LMFDB - Embedded newform 121.8.a.f.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [121,8,Mod(1,121)] 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("121.1"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(121, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	121.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$37.7985880836$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 742x^{4} + 146056x^{2} - 6022080 $ x^6 - 742x^4 + 146056x^2 - 6022080
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$7.47800$ of defining polynomial
Character	$\chi$	$=$	121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+7.47800 q^{2} -8.17483 q^{3} -72.0796 q^{4} +192.856 q^{5} -61.1314 q^{6} +1553.40 q^{7} -1496.19 q^{8} -2120.17 q^{9} +1442.17 q^{10} +589.238 q^{12} +3597.88 q^{13} +11616.3 q^{14} -1576.56 q^{15} -1962.36 q^{16} -7290.09 q^{17} -15854.6 q^{18} +41029.9 q^{19} -13901.0 q^{20} -12698.8 q^{21} -53478.9 q^{23} +12231.1 q^{24} -40931.7 q^{25} +26904.9 q^{26} +35210.4 q^{27} -111969. q^{28} +200115. q^{29} -11789.5 q^{30} +152768. q^{31} +176838. q^{32} -54515.2 q^{34} +299583. q^{35} +152821. q^{36} +408557. q^{37} +306821. q^{38} -29412.1 q^{39} -288550. q^{40} +499543. q^{41} -94961.7 q^{42} -375019. q^{43} -408887. q^{45} -399915. q^{46} +576497. q^{47} +16041.9 q^{48} +1.58952e6 q^{49} -306087. q^{50} +59595.3 q^{51} -259333. q^{52} +353020. q^{53} +263303. q^{54} -2.32419e6 q^{56} -335412. q^{57} +1.49646e6 q^{58} +1.85642e6 q^{59} +113638. q^{60} +1.36048e6 q^{61} +1.14240e6 q^{62} -3.29348e6 q^{63} +1.57358e6 q^{64} +693871. q^{65} -3.19196e6 q^{67} +525466. q^{68} +437181. q^{69} +2.24028e6 q^{70} +4.89246e6 q^{71} +3.17219e6 q^{72} -4.88895e6 q^{73} +3.05519e6 q^{74} +334610. q^{75} -2.95741e6 q^{76} -219943. q^{78} -3.34675e6 q^{79} -378451. q^{80} +4.34898e6 q^{81} +3.73558e6 q^{82} -6.31678e6 q^{83} +915325. q^{84} -1.40593e6 q^{85} -2.80439e6 q^{86} -1.63591e6 q^{87} -902602. q^{89} -3.05766e6 q^{90} +5.58896e6 q^{91} +3.85473e6 q^{92} -1.24885e6 q^{93} +4.31104e6 q^{94} +7.91284e6 q^{95} -1.44562e6 q^{96} +5.93440e6 q^{97} +1.18864e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 16 q^{3} + 716 q^{4} + 240 q^{5} + 3746 q^{9} + 27108 q^{12} - 51264 q^{14} + 88120 q^{15} + 45352 q^{16} + 81900 q^{20} - 55104 q^{23} + 108910 q^{25} + 56928 q^{26} + 73280 q^{27} - 254560 q^{31}+ \cdots + 10649568 q^{97}+O(q^{100}) $ 6 * q - 16 * q^3 + 716 * q^4 + 240 * q^5 + 3746 * q^9 + 27108 * q^12 - 51264 * q^14 + 88120 * q^15 + 45352 * q^16 + 81900 * q^20 - 55104 * q^23 + 108910 * q^25 + 56928 * q^26 + 73280 * q^27 - 254560 * q^31 - 2103776 * q^34 + 2027544 * q^36 - 252272 * q^37 + 2154240 * q^38 + 790240 * q^42 - 1092740 * q^45 + 372072 * q^47 + 7846456 * q^48 + 5017046 * q^49 + 4947636 * q^53 - 9608160 * q^56 + 3784000 * q^58 + 10205904 * q^59 + 18925140 * q^60 + 5409808 * q^64 - 11727568 * q^67 + 7645372 * q^69 + 12576640 * q^70 + 3862176 * q^71 - 5964800 * q^75 - 40017600 * q^78 + 40052040 * q^80 - 11954122 * q^81 + 23841440 * q^82 + 2122368 * q^86 + 3655008 * q^89 - 7026528 * q^91 + 29314212 * q^92 + 19011180 * q^93 + 10649568 * q^97

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 $

$2$	7.47800	0.660968	0.330484	−	0.943812i	$-0.392788\pi$
$2$	7.47800	0.660968	0.330484	+	0.943812i	$0.392788\pi$
$3$	−8.17483	−0.174805	−0.0874027	−	0.996173i	$-0.527857\pi$
$3$	−8.17483	−0.174805	−0.0874027	+	0.996173i	$0.527857\pi$
$4$	−72.0796	−0.563121
$5$	192.856	0.689982	0.344991	−	0.938606i	$-0.387882\pi$
$5$	192.856	0.689982	0.344991	+	0.938606i	$0.387882\pi$
$6$	−61.1314	−0.115541
$7$	1553.40	1.71175	0.855877	−	0.517180i	$-0.173018\pi$
$7$	1553.40	1.71175	0.855877	+	0.517180i	$0.173018\pi$
$8$	−1496.19	−1.03317
$9$	−2120.17	−0.969443
$10$	1442.17	0.456056
$11$	0	0
$11$	0	0
$12$	589.238	0.0984366
$13$	3597.88	0.454197	0.227099	−	0.973872i	$-0.427076\pi$
$13$	3597.88	0.454197	0.227099	+	0.973872i	$0.427076\pi$
$14$	11616.3	1.13141
$15$	−1576.56	−0.120612
$16$	−1962.36	−0.119773
$17$	−7290.09	−0.359883	−0.179942	−	0.983677i	$-0.557591\pi$
$17$	−7290.09	−0.359883	−0.179942	+	0.983677i	$0.557591\pi$
$18$	−15854.6	−0.640771
$19$	41029.9	1.37234	0.686171	−	0.727440i	$-0.259290\pi$
$19$	41029.9	1.37234	0.686171	+	0.727440i	$0.259290\pi$
$20$	−13901.0	−0.388543
$21$	−12698.8	−0.299224
$22$	0	0
$23$	−53478.9	−0.916505	−0.458252	−	0.888822i	$-0.651524\pi$
$23$	−53478.9	−0.916505	−0.458252	+	0.888822i	$0.651524\pi$
$24$	12231.1	0.180604
$25$	−40931.7	−0.523925
$26$	26904.9	0.300210
$27$	35210.4	0.344269
$28$	−111969.	−0.963925
$29$	200115.	1.52365	0.761827	−	0.647781i	$-0.224303\pi$
$29$	200115.	1.52365	0.761827	+	0.647781i	$0.224303\pi$
$30$	−11789.5	−0.0797209
$31$	152768.	0.921015	0.460507	−	0.887656i	$-0.347668\pi$
$31$	152768.	0.921015	0.460507	+	0.887656i	$0.347668\pi$
$32$	176838.	0.954007
$33$	0	0
$34$	−54515.2	−0.237871
$35$	299583.	1.18108
$36$	152821.	0.545914
$37$	408557.	1.32601	0.663004	−	0.748616i	$-0.269281\pi$
$37$	408557.	1.32601	0.663004	+	0.748616i	$0.269281\pi$
$38$	306821.	0.907074
$39$	−29412.1	−0.0793961
$40$	−288550.	−0.712870
$41$	499543.	1.13196	0.565978	−	0.824421i	$-0.308499\pi$
$41$	499543.	1.13196	0.565978	+	0.824421i	$0.308499\pi$
$42$	−94961.7	−0.197777
$43$	−375019.	−0.719305	−0.359653	−	0.933086i	$-0.617105\pi$
$43$	−375019.	−0.719305	−0.359653	+	0.933086i	$0.617105\pi$
$44$	0	0
$45$	−408887.	−0.668898
$46$	−399915.	−0.605780
$47$	576497.	0.809943	0.404971	−	0.914329i	$-0.367281\pi$
$47$	576497.	0.809943	0.404971	+	0.914329i	$0.367281\pi$
$48$	16041.9	0.0209369
$49$	1.58952e6	1.93010
$50$	−306087.	−0.346298
$51$	59595.3	0.0629095
$52$	−259333.	−0.255768
$53$	353020.	0.325712	0.162856	−	0.986650i	$-0.447929\pi$
$53$	353020.	0.325712	0.162856	+	0.986650i	$0.447929\pi$
$54$	263303.	0.227551
$55$	0	0
$56$	−2.32419e6	−1.76854
$57$	−335412.	−0.239893
$58$	1.49646e6	1.00709
$59$	1.85642e6	1.17678	0.588388	−	0.808579i	$-0.299763\pi$
$59$	1.85642e6	1.17678	0.588388	+	0.808579i	$0.299763\pi$
$60$	113638.	0.0679195
$61$	1.36048e6	0.767428	0.383714	−	0.923452i	$-0.374645\pi$
$61$	1.36048e6	0.767428	0.383714	+	0.923452i	$0.374645\pi$
$62$	1.14240e6	0.608761
$63$	−3.29348e6	−1.65945
$64$	1.57358e6	0.750341
$65$	693871.	0.313388
$66$	0	0
$67$	−3.19196e6	−1.29657	−0.648285	−	0.761398i	$-0.724513\pi$
$67$	−3.19196e6	−1.29657	−0.648285	+	0.761398i	$0.724513\pi$
$68$	525466.	0.202658
$69$	437181.	0.160210
$70$	2.24028e6	0.780655
$71$	4.89246e6	1.62227	0.811135	−	0.584860i	$-0.198850\pi$
$71$	4.89246e6	1.62227	0.811135	+	0.584860i	$0.198850\pi$
$72$	3.17219e6	1.00160
$73$	−4.88895e6	−1.47091	−0.735454	−	0.677575i	$-0.763031\pi$
$73$	−4.88895e6	−1.47091	−0.735454	+	0.677575i	$0.763031\pi$
$74$	3.05519e6	0.876449
$75$	334610.	0.0915849
$76$	−2.95741e6	−0.772796
$77$	0	0
$78$	−219943.	−0.0524783
$79$	−3.34675e6	−0.763711	−0.381855	−	0.924222i	$-0.624715\pi$
$79$	−3.34675e6	−0.763711	−0.381855	+	0.924222i	$0.624715\pi$
$80$	−378451.	−0.0826409
$81$	4.34898e6	0.909263
$82$	3.73558e6	0.748186
$83$	−6.31678e6	−1.21261	−0.606307	−	0.795231i	$-0.707350\pi$
$83$	−6.31678e6	−1.21261	−0.606307	+	0.795231i	$0.707350\pi$
$84$	915325.	0.168499
$85$	−1.40593e6	−0.248313
$86$	−2.80439e6	−0.475438
$87$	−1.63591e6	−0.266343
$88$	0	0
$89$	−902602.	−0.135716	−0.0678580	−	0.997695i	$-0.521616\pi$
$89$	−902602.	−0.135716	−0.0678580	+	0.997695i	$0.521616\pi$
$90$	−3.05766e6	−0.442120
$91$	5.58896e6	0.777474
$92$	3.85473e6	0.516104
$93$	−1.24885e6	−0.160998
$94$	4.31104e6	0.535346
$95$	7.91284e6	0.946891
$96$	−1.44562e6	−0.166766
$97$	5.93440e6	0.660200	0.330100	−	0.943946i	$-0.392918\pi$
$97$	5.93440e6	0.660200	0.330100	+	0.943946i	$0.392918\pi$
$98$	1.18864e7	1.27573
$99$	0	0
$100$	2.95034e6	0.295034
$101$	1.88544e7	1.82090	0.910452	−	0.413614i	$-0.135734\pi$
$101$	1.88544e7	1.82090	0.910452	+	0.413614i	$0.135734\pi$
$102$	445653.	0.0415811
$103$	−1.79503e7	−1.61860	−0.809302	−	0.587392i	$-0.800155\pi$
$103$	−1.79503e7	−1.61860	−0.809302	+	0.587392i	$0.800155\pi$
$104$	−5.38313e6	−0.469265
$105$	−2.44904e6	−0.206459
$106$	2.63989e6	0.215285
$107$	7.54117e6	0.595108	0.297554	−	0.954705i	$-0.403829\pi$
$107$	7.54117e6	0.595108	0.297554	+	0.954705i	$0.403829\pi$
$108$	−2.53795e6	−0.193865
$109$	−5.88385e6	−0.435180	−0.217590	−	0.976040i	$-0.569820\pi$
$109$	−5.88385e6	−0.435180	−0.217590	+	0.976040i	$0.569820\pi$
$110$	0	0
$111$	−3.33988e6	−0.231793
$112$	−3.04833e6	−0.205021
$113$	−1.51805e7	−0.989716	−0.494858	−	0.868974i	$-0.664780\pi$
$113$	−1.51805e7	−0.989716	−0.494858	+	0.868974i	$0.664780\pi$
$114$	−2.50821e6	−0.158561
$115$	−1.03137e7	−0.632371
$116$	−1.44242e7	−0.858002
$117$	−7.62812e6	−0.440319
$118$	1.38823e7	0.777811
$119$	−1.13244e7	−0.616031
$120$	2.35885e6	0.124614
$121$	0	0
$122$	1.01737e7	0.507245
$123$	−4.08368e6	−0.197872
$124$	−1.10114e7	−0.518643
$125$	−2.29608e7	−1.05148
$126$	−2.46287e7	−1.09684
$127$	−2.92770e6	−0.126828	−0.0634138	−	0.997987i	$-0.520199\pi$
$127$	−2.92770e6	−0.126828	−0.0634138	+	0.997987i	$0.520199\pi$
$128$	−1.08681e7	−0.458056
$129$	3.06572e6	0.125738
$130$	5.18877e6	0.207139
$131$	−2.66499e7	−1.03573	−0.517864	−	0.855463i	$-0.673273\pi$
$131$	−2.66499e7	−1.03573	−0.517864	+	0.855463i	$0.673273\pi$
$132$	0	0
$133$	6.37359e7	2.34911
$134$	−2.38695e7	−0.856991
$135$	6.79053e6	0.237539
$136$	1.09074e7	0.371822
$137$	−1.83325e7	−0.609114	−0.304557	−	0.952494i	$-0.598508\pi$
$137$	−1.83325e7	−0.609114	−0.304557	+	0.952494i	$0.598508\pi$
$138$	3.26924e6	0.105894
$139$	3.24999e7	1.02643	0.513216	−	0.858260i	$-0.328454\pi$
$139$	3.24999e7	1.02643	0.513216	+	0.858260i	$0.328454\pi$
$140$	−2.15938e7	−0.665091
$141$	−4.71277e6	−0.141582
$142$	3.65858e7	1.07227
$143$	0	0
$144$	4.16053e6	0.116113
$145$	3.85933e7	1.05129
$146$	−3.65595e7	−0.972223
$147$	−1.29941e7	−0.337392
$148$	−2.94486e7	−0.746704
$149$	4.82696e7	1.19542	0.597712	−	0.801711i	$-0.296077\pi$
$149$	4.82696e7	1.19542	0.597712	+	0.801711i	$0.296077\pi$
$150$	2.50221e6	0.0605347
$151$	−5.09805e7	−1.20499	−0.602497	−	0.798121i	$-0.705828\pi$
$151$	−5.09805e7	−1.20499	−0.602497	+	0.798121i	$0.705828\pi$
$152$	−6.13887e7	−1.41787
$153$	1.54562e7	0.348886
$154$	0	0
$155$	2.94622e7	0.635483
$156$	2.12001e6	0.0447097
$157$	−2.37164e7	−0.489103	−0.244551	−	0.969636i	$-0.578641\pi$
$157$	−2.37164e7	−0.489103	−0.244551	+	0.969636i	$0.578641\pi$
$158$	−2.50270e7	−0.504788
$159$	−2.88588e6	−0.0569363
$160$	3.41043e7	0.658247
$161$	−8.30743e7	−1.56883
$162$	3.25216e7	0.600994
$163$	6.01859e7	1.08852	0.544262	−	0.838915i	$-0.316810\pi$
$163$	6.01859e7	1.08852	0.544262	+	0.838915i	$0.316810\pi$
$164$	−3.60068e7	−0.637428
$165$	0	0
$166$	−4.72369e7	−0.801499
$167$	−9.45920e7	−1.57162	−0.785809	−	0.618469i	$-0.787753\pi$
$167$	−9.45920e7	−1.57162	−0.785809	+	0.618469i	$0.787753\pi$
$168$	1.89999e7	0.309150
$169$	−4.98038e7	−0.793705
$170$	−1.05136e7	−0.164127
$171$	−8.69904e7	−1.33041
$172$	2.70312e7	0.405056
$173$	−3.88573e7	−0.570574	−0.285287	−	0.958442i	$-0.592089\pi$
$173$	−3.88573e7	−0.570574	−0.285287	+	0.958442i	$0.592089\pi$
$174$	−1.22333e7	−0.176044
$175$	−6.35834e7	−0.896831
$176$	0	0
$177$	−1.51759e7	−0.205707
$178$	−6.74965e6	−0.0897039
$179$	3.07491e7	0.400725	0.200362	−	0.979722i	$-0.435788\pi$
$179$	3.07491e7	0.400725	0.200362	+	0.979722i	$0.435788\pi$
$180$	2.94724e7	0.376671
$181$	1.34787e7	0.168955	0.0844777	−	0.996425i	$-0.473078\pi$
$181$	1.34787e7	0.168955	0.0844777	+	0.996425i	$0.473078\pi$
$182$	4.17942e7	0.513885
$183$	−1.11217e7	−0.134150
$184$	8.00148e7	0.946908
$185$	7.87925e7	0.914921
$186$	−9.33892e6	−0.106415
$187$	0	0
$188$	−4.15536e7	−0.456096
$189$	5.46960e7	0.589304
$190$	5.91722e7	0.625865
$191$	4.59603e7	0.477272	0.238636	−	0.971109i	$-0.423300\pi$
$191$	4.59603e7	0.477272	0.238636	+	0.971109i	$0.423300\pi$
$192$	−1.28637e7	−0.131164
$193$	3.40597e6	0.0341028	0.0170514	−	0.999855i	$-0.494572\pi$
$193$	3.40597e6	0.0341028	0.0170514	+	0.999855i	$0.494572\pi$
$194$	4.43774e7	0.436371
$195$	−5.67228e6	−0.0547819
$196$	−1.14572e8	−1.08688
$197$	1.60223e8	1.49312	0.746559	−	0.665319i	$-0.231704\pi$
$197$	1.60223e8	1.49312	0.746559	+	0.665319i	$0.231704\pi$
$198$	0	0
$199$	−4.80279e7	−0.432024	−0.216012	−	0.976391i	$-0.569305\pi$
$199$	−4.80279e7	−0.432024	−0.216012	+	0.976391i	$0.569305\pi$
$200$	6.12417e7	0.541306
$201$	2.60938e7	0.226647
$202$	1.40993e8	1.20356
$203$	3.10859e8	2.60812
$204$	−4.29560e6	−0.0354257
$205$	9.63397e7	0.781028
$206$	−1.34232e8	−1.06985
$207$	1.13384e8	0.888499
$208$	−7.06032e6	−0.0544005
$209$	0	0
$210$	−1.83139e7	−0.136463
$211$	1.11962e8	0.820504	0.410252	−	0.911972i	$-0.365441\pi$
$211$	1.11962e8	0.820504	0.410252	+	0.911972i	$0.365441\pi$
$212$	−2.54456e7	−0.183416
$213$	−3.99950e7	−0.283581
$214$	5.63928e7	0.393347
$215$	−7.23245e7	−0.496307
$216$	−5.26816e7	−0.355690
$217$	2.37310e8	1.57655
$218$	−4.39994e7	−0.287640
$219$	3.99663e7	0.257122
$220$	0	0
$221$	−2.62288e7	−0.163458
$222$	−2.49756e7	−0.153208
$223$	1.18645e8	0.716442	0.358221	−	0.933637i	$-0.383383\pi$
$223$	1.18645e8	0.716442	0.358221	+	0.933637i	$0.383383\pi$
$224$	2.74701e8	1.63302
$225$	8.67822e7	0.507916
$226$	−1.13519e8	−0.654170
$227$	2.10716e7	0.119566	0.0597829	−	0.998211i	$-0.480959\pi$
$227$	2.10716e7	0.119566	0.0597829	+	0.998211i	$0.480959\pi$
$228$	2.41764e7	0.135089
$229$	1.18794e8	0.653689	0.326845	−	0.945078i	$-0.394015\pi$
$229$	1.18794e8	0.653689	0.326845	+	0.945078i	$0.394015\pi$
$230$	−7.71259e7	−0.417977
$231$	0	0
$232$	−2.99411e8	−1.57420
$233$	−1.16979e8	−0.605845	−0.302922	−	0.953015i	$-0.597962\pi$
$233$	−1.16979e8	−0.605845	−0.302922	+	0.953015i	$0.597962\pi$
$234$	−5.70431e7	−0.291036
$235$	1.11181e8	0.558846
$236$	−1.33810e8	−0.662668
$237$	2.73592e7	0.133501
$238$	−8.46842e7	−0.407177
$239$	1.87551e8	0.888643	0.444322	−	0.895867i	$-0.353445\pi$
$239$	1.87551e8	0.888643	0.444322	+	0.895867i	$0.353445\pi$
$240$	3.09378e6	0.0144461
$241$	−3.55851e8	−1.63760	−0.818802	−	0.574076i	$-0.805361\pi$
$241$	−3.55851e8	−1.63760	−0.818802	+	0.574076i	$0.805361\pi$
$242$	0	0
$243$	−1.12557e8	−0.503213
$244$	−9.80627e7	−0.432155
$245$	3.06548e8	1.33173
$246$	−3.05377e7	−0.130787
$247$	1.47620e8	0.623315
$248$	−2.28571e8	−0.951567
$249$	5.16386e7	0.211971
$250$	−1.71701e8	−0.694995
$251$	1.26633e8	0.505464	0.252732	−	0.967536i	$-0.418671\pi$
$251$	1.26633e8	0.505464	0.252732	+	0.967536i	$0.418671\pi$
$252$	2.37393e8	0.934470
$253$	0	0
$254$	−2.18934e7	−0.0838290
$255$	1.14933e7	0.0434064
$256$	−2.82690e8	−1.05310
$257$	−4.00529e8	−1.47187	−0.735933	−	0.677054i	$-0.763256\pi$
$257$	−4.00529e8	−1.47187	−0.735933	+	0.677054i	$0.763256\pi$
$258$	2.29254e7	0.0831090
$259$	6.34653e8	2.26980
$260$	−5.00139e7	−0.176475
$261$	−4.24278e8	−1.47710
$262$	−1.99288e8	−0.684583
$263$	4.13139e8	1.40040	0.700198	−	0.713949i	$-0.253095\pi$
$263$	4.13139e8	1.40040	0.700198	+	0.713949i	$0.253095\pi$
$264$	0	0
$265$	6.80820e7	0.224736
$266$	4.76617e8	1.55269
$267$	7.37862e6	0.0237239
$268$	2.30075e8	0.730126
$269$	1.23129e8	0.385681	0.192841	−	0.981230i	$-0.438230\pi$
$269$	1.23129e8	0.385681	0.192841	+	0.981230i	$0.438230\pi$
$270$	5.07796e7	0.157006
$271$	2.53496e7	0.0773711	0.0386855	−	0.999251i	$-0.487683\pi$
$271$	2.53496e7	0.0773711	0.0386855	+	0.999251i	$0.487683\pi$
$272$	1.43057e7	0.0431042
$273$	−4.56888e7	−0.135907
$274$	−1.37090e8	−0.402605
$275$	0	0
$276$	−3.15118e7	−0.0902176
$277$	−3.97696e8	−1.12427	−0.562137	−	0.827044i	$-0.690021\pi$
$277$	−3.97696e8	−1.12427	−0.562137	+	0.827044i	$0.690021\pi$
$278$	2.43034e8	0.678438
$279$	−3.23894e8	−0.892871
$280$	−4.48234e8	−1.22026
$281$	−2.75983e8	−0.742012	−0.371006	−	0.928631i	$-0.620987\pi$
$281$	−2.75983e8	−0.742012	−0.371006	+	0.928631i	$0.620987\pi$
$282$	−3.52421e7	−0.0935813
$283$	−4.81874e7	−0.126381	−0.0631903	−	0.998001i	$-0.520128\pi$
$283$	−4.81874e7	−0.126381	−0.0631903	+	0.998001i	$0.520128\pi$
$284$	−3.52646e8	−0.913535
$285$	−6.46862e7	−0.165522
$286$	0	0
$287$	7.75992e8	1.93763
$288$	−3.74928e8	−0.924856
$289$	−3.57193e8	−0.870484
$290$	2.88600e8	0.694871
$291$	−4.85127e7	−0.115406
$292$	3.52393e8	0.828300
$293$	−3.69039e7	−0.0857109	−0.0428555	−	0.999081i	$-0.513645\pi$
$293$	−3.69039e7	−0.0857109	−0.0428555	+	0.999081i	$0.513645\pi$
$294$	−9.71696e7	−0.223005
$295$	3.58021e8	0.811954
$296$	−6.11280e8	−1.37000
$297$	0	0
$298$	3.60960e8	0.790137
$299$	−1.92410e8	−0.416274
$300$	−2.41185e7	−0.0515735
$301$	−5.82555e8	−1.23127
$302$	−3.81232e8	−0.796463
$303$	−1.54131e8	−0.318304
$304$	−8.05152e7	−0.164369
$305$	2.62376e8	0.529511
$306$	1.15582e8	0.230603
$307$	1.17179e7	0.0231135	0.0115568	−	0.999933i	$-0.496321\pi$
$307$	1.17179e7	0.0231135	0.0115568	+	0.999933i	$0.496321\pi$
$308$	0	0
$309$	1.46741e8	0.282941
$310$	2.20318e8	0.420034
$311$	−2.49341e8	−0.470036	−0.235018	−	0.971991i	$-0.575515\pi$
$311$	−2.49341e8	−0.470036	−0.235018	+	0.971991i	$0.575515\pi$
$312$	4.40062e7	0.0820299
$313$	−3.12569e8	−0.576157	−0.288078	−	0.957607i	$-0.593016\pi$
$313$	−3.12569e8	−0.576157	−0.288078	+	0.957607i	$0.593016\pi$
$314$	−1.77351e8	−0.323281
$315$	−6.35167e8	−1.14499
$316$	2.41233e8	0.430062
$317$	7.33294e7	0.129292	0.0646459	−	0.997908i	$-0.479408\pi$
$317$	7.33294e7	0.129292	0.0646459	+	0.997908i	$0.479408\pi$
$318$	−2.15806e7	−0.0376330
$319$	0	0
$320$	3.03474e8	0.517721
$321$	−6.16478e7	−0.104028
$322$	−6.21229e8	−1.03695
$323$	−2.99111e8	−0.493883
$324$	−3.13472e8	−0.512026
$325$	−1.47267e8	−0.237966
$326$	4.50070e8	0.719479
$327$	4.80995e7	0.0760718
$328$	−7.47413e8	−1.16951
$329$	8.95532e8	1.38642
$330$	0	0
$331$	4.48436e7	0.0679678	0.0339839	−	0.999422i	$-0.489181\pi$
$331$	4.48436e7	0.0679678	0.0339839	+	0.999422i	$0.489181\pi$
$332$	4.55311e8	0.682849
$333$	−8.66210e8	−1.28549
$334$	−7.07359e8	−1.03879
$335$	−6.15588e8	−0.894609
$336$	2.49196e7	0.0358388
$337$	9.11416e8	1.29722	0.648608	−	0.761123i	$-0.275352\pi$
$337$	9.11416e8	1.29722	0.648608	+	0.761123i	$0.275352\pi$
$338$	−3.72433e8	−0.524613
$339$	1.24098e8	0.173008
$340$	1.01339e8	0.139830
$341$	0	0
$342$	−6.50514e8	−0.879357
$343$	1.18987e9	1.59210
$344$	5.61101e8	0.743167
$345$	8.43128e7	0.110542
$346$	−2.90575e8	−0.377131
$347$	−4.90756e7	−0.0630540	−0.0315270	−	0.999503i	$-0.510037\pi$
$347$	−4.90756e7	−0.0630540	−0.0315270	+	0.999503i	$0.510037\pi$
$348$	1.17915e8	0.149983
$349$	5.80029e7	0.0730400	0.0365200	−	0.999333i	$-0.488373\pi$
$349$	5.80029e7	0.0730400	0.0365200	+	0.999333i	$0.488373\pi$
$350$	−4.75477e8	−0.592777
$351$	1.26683e8	0.156366
$352$	0	0
$353$	1.07207e9	1.29722	0.648609	−	0.761122i	$-0.275351\pi$
$353$	1.07207e9	1.29722	0.648609	+	0.761122i	$0.275351\pi$
$354$	−1.13485e8	−0.135966
$355$	9.43538e8	1.11934
$356$	6.50591e7	0.0764246
$357$	9.25755e7	0.107685
$358$	2.29941e8	0.264866
$359$	−3.87304e8	−0.441796	−0.220898	−	0.975297i	$-0.570899\pi$
$359$	−3.87304e8	−0.441796	−0.220898	+	0.975297i	$0.570899\pi$
$360$	6.11775e8	0.691087
$361$	7.89579e8	0.883324
$362$	1.00793e8	0.111674
$363$	0	0
$364$	−4.02850e8	−0.437812
$365$	−9.42861e8	−1.01490
$366$	−8.31680e7	−0.0886691
$367$	−4.32969e8	−0.457220	−0.228610	−	0.973518i	$-0.573418\pi$
$367$	−4.32969e8	−0.457220	−0.228610	+	0.973518i	$0.573418\pi$
$368$	1.04945e8	0.109772
$369$	−1.05912e9	−1.09737
$370$	5.89210e8	0.604734
$371$	5.48383e8	0.557539
$372$	9.00168e7	0.0906616
$373$	−1.36859e9	−1.36551	−0.682754	−	0.730649i	$-0.739218\pi$
$373$	−1.36859e9	−1.36551	−0.682754	+	0.730649i	$0.739218\pi$
$374$	0	0
$375$	1.87700e8	0.183804
$376$	−8.62551e8	−0.836811
$377$	7.19989e8	0.692039
$378$	4.09017e8	0.389511
$379$	5.65482e8	0.533558	0.266779	−	0.963758i	$-0.414041\pi$
$379$	5.65482e8	0.533558	0.266779	+	0.963758i	$0.414041\pi$
$380$	−5.70354e8	−0.533215
$381$	2.39335e7	0.0221701
$382$	3.43691e8	0.315462
$383$	−1.87398e9	−1.70439	−0.852196	−	0.523223i	$-0.824729\pi$
$383$	−1.87398e9	−1.70439	−0.852196	+	0.523223i	$0.824729\pi$
$384$	8.88449e7	0.0800706
$385$	0	0
$386$	2.54698e7	0.0225409
$387$	7.95104e8	0.697326
$388$	−4.27749e8	−0.371773
$389$	1.40118e9	1.20690	0.603451	−	0.797400i	$-0.293792\pi$
$389$	1.40118e9	1.20690	0.603451	+	0.797400i	$0.293792\pi$
$390$	−4.24173e7	−0.0362091
$391$	3.89866e8	0.329835
$392$	−2.37823e9	−1.99413
$393$	2.17858e8	0.181051
$394$	1.19815e9	0.986903
$395$	−6.45441e8	−0.526946
$396$	0	0
$397$	−1.63839e9	−1.31417	−0.657085	−	0.753817i	$-0.728211\pi$
$397$	−1.63839e9	−1.31417	−0.657085	+	0.753817i	$0.728211\pi$
$398$	−3.59152e8	−0.285554
$399$	−5.21031e8	−0.410637
$400$	8.03225e7	0.0627520
$401$	2.47708e9	1.91838	0.959191	−	0.282759i	$-0.0912497\pi$
$401$	2.47708e9	1.91838	0.959191	+	0.282759i	$0.0912497\pi$
$402$	1.95129e8	0.149807
$403$	5.49641e8	0.418322
$404$	−1.35901e9	−1.02539
$405$	8.38725e8	0.627375
$406$	2.32460e9	1.72388
$407$	0	0
$408$	−8.91661e7	−0.0649964
$409$	1.28665e9	0.929886	0.464943	−	0.885341i	$-0.346075\pi$
$409$	1.28665e9	0.929886	0.464943	+	0.885341i	$0.346075\pi$
$410$	7.20428e8	0.516234
$411$	1.49865e8	0.106476
$412$	1.29385e9	0.911471
$413$	2.88377e9	2.01435
$414$	8.47888e8	0.587269
$415$	−1.21823e9	−0.836681
$416$	6.36243e8	0.433308
$417$	−2.65681e8	−0.179426
$418$	0	0
$419$	−6.74343e8	−0.447849	−0.223925	−	0.974606i	$-0.571887\pi$
$419$	−6.74343e8	−0.447849	−0.223925	+	0.974606i	$0.571887\pi$
$420$	1.76526e8	0.116261
$421$	−7.70366e7	−0.0503164	−0.0251582	−	0.999683i	$-0.508009\pi$
$421$	−7.70366e7	−0.0503164	−0.0251582	+	0.999683i	$0.508009\pi$
$422$	8.37249e8	0.542327
$423$	−1.22227e9	−0.785193
$424$	−5.28187e8	−0.336517
$425$	2.98395e8	0.188552
$426$	−2.99083e8	−0.187438
$427$	2.11337e9	1.31365
$428$	−5.43564e8	−0.335118
$429$	0	0
$430$	−5.40842e8	−0.328043
$431$	−2.45305e9	−1.47583	−0.737914	−	0.674895i	$-0.764189\pi$
$431$	−2.45305e9	−1.47583	−0.737914	+	0.674895i	$0.764189\pi$
$432$	−6.90954e7	−0.0412340
$433$	1.61245e9	0.954505	0.477253	−	0.878766i	$-0.341633\pi$
$433$	1.61245e9	0.954505	0.477253	+	0.878766i	$0.341633\pi$
$434$	1.77461e9	1.04205
$435$	−3.15494e8	−0.183772
$436$	4.24105e8	0.245059
$437$	−2.19423e9	−1.25776
$438$	2.98868e8	0.169950
$439$	−1.04636e9	−0.590278	−0.295139	−	0.955454i	$-0.595366\pi$
$439$	−1.04636e9	−0.590278	−0.295139	+	0.955454i	$0.595366\pi$
$440$	0	0
$441$	−3.37006e9	−1.87112
$442$	−1.96139e8	−0.108040
$443$	2.68762e9	1.46878	0.734388	−	0.678730i	$-0.237469\pi$
$443$	2.68762e9	1.46878	0.734388	+	0.678730i	$0.237469\pi$
$444$	2.40737e8	0.130528
$445$	−1.74072e8	−0.0936415
$446$	8.87224e8	0.473545
$447$	−3.94596e8	−0.208966
$448$	2.44440e9	1.28440
$449$	−2.86928e9	−1.49593	−0.747963	−	0.663740i	$-0.768968\pi$
$449$	−2.86928e9	−1.49593	−0.747963	+	0.663740i	$0.768968\pi$
$450$	6.48957e8	0.335716
$451$	0	0
$452$	1.09420e9	0.557330
$453$	4.16757e8	0.210639
$454$	1.57573e8	0.0790292
$455$	1.07786e9	0.536443
$456$	5.01842e8	0.247851
$457$	−1.65308e9	−0.810189	−0.405094	−	0.914275i	$-0.632761\pi$
$457$	−1.65308e9	−0.810189	−0.405094	+	0.914275i	$0.632761\pi$
$458$	8.88343e8	0.432068
$459$	−2.56687e8	−0.123897
$460$	7.43407e8	0.356102
$461$	2.43901e8	0.115947	0.0579736	−	0.998318i	$-0.481536\pi$
$461$	2.43901e8	0.115947	0.0579736	+	0.998318i	$0.481536\pi$
$462$	0	0
$463$	−1.00139e9	−0.468890	−0.234445	−	0.972129i	$-0.575327\pi$
$463$	−1.00139e9	−0.468890	−0.234445	+	0.972129i	$0.575327\pi$
$464$	−3.92696e8	−0.182492
$465$	−2.40848e8	−0.111086
$466$	−8.74767e8	−0.400444
$467$	7.78397e8	0.353665	0.176832	−	0.984241i	$-0.443415\pi$
$467$	7.78397e8	0.353665	0.176832	+	0.984241i	$0.443415\pi$
$468$	5.49832e8	0.247953
$469$	−4.95841e9	−2.21941
$470$	8.31409e8	0.369379
$471$	1.93878e8	0.0854978
$472$	−2.77756e9	−1.21581
$473$	0	0
$474$	2.04592e8	0.0882397
$475$	−1.67942e9	−0.719005
$476$	8.16261e8	0.346900
$477$	−7.48464e8	−0.315760
$478$	1.40251e9	0.587365
$479$	−2.42511e9	−1.00822	−0.504111	−	0.863639i	$-0.668180\pi$
$479$	−2.42511e9	−1.00822	−0.504111	+	0.863639i	$0.668180\pi$
$480$	−2.78797e8	−0.115065
$481$	1.46994e9	0.602270
$482$	−2.66106e9	−1.08240
$483$	6.79118e8	0.274240
$484$	0	0
$485$	1.14448e9	0.455526
$486$	−8.41704e8	−0.332608
$487$	−4.63892e8	−0.181997	−0.0909987	−	0.995851i	$-0.529006\pi$
$487$	−4.63892e8	−0.181997	−0.0909987	+	0.995851i	$0.529006\pi$
$488$	−2.03554e9	−0.792886
$489$	−4.92010e8	−0.190280
$490$	2.29236e9	0.880233
$491$	3.61908e9	1.37979	0.689894	−	0.723910i	$-0.257657\pi$
$491$	3.61908e9	1.37979	0.689894	+	0.723910i	$0.257657\pi$
$492$	2.94350e8	0.111426
$493$	−1.45885e9	−0.548337
$494$	1.10391e9	0.411991
$495$	0	0
$496$	−2.99785e8	−0.110312
$497$	7.59996e9	2.77692
$498$	3.86154e8	0.140106
$499$	2.41596e9	0.870438	0.435219	−	0.900325i	$-0.356671\pi$
$499$	2.41596e9	0.870438	0.435219	+	0.900325i	$0.356671\pi$
$500$	1.65500e9	0.592111
$501$	7.73274e8	0.274727
$502$	9.46963e8	0.334095
$503$	3.19603e8	0.111975	0.0559877	−	0.998431i	$-0.482169\pi$
$503$	3.19603e8	0.111975	0.0559877	+	0.998431i	$0.482169\pi$
$504$	4.92769e9	1.71450
$505$	3.63617e9	1.25639
$506$	0	0
$507$	4.07138e8	0.138744
$508$	2.11027e8	0.0714194
$509$	−1.23039e9	−0.413552	−0.206776	−	0.978388i	$-0.566297\pi$
$509$	−1.23039e9	−0.413552	−0.206776	+	0.978388i	$0.566297\pi$
$510$	8.59468e7	0.0286902
$511$	−7.59451e9	−2.51783
$512$	−7.22836e8	−0.238010
$513$	1.44468e9	0.472455
$514$	−2.99516e9	−0.972856
$515$	−3.46181e9	−1.11681
$516$	−2.20975e8	−0.0708060
$517$	0	0
$518$	4.74594e9	1.50026
$519$	3.17652e8	0.0997393
$520$	−1.03817e9	−0.323784
$521$	6.55557e6	0.00203085	0.00101543	−	0.999999i	$-0.499677\pi$
$521$	6.55557e6	0.00203085	0.00101543	+	0.999999i	$0.499677\pi$
$522$	−3.17275e9	−0.976312
$523$	−3.95738e9	−1.20963	−0.604814	−	0.796367i	$-0.706753\pi$
$523$	−3.95738e9	−1.20963	−0.604814	+	0.796367i	$0.706753\pi$
$524$	1.92091e9	0.583240
$525$	5.19784e8	0.156771
$526$	3.08945e9	0.925617
$527$	−1.11369e9	−0.331458
$528$	0	0
$529$	−5.44837e8	−0.160019
$530$	5.09117e8	0.148543
$531$	−3.93593e9	−1.14082
$532$	−4.59406e9	−1.32284
$533$	1.79729e9	0.514131
$534$	5.51773e7	0.0156807
$535$	1.45436e9	0.410613
$536$	4.77580e9	1.33958
$537$	−2.51369e8	−0.0700488
$538$	9.20761e8	0.254923
$539$	0	0
$540$	−4.89458e8	−0.133764
$541$	−6.06455e9	−1.64668	−0.823338	−	0.567551i	$-0.807891\pi$
$541$	−6.06455e9	−1.64668	−0.823338	+	0.567551i	$0.807891\pi$
$542$	1.89564e8	0.0511398
$543$	−1.10186e8	−0.0295343
$544$	−1.28917e9	−0.343331
$545$	−1.13473e9	−0.300266
$546$	−3.41661e8	−0.0898299
$547$	−6.86147e8	−0.179251	−0.0896255	−	0.995976i	$-0.528567\pi$
$547$	−6.86147e8	−0.179251	−0.0896255	+	0.995976i	$0.528567\pi$
$548$	1.32140e9	0.343005
$549$	−2.88445e9	−0.743978
$550$	0	0
$551$	8.21068e9	2.09097
$552$	−6.54108e8	−0.165525
$553$	−5.19886e9	−1.30728
$554$	−2.97397e9	−0.743109
$555$	−6.44116e8	−0.159933
$556$	−2.34258e9	−0.578006
$557$	−3.68957e9	−0.904654	−0.452327	−	0.891852i	$-0.649406\pi$
$557$	−3.68957e9	−0.904654	−0.452327	+	0.891852i	$0.649406\pi$
$558$	−2.42208e9	−0.590159
$559$	−1.34927e9	−0.326707
$560$	−5.87888e8	−0.141461
$561$	0	0
$562$	−2.06380e9	−0.490446
$563$	4.56958e7	0.0107919	0.00539594	−	0.999985i	$-0.498282\pi$
$563$	4.56958e7	0.0107919	0.00539594	+	0.999985i	$0.498282\pi$
$564$	3.39694e8	0.0797280
$565$	−2.92764e9	−0.682886
$566$	−3.60345e8	−0.0835336
$567$	6.75572e9	1.55643
$568$	−7.32007e9	−1.67608
$569$	6.12558e9	1.39397	0.696987	−	0.717084i	$-0.254524\pi$
$569$	6.12558e9	1.39397	0.696987	+	0.717084i	$0.254524\pi$
$570$	−4.83723e8	−0.109404
$571$	−3.35291e8	−0.0753694	−0.0376847	−	0.999290i	$-0.511998\pi$
$571$	−3.35291e8	−0.0753694	−0.0376847	+	0.999290i	$0.511998\pi$
$572$	0	0
$573$	−3.75718e8	−0.0834297
$574$	5.80286e9	1.28071
$575$	2.18898e9	0.480180
$576$	−3.33626e9	−0.727413
$577$	−7.07448e9	−1.53313	−0.766565	−	0.642167i	$-0.778036\pi$
$577$	−7.07448e9	−1.53313	−0.766565	+	0.642167i	$0.778036\pi$
$578$	−2.67109e9	−0.575362
$579$	−2.78432e7	−0.00596135
$580$	−2.78179e9	−0.592005
$581$	−9.81251e9	−2.07570
$582$	−3.62778e8	−0.0762800
$583$	0	0
$584$	7.31482e9	1.51970
$585$	−1.47113e9	−0.303812
$586$	−2.75968e8	−0.0566522
$587$	4.24719e9	0.866699	0.433350	−	0.901226i	$-0.357332\pi$
$587$	4.24719e9	0.866699	0.433350	+	0.901226i	$0.357332\pi$
$588$	9.36606e8	0.189992
$589$	6.26805e9	1.26395
$590$	2.67728e9	0.536675
$591$	−1.30980e9	−0.261005
$592$	−8.01733e8	−0.158820
$593$	1.46369e8	0.0288242	0.0144121	−	0.999896i	$-0.495412\pi$
$593$	1.46369e8	0.0288242	0.0144121	+	0.999896i	$0.495412\pi$
$594$	0	0
$595$	−2.18398e9	−0.425050
$596$	−3.47925e9	−0.673169
$597$	3.92620e8	0.0755201
$598$	−1.43884e9	−0.275144
$599$	−2.89390e9	−0.550161	−0.275080	−	0.961421i	$-0.588704\pi$
$599$	−2.89390e9	−0.550161	−0.275080	+	0.961421i	$0.588704\pi$
$600$	−5.00641e8	−0.0946231
$601$	6.23231e9	1.17109	0.585543	−	0.810641i	$-0.300881\pi$
$601$	6.23231e9	1.17109	0.585543	+	0.810641i	$0.300881\pi$
$602$	−4.35635e9	−0.813832
$603$	6.76751e9	1.25695
$604$	3.67465e9	0.678558
$605$	0	0
$606$	−1.15259e9	−0.210389
$607$	−2.07734e8	−0.0377006	−0.0188503	−	0.999822i	$-0.506001\pi$
$607$	−2.07734e8	−0.0377006	−0.0188503	+	0.999822i	$0.506001\pi$
$608$	7.25566e9	1.30922
$609$	−2.54122e9	−0.455913
$610$	1.96205e9	0.349990
$611$	2.07417e9	0.367874
$612$	−1.11408e9	−0.196465
$613$	−8.78302e9	−1.54004	−0.770020	−	0.638019i	$-0.779754\pi$
$613$	−8.78302e9	−1.54004	−0.770020	+	0.638019i	$0.779754\pi$
$614$	8.76265e7	0.0152773
$615$	−7.87561e8	−0.136528
$616$	0	0
$617$	1.70674e9	0.292530	0.146265	−	0.989245i	$-0.453275\pi$
$617$	1.70674e9	0.292530	0.146265	+	0.989245i	$0.453275\pi$
$618$	1.09733e9	0.187015
$619$	−7.10301e8	−0.120372	−0.0601859	−	0.998187i	$-0.519169\pi$
$619$	−7.10301e8	−0.120372	−0.0601859	+	0.998187i	$0.519169\pi$
$620$	−2.12362e9	−0.357854
$621$	−1.88301e9	−0.315524
$622$	−1.86457e9	−0.310679
$623$	−1.40210e9	−0.232312
$624$	5.77169e7	0.00950949
$625$	−1.23033e9	−0.201577
$626$	−2.33739e9	−0.380821
$627$	0	0
$628$	1.70947e9	0.275424
$629$	−2.97841e9	−0.477208
$630$	−4.74978e9	−0.756800
$631$	6.59096e9	1.04435	0.522175	−	0.852839i	$-0.325121\pi$
$631$	6.59096e9	1.04435	0.522175	+	0.852839i	$0.325121\pi$
$632$	5.00739e9	0.789045
$633$	−9.15268e8	−0.143428
$634$	5.48357e8	0.0854577
$635$	−5.64624e8	−0.0875087
$636$	2.08013e8	0.0320620
$637$	5.71890e9	0.876646
$638$	0	0
$639$	−1.03729e10	−1.57270
$640$	−2.09597e9	−0.316050
$641$	−9.45580e8	−0.141806	−0.0709031	−	0.997483i	$-0.522588\pi$
$641$	−9.45580e8	−0.141806	−0.0709031	+	0.997483i	$0.522588\pi$
$642$	−4.61002e8	−0.0687591
$643$	7.08661e7	0.0105124	0.00525618	−	0.999986i	$-0.498327\pi$
$643$	7.08661e7	0.0105124	0.00525618	+	0.999986i	$0.498327\pi$
$644$	5.98796e9	0.883442
$645$	5.91241e8	0.0867572
$646$	−2.23675e9	−0.326441
$647$	−1.79125e9	−0.260010	−0.130005	−	0.991513i	$-0.541499\pi$
$647$	−1.79125e9	−0.260010	−0.130005	+	0.991513i	$0.541499\pi$
$648$	−6.50692e9	−0.939426
$649$	0	0
$650$	−1.10126e9	−0.157288
$651$	−1.93997e9	−0.275589
$652$	−4.33817e9	−0.612971
$653$	2.98403e9	0.419380	0.209690	−	0.977768i	$-0.432755\pi$
$653$	2.98403e9	0.419380	0.209690	+	0.977768i	$0.432755\pi$
$654$	3.59688e8	0.0502810
$655$	−5.13958e9	−0.714633
$656$	−9.80281e8	−0.135577
$657$	1.03654e10	1.42596
$658$	6.69679e9	0.916381
$659$	−1.35526e9	−0.184469	−0.0922344	−	0.995737i	$-0.529401\pi$
$659$	−1.35526e9	−0.184469	−0.0922344	+	0.995737i	$0.529401\pi$
$660$	0	0
$661$	−7.47495e9	−1.00671	−0.503353	−	0.864081i	$-0.667901\pi$
$661$	−7.47495e9	−1.00671	−0.503353	+	0.864081i	$0.667901\pi$
$662$	3.35341e8	0.0449245
$663$	2.14416e8	0.0285733
$664$	9.45113e9	1.25284
$665$	1.22918e10	1.62084
$666$	−6.47752e9	−0.849667
$667$	−1.07019e10	−1.39644
$668$	6.81815e9	0.885012
$669$	−9.69900e8	−0.125238
$670$	−4.60337e9	−0.591308
$671$	0	0
$672$	−2.24564e9	−0.285461
$673$	−5.22943e8	−0.0661305	−0.0330653	−	0.999453i	$-0.510527\pi$
$673$	−5.22943e8	−0.0661305	−0.0330653	+	0.999453i	$0.510527\pi$
$674$	6.81557e9	0.857418
$675$	−1.44122e9	−0.180371
$676$	3.58983e9	0.446952
$677$	3.73676e9	0.462844	0.231422	−	0.972853i	$-0.425662\pi$
$677$	3.73676e9	0.462844	0.231422	+	0.972853i	$0.425662\pi$
$678$	9.28003e8	0.114352
$679$	9.21851e9	1.13010
$680$	2.10355e9	0.256550
$681$	−1.72257e8	−0.0209007
$682$	0	0
$683$	1.08906e9	0.130792	0.0653959	−	0.997859i	$-0.479169\pi$
$683$	1.08906e9	0.130792	0.0653959	+	0.997859i	$0.479169\pi$
$684$	6.27023e9	0.749181
$685$	−3.53552e9	−0.420277
$686$	8.89785e9	1.05233
$687$	−9.71124e8	−0.114268
$688$	7.35920e8	0.0861531
$689$	1.27012e9	0.147938
$690$	6.30491e8	0.0730646
$691$	1.15388e10	1.33041	0.665206	−	0.746660i	$-0.268344\pi$
$691$	1.15388e10	1.33041	0.665206	+	0.746660i	$0.268344\pi$
$692$	2.80082e9	0.321302
$693$	0	0
$694$	−3.66988e8	−0.0416767
$695$	6.26779e9	0.708219
$696$	2.44763e9	0.275178
$697$	−3.64171e9	−0.407371
$698$	4.33746e8	0.0482771
$699$	9.56283e8	0.105905
$700$	4.58306e9	0.505025
$701$	−1.69741e10	−1.86112	−0.930558	−	0.366144i	$-0.880678\pi$
$701$	−1.69741e10	−1.86112	−0.930558	+	0.366144i	$0.880678\pi$
$702$	9.47334e8	0.103353
$703$	1.67630e10	1.81974
$704$	0	0
$705$	−9.08884e8	−0.0976892
$706$	8.01696e9	0.857420
$707$	2.92884e10	3.11694
$708$	1.09387e9	0.115838
$709$	1.65944e10	1.74864	0.874318	−	0.485353i	$-0.161309\pi$
$709$	1.65944e10	1.74864	0.874318	+	0.485353i	$0.161309\pi$
$710$	7.05578e9	0.739845
$711$	7.09569e9	0.740374
$712$	1.35047e9	0.140218
$713$	−8.16986e9	−0.844114
$714$	6.92279e8	0.0711766
$715$	0	0
$716$	−2.21638e9	−0.225657
$717$	−1.53320e9	−0.155340
$718$	−2.89626e9	−0.292013
$719$	1.45209e10	1.45694	0.728472	−	0.685076i	$-0.240231\pi$
$719$	1.45209e10	1.45694	0.728472	+	0.685076i	$0.240231\pi$
$720$	8.02382e8	0.0801157
$721$	−2.78840e10	−2.77065
$722$	5.90447e9	0.583849
$723$	2.90903e9	0.286262
$724$	−9.71536e8	−0.0951424
$725$	−8.19103e9	−0.798281
$726$	0	0
$727$	−1.20479e10	−1.16290	−0.581450	−	0.813582i	$-0.697515\pi$
$727$	−1.20479e10	−1.16290	−0.581450	+	0.813582i	$0.697515\pi$
$728$	−8.36217e9	−0.803265
$729$	−8.59107e9	−0.821299
$730$	−7.05072e9	−0.670816
$731$	2.73392e9	0.258866
$732$	8.01647e8	0.0755430
$733$	1.16676e10	1.09425	0.547127	−	0.837050i	$-0.315722\pi$
$733$	1.16676e10	1.09425	0.547127	+	0.837050i	$0.315722\pi$
$734$	−3.23774e9	−0.302208
$735$	−2.50598e9	−0.232794
$736$	−9.45712e9	−0.874352
$737$	0	0
$738$	−7.92007e9	−0.725324
$739$	1.05954e9	0.0965740	0.0482870	−	0.998834i	$-0.484624\pi$
$739$	1.05954e9	0.0965740	0.0482870	+	0.998834i	$0.484624\pi$
$740$	−5.67933e9	−0.515212
$741$	−1.20677e9	−0.108959
$742$	4.10081e9	0.368516
$743$	4.83581e9	0.432522	0.216261	−	0.976336i	$-0.430614\pi$
$743$	4.83581e9	0.432522	0.216261	+	0.976336i	$0.430614\pi$
$744$	1.86853e9	0.166339
$745$	9.30907e9	0.824820
$746$	−1.02343e10	−0.902556
$747$	1.33927e10	1.17556
$748$	0	0
$749$	1.17145e10	1.01868
$750$	1.40362e9	0.121489
$751$	1.48348e10	1.27803	0.639014	−	0.769195i	$-0.279342\pi$
$751$	1.48348e10	1.27803	0.639014	+	0.769195i	$0.279342\pi$
$752$	−1.13129e9	−0.0970090
$753$	−1.03521e9	−0.0883577
$754$	5.38407e9	0.457416
$755$	−9.83189e9	−0.831424
$756$	−3.94246e9	−0.331850
$757$	3.69887e9	0.309908	0.154954	−	0.987922i	$-0.450477\pi$
$757$	3.69887e9	0.309908	0.154954	+	0.987922i	$0.450477\pi$
$758$	4.22867e9	0.352664
$759$	0	0
$760$	−1.18392e10	−0.978302
$761$	−8.66127e8	−0.0712419	−0.0356210	−	0.999365i	$-0.511341\pi$
$761$	−8.66127e8	−0.0712419	−0.0356210	+	0.999365i	$0.511341\pi$
$762$	1.78975e8	0.0146538
$763$	−9.14000e9	−0.744921
$764$	−3.31280e9	−0.268762
$765$	2.98082e9	0.240725
$766$	−1.40136e10	−1.12655
$767$	6.67917e9	0.534489
$768$	2.31094e9	0.184088
$769$	−1.31622e10	−1.04373	−0.521863	−	0.853030i	$-0.674763\pi$
$769$	−1.31622e10	−1.04373	−0.521863	+	0.853030i	$0.674763\pi$
$770$	0	0
$771$	3.27426e9	0.257290
$772$	−2.45501e8	−0.0192040
$773$	−1.46023e10	−1.13709	−0.568544	−	0.822653i	$-0.692493\pi$
$773$	−1.46023e10	−1.13709	−0.568544	+	0.822653i	$0.692493\pi$
$774$	5.94579e9	0.460910
$775$	−6.25305e9	−0.482543
$776$	−8.87901e9	−0.682101
$777$	−5.18819e9	−0.396773
$778$	1.04781e10	0.797723
$779$	2.04962e10	1.55343
$780$	4.08856e8	0.0308488
$781$	0	0
$782$	2.91541e9	0.218010
$783$	7.04612e9	0.524547
$784$	−3.11920e9	−0.231173
$785$	−4.57385e9	−0.337472
$786$	1.62914e9	0.119669
$787$	2.25106e10	1.64618	0.823088	−	0.567914i	$-0.192249\pi$
$787$	2.25106e10	1.64618	0.823088	+	0.567914i	$0.192249\pi$
$788$	−1.15488e10	−0.840807
$789$	−3.37734e9	−0.244797
$790$	−4.82660e9	−0.348295
$791$	−2.35814e10	−1.69415
$792$	0	0
$793$	4.89484e9	0.348564
$794$	−1.22519e10	−0.868623
$795$	−5.56559e8	−0.0392850
$796$	3.46183e9	0.243282
$797$	−3.03700e9	−0.212491	−0.106246	−	0.994340i	$-0.533883\pi$
$797$	−3.03700e9	−0.212491	−0.106246	+	0.994340i	$0.533883\pi$
$798$	−3.89627e9	−0.271418
$799$	−4.20271e9	−0.291485
$800$	−7.23829e9	−0.499829
$801$	1.91367e9	0.131569
$802$	1.85236e10	1.26799
$803$	0	0
$804$	−1.88083e9	−0.127630
$805$	−1.60213e10	−1.08246
$806$	4.11021e9	0.276498
$807$	−1.00656e9	−0.0674191
$808$	−2.82098e10	−1.88131
$809$	5.70405e9	0.378760	0.189380	−	0.981904i	$-0.439352\pi$
$809$	5.70405e9	0.378760	0.189380	+	0.981904i	$0.439352\pi$
$810$	6.27198e9	0.414675
$811$	−2.02335e10	−1.33198	−0.665990	−	0.745961i	$-0.731991\pi$
$811$	−2.02335e10	−1.33198	−0.665990	+	0.745961i	$0.731991\pi$
$812$	−2.24066e10	−1.46869
$813$	−2.07229e8	−0.0135249
$814$	0	0
$815$	1.16072e10	0.751062
$816$	−1.16947e8	−0.00753484
$817$	−1.53870e10	−0.987133
$818$	9.62159e9	0.614625
$819$	−1.18496e10	−0.753717
$820$	−6.94412e9	−0.439814
$821$	1.13512e10	0.715881	0.357941	−	0.933744i	$-0.383479\pi$
$821$	1.13512e10	0.715881	0.357941	+	0.933744i	$0.383479\pi$
$822$	1.12069e9	0.0703775
$823$	1.14403e10	0.715384	0.357692	−	0.933840i	$-0.383564\pi$
$823$	1.14403e10	0.715384	0.357692	+	0.933840i	$0.383564\pi$
$824$	2.68571e10	1.67230
$825$	0	0
$826$	2.15648e10	1.33142
$827$	1.60060e10	0.984041	0.492020	−	0.870584i	$-0.336259\pi$
$827$	1.60060e10	0.984041	0.492020	+	0.870584i	$0.336259\pi$
$828$	−8.17270e9	−0.500333
$829$	−1.65814e10	−1.01083	−0.505416	−	0.862876i	$-0.668661\pi$
$829$	−1.65814e10	−1.01083	−0.505416	+	0.862876i	$0.668661\pi$
$830$	−9.10990e9	−0.553019
$831$	3.25110e9	0.196529
$832$	5.66154e9	0.340803
$833$	−1.15877e10	−0.694610
$834$	−1.98676e9	−0.118595
$835$	−1.82426e10	−1.08439
$836$	0	0
$837$	5.37903e9	0.317077
$838$	−5.04273e9	−0.296014
$839$	−9.85819e9	−0.576276	−0.288138	−	0.957589i	$-0.593036\pi$
$839$	−9.85819e9	−0.576276	−0.288138	+	0.957589i	$0.593036\pi$
$840$	3.66424e9	0.213308
$841$	2.27960e10	1.32152
$842$	−5.76079e8	−0.0332575
$843$	2.25612e9	0.129708
$844$	−8.07014e9	−0.462043
$845$	−9.60495e9	−0.547642
$846$	−9.14015e9	−0.518988
$847$	0	0
$848$	−6.92752e8	−0.0390115
$849$	3.93924e8	0.0220920
$850$	2.23140e9	0.124627
$851$	−2.18491e10	−1.21529
$852$	2.88282e9	0.159691
$853$	1.56754e10	0.864761	0.432381	−	0.901691i	$-0.357674\pi$
$853$	1.56754e10	0.864761	0.432381	+	0.901691i	$0.357674\pi$
$854$	1.58038e10	0.868278
$855$	−1.67766e10	−0.917957
$856$	−1.12831e10	−0.614849
$857$	1.44860e10	0.786169	0.393084	−	0.919502i	$-0.371408\pi$
$857$	1.44860e10	0.786169	0.393084	+	0.919502i	$0.371408\pi$
$858$	0	0
$859$	3.40978e10	1.83548	0.917741	−	0.397180i	$-0.130011\pi$
$859$	3.40978e10	1.83548	0.917741	+	0.397180i	$0.130011\pi$
$860$	5.21312e9	0.279481
$861$	−6.34360e9	−0.338708
$862$	−1.83439e10	−0.975475
$863$	−1.32400e10	−0.701213	−0.350607	−	0.936523i	$-0.614025\pi$
$863$	−1.32400e10	−0.701213	−0.350607	+	0.936523i	$0.614025\pi$
$864$	6.22655e9	0.328435
$865$	−7.49386e9	−0.393685
$866$	1.20579e10	0.630897
$867$	2.92000e9	0.152165
$868$	−1.71052e10	−0.887789
$869$	0	0
$870$	−2.35926e9	−0.121467
$871$	−1.14843e10	−0.588899
$872$	8.80339e9	0.449616
$873$	−1.25819e10	−0.640026
$874$	−1.64085e10	−0.831338
$875$	−3.56673e10	−1.79988
$876$	−2.88076e9	−0.144791
$877$	1.89691e10	0.949618	0.474809	−	0.880089i	$-0.342517\pi$
$877$	1.89691e10	0.949618	0.474809	+	0.880089i	$0.342517\pi$
$878$	−7.82470e9	−0.390155
$879$	3.01684e8	0.0149827
$880$	0	0
$881$	9.55648e9	0.470850	0.235425	−	0.971893i	$-0.424352\pi$
$881$	9.55648e9	0.470850	0.235425	+	0.971893i	$0.424352\pi$
$882$	−2.52013e10	−1.23675
$883$	2.73141e9	0.133513	0.0667567	−	0.997769i	$-0.478735\pi$
$883$	2.73141e9	0.133513	0.0667567	+	0.997769i	$0.478735\pi$
$884$	1.89056e9	0.0920467
$885$	−2.92676e9	−0.141934
$886$	2.00980e10	0.970813
$887$	−1.15789e10	−0.557103	−0.278551	−	0.960421i	$-0.589854\pi$
$887$	−1.15789e10	−0.557103	−0.278551	+	0.960421i	$0.589854\pi$
$888$	4.99711e9	0.239483
$889$	−4.54790e9	−0.217098
$890$	−1.30171e9	−0.0618940
$891$	0	0
$892$	−8.55185e9	−0.403444
$893$	2.36536e10	1.11152
$894$	−2.95079e9	−0.138120
$895$	5.93013e9	0.276493
$896$	−1.68825e10	−0.784079
$897$	1.57292e9	0.0727669
$898$	−2.14564e10	−0.988759
$899$	3.05711e10	1.40331
$900$	−6.25522e9	−0.286018
$901$	−2.57355e9	−0.117218
$902$	0	0
$903$	4.76229e9	0.215233
$904$	2.27129e10	1.02255
$905$	2.59944e9	0.116576
$906$	3.11651e9	0.139226
$907$	−2.58764e10	−1.15154	−0.575769	−	0.817612i	$-0.695297\pi$
$907$	−2.58764e10	−1.15154	−0.575769	+	0.817612i	$0.695297\pi$
$908$	−1.51883e9	−0.0673301
$909$	−3.99745e10	−1.76526
$910$	8.06025e9	0.354571
$911$	2.74713e10	1.20383	0.601914	−	0.798561i	$-0.294405\pi$
$911$	2.74713e10	1.20383	0.601914	+	0.798561i	$0.294405\pi$
$912$	6.58198e8	0.0287326
$913$	0	0
$914$	−1.23617e10	−0.535509
$915$	−2.14488e9	−0.0925613
$916$	−8.56264e9	−0.368106
$917$	−4.13980e10	−1.77291
$918$	−1.91950e9	−0.0818917
$919$	−2.26604e10	−0.963081	−0.481540	−	0.876424i	$-0.659922\pi$
$919$	−2.26604e10	−0.963081	−0.481540	+	0.876424i	$0.659922\pi$
$920$	1.54313e10	0.653349
$921$	−9.57920e7	−0.00404036
$922$	1.82389e9	0.0766374
$923$	1.76025e10	0.736831
$924$	0	0
$925$	−1.67229e10	−0.694729
$926$	−7.48840e9	−0.309921
$927$	3.80577e10	1.56915
$928$	3.53880e10	1.45358
$929$	3.54719e10	1.45154	0.725770	−	0.687937i	$-0.241483\pi$
$929$	3.54719e10	1.45154	0.725770	+	0.687937i	$0.241483\pi$
$930$	−1.80106e9	−0.0734241
$931$	6.52178e10	2.64876
$932$	8.43178e9	0.341164
$933$	2.03832e9	0.0821649
$934$	5.82085e9	0.233761
$935$	0	0
$936$	1.14132e10	0.454925
$937$	2.74457e10	1.08990	0.544949	−	0.838469i	$-0.316549\pi$
$937$	2.74457e10	1.08990	0.544949	+	0.838469i	$0.316549\pi$
$938$	−3.70789e10	−1.46696
$939$	2.55520e9	0.100715
$940$	−8.01385e9	−0.314698
$941$	−2.44345e10	−0.955960	−0.477980	−	0.878371i	$-0.658631\pi$
$941$	−2.44345e10	−0.955960	−0.477980	+	0.878371i	$0.658631\pi$
$942$	1.44982e9	0.0565113
$943$	−2.67150e10	−1.03744
$944$	−3.64295e9	−0.140946
$945$	1.05484e10	0.406609
$946$	0	0
$947$	1.43615e9	0.0549510	0.0274755	−	0.999622i	$-0.491253\pi$
$947$	1.43615e9	0.0549510	0.0274755	+	0.999622i	$0.491253\pi$
$948$	−1.97204e9	−0.0751771
$949$	−1.75898e10	−0.668082
$950$	−1.25587e10	−0.475239
$951$	−5.99456e8	−0.0226009
$952$	1.69436e10	0.636467
$953$	9.69158e9	0.362718	0.181359	−	0.983417i	$-0.441950\pi$
$953$	9.69158e9	0.362718	0.181359	+	0.983417i	$0.441950\pi$
$954$	−5.59701e9	−0.208707
$955$	8.86371e9	0.329309
$956$	−1.35186e10	−0.500414
$957$	0	0
$958$	−1.81349e10	−0.666403
$959$	−2.84777e10	−1.04265
$960$	−2.48085e9	−0.0905004
$961$	−4.17455e9	−0.151732
$962$	1.09922e10	0.398081
$963$	−1.59886e10	−0.576923
$964$	2.56496e10	0.922170
$965$	6.56861e8	0.0235303
$966$	5.07845e9	0.181264
$967$	−1.15862e10	−0.412049	−0.206025	−	0.978547i	$-0.566053\pi$
$967$	−1.15862e10	−0.412049	−0.206025	+	0.978547i	$0.566053\pi$
$968$	0	0
$969$	2.44519e9	0.0863333
$970$	8.55844e9	0.301088
$971$	4.16905e9	0.146140	0.0730701	−	0.997327i	$-0.476720\pi$
$971$	4.16905e9	0.146140	0.0730701	+	0.997327i	$0.476720\pi$
$972$	8.11308e9	0.283370
$973$	5.04854e10	1.75700
$974$	−3.46898e9	−0.120294
$975$	1.20388e9	0.0415977
$976$	−2.66974e9	−0.0919169
$977$	−1.80272e10	−0.618440	−0.309220	−	0.950991i	$-0.600068\pi$
$977$	−1.80272e10	−0.618440	−0.309220	+	0.950991i	$0.600068\pi$
$978$	−3.67925e9	−0.125769
$979$	0	0
$980$	−2.20958e10	−0.749927
$981$	1.24748e10	0.421882
$982$	2.70634e10	0.911996
$983$	4.86933e10	1.63505	0.817526	−	0.575891i	$-0.195345\pi$
$983$	4.86933e10	1.63505	0.817526	+	0.575891i	$0.195345\pi$
$984$	6.10998e9	0.204436
$985$	3.09000e10	1.03022
$986$	−1.09093e10	−0.362433
$987$	−7.32083e9	−0.242354
$988$	−1.06404e10	−0.351002
$989$	2.00556e10	0.659247
$990$	0	0
$991$	2.45831e9	0.0802378	0.0401189	−	0.999195i	$-0.487226\pi$
$991$	2.45831e9	0.0802378	0.0401189	+	0.999195i	$0.487226\pi$
$992$	2.70152e10	0.878654
$993$	−3.66589e8	−0.0118811
$994$	5.68325e10	1.83546
$995$	−9.26245e9	−0.298088
$996$	−3.72209e9	−0.119366
$997$	−1.70304e10	−0.544241	−0.272120	−	0.962263i	$-0.587725\pi$
$997$	−1.70304e10	−0.544241	−0.272120	+	0.962263i	$0.587725\pi$
$998$	1.80665e10	0.575331
$999$	1.43855e10	0.456504

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.8.a.f.1.4	yes	6
11.10	odd	2	inner	121.8.a.f.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.8.a.f.1.3	✓	6	11.10	odd	2	inner
121.8.a.f.1.4	yes	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)

\(f(q)\)	\(=\)	\(q+7.47800 q^{2} -8.17483 q^{3} -72.0796 q^{4} +192.856 q^{5} -61.1314 q^{6} +1553.40 q^{7} -1496.19 q^{8} -2120.17 q^{9} +1442.17 q^{10} +589.238 q^{12} +3597.88 q^{13} +11616.3 q^{14} -1576.56 q^{15} -1962.36 q^{16} -7290.09 q^{17} -15854.6 q^{18} +41029.9 q^{19} -13901.0 q^{20} -12698.8 q^{21} -53478.9 q^{23} +12231.1 q^{24} -40931.7 q^{25} +26904.9 q^{26} +35210.4 q^{27} -111969. q^{28} +200115. q^{29} -11789.5 q^{30} +152768. q^{31} +176838. q^{32} -54515.2 q^{34} +299583. q^{35} +152821. q^{36} +408557. q^{37} +306821. q^{38} -29412.1 q^{39} -288550. q^{40} +499543. q^{41} -94961.7 q^{42} -375019. q^{43} -408887. q^{45} -399915. q^{46} +576497. q^{47} +16041.9 q^{48} +1.58952e6 q^{49} -306087. q^{50} +59595.3 q^{51} -259333. q^{52} +353020. q^{53} +263303. q^{54} -2.32419e6 q^{56} -335412. q^{57} +1.49646e6 q^{58} +1.85642e6 q^{59} +113638. q^{60} +1.36048e6 q^{61} +1.14240e6 q^{62} -3.29348e6 q^{63} +1.57358e6 q^{64} +693871. q^{65} -3.19196e6 q^{67} +525466. q^{68} +437181. q^{69} +2.24028e6 q^{70} +4.89246e6 q^{71} +3.17219e6 q^{72} -4.88895e6 q^{73} +3.05519e6 q^{74} +334610. q^{75} -2.95741e6 q^{76} -219943. q^{78} -3.34675e6 q^{79} -378451. q^{80} +4.34898e6 q^{81} +3.73558e6 q^{82} -6.31678e6 q^{83} +915325. q^{84} -1.40593e6 q^{85} -2.80439e6 q^{86} -1.63591e6 q^{87} -902602. q^{89} -3.05766e6 q^{90} +5.58896e6 q^{91} +3.85473e6 q^{92} -1.24885e6 q^{93} +4.31104e6 q^{94} +7.91284e6 q^{95} -1.44562e6 q^{96} +5.93440e6 q^{97} +1.18864e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 16 q^{3} + 716 q^{4} + 240 q^{5} + 3746 q^{9} + 27108 q^{12} - 51264 q^{14} + 88120 q^{15} + 45352 q^{16} + 81900 q^{20} - 55104 q^{23} + 108910 q^{25} + 56928 q^{26} + 73280 q^{27} - 254560 q^{31}+ \cdots + 10649568 q^{97}+O(q^{100}) \) 6 * q - 16 * q^3 + 716 * q^4 + 240 * q^5 + 3746 * q^9 + 27108 * q^12 - 51264 * q^14 + 88120 * q^15 + 45352 * q^16 + 81900 * q^20 - 55104 * q^23 + 108910 * q^25 + 56928 * q^26 + 73280 * q^27 - 254560 * q^31 - 2103776 * q^34 + 2027544 * q^36 - 252272 * q^37 + 2154240 * q^38 + 790240 * q^42 - 1092740 * q^45 + 372072 * q^47 + 7846456 * q^48 + 5017046 * q^49 + 4947636 * q^53 - 9608160 * q^56 + 3784000 * q^58 + 10205904 * q^59 + 18925140 * q^60 + 5409808 * q^64 - 11727568 * q^67 + 7645372 * q^69 + 12576640 * q^70 + 3862176 * q^71 - 5964800 * q^75 - 40017600 * q^78 + 40052040 * q^80 - 11954122 * q^81 + 23841440 * q^82 + 2122368 * q^86 + 3655008 * q^89 - 7026528 * q^91 + 29314212 * q^92 + 19011180 * q^93 + 10649568 * q^97

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