LMFDB - Embedded newform 333.10.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,10,Mod(1,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, 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("333.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	333.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:	$171.506933443$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 5234 x^{12} + 33102 x^{11} + 10421899 x^{10} - 66002244 x^{9} + \cdots + 51\!\cdots\!20 $ x^14 - 6x^13 - 5234x^12 + 33102x^11 + 10421899x^10 - 66002244x^9 - 9839334124x^8 + 60512691564x^7 + 4405897359639x^6 - 25392014044254x^5 - 798948725725074x^4 + 3805427076948774x^3 + 41503424166638973x^2 - 100457651820986424*x + 51865911118483920
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 37)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-8.01135$ of defining polynomial
Character	$\chi$	$=$	333.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.01135 q^{2} -486.886 q^{4} -557.130 q^{5} -7760.08 q^{7} -5005.76 q^{8} +O(q^{10})$	\(q+5.01135 q^{2} -486.886 q^{4} -557.130 q^{5} -7760.08 q^{7} -5005.76 q^{8} -2791.97 q^{10} +41662.1 q^{11} -13831.9 q^{13} -38888.5 q^{14} +224200. q^{16} -274297. q^{17} +226307. q^{19} +271259. q^{20} +208783. q^{22} -392869. q^{23} -1.64273e6 q^{25} -69316.5 q^{26} +3.77828e6 q^{28} -2.38976e6 q^{29} +9.93724e6 q^{31} +3.68650e6 q^{32} -1.37460e6 q^{34} +4.32337e6 q^{35} +1.87416e6 q^{37} +1.13410e6 q^{38} +2.78886e6 q^{40} +2.24960e7 q^{41} +1.75526e7 q^{43} -2.02847e7 q^{44} -1.96880e6 q^{46} +1.97393e7 q^{47} +1.98653e7 q^{49} -8.23229e6 q^{50} +6.73457e6 q^{52} +6.18106e7 q^{53} -2.32112e7 q^{55} +3.88452e7 q^{56} -1.19759e7 q^{58} +5.98396e7 q^{59} +4.13428e7 q^{61} +4.97989e7 q^{62} -9.63162e7 q^{64} +7.70618e6 q^{65} -7.07839e6 q^{67} +1.33552e8 q^{68} +2.16659e7 q^{70} -3.19253e8 q^{71} -2.31570e8 q^{73} +9.39207e6 q^{74} -1.10186e8 q^{76} -3.23301e8 q^{77} +4.62203e8 q^{79} -1.24909e8 q^{80} +1.12735e8 q^{82} -2.34443e8 q^{83} +1.52819e8 q^{85} +8.79623e7 q^{86} -2.08551e8 q^{88} +1.81605e8 q^{89} +1.07337e8 q^{91} +1.91282e8 q^{92} +9.89203e7 q^{94} -1.26083e8 q^{95} +1.13352e9 q^{97} +9.95518e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 48 q^{2} + 3498 q^{4} - 2841 q^{5} + 6632 q^{7} - 41046 q^{8}+O(q^{10}) $ 14 * q - 48 * q^2 + 3498 * q^4 - 2841 * q^5 + 6632 * q^7 - 41046 * q^8	\( 14 q - 48 q^{2} + 3498 q^{4} - 2841 q^{5} + 6632 q^{7} - 41046 q^{8} + 129003 q^{10} - 44949 q^{11} + 38913 q^{13} - 16434 q^{14} + 859962 q^{16} - 893196 q^{17} + 1532124 q^{19} - 4974963 q^{20} + 3195323 q^{22} - 5911773 q^{23} + 9978791 q^{25} - 10634475 q^{26} + 9469678 q^{28} - 8764377 q^{29} + 13188927 q^{31} - 23982750 q^{32} + 29914960 q^{34} - 29633556 q^{35} + 26238254 q^{37} - 23342796 q^{38} + 42889049 q^{40} - 22153785 q^{41} + 1779790 q^{43} + 83674089 q^{44} - 23239663 q^{46} - 40080072 q^{47} - 170457752 q^{49} + 89214633 q^{50} - 276889277 q^{52} + 102088122 q^{53} - 206797385 q^{55} + 294922194 q^{56} - 527059089 q^{58} - 56191266 q^{59} - 178507397 q^{61} + 27353505 q^{62} - 242330062 q^{64} + 174258810 q^{65} + 287062499 q^{67} - 308827572 q^{68} - 672888452 q^{70} - 224382678 q^{71} + 271440727 q^{73} - 89959728 q^{74} - 229522980 q^{76} - 671279994 q^{77} + 379128625 q^{79} - 1999017183 q^{80} + 551153781 q^{82} - 1664083206 q^{83} + 1982056546 q^{85} - 520253082 q^{86} + 684092585 q^{88} - 3293434692 q^{89} + 1715813946 q^{91} - 3729310881 q^{92} + 998499458 q^{94} - 878402766 q^{95} + 2385468336 q^{97} + 3234447132 q^{98}+O(q^{100}) \) 14 * q - 48 * q^2 + 3498 * q^4 - 2841 * q^5 + 6632 * q^7 - 41046 * q^8 + 129003 * q^10 - 44949 * q^11 + 38913 * q^13 - 16434 * q^14 + 859962 * q^16 - 893196 * q^17 + 1532124 * q^19 - 4974963 * q^20 + 3195323 * q^22 - 5911773 * q^23 + 9978791 * q^25 - 10634475 * q^26 + 9469678 * q^28 - 8764377 * q^29 + 13188927 * q^31 - 23982750 * q^32 + 29914960 * q^34 - 29633556 * q^35 + 26238254 * q^37 - 23342796 * q^38 + 42889049 * q^40 - 22153785 * q^41 + 1779790 * q^43 + 83674089 * q^44 - 23239663 * q^46 - 40080072 * q^47 - 170457752 * q^49 + 89214633 * q^50 - 276889277 * q^52 + 102088122 * q^53 - 206797385 * q^55 + 294922194 * q^56 - 527059089 * q^58 - 56191266 * q^59 - 178507397 * q^61 + 27353505 * q^62 - 242330062 * q^64 + 174258810 * q^65 + 287062499 * q^67 - 308827572 * q^68 - 672888452 * q^70 - 224382678 * q^71 + 271440727 * q^73 - 89959728 * q^74 - 229522980 * q^76 - 671279994 * q^77 + 379128625 * q^79 - 1999017183 * q^80 + 551153781 * q^82 - 1664083206 * q^83 + 1982056546 * q^85 - 520253082 * q^86 + 684092585 * q^88 - 3293434692 * q^89 + 1715813946 * q^91 - 3729310881 * q^92 + 998499458 * q^94 - 878402766 * q^95 + 2385468336 * q^97 + 3234447132 * 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 $

$2$	5.01135	0.221472	0.110736	−	0.993850i	$-0.464679\pi$
$2$	5.01135	0.221472	0.110736	+	0.993850i	$0.464679\pi$
$3$	0	0
$3$	0	0
$4$	−486.886	−0.950950
$5$	−557.130	−0.398650	−0.199325	−	0.979933i	$-0.563875\pi$
$5$	−557.130	−0.398650	−0.199325	+	0.979933i	$0.563875\pi$
$6$	0	0
$7$	−7760.08	−1.22159	−0.610795	−	0.791789i	$-0.709150\pi$
$7$	−7760.08	−1.22159	−0.610795	+	0.791789i	$0.709150\pi$
$8$	−5005.76	−0.432081
$9$	0	0
$10$	−2791.97	−0.0882898
$11$	41662.1	0.857974	0.428987	−	0.903311i	$-0.358871\pi$
$11$	41662.1	0.857974	0.428987	+	0.903311i	$0.358871\pi$
$12$	0	0
$13$	−13831.9	−0.134319	−0.0671595	−	0.997742i	$-0.521394\pi$
$13$	−13831.9	−0.134319	−0.0671595	+	0.997742i	$0.521394\pi$
$14$	−38888.5	−0.270548
$15$	0	0
$16$	224200.	0.855256
$17$	−274297.	−0.796528	−0.398264	−	0.917271i	$-0.630387\pi$
$17$	−274297.	−0.796528	−0.398264	+	0.917271i	$0.630387\pi$
$18$	0	0
$19$	226307.	0.398389	0.199194	−	0.979960i	$-0.436167\pi$
$19$	226307.	0.398389	0.199194	+	0.979960i	$0.436167\pi$
$20$	271259.	0.379096
$21$	0	0
$22$	208783.	0.190017
$23$	−392869.	−0.292733	−0.146367	−	0.989230i	$-0.546758\pi$
$23$	−392869.	−0.292733	−0.146367	+	0.989230i	$0.546758\pi$
$24$	0	0
$25$	−1.64273e6	−0.841078
$26$	−69316.5	−0.0297479
$27$	0	0
$28$	3.77828e6	1.16167
$29$	−2.38976e6	−0.627428	−0.313714	−	0.949518i	$-0.601573\pi$
$29$	−2.38976e6	−0.627428	−0.313714	+	0.949518i	$0.601573\pi$
$30$	0	0
$31$	9.93724e6	1.93258	0.966292	−	0.257450i	$-0.0828823\pi$
$31$	9.93724e6	1.93258	0.966292	+	0.257450i	$0.0828823\pi$
$32$	3.68650e6	0.621497
$33$	0	0
$34$	−1.37460e6	−0.176409
$35$	4.32337e6	0.486986
$36$	0	0
$37$	1.87416e6	0.164399
$37$	1.87416e6	0.164399
$38$	1.13410e6	0.0882321
$39$	0	0
$40$	2.78886e6	0.172249
$41$	2.24960e7	1.24331	0.621653	−	0.783293i	$-0.286461\pi$
$41$	2.24960e7	1.24331	0.621653	+	0.783293i	$0.286461\pi$
$42$	0	0
$43$	1.75526e7	0.782951	0.391475	−	0.920189i	$-0.371965\pi$
$43$	1.75526e7	0.782951	0.391475	+	0.920189i	$0.371965\pi$
$44$	−2.02847e7	−0.815890
$45$	0	0
$46$	−1.96880e6	−0.0648323
$47$	1.97393e7	0.590052	0.295026	−	0.955489i	$-0.404672\pi$
$47$	1.97393e7	0.590052	0.295026	+	0.955489i	$0.404672\pi$
$48$	0	0
$49$	1.98653e7	0.492280
$50$	−8.23229e6	−0.186276
$51$	0	0
$52$	6.73457e6	0.127731
$53$	6.18106e7	1.07602	0.538011	−	0.842938i	$-0.319176\pi$
$53$	6.18106e7	1.07602	0.538011	+	0.842938i	$0.319176\pi$
$54$	0	0
$55$	−2.32112e7	−0.342031
$56$	3.88452e7	0.527826
$57$	0	0
$58$	−1.19759e7	−0.138958
$59$	5.98396e7	0.642917	0.321458	−	0.946924i	$-0.395827\pi$
$59$	5.98396e7	0.642917	0.321458	+	0.946924i	$0.395827\pi$
$60$	0	0
$61$	4.13428e7	0.382310	0.191155	−	0.981560i	$-0.438777\pi$
$61$	4.13428e7	0.382310	0.191155	+	0.981560i	$0.438777\pi$
$62$	4.97989e7	0.428014
$63$	0	0
$64$	−9.63162e7	−0.717612
$65$	7.70618e6	0.0535462
$66$	0	0
$67$	−7.07839e6	−0.0429139	−0.0214569	−	0.999770i	$-0.506830\pi$
$67$	−7.07839e6	−0.0429139	−0.0214569	+	0.999770i	$0.506830\pi$
$68$	1.33552e8	0.757458
$69$	0	0
$70$	2.16659e7	0.107854
$71$	−3.19253e8	−1.49098	−0.745491	−	0.666516i	$-0.767785\pi$
$71$	−3.19253e8	−1.49098	−0.745491	+	0.666516i	$0.767785\pi$
$72$	0	0
$73$	−2.31570e8	−0.954398	−0.477199	−	0.878795i	$-0.658348\pi$
$73$	−2.31570e8	−0.954398	−0.477199	+	0.878795i	$0.658348\pi$
$74$	9.39207e6	0.0364098
$75$	0	0
$76$	−1.10186e8	−0.378848
$77$	−3.23301e8	−1.04809
$78$	0	0
$79$	4.62203e8	1.33509	0.667546	−	0.744569i	$-0.267345\pi$
$79$	4.62203e8	1.33509	0.667546	+	0.744569i	$0.267345\pi$
$80$	−1.24909e8	−0.340948
$81$	0	0
$82$	1.12735e8	0.275358
$83$	−2.34443e8	−0.542232	−0.271116	−	0.962547i	$-0.587393\pi$
$83$	−2.34443e8	−0.542232	−0.271116	+	0.962547i	$0.587393\pi$
$84$	0	0
$85$	1.52819e8	0.317536
$86$	8.79623e7	0.173402
$87$	0	0
$88$	−2.08551e8	−0.370715
$89$	1.81605e8	0.306812	0.153406	−	0.988163i	$-0.450976\pi$
$89$	1.81605e8	0.306812	0.153406	+	0.988163i	$0.450976\pi$
$90$	0	0
$91$	1.07337e8	0.164083
$92$	1.91282e8	0.278375
$93$	0	0
$94$	9.89203e7	0.130680
$95$	−1.26083e8	−0.158818
$96$	0	0
$97$	1.13352e9	1.30004	0.650019	−	0.759918i	$-0.274761\pi$
$97$	1.13352e9	1.30004	0.650019	+	0.759918i	$0.274761\pi$
$98$	9.95518e7	0.109026
$99$	0	0
$100$	7.99824e8	0.799824
$101$	−1.46930e9	−1.40496	−0.702481	−	0.711703i	$-0.747924\pi$
$101$	−1.46930e9	−1.40496	−0.702481	+	0.711703i	$0.747924\pi$
$102$	0	0
$103$	4.13686e8	0.362162	0.181081	−	0.983468i	$-0.442040\pi$
$103$	4.13686e8	0.362162	0.181081	+	0.983468i	$0.442040\pi$
$104$	6.92393e7	0.0580367
$105$	0	0
$106$	3.09754e8	0.238309
$107$	−6.05593e8	−0.446636	−0.223318	−	0.974746i	$-0.571689\pi$
$107$	−6.05593e8	−0.446636	−0.223318	+	0.974746i	$0.571689\pi$
$108$	0	0
$109$	−2.65476e9	−1.80138	−0.900692	−	0.434457i	$-0.856940\pi$
$109$	−2.65476e9	−1.80138	−0.900692	+	0.434457i	$0.856940\pi$
$110$	−1.16319e8	−0.0757504
$111$	0	0
$112$	−1.73981e9	−1.04477
$113$	1.99867e8	0.115316	0.0576578	−	0.998336i	$-0.481637\pi$
$113$	1.99867e8	0.115316	0.0576578	+	0.998336i	$0.481637\pi$
$114$	0	0
$115$	2.18879e8	0.116698
$116$	1.16354e9	0.596653
$117$	0	0
$118$	2.99877e8	0.142388
$119$	2.12857e9	0.973030
$120$	0	0
$121$	−6.22216e8	−0.263881
$122$	2.07183e8	0.0846710
$123$	0	0
$124$	−4.83831e9	−1.83779
$125$	2.00336e9	0.733945
$126$	0	0
$127$	6.46022e8	0.220359	0.110179	−	0.993912i	$-0.464857\pi$
$127$	6.46022e8	0.220359	0.110179	+	0.993912i	$0.464857\pi$
$128$	−2.37016e9	−0.780428
$129$	0	0
$130$	3.86183e7	0.0118590
$131$	8.52345e8	0.252869	0.126434	−	0.991975i	$-0.459647\pi$
$131$	8.52345e8	0.252869	0.126434	+	0.991975i	$0.459647\pi$
$132$	0	0
$133$	−1.75616e9	−0.486668
$134$	−3.54723e7	−0.00950423
$135$	0	0
$136$	1.37307e9	0.344165
$137$	−6.14685e9	−1.49077	−0.745384	−	0.666635i	$-0.767734\pi$
$137$	−6.14685e9	−1.49077	−0.745384	+	0.666635i	$0.767734\pi$
$138$	0	0
$139$	−3.44217e9	−0.782106	−0.391053	−	0.920368i	$-0.627889\pi$
$139$	−3.44217e9	−0.782106	−0.391053	+	0.920368i	$0.627889\pi$
$140$	−2.10499e9	−0.463100
$141$	0	0
$142$	−1.59989e9	−0.330211
$143$	−5.76267e8	−0.115242
$144$	0	0
$145$	1.33141e9	0.250124
$146$	−1.16048e9	−0.211373
$147$	0	0
$148$	−9.12504e8	−0.156335
$149$	−1.15781e10	−1.92441	−0.962206	−	0.272321i	$-0.912209\pi$
$149$	−1.15781e10	−1.92441	−0.962206	+	0.272321i	$0.912209\pi$
$150$	0	0
$151$	4.98356e9	0.780087	0.390044	−	0.920796i	$-0.372460\pi$
$151$	4.98356e9	0.780087	0.390044	+	0.920796i	$0.372460\pi$
$152$	−1.13284e9	−0.172136
$153$	0	0
$154$	−1.62018e9	−0.232123
$155$	−5.53633e9	−0.770424
$156$	0	0
$157$	−2.52347e9	−0.331474	−0.165737	−	0.986170i	$-0.553000\pi$
$157$	−2.52347e9	−0.331474	−0.165737	+	0.986170i	$0.553000\pi$
$158$	2.31626e9	0.295686
$159$	0	0
$160$	−2.05386e9	−0.247759
$161$	3.04869e9	0.357600
$162$	0	0
$163$	1.21081e10	1.34348	0.671742	−	0.740785i	$-0.265546\pi$
$163$	1.21081e10	1.34348	0.671742	+	0.740785i	$0.265546\pi$
$164$	−1.09530e10	−1.18232
$165$	0	0
$166$	−1.17487e9	−0.120089
$167$	1.42256e10	1.41529	0.707647	−	0.706566i	$-0.249757\pi$
$167$	1.42256e10	1.41529	0.707647	+	0.706566i	$0.249757\pi$
$168$	0	0
$169$	−1.04132e10	−0.981958
$170$	7.65829e8	0.0703253
$171$	0	0
$172$	−8.54614e9	−0.744547
$173$	−1.07034e10	−0.908477	−0.454238	−	0.890880i	$-0.650089\pi$
$173$	−1.07034e10	−0.908477	−0.454238	+	0.890880i	$0.650089\pi$
$174$	0	0
$175$	1.27477e10	1.02745
$176$	9.34065e9	0.733787
$177$	0	0
$178$	9.10085e8	0.0679504
$179$	−4.96832e9	−0.361719	−0.180859	−	0.983509i	$-0.557888\pi$
$179$	−4.96832e9	−0.361719	−0.180859	+	0.983509i	$0.557888\pi$
$180$	0	0
$181$	1.41677e10	0.981173	0.490587	−	0.871392i	$-0.336783\pi$
$181$	1.41677e10	0.981173	0.490587	+	0.871392i	$0.336783\pi$
$182$	5.37902e8	0.0363398
$183$	0	0
$184$	1.96661e9	0.126485
$185$	−1.04415e9	−0.0655376
$186$	0	0
$187$	−1.14278e10	−0.683400
$188$	−9.61078e9	−0.561110
$189$	0	0
$190$	−6.31843e8	−0.0351737
$191$	−2.48156e9	−0.134920	−0.0674598	−	0.997722i	$-0.521489\pi$
$191$	−2.48156e9	−0.134920	−0.0674598	+	0.997722i	$0.521489\pi$
$192$	0	0
$193$	−1.76304e9	−0.0914648	−0.0457324	−	0.998954i	$-0.514562\pi$
$193$	−1.76304e9	−0.0914648	−0.0457324	+	0.998954i	$0.514562\pi$
$194$	5.68046e9	0.287922
$195$	0	0
$196$	−9.67214e9	−0.468134
$197$	2.50390e10	1.18446	0.592228	−	0.805771i	$-0.298249\pi$
$197$	2.50390e10	1.18446	0.592228	+	0.805771i	$0.298249\pi$
$198$	0	0
$199$	2.88737e9	0.130516	0.0652579	−	0.997868i	$-0.479213\pi$
$199$	2.88737e9	0.130516	0.0652579	+	0.997868i	$0.479213\pi$
$200$	8.22313e9	0.363414
$201$	0	0
$202$	−7.36317e9	−0.311160
$203$	1.85448e10	0.766459
$204$	0	0
$205$	−1.25332e10	−0.495644
$206$	2.07312e9	0.0802089
$207$	0	0
$208$	−3.10112e9	−0.114877
$209$	9.42844e9	0.341807
$210$	0	0
$211$	−1.82058e10	−0.632323	−0.316162	−	0.948705i	$-0.602394\pi$
$211$	−1.82058e10	−0.632323	−0.316162	+	0.948705i	$0.602394\pi$
$212$	−3.00947e10	−1.02324
$213$	0	0
$214$	−3.03484e9	−0.0989176
$215$	−9.77910e9	−0.312123
$216$	0	0
$217$	−7.71138e10	−2.36082
$218$	−1.33039e10	−0.398957
$219$	0	0
$220$	1.13012e10	0.325254
$221$	3.79406e9	0.106989
$222$	0	0
$223$	4.25562e10	1.15237	0.576184	−	0.817320i	$-0.304541\pi$
$223$	4.25562e10	1.15237	0.576184	+	0.817320i	$0.304541\pi$
$224$	−2.86075e10	−0.759214
$225$	0	0
$226$	1.00160e9	0.0255392
$227$	2.20447e10	0.551047	0.275524	−	0.961294i	$-0.411149\pi$
$227$	2.20447e10	0.551047	0.275524	+	0.961294i	$0.411149\pi$
$228$	0	0
$229$	−2.32919e10	−0.559687	−0.279844	−	0.960046i	$-0.590283\pi$
$229$	−2.32919e10	−0.559687	−0.279844	+	0.960046i	$0.590283\pi$
$230$	1.09688e9	0.0258454
$231$	0	0
$232$	1.19626e10	0.271100
$233$	−1.08068e10	−0.240212	−0.120106	−	0.992761i	$-0.538323\pi$
$233$	−1.08068e10	−0.240212	−0.120106	+	0.992761i	$0.538323\pi$
$234$	0	0
$235$	−1.09973e10	−0.235224
$236$	−2.91351e10	−0.611382
$237$	0	0
$238$	1.06670e10	0.215499
$239$	−7.79226e10	−1.54480	−0.772401	−	0.635135i	$-0.780945\pi$
$239$	−7.79226e10	−1.54480	−0.772401	+	0.635135i	$0.780945\pi$
$240$	0	0
$241$	9.04959e10	1.72803	0.864017	−	0.503463i	$-0.167941\pi$
$241$	9.04959e10	1.72803	0.864017	+	0.503463i	$0.167941\pi$
$242$	−3.11814e9	−0.0584422
$243$	0	0
$244$	−2.01292e10	−0.363558
$245$	−1.10675e10	−0.196247
$246$	0	0
$247$	−3.13026e9	−0.0535112
$248$	−4.97435e10	−0.835033
$249$	0	0
$250$	1.00395e10	0.162549
$251$	−2.33943e9	−0.0372030	−0.0186015	−	0.999827i	$-0.505921\pi$
$251$	−2.33943e9	−0.0372030	−0.0186015	+	0.999827i	$0.505921\pi$
$252$	0	0
$253$	−1.63677e10	−0.251158
$254$	3.23744e9	0.0488033
$255$	0	0
$256$	3.74362e10	0.544769
$257$	−7.48255e10	−1.06992	−0.534959	−	0.844878i	$-0.679673\pi$
$257$	−7.48255e10	−1.06992	−0.534959	+	0.844878i	$0.679673\pi$
$258$	0	0
$259$	−1.45436e10	−0.200828
$260$	−3.75203e9	−0.0509198
$261$	0	0
$262$	4.27140e9	0.0560034
$263$	−1.40183e11	−1.80673	−0.903367	−	0.428868i	$-0.858913\pi$
$263$	−1.40183e11	−1.80673	−0.903367	+	0.428868i	$0.858913\pi$
$264$	0	0
$265$	−3.44365e10	−0.428956
$266$	−8.80074e9	−0.107783
$267$	0	0
$268$	3.44637e9	0.0408090
$269$	6.21510e10	0.723707	0.361854	−	0.932235i	$-0.382144\pi$
$269$	6.21510e10	0.723707	0.361854	+	0.932235i	$0.382144\pi$
$270$	0	0
$271$	−3.11198e10	−0.350489	−0.175245	−	0.984525i	$-0.556072\pi$
$271$	−3.11198e10	−0.350489	−0.175245	+	0.984525i	$0.556072\pi$
$272$	−6.14975e10	−0.681235
$273$	0	0
$274$	−3.08040e10	−0.330164
$275$	−6.84397e10	−0.721623
$276$	0	0
$277$	1.94755e10	0.198761	0.0993803	−	0.995050i	$-0.468314\pi$
$277$	1.94755e10	0.198761	0.0993803	+	0.995050i	$0.468314\pi$
$278$	−1.72499e10	−0.173215
$279$	0	0
$280$	−2.16418e10	−0.210418
$281$	−1.32347e11	−1.26630	−0.633148	−	0.774031i	$-0.718238\pi$
$281$	−1.32347e11	−1.26630	−0.633148	+	0.774031i	$0.718238\pi$
$282$	0	0
$283$	−1.07006e11	−0.991672	−0.495836	−	0.868416i	$-0.665138\pi$
$283$	−1.07006e11	−0.991672	−0.495836	+	0.868416i	$0.665138\pi$
$284$	1.55440e11	1.41785
$285$	0	0
$286$	−2.88787e9	−0.0255230
$287$	−1.74571e11	−1.51881
$288$	0	0
$289$	−4.33490e10	−0.365543
$290$	6.67215e9	0.0553955
$291$	0	0
$292$	1.12748e11	0.907585
$293$	−1.50742e11	−1.19490	−0.597449	−	0.801907i	$-0.703819\pi$
$293$	−1.50742e11	−1.19490	−0.597449	+	0.801907i	$0.703819\pi$
$294$	0	0
$295$	−3.33384e10	−0.256299
$296$	−9.38161e9	−0.0710337
$297$	0	0
$298$	−5.80217e10	−0.426204
$299$	5.43413e9	0.0393197
$300$	0	0
$301$	−1.36210e11	−0.956444
$302$	2.49743e10	0.172768
$303$	0	0
$304$	5.07381e10	0.340725
$305$	−2.30333e10	−0.152408
$306$	0	0
$307$	8.00511e9	0.0514333	0.0257167	−	0.999669i	$-0.491813\pi$
$307$	8.00511e9	0.0514333	0.0257167	+	0.999669i	$0.491813\pi$
$308$	1.57411e11	0.996683
$309$	0	0
$310$	−2.77445e10	−0.170627
$311$	3.02914e11	1.83611	0.918054	−	0.396455i	$-0.129760\pi$
$311$	3.02914e11	1.83611	0.918054	+	0.396455i	$0.129760\pi$
$312$	0	0
$313$	1.49790e11	0.882134	0.441067	−	0.897474i	$-0.354600\pi$
$313$	1.49790e11	0.882134	0.441067	+	0.897474i	$0.354600\pi$
$314$	−1.26460e10	−0.0734124
$315$	0	0
$316$	−2.25040e11	−1.26961
$317$	−1.85636e11	−1.03251	−0.516256	−	0.856434i	$-0.672675\pi$
$317$	−1.85636e11	−1.03251	−0.516256	+	0.856434i	$0.672675\pi$
$318$	0	0
$319$	−9.95626e10	−0.538317
$320$	5.36606e10	0.286076
$321$	0	0
$322$	1.52781e10	0.0791985
$323$	−6.20754e10	−0.317328
$324$	0	0
$325$	2.27221e10	0.112973
$326$	6.06780e10	0.297545
$327$	0	0
$328$	−1.12610e11	−0.537209
$329$	−1.53178e11	−0.720802
$330$	0	0
$331$	3.51664e11	1.61028	0.805141	−	0.593083i	$-0.202089\pi$
$331$	3.51664e11	1.61028	0.805141	+	0.593083i	$0.202089\pi$
$332$	1.14147e11	0.515636
$333$	0	0
$334$	7.12894e10	0.313448
$335$	3.94358e9	0.0171076
$336$	0	0
$337$	−5.13643e10	−0.216934	−0.108467	−	0.994100i	$-0.534594\pi$
$337$	−5.13643e10	−0.216934	−0.108467	+	0.994100i	$0.534594\pi$
$338$	−5.21840e10	−0.217477
$339$	0	0
$340$	−7.44055e10	−0.301960
$341$	4.14006e11	1.65811
$342$	0	0
$343$	1.58991e11	0.620225
$344$	−8.78644e10	−0.338298
$345$	0	0
$346$	−5.36384e10	−0.201202
$347$	−7.76426e10	−0.287487	−0.143743	−	0.989615i	$-0.545914\pi$
$347$	−7.76426e10	−0.287487	−0.143743	+	0.989615i	$0.545914\pi$
$348$	0	0
$349$	−2.73199e11	−0.985745	−0.492872	−	0.870102i	$-0.664053\pi$
$349$	−2.73199e11	−0.985745	−0.492872	+	0.870102i	$0.664053\pi$
$350$	6.38833e10	0.227552
$351$	0	0
$352$	1.53587e11	0.533228
$353$	6.08844e10	0.208699	0.104349	−	0.994541i	$-0.466724\pi$
$353$	6.08844e10	0.208699	0.104349	+	0.994541i	$0.466724\pi$
$354$	0	0
$355$	1.77865e11	0.594379
$356$	−8.84210e10	−0.291763
$357$	0	0
$358$	−2.48980e10	−0.0801107
$359$	−4.64024e11	−1.47440	−0.737200	−	0.675675i	$-0.763852\pi$
$359$	−4.64024e11	−1.47440	−0.737200	+	0.675675i	$0.763852\pi$
$360$	0	0
$361$	−2.71473e11	−0.841286
$362$	7.09992e10	0.217303
$363$	0	0
$364$	−5.22609e10	−0.156034
$365$	1.29015e11	0.380470
$366$	0	0
$367$	1.20513e11	0.346767	0.173384	−	0.984854i	$-0.444530\pi$
$367$	1.20513e11	0.346767	0.173384	+	0.984854i	$0.444530\pi$
$368$	−8.80813e10	−0.250362
$369$	0	0
$370$	−5.23260e9	−0.0145148
$371$	−4.79655e11	−1.31446
$372$	0	0
$373$	8.82896e10	0.236167	0.118084	−	0.993004i	$-0.462325\pi$
$373$	8.82896e10	0.236167	0.118084	+	0.993004i	$0.462325\pi$
$374$	−5.72686e10	−0.151354
$375$	0	0
$376$	−9.88101e10	−0.254951
$377$	3.30550e10	0.0842755
$378$	0	0
$379$	3.63126e11	0.904026	0.452013	−	0.892011i	$-0.350706\pi$
$379$	3.63126e11	0.904026	0.452013	+	0.892011i	$0.350706\pi$
$380$	6.13879e10	0.151028
$381$	0	0
$382$	−1.24360e10	−0.0298809
$383$	−3.84226e11	−0.912414	−0.456207	−	0.889874i	$-0.650792\pi$
$383$	−3.84226e11	−0.912414	−0.456207	+	0.889874i	$0.650792\pi$
$384$	0	0
$385$	1.80121e11	0.417821
$386$	−8.83519e9	−0.0202569
$387$	0	0
$388$	−5.51895e11	−1.23627
$389$	5.61787e11	1.24394	0.621968	−	0.783042i	$-0.286333\pi$
$389$	5.61787e11	1.24394	0.621968	+	0.783042i	$0.286333\pi$
$390$	0	0
$391$	1.07763e11	0.233170
$392$	−9.94410e10	−0.212705
$393$	0	0
$394$	1.25479e11	0.262324
$395$	−2.57507e11	−0.532234
$396$	0	0
$397$	−3.56910e11	−0.721109	−0.360555	−	0.932738i	$-0.617413\pi$
$397$	−3.56910e11	−0.721109	−0.360555	+	0.932738i	$0.617413\pi$
$398$	1.44696e10	0.0289056
$399$	0	0
$400$	−3.68301e11	−0.719337
$401$	−9.30288e9	−0.0179667	−0.00898334	−	0.999960i	$-0.502860\pi$
$401$	−9.30288e9	−0.0179667	−0.00898334	+	0.999960i	$0.502860\pi$
$402$	0	0
$403$	−1.37451e11	−0.259583
$404$	7.15382e11	1.33605
$405$	0	0
$406$	9.29342e10	0.169749
$407$	7.80815e10	0.141050
$408$	0	0
$409$	−7.02687e11	−1.24167	−0.620836	−	0.783941i	$-0.713207\pi$
$409$	−7.02687e11	−1.24167	−0.620836	+	0.783941i	$0.713207\pi$
$410$	−6.28082e10	−0.109771
$411$	0	0
$412$	−2.01418e11	−0.344398
$413$	−4.64361e11	−0.785380
$414$	0	0
$415$	1.30615e11	0.216161
$416$	−5.09913e10	−0.0834788
$417$	0	0
$418$	4.72492e10	0.0757009
$419$	8.94772e11	1.41824	0.709119	−	0.705089i	$-0.249093\pi$
$419$	8.94772e11	1.41824	0.709119	+	0.705089i	$0.249093\pi$
$420$	0	0
$421$	1.49728e11	0.232292	0.116146	−	0.993232i	$-0.462946\pi$
$421$	1.49728e11	0.232292	0.116146	+	0.993232i	$0.462946\pi$
$422$	−9.12356e10	−0.140042
$423$	0	0
$424$	−3.09409e11	−0.464929
$425$	4.50596e11	0.669942
$426$	0	0
$427$	−3.20823e11	−0.467026
$428$	2.94855e11	0.424729
$429$	0	0
$430$	−4.90064e10	−0.0691266
$431$	5.29202e11	0.738710	0.369355	−	0.929288i	$-0.379579\pi$
$431$	5.29202e11	0.738710	0.369355	+	0.929288i	$0.379579\pi$
$432$	0	0
$433$	1.76117e11	0.240772	0.120386	−	0.992727i	$-0.461587\pi$
$433$	1.76117e11	0.240772	0.120386	+	0.992727i	$0.461587\pi$
$434$	−3.86444e11	−0.522857
$435$	0	0
$436$	1.29257e12	1.71303
$437$	−8.89091e10	−0.116622
$438$	0	0
$439$	7.40629e11	0.951723	0.475861	−	0.879520i	$-0.342136\pi$
$439$	7.40629e11	0.951723	0.475861	+	0.879520i	$0.342136\pi$
$440$	1.16190e11	0.147785
$441$	0	0
$442$	1.90133e10	0.0236951
$443$	−2.15106e11	−0.265360	−0.132680	−	0.991159i	$-0.542358\pi$
$443$	−2.15106e11	−0.265360	−0.132680	+	0.991159i	$0.542358\pi$
$444$	0	0
$445$	−1.01178e11	−0.122311
$446$	2.13264e11	0.255217
$447$	0	0
$448$	7.47422e11	0.876627
$449$	1.08175e12	1.25608	0.628040	−	0.778181i	$-0.283858\pi$
$449$	1.08175e12	1.25608	0.628040	+	0.778181i	$0.283858\pi$
$450$	0	0
$451$	9.37231e11	1.06672
$452$	−9.73125e10	−0.109659
$453$	0	0
$454$	1.10474e11	0.122042
$455$	−5.98006e10	−0.0654115
$456$	0	0
$457$	−1.10702e12	−1.18722	−0.593610	−	0.804753i	$-0.702298\pi$
$457$	−1.10702e12	−1.18722	−0.593610	+	0.804753i	$0.702298\pi$
$458$	−1.16724e11	−0.123955
$459$	0	0
$460$	−1.06569e11	−0.110974
$461$	4.82228e9	0.00497277	0.00248639	−	0.999997i	$-0.499209\pi$
$461$	4.82228e9	0.00497277	0.00248639	+	0.999997i	$0.499209\pi$
$462$	0	0
$463$	−7.30180e11	−0.738440	−0.369220	−	0.929342i	$-0.620375\pi$
$463$	−7.30180e11	−0.738440	−0.369220	+	0.929342i	$0.620375\pi$
$464$	−5.35785e11	−0.536612
$465$	0	0
$466$	−5.41565e10	−0.0532003
$467$	−1.23496e12	−1.20150	−0.600752	−	0.799435i	$-0.705132\pi$
$467$	−1.23496e12	−1.20150	−0.600752	+	0.799435i	$0.705132\pi$
$468$	0	0
$469$	5.49289e10	0.0524231
$470$	−5.51114e10	−0.0520956
$471$	0	0
$472$	−2.99543e11	−0.277792
$473$	7.31280e11	0.671751
$474$	0	0
$475$	−3.71762e11	−0.335076
$476$	−1.03637e12	−0.925303
$477$	0	0
$478$	−3.90497e11	−0.342131
$479$	1.11004e12	0.963452	0.481726	−	0.876322i	$-0.340010\pi$
$479$	1.11004e12	0.963452	0.481726	+	0.876322i	$0.340010\pi$
$480$	0	0
$481$	−2.59232e10	−0.0220819
$482$	4.53506e11	0.382711
$483$	0	0
$484$	3.02949e11	0.250937
$485$	−6.31517e11	−0.518260
$486$	0	0
$487$	2.02968e12	1.63511	0.817555	−	0.575850i	$-0.195329\pi$
$487$	2.02968e12	1.63511	0.817555	+	0.575850i	$0.195329\pi$
$488$	−2.06952e11	−0.165189
$489$	0	0
$490$	−5.54633e10	−0.0434634
$491$	6.33964e11	0.492264	0.246132	−	0.969236i	$-0.420840\pi$
$491$	6.33964e11	0.492264	0.246132	+	0.969236i	$0.420840\pi$
$492$	0	0
$493$	6.55505e11	0.499764
$494$	−1.56868e10	−0.0118512
$495$	0	0
$496$	2.22793e12	1.65285
$497$	2.47743e12	1.82137
$498$	0	0
$499$	−6.34178e11	−0.457888	−0.228944	−	0.973440i	$-0.573527\pi$
$499$	−6.34178e11	−0.457888	−0.228944	+	0.973440i	$0.573527\pi$
$500$	−9.75408e11	−0.697945
$501$	0	0
$502$	−1.17237e10	−0.00823944
$503$	−3.33194e11	−0.232082	−0.116041	−	0.993244i	$-0.537020\pi$
$503$	−3.33194e11	−0.232082	−0.116041	+	0.993244i	$0.537020\pi$
$504$	0	0
$505$	8.18591e11	0.560087
$506$	−8.20244e10	−0.0556245
$507$	0	0
$508$	−3.14539e11	−0.209550
$509$	−4.79181e10	−0.0316424	−0.0158212	−	0.999875i	$-0.505036\pi$
$509$	−4.79181e10	−0.0316424	−0.0158212	+	0.999875i	$0.505036\pi$
$510$	0	0
$511$	1.79700e12	1.16588
$512$	1.40113e12	0.901079
$513$	0	0
$514$	−3.74977e11	−0.236957
$515$	−2.30477e11	−0.144376
$516$	0	0
$517$	8.22379e11	0.506250
$518$	−7.28832e10	−0.0444778
$519$	0	0
$520$	−3.85753e10	−0.0231363
$521$	2.52197e12	1.49958	0.749791	−	0.661675i	$-0.230154\pi$
$521$	2.52197e12	1.49958	0.749791	+	0.661675i	$0.230154\pi$
$522$	0	0
$523$	1.64865e12	0.963540	0.481770	−	0.876298i	$-0.339994\pi$
$523$	1.64865e12	0.963540	0.481770	+	0.876298i	$0.339994\pi$
$524$	−4.14995e11	−0.240465
$525$	0	0
$526$	−7.02505e11	−0.400142
$527$	−2.72576e12	−1.53936
$528$	0	0
$529$	−1.64681e12	−0.914307
$530$	−1.72573e11	−0.0950019
$531$	0	0
$532$	8.55052e11	0.462797
$533$	−3.11163e11	−0.167000
$534$	0	0
$535$	3.37394e11	0.178051
$536$	3.54327e10	0.0185423
$537$	0	0
$538$	3.11460e11	0.160281
$539$	8.27630e11	0.422364
$540$	0	0
$541$	−5.60834e11	−0.281480	−0.140740	−	0.990047i	$-0.544948\pi$
$541$	−5.60834e11	−0.281480	−0.140740	+	0.990047i	$0.544948\pi$
$542$	−1.55952e11	−0.0776237
$543$	0	0
$544$	−1.01120e12	−0.495040
$545$	1.47905e12	0.718121
$546$	0	0
$547$	−3.72560e12	−1.77932	−0.889659	−	0.456625i	$-0.849058\pi$
$547$	−3.72560e12	−1.77932	−0.889659	+	0.456625i	$0.849058\pi$
$548$	2.99282e12	1.41765
$549$	0	0
$550$	−3.42975e11	−0.159820
$551$	−5.40821e11	−0.249960
$552$	0	0
$553$	−3.58674e12	−1.63093
$554$	9.75986e10	0.0440200
$555$	0	0
$556$	1.67594e12	0.743743
$557$	1.77269e12	0.780343	0.390171	−	0.920742i	$-0.372416\pi$
$557$	1.77269e12	0.780343	0.390171	+	0.920742i	$0.372416\pi$
$558$	0	0
$559$	−2.42787e11	−0.105165
$560$	9.69301e11	0.416498
$561$	0	0
$562$	−6.63236e11	−0.280449
$563$	−2.82521e12	−1.18512	−0.592561	−	0.805526i	$-0.701883\pi$
$563$	−2.82521e12	−1.18512	−0.592561	+	0.805526i	$0.701883\pi$
$564$	0	0
$565$	−1.11352e11	−0.0459705
$566$	−5.36243e11	−0.219628
$567$	0	0
$568$	1.59811e12	0.644225
$569$	3.08563e12	1.23407	0.617034	−	0.786937i	$-0.288334\pi$
$569$	3.08563e12	1.23407	0.617034	+	0.786937i	$0.288334\pi$
$570$	0	0
$571$	2.61226e12	1.02838	0.514190	−	0.857676i	$-0.328093\pi$
$571$	2.61226e12	1.02838	0.514190	+	0.857676i	$0.328093\pi$
$572$	2.80577e11	0.109590
$573$	0	0
$574$	−8.74835e11	−0.336374
$575$	6.45378e11	0.246212
$576$	0	0
$577$	3.09050e12	1.16075	0.580373	−	0.814350i	$-0.302907\pi$
$577$	3.09050e12	1.16075	0.580373	+	0.814350i	$0.302907\pi$
$578$	−2.17237e11	−0.0809577
$579$	0	0
$580$	−6.48245e11	−0.237855
$581$	1.81930e12	0.662385
$582$	0	0
$583$	2.57516e12	0.923199
$584$	1.15919e12	0.412378
$585$	0	0
$586$	−7.55422e11	−0.264637
$587$	−1.88219e12	−0.654321	−0.327161	−	0.944969i	$-0.606092\pi$
$587$	−1.88219e12	−0.654321	−0.327161	+	0.944969i	$0.606092\pi$
$588$	0	0
$589$	2.24887e12	0.769920
$590$	−1.67070e11	−0.0567630
$591$	0	0
$592$	4.20187e11	0.140603
$593$	4.14376e12	1.37610	0.688048	−	0.725666i	$-0.258468\pi$
$593$	4.14376e12	1.37610	0.688048	+	0.725666i	$0.258468\pi$
$594$	0	0
$595$	−1.18589e12	−0.387898
$596$	5.63721e12	1.83002
$597$	0	0
$598$	2.72323e10	0.00870821
$599$	6.79304e11	0.215597	0.107799	−	0.994173i	$-0.465620\pi$
$599$	6.79304e11	0.215597	0.107799	+	0.994173i	$0.465620\pi$
$600$	0	0
$601$	1.23321e12	0.385567	0.192784	−	0.981241i	$-0.438248\pi$
$601$	1.23321e12	0.385567	0.192784	+	0.981241i	$0.438248\pi$
$602$	−6.82595e11	−0.211826
$603$	0	0
$604$	−2.42643e12	−0.741824
$605$	3.46655e11	0.105196
$606$	0	0
$607$	−2.27029e12	−0.678786	−0.339393	−	0.940645i	$-0.610222\pi$
$607$	−2.27029e12	−0.678786	−0.339393	+	0.940645i	$0.610222\pi$
$608$	8.34281e11	0.247597
$609$	0	0
$610$	−1.15428e11	−0.0337541
$611$	−2.73032e11	−0.0792552
$612$	0	0
$613$	3.36091e12	0.961357	0.480679	−	0.876897i	$-0.340390\pi$
$613$	3.36091e12	0.961357	0.480679	+	0.876897i	$0.340390\pi$
$614$	4.01164e10	0.0113911
$615$	0	0
$616$	1.61837e12	0.452861
$617$	−8.69025e11	−0.241407	−0.120703	−	0.992689i	$-0.538515\pi$
$617$	−8.69025e11	−0.241407	−0.120703	+	0.992689i	$0.538515\pi$
$618$	0	0
$619$	−5.95420e12	−1.63010	−0.815052	−	0.579388i	$-0.803292\pi$
$619$	−5.95420e12	−1.63010	−0.815052	+	0.579388i	$0.803292\pi$
$620$	2.69557e12	0.732634
$621$	0	0
$622$	1.51801e12	0.406647
$623$	−1.40927e12	−0.374799
$624$	0	0
$625$	2.09233e12	0.548491
$626$	7.50652e11	0.195368
$627$	0	0
$628$	1.22864e12	0.315215
$629$	−5.14077e11	−0.130948
$630$	0	0
$631$	3.88933e11	0.0976660	0.0488330	−	0.998807i	$-0.484450\pi$
$631$	3.88933e11	0.0976660	0.0488330	+	0.998807i	$0.484450\pi$
$632$	−2.31368e12	−0.576868
$633$	0	0
$634$	−9.30286e11	−0.228673
$635$	−3.59918e11	−0.0878459
$636$	0	0
$637$	−2.74775e11	−0.0661226
$638$	−4.98942e11	−0.119222
$639$	0	0
$640$	1.32049e12	0.311117
$641$	−4.00334e12	−0.936616	−0.468308	−	0.883565i	$-0.655136\pi$
$641$	−4.00334e12	−0.936616	−0.468308	+	0.883565i	$0.655136\pi$
$642$	0	0
$643$	8.27928e12	1.91004	0.955022	−	0.296535i	$-0.0958311\pi$
$643$	8.27928e12	1.91004	0.955022	+	0.296535i	$0.0958311\pi$
$644$	−1.48437e12	−0.340060
$645$	0	0
$646$	−3.11081e11	−0.0702793
$647$	−3.94109e12	−0.884193	−0.442097	−	0.896967i	$-0.645765\pi$
$647$	−3.94109e12	−0.884193	−0.442097	+	0.896967i	$0.645765\pi$
$648$	0	0
$649$	2.49305e12	0.551606
$650$	1.13868e11	0.0250203
$651$	0	0
$652$	−5.89528e12	−1.27759
$653$	−6.62319e12	−1.42547	−0.712735	−	0.701434i	$-0.752544\pi$
$653$	−6.62319e12	−1.42547	−0.712735	+	0.701434i	$0.752544\pi$
$654$	0	0
$655$	−4.74867e11	−0.100806
$656$	5.04361e12	1.06335
$657$	0	0
$658$	−7.67630e11	−0.159638
$659$	6.40199e12	1.32230	0.661151	−	0.750253i	$-0.270068\pi$
$659$	6.40199e12	1.32230	0.661151	+	0.750253i	$0.270068\pi$
$660$	0	0
$661$	−1.63899e12	−0.333941	−0.166971	−	0.985962i	$-0.553398\pi$
$661$	−1.63899e12	−0.333941	−0.166971	+	0.985962i	$0.553398\pi$
$662$	1.76231e12	0.356633
$663$	0	0
$664$	1.17357e12	0.234288
$665$	9.78411e11	0.194010
$666$	0	0
$667$	9.38863e11	0.183669
$668$	−6.92625e12	−1.34587
$669$	0	0
$670$	1.97626e10	0.00378886
$671$	1.72243e12	0.328012
$672$	0	0
$673$	−5.07685e12	−0.953953	−0.476976	−	0.878916i	$-0.658267\pi$
$673$	−5.07685e12	−0.953953	−0.476976	+	0.878916i	$0.658267\pi$
$674$	−2.57404e11	−0.0480448
$675$	0	0
$676$	5.07003e12	0.933793
$677$	−8.18905e12	−1.49825	−0.749126	−	0.662428i	$-0.769526\pi$
$677$	−8.18905e12	−1.49825	−0.749126	+	0.662428i	$0.769526\pi$
$678$	0	0
$679$	−8.79621e12	−1.58811
$680$	−7.64976e11	−0.137201
$681$	0	0
$682$	2.07473e12	0.367225
$683$	−1.04429e13	−1.83624	−0.918120	−	0.396303i	$-0.870293\pi$
$683$	−1.04429e13	−1.83624	−0.918120	+	0.396303i	$0.870293\pi$
$684$	0	0
$685$	3.42459e12	0.594294
$686$	7.96759e11	0.137363
$687$	0	0
$688$	3.93531e12	0.669623
$689$	−8.54959e11	−0.144530
$690$	0	0
$691$	−5.72108e12	−0.954612	−0.477306	−	0.878737i	$-0.658387\pi$
$691$	−5.72108e12	−0.954612	−0.477306	+	0.878737i	$0.658387\pi$
$692$	5.21133e12	0.863916
$693$	0	0
$694$	−3.89094e11	−0.0636703
$695$	1.91773e12	0.311786
$696$	0	0
$697$	−6.17059e12	−0.990328
$698$	−1.36909e12	−0.218315
$699$	0	0
$700$	−6.20670e12	−0.977056
$701$	−4.40737e12	−0.689364	−0.344682	−	0.938720i	$-0.612013\pi$
$701$	−4.40737e12	−0.689364	−0.344682	+	0.938720i	$0.612013\pi$
$702$	0	0
$703$	4.24136e11	0.0654947
$704$	−4.01274e12	−0.615692
$705$	0	0
$706$	3.05113e11	0.0462210
$707$	1.14019e13	1.71629
$708$	0	0
$709$	1.82952e12	0.271913	0.135956	−	0.990715i	$-0.456589\pi$
$709$	1.82952e12	0.271913	0.135956	+	0.990715i	$0.456589\pi$
$710$	8.91345e11	0.131639
$711$	0	0
$712$	−9.09072e11	−0.132568
$713$	−3.90403e12	−0.565732
$714$	0	0
$715$	3.21056e11	0.0459413
$716$	2.41901e12	0.343976
$717$	0	0
$718$	−2.32538e12	−0.326539
$719$	−8.08941e12	−1.12885	−0.564426	−	0.825484i	$-0.690902\pi$
$719$	−8.08941e12	−1.12885	−0.564426	+	0.825484i	$0.690902\pi$
$720$	0	0
$721$	−3.21024e12	−0.442414
$722$	−1.36044e12	−0.186322
$723$	0	0
$724$	−6.89806e12	−0.933047
$725$	3.92574e12	0.527716
$726$	0	0
$727$	−1.41851e13	−1.88334	−0.941669	−	0.336541i	$-0.890743\pi$
$727$	−1.41851e13	−1.88334	−0.941669	+	0.336541i	$0.890743\pi$
$728$	−5.37303e11	−0.0708970
$729$	0	0
$730$	6.46537e11	0.0842636
$731$	−4.81464e12	−0.623642
$732$	0	0
$733$	−3.22278e12	−0.412347	−0.206173	−	0.978515i	$-0.566101\pi$
$733$	−3.22278e12	−0.412347	−0.206173	+	0.978515i	$0.566101\pi$
$734$	6.03934e11	0.0767993
$735$	0	0
$736$	−1.44831e12	−0.181933
$737$	−2.94901e11	−0.0368190
$738$	0	0
$739$	−6.03232e10	−0.00744019	−0.00372010	−	0.999993i	$-0.501184\pi$
$739$	−6.03232e10	−0.00744019	−0.00372010	+	0.999993i	$0.501184\pi$
$740$	5.08383e11	0.0623230
$741$	0	0
$742$	−2.40372e12	−0.291116
$743$	−1.32585e13	−1.59604	−0.798021	−	0.602630i	$-0.794120\pi$
$743$	−1.32585e13	−1.59604	−0.798021	+	0.602630i	$0.794120\pi$
$744$	0	0
$745$	6.45049e12	0.767167
$746$	4.42450e11	0.0523045
$747$	0	0
$748$	5.56404e12	0.649880
$749$	4.69946e12	0.545606
$750$	0	0
$751$	6.39838e12	0.733991	0.366995	−	0.930223i	$-0.380387\pi$
$751$	6.39838e12	0.733991	0.366995	+	0.930223i	$0.380387\pi$
$752$	4.42555e12	0.504646
$753$	0	0
$754$	1.65650e11	0.0186647
$755$	−2.77649e12	−0.310981
$756$	0	0
$757$	1.23763e13	1.36981	0.684906	−	0.728631i	$-0.259843\pi$
$757$	1.23763e13	1.36981	0.684906	+	0.728631i	$0.259843\pi$
$758$	1.81975e12	0.200217
$759$	0	0
$760$	6.31139e11	0.0686221
$761$	−2.06556e12	−0.223258	−0.111629	−	0.993750i	$-0.535607\pi$
$761$	−2.06556e12	−0.223258	−0.111629	+	0.993750i	$0.535607\pi$
$762$	0	0
$763$	2.06012e13	2.20055
$764$	1.20824e12	0.128302
$765$	0	0
$766$	−1.92549e12	−0.202074
$767$	−8.27697e11	−0.0863559
$768$	0	0
$769$	−1.33067e13	−1.37215	−0.686076	−	0.727529i	$-0.740668\pi$
$769$	−1.33067e13	−1.37215	−0.686076	+	0.727529i	$0.740668\pi$
$770$	9.02648e11	0.0925359
$771$	0	0
$772$	8.58399e11	0.0869784
$773$	−1.16520e13	−1.17379	−0.586897	−	0.809662i	$-0.699650\pi$
$773$	−1.16520e13	−1.17379	−0.586897	+	0.809662i	$0.699650\pi$
$774$	0	0
$775$	−1.63242e13	−1.62545
$776$	−5.67413e12	−0.561722
$777$	0	0
$778$	2.81531e12	0.275497
$779$	5.09101e12	0.495320
$780$	0	0
$781$	−1.33007e13	−1.27922
$782$	5.40036e11	0.0516408
$783$	0	0
$784$	4.45380e12	0.421026
$785$	1.40590e12	0.132142
$786$	0	0
$787$	2.04268e11	0.0189808	0.00949039	−	0.999955i	$-0.496979\pi$
$787$	2.04268e11	0.0189808	0.00949039	+	0.999955i	$0.496979\pi$
$788$	−1.21911e13	−1.12636
$789$	0	0
$790$	−1.29046e12	−0.117875
$791$	−1.55098e12	−0.140868
$792$	0	0
$793$	−5.71850e11	−0.0513515
$794$	−1.78860e12	−0.159706
$795$	0	0
$796$	−1.40582e12	−0.124114
$797$	−4.74583e12	−0.416629	−0.208314	−	0.978062i	$-0.566798\pi$
$797$	−4.74583e12	−0.416629	−0.208314	+	0.978062i	$0.566798\pi$
$798$	0	0
$799$	−5.41442e12	−0.469993
$800$	−6.05592e12	−0.522728
$801$	0	0
$802$	−4.66200e10	−0.00397912
$803$	−9.64770e12	−0.818849
$804$	0	0
$805$	−1.69852e12	−0.142557
$806$	−6.88815e11	−0.0574904
$807$	0	0
$808$	7.35497e12	0.607058
$809$	−7.05649e12	−0.579189	−0.289595	−	0.957149i	$-0.593520\pi$
$809$	−7.05649e12	−0.579189	−0.289595	+	0.957149i	$0.593520\pi$
$810$	0	0
$811$	1.15520e13	0.937696	0.468848	−	0.883279i	$-0.344669\pi$
$811$	1.15520e13	0.937696	0.468848	+	0.883279i	$0.344669\pi$
$812$	−9.02919e12	−0.728864
$813$	0	0
$814$	3.91293e11	0.0312387
$815$	−6.74580e12	−0.535580
$816$	0	0
$817$	3.97229e12	0.311919
$818$	−3.52141e12	−0.274996
$819$	0	0
$820$	6.10224e12	0.471332
$821$	1.01996e13	0.783501	0.391750	−	0.920072i	$-0.371870\pi$
$821$	1.01996e13	0.783501	0.391750	+	0.920072i	$0.371870\pi$
$822$	0	0
$823$	−1.56251e13	−1.18720	−0.593599	−	0.804761i	$-0.702293\pi$
$823$	−1.56251e13	−1.18720	−0.593599	+	0.804761i	$0.702293\pi$
$824$	−2.07082e12	−0.156484
$825$	0	0
$826$	−2.32707e12	−0.173940
$827$	2.15862e13	1.60473	0.802363	−	0.596836i	$-0.203576\pi$
$827$	2.15862e13	1.60473	0.802363	+	0.596836i	$0.203576\pi$
$828$	0	0
$829$	5.93446e12	0.436401	0.218201	−	0.975904i	$-0.429981\pi$
$829$	5.93446e12	0.436401	0.218201	+	0.975904i	$0.429981\pi$
$830$	6.54557e11	0.0478736
$831$	0	0
$832$	1.33224e12	0.0963889
$833$	−5.44899e12	−0.392115
$834$	0	0
$835$	−7.92551e12	−0.564206
$836$	−4.59058e12	−0.325042
$837$	0	0
$838$	4.48401e12	0.314101
$839$	1.13565e13	0.791256	0.395628	−	0.918411i	$-0.370527\pi$
$839$	1.13565e13	0.791256	0.395628	+	0.918411i	$0.370527\pi$
$840$	0	0
$841$	−8.79618e12	−0.606334
$842$	7.50341e11	0.0514463
$843$	0	0
$844$	8.86416e12	0.601308
$845$	5.80149e12	0.391457
$846$	0	0
$847$	4.82845e12	0.322354
$848$	1.38579e13	0.920275
$849$	0	0
$850$	2.25809e12	0.148374
$851$	−7.36299e11	−0.0481251
$852$	0	0
$853$	−1.85007e13	−1.19651	−0.598257	−	0.801304i	$-0.704140\pi$
$853$	−1.85007e13	−1.19651	−0.598257	+	0.801304i	$0.704140\pi$
$854$	−1.60776e12	−0.103433
$855$	0	0
$856$	3.03146e12	0.192983
$857$	−1.96567e13	−1.24479	−0.622396	−	0.782702i	$-0.713841\pi$
$857$	−1.96567e13	−1.24479	−0.622396	+	0.782702i	$0.713841\pi$
$858$	0	0
$859$	−5.75458e12	−0.360616	−0.180308	−	0.983610i	$-0.557709\pi$
$859$	−5.75458e12	−0.360616	−0.180308	+	0.983610i	$0.557709\pi$
$860$	4.76131e12	0.296813
$861$	0	0
$862$	2.65202e12	0.163604
$863$	2.78321e13	1.70804	0.854018	−	0.520243i	$-0.174159\pi$
$863$	2.78321e13	1.70804	0.854018	+	0.520243i	$0.174159\pi$
$864$	0	0
$865$	5.96318e12	0.362164
$866$	8.82583e11	0.0533243
$867$	0	0
$868$	3.75457e13	2.24502
$869$	1.92564e13	1.14547
$870$	0	0
$871$	9.79077e10	0.00576415
$872$	1.32891e13	0.778345
$873$	0	0
$874$	−4.45554e11	−0.0258285
$875$	−1.55462e13	−0.896580
$876$	0	0
$877$	1.39390e13	0.795672	0.397836	−	0.917457i	$-0.369761\pi$
$877$	1.39390e13	0.795672	0.397836	+	0.917457i	$0.369761\pi$
$878$	3.71155e12	0.210780
$879$	0	0
$880$	−5.20396e12	−0.292524
$881$	−2.10534e13	−1.17742	−0.588709	−	0.808345i	$-0.700364\pi$
$881$	−2.10534e13	−1.17742	−0.588709	+	0.808345i	$0.700364\pi$
$882$	0	0
$883$	−1.60235e13	−0.887023	−0.443512	−	0.896269i	$-0.646268\pi$
$883$	−1.60235e13	−0.887023	−0.443512	+	0.896269i	$0.646268\pi$
$884$	−1.84727e12	−0.101741
$885$	0	0
$886$	−1.07797e12	−0.0587699
$887$	7.95565e12	0.431538	0.215769	−	0.976444i	$-0.430774\pi$
$887$	7.95565e12	0.431538	0.215769	+	0.976444i	$0.430774\pi$
$888$	0	0
$889$	−5.01318e12	−0.269188
$890$	−5.07036e11	−0.0270884
$891$	0	0
$892$	−2.07200e13	−1.09584
$893$	4.46714e12	0.235070
$894$	0	0
$895$	2.76800e12	0.144199
$896$	1.83926e13	0.953362
$897$	0	0
$898$	5.42101e12	0.278187
$899$	−2.37477e13	−1.21256
$900$	0	0
$901$	−1.69545e13	−0.857082
$902$	4.69679e12	0.236250
$903$	0	0
$904$	−1.00049e12	−0.0498257
$905$	−7.89325e12	−0.391144
$906$	0	0
$907$	6.51759e12	0.319782	0.159891	−	0.987135i	$-0.448886\pi$
$907$	6.51759e12	0.319782	0.159891	+	0.987135i	$0.448886\pi$
$908$	−1.07333e13	−0.524018
$909$	0	0
$910$	−2.99681e11	−0.0144868
$911$	−1.94390e13	−0.935063	−0.467532	−	0.883976i	$-0.654857\pi$
$911$	−1.94390e13	−0.935063	−0.467532	+	0.883976i	$0.654857\pi$
$912$	0	0
$913$	−9.76738e12	−0.465221
$914$	−5.54764e12	−0.262936
$915$	0	0
$916$	1.13405e13	0.532235
$917$	−6.61427e12	−0.308901
$918$	0	0
$919$	−1.65728e13	−0.766435	−0.383217	−	0.923658i	$-0.625184\pi$
$919$	−1.65728e13	−0.766435	−0.383217	+	0.923658i	$0.625184\pi$
$920$	−1.09566e12	−0.0504231
$921$	0	0
$922$	2.41661e10	0.00110133
$923$	4.41588e12	0.200267
$924$	0	0
$925$	−3.07874e12	−0.138272
$926$	−3.65918e12	−0.163544
$927$	0	0
$928$	−8.80985e12	−0.389944
$929$	2.80460e13	1.23538	0.617690	−	0.786422i	$-0.288069\pi$
$929$	2.80460e13	1.23538	0.617690	+	0.786422i	$0.288069\pi$
$930$	0	0
$931$	4.49566e12	0.196119
$932$	5.26168e12	0.228430
$933$	0	0
$934$	−6.18879e12	−0.266100
$935$	6.36676e12	0.272437
$936$	0	0
$937$	−2.45511e13	−1.04050	−0.520251	−	0.854013i	$-0.674162\pi$
$937$	−2.45511e13	−1.04050	−0.520251	+	0.854013i	$0.674162\pi$
$938$	2.75268e11	0.0116103
$939$	0	0
$940$	5.35445e12	0.223686
$941$	−2.57484e13	−1.07053	−0.535263	−	0.844686i	$-0.679787\pi$
$941$	−2.57484e13	−1.07053	−0.535263	+	0.844686i	$0.679787\pi$
$942$	0	0
$943$	−8.83798e12	−0.363957
$944$	1.34161e13	0.549859
$945$	0	0
$946$	3.66470e12	0.148774
$947$	−3.20045e13	−1.29311	−0.646556	−	0.762867i	$-0.723791\pi$
$947$	−3.20045e13	−1.29311	−0.646556	+	0.762867i	$0.723791\pi$
$948$	0	0
$949$	3.20306e12	0.128194
$950$	−1.86303e12	−0.0742101
$951$	0	0
$952$	−1.06551e13	−0.420428
$953$	−3.87308e13	−1.52103	−0.760517	−	0.649318i	$-0.775054\pi$
$953$	−3.87308e13	−1.52103	−0.760517	+	0.649318i	$0.775054\pi$
$954$	0	0
$955$	1.38255e12	0.0537856
$956$	3.79395e13	1.46903
$957$	0	0
$958$	5.56281e12	0.213378
$959$	4.77001e13	1.82111
$960$	0	0
$961$	7.23091e13	2.73488
$962$	−1.29910e11	−0.00489053
$963$	0	0
$964$	−4.40612e13	−1.64327
$965$	9.82241e11	0.0364624
$966$	0	0
$967$	−3.70138e13	−1.36127	−0.680635	−	0.732622i	$-0.738296\pi$
$967$	−3.70138e13	−1.36127	−0.680635	+	0.732622i	$0.738296\pi$
$968$	3.11467e12	0.114018
$969$	0	0
$970$	−3.16475e12	−0.114780
$971$	−3.26137e13	−1.17737	−0.588686	−	0.808361i	$-0.700355\pi$
$971$	−3.26137e13	−1.17737	−0.588686	+	0.808361i	$0.700355\pi$
$972$	0	0
$973$	2.67115e13	0.955412
$974$	1.01714e13	0.362132
$975$	0	0
$976$	9.26906e12	0.326973
$977$	−2.93187e13	−1.02948	−0.514741	−	0.857346i	$-0.672112\pi$
$977$	−2.93187e13	−1.02948	−0.514741	+	0.857346i	$0.672112\pi$
$978$	0	0
$979$	7.56605e12	0.263237
$980$	5.38864e12	0.186622
$981$	0	0
$982$	3.17701e12	0.109023
$983$	−4.92057e13	−1.68083	−0.840416	−	0.541942i	$-0.817689\pi$
$983$	−4.92057e13	−1.68083	−0.840416	+	0.541942i	$0.817689\pi$
$984$	0	0
$985$	−1.39500e13	−0.472183
$986$	3.28496e12	0.110684
$987$	0	0
$988$	1.52408e12	0.0508865
$989$	−6.89588e12	−0.229196
$990$	0	0
$991$	−1.54085e12	−0.0507492	−0.0253746	−	0.999678i	$-0.508078\pi$
$991$	−1.54085e12	−0.0507492	−0.0253746	+	0.999678i	$0.508078\pi$
$992$	3.66336e13	1.20109
$993$	0	0
$994$	1.24153e13	0.403382
$995$	−1.60864e12	−0.0520301
$996$	0	0
$997$	4.54090e13	1.45551	0.727753	−	0.685839i	$-0.240565\pi$
$997$	4.54090e13	1.45551	0.727753	+	0.685839i	$0.240565\pi$
$998$	−3.17809e12	−0.101409
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.10.a.d.1.9		14
3.2	odd	2		37.10.a.b.1.6	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.a.b.1.6	✓	14	3.2	odd	2
333.10.a.d.1.9		14	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:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	333.a (trivial)

\(f(q)\)	\(=\)	\(q+5.01135 q^{2} -486.886 q^{4} -557.130 q^{5} -7760.08 q^{7} -5005.76 q^{8} +O(q^{10})\)	\(q+5.01135 q^{2} -486.886 q^{4} -557.130 q^{5} -7760.08 q^{7} -5005.76 q^{8} -2791.97 q^{10} +41662.1 q^{11} -13831.9 q^{13} -38888.5 q^{14} +224200. q^{16} -274297. q^{17} +226307. q^{19} +271259. q^{20} +208783. q^{22} -392869. q^{23} -1.64273e6 q^{25} -69316.5 q^{26} +3.77828e6 q^{28} -2.38976e6 q^{29} +9.93724e6 q^{31} +3.68650e6 q^{32} -1.37460e6 q^{34} +4.32337e6 q^{35} +1.87416e6 q^{37} +1.13410e6 q^{38} +2.78886e6 q^{40} +2.24960e7 q^{41} +1.75526e7 q^{43} -2.02847e7 q^{44} -1.96880e6 q^{46} +1.97393e7 q^{47} +1.98653e7 q^{49} -8.23229e6 q^{50} +6.73457e6 q^{52} +6.18106e7 q^{53} -2.32112e7 q^{55} +3.88452e7 q^{56} -1.19759e7 q^{58} +5.98396e7 q^{59} +4.13428e7 q^{61} +4.97989e7 q^{62} -9.63162e7 q^{64} +7.70618e6 q^{65} -7.07839e6 q^{67} +1.33552e8 q^{68} +2.16659e7 q^{70} -3.19253e8 q^{71} -2.31570e8 q^{73} +9.39207e6 q^{74} -1.10186e8 q^{76} -3.23301e8 q^{77} +4.62203e8 q^{79} -1.24909e8 q^{80} +1.12735e8 q^{82} -2.34443e8 q^{83} +1.52819e8 q^{85} +8.79623e7 q^{86} -2.08551e8 q^{88} +1.81605e8 q^{89} +1.07337e8 q^{91} +1.91282e8 q^{92} +9.89203e7 q^{94} -1.26083e8 q^{95} +1.13352e9 q^{97} +9.95518e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 48 q^{2} + 3498 q^{4} - 2841 q^{5} + 6632 q^{7} - 41046 q^{8}+O(q^{10}) \) 14 * q - 48 * q^2 + 3498 * q^4 - 2841 * q^5 + 6632 * q^7 - 41046 * q^8	\( 14 q - 48 q^{2} + 3498 q^{4} - 2841 q^{5} + 6632 q^{7} - 41046 q^{8} + 129003 q^{10} - 44949 q^{11} + 38913 q^{13} - 16434 q^{14} + 859962 q^{16} - 893196 q^{17} + 1532124 q^{19} - 4974963 q^{20} + 3195323 q^{22} - 5911773 q^{23} + 9978791 q^{25} - 10634475 q^{26} + 9469678 q^{28} - 8764377 q^{29} + 13188927 q^{31} - 23982750 q^{32} + 29914960 q^{34} - 29633556 q^{35} + 26238254 q^{37} - 23342796 q^{38} + 42889049 q^{40} - 22153785 q^{41} + 1779790 q^{43} + 83674089 q^{44} - 23239663 q^{46} - 40080072 q^{47} - 170457752 q^{49} + 89214633 q^{50} - 276889277 q^{52} + 102088122 q^{53} - 206797385 q^{55} + 294922194 q^{56} - 527059089 q^{58} - 56191266 q^{59} - 178507397 q^{61} + 27353505 q^{62} - 242330062 q^{64} + 174258810 q^{65} + 287062499 q^{67} - 308827572 q^{68} - 672888452 q^{70} - 224382678 q^{71} + 271440727 q^{73} - 89959728 q^{74} - 229522980 q^{76} - 671279994 q^{77} + 379128625 q^{79} - 1999017183 q^{80} + 551153781 q^{82} - 1664083206 q^{83} + 1982056546 q^{85} - 520253082 q^{86} + 684092585 q^{88} - 3293434692 q^{89} + 1715813946 q^{91} - 3729310881 q^{92} + 998499458 q^{94} - 878402766 q^{95} + 2385468336 q^{97} + 3234447132 q^{98}+O(q^{100}) \) 14 * q - 48 * q^2 + 3498 * q^4 - 2841 * q^5 + 6632 * q^7 - 41046 * q^8 + 129003 * q^10 - 44949 * q^11 + 38913 * q^13 - 16434 * q^14 + 859962 * q^16 - 893196 * q^17 + 1532124 * q^19 - 4974963 * q^20 + 3195323 * q^22 - 5911773 * q^23 + 9978791 * q^25 - 10634475 * q^26 + 9469678 * q^28 - 8764377 * q^29 + 13188927 * q^31 - 23982750 * q^32 + 29914960 * q^34 - 29633556 * q^35 + 26238254 * q^37 - 23342796 * q^38 + 42889049 * q^40 - 22153785 * q^41 + 1779790 * q^43 + 83674089 * q^44 - 23239663 * q^46 - 40080072 * q^47 - 170457752 * q^49 + 89214633 * q^50 - 276889277 * q^52 + 102088122 * q^53 - 206797385 * q^55 + 294922194 * q^56 - 527059089 * q^58 - 56191266 * q^59 - 178507397 * q^61 + 27353505 * q^62 - 242330062 * q^64 + 174258810 * q^65 + 287062499 * q^67 - 308827572 * q^68 - 672888452 * q^70 - 224382678 * q^71 + 271440727 * q^73 - 89959728 * q^74 - 229522980 * q^76 - 671279994 * q^77 + 379128625 * q^79 - 1999017183 * q^80 + 551153781 * q^82 - 1664083206 * q^83 + 1982056546 * q^85 - 520253082 * q^86 + 684092585 * q^88 - 3293434692 * q^89 + 1715813946 * q^91 - 3729310881 * q^92 + 998499458 * q^94 - 878402766 * q^95 + 2385468336 * q^97 + 3234447132 * q^98

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