LMFDB - Embedded newform 387.10.a.c.1.11

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			1.11
Root			$16.4876$ 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)

$f(q)$	$=$	$q+18.4876 q^{2} -170.210 q^{4} +2363.43 q^{5} +7025.62 q^{7} -12612.4 q^{8} +O(q^{10})$	\(q+18.4876 q^{2} -170.210 q^{4} +2363.43 q^{5} +7025.62 q^{7} -12612.4 q^{8} +43694.1 q^{10} +59098.5 q^{11} -84020.4 q^{13} +129887. q^{14} -146025. q^{16} -199182. q^{17} +293458. q^{19} -402279. q^{20} +1.09259e6 q^{22} -366554. q^{23} +3.63268e6 q^{25} -1.55333e6 q^{26} -1.19583e6 q^{28} +1.87481e6 q^{29} +3.91740e6 q^{31} +3.75790e6 q^{32} -3.68239e6 q^{34} +1.66046e7 q^{35} +2.22050e7 q^{37} +5.42532e6 q^{38} -2.98085e7 q^{40} -3.33190e6 q^{41} -3.41880e6 q^{43} -1.00591e7 q^{44} -6.77669e6 q^{46} +4.54124e7 q^{47} +9.00569e6 q^{49} +6.71594e7 q^{50} +1.43011e7 q^{52} -4.88629e7 q^{53} +1.39675e8 q^{55} -8.86099e7 q^{56} +3.46607e7 q^{58} -1.66035e8 q^{59} -1.65599e8 q^{61} +7.24233e7 q^{62} +1.44239e8 q^{64} -1.98576e8 q^{65} +1.13400e7 q^{67} +3.39027e7 q^{68} +3.06978e8 q^{70} +2.09329e8 q^{71} +7.39810e6 q^{73} +4.10516e8 q^{74} -4.99494e7 q^{76} +4.15204e8 q^{77} +5.09343e8 q^{79} -3.45120e8 q^{80} -6.15988e7 q^{82} +4.59491e8 q^{83} -4.70753e8 q^{85} -6.32053e7 q^{86} -7.45374e8 q^{88} +2.28949e8 q^{89} -5.90295e8 q^{91} +6.23911e7 q^{92} +8.39565e8 q^{94} +6.93567e8 q^{95} -9.54121e8 q^{97} +1.66493e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	18.4876	0.817043	0.408521	−	0.912749i	$-0.366045\pi$
$2$	18.4876	0.817043	0.408521	+	0.912749i	$0.366045\pi$
$3$	0	0
$3$	0	0
$4$	−170.210	−0.332441
$5$	2363.43	1.69113	0.845567	−	0.533870i	$-0.179263\pi$
$5$	2363.43	1.69113	0.845567	+	0.533870i	$0.179263\pi$
$6$	0	0
$7$	7025.62	1.10597	0.552985	−	0.833191i	$-0.313489\pi$
$7$	7025.62	1.10597	0.552985	+	0.833191i	$0.313489\pi$
$8$	−12612.4	−1.08866
$9$	0	0
$10$	43694.1	1.38173
$11$	59098.5	1.21705	0.608526	−	0.793534i	$-0.291761\pi$
$11$	59098.5	1.21705	0.608526	+	0.793534i	$0.291761\pi$
$12$	0	0
$13$	−84020.4	−0.815905	−0.407952	−	0.913003i	$-0.633757\pi$
$13$	−84020.4	−0.815905	−0.407952	+	0.913003i	$0.633757\pi$
$14$	129887.	0.903625
$15$	0	0
$16$	−146025.	−0.557042
$17$	−199182.	−0.578402	−0.289201	−	0.957268i	$-0.593390\pi$
$17$	−199182.	−0.578402	−0.289201	+	0.957268i	$0.593390\pi$
$18$	0	0
$19$	293458.	0.516600	0.258300	−	0.966065i	$-0.416838\pi$
$19$	293458.	0.516600	0.258300	+	0.966065i	$0.416838\pi$
$20$	−402279.	−0.562202
$21$	0	0
$22$	1.09259e6	0.994384
$23$	−366554.	−0.273126	−0.136563	−	0.990631i	$-0.543606\pi$
$23$	−366554.	−0.273126	−0.136563	+	0.990631i	$0.543606\pi$
$24$	0	0
$25$	3.63268e6	1.85993
$26$	−1.55333e6	−0.666629
$27$	0	0
$28$	−1.19583e6	−0.367670
$29$	1.87481e6	0.492228	0.246114	−	0.969241i	$-0.420846\pi$
$29$	1.87481e6	0.492228	0.246114	+	0.969241i	$0.420846\pi$
$30$	0	0
$31$	3.91740e6	0.761852	0.380926	−	0.924605i	$-0.375605\pi$
$31$	3.91740e6	0.761852	0.380926	+	0.924605i	$0.375605\pi$
$32$	3.75790e6	0.633534
$33$	0	0
$34$	−3.68239e6	−0.472579
$35$	1.66046e7	1.87034
$36$	0	0
$37$	2.22050e7	1.94779	0.973895	−	0.226997i	$-0.0728907\pi$
$37$	2.22050e7	1.94779	0.973895	+	0.226997i	$0.0728907\pi$
$38$	5.42532e6	0.422084
$39$	0	0
$40$	−2.98085e7	−1.84107
$41$	−3.33190e6	−0.184147	−0.0920736	−	0.995752i	$-0.529350\pi$
$41$	−3.33190e6	−0.184147	−0.0920736	+	0.995752i	$0.529350\pi$
$42$	0	0
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	−1.00591e7	−0.404598
$45$	0	0
$46$	−6.77669e6	−0.223156
$47$	4.54124e7	1.35748	0.678741	−	0.734378i	$-0.262526\pi$
$47$	4.54124e7	1.35748	0.678741	+	0.734378i	$0.262526\pi$
$48$	0	0
$49$	9.00569e6	0.223169
$50$	6.71594e7	1.51964
$51$	0	0
$52$	1.43011e7	0.271240
$53$	−4.88629e7	−0.850624	−0.425312	−	0.905047i	$-0.639836\pi$
$53$	−4.88629e7	−0.850624	−0.425312	+	0.905047i	$0.639836\pi$
$54$	0	0
$55$	1.39675e8	2.05820
$56$	−8.86099e7	−1.20403
$57$	0	0
$58$	3.46607e7	0.402172
$59$	−1.66035e8	−1.78387	−0.891937	−	0.452159i	$-0.850654\pi$
$59$	−1.66035e8	−1.78387	−0.891937	+	0.452159i	$0.850654\pi$
$60$	0	0
$61$	−1.65599e8	−1.53135	−0.765673	−	0.643230i	$-0.777594\pi$
$61$	−1.65599e8	−1.53135	−0.765673	+	0.643230i	$0.777594\pi$
$62$	7.24233e7	0.622466
$63$	0	0
$64$	1.44239e8	1.07467
$65$	−1.98576e8	−1.37980
$66$	0	0
$67$	1.13400e7	0.0687507	0.0343753	−	0.999409i	$-0.489056\pi$
$67$	1.13400e7	0.0687507	0.0343753	+	0.999409i	$0.489056\pi$
$68$	3.39027e7	0.192285
$69$	0	0
$70$	3.06978e8	1.52815
$71$	2.09329e8	0.977611	0.488806	−	0.872393i	$-0.337433\pi$
$71$	2.09329e8	0.977611	0.488806	+	0.872393i	$0.337433\pi$
$72$	0	0
$73$	7.39810e6	0.0304907	0.0152453	−	0.999884i	$-0.495147\pi$
$73$	7.39810e6	0.0304907	0.0152453	+	0.999884i	$0.495147\pi$
$74$	4.10516e8	1.59143
$75$	0	0
$76$	−4.99494e7	−0.171739
$77$	4.15204e8	1.34602
$78$	0	0
$79$	5.09343e8	1.47126	0.735629	−	0.677385i	$-0.236887\pi$
$79$	5.09343e8	1.47126	0.735629	+	0.677385i	$0.236887\pi$
$80$	−3.45120e8	−0.942032
$81$	0	0
$82$	−6.15988e7	−0.150456
$83$	4.59491e8	1.06274	0.531369	−	0.847141i	$-0.321678\pi$
$83$	4.59491e8	1.06274	0.531369	+	0.847141i	$0.321678\pi$
$84$	0	0
$85$	−4.70753e8	−0.978155
$86$	−6.32053e7	−0.124598
$87$	0	0
$88$	−7.45374e8	−1.32496
$89$	2.28949e8	0.386798	0.193399	−	0.981120i	$-0.438049\pi$
$89$	2.28949e8	0.386798	0.193399	+	0.981120i	$0.438049\pi$
$90$	0	0
$91$	−5.90295e8	−0.902366
$92$	6.23911e7	0.0907983
$93$	0	0
$94$	8.39565e8	1.10912
$95$	6.93567e8	0.873639
$96$	0	0
$97$	−9.54121e8	−1.09429	−0.547143	−	0.837039i	$-0.684285\pi$
$97$	−9.54121e8	−1.09429	−0.547143	+	0.837039i	$0.684285\pi$
$98$	1.66493e8	0.182339
$99$	0	0
$100$	−6.18318e8	−0.618318
$101$	−1.29443e9	−1.23775	−0.618876	−	0.785489i	$-0.712412\pi$
$101$	−1.29443e9	−1.23775	−0.618876	+	0.785489i	$0.712412\pi$
$102$	0	0
$103$	5.67850e8	0.497126	0.248563	−	0.968616i	$-0.420042\pi$
$103$	5.67850e8	0.497126	0.248563	+	0.968616i	$0.420042\pi$
$104$	1.05970e9	0.888244
$105$	0	0
$106$	−9.03356e8	−0.694996
$107$	−4.53655e8	−0.334579	−0.167290	−	0.985908i	$-0.553501\pi$
$107$	−4.53655e8	−0.334579	−0.167290	+	0.985908i	$0.553501\pi$
$108$	0	0
$109$	9.29530e8	0.630731	0.315365	−	0.948970i	$-0.397873\pi$
$109$	9.29530e8	0.630731	0.315365	+	0.948970i	$0.397873\pi$
$110$	2.58226e9	1.68164
$111$	0	0
$112$	−1.02592e9	−0.616071
$113$	3.79267e7	0.0218822	0.0109411	−	0.999940i	$-0.496517\pi$
$113$	3.79267e7	0.0218822	0.0109411	+	0.999940i	$0.496517\pi$
$114$	0	0
$115$	−8.66325e8	−0.461892
$116$	−3.19111e8	−0.163637
$117$	0	0
$118$	−3.06957e9	−1.45750
$119$	−1.39938e9	−0.639696
$120$	0	0
$121$	1.13469e9	0.481218
$122$	−3.06152e9	−1.25118
$123$	0	0
$124$	−6.66781e8	−0.253271
$125$	3.96951e9	1.45426
$126$	0	0
$127$	−3.97458e9	−1.35573	−0.677867	−	0.735185i	$-0.737095\pi$
$127$	−3.97458e9	−1.35573	−0.677867	+	0.735185i	$0.737095\pi$
$128$	7.42589e8	0.244514
$129$	0	0
$130$	−3.67119e9	−1.12736
$131$	1.80701e9	0.536093	0.268047	−	0.963406i	$-0.413622\pi$
$131$	1.80701e9	0.536093	0.268047	+	0.963406i	$0.413622\pi$
$132$	0	0
$133$	2.06172e9	0.571344
$134$	2.09649e8	0.0561722
$135$	0	0
$136$	2.51216e9	0.629684
$137$	2.82788e9	0.685834	0.342917	−	0.939366i	$-0.388585\pi$
$137$	2.82788e9	0.685834	0.342917	+	0.939366i	$0.388585\pi$
$138$	0	0
$139$	6.82579e9	1.55091	0.775454	−	0.631404i	$-0.217521\pi$
$139$	6.82579e9	1.55091	0.775454	+	0.631404i	$0.217521\pi$
$140$	−2.82626e9	−0.621779
$141$	0	0
$142$	3.86998e9	0.798750
$143$	−4.96548e9	−0.992999
$144$	0	0
$145$	4.43099e9	0.832424
$146$	1.36773e8	0.0249122
$147$	0	0
$148$	−3.77950e9	−0.647526
$149$	9.22449e9	1.53322	0.766610	−	0.642113i	$-0.221942\pi$
$149$	9.22449e9	1.53322	0.766610	+	0.642113i	$0.221942\pi$
$150$	0	0
$151$	7.71760e9	1.20805	0.604027	−	0.796964i	$-0.293562\pi$
$151$	7.71760e9	1.20805	0.604027	+	0.796964i	$0.293562\pi$
$152$	−3.70121e9	−0.562402
$153$	0	0
$154$	7.67610e9	1.09976
$155$	9.25851e9	1.28839
$156$	0	0
$157$	−1.03691e10	−1.36205	−0.681027	−	0.732259i	$-0.738466\pi$
$157$	−1.03691e10	−1.36205	−0.681027	+	0.732259i	$0.738466\pi$
$158$	9.41652e9	1.20208
$159$	0	0
$160$	8.88153e9	1.07139
$161$	−2.57527e9	−0.302069
$162$	0	0
$163$	1.24179e10	1.37786	0.688929	−	0.724829i	$-0.258081\pi$
$163$	1.24179e10	1.37786	0.688929	+	0.724829i	$0.258081\pi$
$164$	5.67123e8	0.0612181
$165$	0	0
$166$	8.49488e9	0.868302
$167$	−8.49813e8	−0.0845472	−0.0422736	−	0.999106i	$-0.513460\pi$
$167$	−8.49813e8	−0.0845472	−0.0422736	+	0.999106i	$0.513460\pi$
$168$	0	0
$169$	−3.54508e9	−0.334300
$170$	−8.70308e9	−0.799195
$171$	0	0
$172$	5.81914e8	0.0506968
$173$	2.05242e10	1.74204	0.871022	−	0.491244i	$-0.163458\pi$
$173$	2.05242e10	1.74204	0.871022	+	0.491244i	$0.163458\pi$
$174$	0	0
$175$	2.55218e10	2.05703
$176$	−8.62987e9	−0.677949
$177$	0	0
$178$	4.23271e9	0.316030
$179$	−2.24623e8	−0.0163537	−0.00817684	−	0.999967i	$-0.502603\pi$
$179$	−2.24623e8	−0.0163537	−0.00817684	+	0.999967i	$0.502603\pi$
$180$	0	0
$181$	1.28374e10	0.889043	0.444522	−	0.895768i	$-0.353374\pi$
$181$	1.28374e10	0.889043	0.444522	+	0.895768i	$0.353374\pi$
$182$	−1.09131e10	−0.737272
$183$	0	0
$184$	4.62313e9	0.297342
$185$	5.24799e10	3.29397
$186$	0	0
$187$	−1.17714e10	−0.703946
$188$	−7.72964e9	−0.451283
$189$	0	0
$190$	1.28224e10	0.713801
$191$	−1.84958e9	−0.100560	−0.0502798	−	0.998735i	$-0.516011\pi$
$191$	−1.84958e9	−0.100560	−0.0502798	+	0.998735i	$0.516011\pi$
$192$	0	0
$193$	7.73188e9	0.401123	0.200561	−	0.979681i	$-0.435723\pi$
$193$	7.73188e9	0.401123	0.200561	+	0.979681i	$0.435723\pi$
$194$	−1.76394e10	−0.894078
$195$	0	0
$196$	−1.53286e9	−0.0741907
$197$	−2.41118e10	−1.14060	−0.570298	−	0.821438i	$-0.693172\pi$
$197$	−2.41118e10	−1.14060	−0.570298	+	0.821438i	$0.693172\pi$
$198$	0	0
$199$	2.46274e10	1.11322	0.556609	−	0.830775i	$-0.312102\pi$
$199$	2.46274e10	1.11322	0.556609	+	0.830775i	$0.312102\pi$
$200$	−4.58168e10	−2.02484
$201$	0	0
$202$	−2.39309e10	−1.01130
$203$	1.31717e10	0.544390
$204$	0	0
$205$	−7.87472e9	−0.311417
$206$	1.04982e10	0.406173
$207$	0	0
$208$	1.22691e10	0.454493
$209$	1.73429e10	0.628729
$210$	0	0
$211$	−1.54470e10	−0.536504	−0.268252	−	0.963349i	$-0.586446\pi$
$211$	−1.54470e10	−0.536504	−0.268252	+	0.963349i	$0.586446\pi$
$212$	8.31695e9	0.282782
$213$	0	0
$214$	−8.38698e9	−0.273365
$215$	−8.08010e9	−0.257895
$216$	0	0
$217$	2.75222e10	0.842586
$218$	1.71847e10	0.515334
$219$	0	0
$220$	−2.37741e10	−0.684230
$221$	1.67353e10	0.471921
$222$	0	0
$223$	−6.69002e10	−1.81157	−0.905786	−	0.423736i	$-0.860718\pi$
$223$	−6.69002e10	−1.81157	−0.905786	+	0.423736i	$0.860718\pi$
$224$	2.64016e10	0.700670
$225$	0	0
$226$	7.01172e8	0.0178787
$227$	2.18215e10	0.545466	0.272733	−	0.962090i	$-0.412072\pi$
$227$	2.18215e10	0.545466	0.272733	+	0.962090i	$0.412072\pi$
$228$	0	0
$229$	−4.48901e9	−0.107868	−0.0539338	−	0.998545i	$-0.517176\pi$
$229$	−4.48901e9	−0.107868	−0.0539338	+	0.998545i	$0.517176\pi$
$230$	−1.60162e10	−0.377386
$231$	0	0
$232$	−2.36459e10	−0.535870
$233$	−2.75398e9	−0.0612151	−0.0306076	−	0.999531i	$-0.509744\pi$
$233$	−2.75398e9	−0.0612151	−0.0306076	+	0.999531i	$0.509744\pi$
$234$	0	0
$235$	1.07329e11	2.29568
$236$	2.82607e10	0.593033
$237$	0	0
$238$	−2.58711e10	−0.522659
$239$	−2.52877e10	−0.501324	−0.250662	−	0.968075i	$-0.580648\pi$
$239$	−2.52877e10	−0.501324	−0.250662	+	0.968075i	$0.580648\pi$
$240$	0	0
$241$	1.07229e10	0.204755	0.102377	−	0.994746i	$-0.467355\pi$
$241$	1.07229e10	0.204755	0.102377	+	0.994746i	$0.467355\pi$
$242$	2.09776e10	0.393176
$243$	0	0
$244$	2.81866e10	0.509082
$245$	2.12843e10	0.377409
$246$	0	0
$247$	−2.46564e10	−0.421496
$248$	−4.94079e10	−0.829399
$249$	0	0
$250$	7.33866e10	1.18819
$251$	−4.66245e10	−0.741451	−0.370725	−	0.928743i	$-0.620891\pi$
$251$	−4.66245e10	−0.741451	−0.370725	+	0.928743i	$0.620891\pi$
$252$	0	0
$253$	−2.16628e10	−0.332409
$254$	−7.34803e10	−1.10769
$255$	0	0
$256$	−6.01218e10	−0.874888
$257$	2.77809e10	0.397234	0.198617	−	0.980077i	$-0.436355\pi$
$257$	2.77809e10	0.397234	0.198617	+	0.980077i	$0.436355\pi$
$258$	0	0
$259$	1.56004e11	2.15420
$260$	3.37996e10	0.458703
$261$	0	0
$262$	3.34073e10	0.438011
$263$	7.66179e10	0.987482	0.493741	−	0.869609i	$-0.335629\pi$
$263$	7.66179e10	0.987482	0.493741	+	0.869609i	$0.335629\pi$
$264$	0	0
$265$	−1.15484e11	−1.43852
$266$	3.81162e10	0.466812
$267$	0	0
$268$	−1.93018e9	−0.0228556
$269$	5.82715e10	0.678533	0.339266	−	0.940690i	$-0.389821\pi$
$269$	5.82715e10	0.678533	0.339266	+	0.940690i	$0.389821\pi$
$270$	0	0
$271$	5.01640e10	0.564977	0.282488	−	0.959271i	$-0.408840\pi$
$271$	5.01640e10	0.564977	0.282488	+	0.959271i	$0.408840\pi$
$272$	2.90856e10	0.322194
$273$	0	0
$274$	5.22807e10	0.560356
$275$	2.14686e11	2.26364
$276$	0	0
$277$	−6.47834e10	−0.661157	−0.330579	−	0.943778i	$-0.607244\pi$
$277$	−6.47834e10	−0.661157	−0.330579	+	0.943778i	$0.607244\pi$
$278$	1.26192e11	1.26716
$279$	0	0
$280$	−2.09423e11	−2.03617
$281$	−5.01006e10	−0.479363	−0.239682	−	0.970852i	$-0.577043\pi$
$281$	−5.01006e10	−0.479363	−0.239682	+	0.970852i	$0.577043\pi$
$282$	0	0
$283$	2.09526e11	1.94177	0.970887	−	0.239540i	$-0.0769966\pi$
$283$	2.09526e11	1.94177	0.970887	+	0.239540i	$0.0769966\pi$
$284$	−3.56298e10	−0.324998
$285$	0	0
$286$	−9.17996e10	−0.811323
$287$	−2.34087e10	−0.203661
$288$	0	0
$289$	−7.89144e10	−0.665451
$290$	8.19182e10	0.680126
$291$	0	0
$292$	−1.25923e9	−0.0101364
$293$	2.20081e11	1.74453	0.872264	−	0.489035i	$-0.162651\pi$
$293$	2.20081e11	1.74453	0.872264	+	0.489035i	$0.162651\pi$
$294$	0	0
$295$	−3.92411e11	−3.01677
$296$	−2.80058e11	−2.12048
$297$	0	0
$298$	1.70538e11	1.25271
$299$	3.07980e10	0.222845
$300$	0	0
$301$	−2.40192e10	−0.168659
$302$	1.42680e11	0.987031
$303$	0	0
$304$	−4.28522e10	−0.287768
$305$	−3.91382e11	−2.58971
$306$	0	0
$307$	4.15422e10	0.266911	0.133455	−	0.991055i	$-0.457393\pi$
$307$	4.15422e10	0.266911	0.133455	+	0.991055i	$0.457393\pi$
$308$	−7.06717e10	−0.447474
$309$	0	0
$310$	1.71167e11	1.05267
$311$	−7.16229e10	−0.434140	−0.217070	−	0.976156i	$-0.569650\pi$
$311$	−7.16229e10	−0.434140	−0.217070	+	0.976156i	$0.569650\pi$
$312$	0	0
$313$	−1.61891e11	−0.953398	−0.476699	−	0.879067i	$-0.658167\pi$
$313$	−1.61891e11	−0.953398	−0.476699	+	0.879067i	$0.658167\pi$
$314$	−1.91700e11	−1.11286
$315$	0	0
$316$	−8.66953e10	−0.489107
$317$	7.64203e9	0.0425052	0.0212526	−	0.999774i	$-0.493235\pi$
$317$	7.64203e9	0.0425052	0.0212526	+	0.999774i	$0.493235\pi$
$318$	0	0
$319$	1.10799e11	0.599068
$320$	3.40900e11	1.81740
$321$	0	0
$322$	−4.76105e10	−0.246803
$323$	−5.84515e10	−0.298803
$324$	0	0
$325$	−3.05219e11	−1.51753
$326$	2.29577e11	1.12577
$327$	0	0
$328$	4.20233e10	0.200474
$329$	3.19050e11	1.50133
$330$	0	0
$331$	1.41081e11	0.646014	0.323007	−	0.946396i	$-0.395306\pi$
$331$	1.41081e11	0.646014	0.323007	+	0.946396i	$0.395306\pi$
$332$	−7.82100e10	−0.353298
$333$	0	0
$334$	−1.57110e10	−0.0690787
$335$	2.68013e10	0.116267
$336$	0	0
$337$	1.00695e11	0.425279	0.212640	−	0.977131i	$-0.431794\pi$
$337$	1.00695e11	0.425279	0.212640	+	0.977131i	$0.431794\pi$
$338$	−6.55399e10	−0.273137
$339$	0	0
$340$	8.01268e10	0.325179
$341$	2.31513e11	0.927215
$342$	0	0
$343$	−2.20238e11	−0.859151
$344$	4.31193e10	0.166019
$345$	0	0
$346$	3.79443e11	1.42332
$347$	2.91880e11	1.08074	0.540370	−	0.841428i	$-0.318284\pi$
$347$	2.91880e11	1.08074	0.540370	+	0.841428i	$0.318284\pi$
$348$	0	0
$349$	−7.88123e10	−0.284367	−0.142184	−	0.989840i	$-0.545412\pi$
$349$	−7.88123e10	−0.284367	−0.142184	+	0.989840i	$0.545412\pi$
$350$	4.71836e11	1.68068
$351$	0	0
$352$	2.22086e11	0.771045
$353$	4.57862e11	1.56945	0.784726	−	0.619842i	$-0.212803\pi$
$353$	4.57862e11	1.56945	0.784726	+	0.619842i	$0.212803\pi$
$354$	0	0
$355$	4.94734e11	1.65327
$356$	−3.89694e10	−0.128588
$357$	0	0
$358$	−4.15273e9	−0.0133617
$359$	6.39676e10	0.203252	0.101626	−	0.994823i	$-0.467595\pi$
$359$	6.39676e10	0.203252	0.101626	+	0.994823i	$0.467595\pi$
$360$	0	0
$361$	−2.36570e11	−0.733125
$362$	2.37332e11	0.726387
$363$	0	0
$364$	1.00474e11	0.299984
$365$	1.74849e10	0.0515638
$366$	0	0
$367$	5.56082e10	0.160008	0.0800039	−	0.996795i	$-0.474507\pi$
$367$	5.56082e10	0.160008	0.0800039	+	0.996795i	$0.474507\pi$
$368$	5.35261e10	0.152143
$369$	0	0
$370$	9.70226e11	2.69132
$371$	−3.43292e11	−0.940765
$372$	0	0
$373$	−2.47592e11	−0.662289	−0.331145	−	0.943580i	$-0.607435\pi$
$373$	−2.47592e11	−0.662289	−0.331145	+	0.943580i	$0.607435\pi$
$374$	−2.17624e11	−0.575154
$375$	0	0
$376$	−5.72759e11	−1.47784
$377$	−1.57522e11	−0.401612
$378$	0	0
$379$	2.02764e11	0.504794	0.252397	−	0.967624i	$-0.418781\pi$
$379$	2.02764e11	0.504794	0.252397	+	0.967624i	$0.418781\pi$
$380$	−1.18052e11	−0.290434
$381$	0	0
$382$	−3.41943e10	−0.0821615
$383$	7.84097e10	0.186198	0.0930990	−	0.995657i	$-0.470323\pi$
$383$	7.84097e10	0.186198	0.0930990	+	0.995657i	$0.470323\pi$
$384$	0	0
$385$	9.81305e11	2.27631
$386$	1.42944e11	0.327734
$387$	0	0
$388$	1.62401e11	0.363786
$389$	−2.70312e11	−0.598539	−0.299270	−	0.954169i	$-0.596743\pi$
$389$	−2.70312e11	−0.598539	−0.299270	+	0.954169i	$0.596743\pi$
$390$	0	0
$391$	7.30110e10	0.157977
$392$	−1.13583e11	−0.242956
$393$	0	0
$394$	−4.45769e11	−0.931915
$395$	1.20380e12	2.48809
$396$	0	0
$397$	−6.70016e11	−1.35372	−0.676859	−	0.736113i	$-0.736659\pi$
$397$	−6.70016e11	−1.35372	−0.676859	+	0.736113i	$0.736659\pi$
$398$	4.55301e11	0.909546
$399$	0	0
$400$	−5.30463e11	−1.03606
$401$	−3.58493e11	−0.692359	−0.346179	−	0.938168i	$-0.612521\pi$
$401$	−3.58493e11	−0.692359	−0.346179	+	0.938168i	$0.612521\pi$
$402$	0	0
$403$	−3.29142e11	−0.621599
$404$	2.20325e11	0.411480
$405$	0	0
$406$	2.43513e11	0.444790
$407$	1.31228e12	2.37056
$408$	0	0
$409$	−2.93226e11	−0.518140	−0.259070	−	0.965859i	$-0.583416\pi$
$409$	−2.93226e11	−0.518140	−0.259070	+	0.965859i	$0.583416\pi$
$410$	−1.45584e11	−0.254441
$411$	0	0
$412$	−9.66537e10	−0.165265
$413$	−1.16649e12	−1.97291
$414$	0	0
$415$	1.08598e12	1.79723
$416$	−3.15740e11	−0.516904
$417$	0	0
$418$	3.20628e11	0.513699
$419$	2.52617e11	0.400404	0.200202	−	0.979755i	$-0.435840\pi$
$419$	2.52617e11	0.400404	0.200202	+	0.979755i	$0.435840\pi$
$420$	0	0
$421$	1.22137e11	0.189486	0.0947429	−	0.995502i	$-0.469797\pi$
$421$	1.22137e11	0.189486	0.0947429	+	0.995502i	$0.469797\pi$
$422$	−2.85578e11	−0.438347
$423$	0	0
$424$	6.16278e11	0.926042
$425$	−7.23564e11	−1.07579
$426$	0	0
$427$	−1.16343e12	−1.69362
$428$	7.72166e10	0.111228
$429$	0	0
$430$	−1.49381e11	−0.210712
$431$	−1.01246e12	−1.41329	−0.706643	−	0.707571i	$-0.749791\pi$
$431$	−1.01246e12	−1.41329	−0.706643	+	0.707571i	$0.749791\pi$
$432$	0	0
$433$	−9.36722e11	−1.28061	−0.640303	−	0.768123i	$-0.721191\pi$
$433$	−9.36722e11	−1.28061	−0.640303	+	0.768123i	$0.721191\pi$
$434$	5.08818e11	0.688429
$435$	0	0
$436$	−1.58215e11	−0.209681
$437$	−1.07568e11	−0.141097
$438$	0	0
$439$	−5.85451e10	−0.0752316	−0.0376158	−	0.999292i	$-0.511976\pi$
$439$	−5.85451e10	−0.0752316	−0.0376158	+	0.999292i	$0.511976\pi$
$440$	−1.76164e12	−2.24068
$441$	0	0
$442$	3.09396e11	0.385580
$443$	−1.20731e12	−1.48936	−0.744681	−	0.667421i	$-0.767398\pi$
$443$	−1.20731e12	−1.48936	−0.744681	+	0.667421i	$0.767398\pi$
$444$	0	0
$445$	5.41105e11	0.654127
$446$	−1.23682e12	−1.48013
$447$	0	0
$448$	1.01337e12	1.18855
$449$	1.34315e11	0.155961	0.0779807	−	0.996955i	$-0.475153\pi$
$449$	1.34315e11	0.155961	0.0779807	+	0.996955i	$0.475153\pi$
$450$	0	0
$451$	−1.96911e11	−0.224117
$452$	−6.45550e9	−0.00727456
$453$	0	0
$454$	4.03426e11	0.445669
$455$	−1.39512e12	−1.52602
$456$	0	0
$457$	6.04169e11	0.647941	0.323970	−	0.946067i	$-0.394982\pi$
$457$	6.04169e11	0.647941	0.323970	+	0.946067i	$0.394982\pi$
$458$	−8.29909e10	−0.0881325
$459$	0	0
$460$	1.47457e11	0.153552
$461$	7.96508e11	0.821364	0.410682	−	0.911779i	$-0.365291\pi$
$461$	7.96508e11	0.821364	0.410682	+	0.911779i	$0.365291\pi$
$462$	0	0
$463$	1.60119e12	1.61930	0.809652	−	0.586910i	$-0.199656\pi$
$463$	1.60119e12	1.61930	0.809652	+	0.586910i	$0.199656\pi$
$464$	−2.73770e11	−0.274192
$465$	0	0
$466$	−5.09144e10	−0.0500154
$467$	−1.97526e11	−0.192176	−0.0960879	−	0.995373i	$-0.530633\pi$
$467$	−1.97526e11	−0.192176	−0.0960879	+	0.995373i	$0.530633\pi$
$468$	0	0
$469$	7.96706e10	0.0760362
$470$	1.98425e12	1.87567
$471$	0	0
$472$	2.09409e12	1.94204
$473$	−2.02046e11	−0.185599
$474$	0	0
$475$	1.06604e12	0.960841
$476$	2.38188e11	0.212661
$477$	0	0
$478$	−4.67508e11	−0.409604
$479$	1.31380e12	1.14030	0.570149	−	0.821541i	$-0.306885\pi$
$479$	1.31380e12	1.14030	0.570149	+	0.821541i	$0.306885\pi$
$480$	0	0
$481$	−1.86567e12	−1.58921
$482$	1.98240e11	0.167293
$483$	0	0
$484$	−1.93135e11	−0.159977
$485$	−2.25500e12	−1.85058
$486$	0	0
$487$	−1.13531e12	−0.914604	−0.457302	−	0.889312i	$-0.651184\pi$
$487$	−1.13531e12	−0.914604	−0.457302	+	0.889312i	$0.651184\pi$
$488$	2.08860e12	1.66712
$489$	0	0
$490$	3.93495e11	0.308360
$491$	2.16799e11	0.168341	0.0841707	−	0.996451i	$-0.473176\pi$
$491$	2.16799e11	0.168341	0.0841707	+	0.996451i	$0.473176\pi$
$492$	0	0
$493$	−3.73429e11	−0.284706
$494$	−4.55837e11	−0.344380
$495$	0	0
$496$	−5.72040e11	−0.424384
$497$	1.47066e12	1.08121
$498$	0	0
$499$	−1.61040e12	−1.16274	−0.581368	−	0.813641i	$-0.697482\pi$
$499$	−1.61040e12	−1.16274	−0.581368	+	0.813641i	$0.697482\pi$
$500$	−6.75650e11	−0.483456
$501$	0	0
$502$	−8.61973e11	−0.605797
$503$	1.85720e12	1.29361	0.646803	−	0.762657i	$-0.276106\pi$
$503$	1.85720e12	1.29361	0.646803	+	0.762657i	$0.276106\pi$
$504$	0	0
$505$	−3.05930e12	−2.09320
$506$	−4.00493e11	−0.271592
$507$	0	0
$508$	6.76513e11	0.450702
$509$	−1.23771e11	−0.0817312	−0.0408656	−	0.999165i	$-0.513012\pi$
$509$	−1.23771e11	−0.0817312	−0.0408656	+	0.999165i	$0.513012\pi$
$510$	0	0
$511$	5.19762e10	0.0337218
$512$	−1.49171e12	−0.959335
$513$	0	0
$514$	5.13601e11	0.324557
$515$	1.34207e12	0.840705
$516$	0	0
$517$	2.68380e12	1.65213
$518$	2.88413e12	1.76007
$519$	0	0
$520$	2.50452e12	1.50214
$521$	3.54135e11	0.210571	0.105286	−	0.994442i	$-0.466424\pi$
$521$	3.54135e11	0.210571	0.105286	+	0.994442i	$0.466424\pi$
$522$	0	0
$523$	−9.79180e11	−0.572275	−0.286138	−	0.958188i	$-0.592371\pi$
$523$	−9.79180e11	−0.572275	−0.286138	+	0.958188i	$0.592371\pi$
$524$	−3.07571e11	−0.178219
$525$	0	0
$526$	1.41648e12	0.806815
$527$	−7.80277e11	−0.440657
$528$	0	0
$529$	−1.66679e12	−0.925402
$530$	−2.13502e12	−1.17533
$531$	0	0
$532$	−3.50925e11	−0.189938
$533$	2.79948e11	0.150247
$534$	0	0
$535$	−1.07218e12	−0.565818
$536$	−1.43025e11	−0.0748462
$537$	0	0
$538$	1.07730e12	0.554390
$539$	5.32223e11	0.271609
$540$	0	0
$541$	−1.88732e12	−0.947234	−0.473617	−	0.880731i	$-0.657052\pi$
$541$	−1.88732e12	−0.947234	−0.473617	+	0.880731i	$0.657052\pi$
$542$	9.27411e11	0.461610
$543$	0	0
$544$	−7.48506e11	−0.366438
$545$	2.19688e12	1.06665
$546$	0	0
$547$	−9.25517e11	−0.442020	−0.221010	−	0.975272i	$-0.570935\pi$
$547$	−9.25517e11	−0.442020	−0.221010	+	0.975272i	$0.570935\pi$
$548$	−4.81334e11	−0.227999
$549$	0	0
$550$	3.96902e12	1.84949
$551$	5.50178e11	0.254285
$552$	0	0
$553$	3.57845e12	1.62717
$554$	−1.19769e12	−0.540194
$555$	0	0
$556$	−1.16182e12	−0.515586
$557$	−4.04068e12	−1.77871	−0.889356	−	0.457215i	$-0.848847\pi$
$557$	−4.04068e12	−1.77871	−0.889356	+	0.457215i	$0.848847\pi$
$558$	0	0
$559$	2.87249e11	0.124424
$560$	−2.42468e12	−1.04186
$561$	0	0
$562$	−9.26239e11	−0.391660
$563$	1.31953e12	0.553517	0.276758	−	0.960940i	$-0.410740\pi$
$563$	1.31953e12	0.553517	0.276758	+	0.960940i	$0.410740\pi$
$564$	0	0
$565$	8.96371e10	0.0370058
$566$	3.87362e12	1.58651
$567$	0	0
$568$	−2.64014e12	−1.06429
$569$	1.40113e12	0.560366	0.280183	−	0.959947i	$-0.409605\pi$
$569$	1.40113e12	0.560366	0.280183	+	0.959947i	$0.409605\pi$
$570$	0	0
$571$	−7.55062e11	−0.297249	−0.148624	−	0.988894i	$-0.547485\pi$
$571$	−7.55062e11	−0.297249	−0.148624	+	0.988894i	$0.547485\pi$
$572$	8.45173e11	0.330114
$573$	0	0
$574$	−4.32770e11	−0.166400
$575$	−1.33157e12	−0.507995
$576$	0	0
$577$	2.44025e12	0.916521	0.458261	−	0.888818i	$-0.348473\pi$
$577$	2.44025e12	0.916521	0.458261	+	0.888818i	$0.348473\pi$
$578$	−1.45894e12	−0.543702
$579$	0	0
$580$	−7.54198e11	−0.276732
$581$	3.22821e12	1.17536
$582$	0	0
$583$	−2.88772e12	−1.03525
$584$	−9.33078e10	−0.0331940
$585$	0	0
$586$	4.06876e12	1.42535
$587$	5.63814e12	1.96004	0.980019	−	0.198906i	$-0.0637389\pi$
$587$	5.63814e12	1.96004	0.980019	+	0.198906i	$0.0637389\pi$
$588$	0	0
$589$	1.14959e12	0.393573
$590$	−7.25473e12	−2.46483
$591$	0	0
$592$	−3.24248e12	−1.08500
$593$	−2.07785e12	−0.690031	−0.345016	−	0.938597i	$-0.612126\pi$
$593$	−2.07785e12	−0.690031	−0.345016	+	0.938597i	$0.612126\pi$
$594$	0	0
$595$	−3.30733e12	−1.08181
$596$	−1.57010e12	−0.509705
$597$	0	0
$598$	5.69380e11	0.182074
$599$	−2.05195e12	−0.651248	−0.325624	−	0.945499i	$-0.605574\pi$
$599$	−2.05195e12	−0.651248	−0.325624	+	0.945499i	$0.605574\pi$
$600$	0	0
$601$	−3.93140e12	−1.22917	−0.614586	−	0.788850i	$-0.710677\pi$
$601$	−3.93140e12	−1.22917	−0.614586	+	0.788850i	$0.710677\pi$
$602$	−4.44056e11	−0.137801
$603$	0	0
$604$	−1.31361e12	−0.401607
$605$	2.68175e12	0.813803
$606$	0	0
$607$	2.33530e12	0.698221	0.349110	−	0.937082i	$-0.386484\pi$
$607$	2.33530e12	0.698221	0.349110	+	0.937082i	$0.386484\pi$
$608$	1.10278e12	0.327284
$609$	0	0
$610$	−7.23569e12	−2.11590
$611$	−3.81557e12	−1.10758
$612$	0	0
$613$	1.39331e12	0.398544	0.199272	−	0.979944i	$-0.436142\pi$
$613$	1.39331e12	0.398544	0.199272	+	0.979944i	$0.436142\pi$
$614$	7.68013e11	0.218078
$615$	0	0
$616$	−5.23671e12	−1.46536
$617$	−6.75919e11	−0.187764	−0.0938818	−	0.995583i	$-0.529928\pi$
$617$	−6.75919e11	−0.187764	−0.0938818	+	0.995583i	$0.529928\pi$
$618$	0	0
$619$	−3.04638e12	−0.834019	−0.417010	−	0.908902i	$-0.636922\pi$
$619$	−3.04638e12	−0.834019	−0.417010	+	0.908902i	$0.636922\pi$
$620$	−1.57589e12	−0.428315
$621$	0	0
$622$	−1.32413e12	−0.354711
$623$	1.60851e12	0.427787
$624$	0	0
$625$	2.28658e12	0.599414
$626$	−2.99298e12	−0.778967
$627$	0	0
$628$	1.76493e12	0.452802
$629$	−4.42283e12	−1.12661
$630$	0	0
$631$	−5.72611e12	−1.43790	−0.718948	−	0.695064i	$-0.755376\pi$
$631$	−5.72611e12	−1.43790	−0.718948	+	0.695064i	$0.755376\pi$
$632$	−6.42404e12	−1.60170
$633$	0	0
$634$	1.41283e11	0.0347286
$635$	−9.39364e12	−2.29273
$636$	0	0
$637$	−7.56661e11	−0.182085
$638$	2.04840e12	0.489464
$639$	0	0
$640$	1.75506e12	0.413506
$641$	−7.81185e10	−0.0182765	−0.00913825	−	0.999958i	$-0.502909\pi$
$641$	−7.81185e10	−0.0182765	−0.00913825	+	0.999958i	$0.502909\pi$
$642$	0	0
$643$	−1.63383e12	−0.376927	−0.188464	−	0.982080i	$-0.560351\pi$
$643$	−1.63383e12	−0.376927	−0.188464	+	0.982080i	$0.560351\pi$
$644$	4.38336e11	0.100420
$645$	0	0
$646$	−1.08063e12	−0.244134
$647$	−4.02702e12	−0.903471	−0.451735	−	0.892152i	$-0.649195\pi$
$647$	−4.02702e12	−0.903471	−0.451735	+	0.892152i	$0.649195\pi$
$648$	0	0
$649$	−9.81239e12	−2.17107
$650$	−5.64276e12	−1.23988
$651$	0	0
$652$	−2.11365e12	−0.458057
$653$	−5.84257e12	−1.25746	−0.628730	−	0.777623i	$-0.716425\pi$
$653$	−5.84257e12	−1.25746	−0.628730	+	0.777623i	$0.716425\pi$
$654$	0	0
$655$	4.27075e12	0.906605
$656$	4.86542e11	0.102578
$657$	0	0
$658$	5.89846e12	1.22665
$659$	−4.19256e11	−0.0865955	−0.0432977	−	0.999062i	$-0.513786\pi$
$659$	−4.19256e11	−0.0865955	−0.0432977	+	0.999062i	$0.513786\pi$
$660$	0	0
$661$	−4.51791e12	−0.920515	−0.460258	−	0.887785i	$-0.652243\pi$
$661$	−4.51791e12	−0.920515	−0.460258	+	0.887785i	$0.652243\pi$
$662$	2.60824e12	0.527821
$663$	0	0
$664$	−5.79529e12	−1.15696
$665$	4.87274e12	0.966219
$666$	0	0
$667$	−6.87220e11	−0.134440
$668$	1.44647e11	0.0281070
$669$	0	0
$670$	4.95492e11	0.0949948
$671$	−9.78665e12	−1.86373
$672$	0	0
$673$	−3.13452e12	−0.588983	−0.294492	−	0.955654i	$-0.595150\pi$
$673$	−3.13452e12	−0.588983	−0.294492	+	0.955654i	$0.595150\pi$
$674$	1.86161e12	0.347471
$675$	0	0
$676$	6.03407e11	0.111135
$677$	−9.08025e12	−1.66130	−0.830651	−	0.556793i	$-0.812032\pi$
$677$	−9.08025e12	−1.66130	−0.830651	+	0.556793i	$0.812032\pi$
$678$	0	0
$679$	−6.70329e12	−1.21025
$680$	5.93732e12	1.06488
$681$	0	0
$682$	4.28011e12	0.757574
$683$	−9.92561e12	−1.74528	−0.872638	−	0.488367i	$-0.837593\pi$
$683$	−9.92561e12	−1.74528	−0.872638	+	0.488367i	$0.837593\pi$
$684$	0	0
$685$	6.68351e12	1.15984
$686$	−4.07167e12	−0.701963
$687$	0	0
$688$	4.99231e11	0.0849481
$689$	4.10548e12	0.694028
$690$	0	0
$691$	2.83695e12	0.473370	0.236685	−	0.971586i	$-0.423939\pi$
$691$	2.83695e12	0.473370	0.236685	+	0.971586i	$0.423939\pi$
$692$	−3.49342e12	−0.579127
$693$	0	0
$694$	5.39614e12	0.883011
$695$	1.61323e13	2.62279
$696$	0	0
$697$	6.63655e11	0.106511
$698$	−1.45705e12	−0.232340
$699$	0	0
$700$	−4.34406e12	−0.683841
$701$	9.36363e11	0.146458	0.0732290	−	0.997315i	$-0.476670\pi$
$701$	9.36363e11	0.146458	0.0732290	+	0.997315i	$0.476670\pi$
$702$	0	0
$703$	6.51622e12	1.00623
$704$	8.52433e12	1.30793
$705$	0	0
$706$	8.46475e12	1.28231
$707$	−9.09420e12	−1.36892
$708$	0	0
$709$	5.31394e12	0.789785	0.394892	−	0.918727i	$-0.370782\pi$
$709$	5.31394e12	0.789785	0.394892	+	0.918727i	$0.370782\pi$
$710$	9.14643e12	1.35079
$711$	0	0
$712$	−2.88760e12	−0.421092
$713$	−1.43594e12	−0.208082
$714$	0	0
$715$	−1.17356e13	−1.67929
$716$	3.82330e10	0.00543663
$717$	0	0
$718$	1.18261e12	0.166066
$719$	−6.83793e12	−0.954212	−0.477106	−	0.878846i	$-0.658314\pi$
$719$	−6.83793e12	−0.954212	−0.477106	+	0.878846i	$0.658314\pi$
$720$	0	0
$721$	3.98950e12	0.549806
$722$	−4.37361e12	−0.598994
$723$	0	0
$724$	−2.18505e12	−0.295555
$725$	6.81059e12	0.915511
$726$	0	0
$727$	6.36741e12	0.845392	0.422696	−	0.906272i	$-0.361084\pi$
$727$	6.36741e12	0.845392	0.422696	+	0.906272i	$0.361084\pi$
$728$	7.44504e12	0.982371
$729$	0	0
$730$	3.23253e11	0.0421299
$731$	6.80964e11	0.0882055
$732$	0	0
$733$	5.47275e12	0.700226	0.350113	−	0.936708i	$-0.386143\pi$
$733$	5.47275e12	0.700226	0.350113	+	0.936708i	$0.386143\pi$
$734$	1.02806e12	0.130733
$735$	0	0
$736$	−1.37747e12	−0.173035
$737$	6.70178e11	0.0836732
$738$	0	0
$739$	−1.09212e13	−1.34701	−0.673503	−	0.739185i	$-0.735211\pi$
$739$	−1.09212e13	−1.34701	−0.673503	+	0.739185i	$0.735211\pi$
$740$	−8.93260e12	−1.09505
$741$	0	0
$742$	−6.34663e12	−0.768645
$743$	−1.41066e11	−0.0169813	−0.00849066	−	0.999964i	$-0.502703\pi$
$743$	−1.41066e11	−0.0169813	−0.00849066	+	0.999964i	$0.502703\pi$
$744$	0	0
$745$	2.18014e13	2.59288
$746$	−4.57738e12	−0.541118
$747$	0	0
$748$	2.00360e12	0.234021
$749$	−3.18721e12	−0.370034
$750$	0	0
$751$	1.07431e13	1.23240	0.616200	−	0.787590i	$-0.288671\pi$
$751$	1.07431e13	1.23240	0.616200	+	0.787590i	$0.288671\pi$
$752$	−6.63135e12	−0.756174
$753$	0	0
$754$	−2.91221e12	−0.328134
$755$	1.82400e13	2.04298
$756$	0	0
$757$	−3.92377e12	−0.434282	−0.217141	−	0.976140i	$-0.569673\pi$
$757$	−3.92377e12	−0.434282	−0.217141	+	0.976140i	$0.569673\pi$
$758$	3.74861e12	0.412438
$759$	0	0
$760$	−8.74754e12	−0.951097
$761$	−2.65761e12	−0.287250	−0.143625	−	0.989632i	$-0.545876\pi$
$761$	−2.65761e12	−0.287250	−0.143625	+	0.989632i	$0.545876\pi$
$762$	0	0
$763$	6.53052e12	0.697569
$764$	3.14817e11	0.0334302
$765$	0	0
$766$	1.44960e12	0.152132
$767$	1.39503e13	1.45547
$768$	0	0
$769$	3.14923e12	0.324740	0.162370	−	0.986730i	$-0.448086\pi$
$769$	3.14923e12	0.324740	0.162370	+	0.986730i	$0.448086\pi$
$770$	1.81419e13	1.85984
$771$	0	0
$772$	−1.31604e12	−0.133350
$773$	−3.67725e11	−0.0370438	−0.0185219	−	0.999828i	$-0.505896\pi$
$773$	−3.67725e11	−0.0370438	−0.0185219	+	0.999828i	$0.505896\pi$
$774$	0	0
$775$	1.42307e13	1.41699
$776$	1.20338e13	1.19131
$777$	0	0
$778$	−4.99742e12	−0.489032
$779$	−9.77773e11	−0.0951304
$780$	0	0
$781$	1.23710e13	1.18980
$782$	1.34980e12	0.129074
$783$	0	0
$784$	−1.31506e12	−0.124315
$785$	−2.45067e13	−2.30341
$786$	0	0
$787$	−1.46553e13	−1.36179	−0.680895	−	0.732381i	$-0.738409\pi$
$787$	−1.46553e13	−1.36179	−0.680895	+	0.732381i	$0.738409\pi$
$788$	4.10407e12	0.379181
$789$	0	0
$790$	2.22553e13	2.03288
$791$	2.66458e11	0.0242011
$792$	0	0
$793$	1.39137e13	1.24943
$794$	−1.23870e13	−1.10604
$795$	0	0
$796$	−4.19183e12	−0.370079
$797$	2.07106e13	1.81815	0.909075	−	0.416633i	$-0.136790\pi$
$797$	2.07106e13	1.81815	0.909075	+	0.416633i	$0.136790\pi$
$798$	0	0
$799$	−9.04533e12	−0.785171
$800$	1.36512e13	1.17833
$801$	0	0
$802$	−6.62767e12	−0.565687
$803$	4.37217e11	0.0371088
$804$	0	0
$805$	−6.08647e12	−0.510839
$806$	−6.08503e12	−0.507873
$807$	0	0
$808$	1.63259e13	1.34749
$809$	−1.94599e12	−0.159725	−0.0798623	−	0.996806i	$-0.525448\pi$
$809$	−1.94599e12	−0.159725	−0.0798623	+	0.996806i	$0.525448\pi$
$810$	0	0
$811$	1.32679e11	0.0107698	0.00538491	−	0.999986i	$-0.498286\pi$
$811$	1.32679e11	0.0107698	0.00538491	+	0.999986i	$0.498286\pi$
$812$	−2.24196e12	−0.180978
$813$	0	0
$814$	2.42609e13	1.93685
$815$	2.93489e13	2.33014
$816$	0	0
$817$	−1.00327e12	−0.0787807
$818$	−5.42103e12	−0.423343
$819$	0	0
$820$	1.34036e12	0.103528
$821$	−1.39889e13	−1.07458	−0.537290	−	0.843398i	$-0.680552\pi$
$821$	−1.39889e13	−1.07458	−0.537290	+	0.843398i	$0.680552\pi$
$822$	0	0
$823$	−2.70521e12	−0.205543	−0.102771	−	0.994705i	$-0.532771\pi$
$823$	−2.70521e12	−0.205543	−0.102771	+	0.994705i	$0.532771\pi$
$824$	−7.16195e12	−0.541201
$825$	0	0
$826$	−2.15657e13	−1.61195
$827$	7.17939e11	0.0533719	0.0266859	−	0.999644i	$-0.491505\pi$
$827$	7.17939e11	0.0533719	0.0266859	+	0.999644i	$0.491505\pi$
$828$	0	0
$829$	−1.65304e12	−0.121559	−0.0607796	−	0.998151i	$-0.519359\pi$
$829$	−1.65304e12	−0.121559	−0.0607796	+	0.998151i	$0.519359\pi$
$830$	2.00771e13	1.46841
$831$	0	0
$832$	−1.21190e13	−0.876825
$833$	−1.79377e12	−0.129082
$834$	0	0
$835$	−2.00848e12	−0.142981
$836$	−2.95193e12	−0.209016
$837$	0	0
$838$	4.67027e12	0.327148
$839$	−1.51228e13	−1.05366	−0.526832	−	0.849969i	$-0.676620\pi$
$839$	−1.51228e13	−1.05366	−0.526832	+	0.849969i	$0.676620\pi$
$840$	0	0
$841$	−1.09922e13	−0.757711
$842$	2.25801e12	0.154818
$843$	0	0
$844$	2.62923e12	0.178356
$845$	−8.37855e12	−0.565345
$846$	0	0
$847$	7.97187e12	0.532212
$848$	7.13521e12	0.473833
$849$	0	0
$850$	−1.33769e13	−0.878965
$851$	−8.13932e12	−0.531992
$852$	0	0
$853$	−1.14817e13	−0.742568	−0.371284	−	0.928519i	$-0.621082\pi$
$853$	−1.14817e13	−0.742568	−0.371284	+	0.928519i	$0.621082\pi$
$854$	−2.15091e13	−1.38376
$855$	0	0
$856$	5.72168e12	0.364243
$857$	−1.99397e13	−1.26271	−0.631356	−	0.775493i	$-0.717501\pi$
$857$	−1.99397e13	−1.26271	−0.631356	+	0.775493i	$0.717501\pi$
$858$	0	0
$859$	1.38539e13	0.868164	0.434082	−	0.900873i	$-0.357073\pi$
$859$	1.38539e13	0.868164	0.434082	+	0.900873i	$0.357073\pi$
$860$	1.37531e12	0.0857350
$861$	0	0
$862$	−1.87179e13	−1.15471
$863$	2.96018e13	1.81664	0.908321	−	0.418275i	$-0.137365\pi$
$863$	2.96018e13	1.81664	0.908321	+	0.418275i	$0.137365\pi$
$864$	0	0
$865$	4.85076e13	2.94603
$866$	−1.73177e13	−1.04631
$867$	0	0
$868$	−4.68455e12	−0.280110
$869$	3.01014e13	1.79060
$870$	0	0
$871$	−9.52792e11	−0.0560940
$872$	−1.17236e13	−0.686652
$873$	0	0
$874$	−1.98867e12	−0.115282
$875$	2.78883e13	1.60837
$876$	0	0
$877$	−5.98845e12	−0.341835	−0.170918	−	0.985285i	$-0.554673\pi$
$877$	−5.98845e12	−0.341835	−0.170918	+	0.985285i	$0.554673\pi$
$878$	−1.08236e12	−0.0614674
$879$	0	0
$880$	−2.03961e13	−1.14650
$881$	−4.47788e10	−0.00250427	−0.00125213	−	0.999999i	$-0.500399\pi$
$881$	−4.47788e10	−0.00250427	−0.00125213	+	0.999999i	$0.500399\pi$
$882$	0	0
$883$	1.82152e13	1.00835	0.504175	−	0.863601i	$-0.331797\pi$
$883$	1.82152e13	1.00835	0.504175	+	0.863601i	$0.331797\pi$
$884$	−2.84852e12	−0.156886
$885$	0	0
$886$	−2.23201e13	−1.21687
$887$	1.08674e13	0.589483	0.294741	−	0.955577i	$-0.404766\pi$
$887$	1.08674e13	0.589483	0.294741	+	0.955577i	$0.404766\pi$
$888$	0	0
$889$	−2.79239e13	−1.49940
$890$	1.00037e13	0.534450
$891$	0	0
$892$	1.13871e13	0.602241
$893$	1.33266e13	0.701275
$894$	0	0
$895$	−5.30881e11	−0.0276562
$896$	5.21715e12	0.270425
$897$	0	0
$898$	2.48316e12	0.127427
$899$	7.34440e12	0.375005
$900$	0	0
$901$	9.73261e12	0.492003
$902$	−3.64040e12	−0.183113
$903$	0	0
$904$	−4.78347e11	−0.0238224
$905$	3.03403e13	1.50349
$906$	0	0
$907$	−2.21516e13	−1.08686	−0.543429	−	0.839455i	$-0.682874\pi$
$907$	−2.21516e13	−1.08686	−0.543429	+	0.839455i	$0.682874\pi$
$908$	−3.71423e12	−0.181335
$909$	0	0
$910$	−2.57924e13	−1.24682
$911$	−8.34279e12	−0.401309	−0.200654	−	0.979662i	$-0.564307\pi$
$911$	−8.34279e12	−0.401309	−0.200654	+	0.979662i	$0.564307\pi$
$912$	0	0
$913$	2.71553e13	1.29341
$914$	1.11696e13	0.529395
$915$	0	0
$916$	7.64074e11	0.0358596
$917$	1.26954e13	0.592903
$918$	0	0
$919$	−1.73492e13	−0.802341	−0.401170	−	0.916003i	$-0.631396\pi$
$919$	−1.73492e13	−0.802341	−0.401170	+	0.916003i	$0.631396\pi$
$920$	1.09264e13	0.502844
$921$	0	0
$922$	1.47255e13	0.671090
$923$	−1.75879e13	−0.797638
$924$	0	0
$925$	8.06635e13	3.62276
$926$	2.96021e13	1.32304
$927$	0	0
$928$	7.04535e12	0.311844
$929$	1.11298e13	0.490247	0.245124	−	0.969492i	$-0.421171\pi$
$929$	1.11298e13	0.490247	0.245124	+	0.969492i	$0.421171\pi$
$930$	0	0
$931$	2.64279e12	0.115289
$932$	4.68754e11	0.0203504
$933$	0	0
$934$	−3.65178e12	−0.157016
$935$	−2.78208e13	−1.19047
$936$	0	0
$937$	−2.31541e13	−0.981297	−0.490648	−	0.871358i	$-0.663240\pi$
$937$	−2.31541e13	−0.981297	−0.490648	+	0.871358i	$0.663240\pi$
$938$	1.47292e12	0.0621248
$939$	0	0
$940$	−1.82685e13	−0.763179
$941$	−6.27432e12	−0.260864	−0.130432	−	0.991457i	$-0.541636\pi$
$941$	−6.27432e12	−0.260864	−0.130432	+	0.991457i	$0.541636\pi$
$942$	0	0
$943$	1.22132e12	0.0502954
$944$	2.42452e13	0.993693
$945$	0	0
$946$	−3.73534e12	−0.151642
$947$	1.95848e12	0.0791305	0.0395652	−	0.999217i	$-0.487403\pi$
$947$	1.95848e12	0.0791305	0.0395652	+	0.999217i	$0.487403\pi$
$948$	0	0
$949$	−6.21591e11	−0.0248775
$950$	1.97084e13	0.785048
$951$	0	0
$952$	1.76495e13	0.696412
$953$	3.01343e13	1.18343	0.591716	−	0.806146i	$-0.298451\pi$
$953$	3.01343e13	1.18343	0.591716	+	0.806146i	$0.298451\pi$
$954$	0	0
$955$	−4.37136e12	−0.170060
$956$	4.30422e12	0.166661
$957$	0	0
$958$	2.42889e13	0.931672
$959$	1.98676e13	0.758512
$960$	0	0
$961$	−1.10936e13	−0.419581
$962$	−3.44917e13	−1.29845
$963$	0	0
$964$	−1.82514e12	−0.0680689
$965$	1.82738e13	0.678352
$966$	0	0
$967$	−4.59576e13	−1.69020	−0.845099	−	0.534609i	$-0.820459\pi$
$967$	−4.59576e13	−1.69020	−0.845099	+	0.534609i	$0.820459\pi$
$968$	−1.43111e13	−0.523883
$969$	0	0
$970$	−4.16895e13	−1.51201
$971$	−5.92518e11	−0.0213902	−0.0106951	−	0.999943i	$-0.503404\pi$
$971$	−5.92518e11	−0.0213902	−0.0106951	+	0.999943i	$0.503404\pi$
$972$	0	0
$973$	4.79554e13	1.71526
$974$	−2.09891e13	−0.747270
$975$	0	0
$976$	2.41816e13	0.853024
$977$	3.04374e13	1.06876	0.534382	−	0.845243i	$-0.320544\pi$
$977$	3.04374e13	1.06876	0.534382	+	0.845243i	$0.320544\pi$
$978$	0	0
$979$	1.35306e13	0.470753
$980$	−3.62280e12	−0.125466
$981$	0	0
$982$	4.00809e12	0.137542
$983$	−2.48900e13	−0.850225	−0.425113	−	0.905140i	$-0.639765\pi$
$983$	−2.48900e13	−0.850225	−0.425113	+	0.905140i	$0.639765\pi$
$984$	0	0
$985$	−5.69866e13	−1.92890
$986$	−6.90379e12	−0.232617
$987$	0	0
$988$	4.19677e12	0.140123
$989$	1.25318e12	0.0416513
$990$	0	0
$991$	7.06033e12	0.232538	0.116269	−	0.993218i	$-0.462907\pi$
$991$	7.06033e12	0.232538	0.116269	+	0.993218i	$0.462907\pi$
$992$	1.47212e13	0.482660
$993$	0	0
$994$	2.71890e13	0.883394
$995$	5.82052e13	1.88260
$996$	0	0
$997$	−1.27122e13	−0.407468	−0.203734	−	0.979026i	$-0.565308\pi$
$997$	−1.27122e13	−0.407468	−0.203734	+	0.979026i	$0.565308\pi$
$998$	−2.97724e13	−0.950005
$999$	0	0

Twists

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

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

\(f(q)\)	\(=\)	\(q+18.4876 q^{2} -170.210 q^{4} +2363.43 q^{5} +7025.62 q^{7} -12612.4 q^{8} +O(q^{10})\)	\(q+18.4876 q^{2} -170.210 q^{4} +2363.43 q^{5} +7025.62 q^{7} -12612.4 q^{8} +43694.1 q^{10} +59098.5 q^{11} -84020.4 q^{13} +129887. q^{14} -146025. q^{16} -199182. q^{17} +293458. q^{19} -402279. q^{20} +1.09259e6 q^{22} -366554. q^{23} +3.63268e6 q^{25} -1.55333e6 q^{26} -1.19583e6 q^{28} +1.87481e6 q^{29} +3.91740e6 q^{31} +3.75790e6 q^{32} -3.68239e6 q^{34} +1.66046e7 q^{35} +2.22050e7 q^{37} +5.42532e6 q^{38} -2.98085e7 q^{40} -3.33190e6 q^{41} -3.41880e6 q^{43} -1.00591e7 q^{44} -6.77669e6 q^{46} +4.54124e7 q^{47} +9.00569e6 q^{49} +6.71594e7 q^{50} +1.43011e7 q^{52} -4.88629e7 q^{53} +1.39675e8 q^{55} -8.86099e7 q^{56} +3.46607e7 q^{58} -1.66035e8 q^{59} -1.65599e8 q^{61} +7.24233e7 q^{62} +1.44239e8 q^{64} -1.98576e8 q^{65} +1.13400e7 q^{67} +3.39027e7 q^{68} +3.06978e8 q^{70} +2.09329e8 q^{71} +7.39810e6 q^{73} +4.10516e8 q^{74} -4.99494e7 q^{76} +4.15204e8 q^{77} +5.09343e8 q^{79} -3.45120e8 q^{80} -6.15988e7 q^{82} +4.59491e8 q^{83} -4.70753e8 q^{85} -6.32053e7 q^{86} -7.45374e8 q^{88} +2.28949e8 q^{89} -5.90295e8 q^{91} +6.23911e7 q^{92} +8.39565e8 q^{94} +6.93567e8 q^{95} -9.54121e8 q^{97} +1.66493e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) \) 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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