$-0.520148\pi$
$131$	−4.26420e8	−0.126508	−0.0632538	+	0.997997i	$0.520148\pi$
$132$	0	0
$133$	2.36312e8	0.0654868
$134$	4.83301e9	1.29493
$135$	0	0
$136$	4.01719e8	0.100693
$137$	−2.39976e9	−0.582003	−0.291002	−	0.956723i	$-0.593989\pi$
$137$	−2.39976e9	−0.582003	−0.291002	+	0.956723i	$0.593989\pi$
$138$	0	0
$139$	4.62160e8	0.105009	0.0525044	−	0.998621i	$-0.483280\pi$
$139$	4.62160e8	0.105009	0.0525044	+	0.998621i	$0.483280\pi$
$140$	−1.37910e7	−0.00303404
$141$	0	0
$142$	4.45183e9	0.918842
$143$	6.34899e9	1.26968
$144$	0	0
$145$	−2.95468e9	−0.555079
$146$	−6.87923e9	−1.25300
$147$	0	0
$148$	6.79876e8	0.116480
$149$	−1.41734e8	−0.0235578	−0.0117789	−	0.999931i	$-0.503749\pi$
$149$	−1.41734e8	−0.0235578	−0.0117789	+	0.999931i	$0.503749\pi$
$150$	0	0
$151$	−7.41576e9	−1.16081	−0.580403	−	0.814330i	$-0.697105\pi$
$151$	−7.41576e9	−1.16081	−0.580403	+	0.814330i	$0.697105\pi$
$152$	−6.20404e9	−0.942711
$153$	0	0
$154$	−4.04084e8	−0.0578933
$155$	−3.83960e9	−0.534310
$156$	0	0
$157$	−1.10190e10	−1.44742	−0.723709	−	0.690106i	$-0.757564\pi$
$157$	−1.10190e10	−1.44742	−0.723709	+	0.690106i	$0.757564\pi$
$158$	−3.68242e9	−0.470085
$159$	0	0
$160$	7.70098e8	0.0928980
$161$	6.32256e8	0.0741612
$162$	0	0
$163$	−1.12939e10	−1.25314	−0.626571	−	0.779364i	$-0.715542\pi$
$163$	−1.12939e10	−1.25314	−0.626571	+	0.779364i	$0.715542\pi$
$164$	1.07691e9	0.116247
$165$	0	0
$166$	3.44123e9	0.351744
$167$	−2.07229e9	−0.206171	−0.103085	−	0.994673i	$-0.532872\pi$
$167$	−2.07229e9	−0.206171	−0.103085	+	0.994673i	$0.532872\pi$
$168$	0	0
$169$	1.33879e10	1.26247
$170$	−5.11823e8	−0.0470002
$171$	0	0
$172$	−1.97209e8	−0.0171810
$173$	1.50835e10	1.28025	0.640125	−	0.768271i	$-0.278883\pi$
$173$	1.50835e10	1.28025	0.640125	+	0.768271i	$0.278883\pi$
$174$	0	0
$175$	6.68321e8	0.0538659
$176$	1.18192e10	0.928500
$177$	0	0
$178$	−1.31423e10	−0.981253
$179$	−1.57672e10	−1.14793	−0.573967	−	0.818878i	$-0.694596\pi$
$179$	−1.57672e10	−1.14793	−0.573967	+	0.818878i	$0.694596\pi$
$180$	0	0
$181$	6.68229e8	0.0462777	0.0231388	−	0.999732i	$-0.492634\pi$
$181$	6.68229e8	0.0462777	0.0231388	+	0.999732i	$0.492634\pi$
$182$	−1.52701e9	−0.103162
$183$	0	0
$184$	−1.65990e10	−1.06758
$185$	6.82232e9	0.428212
$186$	0	0
$187$	−1.51850e9	−0.0908088
$188$	2.40785e9	0.140579
$189$	0	0
$190$	7.90447e9	0.440029
$191$	3.50164e10	1.90380	0.951901	−	0.306407i	$-0.0991269\pi$
$191$	3.50164e10	1.90380	0.951901	+	0.306407i	$0.0991269\pi$
$192$	0	0
$193$	2.42400e10	1.25755	0.628775	−	0.777587i	$-0.283557\pi$
$193$	2.42400e10	1.25755	0.628775	+	0.777587i	$0.283557\pi$
$194$	2.75591e10	1.39687
$195$	0	0
$196$	−2.31791e9	−0.112187
$197$	−1.04603e10	−0.494819	−0.247409	−	0.968911i	$-0.579579\pi$
$197$	−1.04603e10	−0.494819	−0.247409	+	0.968911i	$0.579579\pi$
$198$	0	0
$199$	−1.66270e10	−0.751580	−0.375790	−	0.926705i	$-0.622629\pi$
$199$	−1.66270e10	−0.751580	−0.375790	+	0.926705i	$0.622629\pi$
$200$	−1.75458e10	−0.775422
$201$	0	0
$202$	−3.96696e10	−1.67640
$203$	2.10835e9	0.0871384
$204$	0	0
$205$	1.08065e10	0.427357
$206$	4.80920e9	0.186067
$207$	0	0
$208$	4.46640e10	1.65452
$209$	2.34513e10	0.850177
$210$	0	0
$211$	2.94765e10	1.02378	0.511888	−	0.859052i	$-0.328946\pi$
$211$	2.94765e10	1.02378	0.511888	+	0.859052i	$0.328946\pi$
$212$	−6.30797e9	−0.214476
$213$	0	0
$214$	−5.29930e10	−1.72726
$215$	−1.97893e9	−0.0631622
$216$	0	0
$217$	2.73978e9	0.0838779
$218$	3.44956e10	1.03445
$219$	0	0
$220$	−1.36860e9	−0.0393891
$221$	−5.73831e9	−0.161815
$222$	0	0
$223$	−3.58102e9	−0.0969694	−0.0484847	−	0.998824i	$-0.515439\pi$
$223$	−3.58102e9	−0.0969694	−0.0484847	+	0.998824i	$0.515439\pi$
$224$	−5.49512e8	−0.0145835
$225$	0	0
$226$	4.73196e10	1.20657
$227$	−2.60470e10	−0.651090	−0.325545	−	0.945527i	$-0.605548\pi$
$227$	−2.60470e10	−0.651090	−0.325545	+	0.945527i	$0.605548\pi$
$228$	0	0
$229$	7.05669e9	0.169567	0.0847836	−	0.996399i	$-0.472980\pi$
$229$	7.05669e9	0.169567	0.0847836	+	0.996399i	$0.472980\pi$
$230$	2.11485e10	0.498315
$231$	0	0
$232$	−5.53516e10	−1.25439
$233$	6.66600e10	1.48171	0.740856	−	0.671664i	$-0.234420\pi$
$233$	6.66600e10	1.48171	0.740856	+	0.671664i	$0.234420\pi$
$234$	0	0
$235$	2.41620e10	0.516805
$236$	−6.27172e9	−0.131608
$237$	0	0
$238$	3.65217e8	0.00737827
$239$	−4.25444e10	−0.843435	−0.421717	−	0.906727i	$-0.638573\pi$
$239$	−4.25444e10	−0.843435	−0.421717	+	0.906727i	$0.638573\pi$
$240$	0	0
$241$	1.80531e10	0.344727	0.172364	−	0.985033i	$-0.444860\pi$
$241$	1.80531e10	0.344727	0.172364	+	0.985033i	$0.444860\pi$
$242$	1.61788e10	0.303234
$243$	0	0
$244$	5.17133e9	0.0934003
$245$	−2.32594e10	−0.412431
$246$	0	0
$247$	8.86209e10	1.51496
$248$	−7.19291e10	−1.20746
$249$	0	0
$250$	4.93386e10	0.798835
$251$	3.95656e10	0.629196	0.314598	−	0.949225i	$-0.398130\pi$
$251$	3.95656e10	0.629196	0.314598	+	0.949225i	$0.398130\pi$
$252$	0	0
$253$	6.27443e10	0.962791
$254$	1.25491e11	1.89173
$255$	0	0
$256$	2.29428e10	0.333862
$257$	−7.15316e10	−1.02282	−0.511410	−	0.859337i	$-0.670876\pi$
$257$	−7.15316e10	−1.02282	−0.511410	+	0.859337i	$0.670876\pi$
$258$	0	0
$259$	−4.86814e9	−0.0672224
$260$	−5.17186e9	−0.0701886
$261$	0	0
$262$	1.01778e10	0.133444
$263$	6.08596e10	0.784384	0.392192	−	0.919883i	$-0.371717\pi$
$263$	6.08596e10	0.784384	0.392192	+	0.919883i	$0.371717\pi$
$264$	0	0
$265$	−6.32983e10	−0.788471
$266$	−5.64032e9	−0.0690774
$267$	0	0
$268$	−1.16803e10	−0.138308
$269$	5.96377e10	0.694441	0.347221	−	0.937783i	$-0.387125\pi$
$269$	5.96377e10	0.694441	0.347221	+	0.937783i	$0.387125\pi$
$270$	0	0
$271$	7.16434e9	0.0806890	0.0403445	−	0.999186i	$-0.487154\pi$
$271$	7.16434e9	0.0806890	0.0403445	+	0.999186i	$0.487154\pi$
$272$	−1.06824e10	−0.118334
$273$	0	0
$274$	5.72776e10	0.613914
$275$	6.63233e10	0.699309
$276$	0	0
$277$	5.21051e10	0.531767	0.265883	−	0.964005i	$-0.414336\pi$
$277$	5.21051e10	0.531767	0.265883	+	0.964005i	$0.414336\pi$
$278$	−1.10308e10	−0.110766
$279$	0	0
$280$	−2.59250e9	−0.0252062
$281$	1.92655e10	0.184333	0.0921663	−	0.995744i	$-0.470621\pi$
$281$	1.92655e10	0.184333	0.0921663	+	0.995744i	$0.470621\pi$
$282$	0	0
$283$	2.24601e10	0.208148	0.104074	−	0.994570i	$-0.466812\pi$
$283$	2.24601e10	0.208148	0.104074	+	0.994570i	$0.466812\pi$
$284$	−1.07591e10	−0.0981392
$285$	0	0
$286$	−1.51538e11	−1.33929
$287$	−7.71106e9	−0.0670881
$288$	0	0
$289$	−1.17215e11	−0.988427
$290$	7.05226e10	0.585514
$291$	0	0
$292$	1.66256e10	0.133830
$293$	−4.53637e10	−0.359587	−0.179794	−	0.983704i	$-0.557543\pi$
$293$	−4.53637e10	−0.359587	−0.179794	+	0.983704i	$0.557543\pi$
$294$	0	0
$295$	−6.29346e10	−0.483827
$296$	1.27806e11	0.967694
$297$	0	0
$298$	3.38291e9	0.0248495
$299$	2.37106e11	1.71563
$300$	0	0
$301$	1.41208e9	0.00991543
$302$	1.77000e11	1.22445
$303$	0	0
$304$	1.64976e11	1.10787
$305$	5.18926e10	0.343365
$306$	0	0
$307$	2.52635e11	1.62320	0.811598	−	0.584216i	$-0.198598\pi$
$307$	2.52635e11	1.62320	0.811598	+	0.584216i	$0.198598\pi$
$308$	9.76582e8	0.00618344
$309$	0	0
$310$	9.16437e10	0.563605
$311$	−1.44034e11	−0.873057	−0.436529	−	0.899690i	$-0.643792\pi$
$311$	−1.44034e11	−0.873057	−0.436529	+	0.899690i	$0.643792\pi$
$312$	0	0
$313$	1.80382e10	0.106229	0.0531147	−	0.998588i	$-0.483085\pi$
$313$	1.80382e10	0.106229	0.0531147	+	0.998588i	$0.483085\pi$
$314$	2.63002e11	1.52678
$315$	0	0
$316$	8.89959e9	0.0502086
$317$	−7.77758e9	−0.0432591	−0.0216296	−	0.999766i	$-0.506885\pi$
$317$	−7.77758e9	−0.0432591	−0.0216296	+	0.999766i	$0.506885\pi$
$318$	0	0
$319$	2.09230e11	1.13127
$320$	6.70762e10	0.357597
$321$	0	0
$322$	−1.50907e10	−0.0782274
$323$	−2.11956e10	−0.108352
$324$	0	0
$325$	2.50631e11	1.24612
$326$	2.69564e11	1.32185
$327$	0	0
$328$	2.02443e11	0.965761
$329$	−1.72410e10	−0.0811300
$330$	0	0
$331$	2.82639e11	1.29421	0.647106	−	0.762400i	$-0.275979\pi$
$331$	2.82639e11	1.29421	0.647106	+	0.762400i	$0.275979\pi$
$332$	−8.31668e9	−0.0375689
$333$	0	0
$334$	4.94616e10	0.217475
$335$	−1.17208e11	−0.508458
$336$	0	0
$337$	1.43617e11	0.606557	0.303279	−	0.952902i	$-0.401919\pi$
$337$	1.43617e11	0.606557	0.303279	+	0.952902i	$0.401919\pi$
$338$	−3.19543e11	−1.33169
$339$	0	0
$340$	1.23696e9	0.00501998
$341$	2.71893e11	1.08894
$342$	0	0
$343$	3.32644e10	0.129765
$344$	−3.70723e10	−0.142737
$345$	0	0
$346$	−3.60014e11	−1.35044
$347$	1.75323e10	0.0649168	0.0324584	−	0.999473i	$-0.489666\pi$
$347$	1.75323e10	0.0649168	0.0324584	+	0.999473i	$0.489666\pi$
$348$	0	0
$349$	6.51688e10	0.235139	0.117570	−	0.993065i	$-0.462490\pi$
$349$	6.51688e10	0.235139	0.117570	+	0.993065i	$0.462490\pi$
$350$	−1.59515e10	−0.0568193
$351$	0	0
$352$	−5.45328e10	−0.189328
$353$	−2.83965e11	−0.973372	−0.486686	−	0.873577i	$-0.661794\pi$
$353$	−2.83965e11	−0.973372	−0.486686	+	0.873577i	$0.661794\pi$
$354$	0	0
$355$	−1.07964e11	−0.360786
$356$	3.17620e10	0.104805
$357$	0	0
$358$	3.76333e11	1.21087
$359$	7.02188e10	0.223115	0.111557	−	0.993758i	$-0.464416\pi$
$359$	7.02188e10	0.223115	0.111557	+	0.993758i	$0.464416\pi$
$360$	0	0
$361$	4.65223e9	0.0144171
$362$	−1.59493e10	−0.0488150
$363$	0	0
$364$	3.69043e9	0.0110185
$365$	1.66832e11	0.491996
$366$	0	0
$367$	−3.53552e11	−1.01732	−0.508658	−	0.860969i	$-0.669858\pi$
$367$	−3.53552e11	−1.01732	−0.508658	+	0.860969i	$0.669858\pi$
$368$	4.41395e11	1.25462
$369$	0	0
$370$	−1.62835e11	−0.451691
$371$	4.51672e10	0.123777
$372$	0	0
$373$	6.13570e11	1.64125	0.820624	−	0.571468i	$-0.193626\pi$
$373$	6.13570e11	1.64125	0.820624	+	0.571468i	$0.193626\pi$
$374$	3.62437e10	0.0957877
$375$	0	0
$376$	4.52638e11	1.16790
$377$	7.90664e11	2.01584
$378$	0	0
$379$	−2.66556e11	−0.663609	−0.331804	−	0.943348i	$-0.607657\pi$
$379$	−2.66556e11	−0.663609	−0.331804	+	0.943348i	$0.607657\pi$
$380$	−1.91033e10	−0.0469984
$381$	0	0
$382$	−8.35774e11	−2.00818
$383$	2.18172e11	0.518090	0.259045	−	0.965865i	$-0.416592\pi$
$383$	2.18172e11	0.518090	0.259045	+	0.965865i	$0.416592\pi$
$384$	0	0
$385$	9.79966e9	0.0227320
$386$	−5.78562e11	−1.32650
$387$	0	0
$388$	−6.66042e10	−0.149197
$389$	−8.62682e10	−0.191019	−0.0955097	−	0.995428i	$-0.530448\pi$
$389$	−8.62682e10	−0.191019	−0.0955097	+	0.995428i	$0.530448\pi$
$390$	0	0
$391$	−5.67092e10	−0.122704
$392$	−4.35730e11	−0.932031
$393$	0	0
$394$	2.49667e11	0.521949
$395$	8.93043e10	0.184580
$396$	0	0
$397$	−9.38797e11	−1.89677	−0.948384	−	0.317124i	$-0.897283\pi$
$397$	−9.38797e11	−1.89677	−0.948384	+	0.317124i	$0.897283\pi$
$398$	3.96854e11	0.792789
$399$	0	0
$400$	4.66572e11	0.911274
$401$	4.13612e11	0.798810	0.399405	−	0.916775i	$-0.369217\pi$
$401$	4.13612e11	0.798810	0.399405	+	0.916775i	$0.369217\pi$
$402$	0	0
$403$	1.02746e12	1.94041
$404$	9.58727e10	0.179052
$405$	0	0
$406$	−5.03221e10	−0.0919161
$407$	−4.83107e11	−0.872708
$408$	0	0
$409$	9.59930e10	0.169623	0.0848115	−	0.996397i	$-0.472971\pi$
$409$	9.59930e10	0.169623	0.0848115	+	0.996397i	$0.472971\pi$
$410$	−2.57929e11	−0.450788
$411$	0	0
$412$	−1.16228e10	−0.0198734
$413$	4.49076e10	0.0759530
$414$	0	0
$415$	−8.34550e10	−0.138113
$416$	−2.06076e11	−0.337370
$417$	0	0
$418$	−5.59738e11	−0.896791
$419$	6.82383e10	0.108160	0.0540798	−	0.998537i	$-0.482777\pi$
$419$	6.82383e10	0.108160	0.0540798	+	0.998537i	$0.482777\pi$
$420$	0	0
$421$	−3.11922e11	−0.483923	−0.241961	−	0.970286i	$-0.577791\pi$
$421$	−3.11922e11	−0.483923	−0.241961	+	0.970286i	$0.577791\pi$
$422$	−7.03546e11	−1.07991
$423$	0	0
$424$	−1.18580e12	−1.78182
$425$	−5.99439e10	−0.0891241
$426$	0	0
$427$	−3.70285e10	−0.0539027
$428$	1.28072e11	0.184484
$429$	0	0
$430$	4.72332e10	0.0666253
$431$	1.57117e11	0.219318	0.109659	−	0.993969i	$-0.465024\pi$
$431$	1.57117e11	0.219318	0.109659	+	0.993969i	$0.465024\pi$
$432$	0	0
$433$	−1.09449e12	−1.49629	−0.748143	−	0.663537i	$-0.769054\pi$
$433$	−1.09449e12	−1.49629	−0.748143	+	0.663537i	$0.769054\pi$
$434$	−6.53933e10	−0.0884768
$435$	0	0
$436$	−8.33681e10	−0.110487
$437$	8.75802e11	1.14879
$438$	0	0
$439$	−7.01115e11	−0.900947	−0.450473	−	0.892790i	$-0.648745\pi$
$439$	−7.01115e11	−0.900947	−0.450473	+	0.892790i	$0.648745\pi$
$440$	−2.57276e11	−0.327237
$441$	0	0
$442$	1.36962e11	0.170687
$443$	−4.23032e11	−0.521863	−0.260932	−	0.965357i	$-0.584030\pi$
$443$	−4.23032e11	−0.521863	−0.260932	+	0.965357i	$0.584030\pi$
$444$	0	0
$445$	3.18721e11	0.385292
$446$	8.54720e10	0.102286
$447$	0	0
$448$	−4.78629e10	−0.0561368
$449$	1.04536e11	0.121383	0.0606916	−	0.998157i	$-0.480669\pi$
$449$	1.04536e11	0.121383	0.0606916	+	0.998157i	$0.480669\pi$
$450$	0	0
$451$	−7.65235e11	−0.870965
$452$	−1.14361e11	−0.128871
$453$	0	0
$454$	6.21690e11	0.686788
$455$	3.70322e10	0.0405069
$456$	0	0
$457$	5.68647e11	0.609845	0.304923	−	0.952377i	$-0.401369\pi$
$457$	5.68647e11	0.609845	0.304923	+	0.952377i	$0.401369\pi$
$458$	−1.68430e11	−0.178864
$459$	0	0
$460$	−5.11112e10	−0.0532238
$461$	1.55226e12	1.60070	0.800349	−	0.599535i	$-0.204648\pi$
$461$	1.55226e12	1.60070	0.800349	+	0.599535i	$0.204648\pi$
$462$	0	0
$463$	1.18555e12	1.19897	0.599483	−	0.800387i	$-0.295373\pi$
$463$	1.18555e12	1.19897	0.599483	+	0.800387i	$0.295373\pi$
$464$	1.47189e12	1.47416
$465$	0	0
$466$	−1.59104e12	−1.56295
$467$	−7.96561e11	−0.774985	−0.387492	−	0.921873i	$-0.626659\pi$
$467$	−7.96561e11	−0.774985	−0.387492	+	0.921873i	$0.626659\pi$
$468$	0	0
$469$	8.36349e10	0.0798196
$470$	−5.76699e11	−0.545141
$471$	0	0
$472$	−1.17898e12	−1.09338
$473$	1.40133e11	0.128726
$474$	0	0
$475$	9.25758e11	0.834404
$476$	−8.82648e8	−0.000788055 0
$477$	0	0
$478$	1.01545e12	0.889679
$479$	1.33615e12	1.15970	0.579848	−	0.814725i	$-0.303112\pi$
$479$	1.33615e12	1.15970	0.579848	+	0.814725i	$0.303112\pi$
$480$	0	0
$481$	−1.82563e12	−1.55510
$482$	−4.30893e11	−0.363628
$483$	0	0
$484$	−3.91006e10	−0.0323877
$485$	−6.68350e11	−0.548487
$486$	0	0
$487$	1.33606e12	1.07633	0.538165	−	0.842839i	$-0.319118\pi$
$487$	1.33606e12	1.07633	0.538165	+	0.842839i	$0.319118\pi$
$488$	9.72129e11	0.775952
$489$	0	0
$490$	5.55157e11	0.435044
$491$	−1.45714e12	−1.13145	−0.565725	−	0.824594i	$-0.691404\pi$
$491$	−1.45714e12	−1.13145	−0.565725	+	0.824594i	$0.691404\pi$
$492$	0	0
$493$	−1.89105e11	−0.144175
$494$	−2.11521e12	−1.59802
$495$	0	0
$496$	1.91272e12	1.41900
$497$	7.70386e10	0.0566376
$498$	0	0
$499$	−9.98947e11	−0.721257	−0.360628	−	0.932710i	$-0.617438\pi$
$499$	−9.98947e11	−0.721257	−0.360628	+	0.932710i	$0.617438\pi$
$500$	−1.19241e11	−0.0853216
$501$	0	0
$502$	−9.44354e11	−0.663694
$503$	−2.25381e12	−1.56986	−0.784930	−	0.619584i	$-0.787301\pi$
$503$	−2.25381e12	−1.56986	−0.784930	+	0.619584i	$0.787301\pi$
$504$	0	0
$505$	9.62049e11	0.658243
$506$	−1.49758e12	−1.01558
$507$	0	0
$508$	−3.03283e11	−0.202051
$509$	−2.45200e12	−1.61916	−0.809581	−	0.587008i	$-0.800306\pi$
$509$	−2.45200e12	−1.61916	−0.809581	+	0.587008i	$0.800306\pi$
$510$	0	0
$511$	−1.19045e11	−0.0772353
$512$	1.21728e12	0.782844
$513$	0	0
$514$	1.70732e12	1.07890
$515$	−1.16630e11	−0.0730600
$516$	0	0
$517$	−1.71098e12	−1.05326
$518$	1.16193e11	0.0709081
$519$	0	0
$520$	−9.72228e11	−0.583113
$521$	−2.99007e12	−1.77791	−0.888957	−	0.457990i	$-0.848570\pi$
$521$	−2.99007e12	−1.77791	−0.888957	+	0.457990i	$0.848570\pi$
$522$	0	0
$523$	1.07354e12	0.627425	0.313713	−	0.949518i	$-0.398427\pi$
$523$	1.07354e12	0.627425	0.313713	+	0.949518i	$0.398427\pi$
$524$	−2.45975e10	−0.0142528
$525$	0	0
$526$	−1.45260e12	−0.827390
$527$	−2.45740e11	−0.138781
$528$	0	0
$529$	5.42065e11	0.300954
$530$	1.51081e12	0.831702
$531$	0	0
$532$	1.36314e10	0.00737799
$533$	−2.89177e12	−1.55200
$534$	0	0
$535$	1.28516e12	0.678213
$536$	−2.19571e12	−1.14904
$537$	0	0
$538$	−1.42344e12	−0.732517
$539$	1.64706e12	0.840545
$540$	0	0
$541$	−2.99583e12	−1.50359	−0.751796	−	0.659395i	$-0.770812\pi$
$541$	−2.99583e12	−1.50359	−0.751796	+	0.659395i	$0.770812\pi$
$542$	−1.70999e11	−0.0851131
$543$	0	0
$544$	4.92875e10	0.0241291
$545$	−8.36570e11	−0.406180
$546$	0	0
$547$	−2.38362e11	−0.113840	−0.0569199	−	0.998379i	$-0.518128\pi$
$547$	−2.38362e11	−0.113840	−0.0569199	+	0.998379i	$0.518128\pi$
$548$	−1.38427e11	−0.0655706
$549$	0	0
$550$	−1.58301e12	−0.737651
$551$	2.92048e12	1.34981
$552$	0	0
$553$	−6.37240e10	−0.0289761
$554$	−1.24365e12	−0.560923
$555$	0	0
$556$	2.66591e10	0.0118307
$557$	3.97940e12	1.75174	0.875870	−	0.482548i	$-0.160289\pi$
$557$	3.97940e12	1.75174	0.875870	+	0.482548i	$0.160289\pi$
$558$	0	0
$559$	5.29554e11	0.229381
$560$	6.89389e10	0.0296222
$561$	0	0
$562$	−4.59830e11	−0.194439
$563$	−9.04378e11	−0.379369	−0.189685	−	0.981845i	$-0.560747\pi$
$563$	−9.04378e11	−0.379369	−0.189685	+	0.981845i	$0.560747\pi$
$564$	0	0
$565$	−1.14757e12	−0.473764
$566$	−5.36078e11	−0.219560
$567$	0	0
$568$	−2.02254e12	−0.815322
$569$	1.36290e12	0.545079	0.272539	−	0.962145i	$-0.412136\pi$
$569$	1.36290e12	0.545079	0.272539	+	0.962145i	$0.412136\pi$
$570$	0	0
$571$	2.48489e12	0.978240	0.489120	−	0.872217i	$-0.337318\pi$
$571$	2.48489e12	0.978240	0.489120	+	0.872217i	$0.337318\pi$
$572$	3.66234e11	0.143046
$573$	0	0
$574$	1.84048e11	0.0707664
$575$	2.47688e12	0.944929
$576$	0	0
$577$	−1.75235e12	−0.658156	−0.329078	−	0.944303i	$-0.606738\pi$
$577$	−1.75235e12	−0.658156	−0.329078	+	0.944303i	$0.606738\pi$
$578$	2.79770e12	1.04262
$579$	0	0
$580$	−1.70437e11	−0.0625373
$581$	5.95502e10	0.0216816
$582$	0	0
$583$	4.48233e12	1.60693
$584$	3.12535e12	1.11184
$585$	0	0
$586$	1.08274e12	0.379303
$587$	−2.44179e12	−0.848862	−0.424431	−	0.905460i	$-0.639526\pi$
$587$	−2.44179e12	−0.848862	−0.424431	+	0.905460i	$0.639526\pi$
$588$	0	0
$589$	3.79515e12	1.29930
$590$	1.50213e12	0.510355
$591$	0	0
$592$	−3.39857e12	−1.13723
$593$	−4.50598e12	−1.49638	−0.748192	−	0.663482i	$-0.769078\pi$
$593$	−4.50598e12	−1.49638	−0.748192	+	0.663482i	$0.769078\pi$
$594$	0	0
$595$	−8.85707e9	−0.00289710
$596$	−8.17574e9	−0.00265411
$597$	0	0
$598$	−5.65926e12	−1.80969
$599$	7.19552e11	0.228371	0.114186	−	0.993459i	$-0.463574\pi$
$599$	7.19552e11	0.228371	0.114186	+	0.993459i	$0.463574\pi$
$600$	0	0
$601$	2.18823e12	0.684160	0.342080	−	0.939671i	$-0.388869\pi$
$601$	2.18823e12	0.684160	0.342080	+	0.939671i	$0.388869\pi$
$602$	−3.37037e10	−0.0104591
$603$	0	0
$604$	−4.27769e11	−0.130781
$605$	−3.92361e11	−0.119066
$606$	0	0
$607$	−4.88532e12	−1.46064	−0.730321	−	0.683104i	$-0.760630\pi$
$607$	−4.88532e12	−1.46064	−0.730321	+	0.683104i	$0.760630\pi$
$608$	−7.61184e11	−0.225904
$609$	0	0
$610$	−1.23857e12	−0.362191
$611$	−6.46566e12	−1.87684
$612$	0	0
$613$	6.65380e11	0.190326	0.0951629	−	0.995462i	$-0.469663\pi$
$613$	6.65380e11	0.190326	0.0951629	+	0.995462i	$0.469663\pi$
$614$	−6.02991e12	−1.71219
$615$	0	0
$616$	1.83582e11	0.0513709
$617$	5.62159e12	1.56162	0.780812	−	0.624767i	$-0.214806\pi$
$617$	5.62159e12	1.56162	0.780812	+	0.624767i	$0.214806\pi$
$618$	0	0
$619$	4.24453e12	1.16204	0.581020	−	0.813889i	$-0.302654\pi$
$619$	4.24453e12	1.16204	0.581020	+	0.813889i	$0.302654\pi$
$620$	−2.21482e11	−0.0601973
$621$	0	0
$622$	3.43781e12	0.920926
$623$	−2.27426e11	−0.0604846
$624$	0	0
$625$	1.96376e12	0.514788
$626$	−4.30538e11	−0.112054
$627$	0	0
$628$	−6.35618e11	−0.163071
$629$	4.36639e11	0.111223
$630$	0	0
$631$	4.66852e12	1.17232	0.586161	−	0.810194i	$-0.300638\pi$
$631$	4.66852e12	1.17232	0.586161	+	0.810194i	$0.300638\pi$
$632$	1.67298e12	0.417123
$633$	0	0
$634$	1.85636e11	0.0456310
$635$	−3.04334e12	−0.742795
$636$	0	0
$637$	6.22414e12	1.49779
$638$	−4.99390e12	−1.19329
$639$	0	0
$640$	−1.99527e12	−0.470101
$641$	3.61791e12	0.846440	0.423220	−	0.906027i	$-0.360900\pi$
$641$	3.61791e12	0.846440	0.423220	+	0.906027i	$0.360900\pi$
$642$	0	0
$643$	−8.06383e12	−1.86034	−0.930169	−	0.367132i	$-0.880340\pi$
$643$	−8.06383e12	−1.86034	−0.930169	+	0.367132i	$0.880340\pi$
$644$	3.64709e10	0.00835527
$645$	0	0
$646$	5.05899e11	0.114292
$647$	−5.05529e12	−1.13417	−0.567083	−	0.823661i	$-0.691928\pi$
$647$	−5.05529e12	−1.13417	−0.567083	+	0.823661i	$0.691928\pi$
$648$	0	0
$649$	4.45657e12	0.986052
$650$	−5.98207e12	−1.31444
$651$	0	0
$652$	−6.51476e11	−0.141184
$653$	1.57457e11	0.0338886	0.0169443	−	0.999856i	$-0.494606\pi$
$653$	1.57457e11	0.0338886	0.0169443	+	0.999856i	$0.494606\pi$
$654$	0	0
$655$	−2.46827e11	−0.0523971
$656$	−5.38329e12	−1.13496
$657$	0	0
$658$	4.11509e11	0.0855782
$659$	−6.64168e11	−0.137181	−0.0685904	−	0.997645i	$-0.521850\pi$
$659$	−6.64168e11	−0.137181	−0.0685904	+	0.997645i	$0.521850\pi$
$660$	0	0
$661$	6.99786e12	1.42580	0.712900	−	0.701265i	$-0.247381\pi$
$661$	6.99786e12	1.42580	0.712900	+	0.701265i	$0.247381\pi$
$662$	−6.74603e12	−1.36517
$663$	0	0
$664$	−1.56341e12	−0.312115
$665$	1.36786e11	0.0271235
$666$	0	0
$667$	7.81378e12	1.52860
$668$	−1.19538e11	−0.0232280
$669$	0	0
$670$	2.79752e12	0.536336
$671$	−3.67466e12	−0.699787
$672$	0	0
$673$	−9.28905e12	−1.74543	−0.872717	−	0.488226i	$-0.837644\pi$
$673$	−9.28905e12	−1.74543	−0.872717	+	0.488226i	$0.837644\pi$
$674$	−3.42786e12	−0.639814
$675$	0	0
$676$	7.72264e11	0.142235
$677$	7.12215e12	1.30305	0.651526	−	0.758626i	$-0.274129\pi$
$677$	7.12215e12	1.30305	0.651526	+	0.758626i	$0.274129\pi$
$678$	0	0
$679$	4.76908e11	0.0861035
$680$	2.32530e11	0.0417050
$681$	0	0
$682$	−6.48955e12	−1.14864
$683$	8.49722e12	1.49411	0.747057	−	0.664760i	$-0.231466\pi$
$683$	8.49722e12	1.49411	0.747057	+	0.664760i	$0.231466\pi$
$684$	0	0
$685$	−1.38907e12	−0.241055
$686$	−7.93958e11	−0.136880
$687$	0	0
$688$	9.85814e11	0.167744
$689$	1.69384e13	2.86343
$690$	0	0
$691$	−1.99151e12	−0.332300	−0.166150	−	0.986100i	$-0.553134\pi$
$691$	−1.99151e12	−0.332300	−0.166150	+	0.986100i	$0.553134\pi$
$692$	8.70073e11	0.144238
$693$	0	0
$694$	−4.18462e11	−0.0684761
$695$	2.67515e11	0.0434927
$696$	0	0
$697$	6.91630e11	0.111001
$698$	−1.55545e12	−0.248032
$699$	0	0
$700$	3.85513e10	0.00606873
$701$	−5.43004e12	−0.849321	−0.424661	−	0.905353i	$-0.639607\pi$
$701$	−5.43004e12	−0.849321	−0.424661	+	0.905353i	$0.639607\pi$
$702$	0	0
$703$	−6.74334e12	−1.04130
$704$	−4.74985e12	−0.728791
$705$	0	0
$706$	6.77769e12	1.02674
$707$	−6.86480e11	−0.103333
$708$	0	0
$709$	1.00333e13	1.49120	0.745599	−	0.666395i	$-0.232163\pi$
$709$	1.00333e13	1.49120	0.745599	+	0.666395i	$0.232163\pi$
$710$	2.57688e12	0.380568
$711$	0	0
$712$	5.97075e12	0.870701
$713$	1.01540e13	1.47141
$714$	0	0
$715$	3.67503e12	0.525877
$716$	−9.09514e11	−0.129330
$717$	0	0
$718$	−1.67599e12	−0.235348
$719$	6.12483e12	0.854701	0.427351	−	0.904086i	$-0.359447\pi$
$719$	6.12483e12	0.854701	0.427351	+	0.904086i	$0.359447\pi$
$720$	0	0
$721$	8.32229e10	0.0114692
$722$	−1.11040e11	−0.0152076
$723$	0	0
$724$	3.85460e10	0.00521381
$725$	8.25949e12	1.11028
$726$	0	0
$727$	−9.66565e12	−1.28329	−0.641647	−	0.767000i	$-0.721749\pi$
$727$	−9.66565e12	−1.28329	−0.641647	+	0.767000i	$0.721749\pi$
$728$	6.93743e11	0.0915393
$729$	0	0
$730$	−3.98195e12	−0.518971
$731$	−1.26655e11	−0.0164056
$732$	0	0
$733$	−6.58742e12	−0.842845	−0.421423	−	0.906864i	$-0.638469\pi$
$733$	−6.58742e12	−0.842845	−0.421423	+	0.906864i	$0.638469\pi$
$734$	8.43859e12	1.07309
$735$	0	0
$736$	−2.03656e12	−0.255827
$737$	8.29982e12	1.03625
$738$	0	0
$739$	−1.58773e13	−1.95829	−0.979147	−	0.203152i	$-0.934882\pi$
$739$	−1.58773e13	−1.95829	−0.979147	+	0.203152i	$0.934882\pi$
$740$	3.93537e11	0.0482440
$741$	0	0
$742$	−1.07805e12	−0.130564
$743$	−9.03557e12	−1.08769	−0.543846	−	0.839185i	$-0.683032\pi$
$743$	−9.03557e12	−1.08769	−0.543846	+	0.839185i	$0.683032\pi$
$744$	0	0
$745$	−8.20407e10	−0.00975722
$746$	−1.46447e13	−1.73124
$747$	0	0
$748$	−8.75929e10	−0.0102308
$749$	−9.17041e11	−0.106468
$750$	0	0
$751$	1.57604e13	1.80795	0.903976	−	0.427583i	$-0.140635\pi$
$751$	1.57604e13	1.80795	0.903976	+	0.427583i	$0.140635\pi$
$752$	−1.20364e13	−1.37251
$753$	0	0
$754$	−1.88716e13	−2.12636
$755$	−4.29252e12	−0.480785
$756$	0	0
$757$	−1.06961e12	−0.118384	−0.0591919	−	0.998247i	$-0.518852\pi$
$757$	−1.06961e12	−0.118384	−0.0591919	+	0.998247i	$0.518852\pi$
$758$	6.36217e12	0.699994
$759$	0	0
$760$	−3.59113e12	−0.390454
$761$	−3.35960e12	−0.363125	−0.181562	−	0.983379i	$-0.558115\pi$
$761$	−3.35960e12	−0.363125	−0.181562	+	0.983379i	$0.558115\pi$
$762$	0	0
$763$	5.96944e11	0.0637636
$764$	2.01988e12	0.214489
$765$	0	0
$766$	−5.20734e12	−0.546496
$767$	1.68411e13	1.75708
$768$	0	0
$769$	−8.70807e12	−0.897952	−0.448976	−	0.893544i	$-0.648211\pi$
$769$	−8.70807e12	−0.897952	−0.448976	+	0.893544i	$0.648211\pi$
$770$	−2.33899e11	−0.0239784
$771$	0	0
$772$	1.39826e12	0.141680
$773$	5.58286e12	0.562405	0.281202	−	0.959649i	$-0.409267\pi$
$773$	5.58286e12	0.562405	0.281202	+	0.959649i	$0.409267\pi$
$774$	0	0
$775$	1.07332e13	1.06873
$776$	−1.25205e13	−1.23950
$777$	0	0
$778$	2.05905e12	0.201493
$779$	−1.06814e13	−1.03922
$780$	0	0
$781$	7.64521e12	0.735292
$782$	1.35354e12	0.129431
$783$	0	0
$784$	1.15868e13	1.09532
$785$	−6.37820e12	−0.599494
$786$	0	0
$787$	1.08054e13	1.00405	0.502025	−	0.864853i	$-0.332588\pi$
$787$	1.08054e13	1.00405	0.502025	+	0.864853i	$0.332588\pi$
$788$	−6.03390e11	−0.0557481
$789$	0	0
$790$	−2.13152e12	−0.194701
$791$	8.18862e11	0.0743732
$792$	0	0
$793$	−1.38863e13	−1.24697
$794$	2.24072e13	2.00077
$795$	0	0
$796$	−9.59109e11	−0.0846758
$797$	1.72340e13	1.51294	0.756472	−	0.654026i	$-0.226921\pi$
$797$	1.72340e13	1.51294	0.756472	+	0.654026i	$0.226921\pi$
$798$	0	0
$799$	1.54640e12	0.134234
$800$	−2.15272e12	−0.185816
$801$	0	0
$802$	−9.87211e12	−0.842608
$803$	−1.18138e13	−1.00270
$804$	0	0
$805$	3.65973e11	0.0307162
$806$	−2.45235e13	−2.04680
$807$	0	0
$808$	1.80226e13	1.48753
$809$	−8.74791e12	−0.718019	−0.359009	−	0.933334i	$-0.616885\pi$
$809$	−8.74791e12	−0.718019	−0.359009	+	0.933334i	$0.616885\pi$
$810$	0	0
$811$	−1.63936e13	−1.33070	−0.665349	−	0.746532i	$-0.731717\pi$
$811$	−1.63936e13	−1.33070	−0.665349	+	0.746532i	$0.731717\pi$
$812$	1.21617e11	0.00981733
$813$	0	0
$814$	1.15308e13	0.920557
$815$	−6.53734e12	−0.519029
$816$	0	0
$817$	1.95602e12	0.153594
$818$	−2.29117e12	−0.178923
$819$	0	0
$820$	6.23357e11	0.0481476
$821$	6.80456e12	0.522704	0.261352	−	0.965244i	$-0.415832\pi$
$821$	6.80456e12	0.522704	0.261352	+	0.965244i	$0.415832\pi$
$822$	0	0
$823$	−1.21597e13	−0.923900	−0.461950	−	0.886906i	$-0.652850\pi$
$823$	−1.21597e13	−0.923900	−0.461950	+	0.886906i	$0.652850\pi$
$824$	−2.18490e12	−0.165104
$825$	0	0
$826$	−1.07186e12	−0.0801174
$827$	6.47949e10	0.00481688	0.00240844	−	0.999997i	$-0.499233\pi$
$827$	6.47949e10	0.00481688	0.00240844	+	0.999997i	$0.499233\pi$
$828$	0	0
$829$	−1.16602e13	−0.857452	−0.428726	−	0.903434i	$-0.641037\pi$
$829$	−1.16602e13	−0.857452	−0.428726	+	0.903434i	$0.641037\pi$
$830$	1.99191e12	0.145686
$831$	0	0
$832$	−1.79494e13	−1.29865
$833$	−1.48864e12	−0.107124
$834$	0	0
$835$	−1.19952e12	−0.0853923
$836$	1.35276e12	0.0957840
$837$	0	0
$838$	−1.62872e12	−0.114090
$839$	3.85423e12	0.268540	0.134270	−	0.990945i	$-0.457131\pi$
$839$	3.85423e12	0.268540	0.134270	+	0.990945i	$0.457131\pi$
$840$	0	0
$841$	1.15490e13	0.796089
$842$	7.44496e12	0.510456
$843$	0	0
$844$	1.70032e12	0.115342
$845$	7.74941e12	0.522893
$846$	0	0
$847$	2.79973e11	0.0186914
$848$	3.15324e13	2.09400
$849$	0	0
$850$	1.43074e12	0.0940106
$851$	−1.80419e13	−1.17923
$852$	0	0
$853$	1.14995e13	0.743717	0.371858	−	0.928289i	$-0.378721\pi$
$853$	1.14995e13	0.743717	0.371858	+	0.928289i	$0.378721\pi$
$854$	8.83798e11	0.0568581
$855$	0	0
$856$	2.40756e13	1.53266
$857$	−4.75467e12	−0.301097	−0.150549	−	0.988603i	$-0.548104\pi$
$857$	−4.75467e12	−0.301097	−0.150549	+	0.988603i	$0.548104\pi$
$858$	0	0
$859$	2.09739e13	1.31434	0.657172	−	0.753741i	$-0.271753\pi$
$859$	2.09739e13	1.31434	0.657172	+	0.753741i	$0.271753\pi$
$860$	−1.14152e11	−0.00711608
$861$	0	0
$862$	−3.75007e12	−0.231343
$863$	7.42352e12	0.455576	0.227788	−	0.973711i	$-0.426851\pi$
$863$	7.42352e12	0.455576	0.227788	+	0.973711i	$0.426851\pi$
$864$	0	0
$865$	8.73089e12	0.530256
$866$	2.61232e13	1.57833
$867$	0	0
$868$	1.58041e11	0.00944999
$869$	−6.32389e12	−0.376180
$870$	0	0
$871$	3.13644e13	1.84653
$872$	−1.56719e13	−0.917904
$873$	0	0
$874$	−2.09037e13	−1.21177
$875$	8.53802e11	0.0492403
$876$	0	0
$877$	8.71674e12	0.497572	0.248786	−	0.968558i	$-0.419968\pi$
$877$	8.71674e12	0.497572	0.248786	+	0.968558i	$0.419968\pi$
$878$	1.67343e13	0.950345
$879$	0	0
$880$	6.84140e12	0.384568
$881$	−7.91000e12	−0.442369	−0.221185	−	0.975232i	$-0.570992\pi$
$881$	−7.91000e12	−0.442369	−0.221185	+	0.975232i	$0.570992\pi$
$882$	0	0
$883$	−1.42391e12	−0.0788244	−0.0394122	−	0.999223i	$-0.512549\pi$
$883$	−1.42391e12	−0.0788244	−0.0394122	+	0.999223i	$0.512549\pi$
$884$	−3.31007e11	−0.0182307
$885$	0	0
$886$	1.00970e13	0.550476
$887$	−2.10969e13	−1.14436	−0.572179	−	0.820129i	$-0.693902\pi$
$887$	−2.10969e13	−1.14436	−0.572179	+	0.820129i	$0.693902\pi$
$888$	0	0
$889$	2.17161e12	0.116607
$890$	−7.60724e12	−0.406417
$891$	0	0
$892$	−2.06567e11	−0.0109249
$893$	−2.38823e13	−1.25674
$894$	0	0
$895$	−9.12666e12	−0.475454
$896$	1.42374e12	0.0737982
$897$	0	0
$898$	−2.49508e12	−0.128038
$899$	3.38598e13	1.72888
$900$	0	0
$901$	−4.05120e12	−0.204796
$902$	1.82647e13	0.918718
$903$	0	0
$904$	−2.14980e13	−1.07063
$905$	3.86795e11	0.0191674
$906$	0	0
$907$	−7.10519e12	−0.348613	−0.174306	−	0.984691i	$-0.555768\pi$
$907$	−7.10519e12	−0.348613	−0.174306	+	0.984691i	$0.555768\pi$
$908$	−1.50249e12	−0.0733541
$909$	0	0
$910$	−8.83887e11	−0.0427278
$911$	2.23287e13	1.07407	0.537034	−	0.843561i	$-0.319545\pi$
$911$	2.23287e13	1.07407	0.537034	+	0.843561i	$0.319545\pi$
$912$	0	0
$913$	5.90969e12	0.281479
$914$	−1.35725e13	−0.643283
$915$	0	0
$916$	4.07057e11	0.0191040
$917$	1.76126e11	0.00822550
$918$	0	0
$919$	−2.55522e13	−1.18170	−0.590852	−	0.806780i	$-0.701208\pi$
$919$	−2.55522e13	−1.18170	−0.590852	+	0.806780i	$0.701208\pi$
$920$	−9.60810e12	−0.442173
$921$	0	0
$922$	−3.70493e13	−1.68846
$923$	2.88907e13	1.31024
$924$	0	0
$925$	−1.90710e13	−0.856517
$926$	−2.82969e13	−1.26470
$927$	0	0
$928$	−6.79117e12	−0.300593
$929$	−4.00707e13	−1.76505	−0.882523	−	0.470270i	$-0.844157\pi$
$929$	−4.00707e13	−1.76505	−0.882523	+	0.470270i	$0.844157\pi$
$930$	0	0
$931$	2.29902e13	1.00292
$932$	3.84520e12	0.166935
$933$	0	0
$934$	1.90124e13	0.817476
$935$	−8.78964e11	−0.0376114
$936$	0	0
$937$	5.88813e12	0.249545	0.124773	−	0.992185i	$-0.460180\pi$
$937$	5.88813e12	0.249545	0.124773	+	0.992185i	$0.460180\pi$
$938$	−1.99620e12	−0.0841961
$939$	0	0
$940$	1.39375e12	0.0582251
$941$	1.42277e13	0.591537	0.295768	−	0.955260i	$-0.404424\pi$
$941$	1.42277e13	0.591537	0.295768	+	0.955260i	$0.404424\pi$
$942$	0	0
$943$	−2.85781e13	−1.17688
$944$	3.13512e13	1.28493
$945$	0	0
$946$	−3.34471e12	−0.135784
$947$	8.76631e12	0.354195	0.177097	−	0.984193i	$-0.443329\pi$
$947$	8.76631e12	0.354195	0.177097	+	0.984193i	$0.443329\pi$
$948$	0	0
$949$	−4.46437e13	−1.78674
$950$	−2.20960e13	−0.880153
$951$	0	0
$952$	−1.65924e11	−0.00654701
$953$	4.63164e13	1.81893	0.909467	−	0.415775i	$-0.136490\pi$
$953$	4.63164e13	1.81893	0.909467	+	0.415775i	$0.136490\pi$
$954$	0	0
$955$	2.02688e13	0.788520
$956$	−2.45412e12	−0.0950244
$957$	0	0
$958$	−3.18912e13	−1.22328
$959$	9.91185e11	0.0378417
$960$	0	0
$961$	1.75610e13	0.664193
$962$	4.35742e13	1.64037
$963$	0	0
$964$	1.04137e12	0.0388382
$965$	1.40310e13	0.520854
$966$	0	0
$967$	−2.72329e12	−0.100155	−0.0500777	−	0.998745i	$-0.515947\pi$
$967$	−2.72329e12	−0.100155	−0.0500777	+	0.998745i	$0.515947\pi$
$968$	−7.35030e12	−0.269070
$969$	0	0
$970$	1.59522e13	0.578560
$971$	4.44982e13	1.60641	0.803203	−	0.595705i	$-0.203127\pi$
$971$	4.44982e13	1.60641	0.803203	+	0.595705i	$0.203127\pi$
$972$	0	0
$973$	−1.90888e11	−0.00682765
$974$	−3.18891e13	−1.13534
$975$	0	0
$976$	−2.58506e13	−0.911897
$977$	8.92268e12	0.313307	0.156653	−	0.987654i	$-0.449929\pi$
$977$	8.92268e12	0.313307	0.156653	+	0.987654i	$0.449929\pi$
$978$	0	0
$979$	−2.25695e13	−0.785235
$980$	−1.34169e12	−0.0464660
$981$	0	0
$982$	3.47792e13	1.19349
$983$	2.04743e13	0.699389	0.349694	−	0.936864i	$-0.386285\pi$
$983$	2.04743e13	0.699389	0.349694	+	0.936864i	$0.386285\pi$
$984$	0	0
$985$	−6.05481e12	−0.204945
$986$	4.51356e12	0.152080
$987$	0	0
$988$	5.11199e12	0.170680
$989$	5.23335e12	0.173939
$990$	0	0
$991$	4.30681e13	1.41848	0.709241	−	0.704966i	$-0.249038\pi$
$991$	4.30681e13	1.41848	0.709241	+	0.704966i	$0.249038\pi$
$992$	−8.82509e12	−0.289346
$993$	0	0
$994$	−1.83876e12	−0.0597429
$995$	−9.62433e12	−0.311291
$996$	0	0
$997$	1.53746e13	0.492806	0.246403	−	0.969167i	$-0.420751\pi$
$997$	1.53746e13	0.492806	0.246403	+	0.969167i	$0.420751\pi$
$998$	2.38429e13	0.760802
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.10.a.c.1.4		15
3.2	odd	2		43.10.a.a.1.12	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.12	✓	15	3.2	odd	2
387.10.a.c.1.4		15	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	387.a (trivial)

\(f(q)\)	\(=\)	\(q-23.8680 q^{2} +57.6838 q^{4} +578.837 q^{5} -413.035 q^{7} +10843.6 q^{8} +O(q^{10})\)	\(q-23.8680 q^{2} +57.6838 q^{4} +578.837 q^{5} -413.035 q^{7} +10843.6 q^{8} -13815.7 q^{10} -40989.1 q^{11} -154895. q^{13} +9858.34 q^{14} -288351. q^{16} +37046.5 q^{17} -572136. q^{19} +33389.5 q^{20} +978329. q^{22} -1.53076e6 q^{23} -1.61807e6 q^{25} +3.69704e6 q^{26} -23825.4 q^{28} -5.10452e6 q^{29} -6.63330e6 q^{31} +1.33042e6 q^{32} -884227. q^{34} -239080. q^{35} +1.17863e7 q^{37} +1.36558e7 q^{38} +6.27670e6 q^{40} +1.86693e7 q^{41} -3.41880e6 q^{43} -2.36440e6 q^{44} +3.65362e7 q^{46} +4.17423e7 q^{47} -4.01830e7 q^{49} +3.86202e7 q^{50} -8.93492e6 q^{52} -1.09354e8 q^{53} -2.37260e7 q^{55} -4.47880e6 q^{56} +1.21835e8 q^{58} -1.08726e8 q^{59} +8.96497e7 q^{61} +1.58324e8 q^{62} +1.15881e8 q^{64} -8.96588e7 q^{65} -2.02489e8 q^{67} +2.13698e6 q^{68} +5.70637e6 q^{70} -1.86518e8 q^{71} +2.88219e8 q^{73} -2.81315e8 q^{74} -3.30030e7 q^{76} +1.69299e7 q^{77} +1.54282e8 q^{79} -1.66908e8 q^{80} -4.45599e8 q^{82} -1.44177e8 q^{83} +2.14439e7 q^{85} +8.16001e7 q^{86} -4.44471e8 q^{88} +5.50623e8 q^{89} +6.39770e7 q^{91} -8.82999e7 q^{92} -9.96306e8 q^{94} -3.31174e8 q^{95} -1.15464e9 q^{97} +9.59090e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) \) 15 * q + 32 * q^2 + 3242 * q^4 + 4717 * q^5 - 9680 * q^7 + 20394 * q^8	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8} - 36237 q^{10} + 104484 q^{11} - 116174 q^{13} - 416064 q^{14} + 996762 q^{16} + 884265 q^{17} - 689535 q^{19} + 3077879 q^{20} - 7276218 q^{22} + 2504077 q^{23} + 1315350 q^{25} + 13343414 q^{26} - 28059568 q^{28} + 18406221 q^{29} - 12033699 q^{31} + 18952630 q^{32} - 30383125 q^{34} + 27855546 q^{35} - 8722847 q^{37} + 63941843 q^{38} - 39665611 q^{40} + 18689389 q^{41} - 51282015 q^{43} + 68723220 q^{44} - 2067521 q^{46} + 104960741 q^{47} + 92663095 q^{49} + 42446347 q^{50} + 149226080 q^{52} + 215907800 q^{53} + 384379852 q^{55} - 430441344 q^{56} + 295963139 q^{58} - 185924544 q^{59} + 247538102 q^{61} - 139798853 q^{62} + 848556290 q^{64} - 94294394 q^{65} + 467904656 q^{67} + 88234341 q^{68} + 647526126 q^{70} + 8252944 q^{71} - 715627902 q^{73} - 725122989 q^{74} + 346300359 q^{76} + 1236779964 q^{77} + 560681783 q^{79} + 1157214179 q^{80} + 941346367 q^{82} + 1442854698 q^{83} + 699302088 q^{85} - 109401632 q^{86} - 1464507256 q^{88} + 396710008 q^{89} - 3278076852 q^{91} - 155864647 q^{92} + 4666638949 q^{94} + 3854114395 q^{95} - 3063837815 q^{97} + 6161086984 q^{98}+O(q^{100}) \) 15 * q + 32 * q^2 + 3242 * q^4 + 4717 * q^5 - 9680 * q^7 + 20394 * q^8 - 36237 * q^10 + 104484 * q^11 - 116174 * q^13 - 416064 * q^14 + 996762 * q^16 + 884265 * q^17 - 689535 * q^19 + 3077879 * q^20 - 7276218 * q^22 + 2504077 * q^23 + 1315350 * q^25 + 13343414 * q^26 - 28059568 * q^28 + 18406221 * q^29 - 12033699 * q^31 + 18952630 * q^32 - 30383125 * q^34 + 27855546 * q^35 - 8722847 * q^37 + 63941843 * q^38 - 39665611 * q^40 + 18689389 * q^41 - 51282015 * q^43 + 68723220 * q^44 - 2067521 * q^46 + 104960741 * q^47 + 92663095 * q^49 + 42446347 * q^50 + 149226080 * q^52 + 215907800 * q^53 + 384379852 * q^55 - 430441344 * q^56 + 295963139 * q^58 - 185924544 * q^59 + 247538102 * q^61 - 139798853 * q^62 + 848556290 * q^64 - 94294394 * q^65 + 467904656 * q^67 + 88234341 * q^68 + 647526126 * q^70 + 8252944 * q^71 - 715627902 * q^73 - 725122989 * q^74 + 346300359 * q^76 + 1236779964 * q^77 + 560681783 * q^79 + 1157214179 * q^80 + 941346367 * q^82 + 1442854698 * q^83 + 699302088 * q^85 - 109401632 * q^86 - 1464507256 * q^88 + 396710008 * q^89 - 3278076852 * q^91 - 155864647 * q^92 + 4666638949 * q^94 + 3854114395 * q^95 - 3063837815 * q^97 + 6161086984 * q^98

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