LMFDB - Embedded newform 387.10.a.c.1.6

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			1.6
Root			$-17.0644$ 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)

$f(q)$	$=$	$q-15.0644 q^{2} -285.063 q^{4} -1876.98 q^{5} -7041.18 q^{7} +12007.3 q^{8} +O(q^{10})$	\(q-15.0644 q^{2} -285.063 q^{4} -1876.98 q^{5} -7041.18 q^{7} +12007.3 q^{8} +28275.7 q^{10} +2479.03 q^{11} +103059. q^{13} +106071. q^{14} -34931.2 q^{16} +529570. q^{17} -431982. q^{19} +535058. q^{20} -37345.2 q^{22} +100577. q^{23} +1.56994e6 q^{25} -1.55253e6 q^{26} +2.00718e6 q^{28} +7.09806e6 q^{29} -3.27053e6 q^{31} -5.62152e6 q^{32} -7.97768e6 q^{34} +1.32162e7 q^{35} -4.41240e6 q^{37} +6.50756e6 q^{38} -2.25375e7 q^{40} -1.81476e7 q^{41} -3.41880e6 q^{43} -706679. q^{44} -1.51514e6 q^{46} -5.52154e7 q^{47} +9.22462e6 q^{49} -2.36502e7 q^{50} -2.93783e7 q^{52} +8.53713e6 q^{53} -4.65310e6 q^{55} -8.45456e7 q^{56} -1.06928e8 q^{58} +1.92252e7 q^{59} -9.01048e6 q^{61} +4.92687e7 q^{62} +1.02570e8 q^{64} -1.93440e8 q^{65} +1.40140e8 q^{67} -1.50961e8 q^{68} -1.99094e8 q^{70} -2.63642e8 q^{71} -1.09424e8 q^{73} +6.64703e7 q^{74} +1.23142e8 q^{76} -1.74553e7 q^{77} -6.39726e7 q^{79} +6.55653e7 q^{80} +2.73383e8 q^{82} -4.71378e8 q^{83} -9.93994e8 q^{85} +5.15023e7 q^{86} +2.97665e7 q^{88} +1.07301e9 q^{89} -7.25657e8 q^{91} -2.86708e7 q^{92} +8.31790e8 q^{94} +8.10822e8 q^{95} -2.81023e8 q^{97} -1.38964e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−15.0644	−0.665761	−0.332880	−	0.942969i	$-0.608020\pi$
$2$	−15.0644	−0.665761	−0.332880	+	0.942969i	$0.608020\pi$
$3$	0	0
$3$	0	0
$4$	−285.063	−0.556763
$5$	−1876.98	−1.34306	−0.671530	−	0.740978i	$-0.734362\pi$
$5$	−1876.98	−1.34306	−0.671530	+	0.740978i	$0.734362\pi$
$6$	0	0
$7$	−7041.18	−1.10842	−0.554210	−	0.832377i	$-0.686980\pi$
$7$	−7041.18	−1.10842	−0.554210	+	0.832377i	$0.686980\pi$
$8$	12007.3	1.03643
$9$	0	0
$10$	28275.7	0.894156
$11$	2479.03	0.0510523	0.0255261	−	0.999674i	$-0.491874\pi$
$11$	2479.03	0.0510523	0.0255261	+	0.999674i	$0.491874\pi$
$12$	0	0
$13$	103059.	1.00079	0.500393	−	0.865799i	$-0.333189\pi$
$13$	103059.	1.00079	0.500393	+	0.865799i	$0.333189\pi$
$14$	106071.	0.737942
$15$	0	0
$16$	−34931.2	−0.133252
$17$	529570.	1.53781	0.768906	−	0.639361i	$-0.220801\pi$
$17$	529570.	1.53781	0.768906	+	0.639361i	$0.220801\pi$
$18$	0	0
$19$	−431982.	−0.760456	−0.380228	−	0.924893i	$-0.624154\pi$
$19$	−431982.	−0.760456	−0.380228	+	0.924893i	$0.624154\pi$
$20$	535058.	0.747766
$21$	0	0
$22$	−37345.2	−0.0339886
$23$	100577.	0.0749419	0.0374709	−	0.999298i	$-0.488070\pi$
$23$	100577.	0.0749419	0.0374709	+	0.999298i	$0.488070\pi$
$24$	0	0
$25$	1.56994e6	0.803808
$26$	−1.55253e6	−0.666283
$27$	0	0
$28$	2.00718e6	0.617127
$29$	7.09806e6	1.86358	0.931792	−	0.362994i	$-0.118245\pi$
$29$	7.09806e6	1.86358	0.931792	+	0.362994i	$0.118245\pi$
$30$	0	0
$31$	−3.27053e6	−0.636049	−0.318025	−	0.948082i	$-0.603020\pi$
$31$	−3.27053e6	−0.636049	−0.318025	+	0.948082i	$0.603020\pi$
$32$	−5.62152e6	−0.947717
$33$	0	0
$34$	−7.97768e6	−1.02381
$35$	1.32162e7	1.48867
$36$	0	0
$37$	−4.41240e6	−0.387050	−0.193525	−	0.981095i	$-0.561992\pi$
$37$	−4.41240e6	−0.387050	−0.193525	+	0.981095i	$0.561992\pi$
$38$	6.50756e6	0.506281
$39$	0	0
$40$	−2.25375e7	−1.39199
$41$	−1.81476e7	−1.00298	−0.501488	−	0.865164i	$-0.667214\pi$
$41$	−1.81476e7	−1.00298	−0.501488	+	0.865164i	$0.667214\pi$
$42$	0	0
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	−706679.	−0.0284240
$45$	0	0
$46$	−1.51514e6	−0.0498933
$47$	−5.52154e7	−1.65052	−0.825259	−	0.564755i	$-0.808971\pi$
$47$	−5.52154e7	−1.65052	−0.825259	+	0.564755i	$0.808971\pi$
$48$	0	0
$49$	9.22462e6	0.228595
$50$	−2.36502e7	−0.535144
$51$	0	0
$52$	−2.93783e7	−0.557200
$53$	8.53713e6	0.148618	0.0743089	−	0.997235i	$-0.476325\pi$
$53$	8.53713e6	0.148618	0.0743089	+	0.997235i	$0.476325\pi$
$54$	0	0
$55$	−4.65310e6	−0.0685662
$56$	−8.45456e7	−1.14880
$57$	0	0
$58$	−1.06928e8	−1.24070
$59$	1.92252e7	0.206556	0.103278	−	0.994653i	$-0.467067\pi$
$59$	1.92252e7	0.206556	0.103278	+	0.994653i	$0.467067\pi$
$60$	0	0
$61$	−9.01048e6	−0.0833228	−0.0416614	−	0.999132i	$-0.513265\pi$
$61$	−9.01048e6	−0.0833228	−0.0416614	+	0.999132i	$0.513265\pi$
$62$	4.92687e7	0.423457
$63$	0	0
$64$	1.02570e8	0.764205
$65$	−1.93440e8	−1.34411
$66$	0	0
$67$	1.40140e8	0.849625	0.424812	−	0.905281i	$-0.360340\pi$
$67$	1.40140e8	0.849625	0.424812	+	0.905281i	$0.360340\pi$
$68$	−1.50961e8	−0.856197
$69$	0	0
$70$	−1.99094e8	−0.991100
$71$	−2.63642e8	−1.23127	−0.615633	−	0.788033i	$-0.711100\pi$
$71$	−2.63642e8	−1.23127	−0.615633	+	0.788033i	$0.711100\pi$
$72$	0	0
$73$	−1.09424e8	−0.450982	−0.225491	−	0.974245i	$-0.572399\pi$
$73$	−1.09424e8	−0.450982	−0.225491	+	0.974245i	$0.572399\pi$
$74$	6.64703e7	0.257683
$75$	0	0
$76$	1.23142e8	0.423394
$77$	−1.74553e7	−0.0565874
$78$	0	0
$79$	−6.39726e7	−0.184787	−0.0923937	−	0.995723i	$-0.529452\pi$
$79$	−6.39726e7	−0.184787	−0.0923937	+	0.995723i	$0.529452\pi$
$80$	6.55653e7	0.178966
$81$	0	0
$82$	2.73383e8	0.667742
$83$	−4.71378e8	−1.09023	−0.545115	−	0.838362i	$-0.683514\pi$
$83$	−4.71378e8	−1.09023	−0.545115	+	0.838362i	$0.683514\pi$
$84$	0	0
$85$	−9.93994e8	−2.06537
$86$	5.15023e7	0.101528
$87$	0	0
$88$	2.97665e7	0.0529122
$89$	1.07301e9	1.81279	0.906395	−	0.422431i	$-0.138823\pi$
$89$	1.07301e9	1.81279	0.906395	+	0.422431i	$0.138823\pi$
$90$	0	0
$91$	−7.25657e8	−1.10929
$92$	−2.86708e7	−0.0417249
$93$	0	0
$94$	8.31790e8	1.09885
$95$	8.10822e8	1.02134
$96$	0	0
$97$	−2.81023e8	−0.322306	−0.161153	−	0.986929i	$-0.551521\pi$
$97$	−2.81023e8	−0.322306	−0.161153	+	0.986929i	$0.551521\pi$
$98$	−1.38964e8	−0.152189
$99$	0	0
$100$	−4.47531e8	−0.447531
$101$	−9.66718e8	−0.924387	−0.462193	−	0.886779i	$-0.652937\pi$
$101$	−9.66718e8	−0.924387	−0.462193	+	0.886779i	$0.652937\pi$
$102$	0	0
$103$	7.64929e8	0.669659	0.334829	−	0.942279i	$-0.391321\pi$
$103$	7.64929e8	0.669659	0.334829	+	0.942279i	$0.391321\pi$
$104$	1.23746e9	1.03725
$105$	0	0
$106$	−1.28607e8	−0.0989438
$107$	6.83281e8	0.503932	0.251966	−	0.967736i	$-0.418923\pi$
$107$	6.83281e8	0.503932	0.251966	+	0.967736i	$0.418923\pi$
$108$	0	0
$109$	1.06256e9	0.721001	0.360501	−	0.932759i	$-0.382606\pi$
$109$	1.06256e9	0.721001	0.360501	+	0.932759i	$0.382606\pi$
$110$	7.00963e7	0.0456487
$111$	0	0
$112$	2.45957e8	0.147699
$113$	2.75197e9	1.58778	0.793889	−	0.608062i	$-0.208053\pi$
$113$	2.75197e9	1.58778	0.793889	+	0.608062i	$0.208053\pi$
$114$	0	0
$115$	−1.88782e8	−0.100651
$116$	−2.02339e9	−1.03757
$117$	0	0
$118$	−2.89617e8	−0.137517
$119$	−3.72880e9	−1.70454
$120$	0	0
$121$	−2.35180e9	−0.997394
$122$	1.35738e8	0.0554730
$123$	0	0
$124$	9.32307e8	0.354129
$125$	7.19235e8	0.263497
$126$	0	0
$127$	4.95413e8	0.168986	0.0844929	−	0.996424i	$-0.473073\pi$
$127$	4.95413e8	0.168986	0.0844929	+	0.996424i	$0.473073\pi$
$128$	1.33306e9	0.438940
$129$	0	0
$130$	2.91407e9	0.894858
$131$	−3.75757e9	−1.11477	−0.557387	−	0.830253i	$-0.688196\pi$
$131$	−3.75757e9	−1.11477	−0.557387	+	0.830253i	$0.688196\pi$
$132$	0	0
$133$	3.04166e9	0.842904
$134$	−2.11114e9	−0.565646
$135$	0	0
$136$	6.35871e9	1.59384
$137$	5.56301e9	1.34917	0.674586	−	0.738197i	$-0.264322\pi$
$137$	5.56301e9	1.34917	0.674586	+	0.738197i	$0.264322\pi$
$138$	0	0
$139$	−2.23267e9	−0.507292	−0.253646	−	0.967297i	$-0.581630\pi$
$139$	−2.23267e9	−0.507292	−0.253646	+	0.967297i	$0.581630\pi$
$140$	−3.76744e9	−0.828838
$141$	0	0
$142$	3.97162e9	0.819728
$143$	2.55487e8	0.0510924
$144$	0	0
$145$	−1.33229e10	−2.50290
$146$	1.64841e9	0.300246
$147$	0	0
$148$	1.25781e9	0.215495
$149$	−2.53385e9	−0.421156	−0.210578	−	0.977577i	$-0.567535\pi$
$149$	−2.53385e9	−0.421156	−0.210578	+	0.977577i	$0.567535\pi$
$150$	0	0
$151$	−8.68661e9	−1.35973	−0.679867	−	0.733335i	$-0.737963\pi$
$151$	−8.68661e9	−1.35973	−0.679867	+	0.733335i	$0.737963\pi$
$152$	−5.18693e9	−0.788160
$153$	0	0
$154$	2.62955e8	0.0376736
$155$	6.13873e9	0.854252
$156$	0	0
$157$	−1.63159e8	−0.0214320	−0.0107160	−	0.999943i	$-0.503411\pi$
$157$	−1.63159e8	−0.0214320	−0.0107160	+	0.999943i	$0.503411\pi$
$158$	9.63712e8	0.123024
$159$	0	0
$160$	1.05515e10	1.27284
$161$	−7.08183e8	−0.0830671
$162$	0	0
$163$	−1.74840e10	−1.93998	−0.969991	−	0.243141i	$-0.921822\pi$
$163$	−1.74840e10	−1.93998	−0.969991	+	0.243141i	$0.921822\pi$
$164$	5.17319e9	0.558420
$165$	0	0
$166$	7.10104e9	0.725831
$167$	−1.29270e10	−1.28610	−0.643048	−	0.765826i	$-0.722331\pi$
$167$	−1.29270e10	−1.28610	−0.643048	+	0.765826i	$0.722331\pi$
$168$	0	0
$169$	1.66620e7	0.00157122
$170$	1.49740e10	1.37504
$171$	0	0
$172$	9.74572e8	0.0849055
$173$	−2.03436e10	−1.72671	−0.863356	−	0.504595i	$-0.831642\pi$
$173$	−2.03436e10	−1.72671	−0.863356	+	0.504595i	$0.831642\pi$
$174$	0	0
$175$	−1.10542e10	−0.890957
$176$	−8.65957e7	−0.00680282
$177$	0	0
$178$	−1.61643e10	−1.20688
$179$	1.34136e10	0.976581	0.488290	−	0.872681i	$-0.337621\pi$
$179$	1.34136e10	0.976581	0.488290	+	0.872681i	$0.337621\pi$
$180$	0	0
$181$	2.32509e10	1.61022	0.805111	−	0.593124i	$-0.202106\pi$
$181$	2.32509e10	1.61022	0.805111	+	0.593124i	$0.202106\pi$
$182$	1.09316e10	0.738522
$183$	0	0
$184$	1.20766e9	0.0776721
$185$	8.28199e9	0.519831
$186$	0	0
$187$	1.31282e9	0.0785088
$188$	1.57399e10	0.918947
$189$	0	0
$190$	−1.22146e10	−0.679966
$191$	2.42046e10	1.31598	0.657988	−	0.753029i	$-0.271408\pi$
$191$	2.42046e10	1.31598	0.657988	+	0.753029i	$0.271408\pi$
$192$	0	0
$193$	−2.49753e10	−1.29570	−0.647848	−	0.761770i	$-0.724331\pi$
$193$	−2.49753e10	−1.29570	−0.647848	+	0.761770i	$0.724331\pi$
$194$	4.23345e9	0.214579
$195$	0	0
$196$	−2.62959e9	−0.127273
$197$	1.22394e10	0.578977	0.289489	−	0.957181i	$-0.406515\pi$
$197$	1.22394e10	0.578977	0.289489	+	0.957181i	$0.406515\pi$
$198$	0	0
$199$	−2.35676e10	−1.06531	−0.532655	−	0.846332i	$-0.678806\pi$
$199$	−2.35676e10	−1.06531	−0.532655	+	0.846332i	$0.678806\pi$
$200$	1.88507e10	0.833092
$201$	0	0
$202$	1.45631e10	0.615420
$203$	−4.99787e10	−2.06563
$204$	0	0
$205$	3.40626e10	1.34706
$206$	−1.15232e10	−0.445832
$207$	0	0
$208$	−3.59998e9	−0.133357
$209$	−1.07090e9	−0.0388230
$210$	0	0
$211$	−5.46004e10	−1.89638	−0.948188	−	0.317710i	$-0.897086\pi$
$211$	−5.46004e10	−1.89638	−0.948188	+	0.317710i	$0.897086\pi$
$212$	−2.43362e9	−0.0827448
$213$	0	0
$214$	−1.02932e10	−0.335498
$215$	6.41703e9	0.204815
$216$	0	0
$217$	2.30284e10	0.705010
$218$	−1.60069e10	−0.480014
$219$	0	0
$220$	1.32642e9	0.0381751
$221$	5.45770e10	1.53902
$222$	0	0
$223$	2.69840e10	0.730693	0.365347	−	0.930872i	$-0.380950\pi$
$223$	2.69840e10	0.730693	0.365347	+	0.930872i	$0.380950\pi$
$224$	3.95821e10	1.05047
$225$	0	0
$226$	−4.14568e10	−1.05708
$227$	−2.28428e10	−0.570995	−0.285498	−	0.958379i	$-0.592159\pi$
$227$	−2.28428e10	−0.570995	−0.285498	+	0.958379i	$0.592159\pi$
$228$	0	0
$229$	4.78347e9	0.114943	0.0574716	−	0.998347i	$-0.481696\pi$
$229$	4.78347e9	0.114943	0.0574716	+	0.998347i	$0.481696\pi$
$230$	2.84389e9	0.0670097
$231$	0	0
$232$	8.52286e10	1.93148
$233$	−2.54149e10	−0.564920	−0.282460	−	0.959279i	$-0.591150\pi$
$233$	−2.54149e10	−0.564920	−0.282460	+	0.959279i	$0.591150\pi$
$234$	0	0
$235$	1.03638e11	2.21674
$236$	−5.48039e9	−0.115003
$237$	0	0
$238$	5.61723e10	1.13482
$239$	−4.29227e10	−0.850936	−0.425468	−	0.904974i	$-0.639890\pi$
$239$	−4.29227e10	−0.850936	−0.425468	+	0.904974i	$0.639890\pi$
$240$	0	0
$241$	3.36684e10	0.642903	0.321451	−	0.946926i	$-0.395829\pi$
$241$	3.36684e10	0.642903	0.321451	+	0.946926i	$0.395829\pi$
$242$	3.54286e10	0.664025
$243$	0	0
$244$	2.56855e9	0.0463910
$245$	−1.73145e10	−0.307016
$246$	0	0
$247$	−4.45196e10	−0.761053
$248$	−3.92703e10	−0.659222
$249$	0	0
$250$	−1.08349e10	−0.175426
$251$	−3.34718e10	−0.532289	−0.266145	−	0.963933i	$-0.585750\pi$
$251$	−3.34718e10	−0.532289	−0.266145	+	0.963933i	$0.585750\pi$
$252$	0	0
$253$	2.49334e8	0.00382595
$254$	−7.46311e9	−0.112504
$255$	0	0
$256$	−7.25976e10	−1.05643
$257$	3.86792e10	0.553068	0.276534	−	0.961004i	$-0.410814\pi$
$257$	3.86792e10	0.553068	0.276534	+	0.961004i	$0.410814\pi$
$258$	0	0
$259$	3.10685e10	0.429014
$260$	5.51425e10	0.748353
$261$	0	0
$262$	5.66057e10	0.742172
$263$	−3.69446e10	−0.476157	−0.238078	−	0.971246i	$-0.576517\pi$
$263$	−3.69446e10	−0.476157	−0.238078	+	0.971246i	$0.576517\pi$
$264$	0	0
$265$	−1.60240e10	−0.199602
$266$	−4.58209e10	−0.561172
$267$	0	0
$268$	−3.99488e10	−0.473039
$269$	1.65605e11	1.92836	0.964182	−	0.265242i	$-0.0854520\pi$
$269$	1.65605e11	1.92836	0.964182	+	0.265242i	$0.0854520\pi$
$270$	0	0
$271$	3.88648e10	0.437718	0.218859	−	0.975756i	$-0.429766\pi$
$271$	3.88648e10	0.437718	0.218859	+	0.975756i	$0.429766\pi$
$272$	−1.84985e10	−0.204917
$273$	0	0
$274$	−8.38036e10	−0.898225
$275$	3.89193e9	0.0410362
$276$	0	0
$277$	1.49820e10	0.152901	0.0764506	−	0.997073i	$-0.475641\pi$
$277$	1.49820e10	0.152901	0.0764506	+	0.997073i	$0.475641\pi$
$278$	3.36339e10	0.337735
$279$	0	0
$280$	1.58691e11	1.54291
$281$	1.83669e11	1.75734	0.878672	−	0.477425i	$-0.158430\pi$
$281$	1.83669e11	1.75734	0.878672	+	0.477425i	$0.158430\pi$
$282$	0	0
$283$	9.42540e10	0.873495	0.436748	−	0.899584i	$-0.356130\pi$
$283$	9.42540e10	0.873495	0.436748	+	0.899584i	$0.356130\pi$
$284$	7.51544e10	0.685523
$285$	0	0
$286$	−3.84876e9	−0.0340153
$287$	1.27780e11	1.11172
$288$	0	0
$289$	1.61857e11	1.36487
$290$	2.00703e11	1.66633
$291$	0	0
$292$	3.11926e10	0.251090
$293$	1.43511e11	1.13758	0.568790	−	0.822483i	$-0.307412\pi$
$293$	1.43511e11	1.13758	0.568790	+	0.822483i	$0.307412\pi$
$294$	0	0
$295$	−3.60854e10	−0.277417
$296$	−5.29810e10	−0.401151
$297$	0	0
$298$	3.81711e10	0.280389
$299$	1.03654e10	0.0750007
$300$	0	0
$301$	2.40724e10	0.169032
$302$	1.30859e11	0.905258
$303$	0	0
$304$	1.50897e10	0.101332
$305$	1.69125e10	0.111907
$306$	0	0
$307$	−2.47841e11	−1.59240	−0.796198	−	0.605037i	$-0.793158\pi$
$307$	−2.47841e11	−1.59240	−0.796198	+	0.605037i	$0.793158\pi$
$308$	4.97586e9	0.0315057
$309$	0	0
$310$	−9.24766e10	−0.568727
$311$	3.23810e11	1.96276	0.981382	−	0.192066i	$-0.0615187\pi$
$311$	3.23810e11	1.96276	0.981382	+	0.192066i	$0.0615187\pi$
$312$	0	0
$313$	2.55636e11	1.50547	0.752735	−	0.658323i	$-0.228734\pi$
$313$	2.55636e11	1.50547	0.752735	+	0.658323i	$0.228734\pi$
$314$	2.45790e9	0.0142686
$315$	0	0
$316$	1.82362e10	0.102883
$317$	−2.16477e11	−1.20405	−0.602025	−	0.798477i	$-0.705639\pi$
$317$	−2.16477e11	−1.20405	−0.602025	+	0.798477i	$0.705639\pi$
$318$	0	0
$319$	1.75963e10	0.0951402
$320$	−1.92522e11	−1.02637
$321$	0	0
$322$	1.06684e10	0.0553028
$323$	−2.28765e11	−1.16944
$324$	0	0
$325$	1.61796e11	0.804440
$326$	2.63387e11	1.29156
$327$	0	0
$328$	−2.17903e11	−1.03952
$329$	3.88782e11	1.82947
$330$	0	0
$331$	−4.68906e10	−0.214714	−0.107357	−	0.994221i	$-0.534239\pi$
$331$	−4.68906e10	−0.214714	−0.107357	+	0.994221i	$0.534239\pi$
$332$	1.34372e11	0.606999
$333$	0	0
$334$	1.94738e11	0.856232
$335$	−2.63041e11	−1.14110
$336$	0	0
$337$	−4.29929e11	−1.81578	−0.907888	−	0.419212i	$-0.862306\pi$
$337$	−4.29929e11	−1.81578	−0.907888	+	0.419212i	$0.862306\pi$
$338$	−2.51003e8	−0.00104605
$339$	0	0
$340$	2.83351e11	1.14992
$341$	−8.10776e9	−0.0324718
$342$	0	0
$343$	2.19185e11	0.855041
$344$	−4.10506e10	−0.158054
$345$	0	0
$346$	3.06465e11	1.14958
$347$	−3.36146e11	−1.24465	−0.622323	−	0.782761i	$-0.713811\pi$
$347$	−3.36146e11	−1.24465	−0.622323	+	0.782761i	$0.713811\pi$
$348$	0	0
$349$	9.78546e10	0.353075	0.176537	−	0.984294i	$-0.443510\pi$
$349$	9.78546e10	0.353075	0.176537	+	0.984294i	$0.443510\pi$
$350$	1.66526e11	0.593164
$351$	0	0
$352$	−1.39359e10	−0.0483831
$353$	1.75851e11	0.602778	0.301389	−	0.953501i	$-0.402550\pi$
$353$	1.75851e11	0.602778	0.301389	+	0.953501i	$0.402550\pi$
$354$	0	0
$355$	4.94851e11	1.65366
$356$	−3.05874e11	−1.00929
$357$	0	0
$358$	−2.02069e11	−0.650169
$359$	−5.43941e10	−0.172833	−0.0864165	−	0.996259i	$-0.527542\pi$
$359$	−5.43941e10	−0.172833	−0.0864165	+	0.996259i	$0.527542\pi$
$360$	0	0
$361$	−1.36080e11	−0.421707
$362$	−3.50261e11	−1.07202
$363$	0	0
$364$	2.06858e11	0.617612
$365$	2.05387e11	0.605695
$366$	0	0
$367$	3.85965e11	1.11058	0.555291	−	0.831656i	$-0.312607\pi$
$367$	3.85965e11	1.11058	0.555291	+	0.831656i	$0.312607\pi$
$368$	−3.51329e9	−0.00998616
$369$	0	0
$370$	−1.24764e11	−0.346083
$371$	−6.01115e10	−0.164731
$372$	0	0
$373$	−1.93481e11	−0.517545	−0.258772	−	0.965938i	$-0.583318\pi$
$373$	−1.93481e11	−0.517545	−0.258772	+	0.965938i	$0.583318\pi$
$374$	−1.97769e10	−0.0522681
$375$	0	0
$376$	−6.62989e11	−1.71065
$377$	7.31519e11	1.86505
$378$	0	0
$379$	1.36906e10	0.0340837	0.0170419	−	0.999855i	$-0.494575\pi$
$379$	1.36906e10	0.0340837	0.0170419	+	0.999855i	$0.494575\pi$
$380$	−2.31135e11	−0.568643
$381$	0	0
$382$	−3.64629e11	−0.876125
$383$	4.49622e11	1.06771	0.533855	−	0.845576i	$-0.320743\pi$
$383$	4.49622e11	1.06771	0.533855	+	0.845576i	$0.320743\pi$
$384$	0	0
$385$	3.27633e10	0.0760002
$386$	3.76239e11	0.862623
$387$	0	0
$388$	8.01090e10	0.179448
$389$	−3.88202e10	−0.0859577	−0.0429789	−	0.999076i	$-0.513685\pi$
$389$	−3.88202e10	−0.0859577	−0.0429789	+	0.999076i	$0.513685\pi$
$390$	0	0
$391$	5.32627e10	0.115247
$392$	1.10763e11	0.236923
$393$	0	0
$394$	−1.84379e11	−0.385460
$395$	1.20075e11	0.248180
$396$	0	0
$397$	−1.19424e11	−0.241288	−0.120644	−	0.992696i	$-0.538496\pi$
$397$	−1.19424e11	−0.241288	−0.120644	+	0.992696i	$0.538496\pi$
$398$	3.55032e11	0.709241
$399$	0	0
$400$	−5.48399e10	−0.107109
$401$	−6.09718e11	−1.17755	−0.588775	−	0.808297i	$-0.700390\pi$
$401$	−6.09718e11	−1.17755	−0.588775	+	0.808297i	$0.700390\pi$
$402$	0	0
$403$	−3.37058e11	−0.636549
$404$	2.75575e11	0.514664
$405$	0	0
$406$	7.52902e11	1.37522
$407$	−1.09385e10	−0.0197598
$408$	0	0
$409$	9.60444e9	0.0169714	0.00848569	−	0.999964i	$-0.497299\pi$
$409$	9.60444e9	0.0169714	0.00848569	+	0.999964i	$0.497299\pi$
$410$	−5.13135e11	−0.896817
$411$	0	0
$412$	−2.18053e11	−0.372841
$413$	−1.35368e11	−0.228950
$414$	0	0
$415$	8.84768e11	1.46424
$416$	−5.79348e11	−0.948462
$417$	0	0
$418$	1.61325e10	0.0258468
$419$	−3.47797e11	−0.551269	−0.275634	−	0.961263i	$-0.588888\pi$
$419$	−3.47797e11	−0.551269	−0.275634	+	0.961263i	$0.588888\pi$
$420$	0	0
$421$	−3.74682e11	−0.581291	−0.290645	−	0.956831i	$-0.593870\pi$
$421$	−3.74682e11	−0.581291	−0.290645	+	0.956831i	$0.593870\pi$
$422$	8.22524e11	1.26253
$423$	0	0
$424$	1.02508e11	0.154032
$425$	8.31393e11	1.23611
$426$	0	0
$427$	6.34444e10	0.0923566
$428$	−1.94778e11	−0.280571
$429$	0	0
$430$	−9.66690e10	−0.136357
$431$	1.23917e12	1.72975	0.864875	−	0.501987i	$-0.167397\pi$
$431$	1.23917e12	1.72975	0.864875	+	0.501987i	$0.167397\pi$
$432$	0	0
$433$	−5.28782e11	−0.722905	−0.361453	−	0.932390i	$-0.617719\pi$
$433$	−5.28782e11	−0.722905	−0.361453	+	0.932390i	$0.617719\pi$
$434$	−3.46910e11	−0.469368
$435$	0	0
$436$	−3.02897e11	−0.401427
$437$	−4.34475e10	−0.0569900
$438$	0	0
$439$	1.10920e12	1.42534	0.712669	−	0.701500i	$-0.247486\pi$
$439$	1.10920e12	1.42534	0.712669	+	0.701500i	$0.247486\pi$
$440$	−5.58712e10	−0.0710642
$441$	0	0
$442$	−8.22172e11	−1.02462
$443$	−1.21790e12	−1.50243	−0.751213	−	0.660059i	$-0.770531\pi$
$443$	−1.21790e12	−1.50243	−0.751213	+	0.660059i	$0.770531\pi$
$444$	0	0
$445$	−2.01402e12	−2.43469
$446$	−4.06500e11	−0.486467
$447$	0	0
$448$	−7.22213e11	−0.847060
$449$	9.78940e11	1.13670	0.568352	−	0.822785i	$-0.307581\pi$
$449$	9.78940e11	1.13670	0.568352	+	0.822785i	$0.307581\pi$
$450$	0	0
$451$	−4.49884e10	−0.0512042
$452$	−7.84482e11	−0.884016
$453$	0	0
$454$	3.44114e11	0.380146
$455$	1.36205e12	1.48984
$456$	0	0
$457$	9.91411e11	1.06324	0.531619	−	0.846983i	$-0.321584\pi$
$457$	9.91411e11	1.06324	0.531619	+	0.846983i	$0.321584\pi$
$458$	−7.20602e10	−0.0765246
$459$	0	0
$460$	5.38146e10	0.0560390
$461$	−1.84663e11	−0.190426	−0.0952130	−	0.995457i	$-0.530353\pi$
$461$	−1.84663e11	−0.190426	−0.0952130	+	0.995457i	$0.530353\pi$
$462$	0	0
$463$	8.46043e11	0.855614	0.427807	−	0.903870i	$-0.359286\pi$
$463$	8.46043e11	0.855614	0.427807	+	0.903870i	$0.359286\pi$
$464$	−2.47944e11	−0.248326
$465$	0	0
$466$	3.82861e11	0.376101
$467$	−1.63330e11	−0.158906	−0.0794530	−	0.996839i	$-0.525317\pi$
$467$	−1.63330e11	−0.158906	−0.0794530	+	0.996839i	$0.525317\pi$
$468$	0	0
$469$	−9.86755e11	−0.941741
$470$	−1.56125e12	−1.47582
$471$	0	0
$472$	2.30843e11	0.214081
$473$	−8.47532e9	−0.00778540
$474$	0	0
$475$	−6.78184e11	−0.611261
$476$	1.06294e12	0.949026
$477$	0	0
$478$	6.46607e11	0.566519
$479$	−1.37723e12	−1.19536	−0.597679	−	0.801736i	$-0.703910\pi$
$479$	−1.37723e12	−1.19536	−0.597679	+	0.801736i	$0.703910\pi$
$480$	0	0
$481$	−4.54737e11	−0.387354
$482$	−5.07195e11	−0.428019
$483$	0	0
$484$	6.70411e11	0.555312
$485$	5.27474e11	0.432876
$486$	0	0
$487$	−2.11605e12	−1.70469	−0.852347	−	0.522977i	$-0.824821\pi$
$487$	−2.11605e12	−1.70469	−0.852347	+	0.522977i	$0.824821\pi$
$488$	−1.08192e11	−0.0863583
$489$	0	0
$490$	2.60833e11	0.204399
$491$	1.23880e11	0.0961907	0.0480954	−	0.998843i	$-0.484685\pi$
$491$	1.23880e11	0.0961907	0.0480954	+	0.998843i	$0.484685\pi$
$492$	0	0
$493$	3.75892e12	2.86584
$494$	6.70663e11	0.506679
$495$	0	0
$496$	1.14244e11	0.0847549
$497$	1.85635e12	1.36476
$498$	0	0
$499$	−2.30366e10	−0.0166328	−0.00831641	−	0.999965i	$-0.502647\pi$
$499$	−2.30366e10	−0.0166328	−0.00831641	+	0.999965i	$0.502647\pi$
$500$	−2.05027e11	−0.146705
$501$	0	0
$502$	5.04234e11	0.354377
$503$	−1.75621e12	−1.22327	−0.611633	−	0.791142i	$-0.709487\pi$
$503$	−1.75621e12	−1.22327	−0.611633	+	0.791142i	$0.709487\pi$
$504$	0	0
$505$	1.81451e12	1.24151
$506$	−3.75608e9	−0.00254717
$507$	0	0
$508$	−1.41224e11	−0.0940850
$509$	−1.05347e12	−0.695650	−0.347825	−	0.937559i	$-0.613080\pi$
$509$	−1.05347e12	−0.695650	−0.347825	+	0.937559i	$0.613080\pi$
$510$	0	0
$511$	7.70473e11	0.499877
$512$	4.11115e11	0.264392
$513$	0	0
$514$	−5.82681e11	−0.368211
$515$	−1.43576e12	−0.899392
$516$	0	0
$517$	−1.36881e11	−0.0842627
$518$	−4.68030e11	−0.285620
$519$	0	0
$520$	−2.32269e12	−1.39308
$521$	7.44126e11	0.442463	0.221231	−	0.975221i	$-0.428992\pi$
$521$	7.44126e11	0.442463	0.221231	+	0.975221i	$0.428992\pi$
$522$	0	0
$523$	9.32642e11	0.545076	0.272538	−	0.962145i	$-0.412137\pi$
$523$	9.32642e11	0.545076	0.272538	+	0.962145i	$0.412137\pi$
$524$	1.07114e12	0.620664
$525$	0	0
$526$	5.56549e11	0.317006
$527$	−1.73198e12	−0.978125
$528$	0	0
$529$	−1.79104e12	−0.994384
$530$	2.41393e11	0.132887
$531$	0	0
$532$	−8.67064e11	−0.469298
$533$	−1.87027e12	−1.00376
$534$	0	0
$535$	−1.28251e12	−0.676811
$536$	1.68271e12	0.880577
$537$	0	0
$538$	−2.49475e12	−1.28383
$539$	2.28681e10	0.0116703
$540$	0	0
$541$	1.74928e12	0.877952	0.438976	−	0.898499i	$-0.355341\pi$
$541$	1.74928e12	0.877952	0.438976	+	0.898499i	$0.355341\pi$
$542$	−5.85477e11	−0.291416
$543$	0	0
$544$	−2.97699e12	−1.45741
$545$	−1.99441e12	−0.968347
$546$	0	0
$547$	−2.83590e12	−1.35440	−0.677202	−	0.735797i	$-0.736808\pi$
$547$	−2.83590e12	−1.35440	−0.677202	+	0.735797i	$0.736808\pi$
$548$	−1.58581e12	−0.751168
$549$	0	0
$550$	−5.86297e10	−0.0273203
$551$	−3.06623e12	−1.41717
$552$	0	0
$553$	4.50443e11	0.204822
$554$	−2.25695e11	−0.101796
$555$	0	0
$556$	6.36450e11	0.282441
$557$	4.44074e11	0.195482	0.0977410	−	0.995212i	$-0.468838\pi$
$557$	4.44074e11	0.195482	0.0977410	+	0.995212i	$0.468838\pi$
$558$	0	0
$559$	−3.52338e11	−0.152618
$560$	−4.61657e11	−0.198369
$561$	0	0
$562$	−2.76687e12	−1.16997
$563$	−2.66977e11	−0.111992	−0.0559959	−	0.998431i	$-0.517833\pi$
$563$	−2.66977e11	−0.111992	−0.0559959	+	0.998431i	$0.517833\pi$
$564$	0	0
$565$	−5.16539e12	−2.13248
$566$	−1.41988e12	−0.581539
$567$	0	0
$568$	−3.16563e12	−1.27612
$569$	−1.98776e12	−0.794985	−0.397492	−	0.917606i	$-0.630119\pi$
$569$	−1.98776e12	−0.794985	−0.397492	+	0.917606i	$0.630119\pi$
$570$	0	0
$571$	1.77358e11	0.0698215	0.0349107	−	0.999390i	$-0.488885\pi$
$571$	1.77358e11	0.0698215	0.0349107	+	0.999390i	$0.488885\pi$
$572$	−7.28297e10	−0.0284463
$573$	0	0
$574$	−1.92494e12	−0.740139
$575$	1.57900e11	0.0602389
$576$	0	0
$577$	−2.44961e12	−0.920039	−0.460020	−	0.887909i	$-0.652158\pi$
$577$	−2.44961e12	−0.920039	−0.460020	+	0.887909i	$0.652158\pi$
$578$	−2.43828e12	−0.908675
$579$	0	0
$580$	3.79787e12	1.39352
$581$	3.31906e12	1.20843
$582$	0	0
$583$	2.11638e10	0.00758727
$584$	−1.31389e12	−0.467412
$585$	0	0
$586$	−2.16192e12	−0.757356
$587$	3.96669e12	1.37898	0.689488	−	0.724297i	$-0.257836\pi$
$587$	3.96669e12	1.37898	0.689488	+	0.724297i	$0.257836\pi$
$588$	0	0
$589$	1.41281e12	0.483687
$590$	5.43606e11	0.184693
$591$	0	0
$592$	1.54131e11	0.0515752
$593$	1.37473e12	0.456531	0.228265	−	0.973599i	$-0.426695\pi$
$593$	1.37473e12	0.456531	0.228265	+	0.973599i	$0.426695\pi$
$594$	0	0
$595$	6.99889e12	2.28930
$596$	7.22307e11	0.234484
$597$	0	0
$598$	−1.56149e11	−0.0499325
$599$	1.83622e12	0.582779	0.291389	−	0.956605i	$-0.405882\pi$
$599$	1.83622e12	0.582779	0.291389	+	0.956605i	$0.405882\pi$
$600$	0	0
$601$	2.11756e12	0.662064	0.331032	−	0.943620i	$-0.392603\pi$
$601$	2.11756e12	0.662064	0.331032	+	0.943620i	$0.392603\pi$
$602$	−3.62637e11	−0.112535
$603$	0	0
$604$	2.47623e12	0.757050
$605$	4.41429e12	1.33956
$606$	0	0
$607$	6.21202e12	1.85731	0.928654	−	0.370947i	$-0.120967\pi$
$607$	6.21202e12	1.85731	0.928654	+	0.370947i	$0.120967\pi$
$608$	2.42839e12	0.720697
$609$	0	0
$610$	−2.54778e11	−0.0745035
$611$	−5.69045e12	−1.65181
$612$	0	0
$613$	1.80823e12	0.517228	0.258614	−	0.965981i	$-0.416734\pi$
$613$	1.80823e12	0.517228	0.258614	+	0.965981i	$0.416734\pi$
$614$	3.73359e12	1.06015
$615$	0	0
$616$	−2.09591e11	−0.0586489
$617$	5.17980e11	0.143890	0.0719449	−	0.997409i	$-0.477079\pi$
$617$	5.17980e11	0.143890	0.0719449	+	0.997409i	$0.477079\pi$
$618$	0	0
$619$	4.80654e12	1.31591	0.657953	−	0.753059i	$-0.271423\pi$
$619$	4.80654e12	1.31591	0.657953	+	0.753059i	$0.271423\pi$
$620$	−1.74992e12	−0.475616
$621$	0	0
$622$	−4.87801e12	−1.30673
$623$	−7.55524e12	−2.00933
$624$	0	0
$625$	−4.41628e12	−1.15770
$626$	−3.85101e12	−1.00228
$627$	0	0
$628$	4.65106e10	0.0119326
$629$	−2.33667e12	−0.595210
$630$	0	0
$631$	6.50796e12	1.63423	0.817114	−	0.576476i	$-0.195572\pi$
$631$	6.50796e12	1.63423	0.817114	+	0.576476i	$0.195572\pi$
$632$	−7.68138e11	−0.191519
$633$	0	0
$634$	3.26110e12	0.801609
$635$	−9.29881e11	−0.226958
$636$	0	0
$637$	9.50680e11	0.228774
$638$	−2.65079e11	−0.0633406
$639$	0	0
$640$	−2.50213e12	−0.589522
$641$	3.48179e12	0.814595	0.407297	−	0.913296i	$-0.366471\pi$
$641$	3.48179e12	0.814595	0.407297	+	0.913296i	$0.366471\pi$
$642$	0	0
$643$	−1.58721e12	−0.366172	−0.183086	−	0.983097i	$-0.558609\pi$
$643$	−1.58721e12	−0.366172	−0.183086	+	0.983097i	$0.558609\pi$
$644$	2.01876e11	0.0462487
$645$	0	0
$646$	3.44621e12	0.778566
$647$	1.50095e12	0.336741	0.168371	−	0.985724i	$-0.446149\pi$
$647$	1.50095e12	0.336741	0.168371	+	0.985724i	$0.446149\pi$
$648$	0	0
$649$	4.76599e10	0.0105451
$650$	−2.43737e12	−0.535564
$651$	0	0
$652$	4.98405e12	1.08011
$653$	6.01788e12	1.29519	0.647596	−	0.761984i	$-0.275774\pi$
$653$	6.01788e12	1.29519	0.647596	+	0.761984i	$0.275774\pi$
$654$	0	0
$655$	7.05290e12	1.49721
$656$	6.33917e11	0.133649
$657$	0	0
$658$	−5.85678e12	−1.21799
$659$	−6.45564e12	−1.33338	−0.666691	−	0.745334i	$-0.732290\pi$
$659$	−6.45564e12	−1.33338	−0.666691	+	0.745334i	$0.732290\pi$
$660$	0	0
$661$	6.32975e12	1.28967	0.644837	−	0.764320i	$-0.276925\pi$
$661$	6.32975e12	1.28967	0.644837	+	0.764320i	$0.276925\pi$
$662$	7.06380e11	0.142948
$663$	0	0
$664$	−5.65998e12	−1.12995
$665$	−5.70914e12	−1.13207
$666$	0	0
$667$	7.13904e11	0.139660
$668$	3.68500e12	0.716051
$669$	0	0
$670$	3.96257e12	0.759697
$671$	−2.23373e10	−0.00425382
$672$	0	0
$673$	−2.05876e12	−0.386846	−0.193423	−	0.981115i	$-0.561959\pi$
$673$	−2.05876e12	−0.386846	−0.193423	+	0.981115i	$0.561959\pi$
$674$	6.47664e12	1.20887
$675$	0	0
$676$	−4.74970e9	−0.000874795 0
$677$	−1.82789e12	−0.334427	−0.167213	−	0.985921i	$-0.553477\pi$
$677$	−1.82789e12	−0.334427	−0.167213	+	0.985921i	$0.553477\pi$
$678$	0	0
$679$	1.97873e12	0.357250
$680$	−1.19352e13	−2.14062
$681$	0	0
$682$	1.22139e11	0.0216184
$683$	5.70420e11	0.100300	0.0501501	−	0.998742i	$-0.484030\pi$
$683$	5.70420e11	0.100300	0.0501501	+	0.998742i	$0.484030\pi$
$684$	0	0
$685$	−1.04417e13	−1.81202
$686$	−3.30190e12	−0.569253
$687$	0	0
$688$	1.19423e11	0.0203208
$689$	8.79829e11	0.148734
$690$	0	0
$691$	7.86912e11	0.131303	0.0656515	−	0.997843i	$-0.479087\pi$
$691$	7.86912e11	0.131303	0.0656515	+	0.997843i	$0.479087\pi$
$692$	5.79919e12	0.961369
$693$	0	0
$694$	5.06386e12	0.828636
$695$	4.19068e12	0.681323
$696$	0	0
$697$	−9.61040e12	−1.54239
$698$	−1.47413e12	−0.235063
$699$	0	0
$700$	3.15114e12	0.496052
$701$	−5.46260e12	−0.854415	−0.427207	−	0.904154i	$-0.640503\pi$
$701$	−5.46260e12	−0.854415	−0.427207	+	0.904154i	$0.640503\pi$
$702$	0	0
$703$	1.90607e12	0.294334
$704$	2.54274e11	0.0390144
$705$	0	0
$706$	−2.64909e12	−0.401306
$707$	6.80684e12	1.02461
$708$	0	0
$709$	−7.21721e12	−1.07266	−0.536329	−	0.844009i	$-0.680189\pi$
$709$	−7.21721e12	−1.07266	−0.536329	+	0.844009i	$0.680189\pi$
$710$	−7.45466e12	−1.10094
$711$	0	0
$712$	1.28839e13	1.87883
$713$	−3.28941e11	−0.0476667
$714$	0	0
$715$	−4.79544e11	−0.0686201
$716$	−3.82373e12	−0.543724
$717$	0	0
$718$	8.19416e11	0.115065
$719$	9.38428e12	1.30955	0.654773	−	0.755825i	$-0.272764\pi$
$719$	9.38428e12	1.30955	0.654773	+	0.755825i	$0.272764\pi$
$720$	0	0
$721$	−5.38600e12	−0.742263
$722$	2.04996e12	0.280756
$723$	0	0
$724$	−6.62795e12	−0.896512
$725$	1.11435e13	1.49796
$726$	0	0
$727$	−1.35930e13	−1.80472	−0.902362	−	0.430980i	$-0.858168\pi$
$727$	−1.35930e13	−1.80472	−0.902362	+	0.430980i	$0.858168\pi$
$728$	−8.71319e12	−1.14970
$729$	0	0
$730$	−3.09403e12	−0.403248
$731$	−1.81050e12	−0.234514
$732$	0	0
$733$	−1.32485e13	−1.69512	−0.847559	−	0.530701i	$-0.821929\pi$
$733$	−1.32485e13	−1.69512	−0.847559	+	0.530701i	$0.821929\pi$
$734$	−5.81435e12	−0.739382
$735$	0	0
$736$	−5.65397e11	−0.0710237
$737$	3.47413e11	0.0433753
$738$	0	0
$739$	−6.06380e10	−0.00747903	−0.00373951	−	0.999993i	$-0.501190\pi$
$739$	−6.06380e10	−0.00747903	−0.00373951	+	0.999993i	$0.501190\pi$
$740$	−2.36089e12	−0.289423
$741$	0	0
$742$	9.05546e11	0.109671
$743$	−8.45052e12	−1.01726	−0.508632	−	0.860984i	$-0.669849\pi$
$743$	−8.45052e12	−1.01726	−0.508632	+	0.860984i	$0.669849\pi$
$744$	0	0
$745$	4.75600e12	0.565638
$746$	2.91468e12	0.344561
$747$	0	0
$748$	−3.74236e11	−0.0437108
$749$	−4.81110e12	−0.558569
$750$	0	0
$751$	5.00951e12	0.574666	0.287333	−	0.957831i	$-0.407231\pi$
$751$	5.00951e12	0.574666	0.287333	+	0.957831i	$0.407231\pi$
$752$	1.92874e12	0.219935
$753$	0	0
$754$	−1.10199e13	−1.24167
$755$	1.63046e13	1.82620
$756$	0	0
$757$	5.80549e12	0.642551	0.321276	−	0.946986i	$-0.395888\pi$
$757$	5.80549e12	0.642551	0.321276	+	0.946986i	$0.395888\pi$
$758$	−2.06242e11	−0.0226916
$759$	0	0
$760$	9.73578e12	1.05855
$761$	−1.32066e13	−1.42745	−0.713723	−	0.700429i	$-0.752992\pi$
$761$	−1.32066e13	−1.42745	−0.713723	+	0.700429i	$0.752992\pi$
$762$	0	0
$763$	−7.48171e12	−0.799172
$764$	−6.89983e12	−0.732686
$765$	0	0
$766$	−6.77331e12	−0.710839
$767$	1.98133e12	0.206718
$768$	0	0
$769$	−8.98106e12	−0.926102	−0.463051	−	0.886332i	$-0.653245\pi$
$769$	−8.98106e12	−0.926102	−0.463051	+	0.886332i	$0.653245\pi$
$770$	−4.93561e11	−0.0505979
$771$	0	0
$772$	7.11952e12	0.721395
$773$	3.75046e12	0.377813	0.188906	−	0.981995i	$-0.439506\pi$
$773$	3.75046e12	0.377813	0.188906	+	0.981995i	$0.439506\pi$
$774$	0	0
$775$	−5.13453e12	−0.511262
$776$	−3.37432e12	−0.334048
$777$	0	0
$778$	5.84805e11	0.0572272
$779$	7.83941e12	0.762719
$780$	0	0
$781$	−6.53577e11	−0.0628589
$782$	−8.02373e11	−0.0767266
$783$	0	0
$784$	−3.22228e11	−0.0304607
$785$	3.06247e11	0.0287845
$786$	0	0
$787$	8.97788e12	0.834233	0.417117	−	0.908853i	$-0.363041\pi$
$787$	8.97788e12	0.834233	0.417117	+	0.908853i	$0.363041\pi$
$788$	−3.48899e12	−0.322353
$789$	0	0
$790$	−1.80887e12	−0.165229
$791$	−1.93771e13	−1.75993
$792$	0	0
$793$	−9.28611e11	−0.0833882
$794$	1.79906e12	0.160640
$795$	0	0
$796$	6.71823e12	0.593125
$797$	9.78357e12	0.858884	0.429442	−	0.903094i	$-0.358710\pi$
$797$	9.78357e12	0.858884	0.429442	+	0.903094i	$0.358710\pi$
$798$	0	0
$799$	−2.92405e13	−2.53819
$800$	−8.82544e12	−0.761783
$801$	0	0
$802$	9.18507e12	0.783967
$803$	−2.71265e11	−0.0230236
$804$	0	0
$805$	1.32925e12	0.111564
$806$	5.07759e12	0.423789
$807$	0	0
$808$	−1.16077e13	−0.958063
$809$	2.21862e13	1.82102	0.910511	−	0.413485i	$-0.135689\pi$
$809$	2.21862e13	1.82102	0.910511	+	0.413485i	$0.135689\pi$
$810$	0	0
$811$	2.78479e12	0.226047	0.113023	−	0.993592i	$-0.463946\pi$
$811$	2.78479e12	0.226047	0.113023	+	0.993592i	$0.463946\pi$
$812$	1.42471e13	1.15007
$813$	0	0
$814$	1.64782e11	0.0131553
$815$	3.28172e13	2.60551
$816$	0	0
$817$	1.47686e12	0.115968
$818$	−1.44685e11	−0.0112989
$819$	0	0
$820$	−9.70998e12	−0.749991
$821$	−1.16501e13	−0.894920	−0.447460	−	0.894304i	$-0.647671\pi$
$821$	−1.16501e13	−0.894920	−0.447460	+	0.894304i	$0.647671\pi$
$822$	0	0
$823$	8.62542e11	0.0655361	0.0327681	−	0.999463i	$-0.489568\pi$
$823$	8.62542e11	0.0655361	0.0327681	+	0.999463i	$0.489568\pi$
$824$	9.18473e12	0.694055
$825$	0	0
$826$	2.03925e12	0.152426
$827$	−3.07127e12	−0.228320	−0.114160	−	0.993462i	$-0.536418\pi$
$827$	−3.07127e12	−0.228320	−0.114160	+	0.993462i	$0.536418\pi$
$828$	0	0
$829$	1.65764e13	1.21897	0.609487	−	0.792796i	$-0.291375\pi$
$829$	1.65764e13	1.21897	0.609487	+	0.792796i	$0.291375\pi$
$830$	−1.33285e13	−0.974835
$831$	0	0
$832$	1.05707e13	0.764805
$833$	4.88509e12	0.351536
$834$	0	0
$835$	2.42637e13	1.72730
$836$	3.05272e11	0.0216152
$837$	0	0
$838$	5.23937e12	0.367013
$839$	−9.91022e12	−0.690486	−0.345243	−	0.938513i	$-0.612203\pi$
$839$	−9.91022e12	−0.690486	−0.345243	+	0.938513i	$0.612203\pi$
$840$	0	0
$841$	3.58753e13	2.47294
$842$	5.64437e12	0.387000
$843$	0	0
$844$	1.55645e13	1.05583
$845$	−3.12742e10	−0.00211024
$846$	0	0
$847$	1.65595e13	1.10553
$848$	−2.98213e11	−0.0198036
$849$	0	0
$850$	−1.25245e13	−0.822951
$851$	−4.43787e11	−0.0290062
$852$	0	0
$853$	−2.84458e13	−1.83970	−0.919852	−	0.392266i	$-0.871691\pi$
$853$	−2.84458e13	−1.83970	−0.919852	+	0.392266i	$0.871691\pi$
$854$	−9.55755e11	−0.0614874
$855$	0	0
$856$	8.20436e12	0.522291
$857$	9.16254e12	0.580232	0.290116	−	0.956991i	$-0.406306\pi$
$857$	9.16254e12	0.580232	0.290116	+	0.956991i	$0.406306\pi$
$858$	0	0
$859$	−1.59098e13	−0.997002	−0.498501	−	0.866889i	$-0.666116\pi$
$859$	−1.59098e13	−0.997002	−0.498501	+	0.866889i	$0.666116\pi$
$860$	−1.82926e12	−0.114033
$861$	0	0
$862$	−1.86674e13	−1.15160
$863$	6.71369e12	0.412015	0.206007	−	0.978550i	$-0.433953\pi$
$863$	6.71369e12	0.412015	0.206007	+	0.978550i	$0.433953\pi$
$864$	0	0
$865$	3.81845e13	2.31908
$866$	7.96581e12	0.481282
$867$	0	0
$868$	−6.56454e12	−0.392523
$869$	−1.58590e11	−0.00943381
$870$	0	0
$871$	1.44427e13	0.850292
$872$	1.27585e13	0.747268
$873$	0	0
$874$	6.54513e11	0.0379417
$875$	−5.06426e12	−0.292065
$876$	0	0
$877$	4.21446e12	0.240571	0.120286	−	0.992739i	$-0.461619\pi$
$877$	4.21446e12	0.240571	0.120286	+	0.992739i	$0.461619\pi$
$878$	−1.67094e13	−0.948934
$879$	0	0
$880$	1.62539e11	0.00913660
$881$	8.50983e12	0.475915	0.237957	−	0.971276i	$-0.423522\pi$
$881$	8.50983e12	0.475915	0.237957	+	0.971276i	$0.423522\pi$
$882$	0	0
$883$	2.12668e13	1.17728	0.588639	−	0.808396i	$-0.299664\pi$
$883$	2.12668e13	1.17728	0.588639	+	0.808396i	$0.299664\pi$
$884$	−1.55579e13	−0.856869
$885$	0	0
$886$	1.83469e13	1.00026
$887$	2.61674e13	1.41940	0.709700	−	0.704504i	$-0.248830\pi$
$887$	2.61674e13	1.41940	0.709700	+	0.704504i	$0.248830\pi$
$888$	0	0
$889$	−3.48829e12	−0.187307
$890$	3.03400e13	1.62092
$891$	0	0
$892$	−7.69214e12	−0.406823
$893$	2.38521e13	1.25515
$894$	0	0
$895$	−2.51772e13	−1.31161
$896$	−9.38632e12	−0.486530
$897$	0	0
$898$	−1.47472e13	−0.756773
$899$	−2.32144e13	−1.18533
$900$	0	0
$901$	4.52101e12	0.228546
$902$	6.77725e11	0.0340898
$903$	0	0
$904$	3.30437e13	1.64562
$905$	−4.36415e13	−2.16262
$906$	0	0
$907$	1.63634e13	0.802861	0.401431	−	0.915889i	$-0.368513\pi$
$907$	1.63634e13	0.802861	0.401431	+	0.915889i	$0.368513\pi$
$908$	6.51162e12	0.317909
$909$	0	0
$910$	−2.05185e13	−0.991878
$911$	3.39916e13	1.63508	0.817540	−	0.575872i	$-0.195337\pi$
$911$	3.39916e13	1.63508	0.817540	+	0.575872i	$0.195337\pi$
$912$	0	0
$913$	−1.16856e12	−0.0556587
$914$	−1.49350e13	−0.707862
$915$	0	0
$916$	−1.36359e12	−0.0639961
$917$	2.64577e13	1.23564
$918$	0	0
$919$	−2.19737e12	−0.101621	−0.0508106	−	0.998708i	$-0.516180\pi$
$919$	−2.19737e12	−0.101621	−0.0508106	+	0.998708i	$0.516180\pi$
$920$	−2.26676e12	−0.104318
$921$	0	0
$922$	2.78185e12	0.126778
$923$	−2.71707e13	−1.23223
$924$	0	0
$925$	−6.92719e12	−0.311114
$926$	−1.27452e13	−0.569634
$927$	0	0
$928$	−3.99019e13	−1.76615
$929$	1.08879e12	0.0479596	0.0239798	−	0.999712i	$-0.492366\pi$
$929$	1.08879e12	0.0479596	0.0239798	+	0.999712i	$0.492366\pi$
$930$	0	0
$931$	−3.98487e12	−0.173836
$932$	7.24484e12	0.314526
$933$	0	0
$934$	2.46048e12	0.105793
$935$	−2.46414e12	−0.105442
$936$	0	0
$937$	3.72812e13	1.58002	0.790008	−	0.613096i	$-0.210076\pi$
$937$	3.72812e13	1.58002	0.790008	+	0.613096i	$0.210076\pi$
$938$	1.48649e13	0.626974
$939$	0	0
$940$	−2.95434e13	−1.23420
$941$	−1.01973e13	−0.423966	−0.211983	−	0.977273i	$-0.567992\pi$
$941$	−1.01973e13	−0.423966	−0.211983	+	0.977273i	$0.567992\pi$
$942$	0	0
$943$	−1.82523e12	−0.0751649
$944$	−6.71561e11	−0.0275240
$945$	0	0
$946$	1.27676e11	0.00518321
$947$	1.73267e13	0.700070	0.350035	−	0.936737i	$-0.386170\pi$
$947$	1.73267e13	0.700070	0.350035	+	0.936737i	$0.386170\pi$
$948$	0	0
$949$	−1.12771e13	−0.451336
$950$	1.02165e13	0.406953
$951$	0	0
$952$	−4.47728e13	−1.76664
$953$	3.24945e13	1.27612	0.638060	−	0.769986i	$-0.279737\pi$
$953$	3.24945e13	1.27612	0.638060	+	0.769986i	$0.279737\pi$
$954$	0	0
$955$	−4.54316e13	−1.76743
$956$	1.22357e13	0.473769
$957$	0	0
$958$	2.07473e13	0.795822
$959$	−3.91701e13	−1.49545
$960$	0	0
$961$	−1.57432e13	−0.595441
$962$	6.85037e12	0.257885
$963$	0	0
$964$	−9.59759e12	−0.357944
$965$	4.68782e13	1.74020
$966$	0	0
$967$	−2.07087e13	−0.761611	−0.380805	−	0.924655i	$-0.624353\pi$
$967$	−2.07087e13	−0.761611	−0.380805	+	0.924655i	$0.624353\pi$
$968$	−2.82388e13	−1.03373
$969$	0	0
$970$	−7.94611e12	−0.288192
$971$	−3.71042e13	−1.33948	−0.669740	−	0.742596i	$-0.733594\pi$
$971$	−3.71042e13	−1.33948	−0.669740	+	0.742596i	$0.733594\pi$
$972$	0	0
$973$	1.57206e13	0.562292
$974$	3.18772e13	1.13492
$975$	0	0
$976$	3.14747e11	0.0111029
$977$	1.12430e13	0.394783	0.197392	−	0.980325i	$-0.436753\pi$
$977$	1.12430e13	0.394783	0.197392	+	0.980325i	$0.436753\pi$
$978$	0	0
$979$	2.66002e12	0.0925471
$980$	4.93570e12	0.170935
$981$	0	0
$982$	−1.86618e12	−0.0640400
$983$	7.97289e12	0.272349	0.136174	−	0.990685i	$-0.456519\pi$
$983$	7.97289e12	0.272349	0.136174	+	0.990685i	$0.456519\pi$
$984$	0	0
$985$	−2.29731e13	−0.777601
$986$	−5.66261e13	−1.90796
$987$	0	0
$988$	1.26909e13	0.423726
$989$	−3.43854e11	−0.0114285
$990$	0	0
$991$	2.75569e13	0.907609	0.453804	−	0.891101i	$-0.350066\pi$
$991$	2.75569e13	0.907609	0.453804	+	0.891101i	$0.350066\pi$
$992$	1.83854e13	0.602795
$993$	0	0
$994$	−2.79649e13	−0.908603
$995$	4.42359e13	1.43077
$996$	0	0
$997$	1.33441e13	0.427722	0.213861	−	0.976864i	$-0.431396\pi$
$997$	1.33441e13	0.427722	0.213861	+	0.976864i	$0.431396\pi$
$998$	3.47033e11	0.0110735
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.10.a.c.1.6		15
3.2	odd	2		43.10.a.a.1.10	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.10	✓	15	3.2	odd	2
387.10.a.c.1.6		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)

\(f(q)\)	\(=\)	\(q-15.0644 q^{2} -285.063 q^{4} -1876.98 q^{5} -7041.18 q^{7} +12007.3 q^{8} +O(q^{10})\)	\(q-15.0644 q^{2} -285.063 q^{4} -1876.98 q^{5} -7041.18 q^{7} +12007.3 q^{8} +28275.7 q^{10} +2479.03 q^{11} +103059. q^{13} +106071. q^{14} -34931.2 q^{16} +529570. q^{17} -431982. q^{19} +535058. q^{20} -37345.2 q^{22} +100577. q^{23} +1.56994e6 q^{25} -1.55253e6 q^{26} +2.00718e6 q^{28} +7.09806e6 q^{29} -3.27053e6 q^{31} -5.62152e6 q^{32} -7.97768e6 q^{34} +1.32162e7 q^{35} -4.41240e6 q^{37} +6.50756e6 q^{38} -2.25375e7 q^{40} -1.81476e7 q^{41} -3.41880e6 q^{43} -706679. q^{44} -1.51514e6 q^{46} -5.52154e7 q^{47} +9.22462e6 q^{49} -2.36502e7 q^{50} -2.93783e7 q^{52} +8.53713e6 q^{53} -4.65310e6 q^{55} -8.45456e7 q^{56} -1.06928e8 q^{58} +1.92252e7 q^{59} -9.01048e6 q^{61} +4.92687e7 q^{62} +1.02570e8 q^{64} -1.93440e8 q^{65} +1.40140e8 q^{67} -1.50961e8 q^{68} -1.99094e8 q^{70} -2.63642e8 q^{71} -1.09424e8 q^{73} +6.64703e7 q^{74} +1.23142e8 q^{76} -1.74553e7 q^{77} -6.39726e7 q^{79} +6.55653e7 q^{80} +2.73383e8 q^{82} -4.71378e8 q^{83} -9.93994e8 q^{85} +5.15023e7 q^{86} +2.97665e7 q^{88} +1.07301e9 q^{89} -7.25657e8 q^{91} -2.86708e7 q^{92} +8.31790e8 q^{94} +8.10822e8 q^{95} -2.81023e8 q^{97} -1.38964e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) \) 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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