LMFDB - Embedded newform 387.10.a.c.1.7

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			1.7
Root			$-0.220103$ 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)

$f(q)$	$=$	$q+1.77990 q^{2} -508.832 q^{4} -1139.29 q^{5} +4324.96 q^{7} -1816.98 q^{8} +O(q^{10})$	\(q+1.77990 q^{2} -508.832 q^{4} -1139.29 q^{5} +4324.96 q^{7} -1816.98 q^{8} -2027.82 q^{10} -30380.9 q^{11} +34108.8 q^{13} +7697.98 q^{14} +257288. q^{16} +566042. q^{17} +246718. q^{19} +579707. q^{20} -54074.8 q^{22} +1.19112e6 q^{23} -655146. q^{25} +60710.1 q^{26} -2.20068e6 q^{28} -7.14721e6 q^{29} -5.75774e6 q^{31} +1.38824e6 q^{32} +1.00750e6 q^{34} -4.92738e6 q^{35} -8.31491e6 q^{37} +439132. q^{38} +2.07006e6 q^{40} +4.50031e6 q^{41} -3.41880e6 q^{43} +1.54588e7 q^{44} +2.12007e6 q^{46} +2.85694e7 q^{47} -2.16483e7 q^{49} -1.16609e6 q^{50} -1.73556e7 q^{52} -2.07892e7 q^{53} +3.46126e7 q^{55} -7.85834e6 q^{56} -1.27213e7 q^{58} +3.59484e6 q^{59} -5.73421e7 q^{61} -1.02482e7 q^{62} -1.29261e8 q^{64} -3.88598e7 q^{65} +1.95331e8 q^{67} -2.88020e8 q^{68} -8.77022e6 q^{70} +4.27590e6 q^{71} -1.36748e8 q^{73} -1.47997e7 q^{74} -1.25538e8 q^{76} -1.31396e8 q^{77} -3.21883e8 q^{79} -2.93125e8 q^{80} +8.01009e6 q^{82} +5.39331e8 q^{83} -6.44885e8 q^{85} -6.08511e6 q^{86} +5.52013e7 q^{88} -2.05645e8 q^{89} +1.47519e8 q^{91} -6.06079e8 q^{92} +5.08506e7 q^{94} -2.81083e8 q^{95} -1.10879e9 q^{97} -3.85318e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.77990	0.0786611	0.0393305	−	0.999226i	$-0.487477\pi$
$2$	1.77990	0.0786611	0.0393305	+	0.999226i	$0.487477\pi$
$3$	0	0
$3$	0	0
$4$	−508.832	−0.993812
$5$	−1139.29	−0.815209	−0.407604	−	0.913159i	$-0.633636\pi$
$5$	−1139.29	−0.815209	−0.407604	+	0.913159i	$0.633636\pi$
$6$	0	0
$7$	4324.96	0.680833	0.340417	−	0.940275i	$-0.389432\pi$
$7$	4324.96	0.680833	0.340417	+	0.940275i	$0.389432\pi$
$8$	−1816.98	−0.156835
$9$	0	0
$10$	−2027.82	−0.0641252
$11$	−30380.9	−0.625652	−0.312826	−	0.949810i	$-0.601276\pi$
$11$	−30380.9	−0.625652	−0.312826	+	0.949810i	$0.601276\pi$
$12$	0	0
$13$	34108.8	0.331224	0.165612	−	0.986191i	$-0.447040\pi$
$13$	34108.8	0.331224	0.165612	+	0.986191i	$0.447040\pi$
$14$	7697.98	0.0535551
$15$	0	0
$16$	257288.	0.981476
$17$	566042.	1.64372	0.821861	−	0.569688i	$-0.192936\pi$
$17$	566042.	1.64372	0.821861	+	0.569688i	$0.192936\pi$
$18$	0	0
$19$	246718.	0.434319	0.217160	−	0.976136i	$-0.430321\pi$
$19$	246718.	0.434319	0.217160	+	0.976136i	$0.430321\pi$
$20$	579707.	0.810165
$21$	0	0
$22$	−54074.8	−0.0492145
$23$	1.19112e6	0.887523	0.443761	−	0.896145i	$-0.353644\pi$
$23$	1.19112e6	0.887523	0.443761	+	0.896145i	$0.353644\pi$
$24$	0	0
$25$	−655146.	−0.335435
$26$	60710.1	0.0260544
$27$	0	0
$28$	−2.20068e6	−0.676621
$29$	−7.14721e6	−1.87649	−0.938243	−	0.345976i	$-0.887548\pi$
$29$	−7.14721e6	−1.87649	−0.938243	+	0.345976i	$0.887548\pi$
$30$	0	0
$31$	−5.75774e6	−1.11976	−0.559879	−	0.828574i	$-0.689152\pi$
$31$	−5.75774e6	−1.11976	−0.559879	+	0.828574i	$0.689152\pi$
$32$	1.38824e6	0.234039
$33$	0	0
$34$	1.00750e6	0.129297
$35$	−4.92738e6	−0.555021
$36$	0	0
$37$	−8.31491e6	−0.729374	−0.364687	−	0.931130i	$-0.618824\pi$
$37$	−8.31491e6	−0.729374	−0.364687	+	0.931130i	$0.618824\pi$
$38$	439132.	0.0341640
$39$	0	0
$40$	2.07006e6	0.127854
$41$	4.50031e6	0.248723	0.124361	−	0.992237i	$-0.460312\pi$
$41$	4.50031e6	0.248723	0.124361	+	0.992237i	$0.460312\pi$
$42$	0	0
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	1.54588e7	0.621781
$45$	0	0
$46$	2.12007e6	0.0698135
$47$	2.85694e7	0.854006	0.427003	−	0.904250i	$-0.359569\pi$
$47$	2.85694e7	0.854006	0.427003	+	0.904250i	$0.359569\pi$
$48$	0	0
$49$	−2.16483e7	−0.536466
$50$	−1.16609e6	−0.0263856
$51$	0	0
$52$	−1.73556e7	−0.329174
$53$	−2.07892e7	−0.361907	−0.180953	−	0.983492i	$-0.557918\pi$
$53$	−2.07892e7	−0.361907	−0.180953	+	0.983492i	$0.557918\pi$
$54$	0	0
$55$	3.46126e7	0.510037
$56$	−7.85834e6	−0.106779
$57$	0	0
$58$	−1.27213e7	−0.147606
$59$	3.59484e6	0.0386229	0.0193115	−	0.999814i	$-0.493853\pi$
$59$	3.59484e6	0.0386229	0.0193115	+	0.999814i	$0.493853\pi$
$60$	0	0
$61$	−5.73421e7	−0.530261	−0.265130	−	0.964213i	$-0.585415\pi$
$61$	−5.73421e7	−0.530261	−0.265130	+	0.964213i	$0.585415\pi$
$62$	−1.02482e7	−0.0880813
$63$	0	0
$64$	−1.29261e8	−0.963066
$65$	−3.88598e7	−0.270016
$66$	0	0
$67$	1.95331e8	1.18422	0.592111	−	0.805856i	$-0.298295\pi$
$67$	1.95331e8	1.18422	0.592111	+	0.805856i	$0.298295\pi$
$68$	−2.88020e8	−1.63355
$69$	0	0
$70$	−8.77022e6	−0.0436586
$71$	4.27590e6	0.0199694	0.00998471	−	0.999950i	$-0.496822\pi$
$71$	4.27590e6	0.0199694	0.00998471	+	0.999950i	$0.496822\pi$
$72$	0	0
$73$	−1.36748e8	−0.563595	−0.281798	−	0.959474i	$-0.590931\pi$
$73$	−1.36748e8	−0.563595	−0.281798	+	0.959474i	$0.590931\pi$
$74$	−1.47997e7	−0.0573733
$75$	0	0
$76$	−1.25538e8	−0.431632
$77$	−1.31396e8	−0.425965
$78$	0	0
$79$	−3.21883e8	−0.929770	−0.464885	−	0.885371i	$-0.653904\pi$
$79$	−3.21883e8	−0.929770	−0.464885	+	0.885371i	$0.653904\pi$
$80$	−2.93125e8	−0.800108
$81$	0	0
$82$	8.01009e6	0.0195648
$83$	5.39331e8	1.24739	0.623697	−	0.781666i	$-0.285630\pi$
$83$	5.39331e8	1.24739	0.623697	+	0.781666i	$0.285630\pi$
$84$	0	0
$85$	−6.44885e8	−1.33998
$86$	−6.08511e6	−0.0119957
$87$	0	0
$88$	5.52013e7	0.0981244
$89$	−2.05645e8	−0.347426	−0.173713	−	0.984796i	$-0.555577\pi$
$89$	−2.05645e8	−0.347426	−0.173713	+	0.984796i	$0.555577\pi$
$90$	0	0
$91$	1.47519e8	0.225508
$92$	−6.06079e8	−0.882031
$93$	0	0
$94$	5.08506e7	0.0671770
$95$	−2.81083e8	−0.354061
$96$	0	0
$97$	−1.10879e9	−1.27168	−0.635840	−	0.771821i	$-0.719346\pi$
$97$	−1.10879e9	−1.27168	−0.635840	+	0.771821i	$0.719346\pi$
$98$	−3.85318e7	−0.0421990
$99$	0	0
$100$	3.33359e8	0.333359
$101$	1.88058e9	1.79823	0.899117	−	0.437709i	$-0.144210\pi$
$101$	1.88058e9	1.79823	0.899117	+	0.437709i	$0.144210\pi$
$102$	0	0
$103$	9.90610e8	0.867232	0.433616	−	0.901098i	$-0.357237\pi$
$103$	9.90610e8	0.867232	0.433616	+	0.901098i	$0.357237\pi$
$104$	−6.19748e7	−0.0519476
$105$	0	0
$106$	−3.70027e7	−0.0284680
$107$	−1.83523e6	−0.00135352	−0.000676759	−	1.00000i	$-0.500215\pi$
$107$	−1.83523e6	−0.00135352	−0.000676759		1.00000i	$0.500215\pi$
$108$	0	0
$109$	−1.28953e9	−0.875007	−0.437503	−	0.899217i	$-0.644137\pi$
$109$	−1.28953e9	−0.875007	−0.437503	+	0.899217i	$0.644137\pi$
$110$	6.16068e7	0.0401201
$111$	0	0
$112$	1.11276e9	0.668221
$113$	1.37637e9	0.794115	0.397057	−	0.917794i	$-0.370031\pi$
$113$	1.37637e9	0.794115	0.397057	+	0.917794i	$0.370031\pi$
$114$	0	0
$115$	−1.35703e9	−0.723517
$116$	3.63673e9	1.86488
$117$	0	0
$118$	6.39844e6	0.00303812
$119$	2.44811e9	1.11910
$120$	0	0
$121$	−1.43495e9	−0.608559
$122$	−1.02063e8	−0.0417109
$123$	0	0
$124$	2.92972e9	1.11283
$125$	2.97157e9	1.08866
$126$	0	0
$127$	−1.41410e9	−0.482352	−0.241176	−	0.970481i	$-0.577533\pi$
$127$	−1.41410e9	−0.482352	−0.241176	+	0.970481i	$0.577533\pi$
$128$	−9.40848e8	−0.309795
$129$	0	0
$130$	−6.91664e7	−0.0212398
$131$	−6.55771e9	−1.94550	−0.972750	−	0.231857i	$-0.925520\pi$
$131$	−6.55771e9	−1.94550	−0.972750	+	0.231857i	$0.925520\pi$
$132$	0	0
$133$	1.06704e9	0.295699
$134$	3.47668e8	0.0931522
$135$	0	0
$136$	−1.02848e9	−0.257794
$137$	−8.93137e8	−0.216609	−0.108304	−	0.994118i	$-0.534542\pi$
$137$	−8.93137e8	−0.216609	−0.108304	+	0.994118i	$0.534542\pi$
$138$	0	0
$139$	4.97678e9	1.13079	0.565395	−	0.824820i	$-0.308724\pi$
$139$	4.97678e9	1.13079	0.565395	+	0.824820i	$0.308724\pi$
$140$	2.50721e9	0.551587
$141$	0	0
$142$	7.61067e6	0.00157082
$143$	−1.03625e9	−0.207231
$144$	0	0
$145$	8.14273e9	1.52973
$146$	−2.43397e8	−0.0443330
$147$	0	0
$148$	4.23089e9	0.724861
$149$	3.83286e9	0.637066	0.318533	−	0.947912i	$-0.396810\pi$
$149$	3.83286e9	0.637066	0.318533	+	0.947912i	$0.396810\pi$
$150$	0	0
$151$	6.11983e9	0.957951	0.478975	−	0.877828i	$-0.341008\pi$
$151$	6.11983e9	0.957951	0.478975	+	0.877828i	$0.341008\pi$
$152$	−4.48280e8	−0.0681166
$153$	0	0
$154$	−2.33871e8	−0.0335069
$155$	6.55972e9	0.912836
$156$	0	0
$157$	−1.04568e10	−1.37357	−0.686783	−	0.726863i	$-0.740978\pi$
$157$	−1.04568e10	−1.37357	−0.686783	+	0.726863i	$0.740978\pi$
$158$	−5.72918e8	−0.0731367
$159$	0	0
$160$	−1.58160e9	−0.190791
$161$	5.15154e9	0.604255
$162$	0	0
$163$	8.35163e9	0.926674	0.463337	−	0.886182i	$-0.346652\pi$
$163$	8.35163e9	0.926674	0.463337	+	0.886182i	$0.346652\pi$
$164$	−2.28990e9	−0.247184
$165$	0	0
$166$	9.59953e8	0.0981213
$167$	8.28252e9	0.824021	0.412011	−	0.911179i	$-0.364827\pi$
$167$	8.28252e9	0.824021	0.412011	+	0.911179i	$0.364827\pi$
$168$	0	0
$169$	−9.44109e9	−0.890291
$170$	−1.14783e9	−0.105404
$171$	0	0
$172$	1.73960e9	0.151555
$173$	−6.37085e9	−0.540742	−0.270371	−	0.962756i	$-0.587146\pi$
$173$	−6.37085e9	−0.540742	−0.270371	+	0.962756i	$0.587146\pi$
$174$	0	0
$175$	−2.83348e9	−0.228375
$176$	−7.81663e9	−0.614063
$177$	0	0
$178$	−3.66026e8	−0.0273289
$179$	1.73831e10	1.26558	0.632789	−	0.774325i	$-0.281910\pi$
$179$	1.73831e10	1.26558	0.632789	+	0.774325i	$0.281910\pi$
$180$	0	0
$181$	−1.20834e10	−0.836826	−0.418413	−	0.908257i	$-0.637414\pi$
$181$	−1.20834e10	−0.836826	−0.418413	+	0.908257i	$0.637414\pi$
$182$	2.62569e8	0.0177387
$183$	0	0
$184$	−2.16423e9	−0.139195
$185$	9.47309e9	0.594592
$186$	0	0
$187$	−1.71969e10	−1.02840
$188$	−1.45370e10	−0.848722
$189$	0	0
$190$	−5.00298e8	−0.0278508
$191$	−2.09279e10	−1.13782	−0.568912	−	0.822398i	$-0.692635\pi$
$191$	−2.09279e10	−1.13782	−0.568912	+	0.822398i	$0.692635\pi$
$192$	0	0
$193$	2.13946e10	1.10993	0.554965	−	0.831874i	$-0.312732\pi$
$193$	2.13946e10	1.10993	0.554965	+	0.831874i	$0.312732\pi$
$194$	−1.97354e9	−0.100032
$195$	0	0
$196$	1.10154e10	0.533147
$197$	2.74114e10	1.29668	0.648340	−	0.761351i	$-0.275464\pi$
$197$	2.74114e10	1.29668	0.648340	+	0.761351i	$0.275464\pi$
$198$	0	0
$199$	4.11872e9	0.186176	0.0930880	−	0.995658i	$-0.470326\pi$
$199$	4.11872e9	0.186176	0.0930880	+	0.995658i	$0.470326\pi$
$200$	1.19038e9	0.0526080
$201$	0	0
$202$	3.34724e9	0.141451
$203$	−3.09114e10	−1.27757
$204$	0	0
$205$	−5.12716e9	−0.202761
$206$	1.76318e9	0.0682174
$207$	0	0
$208$	8.77578e9	0.325088
$209$	−7.49550e9	−0.271733
$210$	0	0
$211$	3.83930e10	1.33346	0.666732	−	0.745298i	$-0.267693\pi$
$211$	3.83930e10	1.33346	0.666732	+	0.745298i	$0.267693\pi$
$212$	1.05782e10	0.359667
$213$	0	0
$214$	−3.26653e6	−0.000106469 0
$215$	3.89500e9	0.124318
$216$	0	0
$217$	−2.49020e10	−0.762368
$218$	−2.29523e9	−0.0688290
$219$	0	0
$220$	−1.76120e10	−0.506881
$221$	1.93070e10	0.544440
$222$	0	0
$223$	3.85620e10	1.04421	0.522105	−	0.852881i	$-0.325147\pi$
$223$	3.85620e10	1.04421	0.522105	+	0.852881i	$0.325147\pi$
$224$	6.00407e9	0.159342
$225$	0	0
$226$	2.44980e9	0.0624659
$227$	1.12890e10	0.282188	0.141094	−	0.989996i	$-0.454938\pi$
$227$	1.12890e10	0.282188	0.141094	+	0.989996i	$0.454938\pi$
$228$	0	0
$229$	3.48087e10	0.836428	0.418214	−	0.908349i	$-0.362656\pi$
$229$	3.48087e10	0.836428	0.418214	+	0.908349i	$0.362656\pi$
$230$	−2.41537e9	−0.0569126
$231$	0	0
$232$	1.29863e10	0.294299
$233$	−2.66211e10	−0.591730	−0.295865	−	0.955230i	$-0.595608\pi$
$233$	−2.66211e10	−0.591730	−0.295865	+	0.955230i	$0.595608\pi$
$234$	0	0
$235$	−3.25488e10	−0.696193
$236$	−1.82917e9	−0.0383839
$237$	0	0
$238$	4.35738e9	0.0880297
$239$	−5.93716e10	−1.17703	−0.588516	−	0.808485i	$-0.700288\pi$
$239$	−5.93716e10	−1.17703	−0.588516	+	0.808485i	$0.700288\pi$
$240$	0	0
$241$	5.18516e10	0.990114	0.495057	−	0.868860i	$-0.335147\pi$
$241$	5.18516e10	0.990114	0.495057	+	0.868860i	$0.335147\pi$
$242$	−2.55406e9	−0.0478699
$243$	0	0
$244$	2.91775e10	0.526980
$245$	2.46637e10	0.437332
$246$	0	0
$247$	8.41524e9	0.143857
$248$	1.04617e10	0.175618
$249$	0	0
$250$	5.28909e9	0.0856350
$251$	7.95240e10	1.26464	0.632320	−	0.774708i	$-0.282103\pi$
$251$	7.95240e10	1.26464	0.632320	+	0.774708i	$0.282103\pi$
$252$	0	0
$253$	−3.61872e10	−0.555281
$254$	−2.51695e9	−0.0379423
$255$	0	0
$256$	6.45068e10	0.938697
$257$	1.13156e10	0.161800	0.0808999	−	0.996722i	$-0.474221\pi$
$257$	1.13156e10	0.161800	0.0808999	+	0.996722i	$0.474221\pi$
$258$	0	0
$259$	−3.59617e10	−0.496582
$260$	1.97731e10	0.268346
$261$	0	0
$262$	−1.16720e10	−0.153035
$263$	1.29655e11	1.67105	0.835525	−	0.549452i	$-0.185163\pi$
$263$	1.29655e11	1.67105	0.835525	+	0.549452i	$0.185163\pi$
$264$	0	0
$265$	2.36849e10	0.295030
$266$	1.89923e9	0.0232600
$267$	0	0
$268$	−9.93904e10	−1.17690
$269$	−2.31009e10	−0.268995	−0.134497	−	0.990914i	$-0.542942\pi$
$269$	−2.31009e10	−0.268995	−0.134497	+	0.990914i	$0.542942\pi$
$270$	0	0
$271$	8.96402e10	1.00958	0.504790	−	0.863242i	$-0.331570\pi$
$271$	8.96402e10	1.00958	0.504790	+	0.863242i	$0.331570\pi$
$272$	1.45636e11	1.61327
$273$	0	0
$274$	−1.58969e9	−0.0170387
$275$	1.99039e10	0.209866
$276$	0	0
$277$	−9.97287e10	−1.01780	−0.508899	−	0.860826i	$-0.669947\pi$
$277$	−9.97287e10	−1.01780	−0.508899	+	0.860826i	$0.669947\pi$
$278$	8.85815e9	0.0889491
$279$	0	0
$280$	8.95292e9	0.0870470
$281$	−1.31117e10	−0.125453	−0.0627265	−	0.998031i	$-0.519980\pi$
$281$	−1.31117e10	−0.125453	−0.0627265	+	0.998031i	$0.519980\pi$
$282$	0	0
$283$	−9.75983e10	−0.904489	−0.452245	−	0.891894i	$-0.649377\pi$
$283$	−9.75983e10	−0.904489	−0.452245	+	0.891894i	$0.649377\pi$
$284$	−2.17572e9	−0.0198459
$285$	0	0
$286$	−1.84443e9	−0.0163010
$287$	1.94637e10	0.169339
$288$	0	0
$289$	2.01816e11	1.70182
$290$	1.44932e10	0.120330
$291$	0	0
$292$	6.95816e10	0.560108
$293$	9.70939e10	0.769640	0.384820	−	0.922992i	$-0.374264\pi$
$293$	9.70939e10	0.769640	0.384820	+	0.922992i	$0.374264\pi$
$294$	0	0
$295$	−4.09556e9	−0.0314857
$296$	1.51080e10	0.114392
$297$	0	0
$298$	6.82209e9	0.0501123
$299$	4.06276e10	0.293969
$300$	0	0
$301$	−1.47862e10	−0.103826
$302$	1.08927e10	0.0753534
$303$	0	0
$304$	6.34775e10	0.426274
$305$	6.53293e10	0.432273
$306$	0	0
$307$	−2.39809e11	−1.54079	−0.770393	−	0.637569i	$-0.779940\pi$
$307$	−2.39809e11	−1.54079	−0.770393	+	0.637569i	$0.779940\pi$
$308$	6.68585e10	0.423329
$309$	0	0
$310$	1.16756e10	0.0718047
$311$	5.16196e10	0.312891	0.156445	−	0.987687i	$-0.449996\pi$
$311$	5.16196e10	0.312891	0.156445	+	0.987687i	$0.449996\pi$
$312$	0	0
$313$	9.12143e10	0.537172	0.268586	−	0.963256i	$-0.413444\pi$
$313$	9.12143e10	0.537172	0.268586	+	0.963256i	$0.413444\pi$
$314$	−1.86120e10	−0.108046
$315$	0	0
$316$	1.63784e11	0.924017
$317$	3.41738e11	1.90076	0.950378	−	0.311099i	$-0.100697\pi$
$317$	3.41738e11	1.90076	0.950378	+	0.311099i	$0.100697\pi$
$318$	0	0
$319$	2.17138e11	1.17403
$320$	1.47265e11	0.785100
$321$	0	0
$322$	9.16920e9	0.0475313
$323$	1.39653e11	0.713901
$324$	0	0
$325$	−2.23462e10	−0.111104
$326$	1.48650e10	0.0728932
$327$	0	0
$328$	−8.17696e9	−0.0390085
$329$	1.23562e11	0.581436
$330$	0	0
$331$	−3.21682e11	−1.47299	−0.736497	−	0.676441i	$-0.763521\pi$
$331$	−3.21682e11	−1.47299	−0.736497	+	0.676441i	$0.763521\pi$
$332$	−2.74429e11	−1.23968
$333$	0	0
$334$	1.47420e10	0.0648184
$335$	−2.22538e11	−0.965389
$336$	0	0
$337$	−4.05004e11	−1.71051	−0.855253	−	0.518211i	$-0.826598\pi$
$337$	−4.05004e11	−1.71051	−0.855253	+	0.518211i	$0.826598\pi$
$338$	−1.68042e10	−0.0700312
$339$	0	0
$340$	3.28138e11	1.33169
$341$	1.74925e11	0.700579
$342$	0	0
$343$	−2.68156e11	−1.04608
$344$	6.21188e9	0.0239172
$345$	0	0
$346$	−1.13395e10	−0.0425353
$347$	8.23031e10	0.304743	0.152371	−	0.988323i	$-0.451309\pi$
$347$	8.23031e10	0.304743	0.152371	+	0.988323i	$0.451309\pi$
$348$	0	0
$349$	3.73070e11	1.34610	0.673048	−	0.739599i	$-0.264985\pi$
$349$	3.73070e11	1.34610	0.673048	+	0.739599i	$0.264985\pi$
$350$	−5.04330e9	−0.0179642
$351$	0	0
$352$	−4.21759e10	−0.146427
$353$	−1.33171e11	−0.456483	−0.228242	−	0.973605i	$-0.573298\pi$
$353$	−1.33171e11	−0.456483	−0.228242	+	0.973605i	$0.573298\pi$
$354$	0	0
$355$	−4.87149e9	−0.0162792
$356$	1.04639e11	0.345276
$357$	0	0
$358$	3.09401e10	0.0995517
$359$	2.99339e11	0.951125	0.475563	−	0.879682i	$-0.342245\pi$
$359$	2.99339e11	0.951125	0.475563	+	0.879682i	$0.342245\pi$
$360$	0	0
$361$	−2.61818e11	−0.811367
$362$	−2.15072e10	−0.0658256
$363$	0	0
$364$	−7.50624e10	−0.224113
$365$	1.55795e11	0.459448
$366$	0	0
$367$	−4.71753e11	−1.35743	−0.678716	−	0.734401i	$-0.737463\pi$
$367$	−4.71753e11	−1.35743	−0.678716	+	0.734401i	$0.737463\pi$
$368$	3.06460e11	0.871082
$369$	0	0
$370$	1.68611e10	0.0467712
$371$	−8.99125e10	−0.246398
$372$	0	0
$373$	5.78431e11	1.54725	0.773627	−	0.633641i	$-0.218441\pi$
$373$	5.78431e11	1.54725	0.773627	+	0.633641i	$0.218441\pi$
$374$	−3.06086e10	−0.0808950
$375$	0	0
$376$	−5.19099e10	−0.133938
$377$	−2.43783e11	−0.621536
$378$	0	0
$379$	2.82375e11	0.702990	0.351495	−	0.936190i	$-0.385673\pi$
$379$	2.82375e11	0.702990	0.351495	+	0.936190i	$0.385673\pi$
$380$	1.43024e11	0.351870
$381$	0	0
$382$	−3.72495e10	−0.0895024
$383$	−1.02581e11	−0.243596	−0.121798	−	0.992555i	$-0.538866\pi$
$383$	−1.02581e11	−0.243596	−0.121798	+	0.992555i	$0.538866\pi$
$384$	0	0
$385$	1.49698e11	0.347250
$386$	3.80801e10	0.0873083
$387$	0	0
$388$	5.64189e11	1.26381
$389$	−3.65492e11	−0.809290	−0.404645	−	0.914474i	$-0.632605\pi$
$389$	−3.65492e11	−0.809290	−0.404645	+	0.914474i	$0.632605\pi$
$390$	0	0
$391$	6.74223e11	1.45884
$392$	3.93345e10	0.0841369
$393$	0	0
$394$	4.87894e10	0.101998
$395$	3.66717e11	0.757957
$396$	0	0
$397$	7.94172e11	1.60457	0.802283	−	0.596944i	$-0.203619\pi$
$397$	7.94172e11	1.60457	0.802283	+	0.596944i	$0.203619\pi$
$398$	7.33090e9	0.0146448
$399$	0	0
$400$	−1.68561e11	−0.329221
$401$	6.31476e11	1.21957	0.609786	−	0.792566i	$-0.291256\pi$
$401$	6.31476e11	1.21957	0.609786	+	0.792566i	$0.291256\pi$
$402$	0	0
$403$	−1.96389e11	−0.370890
$404$	−9.56900e11	−1.78711
$405$	0	0
$406$	−5.50191e10	−0.100495
$407$	2.52614e11	0.456334
$408$	0	0
$409$	−1.73599e11	−0.306755	−0.153377	−	0.988168i	$-0.549015\pi$
$409$	−1.73599e11	−0.306755	−0.153377	+	0.988168i	$0.549015\pi$
$410$	−9.12581e9	−0.0159494
$411$	0	0
$412$	−5.04054e11	−0.861866
$413$	1.55475e10	0.0262958
$414$	0	0
$415$	−6.14453e11	−1.01689
$416$	4.73511e10	0.0775193
$417$	0	0
$418$	−1.33412e10	−0.0213748
$419$	7.33980e11	1.16338	0.581689	−	0.813411i	$-0.302392\pi$
$419$	7.33980e11	1.16338	0.581689	+	0.813411i	$0.302392\pi$
$420$	0	0
$421$	9.33067e11	1.44758	0.723791	−	0.690019i	$-0.242398\pi$
$421$	9.33067e11	1.44758	0.723791	+	0.690019i	$0.242398\pi$
$422$	6.83356e10	0.104892
$423$	0	0
$424$	3.77735e10	0.0567598
$425$	−3.70840e11	−0.551362
$426$	0	0
$427$	−2.48002e11	−0.361019
$428$	9.33825e8	0.00134514
$429$	0	0
$430$	6.93270e9	0.00977900
$431$	−6.98145e11	−0.974536	−0.487268	−	0.873252i	$-0.662007\pi$
$431$	−6.98145e11	−0.974536	−0.487268	+	0.873252i	$0.662007\pi$
$432$	0	0
$433$	5.56024e11	0.760147	0.380074	−	0.924956i	$-0.375899\pi$
$433$	5.56024e11	0.760147	0.380074	+	0.924956i	$0.375899\pi$
$434$	−4.43229e10	−0.0599687
$435$	0	0
$436$	6.56153e11	0.869593
$437$	2.93870e11	0.385468
$438$	0	0
$439$	−1.04816e12	−1.34691	−0.673456	−	0.739228i	$-0.735191\pi$
$439$	−1.04816e12	−1.34691	−0.673456	+	0.739228i	$0.735191\pi$
$440$	−6.28902e10	−0.0799919
$441$	0	0
$442$	3.43645e10	0.0428262
$443$	−5.51262e11	−0.680051	−0.340026	−	0.940416i	$-0.610436\pi$
$443$	−5.51262e11	−0.680051	−0.340026	+	0.940416i	$0.610436\pi$
$444$	0	0
$445$	2.34289e11	0.283225
$446$	6.86364e10	0.0821387
$447$	0	0
$448$	−5.59046e11	−0.655687
$449$	1.10157e12	1.27910	0.639550	−	0.768749i	$-0.279121\pi$
$449$	1.10157e12	1.27910	0.639550	+	0.768749i	$0.279121\pi$
$450$	0	0
$451$	−1.36723e11	−0.155614
$452$	−7.00343e11	−0.789201
$453$	0	0
$454$	2.00932e10	0.0221972
$455$	−1.68067e11	−0.183836
$456$	0	0
$457$	−7.85228e11	−0.842118	−0.421059	−	0.907033i	$-0.638341\pi$
$457$	−7.85228e11	−0.842118	−0.421059	+	0.907033i	$0.638341\pi$
$458$	6.19559e10	0.0657943
$459$	0	0
$460$	6.90499e11	0.719040
$461$	−1.57045e12	−1.61946	−0.809728	−	0.586806i	$-0.800385\pi$
$461$	−1.57045e12	−1.61946	−0.809728	+	0.586806i	$0.800385\pi$
$462$	0	0
$463$	1.25678e11	0.127100	0.0635501	−	0.997979i	$-0.479758\pi$
$463$	1.25678e11	0.127100	0.0635501	+	0.997979i	$0.479758\pi$
$464$	−1.83889e12	−1.84173
$465$	0	0
$466$	−4.73827e10	−0.0465461
$467$	7.17571e11	0.698134	0.349067	−	0.937098i	$-0.386499\pi$
$467$	7.17571e11	0.698134	0.349067	+	0.937098i	$0.386499\pi$
$468$	0	0
$469$	8.44796e11	0.806258
$470$	−5.79335e10	−0.0547633
$471$	0	0
$472$	−6.53173e9	−0.00605744
$473$	1.03866e11	0.0954111
$474$	0	0
$475$	−1.61636e11	−0.145686
$476$	−1.24568e12	−1.11218
$477$	0	0
$478$	−1.05675e11	−0.0925866
$479$	−1.77215e12	−1.53812	−0.769062	−	0.639174i	$-0.779276\pi$
$479$	−1.77215e12	−1.53812	−0.769062	+	0.639174i	$0.779276\pi$
$480$	0	0
$481$	−2.83612e11	−0.241586
$482$	9.22904e10	0.0778834
$483$	0	0
$484$	7.30149e11	0.604794
$485$	1.26324e12	1.03668
$486$	0	0
$487$	2.21711e12	1.78610	0.893051	−	0.449956i	$-0.148560\pi$
$487$	2.21711e12	1.78610	0.893051	+	0.449956i	$0.148560\pi$
$488$	1.04189e11	0.0831637
$489$	0	0
$490$	4.38989e10	0.0344010
$491$	1.36110e12	1.05688	0.528438	−	0.848972i	$-0.322778\pi$
$491$	1.36110e12	1.05688	0.528438	+	0.848972i	$0.322778\pi$
$492$	0	0
$493$	−4.04562e12	−3.08442
$494$	1.49783e10	0.0113159
$495$	0	0
$496$	−1.48140e12	−1.09902
$497$	1.84931e10	0.0135958
$498$	0	0
$499$	2.40786e12	1.73852	0.869258	−	0.494359i	$-0.164597\pi$
$499$	2.40786e12	1.73852	0.869258	+	0.494359i	$0.164597\pi$
$500$	−1.51203e12	−1.08192
$501$	0	0
$502$	1.41545e11	0.0994778
$503$	2.31596e12	1.61315	0.806576	−	0.591130i	$-0.201318\pi$
$503$	2.31596e12	1.61315	0.806576	+	0.591130i	$0.201318\pi$
$504$	0	0
$505$	−2.14253e12	−1.46594
$506$	−6.44095e10	−0.0436790
$507$	0	0
$508$	7.19540e11	0.479367
$509$	−8.58304e10	−0.0566776	−0.0283388	−	0.999598i	$-0.509022\pi$
$509$	−8.58304e10	−0.0566776	−0.0283388	+	0.999598i	$0.509022\pi$
$510$	0	0
$511$	−5.91428e11	−0.383714
$512$	5.96529e11	0.383634
$513$	0	0
$514$	2.01406e10	0.0127273
$515$	−1.12859e12	−0.706975
$516$	0	0
$517$	−8.67964e11	−0.534311
$518$	−6.40080e10	−0.0390616
$519$	0	0
$520$	7.06072e10	0.0423481
$521$	1.42834e12	0.849301	0.424650	−	0.905357i	$-0.360397\pi$
$521$	1.42834e12	0.849301	0.424650	+	0.905357i	$0.360397\pi$
$522$	0	0
$523$	2.06838e12	1.20885	0.604426	−	0.796661i	$-0.293403\pi$
$523$	2.06838e12	1.20885	0.604426	+	0.796661i	$0.293403\pi$
$524$	3.33677e12	1.93346
$525$	0	0
$526$	2.30773e11	0.131447
$527$	−3.25912e12	−1.84057
$528$	0	0
$529$	−3.82390e11	−0.212303
$530$	4.21567e10	0.0232073
$531$	0	0
$532$	−5.42946e11	−0.293869
$533$	1.53500e11	0.0823828
$534$	0	0
$535$	2.09086e9	0.00110340
$536$	−3.54911e11	−0.185728
$537$	0	0
$538$	−4.11172e10	−0.0211594
$539$	6.57695e11	0.335641
$540$	0	0
$541$	1.23040e11	0.0617529	0.0308764	−	0.999523i	$-0.490170\pi$
$541$	1.23040e11	0.0617529	0.0308764	+	0.999523i	$0.490170\pi$
$542$	1.59550e11	0.0794147
$543$	0	0
$544$	7.85801e11	0.384696
$545$	1.46914e12	0.713313
$546$	0	0
$547$	1.80654e12	0.862787	0.431393	−	0.902164i	$-0.358022\pi$
$547$	1.80654e12	0.862787	0.431393	+	0.902164i	$0.358022\pi$
$548$	4.54457e11	0.215268
$549$	0	0
$550$	3.54269e10	0.0165082
$551$	−1.76334e12	−0.814994
$552$	0	0
$553$	−1.39213e12	−0.633019
$554$	−1.77507e11	−0.0800610
$555$	0	0
$556$	−2.53234e12	−1.12379
$557$	6.38748e11	0.281178	0.140589	−	0.990068i	$-0.455100\pi$
$557$	6.38748e11	0.281178	0.140589	+	0.990068i	$0.455100\pi$
$558$	0	0
$559$	−1.16611e11	−0.0505111
$560$	−1.26775e12	−0.544740
$561$	0	0
$562$	−2.33375e10	−0.00986827
$563$	−1.90057e12	−0.797252	−0.398626	−	0.917114i	$-0.630513\pi$
$563$	−1.90057e12	−0.797252	−0.398626	+	0.917114i	$0.630513\pi$
$564$	0	0
$565$	−1.56809e12	−0.647369
$566$	−1.73715e11	−0.0711481
$567$	0	0
$568$	−7.76921e9	−0.00313191
$569$	−1.34358e12	−0.537353	−0.268677	−	0.963230i	$-0.586586\pi$
$569$	−1.34358e12	−0.537353	−0.268677	+	0.963230i	$0.586586\pi$
$570$	0	0
$571$	1.95896e12	0.771193	0.385597	−	0.922667i	$-0.373996\pi$
$571$	1.95896e12	0.771193	0.385597	+	0.922667i	$0.373996\pi$
$572$	5.27279e11	0.205949
$573$	0	0
$574$	3.46433e10	0.0133204
$575$	−7.80356e11	−0.297706
$576$	0	0
$577$	−2.94220e12	−1.10505	−0.552523	−	0.833497i	$-0.686335\pi$
$577$	−2.94220e12	−1.10505	−0.552523	+	0.833497i	$0.686335\pi$
$578$	3.59211e11	0.133867
$579$	0	0
$580$	−4.14328e12	−1.52026
$581$	2.33258e12	0.849267
$582$	0	0
$583$	6.31594e11	0.226428
$584$	2.48467e11	0.0883917
$585$	0	0
$586$	1.72817e11	0.0605407
$587$	5.99434e11	0.208387	0.104193	−	0.994557i	$-0.466774\pi$
$587$	5.99434e11	0.208387	0.104193	+	0.994557i	$0.466774\pi$
$588$	0	0
$589$	−1.42054e12	−0.486333
$590$	−7.28967e9	−0.00247670
$591$	0	0
$592$	−2.13933e12	−0.715862
$593$	−5.53945e11	−0.183959	−0.0919794	−	0.995761i	$-0.529319\pi$
$593$	−5.53945e11	−0.183959	−0.0919794	+	0.995761i	$0.529319\pi$
$594$	0	0
$595$	−2.78910e12	−0.912301
$596$	−1.95028e12	−0.633124
$597$	0	0
$598$	7.23129e10	0.0231239
$599$	1.23783e12	0.392864	0.196432	−	0.980517i	$-0.437065\pi$
$599$	1.23783e12	0.392864	0.196432	+	0.980517i	$0.437065\pi$
$600$	0	0
$601$	−4.88544e12	−1.52745	−0.763727	−	0.645539i	$-0.776633\pi$
$601$	−4.88544e12	−1.52745	−0.763727	+	0.645539i	$0.776633\pi$
$602$	−2.63179e10	−0.00816707
$603$	0	0
$604$	−3.11397e12	−0.952024
$605$	1.63482e12	0.496103
$606$	0	0
$607$	1.73678e12	0.519272	0.259636	−	0.965707i	$-0.416397\pi$
$607$	1.73678e12	0.519272	0.259636	+	0.965707i	$0.416397\pi$
$608$	3.42503e11	0.101648
$609$	0	0
$610$	1.16279e11	0.0340031
$611$	9.74468e11	0.282867
$612$	0	0
$613$	5.18063e12	1.48187	0.740936	−	0.671575i	$-0.234382\pi$
$613$	5.18063e12	1.48187	0.740936	+	0.671575i	$0.234382\pi$
$614$	−4.26835e11	−0.121200
$615$	0	0
$616$	2.38743e11	0.0668064
$617$	−4.99397e12	−1.38728	−0.693638	−	0.720324i	$-0.743993\pi$
$617$	−4.99397e12	−1.38728	−0.693638	+	0.720324i	$0.743993\pi$
$618$	0	0
$619$	1.19615e11	0.0327475	0.0163738	−	0.999866i	$-0.494788\pi$
$619$	1.19615e11	0.0327475	0.0163738	+	0.999866i	$0.494788\pi$
$620$	−3.33780e12	−0.907188
$621$	0	0
$622$	9.18775e10	0.0246123
$623$	−8.89404e11	−0.236539
$624$	0	0
$625$	−2.10590e12	−0.552049
$626$	1.62352e11	0.0422545
$627$	0	0
$628$	5.32074e12	1.36507
$629$	−4.70659e12	−1.19889
$630$	0	0
$631$	6.27030e12	1.57455	0.787275	−	0.616602i	$-0.211491\pi$
$631$	6.27030e12	1.57455	0.787275	+	0.616602i	$0.211491\pi$
$632$	5.84853e11	0.145821
$633$	0	0
$634$	6.08258e11	0.149515
$635$	1.61107e12	0.393217
$636$	0	0
$637$	−7.38399e11	−0.177690
$638$	3.86484e11	0.0923503
$639$	0	0
$640$	1.07190e12	0.252548
$641$	−8.09157e12	−1.89309	−0.946546	−	0.322570i	$-0.895453\pi$
$641$	−8.09157e12	−1.89309	−0.946546	+	0.322570i	$0.895453\pi$
$642$	0	0
$643$	8.41338e11	0.194098	0.0970490	−	0.995280i	$-0.469060\pi$
$643$	8.41338e11	0.194098	0.0970490	+	0.995280i	$0.469060\pi$
$644$	−2.62127e12	−0.600516
$645$	0	0
$646$	2.48567e11	0.0561562
$647$	−2.04314e12	−0.458384	−0.229192	−	0.973381i	$-0.573608\pi$
$647$	−2.04314e12	−0.458384	−0.229192	+	0.973381i	$0.573608\pi$
$648$	0	0
$649$	−1.09214e11	−0.0241645
$650$	−3.97740e10	−0.00873955
$651$	0	0
$652$	−4.24958e12	−0.920941
$653$	−9.39158e11	−0.202129	−0.101065	−	0.994880i	$-0.532225\pi$
$653$	−9.39158e11	−0.202129	−0.101065	+	0.994880i	$0.532225\pi$
$654$	0	0
$655$	7.47112e12	1.58599
$656$	1.15788e12	0.244115
$657$	0	0
$658$	2.19927e11	0.0457364
$659$	4.13790e12	0.854664	0.427332	−	0.904095i	$-0.359454\pi$
$659$	4.13790e12	0.854664	0.427332	+	0.904095i	$0.359454\pi$
$660$	0	0
$661$	1.12840e12	0.229909	0.114954	−	0.993371i	$-0.463328\pi$
$661$	1.12840e12	0.229909	0.114954	+	0.993371i	$0.463328\pi$
$662$	−5.72561e11	−0.115867
$663$	0	0
$664$	−9.79950e11	−0.195636
$665$	−1.21567e12	−0.241056
$666$	0	0
$667$	−8.51317e12	−1.66542
$668$	−4.21441e12	−0.818923
$669$	0	0
$670$	−3.96094e11	−0.0759385
$671$	1.74210e12	0.331759
$672$	0	0
$673$	−3.96514e12	−0.745059	−0.372529	−	0.928020i	$-0.621509\pi$
$673$	−3.96514e12	−0.745059	−0.372529	+	0.928020i	$0.621509\pi$
$674$	−7.20865e11	−0.134550
$675$	0	0
$676$	4.80393e12	0.884782
$677$	−5.57988e11	−0.102088	−0.0510442	−	0.998696i	$-0.516255\pi$
$677$	−5.57988e11	−0.102088	−0.0510442	+	0.998696i	$0.516255\pi$
$678$	0	0
$679$	−4.79548e12	−0.865802
$680$	1.17174e12	0.210156
$681$	0	0
$682$	3.11348e11	0.0551083
$683$	−1.00796e13	−1.77236	−0.886178	−	0.463344i	$-0.846649\pi$
$683$	−1.00796e13	−1.77236	−0.886178	+	0.463344i	$0.846649\pi$
$684$	0	0
$685$	1.01754e12	0.176581
$686$	−4.77290e11	−0.0822855
$687$	0	0
$688$	−8.79616e11	−0.149674
$689$	−7.09095e11	−0.119872
$690$	0	0
$691$	−1.07053e13	−1.78626	−0.893132	−	0.449794i	$-0.851497\pi$
$691$	−1.07053e13	−1.78626	−0.893132	+	0.449794i	$0.851497\pi$
$692$	3.24169e12	0.537396
$693$	0	0
$694$	1.46491e11	0.0239714
$695$	−5.66999e12	−0.921830
$696$	0	0
$697$	2.54737e12	0.408831
$698$	6.64026e11	0.105885
$699$	0	0
$700$	1.44176e12	0.226962
$701$	−9.07245e12	−1.41904	−0.709518	−	0.704687i	$-0.751087\pi$
$701$	−9.07245e12	−1.41904	−0.709518	+	0.704687i	$0.751087\pi$
$702$	0	0
$703$	−2.05144e12	−0.316781
$704$	3.92705e12	0.602544
$705$	0	0
$706$	−2.37031e11	−0.0359074
$707$	8.13344e12	1.22430
$708$	0	0
$709$	1.23204e12	0.183112	0.0915559	−	0.995800i	$-0.470816\pi$
$709$	1.23204e12	0.183112	0.0915559	+	0.995800i	$0.470816\pi$
$710$	−8.67075e9	−0.00128054
$711$	0	0
$712$	3.73651e11	0.0544887
$713$	−6.85814e12	−0.993811
$714$	0	0
$715$	1.18059e12	0.168936
$716$	−8.84508e12	−1.25775
$717$	0	0
$718$	5.32792e11	0.0748165
$719$	7.74691e12	1.08106	0.540528	−	0.841326i	$-0.318224\pi$
$719$	7.74691e12	1.08106	0.540528	+	0.841326i	$0.318224\pi$
$720$	0	0
$721$	4.28435e12	0.590440
$722$	−4.66009e11	−0.0638230
$723$	0	0
$724$	6.14841e12	0.831648
$725$	4.68246e12	0.629439
$726$	0	0
$727$	3.08284e12	0.409304	0.204652	−	0.978835i	$-0.434394\pi$
$727$	3.08284e12	0.409304	0.204652	+	0.978835i	$0.434394\pi$
$728$	−2.68039e11	−0.0353676
$729$	0	0
$730$	2.77299e11	0.0361406
$731$	−1.93519e12	−0.250665
$732$	0	0
$733$	−8.15400e12	−1.04328	−0.521642	−	0.853164i	$-0.674680\pi$
$733$	−8.15400e12	−1.04328	−0.521642	+	0.853164i	$0.674680\pi$
$734$	−8.39672e11	−0.106777
$735$	0	0
$736$	1.65355e12	0.207715
$737$	−5.93431e12	−0.740912
$738$	0	0
$739$	1.08477e13	1.33794	0.668969	−	0.743291i	$-0.266736\pi$
$739$	1.08477e13	1.33794	0.668969	+	0.743291i	$0.266736\pi$
$740$	−4.82021e12	−0.590913
$741$	0	0
$742$	−1.60035e11	−0.0193819
$743$	6.60935e12	0.795626	0.397813	−	0.917467i	$-0.369769\pi$
$743$	6.60935e12	0.795626	0.397813	+	0.917467i	$0.369769\pi$
$744$	0	0
$745$	−4.36673e12	−0.519342
$746$	1.02955e12	0.121709
$747$	0	0
$748$	8.75031e12	1.02204
$749$	−7.93731e9	−0.000921521 0
$750$	0	0
$751$	1.03430e13	1.18650	0.593248	−	0.805020i	$-0.297845\pi$
$751$	1.03430e13	1.18650	0.593248	+	0.805020i	$0.297845\pi$
$752$	7.35057e12	0.838186
$753$	0	0
$754$	−4.33908e11	−0.0488907
$755$	−6.97226e12	−0.780930
$756$	0	0
$757$	7.48200e12	0.828107	0.414054	−	0.910253i	$-0.364113\pi$
$757$	7.48200e12	0.828107	0.414054	+	0.910253i	$0.364113\pi$
$758$	5.02598e11	0.0552979
$759$	0	0
$760$	5.10720e11	0.0555293
$761$	8.49259e12	0.917929	0.458965	−	0.888455i	$-0.348220\pi$
$761$	8.49259e12	0.917929	0.458965	+	0.888455i	$0.348220\pi$
$762$	0	0
$763$	−5.57715e12	−0.595734
$764$	1.06488e13	1.13078
$765$	0	0
$766$	−1.82583e11	−0.0191615
$767$	1.22616e11	0.0127928
$768$	0	0
$769$	−1.35879e13	−1.40115	−0.700573	−	0.713581i	$-0.747072\pi$
$769$	−1.35879e13	−1.40115	−0.700573	+	0.713581i	$0.747072\pi$
$770$	2.66447e11	0.0273151
$771$	0	0
$772$	−1.08862e13	−1.10306
$773$	1.48951e13	1.50050	0.750251	−	0.661153i	$-0.229933\pi$
$773$	1.48951e13	1.50050	0.750251	+	0.661153i	$0.229933\pi$
$774$	0	0
$775$	3.77216e12	0.375606
$776$	2.01465e12	0.199444
$777$	0	0
$778$	−6.50537e11	−0.0636596
$779$	1.11031e12	0.108025
$780$	0	0
$781$	−1.29906e11	−0.0124939
$782$	1.20005e12	0.114754
$783$	0	0
$784$	−5.56986e12	−0.526528
$785$	1.19133e13	1.11974
$786$	0	0
$787$	−1.79246e13	−1.66558	−0.832788	−	0.553592i	$-0.813257\pi$
$787$	−1.79246e13	−1.66558	−0.832788	+	0.553592i	$0.813257\pi$
$788$	−1.39478e13	−1.28866
$789$	0	0
$790$	6.52719e11	0.0596217
$791$	5.95276e12	0.540660
$792$	0	0
$793$	−1.95587e12	−0.175635
$794$	1.41354e12	0.126217
$795$	0	0
$796$	−2.09574e12	−0.185024
$797$	−1.38729e13	−1.21788	−0.608940	−	0.793216i	$-0.708405\pi$
$797$	−1.38729e13	−1.21788	−0.608940	+	0.793216i	$0.708405\pi$
$798$	0	0
$799$	1.61715e13	1.40375
$800$	−9.09498e11	−0.0785049
$801$	0	0
$802$	1.12396e12	0.0959327
$803$	4.15452e12	0.352615
$804$	0	0
$805$	−5.86909e12	−0.492594
$806$	−3.49553e11	−0.0291746
$807$	0	0
$808$	−3.41697e12	−0.282027
$809$	−9.79702e12	−0.804129	−0.402064	−	0.915611i	$-0.631707\pi$
$809$	−9.79702e12	−0.804129	−0.402064	+	0.915611i	$0.631707\pi$
$810$	0	0
$811$	1.11554e13	0.905508	0.452754	−	0.891635i	$-0.350442\pi$
$811$	1.11554e13	0.905508	0.452754	+	0.891635i	$0.350442\pi$
$812$	1.57287e13	1.26967
$813$	0	0
$814$	4.49627e11	0.0358957
$815$	−9.51492e12	−0.755433
$816$	0	0
$817$	−8.43479e11	−0.0662331
$818$	−3.08988e11	−0.0241297
$819$	0	0
$820$	2.60886e12	0.201506
$821$	1.94239e13	1.49208	0.746039	−	0.665902i	$-0.231953\pi$
$821$	1.94239e13	1.49208	0.746039	+	0.665902i	$0.231953\pi$
$822$	0	0
$823$	−1.46781e13	−1.11524	−0.557622	−	0.830095i	$-0.688286\pi$
$823$	−1.46781e13	−1.11524	−0.557622	+	0.830095i	$0.688286\pi$
$824$	−1.79991e12	−0.136013
$825$	0	0
$826$	2.76730e10	0.00206845
$827$	1.77714e13	1.32114	0.660568	−	0.750766i	$-0.270316\pi$
$827$	1.77714e13	1.32114	0.660568	+	0.750766i	$0.270316\pi$
$828$	0	0
$829$	1.08538e13	0.798151	0.399075	−	0.916918i	$-0.369331\pi$
$829$	1.08538e13	0.798151	0.399075	+	0.916918i	$0.369331\pi$
$830$	−1.09366e12	−0.0799894
$831$	0	0
$832$	−4.40892e12	−0.318990
$833$	−1.22539e13	−0.881802
$834$	0	0
$835$	−9.43618e12	−0.671749
$836$	3.81395e12	0.270052
$837$	0	0
$838$	1.30641e12	0.0915126
$839$	−9.83099e12	−0.684965	−0.342482	−	0.939524i	$-0.611268\pi$
$839$	−9.83099e12	−0.684965	−0.342482	+	0.939524i	$0.611268\pi$
$840$	0	0
$841$	3.65754e13	2.52120
$842$	1.66076e12	0.113868
$843$	0	0
$844$	−1.95356e13	−1.32521
$845$	1.07561e13	0.725773
$846$	0	0
$847$	−6.20610e12	−0.414327
$848$	−5.34881e12	−0.355203
$849$	0	0
$850$	−6.60057e11	−0.0433707
$851$	−9.90405e12	−0.647336
$852$	0	0
$853$	2.22566e13	1.43942	0.719712	−	0.694273i	$-0.244274\pi$
$853$	2.22566e13	1.43942	0.719712	+	0.694273i	$0.244274\pi$
$854$	−4.41419e11	−0.0283982
$855$	0	0
$856$	3.33457e9	0.000212280 0
$857$	−6.93260e12	−0.439018	−0.219509	−	0.975610i	$-0.570446\pi$
$857$	−6.93260e12	−0.439018	−0.219509	+	0.975610i	$0.570446\pi$
$858$	0	0
$859$	3.01241e13	1.88775	0.943875	−	0.330303i	$-0.107151\pi$
$859$	3.01241e13	1.88775	0.943875	+	0.330303i	$0.107151\pi$
$860$	−1.98190e12	−0.123549
$861$	0	0
$862$	−1.24263e12	−0.0766581
$863$	2.10193e13	1.28994	0.644971	−	0.764207i	$-0.276869\pi$
$863$	2.10193e13	1.28994	0.644971	+	0.764207i	$0.276869\pi$
$864$	0	0
$865$	7.25824e12	0.440818
$866$	9.89664e11	0.0597940
$867$	0	0
$868$	1.26709e13	0.757651
$869$	9.77908e12	0.581713
$870$	0	0
$871$	6.66249e12	0.392243
$872$	2.34304e12	0.137232
$873$	0	0
$874$	5.23058e11	0.0303214
$875$	1.28519e13	0.741195
$876$	0	0
$877$	1.39399e13	0.795720	0.397860	−	0.917446i	$-0.369753\pi$
$877$	1.39399e13	0.795720	0.397860	+	0.917446i	$0.369753\pi$
$878$	−1.86562e12	−0.105949
$879$	0	0
$880$	8.90540e12	0.500589
$881$	−3.43345e12	−0.192017	−0.0960083	−	0.995381i	$-0.530608\pi$
$881$	−3.43345e12	−0.192017	−0.0960083	+	0.995381i	$0.530608\pi$
$882$	0	0
$883$	1.64420e13	0.910189	0.455095	−	0.890443i	$-0.349605\pi$
$883$	1.64420e13	0.910189	0.455095	+	0.890443i	$0.349605\pi$
$884$	−9.82402e12	−0.541071
$885$	0	0
$886$	−9.81190e11	−0.0534935
$887$	2.76514e13	1.49990	0.749949	−	0.661496i	$-0.230078\pi$
$887$	2.76514e13	1.49990	0.749949	+	0.661496i	$0.230078\pi$
$888$	0	0
$889$	−6.11593e12	−0.328401
$890$	4.17010e11	0.0222788
$891$	0	0
$892$	−1.96216e13	−1.03775
$893$	7.04858e12	0.370911
$894$	0	0
$895$	−1.98044e13	−1.03171
$896$	−4.06913e12	−0.210919
$897$	0	0
$898$	1.96069e12	0.100615
$899$	4.11517e13	2.10121
$900$	0	0
$901$	−1.17676e13	−0.594874
$902$	−2.43354e11	−0.0122408
$903$	0	0
$904$	−2.50084e12	−0.124545
$905$	1.37665e13	0.682188
$906$	0	0
$907$	−1.33233e13	−0.653699	−0.326850	−	0.945076i	$-0.605987\pi$
$907$	−1.33233e13	−0.653699	−0.326850	+	0.945076i	$0.605987\pi$
$908$	−5.74420e12	−0.280442
$909$	0	0
$910$	−2.99142e11	−0.0144607
$911$	2.44420e11	0.0117572	0.00587860	−	0.999983i	$-0.498129\pi$
$911$	2.44420e11	0.0117572	0.00587860	+	0.999983i	$0.498129\pi$
$912$	0	0
$913$	−1.63853e13	−0.780435
$914$	−1.39763e12	−0.0662419
$915$	0	0
$916$	−1.77118e13	−0.831252
$917$	−2.83618e13	−1.32456
$918$	0	0
$919$	1.75324e13	0.810813	0.405407	−	0.914136i	$-0.367130\pi$
$919$	1.75324e13	0.810813	0.405407	+	0.914136i	$0.367130\pi$
$920$	2.46569e12	0.113473
$921$	0	0
$922$	−2.79523e12	−0.127388
$923$	1.45846e11	0.00661434
$924$	0	0
$925$	5.44748e12	0.244657
$926$	2.23695e11	0.00999784
$927$	0	0
$928$	−9.92202e12	−0.439172
$929$	1.10334e13	0.486004	0.243002	−	0.970026i	$-0.421868\pi$
$929$	1.10334e13	0.486004	0.243002	+	0.970026i	$0.421868\pi$
$930$	0	0
$931$	−5.34103e12	−0.232998
$932$	1.35457e13	0.588069
$933$	0	0
$934$	1.27720e12	0.0549159
$935$	1.95922e13	0.838360
$936$	0	0
$937$	−2.57249e13	−1.09025	−0.545124	−	0.838356i	$-0.683517\pi$
$937$	−2.57249e13	−1.09025	−0.545124	+	0.838356i	$0.683517\pi$
$938$	1.50365e12	0.0634211
$939$	0	0
$940$	1.65619e13	0.691886
$941$	8.89212e12	0.369702	0.184851	−	0.982767i	$-0.440820\pi$
$941$	8.89212e12	0.369702	0.184851	+	0.982767i	$0.440820\pi$
$942$	0	0
$943$	5.36041e12	0.220747
$944$	9.24908e11	0.0379075
$945$	0	0
$946$	1.84871e11	0.00750514
$947$	5.49551e12	0.222041	0.111020	−	0.993818i	$-0.464588\pi$
$947$	5.49551e12	0.222041	0.111020	+	0.993818i	$0.464588\pi$
$948$	0	0
$949$	−4.66430e12	−0.186676
$950$	−2.87696e11	−0.0114598
$951$	0	0
$952$	−4.44815e12	−0.175515
$953$	−1.44013e13	−0.565565	−0.282783	−	0.959184i	$-0.591258\pi$
$953$	−1.44013e13	−0.565565	−0.282783	+	0.959184i	$0.591258\pi$
$954$	0	0
$955$	2.38429e13	0.927564
$956$	3.02102e13	1.16975
$957$	0	0
$958$	−3.15425e12	−0.120990
$959$	−3.86278e12	−0.147474
$960$	0	0
$961$	6.71190e12	0.253858
$962$	−5.04799e11	−0.0190034
$963$	0	0
$964$	−2.63837e13	−0.983988
$965$	−2.43746e13	−0.904825
$966$	0	0
$967$	1.72578e13	0.634698	0.317349	−	0.948309i	$-0.397207\pi$
$967$	1.72578e13	0.634698	0.317349	+	0.948309i	$0.397207\pi$
$968$	2.60727e12	0.0954436
$969$	0	0
$970$	2.24843e12	0.0815467
$971$	−1.22438e13	−0.442007	−0.221003	−	0.975273i	$-0.570933\pi$
$971$	−1.22438e13	−0.442007	−0.221003	+	0.975273i	$0.570933\pi$
$972$	0	0
$973$	2.15244e13	0.769879
$974$	3.94622e12	0.140497
$975$	0	0
$976$	−1.47534e13	−0.520438
$977$	5.34352e13	1.87630	0.938149	−	0.346231i	$-0.112539\pi$
$977$	5.34352e13	1.87630	0.938149	+	0.346231i	$0.112539\pi$
$978$	0	0
$979$	6.24766e12	0.217368
$980$	−1.25497e13	−0.434626
$981$	0	0
$982$	2.42262e12	0.0831350
$983$	5.98058e12	0.204293	0.102146	−	0.994769i	$-0.467429\pi$
$983$	5.98058e12	0.204293	0.102146	+	0.994769i	$0.467429\pi$
$984$	0	0
$985$	−3.12295e13	−1.05706
$986$	−7.20079e12	−0.242624
$987$	0	0
$988$	−4.28194e12	−0.142967
$989$	−4.07220e12	−0.135346
$990$	0	0
$991$	−1.53735e13	−0.506340	−0.253170	−	0.967422i	$-0.581473\pi$
$991$	−1.53735e13	−0.506340	−0.253170	+	0.967422i	$0.581473\pi$
$992$	−7.99310e12	−0.262067
$993$	0	0
$994$	3.29158e10	0.00106946
$995$	−4.69241e12	−0.151772
$996$	0	0
$997$	−1.18916e12	−0.0381165	−0.0190583	−	0.999818i	$-0.506067\pi$
$997$	−1.18916e12	−0.0381165	−0.0190583	+	0.999818i	$0.506067\pi$
$998$	4.28574e12	0.136754
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.10.a.c.1.7		15
3.2	odd	2		43.10.a.a.1.9	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.9	✓	15	3.2	odd	2
387.10.a.c.1.7		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)

\(f(q)\)	\(=\)	\(q+1.77990 q^{2} -508.832 q^{4} -1139.29 q^{5} +4324.96 q^{7} -1816.98 q^{8} +O(q^{10})\)	\(q+1.77990 q^{2} -508.832 q^{4} -1139.29 q^{5} +4324.96 q^{7} -1816.98 q^{8} -2027.82 q^{10} -30380.9 q^{11} +34108.8 q^{13} +7697.98 q^{14} +257288. q^{16} +566042. q^{17} +246718. q^{19} +579707. q^{20} -54074.8 q^{22} +1.19112e6 q^{23} -655146. q^{25} +60710.1 q^{26} -2.20068e6 q^{28} -7.14721e6 q^{29} -5.75774e6 q^{31} +1.38824e6 q^{32} +1.00750e6 q^{34} -4.92738e6 q^{35} -8.31491e6 q^{37} +439132. q^{38} +2.07006e6 q^{40} +4.50031e6 q^{41} -3.41880e6 q^{43} +1.54588e7 q^{44} +2.12007e6 q^{46} +2.85694e7 q^{47} -2.16483e7 q^{49} -1.16609e6 q^{50} -1.73556e7 q^{52} -2.07892e7 q^{53} +3.46126e7 q^{55} -7.85834e6 q^{56} -1.27213e7 q^{58} +3.59484e6 q^{59} -5.73421e7 q^{61} -1.02482e7 q^{62} -1.29261e8 q^{64} -3.88598e7 q^{65} +1.95331e8 q^{67} -2.88020e8 q^{68} -8.77022e6 q^{70} +4.27590e6 q^{71} -1.36748e8 q^{73} -1.47997e7 q^{74} -1.25538e8 q^{76} -1.31396e8 q^{77} -3.21883e8 q^{79} -2.93125e8 q^{80} +8.01009e6 q^{82} +5.39331e8 q^{83} -6.44885e8 q^{85} -6.08511e6 q^{86} +5.52013e7 q^{88} -2.05645e8 q^{89} +1.47519e8 q^{91} -6.06079e8 q^{92} +5.08506e7 q^{94} -2.81083e8 q^{95} -1.10879e9 q^{97} -3.85318e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) \) 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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