LMFDB - Embedded newform 50.26.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("50.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$197.998389976$
Analytic rank:	$0$
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			1.2
Root			$107996.$ 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)

$f(q)$	$=$	\(q-4096.00 q^{2} -1.22475e6 q^{3} +1.67772e7 q^{4} +5.01659e9 q^{6} +5.40343e10 q^{7} -6.87195e10 q^{8} +6.52735e11 q^{9} -1.79977e13 q^{11} -2.05480e13 q^{12} -5.05810e13 q^{13} -2.21324e14 q^{14} +2.81475e14 q^{16} -1.91806e15 q^{17} -2.67360e15 q^{18} -3.52431e15 q^{19} -6.61787e16 q^{21} +7.37184e16 q^{22} -1.31301e17 q^{23} +8.41645e16 q^{24} +2.07180e17 q^{26} +2.38280e17 q^{27} +9.06545e17 q^{28} +3.38023e18 q^{29} -1.09603e18 q^{31} -1.15292e18 q^{32} +2.20427e19 q^{33} +7.85638e18 q^{34} +1.09511e19 q^{36} -4.59139e19 q^{37} +1.44356e19 q^{38} +6.19494e19 q^{39} -4.75209e19 q^{41} +2.71068e20 q^{42} +1.40138e20 q^{43} -3.01950e20 q^{44} +5.37807e20 q^{46} -9.40719e20 q^{47} -3.44738e20 q^{48} +1.57863e21 q^{49} +2.34916e21 q^{51} -8.48609e20 q^{52} -4.94559e21 q^{53} -9.75996e20 q^{54} -3.71321e21 q^{56} +4.31641e21 q^{57} -1.38454e22 q^{58} +8.56554e21 q^{59} -2.83544e22 q^{61} +4.48934e21 q^{62} +3.52701e22 q^{63} +4.72237e21 q^{64} -9.02869e22 q^{66} -5.48848e22 q^{67} -3.21797e22 q^{68} +1.60811e23 q^{69} +2.54981e23 q^{71} -4.48556e22 q^{72} -7.34354e22 q^{73} +1.88063e23 q^{74} -5.91281e22 q^{76} -9.72490e23 q^{77} -2.53745e23 q^{78} +3.27839e22 q^{79} -8.44890e23 q^{81} +1.94646e23 q^{82} -1.62267e24 q^{83} -1.11029e24 q^{84} -5.74004e23 q^{86} -4.13995e24 q^{87} +1.23679e24 q^{88} +1.92566e24 q^{89} -2.73311e24 q^{91} -2.20286e24 q^{92} +1.34237e24 q^{93} +3.85318e24 q^{94} +1.41205e24 q^{96} +9.42112e24 q^{97} -6.46609e24 q^{98} -1.17477e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.22475e6	−1.33056	−0.665278	−	0.746595i	$-0.731687\pi$
$3$	−1.22475e6	−1.33056	−0.665278	+	0.746595i	$0.731687\pi$
$4$	1.67772e7	0.500000
$5$	0	0
$5$	0	0
$6$	5.01659e9	0.940846
$7$	5.40343e10	1.47552	0.737758	−	0.675065i	$-0.235885\pi$
$7$	5.40343e10	1.47552	0.737758	+	0.675065i	$0.235885\pi$
$8$	−6.87195e10	−0.353553
$9$	6.52735e11	0.770381
$10$	0	0
$11$	−1.79977e13	−1.72905	−0.864524	−	0.502591i	$-0.832380\pi$
$11$	−1.79977e13	−1.72905	−0.864524	+	0.502591i	$0.832380\pi$
$12$	−2.05480e13	−0.665278
$13$	−5.05810e13	−0.602138	−0.301069	−	0.953602i	$-0.597343\pi$
$13$	−5.05810e13	−0.602138	−0.301069	+	0.953602i	$0.597343\pi$
$14$	−2.21324e14	−1.04335
$15$	0	0
$16$	2.81475e14	0.250000
$17$	−1.91806e15	−0.798456	−0.399228	−	0.916852i	$-0.630722\pi$
$17$	−1.91806e15	−0.798456	−0.399228	+	0.916852i	$0.630722\pi$
$18$	−2.67360e15	−0.544742
$19$	−3.52431e15	−0.365303	−0.182652	−	0.983178i	$-0.558468\pi$
$19$	−3.52431e15	−0.365303	−0.182652	+	0.983178i	$0.558468\pi$
$20$	0	0
$21$	−6.61787e16	−1.96326
$22$	7.37184e16	1.22262
$23$	−1.31301e17	−1.24931	−0.624653	−	0.780902i	$-0.714760\pi$
$23$	−1.31301e17	−1.24931	−0.624653	+	0.780902i	$0.714760\pi$
$24$	8.41645e16	0.470423
$25$	0	0
$26$	2.07180e17	0.425776
$27$	2.38280e17	0.305521
$28$	9.06545e17	0.737758
$29$	3.38023e18	1.77407	0.887037	−	0.461699i	$-0.152760\pi$
$29$	3.38023e18	1.77407	0.887037	+	0.461699i	$0.152760\pi$
$30$	0	0
$31$	−1.09603e18	−0.249920	−0.124960	−	0.992162i	$-0.539880\pi$
$31$	−1.09603e18	−0.249920	−0.124960	+	0.992162i	$0.539880\pi$
$32$	−1.15292e18	−0.176777
$33$	2.20427e19	2.30060
$34$	7.85638e18	0.564594
$35$	0	0
$36$	1.09511e19	0.385190
$37$	−4.59139e19	−1.14663	−0.573314	−	0.819336i	$-0.694343\pi$
$37$	−4.59139e19	−1.14663	−0.573314	+	0.819336i	$0.694343\pi$
$38$	1.44356e19	0.258309
$39$	6.19494e19	0.801178
$40$	0	0
$41$	−4.75209e19	−0.328917	−0.164458	−	0.986384i	$-0.552588\pi$
$41$	−4.75209e19	−0.328917	−0.164458	+	0.986384i	$0.552588\pi$
$42$	2.71068e20	1.38823
$43$	1.40138e20	0.534810	0.267405	−	0.963584i	$-0.413834\pi$
$43$	1.40138e20	0.534810	0.267405	+	0.963584i	$0.413834\pi$
$44$	−3.01950e20	−0.864524
$45$	0	0
$46$	5.37807e20	0.883393
$47$	−9.40719e20	−1.18096	−0.590482	−	0.807051i	$-0.701062\pi$
$47$	−9.40719e20	−1.18096	−0.590482	+	0.807051i	$0.701062\pi$
$48$	−3.44738e20	−0.332639
$49$	1.57863e21	1.17715
$50$	0	0
$51$	2.34916e21	1.06239
$52$	−8.48609e20	−0.301069
$53$	−4.94559e21	−1.38283	−0.691416	−	0.722457i	$-0.743013\pi$
$53$	−4.94559e21	−1.38283	−0.691416	+	0.722457i	$0.743013\pi$
$54$	−9.75996e20	−0.216036
$55$	0	0
$56$	−3.71321e21	−0.521674
$57$	4.31641e21	0.486057
$58$	−1.38454e22	−1.25446
$59$	8.56554e21	0.626765	0.313382	−	0.949627i	$-0.398538\pi$
$59$	8.56554e21	0.626765	0.313382	+	0.949627i	$0.398538\pi$
$60$	0	0
$61$	−2.83544e22	−1.36772	−0.683861	−	0.729612i	$-0.739701\pi$
$61$	−2.83544e22	−1.36772	−0.683861	+	0.729612i	$0.739701\pi$
$62$	4.48934e21	0.176720
$63$	3.52701e22	1.13671
$64$	4.72237e21	0.125000
$65$	0	0
$66$	−9.02869e22	−1.62677
$67$	−5.48848e22	−0.819440	−0.409720	−	0.912211i	$-0.634374\pi$
$67$	−5.48848e22	−0.819440	−0.409720	+	0.912211i	$0.634374\pi$
$68$	−3.21797e22	−0.399228
$69$	1.60811e23	1.66227
$70$	0	0
$71$	2.54981e23	1.84408	0.922038	−	0.387100i	$-0.126523\pi$
$71$	2.54981e23	1.84408	0.922038	+	0.387100i	$0.126523\pi$
$72$	−4.48556e22	−0.272371
$73$	−7.34354e22	−0.375292	−0.187646	−	0.982237i	$-0.560086\pi$
$73$	−7.34354e22	−0.375292	−0.187646	+	0.982237i	$0.560086\pi$
$74$	1.88063e23	0.810789
$75$	0	0
$76$	−5.91281e22	−0.182652
$77$	−9.72490e23	−2.55124
$78$	−2.53745e23	−0.566519
$79$	3.27839e22	0.0624197	0.0312099	−	0.999513i	$-0.490064\pi$
$79$	3.27839e22	0.0624197	0.0312099	+	0.999513i	$0.490064\pi$
$80$	0	0
$81$	−8.44890e23	−1.17689
$82$	1.94646e23	0.232579
$83$	−1.62267e24	−1.66630	−0.833149	−	0.553048i	$-0.813465\pi$
$83$	−1.62267e24	−1.66630	−0.833149	+	0.553048i	$0.813465\pi$
$84$	−1.11029e24	−0.981629
$85$	0	0
$86$	−5.74004e23	−0.378167
$87$	−4.13995e24	−2.36051
$88$	1.23679e24	0.611311
$89$	1.92566e24	0.826429	0.413214	−	0.910634i	$-0.364406\pi$
$89$	1.92566e24	0.826429	0.413214	+	0.910634i	$0.364406\pi$
$90$	0	0
$91$	−2.73311e24	−0.888464
$92$	−2.20286e24	−0.624653
$93$	1.34237e24	0.332533
$94$	3.85318e24	0.835067
$95$	0	0
$96$	1.41205e24	0.235211
$97$	9.42112e24	1.37866	0.689328	−	0.724450i	$-0.257906\pi$
$97$	9.42112e24	1.37866	0.689328	+	0.724450i	$0.257906\pi$
$98$	−6.46609e24	−0.832368
$99$	−1.17477e25	−1.33203
$100$	0	0
$101$	−6.26202e24	−0.552964	−0.276482	−	0.961019i	$-0.589169\pi$
$101$	−6.26202e24	−0.552964	−0.276482	+	0.961019i	$0.589169\pi$
$102$	−9.62214e24	−0.751224
$103$	−9.51652e24	−0.657677	−0.328839	−	0.944386i	$-0.606657\pi$
$103$	−9.51652e24	−0.657677	−0.328839	+	0.944386i	$0.606657\pi$
$104$	3.47590e24	0.212888
$105$	0	0
$106$	2.02571e25	0.977810
$107$	5.03847e24	0.216273	0.108136	−	0.994136i	$-0.465512\pi$
$107$	5.03847e24	0.216273	0.108136	+	0.994136i	$0.465512\pi$
$108$	3.99768e24	0.152761
$109$	−1.74857e25	−0.595461	−0.297730	−	0.954650i	$-0.596230\pi$
$109$	−1.74857e25	−0.595461	−0.297730	+	0.954650i	$0.596230\pi$
$110$	0	0
$111$	5.62333e25	1.52565
$112$	1.52093e25	0.368879
$113$	−4.83834e25	−1.05006	−0.525032	−	0.851082i	$-0.675947\pi$
$113$	−4.83834e25	−1.05006	−0.525032	+	0.851082i	$0.675947\pi$
$114$	−1.76800e25	−0.343694
$115$	0	0
$116$	5.67109e25	0.887037
$117$	−3.30160e25	−0.463875
$118$	−3.50844e25	−0.443189
$119$	−1.03641e26	−1.17813
$120$	0	0
$121$	2.15568e26	1.98961
$122$	1.16140e26	0.967126
$123$	5.82014e25	0.437643
$124$	−1.83883e25	−0.124960
$125$	0	0
$126$	−1.44466e26	−0.803775
$127$	2.16513e26	1.09128	0.545640	−	0.838019i	$-0.316286\pi$
$127$	2.16513e26	1.09128	0.545640	+	0.838019i	$0.316286\pi$
$128$	−1.93428e25	−0.0883883
$129$	−1.71634e26	−0.711594
$130$	0	0
$131$	−3.82649e26	−1.30891	−0.654454	−	0.756102i	$-0.727102\pi$
$131$	−3.82649e26	−1.30891	−0.654454	+	0.756102i	$0.727102\pi$
$132$	3.69815e26	1.15030
$133$	−1.90433e26	−0.539011
$134$	2.24808e26	0.579431
$135$	0	0
$136$	1.31808e26	0.282297
$137$	−8.94431e26	−1.74799	−0.873996	−	0.485933i	$-0.838480\pi$
$137$	−8.94431e26	−1.74799	−0.873996	+	0.485933i	$0.838480\pi$
$138$	−6.58682e26	−1.17540
$139$	−6.14787e26	−1.00240	−0.501199	−	0.865332i	$-0.667107\pi$
$139$	−6.14787e26	−1.00240	−0.501199	+	0.865332i	$0.667107\pi$
$140$	0	0
$141$	1.15215e27	1.57134
$142$	−1.04440e27	−1.30396
$143$	9.10340e26	1.04113
$144$	1.83729e26	0.192595
$145$	0	0
$146$	3.00791e26	0.265372
$147$	−1.93344e27	−1.56626
$148$	−7.70307e26	−0.573314
$149$	−1.52978e27	−1.04665	−0.523325	−	0.852133i	$-0.675309\pi$
$149$	−1.52978e27	−1.04665	−0.523325	+	0.852133i	$0.675309\pi$
$150$	0	0
$151$	−1.66948e27	−0.966873	−0.483436	−	0.875379i	$-0.660612\pi$
$151$	−1.66948e27	−0.966873	−0.483436	+	0.875379i	$0.660612\pi$
$152$	2.42189e26	0.129154
$153$	−1.25199e27	−0.615116
$154$	3.98332e27	1.80400
$155$	0	0
$156$	1.03934e27	0.400589
$157$	−1.97558e27	−0.702988	−0.351494	−	0.936190i	$-0.614326\pi$
$157$	−1.97558e27	−0.702988	−0.351494	+	0.936190i	$0.614326\pi$
$158$	−1.34283e26	−0.0441374
$159$	6.05713e27	1.83994
$160$	0	0
$161$	−7.09473e27	−1.84337
$162$	3.46067e27	0.832190
$163$	4.18722e27	0.932353	0.466176	−	0.884692i	$-0.345631\pi$
$163$	4.18722e27	0.932353	0.466176	+	0.884692i	$0.345631\pi$
$164$	−7.97268e26	−0.164458
$165$	0	0
$166$	6.64644e27	1.17825
$167$	1.83560e27	0.301871	0.150936	−	0.988544i	$-0.451771\pi$
$167$	1.83560e27	0.301871	0.150936	+	0.988544i	$0.451771\pi$
$168$	4.54777e27	0.694116
$169$	−4.49797e27	−0.637430
$170$	0	0
$171$	−2.30044e27	−0.281423
$172$	2.35112e27	0.267405
$173$	7.54567e27	0.798218	0.399109	−	0.916903i	$-0.369319\pi$
$173$	7.54567e27	0.798218	0.399109	+	0.916903i	$0.369319\pi$
$174$	1.69573e28	1.66913
$175$	0	0
$176$	−5.06589e27	−0.432262
$177$	−1.04907e28	−0.833946
$178$	−7.88752e27	−0.584374
$179$	−2.40551e28	−1.66167	−0.830834	−	0.556521i	$-0.812136\pi$
$179$	−2.40551e28	−1.66167	−0.830834	+	0.556521i	$0.812136\pi$
$180$	0	0
$181$	3.05290e28	1.83540	0.917699	−	0.397277i	$-0.130045\pi$
$181$	3.05290e28	1.83540	0.917699	+	0.397277i	$0.130045\pi$
$182$	1.11948e28	0.628239
$183$	3.47272e28	1.81983
$184$	9.02291e27	0.441696
$185$	0	0
$186$	−5.49834e27	−0.235136
$187$	3.45206e28	1.38057
$188$	−1.57826e28	−0.590482
$189$	1.28753e28	0.450801
$190$	0	0
$191$	3.33829e28	1.02472	0.512362	−	0.858769i	$-0.328770\pi$
$191$	3.33829e28	1.02472	0.512362	+	0.858769i	$0.328770\pi$
$192$	−5.78374e27	−0.166320
$193$	2.89791e28	0.780942	0.390471	−	0.920615i	$-0.372312\pi$
$193$	2.89791e28	0.780942	0.390471	+	0.920615i	$0.372312\pi$
$194$	−3.85889e28	−0.974857
$195$	0	0
$196$	2.64851e28	0.588573
$197$	−5.37586e28	−1.12104	−0.560519	−	0.828142i	$-0.689398\pi$
$197$	−5.37586e28	−1.12104	−0.560519	+	0.828142i	$0.689398\pi$
$198$	4.81186e28	0.941885
$199$	2.53738e28	0.466361	0.233180	−	0.972434i	$-0.425087\pi$
$199$	2.53738e28	0.466361	0.233180	+	0.972434i	$0.425087\pi$
$200$	0	0
$201$	6.72204e28	1.09031
$202$	2.56492e28	0.391005
$203$	1.82648e29	2.61767
$204$	3.94123e28	0.531196
$205$	0	0
$206$	3.89797e28	0.465048
$207$	−8.57045e28	−0.962442
$208$	−1.42373e28	−0.150534
$209$	6.34293e28	0.631627
$210$	0	0
$211$	−7.53161e28	−0.665821	−0.332910	−	0.942958i	$-0.608031\pi$
$211$	−7.53161e28	−0.665821	−0.332910	+	0.942958i	$0.608031\pi$
$212$	−8.29731e28	−0.691416
$213$	−3.12289e29	−2.45365
$214$	−2.06376e28	−0.152928
$215$	0	0
$216$	−1.63745e28	−0.108018
$217$	−5.92232e28	−0.368761
$218$	7.16216e28	0.421054
$219$	8.99404e28	0.499348
$220$	0	0
$221$	9.70176e28	0.480781
$222$	−2.30331e29	−1.07880
$223$	−2.07743e29	−0.919848	−0.459924	−	0.887958i	$-0.652123\pi$
$223$	−2.07743e29	−0.919848	−0.459924	+	0.887958i	$0.652123\pi$
$224$	−6.22973e28	−0.260837
$225$	0	0
$226$	1.98179e29	0.742508
$227$	−4.74953e29	−1.68394	−0.841971	−	0.539523i	$-0.818605\pi$
$227$	−4.74953e29	−1.68394	−0.841971	+	0.539523i	$0.818605\pi$
$228$	7.24174e28	0.243028
$229$	4.47901e29	1.42311	0.711555	−	0.702630i	$-0.247991\pi$
$229$	4.47901e29	1.42311	0.711555	+	0.702630i	$0.247991\pi$
$230$	0	0
$231$	1.19106e30	3.39457
$232$	−2.32288e29	−0.627230
$233$	−1.19571e29	−0.305970	−0.152985	−	0.988229i	$-0.548889\pi$
$233$	−1.19571e29	−0.305970	−0.152985	+	0.988229i	$0.548889\pi$
$234$	1.35234e29	0.328009
$235$	0	0
$236$	1.43706e29	0.313382
$237$	−4.01522e28	−0.0830530
$238$	4.24514e29	0.833067
$239$	−1.73647e29	−0.323365	−0.161682	−	0.986843i	$-0.551692\pi$
$239$	−1.73647e29	−0.323365	−0.161682	+	0.986843i	$0.551692\pi$
$240$	0	0
$241$	6.54337e29	1.09796	0.548982	−	0.835834i	$-0.315016\pi$
$241$	6.54337e29	1.09796	0.548982	+	0.835834i	$0.315016\pi$
$242$	−8.82968e29	−1.40687
$243$	8.32891e29	1.26040
$244$	−4.75708e29	−0.683861
$245$	0	0
$246$	−2.38393e29	−0.309460
$247$	1.78263e29	0.219963
$248$	7.53186e28	0.0883601
$249$	1.98737e30	2.21711
$250$	0	0
$251$	6.53799e29	0.659968	0.329984	−	0.943987i	$-0.392957\pi$
$251$	6.53799e29	0.659968	0.329984	+	0.943987i	$0.392957\pi$
$252$	5.91734e29	0.568355
$253$	2.36310e30	2.16011
$254$	−8.86835e29	−0.771652
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	−1.59934e29	−0.120165	−0.0600823	−	0.998193i	$-0.519136\pi$
$257$	−1.59934e29	−0.120165	−0.0600823	+	0.998193i	$0.519136\pi$
$258$	7.03014e29	0.503173
$259$	−2.48092e30	−1.69187
$260$	0	0
$261$	2.20640e30	1.36671
$262$	1.56733e30	0.925538
$263$	−1.44294e30	−0.812461	−0.406231	−	0.913771i	$-0.633157\pi$
$263$	−1.44294e30	−0.812461	−0.406231	+	0.913771i	$0.633157\pi$
$264$	−1.51476e30	−0.813384
$265$	0	0
$266$	7.80015e29	0.381138
$267$	−2.35847e30	−1.09961
$268$	−9.20814e29	−0.409720
$269$	3.68677e30	1.56582	0.782911	−	0.622134i	$-0.213734\pi$
$269$	3.68677e30	1.56582	0.782911	+	0.622134i	$0.213734\pi$
$270$	0	0
$271$	3.98811e30	1.54401	0.772007	−	0.635613i	$-0.219253\pi$
$271$	3.98811e30	1.54401	0.772007	+	0.635613i	$0.219253\pi$
$272$	−5.39887e29	−0.199614
$273$	3.34739e30	1.18215
$274$	3.66359e30	1.23602
$275$	0	0
$276$	2.69796e30	0.831136
$277$	3.61317e30	1.06388	0.531939	−	0.846783i	$-0.321464\pi$
$277$	3.61317e30	1.06388	0.531939	+	0.846783i	$0.321464\pi$
$278$	2.51817e30	0.708802
$279$	−7.15417e29	−0.192534
$280$	0	0
$281$	1.28210e29	0.0315568	0.0157784	−	0.999876i	$-0.494977\pi$
$281$	1.28210e29	0.0315568	0.0157784	+	0.999876i	$0.494977\pi$
$282$	−4.71920e30	−1.11110
$283$	7.90843e30	1.78139	0.890697	−	0.454598i	$-0.150217\pi$
$283$	7.90843e30	1.78139	0.890697	+	0.454598i	$0.150217\pi$
$284$	4.27787e30	0.922038
$285$	0	0
$286$	−3.72875e30	−0.736187
$287$	−2.56776e30	−0.485322
$288$	−7.52552e29	−0.136185
$289$	−2.09166e30	−0.362467
$290$	0	0
$291$	−1.15386e31	−1.83438
$292$	−1.23204e30	−0.187646
$293$	−6.25018e30	−0.912110	−0.456055	−	0.889952i	$-0.650738\pi$
$293$	−6.25018e30	−0.912110	−0.456055	+	0.889952i	$0.650738\pi$
$294$	7.91937e30	1.10751
$295$	0	0
$296$	3.15518e30	0.405394
$297$	−4.28849e30	−0.528261
$298$	6.26600e30	0.740094
$299$	6.64132e30	0.752254
$300$	0	0
$301$	7.57224e30	0.789120
$302$	6.83819e30	0.683682
$303$	7.66943e30	0.735750
$304$	−9.92004e29	−0.0913259
$305$	0	0
$306$	5.12814e30	0.434952
$307$	−2.00082e31	−1.62922	−0.814609	−	0.580010i	$-0.803049\pi$
$307$	−2.00082e31	−1.62922	−0.814609	+	0.580010i	$0.803049\pi$
$308$	−1.63157e31	−1.27562
$309$	1.16554e31	0.875077
$310$	0	0
$311$	−2.26965e31	−1.57201	−0.786003	−	0.618223i	$-0.787853\pi$
$311$	−2.26965e31	−1.57201	−0.786003	+	0.618223i	$0.787853\pi$
$312$	−4.25713e30	−0.283259
$313$	−1.47728e31	−0.944405	−0.472203	−	0.881490i	$-0.656541\pi$
$313$	−1.47728e31	−0.944405	−0.472203	+	0.881490i	$0.656541\pi$
$314$	8.09196e30	0.497088
$315$	0	0
$316$	5.50022e29	0.0312099
$317$	2.36061e30	0.128761	0.0643805	−	0.997925i	$-0.479493\pi$
$317$	2.36061e30	0.128761	0.0643805	+	0.997925i	$0.479493\pi$
$318$	−2.48100e31	−1.30103
$319$	−6.08362e31	−3.06746
$320$	0	0
$321$	−6.17089e30	−0.287763
$322$	2.90600e31	1.30346
$323$	6.75984e30	0.291679
$324$	−1.41749e31	−0.588447
$325$	0	0
$326$	−1.71508e31	−0.659273
$327$	2.14157e31	0.792294
$328$	3.26561e30	0.116290
$329$	−5.08311e31	−1.74253
$330$	0	0
$331$	2.93789e31	0.933653	0.466826	−	0.884349i	$-0.345397\pi$
$331$	2.93789e31	0.933653	0.466826	+	0.884349i	$0.345397\pi$
$332$	−2.72238e31	−0.833149
$333$	−2.99696e31	−0.883341
$334$	−7.51861e30	−0.213455
$335$	0	0
$336$	−1.86277e31	−0.490814
$337$	6.82670e31	1.73315	0.866577	−	0.499044i	$-0.166315\pi$
$337$	6.82670e31	1.73315	0.866577	+	0.499044i	$0.166315\pi$
$338$	1.84237e31	0.450731
$339$	5.92578e31	1.39717
$340$	0	0
$341$	1.97260e31	0.432124
$342$	9.42260e30	0.198996
$343$	1.28367e31	0.261383
$344$	−9.63019e30	−0.189084
$345$	0	0
$346$	−3.09071e31	−0.564425
$347$	1.59692e31	0.281296	0.140648	−	0.990060i	$-0.455081\pi$
$347$	1.59692e31	0.281296	0.140648	+	0.990060i	$0.455081\pi$
$348$	−6.94569e31	−1.18025
$349$	−4.91783e31	−0.806225	−0.403112	−	0.915150i	$-0.632072\pi$
$349$	−4.91783e31	−0.806225	−0.403112	+	0.915150i	$0.632072\pi$
$350$	0	0
$351$	−1.20525e31	−0.183966
$352$	2.07499e31	0.305656
$353$	3.19773e30	0.0454630	0.0227315	−	0.999742i	$-0.492764\pi$
$353$	3.19773e30	0.0454630	0.0227315	+	0.999742i	$0.492764\pi$
$354$	4.29698e31	0.589689
$355$	0	0
$356$	3.23073e31	0.413214
$357$	1.26935e32	1.56758
$358$	9.85296e31	1.17498
$359$	−3.57527e31	−0.411745	−0.205872	−	0.978579i	$-0.566003\pi$
$359$	−3.57527e31	−0.411745	−0.205872	+	0.978579i	$0.566003\pi$
$360$	0	0
$361$	−8.06558e31	−0.866553
$362$	−1.25047e32	−1.29782
$363$	−2.64018e32	−2.64729
$364$	−4.58540e31	−0.444232
$365$	0	0
$366$	−1.42243e32	−1.28682
$367$	2.22256e32	1.94325	0.971623	−	0.236536i	$-0.0760122\pi$
$367$	2.22256e32	1.94325	0.971623	+	0.236536i	$0.0760122\pi$
$368$	−3.69578e31	−0.312327
$369$	−3.10185e31	−0.253391
$370$	0	0
$371$	−2.67231e32	−2.04039
$372$	2.25212e31	0.166266
$373$	−2.11651e32	−1.51099	−0.755493	−	0.655157i	$-0.772603\pi$
$373$	−2.11651e32	−1.51099	−0.755493	+	0.655157i	$0.772603\pi$
$374$	−1.41396e32	−0.976210
$375$	0	0
$376$	6.46457e31	0.417534
$377$	−1.70976e32	−1.06824
$378$	−5.27373e31	−0.318765
$379$	1.57098e32	0.918713	0.459357	−	0.888252i	$-0.348080\pi$
$379$	1.57098e32	0.918713	0.459357	+	0.888252i	$0.348080\pi$
$380$	0	0
$381$	−2.65175e32	−1.45201
$382$	−1.36736e32	−0.724590
$383$	2.04365e32	1.04815	0.524073	−	0.851673i	$-0.324412\pi$
$383$	2.04365e32	1.04815	0.524073	+	0.851673i	$0.324412\pi$
$384$	2.36902e31	0.117606
$385$	0	0
$386$	−1.18699e32	−0.552210
$387$	9.14728e31	0.412007
$388$	1.58060e32	0.689328
$389$	1.78110e32	0.752174	0.376087	−	0.926584i	$-0.377269\pi$
$389$	1.78110e32	0.752174	0.376087	+	0.926584i	$0.377269\pi$
$390$	0	0
$391$	2.51843e32	0.997516
$392$	−1.08483e32	−0.416184
$393$	4.68651e32	1.74158
$394$	2.20195e32	0.792694
$395$	0	0
$396$	−1.97094e32	−0.666013
$397$	−1.81768e32	−0.595163	−0.297581	−	0.954696i	$-0.596180\pi$
$397$	−1.81768e32	−0.595163	−0.297581	+	0.954696i	$0.596180\pi$
$398$	−1.03931e32	−0.329767
$399$	2.33234e32	0.717185
$400$	0	0
$401$	−1.87592e32	−0.541889	−0.270945	−	0.962595i	$-0.587336\pi$
$401$	−1.87592e32	−0.541889	−0.270945	+	0.962595i	$0.587336\pi$
$402$	−2.75335e32	−0.770966
$403$	5.54383e31	0.150486
$404$	−1.05059e32	−0.276482
$405$	0	0
$406$	−7.48128e32	−1.85097
$407$	8.26342e32	1.98258
$408$	−1.61433e32	−0.375612
$409$	−3.48178e32	−0.785706	−0.392853	−	0.919601i	$-0.628512\pi$
$409$	−3.48178e32	−0.785706	−0.392853	+	0.919601i	$0.628512\pi$
$410$	0	0
$411$	1.09546e33	2.32580
$412$	−1.59661e32	−0.328839
$413$	4.62833e32	0.924801
$414$	3.51046e32	0.680549
$415$	0	0
$416$	5.83160e31	0.106444
$417$	7.52964e32	1.33375
$418$	−2.59806e32	−0.446628
$419$	−8.02659e32	−1.33923	−0.669616	−	0.742708i	$-0.733541\pi$
$419$	−8.02659e32	−1.33923	−0.669616	+	0.742708i	$0.733541\pi$
$420$	0	0
$421$	4.26783e32	0.670936	0.335468	−	0.942052i	$-0.391106\pi$
$421$	4.26783e32	0.670936	0.335468	+	0.942052i	$0.391106\pi$
$422$	3.08495e32	0.470806
$423$	−6.14040e32	−0.909792
$424$	3.39858e32	0.488905
$425$	0	0
$426$	1.27914e33	1.73499
$427$	−1.53211e33	−2.01810
$428$	8.45315e31	0.108136
$429$	−1.11494e33	−1.38528
$430$	0	0
$431$	6.47631e32	0.759210	0.379605	−	0.925149i	$-0.376060\pi$
$431$	6.47631e32	0.759210	0.379605	+	0.925149i	$0.376060\pi$
$432$	6.70700e31	0.0763803
$433$	5.41225e32	0.598796	0.299398	−	0.954128i	$-0.403214\pi$
$433$	5.41225e32	0.598796	0.299398	+	0.954128i	$0.403214\pi$
$434$	2.42578e32	0.260753
$435$	0	0
$436$	−2.93362e32	−0.297730
$437$	4.62744e32	0.456376
$438$	−3.68396e32	−0.353092
$439$	−4.19028e32	−0.390334	−0.195167	−	0.980770i	$-0.562525\pi$
$439$	−4.19028e32	−0.390334	−0.195167	+	0.980770i	$0.562525\pi$
$440$	0	0
$441$	1.03043e33	0.906851
$442$	−3.97384e32	−0.339963
$443$	5.75377e32	0.478527	0.239263	−	0.970955i	$-0.423094\pi$
$443$	5.75377e32	0.478527	0.239263	+	0.970955i	$0.423094\pi$
$444$	9.43437e32	0.762827
$445$	0	0
$446$	8.50916e32	0.650431
$447$	1.87361e33	1.39263
$448$	2.55170e32	0.184439
$449$	8.31503e32	0.584500	0.292250	−	0.956342i	$-0.405596\pi$
$449$	8.31503e32	0.584500	0.292250	+	0.956342i	$0.405596\pi$
$450$	0	0
$451$	8.55264e32	0.568714
$452$	−8.11739e32	−0.525032
$453$	2.04470e33	1.28648
$454$	1.94541e33	1.19073
$455$	0	0
$456$	−2.96622e32	−0.171847
$457$	−1.74441e33	−0.983322	−0.491661	−	0.870787i	$-0.663610\pi$
$457$	−1.74441e33	−0.983322	−0.491661	+	0.870787i	$0.663610\pi$
$458$	−1.83460e33	−1.00629
$459$	−4.57037e32	−0.243945
$460$	0	0
$461$	1.31968e33	0.667126	0.333563	−	0.942728i	$-0.391749\pi$
$461$	1.31968e33	0.667126	0.333563	+	0.942728i	$0.391749\pi$
$462$	−4.87859e33	−2.40032
$463$	1.40349e33	0.672121	0.336061	−	0.941840i	$-0.390905\pi$
$463$	1.40349e33	0.672121	0.336061	+	0.941840i	$0.390905\pi$
$464$	9.51451e32	0.443518
$465$	0	0
$466$	4.89765e32	0.216353
$467$	−7.68890e32	−0.330676	−0.165338	−	0.986237i	$-0.552872\pi$
$467$	−7.68890e32	−0.330676	−0.165338	+	0.986237i	$0.552872\pi$
$468$	−5.53917e32	−0.231938
$469$	−2.96566e33	−1.20910
$470$	0	0
$471$	2.41960e33	0.935366
$472$	−5.88619e32	−0.221595
$473$	−2.52215e33	−0.924712
$474$	1.64463e32	0.0587273
$475$	0	0
$476$	−1.73881e33	−0.589067
$477$	−3.22816e33	−1.06531
$478$	7.11256e32	0.228653
$479$	2.68490e33	0.840879	0.420440	−	0.907321i	$-0.361876\pi$
$479$	2.68490e33	0.840879	0.420440	+	0.907321i	$0.361876\pi$
$480$	0	0
$481$	2.32237e33	0.690428
$482$	−2.68016e33	−0.776378
$483$	8.68931e33	2.45271
$484$	3.61664e33	0.994805
$485$	0	0
$486$	−3.41152e33	−0.891240
$487$	−4.59053e33	−1.16883	−0.584415	−	0.811455i	$-0.698676\pi$
$487$	−4.59053e33	−1.16883	−0.584415	+	0.811455i	$0.698676\pi$
$488$	1.94850e33	0.483563
$489$	−5.12831e33	−1.24055
$490$	0	0
$491$	5.15180e33	1.18424	0.592120	−	0.805849i	$-0.298291\pi$
$491$	5.15180e33	1.18424	0.592120	+	0.805849i	$0.298291\pi$
$492$	9.76458e32	0.218821
$493$	−6.48350e33	−1.41652
$494$	−7.30166e32	−0.155537
$495$	0	0
$496$	−3.08505e32	−0.0624800
$497$	1.37777e34	2.72096
$498$	−8.14026e33	−1.56773
$499$	7.46002e33	1.40115	0.700573	−	0.713581i	$-0.252928\pi$
$499$	7.46002e33	1.40115	0.700573	+	0.713581i	$0.252928\pi$
$500$	0	0
$501$	−2.24816e33	−0.401657
$502$	−2.67796e33	−0.466668
$503$	2.55159e33	0.433722	0.216861	−	0.976203i	$-0.430418\pi$
$503$	2.55159e33	0.433722	0.216861	+	0.976203i	$0.430418\pi$
$504$	−2.42374e33	−0.401887
$505$	0	0
$506$	−9.67927e33	−1.52743
$507$	5.50891e33	0.848137
$508$	3.63248e33	0.545640
$509$	8.95543e33	1.31254	0.656272	−	0.754524i	$-0.272132\pi$
$509$	8.95543e33	1.31254	0.656272	+	0.754524i	$0.272132\pi$
$510$	0	0
$511$	−3.96803e33	−0.553750
$512$	−3.24519e32	−0.0441942
$513$	−8.39773e32	−0.111608
$514$	6.55089e32	0.0849692
$515$	0	0
$516$	−2.87954e33	−0.355797
$517$	1.69307e34	2.04194
$518$	1.01619e34	1.19633
$519$	−9.24159e33	−1.06207
$520$	0	0
$521$	8.35519e33	0.915134	0.457567	−	0.889175i	$-0.348721\pi$
$521$	8.35519e33	0.915134	0.457567	+	0.889175i	$0.348721\pi$
$522$	−9.03740e33	−0.966412
$523$	1.81744e34	1.89753	0.948765	−	0.315981i	$-0.102334\pi$
$523$	1.81744e34	1.89753	0.948765	+	0.315981i	$0.102334\pi$
$524$	−6.41978e33	−0.654454
$525$	0	0
$526$	5.91030e33	0.574497
$527$	2.10225e33	0.199550
$528$	6.20447e33	0.575149
$529$	6.19409e33	0.560766
$530$	0	0
$531$	5.59103e33	0.482848
$532$	−3.19494e33	−0.269505
$533$	2.40366e33	0.198053
$534$	9.66028e33	0.777542
$535$	0	0
$536$	3.77165e33	0.289716
$537$	2.94616e34	2.21094
$538$	−1.51010e34	−1.10720
$539$	−2.84117e34	−2.03534
$540$	0	0
$541$	−6.80008e33	−0.465102	−0.232551	−	0.972584i	$-0.574707\pi$
$541$	−6.80008e33	−0.465102	−0.232551	+	0.972584i	$0.574707\pi$
$542$	−1.63353e34	−1.09178
$543$	−3.73905e34	−2.44210
$544$	2.21138e33	0.141148
$545$	0	0
$546$	−1.37109e34	−0.835907
$547$	2.41615e34	1.43973	0.719866	−	0.694113i	$-0.244203\pi$
$547$	2.41615e34	1.43973	0.719866	+	0.694113i	$0.244203\pi$
$548$	−1.50061e34	−0.873996
$549$	−1.85079e34	−1.05367
$550$	0	0
$551$	−1.19130e34	−0.648075
$552$	−1.10509e34	−0.587702
$553$	1.77145e33	0.0921013
$554$	−1.47996e34	−0.752275
$555$	0	0
$556$	−1.03144e34	−0.501199
$557$	1.04132e33	0.0494762	0.0247381	−	0.999694i	$-0.492125\pi$
$557$	1.04132e33	0.0494762	0.0247381	+	0.999694i	$0.492125\pi$
$558$	2.93035e33	0.136142
$559$	−7.08831e33	−0.322029
$560$	0	0
$561$	−4.22793e34	−1.83693
$562$	−5.25148e32	−0.0223140
$563$	−3.05082e34	−1.26783	−0.633915	−	0.773403i	$-0.718553\pi$
$563$	−3.05082e34	−1.26783	−0.633915	+	0.773403i	$0.718553\pi$
$564$	1.93299e34	0.785670
$565$	0	0
$566$	−3.23929e34	−1.25964
$567$	−4.56530e34	−1.73653
$568$	−1.75222e34	−0.651979
$569$	1.30060e34	0.473413	0.236707	−	0.971581i	$-0.423932\pi$
$569$	1.30060e34	0.473413	0.236707	+	0.971581i	$0.423932\pi$
$570$	0	0
$571$	2.50202e34	0.871646	0.435823	−	0.900032i	$-0.356457\pi$
$571$	2.50202e34	0.871646	0.435823	+	0.900032i	$0.356457\pi$
$572$	1.52730e34	0.520563
$573$	−4.08859e34	−1.36345
$574$	1.05175e34	0.343175
$575$	0	0
$576$	3.08245e33	0.0962976
$577$	−6.21101e33	−0.189874	−0.0949368	−	0.995483i	$-0.530265\pi$
$577$	−6.21101e33	−0.189874	−0.0949368	+	0.995483i	$0.530265\pi$
$578$	8.56746e33	0.256303
$579$	−3.54923e34	−1.03909
$580$	0	0
$581$	−8.76796e34	−2.45865
$582$	4.72619e34	1.29710
$583$	8.90089e34	2.39098
$584$	5.04644e33	0.132686
$585$	0	0
$586$	2.56007e34	0.644959
$587$	−2.21731e34	−0.546827	−0.273413	−	0.961897i	$-0.588153\pi$
$587$	−2.21731e34	−0.546827	−0.273413	+	0.961897i	$0.588153\pi$
$588$	−3.24377e34	−0.783130
$589$	3.86275e33	0.0912967
$590$	0	0
$591$	6.58411e34	1.49160
$592$	−1.29236e34	−0.286657
$593$	−4.72404e34	−1.02596	−0.512980	−	0.858401i	$-0.671458\pi$
$593$	−4.72404e34	−1.02596	−0.512980	+	0.858401i	$0.671458\pi$
$594$	1.75656e34	0.373537
$595$	0	0
$596$	−2.56655e34	−0.523325
$597$	−3.10767e34	−0.620519
$598$	−2.72029e34	−0.531924
$599$	9.34743e34	1.79002	0.895008	−	0.446050i	$-0.147170\pi$
$599$	9.34743e34	1.79002	0.895008	+	0.446050i	$0.147170\pi$
$600$	0	0
$601$	1.28681e34	0.236365	0.118183	−	0.992992i	$-0.462293\pi$
$601$	1.28681e34	0.236365	0.118183	+	0.992992i	$0.462293\pi$
$602$	−3.10159e34	−0.557992
$603$	−3.58252e34	−0.631281
$604$	−2.80092e34	−0.483436
$605$	0	0
$606$	−3.14140e34	−0.520254
$607$	6.95915e34	1.12901	0.564505	−	0.825430i	$-0.309067\pi$
$607$	6.95915e34	1.12901	0.564505	+	0.825430i	$0.309067\pi$
$608$	4.06325e33	0.0645771
$609$	−2.23699e35	−3.48296
$610$	0	0
$611$	4.75825e34	0.711103
$612$	−2.10048e34	−0.307558
$613$	1.91426e34	0.274628	0.137314	−	0.990528i	$-0.456153\pi$
$613$	1.91426e34	0.274628	0.137314	+	0.990528i	$0.456153\pi$
$614$	8.19538e34	1.15203
$615$	0	0
$616$	6.68290e34	0.901999
$617$	1.16629e35	1.54255	0.771277	−	0.636499i	$-0.219618\pi$
$617$	1.16629e35	1.54255	0.771277	+	0.636499i	$0.219618\pi$
$618$	−4.77405e34	−0.618773
$619$	−7.21348e33	−0.0916246	−0.0458123	−	0.998950i	$-0.514588\pi$
$619$	−7.21348e33	−0.0916246	−0.0458123	+	0.998950i	$0.514588\pi$
$620$	0	0
$621$	−3.12864e34	−0.381689
$622$	9.29649e34	1.11158
$623$	1.04052e35	1.21941
$624$	1.74372e34	0.200295
$625$	0	0
$626$	6.05093e34	0.667795
$627$	−7.76853e34	−0.840416
$628$	−3.31447e34	−0.351494
$629$	8.80657e34	0.915533
$630$	0	0
$631$	3.50645e34	0.350349	0.175174	−	0.984537i	$-0.443951\pi$
$631$	3.50645e34	0.350349	0.175174	+	0.984537i	$0.443951\pi$
$632$	−2.25289e33	−0.0220687
$633$	9.22438e34	0.885912
$634$	−9.66908e33	−0.0910478
$635$	0	0
$636$	1.01622e35	0.919968
$637$	−7.98490e34	−0.708804
$638$	2.49185e35	2.16902
$639$	1.66435e35	1.42064
$640$	0	0
$641$	−1.17260e35	−0.962551	−0.481276	−	0.876569i	$-0.659826\pi$
$641$	−1.17260e35	−0.962551	−0.481276	+	0.876569i	$0.659826\pi$
$642$	2.52760e34	0.203479
$643$	1.79181e35	1.41467	0.707336	−	0.706877i	$-0.249897\pi$
$643$	1.79181e35	1.41467	0.707336	+	0.706877i	$0.249897\pi$
$644$	−1.19030e35	−0.921685
$645$	0	0
$646$	−2.76883e34	−0.206248
$647$	1.07946e35	0.788686	0.394343	−	0.918963i	$-0.370972\pi$
$647$	1.07946e35	0.788686	0.394343	+	0.918963i	$0.370972\pi$
$648$	5.80604e34	0.416095
$649$	−1.54160e35	−1.08371
$650$	0	0
$651$	7.25338e34	0.490657
$652$	7.02498e34	0.466176
$653$	−1.14134e35	−0.743017	−0.371508	−	0.928430i	$-0.621159\pi$
$653$	−1.14134e35	−0.743017	−0.371508	+	0.928430i	$0.621159\pi$
$654$	−8.77189e34	−0.560236
$655$	0	0
$656$	−1.33759e34	−0.0822292
$657$	−4.79339e34	−0.289118
$658$	2.08204e35	1.23216
$659$	2.00321e35	1.16321	0.581605	−	0.813471i	$-0.302425\pi$
$659$	2.00321e35	1.16321	0.581605	+	0.813471i	$0.302425\pi$
$660$	0	0
$661$	−2.41113e35	−1.34804	−0.674019	−	0.738714i	$-0.735433\pi$
$661$	−2.41113e35	−1.34804	−0.674019	+	0.738714i	$0.735433\pi$
$662$	−1.20336e35	−0.660192
$663$	−1.18823e35	−0.639706
$664$	1.11509e35	0.589126
$665$	0	0
$666$	1.22756e35	0.624616
$667$	−4.43827e35	−2.21636
$668$	3.07962e34	0.150936
$669$	2.54434e35	1.22391
$670$	0	0
$671$	5.10313e35	2.36486
$672$	7.62989e34	0.347058
$673$	4.10824e34	0.183429	0.0917145	−	0.995785i	$-0.470765\pi$
$673$	4.10824e34	0.183429	0.0917145	+	0.995785i	$0.470765\pi$
$674$	−2.79622e35	−1.22552
$675$	0	0
$676$	−7.54634e34	−0.318715
$677$	−2.21198e35	−0.917111	−0.458556	−	0.888666i	$-0.651633\pi$
$677$	−2.21198e35	−0.917111	−0.458556	+	0.888666i	$0.651633\pi$
$678$	−2.42720e35	−0.987949
$679$	5.09063e35	2.03423
$680$	0	0
$681$	5.81700e35	2.24058
$682$	−8.07975e34	−0.305558
$683$	1.93443e35	0.718280	0.359140	−	0.933284i	$-0.383070\pi$
$683$	1.93443e35	0.718280	0.359140	+	0.933284i	$0.383070\pi$
$684$	−3.85950e34	−0.140711
$685$	0	0
$686$	−5.25791e34	−0.184825
$687$	−5.48569e35	−1.89353
$688$	3.94452e34	0.133702
$689$	2.50153e35	0.832655
$690$	0	0
$691$	−1.57151e33	−0.00504479	−0.00252239	−	0.999997i	$-0.500803\pi$
$691$	−1.57151e33	−0.00504479	−0.00252239	+	0.999997i	$0.500803\pi$
$692$	1.26595e35	0.399109
$693$	−6.34778e35	−1.96543
$694$	−6.54097e34	−0.198907
$695$	0	0
$696$	2.84496e35	0.834565
$697$	9.11480e34	0.262626
$698$	2.01435e35	0.570087
$699$	1.46446e35	0.407110
$700$	0	0
$701$	−4.76280e35	−1.27758	−0.638789	−	0.769382i	$-0.720564\pi$
$701$	−4.76280e35	−1.27758	−0.638789	+	0.769382i	$0.720564\pi$
$702$	4.93669e34	0.130083
$703$	1.61815e35	0.418867
$704$	−8.49915e34	−0.216131
$705$	0	0
$706$	−1.30979e34	−0.0321472
$707$	−3.38363e35	−0.815907
$708$	−1.76004e35	−0.416973
$709$	−2.73484e35	−0.636580	−0.318290	−	0.947993i	$-0.603109\pi$
$709$	−2.73484e35	−0.636580	−0.318290	+	0.947993i	$0.603109\pi$
$710$	0	0
$711$	2.13992e34	0.0480870
$712$	−1.32331e35	−0.292187
$713$	1.43909e35	0.312227
$714$	−5.19925e35	−1.10844
$715$	0	0
$716$	−4.03577e35	−0.830834
$717$	2.12674e35	0.430255
$718$	1.46443e35	0.291148
$719$	−1.61873e35	−0.316274	−0.158137	−	0.987417i	$-0.550549\pi$
$719$	−1.61873e35	−0.316274	−0.158137	+	0.987417i	$0.550549\pi$
$720$	0	0
$721$	−5.14218e35	−0.970413
$722$	3.30366e35	0.612746
$723$	−8.01402e35	−1.46090
$724$	5.12191e35	0.917699
$725$	0	0
$726$	1.08142e36	1.87192
$727$	3.12165e35	0.531134	0.265567	−	0.964092i	$-0.414441\pi$
$727$	3.12165e35	0.531134	0.265567	+	0.964092i	$0.414441\pi$
$728$	1.87818e35	0.314119
$729$	−3.04221e35	−0.500144
$730$	0	0
$731$	−2.68793e35	−0.427022
$732$	5.82626e35	0.909916
$733$	−2.02938e35	−0.311576	−0.155788	−	0.987791i	$-0.549792\pi$
$733$	−2.02938e35	−0.311576	−0.155788	+	0.987791i	$0.549792\pi$
$734$	−9.10360e35	−1.37408
$735$	0	0
$736$	1.51379e35	0.220848
$737$	9.87798e35	1.41685
$738$	1.27052e35	0.179175
$739$	6.40360e34	0.0887910	0.0443955	−	0.999014i	$-0.485864\pi$
$739$	6.40360e34	0.0887910	0.0443955	+	0.999014i	$0.485864\pi$
$740$	0	0
$741$	−2.18329e35	−0.292673
$742$	1.09458e36	1.44277
$743$	9.29648e35	1.20492	0.602460	−	0.798149i	$-0.294187\pi$
$743$	9.29648e35	1.20492	0.602460	+	0.798149i	$0.294187\pi$
$744$	−9.22468e34	−0.117568
$745$	0	0
$746$	8.66924e35	1.06843
$747$	−1.05917e36	−1.28369
$748$	5.79160e35	0.690285
$749$	2.72250e35	0.319113
$750$	0	0
$751$	3.56197e35	0.403823	0.201912	−	0.979404i	$-0.435285\pi$
$751$	3.56197e35	0.403823	0.201912	+	0.979404i	$0.435285\pi$
$752$	−2.64789e35	−0.295241
$753$	−8.00743e35	−0.878124
$754$	7.00316e35	0.755357
$755$	0	0
$756$	2.16012e35	0.225401
$757$	−1.75236e36	−1.79856	−0.899278	−	0.437378i	$-0.855907\pi$
$757$	−1.75236e36	−1.79856	−0.899278	+	0.437378i	$0.855907\pi$
$758$	−6.43473e35	−0.649629
$759$	−2.89422e36	−2.87415
$760$	0	0
$761$	−1.03372e36	−0.993332	−0.496666	−	0.867942i	$-0.665443\pi$
$761$	−1.03372e36	−0.993332	−0.496666	+	0.867942i	$0.665443\pi$
$762$	1.08616e36	1.02673
$763$	−9.44830e35	−0.878611
$764$	5.60072e35	0.512362
$765$	0	0
$766$	−8.37079e35	−0.741151
$767$	−4.33254e35	−0.377399
$768$	−9.70351e34	−0.0831598
$769$	1.96647e35	0.165809	0.0829044	−	0.996558i	$-0.473580\pi$
$769$	1.96647e35	0.165809	0.0829044	+	0.996558i	$0.473580\pi$
$770$	0	0
$771$	1.95880e35	0.159886
$772$	4.86189e35	0.390471
$773$	3.07830e35	0.243258	0.121629	−	0.992576i	$-0.461188\pi$
$773$	3.07830e35	0.243258	0.121629	+	0.992576i	$0.461188\pi$
$774$	−3.74672e35	−0.291333
$775$	0	0
$776$	−6.47414e35	−0.487428
$777$	3.03852e36	2.25113
$778$	−7.29538e35	−0.531867
$779$	1.67478e35	0.120155
$780$	0	0
$781$	−4.58906e36	−3.18850
$782$	−1.03155e36	−0.705351
$783$	8.05443e35	0.542017
$784$	4.44346e35	0.294287
$785$	0	0
$786$	−1.91959e36	−1.23148
$787$	2.22687e36	1.40608	0.703042	−	0.711148i	$-0.251825\pi$
$787$	2.22687e36	1.40608	0.703042	+	0.711148i	$0.251825\pi$
$788$	−9.01920e35	−0.560519
$789$	1.76725e36	1.08103
$790$	0	0
$791$	−2.61436e36	−1.54939
$792$	8.07296e35	0.470942
$793$	1.43420e36	0.823557
$794$	7.44521e35	0.420844
$795$	0	0
$796$	4.25702e35	0.233180
$797$	−9.40522e35	−0.507154	−0.253577	−	0.967315i	$-0.581607\pi$
$797$	−9.40522e35	−0.507154	−0.253577	+	0.967315i	$0.581607\pi$
$798$	−9.55327e35	−0.507126
$799$	1.80436e36	0.942948
$800$	0	0
$801$	1.25695e36	0.636665
$802$	7.68378e35	0.383174
$803$	1.32167e36	0.648899
$804$	1.12777e36	0.545156
$805$	0	0
$806$	−2.27075e35	−0.106410
$807$	−4.51539e36	−2.08341
$808$	4.30322e35	0.195502
$809$	2.23971e36	1.00193	0.500963	−	0.865468i	$-0.332979\pi$
$809$	2.23971e36	1.00193	0.500963	+	0.865468i	$0.332979\pi$
$810$	0	0
$811$	−2.70491e35	−0.117325	−0.0586627	−	0.998278i	$-0.518684\pi$
$811$	−2.70491e35	−0.117325	−0.0586627	+	0.998278i	$0.518684\pi$
$812$	3.06433e36	1.30884
$813$	−4.88446e36	−2.05440
$814$	−3.38470e36	−1.40189
$815$	0	0
$816$	6.61228e35	0.265598
$817$	−4.93888e35	−0.195368
$818$	1.42614e36	0.555578
$819$	−1.78400e36	−0.684455
$820$	0	0
$821$	8.72543e35	0.324711	0.162356	−	0.986732i	$-0.448091\pi$
$821$	8.72543e35	0.324711	0.162356	+	0.986732i	$0.448091\pi$
$822$	−4.48700e36	−1.64459
$823$	−5.40468e35	−0.195107	−0.0975534	−	0.995230i	$-0.531102\pi$
$823$	−5.40468e35	−0.195107	−0.0975534	+	0.995230i	$0.531102\pi$
$824$	6.53970e35	0.232524
$825$	0	0
$826$	−1.89576e36	−0.653933
$827$	9.59407e35	0.325975	0.162987	−	0.986628i	$-0.447887\pi$
$827$	9.59407e35	0.325975	0.162987	+	0.986628i	$0.447887\pi$
$828$	−1.43788e36	−0.481221
$829$	−2.44895e36	−0.807326	−0.403663	−	0.914908i	$-0.632263\pi$
$829$	−2.44895e36	−0.807326	−0.403663	+	0.914908i	$0.632263\pi$
$830$	0	0
$831$	−4.42525e36	−1.41555
$832$	−2.38862e35	−0.0752672
$833$	−3.02792e36	−0.939900
$834$	−3.08414e36	−0.943101
$835$	0	0
$836$	1.06417e36	0.315814
$837$	−2.61162e35	−0.0763559
$838$	3.28769e36	0.946980
$839$	5.26267e36	1.49342	0.746709	−	0.665151i	$-0.231633\pi$
$839$	5.26267e36	1.49342	0.746709	+	0.665151i	$0.231633\pi$
$840$	0	0
$841$	7.79561e36	2.14734
$842$	−1.74810e36	−0.474423
$843$	−1.57026e35	−0.0419881
$844$	−1.26359e36	−0.332910
$845$	0	0
$846$	2.51511e36	0.643320
$847$	1.16481e37	2.93570
$848$	−1.39206e36	−0.345708
$849$	−9.68588e36	−2.37024
$850$	0	0
$851$	6.02852e36	1.43249
$852$	−5.23934e36	−1.22682
$853$	2.08360e36	0.480786	0.240393	−	0.970676i	$-0.422724\pi$
$853$	2.08360e36	0.480786	0.240393	+	0.970676i	$0.422724\pi$
$854$	6.27553e36	1.42701
$855$	0	0
$856$	−3.46241e35	−0.0764639
$857$	−4.78596e36	−1.04162	−0.520810	−	0.853673i	$-0.674370\pi$
$857$	−4.78596e36	−1.04162	−0.520810	+	0.853673i	$0.674370\pi$
$858$	4.56681e36	0.979538
$859$	−4.96565e36	−1.04969	−0.524846	−	0.851197i	$-0.675877\pi$
$859$	−4.96565e36	−1.04969	−0.524846	+	0.851197i	$0.675877\pi$
$860$	0	0
$861$	3.14487e36	0.645749
$862$	−2.65270e36	−0.536843
$863$	3.87006e36	0.771939	0.385969	−	0.922512i	$-0.373867\pi$
$863$	3.87006e36	0.771939	0.385969	+	0.922512i	$0.373867\pi$
$864$	−2.74719e35	−0.0540090
$865$	0	0
$866$	−2.21686e36	−0.423413
$867$	2.56178e36	0.482284
$868$	−9.93600e35	−0.184381
$869$	−5.90033e35	−0.107927
$870$	0	0
$871$	2.77613e36	0.493416
$872$	1.20161e36	0.210527
$873$	6.14949e36	1.06209
$874$	−1.89540e36	−0.322706
$875$	0	0
$876$	1.50895e36	0.249674
$877$	9.31488e36	1.51944	0.759718	−	0.650253i	$-0.225337\pi$
$877$	9.31488e36	1.51944	0.759718	+	0.650253i	$0.225337\pi$
$878$	1.71634e36	0.276008
$879$	7.65493e36	1.21361
$880$	0	0
$881$	3.30000e36	0.508528	0.254264	−	0.967135i	$-0.418167\pi$
$881$	3.30000e36	0.508528	0.254264	+	0.967135i	$0.418167\pi$
$882$	−4.22064e36	−0.641241
$883$	−6.02750e36	−0.902876	−0.451438	−	0.892302i	$-0.649089\pi$
$883$	−6.02750e36	−0.902876	−0.451438	+	0.892302i	$0.649089\pi$
$884$	1.62768e36	0.240390
$885$	0	0
$886$	−2.35675e36	−0.338369
$887$	3.09975e36	0.438814	0.219407	−	0.975633i	$-0.429588\pi$
$887$	3.09975e36	0.438814	0.219407	+	0.975633i	$0.429588\pi$
$888$	−3.86432e36	−0.539400
$889$	1.16991e37	1.61020
$890$	0	0
$891$	1.52060e37	2.03491
$892$	−3.48535e36	−0.459924
$893$	3.31538e36	0.431410
$894$	−7.67431e36	−0.984737
$895$	0	0
$896$	−1.04517e36	−0.130418
$897$	−8.13399e36	−1.00092
$898$	−3.40583e36	−0.413304
$899$	−3.70483e36	−0.443377
$900$	0	0
$901$	9.48594e36	1.10413
$902$	−3.50316e36	−0.402141
$903$	−9.27413e36	−1.04997
$904$	3.32488e36	0.371254
$905$	0	0
$906$	−8.37510e36	−0.909678
$907$	−1.94270e36	−0.208120	−0.104060	−	0.994571i	$-0.533183\pi$
$907$	−1.94270e36	−0.208120	−0.104060	+	0.994571i	$0.533183\pi$
$908$	−7.96838e36	−0.841971
$909$	−4.08744e36	−0.425993
$910$	0	0
$911$	−1.71377e37	−1.73769	−0.868845	−	0.495085i	$-0.835137\pi$
$911$	−1.71377e37	−1.73769	−0.868845	+	0.495085i	$0.835137\pi$
$912$	1.21496e36	0.121514
$913$	2.92042e37	2.88111
$914$	7.14510e36	0.695314
$915$	0	0
$916$	7.51453e36	0.711555
$917$	−2.06762e37	−1.93132
$918$	1.87202e36	0.172495
$919$	−8.92079e35	−0.0810886	−0.0405443	−	0.999178i	$-0.512909\pi$
$919$	−8.92079e35	−0.0810886	−0.0405443	+	0.999178i	$0.512909\pi$
$920$	0	0
$921$	2.45052e37	2.16777
$922$	−5.40542e36	−0.471729
$923$	−1.28972e37	−1.11039
$924$	1.99827e37	1.69728
$925$	0	0
$926$	−5.74870e36	−0.475261
$927$	−6.21177e36	−0.506662
$928$	−3.89714e36	−0.313615
$929$	−1.38002e36	−0.109569	−0.0547846	−	0.998498i	$-0.517447\pi$
$929$	−1.38002e36	−0.109569	−0.0547846	+	0.998498i	$0.517447\pi$
$930$	0	0
$931$	−5.56359e36	−0.430016
$932$	−2.00608e36	−0.152985
$933$	2.77976e37	2.09164
$934$	3.14937e36	0.233823
$935$	0	0
$936$	2.26884e36	0.164005
$937$	−1.08251e37	−0.772126	−0.386063	−	0.922472i	$-0.626165\pi$
$937$	−1.08251e37	−0.772126	−0.386063	+	0.922472i	$0.626165\pi$
$938$	1.21473e37	0.854960
$939$	1.80930e37	1.25658
$940$	0	0
$941$	−7.75055e36	−0.524158	−0.262079	−	0.965046i	$-0.584408\pi$
$941$	−7.75055e36	−0.524158	−0.262079	+	0.965046i	$0.584408\pi$
$942$	−9.91066e36	−0.661403
$943$	6.23952e36	0.410918
$944$	2.41098e36	0.156691
$945$	0	0
$946$	1.03307e37	0.653870
$947$	−5.61736e36	−0.350879	−0.175440	−	0.984490i	$-0.556135\pi$
$947$	−5.61736e36	−0.350879	−0.175440	+	0.984490i	$0.556135\pi$
$948$	−6.73642e35	−0.0415265
$949$	3.71444e36	0.225978
$950$	0	0
$951$	−2.89117e36	−0.171324
$952$	7.12216e36	0.416534
$953$	8.09802e36	0.467431	0.233715	−	0.972305i	$-0.424912\pi$
$953$	8.09802e36	0.467431	0.233715	+	0.972305i	$0.424912\pi$
$954$	1.32225e37	0.753286
$955$	0	0
$956$	−2.91331e36	−0.161682
$957$	7.45095e37	4.08143
$958$	−1.09973e37	−0.594591
$959$	−4.83299e37	−2.57919
$960$	0	0
$961$	−1.80315e37	−0.937540
$962$	−9.51244e36	−0.488206
$963$	3.28878e36	0.166612
$964$	1.09779e37	0.548982
$965$	0	0
$966$	−3.55914e37	−1.73433
$967$	8.79417e36	0.423023	0.211511	−	0.977376i	$-0.432161\pi$
$967$	8.79417e36	0.423023	0.211511	+	0.977376i	$0.432161\pi$
$968$	−1.48137e37	−0.703433
$969$	−8.27915e36	−0.388095
$970$	0	0
$971$	−1.66027e37	−0.758472	−0.379236	−	0.925300i	$-0.623813\pi$
$971$	−1.66027e37	−0.758472	−0.379236	+	0.925300i	$0.623813\pi$
$972$	1.39736e37	0.630202
$973$	−3.32196e37	−1.47905
$974$	1.88028e37	0.826487
$975$	0	0
$976$	−7.98106e36	−0.341931
$977$	−2.34433e37	−0.991601	−0.495801	−	0.868436i	$-0.665125\pi$
$977$	−2.34433e37	−0.991601	−0.495801	+	0.868436i	$0.665125\pi$
$978$	2.10056e37	0.877200
$979$	−3.46574e37	−1.42894
$980$	0	0
$981$	−1.14136e37	−0.458732
$982$	−2.11018e37	−0.837385
$983$	3.99283e37	1.56445	0.782225	−	0.622996i	$-0.214085\pi$
$983$	3.99283e37	1.56445	0.782225	+	0.622996i	$0.214085\pi$
$984$	−3.99957e36	−0.154730
$985$	0	0
$986$	2.65564e37	1.00163
$987$	6.22556e37	2.31854
$988$	2.99076e36	0.109981
$989$	−1.84002e37	−0.668141
$990$	0	0
$991$	2.11236e37	0.747907	0.373954	−	0.927447i	$-0.378002\pi$
$991$	2.11236e37	0.747907	0.373954	+	0.927447i	$0.378002\pi$
$992$	1.26364e36	0.0441800
$993$	−3.59819e37	−1.24228
$994$	−5.64335e37	−1.92401
$995$	0	0
$996$	3.33425e37	1.10855
$997$	−2.11846e37	−0.695555	−0.347777	−	0.937577i	$-0.613064\pi$
$997$	−2.11846e37	−0.695555	−0.347777	+	0.937577i	$0.613064\pi$
$998$	−3.05562e37	−0.990760
$999$	−1.09404e37	−0.350319

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.a.i.1.2	✓	5
5.2	odd	4		50.26.b.h.49.4		10
5.3	odd	4		50.26.b.h.49.7		10
5.4	even	2		50.26.a.j.1.4	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.26.a.i.1.2	✓	5	1.1	even	1	trivial
50.26.a.j.1.4	yes	5	5.4	even	2
50.26.b.h.49.4		10	5.2	odd	4
50.26.b.h.49.7		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-4096.00 q^{2} -1.22475e6 q^{3} +1.67772e7 q^{4} +5.01659e9 q^{6} +5.40343e10 q^{7} -6.87195e10 q^{8} +6.52735e11 q^{9} -1.79977e13 q^{11} -2.05480e13 q^{12} -5.05810e13 q^{13} -2.21324e14 q^{14} +2.81475e14 q^{16} -1.91806e15 q^{17} -2.67360e15 q^{18} -3.52431e15 q^{19} -6.61787e16 q^{21} +7.37184e16 q^{22} -1.31301e17 q^{23} +8.41645e16 q^{24} +2.07180e17 q^{26} +2.38280e17 q^{27} +9.06545e17 q^{28} +3.38023e18 q^{29} -1.09603e18 q^{31} -1.15292e18 q^{32} +2.20427e19 q^{33} +7.85638e18 q^{34} +1.09511e19 q^{36} -4.59139e19 q^{37} +1.44356e19 q^{38} +6.19494e19 q^{39} -4.75209e19 q^{41} +2.71068e20 q^{42} +1.40138e20 q^{43} -3.01950e20 q^{44} +5.37807e20 q^{46} -9.40719e20 q^{47} -3.44738e20 q^{48} +1.57863e21 q^{49} +2.34916e21 q^{51} -8.48609e20 q^{52} -4.94559e21 q^{53} -9.75996e20 q^{54} -3.71321e21 q^{56} +4.31641e21 q^{57} -1.38454e22 q^{58} +8.56554e21 q^{59} -2.83544e22 q^{61} +4.48934e21 q^{62} +3.52701e22 q^{63} +4.72237e21 q^{64} -9.02869e22 q^{66} -5.48848e22 q^{67} -3.21797e22 q^{68} +1.60811e23 q^{69} +2.54981e23 q^{71} -4.48556e22 q^{72} -7.34354e22 q^{73} +1.88063e23 q^{74} -5.91281e22 q^{76} -9.72490e23 q^{77} -2.53745e23 q^{78} +3.27839e22 q^{79} -8.44890e23 q^{81} +1.94646e23 q^{82} -1.62267e24 q^{83} -1.11029e24 q^{84} -5.74004e23 q^{86} -4.13995e24 q^{87} +1.23679e24 q^{88} +1.92566e24 q^{89} -2.73311e24 q^{91} -2.20286e24 q^{92} +1.34237e24 q^{93} +3.85318e24 q^{94} +1.41205e24 q^{96} +9.42112e24 q^{97} -6.46609e24 q^{98} -1.17477e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20480 q^{2} - 723995 q^{3} + 83886080 q^{4} + 2965483520 q^{6} - 49218886190 q^{7} - 343597383680 q^{8} + 975375361390 q^{9} - 8837033983815 q^{11} - 12146620497920 q^{12} - 67609989586220 q^{13}+ \cdots - 23\!\cdots\!70 q^{99}+O(q^{100}) \) 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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