LMFDB - Embedded newform 294.8.a.v.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,8,Mod(1,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("294.1"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(294, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	294.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-24,-81,192,-110] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$91.8411974923$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2118x + 33912 $ x^3 - x^2 - 2118*x + 33912
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 42)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-52.1203$ of defining polynomial
Character	$\chi$	$=$	294.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -403.842 q^{5} +216.000 q^{6} -512.000 q^{8} +729.000 q^{9} +3230.74 q^{10} +6474.68 q^{11} -1728.00 q^{12} +11611.3 q^{13} +10903.7 q^{15} +4096.00 q^{16} +20309.0 q^{17} -5832.00 q^{18} -46495.7 q^{19} -25845.9 q^{20} -51797.4 q^{22} -13156.8 q^{23} +13824.0 q^{24} +84963.6 q^{25} -92890.3 q^{26} -19683.0 q^{27} -87278.1 q^{29} -87229.9 q^{30} -250277. q^{31} -32768.0 q^{32} -174816. q^{33} -162472. q^{34} +46656.0 q^{36} +394332. q^{37} +371966. q^{38} -313505. q^{39} +206767. q^{40} -233278. q^{41} +596690. q^{43} +414379. q^{44} -294401. q^{45} +105254. q^{46} -208336. q^{47} -110592. q^{48} -679709. q^{50} -548344. q^{51} +743123. q^{52} -1.10226e6 q^{53} +157464. q^{54} -2.61475e6 q^{55} +1.25538e6 q^{57} +698225. q^{58} -2.13437e6 q^{59} +697839. q^{60} +2.65465e6 q^{61} +2.00222e6 q^{62} +262144. q^{64} -4.68913e6 q^{65} +1.39853e6 q^{66} +77035.5 q^{67} +1.29978e6 q^{68} +355233. q^{69} +1.55255e6 q^{71} -373248. q^{72} +4.66411e6 q^{73} -3.15465e6 q^{74} -2.29402e6 q^{75} -2.97573e6 q^{76} +2.50804e6 q^{78} -2.33491e6 q^{79} -1.65414e6 q^{80} +531441. q^{81} +1.86623e6 q^{82} -5.17043e6 q^{83} -8.20165e6 q^{85} -4.77352e6 q^{86} +2.35651e6 q^{87} -3.31504e6 q^{88} +1.79395e6 q^{89} +2.35521e6 q^{90} -842034. q^{92} +6.75748e6 q^{93} +1.66669e6 q^{94} +1.87769e7 q^{95} +884736. q^{96} +2.34436e6 q^{97} +4.72004e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 24 q^{2} - 81 q^{3} + 192 q^{4} - 110 q^{5} + 648 q^{6} - 1536 q^{8} + 2187 q^{9} + 880 q^{10} + 548 q^{11} - 5184 q^{12} + 9949 q^{13} + 2970 q^{15} + 12288 q^{16} + 20972 q^{17} - 17496 q^{18} - 28383 q^{19}+ \cdots + 399492 q^{99}+O(q^{100}) $ 3 * q - 24 * q^2 - 81 * q^3 + 192 * q^4 - 110 * q^5 + 648 * q^6 - 1536 * q^8 + 2187 * q^9 + 880 * q^10 + 548 * q^11 - 5184 * q^12 + 9949 * q^13 + 2970 * q^15 + 12288 * q^16 + 20972 * q^17 - 17496 * q^18 - 28383 * q^19 - 7040 * q^20 - 4384 * q^22 + 32732 * q^23 + 41472 * q^24 - 22745 * q^25 - 79592 * q^26 - 59049 * q^27 + 117088 * q^29 - 23760 * q^30 + 147865 * q^31 - 98304 * q^32 - 14796 * q^33 - 167776 * q^34 + 139968 * q^36 + 367503 * q^37 + 227064 * q^38 - 268623 * q^39 + 56320 * q^40 - 1437954 * q^41 + 749397 * q^43 + 35072 * q^44 - 80190 * q^45 - 261856 * q^46 - 741486 * q^47 - 331776 * q^48 + 181960 * q^50 - 566244 * q^51 + 636736 * q^52 - 1032432 * q^53 + 472392 * q^54 - 3996280 * q^55 + 766341 * q^57 - 936704 * q^58 - 2389238 * q^59 + 190080 * q^60 + 1238746 * q^61 - 1182920 * q^62 + 786432 * q^64 - 3798390 * q^65 + 118368 * q^66 - 2462497 * q^67 + 1342208 * q^68 - 883764 * q^69 - 636262 * q^71 - 1119744 * q^72 + 4609961 * q^73 - 2940024 * q^74 + 614115 * q^75 - 1816512 * q^76 + 2148984 * q^78 - 6152849 * q^79 - 450560 * q^80 + 1594323 * q^81 + 11503632 * q^82 - 12029884 * q^83 - 9136540 * q^85 - 5995176 * q^86 - 3161376 * q^87 - 280576 * q^88 + 10646976 * q^89 + 641520 * q^90 + 2094848 * q^92 - 3992355 * q^93 + 5931888 * q^94 + 21560930 * q^95 + 2654208 * q^96 + 2281472 * q^97 + 399492 * q^99

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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	64.0000	0.500000
$5$	−403.842	−1.44483	−0.722415	−	0.691460i	$-0.756968\pi$
$5$	−403.842	−1.44483	−0.722415	+	0.691460i	$0.756968\pi$
$6$	216.000	0.408248
$7$	0	0
$7$	0	0
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	3230.74	1.02165
$11$	6474.68	1.46671	0.733354	−	0.679847i	$-0.237954\pi$
$11$	6474.68	1.46671	0.733354	+	0.679847i	$0.237954\pi$
$12$	−1728.00	−0.288675
$13$	11611.3	1.46581	0.732907	−	0.680329i	$-0.238163\pi$
$13$	11611.3	1.46581	0.732907	+	0.680329i	$0.238163\pi$
$14$	0	0
$15$	10903.7	0.834173
$16$	4096.00	0.250000
$17$	20309.0	1.00258	0.501289	−	0.865280i	$-0.332859\pi$
$17$	20309.0	1.00258	0.501289	+	0.865280i	$0.332859\pi$
$18$	−5832.00	−0.235702
$19$	−46495.7	−1.55516	−0.777580	−	0.628784i	$-0.783553\pi$
$19$	−46495.7	−1.55516	−0.777580	+	0.628784i	$0.783553\pi$
$20$	−25845.9	−0.722415
$21$	0	0
$22$	−51797.4	−1.03712
$23$	−13156.8	−0.225477	−0.112739	−	0.993625i	$-0.535962\pi$
$23$	−13156.8	−0.225477	−0.112739	+	0.993625i	$0.535962\pi$
$24$	13824.0	0.204124
$25$	84963.6	1.08753
$26$	−92890.3	−1.03649
$27$	−19683.0	−0.192450
$28$	0	0
$29$	−87278.1	−0.664527	−0.332263	−	0.943187i	$-0.607812\pi$
$29$	−87278.1	−0.664527	−0.332263	+	0.943187i	$0.607812\pi$
$30$	−87229.9	−0.589849
$31$	−250277.	−1.50888	−0.754440	−	0.656369i	$-0.772092\pi$
$31$	−250277.	−1.50888	−0.754440	+	0.656369i	$0.772092\pi$
$32$	−32768.0	−0.176777
$33$	−174816.	−0.846805
$34$	−162472.	−0.708930
$35$	0	0
$36$	46656.0	0.166667
$37$	394332.	1.27984	0.639920	−	0.768442i	$-0.278967\pi$
$37$	394332.	1.27984	0.639920	+	0.768442i	$0.278967\pi$
$38$	371966.	1.09966
$39$	−313505.	−0.846288
$40$	206767.	0.510825
$41$	−233278.	−0.528604	−0.264302	−	0.964440i	$-0.585142\pi$
$41$	−233278.	−0.528604	−0.264302	+	0.964440i	$0.585142\pi$
$42$	0	0
$43$	596690.	1.14448	0.572242	−	0.820085i	$-0.306074\pi$
$43$	596690.	1.14448	0.572242	+	0.820085i	$0.306074\pi$
$44$	414379.	0.733354
$45$	−294401.	−0.481610
$46$	105254.	0.159436
$47$	−208336.	−0.292699	−0.146350	−	0.989233i	$-0.546752\pi$
$47$	−208336.	−0.292699	−0.146350	+	0.989233i	$0.546752\pi$
$48$	−110592.	−0.144338
$49$	0	0
$50$	−679709.	−0.769002
$51$	−548344.	−0.578839
$52$	743123.	0.732907
$53$	−1.10226e6	−1.01700	−0.508498	−	0.861063i	$-0.669799\pi$
$53$	−1.10226e6	−1.01700	−0.508498	+	0.861063i	$0.669799\pi$
$54$	157464.	0.136083
$55$	−2.61475e6	−2.11914
$56$	0	0
$57$	1.25538e6	0.897872
$58$	698225.	0.469891
$59$	−2.13437e6	−1.35297	−0.676484	−	0.736458i	$-0.736497\pi$
$59$	−2.13437e6	−1.35297	−0.676484	+	0.736458i	$0.736497\pi$
$60$	697839.	0.417086
$61$	2.65465e6	1.49745	0.748725	−	0.662880i	$-0.230666\pi$
$61$	2.65465e6	1.49745	0.748725	+	0.662880i	$0.230666\pi$
$62$	2.00222e6	1.06694
$63$	0	0
$64$	262144.	0.125000
$65$	−4.68913e6	−2.11785
$66$	1.39853e6	0.598781
$67$	77035.5	0.0312917	0.0156459	−	0.999878i	$-0.495020\pi$
$67$	77035.5	0.0312917	0.0156459	+	0.999878i	$0.495020\pi$
$68$	1.29978e6	0.501289
$69$	355233.	0.130179
$70$	0	0
$71$	1.55255e6	0.514805	0.257402	−	0.966304i	$-0.417133\pi$
$71$	1.55255e6	0.514805	0.257402	+	0.966304i	$0.417133\pi$
$72$	−373248.	−0.117851
$73$	4.66411e6	1.40326	0.701631	−	0.712540i	$-0.252455\pi$
$73$	4.66411e6	1.40326	0.701631	+	0.712540i	$0.252455\pi$
$74$	−3.15465e6	−0.904983
$75$	−2.29402e6	−0.627888
$76$	−2.97573e6	−0.777580
$77$	0	0
$78$	2.50804e6	0.598416
$79$	−2.33491e6	−0.532814	−0.266407	−	0.963861i	$-0.585836\pi$
$79$	−2.33491e6	−0.532814	−0.266407	+	0.963861i	$0.585836\pi$
$80$	−1.65414e6	−0.361207
$81$	531441.	0.111111
$82$	1.86623e6	0.373780
$83$	−5.17043e6	−0.992552	−0.496276	−	0.868165i	$-0.665300\pi$
$83$	−5.17043e6	−0.992552	−0.496276	+	0.868165i	$0.665300\pi$
$84$	0	0
$85$	−8.20165e6	−1.44855
$86$	−4.77352e6	−0.809272
$87$	2.35651e6	0.383665
$88$	−3.31504e6	−0.518560
$89$	1.79395e6	0.269740	0.134870	−	0.990863i	$-0.456938\pi$
$89$	1.79395e6	0.269740	0.134870	+	0.990863i	$0.456938\pi$
$90$	2.35521e6	0.340550
$91$	0	0
$92$	−842034.	−0.112739
$93$	6.75748e6	0.871153
$94$	1.66669e6	0.206970
$95$	1.87769e7	2.24694
$96$	884736.	0.102062
$97$	2.34436e6	0.260809	0.130404	−	0.991461i	$-0.458372\pi$
$97$	2.34436e6	0.260809	0.130404	+	0.991461i	$0.458372\pi$
$98$	0	0
$99$	4.72004e6	0.488903
$100$	5.43767e6	0.543767
$101$	−1.81159e7	−1.74958	−0.874790	−	0.484502i	$-0.839001\pi$
$101$	−1.81159e7	−1.74958	−0.874790	+	0.484502i	$0.839001\pi$
$102$	4.38675e6	0.409301
$103$	5.85148e6	0.527638	0.263819	−	0.964572i	$-0.415018\pi$
$103$	5.85148e6	0.527638	0.263819	+	0.964572i	$0.415018\pi$
$104$	−5.94498e6	−0.518243
$105$	0	0
$106$	8.81809e6	0.719125
$107$	−2.83619e6	−0.223817	−0.111908	−	0.993719i	$-0.535696\pi$
$107$	−2.83619e6	−0.223817	−0.111908	+	0.993719i	$0.535696\pi$
$108$	−1.25971e6	−0.0962250
$109$	8.15686e6	0.603296	0.301648	−	0.953419i	$-0.402463\pi$
$109$	8.15686e6	0.603296	0.301648	+	0.953419i	$0.402463\pi$
$110$	2.09180e7	1.49846
$111$	−1.06470e7	−0.738916
$112$	0	0
$113$	−1.57932e7	−1.02966	−0.514831	−	0.857292i	$-0.672145\pi$
$113$	−1.57932e7	−1.02966	−0.514831	+	0.857292i	$0.672145\pi$
$114$	−1.00431e7	−0.634892
$115$	5.31327e6	0.325776
$116$	−5.58580e6	−0.332263
$117$	8.46463e6	0.488605
$118$	1.70749e7	0.956692
$119$	0	0
$120$	−5.58272e6	−0.294925
$121$	2.24343e7	1.15123
$122$	−2.12372e7	−1.05886
$123$	6.29851e6	0.305190
$124$	−1.60177e7	−0.754440
$125$	−2.76170e6	−0.126471
$126$	0	0
$127$	3.88646e7	1.68361	0.841805	−	0.539782i	$-0.181493\pi$
$127$	3.88646e7	1.68361	0.841805	+	0.539782i	$0.181493\pi$
$128$	−2.09715e6	−0.0883883
$129$	−1.61106e7	−0.660768
$130$	3.75130e7	1.49755
$131$	−3.02118e6	−0.117416	−0.0587080	−	0.998275i	$-0.518698\pi$
$131$	−3.02118e6	−0.117416	−0.0587080	+	0.998275i	$0.518698\pi$
$132$	−1.11882e7	−0.423402
$133$	0	0
$134$	−616284.	−0.0221266
$135$	7.94883e6	0.278058
$136$	−1.03982e7	−0.354465
$137$	6.61770e6	0.219880	0.109940	−	0.993938i	$-0.464934\pi$
$137$	6.61770e6	0.219880	0.109940	+	0.993938i	$0.464934\pi$
$138$	−2.84187e6	−0.0920506
$139$	2.69156e6	0.0850065	0.0425032	−	0.999096i	$-0.486467\pi$
$139$	2.69156e6	0.0850065	0.0425032	+	0.999096i	$0.486467\pi$
$140$	0	0
$141$	5.62507e6	0.168990
$142$	−1.24204e7	−0.364022
$143$	7.51794e7	2.14992
$144$	2.98598e6	0.0833333
$145$	3.52466e7	0.960128
$146$	−3.73129e7	−0.992256
$147$	0	0
$148$	2.52372e7	0.639920
$149$	4.86318e7	1.20439	0.602196	−	0.798348i	$-0.294292\pi$
$149$	4.86318e7	1.20439	0.602196	+	0.798348i	$0.294292\pi$
$150$	1.83521e7	0.443984
$151$	3.31467e7	0.783469	0.391734	−	0.920078i	$-0.371875\pi$
$151$	3.31467e7	0.783469	0.391734	+	0.920078i	$0.371875\pi$
$152$	2.38058e7	0.549832
$153$	1.48053e7	0.334193
$154$	0	0
$155$	1.01072e8	2.18008
$156$	−2.00643e7	−0.423144
$157$	−2.30428e7	−0.475211	−0.237606	−	0.971362i	$-0.576363\pi$
$157$	−2.30428e7	−0.475211	−0.237606	+	0.971362i	$0.576363\pi$
$158$	1.86793e7	0.376756
$159$	2.97611e7	0.587163
$160$	1.32331e7	0.255412
$161$	0	0
$162$	−4.25153e6	−0.0785674
$163$	−5.68893e7	−1.02890	−0.514451	−	0.857520i	$-0.672004\pi$
$163$	−5.68893e7	−1.02890	−0.514451	+	0.857520i	$0.672004\pi$
$164$	−1.49298e7	−0.264302
$165$	7.05982e7	1.22349
$166$	4.13634e7	0.701840
$167$	2.37567e6	0.0394710	0.0197355	−	0.999805i	$-0.493718\pi$
$167$	2.37567e6	0.0394710	0.0197355	+	0.999805i	$0.493718\pi$
$168$	0	0
$169$	7.20736e7	1.14861
$170$	6.56132e7	1.02428
$171$	−3.38954e7	−0.518387
$172$	3.81882e7	0.572242
$173$	−2.85719e7	−0.419545	−0.209772	−	0.977750i	$-0.567272\pi$
$173$	−2.85719e7	−0.419545	−0.209772	+	0.977750i	$0.567272\pi$
$174$	−1.88521e7	−0.271292
$175$	0	0
$176$	2.65203e7	0.366677
$177$	5.76279e7	0.781136
$178$	−1.43516e7	−0.190735
$179$	4.23793e7	0.552291	0.276146	−	0.961116i	$-0.410943\pi$
$179$	4.23793e7	0.552291	0.276146	+	0.961116i	$0.410943\pi$
$180$	−1.88417e7	−0.240805
$181$	−5.11373e7	−0.641007	−0.320504	−	0.947247i	$-0.603852\pi$
$181$	−5.11373e7	−0.641007	−0.320504	+	0.947247i	$0.603852\pi$
$182$	0	0
$183$	−7.16755e7	−0.864554
$184$	6.73627e6	0.0797182
$185$	−1.59248e8	−1.84915
$186$	−5.40598e7	−0.615998
$187$	1.31495e8	1.47049
$188$	−1.33335e7	−0.146350
$189$	0	0
$190$	−1.50215e8	−1.58883
$191$	1.45227e8	1.50811	0.754053	−	0.656814i	$-0.228096\pi$
$191$	1.45227e8	1.50811	0.754053	+	0.656814i	$0.228096\pi$
$192$	−7.07789e6	−0.0721688
$193$	−3.07683e7	−0.308072	−0.154036	−	0.988065i	$-0.549227\pi$
$193$	−3.07683e7	−0.308072	−0.154036	+	0.988065i	$0.549227\pi$
$194$	−1.87548e7	−0.184420
$195$	1.26607e8	1.22274
$196$	0	0
$197$	6.36237e7	0.592908	0.296454	−	0.955047i	$-0.404196\pi$
$197$	6.36237e7	0.592908	0.296454	+	0.955047i	$0.404196\pi$
$198$	−3.77603e7	−0.345707
$199$	3.15476e7	0.283779	0.141890	−	0.989882i	$-0.454682\pi$
$199$	3.15476e7	0.283779	0.141890	+	0.989882i	$0.454682\pi$
$200$	−4.35013e7	−0.384501
$201$	−2.07996e6	−0.0180663
$202$	1.44927e8	1.23714
$203$	0	0
$204$	−3.50940e7	−0.289419
$205$	9.42076e7	0.763743
$206$	−4.68119e7	−0.373096
$207$	−9.59130e6	−0.0751590
$208$	4.75598e7	0.366453
$209$	−3.01045e8	−2.28097
$210$	0	0
$211$	−1.20761e7	−0.0884987	−0.0442493	−	0.999021i	$-0.514090\pi$
$211$	−1.20761e7	−0.0884987	−0.0442493	+	0.999021i	$0.514090\pi$
$212$	−7.05447e7	−0.508498
$213$	−4.19190e7	−0.297223
$214$	2.26895e7	0.158262
$215$	−2.40969e8	−1.65358
$216$	1.00777e7	0.0680414
$217$	0	0
$218$	−6.52549e7	−0.426594
$219$	−1.25931e8	−0.810174
$220$	−1.67344e8	−1.05957
$221$	2.35814e8	1.46959
$222$	8.51756e7	0.522492
$223$	−2.80825e8	−1.69578	−0.847889	−	0.530173i	$-0.822127\pi$
$223$	−2.80825e8	−1.69578	−0.847889	+	0.530173i	$0.822127\pi$
$224$	0	0
$225$	6.19384e7	0.362511
$226$	1.26345e8	0.728081
$227$	1.63964e8	0.930376	0.465188	−	0.885212i	$-0.345987\pi$
$227$	1.63964e8	0.930376	0.465188	+	0.885212i	$0.345987\pi$
$228$	8.03446e7	0.448936
$229$	−2.69395e7	−0.148240	−0.0741200	−	0.997249i	$-0.523615\pi$
$229$	−2.69395e7	−0.148240	−0.0741200	+	0.997249i	$0.523615\pi$
$230$	−4.25061e7	−0.230358
$231$	0	0
$232$	4.46864e7	0.234946
$233$	−6.74183e7	−0.349166	−0.174583	−	0.984642i	$-0.555858\pi$
$233$	−6.74183e7	−0.349166	−0.174583	+	0.984642i	$0.555858\pi$
$234$	−6.77170e7	−0.345496
$235$	8.41348e7	0.422901
$236$	−1.36600e8	−0.676484
$237$	6.30426e7	0.307620
$238$	0	0
$239$	3.87968e8	1.83824	0.919122	−	0.393973i	$-0.128900\pi$
$239$	3.87968e8	1.83824	0.919122	+	0.393973i	$0.128900\pi$
$240$	4.46617e7	0.208543
$241$	2.31285e8	1.06436	0.532180	−	0.846632i	$-0.321373\pi$
$241$	2.31285e8	1.06436	0.532180	+	0.846632i	$0.321373\pi$
$242$	−1.79474e8	−0.814045
$243$	−1.43489e7	−0.0641500
$244$	1.69897e8	0.748725
$245$	0	0
$246$	−5.03881e7	−0.215802
$247$	−5.39875e8	−2.27958
$248$	1.28142e8	0.533470
$249$	1.39602e8	0.573050
$250$	2.20936e7	0.0894287
$251$	1.20208e8	0.479817	0.239909	−	0.970795i	$-0.422883\pi$
$251$	1.20208e8	0.479817	0.239909	+	0.970795i	$0.422883\pi$
$252$	0	0
$253$	−8.51860e7	−0.330709
$254$	−3.10917e8	−1.19049
$255$	2.21445e8	0.836324
$256$	1.67772e7	0.0625000
$257$	2.32236e8	0.853421	0.426711	−	0.904388i	$-0.359672\pi$
$257$	2.32236e8	0.853421	0.426711	+	0.904388i	$0.359672\pi$
$258$	1.28885e8	0.467233
$259$	0	0
$260$	−3.00104e8	−1.05893
$261$	−6.36258e7	−0.221509
$262$	2.41695e7	0.0830257
$263$	−5.32676e8	−1.80558	−0.902792	−	0.430076i	$-0.858487\pi$
$263$	−5.32676e8	−1.80558	−0.902792	+	0.430076i	$0.858487\pi$
$264$	8.95060e7	0.299391
$265$	4.45140e8	1.46939
$266$	0	0
$267$	−4.84367e7	−0.155735
$268$	4.93027e6	0.0156459
$269$	2.98331e8	0.934469	0.467234	−	0.884133i	$-0.345250\pi$
$269$	2.98331e8	0.934469	0.467234	+	0.884133i	$0.345250\pi$
$270$	−6.35906e7	−0.196616
$271$	5.52332e8	1.68581	0.842903	−	0.538066i	$-0.180845\pi$
$271$	5.52332e8	1.68581	0.842903	+	0.538066i	$0.180845\pi$
$272$	8.31858e7	0.250645
$273$	0	0
$274$	−5.29416e7	−0.155478
$275$	5.50112e8	1.59509
$276$	2.27349e7	0.0650896
$277$	−2.00831e8	−0.567741	−0.283871	−	0.958863i	$-0.591619\pi$
$277$	−2.00831e8	−0.567741	−0.283871	+	0.958863i	$0.591619\pi$
$278$	−2.15325e7	−0.0601087
$279$	−1.82452e8	−0.502960
$280$	0	0
$281$	−3.14684e8	−0.846063	−0.423031	−	0.906115i	$-0.639034\pi$
$281$	−3.14684e8	−0.846063	−0.423031	+	0.906115i	$0.639034\pi$
$282$	−4.50005e7	−0.119494
$283$	3.88847e8	1.01983	0.509914	−	0.860226i	$-0.329677\pi$
$283$	3.88847e8	1.01983	0.509914	+	0.860226i	$0.329677\pi$
$284$	9.93635e7	0.257402
$285$	−5.06977e8	−1.29727
$286$	−6.01435e8	−1.52022
$287$	0	0
$288$	−2.38879e7	−0.0589256
$289$	2.11852e6	0.00516285
$290$	−2.81973e8	−0.678913
$291$	−6.32976e7	−0.150578
$292$	2.98503e8	0.701631
$293$	−8.20380e7	−0.190537	−0.0952684	−	0.995452i	$-0.530371\pi$
$293$	−8.20380e7	−0.190537	−0.0952684	+	0.995452i	$0.530371\pi$
$294$	0	0
$295$	8.61948e8	1.95481
$296$	−2.01898e8	−0.452492
$297$	−1.27441e8	−0.282268
$298$	−3.89054e8	−0.851634
$299$	−1.52767e8	−0.330507
$300$	−1.46817e8	−0.313944
$301$	0	0
$302$	−2.65174e8	−0.553996
$303$	4.89128e8	1.01012
$304$	−1.90446e8	−0.388790
$305$	−1.07206e9	−2.16356
$306$	−1.18442e8	−0.236310
$307$	1.58854e8	0.313338	0.156669	−	0.987651i	$-0.449924\pi$
$307$	1.58854e8	0.313338	0.156669	+	0.987651i	$0.449924\pi$
$308$	0	0
$309$	−1.57990e8	−0.304632
$310$	−8.08579e8	−1.54155
$311$	−5.55220e8	−1.04665	−0.523327	−	0.852132i	$-0.675310\pi$
$311$	−5.55220e8	−1.04665	−0.523327	+	0.852132i	$0.675310\pi$
$312$	1.60514e8	0.299208
$313$	−8.52076e8	−1.57063	−0.785314	−	0.619098i	$-0.787498\pi$
$313$	−8.52076e8	−1.57063	−0.785314	+	0.619098i	$0.787498\pi$
$314$	1.84342e8	0.336025
$315$	0	0
$316$	−1.49434e8	−0.266407
$317$	4.68754e8	0.826490	0.413245	−	0.910620i	$-0.364395\pi$
$317$	4.68754e8	0.826490	0.413245	+	0.910620i	$0.364395\pi$
$318$	−2.38088e8	−0.415187
$319$	−5.65098e8	−0.974667
$320$	−1.05865e8	−0.180604
$321$	7.65772e7	0.129221
$322$	0	0
$323$	−9.44283e8	−1.55917
$324$	3.40122e7	0.0555556
$325$	9.86537e8	1.59412
$326$	4.55114e8	0.727544
$327$	−2.20235e8	−0.348313
$328$	1.19438e8	0.186890
$329$	0	0
$330$	−5.64786e8	−0.865137
$331$	2.48854e8	0.377178	0.188589	−	0.982056i	$-0.439609\pi$
$331$	2.48854e8	0.377178	0.188589	+	0.982056i	$0.439609\pi$
$332$	−3.30907e8	−0.496276
$333$	2.87468e8	0.426613
$334$	−1.90053e7	−0.0279102
$335$	−3.11102e7	−0.0452112
$336$	0	0
$337$	5.86823e8	0.835223	0.417612	−	0.908626i	$-0.362867\pi$
$337$	5.86823e8	0.835223	0.417612	+	0.908626i	$0.362867\pi$
$338$	−5.76588e8	−0.812190
$339$	4.26416e8	0.594476
$340$	−5.24906e8	−0.724277
$341$	−1.62046e9	−2.21309
$342$	2.71163e8	0.366555
$343$	0	0
$344$	−3.05505e8	−0.404636
$345$	−1.43458e8	−0.188087
$346$	2.28575e8	0.296663
$347$	−1.21507e8	−0.156116	−0.0780581	−	0.996949i	$-0.524872\pi$
$347$	−1.21507e8	−0.156116	−0.0780581	+	0.996949i	$0.524872\pi$
$348$	1.50817e8	0.191832
$349$	9.16462e8	1.15405	0.577026	−	0.816725i	$-0.304213\pi$
$349$	9.16462e8	1.15405	0.577026	+	0.816725i	$0.304213\pi$
$350$	0	0
$351$	−2.28545e8	−0.282096
$352$	−2.12162e8	−0.259280
$353$	−1.60587e8	−0.194311	−0.0971556	−	0.995269i	$-0.530974\pi$
$353$	−1.60587e8	−0.194311	−0.0971556	+	0.995269i	$0.530974\pi$
$354$	−4.61024e8	−0.552347
$355$	−6.26987e8	−0.743805
$356$	1.14813e8	0.134870
$357$	0	0
$358$	−3.39034e8	−0.390529
$359$	−8.59549e8	−0.980482	−0.490241	−	0.871587i	$-0.663091\pi$
$359$	−8.59549e8	−0.980482	−0.490241	+	0.871587i	$0.663091\pi$
$360$	1.50733e8	0.170275
$361$	1.26798e9	1.41852
$362$	4.09098e8	0.453261
$363$	−6.05726e8	−0.664665
$364$	0	0
$365$	−1.88357e9	−2.02748
$366$	5.73404e8	0.611332
$367$	−3.77636e8	−0.398788	−0.199394	−	0.979919i	$-0.563897\pi$
$367$	−3.77636e8	−0.398788	−0.199394	+	0.979919i	$0.563897\pi$
$368$	−5.38902e7	−0.0563693
$369$	−1.70060e8	−0.176201
$370$	1.27398e9	1.30755
$371$	0	0
$372$	4.32479e8	0.435576
$373$	7.63699e8	0.761976	0.380988	−	0.924580i	$-0.375584\pi$
$373$	7.63699e8	0.761976	0.380988	+	0.924580i	$0.375584\pi$
$374$	−1.05196e9	−1.03979
$375$	7.45660e7	0.0730182
$376$	1.06668e8	0.103485
$377$	−1.01341e9	−0.974072
$378$	0	0
$379$	7.65774e8	0.722543	0.361271	−	0.932461i	$-0.382343\pi$
$379$	7.65774e8	0.722543	0.361271	+	0.932461i	$0.382343\pi$
$380$	1.20172e9	1.12347
$381$	−1.04935e9	−0.972033
$382$	−1.16182e9	−1.06639
$383$	−1.09578e9	−0.996616	−0.498308	−	0.867000i	$-0.666045\pi$
$383$	−1.09578e9	−0.996616	−0.498308	+	0.867000i	$0.666045\pi$
$384$	5.66231e7	0.0510310
$385$	0	0
$386$	2.46146e8	0.217840
$387$	4.34987e8	0.381494
$388$	1.50039e8	0.130404
$389$	1.39928e9	1.20526	0.602631	−	0.798020i	$-0.294119\pi$
$389$	1.39928e9	1.20526	0.602631	+	0.798020i	$0.294119\pi$
$390$	−1.01285e9	−0.864609
$391$	−2.67202e8	−0.226058
$392$	0	0
$393$	8.15719e7	0.0677902
$394$	−5.08990e8	−0.419249
$395$	9.42935e8	0.769825
$396$	3.02083e8	0.244451
$397$	1.59400e9	1.27856	0.639281	−	0.768973i	$-0.279232\pi$
$397$	1.59400e9	1.27856	0.639281	+	0.768973i	$0.279232\pi$
$398$	−2.52381e8	−0.200662
$399$	0	0
$400$	3.48011e8	0.271883
$401$	−8.35321e8	−0.646916	−0.323458	−	0.946243i	$-0.604845\pi$
$401$	−8.35321e8	−0.646916	−0.323458	+	0.946243i	$0.604845\pi$
$402$	1.66397e7	0.0127748
$403$	−2.90604e9	−2.21174
$404$	−1.15941e9	−0.874790
$405$	−2.14618e8	−0.160537
$406$	0	0
$407$	2.55317e9	1.87715
$408$	2.80752e8	0.204650
$409$	2.24965e9	1.62586	0.812930	−	0.582362i	$-0.197871\pi$
$409$	2.24965e9	1.62586	0.812930	+	0.582362i	$0.197871\pi$
$410$	−7.53661e8	−0.540048
$411$	−1.78678e8	−0.126947
$412$	3.74495e8	0.263819
$413$	0	0
$414$	7.67304e7	0.0531455
$415$	2.08804e9	1.43407
$416$	−3.80479e8	−0.259122
$417$	−7.26721e7	−0.0490785
$418$	2.40836e9	1.61289
$419$	1.75510e9	1.16561	0.582803	−	0.812613i	$-0.301956\pi$
$419$	1.75510e9	1.16561	0.582803	+	0.812613i	$0.301956\pi$
$420$	0	0
$421$	1.57373e9	1.02788	0.513940	−	0.857826i	$-0.328185\pi$
$421$	1.57373e9	1.02788	0.513940	+	0.857826i	$0.328185\pi$
$422$	9.66085e7	0.0625780
$423$	−1.51877e8	−0.0975664
$424$	5.64358e8	0.359562
$425$	1.72553e9	1.09034
$426$	3.35352e8	0.210168
$427$	0	0
$428$	−1.81516e8	−0.111908
$429$	−2.02984e9	−1.24126
$430$	1.92775e9	1.16926
$431$	1.75096e9	1.05343	0.526714	−	0.850042i	$-0.323424\pi$
$431$	1.75096e9	1.05343	0.526714	+	0.850042i	$0.323424\pi$
$432$	−8.06216e7	−0.0481125
$433$	8.68747e8	0.514263	0.257132	−	0.966376i	$-0.417223\pi$
$433$	8.68747e8	0.514263	0.257132	+	0.966376i	$0.417223\pi$
$434$	0	0
$435$	−9.51658e8	−0.554330
$436$	5.22039e8	0.301648
$437$	6.11734e8	0.350653
$438$	1.00745e9	0.572879
$439$	1.23811e9	0.698448	0.349224	−	0.937039i	$-0.386445\pi$
$439$	1.23811e9	0.698448	0.349224	+	0.937039i	$0.386445\pi$
$440$	1.33875e9	0.749231
$441$	0	0
$442$	−1.88651e9	−1.03916
$443$	3.37516e9	1.84451	0.922256	−	0.386579i	$-0.126343\pi$
$443$	3.37516e9	1.84451	0.922256	+	0.386579i	$0.126343\pi$
$444$	−6.81405e8	−0.369458
$445$	−7.24473e8	−0.389729
$446$	2.24660e9	1.19910
$447$	−1.31306e9	−0.695357
$448$	0	0
$449$	2.12595e9	1.10838	0.554192	−	0.832389i	$-0.313027\pi$
$449$	2.12595e9	1.10838	0.554192	+	0.832389i	$0.313027\pi$
$450$	−4.95508e8	−0.256334
$451$	−1.51040e9	−0.775309
$452$	−1.01076e9	−0.514831
$453$	−8.94962e8	−0.452336
$454$	−1.31171e9	−0.657875
$455$	0	0
$456$	−6.42757e8	−0.317446
$457$	−2.00672e9	−0.983515	−0.491758	−	0.870732i	$-0.663645\pi$
$457$	−2.00672e9	−0.983515	−0.491758	+	0.870732i	$0.663645\pi$
$458$	2.15516e8	0.104821
$459$	−3.99743e8	−0.192946
$460$	3.40049e8	0.162888
$461$	1.93015e9	0.917567	0.458783	−	0.888548i	$-0.348285\pi$
$461$	1.93015e9	0.917567	0.458783	+	0.888548i	$0.348285\pi$
$462$	0	0
$463$	−2.08029e9	−0.974072	−0.487036	−	0.873382i	$-0.661922\pi$
$463$	−2.08029e9	−0.974072	−0.487036	+	0.873382i	$0.661922\pi$
$464$	−3.57491e8	−0.166132
$465$	−2.72895e9	−1.25867
$466$	5.39347e8	0.246898
$467$	−3.24798e9	−1.47572	−0.737861	−	0.674953i	$-0.764164\pi$
$467$	−3.24798e9	−1.47572	−0.737861	+	0.674953i	$0.764164\pi$
$468$	5.41736e8	0.244302
$469$	0	0
$470$	−6.73079e8	−0.299036
$471$	6.22156e8	0.274363
$472$	1.09280e9	0.478346
$473$	3.86338e9	1.67862
$474$	−5.04340e8	−0.217520
$475$	−3.95044e9	−1.69129
$476$	0	0
$477$	−8.03549e8	−0.338999
$478$	−3.10374e9	−1.29983
$479$	2.57410e8	0.107017	0.0535083	−	0.998567i	$-0.482960\pi$
$479$	2.57410e8	0.107017	0.0535083	+	0.998567i	$0.482960\pi$
$480$	−3.57294e8	−0.147462
$481$	4.57870e9	1.87601
$482$	−1.85028e9	−0.752616
$483$	0	0
$484$	1.43579e9	0.575617
$485$	−9.46750e8	−0.376824
$486$	1.14791e8	0.0453609
$487$	3.14339e9	1.23324	0.616619	−	0.787262i	$-0.288502\pi$
$487$	3.14339e9	1.23324	0.616619	+	0.787262i	$0.288502\pi$
$488$	−1.35918e9	−0.529429
$489$	1.53601e9	0.594037
$490$	0	0
$491$	−2.17591e9	−0.829575	−0.414788	−	0.909918i	$-0.636144\pi$
$491$	−2.17591e9	−0.829575	−0.414788	+	0.909918i	$0.636144\pi$
$492$	4.03105e8	0.152595
$493$	−1.77254e9	−0.666240
$494$	4.31900e9	1.61190
$495$	−1.90615e9	−0.706382
$496$	−1.02513e9	−0.377220
$497$	0	0
$498$	−1.11681e9	−0.405208
$499$	−3.33819e9	−1.20271	−0.601353	−	0.798983i	$-0.705372\pi$
$499$	−3.33819e9	−1.20271	−0.601353	+	0.798983i	$0.705372\pi$
$500$	−1.76749e8	−0.0632356
$501$	−6.41431e7	−0.0227886
$502$	−9.61665e8	−0.339282
$503$	−3.49207e8	−0.122347	−0.0611737	−	0.998127i	$-0.519484\pi$
$503$	−3.49207e8	−0.122347	−0.0611737	+	0.998127i	$0.519484\pi$
$504$	0	0
$505$	7.31595e9	2.52785
$506$	6.81488e8	0.233847
$507$	−1.94599e9	−0.663150
$508$	2.48734e9	0.841805
$509$	2.10089e9	0.706140	0.353070	−	0.935597i	$-0.385138\pi$
$509$	2.10089e9	0.706140	0.353070	+	0.935597i	$0.385138\pi$
$510$	−1.77156e9	−0.591370
$511$	0	0
$512$	−1.34218e8	−0.0441942
$513$	9.15175e8	0.299291
$514$	−1.85789e9	−0.603460
$515$	−2.36308e9	−0.762347
$516$	−1.03108e9	−0.330384
$517$	−1.34891e9	−0.429304
$518$	0	0
$519$	7.71442e8	0.242224
$520$	2.40083e9	0.748774
$521$	2.98842e9	0.925785	0.462892	−	0.886414i	$-0.346812\pi$
$521$	2.98842e9	0.925785	0.462892	+	0.886414i	$0.346812\pi$
$522$	5.09006e8	0.156630
$523$	3.69544e9	1.12956	0.564782	−	0.825240i	$-0.308960\pi$
$523$	3.69544e9	1.12956	0.564782	+	0.825240i	$0.308960\pi$
$524$	−1.93356e8	−0.0587080
$525$	0	0
$526$	4.26141e9	1.27674
$527$	−5.08288e9	−1.51277
$528$	−7.16048e8	−0.211701
$529$	−3.23172e9	−0.949160
$530$	−3.56112e9	−1.03901
$531$	−1.55595e9	−0.450989
$532$	0	0
$533$	−2.70866e9	−0.774835
$534$	3.87493e8	0.110121
$535$	1.14537e9	0.323377
$536$	−3.94422e7	−0.0110633
$537$	−1.14424e9	−0.318866
$538$	−2.38665e9	−0.660769
$539$	0	0
$540$	5.08725e8	0.139029
$541$	1.46115e9	0.396737	0.198369	−	0.980127i	$-0.436436\pi$
$541$	1.46115e9	0.396737	0.198369	+	0.980127i	$0.436436\pi$
$542$	−4.41866e9	−1.19204
$543$	1.38071e9	0.370086
$544$	−6.65487e8	−0.177232
$545$	−3.29408e9	−0.871659
$546$	0	0
$547$	−3.60184e9	−0.940954	−0.470477	−	0.882412i	$-0.655918\pi$
$547$	−3.60184e9	−0.940954	−0.470477	+	0.882412i	$0.655918\pi$
$548$	4.23532e8	0.109940
$549$	1.93524e9	0.499150
$550$	−4.40089e9	−1.12790
$551$	4.05806e9	1.03345
$552$	−1.81879e8	−0.0460253
$553$	0	0
$554$	1.60664e9	0.401454
$555$	4.29969e9	1.06761
$556$	1.72260e8	0.0425032
$557$	2.93389e9	0.719368	0.359684	−	0.933074i	$-0.382884\pi$
$557$	2.93389e9	0.719368	0.359684	+	0.933074i	$0.382884\pi$
$558$	1.45962e9	0.355647
$559$	6.92835e9	1.67760
$560$	0	0
$561$	−3.55035e9	−0.848988
$562$	2.51747e9	0.598257
$563$	−2.44858e8	−0.0578276	−0.0289138	−	0.999582i	$-0.509205\pi$
$563$	−2.44858e8	−0.0578276	−0.0289138	+	0.999582i	$0.509205\pi$
$564$	3.60004e8	0.0844950
$565$	6.37795e9	1.48769
$566$	−3.11078e9	−0.721127
$567$	0	0
$568$	−7.94908e8	−0.182011
$569$	7.98840e9	1.81789	0.908944	−	0.416919i	$-0.136890\pi$
$569$	7.98840e9	1.81789	0.908944	+	0.416919i	$0.136890\pi$
$570$	4.05582e9	0.917311
$571$	−2.15568e9	−0.484572	−0.242286	−	0.970205i	$-0.577897\pi$
$571$	−2.15568e9	−0.484572	−0.242286	+	0.970205i	$0.577897\pi$
$572$	4.81148e9	1.07496
$573$	−3.92114e9	−0.870705
$574$	0	0
$575$	−1.11785e9	−0.245214
$576$	1.91103e8	0.0416667
$577$	2.84273e9	0.616056	0.308028	−	0.951377i	$-0.400331\pi$
$577$	2.84273e9	0.616056	0.308028	+	0.951377i	$0.400331\pi$
$578$	−1.69481e7	−0.00365069
$579$	8.30743e8	0.177866
$580$	2.25578e9	0.480064
$581$	0	0
$582$	5.06381e8	0.106475
$583$	−7.13679e9	−1.49164
$584$	−2.38802e9	−0.496128
$585$	−3.41838e9	−0.705951
$586$	6.56304e8	0.134730
$587$	−1.27323e9	−0.259821	−0.129910	−	0.991526i	$-0.541469\pi$
$587$	−1.27323e9	−0.259821	−0.129910	+	0.991526i	$0.541469\pi$
$588$	0	0
$589$	1.16368e10	2.34655
$590$	−6.89558e9	−1.38226
$591$	−1.71784e9	−0.342316
$592$	1.61518e9	0.319960
$593$	1.00591e10	1.98093	0.990464	−	0.137768i	$-0.0439929\pi$
$593$	1.00591e10	1.98093	0.990464	+	0.137768i	$0.0439929\pi$
$594$	1.01953e9	0.199594
$595$	0	0
$596$	3.11243e9	0.602196
$597$	−8.51785e8	−0.163840
$598$	1.22214e9	0.233704
$599$	1.34546e9	0.255785	0.127893	−	0.991788i	$-0.459179\pi$
$599$	1.34546e9	0.255785	0.127893	+	0.991788i	$0.459179\pi$
$600$	1.17454e9	0.221992
$601$	−3.26475e9	−0.613465	−0.306732	−	0.951796i	$-0.599236\pi$
$601$	−3.26475e9	−0.613465	−0.306732	+	0.951796i	$0.599236\pi$
$602$	0	0
$603$	5.61589e7	0.0104306
$604$	2.12139e9	0.391734
$605$	−9.05992e9	−1.66334
$606$	−3.91302e9	−0.714263
$607$	−2.44844e9	−0.444353	−0.222177	−	0.975006i	$-0.571316\pi$
$607$	−2.44844e9	−0.444353	−0.222177	+	0.975006i	$0.571316\pi$
$608$	1.52357e9	0.274916
$609$	0	0
$610$	8.57647e9	1.52987
$611$	−2.41905e9	−0.429042
$612$	9.47539e8	0.167096
$613$	5.68631e9	0.997054	0.498527	−	0.866874i	$-0.333874\pi$
$613$	5.68631e9	0.997054	0.498527	+	0.866874i	$0.333874\pi$
$614$	−1.27083e9	−0.221563
$615$	−2.54361e9	−0.440947
$616$	0	0
$617$	−1.09146e10	−1.87072	−0.935361	−	0.353695i	$-0.884925\pi$
$617$	−1.09146e10	−1.87072	−0.935361	+	0.353695i	$0.884925\pi$
$618$	1.26392e9	0.215407
$619$	−5.00460e8	−0.0848110	−0.0424055	−	0.999100i	$-0.513502\pi$
$619$	−5.00460e8	−0.0848110	−0.0424055	+	0.999100i	$0.513502\pi$
$620$	6.46863e9	1.09004
$621$	2.58965e8	0.0433931
$622$	4.44176e9	0.740097
$623$	0	0
$624$	−1.28412e9	−0.211572
$625$	−5.52249e9	−0.904804
$626$	6.81661e9	1.11060
$627$	8.12821e9	1.31692
$628$	−1.47474e9	−0.237606
$629$	8.00850e9	1.28314
$630$	0	0
$631$	4.24339e9	0.672373	0.336186	−	0.941795i	$-0.390863\pi$
$631$	4.24339e9	0.672373	0.336186	+	0.941795i	$0.390863\pi$
$632$	1.19547e9	0.188378
$633$	3.26054e8	0.0510947
$634$	−3.75003e9	−0.584417
$635$	−1.56952e10	−2.43253
$636$	1.90471e9	0.293581
$637$	0	0
$638$	4.52078e9	0.689194
$639$	1.13181e9	0.171602
$640$	8.46919e8	0.127706
$641$	−5.82839e9	−0.874068	−0.437034	−	0.899445i	$-0.643971\pi$
$641$	−5.82839e9	−0.874068	−0.437034	+	0.899445i	$0.643971\pi$
$642$	−6.12617e8	−0.0913727
$643$	−8.45573e9	−1.25433	−0.627166	−	0.778886i	$-0.715785\pi$
$643$	−8.45573e9	−1.25433	−0.627166	+	0.778886i	$0.715785\pi$
$644$	0	0
$645$	6.50616e9	0.954697
$646$	7.55427e9	1.10250
$647$	−1.91911e9	−0.278570	−0.139285	−	0.990252i	$-0.544480\pi$
$647$	−1.91911e9	−0.278570	−0.139285	+	0.990252i	$0.544480\pi$
$648$	−2.72098e8	−0.0392837
$649$	−1.38193e10	−1.98441
$650$	−7.89229e9	−1.12721
$651$	0	0
$652$	−3.64092e9	−0.514451
$653$	1.12995e10	1.58804	0.794021	−	0.607890i	$-0.207984\pi$
$653$	1.12995e10	1.58804	0.794021	+	0.607890i	$0.207984\pi$
$654$	1.76188e9	0.246294
$655$	1.22008e9	0.169646
$656$	−9.55508e8	−0.132151
$657$	3.40014e9	0.467754
$658$	0	0
$659$	−3.23836e9	−0.440784	−0.220392	−	0.975411i	$-0.570734\pi$
$659$	−3.23836e9	−0.440784	−0.220392	+	0.975411i	$0.570734\pi$
$660$	4.51829e9	0.611744
$661$	7.19156e9	0.968541	0.484271	−	0.874918i	$-0.339085\pi$
$661$	7.19156e9	0.968541	0.484271	+	0.874918i	$0.339085\pi$
$662$	−1.99083e9	−0.266705
$663$	−6.36698e9	−0.848470
$664$	2.64726e9	0.350920
$665$	0	0
$666$	−2.29974e9	−0.301661
$667$	1.14830e9	0.149836
$668$	1.52043e8	0.0197355
$669$	7.58228e9	0.979058
$670$	2.48882e8	0.0319691
$671$	1.71880e10	2.19632
$672$	0	0
$673$	−6.55028e9	−0.828337	−0.414168	−	0.910200i	$-0.635928\pi$
$673$	−6.55028e9	−0.828337	−0.414168	+	0.910200i	$0.635928\pi$
$674$	−4.69458e9	−0.590592
$675$	−1.67234e9	−0.209296
$676$	4.61271e9	0.574305
$677$	1.03838e10	1.28616	0.643082	−	0.765797i	$-0.277655\pi$
$677$	1.03838e10	1.28616	0.643082	+	0.765797i	$0.277655\pi$
$678$	−3.41132e9	−0.420358
$679$	0	0
$680$	4.19924e9	0.512141
$681$	−4.42703e9	−0.537153
$682$	1.29637e10	1.56489
$683$	1.26736e9	0.152205	0.0761024	−	0.997100i	$-0.475752\pi$
$683$	1.26736e9	0.152205	0.0761024	+	0.997100i	$0.475752\pi$
$684$	−2.16930e9	−0.259193
$685$	−2.67250e9	−0.317689
$686$	0	0
$687$	7.27366e8	0.0855864
$688$	2.44404e9	0.286121
$689$	−1.27987e10	−1.49073
$690$	1.14767e9	0.132998
$691$	1.49494e10	1.72366	0.861829	−	0.507199i	$-0.169319\pi$
$691$	1.49494e10	1.72366	0.861829	+	0.507199i	$0.169319\pi$
$692$	−1.82860e9	−0.209772
$693$	0	0
$694$	9.72056e8	0.110391
$695$	−1.08697e9	−0.122820
$696$	−1.20653e9	−0.135646
$697$	−4.73766e9	−0.529967
$698$	−7.33170e9	−0.816039
$699$	1.82029e9	0.201591
$700$	0	0
$701$	−1.40054e10	−1.53562	−0.767808	−	0.640680i	$-0.778653\pi$
$701$	−1.40054e10	−1.53562	−0.767808	+	0.640680i	$0.778653\pi$
$702$	1.82836e9	0.199472
$703$	−1.83347e10	−1.99036
$704$	1.69730e9	0.183339
$705$	−2.27164e9	−0.244162
$706$	1.28469e9	0.137399
$707$	0	0
$708$	3.68819e9	0.390568
$709$	−1.38423e10	−1.45864	−0.729319	−	0.684173i	$-0.760163\pi$
$709$	−1.38423e10	−1.45864	−0.729319	+	0.684173i	$0.760163\pi$
$710$	5.01590e9	0.525950
$711$	−1.70215e9	−0.177605
$712$	−9.18503e8	−0.0953676
$713$	3.29284e9	0.340218
$714$	0	0
$715$	−3.03606e10	−3.10627
$716$	2.71228e9	0.276146
$717$	−1.04751e10	−1.06131
$718$	6.87639e9	0.693306
$719$	−1.47656e10	−1.48149	−0.740745	−	0.671786i	$-0.765527\pi$
$719$	−1.47656e10	−1.48149	−0.740745	+	0.671786i	$0.765527\pi$
$720$	−1.20587e9	−0.120402
$721$	0	0
$722$	−1.01438e10	−1.00305
$723$	−6.24470e9	−0.614508
$724$	−3.27279e9	−0.320504
$725$	−7.41546e9	−0.722695
$726$	4.84581e9	0.469989
$727$	1.82026e10	1.75696	0.878481	−	0.477777i	$-0.158557\pi$
$727$	1.82026e10	1.75696	0.878481	+	0.477777i	$0.158557\pi$
$728$	0	0
$729$	3.87420e8	0.0370370
$730$	1.50685e10	1.43364
$731$	1.21182e10	1.14743
$732$	−4.58723e9	−0.432277
$733$	1.09152e10	1.02369	0.511843	−	0.859079i	$-0.328963\pi$
$733$	1.09152e10	1.02369	0.511843	+	0.859079i	$0.328963\pi$
$734$	3.02109e9	0.281986
$735$	0	0
$736$	4.31122e8	0.0398591
$737$	4.98780e8	0.0458958
$738$	1.36048e9	0.124593
$739$	−1.29390e10	−1.17936	−0.589680	−	0.807637i	$-0.700746\pi$
$739$	−1.29390e10	−1.17936	−0.589680	+	0.807637i	$0.700746\pi$
$740$	−1.01919e10	−0.924576
$741$	1.45766e10	1.31611
$742$	0	0
$743$	8.91147e9	0.797056	0.398528	−	0.917156i	$-0.369521\pi$
$743$	8.91147e9	0.797056	0.398528	+	0.917156i	$0.369521\pi$
$744$	−3.45983e9	−0.307999
$745$	−1.96396e10	−1.74014
$746$	−6.10959e9	−0.538798
$747$	−3.76924e9	−0.330851
$748$	8.41565e9	0.735245
$749$	0	0
$750$	−5.96528e8	−0.0516317
$751$	−3.37584e9	−0.290832	−0.145416	−	0.989371i	$-0.546452\pi$
$751$	−3.37584e9	−0.290832	−0.145416	+	0.989371i	$0.546452\pi$
$752$	−8.53344e8	−0.0731748
$753$	−3.24562e9	−0.277023
$754$	8.10729e9	0.688773
$755$	−1.33861e10	−1.13198
$756$	0	0
$757$	4.09781e9	0.343333	0.171667	−	0.985155i	$-0.445085\pi$
$757$	4.09781e9	0.343333	0.171667	+	0.985155i	$0.445085\pi$
$758$	−6.12619e9	−0.510915
$759$	2.30002e9	0.190935
$760$	−9.61379e9	−0.794414
$761$	−8.72641e9	−0.717777	−0.358888	−	0.933380i	$-0.616844\pi$
$761$	−8.72641e9	−0.717777	−0.358888	+	0.933380i	$0.616844\pi$
$762$	8.39476e9	0.687331
$763$	0	0
$764$	9.29455e9	0.754053
$765$	−5.97900e9	−0.482852
$766$	8.76624e9	0.704714
$767$	−2.47828e10	−1.98320
$768$	−4.52985e8	−0.0360844
$769$	−2.27000e10	−1.80005	−0.900024	−	0.435840i	$-0.856451\pi$
$769$	−2.27000e10	−1.80005	−0.900024	+	0.435840i	$0.856451\pi$
$770$	0	0
$771$	−6.27037e9	−0.492723
$772$	−1.96917e9	−0.154036
$773$	1.90370e10	1.48242	0.741209	−	0.671274i	$-0.234253\pi$
$773$	1.90370e10	1.48242	0.741209	+	0.671274i	$0.234253\pi$
$774$	−3.47990e9	−0.269757
$775$	−2.12644e10	−1.64096
$776$	−1.20031e9	−0.0922099
$777$	0	0
$778$	−1.11943e10	−0.852249
$779$	1.08464e10	0.822065
$780$	8.10282e9	0.611371
$781$	1.00523e10	0.755069
$782$	2.13761e9	0.159847
$783$	1.71790e9	0.127888
$784$	0	0
$785$	9.30566e9	0.686599
$786$	−6.52576e8	−0.0479349
$787$	2.27094e10	1.66071	0.830357	−	0.557231i	$-0.188136\pi$
$787$	2.27094e10	1.66071	0.830357	+	0.557231i	$0.188136\pi$
$788$	4.07192e9	0.296454
$789$	1.43822e10	1.04245
$790$	−7.54348e9	−0.544348
$791$	0	0
$792$	−2.41666e9	−0.172853
$793$	3.08239e10	2.19498
$794$	−1.27520e10	−0.904079
$795$	−1.20188e10	−0.848350
$796$	2.01905e9	0.141890
$797$	−5.57990e9	−0.390411	−0.195206	−	0.980762i	$-0.562537\pi$
$797$	−5.57990e9	−0.390411	−0.195206	+	0.980762i	$0.562537\pi$
$798$	0	0
$799$	−4.23110e9	−0.293454
$800$	−2.78409e9	−0.192251
$801$	1.30779e9	0.0899134
$802$	6.68257e9	0.457439
$803$	3.01986e10	2.05818
$804$	−1.33117e8	−0.00903314
$805$	0	0
$806$	2.32483e10	1.56393
$807$	−8.05493e9	−0.539516
$808$	9.27532e9	0.618570
$809$	−9.67457e8	−0.0642409	−0.0321205	−	0.999484i	$-0.510226\pi$
$809$	−9.67457e8	−0.0642409	−0.0321205	+	0.999484i	$0.510226\pi$
$810$	1.71695e9	0.113517
$811$	2.31593e10	1.52459	0.762295	−	0.647229i	$-0.224072\pi$
$811$	2.31593e10	1.52459	0.762295	+	0.647229i	$0.224072\pi$
$812$	0	0
$813$	−1.49130e10	−0.973301
$814$	−2.04254e10	−1.32735
$815$	2.29743e10	1.48659
$816$	−2.24602e9	−0.144710
$817$	−2.77435e10	−1.77986
$818$	−1.79972e10	−1.14966
$819$	0	0
$820$	6.02929e9	0.381872
$821$	−1.86525e10	−1.17635	−0.588174	−	0.808735i	$-0.700153\pi$
$821$	−1.86525e10	−1.17635	−0.588174	+	0.808735i	$0.700153\pi$
$822$	1.42942e9	0.0897654
$823$	−1.44689e10	−0.904766	−0.452383	−	0.891824i	$-0.649426\pi$
$823$	−1.44689e10	−0.904766	−0.452383	+	0.891824i	$0.649426\pi$
$824$	−2.99596e9	−0.186548
$825$	−1.48530e10	−0.920928
$826$	0	0
$827$	2.18964e10	1.34618	0.673092	−	0.739559i	$-0.264966\pi$
$827$	2.18964e10	1.34618	0.673092	+	0.739559i	$0.264966\pi$
$828$	−6.13843e8	−0.0375795
$829$	5.93982e9	0.362103	0.181052	−	0.983474i	$-0.442050\pi$
$829$	5.93982e9	0.362103	0.181052	+	0.983474i	$0.442050\pi$
$830$	−1.67043e10	−1.01404
$831$	5.42242e9	0.327786
$832$	3.04383e9	0.183227
$833$	0	0
$834$	5.81377e8	0.0347038
$835$	−9.59395e8	−0.0570289
$836$	−1.92669e10	−1.14048
$837$	4.92620e9	0.290384
$838$	−1.40408e10	−0.824208
$839$	−2.57848e9	−0.150729	−0.0753646	−	0.997156i	$-0.524012\pi$
$839$	−2.57848e9	−0.150729	−0.0753646	+	0.997156i	$0.524012\pi$
$840$	0	0
$841$	−9.63240e9	−0.558404
$842$	−1.25898e10	−0.726821
$843$	8.49647e9	0.488475
$844$	−7.72868e8	−0.0442493
$845$	−2.91063e10	−1.65955
$846$	1.21501e9	0.0689899
$847$	0	0
$848$	−4.51486e9	−0.254249
$849$	−1.04989e10	−0.588798
$850$	−1.38042e10	−0.770985
$851$	−5.18814e9	−0.288575
$852$	−2.68281e9	−0.148611
$853$	2.41906e10	1.33452	0.667259	−	0.744826i	$-0.267467\pi$
$853$	2.41906e10	1.33452	0.667259	+	0.744826i	$0.267467\pi$
$854$	0	0
$855$	1.36884e10	0.748981
$856$	1.45213e9	0.0791311
$857$	5.94867e9	0.322840	0.161420	−	0.986886i	$-0.448393\pi$
$857$	5.94867e9	0.322840	0.161420	+	0.986886i	$0.448393\pi$
$858$	1.62387e10	0.877702
$859$	1.18132e10	0.635904	0.317952	−	0.948107i	$-0.397005\pi$
$859$	1.18132e10	0.635904	0.317952	+	0.948107i	$0.397005\pi$
$860$	−1.54220e10	−0.826792
$861$	0	0
$862$	−1.40077e10	−0.744887
$863$	−7.31384e8	−0.0387354	−0.0193677	−	0.999812i	$-0.506165\pi$
$863$	−7.31384e8	−0.0387354	−0.0193677	+	0.999812i	$0.506165\pi$
$864$	6.44973e8	0.0340207
$865$	1.15386e10	0.606171
$866$	−6.94997e9	−0.363639
$867$	−5.72000e7	−0.00298077
$868$	0	0
$869$	−1.51178e10	−0.781482
$870$	7.61327e9	0.391971
$871$	8.94482e8	0.0458678
$872$	−4.17631e9	−0.213297
$873$	1.70903e9	0.0869363
$874$	−4.89387e9	−0.247949
$875$	0	0
$876$	−8.05958e9	−0.405087
$877$	−3.16647e10	−1.58517	−0.792587	−	0.609759i	$-0.791266\pi$
$877$	−3.16647e10	−1.58517	−0.792587	+	0.609759i	$0.791266\pi$
$878$	−9.90490e9	−0.493877
$879$	2.21503e9	0.110006
$880$	−1.07100e10	−0.529786
$881$	−1.90621e10	−0.939192	−0.469596	−	0.882881i	$-0.655600\pi$
$881$	−1.90621e10	−0.939192	−0.469596	+	0.882881i	$0.655600\pi$
$882$	0	0
$883$	−2.91186e10	−1.42334	−0.711670	−	0.702514i	$-0.752061\pi$
$883$	−2.91186e10	−1.42334	−0.711670	+	0.702514i	$0.752061\pi$
$884$	1.50921e10	0.734796
$885$	−2.32726e10	−1.12861
$886$	−2.70013e10	−1.30427
$887$	1.70841e9	0.0821979	0.0410989	−	0.999155i	$-0.486914\pi$
$887$	1.70841e9	0.0821979	0.0410989	+	0.999155i	$0.486914\pi$
$888$	5.45124e9	0.261246
$889$	0	0
$890$	5.79579e9	0.275580
$891$	3.44091e9	0.162968
$892$	−1.79728e10	−0.847889
$893$	9.68672e9	0.455194
$894$	1.05045e10	0.491691
$895$	−1.71146e10	−0.797967
$896$	0	0
$897$	4.12472e9	0.190819
$898$	−1.70076e10	−0.783746
$899$	2.18437e10	1.00269
$900$	3.96406e9	0.181256
$901$	−2.23859e10	−1.01962
$902$	1.20832e10	0.548226
$903$	0	0
$904$	8.08610e9	0.364041
$905$	2.06514e10	0.926146
$906$	7.15970e9	0.319850
$907$	−4.73888e9	−0.210887	−0.105444	−	0.994425i	$-0.533626\pi$
$907$	−4.73888e9	−0.210887	−0.105444	+	0.994425i	$0.533626\pi$
$908$	1.04937e10	0.465188
$909$	−1.32065e10	−0.583194
$910$	0	0
$911$	−2.73789e10	−1.19978	−0.599891	−	0.800082i	$-0.704789\pi$
$911$	−2.73789e10	−1.19978	−0.599891	+	0.800082i	$0.704789\pi$
$912$	5.14205e9	0.224468
$913$	−3.34769e10	−1.45578
$914$	1.60538e10	0.695450
$915$	2.89456e10	1.24913
$916$	−1.72413e9	−0.0741200
$917$	0	0
$918$	3.19794e9	0.136434
$919$	9.71719e8	0.0412987	0.0206494	−	0.999787i	$-0.493427\pi$
$919$	9.71719e8	0.0412987	0.0206494	+	0.999787i	$0.493427\pi$
$920$	−2.72039e9	−0.115179
$921$	−4.28905e9	−0.180906
$922$	−1.54412e10	−0.648818
$923$	1.80272e10	0.754608
$924$	0	0
$925$	3.35038e10	1.39187
$926$	1.66423e10	0.688773
$927$	4.26573e9	0.175879
$928$	2.85993e9	0.117473
$929$	4.49858e9	0.184086	0.0920429	−	0.995755i	$-0.470660\pi$
$929$	4.49858e9	0.184086	0.0920429	+	0.995755i	$0.470660\pi$
$930$	2.18316e10	0.890012
$931$	0	0
$932$	−4.31477e9	−0.174583
$933$	1.49909e10	0.604287
$934$	2.59839e10	1.04349
$935$	−5.31030e10	−2.12461
$936$	−4.33389e9	−0.172748
$937$	−2.77390e10	−1.10155	−0.550773	−	0.834655i	$-0.685667\pi$
$937$	−2.77390e10	−1.10155	−0.550773	+	0.834655i	$0.685667\pi$
$938$	0	0
$939$	2.30061e10	0.906802
$940$	5.38463e9	0.211450
$941$	3.87277e10	1.51516	0.757579	−	0.652744i	$-0.226382\pi$
$941$	3.87277e10	1.51516	0.757579	+	0.652744i	$0.226382\pi$
$942$	−4.97725e9	−0.194004
$943$	3.06919e9	0.119188
$944$	−8.74237e9	−0.338242
$945$	0	0
$946$	−3.09070e10	−1.18697
$947$	4.08030e10	1.56123	0.780615	−	0.625012i	$-0.214906\pi$
$947$	4.08030e10	1.56123	0.780615	+	0.625012i	$0.214906\pi$
$948$	4.03472e9	0.153810
$949$	5.41564e10	2.05692
$950$	3.16035e10	1.19592
$951$	−1.26564e10	−0.477174
$952$	0	0
$953$	3.64067e10	1.36256	0.681280	−	0.732023i	$-0.261423\pi$
$953$	3.64067e10	1.36256	0.681280	+	0.732023i	$0.261423\pi$
$954$	6.42839e9	0.239708
$955$	−5.86490e10	−2.17896
$956$	2.48299e10	0.919122
$957$	1.52576e10	0.562724
$958$	−2.05928e9	−0.0756722
$959$	0	0
$960$	2.85835e9	0.104272
$961$	3.51259e10	1.27672
$962$	−3.66296e10	−1.32654
$963$	−2.06758e9	−0.0746055
$964$	1.48023e10	0.532180
$965$	1.24255e10	0.445112
$966$	0	0
$967$	1.98247e10	0.705039	0.352519	−	0.935804i	$-0.385325\pi$
$967$	1.98247e10	0.705039	0.352519	+	0.935804i	$0.385325\pi$
$968$	−1.14864e10	−0.407023
$969$	2.54956e10	0.900187
$970$	7.57400e9	0.266455
$971$	1.77197e10	0.621138	0.310569	−	0.950551i	$-0.399480\pi$
$971$	1.77197e10	0.621138	0.310569	+	0.950551i	$0.399480\pi$
$972$	−9.18330e8	−0.0320750
$973$	0	0
$974$	−2.51471e10	−0.872031
$975$	−2.66365e10	−0.920367
$976$	1.08734e10	0.374363
$977$	2.10651e10	0.722658	0.361329	−	0.932438i	$-0.382323\pi$
$977$	2.10651e10	0.722658	0.361329	+	0.932438i	$0.382323\pi$
$978$	−1.22881e10	−0.420047
$979$	1.16153e10	0.395630
$980$	0	0
$981$	5.94635e9	0.201099
$982$	1.74073e10	0.586598
$983$	−2.51086e9	−0.0843111	−0.0421556	−	0.999111i	$-0.513423\pi$
$983$	−2.51086e9	−0.0843111	−0.0421556	+	0.999111i	$0.513423\pi$
$984$	−3.22484e9	−0.107901
$985$	−2.56940e10	−0.856652
$986$	1.41803e10	0.471103
$987$	0	0
$988$	−3.45520e10	−1.13979
$989$	−7.85053e9	−0.258055
$990$	1.52492e10	0.499487
$991$	3.97074e10	1.29603	0.648013	−	0.761629i	$-0.275600\pi$
$991$	3.97074e10	1.29603	0.648013	+	0.761629i	$0.275600\pi$
$992$	8.20107e9	0.266735
$993$	−6.71905e9	−0.217764
$994$	0	0
$995$	−1.27403e10	−0.410013
$996$	8.93450e9	0.286525
$997$	−3.22916e9	−0.103195	−0.0515973	−	0.998668i	$-0.516431\pi$
$997$	−3.22916e9	−0.103195	−0.0515973	+	0.998668i	$0.516431\pi$
$998$	2.67055e10	0.850442
$999$	−7.76163e9	−0.246305

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.8.a.v.1.1		3
7.2	even	3		42.8.e.e.25.3	✓	6
7.3	odd	6		294.8.e.ba.79.1		6
7.4	even	3		42.8.e.e.37.3	yes	6
7.5	odd	6		294.8.e.ba.67.1		6
7.6	odd	2		294.8.a.w.1.3		3
21.2	odd	6		126.8.g.h.109.1		6
21.11	odd	6		126.8.g.h.37.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.8.e.e.25.3	✓	6	7.2	even	3
42.8.e.e.37.3	yes	6	7.4	even	3
126.8.g.h.37.1		6	21.11	odd	6
126.8.g.h.109.1		6	21.2	odd	6
294.8.a.v.1.1		3	1.1	even	1	trivial
294.8.a.w.1.3		3	7.6	odd	2
294.8.e.ba.67.1		6	7.5	odd	6
294.8.e.ba.79.1		6	7.3	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	294.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -403.842 q^{5} +216.000 q^{6} -512.000 q^{8} +729.000 q^{9} +3230.74 q^{10} +6474.68 q^{11} -1728.00 q^{12} +11611.3 q^{13} +10903.7 q^{15} +4096.00 q^{16} +20309.0 q^{17} -5832.00 q^{18} -46495.7 q^{19} -25845.9 q^{20} -51797.4 q^{22} -13156.8 q^{23} +13824.0 q^{24} +84963.6 q^{25} -92890.3 q^{26} -19683.0 q^{27} -87278.1 q^{29} -87229.9 q^{30} -250277. q^{31} -32768.0 q^{32} -174816. q^{33} -162472. q^{34} +46656.0 q^{36} +394332. q^{37} +371966. q^{38} -313505. q^{39} +206767. q^{40} -233278. q^{41} +596690. q^{43} +414379. q^{44} -294401. q^{45} +105254. q^{46} -208336. q^{47} -110592. q^{48} -679709. q^{50} -548344. q^{51} +743123. q^{52} -1.10226e6 q^{53} +157464. q^{54} -2.61475e6 q^{55} +1.25538e6 q^{57} +698225. q^{58} -2.13437e6 q^{59} +697839. q^{60} +2.65465e6 q^{61} +2.00222e6 q^{62} +262144. q^{64} -4.68913e6 q^{65} +1.39853e6 q^{66} +77035.5 q^{67} +1.29978e6 q^{68} +355233. q^{69} +1.55255e6 q^{71} -373248. q^{72} +4.66411e6 q^{73} -3.15465e6 q^{74} -2.29402e6 q^{75} -2.97573e6 q^{76} +2.50804e6 q^{78} -2.33491e6 q^{79} -1.65414e6 q^{80} +531441. q^{81} +1.86623e6 q^{82} -5.17043e6 q^{83} -8.20165e6 q^{85} -4.77352e6 q^{86} +2.35651e6 q^{87} -3.31504e6 q^{88} +1.79395e6 q^{89} +2.35521e6 q^{90} -842034. q^{92} +6.75748e6 q^{93} +1.66669e6 q^{94} +1.87769e7 q^{95} +884736. q^{96} +2.34436e6 q^{97} +4.72004e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 24 q^{2} - 81 q^{3} + 192 q^{4} - 110 q^{5} + 648 q^{6} - 1536 q^{8} + 2187 q^{9} + 880 q^{10} + 548 q^{11} - 5184 q^{12} + 9949 q^{13} + 2970 q^{15} + 12288 q^{16} + 20972 q^{17} - 17496 q^{18} - 28383 q^{19}+ \cdots + 399492 q^{99}+O(q^{100}) \) 3 * q - 24 * q^2 - 81 * q^3 + 192 * q^4 - 110 * q^5 + 648 * q^6 - 1536 * q^8 + 2187 * q^9 + 880 * q^10 + 548 * q^11 - 5184 * q^12 + 9949 * q^13 + 2970 * q^15 + 12288 * q^16 + 20972 * q^17 - 17496 * q^18 - 28383 * q^19 - 7040 * q^20 - 4384 * q^22 + 32732 * q^23 + 41472 * q^24 - 22745 * q^25 - 79592 * q^26 - 59049 * q^27 + 117088 * q^29 - 23760 * q^30 + 147865 * q^31 - 98304 * q^32 - 14796 * q^33 - 167776 * q^34 + 139968 * q^36 + 367503 * q^37 + 227064 * q^38 - 268623 * q^39 + 56320 * q^40 - 1437954 * q^41 + 749397 * q^43 + 35072 * q^44 - 80190 * q^45 - 261856 * q^46 - 741486 * q^47 - 331776 * q^48 + 181960 * q^50 - 566244 * q^51 + 636736 * q^52 - 1032432 * q^53 + 472392 * q^54 - 3996280 * q^55 + 766341 * q^57 - 936704 * q^58 - 2389238 * q^59 + 190080 * q^60 + 1238746 * q^61 - 1182920 * q^62 + 786432 * q^64 - 3798390 * q^65 + 118368 * q^66 - 2462497 * q^67 + 1342208 * q^68 - 883764 * q^69 - 636262 * q^71 - 1119744 * q^72 + 4609961 * q^73 - 2940024 * q^74 + 614115 * q^75 - 1816512 * q^76 + 2148984 * q^78 - 6152849 * q^79 - 450560 * q^80 + 1594323 * q^81 + 11503632 * q^82 - 12029884 * q^83 - 9136540 * q^85 - 5995176 * q^86 - 3161376 * q^87 - 280576 * q^88 + 10646976 * q^89 + 641520 * q^90 + 2094848 * q^92 - 3992355 * q^93 + 5931888 * q^94 + 21560930 * q^95 + 2654208 * q^96 + 2281472 * q^97 + 399492 * q^99

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