LMFDB - Embedded newform 25.26.a.f.1.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [25,26,Mod(1,25)] 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("25.1"); S:= CuspForms(chi, 26); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 26, names="a")

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	25.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$98.9991949881$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 71168091 x^{10} + \cdots + 10\!\cdots\!36 $ x^12 - 71168091x^10 + 1813581965257740x^8 - 20299276558981985144320x^6 + 100647952747482434827869143040x^4 - 189155799423092547840968636818784256*x^2 + 108016131559589051821063489995287755227136
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{46}\cdot 3^{20}\cdot 5^{36} $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$4680.77$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+9361.55 q^{2} -531494. q^{3} +5.40841e7 q^{4} -4.97561e9 q^{6} -1.37587e10 q^{7} +1.92189e11 q^{8} -5.64803e11 q^{9} -9.26999e12 q^{11} -2.87454e13 q^{12} +1.02027e14 q^{13} -1.28802e14 q^{14} -1.55712e13 q^{16} +3.06292e15 q^{17} -5.28743e15 q^{18} -5.00581e15 q^{19} +7.31265e15 q^{21} -8.67815e16 q^{22} +9.11014e16 q^{23} -1.02148e17 q^{24} +9.55130e17 q^{26} +7.50518e17 q^{27} -7.44125e17 q^{28} +3.16262e18 q^{29} +3.22878e18 q^{31} -6.59458e18 q^{32} +4.92695e18 q^{33} +2.86736e19 q^{34} -3.05468e19 q^{36} -1.59124e19 q^{37} -4.68621e19 q^{38} -5.42268e19 q^{39} -8.10389e19 q^{41} +6.84577e19 q^{42} +3.97592e20 q^{43} -5.01359e20 q^{44} +8.52850e20 q^{46} -9.69576e20 q^{47} +8.27600e18 q^{48} -1.15177e21 q^{49} -1.62792e21 q^{51} +5.51804e21 q^{52} +5.88324e21 q^{53} +7.02601e21 q^{54} -2.64427e21 q^{56} +2.66056e21 q^{57} +2.96070e22 q^{58} +2.11464e22 q^{59} +7.65113e21 q^{61} +3.02264e22 q^{62} +7.77093e21 q^{63} -6.12130e22 q^{64} +4.61238e22 q^{66} +3.72268e22 q^{67} +1.65655e23 q^{68} -4.84199e22 q^{69} -3.96178e22 q^{71} -1.08549e23 q^{72} +4.27194e22 q^{73} -1.48965e23 q^{74} -2.70734e23 q^{76} +1.27543e23 q^{77} -5.07646e23 q^{78} +9.25017e23 q^{79} +7.96549e22 q^{81} -7.58649e23 q^{82} -9.81159e23 q^{83} +3.95498e23 q^{84} +3.72207e24 q^{86} -1.68091e24 q^{87} -1.78160e24 q^{88} +1.32371e24 q^{89} -1.40375e24 q^{91} +4.92714e24 q^{92} -1.71608e24 q^{93} -9.07673e24 q^{94} +3.50498e24 q^{96} -3.52916e24 q^{97} -1.07823e25 q^{98} +5.23572e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 166691544 q^{4} + 10591544184 q^{6} + 3948466041036 q^{9} - 1090673824176 q^{11} + 890646861445848 q^{14} + 22\!\cdots\!32 q^{16} - 63\!\cdots\!60 q^{19} + 13\!\cdots\!44 q^{21} + 12\!\cdots\!20 q^{24}+ \cdots + 10\!\cdots\!72 q^{99}+O(q^{100}) $ 12 * q + 166691544 * q^4 + 10591544184 * q^6 + 3948466041036 * q^9 - 1090673824176 * q^11 + 890646861445848 * q^14 + 2206145875609632 * q^16 - 6329834351210160 * q^19 + 13538972741781744 * q^21 + 1238774108159908320 * q^24 + 487725686068642704 * q^26 + 5990455853511966360 * q^29 - 35669623242168576 * q^31 + 45224081273675172288 * q^34 + 95509342682184062232 * q^36 - 59576177650244745888 * q^39 - 149504768291960577576 * q^41 - 1795327120321140441312 * q^44 - 2632260904857596314776 * q^46 + 1924948130789206201884 * q^49 + 6601362996360626974464 * q^51 + 4543556632841187026640 * q^54 + 6789286242764162655840 * q^56 + 31976684482970870043120 * q^59 + 33892026990475241838024 * q^61 + 45154694563657190239104 * q^64 - 84625057142490628840032 * q^66 - 454638912158488569862128 * q^69 - 118991523615678935618976 * q^71 + 276076790459758393833168 * q^74 + 1770023872374606472757280 * q^76 + 741918285485353377639360 * q^79 + 2020576746978155938317372 * q^81 + 6598941205046486172215328 * q^84 + 6309456694176729359288664 * q^86 - 576066549612764658926520 * q^89 + 12216814388553519240480864 * q^91 + 11673168428062976516959608 * q^94 + 57292208364908004705120384 * q^96 + 10068680551503914801051472 * 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 $

$2$	9361.55	1.61612	0.808058	−	0.589103i	$-0.200519\pi$
$2$	9361.55	1.61612	0.808058	+	0.589103i	$0.200519\pi$
$3$	−531494.	−0.577408	−0.288704	−	0.957418i	$-0.593224\pi$
$3$	−531494.	−0.577408	−0.288704	+	0.957418i	$0.593224\pi$
$4$	5.40841e7	1.61183
$5$	0	0
$5$	0	0
$6$	−4.97561e9	−0.933158
$7$	−1.37587e10	−0.375708	−0.187854	−	0.982197i	$-0.560153\pi$
$7$	−1.37587e10	−0.375708	−0.187854	+	0.982197i	$0.560153\pi$
$8$	1.92189e11	0.988791
$9$	−5.64803e11	−0.666600
$10$	0	0
$11$	−9.26999e12	−0.890576	−0.445288	−	0.895387i	$-0.646899\pi$
$11$	−9.26999e12	−0.890576	−0.445288	+	0.895387i	$0.646899\pi$
$12$	−2.87454e13	−0.930685
$13$	1.02027e14	1.21457	0.607286	−	0.794483i	$-0.292258\pi$
$13$	1.02027e14	1.21457	0.607286	+	0.794483i	$0.292258\pi$
$14$	−1.28802e14	−0.607188
$15$	0	0
$16$	−1.55712e13	−0.0138300
$17$	3.06292e15	1.27504	0.637520	−	0.770434i	$-0.279960\pi$
$17$	3.06292e15	1.27504	0.637520	+	0.770434i	$0.279960\pi$
$18$	−5.28743e15	−1.07730
$19$	−5.00581e15	−0.518864	−0.259432	−	0.965761i	$-0.583535\pi$
$19$	−5.00581e15	−0.518864	−0.259432	+	0.965761i	$0.583535\pi$
$20$	0	0
$21$	7.31265e15	0.216937
$22$	−8.67815e16	−1.43927
$23$	9.11014e16	0.866817	0.433408	−	0.901198i	$-0.357311\pi$
$23$	9.11014e16	0.866817	0.433408	+	0.901198i	$0.357311\pi$
$24$	−1.02148e17	−0.570936
$25$	0	0
$26$	9.55130e17	1.96289
$27$	7.50518e17	0.962308
$28$	−7.44125e17	−0.605578
$29$	3.16262e18	1.65986	0.829930	−	0.557867i	$-0.188380\pi$
$29$	3.16262e18	1.65986	0.829930	+	0.557867i	$0.188380\pi$
$30$	0	0
$31$	3.22878e18	0.736237	0.368119	−	0.929779i	$-0.380002\pi$
$31$	3.22878e18	0.736237	0.368119	+	0.929779i	$0.380002\pi$
$32$	−6.59458e18	−1.01114
$33$	4.92695e18	0.514226
$34$	2.86736e19	2.06061
$35$	0	0
$36$	−3.05468e19	−1.07445
$37$	−1.59124e19	−0.397388	−0.198694	−	0.980062i	$-0.563670\pi$
$37$	−1.59124e19	−0.397388	−0.198694	+	0.980062i	$0.563670\pi$
$38$	−4.68621e19	−0.838545
$39$	−5.42268e19	−0.701303
$40$	0	0
$41$	−8.10389e19	−0.560913	−0.280456	−	0.959867i	$-0.590486\pi$
$41$	−8.10389e19	−0.560913	−0.280456	+	0.959867i	$0.590486\pi$
$42$	6.84577e19	0.350595
$43$	3.97592e20	1.51734	0.758668	−	0.651478i	$-0.225851\pi$
$43$	3.97592e20	1.51734	0.758668	+	0.651478i	$0.225851\pi$
$44$	−5.01359e20	−1.43546
$45$	0	0
$46$	8.52850e20	1.40088
$47$	−9.69576e20	−1.21719	−0.608595	−	0.793481i	$-0.708267\pi$
$47$	−9.69576e20	−1.21719	−0.608595	+	0.793481i	$0.708267\pi$
$48$	8.27600e18	0.00798555
$49$	−1.15177e21	−0.858843
$50$	0	0
$51$	−1.62792e21	−0.736218
$52$	5.51804e21	1.95769
$53$	5.88324e21	1.64501	0.822504	−	0.568759i	$-0.192576\pi$
$53$	5.88324e21	1.64501	0.822504	+	0.568759i	$0.192576\pi$
$54$	7.02601e21	1.55520
$55$	0	0
$56$	−2.64427e21	−0.371497
$57$	2.66056e21	0.299596
$58$	2.96070e22	2.68253
$59$	2.11464e22	1.54734	0.773671	−	0.633588i	$-0.218418\pi$
$59$	2.11464e22	1.54734	0.773671	+	0.633588i	$0.218418\pi$
$60$	0	0
$61$	7.65113e21	0.369065	0.184532	−	0.982826i	$-0.440923\pi$
$61$	7.65113e21	0.369065	0.184532	+	0.982826i	$0.440923\pi$
$62$	3.02264e22	1.18985
$63$	7.77093e21	0.250447
$64$	−6.12130e22	−1.62029
$65$	0	0
$66$	4.61238e22	0.831048
$67$	3.72268e22	0.555802	0.277901	−	0.960610i	$-0.410361\pi$
$67$	3.72268e22	0.555802	0.277901	+	0.960610i	$0.410361\pi$
$68$	1.65655e23	2.05515
$69$	−4.84199e22	−0.500507
$70$	0	0
$71$	−3.96178e22	−0.286524	−0.143262	−	0.989685i	$-0.545759\pi$
$71$	−3.96178e22	−0.286524	−0.143262	+	0.989685i	$0.545759\pi$
$72$	−1.08549e23	−0.659128
$73$	4.27194e22	0.218318	0.109159	−	0.994024i	$-0.465184\pi$
$73$	4.27194e22	0.218318	0.109159	+	0.994024i	$0.465184\pi$
$74$	−1.48965e23	−0.642225
$75$	0	0
$76$	−2.70734e23	−0.836322
$77$	1.27543e23	0.334597
$78$	−5.07646e23	−1.13339
$79$	9.25017e23	1.76121	0.880605	−	0.473851i	$-0.157137\pi$
$79$	9.25017e23	1.76121	0.880605	+	0.473851i	$0.157137\pi$
$80$	0	0
$81$	7.96549e22	0.110956
$82$	−7.58649e23	−0.906500
$83$	−9.81159e23	−1.00754	−0.503771	−	0.863837i	$-0.668054\pi$
$83$	−9.81159e23	−1.00754	−0.503771	+	0.863837i	$0.668054\pi$
$84$	3.95498e23	0.349666
$85$	0	0
$86$	3.72207e24	2.45219
$87$	−1.68091e24	−0.958416
$88$	−1.78160e24	−0.880594
$89$	1.32371e24	0.568091	0.284046	−	0.958811i	$-0.408323\pi$
$89$	1.32371e24	0.568091	0.284046	+	0.958811i	$0.408323\pi$
$90$	0	0
$91$	−1.40375e24	−0.456324
$92$	4.92714e24	1.39716
$93$	−1.71608e24	−0.425109
$94$	−9.07673e24	−1.96712
$95$	0	0
$96$	3.50498e24	0.583842
$97$	−3.52916e24	−0.516445	−0.258223	−	0.966085i	$-0.583137\pi$
$97$	−3.52916e24	−0.516445	−0.258223	+	0.966085i	$0.583137\pi$
$98$	−1.07823e25	−1.38799
$99$	5.23572e24	0.593658
$100$	0	0
$101$	−1.04249e25	−0.920570	−0.460285	−	0.887771i	$-0.652253\pi$
$101$	−1.04249e25	−0.920570	−0.460285	+	0.887771i	$0.652253\pi$
$102$	−1.52399e25	−1.18981
$103$	1.55473e25	1.07446	0.537230	−	0.843436i	$-0.319471\pi$
$103$	1.55473e25	1.07446	0.537230	+	0.843436i	$0.319471\pi$
$104$	1.96085e25	1.20096
$105$	0	0
$106$	5.50762e25	2.65852
$107$	3.91524e25	1.68059	0.840294	−	0.542131i	$-0.182382\pi$
$107$	3.91524e25	1.68059	0.840294	+	0.542131i	$0.182382\pi$
$108$	4.05911e25	1.55108
$109$	1.97006e25	0.670886	0.335443	−	0.942060i	$-0.391114\pi$
$109$	1.97006e25	0.670886	0.335443	+	0.942060i	$0.391114\pi$
$110$	0	0
$111$	8.45735e24	0.229455
$112$	2.14239e23	0.00519604
$113$	−4.21994e25	−0.915853	−0.457926	−	0.888990i	$-0.651408\pi$
$113$	−4.21994e25	−0.915853	−0.457926	+	0.888990i	$0.651408\pi$
$114$	2.49069e25	0.484183
$115$	0	0
$116$	1.71047e26	2.67542
$117$	−5.76251e25	−0.809634
$118$	1.97963e26	2.50068
$119$	−4.21416e25	−0.479043
$120$	0	0
$121$	−2.24143e25	−0.206875
$122$	7.16264e25	0.596452
$123$	4.30717e25	0.323875
$124$	1.74626e26	1.18669
$125$	0	0
$126$	7.27479e25	0.404752
$127$	1.11228e26	0.560619	0.280310	−	0.959910i	$-0.409563\pi$
$127$	1.11228e26	0.560619	0.280310	+	0.959910i	$0.409563\pi$
$128$	−3.51771e26	−1.60744
$129$	−2.11318e26	−0.876122
$130$	0	0
$131$	2.15522e26	0.737227	0.368613	−	0.929583i	$-0.379833\pi$
$131$	2.15522e26	0.737227	0.368613	+	0.929583i	$0.379833\pi$
$132$	2.66470e26	0.828845
$133$	6.88732e25	0.194942
$134$	3.48500e26	0.898241
$135$	0	0
$136$	5.88660e26	1.26075
$137$	−9.54103e26	−1.86461	−0.932305	−	0.361672i	$-0.882206\pi$
$137$	−9.54103e26	−1.86461	−0.932305	+	0.361672i	$0.882206\pi$
$138$	−4.53285e26	−0.808877
$139$	2.71293e26	0.442337	0.221169	−	0.975236i	$-0.429013\pi$
$139$	2.71293e26	0.442337	0.221169	+	0.975236i	$0.429013\pi$
$140$	0	0
$141$	5.15324e26	0.702816
$142$	−3.70884e26	−0.463056
$143$	−9.45790e26	−1.08167
$144$	8.79465e24	0.00921908
$145$	0	0
$146$	3.99919e26	0.352827
$147$	6.12158e26	0.495903
$148$	−8.60608e26	−0.640522
$149$	2.96654e26	0.202966	0.101483	−	0.994837i	$-0.467641\pi$
$149$	2.96654e26	0.202966	0.101483	+	0.994837i	$0.467641\pi$
$150$	0	0
$151$	2.46628e26	0.142834	0.0714169	−	0.997447i	$-0.477248\pi$
$151$	2.46628e26	0.142834	0.0714169	+	0.997447i	$0.477248\pi$
$152$	−9.62063e26	−0.513049
$153$	−1.72994e27	−0.849942
$154$	1.19400e27	0.540747
$155$	0	0
$156$	−2.93281e27	−1.13038
$157$	6.49248e26	0.231028	0.115514	−	0.993306i	$-0.463148\pi$
$157$	6.49248e26	0.231028	0.115514	+	0.993306i	$0.463148\pi$
$158$	8.65959e27	2.84632
$159$	−3.12691e27	−0.949841
$160$	0	0
$161$	−1.25343e27	−0.325670
$162$	7.45693e26	0.179317
$163$	4.33189e26	0.0964567	0.0482283	−	0.998836i	$-0.484642\pi$
$163$	4.33189e26	0.0964567	0.0482283	+	0.998836i	$0.484642\pi$
$164$	−4.38291e27	−0.904097
$165$	0	0
$166$	−9.18516e27	−1.62830
$167$	−1.30454e26	−0.0214536	−0.0107268	−	0.999942i	$-0.503415\pi$
$167$	−1.30454e26	−0.0214536	−0.0107268	+	0.999942i	$0.503415\pi$
$168$	1.40541e27	0.214505
$169$	3.35310e27	0.475185
$170$	0	0
$171$	2.82729e27	0.345875
$172$	2.15034e28	2.44569
$173$	6.64872e27	0.703335	0.351667	−	0.936125i	$-0.385615\pi$
$173$	6.64872e27	0.703335	0.351667	+	0.936125i	$0.385615\pi$
$174$	−1.57359e28	−1.54891
$175$	0	0
$176$	1.44345e26	0.0123167
$177$	−1.12392e28	−0.893447
$178$	1.23920e28	0.918102
$179$	1.37345e28	0.948749	0.474375	−	0.880323i	$-0.342674\pi$
$179$	1.37345e28	0.948749	0.474375	+	0.880323i	$0.342674\pi$
$180$	0	0
$181$	−2.24199e28	−1.34788	−0.673941	−	0.738786i	$-0.735400\pi$
$181$	−2.24199e28	−1.34788	−0.673941	+	0.738786i	$0.735400\pi$
$182$	−1.31413e28	−0.737473
$183$	−4.06653e27	−0.213101
$184$	1.75087e28	0.857101
$185$	0	0
$186$	−1.60652e28	−0.687026
$187$	−2.83932e28	−1.13552
$188$	−5.24386e28	−1.96191
$189$	−1.03261e28	−0.361547
$190$	0	0
$191$	−6.91841e26	−0.0212368	−0.0106184	−	0.999944i	$-0.503380\pi$
$191$	−6.91841e26	−0.0212368	−0.0106184	+	0.999944i	$0.503380\pi$
$192$	3.25343e28	0.935570
$193$	−6.51372e28	−1.75535	−0.877673	−	0.479259i	$-0.840905\pi$
$193$	−6.51372e28	−1.75535	−0.877673	+	0.479259i	$0.840905\pi$
$194$	−3.30384e28	−0.834636
$195$	0	0
$196$	−6.22923e28	−1.38431
$197$	−4.73638e27	−0.0987686	−0.0493843	−	0.998780i	$-0.515726\pi$
$197$	−4.73638e27	−0.0987686	−0.0493843	+	0.998780i	$0.515726\pi$
$198$	4.90144e28	0.959420
$199$	−3.76031e28	−0.691131	−0.345565	−	0.938395i	$-0.612313\pi$
$199$	−3.76031e28	−0.691131	−0.345565	+	0.938395i	$0.612313\pi$
$200$	0	0
$201$	−1.97858e28	−0.320925
$202$	−9.75936e28	−1.48775
$203$	−4.35134e28	−0.623623
$204$	−8.80447e28	−1.18666
$205$	0	0
$206$	1.45547e29	1.73645
$207$	−5.14543e28	−0.577820
$208$	−1.58868e27	−0.0167975
$209$	4.64038e28	0.462088
$210$	0	0
$211$	2.10105e28	0.185740	0.0928700	−	0.995678i	$-0.470396\pi$
$211$	2.10105e28	0.185740	0.0928700	+	0.995678i	$0.470396\pi$
$212$	3.18190e29	2.65148
$213$	2.10566e28	0.165441
$214$	3.66527e29	2.71603
$215$	0	0
$216$	1.44242e29	0.951522
$217$	−4.44237e28	−0.276610
$218$	1.84428e29	1.08423
$219$	−2.27051e28	−0.126058
$220$	0	0
$221$	3.12500e29	1.54863
$222$	7.91739e28	0.370826
$223$	2.96364e29	1.31224	0.656122	−	0.754655i	$-0.272196\pi$
$223$	2.96364e29	1.31224	0.656122	+	0.754655i	$0.272196\pi$
$224$	9.07325e28	0.379894
$225$	0	0
$226$	−3.95051e29	−1.48012
$227$	−2.89017e29	−1.02471	−0.512354	−	0.858775i	$-0.671226\pi$
$227$	−2.89017e29	−1.02471	−0.512354	+	0.858775i	$0.671226\pi$
$228$	1.43894e29	0.482899
$229$	1.38694e29	0.440670	0.220335	−	0.975424i	$-0.429285\pi$
$229$	1.38694e29	0.440670	0.220335	+	0.975424i	$0.429285\pi$
$230$	0	0
$231$	−6.77882e28	−0.193199
$232$	6.07821e29	1.64126
$233$	1.00825e29	0.258000	0.129000	−	0.991645i	$-0.458823\pi$
$233$	1.00825e29	0.258000	0.129000	+	0.991645i	$0.458823\pi$
$234$	−5.39460e29	−1.30846
$235$	0	0
$236$	1.14368e30	2.49405
$237$	−4.91641e29	−1.01694
$238$	−3.94511e29	−0.774189
$239$	−5.29180e29	−0.985438	−0.492719	−	0.870188i	$-0.663997\pi$
$239$	−5.29180e29	−0.985438	−0.492719	+	0.870188i	$0.663997\pi$
$240$	0	0
$241$	−4.04250e28	−0.0678324	−0.0339162	−	0.999425i	$-0.510798\pi$
$241$	−4.04250e28	−0.0678324	−0.0339162	+	0.999425i	$0.510798\pi$
$242$	−2.09832e29	−0.334333
$243$	−6.78242e29	−1.02637
$244$	4.13804e29	0.594870
$245$	0	0
$246$	4.03217e29	0.523420
$247$	−5.10727e29	−0.630198
$248$	6.20538e29	0.727985
$249$	5.21480e29	0.581763
$250$	0	0
$251$	4.46094e29	0.450303	0.225151	−	0.974324i	$-0.427712\pi$
$251$	4.46094e29	0.450303	0.225151	+	0.974324i	$0.427712\pi$
$252$	4.20284e29	0.403678
$253$	−8.44510e29	−0.771966
$254$	1.04127e30	0.906026
$255$	0	0
$256$	−1.23915e30	−0.977517
$257$	−9.74169e29	−0.731931	−0.365965	−	0.930628i	$-0.619261\pi$
$257$	−9.74169e29	−0.731931	−0.365965	+	0.930628i	$0.619261\pi$
$258$	−1.97826e30	−1.41591
$259$	2.18933e29	0.149302
$260$	0	0
$261$	−1.78625e30	−1.10646
$262$	2.01762e30	1.19144
$263$	−1.52948e30	−0.861188	−0.430594	−	0.902546i	$-0.641696\pi$
$263$	−1.52948e30	−0.861188	−0.430594	+	0.902546i	$0.641696\pi$
$264$	9.46907e29	0.508462
$265$	0	0
$266$	6.44759e29	0.315048
$267$	−7.03545e29	−0.328020
$268$	2.01338e30	0.895860
$269$	2.62915e29	0.111663	0.0558317	−	0.998440i	$-0.482219\pi$
$269$	2.62915e29	0.111663	0.0558317	+	0.998440i	$0.482219\pi$
$270$	0	0
$271$	−2.83737e30	−1.09850	−0.549249	−	0.835658i	$-0.685086\pi$
$271$	−2.83737e30	−1.09850	−0.549249	+	0.835658i	$0.685086\pi$
$272$	−4.76933e28	−0.0176338
$273$	7.46087e29	0.263485
$274$	−8.93188e30	−3.01343
$275$	0	0
$276$	−2.61875e30	−0.806733
$277$	−2.96419e30	−0.872788	−0.436394	−	0.899756i	$-0.643745\pi$
$277$	−2.96419e30	−0.872788	−0.436394	+	0.899756i	$0.643745\pi$
$278$	2.53972e30	0.714868
$279$	−1.82363e30	−0.490776
$280$	0	0
$281$	3.78581e30	0.931816	0.465908	−	0.884833i	$-0.345728\pi$
$281$	3.78581e30	0.931816	0.465908	+	0.884833i	$0.345728\pi$
$282$	4.82423e30	1.13583
$283$	5.09128e30	1.14682	0.573412	−	0.819267i	$-0.305619\pi$
$283$	5.09128e30	1.14682	0.573412	+	0.819267i	$0.305619\pi$
$284$	−2.14269e30	−0.461829
$285$	0	0
$286$	−8.85405e30	−1.74810
$287$	1.11499e30	0.210739
$288$	3.72463e30	0.674027
$289$	3.61083e30	0.625727
$290$	0	0
$291$	1.87573e30	0.298200
$292$	2.31044e30	0.351891
$293$	−6.28617e30	−0.917362	−0.458681	−	0.888601i	$-0.651678\pi$
$293$	−6.28617e30	−0.917362	−0.458681	+	0.888601i	$0.651678\pi$
$294$	5.73074e30	0.801437
$295$	0	0
$296$	−3.05820e30	−0.392933
$297$	−6.95730e30	−0.857008
$298$	2.77714e30	0.328016
$299$	9.29481e30	1.05281
$300$	0	0
$301$	−5.47033e30	−0.570075
$302$	2.30882e30	0.230836
$303$	5.54080e30	0.531544
$304$	7.79464e28	0.00717590
$305$	0	0
$306$	−1.61949e31	−1.37360
$307$	1.10314e30	0.0898261	0.0449130	−	0.998991i	$-0.485699\pi$
$307$	1.10314e30	0.0898261	0.0449130	+	0.998991i	$0.485699\pi$
$308$	6.89803e30	0.539313
$309$	−8.26332e30	−0.620402
$310$	0	0
$311$	2.41872e31	1.67525	0.837627	−	0.546242i	$-0.183942\pi$
$311$	2.41872e31	1.67525	0.837627	+	0.546242i	$0.183942\pi$
$312$	−1.04218e31	−0.693443
$313$	−1.66307e31	−1.06318	−0.531589	−	0.847002i	$-0.678405\pi$
$313$	−1.66307e31	−1.06318	−0.531589	+	0.847002i	$0.678405\pi$
$314$	6.07797e30	0.373369
$315$	0	0
$316$	5.00287e31	2.83877
$317$	2.91127e31	1.58797	0.793984	−	0.607939i	$-0.208003\pi$
$317$	2.91127e31	1.58797	0.793984	+	0.607939i	$0.208003\pi$
$318$	−2.92727e31	−1.53505
$319$	−2.93174e31	−1.47823
$320$	0	0
$321$	−2.08093e31	−0.970385
$322$	−1.17341e31	−0.526321
$323$	−1.53324e31	−0.661573
$324$	4.30806e30	0.178842
$325$	0	0
$326$	4.05532e30	0.155885
$327$	−1.04708e31	−0.387375
$328$	−1.55748e31	−0.554625
$329$	1.33401e31	0.457308
$330$	0	0
$331$	1.93746e31	0.615719	0.307860	−	0.951432i	$-0.400387\pi$
$331$	1.93746e31	0.615719	0.307860	+	0.951432i	$0.400387\pi$
$332$	−5.30651e31	−1.62399
$333$	8.98737e30	0.264899
$334$	−1.22125e30	−0.0346715
$335$	0	0
$336$	−1.13867e29	−0.00300024
$337$	2.56947e30	0.0652335	0.0326167	−	0.999468i	$-0.489616\pi$
$337$	2.56947e30	0.0652335	0.0326167	+	0.999468i	$0.489616\pi$
$338$	3.13902e31	0.767954
$339$	2.24287e31	0.528821
$340$	0	0
$341$	−2.99308e31	−0.655675
$342$	2.64678e31	0.558974
$343$	3.42981e31	0.698383
$344$	7.64129e31	1.50033
$345$	0	0
$346$	6.22423e31	1.13667
$347$	3.68925e31	0.649860	0.324930	−	0.945738i	$-0.394659\pi$
$347$	3.68925e31	0.649860	0.324930	+	0.945738i	$0.394659\pi$
$348$	−9.09106e31	−1.54481
$349$	8.90327e31	1.45959	0.729796	−	0.683665i	$-0.239615\pi$
$349$	8.90327e31	1.45959	0.729796	+	0.683665i	$0.239615\pi$
$350$	0	0
$351$	7.65731e31	1.16879
$352$	6.11317e31	0.900499
$353$	1.18792e32	1.68890	0.844448	−	0.535638i	$-0.179929\pi$
$353$	1.18792e32	1.68890	0.844448	+	0.535638i	$0.179929\pi$
$354$	−1.05216e32	−1.44391
$355$	0	0
$356$	7.15917e31	0.915668
$357$	2.23980e31	0.276603
$358$	1.28577e32	1.53329
$359$	−3.43106e31	−0.395137	−0.197569	−	0.980289i	$-0.563305\pi$
$359$	−3.43106e31	−0.395137	−0.197569	+	0.980289i	$0.563305\pi$
$360$	0	0
$361$	−6.80184e31	−0.730780
$362$	−2.09885e32	−2.17833
$363$	1.19130e31	0.119451
$364$	−7.59208e31	−0.735518
$365$	0	0
$366$	−3.80690e31	−0.344396
$367$	1.81832e32	1.58981	0.794904	−	0.606735i	$-0.207521\pi$
$367$	1.81832e32	1.58981	0.794904	+	0.606735i	$0.207521\pi$
$368$	−1.41856e30	−0.0119881
$369$	4.57710e31	0.373904
$370$	0	0
$371$	−8.09454e31	−0.618043
$372$	−9.28126e31	−0.685205
$373$	4.57515e31	0.326621	0.163311	−	0.986575i	$-0.447783\pi$
$373$	4.57515e31	0.326621	0.163311	+	0.986575i	$0.447783\pi$
$374$	−2.65804e32	−1.83513
$375$	0	0
$376$	−1.86342e32	−1.20355
$377$	3.22672e32	2.01602
$378$	−9.66685e31	−0.584302
$379$	−5.21676e31	−0.305078	−0.152539	−	0.988297i	$-0.548745\pi$
$379$	−5.21676e31	−0.305078	−0.152539	+	0.988297i	$0.548745\pi$
$380$	0	0
$381$	−5.91171e31	−0.323706
$382$	−6.47670e30	−0.0343212
$383$	−1.65045e32	−0.846481	−0.423240	−	0.906017i	$-0.639107\pi$
$383$	−1.65045e32	−0.846481	−0.423240	+	0.906017i	$0.639107\pi$
$384$	1.86964e32	0.928149
$385$	0	0
$386$	−6.09785e32	−2.83684
$387$	−2.24561e32	−1.01146
$388$	−1.90871e32	−0.832423
$389$	2.98846e32	1.26205	0.631025	−	0.775762i	$-0.282634\pi$
$389$	2.98846e32	1.26205	0.631025	+	0.775762i	$0.282634\pi$
$390$	0	0
$391$	2.79036e32	1.10523
$392$	−2.21358e32	−0.849217
$393$	−1.14549e32	−0.425681
$394$	−4.43399e31	−0.159622
$395$	0	0
$396$	2.83169e32	0.956877
$397$	−3.98902e32	−1.30612	−0.653062	−	0.757304i	$-0.726516\pi$
$397$	−3.98902e32	−1.30612	−0.653062	+	0.757304i	$0.726516\pi$
$398$	−3.52023e32	−1.11695
$399$	−3.66057e31	−0.112561
$400$	0	0
$401$	1.04555e32	0.302024	0.151012	−	0.988532i	$-0.451747\pi$
$401$	1.04555e32	0.302024	0.151012	+	0.988532i	$0.451747\pi$
$402$	−1.85226e32	−0.518651
$403$	3.29423e32	0.894213
$404$	−5.63824e32	−1.48380
$405$	0	0
$406$	−4.07352e32	−1.00785
$407$	1.47508e32	0.353904
$408$	−3.12869e32	−0.727966
$409$	5.94901e32	1.34247	0.671234	−	0.741246i	$-0.265765\pi$
$409$	5.94901e32	1.34247	0.671234	+	0.741246i	$0.265765\pi$
$410$	0	0
$411$	5.07100e32	1.07664
$412$	8.40864e32	1.73185
$413$	−2.90946e32	−0.581349
$414$	−4.81692e32	−0.933825
$415$	0	0
$416$	−6.72825e32	−1.22810
$417$	−1.44191e32	−0.255409
$418$	4.34411e32	0.746788
$419$	−1.11614e33	−1.86227	−0.931136	−	0.364671i	$-0.881181\pi$
$419$	−1.11614e33	−1.86227	−0.931136	+	0.364671i	$0.881181\pi$
$420$	0	0
$421$	−4.92553e32	−0.774331	−0.387166	−	0.922010i	$-0.626546\pi$
$421$	−4.92553e32	−0.774331	−0.387166	+	0.922010i	$0.626546\pi$
$422$	1.96691e32	0.300177
$423$	5.47619e32	0.811379
$424$	1.13070e33	1.62657
$425$	0	0
$426$	1.97123e32	0.267372
$427$	−1.05269e32	−0.138661
$428$	2.11752e33	2.70883
$429$	5.02682e32	0.624564
$430$	0	0
$431$	−4.71497e31	−0.0552730	−0.0276365	−	0.999618i	$-0.508798\pi$
$431$	−4.71497e31	−0.0552730	−0.0276365	+	0.999618i	$0.508798\pi$
$432$	−1.16865e31	−0.0133087
$433$	−3.61224e30	−0.00399648	−0.00199824	−	0.999998i	$-0.500636\pi$
$433$	−3.61224e30	−0.00399648	−0.00199824	+	0.999998i	$0.500636\pi$
$434$	−4.15875e32	−0.447034
$435$	0	0
$436$	1.06549e33	1.08136
$437$	−4.56036e32	−0.449760
$438$	−2.12555e32	−0.203725
$439$	3.57029e32	0.332580	0.166290	−	0.986077i	$-0.446821\pi$
$439$	3.57029e32	0.332580	0.166290	+	0.986077i	$0.446821\pi$
$440$	0	0
$441$	6.50522e32	0.572505
$442$	2.92549e33	2.50276
$443$	−1.54821e33	−1.28761	−0.643805	−	0.765190i	$-0.722645\pi$
$443$	−1.54821e33	−1.28761	−0.643805	+	0.765190i	$0.722645\pi$
$444$	4.57408e32	0.369842
$445$	0	0
$446$	2.77442e33	2.12074
$447$	−1.57670e32	−0.117194
$448$	8.42208e32	0.608757
$449$	2.49721e33	1.75540	0.877701	−	0.479209i	$-0.159076\pi$
$449$	2.49721e33	1.75540	0.877701	+	0.479209i	$0.159076\pi$
$450$	0	0
$451$	7.51230e32	0.499535
$452$	−2.28232e33	−1.47620
$453$	−1.31082e32	−0.0824734
$454$	−2.70564e33	−1.65605
$455$	0	0
$456$	5.11331e32	0.296238
$457$	−3.97112e32	−0.223851	−0.111926	−	0.993717i	$-0.535702\pi$
$457$	−3.97112e32	−0.223851	−0.111926	+	0.993717i	$0.535702\pi$
$458$	1.29839e33	0.712174
$459$	2.29878e33	1.22698
$460$	0	0
$461$	−8.07920e32	−0.408420	−0.204210	−	0.978927i	$-0.565463\pi$
$461$	−8.07920e32	−0.408420	−0.204210	+	0.978927i	$0.565463\pi$
$462$	−6.34602e32	−0.312232
$463$	−9.97158e32	−0.477531	−0.238766	−	0.971077i	$-0.576743\pi$
$463$	−9.97158e32	−0.477531	−0.238766	+	0.971077i	$0.576743\pi$
$464$	−4.92457e31	−0.0229559
$465$	0	0
$466$	9.43880e32	0.416959
$467$	−3.43650e33	−1.47793	−0.738967	−	0.673742i	$-0.764686\pi$
$467$	−3.43650e33	−1.47793	−0.738967	+	0.673742i	$0.764686\pi$
$468$	−3.11660e33	−1.30499
$469$	−5.12190e32	−0.208819
$470$	0	0
$471$	−3.45072e32	−0.133398
$472$	4.06411e33	1.53000
$473$	−3.68567e33	−1.35130
$474$	−4.60252e33	−1.64349
$475$	0	0
$476$	−2.27919e33	−0.772136
$477$	−3.32287e33	−1.09656
$478$	−4.95394e33	−1.59258
$479$	4.30103e33	1.34704	0.673518	−	0.739171i	$-0.264782\pi$
$479$	4.30103e33	1.34704	0.673518	+	0.739171i	$0.264782\pi$
$480$	0	0
$481$	−1.62350e33	−0.482656
$482$	−3.78440e32	−0.109625
$483$	6.66193e32	0.188045
$484$	−1.21225e33	−0.333447
$485$	0	0
$486$	−6.34939e33	−1.65874
$487$	1.77385e33	0.451654	0.225827	−	0.974167i	$-0.427492\pi$
$487$	1.77385e33	0.451654	0.225827	+	0.974167i	$0.427492\pi$
$488$	1.47047e33	0.364928
$489$	−2.30237e32	−0.0556948
$490$	0	0
$491$	7.59245e33	1.74527	0.872637	−	0.488370i	$-0.162408\pi$
$491$	7.59245e33	1.74527	0.872637	+	0.488370i	$0.162408\pi$
$492$	2.32949e33	0.522033
$493$	9.68683e33	2.11639
$494$	−4.78120e33	−1.01847
$495$	0	0
$496$	−5.02760e31	−0.0101822
$497$	5.45088e32	0.107649
$498$	4.88186e33	0.940196
$499$	2.93681e33	0.551593	0.275797	−	0.961216i	$-0.411058\pi$
$499$	2.93681e33	0.551593	0.275797	+	0.961216i	$0.411058\pi$
$500$	0	0
$501$	6.93353e31	0.0123875
$502$	4.17613e33	0.727742
$503$	−4.24338e33	−0.721294	−0.360647	−	0.932702i	$-0.617444\pi$
$503$	−4.24338e33	−0.721294	−0.360647	+	0.932702i	$0.617444\pi$
$504$	1.49349e33	0.247640
$505$	0	0
$506$	−7.90592e33	−1.24759
$507$	−1.78215e33	−0.274376
$508$	6.01567e33	0.903624
$509$	2.39447e33	0.350943	0.175472	−	0.984484i	$-0.443855\pi$
$509$	2.39447e33	0.350943	0.175472	+	0.984484i	$0.443855\pi$
$510$	0	0
$511$	−5.87761e32	−0.0820237
$512$	2.03101e32	0.0276591
$513$	−3.75695e33	−0.499307
$514$	−9.11972e33	−1.18289
$515$	0	0
$516$	−1.14289e34	−1.41216
$517$	8.98796e33	1.08400
$518$	2.04955e33	0.241289
$519$	−3.53376e33	−0.406111
$520$	0	0
$521$	8.32276e33	0.911582	0.455791	−	0.890087i	$-0.349356\pi$
$521$	8.32276e33	0.911582	0.455791	+	0.890087i	$0.349356\pi$
$522$	−1.67221e34	−1.78817
$523$	1.32749e34	1.38599	0.692993	−	0.720944i	$-0.256292\pi$
$523$	1.32749e34	1.38599	0.692993	+	0.720944i	$0.256292\pi$
$524$	1.16563e34	1.18829
$525$	0	0
$526$	−1.43183e34	−1.39178
$527$	9.88950e33	0.938732
$528$	−7.67185e31	−0.00711174
$529$	−2.74629e33	−0.248629
$530$	0	0
$531$	−1.19435e34	−1.03146
$532$	3.72494e33	0.314213
$533$	−8.26815e33	−0.681269
$534$	−6.58627e33	−0.530119
$535$	0	0
$536$	7.15459e33	0.549572
$537$	−7.29983e33	−0.547815
$538$	2.46129e33	0.180461
$539$	1.06769e34	0.764865
$540$	0	0
$541$	1.45952e34	0.998260	0.499130	−	0.866527i	$-0.333653\pi$
$541$	1.45952e34	0.998260	0.499130	+	0.866527i	$0.333653\pi$
$542$	−2.65622e34	−1.77530
$543$	1.19160e34	0.778277
$544$	−2.01986e34	−1.28925
$545$	0	0
$546$	6.98453e33	0.425823
$547$	3.28646e34	1.95834	0.979168	−	0.203054i	$-0.0650867\pi$
$547$	3.28646e34	1.95834	0.979168	+	0.203054i	$0.0650867\pi$
$548$	−5.16018e34	−3.00544
$549$	−4.32138e33	−0.246019
$550$	0	0
$551$	−1.58314e34	−0.861242
$552$	−9.30579e33	−0.494897
$553$	−1.27270e34	−0.661701
$554$	−2.77494e34	−1.41053
$555$	0	0
$556$	1.46726e34	0.712973
$557$	−2.79942e34	−1.33008	−0.665042	−	0.746806i	$-0.731586\pi$
$557$	−2.79942e34	−1.33008	−0.665042	+	0.746806i	$0.731586\pi$
$558$	−1.70720e34	−0.793151
$559$	4.05651e34	1.84291
$560$	0	0
$561$	1.50908e34	0.655658
$562$	3.54410e34	1.50592
$563$	2.94294e34	1.22300	0.611500	−	0.791244i	$-0.290566\pi$
$563$	2.94294e34	1.22300	0.611500	+	0.791244i	$0.290566\pi$
$564$	2.78708e34	1.13282
$565$	0	0
$566$	4.76623e34	1.85340
$567$	−1.09594e33	−0.0416869
$568$	−7.61413e33	−0.283313
$569$	1.44033e34	0.524275	0.262137	−	0.965031i	$-0.415573\pi$
$569$	1.44033e34	0.524275	0.262137	+	0.965031i	$0.415573\pi$
$570$	0	0
$571$	−6.02200e33	−0.209792	−0.104896	−	0.994483i	$-0.533451\pi$
$571$	−6.02200e33	−0.209792	−0.104896	+	0.994483i	$0.533451\pi$
$572$	−5.11522e34	−1.74347
$573$	3.67710e32	0.0122623
$574$	1.04380e34	0.340579
$575$	0	0
$576$	3.45732e34	1.08009
$577$	3.36622e34	1.02907	0.514534	−	0.857470i	$-0.327965\pi$
$577$	3.36622e34	1.02907	0.514534	+	0.857470i	$0.327965\pi$
$578$	3.38030e34	1.01125
$579$	3.46201e34	1.01355
$580$	0	0
$581$	1.34994e34	0.378542
$582$	1.75597e34	0.481925
$583$	−5.45376e34	−1.46500
$584$	8.21021e33	0.215871
$585$	0	0
$586$	−5.88482e34	−1.48256
$587$	2.29972e34	0.567152	0.283576	−	0.958950i	$-0.408479\pi$
$587$	2.29972e34	0.567152	0.283576	+	0.958950i	$0.408479\pi$
$588$	3.31080e34	0.799312
$589$	−1.61627e34	−0.382007
$590$	0	0
$591$	2.51736e33	0.0570298
$592$	2.47775e32	0.00549587
$593$	2.56446e34	0.556945	0.278472	−	0.960444i	$-0.410172\pi$
$593$	2.56446e34	0.556945	0.278472	+	0.960444i	$0.410172\pi$
$594$	−6.51311e34	−1.38503
$595$	0	0
$596$	1.60443e34	0.327146
$597$	1.99858e34	0.399064
$598$	8.70138e34	1.70147
$599$	−6.53223e34	−1.25091	−0.625455	−	0.780260i	$-0.715087\pi$
$599$	−6.53223e34	−1.25091	−0.625455	+	0.780260i	$0.715087\pi$
$600$	0	0
$601$	1.46105e34	0.268370	0.134185	−	0.990956i	$-0.457158\pi$
$601$	1.46105e34	0.268370	0.134185	+	0.990956i	$0.457158\pi$
$602$	−5.12107e34	−0.921308
$603$	−2.10258e34	−0.370498
$604$	1.33387e34	0.230224
$605$	0	0
$606$	5.18704e34	0.859038
$607$	1.63446e34	0.265165	0.132582	−	0.991172i	$-0.457673\pi$
$607$	1.63446e34	0.265165	0.132582	+	0.991172i	$0.457673\pi$
$608$	3.30112e34	0.524646
$609$	2.31271e34	0.360085
$610$	0	0
$611$	−9.89229e34	−1.47837
$612$	−9.35625e34	−1.36996
$613$	6.22253e34	0.892712	0.446356	−	0.894855i	$-0.352722\pi$
$613$	6.22253e34	0.892712	0.446356	+	0.894855i	$0.352722\pi$
$614$	1.03271e34	0.145169
$615$	0	0
$616$	2.45124e34	0.330846
$617$	−4.34980e34	−0.575314	−0.287657	−	0.957733i	$-0.592876\pi$
$617$	−4.34980e34	−0.575314	−0.287657	+	0.957733i	$0.592876\pi$
$618$	−7.73574e34	−1.00264
$619$	−1.76940e34	−0.224747	−0.112373	−	0.993666i	$-0.535845\pi$
$619$	−1.76940e34	−0.224747	−0.112373	+	0.993666i	$0.535845\pi$
$620$	0	0
$621$	6.83733e34	0.834145
$622$	2.26430e35	2.70741
$623$	−1.82125e34	−0.213437
$624$	8.44376e32	0.00969903
$625$	0	0
$626$	−1.55689e35	−1.71822
$627$	−2.46633e34	−0.266813
$628$	3.51140e34	0.372379
$629$	−4.87384e34	−0.506685
$630$	0	0
$631$	1.04208e35	1.04120	0.520601	−	0.853800i	$-0.325708\pi$
$631$	1.04208e35	1.04120	0.520601	+	0.853800i	$0.325708\pi$
$632$	1.77778e35	1.74147
$633$	−1.11669e34	−0.107248
$634$	2.72540e35	2.56634
$635$	0	0
$636$	−1.69116e35	−1.53098
$637$	−1.17511e35	−1.04313
$638$	−2.74457e35	−2.38899
$639$	2.23762e34	0.190997
$640$	0	0
$641$	−8.19994e34	−0.673109	−0.336555	−	0.941664i	$-0.609262\pi$
$641$	−8.19994e34	−0.673109	−0.336555	+	0.941664i	$0.609262\pi$
$642$	−1.94807e35	−1.56825
$643$	5.73324e34	0.452650	0.226325	−	0.974052i	$-0.427329\pi$
$643$	5.73324e34	0.452650	0.226325	+	0.974052i	$0.427329\pi$
$644$	−6.77908e34	−0.524925
$645$	0	0
$646$	−1.43535e35	−1.06918
$647$	−1.81756e35	−1.32796	−0.663979	−	0.747751i	$-0.731134\pi$
$647$	−1.81756e35	−1.32796	−0.663979	+	0.747751i	$0.731134\pi$
$648$	1.53088e34	0.109712
$649$	−1.96027e35	−1.37803
$650$	0	0
$651$	2.36110e34	0.159717
$652$	2.34286e34	0.155472
$653$	−1.90602e35	−1.24083	−0.620415	−	0.784274i	$-0.713036\pi$
$653$	−1.90602e35	−1.24083	−0.620415	+	0.784274i	$0.713036\pi$
$654$	−9.80226e34	−0.626043
$655$	0	0
$656$	1.26187e33	0.00775742
$657$	−2.41280e34	−0.145531
$658$	1.24884e35	0.739064
$659$	−6.08809e34	−0.353520	−0.176760	−	0.984254i	$-0.556562\pi$
$659$	−6.08809e34	−0.353520	−0.176760	+	0.984254i	$0.556562\pi$
$660$	0	0
$661$	−2.17257e35	−1.21466	−0.607332	−	0.794448i	$-0.707760\pi$
$661$	−2.17257e35	−1.21466	−0.607332	+	0.794448i	$0.707760\pi$
$662$	1.81376e35	0.995074
$663$	−1.66092e35	−0.894190
$664$	−1.88568e35	−0.996249
$665$	0	0
$666$	8.41357e34	0.428107
$667$	2.88119e35	1.43879
$668$	−7.05547e33	−0.0345796
$669$	−1.57516e35	−0.757700
$670$	0	0
$671$	−7.09259e34	−0.328680
$672$	−4.82238e34	−0.219354
$673$	−7.80776e34	−0.348609	−0.174304	−	0.984692i	$-0.555768\pi$
$673$	−7.80776e34	−0.348609	−0.174304	+	0.984692i	$0.555768\pi$
$674$	2.40542e34	0.105425
$675$	0	0
$676$	1.81349e35	0.765918
$677$	−2.43537e35	−1.00973	−0.504866	−	0.863198i	$-0.668458\pi$
$677$	−2.43537e35	−1.00973	−0.504866	+	0.863198i	$0.668458\pi$
$678$	2.09968e35	0.854636
$679$	4.85565e34	0.194033
$680$	0	0
$681$	1.53611e35	0.591674
$682$	−2.80199e35	−1.05965
$683$	4.30905e35	1.60001	0.800004	−	0.599994i	$-0.204830\pi$
$683$	4.30905e35	1.60001	0.800004	+	0.599994i	$0.204830\pi$
$684$	1.52912e35	0.557492
$685$	0	0
$686$	3.21083e35	1.12867
$687$	−7.37149e34	−0.254446
$688$	−6.19098e33	−0.0209848
$689$	6.00249e35	1.99798
$690$	0	0
$691$	2.98951e35	0.959675	0.479838	−	0.877357i	$-0.340696\pi$
$691$	2.98951e35	0.959675	0.479838	+	0.877357i	$0.340696\pi$
$692$	3.59590e35	1.13366
$693$	−7.20364e34	−0.223042
$694$	3.45371e35	1.05025
$695$	0	0
$696$	−3.23053e35	−0.947674
$697$	−2.48215e35	−0.715186
$698$	8.33483e35	2.35887
$699$	−5.35880e34	−0.148971
$700$	0	0
$701$	−5.64961e35	−1.51546	−0.757728	−	0.652570i	$-0.773691\pi$
$701$	−5.64961e35	−1.51546	−0.757728	+	0.652570i	$0.773691\pi$
$702$	7.16843e35	1.88890
$703$	7.96544e34	0.206190
$704$	5.67444e35	1.44299
$705$	0	0
$706$	1.11208e36	2.72945
$707$	1.43433e35	0.345866
$708$	−6.07861e35	−1.44009
$709$	−3.85512e35	−0.897345	−0.448672	−	0.893696i	$-0.648103\pi$
$709$	−3.85512e35	−0.897345	−0.448672	+	0.893696i	$0.648103\pi$
$710$	0	0
$711$	−5.22452e35	−1.17402
$712$	2.54403e35	0.561724
$713$	2.94147e35	0.638183
$714$	2.09680e35	0.447023
$715$	0	0
$716$	7.42821e35	1.52922
$717$	2.81256e35	0.569000
$718$	−3.21200e35	−0.638588
$719$	−9.36871e35	−1.83050	−0.915248	−	0.402892i	$-0.868005\pi$
$719$	−9.36871e35	−1.83050	−0.915248	+	0.402892i	$0.868005\pi$
$720$	0	0
$721$	−2.13910e35	−0.403684
$722$	−6.36757e35	−1.18102
$723$	2.14856e34	0.0391669
$724$	−1.21256e36	−2.17256
$725$	0	0
$726$	1.11525e35	0.193047
$727$	−3.25564e35	−0.553931	−0.276966	−	0.960880i	$-0.589329\pi$
$727$	−3.25564e35	−0.553931	−0.276966	+	0.960880i	$0.589329\pi$
$728$	−2.69787e35	−0.451210
$729$	2.92991e35	0.481681
$730$	0	0
$731$	1.21779e36	1.93466
$732$	−2.19935e35	−0.343483
$733$	−2.07689e35	−0.318870	−0.159435	−	0.987208i	$-0.550967\pi$
$733$	−2.07689e35	−0.318870	−0.159435	+	0.987208i	$0.550967\pi$
$734$	1.70223e36	2.56931
$735$	0	0
$736$	−6.00776e35	−0.876475
$737$	−3.45092e35	−0.494984
$738$	4.28487e35	0.604273
$739$	−1.12620e36	−1.56156	−0.780781	−	0.624805i	$-0.785179\pi$
$739$	−1.12620e36	−1.56156	−0.780781	+	0.624805i	$0.785179\pi$
$740$	0	0
$741$	2.71449e35	0.363881
$742$	−7.57774e35	−0.998829
$743$	−7.41657e35	−0.961264	−0.480632	−	0.876922i	$-0.659593\pi$
$743$	−7.41657e35	−0.961264	−0.480632	+	0.876922i	$0.659593\pi$
$744$	−3.29812e35	−0.420344
$745$	0	0
$746$	4.28304e35	0.527858
$747$	5.54161e35	0.671628
$748$	−1.53562e36	−1.83027
$749$	−5.38685e35	−0.631411
$750$	0	0
$751$	−9.24971e35	−1.04865	−0.524323	−	0.851520i	$-0.675681\pi$
$751$	−9.24971e35	−1.04865	−0.524323	+	0.851520i	$0.675681\pi$
$752$	1.50975e34	0.0168338
$753$	−2.37096e35	−0.260008
$754$	3.02071e36	3.25812
$755$	0	0
$756$	−5.58479e35	−0.582753
$757$	2.20319e35	0.226127	0.113064	−	0.993588i	$-0.463934\pi$
$757$	2.20319e35	0.226127	0.113064	+	0.993588i	$0.463934\pi$
$758$	−4.88369e35	−0.493041
$759$	4.48852e35	0.445739
$760$	0	0
$761$	−3.87186e35	−0.372059	−0.186029	−	0.982544i	$-0.559562\pi$
$761$	−3.87186e35	−0.372059	−0.186029	+	0.982544i	$0.559562\pi$
$762$	−5.53427e35	−0.523147
$763$	−2.71054e35	−0.252057
$764$	−3.74176e34	−0.0342302
$765$	0	0
$766$	−1.54507e36	−1.36801
$767$	2.15750e36	1.87936
$768$	6.58601e35	0.564426
$769$	−5.73844e35	−0.483854	−0.241927	−	0.970294i	$-0.577779\pi$
$769$	−5.73844e35	−0.483854	−0.241927	+	0.970294i	$0.577779\pi$
$770$	0	0
$771$	5.17765e35	0.422623
$772$	−3.52289e36	−2.82932
$773$	−1.94109e35	−0.153392	−0.0766959	−	0.997055i	$-0.524437\pi$
$773$	−1.94109e35	−0.153392	−0.0766959	+	0.997055i	$0.524437\pi$
$774$	−2.10224e36	−1.63463
$775$	0	0
$776$	−6.78267e35	−0.510657
$777$	−1.16362e35	−0.0862080
$778$	2.79766e36	2.03962
$779$	4.05665e35	0.291038
$780$	0	0
$781$	3.67257e35	0.255171
$782$	2.61221e36	1.78617
$783$	2.37360e36	1.59730
$784$	1.79344e34	0.0118778
$785$	0	0
$786$	−1.07235e36	−0.687949
$787$	−7.50226e35	−0.473705	−0.236852	−	0.971546i	$-0.576116\pi$
$787$	−7.50226e35	−0.473705	−0.236852	+	0.971546i	$0.576116\pi$
$788$	−2.56163e35	−0.159198
$789$	8.12912e35	0.497257
$790$	0	0
$791$	5.80607e35	0.344093
$792$	1.00625e36	0.587004
$793$	7.80622e35	0.448256
$794$	−3.73434e36	−2.11085
$795$	0	0
$796$	−2.03373e36	−1.11399
$797$	2.78320e36	1.50077	0.750387	−	0.660998i	$-0.229867\pi$
$797$	2.78320e36	1.50077	0.750387	+	0.660998i	$0.229867\pi$
$798$	−3.42686e35	−0.181911
$799$	−2.96973e36	−1.55197
$800$	0	0
$801$	−7.47636e35	−0.378690
$802$	9.78801e35	0.488107
$803$	−3.96008e35	−0.194429
$804$	−1.07010e36	−0.517276
$805$	0	0
$806$	3.08391e36	1.44515
$807$	−1.39738e35	−0.0644754
$808$	−2.00357e36	−0.910252
$809$	2.84960e36	1.27476	0.637379	−	0.770550i	$-0.280018\pi$
$809$	2.84960e36	1.27476	0.637379	+	0.770550i	$0.280018\pi$
$810$	0	0
$811$	−2.18452e36	−0.947535	−0.473767	−	0.880650i	$-0.657106\pi$
$811$	−2.18452e36	−0.947535	−0.473767	+	0.880650i	$0.657106\pi$
$812$	−2.35338e36	−1.00518
$813$	1.50804e36	0.634282
$814$	1.38090e36	0.571950
$815$	0	0
$816$	2.53487e34	0.0101819
$817$	−1.99027e36	−0.787291
$818$	5.56920e36	2.16958
$819$	7.92844e35	0.304186
$820$	0	0
$821$	−3.44892e36	−1.28349	−0.641746	−	0.766917i	$-0.721790\pi$
$821$	−3.44892e36	−1.28349	−0.641746	+	0.766917i	$0.721790\pi$
$822$	4.74724e36	1.73998
$823$	6.75510e35	0.243856	0.121928	−	0.992539i	$-0.461092\pi$
$823$	6.75510e35	0.243856	0.121928	+	0.992539i	$0.461092\pi$
$824$	2.98803e36	1.06242
$825$	0	0
$826$	−2.72370e36	−0.939527
$827$	−1.98402e36	−0.674105	−0.337053	−	0.941486i	$-0.609430\pi$
$827$	−1.98402e36	−0.674105	−0.337053	+	0.941486i	$0.609430\pi$
$828$	−2.78286e36	−0.931349
$829$	1.25430e36	0.413496	0.206748	−	0.978394i	$-0.433712\pi$
$829$	1.25430e36	0.413496	0.206748	+	0.978394i	$0.433712\pi$
$830$	0	0
$831$	1.57545e36	0.503955
$832$	−6.24537e36	−1.96796
$833$	−3.52777e36	−1.09506
$834$	−1.34985e36	−0.412771
$835$	0	0
$836$	2.50971e36	0.744808
$837$	2.42326e36	0.708487
$838$	−1.04488e37	−3.00965
$839$	3.59072e36	1.01896	0.509480	−	0.860483i	$-0.329838\pi$
$839$	3.59072e36	1.01896	0.509480	+	0.860483i	$0.329838\pi$
$840$	0	0
$841$	6.37178e36	1.75514
$842$	−4.61106e36	−1.25141
$843$	−2.01214e36	−0.538038
$844$	1.13633e36	0.299381
$845$	0	0
$846$	5.12656e36	1.31128
$847$	3.08390e35	0.0777245
$848$	−9.16091e34	−0.0227505
$849$	−2.70599e36	−0.662185
$850$	0	0
$851$	−1.44964e36	−0.344462
$852$	1.13883e36	0.266664
$853$	−4.77260e35	−0.110127	−0.0550633	−	0.998483i	$-0.517536\pi$
$853$	−4.77260e35	−0.110127	−0.0550633	+	0.998483i	$0.517536\pi$
$854$	−9.85483e35	−0.224092
$855$	0	0
$856$	7.52468e36	1.66175
$857$	3.37504e36	0.734545	0.367272	−	0.930113i	$-0.380292\pi$
$857$	3.37504e36	0.734545	0.367272	+	0.930113i	$0.380292\pi$
$858$	4.70588e36	1.00937
$859$	4.53153e36	0.957923	0.478961	−	0.877836i	$-0.341013\pi$
$859$	4.53153e36	0.957923	0.478961	+	0.877836i	$0.341013\pi$
$860$	0	0
$861$	−5.92608e35	−0.121683
$862$	−4.41394e35	−0.0893276
$863$	2.57027e36	0.512677	0.256338	−	0.966587i	$-0.417484\pi$
$863$	2.57027e36	0.512677	0.256338	+	0.966587i	$0.417484\pi$
$864$	−4.94935e36	−0.973030
$865$	0	0
$866$	−3.38162e34	−0.00645878
$867$	−1.91914e36	−0.361299
$868$	−2.40262e36	−0.445849
$869$	−8.57490e36	−1.56849
$870$	0	0
$871$	3.79814e36	0.675062
$872$	3.78625e36	0.663366
$873$	1.99328e36	0.344262
$874$	−4.26920e36	−0.726865
$875$	0	0
$876$	−1.22798e36	−0.203185
$877$	−1.02943e37	−1.67919	−0.839595	−	0.543213i	$-0.817208\pi$
$877$	−1.02943e37	−1.67919	−0.839595	+	0.543213i	$0.817208\pi$
$878$	3.34234e36	0.537488
$879$	3.34106e36	0.529692
$880$	0	0
$881$	−1.32860e36	−0.204737	−0.102369	−	0.994747i	$-0.532642\pi$
$881$	−1.32860e36	−0.204737	−0.102369	+	0.994747i	$0.532642\pi$
$882$	6.08989e36	0.925235
$883$	−8.24109e36	−1.23446	−0.617228	−	0.786784i	$-0.711745\pi$
$883$	−8.24109e36	−1.23446	−0.617228	+	0.786784i	$0.711745\pi$
$884$	1.69013e37	2.49613
$885$	0	0
$886$	−1.44937e37	−2.08093
$887$	2.45432e36	0.347445	0.173722	−	0.984795i	$-0.444421\pi$
$887$	2.45432e36	0.347445	0.173722	+	0.984795i	$0.444421\pi$
$888$	1.62541e36	0.226883
$889$	−1.53035e36	−0.210629
$890$	0	0
$891$	−7.38400e35	−0.0988144
$892$	1.60286e37	2.11512
$893$	4.85351e36	0.631557
$894$	−1.47604e36	−0.189399
$895$	0	0
$896$	4.83989e36	0.603928
$897$	−4.94014e36	−0.607902
$898$	2.33778e37	2.83693
$899$	1.02114e37	1.22205
$900$	0	0
$901$	1.80199e37	2.09745
$902$	7.03267e36	0.807307
$903$	2.90745e36	0.329166
$904$	−8.11028e36	−0.905587
$905$	0	0
$906$	−1.22713e36	−0.133287
$907$	−7.87438e36	−0.843578	−0.421789	−	0.906694i	$-0.638598\pi$
$907$	−7.87438e36	−0.843578	−0.421789	+	0.906694i	$0.638598\pi$
$908$	−1.56312e37	−1.65166
$909$	5.88804e36	0.613652
$910$	0	0
$911$	−1.36078e37	−1.37978	−0.689889	−	0.723915i	$-0.742341\pi$
$911$	−1.36078e37	−1.37978	−0.689889	+	0.723915i	$0.742341\pi$
$912$	−4.14280e34	−0.00414342
$913$	9.09534e36	0.897293
$914$	−3.71758e36	−0.361770
$915$	0	0
$916$	7.50112e36	0.710286
$917$	−2.96530e36	−0.276982
$918$	2.15201e37	1.98294
$919$	−9.86137e35	−0.0896382	−0.0448191	−	0.998995i	$-0.514271\pi$
$919$	−9.86137e35	−0.0896382	−0.0448191	+	0.998995i	$0.514271\pi$
$920$	0	0
$921$	−5.86315e35	−0.0518663
$922$	−7.56338e36	−0.660054
$923$	−4.04209e36	−0.348004
$924$	−3.66626e36	−0.311404
$925$	0	0
$926$	−9.33494e36	−0.771746
$927$	−8.78117e36	−0.716236
$928$	−2.08561e37	−1.67835
$929$	3.38052e36	0.268403	0.134202	−	0.990954i	$-0.457153\pi$
$929$	3.38052e36	0.268403	0.134202	+	0.990954i	$0.457153\pi$
$930$	0	0
$931$	5.76553e36	0.445623
$932$	5.45304e36	0.415853
$933$	−1.28554e37	−0.967305
$934$	−3.21709e37	−2.38851
$935$	0	0
$936$	−1.10749e37	−0.800559
$937$	1.23256e37	0.879151	0.439576	−	0.898206i	$-0.355129\pi$
$937$	1.23256e37	0.879151	0.439576	+	0.898206i	$0.355129\pi$
$938$	−4.79489e36	−0.337476
$939$	8.83912e36	0.613888
$940$	0	0
$941$	6.55312e36	0.443178	0.221589	−	0.975140i	$-0.428876\pi$
$941$	6.55312e36	0.443178	0.221589	+	0.975140i	$0.428876\pi$
$942$	−3.23040e36	−0.215586
$943$	−7.38276e36	−0.486208
$944$	−3.29275e35	−0.0213997
$945$	0	0
$946$	−3.45036e37	−2.18386
$947$	−1.42694e37	−0.891316	−0.445658	−	0.895203i	$-0.647030\pi$
$947$	−1.42694e37	−0.891316	−0.445658	+	0.895203i	$0.647030\pi$
$948$	−2.65900e37	−1.63913
$949$	4.35853e36	0.265163
$950$	0	0
$951$	−1.54732e37	−0.916905
$952$	−8.09918e36	−0.473673
$953$	−2.38480e36	−0.137655	−0.0688274	−	0.997629i	$-0.521926\pi$
$953$	−2.38480e36	−0.137655	−0.0688274	+	0.997629i	$0.521926\pi$
$954$	−3.11072e37	−1.77217
$955$	0	0
$956$	−2.86202e37	−1.58836
$957$	1.55820e37	0.853543
$958$	4.02643e37	2.17697
$959$	1.31272e37	0.700549
$960$	0	0
$961$	−8.80775e36	−0.457955
$962$	−1.51984e37	−0.780028
$963$	−2.21134e37	−1.12028
$964$	−2.18635e36	−0.109334
$965$	0	0
$966$	6.23659e36	0.303902
$967$	1.64185e37	0.789774	0.394887	−	0.918730i	$-0.370784\pi$
$967$	1.64185e37	0.789774	0.394887	+	0.918730i	$0.370784\pi$
$968$	−4.30778e36	−0.204556
$969$	8.14906e36	0.381997
$970$	0	0
$971$	2.07297e37	0.947007	0.473503	−	0.880792i	$-0.342989\pi$
$971$	2.07297e37	0.947007	0.473503	+	0.880792i	$0.342989\pi$
$972$	−3.66821e37	−1.65434
$973$	−3.73263e36	−0.166190
$974$	1.66060e37	0.729925
$975$	0	0
$976$	−1.19137e35	−0.00510417
$977$	3.93106e36	0.166275	0.0831376	−	0.996538i	$-0.473506\pi$
$977$	3.93106e36	0.166275	0.0831376	+	0.996538i	$0.473506\pi$
$978$	−2.15538e36	−0.0900093
$979$	−1.22708e37	−0.505929
$980$	0	0
$981$	−1.11270e37	−0.447213
$982$	7.10771e37	2.82056
$983$	9.80814e36	0.384298	0.192149	−	0.981366i	$-0.438454\pi$
$983$	9.80814e36	0.384298	0.192149	+	0.981366i	$0.438454\pi$
$984$	8.27792e36	0.320245
$985$	0	0
$986$	9.06837e37	3.42033
$987$	−7.09017e36	−0.264054
$988$	−2.76222e37	−1.01577
$989$	3.62212e37	1.31525
$990$	0	0
$991$	−9.07369e36	−0.321265	−0.160632	−	0.987014i	$-0.551353\pi$
$991$	−9.07369e36	−0.321265	−0.160632	+	0.987014i	$0.551353\pi$
$992$	−2.12925e37	−0.744441
$993$	−1.02975e37	−0.355521
$994$	5.10287e36	0.173974
$995$	0	0
$996$	2.82038e37	0.937704
$997$	1.44463e37	0.474315	0.237158	−	0.971471i	$-0.423784\pi$
$997$	1.44463e37	0.474315	0.237158	+	0.971471i	$0.423784\pi$
$998$	2.74931e37	0.891439
$999$	−1.19425e37	−0.382409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.26.a.f.1.11		12
5.2	odd	4		5.26.b.a.4.11	yes	12
5.3	odd	4		5.26.b.a.4.2	✓	12
5.4	even	2	inner	25.26.a.f.1.2		12
15.2	even	4		45.26.b.b.19.2		12
15.8	even	4		45.26.b.b.19.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.26.b.a.4.2	✓	12	5.3	odd	4
5.26.b.a.4.11	yes	12	5.2	odd	4
25.26.a.f.1.2		12	5.4	even	2	inner
25.26.a.f.1.11		12	1.1	even	1	trivial
45.26.b.b.19.2		12	15.2	even	4
45.26.b.b.19.11		12	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+9361.55 q^{2} -531494. q^{3} +5.40841e7 q^{4} -4.97561e9 q^{6} -1.37587e10 q^{7} +1.92189e11 q^{8} -5.64803e11 q^{9} -9.26999e12 q^{11} -2.87454e13 q^{12} +1.02027e14 q^{13} -1.28802e14 q^{14} -1.55712e13 q^{16} +3.06292e15 q^{17} -5.28743e15 q^{18} -5.00581e15 q^{19} +7.31265e15 q^{21} -8.67815e16 q^{22} +9.11014e16 q^{23} -1.02148e17 q^{24} +9.55130e17 q^{26} +7.50518e17 q^{27} -7.44125e17 q^{28} +3.16262e18 q^{29} +3.22878e18 q^{31} -6.59458e18 q^{32} +4.92695e18 q^{33} +2.86736e19 q^{34} -3.05468e19 q^{36} -1.59124e19 q^{37} -4.68621e19 q^{38} -5.42268e19 q^{39} -8.10389e19 q^{41} +6.84577e19 q^{42} +3.97592e20 q^{43} -5.01359e20 q^{44} +8.52850e20 q^{46} -9.69576e20 q^{47} +8.27600e18 q^{48} -1.15177e21 q^{49} -1.62792e21 q^{51} +5.51804e21 q^{52} +5.88324e21 q^{53} +7.02601e21 q^{54} -2.64427e21 q^{56} +2.66056e21 q^{57} +2.96070e22 q^{58} +2.11464e22 q^{59} +7.65113e21 q^{61} +3.02264e22 q^{62} +7.77093e21 q^{63} -6.12130e22 q^{64} +4.61238e22 q^{66} +3.72268e22 q^{67} +1.65655e23 q^{68} -4.84199e22 q^{69} -3.96178e22 q^{71} -1.08549e23 q^{72} +4.27194e22 q^{73} -1.48965e23 q^{74} -2.70734e23 q^{76} +1.27543e23 q^{77} -5.07646e23 q^{78} +9.25017e23 q^{79} +7.96549e22 q^{81} -7.58649e23 q^{82} -9.81159e23 q^{83} +3.95498e23 q^{84} +3.72207e24 q^{86} -1.68091e24 q^{87} -1.78160e24 q^{88} +1.32371e24 q^{89} -1.40375e24 q^{91} +4.92714e24 q^{92} -1.71608e24 q^{93} -9.07673e24 q^{94} +3.50498e24 q^{96} -3.52916e24 q^{97} -1.07823e25 q^{98} +5.23572e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 166691544 q^{4} + 10591544184 q^{6} + 3948466041036 q^{9} - 1090673824176 q^{11} + 890646861445848 q^{14} + 22\!\cdots\!32 q^{16} - 63\!\cdots\!60 q^{19} + 13\!\cdots\!44 q^{21} + 12\!\cdots\!20 q^{24}+ \cdots + 10\!\cdots\!72 q^{99}+O(q^{100}) \) 12 * q + 166691544 * q^4 + 10591544184 * q^6 + 3948466041036 * q^9 - 1090673824176 * q^11 + 890646861445848 * q^14 + 2206145875609632 * q^16 - 6329834351210160 * q^19 + 13538972741781744 * q^21 + 1238774108159908320 * q^24 + 487725686068642704 * q^26 + 5990455853511966360 * q^29 - 35669623242168576 * q^31 + 45224081273675172288 * q^34 + 95509342682184062232 * q^36 - 59576177650244745888 * q^39 - 149504768291960577576 * q^41 - 1795327120321140441312 * q^44 - 2632260904857596314776 * q^46 + 1924948130789206201884 * q^49 + 6601362996360626974464 * q^51 + 4543556632841187026640 * q^54 + 6789286242764162655840 * q^56 + 31976684482970870043120 * q^59 + 33892026990475241838024 * q^61 + 45154694563657190239104 * q^64 - 84625057142490628840032 * q^66 - 454638912158488569862128 * q^69 - 118991523615678935618976 * q^71 + 276076790459758393833168 * q^74 + 1770023872374606472757280 * q^76 + 741918285485353377639360 * q^79 + 2020576746978155938317372 * q^81 + 6598941205046486172215328 * q^84 + 6309456694176729359288664 * q^86 - 576066549612764658926520 * q^89 + 12216814388553519240480864 * q^91 + 11673168428062976516959608 * q^94 + 57292208364908004705120384 * q^96 + 10068680551503914801051472 * q^99

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