LMFDB - Embedded newform 50.26.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,26,Mod(1,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 26, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("50.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	50.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$197.998389976$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{106705}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 26676 $ x^2 - x - 26676
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{7}\cdot 3\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 2)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$163.829$ 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)

$f(q)$	$=$	\(q-4096.00 q^{2} -1.75788e6 q^{3} +1.67772e7 q^{4} +7.20027e9 q^{6} +3.04153e10 q^{7} -6.87195e10 q^{8} +2.24285e12 q^{9} +2.58704e12 q^{11} -2.94923e13 q^{12} +9.57327e13 q^{13} -1.24581e14 q^{14} +2.81475e14 q^{16} +1.64685e15 q^{17} -9.18671e15 q^{18} +4.95030e15 q^{19} -5.34664e16 q^{21} -1.05965e16 q^{22} +1.07650e16 q^{23} +1.20801e17 q^{24} -3.92121e17 q^{26} -2.45323e18 q^{27} +5.10284e17 q^{28} -1.36741e18 q^{29} -4.42000e18 q^{31} -1.15292e18 q^{32} -4.54771e18 q^{33} -6.74549e18 q^{34} +3.76288e19 q^{36} -1.01944e19 q^{37} -2.02764e19 q^{38} -1.68287e20 q^{39} +1.58687e20 q^{41} +2.18999e20 q^{42} -1.83575e20 q^{43} +4.34034e19 q^{44} -4.40934e19 q^{46} -1.40203e21 q^{47} -4.94799e20 q^{48} -4.15978e20 q^{49} -2.89496e21 q^{51} +1.60613e21 q^{52} +1.99903e21 q^{53} +1.00484e22 q^{54} -2.09012e21 q^{56} -8.70202e21 q^{57} +5.60091e21 q^{58} -4.16691e21 q^{59} +3.42128e22 q^{61} +1.81043e22 q^{62} +6.82170e22 q^{63} +4.72237e21 q^{64} +1.86274e22 q^{66} -8.67051e22 q^{67} +2.76295e22 q^{68} -1.89236e22 q^{69} -5.13159e22 q^{71} -1.54128e23 q^{72} -3.49147e22 q^{73} +4.17563e22 q^{74} +8.30522e22 q^{76} +7.86857e22 q^{77} +6.89302e23 q^{78} +2.91588e23 q^{79} +2.41214e24 q^{81} -6.49981e23 q^{82} +1.64916e24 q^{83} -8.97018e23 q^{84} +7.51925e23 q^{86} +2.40374e24 q^{87} -1.77780e23 q^{88} +8.74435e23 q^{89} +2.91174e24 q^{91} +1.80607e23 q^{92} +7.76982e24 q^{93} +5.74273e24 q^{94} +2.02670e24 q^{96} -1.00608e25 q^{97} +1.70384e24 q^{98} +5.80235e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8192 q^{2} - 379848 q^{3} + 33554432 q^{4} + 1555857408 q^{6} + 376536944 q^{7} - 137438953472 q^{8} + 3294531432666 q^{9} + 8323034610264 q^{11} - 6372791943168 q^{12} + 106467053152292 q^{13} - 1542295322624 q^{14}+ \cdots + 11\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 8192 * q^2 - 379848 * q^3 + 33554432 * q^4 + 1555857408 * q^6 + 376536944 * q^7 - 137438953472 * q^8 + 3294531432666 * q^9 + 8323034610264 * q^11 - 6372791943168 * q^12 + 106467053152292 * q^13 - 1542295322624 * q^14 + 562949953421312 * q^16 - 1327878920113956 * q^17 - 13494400748199936 * q^18 - 477079242949400 * q^19 - 94860791661752256 * q^21 - 34091149763641344 * q^22 + 115305025781473872 * q^23 + 26102955799216128 * q^24 - 436089049711788032 * q^26 - 2171569557205152720 * q^27 + 6317241641467904 * q^28 + 1724412645206435580 * q^29 - 8688082288351126976 * q^31 - 2305843009213693952 * q^32 + 3356662204005020064 * q^33 + 5438992056786763776 * q^34 + 55273065464626937856 * q^36 + 34908364049750170484 * q^37 + 1954116579120742400 * q^38 - 153494373835331105808 * q^39 + 83014324355953468884 * q^41 + 388549802646537240576 * q^42 - 44539608583471901848 * q^43 + 139637349431874945024 * q^44 - 472289385600916979712 * q^46 - 1869360732054674599776 * q^47 - 106917706953589260288 * q^48 - 854718643011973772046 * q^49 - 6994225992587553820656 * q^51 + 1786220747619483779072 * q^52 + 3242170458210097794132 * q^53 + 8894748906312305541120 * q^54 - 25875421763452534784 * q^56 - 16181115057055601354400 * q^57 - 7063194194765560135680 * q^58 - 17413675430632049453640 * q^59 + 33975859953090212810044 * q^61 + 35586385053086216093696 * q^62 + 36625774166984600306352 * q^63 + 9444732965739290427392 * q^64 - 13748888387604562182144 * q^66 - 33012908196969622380616 * q^67 - 22278111464598584426496 * q^68 + 125135868082548386734272 * q^69 - 278348008145600813615856 * q^71 - 226398476143111937458176 * q^72 - 313442631796571689392148 * q^73 - 142984659147776698302464 * q^74 - 8004061508078560870400 * q^76 - 93616352280445975603392 * q^77 + 628712955229516209389568 * q^78 + 928546182288781647817120 * q^79 + 1909195802481672047728242 * q^81 - 340026672561985408548864 * q^82 + 452542629950725008985752 * q^83 - 1591499991640216537399296 * q^84 + 182434236757900909969408 * q^86 + 6664364855011895770504080 * q^87 - 571954583272959774818304 * q^88 - 2346904179674200701244620 * q^89 + 2589295264446210583737824 * q^91 + 1934497323421355948900352 * q^92 + 1888263951389289833389824 * q^93 + 7656901558495947160682496 * q^94 + 437934927681901610139648 * q^96 - 13645482361777595497674436 * q^97 + 3500927561777044570300416 * q^98 + 11834785687944312803841912 * 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 $

$2$	−4096.00	−0.707107
$2$	−4096.00	−0.707107
$3$	−1.75788e6	−1.90974	−0.954868	−	0.297031i	$-0.904004\pi$
$3$	−1.75788e6	−1.90974	−0.954868	+	0.297031i	$0.904004\pi$
$4$	1.67772e7	0.500000
$5$	0	0
$5$	0	0
$6$	7.20027e9	1.35039
$7$	3.04153e10	0.830552	0.415276	−	0.909696i	$-0.363685\pi$
$7$	3.04153e10	0.830552	0.415276	+	0.909696i	$0.363685\pi$
$8$	−6.87195e10	−0.353553
$9$	2.24285e12	2.64709
$10$	0	0
$11$	2.58704e12	0.248539	0.124270	−	0.992248i	$-0.460341\pi$
$11$	2.58704e12	0.248539	0.124270	+	0.992248i	$0.460341\pi$
$12$	−2.94923e13	−0.954868
$13$	9.57327e13	1.13964	0.569821	−	0.821769i	$-0.307012\pi$
$13$	9.57327e13	1.13964	0.569821	+	0.821769i	$0.307012\pi$
$14$	−1.24581e14	−0.587289
$15$	0	0
$16$	2.81475e14	0.250000
$17$	1.64685e15	0.685555	0.342777	−	0.939417i	$-0.388632\pi$
$17$	1.64685e15	0.685555	0.342777	+	0.939417i	$0.388632\pi$
$18$	−9.18671e15	−1.87178
$19$	4.95030e15	0.513111	0.256555	−	0.966530i	$-0.417412\pi$
$19$	4.95030e15	0.513111	0.256555	+	0.966530i	$0.417412\pi$
$20$	0	0
$21$	−5.34664e16	−1.58613
$22$	−1.05965e16	−0.175744
$23$	1.07650e16	0.102427	0.0512136	−	0.998688i	$-0.483691\pi$
$23$	1.07650e16	0.102427	0.0512136	+	0.998688i	$0.483691\pi$
$24$	1.20801e17	0.675194
$25$	0	0
$26$	−3.92121e17	−0.805849
$27$	−2.45323e18	−3.14551
$28$	5.10284e17	0.415276
$29$	−1.36741e18	−0.717668	−0.358834	−	0.933401i	$-0.616826\pi$
$29$	−1.36741e18	−0.717668	−0.358834	+	0.933401i	$0.616826\pi$
$30$	0	0
$31$	−4.42000e18	−1.00786	−0.503931	−	0.863744i	$-0.668113\pi$
$31$	−4.42000e18	−1.00786	−0.503931	+	0.863744i	$0.668113\pi$
$32$	−1.15292e18	−0.176777
$33$	−4.54771e18	−0.474645
$34$	−6.74549e18	−0.484760
$35$	0	0
$36$	3.76288e19	1.32355
$37$	−1.01944e19	−0.254590	−0.127295	−	0.991865i	$-0.540629\pi$
$37$	−1.01944e19	−0.254590	−0.127295	+	0.991865i	$0.540629\pi$
$38$	−2.02764e19	−0.362824
$39$	−1.68287e20	−2.17642
$40$	0	0
$41$	1.58687e20	1.09835	0.549177	−	0.835706i	$-0.314941\pi$
$41$	1.58687e20	1.09835	0.549177	+	0.835706i	$0.314941\pi$
$42$	2.18999e20	1.12157
$43$	−1.83575e20	−0.700582	−0.350291	−	0.936641i	$-0.613917\pi$
$43$	−1.83575e20	−0.700582	−0.350291	+	0.936641i	$0.613917\pi$
$44$	4.34034e19	0.124270
$45$	0	0
$46$	−4.40934e19	−0.0724270
$47$	−1.40203e21	−1.76009	−0.880045	−	0.474890i	$-0.842488\pi$
$47$	−1.40203e21	−1.76009	−0.880045	+	0.474890i	$0.842488\pi$
$48$	−4.94799e20	−0.477434
$49$	−4.15978e20	−0.310184
$50$	0	0
$51$	−2.89496e21	−1.30923
$52$	1.60613e21	0.569821
$53$	1.99903e21	0.558946	0.279473	−	0.960154i	$-0.409840\pi$
$53$	1.99903e21	0.558946	0.279473	+	0.960154i	$0.409840\pi$
$54$	1.00484e22	2.22421
$55$	0	0
$56$	−2.09012e21	−0.293644
$57$	−8.70202e21	−0.979906
$58$	5.60091e21	0.507468
$59$	−4.16691e21	−0.304905	−0.152452	−	0.988311i	$-0.548717\pi$
$59$	−4.16691e21	−0.304905	−0.152452	+	0.988311i	$0.548717\pi$
$60$	0	0
$61$	3.42128e22	1.65031	0.825156	−	0.564904i	$-0.191087\pi$
$61$	3.42128e22	1.65031	0.825156	+	0.564904i	$0.191087\pi$
$62$	1.81043e22	0.712666
$63$	6.82170e22	2.19855
$64$	4.72237e21	0.125000
$65$	0	0
$66$	1.86274e22	0.335624
$67$	−8.67051e22	−1.29452	−0.647261	−	0.762268i	$-0.724086\pi$
$67$	−8.67051e22	−1.29452	−0.647261	+	0.762268i	$0.724086\pi$
$68$	2.76295e22	0.342777
$69$	−1.89236e22	−0.195609
$70$	0	0
$71$	−5.13159e22	−0.371127	−0.185564	−	0.982632i	$-0.559411\pi$
$71$	−5.13159e22	−0.371127	−0.185564	+	0.982632i	$0.559411\pi$
$72$	−1.54128e23	−0.935888
$73$	−3.49147e22	−0.178432	−0.0892159	−	0.996012i	$-0.528436\pi$
$73$	−3.49147e22	−0.178432	−0.0892159	+	0.996012i	$0.528436\pi$
$74$	4.17563e22	0.180022
$75$	0	0
$76$	8.30522e22	0.256555
$77$	7.86857e22	0.206425
$78$	6.89302e23	1.53896
$79$	2.91588e23	0.555176	0.277588	−	0.960700i	$-0.410465\pi$
$79$	2.91588e23	0.555176	0.277588	+	0.960700i	$0.410465\pi$
$80$	0	0
$81$	2.41214e24	3.36000
$82$	−6.49981e23	−0.776654
$83$	1.64916e24	1.69351	0.846753	−	0.531986i	$-0.178554\pi$
$83$	1.64916e24	1.69351	0.846753	+	0.531986i	$0.178554\pi$
$84$	−8.97018e23	−0.793067
$85$	0	0
$86$	7.51925e23	0.495386
$87$	2.40374e24	1.37056
$88$	−1.77780e23	−0.0878720
$89$	8.74435e23	0.375277	0.187639	−	0.982238i	$-0.439917\pi$
$89$	8.74435e23	0.375277	0.187639	+	0.982238i	$0.439917\pi$
$90$	0	0
$91$	2.91174e24	0.946532
$92$	1.80607e23	0.0512136
$93$	7.76982e24	1.92475
$94$	5.74273e24	1.24457
$95$	0	0
$96$	2.02670e24	0.337597
$97$	−1.00608e25	−1.47227	−0.736134	−	0.676835i	$-0.763351\pi$
$97$	−1.00608e25	−1.47227	−0.736134	+	0.676835i	$0.763351\pi$
$98$	1.70384e24	0.219333
$99$	5.80235e24	0.657907
$100$	0	0
$101$	−1.42151e25	−1.25526	−0.627628	−	0.778513i	$-0.715974\pi$
$101$	−1.42151e25	−1.25526	−0.627628	+	0.778513i	$0.715974\pi$
$102$	1.18578e25	0.925764
$103$	−1.03211e25	−0.713283	−0.356642	−	0.934241i	$-0.616078\pi$
$103$	−1.03211e25	−0.713283	−0.356642	+	0.934241i	$0.616078\pi$
$104$	−6.57870e24	−0.402924
$105$	0	0
$106$	−8.18801e24	−0.395235
$107$	1.74396e25	0.748582	0.374291	−	0.927311i	$-0.377886\pi$
$107$	1.74396e25	0.748582	0.374291	+	0.927311i	$0.377886\pi$
$108$	−4.11583e25	−1.57275
$109$	−1.65117e25	−0.562292	−0.281146	−	0.959665i	$-0.590714\pi$
$109$	−1.65117e25	−0.562292	−0.281146	+	0.959665i	$0.590714\pi$
$110$	0	0
$111$	1.79205e25	0.486199
$112$	8.56115e24	0.207638
$113$	−6.96039e25	−1.51061	−0.755306	−	0.655372i	$-0.772512\pi$
$113$	−6.96039e25	−1.51061	−0.755306	+	0.655372i	$0.772512\pi$
$114$	3.56435e25	0.692898
$115$	0	0
$116$	−2.29413e25	−0.358834
$117$	2.14714e26	3.01674
$118$	1.70677e25	0.215600
$119$	5.00894e25	0.569389
$120$	0	0
$121$	−1.01654e26	−0.938228
$122$	−1.40136e26	−1.16695
$123$	−2.78952e26	−2.09757
$124$	−7.41552e25	−0.503931
$125$	0	0
$126$	−2.79417e26	−1.55461
$127$	6.18922e25	0.311953	0.155977	−	0.987761i	$-0.450148\pi$
$127$	6.18922e25	0.311953	0.155977	+	0.987761i	$0.450148\pi$
$128$	−1.93428e25	−0.0883883
$129$	3.22703e26	1.33793
$130$	0	0
$131$	−1.39682e26	−0.477805	−0.238902	−	0.971044i	$-0.576788\pi$
$131$	−1.39682e26	−0.477805	−0.238902	+	0.971044i	$0.576788\pi$
$132$	−7.62979e25	−0.237322
$133$	1.50565e26	0.426165
$134$	3.55144e26	0.915366
$135$	0	0
$136$	−1.13171e26	−0.242380
$137$	6.92418e26	1.35320	0.676599	−	0.736352i	$-0.263453\pi$
$137$	6.92418e26	1.35320	0.676599	+	0.736352i	$0.263453\pi$
$138$	7.75109e25	0.138317
$139$	−8.06682e26	−1.31528	−0.657639	−	0.753333i	$-0.728445\pi$
$139$	−8.06682e26	−1.31528	−0.657639	+	0.753333i	$0.728445\pi$
$140$	0	0
$141$	2.46460e27	3.36131
$142$	2.10190e26	0.262427
$143$	2.47665e26	0.283246
$144$	6.31306e26	0.661773
$145$	0	0
$146$	1.43010e26	0.126170
$147$	7.31239e26	0.592369
$148$	−1.71034e26	−0.127295
$149$	−4.24039e26	−0.290120	−0.145060	−	0.989423i	$-0.546337\pi$
$149$	−4.24039e26	−0.290120	−0.145060	+	0.989423i	$0.546337\pi$
$150$	0	0
$151$	2.51382e27	1.45587	0.727934	−	0.685647i	$-0.240481\pi$
$151$	2.51382e27	1.45587	0.727934	+	0.685647i	$0.240481\pi$
$152$	−3.40182e26	−0.181412
$153$	3.69363e27	1.81473
$154$	−3.22297e26	−0.145964
$155$	0	0
$156$	−2.82338e27	−1.08821
$157$	−4.75882e27	−1.69338	−0.846689	−	0.532088i	$-0.821407\pi$
$157$	−4.75882e27	−1.69338	−0.846689	+	0.532088i	$0.821407\pi$
$158$	−1.19434e27	−0.392569
$159$	−3.51404e27	−1.06744
$160$	0	0
$161$	3.27420e26	0.0850712
$162$	−9.88012e27	−2.37588
$163$	−7.59899e26	−0.169204	−0.0846020	−	0.996415i	$-0.526962\pi$
$163$	−7.59899e26	−0.169204	−0.0846020	+	0.996415i	$0.526962\pi$
$164$	2.66232e27	0.549177
$165$	0	0
$166$	−6.75496e27	−1.19749
$167$	1.00207e28	1.64794	0.823970	−	0.566634i	$-0.191755\pi$
$167$	1.00207e28	1.64794	0.823970	+	0.566634i	$0.191755\pi$
$168$	3.67419e27	0.560783
$169$	2.10835e27	0.298785
$170$	0	0
$171$	1.11028e28	1.35825
$172$	−3.07989e27	−0.350291
$173$	7.89989e27	0.835689	0.417845	−	0.908518i	$-0.362786\pi$
$173$	7.89989e27	0.835689	0.417845	+	0.908518i	$0.362786\pi$
$174$	−9.84571e27	−0.969129
$175$	0	0
$176$	7.28188e26	0.0621349
$177$	7.32493e27	0.582288
$178$	−3.58168e27	−0.265361
$179$	−8.08087e27	−0.558207	−0.279103	−	0.960261i	$-0.590037\pi$
$179$	−8.08087e27	−0.558207	−0.279103	+	0.960261i	$0.590037\pi$
$180$	0	0
$181$	1.80674e27	0.108621	0.0543104	−	0.998524i	$-0.482704\pi$
$181$	1.80674e27	0.108621	0.0543104	+	0.998524i	$0.482704\pi$
$182$	−1.19265e28	−0.669299
$183$	−6.01420e28	−3.15166
$184$	−7.39765e26	−0.0362135
$185$	0	0
$186$	−3.18252e28	−1.36100
$187$	4.26047e27	0.170387
$188$	−2.35222e28	−0.880045
$189$	−7.46157e28	−2.61251
$190$	0	0
$191$	−4.93091e28	−1.51360	−0.756798	−	0.653649i	$-0.773237\pi$
$191$	−4.93091e28	−1.51360	−0.756798	+	0.653649i	$0.773237\pi$
$192$	−8.30135e27	−0.238717
$193$	−1.42443e28	−0.383861	−0.191931	−	0.981408i	$-0.561475\pi$
$193$	−1.42443e28	−0.383861	−0.191931	+	0.981408i	$0.561475\pi$
$194$	4.12092e28	1.04105
$195$	0	0
$196$	−6.97895e27	−0.155092
$197$	−3.59073e28	−0.748781	−0.374390	−	0.927271i	$-0.622148\pi$
$197$	−3.59073e28	−0.748781	−0.374390	+	0.927271i	$0.622148\pi$
$198$	−2.37664e28	−0.465210
$199$	−8.11996e28	−1.49242	−0.746209	−	0.665712i	$-0.768128\pi$
$199$	−8.11996e28	−1.49242	−0.746209	+	0.665712i	$0.768128\pi$
$200$	0	0
$201$	1.52417e29	2.47220
$202$	5.82250e28	0.887601
$203$	−4.15902e28	−0.596060
$204$	−4.85694e28	−0.654614
$205$	0	0
$206$	4.22753e28	0.504367
$207$	2.41443e28	0.271134
$208$	2.69464e28	0.284911
$209$	1.28066e28	0.127528
$210$	0	0
$211$	−1.03285e29	−0.913075	−0.456537	−	0.889704i	$-0.650911\pi$
$211$	−1.03285e29	−0.913075	−0.456537	+	0.889704i	$0.650911\pi$
$212$	3.35381e28	0.279473
$213$	9.02072e28	0.708755
$214$	−7.14326e28	−0.529327
$215$	0	0
$216$	1.68585e29	1.11211
$217$	−1.34436e29	−0.837081
$218$	6.76321e28	0.397600
$219$	6.13758e28	0.340757
$220$	0	0
$221$	1.57657e29	0.781287
$222$	−7.34025e28	−0.343795
$223$	−1.15542e29	−0.511597	−0.255799	−	0.966730i	$-0.582338\pi$
$223$	−1.15542e29	−0.511597	−0.255799	+	0.966730i	$0.582338\pi$
$224$	−3.50665e28	−0.146822
$225$	0	0
$226$	2.85098e29	1.06816
$227$	9.01151e28	0.319502	0.159751	−	0.987157i	$-0.448931\pi$
$227$	9.01151e28	0.319502	0.159751	+	0.987157i	$0.448931\pi$
$228$	−1.45996e29	−0.489953
$229$	3.69415e29	1.17374	0.586869	−	0.809682i	$-0.300360\pi$
$229$	3.69415e29	1.17374	0.586869	+	0.809682i	$0.300360\pi$
$230$	0	0
$231$	−1.38320e29	−0.394217
$232$	9.39676e28	0.253734
$233$	−4.10753e28	−0.105107	−0.0525536	−	0.998618i	$-0.516736\pi$
$233$	−4.10753e28	−0.105107	−0.0525536	+	0.998618i	$0.516736\pi$
$234$	−8.79469e29	−2.13316
$235$	0	0
$236$	−6.99092e28	−0.152452
$237$	−5.12576e29	−1.06024
$238$	−2.05166e29	−0.402618
$239$	−6.49097e29	−1.20875	−0.604374	−	0.796701i	$-0.706577\pi$
$239$	−6.49097e29	−1.20875	−0.604374	+	0.796701i	$0.706577\pi$
$240$	0	0
$241$	1.68781e29	0.283212	0.141606	−	0.989923i	$-0.454773\pi$
$241$	1.68781e29	0.283212	0.141606	+	0.989923i	$0.454773\pi$
$242$	4.16376e29	0.663427
$243$	−2.16165e30	−3.27121
$244$	5.73996e29	0.825156
$245$	0	0
$246$	1.14259e30	1.48320
$247$	4.73905e29	0.584763
$248$	3.03740e29	0.356333
$249$	−2.89903e30	−3.23415
$250$	0	0
$251$	2.65029e29	0.267530	0.133765	−	0.991013i	$-0.457293\pi$
$251$	2.65029e29	0.267530	0.133765	+	0.991013i	$0.457293\pi$
$252$	1.14449e30	1.09927
$253$	2.78495e28	0.0254572
$254$	−2.53510e29	−0.220584
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	−1.11592e30	−0.838433	−0.419217	−	0.907886i	$-0.637695\pi$
$257$	−1.11592e30	−0.838433	−0.419217	+	0.907886i	$0.637695\pi$
$258$	−1.32179e30	−0.946057
$259$	−3.10066e29	−0.211450
$260$	0	0
$261$	−3.06689e30	−1.89973
$262$	5.72139e29	0.337859
$263$	−1.53721e30	−0.865541	−0.432770	−	0.901504i	$-0.642464\pi$
$263$	−1.53721e30	−0.865541	−0.432770	+	0.901504i	$0.642464\pi$
$264$	3.12516e29	0.167812
$265$	0	0
$266$	−6.16713e29	−0.301344
$267$	−1.53715e30	−0.716681
$268$	−1.45467e30	−0.647261
$269$	2.34612e30	0.996431	0.498216	−	0.867053i	$-0.333989\pi$
$269$	2.34612e30	0.996431	0.498216	+	0.867053i	$0.333989\pi$
$270$	0	0
$271$	−1.54578e30	−0.598454	−0.299227	−	0.954182i	$-0.596729\pi$
$271$	−1.54578e30	−0.598454	−0.299227	+	0.954182i	$0.596729\pi$
$272$	4.63547e29	0.171389
$273$	−5.11849e30	−1.80763
$274$	−2.83614e30	−0.956855
$275$	0	0
$276$	−3.17485e29	−0.0978045
$277$	1.21614e30	0.358085	0.179042	−	0.983841i	$-0.442700\pi$
$277$	1.21614e30	0.358085	0.179042	+	0.983841i	$0.442700\pi$
$278$	3.30417e30	0.930042
$279$	−9.91339e30	−2.66790
$280$	0	0
$281$	5.09885e30	1.25500	0.627499	−	0.778617i	$-0.284079\pi$
$281$	5.09885e30	1.25500	0.627499	+	0.778617i	$0.284079\pi$
$282$	−1.00950e31	−2.37680
$283$	1.56288e30	0.352042	0.176021	−	0.984386i	$-0.443677\pi$
$283$	1.56288e30	0.352042	0.176021	+	0.984386i	$0.443677\pi$
$284$	−8.60939e29	−0.185564
$285$	0	0
$286$	−1.01444e30	−0.200285
$287$	4.82651e30	0.912240
$288$	−2.58583e30	−0.467944
$289$	−3.05852e30	−0.530015
$290$	0	0
$291$	1.76857e31	2.81164
$292$	−5.85771e29	−0.0892159
$293$	4.17112e30	0.608706	0.304353	−	0.952559i	$-0.401560\pi$
$293$	4.17112e30	0.608706	0.304353	+	0.952559i	$0.401560\pi$
$294$	−2.99515e30	−0.418868
$295$	0	0
$296$	7.00555e29	0.0900110
$297$	−6.34661e30	−0.781783
$298$	1.73686e30	0.205146
$299$	1.03056e30	0.116730
$300$	0	0
$301$	−5.58350e30	−0.581870
$302$	−1.02966e31	−1.02945
$303$	2.49884e31	2.39721
$304$	1.39338e30	0.128278
$305$	0	0
$306$	−1.51291e31	−1.28320
$307$	−7.69994e30	−0.626986	−0.313493	−	0.949591i	$-0.601499\pi$
$307$	−7.69994e30	−0.626986	−0.313493	+	0.949591i	$0.601499\pi$
$308$	1.32013e30	0.103212
$309$	1.81433e31	1.36218
$310$	0	0
$311$	1.54260e31	1.06843	0.534217	−	0.845347i	$-0.320606\pi$
$311$	1.54260e31	1.06843	0.534217	+	0.845347i	$0.320606\pi$
$312$	1.15646e31	0.769479
$313$	−1.62517e31	−1.03895	−0.519476	−	0.854485i	$-0.673873\pi$
$313$	−1.62517e31	−1.03895	−0.519476	+	0.854485i	$0.673873\pi$
$314$	1.94921e31	1.19740
$315$	0	0
$316$	4.89203e30	0.277588
$317$	2.29098e31	1.24963	0.624814	−	0.780773i	$-0.285175\pi$
$317$	2.29098e31	1.24963	0.624814	+	0.780773i	$0.285175\pi$
$318$	1.43935e31	0.754794
$319$	−3.53755e30	−0.178369
$320$	0	0
$321$	−3.06567e31	−1.42959
$322$	−1.34111e30	−0.0601544
$323$	8.15239e30	0.351765
$324$	4.04690e31	1.68000
$325$	0	0
$326$	3.11255e30	0.119645
$327$	2.90256e31	1.07383
$328$	−1.09049e31	−0.388327
$329$	−4.26433e31	−1.46185
$330$	0	0
$331$	3.45199e31	1.09703	0.548517	−	0.836140i	$-0.315193\pi$
$331$	3.45199e31	1.09703	0.548517	+	0.836140i	$0.315193\pi$
$332$	2.76683e31	0.846753
$333$	−2.28645e31	−0.673922
$334$	−4.10447e31	−1.16527
$335$	0	0
$336$	−1.50495e31	−0.396534
$337$	5.27735e31	1.33981	0.669904	−	0.742448i	$-0.266335\pi$
$337$	5.27735e31	1.33981	0.669904	+	0.742448i	$0.266335\pi$
$338$	−8.63579e30	−0.211273
$339$	1.22355e32	2.88487
$340$	0	0
$341$	−1.14347e31	−0.250493
$342$	−4.54770e31	−0.960429
$343$	−5.34411e31	−1.08818
$344$	1.26152e31	0.247693
$345$	0	0
$346$	−3.23580e31	−0.590922
$347$	−4.40093e30	−0.0775222	−0.0387611	−	0.999249i	$-0.512341\pi$
$347$	−4.40093e30	−0.0775222	−0.0387611	+	0.999249i	$0.512341\pi$
$348$	4.03280e31	0.685278
$349$	2.98069e31	0.488651	0.244326	−	0.969693i	$-0.421433\pi$
$349$	2.98069e31	0.488651	0.244326	+	0.969693i	$0.421433\pi$
$350$	0	0
$351$	−2.34854e32	−3.58476
$352$	−2.98266e30	−0.0439360
$353$	−4.46084e31	−0.634209	−0.317105	−	0.948391i	$-0.602711\pi$
$353$	−4.46084e31	−0.634209	−0.317105	+	0.948391i	$0.602711\pi$
$354$	−3.00029e31	−0.411740
$355$	0	0
$356$	1.46706e31	0.187639
$357$	−8.80511e31	−1.08738
$358$	3.30992e31	0.394712
$359$	4.38054e31	0.504483	0.252242	−	0.967664i	$-0.418832\pi$
$359$	4.38054e31	0.504483	0.252242	+	0.967664i	$0.418832\pi$
$360$	0	0
$361$	−6.85711e31	−0.736717
$362$	−7.40039e30	−0.0768065
$363$	1.78696e32	1.79177
$364$	4.88509e31	0.473266
$365$	0	0
$366$	2.46342e32	2.22856
$367$	7.76735e31	0.679121	0.339560	−	0.940584i	$-0.389722\pi$
$367$	7.76735e31	0.679121	0.339560	+	0.940584i	$0.389722\pi$
$368$	3.03008e30	0.0256068
$369$	3.55911e32	2.90744
$370$	0	0
$371$	6.08010e31	0.464234
$372$	1.30356e32	0.962374
$373$	2.37205e32	1.69342	0.846708	−	0.532058i	$-0.178581\pi$
$373$	2.37205e32	1.69342	0.846708	+	0.532058i	$0.178581\pi$
$374$	−1.74509e31	−0.120482
$375$	0	0
$376$	9.63470e31	0.622286
$377$	−1.30906e32	−0.817884
$378$	3.05626e32	1.84732
$379$	−1.38944e32	−0.812551	−0.406276	−	0.913751i	$-0.633173\pi$
$379$	−1.38944e32	−0.812551	−0.406276	+	0.913751i	$0.633173\pi$
$380$	0	0
$381$	−1.08799e32	−0.595748
$382$	2.01970e32	1.07027
$383$	3.79085e31	0.194425	0.0972125	−	0.995264i	$-0.469007\pi$
$383$	3.79085e31	0.194425	0.0972125	+	0.995264i	$0.469007\pi$
$384$	3.40023e31	0.168798
$385$	0	0
$386$	5.83446e31	0.271431
$387$	−4.11732e32	−1.85450
$388$	−1.68793e32	−0.736134
$389$	−2.20209e32	−0.929963	−0.464982	−	0.885320i	$-0.653939\pi$
$389$	−2.20209e32	−0.929963	−0.464982	+	0.885320i	$0.653939\pi$
$390$	0	0
$391$	1.77283e31	0.0702195
$392$	2.85858e31	0.109667
$393$	2.45545e32	0.912481
$394$	1.47076e32	0.529468
$395$	0	0
$396$	9.73473e31	0.328953
$397$	−2.18941e32	−0.716877	−0.358439	−	0.933553i	$-0.616691\pi$
$397$	−2.18941e32	−0.716877	−0.358439	+	0.933553i	$0.616691\pi$
$398$	3.32594e32	1.05530
$399$	−2.64675e32	−0.813863
$400$	0	0
$401$	2.99036e32	0.863810	0.431905	−	0.901919i	$-0.357842\pi$
$401$	2.99036e32	0.863810	0.431905	+	0.901919i	$0.357842\pi$
$402$	−6.24300e32	−1.74811
$403$	−4.23138e32	−1.14860
$404$	−2.38490e32	−0.627628
$405$	0	0
$406$	1.70353e32	0.421478
$407$	−2.63734e31	−0.0632755
$408$	1.98940e32	0.462882
$409$	7.12330e31	0.160746	0.0803730	−	0.996765i	$-0.474389\pi$
$409$	7.12330e31	0.160746	0.0803730	+	0.996765i	$0.474389\pi$
$410$	0	0
$411$	−1.21719e33	−2.58425
$412$	−1.73160e32	−0.356642
$413$	−1.26738e32	−0.253239
$414$	−9.88949e31	−0.191721
$415$	0	0
$416$	−1.10372e32	−0.201462
$417$	1.41805e33	2.51183
$418$	−5.24560e31	−0.0901761
$419$	2.94461e32	0.491307	0.245654	−	0.969358i	$-0.420997\pi$
$419$	2.94461e32	0.491307	0.245654	+	0.969358i	$0.420997\pi$
$420$	0	0
$421$	1.01892e33	1.60182	0.800908	−	0.598787i	$-0.204350\pi$
$421$	1.01892e33	1.60182	0.800908	+	0.598787i	$0.204350\pi$
$422$	4.23055e32	0.645641
$423$	−3.14455e33	−4.65912
$424$	−1.37372e32	−0.197617
$425$	0	0
$426$	−3.69489e32	−0.501166
$427$	1.04059e33	1.37067
$428$	2.92588e32	0.374291
$429$	−4.35365e32	−0.540925
$430$	0	0
$431$	−6.79497e32	−0.796565	−0.398283	−	0.917263i	$-0.630394\pi$
$431$	−6.79497e32	−0.796565	−0.398283	+	0.917263i	$0.630394\pi$
$432$	−6.90523e32	−0.786377
$433$	7.24164e32	0.801195	0.400597	−	0.916254i	$-0.368803\pi$
$433$	7.24164e32	0.801195	0.400597	+	0.916254i	$0.368803\pi$
$434$	5.50648e32	0.591906
$435$	0	0
$436$	−2.77021e32	−0.281146
$437$	5.32899e31	0.0525566
$438$	−2.51395e32	−0.240952
$439$	−9.13459e32	−0.850908	−0.425454	−	0.904980i	$-0.639886\pi$
$439$	−9.13459e32	−0.850908	−0.425454	+	0.904980i	$0.639886\pi$
$440$	0	0
$441$	−9.32976e32	−0.821085
$442$	−6.45764e32	−0.552453
$443$	3.52555e32	0.293211	0.146605	−	0.989195i	$-0.453165\pi$
$443$	3.52555e32	0.293211	0.146605	+	0.989195i	$0.453165\pi$
$444$	3.00657e32	0.243099
$445$	0	0
$446$	4.73259e32	0.361754
$447$	7.45409e32	0.554052
$448$	1.43632e32	0.103819
$449$	3.70918e32	0.260735	0.130367	−	0.991466i	$-0.458384\pi$
$449$	3.70918e32	0.260735	0.130367	+	0.991466i	$0.458384\pi$
$450$	0	0
$451$	4.10530e32	0.272984
$452$	−1.16776e33	−0.755306
$453$	−4.41899e33	−2.78032
$454$	−3.69111e32	−0.225922
$455$	0	0
$456$	5.97998e32	0.346449
$457$	−1.76958e33	−0.997512	−0.498756	−	0.866742i	$-0.666210\pi$
$457$	−1.76958e33	−0.997512	−0.498756	+	0.866742i	$0.666210\pi$
$458$	−1.51313e33	−0.829959
$459$	−4.04009e33	−2.15642
$460$	0	0
$461$	7.01018e32	0.354379	0.177189	−	0.984177i	$-0.443299\pi$
$461$	7.01018e32	0.354379	0.177189	+	0.984177i	$0.443299\pi$
$462$	5.66559e32	0.278753
$463$	9.20521e32	0.440830	0.220415	−	0.975406i	$-0.429259\pi$
$463$	9.20521e32	0.440830	0.220415	+	0.975406i	$0.429259\pi$
$464$	−3.84891e32	−0.179417
$465$	0	0
$466$	1.68245e32	0.0743219
$467$	1.84600e33	0.793908	0.396954	−	0.917838i	$-0.370067\pi$
$467$	1.84600e33	0.793908	0.396954	+	0.917838i	$0.370067\pi$
$468$	3.60231e33	1.50837
$469$	−2.63716e33	−1.07517
$470$	0	0
$471$	8.36543e33	3.23390
$472$	2.86348e32	0.107800
$473$	−4.74918e32	−0.174122
$474$	2.09951e33	0.749703
$475$	0	0
$476$	8.40360e32	0.284694
$477$	4.48351e33	1.47958
$478$	2.65870e33	0.854714
$479$	−3.88481e32	−0.121668	−0.0608339	−	0.998148i	$-0.519376\pi$
$479$	−3.88481e32	−0.121668	−0.0608339	+	0.998148i	$0.519376\pi$
$480$	0	0
$481$	−9.75939e32	−0.290141
$482$	−6.91328e32	−0.200261
$483$	−5.75566e32	−0.162463
$484$	−1.70548e33	−0.469114
$485$	0	0
$486$	8.85414e33	2.31309
$487$	−4.26102e33	−1.08493	−0.542465	−	0.840078i	$-0.682509\pi$
$487$	−4.26102e33	−1.08493	−0.542465	+	0.840078i	$0.682509\pi$
$488$	−2.35109e33	−0.583474
$489$	1.33581e33	0.323135
$490$	0	0
$491$	−4.52548e33	−1.04027	−0.520134	−	0.854084i	$-0.674118\pi$
$491$	−4.52548e33	−1.04027	−0.520134	+	0.854084i	$0.674118\pi$
$492$	−4.68004e33	−1.04878
$493$	−2.25191e33	−0.492000
$494$	−1.94112e33	−0.413490
$495$	0	0
$496$	−1.24412e33	−0.251965
$497$	−1.56079e33	−0.308241
$498$	1.18744e34	2.28689
$499$	4.45020e33	0.835840	0.417920	−	0.908484i	$-0.362759\pi$
$499$	4.45020e33	0.835840	0.417920	+	0.908484i	$0.362759\pi$
$500$	0	0
$501$	−1.76151e34	−3.14713
$502$	−1.08556e33	−0.189172
$503$	−2.29032e33	−0.389311	−0.194656	−	0.980872i	$-0.562359\pi$
$503$	−2.29032e33	−0.389311	−0.194656	+	0.980872i	$0.562359\pi$
$504$	−4.68784e33	−0.777304
$505$	0	0
$506$	−1.14072e32	−0.0180010
$507$	−3.70622e33	−0.570600
$508$	1.03838e33	0.155977
$509$	5.35889e33	0.785421	0.392711	−	0.919662i	$-0.371537\pi$
$509$	5.35889e33	0.785421	0.392711	+	0.919662i	$0.371537\pi$
$510$	0	0
$511$	−1.06194e33	−0.148197
$512$	−3.24519e32	−0.0441942
$513$	−1.21442e34	−1.61400
$514$	4.57080e33	0.592862
$515$	0	0
$516$	5.41407e33	0.668963
$517$	−3.62712e33	−0.437452
$518$	1.27003e33	0.149518
$519$	−1.38871e34	−1.59595
$520$	0	0
$521$	−1.14090e34	−1.24961	−0.624807	−	0.780779i	$-0.714822\pi$
$521$	−1.14090e34	−1.24961	−0.624807	+	0.780779i	$0.714822\pi$
$522$	1.25620e34	1.34331
$523$	−1.37717e34	−1.43786	−0.718928	−	0.695085i	$-0.755367\pi$
$523$	−1.37717e34	−1.43786	−0.718928	+	0.695085i	$0.755367\pi$
$524$	−2.34348e33	−0.238902
$525$	0	0
$526$	6.29643e33	0.612030
$527$	−7.27906e33	−0.690944
$528$	−1.28007e33	−0.118661
$529$	−1.09299e34	−0.989509
$530$	0	0
$531$	−9.34576e33	−0.807111
$532$	2.52606e33	0.213083
$533$	1.51915e34	1.25173
$534$	6.29617e33	0.506770
$535$	0	0
$536$	5.95833e33	0.457683
$537$	1.42052e34	1.06603
$538$	−9.60972e33	−0.704583
$539$	−1.07615e33	−0.0770929
$540$	0	0
$541$	−1.58682e34	−1.08533	−0.542667	−	0.839948i	$-0.682585\pi$
$541$	−1.58682e34	−1.08533	−0.542667	+	0.839948i	$0.682585\pi$
$542$	6.33151e33	0.423171
$543$	−3.17603e33	−0.207437
$544$	−1.89869e33	−0.121190
$545$	0	0
$546$	2.09653e34	1.27818
$547$	8.29322e33	0.494176	0.247088	−	0.968993i	$-0.420526\pi$
$547$	8.29322e33	0.494176	0.247088	+	0.968993i	$0.420526\pi$
$548$	1.16168e34	0.676599
$549$	7.67343e34	4.36853
$550$	0	0
$551$	−6.76908e33	−0.368243
$552$	1.30042e33	0.0691583
$553$	8.86874e33	0.461103
$554$	−4.98130e33	−0.253204
$555$	0	0
$556$	−1.35339e34	−0.657639
$557$	−3.56496e34	−1.69381	−0.846905	−	0.531744i	$-0.821537\pi$
$557$	−3.56496e34	−1.69381	−0.846905	+	0.531744i	$0.821537\pi$
$558$	4.06052e34	1.88649
$559$	−1.75742e34	−0.798413
$560$	0	0
$561$	−7.48939e33	−0.325395
$562$	−2.08849e34	−0.887417
$563$	−1.62059e34	−0.673471	−0.336735	−	0.941599i	$-0.609323\pi$
$563$	−1.62059e34	−0.673471	−0.336735	+	0.941599i	$0.609323\pi$
$564$	4.13492e34	1.68065
$565$	0	0
$566$	−6.40155e33	−0.248931
$567$	7.33659e34	2.79065
$568$	3.52641e33	0.131213
$569$	4.19926e34	1.52851	0.764257	−	0.644912i	$-0.223106\pi$
$569$	4.19926e34	1.52851	0.764257	+	0.644912i	$0.223106\pi$
$570$	0	0
$571$	2.27922e34	0.794026	0.397013	−	0.917813i	$-0.370047\pi$
$571$	2.27922e34	0.794026	0.397013	+	0.917813i	$0.370047\pi$
$572$	4.15513e33	0.141623
$573$	8.66794e34	2.89057
$574$	−1.97694e34	−0.645051
$575$	0	0
$576$	1.05916e34	0.330886
$577$	1.30064e34	0.397613	0.198807	−	0.980039i	$-0.436293\pi$
$577$	1.30064e34	0.397613	0.198807	+	0.980039i	$0.436293\pi$
$578$	1.25277e34	0.374777
$579$	2.50397e34	0.733074
$580$	0	0
$581$	5.01597e34	1.40655
$582$	−7.24407e34	−1.98813
$583$	5.17157e33	0.138920
$584$	2.39932e33	0.0630851
$585$	0	0
$586$	−1.70849e34	−0.430420
$587$	−3.13619e34	−0.773440	−0.386720	−	0.922197i	$-0.626392\pi$
$587$	−3.13619e34	−0.773440	−0.386720	+	0.922197i	$0.626392\pi$
$588$	1.22681e34	0.296185
$589$	−2.18803e34	−0.517145
$590$	0	0
$591$	6.31206e34	1.42997
$592$	−2.86947e33	−0.0636474
$593$	6.43753e34	1.39809	0.699046	−	0.715077i	$-0.253608\pi$
$593$	6.43753e34	1.39809	0.699046	+	0.715077i	$0.253608\pi$
$594$	2.59957e34	0.552804
$595$	0	0
$596$	−7.11419e33	−0.145060
$597$	1.42739e35	2.85012
$598$	−4.22118e33	−0.0825409
$599$	−9.82124e34	−1.88075	−0.940375	−	0.340140i	$-0.889526\pi$
$599$	−9.82124e34	−1.88075	−0.940375	+	0.340140i	$0.889526\pi$
$600$	0	0
$601$	1.10144e34	0.202316	0.101158	−	0.994870i	$-0.467745\pi$
$601$	1.10144e34	0.202316	0.101158	+	0.994870i	$0.467745\pi$
$602$	2.28700e34	0.411444
$603$	−1.94467e35	−3.42672
$604$	4.21749e34	0.727934
$605$	0	0
$606$	−1.02353e35	−1.69508
$607$	−9.06735e34	−1.47103	−0.735516	−	0.677508i	$-0.763060\pi$
$607$	−9.06735e34	−1.47103	−0.735516	+	0.677508i	$0.763060\pi$
$608$	−5.70730e33	−0.0907060
$609$	7.31105e34	1.13832
$610$	0	0
$611$	−1.34220e35	−2.00587
$612$	6.19689e34	0.907363
$613$	−2.62922e34	−0.377199	−0.188599	−	0.982054i	$-0.560395\pi$
$613$	−2.62922e34	−0.377199	−0.188599	+	0.982054i	$0.560395\pi$
$614$	3.15390e34	0.443346
$615$	0	0
$616$	−5.40724e33	−0.0729822
$617$	−6.11422e34	−0.808679	−0.404340	−	0.914609i	$-0.632499\pi$
$617$	−6.11422e34	−0.808679	−0.404340	+	0.914609i	$0.632499\pi$
$618$	−7.43150e34	−0.963208
$619$	−4.66687e34	−0.592779	−0.296389	−	0.955067i	$-0.595783\pi$
$619$	−4.66687e34	−0.592779	−0.296389	+	0.955067i	$0.595783\pi$
$620$	0	0
$621$	−2.64090e34	−0.322186
$622$	−6.31848e34	−0.755497
$623$	2.65962e34	0.311687
$624$	−4.73685e34	−0.544104
$625$	0	0
$626$	6.65672e34	0.734651
$627$	−2.25125e34	−0.243545
$628$	−7.98398e34	−0.846689
$629$	−1.67886e34	−0.174535
$630$	0	0
$631$	−7.88083e33	−0.0787417	−0.0393709	−	0.999225i	$-0.512535\pi$
$631$	−7.88083e33	−0.0787417	−0.0393709	+	0.999225i	$0.512535\pi$
$632$	−2.00378e34	−0.196284
$633$	1.81562e35	1.74373
$634$	−9.38386e34	−0.883621
$635$	0	0
$636$	−5.89559e34	−0.533720
$637$	−3.98227e34	−0.353499
$638$	1.44898e34	0.126126
$639$	−1.15094e35	−0.982408
$640$	0	0
$641$	3.14908e34	0.258499	0.129250	−	0.991612i	$-0.458743\pi$
$641$	3.14908e34	0.258499	0.129250	+	0.991612i	$0.458743\pi$
$642$	1.25570e35	1.01088
$643$	−8.32480e34	−0.657259	−0.328630	−	0.944459i	$-0.606587\pi$
$643$	−8.32480e34	−0.657259	−0.328630	+	0.944459i	$0.606587\pi$
$644$	5.49320e33	0.0425356
$645$	0	0
$646$	−3.33922e34	−0.248736
$647$	1.33124e35	0.972641	0.486321	−	0.873780i	$-0.338339\pi$
$647$	1.33124e35	0.972641	0.486321	+	0.873780i	$0.338339\pi$
$648$	−1.65761e35	−1.18794
$649$	−1.07800e34	−0.0757809
$650$	0	0
$651$	2.36321e35	1.59860
$652$	−1.27490e34	−0.0846020
$653$	−2.06756e35	−1.34599	−0.672997	−	0.739645i	$-0.734993\pi$
$653$	−2.06756e35	−1.34599	−0.672997	+	0.739645i	$0.734993\pi$
$654$	−1.18889e35	−0.759311
$655$	0	0
$656$	4.46664e34	0.274589
$657$	−7.83084e34	−0.472325
$658$	1.74667e35	1.03368
$659$	−2.57849e35	−1.49726	−0.748632	−	0.662986i	$-0.769289\pi$
$659$	−2.57849e35	−1.49726	−0.748632	+	0.662986i	$0.769289\pi$
$660$	0	0
$661$	−3.31671e34	−0.185434	−0.0927170	−	0.995692i	$-0.529555\pi$
$661$	−3.31671e34	−0.185434	−0.0927170	+	0.995692i	$0.529555\pi$
$662$	−1.41394e35	−0.775720
$663$	−2.77142e35	−1.49205
$664$	−1.13329e35	−0.598745
$665$	0	0
$666$	9.36532e34	0.476535
$667$	−1.47201e34	−0.0735087
$668$	1.68119e35	0.823970
$669$	2.03109e35	0.977016
$670$	0	0
$671$	8.85101e34	0.410168
$672$	6.16426e34	0.280392
$673$	2.87165e35	1.28216	0.641082	−	0.767472i	$-0.278486\pi$
$673$	2.87165e35	1.28216	0.641082	+	0.767472i	$0.278486\pi$
$674$	−2.16160e35	−0.947387
$675$	0	0
$676$	3.53722e34	0.149392
$677$	−3.20244e35	−1.32777	−0.663885	−	0.747835i	$-0.731093\pi$
$677$	−3.20244e35	−1.32777	−0.663885	+	0.747835i	$0.731093\pi$
$678$	−5.01167e35	−2.03991
$679$	−3.06003e35	−1.22280
$680$	0	0
$681$	−1.58411e35	−0.610165
$682$	4.68366e34	0.177125
$683$	4.34050e35	1.61169	0.805843	−	0.592129i	$-0.201712\pi$
$683$	4.34050e35	1.61169	0.805843	+	0.592129i	$0.201712\pi$
$684$	1.86274e35	0.679126
$685$	0	0
$686$	2.18895e35	0.769456
$687$	−6.49388e35	−2.24153
$688$	−5.16719e34	−0.175145
$689$	1.91372e35	0.636999
$690$	0	0
$691$	3.59659e35	1.15456	0.577279	−	0.816547i	$-0.304114\pi$
$691$	3.59659e35	1.15456	0.577279	+	0.816547i	$0.304114\pi$
$692$	1.32538e35	0.417845
$693$	1.76480e35	0.546425
$694$	1.80262e34	0.0548165
$695$	0	0
$696$	−1.65184e35	−0.484565
$697$	2.61333e35	0.752982
$698$	−1.22089e35	−0.345529
$699$	7.22055e34	0.200727
$700$	0	0
$701$	−4.01671e34	−0.107745	−0.0538723	−	0.998548i	$-0.517156\pi$
$701$	−4.01671e34	−0.107745	−0.0538723	+	0.998548i	$0.517156\pi$
$702$	9.61963e35	2.53481
$703$	−5.04654e34	−0.130633
$704$	1.22170e34	0.0310674
$705$	0	0
$706$	1.82716e35	0.448454
$707$	−4.32357e35	−1.04256
$708$	1.22892e35	0.291144
$709$	−2.37128e34	−0.0551957	−0.0275979	−	0.999619i	$-0.508786\pi$
$709$	−2.37128e34	−0.0551957	−0.0275979	+	0.999619i	$0.508786\pi$
$710$	0	0
$711$	6.53988e35	1.46960
$712$	−6.00907e34	−0.132681
$713$	−4.75812e34	−0.103232
$714$	3.60657e35	0.768895
$715$	0	0
$716$	−1.35574e35	−0.279103
$717$	1.14103e36	2.30839
$718$	−1.79427e35	−0.356724
$719$	−8.41947e35	−1.64503	−0.822514	−	0.568744i	$-0.807429\pi$
$719$	−8.41947e35	−1.64503	−0.822514	+	0.568744i	$0.807429\pi$
$720$	0	0
$721$	−3.13920e35	−0.592419
$722$	2.80867e35	0.520938
$723$	−2.96697e35	−0.540859
$724$	3.03120e34	0.0543104
$725$	0	0
$726$	−7.31938e35	−1.26697
$727$	−8.07486e35	−1.37390	−0.686950	−	0.726705i	$-0.741051\pi$
$727$	−8.07486e35	−1.37390	−0.686950	+	0.726705i	$0.741051\pi$
$728$	−2.00093e35	−0.334650
$729$	1.75615e36	2.88714
$730$	0	0
$731$	−3.02321e35	−0.480287
$732$	−1.00902e36	−1.57583
$733$	9.32041e35	1.43099	0.715493	−	0.698620i	$-0.246202\pi$
$733$	9.32041e35	1.43099	0.715493	+	0.698620i	$0.246202\pi$
$734$	−3.18151e35	−0.480211
$735$	0	0
$736$	−1.24112e34	−0.0181068
$737$	−2.24310e35	−0.321740
$738$	−1.45781e36	−2.05587
$739$	−9.24490e34	−0.128188	−0.0640939	−	0.997944i	$-0.520416\pi$
$739$	−9.24490e34	−0.128188	−0.0640939	+	0.997944i	$0.520416\pi$
$740$	0	0
$741$	−8.33068e35	−1.11674
$742$	−2.49041e35	−0.328263
$743$	−3.86129e35	−0.500463	−0.250232	−	0.968186i	$-0.580507\pi$
$743$	−3.86129e35	−0.500463	−0.250232	+	0.968186i	$0.580507\pi$
$744$	−5.33938e35	−0.680501
$745$	0	0
$746$	−9.71592e35	−1.19743
$747$	3.69882e36	4.48287
$748$	7.14788e34	0.0851937
$749$	5.30431e35	0.621736
$750$	0	0
$751$	5.31819e35	0.602927	0.301463	−	0.953478i	$-0.402525\pi$
$751$	5.31819e35	0.602927	0.301463	+	0.953478i	$0.402525\pi$
$752$	−3.94637e35	−0.440023
$753$	−4.65889e35	−0.510911
$754$	5.36190e35	0.578332
$755$	0	0
$756$	−1.25184e36	−1.30625
$757$	−1.46803e36	−1.50674	−0.753368	−	0.657599i	$-0.771572\pi$
$757$	−1.46803e36	−1.50674	−0.753368	+	0.657599i	$0.771572\pi$
$758$	5.69116e35	0.574560
$759$	−4.89561e34	−0.0486166
$760$	0	0
$761$	1.26153e36	1.21225	0.606123	−	0.795371i	$-0.292724\pi$
$761$	1.26153e36	1.21225	0.606123	+	0.795371i	$0.292724\pi$
$762$	4.45641e35	0.421257
$763$	−5.02210e35	−0.467012
$764$	−8.27269e35	−0.756798
$765$	0	0
$766$	−1.55273e35	−0.137479
$767$	−3.98910e35	−0.347482
$768$	−1.39274e35	−0.119358
$769$	−9.78483e35	−0.825039	−0.412519	−	0.910949i	$-0.635351\pi$
$769$	−9.78483e35	−0.825039	−0.412519	+	0.910949i	$0.635351\pi$
$770$	0	0
$771$	1.96165e36	1.60119
$772$	−2.38980e35	−0.191931
$773$	1.97217e36	1.55848	0.779238	−	0.626728i	$-0.215606\pi$
$773$	1.97217e36	1.55848	0.779238	+	0.626728i	$0.215606\pi$
$774$	1.68646e36	1.31133
$775$	0	0
$776$	6.91375e35	0.520526
$777$	5.45059e35	0.403813
$778$	9.01978e35	0.657583
$779$	7.85547e35	0.563578
$780$	0	0
$781$	−1.32757e35	−0.0922398
$782$	−7.26151e34	−0.0496527
$783$	3.35457e36	2.25743
$784$	−1.17087e35	−0.0775459
$785$	0	0
$786$	−1.00575e36	−0.645222
$787$	2.25189e35	0.142188	0.0710940	−	0.997470i	$-0.477351\pi$
$787$	2.25189e35	0.142188	0.0710940	+	0.997470i	$0.477351\pi$
$788$	−6.02424e35	−0.374390
$789$	2.70224e36	1.65295
$790$	0	0
$791$	−2.11702e36	−1.25464
$792$	−3.98735e35	−0.232605
$793$	3.27529e36	1.88077
$794$	8.96781e35	0.506909
$795$	0	0
$796$	−1.36230e36	−0.746209
$797$	−3.69113e36	−1.99035	−0.995177	−	0.0980978i	$-0.968724\pi$
$797$	−3.69113e36	−1.99035	−0.995177	+	0.0980978i	$0.968724\pi$
$798$	1.08411e36	0.575488
$799$	−2.30893e36	−1.20664
$800$	0	0
$801$	1.96123e36	0.993393
$802$	−1.22485e36	−0.610806
$803$	−9.03258e34	−0.0443473
$804$	2.55713e36	1.23610
$805$	0	0
$806$	1.73317e36	0.812184
$807$	−4.12420e36	−1.90292
$808$	9.76854e35	0.443800
$809$	−2.93815e36	−1.31437	−0.657185	−	0.753730i	$-0.728253\pi$
$809$	−2.93815e36	−1.31437	−0.657185	+	0.753730i	$0.728253\pi$
$810$	0	0
$811$	−2.44583e36	−1.06088	−0.530439	−	0.847723i	$-0.677973\pi$
$811$	−2.44583e36	−1.06088	−0.530439	+	0.847723i	$0.677973\pi$
$812$	−6.97767e35	−0.298030
$813$	2.71729e36	1.14289
$814$	1.08025e35	0.0447426
$815$	0	0
$816$	−8.14859e35	−0.327307
$817$	−9.08753e35	−0.359476
$818$	−2.91771e35	−0.113665
$819$	6.53060e36	2.50556
$820$	0	0
$821$	3.33815e36	1.24227	0.621136	−	0.783703i	$-0.286672\pi$
$821$	3.33815e36	1.24227	0.621136	+	0.783703i	$0.286672\pi$
$822$	4.98560e36	1.82734
$823$	−2.54036e36	−0.917058	−0.458529	−	0.888679i	$-0.651623\pi$
$823$	−2.54036e36	−0.917058	−0.458529	+	0.888679i	$0.651623\pi$
$824$	7.09263e35	0.252184
$825$	0	0
$826$	5.19119e35	0.179067
$827$	3.63276e36	1.23429	0.617146	−	0.786849i	$-0.288289\pi$
$827$	3.63276e36	1.23429	0.617146	+	0.786849i	$0.288289\pi$
$828$	4.05074e35	0.135567
$829$	1.07727e36	0.355135	0.177567	−	0.984109i	$-0.443177\pi$
$829$	1.07727e36	0.355135	0.177567	+	0.984109i	$0.443177\pi$
$830$	0	0
$831$	−2.13782e36	−0.683847
$832$	4.52085e35	0.142455
$833$	−6.85052e35	−0.212648
$834$	−5.80833e36	−1.77613
$835$	0	0
$836$	2.14860e35	0.0637641
$837$	1.08433e37	3.17024
$838$	−1.20611e36	−0.347407
$839$	−2.96808e36	−0.842269	−0.421134	−	0.906998i	$-0.638368\pi$
$839$	−2.96808e36	−0.842269	−0.421134	+	0.906998i	$0.638368\pi$
$840$	0	0
$841$	−1.76056e36	−0.484953
$842$	−4.17349e36	−1.13266
$843$	−8.96316e36	−2.39671
$844$	−1.73283e36	−0.456537
$845$	0	0
$846$	1.28801e37	3.29450
$847$	−3.09185e36	−0.779247
$848$	5.62676e35	0.139737
$849$	−2.74735e36	−0.672308
$850$	0	0
$851$	−1.09743e35	−0.0260769
$852$	1.51343e36	0.354378
$853$	−6.13786e36	−1.41630	−0.708148	−	0.706064i	$-0.750469\pi$
$853$	−6.13786e36	−1.41630	−0.708148	+	0.706064i	$0.750469\pi$
$854$	−4.26227e36	−0.969210
$855$	0	0
$856$	−1.19844e36	−0.264664
$857$	−3.16481e36	−0.688791	−0.344395	−	0.938825i	$-0.611916\pi$
$857$	−3.16481e36	−0.688791	−0.344395	+	0.938825i	$0.611916\pi$
$858$	1.78325e36	0.382492
$859$	5.65370e36	1.19514	0.597569	−	0.801818i	$-0.296134\pi$
$859$	5.65370e36	1.19514	0.597569	+	0.801818i	$0.296134\pi$
$860$	0	0
$861$	−8.48442e36	−1.74214
$862$	2.78322e36	0.563257
$863$	8.00828e36	1.59736	0.798682	−	0.601753i	$-0.205531\pi$
$863$	8.00828e36	1.59736	0.798682	+	0.601753i	$0.205531\pi$
$864$	2.82838e36	0.556053
$865$	0	0
$866$	−2.96617e36	−0.566530
$867$	5.37651e36	1.01219
$868$	−2.25545e36	−0.418540
$869$	7.54351e35	0.137983
$870$	0	0
$871$	−8.30052e36	−1.47529
$872$	1.13468e36	0.198800
$873$	−2.25649e37	−3.89723
$874$	−2.18275e35	−0.0371631
$875$	0	0
$876$	1.02971e36	0.170379
$877$	−3.29560e36	−0.537575	−0.268788	−	0.963199i	$-0.586623\pi$
$877$	−3.29560e36	−0.537575	−0.268788	+	0.963199i	$0.586623\pi$
$878$	3.74153e36	0.601683
$879$	−7.33233e36	−1.16247
$880$	0	0
$881$	−8.05386e36	−1.24109	−0.620547	−	0.784169i	$-0.713090\pi$
$881$	−8.05386e36	−1.24109	−0.620547	+	0.784169i	$0.713090\pi$
$882$	3.82147e36	0.580595
$883$	4.91849e35	0.0736754	0.0368377	−	0.999321i	$-0.488272\pi$
$883$	4.91849e35	0.0736754	0.0368377	+	0.999321i	$0.488272\pi$
$884$	2.64505e36	0.390644
$885$	0	0
$886$	−1.44406e36	−0.207331
$887$	−7.79484e36	−1.10347	−0.551737	−	0.834018i	$-0.686035\pi$
$887$	−7.79484e36	−1.10347	−0.551737	+	0.834018i	$0.686035\pi$
$888$	−1.23149e36	−0.171897
$889$	1.88247e36	0.259093
$890$	0	0
$891$	6.24031e36	0.835093
$892$	−1.93847e36	−0.255799
$893$	−6.94048e36	−0.903121
$894$	−3.05319e36	−0.391774
$895$	0	0
$896$	−5.88318e35	−0.0734111
$897$	−1.81160e36	−0.222924
$898$	−1.51928e36	−0.184367
$899$	6.04394e36	0.723309
$900$	0	0
$901$	3.29209e36	0.383188
$902$	−1.68153e36	−0.193029
$903$	9.81513e36	1.11122
$904$	4.78314e36	0.534082
$905$	0	0
$906$	1.81002e37	1.96599
$907$	1.31417e37	1.40786	0.703932	−	0.710268i	$-0.251426\pi$
$907$	1.31417e37	1.40786	0.703932	+	0.710268i	$0.251426\pi$
$908$	1.51188e36	0.159751
$909$	−3.18823e37	−3.32278
$910$	0	0
$911$	1.44767e37	1.46788	0.733940	−	0.679214i	$-0.237679\pi$
$911$	1.44767e37	1.46788	0.733940	+	0.679214i	$0.237679\pi$
$912$	−2.44940e36	−0.244977
$913$	4.26645e36	0.420903
$914$	7.24821e36	0.705347
$915$	0	0
$916$	6.19776e36	0.586869
$917$	−4.24848e36	−0.396842
$918$	1.65482e37	1.52482
$919$	−1.03191e37	−0.937990	−0.468995	−	0.883201i	$-0.655384\pi$
$919$	−1.03191e37	−0.937990	−0.468995	+	0.883201i	$0.655384\pi$
$920$	0	0
$921$	1.35356e37	1.19738
$922$	−2.87137e36	−0.250584
$923$	−4.91262e36	−0.422953
$924$	−2.32062e36	−0.197108
$925$	0	0
$926$	−3.77045e36	−0.311714
$927$	−2.31487e37	−1.88813
$928$	1.57651e36	0.126867
$929$	−2.17912e37	−1.73015	−0.865075	−	0.501642i	$-0.832729\pi$
$929$	−2.17912e37	−1.73015	−0.865075	+	0.501642i	$0.832729\pi$
$930$	0	0
$931$	−2.05921e36	−0.159159
$932$	−6.89130e35	−0.0525536
$933$	−2.71170e37	−2.04043
$934$	−7.56121e36	−0.561378
$935$	0	0
$936$	−1.47550e37	−1.06658
$937$	2.08020e37	1.48375	0.741873	−	0.670540i	$-0.233938\pi$
$937$	2.08020e37	1.48375	0.741873	+	0.670540i	$0.233938\pi$
$938$	1.08018e37	0.760258
$939$	2.85686e37	1.98413
$940$	0	0
$941$	2.39454e37	1.61939	0.809695	−	0.586851i	$-0.199632\pi$
$941$	2.39454e37	1.61939	0.809695	+	0.586851i	$0.199632\pi$
$942$	−3.42648e37	−2.28672
$943$	1.70826e36	0.112501
$944$	−1.17288e36	−0.0762262
$945$	0	0
$946$	1.94526e36	0.123123
$947$	8.06134e36	0.503539	0.251769	−	0.967787i	$-0.418988\pi$
$947$	8.06134e36	0.503539	0.251769	+	0.967787i	$0.418988\pi$
$948$	−8.59960e36	−0.530120
$949$	−3.34248e36	−0.203348
$950$	0	0
$951$	−4.02727e37	−2.38646
$952$	−3.44212e36	−0.201309
$953$	1.92589e37	1.11166	0.555829	−	0.831297i	$-0.312401\pi$
$953$	1.92589e37	1.11166	0.555829	+	0.831297i	$0.312401\pi$
$954$	−1.83645e37	−1.04622
$955$	0	0
$956$	−1.08900e37	−0.604374
$957$	6.21858e36	0.340637
$958$	1.59122e36	0.0860321
$959$	2.10601e37	1.12390
$960$	0	0
$961$	3.03575e35	0.0157842
$962$	3.99745e36	0.205161
$963$	3.91144e37	1.98157
$964$	2.83168e36	0.141606
$965$	0	0
$966$	2.35752e36	0.114879
$967$	−2.29324e37	−1.10311	−0.551554	−	0.834139i	$-0.685965\pi$
$967$	−2.29324e37	−1.10311	−0.551554	+	0.834139i	$0.685965\pi$
$968$	6.98563e36	0.331714
$969$	−1.43309e37	−0.671779
$970$	0	0
$971$	2.10199e37	0.960265	0.480132	−	0.877196i	$-0.340589\pi$
$971$	2.10199e37	0.960265	0.480132	+	0.877196i	$0.340589\pi$
$972$	−3.62665e37	−1.63560
$973$	−2.45355e37	−1.09241
$974$	1.74531e37	0.767161
$975$	0	0
$976$	9.63006e36	0.412578
$977$	3.52592e37	1.49139	0.745694	−	0.666289i	$-0.232118\pi$
$977$	3.52592e37	1.49139	0.745694	+	0.666289i	$0.232118\pi$
$978$	−5.47148e36	−0.228491
$979$	2.26220e36	0.0932712
$980$	0	0
$981$	−3.70334e37	−1.48844
$982$	1.85363e37	0.735581
$983$	−7.31962e36	−0.286794	−0.143397	−	0.989665i	$-0.545803\pi$
$983$	−7.31962e36	−0.286794	−0.143397	+	0.989665i	$0.545803\pi$
$984$	1.91694e37	0.741602
$985$	0	0
$986$	9.22384e36	0.347897
$987$	7.49617e37	2.79174
$988$	7.95081e36	0.292381
$989$	−1.97619e36	−0.0717587
$990$	0	0
$991$	1.16985e37	0.414200	0.207100	−	0.978320i	$-0.433597\pi$
$991$	1.16985e37	0.414200	0.207100	+	0.978320i	$0.433597\pi$
$992$	5.09591e36	0.178166
$993$	−6.06819e37	−2.09504
$994$	6.39300e36	0.217959
$995$	0	0
$996$	−4.86376e37	−1.61708
$997$	−2.33411e37	−0.766358	−0.383179	−	0.923674i	$-0.625171\pi$
$997$	−2.33411e37	−0.766358	−0.383179	+	0.923674i	$0.625171\pi$
$998$	−1.82280e37	−0.591028
$999$	2.50092e37	0.800814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.a.c.1.1		2
5.2	odd	4		50.26.b.e.49.2		4
5.3	odd	4		50.26.b.e.49.3		4
5.4	even	2		2.26.a.b.1.2	✓	2
15.14	odd	2		18.26.a.e.1.2		2
20.19	odd	2		16.26.a.c.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.26.a.b.1.2	✓	2	5.4	even	2
16.26.a.c.1.1		2	20.19	odd	2
18.26.a.e.1.2		2	15.14	odd	2
50.26.a.c.1.1		2	1.1	even	1	trivial
50.26.b.e.49.2		4	5.2	odd	4
50.26.b.e.49.3		4	5.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	50.a (trivial)

\(f(q)\)	\(=\)	\(q-4096.00 q^{2} -1.75788e6 q^{3} +1.67772e7 q^{4} +7.20027e9 q^{6} +3.04153e10 q^{7} -6.87195e10 q^{8} +2.24285e12 q^{9} +2.58704e12 q^{11} -2.94923e13 q^{12} +9.57327e13 q^{13} -1.24581e14 q^{14} +2.81475e14 q^{16} +1.64685e15 q^{17} -9.18671e15 q^{18} +4.95030e15 q^{19} -5.34664e16 q^{21} -1.05965e16 q^{22} +1.07650e16 q^{23} +1.20801e17 q^{24} -3.92121e17 q^{26} -2.45323e18 q^{27} +5.10284e17 q^{28} -1.36741e18 q^{29} -4.42000e18 q^{31} -1.15292e18 q^{32} -4.54771e18 q^{33} -6.74549e18 q^{34} +3.76288e19 q^{36} -1.01944e19 q^{37} -2.02764e19 q^{38} -1.68287e20 q^{39} +1.58687e20 q^{41} +2.18999e20 q^{42} -1.83575e20 q^{43} +4.34034e19 q^{44} -4.40934e19 q^{46} -1.40203e21 q^{47} -4.94799e20 q^{48} -4.15978e20 q^{49} -2.89496e21 q^{51} +1.60613e21 q^{52} +1.99903e21 q^{53} +1.00484e22 q^{54} -2.09012e21 q^{56} -8.70202e21 q^{57} +5.60091e21 q^{58} -4.16691e21 q^{59} +3.42128e22 q^{61} +1.81043e22 q^{62} +6.82170e22 q^{63} +4.72237e21 q^{64} +1.86274e22 q^{66} -8.67051e22 q^{67} +2.76295e22 q^{68} -1.89236e22 q^{69} -5.13159e22 q^{71} -1.54128e23 q^{72} -3.49147e22 q^{73} +4.17563e22 q^{74} +8.30522e22 q^{76} +7.86857e22 q^{77} +6.89302e23 q^{78} +2.91588e23 q^{79} +2.41214e24 q^{81} -6.49981e23 q^{82} +1.64916e24 q^{83} -8.97018e23 q^{84} +7.51925e23 q^{86} +2.40374e24 q^{87} -1.77780e23 q^{88} +8.74435e23 q^{89} +2.91174e24 q^{91} +1.80607e23 q^{92} +7.76982e24 q^{93} +5.74273e24 q^{94} +2.02670e24 q^{96} -1.00608e25 q^{97} +1.70384e24 q^{98} +5.80235e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8192 q^{2} - 379848 q^{3} + 33554432 q^{4} + 1555857408 q^{6} + 376536944 q^{7} - 137438953472 q^{8} + 3294531432666 q^{9} + 8323034610264 q^{11} - 6372791943168 q^{12} + 106467053152292 q^{13} - 1542295322624 q^{14}+ \cdots + 11\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 8192 * q^2 - 379848 * q^3 + 33554432 * q^4 + 1555857408 * q^6 + 376536944 * q^7 - 137438953472 * q^8 + 3294531432666 * q^9 + 8323034610264 * q^11 - 6372791943168 * q^12 + 106467053152292 * q^13 - 1542295322624 * q^14 + 562949953421312 * q^16 - 1327878920113956 * q^17 - 13494400748199936 * q^18 - 477079242949400 * q^19 - 94860791661752256 * q^21 - 34091149763641344 * q^22 + 115305025781473872 * q^23 + 26102955799216128 * q^24 - 436089049711788032 * q^26 - 2171569557205152720 * q^27 + 6317241641467904 * q^28 + 1724412645206435580 * q^29 - 8688082288351126976 * q^31 - 2305843009213693952 * q^32 + 3356662204005020064 * q^33 + 5438992056786763776 * q^34 + 55273065464626937856 * q^36 + 34908364049750170484 * q^37 + 1954116579120742400 * q^38 - 153494373835331105808 * q^39 + 83014324355953468884 * q^41 + 388549802646537240576 * q^42 - 44539608583471901848 * q^43 + 139637349431874945024 * q^44 - 472289385600916979712 * q^46 - 1869360732054674599776 * q^47 - 106917706953589260288 * q^48 - 854718643011973772046 * q^49 - 6994225992587553820656 * q^51 + 1786220747619483779072 * q^52 + 3242170458210097794132 * q^53 + 8894748906312305541120 * q^54 - 25875421763452534784 * q^56 - 16181115057055601354400 * q^57 - 7063194194765560135680 * q^58 - 17413675430632049453640 * q^59 + 33975859953090212810044 * q^61 + 35586385053086216093696 * q^62 + 36625774166984600306352 * q^63 + 9444732965739290427392 * q^64 - 13748888387604562182144 * q^66 - 33012908196969622380616 * q^67 - 22278111464598584426496 * q^68 + 125135868082548386734272 * q^69 - 278348008145600813615856 * q^71 - 226398476143111937458176 * q^72 - 313442631796571689392148 * q^73 - 142984659147776698302464 * q^74 - 8004061508078560870400 * q^76 - 93616352280445975603392 * q^77 + 628712955229516209389568 * q^78 + 928546182288781647817120 * q^79 + 1909195802481672047728242 * q^81 - 340026672561985408548864 * q^82 + 452542629950725008985752 * q^83 - 1591499991640216537399296 * q^84 + 182434236757900909969408 * q^86 + 6664364855011895770504080 * q^87 - 571954583272959774818304 * q^88 - 2346904179674200701244620 * q^89 + 2589295264446210583737824 * q^91 + 1934497323421355948900352 * q^92 + 1888263951389289833389824 * q^93 + 7656901558495947160682496 * q^94 + 437934927681901610139648 * q^96 - 13645482361777595497674436 * q^97 + 3500927561777044570300416 * q^98 + 11834785687944312803841912 * q^99

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