LMFDB - Embedded newform 75.14.a.c.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [75,14,Mod(1,75)] 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("75.1"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(75, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 14, names="a")

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	75.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-131] 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:	$80.4231967139$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{3121}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 780 $ x^2 - x - 780
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 15)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-27.4330$ of defining polynomial
Character	$\chi$	$=$	75.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+18.2989 q^{2} -729.000 q^{3} -7857.15 q^{4} -13339.9 q^{6} -112047. q^{7} -293681. q^{8} +531441. q^{9} +143727. q^{11} +5.72786e6 q^{12} -627845. q^{13} -2.05033e6 q^{14} +5.89918e7 q^{16} -7.51428e7 q^{17} +9.72477e6 q^{18} +3.68418e8 q^{19} +8.16820e7 q^{21} +2.63004e6 q^{22} -2.64060e8 q^{23} +2.14094e8 q^{24} -1.14888e7 q^{26} -3.87420e8 q^{27} +8.80367e8 q^{28} +5.37538e9 q^{29} -1.57044e9 q^{31} +3.48532e9 q^{32} -1.04777e8 q^{33} -1.37503e9 q^{34} -4.17561e9 q^{36} +1.85013e10 q^{37} +6.74163e9 q^{38} +4.57699e8 q^{39} -8.47428e9 q^{41} +1.49469e9 q^{42} -6.20298e9 q^{43} -1.12928e9 q^{44} -4.83201e9 q^{46} -3.77183e9 q^{47} -4.30050e10 q^{48} -8.43346e10 q^{49} +5.47791e10 q^{51} +4.93307e9 q^{52} -2.30272e11 q^{53} -7.08936e9 q^{54} +3.29060e10 q^{56} -2.68577e11 q^{57} +9.83633e10 q^{58} +4.11830e11 q^{59} -4.06580e11 q^{61} -2.87372e10 q^{62} -5.95462e10 q^{63} -4.19483e11 q^{64} -1.91730e9 q^{66} -2.96486e11 q^{67} +5.90409e11 q^{68} +1.92500e11 q^{69} -3.97640e11 q^{71} -1.56074e11 q^{72} +1.37728e12 q^{73} +3.38553e11 q^{74} -2.89472e12 q^{76} -1.61041e10 q^{77} +8.37537e9 q^{78} -4.66466e11 q^{79} +2.82430e11 q^{81} -1.55070e11 q^{82} -4.77278e12 q^{83} -6.41788e11 q^{84} -1.13508e11 q^{86} -3.91865e12 q^{87} -4.22098e10 q^{88} +6.88111e12 q^{89} +7.03479e10 q^{91} +2.07476e12 q^{92} +1.14485e12 q^{93} -6.90203e10 q^{94} -2.54080e12 q^{96} -1.38827e13 q^{97} -1.54323e12 q^{98} +7.63823e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 131 q^{2} - 1458 q^{3} + 6241 q^{4} + 95499 q^{6} - 496272 q^{7} - 1175463 q^{8} + 1062882 q^{9} + 6245888 q^{11} - 4549689 q^{12} - 1761164 q^{13} + 55314084 q^{14} + 75148705 q^{16} - 48151604 q^{17}+ \cdots + 3319320964608 q^{99}+O(q^{100}) $ 2 * q - 131 * q^2 - 1458 * q^3 + 6241 * q^4 + 95499 * q^6 - 496272 * q^7 - 1175463 * q^8 + 1062882 * q^9 + 6245888 * q^11 - 4549689 * q^12 - 1761164 * q^13 + 55314084 * q^14 + 75148705 * q^16 - 48151604 * q^17 - 69618771 * q^18 + 38475344 * q^19 + 361782288 * q^21 - 908415728 * q^22 - 734264616 * q^23 + 856912527 * q^24 + 157714454 * q^26 - 774840978 * q^27 - 4536499884 * q^28 + 1126474708 * q^29 + 6100104312 * q^31 + 8296660073 * q^32 - 4553252352 * q^33 - 5404788238 * q^34 + 3316723281 * q^36 + 46819674548 * q^37 + 56001723484 * q^38 + 1283888556 * q^39 - 29607909788 * q^41 - 40323967236 * q^42 + 63189768520 * q^43 + 84899911888 * q^44 + 65368954992 * q^46 - 105004415960 * q^47 - 54783405945 * q^48 - 33594444590 * q^49 + 35102519316 * q^51 - 11044638034 * q^52 - 48425833796 * q^53 + 50752084059 * q^54 + 371708899380 * q^56 - 28048525776 * q^57 + 732719858498 * q^58 + 722768180096 * q^59 - 229984402180 * q^61 - 1173940563384 * q^62 - 263739287952 * q^63 - 1270168541071 * q^64 + 662235065712 * q^66 - 359062188984 * q^67 + 970935017018 * q^68 + 535278905064 * q^69 + 736545668224 * q^71 - 624689232183 * q^72 + 1494470740204 * q^73 - 3889351112906 * q^74 - 7546301154644 * q^76 - 2360709208704 * q^77 - 114973836966 * q^78 + 3526348590120 * q^79 + 564859072962 * q^81 + 3000156702386 * q^82 - 5631050986968 * q^83 + 3307108415436 * q^84 - 10473766954252 * q^86 - 821200062132 * q^87 - 5422984137648 * q^88 + 5913121459764 * q^89 + 505797926592 * q^91 - 4554248300592 * q^92 - 4446976043448 * q^93 + 15044889696176 * q^94 - 6048265193217 * q^96 - 16383233322244 * q^97 - 9118668656251 * q^98 + 3319320964608 * 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 $

$2$	18.2989	0.202176	0.101088	−	0.994877i	$-0.467768\pi$
$2$	18.2989	0.202176	0.101088	+	0.994877i	$0.467768\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	−7857.15	−0.959125
$5$	0	0
$5$	0	0
$6$	−13339.9	−0.116726
$7$	−112047.	−0.359966	−0.179983	−	0.983670i	$-0.557604\pi$
$7$	−112047.	−0.359966	−0.179983	+	0.983670i	$0.557604\pi$
$8$	−293681.	−0.396088
$9$	531441.	0.333333
$10$	0	0
$11$	143727.	0.0244616	0.0122308	−	0.999925i	$-0.496107\pi$
$11$	143727.	0.0244616	0.0122308	+	0.999925i	$0.496107\pi$
$12$	5.72786e6	0.553751
$13$	−627845.	−0.0360762	−0.0180381	−	0.999837i	$-0.505742\pi$
$13$	−627845.	−0.0360762	−0.0180381	+	0.999837i	$0.505742\pi$
$14$	−2.05033e6	−0.0727764
$15$	0	0
$16$	5.89918e7	0.879046
$17$	−7.51428e7	−0.755039	−0.377520	−	0.926002i	$-0.623223\pi$
$17$	−7.51428e7	−0.755039	−0.377520	+	0.926002i	$0.623223\pi$
$18$	9.72477e6	0.0673919
$19$	3.68418e8	1.79656	0.898282	−	0.439420i	$-0.144816\pi$
$19$	3.68418e8	1.79656	0.898282	+	0.439420i	$0.144816\pi$
$20$	0	0
$21$	8.16820e7	0.207827
$22$	2.63004e6	0.00494555
$23$	−2.64060e8	−0.371939	−0.185970	−	0.982555i	$-0.559543\pi$
$23$	−2.64060e8	−0.371939	−0.185970	+	0.982555i	$0.559543\pi$
$24$	2.14094e8	0.228681
$25$	0	0
$26$	−1.14888e7	−0.00729373
$27$	−3.87420e8	−0.192450
$28$	8.80367e8	0.345252
$29$	5.37538e9	1.67812	0.839058	−	0.544042i	$-0.183107\pi$
$29$	5.37538e9	1.67812	0.839058	+	0.544042i	$0.183107\pi$
$30$	0	0
$31$	−1.57044e9	−0.317812	−0.158906	−	0.987294i	$-0.550797\pi$
$31$	−1.57044e9	−0.317812	−0.158906	+	0.987294i	$0.550797\pi$
$32$	3.48532e9	0.573809
$33$	−1.04777e8	−0.0141229
$34$	−1.37503e9	−0.152651
$35$	0	0
$36$	−4.17561e9	−0.319708
$37$	1.85013e10	1.18547	0.592735	−	0.805397i	$-0.298048\pi$
$37$	1.85013e10	1.18547	0.592735	+	0.805397i	$0.298048\pi$
$38$	6.74163e9	0.363222
$39$	4.57699e8	0.0208286
$40$	0	0
$41$	−8.47428e9	−0.278617	−0.139309	−	0.990249i	$-0.544488\pi$
$41$	−8.47428e9	−0.278617	−0.139309	+	0.990249i	$0.544488\pi$
$42$	1.49469e9	0.0420175
$43$	−6.20298e9	−0.149643	−0.0748214	−	0.997197i	$-0.523839\pi$
$43$	−6.20298e9	−0.149643	−0.0748214	+	0.997197i	$0.523839\pi$
$44$	−1.12928e9	−0.0234617
$45$	0	0
$46$	−4.83201e9	−0.0751972
$47$	−3.77183e9	−0.0510407	−0.0255203	−	0.999674i	$-0.508124\pi$
$47$	−3.77183e9	−0.0510407	−0.0255203	+	0.999674i	$0.508124\pi$
$48$	−4.30050e10	−0.507517
$49$	−8.43346e10	−0.870424
$50$	0	0
$51$	5.47791e10	0.435922
$52$	4.93307e9	0.0346016
$53$	−2.30272e11	−1.42708	−0.713540	−	0.700614i	$-0.752909\pi$
$53$	−2.30272e11	−1.42708	−0.713540	+	0.700614i	$0.752909\pi$
$54$	−7.08936e9	−0.0389088
$55$	0	0
$56$	3.29060e10	0.142578
$57$	−2.68577e11	−1.03725
$58$	9.83633e10	0.339275
$59$	4.11830e11	1.27110	0.635551	−	0.772059i	$-0.280773\pi$
$59$	4.11830e11	1.27110	0.635551	+	0.772059i	$0.280773\pi$
$60$	0	0
$61$	−4.06580e11	−1.01042	−0.505210	−	0.862996i	$-0.668585\pi$
$61$	−4.06580e11	−1.01042	−0.505210	+	0.862996i	$0.668585\pi$
$62$	−2.87372e10	−0.0642538
$63$	−5.95462e10	−0.119989
$64$	−4.19483e11	−0.763035
$65$	0	0
$66$	−1.91730e9	−0.00285531
$67$	−2.96486e11	−0.400423	−0.200211	−	0.979753i	$-0.564163\pi$
$67$	−2.96486e11	−0.400423	−0.200211	+	0.979753i	$0.564163\pi$
$68$	5.90409e11	0.724177
$69$	1.92500e11	0.214739
$70$	0	0
$71$	−3.97640e11	−0.368393	−0.184196	−	0.982889i	$-0.558968\pi$
$71$	−3.97640e11	−0.368393	−0.184196	+	0.982889i	$0.558968\pi$
$72$	−1.56074e11	−0.132029
$73$	1.37728e12	1.06518	0.532591	−	0.846373i	$-0.321219\pi$
$73$	1.37728e12	1.06518	0.532591	+	0.846373i	$0.321219\pi$
$74$	3.38553e11	0.239673
$75$	0	0
$76$	−2.89472e12	−1.72313
$77$	−1.61041e10	−0.00880535
$78$	8.37537e9	0.00421104
$79$	−4.66466e11	−0.215896	−0.107948	−	0.994157i	$-0.534428\pi$
$79$	−4.66466e11	−0.215896	−0.107948	+	0.994157i	$0.534428\pi$
$80$	0	0
$81$	2.82430e11	0.111111
$82$	−1.55070e11	−0.0563297
$83$	−4.77278e12	−1.60237	−0.801186	−	0.598415i	$-0.795797\pi$
$83$	−4.77278e12	−1.60237	−0.801186	+	0.598415i	$0.795797\pi$
$84$	−6.41788e11	−0.199332
$85$	0	0
$86$	−1.13508e11	−0.0302541
$87$	−3.91865e12	−0.968861
$88$	−4.22098e10	−0.00968894
$89$	6.88111e12	1.46765	0.733827	−	0.679336i	$-0.237732\pi$
$89$	6.88111e12	1.46765	0.733827	+	0.679336i	$0.237732\pi$
$90$	0	0
$91$	7.03479e10	0.0129862
$92$	2.07476e12	0.356736
$93$	1.14485e12	0.183489
$94$	−6.90203e10	−0.0103192
$95$	0	0
$96$	−2.54080e12	−0.331289
$97$	−1.38827e13	−1.69223	−0.846113	−	0.533004i	$-0.821063\pi$
$97$	−1.38827e13	−1.69223	−0.846113	+	0.533004i	$0.821063\pi$
$98$	−1.54323e12	−0.175979
$99$	7.63823e10	0.00815387
$100$	0	0
$101$	−1.02752e13	−0.963162	−0.481581	−	0.876402i	$-0.659937\pi$
$101$	−1.02752e13	−0.963162	−0.481581	+	0.876402i	$0.659937\pi$
$102$	1.00240e12	0.0881329
$103$	−1.05918e13	−0.874036	−0.437018	−	0.899453i	$-0.643965\pi$
$103$	−1.05918e13	−0.874036	−0.437018	+	0.899453i	$0.643965\pi$
$104$	1.84386e11	0.0142893
$105$	0	0
$106$	−4.21372e12	−0.288521
$107$	−1.26172e13	−0.812774	−0.406387	−	0.913701i	$-0.633211\pi$
$107$	−1.26172e13	−0.812774	−0.406387	+	0.913701i	$0.633211\pi$
$108$	3.04402e12	0.184584
$109$	1.49988e13	0.856612	0.428306	−	0.903634i	$-0.359110\pi$
$109$	1.49988e13	0.856612	0.428306	+	0.903634i	$0.359110\pi$
$110$	0	0
$111$	−1.34874e13	−0.684432
$112$	−6.60983e12	−0.316427
$113$	3.11837e13	1.40902	0.704512	−	0.709693i	$-0.251166\pi$
$113$	3.11837e13	1.40902	0.704512	+	0.709693i	$0.251166\pi$
$114$	−4.91465e12	−0.209706
$115$	0	0
$116$	−4.22352e13	−1.60952
$117$	−3.33662e11	−0.0120254
$118$	7.53603e12	0.256986
$119$	8.41950e12	0.271789
$120$	0	0
$121$	−3.45021e13	−0.999402
$122$	−7.43996e12	−0.204283
$123$	6.17775e12	0.160860
$124$	1.23392e13	0.304821
$125$	0	0
$126$	−1.08963e12	−0.0242588
$127$	−6.92694e13	−1.46493	−0.732466	−	0.680804i	$-0.761631\pi$
$127$	−6.92694e13	−1.46493	−0.732466	+	0.680804i	$0.761631\pi$
$128$	−3.62278e13	−0.728077
$129$	4.52198e12	0.0863963
$130$	0	0
$131$	−3.60740e13	−0.623636	−0.311818	−	0.950142i	$-0.600938\pi$
$131$	−3.60740e13	−0.623636	−0.311818	+	0.950142i	$0.600938\pi$
$132$	8.23247e11	0.0135456
$133$	−4.12800e13	−0.646702
$134$	−5.42537e12	−0.0809558
$135$	0	0
$136$	2.20680e13	0.299062
$137$	−8.46431e13	−1.09372	−0.546862	−	0.837223i	$-0.684178\pi$
$137$	−8.46431e13	−1.09372	−0.546862	+	0.837223i	$0.684178\pi$
$138$	3.52253e12	0.0434151
$139$	1.23811e13	0.145600	0.0728002	−	0.997347i	$-0.476806\pi$
$139$	1.23811e13	0.145600	0.0728002	+	0.997347i	$0.476806\pi$
$140$	0	0
$141$	2.74967e12	0.0294683
$142$	−7.27637e12	−0.0744801
$143$	−9.02380e10	−0.000882481 0
$144$	3.13506e13	0.293015
$145$	0	0
$146$	2.52027e13	0.215354
$147$	6.14799e13	0.502540
$148$	−1.45367e14	−1.13701
$149$	−1.01554e14	−0.760303	−0.380152	−	0.924924i	$-0.624128\pi$
$149$	−1.01554e14	−0.760303	−0.380152	+	0.924924i	$0.624128\pi$
$150$	0	0
$151$	−6.26055e13	−0.429796	−0.214898	−	0.976636i	$-0.568942\pi$
$151$	−6.26055e13	−0.429796	−0.214898	+	0.976636i	$0.568942\pi$
$152$	−1.08198e14	−0.711597
$153$	−3.99340e13	−0.251680
$154$	−2.94687e11	−0.00178023
$155$	0	0
$156$	−3.59621e12	−0.0199772
$157$	3.46935e14	1.84885	0.924423	−	0.381368i	$-0.124547\pi$
$157$	3.46935e14	1.84885	0.924423	+	0.381368i	$0.124547\pi$
$158$	−8.53580e12	−0.0436489
$159$	1.67868e14	0.823925
$160$	0	0
$161$	2.95871e13	0.133886
$162$	5.16814e12	0.0224640
$163$	4.29452e14	1.79347	0.896736	−	0.442565i	$-0.145931\pi$
$163$	4.29452e14	1.79347	0.896736	+	0.442565i	$0.145931\pi$
$164$	6.65837e13	0.267229
$165$	0	0
$166$	−8.73364e13	−0.323961
$167$	3.09663e14	1.10467	0.552334	−	0.833623i	$-0.313737\pi$
$167$	3.09663e14	1.10467	0.552334	+	0.833623i	$0.313737\pi$
$168$	−2.39885e13	−0.0823175
$169$	−3.02481e14	−0.998699
$170$	0	0
$171$	1.95793e14	0.598855
$172$	4.87378e13	0.143526
$173$	−4.50613e13	−0.127792	−0.0638960	−	0.997957i	$-0.520353\pi$
$173$	−4.50613e13	−0.127792	−0.0638960	+	0.997957i	$0.520353\pi$
$174$	−7.17069e13	−0.195880
$175$	0	0
$176$	8.47869e12	0.0215029
$177$	−3.00224e14	−0.733871
$178$	1.25917e14	0.296724
$179$	1.74245e14	0.395926	0.197963	−	0.980209i	$-0.436567\pi$
$179$	1.74245e14	0.395926	0.197963	+	0.980209i	$0.436567\pi$
$180$	0	0
$181$	6.89956e14	1.45851	0.729257	−	0.684240i	$-0.239866\pi$
$181$	6.89956e14	1.45851	0.729257	+	0.684240i	$0.239866\pi$
$182$	1.28729e12	0.00262549
$183$	2.96397e14	0.583367
$184$	7.75496e13	0.147321
$185$	0	0
$186$	2.09494e13	0.0370970
$187$	−1.08000e13	−0.0184695
$188$	2.96359e13	0.0489544
$189$	4.34092e13	0.0692755
$190$	0	0
$191$	7.52391e14	1.12131	0.560656	−	0.828049i	$-0.310549\pi$
$191$	7.52391e14	1.12131	0.560656	+	0.828049i	$0.310549\pi$
$192$	3.05803e14	0.440539
$193$	−4.18449e14	−0.582801	−0.291400	−	0.956601i	$-0.594121\pi$
$193$	−4.18449e14	−0.582801	−0.291400	+	0.956601i	$0.594121\pi$
$194$	−2.54038e14	−0.342127
$195$	0	0
$196$	6.62629e14	0.834846
$197$	5.04365e14	0.614772	0.307386	−	0.951585i	$-0.400546\pi$
$197$	5.04365e14	0.614772	0.307386	+	0.951585i	$0.400546\pi$
$198$	1.39771e12	0.00164852
$199$	−1.01359e15	−1.15696	−0.578479	−	0.815697i	$-0.696354\pi$
$199$	−1.01359e15	−1.15696	−0.578479	+	0.815697i	$0.696354\pi$
$200$	0	0
$201$	2.16139e14	0.231184
$202$	−1.88024e14	−0.194728
$203$	−6.02293e14	−0.604065
$204$	−4.30408e14	−0.418104
$205$	0	0
$206$	−1.93819e14	−0.176709
$207$	−1.40333e14	−0.123980
$208$	−3.70377e13	−0.0317126
$209$	5.29515e13	0.0439468
$210$	0	0
$211$	6.68511e14	0.521522	0.260761	−	0.965403i	$-0.416027\pi$
$211$	6.68511e14	0.521522	0.260761	+	0.965403i	$0.416027\pi$
$212$	1.80928e15	1.36875
$213$	2.89880e14	0.212692
$214$	−2.30881e14	−0.164323
$215$	0	0
$216$	1.13778e14	0.0762271
$217$	1.75962e14	0.114401
$218$	2.74461e14	0.173186
$219$	−1.00404e15	−0.614983
$220$	0	0
$221$	4.71780e13	0.0272389
$222$	−2.46805e14	−0.138376
$223$	6.64343e14	0.361752	0.180876	−	0.983506i	$-0.442107\pi$
$223$	6.64343e14	0.361752	0.180876	+	0.983506i	$0.442107\pi$
$224$	−3.90518e14	−0.206552
$225$	0	0
$226$	5.70627e14	0.284870
$227$	2.74872e15	1.33341	0.666703	−	0.745324i	$-0.267705\pi$
$227$	2.74872e15	1.33341	0.666703	+	0.745324i	$0.267705\pi$
$228$	2.11025e15	0.994849
$229$	1.93108e15	0.884851	0.442426	−	0.896805i	$-0.354118\pi$
$229$	1.93108e15	0.884851	0.442426	+	0.896805i	$0.354118\pi$
$230$	0	0
$231$	1.17399e13	0.00508377
$232$	−1.57865e15	−0.664681
$233$	−3.04503e15	−1.24674	−0.623372	−	0.781925i	$-0.714238\pi$
$233$	−3.04503e15	−1.24674	−0.623372	+	0.781925i	$0.714238\pi$
$234$	−6.10564e12	−0.00243124
$235$	0	0
$236$	−3.23581e15	−1.21914
$237$	3.40054e14	0.124647
$238$	1.54067e14	0.0549491
$239$	1.63875e15	0.568756	0.284378	−	0.958712i	$-0.408213\pi$
$239$	1.63875e15	0.568756	0.284378	+	0.958712i	$0.408213\pi$
$240$	0	0
$241$	−2.33624e14	−0.0768081	−0.0384041	−	0.999262i	$-0.512227\pi$
$241$	−2.33624e14	−0.0768081	−0.0384041	+	0.999262i	$0.512227\pi$
$242$	−6.31348e14	−0.202055
$243$	−2.05891e14	−0.0641500
$244$	3.19456e15	0.969120
$245$	0	0
$246$	1.13046e14	0.0325219
$247$	−2.31309e14	−0.0648131
$248$	4.61208e14	0.125881
$249$	3.47935e15	0.925130
$250$	0	0
$251$	−3.58149e15	−0.904033	−0.452016	−	0.892010i	$-0.649295\pi$
$251$	−3.58149e15	−0.904033	−0.452016	+	0.892010i	$0.649295\pi$
$252$	4.67863e14	0.115084
$253$	−3.79525e13	−0.00909824
$254$	−1.26755e15	−0.296174
$255$	0	0
$256$	2.77348e15	0.615836
$257$	−7.60591e15	−1.64659	−0.823296	−	0.567612i	$-0.807867\pi$
$257$	−7.60591e15	−1.64659	−0.823296	+	0.567612i	$0.807867\pi$
$258$	8.27470e13	0.0174672
$259$	−2.07301e15	−0.426729
$260$	0	0
$261$	2.85670e15	0.559372
$262$	−6.60113e14	−0.126084
$263$	−7.86154e15	−1.46486	−0.732428	−	0.680844i	$-0.761613\pi$
$263$	−7.86154e15	−1.46486	−0.732428	+	0.680844i	$0.761613\pi$
$264$	3.07710e13	0.00559391
$265$	0	0
$266$	−7.55378e14	−0.130748
$267$	−5.01633e15	−0.847350
$268$	2.32954e15	0.384055
$269$	−6.04452e15	−0.972685	−0.486343	−	0.873768i	$-0.661669\pi$
$269$	−6.04452e15	−0.972685	−0.486343	+	0.873768i	$0.661669\pi$
$270$	0	0
$271$	−1.14219e16	−1.75162	−0.875809	−	0.482658i	$-0.839672\pi$
$271$	−1.14219e16	−1.75162	−0.875809	+	0.482658i	$0.839672\pi$
$272$	−4.43281e15	−0.663714
$273$	−5.12836e13	−0.00749758
$274$	−1.54887e15	−0.221125
$275$	0	0
$276$	−1.51250e15	−0.205962
$277$	1.65973e15	0.220760	0.110380	−	0.993889i	$-0.464793\pi$
$277$	1.65973e15	0.220760	0.110380	+	0.993889i	$0.464793\pi$
$278$	2.26560e14	0.0294369
$279$	−8.34595e14	−0.105937
$280$	0	0
$281$	−1.28234e16	−1.55386	−0.776930	−	0.629587i	$-0.783224\pi$
$281$	−1.28234e16	−1.55386	−0.776930	+	0.629587i	$0.783224\pi$
$282$	5.03158e13	0.00595779
$283$	1.55354e16	1.79767	0.898837	−	0.438283i	$-0.144413\pi$
$283$	1.55354e16	1.79767	0.898837	+	0.438283i	$0.144413\pi$
$284$	3.12432e15	0.353335
$285$	0	0
$286$	−1.65125e12	−0.000178416 0
$287$	9.49515e14	0.100293
$288$	1.85224e15	0.191270
$289$	−4.25813e15	−0.429916
$290$	0	0
$291$	1.01205e16	0.977007
$292$	−1.08215e16	−1.02164
$293$	−1.56366e16	−1.44378	−0.721891	−	0.692007i	$-0.756727\pi$
$293$	−1.56366e16	−1.44378	−0.721891	+	0.692007i	$0.756727\pi$
$294$	1.12501e15	0.101601
$295$	0	0
$296$	−5.43348e15	−0.469550
$297$	−5.56827e13	−0.00470764
$298$	−1.85833e15	−0.153715
$299$	1.65789e14	0.0134182
$300$	0	0
$301$	6.95024e14	0.0538663
$302$	−1.14561e15	−0.0868944
$303$	7.49059e15	0.556082
$304$	2.17336e16	1.57926
$305$	0	0
$306$	−7.30747e14	−0.0508836
$307$	4.73925e15	0.323080	0.161540	−	0.986866i	$-0.448354\pi$
$307$	4.73925e15	0.323080	0.161540	+	0.986866i	$0.448354\pi$
$308$	1.26532e14	0.00844543
$309$	7.72145e15	0.504625
$310$	0	0
$311$	−2.24003e16	−1.40382	−0.701911	−	0.712265i	$-0.747670\pi$
$311$	−2.24003e16	−1.40382	−0.701911	+	0.712265i	$0.747670\pi$
$312$	−1.34418e14	−0.00824995
$313$	2.48799e15	0.149558	0.0747791	−	0.997200i	$-0.476175\pi$
$313$	2.48799e15	0.149558	0.0747791	+	0.997200i	$0.476175\pi$
$314$	6.34852e15	0.373792
$315$	0	0
$316$	3.66510e15	0.207071
$317$	7.02646e14	0.0388912	0.0194456	−	0.999811i	$-0.493810\pi$
$317$	7.02646e14	0.0388912	0.0194456	+	0.999811i	$0.493810\pi$
$318$	3.07180e15	0.166578
$319$	7.72585e14	0.0410494
$320$	0	0
$321$	9.19797e15	0.469255
$322$	5.41410e14	0.0270684
$323$	−2.76840e16	−1.35648
$324$	−2.21909e15	−0.106569
$325$	0	0
$326$	7.85848e15	0.362597
$327$	−1.09341e16	−0.494565
$328$	2.48874e15	0.110357
$329$	4.22621e14	0.0183729
$330$	0	0
$331$	2.99883e16	1.25334	0.626672	−	0.779283i	$-0.284417\pi$
$331$	2.99883e16	1.25334	0.626672	+	0.779283i	$0.284417\pi$
$332$	3.75004e16	1.53688
$333$	9.83234e15	0.395157
$334$	5.66648e15	0.223337
$335$	0	0
$336$	4.81856e15	0.182689
$337$	−2.60291e16	−0.967975	−0.483987	−	0.875075i	$-0.660812\pi$
$337$	−2.60291e16	−0.967975	−0.483987	+	0.875075i	$0.660812\pi$
$338$	−5.53506e15	−0.201913
$339$	−2.27329e16	−0.813500
$340$	0	0
$341$	−2.25714e14	−0.00777419
$342$	3.58278e15	0.121074
$343$	2.03055e16	0.673289
$344$	1.82170e15	0.0592717
$345$	0	0
$346$	−8.24570e14	−0.0258365
$347$	5.96465e16	1.83419	0.917093	−	0.398674i	$-0.130530\pi$
$347$	5.96465e16	1.83419	0.917093	+	0.398674i	$0.130530\pi$
$348$	3.07894e16	0.929259
$349$	−2.72283e16	−0.806595	−0.403298	−	0.915069i	$-0.632136\pi$
$349$	−2.72283e16	−0.806595	−0.403298	+	0.915069i	$0.632136\pi$
$350$	0	0
$351$	2.43240e14	0.00694286
$352$	5.00933e14	0.0140363
$353$	−5.67802e16	−1.56193	−0.780964	−	0.624576i	$-0.785272\pi$
$353$	−5.67802e16	−1.56193	−0.780964	+	0.624576i	$0.785272\pi$
$354$	−5.49376e15	−0.148371
$355$	0	0
$356$	−5.40659e16	−1.40766
$357$	−6.13782e15	−0.156917
$358$	3.18848e15	0.0800467
$359$	−7.02312e16	−1.73147	−0.865737	−	0.500499i	$-0.833150\pi$
$359$	−7.02312e16	−1.73147	−0.865737	+	0.500499i	$0.833150\pi$
$360$	0	0
$361$	9.36790e16	2.22764
$362$	1.26254e16	0.294876
$363$	2.51520e16	0.577005
$364$	−5.52734e14	−0.0124554
$365$	0	0
$366$	5.42373e15	0.117943
$367$	2.11880e16	0.452649	0.226324	−	0.974052i	$-0.427329\pi$
$367$	2.11880e16	0.452649	0.226324	+	0.974052i	$0.427329\pi$
$368$	−1.55774e16	−0.326952
$369$	−4.50358e15	−0.0928724
$370$	0	0
$371$	2.58012e16	0.513700
$372$	−8.99526e15	−0.175989
$373$	−2.26994e16	−0.436421	−0.218211	−	0.975902i	$-0.570022\pi$
$373$	−2.26994e16	−0.436421	−0.218211	+	0.975902i	$0.570022\pi$
$374$	−1.97628e14	−0.00373408
$375$	0	0
$376$	1.10772e15	0.0202166
$377$	−3.37490e15	−0.0605400
$378$	7.94338e14	0.0140058
$379$	−3.61052e16	−0.625770	−0.312885	−	0.949791i	$-0.601296\pi$
$379$	−3.61052e16	−0.625770	−0.312885	+	0.949791i	$0.601296\pi$
$380$	0	0
$381$	5.04974e16	0.845779
$382$	1.37679e16	0.226702
$383$	−2.14417e16	−0.347110	−0.173555	−	0.984824i	$-0.555525\pi$
$383$	−2.14417e16	−0.347110	−0.173555	+	0.984824i	$0.555525\pi$
$384$	2.64101e16	0.420355
$385$	0	0
$386$	−7.65714e15	−0.117828
$387$	−3.29652e15	−0.0498809
$388$	1.09079e17	1.62306
$389$	6.52962e16	0.955466	0.477733	−	0.878505i	$-0.341459\pi$
$389$	6.52962e16	0.955466	0.477733	+	0.878505i	$0.341459\pi$
$390$	0	0
$391$	1.98422e16	0.280829
$392$	2.47675e16	0.344764
$393$	2.62980e16	0.360056
$394$	9.22930e15	0.124292
$395$	0	0
$396$	−6.00147e14	−0.00782058
$397$	−3.27384e16	−0.419680	−0.209840	−	0.977736i	$-0.567294\pi$
$397$	−3.27384e16	−0.419680	−0.209840	+	0.977736i	$0.567294\pi$
$398$	−1.85476e16	−0.233909
$399$	3.00931e16	0.373374
$400$	0	0
$401$	3.67179e16	0.441001	0.220501	−	0.975387i	$-0.429231\pi$
$401$	3.67179e16	0.441001	0.220501	+	0.975387i	$0.429231\pi$
$402$	3.95509e15	0.0467398
$403$	9.85991e14	0.0114654
$404$	8.07334e16	0.923793
$405$	0	0
$406$	−1.10213e16	−0.122127
$407$	2.65913e15	0.0289985
$408$	−1.60876e16	−0.172663
$409$	2.37728e14	0.00251119	0.00125559	−	0.999999i	$-0.499600\pi$
$409$	2.37728e14	0.00251119	0.00125559	+	0.999999i	$0.499600\pi$
$410$	0	0
$411$	6.17048e16	0.631462
$412$	8.32217e16	0.838310
$413$	−4.61442e16	−0.457553
$414$	−2.56793e15	−0.0250657
$415$	0	0
$416$	−2.18824e15	−0.0207008
$417$	−9.02581e15	−0.0840624
$418$	9.68953e14	0.00888499
$419$	−1.07748e17	−0.972785	−0.486392	−	0.873741i	$-0.661687\pi$
$419$	−1.07748e17	−0.972785	−0.486392	+	0.873741i	$0.661687\pi$
$420$	0	0
$421$	−4.46846e15	−0.0391133	−0.0195566	−	0.999809i	$-0.506225\pi$
$421$	−4.46846e15	−0.0391133	−0.0195566	+	0.999809i	$0.506225\pi$
$422$	1.22330e16	0.105439
$423$	−2.00451e15	−0.0170136
$424$	6.76266e16	0.565249
$425$	0	0
$426$	5.30447e15	0.0430011
$427$	4.55559e16	0.363717
$428$	9.91356e16	0.779552
$429$	6.57835e13	0.000509501 0
$430$	0	0
$431$	−2.38034e17	−1.78869	−0.894347	−	0.447373i	$-0.852360\pi$
$431$	−2.38034e17	−1.78869	−0.894347	+	0.447373i	$0.852360\pi$
$432$	−2.28546e16	−0.169172
$433$	−1.52333e16	−0.111077	−0.0555384	−	0.998457i	$-0.517688\pi$
$433$	−1.52333e16	−0.111077	−0.0555384	+	0.998457i	$0.517688\pi$
$434$	3.21991e15	0.0231292
$435$	0	0
$436$	−1.17848e17	−0.821598
$437$	−9.72846e16	−0.668213
$438$	−1.83727e16	−0.124335
$439$	−1.46731e17	−0.978370	−0.489185	−	0.872180i	$-0.662706\pi$
$439$	−1.46731e17	−0.978370	−0.489185	+	0.872180i	$0.662706\pi$
$440$	0	0
$441$	−4.48188e16	−0.290141
$442$	8.63304e14	0.00550705
$443$	−1.80890e17	−1.13708	−0.568540	−	0.822656i	$-0.692492\pi$
$443$	−1.80890e17	−1.13708	−0.568540	+	0.822656i	$0.692492\pi$
$444$	1.05973e17	0.656455
$445$	0	0
$446$	1.21567e16	0.0731375
$447$	7.40330e16	0.438961
$448$	4.70017e16	0.274667
$449$	−2.86599e17	−1.65072	−0.825360	−	0.564607i	$-0.809028\pi$
$449$	−2.86599e17	−1.65072	−0.825360	+	0.564607i	$0.809028\pi$
$450$	0	0
$451$	−1.21798e15	−0.00681542
$452$	−2.45015e17	−1.35143
$453$	4.56394e16	0.248143
$454$	5.02984e16	0.269582
$455$	0	0
$456$	7.88760e16	0.410841
$457$	−2.00560e17	−1.02989	−0.514943	−	0.857224i	$-0.672187\pi$
$457$	−2.00560e17	−1.02989	−0.514943	+	0.857224i	$0.672187\pi$
$458$	3.53366e16	0.178895
$459$	2.91119e16	0.145307
$460$	0	0
$461$	−7.03451e16	−0.341332	−0.170666	−	0.985329i	$-0.554592\pi$
$461$	−7.03451e16	−0.341332	−0.170666	+	0.985329i	$0.554592\pi$
$462$	2.14827e14	0.00102782
$463$	−1.71885e17	−0.810891	−0.405446	−	0.914119i	$-0.632884\pi$
$463$	−1.71885e17	−0.810891	−0.405446	+	0.914119i	$0.632884\pi$
$464$	3.17103e17	1.47514
$465$	0	0
$466$	−5.57205e16	−0.252062
$467$	−5.37684e16	−0.239865	−0.119933	−	0.992782i	$-0.538268\pi$
$467$	−5.37684e16	−0.239865	−0.119933	+	0.992782i	$0.538268\pi$
$468$	2.62164e15	0.0115339
$469$	3.32203e16	0.144139
$470$	0	0
$471$	−2.52916e17	−1.06743
$472$	−1.20947e17	−0.503467
$473$	−8.91535e14	−0.00366050
$474$	6.22260e15	0.0252007
$475$	0	0
$476$	−6.61533e16	−0.260679
$477$	−1.22376e17	−0.475693
$478$	2.99872e16	0.114989
$479$	1.45707e17	0.551188	0.275594	−	0.961274i	$-0.411125\pi$
$479$	1.45707e17	0.551188	0.275594	+	0.961274i	$0.411125\pi$
$480$	0	0
$481$	−1.16159e16	−0.0427672
$482$	−4.27506e15	−0.0155287
$483$	−2.15690e16	−0.0772989
$484$	2.71088e17	0.958551
$485$	0	0
$486$	−3.76757e15	−0.0129696
$487$	−2.20545e17	−0.749132	−0.374566	−	0.927200i	$-0.622208\pi$
$487$	−2.20545e17	−0.749132	−0.374566	+	0.927200i	$0.622208\pi$
$488$	1.19405e17	0.400215
$489$	−3.13070e17	−1.03546
$490$	0	0
$491$	−2.43820e16	−0.0785309	−0.0392654	−	0.999229i	$-0.512502\pi$
$491$	−2.43820e16	−0.0785309	−0.0392654	+	0.999229i	$0.512502\pi$
$492$	−4.85395e16	−0.154285
$493$	−4.03921e17	−1.26704
$494$	−4.23270e15	−0.0131036
$495$	0	0
$496$	−9.26429e16	−0.279371
$497$	4.45543e16	0.132609
$498$	6.36682e16	0.187039
$499$	2.54719e17	0.738599	0.369299	−	0.929311i	$-0.379598\pi$
$499$	2.54719e17	0.738599	0.369299	+	0.929311i	$0.379598\pi$
$500$	0	0
$501$	−2.25744e17	−0.637781
$502$	−6.55371e16	−0.182774
$503$	3.72489e17	1.02547	0.512733	−	0.858548i	$-0.328633\pi$
$503$	3.72489e17	1.02547	0.512733	+	0.858548i	$0.328633\pi$
$504$	1.74876e16	0.0475260
$505$	0	0
$506$	−6.94488e14	−0.00183944
$507$	2.20509e17	0.576599
$508$	5.44260e17	1.40505
$509$	−1.62073e17	−0.413091	−0.206546	−	0.978437i	$-0.566222\pi$
$509$	−1.62073e17	−0.413091	−0.206546	+	0.978437i	$0.566222\pi$
$510$	0	0
$511$	−1.54320e17	−0.383429
$512$	3.47530e17	0.852584
$513$	−1.42733e17	−0.345749
$514$	−1.39180e17	−0.332901
$515$	0	0
$516$	−3.55298e16	−0.0828648
$517$	−5.42113e14	−0.00124854
$518$	−3.79337e16	−0.0862743
$519$	3.28497e16	0.0737808
$520$	0	0
$521$	1.71142e17	0.374896	0.187448	−	0.982275i	$-0.439978\pi$
$521$	1.71142e17	0.374896	0.187448	+	0.982275i	$0.439978\pi$
$522$	5.22743e16	0.113092
$523$	−4.86625e17	−1.03976	−0.519880	−	0.854239i	$-0.674023\pi$
$523$	−4.86625e17	−1.03976	−0.519880	+	0.854239i	$0.674023\pi$
$524$	2.83439e17	0.598145
$525$	0	0
$526$	−1.43857e17	−0.296159
$527$	1.18007e17	0.239960
$528$	−6.18096e15	−0.0124147
$529$	−4.34308e17	−0.861661
$530$	0	0
$531$	2.18863e17	0.423700
$532$	3.24343e17	0.620268
$533$	5.32053e15	0.0100514
$534$	−9.17932e16	−0.171314
$535$	0	0
$536$	8.70725e16	0.158602
$537$	−1.27024e17	−0.228588
$538$	−1.10608e17	−0.196653
$539$	−1.21211e16	−0.0212920
$540$	0	0
$541$	2.80840e17	0.481589	0.240795	−	0.970576i	$-0.422592\pi$
$541$	2.80840e17	0.481589	0.240795	+	0.970576i	$0.422592\pi$
$542$	−2.09009e17	−0.354135
$543$	−5.02978e17	−0.842073
$544$	−2.61897e17	−0.433249
$545$	0	0
$546$	−9.38432e14	−0.00151583
$547$	6.77006e17	1.08062	0.540312	−	0.841464i	$-0.318306\pi$
$547$	6.77006e17	1.08062	0.540312	+	0.841464i	$0.318306\pi$
$548$	6.65054e17	1.04902
$549$	−2.16073e17	−0.336807
$550$	0	0
$551$	1.98039e18	3.01484
$552$	−5.65336e16	−0.0850556
$553$	5.22660e16	0.0777152
$554$	3.03713e16	0.0446323
$555$	0	0
$556$	−9.72800e16	−0.139649
$557$	4.76254e17	0.675740	0.337870	−	0.941193i	$-0.390294\pi$
$557$	4.76254e17	0.675740	0.337870	+	0.941193i	$0.390294\pi$
$558$	−1.52721e16	−0.0214179
$559$	3.89451e15	0.00539854
$560$	0	0
$561$	7.87322e15	0.0106634
$562$	−2.34654e17	−0.314153
$563$	1.40153e17	0.185480	0.0927400	−	0.995690i	$-0.470437\pi$
$563$	1.40153e17	0.185480	0.0927400	+	0.995690i	$0.470437\pi$
$564$	−2.16045e16	−0.0282638
$565$	0	0
$566$	2.84280e17	0.363446
$567$	−3.16453e16	−0.0399962
$568$	1.16780e17	0.145916
$569$	4.19192e17	0.517825	0.258912	−	0.965901i	$-0.416636\pi$
$569$	4.19192e17	0.517825	0.258912	+	0.965901i	$0.416636\pi$
$570$	0	0
$571$	4.21896e17	0.509414	0.254707	−	0.967018i	$-0.418021\pi$
$571$	4.21896e17	0.509414	0.254707	+	0.967018i	$0.418021\pi$
$572$	7.09014e14	0.000846410 0
$573$	−5.48493e17	−0.647390
$574$	1.73750e16	0.0202768
$575$	0	0
$576$	−2.22930e17	−0.254345
$577$	2.42814e17	0.273924	0.136962	−	0.990576i	$-0.456266\pi$
$577$	2.42814e17	0.273924	0.136962	+	0.990576i	$0.456266\pi$
$578$	−7.79190e16	−0.0869185
$579$	3.05049e17	0.336480
$580$	0	0
$581$	5.34774e17	0.576800
$582$	1.85194e17	0.197527
$583$	−3.30963e16	−0.0349087
$584$	−4.04481e17	−0.421905
$585$	0	0
$586$	−2.86131e17	−0.291898
$587$	−1.71527e18	−1.73055	−0.865274	−	0.501299i	$-0.832856\pi$
$587$	−1.71527e18	−1.73055	−0.865274	+	0.501299i	$0.832856\pi$
$588$	−4.83057e17	−0.481998
$589$	−5.78578e17	−0.570969
$590$	0	0
$591$	−3.67682e17	−0.354939
$592$	1.09142e18	1.04208
$593$	1.76024e18	1.66232	0.831161	−	0.556031i	$-0.187676\pi$
$593$	1.76024e18	1.66232	0.831161	+	0.556031i	$0.187676\pi$
$594$	−1.01893e15	−0.000951771 0
$595$	0	0
$596$	7.97926e17	0.729226
$597$	7.38908e17	0.667970
$598$	3.03375e15	0.00271283
$599$	−1.01218e18	−0.895328	−0.447664	−	0.894202i	$-0.647744\pi$
$599$	−1.01218e18	−0.895328	−0.447664	+	0.894202i	$0.647744\pi$
$600$	0	0
$601$	−1.00124e18	−0.866669	−0.433335	−	0.901233i	$-0.642663\pi$
$601$	−1.00124e18	−0.866669	−0.433335	+	0.901233i	$0.642663\pi$
$602$	1.27181e16	0.0108905
$603$	−1.57565e17	−0.133474
$604$	4.91901e17	0.412228
$605$	0	0
$606$	1.37069e17	0.112426
$607$	1.81791e18	1.47518	0.737590	−	0.675249i	$-0.235964\pi$
$607$	1.81791e18	1.47518	0.737590	+	0.675249i	$0.235964\pi$
$608$	1.28405e18	1.03089
$609$	4.39072e17	0.348757
$610$	0	0
$611$	2.36812e15	0.00184135
$612$	3.13767e17	0.241392
$613$	1.45199e18	1.10527	0.552637	−	0.833422i	$-0.313622\pi$
$613$	1.45199e18	1.10527	0.552637	+	0.833422i	$0.313622\pi$
$614$	8.67229e16	0.0653190
$615$	0	0
$616$	4.72947e15	0.00348769
$617$	−7.36777e17	−0.537629	−0.268814	−	0.963192i	$-0.586632\pi$
$617$	−7.36777e17	−0.537629	−0.268814	+	0.963192i	$0.586632\pi$
$618$	1.41294e17	0.102023
$619$	3.78289e16	0.0270293	0.0135147	−	0.999909i	$-0.495698\pi$
$619$	3.78289e16	0.0270293	0.0135147	+	0.999909i	$0.495698\pi$
$620$	0	0
$621$	1.02302e17	0.0715798
$622$	−4.09901e17	−0.283819
$623$	−7.71006e17	−0.528306
$624$	2.70004e16	0.0183093
$625$	0	0
$626$	4.55273e16	0.0302370
$627$	−3.86017e16	−0.0253727
$628$	−2.72592e18	−1.77327
$629$	−1.39024e18	−0.895077
$630$	0	0
$631$	1.18325e18	0.746253	0.373127	−	0.927780i	$-0.378286\pi$
$631$	1.18325e18	0.746253	0.373127	+	0.927780i	$0.378286\pi$
$632$	1.36992e17	0.0855137
$633$	−4.87344e17	−0.301101
$634$	1.28576e16	0.00786286
$635$	0	0
$636$	−1.31897e18	−0.790247
$637$	5.29490e16	0.0314016
$638$	1.41374e16	0.00829920
$639$	−2.11322e17	−0.122798
$640$	0	0
$641$	2.00244e17	0.114020	0.0570102	−	0.998374i	$-0.481843\pi$
$641$	2.00244e17	0.114020	0.0570102	+	0.998374i	$0.481843\pi$
$642$	1.68312e17	0.0948721
$643$	−2.12199e18	−1.18406	−0.592028	−	0.805917i	$-0.701673\pi$
$643$	−2.12199e18	−1.18406	−0.592028	+	0.805917i	$0.701673\pi$
$644$	−2.32470e17	−0.128413
$645$	0	0
$646$	−5.06586e17	−0.274247
$647$	1.12704e18	0.604032	0.302016	−	0.953303i	$-0.402340\pi$
$647$	1.12704e18	0.604032	0.302016	+	0.953303i	$0.402340\pi$
$648$	−8.29443e16	−0.0440097
$649$	5.91910e16	0.0310932
$650$	0	0
$651$	−1.28277e17	−0.0660497
$652$	−3.37427e18	−1.72016
$653$	2.48373e18	1.25363	0.626813	−	0.779169i	$-0.284359\pi$
$653$	2.48373e18	1.25363	0.626813	+	0.779169i	$0.284359\pi$
$654$	−2.00082e17	−0.0999891
$655$	0	0
$656$	−4.99913e17	−0.244917
$657$	7.31943e17	0.355060
$658$	7.73349e15	0.00371456
$659$	3.56057e18	1.69342	0.846709	−	0.532056i	$-0.178580\pi$
$659$	3.56057e18	1.69342	0.846709	+	0.532056i	$0.178580\pi$
$660$	0	0
$661$	−1.25090e18	−0.583329	−0.291664	−	0.956521i	$-0.594209\pi$
$661$	−1.25090e18	−0.583329	−0.291664	+	0.956521i	$0.594209\pi$
$662$	5.48752e17	0.253396
$663$	−3.43928e16	−0.0157264
$664$	1.40167e18	0.634680
$665$	0	0
$666$	1.79921e17	0.0798911
$667$	−1.41942e18	−0.624158
$668$	−2.43307e18	−1.05952
$669$	−4.84306e17	−0.208858
$670$	0	0
$671$	−5.84364e16	−0.0247165
$672$	2.84688e17	0.119253
$673$	−2.74283e18	−1.13789	−0.568946	−	0.822375i	$-0.692648\pi$
$673$	−2.74283e18	−1.13789	−0.568946	+	0.822375i	$0.692648\pi$
$674$	−4.76302e17	−0.195701
$675$	0	0
$676$	2.37664e18	0.957877
$677$	−4.19537e18	−1.67473	−0.837364	−	0.546646i	$-0.815905\pi$
$677$	−4.19537e18	−1.67473	−0.837364	+	0.546646i	$0.815905\pi$
$678$	−4.15987e17	−0.164470
$679$	1.55551e18	0.609144
$680$	0	0
$681$	−2.00382e18	−0.769842
$682$	−4.13031e15	−0.00157175
$683$	2.74346e18	1.03410	0.517052	−	0.855954i	$-0.327029\pi$
$683$	2.74346e18	1.03410	0.517052	+	0.855954i	$0.327029\pi$
$684$	−1.53837e18	−0.574376
$685$	0	0
$686$	3.71567e17	0.136123
$687$	−1.40776e18	−0.510869
$688$	−3.65925e17	−0.131543
$689$	1.44575e17	0.0514836
$690$	0	0
$691$	−5.46424e18	−1.90951	−0.954756	−	0.297390i	$-0.903884\pi$
$691$	−5.46424e18	−1.90951	−0.954756	+	0.297390i	$0.903884\pi$
$692$	3.54053e17	0.122569
$693$	−8.55838e15	−0.00293512
$694$	1.09146e18	0.370828
$695$	0	0
$696$	1.15083e18	0.383754
$697$	6.36782e17	0.210367
$698$	−4.98248e17	−0.163074
$699$	2.21982e18	0.719808
$700$	0	0
$701$	−5.09836e18	−1.62279	−0.811397	−	0.584495i	$-0.801293\pi$
$701$	−5.09836e18	−1.62279	−0.811397	+	0.584495i	$0.801293\pi$
$702$	4.45101e15	0.00140368
$703$	6.81621e18	2.12977
$704$	−6.02909e16	−0.0186651
$705$	0	0
$706$	−1.03901e18	−0.315784
$707$	1.15130e18	0.346706
$708$	2.35891e18	0.703874
$709$	−2.21731e18	−0.655580	−0.327790	−	0.944751i	$-0.606304\pi$
$709$	−2.21731e18	−0.655580	−0.327790	+	0.944751i	$0.606304\pi$
$710$	0	0
$711$	−2.47899e17	−0.0719653
$712$	−2.02085e18	−0.581320
$713$	4.14691e17	0.118207
$714$	−1.12315e17	−0.0317249
$715$	0	0
$716$	−1.36907e18	−0.379743
$717$	−1.19465e18	−0.328371
$718$	−1.28515e18	−0.350062
$719$	5.05135e18	1.36355	0.681773	−	0.731563i	$-0.261209\pi$
$719$	5.05135e18	1.36355	0.681773	+	0.731563i	$0.261209\pi$
$720$	0	0
$721$	1.18678e18	0.314623
$722$	1.71422e18	0.450375
$723$	1.70312e17	0.0443452
$724$	−5.42109e18	−1.39890
$725$	0	0
$726$	4.60253e17	0.116656
$727$	−2.06443e18	−0.518594	−0.259297	−	0.965798i	$-0.583491\pi$
$727$	−2.06443e18	−0.518594	−0.259297	+	0.965798i	$0.583491\pi$
$728$	−2.06599e16	−0.00514367
$729$	1.50095e17	0.0370370
$730$	0	0
$731$	4.66110e17	0.112986
$732$	−2.32884e18	−0.559522
$733$	2.95043e18	0.702603	0.351301	−	0.936262i	$-0.385739\pi$
$733$	2.95043e18	0.702603	0.351301	+	0.936262i	$0.385739\pi$
$734$	3.87717e17	0.0915147
$735$	0	0
$736$	−9.20335e17	−0.213422
$737$	−4.26130e16	−0.00979498
$738$	−8.24104e16	−0.0187766
$739$	−1.77031e18	−0.399816	−0.199908	−	0.979815i	$-0.564064\pi$
$739$	−1.77031e18	−0.399816	−0.199908	+	0.979815i	$0.564064\pi$
$740$	0	0
$741$	1.68625e17	0.0374199
$742$	4.72133e17	0.103858
$743$	−8.75773e18	−1.90970	−0.954848	−	0.297094i	$-0.903983\pi$
$743$	−8.75773e18	−1.90970	−0.954848	+	0.297094i	$0.903983\pi$
$744$	−3.36221e17	−0.0726776
$745$	0	0
$746$	−4.15372e17	−0.0882339
$747$	−2.53645e18	−0.534124
$748$	8.48575e16	0.0177145
$749$	1.41372e18	0.292571
$750$	0	0
$751$	3.32951e18	0.677205	0.338602	−	0.940930i	$-0.390046\pi$
$751$	3.32951e18	0.677205	0.338602	+	0.940930i	$0.390046\pi$
$752$	−2.22507e17	−0.0448671
$753$	2.61090e18	0.521944
$754$	−6.17569e16	−0.0122397
$755$	0	0
$756$	−3.41072e17	−0.0664439
$757$	−1.11835e17	−0.0216001	−0.0108000	−	0.999942i	$-0.503438\pi$
$757$	−1.11835e17	−0.0216001	−0.0108000	+	0.999942i	$0.503438\pi$
$758$	−6.60685e17	−0.126516
$759$	2.76674e16	0.00525287
$760$	0	0
$761$	1.10635e18	0.206486	0.103243	−	0.994656i	$-0.467078\pi$
$761$	1.10635e18	0.206486	0.103243	+	0.994656i	$0.467078\pi$
$762$	9.24045e17	0.170996
$763$	−1.68057e18	−0.308351
$764$	−5.91165e18	−1.07548
$765$	0	0
$766$	−3.92359e17	−0.0701773
$767$	−2.58565e17	−0.0458565
$768$	−2.02186e18	−0.355553
$769$	7.10729e18	1.23932	0.619659	−	0.784871i	$-0.287271\pi$
$769$	7.10729e18	1.23932	0.619659	+	0.784871i	$0.287271\pi$
$770$	0	0
$771$	5.54471e18	0.950661
$772$	3.28782e18	0.558979
$773$	−4.57751e18	−0.771724	−0.385862	−	0.922556i	$-0.626096\pi$
$773$	−4.57751e18	−0.771724	−0.385862	+	0.922556i	$0.626096\pi$
$774$	−6.03226e16	−0.0100847
$775$	0	0
$776$	4.07709e18	0.670270
$777$	1.51122e18	0.246372
$778$	1.19485e18	0.193172
$779$	−3.12208e18	−0.500554
$780$	0	0
$781$	−5.71515e16	−0.00901148
$782$	3.63091e17	0.0567768
$783$	−2.08253e18	−0.322954
$784$	−4.97504e18	−0.765143
$785$	0	0
$786$	4.81223e17	0.0727947
$787$	8.42386e18	1.26379	0.631896	−	0.775053i	$-0.282277\pi$
$787$	8.42386e18	1.26379	0.631896	+	0.775053i	$0.282277\pi$
$788$	−3.96287e18	−0.589643
$789$	5.73106e18	0.845736
$790$	0	0
$791$	−3.49403e18	−0.507201
$792$	−2.24320e16	−0.00322965
$793$	2.55269e17	0.0364521
$794$	−5.99075e17	−0.0848492
$795$	0	0
$796$	7.96393e18	1.10967
$797$	4.95824e18	0.685249	0.342625	−	0.939472i	$-0.388684\pi$
$797$	4.95824e18	0.685249	0.342625	+	0.939472i	$0.388684\pi$
$798$	5.50670e17	0.0754871
$799$	2.83426e17	0.0385377
$800$	0	0
$801$	3.65691e18	0.489218
$802$	6.71897e17	0.0891598
$803$	1.97952e17	0.0260560
$804$	−1.69823e18	−0.221734
$805$	0	0
$806$	1.80425e16	0.00231803
$807$	4.40646e18	0.561580
$808$	3.01762e18	0.381497
$809$	−2.91720e18	−0.365848	−0.182924	−	0.983127i	$-0.558556\pi$
$809$	−2.91720e18	−0.365848	−0.182924	+	0.983127i	$0.558556\pi$
$810$	0	0
$811$	2.27898e18	0.281258	0.140629	−	0.990062i	$-0.455088\pi$
$811$	2.27898e18	0.281258	0.140629	+	0.990062i	$0.455088\pi$
$812$	4.73231e18	0.579374
$813$	8.32659e18	1.01130
$814$	4.86590e16	0.00586280
$815$	0	0
$816$	3.23152e18	0.383195
$817$	−2.28529e18	−0.268843
$818$	4.35016e15	0.000507702 0
$819$	3.73857e16	0.00432873
$820$	0	0
$821$	−9.35907e18	−1.06660	−0.533301	−	0.845926i	$-0.679049\pi$
$821$	−9.35907e18	−1.06660	−0.533301	+	0.845926i	$0.679049\pi$
$822$	1.12913e18	0.127666
$823$	1.20581e19	1.35264	0.676319	−	0.736609i	$-0.263574\pi$
$823$	1.20581e19	1.35264	0.676319	+	0.736609i	$0.263574\pi$
$824$	3.11063e18	0.346195
$825$	0	0
$826$	−8.44386e17	−0.0925062
$827$	7.53213e18	0.818714	0.409357	−	0.912374i	$-0.365753\pi$
$827$	7.53213e18	0.818714	0.409357	+	0.912374i	$0.365753\pi$
$828$	1.10261e18	0.118912
$829$	1.09464e19	1.17130	0.585649	−	0.810565i	$-0.300840\pi$
$829$	1.09464e19	1.17130	0.585649	+	0.810565i	$0.300840\pi$
$830$	0	0
$831$	−1.20995e18	−0.127456
$832$	2.63370e17	0.0275274
$833$	6.33714e18	0.657205
$834$	−1.65162e17	−0.0169954
$835$	0	0
$836$	−4.16048e17	−0.0421505
$837$	6.08420e17	0.0611629
$838$	−1.97166e18	−0.196674
$839$	−1.38440e19	−1.37028	−0.685139	−	0.728413i	$-0.740258\pi$
$839$	−1.38440e19	−1.37028	−0.685139	+	0.728413i	$0.740258\pi$
$840$	0	0
$841$	1.86341e19	1.81607
$842$	−8.17677e16	−0.00790775
$843$	9.34826e18	0.897122
$844$	−5.25259e18	−0.500204
$845$	0	0
$846$	−3.66802e16	−0.00343973
$847$	3.86584e18	0.359751
$848$	−1.35842e19	−1.25447
$849$	−1.13253e19	−1.03789
$850$	0	0
$851$	−4.88546e18	−0.440923
$852$	−2.27763e18	−0.203998
$853$	−1.10709e19	−0.984039	−0.492020	−	0.870584i	$-0.663741\pi$
$853$	−1.10709e19	−0.984039	−0.492020	+	0.870584i	$0.663741\pi$
$854$	8.33622e17	0.0735348
$855$	0	0
$856$	3.70545e18	0.321930
$857$	3.38629e18	0.291977	0.145989	−	0.989286i	$-0.453364\pi$
$857$	3.38629e18	0.291977	0.145989	+	0.989286i	$0.453364\pi$
$858$	1.20376e15	0.000103009 0
$859$	5.43237e18	0.461354	0.230677	−	0.973030i	$-0.425906\pi$
$859$	5.43237e18	0.461354	0.230677	+	0.973030i	$0.425906\pi$
$860$	0	0
$861$	−6.92196e17	−0.0579040
$862$	−4.35575e18	−0.361631
$863$	−1.86531e18	−0.153703	−0.0768513	−	0.997043i	$-0.524487\pi$
$863$	−1.86531e18	−0.153703	−0.0768513	+	0.997043i	$0.524487\pi$
$864$	−1.35028e18	−0.110430
$865$	0	0
$866$	−2.78752e17	−0.0224570
$867$	3.10418e18	0.248212
$868$	−1.38256e18	−0.109725
$869$	−6.70437e16	−0.00528116
$870$	0	0
$871$	1.86147e17	0.0144457
$872$	−4.40487e18	−0.339294
$873$	−7.37784e18	−0.564075
$874$	−1.78020e18	−0.135097
$875$	0	0
$876$	7.88887e18	0.589845
$877$	−1.78738e19	−1.32654	−0.663269	−	0.748381i	$-0.730831\pi$
$877$	−1.78738e19	−1.32654	−0.663269	+	0.748381i	$0.730831\pi$
$878$	−2.68501e18	−0.197803
$879$	1.13991e19	0.833568
$880$	0	0
$881$	3.72462e18	0.268372	0.134186	−	0.990956i	$-0.457158\pi$
$881$	3.72462e18	0.268372	0.134186	+	0.990956i	$0.457158\pi$
$882$	−8.20134e17	−0.0586596
$883$	1.78621e19	1.26820	0.634102	−	0.773250i	$-0.281370\pi$
$883$	1.78621e19	1.26820	0.634102	+	0.773250i	$0.281370\pi$
$884$	−3.70685e17	−0.0261255
$885$	0	0
$886$	−3.31009e18	−0.229890
$887$	−1.20818e19	−0.832967	−0.416483	−	0.909143i	$-0.636738\pi$
$887$	−1.20818e19	−0.832967	−0.416483	+	0.909143i	$0.636738\pi$
$888$	3.96101e18	0.271095
$889$	7.76141e18	0.527326
$890$	0	0
$891$	4.05927e16	0.00271796
$892$	−5.21985e18	−0.346965
$893$	−1.38961e18	−0.0916978
$894$	1.35472e18	0.0887474
$895$	0	0
$896$	4.05920e18	0.262083
$897$	−1.20860e17	−0.00774697
$898$	−5.24444e18	−0.333736
$899$	−8.44170e18	−0.533325
$900$	0	0
$901$	1.73033e19	1.07750
$902$	−2.22877e16	−0.00137791
$903$	−5.06672e17	−0.0310997
$904$	−9.15808e18	−0.558097
$905$	0	0
$906$	8.35150e17	0.0501685
$907$	1.97495e19	1.17790	0.588951	−	0.808168i	$-0.299541\pi$
$907$	1.97495e19	1.17790	0.588951	+	0.808168i	$0.299541\pi$
$908$	−2.15971e19	−1.27890
$909$	−5.46064e18	−0.321054
$910$	0	0
$911$	−2.11213e19	−1.22420	−0.612100	−	0.790781i	$-0.709675\pi$
$911$	−2.11213e19	−1.22420	−0.612100	+	0.790781i	$0.709675\pi$
$912$	−1.58438e19	−0.911787
$913$	−6.85975e17	−0.0391966
$914$	−3.67002e18	−0.208218
$915$	0	0
$916$	−1.51728e19	−0.848683
$917$	4.04197e18	0.224488
$918$	5.32714e17	0.0293776
$919$	−2.23735e18	−0.122513	−0.0612566	−	0.998122i	$-0.519511\pi$
$919$	−2.23735e18	−0.122513	−0.0612566	+	0.998122i	$0.519511\pi$
$920$	0	0
$921$	−3.45491e18	−0.186530
$922$	−1.28723e18	−0.0690092
$923$	2.49656e17	0.0132902
$924$	−9.22421e16	−0.00487597
$925$	0	0
$926$	−3.14531e18	−0.163943
$927$	−5.62894e18	−0.291345
$928$	1.87349e19	0.962919
$929$	2.69207e19	1.37399	0.686996	−	0.726662i	$-0.258929\pi$
$929$	2.69207e19	1.37399	0.686996	+	0.726662i	$0.258929\pi$
$930$	0	0
$931$	−3.10704e19	−1.56377
$932$	2.39252e19	1.19578
$933$	1.63298e19	0.810497
$934$	−9.83900e17	−0.0484949
$935$	0	0
$936$	9.79904e16	0.00476311
$937$	−1.74551e19	−0.842588	−0.421294	−	0.906924i	$-0.638424\pi$
$937$	−1.74551e19	−0.842588	−0.421294	+	0.906924i	$0.638424\pi$
$938$	6.07894e17	0.0291413
$939$	−1.81374e18	−0.0863474
$940$	0	0
$941$	−2.30287e19	−1.08128	−0.540638	−	0.841255i	$-0.681817\pi$
$941$	−2.30287e19	−1.08128	−0.540638	+	0.841255i	$0.681817\pi$
$942$	−4.62807e18	−0.215809
$943$	2.23772e18	0.103629
$944$	2.42946e19	1.11736
$945$	0	0
$946$	−1.63141e16	−0.000740065 0
$947$	2.31518e18	0.104306	0.0521532	−	0.998639i	$-0.483392\pi$
$947$	2.31518e18	0.104306	0.0521532	+	0.998639i	$0.483392\pi$
$948$	−2.67186e18	−0.119553
$949$	−8.64718e17	−0.0384277
$950$	0	0
$951$	−5.12229e17	−0.0224538
$952$	−2.47265e18	−0.107652
$953$	−1.88776e19	−0.816288	−0.408144	−	0.912917i	$-0.633824\pi$
$953$	−1.88776e19	−0.816288	−0.408144	+	0.912917i	$0.633824\pi$
$954$	−2.23934e18	−0.0961737
$955$	0	0
$956$	−1.28759e19	−0.545508
$957$	−5.63215e17	−0.0236999
$958$	2.66627e18	0.111437
$959$	9.48398e18	0.393704
$960$	0	0
$961$	−2.19513e19	−0.898996
$962$	−2.12558e17	−0.00864650
$963$	−6.70532e18	−0.270925
$964$	1.83562e18	0.0736686
$965$	0	0
$966$	−3.94688e17	−0.0156280
$967$	−3.58183e18	−0.140875	−0.0704374	−	0.997516i	$-0.522439\pi$
$967$	−3.58183e18	−0.140875	−0.0704374	+	0.997516i	$0.522439\pi$
$968$	1.01326e19	0.395851
$969$	2.01816e19	0.783162
$970$	0	0
$971$	3.44871e19	1.32048	0.660240	−	0.751055i	$-0.270455\pi$
$971$	3.44871e19	1.32048	0.660240	+	0.751055i	$0.270455\pi$
$972$	1.61772e18	0.0615279
$973$	−1.38726e18	−0.0524112
$974$	−4.03572e18	−0.151456
$975$	0	0
$976$	−2.39849e19	−0.888206
$977$	−1.61246e19	−0.593162	−0.296581	−	0.955008i	$-0.595846\pi$
$977$	−1.61246e19	−0.593162	−0.296581	+	0.955008i	$0.595846\pi$
$978$	−5.72883e18	−0.209345
$979$	9.89000e17	0.0359012
$980$	0	0
$981$	7.97098e18	0.285537
$982$	−4.46164e17	−0.0158770
$983$	1.25333e19	0.443065	0.221532	−	0.975153i	$-0.428894\pi$
$983$	1.25333e19	0.443065	0.221532	+	0.975153i	$0.428894\pi$
$984$	−1.81429e18	−0.0637146
$985$	0	0
$986$	−7.39130e18	−0.256166
$987$	−3.08091e17	−0.0106076
$988$	1.81743e18	0.0621639
$989$	1.63796e18	0.0556581
$990$	0	0
$991$	−5.10124e18	−0.171079	−0.0855396	−	0.996335i	$-0.527261\pi$
$991$	−5.10124e18	−0.171079	−0.0855396	+	0.996335i	$0.527261\pi$
$992$	−5.47348e18	−0.182363
$993$	−2.18615e19	−0.723618
$994$	8.15292e17	0.0268103
$995$	0	0
$996$	−2.73378e19	−0.887315
$997$	−2.50551e18	−0.0807939	−0.0403969	−	0.999184i	$-0.512862\pi$
$997$	−2.50551e18	−0.0807939	−0.0403969	+	0.999184i	$0.512862\pi$
$998$	4.66108e18	0.149327
$999$	−7.16778e18	−0.228144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.14.a.c.1.2		2
5.2	odd	4		75.14.b.e.49.3		4
5.3	odd	4		75.14.b.e.49.2		4
5.4	even	2		15.14.a.c.1.1	✓	2
15.14	odd	2		45.14.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.14.a.c.1.1	✓	2	5.4	even	2
45.14.a.b.1.2		2	15.14	odd	2
75.14.a.c.1.2		2	1.1	even	1	trivial
75.14.b.e.49.2		4	5.3	odd	4
75.14.b.e.49.3		4	5.2	odd	4

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	75.a (trivial)

\(f(q)\)	\(=\)	\(q+18.2989 q^{2} -729.000 q^{3} -7857.15 q^{4} -13339.9 q^{6} -112047. q^{7} -293681. q^{8} +531441. q^{9} +143727. q^{11} +5.72786e6 q^{12} -627845. q^{13} -2.05033e6 q^{14} +5.89918e7 q^{16} -7.51428e7 q^{17} +9.72477e6 q^{18} +3.68418e8 q^{19} +8.16820e7 q^{21} +2.63004e6 q^{22} -2.64060e8 q^{23} +2.14094e8 q^{24} -1.14888e7 q^{26} -3.87420e8 q^{27} +8.80367e8 q^{28} +5.37538e9 q^{29} -1.57044e9 q^{31} +3.48532e9 q^{32} -1.04777e8 q^{33} -1.37503e9 q^{34} -4.17561e9 q^{36} +1.85013e10 q^{37} +6.74163e9 q^{38} +4.57699e8 q^{39} -8.47428e9 q^{41} +1.49469e9 q^{42} -6.20298e9 q^{43} -1.12928e9 q^{44} -4.83201e9 q^{46} -3.77183e9 q^{47} -4.30050e10 q^{48} -8.43346e10 q^{49} +5.47791e10 q^{51} +4.93307e9 q^{52} -2.30272e11 q^{53} -7.08936e9 q^{54} +3.29060e10 q^{56} -2.68577e11 q^{57} +9.83633e10 q^{58} +4.11830e11 q^{59} -4.06580e11 q^{61} -2.87372e10 q^{62} -5.95462e10 q^{63} -4.19483e11 q^{64} -1.91730e9 q^{66} -2.96486e11 q^{67} +5.90409e11 q^{68} +1.92500e11 q^{69} -3.97640e11 q^{71} -1.56074e11 q^{72} +1.37728e12 q^{73} +3.38553e11 q^{74} -2.89472e12 q^{76} -1.61041e10 q^{77} +8.37537e9 q^{78} -4.66466e11 q^{79} +2.82430e11 q^{81} -1.55070e11 q^{82} -4.77278e12 q^{83} -6.41788e11 q^{84} -1.13508e11 q^{86} -3.91865e12 q^{87} -4.22098e10 q^{88} +6.88111e12 q^{89} +7.03479e10 q^{91} +2.07476e12 q^{92} +1.14485e12 q^{93} -6.90203e10 q^{94} -2.54080e12 q^{96} -1.38827e13 q^{97} -1.54323e12 q^{98} +7.63823e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 131 q^{2} - 1458 q^{3} + 6241 q^{4} + 95499 q^{6} - 496272 q^{7} - 1175463 q^{8} + 1062882 q^{9} + 6245888 q^{11} - 4549689 q^{12} - 1761164 q^{13} + 55314084 q^{14} + 75148705 q^{16} - 48151604 q^{17}+ \cdots + 3319320964608 q^{99}+O(q^{100}) \) 2 * q - 131 * q^2 - 1458 * q^3 + 6241 * q^4 + 95499 * q^6 - 496272 * q^7 - 1175463 * q^8 + 1062882 * q^9 + 6245888 * q^11 - 4549689 * q^12 - 1761164 * q^13 + 55314084 * q^14 + 75148705 * q^16 - 48151604 * q^17 - 69618771 * q^18 + 38475344 * q^19 + 361782288 * q^21 - 908415728 * q^22 - 734264616 * q^23 + 856912527 * q^24 + 157714454 * q^26 - 774840978 * q^27 - 4536499884 * q^28 + 1126474708 * q^29 + 6100104312 * q^31 + 8296660073 * q^32 - 4553252352 * q^33 - 5404788238 * q^34 + 3316723281 * q^36 + 46819674548 * q^37 + 56001723484 * q^38 + 1283888556 * q^39 - 29607909788 * q^41 - 40323967236 * q^42 + 63189768520 * q^43 + 84899911888 * q^44 + 65368954992 * q^46 - 105004415960 * q^47 - 54783405945 * q^48 - 33594444590 * q^49 + 35102519316 * q^51 - 11044638034 * q^52 - 48425833796 * q^53 + 50752084059 * q^54 + 371708899380 * q^56 - 28048525776 * q^57 + 732719858498 * q^58 + 722768180096 * q^59 - 229984402180 * q^61 - 1173940563384 * q^62 - 263739287952 * q^63 - 1270168541071 * q^64 + 662235065712 * q^66 - 359062188984 * q^67 + 970935017018 * q^68 + 535278905064 * q^69 + 736545668224 * q^71 - 624689232183 * q^72 + 1494470740204 * q^73 - 3889351112906 * q^74 - 7546301154644 * q^76 - 2360709208704 * q^77 - 114973836966 * q^78 + 3526348590120 * q^79 + 564859072962 * q^81 + 3000156702386 * q^82 - 5631050986968 * q^83 + 3307108415436 * q^84 - 10473766954252 * q^86 - 821200062132 * q^87 - 5422984137648 * q^88 + 5913121459764 * q^89 + 505797926592 * q^91 - 4554248300592 * q^92 - 4446976043448 * q^93 + 15044889696176 * q^94 - 6048265193217 * q^96 - 16383233322244 * q^97 - 9118668656251 * q^98 + 3319320964608 * q^99

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