LMFDB - Embedded newform 387.10.a.c.1.5

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			1.5
Root			$-22.4329$ 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)

$f(q)$	$=$	$q-20.4329 q^{2} -94.4979 q^{4} +2583.58 q^{5} -1769.99 q^{7} +12392.5 q^{8} +O(q^{10})$	\(q-20.4329 q^{2} -94.4979 q^{4} +2583.58 q^{5} -1769.99 q^{7} +12392.5 q^{8} -52790.0 q^{10} +74570.0 q^{11} +7100.10 q^{13} +36165.9 q^{14} -204831. q^{16} +268650. q^{17} +572153. q^{19} -244143. q^{20} -1.52368e6 q^{22} -1.28932e6 q^{23} +4.72177e6 q^{25} -145075. q^{26} +167260. q^{28} +6.39915e6 q^{29} -2.00450e6 q^{31} -2.15967e6 q^{32} -5.48930e6 q^{34} -4.57291e6 q^{35} +1.49299e7 q^{37} -1.16907e7 q^{38} +3.20170e7 q^{40} +1.77326e7 q^{41} -3.41880e6 q^{43} -7.04671e6 q^{44} +2.63445e7 q^{46} -1.13138e7 q^{47} -3.72207e7 q^{49} -9.64794e7 q^{50} -670945. q^{52} +1.02987e8 q^{53} +1.92658e8 q^{55} -2.19346e7 q^{56} -1.30753e8 q^{58} +8.07005e7 q^{59} +6.21644e7 q^{61} +4.09577e7 q^{62} +1.49002e8 q^{64} +1.83437e7 q^{65} +1.55110e8 q^{67} -2.53869e7 q^{68} +9.34377e7 q^{70} +1.87869e8 q^{71} +4.82049e7 q^{73} -3.05060e8 q^{74} -5.40673e7 q^{76} -1.31988e8 q^{77} -4.54354e8 q^{79} -5.29198e8 q^{80} -3.62328e8 q^{82} -1.00047e8 q^{83} +6.94081e8 q^{85} +6.98559e7 q^{86} +9.24108e8 q^{88} -1.13769e9 q^{89} -1.25671e7 q^{91} +1.21838e8 q^{92} +2.31174e8 q^{94} +1.47821e9 q^{95} -2.37271e8 q^{97} +7.60527e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−20.4329	−0.903014	−0.451507	−	0.892268i	$-0.649113\pi$
$2$	−20.4329	−0.903014	−0.451507	+	0.892268i	$0.649113\pi$
$3$	0	0
$3$	0	0
$4$	−94.4979	−0.184566
$5$	2583.58	1.84866	0.924331	−	0.381592i	$-0.124624\pi$
$5$	2583.58	1.84866	0.924331	+	0.381592i	$0.124624\pi$
$6$	0	0
$7$	−1769.99	−0.278631	−0.139315	−	0.990248i	$-0.544490\pi$
$7$	−1769.99	−0.278631	−0.139315	+	0.990248i	$0.544490\pi$
$8$	12392.5	1.06968
$9$	0	0
$10$	−52790.0	−1.66937
$11$	74570.0	1.53567	0.767833	−	0.640650i	$-0.221335\pi$
$11$	74570.0	1.53567	0.767833	+	0.640650i	$0.221335\pi$
$12$	0	0
$13$	7100.10	0.0689476	0.0344738	−	0.999406i	$-0.489024\pi$
$13$	7100.10	0.0689476	0.0344738	+	0.999406i	$0.489024\pi$
$14$	36165.9	0.251608
$15$	0	0
$16$	−204831.	−0.781369
$17$	268650.	0.780131	0.390065	−	0.920787i	$-0.372452\pi$
$17$	268650.	0.780131	0.390065	+	0.920787i	$0.372452\pi$
$18$	0	0
$19$	572153.	1.00721	0.503606	−	0.863933i	$-0.332006\pi$
$19$	572153.	1.00721	0.503606	+	0.863933i	$0.332006\pi$
$20$	−244143.	−0.341201
$21$	0	0
$22$	−1.52368e6	−1.38673
$23$	−1.28932e6	−0.960694	−0.480347	−	0.877079i	$-0.659489\pi$
$23$	−1.28932e6	−0.960694	−0.480347	+	0.877079i	$0.659489\pi$
$24$	0	0
$25$	4.72177e6	2.41755
$26$	−145075.	−0.0622606
$27$	0	0
$28$	167260.	0.0514259
$29$	6.39915e6	1.68009	0.840043	−	0.542520i	$-0.182530\pi$
$29$	6.39915e6	1.68009	0.840043	+	0.542520i	$0.182530\pi$
$30$	0	0
$31$	−2.00450e6	−0.389833	−0.194916	−	0.980820i	$-0.562444\pi$
$31$	−2.00450e6	−0.389833	−0.194916	+	0.980820i	$0.562444\pi$
$32$	−2.15967e6	−0.364093
$33$	0	0
$34$	−5.48930e6	−0.704469
$35$	−4.57291e6	−0.515094
$36$	0	0
$37$	1.49299e7	1.30963	0.654815	−	0.755789i	$-0.272746\pi$
$37$	1.49299e7	1.30963	0.654815	+	0.755789i	$0.272746\pi$
$38$	−1.16907e7	−0.909527
$39$	0	0
$40$	3.20170e7	1.97748
$41$	1.77326e7	0.980042	0.490021	−	0.871711i	$-0.336989\pi$
$41$	1.77326e7	0.980042	0.490021	+	0.871711i	$0.336989\pi$
$42$	0	0
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	−7.04671e6	−0.283432
$45$	0	0
$46$	2.63445e7	0.867520
$47$	−1.13138e7	−0.338196	−0.169098	−	0.985599i	$-0.554086\pi$
$47$	−1.13138e7	−0.338196	−0.169098	+	0.985599i	$0.554086\pi$
$48$	0	0
$49$	−3.72207e7	−0.922365
$50$	−9.64794e7	−2.18308
$51$	0	0
$52$	−670945.	−0.0127254
$53$	1.02987e8	1.79283	0.896417	−	0.443211i	$-0.146161\pi$
$53$	1.02987e8	1.79283	0.896417	+	0.443211i	$0.146161\pi$
$54$	0	0
$55$	1.92658e8	2.83893
$56$	−2.19346e7	−0.298046
$57$	0	0
$58$	−1.30753e8	−1.51714
$59$	8.07005e7	0.867046	0.433523	−	0.901143i	$-0.357270\pi$
$59$	8.07005e7	0.867046	0.433523	+	0.901143i	$0.357270\pi$
$60$	0	0
$61$	6.21644e7	0.574854	0.287427	−	0.957803i	$-0.407200\pi$
$61$	6.21644e7	0.574854	0.287427	+	0.957803i	$0.407200\pi$
$62$	4.09577e7	0.352024
$63$	0	0
$64$	1.49002e8	1.11015
$65$	1.83437e7	0.127461
$66$	0	0
$67$	1.55110e8	0.940381	0.470191	−	0.882565i	$-0.344185\pi$
$67$	1.55110e8	0.940381	0.470191	+	0.882565i	$0.344185\pi$
$68$	−2.53869e7	−0.143986
$69$	0	0
$70$	9.34377e7	0.465137
$71$	1.87869e8	0.877390	0.438695	−	0.898636i	$-0.355441\pi$
$71$	1.87869e8	0.877390	0.438695	+	0.898636i	$0.355441\pi$
$72$	0	0
$73$	4.82049e7	0.198673	0.0993363	−	0.995054i	$-0.468328\pi$
$73$	4.82049e7	0.198673	0.0993363	+	0.995054i	$0.468328\pi$
$74$	−3.05060e8	−1.18261
$75$	0	0
$76$	−5.40673e7	−0.185898
$77$	−1.31988e8	−0.427884
$78$	0	0
$79$	−4.54354e8	−1.31242	−0.656210	−	0.754579i	$-0.727841\pi$
$79$	−4.54354e8	−1.31242	−0.656210	+	0.754579i	$0.727841\pi$
$80$	−5.29198e8	−1.44449
$81$	0	0
$82$	−3.62328e8	−0.884991
$83$	−1.00047e8	−0.231394	−0.115697	−	0.993285i	$-0.536910\pi$
$83$	−1.00047e8	−0.231394	−0.115697	+	0.993285i	$0.536910\pi$
$84$	0	0
$85$	6.94081e8	1.44220
$86$	6.98559e7	0.137708
$87$	0	0
$88$	9.24108e8	1.64267
$89$	−1.13769e9	−1.92207	−0.961034	−	0.276431i	$-0.910848\pi$
$89$	−1.13769e9	−1.92207	−0.961034	+	0.276431i	$0.910848\pi$
$90$	0	0
$91$	−1.25671e7	−0.0192109
$92$	1.21838e8	0.177312
$93$	0	0
$94$	2.31174e8	0.305396
$95$	1.47821e9	1.86200
$96$	0	0
$97$	−2.37271e8	−0.272127	−0.136064	−	0.990700i	$-0.543445\pi$
$97$	−2.37271e8	−0.272127	−0.136064	+	0.990700i	$0.543445\pi$
$98$	7.60527e8	0.832908
$99$	0	0
$100$	−4.46198e8	−0.446198
$101$	7.88795e8	0.754254	0.377127	−	0.926162i	$-0.376912\pi$
$101$	7.88795e8	0.754254	0.377127	+	0.926162i	$0.376912\pi$
$102$	0	0
$103$	−1.40500e9	−1.23001	−0.615004	−	0.788524i	$-0.710845\pi$
$103$	−1.40500e9	−1.23001	−0.615004	+	0.788524i	$0.710845\pi$
$104$	8.79879e7	0.0737518
$105$	0	0
$106$	−2.10432e9	−1.61895
$107$	−1.23319e9	−0.909499	−0.454749	−	0.890619i	$-0.650271\pi$
$107$	−1.23319e9	−0.909499	−0.454749	+	0.890619i	$0.650271\pi$
$108$	0	0
$109$	5.28937e8	0.358909	0.179455	−	0.983766i	$-0.442567\pi$
$109$	5.28937e8	0.358909	0.179455	+	0.983766i	$0.442567\pi$
$110$	−3.93655e9	−2.56359
$111$	0	0
$112$	3.62549e8	0.217714
$113$	−6.54283e8	−0.377496	−0.188748	−	0.982026i	$-0.560443\pi$
$113$	−6.54283e8	−0.377496	−0.188748	+	0.982026i	$0.560443\pi$
$114$	0	0
$115$	−3.33106e9	−1.77600
$116$	−6.04706e8	−0.310087
$117$	0	0
$118$	−1.64894e9	−0.782954
$119$	−4.75508e8	−0.217369
$120$	0	0
$121$	3.20273e9	1.35827
$122$	−1.27020e9	−0.519101
$123$	0	0
$124$	1.89421e8	0.0719500
$125$	7.15304e9	2.62057
$126$	0	0
$127$	−3.42183e9	−1.16719	−0.583595	−	0.812045i	$-0.698354\pi$
$127$	−3.42183e9	−1.16719	−0.583595	+	0.812045i	$0.698354\pi$
$128$	−1.93878e9	−0.638388
$129$	0	0
$130$	−3.74814e8	−0.115099
$131$	−2.65085e9	−0.786439	−0.393220	−	0.919445i	$-0.628639\pi$
$131$	−2.65085e9	−0.786439	−0.393220	+	0.919445i	$0.628639\pi$
$132$	0	0
$133$	−1.01270e9	−0.280641
$134$	−3.16935e9	−0.849177
$135$	0	0
$136$	3.32925e9	0.834490
$137$	9.18404e7	0.0222736	0.0111368	−	0.999938i	$-0.496455\pi$
$137$	9.18404e7	0.0222736	0.0111368	+	0.999938i	$0.496455\pi$
$138$	0	0
$139$	7.61102e7	0.0172932	0.00864662	−	0.999963i	$-0.497248\pi$
$139$	7.61102e7	0.0172932	0.00864662	+	0.999963i	$0.497248\pi$
$140$	4.32131e8	0.0950690
$141$	0	0
$142$	−3.83870e9	−0.792295
$143$	5.29454e8	0.105881
$144$	0	0
$145$	1.65327e10	3.10591
$146$	−9.84964e8	−0.179404
$147$	0	0
$148$	−1.41084e9	−0.241714
$149$	−4.91840e9	−0.817495	−0.408748	−	0.912647i	$-0.634034\pi$
$149$	−4.91840e9	−0.817495	−0.408748	+	0.912647i	$0.634034\pi$
$150$	0	0
$151$	−6.55107e9	−1.02545	−0.512727	−	0.858552i	$-0.671365\pi$
$151$	−6.55107e9	−1.02545	−0.512727	+	0.858552i	$0.671365\pi$
$152$	7.09041e9	1.07739
$153$	0	0
$154$	2.69689e9	0.386385
$155$	−5.17879e9	−0.720668
$156$	0	0
$157$	−2.66784e9	−0.350438	−0.175219	−	0.984530i	$-0.556063\pi$
$157$	−2.66784e9	−0.350438	−0.175219	+	0.984530i	$0.556063\pi$
$158$	9.28376e9	1.18513
$159$	0	0
$160$	−5.57968e9	−0.673084
$161$	2.28208e9	0.267679
$162$	0	0
$163$	−9.83535e8	−0.109130	−0.0545652	−	0.998510i	$-0.517377\pi$
$163$	−9.83535e8	−0.109130	−0.0545652	+	0.998510i	$0.517377\pi$
$164$	−1.67569e9	−0.180883
$165$	0	0
$166$	2.04425e9	0.208952
$167$	−9.80315e9	−0.975307	−0.487654	−	0.873037i	$-0.662147\pi$
$167$	−9.80315e9	−0.975307	−0.487654	+	0.873037i	$0.662147\pi$
$168$	0	0
$169$	−1.05541e10	−0.995246
$170$	−1.41821e10	−1.30232
$171$	0	0
$172$	3.23070e8	0.0281461
$173$	3.11130e9	0.264079	0.132040	−	0.991244i	$-0.457847\pi$
$173$	3.11130e9	0.264079	0.132040	+	0.991244i	$0.457847\pi$
$174$	0	0
$175$	−8.35749e9	−0.673604
$176$	−1.52743e10	−1.19992
$177$	0	0
$178$	2.32463e10	1.73565
$179$	1.52460e10	1.10999	0.554993	−	0.831855i	$-0.312721\pi$
$179$	1.52460e10	1.10999	0.554993	+	0.831855i	$0.312721\pi$
$180$	0	0
$181$	−2.42388e10	−1.67864	−0.839319	−	0.543640i	$-0.817046\pi$
$181$	−2.42388e10	−1.67864	−0.839319	+	0.543640i	$0.817046\pi$
$182$	2.56782e8	0.0173477
$183$	0	0
$184$	−1.59779e10	−1.02763
$185$	3.85726e10	2.42106
$186$	0	0
$187$	2.00333e10	1.19802
$188$	1.06913e9	0.0624197
$189$	0	0
$190$	−3.02040e10	−1.68141
$191$	−8.62554e9	−0.468960	−0.234480	−	0.972121i	$-0.575339\pi$
$191$	−8.62554e9	−0.468960	−0.234480	+	0.972121i	$0.575339\pi$
$192$	0	0
$193$	3.46237e10	1.79624	0.898122	−	0.439747i	$-0.144932\pi$
$193$	3.46237e10	1.79624	0.898122	+	0.439747i	$0.144932\pi$
$194$	4.84813e9	0.245735
$195$	0	0
$196$	3.51728e9	0.170237
$197$	2.05360e10	0.971444	0.485722	−	0.874113i	$-0.338557\pi$
$197$	2.05360e10	0.971444	0.485722	+	0.874113i	$0.338557\pi$
$198$	0	0
$199$	−1.56130e10	−0.705745	−0.352873	−	0.935671i	$-0.614795\pi$
$199$	−1.56130e10	−0.705745	−0.352873	+	0.935671i	$0.614795\pi$
$200$	5.85146e10	2.58600
$201$	0	0
$202$	−1.61173e10	−0.681102
$203$	−1.13264e10	−0.468124
$204$	0	0
$205$	4.58136e10	1.81177
$206$	2.87081e10	1.11071
$207$	0	0
$208$	−1.45432e9	−0.0538735
$209$	4.26655e10	1.54674
$210$	0	0
$211$	−3.30552e10	−1.14807	−0.574036	−	0.818830i	$-0.694623\pi$
$211$	−3.30552e10	−1.14807	−0.574036	+	0.818830i	$0.694623\pi$
$212$	−9.73204e9	−0.330897
$213$	0	0
$214$	2.51976e10	0.821290
$215$	−8.83276e9	−0.281918
$216$	0	0
$217$	3.54794e9	0.108619
$218$	−1.08077e10	−0.324100
$219$	0	0
$220$	−1.82058e10	−0.523970
$221$	1.90744e9	0.0537882
$222$	0	0
$223$	2.45049e10	0.663560	0.331780	−	0.943357i	$-0.392351\pi$
$223$	2.45049e10	0.663560	0.331780	+	0.943357i	$0.392351\pi$
$224$	3.82259e9	0.101447
$225$	0	0
$226$	1.33689e10	0.340884
$227$	2.42024e10	0.604981	0.302490	−	0.953152i	$-0.402182\pi$
$227$	2.42024e10	0.604981	0.302490	+	0.953152i	$0.402182\pi$
$228$	0	0
$229$	−3.44206e10	−0.827102	−0.413551	−	0.910481i	$-0.635712\pi$
$229$	−3.44206e10	−0.827102	−0.413551	+	0.910481i	$0.635712\pi$
$230$	6.80631e10	1.60375
$231$	0	0
$232$	7.93014e10	1.79715
$233$	−4.12963e10	−0.917929	−0.458964	−	0.888455i	$-0.651779\pi$
$233$	−4.12963e10	−0.917929	−0.458964	+	0.888455i	$0.651779\pi$
$234$	0	0
$235$	−2.92302e10	−0.625211
$236$	−7.62603e9	−0.160027
$237$	0	0
$238$	9.71600e9	0.196287
$239$	2.39540e10	0.474883	0.237442	−	0.971402i	$-0.423691\pi$
$239$	2.39540e10	0.474883	0.237442	+	0.971402i	$0.423691\pi$
$240$	0	0
$241$	3.26986e10	0.624385	0.312192	−	0.950019i	$-0.398937\pi$
$241$	3.26986e10	0.624385	0.312192	+	0.950019i	$0.398937\pi$
$242$	−6.54410e10	−1.22654
$243$	0	0
$244$	−5.87441e9	−0.106099
$245$	−9.61629e10	−1.70514
$246$	0	0
$247$	4.06234e9	0.0694449
$248$	−2.48407e10	−0.416996
$249$	0	0
$250$	−1.46157e11	−2.36641
$251$	4.46019e10	0.709286	0.354643	−	0.935002i	$-0.384602\pi$
$251$	4.46019e10	0.709286	0.354643	+	0.935002i	$0.384602\pi$
$252$	0	0
$253$	−9.61445e10	−1.47531
$254$	6.99178e10	1.05399
$255$	0	0
$256$	−3.66740e10	−0.533677
$257$	−4.55935e10	−0.651935	−0.325967	−	0.945381i	$-0.605690\pi$
$257$	−4.55935e10	−0.651935	−0.325967	+	0.945381i	$0.605690\pi$
$258$	0	0
$259$	−2.64257e10	−0.364904
$260$	−1.73344e9	−0.0235250
$261$	0	0
$262$	5.41646e10	0.710165
$263$	8.02154e10	1.03385	0.516924	−	0.856031i	$-0.327077\pi$
$263$	8.02154e10	1.03385	0.516924	+	0.856031i	$0.327077\pi$
$264$	0	0
$265$	2.66075e11	3.31434
$266$	2.06925e10	0.253422
$267$	0	0
$268$	−1.46576e10	−0.173563
$269$	−1.79789e10	−0.209352	−0.104676	−	0.994506i	$-0.533381\pi$
$269$	−1.79789e10	−0.209352	−0.104676	+	0.994506i	$0.533381\pi$
$270$	0	0
$271$	−5.80992e10	−0.654347	−0.327173	−	0.944964i	$-0.606096\pi$
$271$	−5.80992e10	−0.654347	−0.327173	+	0.944964i	$0.606096\pi$
$272$	−5.50280e10	−0.609570
$273$	0	0
$274$	−1.87656e9	−0.0201134
$275$	3.52103e11	3.71255
$276$	0	0
$277$	7.56051e10	0.771600	0.385800	−	0.922582i	$-0.373925\pi$
$277$	7.56051e10	0.771600	0.385800	+	0.922582i	$0.373925\pi$
$278$	−1.55515e9	−0.0156160
$279$	0	0
$280$	−5.66698e10	−0.550986
$281$	−7.81929e10	−0.748151	−0.374075	−	0.927398i	$-0.622040\pi$
$281$	−7.81929e10	−0.748151	−0.374075	+	0.927398i	$0.622040\pi$
$282$	0	0
$283$	1.17607e11	1.08992	0.544961	−	0.838462i	$-0.316545\pi$
$283$	1.17607e11	1.08992	0.544961	+	0.838462i	$0.316545\pi$
$284$	−1.77532e10	−0.161937
$285$	0	0
$286$	−1.08183e10	−0.0956116
$287$	−3.13865e10	−0.273070
$288$	0	0
$289$	−4.64148e10	−0.391396
$290$	−3.37811e11	−2.80468
$291$	0	0
$292$	−4.55526e9	−0.0366683
$293$	−1.39474e11	−1.10557	−0.552787	−	0.833323i	$-0.686436\pi$
$293$	−1.39474e11	−1.10557	−0.552787	+	0.833323i	$0.686436\pi$
$294$	0	0
$295$	2.08496e11	1.60287
$296$	1.85019e11	1.40089
$297$	0	0
$298$	1.00497e11	0.738209
$299$	−9.15429e9	−0.0662375
$300$	0	0
$301$	6.05124e9	0.0424908
$302$	1.33857e11	0.925999
$303$	0	0
$304$	−1.17195e11	−0.787005
$305$	1.60607e11	1.06271
$306$	0	0
$307$	3.89983e10	0.250567	0.125283	−	0.992121i	$-0.460016\pi$
$307$	3.89983e10	0.250567	0.125283	+	0.992121i	$0.460016\pi$
$308$	1.24726e10	0.0789730
$309$	0	0
$310$	1.05817e11	0.650773
$311$	−2.46919e11	−1.49669	−0.748347	−	0.663308i	$-0.769152\pi$
$311$	−2.46919e11	−1.49669	−0.748347	+	0.663308i	$0.769152\pi$
$312$	0	0
$313$	1.43556e11	0.845416	0.422708	−	0.906266i	$-0.361080\pi$
$313$	1.43556e11	0.845416	0.422708	+	0.906266i	$0.361080\pi$
$314$	5.45115e10	0.316450
$315$	0	0
$316$	4.29355e10	0.242228
$317$	2.92123e11	1.62480	0.812399	−	0.583102i	$-0.198161\pi$
$317$	2.92123e11	1.62480	0.812399	+	0.583102i	$0.198161\pi$
$318$	0	0
$319$	4.77184e11	2.58005
$320$	3.84958e11	2.05229
$321$	0	0
$322$	−4.66294e10	−0.241718
$323$	1.53709e11	0.785758
$324$	0	0
$325$	3.35251e10	0.166684
$326$	2.00964e10	0.0985462
$327$	0	0
$328$	2.19751e11	1.04833
$329$	2.00253e10	0.0942320
$330$	0	0
$331$	−3.59742e10	−0.164727	−0.0823636	−	0.996602i	$-0.526247\pi$
$331$	−3.59742e10	−0.164727	−0.0823636	+	0.996602i	$0.526247\pi$
$332$	9.45423e9	0.0427076
$333$	0	0
$334$	2.00306e11	0.880716
$335$	4.00740e11	1.73845
$336$	0	0
$337$	4.12227e11	1.74101	0.870506	−	0.492157i	$-0.163791\pi$
$337$	4.12227e11	1.74101	0.870506	+	0.492157i	$0.163791\pi$
$338$	2.15650e11	0.898721
$339$	0	0
$340$	−6.55892e10	−0.266181
$341$	−1.49475e11	−0.598653
$342$	0	0
$343$	1.37306e11	0.535630
$344$	−4.23675e10	−0.163125
$345$	0	0
$346$	−6.35728e10	−0.238467
$347$	7.23809e10	0.268004	0.134002	−	0.990981i	$-0.457217\pi$
$347$	7.23809e10	0.268004	0.134002	+	0.990981i	$0.457217\pi$
$348$	0	0
$349$	2.59445e11	0.936119	0.468060	−	0.883697i	$-0.344953\pi$
$349$	2.59445e11	0.936119	0.468060	+	0.883697i	$0.344953\pi$
$350$	1.70767e11	0.608273
$351$	0	0
$352$	−1.61046e11	−0.559125
$353$	−8.53217e10	−0.292465	−0.146232	−	0.989250i	$-0.546715\pi$
$353$	−8.53217e10	−0.292465	−0.146232	+	0.989250i	$0.546715\pi$
$354$	0	0
$355$	4.85375e11	1.62200
$356$	1.07509e11	0.354749
$357$	0	0
$358$	−3.11520e11	−1.00233
$359$	2.92377e11	0.929005	0.464503	−	0.885572i	$-0.346233\pi$
$359$	2.92377e11	0.929005	0.464503	+	0.885572i	$0.346233\pi$
$360$	0	0
$361$	4.67171e9	0.0144775
$362$	4.95267e11	1.51583
$363$	0	0
$364$	1.18756e9	0.00354569
$365$	1.24541e11	0.367278
$366$	0	0
$367$	5.23535e11	1.50643	0.753214	−	0.657775i	$-0.228502\pi$
$367$	5.23535e11	1.50643	0.753214	+	0.657775i	$0.228502\pi$
$368$	2.64093e11	0.750656
$369$	0	0
$370$	−7.88149e11	−2.18625
$371$	−1.82285e11	−0.499539
$372$	0	0
$373$	2.22087e11	0.594063	0.297032	−	0.954868i	$-0.404003\pi$
$373$	2.22087e11	0.594063	0.297032	+	0.954868i	$0.404003\pi$
$374$	−4.09337e11	−1.08183
$375$	0	0
$376$	−1.40206e11	−0.361762
$377$	4.54346e10	0.115838
$378$	0	0
$379$	5.93299e10	0.147706	0.0738528	−	0.997269i	$-0.476470\pi$
$379$	5.93299e10	0.147706	0.0738528	+	0.997269i	$0.476470\pi$
$380$	−1.39687e11	−0.343662
$381$	0	0
$382$	1.76244e11	0.423478
$383$	−3.66860e11	−0.871175	−0.435587	−	0.900146i	$-0.643459\pi$
$383$	−3.66860e11	−0.871175	−0.435587	+	0.900146i	$0.643459\pi$
$384$	0	0
$385$	−3.41002e11	−0.791013
$386$	−7.07461e11	−1.62203
$387$	0	0
$388$	2.24216e10	0.0502255
$389$	8.75015e11	1.93750	0.968751	−	0.248035i	$-0.0797846\pi$
$389$	8.75015e11	1.93750	0.968751	+	0.248035i	$0.0797846\pi$
$390$	0	0
$391$	−3.46376e11	−0.749467
$392$	−4.61258e11	−0.986635
$393$	0	0
$394$	−4.19609e11	−0.877227
$395$	−1.17386e12	−2.42622
$396$	0	0
$397$	−5.04810e11	−1.01993	−0.509965	−	0.860195i	$-0.670342\pi$
$397$	−5.04810e11	−1.01993	−0.509965	+	0.860195i	$0.670342\pi$
$398$	3.19019e11	0.637298
$399$	0	0
$400$	−9.67167e11	−1.88900
$401$	−7.68568e11	−1.48434	−0.742169	−	0.670213i	$-0.766203\pi$
$401$	−7.68568e11	−1.48434	−0.742169	+	0.670213i	$0.766203\pi$
$402$	0	0
$403$	−1.42321e10	−0.0268780
$404$	−7.45395e10	−0.139210
$405$	0	0
$406$	2.31431e11	0.422722
$407$	1.11332e12	2.01116
$408$	0	0
$409$	−6.22133e11	−1.09933	−0.549665	−	0.835385i	$-0.685245\pi$
$409$	−6.22133e11	−1.09933	−0.549665	+	0.835385i	$0.685245\pi$
$410$	−9.36103e11	−1.63605
$411$	0	0
$412$	1.32769e11	0.227018
$413$	−1.42839e11	−0.241586
$414$	0	0
$415$	−2.58479e11	−0.427769
$416$	−1.53338e10	−0.0251033
$417$	0	0
$418$	−8.71778e11	−1.39673
$419$	1.15967e12	1.83812	0.919058	−	0.394122i	$-0.128951\pi$
$419$	1.15967e12	1.83812	0.919058	+	0.394122i	$0.128951\pi$
$420$	0	0
$421$	8.01209e10	0.124302	0.0621508	−	0.998067i	$-0.480204\pi$
$421$	8.01209e10	0.124302	0.0621508	+	0.998067i	$0.480204\pi$
$422$	6.75413e11	1.03672
$423$	0	0
$424$	1.27626e12	1.91776
$425$	1.26851e12	1.88600
$426$	0	0
$427$	−1.10030e11	−0.160172
$428$	1.16534e11	0.167863
$429$	0	0
$430$	1.80479e11	0.254576
$431$	−3.08981e11	−0.431304	−0.215652	−	0.976470i	$-0.569188\pi$
$431$	−3.08981e11	−0.431304	−0.215652	+	0.976470i	$0.569188\pi$
$432$	0	0
$433$	7.06997e11	0.966544	0.483272	−	0.875470i	$-0.339448\pi$
$433$	7.06997e11	0.966544	0.483272	+	0.875470i	$0.339448\pi$
$434$	−7.24946e10	−0.0980848
$435$	0	0
$436$	−4.99834e10	−0.0662425
$437$	−7.37688e11	−0.967623
$438$	0	0
$439$	−1.15067e12	−1.47864	−0.739318	−	0.673356i	$-0.764852\pi$
$439$	−1.15067e12	−1.47864	−0.739318	+	0.673356i	$0.764852\pi$
$440$	2.38751e12	3.03674
$441$	0	0
$442$	−3.89746e10	−0.0485714
$443$	−1.45765e12	−1.79819	−0.899095	−	0.437754i	$-0.855774\pi$
$443$	−1.45765e12	−1.79819	−0.899095	+	0.437754i	$0.855774\pi$
$444$	0	0
$445$	−2.93931e12	−3.55325
$446$	−5.00705e11	−0.599204
$447$	0	0
$448$	−2.63731e11	−0.309322
$449$	−1.51686e12	−1.76132	−0.880658	−	0.473753i	$-0.842899\pi$
$449$	−1.51686e12	−1.76132	−0.880658	+	0.473753i	$0.842899\pi$
$450$	0	0
$451$	1.32232e12	1.50502
$452$	6.18284e10	0.0696731
$453$	0	0
$454$	−4.94524e11	−0.546306
$455$	−3.24681e10	−0.0355145
$456$	0	0
$457$	−1.58795e12	−1.70300	−0.851501	−	0.524354i	$-0.824307\pi$
$457$	−1.58795e12	−1.70300	−0.851501	+	0.524354i	$0.824307\pi$
$458$	7.03312e11	0.746884
$459$	0	0
$460$	3.14778e11	0.327789
$461$	5.06836e11	0.522653	0.261326	−	0.965251i	$-0.415840\pi$
$461$	5.06836e11	0.522653	0.261326	+	0.965251i	$0.415840\pi$
$462$	0	0
$463$	−1.40219e12	−1.41806	−0.709028	−	0.705180i	$-0.750866\pi$
$463$	−1.40219e12	−1.41806	−0.709028	+	0.705180i	$0.750866\pi$
$464$	−1.31075e12	−1.31277
$465$	0	0
$466$	8.43801e11	0.828902
$467$	9.39462e11	0.914015	0.457008	−	0.889463i	$-0.348921\pi$
$467$	9.39462e11	0.914015	0.457008	+	0.889463i	$0.348921\pi$
$468$	0	0
$469$	−2.74543e11	−0.262019
$470$	5.97257e11	0.564574
$471$	0	0
$472$	1.00008e12	0.927461
$473$	−2.54940e11	−0.234187
$474$	0	0
$475$	2.70158e12	2.43499
$476$	4.49346e10	0.0401189
$477$	0	0
$478$	−4.89448e11	−0.428826
$479$	9.05240e11	0.785695	0.392847	−	0.919604i	$-0.371490\pi$
$479$	9.05240e11	0.785695	0.392847	+	0.919604i	$0.371490\pi$
$480$	0	0
$481$	1.06004e11	0.0902959
$482$	−6.68126e11	−0.563828
$483$	0	0
$484$	−3.02652e11	−0.250691
$485$	−6.13010e11	−0.503071
$486$	0	0
$487$	−6.82703e11	−0.549986	−0.274993	−	0.961446i	$-0.588675\pi$
$487$	−6.82703e11	−0.549986	−0.274993	+	0.961446i	$0.588675\pi$
$488$	7.70372e11	0.614909
$489$	0	0
$490$	1.96488e12	1.53976
$491$	−2.15045e11	−0.166979	−0.0834897	−	0.996509i	$-0.526607\pi$
$491$	−2.15045e11	−0.166979	−0.0834897	+	0.996509i	$0.526607\pi$
$492$	0	0
$493$	1.71913e12	1.31069
$494$	−8.30053e10	−0.0627097
$495$	0	0
$496$	4.10584e11	0.304603
$497$	−3.32526e11	−0.244468
$498$	0	0
$499$	−5.06026e10	−0.0365359	−0.0182680	−	0.999833i	$-0.505815\pi$
$499$	−5.06026e10	−0.0365359	−0.0182680	+	0.999833i	$0.505815\pi$
$500$	−6.75947e11	−0.483668
$501$	0	0
$502$	−9.11345e11	−0.640495
$503$	−2.64497e12	−1.84232	−0.921161	−	0.389183i	$-0.872758\pi$
$503$	−2.64497e12	−1.84232	−0.921161	+	0.389183i	$0.872758\pi$
$504$	0	0
$505$	2.03792e12	1.39436
$506$	1.96451e12	1.33222
$507$	0	0
$508$	3.23356e11	0.215424
$509$	−1.81937e12	−1.20141	−0.600703	−	0.799472i	$-0.705113\pi$
$509$	−1.81937e12	−1.20141	−0.600703	+	0.799472i	$0.705113\pi$
$510$	0	0
$511$	−8.53221e10	−0.0553563
$512$	1.74201e12	1.12031
$513$	0	0
$514$	9.31607e11	0.588706
$515$	−3.62992e12	−2.27387
$516$	0	0
$517$	−8.43671e11	−0.519357
$518$	5.39954e11	0.329513
$519$	0	0
$520$	2.27324e11	0.136342
$521$	6.58651e11	0.391639	0.195819	−	0.980640i	$-0.437263\pi$
$521$	6.58651e11	0.391639	0.195819	+	0.980640i	$0.437263\pi$
$522$	0	0
$523$	−2.09316e12	−1.22333	−0.611666	−	0.791116i	$-0.709500\pi$
$523$	−2.09316e12	−1.22333	−0.611666	+	0.791116i	$0.709500\pi$
$524$	2.50500e11	0.145150
$525$	0	0
$526$	−1.63903e12	−0.933579
$527$	−5.38510e11	−0.304120
$528$	0	0
$529$	−1.38810e11	−0.0770672
$530$	−5.43667e12	−2.99290
$531$	0	0
$532$	9.56985e10	0.0517968
$533$	1.25903e11	0.0675716
$534$	0	0
$535$	−3.18604e12	−1.68135
$536$	1.92220e12	1.00591
$537$	0	0
$538$	3.67360e11	0.189048
$539$	−2.77555e12	−1.41644
$540$	0	0
$541$	2.75220e12	1.38131	0.690656	−	0.723184i	$-0.257322\pi$
$541$	2.75220e12	1.38131	0.690656	+	0.723184i	$0.257322\pi$
$542$	1.18713e12	0.590884
$543$	0	0
$544$	−5.80196e11	−0.284040
$545$	1.36655e12	0.663502
$546$	0	0
$547$	−1.67438e12	−0.799669	−0.399835	−	0.916587i	$-0.630932\pi$
$547$	−1.67438e12	−0.799669	−0.399835	+	0.916587i	$0.630932\pi$
$548$	−8.67873e9	−0.00411096
$549$	0	0
$550$	−7.19447e12	−3.35248
$551$	3.66129e12	1.69220
$552$	0	0
$553$	8.04202e11	0.365681
$554$	−1.54483e12	−0.696765
$555$	0	0
$556$	−7.19226e9	−0.00319175
$557$	−2.66058e12	−1.17119	−0.585596	−	0.810603i	$-0.699140\pi$
$557$	−2.66058e12	−1.17119	−0.585596	+	0.810603i	$0.699140\pi$
$558$	0	0
$559$	−2.42738e10	−0.0105144
$560$	9.36675e11	0.402479
$561$	0	0
$562$	1.59771e12	0.675590
$563$	1.80763e12	0.758268	0.379134	−	0.925342i	$-0.376222\pi$
$563$	1.80763e12	0.758268	0.379134	+	0.925342i	$0.376222\pi$
$564$	0	0
$565$	−1.69040e12	−0.697863
$566$	−2.40305e12	−0.984214
$567$	0	0
$568$	2.32817e12	0.938526
$569$	3.50663e12	1.40244	0.701220	−	0.712944i	$-0.252639\pi$
$569$	3.50663e12	1.40244	0.701220	+	0.712944i	$0.252639\pi$
$570$	0	0
$571$	2.95802e12	1.16450	0.582248	−	0.813011i	$-0.302173\pi$
$571$	2.95802e12	1.16450	0.582248	+	0.813011i	$0.302173\pi$
$572$	−5.00323e10	−0.0195420
$573$	0	0
$574$	6.41316e11	0.246586
$575$	−6.08787e12	−2.32252
$576$	0	0
$577$	−9.05526e11	−0.340103	−0.170051	−	0.985435i	$-0.554393\pi$
$577$	−9.05526e11	−0.340103	−0.170051	+	0.985435i	$0.554393\pi$
$578$	9.48387e11	0.353436
$579$	0	0
$580$	−1.56231e12	−0.573246
$581$	1.77082e11	0.0644735
$582$	0	0
$583$	7.67972e12	2.75320
$584$	5.97378e11	0.212516
$585$	0	0
$586$	2.84985e12	0.998348
$587$	6.85640e11	0.238355	0.119178	−	0.992873i	$-0.461974\pi$
$587$	6.85640e11	0.238355	0.119178	+	0.992873i	$0.461974\pi$
$588$	0	0
$589$	−1.14688e12	−0.392644
$590$	−4.26018e12	−1.44742
$591$	0	0
$592$	−3.05811e12	−1.02330
$593$	6.58143e11	0.218562	0.109281	−	0.994011i	$-0.465145\pi$
$593$	6.58143e11	0.218562	0.109281	+	0.994011i	$0.465145\pi$
$594$	0	0
$595$	−1.22852e12	−0.401841
$596$	4.64778e11	0.150882
$597$	0	0
$598$	1.87048e11	0.0598134
$599$	1.58033e12	0.501564	0.250782	−	0.968044i	$-0.419312\pi$
$599$	1.58033e12	0.501564	0.250782	+	0.968044i	$0.419312\pi$
$600$	0	0
$601$	−1.50248e12	−0.469756	−0.234878	−	0.972025i	$-0.575469\pi$
$601$	−1.50248e12	−0.469756	−0.234878	+	0.972025i	$0.575469\pi$
$602$	−1.23644e11	−0.0383698
$603$	0	0
$604$	6.19063e11	0.189264
$605$	8.27452e12	2.51098
$606$	0	0
$607$	5.26894e12	1.57534	0.787670	−	0.616097i	$-0.211287\pi$
$607$	5.26894e12	1.57534	0.787670	+	0.616097i	$0.211287\pi$
$608$	−1.23566e12	−0.366719
$609$	0	0
$610$	−3.28166e12	−0.959642
$611$	−8.03292e10	−0.0233178
$612$	0	0
$613$	2.66173e12	0.761364	0.380682	−	0.924706i	$-0.375689\pi$
$613$	2.66173e12	0.761364	0.380682	+	0.924706i	$0.375689\pi$
$614$	−7.96848e11	−0.226265
$615$	0	0
$616$	−1.63566e12	−0.457699
$617$	−3.08426e12	−0.856777	−0.428388	−	0.903595i	$-0.640918\pi$
$617$	−3.08426e12	−0.856777	−0.428388	+	0.903595i	$0.640918\pi$
$618$	0	0
$619$	1.96063e12	0.536769	0.268384	−	0.963312i	$-0.413510\pi$
$619$	1.96063e12	0.536769	0.268384	+	0.963312i	$0.413510\pi$
$620$	4.89385e11	0.133011
$621$	0	0
$622$	5.04526e12	1.35153
$623$	2.01370e12	0.535547
$624$	0	0
$625$	9.25824e12	2.42699
$626$	−2.93325e12	−0.763423
$627$	0	0
$628$	2.52105e11	0.0646790
$629$	4.01092e12	1.02168
$630$	0	0
$631$	1.03708e12	0.260424	0.130212	−	0.991486i	$-0.458434\pi$
$631$	1.03708e12	0.260424	0.130212	+	0.991486i	$0.458434\pi$
$632$	−5.63058e12	−1.40387
$633$	0	0
$634$	−5.96892e12	−1.46722
$635$	−8.84058e12	−2.15774
$636$	0	0
$637$	−2.64271e11	−0.0635948
$638$	−9.75025e12	−2.32982
$639$	0	0
$640$	−5.00901e12	−1.18016
$641$	−5.27910e12	−1.23509	−0.617545	−	0.786535i	$-0.711873\pi$
$641$	−5.27910e12	−1.23509	−0.617545	+	0.786535i	$0.711873\pi$
$642$	0	0
$643$	3.47722e11	0.0802201	0.0401100	−	0.999195i	$-0.487229\pi$
$643$	3.47722e11	0.0802201	0.0401100	+	0.999195i	$0.487229\pi$
$644$	−2.15652e11	−0.0494045
$645$	0	0
$646$	−3.14072e12	−0.709550
$647$	−7.11791e11	−0.159692	−0.0798460	−	0.996807i	$-0.525443\pi$
$647$	−7.11791e11	−0.159692	−0.0798460	+	0.996807i	$0.525443\pi$
$648$	0	0
$649$	6.01783e12	1.33149
$650$	−6.85013e11	−0.150518
$651$	0	0
$652$	9.29420e10	0.0201418
$653$	1.71011e12	0.368056	0.184028	−	0.982921i	$-0.441086\pi$
$653$	1.71011e12	0.368056	0.184028	+	0.982921i	$0.441086\pi$
$654$	0	0
$655$	−6.84870e12	−1.45386
$656$	−3.63219e12	−0.765775
$657$	0	0
$658$	−4.09175e11	−0.0850928
$659$	3.21878e12	0.664825	0.332412	−	0.943134i	$-0.392137\pi$
$659$	3.21878e12	0.664825	0.332412	+	0.943134i	$0.392137\pi$
$660$	0	0
$661$	−1.29023e12	−0.262882	−0.131441	−	0.991324i	$-0.541960\pi$
$661$	−1.29023e12	−0.262882	−0.131441	+	0.991324i	$0.541960\pi$
$662$	7.35056e11	0.148751
$663$	0	0
$664$	−1.23983e12	−0.247518
$665$	−2.61641e12	−0.518809
$666$	0	0
$667$	−8.25054e12	−1.61405
$668$	9.26377e11	0.180009
$669$	0	0
$670$	−8.18827e12	−1.56984
$671$	4.63560e12	0.882784
$672$	0	0
$673$	−2.68951e12	−0.505365	−0.252682	−	0.967549i	$-0.581313\pi$
$673$	−2.68951e12	−0.505365	−0.252682	+	0.967549i	$0.581313\pi$
$674$	−8.42298e12	−1.57216
$675$	0	0
$676$	9.97340e11	0.183689
$677$	−3.07951e12	−0.563421	−0.281710	−	0.959500i	$-0.590902\pi$
$677$	−3.07951e12	−0.563421	−0.281710	+	0.959500i	$0.590902\pi$
$678$	0	0
$679$	4.19967e11	0.0758231
$680$	8.60139e12	1.54269
$681$	0	0
$682$	3.05421e12	0.540592
$683$	1.87777e12	0.330178	0.165089	−	0.986279i	$-0.447209\pi$
$683$	1.87777e12	0.330178	0.165089	+	0.986279i	$0.447209\pi$
$684$	0	0
$685$	2.37277e11	0.0411764
$686$	−2.80555e12	−0.483681
$687$	0	0
$688$	7.00277e11	0.119158
$689$	7.31216e11	0.123612
$690$	0	0
$691$	−1.40579e12	−0.234568	−0.117284	−	0.993098i	$-0.537419\pi$
$691$	−1.40579e12	−0.234568	−0.117284	+	0.993098i	$0.537419\pi$
$692$	−2.94012e11	−0.0487402
$693$	0	0
$694$	−1.47895e12	−0.242011
$695$	1.96637e11	0.0319693
$696$	0	0
$697$	4.76387e12	0.764561
$698$	−5.30121e12	−0.845328
$699$	0	0
$700$	7.89765e11	0.124325
$701$	1.02642e13	1.60544	0.802720	−	0.596356i	$-0.203385\pi$
$701$	1.02642e13	1.60544	0.802720	+	0.596356i	$0.203385\pi$
$702$	0	0
$703$	8.54219e12	1.31908
$704$	1.11111e13	1.70482
$705$	0	0
$706$	1.74337e12	0.264100
$707$	−1.39616e12	−0.210159
$708$	0	0
$709$	−6.07076e12	−0.902267	−0.451133	−	0.892457i	$-0.648980\pi$
$709$	−6.07076e12	−0.902267	−0.451133	+	0.892457i	$0.648980\pi$
$710$	−9.91761e12	−1.46469
$711$	0	0
$712$	−1.40988e13	−2.05600
$713$	2.58444e12	0.374510
$714$	0	0
$715$	1.36789e12	0.195737
$716$	−1.44072e12	−0.204866
$717$	0	0
$718$	−5.97410e12	−0.838905
$719$	4.59470e12	0.641175	0.320588	−	0.947219i	$-0.396120\pi$
$719$	4.59470e12	0.641175	0.320588	+	0.947219i	$0.396120\pi$
$720$	0	0
$721$	2.48683e12	0.342718
$722$	−9.54564e10	−0.0130734
$723$	0	0
$724$	2.29051e12	0.309820
$725$	3.02153e13	4.06169
$726$	0	0
$727$	3.53648e12	0.469533	0.234767	−	0.972052i	$-0.424567\pi$
$727$	3.53648e12	0.469533	0.234767	+	0.972052i	$0.424567\pi$
$728$	−1.55738e11	−0.0205495
$729$	0	0
$730$	−2.54474e12	−0.331657
$731$	−9.18463e11	−0.118969
$732$	0	0
$733$	−5.36402e12	−0.686314	−0.343157	−	0.939278i	$-0.611496\pi$
$733$	−5.36402e12	−0.686314	−0.343157	+	0.939278i	$0.611496\pi$
$734$	−1.06973e13	−1.36033
$735$	0	0
$736$	2.78450e12	0.349782
$737$	1.15666e13	1.44411
$738$	0	0
$739$	1.14197e12	0.140850	0.0704249	−	0.997517i	$-0.477564\pi$
$739$	1.14197e12	0.140850	0.0704249	+	0.997517i	$0.477564\pi$
$740$	−3.64503e12	−0.446847
$741$	0	0
$742$	3.72462e12	0.451091
$743$	6.88545e11	0.0828863	0.0414431	−	0.999141i	$-0.486804\pi$
$743$	6.88545e11	0.0828863	0.0414431	+	0.999141i	$0.486804\pi$
$744$	0	0
$745$	−1.27071e13	−1.51127
$746$	−4.53787e12	−0.536447
$747$	0	0
$748$	−1.89310e12	−0.221114
$749$	2.18273e12	0.253414
$750$	0	0
$751$	4.45256e12	0.510776	0.255388	−	0.966839i	$-0.417797\pi$
$751$	4.45256e12	0.510776	0.255388	+	0.966839i	$0.417797\pi$
$752$	2.31742e12	0.264256
$753$	0	0
$754$	−9.28359e11	−0.104603
$755$	−1.69252e13	−1.89572
$756$	0	0
$757$	8.14319e12	0.901287	0.450643	−	0.892704i	$-0.351195\pi$
$757$	8.14319e12	0.901287	0.450643	+	0.892704i	$0.351195\pi$
$758$	−1.21228e12	−0.133380
$759$	0	0
$760$	1.83186e13	1.99174
$761$	7.09695e12	0.767080	0.383540	−	0.923524i	$-0.374705\pi$
$761$	7.09695e12	0.767080	0.383540	+	0.923524i	$0.374705\pi$
$762$	0	0
$763$	−9.36212e11	−0.100003
$764$	8.15096e11	0.0865543
$765$	0	0
$766$	7.49599e12	0.786683
$767$	5.72981e11	0.0597807
$768$	0	0
$769$	−1.45984e13	−1.50535	−0.752673	−	0.658395i	$-0.771236\pi$
$769$	−1.45984e13	−1.50535	−0.752673	+	0.658395i	$0.771236\pi$
$770$	6.96765e12	0.714295
$771$	0	0
$772$	−3.27187e12	−0.331526
$773$	−4.52458e11	−0.0455796	−0.0227898	−	0.999740i	$-0.507255\pi$
$773$	−4.52458e11	−0.0455796	−0.0227898	+	0.999740i	$0.507255\pi$
$774$	0	0
$775$	−9.46479e12	−0.942439
$776$	−2.94038e12	−0.291089
$777$	0	0
$778$	−1.78791e13	−1.74959
$779$	1.01458e13	0.987111
$780$	0	0
$781$	1.40094e13	1.34738
$782$	7.07746e12	0.676779
$783$	0	0
$784$	7.62397e12	0.720707
$785$	−6.89257e12	−0.647840
$786$	0	0
$787$	1.47638e13	1.37187	0.685935	−	0.727663i	$-0.259394\pi$
$787$	1.47638e13	1.37187	0.685935	+	0.727663i	$0.259394\pi$
$788$	−1.94061e12	−0.179296
$789$	0	0
$790$	2.39854e13	2.19091
$791$	1.15807e12	0.105182
$792$	0	0
$793$	4.41373e11	0.0396348
$794$	1.03147e13	0.921011
$795$	0	0
$796$	1.47540e12	0.130257
$797$	1.34285e13	1.17887	0.589435	−	0.807816i	$-0.299351\pi$
$797$	1.34285e13	1.17887	0.589435	+	0.807816i	$0.299351\pi$
$798$	0	0
$799$	−3.03946e12	−0.263837
$800$	−1.01975e13	−0.880212
$801$	0	0
$802$	1.57041e13	1.34038
$803$	3.59464e12	0.305095
$804$	0	0
$805$	5.89594e12	0.494848
$806$	2.90803e11	0.0242712
$807$	0	0
$808$	9.77513e12	0.806810
$809$	−6.69281e12	−0.549338	−0.274669	−	0.961539i	$-0.588568\pi$
$809$	−6.69281e12	−0.549338	−0.274669	+	0.961539i	$0.588568\pi$
$810$	0	0
$811$	−3.84593e11	−0.0312182	−0.0156091	−	0.999878i	$-0.504969\pi$
$811$	−3.84593e11	−0.0312182	−0.0156091	+	0.999878i	$0.504969\pi$
$812$	1.07032e12	0.0863998
$813$	0	0
$814$	−2.27484e13	−1.81610
$815$	−2.54104e12	−0.201745
$816$	0	0
$817$	−1.95608e12	−0.153599
$818$	1.27120e13	0.992711
$819$	0	0
$820$	−4.32929e12	−0.334391
$821$	2.49941e13	1.91997	0.959983	−	0.280057i	$-0.0903534\pi$
$821$	2.49941e13	1.91997	0.959983	+	0.280057i	$0.0903534\pi$
$822$	0	0
$823$	6.40992e12	0.487027	0.243514	−	0.969897i	$-0.421700\pi$
$823$	6.40992e12	0.487027	0.243514	+	0.969897i	$0.421700\pi$
$824$	−1.74114e13	−1.31571
$825$	0	0
$826$	2.91861e12	0.218155
$827$	−1.16763e13	−0.868019	−0.434010	−	0.900908i	$-0.642902\pi$
$827$	−1.16763e13	−0.868019	−0.434010	+	0.900908i	$0.642902\pi$
$828$	0	0
$829$	−1.45512e13	−1.07005	−0.535024	−	0.844837i	$-0.679698\pi$
$829$	−1.45512e13	−1.07005	−0.535024	+	0.844837i	$0.679698\pi$
$830$	5.28148e12	0.386282
$831$	0	0
$832$	1.05793e12	0.0765422
$833$	−9.99937e12	−0.719565
$834$	0	0
$835$	−2.53272e13	−1.80301
$836$	−4.03180e12	−0.285477
$837$	0	0
$838$	−2.36955e13	−1.65984
$839$	1.63671e13	1.14036	0.570180	−	0.821519i	$-0.306873\pi$
$839$	1.63671e13	1.14036	0.570180	+	0.821519i	$0.306873\pi$
$840$	0	0
$841$	2.64420e13	1.82269
$842$	−1.63710e12	−0.112246
$843$	0	0
$844$	3.12365e12	0.211895
$845$	−2.72674e13	−1.83987
$846$	0	0
$847$	−5.66880e12	−0.378456
$848$	−2.10949e13	−1.40087
$849$	0	0
$850$	−2.59192e13	−1.70309
$851$	−1.92494e13	−1.25815
$852$	0	0
$853$	5.19459e12	0.335954	0.167977	−	0.985791i	$-0.446276\pi$
$853$	5.19459e12	0.335954	0.167977	+	0.985791i	$0.446276\pi$
$854$	2.24823e12	0.144638
$855$	0	0
$856$	−1.52823e13	−0.972872
$857$	2.66688e12	0.168885	0.0844423	−	0.996428i	$-0.473089\pi$
$857$	2.66688e12	0.168885	0.0844423	+	0.996428i	$0.473089\pi$
$858$	0	0
$859$	−1.08042e13	−0.677054	−0.338527	−	0.940957i	$-0.609929\pi$
$859$	−1.08042e13	−0.677054	−0.338527	+	0.940957i	$0.609929\pi$
$860$	8.34677e11	0.0520326
$861$	0	0
$862$	6.31336e12	0.389474
$863$	1.34009e13	0.822407	0.411204	−	0.911544i	$-0.365109\pi$
$863$	1.34009e13	0.822407	0.411204	+	0.911544i	$0.365109\pi$
$864$	0	0
$865$	8.03830e12	0.488193
$866$	−1.44460e13	−0.872803
$867$	0	0
$868$	−3.35273e11	−0.0200475
$869$	−3.38812e13	−2.01544
$870$	0	0
$871$	1.10130e12	0.0648370
$872$	6.55485e12	0.383918
$873$	0	0
$874$	1.50731e13	0.873777
$875$	−1.26608e13	−0.730171
$876$	0	0
$877$	7.67119e12	0.437890	0.218945	−	0.975737i	$-0.429739\pi$
$877$	7.67119e12	0.437890	0.218945	+	0.975737i	$0.429739\pi$
$878$	2.35115e13	1.33523
$879$	0	0
$880$	−3.94623e13	−2.21825
$881$	2.06346e13	1.15400	0.576998	−	0.816746i	$-0.304224\pi$
$881$	2.06346e13	1.15400	0.576998	+	0.816746i	$0.304224\pi$
$882$	0	0
$883$	−2.76514e13	−1.53071	−0.765357	−	0.643606i	$-0.777438\pi$
$883$	−2.76514e13	−1.53071	−0.765357	+	0.643606i	$0.777438\pi$
$884$	−1.80250e11	−0.00992748
$885$	0	0
$886$	2.97839e13	1.62379
$887$	8.21082e12	0.445379	0.222690	−	0.974889i	$-0.428516\pi$
$887$	8.21082e12	0.445379	0.222690	+	0.974889i	$0.428516\pi$
$888$	0	0
$889$	6.05660e12	0.325215
$890$	6.00586e13	3.20863
$891$	0	0
$892$	−2.31566e12	−0.122471
$893$	−6.47324e12	−0.340636
$894$	0	0
$895$	3.93893e13	2.05199
$896$	3.43162e12	0.177875
$897$	0	0
$898$	3.09938e13	1.59049
$899$	−1.28271e13	−0.654952
$900$	0	0
$901$	2.76675e13	1.39865
$902$	−2.70188e13	−1.35905
$903$	0	0
$904$	−8.10820e12	−0.403800
$905$	−6.26229e13	−3.10323
$906$	0	0
$907$	2.10695e13	1.03376	0.516881	−	0.856057i	$-0.327093\pi$
$907$	2.10695e13	1.03376	0.516881	+	0.856057i	$0.327093\pi$
$908$	−2.28707e12	−0.111659
$909$	0	0
$910$	6.63417e11	0.0320701
$911$	−2.33428e13	−1.12285	−0.561423	−	0.827529i	$-0.689746\pi$
$911$	−2.33428e13	−1.12285	−0.561423	+	0.827529i	$0.689746\pi$
$912$	0	0
$913$	−7.46050e12	−0.355344
$914$	3.24464e13	1.53783
$915$	0	0
$916$	3.25268e12	0.152655
$917$	4.69198e12	0.219126
$918$	0	0
$919$	−2.76026e13	−1.27653	−0.638264	−	0.769818i	$-0.720347\pi$
$919$	−2.76026e13	−1.27653	−0.638264	+	0.769818i	$0.720347\pi$
$920$	−4.12802e13	−1.89975
$921$	0	0
$922$	−1.03561e13	−0.471962
$923$	1.33389e12	0.0604939
$924$	0	0
$925$	7.04956e13	3.16610
$926$	2.86508e13	1.28052
$927$	0	0
$928$	−1.38200e13	−0.611707
$929$	1.82656e13	0.804570	0.402285	−	0.915514i	$-0.368216\pi$
$929$	1.82656e13	0.804570	0.402285	+	0.915514i	$0.368216\pi$
$930$	0	0
$931$	−2.12960e13	−0.929018
$932$	3.90241e12	0.169419
$933$	0	0
$934$	−1.91959e13	−0.825368
$935$	5.17576e13	2.21473
$936$	0	0
$937$	1.64822e12	0.0698534	0.0349267	−	0.999390i	$-0.488880\pi$
$937$	1.64822e12	0.0698534	0.0349267	+	0.999390i	$0.488880\pi$
$938$	5.60971e12	0.236607
$939$	0	0
$940$	2.76219e12	0.115393
$941$	1.96652e13	0.817608	0.408804	−	0.912622i	$-0.365946\pi$
$941$	1.96652e13	0.817608	0.408804	+	0.912622i	$0.365946\pi$
$942$	0	0
$943$	−2.28630e13	−0.941521
$944$	−1.65300e13	−0.677483
$945$	0	0
$946$	5.20915e12	0.211474
$947$	2.10340e13	0.849860	0.424930	−	0.905226i	$-0.360299\pi$
$947$	2.10340e13	0.849860	0.424930	+	0.905226i	$0.360299\pi$
$948$	0	0
$949$	3.42259e11	0.0136980
$950$	−5.52010e13	−2.19883
$951$	0	0
$952$	−5.89273e12	−0.232515
$953$	−1.36899e13	−0.537629	−0.268814	−	0.963192i	$-0.586632\pi$
$953$	−1.36899e13	−0.537629	−0.268814	+	0.963192i	$0.586632\pi$
$954$	0	0
$955$	−2.22848e13	−0.866949
$956$	−2.26360e12	−0.0876474
$957$	0	0
$958$	−1.84966e13	−0.709493
$959$	−1.62556e11	−0.00620612
$960$	0	0
$961$	−2.24216e13	−0.848031
$962$	−2.16596e12	−0.0815384
$963$	0	0
$964$	−3.08995e12	−0.115240
$965$	8.94531e13	3.32065
$966$	0	0
$967$	1.15243e12	0.0423835	0.0211917	−	0.999775i	$-0.493254\pi$
$967$	1.15243e12	0.0423835	0.0211917	+	0.999775i	$0.493254\pi$
$968$	3.96898e13	1.45291
$969$	0	0
$970$	1.25255e13	0.454280
$971$	3.56388e13	1.28658	0.643290	−	0.765623i	$-0.277569\pi$
$971$	3.56388e13	1.28658	0.643290	+	0.765623i	$0.277569\pi$
$972$	0	0
$973$	−1.34714e11	−0.00481843
$974$	1.39496e13	0.496645
$975$	0	0
$976$	−1.27332e13	−0.449173
$977$	2.68281e13	0.942029	0.471014	−	0.882126i	$-0.343888\pi$
$977$	2.68281e13	0.942029	0.471014	+	0.882126i	$0.343888\pi$
$978$	0	0
$979$	−8.48374e13	−2.95165
$980$	9.08719e12	0.314711
$981$	0	0
$982$	4.39399e12	0.150785
$983$	3.23922e12	0.110649	0.0553247	−	0.998468i	$-0.482381\pi$
$983$	3.23922e12	0.110649	0.0553247	+	0.998468i	$0.482381\pi$
$984$	0	0
$985$	5.30565e13	1.79587
$986$	−3.51269e13	−1.18357
$987$	0	0
$988$	−3.83883e11	−0.0128172
$989$	4.40792e12	0.146504
$990$	0	0
$991$	−1.57632e13	−0.519174	−0.259587	−	0.965720i	$-0.583586\pi$
$991$	−1.57632e13	−0.519174	−0.259587	+	0.965720i	$0.583586\pi$
$992$	4.32905e12	0.141935
$993$	0	0
$994$	6.79446e12	0.220758
$995$	−4.03375e13	−1.30468
$996$	0	0
$997$	−6.52488e12	−0.209144	−0.104572	−	0.994517i	$-0.533347\pi$
$997$	−6.52488e12	−0.209144	−0.104572	+	0.994517i	$0.533347\pi$
$998$	1.03396e12	0.0329924
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.10.a.c.1.5		15
3.2	odd	2		43.10.a.a.1.11	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.11	✓	15	3.2	odd	2
387.10.a.c.1.5		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)

\(f(q)\)	\(=\)	\(q-20.4329 q^{2} -94.4979 q^{4} +2583.58 q^{5} -1769.99 q^{7} +12392.5 q^{8} +O(q^{10})\)	\(q-20.4329 q^{2} -94.4979 q^{4} +2583.58 q^{5} -1769.99 q^{7} +12392.5 q^{8} -52790.0 q^{10} +74570.0 q^{11} +7100.10 q^{13} +36165.9 q^{14} -204831. q^{16} +268650. q^{17} +572153. q^{19} -244143. q^{20} -1.52368e6 q^{22} -1.28932e6 q^{23} +4.72177e6 q^{25} -145075. q^{26} +167260. q^{28} +6.39915e6 q^{29} -2.00450e6 q^{31} -2.15967e6 q^{32} -5.48930e6 q^{34} -4.57291e6 q^{35} +1.49299e7 q^{37} -1.16907e7 q^{38} +3.20170e7 q^{40} +1.77326e7 q^{41} -3.41880e6 q^{43} -7.04671e6 q^{44} +2.63445e7 q^{46} -1.13138e7 q^{47} -3.72207e7 q^{49} -9.64794e7 q^{50} -670945. q^{52} +1.02987e8 q^{53} +1.92658e8 q^{55} -2.19346e7 q^{56} -1.30753e8 q^{58} +8.07005e7 q^{59} +6.21644e7 q^{61} +4.09577e7 q^{62} +1.49002e8 q^{64} +1.83437e7 q^{65} +1.55110e8 q^{67} -2.53869e7 q^{68} +9.34377e7 q^{70} +1.87869e8 q^{71} +4.82049e7 q^{73} -3.05060e8 q^{74} -5.40673e7 q^{76} -1.31988e8 q^{77} -4.54354e8 q^{79} -5.29198e8 q^{80} -3.62328e8 q^{82} -1.00047e8 q^{83} +6.94081e8 q^{85} +6.98559e7 q^{86} +9.24108e8 q^{88} -1.13769e9 q^{89} -1.25671e7 q^{91} +1.21838e8 q^{92} +2.31174e8 q^{94} +1.47821e9 q^{95} -2.37271e8 q^{97} +7.60527e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) \) 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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