LMFDB - Embedded newform 153.10.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,10,Mod(1,153)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, 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("153.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	153.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:	$78.8004829331$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 1596x^{3} + 5754x^{2} + 488987x - 2711704 $ x^5 - 2x^4 - 1596x^3 + 5754x^2 + 488987x - 2711704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-21.1654$ of defining polynomial
Character	$\chi$	$=$	153.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+28.1654 q^{2} +281.287 q^{4} -762.851 q^{5} +5573.11 q^{7} -6498.11 q^{8} +O(q^{10})$	\(q+28.1654 q^{2} +281.287 q^{4} -762.851 q^{5} +5573.11 q^{7} -6498.11 q^{8} -21486.0 q^{10} +47641.7 q^{11} -92260.9 q^{13} +156969. q^{14} -327041. q^{16} +83521.0 q^{17} -8373.93 q^{19} -214580. q^{20} +1.34184e6 q^{22} -364592. q^{23} -1.37118e6 q^{25} -2.59856e6 q^{26} +1.56764e6 q^{28} +3.50595e6 q^{29} -5.20629e6 q^{31} -5.88418e6 q^{32} +2.35240e6 q^{34} -4.25145e6 q^{35} -499530. q^{37} -235855. q^{38} +4.95709e6 q^{40} +5.43648e6 q^{41} -3.54411e7 q^{43} +1.34010e7 q^{44} -1.02689e7 q^{46} -1.21753e7 q^{47} -9.29403e6 q^{49} -3.86199e7 q^{50} -2.59518e7 q^{52} -1.04471e8 q^{53} -3.63435e7 q^{55} -3.62147e7 q^{56} +9.87464e7 q^{58} -4.16714e7 q^{59} +5.67537e7 q^{61} -1.46637e8 q^{62} +1.71477e6 q^{64} +7.03813e7 q^{65} -1.74621e8 q^{67} +2.34934e7 q^{68} -1.19744e8 q^{70} -3.46330e7 q^{71} -3.93220e8 q^{73} -1.40694e7 q^{74} -2.35548e6 q^{76} +2.65512e8 q^{77} +1.85772e8 q^{79} +2.49483e8 q^{80} +1.53120e8 q^{82} -3.62239e8 q^{83} -6.37141e7 q^{85} -9.98211e8 q^{86} -3.09581e8 q^{88} +5.04798e7 q^{89} -5.14180e8 q^{91} -1.02555e8 q^{92} -3.42920e8 q^{94} +6.38806e6 q^{95} -9.67620e8 q^{97} -2.61770e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 33 q^{2} + 853 q^{4} - 1480 q^{5} - 13202 q^{7} + 42423 q^{8}+O(q^{10}) $ 5 * q + 33 * q^2 + 853 * q^4 - 1480 * q^5 - 13202 * q^7 + 42423 * q^8	\( 5 q + 33 q^{2} + 853 q^{4} - 1480 q^{5} - 13202 q^{7} + 42423 q^{8} - 89328 q^{10} + 68036 q^{11} - 158862 q^{13} + 84700 q^{14} + 350225 q^{16} + 417605 q^{17} - 370992 q^{19} - 1632640 q^{20} + 122290 q^{22} - 1645870 q^{23} + 3270239 q^{25} - 734846 q^{26} + 183372 q^{28} - 3668616 q^{29} - 7262362 q^{31} + 5605919 q^{32} + 2756193 q^{34} + 26503988 q^{35} - 31420708 q^{37} - 18513700 q^{38} - 53930464 q^{40} + 7996938 q^{41} - 56908268 q^{43} - 43323054 q^{44} - 32063472 q^{46} + 16903336 q^{47} - 11784059 q^{49} - 85921093 q^{50} + 173619082 q^{52} + 83362982 q^{53} + 6363364 q^{55} - 317409372 q^{56} + 64577488 q^{58} + 37946604 q^{59} - 77685452 q^{61} - 324855300 q^{62} + 131623105 q^{64} + 40321288 q^{65} - 304503600 q^{67} + 71243413 q^{68} - 122787392 q^{70} + 476602922 q^{71} - 289980486 q^{73} - 262289012 q^{74} - 1031276084 q^{76} + 143385648 q^{77} - 828240610 q^{79} - 912750944 q^{80} - 1109615654 q^{82} - 194681148 q^{83} - 123611080 q^{85} - 1164707144 q^{86} - 1017979978 q^{88} - 376848106 q^{89} + 194543664 q^{91} - 2506713088 q^{92} - 2244811104 q^{94} - 1498679864 q^{95} + 692035246 q^{97} - 871744055 q^{98}+O(q^{100}) \) 5 * q + 33 * q^2 + 853 * q^4 - 1480 * q^5 - 13202 * q^7 + 42423 * q^8 - 89328 * q^10 + 68036 * q^11 - 158862 * q^13 + 84700 * q^14 + 350225 * q^16 + 417605 * q^17 - 370992 * q^19 - 1632640 * q^20 + 122290 * q^22 - 1645870 * q^23 + 3270239 * q^25 - 734846 * q^26 + 183372 * q^28 - 3668616 * q^29 - 7262362 * q^31 + 5605919 * q^32 + 2756193 * q^34 + 26503988 * q^35 - 31420708 * q^37 - 18513700 * q^38 - 53930464 * q^40 + 7996938 * q^41 - 56908268 * q^43 - 43323054 * q^44 - 32063472 * q^46 + 16903336 * q^47 - 11784059 * q^49 - 85921093 * q^50 + 173619082 * q^52 + 83362982 * q^53 + 6363364 * q^55 - 317409372 * q^56 + 64577488 * q^58 + 37946604 * q^59 - 77685452 * q^61 - 324855300 * q^62 + 131623105 * q^64 + 40321288 * q^65 - 304503600 * q^67 + 71243413 * q^68 - 122787392 * q^70 + 476602922 * q^71 - 289980486 * q^73 - 262289012 * q^74 - 1031276084 * q^76 + 143385648 * q^77 - 828240610 * q^79 - 912750944 * q^80 - 1109615654 * q^82 - 194681148 * q^83 - 123611080 * q^85 - 1164707144 * q^86 - 1017979978 * q^88 - 376848106 * q^89 + 194543664 * q^91 - 2506713088 * q^92 - 2244811104 * q^94 - 1498679864 * q^95 + 692035246 * q^97 - 871744055 * 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 $

$2$	28.1654	1.24474	0.622372	−	0.782721i	$-0.286169\pi$
$2$	28.1654	1.24474	0.622372	+	0.782721i	$0.286169\pi$
$3$	0	0
$3$	0	0
$4$	281.287	0.549389
$5$	−762.851	−0.545852	−0.272926	−	0.962035i	$-0.587991\pi$
$5$	−762.851	−0.545852	−0.272926	+	0.962035i	$0.587991\pi$
$6$	0	0
$7$	5573.11	0.877317	0.438659	−	0.898654i	$-0.355454\pi$
$7$	5573.11	0.877317	0.438659	+	0.898654i	$0.355454\pi$
$8$	−6498.11	−0.560896
$9$	0	0
$10$	−21486.0	−0.679446
$11$	47641.7	0.981115	0.490558	−	0.871409i	$-0.336793\pi$
$11$	47641.7	0.981115	0.490558	+	0.871409i	$0.336793\pi$
$12$	0	0
$13$	−92260.9	−0.895927	−0.447963	−	0.894052i	$-0.647851\pi$
$13$	−92260.9	−0.895927	−0.447963	+	0.894052i	$0.647851\pi$
$14$	156969.	1.09204
$15$	0	0
$16$	−327041.	−1.24756
$17$	83521.0	0.242536
$17$	83521.0	0.242536
$18$	0	0
$19$	−8373.93	−0.0147414	−0.00737069	−	0.999973i	$-0.502346\pi$
$19$	−8373.93	−0.0147414	−0.00737069	+	0.999973i	$0.502346\pi$
$20$	−214580.	−0.299885
$21$	0	0
$22$	1.34184e6	1.22124
$23$	−364592.	−0.271664	−0.135832	−	0.990732i	$-0.543371\pi$
$23$	−364592.	−0.271664	−0.135832	+	0.990732i	$0.543371\pi$
$24$	0	0
$25$	−1.37118e6	−0.702046
$26$	−2.59856e6	−1.11520
$27$	0	0
$28$	1.56764e6	0.481988
$29$	3.50595e6	0.920482	0.460241	−	0.887794i	$-0.347763\pi$
$29$	3.50595e6	0.920482	0.460241	+	0.887794i	$0.347763\pi$
$30$	0	0
$31$	−5.20629e6	−1.01251	−0.506257	−	0.862383i	$-0.668971\pi$
$31$	−5.20629e6	−1.01251	−0.506257	+	0.862383i	$0.668971\pi$
$32$	−5.88418e6	−0.991999
$33$	0	0
$34$	2.35240e6	0.301895
$35$	−4.25145e6	−0.478885
$36$	0	0
$37$	−499530.	−0.0438182	−0.0219091	−	0.999760i	$-0.506974\pi$
$37$	−499530.	−0.0438182	−0.0219091	+	0.999760i	$0.506974\pi$
$38$	−235855.	−0.0183493
$39$	0	0
$40$	4.95709e6	0.306166
$41$	5.43648e6	0.300463	0.150231	−	0.988651i	$-0.451998\pi$
$41$	5.43648e6	0.300463	0.150231	+	0.988651i	$0.451998\pi$
$42$	0	0
$43$	−3.54411e7	−1.58088	−0.790440	−	0.612539i	$-0.790148\pi$
$43$	−3.54411e7	−1.58088	−0.790440	+	0.612539i	$0.790148\pi$
$44$	1.34010e7	0.539014
$45$	0	0
$46$	−1.02689e7	−0.338152
$47$	−1.21753e7	−0.363947	−0.181973	−	0.983303i	$-0.558248\pi$
$47$	−1.21753e7	−0.363947	−0.181973	+	0.983303i	$0.558248\pi$
$48$	0	0
$49$	−9.29403e6	−0.230315
$50$	−3.86199e7	−0.873868
$51$	0	0
$52$	−2.59518e7	−0.492212
$53$	−1.04471e8	−1.81867	−0.909336	−	0.416063i	$-0.863410\pi$
$53$	−1.04471e8	−1.81867	−0.909336	+	0.416063i	$0.863410\pi$
$54$	0	0
$55$	−3.63435e7	−0.535543
$56$	−3.62147e7	−0.492083
$57$	0	0
$58$	9.87464e7	1.14576
$59$	−4.16714e7	−0.447718	−0.223859	−	0.974622i	$-0.571865\pi$
$59$	−4.16714e7	−0.447718	−0.223859	+	0.974622i	$0.571865\pi$
$60$	0	0
$61$	5.67537e7	0.524819	0.262410	−	0.964957i	$-0.415483\pi$
$61$	5.67537e7	0.524819	0.262410	+	0.964957i	$0.415483\pi$
$62$	−1.46637e8	−1.26032
$63$	0	0
$64$	1.71477e6	0.0127760
$65$	7.03813e7	0.489043
$66$	0	0
$67$	−1.74621e8	−1.05867	−0.529333	−	0.848414i	$-0.677558\pi$
$67$	−1.74621e8	−1.05867	−0.529333	+	0.848414i	$0.677558\pi$
$68$	2.34934e7	0.133246
$69$	0	0
$70$	−1.19744e8	−0.596089
$71$	−3.46330e7	−0.161744	−0.0808719	−	0.996725i	$-0.525770\pi$
$71$	−3.46330e7	−0.161744	−0.0808719	+	0.996725i	$0.525770\pi$
$72$	0	0
$73$	−3.93220e8	−1.62063	−0.810314	−	0.585996i	$-0.800703\pi$
$73$	−3.93220e8	−1.62063	−0.810314	+	0.585996i	$0.800703\pi$
$74$	−1.40694e7	−0.0545424
$75$	0	0
$76$	−2.35548e6	−0.00809875
$77$	2.65512e8	0.860749
$78$	0	0
$79$	1.85772e8	0.536609	0.268305	−	0.963334i	$-0.413537\pi$
$79$	1.85772e8	0.536609	0.268305	+	0.963334i	$0.413537\pi$
$80$	2.49483e8	0.680983
$81$	0	0
$82$	1.53120e8	0.373999
$83$	−3.62239e8	−0.837807	−0.418903	−	0.908031i	$-0.637585\pi$
$83$	−3.62239e8	−0.837807	−0.418903	+	0.908031i	$0.637585\pi$
$84$	0	0
$85$	−6.37141e7	−0.132388
$86$	−9.98211e8	−1.96779
$87$	0	0
$88$	−3.09581e8	−0.550303
$89$	5.04798e7	0.0852831	0.0426416	−	0.999090i	$-0.486423\pi$
$89$	5.04798e7	0.0852831	0.0426416	+	0.999090i	$0.486423\pi$
$90$	0	0
$91$	−5.14180e8	−0.786012
$92$	−1.02555e8	−0.149249
$93$	0	0
$94$	−3.42920e8	−0.453020
$95$	6.38806e6	0.00804661
$96$	0	0
$97$	−9.67620e8	−1.10977	−0.554884	−	0.831928i	$-0.687237\pi$
$97$	−9.67620e8	−1.10977	−0.554884	+	0.831928i	$0.687237\pi$
$98$	−2.61770e8	−0.286683
$99$	0	0
$100$	−3.85696e8	−0.385696
$101$	−1.60604e9	−1.53572	−0.767858	−	0.640621i	$-0.778677\pi$
$101$	−1.60604e9	−1.53572	−0.767858	+	0.640621i	$0.778677\pi$
$102$	0	0
$103$	1.76819e9	1.54796	0.773982	−	0.633208i	$-0.218262\pi$
$103$	1.76819e9	1.54796	0.773982	+	0.633208i	$0.218262\pi$
$104$	5.99522e8	0.502522
$105$	0	0
$106$	−2.94246e9	−2.26378
$107$	2.59627e9	1.91479	0.957397	−	0.288774i	$-0.0932477\pi$
$107$	2.59627e9	1.91479	0.957397	+	0.288774i	$0.0932477\pi$
$108$	0	0
$109$	2.64333e9	1.79363	0.896814	−	0.442408i	$-0.145876\pi$
$109$	2.64333e9	1.79363	0.896814	+	0.442408i	$0.145876\pi$
$110$	−1.02363e9	−0.666614
$111$	0	0
$112$	−1.82263e9	−1.09451
$113$	−9.53189e8	−0.549954	−0.274977	−	0.961451i	$-0.588670\pi$
$113$	−9.53189e8	−0.549954	−0.274977	+	0.961451i	$0.588670\pi$
$114$	0	0
$115$	2.78129e8	0.148288
$116$	9.86179e8	0.505702
$117$	0	0
$118$	−1.17369e9	−0.557294
$119$	4.65472e8	0.212781
$120$	0	0
$121$	−8.82187e7	−0.0374133
$122$	1.59849e9	0.653266
$123$	0	0
$124$	−1.46446e9	−0.556264
$125$	2.53595e9	0.929065
$126$	0	0
$127$	9.64764e8	0.329082	0.164541	−	0.986370i	$-0.447386\pi$
$127$	9.64764e8	0.329082	0.164541	+	0.986370i	$0.447386\pi$
$128$	3.06100e9	1.00790
$129$	0	0
$130$	1.98231e9	0.608734
$131$	5.24089e9	1.55483	0.777417	−	0.628985i	$-0.216529\pi$
$131$	5.24089e9	1.55483	0.777417	+	0.628985i	$0.216529\pi$
$132$	0	0
$133$	−4.66689e7	−0.0129329
$134$	−4.91825e9	−1.31777
$135$	0	0
$136$	−5.42729e8	−0.136037
$137$	−3.09452e9	−0.750500	−0.375250	−	0.926924i	$-0.622443\pi$
$137$	−3.09452e9	−0.750500	−0.375250	+	0.926924i	$0.622443\pi$
$138$	0	0
$139$	−6.10981e8	−0.138823	−0.0694115	−	0.997588i	$-0.522112\pi$
$139$	−6.10981e8	−0.138823	−0.0694115	+	0.997588i	$0.522112\pi$
$140$	−1.19588e9	−0.263094
$141$	0	0
$142$	−9.75450e8	−0.201330
$143$	−4.39546e9	−0.879007
$144$	0	0
$145$	−2.67452e9	−0.502446
$146$	−1.10752e10	−2.01727
$147$	0	0
$148$	−1.40511e8	−0.0240732
$149$	−2.02582e9	−0.336716	−0.168358	−	0.985726i	$-0.553846\pi$
$149$	−2.02582e9	−0.336716	−0.168358	+	0.985726i	$0.553846\pi$
$150$	0	0
$151$	−7.09269e9	−1.11024	−0.555118	−	0.831772i	$-0.687327\pi$
$151$	−7.09269e9	−1.11024	−0.555118	+	0.831772i	$0.687327\pi$
$152$	5.44147e7	0.00826838
$153$	0	0
$154$	7.47825e9	1.07141
$155$	3.97162e9	0.552682
$156$	0	0
$157$	−8.25715e9	−1.08463	−0.542315	−	0.840175i	$-0.682452\pi$
$157$	−8.25715e9	−1.08463	−0.542315	+	0.840175i	$0.682452\pi$
$158$	5.23233e9	0.667941
$159$	0	0
$160$	4.48875e9	0.541484
$161$	−2.03191e9	−0.238335
$162$	0	0
$163$	−6.13273e9	−0.680471	−0.340235	−	0.940340i	$-0.610507\pi$
$163$	−6.13273e9	−0.680471	−0.340235	+	0.940340i	$0.610507\pi$
$164$	1.52921e9	0.165071
$165$	0	0
$166$	−1.02026e10	−1.04286
$167$	1.53224e10	1.52442	0.762208	−	0.647332i	$-0.224115\pi$
$167$	1.53224e10	1.52442	0.762208	+	0.647332i	$0.224115\pi$
$168$	0	0
$169$	−2.09243e9	−0.197315
$170$	−1.79453e9	−0.164790
$171$	0	0
$172$	−9.96912e9	−0.868518
$173$	−1.45473e10	−1.23474	−0.617370	−	0.786673i	$-0.711802\pi$
$173$	−1.45473e10	−1.23474	−0.617370	+	0.786673i	$0.711802\pi$
$174$	0	0
$175$	−7.64176e9	−0.615917
$176$	−1.55808e10	−1.22400
$177$	0	0
$178$	1.42178e9	0.106156
$179$	−4.64898e9	−0.338469	−0.169235	−	0.985576i	$-0.554130\pi$
$179$	−4.64898e9	−0.338469	−0.169235	+	0.985576i	$0.554130\pi$
$180$	0	0
$181$	1.08585e9	0.0751997	0.0375998	−	0.999293i	$-0.488029\pi$
$181$	1.08585e9	0.0751997	0.0375998	+	0.999293i	$0.488029\pi$
$182$	−1.44821e10	−0.978384
$183$	0	0
$184$	2.36916e9	0.152375
$185$	3.81067e8	0.0239182
$186$	0	0
$187$	3.97908e9	0.237955
$188$	−3.42474e9	−0.199948
$189$	0	0
$190$	1.79922e8	0.0100160
$191$	3.78328e9	0.205693	0.102846	−	0.994697i	$-0.467205\pi$
$191$	3.78328e9	0.205693	0.102846	+	0.994697i	$0.467205\pi$
$192$	0	0
$193$	3.16352e10	1.64121	0.820603	−	0.571499i	$-0.193638\pi$
$193$	3.16352e10	1.64121	0.820603	+	0.571499i	$0.193638\pi$
$194$	−2.72534e10	−1.38138
$195$	0	0
$196$	−2.61429e9	−0.126532
$197$	−1.24212e10	−0.587576	−0.293788	−	0.955871i	$-0.594916\pi$
$197$	−1.24212e10	−0.587576	−0.293788	+	0.955871i	$0.594916\pi$
$198$	0	0
$199$	4.01627e10	1.81545	0.907724	−	0.419568i	$-0.137818\pi$
$199$	4.01627e10	1.81545	0.907724	+	0.419568i	$0.137818\pi$
$200$	8.91010e9	0.393775
$201$	0	0
$202$	−4.52347e10	−1.91157
$203$	1.95391e10	0.807554
$204$	0	0
$205$	−4.14722e9	−0.164008
$206$	4.98016e10	1.92682
$207$	0	0
$208$	3.01731e10	1.11772
$209$	−3.98948e8	−0.0144630
$210$	0	0
$211$	1.34292e10	0.466422	0.233211	−	0.972426i	$-0.425077\pi$
$211$	1.34292e10	0.466422	0.233211	+	0.972426i	$0.425077\pi$
$212$	−2.93863e10	−0.999158
$213$	0	0
$214$	7.31247e10	2.38343
$215$	2.70363e10	0.862926
$216$	0	0
$217$	−2.90153e10	−0.888296
$218$	7.44503e10	2.23261
$219$	0	0
$220$	−1.02230e10	−0.294221
$221$	−7.70572e9	−0.217294
$222$	0	0
$223$	−4.41977e10	−1.19682	−0.598409	−	0.801191i	$-0.704200\pi$
$223$	−4.41977e10	−1.19682	−0.598409	+	0.801191i	$0.704200\pi$
$224$	−3.27932e10	−0.870297
$225$	0	0
$226$	−2.68469e10	−0.684552
$227$	3.42932e10	0.857218	0.428609	−	0.903490i	$-0.359004\pi$
$227$	3.42932e10	0.857218	0.428609	+	0.903490i	$0.359004\pi$
$228$	0	0
$229$	5.87161e10	1.41090	0.705452	−	0.708757i	$-0.250744\pi$
$229$	5.87161e10	1.41090	0.705452	+	0.708757i	$0.250744\pi$
$230$	7.83361e9	0.184581
$231$	0	0
$232$	−2.27821e10	−0.516294
$233$	−8.16442e10	−1.81478	−0.907390	−	0.420290i	$-0.861928\pi$
$233$	−8.16442e10	−1.81478	−0.907390	+	0.420290i	$0.861928\pi$
$234$	0	0
$235$	9.28790e9	0.198661
$236$	−1.17216e10	−0.245971
$237$	0	0
$238$	1.31102e10	0.264858
$239$	6.99278e10	1.38631	0.693153	−	0.720790i	$-0.256221\pi$
$239$	6.99278e10	1.38631	0.693153	+	0.720790i	$0.256221\pi$
$240$	0	0
$241$	2.20186e10	0.420448	0.210224	−	0.977653i	$-0.432581\pi$
$241$	2.20186e10	0.420448	0.210224	+	0.977653i	$0.432581\pi$
$242$	−2.48471e9	−0.0465700
$243$	0	0
$244$	1.59641e10	0.288330
$245$	7.08996e9	0.125718
$246$	0	0
$247$	7.72586e8	0.0132072
$248$	3.38311e10	0.567915
$249$	0	0
$250$	7.14260e10	1.15645
$251$	7.51995e10	1.19587	0.597934	−	0.801545i	$-0.295988\pi$
$251$	7.51995e10	1.19587	0.597934	+	0.801545i	$0.295988\pi$
$252$	0	0
$253$	−1.73698e10	−0.266534
$254$	2.71729e10	0.409623
$255$	0	0
$256$	8.53361e10	1.24180
$257$	4.88179e10	0.698039	0.349020	−	0.937115i	$-0.386515\pi$
$257$	4.88179e10	0.698039	0.349020	+	0.937115i	$0.386515\pi$
$258$	0	0
$259$	−2.78394e9	−0.0384424
$260$	1.97973e10	0.268675
$261$	0	0
$262$	1.47612e11	1.93537
$263$	−1.51056e10	−0.194687	−0.0973437	−	0.995251i	$-0.531035\pi$
$263$	−1.51056e10	−0.194687	−0.0973437	+	0.995251i	$0.531035\pi$
$264$	0	0
$265$	7.96958e10	0.992725
$266$	−1.31444e9	−0.0160981
$267$	0	0
$268$	−4.91185e10	−0.581619
$269$	−7.34701e9	−0.0855511	−0.0427755	−	0.999085i	$-0.513620\pi$
$269$	−7.34701e9	−0.0855511	−0.0427755	+	0.999085i	$0.513620\pi$
$270$	0	0
$271$	9.26149e10	1.04308	0.521542	−	0.853226i	$-0.325357\pi$
$271$	9.26149e10	1.04308	0.521542	+	0.853226i	$0.325357\pi$
$272$	−2.73148e10	−0.302578
$273$	0	0
$274$	−8.71583e10	−0.934181
$275$	−6.53255e10	−0.688788
$276$	0	0
$277$	2.09446e10	0.213753	0.106877	−	0.994272i	$-0.465915\pi$
$277$	2.09446e10	0.213753	0.106877	+	0.994272i	$0.465915\pi$
$278$	−1.72085e10	−0.172799
$279$	0	0
$280$	2.76264e10	0.268605
$281$	7.54010e10	0.721438	0.360719	−	0.932675i	$-0.382531\pi$
$281$	7.54010e10	0.721438	0.360719	+	0.932675i	$0.382531\pi$
$282$	0	0
$283$	−1.56859e11	−1.45368	−0.726842	−	0.686805i	$-0.759013\pi$
$283$	−1.56859e11	−1.45368	−0.726842	+	0.686805i	$0.759013\pi$
$284$	−9.74181e9	−0.0888602
$285$	0	0
$286$	−1.23800e11	−1.09414
$287$	3.02981e10	0.263601
$288$	0	0
$289$	6.97576e9	0.0588235
$290$	−7.53288e10	−0.625417
$291$	0	0
$292$	−1.10608e11	−0.890355
$293$	1.90997e11	1.51399	0.756994	−	0.653422i	$-0.226667\pi$
$293$	1.90997e11	1.51399	0.756994	+	0.653422i	$0.226667\pi$
$294$	0	0
$295$	3.17891e10	0.244387
$296$	3.24600e9	0.0245774
$297$	0	0
$298$	−5.70580e10	−0.419125
$299$	3.36376e10	0.243391
$300$	0	0
$301$	−1.97517e11	−1.38693
$302$	−1.99768e11	−1.38196
$303$	0	0
$304$	2.73862e9	0.0183908
$305$	−4.32946e10	−0.286473
$306$	0	0
$307$	7.83989e10	0.503718	0.251859	−	0.967764i	$-0.418958\pi$
$307$	7.83989e10	0.503718	0.251859	+	0.967764i	$0.418958\pi$
$308$	7.46852e10	0.472886
$309$	0	0
$310$	1.11862e11	0.687948
$311$	2.81000e11	1.70328	0.851639	−	0.524130i	$-0.175609\pi$
$311$	2.81000e11	1.70328	0.851639	+	0.524130i	$0.175609\pi$
$312$	0	0
$313$	−8.83831e10	−0.520499	−0.260249	−	0.965541i	$-0.583805\pi$
$313$	−8.83831e10	−0.520499	−0.260249	+	0.965541i	$0.583805\pi$
$314$	−2.32566e11	−1.35009
$315$	0	0
$316$	5.22552e10	0.294807
$317$	−2.32664e11	−1.29409	−0.647043	−	0.762454i	$-0.723994\pi$
$317$	−2.32664e11	−1.29409	−0.647043	+	0.762454i	$0.723994\pi$
$318$	0	0
$319$	1.67029e11	0.903098
$320$	−1.30811e9	−0.00697382
$321$	0	0
$322$	−5.72295e10	−0.296667
$323$	−6.99399e8	−0.00357531
$324$	0	0
$325$	1.26507e11	0.628982
$326$	−1.72730e11	−0.847012
$327$	0	0
$328$	−3.53269e10	−0.168528
$329$	−6.78540e10	−0.319297
$330$	0	0
$331$	−1.08788e11	−0.498144	−0.249072	−	0.968485i	$-0.580126\pi$
$331$	−1.08788e11	−0.498144	−0.249072	+	0.968485i	$0.580126\pi$
$332$	−1.01893e11	−0.460282
$333$	0	0
$334$	4.31562e11	1.89751
$335$	1.33209e11	0.577874
$336$	0	0
$337$	1.67127e11	0.705849	0.352925	−	0.935652i	$-0.385187\pi$
$337$	1.67127e11	0.705849	0.352925	+	0.935652i	$0.385187\pi$
$338$	−5.89339e10	−0.245607
$339$	0	0
$340$	−1.79219e10	−0.0727327
$341$	−2.48037e11	−0.993393
$342$	0	0
$343$	−2.76692e11	−1.07938
$344$	2.30300e11	0.886709
$345$	0	0
$346$	−4.09731e11	−1.53694
$347$	−4.77989e11	−1.76985	−0.884923	−	0.465737i	$-0.845789\pi$
$347$	−4.77989e11	−1.76985	−0.884923	+	0.465737i	$0.845789\pi$
$348$	0	0
$349$	−4.80098e11	−1.73227	−0.866134	−	0.499811i	$-0.833403\pi$
$349$	−4.80098e11	−1.73227	−0.866134	+	0.499811i	$0.833403\pi$
$350$	−2.15233e11	−0.766659
$351$	0	0
$352$	−2.80332e11	−0.973265
$353$	2.98926e11	1.02466	0.512328	−	0.858790i	$-0.328783\pi$
$353$	2.98926e11	1.02466	0.512328	+	0.858790i	$0.328783\pi$
$354$	0	0
$355$	2.64198e10	0.0882881
$356$	1.41993e10	0.0468536
$357$	0	0
$358$	−1.30940e11	−0.421308
$359$	−3.68878e11	−1.17208	−0.586041	−	0.810282i	$-0.699314\pi$
$359$	−3.68878e11	−1.17208	−0.586041	+	0.810282i	$0.699314\pi$
$360$	0	0
$361$	−3.22618e11	−0.999783
$362$	3.05833e10	0.0936044
$363$	0	0
$364$	−1.44632e11	−0.431826
$365$	2.99969e11	0.884622
$366$	0	0
$367$	−6.01112e11	−1.72965	−0.864825	−	0.502074i	$-0.832571\pi$
$367$	−6.01112e11	−1.72965	−0.864825	+	0.502074i	$0.832571\pi$
$368$	1.19236e11	0.338917
$369$	0	0
$370$	1.07329e10	0.0297721
$371$	−5.82229e11	−1.59555
$372$	0	0
$373$	3.28495e11	0.878697	0.439349	−	0.898317i	$-0.355209\pi$
$373$	3.28495e11	0.878697	0.439349	+	0.898317i	$0.355209\pi$
$374$	1.12072e11	0.296194
$375$	0	0
$376$	7.91161e10	0.204136
$377$	−3.23462e11	−0.824684
$378$	0	0
$379$	1.10170e11	0.274276	0.137138	−	0.990552i	$-0.456210\pi$
$379$	1.10170e11	0.274276	0.137138	+	0.990552i	$0.456210\pi$
$380$	1.79688e9	0.00442072
$381$	0	0
$382$	1.06557e11	0.256035
$383$	−4.46966e11	−1.06140	−0.530702	−	0.847559i	$-0.678072\pi$
$383$	−4.46966e11	−1.06140	−0.530702	+	0.847559i	$0.678072\pi$
$384$	0	0
$385$	−2.02546e11	−0.469841
$386$	8.91017e11	2.04288
$387$	0	0
$388$	−2.72179e11	−0.609694
$389$	−5.35885e11	−1.18658	−0.593292	−	0.804987i	$-0.702172\pi$
$389$	−5.35885e11	−1.18658	−0.593292	+	0.804987i	$0.702172\pi$
$390$	0	0
$391$	−3.04511e10	−0.0658882
$392$	6.03936e10	0.129183
$393$	0	0
$394$	−3.49846e11	−0.731382
$395$	−1.41716e11	−0.292909
$396$	0	0
$397$	−5.15293e11	−1.04111	−0.520555	−	0.853828i	$-0.674275\pi$
$397$	−5.15293e11	−1.04111	−0.520555	+	0.853828i	$0.674275\pi$
$398$	1.13120e12	2.25977
$399$	0	0
$400$	4.48433e11	0.875845
$401$	4.93193e11	0.952504	0.476252	−	0.879309i	$-0.341995\pi$
$401$	4.93193e11	0.952504	0.476252	+	0.879309i	$0.341995\pi$
$402$	0	0
$403$	4.80337e11	0.907138
$404$	−4.51759e11	−0.843705
$405$	0	0
$406$	5.50325e11	1.00520
$407$	−2.37985e10	−0.0429907
$408$	0	0
$409$	−2.86274e11	−0.505857	−0.252928	−	0.967485i	$-0.581394\pi$
$409$	−2.86274e11	−0.505857	−0.252928	+	0.967485i	$0.581394\pi$
$410$	−1.16808e11	−0.204148
$411$	0	0
$412$	4.97368e11	0.850434
$413$	−2.32239e11	−0.392790
$414$	0	0
$415$	2.76334e11	0.457318
$416$	5.42880e11	0.888758
$417$	0	0
$418$	−1.12365e10	−0.0180027
$419$	1.66697e11	0.264219	0.132110	−	0.991235i	$-0.457825\pi$
$419$	1.66697e11	0.264219	0.132110	+	0.991235i	$0.457825\pi$
$420$	0	0
$421$	−5.15187e11	−0.799274	−0.399637	−	0.916674i	$-0.630864\pi$
$421$	−5.15187e11	−0.799274	−0.399637	+	0.916674i	$0.630864\pi$
$422$	3.78238e11	0.580576
$423$	0	0
$424$	6.78864e11	1.02009
$425$	−1.14523e11	−0.170271
$426$	0	0
$427$	3.16295e11	0.460433
$428$	7.30296e11	1.05197
$429$	0	0
$430$	7.61486e11	1.07412
$431$	−5.42449e10	−0.0757202	−0.0378601	−	0.999283i	$-0.512054\pi$
$431$	−5.42449e10	−0.0757202	−0.0378601	+	0.999283i	$0.512054\pi$
$432$	0	0
$433$	−2.49025e11	−0.340445	−0.170222	−	0.985406i	$-0.554449\pi$
$433$	−2.49025e11	−0.340445	−0.170222	+	0.985406i	$0.554449\pi$
$434$	−8.17225e11	−1.10570
$435$	0	0
$436$	7.43535e11	0.985399
$437$	3.05307e9	0.00400470
$438$	0	0
$439$	2.46288e11	0.316485	0.158242	−	0.987400i	$-0.449417\pi$
$439$	2.46288e11	0.316485	0.158242	+	0.987400i	$0.449417\pi$
$440$	2.36164e11	0.300384
$441$	0	0
$442$	−2.17034e11	−0.270476
$443$	1.20603e12	1.48779	0.743895	−	0.668297i	$-0.232976\pi$
$443$	1.20603e12	1.48779	0.743895	+	0.668297i	$0.232976\pi$
$444$	0	0
$445$	−3.85086e10	−0.0465519
$446$	−1.24484e12	−1.48973
$447$	0	0
$448$	9.55660e9	0.0112086
$449$	1.43303e12	1.66398	0.831988	−	0.554794i	$-0.187203\pi$
$449$	1.43303e12	1.66398	0.831988	+	0.554794i	$0.187203\pi$
$450$	0	0
$451$	2.59003e11	0.294788
$452$	−2.68120e11	−0.302138
$453$	0	0
$454$	9.65879e11	1.06702
$455$	3.92243e11	0.429046
$456$	0	0
$457$	−1.45072e12	−1.55582	−0.777911	−	0.628375i	$-0.783721\pi$
$457$	−1.45072e12	−1.55582	−0.777911	+	0.628375i	$0.783721\pi$
$458$	1.65376e12	1.75622
$459$	0	0
$460$	7.82342e10	0.0814679
$461$	−4.79650e11	−0.494619	−0.247309	−	0.968937i	$-0.579546\pi$
$461$	−4.79650e11	−0.494619	−0.247309	+	0.968937i	$0.579546\pi$
$462$	0	0
$463$	−1.02183e11	−0.103339	−0.0516697	−	0.998664i	$-0.516454\pi$
$463$	−1.02183e11	−0.103339	−0.0516697	+	0.998664i	$0.516454\pi$
$464$	−1.14659e12	−1.14836
$465$	0	0
$466$	−2.29954e12	−2.25894
$467$	9.48806e11	0.923106	0.461553	−	0.887113i	$-0.347292\pi$
$467$	9.48806e11	0.923106	0.461553	+	0.887113i	$0.347292\pi$
$468$	0	0
$469$	−9.73180e11	−0.928785
$470$	2.61597e11	0.247282
$471$	0	0
$472$	2.70785e11	0.251123
$473$	−1.68847e12	−1.55103
$474$	0	0
$475$	1.14822e10	0.0103491
$476$	1.30931e11	0.116899
$477$	0	0
$478$	1.96954e12	1.72560
$479$	−1.54645e12	−1.34223	−0.671114	−	0.741354i	$-0.734184\pi$
$479$	−1.54645e12	−1.34223	−0.671114	+	0.741354i	$0.734184\pi$
$480$	0	0
$481$	4.60871e10	0.0392579
$482$	6.20161e11	0.523350
$483$	0	0
$484$	−2.48148e10	−0.0205545
$485$	7.38150e11	0.605768
$486$	0	0
$487$	−8.16740e11	−0.657966	−0.328983	−	0.944336i	$-0.606706\pi$
$487$	−8.16740e11	−0.657966	−0.328983	+	0.944336i	$0.606706\pi$
$488$	−3.68792e11	−0.294369
$489$	0	0
$490$	1.99691e11	0.156486
$491$	−2.36995e11	−0.184023	−0.0920116	−	0.995758i	$-0.529330\pi$
$491$	−2.36995e11	−0.184023	−0.0920116	+	0.995758i	$0.529330\pi$
$492$	0	0
$493$	2.92821e11	0.223250
$494$	2.17602e10	0.0164396
$495$	0	0
$496$	1.70267e12	1.26317
$497$	−1.93014e11	−0.141901
$498$	0	0
$499$	1.95695e12	1.41295	0.706477	−	0.707736i	$-0.250283\pi$
$499$	1.95695e12	1.41295	0.706477	+	0.707736i	$0.250283\pi$
$500$	7.13330e11	0.510418
$501$	0	0
$502$	2.11802e12	1.48855
$503$	−1.25952e12	−0.877302	−0.438651	−	0.898658i	$-0.644544\pi$
$503$	−1.25952e12	−0.877302	−0.438651	+	0.898658i	$0.644544\pi$
$504$	0	0
$505$	1.22517e12	0.838273
$506$	−4.89226e11	−0.331766
$507$	0	0
$508$	2.71376e11	0.180794
$509$	−8.63543e11	−0.570235	−0.285118	−	0.958493i	$-0.592033\pi$
$509$	−8.63543e11	−0.570235	−0.285118	+	0.958493i	$0.592033\pi$
$510$	0	0
$511$	−2.19146e12	−1.42180
$512$	8.36291e11	0.537827
$513$	0	0
$514$	1.37497e12	0.868881
$515$	−1.34886e12	−0.844958
$516$	0	0
$517$	−5.80049e11	−0.357073
$518$	−7.84106e10	−0.0478510
$519$	0	0
$520$	−4.57345e11	−0.274302
$521$	−8.44577e11	−0.502192	−0.251096	−	0.967962i	$-0.580791\pi$
$521$	−8.44577e11	−0.502192	−0.251096	+	0.967962i	$0.580791\pi$
$522$	0	0
$523$	9.06283e11	0.529671	0.264835	−	0.964294i	$-0.414682\pi$
$523$	9.06283e11	0.529671	0.264835	+	0.964294i	$0.414682\pi$
$524$	1.47419e12	0.854209
$525$	0	0
$526$	−4.25455e11	−0.242336
$527$	−4.34835e11	−0.245571
$528$	0	0
$529$	−1.66823e12	−0.926199
$530$	2.24466e12	1.23569
$531$	0	0
$532$	−1.31273e10	−0.00710517
$533$	−5.01575e11	−0.269193
$534$	0	0
$535$	−1.98056e12	−1.04519
$536$	1.13470e12	0.593801
$537$	0	0
$538$	−2.06931e11	−0.106489
$539$	−4.42783e11	−0.225965
$540$	0	0
$541$	1.55099e12	0.778435	0.389217	−	0.921146i	$-0.372745\pi$
$541$	1.55099e12	0.778435	0.389217	+	0.921146i	$0.372745\pi$
$542$	2.60853e12	1.29837
$543$	0	0
$544$	−4.91453e11	−0.240595
$545$	−2.01647e12	−0.979054
$546$	0	0
$547$	−2.93476e12	−1.40162	−0.700808	−	0.713350i	$-0.747177\pi$
$547$	−2.93476e12	−1.40162	−0.700808	+	0.713350i	$0.747177\pi$
$548$	−8.70449e11	−0.412317
$549$	0	0
$550$	−1.83992e12	−0.857365
$551$	−2.93586e10	−0.0135692
$552$	0	0
$553$	1.03533e12	0.470776
$554$	5.89912e11	0.266068
$555$	0	0
$556$	−1.71861e11	−0.0762678
$557$	2.35783e12	1.03792	0.518961	−	0.854798i	$-0.326319\pi$
$557$	2.35783e12	1.03792	0.518961	+	0.854798i	$0.326319\pi$
$558$	0	0
$559$	3.26983e12	1.41635
$560$	1.39040e12	0.597438
$561$	0	0
$562$	2.12370e12	0.898006
$563$	−2.31243e12	−0.970020	−0.485010	−	0.874509i	$-0.661184\pi$
$563$	−2.31243e12	−0.970020	−0.485010	+	0.874509i	$0.661184\pi$
$564$	0	0
$565$	7.27141e11	0.300193
$566$	−4.41798e12	−1.80946
$567$	0	0
$568$	2.25049e11	0.0907214
$569$	8.35674e11	0.334220	0.167110	−	0.985938i	$-0.446557\pi$
$569$	8.35674e11	0.334220	0.167110	+	0.985938i	$0.446557\pi$
$570$	0	0
$571$	−2.79849e12	−1.10169	−0.550846	−	0.834607i	$-0.685695\pi$
$571$	−2.79849e12	−1.10169	−0.550846	+	0.834607i	$0.685695\pi$
$572$	−1.23639e12	−0.482917
$573$	0	0
$574$	8.53357e11	0.328116
$575$	4.99923e11	0.190721
$576$	0	0
$577$	4.23010e12	1.58876	0.794382	−	0.607419i	$-0.207795\pi$
$577$	4.23010e12	1.58876	0.794382	+	0.607419i	$0.207795\pi$
$578$	1.96475e11	0.0732203
$579$	0	0
$580$	−7.52308e11	−0.276038
$581$	−2.01880e12	−0.735022
$582$	0	0
$583$	−4.97717e12	−1.78433
$584$	2.55519e12	0.909003
$585$	0	0
$586$	5.37950e12	1.88453
$587$	9.29095e11	0.322990	0.161495	−	0.986874i	$-0.448368\pi$
$587$	9.29095e11	0.322990	0.161495	+	0.986874i	$0.448368\pi$
$588$	0	0
$589$	4.35971e10	0.0149259
$590$	8.95350e11	0.304200
$591$	0	0
$592$	1.63367e11	0.0546658
$593$	−3.56436e12	−1.18368	−0.591841	−	0.806055i	$-0.701599\pi$
$593$	−3.56436e12	−1.18368	−0.591841	+	0.806055i	$0.701599\pi$
$594$	0	0
$595$	−3.55086e11	−0.116147
$596$	−5.69838e11	−0.184988
$597$	0	0
$598$	9.47415e11	0.302960
$599$	5.69493e12	1.80746	0.903728	−	0.428106i	$-0.140819\pi$
$599$	5.69493e12	1.80746	0.903728	+	0.428106i	$0.140819\pi$
$600$	0	0
$601$	−3.23003e12	−1.00989	−0.504943	−	0.863153i	$-0.668486\pi$
$601$	−3.23003e12	−1.00989	−0.504943	+	0.863153i	$0.668486\pi$
$602$	−5.56314e12	−1.72638
$603$	0	0
$604$	−1.99508e12	−0.609951
$605$	6.72977e10	0.0204221
$606$	0	0
$607$	−1.62163e12	−0.484846	−0.242423	−	0.970171i	$-0.577942\pi$
$607$	−1.62163e12	−0.484846	−0.242423	+	0.970171i	$0.577942\pi$
$608$	4.92737e10	0.0146234
$609$	0	0
$610$	−1.21941e12	−0.356586
$611$	1.12330e12	0.326070
$612$	0	0
$613$	3.22227e12	0.921700	0.460850	−	0.887478i	$-0.347545\pi$
$613$	3.22227e12	0.921700	0.460850	+	0.887478i	$0.347545\pi$
$614$	2.20813e12	0.627000
$615$	0	0
$616$	−1.72533e12	−0.482790
$617$	3.76562e12	1.04605	0.523026	−	0.852317i	$-0.324803\pi$
$617$	3.76562e12	1.04605	0.523026	+	0.852317i	$0.324803\pi$
$618$	0	0
$619$	3.75883e12	1.02907	0.514535	−	0.857470i	$-0.327965\pi$
$619$	3.75883e12	1.02907	0.514535	+	0.857470i	$0.327965\pi$
$620$	1.11717e12	0.303637
$621$	0	0
$622$	7.91448e12	2.12014
$623$	2.81330e11	0.0748203
$624$	0	0
$625$	7.43541e11	0.194915
$626$	−2.48934e12	−0.647888
$627$	0	0
$628$	−2.32263e12	−0.595884
$629$	−4.17213e10	−0.0106275
$630$	0	0
$631$	−5.72141e12	−1.43672	−0.718358	−	0.695673i	$-0.755106\pi$
$631$	−5.72141e12	−1.43672	−0.718358	+	0.695673i	$0.755106\pi$
$632$	−1.20717e12	−0.300982
$633$	0	0
$634$	−6.55307e12	−1.61081
$635$	−7.35971e11	−0.179630
$636$	0	0
$637$	8.57475e11	0.206345
$638$	4.70444e12	1.12413
$639$	0	0
$640$	−2.33508e12	−0.550165
$641$	2.45043e12	0.573299	0.286650	−	0.958035i	$-0.407458\pi$
$641$	2.45043e12	0.573299	0.286650	+	0.958035i	$0.407458\pi$
$642$	0	0
$643$	5.20042e12	1.19975	0.599873	−	0.800095i	$-0.295218\pi$
$643$	5.20042e12	1.19975	0.599873	+	0.800095i	$0.295218\pi$
$644$	−5.71551e11	−0.130939
$645$	0	0
$646$	−1.96988e10	−0.00445035
$647$	−9.06811e11	−0.203445	−0.101723	−	0.994813i	$-0.532435\pi$
$647$	−9.06811e11	−0.203445	−0.101723	+	0.994813i	$0.532435\pi$
$648$	0	0
$649$	−1.98530e12	−0.439262
$650$	3.56310e12	0.782922
$651$	0	0
$652$	−1.72506e12	−0.373843
$653$	−5.74944e12	−1.23742	−0.618708	−	0.785621i	$-0.712344\pi$
$653$	−5.74944e12	−1.23742	−0.618708	+	0.785621i	$0.712344\pi$
$654$	0	0
$655$	−3.99802e12	−0.848709
$656$	−1.77795e12	−0.374845
$657$	0	0
$658$	−1.91113e12	−0.397443
$659$	1.14504e12	0.236503	0.118252	−	0.992984i	$-0.462271\pi$
$659$	1.14504e12	0.236503	0.118252	+	0.992984i	$0.462271\pi$
$660$	0	0
$661$	−2.18103e12	−0.444380	−0.222190	−	0.975003i	$-0.571321\pi$
$661$	−2.18103e12	−0.444380	−0.222190	+	0.975003i	$0.571321\pi$
$662$	−3.06405e12	−0.620062
$663$	0	0
$664$	2.35387e12	0.469922
$665$	3.56014e10	0.00705943
$666$	0	0
$667$	−1.27824e12	−0.250062
$668$	4.31000e12	0.837497
$669$	0	0
$670$	3.75189e12	0.719306
$671$	2.70384e12	0.514908
$672$	0	0
$673$	−5.45288e12	−1.02461	−0.512304	−	0.858804i	$-0.671208\pi$
$673$	−5.45288e12	−1.02461	−0.512304	+	0.858804i	$0.671208\pi$
$674$	4.70719e12	0.878602
$675$	0	0
$676$	−5.88573e11	−0.108403
$677$	4.84898e12	0.887159	0.443579	−	0.896235i	$-0.353708\pi$
$677$	4.84898e12	0.887159	0.443579	+	0.896235i	$0.353708\pi$
$678$	0	0
$679$	−5.39266e12	−0.973618
$680$	4.14021e11	0.0742561
$681$	0	0
$682$	−6.98604e12	−1.23652
$683$	1.30756e11	0.0229916	0.0114958	−	0.999934i	$-0.496341\pi$
$683$	1.30756e11	0.0229916	0.0114958	+	0.999934i	$0.496341\pi$
$684$	0	0
$685$	2.36066e12	0.409662
$686$	−7.79312e12	−1.34355
$687$	0	0
$688$	1.15907e13	1.97224
$689$	9.63859e12	1.62940
$690$	0	0
$691$	3.22565e12	0.538227	0.269113	−	0.963108i	$-0.413269\pi$
$691$	3.22565e12	0.538227	0.269113	+	0.963108i	$0.413269\pi$
$692$	−4.09198e12	−0.678353
$693$	0	0
$694$	−1.34627e13	−2.20301
$695$	4.66088e11	0.0757767
$696$	0	0
$697$	4.54060e11	0.0728729
$698$	−1.35221e13	−2.15623
$699$	0	0
$700$	−2.14953e12	−0.338378
$701$	−8.43820e12	−1.31983	−0.659916	−	0.751339i	$-0.729408\pi$
$701$	−8.43820e12	−1.31983	−0.659916	+	0.751339i	$0.729408\pi$
$702$	0	0
$703$	4.18303e9	0.000645940 0
$704$	8.16945e10	0.0125348
$705$	0	0
$706$	8.41936e12	1.27543
$707$	−8.95065e12	−1.34731
$708$	0	0
$709$	5.72297e12	0.850576	0.425288	−	0.905058i	$-0.360173\pi$
$709$	5.72297e12	0.850576	0.425288	+	0.905058i	$0.360173\pi$
$710$	7.44123e11	0.109896
$711$	0	0
$712$	−3.28024e11	−0.0478349
$713$	1.89817e12	0.275064
$714$	0	0
$715$	3.35308e12	0.479808
$716$	−1.30770e12	−0.185951
$717$	0	0
$718$	−1.03896e13	−1.45894
$719$	6.14814e12	0.857954	0.428977	−	0.903316i	$-0.358874\pi$
$719$	6.14814e12	0.857954	0.428977	+	0.903316i	$0.358874\pi$
$720$	0	0
$721$	9.85431e12	1.35805
$722$	−9.08664e12	−1.24447
$723$	0	0
$724$	3.05435e11	0.0413138
$725$	−4.80731e12	−0.646220
$726$	0	0
$727$	−9.21269e12	−1.22316	−0.611578	−	0.791184i	$-0.709465\pi$
$727$	−9.21269e12	−1.22316	−0.611578	+	0.791184i	$0.709465\pi$
$728$	3.34120e12	0.440871
$729$	0	0
$730$	8.44872e12	1.10113
$731$	−2.96008e12	−0.383420
$732$	0	0
$733$	−8.69962e12	−1.11310	−0.556548	−	0.830816i	$-0.687874\pi$
$733$	−8.69962e12	−1.11310	−0.556548	+	0.830816i	$0.687874\pi$
$734$	−1.69305e13	−2.15297
$735$	0	0
$736$	2.14533e12	0.269490
$737$	−8.31921e12	−1.03867
$738$	0	0
$739$	−8.74888e12	−1.07908	−0.539539	−	0.841961i	$-0.681401\pi$
$739$	−8.74888e12	−1.07908	−0.539539	+	0.841961i	$0.681401\pi$
$740$	1.07189e11	0.0131404
$741$	0	0
$742$	−1.63987e13	−1.98605
$743$	4.65215e11	0.0560021	0.0280010	−	0.999608i	$-0.491086\pi$
$743$	4.65215e11	0.0560021	0.0280010	+	0.999608i	$0.491086\pi$
$744$	0	0
$745$	1.54540e12	0.183797
$746$	9.25219e12	1.09375
$747$	0	0
$748$	1.11926e12	0.130730
$749$	1.44693e13	1.67988
$750$	0	0
$751$	−8.93867e12	−1.02540	−0.512700	−	0.858568i	$-0.671355\pi$
$751$	−8.93867e12	−1.02540	−0.512700	+	0.858568i	$0.671355\pi$
$752$	3.98180e12	0.454045
$753$	0	0
$754$	−9.11043e12	−1.02652
$755$	5.41067e12	0.606024
$756$	0	0
$757$	6.47580e12	0.716741	0.358371	−	0.933579i	$-0.383332\pi$
$757$	6.47580e12	0.716741	0.358371	+	0.933579i	$0.383332\pi$
$758$	3.10298e12	0.341403
$759$	0	0
$760$	−4.15103e10	−0.00451331
$761$	−1.50384e12	−0.162544	−0.0812720	−	0.996692i	$-0.525898\pi$
$761$	−1.50384e12	−0.162544	−0.0812720	+	0.996692i	$0.525898\pi$
$762$	0	0
$763$	1.47316e13	1.57358
$764$	1.06419e12	0.113005
$765$	0	0
$766$	−1.25890e13	−1.32118
$767$	3.84464e12	0.401122
$768$	0	0
$769$	1.49083e13	1.53731	0.768653	−	0.639666i	$-0.220927\pi$
$769$	1.49083e13	1.53731	0.768653	+	0.639666i	$0.220927\pi$
$770$	−5.70479e12	−0.584832
$771$	0	0
$772$	8.89858e12	0.901660
$773$	2.45775e11	0.0247588	0.0123794	−	0.999923i	$-0.496059\pi$
$773$	2.45775e11	0.0247588	0.0123794	+	0.999923i	$0.496059\pi$
$774$	0	0
$775$	7.13878e12	0.710831
$776$	6.28770e12	0.622464
$777$	0	0
$778$	−1.50934e13	−1.47699
$779$	−4.55247e10	−0.00442924
$780$	0	0
$781$	−1.64997e12	−0.158689
$782$	−8.57666e11	−0.0820140
$783$	0	0
$784$	3.03952e12	0.287332
$785$	6.29898e12	0.592047
$786$	0	0
$787$	8.04995e12	0.748009	0.374004	−	0.927427i	$-0.377984\pi$
$787$	8.04995e12	0.748009	0.374004	+	0.927427i	$0.377984\pi$
$788$	−3.49391e12	−0.322808
$789$	0	0
$790$	−3.99149e12	−0.364597
$791$	−5.31223e12	−0.482484
$792$	0	0
$793$	−5.23615e12	−0.470200
$794$	−1.45134e13	−1.29592
$795$	0	0
$796$	1.12972e13	0.997387
$797$	−2.27278e12	−0.199524	−0.0997618	−	0.995011i	$-0.531808\pi$
$797$	−2.27278e12	−0.199524	−0.0997618	+	0.995011i	$0.531808\pi$
$798$	0	0
$799$	−1.01689e12	−0.0882700
$800$	8.06829e12	0.696429
$801$	0	0
$802$	1.38909e13	1.18562
$803$	−1.87337e13	−1.59002
$804$	0	0
$805$	1.55005e12	0.130096
$806$	1.35289e13	1.12916
$807$	0	0
$808$	1.04362e13	0.861376
$809$	−2.47519e12	−0.203161	−0.101581	−	0.994827i	$-0.532390\pi$
$809$	−2.47519e12	−0.203161	−0.101581	+	0.994827i	$0.532390\pi$
$810$	0	0
$811$	2.45293e13	1.99110	0.995548	−	0.0942611i	$-0.0300488\pi$
$811$	2.45293e13	1.99110	0.995548	+	0.0942611i	$0.0300488\pi$
$812$	5.49609e12	0.443661
$813$	0	0
$814$	−6.70292e11	−0.0535124
$815$	4.67836e12	0.371436
$816$	0	0
$817$	2.96781e11	0.0233044
$818$	−8.06302e12	−0.629662
$819$	0	0
$820$	−1.16656e12	−0.0901042
$821$	8.21852e12	0.631319	0.315660	−	0.948872i	$-0.397774\pi$
$821$	8.21852e12	0.631319	0.315660	+	0.948872i	$0.397774\pi$
$822$	0	0
$823$	1.55798e12	0.118376	0.0591878	−	0.998247i	$-0.481149\pi$
$823$	1.55798e12	0.118376	0.0591878	+	0.998247i	$0.481149\pi$
$824$	−1.14899e13	−0.868246
$825$	0	0
$826$	−6.54110e12	−0.488923
$827$	−1.18962e13	−0.884367	−0.442184	−	0.896924i	$-0.645796\pi$
$827$	−1.18962e13	−0.884367	−0.442184	+	0.896924i	$0.645796\pi$
$828$	0	0
$829$	−8.80333e12	−0.647368	−0.323684	−	0.946165i	$-0.604922\pi$
$829$	−8.80333e12	−0.647368	−0.323684	+	0.946165i	$0.604922\pi$
$830$	7.78305e12	0.569244
$831$	0	0
$832$	−1.58206e11	−0.0114464
$833$	−7.76247e11	−0.0558595
$834$	0	0
$835$	−1.16887e13	−0.832105
$836$	−1.12219e11	−0.00794581
$837$	0	0
$838$	4.69508e12	0.328886
$839$	6.42832e12	0.447887	0.223944	−	0.974602i	$-0.428107\pi$
$839$	6.42832e12	0.447887	0.223944	+	0.974602i	$0.428107\pi$
$840$	0	0
$841$	−2.21544e12	−0.152714
$842$	−1.45104e13	−0.994892
$843$	0	0
$844$	3.77746e12	0.256247
$845$	1.59621e12	0.107705
$846$	0	0
$847$	−4.91653e11	−0.0328234
$848$	3.41663e13	2.26890
$849$	0	0
$850$	−3.22557e12	−0.211944
$851$	1.82125e11	0.0119038
$852$	0	0
$853$	−1.34906e13	−0.872492	−0.436246	−	0.899827i	$-0.643692\pi$
$853$	−1.34906e13	−0.872492	−0.436246	+	0.899827i	$0.643692\pi$
$854$	8.90855e12	0.573121
$855$	0	0
$856$	−1.68708e13	−1.07400
$857$	2.46136e13	1.55870	0.779348	−	0.626592i	$-0.215551\pi$
$857$	2.46136e13	1.55870	0.779348	+	0.626592i	$0.215551\pi$
$858$	0	0
$859$	2.45934e13	1.54117	0.770583	−	0.637340i	$-0.219965\pi$
$859$	2.45934e13	1.54117	0.770583	+	0.637340i	$0.219965\pi$
$860$	7.60495e12	0.474082
$861$	0	0
$862$	−1.52783e12	−0.0942523
$863$	−1.57068e12	−0.0963918	−0.0481959	−	0.998838i	$-0.515347\pi$
$863$	−1.57068e12	−0.0963918	−0.0481959	+	0.998838i	$0.515347\pi$
$864$	0	0
$865$	1.10974e13	0.673985
$866$	−7.01386e12	−0.423767
$867$	0	0
$868$	−8.16162e12	−0.488020
$869$	8.85048e12	0.526475
$870$	0	0
$871$	1.61106e13	0.948487
$872$	−1.71767e13	−1.00604
$873$	0	0
$874$	8.59908e10	0.00498483
$875$	1.41331e13	0.815084
$876$	0	0
$877$	−2.26638e12	−0.129370	−0.0646852	−	0.997906i	$-0.520604\pi$
$877$	−2.26638e12	−0.129370	−0.0646852	+	0.997906i	$0.520604\pi$
$878$	6.93678e12	0.393942
$879$	0	0
$880$	1.18858e13	0.668123
$881$	2.20342e13	1.23227	0.616134	−	0.787641i	$-0.288698\pi$
$881$	2.20342e13	1.23227	0.616134	+	0.787641i	$0.288698\pi$
$882$	0	0
$883$	7.71424e12	0.427041	0.213521	−	0.976939i	$-0.431507\pi$
$883$	7.71424e12	0.427041	0.213521	+	0.976939i	$0.431507\pi$
$884$	−2.16752e12	−0.119379
$885$	0	0
$886$	3.39683e13	1.85192
$887$	3.10912e13	1.68648	0.843239	−	0.537539i	$-0.180646\pi$
$887$	3.10912e13	1.68648	0.843239	+	0.537539i	$0.180646\pi$
$888$	0	0
$889$	5.37674e12	0.288709
$890$	−1.08461e12	−0.0579452
$891$	0	0
$892$	−1.24322e13	−0.657518
$893$	1.01955e11	0.00536508
$894$	0	0
$895$	3.54648e12	0.184754
$896$	1.70593e13	0.884249
$897$	0	0
$898$	4.03618e13	2.07122
$899$	−1.82530e13	−0.932000
$900$	0	0
$901$	−8.72552e12	−0.441093
$902$	7.29491e12	0.366936
$903$	0	0
$904$	6.19393e12	0.308467
$905$	−8.28341e11	−0.0410479
$906$	0	0
$907$	−9.61906e12	−0.471954	−0.235977	−	0.971759i	$-0.575829\pi$
$907$	−9.61906e12	−0.471954	−0.235977	+	0.971759i	$0.575829\pi$
$908$	9.64623e12	0.470946
$909$	0	0
$910$	1.10477e13	0.534052
$911$	1.52076e13	0.731525	0.365762	−	0.930708i	$-0.380808\pi$
$911$	1.52076e13	0.731525	0.365762	+	0.930708i	$0.380808\pi$
$912$	0	0
$913$	−1.72577e13	−0.821985
$914$	−4.08600e13	−1.93660
$915$	0	0
$916$	1.65161e13	0.775135
$917$	2.92081e13	1.36408
$918$	0	0
$919$	1.96701e13	0.909675	0.454838	−	0.890574i	$-0.349697\pi$
$919$	1.96701e13	0.909675	0.454838	+	0.890574i	$0.349697\pi$
$920$	−1.80732e12	−0.0831742
$921$	0	0
$922$	−1.35095e13	−0.615674
$923$	3.19527e12	0.144911
$924$	0	0
$925$	6.84948e11	0.0307624
$926$	−2.87803e12	−0.128631
$927$	0	0
$928$	−2.06297e13	−0.913116
$929$	−3.18903e13	−1.40471	−0.702357	−	0.711825i	$-0.747869\pi$
$929$	−3.18903e13	−1.40471	−0.702357	+	0.711825i	$0.747869\pi$
$930$	0	0
$931$	7.78276e10	0.00339516
$932$	−2.29655e13	−0.997020
$933$	0	0
$934$	2.67235e13	1.14903
$935$	−3.03544e12	−0.129888
$936$	0	0
$937$	−2.61645e13	−1.10888	−0.554439	−	0.832224i	$-0.687067\pi$
$937$	−2.61645e13	−1.10888	−0.554439	+	0.832224i	$0.687067\pi$
$938$	−2.74099e13	−1.15610
$939$	0	0
$940$	2.61257e12	0.109142
$941$	−3.93723e13	−1.63696	−0.818479	−	0.574536i	$-0.805183\pi$
$941$	−3.93723e13	−1.63696	−0.818479	+	0.574536i	$0.805183\pi$
$942$	0	0
$943$	−1.98210e12	−0.0816249
$944$	1.36282e13	0.558555
$945$	0	0
$946$	−4.75564e13	−1.93063
$947$	2.26031e13	0.913258	0.456629	−	0.889657i	$-0.349057\pi$
$947$	2.26031e13	0.913258	0.456629	+	0.889657i	$0.349057\pi$
$948$	0	0
$949$	3.62789e13	1.45196
$950$	3.23400e11	0.0128820
$951$	0	0
$952$	−3.02469e12	−0.119348
$953$	3.27556e13	1.28637	0.643187	−	0.765709i	$-0.277612\pi$
$953$	3.27556e13	1.28637	0.643187	+	0.765709i	$0.277612\pi$
$954$	0	0
$955$	−2.88608e12	−0.112278
$956$	1.96698e13	0.761621
$957$	0	0
$958$	−4.35563e13	−1.67073
$959$	−1.72461e13	−0.658427
$960$	0	0
$961$	6.65864e11	0.0251843
$962$	1.29806e12	0.0488660
$963$	0	0
$964$	6.19354e12	0.230989
$965$	−2.41329e13	−0.895854
$966$	0	0
$967$	2.07251e13	0.762217	0.381108	−	0.924530i	$-0.375543\pi$
$967$	2.07251e13	0.762217	0.381108	+	0.924530i	$0.375543\pi$
$968$	5.73255e11	0.0209850
$969$	0	0
$970$	2.07902e13	0.754027
$971$	−5.19068e13	−1.87386	−0.936932	−	0.349512i	$-0.886348\pi$
$971$	−5.19068e13	−1.87386	−0.936932	+	0.349512i	$0.886348\pi$
$972$	0	0
$973$	−3.40507e12	−0.121792
$974$	−2.30038e13	−0.819000
$975$	0	0
$976$	−1.85608e13	−0.654744
$977$	−2.18772e12	−0.0768185	−0.0384093	−	0.999262i	$-0.512229\pi$
$977$	−2.18772e12	−0.0768185	−0.0384093	+	0.999262i	$0.512229\pi$
$978$	0	0
$979$	2.40494e12	0.0836725
$980$	1.99431e12	0.0690679
$981$	0	0
$982$	−6.67505e12	−0.229062
$983$	1.84743e13	0.631068	0.315534	−	0.948914i	$-0.397816\pi$
$983$	1.84743e13	0.631068	0.315534	+	0.948914i	$0.397816\pi$
$984$	0	0
$985$	9.47549e12	0.320729
$986$	8.24740e12	0.277889
$987$	0	0
$988$	2.17319e11	0.00725589
$989$	1.29215e13	0.429468
$990$	0	0
$991$	−3.55303e13	−1.17022	−0.585110	−	0.810954i	$-0.698949\pi$
$991$	−3.55303e13	−1.17022	−0.585110	+	0.810954i	$0.698949\pi$
$992$	3.06348e13	1.00441
$993$	0	0
$994$	−5.43629e12	−0.176630
$995$	−3.06381e13	−0.990965
$996$	0	0
$997$	5.54350e13	1.77687	0.888435	−	0.459003i	$-0.151793\pi$
$997$	5.54350e13	1.77687	0.888435	+	0.459003i	$0.151793\pi$
$998$	5.51183e13	1.75877
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.10.a.c.1.4		5
3.2	odd	2		17.10.a.a.1.2	✓	5
12.11	even	2		272.10.a.f.1.2		5
51.50	odd	2		289.10.a.a.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.a.1.2	✓	5	3.2	odd	2
153.10.a.c.1.4		5	1.1	even	1	trivial
272.10.a.f.1.2		5	12.11	even	2
289.10.a.a.1.2		5	51.50	odd	2

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	153.a (trivial)

\(f(q)\)	\(=\)	\(q+28.1654 q^{2} +281.287 q^{4} -762.851 q^{5} +5573.11 q^{7} -6498.11 q^{8} +O(q^{10})\)	\(q+28.1654 q^{2} +281.287 q^{4} -762.851 q^{5} +5573.11 q^{7} -6498.11 q^{8} -21486.0 q^{10} +47641.7 q^{11} -92260.9 q^{13} +156969. q^{14} -327041. q^{16} +83521.0 q^{17} -8373.93 q^{19} -214580. q^{20} +1.34184e6 q^{22} -364592. q^{23} -1.37118e6 q^{25} -2.59856e6 q^{26} +1.56764e6 q^{28} +3.50595e6 q^{29} -5.20629e6 q^{31} -5.88418e6 q^{32} +2.35240e6 q^{34} -4.25145e6 q^{35} -499530. q^{37} -235855. q^{38} +4.95709e6 q^{40} +5.43648e6 q^{41} -3.54411e7 q^{43} +1.34010e7 q^{44} -1.02689e7 q^{46} -1.21753e7 q^{47} -9.29403e6 q^{49} -3.86199e7 q^{50} -2.59518e7 q^{52} -1.04471e8 q^{53} -3.63435e7 q^{55} -3.62147e7 q^{56} +9.87464e7 q^{58} -4.16714e7 q^{59} +5.67537e7 q^{61} -1.46637e8 q^{62} +1.71477e6 q^{64} +7.03813e7 q^{65} -1.74621e8 q^{67} +2.34934e7 q^{68} -1.19744e8 q^{70} -3.46330e7 q^{71} -3.93220e8 q^{73} -1.40694e7 q^{74} -2.35548e6 q^{76} +2.65512e8 q^{77} +1.85772e8 q^{79} +2.49483e8 q^{80} +1.53120e8 q^{82} -3.62239e8 q^{83} -6.37141e7 q^{85} -9.98211e8 q^{86} -3.09581e8 q^{88} +5.04798e7 q^{89} -5.14180e8 q^{91} -1.02555e8 q^{92} -3.42920e8 q^{94} +6.38806e6 q^{95} -9.67620e8 q^{97} -2.61770e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 33 q^{2} + 853 q^{4} - 1480 q^{5} - 13202 q^{7} + 42423 q^{8}+O(q^{10}) \) 5 * q + 33 * q^2 + 853 * q^4 - 1480 * q^5 - 13202 * q^7 + 42423 * q^8	\( 5 q + 33 q^{2} + 853 q^{4} - 1480 q^{5} - 13202 q^{7} + 42423 q^{8} - 89328 q^{10} + 68036 q^{11} - 158862 q^{13} + 84700 q^{14} + 350225 q^{16} + 417605 q^{17} - 370992 q^{19} - 1632640 q^{20} + 122290 q^{22} - 1645870 q^{23} + 3270239 q^{25} - 734846 q^{26} + 183372 q^{28} - 3668616 q^{29} - 7262362 q^{31} + 5605919 q^{32} + 2756193 q^{34} + 26503988 q^{35} - 31420708 q^{37} - 18513700 q^{38} - 53930464 q^{40} + 7996938 q^{41} - 56908268 q^{43} - 43323054 q^{44} - 32063472 q^{46} + 16903336 q^{47} - 11784059 q^{49} - 85921093 q^{50} + 173619082 q^{52} + 83362982 q^{53} + 6363364 q^{55} - 317409372 q^{56} + 64577488 q^{58} + 37946604 q^{59} - 77685452 q^{61} - 324855300 q^{62} + 131623105 q^{64} + 40321288 q^{65} - 304503600 q^{67} + 71243413 q^{68} - 122787392 q^{70} + 476602922 q^{71} - 289980486 q^{73} - 262289012 q^{74} - 1031276084 q^{76} + 143385648 q^{77} - 828240610 q^{79} - 912750944 q^{80} - 1109615654 q^{82} - 194681148 q^{83} - 123611080 q^{85} - 1164707144 q^{86} - 1017979978 q^{88} - 376848106 q^{89} + 194543664 q^{91} - 2506713088 q^{92} - 2244811104 q^{94} - 1498679864 q^{95} + 692035246 q^{97} - 871744055 q^{98}+O(q^{100}) \) 5 * q + 33 * q^2 + 853 * q^4 - 1480 * q^5 - 13202 * q^7 + 42423 * q^8 - 89328 * q^10 + 68036 * q^11 - 158862 * q^13 + 84700 * q^14 + 350225 * q^16 + 417605 * q^17 - 370992 * q^19 - 1632640 * q^20 + 122290 * q^22 - 1645870 * q^23 + 3270239 * q^25 - 734846 * q^26 + 183372 * q^28 - 3668616 * q^29 - 7262362 * q^31 + 5605919 * q^32 + 2756193 * q^34 + 26503988 * q^35 - 31420708 * q^37 - 18513700 * q^38 - 53930464 * q^40 + 7996938 * q^41 - 56908268 * q^43 - 43323054 * q^44 - 32063472 * q^46 + 16903336 * q^47 - 11784059 * q^49 - 85921093 * q^50 + 173619082 * q^52 + 83362982 * q^53 + 6363364 * q^55 - 317409372 * q^56 + 64577488 * q^58 + 37946604 * q^59 - 77685452 * q^61 - 324855300 * q^62 + 131623105 * q^64 + 40321288 * q^65 - 304503600 * q^67 + 71243413 * q^68 - 122787392 * q^70 + 476602922 * q^71 - 289980486 * q^73 - 262289012 * q^74 - 1031276084 * q^76 + 143385648 * q^77 - 828240610 * q^79 - 912750944 * q^80 - 1109615654 * q^82 - 194681148 * q^83 - 123611080 * q^85 - 1164707144 * q^86 - 1017979978 * q^88 - 376848106 * q^89 + 194543664 * q^91 - 2506713088 * q^92 - 2244811104 * q^94 - 1498679864 * q^95 + 692035246 * q^97 - 871744055 * q^98

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