LMFDB - Embedded newform 50.26.a.l.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("50.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$197.998389976$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2 x^{5} - 27590779188 x^{4} + 26487255863952 x^{3} + \cdots - 30\!\cdots\!08 $ x^6 - 2x^5 - 27590779188x^4 + 26487255863952x^3 + 180405425727179733780x^2 - 1479960352440847053525960*x - 3018239644098422083113677808
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{4}\cdot 5^{18} $
Twist minimal:	no (minimal twist has level 10)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-115041.$ of defining polynomial
Character	$\chi$	$=$	50.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4096.00 q^{2} +1.01684e6 q^{3} +1.67772e7 q^{4} +4.16497e9 q^{6} -1.16326e10 q^{7} +6.87195e10 q^{8} +1.86674e11 q^{9} -5.94667e12 q^{11} +1.70597e13 q^{12} -8.19186e13 q^{13} -4.76472e13 q^{14} +2.81475e14 q^{16} +1.37679e15 q^{17} +7.64617e14 q^{18} +4.66320e15 q^{19} -1.18285e16 q^{21} -2.43576e16 q^{22} +9.70196e16 q^{23} +6.98767e16 q^{24} -3.35539e17 q^{26} -6.71739e17 q^{27} -1.95163e17 q^{28} -1.92842e18 q^{29} +5.14163e18 q^{31} +1.15292e18 q^{32} -6.04681e18 q^{33} +5.63933e18 q^{34} +3.13187e18 q^{36} -4.77086e19 q^{37} +1.91005e19 q^{38} -8.32981e19 q^{39} +1.13507e20 q^{41} -4.84495e19 q^{42} +9.41611e18 q^{43} -9.97685e19 q^{44} +3.97392e20 q^{46} -1.09883e21 q^{47} +2.86215e20 q^{48} -1.20575e21 q^{49} +1.39998e21 q^{51} -1.37437e21 q^{52} +6.11805e20 q^{53} -2.75144e21 q^{54} -7.99387e20 q^{56} +4.74172e21 q^{57} -7.89879e21 q^{58} -1.74642e22 q^{59} +2.94578e21 q^{61} +2.10601e22 q^{62} -2.17151e21 q^{63} +4.72237e21 q^{64} -2.47677e22 q^{66} -5.85392e22 q^{67} +2.30987e22 q^{68} +9.86533e22 q^{69} -2.27224e23 q^{71} +1.28281e22 q^{72} -2.69974e23 q^{73} -1.95415e23 q^{74} +7.82355e22 q^{76} +6.91753e22 q^{77} -3.41189e23 q^{78} -9.35155e23 q^{79} -8.41218e23 q^{81} +4.64926e23 q^{82} +1.71255e24 q^{83} -1.98449e23 q^{84} +3.85684e22 q^{86} -1.96089e24 q^{87} -4.08652e23 q^{88} -2.89830e24 q^{89} +9.52927e23 q^{91} +1.62772e24 q^{92} +5.22821e24 q^{93} -4.50081e24 q^{94} +1.17234e24 q^{96} +1.13099e24 q^{97} -4.93876e24 q^{98} -1.11009e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 24576 q^{2} - 801416 q^{3} + 100663296 q^{4} - 3282599936 q^{6} - 34007705352 q^{7} + 412316860416 q^{8} + 541468782118 q^{9} + 9861544614312 q^{11} - 13445529337856 q^{12} - 30787386783696 q^{13}+ \cdots - 20\!\cdots\!64 q^{99}+O(q^{100}) $ 6 * q + 24576 * q^2 - 801416 * q^3 + 100663296 * q^4 - 3282599936 * q^6 - 34007705352 * q^7 + 412316860416 * q^8 + 541468782118 * q^9 + 9861544614312 * q^11 - 13445529337856 * q^12 - 30787386783696 * q^13 - 139295561121792 * q^14 + 1688849860263936 * q^16 - 3432836939805312 * q^17 + 2217856131555328 * q^18 + 2007656488916520 * q^19 - 28181710291014728 * q^21 + 40392886740221952 * q^22 - 135711886432707576 * q^23 - 55072888167858176 * q^24 - 126105136266018816 * q^26 - 788054364552235760 * q^27 - 570554618354860032 * q^28 - 2926032031655504820 * q^29 + 79292935777014912 * q^31 + 6917529027641081856 * q^32 + 6844843638395003168 * q^33 - 14060900105442557952 * q^34 + 9084338714850623488 * q^36 - 3345885298190974032 * q^37 + 8223360978602065920 * q^38 + 124726636622561793456 * q^39 + 103229301719876244012 * q^41 - 115432285351996325888 * q^42 - 166390524239317503336 * q^43 + 165449264087949115392 * q^44 - 555875886828370231296 * q^46 - 405906243391034677992 * q^47 - 225578549935547088896 * q^48 + 1716280748139027694542 * q^49 - 1516225893661962013568 * q^51 - 516526638145613070336 * q^52 - 9772760301640799789616 * q^53 - 3227870677205957672960 * q^54 - 2336991716781506691072 * q^56 - 26174725126915157341920 * q^57 - 11985027201660947742720 * q^58 - 12499075130880780168840 * q^59 + 3687285610311118296612 * q^61 + 324783864942653079552 * q^62 - 93007818034972665339656 * q^63 + 28334198897217871282176 * q^64 + 28036479542865932976128 * q^66 - 16759935062266648886712 * q^67 - 57593446831892717371392 * q^68 + 185125325982378999854536 * q^69 + 74568876221253661649712 * q^71 + 37209451376028153806848 * q^72 - 381797761857106829638176 * q^73 - 13704746181390229635072 * q^74 + 33682886568354062008320 * q^76 + 80271541631956375339296 * q^77 + 510880303606013105995776 * q^78 - 400850316873811624799520 * q^79 - 1432110118616113828343714 * q^81 + 422827219844613095473152 * q^82 + 2423159733509985740001144 * q^83 - 472810640801776950837248 * q^84 - 681535587284244493664256 * q^86 + 1231328665433636473947120 * q^87 + 677680185704239576645632 * q^88 + 2982172528060341024616740 * q^89 - 7001711719121019241314768 * q^91 - 2276867632449004467388416 * q^92 + 8806417055581711481018368 * q^93 - 1662591972929678041055232 * q^94 - 923969740536000876118016 * q^96 + 4960469410756873985567808 * q^97 + 7029885944377457436844032 * q^98 - 2053720289282411723573464 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	4096.00	0.707107
$2$	4096.00	0.707107
$3$	1.01684e6	1.10468	0.552340	−	0.833619i	$-0.313735\pi$
$3$	1.01684e6	1.10468	0.552340	+	0.833619i	$0.313735\pi$
$4$	1.67772e7	0.500000
$5$	0	0
$5$	0	0
$6$	4.16497e9	0.781127
$7$	−1.16326e10	−0.317652	−0.158826	−	0.987307i	$-0.550771\pi$
$7$	−1.16326e10	−0.317652	−0.158826	+	0.987307i	$0.550771\pi$
$8$	6.87195e10	0.353553
$9$	1.86674e11	0.220319
$10$	0	0
$11$	−5.94667e12	−0.571301	−0.285651	−	0.958334i	$-0.592210\pi$
$11$	−5.94667e12	−0.571301	−0.285651	+	0.958334i	$0.592210\pi$
$12$	1.70597e13	0.552340
$13$	−8.19186e13	−0.975193	−0.487597	−	0.873069i	$-0.662126\pi$
$13$	−8.19186e13	−0.975193	−0.487597	+	0.873069i	$0.662126\pi$
$14$	−4.76472e13	−0.224614
$15$	0	0
$16$	2.81475e14	0.250000
$17$	1.37679e15	0.573134	0.286567	−	0.958060i	$-0.407486\pi$
$17$	1.37679e15	0.573134	0.286567	+	0.958060i	$0.407486\pi$
$18$	7.64617e14	0.155789
$19$	4.66320e15	0.483352	0.241676	−	0.970357i	$-0.422303\pi$
$19$	4.66320e15	0.483352	0.241676	+	0.970357i	$0.422303\pi$
$20$	0	0
$21$	−1.18285e16	−0.350904
$22$	−2.43576e16	−0.403971
$23$	9.70196e16	0.923127	0.461563	−	0.887107i	$-0.347289\pi$
$23$	9.70196e16	0.923127	0.461563	+	0.887107i	$0.347289\pi$
$24$	6.98767e16	0.390564
$25$	0	0
$26$	−3.35539e17	−0.689566
$27$	−6.71739e17	−0.861298
$28$	−1.95163e17	−0.158826
$29$	−1.92842e18	−1.01211	−0.506053	−	0.862503i	$-0.668896\pi$
$29$	−1.92842e18	−1.01211	−0.506053	+	0.862503i	$0.668896\pi$
$30$	0	0
$31$	5.14163e18	1.17241	0.586205	−	0.810163i	$-0.300621\pi$
$31$	5.14163e18	1.17241	0.586205	+	0.810163i	$0.300621\pi$
$32$	1.15292e18	0.176777
$33$	−6.04681e18	−0.631105
$34$	5.63933e18	0.405267
$35$	0	0
$36$	3.13187e18	0.110160
$37$	−4.77086e19	−1.19145	−0.595725	−	0.803189i	$-0.703135\pi$
$37$	−4.77086e19	−1.19145	−0.595725	+	0.803189i	$0.703135\pi$
$38$	1.91005e19	0.341782
$39$	−8.32981e19	−1.07728
$40$	0	0
$41$	1.13507e20	0.785644	0.392822	−	0.919615i	$-0.371499\pi$
$41$	1.13507e20	0.785644	0.392822	+	0.919615i	$0.371499\pi$
$42$	−4.84495e19	−0.248127
$43$	9.41611e18	0.0359348	0.0179674	−	0.999839i	$-0.494280\pi$
$43$	9.41611e18	0.0359348	0.0179674	+	0.999839i	$0.494280\pi$
$44$	−9.97685e19	−0.285651
$45$	0	0
$46$	3.97392e20	0.652749
$47$	−1.09883e21	−1.37946	−0.689728	−	0.724069i	$-0.742270\pi$
$47$	−1.09883e21	−1.37946	−0.689728	+	0.724069i	$0.742270\pi$
$48$	2.86215e20	0.276170
$49$	−1.20575e21	−0.899097
$50$	0	0
$51$	1.39998e21	0.633130
$52$	−1.37437e21	−0.487597
$53$	6.11805e20	0.171066	0.0855331	−	0.996335i	$-0.472741\pi$
$53$	6.11805e20	0.171066	0.0855331	+	0.996335i	$0.472741\pi$
$54$	−2.75144e21	−0.609030
$55$	0	0
$56$	−7.99387e20	−0.112307
$57$	4.74172e21	0.533950
$58$	−7.89879e21	−0.715667
$59$	−1.74642e22	−1.27791	−0.638954	−	0.769245i	$-0.720632\pi$
$59$	−1.74642e22	−1.27791	−0.638954	+	0.769245i	$0.720632\pi$
$60$	0	0
$61$	2.94578e21	0.142095	0.0710473	−	0.997473i	$-0.477366\pi$
$61$	2.94578e21	0.142095	0.0710473	+	0.997473i	$0.477366\pi$
$62$	2.10601e22	0.829019
$63$	−2.17151e21	−0.0699849
$64$	4.72237e21	0.125000
$65$	0	0
$66$	−2.47677e22	−0.446259
$67$	−5.85392e22	−0.874001	−0.437000	−	0.899461i	$-0.643959\pi$
$67$	−5.85392e22	−0.874001	−0.437000	+	0.899461i	$0.643959\pi$
$68$	2.30987e22	0.286567
$69$	9.86533e22	1.01976
$70$	0	0
$71$	−2.27224e23	−1.64333	−0.821665	−	0.569970i	$-0.806955\pi$
$71$	−2.27224e23	−1.64333	−0.821665	+	0.569970i	$0.806955\pi$
$72$	1.28281e22	0.0778946
$73$	−2.69974e23	−1.37971	−0.689853	−	0.723949i	$-0.742325\pi$
$73$	−2.69974e23	−1.37971	−0.689853	+	0.723949i	$0.742325\pi$
$74$	−1.95415e23	−0.842482
$75$	0	0
$76$	7.82355e22	0.241676
$77$	6.91753e22	0.181475
$78$	−3.41189e23	−0.761750
$79$	−9.35155e23	−1.78051	−0.890257	−	0.455459i	$-0.849475\pi$
$79$	−9.35155e23	−1.78051	−0.890257	+	0.455459i	$0.849475\pi$
$80$	0	0
$81$	−8.41218e23	−1.17178
$82$	4.64926e23	0.555534
$83$	1.71255e24	1.75860	0.879302	−	0.476264i	$-0.158009\pi$
$83$	1.71255e24	1.75860	0.879302	+	0.476264i	$0.158009\pi$
$84$	−1.98449e23	−0.175452
$85$	0	0
$86$	3.85684e22	0.0254098
$87$	−1.96089e24	−1.11805
$88$	−4.08652e23	−0.201985
$89$	−2.89830e24	−1.24385	−0.621926	−	0.783076i	$-0.713650\pi$
$89$	−2.89830e24	−1.24385	−0.621926	+	0.783076i	$0.713650\pi$
$90$	0	0
$91$	9.52927e23	0.309772
$92$	1.62772e24	0.461563
$93$	5.22821e24	1.29514
$94$	−4.50081e24	−0.975422
$95$	0	0
$96$	1.17234e24	0.195282
$97$	1.13099e24	0.165506	0.0827529	−	0.996570i	$-0.473629\pi$
$97$	1.13099e24	0.165506	0.0827529	+	0.996570i	$0.473629\pi$
$98$	−4.93876e24	−0.635758
$99$	−1.11009e24	−0.125869
$100$	0	0
$101$	−1.20834e25	−1.06702	−0.533510	−	0.845794i	$-0.679127\pi$
$101$	−1.20834e25	−1.06702	−0.533510	+	0.845794i	$0.679127\pi$
$102$	5.73430e24	0.447691
$103$	1.70464e23	0.0117806	0.00589030	−	0.999983i	$-0.498125\pi$
$103$	1.70464e23	0.0117806	0.00589030	+	0.999983i	$0.498125\pi$
$104$	−5.62940e24	−0.344783
$105$	0	0
$106$	2.50595e24	0.120962
$107$	−1.25315e25	−0.537906	−0.268953	−	0.963153i	$-0.586678\pi$
$107$	−1.25315e25	−0.537906	−0.268953	+	0.963153i	$0.586678\pi$
$108$	−1.12699e25	−0.430649
$109$	5.31922e25	1.81141	0.905704	−	0.423910i	$-0.139343\pi$
$109$	5.31922e25	1.81141	0.905704	+	0.423910i	$0.139343\pi$
$110$	0	0
$111$	−4.85120e25	−1.31617
$112$	−3.27429e24	−0.0794130
$113$	−1.81999e25	−0.394991	−0.197496	−	0.980304i	$-0.563281\pi$
$113$	−1.81999e25	−0.394991	−0.197496	+	0.980304i	$0.563281\pi$
$114$	1.94221e25	0.377560
$115$	0	0
$116$	−3.23535e25	−0.506053
$117$	−1.52921e25	−0.214854
$118$	−7.15335e25	−0.903617
$119$	−1.60157e25	−0.182057
$120$	0	0
$121$	−7.29842e25	−0.673615
$122$	1.20659e25	0.100476
$123$	1.15419e26	0.867886
$124$	8.62622e25	0.586205
$125$	0	0
$126$	−8.89449e24	−0.0494868
$127$	4.54166e25	0.228912	0.114456	−	0.993428i	$-0.463488\pi$
$127$	4.54166e25	0.228912	0.114456	+	0.993428i	$0.463488\pi$
$128$	1.93428e25	0.0883883
$129$	9.57467e24	0.0396965
$130$	0	0
$131$	3.22369e26	1.10271	0.551356	−	0.834270i	$-0.314110\pi$
$131$	3.22369e26	1.10271	0.551356	+	0.834270i	$0.314110\pi$
$132$	−1.01449e26	−0.315553
$133$	−5.42452e25	−0.153538
$134$	−2.39777e26	−0.618012
$135$	0	0
$136$	9.46123e25	0.202634
$137$	5.61602e26	1.09754	0.548771	−	0.835973i	$-0.315096\pi$
$137$	5.61602e26	1.09754	0.548771	+	0.835973i	$0.315096\pi$
$138$	4.04084e26	0.721079
$139$	−7.44482e26	−1.21386	−0.606931	−	0.794755i	$-0.707600\pi$
$139$	−7.44482e26	−1.21386	−0.606931	+	0.794755i	$0.707600\pi$
$140$	0	0
$141$	−1.11733e27	−1.52386
$142$	−9.30710e26	−1.16201
$143$	4.87143e26	0.557129
$144$	5.25441e25	0.0550798
$145$	0	0
$146$	−1.10581e27	−0.975600
$147$	−1.22606e27	−0.993215
$148$	−8.00418e26	−0.595725
$149$	−9.58450e26	−0.655754	−0.327877	−	0.944720i	$-0.606333\pi$
$149$	−9.58450e26	−0.655754	−0.327877	+	0.944720i	$0.606333\pi$
$150$	0	0
$151$	8.90889e26	0.515955	0.257978	−	0.966151i	$-0.416944\pi$
$151$	8.90889e26	0.515955	0.257978	+	0.966151i	$0.416944\pi$
$152$	3.20452e26	0.170891
$153$	2.57011e26	0.126273
$154$	2.83342e26	0.128322
$155$	0	0
$156$	−1.39751e27	−0.538639
$157$	4.44904e27	1.58314	0.791572	−	0.611076i	$-0.209263\pi$
$157$	4.44904e27	1.58314	0.791572	+	0.611076i	$0.209263\pi$
$158$	−3.83040e27	−1.25901
$159$	6.22107e26	0.188974
$160$	0	0
$161$	−1.12859e27	−0.293233
$162$	−3.44563e27	−0.828573
$163$	−1.89357e27	−0.421634	−0.210817	−	0.977526i	$-0.567612\pi$
$163$	−1.89357e27	−0.421634	−0.210817	+	0.977526i	$0.567612\pi$
$164$	1.90434e27	0.392822
$165$	0	0
$166$	7.01462e27	1.24352
$167$	−2.78772e27	−0.458451	−0.229226	−	0.973373i	$-0.573619\pi$
$167$	−2.78772e27	−0.458451	−0.229226	+	0.973373i	$0.573619\pi$
$168$	−8.12848e26	−0.124063
$169$	−3.45751e26	−0.0489982
$170$	0	0
$171$	8.70498e26	0.106492
$172$	1.57976e26	0.0179674
$173$	1.54571e28	1.63513	0.817565	−	0.575836i	$-0.195323\pi$
$173$	1.54571e28	1.63513	0.817565	+	0.575836i	$0.195323\pi$
$174$	−8.03180e27	−0.790583
$175$	0	0
$176$	−1.67384e27	−0.142825
$177$	−1.77583e28	−1.41168
$178$	−1.18715e28	−0.879536
$179$	1.48885e28	1.02846	0.514232	−	0.857651i	$-0.328077\pi$
$179$	1.48885e28	1.02846	0.514232	+	0.857651i	$0.328077\pi$
$180$	0	0
$181$	2.99166e28	1.79858	0.899291	−	0.437351i	$-0.144083\pi$
$181$	2.99166e28	1.79858	0.899291	+	0.437351i	$0.144083\pi$
$182$	3.90319e27	0.219042
$183$	2.99539e27	0.156969
$184$	6.66713e27	0.326375
$185$	0	0
$186$	2.14148e28	0.915802
$187$	−8.18732e27	−0.327432
$188$	−1.84353e28	−0.689728
$189$	7.81408e27	0.273593
$190$	0	0
$191$	1.13139e28	0.347292	0.173646	−	0.984808i	$-0.444445\pi$
$191$	1.13139e28	0.347292	0.173646	+	0.984808i	$0.444445\pi$
$192$	4.80189e27	0.138085
$193$	6.86928e26	0.0185116	0.00925582	−	0.999957i	$-0.497054\pi$
$193$	6.86928e26	0.0185116	0.00925582	+	0.999957i	$0.497054\pi$
$194$	4.63255e27	0.117030
$195$	0	0
$196$	−2.02291e28	−0.449549
$197$	−7.22234e28	−1.50609	−0.753044	−	0.657970i	$-0.771415\pi$
$197$	−7.22234e28	−1.50609	−0.753044	+	0.657970i	$0.771415\pi$
$198$	−4.54692e27	−0.0890026
$199$	6.41046e28	1.17822	0.589110	−	0.808053i	$-0.299479\pi$
$199$	6.41046e28	1.17822	0.589110	+	0.808053i	$0.299479\pi$
$200$	0	0
$201$	−5.95250e28	−0.965492
$202$	−4.94936e28	−0.754497
$203$	2.24325e28	0.321497
$204$	2.34877e28	0.316565
$205$	0	0
$206$	6.98220e26	0.00833014
$207$	1.81110e28	0.203383
$208$	−2.30580e28	−0.243798
$209$	−2.77305e28	−0.276140
$210$	0	0
$211$	−2.74461e28	−0.242633	−0.121317	−	0.992614i	$-0.538712\pi$
$211$	−2.74461e28	−0.242633	−0.121317	+	0.992614i	$0.538712\pi$
$212$	1.02644e28	0.0855331
$213$	−2.31050e29	−1.81536
$214$	−5.13290e28	−0.380357
$215$	0	0
$216$	−4.61616e28	−0.304515
$217$	−5.98106e28	−0.372419
$218$	2.17875e29	1.28086
$219$	−2.74521e29	−1.52414
$220$	0	0
$221$	−1.12785e29	−0.558917
$222$	−1.98705e29	−0.930673
$223$	−2.58596e29	−1.14502	−0.572508	−	0.819899i	$-0.694029\pi$
$223$	−2.58596e29	−1.14502	−0.572508	+	0.819899i	$0.694029\pi$
$224$	−1.34115e28	−0.0561535
$225$	0	0
$226$	−7.45466e28	−0.279301
$227$	−4.86361e29	−1.72439	−0.862194	−	0.506578i	$-0.830910\pi$
$227$	−4.86361e29	−1.72439	−0.862194	+	0.506578i	$0.830910\pi$
$228$	7.95529e28	0.266975
$229$	−4.91096e29	−1.56035	−0.780176	−	0.625560i	$-0.784870\pi$
$229$	−4.91096e29	−1.56035	−0.780176	+	0.625560i	$0.784870\pi$
$230$	0	0
$231$	7.03402e28	0.200472
$232$	−1.32520e29	−0.357833
$233$	−2.93368e29	−0.750696	−0.375348	−	0.926884i	$-0.622477\pi$
$233$	−2.93368e29	−0.750696	−0.375348	+	0.926884i	$0.622477\pi$
$234$	−6.26363e28	−0.151925
$235$	0	0
$236$	−2.93001e29	−0.638954
$237$	−9.50903e29	−1.96690
$238$	−6.56002e28	−0.128734
$239$	−2.65452e28	−0.0494324	−0.0247162	−	0.999695i	$-0.507868\pi$
$239$	−2.65452e28	−0.0494324	−0.0247162	+	0.999695i	$0.507868\pi$
$240$	0	0
$241$	−6.46401e27	−0.0108465	−0.00542324	−	0.999985i	$-0.501726\pi$
$241$	−6.46401e27	−0.0108465	−0.00542324	+	0.999985i	$0.501726\pi$
$242$	−2.98943e29	−0.476318
$243$	−2.86226e29	−0.433143
$244$	4.94220e28	0.0710473
$245$	0	0
$246$	4.72755e29	0.613688
$247$	−3.82003e29	−0.471362
$248$	3.53330e29	0.414510
$249$	1.74139e30	1.94270
$250$	0	0
$251$	−5.06787e29	−0.511569	−0.255785	−	0.966734i	$-0.582334\pi$
$251$	−5.06787e29	−0.511569	−0.255785	+	0.966734i	$0.582334\pi$
$252$	−3.64318e28	−0.0349924
$253$	−5.76943e29	−0.527383
$254$	1.86026e29	0.161865
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	−8.16135e29	−0.613194	−0.306597	−	0.951839i	$-0.599190\pi$
$257$	−8.16135e29	−0.613194	−0.306597	+	0.951839i	$0.599190\pi$
$258$	3.92178e28	0.0280697
$259$	5.54976e29	0.378466
$260$	0	0
$261$	−3.59985e29	−0.222986
$262$	1.32042e30	0.779736
$263$	−1.16241e30	−0.654505	−0.327253	−	0.944937i	$-0.606123\pi$
$263$	−1.16241e30	−0.654505	−0.327253	+	0.944937i	$0.606123\pi$
$264$	−4.15533e29	−0.223129
$265$	0	0
$266$	−2.22188e29	−0.108568
$267$	−2.94711e30	−1.37406
$268$	−9.82125e29	−0.437000
$269$	1.07881e30	0.458184	0.229092	−	0.973405i	$-0.426424\pi$
$269$	1.07881e30	0.458184	0.229092	+	0.973405i	$0.426424\pi$
$270$	0	0
$271$	2.07856e30	0.804723	0.402362	−	0.915481i	$-0.368189\pi$
$271$	2.07856e30	0.804723	0.402362	+	0.915481i	$0.368189\pi$
$272$	3.87532e29	0.143284
$273$	9.68974e29	0.342199
$274$	2.30032e30	0.776080
$275$	0	0
$276$	1.65513e30	0.509880
$277$	−4.81866e30	−1.41883	−0.709413	−	0.704793i	$-0.751040\pi$
$277$	−4.81866e30	−1.41883	−0.709413	+	0.704793i	$0.751040\pi$
$278$	−3.04940e30	−0.858330
$279$	9.59809e29	0.258305
$280$	0	0
$281$	3.81522e30	0.939054	0.469527	−	0.882918i	$-0.344424\pi$
$281$	3.81522e30	0.939054	0.469527	+	0.882918i	$0.344424\pi$
$282$	−4.57660e30	−1.07753
$283$	3.50448e30	0.789392	0.394696	−	0.918812i	$-0.370850\pi$
$283$	3.50448e30	0.789392	0.394696	+	0.918812i	$0.370850\pi$
$284$	−3.81219e30	−0.821665
$285$	0	0
$286$	1.99534e30	0.393950
$287$	−1.32039e30	−0.249561
$288$	2.15220e29	0.0389473
$289$	−3.87508e30	−0.671517
$290$	0	0
$291$	1.15004e30	0.182831
$292$	−4.52942e30	−0.689853
$293$	−1.01157e30	−0.147622	−0.0738111	−	0.997272i	$-0.523516\pi$
$293$	−1.01157e30	−0.147622	−0.0738111	+	0.997272i	$0.523516\pi$
$294$	−5.02192e30	−0.702309
$295$	0	0
$296$	−3.27851e30	−0.421241
$297$	3.99461e30	0.492061
$298$	−3.92581e30	−0.463688
$299$	−7.94771e30	−0.900227
$300$	0	0
$301$	−1.09534e29	−0.0114148
$302$	3.64908e30	0.364835
$303$	−1.22869e31	−1.17872
$304$	1.31257e30	0.120838
$305$	0	0
$306$	1.05272e30	0.0892882
$307$	1.27764e31	1.04035	0.520174	−	0.854060i	$-0.325867\pi$
$307$	1.27764e31	1.04035	0.520174	+	0.854060i	$0.325867\pi$
$308$	1.16057e30	0.0907375
$309$	1.73334e29	0.0130138
$310$	0	0
$311$	−1.19771e31	−0.829556	−0.414778	−	0.909923i	$-0.636141\pi$
$311$	−1.19771e31	−0.829556	−0.414778	+	0.909923i	$0.636141\pi$
$312$	−5.72420e30	−0.380875
$313$	2.39996e31	1.53426	0.767130	−	0.641492i	$-0.221684\pi$
$313$	2.39996e31	1.53426	0.767130	+	0.641492i	$0.221684\pi$
$314$	1.82233e31	1.11945
$315$	0	0
$316$	−1.56893e31	−0.890257
$317$	5.21982e30	0.284718	0.142359	−	0.989815i	$-0.454531\pi$
$317$	5.21982e30	0.284718	0.142359	+	0.989815i	$0.454531\pi$
$318$	2.54815e30	0.133625
$319$	1.14677e31	0.578217
$320$	0	0
$321$	−1.27425e31	−0.594214
$322$	−4.62271e30	−0.207347
$323$	6.42025e30	0.277026
$324$	−1.41133e31	−0.585889
$325$	0	0
$326$	−7.75605e30	−0.298140
$327$	5.40879e31	2.00103
$328$	7.80017e30	0.277767
$329$	1.27823e31	0.438187
$330$	0	0
$331$	2.99801e31	0.952759	0.476379	−	0.879240i	$-0.341949\pi$
$331$	2.99801e31	0.952759	0.476379	+	0.879240i	$0.341949\pi$
$332$	2.87319e31	0.879302
$333$	−8.90596e30	−0.262499
$334$	−1.14185e31	−0.324174
$335$	0	0
$336$	−3.32943e30	−0.0877260
$337$	−2.25223e31	−0.571792	−0.285896	−	0.958261i	$-0.592291\pi$
$337$	−2.25223e31	−0.571792	−0.285896	+	0.958261i	$0.592291\pi$
$338$	−1.41620e30	−0.0346469
$339$	−1.85063e31	−0.436339
$340$	0	0
$341$	−3.05756e31	−0.669800
$342$	3.56556e30	0.0753011
$343$	2.96262e31	0.603252
$344$	6.47070e29	0.0127049
$345$	0	0
$346$	6.33124e31	1.15621
$347$	1.77495e31	0.312656	0.156328	−	0.987705i	$-0.450034\pi$
$347$	1.77495e31	0.312656	0.156328	+	0.987705i	$0.450034\pi$
$348$	−3.28983e31	−0.559027
$349$	6.99151e31	1.14618	0.573091	−	0.819492i	$-0.305744\pi$
$349$	6.99151e31	1.14618	0.573091	+	0.819492i	$0.305744\pi$
$350$	0	0
$351$	5.50279e31	0.839932
$352$	−6.85604e30	−0.100993
$353$	5.98918e31	0.851498	0.425749	−	0.904841i	$-0.360011\pi$
$353$	5.98918e31	0.851498	0.425749	+	0.904841i	$0.360011\pi$
$354$	−7.27381e31	−0.998208
$355$	0	0
$356$	−4.86255e31	−0.621926
$357$	−1.62854e31	−0.201115
$358$	6.09835e31	0.727234
$359$	2.70071e31	0.311027	0.155513	−	0.987834i	$-0.450297\pi$
$359$	2.70071e31	0.311027	0.155513	+	0.987834i	$0.450297\pi$
$360$	0	0
$361$	−7.13311e31	−0.766371
$362$	1.22538e32	1.27179
$363$	−7.42132e31	−0.744129
$364$	1.59875e31	0.154886
$365$	0	0
$366$	1.22691e31	0.110994
$367$	1.68905e32	1.47678	0.738392	−	0.674372i	$-0.235585\pi$
$367$	1.68905e32	1.47678	0.738392	+	0.674372i	$0.235585\pi$
$368$	2.73086e31	0.230782
$369$	2.11889e31	0.173093
$370$	0	0
$371$	−7.11689e30	−0.0543396
$372$	8.77149e31	0.647570
$373$	5.83575e31	0.416616	0.208308	−	0.978063i	$-0.433204\pi$
$373$	5.83575e31	0.416616	0.208308	+	0.978063i	$0.433204\pi$
$374$	−3.35352e31	−0.231530
$375$	0	0
$376$	−7.55111e31	−0.487711
$377$	1.57973e32	0.986998
$378$	3.20065e31	0.193460
$379$	−1.51743e32	−0.887399	−0.443700	−	0.896176i	$-0.646334\pi$
$379$	−1.51743e32	−0.887399	−0.443700	+	0.896176i	$0.646334\pi$
$380$	0	0
$381$	4.61814e31	0.252874
$382$	4.63416e31	0.245572
$383$	−2.03117e32	−1.04174	−0.520872	−	0.853635i	$-0.674393\pi$
$383$	−2.03117e32	−1.04174	−0.520872	+	0.853635i	$0.674393\pi$
$384$	1.96685e31	0.0976409
$385$	0	0
$386$	2.81366e30	0.0130897
$387$	1.75774e30	0.00791714
$388$	1.89749e31	0.0827529
$389$	4.00318e32	1.69058	0.845289	−	0.534310i	$-0.179428\pi$
$389$	4.00318e32	1.69058	0.845289	+	0.534310i	$0.179428\pi$
$390$	0	0
$391$	1.33576e32	0.529076
$392$	−8.28586e31	−0.317879
$393$	3.27798e32	1.21815
$394$	−2.95827e32	−1.06496
$395$	0	0
$396$	−1.86242e31	−0.0629343
$397$	−9.71109e31	−0.317970	−0.158985	−	0.987281i	$-0.550822\pi$
$397$	−9.71109e31	−0.317970	−0.158985	+	0.987281i	$0.550822\pi$
$398$	2.62573e32	0.833127
$399$	−5.51586e31	−0.169610
$400$	0	0
$401$	1.47073e32	0.424842	0.212421	−	0.977178i	$-0.431865\pi$
$401$	1.47073e32	0.424842	0.212421	+	0.977178i	$0.431865\pi$
$402$	−2.43814e32	−0.682706
$403$	−4.21195e32	−1.14333
$404$	−2.02726e32	−0.533510
$405$	0	0
$406$	9.18836e31	0.227333
$407$	2.83708e32	0.680676
$408$	9.62056e31	0.223845
$409$	−4.55653e32	−1.02824	−0.514118	−	0.857720i	$-0.671881\pi$
$409$	−4.55653e32	−1.02824	−0.514118	+	0.857720i	$0.671881\pi$
$410$	0	0
$411$	5.71059e32	1.21243
$412$	2.85991e30	0.00589030
$413$	2.03155e32	0.405930
$414$	7.41828e31	0.143813
$415$	0	0
$416$	−9.44457e31	−0.172391
$417$	−7.57019e32	−1.34093
$418$	−1.13584e32	−0.195260
$419$	1.07085e33	1.78670	0.893350	−	0.449361i	$-0.148348\pi$
$419$	1.07085e33	1.78670	0.893350	+	0.449361i	$0.148348\pi$
$420$	0	0
$421$	4.34132e32	0.682489	0.341244	−	0.939975i	$-0.389152\pi$
$421$	4.34132e32	0.682489	0.341244	+	0.939975i	$0.389152\pi$
$422$	−1.12419e32	−0.171568
$423$	−2.05123e32	−0.303921
$424$	4.20429e31	0.0604811
$425$	0	0
$426$	−9.46382e32	−1.28365
$427$	−3.42671e31	−0.0451366
$428$	−2.10244e32	−0.268953
$429$	4.95346e32	0.615450
$430$	0	0
$431$	−7.49364e32	−0.878470	−0.439235	−	0.898372i	$-0.644750\pi$
$431$	−7.49364e32	−0.878470	−0.439235	+	0.898372i	$0.644750\pi$
$432$	−1.89078e32	−0.215325
$433$	3.10398e32	0.343416	0.171708	−	0.985148i	$-0.445072\pi$
$433$	3.10398e32	0.343416	0.171708	+	0.985148i	$0.445072\pi$
$434$	−2.44984e32	−0.263340
$435$	0	0
$436$	8.92417e32	0.905704
$437$	4.52421e32	0.446195
$438$	−1.12444e33	−1.07773
$439$	3.93993e32	0.367013	0.183507	−	0.983018i	$-0.441255\pi$
$439$	3.93993e32	0.367013	0.183507	+	0.983018i	$0.441255\pi$
$440$	0	0
$441$	−2.25082e32	−0.198088
$442$	−4.61966e32	−0.395214
$443$	−1.28865e33	−1.07174	−0.535869	−	0.844301i	$-0.680016\pi$
$443$	−1.28865e33	−1.07174	−0.535869	+	0.844301i	$0.680016\pi$
$444$	−8.13897e32	−0.658085
$445$	0	0
$446$	−1.05921e33	−0.809649
$447$	−9.74590e32	−0.724399
$448$	−5.49335e31	−0.0397065
$449$	2.64778e33	1.86124	0.930619	−	0.365990i	$-0.119269\pi$
$449$	2.64778e33	1.86124	0.930619	+	0.365990i	$0.119269\pi$
$450$	0	0
$451$	−6.74991e32	−0.448839
$452$	−3.05343e32	−0.197496
$453$	9.05891e32	0.569966
$454$	−1.99213e33	−1.21933
$455$	0	0
$456$	3.25849e32	0.188780
$457$	−3.41528e33	−1.92519	−0.962594	−	0.270947i	$-0.912663\pi$
$457$	−3.41528e33	−1.92519	−0.962594	+	0.270947i	$0.912663\pi$
$458$	−2.01153e33	−1.10334
$459$	−9.24844e32	−0.493639
$460$	0	0
$461$	−3.55950e33	−1.79940	−0.899700	−	0.436510i	$-0.856214\pi$
$461$	−3.55950e33	−1.79940	−0.899700	+	0.436510i	$0.856214\pi$
$462$	2.88113e32	0.141755
$463$	2.37447e33	1.13712	0.568558	−	0.822643i	$-0.307501\pi$
$463$	2.37447e33	1.13712	0.568558	+	0.822643i	$0.307501\pi$
$464$	−5.42801e32	−0.253026
$465$	0	0
$466$	−1.20164e33	−0.530822
$467$	−1.47044e33	−0.632392	−0.316196	−	0.948694i	$-0.602406\pi$
$467$	−1.47044e33	−0.632392	−0.316196	+	0.948694i	$0.602406\pi$
$468$	−2.56558e32	−0.107427
$469$	6.80964e32	0.277628
$470$	0	0
$471$	4.52396e33	1.74887
$472$	−1.20013e33	−0.451808
$473$	−5.59945e31	−0.0205296
$474$	−3.89490e33	−1.39081
$475$	0	0
$476$	−2.68698e32	−0.0910286
$477$	1.14208e32	0.0376892
$478$	−1.08729e32	−0.0349540
$479$	−1.56346e33	−0.489657	−0.244829	−	0.969566i	$-0.578732\pi$
$479$	−1.56346e33	−0.489657	−0.244829	+	0.969566i	$0.578732\pi$
$480$	0	0
$481$	3.90823e33	1.16189
$482$	−2.64766e31	−0.00766962
$483$	−1.14760e33	−0.323929
$484$	−1.22447e33	−0.336807
$485$	0	0
$486$	−1.17238e33	−0.306278
$487$	−4.18200e33	−1.06481	−0.532405	−	0.846490i	$-0.678711\pi$
$487$	−4.18200e33	−1.06481	−0.532405	+	0.846490i	$0.678711\pi$
$488$	2.02432e32	0.0502380
$489$	−1.92545e33	−0.465771
$490$	0	0
$491$	4.13591e32	0.0950719	0.0475360	−	0.998870i	$-0.484863\pi$
$491$	4.13591e32	0.0950719	0.0475360	+	0.998870i	$0.484863\pi$
$492$	1.93641e33	0.433943
$493$	−2.65502e33	−0.580072
$494$	−1.56468e33	−0.333303
$495$	0	0
$496$	1.44724e33	0.293103
$497$	2.64321e33	0.522007
$498$	7.13275e33	1.37369
$499$	5.19785e33	0.976264	0.488132	−	0.872770i	$-0.337679\pi$
$499$	5.19785e33	0.976264	0.488132	+	0.872770i	$0.337679\pi$
$500$	0	0
$501$	−2.83466e33	−0.506442
$502$	−2.07580e33	−0.361734
$503$	−3.59933e33	−0.611817	−0.305909	−	0.952061i	$-0.598960\pi$
$503$	−3.59933e33	−0.611817	−0.305909	+	0.952061i	$0.598960\pi$
$504$	−1.49225e32	−0.0247434
$505$	0	0
$506$	−2.36316e33	−0.372916
$507$	−3.51573e32	−0.0541273
$508$	7.61964e32	0.114456
$509$	1.19327e34	1.74891	0.874453	−	0.485109i	$-0.161220\pi$
$509$	1.19327e34	1.74891	0.874453	+	0.485109i	$0.161220\pi$
$510$	0	0
$511$	3.14051e33	0.438267
$512$	3.24519e32	0.0441942
$513$	−3.13245e33	−0.416310
$514$	−3.34289e33	−0.433594
$515$	0	0
$516$	1.60636e32	0.0198483
$517$	6.53438e33	0.788085
$518$	2.27318e33	0.267616
$519$	1.57174e34	1.80630
$520$	0	0
$521$	1.63355e34	1.78921	0.894605	−	0.446859i	$-0.147457\pi$
$521$	1.63355e34	1.78921	0.894605	+	0.446859i	$0.147457\pi$
$522$	−1.47450e33	−0.157675
$523$	−9.46552e33	−0.988265	−0.494133	−	0.869387i	$-0.664514\pi$
$523$	−9.46552e33	−0.988265	−0.494133	+	0.869387i	$0.664514\pi$
$524$	5.40846e33	0.551356
$525$	0	0
$526$	−4.76124e33	−0.462805
$527$	7.07895e33	0.671949
$528$	−1.70202e33	−0.157776
$529$	−1.63297e33	−0.147837
$530$	0	0
$531$	−3.26012e33	−0.281548
$532$	−9.10083e32	−0.0767689
$533$	−9.29836e33	−0.766155
$534$	−1.20714e34	−0.971607
$535$	0	0
$536$	−4.02278e33	−0.309006
$537$	1.51393e34	1.13612
$538$	4.41879e33	0.323985
$539$	7.17020e33	0.513655
$540$	0	0
$541$	1.13679e34	0.777528	0.388764	−	0.921337i	$-0.372902\pi$
$541$	1.13679e34	0.777528	0.388764	+	0.921337i	$0.372902\pi$
$542$	8.51379e33	0.569025
$543$	3.04204e34	1.98686
$544$	1.58733e33	0.101317
$545$	0	0
$546$	3.96892e33	0.241971
$547$	−2.60600e34	−1.55286	−0.776430	−	0.630204i	$-0.782971\pi$
$547$	−2.60600e34	−1.55286	−0.776430	+	0.630204i	$0.782971\pi$
$548$	9.42211e33	0.548771
$549$	5.49901e32	0.0313062
$550$	0	0
$551$	−8.99258e33	−0.489203
$552$	6.77940e33	0.360540
$553$	1.08783e34	0.565584
$554$	−1.97372e34	−1.00326
$555$	0	0
$556$	−1.24903e34	−0.606931
$557$	3.30593e34	1.57074	0.785368	−	0.619029i	$-0.212474\pi$
$557$	3.30593e34	1.57074	0.785368	+	0.619029i	$0.212474\pi$
$558$	3.93138e33	0.182649
$559$	−7.71354e32	−0.0350434
$560$	0	0
$561$	−8.32519e33	−0.361708
$562$	1.56271e34	0.664011
$563$	1.77408e34	0.737255	0.368628	−	0.929577i	$-0.379828\pi$
$563$	1.77408e34	0.737255	0.368628	+	0.929577i	$0.379828\pi$
$564$	−1.87458e34	−0.761929
$565$	0	0
$566$	1.43543e34	0.558184
$567$	9.78556e33	0.372218
$568$	−1.56147e34	−0.581005
$569$	−3.24647e34	−1.18170	−0.590851	−	0.806781i	$-0.701208\pi$
$569$	−3.24647e34	−1.18170	−0.590851	+	0.806781i	$0.701208\pi$
$570$	0	0
$571$	−1.08523e34	−0.378068	−0.189034	−	0.981971i	$-0.560536\pi$
$571$	−1.08523e34	−0.378068	−0.189034	+	0.981971i	$0.560536\pi$
$572$	8.17290e33	0.278565
$573$	1.15044e34	0.383646
$574$	−5.40830e33	−0.176467
$575$	0	0
$576$	8.81543e32	0.0275399
$577$	5.40061e34	1.65099	0.825497	−	0.564406i	$-0.190895\pi$
$577$	5.40061e34	1.65099	0.825497	+	0.564406i	$0.190895\pi$
$578$	−1.58723e34	−0.474834
$579$	6.98496e32	0.0204495
$580$	0	0
$581$	−1.99215e34	−0.558625
$582$	4.71056e33	0.129281
$583$	−3.63820e33	−0.0977304
$584$	−1.85525e34	−0.487800
$585$	0	0
$586$	−4.14340e33	−0.104385
$587$	−5.41910e34	−1.33644	−0.668222	−	0.743962i	$-0.732944\pi$
$587$	−5.41910e34	−1.33644	−0.668222	+	0.743962i	$0.732944\pi$
$588$	−2.05698e34	−0.496608
$589$	2.39764e34	0.566687
$590$	0	0
$591$	−7.34396e34	−1.66375
$592$	−1.34288e34	−0.297862
$593$	3.87147e34	0.840799	0.420400	−	0.907339i	$-0.361890\pi$
$593$	3.87147e34	0.840799	0.420400	+	0.907339i	$0.361890\pi$
$594$	1.63619e34	0.347939
$595$	0	0
$596$	−1.60801e34	−0.327877
$597$	6.51841e34	1.30156
$598$	−3.25538e34	−0.636557
$599$	9.20898e33	0.176350	0.0881751	−	0.996105i	$-0.471896\pi$
$599$	9.20898e33	0.176350	0.0881751	+	0.996105i	$0.471896\pi$
$600$	0	0
$601$	3.98144e34	0.731324	0.365662	−	0.930748i	$-0.380843\pi$
$601$	3.98144e34	0.731324	0.365662	+	0.930748i	$0.380843\pi$
$602$	−4.48651e32	−0.00807147
$603$	−1.09277e34	−0.192559
$604$	1.49466e34	0.257978
$605$	0	0
$606$	−5.03271e34	−0.833478
$607$	−3.32966e34	−0.540184	−0.270092	−	0.962835i	$-0.587054\pi$
$607$	−3.32966e34	−0.540184	−0.270092	+	0.962835i	$0.587054\pi$
$608$	5.37630e33	0.0854454
$609$	2.28103e34	0.355152
$610$	0	0
$611$	9.00147e34	1.34524
$612$	4.31193e33	0.0631363
$613$	−5.68278e34	−0.815277	−0.407639	−	0.913143i	$-0.633648\pi$
$613$	−5.68278e34	−0.815277	−0.407639	+	0.913143i	$0.633648\pi$
$614$	5.23321e34	0.735637
$615$	0	0
$616$	4.75369e33	0.0641611
$617$	−9.70987e33	−0.128425	−0.0642124	−	0.997936i	$-0.520454\pi$
$617$	−9.70987e33	−0.128425	−0.0642124	+	0.997936i	$0.520454\pi$
$618$	7.09978e32	0.00920214
$619$	3.18717e34	0.404829	0.202415	−	0.979300i	$-0.435121\pi$
$619$	3.18717e34	0.404829	0.202415	+	0.979300i	$0.435121\pi$
$620$	0	0
$621$	−6.51718e34	−0.795087
$622$	−4.90581e34	−0.586584
$623$	3.37148e34	0.395112
$624$	−2.34463e34	−0.269319
$625$	0	0
$626$	9.83022e34	1.08489
$627$	−2.81975e34	−0.305046
$628$	7.46425e34	0.791572
$629$	−6.56848e34	−0.682860
$630$	0	0
$631$	1.18827e35	1.18726	0.593632	−	0.804737i	$-0.297693\pi$
$631$	1.18827e35	1.18726	0.593632	+	0.804737i	$0.297693\pi$
$632$	−6.42634e34	−0.629506
$633$	−2.79083e34	−0.268032
$634$	2.13804e34	0.201326
$635$	0	0
$636$	1.04372e34	0.0944868
$637$	9.87734e34	0.876793
$638$	4.69715e34	0.408861
$639$	−4.24168e34	−0.362057
$640$	0	0
$641$	1.95210e35	1.60242	0.801212	−	0.598381i	$-0.204189\pi$
$641$	1.95210e35	1.60242	0.801212	+	0.598381i	$0.204189\pi$
$642$	−5.21934e34	−0.420173
$643$	−5.50965e34	−0.434998	−0.217499	−	0.976061i	$-0.569790\pi$
$643$	−5.50965e34	−0.434998	−0.217499	+	0.976061i	$0.569790\pi$
$644$	−1.89346e34	−0.146617
$645$	0	0
$646$	2.62973e34	0.195887
$647$	−1.62013e35	−1.18371	−0.591855	−	0.806045i	$-0.701604\pi$
$647$	−1.62013e35	−1.18371	−0.591855	+	0.806045i	$0.701604\pi$
$648$	−5.78080e34	−0.414286
$649$	1.03854e35	0.730070
$650$	0	0
$651$	−6.08178e34	−0.411404
$652$	−3.17688e34	−0.210817
$653$	6.88298e34	0.448086	0.224043	−	0.974579i	$-0.428074\pi$
$653$	6.88298e34	0.448086	0.224043	+	0.974579i	$0.428074\pi$
$654$	2.21544e35	1.41494
$655$	0	0
$656$	3.19495e34	0.196411
$657$	−5.03972e34	−0.303976
$658$	5.23562e34	0.309845
$659$	−8.31458e34	−0.482806	−0.241403	−	0.970425i	$-0.577608\pi$
$659$	−8.31458e34	−0.482806	−0.241403	+	0.970425i	$0.577608\pi$
$660$	0	0
$661$	−9.81505e34	−0.548749	−0.274375	−	0.961623i	$-0.588471\pi$
$661$	−9.81505e34	−0.548749	−0.274375	+	0.961623i	$0.588471\pi$
$662$	1.22798e35	0.673702
$663$	−1.14684e35	−0.617424
$664$	1.17686e35	0.621761
$665$	0	0
$666$	−3.64788e34	−0.185615
$667$	−1.87094e35	−0.934302
$668$	−4.67702e34	−0.229226
$669$	−2.62951e35	−1.26488
$670$	0	0
$671$	−1.75176e34	−0.0811788
$672$	−1.36373e34	−0.0620317
$673$	−1.38294e34	−0.0617470	−0.0308735	−	0.999523i	$-0.509829\pi$
$673$	−1.38294e34	−0.0617470	−0.0308735	+	0.999523i	$0.509829\pi$
$674$	−9.22512e34	−0.404318
$675$	0	0
$676$	−5.80074e33	−0.0244991
$677$	−3.23088e35	−1.33956	−0.669780	−	0.742559i	$-0.733612\pi$
$677$	−3.23088e35	−1.33956	−0.669780	+	0.742559i	$0.733612\pi$
$678$	−7.58020e34	−0.308538
$679$	−1.31564e34	−0.0525732
$680$	0	0
$681$	−4.94551e35	−1.90490
$682$	−1.25238e35	−0.473620
$683$	−4.94645e35	−1.83669	−0.918343	−	0.395785i	$-0.870473\pi$
$683$	−4.94645e35	−1.83669	−0.918343	+	0.395785i	$0.870473\pi$
$684$	1.46045e34	0.0532459
$685$	0	0
$686$	1.21349e35	0.426564
$687$	−4.99365e35	−1.72369
$688$	2.65040e33	0.00898371
$689$	−5.01182e34	−0.166823
$690$	0	0
$691$	−3.23399e35	−1.03816	−0.519079	−	0.854726i	$-0.673725\pi$
$691$	−3.23399e35	−1.03816	−0.519079	+	0.854726i	$0.673725\pi$
$692$	2.59328e35	0.817565
$693$	1.29132e34	0.0399824
$694$	7.27017e34	0.221081
$695$	0	0
$696$	−1.34751e35	−0.395292
$697$	1.56276e35	0.450279
$698$	2.86372e35	0.810472
$699$	−2.98308e35	−0.829279
$700$	0	0
$701$	3.02063e35	0.810256	0.405128	−	0.914260i	$-0.367227\pi$
$701$	3.02063e35	0.810256	0.405128	+	0.914260i	$0.367227\pi$
$702$	2.25394e35	0.593922
$703$	−2.22475e35	−0.575890
$704$	−2.80823e34	−0.0714127
$705$	0	0
$706$	2.45317e35	0.602100
$707$	1.40562e35	0.338941
$708$	−2.97935e35	−0.705840
$709$	−4.34959e35	−1.01244	−0.506222	−	0.862403i	$-0.668958\pi$
$709$	−4.34959e35	−1.01244	−0.506222	+	0.862403i	$0.668958\pi$
$710$	0	0
$711$	−1.74569e35	−0.392281
$712$	−1.99170e35	−0.439768
$713$	4.98839e35	1.08228
$714$	−6.67049e34	−0.142210
$715$	0	0
$716$	2.49788e35	0.514232
$717$	−2.69922e34	−0.0546071
$718$	1.10621e35	0.219929
$719$	−2.50423e35	−0.489286	−0.244643	−	0.969613i	$-0.578671\pi$
$719$	−2.50423e35	−0.489286	−0.244643	+	0.969613i	$0.578671\pi$
$720$	0	0
$721$	−1.98294e33	−0.00374213
$722$	−2.92172e35	−0.541906
$723$	−6.57286e33	−0.0119819
$724$	5.01917e35	0.899291
$725$	0	0
$726$	−3.03977e35	−0.526179
$727$	6.25077e34	0.106354	0.0531770	−	0.998585i	$-0.483065\pi$
$727$	6.25077e34	0.106354	0.0531770	+	0.998585i	$0.483065\pi$
$728$	6.54847e34	0.109521
$729$	4.21708e35	0.693294
$730$	0	0
$731$	1.29640e34	0.0205955
$732$	5.02542e34	0.0784845
$733$	8.87732e35	1.36296	0.681479	−	0.731838i	$-0.261337\pi$
$733$	8.87732e35	1.36296	0.681479	+	0.731838i	$0.261337\pi$
$734$	6.91835e35	1.04424
$735$	0	0
$736$	1.11856e35	0.163187
$737$	3.48113e35	0.499318
$738$	8.67896e34	0.122395
$739$	−6.31553e35	−0.875698	−0.437849	−	0.899048i	$-0.644260\pi$
$739$	−6.31553e35	−0.875698	−0.437849	+	0.899048i	$0.644260\pi$
$740$	0	0
$741$	−3.88435e35	−0.520704
$742$	−2.91508e34	−0.0384239
$743$	1.51703e35	0.196623	0.0983113	−	0.995156i	$-0.468656\pi$
$743$	1.51703e35	0.196623	0.0983113	+	0.995156i	$0.468656\pi$
$744$	3.59280e35	0.457901
$745$	0	0
$746$	2.39032e35	0.294592
$747$	3.19689e35	0.387455
$748$	−1.37360e35	−0.163716
$749$	1.45774e35	0.170867
$750$	0	0
$751$	1.36888e36	1.55191	0.775954	−	0.630789i	$-0.217269\pi$
$751$	1.36888e36	1.55191	0.775954	+	0.630789i	$0.217269\pi$
$752$	−3.09293e35	−0.344864
$753$	−5.15322e35	−0.565121
$754$	6.47058e35	0.697913
$755$	0	0
$756$	1.31099e35	0.136797
$757$	1.53344e36	1.57386	0.786931	−	0.617040i	$-0.211669\pi$
$757$	1.53344e36	1.57386	0.786931	+	0.617040i	$0.211669\pi$
$758$	−6.21540e35	−0.627486
$759$	−5.86659e35	−0.582590
$760$	0	0
$761$	−1.14959e36	−1.10467	−0.552337	−	0.833621i	$-0.686264\pi$
$761$	−1.14959e36	−1.10467	−0.552337	+	0.833621i	$0.686264\pi$
$762$	1.89159e35	0.178809
$763$	−6.18764e35	−0.575398
$764$	1.89815e35	0.173646
$765$	0	0
$766$	−8.31967e35	−0.736625
$767$	1.43065e36	1.24621
$768$	8.05623e34	0.0690425
$769$	1.22160e36	1.03003	0.515015	−	0.857181i	$-0.327786\pi$
$769$	1.22160e36	1.03003	0.515015	+	0.857181i	$0.327786\pi$
$770$	0	0
$771$	−8.29879e35	−0.677384
$772$	1.15247e34	0.00925582
$773$	6.78971e35	0.536547	0.268273	−	0.963343i	$-0.413547\pi$
$773$	6.78971e35	0.536547	0.268273	+	0.963343i	$0.413547\pi$
$774$	7.19971e33	0.00559826
$775$	0	0
$776$	7.77212e34	0.0585151
$777$	5.64322e35	0.418084
$778$	1.63970e36	1.19542
$779$	5.29307e35	0.379743
$780$	0	0
$781$	1.35123e36	0.938837
$782$	5.47126e35	0.374113
$783$	1.29539e36	0.871725
$784$	−3.39389e35	−0.224774
$785$	0	0
$786$	1.34266e36	0.861359
$787$	9.85723e35	0.622402	0.311201	−	0.950344i	$-0.399269\pi$
$787$	9.85723e35	0.622402	0.311201	+	0.950344i	$0.399269\pi$
$788$	−1.21171e36	−0.753044
$789$	−1.18199e36	−0.723019
$790$	0	0
$791$	2.11712e35	0.125470
$792$	−7.62847e34	−0.0445013
$793$	−2.41314e35	−0.138570
$794$	−3.97766e35	−0.224839
$795$	0	0
$796$	1.07550e36	0.589110
$797$	−1.15299e36	−0.621722	−0.310861	−	0.950455i	$-0.600617\pi$
$797$	−1.15299e36	−0.621722	−0.310861	+	0.950455i	$0.600617\pi$
$798$	−2.25930e35	−0.119933
$799$	−1.51286e36	−0.790613
$800$	0	0
$801$	−5.41038e35	−0.274045
$802$	6.02410e35	0.300409
$803$	1.60545e36	0.788228
$804$	−9.98663e35	−0.482746
$805$	0	0
$806$	−1.72522e36	−0.808454
$807$	1.09697e36	0.506147
$808$	−8.30366e35	−0.377248
$809$	−1.76491e36	−0.789526	−0.394763	−	0.918783i	$-0.629173\pi$
$809$	−1.76491e36	−0.789526	−0.394763	+	0.918783i	$0.629173\pi$
$810$	0	0
$811$	3.26639e36	1.41680	0.708398	−	0.705814i	$-0.249418\pi$
$811$	3.26639e36	1.41680	0.708398	+	0.705814i	$0.249418\pi$
$812$	3.76355e35	0.160749
$813$	2.11356e36	0.888962
$814$	1.16207e36	0.481311
$815$	0	0
$816$	3.94058e35	0.158283
$817$	4.39092e34	0.0173692
$818$	−1.86635e36	−0.727072
$819$	1.77887e35	0.0682488
$820$	0	0
$821$	8.67287e35	0.322755	0.161378	−	0.986893i	$-0.448406\pi$
$821$	8.67287e35	0.322755	0.161378	+	0.986893i	$0.448406\pi$
$822$	2.33906e36	0.857320
$823$	−1.77728e36	−0.641589	−0.320794	−	0.947149i	$-0.603950\pi$
$823$	−1.77728e36	−0.641589	−0.320794	+	0.947149i	$0.603950\pi$
$824$	1.17142e34	0.00416507
$825$	0	0
$826$	8.32121e35	0.287036
$827$	−1.78322e36	−0.605880	−0.302940	−	0.953010i	$-0.597968\pi$
$827$	−1.78322e36	−0.605880	−0.302940	+	0.953010i	$0.597968\pi$
$828$	3.03853e35	0.101691
$829$	−2.64368e36	−0.871521	−0.435760	−	0.900063i	$-0.643521\pi$
$829$	−2.64368e36	−0.871521	−0.435760	+	0.900063i	$0.643521\pi$
$830$	0	0
$831$	−4.89981e36	−1.56735
$832$	−3.86850e35	−0.121899
$833$	−1.66007e36	−0.515303
$834$	−3.10075e36	−0.948180
$835$	0	0
$836$	−4.65240e35	−0.138070
$837$	−3.45383e36	−1.00980
$838$	4.38619e36	1.26339
$839$	6.66972e36	1.89271	0.946354	−	0.323133i	$-0.104736\pi$
$839$	6.66972e36	1.89271	0.946354	+	0.323133i	$0.104736\pi$
$840$	0	0
$841$	8.84259e34	0.0243573
$842$	1.77820e36	0.482593
$843$	3.87947e36	1.03735
$844$	−4.60469e35	−0.121317
$845$	0	0
$846$	−8.40185e35	−0.214904
$847$	8.48997e35	0.213975
$848$	1.72208e35	0.0427666
$849$	3.56349e36	0.872026
$850$	0	0
$851$	−4.62867e36	−1.09986
$852$	−3.87638e36	−0.907678
$853$	−5.04065e36	−1.16312	−0.581559	−	0.813504i	$-0.697557\pi$
$853$	−5.04065e36	−1.16312	−0.581559	+	0.813504i	$0.697557\pi$
$854$	−1.40358e35	−0.0319164
$855$	0	0
$856$	−8.61159e35	−0.190178
$857$	1.92537e36	0.419038	0.209519	−	0.977805i	$-0.432810\pi$
$857$	1.92537e36	0.419038	0.209519	+	0.977805i	$0.432810\pi$
$858$	2.02894e36	0.435189
$859$	4.40642e36	0.931474	0.465737	−	0.884923i	$-0.345789\pi$
$859$	4.40642e36	0.931474	0.465737	+	0.884923i	$0.345789\pi$
$860$	0	0
$861$	−1.34262e36	−0.275686
$862$	−3.06940e36	−0.621172
$863$	−8.01223e36	−1.59815	−0.799077	−	0.601229i	$-0.794678\pi$
$863$	−8.01223e36	−1.59815	−0.799077	+	0.601229i	$0.794678\pi$
$864$	−7.74462e35	−0.152257
$865$	0	0
$866$	1.27139e36	0.242831
$867$	−3.94033e36	−0.741812
$868$	−1.00346e36	−0.186209
$869$	5.56106e36	1.01721
$870$	0	0
$871$	4.79545e36	0.852319
$872$	3.65534e36	0.640430
$873$	2.11127e35	0.0364641
$874$	1.85312e36	0.315508
$875$	0	0
$876$	−4.60569e36	−0.762068
$877$	4.46078e36	0.727639	0.363820	−	0.931469i	$-0.381472\pi$
$877$	4.46078e36	0.727639	0.363820	+	0.931469i	$0.381472\pi$
$878$	1.61379e36	0.259518
$879$	−1.02861e36	−0.163075
$880$	0	0
$881$	3.24157e36	0.499525	0.249762	−	0.968307i	$-0.419648\pi$
$881$	3.24157e36	0.499525	0.249762	+	0.968307i	$0.419648\pi$
$882$	−9.21937e35	−0.140070
$883$	4.92118e35	0.0737157	0.0368579	−	0.999321i	$-0.488265\pi$
$883$	4.92118e35	0.0737157	0.0368579	+	0.999321i	$0.488265\pi$
$884$	−1.89221e36	−0.279458
$885$	0	0
$886$	−5.27831e36	−0.757833
$887$	−1.07566e37	−1.52276	−0.761380	−	0.648306i	$-0.775478\pi$
$887$	−1.07566e37	−1.52276	−0.761380	+	0.648306i	$0.775478\pi$
$888$	−3.33372e36	−0.465337
$889$	−5.28314e35	−0.0727143
$890$	0	0
$891$	5.00244e36	0.669439
$892$	−4.33853e36	−0.572508
$893$	−5.12407e36	−0.666763
$894$	−3.99192e36	−0.512228
$895$	0	0
$896$	−2.25007e35	−0.0280767
$897$	−8.08154e36	−0.994463
$898$	1.08453e37	1.31609
$899$	−9.91520e36	−1.18660
$900$	0	0
$901$	8.42327e35	0.0980439
$902$	−2.76476e36	−0.317377
$903$	−1.11378e35	−0.0126097
$904$	−1.25069e36	−0.139651
$905$	0	0
$906$	3.71053e36	0.403026
$907$	−5.76079e35	−0.0617151	−0.0308575	−	0.999524i	$-0.509824\pi$
$907$	−5.76079e35	−0.0617151	−0.0308575	+	0.999524i	$0.509824\pi$
$908$	−8.15978e36	−0.862194
$909$	−2.25566e36	−0.235085
$910$	0	0
$911$	−2.28818e36	−0.232012	−0.116006	−	0.993249i	$-0.537009\pi$
$911$	−2.28818e36	−0.232012	−0.116006	+	0.993249i	$0.537009\pi$
$912$	1.33468e36	0.133487
$913$	−1.01840e37	−1.00469
$914$	−1.39890e37	−1.36131
$915$	0	0
$916$	−8.23922e36	−0.780176
$917$	−3.75000e36	−0.350279
$918$	−3.78816e36	−0.349056
$919$	3.48143e36	0.316457	0.158228	−	0.987403i	$-0.449422\pi$
$919$	3.48143e36	0.316457	0.158228	+	0.987403i	$0.449422\pi$
$920$	0	0
$921$	1.29915e37	1.14925
$922$	−1.45797e37	−1.27237
$923$	1.86139e37	1.60256
$924$	1.18011e36	0.100236
$925$	0	0
$926$	9.72584e36	0.804063
$927$	3.18212e34	0.00259549
$928$	−2.22331e36	−0.178917
$929$	−4.39451e36	−0.348910	−0.174455	−	0.984665i	$-0.555816\pi$
$929$	−4.39451e36	−0.348910	−0.174455	+	0.984665i	$0.555816\pi$
$930$	0	0
$931$	−5.62265e36	−0.434581
$932$	−4.92190e36	−0.375348
$933$	−1.21788e37	−0.916394
$934$	−6.02292e36	−0.447168
$935$	0	0
$936$	−1.05086e36	−0.0759623
$937$	−2.04937e37	−1.46176	−0.730878	−	0.682508i	$-0.760889\pi$
$937$	−2.04937e37	−1.46176	−0.730878	+	0.682508i	$0.760889\pi$
$938$	2.78923e36	0.196313
$939$	2.44037e37	1.69487
$940$	0	0
$941$	−7.85670e36	−0.531337	−0.265668	−	0.964064i	$-0.585593\pi$
$941$	−7.85670e36	−0.531337	−0.265668	+	0.964064i	$0.585593\pi$
$942$	1.85301e37	1.23664
$943$	1.10124e37	0.725249
$944$	−4.91574e36	−0.319477
$945$	0	0
$946$	−2.29353e35	−0.0145166
$947$	7.10609e36	0.443870	0.221935	−	0.975061i	$-0.428763\pi$
$947$	7.10609e36	0.443870	0.221935	+	0.975061i	$0.428763\pi$
$948$	−1.59535e37	−0.983449
$949$	2.21159e37	1.34548
$950$	0	0
$951$	5.30772e36	0.314522
$952$	−1.10059e36	−0.0643670
$953$	1.19839e37	0.691729	0.345864	−	0.938285i	$-0.387586\pi$
$953$	1.19839e37	0.691729	0.345864	+	0.938285i	$0.387586\pi$
$954$	4.67796e35	0.0266503
$955$	0	0
$956$	−4.45354e35	−0.0247162
$957$	1.16608e37	0.638745
$958$	−6.40392e36	−0.346240
$959$	−6.53289e36	−0.348637
$960$	0	0
$961$	7.20357e36	0.374546
$962$	1.60081e37	0.821583
$963$	−2.33931e36	−0.118511
$964$	−1.08448e35	−0.00542324
$965$	0	0
$966$	−4.70055e36	−0.229052
$967$	3.63759e37	1.74978	0.874890	−	0.484322i	$-0.160934\pi$
$967$	3.63759e37	1.74978	0.874890	+	0.484322i	$0.160934\pi$
$968$	−5.01544e36	−0.238159
$969$	6.52836e36	0.306025
$970$	0	0
$971$	−2.46036e36	−0.112398	−0.0561990	−	0.998420i	$-0.517898\pi$
$971$	−2.46036e36	−0.112398	−0.0561990	+	0.998420i	$0.517898\pi$
$972$	−4.80208e36	−0.216572
$973$	8.66027e36	0.385586
$974$	−1.71295e37	−0.752934
$975$	0	0
$976$	8.29163e35	0.0355236
$977$	−7.12253e36	−0.301268	−0.150634	−	0.988590i	$-0.548131\pi$
$977$	−7.12253e36	−0.301268	−0.150634	+	0.988590i	$0.548131\pi$
$978$	−7.88666e36	−0.329350
$979$	1.72353e37	0.710614
$980$	0	0
$981$	9.92960e36	0.399088
$982$	1.69407e36	0.0672260
$983$	3.14802e37	1.23344	0.616720	−	0.787183i	$-0.288461\pi$
$983$	3.14802e37	1.23344	0.616720	+	0.787183i	$0.288461\pi$
$984$	7.93152e36	0.306844
$985$	0	0
$986$	−1.08750e37	−0.410173
$987$	1.29975e37	0.484057
$988$	−6.40894e36	−0.235681
$989$	9.13547e35	0.0331724
$990$	0	0
$991$	2.04047e37	0.722454	0.361227	−	0.932478i	$-0.382358\pi$
$991$	2.04047e37	0.722454	0.361227	+	0.932478i	$0.382358\pi$
$992$	5.92790e36	0.207255
$993$	3.04849e37	1.05249
$994$	1.08266e37	0.369115
$995$	0	0
$996$	2.92157e37	0.971348
$997$	−1.06204e37	−0.348700	−0.174350	−	0.984684i	$-0.555782\pi$
$997$	−1.06204e37	−0.348700	−0.174350	+	0.984684i	$0.555782\pi$
$998$	2.12904e37	0.690323
$999$	3.20478e37	1.02619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.a.l.1.5		6
5.2	odd	4		10.26.b.a.9.8	yes	12
5.3	odd	4		10.26.b.a.9.5	✓	12
5.4	even	2		50.26.a.k.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.b.a.9.5	✓	12	5.3	odd	4
10.26.b.a.9.8	yes	12	5.2	odd	4
50.26.a.k.1.2		6	5.4	even	2
50.26.a.l.1.5		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+4096.00 q^{2} +1.01684e6 q^{3} +1.67772e7 q^{4} +4.16497e9 q^{6} -1.16326e10 q^{7} +6.87195e10 q^{8} +1.86674e11 q^{9} -5.94667e12 q^{11} +1.70597e13 q^{12} -8.19186e13 q^{13} -4.76472e13 q^{14} +2.81475e14 q^{16} +1.37679e15 q^{17} +7.64617e14 q^{18} +4.66320e15 q^{19} -1.18285e16 q^{21} -2.43576e16 q^{22} +9.70196e16 q^{23} +6.98767e16 q^{24} -3.35539e17 q^{26} -6.71739e17 q^{27} -1.95163e17 q^{28} -1.92842e18 q^{29} +5.14163e18 q^{31} +1.15292e18 q^{32} -6.04681e18 q^{33} +5.63933e18 q^{34} +3.13187e18 q^{36} -4.77086e19 q^{37} +1.91005e19 q^{38} -8.32981e19 q^{39} +1.13507e20 q^{41} -4.84495e19 q^{42} +9.41611e18 q^{43} -9.97685e19 q^{44} +3.97392e20 q^{46} -1.09883e21 q^{47} +2.86215e20 q^{48} -1.20575e21 q^{49} +1.39998e21 q^{51} -1.37437e21 q^{52} +6.11805e20 q^{53} -2.75144e21 q^{54} -7.99387e20 q^{56} +4.74172e21 q^{57} -7.89879e21 q^{58} -1.74642e22 q^{59} +2.94578e21 q^{61} +2.10601e22 q^{62} -2.17151e21 q^{63} +4.72237e21 q^{64} -2.47677e22 q^{66} -5.85392e22 q^{67} +2.30987e22 q^{68} +9.86533e22 q^{69} -2.27224e23 q^{71} +1.28281e22 q^{72} -2.69974e23 q^{73} -1.95415e23 q^{74} +7.82355e22 q^{76} +6.91753e22 q^{77} -3.41189e23 q^{78} -9.35155e23 q^{79} -8.41218e23 q^{81} +4.64926e23 q^{82} +1.71255e24 q^{83} -1.98449e23 q^{84} +3.85684e22 q^{86} -1.96089e24 q^{87} -4.08652e23 q^{88} -2.89830e24 q^{89} +9.52927e23 q^{91} +1.62772e24 q^{92} +5.22821e24 q^{93} -4.50081e24 q^{94} +1.17234e24 q^{96} +1.13099e24 q^{97} -4.93876e24 q^{98} -1.11009e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 24576 q^{2} - 801416 q^{3} + 100663296 q^{4} - 3282599936 q^{6} - 34007705352 q^{7} + 412316860416 q^{8} + 541468782118 q^{9} + 9861544614312 q^{11} - 13445529337856 q^{12} - 30787386783696 q^{13}+ \cdots - 20\!\cdots\!64 q^{99}+O(q^{100}) \) 6 * q + 24576 * q^2 - 801416 * q^3 + 100663296 * q^4 - 3282599936 * q^6 - 34007705352 * q^7 + 412316860416 * q^8 + 541468782118 * q^9 + 9861544614312 * q^11 - 13445529337856 * q^12 - 30787386783696 * q^13 - 139295561121792 * q^14 + 1688849860263936 * q^16 - 3432836939805312 * q^17 + 2217856131555328 * q^18 + 2007656488916520 * q^19 - 28181710291014728 * q^21 + 40392886740221952 * q^22 - 135711886432707576 * q^23 - 55072888167858176 * q^24 - 126105136266018816 * q^26 - 788054364552235760 * q^27 - 570554618354860032 * q^28 - 2926032031655504820 * q^29 + 79292935777014912 * q^31 + 6917529027641081856 * q^32 + 6844843638395003168 * q^33 - 14060900105442557952 * q^34 + 9084338714850623488 * q^36 - 3345885298190974032 * q^37 + 8223360978602065920 * q^38 + 124726636622561793456 * q^39 + 103229301719876244012 * q^41 - 115432285351996325888 * q^42 - 166390524239317503336 * q^43 + 165449264087949115392 * q^44 - 555875886828370231296 * q^46 - 405906243391034677992 * q^47 - 225578549935547088896 * q^48 + 1716280748139027694542 * q^49 - 1516225893661962013568 * q^51 - 516526638145613070336 * q^52 - 9772760301640799789616 * q^53 - 3227870677205957672960 * q^54 - 2336991716781506691072 * q^56 - 26174725126915157341920 * q^57 - 11985027201660947742720 * q^58 - 12499075130880780168840 * q^59 + 3687285610311118296612 * q^61 + 324783864942653079552 * q^62 - 93007818034972665339656 * q^63 + 28334198897217871282176 * q^64 + 28036479542865932976128 * q^66 - 16759935062266648886712 * q^67 - 57593446831892717371392 * q^68 + 185125325982378999854536 * q^69 + 74568876221253661649712 * q^71 + 37209451376028153806848 * q^72 - 381797761857106829638176 * q^73 - 13704746181390229635072 * q^74 + 33682886568354062008320 * q^76 + 80271541631956375339296 * q^77 + 510880303606013105995776 * q^78 - 400850316873811624799520 * q^79 - 1432110118616113828343714 * q^81 + 422827219844613095473152 * q^82 + 2423159733509985740001144 * q^83 - 472810640801776950837248 * q^84 - 681535587284244493664256 * q^86 + 1231328665433636473947120 * q^87 + 677680185704239576645632 * q^88 + 2982172528060341024616740 * q^89 - 7001711719121019241314768 * q^91 - 2276867632449004467388416 * q^92 + 8806417055581711481018368 * q^93 - 1662591972929678041055232 * q^94 - 923969740536000876118016 * q^96 + 4960469410756873985567808 * q^97 + 7029885944377457436844032 * q^98 - 2053720289282411723573464 * q^99

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