LMFDB - Embedded newform 50.26.a.i.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [50,26,Mod(1,50)] 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("50.1"); S:= CuspForms(chi, 26); N := Newforms(S);

sage: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")

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

Newform invariants

comment:select newform

sage:traces = [5,-20480,-723995] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$197.998389976$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 25534923283x^{3} - 31863478542482x^{2} + 141941149085067124800x + 2515032055818200956928000 $ x^5 - 25534923283x^3 - 31863478542482x^2 + 141941149085067124800*x + 2515032055818200956928000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{19}\cdot 3^{5}\cdot 5^{12} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-136720.$ 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)

$f(q)$	$=$	\(q-4096.00 q^{2} +1.22241e6 q^{3} +1.67772e7 q^{4} -5.00697e9 q^{6} -6.80801e10 q^{7} -6.87195e10 q^{8} +6.46987e11 q^{9} -1.63529e13 q^{11} +2.05086e13 q^{12} -1.23277e14 q^{13} +2.78856e14 q^{14} +2.81475e14 q^{16} -1.24327e15 q^{17} -2.65006e15 q^{18} +1.08089e16 q^{19} -8.32215e16 q^{21} +6.69815e16 q^{22} -1.26942e17 q^{23} -8.40031e16 q^{24} +5.04942e17 q^{26} -2.44849e17 q^{27} -1.14219e18 q^{28} -1.19617e18 q^{29} +3.33827e18 q^{31} -1.15292e18 q^{32} -1.99899e19 q^{33} +5.09242e18 q^{34} +1.08546e19 q^{36} -5.02410e19 q^{37} -4.42734e19 q^{38} -1.50694e20 q^{39} -2.63431e20 q^{41} +3.40875e20 q^{42} -1.36754e20 q^{43} -2.74356e20 q^{44} +5.19955e20 q^{46} +7.03907e20 q^{47} +3.44077e20 q^{48} +3.29383e21 q^{49} -1.51978e21 q^{51} -2.06824e21 q^{52} +3.75972e21 q^{53} +1.00290e21 q^{54} +4.67843e21 q^{56} +1.32129e22 q^{57} +4.89952e21 q^{58} -6.89657e21 q^{59} +1.54607e22 q^{61} -1.36736e22 q^{62} -4.40470e22 q^{63} +4.72237e21 q^{64} +8.18786e22 q^{66} +8.66895e22 q^{67} -2.08585e22 q^{68} -1.55175e23 q^{69} +4.41872e22 q^{71} -4.44606e22 q^{72} +8.03151e22 q^{73} +2.05787e23 q^{74} +1.81344e23 q^{76} +1.11331e24 q^{77} +6.17244e23 q^{78} -5.07310e23 q^{79} -8.47490e23 q^{81} +1.07901e24 q^{82} -5.22032e23 q^{83} -1.39623e24 q^{84} +5.60143e23 q^{86} -1.46221e24 q^{87} +1.12376e24 q^{88} -1.15373e24 q^{89} +8.39270e24 q^{91} -2.12974e24 q^{92} +4.08072e24 q^{93} -2.88320e24 q^{94} -1.40934e24 q^{96} +4.89110e24 q^{97} -1.34915e25 q^{98} -1.05801e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 20480 q^{2} - 723995 q^{3} + 83886080 q^{4} + 2965483520 q^{6} - 49218886190 q^{7} - 343597383680 q^{8} + 975375361390 q^{9} - 8837033983815 q^{11} - 12146620497920 q^{12} - 67609989586220 q^{13}+ \cdots - 23\!\cdots\!70 q^{99}+O(q^{100}) $ 5 * q - 20480 * q^2 - 723995 * q^3 + 83886080 * q^4 + 2965483520 * q^6 - 49218886190 * q^7 - 343597383680 * q^8 + 975375361390 * q^9 - 8837033983815 * q^11 - 12146620497920 * q^12 - 67609989586220 * q^13 + 201600557834240 * q^14 + 1407374883553280 * q^16 - 1543441123223415 * q^17 - 3995137480253440 * q^18 + 6828205451077225 * q^19 - 56457058818760990 * q^21 + 36196491197706240 * q^22 - 175655399207336370 * q^23 + 49752557559480320 * q^24 + 276930517345157120 * q^26 - 1102363638369718625 * q^27 - 825755884889047040 * q^28 + 2616960879251719800 * q^29 + 1381921297247629210 * q^31 - 5764607523034234880 * q^32 - 14683366800887949615 * q^33 + 6321934840723107840 * q^34 + 16364083119118090240 * q^36 - 68054744257794520190 * q^37 - 27968329527612313600 * q^38 - 76418447091053627020 * q^39 + 110646765257217206385 * q^41 + 231248112921645015040 * q^42 + 169174323273383550580 * q^43 - 148260827945804759040 * q^44 + 719484515153249771520 * q^46 + 1653792144435756647460 * q^47 - 203786475763631390720 * q^48 + 4971416583743605737585 * q^49 - 954942568710765966615 * q^51 - 1134307399045763563520 * q^52 - 4245089483221901865570 * q^53 + 4515281462762367488000 * q^54 + 3382296104505536675840 * q^56 + 11353190237350969575425 * q^57 - 10719071761415044300800 * q^58 + 33041536388165595960600 * q^59 - 11589871696744004976590 * q^61 - 5660349633526289244160 * q^62 - 87882675280033083250420 * q^63 + 23611832414348226068480 * q^64 + 60143070416437041623040 * q^66 + 92154529366841541565735 * q^67 - 25894645107601849712640 * q^68 + 67961625053826065275230 * q^69 + 177839620469327433418260 * q^71 - 67027284455907697623040 * q^72 - 192252066408262024306145 * q^73 + 278752232479926354698240 * q^74 + 114558277745100036505600 * q^76 - 420363080385387083988630 * q^77 + 313009959284955656273920 * q^78 - 220198603705551780910250 * q^79 - 1595228143213014227240195 * q^81 - 453209150493561677352960 * q^82 - 1018803599085572371644645 * q^83 - 947192270527057981603840 * q^84 - 692938028127779023175680 * q^86 - 6970820850065961522685800 * q^87 + 607276351266016293027840 * q^88 - 5932331377929555403184925 * q^89 + 3355259607310216720714760 * q^91 - 2947008574067711064145920 * q^92 - 3721806140580454551574390 * q^93 - 6773932623608859227996160 * q^94 + 834709404727834176389120 * q^96 + 377622858226960257754810 * q^97 - 20362922327013809101148160 * q^98 - 23196936518287622996926170 * 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
$3$	1.22241e6	1.32801	0.664003	−	0.747730i	$-0.268856\pi$
$3$	1.22241e6	1.32801	0.664003	+	0.747730i	$0.268856\pi$
$4$	1.67772e7	0.500000
$5$	0	0
$5$	0	0
$6$	−5.00697e9	−0.939041
$7$	−6.80801e10	−1.85907	−0.929533	−	0.368739i	$-0.879789\pi$
$7$	−6.80801e10	−1.85907	−0.929533	+	0.368739i	$0.879789\pi$
$8$	−6.87195e10	−0.353553
$9$	6.46987e11	0.763597
$10$	0	0
$11$	−1.63529e13	−1.57104	−0.785519	−	0.618838i	$-0.787604\pi$
$11$	−1.63529e13	−1.57104	−0.785519	+	0.618838i	$0.787604\pi$
$12$	2.05086e13	0.664003
$13$	−1.23277e14	−1.46754	−0.733769	−	0.679399i	$-0.762241\pi$
$13$	−1.23277e14	−1.46754	−0.733769	+	0.679399i	$0.762241\pi$
$14$	2.78856e14	1.31456
$15$	0	0
$16$	2.81475e14	0.250000
$17$	−1.24327e15	−0.517550	−0.258775	−	0.965938i	$-0.583319\pi$
$17$	−1.24327e15	−0.517550	−0.258775	+	0.965938i	$0.583319\pi$
$18$	−2.65006e15	−0.539945
$19$	1.08089e16	1.12037	0.560187	−	0.828366i	$-0.310729\pi$
$19$	1.08089e16	1.12037	0.560187	+	0.828366i	$0.310729\pi$
$20$	0	0
$21$	−8.32215e16	−2.46885
$22$	6.69815e16	1.11089
$23$	−1.26942e17	−1.20784	−0.603918	−	0.797046i	$-0.706395\pi$
$23$	−1.26942e17	−1.20784	−0.603918	+	0.797046i	$0.706395\pi$
$24$	−8.40031e16	−0.469521
$25$	0	0
$26$	5.04942e17	1.03771
$27$	−2.44849e17	−0.313944
$28$	−1.14219e18	−0.929533
$29$	−1.19617e18	−0.627797	−0.313898	−	0.949457i	$-0.601635\pi$
$29$	−1.19617e18	−0.627797	−0.313898	+	0.949457i	$0.601635\pi$
$30$	0	0
$31$	3.33827e18	0.761203	0.380602	−	0.924739i	$-0.375717\pi$
$31$	3.33827e18	0.761203	0.380602	+	0.924739i	$0.375717\pi$
$32$	−1.15292e18	−0.176777
$33$	−1.99899e19	−2.08635
$34$	5.09242e18	0.365963
$35$	0	0
$36$	1.08546e19	0.381799
$37$	−5.02410e19	−1.25469	−0.627346	−	0.778741i	$-0.715859\pi$
$37$	−5.02410e19	−1.25469	−0.627346	+	0.778741i	$0.715859\pi$
$38$	−4.42734e19	−0.792224
$39$	−1.50694e20	−1.94890
$40$	0	0
$41$	−2.63431e20	−1.82335	−0.911673	−	0.410917i	$-0.865209\pi$
$41$	−2.63431e20	−1.82335	−0.911673	+	0.410917i	$0.865209\pi$
$42$	3.40875e20	1.74574
$43$	−1.36754e20	−0.521895	−0.260947	−	0.965353i	$-0.584035\pi$
$43$	−1.36754e20	−0.521895	−0.260947	+	0.965353i	$0.584035\pi$
$44$	−2.74356e20	−0.785519
$45$	0	0
$46$	5.19955e20	0.854069
$47$	7.03907e20	0.883674	0.441837	−	0.897095i	$-0.354327\pi$
$47$	7.03907e20	0.883674	0.441837	+	0.897095i	$0.354327\pi$
$48$	3.44077e20	0.332001
$49$	3.29383e21	2.45613
$50$	0	0
$51$	−1.51978e21	−0.687309
$52$	−2.06824e21	−0.733769
$53$	3.75972e21	1.05125	0.525626	−	0.850716i	$-0.323831\pi$
$53$	3.75972e21	1.05125	0.525626	+	0.850716i	$0.323831\pi$
$54$	1.00290e21	0.221992
$55$	0	0
$56$	4.67843e21	0.657279
$57$	1.32129e22	1.48786
$58$	4.89952e21	0.443919
$59$	−6.89657e21	−0.504642	−0.252321	−	0.967644i	$-0.581194\pi$
$59$	−6.89657e21	−0.504642	−0.252321	+	0.967644i	$0.581194\pi$
$60$	0	0
$61$	1.54607e22	0.745773	0.372886	−	0.927877i	$-0.378368\pi$
$61$	1.54607e22	0.745773	0.372886	+	0.927877i	$0.378368\pi$
$62$	−1.36736e22	−0.538252
$63$	−4.40470e22	−1.41958
$64$	4.72237e21	0.125000
$65$	0	0
$66$	8.18786e22	1.47527
$67$	8.66895e22	1.29429	0.647145	−	0.762367i	$-0.275963\pi$
$67$	8.66895e22	1.29429	0.647145	+	0.762367i	$0.275963\pi$
$68$	−2.08585e22	−0.258775
$69$	−1.55175e23	−1.60401
$70$	0	0
$71$	4.41872e22	0.319571	0.159785	−	0.987152i	$-0.448920\pi$
$71$	4.41872e22	0.319571	0.159785	+	0.987152i	$0.448920\pi$
$72$	−4.44606e22	−0.269972
$73$	8.03151e22	0.410451	0.205226	−	0.978715i	$-0.434207\pi$
$73$	8.03151e22	0.410451	0.205226	+	0.978715i	$0.434207\pi$
$74$	2.05787e23	0.887201
$75$	0	0
$76$	1.81344e23	0.560187
$77$	1.11331e24	2.92066
$78$	6.17244e23	1.37808
$79$	−5.07310e23	−0.965906	−0.482953	−	0.875646i	$-0.660436\pi$
$79$	−5.07310e23	−0.965906	−0.482953	+	0.875646i	$0.660436\pi$
$80$	0	0
$81$	−8.47490e23	−1.18052
$82$	1.07901e24	1.28930
$83$	−5.22032e23	−0.536070	−0.268035	−	0.963409i	$-0.586374\pi$
$83$	−5.22032e23	−0.536070	−0.268035	+	0.963409i	$0.586374\pi$
$84$	−1.39623e24	−1.23442
$85$	0	0
$86$	5.60143e23	0.369035
$87$	−1.46221e24	−0.833717
$88$	1.12376e24	0.555446
$89$	−1.15373e24	−0.495142	−0.247571	−	0.968870i	$-0.579632\pi$
$89$	−1.15373e24	−0.495142	−0.247571	+	0.968870i	$0.579632\pi$
$90$	0	0
$91$	8.39270e24	2.72825
$92$	−2.12974e24	−0.603918
$93$	4.08072e24	1.01088
$94$	−2.88320e24	−0.624852
$95$	0	0
$96$	−1.40934e24	−0.234760
$97$	4.89110e24	0.715748	0.357874	−	0.933770i	$-0.383502\pi$
$97$	4.89110e24	0.715748	0.357874	+	0.933770i	$0.383502\pi$
$98$	−1.34915e25	−1.73674
$99$	−1.05801e25	−1.19964
$100$	0	0
$101$	1.39348e25	1.23051	0.615255	−	0.788328i	$-0.289053\pi$
$101$	1.39348e25	1.23051	0.615255	+	0.788328i	$0.289053\pi$
$102$	6.22500e24	0.486001
$103$	−1.11068e25	−0.767579	−0.383789	−	0.923421i	$-0.625381\pi$
$103$	−1.11068e25	−0.767579	−0.383789	+	0.923421i	$0.625381\pi$
$104$	8.47152e24	0.518853
$105$	0	0
$106$	−1.53998e25	−0.743348
$107$	−2.28767e25	−0.981967	−0.490983	−	0.871169i	$-0.663362\pi$
$107$	−2.28767e25	−0.981967	−0.490983	+	0.871169i	$0.663362\pi$
$108$	−4.10789e24	−0.156972
$109$	3.92414e25	1.33633	0.668164	−	0.744014i	$-0.267081\pi$
$109$	3.92414e25	1.33633	0.668164	+	0.744014i	$0.267081\pi$
$110$	0	0
$111$	−6.14149e25	−1.66624
$112$	−1.91628e25	−0.464766
$113$	−2.95166e25	−0.640599	−0.320299	−	0.947316i	$-0.603784\pi$
$113$	−2.95166e25	−0.640599	−0.320299	+	0.947316i	$0.603784\pi$
$114$	−5.41201e25	−1.05208
$115$	0	0
$116$	−2.00685e25	−0.313898
$117$	−7.97585e25	−1.12061
$118$	2.82484e25	0.356835
$119$	8.46417e25	0.962160
$120$	0	0
$121$	1.59071e26	1.46816
$122$	−6.33271e25	−0.527341
$123$	−3.22020e26	−2.42141
$124$	5.60069e25	0.380602
$125$	0	0
$126$	1.80416e26	1.00379
$127$	−3.71288e25	−0.187139	−0.0935696	−	0.995613i	$-0.529828\pi$
$127$	−3.71288e25	−0.187139	−0.0935696	+	0.995613i	$0.529828\pi$
$128$	−1.93428e25	−0.0883883
$129$	−1.67168e26	−0.693079
$130$	0	0
$131$	−2.02734e26	−0.693482	−0.346741	−	0.937961i	$-0.612712\pi$
$131$	−2.02734e26	−0.693482	−0.346741	+	0.937961i	$0.612712\pi$
$132$	−3.35375e26	−1.04317
$133$	−7.35874e26	−2.08285
$134$	−3.55080e26	−0.915201
$135$	0	0
$136$	8.54366e25	0.182982
$137$	−4.21478e26	−0.823697	−0.411848	−	0.911252i	$-0.635117\pi$
$137$	−4.21478e26	−0.823697	−0.411848	+	0.911252i	$0.635117\pi$
$138$	6.35596e26	1.13421
$139$	−2.61876e26	−0.426983	−0.213491	−	0.976945i	$-0.568484\pi$
$139$	−2.61876e26	−0.426983	−0.213491	+	0.976945i	$0.568484\pi$
$140$	0	0
$141$	8.60460e26	1.17352
$142$	−1.80991e26	−0.225971
$143$	2.01593e27	2.30556
$144$	1.82111e26	0.190899
$145$	0	0
$146$	−3.28971e26	−0.290233
$147$	4.02640e27	3.26175
$148$	−8.42905e26	−0.627346
$149$	5.33091e26	0.364732	0.182366	−	0.983231i	$-0.441625\pi$
$149$	5.33091e26	0.364732	0.182366	+	0.983231i	$0.441625\pi$
$150$	0	0
$151$	−1.15195e26	−0.0667148	−0.0333574	−	0.999443i	$-0.510620\pi$
$151$	−1.15195e26	−0.0667148	−0.0333574	+	0.999443i	$0.510620\pi$
$152$	−7.42784e26	−0.396112
$153$	−8.04377e26	−0.395200
$154$	−4.56011e27	−2.06522
$155$	0	0
$156$	−2.52823e27	−0.974449
$157$	−7.11181e26	−0.253066	−0.126533	−	0.991962i	$-0.540385\pi$
$157$	−7.11181e26	−0.253066	−0.126533	+	0.991962i	$0.540385\pi$
$158$	2.07794e27	0.682999
$159$	4.59590e27	1.39607
$160$	0	0
$161$	8.64224e27	2.24545
$162$	3.47132e27	0.834751
$163$	−4.92749e27	−1.09719	−0.548594	−	0.836089i	$-0.684837\pi$
$163$	−4.92749e27	−1.09719	−0.548594	+	0.836089i	$0.684837\pi$
$164$	−4.41964e27	−0.911673
$165$	0	0
$166$	2.13825e27	0.379059
$167$	−1.54847e26	−0.0254651	−0.0127326	−	0.999919i	$-0.504053\pi$
$167$	−1.54847e26	−0.0254651	−0.0127326	+	0.999919i	$0.504053\pi$
$168$	5.71894e27	0.872870
$169$	8.14076e27	1.15367
$170$	0	0
$171$	6.99325e27	0.855515
$172$	−2.29434e27	−0.260947
$173$	1.24940e28	1.32168	0.660840	−	0.750527i	$-0.270200\pi$
$173$	1.24940e28	1.32168	0.660840	+	0.750527i	$0.270200\pi$
$174$	5.98921e27	0.589527
$175$	0	0
$176$	−4.60293e27	−0.392759
$177$	−8.43041e27	−0.670167
$178$	4.72569e27	0.350118
$179$	1.81393e28	1.25302	0.626509	−	0.779414i	$-0.284483\pi$
$179$	1.81393e28	1.25302	0.626509	+	0.779414i	$0.284483\pi$
$180$	0	0
$181$	−2.28334e28	−1.37274	−0.686369	−	0.727254i	$-0.740796\pi$
$181$	−2.28334e28	−1.37274	−0.686369	+	0.727254i	$0.740796\pi$
$182$	−3.43765e28	−1.92916
$183$	1.88993e28	0.990390
$184$	8.72340e27	0.427035
$185$	0	0
$186$	−1.67146e28	−0.714801
$187$	2.03310e28	0.813091
$188$	1.18096e28	0.441837
$189$	1.66694e28	0.583642
$190$	0	0
$191$	−3.88305e28	−1.19195	−0.595973	−	0.803005i	$-0.703233\pi$
$191$	−3.88305e28	−1.19195	−0.595973	+	0.803005i	$0.703233\pi$
$192$	5.77265e27	0.166001
$193$	−5.16030e28	−1.39062	−0.695310	−	0.718710i	$-0.744733\pi$
$193$	−5.16030e28	−1.39062	−0.695310	+	0.718710i	$0.744733\pi$
$194$	−2.00340e28	−0.506110
$195$	0	0
$196$	5.52613e28	1.22806
$197$	−4.39578e28	−0.916659	−0.458330	−	0.888782i	$-0.651552\pi$
$197$	−4.39578e28	−0.916659	−0.458330	+	0.888782i	$0.651552\pi$
$198$	4.33362e28	0.848274
$199$	6.89463e28	1.26721	0.633604	−	0.773658i	$-0.281575\pi$
$199$	6.89463e28	1.26721	0.633604	+	0.773658i	$0.281575\pi$
$200$	0	0
$201$	1.05970e29	1.71882
$202$	−5.70771e28	−0.870102
$203$	8.14356e28	1.16712
$204$	−2.54976e28	−0.343655
$205$	0	0
$206$	4.54934e28	0.542760
$207$	−8.21300e28	−0.922301
$208$	−3.46993e28	−0.366885
$209$	−1.76758e29	−1.76015
$210$	0	0
$211$	2.04578e29	1.80854	0.904269	−	0.426962i	$-0.140416\pi$
$211$	2.04578e29	1.80854	0.904269	+	0.426962i	$0.140416\pi$
$212$	6.30776e28	0.525626
$213$	5.40147e28	0.424392
$214$	9.37031e28	0.694355
$215$	0	0
$216$	1.68259e28	0.110996
$217$	−2.27270e29	−1.41513
$218$	−1.60733e29	−0.944926
$219$	9.81777e28	0.545081
$220$	0	0
$221$	1.53266e29	0.759525
$222$	2.51556e29	1.17821
$223$	3.97032e29	1.75798	0.878991	−	0.476839i	$-0.158217\pi$
$223$	3.97032e29	1.75798	0.878991	+	0.476839i	$0.158217\pi$
$224$	7.84910e28	0.328639
$225$	0	0
$226$	1.20900e29	0.452972
$227$	3.06368e29	1.08623	0.543113	−	0.839660i	$-0.317246\pi$
$227$	3.06368e29	1.08623	0.543113	+	0.839660i	$0.317246\pi$
$228$	2.21676e29	0.743931
$229$	2.92488e28	0.0929319	0.0464660	−	0.998920i	$-0.485204\pi$
$229$	2.92488e28	0.0929319	0.0464660	+	0.998920i	$0.485204\pi$
$230$	0	0
$231$	1.36091e30	3.87865
$232$	8.22004e28	0.221960
$233$	3.00032e29	0.767748	0.383874	−	0.923385i	$-0.374590\pi$
$233$	3.00032e29	0.767748	0.383874	+	0.923385i	$0.374590\pi$
$234$	3.26691e29	0.792390
$235$	0	0
$236$	−1.15705e29	−0.252321
$237$	−6.20139e29	−1.28273
$238$	−3.46692e29	−0.680350
$239$	−7.62279e29	−1.41952	−0.709758	−	0.704445i	$-0.751196\pi$
$239$	−7.62279e29	−1.41952	−0.709758	+	0.704445i	$0.751196\pi$
$240$	0	0
$241$	−5.68961e29	−0.954705	−0.477352	−	0.878712i	$-0.658403\pi$
$241$	−5.68961e29	−0.954705	−0.477352	+	0.878712i	$0.658403\pi$
$242$	−6.51553e29	−1.03814
$243$	−8.28519e29	−1.25379
$244$	2.59388e29	0.372886
$245$	0	0
$246$	1.31899e30	1.71220
$247$	−1.33249e30	−1.64419
$248$	−2.29404e29	−0.269126
$249$	−6.38136e29	−0.711903
$250$	0	0
$251$	7.84848e29	0.792253	0.396127	−	0.918196i	$-0.370354\pi$
$251$	7.84848e29	0.792253	0.396127	+	0.918196i	$0.370354\pi$
$252$	−7.38986e29	−0.709789
$253$	2.07587e30	1.89756
$254$	1.52080e29	0.132327
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	−1.93819e30	−1.45624	−0.728119	−	0.685450i	$-0.759605\pi$
$257$	−1.93819e30	−1.45624	−0.728119	+	0.685450i	$0.759605\pi$
$258$	6.84722e29	0.490081
$259$	3.42041e30	2.33255
$260$	0	0
$261$	−7.73909e29	−0.479384
$262$	8.30399e29	0.490366
$263$	−7.76661e29	−0.437305	−0.218653	−	0.975803i	$-0.570166\pi$
$263$	−7.76661e29	−0.437305	−0.218653	+	0.975803i	$0.570166\pi$
$264$	1.37369e30	0.737634
$265$	0	0
$266$	3.01414e30	1.47280
$267$	−1.41033e30	−0.657551
$268$	1.45441e30	0.647145
$269$	1.26958e30	0.539209	0.269604	−	0.962971i	$-0.413107\pi$
$269$	1.26958e30	0.539209	0.269604	+	0.962971i	$0.413107\pi$
$270$	0	0
$271$	−2.59506e29	−0.100469	−0.0502344	−	0.998737i	$-0.515997\pi$
$271$	−2.59506e29	−0.100469	−0.0502344	+	0.998737i	$0.515997\pi$
$272$	−3.49948e29	−0.129388
$273$	1.02593e31	3.62313
$274$	1.72637e30	0.582442
$275$	0	0
$276$	−2.60340e30	−0.802006
$277$	−4.20101e30	−1.23696	−0.618482	−	0.785799i	$-0.712252\pi$
$277$	−4.20101e30	−1.23696	−0.618482	+	0.785799i	$0.712252\pi$
$278$	1.07264e30	0.301922
$279$	2.15982e30	0.581253
$280$	0	0
$281$	7.34654e30	1.80823	0.904115	−	0.427290i	$-0.140532\pi$
$281$	7.34654e30	1.80823	0.904115	+	0.427290i	$0.140532\pi$
$282$	−3.52444e30	−0.829806
$283$	−7.45011e30	−1.67816	−0.839078	−	0.544011i	$-0.816905\pi$
$283$	−7.45011e30	−1.67816	−0.839078	+	0.544011i	$0.816905\pi$
$284$	7.41339e29	0.159785
$285$	0	0
$286$	−8.25727e30	−1.63028
$287$	1.79344e31	3.38972
$288$	−7.45926e29	−0.134986
$289$	−4.22492e30	−0.732142
$290$	0	0
$291$	5.97891e30	0.950517
$292$	1.34746e30	0.205226
$293$	−3.40180e30	−0.496436	−0.248218	−	0.968704i	$-0.579845\pi$
$293$	−3.40180e30	−0.496436	−0.248218	+	0.968704i	$0.579845\pi$
$294$	−1.64921e31	−2.30640
$295$	0	0
$296$	3.45254e30	0.443601
$297$	4.00400e30	0.493217
$298$	−2.18354e30	−0.257904
$299$	1.56490e31	1.77255
$300$	0	0
$301$	9.31020e30	0.970237
$302$	4.71839e29	0.0471745
$303$	1.70340e31	1.63412
$304$	3.04245e30	0.280093
$305$	0	0
$306$	3.29473e30	0.279449
$307$	−2.05490e31	−1.67325	−0.836624	−	0.547778i	$-0.815474\pi$
$307$	−2.05490e31	−1.67325	−0.836624	+	0.547778i	$0.815474\pi$
$308$	1.86782e31	1.46033
$309$	−1.35770e31	−1.01935
$310$	0	0
$311$	−7.23094e28	−0.00500829	−0.00250415	−	0.999997i	$-0.500797\pi$
$311$	−7.23094e28	−0.00500829	−0.00250415	+	0.999997i	$0.500797\pi$
$312$	1.03556e31	0.689040
$313$	−1.14602e31	−0.732635	−0.366318	−	0.930490i	$-0.619382\pi$
$313$	−1.14602e31	−0.732635	−0.366318	+	0.930490i	$0.619382\pi$
$314$	2.91300e30	0.178945
$315$	0	0
$316$	−8.51125e30	−0.482953
$317$	2.43704e31	1.32929	0.664647	−	0.747158i	$-0.268582\pi$
$317$	2.43704e31	1.32929	0.664647	+	0.747158i	$0.268582\pi$
$318$	−1.88248e31	−0.987170
$319$	1.95609e31	0.986292
$320$	0	0
$321$	−2.79646e31	−1.30406
$322$	−3.53986e31	−1.58777
$323$	−1.34384e31	−0.579850
$324$	−1.42185e31	−0.590258
$325$	0	0
$326$	2.01830e31	0.775828
$327$	4.79689e31	1.77465
$328$	1.81029e31	0.644650
$329$	−4.79220e31	−1.64281
$330$	0	0
$331$	−3.61088e31	−1.14753	−0.573764	−	0.819021i	$-0.694517\pi$
$331$	−3.61088e31	−1.14753	−0.573764	+	0.819021i	$0.694517\pi$
$332$	−8.75825e30	−0.268035
$333$	−3.25053e31	−0.958079
$334$	6.34252e29	0.0180066
$335$	0	0
$336$	−2.34248e31	−0.617212
$337$	−5.01811e31	−1.27399	−0.636995	−	0.770868i	$-0.719823\pi$
$337$	−5.01811e31	−1.27399	−0.636995	+	0.770868i	$0.719823\pi$
$338$	−3.33446e31	−0.815767
$339$	−3.60813e31	−0.850718
$340$	0	0
$341$	−5.45905e31	−1.19588
$342$	−2.86443e31	−0.604940
$343$	−1.32944e32	−2.70703
$344$	9.39763e30	0.184518
$345$	0	0
$346$	−5.11756e31	−0.934569
$347$	−2.69651e31	−0.474988	−0.237494	−	0.971389i	$-0.576326\pi$
$347$	−2.69651e31	−0.474988	−0.237494	+	0.971389i	$0.576326\pi$
$348$	−2.45318e31	−0.416859
$349$	4.66669e31	0.765052	0.382526	−	0.923945i	$-0.375054\pi$
$349$	4.66669e31	0.765052	0.382526	+	0.923945i	$0.375054\pi$
$350$	0	0
$351$	3.01842e31	0.460725
$352$	1.88536e31	0.277723
$353$	−6.63592e31	−0.943446	−0.471723	−	0.881747i	$-0.656368\pi$
$353$	−6.63592e31	−0.943446	−0.471723	+	0.881747i	$0.656368\pi$
$354$	3.45310e31	0.473879
$355$	0	0
$356$	−1.93564e31	−0.247571
$357$	1.03466e32	1.27775
$358$	−7.42985e31	−0.886017
$359$	−7.18124e31	−0.827025	−0.413513	−	0.910498i	$-0.635698\pi$
$359$	−7.18124e31	−0.827025	−0.413513	+	0.910498i	$0.635698\pi$
$360$	0	0
$361$	2.37566e31	0.255238
$362$	9.35254e31	0.970672
$363$	1.94449e32	1.94972
$364$	1.40806e32	1.36413
$365$	0	0
$366$	−7.74114e31	−0.700311
$367$	8.09654e31	0.707903	0.353951	−	0.935264i	$-0.384838\pi$
$367$	8.09654e31	0.707903	0.353951	+	0.935264i	$0.384838\pi$
$368$	−3.57310e31	−0.301959
$369$	−1.70437e32	−1.39230
$370$	0	0
$371$	−2.55962e32	−1.95435
$372$	6.84632e31	0.505441
$373$	1.63975e32	1.17063	0.585313	−	0.810807i	$-0.300972\pi$
$373$	1.63975e32	1.17063	0.585313	+	0.810807i	$0.300972\pi$
$374$	−8.32758e31	−0.574942
$375$	0	0
$376$	−4.83721e31	−0.312426
$377$	1.47460e32	0.921316
$378$	−6.82777e31	−0.412697
$379$	−5.11219e31	−0.298963	−0.149481	−	0.988765i	$-0.547760\pi$
$379$	−5.11219e31	−0.298963	−0.149481	+	0.988765i	$0.547760\pi$
$380$	0	0
$381$	−4.53865e31	−0.248522
$382$	1.59050e32	0.842833
$383$	2.90570e32	1.49028	0.745138	−	0.666911i	$-0.232384\pi$
$383$	2.90570e32	1.49028	0.745138	+	0.666911i	$0.232384\pi$
$384$	−2.36448e31	−0.117380
$385$	0	0
$386$	2.11366e32	0.983317
$387$	−8.84778e31	−0.398518
$388$	8.20591e31	0.357874
$389$	9.70428e31	0.409820	0.204910	−	0.978781i	$-0.434310\pi$
$389$	9.70428e31	0.409820	0.204910	+	0.978781i	$0.434310\pi$
$390$	0	0
$391$	1.57823e32	0.625116
$392$	−2.26350e32	−0.868371
$393$	−2.47823e32	−0.920948
$394$	1.80051e32	0.648176
$395$	0	0
$396$	−1.77505e32	−0.599820
$397$	4.94379e32	1.61875	0.809373	−	0.587295i	$-0.199807\pi$
$397$	4.94379e32	1.61875	0.809373	+	0.587295i	$0.199807\pi$
$398$	−2.82404e32	−0.896051
$399$	−8.99536e32	−2.76603
$400$	0	0
$401$	4.47162e31	0.129170	0.0645848	−	0.997912i	$-0.479428\pi$
$401$	4.47162e31	0.129170	0.0645848	+	0.997912i	$0.479428\pi$
$402$	−4.34052e32	−1.21539
$403$	−4.11531e32	−1.11709
$404$	2.33788e32	0.615255
$405$	0	0
$406$	−3.33560e32	−0.825275
$407$	8.21587e32	1.97117
$408$	1.04438e32	0.243001
$409$	3.47804e32	0.784863	0.392431	−	0.919781i	$-0.371634\pi$
$409$	3.47804e32	0.784863	0.392431	+	0.919781i	$0.371634\pi$
$410$	0	0
$411$	−5.15217e32	−1.09387
$412$	−1.86341e32	−0.383789
$413$	4.69519e32	0.938162
$414$	3.36404e32	0.652165
$415$	0	0
$416$	1.42128e32	0.259427
$417$	−3.20119e32	−0.567035
$418$	7.23999e32	1.24461
$419$	−1.64856e32	−0.275061	−0.137531	−	0.990498i	$-0.543917\pi$
$419$	−1.64856e32	−0.275061	−0.137531	+	0.990498i	$0.543917\pi$
$420$	0	0
$421$	4.59846e32	0.722914	0.361457	−	0.932389i	$-0.382279\pi$
$421$	4.59846e32	0.722914	0.361457	+	0.932389i	$0.382279\pi$
$422$	−8.37951e32	−1.27883
$423$	4.55419e32	0.674771
$424$	−2.58366e32	−0.371674
$425$	0	0
$426$	−2.21244e32	−0.300090
$427$	−1.05257e33	−1.38644
$428$	−3.83808e32	−0.490983
$429$	2.46429e33	3.06179
$430$	0	0
$431$	7.08014e32	0.829996	0.414998	−	0.909822i	$-0.363782\pi$
$431$	7.08014e32	0.829996	0.414998	+	0.909822i	$0.363782\pi$
$432$	−6.89190e31	−0.0784860
$433$	1.74438e32	0.192993	0.0964964	−	0.995333i	$-0.469236\pi$
$433$	1.74438e32	0.192993	0.0964964	+	0.995333i	$0.469236\pi$
$434$	9.30898e32	1.00065
$435$	0	0
$436$	6.58361e32	0.668164
$437$	−1.37211e33	−1.35323
$438$	−4.02136e32	−0.385431
$439$	−9.83917e32	−0.916541	−0.458271	−	0.888813i	$-0.651531\pi$
$439$	−9.83917e32	−0.916541	−0.458271	+	0.888813i	$0.651531\pi$
$440$	0	0
$441$	2.13107e33	1.87549
$442$	−6.27777e32	−0.537065
$443$	−9.66613e32	−0.803908	−0.401954	−	0.915660i	$-0.631669\pi$
$443$	−9.66613e32	−0.803908	−0.401954	+	0.915660i	$0.631669\pi$
$444$	−1.03037e33	−0.833118
$445$	0	0
$446$	−1.62624e33	−1.24308
$447$	6.51654e32	0.484365
$448$	−3.21499e32	−0.232383
$449$	5.74227e32	0.403650	0.201825	−	0.979422i	$-0.435313\pi$
$449$	5.74227e32	0.403650	0.201825	+	0.979422i	$0.435313\pi$
$450$	0	0
$451$	4.30787e33	2.86454
$452$	−4.95207e32	−0.320299
$453$	−1.40815e32	−0.0885977
$454$	−1.25488e33	−0.768078
$455$	0	0
$456$	−9.07984e32	−0.526039
$457$	3.19404e33	1.80048	0.900238	−	0.435398i	$-0.143392\pi$
$457$	3.19404e33	1.80048	0.900238	+	0.435398i	$0.143392\pi$
$458$	−1.19803e32	−0.0657128
$459$	3.04413e32	0.162482
$460$	0	0
$461$	2.15114e33	1.08745	0.543723	−	0.839264i	$-0.317014\pi$
$461$	2.15114e33	1.08745	0.543723	+	0.839264i	$0.317014\pi$
$462$	−5.57430e33	−2.74262
$463$	6.57140e32	0.314699	0.157350	−	0.987543i	$-0.449705\pi$
$463$	6.57140e32	0.314699	0.157350	+	0.987543i	$0.449705\pi$
$464$	−3.36693e32	−0.156949
$465$	0	0
$466$	−1.22893e33	−0.542880
$467$	1.92599e32	0.0828312	0.0414156	−	0.999142i	$-0.486813\pi$
$467$	1.92599e32	0.0828312	0.0414156	+	0.999142i	$0.486813\pi$
$468$	−1.33813e33	−0.560304
$469$	−5.90183e33	−2.40617
$470$	0	0
$471$	−8.69352e32	−0.336074
$472$	4.73929e32	0.178418
$473$	2.23632e33	0.819916
$474$	2.54009e33	0.907026
$475$	0	0
$476$	1.42005e33	0.481080
$477$	2.43249e33	0.802734
$478$	3.12230e33	1.00375
$479$	3.90669e33	1.22353	0.611766	−	0.791039i	$-0.290459\pi$
$479$	3.90669e33	1.22353	0.611766	+	0.791039i	$0.290459\pi$
$480$	0	0
$481$	6.19355e33	1.84131
$482$	2.33046e33	0.675078
$483$	1.05643e34	2.98196
$484$	2.66876e33	0.734079
$485$	0	0
$486$	3.39361e33	0.886562
$487$	4.17680e33	1.06349	0.531743	−	0.846906i	$-0.321537\pi$
$487$	4.17680e33	1.06349	0.531743	+	0.846906i	$0.321537\pi$
$488$	−1.06245e33	−0.263670
$489$	−6.02339e33	−1.45707
$490$	0	0
$491$	−1.40550e33	−0.323083	−0.161541	−	0.986866i	$-0.551647\pi$
$491$	−1.40550e33	−0.323083	−0.161541	+	0.986866i	$0.551647\pi$
$492$	−5.40260e33	−1.21071
$493$	1.48716e33	0.324916
$494$	5.45788e33	1.16262
$495$	0	0
$496$	9.39640e32	0.190301
$497$	−3.00827e33	−0.594103
$498$	2.61380e33	0.503392
$499$	8.69572e32	0.163323	0.0816617	−	0.996660i	$-0.473977\pi$
$499$	8.69572e32	0.163323	0.0816617	+	0.996660i	$0.473977\pi$
$500$	0	0
$501$	−1.89285e32	−0.0338178
$502$	−3.21474e33	−0.560208
$503$	−7.81824e33	−1.32895	−0.664476	−	0.747310i	$-0.731345\pi$
$503$	−7.81824e33	−1.32895	−0.664476	+	0.747310i	$0.731345\pi$
$504$	3.02688e33	0.501897
$505$	0	0
$506$	−8.50278e33	−1.34177
$507$	9.95131e33	1.53208
$508$	−6.22918e32	−0.0935696
$509$	−7.92846e33	−1.16203	−0.581014	−	0.813894i	$-0.697344\pi$
$509$	−7.92846e33	−1.16203	−0.581014	+	0.813894i	$0.697344\pi$
$510$	0	0
$511$	−5.46786e33	−0.763056
$512$	−3.24519e32	−0.0441942
$513$	−2.64656e33	−0.351734
$514$	7.93883e33	1.02972
$515$	0	0
$516$	−2.80462e33	−0.346539
$517$	−1.15109e34	−1.38828
$518$	−1.40100e34	−1.64936
$519$	1.52728e34	1.75520
$520$	0	0
$521$	−3.29787e33	−0.361212	−0.180606	−	0.983556i	$-0.557806\pi$
$521$	−3.29787e33	−0.361212	−0.180606	+	0.983556i	$0.557806\pi$
$522$	3.16993e33	0.338976
$523$	−1.60818e33	−0.167905	−0.0839524	−	0.996470i	$-0.526754\pi$
$523$	−1.60818e33	−0.167905	−0.0839524	+	0.996470i	$0.526754\pi$
$524$	−3.40131e33	−0.346741
$525$	0	0
$526$	3.18120e33	0.309221
$527$	−4.15036e33	−0.393961
$528$	−5.62665e33	−0.521586
$529$	5.06855e33	0.458868
$530$	0	0
$531$	−4.46199e33	−0.385343
$532$	−1.23459e34	−1.04142
$533$	3.24750e34	2.67583
$534$	5.77671e33	0.464959
$535$	0	0
$536$	−5.95726e33	−0.457601
$537$	2.21736e34	1.66401
$538$	−5.20020e33	−0.381278
$539$	−5.38637e34	−3.85866
$540$	0	0
$541$	−1.05559e34	−0.721990	−0.360995	−	0.932568i	$-0.617563\pi$
$541$	−1.05559e34	−0.721990	−0.360995	+	0.932568i	$0.617563\pi$
$542$	1.06294e33	0.0710422
$543$	−2.79116e34	−1.82300
$544$	1.43339e33	0.0914908
$545$	0	0
$546$	−4.20220e34	−2.56194
$547$	2.41768e34	1.44065	0.720324	−	0.693638i	$-0.243993\pi$
$547$	2.41768e34	1.44065	0.720324	+	0.693638i	$0.243993\pi$
$548$	−7.07122e33	−0.411848
$549$	1.00029e34	0.569470
$550$	0	0
$551$	−1.29294e34	−0.703367
$552$	1.06635e34	0.567104
$553$	3.45377e34	1.79568
$554$	1.72073e34	0.874665
$555$	0	0
$556$	−4.39355e33	−0.213491
$557$	−1.98926e34	−0.945153	−0.472576	−	0.881290i	$-0.656676\pi$
$557$	−1.98926e34	−0.945153	−0.472576	+	0.881290i	$0.656676\pi$
$558$	−8.84662e33	−0.411008
$559$	1.68585e34	0.765901
$560$	0	0
$561$	2.48527e34	1.07979
$562$	−3.00914e34	−1.27861
$563$	−3.43624e34	−1.42800	−0.714001	−	0.700145i	$-0.753119\pi$
$563$	−3.43624e34	−1.42800	−0.714001	+	0.700145i	$0.753119\pi$
$564$	1.44361e34	0.586762
$565$	0	0
$566$	3.05157e34	1.18664
$567$	5.76972e34	2.19466
$568$	−3.03652e33	−0.112985
$569$	−4.74393e34	−1.72677	−0.863386	−	0.504544i	$-0.831661\pi$
$569$	−4.74393e34	−1.72677	−0.863386	+	0.504544i	$0.831661\pi$
$570$	0	0
$571$	−4.26964e33	−0.148744	−0.0743721	−	0.997231i	$-0.523695\pi$
$571$	−4.26964e33	−0.148744	−0.0743721	+	0.997231i	$0.523695\pi$
$572$	3.38218e34	1.15278
$573$	−4.74667e34	−1.58291
$574$	−7.34594e34	−2.39689
$575$	0	0
$576$	3.05531e33	0.0954497
$577$	−1.96194e34	−0.599775	−0.299887	−	0.953975i	$-0.596949\pi$
$577$	−1.96194e34	−0.599775	−0.299887	+	0.953975i	$0.596949\pi$
$578$	1.73053e34	0.517702
$579$	−6.30798e34	−1.84675
$580$	0	0
$581$	3.55400e34	0.996589
$582$	−2.44896e34	−0.672117
$583$	−6.14824e34	−1.65156
$584$	−5.51921e33	−0.145116
$585$	0	0
$586$	1.39338e34	0.351033
$587$	4.23298e34	1.04393	0.521963	−	0.852968i	$-0.325200\pi$
$587$	4.23298e34	1.04393	0.521963	+	0.852968i	$0.325200\pi$
$588$	6.75518e34	1.63087
$589$	3.60832e34	0.852832
$590$	0	0
$591$	−5.37343e34	−1.21733
$592$	−1.41416e34	−0.313673
$593$	−2.29135e34	−0.497631	−0.248816	−	0.968551i	$-0.580041\pi$
$593$	−2.29135e34	−0.497631	−0.248816	+	0.968551i	$0.580041\pi$
$594$	−1.64004e34	−0.348757
$595$	0	0
$596$	8.94379e33	0.182366
$597$	8.42804e34	1.68286
$598$	−6.40984e34	−1.25338
$599$	1.21937e34	0.233508	0.116754	−	0.993161i	$-0.462751\pi$
$599$	1.21937e34	0.233508	0.116754	+	0.993161i	$0.462751\pi$
$600$	0	0
$601$	−2.38798e33	−0.0438631	−0.0219315	−	0.999759i	$-0.506982\pi$
$601$	−2.38798e33	−0.0438631	−0.0219315	+	0.999759i	$0.506982\pi$
$602$	−3.81346e34	−0.686061
$603$	5.60870e34	0.988317
$604$	−1.93265e33	−0.0333574
$605$	0	0
$606$	−6.97714e34	−1.15550
$607$	2.92481e34	0.474504	0.237252	−	0.971448i	$-0.423753\pi$
$607$	2.92481e34	0.474504	0.237252	+	0.971448i	$0.423753\pi$
$608$	−1.24619e34	−0.198056
$609$	9.95473e34	1.54993
$610$	0	0
$611$	−8.67754e34	−1.29682
$612$	−1.34952e34	−0.197600
$613$	−6.94539e34	−0.996416	−0.498208	−	0.867057i	$-0.666008\pi$
$613$	−6.94539e34	−0.996416	−0.498208	+	0.867057i	$0.666008\pi$
$614$	8.41686e34	1.18316
$615$	0	0
$616$	−7.65059e34	−1.03261
$617$	4.20916e34	0.556713	0.278356	−	0.960478i	$-0.410210\pi$
$617$	4.20916e34	0.556713	0.278356	+	0.960478i	$0.410210\pi$
$618$	5.56114e34	0.720788
$619$	5.93194e34	0.753466	0.376733	−	0.926322i	$-0.377047\pi$
$619$	5.93194e34	0.753466	0.376733	+	0.926322i	$0.377047\pi$
$620$	0	0
$621$	3.10817e34	0.379193
$622$	2.96179e32	0.00354140
$623$	7.85462e34	0.920502
$624$	−4.24167e34	−0.487225
$625$	0	0
$626$	4.69410e34	0.518051
$627$	−2.16069e35	−2.33749
$628$	−1.19316e34	−0.126533
$629$	6.24630e34	0.649366
$630$	0	0
$631$	1.46762e35	1.46638	0.733192	−	0.680022i	$-0.238030\pi$
$631$	1.46762e35	1.46638	0.733192	+	0.680022i	$0.238030\pi$
$632$	3.48621e34	0.341499
$633$	2.50077e35	2.40175
$634$	−9.98210e34	−0.939953
$635$	0	0
$636$	7.71065e34	0.698034
$637$	−4.06053e35	−3.60446
$638$	−8.01215e34	−0.697414
$639$	2.85886e34	0.244024
$640$	0	0
$641$	1.22792e35	1.00796	0.503982	−	0.863714i	$-0.331868\pi$
$641$	1.22792e35	1.00796	0.503982	+	0.863714i	$0.331868\pi$
$642$	1.14543e35	0.922107
$643$	−1.26806e34	−0.100116	−0.0500579	−	0.998746i	$-0.515941\pi$
$643$	−1.26806e34	−0.100116	−0.0500579	+	0.998746i	$0.515941\pi$
$644$	1.44993e35	1.12272
$645$	0	0
$646$	5.50436e34	0.410016
$647$	−3.01852e34	−0.220541	−0.110271	−	0.993902i	$-0.535172\pi$
$647$	−3.01852e34	−0.220541	−0.110271	+	0.993902i	$0.535172\pi$
$648$	5.82391e34	0.417376
$649$	1.12779e35	0.792811
$650$	0	0
$651$	−2.77816e35	−1.87930
$652$	−8.26696e34	−0.548594
$653$	−1.81062e35	−1.17872	−0.589361	−	0.807870i	$-0.700620\pi$
$653$	−1.81062e35	−1.17872	−0.589361	+	0.807870i	$0.700620\pi$
$654$	−1.96481e35	−1.25487
$655$	0	0
$656$	−7.41493e34	−0.455836
$657$	5.19629e34	0.313420
$658$	1.96289e35	1.16164
$659$	−2.69289e35	−1.56369	−0.781847	−	0.623471i	$-0.785722\pi$
$659$	−2.69289e35	−1.56369	−0.781847	+	0.623471i	$0.785722\pi$
$660$	0	0
$661$	3.11605e35	1.74215	0.871075	−	0.491150i	$-0.163423\pi$
$661$	3.11605e35	1.74215	0.871075	+	0.491150i	$0.163423\pi$
$662$	1.47902e35	0.811424
$663$	1.87353e35	1.00865
$664$	3.58738e34	0.189529
$665$	0	0
$666$	1.33142e35	0.677464
$667$	1.51845e35	0.758276
$668$	−2.59789e33	−0.0127326
$669$	4.85334e35	2.33461
$670$	0	0
$671$	−2.52828e35	−1.17164
$672$	9.59479e34	0.436435
$673$	1.24919e35	0.557752	0.278876	−	0.960327i	$-0.410038\pi$
$673$	1.24919e35	0.557752	0.278876	+	0.960327i	$0.410038\pi$
$674$	2.05542e35	0.900848
$675$	0	0
$676$	1.36579e35	0.576834
$677$	−2.88499e35	−1.19615	−0.598075	−	0.801440i	$-0.704067\pi$
$677$	−2.88499e35	−1.19615	−0.598075	+	0.801440i	$0.704067\pi$
$678$	1.47789e35	0.601549
$679$	−3.32987e35	−1.33062
$680$	0	0
$681$	3.74506e35	1.44251
$682$	2.23603e35	0.845614
$683$	−3.81708e34	−0.141733	−0.0708667	−	0.997486i	$-0.522577\pi$
$683$	−3.81708e34	−0.141733	−0.0708667	+	0.997486i	$0.522577\pi$
$684$	1.17327e35	0.427757
$685$	0	0
$686$	5.44540e35	1.91416
$687$	3.57539e34	0.123414
$688$	−3.84927e34	−0.130474
$689$	−4.63486e35	−1.54275
$690$	0	0
$691$	−2.01041e35	−0.645372	−0.322686	−	0.946506i	$-0.604586\pi$
$691$	−2.01041e35	−0.645372	−0.322686	+	0.946506i	$0.604586\pi$
$692$	2.09615e35	0.660840
$693$	7.20296e35	2.23021
$694$	1.10449e35	0.335867
$695$	0	0
$696$	1.00482e35	0.294764
$697$	3.27515e35	0.943673
$698$	−1.91148e35	−0.540974
$699$	3.66761e35	1.01957
$700$	0	0
$701$	1.78724e35	0.479411	0.239705	−	0.970846i	$-0.422949\pi$
$701$	1.78724e35	0.479411	0.239705	+	0.970846i	$0.422949\pi$
$702$	−1.23635e35	−0.325781
$703$	−5.43052e35	−1.40572
$704$	−7.72244e34	−0.196380
$705$	0	0
$706$	2.71807e35	0.667117
$707$	−9.48686e35	−2.28760
$708$	−1.41439e35	−0.335083
$709$	5.59205e33	0.0130165	0.00650824	−	0.999979i	$-0.497928\pi$
$709$	5.59205e33	0.0130165	0.00650824	+	0.999979i	$0.497928\pi$
$710$	0	0
$711$	−3.28223e35	−0.737564
$712$	7.92839e34	0.175059
$713$	−4.23768e35	−0.919409
$714$	−4.23799e35	−0.903508
$715$	0	0
$716$	3.04327e35	0.626509
$717$	−9.31815e35	−1.88512
$718$	2.94144e35	0.584795
$719$	3.90750e35	0.763463	0.381732	−	0.924273i	$-0.375328\pi$
$719$	3.90750e35	0.763463	0.381732	+	0.924273i	$0.375328\pi$
$720$	0	0
$721$	7.56151e35	1.42698
$722$	−9.73071e34	−0.180480
$723$	−6.95501e35	−1.26785
$724$	−3.83080e35	−0.686369
$725$	0	0
$726$	−7.96462e35	−1.37866
$727$	9.31579e35	1.58504	0.792518	−	0.609848i	$-0.208770\pi$
$727$	9.31579e35	1.58504	0.792518	+	0.609848i	$0.208770\pi$
$728$	−5.76742e35	−0.964582
$729$	−2.94718e35	−0.484520
$730$	0	0
$731$	1.70021e35	0.270107
$732$	3.17077e35	0.495195
$733$	−2.49884e35	−0.383653	−0.191826	−	0.981429i	$-0.561441\pi$
$733$	−2.49884e35	−0.383653	−0.191826	+	0.981429i	$0.561441\pi$
$734$	−3.31634e35	−0.500563
$735$	0	0
$736$	1.46354e35	0.213517
$737$	−1.41763e36	−2.03338
$738$	6.98109e35	0.984506
$739$	−1.12909e35	−0.156558	−0.0782788	−	0.996932i	$-0.524942\pi$
$739$	−1.12909e35	−0.156558	−0.0782788	+	0.996932i	$0.524942\pi$
$740$	0	0
$741$	−1.62885e36	−2.18349
$742$	1.04842e36	1.38193
$743$	−3.71494e35	−0.481495	−0.240748	−	0.970588i	$-0.577393\pi$
$743$	−3.71494e35	−0.481495	−0.240748	+	0.970588i	$0.577393\pi$
$744$	−2.80425e35	−0.357401
$745$	0	0
$746$	−6.71643e35	−0.827758
$747$	−3.37748e35	−0.409342
$748$	3.41098e35	0.406545
$749$	1.55745e36	1.82554
$750$	0	0
$751$	−6.99646e35	−0.793194	−0.396597	−	0.917993i	$-0.629809\pi$
$751$	−6.99646e35	−0.793194	−0.396597	+	0.917993i	$0.629809\pi$
$752$	1.98132e35	0.220918
$753$	9.59403e35	1.05212
$754$	−6.03998e35	−0.651469
$755$	0	0
$756$	2.79666e35	0.291821
$757$	−7.64525e35	−0.784681	−0.392341	−	0.919820i	$-0.628335\pi$
$757$	−7.64525e35	−0.784681	−0.392341	+	0.919820i	$0.628335\pi$
$758$	2.09395e35	0.211399
$759$	2.53756e36	2.51996
$760$	0	0
$761$	−7.74903e35	−0.744628	−0.372314	−	0.928107i	$-0.621436\pi$
$761$	−7.74903e35	−0.744628	−0.372314	+	0.928107i	$0.621436\pi$
$762$	1.85903e35	0.175731
$763$	−2.67156e36	−2.48432
$764$	−6.51468e35	−0.595973
$765$	0	0
$766$	−1.19018e36	−1.05378
$767$	8.50187e35	0.740581
$768$	9.68490e34	0.0830003
$769$	−1.04301e36	−0.879447	−0.439723	−	0.898133i	$-0.644923\pi$
$769$	−1.04301e36	−0.879447	−0.439723	+	0.898133i	$0.644923\pi$
$770$	0	0
$771$	−2.36926e36	−1.93389
$772$	−8.65755e35	−0.695310
$773$	1.42237e36	1.12400	0.562002	−	0.827136i	$-0.310031\pi$
$773$	1.42237e36	1.12400	0.562002	+	0.827136i	$0.310031\pi$
$774$	3.62405e35	0.281794
$775$	0	0
$776$	−3.36114e35	−0.253055
$777$	4.18114e36	3.09764
$778$	−3.97487e35	−0.289786
$779$	−2.84741e36	−2.04283
$780$	0	0
$781$	−7.22590e35	−0.502058
$782$	−6.46443e35	−0.442024
$783$	2.92882e35	0.197093
$784$	9.27131e35	0.614031
$785$	0	0
$786$	1.01508e36	0.651209
$787$	2.40737e36	1.52005	0.760026	−	0.649892i	$-0.225186\pi$
$787$	2.40737e36	1.52005	0.760026	+	0.649892i	$0.225186\pi$
$788$	−7.37489e35	−0.458330
$789$	−9.49395e35	−0.580743
$790$	0	0
$791$	2.00949e36	1.19092
$792$	7.27061e35	0.424137
$793$	−1.90595e36	−1.09445
$794$	−2.02498e36	−1.14463
$795$	0	0
$796$	1.15673e36	0.633604
$797$	−9.73330e35	−0.524845	−0.262423	−	0.964953i	$-0.584521\pi$
$797$	−9.73330e35	−0.524845	−0.262423	+	0.964953i	$0.584521\pi$
$798$	3.68450e36	1.95588
$799$	−8.75143e35	−0.457345
$800$	0	0
$801$	−7.46450e35	−0.378089
$802$	−1.83158e35	−0.0913368
$803$	−1.31339e36	−0.644834
$804$	1.77788e36	0.859412
$805$	0	0
$806$	1.68563e36	0.789905
$807$	1.55194e36	0.716072
$808$	−9.57595e35	−0.435051
$809$	3.20638e36	1.43436	0.717179	−	0.696889i	$-0.245433\pi$
$809$	3.20638e36	1.43436	0.717179	+	0.696889i	$0.245433\pi$
$810$	0	0
$811$	2.99227e36	1.29790	0.648948	−	0.760833i	$-0.275209\pi$
$811$	2.99227e36	1.29790	0.648948	+	0.760833i	$0.275209\pi$
$812$	1.36626e36	0.583558
$813$	−3.17222e35	−0.133423
$814$	−3.36522e36	−1.39383
$815$	0	0
$816$	−4.27779e35	−0.171827
$817$	−1.47816e36	−0.584717
$818$	−1.42461e36	−0.554982
$819$	5.42997e36	2.08328
$820$	0	0
$821$	−4.26235e36	−1.58621	−0.793103	−	0.609087i	$-0.791536\pi$
$821$	−4.26235e36	−1.58621	−0.793103	+	0.609087i	$0.791536\pi$
$822$	2.11033e36	0.773485
$823$	5.35214e36	1.93210	0.966051	−	0.258352i	$-0.0831796\pi$
$823$	5.35214e36	1.93210	0.966051	+	0.258352i	$0.0831796\pi$
$824$	7.63252e35	0.271380
$825$	0	0
$826$	−1.92315e36	−0.663381
$827$	3.57743e36	1.21549	0.607747	−	0.794131i	$-0.292074\pi$
$827$	3.57743e36	1.21549	0.607747	+	0.794131i	$0.292074\pi$
$828$	−1.37791e36	−0.461150
$829$	−4.26555e36	−1.40619	−0.703095	−	0.711096i	$-0.748199\pi$
$829$	−4.26555e36	−1.40619	−0.703095	+	0.711096i	$0.748199\pi$
$830$	0	0
$831$	−5.13534e36	−1.64269
$832$	−5.82158e35	−0.183442
$833$	−4.09511e36	−1.27117
$834$	1.31121e36	0.400955
$835$	0	0
$836$	−2.96550e36	−0.880075
$837$	−8.17374e35	−0.238975
$838$	6.75250e35	0.194498
$839$	−5.62994e36	−1.59764	−0.798820	−	0.601570i	$-0.794542\pi$
$839$	−5.62994e36	−1.59764	−0.798820	+	0.601570i	$0.794542\pi$
$840$	0	0
$841$	−2.19953e36	−0.605871
$842$	−1.88353e36	−0.511177
$843$	8.98045e36	2.40134
$844$	3.43225e36	0.904269
$845$	0	0
$846$	−1.86540e36	−0.477135
$847$	−1.08295e37	−2.72940
$848$	1.05827e36	0.262813
$849$	−9.10706e36	−2.22860
$850$	0	0
$851$	6.37771e36	1.51546
$852$	9.06217e35	0.212196
$853$	−4.55647e36	−1.05139	−0.525697	−	0.850672i	$-0.676195\pi$
$853$	−4.55647e36	−1.05139	−0.525697	+	0.850672i	$0.676195\pi$
$854$	4.31131e36	0.980361
$855$	0	0
$856$	1.57208e36	0.347178
$857$	7.95266e35	0.173082	0.0865411	−	0.996248i	$-0.472419\pi$
$857$	7.95266e35	0.173082	0.0865411	+	0.996248i	$0.472419\pi$
$858$	−1.00937e37	−2.16501
$859$	1.26545e36	0.267505	0.133752	−	0.991015i	$-0.457297\pi$
$859$	1.26545e36	0.267505	0.133752	+	0.991015i	$0.457297\pi$
$860$	0	0
$861$	2.19231e37	4.50156
$862$	−2.90003e36	−0.586896
$863$	−3.32635e36	−0.663487	−0.331744	−	0.943370i	$-0.607637\pi$
$863$	−3.32635e36	−0.663487	−0.331744	+	0.943370i	$0.607637\pi$
$864$	2.82292e35	0.0554979
$865$	0	0
$866$	−7.14496e35	−0.136467
$867$	−5.16456e36	−0.972288
$868$	−3.81296e36	−0.707563
$869$	8.29600e36	1.51747
$870$	0	0
$871$	−1.06868e37	−1.89942
$872$	−2.69665e36	−0.472463
$873$	3.16448e36	0.546543
$874$	5.62016e36	0.956877
$875$	0	0
$876$	1.64715e36	0.272541
$877$	−5.26043e36	−0.858078	−0.429039	−	0.903286i	$-0.641148\pi$
$877$	−5.26043e36	−0.858078	−0.429039	+	0.903286i	$0.641148\pi$
$878$	4.03012e36	0.648093
$879$	−4.15838e36	−0.659269
$880$	0	0
$881$	5.34809e36	0.824137	0.412069	−	0.911153i	$-0.364806\pi$
$881$	5.34809e36	0.824137	0.412069	+	0.911153i	$0.364806\pi$
$882$	−8.72885e36	−1.32617
$883$	−3.32166e36	−0.497560	−0.248780	−	0.968560i	$-0.580030\pi$
$883$	−3.32166e36	−0.497560	−0.248780	+	0.968560i	$0.580030\pi$
$884$	2.57137e36	0.379762
$885$	0	0
$886$	3.95925e36	0.568449
$887$	−8.17924e36	−1.15789	−0.578945	−	0.815366i	$-0.696536\pi$
$887$	−8.17924e36	−1.15789	−0.578945	+	0.815366i	$0.696536\pi$
$888$	4.22040e36	0.589104
$889$	2.52773e36	0.347904
$890$	0	0
$891$	1.38589e37	1.85464
$892$	6.66109e36	0.878991
$893$	7.60848e36	0.990045
$894$	−2.66917e36	−0.342498
$895$	0	0
$896$	1.31686e36	0.164320
$897$	1.91295e37	2.35395
$898$	−2.35204e36	−0.285423
$899$	−3.99315e36	−0.477881
$900$	0	0
$901$	−4.67433e36	−0.544076
$902$	−1.76450e37	−2.02554
$903$	1.13808e37	1.28848
$904$	2.02837e36	0.226486
$905$	0	0
$906$	5.76779e35	0.0626480
$907$	1.71298e37	1.83511	0.917553	−	0.397615i	$-0.130162\pi$
$907$	1.71298e37	1.83511	0.917553	+	0.397615i	$0.130162\pi$
$908$	5.14000e36	0.543113
$909$	9.01567e36	0.939614
$910$	0	0
$911$	6.12131e36	0.620676	0.310338	−	0.950626i	$-0.399558\pi$
$911$	6.12131e36	0.620676	0.310338	+	0.950626i	$0.399558\pi$
$912$	3.71910e36	0.371966
$913$	8.53675e36	0.842186
$914$	−1.30828e37	−1.27313
$915$	0	0
$916$	4.90714e35	0.0464660
$917$	1.38022e37	1.28923
$918$	−1.24687e36	−0.114892
$919$	−1.52693e36	−0.138795	−0.0693977	−	0.997589i	$-0.522108\pi$
$919$	−1.52693e36	−0.138795	−0.0693977	+	0.997589i	$0.522108\pi$
$920$	0	0
$921$	−2.51192e37	−2.22208
$922$	−8.81109e36	−0.768941
$923$	−5.44726e36	−0.468983
$924$	2.28323e37	1.93933
$925$	0	0
$926$	−2.69165e36	−0.222526
$927$	−7.18595e36	−0.586121
$928$	1.37909e36	0.110980
$929$	1.93910e36	0.153959	0.0769793	−	0.997033i	$-0.475472\pi$
$929$	1.93910e36	0.153959	0.0769793	+	0.997033i	$0.475472\pi$
$930$	0	0
$931$	3.56028e37	2.75178
$932$	5.03370e36	0.383874
$933$	−8.83914e34	−0.00665104
$934$	−7.88887e35	−0.0585705
$935$	0	0
$936$	5.48097e36	0.396195
$937$	1.01514e37	0.724069	0.362035	−	0.932165i	$-0.382082\pi$
$937$	1.01514e37	0.724069	0.362035	+	0.932165i	$0.382082\pi$
$938$	2.41739e37	1.70142
$939$	−1.40090e37	−0.972944
$940$	0	0
$941$	4.58463e36	0.310051	0.155026	−	0.987910i	$-0.450454\pi$
$941$	4.58463e36	0.310051	0.155026	+	0.987910i	$0.450454\pi$
$942$	3.56087e36	0.237640
$943$	3.34405e37	2.20230
$944$	−1.94121e36	−0.126160
$945$	0	0
$946$	−9.15996e36	−0.579768
$947$	−2.00468e37	−1.25219	−0.626094	−	0.779748i	$-0.715347\pi$
$947$	−2.00468e37	−1.25219	−0.626094	+	0.779748i	$0.715347\pi$
$948$	−1.04042e37	−0.641364
$949$	−9.90099e36	−0.602353
$950$	0	0
$951$	2.97905e37	1.76531
$952$	−5.81653e36	−0.340175
$953$	−2.53894e37	−1.46552	−0.732758	−	0.680489i	$-0.761767\pi$
$953$	−2.53894e37	−1.46552	−0.732758	+	0.680489i	$0.761767\pi$
$954$	−9.96348e36	−0.567619
$955$	0	0
$956$	−1.27889e37	−0.709758
$957$	2.39114e37	1.30980
$958$	−1.60018e37	−0.865168
$959$	2.86942e37	1.53131
$960$	0	0
$961$	−8.08873e36	−0.420570
$962$	−2.53688e37	−1.30200
$963$	−1.48010e37	−0.749827
$964$	−9.54557e36	−0.477352
$965$	0	0
$966$	−4.32715e37	−2.10857
$967$	3.53299e37	1.69946	0.849731	−	0.527216i	$-0.176764\pi$
$967$	3.53299e37	1.69946	0.849731	+	0.527216i	$0.176764\pi$
$968$	−1.09312e37	−0.519072
$969$	−1.64272e37	−0.770043
$970$	0	0
$971$	−2.42162e37	−1.10628	−0.553141	−	0.833088i	$-0.686571\pi$
$971$	−2.42162e37	−1.10628	−0.553141	+	0.833088i	$0.686571\pi$
$972$	−1.39002e37	−0.626894
$973$	1.78285e37	0.793789
$974$	−1.71082e37	−0.751998
$975$	0	0
$976$	4.35180e36	0.186443
$977$	−2.74750e36	−0.116213	−0.0581066	−	0.998310i	$-0.518506\pi$
$977$	−2.74750e36	−0.116213	−0.0581066	+	0.998310i	$0.518506\pi$
$978$	2.46718e37	1.03030
$979$	1.88669e37	0.777887
$980$	0	0
$981$	2.53887e37	1.02042
$982$	5.75695e36	0.228454
$983$	2.03235e37	0.796303	0.398152	−	0.917320i	$-0.369652\pi$
$983$	2.03235e37	0.796303	0.398152	+	0.917320i	$0.369652\pi$
$984$	2.21290e37	0.856099
$985$	0	0
$986$	−6.09141e36	−0.229751
$987$	−5.85802e37	−2.18166
$988$	−2.23555e37	−0.822096
$989$	1.73598e37	0.630363
$990$	0	0
$991$	1.72765e37	0.611695	0.305847	−	0.952081i	$-0.401060\pi$
$991$	1.72765e37	0.611695	0.305847	+	0.952081i	$0.401060\pi$
$992$	−3.84877e36	−0.134563
$993$	−4.41396e37	−1.52392
$994$	1.23219e37	0.420095
$995$	0	0
$996$	−1.07061e37	−0.355952
$997$	−7.90582e36	−0.259572	−0.129786	−	0.991542i	$-0.541429\pi$
$997$	−7.90582e36	−0.259572	−0.129786	+	0.991542i	$0.541429\pi$
$998$	−3.56177e36	−0.115487
$999$	1.23015e37	0.393903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.a.i.1.5	✓	5
5.2	odd	4		50.26.b.h.49.1		10
5.3	odd	4		50.26.b.h.49.10		10
5.4	even	2		50.26.a.j.1.1	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.26.a.i.1.5	✓	5	1.1	even	1	trivial
50.26.a.j.1.1	yes	5	5.4	even	2
50.26.b.h.49.1		10	5.2	odd	4
50.26.b.h.49.10		10	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4096.00 q^{2} +1.22241e6 q^{3} +1.67772e7 q^{4} -5.00697e9 q^{6} -6.80801e10 q^{7} -6.87195e10 q^{8} +6.46987e11 q^{9} -1.63529e13 q^{11} +2.05086e13 q^{12} -1.23277e14 q^{13} +2.78856e14 q^{14} +2.81475e14 q^{16} -1.24327e15 q^{17} -2.65006e15 q^{18} +1.08089e16 q^{19} -8.32215e16 q^{21} +6.69815e16 q^{22} -1.26942e17 q^{23} -8.40031e16 q^{24} +5.04942e17 q^{26} -2.44849e17 q^{27} -1.14219e18 q^{28} -1.19617e18 q^{29} +3.33827e18 q^{31} -1.15292e18 q^{32} -1.99899e19 q^{33} +5.09242e18 q^{34} +1.08546e19 q^{36} -5.02410e19 q^{37} -4.42734e19 q^{38} -1.50694e20 q^{39} -2.63431e20 q^{41} +3.40875e20 q^{42} -1.36754e20 q^{43} -2.74356e20 q^{44} +5.19955e20 q^{46} +7.03907e20 q^{47} +3.44077e20 q^{48} +3.29383e21 q^{49} -1.51978e21 q^{51} -2.06824e21 q^{52} +3.75972e21 q^{53} +1.00290e21 q^{54} +4.67843e21 q^{56} +1.32129e22 q^{57} +4.89952e21 q^{58} -6.89657e21 q^{59} +1.54607e22 q^{61} -1.36736e22 q^{62} -4.40470e22 q^{63} +4.72237e21 q^{64} +8.18786e22 q^{66} +8.66895e22 q^{67} -2.08585e22 q^{68} -1.55175e23 q^{69} +4.41872e22 q^{71} -4.44606e22 q^{72} +8.03151e22 q^{73} +2.05787e23 q^{74} +1.81344e23 q^{76} +1.11331e24 q^{77} +6.17244e23 q^{78} -5.07310e23 q^{79} -8.47490e23 q^{81} +1.07901e24 q^{82} -5.22032e23 q^{83} -1.39623e24 q^{84} +5.60143e23 q^{86} -1.46221e24 q^{87} +1.12376e24 q^{88} -1.15373e24 q^{89} +8.39270e24 q^{91} -2.12974e24 q^{92} +4.08072e24 q^{93} -2.88320e24 q^{94} -1.40934e24 q^{96} +4.89110e24 q^{97} -1.34915e25 q^{98} -1.05801e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20480 q^{2} - 723995 q^{3} + 83886080 q^{4} + 2965483520 q^{6} - 49218886190 q^{7} - 343597383680 q^{8} + 975375361390 q^{9} - 8837033983815 q^{11} - 12146620497920 q^{12} - 67609989586220 q^{13}+ \cdots - 23\!\cdots\!70 q^{99}+O(q^{100}) \) 5 * q - 20480 * q^2 - 723995 * q^3 + 83886080 * q^4 + 2965483520 * q^6 - 49218886190 * q^7 - 343597383680 * q^8 + 975375361390 * q^9 - 8837033983815 * q^11 - 12146620497920 * q^12 - 67609989586220 * q^13 + 201600557834240 * q^14 + 1407374883553280 * q^16 - 1543441123223415 * q^17 - 3995137480253440 * q^18 + 6828205451077225 * q^19 - 56457058818760990 * q^21 + 36196491197706240 * q^22 - 175655399207336370 * q^23 + 49752557559480320 * q^24 + 276930517345157120 * q^26 - 1102363638369718625 * q^27 - 825755884889047040 * q^28 + 2616960879251719800 * q^29 + 1381921297247629210 * q^31 - 5764607523034234880 * q^32 - 14683366800887949615 * q^33 + 6321934840723107840 * q^34 + 16364083119118090240 * q^36 - 68054744257794520190 * q^37 - 27968329527612313600 * q^38 - 76418447091053627020 * q^39 + 110646765257217206385 * q^41 + 231248112921645015040 * q^42 + 169174323273383550580 * q^43 - 148260827945804759040 * q^44 + 719484515153249771520 * q^46 + 1653792144435756647460 * q^47 - 203786475763631390720 * q^48 + 4971416583743605737585 * q^49 - 954942568710765966615 * q^51 - 1134307399045763563520 * q^52 - 4245089483221901865570 * q^53 + 4515281462762367488000 * q^54 + 3382296104505536675840 * q^56 + 11353190237350969575425 * q^57 - 10719071761415044300800 * q^58 + 33041536388165595960600 * q^59 - 11589871696744004976590 * q^61 - 5660349633526289244160 * q^62 - 87882675280033083250420 * q^63 + 23611832414348226068480 * q^64 + 60143070416437041623040 * q^66 + 92154529366841541565735 * q^67 - 25894645107601849712640 * q^68 + 67961625053826065275230 * q^69 + 177839620469327433418260 * q^71 - 67027284455907697623040 * q^72 - 192252066408262024306145 * q^73 + 278752232479926354698240 * q^74 + 114558277745100036505600 * q^76 - 420363080385387083988630 * q^77 + 313009959284955656273920 * q^78 - 220198603705551780910250 * q^79 - 1595228143213014227240195 * q^81 - 453209150493561677352960 * q^82 - 1018803599085572371644645 * q^83 - 947192270527057981603840 * q^84 - 692938028127779023175680 * q^86 - 6970820850065961522685800 * q^87 + 607276351266016293027840 * q^88 - 5932331377929555403184925 * q^89 + 3355259607310216720714760 * q^91 - 2947008574067711064145920 * q^92 - 3721806140580454551574390 * q^93 - 6773932623608859227996160 * q^94 + 834709404727834176389120 * q^96 + 377622858226960257754810 * q^97 - 20362922327013809101148160 * q^98 - 23196936518287622996926170 * q^99

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