LMFDB - Embedded newform 387.10.a.c.1.14

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			1.14
Root			$39.2075$ 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)

$f(q)$	$=$	$q+41.2075 q^{2} +1186.05 q^{4} +1998.59 q^{5} -10690.1 q^{7} +27776.1 q^{8} +O(q^{10})$	\(q+41.2075 q^{2} +1186.05 q^{4} +1998.59 q^{5} -10690.1 q^{7} +27776.1 q^{8} +82356.9 q^{10} -36286.0 q^{11} +164599. q^{13} -440512. q^{14} +537322. q^{16} +397627. q^{17} +501060. q^{19} +2.37044e6 q^{20} -1.49525e6 q^{22} -342901. q^{23} +2.04125e6 q^{25} +6.78271e6 q^{26} -1.26790e7 q^{28} +205168. q^{29} -4.44691e6 q^{31} +7.92032e6 q^{32} +1.63852e7 q^{34} -2.13651e7 q^{35} +9.29370e6 q^{37} +2.06474e7 q^{38} +5.55131e7 q^{40} +2.39332e6 q^{41} -3.41880e6 q^{43} -4.30372e7 q^{44} -1.41301e7 q^{46} +4.72891e7 q^{47} +7.39245e7 q^{49} +8.41146e7 q^{50} +1.95224e8 q^{52} +9.18336e7 q^{53} -7.25209e7 q^{55} -2.96929e8 q^{56} +8.45447e6 q^{58} -1.40816e8 q^{59} +8.99461e7 q^{61} -1.83246e8 q^{62} +5.12674e7 q^{64} +3.28967e8 q^{65} +2.51089e8 q^{67} +4.71607e8 q^{68} -8.80403e8 q^{70} -3.30330e8 q^{71} -1.51643e8 q^{73} +3.82970e8 q^{74} +5.94285e8 q^{76} +3.87900e8 q^{77} +2.48990e8 q^{79} +1.07389e9 q^{80} +9.86226e7 q^{82} +2.98476e8 q^{83} +7.94694e8 q^{85} -1.40880e8 q^{86} -1.00788e9 q^{88} +8.14630e8 q^{89} -1.75958e9 q^{91} -4.06699e8 q^{92} +1.94866e9 q^{94} +1.00142e9 q^{95} +9.42482e8 q^{97} +3.04624e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	41.2075	1.82113	0.910565	−	0.413366i	$-0.135647\pi$
$2$	41.2075	1.82113	0.910565	+	0.413366i	$0.135647\pi$
$3$	0	0
$3$	0	0
$4$	1186.05	2.31651
$5$	1998.59	1.43008	0.715038	−	0.699085i	$-0.246409\pi$
$5$	1998.59	1.43008	0.715038	+	0.699085i	$0.246409\pi$
$6$	0	0
$7$	−10690.1	−1.68283	−0.841415	−	0.540389i	$-0.818277\pi$
$7$	−10690.1	−1.68283	−0.841415	+	0.540389i	$0.818277\pi$
$8$	27776.1	2.39754
$9$	0	0
$10$	82356.9	2.60435
$11$	−36286.0	−0.747260	−0.373630	−	0.927578i	$-0.621887\pi$
$11$	−36286.0	−0.747260	−0.373630	+	0.927578i	$0.621887\pi$
$12$	0	0
$13$	164599.	1.59839	0.799194	−	0.601073i	$-0.205260\pi$
$13$	164599.	1.59839	0.799194	+	0.601073i	$0.205260\pi$
$14$	−440512.	−3.06465
$15$	0	0
$16$	537322.	2.04972
$17$	397627.	1.15466	0.577332	−	0.816510i	$-0.304094\pi$
$17$	397627.	1.15466	0.577332	+	0.816510i	$0.304094\pi$
$18$	0	0
$19$	501060.	0.882061	0.441031	−	0.897492i	$-0.354613\pi$
$19$	501060.	0.882061	0.441031	+	0.897492i	$0.354613\pi$
$20$	2.37044e6	3.31279
$21$	0	0
$22$	−1.49525e6	−1.36086
$23$	−342901.	−0.255501	−0.127751	−	0.991806i	$-0.540776\pi$
$23$	−342901.	−0.255501	−0.127751	+	0.991806i	$0.540776\pi$
$24$	0	0
$25$	2.04125e6	1.04512
$26$	6.78271e6	2.91087
$27$	0	0
$28$	−1.26790e7	−3.89830
$29$	205168.	0.0538666	0.0269333	−	0.999637i	$-0.491426\pi$
$29$	205168.	0.0538666	0.0269333	+	0.999637i	$0.491426\pi$
$30$	0	0
$31$	−4.44691e6	−0.864829	−0.432415	−	0.901675i	$-0.642338\pi$
$31$	−4.44691e6	−0.864829	−0.432415	+	0.901675i	$0.642338\pi$
$32$	7.92032e6	1.33527
$33$	0	0
$34$	1.63852e7	2.10279
$35$	−2.13651e7	−2.40658
$36$	0	0
$37$	9.29370e6	0.815231	0.407616	−	0.913154i	$-0.366360\pi$
$37$	9.29370e6	0.815231	0.407616	+	0.913154i	$0.366360\pi$
$38$	2.06474e7	1.60635
$39$	0	0
$40$	5.55131e7	3.42867
$41$	2.39332e6	0.132274	0.0661368	−	0.997811i	$-0.478933\pi$
$41$	2.39332e6	0.132274	0.0661368	+	0.997811i	$0.478933\pi$
$42$	0	0
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	−4.30372e7	−1.73104
$45$	0	0
$46$	−1.41301e7	−0.465301
$47$	4.72891e7	1.41358	0.706790	−	0.707423i	$-0.250143\pi$
$47$	4.72891e7	1.41358	0.706790	+	0.707423i	$0.250143\pi$
$48$	0	0
$49$	7.39245e7	1.83192
$50$	8.41146e7	1.90330
$51$	0	0
$52$	1.95224e8	3.70269
$53$	9.18336e7	1.59868	0.799338	−	0.600882i	$-0.205184\pi$
$53$	9.18336e7	1.59868	0.799338	+	0.600882i	$0.205184\pi$
$54$	0	0
$55$	−7.25209e7	−1.06864
$56$	−2.96929e8	−4.03466
$57$	0	0
$58$	8.45447e6	0.0980980
$59$	−1.40816e8	−1.51293	−0.756464	−	0.654035i	$-0.773075\pi$
$59$	−1.40816e8	−1.51293	−0.756464	+	0.654035i	$0.773075\pi$
$60$	0	0
$61$	8.99461e7	0.831760	0.415880	−	0.909420i	$-0.363474\pi$
$61$	8.99461e7	0.831760	0.415880	+	0.909420i	$0.363474\pi$
$62$	−1.83246e8	−1.57497
$63$	0	0
$64$	5.12674e7	0.381972
$65$	3.28967e8	2.28582
$66$	0	0
$67$	2.51089e8	1.52227	0.761135	−	0.648593i	$-0.224642\pi$
$67$	2.51089e8	1.52227	0.761135	+	0.648593i	$0.224642\pi$
$68$	4.71607e8	2.67479
$69$	0	0
$70$	−8.80403e8	−4.38269
$71$	−3.30330e8	−1.54271	−0.771357	−	0.636402i	$-0.780422\pi$
$71$	−3.30330e8	−1.54271	−0.771357	+	0.636402i	$0.780422\pi$
$72$	0	0
$73$	−1.51643e8	−0.624986	−0.312493	−	0.949920i	$-0.601164\pi$
$73$	−1.51643e8	−0.624986	−0.312493	+	0.949920i	$0.601164\pi$
$74$	3.82970e8	1.48464
$75$	0	0
$76$	5.94285e8	2.04331
$77$	3.87900e8	1.25751
$78$	0	0
$79$	2.48990e8	0.719217	0.359608	−	0.933103i	$-0.382910\pi$
$79$	2.48990e8	0.719217	0.359608	+	0.933103i	$0.382910\pi$
$80$	1.07389e9	2.93126
$81$	0	0
$82$	9.86226e7	0.240887
$83$	2.98476e8	0.690331	0.345166	−	0.938542i	$-0.387823\pi$
$83$	2.98476e8	0.690331	0.345166	+	0.938542i	$0.387823\pi$
$84$	0	0
$85$	7.94694e8	1.65126
$86$	−1.40880e8	−0.277720
$87$	0	0
$88$	−1.00788e9	−1.79159
$89$	8.14630e8	1.37628	0.688138	−	0.725580i	$-0.258428\pi$
$89$	8.14630e8	1.37628	0.688138	+	0.725580i	$0.258428\pi$
$90$	0	0
$91$	−1.75958e9	−2.68982
$92$	−4.06699e8	−0.591872
$93$	0	0
$94$	1.94866e9	2.57431
$95$	1.00142e9	1.26142
$96$	0	0
$97$	9.42482e8	1.08094	0.540468	−	0.841364i	$-0.318247\pi$
$97$	9.42482e8	1.08094	0.540468	+	0.841364i	$0.318247\pi$
$98$	3.04624e9	3.33616
$99$	0	0
$100$	2.42103e9	2.42103
$101$	6.02282e8	0.575909	0.287954	−	0.957644i	$-0.407025\pi$
$101$	6.02282e8	0.575909	0.287954	+	0.957644i	$0.407025\pi$
$102$	0	0
$103$	−5.70962e8	−0.499850	−0.249925	−	0.968265i	$-0.580406\pi$
$103$	−5.70962e8	−0.499850	−0.249925	+	0.968265i	$0.580406\pi$
$104$	4.57192e9	3.83220
$105$	0	0
$106$	3.78423e9	2.91140
$107$	−5.23029e8	−0.385743	−0.192872	−	0.981224i	$-0.561780\pi$
$107$	−5.23029e8	−0.385743	−0.192872	+	0.981224i	$0.561780\pi$
$108$	0	0
$109$	1.69448e9	1.14979	0.574895	−	0.818227i	$-0.305043\pi$
$109$	1.69448e9	1.14979	0.574895	+	0.818227i	$0.305043\pi$
$110$	−2.98840e9	−1.94613
$111$	0	0
$112$	−5.74402e9	−3.44933
$113$	−3.15269e9	−1.81898	−0.909489	−	0.415727i	$-0.863527\pi$
$113$	−3.15269e9	−1.81898	−0.909489	+	0.415727i	$0.863527\pi$
$114$	0	0
$115$	−6.85319e8	−0.365387
$116$	2.43341e8	0.124783
$117$	0	0
$118$	−5.80267e9	−2.75524
$119$	−4.25067e9	−1.94310
$120$	0	0
$121$	−1.04128e9	−0.441602
$122$	3.70645e9	1.51474
$123$	0	0
$124$	−5.27428e9	−2.00339
$125$	1.76121e8	0.0645233
$126$	0	0
$127$	9.03372e8	0.308141	0.154071	−	0.988060i	$-0.450762\pi$
$127$	9.03372e8	0.308141	0.154071	+	0.988060i	$0.450762\pi$
$128$	−1.94260e9	−0.639646
$129$	0	0
$130$	1.35559e10	4.16277
$131$	−1.08637e9	−0.322299	−0.161149	−	0.986930i	$-0.551520\pi$
$131$	−1.08637e9	−0.322299	−0.161149	+	0.986930i	$0.551520\pi$
$132$	0	0
$133$	−5.35638e9	−1.48436
$134$	1.03468e10	2.77225
$135$	0	0
$136$	1.10445e10	2.76835
$137$	5.85232e8	0.141934	0.0709668	−	0.997479i	$-0.477392\pi$
$137$	5.85232e8	0.141934	0.0709668	+	0.997479i	$0.477392\pi$
$138$	0	0
$139$	6.47466e8	0.147113	0.0735564	−	0.997291i	$-0.476565\pi$
$139$	6.47466e8	0.147113	0.0735564	+	0.997291i	$0.476565\pi$
$140$	−2.53402e10	−5.57486
$141$	0	0
$142$	−1.36121e10	−2.80948
$143$	−5.97264e9	−1.19441
$144$	0	0
$145$	4.10048e8	0.0770333
$146$	−6.24883e9	−1.13818
$147$	0	0
$148$	1.10228e10	1.88849
$149$	5.65496e9	0.939921	0.469960	−	0.882687i	$-0.344268\pi$
$149$	5.65496e9	0.939921	0.469960	+	0.882687i	$0.344268\pi$
$150$	0	0
$151$	−5.68427e9	−0.889772	−0.444886	−	0.895587i	$-0.646756\pi$
$151$	−5.68427e9	−0.889772	−0.444886	+	0.895587i	$0.646756\pi$
$152$	1.39175e10	2.11478
$153$	0	0
$154$	1.59844e10	2.29009
$155$	−8.88756e9	−1.23677
$156$	0	0
$157$	−4.76925e9	−0.626471	−0.313236	−	0.949675i	$-0.601413\pi$
$157$	−4.76925e9	−0.626471	−0.313236	+	0.949675i	$0.601413\pi$
$158$	1.02602e10	1.30979
$159$	0	0
$160$	1.58295e10	1.90953
$161$	3.66564e9	0.429965
$162$	0	0
$163$	−3.07695e9	−0.341411	−0.170705	−	0.985322i	$-0.554605\pi$
$163$	−3.07695e9	−0.341411	−0.170705	+	0.985322i	$0.554605\pi$
$164$	2.83861e9	0.306414
$165$	0	0
$166$	1.22994e10	1.25718
$167$	−1.83022e9	−0.182087	−0.0910437	−	0.995847i	$-0.529020\pi$
$167$	−1.83022e9	−0.182087	−0.0910437	+	0.995847i	$0.529020\pi$
$168$	0	0
$169$	1.64884e10	1.55485
$170$	3.27473e10	3.00715
$171$	0	0
$172$	−4.05489e9	−0.353265
$173$	−7.61751e9	−0.646555	−0.323278	−	0.946304i	$-0.604785\pi$
$173$	−7.61751e9	−0.646555	−0.323278	+	0.946304i	$0.604785\pi$
$174$	0	0
$175$	−2.18211e10	−1.75876
$176$	−1.94973e10	−1.53167
$177$	0	0
$178$	3.35689e10	2.50638
$179$	2.69122e9	0.195934	0.0979672	−	0.995190i	$-0.468766\pi$
$179$	2.69122e9	0.195934	0.0979672	+	0.995190i	$0.468766\pi$
$180$	0	0
$181$	−1.34253e10	−0.929761	−0.464881	−	0.885373i	$-0.653903\pi$
$181$	−1.34253e10	−0.929761	−0.464881	+	0.885373i	$0.653903\pi$
$182$	−7.25078e10	−4.89850
$183$	0	0
$184$	−9.52444e9	−0.612575
$185$	1.85743e10	1.16584
$186$	0	0
$187$	−1.44283e10	−0.862834
$188$	5.60874e10	3.27458
$189$	0	0
$190$	4.12658e10	2.29720
$191$	2.22480e10	1.20960	0.604799	−	0.796378i	$-0.293254\pi$
$191$	2.22480e10	1.20960	0.604799	+	0.796378i	$0.293254\pi$
$192$	0	0
$193$	−2.60547e10	−1.35169	−0.675847	−	0.737042i	$-0.736222\pi$
$193$	−2.60547e10	−1.35169	−0.675847	+	0.737042i	$0.736222\pi$
$194$	3.88373e10	1.96853
$195$	0	0
$196$	8.76785e10	4.24366
$197$	−8.60900e9	−0.407244	−0.203622	−	0.979050i	$-0.565271\pi$
$197$	−8.60900e9	−0.407244	−0.203622	+	0.979050i	$0.565271\pi$
$198$	0	0
$199$	−4.77571e9	−0.215873	−0.107937	−	0.994158i	$-0.534424\pi$
$199$	−4.77571e9	−0.215873	−0.107937	+	0.994158i	$0.534424\pi$
$200$	5.66979e10	2.50572
$201$	0	0
$202$	2.48185e10	1.04880
$203$	−2.19327e9	−0.0906483
$204$	0	0
$205$	4.78327e9	0.189161
$206$	−2.35279e10	−0.910291
$207$	0	0
$208$	8.84427e10	3.27625
$209$	−1.81815e10	−0.659129
$210$	0	0
$211$	1.74070e10	0.604578	0.302289	−	0.953216i	$-0.402249\pi$
$211$	1.74070e10	0.604578	0.302289	+	0.953216i	$0.402249\pi$
$212$	1.08920e11	3.70335
$213$	0	0
$214$	−2.15527e10	−0.702489
$215$	−6.83279e9	−0.218085
$216$	0	0
$217$	4.75378e10	1.45536
$218$	6.98254e10	2.09392
$219$	0	0
$220$	−8.60138e10	−2.47552
$221$	6.54490e10	1.84560
$222$	0	0
$223$	4.18882e10	1.13428	0.567140	−	0.823622i	$-0.308050\pi$
$223$	4.18882e10	1.13428	0.567140	+	0.823622i	$0.308050\pi$
$224$	−8.46690e10	−2.24703
$225$	0	0
$226$	−1.29914e11	−3.31260
$227$	−6.69191e9	−0.167276	−0.0836380	−	0.996496i	$-0.526654\pi$
$227$	−6.69191e9	−0.167276	−0.0836380	+	0.996496i	$0.526654\pi$
$228$	0	0
$229$	−4.12032e10	−0.990081	−0.495041	−	0.868870i	$-0.664847\pi$
$229$	−4.12032e10	−0.990081	−0.495041	+	0.868870i	$0.664847\pi$
$230$	−2.82403e10	−0.665416
$231$	0	0
$232$	5.69877e9	0.129147
$233$	7.86029e10	1.74718	0.873588	−	0.486666i	$-0.161787\pi$
$233$	7.86029e10	1.74718	0.873588	+	0.486666i	$0.161787\pi$
$234$	0	0
$235$	9.45116e10	2.02153
$236$	−1.67016e11	−3.50472
$237$	0	0
$238$	−1.75159e11	−3.53864
$239$	−3.00733e10	−0.596198	−0.298099	−	0.954535i	$-0.596353\pi$
$239$	−3.00733e10	−0.596198	−0.298099	+	0.954535i	$0.596353\pi$
$240$	0	0
$241$	1.44474e10	0.275875	0.137937	−	0.990441i	$-0.455953\pi$
$241$	1.44474e10	0.275875	0.137937	+	0.990441i	$0.455953\pi$
$242$	−4.29083e10	−0.804215
$243$	0	0
$244$	1.06681e11	1.92678
$245$	1.47745e11	2.61978
$246$	0	0
$247$	8.24741e10	1.40988
$248$	−1.23518e11	−2.07346
$249$	0	0
$250$	7.25751e9	0.117505
$251$	4.66837e10	0.742392	0.371196	−	0.928555i	$-0.378948\pi$
$251$	4.66837e10	0.742392	0.371196	+	0.928555i	$0.378948\pi$
$252$	0	0
$253$	1.24425e10	0.190926
$254$	3.72256e10	0.561165
$255$	0	0
$256$	−1.06299e11	−1.54685
$257$	−6.18273e10	−0.884059	−0.442030	−	0.897000i	$-0.645741\pi$
$257$	−6.18273e10	−0.884059	−0.442030	+	0.897000i	$0.645741\pi$
$258$	0	0
$259$	−9.93505e10	−1.37190
$260$	3.90172e11	5.29513
$261$	0	0
$262$	−4.47667e10	−0.586948
$263$	−6.15683e10	−0.793517	−0.396759	−	0.917923i	$-0.629865\pi$
$263$	−6.15683e10	−0.793517	−0.396759	+	0.917923i	$0.629865\pi$
$264$	0	0
$265$	1.83538e11	2.28623
$266$	−2.20723e11	−2.70321
$267$	0	0
$268$	2.97806e11	3.52636
$269$	−5.70312e10	−0.664091	−0.332045	−	0.943263i	$-0.607739\pi$
$269$	−5.70312e10	−0.664091	−0.332045	+	0.943263i	$0.607739\pi$
$270$	0	0
$271$	−9.67574e10	−1.08974	−0.544870	−	0.838521i	$-0.683421\pi$
$271$	−9.67574e10	−1.08974	−0.544870	+	0.838521i	$0.683421\pi$
$272$	2.13654e11	2.36674
$273$	0	0
$274$	2.41159e10	0.258480
$275$	−7.40687e10	−0.780976
$276$	0	0
$277$	−1.10031e11	−1.12294	−0.561471	−	0.827497i	$-0.689764\pi$
$277$	−1.10031e11	−1.12294	−0.561471	+	0.827497i	$0.689764\pi$
$278$	2.66804e10	0.267911
$279$	0	0
$280$	−5.93440e11	−5.76987
$281$	4.71720e10	0.451342	0.225671	−	0.974204i	$-0.427543\pi$
$281$	4.71720e10	0.451342	0.225671	+	0.974204i	$0.427543\pi$
$282$	0	0
$283$	6.65135e10	0.616411	0.308206	−	0.951320i	$-0.400271\pi$
$283$	6.65135e10	0.616411	0.308206	+	0.951320i	$0.400271\pi$
$284$	−3.91790e11	−3.57372
$285$	0	0
$286$	−2.46117e11	−2.17518
$287$	−2.55848e10	−0.222594
$288$	0	0
$289$	3.95191e10	0.333247
$290$	1.68970e10	0.140288
$291$	0	0
$292$	−1.79857e11	−1.44779
$293$	−5.04654e10	−0.400027	−0.200013	−	0.979793i	$-0.564099\pi$
$293$	−5.04654e10	−0.400027	−0.200013	+	0.979793i	$0.564099\pi$
$294$	0	0
$295$	−2.81434e11	−2.16360
$296$	2.58143e11	1.95455
$297$	0	0
$298$	2.33027e11	1.71172
$299$	−5.64412e10	−0.408391
$300$	0	0
$301$	3.65473e10	0.256629
$302$	−2.34234e11	−1.62039
$303$	0	0
$304$	2.69231e11	1.80798
$305$	1.79766e11	1.18948
$306$	0	0
$307$	9.46104e10	0.607878	0.303939	−	0.952692i	$-0.401698\pi$
$307$	9.46104e10	0.607878	0.303939	+	0.952692i	$0.401698\pi$
$308$	4.60071e11	2.91304
$309$	0	0
$310$	−3.66234e11	−2.25232
$311$	−1.39290e10	−0.0844302	−0.0422151	−	0.999109i	$-0.513441\pi$
$311$	−1.39290e10	−0.0844302	−0.0422151	+	0.999109i	$0.513441\pi$
$312$	0	0
$313$	−1.97862e11	−1.16523	−0.582617	−	0.812747i	$-0.697971\pi$
$313$	−1.97862e11	−1.16523	−0.582617	+	0.812747i	$0.697971\pi$
$314$	−1.96529e11	−1.14089
$315$	0	0
$316$	2.95316e11	1.66608
$317$	8.01606e10	0.445856	0.222928	−	0.974835i	$-0.428439\pi$
$317$	8.01606e10	0.445856	0.222928	+	0.974835i	$0.428439\pi$
$318$	0	0
$319$	−7.44473e9	−0.0402523
$320$	1.02463e11	0.546249
$321$	0	0
$322$	1.51052e11	0.783023
$323$	1.99235e11	1.01848
$324$	0	0
$325$	3.35988e11	1.67051
$326$	−1.26793e11	−0.621753
$327$	0	0
$328$	6.64771e10	0.317132
$329$	−5.05524e11	−2.37881
$330$	0	0
$331$	3.39745e11	1.55570	0.777851	−	0.628448i	$-0.216310\pi$
$331$	3.39745e11	1.55570	0.777851	+	0.628448i	$0.216310\pi$
$332$	3.54009e11	1.59916
$333$	0	0
$334$	−7.54188e10	−0.331605
$335$	5.01825e11	2.17696
$336$	0	0
$337$	−1.99608e11	−0.843030	−0.421515	−	0.906821i	$-0.638502\pi$
$337$	−1.99608e11	−0.843030	−0.421515	+	0.906821i	$0.638502\pi$
$338$	6.79444e11	2.83158
$339$	0	0
$340$	9.42550e11	3.82516
$341$	1.61360e11	0.646253
$342$	0	0
$343$	−3.58875e11	−1.39997
$344$	−9.49609e10	−0.365622
$345$	0	0
$346$	−3.13898e11	−1.17746
$347$	−3.63746e11	−1.34684	−0.673420	−	0.739260i	$-0.735175\pi$
$347$	−3.63746e11	−1.34684	−0.673420	+	0.739260i	$0.735175\pi$
$348$	0	0
$349$	−1.07178e11	−0.386715	−0.193357	−	0.981128i	$-0.561938\pi$
$349$	−1.07178e11	−0.386715	−0.193357	+	0.981128i	$0.561938\pi$
$350$	−8.99193e11	−3.20293
$351$	0	0
$352$	−2.87397e11	−0.997791
$353$	−1.04485e11	−0.358152	−0.179076	−	0.983835i	$-0.557311\pi$
$353$	−1.04485e11	−0.358152	−0.179076	+	0.983835i	$0.557311\pi$
$354$	0	0
$355$	−6.60195e11	−2.20620
$356$	9.66196e11	3.18816
$357$	0	0
$358$	1.10898e11	0.356822
$359$	−1.05990e9	−0.00336774	−0.00168387	−	0.999999i	$-0.500536\pi$
$359$	−1.05990e9	−0.00336774	−0.00168387	+	0.999999i	$0.500536\pi$
$360$	0	0
$361$	−7.16263e10	−0.221968
$362$	−5.53224e11	−1.69322
$363$	0	0
$364$	−2.08696e12	−6.23100
$365$	−3.03073e11	−0.893778
$366$	0	0
$367$	−9.86256e10	−0.283787	−0.141893	−	0.989882i	$-0.545319\pi$
$367$	−9.86256e10	−0.283787	−0.141893	+	0.989882i	$0.545319\pi$
$368$	−1.84248e11	−0.523707
$369$	0	0
$370$	7.65401e11	2.12315
$371$	−9.81710e11	−2.69030
$372$	0	0
$373$	−3.53431e11	−0.945398	−0.472699	−	0.881224i	$-0.656720\pi$
$373$	−3.53431e11	−0.945398	−0.472699	+	0.881224i	$0.656720\pi$
$374$	−5.94553e11	−1.57133
$375$	0	0
$376$	1.31351e12	3.38912
$377$	3.37705e10	0.0860997
$378$	0	0
$379$	−8.14234e9	−0.0202709	−0.0101354	−	0.999949i	$-0.503226\pi$
$379$	−8.14234e9	−0.0202709	−0.0101354	+	0.999949i	$0.503226\pi$
$380$	1.18773e12	2.92209
$381$	0	0
$382$	9.16784e11	2.20283
$383$	−4.12171e11	−0.978774	−0.489387	−	0.872067i	$-0.662779\pi$
$383$	−4.12171e11	−0.978774	−0.489387	+	0.872067i	$0.662779\pi$
$384$	0	0
$385$	7.75255e11	1.79834
$386$	−1.07365e12	−2.46161
$387$	0	0
$388$	1.11784e12	2.50400
$389$	5.55473e11	1.22996	0.614979	−	0.788544i	$-0.289165\pi$
$389$	5.55473e11	1.22996	0.614979	+	0.788544i	$0.289165\pi$
$390$	0	0
$391$	−1.36346e11	−0.295018
$392$	2.05333e12	4.39210
$393$	0	0
$394$	−3.54755e11	−0.741644
$395$	4.97629e11	1.02854
$396$	0	0
$397$	−6.23323e11	−1.25938	−0.629689	−	0.776847i	$-0.716818\pi$
$397$	−6.23323e11	−1.25938	−0.629689	+	0.776847i	$0.716818\pi$
$398$	−1.96795e11	−0.393134
$399$	0	0
$400$	1.09681e12	2.14220
$401$	−5.35221e11	−1.03367	−0.516836	−	0.856084i	$-0.672890\pi$
$401$	−5.35221e11	−1.03367	−0.516836	+	0.856084i	$0.672890\pi$
$402$	0	0
$403$	−7.31957e11	−1.38233
$404$	7.14339e11	1.33410
$405$	0	0
$406$	−9.03790e10	−0.165082
$407$	−3.37231e11	−0.609190
$408$	0	0
$409$	−5.78560e11	−1.02234	−0.511168	−	0.859481i	$-0.670787\pi$
$409$	−5.78560e11	−1.02234	−0.511168	+	0.859481i	$0.670787\pi$
$410$	1.97106e11	0.344488
$411$	0	0
$412$	−6.77192e11	−1.15791
$413$	1.50534e12	2.54600
$414$	0	0
$415$	5.96531e11	0.987227
$416$	1.30368e12	2.13427
$417$	0	0
$418$	−7.49212e11	−1.20036
$419$	8.98515e11	1.42417	0.712086	−	0.702093i	$-0.247751\pi$
$419$	8.98515e11	1.42417	0.712086	+	0.702093i	$0.247751\pi$
$420$	0	0
$421$	5.58393e11	0.866304	0.433152	−	0.901321i	$-0.357401\pi$
$421$	5.58393e11	0.866304	0.433152	+	0.901321i	$0.357401\pi$
$422$	7.17297e11	1.10102
$423$	0	0
$424$	2.55078e12	3.83289
$425$	8.11654e11	1.20676
$426$	0	0
$427$	−9.61532e11	−1.39971
$428$	−6.20341e11	−0.893580
$429$	0	0
$430$	−2.81562e11	−0.397160
$431$	3.49762e11	0.488230	0.244115	−	0.969746i	$-0.421503\pi$
$431$	3.49762e11	0.488230	0.244115	+	0.969746i	$0.421503\pi$
$432$	0	0
$433$	−9.15456e11	−1.25153	−0.625766	−	0.780011i	$-0.715214\pi$
$433$	−9.15456e11	−1.25153	−0.625766	+	0.780011i	$0.715214\pi$
$434$	1.95891e12	2.65040
$435$	0	0
$436$	2.00975e12	2.66350
$437$	−1.71814e11	−0.225368
$438$	0	0
$439$	−1.38571e12	−1.78066	−0.890332	−	0.455312i	$-0.849528\pi$
$439$	−1.38571e12	−1.78066	−0.890332	+	0.455312i	$0.849528\pi$
$440$	−2.01435e12	−2.56211
$441$	0	0
$442$	2.69699e12	3.36108
$443$	−1.31854e12	−1.62658	−0.813292	−	0.581856i	$-0.802327\pi$
$443$	−1.31854e12	−1.62658	−0.813292	+	0.581856i	$0.802327\pi$
$444$	0	0
$445$	1.62811e12	1.96818
$446$	1.72611e12	2.06567
$447$	0	0
$448$	−5.48053e11	−0.642794
$449$	3.56492e11	0.413944	0.206972	−	0.978347i	$-0.433639\pi$
$449$	3.56492e11	0.413944	0.206972	+	0.978347i	$0.433639\pi$
$450$	0	0
$451$	−8.68440e10	−0.0988428
$452$	−3.73926e12	−4.21369
$453$	0	0
$454$	−2.75756e11	−0.304631
$455$	−3.51668e12	−3.84664
$456$	0	0
$457$	1.30599e12	1.40061	0.700307	−	0.713842i	$-0.253047\pi$
$457$	1.30599e12	1.40061	0.700307	+	0.713842i	$0.253047\pi$
$458$	−1.69788e12	−1.80307
$459$	0	0
$460$	−8.12826e11	−0.846423
$461$	8.59137e11	0.885948	0.442974	−	0.896534i	$-0.353923\pi$
$461$	8.59137e11	0.885948	0.442974	+	0.896534i	$0.353923\pi$
$462$	0	0
$463$	4.67927e11	0.473221	0.236610	−	0.971605i	$-0.423964\pi$
$463$	4.67927e11	0.473221	0.236610	+	0.971605i	$0.423964\pi$
$464$	1.10241e11	0.110411
$465$	0	0
$466$	3.23902e12	3.18183
$467$	−1.06844e12	−1.03950	−0.519748	−	0.854320i	$-0.673974\pi$
$467$	−1.06844e12	−1.03950	−0.519748	+	0.854320i	$0.673974\pi$
$468$	0	0
$469$	−2.68417e12	−2.56172
$470$	3.89458e12	3.68146
$471$	0	0
$472$	−3.91132e12	−3.62731
$473$	1.24055e11	0.113956
$474$	0	0
$475$	1.02279e12	0.921859
$476$	−5.04152e12	−4.50122
$477$	0	0
$478$	−1.23925e12	−1.08575
$479$	−1.71944e12	−1.49237	−0.746185	−	0.665739i	$-0.768116\pi$
$479$	−1.71944e12	−1.49237	−0.746185	+	0.665739i	$0.768116\pi$
$480$	0	0
$481$	1.52973e12	1.30306
$482$	5.95340e11	0.502404
$483$	0	0
$484$	−1.23501e12	−1.02298
$485$	1.88364e12	1.54582
$486$	0	0
$487$	1.43644e12	1.15720	0.578598	−	0.815613i	$-0.303600\pi$
$487$	1.43644e12	1.15720	0.578598	+	0.815613i	$0.303600\pi$
$488$	2.49835e12	1.99418
$489$	0	0
$490$	6.08819e12	4.77096
$491$	2.21628e12	1.72091	0.860453	−	0.509530i	$-0.170181\pi$
$491$	2.21628e12	1.72091	0.860453	+	0.509530i	$0.170181\pi$
$492$	0	0
$493$	8.15804e10	0.0621978
$494$	3.39855e12	2.56757
$495$	0	0
$496$	−2.38942e12	−1.77266
$497$	3.53126e12	2.59613
$498$	0	0
$499$	1.04835e12	0.756927	0.378464	−	0.925616i	$-0.376453\pi$
$499$	1.04835e12	0.756927	0.378464	+	0.925616i	$0.376453\pi$
$500$	2.08890e11	0.149469
$501$	0	0
$502$	1.92372e12	1.35199
$503$	−2.02850e12	−1.41292	−0.706462	−	0.707751i	$-0.749710\pi$
$503$	−2.02850e12	−1.41292	−0.706462	+	0.707751i	$0.749710\pi$
$504$	0	0
$505$	1.20372e12	0.823593
$506$	5.12724e11	0.347701
$507$	0	0
$508$	1.07145e12	0.713813
$509$	1.00903e12	0.666303	0.333152	−	0.942873i	$-0.391888\pi$
$509$	1.00903e12	0.666303	0.333152	+	0.942873i	$0.391888\pi$
$510$	0	0
$511$	1.62108e12	1.05175
$512$	−3.38569e12	−2.17737
$513$	0	0
$514$	−2.54775e12	−1.60999
$515$	−1.14112e12	−0.714823
$516$	0	0
$517$	−1.71593e12	−1.05631
$518$	−4.09398e12	−2.49840
$519$	0	0
$520$	9.13741e12	5.48034
$521$	−9.68502e11	−0.575878	−0.287939	−	0.957649i	$-0.592970\pi$
$521$	−9.68502e11	−0.575878	−0.287939	+	0.957649i	$0.592970\pi$
$522$	0	0
$523$	−2.51347e12	−1.46898	−0.734490	−	0.678619i	$-0.762579\pi$
$523$	−2.51347e12	−1.46898	−0.734490	+	0.678619i	$0.762579\pi$
$524$	−1.28850e12	−0.746610
$525$	0	0
$526$	−2.53707e12	−1.44510
$527$	−1.76821e12	−0.998587
$528$	0	0
$529$	−1.68357e12	−0.934719
$530$	7.56314e12	4.16352
$531$	0	0
$532$	−6.35296e12	−3.43854
$533$	3.93938e11	0.211425
$534$	0	0
$535$	−1.04532e12	−0.551643
$536$	6.97428e12	3.64971
$537$	0	0
$538$	−2.35011e12	−1.20940
$539$	−2.68242e12	−1.36892
$540$	0	0
$541$	8.92784e11	0.448083	0.224042	−	0.974580i	$-0.428075\pi$
$541$	8.92784e11	0.448083	0.224042	+	0.974580i	$0.428075\pi$
$542$	−3.98713e12	−1.98456
$543$	0	0
$544$	3.14933e12	1.54178
$545$	3.38658e12	1.64429
$546$	0	0
$547$	9.58310e11	0.457681	0.228841	−	0.973464i	$-0.426507\pi$
$547$	9.58310e11	0.457681	0.228841	+	0.973464i	$0.426507\pi$
$548$	6.94117e11	0.328791
$549$	0	0
$550$	−3.05218e12	−1.42226
$551$	1.02802e11	0.0475136
$552$	0	0
$553$	−2.66172e12	−1.21032
$554$	−4.53411e12	−2.04502
$555$	0	0
$556$	7.67930e11	0.340789
$557$	1.35685e12	0.597289	0.298645	−	0.954364i	$-0.403465\pi$
$557$	1.35685e12	0.597289	0.298645	+	0.954364i	$0.403465\pi$
$558$	0	0
$559$	−5.62732e11	−0.243752
$560$	−1.14800e13	−4.93281
$561$	0	0
$562$	1.94384e12	0.821953
$563$	1.64809e12	0.691341	0.345670	−	0.938356i	$-0.387652\pi$
$563$	1.64809e12	0.691341	0.345670	+	0.938356i	$0.387652\pi$
$564$	0	0
$565$	−6.30093e12	−2.60128
$566$	2.74085e12	1.12257
$567$	0	0
$568$	−9.17528e12	−3.69872
$569$	−1.46538e12	−0.586066	−0.293033	−	0.956102i	$-0.594665\pi$
$569$	−1.46538e12	−0.586066	−0.293033	+	0.956102i	$0.594665\pi$
$570$	0	0
$571$	7.35186e11	0.289424	0.144712	−	0.989474i	$-0.453774\pi$
$571$	7.35186e11	0.289424	0.144712	+	0.989474i	$0.453774\pi$
$572$	−7.08388e12	−2.76687
$573$	0	0
$574$	−1.05428e12	−0.405373
$575$	−6.99945e11	−0.267029
$576$	0	0
$577$	−4.52671e12	−1.70017	−0.850083	−	0.526649i	$-0.823448\pi$
$577$	−4.52671e12	−1.70017	−0.850083	+	0.526649i	$0.823448\pi$
$578$	1.62848e12	0.606886
$579$	0	0
$580$	4.86339e11	0.178449
$581$	−3.19073e12	−1.16171
$582$	0	0
$583$	−3.33227e12	−1.19463
$584$	−4.21206e12	−1.49843
$585$	0	0
$586$	−2.07955e12	−0.728501
$587$	1.38198e12	0.480429	0.240214	−	0.970720i	$-0.422782\pi$
$587$	1.38198e12	0.480429	0.240214	+	0.970720i	$0.422782\pi$
$588$	0	0
$589$	−2.22817e12	−0.762833
$590$	−1.15972e13	−3.94020
$591$	0	0
$592$	4.99371e12	1.67100
$593$	−4.26421e12	−1.41609	−0.708047	−	0.706165i	$-0.750424\pi$
$593$	−4.26421e12	−1.41609	−0.708047	+	0.706165i	$0.750424\pi$
$594$	0	0
$595$	−8.49535e12	−2.77878
$596$	6.70709e12	2.17734
$597$	0	0
$598$	−2.32580e12	−0.743732
$599$	−1.35010e12	−0.428493	−0.214246	−	0.976780i	$-0.568730\pi$
$599$	−1.35010e12	−0.428493	−0.214246	+	0.976780i	$0.568730\pi$
$600$	0	0
$601$	3.69329e12	1.15472	0.577362	−	0.816488i	$-0.304082\pi$
$601$	3.69329e12	1.15472	0.577362	+	0.816488i	$0.304082\pi$
$602$	1.50602e12	0.467355
$603$	0	0
$604$	−6.74186e12	−2.06117
$605$	−2.08108e12	−0.631525
$606$	0	0
$607$	−6.36583e12	−1.90329	−0.951647	−	0.307193i	$-0.900610\pi$
$607$	−6.36583e12	−1.90329	−0.951647	+	0.307193i	$0.900610\pi$
$608$	3.96856e12	1.17779
$609$	0	0
$610$	7.40768e12	2.16620
$611$	7.78374e12	2.25945
$612$	0	0
$613$	−1.03194e12	−0.295178	−0.147589	−	0.989049i	$-0.547151\pi$
$613$	−1.03194e12	−0.295178	−0.147589	+	0.989049i	$0.547151\pi$
$614$	3.89866e12	1.10702
$615$	0	0
$616$	1.07744e13	3.01494
$617$	−2.40238e12	−0.667357	−0.333679	−	0.942687i	$-0.608290\pi$
$617$	−2.40238e12	−0.667357	−0.333679	+	0.942687i	$0.608290\pi$
$618$	0	0
$619$	1.91546e12	0.524403	0.262201	−	0.965013i	$-0.415552\pi$
$619$	1.91546e12	0.524403	0.262201	+	0.965013i	$0.415552\pi$
$620$	−1.05411e13	−2.86500
$621$	0	0
$622$	−5.73978e11	−0.153758
$623$	−8.70847e12	−2.31604
$624$	0	0
$625$	−3.63482e12	−0.952845
$626$	−8.15340e12	−2.12204
$627$	0	0
$628$	−5.65659e12	−1.45123
$629$	3.69542e12	0.941318
$630$	0	0
$631$	4.65531e12	1.16901	0.584503	−	0.811391i	$-0.301289\pi$
$631$	4.65531e12	1.16901	0.584503	+	0.811391i	$0.301289\pi$
$632$	6.91597e12	1.72435
$633$	0	0
$634$	3.30322e12	0.811961
$635$	1.80547e12	0.440665
$636$	0	0
$637$	1.21679e13	2.92812
$638$	−3.06779e11	−0.0733047
$639$	0	0
$640$	−3.88248e12	−0.914742
$641$	−5.52343e12	−1.29225	−0.646127	−	0.763230i	$-0.723612\pi$
$641$	−5.52343e12	−1.29225	−0.646127	+	0.763230i	$0.723612\pi$
$642$	0	0
$643$	1.72571e12	0.398124	0.199062	−	0.979987i	$-0.436211\pi$
$643$	1.72571e12	0.398124	0.199062	+	0.979987i	$0.436211\pi$
$644$	4.34765e12	0.996021
$645$	0	0
$646$	8.20997e12	1.85479
$647$	5.22795e12	1.17290	0.586452	−	0.809984i	$-0.300524\pi$
$647$	5.22795e12	1.17290	0.586452	+	0.809984i	$0.300524\pi$
$648$	0	0
$649$	5.10965e12	1.13055
$650$	1.38452e13	3.04221
$651$	0	0
$652$	−3.64944e12	−0.790882
$653$	7.44348e12	1.60202	0.801008	−	0.598654i	$-0.204297\pi$
$653$	7.44348e12	1.60202	0.801008	+	0.598654i	$0.204297\pi$
$654$	0	0
$655$	−2.17122e12	−0.460912
$656$	1.28598e12	0.271124
$657$	0	0
$658$	−2.08314e13	−4.33213
$659$	1.96795e11	0.0406471	0.0203236	−	0.999793i	$-0.493530\pi$
$659$	1.96795e11	0.0406471	0.0203236	+	0.999793i	$0.493530\pi$
$660$	0	0
$661$	−5.13401e12	−1.04605	−0.523023	−	0.852319i	$-0.675196\pi$
$661$	−5.13401e12	−1.04605	−0.523023	+	0.852319i	$0.675196\pi$
$662$	1.40000e13	2.83314
$663$	0	0
$664$	8.29049e12	1.65510
$665$	−1.07052e13	−2.12275
$666$	0	0
$667$	−7.03524e10	−0.0137630
$668$	−2.17074e12	−0.421808
$669$	0	0
$670$	2.06790e13	3.96453
$671$	−3.26378e12	−0.621541
$672$	0	0
$673$	−8.52529e11	−0.160192	−0.0800961	−	0.996787i	$-0.525523\pi$
$673$	−8.52529e11	−0.160192	−0.0800961	+	0.996787i	$0.525523\pi$
$674$	−8.22534e12	−1.53527
$675$	0	0
$676$	1.95561e13	3.60182
$677$	1.41760e12	0.259361	0.129681	−	0.991556i	$-0.458605\pi$
$677$	1.41760e12	0.259361	0.129681	+	0.991556i	$0.458605\pi$
$678$	0	0
$679$	−1.00752e13	−1.81903
$680$	2.20735e13	3.95896
$681$	0	0
$682$	6.64925e12	1.17691
$683$	1.05881e12	0.186176	0.0930880	−	0.995658i	$-0.470326\pi$
$683$	1.05881e12	0.186176	0.0930880	+	0.995658i	$0.470326\pi$
$684$	0	0
$685$	1.16964e12	0.202976
$686$	−1.47883e13	−2.54954
$687$	0	0
$688$	−1.83700e12	−0.312580
$689$	1.51157e13	2.55531
$690$	0	0
$691$	−2.62758e12	−0.438434	−0.219217	−	0.975676i	$-0.570350\pi$
$691$	−2.62758e12	−0.438434	−0.219217	+	0.975676i	$0.570350\pi$
$692$	−9.03478e12	−1.49775
$693$	0	0
$694$	−1.49891e13	−2.45277
$695$	1.29402e12	0.210382
$696$	0	0
$697$	9.51648e11	0.152732
$698$	−4.41653e12	−0.704258
$699$	0	0
$700$	−2.58811e13	−4.07418
$701$	−4.78305e11	−0.0748124	−0.0374062	−	0.999300i	$-0.511910\pi$
$701$	−4.78305e11	−0.0748124	−0.0374062	+	0.999300i	$0.511910\pi$
$702$	0	0
$703$	4.65670e12	0.719084
$704$	−1.86029e12	−0.285432
$705$	0	0
$706$	−4.30555e12	−0.652241
$707$	−6.43845e12	−0.969156
$708$	0	0
$709$	−1.43959e12	−0.213959	−0.106979	−	0.994261i	$-0.534118\pi$
$709$	−1.43959e12	−0.213959	−0.106979	+	0.994261i	$0.534118\pi$
$710$	−2.72050e13	−4.01778
$711$	0	0
$712$	2.26272e13	3.29968
$713$	1.52485e12	0.220965
$714$	0	0
$715$	−1.19369e13	−1.70810
$716$	3.19193e12	0.453885
$717$	0	0
$718$	−4.36757e10	−0.00613310
$719$	5.06222e12	0.706417	0.353209	−	0.935545i	$-0.385091\pi$
$719$	5.06222e12	0.706417	0.353209	+	0.935545i	$0.385091\pi$
$720$	0	0
$721$	6.10363e12	0.841162
$722$	−2.95154e12	−0.404232
$723$	0	0
$724$	−1.59232e13	−2.15380
$725$	4.18799e11	0.0562970
$726$	0	0
$727$	7.74749e12	1.02862	0.514311	−	0.857604i	$-0.328048\pi$
$727$	7.74749e12	1.02862	0.514311	+	0.857604i	$0.328048\pi$
$728$	−4.88742e13	−6.44895
$729$	0	0
$730$	−1.24889e13	−1.62769
$731$	−1.35941e12	−0.176084
$732$	0	0
$733$	6.14525e10	0.00786270	0.00393135	−	0.999992i	$-0.498749\pi$
$733$	6.14525e10	0.00786270	0.00393135	+	0.999992i	$0.498749\pi$
$734$	−4.06411e12	−0.516813
$735$	0	0
$736$	−2.71588e12	−0.341162
$737$	−9.11103e12	−1.13753
$738$	0	0
$739$	1.45629e13	1.79617	0.898086	−	0.439819i	$-0.144957\pi$
$739$	1.45629e13	1.79617	0.898086	+	0.439819i	$0.144957\pi$
$740$	2.20302e13	2.70069
$741$	0	0
$742$	−4.04538e13	−4.89938
$743$	3.15672e12	0.380003	0.190001	−	0.981784i	$-0.439151\pi$
$743$	3.15672e12	0.380003	0.190001	+	0.981784i	$0.439151\pi$
$744$	0	0
$745$	1.13020e13	1.34416
$746$	−1.45640e13	−1.72169
$747$	0	0
$748$	−1.71127e13	−1.99877
$749$	5.59122e12	0.649141
$750$	0	0
$751$	−6.68968e12	−0.767407	−0.383704	−	0.923456i	$-0.625352\pi$
$751$	−6.68968e12	−0.767407	−0.383704	+	0.923456i	$0.625352\pi$
$752$	2.54095e13	2.89744
$753$	0	0
$754$	1.39160e12	0.156799
$755$	−1.13605e13	−1.27244
$756$	0	0
$757$	1.05129e12	0.116357	0.0581783	−	0.998306i	$-0.481471\pi$
$757$	1.05129e12	0.116357	0.0581783	+	0.998306i	$0.481471\pi$
$758$	−3.35525e11	−0.0369159
$759$	0	0
$760$	2.78154e13	3.02430
$761$	9.91519e12	1.07169	0.535846	−	0.844315i	$-0.319993\pi$
$761$	9.91519e12	1.07169	0.535846	+	0.844315i	$0.319993\pi$
$762$	0	0
$763$	−1.81142e13	−1.93490
$764$	2.63873e13	2.80205
$765$	0	0
$766$	−1.69845e13	−1.78247
$767$	−2.31782e13	−2.41825
$768$	0	0
$769$	8.72311e12	0.899503	0.449752	−	0.893154i	$-0.351512\pi$
$769$	8.72311e12	0.899503	0.449752	+	0.893154i	$0.351512\pi$
$770$	3.19463e13	3.27501
$771$	0	0
$772$	−3.09023e13	−3.13122
$773$	−4.56418e12	−0.459785	−0.229893	−	0.973216i	$-0.573837\pi$
$773$	−4.56418e12	−0.459785	−0.229893	+	0.973216i	$0.573837\pi$
$774$	0	0
$775$	−9.07724e12	−0.903849
$776$	2.61785e13	2.59159
$777$	0	0
$778$	2.28897e13	2.23991
$779$	1.19920e12	0.116673
$780$	0	0
$781$	1.19864e13	1.15281
$782$	−5.61849e12	−0.537266
$783$	0	0
$784$	3.97212e13	3.75492
$785$	−9.53178e12	−0.895902
$786$	0	0
$787$	3.65924e12	0.340020	0.170010	−	0.985442i	$-0.445620\pi$
$787$	3.65924e12	0.340020	0.170010	+	0.985442i	$0.445620\pi$
$788$	−1.02107e13	−0.943386
$789$	0	0
$790$	2.05060e13	1.87310
$791$	3.37025e13	3.06103
$792$	0	0
$793$	1.48050e13	1.32948
$794$	−2.56856e13	−2.29349
$795$	0	0
$796$	−5.66426e12	−0.500074
$797$	−5.96161e12	−0.523360	−0.261680	−	0.965155i	$-0.584277\pi$
$797$	−5.96161e12	−0.523360	−0.261680	+	0.965155i	$0.584277\pi$
$798$	0	0
$799$	1.88034e13	1.63221
$800$	1.61673e13	1.39551
$801$	0	0
$802$	−2.20551e13	−1.88245
$803$	5.50252e12	0.467027
$804$	0	0
$805$	7.32612e12	0.614883
$806$	−3.01621e13	−2.51741
$807$	0	0
$808$	1.67290e13	1.38076
$809$	−3.36558e12	−0.276243	−0.138121	−	0.990415i	$-0.544106\pi$
$809$	−3.36558e12	−0.276243	−0.138121	+	0.990415i	$0.544106\pi$
$810$	0	0
$811$	−1.91615e13	−1.55537	−0.777687	−	0.628651i	$-0.783607\pi$
$811$	−1.91615e13	−1.55537	−0.777687	+	0.628651i	$0.783607\pi$
$812$	−2.60134e12	−0.209988
$813$	0	0
$814$	−1.38964e13	−1.10941
$815$	−6.14958e12	−0.488243
$816$	0	0
$817$	−1.71303e12	−0.134513
$818$	−2.38410e13	−1.86181
$819$	0	0
$820$	5.67322e12	0.438195
$821$	−2.01302e13	−1.54634	−0.773169	−	0.634200i	$-0.781330\pi$
$821$	−2.01302e13	−1.54634	−0.773169	+	0.634200i	$0.781330\pi$
$822$	0	0
$823$	2.08369e12	0.158319	0.0791596	−	0.996862i	$-0.474776\pi$
$823$	2.08369e12	0.158319	0.0791596	+	0.996862i	$0.474776\pi$
$824$	−1.58591e13	−1.19841
$825$	0	0
$826$	6.20311e13	4.63660
$827$	1.11909e13	0.831934	0.415967	−	0.909380i	$-0.363443\pi$
$827$	1.11909e13	0.831934	0.415967	+	0.909380i	$0.363443\pi$
$828$	0	0
$829$	1.03196e13	0.758868	0.379434	−	0.925219i	$-0.376119\pi$
$829$	1.03196e13	0.758868	0.379434	+	0.925219i	$0.376119\pi$
$830$	2.45815e13	1.79787
$831$	0	0
$832$	8.43857e12	0.610540
$833$	2.93943e13	2.11525
$834$	0	0
$835$	−3.65787e12	−0.260399
$836$	−2.15642e13	−1.52688
$837$	0	0
$838$	3.70255e13	2.59360
$839$	8.02040e12	0.558814	0.279407	−	0.960173i	$-0.409862\pi$
$839$	8.02040e12	0.558814	0.279407	+	0.960173i	$0.409862\pi$
$840$	0	0
$841$	−1.44651e13	−0.997098
$842$	2.30100e13	1.57765
$843$	0	0
$844$	2.06456e13	1.40051
$845$	3.29535e13	2.22355
$846$	0	0
$847$	1.11313e13	0.743142
$848$	4.93442e13	3.27684
$849$	0	0
$850$	3.34462e13	2.19767
$851$	−3.18682e12	−0.208293
$852$	0	0
$853$	−1.47888e13	−0.956448	−0.478224	−	0.878238i	$-0.658719\pi$
$853$	−1.47888e13	−0.956448	−0.478224	+	0.878238i	$0.658719\pi$
$854$	−3.96223e13	−2.54905
$855$	0	0
$856$	−1.45277e13	−0.924836
$857$	9.11573e12	0.577268	0.288634	−	0.957439i	$-0.406799\pi$
$857$	9.11573e12	0.577268	0.288634	+	0.957439i	$0.406799\pi$
$858$	0	0
$859$	−2.57161e13	−1.61152	−0.805760	−	0.592242i	$-0.798243\pi$
$859$	−2.57161e13	−1.61152	−0.805760	+	0.592242i	$0.798243\pi$
$860$	−8.10406e12	−0.505196
$861$	0	0
$862$	1.44128e13	0.889130
$863$	1.98415e13	1.21766	0.608829	−	0.793302i	$-0.291640\pi$
$863$	1.98415e13	1.21766	0.608829	+	0.793302i	$0.291640\pi$
$864$	0	0
$865$	−1.52243e13	−0.924623
$866$	−3.77236e13	−2.27920
$867$	0	0
$868$	5.63825e13	3.37136
$869$	−9.03484e12	−0.537442
$870$	0	0
$871$	4.13291e13	2.43318
$872$	4.70662e13	2.75667
$873$	0	0
$874$	−7.08002e12	−0.410424
$875$	−1.88275e12	−0.108582
$876$	0	0
$877$	3.27261e13	1.86808	0.934041	−	0.357166i	$-0.116257\pi$
$877$	3.27261e13	1.86808	0.934041	+	0.357166i	$0.116257\pi$
$878$	−5.71016e13	−3.24282
$879$	0	0
$880$	−3.89671e13	−2.19041
$881$	1.23728e13	0.691950	0.345975	−	0.938244i	$-0.387548\pi$
$881$	1.23728e13	0.691950	0.345975	+	0.938244i	$0.387548\pi$
$882$	0	0
$883$	−2.40830e13	−1.33318	−0.666589	−	0.745426i	$-0.732246\pi$
$883$	−2.40830e13	−1.33318	−0.666589	+	0.745426i	$0.732246\pi$
$884$	7.76261e13	4.27536
$885$	0	0
$886$	−5.43337e13	−2.96222
$887$	1.12077e13	0.607941	0.303971	−	0.952681i	$-0.401688\pi$
$887$	1.12077e13	0.607941	0.303971	+	0.952681i	$0.401688\pi$
$888$	0	0
$889$	−9.65712e12	−0.518549
$890$	6.70905e13	3.58431
$891$	0	0
$892$	4.96817e13	2.62757
$893$	2.36947e13	1.24686
$894$	0	0
$895$	5.37865e12	0.280201
$896$	2.07666e13	1.07642
$897$	0	0
$898$	1.46901e13	0.753845
$899$	−9.12365e11	−0.0465854
$900$	0	0
$901$	3.65155e13	1.84593
$902$	−3.57862e12	−0.180006
$903$	0	0
$904$	−8.75693e13	−4.36108
$905$	−2.68318e13	−1.32963
$906$	0	0
$907$	9.35683e11	0.0459088	0.0229544	−	0.999737i	$-0.492693\pi$
$907$	9.35683e11	0.0459088	0.0229544	+	0.999737i	$0.492693\pi$
$908$	−7.93697e12	−0.387497
$909$	0	0
$910$	−1.44914e14	−7.00524
$911$	−1.46656e13	−0.705452	−0.352726	−	0.935727i	$-0.614745\pi$
$911$	−1.46656e13	−0.705452	−0.352726	+	0.935727i	$0.614745\pi$
$912$	0	0
$913$	−1.08305e13	−0.515857
$914$	5.38167e13	2.55070
$915$	0	0
$916$	−4.88692e13	−2.29354
$917$	1.16134e13	0.542374
$918$	0	0
$919$	−2.92432e13	−1.35240	−0.676199	−	0.736719i	$-0.736374\pi$
$919$	−2.92432e13	−1.35240	−0.676199	+	0.736719i	$0.736374\pi$
$920$	−1.90355e13	−0.876029
$921$	0	0
$922$	3.54029e13	1.61343
$923$	−5.43720e13	−2.46586
$924$	0	0
$925$	1.89707e13	0.852014
$926$	1.92821e13	0.861796
$927$	0	0
$928$	1.62500e12	0.0719262
$929$	7.23318e11	0.0318609	0.0159305	−	0.999873i	$-0.494929\pi$
$929$	7.23318e11	0.0318609	0.0159305	+	0.999873i	$0.494929\pi$
$930$	0	0
$931$	3.70406e13	1.61586
$932$	9.32273e13	4.04736
$933$	0	0
$934$	−4.40276e13	−1.89306
$935$	−2.88362e13	−1.23392
$936$	0	0
$937$	3.23620e13	1.37154	0.685768	−	0.727821i	$-0.259467\pi$
$937$	3.23620e13	1.37154	0.685768	+	0.727821i	$0.259467\pi$
$938$	−1.10608e14	−4.66523
$939$	0	0
$940$	1.12096e14	4.68290
$941$	−3.92794e12	−0.163309	−0.0816547	−	0.996661i	$-0.526020\pi$
$941$	−3.92794e12	−0.163309	−0.0816547	+	0.996661i	$0.526020\pi$
$942$	0	0
$943$	−8.20671e11	−0.0337961
$944$	−7.56636e13	−3.10108
$945$	0	0
$946$	5.11197e12	0.207529
$947$	−4.49509e13	−1.81620	−0.908099	−	0.418755i	$-0.862467\pi$
$947$	−4.49509e13	−1.81620	−0.908099	+	0.418755i	$0.862467\pi$
$948$	0	0
$949$	−2.49603e13	−0.998970
$950$	4.21465e13	1.67882
$951$	0	0
$952$	−1.18067e14	−4.65867
$953$	1.50521e13	0.591126	0.295563	−	0.955323i	$-0.404493\pi$
$953$	1.50521e13	0.591126	0.295563	+	0.955323i	$0.404493\pi$
$954$	0	0
$955$	4.44647e13	1.72982
$956$	−3.56686e13	−1.38110
$957$	0	0
$958$	−7.08536e13	−2.71780
$959$	−6.25618e12	−0.238850
$960$	0	0
$961$	−6.66464e12	−0.252070
$962$	6.30365e13	2.37303
$963$	0	0
$964$	1.71354e13	0.639068
$965$	−5.20728e13	−1.93303
$966$	0	0
$967$	−7.83639e12	−0.288202	−0.144101	−	0.989563i	$-0.546029\pi$
$967$	−7.83639e12	−0.288202	−0.144101	+	0.989563i	$0.546029\pi$
$968$	−2.89226e13	−1.05876
$969$	0	0
$970$	7.76199e13	2.81514
$971$	1.42988e13	0.516195	0.258098	−	0.966119i	$-0.416904\pi$
$971$	1.42988e13	0.516195	0.258098	+	0.966119i	$0.416904\pi$
$972$	0	0
$973$	−6.92147e12	−0.247566
$974$	5.91920e13	2.10741
$975$	0	0
$976$	4.83300e13	1.70488
$977$	−5.21673e13	−1.83178	−0.915888	−	0.401433i	$-0.868512\pi$
$977$	−5.21673e13	−1.83178	−0.915888	+	0.401433i	$0.868512\pi$
$978$	0	0
$979$	−2.95597e13	−1.02844
$980$	1.75234e14	6.06876
$981$	0	0
$982$	9.13271e13	3.13399
$983$	2.02089e13	0.690322	0.345161	−	0.938544i	$-0.387824\pi$
$983$	2.02089e13	0.690322	0.345161	+	0.938544i	$0.387824\pi$
$984$	0	0
$985$	−1.72059e13	−0.582390
$986$	3.36172e12	0.113270
$987$	0	0
$988$	9.78188e13	3.26600
$989$	1.17231e12	0.0389636
$990$	0	0
$991$	1.19883e13	0.394846	0.197423	−	0.980318i	$-0.436743\pi$
$991$	1.19883e13	0.394846	0.197423	+	0.980318i	$0.436743\pi$
$992$	−3.52209e13	−1.15478
$993$	0	0
$994$	1.45514e14	4.72788
$995$	−9.54470e12	−0.308716
$996$	0	0
$997$	−1.83297e13	−0.587525	−0.293763	−	0.955878i	$-0.594908\pi$
$997$	−1.83297e13	−0.587525	−0.293763	+	0.955878i	$0.594908\pi$
$998$	4.31999e13	1.37846
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.10.a.c.1.14		15
3.2	odd	2		43.10.a.a.1.2	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.2	✓	15	3.2	odd	2
387.10.a.c.1.14		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)

\(f(q)\)	\(=\)	\(q+41.2075 q^{2} +1186.05 q^{4} +1998.59 q^{5} -10690.1 q^{7} +27776.1 q^{8} +O(q^{10})\)	\(q+41.2075 q^{2} +1186.05 q^{4} +1998.59 q^{5} -10690.1 q^{7} +27776.1 q^{8} +82356.9 q^{10} -36286.0 q^{11} +164599. q^{13} -440512. q^{14} +537322. q^{16} +397627. q^{17} +501060. q^{19} +2.37044e6 q^{20} -1.49525e6 q^{22} -342901. q^{23} +2.04125e6 q^{25} +6.78271e6 q^{26} -1.26790e7 q^{28} +205168. q^{29} -4.44691e6 q^{31} +7.92032e6 q^{32} +1.63852e7 q^{34} -2.13651e7 q^{35} +9.29370e6 q^{37} +2.06474e7 q^{38} +5.55131e7 q^{40} +2.39332e6 q^{41} -3.41880e6 q^{43} -4.30372e7 q^{44} -1.41301e7 q^{46} +4.72891e7 q^{47} +7.39245e7 q^{49} +8.41146e7 q^{50} +1.95224e8 q^{52} +9.18336e7 q^{53} -7.25209e7 q^{55} -2.96929e8 q^{56} +8.45447e6 q^{58} -1.40816e8 q^{59} +8.99461e7 q^{61} -1.83246e8 q^{62} +5.12674e7 q^{64} +3.28967e8 q^{65} +2.51089e8 q^{67} +4.71607e8 q^{68} -8.80403e8 q^{70} -3.30330e8 q^{71} -1.51643e8 q^{73} +3.82970e8 q^{74} +5.94285e8 q^{76} +3.87900e8 q^{77} +2.48990e8 q^{79} +1.07389e9 q^{80} +9.86226e7 q^{82} +2.98476e8 q^{83} +7.94694e8 q^{85} -1.40880e8 q^{86} -1.00788e9 q^{88} +8.14630e8 q^{89} -1.75958e9 q^{91} -4.06699e8 q^{92} +1.94866e9 q^{94} +1.00142e9 q^{95} +9.42482e8 q^{97} +3.04624e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) \) 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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