LMFDB - Embedded newform 387.10.a.c.1.1

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			1.1
Root			$-45.0936$ 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)

$f(q)$	$=$	$q-43.0936 q^{2} +1345.05 q^{4} +1330.99 q^{5} -743.545 q^{7} -35899.3 q^{8} +O(q^{10})$	\(q-43.0936 q^{2} +1345.05 q^{4} +1330.99 q^{5} -743.545 q^{7} -35899.3 q^{8} -57356.9 q^{10} +60876.5 q^{11} -104090. q^{13} +32042.0 q^{14} +858359. q^{16} +344506. q^{17} -626694. q^{19} +1.79025e6 q^{20} -2.62338e6 q^{22} -1.13084e6 q^{23} -181604. q^{25} +4.48560e6 q^{26} -1.00011e6 q^{28} -3.51526e6 q^{29} -6.97177e6 q^{31} -1.86093e7 q^{32} -1.48460e7 q^{34} -989648. q^{35} +7.60065e6 q^{37} +2.70065e7 q^{38} -4.77814e7 q^{40} -3.04443e7 q^{41} -3.41880e6 q^{43} +8.18822e7 q^{44} +4.87317e7 q^{46} -3.57930e7 q^{47} -3.98007e7 q^{49} +7.82595e6 q^{50} -1.40006e8 q^{52} +9.41168e7 q^{53} +8.10257e7 q^{55} +2.66927e7 q^{56} +1.51485e8 q^{58} +1.25011e8 q^{59} +1.62742e8 q^{61} +3.00439e8 q^{62} +3.62462e8 q^{64} -1.38542e8 q^{65} +1.76153e8 q^{67} +4.63379e8 q^{68} +4.26474e7 q^{70} +7.75938e7 q^{71} -4.14592e8 q^{73} -3.27539e8 q^{74} -8.42937e8 q^{76} -4.52644e7 q^{77} +3.87411e8 q^{79} +1.14246e9 q^{80} +1.31195e9 q^{82} -1.61425e7 q^{83} +4.58532e8 q^{85} +1.47328e8 q^{86} -2.18542e9 q^{88} +1.53813e8 q^{89} +7.73955e7 q^{91} -1.52103e9 q^{92} +1.54245e9 q^{94} -8.34120e8 q^{95} +1.02217e9 q^{97} +1.71516e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−43.0936	−1.90448	−0.952242	−	0.305345i	$-0.901228\pi$
$2$	−43.0936	−1.90448	−0.952242	+	0.305345i	$0.901228\pi$
$3$	0	0
$3$	0	0
$4$	1345.05	2.62706
$5$	1330.99	0.952375	0.476188	−	0.879344i	$-0.342018\pi$
$5$	1330.99	0.952375	0.476188	+	0.879344i	$0.342018\pi$
$6$	0	0
$7$	−743.545	−0.117049	−0.0585243	−	0.998286i	$-0.518640\pi$
$7$	−743.545	−0.117049	−0.0585243	+	0.998286i	$0.518640\pi$
$8$	−35899.3	−3.09871
$9$	0	0
$10$	−57356.9	−1.81378
$11$	60876.5	1.25367	0.626834	−	0.779153i	$-0.284350\pi$
$11$	60876.5	1.25367	0.626834	+	0.779153i	$0.284350\pi$
$12$	0	0
$13$	−104090.	−1.01080	−0.505398	−	0.862887i	$-0.668654\pi$
$13$	−104090.	−1.01080	−0.505398	+	0.862887i	$0.668654\pi$
$14$	32042.0	0.222917
$15$	0	0
$16$	858359.	3.27438
$17$	344506.	1.00041	0.500203	−	0.865908i	$-0.333259\pi$
$17$	344506.	1.00041	0.500203	+	0.865908i	$0.333259\pi$
$18$	0	0
$19$	−626694.	−1.10323	−0.551613	−	0.834100i	$-0.685987\pi$
$19$	−626694.	−1.10323	−0.551613	+	0.834100i	$0.685987\pi$
$20$	1.79025e6	2.50195
$21$	0	0
$22$	−2.62338e6	−2.38759
$23$	−1.13084e6	−0.842605	−0.421303	−	0.906920i	$-0.638427\pi$
$23$	−1.13084e6	−0.842605	−0.421303	+	0.906920i	$0.638427\pi$
$24$	0	0
$25$	−181604.	−0.0929811
$26$	4.48560e6	1.92504
$27$	0	0
$28$	−1.00011e6	−0.307494
$29$	−3.51526e6	−0.922924	−0.461462	−	0.887160i	$-0.652675\pi$
$29$	−3.51526e6	−0.922924	−0.461462	+	0.887160i	$0.652675\pi$
$30$	0	0
$31$	−6.97177e6	−1.35586	−0.677931	−	0.735125i	$-0.737123\pi$
$31$	−6.97177e6	−1.35586	−0.677931	+	0.735125i	$0.737123\pi$
$32$	−1.86093e7	−3.13730
$33$	0	0
$34$	−1.48460e7	−1.90526
$35$	−989648.	−0.111474
$36$	0	0
$37$	7.60065e6	0.666719	0.333360	−	0.942800i	$-0.391818\pi$
$37$	7.60065e6	0.666719	0.333360	+	0.942800i	$0.391818\pi$
$38$	2.70065e7	2.10108
$39$	0	0
$40$	−4.77814e7	−2.95113
$41$	−3.04443e7	−1.68259	−0.841296	−	0.540575i	$-0.818207\pi$
$41$	−3.04443e7	−1.68259	−0.841296	+	0.540575i	$0.818207\pi$
$42$	0	0
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	8.18822e7	3.29346
$45$	0	0
$46$	4.87317e7	1.60473
$47$	−3.57930e7	−1.06994	−0.534968	−	0.844872i	$-0.679676\pi$
$47$	−3.57930e7	−1.06994	−0.534968	+	0.844872i	$0.679676\pi$
$48$	0	0
$49$	−3.98007e7	−0.986300
$50$	7.82595e6	0.177081
$51$	0	0
$52$	−1.40006e8	−2.65542
$53$	9.41168e7	1.63842	0.819211	−	0.573492i	$-0.194412\pi$
$53$	9.41168e7	1.63842	0.819211	+	0.573492i	$0.194412\pi$
$54$	0	0
$55$	8.10257e7	1.19396
$56$	2.66927e7	0.362699
$57$	0	0
$58$	1.51485e8	1.75769
$59$	1.25011e8	1.34312	0.671561	−	0.740949i	$-0.265624\pi$
$59$	1.25011e8	1.34312	0.671561	+	0.740949i	$0.265624\pi$
$60$	0	0
$61$	1.62742e8	1.50493	0.752464	−	0.658633i	$-0.228865\pi$
$61$	1.62742e8	1.50493	0.752464	+	0.658633i	$0.228865\pi$
$62$	3.00439e8	2.58222
$63$	0	0
$64$	3.62462e8	2.70055
$65$	−1.38542e8	−0.962656
$66$	0	0
$67$	1.76153e8	1.06796	0.533978	−	0.845498i	$-0.320697\pi$
$67$	1.76153e8	1.06796	0.533978	+	0.845498i	$0.320697\pi$
$68$	4.63379e8	2.62813
$69$	0	0
$70$	4.26474e7	0.212301
$71$	7.75938e7	0.362380	0.181190	−	0.983448i	$-0.442005\pi$
$71$	7.75938e7	0.362380	0.181190	+	0.983448i	$0.442005\pi$
$72$	0	0
$73$	−4.14592e8	−1.70871	−0.854354	−	0.519692i	$-0.826047\pi$
$73$	−4.14592e8	−1.70871	−0.854354	+	0.519692i	$0.826047\pi$
$74$	−3.27539e8	−1.26976
$75$	0	0
$76$	−8.42937e8	−2.89824
$77$	−4.52644e7	−0.146740
$78$	0	0
$79$	3.87411e8	1.11905	0.559526	−	0.828813i	$-0.310983\pi$
$79$	3.87411e8	1.11905	0.559526	+	0.828813i	$0.310983\pi$
$80$	1.14246e9	3.11844
$81$	0	0
$82$	1.31195e9	3.20447
$83$	−1.61425e7	−0.0373354	−0.0186677	−	0.999826i	$-0.505942\pi$
$83$	−1.61425e7	−0.0373354	−0.0186677	+	0.999826i	$0.505942\pi$
$84$	0	0
$85$	4.58532e8	0.952763
$86$	1.47328e8	0.290431
$87$	0	0
$88$	−2.18542e9	−3.88475
$89$	1.53813e8	0.259859	0.129929	−	0.991523i	$-0.458525\pi$
$89$	1.53813e8	0.259859	0.129929	+	0.991523i	$0.458525\pi$
$90$	0	0
$91$	7.73955e7	0.118312
$92$	−1.52103e9	−2.21357
$93$	0	0
$94$	1.54245e9	2.03768
$95$	−8.34120e8	−1.05069
$96$	0	0
$97$	1.02217e9	1.17233	0.586167	−	0.810190i	$-0.300636\pi$
$97$	1.02217e9	1.17233	0.586167	+	0.810190i	$0.300636\pi$
$98$	1.71516e9	1.87839
$99$	0	0
$100$	−2.44267e8	−0.244267
$101$	6.67110e8	0.637898	0.318949	−	0.947772i	$-0.396670\pi$
$101$	6.67110e8	0.637898	0.318949	+	0.947772i	$0.396670\pi$
$102$	0	0
$103$	6.79368e7	0.0594754	0.0297377	−	0.999558i	$-0.490533\pi$
$103$	6.79368e7	0.0594754	0.0297377	+	0.999558i	$0.490533\pi$
$104$	3.73675e9	3.13216
$105$	0	0
$106$	−4.05583e9	−3.12035
$107$	1.71864e9	1.26753	0.633766	−	0.773525i	$-0.281508\pi$
$107$	1.71864e9	1.26753	0.633766	+	0.773525i	$0.281508\pi$
$108$	0	0
$109$	−1.49887e9	−1.01706	−0.508530	−	0.861045i	$-0.669811\pi$
$109$	−1.49887e9	−1.01706	−0.508530	+	0.861045i	$0.669811\pi$
$110$	−3.49169e9	−2.27388
$111$	0	0
$112$	−6.38229e8	−0.383262
$113$	4.77264e8	0.275363	0.137681	−	0.990477i	$-0.456035\pi$
$113$	4.77264e8	0.275363	0.137681	+	0.990477i	$0.456035\pi$
$114$	0	0
$115$	−1.50512e9	−0.802476
$116$	−4.72821e9	−2.42458
$117$	0	0
$118$	−5.38718e9	−2.55795
$119$	−2.56156e8	−0.117096
$120$	0	0
$121$	1.34800e9	0.571684
$122$	−7.01314e9	−2.86611
$123$	0	0
$124$	−9.37741e9	−3.56193
$125$	−2.84129e9	−1.04093
$126$	0	0
$127$	1.95999e9	0.668556	0.334278	−	0.942475i	$-0.391508\pi$
$127$	1.95999e9	0.668556	0.334278	+	0.942475i	$0.391508\pi$
$128$	−6.09179e9	−2.00586
$129$	0	0
$130$	5.97027e9	1.83336
$131$	3.31045e9	0.982123	0.491061	−	0.871125i	$-0.336609\pi$
$131$	3.31045e9	0.982123	0.491061	+	0.871125i	$0.336609\pi$
$132$	0	0
$133$	4.65975e8	0.129131
$134$	−7.59106e9	−2.03391
$135$	0	0
$136$	−1.23675e10	−3.09997
$137$	6.47943e9	1.57143	0.785713	−	0.618591i	$-0.212296\pi$
$137$	6.47943e9	1.57143	0.785713	+	0.618591i	$0.212296\pi$
$138$	0	0
$139$	−6.83083e9	−1.55206	−0.776028	−	0.630699i	$-0.782768\pi$
$139$	−6.83083e9	−1.55206	−0.776028	+	0.630699i	$0.782768\pi$
$140$	−1.33113e9	−0.292849
$141$	0	0
$142$	−3.34379e9	−0.690147
$143$	−6.33662e9	−1.26720
$144$	0	0
$145$	−4.67875e9	−0.878970
$146$	1.78662e10	3.25421
$147$	0	0
$148$	1.02233e10	1.75151
$149$	5.71164e9	0.949341	0.474671	−	0.880164i	$-0.342567\pi$
$149$	5.71164e9	0.949341	0.474671	+	0.880164i	$0.342567\pi$
$150$	0	0
$151$	6.90224e9	1.08042	0.540211	−	0.841530i	$-0.318344\pi$
$151$	6.90224e9	1.08042	0.540211	+	0.841530i	$0.318344\pi$
$152$	2.24979e10	3.41857
$153$	0	0
$154$	1.95061e9	0.279464
$155$	−9.27933e9	−1.29129
$156$	0	0
$157$	6.65621e8	0.0874336	0.0437168	−	0.999044i	$-0.486080\pi$
$157$	6.65621e8	0.0874336	0.0437168	+	0.999044i	$0.486080\pi$
$158$	−1.66949e10	−2.13122
$159$	0	0
$160$	−2.47687e10	−2.98788
$161$	8.40827e8	0.0986258
$162$	0	0
$163$	−7.03047e9	−0.780082	−0.390041	−	0.920798i	$-0.627539\pi$
$163$	−7.03047e9	−0.780082	−0.390041	+	0.920798i	$0.627539\pi$
$164$	−4.09492e10	−4.42027
$165$	0	0
$166$	6.95639e8	0.0711046
$167$	−7.10666e9	−0.707036	−0.353518	−	0.935428i	$-0.615015\pi$
$167$	−7.10666e9	−0.707036	−0.353518	+	0.935428i	$0.615015\pi$
$168$	0	0
$169$	2.30190e8	0.0217068
$170$	−1.97598e10	−1.81452
$171$	0	0
$172$	−4.59847e9	−0.400623
$173$	1.52722e10	1.29627	0.648134	−	0.761527i	$-0.275550\pi$
$173$	1.52722e10	1.29627	0.648134	+	0.761527i	$0.275550\pi$
$174$	0	0
$175$	1.35031e8	0.0108833
$176$	5.22539e10	4.10499
$177$	0	0
$178$	−6.62834e9	−0.494897
$179$	3.28112e8	0.0238882	0.0119441	−	0.999929i	$-0.496198\pi$
$179$	3.28112e8	0.0238882	0.0119441	+	0.999929i	$0.496198\pi$
$180$	0	0
$181$	1.38266e9	0.0957554	0.0478777	−	0.998853i	$-0.484754\pi$
$181$	1.38266e9	0.0957554	0.0478777	+	0.998853i	$0.484754\pi$
$182$	−3.33525e9	−0.225324
$183$	0	0
$184$	4.05961e10	2.61099
$185$	1.01164e10	0.634967
$186$	0	0
$187$	2.09723e10	1.25418
$188$	−4.81436e10	−2.81079
$189$	0	0
$190$	3.59452e10	2.00101
$191$	−1.10617e10	−0.601411	−0.300706	−	0.953717i	$-0.597222\pi$
$191$	−1.10617e10	−0.601411	−0.300706	+	0.953717i	$0.597222\pi$
$192$	0	0
$193$	1.56904e10	0.814005	0.407003	−	0.913427i	$-0.366574\pi$
$193$	1.56904e10	0.814005	0.407003	+	0.913427i	$0.366574\pi$
$194$	−4.40490e10	−2.23269
$195$	0	0
$196$	−5.35342e10	−2.59107
$197$	1.54645e10	0.731538	0.365769	−	0.930706i	$-0.380806\pi$
$197$	1.54645e10	0.731538	0.365769	+	0.930706i	$0.380806\pi$
$198$	0	0
$199$	1.72181e10	0.778300	0.389150	−	0.921174i	$-0.372769\pi$
$199$	1.72181e10	0.778300	0.389150	+	0.921174i	$0.372769\pi$
$200$	6.51944e9	0.288121
$201$	0	0
$202$	−2.87482e10	−1.21487
$203$	2.61375e9	0.108027
$204$	0	0
$205$	−4.05209e10	−1.60246
$206$	−2.92764e9	−0.113270
$207$	0	0
$208$	−8.93464e10	−3.30973
$209$	−3.81509e10	−1.38308
$210$	0	0
$211$	2.45117e10	0.851337	0.425669	−	0.904879i	$-0.360039\pi$
$211$	2.45117e10	0.851337	0.425669	+	0.904879i	$0.360039\pi$
$212$	1.26592e11	4.30423
$213$	0	0
$214$	−7.40625e10	−2.41400
$215$	−4.55037e9	−0.145236
$216$	0	0
$217$	5.18383e9	0.158702
$218$	6.45918e10	1.93697
$219$	0	0
$220$	1.08984e11	3.13661
$221$	−3.58596e10	−1.01121
$222$	0	0
$223$	3.43688e9	0.0930664	0.0465332	−	0.998917i	$-0.485183\pi$
$223$	3.43688e9	0.0930664	0.0465332	+	0.998917i	$0.485183\pi$
$224$	1.38369e10	0.367216
$225$	0	0
$226$	−2.05670e10	−0.524424
$227$	−1.17388e10	−0.293431	−0.146716	−	0.989179i	$-0.546870\pi$
$227$	−1.17388e10	−0.293431	−0.146716	+	0.989179i	$0.546870\pi$
$228$	0	0
$229$	−8.32583e8	−0.0200064	−0.0100032	−	0.999950i	$-0.503184\pi$
$229$	−8.32583e8	−0.0200064	−0.0100032	+	0.999950i	$0.503184\pi$
$230$	6.48612e10	1.52830
$231$	0	0
$232$	1.26195e11	2.85987
$233$	7.38751e9	0.164209	0.0821044	−	0.996624i	$-0.473836\pi$
$233$	7.38751e9	0.164209	0.0821044	+	0.996624i	$0.473836\pi$
$234$	0	0
$235$	−4.76400e10	−1.01898
$236$	1.68147e11	3.52846
$237$	0	0
$238$	1.10387e10	0.223008
$239$	−3.60402e10	−0.714492	−0.357246	−	0.934010i	$-0.616284\pi$
$239$	−3.60402e10	−0.714492	−0.357246	+	0.934010i	$0.616284\pi$
$240$	0	0
$241$	5.35383e10	1.02232	0.511161	−	0.859485i	$-0.329216\pi$
$241$	5.35383e10	1.02232	0.511161	+	0.859485i	$0.329216\pi$
$242$	−5.80902e10	−1.08876
$243$	0	0
$244$	2.18897e11	3.95354
$245$	−5.29742e10	−0.939327
$246$	0	0
$247$	6.52325e10	1.11514
$248$	2.50282e11	4.20142
$249$	0	0
$250$	1.22441e11	1.98243
$251$	−8.37307e10	−1.33154	−0.665768	−	0.746159i	$-0.731896\pi$
$251$	−8.37307e10	−1.33154	−0.665768	+	0.746159i	$0.731896\pi$
$252$	0	0
$253$	−6.88413e10	−1.05635
$254$	−8.44630e10	−1.27325
$255$	0	0
$256$	7.69365e10	1.11957
$257$	9.28756e10	1.32801	0.664007	−	0.747726i	$-0.268854\pi$
$257$	9.28756e10	1.32801	0.664007	+	0.747726i	$0.268854\pi$
$258$	0	0
$259$	−5.65143e9	−0.0780386
$260$	−1.86346e11	−2.52896
$261$	0	0
$262$	−1.42659e11	−1.87044
$263$	−4.81389e10	−0.620434	−0.310217	−	0.950666i	$-0.600402\pi$
$263$	−4.81389e10	−0.620434	−0.310217	+	0.950666i	$0.600402\pi$
$264$	0	0
$265$	1.25268e11	1.56039
$266$	−2.00805e10	−0.245928
$267$	0	0
$268$	2.36935e11	2.80558
$269$	5.22733e10	0.608688	0.304344	−	0.952562i	$-0.401563\pi$
$269$	5.22733e10	0.608688	0.304344	+	0.952562i	$0.401563\pi$
$270$	0	0
$271$	−1.23731e9	−0.0139354	−0.00696768	−	0.999976i	$-0.502218\pi$
$271$	−1.23731e9	−0.0139354	−0.00696768	+	0.999976i	$0.502218\pi$
$272$	2.95710e11	3.27571
$273$	0	0
$274$	−2.79221e11	−2.99276
$275$	−1.10554e10	−0.116567
$276$	0	0
$277$	−1.26159e10	−0.128754	−0.0643768	−	0.997926i	$-0.520506\pi$
$277$	−1.26159e10	−0.128754	−0.0643768	+	0.997926i	$0.520506\pi$
$278$	2.94365e11	2.95586
$279$	0	0
$280$	3.55276e10	0.345426
$281$	−3.54512e10	−0.339197	−0.169599	−	0.985513i	$-0.554247\pi$
$281$	−3.54512e10	−0.339197	−0.169599	+	0.985513i	$0.554247\pi$
$282$	0	0
$283$	−4.93389e10	−0.457247	−0.228624	−	0.973515i	$-0.573422\pi$
$283$	−4.93389e10	−0.457247	−0.228624	+	0.973515i	$0.573422\pi$
$284$	1.04368e11	0.951994
$285$	0	0
$286$	2.73068e11	2.41337
$287$	2.26367e10	0.196945
$288$	0	0
$289$	9.64955e7	0.000813704 0
$290$	2.01624e11	1.67398
$291$	0	0
$292$	−5.57648e11	−4.48888
$293$	−8.58588e9	−0.0680582	−0.0340291	−	0.999421i	$-0.510834\pi$
$293$	−8.58588e9	−0.0680582	−0.0340291	+	0.999421i	$0.510834\pi$
$294$	0	0
$295$	1.66388e11	1.27916
$296$	−2.72858e11	−2.06597
$297$	0	0
$298$	−2.46135e11	−1.80800
$299$	1.17708e11	0.851701
$300$	0	0
$301$	2.54203e9	0.0178497
$302$	−2.97442e11	−2.05765
$303$	0	0
$304$	−5.37928e11	−3.61238
$305$	2.16607e11	1.43326
$306$	0	0
$307$	−1.78128e11	−1.14448	−0.572241	−	0.820085i	$-0.693926\pi$
$307$	−1.78128e11	−1.14448	−0.572241	+	0.820085i	$0.693926\pi$
$308$	−6.08831e10	−0.385495
$309$	0	0
$310$	3.99879e11	2.45924
$311$	1.70733e11	1.03489	0.517447	−	0.855715i	$-0.326882\pi$
$311$	1.70733e11	1.03489	0.517447	+	0.855715i	$0.326882\pi$
$312$	0	0
$313$	1.90876e11	1.12409	0.562046	−	0.827106i	$-0.310015\pi$
$313$	1.90876e11	1.12409	0.562046	+	0.827106i	$0.310015\pi$
$314$	−2.86840e10	−0.166516
$315$	0	0
$316$	5.21089e11	2.93982
$317$	−9.34241e10	−0.519628	−0.259814	−	0.965659i	$-0.583661\pi$
$317$	−9.34241e10	−0.519628	−0.259814	+	0.965659i	$0.583661\pi$
$318$	0	0
$319$	−2.13997e11	−1.15704
$320$	4.82431e11	2.57194
$321$	0	0
$322$	−3.62342e10	−0.187831
$323$	−2.15900e11	−1.10367
$324$	0	0
$325$	1.89031e10	0.0939849
$326$	3.02968e11	1.48565
$327$	0	0
$328$	1.09293e12	5.21386
$329$	2.66137e10	0.125235
$330$	0	0
$331$	5.97363e10	0.273535	0.136767	−	0.990603i	$-0.456329\pi$
$331$	5.97363e10	0.273535	0.136767	+	0.990603i	$0.456329\pi$
$332$	−2.17126e10	−0.0980822
$333$	0	0
$334$	3.06251e11	1.34654
$335$	2.34457e11	1.01710
$336$	0	0
$337$	1.79056e11	0.756230	0.378115	−	0.925759i	$-0.376572\pi$
$337$	1.79056e11	0.756230	0.378115	+	0.925759i	$0.376572\pi$
$338$	−9.91969e9	−0.0413403
$339$	0	0
$340$	6.16751e11	2.50296
$341$	−4.24417e11	−1.69980
$342$	0	0
$343$	5.95984e10	0.232494
$344$	1.22732e11	0.472548
$345$	0	0
$346$	−6.58134e11	−2.46872
$347$	3.88777e11	1.43952	0.719760	−	0.694223i	$-0.244252\pi$
$347$	3.88777e11	1.43952	0.719760	+	0.694223i	$0.244252\pi$
$348$	0	0
$349$	−4.77801e11	−1.72398	−0.861991	−	0.506923i	$-0.830783\pi$
$349$	−4.77801e11	−1.72398	−0.861991	+	0.506923i	$0.830783\pi$
$350$	−5.81895e9	−0.0207271
$351$	0	0
$352$	−1.13287e12	−3.93313
$353$	5.04077e11	1.72787	0.863933	−	0.503606i	$-0.167994\pi$
$353$	5.04077e11	1.72787	0.863933	+	0.503606i	$0.167994\pi$
$354$	0	0
$355$	1.03276e11	0.345122
$356$	2.06887e11	0.682665
$357$	0	0
$358$	−1.41395e10	−0.0454946
$359$	−4.17951e11	−1.32801	−0.664004	−	0.747729i	$-0.731144\pi$
$359$	−4.17951e11	−1.32801	−0.664004	+	0.747729i	$0.731144\pi$
$360$	0	0
$361$	7.00577e10	0.217107
$362$	−5.95839e10	−0.182365
$363$	0	0
$364$	1.04101e11	0.310813
$365$	−5.51816e11	−1.62733
$366$	0	0
$367$	5.55628e11	1.59877	0.799387	−	0.600817i	$-0.205158\pi$
$367$	5.55628e11	1.59877	0.799387	+	0.600817i	$0.205158\pi$
$368$	−9.70662e11	−2.75901
$369$	0	0
$370$	−4.35950e11	−1.20928
$371$	−6.99801e10	−0.191775
$372$	0	0
$373$	−6.91524e11	−1.84977	−0.924885	−	0.380247i	$-0.875839\pi$
$373$	−6.91524e11	−1.84977	−0.924885	+	0.380247i	$0.875839\pi$
$374$	−9.03772e11	−2.38856
$375$	0	0
$376$	1.28494e12	3.31542
$377$	3.65902e11	0.932887
$378$	0	0
$379$	5.21767e11	1.29897	0.649486	−	0.760373i	$-0.274984\pi$
$379$	5.21767e11	1.29897	0.649486	+	0.760373i	$0.274984\pi$
$380$	−1.12194e12	−2.76021
$381$	0	0
$382$	4.76688e11	1.14538
$383$	6.52757e11	1.55009	0.775045	−	0.631906i	$-0.217727\pi$
$383$	6.52757e11	1.55009	0.775045	+	0.631906i	$0.217727\pi$
$384$	0	0
$385$	−6.02463e10	−0.139752
$386$	−6.76157e11	−1.55026
$387$	0	0
$388$	1.37488e12	3.07979
$389$	−3.45861e11	−0.765823	−0.382912	−	0.923785i	$-0.625079\pi$
$389$	−3.45861e11	−0.765823	−0.382912	+	0.923785i	$0.625079\pi$
$390$	0	0
$391$	−3.89579e11	−0.842948
$392$	1.42882e12	3.05625
$393$	0	0
$394$	−6.66419e11	−1.39320
$395$	5.15639e11	1.06576
$396$	0	0
$397$	1.97139e11	0.398305	0.199152	−	0.979969i	$-0.436181\pi$
$397$	1.97139e11	0.398305	0.199152	+	0.979969i	$0.436181\pi$
$398$	−7.41990e11	−1.48226
$399$	0	0
$400$	−1.55881e11	−0.304455
$401$	9.67496e11	1.86853	0.934263	−	0.356584i	$-0.116059\pi$
$401$	9.67496e11	1.86853	0.934263	+	0.356584i	$0.116059\pi$
$402$	0	0
$403$	7.25691e11	1.37050
$404$	8.97300e11	1.67580
$405$	0	0
$406$	−1.12636e11	−0.205736
$407$	4.62701e11	0.835845
$408$	0	0
$409$	−7.33241e11	−1.29566	−0.647831	−	0.761784i	$-0.724324\pi$
$409$	−7.33241e11	−1.29566	−0.647831	+	0.761784i	$0.724324\pi$
$410$	1.74619e12	3.05186
$411$	0	0
$412$	9.13786e10	0.156245
$413$	−9.29516e10	−0.157211
$414$	0	0
$415$	−2.14855e10	−0.0355573
$416$	1.93704e12	3.17116
$417$	0	0
$418$	1.64406e12	2.63405
$419$	−1.00496e11	−0.159289	−0.0796443	−	0.996823i	$-0.525378\pi$
$419$	−1.00496e11	−0.159289	−0.0796443	+	0.996823i	$0.525378\pi$
$420$	0	0
$421$	8.88132e10	0.137787	0.0688935	−	0.997624i	$-0.478053\pi$
$421$	8.88132e10	0.137787	0.0688935	+	0.997624i	$0.478053\pi$
$422$	−1.05629e12	−1.62136
$423$	0	0
$424$	−3.37872e12	−5.07699
$425$	−6.25636e10	−0.0930189
$426$	0	0
$427$	−1.21006e11	−0.176150
$428$	2.31167e12	3.32988
$429$	0	0
$430$	1.96092e11	0.276599
$431$	−4.61691e11	−0.644471	−0.322236	−	0.946660i	$-0.604434\pi$
$431$	−4.61691e11	−0.644471	−0.322236	+	0.946660i	$0.604434\pi$
$432$	0	0
$433$	5.27475e11	0.721119	0.360559	−	0.932736i	$-0.382586\pi$
$433$	5.27475e11	0.721119	0.360559	+	0.932736i	$0.382586\pi$
$434$	−2.23390e11	−0.302245
$435$	0	0
$436$	−2.01607e12	−2.67187
$437$	7.08688e11	0.929584
$438$	0	0
$439$	7.31485e11	0.939973	0.469986	−	0.882674i	$-0.344259\pi$
$439$	7.31485e11	0.939973	0.469986	+	0.882674i	$0.344259\pi$
$440$	−2.90876e12	−3.69974
$441$	0	0
$442$	1.54532e12	1.92583
$443$	4.46593e11	0.550929	0.275464	−	0.961311i	$-0.411168\pi$
$443$	4.46593e11	0.550929	0.275464	+	0.961311i	$0.411168\pi$
$444$	0	0
$445$	2.04723e11	0.247483
$446$	−1.48108e11	−0.177243
$447$	0	0
$448$	−2.69507e11	−0.316096
$449$	3.25387e11	0.377826	0.188913	−	0.981994i	$-0.439504\pi$
$449$	3.25387e11	0.377826	0.188913	+	0.981994i	$0.439504\pi$
$450$	0	0
$451$	−1.85334e12	−2.10941
$452$	6.41945e11	0.723394
$453$	0	0
$454$	5.05865e11	0.558835
$455$	1.03012e11	0.112678
$456$	0	0
$457$	−1.70489e12	−1.82841	−0.914203	−	0.405257i	$-0.867182\pi$
$457$	−1.70489e12	−1.82841	−0.914203	+	0.405257i	$0.867182\pi$
$458$	3.58790e10	0.0381018
$459$	0	0
$460$	−2.02447e12	−2.10815
$461$	4.25542e11	0.438821	0.219411	−	0.975633i	$-0.429587\pi$
$461$	4.25542e11	0.438821	0.219411	+	0.975633i	$0.429587\pi$
$462$	0	0
$463$	1.43391e12	1.45013	0.725065	−	0.688681i	$-0.241810\pi$
$463$	1.43391e12	1.45013	0.725065	+	0.688681i	$0.241810\pi$
$464$	−3.01735e12	−3.02200
$465$	0	0
$466$	−3.18354e11	−0.312733
$467$	3.64292e11	0.354424	0.177212	−	0.984173i	$-0.443292\pi$
$467$	3.64292e11	0.354424	0.177212	+	0.984173i	$0.443292\pi$
$468$	0	0
$469$	−1.30978e11	−0.125003
$470$	2.05298e12	1.94063
$471$	0	0
$472$	−4.48782e12	−4.16194
$473$	−2.08125e11	−0.191183
$474$	0	0
$475$	1.13810e11	0.102579
$476$	−3.44543e11	−0.307619
$477$	0	0
$478$	1.55310e12	1.36074
$479$	−1.17368e12	−1.01869	−0.509344	−	0.860563i	$-0.670112\pi$
$479$	−1.17368e12	−1.01869	−0.509344	+	0.860563i	$0.670112\pi$
$480$	0	0
$481$	−7.91150e11	−0.673917
$482$	−2.30716e12	−1.94700
$483$	0	0
$484$	1.81314e12	1.50185
$485$	1.36050e12	1.11650
$486$	0	0
$487$	−2.54555e11	−0.205070	−0.102535	−	0.994729i	$-0.532695\pi$
$487$	−2.54555e11	−0.205070	−0.102535	+	0.994729i	$0.532695\pi$
$488$	−5.84233e12	−4.66333
$489$	0	0
$490$	2.28285e12	1.78893
$491$	1.23895e11	0.0962028	0.0481014	−	0.998842i	$-0.484683\pi$
$491$	1.23895e11	0.0962028	0.0481014	+	0.998842i	$0.484683\pi$
$492$	0	0
$493$	−1.21103e12	−0.923300
$494$	−2.81110e12	−2.12376
$495$	0	0
$496$	−5.98429e12	−4.43961
$497$	−5.76945e10	−0.0424161
$498$	0	0
$499$	−1.43556e12	−1.03650	−0.518250	−	0.855229i	$-0.673416\pi$
$499$	−1.43556e12	−1.03650	−0.518250	+	0.855229i	$0.673416\pi$
$500$	−3.82169e12	−2.73458
$501$	0	0
$502$	3.60825e12	2.53589
$503$	2.19255e12	1.52719	0.763595	−	0.645695i	$-0.223432\pi$
$503$	2.19255e12	1.52719	0.763595	+	0.645695i	$0.223432\pi$
$504$	0	0
$505$	8.87914e11	0.607519
$506$	2.96662e12	2.01180
$507$	0	0
$508$	2.63630e12	1.75633
$509$	−8.92806e11	−0.589559	−0.294779	−	0.955565i	$-0.595246\pi$
$509$	−8.92806e11	−0.589559	−0.294779	+	0.955565i	$0.595246\pi$
$510$	0	0
$511$	3.08268e11	0.200002
$512$	−1.96471e11	−0.126352
$513$	0	0
$514$	−4.00234e12	−2.52918
$515$	9.04228e10	0.0566429
$516$	0	0
$517$	−2.17895e12	−1.34135
$518$	2.43540e11	0.148623
$519$	0	0
$520$	4.97356e12	2.98299
$521$	−1.73495e12	−1.03161	−0.515807	−	0.856705i	$-0.672508\pi$
$521$	−1.73495e12	−1.03161	−0.515807	+	0.856705i	$0.672508\pi$
$522$	0	0
$523$	2.26368e12	1.32299	0.661497	−	0.749948i	$-0.269921\pi$
$523$	2.26368e12	1.32299	0.661497	+	0.749948i	$0.269921\pi$
$524$	4.45273e12	2.58009
$525$	0	0
$526$	2.07448e12	1.18161
$527$	−2.40182e12	−1.35641
$528$	0	0
$529$	−5.22364e11	−0.290017
$530$	−5.39825e12	−2.97174
$531$	0	0
$532$	6.26762e11	0.339235
$533$	3.16894e12	1.70076
$534$	0	0
$535$	2.28749e12	1.20717
$536$	−6.32376e12	−3.30928
$537$	0	0
$538$	−2.25264e12	−1.15924
$539$	−2.42293e12	−1.23649
$540$	0	0
$541$	7.85800e11	0.394388	0.197194	−	0.980364i	$-0.436817\pi$
$541$	7.85800e11	0.394388	0.197194	+	0.980364i	$0.436817\pi$
$542$	5.33202e10	0.0265397
$543$	0	0
$544$	−6.41102e12	−3.13857
$545$	−1.99498e12	−0.968622
$546$	0	0
$547$	−8.14762e11	−0.389124	−0.194562	−	0.980890i	$-0.562329\pi$
$547$	−8.14762e11	−0.389124	−0.194562	+	0.980890i	$0.562329\pi$
$548$	8.71518e12	4.12823
$549$	0	0
$550$	4.76417e11	0.222001
$551$	2.20299e12	1.01819
$552$	0	0
$553$	−2.88058e11	−0.130984
$554$	5.43664e11	0.245209
$555$	0	0
$556$	−9.18784e12	−4.07734
$557$	−2.73409e12	−1.20355	−0.601775	−	0.798666i	$-0.705540\pi$
$557$	−2.73409e12	−1.20355	−0.601775	+	0.798666i	$0.705540\pi$
$558$	0	0
$559$	3.55862e11	0.154145
$560$	−8.49473e11	−0.365009
$561$	0	0
$562$	1.52772e12	0.645996
$563$	−9.71533e11	−0.407540	−0.203770	−	0.979019i	$-0.565319\pi$
$563$	−9.71533e11	−0.407540	−0.203770	+	0.979019i	$0.565319\pi$
$564$	0	0
$565$	6.35231e11	0.262249
$566$	2.12619e12	0.870820
$567$	0	0
$568$	−2.78556e12	−1.12291
$569$	−2.53670e12	−1.01453	−0.507265	−	0.861790i	$-0.669343\pi$
$569$	−2.53670e12	−1.01453	−0.507265	+	0.861790i	$0.669343\pi$
$570$	0	0
$571$	4.31961e12	1.70052	0.850261	−	0.526361i	$-0.176444\pi$
$571$	4.31961e12	1.70052	0.850261	+	0.526361i	$0.176444\pi$
$572$	−8.52310e12	−3.32901
$573$	0	0
$574$	−9.75497e11	−0.375079
$575$	2.05364e11	0.0783464
$576$	0	0
$577$	1.89784e12	0.712801	0.356401	−	0.934333i	$-0.384004\pi$
$577$	1.89784e12	0.712801	0.356401	+	0.934333i	$0.384004\pi$
$578$	−4.15833e9	−0.00154969
$579$	0	0
$580$	−6.29318e12	−2.30911
$581$	1.20027e10	0.00437005
$582$	0	0
$583$	5.72950e12	2.05404
$584$	1.48835e13	5.29479
$585$	0	0
$586$	3.69996e11	0.129616
$587$	−2.77649e12	−0.965216	−0.482608	−	0.875837i	$-0.660310\pi$
$587$	−2.77649e12	−0.965216	−0.482608	+	0.875837i	$0.660310\pi$
$588$	0	0
$589$	4.36917e12	1.49582
$590$	−7.17026e12	−2.43613
$591$	0	0
$592$	6.52409e12	2.18309
$593$	2.88583e11	0.0958352	0.0479176	−	0.998851i	$-0.484742\pi$
$593$	2.88583e11	0.0958352	0.0479176	+	0.998851i	$0.484742\pi$
$594$	0	0
$595$	−3.40940e11	−0.111520
$596$	7.68246e12	2.49397
$597$	0	0
$598$	−5.07247e12	−1.62205
$599$	−2.66006e12	−0.844250	−0.422125	−	0.906538i	$-0.638716\pi$
$599$	−2.66006e12	−0.844250	−0.422125	+	0.906538i	$0.638716\pi$
$600$	0	0
$601$	3.96050e12	1.23827	0.619134	−	0.785286i	$-0.287484\pi$
$601$	3.96050e12	1.23827	0.619134	+	0.785286i	$0.287484\pi$
$602$	−1.09545e11	−0.0339946
$603$	0	0
$604$	9.28388e12	2.83833
$605$	1.79417e12	0.544458
$606$	0	0
$607$	6.64259e12	1.98604	0.993020	−	0.117944i	$-0.0376303\pi$
$607$	6.64259e12	1.98604	0.993020	+	0.117944i	$0.0376303\pi$
$608$	1.16623e13	3.46115
$609$	0	0
$610$	−9.33438e12	−2.72962
$611$	3.72569e12	1.08149
$612$	0	0
$613$	−5.81304e12	−1.66277	−0.831383	−	0.555700i	$-0.812450\pi$
$613$	−5.81304e12	−1.66277	−0.831383	+	0.555700i	$0.812450\pi$
$614$	7.67616e12	2.17965
$615$	0	0
$616$	1.62496e12	0.454705
$617$	4.96503e12	1.37924	0.689618	−	0.724173i	$-0.257778\pi$
$617$	4.96503e12	1.37924	0.689618	+	0.724173i	$0.257778\pi$
$618$	0	0
$619$	−1.48949e11	−0.0407784	−0.0203892	−	0.999792i	$-0.506491\pi$
$619$	−1.48949e11	−0.0407784	−0.0203892	+	0.999792i	$0.506491\pi$
$620$	−1.24812e13	−3.39230
$621$	0	0
$622$	−7.35749e12	−1.97094
$623$	−1.14367e11	−0.0304161
$624$	0	0
$625$	−3.42702e12	−0.898373
$626$	−8.22552e12	−2.14081
$627$	0	0
$628$	8.95296e11	0.229693
$629$	2.61847e12	0.666990
$630$	0	0
$631$	−6.80747e11	−0.170944	−0.0854719	−	0.996341i	$-0.527240\pi$
$631$	−6.80747e11	−0.170944	−0.0854719	+	0.996341i	$0.527240\pi$
$632$	−1.39078e13	−3.46762
$633$	0	0
$634$	4.02598e12	0.989622
$635$	2.60872e12	0.636716
$636$	0	0
$637$	4.14285e12	0.996947
$638$	9.22187e12	2.20357
$639$	0	0
$640$	−8.10808e12	−1.91033
$641$	3.88893e12	0.909848	0.454924	−	0.890530i	$-0.349666\pi$
$641$	3.88893e12	0.909848	0.454924	+	0.890530i	$0.349666\pi$
$642$	0	0
$643$	−3.00480e11	−0.0693213	−0.0346606	−	0.999399i	$-0.511035\pi$
$643$	−3.00480e11	−0.0693213	−0.0346606	+	0.999399i	$0.511035\pi$
$644$	1.13096e12	0.259096
$645$	0	0
$646$	9.30389e12	2.10193
$647$	2.32257e12	0.521074	0.260537	−	0.965464i	$-0.416100\pi$
$647$	2.32257e12	0.521074	0.260537	+	0.965464i	$0.416100\pi$
$648$	0	0
$649$	7.61026e12	1.68383
$650$	−8.14602e11	−0.178993
$651$	0	0
$652$	−9.45636e12	−2.04932
$653$	5.89953e12	1.26972	0.634860	−	0.772627i	$-0.281058\pi$
$653$	5.89953e12	1.26972	0.634860	+	0.772627i	$0.281058\pi$
$654$	0	0
$655$	4.40615e12	0.935349
$656$	−2.61321e13	−5.50944
$657$	0	0
$658$	−1.14688e12	−0.238507
$659$	2.83678e12	0.585924	0.292962	−	0.956124i	$-0.405359\pi$
$659$	2.83678e12	0.585924	0.292962	+	0.956124i	$0.405359\pi$
$660$	0	0
$661$	6.55557e12	1.33568	0.667842	−	0.744303i	$-0.267218\pi$
$661$	6.55557e12	1.33568	0.667842	+	0.744303i	$0.267218\pi$
$662$	−2.57425e12	−0.520942
$663$	0	0
$664$	5.79505e11	0.115691
$665$	6.20206e11	0.122981
$666$	0	0
$667$	3.97518e12	0.777661
$668$	−9.55884e12	−1.85742
$669$	0	0
$670$	−1.01036e13	−1.93704
$671$	9.90718e12	1.88668
$672$	0	0
$673$	−7.59974e11	−0.142801	−0.0714004	−	0.997448i	$-0.522747\pi$
$673$	−7.59974e11	−0.142801	−0.0714004	+	0.997448i	$0.522747\pi$
$674$	−7.71615e12	−1.44023
$675$	0	0
$676$	3.09618e11	0.0570250
$677$	7.68314e12	1.40569	0.702845	−	0.711343i	$-0.251913\pi$
$677$	7.68314e12	1.40569	0.702845	+	0.711343i	$0.251913\pi$
$678$	0	0
$679$	−7.60031e11	−0.137220
$680$	−1.64610e13	−2.95233
$681$	0	0
$682$	1.82896e13	3.23725
$683$	3.85374e12	0.677624	0.338812	−	0.940854i	$-0.389975\pi$
$683$	3.85374e12	0.677624	0.338812	+	0.940854i	$0.389975\pi$
$684$	0	0
$685$	8.62402e12	1.49659
$686$	−2.56831e12	−0.442780
$687$	0	0
$688$	−2.93456e12	−0.499338
$689$	−9.79660e12	−1.65611
$690$	0	0
$691$	1.15096e11	0.0192048	0.00960239	−	0.999954i	$-0.496943\pi$
$691$	1.15096e11	0.0192048	0.00960239	+	0.999954i	$0.496943\pi$
$692$	2.05420e13	3.40537
$693$	0	0
$694$	−1.67538e13	−2.74154
$695$	−9.09174e12	−1.47814
$696$	0	0
$697$	−1.04882e13	−1.68328
$698$	2.05902e13	3.28330
$699$	0	0
$700$	1.81624e11	0.0285911
$701$	2.15689e12	0.337362	0.168681	−	0.985671i	$-0.446049\pi$
$701$	2.15689e12	0.337362	0.168681	+	0.985671i	$0.446049\pi$
$702$	0	0
$703$	−4.76328e12	−0.735542
$704$	2.20654e13	3.38559
$705$	0	0
$706$	−2.17224e13	−3.29069
$707$	−4.96027e11	−0.0746651
$708$	0	0
$709$	9.13106e12	1.35710	0.678552	−	0.734552i	$-0.262608\pi$
$709$	9.13106e12	1.35710	0.678552	+	0.734552i	$0.262608\pi$
$710$	−4.45054e12	−0.657279
$711$	0	0
$712$	−5.52177e12	−0.805227
$713$	7.88393e12	1.14246
$714$	0	0
$715$	−8.43395e12	−1.20685
$716$	4.41328e11	0.0627556
$717$	0	0
$718$	1.80110e13	2.52917
$719$	−7.17755e12	−1.00160	−0.500802	−	0.865562i	$-0.666962\pi$
$719$	−7.17755e12	−1.00160	−0.500802	+	0.865562i	$0.666962\pi$
$720$	0	0
$721$	−5.05141e10	−0.00696151
$722$	−3.01904e12	−0.413477
$723$	0	0
$724$	1.85976e12	0.251555
$725$	6.38384e11	0.0858145
$726$	0	0
$727$	1.54751e12	0.205461	0.102730	−	0.994709i	$-0.467242\pi$
$727$	1.54751e12	0.205461	0.102730	+	0.994709i	$0.467242\pi$
$728$	−2.77844e12	−0.366615
$729$	0	0
$730$	2.37797e13	3.09923
$731$	−1.17780e12	−0.152561
$732$	0	0
$733$	5.60399e12	0.717017	0.358508	−	0.933527i	$-0.383285\pi$
$733$	5.60399e12	0.717017	0.358508	+	0.933527i	$0.383285\pi$
$734$	−2.39440e13	−3.04484
$735$	0	0
$736$	2.10441e13	2.64350
$737$	1.07236e13	1.33886
$738$	0	0
$739$	−1.36939e12	−0.168899	−0.0844494	−	0.996428i	$-0.526913\pi$
$739$	−1.36939e12	−0.168899	−0.0844494	+	0.996428i	$0.526913\pi$
$740$	1.36070e13	1.66810
$741$	0	0
$742$	3.01569e12	0.365232
$743$	4.16784e12	0.501720	0.250860	−	0.968023i	$-0.419287\pi$
$743$	4.16784e12	0.501720	0.250860	+	0.968023i	$0.419287\pi$
$744$	0	0
$745$	7.60210e12	0.904129
$746$	2.98002e13	3.52286
$747$	0	0
$748$	2.82089e13	3.29480
$749$	−1.27789e12	−0.148363
$750$	0	0
$751$	−4.35477e12	−0.499557	−0.249779	−	0.968303i	$-0.580358\pi$
$751$	−4.35477e12	−0.499557	−0.249779	+	0.968303i	$0.580358\pi$
$752$	−3.07233e13	−3.50338
$753$	0	0
$754$	−1.57680e13	−1.77667
$755$	9.18677e12	1.02897
$756$	0	0
$757$	1.07979e13	1.19511	0.597556	−	0.801827i	$-0.296138\pi$
$757$	1.07979e13	1.19511	0.597556	+	0.801827i	$0.296138\pi$
$758$	−2.24848e13	−2.47387
$759$	0	0
$760$	2.99443e13	3.25577
$761$	1.64930e13	1.78266	0.891328	−	0.453359i	$-0.149774\pi$
$761$	1.64930e13	1.78266	0.891328	+	0.453359i	$0.149774\pi$
$762$	0	0
$763$	1.11448e12	0.119045
$764$	−1.48786e13	−1.57994
$765$	0	0
$766$	−2.81296e13	−2.95212
$767$	−1.30124e13	−1.35762
$768$	0	0
$769$	1.66475e13	1.71665	0.858323	−	0.513109i	$-0.171506\pi$
$769$	1.66475e13	1.71665	0.858323	+	0.513109i	$0.171506\pi$
$770$	2.59623e12	0.266155
$771$	0	0
$772$	2.11045e13	2.13844
$773$	−1.53370e12	−0.154502	−0.0772509	−	0.997012i	$-0.524614\pi$
$773$	−1.53370e12	−0.154502	−0.0772509	+	0.997012i	$0.524614\pi$
$774$	0	0
$775$	1.26610e12	0.126070
$776$	−3.66952e13	−3.63272
$777$	0	0
$778$	1.49044e13	1.45850
$779$	1.90793e13	1.85628
$780$	0	0
$781$	4.72364e12	0.454304
$782$	1.67884e13	1.60538
$783$	0	0
$784$	−3.41633e13	−3.22952
$785$	8.85931e11	0.0832696
$786$	0	0
$787$	−5.66934e12	−0.526801	−0.263400	−	0.964687i	$-0.584844\pi$
$787$	−5.66934e12	−0.526801	−0.263400	+	0.964687i	$0.584844\pi$
$788$	2.08005e13	1.92179
$789$	0	0
$790$	−2.22207e13	−2.02972
$791$	−3.54867e11	−0.0322308
$792$	0	0
$793$	−1.69398e13	−1.52117
$794$	−8.49542e12	−0.758565
$795$	0	0
$796$	2.31593e13	2.04464
$797$	−1.69239e13	−1.48572	−0.742860	−	0.669446i	$-0.766531\pi$
$797$	−1.69239e13	−1.48572	−0.742860	+	0.669446i	$0.766531\pi$
$798$	0	0
$799$	−1.23309e13	−1.07037
$800$	3.37952e12	0.291709
$801$	0	0
$802$	−4.16928e13	−3.55858
$803$	−2.52389e13	−2.14215
$804$	0	0
$805$	1.11913e12	0.0939287
$806$	−3.12726e13	−2.61009
$807$	0	0
$808$	−2.39488e13	−1.97666
$809$	−1.54138e13	−1.26515	−0.632575	−	0.774499i	$-0.718002\pi$
$809$	−1.54138e13	−1.26515	−0.632575	+	0.774499i	$0.718002\pi$
$810$	0	0
$811$	−6.33063e12	−0.513870	−0.256935	−	0.966429i	$-0.582713\pi$
$811$	−6.33063e12	−0.513870	−0.256935	+	0.966429i	$0.582713\pi$
$812$	3.51564e12	0.283793
$813$	0	0
$814$	−1.99394e13	−1.59185
$815$	−9.35745e12	−0.742931
$816$	0	0
$817$	2.14254e12	0.168240
$818$	3.15979e13	2.46757
$819$	0	0
$820$	−5.45028e13	−4.20975
$821$	1.35648e13	1.04200	0.521000	−	0.853557i	$-0.325559\pi$
$821$	1.35648e13	1.04200	0.521000	+	0.853557i	$0.325559\pi$
$822$	0	0
$823$	6.80965e11	0.0517399	0.0258700	−	0.999665i	$-0.491764\pi$
$823$	6.80965e11	0.0517399	0.0258700	+	0.999665i	$0.491764\pi$
$824$	−2.43888e12	−0.184297
$825$	0	0
$826$	4.00562e12	0.299405
$827$	−2.18527e13	−1.62454	−0.812270	−	0.583281i	$-0.801769\pi$
$827$	−2.18527e13	−1.62454	−0.812270	+	0.583281i	$0.801769\pi$
$828$	0	0
$829$	−8.42772e12	−0.619747	−0.309874	−	0.950778i	$-0.600287\pi$
$829$	−8.42772e12	−0.619747	−0.309874	+	0.950778i	$0.600287\pi$
$830$	9.25885e11	0.0677183
$831$	0	0
$832$	−3.77286e13	−2.72970
$833$	−1.37116e13	−0.986701
$834$	0	0
$835$	−9.45886e12	−0.673364
$836$	−5.13151e13	−3.63343
$837$	0	0
$838$	4.33072e12	0.303363
$839$	1.21585e13	0.847130	0.423565	−	0.905866i	$-0.360779\pi$
$839$	1.21585e13	0.847130	0.423565	+	0.905866i	$0.360779\pi$
$840$	0	0
$841$	−2.15012e12	−0.148211
$842$	−3.82728e12	−0.262413
$843$	0	0
$844$	3.29695e13	2.23651
$845$	3.06379e11	0.0206730
$846$	0	0
$847$	−1.00230e12	−0.0669149
$848$	8.07860e13	5.36482
$849$	0	0
$850$	2.69609e12	0.177153
$851$	−8.59508e12	−0.561781
$852$	0	0
$853$	1.08092e13	0.699072	0.349536	−	0.936923i	$-0.386339\pi$
$853$	1.08092e13	0.699072	0.349536	+	0.936923i	$0.386339\pi$
$854$	5.21459e12	0.335475
$855$	0	0
$856$	−6.16981e13	−3.92771
$857$	−5.36363e12	−0.339660	−0.169830	−	0.985473i	$-0.554322\pi$
$857$	−5.36363e12	−0.339660	−0.169830	+	0.985473i	$0.554322\pi$
$858$	0	0
$859$	−9.61783e12	−0.602709	−0.301355	−	0.953512i	$-0.597439\pi$
$859$	−9.61783e12	−0.602709	−0.301355	+	0.953512i	$0.597439\pi$
$860$	−6.12050e12	−0.381543
$861$	0	0
$862$	1.98959e13	1.22738
$863$	−1.95919e13	−1.20234	−0.601171	−	0.799121i	$-0.705299\pi$
$863$	−1.95919e13	−1.20234	−0.601171	+	0.799121i	$0.705299\pi$
$864$	0	0
$865$	2.03271e13	1.23453
$866$	−2.27308e13	−1.37336
$867$	0	0
$868$	6.97253e12	0.416919
$869$	2.35842e13	1.40292
$870$	0	0
$871$	−1.83357e13	−1.07948
$872$	5.38085e13	3.15157
$873$	0	0
$874$	−3.05399e13	−1.77038
$875$	2.11263e12	0.121839
$876$	0	0
$877$	1.92311e13	1.09775	0.548877	−	0.835903i	$-0.315056\pi$
$877$	1.92311e13	1.09775	0.548877	+	0.835903i	$0.315056\pi$
$878$	−3.15223e13	−1.79016
$879$	0	0
$880$	6.95492e13	3.90949
$881$	−1.63419e13	−0.913925	−0.456963	−	0.889486i	$-0.651063\pi$
$881$	−1.63419e13	−0.913925	−0.456963	+	0.889486i	$0.651063\pi$
$882$	0	0
$883$	−3.37986e13	−1.87101	−0.935503	−	0.353319i	$-0.885053\pi$
$883$	−3.37986e13	−1.87101	−0.935503	+	0.353319i	$0.885053\pi$
$884$	−4.82331e13	−2.65650
$885$	0	0
$886$	−1.92453e13	−1.04924
$887$	1.58038e13	0.857244	0.428622	−	0.903484i	$-0.358999\pi$
$887$	1.58038e13	0.857244	0.428622	+	0.903484i	$0.358999\pi$
$888$	0	0
$889$	−1.45734e12	−0.0782535
$890$	−8.82222e12	−0.471328
$891$	0	0
$892$	4.62279e12	0.244491
$893$	2.24313e13	1.18038
$894$	0	0
$895$	4.36712e11	0.0227505
$896$	4.52952e12	0.234783
$897$	0	0
$898$	−1.40221e13	−0.719564
$899$	2.45076e13	1.25136
$900$	0	0
$901$	3.24238e13	1.63909
$902$	7.98671e13	4.01734
$903$	0	0
$904$	−1.71334e13	−0.853269
$905$	1.84031e12	0.0911951
$906$	0	0
$907$	−8.09983e12	−0.397414	−0.198707	−	0.980059i	$-0.563674\pi$
$907$	−8.09983e12	−0.397414	−0.198707	+	0.980059i	$0.563674\pi$
$908$	−1.57893e13	−0.770861
$909$	0	0
$910$	−4.43916e12	−0.214593
$911$	4.04038e12	0.194352	0.0971760	−	0.995267i	$-0.469019\pi$
$911$	4.04038e12	0.194352	0.0971760	+	0.995267i	$0.469019\pi$
$912$	0	0
$913$	−9.82701e11	−0.0468062
$914$	7.34696e13	3.48217
$915$	0	0
$916$	−1.11987e12	−0.0525579
$917$	−2.46147e12	−0.114956
$918$	0	0
$919$	−1.35982e13	−0.628869	−0.314435	−	0.949279i	$-0.601815\pi$
$919$	−1.35982e13	−0.628869	−0.314435	+	0.949279i	$0.601815\pi$
$920$	5.40329e13	2.48664
$921$	0	0
$922$	−1.83381e13	−0.835728
$923$	−8.07672e12	−0.366292
$924$	0	0
$925$	−1.38031e12	−0.0619923
$926$	−6.17922e13	−2.76175
$927$	0	0
$928$	6.54165e13	2.89549
$929$	1.80722e13	0.796049	0.398024	−	0.917375i	$-0.369696\pi$
$929$	1.80722e13	0.796049	0.398024	+	0.917375i	$0.369696\pi$
$930$	0	0
$931$	2.49429e13	1.08811
$932$	9.93660e12	0.431386
$933$	0	0
$934$	−1.56986e13	−0.674995
$935$	2.79138e13	1.19445
$936$	0	0
$937$	−2.82959e13	−1.19921	−0.599606	−	0.800295i	$-0.704676\pi$
$937$	−2.82959e13	−1.19921	−0.599606	+	0.800295i	$0.704676\pi$
$938$	5.64430e12	0.238066
$939$	0	0
$940$	−6.40784e13	−2.67692
$941$	−1.67782e13	−0.697579	−0.348789	−	0.937201i	$-0.613407\pi$
$941$	−1.67782e13	−0.697579	−0.348789	+	0.937201i	$0.613407\pi$
$942$	0	0
$943$	3.44275e13	1.41776
$944$	1.07305e14	4.39789
$945$	0	0
$946$	8.96883e12	0.364104
$947$	9.22630e12	0.372780	0.186390	−	0.982476i	$-0.440321\pi$
$947$	9.22630e12	0.372780	0.186390	+	0.982476i	$0.440321\pi$
$948$	0	0
$949$	4.31548e13	1.72715
$950$	−4.90448e12	−0.195360
$951$	0	0
$952$	9.19581e12	0.362847
$953$	2.41710e13	0.949241	0.474620	−	0.880191i	$-0.342585\pi$
$953$	2.41710e13	0.949241	0.474620	+	0.880191i	$0.342585\pi$
$954$	0	0
$955$	−1.47229e13	−0.572769
$956$	−4.84761e13	−1.87701
$957$	0	0
$958$	5.05782e13	1.94007
$959$	−4.81775e12	−0.183933
$960$	0	0
$961$	2.21660e13	0.838364
$962$	3.40935e13	1.28346
$963$	0	0
$964$	7.20119e13	2.68570
$965$	2.08837e13	0.775239
$966$	0	0
$967$	4.39048e13	1.61470	0.807352	−	0.590070i	$-0.200900\pi$
$967$	4.39048e13	1.61470	0.807352	+	0.590070i	$0.200900\pi$
$968$	−4.83923e13	−1.77148
$969$	0	0
$970$	−5.86286e13	−2.12636
$971$	1.38873e13	0.501339	0.250670	−	0.968073i	$-0.419349\pi$
$971$	1.38873e13	0.501339	0.250670	+	0.968073i	$0.419349\pi$
$972$	0	0
$973$	5.07904e12	0.181666
$974$	1.09697e13	0.390552
$975$	0	0
$976$	1.39691e14	4.92771
$977$	1.29967e13	0.456359	0.228179	−	0.973619i	$-0.426723\pi$
$977$	1.29967e13	0.456359	0.228179	+	0.973619i	$0.426723\pi$
$978$	0	0
$979$	9.36359e12	0.325777
$980$	−7.12532e13	−2.46767
$981$	0	0
$982$	−5.33909e12	−0.183217
$983$	1.69991e12	0.0580679	0.0290340	−	0.999578i	$-0.490757\pi$
$983$	1.69991e12	0.0580679	0.0290340	+	0.999578i	$0.490757\pi$
$984$	0	0
$985$	2.05830e13	0.696699
$986$	5.21875e13	1.75841
$987$	0	0
$988$	8.77412e13	2.92953
$989$	3.86610e12	0.128496
$990$	0	0
$991$	−3.65973e13	−1.20536	−0.602681	−	0.797982i	$-0.705901\pi$
$991$	−3.65973e13	−1.20536	−0.602681	+	0.797982i	$0.705901\pi$
$992$	1.29740e14	4.25374
$993$	0	0
$994$	2.48626e12	0.0807808
$995$	2.29171e13	0.741234
$996$	0	0
$997$	−7.31096e12	−0.234340	−0.117170	−	0.993112i	$-0.537382\pi$
$997$	−7.31096e12	−0.234340	−0.117170	+	0.993112i	$0.537382\pi$
$998$	6.18635e13	1.97400
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.10.a.c.1.1		15
3.2	odd	2		43.10.a.a.1.15	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.15	✓	15	3.2	odd	2
387.10.a.c.1.1		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)

\(f(q)\)	\(=\)	\(q-43.0936 q^{2} +1345.05 q^{4} +1330.99 q^{5} -743.545 q^{7} -35899.3 q^{8} +O(q^{10})\)	\(q-43.0936 q^{2} +1345.05 q^{4} +1330.99 q^{5} -743.545 q^{7} -35899.3 q^{8} -57356.9 q^{10} +60876.5 q^{11} -104090. q^{13} +32042.0 q^{14} +858359. q^{16} +344506. q^{17} -626694. q^{19} +1.79025e6 q^{20} -2.62338e6 q^{22} -1.13084e6 q^{23} -181604. q^{25} +4.48560e6 q^{26} -1.00011e6 q^{28} -3.51526e6 q^{29} -6.97177e6 q^{31} -1.86093e7 q^{32} -1.48460e7 q^{34} -989648. q^{35} +7.60065e6 q^{37} +2.70065e7 q^{38} -4.77814e7 q^{40} -3.04443e7 q^{41} -3.41880e6 q^{43} +8.18822e7 q^{44} +4.87317e7 q^{46} -3.57930e7 q^{47} -3.98007e7 q^{49} +7.82595e6 q^{50} -1.40006e8 q^{52} +9.41168e7 q^{53} +8.10257e7 q^{55} +2.66927e7 q^{56} +1.51485e8 q^{58} +1.25011e8 q^{59} +1.62742e8 q^{61} +3.00439e8 q^{62} +3.62462e8 q^{64} -1.38542e8 q^{65} +1.76153e8 q^{67} +4.63379e8 q^{68} +4.26474e7 q^{70} +7.75938e7 q^{71} -4.14592e8 q^{73} -3.27539e8 q^{74} -8.42937e8 q^{76} -4.52644e7 q^{77} +3.87411e8 q^{79} +1.14246e9 q^{80} +1.31195e9 q^{82} -1.61425e7 q^{83} +4.58532e8 q^{85} +1.47328e8 q^{86} -2.18542e9 q^{88} +1.53813e8 q^{89} +7.73955e7 q^{91} -1.52103e9 q^{92} +1.54245e9 q^{94} -8.34120e8 q^{95} +1.02217e9 q^{97} +1.71516e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) \) 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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