LMFDB - Embedded newform 50.18.a.j.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [50,18,Mod(1,50)] 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("50.1"); S:= CuspForms(chi, 18); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(50, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 18, names="a")

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	50.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,-1024,1904] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$91.6110436723$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 278100x^{2} + 44986027x - 279418975 $ x^4 - x^3 - 278100x^2 + 44986027x - 279418975
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2}\cdot 5^{7} $
Twist minimal:	no (minimal twist has level 10)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-594.906$ of defining polynomial
Character	$\chi$	$=$	50.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-256.000 q^{2} +20214.2 q^{3} +65536.0 q^{4} -5.17482e6 q^{6} +1.76306e7 q^{7} -1.67772e7 q^{8} +2.79472e8 q^{9} +4.98950e8 q^{11} +1.32475e9 q^{12} +5.00327e9 q^{13} -4.51344e9 q^{14} +4.29497e9 q^{16} -1.61697e10 q^{17} -7.15448e10 q^{18} +3.43950e10 q^{19} +3.56388e11 q^{21} -1.27731e11 q^{22} -4.72599e11 q^{23} -3.39137e11 q^{24} -1.28084e12 q^{26} +3.03883e12 q^{27} +1.15544e12 q^{28} +3.30807e12 q^{29} +3.23730e12 q^{31} -1.09951e12 q^{32} +1.00859e13 q^{33} +4.13944e12 q^{34} +1.83155e13 q^{36} +5.76908e11 q^{37} -8.80513e12 q^{38} +1.01137e14 q^{39} -5.68215e13 q^{41} -9.12354e13 q^{42} -5.07446e12 q^{43} +3.26992e13 q^{44} +1.20985e14 q^{46} +3.32325e13 q^{47} +8.68191e13 q^{48} +7.82089e13 q^{49} -3.26857e14 q^{51} +3.27894e14 q^{52} -6.11026e14 q^{53} -7.77940e14 q^{54} -2.95793e14 q^{56} +6.95266e14 q^{57} -8.46865e14 q^{58} -8.63122e14 q^{59} -8.57703e14 q^{61} -8.28749e14 q^{62} +4.92727e15 q^{63} +2.81475e14 q^{64} -2.58198e15 q^{66} -4.06389e14 q^{67} -1.05970e15 q^{68} -9.55319e15 q^{69} -9.53517e15 q^{71} -4.68876e15 q^{72} +6.07142e15 q^{73} -1.47688e14 q^{74} +2.25411e15 q^{76} +8.79681e15 q^{77} -2.58910e16 q^{78} +1.38305e16 q^{79} +2.53363e16 q^{81} +1.45463e16 q^{82} +1.96416e16 q^{83} +2.33563e16 q^{84} +1.29906e15 q^{86} +6.68698e16 q^{87} -8.37099e15 q^{88} +2.45918e16 q^{89} +8.82108e16 q^{91} -3.09722e16 q^{92} +6.54393e16 q^{93} -8.50752e15 q^{94} -2.22257e16 q^{96} -3.63292e16 q^{97} -2.00215e16 q^{98} +1.39443e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 1024 q^{2} + 1904 q^{3} + 262144 q^{4} - 487424 q^{6} + 27852528 q^{7} - 67108864 q^{8} + 181591252 q^{9} + 73116048 q^{11} + 124780544 q^{12} + 5260514784 q^{13} - 7130247168 q^{14} + 17179869184 q^{16}+ \cdots + 11\!\cdots\!24 q^{99}+O(q^{100}) $ 4 * q - 1024 * q^2 + 1904 * q^3 + 262144 * q^4 - 487424 * q^6 + 27852528 * q^7 - 67108864 * q^8 + 181591252 * q^9 + 73116048 * q^11 + 124780544 * q^12 + 5260514784 * q^13 - 7130247168 * q^14 + 17179869184 * q^16 + 27652825088 * q^17 - 46487360512 * q^18 + 27132089040 * q^19 + 257721166528 * q^21 - 18717708288 * q^22 + 267096076304 * q^23 - 31943819264 * q^24 - 1346691784704 * q^26 + 3653720352800 * q^27 + 1825343275008 * q^28 - 830121541560 * q^29 - 3027738496832 * q^31 - 4398046511104 * q^32 + 19883640874048 * q^33 - 7079123222528 * q^34 + 11900764291072 * q^36 + 11753219425248 * q^37 - 6945814794240 * q^38 + 30023617116384 * q^39 - 109960914985992 * q^41 - 65976618631168 * q^42 - 57843805555536 * q^43 + 4791733321728 * q^44 - 68376595533824 * q^46 - 22344329926352 * q^47 + 8177617731584 * q^48 - 398604472020732 * q^49 - 1314685175765312 * q^51 + 344753096884224 * q^52 - 1100693686082016 * q^53 - 935352410316800 * q^54 - 467287878402048 * q^56 - 95996606285760 * q^57 + 212511114639360 * q^58 + 77705278880880 * q^59 - 3175222034484472 * q^61 + 775101055188992 * q^62 + 6027001010119664 * q^63 + 1125899906842624 * q^64 - 5090212063756288 * q^66 + 5846012954016528 * q^67 + 1812255544967168 * q^68 - 10410680115629696 * q^69 - 16574513271866592 * q^71 - 3046595658514432 * q^72 + 5319423834293184 * q^73 - 3008824172863488 * q^74 + 1778128587325440 * q^76 + 17129208918876736 * q^77 - 7686045981794304 * q^78 + 9677334395854080 * q^79 + 27216187312417924 * q^81 + 28149994236413952 * q^82 - 16561108625266576 * q^83 + 16890014369579008 * q^84 + 14808014222217216 * q^86 + 92228129920815840 * q^87 - 1226683730362368 * q^88 + 21784615149779160 * q^89 + 166710153944985888 * q^91 + 17504408456658944 * q^92 + 116588278209594368 * q^93 + 5720148461146112 * q^94 - 2093470139285504 * q^96 + 256361495844924288 * q^97 + 102042744837307392 * q^98 + 118340668209625424 * 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 $

$2$	−256.000	−0.707107
$2$	−256.000	−0.707107
$3$	20214.2	1.77879	0.889395	−	0.457139i	$-0.151126\pi$
$3$	20214.2	1.77879	0.889395	+	0.457139i	$0.151126\pi$
$4$	65536.0	0.500000
$5$	0	0
$5$	0	0
$6$	−5.17482e6	−1.25780
$7$	1.76306e7	1.15594	0.577969	−	0.816059i	$-0.303845\pi$
$7$	1.76306e7	1.15594	0.577969	+	0.816059i	$0.303845\pi$
$8$	−1.67772e7	−0.353553
$9$	2.79472e8	2.16410
$10$	0	0
$11$	4.98950e8	0.701810	0.350905	−	0.936411i	$-0.385874\pi$
$11$	4.98950e8	0.701810	0.350905	+	0.936411i	$0.385874\pi$
$12$	1.32475e9	0.889395
$13$	5.00327e9	1.70112	0.850561	−	0.525877i	$-0.176263\pi$
$13$	5.00327e9	1.70112	0.850561	+	0.525877i	$0.176263\pi$
$14$	−4.51344e9	−0.817372
$15$	0	0
$16$	4.29497e9	0.250000
$17$	−1.61697e10	−0.562194	−0.281097	−	0.959679i	$-0.590698\pi$
$17$	−1.61697e10	−0.562194	−0.281097	+	0.959679i	$0.590698\pi$
$18$	−7.15448e10	−1.53025
$19$	3.43950e10	0.464612	0.232306	−	0.972643i	$-0.425373\pi$
$19$	3.43950e10	0.464612	0.232306	+	0.972643i	$0.425373\pi$
$20$	0	0
$21$	3.56388e11	2.05617
$22$	−1.27731e11	−0.496254
$23$	−4.72599e11	−1.25836	−0.629182	−	0.777258i	$-0.716610\pi$
$23$	−4.72599e11	−1.25836	−0.629182	+	0.777258i	$0.716610\pi$
$24$	−3.39137e11	−0.628898
$25$	0	0
$26$	−1.28084e12	−1.20287
$27$	3.03883e12	2.07068
$28$	1.15544e12	0.577969
$29$	3.30807e12	1.22798	0.613990	−	0.789314i	$-0.289563\pi$
$29$	3.30807e12	1.22798	0.613990	+	0.789314i	$0.289563\pi$
$30$	0	0
$31$	3.23730e12	0.681724	0.340862	−	0.940113i	$-0.389281\pi$
$31$	3.23730e12	0.681724	0.340862	+	0.940113i	$0.389281\pi$
$32$	−1.09951e12	−0.176777
$33$	1.00859e13	1.24837
$34$	4.13944e12	0.397531
$35$	0	0
$36$	1.83155e13	1.08205
$37$	5.76908e11	0.0270017	0.0135009	−	0.999909i	$-0.495702\pi$
$37$	5.76908e11	0.0270017	0.0135009	+	0.999909i	$0.495702\pi$
$38$	−8.80513e12	−0.328530
$39$	1.01137e14	3.02594
$40$	0	0
$41$	−5.68215e13	−1.11135	−0.555674	−	0.831400i	$-0.687540\pi$
$41$	−5.68215e13	−1.11135	−0.555674	+	0.831400i	$0.687540\pi$
$42$	−9.12354e13	−1.45393
$43$	−5.07446e12	−0.0662076	−0.0331038	−	0.999452i	$-0.510539\pi$
$43$	−5.07446e12	−0.0662076	−0.0331038	+	0.999452i	$0.510539\pi$
$44$	3.26992e13	0.350905
$45$	0	0
$46$	1.20985e14	0.889798
$47$	3.32325e13	0.203578	0.101789	−	0.994806i	$-0.467543\pi$
$47$	3.32325e13	0.203578	0.101789	+	0.994806i	$0.467543\pi$
$48$	8.68191e13	0.444698
$49$	7.82089e13	0.336193
$50$	0	0
$51$	−3.26857e14	−1.00003
$52$	3.27894e14	0.850561
$53$	−6.11026e14	−1.34808	−0.674039	−	0.738696i	$-0.735442\pi$
$53$	−6.11026e14	−1.34808	−0.674039	+	0.738696i	$0.735442\pi$
$54$	−7.77940e14	−1.46420
$55$	0	0
$56$	−2.95793e14	−0.408686
$57$	6.95266e14	0.826447
$58$	−8.46865e14	−0.868313
$59$	−8.63122e14	−0.765297	−0.382648	−	0.923894i	$-0.624988\pi$
$59$	−8.63122e14	−0.765297	−0.382648	+	0.923894i	$0.624988\pi$
$60$	0	0
$61$	−8.57703e14	−0.572840	−0.286420	−	0.958104i	$-0.592465\pi$
$61$	−8.57703e14	−0.572840	−0.286420	+	0.958104i	$0.592465\pi$
$62$	−8.28749e14	−0.482051
$63$	4.92727e15	2.50156
$64$	2.81475e14	0.125000
$65$	0	0
$66$	−2.58198e15	−0.882733
$67$	−4.06389e14	−0.122266	−0.0611331	−	0.998130i	$-0.519471\pi$
$67$	−4.06389e14	−0.122266	−0.0611331	+	0.998130i	$0.519471\pi$
$68$	−1.05970e15	−0.281097
$69$	−9.55319e15	−2.23837
$70$	0	0
$71$	−9.53517e15	−1.75240	−0.876198	−	0.481951i	$-0.839928\pi$
$71$	−9.53517e15	−1.75240	−0.876198	+	0.481951i	$0.839928\pi$
$72$	−4.68876e15	−0.765124
$73$	6.07142e15	0.881142	0.440571	−	0.897718i	$-0.354776\pi$
$73$	6.07142e15	0.881142	0.440571	+	0.897718i	$0.354776\pi$
$74$	−1.47688e14	−0.0190931
$75$	0	0
$76$	2.25411e15	0.232306
$77$	8.79681e15	0.811249
$78$	−2.58910e16	−2.13966
$79$	1.38305e16	1.02567	0.512836	−	0.858486i	$-0.328595\pi$
$79$	1.38305e16	1.02567	0.512836	+	0.858486i	$0.328595\pi$
$80$	0	0
$81$	2.53363e16	1.51922
$82$	1.45463e16	0.785842
$83$	1.96416e16	0.957222	0.478611	−	0.878027i	$-0.341140\pi$
$83$	1.96416e16	0.957222	0.478611	+	0.878027i	$0.341140\pi$
$84$	2.33563e16	1.02809
$85$	0	0
$86$	1.29906e15	0.0468158
$87$	6.68698e16	2.18432
$88$	−8.37099e15	−0.248127
$89$	2.45918e16	0.662178	0.331089	−	0.943600i	$-0.392584\pi$
$89$	2.45918e16	0.662178	0.331089	+	0.943600i	$0.392584\pi$
$90$	0	0
$91$	8.82108e16	1.96639
$92$	−3.09722e16	−0.629182
$93$	6.54393e16	1.21264
$94$	−8.50752e15	−0.143951
$95$	0	0
$96$	−2.22257e16	−0.314449
$97$	−3.63292e16	−0.470647	−0.235324	−	0.971917i	$-0.575615\pi$
$97$	−3.63292e16	−0.470647	−0.235324	+	0.971917i	$0.575615\pi$
$98$	−2.00215e16	−0.237725
$99$	1.39443e17	1.51878
$100$	0	0
$101$	−1.67053e17	−1.53505	−0.767527	−	0.641017i	$-0.778513\pi$
$101$	−1.67053e17	−1.53505	−0.767527	+	0.641017i	$0.778513\pi$
$102$	8.36754e16	0.707125
$103$	−1.13488e16	−0.0882739	−0.0441370	−	0.999025i	$-0.514054\pi$
$103$	−1.13488e16	−0.0882739	−0.0441370	+	0.999025i	$0.514054\pi$
$104$	−8.39409e16	−0.601437
$105$	0	0
$106$	1.56423e17	0.953235
$107$	1.72393e17	0.969970	0.484985	−	0.874522i	$-0.338825\pi$
$107$	1.72393e17	0.969970	0.484985	+	0.874522i	$0.338825\pi$
$108$	1.99153e17	1.03534
$109$	−3.17806e17	−1.52770	−0.763848	−	0.645396i	$-0.776693\pi$
$109$	−3.17806e17	−1.52770	−0.763848	+	0.645396i	$0.776693\pi$
$110$	0	0
$111$	1.16617e16	0.0480304
$112$	7.57230e16	0.288985
$113$	3.07271e17	1.08731	0.543657	−	0.839307i	$-0.317039\pi$
$113$	3.07271e17	1.08731	0.543657	+	0.839307i	$0.317039\pi$
$114$	−1.77988e17	−0.584386
$115$	0	0
$116$	2.16798e17	0.613990
$117$	1.39827e18	3.68139
$118$	2.20959e17	0.541147
$119$	−2.85082e17	−0.649862
$120$	0	0
$121$	−2.56496e17	−0.507463
$122$	2.19572e17	0.405059
$123$	−1.14860e18	−1.97686
$124$	2.12160e17	0.340862
$125$	0	0
$126$	−1.26138e18	−1.76887
$127$	−8.22015e17	−1.07782	−0.538912	−	0.842362i	$-0.681165\pi$
$127$	−8.22015e17	−1.07782	−0.538912	+	0.842362i	$0.681165\pi$
$128$	−7.20576e16	−0.0883883
$129$	−1.02576e17	−0.117769
$130$	0	0
$131$	2.64662e17	0.266616	0.133308	−	0.991075i	$-0.457440\pi$
$131$	2.64662e17	0.266616	0.133308	+	0.991075i	$0.457440\pi$
$132$	6.60987e17	0.624186
$133$	6.06406e17	0.537062
$134$	1.04036e17	0.0864553
$135$	0	0
$136$	2.71283e17	0.198766
$137$	−1.71830e17	−0.118297	−0.0591486	−	0.998249i	$-0.518839\pi$
$137$	−1.71830e17	−0.118297	−0.0591486	+	0.998249i	$0.518839\pi$
$138$	2.44562e18	1.58276
$139$	2.86799e18	1.74563	0.872814	−	0.488053i	$-0.162293\pi$
$139$	2.86799e18	1.74563	0.872814	+	0.488053i	$0.162293\pi$
$140$	0	0
$141$	6.71767e17	0.362123
$142$	2.44100e18	1.23913
$143$	2.49638e18	1.19386
$144$	1.20032e18	0.541024
$145$	0	0
$146$	−1.55428e18	−0.623061
$147$	1.58093e18	0.598018
$148$	3.78082e16	0.0135009
$149$	2.17323e18	0.732863	0.366431	−	0.930445i	$-0.380579\pi$
$149$	2.17323e18	0.732863	0.366431	+	0.930445i	$0.380579\pi$
$150$	0	0
$151$	1.81870e18	0.547591	0.273796	−	0.961788i	$-0.411721\pi$
$151$	1.81870e18	0.547591	0.273796	+	0.961788i	$0.411721\pi$
$152$	−5.77053e17	−0.164265
$153$	−4.51898e18	−1.21664
$154$	−2.25198e18	−0.573639
$155$	0	0
$156$	6.62810e18	1.51297
$157$	6.73380e18	1.45584	0.727919	−	0.685663i	$-0.240488\pi$
$157$	6.73380e18	1.45584	0.727919	+	0.685663i	$0.240488\pi$
$158$	−3.54062e18	−0.725260
$159$	−1.23514e19	−2.39795
$160$	0	0
$161$	−8.33222e18	−1.45459
$162$	−6.48609e18	−1.07425
$163$	1.37505e18	0.216134	0.108067	−	0.994144i	$-0.465534\pi$
$163$	1.37505e18	0.216134	0.108067	+	0.994144i	$0.465534\pi$
$164$	−3.72386e18	−0.555674
$165$	0	0
$166$	−5.02825e18	−0.676858
$167$	−5.07885e18	−0.649644	−0.324822	−	0.945775i	$-0.605304\pi$
$167$	−5.07885e18	−0.649644	−0.324822	+	0.945775i	$0.605304\pi$
$168$	−5.97921e18	−0.726967
$169$	1.63823e19	1.89381
$170$	0	0
$171$	9.61244e18	1.00546
$172$	−3.32560e17	−0.0331038
$173$	1.55546e19	1.47390	0.736949	−	0.675948i	$-0.236266\pi$
$173$	1.55546e19	1.47390	0.736949	+	0.675948i	$0.236266\pi$
$174$	−1.71187e19	−1.54455
$175$	0	0
$176$	2.14297e18	0.175452
$177$	−1.74473e19	−1.36130
$178$	−6.29549e18	−0.468230
$179$	−6.70360e18	−0.475398	−0.237699	−	0.971339i	$-0.576393\pi$
$179$	−6.70360e18	−0.475398	−0.237699	+	0.971339i	$0.576393\pi$
$180$	0	0
$181$	1.39268e19	0.898637	0.449318	−	0.893372i	$-0.351667\pi$
$181$	1.39268e19	0.898637	0.449318	+	0.893372i	$0.351667\pi$
$182$	−2.25820e19	−1.39045
$183$	−1.73377e19	−1.01896
$184$	7.92890e18	0.444899
$185$	0	0
$186$	−1.67524e19	−0.857469
$187$	−8.06788e18	−0.394553
$188$	2.17792e18	0.101789
$189$	5.35765e19	2.39358
$190$	0	0
$191$	−1.88045e18	−0.0768205	−0.0384103	−	0.999262i	$-0.512229\pi$
$191$	−1.88045e18	−0.0768205	−0.0384103	+	0.999262i	$0.512229\pi$
$192$	5.68978e18	0.222349
$193$	2.08963e18	0.0781325	0.0390663	−	0.999237i	$-0.487562\pi$
$193$	2.08963e18	0.0781325	0.0390663	+	0.999237i	$0.487562\pi$
$194$	9.30026e18	0.332798
$195$	0	0
$196$	5.12550e18	0.168097
$197$	3.11134e18	0.0977202	0.0488601	−	0.998806i	$-0.484441\pi$
$197$	3.11134e18	0.0977202	0.0488601	+	0.998806i	$0.484441\pi$
$198$	−3.56973e19	−1.07394
$199$	−2.90090e19	−0.836144	−0.418072	−	0.908414i	$-0.637294\pi$
$199$	−2.90090e19	−0.836144	−0.418072	+	0.908414i	$0.637294\pi$
$200$	0	0
$201$	−8.21482e18	−0.217486
$202$	4.27656e19	1.08545
$203$	5.83233e19	1.41947
$204$	−2.14209e19	−0.500013
$205$	0	0
$206$	2.90529e18	0.0624191
$207$	−1.32078e20	−2.72322
$208$	2.14889e19	0.425280
$209$	1.71614e19	0.326069
$210$	0	0
$211$	3.27307e19	0.573528	0.286764	−	0.958001i	$-0.407420\pi$
$211$	3.27307e19	0.573528	0.286764	+	0.958001i	$0.407420\pi$
$212$	−4.00442e19	−0.674039
$213$	−1.92745e20	−3.11715
$214$	−4.41327e19	−0.685873
$215$	0	0
$216$	−5.09831e19	−0.732098
$217$	5.70756e19	0.788031
$218$	8.13584e19	1.08024
$219$	1.22729e20	1.56737
$220$	0	0
$221$	−8.09014e19	−0.956361
$222$	−2.98539e18	−0.0339626
$223$	−4.94295e19	−0.541246	−0.270623	−	0.962685i	$-0.587230\pi$
$223$	−4.94295e19	−0.541246	−0.270623	+	0.962685i	$0.587230\pi$
$224$	−1.93851e19	−0.204343
$225$	0	0
$226$	−7.86615e19	−0.768848
$227$	−1.02192e20	−0.962052	−0.481026	−	0.876706i	$-0.659736\pi$
$227$	−1.02192e20	−0.962052	−0.481026	+	0.876706i	$0.659736\pi$
$228$	4.55650e19	0.413223
$229$	−1.74856e20	−1.52785	−0.763923	−	0.645308i	$-0.776729\pi$
$229$	−1.74856e20	−1.52785	−0.763923	+	0.645308i	$0.776729\pi$
$230$	0	0
$231$	1.77820e20	1.44304
$232$	−5.55002e19	−0.434157
$233$	1.22044e20	0.920430	0.460215	−	0.887807i	$-0.347772\pi$
$233$	1.22044e20	0.920430	0.460215	+	0.887807i	$0.347772\pi$
$234$	−3.57958e20	−2.60314
$235$	0	0
$236$	−5.65656e19	−0.382648
$237$	2.79573e20	1.82446
$238$	7.29811e19	0.459522
$239$	2.03446e20	1.23614	0.618069	−	0.786124i	$-0.287915\pi$
$239$	2.03446e20	1.23614	0.618069	+	0.786124i	$0.287915\pi$
$240$	0	0
$241$	−2.15084e20	−1.21749	−0.608743	−	0.793368i	$-0.708326\pi$
$241$	−2.15084e20	−1.21749	−0.608743	+	0.793368i	$0.708326\pi$
$242$	6.56629e19	0.358831
$243$	1.19717e20	0.631687
$244$	−5.62104e19	−0.286420
$245$	0	0
$246$	2.94041e20	1.39785
$247$	1.72088e20	0.790361
$248$	−5.43129e19	−0.241026
$249$	3.97038e20	1.70270
$250$	0	0
$251$	−1.40847e19	−0.0564315	−0.0282158	−	0.999602i	$-0.508983\pi$
$251$	−1.40847e19	−0.0564315	−0.0282158	+	0.999602i	$0.508983\pi$
$252$	3.22913e20	1.25078
$253$	−2.35803e20	−0.883132
$254$	2.10436e20	0.762137
$255$	0	0
$256$	1.84467e19	0.0625000
$257$	−1.66925e20	−0.547129	−0.273564	−	0.961854i	$-0.588203\pi$
$257$	−1.66925e20	−0.547129	−0.273564	+	0.961854i	$0.588203\pi$
$258$	2.62594e19	0.0832756
$259$	1.01712e19	0.0312123
$260$	0	0
$261$	9.24512e20	2.65747
$262$	−6.77536e19	−0.188526
$263$	−2.85711e20	−0.769667	−0.384834	−	0.922986i	$-0.625741\pi$
$263$	−2.85711e20	−0.769667	−0.384834	+	0.922986i	$0.625741\pi$
$264$	−1.69213e20	−0.441366
$265$	0	0
$266$	−1.55240e20	−0.379760
$267$	4.97102e20	1.17788
$268$	−2.66331e19	−0.0611331
$269$	4.15461e20	0.923923	0.461962	−	0.886900i	$-0.347146\pi$
$269$	4.15461e20	0.923923	0.461962	+	0.886900i	$0.347146\pi$
$270$	0	0
$271$	2.65437e20	0.554272	0.277136	−	0.960831i	$-0.410615\pi$
$271$	2.65437e20	0.554272	0.277136	+	0.960831i	$0.410615\pi$
$272$	−6.94484e19	−0.140549
$273$	1.78311e21	3.49780
$274$	4.39885e19	0.0836487
$275$	0	0
$276$	−6.26078e20	−1.11918
$277$	1.04764e21	1.81608	0.908039	−	0.418886i	$-0.137579\pi$
$277$	1.04764e21	1.81608	0.908039	+	0.418886i	$0.137579\pi$
$278$	−7.34205e20	−1.23435
$279$	9.04734e20	1.47532
$280$	0	0
$281$	−4.31210e20	−0.661736	−0.330868	−	0.943677i	$-0.607342\pi$
$281$	−4.31210e20	−0.661736	−0.330868	+	0.943677i	$0.607342\pi$
$282$	−1.71972e20	−0.256060
$283$	5.09227e20	0.735745	0.367872	−	0.929876i	$-0.380086\pi$
$283$	5.09227e20	0.735745	0.367872	+	0.929876i	$0.380086\pi$
$284$	−6.24897e20	−0.876198
$285$	0	0
$286$	−6.39074e20	−0.844189
$287$	−1.00180e21	−1.28465
$288$	−3.07283e20	−0.382562
$289$	−5.65781e20	−0.683938
$290$	0	0
$291$	−7.34363e20	−0.837183
$292$	3.97896e20	0.440571
$293$	6.39057e20	0.687329	0.343664	−	0.939093i	$-0.388332\pi$
$293$	6.39057e20	0.687329	0.343664	+	0.939093i	$0.388332\pi$
$294$	−4.04717e20	−0.422862
$295$	0	0
$296$	−9.67890e18	−0.00954655
$297$	1.51622e21	1.45323
$298$	−5.56347e20	−0.518212
$299$	−2.36454e21	−2.14063
$300$	0	0
$301$	−8.94659e19	−0.0765319
$302$	−4.65587e20	−0.387205
$303$	−3.37684e21	−2.73054
$304$	1.47726e20	0.116153
$305$	0	0
$306$	1.15686e21	0.860296
$307$	−2.65100e21	−1.91749	−0.958746	−	0.284265i	$-0.908251\pi$
$307$	−2.65100e21	−1.91749	−0.958746	+	0.284265i	$0.908251\pi$
$308$	5.76508e20	0.405624
$309$	−2.29406e20	−0.157021
$310$	0	0
$311$	−2.17669e21	−1.41037	−0.705185	−	0.709023i	$-0.749136\pi$
$311$	−2.17669e21	−1.41037	−0.705185	+	0.709023i	$0.749136\pi$
$312$	−1.69679e21	−1.06983
$313$	−6.47134e19	−0.0397070	−0.0198535	−	0.999803i	$-0.506320\pi$
$313$	−6.47134e19	−0.0397070	−0.0198535	+	0.999803i	$0.506320\pi$
$314$	−1.72385e21	−1.02943
$315$	0	0
$316$	9.06398e20	0.512836
$317$	3.20908e21	1.76757	0.883785	−	0.467893i	$-0.154987\pi$
$317$	3.20908e21	1.76757	0.883785	+	0.467893i	$0.154987\pi$
$318$	3.16195e21	1.69561
$319$	1.65056e21	0.861808
$320$	0	0
$321$	3.48479e21	1.72537
$322$	2.13305e21	1.02855
$323$	−5.56158e20	−0.261202
$324$	1.66044e21	0.759609
$325$	0	0
$326$	−3.52012e20	−0.152830
$327$	−6.42418e21	−2.71745
$328$	9.53307e20	0.392921
$329$	5.85910e20	0.235324
$330$	0	0
$331$	−4.59189e21	−1.75167	−0.875837	−	0.482608i	$-0.839690\pi$
$331$	−4.59189e21	−1.75167	−0.875837	+	0.482608i	$0.839690\pi$
$332$	1.28723e21	0.478611
$333$	1.61229e20	0.0584344
$334$	1.30019e21	0.459368
$335$	0	0
$336$	1.53068e21	0.514043
$337$	−3.38339e21	−1.10789	−0.553946	−	0.832552i	$-0.686879\pi$
$337$	−3.38339e21	−1.10789	−0.553946	+	0.832552i	$0.686879\pi$
$338$	−4.19386e21	−1.33913
$339$	6.21123e21	1.93411
$340$	0	0
$341$	1.61525e21	0.478440
$342$	−2.46078e21	−0.710971
$343$	−2.72255e21	−0.767319
$344$	8.51353e19	0.0234079
$345$	0	0
$346$	−3.98198e21	−1.04220
$347$	−7.94764e20	−0.202973	−0.101486	−	0.994837i	$-0.532360\pi$
$347$	−7.94764e20	−0.202973	−0.101486	+	0.994837i	$0.532360\pi$
$348$	4.38238e21	1.09216
$349$	−5.52679e20	−0.134418	−0.0672089	−	0.997739i	$-0.521409\pi$
$349$	−5.52679e20	−0.134418	−0.0672089	+	0.997739i	$0.521409\pi$
$350$	0	0
$351$	1.52041e22	3.52249
$352$	−5.48601e20	−0.124064
$353$	−4.24483e21	−0.937076	−0.468538	−	0.883443i	$-0.655219\pi$
$353$	−4.24483e21	−0.937076	−0.468538	+	0.883443i	$0.655219\pi$
$354$	4.46650e21	0.962587
$355$	0	0
$356$	1.61165e21	0.331089
$357$	−5.76270e21	−1.15597
$358$	1.71612e21	0.336157
$359$	−6.15257e21	−1.17694	−0.588469	−	0.808520i	$-0.700269\pi$
$359$	−6.15257e21	−1.17694	−0.588469	+	0.808520i	$0.700269\pi$
$360$	0	0
$361$	−4.29737e21	−0.784136
$362$	−3.56527e21	−0.635432
$363$	−5.18484e21	−0.902671
$364$	5.78098e21	0.983196
$365$	0	0
$366$	4.43846e21	0.720516
$367$	1.53580e21	0.243598	0.121799	−	0.992555i	$-0.461134\pi$
$367$	1.53580e21	0.243598	0.121799	+	0.992555i	$0.461134\pi$
$368$	−2.02980e21	−0.314591
$369$	−1.58800e22	−2.40506
$370$	0	0
$371$	−1.07728e22	−1.55829
$372$	4.28863e21	0.606322
$373$	1.00414e22	1.38762	0.693808	−	0.720160i	$-0.255931\pi$
$373$	1.00414e22	1.38762	0.693808	+	0.720160i	$0.255931\pi$
$374$	2.06538e21	0.278991
$375$	0	0
$376$	−5.57549e20	−0.0719757
$377$	1.65511e22	2.08894
$378$	−1.37156e22	−1.69252
$379$	−1.19831e22	−1.44589	−0.722944	−	0.690907i	$-0.757212\pi$
$379$	−1.19831e22	−1.44589	−0.722944	+	0.690907i	$0.757212\pi$
$380$	0	0
$381$	−1.66163e22	−1.91722
$382$	4.81394e20	0.0543203
$383$	1.12305e22	1.23940	0.619699	−	0.784839i	$-0.287255\pi$
$383$	1.12305e22	1.23940	0.619699	+	0.784839i	$0.287255\pi$
$384$	−1.45658e21	−0.157224
$385$	0	0
$386$	−5.34945e20	−0.0552480
$387$	−1.41817e21	−0.143280
$388$	−2.38087e21	−0.235324
$389$	−2.54158e21	−0.245772	−0.122886	−	0.992421i	$-0.539215\pi$
$389$	−2.54158e21	−0.245772	−0.122886	+	0.992421i	$0.539215\pi$
$390$	0	0
$391$	7.64179e21	0.707445
$392$	−1.31213e21	−0.118862
$393$	5.34993e21	0.474254
$394$	−7.96503e20	−0.0690986
$395$	0	0
$396$	9.13850e21	0.759392
$397$	−3.06633e21	−0.249402	−0.124701	−	0.992194i	$-0.539797\pi$
$397$	−3.06633e21	−0.249402	−0.124701	+	0.992194i	$0.539797\pi$
$398$	7.42630e21	0.591243
$399$	1.22580e22	0.955322
$400$	0	0
$401$	−1.31178e22	−0.979793	−0.489897	−	0.871781i	$-0.662965\pi$
$401$	−1.31178e22	−0.979793	−0.489897	+	0.871781i	$0.662965\pi$
$402$	2.10299e21	0.153786
$403$	1.61971e22	1.15969
$404$	−1.09480e22	−0.767527
$405$	0	0
$406$	−1.49308e22	−1.00372
$407$	2.87848e20	0.0189501
$408$	5.48375e21	0.353563
$409$	2.29036e21	0.144629	0.0723146	−	0.997382i	$-0.476961\pi$
$409$	2.29036e21	0.144629	0.0723146	+	0.997382i	$0.476961\pi$
$410$	0	0
$411$	−3.47340e21	−0.210426
$412$	−7.43753e20	−0.0441370
$413$	−1.52174e22	−0.884636
$414$	3.38120e22	1.92561
$415$	0	0
$416$	−5.50115e21	−0.300719
$417$	5.79740e22	3.10511
$418$	−4.39332e21	−0.230566
$419$	−9.99153e21	−0.513822	−0.256911	−	0.966435i	$-0.582705\pi$
$419$	−9.99153e21	−0.513822	−0.256911	+	0.966435i	$0.582705\pi$
$420$	0	0
$421$	2.42321e22	1.19672	0.598361	−	0.801227i	$-0.295819\pi$
$421$	2.42321e22	1.19672	0.598361	+	0.801227i	$0.295819\pi$
$422$	−8.37906e21	−0.405546
$423$	9.28754e21	0.440563
$424$	1.02513e22	0.476617
$425$	0	0
$426$	4.93428e22	2.20416
$427$	−1.51219e22	−0.662168
$428$	1.12980e22	0.484985
$429$	5.04622e22	2.12363
$430$	0	0
$431$	−3.74076e21	−0.151322	−0.0756611	−	0.997134i	$-0.524107\pi$
$431$	−3.74076e21	−0.151322	−0.0756611	+	0.997134i	$0.524107\pi$
$432$	1.30517e22	0.517671
$433$	−3.00276e22	−1.16781	−0.583907	−	0.811820i	$-0.698477\pi$
$433$	−3.00276e22	−1.16781	−0.583907	+	0.811820i	$0.698477\pi$
$434$	−1.46114e22	−0.557222
$435$	0	0
$436$	−2.08277e22	−0.763848
$437$	−1.62551e22	−0.584650
$438$	−3.14185e22	−1.10830
$439$	−4.88091e22	−1.68870	−0.844349	−	0.535793i	$-0.820013\pi$
$439$	−4.88091e22	−1.68870	−0.844349	+	0.535793i	$0.820013\pi$
$440$	0	0
$441$	2.18572e22	0.727555
$442$	2.07108e22	0.676249
$443$	8.85676e20	0.0283689	0.0141845	−	0.999899i	$-0.495485\pi$
$443$	8.85676e20	0.0283689	0.0141845	+	0.999899i	$0.495485\pi$
$444$	7.64261e20	0.0240152
$445$	0	0
$446$	1.26540e22	0.382719
$447$	4.39300e22	1.30361
$448$	4.96258e21	0.144492
$449$	1.07587e18	3.07374e−5 0	1.53687e−5	−	1.00000i	$-0.499995\pi$
$449$	1.07587e18	3.07374e−5 0	1.53687e−5		1.00000i	$0.499995\pi$
$450$	0	0
$451$	−2.83511e22	−0.779955
$452$	2.01373e22	0.543657
$453$	3.67634e22	0.974050
$454$	2.61612e22	0.680274
$455$	0	0
$456$	−1.16646e22	−0.292193
$457$	4.30315e21	0.105803	0.0529016	−	0.998600i	$-0.483153\pi$
$457$	4.30315e21	0.105803	0.0529016	+	0.998600i	$0.483153\pi$
$458$	4.47632e22	1.08035
$459$	−4.91369e22	−1.16413
$460$	0	0
$461$	−3.48054e22	−0.794674	−0.397337	−	0.917673i	$-0.630066\pi$
$461$	−3.48054e22	−0.794674	−0.397337	+	0.917673i	$0.630066\pi$
$462$	−4.55219e22	−1.02038
$463$	2.06561e21	0.0454579	0.0227290	−	0.999742i	$-0.492765\pi$
$463$	2.06561e21	0.0454579	0.0227290	+	0.999742i	$0.492765\pi$
$464$	1.42080e22	0.306995
$465$	0	0
$466$	−3.12432e22	−0.650843
$467$	−2.27698e22	−0.465763	−0.232882	−	0.972505i	$-0.574815\pi$
$467$	−2.27698e22	−0.465763	−0.232882	+	0.972505i	$0.574815\pi$
$468$	9.16372e22	1.84070
$469$	−7.16490e21	−0.141332
$470$	0	0
$471$	1.36118e23	2.58963
$472$	1.44808e22	0.270573
$473$	−2.53190e21	−0.0464651
$474$	−7.15706e22	−1.29009
$475$	0	0
$476$	−1.86831e22	−0.324931
$477$	−1.70765e23	−2.91737
$478$	−5.20822e22	−0.874081
$479$	2.90207e22	0.478471	0.239236	−	0.970962i	$-0.423103\pi$
$479$	2.90207e22	0.478471	0.239236	+	0.970962i	$0.423103\pi$
$480$	0	0
$481$	2.88642e21	0.0459332
$482$	5.50616e22	0.860892
$483$	−1.68429e23	−2.58741
$484$	−1.68097e22	−0.253732
$485$	0	0
$486$	−3.06475e22	−0.446670
$487$	−2.68073e22	−0.383934	−0.191967	−	0.981401i	$-0.561487\pi$
$487$	−2.68073e22	−0.383934	−0.191967	+	0.981401i	$0.561487\pi$
$488$	1.43899e22	0.202530
$489$	2.77954e22	0.384457
$490$	0	0
$491$	−9.88548e22	−1.32070	−0.660351	−	0.750957i	$-0.729593\pi$
$491$	−9.88548e22	−1.32070	−0.660351	+	0.750957i	$0.729593\pi$
$492$	−7.52746e22	−0.988428
$493$	−5.34905e22	−0.690363
$494$	−4.40544e22	−0.558869
$495$	0	0
$496$	1.39041e22	0.170431
$497$	−1.68111e23	−2.02566
$498$	−1.01642e23	−1.20399
$499$	1.20742e23	1.40606	0.703030	−	0.711160i	$-0.251830\pi$
$499$	1.20742e23	1.40606	0.703030	+	0.711160i	$0.251830\pi$
$500$	0	0
$501$	−1.02665e23	−1.15558
$502$	3.60569e21	0.0399031
$503$	7.15920e22	0.778998	0.389499	−	0.921027i	$-0.372648\pi$
$503$	7.15920e22	0.778998	0.389499	+	0.921027i	$0.372648\pi$
$504$	−8.26658e22	−0.884436
$505$	0	0
$506$	6.03657e22	0.624469
$507$	3.31154e23	3.36870
$508$	−5.38716e22	−0.538912
$509$	−9.08719e22	−0.893981	−0.446991	−	0.894539i	$-0.647504\pi$
$509$	−9.08719e22	−0.893981	−0.446991	+	0.894539i	$0.647504\pi$
$510$	0	0
$511$	1.07043e23	1.01855
$512$	−4.72237e21	−0.0441942
$513$	1.04521e23	0.962064
$514$	4.27328e22	0.386878
$515$	0	0
$516$	−6.72241e21	−0.0588847
$517$	1.65814e22	0.142873
$518$	−2.60384e21	−0.0220705
$519$	3.14424e23	2.62176
$520$	0	0
$521$	3.85520e22	0.311119	0.155559	−	0.987827i	$-0.450282\pi$
$521$	3.85520e22	0.311119	0.155559	+	0.987827i	$0.450282\pi$
$522$	−2.36675e23	−1.87911
$523$	1.28297e23	1.00219	0.501097	−	0.865391i	$-0.332930\pi$
$523$	1.28297e23	1.00219	0.501097	+	0.865391i	$0.332930\pi$
$524$	1.73449e22	0.133308
$525$	0	0
$526$	7.31420e22	0.544237
$527$	−5.23462e22	−0.383261
$528$	4.33184e22	0.312093
$529$	8.22998e22	0.583479
$530$	0	0
$531$	−2.41218e23	−1.65618
$532$	3.97414e22	0.268531
$533$	−2.84293e23	−1.89054
$534$	−1.27258e23	−0.832884
$535$	0	0
$536$	6.81808e21	0.0432276
$537$	−1.35508e23	−0.845633
$538$	−1.06358e23	−0.653312
$539$	3.90223e22	0.235944
$540$	0	0
$541$	3.40003e23	1.99207	0.996037	−	0.0889412i	$-0.0283483\pi$
$541$	3.40003e23	1.99207	0.996037	+	0.0889412i	$0.0283483\pi$
$542$	−6.79519e22	−0.391929
$543$	2.81519e23	1.59849
$544$	1.77788e22	0.0993828
$545$	0	0
$546$	−4.56475e23	−2.47332
$547$	−2.66900e23	−1.42383	−0.711913	−	0.702268i	$-0.752171\pi$
$547$	−2.66900e23	−1.42383	−0.711913	+	0.702268i	$0.752171\pi$
$548$	−1.12611e22	−0.0591486
$549$	−2.39704e23	−1.23968
$550$	0	0
$551$	1.13781e23	0.570534
$552$	1.60276e23	0.791382
$553$	2.43841e23	1.18561
$554$	−2.68196e23	−1.28416
$555$	0	0
$556$	1.87957e23	0.872814
$557$	2.58262e22	0.118111	0.0590555	−	0.998255i	$-0.481191\pi$
$557$	2.58262e22	0.118111	0.0590555	+	0.998255i	$0.481191\pi$
$558$	−2.31612e23	−1.04321
$559$	−2.53889e22	−0.112627
$560$	0	0
$561$	−1.63085e23	−0.701828
$562$	1.10390e23	0.467918
$563$	−1.41028e22	−0.0588822	−0.0294411	−	0.999567i	$-0.509373\pi$
$563$	−1.41028e22	−0.0588822	−0.0294411	+	0.999567i	$0.509373\pi$
$564$	4.40249e22	0.181061
$565$	0	0
$566$	−1.30362e23	−0.520250
$567$	4.46695e23	1.75612
$568$	1.59974e23	0.619566
$569$	−2.13811e23	−0.815785	−0.407892	−	0.913030i	$-0.633736\pi$
$569$	−2.13811e23	−0.815785	−0.407892	+	0.913030i	$0.633736\pi$
$570$	0	0
$571$	1.13718e23	0.421136	0.210568	−	0.977579i	$-0.432469\pi$
$571$	1.13718e23	0.421136	0.210568	+	0.977579i	$0.432469\pi$
$572$	1.63603e23	0.596932
$573$	−3.80116e22	−0.136648
$574$	2.56461e23	0.908385
$575$	0	0
$576$	7.86643e22	0.270512
$577$	2.79237e23	0.946191	0.473096	−	0.881011i	$-0.343136\pi$
$577$	2.79237e23	0.946191	0.473096	+	0.881011i	$0.343136\pi$
$578$	1.44840e23	0.483617
$579$	4.22401e22	0.138981
$580$	0	0
$581$	3.46294e23	1.10649
$582$	1.87997e23	0.591978
$583$	−3.04872e23	−0.946094
$584$	−1.01861e23	−0.311531
$585$	0	0
$586$	−1.63599e23	−0.486015
$587$	6.02342e23	1.76368	0.881840	−	0.471549i	$-0.156305\pi$
$587$	6.02342e23	1.76368	0.881840	+	0.471549i	$0.156305\pi$
$588$	1.03608e23	0.299009
$589$	1.11347e23	0.316737
$590$	0	0
$591$	6.28931e22	0.173824
$592$	2.47780e21	0.00675043
$593$	−3.93286e23	−1.05619	−0.528097	−	0.849184i	$-0.677094\pi$
$593$	−3.93286e23	−1.05619	−0.528097	+	0.849184i	$0.677094\pi$
$594$	−3.88153e23	−1.02759
$595$	0	0
$596$	1.42425e23	0.366431
$597$	−5.86392e23	−1.48733
$598$	6.05322e23	1.51365
$599$	−3.72267e23	−0.917754	−0.458877	−	0.888500i	$-0.651748\pi$
$599$	−3.72267e23	−0.917754	−0.458877	+	0.888500i	$0.651748\pi$
$600$	0	0
$601$	−2.05419e23	−0.492275	−0.246138	−	0.969235i	$-0.579162\pi$
$601$	−2.05419e23	−0.492275	−0.246138	+	0.969235i	$0.579162\pi$
$602$	2.29033e22	0.0541162
$603$	−1.13574e23	−0.264596
$604$	1.19190e23	0.273796
$605$	0	0
$606$	8.64471e23	1.93078
$607$	−6.45041e22	−0.142064	−0.0710319	−	0.997474i	$-0.522629\pi$
$607$	−6.45041e22	−0.142064	−0.0710319	+	0.997474i	$0.522629\pi$
$608$	−3.78177e22	−0.0821325
$609$	1.17896e24	2.52494
$610$	0	0
$611$	1.66271e23	0.346311
$612$	−2.96156e23	−0.608321
$613$	8.33557e22	0.168858	0.0844289	−	0.996430i	$-0.473093\pi$
$613$	8.33557e22	0.168858	0.0844289	+	0.996430i	$0.473093\pi$
$614$	6.78656e23	1.35587
$615$	0	0
$616$	−1.47586e23	−0.286820
$617$	1.53109e23	0.293479	0.146739	−	0.989175i	$-0.453122\pi$
$617$	1.53109e23	0.293479	0.146739	+	0.989175i	$0.453122\pi$
$618$	5.87279e22	0.111031
$619$	9.76593e23	1.82114	0.910569	−	0.413356i	$-0.135644\pi$
$619$	9.76593e23	1.82114	0.910569	+	0.413356i	$0.135644\pi$
$620$	0	0
$621$	−1.43615e24	−2.60567
$622$	5.57233e23	0.997283
$623$	4.33568e23	0.765437
$624$	4.34379e23	0.756485
$625$	0	0
$626$	1.65666e22	0.0280771
$627$	3.46903e23	0.580008
$628$	4.41306e23	0.727919
$629$	−9.32843e21	−0.0151802
$630$	0	0
$631$	−6.02040e23	−0.953621	−0.476811	−	0.879006i	$-0.658207\pi$
$631$	−6.02040e23	−0.953621	−0.476811	+	0.879006i	$0.658207\pi$
$632$	−2.32038e23	−0.362630
$633$	6.61624e23	1.02019
$634$	−8.21524e23	−1.24986
$635$	0	0
$636$	−8.09460e23	−1.19897
$637$	3.91300e23	0.571906
$638$	−4.22544e23	−0.609391
$639$	−2.66481e24	−3.79236
$640$	0	0
$641$	8.13646e23	1.12757	0.563783	−	0.825923i	$-0.309345\pi$
$641$	8.13646e23	1.12757	0.563783	+	0.825923i	$0.309345\pi$
$642$	−8.92105e23	−1.22002
$643$	1.02063e23	0.137745	0.0688726	−	0.997625i	$-0.478060\pi$
$643$	1.02063e23	0.137745	0.0688726	+	0.997625i	$0.478060\pi$
$644$	−5.46060e23	−0.727295
$645$	0	0
$646$	1.42376e23	0.184698
$647$	−9.71752e23	−1.24414	−0.622070	−	0.782962i	$-0.713708\pi$
$647$	−9.71752e23	−1.24414	−0.622070	+	0.782962i	$0.713708\pi$
$648$	−4.25072e23	−0.537125
$649$	−4.30655e23	−0.537093
$650$	0	0
$651$	1.15374e24	1.40174
$652$	9.01151e22	0.108067
$653$	−5.73338e23	−0.678655	−0.339327	−	0.940668i	$-0.610199\pi$
$653$	−5.73338e23	−0.678655	−0.339327	+	0.940668i	$0.610199\pi$
$654$	1.64459e24	1.92153
$655$	0	0
$656$	−2.44047e23	−0.277837
$657$	1.69679e24	1.90688
$658$	−1.49993e23	−0.166399
$659$	6.64180e22	0.0727377	0.0363689	−	0.999338i	$-0.488421\pi$
$659$	6.64180e22	0.0727377	0.0363689	+	0.999338i	$0.488421\pi$
$660$	0	0
$661$	−2.25960e23	−0.241168	−0.120584	−	0.992703i	$-0.538477\pi$
$661$	−2.25960e23	−0.241168	−0.120584	+	0.992703i	$0.538477\pi$
$662$	1.17552e24	1.23862
$663$	−1.63535e24	−1.70117
$664$	−3.29531e23	−0.338429
$665$	0	0
$666$	−4.12747e22	−0.0413193
$667$	−1.56339e24	−1.54525
$668$	−3.32848e23	−0.324822
$669$	−9.99176e23	−0.962764
$670$	0	0
$671$	−4.27951e23	−0.402025
$672$	−3.91853e23	−0.363483
$673$	−2.25201e23	−0.206273	−0.103136	−	0.994667i	$-0.532888\pi$
$673$	−2.25201e23	−0.206273	−0.103136	+	0.994667i	$0.532888\pi$
$674$	8.66147e23	0.783398
$675$	0	0
$676$	1.07363e24	0.946907
$677$	−6.00722e23	−0.523203	−0.261601	−	0.965176i	$-0.584251\pi$
$677$	−6.00722e23	−0.523203	−0.261601	+	0.965176i	$0.584251\pi$
$678$	−1.59008e24	−1.36762
$679$	−6.40506e23	−0.544039
$680$	0	0
$681$	−2.06573e24	−1.71129
$682$	−4.13504e23	−0.338308
$683$	2.10638e24	1.70200	0.851002	−	0.525163i	$-0.175995\pi$
$683$	2.10638e24	1.70200	0.851002	+	0.525163i	$0.175995\pi$
$684$	6.29961e23	0.502732
$685$	0	0
$686$	6.96973e23	0.542577
$687$	−3.53457e24	−2.71772
$688$	−2.17946e22	−0.0165519
$689$	−3.05713e24	−2.29324
$690$	0	0
$691$	1.47665e24	1.08072	0.540360	−	0.841434i	$-0.318288\pi$
$691$	1.47665e24	1.08072	0.540360	+	0.841434i	$0.318288\pi$
$692$	1.01939e24	0.736949
$693$	2.45846e24	1.75562
$694$	2.03460e23	0.143523
$695$	0	0
$696$	−1.12189e24	−0.772274
$697$	9.18787e23	0.624793
$698$	1.41486e23	0.0950478
$699$	2.46701e24	1.63725
$700$	0	0
$701$	−1.95160e24	−1.26412	−0.632059	−	0.774920i	$-0.717790\pi$
$701$	−1.95160e24	−1.26412	−0.632059	+	0.774920i	$0.717790\pi$
$702$	−3.89224e24	−2.49077
$703$	1.98428e22	0.0125453
$704$	1.40442e23	0.0877262
$705$	0	0
$706$	1.08668e24	0.662613
$707$	−2.94526e24	−1.77443
$708$	−1.14342e24	−0.680652
$709$	1.53951e24	0.905505	0.452752	−	0.891636i	$-0.350442\pi$
$709$	1.53951e24	0.905505	0.452752	+	0.891636i	$0.350442\pi$
$710$	0	0
$711$	3.86525e24	2.21966
$712$	−4.12581e23	−0.234115
$713$	−1.52994e24	−0.857856
$714$	1.47525e24	0.817393
$715$	0	0
$716$	−4.39327e23	−0.237699
$717$	4.11249e24	2.19883
$718$	1.57506e24	0.832221
$719$	2.84029e24	1.48309	0.741545	−	0.670903i	$-0.234093\pi$
$719$	2.84029e24	1.48309	0.741545	+	0.670903i	$0.234093\pi$
$720$	0	0
$721$	−2.00086e23	−0.102039
$722$	1.10013e24	0.554468
$723$	−4.34775e24	−2.16565
$724$	9.12708e23	0.449318
$725$	0	0
$726$	1.32732e24	0.638285
$727$	6.98622e23	0.332047	0.166024	−	0.986122i	$-0.446907\pi$
$727$	6.98622e23	0.332047	0.166024	+	0.986122i	$0.446907\pi$
$728$	−1.47993e24	−0.695224
$729$	−8.51957e23	−0.395579
$730$	0	0
$731$	8.20525e22	0.0372215
$732$	−1.13625e24	−0.509481
$733$	2.64577e24	1.17265	0.586326	−	0.810075i	$-0.300574\pi$
$733$	2.64577e24	1.17265	0.586326	+	0.810075i	$0.300574\pi$
$734$	−3.93166e23	−0.172250
$735$	0	0
$736$	5.19628e23	0.222449
$737$	−2.02768e23	−0.0858076
$738$	4.06528e24	1.70064
$739$	−8.69279e22	−0.0359486	−0.0179743	−	0.999838i	$-0.505722\pi$
$739$	−8.69279e22	−0.0359486	−0.0179743	+	0.999838i	$0.505722\pi$
$740$	0	0
$741$	3.47860e24	1.40589
$742$	2.75783e24	1.10188
$743$	−5.50364e23	−0.217393	−0.108696	−	0.994075i	$-0.534668\pi$
$743$	−5.50364e23	−0.217393	−0.108696	+	0.994075i	$0.534668\pi$
$744$	−1.09789e24	−0.428734
$745$	0	0
$746$	−2.57060e24	−0.981193
$747$	5.48927e24	2.07152
$748$	−5.28736e23	−0.197277
$749$	3.03941e24	1.12123
$750$	0	0
$751$	−2.95235e24	−1.06470	−0.532352	−	0.846523i	$-0.678692\pi$
$751$	−2.95235e24	−1.06470	−0.532352	+	0.846523i	$0.678692\pi$
$752$	1.42732e23	0.0508945
$753$	−2.84711e23	−0.100380
$754$	−4.23709e24	−1.47711
$755$	0	0
$756$	3.51119e24	1.19679
$757$	−4.84963e24	−1.63453	−0.817266	−	0.576261i	$-0.804511\pi$
$757$	−4.84963e24	−1.63453	−0.817266	+	0.576261i	$0.804511\pi$
$758$	3.06766e24	1.02240
$759$	−4.76657e24	−1.57091
$760$	0	0
$761$	−4.97641e24	−1.60379	−0.801893	−	0.597468i	$-0.796173\pi$
$761$	−4.97641e24	−1.60379	−0.801893	+	0.597468i	$0.796173\pi$
$762$	4.25378e24	1.35568
$763$	−5.60313e24	−1.76592
$764$	−1.23237e23	−0.0384103
$765$	0	0
$766$	−2.87502e24	−0.876387
$767$	−4.31843e24	−1.30186
$768$	3.72885e23	0.111174
$769$	−4.91902e23	−0.145046	−0.0725228	−	0.997367i	$-0.523105\pi$
$769$	−4.91902e23	−0.145046	−0.0725228	+	0.997367i	$0.523105\pi$
$770$	0	0
$771$	−3.37424e24	−0.973227
$772$	1.36946e23	0.0390663
$773$	−2.61117e24	−0.736732	−0.368366	−	0.929681i	$-0.620083\pi$
$773$	−2.61117e24	−0.736732	−0.368366	+	0.929681i	$0.620083\pi$
$774$	3.63051e23	0.101314
$775$	0	0
$776$	6.09502e23	0.166399
$777$	2.05603e23	0.0555202
$778$	6.50645e23	0.173787
$779$	−1.95438e24	−0.516345
$780$	0	0
$781$	−4.75757e24	−1.22985
$782$	−1.95630e24	−0.500239
$783$	1.00526e25	2.54276
$784$	3.35904e23	0.0840484
$785$	0	0
$786$	−1.36958e24	−0.335348
$787$	4.37257e24	1.05914	0.529568	−	0.848268i	$-0.322354\pi$
$787$	4.37257e24	1.05914	0.529568	+	0.848268i	$0.322354\pi$
$788$	2.03905e23	0.0488601
$789$	−5.77540e24	−1.36908
$790$	0	0
$791$	5.41739e24	1.25687
$792$	−2.33946e24	−0.536971
$793$	−4.29132e24	−0.974471
$794$	7.84981e23	0.176354
$795$	0	0
$796$	−1.90113e24	−0.418072
$797$	1.47316e24	0.320519	0.160260	−	0.987075i	$-0.448767\pi$
$797$	1.47316e24	0.320519	0.160260	+	0.987075i	$0.448767\pi$
$798$	−3.13805e24	−0.675514
$799$	−5.37360e23	−0.114450
$800$	0	0
$801$	6.87271e24	1.43302
$802$	3.35816e24	0.692818
$803$	3.02934e24	0.618394
$804$	−5.38366e23	−0.108743
$805$	0	0
$806$	−4.14645e24	−0.820028
$807$	8.39819e24	1.64347
$808$	2.80269e24	0.542723
$809$	−1.91465e24	−0.366882	−0.183441	−	0.983031i	$-0.558724\pi$
$809$	−1.91465e24	−0.366882	−0.183441	+	0.983031i	$0.558724\pi$
$810$	0	0
$811$	−4.84935e24	−0.909927	−0.454964	−	0.890510i	$-0.650348\pi$
$811$	−4.84935e24	−0.909927	−0.454964	+	0.890510i	$0.650348\pi$
$812$	3.82228e24	0.709735
$813$	5.36559e24	0.985933
$814$	−7.36891e22	−0.0133997
$815$	0	0
$816$	−1.40384e24	−0.250006
$817$	−1.74536e23	−0.0307608
$818$	−5.86332e23	−0.102268
$819$	2.46524e25	4.25546
$820$	0	0
$821$	2.84679e24	0.481326	0.240663	−	0.970609i	$-0.422635\pi$
$821$	2.84679e24	0.481326	0.240663	+	0.970609i	$0.422635\pi$
$822$	8.89190e23	0.148794
$823$	9.76200e24	1.61674	0.808370	−	0.588674i	$-0.200350\pi$
$823$	9.76200e24	1.61674	0.808370	+	0.588674i	$0.200350\pi$
$824$	1.90401e23	0.0312095
$825$	0	0
$826$	3.89565e24	0.625532
$827$	4.92807e24	0.783213	0.391607	−	0.920133i	$-0.371919\pi$
$827$	4.92807e24	0.783213	0.391607	+	0.920133i	$0.371919\pi$
$828$	−8.65587e24	−1.36161
$829$	2.49105e24	0.387854	0.193927	−	0.981016i	$-0.437877\pi$
$829$	2.49105e24	0.387854	0.193927	+	0.981016i	$0.437877\pi$
$830$	0	0
$831$	2.11772e25	3.23042
$832$	1.40829e24	0.212640
$833$	−1.26461e24	−0.189006
$834$	−1.48413e25	−2.19564
$835$	0	0
$836$	1.12469e24	0.163034
$837$	9.83759e24	1.41163
$838$	2.55783e24	0.363327
$839$	9.44495e23	0.132808	0.0664038	−	0.997793i	$-0.478847\pi$
$839$	9.44495e23	0.132808	0.0664038	+	0.997793i	$0.478847\pi$
$840$	0	0
$841$	3.68616e24	0.507935
$842$	−6.20341e24	−0.846210
$843$	−8.71654e24	−1.17709
$844$	2.14504e24	0.286764
$845$	0	0
$846$	−2.37761e24	−0.311525
$847$	−4.52218e24	−0.586596
$848$	−2.62434e24	−0.337019
$849$	1.02936e25	1.30874
$850$	0	0
$851$	−2.72646e23	−0.0339780
$852$	−1.26318e25	−1.55857
$853$	1.00068e25	1.22244	0.611221	−	0.791460i	$-0.290679\pi$
$853$	1.00068e25	1.22244	0.611221	+	0.791460i	$0.290679\pi$
$854$	3.87120e24	0.468223
$855$	0	0
$856$	−2.89228e24	−0.342936
$857$	−1.02788e25	−1.20671	−0.603356	−	0.797472i	$-0.706170\pi$
$857$	−1.02788e25	−1.20671	−0.603356	+	0.797472i	$0.706170\pi$
$858$	−1.29183e25	−1.50164
$859$	−9.78146e24	−1.12580	−0.562900	−	0.826525i	$-0.690315\pi$
$859$	−9.78146e24	−1.12580	−0.562900	+	0.826525i	$0.690315\pi$
$860$	0	0
$861$	−2.02505e25	−2.28512
$862$	9.57634e23	0.107001
$863$	−1.30891e25	−1.44816	−0.724081	−	0.689715i	$-0.757736\pi$
$863$	−1.30891e25	−1.44816	−0.724081	+	0.689715i	$0.757736\pi$
$864$	−3.34123e24	−0.366049
$865$	0	0
$866$	7.68707e24	0.825770
$867$	−1.14368e25	−1.21658
$868$	3.74051e24	0.394015
$869$	6.90075e24	0.719827
$870$	0	0
$871$	−2.03327e24	−0.207990
$872$	5.33190e24	0.540122
$873$	−1.01530e25	−1.01853
$874$	4.16129e24	0.413410
$875$	0	0
$876$	8.04314e24	0.783684
$877$	9.63915e22	0.00930127	0.00465063	−	0.999989i	$-0.498520\pi$
$877$	9.63915e22	0.00930127	0.00465063	+	0.999989i	$0.498520\pi$
$878$	1.24951e25	1.19409
$879$	1.29180e25	1.22261
$880$	0	0
$881$	−1.24804e25	−1.15859	−0.579297	−	0.815116i	$-0.696673\pi$
$881$	−1.24804e25	−1.15859	−0.579297	+	0.815116i	$0.696673\pi$
$882$	−5.59544e24	−0.514459
$883$	1.82649e25	1.66322	0.831611	−	0.555359i	$-0.187419\pi$
$883$	1.82649e25	1.66322	0.831611	+	0.555359i	$0.187419\pi$
$884$	−5.30195e24	−0.478180
$885$	0	0
$886$	−2.26733e23	−0.0200599
$887$	9.15990e24	0.802675	0.401338	−	0.915930i	$-0.368545\pi$
$887$	9.15990e24	0.802675	0.401338	+	0.915930i	$0.368545\pi$
$888$	−1.95651e23	−0.0169813
$889$	−1.44926e25	−1.24590
$890$	0	0
$891$	1.26415e25	1.06620
$892$	−3.23941e24	−0.270623
$893$	1.14303e24	0.0945847
$894$	−1.12461e25	−0.921791
$895$	0	0
$896$	−1.27042e24	−0.102171
$897$	−4.77972e25	−3.80773
$898$	−2.75424e20	−2.17346e−5 0
$899$	1.07092e25	0.837143
$900$	0	0
$901$	9.88011e24	0.757881
$902$	7.25788e24	0.551511
$903$	−1.80848e24	−0.136134
$904$	−5.15516e24	−0.384424
$905$	0	0
$906$	−9.41144e24	−0.688758
$907$	2.04267e25	1.48093	0.740467	−	0.672092i	$-0.234604\pi$
$907$	2.04267e25	1.48093	0.740467	+	0.672092i	$0.234604\pi$
$908$	−6.69728e24	−0.481026
$909$	−4.66867e25	−3.32200
$910$	0	0
$911$	7.78026e24	0.543360	0.271680	−	0.962388i	$-0.412421\pi$
$911$	7.78026e24	0.543360	0.271680	+	0.962388i	$0.412421\pi$
$912$	2.98615e24	0.206612
$913$	9.80017e24	0.671788
$914$	−1.10161e24	−0.0748141
$915$	0	0
$916$	−1.14594e25	−0.763923
$917$	4.66617e24	0.308192
$918$	1.25791e25	0.823162
$919$	−1.92668e25	−1.24919	−0.624594	−	0.780949i	$-0.714736\pi$
$919$	−1.92668e25	−1.24919	−0.624594	+	0.780949i	$0.714736\pi$
$920$	0	0
$921$	−5.35877e25	−3.41082
$922$	8.91018e24	0.561919
$923$	−4.77070e25	−2.98104
$924$	1.16536e25	0.721521
$925$	0	0
$926$	−5.28796e23	−0.0321436
$927$	−3.17166e24	−0.191033
$928$	−3.63726e24	−0.217078
$929$	1.92204e25	1.13666	0.568328	−	0.822802i	$-0.307590\pi$
$929$	1.92204e25	1.13666	0.568328	+	0.822802i	$0.307590\pi$
$930$	0	0
$931$	2.69000e24	0.156199
$932$	7.99827e24	0.460215
$933$	−4.39999e25	−2.50875
$934$	5.82906e24	0.329344
$935$	0	0
$936$	−2.34591e25	−1.30157
$937$	−2.49742e25	−1.37311	−0.686554	−	0.727079i	$-0.740878\pi$
$937$	−2.49742e25	−1.37311	−0.686554	+	0.727079i	$0.740878\pi$
$938$	1.83421e24	0.0999370
$939$	−1.30813e24	−0.0706304
$940$	0	0
$941$	2.13047e25	1.12970	0.564851	−	0.825193i	$-0.308934\pi$
$941$	2.13047e25	1.12970	0.564851	+	0.825193i	$0.308934\pi$
$942$	−3.48462e25	−1.83115
$943$	2.68538e25	1.39848
$944$	−3.70708e24	−0.191324
$945$	0	0
$946$	6.48167e23	0.0328558
$947$	−1.70570e25	−0.856893	−0.428447	−	0.903567i	$-0.640939\pi$
$947$	−1.70570e25	−0.856893	−0.428447	+	0.903567i	$0.640939\pi$
$948$	1.83221e25	0.912229
$949$	3.03769e25	1.49893
$950$	0	0
$951$	6.48688e25	3.14414
$952$	4.78289e24	0.229761
$953$	−6.64867e24	−0.316552	−0.158276	−	0.987395i	$-0.550594\pi$
$953$	−6.64867e24	−0.316552	−0.158276	+	0.987395i	$0.550594\pi$
$954$	4.37157e25	2.06289
$955$	0	0
$956$	1.33330e25	0.618069
$957$	3.33647e25	1.53298
$958$	−7.42929e24	−0.338330
$959$	−3.02947e24	−0.136744
$960$	0	0
$961$	−1.20700e25	−0.535253
$962$	−7.38924e23	−0.0324797
$963$	4.81791e25	2.09911
$964$	−1.40958e25	−0.608743
$965$	0	0
$966$	4.31178e25	1.82958
$967$	1.05112e25	0.442105	0.221052	−	0.975262i	$-0.429051\pi$
$967$	1.05112e25	0.442105	0.221052	+	0.975262i	$0.429051\pi$
$968$	4.30328e24	0.179415
$969$	−1.12423e25	−0.464624
$970$	0	0
$971$	−2.13371e25	−0.866507	−0.433254	−	0.901272i	$-0.642635\pi$
$971$	−2.13371e25	−0.866507	−0.433254	+	0.901272i	$0.642635\pi$
$972$	7.84576e24	0.315843
$973$	5.05645e25	2.01784
$974$	6.86266e24	0.271482
$975$	0	0
$976$	−3.68381e24	−0.143210
$977$	−1.33440e25	−0.514260	−0.257130	−	0.966377i	$-0.582777\pi$
$977$	−1.33440e25	−0.514260	−0.257130	+	0.966377i	$0.582777\pi$
$978$	−7.11563e24	−0.271852
$979$	1.22701e25	0.464723
$980$	0	0
$981$	−8.88179e25	−3.30608
$982$	2.53068e25	0.933878
$983$	−1.31969e25	−0.482800	−0.241400	−	0.970426i	$-0.577607\pi$
$983$	−1.31969e25	−0.482800	−0.241400	+	0.970426i	$0.577607\pi$
$984$	1.92703e25	0.698924
$985$	0	0
$986$	1.36936e25	0.488161
$987$	1.18437e25	0.418592
$988$	1.12779e25	0.395180
$989$	2.39818e24	0.0833132
$990$	0	0
$991$	4.80007e25	1.63916	0.819580	−	0.572964i	$-0.194207\pi$
$991$	4.80007e25	1.63916	0.819580	+	0.572964i	$0.194207\pi$
$992$	−3.55945e24	−0.120513
$993$	−9.28211e25	−3.11586
$994$	4.30364e25	1.43236
$995$	0	0
$996$	2.60203e25	0.851349
$997$	1.30477e25	0.423276	0.211638	−	0.977348i	$-0.432120\pi$
$997$	1.30477e25	0.423276	0.211638	+	0.977348i	$0.432120\pi$
$998$	−3.09100e25	−0.994234
$999$	1.75312e24	0.0559121

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.18.a.j.1.4		4
5.2	odd	4		10.18.b.a.9.1	✓	8
5.3	odd	4		10.18.b.a.9.8	yes	8
5.4	even	2		50.18.a.k.1.1		4
15.2	even	4		90.18.c.b.19.8		8
15.8	even	4		90.18.c.b.19.4		8
20.3	even	4		80.18.c.a.49.1		8
20.7	even	4		80.18.c.a.49.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.18.b.a.9.1	✓	8	5.2	odd	4
10.18.b.a.9.8	yes	8	5.3	odd	4
50.18.a.j.1.4		4	1.1	even	1	trivial
50.18.a.k.1.1		4	5.4	even	2
80.18.c.a.49.1		8	20.3	even	4
80.18.c.a.49.8		8	20.7	even	4
90.18.c.b.19.4		8	15.8	even	4
90.18.c.b.19.8		8	15.2	even	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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	50.a (trivial)

\(f(q)\)	\(=\)	\(q-256.000 q^{2} +20214.2 q^{3} +65536.0 q^{4} -5.17482e6 q^{6} +1.76306e7 q^{7} -1.67772e7 q^{8} +2.79472e8 q^{9} +4.98950e8 q^{11} +1.32475e9 q^{12} +5.00327e9 q^{13} -4.51344e9 q^{14} +4.29497e9 q^{16} -1.61697e10 q^{17} -7.15448e10 q^{18} +3.43950e10 q^{19} +3.56388e11 q^{21} -1.27731e11 q^{22} -4.72599e11 q^{23} -3.39137e11 q^{24} -1.28084e12 q^{26} +3.03883e12 q^{27} +1.15544e12 q^{28} +3.30807e12 q^{29} +3.23730e12 q^{31} -1.09951e12 q^{32} +1.00859e13 q^{33} +4.13944e12 q^{34} +1.83155e13 q^{36} +5.76908e11 q^{37} -8.80513e12 q^{38} +1.01137e14 q^{39} -5.68215e13 q^{41} -9.12354e13 q^{42} -5.07446e12 q^{43} +3.26992e13 q^{44} +1.20985e14 q^{46} +3.32325e13 q^{47} +8.68191e13 q^{48} +7.82089e13 q^{49} -3.26857e14 q^{51} +3.27894e14 q^{52} -6.11026e14 q^{53} -7.77940e14 q^{54} -2.95793e14 q^{56} +6.95266e14 q^{57} -8.46865e14 q^{58} -8.63122e14 q^{59} -8.57703e14 q^{61} -8.28749e14 q^{62} +4.92727e15 q^{63} +2.81475e14 q^{64} -2.58198e15 q^{66} -4.06389e14 q^{67} -1.05970e15 q^{68} -9.55319e15 q^{69} -9.53517e15 q^{71} -4.68876e15 q^{72} +6.07142e15 q^{73} -1.47688e14 q^{74} +2.25411e15 q^{76} +8.79681e15 q^{77} -2.58910e16 q^{78} +1.38305e16 q^{79} +2.53363e16 q^{81} +1.45463e16 q^{82} +1.96416e16 q^{83} +2.33563e16 q^{84} +1.29906e15 q^{86} +6.68698e16 q^{87} -8.37099e15 q^{88} +2.45918e16 q^{89} +8.82108e16 q^{91} -3.09722e16 q^{92} +6.54393e16 q^{93} -8.50752e15 q^{94} -2.22257e16 q^{96} -3.63292e16 q^{97} -2.00215e16 q^{98} +1.39443e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1024 q^{2} + 1904 q^{3} + 262144 q^{4} - 487424 q^{6} + 27852528 q^{7} - 67108864 q^{8} + 181591252 q^{9} + 73116048 q^{11} + 124780544 q^{12} + 5260514784 q^{13} - 7130247168 q^{14} + 17179869184 q^{16}+ \cdots + 11\!\cdots\!24 q^{99}+O(q^{100}) \) 4 * q - 1024 * q^2 + 1904 * q^3 + 262144 * q^4 - 487424 * q^6 + 27852528 * q^7 - 67108864 * q^8 + 181591252 * q^9 + 73116048 * q^11 + 124780544 * q^12 + 5260514784 * q^13 - 7130247168 * q^14 + 17179869184 * q^16 + 27652825088 * q^17 - 46487360512 * q^18 + 27132089040 * q^19 + 257721166528 * q^21 - 18717708288 * q^22 + 267096076304 * q^23 - 31943819264 * q^24 - 1346691784704 * q^26 + 3653720352800 * q^27 + 1825343275008 * q^28 - 830121541560 * q^29 - 3027738496832 * q^31 - 4398046511104 * q^32 + 19883640874048 * q^33 - 7079123222528 * q^34 + 11900764291072 * q^36 + 11753219425248 * q^37 - 6945814794240 * q^38 + 30023617116384 * q^39 - 109960914985992 * q^41 - 65976618631168 * q^42 - 57843805555536 * q^43 + 4791733321728 * q^44 - 68376595533824 * q^46 - 22344329926352 * q^47 + 8177617731584 * q^48 - 398604472020732 * q^49 - 1314685175765312 * q^51 + 344753096884224 * q^52 - 1100693686082016 * q^53 - 935352410316800 * q^54 - 467287878402048 * q^56 - 95996606285760 * q^57 + 212511114639360 * q^58 + 77705278880880 * q^59 - 3175222034484472 * q^61 + 775101055188992 * q^62 + 6027001010119664 * q^63 + 1125899906842624 * q^64 - 5090212063756288 * q^66 + 5846012954016528 * q^67 + 1812255544967168 * q^68 - 10410680115629696 * q^69 - 16574513271866592 * q^71 - 3046595658514432 * q^72 + 5319423834293184 * q^73 - 3008824172863488 * q^74 + 1778128587325440 * q^76 + 17129208918876736 * q^77 - 7686045981794304 * q^78 + 9677334395854080 * q^79 + 27216187312417924 * q^81 + 28149994236413952 * q^82 - 16561108625266576 * q^83 + 16890014369579008 * q^84 + 14808014222217216 * q^86 + 92228129920815840 * q^87 - 1226683730362368 * q^88 + 21784615149779160 * q^89 + 166710153944985888 * q^91 + 17504408456658944 * q^92 + 116588278209594368 * q^93 + 5720148461146112 * q^94 - 2093470139285504 * q^96 + 256361495844924288 * q^97 + 102042744837307392 * q^98 + 118340668209625424 * q^99

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