LMFDB - Embedded newform 387.10.a.c.1.8

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			1.8
Root			$2.38595$ 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)

$f(q)$	$=$	$q+4.38595 q^{2} -492.763 q^{4} +1237.15 q^{5} +12549.3 q^{7} -4406.84 q^{8} +O(q^{10})$	\(q+4.38595 q^{2} -492.763 q^{4} +1237.15 q^{5} +12549.3 q^{7} -4406.84 q^{8} +5426.06 q^{10} -27918.0 q^{11} -139652. q^{13} +55040.4 q^{14} +232967. q^{16} +408645. q^{17} -157490. q^{19} -609620. q^{20} -122447. q^{22} +730739. q^{23} -422597. q^{25} -612508. q^{26} -6.18382e6 q^{28} +6.14391e6 q^{29} +6.18625e6 q^{31} +3.27808e6 q^{32} +1.79230e6 q^{34} +1.55253e7 q^{35} -2.16507e7 q^{37} -690744. q^{38} -5.45190e6 q^{40} -2.42738e7 q^{41} -3.41880e6 q^{43} +1.37570e7 q^{44} +3.20499e6 q^{46} +3.21569e7 q^{47} +1.17130e8 q^{49} -1.85349e6 q^{50} +6.88155e7 q^{52} +6.96541e7 q^{53} -3.45386e7 q^{55} -5.53026e7 q^{56} +2.69469e7 q^{58} +1.12041e8 q^{59} +8.03385e7 q^{61} +2.71326e7 q^{62} -1.04901e8 q^{64} -1.72770e8 q^{65} -5.78429e7 q^{67} -2.01366e8 q^{68} +6.80930e7 q^{70} -3.11039e8 q^{71} -3.23803e7 q^{73} -9.49590e7 q^{74} +7.76054e7 q^{76} -3.50350e8 q^{77} +2.36871e8 q^{79} +2.88214e8 q^{80} -1.06464e8 q^{82} -4.61987e8 q^{83} +5.05554e8 q^{85} -1.49947e7 q^{86} +1.23030e8 q^{88} -6.16826e8 q^{89} -1.75253e9 q^{91} -3.60082e8 q^{92} +1.41038e8 q^{94} -1.94838e8 q^{95} -1.00137e9 q^{97} +5.13728e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.38595	0.193833	0.0969167	−	0.995292i	$-0.469102\pi$
$2$	4.38595	0.193833	0.0969167	+	0.995292i	$0.469102\pi$
$3$	0	0
$3$	0	0
$4$	−492.763	−0.962429
$5$	1237.15	0.885229	0.442614	−	0.896712i	$-0.354051\pi$
$5$	1237.15	0.885229	0.442614	+	0.896712i	$0.354051\pi$
$6$	0	0
$7$	12549.3	1.97550	0.987750	−	0.156046i	$-0.0498748\pi$
$7$	12549.3	1.97550	0.987750	+	0.156046i	$0.0498748\pi$
$8$	−4406.84	−0.380384
$9$	0	0
$10$	5426.06	0.171587
$11$	−27918.0	−0.574933	−0.287467	−	0.957791i	$-0.592813\pi$
$11$	−27918.0	−0.574933	−0.287467	+	0.957791i	$0.592813\pi$
$12$	0	0
$13$	−139652.	−1.35613	−0.678067	−	0.735000i	$-0.737182\pi$
$13$	−139652.	−1.35613	−0.678067	+	0.735000i	$0.737182\pi$
$14$	55040.4	0.382918
$15$	0	0
$16$	232967.	0.888697
$17$	408645.	1.18666	0.593330	−	0.804959i	$-0.297813\pi$
$17$	408645.	1.18666	0.593330	+	0.804959i	$0.297813\pi$
$18$	0	0
$19$	−157490.	−0.277244	−0.138622	−	0.990345i	$-0.544267\pi$
$19$	−157490.	−0.277244	−0.138622	+	0.990345i	$0.544267\pi$
$20$	−609620.	−0.851970
$21$	0	0
$22$	−122447.	−0.111441
$23$	730739.	0.544487	0.272243	−	0.962228i	$-0.412234\pi$
$23$	730739.	0.544487	0.272243	+	0.962228i	$0.412234\pi$
$24$	0	0
$25$	−422597.	−0.216370
$26$	−612508.	−0.262864
$27$	0	0
$28$	−6.18382e6	−1.90128
$29$	6.14391e6	1.61307	0.806537	−	0.591184i	$-0.201339\pi$
$29$	6.14391e6	1.61307	0.806537	+	0.591184i	$0.201339\pi$
$30$	0	0
$31$	6.18625e6	1.20309	0.601547	−	0.798837i	$-0.294551\pi$
$31$	6.18625e6	1.20309	0.601547	+	0.798837i	$0.294551\pi$
$32$	3.27808e6	0.552644
$33$	0	0
$34$	1.79230e6	0.230015
$35$	1.55253e7	1.74877
$36$	0	0
$37$	−2.16507e7	−1.89917	−0.949587	−	0.313503i	$-0.898497\pi$
$37$	−2.16507e7	−1.89917	−0.949587	+	0.313503i	$0.898497\pi$
$38$	−690744.	−0.0537392
$39$	0	0
$40$	−5.45190e6	−0.336727
$41$	−2.42738e7	−1.34156	−0.670780	−	0.741657i	$-0.734040\pi$
$41$	−2.42738e7	−1.34156	−0.670780	+	0.741657i	$0.734040\pi$
$42$	0	0
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	1.37570e7	0.553332
$45$	0	0
$46$	3.20499e6	0.105540
$47$	3.21569e7	0.961243	0.480622	−	0.876928i	$-0.340411\pi$
$47$	3.21569e7	0.961243	0.480622	+	0.876928i	$0.340411\pi$
$48$	0	0
$49$	1.17130e8	2.90260
$50$	−1.85349e6	−0.0419397
$51$	0	0
$52$	6.88155e7	1.30518
$53$	6.96541e7	1.21257	0.606283	−	0.795249i	$-0.292660\pi$
$53$	6.96541e7	1.21257	0.606283	+	0.795249i	$0.292660\pi$
$54$	0	0
$55$	−3.45386e7	−0.508947
$56$	−5.53026e7	−0.751449
$57$	0	0
$58$	2.69469e7	0.312668
$59$	1.12041e8	1.20377	0.601886	−	0.798582i	$-0.294416\pi$
$59$	1.12041e8	1.20377	0.601886	+	0.798582i	$0.294416\pi$
$60$	0	0
$61$	8.03385e7	0.742915	0.371458	−	0.928450i	$-0.378858\pi$
$61$	8.03385e7	0.742915	0.371458	+	0.928450i	$0.378858\pi$
$62$	2.71326e7	0.233200
$63$	0	0
$64$	−1.04901e8	−0.781577
$65$	−1.72770e8	−1.20049
$66$	0	0
$67$	−5.78429e7	−0.350682	−0.175341	−	0.984508i	$-0.556103\pi$
$67$	−5.78429e7	−0.350682	−0.175341	+	0.984508i	$0.556103\pi$
$68$	−2.01366e8	−1.14208
$69$	0	0
$70$	6.80930e7	0.338970
$71$	−3.11039e8	−1.45262	−0.726311	−	0.687366i	$-0.758767\pi$
$71$	−3.11039e8	−1.45262	−0.726311	+	0.687366i	$0.758767\pi$
$72$	0	0
$73$	−3.23803e7	−0.133453	−0.0667265	−	0.997771i	$-0.521255\pi$
$73$	−3.23803e7	−0.133453	−0.0667265	+	0.997771i	$0.521255\pi$
$74$	−9.49590e7	−0.368124
$75$	0	0
$76$	7.76054e7	0.266828
$77$	−3.50350e8	−1.13578
$78$	0	0
$79$	2.36871e8	0.684210	0.342105	−	0.939662i	$-0.388860\pi$
$79$	2.36871e8	0.684210	0.342105	+	0.939662i	$0.388860\pi$
$80$	2.88214e8	0.786701
$81$	0	0
$82$	−1.06464e8	−0.260039
$83$	−4.61987e8	−1.06851	−0.534255	−	0.845324i	$-0.679408\pi$
$83$	−4.61987e8	−1.06851	−0.534255	+	0.845324i	$0.679408\pi$
$84$	0	0
$85$	5.05554e8	1.05047
$86$	−1.49947e7	−0.0295593
$87$	0	0
$88$	1.23030e8	0.218696
$89$	−6.16826e8	−1.04210	−0.521048	−	0.853527i	$-0.674459\pi$
$89$	−6.16826e8	−1.04210	−0.521048	+	0.853527i	$0.674459\pi$
$90$	0	0
$91$	−1.75253e9	−2.67904
$92$	−3.60082e8	−0.524029
$93$	0	0
$94$	1.41038e8	0.186321
$95$	−1.94838e8	−0.245425
$96$	0	0
$97$	−1.00137e9	−1.14848	−0.574240	−	0.818687i	$-0.694702\pi$
$97$	−1.00137e9	−1.14848	−0.574240	+	0.818687i	$0.694702\pi$
$98$	5.13728e8	0.562621
$99$	0	0
$100$	2.08240e8	0.208240
$101$	3.05585e8	0.292203	0.146102	−	0.989270i	$-0.453327\pi$
$101$	3.05585e8	0.292203	0.146102	+	0.989270i	$0.453327\pi$
$102$	0	0
$103$	−3.81600e8	−0.334073	−0.167036	−	0.985951i	$-0.553420\pi$
$103$	−3.81600e8	−0.334073	−0.167036	+	0.985951i	$0.553420\pi$
$104$	6.15425e8	0.515852
$105$	0	0
$106$	3.05499e8	0.235036
$107$	1.99829e9	1.47378	0.736888	−	0.676015i	$-0.236295\pi$
$107$	1.99829e9	1.47378	0.736888	+	0.676015i	$0.236295\pi$
$108$	0	0
$109$	5.64232e8	0.382859	0.191429	−	0.981506i	$-0.438688\pi$
$109$	5.64232e8	0.382859	0.191429	+	0.981506i	$0.438688\pi$
$110$	−1.51485e8	−0.0986510
$111$	0	0
$112$	2.92356e9	1.75562
$113$	−9.01181e8	−0.519947	−0.259973	−	0.965616i	$-0.583714\pi$
$113$	−9.01181e8	−0.519947	−0.259973	+	0.965616i	$0.583714\pi$
$114$	0	0
$115$	9.04030e8	0.481995
$116$	−3.02750e9	−1.55247
$117$	0	0
$118$	4.91407e8	0.233331
$119$	5.12820e9	2.34425
$120$	0	0
$121$	−1.57853e9	−0.669452
$122$	3.52361e8	0.144002
$123$	0	0
$124$	−3.04836e9	−1.15789
$125$	−2.93911e9	−1.07677
$126$	0	0
$127$	3.22590e9	1.10036	0.550179	−	0.835047i	$-0.314559\pi$
$127$	3.22590e9	1.10036	0.550179	+	0.835047i	$0.314559\pi$
$128$	−2.13847e9	−0.704139
$129$	0	0
$130$	−7.57761e8	−0.232695
$131$	3.22175e9	0.955808	0.477904	−	0.878412i	$-0.341397\pi$
$131$	3.22175e9	0.955808	0.477904	+	0.878412i	$0.341397\pi$
$132$	0	0
$133$	−1.97639e9	−0.547696
$134$	−2.53696e8	−0.0679739
$135$	0	0
$136$	−1.80084e9	−0.451387
$137$	4.02495e9	0.976153	0.488077	−	0.872801i	$-0.337699\pi$
$137$	4.02495e9	0.976153	0.488077	+	0.872801i	$0.337699\pi$
$138$	0	0
$139$	2.36428e9	0.537196	0.268598	−	0.963252i	$-0.413440\pi$
$139$	2.36428e9	0.537196	0.268598	+	0.963252i	$0.413440\pi$
$140$	−7.65028e9	−1.68307
$141$	0	0
$142$	−1.36420e9	−0.281567
$143$	3.89881e9	0.779686
$144$	0	0
$145$	7.60091e9	1.42794
$146$	−1.42018e8	−0.0258676
$147$	0	0
$148$	1.06687e10	1.82782
$149$	−3.40025e9	−0.565161	−0.282581	−	0.959244i	$-0.591190\pi$
$149$	−3.40025e9	−0.565161	−0.282581	+	0.959244i	$0.591190\pi$
$150$	0	0
$151$	−2.71186e9	−0.424494	−0.212247	−	0.977216i	$-0.568078\pi$
$151$	−2.71186e9	−0.424494	−0.212247	+	0.977216i	$0.568078\pi$
$152$	6.94035e8	0.105459
$153$	0	0
$154$	−1.53662e9	−0.220152
$155$	7.65329e9	1.06501
$156$	0	0
$157$	2.25484e9	0.296188	0.148094	−	0.988973i	$-0.452686\pi$
$157$	2.25484e9	0.296188	0.148094	+	0.988973i	$0.452686\pi$
$158$	1.03890e9	0.132623
$159$	0	0
$160$	4.05547e9	0.489216
$161$	9.17024e9	1.07563
$162$	0	0
$163$	2.12327e9	0.235592	0.117796	−	0.993038i	$-0.462417\pi$
$163$	2.12327e9	0.235592	0.117796	+	0.993038i	$0.462417\pi$
$164$	1.19612e10	1.29116
$165$	0	0
$166$	−2.02625e9	−0.207113
$167$	7.94637e9	0.790578	0.395289	−	0.918557i	$-0.370645\pi$
$167$	7.94637e9	0.790578	0.395289	+	0.918557i	$0.370645\pi$
$168$	0	0
$169$	8.89824e9	0.839100
$170$	2.21733e9	0.203616
$171$	0	0
$172$	1.68466e9	0.146769
$173$	1.13404e10	0.962548	0.481274	−	0.876570i	$-0.340174\pi$
$173$	1.13404e10	0.962548	0.481274	+	0.876570i	$0.340174\pi$
$174$	0	0
$175$	−5.30328e9	−0.427438
$176$	−6.50396e9	−0.510941
$177$	0	0
$178$	−2.70537e9	−0.201993
$179$	1.54500e10	1.12484	0.562420	−	0.826852i	$-0.309870\pi$
$179$	1.54500e10	1.12484	0.562420	+	0.826852i	$0.309870\pi$
$180$	0	0
$181$	1.12851e10	0.781540	0.390770	−	0.920488i	$-0.372209\pi$
$181$	1.12851e10	0.781540	0.390770	+	0.920488i	$0.372209\pi$
$182$	−7.68652e9	−0.519288
$183$	0	0
$184$	−3.22025e9	−0.207114
$185$	−2.67851e10	−1.68120
$186$	0	0
$187$	−1.14086e10	−0.682250
$188$	−1.58457e10	−0.925128
$189$	0	0
$190$	−8.54551e8	−0.0475715
$191$	−1.87758e10	−1.02082	−0.510409	−	0.859932i	$-0.670506\pi$
$191$	−1.87758e10	−1.02082	−0.510409	+	0.859932i	$0.670506\pi$
$192$	0	0
$193$	2.54039e9	0.131793	0.0658966	−	0.997826i	$-0.479009\pi$
$193$	2.54039e9	0.131793	0.0658966	+	0.997826i	$0.479009\pi$
$194$	−4.39197e9	−0.222614
$195$	0	0
$196$	−5.77175e10	−2.79354
$197$	2.66438e10	1.26037	0.630186	−	0.776444i	$-0.282979\pi$
$197$	2.66438e10	1.26037	0.630186	+	0.776444i	$0.282979\pi$
$198$	0	0
$199$	2.48904e10	1.12511	0.562553	−	0.826761i	$-0.309819\pi$
$199$	2.48904e10	1.12511	0.562553	+	0.826761i	$0.309819\pi$
$200$	1.86232e9	0.0823036
$201$	0	0
$202$	1.34028e9	0.0566388
$203$	7.71016e10	3.18663
$204$	0	0
$205$	−3.00302e10	−1.18759
$206$	−1.67368e9	−0.0647545
$207$	0	0
$208$	−3.25343e10	−1.20519
$209$	4.39681e9	0.159397
$210$	0	0
$211$	2.83390e10	0.984267	0.492134	−	0.870520i	$-0.336217\pi$
$211$	2.83390e10	0.984267	0.492134	+	0.870520i	$0.336217\pi$
$212$	−3.43230e10	−1.16701
$213$	0	0
$214$	8.76440e9	0.285667
$215$	−4.22955e9	−0.134996
$216$	0	0
$217$	7.76329e10	2.37671
$218$	2.47470e9	0.0742109
$219$	0	0
$220$	1.70194e10	0.489826
$221$	−5.70682e10	−1.60927
$222$	0	0
$223$	−8.66457e9	−0.234626	−0.117313	−	0.993095i	$-0.537428\pi$
$223$	−8.66457e9	−0.234626	−0.117313	+	0.993095i	$0.537428\pi$
$224$	4.11375e10	1.09175
$225$	0	0
$226$	−3.95254e9	−0.100783
$227$	1.92752e10	0.481817	0.240908	−	0.970548i	$-0.422555\pi$
$227$	1.92752e10	0.481817	0.240908	+	0.970548i	$0.422555\pi$
$228$	0	0
$229$	−2.30675e9	−0.0554294	−0.0277147	−	0.999616i	$-0.508823\pi$
$229$	−2.30675e9	−0.0554294	−0.0277147	+	0.999616i	$0.508823\pi$
$230$	3.96503e9	0.0934268
$231$	0	0
$232$	−2.70753e10	−0.613588
$233$	2.20050e10	0.489125	0.244562	−	0.969634i	$-0.421356\pi$
$233$	2.20050e10	0.489125	0.244562	+	0.969634i	$0.421356\pi$
$234$	0	0
$235$	3.97827e10	0.850920
$236$	−5.52098e10	−1.15854
$237$	0	0
$238$	2.24920e10	0.454394
$239$	3.65120e10	0.723845	0.361922	−	0.932208i	$-0.382121\pi$
$239$	3.65120e10	0.723845	0.361922	+	0.932208i	$0.382121\pi$
$240$	0	0
$241$	8.05560e10	1.53823	0.769115	−	0.639110i	$-0.220697\pi$
$241$	8.05560e10	1.53823	0.769115	+	0.639110i	$0.220697\pi$
$242$	−6.92337e9	−0.129762
$243$	0	0
$244$	−3.95879e10	−0.715003
$245$	1.44907e11	2.56946
$246$	0	0
$247$	2.19939e10	0.375980
$248$	−2.72618e10	−0.457638
$249$	0	0
$250$	−1.28908e10	−0.208713
$251$	−2.34339e10	−0.372661	−0.186330	−	0.982487i	$-0.559659\pi$
$251$	−2.34339e10	−0.372661	−0.186330	+	0.982487i	$0.559659\pi$
$252$	0	0
$253$	−2.04008e10	−0.313043
$254$	1.41486e10	0.213286
$255$	0	0
$256$	4.43303e10	0.645091
$257$	1.48746e10	0.212689	0.106345	−	0.994329i	$-0.466085\pi$
$257$	1.48746e10	0.212689	0.106345	+	0.994329i	$0.466085\pi$
$258$	0	0
$259$	−2.71701e11	−3.75182
$260$	8.51348e10	1.15539
$261$	0	0
$262$	1.41304e10	0.185268
$263$	1.29482e10	0.166882	0.0834410	−	0.996513i	$-0.473409\pi$
$263$	1.29482e10	0.166882	0.0834410	+	0.996513i	$0.473409\pi$
$264$	0	0
$265$	8.61722e10	1.07340
$266$	−8.66833e9	−0.106162
$267$	0	0
$268$	2.85028e10	0.337506
$269$	−1.38611e11	−1.61403	−0.807016	−	0.590529i	$-0.798919\pi$
$269$	−1.38611e11	−1.61403	−0.807016	+	0.590529i	$0.798919\pi$
$270$	0	0
$271$	−3.55761e10	−0.400679	−0.200339	−	0.979727i	$-0.564204\pi$
$271$	−3.55761e10	−0.400679	−0.200339	+	0.979727i	$0.564204\pi$
$272$	9.52008e10	1.05458
$273$	0	0
$274$	1.76532e10	0.189211
$275$	1.17981e10	0.124398
$276$	0	0
$277$	1.13489e11	1.15823	0.579114	−	0.815247i	$-0.303399\pi$
$277$	1.13489e11	1.15823	0.579114	+	0.815247i	$0.303399\pi$
$278$	1.03696e10	0.104126
$279$	0	0
$280$	−6.84174e10	−0.665205
$281$	−2.84629e10	−0.272334	−0.136167	−	0.990686i	$-0.543478\pi$
$281$	−2.84629e10	−0.272334	−0.136167	+	0.990686i	$0.543478\pi$
$282$	0	0
$283$	1.03614e11	0.960243	0.480121	−	0.877202i	$-0.340593\pi$
$283$	1.03614e11	0.960243	0.480121	+	0.877202i	$0.340593\pi$
$284$	1.53269e11	1.39805
$285$	0	0
$286$	1.71000e10	0.151129
$287$	−3.04618e11	−2.65025
$288$	0	0
$289$	4.84032e10	0.408163
$290$	3.33372e10	0.276782
$291$	0	0
$292$	1.59558e10	0.128439
$293$	1.91800e11	1.52035	0.760176	−	0.649717i	$-0.225112\pi$
$293$	1.91800e11	1.52035	0.760176	+	0.649717i	$0.225112\pi$
$294$	0	0
$295$	1.38611e11	1.06561
$296$	9.54114e10	0.722416
$297$	0	0
$298$	−1.49133e10	−0.109547
$299$	−1.02049e11	−0.738397
$300$	0	0
$301$	−4.29034e10	−0.301261
$302$	−1.18941e10	−0.0822811
$303$	0	0
$304$	−3.66900e10	−0.246386
$305$	9.93904e10	0.657650
$306$	0	0
$307$	−5.93480e10	−0.381315	−0.190657	−	0.981657i	$-0.561062\pi$
$307$	−5.93480e10	−0.381315	−0.190657	+	0.981657i	$0.561062\pi$
$308$	1.72640e11	1.09311
$309$	0	0
$310$	3.35670e10	0.206435
$311$	1.46203e11	0.886205	0.443102	−	0.896471i	$-0.353878\pi$
$311$	1.46203e11	0.886205	0.443102	+	0.896471i	$0.353878\pi$
$312$	0	0
$313$	−1.38227e11	−0.814036	−0.407018	−	0.913420i	$-0.633431\pi$
$313$	−1.38227e11	−0.814036	−0.407018	+	0.913420i	$0.633431\pi$
$314$	9.88963e9	0.0574112
$315$	0	0
$316$	−1.16721e11	−0.658504
$317$	−5.56681e10	−0.309628	−0.154814	−	0.987944i	$-0.549478\pi$
$317$	−5.56681e10	−0.309628	−0.154814	+	0.987944i	$0.549478\pi$
$318$	0	0
$319$	−1.71526e11	−0.927409
$320$	−1.29778e11	−0.691874
$321$	0	0
$322$	4.02202e10	0.208494
$323$	−6.43577e10	−0.328995
$324$	0	0
$325$	5.90166e10	0.293426
$326$	9.31255e9	0.0456656
$327$	0	0
$328$	1.06971e11	0.510308
$329$	4.03545e11	1.89894
$330$	0	0
$331$	2.09845e11	0.960888	0.480444	−	0.877025i	$-0.340476\pi$
$331$	2.09845e11	0.960888	0.480444	+	0.877025i	$0.340476\pi$
$332$	2.27650e11	1.02836
$333$	0	0
$334$	3.48524e10	0.153240
$335$	−7.15600e10	−0.310434
$336$	0	0
$337$	2.40308e11	1.01493	0.507463	−	0.861673i	$-0.330583\pi$
$337$	2.40308e11	1.01493	0.507463	+	0.861673i	$0.330583\pi$
$338$	3.90272e10	0.162646
$339$	0	0
$340$	−2.49118e11	−1.01100
$341$	−1.72708e11	−0.691699
$342$	0	0
$343$	9.63491e11	3.75858
$344$	1.50661e10	0.0580081
$345$	0	0
$346$	4.97386e10	0.186574
$347$	−1.62927e10	−0.0603266	−0.0301633	−	0.999545i	$-0.509603\pi$
$347$	−1.62927e10	−0.0603266	−0.0301633	+	0.999545i	$0.509603\pi$
$348$	0	0
$349$	−1.41443e11	−0.510347	−0.255174	−	0.966895i	$-0.582133\pi$
$349$	−1.41443e11	−0.510347	−0.255174	+	0.966895i	$0.582133\pi$
$350$	−2.32599e10	−0.0828518
$351$	0	0
$352$	−9.15176e10	−0.317733
$353$	−3.15790e10	−0.108246	−0.0541230	−	0.998534i	$-0.517236\pi$
$353$	−3.15790e10	−0.108246	−0.0541230	+	0.998534i	$0.517236\pi$
$354$	0	0
$355$	−3.84801e11	−1.28590
$356$	3.03949e11	1.00294
$357$	0	0
$358$	6.77631e10	0.218032
$359$	−9.18482e10	−0.291840	−0.145920	−	0.989296i	$-0.546614\pi$
$359$	−9.18482e10	−0.291840	−0.145920	+	0.989296i	$0.546614\pi$
$360$	0	0
$361$	−2.97885e11	−0.923136
$362$	4.94958e10	0.151489
$363$	0	0
$364$	8.63584e11	2.57839
$365$	−4.00591e10	−0.118136
$366$	0	0
$367$	2.61752e11	0.753169	0.376584	−	0.926382i	$-0.377098\pi$
$367$	2.61752e11	0.753169	0.376584	+	0.926382i	$0.377098\pi$
$368$	1.70238e11	0.483884
$369$	0	0
$370$	−1.17478e11	−0.325874
$371$	8.74107e11	2.39542
$372$	0	0
$373$	2.92272e11	0.781803	0.390902	−	0.920433i	$-0.372163\pi$
$373$	2.92272e11	0.781803	0.390902	+	0.920433i	$0.372163\pi$
$374$	−5.00374e10	−0.132243
$375$	0	0
$376$	−1.41710e11	−0.365642
$377$	−8.58011e11	−2.18754
$378$	0	0
$379$	4.04776e11	1.00772	0.503859	−	0.863786i	$-0.331913\pi$
$379$	4.04776e11	1.00772	0.503859	+	0.863786i	$0.331913\pi$
$380$	9.60092e10	0.236204
$381$	0	0
$382$	−8.23497e10	−0.197869
$383$	6.03567e11	1.43328	0.716640	−	0.697443i	$-0.245679\pi$
$383$	6.03567e11	1.43328	0.716640	+	0.697443i	$0.245679\pi$
$384$	0	0
$385$	−4.33434e11	−1.00543
$386$	1.11420e10	0.0255459
$387$	0	0
$388$	4.93440e11	1.10533
$389$	4.00613e11	0.887057	0.443529	−	0.896260i	$-0.353726\pi$
$389$	4.00613e11	0.887057	0.443529	+	0.896260i	$0.353726\pi$
$390$	0	0
$391$	2.98613e11	0.646121
$392$	−5.16175e11	−1.10410
$393$	0	0
$394$	1.16859e11	0.244302
$395$	2.93044e11	0.605683
$396$	0	0
$397$	−7.65107e11	−1.54584	−0.772920	−	0.634503i	$-0.781205\pi$
$397$	−7.65107e11	−1.54584	−0.772920	+	0.634503i	$0.781205\pi$
$398$	1.09168e11	0.218083
$399$	0	0
$400$	−9.84510e10	−0.192287
$401$	−5.13976e11	−0.992643	−0.496322	−	0.868139i	$-0.665316\pi$
$401$	−5.13976e11	−0.992643	−0.496322	+	0.868139i	$0.665316\pi$
$402$	0	0
$403$	−8.63924e11	−1.63156
$404$	−1.50581e11	−0.281225
$405$	0	0
$406$	3.38164e11	0.617675
$407$	6.04445e11	1.09190
$408$	0	0
$409$	3.29917e11	0.582975	0.291488	−	0.956575i	$-0.405850\pi$
$409$	3.29917e11	0.582975	0.291488	+	0.956575i	$0.405850\pi$
$410$	−1.31711e11	−0.230194
$411$	0	0
$412$	1.88039e11	0.321521
$413$	1.40603e12	2.37805
$414$	0	0
$415$	−5.71545e11	−0.945875
$416$	−4.57792e11	−0.749459
$417$	0	0
$418$	1.92842e10	0.0308964
$419$	−1.13273e11	−0.179541	−0.0897707	−	0.995962i	$-0.528613\pi$
$419$	−1.13273e11	−0.179541	−0.0897707	+	0.995962i	$0.528613\pi$
$420$	0	0
$421$	−5.70807e11	−0.885564	−0.442782	−	0.896629i	$-0.646008\pi$
$421$	−5.70807e11	−0.885564	−0.442782	+	0.896629i	$0.646008\pi$
$422$	1.24293e11	0.190784
$423$	0	0
$424$	−3.06955e11	−0.461241
$425$	−1.72692e11	−0.256757
$426$	0	0
$427$	1.00819e12	1.46763
$428$	−9.84684e11	−1.41840
$429$	0	0
$430$	−1.85506e10	−0.0261668
$431$	5.38814e11	0.752127	0.376064	−	0.926594i	$-0.377277\pi$
$431$	5.38814e11	0.752127	0.376064	+	0.926594i	$0.377277\pi$
$432$	0	0
$433$	−8.64588e11	−1.18199	−0.590995	−	0.806675i	$-0.701265\pi$
$433$	−8.64588e11	−1.18199	−0.590995	+	0.806675i	$0.701265\pi$
$434$	3.40494e11	0.460687
$435$	0	0
$436$	−2.78033e11	−0.368474
$437$	−1.15084e11	−0.150956
$438$	0	0
$439$	−3.81449e10	−0.0490170	−0.0245085	−	0.999700i	$-0.507802\pi$
$439$	−3.81449e10	−0.0490170	−0.0245085	+	0.999700i	$0.507802\pi$
$440$	1.52206e11	0.193596
$441$	0	0
$442$	−2.50298e11	−0.311931
$443$	−4.04411e11	−0.498891	−0.249446	−	0.968389i	$-0.580248\pi$
$443$	−4.04411e11	−0.498891	−0.249446	+	0.968389i	$0.580248\pi$
$444$	0	0
$445$	−7.63103e11	−0.922494
$446$	−3.80024e10	−0.0454783
$447$	0	0
$448$	−1.31644e12	−1.54400
$449$	−5.23002e11	−0.607288	−0.303644	−	0.952786i	$-0.598203\pi$
$449$	−5.23002e11	−0.607288	−0.303644	+	0.952786i	$0.598203\pi$
$450$	0	0
$451$	6.77675e11	0.771307
$452$	4.44069e11	0.500412
$453$	0	0
$454$	8.45400e10	0.0933923
$455$	−2.16814e12	−2.37157
$456$	0	0
$457$	−1.62214e12	−1.73966	−0.869832	−	0.493347i	$-0.835773\pi$
$457$	−1.62214e12	−1.73966	−0.869832	+	0.493347i	$0.835773\pi$
$458$	−1.01173e10	−0.0107441
$459$	0	0
$460$	−4.45473e11	−0.463886
$461$	5.64486e11	0.582102	0.291051	−	0.956708i	$-0.405995\pi$
$461$	5.64486e11	0.582102	0.291051	+	0.956708i	$0.405995\pi$
$462$	0	0
$463$	−1.76040e11	−0.178031	−0.0890156	−	0.996030i	$-0.528372\pi$
$463$	−1.76040e11	−0.178031	−0.0890156	+	0.996030i	$0.528372\pi$
$464$	1.43133e12	1.43353
$465$	0	0
$466$	9.65129e10	0.0948088
$467$	−1.36802e11	−0.133097	−0.0665483	−	0.997783i	$-0.521199\pi$
$467$	−1.36802e11	−0.133097	−0.0665483	+	0.997783i	$0.521199\pi$
$468$	0	0
$469$	−7.25885e11	−0.692772
$470$	1.74485e11	0.164937
$471$	0	0
$472$	−4.93748e11	−0.457896
$473$	9.54461e10	0.0876765
$474$	0	0
$475$	6.65549e10	0.0599872
$476$	−2.52699e12	−2.25617
$477$	0	0
$478$	1.60140e11	0.140305
$479$	4.86473e11	0.422230	0.211115	−	0.977461i	$-0.432291\pi$
$479$	4.86473e11	0.422230	0.211115	+	0.977461i	$0.432291\pi$
$480$	0	0
$481$	3.02357e12	2.57554
$482$	3.53315e11	0.298160
$483$	0	0
$484$	7.77843e11	0.644300
$485$	−1.23884e12	−1.01667
$486$	0	0
$487$	−8.10600e11	−0.653020	−0.326510	−	0.945194i	$-0.605873\pi$
$487$	−8.10600e11	−0.653020	−0.326510	+	0.945194i	$0.605873\pi$
$488$	−3.54039e11	−0.282593
$489$	0	0
$490$	6.35556e11	0.498048
$491$	−1.12030e12	−0.869893	−0.434947	−	0.900456i	$-0.643233\pi$
$491$	−1.12030e12	−0.869893	−0.434947	+	0.900456i	$0.643233\pi$
$492$	0	0
$493$	2.51068e12	1.91417
$494$	9.64640e10	0.0728776
$495$	0	0
$496$	1.44119e12	1.06919
$497$	−3.90331e12	−2.86966
$498$	0	0
$499$	1.93337e12	1.39593	0.697963	−	0.716134i	$-0.254090\pi$
$499$	1.93337e12	1.39593	0.697963	+	0.716134i	$0.254090\pi$
$500$	1.44829e12	1.03631
$501$	0	0
$502$	−1.02780e11	−0.0722341
$503$	9.53953e11	0.664463	0.332232	−	0.943198i	$-0.392198\pi$
$503$	9.53953e11	0.664463	0.332232	+	0.943198i	$0.392198\pi$
$504$	0	0
$505$	3.78052e11	0.258667
$506$	−8.94768e10	−0.0606783
$507$	0	0
$508$	−1.58961e12	−1.05902
$509$	2.27539e12	1.50254	0.751270	−	0.659995i	$-0.229442\pi$
$509$	2.27539e12	1.50254	0.751270	+	0.659995i	$0.229442\pi$
$510$	0	0
$511$	−4.06349e11	−0.263636
$512$	1.28933e12	0.829180
$513$	0	0
$514$	6.52392e10	0.0412263
$515$	−4.72095e11	−0.295731
$516$	0	0
$517$	−8.97755e11	−0.552650
$518$	−1.19167e12	−0.727228
$519$	0	0
$520$	7.61370e11	0.456647
$521$	−8.63866e11	−0.513661	−0.256830	−	0.966456i	$-0.582678\pi$
$521$	−8.63866e11	−0.513661	−0.256830	+	0.966456i	$0.582678\pi$
$522$	0	0
$523$	−3.96246e11	−0.231583	−0.115792	−	0.993274i	$-0.536940\pi$
$523$	−3.96246e11	−0.231583	−0.115792	+	0.993274i	$0.536940\pi$
$524$	−1.58756e12	−0.919897
$525$	0	0
$526$	5.67903e10	0.0323473
$527$	2.52798e12	1.42767
$528$	0	0
$529$	−1.26717e12	−0.703534
$530$	3.77947e11	0.208061
$531$	0	0
$532$	9.73891e11	0.527118
$533$	3.38989e12	1.81933
$534$	0	0
$535$	2.47217e12	1.30463
$536$	2.54904e11	0.133394
$537$	0	0
$538$	−6.07941e11	−0.312854
$539$	−3.27004e12	−1.66880
$540$	0	0
$541$	−3.00813e12	−1.50976	−0.754881	−	0.655862i	$-0.772305\pi$
$541$	−3.00813e12	−1.50976	−0.754881	+	0.655862i	$0.772305\pi$
$542$	−1.56035e11	−0.0776650
$543$	0	0
$544$	1.33957e12	0.655800
$545$	6.98037e11	0.338918
$546$	0	0
$547$	−1.67014e12	−0.797645	−0.398823	−	0.917028i	$-0.630581\pi$
$547$	−1.67014e12	−0.797645	−0.398823	+	0.917028i	$0.630581\pi$
$548$	−1.98335e12	−0.939478
$549$	0	0
$550$	5.17457e10	0.0241125
$551$	−9.67606e11	−0.447215
$552$	0	0
$553$	2.97255e12	1.35166
$554$	4.97756e11	0.224503
$555$	0	0
$556$	−1.16503e12	−0.517012
$557$	3.27102e12	1.43991	0.719954	−	0.694022i	$-0.244163\pi$
$557$	3.27102e12	1.43991	0.719954	+	0.694022i	$0.244163\pi$
$558$	0	0
$559$	4.77443e11	0.206809
$560$	3.61687e12	1.55413
$561$	0	0
$562$	−1.24837e11	−0.0527874
$563$	3.16570e12	1.32795	0.663976	−	0.747754i	$-0.268868\pi$
$563$	3.16570e12	1.32795	0.663976	+	0.747754i	$0.268868\pi$
$564$	0	0
$565$	−1.11489e12	−0.460272
$566$	4.54448e11	0.186127
$567$	0	0
$568$	1.37070e12	0.552555
$569$	3.41258e12	1.36483	0.682414	−	0.730966i	$-0.260930\pi$
$569$	3.41258e12	1.36483	0.682414	+	0.730966i	$0.260930\pi$
$570$	0	0
$571$	5.10789e11	0.201085	0.100542	−	0.994933i	$-0.467942\pi$
$571$	5.10789e11	0.201085	0.100542	+	0.994933i	$0.467942\pi$
$572$	−1.92119e12	−0.750393
$573$	0	0
$574$	−1.33604e12	−0.513707
$575$	−3.08808e11	−0.117810
$576$	0	0
$577$	3.29567e12	1.23781	0.618903	−	0.785467i	$-0.287577\pi$
$577$	3.29567e12	1.23781	0.618903	+	0.785467i	$0.287577\pi$
$578$	2.12294e11	0.0791157
$579$	0	0
$580$	−3.74545e12	−1.37429
$581$	−5.79759e12	−2.11084
$582$	0	0
$583$	−1.94460e12	−0.697144
$584$	1.42695e11	0.0507634
$585$	0	0
$586$	8.41226e11	0.294695
$587$	−3.75472e12	−1.30529	−0.652644	−	0.757665i	$-0.726340\pi$
$587$	−3.75472e12	−1.30529	−0.652644	+	0.757665i	$0.726340\pi$
$588$	0	0
$589$	−9.74274e11	−0.333551
$590$	6.07942e11	0.206551
$591$	0	0
$592$	−5.04390e12	−1.68779
$593$	7.28844e11	0.242041	0.121020	−	0.992650i	$-0.461383\pi$
$593$	7.28844e11	0.242041	0.121020	+	0.992650i	$0.461383\pi$
$594$	0	0
$595$	6.34432e12	2.07520
$596$	1.67552e12	0.543927
$597$	0	0
$598$	−4.47583e11	−0.143126
$599$	−1.79149e12	−0.568582	−0.284291	−	0.958738i	$-0.591758\pi$
$599$	−1.79149e12	−0.568582	−0.284291	+	0.958738i	$0.591758\pi$
$600$	0	0
$601$	3.67032e11	0.114754	0.0573772	−	0.998353i	$-0.481726\pi$
$601$	3.67032e11	0.114754	0.0573772	+	0.998353i	$0.481726\pi$
$602$	−1.88172e11	−0.0583944
$603$	0	0
$604$	1.33631e12	0.408545
$605$	−1.95287e12	−0.592618
$606$	0	0
$607$	−3.38377e12	−1.01170	−0.505850	−	0.862622i	$-0.668821\pi$
$607$	−3.38377e12	−1.01170	−0.505850	+	0.862622i	$0.668821\pi$
$608$	−5.16266e11	−0.153217
$609$	0	0
$610$	4.35921e11	0.127475
$611$	−4.49078e12	−1.30357
$612$	0	0
$613$	3.01980e11	0.0863786	0.0431893	−	0.999067i	$-0.486248\pi$
$613$	3.01980e11	0.0863786	0.0431893	+	0.999067i	$0.486248\pi$
$614$	−2.60298e11	−0.0739116
$615$	0	0
$616$	1.54394e12	0.432033
$617$	−3.65251e12	−1.01463	−0.507315	−	0.861761i	$-0.669362\pi$
$617$	−3.65251e12	−1.01463	−0.507315	+	0.861761i	$0.669362\pi$
$618$	0	0
$619$	1.83928e10	0.00503546	0.00251773	−	0.999997i	$-0.499199\pi$
$619$	1.83928e10	0.00503546	0.00251773	+	0.999997i	$0.499199\pi$
$620$	−3.77126e12	−1.02500
$621$	0	0
$622$	6.41239e11	0.171776
$623$	−7.74071e12	−2.05866
$624$	0	0
$625$	−2.81072e12	−0.736815
$626$	−6.06257e11	−0.157787
$627$	0	0
$628$	−1.11110e12	−0.285060
$629$	−8.84747e12	−2.25367
$630$	0	0
$631$	−3.45921e12	−0.868650	−0.434325	−	0.900756i	$-0.643013\pi$
$631$	−3.45921e12	−0.868650	−0.434325	+	0.900756i	$0.643013\pi$
$632$	−1.04385e12	−0.260263
$633$	0	0
$634$	−2.44157e11	−0.0600162
$635$	3.99091e12	0.974069
$636$	0	0
$637$	−1.63575e13	−3.93631
$638$	−7.52304e11	−0.179763
$639$	0	0
$640$	−2.64560e12	−0.623325
$641$	1.71702e12	0.401710	0.200855	−	0.979621i	$-0.435628\pi$
$641$	1.71702e12	0.401710	0.200855	+	0.979621i	$0.435628\pi$
$642$	0	0
$643$	−5.95110e11	−0.137293	−0.0686464	−	0.997641i	$-0.521868\pi$
$643$	−5.95110e11	−0.137293	−0.0686464	+	0.997641i	$0.521868\pi$
$644$	−4.51876e12	−1.03522
$645$	0	0
$646$	−2.82270e11	−0.0637702
$647$	2.77664e12	0.622946	0.311473	−	0.950255i	$-0.399178\pi$
$647$	2.77664e12	0.622946	0.311473	+	0.950255i	$0.399178\pi$
$648$	0	0
$649$	−3.12797e12	−0.692088
$650$	2.58844e11	0.0568758
$651$	0	0
$652$	−1.04627e12	−0.226740
$653$	−2.92497e12	−0.629523	−0.314761	−	0.949171i	$-0.601925\pi$
$653$	−2.92497e12	−0.629523	−0.314761	+	0.949171i	$0.601925\pi$
$654$	0	0
$655$	3.98577e12	0.846109
$656$	−5.65498e12	−1.19224
$657$	0	0
$658$	1.76993e12	0.368077
$659$	3.06130e12	0.632299	0.316149	−	0.948709i	$-0.397610\pi$
$659$	3.06130e12	0.632299	0.316149	+	0.948709i	$0.397610\pi$
$660$	0	0
$661$	7.09295e12	1.44517	0.722587	−	0.691280i	$-0.242953\pi$
$661$	7.09295e12	1.44517	0.722587	+	0.691280i	$0.242953\pi$
$662$	9.20370e11	0.186252
$663$	0	0
$664$	2.03590e12	0.406444
$665$	−2.44508e12	−0.484836
$666$	0	0
$667$	4.48960e12	0.878297
$668$	−3.91568e12	−0.760875
$669$	0	0
$670$	−3.13859e11	−0.0601724
$671$	−2.24289e12	−0.427127
$672$	0	0
$673$	3.65617e12	0.687003	0.343502	−	0.939152i	$-0.388387\pi$
$673$	3.65617e12	0.687003	0.343502	+	0.939152i	$0.388387\pi$
$674$	1.05398e12	0.196727
$675$	0	0
$676$	−4.38473e12	−0.807574
$677$	1.69929e12	0.310898	0.155449	−	0.987844i	$-0.450318\pi$
$677$	1.69929e12	0.310898	0.155449	+	0.987844i	$0.450318\pi$
$678$	0	0
$679$	−1.25665e13	−2.26882
$680$	−2.22790e12	−0.399581
$681$	0	0
$682$	−7.57488e11	−0.134074
$683$	3.57423e12	0.628477	0.314239	−	0.949344i	$-0.398251\pi$
$683$	3.57423e12	0.628477	0.314239	+	0.949344i	$0.398251\pi$
$684$	0	0
$685$	4.97945e12	0.864119
$686$	4.22582e12	0.728539
$687$	0	0
$688$	−7.96467e11	−0.135525
$689$	−9.72735e12	−1.64440
$690$	0	0
$691$	9.20422e11	0.153580	0.0767902	−	0.997047i	$-0.475533\pi$
$691$	9.20422e11	0.153580	0.0767902	+	0.997047i	$0.475533\pi$
$692$	−5.58815e12	−0.926384
$693$	0	0
$694$	−7.14588e10	−0.0116933
$695$	2.92496e12	0.475541
$696$	0	0
$697$	−9.91937e12	−1.59198
$698$	−6.20360e11	−0.0989224
$699$	0	0
$700$	2.61326e12	0.411379
$701$	−3.78617e11	−0.0592200	−0.0296100	−	0.999562i	$-0.509427\pi$
$701$	−3.78617e11	−0.0592200	−0.0296100	+	0.999562i	$0.509427\pi$
$702$	0	0
$703$	3.40978e12	0.526535
$704$	2.92864e12	0.449354
$705$	0	0
$706$	−1.38504e11	−0.0209817
$707$	3.83486e12	0.577248
$708$	0	0
$709$	−4.49168e12	−0.667576	−0.333788	−	0.942648i	$-0.608327\pi$
$709$	−4.49168e12	−0.667576	−0.333788	+	0.942648i	$0.608327\pi$
$710$	−1.68772e12	−0.249251
$711$	0	0
$712$	2.71826e12	0.396397
$713$	4.52054e12	0.655069
$714$	0	0
$715$	4.82339e12	0.690201
$716$	−7.61321e12	−1.08258
$717$	0	0
$718$	−4.02842e11	−0.0565684
$719$	8.71449e12	1.21608	0.608039	−	0.793907i	$-0.291956\pi$
$719$	8.71449e12	1.21608	0.608039	+	0.793907i	$0.291956\pi$
$720$	0	0
$721$	−4.78880e12	−0.659961
$722$	−1.30651e12	−0.178935
$723$	0	0
$724$	−5.56087e12	−0.752176
$725$	−2.59640e12	−0.349020
$726$	0	0
$727$	1.20858e13	1.60461	0.802306	−	0.596913i	$-0.203606\pi$
$727$	1.20858e13	1.60461	0.802306	+	0.596913i	$0.203606\pi$
$728$	7.72313e12	1.01907
$729$	0	0
$730$	−1.75697e11	−0.0228988
$731$	−1.39708e12	−0.180964
$732$	0	0
$733$	−2.17693e12	−0.278534	−0.139267	−	0.990255i	$-0.544475\pi$
$733$	−2.17693e12	−0.278534	−0.139267	+	0.990255i	$0.544475\pi$
$734$	1.14803e12	0.145989
$735$	0	0
$736$	2.39542e12	0.300907
$737$	1.61486e12	0.201619
$738$	0	0
$739$	1.41514e13	1.74542	0.872709	−	0.488240i	$-0.162361\pi$
$739$	1.41514e13	1.74542	0.872709	+	0.488240i	$0.162361\pi$
$740$	1.31987e13	1.61804
$741$	0	0
$742$	3.83379e12	0.464313
$743$	1.36261e13	1.64030	0.820148	−	0.572152i	$-0.193891\pi$
$743$	1.36261e13	1.64030	0.820148	+	0.572152i	$0.193891\pi$
$744$	0	0
$745$	−4.20660e12	−0.500297
$746$	1.28189e12	0.151540
$747$	0	0
$748$	5.62172e12	0.656617
$749$	2.50770e13	2.91144
$750$	0	0
$751$	−1.39601e13	−1.60143	−0.800715	−	0.599046i	$-0.795547\pi$
$751$	−1.39601e13	−1.60143	−0.800715	+	0.599046i	$0.795547\pi$
$752$	7.49148e12	0.854254
$753$	0	0
$754$	−3.76319e12	−0.424019
$755$	−3.35497e12	−0.375774
$756$	0	0
$757$	6.22034e12	0.688467	0.344233	−	0.938884i	$-0.388139\pi$
$757$	6.22034e12	0.688467	0.344233	+	0.938884i	$0.388139\pi$
$758$	1.77533e12	0.195329
$759$	0	0
$760$	8.58622e11	0.0933557
$761$	7.99871e12	0.864548	0.432274	−	0.901742i	$-0.357711\pi$
$761$	7.99871e12	0.864548	0.432274	+	0.901742i	$0.357711\pi$
$762$	0	0
$763$	7.08070e12	0.756338
$764$	9.25202e12	0.982464
$765$	0	0
$766$	2.64721e12	0.277818
$767$	−1.56468e13	−1.63248
$768$	0	0
$769$	−1.87310e13	−1.93149	−0.965745	−	0.259493i	$-0.916444\pi$
$769$	−1.87310e13	−1.93149	−0.965745	+	0.259493i	$0.916444\pi$
$770$	−1.90102e12	−0.194885
$771$	0	0
$772$	−1.25181e12	−0.126842
$773$	7.45839e12	0.751342	0.375671	−	0.926753i	$-0.377412\pi$
$773$	7.45839e12	0.751342	0.375671	+	0.926753i	$0.377412\pi$
$774$	0	0
$775$	−2.61429e12	−0.260313
$776$	4.41289e12	0.436863
$777$	0	0
$778$	1.75707e12	0.171941
$779$	3.82288e12	0.371939
$780$	0	0
$781$	8.68360e12	0.835161
$782$	1.30970e12	0.125240
$783$	0	0
$784$	2.72875e13	2.57953
$785$	2.78957e12	0.262194
$786$	0	0
$787$	−1.24079e13	−1.15295	−0.576476	−	0.817114i	$-0.695573\pi$
$787$	−1.24079e13	−1.15295	−0.576476	+	0.817114i	$0.695573\pi$
$788$	−1.31291e13	−1.21302
$789$	0	0
$790$	1.28527e12	0.117402
$791$	−1.13092e13	−1.02715
$792$	0	0
$793$	−1.12194e13	−1.00749
$794$	−3.35572e12	−0.299636
$795$	0	0
$796$	−1.22651e13	−1.08283
$797$	−4.11416e12	−0.361176	−0.180588	−	0.983559i	$-0.557800\pi$
$797$	−4.11416e12	−0.361176	−0.180588	+	0.983559i	$0.557800\pi$
$798$	0	0
$799$	1.31408e13	1.14067
$800$	−1.38531e12	−0.119575
$801$	0	0
$802$	−2.25427e12	−0.192408
$803$	9.03993e11	0.0767265
$804$	0	0
$805$	1.13449e13	0.952181
$806$	−3.78913e12	−0.316251
$807$	0	0
$808$	−1.34666e12	−0.111150
$809$	−1.87181e13	−1.53636	−0.768182	−	0.640231i	$-0.778838\pi$
$809$	−1.87181e13	−1.53636	−0.768182	+	0.640231i	$0.778838\pi$
$810$	0	0
$811$	−1.17522e13	−0.953949	−0.476975	−	0.878917i	$-0.658267\pi$
$811$	−1.17522e13	−0.953949	−0.476975	+	0.878917i	$0.658267\pi$
$812$	−3.79928e13	−3.06690
$813$	0	0
$814$	2.65107e12	0.211646
$815$	2.62679e12	0.208553
$816$	0	0
$817$	5.38428e11	0.0422793
$818$	1.44700e12	0.113000
$819$	0	0
$820$	1.47978e13	1.14297
$821$	−2.29795e13	−1.76521	−0.882605	−	0.470115i	$-0.844213\pi$
$821$	−2.29795e13	−1.76521	−0.882605	+	0.470115i	$0.844213\pi$
$822$	0	0
$823$	7.89246e12	0.599671	0.299836	−	0.953991i	$-0.403068\pi$
$823$	7.89246e12	0.599671	0.299836	+	0.953991i	$0.403068\pi$
$824$	1.68165e12	0.127076
$825$	0	0
$826$	6.16680e12	0.460946
$827$	1.43874e13	1.06957	0.534784	−	0.844989i	$-0.320393\pi$
$827$	1.43874e13	1.06957	0.534784	+	0.844989i	$0.320393\pi$
$828$	0	0
$829$	−1.40139e12	−0.103053	−0.0515267	−	0.998672i	$-0.516409\pi$
$829$	−1.40139e12	−0.103053	−0.0515267	+	0.998672i	$0.516409\pi$
$830$	−2.50677e12	−0.183342
$831$	0	0
$832$	1.46497e13	1.05992
$833$	4.78648e13	3.44440
$834$	0	0
$835$	9.83081e12	0.699842
$836$	−2.16659e12	−0.153408
$837$	0	0
$838$	−4.96811e11	−0.0348011
$839$	2.01539e13	1.40420	0.702101	−	0.712078i	$-0.252246\pi$
$839$	2.01539e13	1.40420	0.702101	+	0.712078i	$0.252246\pi$
$840$	0	0
$841$	2.32405e13	1.60200
$842$	−2.50353e12	−0.171652
$843$	0	0
$844$	−1.39644e13	−0.947287
$845$	1.10084e13	0.742796
$846$	0	0
$847$	−1.98094e13	−1.32250
$848$	1.62271e13	1.07760
$849$	0	0
$850$	−7.57420e11	−0.0497682
$851$	−1.58210e13	−1.03407
$852$	0	0
$853$	−1.31259e13	−0.848907	−0.424453	−	0.905450i	$-0.639534\pi$
$853$	−1.31259e13	−0.848907	−0.424453	+	0.905450i	$0.639534\pi$
$854$	4.42187e12	0.284476
$855$	0	0
$856$	−8.80615e12	−0.560601
$857$	8.66664e12	0.548829	0.274414	−	0.961612i	$-0.411516\pi$
$857$	8.66664e12	0.548829	0.274414	+	0.961612i	$0.411516\pi$
$858$	0	0
$859$	1.00716e13	0.631143	0.315571	−	0.948902i	$-0.397804\pi$
$859$	1.00716e13	0.631143	0.315571	+	0.948902i	$0.397804\pi$
$860$	2.08417e12	0.129924
$861$	0	0
$862$	2.36321e12	0.145787
$863$	8.56376e12	0.525552	0.262776	−	0.964857i	$-0.415362\pi$
$863$	8.56376e12	0.525552	0.262776	+	0.964857i	$0.415362\pi$
$864$	0	0
$865$	1.40298e13	0.852075
$866$	−3.79204e12	−0.229109
$867$	0	0
$868$	−3.82546e13	−2.28742
$869$	−6.61296e12	−0.393375
$870$	0	0
$871$	8.07788e12	0.475571
$872$	−2.48648e12	−0.145634
$873$	0	0
$874$	−5.04754e11	−0.0292603
$875$	−3.68837e13	−2.12715
$876$	0	0
$877$	−1.86361e12	−0.106379	−0.0531896	−	0.998584i	$-0.516939\pi$
$877$	−1.86361e12	−0.106379	−0.0531896	+	0.998584i	$0.516939\pi$
$878$	−1.67302e11	−0.00950113
$879$	0	0
$880$	−8.04635e12	−0.452300
$881$	−1.12984e13	−0.631868	−0.315934	−	0.948781i	$-0.602318\pi$
$881$	−1.12984e13	−0.631868	−0.315934	+	0.948781i	$0.602318\pi$
$882$	0	0
$883$	−1.69207e13	−0.936690	−0.468345	−	0.883546i	$-0.655150\pi$
$883$	−1.69207e13	−0.936690	−0.468345	+	0.883546i	$0.655150\pi$
$884$	2.81211e13	1.54881
$885$	0	0
$886$	−1.77373e12	−0.0967018
$887$	−1.15592e13	−0.627004	−0.313502	−	0.949588i	$-0.601502\pi$
$887$	−1.15592e13	−0.627004	−0.313502	+	0.949588i	$0.601502\pi$
$888$	0	0
$889$	4.04827e13	2.17376
$890$	−3.34693e12	−0.178810
$891$	0	0
$892$	4.26959e12	0.225810
$893$	−5.06439e12	−0.266499
$894$	0	0
$895$	1.91139e13	0.995741
$896$	−2.68362e13	−1.39103
$897$	0	0
$898$	−2.29386e12	−0.117713
$899$	3.80078e13	1.94068
$900$	0	0
$901$	2.84638e13	1.43890
$902$	2.97225e12	0.149505
$903$	0	0
$904$	3.97136e12	0.197780
$905$	1.39613e13	0.691842
$906$	0	0
$907$	−8.82407e12	−0.432948	−0.216474	−	0.976288i	$-0.569456\pi$
$907$	−8.82407e12	−0.432948	−0.216474	+	0.976288i	$0.569456\pi$
$908$	−9.49810e12	−0.463714
$909$	0	0
$910$	−9.50934e12	−0.459689
$911$	9.12800e12	0.439079	0.219540	−	0.975604i	$-0.429544\pi$
$911$	9.12800e12	0.439079	0.219540	+	0.975604i	$0.429544\pi$
$912$	0	0
$913$	1.28978e13	0.614321
$914$	−7.11463e12	−0.337205
$915$	0	0
$916$	1.13668e12	0.0533468
$917$	4.04306e13	1.88820
$918$	0	0
$919$	−1.89826e13	−0.877881	−0.438940	−	0.898516i	$-0.644646\pi$
$919$	−1.89826e13	−0.877881	−0.438940	+	0.898516i	$0.644646\pi$
$920$	−3.98392e12	−0.183343
$921$	0	0
$922$	2.47581e12	0.112831
$923$	4.34373e13	1.96995
$924$	0	0
$925$	9.14953e12	0.410924
$926$	−7.72101e11	−0.0345084
$927$	0	0
$928$	2.01403e13	0.891455
$929$	−1.66439e13	−0.733136	−0.366568	−	0.930391i	$-0.619467\pi$
$929$	−1.66439e13	−0.733136	−0.366568	+	0.930391i	$0.619467\pi$
$930$	0	0
$931$	−1.84469e13	−0.804729
$932$	−1.08433e13	−0.470748
$933$	0	0
$934$	−6.00008e11	−0.0257986
$935$	−1.41141e13	−0.603948
$936$	0	0
$937$	1.20784e13	0.511896	0.255948	−	0.966691i	$-0.417612\pi$
$937$	1.20784e13	0.511896	0.255948	+	0.966691i	$0.417612\pi$
$938$	−3.18370e12	−0.134282
$939$	0	0
$940$	−1.96035e13	−0.818950
$941$	1.09033e13	0.453320	0.226660	−	0.973974i	$-0.427219\pi$
$941$	1.09033e13	0.453320	0.226660	+	0.973974i	$0.427219\pi$
$942$	0	0
$943$	−1.77378e13	−0.730461
$944$	2.61019e13	1.06979
$945$	0	0
$946$	4.18622e11	0.0169946
$947$	−2.49583e13	−1.00842	−0.504209	−	0.863582i	$-0.668216\pi$
$947$	−2.49583e13	−1.00842	−0.504209	+	0.863582i	$0.668216\pi$
$948$	0	0
$949$	4.52198e12	0.180980
$950$	2.91907e11	0.0116275
$951$	0	0
$952$	−2.25992e13	−0.891715
$953$	1.44768e13	0.568530	0.284265	−	0.958746i	$-0.408250\pi$
$953$	1.44768e13	0.568530	0.284265	+	0.958746i	$0.408250\pi$
$954$	0	0
$955$	−2.32284e13	−0.903657
$956$	−1.79918e13	−0.696649
$957$	0	0
$958$	2.13365e12	0.0818423
$959$	5.05102e13	1.92839
$960$	0	0
$961$	1.18301e13	0.447437
$962$	1.32612e13	0.499225
$963$	0	0
$964$	−3.96951e13	−1.48044
$965$	3.14284e12	0.116667
$966$	0	0
$967$	−1.31877e12	−0.0485007	−0.0242504	−	0.999706i	$-0.507720\pi$
$967$	−1.31877e12	−0.0485007	−0.0242504	+	0.999706i	$0.507720\pi$
$968$	6.95635e12	0.254649
$969$	0	0
$970$	−5.43351e12	−0.197064
$971$	5.24865e13	1.89479	0.947394	−	0.320069i	$-0.103706\pi$
$971$	5.24865e13	1.89479	0.947394	+	0.320069i	$0.103706\pi$
$972$	0	0
$973$	2.96700e13	1.06123
$974$	−3.55525e12	−0.126577
$975$	0	0
$976$	1.87162e13	0.660227
$977$	−5.15657e13	−1.81065	−0.905327	−	0.424714i	$-0.860375\pi$
$977$	−5.15657e13	−1.81065	−0.905327	+	0.424714i	$0.860375\pi$
$978$	0	0
$979$	1.72206e13	0.599135
$980$	−7.14050e13	−2.47293
$981$	0	0
$982$	−4.91356e12	−0.168614
$983$	−2.11520e13	−0.722537	−0.361269	−	0.932462i	$-0.617656\pi$
$983$	−2.11520e13	−0.722537	−0.361269	+	0.932462i	$0.617656\pi$
$984$	0	0
$985$	3.29623e13	1.11572
$986$	1.10117e13	0.371030
$987$	0	0
$988$	−1.08378e13	−0.361854
$989$	−2.49825e12	−0.0830334
$990$	0	0
$991$	−4.73443e13	−1.55932	−0.779661	−	0.626201i	$-0.784609\pi$
$991$	−4.73443e13	−1.55932	−0.779661	+	0.626201i	$0.784609\pi$
$992$	2.02791e13	0.664883
$993$	0	0
$994$	−1.71197e13	−0.556235
$995$	3.07931e13	0.995977
$996$	0	0
$997$	−1.49776e13	−0.480081	−0.240041	−	0.970763i	$-0.577161\pi$
$997$	−1.49776e13	−0.480081	−0.240041	+	0.970763i	$0.577161\pi$
$998$	8.47966e12	0.270577
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.10.a.c.1.8		15
3.2	odd	2		43.10.a.a.1.8	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.8	✓	15	3.2	odd	2
387.10.a.c.1.8		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)

\(f(q)\)	\(=\)	\(q+4.38595 q^{2} -492.763 q^{4} +1237.15 q^{5} +12549.3 q^{7} -4406.84 q^{8} +O(q^{10})\)	\(q+4.38595 q^{2} -492.763 q^{4} +1237.15 q^{5} +12549.3 q^{7} -4406.84 q^{8} +5426.06 q^{10} -27918.0 q^{11} -139652. q^{13} +55040.4 q^{14} +232967. q^{16} +408645. q^{17} -157490. q^{19} -609620. q^{20} -122447. q^{22} +730739. q^{23} -422597. q^{25} -612508. q^{26} -6.18382e6 q^{28} +6.14391e6 q^{29} +6.18625e6 q^{31} +3.27808e6 q^{32} +1.79230e6 q^{34} +1.55253e7 q^{35} -2.16507e7 q^{37} -690744. q^{38} -5.45190e6 q^{40} -2.42738e7 q^{41} -3.41880e6 q^{43} +1.37570e7 q^{44} +3.20499e6 q^{46} +3.21569e7 q^{47} +1.17130e8 q^{49} -1.85349e6 q^{50} +6.88155e7 q^{52} +6.96541e7 q^{53} -3.45386e7 q^{55} -5.53026e7 q^{56} +2.69469e7 q^{58} +1.12041e8 q^{59} +8.03385e7 q^{61} +2.71326e7 q^{62} -1.04901e8 q^{64} -1.72770e8 q^{65} -5.78429e7 q^{67} -2.01366e8 q^{68} +6.80930e7 q^{70} -3.11039e8 q^{71} -3.23803e7 q^{73} -9.49590e7 q^{74} +7.76054e7 q^{76} -3.50350e8 q^{77} +2.36871e8 q^{79} +2.88214e8 q^{80} -1.06464e8 q^{82} -4.61987e8 q^{83} +5.05554e8 q^{85} -1.49947e7 q^{86} +1.23030e8 q^{88} -6.16826e8 q^{89} -1.75253e9 q^{91} -3.60082e8 q^{92} +1.41038e8 q^{94} -1.94838e8 q^{95} -1.00137e9 q^{97} +5.13728e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) \) 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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