LMFDB - Embedded newform 387.10.a.c.1.10

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			1.10
Root			$15.9205$ 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)

$f(q)$	$=$	$q+17.9205 q^{2} -190.855 q^{4} -238.484 q^{5} -4524.82 q^{7} -12595.5 q^{8} +O(q^{10})$	\(q+17.9205 q^{2} -190.855 q^{4} -238.484 q^{5} -4524.82 q^{7} -12595.5 q^{8} -4273.75 q^{10} -66772.1 q^{11} +45566.0 q^{13} -81087.1 q^{14} -128001. q^{16} -494574. q^{17} -1.08372e6 q^{19} +45515.8 q^{20} -1.19659e6 q^{22} -1.35193e6 q^{23} -1.89625e6 q^{25} +816566. q^{26} +863584. q^{28} +4.85463e6 q^{29} +5.69784e6 q^{31} +4.15507e6 q^{32} -8.86302e6 q^{34} +1.07910e6 q^{35} -1.59658e7 q^{37} -1.94208e7 q^{38} +3.00383e6 q^{40} -1.10007e7 q^{41} -3.41880e6 q^{43} +1.27438e7 q^{44} -2.42274e7 q^{46} -2.98409e7 q^{47} -1.98796e7 q^{49} -3.39818e7 q^{50} -8.69648e6 q^{52} -7.43943e6 q^{53} +1.59241e7 q^{55} +5.69925e7 q^{56} +8.69975e7 q^{58} -1.08119e8 q^{59} +1.99515e8 q^{61} +1.02108e8 q^{62} +1.39997e8 q^{64} -1.08667e7 q^{65} -2.61727e8 q^{67} +9.43918e7 q^{68} +1.93380e7 q^{70} -6.58887e7 q^{71} -4.01146e8 q^{73} -2.86115e8 q^{74} +2.06832e8 q^{76} +3.02132e8 q^{77} +1.23252e8 q^{79} +3.05261e7 q^{80} -1.97139e8 q^{82} +3.81346e8 q^{83} +1.17948e8 q^{85} -6.12667e7 q^{86} +8.41030e8 q^{88} +3.81633e8 q^{89} -2.06178e8 q^{91} +2.58023e8 q^{92} -5.34765e8 q^{94} +2.58449e8 q^{95} -5.93343e8 q^{97} -3.56253e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	17.9205	0.791983	0.395991	−	0.918254i	$-0.370401\pi$
$2$	17.9205	0.791983	0.395991	+	0.918254i	$0.370401\pi$
$3$	0	0
$3$	0	0
$4$	−190.855	−0.372763
$5$	−238.484	−0.170645	−0.0853226	−	0.996353i	$-0.527192\pi$
$5$	−238.484	−0.170645	−0.0853226	+	0.996353i	$0.527192\pi$
$6$	0	0
$7$	−4524.82	−0.712295	−0.356148	−	0.934430i	$-0.615910\pi$
$7$	−4524.82	−0.712295	−0.356148	+	0.934430i	$0.615910\pi$
$8$	−12595.5	−1.08720
$9$	0	0
$10$	−4273.75	−0.135148
$11$	−66772.1	−1.37508	−0.687540	−	0.726146i	$-0.741310\pi$
$11$	−66772.1	−1.37508	−0.687540	+	0.726146i	$0.741310\pi$
$12$	0	0
$13$	45566.0	0.442482	0.221241	−	0.975219i	$-0.428989\pi$
$13$	45566.0	0.442482	0.221241	+	0.975219i	$0.428989\pi$
$14$	−81087.1	−0.564126
$15$	0	0
$16$	−128001.	−0.488284
$17$	−494574.	−1.43619	−0.718094	−	0.695947i	$-0.754985\pi$
$17$	−494574.	−1.43619	−0.718094	+	0.695947i	$0.754985\pi$
$18$	0	0
$19$	−1.08372e6	−1.90776	−0.953881	−	0.300184i	$-0.902952\pi$
$19$	−1.08372e6	−1.90776	−0.953881	+	0.300184i	$0.902952\pi$
$20$	45515.8	0.0636103
$21$	0	0
$22$	−1.19659e6	−1.08904
$23$	−1.35193e6	−1.00735	−0.503675	−	0.863893i	$-0.668019\pi$
$23$	−1.35193e6	−1.00735	−0.503675	+	0.863893i	$0.668019\pi$
$24$	0	0
$25$	−1.89625e6	−0.970880
$26$	816566.	0.350438
$27$	0	0
$28$	863584.	0.265518
$29$	4.85463e6	1.27457	0.637287	−	0.770627i	$-0.280057\pi$
$29$	4.85463e6	1.27457	0.637287	+	0.770627i	$0.280057\pi$
$30$	0	0
$31$	5.69784e6	1.10811	0.554054	−	0.832481i	$-0.313080\pi$
$31$	5.69784e6	1.10811	0.554054	+	0.832481i	$0.313080\pi$
$32$	4.15507e6	0.700492
$33$	0	0
$34$	−8.86302e6	−1.13744
$35$	1.07910e6	0.121550
$36$	0	0
$37$	−1.59658e7	−1.40050	−0.700249	−	0.713898i	$-0.746928\pi$
$37$	−1.59658e7	−1.40050	−0.700249	+	0.713898i	$0.746928\pi$
$38$	−1.94208e7	−1.51091
$39$	0	0
$40$	3.00383e6	0.185526
$41$	−1.10007e7	−0.607988	−0.303994	−	0.952674i	$-0.598320\pi$
$41$	−1.10007e7	−0.607988	−0.303994	+	0.952674i	$0.598320\pi$
$42$	0	0
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	1.27438e7	0.512580
$45$	0	0
$46$	−2.42274e7	−0.797803
$47$	−2.98409e7	−0.892014	−0.446007	−	0.895029i	$-0.647154\pi$
$47$	−2.98409e7	−0.892014	−0.446007	+	0.895029i	$0.647154\pi$
$48$	0	0
$49$	−1.98796e7	−0.492635
$50$	−3.39818e7	−0.768920
$51$	0	0
$52$	−8.69648e6	−0.164941
$53$	−7.43943e6	−0.129509	−0.0647543	−	0.997901i	$-0.520626\pi$
$53$	−7.43943e6	−0.129509	−0.0647543	+	0.997901i	$0.520626\pi$
$54$	0	0
$55$	1.59241e7	0.234651
$56$	5.69925e7	0.774411
$57$	0	0
$58$	8.69975e7	1.00944
$59$	−1.08119e8	−1.16163	−0.580815	−	0.814036i	$-0.697266\pi$
$59$	−1.08119e8	−1.16163	−0.580815	+	0.814036i	$0.697266\pi$
$60$	0	0
$61$	1.99515e8	1.84497	0.922487	−	0.386028i	$-0.126153\pi$
$61$	1.99515e8	1.84497	0.922487	+	0.386028i	$0.126153\pi$
$62$	1.02108e8	0.877603
$63$	0	0
$64$	1.39997e8	1.04306
$65$	−1.08667e7	−0.0755073
$66$	0	0
$67$	−2.61727e8	−1.58677	−0.793383	−	0.608723i	$-0.791682\pi$
$67$	−2.61727e8	−1.58677	−0.793383	+	0.608723i	$0.791682\pi$
$68$	9.43918e7	0.535358
$69$	0	0
$70$	1.93380e7	0.0962653
$71$	−6.58887e7	−0.307715	−0.153857	−	0.988093i	$-0.549170\pi$
$71$	−6.58887e7	−0.307715	−0.153857	+	0.988093i	$0.549170\pi$
$72$	0	0
$73$	−4.01146e8	−1.65329	−0.826646	−	0.562722i	$-0.809754\pi$
$73$	−4.01146e8	−1.65329	−0.826646	+	0.562722i	$0.809754\pi$
$74$	−2.86115e8	−1.10917
$75$	0	0
$76$	2.06832e8	0.711144
$77$	3.02132e8	0.979464
$78$	0	0
$79$	1.23252e8	0.356019	0.178009	−	0.984029i	$-0.443034\pi$
$79$	1.23252e8	0.356019	0.178009	+	0.984029i	$0.443034\pi$
$80$	3.05261e7	0.0833233
$81$	0	0
$82$	−1.97139e8	−0.481516
$83$	3.81346e8	0.881998	0.440999	−	0.897507i	$-0.354624\pi$
$83$	3.81346e8	0.881998	0.440999	+	0.897507i	$0.354624\pi$
$84$	0	0
$85$	1.17948e8	0.245078
$86$	−6.12667e7	−0.120776
$87$	0	0
$88$	8.41030e8	1.49499
$89$	3.81633e8	0.644749	0.322375	−	0.946612i	$-0.395519\pi$
$89$	3.81633e8	0.644749	0.322375	+	0.946612i	$0.395519\pi$
$90$	0	0
$91$	−2.06178e8	−0.315178
$92$	2.58023e8	0.375503
$93$	0	0
$94$	−5.34765e8	−0.706460
$95$	2.58449e8	0.325550
$96$	0	0
$97$	−5.93343e8	−0.680507	−0.340254	−	0.940334i	$-0.610513\pi$
$97$	−5.93343e8	−0.680507	−0.340254	+	0.940334i	$0.610513\pi$
$98$	−3.56253e8	−0.390159
$99$	0	0
$100$	3.61909e8	0.361909
$101$	−1.22816e8	−0.117438	−0.0587190	−	0.998275i	$-0.518702\pi$
$101$	−1.22816e8	−0.117438	−0.0587190	+	0.998275i	$0.518702\pi$
$102$	0	0
$103$	−1.45390e9	−1.27282	−0.636408	−	0.771353i	$-0.719580\pi$
$103$	−1.45390e9	−1.27282	−0.636408	+	0.771353i	$0.719580\pi$
$104$	−5.73927e8	−0.481068
$105$	0	0
$106$	−1.33319e8	−0.102569
$107$	1.05553e9	0.778475	0.389237	−	0.921138i	$-0.372739\pi$
$107$	1.05553e9	0.778475	0.389237	+	0.921138i	$0.372739\pi$
$108$	0	0
$109$	−1.48849e9	−1.01001	−0.505006	−	0.863116i	$-0.668510\pi$
$109$	−1.48849e9	−1.01001	−0.505006	+	0.863116i	$0.668510\pi$
$110$	2.85368e8	0.185839
$111$	0	0
$112$	5.79180e8	0.347802
$113$	2.40872e9	1.38974	0.694869	−	0.719137i	$-0.255462\pi$
$113$	2.40872e9	1.38974	0.694869	+	0.719137i	$0.255462\pi$
$114$	0	0
$115$	3.22414e8	0.171899
$116$	−9.26530e8	−0.475115
$117$	0	0
$118$	−1.93755e9	−0.919991
$119$	2.23786e9	1.02299
$120$	0	0
$121$	2.10057e9	0.890847
$122$	3.57541e9	1.46119
$123$	0	0
$124$	−1.08746e9	−0.413062
$125$	9.18014e8	0.336321
$126$	0	0
$127$	1.63138e9	0.556464	0.278232	−	0.960514i	$-0.410252\pi$
$127$	1.63138e9	0.556464	0.278232	+	0.960514i	$0.410252\pi$
$128$	3.81431e8	0.125595
$129$	0	0
$130$	−1.94738e8	−0.0598005
$131$	2.34159e9	0.694690	0.347345	−	0.937737i	$-0.387083\pi$
$131$	2.34159e9	0.694690	0.347345	+	0.937737i	$0.387083\pi$
$132$	0	0
$133$	4.90362e9	1.35889
$134$	−4.69029e9	−1.25669
$135$	0	0
$136$	6.22942e9	1.56143
$137$	−4.87195e9	−1.18157	−0.590786	−	0.806828i	$-0.701182\pi$
$137$	−4.87195e9	−1.18157	−0.590786	+	0.806828i	$0.701182\pi$
$138$	0	0
$139$	3.89560e9	0.885131	0.442566	−	0.896736i	$-0.354068\pi$
$139$	3.89560e9	0.885131	0.442566	+	0.896736i	$0.354068\pi$
$140$	−2.05951e8	−0.0453093
$141$	0	0
$142$	−1.18076e9	−0.243705
$143$	−3.04254e9	−0.608448
$144$	0	0
$145$	−1.15775e9	−0.217500
$146$	−7.18875e9	−1.30938
$147$	0	0
$148$	3.04715e9	0.522055
$149$	−3.97719e9	−0.661056	−0.330528	−	0.943796i	$-0.607227\pi$
$149$	−3.97719e9	−0.661056	−0.330528	+	0.943796i	$0.607227\pi$
$150$	0	0
$151$	1.04756e9	0.163977	0.0819886	−	0.996633i	$-0.473873\pi$
$151$	1.04756e9	0.163977	0.0819886	+	0.996633i	$0.473873\pi$
$152$	1.36500e10	2.07413
$153$	0	0
$154$	5.41436e9	0.775718
$155$	−1.35884e9	−0.189093
$156$	0	0
$157$	−6.06273e9	−0.796379	−0.398189	−	0.917303i	$-0.630361\pi$
$157$	−6.06273e9	−0.796379	−0.398189	+	0.917303i	$0.630361\pi$
$158$	2.20874e9	0.281961
$159$	0	0
$160$	−9.90917e8	−0.119536
$161$	6.11726e9	0.717530
$162$	0	0
$163$	4.36837e9	0.484702	0.242351	−	0.970189i	$-0.422081\pi$
$163$	4.36837e9	0.484702	0.242351	+	0.970189i	$0.422081\pi$
$164$	2.09955e9	0.226636
$165$	0	0
$166$	6.83392e9	0.698528
$167$	9.06833e9	0.902200	0.451100	−	0.892473i	$-0.351032\pi$
$167$	9.06833e9	0.902200	0.451100	+	0.892473i	$0.351032\pi$
$168$	0	0
$169$	−8.52824e9	−0.804210
$170$	2.11369e9	0.194098
$171$	0	0
$172$	6.52495e8	0.0568459
$173$	1.41700e10	1.20272	0.601359	−	0.798979i	$-0.294626\pi$
$173$	1.41700e10	1.20272	0.601359	+	0.798979i	$0.294626\pi$
$174$	0	0
$175$	8.58019e9	0.691554
$176$	8.54688e9	0.671430
$177$	0	0
$178$	6.83906e9	0.510630
$179$	−2.05552e10	−1.49652	−0.748260	−	0.663405i	$-0.769111\pi$
$179$	−2.05552e10	−1.49652	−0.748260	+	0.663405i	$0.769111\pi$
$180$	0	0
$181$	−1.98258e10	−1.37302	−0.686511	−	0.727119i	$-0.740859\pi$
$181$	−1.98258e10	−1.37302	−0.686511	+	0.727119i	$0.740859\pi$
$182$	−3.69481e9	−0.249615
$183$	0	0
$184$	1.70283e10	1.09519
$185$	3.80758e9	0.238988
$186$	0	0
$187$	3.30238e10	1.97487
$188$	5.69528e9	0.332510
$189$	0	0
$190$	4.63154e9	0.257830
$191$	1.93769e10	1.05350	0.526750	−	0.850020i	$-0.323410\pi$
$191$	1.93769e10	1.05350	0.526750	+	0.850020i	$0.323410\pi$
$192$	0	0
$193$	2.44314e10	1.26748	0.633740	−	0.773546i	$-0.281519\pi$
$193$	2.44314e10	1.26748	0.633740	+	0.773546i	$0.281519\pi$
$194$	−1.06330e10	−0.538950
$195$	0	0
$196$	3.79412e9	0.183636
$197$	1.22473e10	0.579354	0.289677	−	0.957124i	$-0.406452\pi$
$197$	1.22473e10	0.579354	0.289677	+	0.957124i	$0.406452\pi$
$198$	0	0
$199$	−2.12982e10	−0.962731	−0.481366	−	0.876520i	$-0.659859\pi$
$199$	−2.12982e10	−0.962731	−0.481366	+	0.876520i	$0.659859\pi$
$200$	2.38843e10	1.05555
$201$	0	0
$202$	−2.20092e9	−0.0930088
$203$	−2.19663e10	−0.907873
$204$	0	0
$205$	2.62350e9	0.103750
$206$	−2.60546e10	−1.00805
$207$	0	0
$208$	−5.83247e9	−0.216057
$209$	7.23620e10	2.62333
$210$	0	0
$211$	−3.57352e10	−1.24115	−0.620576	−	0.784146i	$-0.713101\pi$
$211$	−3.57352e10	−1.24115	−0.620576	+	0.784146i	$0.713101\pi$
$212$	1.41985e9	0.0482761
$213$	0	0
$214$	1.89157e10	0.616538
$215$	8.15329e8	0.0260231
$216$	0	0
$217$	−2.57817e10	−0.789301
$218$	−2.66745e10	−0.799912
$219$	0	0
$220$	−3.03919e9	−0.0874692
$221$	−2.25357e10	−0.635487
$222$	0	0
$223$	1.10106e10	0.298153	0.149076	−	0.988826i	$-0.452370\pi$
$223$	1.10106e10	0.298153	0.149076	+	0.988826i	$0.452370\pi$
$224$	−1.88009e10	−0.498958
$225$	0	0
$226$	4.31655e10	1.10065
$227$	−1.50858e10	−0.377096	−0.188548	−	0.982064i	$-0.560378\pi$
$227$	−1.50858e10	−0.377096	−0.188548	+	0.982064i	$0.560378\pi$
$228$	0	0
$229$	1.14580e10	0.275327	0.137664	−	0.990479i	$-0.456041\pi$
$229$	1.14580e10	0.275327	0.137664	+	0.990479i	$0.456041\pi$
$230$	5.77783e9	0.136141
$231$	0	0
$232$	−6.11466e10	−1.38572
$233$	1.02658e10	0.228187	0.114094	−	0.993470i	$-0.463604\pi$
$233$	1.02658e10	0.228187	0.114094	+	0.993470i	$0.463604\pi$
$234$	0	0
$235$	7.11658e9	0.152218
$236$	2.06350e10	0.433013
$237$	0	0
$238$	4.01036e10	0.810190
$239$	−3.71284e10	−0.736064	−0.368032	−	0.929813i	$-0.619968\pi$
$239$	−3.71284e10	−0.736064	−0.368032	+	0.929813i	$0.619968\pi$
$240$	0	0
$241$	4.83626e10	0.923492	0.461746	−	0.887012i	$-0.347223\pi$
$241$	4.83626e10	0.923492	0.461746	+	0.887012i	$0.347223\pi$
$242$	3.76433e10	0.705536
$243$	0	0
$244$	−3.80783e10	−0.687739
$245$	4.74096e9	0.0840658
$246$	0	0
$247$	−4.93806e10	−0.844150
$248$	−7.17672e10	−1.20474
$249$	0	0
$250$	1.64513e10	0.266360
$251$	−3.34140e10	−0.531369	−0.265684	−	0.964060i	$-0.585598\pi$
$251$	−3.34140e10	−0.531369	−0.265684	+	0.964060i	$0.585598\pi$
$252$	0	0
$253$	9.02715e10	1.38519
$254$	2.92351e10	0.440710
$255$	0	0
$256$	−6.48432e10	−0.943593
$257$	8.20412e10	1.17309	0.586547	−	0.809915i	$-0.300487\pi$
$257$	8.20412e10	1.17309	0.586547	+	0.809915i	$0.300487\pi$
$258$	0	0
$259$	7.22423e10	0.997569
$260$	2.07397e9	0.0281464
$261$	0	0
$262$	4.19626e10	0.550182
$263$	−4.19397e10	−0.540536	−0.270268	−	0.962785i	$-0.587112\pi$
$263$	−4.19397e10	−0.540536	−0.270268	+	0.962785i	$0.587112\pi$
$264$	0	0
$265$	1.77418e9	0.0221000
$266$	8.78754e10	1.07622
$267$	0	0
$268$	4.99520e10	0.591488
$269$	−1.06374e11	−1.23866	−0.619328	−	0.785132i	$-0.712595\pi$
$269$	−1.06374e11	−1.23866	−0.619328	+	0.785132i	$0.712595\pi$
$270$	0	0
$271$	−8.12651e10	−0.915255	−0.457628	−	0.889144i	$-0.651301\pi$
$271$	−8.12651e10	−0.915255	−0.457628	+	0.889144i	$0.651301\pi$
$272$	6.33058e10	0.701267
$273$	0	0
$274$	−8.73079e10	−0.935785
$275$	1.26617e11	1.33504
$276$	0	0
$277$	2.01089e10	0.205225	0.102612	−	0.994721i	$-0.467280\pi$
$277$	2.01089e10	0.205225	0.102612	+	0.994721i	$0.467280\pi$
$278$	6.98112e10	0.701009
$279$	0	0
$280$	−1.35918e10	−0.132149
$281$	1.16967e11	1.11914	0.559572	−	0.828782i	$-0.310965\pi$
$281$	1.16967e11	1.11914	0.559572	+	0.828782i	$0.310965\pi$
$282$	0	0
$283$	−9.10743e10	−0.844028	−0.422014	−	0.906589i	$-0.638677\pi$
$283$	−9.10743e10	−0.844028	−0.422014	+	0.906589i	$0.638677\pi$
$284$	1.25752e10	0.114705
$285$	0	0
$286$	−5.45238e10	−0.481880
$287$	4.97764e10	0.433067
$288$	0	0
$289$	1.26015e11	1.06263
$290$	−2.07475e10	−0.172256
$291$	0	0
$292$	7.65607e10	0.616287
$293$	7.51554e10	0.595739	0.297869	−	0.954607i	$-0.403724\pi$
$293$	7.51554e10	0.595739	0.297869	+	0.954607i	$0.403724\pi$
$294$	0	0
$295$	2.57846e10	0.198226
$296$	2.01098e11	1.52263
$297$	0	0
$298$	−7.12733e10	−0.523545
$299$	−6.16021e10	−0.445734
$300$	0	0
$301$	1.54695e10	0.108624
$302$	1.87729e10	0.129867
$303$	0	0
$304$	1.38716e11	0.931530
$305$	−4.75810e10	−0.314836
$306$	0	0
$307$	2.57354e10	0.165352	0.0826759	−	0.996576i	$-0.473653\pi$
$307$	2.57354e10	0.165352	0.0826759	+	0.996576i	$0.473653\pi$
$308$	−5.76634e10	−0.365108
$309$	0	0
$310$	−2.43511e10	−0.149759
$311$	−5.97715e10	−0.362304	−0.181152	−	0.983455i	$-0.557983\pi$
$311$	−5.97715e10	−0.362304	−0.181152	+	0.983455i	$0.557983\pi$
$312$	0	0
$313$	−6.89838e10	−0.406254	−0.203127	−	0.979152i	$-0.565110\pi$
$313$	−6.89838e10	−0.406254	−0.203127	+	0.979152i	$0.565110\pi$
$314$	−1.08647e11	−0.630718
$315$	0	0
$316$	−2.35233e10	−0.132711
$317$	3.11421e11	1.73213	0.866067	−	0.499928i	$-0.166640\pi$
$317$	3.11421e11	1.73213	0.866067	+	0.499928i	$0.166640\pi$
$318$	0	0
$319$	−3.24154e11	−1.75264
$320$	−3.33871e10	−0.177993
$321$	0	0
$322$	1.09624e11	0.568271
$323$	5.35978e11	2.73990
$324$	0	0
$325$	−8.64045e10	−0.429597
$326$	7.82835e10	0.383876
$327$	0	0
$328$	1.38560e11	0.661007
$329$	1.35025e11	0.635378
$330$	0	0
$331$	−1.00401e11	−0.459738	−0.229869	−	0.973222i	$-0.573830\pi$
$331$	−1.00401e11	−0.459738	−0.229869	+	0.973222i	$0.573830\pi$
$332$	−7.27818e10	−0.328777
$333$	0	0
$334$	1.62509e11	0.714527
$335$	6.24178e10	0.270774
$336$	0	0
$337$	−3.46652e11	−1.46406	−0.732030	−	0.681273i	$-0.761427\pi$
$337$	−3.46652e11	−1.46406	−0.732030	+	0.681273i	$0.761427\pi$
$338$	−1.52831e11	−0.636920
$339$	0	0
$340$	−2.25109e10	−0.0913562
$341$	−3.80457e11	−1.52374
$342$	0	0
$343$	2.72544e11	1.06320
$344$	4.30616e10	0.165797
$345$	0	0
$346$	2.53935e11	0.952531
$347$	−4.59014e10	−0.169959	−0.0849794	−	0.996383i	$-0.527082\pi$
$347$	−4.59014e10	−0.169959	−0.0849794	+	0.996383i	$0.527082\pi$
$348$	0	0
$349$	−5.52760e11	−1.99445	−0.997224	−	0.0744645i	$-0.976275\pi$
$349$	−5.52760e11	−1.99445	−0.997224	+	0.0744645i	$0.976275\pi$
$350$	1.53762e11	0.547698
$351$	0	0
$352$	−2.77443e11	−0.963234
$353$	3.24055e11	1.11079	0.555395	−	0.831586i	$-0.312567\pi$
$353$	3.24055e11	1.11079	0.555395	+	0.831586i	$0.312567\pi$
$354$	0	0
$355$	1.57134e10	0.0525100
$356$	−7.28365e10	−0.240339
$357$	0	0
$358$	−3.68360e11	−1.18522
$359$	−2.90617e11	−0.923413	−0.461707	−	0.887033i	$-0.652763\pi$
$359$	−2.90617e11	−0.923413	−0.461707	+	0.887033i	$0.652763\pi$
$360$	0	0
$361$	8.51753e11	2.63956
$362$	−3.55289e11	−1.08741
$363$	0	0
$364$	3.93500e10	0.117487
$365$	9.56668e10	0.282126
$366$	0	0
$367$	−1.08398e11	−0.311906	−0.155953	−	0.987764i	$-0.549845\pi$
$367$	−1.08398e11	−0.311906	−0.155953	+	0.987764i	$0.549845\pi$
$368$	1.73048e11	0.491872
$369$	0	0
$370$	6.82339e10	0.189275
$371$	3.36621e10	0.0922483
$372$	0	0
$373$	−4.17071e11	−1.11563	−0.557815	−	0.829965i	$-0.688360\pi$
$373$	−4.17071e11	−1.11563	−0.557815	+	0.829965i	$0.688360\pi$
$374$	5.91803e11	1.56407
$375$	0	0
$376$	3.75862e11	0.969802
$377$	2.21206e11	0.563976
$378$	0	0
$379$	−2.63908e11	−0.657015	−0.328508	−	0.944501i	$-0.606546\pi$
$379$	−2.63908e11	−0.657015	−0.328508	+	0.944501i	$0.606546\pi$
$380$	−4.93262e10	−0.121353
$381$	0	0
$382$	3.47245e11	0.834354
$383$	−8.16196e11	−1.93821	−0.969103	−	0.246658i	$-0.920667\pi$
$383$	−8.16196e11	−1.93821	−0.969103	+	0.246658i	$0.920667\pi$
$384$	0	0
$385$	−7.20536e10	−0.167141
$386$	4.37824e11	1.00382
$387$	0	0
$388$	1.13242e11	0.253668
$389$	−6.95765e11	−1.54060	−0.770299	−	0.637683i	$-0.779893\pi$
$389$	−6.95765e11	−1.54060	−0.770299	+	0.637683i	$0.779893\pi$
$390$	0	0
$391$	6.68631e11	1.44674
$392$	2.50394e11	0.535595
$393$	0	0
$394$	2.19479e11	0.458838
$395$	−2.93937e10	−0.0607528
$396$	0	0
$397$	2.39129e10	0.0483143	0.0241571	−	0.999708i	$-0.492310\pi$
$397$	2.39129e10	0.0483143	0.0241571	+	0.999708i	$0.492310\pi$
$398$	−3.81676e11	−0.762466
$399$	0	0
$400$	2.42721e11	0.474065
$401$	1.31846e11	0.254634	0.127317	−	0.991862i	$-0.459363\pi$
$401$	1.31846e11	0.254634	0.127317	+	0.991862i	$0.459363\pi$
$402$	0	0
$403$	2.59627e11	0.490318
$404$	2.34400e10	0.0437766
$405$	0	0
$406$	−3.93648e11	−0.719020
$407$	1.06607e12	1.92580
$408$	0	0
$409$	2.22821e11	0.393732	0.196866	−	0.980430i	$-0.436924\pi$
$409$	2.22821e11	0.393732	0.196866	+	0.980430i	$0.436924\pi$
$410$	4.70145e10	0.0821683
$411$	0	0
$412$	2.77483e11	0.474459
$413$	4.89219e11	0.827423
$414$	0	0
$415$	−9.09449e10	−0.150509
$416$	1.89330e11	0.309955
$417$	0	0
$418$	1.29677e12	2.07763
$419$	8.93132e11	1.41564	0.707820	−	0.706393i	$-0.249679\pi$
$419$	8.93132e11	1.41564	0.707820	+	0.706393i	$0.249679\pi$
$420$	0	0
$421$	4.93105e11	0.765014	0.382507	−	0.923953i	$-0.375061\pi$
$421$	4.93105e11	0.765014	0.382507	+	0.923953i	$0.375061\pi$
$422$	−6.40393e11	−0.982971
$423$	0	0
$424$	9.37036e10	0.140802
$425$	9.37836e11	1.39437
$426$	0	0
$427$	−9.02768e11	−1.31417
$428$	−2.01453e11	−0.290187
$429$	0	0
$430$	1.46111e10	0.0206099
$431$	−1.09242e12	−1.52490	−0.762449	−	0.647048i	$-0.776003\pi$
$431$	−1.09242e12	−1.52490	−0.762449	+	0.647048i	$0.776003\pi$
$432$	0	0
$433$	−6.73980e11	−0.921406	−0.460703	−	0.887554i	$-0.652403\pi$
$433$	−6.73980e11	−0.921406	−0.460703	+	0.887554i	$0.652403\pi$
$434$	−4.62021e11	−0.625112
$435$	0	0
$436$	2.84085e11	0.376495
$437$	1.46511e12	1.92178
$438$	0	0
$439$	2.78225e11	0.357524	0.178762	−	0.983892i	$-0.442791\pi$
$439$	2.78225e11	0.357524	0.178762	+	0.983892i	$0.442791\pi$
$440$	−2.00572e11	−0.255114
$441$	0	0
$442$	−4.03852e11	−0.503294
$443$	−3.25574e11	−0.401636	−0.200818	−	0.979629i	$-0.564360\pi$
$443$	−3.25574e11	−0.401636	−0.200818	+	0.979629i	$0.564360\pi$
$444$	0	0
$445$	−9.10133e10	−0.110023
$446$	1.97316e11	0.236132
$447$	0	0
$448$	−6.33463e11	−0.742968
$449$	−9.27680e11	−1.07718	−0.538592	−	0.842567i	$-0.681044\pi$
$449$	−9.27680e11	−1.07718	−0.538592	+	0.842567i	$0.681044\pi$
$450$	0	0
$451$	7.34544e11	0.836032
$452$	−4.59715e11	−0.518043
$453$	0	0
$454$	−2.70346e11	−0.298654
$455$	4.91700e10	0.0537835
$456$	0	0
$457$	1.08416e12	1.16271	0.581355	−	0.813650i	$-0.302523\pi$
$457$	1.08416e12	1.16271	0.581355	+	0.813650i	$0.302523\pi$
$458$	2.05333e11	0.218055
$459$	0	0
$460$	−6.15343e10	−0.0640777
$461$	−5.03578e11	−0.519293	−0.259647	−	0.965704i	$-0.583606\pi$
$461$	−5.03578e11	−0.519293	−0.259647	+	0.965704i	$0.583606\pi$
$462$	0	0
$463$	−1.27085e12	−1.28523	−0.642613	−	0.766191i	$-0.722150\pi$
$463$	−1.27085e12	−1.28523	−0.642613	+	0.766191i	$0.722150\pi$
$464$	−6.21396e11	−0.622354
$465$	0	0
$466$	1.83968e11	0.180720
$467$	−1.68815e12	−1.64243	−0.821214	−	0.570621i	$-0.806703\pi$
$467$	−1.68815e12	−1.64243	−0.821214	+	0.570621i	$0.806703\pi$
$468$	0	0
$469$	1.18427e12	1.13025
$470$	1.27533e11	0.120554
$471$	0	0
$472$	1.36181e12	1.26293
$473$	2.28281e11	0.209698
$474$	0	0
$475$	2.05500e12	1.85221
$476$	−4.27106e11	−0.381333
$477$	0	0
$478$	−6.65360e11	−0.582950
$479$	1.34770e12	1.16972	0.584862	−	0.811133i	$-0.301149\pi$
$479$	1.34770e12	1.16972	0.584862	+	0.811133i	$0.301149\pi$
$480$	0	0
$481$	−7.27496e11	−0.619695
$482$	8.66684e11	0.731390
$483$	0	0
$484$	−4.00904e11	−0.332075
$485$	1.41503e11	0.116125
$486$	0	0
$487$	4.15547e11	0.334765	0.167382	−	0.985892i	$-0.446469\pi$
$487$	4.15547e11	0.334765	0.167382	+	0.985892i	$0.446469\pi$
$488$	−2.51299e12	−2.00587
$489$	0	0
$490$	8.49606e10	0.0665787
$491$	−2.51440e11	−0.195239	−0.0976197	−	0.995224i	$-0.531123\pi$
$491$	−2.51440e11	−0.195239	−0.0976197	+	0.995224i	$0.531123\pi$
$492$	0	0
$493$	−2.40097e12	−1.83053
$494$	−8.84925e11	−0.668552
$495$	0	0
$496$	−7.29327e11	−0.541072
$497$	2.98134e11	0.219184
$498$	0	0
$499$	−1.18872e12	−0.858273	−0.429137	−	0.903240i	$-0.641182\pi$
$499$	−1.18872e12	−0.858273	−0.429137	+	0.903240i	$0.641182\pi$
$500$	−1.75207e11	−0.125368
$501$	0	0
$502$	−5.98796e11	−0.420835
$503$	2.74830e10	0.0191430	0.00957148	−	0.999954i	$-0.496953\pi$
$503$	2.74830e10	0.0191430	0.00957148	+	0.999954i	$0.496953\pi$
$504$	0	0
$505$	2.92896e10	0.0200402
$506$	1.61771e12	1.09704
$507$	0	0
$508$	−3.11356e11	−0.207430
$509$	2.56804e12	1.69579	0.847894	−	0.530165i	$-0.177870\pi$
$509$	2.56804e12	1.69579	0.847894	+	0.530165i	$0.177870\pi$
$510$	0	0
$511$	1.81511e12	1.17763
$512$	−1.35732e12	−0.872904
$513$	0	0
$514$	1.47022e12	0.929070
$515$	3.46730e11	0.217200
$516$	0	0
$517$	1.99254e12	1.22659
$518$	1.29462e12	0.790057
$519$	0	0
$520$	1.36872e11	0.0820920
$521$	5.58805e11	0.332269	0.166135	−	0.986103i	$-0.446871\pi$
$521$	5.58805e11	0.332269	0.166135	+	0.986103i	$0.446871\pi$
$522$	0	0
$523$	−1.74645e12	−1.02070	−0.510350	−	0.859967i	$-0.670484\pi$
$523$	−1.74645e12	−1.02070	−0.510350	+	0.859967i	$0.670484\pi$
$524$	−4.46905e11	−0.258955
$525$	0	0
$526$	−7.51581e11	−0.428095
$527$	−2.81800e12	−1.59145
$528$	0	0
$529$	2.65711e10	0.0147523
$530$	3.17943e10	0.0175028
$531$	0	0
$532$	−9.35880e11	−0.506545
$533$	−5.01260e11	−0.269024
$534$	0	0
$535$	−2.51727e11	−0.132843
$536$	3.29660e12	1.72514
$537$	0	0
$538$	−1.90628e12	−0.980994
$539$	1.32740e12	0.677413
$540$	0	0
$541$	1.23556e12	0.620122	0.310061	−	0.950717i	$-0.399650\pi$
$541$	1.23556e12	0.620122	0.310061	+	0.950717i	$0.399650\pi$
$542$	−1.45631e12	−0.724866
$543$	0	0
$544$	−2.05499e12	−1.00604
$545$	3.54981e11	0.172354
$546$	0	0
$547$	−1.66722e11	−0.0796251	−0.0398126	−	0.999207i	$-0.512676\pi$
$547$	−1.66722e11	−0.0796251	−0.0398126	+	0.999207i	$0.512676\pi$
$548$	9.29835e11	0.440447
$549$	0	0
$550$	2.26904e12	1.05733
$551$	−5.26104e12	−2.43158
$552$	0	0
$553$	−5.57694e11	−0.253590
$554$	3.60362e11	0.162534
$555$	0	0
$556$	−7.43494e11	−0.329945
$557$	−5.10355e11	−0.224659	−0.112330	−	0.993671i	$-0.535831\pi$
$557$	−5.10355e11	−0.224659	−0.112330	+	0.993671i	$0.535831\pi$
$558$	0	0
$559$	−1.55781e11	−0.0674778
$560$	−1.38125e11	−0.0593508
$561$	0	0
$562$	2.09612e12	0.886343
$563$	−6.39701e11	−0.268342	−0.134171	−	0.990958i	$-0.542837\pi$
$563$	−6.39701e11	−0.268342	−0.134171	+	0.990958i	$0.542837\pi$
$564$	0	0
$565$	−5.74440e11	−0.237152
$566$	−1.63210e12	−0.668456
$567$	0	0
$568$	8.29903e11	0.334549
$569$	−2.50583e12	−1.00218	−0.501090	−	0.865395i	$-0.667067\pi$
$569$	−2.50583e12	−1.00218	−0.501090	+	0.865395i	$0.667067\pi$
$570$	0	0
$571$	−2.06826e12	−0.814220	−0.407110	−	0.913379i	$-0.633463\pi$
$571$	−2.06826e12	−0.814220	−0.407110	+	0.913379i	$0.633463\pi$
$572$	5.80683e11	0.226807
$573$	0	0
$574$	8.92019e11	0.342982
$575$	2.56360e12	0.978015
$576$	0	0
$577$	−1.61115e12	−0.605124	−0.302562	−	0.953130i	$-0.597842\pi$
$577$	−1.61115e12	−0.605124	−0.302562	+	0.953130i	$0.597842\pi$
$578$	2.25826e12	0.841587
$579$	0	0
$580$	2.20962e11	0.0810760
$581$	−1.72552e12	−0.628243
$582$	0	0
$583$	4.96747e11	0.178085
$584$	5.05265e12	1.79747
$585$	0	0
$586$	1.34682e12	0.471815
$587$	−2.54415e12	−0.884446	−0.442223	−	0.896905i	$-0.645810\pi$
$587$	−2.54415e12	−0.884446	−0.442223	+	0.896905i	$0.645810\pi$
$588$	0	0
$589$	−6.17484e12	−2.11401
$590$	4.62074e11	0.156992
$591$	0	0
$592$	2.04363e12	0.683841
$593$	−1.32235e11	−0.0439137	−0.0219569	−	0.999759i	$-0.506990\pi$
$593$	−1.32235e11	−0.0439137	−0.0219569	+	0.999759i	$0.506990\pi$
$594$	0	0
$595$	−5.33693e11	−0.174568
$596$	7.59066e11	0.246417
$597$	0	0
$598$	−1.10394e12	−0.353013
$599$	−2.32737e12	−0.738660	−0.369330	−	0.929298i	$-0.620413\pi$
$599$	−2.32737e12	−0.738660	−0.369330	+	0.929298i	$0.620413\pi$
$600$	0	0
$601$	−5.87945e12	−1.83824	−0.919119	−	0.393981i	$-0.871098\pi$
$601$	−5.87945e12	−1.83824	−0.919119	+	0.393981i	$0.871098\pi$
$602$	2.77221e11	0.0860284
$603$	0	0
$604$	−1.99932e11	−0.0611247
$605$	−5.00952e11	−0.152019
$606$	0	0
$607$	−2.28556e12	−0.683351	−0.341675	−	0.939818i	$-0.610994\pi$
$607$	−2.28556e12	−0.683351	−0.341675	+	0.939818i	$0.610994\pi$
$608$	−4.50292e12	−1.33637
$609$	0	0
$610$	−8.52676e11	−0.249345
$611$	−1.35973e12	−0.394700
$612$	0	0
$613$	−2.72675e12	−0.779960	−0.389980	−	0.920823i	$-0.627518\pi$
$613$	−2.72675e12	−0.779960	−0.389980	+	0.920823i	$0.627518\pi$
$614$	4.61192e11	0.130956
$615$	0	0
$616$	−3.80551e12	−1.06488
$617$	−1.68755e12	−0.468784	−0.234392	−	0.972142i	$-0.575310\pi$
$617$	−1.68755e12	−0.468784	−0.234392	+	0.972142i	$0.575310\pi$
$618$	0	0
$619$	−5.29229e12	−1.44889	−0.724445	−	0.689332i	$-0.757904\pi$
$619$	−5.29229e12	−1.44889	−0.724445	+	0.689332i	$0.757904\pi$
$620$	2.59341e11	0.0704871
$621$	0	0
$622$	−1.07114e12	−0.286938
$623$	−1.72682e12	−0.459252
$624$	0	0
$625$	3.48468e12	0.913489
$626$	−1.23623e12	−0.321746
$627$	0	0
$628$	1.15710e12	0.296861
$629$	7.89626e12	2.01138
$630$	0	0
$631$	−2.78836e12	−0.700191	−0.350095	−	0.936714i	$-0.613851\pi$
$631$	−2.78836e12	−0.700191	−0.350095	+	0.936714i	$0.613851\pi$
$632$	−1.55243e12	−0.387065
$633$	0	0
$634$	5.58083e12	1.37182
$635$	−3.89057e11	−0.0949579
$636$	0	0
$637$	−9.05833e11	−0.217982
$638$	−5.80901e12	−1.38806
$639$	0	0
$640$	−9.09650e10	−0.0214321
$641$	−5.16942e12	−1.20943	−0.604715	−	0.796442i	$-0.706713\pi$
$641$	−5.16942e12	−1.20943	−0.604715	+	0.796442i	$0.706713\pi$
$642$	0	0
$643$	−3.58293e12	−0.826589	−0.413294	−	0.910598i	$-0.635622\pi$
$643$	−3.58293e12	−0.826589	−0.413294	+	0.910598i	$0.635622\pi$
$644$	−1.16751e12	−0.267469
$645$	0	0
$646$	9.60500e12	2.16996
$647$	−3.89598e12	−0.874074	−0.437037	−	0.899444i	$-0.643972\pi$
$647$	−3.89598e12	−0.874074	−0.437037	+	0.899444i	$0.643972\pi$
$648$	0	0
$649$	7.21933e12	1.59733
$650$	−1.54841e12	−0.340233
$651$	0	0
$652$	−8.33725e11	−0.180679
$653$	6.62700e10	0.0142629	0.00713145	−	0.999975i	$-0.497730\pi$
$653$	6.62700e10	0.0142629	0.00713145	+	0.999975i	$0.497730\pi$
$654$	0	0
$655$	−5.58432e11	−0.118545
$656$	1.40810e12	0.296871
$657$	0	0
$658$	2.41971e12	0.503208
$659$	−1.84962e12	−0.382030	−0.191015	−	0.981587i	$-0.561178\pi$
$659$	−1.84962e12	−0.382030	−0.191015	+	0.981587i	$0.561178\pi$
$660$	0	0
$661$	−3.74337e12	−0.762705	−0.381352	−	0.924430i	$-0.624542\pi$
$661$	−3.74337e12	−0.762705	−0.381352	+	0.924430i	$0.624542\pi$
$662$	−1.79923e12	−0.364104
$663$	0	0
$664$	−4.80325e12	−0.958913
$665$	−1.16943e12	−0.231888
$666$	0	0
$667$	−6.56314e12	−1.28394
$668$	−1.73073e12	−0.336307
$669$	0	0
$670$	1.11856e12	0.214448
$671$	−1.33220e13	−2.53699
$672$	0	0
$673$	2.59774e12	0.488122	0.244061	−	0.969760i	$-0.421520\pi$
$673$	2.59774e12	0.488122	0.244061	+	0.969760i	$0.421520\pi$
$674$	−6.21218e12	−1.15951
$675$	0	0
$676$	1.62766e12	0.299780
$677$	7.57984e12	1.38679	0.693396	−	0.720557i	$-0.256114\pi$
$677$	7.57984e12	1.38679	0.693396	+	0.720557i	$0.256114\pi$
$678$	0	0
$679$	2.68477e12	0.484722
$680$	−1.48562e12	−0.266450
$681$	0	0
$682$	−6.81798e12	−1.20677
$683$	9.09946e12	1.60001	0.800004	−	0.599994i	$-0.204830\pi$
$683$	9.09946e12	1.60001	0.800004	+	0.599994i	$0.204830\pi$
$684$	0	0
$685$	1.16188e12	0.201630
$686$	4.88414e12	0.842034
$687$	0	0
$688$	4.37609e11	0.0744626
$689$	−3.38985e11	−0.0573052
$690$	0	0
$691$	1.40526e10	0.00234480	0.00117240	−	0.999999i	$-0.499627\pi$
$691$	1.40526e10	0.00234480	0.00117240	+	0.999999i	$0.499627\pi$
$692$	−2.70442e12	−0.448329
$693$	0	0
$694$	−8.22578e11	−0.134604
$695$	−9.29037e11	−0.151043
$696$	0	0
$697$	5.44068e12	0.873184
$698$	−9.90576e12	−1.57957
$699$	0	0
$700$	−1.63757e12	−0.257786
$701$	9.00853e12	1.40904	0.704519	−	0.709685i	$-0.251163\pi$
$701$	9.00853e12	1.40904	0.704519	+	0.709685i	$0.251163\pi$
$702$	0	0
$703$	1.73024e13	2.67182
$704$	−9.34793e12	−1.43429
$705$	0	0
$706$	5.80723e12	0.879727
$707$	5.55720e11	0.0836505
$708$	0	0
$709$	−1.15494e13	−1.71653	−0.858264	−	0.513209i	$-0.828457\pi$
$709$	−1.15494e13	−1.71653	−0.858264	+	0.513209i	$0.828457\pi$
$710$	2.81592e11	0.0415870
$711$	0	0
$712$	−4.80687e12	−0.700974
$713$	−7.70309e12	−1.11625
$714$	0	0
$715$	7.25596e11	0.103829
$716$	3.92306e12	0.557848
$717$	0	0
$718$	−5.20801e12	−0.731327
$719$	2.80308e12	0.391161	0.195580	−	0.980688i	$-0.437341\pi$
$719$	2.80308e12	0.391161	0.195580	+	0.980688i	$0.437341\pi$
$720$	0	0
$721$	6.57861e12	0.906621
$722$	1.52639e13	2.09048
$723$	0	0
$724$	3.78386e12	0.511813
$725$	−9.20559e12	−1.23746
$726$	0	0
$727$	−5.45780e12	−0.724625	−0.362312	−	0.932057i	$-0.618013\pi$
$727$	−5.45780e12	−0.724625	−0.362312	+	0.932057i	$0.618013\pi$
$728$	2.59692e12	0.342663
$729$	0	0
$730$	1.71440e12	0.223439
$731$	1.69085e12	0.219016
$732$	0	0
$733$	−3.95238e12	−0.505697	−0.252849	−	0.967506i	$-0.581367\pi$
$733$	−3.95238e12	−0.505697	−0.252849	+	0.967506i	$0.581367\pi$
$734$	−1.94255e12	−0.247024
$735$	0	0
$736$	−5.61738e12	−0.705640
$737$	1.74761e13	2.18193
$738$	0	0
$739$	2.12821e11	0.0262491	0.0131246	−	0.999914i	$-0.495822\pi$
$739$	2.12821e11	0.0262491	0.0131246	+	0.999914i	$0.495822\pi$
$740$	−7.26696e11	−0.0890861
$741$	0	0
$742$	6.03242e11	0.0730591
$743$	4.10800e12	0.494516	0.247258	−	0.968950i	$-0.420470\pi$
$743$	4.10800e12	0.494516	0.247258	+	0.968950i	$0.420470\pi$
$744$	0	0
$745$	9.48495e11	0.112806
$746$	−7.47413e12	−0.883560
$747$	0	0
$748$	−6.30274e12	−0.736161
$749$	−4.77609e12	−0.554504
$750$	0	0
$751$	5.19165e12	0.595560	0.297780	−	0.954634i	$-0.403754\pi$
$751$	5.19165e12	0.595560	0.297780	+	0.954634i	$0.403754\pi$
$752$	3.81966e12	0.435556
$753$	0	0
$754$	3.96412e12	0.446659
$755$	−2.49826e11	−0.0279819
$756$	0	0
$757$	−1.20035e13	−1.32854	−0.664272	−	0.747491i	$-0.731258\pi$
$757$	−1.20035e13	−1.32854	−0.664272	+	0.747491i	$0.731258\pi$
$758$	−4.72936e12	−0.520345
$759$	0	0
$760$	−3.25530e12	−0.353940
$761$	1.27185e12	0.137469	0.0687345	−	0.997635i	$-0.478104\pi$
$761$	1.27185e12	0.137469	0.0687345	+	0.997635i	$0.478104\pi$
$762$	0	0
$763$	6.73515e12	0.719427
$764$	−3.69818e12	−0.392706
$765$	0	0
$766$	−1.46267e13	−1.53502
$767$	−4.92654e12	−0.514000
$768$	0	0
$769$	1.49703e13	1.54370	0.771849	−	0.635806i	$-0.219332\pi$
$769$	1.49703e13	1.54370	0.771849	+	0.635806i	$0.219332\pi$
$770$	−1.29124e12	−0.132373
$771$	0	0
$772$	−4.66286e12	−0.472470
$773$	−1.59529e13	−1.60706	−0.803529	−	0.595266i	$-0.797047\pi$
$773$	−1.59529e13	−1.60706	−0.803529	+	0.595266i	$0.797047\pi$
$774$	0	0
$775$	−1.08045e13	−1.07584
$776$	7.47346e12	0.739851
$777$	0	0
$778$	−1.24685e13	−1.22013
$779$	1.19217e13	1.15990
$780$	0	0
$781$	4.39953e12	0.423133
$782$	1.19822e13	1.14579
$783$	0	0
$784$	2.54460e12	0.240546
$785$	1.44586e12	0.135898
$786$	0	0
$787$	−4.64442e12	−0.431564	−0.215782	−	0.976442i	$-0.569230\pi$
$787$	−4.64442e12	−0.431564	−0.215782	+	0.976442i	$0.569230\pi$
$788$	−2.33747e12	−0.215962
$789$	0	0
$790$	−5.26750e11	−0.0481152
$791$	−1.08990e13	−0.989904
$792$	0	0
$793$	9.09107e12	0.816368
$794$	4.28532e11	0.0382641
$795$	0	0
$796$	4.06487e12	0.358871
$797$	−1.24077e13	−1.08925	−0.544625	−	0.838680i	$-0.683328\pi$
$797$	−1.24077e13	−1.08925	−0.544625	+	0.838680i	$0.683328\pi$
$798$	0	0
$799$	1.47585e13	1.28110
$800$	−7.87905e12	−0.680094
$801$	0	0
$802$	2.36275e12	0.201666
$803$	2.67854e13	2.27341
$804$	0	0
$805$	−1.45887e12	−0.122443
$806$	4.65266e12	0.388323
$807$	0	0
$808$	1.54693e12	0.127679
$809$	9.50544e12	0.780196	0.390098	−	0.920773i	$-0.372441\pi$
$809$	9.50544e12	0.780196	0.390098	+	0.920773i	$0.372441\pi$
$810$	0	0
$811$	−6.56385e12	−0.532801	−0.266400	−	0.963862i	$-0.585834\pi$
$811$	−6.56385e12	−0.532801	−0.266400	+	0.963862i	$0.585834\pi$
$812$	4.19238e12	0.338422
$813$	0	0
$814$	1.91045e13	1.52520
$815$	−1.04179e12	−0.0827121
$816$	0	0
$817$	3.70501e12	0.290931
$818$	3.99306e12	0.311829
$819$	0	0
$820$	−5.00708e11	−0.0386743
$821$	−3.96939e12	−0.304915	−0.152458	−	0.988310i	$-0.548719\pi$
$821$	−3.96939e12	−0.304915	−0.152458	+	0.988310i	$0.548719\pi$
$822$	0	0
$823$	2.57352e13	1.95537	0.977683	−	0.210086i	$-0.0673743\pi$
$823$	2.57352e13	1.95537	0.977683	+	0.210086i	$0.0673743\pi$
$824$	1.83126e13	1.38381
$825$	0	0
$826$	8.76706e12	0.655305
$827$	1.59944e13	1.18903	0.594516	−	0.804084i	$-0.297344\pi$
$827$	1.59944e13	1.18903	0.594516	+	0.804084i	$0.297344\pi$
$828$	0	0
$829$	5.84546e12	0.429856	0.214928	−	0.976630i	$-0.431048\pi$
$829$	5.84546e12	0.429856	0.214928	+	0.976630i	$0.431048\pi$
$830$	−1.62978e12	−0.119200
$831$	0	0
$832$	6.37911e12	0.461536
$833$	9.83194e12	0.707516
$834$	0	0
$835$	−2.16265e12	−0.153956
$836$	−1.38106e13	−0.977881
$837$	0	0
$838$	1.60054e13	1.12116
$839$	2.45685e12	0.171178	0.0855892	−	0.996331i	$-0.472723\pi$
$839$	2.45685e12	0.171178	0.0855892	+	0.996331i	$0.472723\pi$
$840$	0	0
$841$	9.06028e12	0.624539
$842$	8.83669e12	0.605878
$843$	0	0
$844$	6.82023e12	0.462656
$845$	2.03385e12	0.137234
$846$	0	0
$847$	−9.50471e12	−0.634546
$848$	9.52253e11	0.0632370
$849$	0	0
$850$	1.68065e13	1.10431
$851$	2.15847e13	1.41079
$852$	0	0
$853$	1.38158e11	0.00893523	0.00446761	−	0.999990i	$-0.498578\pi$
$853$	1.38158e11	0.00893523	0.00446761	+	0.999990i	$0.498578\pi$
$854$	−1.61781e13	−1.04080
$855$	0	0
$856$	−1.32950e13	−0.846361
$857$	4.58334e12	0.290248	0.145124	−	0.989414i	$-0.453642\pi$
$857$	4.58334e12	0.290248	0.145124	+	0.989414i	$0.453642\pi$
$858$	0	0
$859$	1.34992e13	0.845938	0.422969	−	0.906144i	$-0.360988\pi$
$859$	1.34992e13	0.845938	0.422969	+	0.906144i	$0.360988\pi$
$860$	−1.55609e11	−0.00970047
$861$	0	0
$862$	−1.95767e13	−1.20769
$863$	−1.87111e13	−1.14829	−0.574144	−	0.818754i	$-0.694665\pi$
$863$	−1.87111e13	−1.14829	−0.574144	+	0.818754i	$0.694665\pi$
$864$	0	0
$865$	−3.37932e12	−0.205238
$866$	−1.20781e13	−0.729738
$867$	0	0
$868$	4.92056e12	0.294222
$869$	−8.22981e12	−0.489554
$870$	0	0
$871$	−1.19259e13	−0.702115
$872$	1.87483e13	1.09809
$873$	0	0
$874$	2.62556e13	1.52202
$875$	−4.15385e12	−0.239560
$876$	0	0
$877$	−2.55346e13	−1.45757	−0.728786	−	0.684741i	$-0.759915\pi$
$877$	−2.55346e13	−1.45757	−0.728786	+	0.684741i	$0.759915\pi$
$878$	4.98593e12	0.283153
$879$	0	0
$880$	−2.03829e12	−0.114576
$881$	−3.99929e12	−0.223662	−0.111831	−	0.993727i	$-0.535671\pi$
$881$	−3.99929e12	−0.223662	−0.111831	+	0.993727i	$0.535671\pi$
$882$	0	0
$883$	−1.35158e12	−0.0748204	−0.0374102	−	0.999300i	$-0.511911\pi$
$883$	−1.35158e12	−0.0748204	−0.0374102	+	0.999300i	$0.511911\pi$
$884$	4.30105e12	0.236886
$885$	0	0
$886$	−5.83445e12	−0.318089
$887$	1.75151e13	0.950074	0.475037	−	0.879966i	$-0.342435\pi$
$887$	1.75151e13	0.950074	0.475037	+	0.879966i	$0.342435\pi$
$888$	0	0
$889$	−7.38168e12	−0.396367
$890$	−1.63101e12	−0.0871365
$891$	0	0
$892$	−2.10143e12	−0.111140
$893$	3.23391e13	1.70175
$894$	0	0
$895$	4.90208e12	0.255374
$896$	−1.72591e12	−0.0894604
$897$	0	0
$898$	−1.66245e13	−0.853111
$899$	2.76609e13	1.41237
$900$	0	0
$901$	3.67935e12	0.185999
$902$	1.31634e13	0.662123
$903$	0	0
$904$	−3.03391e13	−1.51093
$905$	4.72814e12	0.234300
$906$	0	0
$907$	3.20478e13	1.57241	0.786204	−	0.617967i	$-0.212044\pi$
$907$	3.20478e13	1.57241	0.786204	+	0.617967i	$0.212044\pi$
$908$	2.87920e12	0.140568
$909$	0	0
$910$	8.81153e11	0.0425956
$911$	−3.17963e13	−1.52948	−0.764740	−	0.644340i	$-0.777132\pi$
$911$	−3.17963e13	−1.52948	−0.764740	+	0.644340i	$0.777132\pi$
$912$	0	0
$913$	−2.54633e13	−1.21282
$914$	1.94287e13	0.920846
$915$	0	0
$916$	−2.18682e12	−0.102632
$917$	−1.05953e13	−0.494824
$918$	0	0
$919$	6.46550e12	0.299008	0.149504	−	0.988761i	$-0.452232\pi$
$919$	6.46550e12	0.299008	0.149504	+	0.988761i	$0.452232\pi$
$920$	−4.06098e12	−0.186890
$921$	0	0
$922$	−9.02438e12	−0.411271
$923$	−3.00228e12	−0.136158
$924$	0	0
$925$	3.02751e13	1.35972
$926$	−2.27743e13	−1.01788
$927$	0	0
$928$	2.01713e13	0.892829
$929$	−3.58746e12	−0.158022	−0.0790109	−	0.996874i	$-0.525176\pi$
$929$	−3.58746e12	−0.158022	−0.0790109	+	0.996874i	$0.525176\pi$
$930$	0	0
$931$	2.15439e13	0.939831
$932$	−1.95928e12	−0.0850598
$933$	0	0
$934$	−3.02526e13	−1.30077
$935$	−7.87563e12	−0.337002
$936$	0	0
$937$	4.03654e13	1.71073	0.855364	−	0.518027i	$-0.173333\pi$
$937$	4.03654e13	1.71073	0.855364	+	0.518027i	$0.173333\pi$
$938$	2.12227e13	0.895135
$939$	0	0
$940$	−1.35823e12	−0.0567413
$941$	1.34172e13	0.557840	0.278920	−	0.960314i	$-0.410023\pi$
$941$	1.34172e13	0.557840	0.278920	+	0.960314i	$0.410023\pi$
$942$	0	0
$943$	1.48723e13	0.612456
$944$	1.38393e13	0.567205
$945$	0	0
$946$	4.09091e12	0.166077
$947$	8.00627e12	0.323486	0.161743	−	0.986833i	$-0.448288\pi$
$947$	8.00627e12	0.323486	0.161743	+	0.986833i	$0.448288\pi$
$948$	0	0
$949$	−1.82786e13	−0.731552
$950$	3.68266e13	1.46692
$951$	0	0
$952$	−2.81870e13	−1.11220
$953$	2.74035e13	1.07619	0.538094	−	0.842885i	$-0.319145\pi$
$953$	2.74035e13	1.07619	0.538094	+	0.842885i	$0.319145\pi$
$954$	0	0
$955$	−4.62108e12	−0.179775
$956$	7.08614e12	0.274378
$957$	0	0
$958$	2.41515e13	0.926402
$959$	2.20447e13	0.841628
$960$	0	0
$961$	6.02571e12	0.227904
$962$	−1.30371e13	−0.490788
$963$	0	0
$964$	−9.23024e12	−0.344244
$965$	−5.82650e12	−0.216289
$966$	0	0
$967$	−1.14021e13	−0.419341	−0.209671	−	0.977772i	$-0.567239\pi$
$967$	−1.14021e13	−0.419341	−0.209671	+	0.977772i	$0.567239\pi$
$968$	−2.64578e13	−0.968534
$969$	0	0
$970$	2.53580e12	0.0919692
$971$	−3.11540e13	−1.12467	−0.562337	−	0.826908i	$-0.690098\pi$
$971$	−3.11540e13	−1.12467	−0.562337	+	0.826908i	$0.690098\pi$
$972$	0	0
$973$	−1.76269e13	−0.630475
$974$	7.44682e12	0.265128
$975$	0	0
$976$	−2.55380e13	−0.900872
$977$	4.42114e13	1.55242	0.776209	−	0.630475i	$-0.217140\pi$
$977$	4.42114e13	1.55242	0.776209	+	0.630475i	$0.217140\pi$
$978$	0	0
$979$	−2.54824e13	−0.886582
$980$	−9.04836e11	−0.0313367
$981$	0	0
$982$	−4.50594e12	−0.154626
$983$	−1.16477e13	−0.397877	−0.198939	−	0.980012i	$-0.563749\pi$
$983$	−1.16477e13	−0.397877	−0.198939	+	0.980012i	$0.563749\pi$
$984$	0	0
$985$	−2.92079e12	−0.0988639
$986$	−4.30267e13	−1.44975
$987$	0	0
$988$	9.42452e12	0.314668
$989$	4.62199e12	0.153619
$990$	0	0
$991$	4.19672e12	0.138222	0.0691112	−	0.997609i	$-0.477984\pi$
$991$	4.19672e12	0.138222	0.0691112	+	0.997609i	$0.477984\pi$
$992$	2.36749e13	0.776222
$993$	0	0
$994$	5.34273e12	0.173590
$995$	5.07929e12	0.164285
$996$	0	0
$997$	3.39392e13	1.08786	0.543930	−	0.839131i	$-0.316936\pi$
$997$	3.39392e13	1.08786	0.543930	+	0.839131i	$0.316936\pi$
$998$	−2.13024e13	−0.679737
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.10.a.c.1.10		15
3.2	odd	2		43.10.a.a.1.6	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.6	✓	15	3.2	odd	2
387.10.a.c.1.10		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)

\(f(q)\)	\(=\)	\(q+17.9205 q^{2} -190.855 q^{4} -238.484 q^{5} -4524.82 q^{7} -12595.5 q^{8} +O(q^{10})\)	\(q+17.9205 q^{2} -190.855 q^{4} -238.484 q^{5} -4524.82 q^{7} -12595.5 q^{8} -4273.75 q^{10} -66772.1 q^{11} +45566.0 q^{13} -81087.1 q^{14} -128001. q^{16} -494574. q^{17} -1.08372e6 q^{19} +45515.8 q^{20} -1.19659e6 q^{22} -1.35193e6 q^{23} -1.89625e6 q^{25} +816566. q^{26} +863584. q^{28} +4.85463e6 q^{29} +5.69784e6 q^{31} +4.15507e6 q^{32} -8.86302e6 q^{34} +1.07910e6 q^{35} -1.59658e7 q^{37} -1.94208e7 q^{38} +3.00383e6 q^{40} -1.10007e7 q^{41} -3.41880e6 q^{43} +1.27438e7 q^{44} -2.42274e7 q^{46} -2.98409e7 q^{47} -1.98796e7 q^{49} -3.39818e7 q^{50} -8.69648e6 q^{52} -7.43943e6 q^{53} +1.59241e7 q^{55} +5.69925e7 q^{56} +8.69975e7 q^{58} -1.08119e8 q^{59} +1.99515e8 q^{61} +1.02108e8 q^{62} +1.39997e8 q^{64} -1.08667e7 q^{65} -2.61727e8 q^{67} +9.43918e7 q^{68} +1.93380e7 q^{70} -6.58887e7 q^{71} -4.01146e8 q^{73} -2.86115e8 q^{74} +2.06832e8 q^{76} +3.02132e8 q^{77} +1.23252e8 q^{79} +3.05261e7 q^{80} -1.97139e8 q^{82} +3.81346e8 q^{83} +1.17948e8 q^{85} -6.12667e7 q^{86} +8.41030e8 q^{88} +3.81633e8 q^{89} -2.06178e8 q^{91} +2.58023e8 q^{92} -5.34765e8 q^{94} +2.58449e8 q^{95} -5.93343e8 q^{97} -3.56253e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) \) 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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