LMFDB - Embedded newform 245.10.a.e.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,10,Mod(1,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	245.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,-19,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$126.183779860$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 648x^{2} + 6926x - 8308 $ x^4 - x^3 - 648x^2 + 6926x - 8308
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 3^{2}\cdot 5 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.37673$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-25.9629 q^{2} +209.523 q^{3} +162.070 q^{4} +625.000 q^{5} -5439.82 q^{6} +9085.18 q^{8} +24216.9 q^{9} -16226.8 q^{10} +43490.0 q^{11} +33957.4 q^{12} -67126.8 q^{13} +130952. q^{15} -318857. q^{16} +261183. q^{17} -628740. q^{18} -744649. q^{19} +101294. q^{20} -1.12912e6 q^{22} -2.12319e6 q^{23} +1.90355e6 q^{24} +390625. q^{25} +1.74280e6 q^{26} +949956. q^{27} +2.19162e6 q^{29} -3.39989e6 q^{30} +1.20634e6 q^{31} +3.62683e6 q^{32} +9.11216e6 q^{33} -6.78107e6 q^{34} +3.92484e6 q^{36} -7.82577e6 q^{37} +1.93332e7 q^{38} -1.40646e7 q^{39} +5.67824e6 q^{40} -2.84010e7 q^{41} -836250. q^{43} +7.04843e6 q^{44} +1.51356e7 q^{45} +5.51241e7 q^{46} -4.69259e7 q^{47} -6.68079e7 q^{48} -1.01417e7 q^{50} +5.47240e7 q^{51} -1.08793e7 q^{52} -1.18469e7 q^{53} -2.46636e7 q^{54} +2.71813e7 q^{55} -1.56021e8 q^{57} -5.69006e7 q^{58} -1.31445e8 q^{59} +2.12234e7 q^{60} +1.79312e8 q^{61} -3.13200e7 q^{62} +6.90919e7 q^{64} -4.19543e7 q^{65} -2.36578e8 q^{66} -2.11309e8 q^{67} +4.23300e7 q^{68} -4.44857e8 q^{69} -3.50475e8 q^{71} +2.20015e8 q^{72} +2.82794e8 q^{73} +2.03179e8 q^{74} +8.18449e7 q^{75} -1.20685e8 q^{76} +3.65158e8 q^{78} -3.47506e6 q^{79} -1.99286e8 q^{80} -2.77624e8 q^{81} +7.37370e8 q^{82} -1.95999e8 q^{83} +1.63240e8 q^{85} +2.17115e7 q^{86} +4.59194e8 q^{87} +3.95115e8 q^{88} +3.37238e8 q^{89} -3.92962e8 q^{90} -3.44106e8 q^{92} +2.52755e8 q^{93} +1.21833e9 q^{94} -4.65406e8 q^{95} +7.59905e8 q^{96} +1.63718e8 q^{97} +1.05319e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 19 q^{2} + 18 q^{3} + 1729 q^{4} + 2500 q^{5} + 144 q^{6} - 30495 q^{8} + 5382 q^{9} - 11875 q^{10} + 82438 q^{11} - 41328 q^{12} + 72962 q^{13} + 11250 q^{15} + 64257 q^{16} + 357542 q^{17} - 965367 q^{18}+ \cdots + 1222369524 q^{99}+O(q^{100}) $ 4 * q - 19 * q^2 + 18 * q^3 + 1729 * q^4 + 2500 * q^5 + 144 * q^6 - 30495 * q^8 + 5382 * q^9 - 11875 * q^10 + 82438 * q^11 - 41328 * q^12 + 72962 * q^13 + 11250 * q^15 + 64257 * q^16 + 357542 * q^17 - 965367 * q^18 - 300732 * q^19 + 1080625 * q^20 - 5595068 * q^22 - 2340836 * q^23 + 7636320 * q^24 + 1562500 * q^25 - 1305666 * q^26 + 4240350 * q^27 - 1372022 * q^29 + 90000 * q^30 + 4590888 * q^31 - 10529439 * q^32 - 2000034 * q^33 + 7199478 * q^34 - 9144243 * q^36 - 38868456 * q^37 + 15477280 * q^38 - 46666242 * q^39 - 19059375 * q^40 - 57287084 * q^41 - 43403452 * q^43 + 87639348 * q^44 + 3363750 * q^45 + 28892416 * q^46 - 91822222 * q^47 - 156168864 * q^48 - 7421875 * q^50 + 86342634 * q^51 - 1953386 * q^52 - 61086884 * q^53 - 187589520 * q^54 + 51523750 * q^55 - 79928892 * q^57 + 29615390 * q^58 - 72569680 * q^59 - 25830000 * q^60 + 225681036 * q^61 - 190286472 * q^62 + 141443393 * q^64 + 45601250 * q^65 + 119673648 * q^66 - 4429720 * q^67 - 15339698 * q^68 - 348300612 * q^69 - 470468984 * q^71 + 298610685 * q^72 + 168326464 * q^73 + 927809502 * q^74 + 7031250 * q^75 + 892265344 * q^76 + 281290896 * q^78 - 598805646 * q^79 + 40160625 * q^80 - 847155996 * q^81 + 1821993318 * q^82 + 1159074304 * q^83 + 223463750 * q^85 + 706791156 * q^86 + 421480998 * q^87 - 1992103900 * q^88 + 1380153012 * q^89 - 603354375 * q^90 + 710319264 * q^92 - 1601969400 * q^93 - 2466744152 * q^94 - 187957500 * q^95 + 799321824 * q^96 - 754874082 * q^97 + 1222369524 * 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 $

$2$	−25.9629	−1.14741	−0.573704	−	0.819063i	$-0.694494\pi$
$2$	−25.9629	−1.14741	−0.573704	+	0.819063i	$0.694494\pi$
$3$	209.523	1.49343	0.746717	−	0.665142i	$-0.231629\pi$
$3$	209.523	1.49343	0.746717	+	0.665142i	$0.231629\pi$
$4$	162.070	0.316543
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−5439.82	−1.71358
$7$	0	0
$7$	0	0
$8$	9085.18	0.784203
$9$	24216.9	1.23035
$10$	−16226.8	−0.513136
$11$	43490.0	0.895617	0.447809	−	0.894129i	$-0.352205\pi$
$11$	43490.0	0.895617	0.447809	+	0.894129i	$0.352205\pi$
$12$	33957.4	0.472736
$13$	−67126.8	−0.651855	−0.325928	−	0.945395i	$-0.605677\pi$
$13$	−67126.8	−0.651855	−0.325928	+	0.945395i	$0.605677\pi$
$14$	0	0
$15$	130952.	0.667884
$16$	−318857.	−1.21634
$17$	261183.	0.758448	0.379224	−	0.925305i	$-0.376191\pi$
$17$	261183.	0.758448	0.379224	+	0.925305i	$0.376191\pi$
$18$	−628740.	−1.41171
$19$	−744649.	−1.31087	−0.655437	−	0.755250i	$-0.727515\pi$
$19$	−744649.	−1.31087	−0.655437	+	0.755250i	$0.727515\pi$
$20$	101294.	0.141562
$21$	0	0
$22$	−1.12912e6	−1.02764
$23$	−2.12319e6	−1.58203	−0.791013	−	0.611799i	$-0.790446\pi$
$23$	−2.12319e6	−1.58203	−0.791013	+	0.611799i	$0.790446\pi$
$24$	1.90355e6	1.17116
$25$	390625.	0.200000
$26$	1.74280e6	0.747943
$27$	949956.	0.344006
$28$	0	0
$29$	2.19162e6	0.575405	0.287702	−	0.957720i	$-0.407109\pi$
$29$	2.19162e6	0.575405	0.287702	+	0.957720i	$0.407109\pi$
$30$	−3.39989e6	−0.766335
$31$	1.20634e6	0.234607	0.117303	−	0.993096i	$-0.462575\pi$
$31$	1.20634e6	0.234607	0.117303	+	0.993096i	$0.462575\pi$
$32$	3.62683e6	0.611438
$33$	9.11216e6	1.33755
$34$	−6.78107e6	−0.870248
$35$	0	0
$36$	3.92484e6	0.389458
$37$	−7.82577e6	−0.686467	−0.343233	−	0.939250i	$-0.611522\pi$
$37$	−7.82577e6	−0.686467	−0.343233	+	0.939250i	$0.611522\pi$
$38$	1.93332e7	1.50411
$39$	−1.40646e7	−0.973503
$40$	5.67824e6	0.350706
$41$	−2.84010e7	−1.56966	−0.784830	−	0.619711i	$-0.787250\pi$
$41$	−2.84010e7	−1.56966	−0.784830	+	0.619711i	$0.787250\pi$
$42$	0	0
$43$	−836250.	−0.0373017	−0.0186508	−	0.999826i	$-0.505937\pi$
$43$	−836250.	−0.0373017	−0.0186508	+	0.999826i	$0.505937\pi$
$44$	7.04843e6	0.283501
$45$	1.51356e7	0.550227
$46$	5.51241e7	1.81523
$47$	−4.69259e7	−1.40273	−0.701363	−	0.712804i	$-0.747425\pi$
$47$	−4.69259e7	−1.40273	−0.701363	+	0.712804i	$0.747425\pi$
$48$	−6.68079e7	−1.81653
$49$	0	0
$50$	−1.01417e7	−0.229481
$51$	5.47240e7	1.13269
$52$	−1.08793e7	−0.206340
$53$	−1.18469e7	−0.206235	−0.103118	−	0.994669i	$-0.532882\pi$
$53$	−1.18469e7	−0.206235	−0.103118	+	0.994669i	$0.532882\pi$
$54$	−2.46636e7	−0.394715
$55$	2.71813e7	0.400532
$56$	0	0
$57$	−1.56021e8	−1.95770
$58$	−5.69006e7	−0.660224
$59$	−1.31445e8	−1.41224	−0.706120	−	0.708092i	$-0.749556\pi$
$59$	−1.31445e8	−1.41224	−0.706120	+	0.708092i	$0.749556\pi$
$60$	2.12234e7	0.211414
$61$	1.79312e8	1.65815	0.829077	−	0.559135i	$-0.188867\pi$
$61$	1.79312e8	1.65815	0.829077	+	0.559135i	$0.188867\pi$
$62$	−3.13200e7	−0.269190
$63$	0	0
$64$	6.90919e7	0.514775
$65$	−4.19543e7	−0.291518
$66$	−2.36578e8	−1.53471
$67$	−2.11309e8	−1.28109	−0.640547	−	0.767919i	$-0.721292\pi$
$67$	−2.11309e8	−1.28109	−0.640547	+	0.767919i	$0.721292\pi$
$68$	4.23300e7	0.240081
$69$	−4.44857e8	−2.36265
$70$	0	0
$71$	−3.50475e8	−1.63680	−0.818398	−	0.574651i	$-0.805138\pi$
$71$	−3.50475e8	−1.63680	−0.818398	+	0.574651i	$0.805138\pi$
$72$	2.20015e8	0.964841
$73$	2.82794e8	1.16551	0.582757	−	0.812646i	$-0.301974\pi$
$73$	2.82794e8	1.16551	0.582757	+	0.812646i	$0.301974\pi$
$74$	2.03179e8	0.787657
$75$	8.18449e7	0.298687
$76$	−1.20685e8	−0.414948
$77$	0	0
$78$	3.65158e8	1.11700
$79$	−3.47506e6	−0.0100378	−0.00501892	−	0.999987i	$-0.501598\pi$
$79$	−3.47506e6	−0.0100378	−0.00501892	+	0.999987i	$0.501598\pi$
$80$	−1.99286e8	−0.543965
$81$	−2.77624e8	−0.716595
$82$	7.37370e8	1.80104
$83$	−1.95999e8	−0.453318	−0.226659	−	0.973974i	$-0.572780\pi$
$83$	−1.95999e8	−0.453318	−0.226659	+	0.973974i	$0.572780\pi$
$84$	0	0
$85$	1.63240e8	0.339188
$86$	2.17115e7	0.0428002
$87$	4.59194e8	0.859330
$88$	3.95115e8	0.702346
$89$	3.37238e8	0.569747	0.284873	−	0.958565i	$-0.408048\pi$
$89$	3.37238e8	0.569747	0.284873	+	0.958565i	$0.408048\pi$
$90$	−3.92962e8	−0.631335
$91$	0	0
$92$	−3.44106e8	−0.500780
$93$	2.52755e8	0.350370
$94$	1.21833e9	1.60950
$95$	−4.65406e8	−0.586240
$96$	7.59905e8	0.913143
$97$	1.63718e8	0.187769	0.0938847	−	0.995583i	$-0.470072\pi$
$97$	1.63718e8	0.187769	0.0938847	+	0.995583i	$0.470072\pi$
$98$	0	0
$99$	1.05319e9	1.10192
$100$	6.33086e7	0.0633086
$101$	1.76637e9	1.68902	0.844510	−	0.535540i	$-0.179892\pi$
$101$	1.76637e9	1.68902	0.844510	+	0.535540i	$0.179892\pi$
$102$	−1.42079e9	−1.29966
$103$	1.92191e8	0.168254	0.0841269	−	0.996455i	$-0.473190\pi$
$103$	1.92191e8	0.168254	0.0841269	+	0.996455i	$0.473190\pi$
$104$	−6.09859e8	−0.511187
$105$	0	0
$106$	3.07579e8	0.236636
$107$	1.72802e9	1.27445	0.637225	−	0.770678i	$-0.280082\pi$
$107$	1.72802e9	1.27445	0.637225	+	0.770678i	$0.280082\pi$
$108$	1.53959e8	0.108893
$109$	5.28362e8	0.358519	0.179260	−	0.983802i	$-0.442630\pi$
$109$	5.28362e8	0.358519	0.179260	+	0.983802i	$0.442630\pi$
$110$	−7.05703e8	−0.459573
$111$	−1.63968e9	−1.02519
$112$	0	0
$113$	2.74144e9	1.58171	0.790853	−	0.612006i	$-0.209637\pi$
$113$	2.74144e9	1.58171	0.790853	+	0.612006i	$0.209637\pi$
$114$	4.05076e9	2.24628
$115$	−1.32699e9	−0.707504
$116$	3.55196e8	0.182141
$117$	−1.62560e9	−0.802007
$118$	3.41268e9	1.62041
$119$	0	0
$120$	1.18972e9	0.523757
$121$	−4.66567e8	−0.197870
$122$	−4.65545e9	−1.90258
$123$	−5.95065e9	−2.34418
$124$	1.95511e8	0.0742632
$125$	2.44141e8	0.0894427
$126$	0	0
$127$	2.75922e8	0.0941175	0.0470587	−	0.998892i	$-0.485015\pi$
$127$	2.75922e8	0.0941175	0.0470587	+	0.998892i	$0.485015\pi$
$128$	−3.65076e9	−1.20209
$129$	−1.75214e8	−0.0557076
$130$	1.08925e9	0.334490
$131$	−4.12137e9	−1.22270	−0.611352	−	0.791359i	$-0.709374\pi$
$131$	−4.12137e9	−1.22270	−0.611352	+	0.791359i	$0.709374\pi$
$132$	1.47681e9	0.423391
$133$	0	0
$134$	5.48618e9	1.46994
$135$	5.93723e8	0.153844
$136$	2.37290e9	0.594777
$137$	−5.56659e9	−1.35004	−0.675020	−	0.737799i	$-0.735865\pi$
$137$	−5.56659e9	−1.35004	−0.675020	+	0.737799i	$0.735865\pi$
$138$	1.15498e10	2.71093
$139$	−1.51553e8	−0.0344349	−0.0172175	−	0.999852i	$-0.505481\pi$
$139$	−1.51553e8	−0.0344349	−0.0172175	+	0.999852i	$0.505481\pi$
$140$	0	0
$141$	−9.83207e9	−2.09488
$142$	9.09934e9	1.87807
$143$	−2.91935e9	−0.583813
$144$	−7.72173e9	−1.49652
$145$	1.36976e9	0.257329
$146$	−7.34215e9	−1.33732
$147$	0	0
$148$	−1.26832e9	−0.217296
$149$	−1.49119e9	−0.247853	−0.123927	−	0.992291i	$-0.539549\pi$
$149$	−1.49119e9	−0.247853	−0.123927	+	0.992291i	$0.539549\pi$
$150$	−2.12493e9	−0.342715
$151$	−1.06694e10	−1.67010	−0.835051	−	0.550173i	$-0.814562\pi$
$151$	−1.06694e10	−1.67010	−0.835051	+	0.550173i	$0.814562\pi$
$152$	−6.76527e9	−1.02799
$153$	6.32505e9	0.933153
$154$	0	0
$155$	7.53960e8	0.104919
$156$	−2.27945e9	−0.308156
$157$	9.03073e9	1.18625	0.593123	−	0.805112i	$-0.297895\pi$
$157$	9.03073e9	1.18625	0.593123	+	0.805112i	$0.297895\pi$
$158$	9.02225e7	0.0115175
$159$	−2.48220e9	−0.307999
$160$	2.26677e9	0.273443
$161$	0	0
$162$	7.20790e9	0.822226
$163$	−5.34934e9	−0.593549	−0.296774	−	0.954948i	$-0.595911\pi$
$163$	−5.34934e9	−0.593549	−0.296774	+	0.954948i	$0.595911\pi$
$164$	−4.60295e9	−0.496865
$165$	5.69510e9	0.598168
$166$	5.08870e9	0.520141
$167$	−9.41973e9	−0.937162	−0.468581	−	0.883421i	$-0.655235\pi$
$167$	−9.41973e9	−0.937162	−0.468581	+	0.883421i	$0.655235\pi$
$168$	0	0
$169$	−6.09849e9	−0.575085
$170$	−4.23817e9	−0.389187
$171$	−1.80331e10	−1.61283
$172$	−1.35531e8	−0.0118076
$173$	1.38243e10	1.17337	0.586687	−	0.809814i	$-0.300432\pi$
$173$	1.38243e10	1.17337	0.586687	+	0.809814i	$0.300432\pi$
$174$	−1.19220e10	−0.986001
$175$	0	0
$176$	−1.38671e10	−1.08938
$177$	−2.75407e10	−2.10909
$178$	−8.75567e9	−0.653731
$179$	2.20063e10	1.60217	0.801084	−	0.598552i	$-0.204257\pi$
$179$	2.20063e10	1.60217	0.801084	+	0.598552i	$0.204257\pi$
$180$	2.45302e9	0.174171
$181$	1.83559e8	0.0127122	0.00635611	−	0.999980i	$-0.497977\pi$
$181$	1.83559e8	0.0127122	0.00635611	+	0.999980i	$0.497977\pi$
$182$	0	0
$183$	3.75700e10	2.47634
$184$	−1.92896e10	−1.24063
$185$	−4.89111e9	−0.306997
$186$	−6.56225e9	−0.402017
$187$	1.13589e10	0.679279
$188$	−7.60529e9	−0.444023
$189$	0	0
$190$	1.20833e10	0.672656
$191$	−2.04034e10	−1.10931	−0.554654	−	0.832081i	$-0.687150\pi$
$191$	−2.04034e10	−1.10931	−0.554654	+	0.832081i	$0.687150\pi$
$192$	1.44764e10	0.768783
$193$	9.14597e9	0.474484	0.237242	−	0.971451i	$-0.423756\pi$
$193$	9.14597e9	0.474484	0.237242	+	0.971451i	$0.423756\pi$
$194$	−4.25060e9	−0.215448
$195$	−8.79039e9	−0.435364
$196$	0	0
$197$	−2.08681e10	−0.987152	−0.493576	−	0.869703i	$-0.664311\pi$
$197$	−2.08681e10	−0.987152	−0.493576	+	0.869703i	$0.664311\pi$
$198$	−2.73439e10	−1.26435
$199$	−4.12889e10	−1.86635	−0.933177	−	0.359416i	$-0.882976\pi$
$199$	−4.12889e10	−1.86635	−0.933177	+	0.359416i	$0.882976\pi$
$200$	3.54890e9	0.156841
$201$	−4.42741e10	−1.91323
$202$	−4.58599e10	−1.93799
$203$	0	0
$204$	8.86912e9	0.358546
$205$	−1.77506e10	−0.701973
$206$	−4.98982e9	−0.193056
$207$	−5.14171e10	−1.94644
$208$	2.14039e10	0.792880
$209$	−3.23848e10	−1.17404
$210$	0	0
$211$	−3.01901e10	−1.04856	−0.524280	−	0.851546i	$-0.675666\pi$
$211$	−3.01901e10	−1.04856	−0.524280	+	0.851546i	$0.675666\pi$
$212$	−1.92003e9	−0.0652823
$213$	−7.34326e10	−2.44445
$214$	−4.48644e10	−1.46231
$215$	−5.22657e8	−0.0166818
$216$	8.63052e9	0.269771
$217$	0	0
$218$	−1.37178e10	−0.411367
$219$	5.92519e10	1.74062
$220$	4.40527e9	0.126786
$221$	−1.75324e10	−0.494398
$222$	4.25708e10	1.17631
$223$	−8.91955e9	−0.241530	−0.120765	−	0.992681i	$-0.538535\pi$
$223$	−8.91955e9	−0.241530	−0.120765	+	0.992681i	$0.538535\pi$
$224$	0	0
$225$	9.45973e9	0.246069
$226$	−7.11756e10	−1.81486
$227$	−1.85212e10	−0.462971	−0.231486	−	0.972838i	$-0.574359\pi$
$227$	−1.85212e10	−0.462971	−0.231486	+	0.972838i	$0.574359\pi$
$228$	−2.52864e10	−0.619697
$229$	6.14911e10	1.47758	0.738792	−	0.673933i	$-0.235396\pi$
$229$	6.14911e10	1.47758	0.738792	+	0.673933i	$0.235396\pi$
$230$	3.44526e10	0.811795
$231$	0	0
$232$	1.99112e10	0.451234
$233$	7.22531e10	1.60603	0.803017	−	0.595956i	$-0.203227\pi$
$233$	7.22531e10	1.60603	0.803017	+	0.595956i	$0.203227\pi$
$234$	4.22053e10	0.920229
$235$	−2.93287e10	−0.627318
$236$	−2.13032e10	−0.447035
$237$	−7.28105e8	−0.0149909
$238$	0	0
$239$	−5.51824e10	−1.09398	−0.546991	−	0.837139i	$-0.684227\pi$
$239$	−5.51824e10	−1.09398	−0.546991	+	0.837139i	$0.684227\pi$
$240$	−4.17550e10	−0.812377
$241$	−6.33057e10	−1.20883	−0.604416	−	0.796669i	$-0.706594\pi$
$241$	−6.33057e10	−1.20883	−0.604416	+	0.796669i	$0.706594\pi$
$242$	1.21134e10	0.227038
$243$	−7.68665e10	−1.41419
$244$	2.90611e10	0.524877
$245$	0	0
$246$	1.54496e11	2.68973
$247$	4.99860e10	0.854499
$248$	1.09598e10	0.183980
$249$	−4.10664e10	−0.677001
$250$	−6.33859e9	−0.102627
$251$	6.18704e10	0.983900	0.491950	−	0.870623i	$-0.336284\pi$
$251$	6.18704e10	0.983900	0.491950	+	0.870623i	$0.336284\pi$
$252$	0	0
$253$	−9.23376e10	−1.41689
$254$	−7.16373e9	−0.107991
$255$	3.42025e10	0.506555
$256$	5.94092e10	0.864517
$257$	−1.05744e10	−0.151202	−0.0756010	−	0.997138i	$-0.524088\pi$
$257$	−1.05744e10	−0.151202	−0.0756010	+	0.997138i	$0.524088\pi$
$258$	4.54905e9	0.0639193
$259$	0	0
$260$	−6.79953e9	−0.0922782
$261$	5.30742e10	0.707947
$262$	1.07003e11	1.40294
$263$	−9.17838e10	−1.18295	−0.591473	−	0.806325i	$-0.701453\pi$
$263$	−9.17838e10	−1.18295	−0.591473	+	0.806325i	$0.701453\pi$
$264$	8.27856e10	1.04891
$265$	−7.40430e9	−0.0922312
$266$	0	0
$267$	7.06592e10	0.850879
$268$	−3.42469e10	−0.405522
$269$	1.18137e11	1.37562	0.687811	−	0.725890i	$-0.258572\pi$
$269$	1.18137e11	1.37562	0.687811	+	0.725890i	$0.258572\pi$
$270$	−1.54147e10	−0.176522
$271$	7.96797e10	0.897399	0.448700	−	0.893683i	$-0.351887\pi$
$271$	7.96797e10	0.897399	0.448700	+	0.893683i	$0.351887\pi$
$272$	−8.32802e10	−0.922533
$273$	0	0
$274$	1.44525e11	1.54905
$275$	1.69883e10	0.179123
$276$	−7.20981e10	−0.747882
$277$	3.15470e9	0.0321958	0.0160979	−	0.999870i	$-0.494876\pi$
$277$	3.15470e9	0.0321958	0.0160979	+	0.999870i	$0.494876\pi$
$278$	3.93476e9	0.0395109
$279$	2.92137e10	0.288648
$280$	0	0
$281$	−1.15513e11	−1.10523	−0.552614	−	0.833438i	$-0.686369\pi$
$281$	−1.15513e11	−1.10523	−0.552614	+	0.833438i	$0.686369\pi$
$282$	2.55269e11	2.40368
$283$	6.39337e10	0.592504	0.296252	−	0.955110i	$-0.404263\pi$
$283$	6.39337e10	0.592504	0.296252	+	0.955110i	$0.404263\pi$
$284$	−5.68016e10	−0.518117
$285$	−9.75132e10	−0.875511
$286$	7.57946e10	0.669871
$287$	0	0
$288$	8.78306e10	0.752280
$289$	−5.03711e10	−0.424757
$290$	−3.55629e10	−0.295261
$291$	3.43028e10	0.280421
$292$	4.58325e10	0.368936
$293$	−8.43668e10	−0.668756	−0.334378	−	0.942439i	$-0.608526\pi$
$293$	−8.43668e10	−0.668756	−0.334378	+	0.942439i	$0.608526\pi$
$294$	0	0
$295$	−8.21528e10	−0.631573
$296$	−7.10986e10	−0.538329
$297$	4.13136e10	0.308098
$298$	3.87156e10	0.284389
$299$	1.42523e11	1.03125
$300$	1.32646e10	0.0945473
$301$	0	0
$302$	2.77008e11	1.91629
$303$	3.70094e11	2.52244
$304$	2.37437e11	1.59447
$305$	1.12070e11	0.741549
$306$	−1.64216e11	−1.07071
$307$	−9.93740e10	−0.638484	−0.319242	−	0.947673i	$-0.603428\pi$
$307$	−9.93740e10	−0.638484	−0.319242	+	0.947673i	$0.603428\pi$
$308$	0	0
$309$	4.02684e10	0.251276
$310$	−1.95750e10	−0.120385
$311$	−2.24958e11	−1.36358	−0.681788	−	0.731550i	$-0.738797\pi$
$311$	−2.24958e11	−1.36358	−0.681788	+	0.731550i	$0.738797\pi$
$312$	−1.27780e11	−0.763424
$313$	−1.79613e11	−1.05776	−0.528881	−	0.848696i	$-0.677388\pi$
$313$	−1.79613e11	−1.05776	−0.528881	+	0.848696i	$0.677388\pi$
$314$	−2.34464e11	−1.36111
$315$	0	0
$316$	−5.63204e8	−0.00317741
$317$	1.89181e11	1.05223	0.526114	−	0.850414i	$-0.323649\pi$
$317$	1.89181e11	1.05223	0.526114	+	0.850414i	$0.323649\pi$
$318$	6.44449e10	0.353400
$319$	9.53134e10	0.515343
$320$	4.31825e10	0.230214
$321$	3.62061e11	1.90331
$322$	0	0
$323$	−1.94490e11	−0.994228
$324$	−4.49945e10	−0.226833
$325$	−2.62214e10	−0.130371
$326$	1.38884e11	0.681042
$327$	1.10704e11	0.535425
$328$	−2.58028e11	−1.23093
$329$	0	0
$330$	−1.47861e11	−0.686343
$331$	−2.82309e11	−1.29270	−0.646351	−	0.763040i	$-0.723706\pi$
$331$	−2.82309e11	−1.29270	−0.646351	+	0.763040i	$0.723706\pi$
$332$	−3.17656e10	−0.143495
$333$	−1.89516e11	−0.844591
$334$	2.44563e11	1.07531
$335$	−1.32068e11	−0.572923
$336$	0	0
$337$	−2.97708e11	−1.25735	−0.628675	−	0.777668i	$-0.716403\pi$
$337$	−2.97708e11	−1.25735	−0.628675	+	0.777668i	$0.716403\pi$
$338$	1.58334e11	0.659857
$339$	5.74395e11	2.36217
$340$	2.64563e10	0.107368
$341$	5.24636e10	0.210118
$342$	4.68191e11	1.85057
$343$	0	0
$344$	−7.59749e9	−0.0292521
$345$	−2.78036e11	−1.05661
$346$	−3.58919e11	−1.34634
$347$	−3.44149e11	−1.27428	−0.637139	−	0.770749i	$-0.719882\pi$
$347$	−3.44149e11	−1.27428	−0.637139	+	0.770749i	$0.719882\pi$
$348$	7.44217e10	0.272015
$349$	3.88686e11	1.40244	0.701220	−	0.712945i	$-0.252639\pi$
$349$	3.88686e11	1.40244	0.701220	+	0.712945i	$0.252639\pi$
$350$	0	0
$351$	−6.37675e10	−0.224242
$352$	1.57731e11	0.547614
$353$	−1.33667e11	−0.458181	−0.229091	−	0.973405i	$-0.573575\pi$
$353$	−1.33667e11	−0.458181	−0.229091	+	0.973405i	$0.573575\pi$
$354$	7.15034e11	2.41998
$355$	−2.19047e11	−0.731998
$356$	5.46562e10	0.180349
$357$	0	0
$358$	−5.71346e11	−1.83834
$359$	1.55733e11	0.494831	0.247415	−	0.968909i	$-0.420419\pi$
$359$	1.55733e11	0.494831	0.247415	+	0.968909i	$0.420419\pi$
$360$	1.37509e11	0.431490
$361$	2.31815e11	0.718388
$362$	−4.76571e9	−0.0145861
$363$	−9.77566e10	−0.295506
$364$	0	0
$365$	1.76746e11	0.521234
$366$	−9.75424e11	−2.84137
$367$	−4.25431e11	−1.22414	−0.612071	−	0.790803i	$-0.709663\pi$
$367$	−4.25431e11	−1.22414	−0.612071	+	0.790803i	$0.709663\pi$
$368$	6.76995e11	1.92429
$369$	−6.87783e11	−1.93122
$370$	1.26987e11	0.352251
$371$	0	0
$372$	4.09641e10	0.110907
$373$	−4.92563e11	−1.31757	−0.658783	−	0.752333i	$-0.728929\pi$
$373$	−4.92563e11	−1.31757	−0.658783	+	0.752333i	$0.728929\pi$
$374$	−2.94909e11	−0.779409
$375$	5.11531e10	0.133577
$376$	−4.26331e11	−1.10002
$377$	−1.47116e11	−0.375081
$378$	0	0
$379$	3.59952e11	0.896124	0.448062	−	0.894003i	$-0.352114\pi$
$379$	3.59952e11	0.896124	0.448062	+	0.894003i	$0.352114\pi$
$380$	−7.54284e10	−0.185570
$381$	5.78121e10	0.140558
$382$	5.29731e11	1.27283
$383$	−1.79352e11	−0.425905	−0.212953	−	0.977063i	$-0.568308\pi$
$383$	−1.79352e11	−0.425905	−0.212953	+	0.977063i	$0.568308\pi$
$384$	−7.64919e11	−1.79525
$385$	0	0
$386$	−2.37456e11	−0.544427
$387$	−2.02514e10	−0.0458940
$388$	2.65339e10	0.0594371
$389$	4.87473e11	1.07939	0.539694	−	0.841861i	$-0.318540\pi$
$389$	4.87473e11	1.07939	0.539694	+	0.841861i	$0.318540\pi$
$390$	2.28224e11	0.499539
$391$	−5.54542e11	−1.19988
$392$	0	0
$393$	−8.63522e11	−1.82603
$394$	5.41795e11	1.13267
$395$	−2.17191e9	−0.00448906
$396$	1.70691e11	0.348805
$397$	3.74858e11	0.757372	0.378686	−	0.925525i	$-0.376376\pi$
$397$	3.74858e11	0.757372	0.378686	+	0.925525i	$0.376376\pi$
$398$	1.07198e12	2.14147
$399$	0	0
$400$	−1.24554e11	−0.243269
$401$	−1.53956e11	−0.297336	−0.148668	−	0.988887i	$-0.547499\pi$
$401$	−1.53956e11	−0.297336	−0.148668	+	0.988887i	$0.547499\pi$
$402$	1.14948e12	2.19525
$403$	−8.09776e10	−0.152930
$404$	2.86275e11	0.534648
$405$	−1.73515e11	−0.320471
$406$	0	0
$407$	−3.40343e11	−0.614811
$408$	4.97177e11	0.888260
$409$	9.95183e11	1.75852	0.879261	−	0.476340i	$-0.158037\pi$
$409$	9.95183e11	1.75852	0.879261	+	0.476340i	$0.158037\pi$
$410$	4.60856e11	0.805449
$411$	−1.16633e12	−2.01620
$412$	3.11484e10	0.0532596
$413$	0	0
$414$	1.33494e12	2.23336
$415$	−1.22500e11	−0.202730
$416$	−2.43458e11	−0.398569
$417$	−3.17539e10	−0.0514263
$418$	8.40802e11	1.34710
$419$	−1.86666e11	−0.295870	−0.147935	−	0.988997i	$-0.547263\pi$
$419$	−1.86666e11	−0.295870	−0.147935	+	0.988997i	$0.547263\pi$
$420$	0	0
$421$	1.54125e11	0.239114	0.119557	−	0.992827i	$-0.461853\pi$
$421$	1.54125e11	0.239114	0.119557	+	0.992827i	$0.461853\pi$
$422$	7.83822e11	1.20313
$423$	−1.13640e12	−1.72584
$424$	−1.07631e11	−0.161730
$425$	1.02025e11	0.151690
$426$	1.90652e12	2.80478
$427$	0	0
$428$	2.80061e11	0.403418
$429$	−6.11670e11	−0.871886
$430$	1.35697e10	0.0191408
$431$	8.64666e11	1.20698	0.603491	−	0.797370i	$-0.293776\pi$
$431$	8.64666e11	1.20698	0.603491	+	0.797370i	$0.293776\pi$
$432$	−3.02900e11	−0.418430
$433$	9.90737e11	1.35445	0.677225	−	0.735776i	$-0.263182\pi$
$433$	9.90737e11	1.35445	0.677225	+	0.735776i	$0.263182\pi$
$434$	0	0
$435$	2.86996e11	0.384304
$436$	8.56317e10	0.113487
$437$	1.58103e12	2.07384
$438$	−1.53835e12	−1.99720
$439$	−5.91950e11	−0.760668	−0.380334	−	0.924849i	$-0.624191\pi$
$439$	−5.91950e11	−0.760668	−0.380334	+	0.924849i	$0.624191\pi$
$440$	2.46947e11	0.314099
$441$	0	0
$442$	4.55192e11	0.567276
$443$	−9.35260e11	−1.15376	−0.576880	−	0.816829i	$-0.695730\pi$
$443$	−9.35260e11	−1.15376	−0.576880	+	0.816829i	$0.695730\pi$
$444$	−2.65743e11	−0.324518
$445$	2.10774e11	0.254798
$446$	2.31577e11	0.277133
$447$	−3.12439e11	−0.370153
$448$	0	0
$449$	−9.09288e11	−1.05583	−0.527913	−	0.849298i	$-0.677025\pi$
$449$	−9.09288e11	−1.05583	−0.527913	+	0.849298i	$0.677025\pi$
$450$	−2.45602e11	−0.282342
$451$	−1.23516e12	−1.40581
$452$	4.44305e11	0.500678
$453$	−2.23548e12	−2.49419
$454$	4.80865e11	0.531216
$455$	0	0
$456$	−1.41748e12	−1.53524
$457$	2.30997e11	0.247733	0.123866	−	0.992299i	$-0.460471\pi$
$457$	2.30997e11	0.247733	0.123866	+	0.992299i	$0.460471\pi$
$458$	−1.59648e12	−1.69539
$459$	2.48113e11	0.260911
$460$	−2.15066e11	−0.223956
$461$	1.22394e12	1.26213	0.631066	−	0.775729i	$-0.282618\pi$
$461$	1.22394e12	1.26213	0.631066	+	0.775729i	$0.282618\pi$
$462$	0	0
$463$	7.72436e10	0.0781175	0.0390587	−	0.999237i	$-0.487564\pi$
$463$	7.72436e10	0.0781175	0.0390587	+	0.999237i	$0.487564\pi$
$464$	−6.98813e11	−0.699890
$465$	1.57972e11	0.156690
$466$	−1.87590e12	−1.84278
$467$	−3.92470e11	−0.381839	−0.190920	−	0.981606i	$-0.561147\pi$
$467$	−3.92470e11	−0.381839	−0.190920	+	0.981606i	$0.561147\pi$
$468$	−2.63462e11	−0.253870
$469$	0	0
$470$	7.61457e11	0.719789
$471$	1.89215e12	1.77158
$472$	−1.19420e12	−1.10748
$473$	−3.63685e10	−0.0334080
$474$	1.89037e10	0.0172006
$475$	−2.90879e11	−0.262175
$476$	0	0
$477$	−2.86895e11	−0.253741
$478$	1.43269e12	1.25524
$479$	1.62209e12	1.40788	0.703941	−	0.710259i	$-0.251422\pi$
$479$	1.62209e12	1.40788	0.703941	+	0.710259i	$0.251422\pi$
$480$	4.74940e11	0.408370
$481$	5.25319e11	0.447477
$482$	1.64360e12	1.38702
$483$	0	0
$484$	−7.56166e10	−0.0626344
$485$	1.02324e11	0.0839730
$486$	1.99567e12	1.62266
$487$	6.21478e11	0.500663	0.250332	−	0.968160i	$-0.419460\pi$
$487$	6.21478e11	0.500663	0.250332	+	0.968160i	$0.419460\pi$
$488$	1.62908e12	1.30033
$489$	−1.12081e12	−0.886426
$490$	0	0
$491$	−2.43192e12	−1.88835	−0.944176	−	0.329442i	$-0.893139\pi$
$491$	−2.43192e12	−1.88835	−0.944176	+	0.329442i	$0.893139\pi$
$492$	−9.64423e11	−0.742035
$493$	5.72414e11	0.436415
$494$	−1.29778e12	−0.980459
$495$	6.58246e11	0.492793
$496$	−3.84649e11	−0.285363
$497$	0	0
$498$	1.06620e12	0.776796
$499$	−1.10777e11	−0.0799827	−0.0399913	−	0.999200i	$-0.512733\pi$
$499$	−1.10777e11	−0.0799827	−0.0399913	+	0.999200i	$0.512733\pi$
$500$	3.95679e10	0.0283125
$501$	−1.97365e12	−1.39959
$502$	−1.60633e12	−1.12893
$503$	7.14662e11	0.497788	0.248894	−	0.968531i	$-0.419933\pi$
$503$	7.14662e11	0.497788	0.248894	+	0.968531i	$0.419933\pi$
$504$	0	0
$505$	1.10398e12	0.755353
$506$	2.39735e12	1.62575
$507$	−1.27777e12	−0.858851
$508$	4.47188e10	0.0297922
$509$	1.21131e12	0.799884	0.399942	−	0.916541i	$-0.369030\pi$
$509$	1.21131e12	0.799884	0.399942	+	0.916541i	$0.369030\pi$
$510$	−8.87994e11	−0.581225
$511$	0	0
$512$	3.26759e11	0.210142
$513$	−7.07384e11	−0.450949
$514$	2.74542e11	0.173490
$515$	1.20119e11	0.0752454
$516$	−2.83969e10	−0.0176339
$517$	−2.04081e12	−1.25630
$518$	0	0
$519$	2.89651e12	1.75236
$520$	−3.81162e11	−0.228610
$521$	7.89014e11	0.469154	0.234577	−	0.972098i	$-0.424630\pi$
$521$	7.89014e11	0.469154	0.234577	+	0.972098i	$0.424630\pi$
$522$	−1.37796e12	−0.812304
$523$	2.34542e12	1.37077	0.685383	−	0.728183i	$-0.259635\pi$
$523$	2.34542e12	1.37077	0.685383	+	0.728183i	$0.259635\pi$
$524$	−6.67951e11	−0.387038
$525$	0	0
$526$	2.38297e12	1.35732
$527$	3.15075e11	0.177937
$528$	−2.90548e12	−1.62691
$529$	2.70679e12	1.50281
$530$	1.92237e11	0.105827
$531$	−3.18318e12	−1.73754
$532$	0	0
$533$	1.90647e12	1.02319
$534$	−1.83451e12	−0.976305
$535$	1.08001e12	0.569951
$536$	−1.91978e12	−1.00464
$537$	4.61082e12	2.39273
$538$	−3.06716e12	−1.57840
$539$	0	0
$540$	9.62247e10	0.0486984
$541$	1.88358e12	0.945357	0.472678	−	0.881235i	$-0.343287\pi$
$541$	1.88358e12	0.945357	0.472678	+	0.881235i	$0.343287\pi$
$542$	−2.06871e12	−1.02968
$543$	3.84598e10	0.0189849
$544$	9.47269e11	0.463744
$545$	3.30226e11	0.160335
$546$	0	0
$547$	−2.08933e12	−0.997846	−0.498923	−	0.866646i	$-0.666271\pi$
$547$	−2.08933e12	−0.997846	−0.498923	+	0.866646i	$0.666271\pi$
$548$	−9.02178e11	−0.427346
$549$	4.34238e12	2.04010
$550$	−4.41064e11	−0.205527
$551$	−1.63199e12	−0.754283
$552$	−4.04161e12	−1.85280
$553$	0	0
$554$	−8.19051e10	−0.0369417
$555$	−1.02480e12	−0.458480
$556$	−2.45623e10	−0.0109001
$557$	−2.51383e12	−1.10659	−0.553297	−	0.832984i	$-0.686630\pi$
$557$	−2.51383e12	−1.10659	−0.553297	+	0.832984i	$0.686630\pi$
$558$	−7.58472e11	−0.331196
$559$	5.61348e10	0.0243153
$560$	0	0
$561$	2.37994e12	1.01446
$562$	2.99904e12	1.26815
$563$	−8.76468e11	−0.367662	−0.183831	−	0.982958i	$-0.558850\pi$
$563$	−8.76468e11	−0.367662	−0.183831	+	0.982958i	$0.558850\pi$
$564$	−1.59348e12	−0.663120
$565$	1.71340e12	0.707360
$566$	−1.65990e12	−0.679843
$567$	0	0
$568$	−3.18413e12	−1.28358
$569$	−1.75549e12	−0.702091	−0.351046	−	0.936358i	$-0.614174\pi$
$569$	−1.75549e12	−0.702091	−0.351046	+	0.936358i	$0.614174\pi$
$570$	2.53172e12	1.00457
$571$	2.32441e12	0.915060	0.457530	−	0.889194i	$-0.348734\pi$
$571$	2.32441e12	0.915060	0.457530	+	0.889194i	$0.348734\pi$
$572$	−4.73139e11	−0.184802
$573$	−4.27498e12	−1.65668
$574$	0	0
$575$	−8.29372e11	−0.316405
$576$	1.67319e12	0.633351
$577$	−3.74722e12	−1.40740	−0.703700	−	0.710497i	$-0.748470\pi$
$577$	−3.74722e12	−1.40740	−0.703700	+	0.710497i	$0.748470\pi$
$578$	1.30778e12	0.487370
$579$	1.91629e12	0.708611
$580$	2.21997e11	0.0814557
$581$	0	0
$582$	−8.90598e11	−0.321757
$583$	−5.15221e11	−0.184708
$584$	2.56924e12	0.914000
$585$	−1.01600e12	−0.358669
$586$	2.19040e12	0.767335
$587$	5.13023e12	1.78347	0.891734	−	0.452561i	$-0.149489\pi$
$587$	5.13023e12	1.78347	0.891734	+	0.452561i	$0.149489\pi$
$588$	0	0
$589$	−8.98298e11	−0.307540
$590$	2.13292e12	0.724671
$591$	−4.37234e12	−1.47425
$592$	2.49530e12	0.834979
$593$	−5.25654e11	−0.174564	−0.0872819	−	0.996184i	$-0.527818\pi$
$593$	−5.25654e11	−0.174564	−0.0872819	+	0.996184i	$0.527818\pi$
$594$	−1.07262e12	−0.353514
$595$	0	0
$596$	−2.41677e11	−0.0784563
$597$	−8.65097e12	−2.78728
$598$	−3.70031e12	−1.18327
$599$	4.45408e12	1.41364	0.706818	−	0.707396i	$-0.250130\pi$
$599$	4.45408e12	1.41364	0.706818	+	0.707396i	$0.250130\pi$
$600$	7.43576e11	0.234231
$601$	1.48564e12	0.464491	0.232245	−	0.972657i	$-0.425393\pi$
$601$	1.48564e12	0.464491	0.232245	+	0.972657i	$0.425393\pi$
$602$	0	0
$603$	−5.11725e12	−1.57619
$604$	−1.72919e12	−0.528659
$605$	−2.91605e11	−0.0884902
$606$	−9.60871e12	−2.89427
$607$	−1.33914e12	−0.400385	−0.200192	−	0.979757i	$-0.564157\pi$
$607$	−1.33914e12	−0.400385	−0.200192	+	0.979757i	$0.564157\pi$
$608$	−2.70072e12	−0.801518
$609$	0	0
$610$	−2.90966e12	−0.850859
$611$	3.14999e12	0.914374
$612$	1.02510e12	0.295383
$613$	−3.77297e12	−1.07922	−0.539612	−	0.841914i	$-0.681429\pi$
$613$	−3.77297e12	−1.07922	−0.539612	+	0.841914i	$0.681429\pi$
$614$	2.58003e12	0.732602
$615$	−3.71916e12	−1.04835
$616$	0	0
$617$	8.47795e11	0.235509	0.117755	−	0.993043i	$-0.462430\pi$
$617$	8.47795e11	0.235509	0.117755	+	0.993043i	$0.462430\pi$
$618$	−1.04548e12	−0.288316
$619$	−1.05795e12	−0.289640	−0.144820	−	0.989458i	$-0.546260\pi$
$619$	−1.05795e12	−0.289640	−0.144820	+	0.989458i	$0.546260\pi$
$620$	1.22194e11	0.0332115
$621$	−2.01694e12	−0.544227
$622$	5.84055e12	1.56458
$623$	0	0
$624$	4.48460e12	1.18411
$625$	1.52588e11	0.0400000
$626$	4.66327e12	1.21368
$627$	−6.78536e12	−1.75335
$628$	1.46361e12	0.375498
$629$	−2.04396e12	−0.520649
$630$	0	0
$631$	6.07455e12	1.52539	0.762696	−	0.646757i	$-0.223875\pi$
$631$	6.07455e12	1.52539	0.762696	+	0.646757i	$0.223875\pi$
$632$	−3.15716e10	−0.00787171
$633$	−6.32552e12	−1.56596
$634$	−4.91167e12	−1.20733
$635$	1.72451e11	0.0420906
$636$	−4.02290e11	−0.0974949
$637$	0	0
$638$	−2.47461e12	−0.591308
$639$	−8.48742e12	−2.01383
$640$	−2.28173e12	−0.537593
$641$	1.55196e12	0.363094	0.181547	−	0.983382i	$-0.441890\pi$
$641$	1.55196e12	0.363094	0.181547	+	0.983382i	$0.441890\pi$
$642$	−9.40013e12	−2.18387
$643$	7.39291e12	1.70556	0.852778	−	0.522273i	$-0.174916\pi$
$643$	7.39291e12	1.70556	0.852778	+	0.522273i	$0.174916\pi$
$644$	0	0
$645$	−1.09509e11	−0.0249132
$646$	5.04952e12	1.14078
$647$	−3.70849e11	−0.0832009	−0.0416004	−	0.999134i	$-0.513246\pi$
$647$	−3.70849e11	−0.0832009	−0.0416004	+	0.999134i	$0.513246\pi$
$648$	−2.52226e12	−0.561956
$649$	−5.71652e12	−1.26483
$650$	6.80783e11	0.149589
$651$	0	0
$652$	−8.66969e11	−0.187884
$653$	5.70367e12	1.22757	0.613783	−	0.789475i	$-0.289647\pi$
$653$	5.70367e12	1.22757	0.613783	+	0.789475i	$0.289647\pi$
$654$	−2.87419e12	−0.614350
$655$	−2.57586e12	−0.546810
$656$	9.05585e12	1.90925
$657$	6.84840e12	1.43399
$658$	0	0
$659$	−1.72578e12	−0.356451	−0.178226	−	0.983990i	$-0.557036\pi$
$659$	−1.72578e12	−0.356451	−0.178226	+	0.983990i	$0.557036\pi$
$660$	9.23005e11	0.189346
$661$	−6.91726e11	−0.140938	−0.0704690	−	0.997514i	$-0.522450\pi$
$661$	−6.91726e11	−0.140938	−0.0704690	+	0.997514i	$0.522450\pi$
$662$	7.32955e12	1.48326
$663$	−3.67345e12	−0.738351
$664$	−1.78069e12	−0.355494
$665$	0	0
$666$	4.92038e12	0.969090
$667$	−4.65322e12	−0.910306
$668$	−1.52666e12	−0.296652
$669$	−1.86885e12	−0.360709
$670$	3.42886e12	0.657376
$671$	7.79827e12	1.48507
$672$	0	0
$673$	−3.11235e12	−0.584818	−0.292409	−	0.956293i	$-0.594457\pi$
$673$	−3.11235e12	−0.584818	−0.292409	+	0.956293i	$0.594457\pi$
$674$	7.72936e12	1.44269
$675$	3.71077e11	0.0688013
$676$	−9.88383e11	−0.182039
$677$	−6.18272e12	−1.13118	−0.565589	−	0.824687i	$-0.691351\pi$
$677$	−6.18272e12	−1.13118	−0.565589	+	0.824687i	$0.691351\pi$
$678$	−1.49129e13	−2.71037
$679$	0	0
$680$	1.48306e12	0.265992
$681$	−3.88063e12	−0.691417
$682$	−1.36210e12	−0.241091
$683$	9.17110e12	1.61261	0.806303	−	0.591503i	$-0.201465\pi$
$683$	9.17110e12	1.61261	0.806303	+	0.591503i	$0.201465\pi$
$684$	−2.92263e12	−0.510530
$685$	−3.47912e12	−0.603756
$686$	0	0
$687$	1.28838e13	2.20668
$688$	2.66644e11	0.0453716
$689$	7.95244e11	0.134435
$690$	7.21861e12	1.21236
$691$	6.21607e12	1.03721	0.518603	−	0.855015i	$-0.326452\pi$
$691$	6.21607e12	1.03721	0.518603	+	0.855015i	$0.326452\pi$
$692$	2.24051e12	0.371423
$693$	0	0
$694$	8.93509e12	1.46211
$695$	−9.47209e10	−0.0153998
$696$	4.17186e12	0.673889
$697$	−7.41786e12	−1.19050
$698$	−1.00914e13	−1.60917
$699$	1.51387e13	2.39851
$700$	0	0
$701$	9.62999e12	1.50624	0.753121	−	0.657882i	$-0.228547\pi$
$701$	9.62999e12	1.50624	0.753121	+	0.657882i	$0.228547\pi$
$702$	1.65559e12	0.257297
$703$	5.82746e12	0.899871
$704$	3.00481e12	0.461041
$705$	−6.14504e12	−0.936858
$706$	3.47037e12	0.525721
$707$	0	0
$708$	−4.46352e12	−0.667617
$709$	−8.38186e12	−1.24575	−0.622877	−	0.782320i	$-0.714036\pi$
$709$	−8.38186e12	−1.24575	−0.622877	+	0.782320i	$0.714036\pi$
$710$	5.68709e12	0.839899
$711$	−8.41552e10	−0.0123500
$712$	3.06387e12	0.446797
$713$	−2.56128e12	−0.371155
$714$	0	0
$715$	−1.82459e12	−0.261089
$716$	3.56656e12	0.507156
$717$	−1.15620e13	−1.63379
$718$	−4.04328e12	−0.567773
$719$	2.10248e12	0.293395	0.146697	−	0.989181i	$-0.453136\pi$
$719$	2.10248e12	0.293395	0.146697	+	0.989181i	$0.453136\pi$
$720$	−4.82608e12	−0.669266
$721$	0	0
$722$	−6.01858e12	−0.824284
$723$	−1.32640e13	−1.80531
$724$	2.97494e10	0.00402397
$725$	8.56100e11	0.115081
$726$	2.53804e12	0.339066
$727$	1.36288e12	0.180947	0.0904736	−	0.995899i	$-0.471162\pi$
$727$	1.36288e12	0.180947	0.0904736	+	0.995899i	$0.471162\pi$
$728$	0	0
$729$	−1.06408e13	−1.39541
$730$	−4.58884e12	−0.598068
$731$	−2.18415e11	−0.0282914
$732$	6.08897e12	0.783870
$733$	6.10310e12	0.780878	0.390439	−	0.920629i	$-0.372323\pi$
$733$	6.10310e12	0.780878	0.390439	+	0.920629i	$0.372323\pi$
$734$	1.10454e13	1.40459
$735$	0	0
$736$	−7.70046e12	−0.967312
$737$	−9.18982e12	−1.14737
$738$	1.78568e13	2.21590
$739$	5.95459e12	0.734432	0.367216	−	0.930136i	$-0.380311\pi$
$739$	5.95459e12	0.734432	0.367216	+	0.930136i	$0.380311\pi$
$740$	−7.92702e11	−0.0971779
$741$	1.04732e13	1.27614
$742$	0	0
$743$	−1.59757e13	−1.92314	−0.961569	−	0.274563i	$-0.911467\pi$
$743$	−1.59757e13	−1.92314	−0.961569	+	0.274563i	$0.911467\pi$
$744$	2.29633e12	0.274761
$745$	−9.31994e11	−0.110843
$746$	1.27884e13	1.51178
$747$	−4.74650e12	−0.557738
$748$	1.84093e12	0.215021
$749$	0	0
$750$	−1.32808e12	−0.153267
$751$	6.94141e12	0.796284	0.398142	−	0.917324i	$-0.369655\pi$
$751$	6.94141e12	0.796284	0.398142	+	0.917324i	$0.369655\pi$
$752$	1.49627e13	1.70620
$753$	1.29633e13	1.46939
$754$	3.81956e12	0.430370
$755$	−6.66836e12	−0.746892
$756$	0	0
$757$	8.41151e12	0.930984	0.465492	−	0.885052i	$-0.345877\pi$
$757$	8.41151e12	0.930984	0.465492	+	0.885052i	$0.345877\pi$
$758$	−9.34538e12	−1.02822
$759$	−1.93469e13	−2.11603
$760$	−4.22830e12	−0.459731
$761$	−1.50892e13	−1.63093	−0.815467	−	0.578803i	$-0.803520\pi$
$761$	−1.50892e13	−1.63093	−0.815467	+	0.578803i	$0.803520\pi$
$762$	−1.50097e12	−0.161278
$763$	0	0
$764$	−3.30678e12	−0.351144
$765$	3.95316e12	0.417319
$766$	4.65650e12	0.488687
$767$	8.82346e12	0.920576
$768$	1.24476e13	1.29110
$769$	−8.73448e12	−0.900676	−0.450338	−	0.892858i	$-0.648697\pi$
$769$	−8.73448e12	−0.900676	−0.450338	+	0.892858i	$0.648697\pi$
$770$	0	0
$771$	−2.21559e12	−0.225810
$772$	1.48229e12	0.150195
$773$	−9.26595e12	−0.933431	−0.466716	−	0.884407i	$-0.654563\pi$
$773$	−9.26595e12	−0.933431	−0.466716	+	0.884407i	$0.654563\pi$
$774$	5.25784e11	0.0526591
$775$	4.71225e11	0.0469214
$776$	1.48741e12	0.147249
$777$	0	0
$778$	−1.26562e13	−1.23850
$779$	2.11488e13	2.05762
$780$	−1.42466e12	−0.137811
$781$	−1.52422e13	−1.46594
$782$	1.43975e13	1.37676
$783$	2.08194e12	0.197943
$784$	0	0
$785$	5.64421e12	0.530505
$786$	2.24195e13	2.09520
$787$	−8.04278e12	−0.747343	−0.373671	−	0.927561i	$-0.621901\pi$
$787$	−8.04278e12	−0.747343	−0.373671	+	0.927561i	$0.621901\pi$
$788$	−3.38209e12	−0.312476
$789$	−1.92308e13	−1.76665
$790$	5.63891e10	0.00515078
$791$	0	0
$792$	9.56845e12	0.864128
$793$	−1.20366e13	−1.08088
$794$	−9.73239e12	−0.869015
$795$	−1.55137e12	−0.137741
$796$	−6.69169e12	−0.590782
$797$	3.62841e12	0.318533	0.159266	−	0.987236i	$-0.449087\pi$
$797$	3.62841e12	0.318533	0.159266	+	0.987236i	$0.449087\pi$
$798$	0	0
$799$	−1.22563e13	−1.06389
$800$	1.41673e12	0.122288
$801$	8.16686e12	0.700985
$802$	3.99714e12	0.341165
$803$	1.22987e13	1.04385
$804$	−7.17550e12	−0.605620
$805$	0	0
$806$	2.10241e12	0.175473
$807$	2.47523e13	2.05440
$808$	1.60478e13	1.32453
$809$	1.27049e13	1.04280	0.521402	−	0.853311i	$-0.325409\pi$
$809$	1.27049e13	1.04280	0.521402	+	0.853311i	$0.325409\pi$
$810$	4.50494e12	0.367711
$811$	−6.90849e12	−0.560776	−0.280388	−	0.959887i	$-0.590463\pi$
$811$	−6.90849e12	−0.560776	−0.280388	+	0.959887i	$0.590463\pi$
$812$	0	0
$813$	1.66947e13	1.34021
$814$	8.83627e12	0.705439
$815$	−3.34334e12	−0.265443
$816$	−1.74491e13	−1.37774
$817$	6.22713e11	0.0488978
$818$	−2.58378e13	−2.01774
$819$	0	0
$820$	−2.87684e12	−0.222205
$821$	−1.57014e13	−1.20613	−0.603067	−	0.797691i	$-0.706055\pi$
$821$	−1.57014e13	−1.20613	−0.603067	+	0.797691i	$0.706055\pi$
$822$	3.02812e13	2.31340
$823$	1.02697e13	0.780295	0.390147	−	0.920752i	$-0.372424\pi$
$823$	1.02697e13	0.780295	0.390147	+	0.920752i	$0.372424\pi$
$824$	1.74609e12	0.131945
$825$	3.55944e12	0.267509
$826$	0	0
$827$	−2.06564e13	−1.53561	−0.767804	−	0.640684i	$-0.778651\pi$
$827$	−2.06564e13	−1.53561	−0.767804	+	0.640684i	$0.778651\pi$
$828$	−8.33318e12	−0.616132
$829$	9.01114e12	0.662650	0.331325	−	0.943517i	$-0.392504\pi$
$829$	9.01114e12	0.662650	0.331325	+	0.943517i	$0.392504\pi$
$830$	3.18044e12	0.232614
$831$	6.60983e11	0.0480823
$832$	−4.63792e12	−0.335559
$833$	0	0
$834$	8.24423e11	0.0590069
$835$	−5.88733e12	−0.419111
$836$	−5.24861e12	−0.371634
$837$	1.14597e12	0.0807063
$838$	4.84637e12	0.339483
$839$	5.25303e12	0.366000	0.183000	−	0.983113i	$-0.441419\pi$
$839$	5.25303e12	0.366000	0.183000	+	0.983113i	$0.441419\pi$
$840$	0	0
$841$	−9.70396e12	−0.668909
$842$	−4.00153e12	−0.274361
$843$	−2.42026e13	−1.65058
$844$	−4.89291e12	−0.331915
$845$	−3.81155e12	−0.257186
$846$	2.95042e13	1.98024
$847$	0	0
$848$	3.77746e12	0.250853
$849$	1.33956e13	0.884865
$850$	−2.64886e12	−0.174050
$851$	1.66156e13	1.08601
$852$	−1.19012e13	−0.773773
$853$	−2.16481e13	−1.40007	−0.700035	−	0.714109i	$-0.746832\pi$
$853$	−2.16481e13	−1.40007	−0.700035	+	0.714109i	$0.746832\pi$
$854$	0	0
$855$	−1.12707e13	−0.721278
$856$	1.56994e13	0.999427
$857$	2.18253e13	1.38212	0.691061	−	0.722796i	$-0.257143\pi$
$857$	2.18253e13	1.38212	0.691061	+	0.722796i	$0.257143\pi$
$858$	1.58807e13	1.00041
$859$	8.56506e12	0.536737	0.268368	−	0.963316i	$-0.413516\pi$
$859$	8.56506e12	0.536737	0.268368	+	0.963316i	$0.413516\pi$
$860$	−8.47070e10	−0.00528052
$861$	0	0
$862$	−2.24492e13	−1.38490
$863$	−3.29505e12	−0.202215	−0.101108	−	0.994876i	$-0.532239\pi$
$863$	−3.29505e12	−0.202215	−0.101108	+	0.994876i	$0.532239\pi$
$864$	3.44533e12	0.210339
$865$	8.64020e12	0.524749
$866$	−2.57224e13	−1.55411
$867$	−1.05539e13	−0.634347
$868$	0	0
$869$	−1.51130e11	−0.00899007
$870$	−7.45125e12	−0.440953
$871$	1.41845e13	0.835088
$872$	4.80026e12	0.281152
$873$	3.96475e12	0.231021
$874$	−4.10481e13	−2.37953
$875$	0	0
$876$	9.60296e12	0.550981
$877$	−5.03789e12	−0.287574	−0.143787	−	0.989609i	$-0.545928\pi$
$877$	−5.03789e12	−0.287574	−0.143787	+	0.989609i	$0.545928\pi$
$878$	1.53687e13	0.872796
$879$	−1.76768e13	−0.998742
$880$	−8.66694e12	−0.487185
$881$	1.87408e13	1.04808	0.524042	−	0.851692i	$-0.324423\pi$
$881$	1.87408e13	1.04808	0.524042	+	0.851692i	$0.324423\pi$
$882$	0	0
$883$	3.35081e13	1.85493	0.927463	−	0.373914i	$-0.121984\pi$
$883$	3.35081e13	1.85493	0.927463	+	0.373914i	$0.121984\pi$
$884$	−2.84148e12	−0.156498
$885$	−1.72129e13	−0.943213
$886$	2.42820e13	1.32383
$887$	1.04883e13	0.568917	0.284459	−	0.958688i	$-0.408186\pi$
$887$	1.04883e13	0.568917	0.284459	+	0.958688i	$0.408186\pi$
$888$	−1.48968e13	−0.803959
$889$	0	0
$890$	−5.47229e12	−0.292358
$891$	−1.20738e13	−0.641795
$892$	−1.44559e12	−0.0764547
$893$	3.49434e13	1.83880
$894$	8.11180e12	0.424716
$895$	1.37539e13	0.716512
$896$	0	0
$897$	2.98619e13	1.54011
$898$	2.36077e13	1.21146
$899$	2.64383e12	0.134994
$900$	1.53314e12	0.0778915
$901$	−3.09421e12	−0.156419
$902$	3.20682e13	1.61304
$903$	0	0
$904$	2.49065e13	1.24038
$905$	1.14724e11	0.00568508
$906$	5.80395e13	2.86185
$907$	−3.18949e13	−1.56491	−0.782454	−	0.622709i	$-0.786032\pi$
$907$	−3.18949e13	−1.56491	−0.782454	+	0.622709i	$0.786032\pi$
$908$	−3.00174e12	−0.146550
$909$	4.27759e13	2.07808
$910$	0	0
$911$	2.29508e13	1.10399	0.551995	−	0.833848i	$-0.313867\pi$
$911$	2.29508e13	1.10399	0.551995	+	0.833848i	$0.313867\pi$
$912$	4.97485e13	2.38124
$913$	−8.52401e12	−0.405999
$914$	−5.99734e12	−0.284250
$915$	2.34812e13	1.10745
$916$	9.96587e12	0.467719
$917$	0	0
$918$	−6.44172e12	−0.299371
$919$	1.75653e13	0.812334	0.406167	−	0.913799i	$-0.366865\pi$
$919$	1.75653e13	0.812334	0.406167	+	0.913799i	$0.366865\pi$
$920$	−1.20560e13	−0.554827
$921$	−2.08212e13	−0.953534
$922$	−3.17769e13	−1.44818
$923$	2.35263e13	1.06695
$924$	0	0
$925$	−3.05694e12	−0.137293
$926$	−2.00547e12	−0.0896326
$927$	4.65426e12	0.207010
$928$	7.94863e12	0.351825
$929$	−1.93752e13	−0.853446	−0.426723	−	0.904382i	$-0.640332\pi$
$929$	−1.93752e13	−0.853446	−0.426723	+	0.904382i	$0.640332\pi$
$930$	−4.10141e12	−0.179788
$931$	0	0
$932$	1.17101e13	0.508379
$933$	−4.71338e13	−2.03641
$934$	1.01896e13	0.438125
$935$	7.09929e12	0.303783
$936$	−1.47689e13	−0.628937
$937$	−4.08529e12	−0.173139	−0.0865696	−	0.996246i	$-0.527590\pi$
$937$	−4.08529e12	−0.173139	−0.0865696	+	0.996246i	$0.527590\pi$
$938$	0	0
$939$	−3.76331e13	−1.57970
$940$	−4.75331e12	−0.198573
$941$	1.06000e12	0.0440709	0.0220355	−	0.999757i	$-0.492985\pi$
$941$	1.06000e12	0.0440709	0.0220355	+	0.999757i	$0.492985\pi$
$942$	−4.91255e13	−2.03272
$943$	6.03006e13	2.48324
$944$	4.19120e13	1.71777
$945$	0	0
$946$	9.44231e11	0.0383326
$947$	−1.29151e13	−0.521824	−0.260912	−	0.965363i	$-0.584023\pi$
$947$	−1.29151e13	−0.521824	−0.260912	+	0.965363i	$0.584023\pi$
$948$	−1.18004e11	−0.00474526
$949$	−1.89831e13	−0.759747
$950$	7.55204e12	0.300821
$951$	3.96377e13	1.57143
$952$	0	0
$953$	8.70094e12	0.341702	0.170851	−	0.985297i	$-0.445348\pi$
$953$	8.70094e12	0.341702	0.170851	+	0.985297i	$0.445348\pi$
$954$	7.44861e12	0.291144
$955$	−1.27521e13	−0.496098
$956$	−8.94342e12	−0.346292
$957$	1.99704e13	0.769630
$958$	−4.21142e13	−1.61541
$959$	0	0
$960$	9.04772e12	0.343810
$961$	−2.49844e13	−0.944960
$962$	−1.36388e13	−0.513438
$963$	4.18474e13	1.56801
$964$	−1.02600e13	−0.382648
$965$	5.71623e12	0.212196
$966$	0	0
$967$	−4.84084e13	−1.78033	−0.890167	−	0.455635i	$-0.849412\pi$
$967$	−4.84084e13	−1.78033	−0.890167	+	0.455635i	$0.849412\pi$
$968$	−4.23885e12	−0.155170
$969$	−4.07502e13	−1.48481
$970$	−2.65662e12	−0.0963512
$971$	−2.67952e13	−0.967319	−0.483660	−	0.875256i	$-0.660693\pi$
$971$	−2.67952e13	−0.967319	−0.483660	+	0.875256i	$0.660693\pi$
$972$	−1.24578e13	−0.447653
$973$	0	0
$974$	−1.61354e13	−0.574465
$975$	−5.49399e12	−0.194701
$976$	−5.71749e13	−2.01688
$977$	4.21970e12	0.148169	0.0740843	−	0.997252i	$-0.476397\pi$
$977$	4.21970e12	0.148169	0.0740843	+	0.997252i	$0.476397\pi$
$978$	2.90994e13	1.01709
$979$	1.46665e13	0.510275
$980$	0	0
$981$	1.27953e13	0.441103
$982$	6.31396e13	2.16671
$983$	4.74505e13	1.62088	0.810438	−	0.585825i	$-0.199229\pi$
$983$	4.74505e13	1.62088	0.810438	+	0.585825i	$0.199229\pi$
$984$	−5.40628e13	−1.83832
$985$	−1.30425e13	−0.441468
$986$	−1.48615e13	−0.500745
$987$	0	0
$988$	8.10123e12	0.270486
$989$	1.77552e12	0.0590122
$990$	−1.70899e13	−0.565434
$991$	−1.04090e13	−0.342830	−0.171415	−	0.985199i	$-0.554834\pi$
$991$	−1.04090e13	−0.342830	−0.171415	+	0.985199i	$0.554834\pi$
$992$	4.37518e12	0.143448
$993$	−5.91502e13	−1.93057
$994$	0	0
$995$	−2.58055e13	−0.834659
$996$	−6.65563e12	−0.214300
$997$	−2.11445e13	−0.677749	−0.338874	−	0.940832i	$-0.610046\pi$
$997$	−2.11445e13	−0.677749	−0.338874	+	0.940832i	$0.610046\pi$
$998$	2.87608e12	0.0917727
$999$	−7.43414e12	−0.236149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.10.a.e.1.2		4
7.6	odd	2		35.10.a.c.1.2	✓	4
21.20	even	2		315.10.a.g.1.3		4
35.13	even	4		175.10.b.e.99.6		8
35.27	even	4		175.10.b.e.99.3		8
35.34	odd	2		175.10.a.e.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.c.1.2	✓	4	7.6	odd	2
175.10.a.e.1.3		4	35.34	odd	2
175.10.b.e.99.3		8	35.27	even	4
175.10.b.e.99.6		8	35.13	even	4
245.10.a.e.1.2		4	1.1	even	1	trivial
315.10.a.g.1.3		4	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q-25.9629 q^{2} +209.523 q^{3} +162.070 q^{4} +625.000 q^{5} -5439.82 q^{6} +9085.18 q^{8} +24216.9 q^{9} -16226.8 q^{10} +43490.0 q^{11} +33957.4 q^{12} -67126.8 q^{13} +130952. q^{15} -318857. q^{16} +261183. q^{17} -628740. q^{18} -744649. q^{19} +101294. q^{20} -1.12912e6 q^{22} -2.12319e6 q^{23} +1.90355e6 q^{24} +390625. q^{25} +1.74280e6 q^{26} +949956. q^{27} +2.19162e6 q^{29} -3.39989e6 q^{30} +1.20634e6 q^{31} +3.62683e6 q^{32} +9.11216e6 q^{33} -6.78107e6 q^{34} +3.92484e6 q^{36} -7.82577e6 q^{37} +1.93332e7 q^{38} -1.40646e7 q^{39} +5.67824e6 q^{40} -2.84010e7 q^{41} -836250. q^{43} +7.04843e6 q^{44} +1.51356e7 q^{45} +5.51241e7 q^{46} -4.69259e7 q^{47} -6.68079e7 q^{48} -1.01417e7 q^{50} +5.47240e7 q^{51} -1.08793e7 q^{52} -1.18469e7 q^{53} -2.46636e7 q^{54} +2.71813e7 q^{55} -1.56021e8 q^{57} -5.69006e7 q^{58} -1.31445e8 q^{59} +2.12234e7 q^{60} +1.79312e8 q^{61} -3.13200e7 q^{62} +6.90919e7 q^{64} -4.19543e7 q^{65} -2.36578e8 q^{66} -2.11309e8 q^{67} +4.23300e7 q^{68} -4.44857e8 q^{69} -3.50475e8 q^{71} +2.20015e8 q^{72} +2.82794e8 q^{73} +2.03179e8 q^{74} +8.18449e7 q^{75} -1.20685e8 q^{76} +3.65158e8 q^{78} -3.47506e6 q^{79} -1.99286e8 q^{80} -2.77624e8 q^{81} +7.37370e8 q^{82} -1.95999e8 q^{83} +1.63240e8 q^{85} +2.17115e7 q^{86} +4.59194e8 q^{87} +3.95115e8 q^{88} +3.37238e8 q^{89} -3.92962e8 q^{90} -3.44106e8 q^{92} +2.52755e8 q^{93} +1.21833e9 q^{94} -4.65406e8 q^{95} +7.59905e8 q^{96} +1.63718e8 q^{97} +1.05319e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 19 q^{2} + 18 q^{3} + 1729 q^{4} + 2500 q^{5} + 144 q^{6} - 30495 q^{8} + 5382 q^{9} - 11875 q^{10} + 82438 q^{11} - 41328 q^{12} + 72962 q^{13} + 11250 q^{15} + 64257 q^{16} + 357542 q^{17} - 965367 q^{18}+ \cdots + 1222369524 q^{99}+O(q^{100}) \) 4 * q - 19 * q^2 + 18 * q^3 + 1729 * q^4 + 2500 * q^5 + 144 * q^6 - 30495 * q^8 + 5382 * q^9 - 11875 * q^10 + 82438 * q^11 - 41328 * q^12 + 72962 * q^13 + 11250 * q^15 + 64257 * q^16 + 357542 * q^17 - 965367 * q^18 - 300732 * q^19 + 1080625 * q^20 - 5595068 * q^22 - 2340836 * q^23 + 7636320 * q^24 + 1562500 * q^25 - 1305666 * q^26 + 4240350 * q^27 - 1372022 * q^29 + 90000 * q^30 + 4590888 * q^31 - 10529439 * q^32 - 2000034 * q^33 + 7199478 * q^34 - 9144243 * q^36 - 38868456 * q^37 + 15477280 * q^38 - 46666242 * q^39 - 19059375 * q^40 - 57287084 * q^41 - 43403452 * q^43 + 87639348 * q^44 + 3363750 * q^45 + 28892416 * q^46 - 91822222 * q^47 - 156168864 * q^48 - 7421875 * q^50 + 86342634 * q^51 - 1953386 * q^52 - 61086884 * q^53 - 187589520 * q^54 + 51523750 * q^55 - 79928892 * q^57 + 29615390 * q^58 - 72569680 * q^59 - 25830000 * q^60 + 225681036 * q^61 - 190286472 * q^62 + 141443393 * q^64 + 45601250 * q^65 + 119673648 * q^66 - 4429720 * q^67 - 15339698 * q^68 - 348300612 * q^69 - 470468984 * q^71 + 298610685 * q^72 + 168326464 * q^73 + 927809502 * q^74 + 7031250 * q^75 + 892265344 * q^76 + 281290896 * q^78 - 598805646 * q^79 + 40160625 * q^80 - 847155996 * q^81 + 1821993318 * q^82 + 1159074304 * q^83 + 223463750 * q^85 + 706791156 * q^86 + 421480998 * q^87 - 1992103900 * q^88 + 1380153012 * q^89 - 603354375 * q^90 + 710319264 * q^92 - 1601969400 * q^93 - 2466744152 * q^94 - 187957500 * q^95 + 799321824 * q^96 - 754874082 * q^97 + 1222369524 * q^99

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