LMFDB - Embedded newform 50.26.a.c.1.2

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			1.2
Root			$-162.829$ 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)

$f(q)$	$=$	\(q-4096.00 q^{2} +1.37803e6 q^{3} +1.67772e7 q^{4} -5.64442e9 q^{6} -3.00388e10 q^{7} -6.87195e10 q^{8} +1.05168e12 q^{9} +5.73599e12 q^{11} +2.31195e13 q^{12} +1.07343e13 q^{13} +1.23039e14 q^{14} +2.81475e14 q^{16} -2.97473e15 q^{17} -4.30769e15 q^{18} -5.42738e15 q^{19} -4.13944e16 q^{21} -2.34946e16 q^{22} +1.04540e17 q^{23} -9.46976e16 q^{24} -4.39677e16 q^{26} +2.81659e17 q^{27} -5.03967e17 q^{28} +3.09182e18 q^{29} -4.26809e18 q^{31} -1.15292e18 q^{32} +7.90437e18 q^{33} +1.21845e19 q^{34} +1.76443e19 q^{36} +4.51028e19 q^{37} +2.22305e19 q^{38} +1.47922e19 q^{39} -7.56724e19 q^{41} +1.69551e20 q^{42} +1.39036e20 q^{43} +9.62339e19 q^{44} -4.28196e20 q^{46} -4.67328e20 q^{47} +3.87881e20 q^{48} -4.38741e20 q^{49} -4.09927e21 q^{51} +1.80092e20 q^{52} +1.24315e21 q^{53} -1.15368e21 q^{54} +2.06425e21 q^{56} -7.47909e21 q^{57} -1.26641e22 q^{58} -1.32468e22 q^{59} -2.36984e20 q^{61} +1.74821e22 q^{62} -3.15912e22 q^{63} +4.72237e21 q^{64} -3.23763e22 q^{66} +5.36922e22 q^{67} -4.99076e22 q^{68} +1.44059e23 q^{69} -2.27032e23 q^{71} -7.22710e22 q^{72} -2.78528e23 q^{73} -1.84741e23 q^{74} -9.10563e22 q^{76} -1.72302e23 q^{77} -6.05889e22 q^{78} +6.36958e23 q^{79} -5.02942e23 q^{81} +3.09954e23 q^{82} -1.19662e24 q^{83} -6.94482e23 q^{84} -5.69491e23 q^{86} +4.26063e24 q^{87} -3.94174e23 q^{88} -3.22134e24 q^{89} -3.22445e23 q^{91} +1.75389e24 q^{92} -5.88156e24 q^{93} +1.91418e24 q^{94} -1.58876e24 q^{96} -3.58465e24 q^{97} +1.79708e24 q^{98} +6.03243e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.37803e6	1.49707	0.748537	−	0.663093i	$-0.230757\pi$
$3$	1.37803e6	1.49707	0.748537	+	0.663093i	$0.230757\pi$
$4$	1.67772e7	0.500000
$5$	0	0
$5$	0	0
$6$	−5.64442e9	−1.05859
$7$	−3.00388e10	−0.820270	−0.410135	−	0.912025i	$-0.634518\pi$
$7$	−3.00388e10	−0.820270	−0.410135	+	0.912025i	$0.634518\pi$
$8$	−6.87195e10	−0.353553
$9$	1.05168e12	1.24123
$10$	0	0
$11$	5.73599e12	0.551061	0.275531	−	0.961292i	$-0.411146\pi$
$11$	5.73599e12	0.551061	0.275531	+	0.961292i	$0.411146\pi$
$12$	2.31195e13	0.748537
$13$	1.07343e13	0.127786	0.0638928	−	0.997957i	$-0.479648\pi$
$13$	1.07343e13	0.127786	0.0638928	+	0.997957i	$0.479648\pi$
$14$	1.23039e14	0.580018
$15$	0	0
$16$	2.81475e14	0.250000
$17$	−2.97473e15	−1.23833	−0.619164	−	0.785262i	$-0.712528\pi$
$17$	−2.97473e15	−1.23833	−0.619164	+	0.785262i	$0.712528\pi$
$18$	−4.30769e15	−0.877683
$19$	−5.42738e15	−0.562561	−0.281281	−	0.959626i	$-0.590759\pi$
$19$	−5.42738e15	−0.562561	−0.281281	+	0.959626i	$0.590759\pi$
$20$	0	0
$21$	−4.13944e16	−1.22800
$22$	−2.34946e16	−0.389659
$23$	1.04540e17	0.994683	0.497341	−	0.867555i	$-0.334310\pi$
$23$	1.04540e17	0.994683	0.497341	+	0.867555i	$0.334310\pi$
$24$	−9.46976e16	−0.529296
$25$	0	0
$26$	−4.39677e16	−0.0903581
$27$	2.81659e17	0.361141
$28$	−5.03967e17	−0.410135
$29$	3.09182e18	1.62270	0.811352	−	0.584558i	$-0.198732\pi$
$29$	3.09182e18	1.62270	0.811352	+	0.584558i	$0.198732\pi$
$30$	0	0
$31$	−4.26809e18	−0.973222	−0.486611	−	0.873619i	$-0.661767\pi$
$31$	−4.26809e18	−0.973222	−0.486611	+	0.873619i	$0.661767\pi$
$32$	−1.15292e18	−0.176777
$33$	7.90437e18	0.824980
$34$	1.21845e19	0.875630
$35$	0	0
$36$	1.76443e19	0.620616
$37$	4.51028e19	1.12637	0.563186	−	0.826330i	$-0.309576\pi$
$37$	4.51028e19	1.12637	0.563186	+	0.826330i	$0.309576\pi$
$38$	2.22305e19	0.397791
$39$	1.47922e19	0.191305
$40$	0	0
$41$	−7.56724e19	−0.523769	−0.261884	−	0.965099i	$-0.584344\pi$
$41$	−7.56724e19	−0.523769	−0.261884	+	0.965099i	$0.584344\pi$
$42$	1.69551e20	0.868330
$43$	1.39036e20	0.530605	0.265302	−	0.964165i	$-0.414528\pi$
$43$	1.39036e20	0.530605	0.265302	+	0.964165i	$0.414528\pi$
$44$	9.62339e19	0.275531
$45$	0	0
$46$	−4.28196e20	−0.703347
$47$	−4.67328e20	−0.586676	−0.293338	−	0.956009i	$-0.594766\pi$
$47$	−4.67328e20	−0.586676	−0.293338	+	0.956009i	$0.594766\pi$
$48$	3.87881e20	0.374269
$49$	−4.38741e20	−0.327158
$50$	0	0
$51$	−4.09927e21	−1.85387
$52$	1.80092e20	0.0638928
$53$	1.24315e21	0.347595	0.173797	−	0.984781i	$-0.444396\pi$
$53$	1.24315e21	0.347595	0.173797	+	0.984781i	$0.444396\pi$
$54$	−1.15368e21	−0.255365
$55$	0	0
$56$	2.06425e21	0.290009
$57$	−7.47909e21	−0.842196
$58$	−1.26641e22	−1.14743
$59$	−1.32468e22	−0.969303	−0.484652	−	0.874707i	$-0.661054\pi$
$59$	−1.32468e22	−0.969303	−0.484652	+	0.874707i	$0.661054\pi$
$60$	0	0
$61$	−2.36984e20	−0.0114313	−0.00571565	−	0.999984i	$-0.501819\pi$
$61$	−2.36984e20	−0.0114313	−0.00571565	+	0.999984i	$0.501819\pi$
$62$	1.74821e22	0.688172
$63$	−3.15912e22	−1.01814
$64$	4.72237e21	0.125000
$65$	0	0
$66$	−3.23763e22	−0.583349
$67$	5.36922e22	0.801634	0.400817	−	0.916158i	$-0.368726\pi$
$67$	5.36922e22	0.801634	0.400817	+	0.916158i	$0.368726\pi$
$68$	−4.99076e22	−0.619164
$69$	1.44059e23	1.48911
$70$	0	0
$71$	−2.27032e23	−1.64194	−0.820971	−	0.570970i	$-0.806567\pi$
$71$	−2.27032e23	−1.64194	−0.820971	+	0.570970i	$0.806567\pi$
$72$	−7.22710e22	−0.438842
$73$	−2.78528e23	−1.42342	−0.711710	−	0.702473i	$-0.752079\pi$
$73$	−2.78528e23	−1.42342	−0.711710	+	0.702473i	$0.752079\pi$
$74$	−1.84741e23	−0.796465
$75$	0	0
$76$	−9.10563e22	−0.281281
$77$	−1.72302e23	−0.452019
$78$	−6.05889e22	−0.135273
$79$	6.36958e23	1.21275	0.606376	−	0.795178i	$-0.292622\pi$
$79$	6.36958e23	1.21275	0.606376	+	0.795178i	$0.292622\pi$
$80$	0	0
$81$	−5.02942e23	−0.700576
$82$	3.09954e23	0.370360
$83$	−1.19662e24	−1.22880	−0.614398	−	0.788996i	$-0.710601\pi$
$83$	−1.19662e24	−1.22880	−0.614398	+	0.788996i	$0.710601\pi$
$84$	−6.94482e23	−0.614002
$85$	0	0
$86$	−5.69491e23	−0.375194
$87$	4.26063e24	2.42931
$88$	−3.94174e23	−0.194830
$89$	−3.22134e24	−1.38249	−0.691244	−	0.722621i	$-0.742937\pi$
$89$	−3.22134e24	−1.38249	−0.691244	+	0.722621i	$0.742937\pi$
$90$	0	0
$91$	−3.22445e23	−0.104819
$92$	1.75389e24	0.497341
$93$	−5.88156e24	−1.45699
$94$	1.91418e24	0.414843
$95$	0	0
$96$	−1.58876e24	−0.264648
$97$	−3.58465e24	−0.524566	−0.262283	−	0.964991i	$-0.584475\pi$
$97$	−3.58465e24	−0.524566	−0.262283	+	0.964991i	$0.584475\pi$
$98$	1.79708e24	0.231335
$99$	6.03243e24	0.683994
$100$	0	0
$101$	−3.40630e24	−0.300792	−0.150396	−	0.988626i	$-0.548055\pi$
$101$	−3.40630e24	−0.300792	−0.150396	+	0.988626i	$0.548055\pi$
$102$	1.67906e25	1.31088
$103$	−8.27075e24	−0.571583	−0.285792	−	0.958292i	$-0.592257\pi$
$103$	−8.27075e24	−0.571583	−0.285792	+	0.958292i	$0.592257\pi$
$104$	−7.37656e23	−0.0451791
$105$	0	0
$106$	−5.09192e24	−0.245787
$107$	−1.57986e25	−0.678142	−0.339071	−	0.940761i	$-0.610113\pi$
$107$	−1.57986e25	−0.678142	−0.339071	+	0.940761i	$0.610113\pi$
$108$	4.72546e24	0.180571
$109$	3.00869e25	1.02458	0.512290	−	0.858813i	$-0.328797\pi$
$109$	3.00869e25	1.02458	0.512290	+	0.858813i	$0.328797\pi$
$110$	0	0
$111$	6.21530e25	1.68626
$112$	−8.45516e24	−0.205067
$113$	8.06745e25	1.75088	0.875439	−	0.483329i	$-0.160572\pi$
$113$	8.06745e25	1.75088	0.875439	+	0.483329i	$0.160572\pi$
$114$	3.06344e25	0.595523
$115$	0	0
$116$	5.18722e25	0.811352
$117$	1.12891e25	0.158612
$118$	5.42587e25	0.685401
$119$	8.93571e25	1.01576
$120$	0	0
$121$	−7.54455e25	−0.696332
$122$	9.70685e23	0.00808315
$123$	−1.04279e26	−0.784121
$124$	−7.16066e25	−0.486611
$125$	0	0
$126$	1.29398e26	0.719937
$127$	1.32973e26	0.670221	0.335111	−	0.942179i	$-0.391226\pi$
$127$	1.32973e26	0.670221	0.335111	+	0.942179i	$0.391226\pi$
$128$	−1.93428e25	−0.0883883
$129$	1.91596e26	0.794355
$130$	0	0
$131$	6.73908e25	0.230520	0.115260	−	0.993335i	$-0.463230\pi$
$131$	6.73908e25	0.230520	0.115260	+	0.993335i	$0.463230\pi$
$132$	1.32613e26	0.412490
$133$	1.63032e26	0.461452
$134$	−2.19923e26	−0.566841
$135$	0	0
$136$	2.04422e26	0.437815
$137$	3.22963e26	0.631170	0.315585	−	0.948897i	$-0.397799\pi$
$137$	3.22963e26	0.631170	0.315585	+	0.948897i	$0.397799\pi$
$138$	−5.90067e26	−1.05296
$139$	−9.21581e25	−0.150262	−0.0751309	−	0.997174i	$-0.523937\pi$
$139$	−9.21581e25	−0.150262	−0.0751309	+	0.997174i	$0.523937\pi$
$140$	0	0
$141$	−6.43992e26	−0.878298
$142$	9.29923e26	1.16103
$143$	6.15719e25	0.0704177
$144$	2.96022e26	0.310308
$145$	0	0
$146$	1.14085e27	1.00651
$147$	−6.04599e26	−0.489779
$148$	7.56699e26	0.563186
$149$	−7.12667e26	−0.487594	−0.243797	−	0.969826i	$-0.578393\pi$
$149$	−7.12667e26	−0.487594	−0.243797	+	0.969826i	$0.578393\pi$
$150$	0	0
$151$	−3.06161e27	−1.77312	−0.886559	−	0.462616i	$-0.846911\pi$
$151$	−3.06161e27	−1.77312	−0.886559	+	0.462616i	$0.846911\pi$
$152$	3.72966e26	0.198895
$153$	−3.12846e27	−1.53705
$154$	7.05749e26	0.319626
$155$	0	0
$156$	2.48172e26	0.0956523
$157$	−2.38960e27	−0.850315	−0.425157	−	0.905119i	$-0.639781\pi$
$157$	−2.38960e27	−0.850315	−0.425157	+	0.905119i	$0.639781\pi$
$158$	−2.60898e27	−0.857546
$159$	1.71309e27	0.520375
$160$	0	0
$161$	−3.14025e27	−0.815908
$162$	2.06005e27	0.495382
$163$	−6.63092e27	−1.47648	−0.738242	−	0.674536i	$-0.764344\pi$
$163$	−6.63092e27	−1.47648	−0.738242	+	0.674536i	$0.764344\pi$
$164$	−1.26957e27	−0.261884
$165$	0	0
$166$	4.90135e27	0.868890
$167$	−4.06997e27	−0.669323	−0.334662	−	0.942338i	$-0.608622\pi$
$167$	−4.06997e27	−0.669323	−0.334662	+	0.942338i	$0.608622\pi$
$168$	2.84460e27	0.434165
$169$	−6.94118e27	−0.983671
$170$	0	0
$171$	−5.70787e27	−0.698269
$172$	2.33263e27	0.265302
$173$	8.68916e27	0.919182	0.459591	−	0.888131i	$-0.347996\pi$
$173$	8.68916e27	0.919182	0.459591	+	0.888131i	$0.347996\pi$
$174$	−1.74515e28	−1.71778
$175$	0	0
$176$	1.61454e27	0.137765
$177$	−1.82545e28	−1.45112
$178$	1.31946e28	0.977567
$179$	−4.31406e27	−0.298005	−0.149002	−	0.988837i	$-0.547606\pi$
$179$	−4.31406e27	−0.298005	−0.149002	+	0.988837i	$0.547606\pi$
$180$	0	0
$181$	2.22969e28	1.34049	0.670243	−	0.742142i	$-0.266190\pi$
$181$	2.22969e28	1.34049	0.670243	+	0.742142i	$0.266190\pi$
$182$	1.32074e27	0.0741180
$183$	−3.26571e26	−0.0171135
$184$	−7.18394e27	−0.351674
$185$	0	0
$186$	2.40909e28	1.03024
$187$	−1.70630e28	−0.682394
$188$	−7.84046e27	−0.293338
$189$	−8.46070e27	−0.296233
$190$	0	0
$191$	−1.91337e28	−0.587329	−0.293665	−	0.955908i	$-0.594875\pi$
$191$	−1.91337e28	−0.587329	−0.293665	+	0.955908i	$0.594875\pi$
$192$	6.50757e27	0.187134
$193$	5.96748e28	1.60814	0.804071	−	0.594533i	$-0.202663\pi$
$193$	5.96748e28	1.60814	0.804071	+	0.594533i	$0.202663\pi$
$194$	1.46827e28	0.370924
$195$	0	0
$196$	−7.36085e27	−0.163579
$197$	−6.24204e28	−1.30166	−0.650832	−	0.759222i	$-0.725580\pi$
$197$	−6.24204e28	−1.30166	−0.650832	+	0.759222i	$0.725580\pi$
$198$	−2.47088e28	−0.483657
$199$	−3.24229e28	−0.595921	−0.297960	−	0.954578i	$-0.596306\pi$
$199$	−3.24229e28	−0.595921	−0.297960	+	0.954578i	$0.596306\pi$
$200$	0	0
$201$	7.39895e28	1.20011
$202$	1.39522e28	0.212692
$203$	−9.28745e28	−1.33106
$204$	−6.87743e28	−0.926934
$205$	0	0
$206$	3.38770e28	0.404171
$207$	1.09943e29	1.23463
$208$	3.02144e27	0.0319464
$209$	−3.11314e28	−0.310006
$210$	0	0
$211$	3.82197e28	0.337875	0.168938	−	0.985627i	$-0.445966\pi$
$211$	3.82197e28	0.337875	0.168938	+	0.985627i	$0.445966\pi$
$212$	2.08565e28	0.173797
$213$	−3.12857e29	−2.45811
$214$	6.47109e28	0.479519
$215$	0	0
$216$	−1.93555e28	−0.127683
$217$	1.28208e29	0.798305
$218$	−1.23236e29	−0.724487
$219$	−3.83820e29	−2.13097
$220$	0	0
$221$	−3.19316e28	−0.158241
$222$	−2.54579e29	−1.19237
$223$	−3.11100e29	−1.37749	−0.688746	−	0.725003i	$-0.741839\pi$
$223$	−3.11100e29	−1.37749	−0.688746	+	0.725003i	$0.741839\pi$
$224$	3.46323e28	0.145005
$225$	0	0
$226$	−3.30443e29	−1.23806
$227$	1.05572e29	0.374304	0.187152	−	0.982331i	$-0.440074\pi$
$227$	1.05572e29	0.374304	0.187152	+	0.982331i	$0.440074\pi$
$228$	−1.25478e29	−0.421098
$229$	−3.70322e29	−1.17662	−0.588310	−	0.808635i	$-0.700207\pi$
$229$	−3.70322e29	−1.17662	−0.588310	+	0.808635i	$0.700207\pi$
$230$	0	0
$231$	−2.37438e29	−0.676706
$232$	−2.12468e29	−0.573713
$233$	6.84781e28	0.175228	0.0876138	−	0.996155i	$-0.472076\pi$
$233$	6.84781e28	0.175228	0.0876138	+	0.996155i	$0.472076\pi$
$234$	−4.62400e28	−0.112155
$235$	0	0
$236$	−2.22244e29	−0.484652
$237$	8.77748e29	1.81558
$238$	−3.66007e29	−0.718253
$239$	3.87773e29	0.722111	0.361055	−	0.932544i	$-0.382417\pi$
$239$	3.87773e29	0.722111	0.361055	+	0.932544i	$0.382417\pi$
$240$	0	0
$241$	1.03723e30	1.74046	0.870230	−	0.492646i	$-0.163970\pi$
$241$	1.03723e30	1.74046	0.870230	+	0.492646i	$0.163970\pi$
$242$	3.09025e29	0.492381
$243$	−9.31717e29	−1.40996
$244$	−3.97593e27	−0.00571565
$245$	0	0
$246$	4.27127e29	0.554457
$247$	−5.82591e28	−0.0718873
$248$	2.93301e29	0.344086
$249$	−1.64898e30	−1.83960
$250$	0	0
$251$	1.47990e30	1.49386	0.746930	−	0.664903i	$-0.231527\pi$
$251$	1.47990e30	1.49386	0.746930	+	0.664903i	$0.231527\pi$
$252$	−5.30013e29	−0.509072
$253$	5.99641e29	0.548131
$254$	−5.44659e29	−0.473918
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	−6.75384e29	−0.507442	−0.253721	−	0.967277i	$-0.581655\pi$
$257$	−6.75384e29	−0.507442	−0.253721	+	0.967277i	$0.581655\pi$
$258$	−7.84776e29	−0.561694
$259$	−1.35483e30	−0.923929
$260$	0	0
$261$	3.25161e30	2.01415
$262$	−2.76033e29	−0.163003
$263$	−1.42102e30	−0.800119	−0.400059	−	0.916489i	$-0.631011\pi$
$263$	−1.42102e30	−0.800119	−0.400059	+	0.916489i	$0.631011\pi$
$264$	−5.43184e29	−0.291674
$265$	0	0
$266$	−6.67778e29	−0.326296
$267$	−4.43911e30	−2.06969
$268$	9.00805e29	0.400817
$269$	−1.90129e30	−0.807504	−0.403752	−	0.914868i	$-0.632294\pi$
$269$	−1.90129e30	−0.807504	−0.403752	+	0.914868i	$0.632294\pi$
$270$	0	0
$271$	−1.45800e30	−0.564471	−0.282236	−	0.959345i	$-0.591076\pi$
$271$	−1.45800e30	−0.564471	−0.282236	+	0.959345i	$0.591076\pi$
$272$	−8.37311e29	−0.309582
$273$	−4.44340e29	−0.156921
$274$	−1.32286e30	−0.446304
$275$	0	0
$276$	2.41692e30	0.744557
$277$	5.31088e29	0.156376	0.0781879	−	0.996939i	$-0.475087\pi$
$277$	5.31088e29	0.156376	0.0781879	+	0.996939i	$0.475087\pi$
$278$	3.77479e29	0.106251
$279$	−4.48867e30	−1.20799
$280$	0	0
$281$	−3.64974e30	−0.898323	−0.449161	−	0.893451i	$-0.648277\pi$
$281$	−3.64974e30	−0.898323	−0.449161	+	0.893451i	$0.648277\pi$
$282$	2.63779e30	0.621050
$283$	1.43965e30	0.324285	0.162143	−	0.986767i	$-0.448160\pi$
$283$	1.43965e30	0.324285	0.162143	+	0.986767i	$0.448160\pi$
$284$	−3.80897e30	−0.820971
$285$	0	0
$286$	−2.52199e29	−0.0497929
$287$	2.27311e30	0.429632
$288$	−1.21251e30	−0.219421
$289$	3.07837e30	0.533456
$290$	0	0
$291$	−4.93976e30	−0.785315
$292$	−4.67292e30	−0.711710
$293$	−1.24504e31	−1.81692	−0.908462	−	0.417967i	$-0.862743\pi$
$293$	−1.24504e31	−1.81692	−0.908462	+	0.417967i	$0.862743\pi$
$294$	2.47644e30	0.346326
$295$	0	0
$296$	−3.09944e30	−0.398233
$297$	1.61559e30	0.199011
$298$	2.91909e30	0.344781
$299$	1.12217e30	0.127106
$300$	0	0
$301$	−4.17647e30	−0.435239
$302$	1.25403e31	1.25378
$303$	−4.69399e30	−0.450307
$304$	−1.52767e30	−0.140640
$305$	0	0
$306$	1.28142e31	1.08686
$307$	−2.27193e31	−1.84997	−0.924986	−	0.380001i	$-0.875924\pi$
$307$	−2.27193e31	−1.84997	−0.924986	+	0.380001i	$0.875924\pi$
$308$	−2.89075e30	−0.226009
$309$	−1.13974e31	−0.855703
$310$	0	0
$311$	−1.84336e31	−1.27675	−0.638374	−	0.769726i	$-0.720393\pi$
$311$	−1.84336e31	−1.27675	−0.638374	+	0.769726i	$0.720393\pi$
$312$	−1.01651e30	−0.0676364
$313$	−4.98693e30	−0.318808	−0.159404	−	0.987213i	$-0.550957\pi$
$313$	−4.98693e30	−0.318808	−0.159404	+	0.987213i	$0.550957\pi$
$314$	9.78780e30	0.601263
$315$	0	0
$316$	1.06864e31	0.606376
$317$	8.79478e30	0.479716	0.239858	−	0.970808i	$-0.422899\pi$
$317$	8.79478e30	0.479716	0.239858	+	0.970808i	$0.422899\pi$
$318$	−7.01683e30	−0.367961
$319$	1.77347e31	0.894209
$320$	0	0
$321$	−2.17709e31	−1.01523
$322$	1.28625e31	0.576934
$323$	1.61450e31	0.696635
$324$	−8.43797e30	−0.350288
$325$	0	0
$326$	2.71602e31	1.04403
$327$	4.14606e31	1.53387
$328$	5.20017e30	0.185180
$329$	1.40380e31	0.481233
$330$	0	0
$331$	5.97122e31	1.89764	0.948818	−	0.315822i	$-0.102280\pi$
$331$	5.97122e31	1.89764	0.948818	+	0.315822i	$0.102280\pi$
$332$	−2.00759e31	−0.614398
$333$	4.74337e31	1.39809
$334$	1.66706e31	0.473283
$335$	0	0
$336$	−1.16515e31	−0.307001
$337$	−1.08428e31	−0.275275	−0.137638	−	0.990483i	$-0.543951\pi$
$337$	−1.08428e31	−0.275275	−0.137638	+	0.990483i	$0.543951\pi$
$338$	2.84311e31	0.695560
$339$	1.11172e32	2.62119
$340$	0	0
$341$	−2.44817e31	−0.536305
$342$	2.33794e31	0.493751
$343$	5.34633e31	1.08863
$344$	−9.55447e30	−0.187597
$345$	0	0
$346$	−3.55908e31	−0.649960
$347$	−7.20193e30	−0.126862	−0.0634308	−	0.997986i	$-0.520204\pi$
$347$	−7.20193e30	−0.126862	−0.0634308	+	0.997986i	$0.520204\pi$
$348$	7.14814e31	1.21465
$349$	5.27779e31	0.865235	0.432618	−	0.901577i	$-0.357590\pi$
$349$	5.27779e31	0.865235	0.432618	+	0.901577i	$0.357590\pi$
$350$	0	0
$351$	3.02342e30	0.0461487
$352$	−6.61315e30	−0.0974148
$353$	5.67715e31	0.807135	0.403567	−	0.914950i	$-0.367770\pi$
$353$	5.67715e31	0.807135	0.403567	+	0.914950i	$0.367770\pi$
$354$	7.47702e31	1.02610
$355$	0	0
$356$	−5.40451e31	−0.691244
$357$	1.23137e32	1.52067
$358$	1.76704e31	0.210721
$359$	2.18925e31	0.252125	0.126062	−	0.992022i	$-0.459766\pi$
$359$	2.18925e31	0.252125	0.126062	+	0.992022i	$0.459766\pi$
$360$	0	0
$361$	−6.36201e31	−0.683525
$362$	−9.13280e31	−0.947866
$363$	−1.03966e32	−1.04246
$364$	−5.40974e30	−0.0524094
$365$	0	0
$366$	1.33763e30	0.0121011
$367$	−1.00500e32	−0.878699	−0.439349	−	0.898316i	$-0.644791\pi$
$367$	−1.00500e32	−0.878699	−0.439349	+	0.898316i	$0.644791\pi$
$368$	2.94254e31	0.248671
$369$	−7.95833e31	−0.650118
$370$	0	0
$371$	−3.73425e31	−0.285122
$372$	−9.86761e31	−0.728493
$373$	−6.31052e31	−0.450510	−0.225255	−	0.974300i	$-0.572322\pi$
$373$	−6.31052e31	−0.450510	−0.225255	+	0.974300i	$0.572322\pi$
$374$	6.98901e31	0.482526
$375$	0	0
$376$	3.21145e31	0.207421
$377$	3.31886e31	0.207358
$378$	3.46550e31	0.209468
$379$	−8.85755e31	−0.517993	−0.258996	−	0.965878i	$-0.583392\pi$
$379$	−8.85755e31	−0.517993	−0.258996	+	0.965878i	$0.583392\pi$
$380$	0	0
$381$	1.83241e32	1.00337
$382$	7.83716e31	0.415305
$383$	−9.08315e31	−0.465856	−0.232928	−	0.972494i	$-0.574831\pi$
$383$	−9.08315e31	−0.465856	−0.232928	+	0.972494i	$0.574831\pi$
$384$	−2.66550e31	−0.132324
$385$	0	0
$386$	−2.44428e32	−1.13713
$387$	1.46221e32	0.658603
$388$	−6.01405e31	−0.262283
$389$	7.13043e31	0.301124	0.150562	−	0.988601i	$-0.451892\pi$
$389$	7.13043e31	0.301124	0.150562	+	0.988601i	$0.451892\pi$
$390$	0	0
$391$	−3.10978e32	−1.23174
$392$	3.01500e31	0.115668
$393$	9.28666e31	0.345106
$394$	2.55674e32	0.920416
$395$	0	0
$396$	1.01207e32	0.341997
$397$	−2.99427e31	−0.0980413	−0.0490206	−	0.998798i	$-0.515610\pi$
$397$	−2.99427e31	−0.0980413	−0.0490206	+	0.998798i	$0.515610\pi$
$398$	1.32804e32	0.421380
$399$	2.24663e32	0.690828
$400$	0	0
$401$	−5.00588e32	−1.44603	−0.723013	−	0.690835i	$-0.757243\pi$
$401$	−5.00588e32	−1.44603	−0.723013	+	0.690835i	$0.757243\pi$
$402$	−3.03061e32	−0.848603
$403$	−4.58150e31	−0.124364
$404$	−5.71482e31	−0.150396
$405$	0	0
$406$	3.80414e32	0.941198
$407$	2.58709e32	0.620700
$408$	2.81699e32	0.655441
$409$	−2.78379e32	−0.628195	−0.314097	−	0.949391i	$-0.601702\pi$
$409$	−2.78379e32	−0.628195	−0.314097	+	0.949391i	$0.601702\pi$
$410$	0	0
$411$	4.45054e32	0.944908
$412$	−1.38760e32	−0.285792
$413$	3.97916e32	0.795090
$414$	−4.50326e32	−0.873016
$415$	0	0
$416$	−1.23758e31	−0.0225895
$417$	−1.26997e32	−0.224953
$418$	1.27514e32	0.219207
$419$	−6.36828e32	−1.06254	−0.531272	−	0.847201i	$-0.678286\pi$
$419$	−6.36828e32	−1.06254	−0.531272	+	0.847201i	$0.678286\pi$
$420$	0	0
$421$	−3.92275e32	−0.616686	−0.308343	−	0.951275i	$-0.599775\pi$
$421$	−3.92275e32	−0.616686	−0.308343	+	0.951275i	$0.599775\pi$
$422$	−1.56548e32	−0.238914
$423$	−4.91480e32	−0.728201
$424$	−8.54283e31	−0.122893
$425$	0	0
$426$	1.28146e33	1.73815
$427$	7.11870e30	0.00937675
$428$	−2.65056e32	−0.339071
$429$	8.48480e31	0.105421
$430$	0	0
$431$	2.44178e32	0.286247	0.143124	−	0.989705i	$-0.454285\pi$
$431$	2.44178e32	0.286247	0.143124	+	0.989705i	$0.454285\pi$
$432$	7.92800e31	0.0902853
$433$	−9.12872e32	−1.00998	−0.504988	−	0.863126i	$-0.668503\pi$
$433$	−9.12872e32	−1.00998	−0.504988	+	0.863126i	$0.668503\pi$
$434$	−5.25140e32	−0.564487
$435$	0	0
$436$	5.04774e32	0.512290
$437$	−5.67378e32	−0.559570
$438$	1.57213e33	1.50682
$439$	6.07601e32	0.565995	0.282997	−	0.959121i	$-0.408671\pi$
$439$	6.07601e32	0.565995	0.282997	+	0.959121i	$0.408671\pi$
$440$	0	0
$441$	−4.61416e32	−0.406078
$442$	1.30792e32	0.111893
$443$	−9.06289e32	−0.753737	−0.376869	−	0.926267i	$-0.622999\pi$
$443$	−9.06289e32	−0.753737	−0.376869	+	0.926267i	$0.622999\pi$
$444$	1.04275e33	0.843131
$445$	0	0
$446$	1.27427e33	0.974034
$447$	−9.82078e32	−0.729965
$448$	−1.41854e32	−0.102534
$449$	−1.21579e33	−0.854630	−0.427315	−	0.904103i	$-0.640540\pi$
$449$	−1.21579e33	−0.854630	−0.427315	+	0.904103i	$0.640540\pi$
$450$	0	0
$451$	−4.34056e32	−0.288629
$452$	1.35349e33	0.875439
$453$	−4.21899e33	−2.65449
$454$	−4.32422e32	−0.264673
$455$	0	0
$456$	5.13959e32	0.297761
$457$	5.59530e32	0.315407	0.157703	−	0.987487i	$-0.449591\pi$
$457$	5.59530e32	0.315407	0.157703	+	0.987487i	$0.449591\pi$
$458$	1.51684e33	0.831997
$459$	−8.37859e32	−0.447211
$460$	0	0
$461$	−3.78592e32	−0.191386	−0.0956930	−	0.995411i	$-0.530507\pi$
$461$	−3.78592e32	−0.191386	−0.0956930	+	0.995411i	$0.530507\pi$
$462$	9.72545e32	0.478503
$463$	−2.77039e33	−1.32672	−0.663359	−	0.748301i	$-0.730870\pi$
$463$	−2.77039e33	−1.32672	−0.663359	+	0.748301i	$0.730870\pi$
$464$	8.70270e32	0.405676
$465$	0	0
$466$	−2.80486e32	−0.123905
$467$	2.31922e33	0.997428	0.498714	−	0.866767i	$-0.333806\pi$
$467$	2.31922e33	0.997428	0.498714	+	0.866767i	$0.333806\pi$
$468$	1.89399e32	0.0793058
$469$	−1.61285e33	−0.657556
$470$	0	0
$471$	−3.29294e33	−1.27298
$472$	9.10311e32	0.342700
$473$	7.97508e32	0.292396
$474$	−3.59526e33	−1.28381
$475$	0	0
$476$	1.49916e33	0.507881
$477$	1.30739e33	0.431446
$478$	−1.58832e33	−0.510609
$479$	2.24376e33	0.702720	0.351360	−	0.936240i	$-0.385719\pi$
$479$	2.24376e33	0.702720	0.351360	+	0.936240i	$0.385719\pi$
$480$	0	0
$481$	4.84147e32	0.143934
$482$	−4.24851e33	−1.23069
$483$	−4.32737e33	−1.22148
$484$	−1.26577e33	−0.348166
$485$	0	0
$486$	3.81631e33	0.996989
$487$	−3.71393e32	−0.0945632	−0.0472816	−	0.998882i	$-0.515056\pi$
$487$	−3.71393e32	−0.0945632	−0.0472816	+	0.998882i	$0.515056\pi$
$488$	1.62854e31	0.00404157
$489$	−9.13761e33	−2.21041
$490$	0	0
$491$	−2.65508e33	−0.610323	−0.305161	−	0.952301i	$-0.598710\pi$
$491$	−2.65508e33	−0.610323	−0.305161	+	0.952301i	$0.598710\pi$
$492$	−1.74951e33	−0.392060
$493$	−9.19732e33	−2.00944
$494$	2.38629e32	0.0508320
$495$	0	0
$496$	−1.20136e33	−0.243306
$497$	6.81976e33	1.34684
$498$	6.75421e33	1.30079
$499$	−2.39117e33	−0.449111	−0.224556	−	0.974461i	$-0.572093\pi$
$499$	−2.39117e33	−0.449111	−0.224556	+	0.974461i	$0.572093\pi$
$500$	0	0
$501$	−5.60855e33	−1.00203
$502$	−6.06166e33	−1.05632
$503$	6.34146e33	1.07793	0.538964	−	0.842329i	$-0.318816\pi$
$503$	6.34146e33	1.07793	0.538964	+	0.842329i	$0.318816\pi$
$504$	2.17093e33	0.359968
$505$	0	0
$506$	−2.45613e33	−0.387587
$507$	−9.56517e33	−1.47263
$508$	2.23092e33	0.335111
$509$	−3.62528e32	−0.0531337	−0.0265668	−	0.999647i	$-0.508457\pi$
$509$	−3.62528e32	−0.0531337	−0.0265668	+	0.999647i	$0.508457\pi$
$510$	0	0
$511$	8.36664e33	1.16759
$512$	−3.24519e32	−0.0441942
$513$	−1.52867e33	−0.203164
$514$	2.76637e33	0.358816
$515$	0	0
$516$	3.21444e33	0.397177
$517$	−2.68059e33	−0.323295
$518$	5.54939e33	0.653316
$519$	1.19739e34	1.37608
$520$	0	0
$521$	8.23573e33	0.902050	0.451025	−	0.892511i	$-0.351058\pi$
$521$	8.23573e33	0.902050	0.451025	+	0.892511i	$0.351058\pi$
$522$	−1.33186e34	−1.42422
$523$	1.20443e34	1.25750	0.628752	−	0.777606i	$-0.283566\pi$
$523$	1.20443e34	1.25750	0.628752	+	0.777606i	$0.283566\pi$
$524$	1.13063e33	0.115260
$525$	0	0
$526$	5.82051e33	0.565770
$527$	1.26964e34	1.20517
$528$	2.22488e33	0.206245
$529$	−1.17149e32	−0.0106057
$530$	0	0
$531$	−1.39314e34	−1.20313
$532$	2.73522e33	0.230726
$533$	−8.12291e32	−0.0669301
$534$	1.81826e34	1.46349
$535$	0	0
$536$	−3.68970e33	−0.283420
$537$	−5.94490e33	−0.446135
$538$	7.78769e33	0.570992
$539$	−2.51661e33	−0.180284
$540$	0	0
$541$	1.30366e34	0.891657	0.445829	−	0.895118i	$-0.352909\pi$
$541$	1.30366e34	0.891657	0.445829	+	0.895118i	$0.352909\pi$
$542$	5.97197e33	0.399141
$543$	3.07258e34	2.00681
$544$	3.42963e33	0.218907
$545$	0	0
$546$	1.82002e33	0.110960
$547$	1.78334e34	1.06266	0.531328	−	0.847166i	$-0.321693\pi$
$547$	1.78334e34	1.06266	0.531328	+	0.847166i	$0.321693\pi$
$548$	5.41843e33	0.315585
$549$	−2.49231e32	−0.0141889
$550$	0	0
$551$	−1.67805e34	−0.912871
$552$	−9.89969e33	−0.526481
$553$	−1.91334e34	−0.994784
$554$	−2.17534e33	−0.110574
$555$	0	0
$556$	−1.54616e33	−0.0751309
$557$	−8.73339e33	−0.414947	−0.207474	−	0.978241i	$-0.566524\pi$
$557$	−8.73339e33	−0.414947	−0.207474	+	0.978241i	$0.566524\pi$
$558$	1.83856e34	0.854181
$559$	1.49245e33	0.0678037
$560$	0	0
$561$	−2.35134e34	−1.02160
$562$	1.49493e34	0.635210
$563$	−3.82416e34	−1.58921	−0.794606	−	0.607126i	$-0.792322\pi$
$563$	−3.82416e34	−1.58921	−0.794606	+	0.607126i	$0.792322\pi$
$564$	−1.08044e34	−0.439149
$565$	0	0
$566$	−5.89682e33	−0.229304
$567$	1.51078e34	0.574661
$568$	1.56015e34	0.580514
$569$	3.49591e34	1.27250	0.636248	−	0.771484i	$-0.280485\pi$
$569$	3.49591e34	1.27250	0.636248	+	0.771484i	$0.280485\pi$
$570$	0	0
$571$	−3.60524e34	−1.25598	−0.627989	−	0.778222i	$-0.716122\pi$
$571$	−3.60524e34	−1.25598	−0.627989	+	0.778222i	$0.716122\pi$
$572$	1.03301e33	0.0352089
$573$	−2.63668e34	−0.879276
$574$	−9.31065e33	−0.303795
$575$	0	0
$576$	4.96642e33	0.155154
$577$	4.45926e34	1.36322	0.681609	−	0.731717i	$-0.261281\pi$
$577$	4.45926e34	1.36322	0.681609	+	0.731717i	$0.261281\pi$
$578$	−1.26090e34	−0.377210
$579$	8.22337e34	2.40751
$580$	0	0
$581$	3.59450e34	1.00794
$582$	2.02333e34	0.555301
$583$	7.13067e33	0.191546
$584$	1.91403e34	0.503255
$585$	0	0
$586$	5.09967e34	1.28476
$587$	2.50958e34	0.618905	0.309452	−	0.950915i	$-0.399854\pi$
$587$	2.50958e34	0.618905	0.309452	+	0.950915i	$0.399854\pi$
$588$	−1.01435e34	−0.244890
$589$	2.31645e34	0.547497
$590$	0	0
$591$	−8.60173e34	−1.94869
$592$	1.26953e34	0.281593
$593$	4.88078e33	0.106000	0.0530000	−	0.998595i	$-0.483122\pi$
$593$	4.88078e33	0.106000	0.0530000	+	0.998595i	$0.483122\pi$
$594$	−6.61748e33	−0.140722
$595$	0	0
$596$	−1.19566e34	−0.243797
$597$	−4.46798e34	−0.892138
$598$	−4.59639e33	−0.0898777
$599$	4.61838e34	0.884412	0.442206	−	0.896914i	$-0.354196\pi$
$599$	4.61838e34	0.884412	0.442206	+	0.896914i	$0.354196\pi$
$600$	0	0
$601$	−3.07405e34	−0.564651	−0.282325	−	0.959319i	$-0.591106\pi$
$601$	−3.07405e34	−0.564651	−0.282325	+	0.959319i	$0.591106\pi$
$602$	1.71068e34	0.307760
$603$	5.64671e34	0.995013
$604$	−5.13652e34	−0.886559
$605$	0	0
$606$	1.92266e34	0.318415
$607$	−1.03737e35	−1.68297	−0.841484	−	0.540282i	$-0.818318\pi$
$607$	−1.03737e35	−1.68297	−0.841484	+	0.540282i	$0.818318\pi$
$608$	6.25734e33	0.0994477
$609$	−1.27984e35	−1.99269
$610$	0	0
$611$	−5.01644e33	−0.0749688
$612$	−5.24869e34	−0.768526
$613$	−2.85744e34	−0.409941	−0.204970	−	0.978768i	$-0.565710\pi$
$613$	−2.85744e34	−0.409941	−0.204970	+	0.978768i	$0.565710\pi$
$614$	9.30582e34	1.30813
$615$	0	0
$616$	1.18405e34	0.159813
$617$	−5.36336e34	−0.709370	−0.354685	−	0.934986i	$-0.615412\pi$
$617$	−5.36336e34	−0.709370	−0.354685	+	0.934986i	$0.615412\pi$
$618$	4.66836e34	0.605073
$619$	6.60909e34	0.839477	0.419738	−	0.907645i	$-0.362122\pi$
$619$	6.60909e34	0.839477	0.419738	+	0.907645i	$0.362122\pi$
$620$	0	0
$621$	2.94447e34	0.359221
$622$	7.55041e34	0.902798
$623$	9.67651e34	1.13401
$624$	4.16364e33	0.0478262
$625$	0	0
$626$	2.04264e34	0.225431
$627$	−4.29000e34	−0.464102
$628$	−4.00908e34	−0.425157
$629$	−1.34168e35	−1.39482
$630$	0	0
$631$	8.62816e34	0.862087	0.431043	−	0.902331i	$-0.358146\pi$
$631$	8.62816e34	0.862087	0.431043	+	0.902331i	$0.358146\pi$
$632$	−4.37714e34	−0.428773
$633$	5.26679e34	0.505824
$634$	−3.60234e34	−0.339210
$635$	0	0
$636$	2.87409e34	0.260188
$637$	−4.70958e33	−0.0418061
$638$	−7.26412e34	−0.632302
$639$	−2.38765e35	−2.03803
$640$	0	0
$641$	1.77093e35	1.45370	0.726850	−	0.686796i	$-0.240983\pi$
$641$	1.77093e35	1.45370	0.726850	+	0.686796i	$0.240983\pi$
$642$	8.91737e34	0.717875
$643$	7.98617e34	0.630524	0.315262	−	0.949005i	$-0.397908\pi$
$643$	7.98617e34	0.630524	0.315262	+	0.949005i	$0.397908\pi$
$644$	−5.26847e34	−0.407954
$645$	0	0
$646$	−6.61298e34	−0.492596
$647$	2.16671e35	1.58306	0.791530	−	0.611130i	$-0.209285\pi$
$647$	2.16671e35	1.58306	0.791530	+	0.611130i	$0.209285\pi$
$648$	3.45619e34	0.247691
$649$	−7.59833e34	−0.534145
$650$	0	0
$651$	1.76675e35	1.19512
$652$	−1.11248e35	−0.738242
$653$	−2.41184e35	−1.57013	−0.785063	−	0.619416i	$-0.787369\pi$
$653$	−2.41184e35	−1.57013	−0.785063	+	0.619416i	$0.787369\pi$
$654$	−1.69823e35	−1.08461
$655$	0	0
$656$	−2.12999e34	−0.130942
$657$	−2.92923e35	−1.76679
$658$	−5.74995e34	−0.340283
$659$	2.18788e35	1.27045	0.635223	−	0.772329i	$-0.280908\pi$
$659$	2.18788e35	1.27045	0.635223	+	0.772329i	$0.280908\pi$
$660$	0	0
$661$	−8.90411e34	−0.497820	−0.248910	−	0.968527i	$-0.580072\pi$
$661$	−8.90411e34	−0.497820	−0.248910	+	0.968527i	$0.580072\pi$
$662$	−2.44581e35	−1.34183
$663$	−4.40028e34	−0.236898
$664$	8.22310e34	0.434445
$665$	0	0
$666$	−1.94289e35	−0.988597
$667$	3.23219e35	1.61408
$668$	−6.82828e34	−0.334662
$669$	−4.28705e35	−2.06221
$670$	0	0
$671$	−1.35934e33	−0.00629934
$672$	4.77244e34	0.217083
$673$	−2.39665e35	−1.07008	−0.535040	−	0.844827i	$-0.679703\pi$
$673$	−2.39665e35	−1.07008	−0.535040	+	0.844827i	$0.679703\pi$
$674$	4.44120e34	0.194649
$675$	0	0
$676$	−1.16454e35	−0.491835
$677$	3.79216e34	0.157227	0.0786137	−	0.996905i	$-0.474951\pi$
$677$	3.79216e34	0.157227	0.0786137	+	0.996905i	$0.474951\pi$
$678$	−4.55360e35	−1.85346
$679$	1.07679e35	0.430286
$680$	0	0
$681$	1.45481e35	0.560361
$682$	1.00277e35	0.379225
$683$	3.21208e35	1.19269	0.596345	−	0.802729i	$-0.296619\pi$
$683$	3.21208e35	1.19269	0.596345	+	0.802729i	$0.296619\pi$
$684$	−9.57621e34	−0.349134
$685$	0	0
$686$	−2.18986e35	−0.769776
$687$	−5.10316e35	−1.76149
$688$	3.91351e34	0.132651
$689$	1.33443e34	0.0444177
$690$	0	0
$691$	8.34540e34	0.267899	0.133950	−	0.990988i	$-0.457234\pi$
$691$	8.34540e34	0.267899	0.133950	+	0.990988i	$0.457234\pi$
$692$	1.45780e35	0.459591
$693$	−1.81207e35	−0.561060
$694$	2.94991e34	0.0897047
$695$	0	0
$696$	−2.92788e35	−0.858890
$697$	2.25105e35	0.648597
$698$	−2.16178e35	−0.611814
$699$	9.43649e34	0.262329
$700$	0	0
$701$	1.50008e35	0.402383	0.201191	−	0.979552i	$-0.435519\pi$
$701$	1.50008e35	0.402383	0.201191	+	0.979552i	$0.435519\pi$
$702$	−1.23839e34	−0.0326320
$703$	−2.44790e35	−0.633653
$704$	2.70874e34	0.0688827
$705$	0	0
$706$	−2.32536e35	−0.570731
$707$	1.02321e35	0.246730
$708$	−3.06259e35	−0.725559
$709$	−2.12042e35	−0.493564	−0.246782	−	0.969071i	$-0.579373\pi$
$709$	−2.12042e35	−0.493564	−0.246782	+	0.969071i	$0.579373\pi$
$710$	0	0
$711$	6.69877e35	1.50531
$712$	2.21369e35	0.488783
$713$	−4.46186e35	−0.968048
$714$	−5.04369e35	−1.07528
$715$	0	0
$716$	−7.23778e34	−0.149002
$717$	5.34363e35	1.08105
$718$	−8.96718e34	−0.178279
$719$	3.27911e35	0.640686	0.320343	−	0.947302i	$-0.396202\pi$
$719$	3.27911e35	0.640686	0.320343	+	0.947302i	$0.396202\pi$
$720$	0	0
$721$	2.48443e35	0.468853
$722$	2.60588e35	0.483325
$723$	1.42934e36	2.60560
$724$	3.74080e35	0.670243
$725$	0	0
$726$	4.25846e35	0.737131
$727$	−2.40795e35	−0.409701	−0.204850	−	0.978793i	$-0.565671\pi$
$727$	−2.40795e35	−0.409701	−0.204850	+	0.978793i	$0.565671\pi$
$728$	2.21583e34	0.0370590
$729$	−8.57797e35	−1.41023
$730$	0	0
$731$	−4.13594e35	−0.657063
$732$	−5.47895e33	−0.00855675
$733$	3.39196e35	0.520776	0.260388	−	0.965504i	$-0.416150\pi$
$733$	3.39196e35	0.520776	0.260388	+	0.965504i	$0.416150\pi$
$734$	4.11648e35	0.621334
$735$	0	0
$736$	−1.20526e35	−0.175837
$737$	3.07978e35	0.441749
$738$	3.25973e35	0.459703
$739$	1.23366e36	1.71057	0.855284	−	0.518159i	$-0.173383\pi$
$739$	1.23366e36	1.71057	0.855284	+	0.518159i	$0.173383\pi$
$740$	0	0
$741$	−8.02829e34	−0.107621
$742$	1.52955e35	0.201611
$743$	6.24478e35	0.809389	0.404694	−	0.914452i	$-0.367378\pi$
$743$	6.24478e35	0.809389	0.404694	+	0.914452i	$0.367378\pi$
$744$	4.04177e35	0.515122
$745$	0	0
$746$	2.58479e35	0.318559
$747$	−1.25846e36	−1.52522
$748$	−2.86270e35	−0.341197
$749$	4.74570e35	0.556259
$750$	0	0
$751$	−4.41291e35	−0.500294	−0.250147	−	0.968208i	$-0.580479\pi$
$751$	−4.41291e35	−0.500294	−0.250147	+	0.968208i	$0.580479\pi$
$752$	−1.31541e35	−0.146669
$753$	2.03934e36	2.23642
$754$	−1.35940e35	−0.146625
$755$	0	0
$756$	−1.41947e35	−0.148117
$757$	−1.83266e35	−0.188098	−0.0940489	−	0.995568i	$-0.529981\pi$
$757$	−1.83266e35	−0.188098	−0.0940489	+	0.995568i	$0.529981\pi$
$758$	3.62805e35	0.366276
$759$	8.26323e35	0.820593
$760$	0	0
$761$	1.88027e36	1.80681	0.903406	−	0.428787i	$-0.141059\pi$
$761$	1.88027e36	1.80681	0.903406	+	0.428787i	$0.141059\pi$
$762$	−7.50557e35	−0.709490
$763$	−9.03772e35	−0.840431
$764$	−3.21010e35	−0.293665
$765$	0	0
$766$	3.72046e35	0.329410
$767$	−1.42195e35	−0.123863
$768$	1.09179e35	0.0935671
$769$	1.28453e36	1.08309	0.541546	−	0.840671i	$-0.317839\pi$
$769$	1.28453e36	1.08309	0.541546	+	0.840671i	$0.317839\pi$
$770$	0	0
$771$	−9.30700e35	−0.759679
$772$	1.00118e36	0.804071
$773$	1.04808e36	0.828226	0.414113	−	0.910225i	$-0.364092\pi$
$773$	1.04808e36	0.828226	0.414113	+	0.910225i	$0.364092\pi$
$774$	−5.98923e35	−0.465703
$775$	0	0
$776$	2.46335e35	0.185462
$777$	−1.86700e36	−1.38319
$778$	−2.92063e35	−0.212927
$779$	4.10703e35	0.294652
$780$	0	0
$781$	−1.30225e36	−0.904811
$782$	1.27377e36	0.870974
$783$	8.70840e35	0.586025
$784$	−1.23495e35	−0.0817894
$785$	0	0
$786$	−3.80382e35	−0.244027
$787$	8.93146e35	0.563947	0.281974	−	0.959422i	$-0.409011\pi$
$787$	8.93146e35	0.563947	0.281974	+	0.959422i	$0.409011\pi$
$788$	−1.04724e36	−0.650832
$789$	−1.95822e36	−1.19784
$790$	0	0
$791$	−2.42336e36	−1.43619
$792$	−4.14546e35	−0.241829
$793$	−2.54386e33	−0.00146076
$794$	1.22645e35	0.0693257
$795$	0	0
$796$	−5.43966e35	−0.297960
$797$	1.02840e36	0.554540	0.277270	−	0.960792i	$-0.410570\pi$
$797$	1.02840e36	0.554540	0.277270	+	0.960792i	$0.410570\pi$
$798$	−9.20219e35	−0.488489
$799$	1.39017e36	0.726498
$800$	0	0
$801$	−3.38782e36	−1.71599
$802$	2.05041e36	1.02249
$803$	−1.59763e36	−0.784392
$804$	1.24134e36	0.600053
$805$	0	0
$806$	1.87658e35	0.0879385
$807$	−2.62004e36	−1.20889
$808$	2.34079e35	0.106346
$809$	1.33897e36	0.598981	0.299490	−	0.954099i	$-0.403183\pi$
$809$	1.33897e36	0.598981	0.299490	+	0.954099i	$0.403183\pi$
$810$	0	0
$811$	1.29485e36	0.561643	0.280821	−	0.959760i	$-0.409393\pi$
$811$	1.29485e36	0.561643	0.280821	+	0.959760i	$0.409393\pi$
$812$	−1.55818e36	−0.665528
$813$	−2.00917e36	−0.845055
$814$	−1.05967e36	−0.438901
$815$	0	0
$816$	−1.15384e36	−0.463467
$817$	−7.54600e35	−0.298498
$818$	1.14024e36	0.444201
$819$	−3.39110e35	−0.130104
$820$	0	0
$821$	3.91664e34	0.0145755	0.00728777	−	0.999973i	$-0.497680\pi$
$821$	3.91664e34	0.0145755	0.00728777	+	0.999973i	$0.497680\pi$
$822$	−1.82294e36	−0.668151
$823$	3.40400e36	1.22883	0.614414	−	0.788984i	$-0.289392\pi$
$823$	3.40400e36	1.22883	0.614414	+	0.788984i	$0.289392\pi$
$824$	5.68362e35	0.202085
$825$	0	0
$826$	−1.62987e36	−0.562213
$827$	5.02186e36	1.70626	0.853132	−	0.521696i	$-0.174700\pi$
$827$	5.02186e36	1.70626	0.853132	+	0.521696i	$0.174700\pi$
$828$	1.84453e36	0.617316
$829$	8.20485e35	0.270482	0.135241	−	0.990813i	$-0.456819\pi$
$829$	8.20485e35	0.270482	0.135241	+	0.990813i	$0.456819\pi$
$830$	0	0
$831$	7.31856e35	0.234106
$832$	5.06913e34	0.0159732
$833$	1.30513e36	0.405128
$834$	5.20178e35	0.159066
$835$	0	0
$836$	−5.22298e35	−0.155003
$837$	−1.20215e36	−0.351471
$838$	2.60845e36	0.751332
$839$	−5.38664e36	−1.52860	−0.764300	−	0.644861i	$-0.776915\pi$
$839$	−5.38664e36	−1.52860	−0.764300	+	0.644861i	$0.776915\pi$
$840$	0	0
$841$	5.92900e36	1.63317
$842$	1.60676e36	0.436063
$843$	−5.02945e36	−1.34486
$844$	6.41220e35	0.168938
$845$	0	0
$846$	2.01310e36	0.514916
$847$	2.26629e36	0.571180
$848$	3.49914e35	0.0868987
$849$	1.98389e36	0.485479
$850$	0	0
$851$	4.71505e36	1.12038
$852$	−5.24887e36	−1.22905
$853$	−9.55369e35	−0.220449	−0.110225	−	0.993907i	$-0.535157\pi$
$853$	−9.55369e35	−0.220449	−0.110225	+	0.993907i	$0.535157\pi$
$854$	−2.91582e34	−0.00663036
$855$	0	0
$856$	1.08567e36	0.239759
$857$	5.39118e36	1.17334	0.586669	−	0.809827i	$-0.300439\pi$
$857$	5.39118e36	1.17334	0.586669	+	0.809827i	$0.300439\pi$
$858$	−3.47537e35	−0.0745436
$859$	5.48992e36	1.16052	0.580258	−	0.814432i	$-0.302952\pi$
$859$	5.48992e36	1.16052	0.580258	+	0.814432i	$0.302952\pi$
$860$	0	0
$861$	3.13241e36	0.643190
$862$	−1.00016e36	−0.202407
$863$	2.89510e36	0.577469	0.288735	−	0.957409i	$-0.406766\pi$
$863$	2.89510e36	0.577469	0.288735	+	0.957409i	$0.406766\pi$
$864$	−3.24731e35	−0.0638413
$865$	0	0
$866$	3.73912e36	0.714161
$867$	4.24209e36	0.798623
$868$	2.15097e36	0.399152
$869$	3.65359e36	0.668301
$870$	0	0
$871$	5.76349e35	0.102437
$872$	−2.06755e36	−0.362244
$873$	−3.76991e36	−0.651108
$874$	2.32398e36	0.395676
$875$	0	0
$876$	−6.43943e36	−1.06548
$877$	−2.04429e36	−0.333463	−0.166731	−	0.986002i	$-0.553321\pi$
$877$	−2.04429e36	−0.333463	−0.166731	+	0.986002i	$0.553321\pi$
$878$	−2.48874e36	−0.400219
$879$	−1.71570e37	−2.72007
$880$	0	0
$881$	−1.76163e36	−0.271466	−0.135733	−	0.990745i	$-0.543339\pi$
$881$	−1.76163e36	−0.271466	−0.135733	+	0.990745i	$0.543339\pi$
$882$	1.88996e36	0.287141
$883$	−1.25672e37	−1.88248	−0.941240	−	0.337738i	$-0.890338\pi$
$883$	−1.25672e37	−1.88248	−0.941240	+	0.337738i	$0.890338\pi$
$884$	−5.35724e35	−0.0791203
$885$	0	0
$886$	3.71216e36	0.532973
$887$	−8.81003e36	−1.24719	−0.623595	−	0.781748i	$-0.714328\pi$
$887$	−8.81003e36	−1.24719	−0.623595	+	0.781748i	$0.714328\pi$
$888$	−4.27112e36	−0.596184
$889$	−3.99436e36	−0.549762
$890$	0	0
$891$	−2.88487e36	−0.386060
$892$	−5.21939e36	−0.688746
$893$	2.53636e36	0.330041
$894$	4.02259e36	0.516163
$895$	0	0
$896$	5.81034e35	0.0725023
$897$	1.54638e36	0.190288
$898$	4.97986e36	0.604315
$899$	−1.31962e37	−1.57925
$900$	0	0
$901$	−3.69802e36	−0.430436
$902$	1.77789e36	0.204091
$903$	−5.75530e36	−0.651585
$904$	−5.54391e36	−0.619029
$905$	0	0
$906$	1.72810e37	1.87701
$907$	1.59523e37	1.70896	0.854482	−	0.519481i	$-0.173875\pi$
$907$	1.59523e37	1.70896	0.854482	+	0.519481i	$0.173875\pi$
$908$	1.77120e36	0.187152
$909$	−3.58234e36	−0.373352
$910$	0	0
$911$	−1.71775e36	−0.174172	−0.0870862	−	0.996201i	$-0.527756\pi$
$911$	−1.71775e36	−0.174172	−0.0870862	+	0.996201i	$0.527756\pi$
$912$	−2.10518e36	−0.210549
$913$	−6.86379e36	−0.677142
$914$	−2.29183e36	−0.223026
$915$	0	0
$916$	−6.21298e36	−0.588310
$917$	−2.02434e36	−0.189089
$918$	3.43187e36	0.316226
$919$	−7.70373e35	−0.0700256	−0.0350128	−	0.999387i	$-0.511147\pi$
$919$	−7.70373e35	−0.0700256	−0.0350128	+	0.999387i	$0.511147\pi$
$920$	0	0
$921$	−3.13079e37	−2.76955
$922$	1.55071e36	0.135330
$923$	−2.43703e36	−0.209817
$924$	−3.98354e36	−0.338353
$925$	0	0
$926$	1.13475e37	0.938132
$927$	−8.69819e36	−0.709467
$928$	−3.56463e36	−0.286856
$929$	1.66420e37	1.32132	0.660662	−	0.750684i	$-0.270276\pi$
$929$	1.66420e37	1.32132	0.660662	+	0.750684i	$0.270276\pi$
$930$	0	0
$931$	2.38121e36	0.184046
$932$	1.14887e36	0.0876138
$933$	−2.54021e37	−1.91139
$934$	−9.49954e36	−0.705288
$935$	0	0
$936$	−7.75779e35	−0.0560777
$937$	−9.66427e36	−0.689325	−0.344663	−	0.938727i	$-0.612007\pi$
$937$	−9.66427e36	−0.689325	−0.344663	+	0.938727i	$0.612007\pi$
$938$	6.60622e36	0.464962
$939$	−6.87214e36	−0.477279
$940$	0	0
$941$	−1.33808e37	−0.904923	−0.452461	−	0.891784i	$-0.649454\pi$
$941$	−1.33808e37	−0.904923	−0.452461	+	0.891784i	$0.649454\pi$
$942$	1.34879e37	0.900136
$943$	−7.91080e36	−0.520984
$944$	−3.72863e36	−0.242326
$945$	0	0
$946$	−3.26659e36	−0.206755
$947$	−2.63078e37	−1.64328	−0.821638	−	0.570010i	$-0.806939\pi$
$947$	−2.63078e37	−1.64328	−0.821638	+	0.570010i	$0.806939\pi$
$948$	1.47262e37	0.907791
$949$	−2.98981e36	−0.181893
$950$	0	0
$951$	1.21195e37	0.718170
$952$	−6.14058e36	−0.359126
$953$	9.10378e36	0.525485	0.262742	−	0.964866i	$-0.415373\pi$
$953$	9.10378e36	0.525485	0.262742	+	0.964866i	$0.415373\pi$
$954$	−5.35508e36	−0.305078
$955$	0	0
$956$	6.50575e36	0.361055
$957$	2.44389e37	1.33870
$958$	−9.19044e36	−0.496898
$959$	−9.70142e36	−0.517729
$960$	0	0
$961$	−1.01623e36	−0.0528386
$962$	−1.98307e36	−0.101777
$963$	−1.66151e37	−0.841731
$964$	1.74019e37	0.870230
$965$	0	0
$966$	1.77249e37	0.863713
$967$	1.34794e36	0.0648394	0.0324197	−	0.999474i	$-0.489679\pi$
$967$	1.34794e36	0.0648394	0.0324197	+	0.999474i	$0.489679\pi$
$968$	5.18457e36	0.246190
$969$	2.22483e37	1.04291
$970$	0	0
$971$	3.82504e36	0.174741	0.0873707	−	0.996176i	$-0.472154\pi$
$971$	3.82504e36	0.174741	0.0873707	+	0.996176i	$0.472154\pi$
$972$	−1.56316e37	−0.704978
$973$	2.76831e36	0.123255
$974$	1.52123e36	0.0668663
$975$	0	0
$976$	−6.67050e34	−0.00285782
$977$	−1.16914e37	−0.494522	−0.247261	−	0.968949i	$-0.579530\pi$
$977$	−1.16914e37	−0.494522	−0.247261	+	0.968949i	$0.579530\pi$
$978$	3.74277e37	1.56299
$979$	−1.84776e37	−0.761835
$980$	0	0
$981$	3.16418e37	1.27174
$982$	1.08752e37	0.431563
$983$	−1.38138e37	−0.541244	−0.270622	−	0.962686i	$-0.587229\pi$
$983$	−1.38138e37	−0.541244	−0.270622	+	0.962686i	$0.587229\pi$
$984$	7.16600e36	0.277228
$985$	0	0
$986$	3.76722e37	1.42089
$987$	1.93447e37	0.720441
$988$	−9.77426e35	−0.0359436
$989$	1.45348e37	0.527784
$990$	0	0
$991$	−3.79186e37	−1.34255	−0.671276	−	0.741207i	$-0.734254\pi$
$991$	−3.79186e37	−1.34255	−0.671276	+	0.741207i	$0.734254\pi$
$992$	4.92077e36	0.172043
$993$	8.22853e37	2.84090
$994$	−2.79338e37	−0.952356
$995$	0	0
$996$	−2.76653e37	−0.919799
$997$	−5.34619e37	−1.75531	−0.877657	−	0.479289i	$-0.840894\pi$
$997$	−5.34619e37	−1.75531	−0.877657	+	0.479289i	$0.840894\pi$
$998$	9.79424e36	0.317570
$999$	1.27036e37	0.406779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.a.c.1.2		2
5.2	odd	4		50.26.b.e.49.1		4
5.3	odd	4		50.26.b.e.49.4		4
5.4	even	2		2.26.a.b.1.1	✓	2
15.14	odd	2		18.26.a.e.1.1		2
20.19	odd	2		16.26.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.26.a.b.1.1	✓	2	5.4	even	2
16.26.a.c.1.2		2	20.19	odd	2
18.26.a.e.1.1		2	15.14	odd	2
50.26.a.c.1.2		2	1.1	even	1	trivial
50.26.b.e.49.1		4	5.2	odd	4
50.26.b.e.49.4		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)

\(f(q)\)	\(=\)	\(q-4096.00 q^{2} +1.37803e6 q^{3} +1.67772e7 q^{4} -5.64442e9 q^{6} -3.00388e10 q^{7} -6.87195e10 q^{8} +1.05168e12 q^{9} +5.73599e12 q^{11} +2.31195e13 q^{12} +1.07343e13 q^{13} +1.23039e14 q^{14} +2.81475e14 q^{16} -2.97473e15 q^{17} -4.30769e15 q^{18} -5.42738e15 q^{19} -4.13944e16 q^{21} -2.34946e16 q^{22} +1.04540e17 q^{23} -9.46976e16 q^{24} -4.39677e16 q^{26} +2.81659e17 q^{27} -5.03967e17 q^{28} +3.09182e18 q^{29} -4.26809e18 q^{31} -1.15292e18 q^{32} +7.90437e18 q^{33} +1.21845e19 q^{34} +1.76443e19 q^{36} +4.51028e19 q^{37} +2.22305e19 q^{38} +1.47922e19 q^{39} -7.56724e19 q^{41} +1.69551e20 q^{42} +1.39036e20 q^{43} +9.62339e19 q^{44} -4.28196e20 q^{46} -4.67328e20 q^{47} +3.87881e20 q^{48} -4.38741e20 q^{49} -4.09927e21 q^{51} +1.80092e20 q^{52} +1.24315e21 q^{53} -1.15368e21 q^{54} +2.06425e21 q^{56} -7.47909e21 q^{57} -1.26641e22 q^{58} -1.32468e22 q^{59} -2.36984e20 q^{61} +1.74821e22 q^{62} -3.15912e22 q^{63} +4.72237e21 q^{64} -3.23763e22 q^{66} +5.36922e22 q^{67} -4.99076e22 q^{68} +1.44059e23 q^{69} -2.27032e23 q^{71} -7.22710e22 q^{72} -2.78528e23 q^{73} -1.84741e23 q^{74} -9.10563e22 q^{76} -1.72302e23 q^{77} -6.05889e22 q^{78} +6.36958e23 q^{79} -5.02942e23 q^{81} +3.09954e23 q^{82} -1.19662e24 q^{83} -6.94482e23 q^{84} -5.69491e23 q^{86} +4.26063e24 q^{87} -3.94174e23 q^{88} -3.22134e24 q^{89} -3.22445e23 q^{91} +1.75389e24 q^{92} -5.88156e24 q^{93} +1.91418e24 q^{94} -1.58876e24 q^{96} -3.58465e24 q^{97} +1.79708e24 q^{98} +6.03243e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8192 q^{2} - 379848 q^{3} + 33554432 q^{4} + 1555857408 q^{6} + 376536944 q^{7} - 137438953472 q^{8} + 3294531432666 q^{9} + 8323034610264 q^{11} - 6372791943168 q^{12} + 106467053152292 q^{13} - 1542295322624 q^{14}+ \cdots + 11\!\cdots\!12 q^{99}+O(q^{100}) \) 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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