LMFDB - Embedded newform 387.10.a.c.1.9

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			1.9
Root			$7.62988$ 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)

$f(q)$	$=$	$q+9.62988 q^{2} -419.265 q^{4} -636.384 q^{5} -3288.51 q^{7} -8967.97 q^{8} +O(q^{10})$	\(q+9.62988 q^{2} -419.265 q^{4} -636.384 q^{5} -3288.51 q^{7} -8967.97 q^{8} -6128.30 q^{10} +71891.5 q^{11} -56499.0 q^{13} -31667.9 q^{14} +128303. q^{16} -227428. q^{17} -258196. q^{19} +266814. q^{20} +692307. q^{22} +205452. q^{23} -1.54814e6 q^{25} -544079. q^{26} +1.37876e6 q^{28} -568487. q^{29} -6.46168e6 q^{31} +5.82715e6 q^{32} -2.19010e6 q^{34} +2.09275e6 q^{35} -1.41255e7 q^{37} -2.48640e6 q^{38} +5.70707e6 q^{40} +1.35846e7 q^{41} -3.41880e6 q^{43} -3.01416e7 q^{44} +1.97848e6 q^{46} -2.14428e7 q^{47} -2.95393e7 q^{49} -1.49084e7 q^{50} +2.36881e7 q^{52} -3.02124e7 q^{53} -4.57506e7 q^{55} +2.94912e7 q^{56} -5.47446e6 q^{58} -1.16373e8 q^{59} -1.09646e8 q^{61} -6.22252e7 q^{62} -9.57661e6 q^{64} +3.59551e7 q^{65} +1.24276e8 q^{67} +9.53526e7 q^{68} +2.01529e7 q^{70} -2.04397e8 q^{71} +1.16000e8 q^{73} -1.36027e8 q^{74} +1.08253e8 q^{76} -2.36416e8 q^{77} +4.47267e8 q^{79} -8.16502e7 q^{80} +1.30818e8 q^{82} +5.31305e8 q^{83} +1.44731e8 q^{85} -3.29226e7 q^{86} -6.44721e8 q^{88} -2.15750e7 q^{89} +1.85797e8 q^{91} -8.61388e7 q^{92} -2.06492e8 q^{94} +1.64312e8 q^{95} +9.39408e8 q^{97} -2.84460e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	9.62988	0.425585	0.212792	−	0.977097i	$-0.431744\pi$
$2$	9.62988	0.425585	0.212792	+	0.977097i	$0.431744\pi$
$3$	0	0
$3$	0	0
$4$	−419.265	−0.818878
$5$	−636.384	−0.455359	−0.227680	−	0.973736i	$-0.573114\pi$
$5$	−636.384	−0.455359	−0.227680	+	0.973736i	$0.573114\pi$
$6$	0	0
$7$	−3288.51	−0.517675	−0.258838	−	0.965921i	$-0.583339\pi$
$7$	−3288.51	−0.517675	−0.258838	+	0.965921i	$0.583339\pi$
$8$	−8967.97	−0.774086
$9$	0	0
$10$	−6128.30	−0.193794
$11$	71891.5	1.48051	0.740254	−	0.672327i	$-0.234705\pi$
$11$	71891.5	1.48051	0.740254	+	0.672327i	$0.234705\pi$
$12$	0	0
$13$	−56499.0	−0.548651	−0.274325	−	0.961637i	$-0.588455\pi$
$13$	−56499.0	−0.548651	−0.274325	+	0.961637i	$0.588455\pi$
$14$	−31667.9	−0.220315
$15$	0	0
$16$	128303.	0.489439
$17$	−227428.	−0.660425	−0.330212	−	0.943907i	$-0.607120\pi$
$17$	−227428.	−0.660425	−0.330212	+	0.943907i	$0.607120\pi$
$18$	0	0
$19$	−258196.	−0.454526	−0.227263	−	0.973833i	$-0.572978\pi$
$19$	−258196.	−0.454526	−0.227263	+	0.973833i	$0.572978\pi$
$20$	266814.	0.372884
$21$	0	0
$22$	692307.	0.630081
$23$	205452.	0.153086	0.0765429	−	0.997066i	$-0.475612\pi$
$23$	205452.	0.153086	0.0765429	+	0.997066i	$0.475612\pi$
$24$	0	0
$25$	−1.54814e6	−0.792648
$26$	−544079.	−0.233497
$27$	0	0
$28$	1.37876e6	0.423913
$29$	−568487.	−0.149255	−0.0746276	−	0.997211i	$-0.523777\pi$
$29$	−568487.	−0.149255	−0.0746276	+	0.997211i	$0.523777\pi$
$30$	0	0
$31$	−6.46168e6	−1.25666	−0.628330	−	0.777947i	$-0.716261\pi$
$31$	−6.46168e6	−1.25666	−0.628330	+	0.777947i	$0.716261\pi$
$32$	5.82715e6	0.982384
$33$	0	0
$34$	−2.19010e6	−0.281066
$35$	2.09275e6	0.235728
$36$	0	0
$37$	−1.41255e7	−1.23907	−0.619535	−	0.784969i	$-0.712679\pi$
$37$	−1.41255e7	−1.23907	−0.619535	+	0.784969i	$0.712679\pi$
$38$	−2.48640e6	−0.193439
$39$	0	0
$40$	5.70707e6	0.352487
$41$	1.35846e7	0.750791	0.375395	−	0.926865i	$-0.377507\pi$
$41$	1.35846e7	0.750791	0.375395	+	0.926865i	$0.377507\pi$
$42$	0	0
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	−3.01416e7	−1.21235
$45$	0	0
$46$	1.97848e6	0.0651509
$47$	−2.14428e7	−0.640976	−0.320488	−	0.947253i	$-0.603847\pi$
$47$	−2.14428e7	−0.640976	−0.320488	+	0.947253i	$0.603847\pi$
$48$	0	0
$49$	−2.95393e7	−0.732012
$50$	−1.49084e7	−0.337339
$51$	0	0
$52$	2.36881e7	0.449278
$53$	−3.02124e7	−0.525949	−0.262975	−	0.964803i	$-0.584704\pi$
$53$	−3.02124e7	−0.525949	−0.262975	+	0.964803i	$0.584704\pi$
$54$	0	0
$55$	−4.57506e7	−0.674163
$56$	2.94912e7	0.400725
$57$	0	0
$58$	−5.47446e6	−0.0635207
$59$	−1.16373e8	−1.25031	−0.625154	−	0.780501i	$-0.714964\pi$
$59$	−1.16373e8	−1.25031	−0.625154	+	0.780501i	$0.714964\pi$
$60$	0	0
$61$	−1.09646e8	−1.01393	−0.506965	−	0.861967i	$-0.669233\pi$
$61$	−1.09646e8	−1.01393	−0.506965	+	0.861967i	$0.669233\pi$
$62$	−6.22252e7	−0.534815
$63$	0	0
$64$	−9.57661e6	−0.0713513
$65$	3.59551e7	0.249833
$66$	0	0
$67$	1.24276e8	0.753444	0.376722	−	0.926326i	$-0.377051\pi$
$67$	1.24276e8	0.753444	0.376722	+	0.926326i	$0.377051\pi$
$68$	9.53526e7	0.540807
$69$	0	0
$70$	2.01529e7	0.100322
$71$	−2.04397e8	−0.954578	−0.477289	−	0.878746i	$-0.658380\pi$
$71$	−2.04397e8	−0.954578	−0.477289	+	0.878746i	$0.658380\pi$
$72$	0	0
$73$	1.16000e8	0.478086	0.239043	−	0.971009i	$-0.423166\pi$
$73$	1.16000e8	0.478086	0.239043	+	0.971009i	$0.423166\pi$
$74$	−1.36027e8	−0.527329
$75$	0	0
$76$	1.08253e8	0.372201
$77$	−2.36416e8	−0.766422
$78$	0	0
$79$	4.47267e8	1.29195	0.645974	−	0.763359i	$-0.276451\pi$
$79$	4.47267e8	1.29195	0.645974	+	0.763359i	$0.276451\pi$
$80$	−8.16502e7	−0.222870
$81$	0	0
$82$	1.30818e8	0.319525
$83$	5.31305e8	1.22883	0.614416	−	0.788982i	$-0.289392\pi$
$83$	5.31305e8	1.22883	0.614416	+	0.788982i	$0.289392\pi$
$84$	0	0
$85$	1.44731e8	0.300730
$86$	−3.29226e7	−0.0649010
$87$	0	0
$88$	−6.44721e8	−1.14604
$89$	−2.15750e7	−0.0364499	−0.0182249	−	0.999834i	$-0.505802\pi$
$89$	−2.15750e7	−0.0364499	−0.0182249	+	0.999834i	$0.505802\pi$
$90$	0	0
$91$	1.85797e8	0.284023
$92$	−8.61388e7	−0.125358
$93$	0	0
$94$	−2.06492e8	−0.272790
$95$	1.64312e8	0.206972
$96$	0	0
$97$	9.39408e8	1.07741	0.538705	−	0.842494i	$-0.318914\pi$
$97$	9.39408e8	1.07741	0.538705	+	0.842494i	$0.318914\pi$
$98$	−2.84460e8	−0.311533
$99$	0	0
$100$	6.49082e8	0.649082
$101$	−1.98427e8	−0.189738	−0.0948691	−	0.995490i	$-0.530243\pi$
$101$	−1.98427e8	−0.189738	−0.0948691	+	0.995490i	$0.530243\pi$
$102$	0	0
$103$	−3.43220e8	−0.300473	−0.150236	−	0.988650i	$-0.548003\pi$
$103$	−3.43220e8	−0.300473	−0.150236	+	0.988650i	$0.548003\pi$
$104$	5.06682e8	0.424703
$105$	0	0
$106$	−2.90942e8	−0.223836
$107$	−1.59458e9	−1.17603	−0.588017	−	0.808849i	$-0.700091\pi$
$107$	−1.59458e9	−1.17603	−0.588017	+	0.808849i	$0.700091\pi$
$108$	0	0
$109$	−1.36307e8	−0.0924912	−0.0462456	−	0.998930i	$-0.514726\pi$
$109$	−1.36307e8	−0.0924912	−0.0462456	+	0.998930i	$0.514726\pi$
$110$	−4.40573e8	−0.286913
$111$	0	0
$112$	−4.21926e8	−0.253370
$113$	−6.49652e8	−0.374824	−0.187412	−	0.982281i	$-0.560010\pi$
$113$	−6.49652e8	−0.374824	−0.187412	+	0.982281i	$0.560010\pi$
$114$	0	0
$115$	−1.30746e8	−0.0697090
$116$	2.38347e8	0.122222
$117$	0	0
$118$	−1.12065e9	−0.532112
$119$	7.47897e8	0.341885
$120$	0	0
$121$	2.81045e9	1.19190
$122$	−1.05588e9	−0.431513
$123$	0	0
$124$	2.70916e9	1.02905
$125$	2.22815e9	0.816299
$126$	0	0
$127$	8.75307e8	0.298568	0.149284	−	0.988794i	$-0.452303\pi$
$127$	8.75307e8	0.298568	0.149284	+	0.988794i	$0.452303\pi$
$128$	−3.07572e9	−1.01275
$129$	0	0
$130$	3.46243e8	0.106325
$131$	5.17356e9	1.53486	0.767429	−	0.641134i	$-0.221536\pi$
$131$	5.17356e9	1.53486	0.767429	+	0.641134i	$0.221536\pi$
$132$	0	0
$133$	8.49079e8	0.235297
$134$	1.19676e9	0.320654
$135$	0	0
$136$	2.03957e9	0.511226
$137$	−2.77573e9	−0.673185	−0.336593	−	0.941650i	$-0.609275\pi$
$137$	−2.77573e9	−0.673185	−0.336593	+	0.941650i	$0.609275\pi$
$138$	0	0
$139$	−5.81753e9	−1.32182	−0.660910	−	0.750465i	$-0.729830\pi$
$139$	−5.81753e9	−1.32182	−0.660910	+	0.750465i	$0.729830\pi$
$140$	−8.77419e8	−0.193033
$141$	0	0
$142$	−1.96832e9	−0.406253
$143$	−4.06180e9	−0.812281
$144$	0	0
$145$	3.61776e8	0.0679648
$146$	1.11707e9	0.203466
$147$	0	0
$148$	5.92233e9	1.01465
$149$	9.17312e9	1.52468	0.762340	−	0.647176i	$-0.224050\pi$
$149$	9.17312e9	1.52468	0.762340	+	0.647176i	$0.224050\pi$
$150$	0	0
$151$	1.08986e10	1.70598	0.852990	−	0.521927i	$-0.174787\pi$
$151$	1.08986e10	1.70598	0.852990	+	0.521927i	$0.174787\pi$
$152$	2.31550e9	0.351842
$153$	0	0
$154$	−2.27665e9	−0.326177
$155$	4.11211e9	0.572232
$156$	0	0
$157$	6.31663e9	0.829730	0.414865	−	0.909883i	$-0.363829\pi$
$157$	6.31663e9	0.829730	0.414865	+	0.909883i	$0.363829\pi$
$158$	4.30713e9	0.549833
$159$	0	0
$160$	−3.70830e9	−0.447338
$161$	−6.75629e8	−0.0792487
$162$	0	0
$163$	1.41043e10	1.56498	0.782489	−	0.622665i	$-0.213950\pi$
$163$	1.41043e10	1.56498	0.782489	+	0.622665i	$0.213950\pi$
$164$	−5.69555e9	−0.614806
$165$	0	0
$166$	5.11640e9	0.522972
$167$	9.73712e9	0.968739	0.484369	−	0.874864i	$-0.339049\pi$
$167$	9.73712e9	0.968739	0.484369	+	0.874864i	$0.339049\pi$
$168$	0	0
$169$	−7.41236e9	−0.698983
$170$	1.39375e9	0.127986
$171$	0	0
$172$	1.43339e9	0.124878
$173$	2.77504e9	0.235539	0.117769	−	0.993041i	$-0.462426\pi$
$173$	2.77504e9	0.235539	0.117769	+	0.993041i	$0.462426\pi$
$174$	0	0
$175$	5.09107e9	0.410334
$176$	9.22393e9	0.724618
$177$	0	0
$178$	−2.07765e8	−0.0155125
$179$	1.51599e10	1.10372	0.551860	−	0.833937i	$-0.313918\pi$
$179$	1.51599e10	1.10372	0.551860	+	0.833937i	$0.313918\pi$
$180$	0	0
$181$	−1.80133e10	−1.24750	−0.623749	−	0.781624i	$-0.714391\pi$
$181$	−1.80133e10	−1.24750	−0.623749	+	0.781624i	$0.714391\pi$
$182$	1.78921e9	0.120876
$183$	0	0
$184$	−1.84249e9	−0.118502
$185$	8.98924e9	0.564222
$186$	0	0
$187$	−1.63501e10	−0.977764
$188$	8.99024e9	0.524881
$189$	0	0
$190$	1.58230e9	0.0880843
$191$	−1.94270e9	−0.105623	−0.0528113	−	0.998605i	$-0.516818\pi$
$191$	−1.94270e9	−0.105623	−0.0528113	+	0.998605i	$0.516818\pi$
$192$	0	0
$193$	−4.22076e8	−0.0218969	−0.0109485	−	0.999940i	$-0.503485\pi$
$193$	−4.22076e8	−0.0218969	−0.0109485	+	0.999940i	$0.503485\pi$
$194$	9.04638e9	0.458529
$195$	0	0
$196$	1.23848e10	0.599429
$197$	−2.39596e10	−1.13339	−0.566697	−	0.823926i	$-0.691779\pi$
$197$	−2.39596e10	−1.13339	−0.566697	+	0.823926i	$0.691779\pi$
$198$	0	0
$199$	−3.27995e10	−1.48261	−0.741307	−	0.671166i	$-0.765794\pi$
$199$	−3.27995e10	−1.48261	−0.741307	+	0.671166i	$0.765794\pi$
$200$	1.38837e10	0.613578
$201$	0	0
$202$	−1.91083e9	−0.0807496
$203$	1.86947e9	0.0772658
$204$	0	0
$205$	−8.64501e9	−0.341880
$206$	−3.30516e9	−0.127876
$207$	0	0
$208$	−7.24902e9	−0.268531
$209$	−1.85621e10	−0.672929
$210$	0	0
$211$	−7.88494e9	−0.273859	−0.136930	−	0.990581i	$-0.543723\pi$
$211$	−7.88494e9	−0.273859	−0.136930	+	0.990581i	$0.543723\pi$
$212$	1.26670e10	0.430688
$213$	0	0
$214$	−1.53556e10	−0.500502
$215$	2.17567e9	0.0694416
$216$	0	0
$217$	2.12493e10	0.650542
$218$	−1.31262e9	−0.0393628
$219$	0	0
$220$	1.91817e10	0.552057
$221$	1.28494e10	0.362342
$222$	0	0
$223$	1.50654e10	0.407952	0.203976	−	0.978976i	$-0.434614\pi$
$223$	1.50654e10	0.407952	0.203976	+	0.978976i	$0.434614\pi$
$224$	−1.91626e10	−0.508556
$225$	0	0
$226$	−6.25607e9	−0.159519
$227$	−2.82057e10	−0.705051	−0.352525	−	0.935802i	$-0.614677\pi$
$227$	−2.82057e10	−0.705051	−0.352525	+	0.935802i	$0.614677\pi$
$228$	0	0
$229$	2.85908e10	0.687016	0.343508	−	0.939150i	$-0.388385\pi$
$229$	2.85908e10	0.687016	0.343508	+	0.939150i	$0.388385\pi$
$230$	−1.25907e9	−0.0296671
$231$	0	0
$232$	5.09818e9	0.115536
$233$	−3.60569e10	−0.801469	−0.400735	−	0.916194i	$-0.631245\pi$
$233$	−3.60569e10	−0.801469	−0.400735	+	0.916194i	$0.631245\pi$
$234$	0	0
$235$	1.36459e10	0.291874
$236$	4.87910e10	1.02385
$237$	0	0
$238$	7.20216e9	0.145501
$239$	6.82558e10	1.35316	0.676580	−	0.736369i	$-0.263461\pi$
$239$	6.82558e10	1.35316	0.676580	+	0.736369i	$0.263461\pi$
$240$	0	0
$241$	−4.14356e10	−0.791219	−0.395610	−	0.918419i	$-0.629467\pi$
$241$	−4.14356e10	−0.791219	−0.395610	+	0.918419i	$0.629467\pi$
$242$	2.70643e10	0.507256
$243$	0	0
$244$	4.59707e10	0.830285
$245$	1.87984e10	0.333329
$246$	0	0
$247$	1.45878e10	0.249376
$248$	5.79482e10	0.972764
$249$	0	0
$250$	2.14568e10	0.347404
$251$	4.84151e10	0.769927	0.384963	−	0.922932i	$-0.374214\pi$
$251$	4.84151e10	0.769927	0.384963	+	0.922932i	$0.374214\pi$
$252$	0	0
$253$	1.47702e10	0.226645
$254$	8.42910e9	0.127066
$255$	0	0
$256$	−2.47156e10	−0.359659
$257$	−1.70355e10	−0.243588	−0.121794	−	0.992555i	$-0.538865\pi$
$257$	−1.70355e10	−0.243588	−0.121794	+	0.992555i	$0.538865\pi$
$258$	0	0
$259$	4.64518e10	0.641436
$260$	−1.50747e10	−0.204583
$261$	0	0
$262$	4.98207e10	0.653212
$263$	−5.93948e10	−0.765504	−0.382752	−	0.923851i	$-0.625024\pi$
$263$	−5.93948e10	−0.765504	−0.382752	+	0.923851i	$0.625024\pi$
$264$	0	0
$265$	1.92267e10	0.239496
$266$	8.17653e9	0.100139
$267$	0	0
$268$	−5.21047e10	−0.616978
$269$	1.07712e11	1.25423	0.627117	−	0.778925i	$-0.284235\pi$
$269$	1.07712e11	1.25423	0.627117	+	0.778925i	$0.284235\pi$
$270$	0	0
$271$	1.11447e11	1.25518	0.627592	−	0.778543i	$-0.284041\pi$
$271$	1.11447e11	1.25518	0.627592	+	0.778543i	$0.284041\pi$
$272$	−2.91797e10	−0.323237
$273$	0	0
$274$	−2.67299e10	−0.286497
$275$	−1.11298e11	−1.17352
$276$	0	0
$277$	1.47167e10	0.150194	0.0750968	−	0.997176i	$-0.476073\pi$
$277$	1.47167e10	0.150194	0.0750968	+	0.997176i	$0.476073\pi$
$278$	−5.60222e10	−0.562546
$279$	0	0
$280$	−1.87677e10	−0.182474
$281$	−1.28452e11	−1.22903	−0.614513	−	0.788906i	$-0.710648\pi$
$281$	−1.28452e11	−1.22903	−0.614513	+	0.788906i	$0.710648\pi$
$282$	0	0
$283$	−1.55862e10	−0.144445	−0.0722224	−	0.997389i	$-0.523009\pi$
$283$	−1.55862e10	−0.144445	−0.0722224	+	0.997389i	$0.523009\pi$
$284$	8.56965e10	0.781682
$285$	0	0
$286$	−3.91147e10	−0.345694
$287$	−4.46730e10	−0.388666
$288$	0	0
$289$	−6.68645e10	−0.563839
$290$	3.48386e9	0.0289248
$291$	0	0
$292$	−4.86349e10	−0.391494
$293$	1.78122e11	1.41193	0.705965	−	0.708247i	$-0.250514\pi$
$293$	1.78122e11	1.41193	0.705965	+	0.708247i	$0.250514\pi$
$294$	0	0
$295$	7.40577e10	0.569339
$296$	1.26677e11	0.959148
$297$	0	0
$298$	8.83360e10	0.648881
$299$	−1.16078e10	−0.0839906
$300$	0	0
$301$	1.12427e10	0.0789447
$302$	1.04952e11	0.726039
$303$	0	0
$304$	−3.31274e10	−0.222462
$305$	6.97768e10	0.461702
$306$	0	0
$307$	1.52485e11	0.979725	0.489863	−	0.871800i	$-0.337047\pi$
$307$	1.52485e11	0.979725	0.489863	+	0.871800i	$0.337047\pi$
$308$	9.91209e10	0.627606
$309$	0	0
$310$	3.95991e10	0.243533
$311$	2.83289e11	1.71715	0.858574	−	0.512690i	$-0.171351\pi$
$311$	2.83289e11	1.71715	0.858574	+	0.512690i	$0.171351\pi$
$312$	0	0
$313$	−2.44015e11	−1.43704	−0.718518	−	0.695508i	$-0.755179\pi$
$313$	−2.44015e11	−1.43704	−0.718518	+	0.695508i	$0.755179\pi$
$314$	6.08284e10	0.353120
$315$	0	0
$316$	−1.87524e11	−1.05795
$317$	1.70636e11	0.949084	0.474542	−	0.880233i	$-0.342614\pi$
$317$	1.70636e11	0.949084	0.474542	+	0.880233i	$0.342614\pi$
$318$	0	0
$319$	−4.08694e10	−0.220974
$320$	6.09440e9	0.0324905
$321$	0	0
$322$	−6.50623e9	−0.0337270
$323$	5.87209e10	0.300180
$324$	0	0
$325$	8.74684e10	0.434887
$326$	1.35823e11	0.666030
$327$	0	0
$328$	−1.21826e11	−0.581177
$329$	7.05149e10	0.331818
$330$	0	0
$331$	3.68117e11	1.68562	0.842811	−	0.538210i	$-0.180899\pi$
$331$	3.68117e11	1.68562	0.842811	+	0.538210i	$0.180899\pi$
$332$	−2.22758e11	−1.00626
$333$	0	0
$334$	9.37673e10	0.412280
$335$	−7.90873e10	−0.343088
$336$	0	0
$337$	−4.28944e10	−0.181162	−0.0905808	−	0.995889i	$-0.528872\pi$
$337$	−4.28944e10	−0.181162	−0.0905808	+	0.995889i	$0.528872\pi$
$338$	−7.13801e10	−0.297476
$339$	0	0
$340$	−6.06808e10	−0.246261
$341$	−4.64540e11	−1.86050
$342$	0	0
$343$	2.29843e11	0.896620
$344$	3.06597e10	0.118047
$345$	0	0
$346$	2.67233e10	0.100242
$347$	−1.60170e11	−0.593059	−0.296529	−	0.955024i	$-0.595829\pi$
$347$	−1.60170e11	−0.593059	−0.296529	+	0.955024i	$0.595829\pi$
$348$	0	0
$349$	3.04550e11	1.09887	0.549433	−	0.835538i	$-0.314844\pi$
$349$	3.04550e11	1.09887	0.549433	+	0.835538i	$0.314844\pi$
$350$	4.90264e10	0.174632
$351$	0	0
$352$	4.18923e11	1.45443
$353$	1.58317e11	0.542676	0.271338	−	0.962484i	$-0.412534\pi$
$353$	1.58317e11	0.542676	0.271338	+	0.962484i	$0.412534\pi$
$354$	0	0
$355$	1.30075e11	0.434676
$356$	9.04566e9	0.0298480
$357$	0	0
$358$	1.45988e11	0.469726
$359$	3.29410e11	1.04668	0.523338	−	0.852125i	$-0.324686\pi$
$359$	3.29410e11	1.04668	0.523338	+	0.852125i	$0.324686\pi$
$360$	0	0
$361$	−2.56023e11	−0.793406
$362$	−1.73466e11	−0.530916
$363$	0	0
$364$	−7.78984e10	−0.232580
$365$	−7.38207e10	−0.217701
$366$	0	0
$367$	5.66994e11	1.63148	0.815738	−	0.578421i	$-0.196331\pi$
$367$	5.66994e11	1.63148	0.815738	+	0.578421i	$0.196331\pi$
$368$	2.63602e10	0.0749261
$369$	0	0
$370$	8.65653e10	0.240124
$371$	9.93536e10	0.272271
$372$	0	0
$373$	−4.36684e11	−1.16809	−0.584046	−	0.811720i	$-0.698531\pi$
$373$	−4.36684e11	−1.16809	−0.584046	+	0.811720i	$0.698531\pi$
$374$	−1.57450e11	−0.416121
$375$	0	0
$376$	1.92299e11	0.496171
$377$	3.21190e10	0.0818890
$378$	0	0
$379$	−5.72159e11	−1.42443	−0.712213	−	0.701963i	$-0.752307\pi$
$379$	−5.72159e11	−1.42443	−0.712213	+	0.701963i	$0.752307\pi$
$380$	−6.88903e10	−0.169485
$381$	0	0
$382$	−1.87080e10	−0.0449513
$383$	6.60393e11	1.56822	0.784111	−	0.620620i	$-0.213119\pi$
$383$	6.60393e11	1.56822	0.784111	+	0.620620i	$0.213119\pi$
$384$	0	0
$385$	1.50451e11	0.348997
$386$	−4.06454e9	−0.00931899
$387$	0	0
$388$	−3.93861e11	−0.882268
$389$	5.55324e11	1.22963	0.614814	−	0.788672i	$-0.289231\pi$
$389$	5.55324e11	1.22963	0.614814	+	0.788672i	$0.289231\pi$
$390$	0	0
$391$	−4.67254e10	−0.101102
$392$	2.64908e11	0.566641
$393$	0	0
$394$	−2.30728e11	−0.482355
$395$	−2.84634e11	−0.588301
$396$	0	0
$397$	−7.47227e11	−1.50972	−0.754858	−	0.655889i	$-0.772294\pi$
$397$	−7.47227e11	−1.50972	−0.754858	+	0.655889i	$0.772294\pi$
$398$	−3.15855e11	−0.630978
$399$	0	0
$400$	−1.98632e11	−0.387953
$401$	4.59550e11	0.887530	0.443765	−	0.896143i	$-0.353643\pi$
$401$	4.59550e11	0.887530	0.443765	+	0.896143i	$0.353643\pi$
$402$	0	0
$403$	3.65079e11	0.689468
$404$	8.31936e10	0.155372
$405$	0	0
$406$	1.80028e10	0.0328831
$407$	−1.01550e12	−1.83445
$408$	0	0
$409$	4.85966e11	0.858718	0.429359	−	0.903134i	$-0.358739\pi$
$409$	4.85966e11	0.858718	0.429359	+	0.903134i	$0.358739\pi$
$410$	−8.32504e10	−0.145499
$411$	0	0
$412$	1.43900e11	0.246050
$413$	3.82692e11	0.647253
$414$	0	0
$415$	−3.38114e11	−0.559560
$416$	−3.29228e11	−0.538985
$417$	0	0
$418$	−1.78751e11	−0.286388
$419$	−6.23327e11	−0.987991	−0.493995	−	0.869465i	$-0.664464\pi$
$419$	−6.23327e11	−0.987991	−0.493995	+	0.869465i	$0.664464\pi$
$420$	0	0
$421$	−1.20079e11	−0.186294	−0.0931468	−	0.995652i	$-0.529693\pi$
$421$	−1.20079e11	−0.186294	−0.0931468	+	0.995652i	$0.529693\pi$
$422$	−7.59311e10	−0.116550
$423$	0	0
$424$	2.70944e11	0.407130
$425$	3.52090e11	0.523484
$426$	0	0
$427$	3.60571e11	0.524886
$428$	6.68553e11	0.963028
$429$	0	0
$430$	2.09514e10	0.0295533
$431$	1.24998e12	1.74485	0.872423	−	0.488752i	$-0.162548\pi$
$431$	1.24998e12	1.74485	0.872423	+	0.488752i	$0.162548\pi$
$432$	0	0
$433$	3.88881e10	0.0531644	0.0265822	−	0.999647i	$-0.491538\pi$
$433$	3.88881e10	0.0531644	0.0265822	+	0.999647i	$0.491538\pi$
$434$	2.04628e11	0.276861
$435$	0	0
$436$	5.71490e10	0.0757390
$437$	−5.30468e10	−0.0695814
$438$	0	0
$439$	−5.52309e11	−0.709728	−0.354864	−	0.934918i	$-0.615473\pi$
$439$	−5.52309e11	−0.709728	−0.354864	+	0.934918i	$0.615473\pi$
$440$	4.10290e11	0.521860
$441$	0	0
$442$	1.23739e11	0.154207
$443$	1.47315e12	1.81731	0.908656	−	0.417546i	$-0.137110\pi$
$443$	1.47315e12	1.81731	0.908656	+	0.417546i	$0.137110\pi$
$444$	0	0
$445$	1.37300e10	0.0165978
$446$	1.45078e11	0.173618
$447$	0	0
$448$	3.14927e10	0.0369368
$449$	−7.85918e11	−0.912575	−0.456288	−	0.889832i	$-0.650821\pi$
$449$	−7.85918e11	−0.912575	−0.456288	+	0.889832i	$0.650821\pi$
$450$	0	0
$451$	9.76616e11	1.11155
$452$	2.72377e11	0.306935
$453$	0	0
$454$	−2.71617e11	−0.300059
$455$	−1.18238e11	−0.129332
$456$	0	0
$457$	−1.62167e12	−1.73916	−0.869579	−	0.493794i	$-0.835610\pi$
$457$	−1.62167e12	−1.73916	−0.869579	+	0.493794i	$0.835610\pi$
$458$	2.75326e11	0.292383
$459$	0	0
$460$	5.48174e10	0.0570831
$461$	8.89063e11	0.916808	0.458404	−	0.888744i	$-0.348421\pi$
$461$	8.89063e11	0.916808	0.458404	+	0.888744i	$0.348421\pi$
$462$	0	0
$463$	4.38923e11	0.443889	0.221944	−	0.975059i	$-0.428760\pi$
$463$	4.38923e11	0.443889	0.221944	+	0.975059i	$0.428760\pi$
$464$	−7.29388e10	−0.0730513
$465$	0	0
$466$	−3.47224e11	−0.341093
$467$	−6.08342e11	−0.591864	−0.295932	−	0.955209i	$-0.595630\pi$
$467$	−6.08342e11	−0.591864	−0.295932	+	0.955209i	$0.595630\pi$
$468$	0	0
$469$	−4.08683e11	−0.390039
$470$	1.31408e11	0.124217
$471$	0	0
$472$	1.04363e12	0.967846
$473$	−2.45783e11	−0.225775
$474$	0	0
$475$	3.99724e11	0.360279
$476$	−3.13567e11	−0.279962
$477$	0	0
$478$	6.57296e11	0.575884
$479$	−2.16565e12	−1.87965	−0.939827	−	0.341650i	$-0.889014\pi$
$479$	−2.16565e12	−1.87965	−0.939827	+	0.341650i	$0.889014\pi$
$480$	0	0
$481$	7.98077e11	0.679817
$482$	−3.99020e11	−0.336731
$483$	0	0
$484$	−1.17832e12	−0.976023
$485$	−5.97824e11	−0.490609
$486$	0	0
$487$	1.64181e12	1.32264	0.661320	−	0.750104i	$-0.269996\pi$
$487$	1.64181e12	1.32264	0.661320	+	0.750104i	$0.269996\pi$
$488$	9.83301e11	0.784869
$489$	0	0
$490$	1.81026e11	0.141860
$491$	−1.52108e12	−1.18109	−0.590547	−	0.807003i	$-0.701088\pi$
$491$	−1.52108e12	−1.18109	−0.590547	+	0.807003i	$0.701088\pi$
$492$	0	0
$493$	1.29290e11	0.0985718
$494$	1.40479e11	0.106130
$495$	0	0
$496$	−8.29056e11	−0.615058
$497$	6.72160e11	0.494161
$498$	0	0
$499$	−4.02982e11	−0.290960	−0.145480	−	0.989361i	$-0.546473\pi$
$499$	−4.02982e11	−0.290960	−0.145480	+	0.989361i	$0.546473\pi$
$500$	−9.34186e11	−0.668449
$501$	0	0
$502$	4.66232e11	0.327669
$503$	4.10239e11	0.285747	0.142873	−	0.989741i	$-0.454366\pi$
$503$	4.10239e11	0.285747	0.142873	+	0.989741i	$0.454366\pi$
$504$	0	0
$505$	1.26276e11	0.0863990
$506$	1.42236e11	0.0964564
$507$	0	0
$508$	−3.66986e11	−0.244491
$509$	−1.26933e12	−0.838192	−0.419096	−	0.907942i	$-0.637653\pi$
$509$	−1.26933e12	−0.838192	−0.419096	+	0.907942i	$0.637653\pi$
$510$	0	0
$511$	−3.81467e11	−0.247493
$512$	1.33676e12	0.859684
$513$	0	0
$514$	−1.64050e11	−0.103667
$515$	2.18420e11	0.136823
$516$	0	0
$517$	−1.54156e12	−0.948970
$518$	4.47325e11	0.272985
$519$	0	0
$520$	−3.22444e11	−0.193392
$521$	−2.92628e12	−1.73999	−0.869994	−	0.493062i	$-0.835878\pi$
$521$	−2.92628e12	−1.73999	−0.869994	+	0.493062i	$0.835878\pi$
$522$	0	0
$523$	2.35078e12	1.37390	0.686950	−	0.726705i	$-0.258949\pi$
$523$	2.35078e12	1.37390	0.686950	+	0.726705i	$0.258949\pi$
$524$	−2.16909e12	−1.25686
$525$	0	0
$526$	−5.71964e11	−0.325786
$527$	1.46957e12	0.829930
$528$	0	0
$529$	−1.75894e12	−0.976565
$530$	1.85151e11	0.101926
$531$	0	0
$532$	−3.55989e11	−0.192679
$533$	−7.67516e11	−0.411922
$534$	0	0
$535$	1.01477e12	0.535518
$536$	−1.11450e12	−0.583231
$537$	0	0
$538$	1.03725e12	0.533782
$539$	−2.12363e12	−1.08375
$540$	0	0
$541$	3.12960e12	1.57073	0.785364	−	0.619034i	$-0.212476\pi$
$541$	3.12960e12	1.57073	0.785364	+	0.619034i	$0.212476\pi$
$542$	1.07322e12	0.534187
$543$	0	0
$544$	−1.32526e12	−0.648790
$545$	8.67439e10	0.0421167
$546$	0	0
$547$	−2.95721e12	−1.41234	−0.706169	−	0.708043i	$-0.749578\pi$
$547$	−2.95721e12	−1.41234	−0.706169	+	0.708043i	$0.749578\pi$
$548$	1.16377e12	0.551257
$549$	0	0
$550$	−1.07179e12	−0.499433
$551$	1.46781e11	0.0678403
$552$	0	0
$553$	−1.47084e12	−0.668810
$554$	1.41720e11	0.0639201
$555$	0	0
$556$	2.43909e12	1.08241
$557$	1.07910e12	0.475021	0.237511	−	0.971385i	$-0.423669\pi$
$557$	1.07910e12	0.475021	0.237511	+	0.971385i	$0.423669\pi$
$558$	0	0
$559$	1.93159e11	0.0836684
$560$	2.68507e11	0.115375
$561$	0	0
$562$	−1.23697e12	−0.523055
$563$	−1.53793e12	−0.645132	−0.322566	−	0.946547i	$-0.604545\pi$
$563$	−1.53793e12	−0.645132	−0.322566	+	0.946547i	$0.604545\pi$
$564$	0	0
$565$	4.13428e11	0.170680
$566$	−1.50093e11	−0.0614735
$567$	0	0
$568$	1.83302e12	0.738925
$569$	−2.07875e12	−0.831377	−0.415688	−	0.909507i	$-0.636459\pi$
$569$	−2.07875e12	−0.831377	−0.415688	+	0.909507i	$0.636459\pi$
$570$	0	0
$571$	−1.16515e12	−0.458689	−0.229345	−	0.973345i	$-0.573658\pi$
$571$	−1.16515e12	−0.458689	−0.229345	+	0.973345i	$0.573658\pi$
$572$	1.70297e12	0.665159
$573$	0	0
$574$	−4.30195e11	−0.165410
$575$	−3.18068e11	−0.121343
$576$	0	0
$577$	7.45248e11	0.279904	0.139952	−	0.990158i	$-0.455305\pi$
$577$	7.45248e11	0.279904	0.139952	+	0.990158i	$0.455305\pi$
$578$	−6.43897e11	−0.239961
$579$	0	0
$580$	−1.51680e11	−0.0556548
$581$	−1.74720e12	−0.636136
$582$	0	0
$583$	−2.17202e12	−0.778672
$584$	−1.04029e12	−0.370080
$585$	0	0
$586$	1.71529e12	0.600895
$587$	2.49286e11	0.0866615	0.0433308	−	0.999061i	$-0.486203\pi$
$587$	2.49286e11	0.0866615	0.0433308	+	0.999061i	$0.486203\pi$
$588$	0	0
$589$	1.66838e12	0.571184
$590$	7.13167e11	0.242302
$591$	0	0
$592$	−1.81235e12	−0.606449
$593$	3.10748e12	1.03196	0.515980	−	0.856601i	$-0.327428\pi$
$593$	3.10748e12	1.03196	0.515980	+	0.856601i	$0.327428\pi$
$594$	0	0
$595$	−4.75950e11	−0.155681
$596$	−3.84597e12	−1.24853
$597$	0	0
$598$	−1.11782e11	−0.0357451
$599$	−2.25538e12	−0.715811	−0.357906	−	0.933758i	$-0.616509\pi$
$599$	−2.25538e12	−0.715811	−0.357906	+	0.933758i	$0.616509\pi$
$600$	0	0
$601$	6.65807e11	0.208168	0.104084	−	0.994569i	$-0.466809\pi$
$601$	6.65807e11	0.208168	0.104084	+	0.994569i	$0.466809\pi$
$602$	1.08266e11	0.0335977
$603$	0	0
$604$	−4.56940e12	−1.39699
$605$	−1.78852e12	−0.542744
$606$	0	0
$607$	7.48544e11	0.223804	0.111902	−	0.993719i	$-0.464306\pi$
$607$	7.48544e11	0.223804	0.111902	+	0.993719i	$0.464306\pi$
$608$	−1.50455e12	−0.446519
$609$	0	0
$610$	6.71943e11	0.196493
$611$	1.21150e12	0.351672
$612$	0	0
$613$	−2.50001e12	−0.715103	−0.357552	−	0.933893i	$-0.616388\pi$
$613$	−2.50001e12	−0.715103	−0.357552	+	0.933893i	$0.616388\pi$
$614$	1.46841e12	0.416956
$615$	0	0
$616$	2.12017e12	0.593277
$617$	−1.56036e12	−0.433451	−0.216726	−	0.976233i	$-0.569538\pi$
$617$	−1.56036e12	−0.433451	−0.216726	+	0.976233i	$0.569538\pi$
$618$	0	0
$619$	−1.65116e12	−0.452045	−0.226023	−	0.974122i	$-0.572572\pi$
$619$	−1.65116e12	−0.452045	−0.226023	+	0.974122i	$0.572572\pi$
$620$	−1.72407e12	−0.468588
$621$	0	0
$622$	2.72804e12	0.730792
$623$	7.09496e10	0.0188692
$624$	0	0
$625$	1.60575e12	0.420939
$626$	−2.34984e12	−0.611580
$627$	0	0
$628$	−2.64834e12	−0.679448
$629$	3.21253e12	0.818313
$630$	0	0
$631$	−9.48276e9	−0.00238124	−0.00119062	−	0.999999i	$-0.500379\pi$
$631$	−9.48276e9	−0.00238124	−0.00119062	+	0.999999i	$0.500379\pi$
$632$	−4.01108e12	−1.00008
$633$	0	0
$634$	1.64321e12	0.403916
$635$	−5.57031e11	−0.135956
$636$	0	0
$637$	1.66894e12	0.401619
$638$	−3.93568e11	−0.0940429
$639$	0	0
$640$	1.95734e12	0.461165
$641$	−2.83779e12	−0.663925	−0.331963	−	0.943293i	$-0.607711\pi$
$641$	−2.83779e12	−0.663925	−0.331963	+	0.943293i	$0.607711\pi$
$642$	0	0
$643$	6.64160e12	1.53223	0.766114	−	0.642704i	$-0.222188\pi$
$643$	6.64160e12	1.53223	0.766114	+	0.642704i	$0.222188\pi$
$644$	2.83268e11	0.0648950
$645$	0	0
$646$	5.65475e11	0.127752
$647$	1.93866e12	0.434943	0.217471	−	0.976067i	$-0.430219\pi$
$647$	1.93866e12	0.434943	0.217471	+	0.976067i	$0.430219\pi$
$648$	0	0
$649$	−8.36621e12	−1.85109
$650$	8.42310e11	0.185081
$651$	0	0
$652$	−5.91346e12	−1.28153
$653$	−3.90359e11	−0.0840147	−0.0420073	−	0.999117i	$-0.513375\pi$
$653$	−3.90359e11	−0.0840147	−0.0420073	+	0.999117i	$0.513375\pi$
$654$	0	0
$655$	−3.29237e12	−0.698912
$656$	1.74295e12	0.367466
$657$	0	0
$658$	6.79050e11	0.141216
$659$	−4.87974e12	−1.00789	−0.503944	−	0.863737i	$-0.668118\pi$
$659$	−4.87974e12	−1.00789	−0.503944	+	0.863737i	$0.668118\pi$
$660$	0	0
$661$	−8.13003e12	−1.65648	−0.828239	−	0.560376i	$-0.810657\pi$
$661$	−8.13003e12	−1.65648	−0.828239	+	0.560376i	$0.810657\pi$
$662$	3.54492e12	0.717375
$663$	0	0
$664$	−4.76473e12	−0.951222
$665$	−5.40340e11	−0.107145
$666$	0	0
$667$	−1.16797e11	−0.0228488
$668$	−4.08244e12	−0.793279
$669$	0	0
$670$	−7.61601e11	−0.146013
$671$	−7.88261e12	−1.50113
$672$	0	0
$673$	7.83754e12	1.47269	0.736346	−	0.676606i	$-0.236550\pi$
$673$	7.83754e12	1.47269	0.736346	+	0.676606i	$0.236550\pi$
$674$	−4.13068e11	−0.0770996
$675$	0	0
$676$	3.10775e12	0.572381
$677$	−3.51888e12	−0.643807	−0.321903	−	0.946773i	$-0.604323\pi$
$677$	−3.51888e12	−0.643807	−0.321903	+	0.946773i	$0.604323\pi$
$678$	0	0
$679$	−3.08925e12	−0.557749
$680$	−1.29795e12	−0.232791
$681$	0	0
$682$	−4.47347e12	−0.791798
$683$	−9.44474e12	−1.66072	−0.830361	−	0.557226i	$-0.811866\pi$
$683$	−9.44474e12	−1.66072	−0.830361	+	0.557226i	$0.811866\pi$
$684$	0	0
$685$	1.76643e12	0.306541
$686$	2.21336e12	0.381588
$687$	0	0
$688$	−4.38644e11	−0.0746387
$689$	1.70697e12	0.288562
$690$	0	0
$691$	−3.85564e12	−0.643346	−0.321673	−	0.946851i	$-0.604245\pi$
$691$	−3.85564e12	−0.643346	−0.321673	+	0.946851i	$0.604245\pi$
$692$	−1.16348e12	−0.192877
$693$	0	0
$694$	−1.54241e12	−0.252397
$695$	3.70219e12	0.601903
$696$	0	0
$697$	−3.08951e12	−0.495841
$698$	2.93278e12	0.467660
$699$	0	0
$700$	−2.13451e12	−0.336014
$701$	2.65363e12	0.415059	0.207529	−	0.978229i	$-0.433458\pi$
$701$	2.65363e12	0.415059	0.207529	+	0.978229i	$0.433458\pi$
$702$	0	0
$703$	3.64715e12	0.563189
$704$	−6.88477e11	−0.105636
$705$	0	0
$706$	1.52457e12	0.230954
$707$	6.52528e11	0.0982228
$708$	0	0
$709$	−8.34085e12	−1.23966	−0.619830	−	0.784736i	$-0.712798\pi$
$709$	−8.34085e12	−1.23966	−0.619830	+	0.784736i	$0.712798\pi$
$710$	1.25260e12	0.184991
$711$	0	0
$712$	1.93484e11	0.0282154
$713$	−1.32756e12	−0.192377
$714$	0	0
$715$	2.58487e12	0.369880
$716$	−6.35603e12	−0.903811
$717$	0	0
$718$	3.17218e12	0.445449
$719$	1.03986e13	1.45110	0.725549	−	0.688170i	$-0.241586\pi$
$719$	1.03986e13	1.45110	0.725549	+	0.688170i	$0.241586\pi$
$720$	0	0
$721$	1.12868e12	0.155547
$722$	−2.46547e12	−0.337662
$723$	0	0
$724$	7.55236e12	1.02155
$725$	8.80098e11	0.118307
$726$	0	0
$727$	−5.23334e12	−0.694822	−0.347411	−	0.937713i	$-0.612939\pi$
$727$	−5.23334e12	−0.694822	−0.347411	+	0.937713i	$0.612939\pi$
$728$	−1.66623e12	−0.219858
$729$	0	0
$730$	−7.10884e11	−0.0926501
$731$	7.77530e11	0.100714
$732$	0	0
$733$	−1.15223e12	−0.147425	−0.0737123	−	0.997280i	$-0.523485\pi$
$733$	−1.15223e12	−0.147425	−0.0737123	+	0.997280i	$0.523485\pi$
$734$	5.46008e12	0.694331
$735$	0	0
$736$	1.19720e12	0.150389
$737$	8.93440e12	1.11548
$738$	0	0
$739$	−5.82737e12	−0.718741	−0.359371	−	0.933195i	$-0.617009\pi$
$739$	−5.82737e12	−0.718741	−0.359371	+	0.933195i	$0.617009\pi$
$740$	−3.76888e12	−0.462029
$741$	0	0
$742$	9.56763e11	0.115874
$743$	6.73156e12	0.810338	0.405169	−	0.914242i	$-0.367213\pi$
$743$	6.73156e12	0.810338	0.405169	+	0.914242i	$0.367213\pi$
$744$	0	0
$745$	−5.83763e12	−0.694278
$746$	−4.20521e12	−0.497122
$747$	0	0
$748$	6.85504e12	0.800669
$749$	5.24379e12	0.608804
$750$	0	0
$751$	−1.31942e13	−1.51357	−0.756784	−	0.653665i	$-0.773231\pi$
$751$	−1.31942e13	−1.51357	−0.756784	+	0.653665i	$0.773231\pi$
$752$	−2.75119e12	−0.313719
$753$	0	0
$754$	3.09302e11	0.0348507
$755$	−6.93569e12	−0.776834
$756$	0	0
$757$	−7.77025e12	−0.860010	−0.430005	−	0.902826i	$-0.641488\pi$
$757$	−7.77025e12	−0.860010	−0.430005	+	0.902826i	$0.641488\pi$
$758$	−5.50982e12	−0.606214
$759$	0	0
$760$	−1.47354e12	−0.160215
$761$	1.84489e13	1.99407	0.997035	−	0.0769500i	$-0.0245182\pi$
$761$	1.84489e13	1.99407	0.997035	+	0.0769500i	$0.0245182\pi$
$762$	0	0
$763$	4.48248e11	0.0478804
$764$	8.14509e11	0.0864920
$765$	0	0
$766$	6.35950e12	0.667411
$767$	6.57494e12	0.685982
$768$	0	0
$769$	1.24516e13	1.28397	0.641985	−	0.766717i	$-0.278111\pi$
$769$	1.24516e13	1.28397	0.641985	+	0.766717i	$0.278111\pi$
$770$	1.44883e12	0.148528
$771$	0	0
$772$	1.76962e11	0.0179309
$773$	1.48775e13	1.49873	0.749365	−	0.662157i	$-0.230359\pi$
$773$	1.48775e13	1.49873	0.749365	+	0.662157i	$0.230359\pi$
$774$	0	0
$775$	1.00036e13	0.996090
$776$	−8.42459e12	−0.834009
$777$	0	0
$778$	5.34771e12	0.523310
$779$	−3.50748e12	−0.341254
$780$	0	0
$781$	−1.46944e13	−1.41326
$782$	−4.49960e11	−0.0430273
$783$	0	0
$784$	−3.79000e12	−0.358275
$785$	−4.01980e12	−0.377825
$786$	0	0
$787$	1.10622e13	1.02791	0.513956	−	0.857816i	$-0.328179\pi$
$787$	1.10622e13	1.02791	0.513956	+	0.857816i	$0.328179\pi$
$788$	1.00454e13	0.928112
$789$	0	0
$790$	−2.74099e12	−0.250372
$791$	2.13638e12	0.194037
$792$	0	0
$793$	6.19488e12	0.556293
$794$	−7.19570e12	−0.642512
$795$	0	0
$796$	1.37517e13	1.21408
$797$	5.04498e12	0.442891	0.221446	−	0.975173i	$-0.428923\pi$
$797$	5.04498e12	0.442891	0.221446	+	0.975173i	$0.428923\pi$
$798$	0	0
$799$	4.87670e12	0.423316
$800$	−9.02124e12	−0.778684
$801$	0	0
$802$	4.42541e12	0.377719
$803$	8.33943e12	0.707810
$804$	0	0
$805$	4.29960e11	0.0360866
$806$	3.51566e12	0.293427
$807$	0	0
$808$	1.77949e12	0.146874
$809$	−1.42809e11	−0.0117216	−0.00586079	−	0.999983i	$-0.501866\pi$
$809$	−1.42809e11	−0.0117216	−0.00586079	+	0.999983i	$0.501866\pi$
$810$	0	0
$811$	2.03598e13	1.65264	0.826322	−	0.563197i	$-0.190429\pi$
$811$	2.03598e13	1.65264	0.826322	+	0.563197i	$0.190429\pi$
$812$	−7.83805e11	−0.0632712
$813$	0	0
$814$	−9.77918e12	−0.780715
$815$	−8.97577e12	−0.712627
$816$	0	0
$817$	8.82721e11	0.0693145
$818$	4.67979e12	0.365457
$819$	0	0
$820$	3.62455e12	0.279958
$821$	1.84922e11	0.0142051	0.00710255	−	0.999975i	$-0.497739\pi$
$821$	1.84922e11	0.0142051	0.00710255	+	0.999975i	$0.497739\pi$
$822$	0	0
$823$	2.87069e12	0.218116	0.109058	−	0.994035i	$-0.465217\pi$
$823$	2.87069e12	0.218116	0.109058	+	0.994035i	$0.465217\pi$
$824$	3.07799e12	0.232592
$825$	0	0
$826$	3.68528e12	0.275461
$827$	−2.25945e13	−1.67969	−0.839844	−	0.542828i	$-0.817353\pi$
$827$	−2.25945e13	−1.67969	−0.839844	+	0.542828i	$0.817353\pi$
$828$	0	0
$829$	−1.25049e12	−0.0919570	−0.0459785	−	0.998942i	$-0.514641\pi$
$829$	−1.25049e12	−0.0919570	−0.0459785	+	0.998942i	$0.514641\pi$
$830$	−3.25600e12	−0.238140
$831$	0	0
$832$	5.41069e11	0.0391469
$833$	6.71806e12	0.483439
$834$	0	0
$835$	−6.19655e12	−0.441124
$836$	7.78245e12	0.551046
$837$	0	0
$838$	−6.00256e12	−0.420474
$839$	9.40360e12	0.655187	0.327594	−	0.944819i	$-0.393762\pi$
$839$	9.40360e12	0.655187	0.327594	+	0.944819i	$0.393762\pi$
$840$	0	0
$841$	−1.41840e13	−0.977723
$842$	−1.15635e12	−0.0792837
$843$	0	0
$844$	3.30588e12	0.224257
$845$	4.71711e12	0.318288
$846$	0	0
$847$	−9.24217e12	−0.617019
$848$	−3.87635e12	−0.257420
$849$	0	0
$850$	3.39058e12	0.222787
$851$	−2.90211e12	−0.189684
$852$	0	0
$853$	4.97590e12	0.321811	0.160905	−	0.986970i	$-0.448559\pi$
$853$	4.97590e12	0.321811	0.160905	+	0.986970i	$0.448559\pi$
$854$	3.47225e12	0.223384
$855$	0	0
$856$	1.43002e13	0.910352
$857$	2.45954e13	1.55755	0.778773	−	0.627306i	$-0.215842\pi$
$857$	2.45954e13	1.55755	0.778773	+	0.627306i	$0.215842\pi$
$858$	0	0
$859$	4.12964e12	0.258787	0.129394	−	0.991593i	$-0.458697\pi$
$859$	4.12964e12	0.258787	0.129394	+	0.991593i	$0.458697\pi$
$860$	−9.12183e11	−0.0568642
$861$	0	0
$862$	1.20372e13	0.742579
$863$	5.44656e11	0.0334252	0.0167126	−	0.999860i	$-0.494680\pi$
$863$	5.44656e11	0.0334252	0.0167126	+	0.999860i	$0.494680\pi$
$864$	0	0
$865$	−1.76599e12	−0.107255
$866$	3.74488e11	0.0226260
$867$	0	0
$868$	−8.90909e12	−0.532715
$869$	3.21547e13	1.91274
$870$	0	0
$871$	−7.02148e12	−0.413377
$872$	1.22240e12	0.0715961
$873$	0	0
$874$	−5.10835e11	−0.0296128
$875$	−7.32728e12	−0.422578
$876$	0	0
$877$	2.79747e13	1.59686	0.798431	−	0.602087i	$-0.205664\pi$
$877$	2.79747e13	1.59686	0.798431	+	0.602087i	$0.205664\pi$
$878$	−5.31867e12	−0.302049
$879$	0	0
$880$	−5.86996e12	−0.329961
$881$	−2.31406e13	−1.29415	−0.647073	−	0.762428i	$-0.724007\pi$
$881$	−2.31406e13	−1.29415	−0.647073	+	0.762428i	$0.724007\pi$
$882$	0	0
$883$	−2.00961e13	−1.11247	−0.556235	−	0.831025i	$-0.687754\pi$
$883$	−2.00961e13	−1.11247	−0.556235	+	0.831025i	$0.687754\pi$
$884$	−5.38733e12	−0.296714
$885$	0	0
$886$	1.41862e13	0.773420
$887$	−1.62218e12	−0.0879916	−0.0439958	−	0.999032i	$-0.514009\pi$
$887$	−1.62218e12	−0.0879916	−0.0439958	+	0.999032i	$0.514009\pi$
$888$	0	0
$889$	−2.87845e12	−0.154561
$890$	1.32218e11	0.00706376
$891$	0	0
$892$	−6.31641e12	−0.334063
$893$	5.53646e12	0.291340
$894$	0	0
$895$	−9.64754e12	−0.502589
$896$	1.01145e13	0.524276
$897$	0	0
$898$	−7.56829e12	−0.388378
$899$	3.67338e12	0.187563
$900$	0	0
$901$	6.87113e12	0.347350
$902$	9.40470e12	0.473059
$903$	0	0
$904$	5.82606e12	0.290146
$905$	1.14634e13	0.568060
$906$	0	0
$907$	3.75549e13	1.84261	0.921306	−	0.388839i	$-0.127124\pi$
$907$	3.75549e13	1.84261	0.921306	+	0.388839i	$0.127124\pi$
$908$	1.18257e13	0.577350
$909$	0	0
$910$	−1.13862e12	−0.0550419
$911$	1.18903e13	0.571951	0.285975	−	0.958237i	$-0.407682\pi$
$911$	1.18903e13	0.571951	0.285975	+	0.958237i	$0.407682\pi$
$912$	0	0
$913$	3.81963e13	1.81929
$914$	−1.56165e13	−0.740159
$915$	0	0
$916$	−1.19871e13	−0.562582
$917$	−1.70133e13	−0.794558
$918$	0	0
$919$	−2.35907e11	−0.0109099	−0.00545495	−	0.999985i	$-0.501736\pi$
$919$	−2.35907e11	−0.0109099	−0.00545495	+	0.999985i	$0.501736\pi$
$920$	1.17253e12	0.0539608
$921$	0	0
$922$	8.56157e12	0.390179
$923$	1.15482e13	0.523730
$924$	0	0
$925$	2.18683e13	0.982147
$926$	4.22678e12	0.188912
$927$	0	0
$928$	−3.31266e12	−0.146626
$929$	1.46785e11	0.00646562	0.00323281	−	0.999995i	$-0.498971\pi$
$929$	1.46785e11	0.00646562	0.00323281	+	0.999995i	$0.498971\pi$
$930$	0	0
$931$	7.62694e12	0.332718
$932$	1.51174e13	0.656305
$933$	0	0
$934$	−5.85826e12	−0.251888
$935$	1.04050e13	0.445234
$936$	0	0
$937$	2.39861e13	1.01656	0.508279	−	0.861193i	$-0.330282\pi$
$937$	2.39861e13	1.01656	0.508279	+	0.861193i	$0.330282\pi$
$938$	−3.93556e12	−0.165995
$939$	0	0
$940$	−5.72124e12	−0.239010
$941$	1.94273e12	0.0807716	0.0403858	−	0.999184i	$-0.487141\pi$
$941$	1.94273e12	0.0807716	0.0403858	+	0.999184i	$0.487141\pi$
$942$	0	0
$943$	2.79098e12	0.114935
$944$	−1.49310e13	−0.611949
$945$	0	0
$946$	−2.36686e12	−0.0960865
$947$	−3.34211e12	−0.135035	−0.0675173	−	0.997718i	$-0.521508\pi$
$947$	−3.34211e12	−0.135035	−0.0675173	+	0.997718i	$0.521508\pi$
$948$	0	0
$949$	−6.55390e12	−0.262302
$950$	3.84929e12	0.153329
$951$	0	0
$952$	−6.70712e12	−0.264649
$953$	2.86874e13	1.12661	0.563304	−	0.826250i	$-0.309530\pi$
$953$	2.86874e13	1.12661	0.563304	+	0.826250i	$0.309530\pi$
$954$	0	0
$955$	1.23631e12	0.0480962
$956$	−2.86173e13	−1.10807
$957$	0	0
$958$	−2.08549e13	−0.799952
$959$	9.12800e12	0.348491
$960$	0	0
$961$	1.53137e13	0.579196
$962$	7.68539e12	0.289320
$963$	0	0
$964$	1.73725e13	0.647912
$965$	2.68603e11	0.00997097
$966$	0	0
$967$	−3.93409e13	−1.44685	−0.723427	−	0.690401i	$-0.757434\pi$
$967$	−3.93409e13	−1.44685	−0.723427	+	0.690401i	$0.757434\pi$
$968$	−2.52040e13	−0.922636
$969$	0	0
$970$	−5.75697e12	−0.208796
$971$	1.16162e13	0.419353	0.209676	−	0.977771i	$-0.432759\pi$
$971$	1.16162e13	0.419353	0.209676	+	0.977771i	$0.432759\pi$
$972$	0	0
$973$	1.91310e13	0.684274
$974$	1.58104e13	0.562895
$975$	0	0
$976$	−1.40679e13	−0.496256
$977$	−3.35215e13	−1.17706	−0.588530	−	0.808476i	$-0.700293\pi$
$977$	−3.35215e13	−1.17706	−0.588530	+	0.808476i	$0.700293\pi$
$978$	0	0
$979$	−1.55106e12	−0.0539643
$980$	−7.88150e12	−0.272955
$981$	0	0
$982$	−1.46478e13	−0.502655
$983$	5.05172e13	1.72563	0.862817	−	0.505516i	$-0.168698\pi$
$983$	5.05172e13	1.72563	0.862817	+	0.505516i	$0.168698\pi$
$984$	0	0
$985$	1.52475e13	0.516102
$986$	1.24504e12	0.0419507
$987$	0	0
$988$	−6.11617e12	−0.204208
$989$	−7.02399e11	−0.0233454
$990$	0	0
$991$	5.31629e13	1.75096	0.875482	−	0.483250i	$-0.160544\pi$
$991$	5.31629e13	1.75096	0.875482	+	0.483250i	$0.160544\pi$
$992$	−3.76532e13	−1.23452
$993$	0	0
$994$	6.47282e12	0.210307
$995$	2.08731e13	0.675122
$996$	0	0
$997$	−4.26532e13	−1.36717	−0.683586	−	0.729870i	$-0.739581\pi$
$997$	−4.26532e13	−1.36717	−0.683586	+	0.729870i	$0.739581\pi$
$998$	−3.88067e12	−0.123828
$999$	0	0

Twists

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

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

\(f(q)\)	\(=\)	\(q+9.62988 q^{2} -419.265 q^{4} -636.384 q^{5} -3288.51 q^{7} -8967.97 q^{8} +O(q^{10})\)	\(q+9.62988 q^{2} -419.265 q^{4} -636.384 q^{5} -3288.51 q^{7} -8967.97 q^{8} -6128.30 q^{10} +71891.5 q^{11} -56499.0 q^{13} -31667.9 q^{14} +128303. q^{16} -227428. q^{17} -258196. q^{19} +266814. q^{20} +692307. q^{22} +205452. q^{23} -1.54814e6 q^{25} -544079. q^{26} +1.37876e6 q^{28} -568487. q^{29} -6.46168e6 q^{31} +5.82715e6 q^{32} -2.19010e6 q^{34} +2.09275e6 q^{35} -1.41255e7 q^{37} -2.48640e6 q^{38} +5.70707e6 q^{40} +1.35846e7 q^{41} -3.41880e6 q^{43} -3.01416e7 q^{44} +1.97848e6 q^{46} -2.14428e7 q^{47} -2.95393e7 q^{49} -1.49084e7 q^{50} +2.36881e7 q^{52} -3.02124e7 q^{53} -4.57506e7 q^{55} +2.94912e7 q^{56} -5.47446e6 q^{58} -1.16373e8 q^{59} -1.09646e8 q^{61} -6.22252e7 q^{62} -9.57661e6 q^{64} +3.59551e7 q^{65} +1.24276e8 q^{67} +9.53526e7 q^{68} +2.01529e7 q^{70} -2.04397e8 q^{71} +1.16000e8 q^{73} -1.36027e8 q^{74} +1.08253e8 q^{76} -2.36416e8 q^{77} +4.47267e8 q^{79} -8.16502e7 q^{80} +1.30818e8 q^{82} +5.31305e8 q^{83} +1.44731e8 q^{85} -3.29226e7 q^{86} -6.44721e8 q^{88} -2.15750e7 q^{89} +1.85797e8 q^{91} -8.61388e7 q^{92} -2.06492e8 q^{94} +1.64312e8 q^{95} +9.39408e8 q^{97} -2.84460e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) \) 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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