LMFDB - Embedded newform 387.10.a.c.1.15

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			1.15
Root			$40.4171$ 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)

$f(q)$	$=$	$q+42.4171 q^{2} +1287.21 q^{4} -267.050 q^{5} +1084.23 q^{7} +32882.2 q^{8} +O(q^{10})$	\(q+42.4171 q^{2} +1287.21 q^{4} -267.050 q^{5} +1084.23 q^{7} +32882.2 q^{8} -11327.5 q^{10} +49756.6 q^{11} +90530.0 q^{13} +45990.0 q^{14} +735714. q^{16} -139514. q^{17} -189921. q^{19} -343749. q^{20} +2.11053e6 q^{22} +94945.1 q^{23} -1.88181e6 q^{25} +3.84002e6 q^{26} +1.39564e6 q^{28} +4.15457e6 q^{29} +7.48504e6 q^{31} +1.43712e7 q^{32} -5.91779e6 q^{34} -289544. q^{35} +3.13035e6 q^{37} -8.05590e6 q^{38} -8.78117e6 q^{40} +7.85257e6 q^{41} -3.41880e6 q^{43} +6.40472e7 q^{44} +4.02729e6 q^{46} +2.99064e7 q^{47} -3.91780e7 q^{49} -7.98209e7 q^{50} +1.16531e8 q^{52} -2.07014e7 q^{53} -1.32875e7 q^{55} +3.56519e7 q^{56} +1.76225e8 q^{58} +1.16826e8 q^{59} -1.04732e8 q^{61} +3.17494e8 q^{62} +2.32899e8 q^{64} -2.41760e7 q^{65} -1.64575e8 q^{67} -1.79584e8 q^{68} -1.22816e7 q^{70} +8.20184e7 q^{71} -3.51380e8 q^{73} +1.32780e8 q^{74} -2.44468e8 q^{76} +5.39478e7 q^{77} +5.29284e8 q^{79} -1.96472e8 q^{80} +3.33083e8 q^{82} +7.19804e8 q^{83} +3.72572e7 q^{85} -1.45016e8 q^{86} +1.63611e9 q^{88} -6.64822e8 q^{89} +9.81556e7 q^{91} +1.22214e8 q^{92} +1.26854e9 q^{94} +5.07183e7 q^{95} +3.05873e8 q^{97} -1.66182e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	42.4171	1.87459	0.937294	−	0.348539i	$-0.113322\pi$
$2$	42.4171	1.87459	0.937294	+	0.348539i	$0.113322\pi$
$3$	0	0
$3$	0	0
$4$	1287.21	2.51408
$5$	−267.050	−0.191085	−0.0955426	−	0.995425i	$-0.530459\pi$
$5$	−267.050	−0.191085	−0.0955426	+	0.995425i	$0.530459\pi$
$6$	0	0
$7$	1084.23	0.170680	0.0853398	−	0.996352i	$-0.472802\pi$
$7$	1084.23	0.170680	0.0853398	+	0.996352i	$0.472802\pi$
$8$	32882.2	2.83828
$9$	0	0
$10$	−11327.5	−0.358206
$11$	49756.6	1.02467	0.512335	−	0.858786i	$-0.328781\pi$
$11$	49756.6	1.02467	0.512335	+	0.858786i	$0.328781\pi$
$12$	0	0
$13$	90530.0	0.879118	0.439559	−	0.898214i	$-0.355135\pi$
$13$	90530.0	0.879118	0.439559	+	0.898214i	$0.355135\pi$
$14$	45990.0	0.319954
$15$	0	0
$16$	735714.	2.80653
$17$	−139514.	−0.405134	−0.202567	−	0.979268i	$-0.564928\pi$
$17$	−139514.	−0.405134	−0.202567	+	0.979268i	$0.564928\pi$
$18$	0	0
$19$	−189921.	−0.334335	−0.167168	−	0.985929i	$-0.553462\pi$
$19$	−189921.	−0.334335	−0.167168	+	0.985929i	$0.553462\pi$
$20$	−343749.	−0.480404
$21$	0	0
$22$	2.11053e6	1.92083
$23$	94945.1	0.0707452	0.0353726	−	0.999374i	$-0.488738\pi$
$23$	94945.1	0.0707452	0.0353726	+	0.999374i	$0.488738\pi$
$24$	0	0
$25$	−1.88181e6	−0.963486
$26$	3.84002e6	1.64798
$27$	0	0
$28$	1.39564e6	0.429103
$29$	4.15457e6	1.09077	0.545387	−	0.838184i	$-0.316383\pi$
$29$	4.15457e6	1.09077	0.545387	+	0.838184i	$0.316383\pi$
$30$	0	0
$31$	7.48504e6	1.45568	0.727841	−	0.685745i	$-0.240524\pi$
$31$	7.48504e6	1.45568	0.727841	+	0.685745i	$0.240524\pi$
$32$	1.43712e7	2.42280
$33$	0	0
$34$	−5.91779e6	−0.759460
$35$	−289544.	−0.0326143
$36$	0	0
$37$	3.13035e6	0.274590	0.137295	−	0.990530i	$-0.456159\pi$
$37$	3.13035e6	0.274590	0.137295	+	0.990530i	$0.456159\pi$
$38$	−8.05590e6	−0.626741
$39$	0	0
$40$	−8.78117e6	−0.542353
$41$	7.85257e6	0.433995	0.216997	−	0.976172i	$-0.430374\pi$
$41$	7.85257e6	0.433995	0.216997	+	0.976172i	$0.430374\pi$
$42$	0	0
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	6.40472e7	2.57610
$45$	0	0
$46$	4.02729e6	0.132618
$47$	2.99064e7	0.893973	0.446986	−	0.894541i	$-0.352497\pi$
$47$	2.99064e7	0.893973	0.446986	+	0.894541i	$0.352497\pi$
$48$	0	0
$49$	−3.91780e7	−0.970868
$50$	−7.98209e7	−1.80614
$51$	0	0
$52$	1.16531e8	2.21017
$53$	−2.07014e7	−0.360378	−0.180189	−	0.983632i	$-0.557671\pi$
$53$	−2.07014e7	−0.360378	−0.180189	+	0.983632i	$0.557671\pi$
$54$	0	0
$55$	−1.32875e7	−0.195799
$56$	3.56519e7	0.484437
$57$	0	0
$58$	1.76225e8	2.04475
$59$	1.16826e8	1.25518	0.627590	−	0.778544i	$-0.284041\pi$
$59$	1.16826e8	1.25518	0.627590	+	0.778544i	$0.284041\pi$
$60$	0	0
$61$	−1.04732e8	−0.968486	−0.484243	−	0.874934i	$-0.660905\pi$
$61$	−1.04732e8	−0.968486	−0.484243	+	0.874934i	$0.660905\pi$
$62$	3.17494e8	2.72881
$63$	0	0
$64$	2.32899e8	1.73523
$65$	−2.41760e7	−0.167986
$66$	0	0
$67$	−1.64575e8	−0.997764	−0.498882	−	0.866670i	$-0.666256\pi$
$67$	−1.64575e8	−0.997764	−0.498882	+	0.866670i	$0.666256\pi$
$68$	−1.79584e8	−1.01854
$69$	0	0
$70$	−1.22816e7	−0.0611385
$71$	8.20184e7	0.383044	0.191522	−	0.981488i	$-0.438658\pi$
$71$	8.20184e7	0.383044	0.191522	+	0.981488i	$0.438658\pi$
$72$	0	0
$73$	−3.51380e8	−1.44819	−0.724093	−	0.689702i	$-0.757741\pi$
$73$	−3.51380e8	−1.44819	−0.724093	+	0.689702i	$0.757741\pi$
$74$	1.32780e8	0.514744
$75$	0	0
$76$	−2.44468e8	−0.840546
$77$	5.39478e7	0.174890
$78$	0	0
$79$	5.29284e8	1.52886	0.764428	−	0.644709i	$-0.223022\pi$
$79$	5.29284e8	1.52886	0.764428	+	0.644709i	$0.223022\pi$
$80$	−1.96472e8	−0.536285
$81$	0	0
$82$	3.33083e8	0.813561
$83$	7.19804e8	1.66480	0.832402	−	0.554172i	$-0.186965\pi$
$83$	7.19804e8	1.66480	0.832402	+	0.554172i	$0.186965\pi$
$84$	0	0
$85$	3.72572e7	0.0774151
$86$	−1.45016e8	−0.285872
$87$	0	0
$88$	1.63611e9	2.90830
$89$	−6.64822e8	−1.12318	−0.561591	−	0.827415i	$-0.689811\pi$
$89$	−6.64822e8	−1.12318	−0.561591	+	0.827415i	$0.689811\pi$
$90$	0	0
$91$	9.81556e7	0.150048
$92$	1.22214e8	0.177859
$93$	0	0
$94$	1.26854e9	1.67583
$95$	5.07183e7	0.0638865
$96$	0	0
$97$	3.05873e8	0.350807	0.175403	−	0.984497i	$-0.443877\pi$
$97$	3.05873e8	0.350807	0.175403	+	0.984497i	$0.443877\pi$
$98$	−1.66182e9	−1.81998
$99$	0	0
$100$	−2.42228e9	−2.42228
$101$	1.49507e9	1.42960	0.714800	−	0.699328i	$-0.246518\pi$
$101$	1.49507e9	1.42960	0.714800	+	0.699328i	$0.246518\pi$
$102$	0	0
$103$	8.69690e8	0.761372	0.380686	−	0.924704i	$-0.375688\pi$
$103$	8.69690e8	0.761372	0.380686	+	0.924704i	$0.375688\pi$
$104$	2.97682e9	2.49518
$105$	0	0
$106$	−8.78094e8	−0.675561
$107$	1.70820e9	1.25983	0.629915	−	0.776664i	$-0.283090\pi$
$107$	1.70820e9	1.25983	0.629915	+	0.776664i	$0.283090\pi$
$108$	0	0
$109$	1.88987e9	1.28237	0.641183	−	0.767388i	$-0.278444\pi$
$109$	1.88987e9	1.28237	0.641183	+	0.767388i	$0.278444\pi$
$110$	−5.63617e8	−0.367043
$111$	0	0
$112$	7.97686e8	0.479017
$113$	1.37931e9	0.795809	0.397904	−	0.917427i	$-0.369738\pi$
$113$	1.37931e9	0.795809	0.397904	+	0.917427i	$0.369738\pi$
$114$	0	0
$115$	−2.53550e7	−0.0135184
$116$	5.34780e9	2.74230
$117$	0	0
$118$	4.95543e9	2.35295
$119$	−1.51266e8	−0.0691481
$120$	0	0
$121$	1.17776e8	0.0499485
$122$	−4.44241e9	−1.81551
$123$	0	0
$124$	9.63482e9	3.65971
$125$	1.02412e9	0.375193
$126$	0	0
$127$	−2.53906e9	−0.866078	−0.433039	−	0.901375i	$-0.642559\pi$
$127$	−2.53906e9	−0.866078	−0.433039	+	0.901375i	$0.642559\pi$
$128$	2.52083e9	0.830039
$129$	0	0
$130$	−1.02548e9	−0.314905
$131$	−3.77650e9	−1.12039	−0.560195	−	0.828361i	$-0.689274\pi$
$131$	−3.77650e9	−1.12039	−0.560195	+	0.828361i	$0.689274\pi$
$132$	0	0
$133$	−2.05919e8	−0.0570642
$134$	−6.98080e9	−1.87040
$135$	0	0
$136$	−4.58753e9	−1.14988
$137$	1.89296e9	0.459091	0.229545	−	0.973298i	$-0.426276\pi$
$137$	1.89296e9	0.459091	0.229545	+	0.973298i	$0.426276\pi$
$138$	0	0
$139$	4.91789e9	1.11741	0.558705	−	0.829367i	$-0.311298\pi$
$139$	4.91789e9	1.11741	0.558705	+	0.829367i	$0.311298\pi$
$140$	−3.72704e8	−0.0819951
$141$	0	0
$142$	3.47898e9	0.718050
$143$	4.50447e9	0.900806
$144$	0	0
$145$	−1.10948e9	−0.208431
$146$	−1.49045e10	−2.71475
$147$	0	0
$148$	4.02942e9	0.690343
$149$	−1.00447e10	−1.66955	−0.834773	−	0.550594i	$-0.814401\pi$
$149$	−1.00447e10	−1.66955	−0.834773	+	0.550594i	$0.814401\pi$
$150$	0	0
$151$	6.32434e8	0.0989963	0.0494981	−	0.998774i	$-0.484238\pi$
$151$	6.32434e8	0.0989963	0.0494981	+	0.998774i	$0.484238\pi$
$152$	−6.24501e9	−0.948937
$153$	0	0
$154$	2.28831e9	0.327847
$155$	−1.99888e9	−0.278159
$156$	0	0
$157$	2.92391e9	0.384075	0.192037	−	0.981388i	$-0.438490\pi$
$157$	2.92391e9	0.384075	0.192037	+	0.981388i	$0.438490\pi$
$158$	2.24507e10	2.86598
$159$	0	0
$160$	−3.83782e9	−0.462961
$161$	1.02943e8	0.0120748
$162$	0	0
$163$	−1.56060e10	−1.73160	−0.865800	−	0.500389i	$-0.833190\pi$
$163$	−1.56060e10	−1.73160	−0.865800	+	0.500389i	$0.833190\pi$
$164$	1.01079e10	1.09110
$165$	0	0
$166$	3.05320e10	3.12082
$167$	−1.67291e10	−1.66436	−0.832182	−	0.554502i	$-0.812909\pi$
$167$	−1.67291e10	−1.66436	−0.832182	+	0.554502i	$0.812909\pi$
$168$	0	0
$169$	−2.40883e9	−0.227151
$170$	1.58034e9	0.145121
$171$	0	0
$172$	−4.40071e9	−0.383394
$173$	−1.01069e10	−0.857847	−0.428924	−	0.903341i	$-0.641107\pi$
$173$	−1.01069e10	−0.857847	−0.428924	+	0.903341i	$0.641107\pi$
$174$	0	0
$175$	−2.04032e9	−0.164447
$176$	3.66067e10	2.87576
$177$	0	0
$178$	−2.81998e10	−2.10551
$179$	1.86270e10	1.35614	0.678068	−	0.734999i	$-0.262817\pi$
$179$	1.86270e10	1.35614	0.678068	+	0.734999i	$0.262817\pi$
$180$	0	0
$181$	−1.34573e10	−0.931978	−0.465989	−	0.884791i	$-0.654301\pi$
$181$	−1.34573e10	−0.931978	−0.465989	+	0.884791i	$0.654301\pi$
$182$	4.16348e9	0.281277
$183$	0	0
$184$	3.12200e9	0.200795
$185$	−8.35959e8	−0.0524701
$186$	0	0
$187$	−6.94176e9	−0.415129
$188$	3.84959e10	2.24752
$189$	0	0
$190$	2.15132e9	0.119761
$191$	2.59444e10	1.41056	0.705282	−	0.708926i	$-0.250820\pi$
$191$	2.59444e10	1.41056	0.705282	+	0.708926i	$0.250820\pi$
$192$	0	0
$193$	3.54739e10	1.84035	0.920176	−	0.391505i	$-0.128045\pi$
$193$	3.54739e10	1.84035	0.920176	+	0.391505i	$0.128045\pi$
$194$	1.29742e10	0.657618
$195$	0	0
$196$	−5.04304e10	−2.44084
$197$	−1.96576e10	−0.929894	−0.464947	−	0.885339i	$-0.653927\pi$
$197$	−1.96576e10	−0.929894	−0.464947	+	0.885339i	$0.653927\pi$
$198$	0	0
$199$	1.91082e10	0.863737	0.431869	−	0.901937i	$-0.357854\pi$
$199$	1.91082e10	0.863737	0.431869	+	0.901937i	$0.357854\pi$
$200$	−6.18780e10	−2.73465
$201$	0	0
$202$	6.34164e10	2.67991
$203$	4.50452e9	0.186173
$204$	0	0
$205$	−2.09702e9	−0.0829299
$206$	3.68897e10	1.42726
$207$	0	0
$208$	6.66042e10	2.46727
$209$	−9.44983e9	−0.342583
$210$	0	0
$211$	−2.94149e9	−0.102164	−0.0510818	−	0.998694i	$-0.516267\pi$
$211$	−2.94149e9	−0.102164	−0.0510818	+	0.998694i	$0.516267\pi$
$212$	−2.66471e10	−0.906020
$213$	0	0
$214$	7.24570e10	2.36166
$215$	9.12989e8	0.0291402
$216$	0	0
$217$	8.11554e9	0.248455
$218$	8.01627e10	2.40391
$219$	0	0
$220$	−1.71038e10	−0.492255
$221$	−1.26302e10	−0.356161
$222$	0	0
$223$	−4.30635e7	−0.00116610	−0.000583052	−	1.00000i	$-0.500186\pi$
$223$	−4.30635e7	−0.00116610	−0.000583052		1.00000i	$0.500186\pi$
$224$	1.55817e10	0.413523
$225$	0	0
$226$	5.85063e10	1.49181
$227$	5.87731e10	1.46914	0.734569	−	0.678534i	$-0.237385\pi$
$227$	5.87731e10	1.46914	0.734569	+	0.678534i	$0.237385\pi$
$228$	0	0
$229$	−4.67848e9	−0.112420	−0.0562101	−	0.998419i	$-0.517902\pi$
$229$	−4.67848e9	−0.112420	−0.0562101	+	0.998419i	$0.517902\pi$
$230$	−1.07549e9	−0.0253414
$231$	0	0
$232$	1.36611e11	3.09592
$233$	6.22080e10	1.38275	0.691377	−	0.722494i	$-0.257004\pi$
$233$	6.22080e10	1.38275	0.691377	+	0.722494i	$0.257004\pi$
$234$	0	0
$235$	−7.98650e9	−0.170825
$236$	1.50380e11	3.15563
$237$	0	0
$238$	−6.41627e9	−0.129624
$239$	−8.17154e10	−1.61999	−0.809997	−	0.586434i	$-0.800531\pi$
$239$	−8.17154e10	−1.61999	−0.809997	+	0.586434i	$0.800531\pi$
$240$	0	0
$241$	−7.26673e9	−0.138759	−0.0693796	−	0.997590i	$-0.522102\pi$
$241$	−7.26673e9	−0.138759	−0.0693796	+	0.997590i	$0.522102\pi$
$242$	4.99571e9	0.0936328
$243$	0	0
$244$	−1.34812e11	−2.43485
$245$	1.04625e10	0.185519
$246$	0	0
$247$	−1.71935e10	−0.293920
$248$	2.46124e11	4.13164
$249$	0	0
$250$	4.34401e10	0.703333
$251$	−6.85052e10	−1.08941	−0.544706	−	0.838627i	$-0.683359\pi$
$251$	−6.85052e10	−1.08941	−0.544706	+	0.838627i	$0.683359\pi$
$252$	0	0
$253$	4.72415e9	0.0724905
$254$	−1.07700e11	−1.62354
$255$	0	0
$256$	−1.23178e10	−0.179247
$257$	−1.40768e10	−0.201281	−0.100641	−	0.994923i	$-0.532089\pi$
$257$	−1.40768e10	−0.201281	−0.100641	+	0.994923i	$0.532089\pi$
$258$	0	0
$259$	3.39403e9	0.0468670
$260$	−3.11196e10	−0.422332
$261$	0	0
$262$	−1.60188e11	−2.10027
$263$	−4.75236e10	−0.612503	−0.306252	−	0.951951i	$-0.599075\pi$
$263$	−4.75236e10	−0.612503	−0.306252	+	0.951951i	$0.599075\pi$
$264$	0	0
$265$	5.52830e9	0.0688629
$266$	−8.73448e9	−0.106972
$267$	0	0
$268$	−2.11843e11	−2.50846
$269$	−3.74937e10	−0.436589	−0.218294	−	0.975883i	$-0.570049\pi$
$269$	−3.74937e10	−0.436589	−0.218294	+	0.975883i	$0.570049\pi$
$270$	0	0
$271$	9.32440e10	1.05017	0.525084	−	0.851050i	$-0.324034\pi$
$271$	9.32440e10	1.05017	0.525084	+	0.851050i	$0.324034\pi$
$272$	−1.02643e11	−1.13702
$273$	0	0
$274$	8.02938e10	0.860606
$275$	−9.36325e10	−0.987256
$276$	0	0
$277$	−1.14756e11	−1.17116	−0.585582	−	0.810614i	$-0.699134\pi$
$277$	−1.14756e11	−1.17116	−0.585582	+	0.810614i	$0.699134\pi$
$278$	2.08603e11	2.09468
$279$	0	0
$280$	−9.52084e9	−0.0925686
$281$	−1.15044e11	−1.10074	−0.550372	−	0.834920i	$-0.685514\pi$
$281$	−1.15044e11	−1.10074	−0.550372	+	0.834920i	$0.685514\pi$
$282$	0	0
$283$	−3.96421e10	−0.367382	−0.183691	−	0.982984i	$-0.558805\pi$
$283$	−3.96421e10	−0.367382	−0.183691	+	0.982984i	$0.558805\pi$
$284$	1.05575e11	0.963004
$285$	0	0
$286$	1.91066e11	1.68864
$287$	8.51402e9	0.0740740
$288$	0	0
$289$	−9.91236e10	−0.835866
$290$	−4.70607e10	−0.390722
$291$	0	0
$292$	−4.52300e11	−3.64086
$293$	−1.46620e11	−1.16222	−0.581109	−	0.813825i	$-0.697381\pi$
$293$	−1.46620e11	−1.16222	−0.581109	+	0.813825i	$0.697381\pi$
$294$	0	0
$295$	−3.11984e10	−0.239846
$296$	1.02933e11	0.779364
$297$	0	0
$298$	−4.26067e11	−3.12971
$299$	8.59537e9	0.0621934
$300$	0	0
$301$	−3.70678e9	−0.0260284
$302$	2.68260e10	0.185577
$303$	0	0
$304$	−1.39728e11	−0.938320
$305$	2.79685e10	0.185063
$306$	0	0
$307$	2.04547e11	1.31423	0.657114	−	0.753792i	$-0.271777\pi$
$307$	2.04547e11	1.31423	0.657114	+	0.753792i	$0.271777\pi$
$308$	6.94422e10	0.439688
$309$	0	0
$310$	−8.47866e10	−0.521434
$311$	−2.05452e11	−1.24534	−0.622671	−	0.782483i	$-0.713953\pi$
$311$	−2.05452e11	−1.24534	−0.622671	+	0.782483i	$0.713953\pi$
$312$	0	0
$313$	2.06361e11	1.21528	0.607642	−	0.794211i	$-0.292116\pi$
$313$	2.06361e11	1.21528	0.607642	+	0.794211i	$0.292116\pi$
$314$	1.24024e11	0.719982
$315$	0	0
$316$	6.81299e11	3.84367
$317$	2.13970e10	0.119011	0.0595053	−	0.998228i	$-0.481048\pi$
$317$	2.13970e10	0.119011	0.0595053	+	0.998228i	$0.481048\pi$
$318$	0	0
$319$	2.06717e11	1.11768
$320$	−6.21955e10	−0.331577
$321$	0	0
$322$	4.36653e9	0.0226352
$323$	2.64967e10	0.135450
$324$	0	0
$325$	−1.70360e11	−0.847018
$326$	−6.61962e11	−3.24604
$327$	0	0
$328$	2.58209e11	1.23180
$329$	3.24256e10	0.152583
$330$	0	0
$331$	1.60601e11	0.735396	0.367698	−	0.929945i	$-0.380146\pi$
$331$	1.60601e11	0.735396	0.367698	+	0.929945i	$0.380146\pi$
$332$	9.26539e11	4.18545
$333$	0	0
$334$	−7.09600e11	−3.12000
$335$	4.39498e10	0.190658
$336$	0	0
$337$	−3.08563e11	−1.30320	−0.651598	−	0.758564i	$-0.725901\pi$
$337$	−3.08563e11	−1.30320	−0.651598	+	0.758564i	$0.725901\pi$
$338$	−1.02175e11	−0.425815
$339$	0	0
$340$	4.79579e10	0.194628
$341$	3.72431e11	1.49159
$342$	0	0
$343$	−8.62309e10	−0.336387
$344$	−1.12418e11	−0.432834
$345$	0	0
$346$	−4.28705e11	−1.60811
$347$	−1.34264e11	−0.497138	−0.248569	−	0.968614i	$-0.579960\pi$
$347$	−1.34264e11	−0.497138	−0.248569	+	0.968614i	$0.579960\pi$
$348$	0	0
$349$	2.70503e11	0.976016	0.488008	−	0.872839i	$-0.337724\pi$
$349$	2.70503e11	0.976016	0.488008	+	0.872839i	$0.337724\pi$
$350$	−8.65445e10	−0.308271
$351$	0	0
$352$	7.15062e11	2.48257
$353$	−1.67866e10	−0.0575408	−0.0287704	−	0.999586i	$-0.509159\pi$
$353$	−1.67866e10	−0.0575408	−0.0287704	+	0.999586i	$0.509159\pi$
$354$	0	0
$355$	−2.19030e10	−0.0731940
$356$	−8.55766e11	−2.82377
$357$	0	0
$358$	7.90102e11	2.54220
$359$	−4.80875e11	−1.52794	−0.763972	−	0.645250i	$-0.776753\pi$
$359$	−4.80875e11	−1.52794	−0.763972	+	0.645250i	$0.776753\pi$
$360$	0	0
$361$	−2.86618e11	−0.888220
$362$	−5.70821e11	−1.74707
$363$	0	0
$364$	1.26347e11	0.377232
$365$	9.38359e10	0.276727
$366$	0	0
$367$	−5.91797e11	−1.70285	−0.851424	−	0.524479i	$-0.824260\pi$
$367$	−5.91797e11	−1.70285	−0.851424	+	0.524479i	$0.824260\pi$
$368$	6.98524e10	0.198548
$369$	0	0
$370$	−3.54589e10	−0.0983599
$371$	−2.24452e10	−0.0615092
$372$	0	0
$373$	−5.20908e11	−1.39338	−0.696692	−	0.717370i	$-0.745346\pi$
$373$	−5.20908e11	−1.39338	−0.696692	+	0.717370i	$0.745346\pi$
$374$	−2.94450e11	−0.778195
$375$	0	0
$376$	9.83388e11	2.53735
$377$	3.76113e11	0.958919
$378$	0	0
$379$	−9.96613e10	−0.248113	−0.124057	−	0.992275i	$-0.539590\pi$
$379$	−9.96613e10	−0.248113	−0.124057	+	0.992275i	$0.539590\pi$
$380$	6.52852e10	0.160616
$381$	0	0
$382$	1.10049e12	2.64423
$383$	3.57401e11	0.848714	0.424357	−	0.905495i	$-0.360500\pi$
$383$	3.57401e11	0.848714	0.424357	+	0.905495i	$0.360500\pi$
$384$	0	0
$385$	−1.44067e10	−0.0334189
$386$	1.50470e12	3.44990
$387$	0	0
$388$	3.93722e11	0.881956
$389$	4.67526e11	1.03522	0.517610	−	0.855617i	$-0.326822\pi$
$389$	4.67526e11	1.03522	0.517610	+	0.855617i	$0.326822\pi$
$390$	0	0
$391$	−1.32462e10	−0.0286613
$392$	−1.28826e12	−2.75560
$393$	0	0
$394$	−8.33820e11	−1.74317
$395$	−1.41345e11	−0.292142
$396$	0	0
$397$	−9.97116e10	−0.201460	−0.100730	−	0.994914i	$-0.532118\pi$
$397$	−9.97116e10	−0.201460	−0.100730	+	0.994914i	$0.532118\pi$
$398$	8.10516e11	1.61915
$399$	0	0
$400$	−1.38447e12	−2.70405
$401$	4.32588e11	0.835459	0.417729	−	0.908572i	$-0.362826\pi$
$401$	4.32588e11	0.835459	0.417729	+	0.908572i	$0.362826\pi$
$402$	0	0
$403$	6.77621e11	1.27972
$404$	1.92447e12	3.59413
$405$	0	0
$406$	1.91069e11	0.348998
$407$	1.55756e11	0.281364
$408$	0	0
$409$	−8.08953e11	−1.42945	−0.714724	−	0.699406i	$-0.753448\pi$
$409$	−8.08953e11	−1.42945	−0.714724	+	0.699406i	$0.753448\pi$
$410$	−8.89497e10	−0.155459
$411$	0	0
$412$	1.11947e12	1.91415
$413$	1.26667e11	0.214234
$414$	0	0
$415$	−1.92223e11	−0.318119
$416$	1.30102e12	2.12993
$417$	0	0
$418$	−4.00835e11	−0.642202
$419$	−7.28742e11	−1.15508	−0.577538	−	0.816364i	$-0.695986\pi$
$419$	−7.28742e11	−1.15508	−0.577538	+	0.816364i	$0.695986\pi$
$420$	0	0
$421$	−6.26279e11	−0.971625	−0.485812	−	0.874063i	$-0.661476\pi$
$421$	−6.26279e11	−0.971625	−0.485812	+	0.874063i	$0.661476\pi$
$422$	−1.24769e11	−0.191515
$423$	0	0
$424$	−6.80707e11	−1.02285
$425$	2.62539e11	0.390341
$426$	0	0
$427$	−1.13553e11	−0.165301
$428$	2.19881e12	3.16732
$429$	0	0
$430$	3.87264e10	0.0546259
$431$	−9.36909e11	−1.30782	−0.653912	−	0.756570i	$-0.726873\pi$
$431$	−9.36909e11	−1.30782	−0.653912	+	0.756570i	$0.726873\pi$
$432$	0	0
$433$	−2.08675e11	−0.285282	−0.142641	−	0.989774i	$-0.545560\pi$
$433$	−2.08675e11	−0.285282	−0.142641	+	0.989774i	$0.545560\pi$
$434$	3.44237e11	0.465752
$435$	0	0
$436$	2.43266e12	3.22397
$437$	−1.80321e10	−0.0236526
$438$	0	0
$439$	4.01235e10	0.0515594	0.0257797	−	0.999668i	$-0.491793\pi$
$439$	4.01235e10	0.0515594	0.0257797	+	0.999668i	$0.491793\pi$
$440$	−4.36921e11	−0.555733
$441$	0	0
$442$	−5.35738e11	−0.667655
$443$	4.49679e11	0.554735	0.277367	−	0.960764i	$-0.410538\pi$
$443$	4.49679e11	0.554735	0.277367	+	0.960764i	$0.410538\pi$
$444$	0	0
$445$	1.77540e11	0.214624
$446$	−1.82663e9	−0.00218597
$447$	0	0
$448$	2.52516e11	0.296168
$449$	−2.85367e11	−0.331357	−0.165678	−	0.986180i	$-0.552981\pi$
$449$	−2.85367e11	−0.331357	−0.165678	+	0.986180i	$0.552981\pi$
$450$	0	0
$451$	3.90717e11	0.444701
$452$	1.77546e12	2.00073
$453$	0	0
$454$	2.49299e12	2.75403
$455$	−2.62124e10	−0.0286719
$456$	0	0
$457$	3.04646e11	0.326718	0.163359	−	0.986567i	$-0.447767\pi$
$457$	3.04646e11	0.326718	0.163359	+	0.986567i	$0.447767\pi$
$458$	−1.98447e11	−0.210742
$459$	0	0
$460$	−3.26373e10	−0.0339863
$461$	−6.14100e11	−0.633265	−0.316632	−	0.948548i	$-0.602552\pi$
$461$	−6.14100e11	−0.633265	−0.316632	+	0.948548i	$0.602552\pi$
$462$	0	0
$463$	−1.91905e11	−0.194076	−0.0970382	−	0.995281i	$-0.530937\pi$
$463$	−1.91905e11	−0.194076	−0.0970382	+	0.995281i	$0.530937\pi$
$464$	3.05657e12	3.06129
$465$	0	0
$466$	2.63868e12	2.59209
$467$	−3.82929e11	−0.372556	−0.186278	−	0.982497i	$-0.559643\pi$
$467$	−3.82929e11	−0.372556	−0.186278	+	0.982497i	$0.559643\pi$
$468$	0	0
$469$	−1.78438e11	−0.170298
$470$	−3.38764e11	−0.320226
$471$	0	0
$472$	3.84150e12	3.56255
$473$	−1.70108e11	−0.156261
$474$	0	0
$475$	3.57395e11	0.322127
$476$	−1.94711e11	−0.173844
$477$	0	0
$478$	−3.46613e12	−3.03682
$479$	1.69714e11	0.147302	0.0736510	−	0.997284i	$-0.476535\pi$
$479$	1.69714e11	0.147302	0.0736510	+	0.997284i	$0.476535\pi$
$480$	0	0
$481$	2.83391e11	0.241397
$482$	−3.08233e11	−0.260117
$483$	0	0
$484$	1.51602e11	0.125575
$485$	−8.16831e10	−0.0670339
$486$	0	0
$487$	2.46356e11	0.198465	0.0992324	−	0.995064i	$-0.468361\pi$
$487$	2.46356e11	0.198465	0.0992324	+	0.995064i	$0.468361\pi$
$488$	−3.44380e12	−2.74884
$489$	0	0
$490$	4.43788e11	0.347771
$491$	−1.01928e12	−0.791458	−0.395729	−	0.918367i	$-0.629508\pi$
$491$	−1.01928e12	−0.791458	−0.395729	+	0.918367i	$0.629508\pi$
$492$	0	0
$493$	−5.79622e11	−0.441910
$494$	−7.29300e11	−0.550979
$495$	0	0
$496$	5.50685e12	4.08541
$497$	8.89271e10	0.0653778
$498$	0	0
$499$	1.06244e12	0.767101	0.383550	−	0.923520i	$-0.374701\pi$
$499$	1.06244e12	0.767101	0.383550	+	0.923520i	$0.374701\pi$
$500$	1.31825e12	0.943266
$501$	0	0
$502$	−2.90579e12	−2.04220
$503$	2.56713e12	1.78810	0.894051	−	0.447965i	$-0.147851\pi$
$503$	2.56713e12	1.78810	0.894051	+	0.447965i	$0.147851\pi$
$504$	0	0
$505$	−3.99257e11	−0.273175
$506$	2.00385e11	0.135890
$507$	0	0
$508$	−3.26831e12	−2.17739
$509$	−2.54412e12	−1.67999	−0.839997	−	0.542590i	$-0.817444\pi$
$509$	−2.54412e12	−1.67999	−0.839997	+	0.542590i	$0.817444\pi$
$510$	0	0
$511$	−3.80978e11	−0.247176
$512$	−1.81315e12	−1.16605
$513$	0	0
$514$	−5.97095e11	−0.377320
$515$	−2.32250e11	−0.145487
$516$	0	0
$517$	1.48804e12	0.916027
$518$	1.43965e11	0.0878563
$519$	0	0
$520$	−7.94959e11	−0.476793
$521$	1.73418e12	1.03116	0.515579	−	0.856842i	$-0.327577\pi$
$521$	1.73418e12	1.03116	0.515579	+	0.856842i	$0.327577\pi$
$522$	0	0
$523$	1.03596e12	0.605457	0.302729	−	0.953077i	$-0.402102\pi$
$523$	1.03596e12	0.605457	0.302729	+	0.953077i	$0.402102\pi$
$524$	−4.86115e12	−2.81675
$525$	0	0
$526$	−2.01581e12	−1.14819
$527$	−1.04427e12	−0.589747
$528$	0	0
$529$	−1.79214e12	−0.994995
$530$	2.34495e11	0.129090
$531$	0	0
$532$	−2.65061e11	−0.143464
$533$	7.10892e11	0.381532
$534$	0	0
$535$	−4.56175e11	−0.240735
$536$	−5.41159e12	−2.83194
$537$	0	0
$538$	−1.59037e12	−0.818424
$539$	−1.94937e12	−0.994820
$540$	0	0
$541$	−2.94842e12	−1.47980	−0.739898	−	0.672719i	$-0.765126\pi$
$541$	−2.94842e12	−1.47980	−0.739898	+	0.672719i	$0.765126\pi$
$542$	3.95514e12	1.96863
$543$	0	0
$544$	−2.00499e12	−0.981559
$545$	−5.04688e11	−0.245041
$546$	0	0
$547$	2.32179e12	1.10887	0.554435	−	0.832227i	$-0.312935\pi$
$547$	2.32179e12	1.10887	0.554435	+	0.832227i	$0.312935\pi$
$548$	2.43663e12	1.15419
$549$	0	0
$550$	−3.97162e12	−1.85070
$551$	−7.89040e11	−0.364684
$552$	0	0
$553$	5.73867e11	0.260944
$554$	−4.86763e12	−2.19545
$555$	0	0
$556$	6.33036e12	2.80926
$557$	−2.16532e12	−0.953176	−0.476588	−	0.879127i	$-0.658127\pi$
$557$	−2.16532e12	−0.953176	−0.476588	+	0.879127i	$0.658127\pi$
$558$	0	0
$559$	−3.09504e11	−0.134064
$560$	−2.13022e11	−0.0915330
$561$	0	0
$562$	−4.87984e12	−2.06344
$563$	1.91225e12	0.802154	0.401077	−	0.916044i	$-0.368636\pi$
$563$	1.91225e12	0.802154	0.401077	+	0.916044i	$0.368636\pi$
$564$	0	0
$565$	−3.68344e11	−0.152067
$566$	−1.68150e12	−0.688690
$567$	0	0
$568$	2.69694e12	1.08719
$569$	−2.85153e12	−1.14044	−0.570220	−	0.821492i	$-0.693142\pi$
$569$	−2.85153e12	−1.14044	−0.570220	+	0.821492i	$0.693142\pi$
$570$	0	0
$571$	−2.16577e12	−0.852608	−0.426304	−	0.904580i	$-0.640185\pi$
$571$	−2.16577e12	−0.852608	−0.426304	+	0.904580i	$0.640185\pi$
$572$	5.79819e12	2.26470
$573$	0	0
$574$	3.61140e11	0.138858
$575$	−1.78669e11	−0.0681621
$576$	0	0
$577$	−2.81611e12	−1.05769	−0.528845	−	0.848718i	$-0.677375\pi$
$577$	−2.81611e12	−1.05769	−0.528845	+	0.848718i	$0.677375\pi$
$578$	−4.20454e12	−1.56691
$579$	0	0
$580$	−1.42813e12	−0.524012
$581$	7.80436e11	0.284148
$582$	0	0
$583$	−1.03003e12	−0.369269
$584$	−1.15541e13	−4.11036
$585$	0	0
$586$	−6.21918e12	−2.17868
$587$	1.61735e12	0.562255	0.281128	−	0.959670i	$-0.409292\pi$
$587$	1.61735e12	0.562255	0.281128	+	0.959670i	$0.409292\pi$
$588$	0	0
$589$	−1.42157e12	−0.486686
$590$	−1.32334e12	−0.449613
$591$	0	0
$592$	2.30304e12	0.770645
$593$	−2.81752e12	−0.935665	−0.467833	−	0.883817i	$-0.654965\pi$
$593$	−2.81752e12	−0.935665	−0.467833	+	0.883817i	$0.654965\pi$
$594$	0	0
$595$	4.03956e10	0.0132132
$596$	−1.29296e13	−4.19738
$597$	0	0
$598$	3.64591e11	0.116587
$599$	−1.84733e12	−0.586305	−0.293152	−	0.956066i	$-0.594704\pi$
$599$	−1.84733e12	−0.586305	−0.293152	+	0.956066i	$0.594704\pi$
$600$	0	0
$601$	1.93095e12	0.603720	0.301860	−	0.953352i	$-0.402392\pi$
$601$	1.93095e12	0.603720	0.301860	+	0.953352i	$0.402392\pi$
$602$	−1.57231e11	−0.0487925
$603$	0	0
$604$	8.14075e11	0.248885
$605$	−3.14520e10	−0.00954441
$606$	0	0
$607$	2.77322e12	0.829155	0.414578	−	0.910014i	$-0.363929\pi$
$607$	2.77322e12	0.829155	0.414578	+	0.910014i	$0.363929\pi$
$608$	−2.72939e12	−0.810027
$609$	0	0
$610$	1.18634e12	0.346918
$611$	2.70743e12	0.785908
$612$	0	0
$613$	−6.12373e12	−1.75164	−0.875819	−	0.482640i	$-0.839678\pi$
$613$	−6.12373e12	−1.75164	−0.875819	+	0.482640i	$0.839678\pi$
$614$	8.67629e12	2.46364
$615$	0	0
$616$	1.77392e12	0.496388
$617$	5.57842e12	1.54963	0.774815	−	0.632188i	$-0.217843\pi$
$617$	5.57842e12	1.54963	0.774815	+	0.632188i	$0.217843\pi$
$618$	0	0
$619$	−1.98413e12	−0.543203	−0.271602	−	0.962410i	$-0.587553\pi$
$619$	−1.98413e12	−0.543203	−0.271602	+	0.962410i	$0.587553\pi$
$620$	−2.57298e12	−0.699315
$621$	0	0
$622$	−8.71468e12	−2.33451
$623$	−7.20822e11	−0.191704
$624$	0	0
$625$	3.40192e12	0.891793
$626$	8.75322e12	2.27816
$627$	0	0
$628$	3.76369e12	0.965596
$629$	−4.36729e11	−0.111246
$630$	0	0
$631$	−5.57032e12	−1.39878	−0.699388	−	0.714743i	$-0.746544\pi$
$631$	−5.57032e12	−1.39878	−0.699388	+	0.714743i	$0.746544\pi$
$632$	1.74040e13	4.33932
$633$	0	0
$634$	9.07598e11	0.223096
$635$	6.78056e11	0.165495
$636$	0	0
$637$	−3.54679e12	−0.853508
$638$	8.76835e12	2.09520
$639$	0	0
$640$	−6.73187e11	−0.158608
$641$	5.38235e12	1.25925	0.629623	−	0.776901i	$-0.283209\pi$
$641$	5.38235e12	1.25925	0.629623	+	0.776901i	$0.283209\pi$
$642$	0	0
$643$	7.27179e11	0.167761	0.0838807	−	0.996476i	$-0.473269\pi$
$643$	7.27179e11	0.167761	0.0838807	+	0.996476i	$0.473269\pi$
$644$	1.32509e11	0.0303570
$645$	0	0
$646$	1.12391e12	0.253914
$647$	−1.81068e12	−0.406231	−0.203116	−	0.979155i	$-0.565107\pi$
$647$	−1.81068e12	−0.406231	−0.203116	+	0.979155i	$0.565107\pi$
$648$	0	0
$649$	5.81288e12	1.28615
$650$	−7.22618e12	−1.58781
$651$	0	0
$652$	−2.00882e13	−4.35339
$653$	3.82339e12	0.822886	0.411443	−	0.911435i	$-0.365025\pi$
$653$	3.82339e12	0.822886	0.411443	+	0.911435i	$0.365025\pi$
$654$	0	0
$655$	1.00851e12	0.214090
$656$	5.77724e12	1.21802
$657$	0	0
$658$	1.37540e12	0.286030
$659$	−3.40517e12	−0.703323	−0.351661	−	0.936127i	$-0.614383\pi$
$659$	−3.40517e12	−0.703323	−0.351661	+	0.936127i	$0.614383\pi$
$660$	0	0
$661$	1.30545e12	0.265982	0.132991	−	0.991117i	$-0.457542\pi$
$661$	1.30545e12	0.265982	0.132991	+	0.991117i	$0.457542\pi$
$662$	6.81221e12	1.37857
$663$	0	0
$664$	2.36687e13	4.72518
$665$	5.49905e10	0.0109041
$666$	0	0
$667$	3.94456e11	0.0771671
$668$	−2.15339e13	−4.18435
$669$	0	0
$670$	1.86422e12	0.357405
$671$	−5.21109e12	−0.992379
$672$	0	0
$673$	−1.13952e12	−0.214119	−0.107059	−	0.994253i	$-0.534143\pi$
$673$	−1.13952e12	−0.214119	−0.107059	+	0.994253i	$0.534143\pi$
$674$	−1.30884e13	−2.44296
$675$	0	0
$676$	−3.10067e12	−0.571077
$677$	2.85019e12	0.521464	0.260732	−	0.965411i	$-0.416036\pi$
$677$	2.85019e12	0.521464	0.260732	+	0.965411i	$0.416036\pi$
$678$	0	0
$679$	3.31637e11	0.0598755
$680$	1.22510e12	0.219726
$681$	0	0
$682$	1.57974e13	2.79613
$683$	−6.16518e12	−1.08406	−0.542029	−	0.840360i	$-0.682344\pi$
$683$	−6.16518e12	−1.08406	−0.542029	+	0.840360i	$0.682344\pi$
$684$	0	0
$685$	−5.05514e11	−0.0877254
$686$	−3.65766e12	−0.630587
$687$	0	0
$688$	−2.51526e12	−0.427991
$689$	−1.87410e12	−0.316815
$690$	0	0
$691$	9.71088e12	1.62034	0.810172	−	0.586192i	$-0.199374\pi$
$691$	9.71088e12	1.62034	0.810172	+	0.586192i	$0.199374\pi$
$692$	−1.30097e13	−2.15670
$693$	0	0
$694$	−5.69509e12	−0.931929
$695$	−1.31332e12	−0.213520
$696$	0	0
$697$	−1.09555e12	−0.175826
$698$	1.14739e13	1.82963
$699$	0	0
$700$	−2.62632e12	−0.413435
$701$	−3.33352e12	−0.521402	−0.260701	−	0.965420i	$-0.583954\pi$
$701$	−3.33352e12	−0.521402	−0.260701	+	0.965420i	$0.583954\pi$
$702$	0	0
$703$	−5.94520e11	−0.0918052
$704$	1.15882e13	1.77804
$705$	0	0
$706$	−7.12037e11	−0.107865
$707$	1.62100e12	0.244004
$708$	0	0
$709$	−6.12092e12	−0.909723	−0.454861	−	0.890562i	$-0.650311\pi$
$709$	−6.12092e12	−0.909723	−0.454861	+	0.890562i	$0.650311\pi$
$710$	−9.29061e11	−0.137209
$711$	0	0
$712$	−2.18608e13	−3.18791
$713$	7.10668e11	0.102983
$714$	0	0
$715$	−1.20292e12	−0.172131
$716$	2.39768e13	3.40944
$717$	0	0
$718$	−2.03973e13	−2.86427
$719$	−2.16423e12	−0.302012	−0.151006	−	0.988533i	$-0.548251\pi$
$719$	−2.16423e12	−0.302012	−0.151006	+	0.988533i	$0.548251\pi$
$720$	0	0
$721$	9.42947e11	0.129951
$722$	−1.21575e13	−1.66505
$723$	0	0
$724$	−1.73224e13	−2.34307
$725$	−7.81810e12	−1.05095
$726$	0	0
$727$	1.22681e13	1.62882	0.814412	−	0.580287i	$-0.197060\pi$
$727$	1.22681e13	1.62882	0.814412	+	0.580287i	$0.197060\pi$
$728$	3.22757e12	0.425877
$729$	0	0
$730$	3.98025e12	0.518749
$731$	4.76972e11	0.0617824
$732$	0	0
$733$	−1.22993e13	−1.57367	−0.786833	−	0.617166i	$-0.788281\pi$
$733$	−1.22993e13	−1.57367	−0.786833	+	0.617166i	$0.788281\pi$
$734$	−2.51023e13	−3.19214
$735$	0	0
$736$	1.36447e12	0.171402
$737$	−8.18871e12	−1.02238
$738$	0	0
$739$	2.39881e12	0.295867	0.147933	−	0.988997i	$-0.452738\pi$
$739$	2.39881e12	0.295867	0.147933	+	0.988997i	$0.452738\pi$
$740$	−1.07605e12	−0.131914
$741$	0	0
$742$	−9.52059e11	−0.115304
$743$	9.39278e12	1.13069	0.565346	−	0.824854i	$-0.308742\pi$
$743$	9.39278e12	1.13069	0.565346	+	0.824854i	$0.308742\pi$
$744$	0	0
$745$	2.68243e12	0.319026
$746$	−2.20954e13	−2.61202
$747$	0	0
$748$	−8.93551e12	−1.04367
$749$	1.85209e12	0.215027
$750$	0	0
$751$	−1.66561e13	−1.91070	−0.955352	−	0.295469i	$-0.904524\pi$
$751$	−1.66561e13	−1.91070	−0.955352	+	0.295469i	$0.904524\pi$
$752$	2.20026e13	2.50896
$753$	0	0
$754$	1.59536e13	1.79758
$755$	−1.68891e11	−0.0189167
$756$	0	0
$757$	−1.58067e13	−1.74949	−0.874743	−	0.484587i	$-0.838970\pi$
$757$	−1.58067e13	−1.74949	−0.874743	+	0.484587i	$0.838970\pi$
$758$	−4.22734e12	−0.465111
$759$	0	0
$760$	1.66773e12	0.181328
$761$	1.76096e13	1.90335	0.951673	−	0.307112i	$-0.0993627\pi$
$761$	1.76096e13	1.90335	0.951673	+	0.307112i	$0.0993627\pi$
$762$	0	0
$763$	2.04906e12	0.218874
$764$	3.33959e13	3.54628
$765$	0	0
$766$	1.51599e13	1.59099
$767$	1.05763e13	1.10345
$768$	0	0
$769$	−1.26882e13	−1.30838	−0.654188	−	0.756332i	$-0.726989\pi$
$769$	−1.26882e13	−1.30838	−0.654188	+	0.756332i	$0.726989\pi$
$770$	−6.11092e11	−0.0626467
$771$	0	0
$772$	4.56623e13	4.62680
$773$	−1.57233e12	−0.158393	−0.0791965	−	0.996859i	$-0.525235\pi$
$773$	−1.57233e12	−0.158393	−0.0791965	+	0.996859i	$0.525235\pi$
$774$	0	0
$775$	−1.40854e13	−1.40253
$776$	1.00577e13	0.995687
$777$	0	0
$778$	1.98311e13	1.94061
$779$	−1.49137e12	−0.145100
$780$	0	0
$781$	4.08096e12	0.392494
$782$	−5.61865e11	−0.0537281
$783$	0	0
$784$	−2.88238e13	−2.72477
$785$	−7.80830e11	−0.0733910
$786$	0	0
$787$	−7.00350e12	−0.650772	−0.325386	−	0.945581i	$-0.605494\pi$
$787$	−7.00350e12	−0.650772	−0.325386	+	0.945581i	$0.605494\pi$
$788$	−2.53035e13	−2.33783
$789$	0	0
$790$	−5.99544e12	−0.547645
$791$	1.49549e12	0.135828
$792$	0	0
$793$	−9.48135e12	−0.851414
$794$	−4.22948e12	−0.377654
$795$	0	0
$796$	2.45963e13	2.17151
$797$	−6.34176e12	−0.556734	−0.278367	−	0.960475i	$-0.589793\pi$
$797$	−6.34176e12	−0.556734	−0.278367	+	0.960475i	$0.589793\pi$
$798$	0	0
$799$	−4.17238e12	−0.362179
$800$	−2.70438e13	−2.33434
$801$	0	0
$802$	1.83491e13	1.56614
$803$	−1.74835e13	−1.48391
$804$	0	0
$805$	−2.74908e10	−0.00230731
$806$	2.87427e13	2.39894
$807$	0	0
$808$	4.91611e13	4.05761
$809$	1.84767e13	1.51654	0.758272	−	0.651938i	$-0.226044\pi$
$809$	1.84767e13	1.51654	0.758272	+	0.651938i	$0.226044\pi$
$810$	0	0
$811$	9.90436e12	0.803956	0.401978	−	0.915649i	$-0.368323\pi$
$811$	9.90436e12	0.803956	0.401978	+	0.915649i	$0.368323\pi$
$812$	5.79826e12	0.468054
$813$	0	0
$814$	6.60671e12	0.527443
$815$	4.16758e12	0.330883
$816$	0	0
$817$	6.49302e11	0.0509856
$818$	−3.43135e13	−2.67963
$819$	0	0
$820$	−2.69931e12	−0.208493
$821$	6.67366e12	0.512649	0.256324	−	0.966591i	$-0.417488\pi$
$821$	6.67366e12	0.512649	0.256324	+	0.966591i	$0.417488\pi$
$822$	0	0
$823$	−1.21283e13	−0.921512	−0.460756	−	0.887527i	$-0.652422\pi$
$823$	−1.21283e13	−0.921512	−0.460756	+	0.887527i	$0.652422\pi$
$824$	2.85973e13	2.16099
$825$	0	0
$826$	5.37284e12	0.401600
$827$	1.18283e13	0.879318	0.439659	−	0.898165i	$-0.355099\pi$
$827$	1.18283e13	0.879318	0.439659	+	0.898165i	$0.355099\pi$
$828$	0	0
$829$	7.07948e12	0.520602	0.260301	−	0.965527i	$-0.416178\pi$
$829$	7.07948e12	0.520602	0.260301	+	0.965527i	$0.416178\pi$
$830$	−8.15356e12	−0.596343
$831$	0	0
$832$	2.10843e13	1.52547
$833$	5.46590e12	0.393332
$834$	0	0
$835$	4.46750e12	0.318035
$836$	−1.21639e13	−0.861282
$837$	0	0
$838$	−3.09111e13	−2.16529
$839$	2.29506e12	0.159906	0.0799532	−	0.996799i	$-0.474523\pi$
$839$	2.29506e12	0.159906	0.0799532	+	0.996799i	$0.474523\pi$
$840$	0	0
$841$	2.75328e12	0.189788
$842$	−2.65649e13	−1.82140
$843$	0	0
$844$	−3.78632e12	−0.256848
$845$	6.43276e11	0.0434053
$846$	0	0
$847$	1.27697e11	0.00852519
$848$	−1.52303e13	−1.01141
$849$	0	0
$850$	1.11362e13	0.731729
$851$	2.97211e11	0.0194260
$852$	0	0
$853$	1.07725e13	0.696700	0.348350	−	0.937365i	$-0.386742\pi$
$853$	1.07725e13	0.696700	0.348350	+	0.937365i	$0.386742\pi$
$854$	−4.81661e12	−0.309871
$855$	0	0
$856$	5.61694e13	3.57575
$857$	−1.70306e13	−1.07849	−0.539246	−	0.842148i	$-0.681291\pi$
$857$	−1.70306e13	−1.07849	−0.539246	+	0.842148i	$0.681291\pi$
$858$	0	0
$859$	1.68432e13	1.05549	0.527747	−	0.849402i	$-0.323037\pi$
$859$	1.68432e13	1.05549	0.527747	+	0.849402i	$0.323037\pi$
$860$	1.17521e12	0.0732609
$861$	0	0
$862$	−3.97409e13	−2.45163
$863$	−2.85773e13	−1.75377	−0.876886	−	0.480699i	$-0.840383\pi$
$863$	−2.85773e13	−1.75377	−0.876886	+	0.480699i	$0.840383\pi$
$864$	0	0
$865$	2.69904e12	0.163922
$866$	−8.85139e12	−0.534787
$867$	0	0
$868$	1.04464e13	0.624637
$869$	2.63354e13	1.56657
$870$	0	0
$871$	−1.48990e13	−0.877153
$872$	6.21429e13	3.63971
$873$	0	0
$874$	−7.64868e11	−0.0443389
$875$	1.11038e12	0.0640378
$876$	0	0
$877$	−1.62714e12	−0.0928807	−0.0464404	−	0.998921i	$-0.514788\pi$
$877$	−1.62714e12	−0.0928807	−0.0464404	+	0.998921i	$0.514788\pi$
$878$	1.70192e12	0.0966527
$879$	0	0
$880$	−9.77579e12	−0.549516
$881$	−9.31457e12	−0.520920	−0.260460	−	0.965485i	$-0.583874\pi$
$881$	−9.31457e12	−0.520920	−0.260460	+	0.965485i	$0.583874\pi$
$882$	0	0
$883$	−1.11738e12	−0.0618553	−0.0309277	−	0.999522i	$-0.509846\pi$
$883$	−1.11738e12	−0.0618553	−0.0309277	+	0.999522i	$0.509846\pi$
$884$	−1.62578e13	−0.895417
$885$	0	0
$886$	1.90741e13	1.03990
$887$	1.85575e13	1.00661	0.503307	−	0.864108i	$-0.332116\pi$
$887$	1.85575e13	1.00661	0.503307	+	0.864108i	$0.332116\pi$
$888$	0	0
$889$	−2.75294e12	−0.147822
$890$	7.53075e12	0.402331
$891$	0	0
$892$	−5.54318e10	−0.00293168
$893$	−5.67986e12	−0.298886
$894$	0	0
$895$	−4.97432e12	−0.259138
$896$	2.73317e12	0.141671
$897$	0	0
$898$	−1.21045e13	−0.621158
$899$	3.10971e13	1.58782
$900$	0	0
$901$	2.88814e12	0.146001
$902$	1.65731e13	0.833632
$903$	0	0
$904$	4.53547e13	2.25873
$905$	3.59378e12	0.178087
$906$	0	0
$907$	−1.49318e13	−0.732620	−0.366310	−	0.930493i	$-0.619379\pi$
$907$	−1.49318e13	−0.732620	−0.366310	+	0.930493i	$0.619379\pi$
$908$	7.56533e13	3.69353
$909$	0	0
$910$	−1.11185e12	−0.0537479
$911$	2.77113e13	1.33298	0.666490	−	0.745514i	$-0.267796\pi$
$911$	2.77113e13	1.33298	0.666490	+	0.745514i	$0.267796\pi$
$912$	0	0
$913$	3.58151e13	1.70587
$914$	1.29222e13	0.612462
$915$	0	0
$916$	−6.02218e12	−0.282634
$917$	−4.09461e12	−0.191228
$918$	0	0
$919$	2.32626e13	1.07582	0.537909	−	0.843003i	$-0.319214\pi$
$919$	2.32626e13	1.07582	0.537909	+	0.843003i	$0.319214\pi$
$920$	−8.33728e11	−0.0383689
$921$	0	0
$922$	−2.60484e13	−1.18711
$923$	7.42512e12	0.336741
$924$	0	0
$925$	−5.89072e12	−0.264564
$926$	−8.14007e12	−0.363813
$927$	0	0
$928$	5.97061e13	2.64273
$929$	2.61747e13	1.15295	0.576476	−	0.817114i	$-0.304428\pi$
$929$	2.61747e13	1.15295	0.576476	+	0.817114i	$0.304428\pi$
$930$	0	0
$931$	7.44074e12	0.324595
$932$	8.00748e13	3.47636
$933$	0	0
$934$	−1.62427e13	−0.698390
$935$	1.85380e12	0.0793249
$936$	0	0
$937$	1.82019e12	0.0771417	0.0385709	−	0.999256i	$-0.487719\pi$
$937$	1.82019e12	0.0771417	0.0385709	+	0.999256i	$0.487719\pi$
$938$	−7.56882e12	−0.319239
$939$	0	0
$940$	−1.02803e13	−0.429468
$941$	−3.78437e13	−1.57340	−0.786702	−	0.617332i	$-0.788213\pi$
$941$	−3.78437e13	−1.57340	−0.786702	+	0.617332i	$0.788213\pi$
$942$	0	0
$943$	7.45562e11	0.0307030
$944$	8.59507e13	3.52270
$945$	0	0
$946$	−7.21549e12	−0.292925
$947$	−1.25246e13	−0.506045	−0.253022	−	0.967460i	$-0.581425\pi$
$947$	−1.25246e13	−0.506045	−0.253022	+	0.967460i	$0.581425\pi$
$948$	0	0
$949$	−3.18104e13	−1.27313
$950$	1.51597e13	0.603856
$951$	0	0
$952$	−4.97396e12	−0.196262
$953$	−6.72806e12	−0.264224	−0.132112	−	0.991235i	$-0.542176\pi$
$953$	−6.72806e12	−0.264224	−0.132112	+	0.991235i	$0.542176\pi$
$954$	0	0
$955$	−6.92844e12	−0.269538
$956$	−1.05185e14	−4.07280
$957$	0	0
$958$	7.19879e12	0.276131
$959$	2.05241e12	0.0783574
$960$	0	0
$961$	2.95863e13	1.11901
$962$	1.20206e13	0.452521
$963$	0	0
$964$	−9.35380e12	−0.348852
$965$	−9.47329e12	−0.351664
$966$	0	0
$967$	4.50859e13	1.65814	0.829071	−	0.559143i	$-0.188870\pi$
$967$	4.50859e13	1.65814	0.829071	+	0.559143i	$0.188870\pi$
$968$	3.87272e12	0.141768
$969$	0	0
$970$	−3.46476e12	−0.125661
$971$	−6.75879e12	−0.243996	−0.121998	−	0.992530i	$-0.538930\pi$
$971$	−6.75879e12	−0.243996	−0.121998	+	0.992530i	$0.538930\pi$
$972$	0	0
$973$	5.33214e12	0.190719
$974$	1.04497e13	0.372040
$975$	0	0
$976$	−7.70525e13	−2.71808
$977$	−2.58525e13	−0.907772	−0.453886	−	0.891060i	$-0.649963\pi$
$977$	−2.58525e13	−0.907772	−0.453886	+	0.891060i	$0.649963\pi$
$978$	0	0
$979$	−3.30793e13	−1.15089
$980$	1.34674e13	0.466409
$981$	0	0
$982$	−4.32350e13	−1.48366
$983$	−1.85340e13	−0.633109	−0.316554	−	0.948574i	$-0.602526\pi$
$983$	−1.85340e13	−0.633109	−0.316554	+	0.948574i	$0.602526\pi$
$984$	0	0
$985$	5.24957e12	0.177689
$986$	−2.45859e13	−0.828399
$987$	0	0
$988$	−2.21317e13	−0.738939
$989$	−3.24598e11	−0.0107885
$990$	0	0
$991$	−4.66998e12	−0.153809	−0.0769047	−	0.997038i	$-0.524504\pi$
$991$	−4.66998e12	−0.153809	−0.0769047	+	0.997038i	$0.524504\pi$
$992$	1.07569e14	3.52683
$993$	0	0
$994$	3.77203e12	0.122556
$995$	−5.10285e12	−0.165047
$996$	0	0
$997$	3.66040e13	1.17328	0.586639	−	0.809849i	$-0.300451\pi$
$997$	3.66040e13	1.17328	0.586639	+	0.809849i	$0.300451\pi$
$998$	4.50657e13	1.43800
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.10.a.c.1.15		15
3.2	odd	2		43.10.a.a.1.1	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.1	✓	15	3.2	odd	2
387.10.a.c.1.15		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)

\(f(q)\)	\(=\)	\(q+42.4171 q^{2} +1287.21 q^{4} -267.050 q^{5} +1084.23 q^{7} +32882.2 q^{8} +O(q^{10})\)	\(q+42.4171 q^{2} +1287.21 q^{4} -267.050 q^{5} +1084.23 q^{7} +32882.2 q^{8} -11327.5 q^{10} +49756.6 q^{11} +90530.0 q^{13} +45990.0 q^{14} +735714. q^{16} -139514. q^{17} -189921. q^{19} -343749. q^{20} +2.11053e6 q^{22} +94945.1 q^{23} -1.88181e6 q^{25} +3.84002e6 q^{26} +1.39564e6 q^{28} +4.15457e6 q^{29} +7.48504e6 q^{31} +1.43712e7 q^{32} -5.91779e6 q^{34} -289544. q^{35} +3.13035e6 q^{37} -8.05590e6 q^{38} -8.78117e6 q^{40} +7.85257e6 q^{41} -3.41880e6 q^{43} +6.40472e7 q^{44} +4.02729e6 q^{46} +2.99064e7 q^{47} -3.91780e7 q^{49} -7.98209e7 q^{50} +1.16531e8 q^{52} -2.07014e7 q^{53} -1.32875e7 q^{55} +3.56519e7 q^{56} +1.76225e8 q^{58} +1.16826e8 q^{59} -1.04732e8 q^{61} +3.17494e8 q^{62} +2.32899e8 q^{64} -2.41760e7 q^{65} -1.64575e8 q^{67} -1.79584e8 q^{68} -1.22816e7 q^{70} +8.20184e7 q^{71} -3.51380e8 q^{73} +1.32780e8 q^{74} -2.44468e8 q^{76} +5.39478e7 q^{77} +5.29284e8 q^{79} -1.96472e8 q^{80} +3.33083e8 q^{82} +7.19804e8 q^{83} +3.72572e7 q^{85} -1.45016e8 q^{86} +1.63611e9 q^{88} -6.64822e8 q^{89} +9.81556e7 q^{91} +1.22214e8 q^{92} +1.26854e9 q^{94} +5.07183e7 q^{95} +3.05873e8 q^{97} -1.66182e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) \) 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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