LMFDB - Embedded newform 387.10.a.c.1.3

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			1.3
Root			$-28.3075$ 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)

$f(q)$	$=$	$q-26.3075 q^{2} +180.084 q^{4} -879.044 q^{5} +8431.97 q^{7} +8731.88 q^{8} +O(q^{10})$	\(q-26.3075 q^{2} +180.084 q^{4} -879.044 q^{5} +8431.97 q^{7} +8731.88 q^{8} +23125.4 q^{10} +44408.6 q^{11} -47197.0 q^{13} -221824. q^{14} -321917. q^{16} -106312. q^{17} -840557. q^{19} -158302. q^{20} -1.16828e6 q^{22} +2.20694e6 q^{23} -1.18041e6 q^{25} +1.24163e6 q^{26} +1.51846e6 q^{28} +5.29576e6 q^{29} +8.55848e6 q^{31} +3.99810e6 q^{32} +2.79681e6 q^{34} -7.41208e6 q^{35} +1.40897e7 q^{37} +2.21129e7 q^{38} -7.67571e6 q^{40} +3.26833e7 q^{41} -3.41880e6 q^{43} +7.99729e6 q^{44} -5.80590e7 q^{46} -1.82676e7 q^{47} +3.07445e7 q^{49} +3.10535e7 q^{50} -8.49942e6 q^{52} +1.58212e7 q^{53} -3.90372e7 q^{55} +7.36269e7 q^{56} -1.39318e8 q^{58} -5.21983e7 q^{59} -5.19929e7 q^{61} -2.25152e8 q^{62} +5.96414e7 q^{64} +4.14882e7 q^{65} -5.12923e7 q^{67} -1.91451e7 q^{68} +1.94993e8 q^{70} -1.33738e8 q^{71} +2.51019e8 q^{73} -3.70665e8 q^{74} -1.51371e8 q^{76} +3.74452e8 q^{77} -5.19381e8 q^{79} +2.82979e8 q^{80} -8.59815e8 q^{82} +9.09782e6 q^{83} +9.34532e7 q^{85} +8.99401e7 q^{86} +3.87771e8 q^{88} -2.78479e8 q^{89} -3.97963e8 q^{91} +3.97434e8 q^{92} +4.80576e8 q^{94} +7.38887e8 q^{95} +1.06067e9 q^{97} -8.08811e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−26.3075	−1.16264	−0.581319	−	0.813676i	$-0.697463\pi$
$2$	−26.3075	−1.16264	−0.581319	+	0.813676i	$0.697463\pi$
$3$	0	0
$3$	0	0
$4$	180.084	0.351727
$5$	−879.044	−0.628993	−0.314496	−	0.949259i	$-0.601836\pi$
$5$	−879.044	−0.628993	−0.314496	+	0.949259i	$0.601836\pi$
$6$	0	0
$7$	8431.97	1.32736	0.663679	−	0.748018i	$-0.268994\pi$
$7$	8431.97	1.32736	0.663679	+	0.748018i	$0.268994\pi$
$8$	8731.88	0.753707
$9$	0	0
$10$	23125.4	0.731291
$11$	44408.6	0.914535	0.457268	−	0.889329i	$-0.348828\pi$
$11$	44408.6	0.914535	0.457268	+	0.889329i	$0.348828\pi$
$12$	0	0
$13$	−47197.0	−0.458320	−0.229160	−	0.973389i	$-0.573598\pi$
$13$	−47197.0	−0.458320	−0.229160	+	0.973389i	$0.573598\pi$
$14$	−221824.	−1.54324
$15$	0	0
$16$	−321917.	−1.22801
$17$	−106312.	−0.308719	−0.154359	−	0.988015i	$-0.549331\pi$
$17$	−106312.	−0.308719	−0.154359	+	0.988015i	$0.549331\pi$
$18$	0	0
$19$	−840557.	−1.47971	−0.739854	−	0.672768i	$-0.765105\pi$
$19$	−840557.	−1.47971	−0.739854	+	0.672768i	$0.765105\pi$
$20$	−158302.	−0.221234
$21$	0	0
$22$	−1.16828e6	−1.06327
$23$	2.20694e6	1.64443	0.822214	−	0.569178i	$-0.192738\pi$
$23$	2.20694e6	1.64443	0.822214	+	0.569178i	$0.192738\pi$
$24$	0	0
$25$	−1.18041e6	−0.604368
$26$	1.24163e6	0.532860
$27$	0	0
$28$	1.51846e6	0.466867
$29$	5.29576e6	1.39039	0.695196	−	0.718820i	$-0.255317\pi$
$29$	5.29576e6	1.39039	0.695196	+	0.718820i	$0.255317\pi$
$30$	0	0
$31$	8.55848e6	1.66444	0.832222	−	0.554443i	$-0.187068\pi$
$31$	8.55848e6	1.66444	0.832222	+	0.554443i	$0.187068\pi$
$32$	3.99810e6	0.674029
$33$	0	0
$34$	2.79681e6	0.358928
$35$	−7.41208e6	−0.834898
$36$	0	0
$37$	1.40897e7	1.23593	0.617965	−	0.786205i	$-0.287957\pi$
$37$	1.40897e7	1.23593	0.617965	+	0.786205i	$0.287957\pi$
$38$	2.21129e7	1.72036
$39$	0	0
$40$	−7.67571e6	−0.474076
$41$	3.26833e7	1.80633	0.903167	−	0.429288i	$-0.141236\pi$
$41$	3.26833e7	1.80633	0.903167	+	0.429288i	$0.141236\pi$
$42$	0	0
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	7.99729e6	0.321666
$45$	0	0
$46$	−5.80590e7	−1.91187
$47$	−1.82676e7	−0.546062	−0.273031	−	0.962005i	$-0.588026\pi$
$47$	−1.82676e7	−0.546062	−0.273031	+	0.962005i	$0.588026\pi$
$48$	0	0
$49$	3.07445e7	0.761878
$50$	3.10535e7	0.702661
$51$	0	0
$52$	−8.49942e6	−0.161203
$53$	1.58212e7	0.275422	0.137711	−	0.990472i	$-0.456026\pi$
$53$	1.58212e7	0.275422	0.137711	+	0.990472i	$0.456026\pi$
$54$	0	0
$55$	−3.90372e7	−0.575236
$56$	7.36269e7	1.00044
$57$	0	0
$58$	−1.39318e8	−1.61652
$59$	−5.21983e7	−0.560819	−0.280409	−	0.959881i	$-0.590470\pi$
$59$	−5.21983e7	−0.560819	−0.280409	+	0.959881i	$0.590470\pi$
$60$	0	0
$61$	−5.19929e7	−0.480794	−0.240397	−	0.970675i	$-0.577278\pi$
$61$	−5.19929e7	−0.480794	−0.240397	+	0.970675i	$0.577278\pi$
$62$	−2.25152e8	−1.93515
$63$	0	0
$64$	5.96414e7	0.444363
$65$	4.14882e7	0.288280
$66$	0	0
$67$	−5.12923e7	−0.310968	−0.155484	−	0.987838i	$-0.549694\pi$
$67$	−5.12923e7	−0.310968	−0.155484	+	0.987838i	$0.549694\pi$
$68$	−1.91451e7	−0.108585
$69$	0	0
$70$	1.94993e8	0.970685
$71$	−1.33738e8	−0.624588	−0.312294	−	0.949986i	$-0.601097\pi$
$71$	−1.33738e8	−0.624588	−0.312294	+	0.949986i	$0.601097\pi$
$72$	0	0
$73$	2.51019e8	1.03455	0.517277	−	0.855818i	$-0.326946\pi$
$73$	2.51019e8	1.03455	0.517277	+	0.855818i	$0.326946\pi$
$74$	−3.70665e8	−1.43694
$75$	0	0
$76$	−1.51371e8	−0.520453
$77$	3.74452e8	1.21391
$78$	0	0
$79$	−5.19381e8	−1.50025	−0.750126	−	0.661295i	$-0.770007\pi$
$79$	−5.19381e8	−1.50025	−0.750126	+	0.661295i	$0.770007\pi$
$80$	2.82979e8	0.772413
$81$	0	0
$82$	−8.59815e8	−2.10011
$83$	9.09782e6	0.0210419	0.0105210	−	0.999945i	$-0.496651\pi$
$83$	9.09782e6	0.0210419	0.0105210	+	0.999945i	$0.496651\pi$
$84$	0	0
$85$	9.34532e7	0.194182
$86$	8.99401e7	0.177301
$87$	0	0
$88$	3.87771e8	0.689292
$89$	−2.78479e8	−0.470476	−0.235238	−	0.971938i	$-0.575587\pi$
$89$	−2.78479e8	−0.470476	−0.235238	+	0.971938i	$0.575587\pi$
$90$	0	0
$91$	−3.97963e8	−0.608355
$92$	3.97434e8	0.578389
$93$	0	0
$94$	4.80576e8	0.634873
$95$	7.38887e8	0.930726
$96$	0	0
$97$	1.06067e9	1.21649	0.608244	−	0.793750i	$-0.291874\pi$
$97$	1.06067e9	1.21649	0.608244	+	0.793750i	$0.291874\pi$
$98$	−8.08811e8	−0.885788
$99$	0	0
$100$	−2.12572e8	−0.212572
$101$	9.68968e8	0.926538	0.463269	−	0.886218i	$-0.346676\pi$
$101$	9.68968e8	0.926538	0.463269	+	0.886218i	$0.346676\pi$
$102$	0	0
$103$	−9.31835e8	−0.815777	−0.407888	−	0.913032i	$-0.633735\pi$
$103$	−9.31835e8	−0.815777	−0.407888	+	0.913032i	$0.633735\pi$
$104$	−4.12118e8	−0.345439
$105$	0	0
$106$	−4.16216e8	−0.320216
$107$	−4.53416e8	−0.334403	−0.167202	−	0.985923i	$-0.553473\pi$
$107$	−4.53416e8	−0.334403	−0.167202	+	0.985923i	$0.553473\pi$
$108$	0	0
$109$	−2.45730e8	−0.166740	−0.0833698	−	0.996519i	$-0.526568\pi$
$109$	−2.45730e8	−0.166740	−0.0833698	+	0.996519i	$0.526568\pi$
$110$	1.02697e9	0.668791
$111$	0	0
$112$	−2.71439e9	−1.63001
$113$	−1.88661e9	−1.08850	−0.544251	−	0.838922i	$-0.683186\pi$
$113$	−1.88661e9	−1.08850	−0.544251	+	0.838922i	$0.683186\pi$
$114$	0	0
$115$	−1.94000e9	−1.03433
$116$	9.53682e8	0.489038
$117$	0	0
$118$	1.37321e9	0.652029
$119$	−8.96422e8	−0.409780
$120$	0	0
$121$	−3.85821e8	−0.163626
$122$	1.36780e9	0.558990
$123$	0	0
$124$	1.54125e9	0.585429
$125$	2.75451e9	1.00914
$126$	0	0
$127$	4.85598e9	1.65638	0.828190	−	0.560447i	$-0.189371\pi$
$127$	4.85598e9	1.65638	0.828190	+	0.560447i	$0.189371\pi$
$128$	−3.61604e9	−1.19066
$129$	0	0
$130$	−1.09145e9	−0.335165
$131$	2.84855e9	0.845089	0.422545	−	0.906342i	$-0.361137\pi$
$131$	2.84855e9	0.845089	0.422545	+	0.906342i	$0.361137\pi$
$132$	0	0
$133$	−7.08755e9	−1.96410
$134$	1.34937e9	0.361543
$135$	0	0
$136$	−9.28305e8	−0.232684
$137$	2.63584e9	0.639258	0.319629	−	0.947543i	$-0.396442\pi$
$137$	2.63584e9	0.639258	0.319629	+	0.947543i	$0.396442\pi$
$138$	0	0
$139$	−1.99731e9	−0.453814	−0.226907	−	0.973916i	$-0.572861\pi$
$139$	−1.99731e9	−0.453814	−0.226907	+	0.973916i	$0.572861\pi$
$140$	−1.33480e9	−0.293656
$141$	0	0
$142$	3.51832e9	0.726169
$143$	−2.09595e9	−0.419150
$144$	0	0
$145$	−4.65521e9	−0.874547
$146$	−6.60368e9	−1.20281
$147$	0	0
$148$	2.53733e9	0.434710
$149$	−1.72984e9	−0.287520	−0.143760	−	0.989613i	$-0.545919\pi$
$149$	−1.72984e9	−0.287520	−0.143760	+	0.989613i	$0.545919\pi$
$150$	0	0
$151$	9.37624e8	0.146768	0.0733841	−	0.997304i	$-0.476620\pi$
$151$	9.37624e8	0.146768	0.0733841	+	0.997304i	$0.476620\pi$
$152$	−7.33964e9	−1.11527
$153$	0	0
$154$	−9.85090e9	−1.41134
$155$	−7.52329e9	−1.04692
$156$	0	0
$157$	7.92803e9	1.04140	0.520699	−	0.853740i	$-0.325671\pi$
$157$	7.92803e9	1.04140	0.520699	+	0.853740i	$0.325671\pi$
$158$	1.36636e10	1.74425
$159$	0	0
$160$	−3.51451e9	−0.423960
$161$	1.86088e10	2.18274
$162$	0	0
$163$	2.00486e9	0.222454	0.111227	−	0.993795i	$-0.464522\pi$
$163$	2.00486e9	0.222454	0.111227	+	0.993795i	$0.464522\pi$
$164$	5.88574e9	0.635336
$165$	0	0
$166$	−2.39341e8	−0.0244642
$167$	−1.17331e10	−1.16731	−0.583656	−	0.812001i	$-0.698378\pi$
$167$	−1.17331e10	−1.16731	−0.583656	+	0.812001i	$0.698378\pi$
$168$	0	0
$169$	−8.37695e9	−0.789943
$170$	−2.45852e9	−0.225763
$171$	0	0
$172$	−6.15671e8	−0.0536378
$173$	4.43977e9	0.376837	0.188418	−	0.982089i	$-0.439664\pi$
$173$	4.43977e9	0.376837	0.188418	+	0.982089i	$0.439664\pi$
$174$	0	0
$175$	−9.95315e9	−0.802212
$176$	−1.42959e10	−1.12306
$177$	0	0
$178$	7.32608e9	0.546993
$179$	−8.09413e8	−0.0589294	−0.0294647	−	0.999566i	$-0.509380\pi$
$179$	−8.09413e8	−0.0589294	−0.0294647	+	0.999566i	$0.509380\pi$
$180$	0	0
$181$	−2.74859e10	−1.90352	−0.951758	−	0.306850i	$-0.900725\pi$
$181$	−2.74859e10	−1.90352	−0.951758	+	0.306850i	$0.900725\pi$
$182$	1.04694e10	0.707296
$183$	0	0
$184$	1.92707e10	1.23942
$185$	−1.23855e10	−0.777391
$186$	0	0
$187$	−4.72118e9	−0.282334
$188$	−3.28971e9	−0.192065
$189$	0	0
$190$	−1.94383e10	−1.08210
$191$	−2.57143e10	−1.39805	−0.699027	−	0.715095i	$-0.746383\pi$
$191$	−2.57143e10	−1.39805	−0.699027	+	0.715095i	$0.746383\pi$
$192$	0	0
$193$	−3.15862e10	−1.63866	−0.819330	−	0.573322i	$-0.805654\pi$
$193$	−3.15862e10	−1.63866	−0.819330	+	0.573322i	$0.805654\pi$
$194$	−2.79036e10	−1.41433
$195$	0	0
$196$	5.53660e9	0.267973
$197$	8.04167e9	0.380407	0.190203	−	0.981745i	$-0.439085\pi$
$197$	8.04167e9	0.380407	0.190203	+	0.981745i	$0.439085\pi$
$198$	0	0
$199$	2.69320e10	1.21739	0.608695	−	0.793404i	$-0.291693\pi$
$199$	2.69320e10	1.21739	0.608695	+	0.793404i	$0.291693\pi$
$200$	−1.03072e10	−0.455516
$201$	0	0
$202$	−2.54911e10	−1.07723
$203$	4.46537e10	1.84555
$204$	0	0
$205$	−2.87301e10	−1.13617
$206$	2.45142e10	0.948453
$207$	0	0
$208$	1.51935e10	0.562824
$209$	−3.73280e10	−1.35324
$210$	0	0
$211$	3.31590e10	1.15168	0.575838	−	0.817564i	$-0.304676\pi$
$211$	3.31590e10	1.15168	0.575838	+	0.817564i	$0.304676\pi$
$212$	2.84915e9	0.0968731
$213$	0	0
$214$	1.19282e10	0.388790
$215$	3.00528e9	0.0959205
$216$	0	0
$217$	7.21649e10	2.20931
$218$	6.46454e9	0.193858
$219$	0	0
$220$	−7.02997e9	−0.202326
$221$	5.01762e9	0.141492
$222$	0	0
$223$	−9.20954e8	−0.0249383	−0.0124691	−	0.999922i	$-0.503969\pi$
$223$	−9.20954e8	−0.0249383	−0.0124691	+	0.999922i	$0.503969\pi$
$224$	3.37119e10	0.894678
$225$	0	0
$226$	4.96320e10	1.26553
$227$	1.44593e10	0.361436	0.180718	−	0.983535i	$-0.442158\pi$
$227$	1.44593e10	0.361436	0.180718	+	0.983535i	$0.442158\pi$
$228$	0	0
$229$	1.65510e10	0.397709	0.198855	−	0.980029i	$-0.436278\pi$
$229$	1.65510e10	0.397709	0.198855	+	0.980029i	$0.436278\pi$
$230$	5.10365e10	1.20256
$231$	0	0
$232$	4.62419e10	1.04795
$233$	−3.78508e10	−0.841344	−0.420672	−	0.907213i	$-0.638206\pi$
$233$	−3.78508e10	−0.841344	−0.420672	+	0.907213i	$0.638206\pi$
$234$	0	0
$235$	1.60581e10	0.343469
$236$	−9.40008e9	−0.197255
$237$	0	0
$238$	2.35826e10	0.476426
$239$	8.76102e10	1.73686	0.868429	−	0.495814i	$-0.165130\pi$
$239$	8.76102e10	1.73686	0.868429	+	0.495814i	$0.165130\pi$
$240$	0	0
$241$	1.20041e10	0.229221	0.114610	−	0.993411i	$-0.463438\pi$
$241$	1.20041e10	0.229221	0.114610	+	0.993411i	$0.463438\pi$
$242$	1.01500e10	0.190237
$243$	0	0
$244$	−9.36308e9	−0.169108
$245$	−2.70258e10	−0.479216
$246$	0	0
$247$	3.96717e10	0.678180
$248$	7.47316e10	1.25450
$249$	0	0
$250$	−7.24643e10	−1.17326
$251$	3.64728e10	0.580013	0.290006	−	0.957025i	$-0.406343\pi$
$251$	3.64728e10	0.580013	0.290006	+	0.957025i	$0.406343\pi$
$252$	0	0
$253$	9.80071e10	1.50389
$254$	−1.27749e11	−1.92577
$255$	0	0
$256$	6.45926e10	0.939946
$257$	5.66916e10	0.810624	0.405312	−	0.914178i	$-0.367163\pi$
$257$	5.66916e10	0.810624	0.405312	+	0.914178i	$0.367163\pi$
$258$	0	0
$259$	1.18804e11	1.64052
$260$	7.47137e9	0.101396
$261$	0	0
$262$	−7.49381e10	−0.982533
$263$	−1.18478e11	−1.52700	−0.763498	−	0.645811i	$-0.776520\pi$
$263$	−1.18478e11	−1.52700	−0.763498	+	0.645811i	$0.776520\pi$
$264$	0	0
$265$	−1.39075e10	−0.173238
$266$	1.86456e11	2.28354
$267$	0	0
$268$	−9.23693e9	−0.109376
$269$	1.35889e11	1.58234	0.791168	−	0.611598i	$-0.209473\pi$
$269$	1.35889e11	1.58234	0.791168	+	0.611598i	$0.209473\pi$
$270$	0	0
$271$	1.48062e11	1.66756	0.833782	−	0.552094i	$-0.186171\pi$
$271$	1.48062e11	1.66756	0.833782	+	0.552094i	$0.186171\pi$
$272$	3.42237e10	0.379111
$273$	0	0
$274$	−6.93422e10	−0.743225
$275$	−5.24202e10	−0.552716
$276$	0	0
$277$	−1.40075e11	−1.42955	−0.714777	−	0.699353i	$-0.753472\pi$
$277$	−1.40075e11	−1.42955	−0.714777	+	0.699353i	$0.753472\pi$
$278$	5.25441e10	0.527621
$279$	0	0
$280$	−6.47213e10	−0.629269
$281$	1.76496e11	1.68872	0.844358	−	0.535780i	$-0.179982\pi$
$281$	1.76496e11	1.68872	0.844358	+	0.535780i	$0.179982\pi$
$282$	0	0
$283$	−1.68090e11	−1.55776	−0.778882	−	0.627170i	$-0.784213\pi$
$283$	−1.68090e11	−1.55776	−0.778882	+	0.627170i	$0.784213\pi$
$284$	−2.40841e10	−0.219684
$285$	0	0
$286$	5.51393e10	0.487319
$287$	2.75584e11	2.39765
$288$	0	0
$289$	−1.07286e11	−0.904693
$290$	1.22467e11	1.01678
$291$	0	0
$292$	4.52045e10	0.363880
$293$	−1.44737e11	−1.14729	−0.573646	−	0.819103i	$-0.694471\pi$
$293$	−1.44737e11	−1.14729	−0.573646	+	0.819103i	$0.694471\pi$
$294$	0	0
$295$	4.58846e10	0.352751
$296$	1.23030e11	0.931530
$297$	0	0
$298$	4.55079e10	0.334282
$299$	−1.04161e11	−0.753675
$300$	0	0
$301$	−2.88272e10	−0.202420
$302$	−2.46665e10	−0.170638
$303$	0	0
$304$	2.70589e11	1.81710
$305$	4.57040e10	0.302416
$306$	0	0
$307$	−5.43835e10	−0.349418	−0.174709	−	0.984620i	$-0.555898\pi$
$307$	−5.43835e10	−0.349418	−0.174709	+	0.984620i	$0.555898\pi$
$308$	6.74329e10	0.426966
$309$	0	0
$310$	1.97919e11	1.21719
$311$	−2.25354e10	−0.136598	−0.0682990	−	0.997665i	$-0.521757\pi$
$311$	−2.25354e10	−0.136598	−0.0682990	+	0.997665i	$0.521757\pi$
$312$	0	0
$313$	−1.33449e11	−0.785896	−0.392948	−	0.919561i	$-0.628545\pi$
$313$	−1.33449e11	−0.785896	−0.392948	+	0.919561i	$0.628545\pi$
$314$	−2.08567e11	−1.21077
$315$	0	0
$316$	−9.35322e10	−0.527678
$317$	1.53990e11	0.856495	0.428247	−	0.903662i	$-0.359131\pi$
$317$	1.53990e11	0.856495	0.428247	+	0.903662i	$0.359131\pi$
$318$	0	0
$319$	2.35178e11	1.27156
$320$	−5.24274e10	−0.279501
$321$	0	0
$322$	−4.89552e11	−2.53774
$323$	8.93615e10	0.456814
$324$	0	0
$325$	5.57116e10	0.276994
$326$	−5.27429e10	−0.258633
$327$	0	0
$328$	2.85386e11	1.36145
$329$	−1.54032e11	−0.724820
$330$	0	0
$331$	2.39934e11	1.09867	0.549333	−	0.835603i	$-0.314882\pi$
$331$	2.39934e11	1.09867	0.549333	+	0.835603i	$0.314882\pi$
$332$	1.63837e9	0.00740101
$333$	0	0
$334$	3.08667e11	1.35716
$335$	4.50882e10	0.195597
$336$	0	0
$337$	3.87512e10	0.163663	0.0818315	−	0.996646i	$-0.473923\pi$
$337$	3.87512e10	0.163663	0.0818315	+	0.996646i	$0.473923\pi$
$338$	2.20376e11	0.918417
$339$	0	0
$340$	1.68294e10	0.0682990
$341$	3.80071e11	1.52219
$342$	0	0
$343$	−8.10235e10	−0.316073
$344$	−2.98525e10	−0.114939
$345$	0	0
$346$	−1.16799e11	−0.438124
$347$	5.45577e10	0.202010	0.101005	−	0.994886i	$-0.467794\pi$
$347$	5.45577e10	0.202010	0.101005	+	0.994886i	$0.467794\pi$
$348$	0	0
$349$	−6.33934e10	−0.228733	−0.114367	−	0.993439i	$-0.536484\pi$
$349$	−6.33934e10	−0.228733	−0.114367	+	0.993439i	$0.536484\pi$
$350$	2.61842e11	0.932682
$351$	0	0
$352$	1.77550e11	0.616424
$353$	1.99546e11	0.684002	0.342001	−	0.939700i	$-0.388895\pi$
$353$	1.99546e11	0.684002	0.342001	+	0.939700i	$0.388895\pi$
$354$	0	0
$355$	1.17562e11	0.392861
$356$	−5.01496e10	−0.165479
$357$	0	0
$358$	2.12936e10	0.0685135
$359$	−4.39428e11	−1.39625	−0.698125	−	0.715976i	$-0.745982\pi$
$359$	−4.39428e11	−1.39625	−0.698125	+	0.715976i	$0.745982\pi$
$360$	0	0
$361$	3.83848e11	1.18954
$362$	7.23085e11	2.21310
$363$	0	0
$364$	−7.16669e10	−0.213975
$365$	−2.20657e11	−0.650728
$366$	0	0
$367$	−2.34148e11	−0.673742	−0.336871	−	0.941551i	$-0.609369\pi$
$367$	−2.34148e11	−0.673742	−0.336871	+	0.941551i	$0.609369\pi$
$368$	−7.10451e11	−2.01938
$369$	0	0
$370$	3.25831e11	0.903825
$371$	1.33404e11	0.365583
$372$	0	0
$373$	5.75087e11	1.53831	0.769155	−	0.639063i	$-0.220678\pi$
$373$	5.75087e11	1.53831	0.769155	+	0.639063i	$0.220678\pi$
$374$	1.24202e11	0.328252
$375$	0	0
$376$	−1.59511e11	−0.411571
$377$	−2.49944e11	−0.637245
$378$	0	0
$379$	−3.66818e11	−0.913218	−0.456609	−	0.889667i	$-0.650936\pi$
$379$	−3.66818e11	−0.913218	−0.456609	+	0.889667i	$0.650936\pi$
$380$	1.33062e11	0.327361
$381$	0	0
$382$	6.76478e11	1.62543
$383$	−5.74114e11	−1.36334	−0.681669	−	0.731660i	$-0.738746\pi$
$383$	−5.74114e11	−1.36334	−0.681669	+	0.731660i	$0.738746\pi$
$384$	0	0
$385$	−3.29160e11	−0.763544
$386$	8.30953e11	1.90517
$387$	0	0
$388$	1.91010e11	0.427871
$389$	2.56613e11	0.568205	0.284102	−	0.958794i	$-0.408304\pi$
$389$	2.56613e11	0.568205	0.284102	+	0.958794i	$0.408304\pi$
$390$	0	0
$391$	−2.34625e11	−0.507666
$392$	2.68457e11	0.574233
$393$	0	0
$394$	−2.11556e11	−0.442275
$395$	4.56559e11	0.943647
$396$	0	0
$397$	4.87408e11	0.984771	0.492385	−	0.870377i	$-0.336125\pi$
$397$	4.87408e11	0.984771	0.492385	+	0.870377i	$0.336125\pi$
$398$	−7.08513e11	−1.41538
$399$	0	0
$400$	3.79993e11	0.742173
$401$	2.25451e10	0.0435414	0.0217707	−	0.999763i	$-0.493070\pi$
$401$	2.25451e10	0.0435414	0.0217707	+	0.999763i	$0.493070\pi$
$402$	0	0
$403$	−4.03934e11	−0.762848
$404$	1.74496e11	0.325888
$405$	0	0
$406$	−1.17473e12	−2.14570
$407$	6.25704e11	1.13030
$408$	0	0
$409$	−5.20640e11	−0.919988	−0.459994	−	0.887922i	$-0.652149\pi$
$409$	−5.20640e11	−0.919988	−0.459994	+	0.887922i	$0.652149\pi$
$410$	7.55816e11	1.32096
$411$	0	0
$412$	−1.67809e11	−0.286930
$413$	−4.40135e11	−0.744407
$414$	0	0
$415$	−7.99738e9	−0.0132352
$416$	−1.88698e11	−0.308921
$417$	0	0
$418$	9.82006e11	1.57333
$419$	8.78483e11	1.39242	0.696210	−	0.717838i	$-0.254868\pi$
$419$	8.78483e11	1.39242	0.696210	+	0.717838i	$0.254868\pi$
$420$	0	0
$421$	7.17609e10	0.111332	0.0556658	−	0.998449i	$-0.482272\pi$
$421$	7.17609e10	0.111332	0.0556658	+	0.998449i	$0.482272\pi$
$422$	−8.72329e11	−1.33898
$423$	0	0
$424$	1.38149e11	0.207587
$425$	1.25492e11	0.186580
$426$	0	0
$427$	−4.38402e11	−0.638186
$428$	−8.16531e10	−0.117618
$429$	0	0
$430$	−7.90613e10	−0.111521
$431$	1.77962e11	0.248416	0.124208	−	0.992256i	$-0.460361\pi$
$431$	1.77962e11	0.248416	0.124208	+	0.992256i	$0.460361\pi$
$432$	0	0
$433$	−1.21148e12	−1.65622	−0.828112	−	0.560563i	$-0.810585\pi$
$433$	−1.21148e12	−1.65622	−0.828112	+	0.560563i	$0.810585\pi$
$434$	−1.89848e12	−2.56863
$435$	0	0
$436$	−4.42520e10	−0.0586468
$437$	−1.85506e12	−2.43327
$438$	0	0
$439$	−5.87231e11	−0.754603	−0.377302	−	0.926090i	$-0.623148\pi$
$439$	−5.87231e11	−0.754603	−0.377302	+	0.926090i	$0.623148\pi$
$440$	−3.40868e11	−0.433560
$441$	0	0
$442$	−1.32001e11	−0.164504
$443$	1.21527e12	1.49919	0.749593	−	0.661899i	$-0.230249\pi$
$443$	1.21527e12	1.49919	0.749593	+	0.661899i	$0.230249\pi$
$444$	0	0
$445$	2.44795e11	0.295926
$446$	2.42280e10	0.0289942
$447$	0	0
$448$	5.02894e11	0.589828
$449$	1.69159e12	1.96421	0.982103	−	0.188342i	$-0.0603115\pi$
$449$	1.69159e12	1.96421	0.982103	+	0.188342i	$0.0603115\pi$
$450$	0	0
$451$	1.45142e12	1.65196
$452$	−3.39749e11	−0.382855
$453$	0	0
$454$	−3.80388e11	−0.420219
$455$	3.49827e11	0.382651
$456$	0	0
$457$	−3.52686e11	−0.378239	−0.189119	−	0.981954i	$-0.560563\pi$
$457$	−3.52686e11	−0.378239	−0.189119	+	0.981954i	$0.560563\pi$
$458$	−4.35416e11	−0.462392
$459$	0	0
$460$	−3.49362e11	−0.363803
$461$	7.83575e11	0.808028	0.404014	−	0.914753i	$-0.367615\pi$
$461$	7.83575e11	0.808028	0.404014	+	0.914753i	$0.367615\pi$
$462$	0	0
$463$	8.28011e11	0.837378	0.418689	−	0.908130i	$-0.362490\pi$
$463$	8.28011e11	0.837378	0.418689	+	0.908130i	$0.362490\pi$
$464$	−1.70479e12	−1.70742
$465$	0	0
$466$	9.95760e11	0.978179
$467$	9.44763e11	0.919172	0.459586	−	0.888133i	$-0.347998\pi$
$467$	9.44763e11	0.919172	0.459586	+	0.888133i	$0.347998\pi$
$468$	0	0
$469$	−4.32495e11	−0.412766
$470$	−4.22447e11	−0.399330
$471$	0	0
$472$	−4.55789e11	−0.422693
$473$	−1.51824e11	−0.139465
$474$	0	0
$475$	9.92199e11	0.894288
$476$	−1.61431e11	−0.144131
$477$	0	0
$478$	−2.30480e12	−2.01934
$479$	1.31925e12	1.14503	0.572514	−	0.819895i	$-0.305968\pi$
$479$	1.31925e12	1.14503	0.572514	+	0.819895i	$0.305968\pi$
$480$	0	0
$481$	−6.64991e11	−0.566452
$482$	−3.15798e11	−0.266500
$483$	0	0
$484$	−6.94801e10	−0.0575515
$485$	−9.32376e11	−0.765162
$486$	0	0
$487$	−7.98399e11	−0.643190	−0.321595	−	0.946877i	$-0.604219\pi$
$487$	−7.98399e11	−0.643190	−0.321595	+	0.946877i	$0.604219\pi$
$488$	−4.53995e11	−0.362378
$489$	0	0
$490$	7.10981e11	0.557154
$491$	−9.36951e11	−0.727529	−0.363765	−	0.931491i	$-0.618509\pi$
$491$	−9.36951e11	−0.727529	−0.363765	+	0.931491i	$0.618509\pi$
$492$	0	0
$493$	−5.63004e11	−0.429240
$494$	−1.04366e12	−0.788478
$495$	0	0
$496$	−2.75512e12	−2.04396
$497$	−1.12768e12	−0.829051
$498$	0	0
$499$	6.92404e11	0.499928	0.249964	−	0.968255i	$-0.419581\pi$
$499$	6.92404e11	0.499928	0.249964	+	0.968255i	$0.419581\pi$
$500$	4.96044e11	0.354940
$501$	0	0
$502$	−9.59508e11	−0.674345
$503$	−4.51453e11	−0.314454	−0.157227	−	0.987563i	$-0.550255\pi$
$503$	−4.51453e11	−0.314454	−0.157227	+	0.987563i	$0.550255\pi$
$504$	0	0
$505$	−8.51766e11	−0.582786
$506$	−2.57832e12	−1.74848
$507$	0	0
$508$	8.74484e11	0.582593
$509$	1.19633e12	0.789987	0.394993	−	0.918684i	$-0.370747\pi$
$509$	1.19633e12	0.789987	0.394993	+	0.918684i	$0.370747\pi$
$510$	0	0
$511$	2.11658e12	1.37322
$512$	1.52144e11	0.0978454
$513$	0	0
$514$	−1.49141e12	−0.942462
$515$	8.19124e11	0.513118
$516$	0	0
$517$	−8.11241e11	−0.499393
$518$	−3.12543e12	−1.90733
$519$	0	0
$520$	3.62270e11	0.217279
$521$	2.45881e12	1.46203	0.731013	−	0.682364i	$-0.239048\pi$
$521$	2.45881e12	1.46203	0.731013	+	0.682364i	$0.239048\pi$
$522$	0	0
$523$	7.38007e11	0.431323	0.215662	−	0.976468i	$-0.430809\pi$
$523$	7.38007e11	0.431323	0.215662	+	0.976468i	$0.430809\pi$
$524$	5.12978e11	0.297240
$525$	0	0
$526$	3.11686e12	1.77534
$527$	−9.09872e11	−0.513845
$528$	0	0
$529$	3.06943e12	1.70415
$530$	3.65872e11	0.201413
$531$	0	0
$532$	−1.27635e12	−0.690827
$533$	−1.54255e12	−0.827880
$534$	0	0
$535$	3.98573e11	0.210337
$536$	−4.47878e11	−0.234379
$537$	0	0
$538$	−3.57490e12	−1.83968
$539$	1.36532e12	0.696764
$540$	0	0
$541$	−5.43907e11	−0.272984	−0.136492	−	0.990641i	$-0.543583\pi$
$541$	−5.43907e11	−0.272984	−0.136492	+	0.990641i	$0.543583\pi$
$542$	−3.89514e12	−1.93877
$543$	0	0
$544$	−4.25047e11	−0.208086
$545$	2.16008e11	0.104878
$546$	0	0
$547$	3.81622e12	1.82260	0.911298	−	0.411747i	$-0.135081\pi$
$547$	3.81622e12	1.82260	0.911298	+	0.411747i	$0.135081\pi$
$548$	4.74672e11	0.224844
$549$	0	0
$550$	1.37904e12	0.642608
$551$	−4.45139e12	−2.05737
$552$	0	0
$553$	−4.37940e12	−1.99137
$554$	3.68501e12	1.66205
$555$	0	0
$556$	−3.59683e11	−0.159618
$557$	−3.04799e12	−1.34173	−0.670865	−	0.741580i	$-0.734077\pi$
$557$	−3.04799e12	−1.34173	−0.670865	+	0.741580i	$0.734077\pi$
$558$	0	0
$559$	1.61357e11	0.0698932
$560$	2.38607e12	1.02527
$561$	0	0
$562$	−4.64317e12	−1.96336
$563$	3.04470e12	1.27719	0.638597	−	0.769542i	$-0.279515\pi$
$563$	3.04470e12	1.27719	0.638597	+	0.769542i	$0.279515\pi$
$564$	0	0
$565$	1.65842e12	0.684661
$566$	4.42201e12	1.81112
$567$	0	0
$568$	−1.16779e12	−0.470756
$569$	−1.54929e12	−0.619624	−0.309812	−	0.950798i	$-0.600266\pi$
$569$	−1.54929e12	−0.619624	−0.309812	+	0.950798i	$0.600266\pi$
$570$	0	0
$571$	3.65555e11	0.143910	0.0719549	−	0.997408i	$-0.477076\pi$
$571$	3.65555e11	0.143910	0.0719549	+	0.997408i	$0.477076\pi$
$572$	−3.77448e11	−0.147426
$573$	0	0
$574$	−7.24994e12	−2.78760
$575$	−2.60508e12	−0.993840
$576$	0	0
$577$	−7.02681e11	−0.263917	−0.131958	−	0.991255i	$-0.542127\pi$
$577$	−7.02681e11	−0.263917	−0.131958	+	0.991255i	$0.542127\pi$
$578$	2.82241e12	1.05183
$579$	0	0
$580$	−8.38329e11	−0.307601
$581$	7.67125e10	0.0279302
$582$	0	0
$583$	7.02598e11	0.251883
$584$	2.19187e12	0.779751
$585$	0	0
$586$	3.80765e12	1.33388
$587$	1.17216e12	0.407488	0.203744	−	0.979024i	$-0.434689\pi$
$587$	1.17216e12	0.407488	0.203744	+	0.979024i	$0.434689\pi$
$588$	0	0
$589$	−7.19389e12	−2.46289
$590$	−1.20711e12	−0.410122
$591$	0	0
$592$	−4.53571e12	−1.51774
$593$	2.02177e12	0.671406	0.335703	−	0.941968i	$-0.391026\pi$
$593$	2.02177e12	0.671406	0.335703	+	0.941968i	$0.391026\pi$
$594$	0	0
$595$	7.87995e11	0.257749
$596$	−3.11517e11	−0.101129
$597$	0	0
$598$	2.74021e12	0.876251
$599$	−3.38829e12	−1.07538	−0.537688	−	0.843144i	$-0.680702\pi$
$599$	−3.38829e12	−1.07538	−0.537688	+	0.843144i	$0.680702\pi$
$600$	0	0
$601$	3.27712e12	1.02461	0.512303	−	0.858805i	$-0.328792\pi$
$601$	3.27712e12	1.02461	0.512303	+	0.858805i	$0.328792\pi$
$602$	7.58372e11	0.235341
$603$	0	0
$604$	1.68851e11	0.0516223
$605$	3.39153e11	0.102919
$606$	0	0
$607$	2.63454e12	0.787692	0.393846	−	0.919177i	$-0.371144\pi$
$607$	2.63454e12	0.787692	0.393846	+	0.919177i	$0.371144\pi$
$608$	−3.36063e12	−0.997367
$609$	0	0
$610$	−1.20236e12	−0.351601
$611$	8.62177e11	0.250271
$612$	0	0
$613$	1.97763e12	0.565682	0.282841	−	0.959167i	$-0.408723\pi$
$613$	1.97763e12	0.565682	0.282841	+	0.959167i	$0.408723\pi$
$614$	1.43069e12	0.406246
$615$	0	0
$616$	3.26967e12	0.914936
$617$	1.80428e12	0.501211	0.250605	−	0.968089i	$-0.419370\pi$
$617$	1.80428e12	0.501211	0.250605	+	0.968089i	$0.419370\pi$
$618$	0	0
$619$	4.19267e12	1.14784	0.573922	−	0.818910i	$-0.305421\pi$
$619$	4.19267e12	1.14784	0.573922	+	0.818910i	$0.305421\pi$
$620$	−1.35482e12	−0.368231
$621$	0	0
$622$	5.92851e11	0.158814
$623$	−2.34813e12	−0.624489
$624$	0	0
$625$	−1.15858e11	−0.0303715
$626$	3.51070e12	0.913712
$627$	0	0
$628$	1.42771e12	0.366288
$629$	−1.49791e12	−0.381555
$630$	0	0
$631$	7.60008e12	1.90847	0.954236	−	0.299054i	$-0.0966711\pi$
$631$	7.60008e12	1.90847	0.954236	+	0.299054i	$0.0966711\pi$
$632$	−4.53517e12	−1.13075
$633$	0	0
$634$	−4.05108e12	−0.995793
$635$	−4.26862e12	−1.04185
$636$	0	0
$637$	−1.45105e12	−0.349184
$638$	−6.18693e12	−1.47837
$639$	0	0
$640$	3.17866e12	0.748918
$641$	−2.51743e12	−0.588974	−0.294487	−	0.955655i	$-0.595149\pi$
$641$	−2.51743e12	−0.588974	−0.294487	+	0.955655i	$0.595149\pi$
$642$	0	0
$643$	1.22772e12	0.283238	0.141619	−	0.989921i	$-0.454769\pi$
$643$	1.22772e12	0.283238	0.141619	+	0.989921i	$0.454769\pi$
$644$	3.35116e12	0.767729
$645$	0	0
$646$	−2.35088e12	−0.531109
$647$	1.27600e12	0.286274	0.143137	−	0.989703i	$-0.454281\pi$
$647$	1.27600e12	0.286274	0.143137	+	0.989703i	$0.454281\pi$
$648$	0	0
$649$	−2.31806e12	−0.512888
$650$	−1.46563e12	−0.322044
$651$	0	0
$652$	3.61043e11	0.0782430
$653$	5.09778e12	1.09717	0.548583	−	0.836096i	$-0.315168\pi$
$653$	5.09778e12	1.09717	0.548583	+	0.836096i	$0.315168\pi$
$654$	0	0
$655$	−2.50400e12	−0.531555
$656$	−1.05213e13	−2.21821
$657$	0	0
$658$	4.05220e12	0.842703
$659$	5.41368e12	1.11817	0.559085	−	0.829110i	$-0.311153\pi$
$659$	5.41368e12	1.11817	0.559085	+	0.829110i	$0.311153\pi$
$660$	0	0
$661$	−6.99933e11	−0.142610	−0.0713050	−	0.997455i	$-0.522716\pi$
$661$	−6.99933e11	−0.142610	−0.0713050	+	0.997455i	$0.522716\pi$
$662$	−6.31206e12	−1.27735
$663$	0	0
$664$	7.94410e10	0.0158595
$665$	6.23027e12	1.23541
$666$	0	0
$667$	1.16874e13	2.28640
$668$	−2.11294e12	−0.410575
$669$	0	0
$670$	−1.18616e12	−0.227408
$671$	−2.30893e12	−0.439703
$672$	0	0
$673$	9.59739e12	1.80337	0.901686	−	0.432391i	$-0.142330\pi$
$673$	9.59739e12	1.80337	0.901686	+	0.432391i	$0.142330\pi$
$674$	−1.01945e12	−0.190281
$675$	0	0
$676$	−1.50855e12	−0.277844
$677$	−6.93140e12	−1.26815	−0.634077	−	0.773270i	$-0.718620\pi$
$677$	−6.93140e12	−1.26815	−0.634077	+	0.773270i	$0.718620\pi$
$678$	0	0
$679$	8.94354e12	1.61471
$680$	8.16022e11	0.146356
$681$	0	0
$682$	−9.99870e12	−1.76976
$683$	1.01426e13	1.78343	0.891715	−	0.452597i	$-0.149503\pi$
$683$	1.01426e13	1.78343	0.891715	+	0.452597i	$0.149503\pi$
$684$	0	0
$685$	−2.31702e12	−0.402089
$686$	2.13152e12	0.367478
$687$	0	0
$688$	1.10057e12	0.187271
$689$	−7.46713e11	−0.126231
$690$	0	0
$691$	−1.50973e12	−0.251911	−0.125955	−	0.992036i	$-0.540200\pi$
$691$	−1.50973e12	−0.251911	−0.125955	+	0.992036i	$0.540200\pi$
$692$	7.99532e11	0.132543
$693$	0	0
$694$	−1.43528e12	−0.234865
$695$	1.75572e12	0.285446
$696$	0	0
$697$	−3.47463e12	−0.557650
$698$	1.66772e12	0.265934
$699$	0	0
$700$	−1.79240e12	−0.282159
$701$	−3.00850e12	−0.470565	−0.235282	−	0.971927i	$-0.575601\pi$
$701$	−3.00850e12	−0.470565	−0.235282	+	0.971927i	$0.575601\pi$
$702$	0	0
$703$	−1.18432e13	−1.82882
$704$	2.64859e12	0.406385
$705$	0	0
$706$	−5.24956e12	−0.795247
$707$	8.17031e12	1.22985
$708$	0	0
$709$	6.68286e12	0.993240	0.496620	−	0.867968i	$-0.334574\pi$
$709$	6.68286e12	0.993240	0.496620	+	0.867968i	$0.334574\pi$
$710$	−3.09276e12	−0.456755
$711$	0	0
$712$	−2.43164e12	−0.354601
$713$	1.88880e13	2.73706
$714$	0	0
$715$	1.84244e12	0.263642
$716$	−1.45762e11	−0.0207270
$717$	0	0
$718$	1.15603e13	1.62333
$719$	4.40326e12	0.614461	0.307230	−	0.951635i	$-0.400598\pi$
$719$	4.40326e12	0.614461	0.307230	+	0.951635i	$0.400598\pi$
$720$	0	0
$721$	−7.85720e12	−1.08283
$722$	−1.00981e13	−1.38300
$723$	0	0
$724$	−4.94977e12	−0.669517
$725$	−6.25115e12	−0.840309
$726$	0	0
$727$	5.60251e11	0.0743837	0.0371919	−	0.999308i	$-0.488159\pi$
$727$	5.60251e11	0.0743837	0.0371919	+	0.999308i	$0.488159\pi$
$728$	−3.47497e12	−0.458521
$729$	0	0
$730$	5.80492e12	0.756560
$731$	3.63460e11	0.0470792
$732$	0	0
$733$	1.16288e13	1.48787	0.743937	−	0.668249i	$-0.232956\pi$
$733$	1.16288e13	1.48787	0.743937	+	0.668249i	$0.232956\pi$
$734$	6.15985e12	0.783317
$735$	0	0
$736$	8.82357e12	1.10839
$737$	−2.27782e12	−0.284391
$738$	0	0
$739$	−8.52376e12	−1.05131	−0.525656	−	0.850697i	$-0.676180\pi$
$739$	−8.52376e12	−1.05131	−0.525656	+	0.850697i	$0.676180\pi$
$740$	−2.23043e12	−0.273429
$741$	0	0
$742$	−3.50952e12	−0.425041
$743$	−7.66343e12	−0.922515	−0.461258	−	0.887266i	$-0.652602\pi$
$743$	−7.66343e12	−0.922515	−0.461258	+	0.887266i	$0.652602\pi$
$744$	0	0
$745$	1.52061e12	0.180848
$746$	−1.51291e13	−1.78850
$747$	0	0
$748$	−8.50209e11	−0.0993045
$749$	−3.82319e12	−0.443872
$750$	0	0
$751$	−3.80411e12	−0.436389	−0.218194	−	0.975905i	$-0.570017\pi$
$751$	−3.80411e12	−0.436389	−0.218194	+	0.975905i	$0.570017\pi$
$752$	5.88066e12	0.670573
$753$	0	0
$754$	6.57540e12	0.740885
$755$	−8.24213e11	−0.0923162
$756$	0	0
$757$	−1.39063e13	−1.53915	−0.769575	−	0.638556i	$-0.779532\pi$
$757$	−1.39063e13	−1.53915	−0.769575	+	0.638556i	$0.779532\pi$
$758$	9.65007e12	1.06174
$759$	0	0
$760$	6.45187e12	0.701495
$761$	−1.60656e13	−1.73646	−0.868230	−	0.496162i	$-0.834742\pi$
$761$	−1.60656e13	−1.73646	−0.868230	+	0.496162i	$0.834742\pi$
$762$	0	0
$763$	−2.07199e12	−0.221323
$764$	−4.63073e12	−0.491733
$765$	0	0
$766$	1.51035e13	1.58507
$767$	2.46360e12	0.257034
$768$	0	0
$769$	9.39173e12	0.968449	0.484225	−	0.874944i	$-0.339102\pi$
$769$	9.39173e12	0.968449	0.484225	+	0.874944i	$0.339102\pi$
$770$	8.65938e12	0.887725
$771$	0	0
$772$	−5.68816e12	−0.576360
$773$	−7.25850e11	−0.0731205	−0.0365602	−	0.999331i	$-0.511640\pi$
$773$	−7.25850e11	−0.0731205	−0.0365602	+	0.999331i	$0.511640\pi$
$774$	0	0
$775$	−1.01025e13	−1.00594
$776$	9.26164e12	0.916875
$777$	0	0
$778$	−6.75083e12	−0.660616
$779$	−2.74722e13	−2.67285
$780$	0	0
$781$	−5.93914e12	−0.571207
$782$	6.17239e12	0.590232
$783$	0	0
$784$	−9.89718e12	−0.935598
$785$	−6.96909e12	−0.655032
$786$	0	0
$787$	2.02032e12	0.187730	0.0938649	−	0.995585i	$-0.470078\pi$
$787$	2.02032e12	0.187730	0.0938649	+	0.995585i	$0.470078\pi$
$788$	1.44818e12	0.133799
$789$	0	0
$790$	−1.20109e13	−1.09712
$791$	−1.59079e13	−1.44483
$792$	0	0
$793$	2.45391e12	0.220358
$794$	−1.28225e13	−1.14493
$795$	0	0
$796$	4.85002e12	0.428189
$797$	1.88088e13	1.65119	0.825597	−	0.564260i	$-0.190838\pi$
$797$	1.88088e13	1.65119	0.825597	+	0.564260i	$0.190838\pi$
$798$	0	0
$799$	1.94207e12	0.168580
$800$	−4.71938e12	−0.407362
$801$	0	0
$802$	−5.93104e11	−0.0506228
$803$	1.11474e13	0.946136
$804$	0	0
$805$	−1.63580e13	−1.37293
$806$	1.06265e13	0.886916
$807$	0	0
$808$	8.46091e12	0.698338
$809$	7.98963e12	0.655780	0.327890	−	0.944716i	$-0.393662\pi$
$809$	7.98963e12	0.655780	0.327890	+	0.944716i	$0.393662\pi$
$810$	0	0
$811$	1.98323e13	1.60982	0.804912	−	0.593395i	$-0.202213\pi$
$811$	1.98323e13	1.60982	0.804912	+	0.593395i	$0.202213\pi$
$812$	8.04142e12	0.649128
$813$	0	0
$814$	−1.64607e13	−1.31413
$815$	−1.76236e12	−0.139922
$816$	0	0
$817$	2.87370e12	0.225653
$818$	1.36967e13	1.06961
$819$	0	0
$820$	−5.17382e12	−0.399622
$821$	−1.32468e13	−1.01757	−0.508787	−	0.860892i	$-0.669906\pi$
$821$	−1.32468e13	−1.01757	−0.508787	+	0.860892i	$0.669906\pi$
$822$	0	0
$823$	−1.59550e13	−1.21227	−0.606133	−	0.795363i	$-0.707280\pi$
$823$	−1.59550e13	−1.21227	−0.606133	+	0.795363i	$0.707280\pi$
$824$	−8.13667e12	−0.614857
$825$	0	0
$826$	1.15788e13	0.865475
$827$	1.55293e13	1.15445	0.577226	−	0.816584i	$-0.304135\pi$
$827$	1.55293e13	1.15445	0.577226	+	0.816584i	$0.304135\pi$
$828$	0	0
$829$	9.57611e12	0.704196	0.352098	−	0.935963i	$-0.385468\pi$
$829$	9.57611e12	0.704196	0.352098	+	0.935963i	$0.385468\pi$
$830$	2.10391e11	0.0153878
$831$	0	0
$832$	−2.81489e12	−0.203660
$833$	−3.26852e12	−0.235206
$834$	0	0
$835$	1.03139e13	0.734231
$836$	−6.72217e12	−0.475972
$837$	0	0
$838$	−2.31107e13	−1.61888
$839$	−7.28075e12	−0.507279	−0.253640	−	0.967299i	$-0.581628\pi$
$839$	−7.28075e12	−0.507279	−0.253640	+	0.967299i	$0.581628\pi$
$840$	0	0
$841$	1.35379e13	0.933191
$842$	−1.88785e12	−0.129438
$843$	0	0
$844$	5.97140e12	0.405075
$845$	7.36371e12	0.496868
$846$	0	0
$847$	−3.25323e12	−0.217190
$848$	−5.09311e12	−0.338222
$849$	0	0
$850$	−3.30137e12	−0.216925
$851$	3.10951e13	2.03240
$852$	0	0
$853$	−1.46073e13	−0.944710	−0.472355	−	0.881408i	$-0.656596\pi$
$853$	−1.46073e13	−0.944710	−0.472355	+	0.881408i	$0.656596\pi$
$854$	1.15333e13	0.741979
$855$	0	0
$856$	−3.95918e12	−0.252042
$857$	5.33231e12	0.337677	0.168839	−	0.985644i	$-0.445998\pi$
$857$	5.33231e12	0.337677	0.168839	+	0.985644i	$0.445998\pi$
$858$	0	0
$859$	−2.80034e13	−1.75486	−0.877429	−	0.479707i	$-0.840743\pi$
$859$	−2.80034e13	−1.75486	−0.877429	+	0.479707i	$0.840743\pi$
$860$	5.41202e11	0.0337378
$861$	0	0
$862$	−4.68174e12	−0.288818
$863$	−1.68340e13	−1.03309	−0.516545	−	0.856260i	$-0.672782\pi$
$863$	−1.68340e13	−1.03309	−0.516545	+	0.856260i	$0.672782\pi$
$864$	0	0
$865$	−3.90275e12	−0.237027
$866$	3.18709e13	1.92559
$867$	0	0
$868$	1.29957e13	0.777074
$869$	−2.30650e13	−1.37203
$870$	0	0
$871$	2.42084e12	0.142523
$872$	−2.14568e12	−0.125673
$873$	0	0
$874$	4.88019e13	2.82902
$875$	2.32260e13	1.33948
$876$	0	0
$877$	2.28783e13	1.30595	0.652973	−	0.757381i	$-0.273522\pi$
$877$	2.28783e13	1.30595	0.652973	+	0.757381i	$0.273522\pi$
$878$	1.54486e13	0.877330
$879$	0	0
$880$	1.25667e13	0.706398
$881$	−2.40339e13	−1.34410	−0.672052	−	0.740504i	$-0.734587\pi$
$881$	−2.40339e13	−1.34410	−0.672052	+	0.740504i	$0.734587\pi$
$882$	0	0
$883$	−2.37323e13	−1.31376	−0.656882	−	0.753993i	$-0.728125\pi$
$883$	−2.37323e13	−1.31376	−0.656882	+	0.753993i	$0.728125\pi$
$884$	9.03592e11	0.0497665
$885$	0	0
$886$	−3.19707e13	−1.74301
$887$	−1.92837e12	−0.104600	−0.0523002	−	0.998631i	$-0.516655\pi$
$887$	−1.92837e12	−0.104600	−0.0523002	+	0.998631i	$0.516655\pi$
$888$	0	0
$889$	4.09455e13	2.19861
$890$	−6.43995e12	−0.344055
$891$	0	0
$892$	−1.65849e11	−0.00877145
$893$	1.53550e13	0.808013
$894$	0	0
$895$	7.11510e11	0.0370661
$896$	−3.04904e13	−1.58043
$897$	0	0
$898$	−4.45016e13	−2.28366
$899$	4.53237e13	2.31423
$900$	0	0
$901$	−1.68199e12	−0.0850279
$902$	−3.81832e13	−1.92063
$903$	0	0
$904$	−1.64737e13	−0.820412
$905$	2.41613e13	1.19730
$906$	0	0
$907$	−7.87264e12	−0.386267	−0.193134	−	0.981172i	$-0.561865\pi$
$907$	−7.87264e12	−0.386267	−0.193134	+	0.981172i	$0.561865\pi$
$908$	2.60389e12	0.127127
$909$	0	0
$910$	−9.20308e12	−0.444884
$911$	−5.84560e12	−0.281188	−0.140594	−	0.990067i	$-0.544901\pi$
$911$	−5.84560e12	−0.281188	−0.140594	+	0.990067i	$0.544901\pi$
$912$	0	0
$913$	4.04022e11	0.0192436
$914$	9.27830e12	0.439755
$915$	0	0
$916$	2.98058e12	0.139885
$917$	2.40189e13	1.12174
$918$	0	0
$919$	1.30582e13	0.603898	0.301949	−	0.953324i	$-0.402363\pi$
$919$	1.30582e13	0.603898	0.301949	+	0.953324i	$0.402363\pi$
$920$	−1.69398e13	−0.779585
$921$	0	0
$922$	−2.06139e13	−0.939444
$923$	6.31204e12	0.286261
$924$	0	0
$925$	−1.66316e13	−0.746957
$926$	−2.17829e13	−0.973567
$927$	0	0
$928$	2.11730e13	0.937165
$929$	−3.22164e11	−0.0141908	−0.00709538	−	0.999975i	$-0.502259\pi$
$929$	−3.22164e11	−0.0141908	−0.00709538	+	0.999975i	$0.502259\pi$
$930$	0	0
$931$	−2.58425e13	−1.12736
$932$	−6.81633e12	−0.295923
$933$	0	0
$934$	−2.48543e13	−1.06866
$935$	4.15013e12	0.177586
$936$	0	0
$937$	−2.39611e13	−1.01550	−0.507748	−	0.861506i	$-0.669522\pi$
$937$	−2.39611e13	−1.01550	−0.507748	+	0.861506i	$0.669522\pi$
$938$	1.13779e13	0.479897
$939$	0	0
$940$	2.89180e12	0.120807
$941$	−1.17349e13	−0.487895	−0.243947	−	0.969788i	$-0.578442\pi$
$941$	−1.17349e13	−0.487895	−0.243947	+	0.969788i	$0.578442\pi$
$942$	0	0
$943$	7.21300e13	2.97039
$944$	1.68035e13	0.688694
$945$	0	0
$946$	3.99412e12	0.162148
$947$	4.64389e13	1.87632	0.938160	−	0.346203i	$-0.112529\pi$
$947$	4.64389e13	1.87632	0.938160	+	0.346203i	$0.112529\pi$
$948$	0	0
$949$	−1.18473e13	−0.474157
$950$	−2.61023e13	−1.03973
$951$	0	0
$952$	−7.82744e12	−0.308854
$953$	8.15486e12	0.320257	0.160128	−	0.987096i	$-0.448809\pi$
$953$	8.15486e12	0.320257	0.160128	+	0.987096i	$0.448809\pi$
$954$	0	0
$955$	2.26040e13	0.879366
$956$	1.57772e13	0.610899
$957$	0	0
$958$	−3.47060e13	−1.33125
$959$	2.22253e13	0.848523
$960$	0	0
$961$	4.68080e13	1.77037
$962$	1.74942e13	0.658578
$963$	0	0
$964$	2.16175e12	0.0806230
$965$	2.77656e13	1.03071
$966$	0	0
$967$	2.76860e13	1.01822	0.509109	−	0.860702i	$-0.329975\pi$
$967$	2.76860e13	1.01822	0.509109	+	0.860702i	$0.329975\pi$
$968$	−3.36894e12	−0.123326
$969$	0	0
$970$	2.45285e13	0.889606
$971$	2.46465e13	0.889750	0.444875	−	0.895593i	$-0.353248\pi$
$971$	2.46465e13	0.889750	0.444875	+	0.895593i	$0.353248\pi$
$972$	0	0
$973$	−1.68412e13	−0.602373
$974$	2.10039e13	0.747797
$975$	0	0
$976$	1.67374e13	0.590423
$977$	4.94639e12	0.173685	0.0868427	−	0.996222i	$-0.472322\pi$
$977$	4.94639e12	0.173685	0.0868427	+	0.996222i	$0.472322\pi$
$978$	0	0
$979$	−1.23669e13	−0.430267
$980$	−4.86691e12	−0.168553
$981$	0	0
$982$	2.46488e13	0.845853
$983$	3.98081e13	1.35982	0.679908	−	0.733297i	$-0.262020\pi$
$983$	3.98081e13	1.35982	0.679908	+	0.733297i	$0.262020\pi$
$984$	0	0
$985$	−7.06899e12	−0.239273
$986$	1.48112e13	0.499051
$987$	0	0
$988$	7.14425e12	0.238534
$989$	−7.54508e12	−0.250773
$990$	0	0
$991$	2.28757e13	0.753430	0.376715	−	0.926329i	$-0.377054\pi$
$991$	2.28757e13	0.753430	0.376715	+	0.926329i	$0.377054\pi$
$992$	3.42177e13	1.12188
$993$	0	0
$994$	2.96664e13	0.963886
$995$	−2.36744e13	−0.765730
$996$	0	0
$997$	4.85768e13	1.55704	0.778521	−	0.627618i	$-0.215970\pi$
$997$	4.85768e13	1.55704	0.778521	+	0.627618i	$0.215970\pi$
$998$	−1.82154e13	−0.581235
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.10.a.c.1.3		15
3.2	odd	2		43.10.a.a.1.13	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.13	✓	15	3.2	odd	2
387.10.a.c.1.3		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)

\(f(q)\)	\(=\)	\(q-26.3075 q^{2} +180.084 q^{4} -879.044 q^{5} +8431.97 q^{7} +8731.88 q^{8} +O(q^{10})\)	\(q-26.3075 q^{2} +180.084 q^{4} -879.044 q^{5} +8431.97 q^{7} +8731.88 q^{8} +23125.4 q^{10} +44408.6 q^{11} -47197.0 q^{13} -221824. q^{14} -321917. q^{16} -106312. q^{17} -840557. q^{19} -158302. q^{20} -1.16828e6 q^{22} +2.20694e6 q^{23} -1.18041e6 q^{25} +1.24163e6 q^{26} +1.51846e6 q^{28} +5.29576e6 q^{29} +8.55848e6 q^{31} +3.99810e6 q^{32} +2.79681e6 q^{34} -7.41208e6 q^{35} +1.40897e7 q^{37} +2.21129e7 q^{38} -7.67571e6 q^{40} +3.26833e7 q^{41} -3.41880e6 q^{43} +7.99729e6 q^{44} -5.80590e7 q^{46} -1.82676e7 q^{47} +3.07445e7 q^{49} +3.10535e7 q^{50} -8.49942e6 q^{52} +1.58212e7 q^{53} -3.90372e7 q^{55} +7.36269e7 q^{56} -1.39318e8 q^{58} -5.21983e7 q^{59} -5.19929e7 q^{61} -2.25152e8 q^{62} +5.96414e7 q^{64} +4.14882e7 q^{65} -5.12923e7 q^{67} -1.91451e7 q^{68} +1.94993e8 q^{70} -1.33738e8 q^{71} +2.51019e8 q^{73} -3.70665e8 q^{74} -1.51371e8 q^{76} +3.74452e8 q^{77} -5.19381e8 q^{79} +2.82979e8 q^{80} -8.59815e8 q^{82} +9.09782e6 q^{83} +9.34532e7 q^{85} +8.99401e7 q^{86} +3.87771e8 q^{88} -2.78479e8 q^{89} -3.97963e8 q^{91} +3.97434e8 q^{92} +4.80576e8 q^{94} +7.38887e8 q^{95} +1.06067e9 q^{97} -8.08811e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) \) 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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