LMFDB - Embedded newform 50.26.a.i.1.4

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			1.4
Root			$-74281.7$ 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)

$f(q)$	$=$	\(q-4096.00 q^{2} +598018. q^{3} +1.67772e7 q^{4} -2.44948e9 q^{6} +1.45531e10 q^{7} -6.87195e10 q^{8} -4.89664e11 q^{9} -2.61864e12 q^{11} +1.00331e13 q^{12} +1.51962e14 q^{13} -5.96094e13 q^{14} +2.81475e14 q^{16} +3.15464e15 q^{17} +2.00566e15 q^{18} -8.10963e15 q^{19} +8.70300e15 q^{21} +1.07260e16 q^{22} +9.27767e15 q^{23} -4.10955e16 q^{24} -6.22436e17 q^{26} -7.99521e17 q^{27} +2.44160e17 q^{28} +1.39333e18 q^{29} -1.42368e17 q^{31} -1.15292e18 q^{32} -1.56599e18 q^{33} -1.29214e19 q^{34} -8.21519e18 q^{36} +5.37730e19 q^{37} +3.32170e19 q^{38} +9.08759e19 q^{39} -7.26333e19 q^{41} -3.56475e19 q^{42} -3.12589e20 q^{43} -4.39335e19 q^{44} -3.80013e19 q^{46} +2.45817e19 q^{47} +1.68327e20 q^{48} -1.12928e21 q^{49} +1.88653e21 q^{51} +2.54950e21 q^{52} +6.91634e20 q^{53} +3.27484e21 q^{54} -1.00008e21 q^{56} -4.84970e21 q^{57} -5.70708e21 q^{58} +9.21095e21 q^{59} +1.19113e22 q^{61} +5.83140e20 q^{62} -7.12611e21 q^{63} +4.72237e21 q^{64} +6.41431e21 q^{66} +1.17804e23 q^{67} +5.29260e22 q^{68} +5.54821e21 q^{69} +1.28366e23 q^{71} +3.36494e22 q^{72} +2.12900e22 q^{73} -2.20254e23 q^{74} -1.36057e23 q^{76} -3.81093e22 q^{77} -3.72228e23 q^{78} -2.44555e23 q^{79} -6.32412e22 q^{81} +2.97506e23 q^{82} +4.71841e23 q^{83} +1.46012e23 q^{84} +1.28037e24 q^{86} +8.33235e23 q^{87} +1.79952e23 q^{88} -3.32650e24 q^{89} +2.21152e24 q^{91} +1.55653e23 q^{92} -8.51387e22 q^{93} -1.00687e23 q^{94} -6.89467e23 q^{96} -2.17673e24 q^{97} +4.62552e24 q^{98} +1.28225e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	598018.	0.649678	0.324839	−	0.945769i	$-0.394690\pi$
$3$	598018.	0.649678	0.324839	+	0.945769i	$0.394690\pi$
$4$	1.67772e7	0.500000
$5$	0	0
$5$	0	0
$6$	−2.44948e9	−0.459392
$7$	1.45531e10	0.397401	0.198701	−	0.980060i	$-0.436328\pi$
$7$	1.45531e10	0.397401	0.198701	+	0.980060i	$0.436328\pi$
$8$	−6.87195e10	−0.353553
$9$	−4.89664e11	−0.577918
$10$	0	0
$11$	−2.61864e12	−0.251575	−0.125788	−	0.992057i	$-0.540146\pi$
$11$	−2.61864e12	−0.251575	−0.125788	+	0.992057i	$0.540146\pi$
$12$	1.00331e13	0.324839
$13$	1.51962e14	1.80902	0.904509	−	0.426454i	$-0.140237\pi$
$13$	1.51962e14	1.80902	0.904509	+	0.426454i	$0.140237\pi$
$14$	−5.96094e13	−0.281005
$15$	0	0
$16$	2.81475e14	0.250000
$17$	3.15464e15	1.31322	0.656611	−	0.754230i	$-0.271990\pi$
$17$	3.15464e15	1.31322	0.656611	+	0.754230i	$0.271990\pi$
$18$	2.00566e15	0.408650
$19$	−8.10963e15	−0.840584	−0.420292	−	0.907389i	$-0.638072\pi$
$19$	−8.10963e15	−0.840584	−0.420292	+	0.907389i	$0.638072\pi$
$20$	0	0
$21$	8.70300e15	0.258183
$22$	1.07260e16	0.177890
$23$	9.27767e15	0.0882756	0.0441378	−	0.999025i	$-0.485946\pi$
$23$	9.27767e15	0.0882756	0.0441378	+	0.999025i	$0.485946\pi$
$24$	−4.10955e16	−0.229696
$25$	0	0
$26$	−6.22436e17	−1.27917
$27$	−7.99521e17	−1.02514
$28$	2.44160e17	0.198701
$29$	1.39333e18	0.731272	0.365636	−	0.930758i	$-0.380852\pi$
$29$	1.39333e18	0.731272	0.365636	+	0.930758i	$0.380852\pi$
$30$	0	0
$31$	−1.42368e17	−0.0324633	−0.0162316	−	0.999868i	$-0.505167\pi$
$31$	−1.42368e17	−0.0324633	−0.0162316	+	0.999868i	$0.505167\pi$
$32$	−1.15292e18	−0.176777
$33$	−1.56599e18	−0.163443
$34$	−1.29214e19	−0.928588
$35$	0	0
$36$	−8.21519e18	−0.288959
$37$	5.37730e19	1.34290	0.671449	−	0.741051i	$-0.265672\pi$
$37$	5.37730e19	1.34290	0.671449	+	0.741051i	$0.265672\pi$
$38$	3.32170e19	0.594382
$39$	9.08759e19	1.17528
$40$	0	0
$41$	−7.26333e19	−0.502733	−0.251367	−	0.967892i	$-0.580880\pi$
$41$	−7.26333e19	−0.502733	−0.251367	+	0.967892i	$0.580880\pi$
$42$	−3.56475e19	−0.182563
$43$	−3.12589e20	−1.19294	−0.596469	−	0.802636i	$-0.703430\pi$
$43$	−3.12589e20	−1.19294	−0.596469	+	0.802636i	$0.703430\pi$
$44$	−4.39335e19	−0.125788
$45$	0	0
$46$	−3.80013e19	−0.0624203
$47$	2.45817e19	0.0308595	0.0154297	−	0.999881i	$-0.495088\pi$
$47$	2.45817e19	0.0308595	0.0154297	+	0.999881i	$0.495088\pi$
$48$	1.68327e20	0.162420
$49$	−1.12928e21	−0.842072
$50$	0	0
$51$	1.88653e21	0.853171
$52$	2.54950e21	0.904509
$53$	6.91634e20	0.193387	0.0966936	−	0.995314i	$-0.469173\pi$
$53$	6.91634e20	0.193387	0.0966936	+	0.995314i	$0.469173\pi$
$54$	3.27484e21	0.724883
$55$	0	0
$56$	−1.00008e21	−0.140503
$57$	−4.84970e21	−0.546109
$58$	−5.70708e21	−0.517087
$59$	9.21095e21	0.673991	0.336996	−	0.941506i	$-0.390589\pi$
$59$	9.21095e21	0.673991	0.336996	+	0.941506i	$0.390589\pi$
$60$	0	0
$61$	1.19113e22	0.574561	0.287281	−	0.957846i	$-0.407249\pi$
$61$	1.19113e22	0.574561	0.287281	+	0.957846i	$0.407249\pi$
$62$	5.83140e20	0.0229550
$63$	−7.12611e21	−0.229666
$64$	4.72237e21	0.125000
$65$	0	0
$66$	6.41431e21	0.115572
$67$	1.17804e23	1.75884	0.879418	−	0.476050i	$-0.157932\pi$
$67$	1.17804e23	1.75884	0.879418	+	0.476050i	$0.157932\pi$
$68$	5.29260e22	0.656611
$69$	5.54821e21	0.0573508
$70$	0	0
$71$	1.28366e23	0.928367	0.464184	−	0.885739i	$-0.346348\pi$
$71$	1.28366e23	0.928367	0.464184	+	0.885739i	$0.346348\pi$
$72$	3.36494e22	0.204325
$73$	2.12900e22	0.108803	0.0544013	−	0.998519i	$-0.482675\pi$
$73$	2.12900e22	0.108803	0.0544013	+	0.998519i	$0.482675\pi$
$74$	−2.20254e23	−0.949572
$75$	0	0
$76$	−1.36057e23	−0.420292
$77$	−3.81093e22	−0.0999763
$78$	−3.72228e23	−0.831048
$79$	−2.44555e23	−0.465627	−0.232813	−	0.972521i	$-0.574793\pi$
$79$	−2.44555e23	−0.465627	−0.232813	+	0.972521i	$0.574793\pi$
$80$	0	0
$81$	−6.32412e22	−0.0880922
$82$	2.97506e23	0.355486
$83$	4.71841e23	0.484529	0.242264	−	0.970210i	$-0.422110\pi$
$83$	4.71841e23	0.484529	0.242264	+	0.970210i	$0.422110\pi$
$84$	1.46012e23	0.129092
$85$	0	0
$86$	1.28037e24	0.843535
$87$	8.33235e23	0.475091
$88$	1.79952e23	0.0889452
$89$	−3.32650e24	−1.42762	−0.713810	−	0.700340i	$-0.753032\pi$
$89$	−3.32650e24	−1.42762	−0.713810	+	0.700340i	$0.753032\pi$
$90$	0	0
$91$	2.21152e24	0.718907
$92$	1.55653e23	0.0441378
$93$	−8.51387e22	−0.0210907
$94$	−1.00687e23	−0.0218209
$95$	0	0
$96$	−6.89467e23	−0.114848
$97$	−2.17673e24	−0.318535	−0.159268	−	0.987235i	$-0.550913\pi$
$97$	−2.17673e24	−0.318535	−0.159268	+	0.987235i	$0.550913\pi$
$98$	4.62552e24	0.595435
$99$	1.28225e24	0.145390
$100$	0	0
$101$	9.49877e23	0.0838784	0.0419392	−	0.999120i	$-0.486646\pi$
$101$	9.49877e23	0.0838784	0.0419392	+	0.999120i	$0.486646\pi$
$102$	−7.72722e24	−0.603283
$103$	−1.58249e25	−1.09364	−0.546822	−	0.837249i	$-0.684163\pi$
$103$	−1.58249e25	−1.09364	−0.546822	+	0.837249i	$0.684163\pi$
$104$	−1.04427e25	−0.639585
$105$	0	0
$106$	−2.83293e24	−0.136745
$107$	5.57078e24	0.239121	0.119561	−	0.992827i	$-0.461851\pi$
$107$	5.57078e24	0.239121	0.119561	+	0.992827i	$0.461851\pi$
$108$	−1.34137e25	−0.512570
$109$	−6.15233e24	−0.209512	−0.104756	−	0.994498i	$-0.533406\pi$
$109$	−6.15233e24	−0.209512	−0.104756	+	0.994498i	$0.533406\pi$
$110$	0	0
$111$	3.21572e25	0.872451
$112$	4.09633e24	0.0993504
$113$	−7.53762e25	−1.63589	−0.817945	−	0.575297i	$-0.804886\pi$
$113$	−7.53762e25	−1.63589	−0.817945	+	0.575297i	$0.804886\pi$
$114$	1.98644e25	0.386157
$115$	0	0
$116$	2.33762e25	0.365636
$117$	−7.44102e25	−1.04546
$118$	−3.77280e25	−0.476584
$119$	4.59097e25	0.521876
$120$	0	0
$121$	−1.01490e26	−0.936710
$122$	−4.87887e25	−0.406276
$123$	−4.34360e25	−0.326615
$124$	−2.38854e24	−0.0162316
$125$	0	0
$126$	2.91886e25	0.162398
$127$	−1.42556e26	−0.718520	−0.359260	−	0.933238i	$-0.616971\pi$
$127$	−1.42556e26	−0.718520	−0.359260	+	0.933238i	$0.616971\pi$
$128$	−1.93428e25	−0.0883883
$129$	−1.86934e26	−0.775026
$130$	0	0
$131$	5.35467e26	1.83165	0.915823	−	0.401582i	$-0.131540\pi$
$131$	5.35467e26	1.83165	0.915823	+	0.401582i	$0.131540\pi$
$132$	−2.62730e25	−0.0817214
$133$	−1.18020e26	−0.334049
$134$	−4.82526e26	−1.24368
$135$	0	0
$136$	−2.16785e26	−0.464294
$137$	2.89135e26	0.565059	0.282530	−	0.959259i	$-0.408826\pi$
$137$	2.89135e26	0.565059	0.282530	+	0.959259i	$0.408826\pi$
$138$	−2.27255e25	−0.0405531
$139$	5.79091e26	0.944195	0.472097	−	0.881546i	$-0.343497\pi$
$139$	5.79091e26	0.944195	0.472097	+	0.881546i	$0.343497\pi$
$140$	0	0
$141$	1.47003e25	0.0200487
$142$	−5.25786e26	−0.656455
$143$	−3.97934e26	−0.455104
$144$	−1.37828e26	−0.144480
$145$	0	0
$146$	−8.72037e25	−0.0769351
$147$	−6.75327e26	−0.547076
$148$	9.02161e26	0.671449
$149$	−1.63954e27	−1.12174	−0.560871	−	0.827903i	$-0.689534\pi$
$149$	−1.63954e27	−1.12174	−0.560871	+	0.827903i	$0.689534\pi$
$150$	0	0
$151$	8.73769e26	0.506040	0.253020	−	0.967461i	$-0.418576\pi$
$151$	8.73769e26	0.506040	0.253020	+	0.967461i	$0.418576\pi$
$152$	5.57289e26	0.297191
$153$	−1.54471e27	−0.758935
$154$	1.56096e26	0.0706939
$155$	0	0
$156$	1.52465e27	0.587640
$157$	5.11473e27	1.82002	0.910011	−	0.414583i	$-0.136073\pi$
$157$	5.11473e27	1.82002	0.910011	+	0.414583i	$0.136073\pi$
$158$	1.00170e27	0.329248
$159$	4.13609e26	0.125639
$160$	0	0
$161$	1.35019e26	0.0350809
$162$	2.59036e26	0.0622906
$163$	8.90978e27	1.98391	0.991955	−	0.126591i	$-0.0404036\pi$
$163$	8.90978e27	1.98391	0.991955	+	0.126591i	$0.0404036\pi$
$164$	−1.21858e27	−0.251367
$165$	0	0
$166$	−1.93266e27	−0.342614
$167$	−4.51191e27	−0.742002	−0.371001	−	0.928632i	$-0.620985\pi$
$167$	−4.51191e27	−0.742002	−0.371001	+	0.928632i	$0.620985\pi$
$168$	−5.98066e26	−0.0912815
$169$	1.60360e28	2.27255
$170$	0	0
$171$	3.97099e27	0.485789
$172$	−5.24438e27	−0.596469
$173$	−4.73770e27	−0.501177	−0.250588	−	0.968094i	$-0.580624\pi$
$173$	−4.73770e27	−0.501177	−0.250588	+	0.968094i	$0.580624\pi$
$174$	−3.41293e27	−0.335940
$175$	0	0
$176$	−7.37082e26	−0.0628938
$177$	5.50831e27	0.437877
$178$	1.36253e28	1.00948
$179$	1.61045e28	1.11246	0.556230	−	0.831029i	$-0.312248\pi$
$179$	1.61045e28	1.11246	0.556230	+	0.831029i	$0.312248\pi$
$180$	0	0
$181$	1.83661e27	0.110417	0.0552085	−	0.998475i	$-0.482418\pi$
$181$	1.83661e27	0.110417	0.0552085	+	0.998475i	$0.482418\pi$
$182$	−9.05837e27	−0.508344
$183$	7.12317e27	0.373280
$184$	−6.37557e26	−0.0312102
$185$	0	0
$186$	3.48728e26	0.0149134
$187$	−8.26087e27	−0.330374
$188$	4.12412e26	0.0154297
$189$	−1.16355e28	−0.407392
$190$	0	0
$191$	−8.82845e27	−0.270999	−0.135499	−	0.990777i	$-0.543264\pi$
$191$	−8.82845e27	−0.270999	−0.135499	+	0.990777i	$0.543264\pi$
$192$	2.82406e27	0.0812098
$193$	4.86040e28	1.30980	0.654901	−	0.755714i	$-0.272710\pi$
$193$	4.86040e28	1.30980	0.654901	+	0.755714i	$0.272710\pi$
$194$	8.91587e27	0.225238
$195$	0	0
$196$	−1.89461e28	−0.421036
$197$	−8.10600e28	−1.69036	−0.845179	−	0.534484i	$-0.820506\pi$
$197$	−8.10600e28	−1.69036	−0.845179	+	0.534484i	$0.820506\pi$
$198$	−5.25211e27	−0.102806
$199$	2.19750e28	0.403893	0.201946	−	0.979397i	$-0.435273\pi$
$199$	2.19750e28	0.403893	0.201946	+	0.979397i	$0.435273\pi$
$200$	0	0
$201$	7.04489e28	1.14268
$202$	−3.89069e27	−0.0593110
$203$	2.02772e28	0.290608
$204$	3.16507e28	0.426586
$205$	0	0
$206$	6.48189e28	0.773323
$207$	−4.54294e27	−0.0510161
$208$	4.27735e28	0.452255
$209$	2.12362e28	0.211470
$210$	0	0
$211$	1.16957e29	1.03394	0.516971	−	0.856003i	$-0.327059\pi$
$211$	1.16957e29	1.03394	0.516971	+	0.856003i	$0.327059\pi$
$212$	1.16037e28	0.0966936
$213$	7.67650e28	0.603140
$214$	−2.28179e28	−0.169084
$215$	0	0
$216$	5.49427e28	0.362441
$217$	−2.07190e27	−0.0129009
$218$	2.52000e28	0.148147
$219$	1.27318e28	0.0706867
$220$	0	0
$221$	4.79385e29	2.37564
$222$	−1.31716e29	−0.616916
$223$	−1.81556e29	−0.803898	−0.401949	−	0.915662i	$-0.631667\pi$
$223$	−1.81556e29	−0.803898	−0.401949	+	0.915662i	$0.631667\pi$
$224$	−1.67786e28	−0.0702513
$225$	0	0
$226$	3.08741e29	1.15675
$227$	−2.82277e29	−1.00081	−0.500406	−	0.865791i	$-0.666816\pi$
$227$	−2.82277e29	−1.00081	−0.500406	+	0.865791i	$0.666816\pi$
$228$	−8.13645e28	−0.273054
$229$	−6.39963e28	−0.203335	−0.101667	−	0.994818i	$-0.532418\pi$
$229$	−6.39963e28	−0.203335	−0.101667	+	0.994818i	$0.532418\pi$
$230$	0	0
$231$	−2.27900e28	−0.0649524
$232$	−9.57488e28	−0.258544
$233$	5.09485e29	1.30371	0.651856	−	0.758342i	$-0.273990\pi$
$233$	5.09485e29	1.30371	0.651856	+	0.758342i	$0.273990\pi$
$234$	3.04784e29	0.739255
$235$	0	0
$236$	1.54534e29	0.336996
$237$	−1.46248e29	−0.302507
$238$	−1.88046e29	−0.369022
$239$	−2.78735e29	−0.519060	−0.259530	−	0.965735i	$-0.583568\pi$
$239$	−2.78735e29	−0.519060	−0.259530	+	0.965735i	$0.583568\pi$
$240$	0	0
$241$	1.16488e30	1.95465	0.977326	−	0.211741i	$-0.0679133\pi$
$241$	1.16488e30	1.95465	0.977326	+	0.211741i	$0.0679133\pi$
$242$	4.15702e29	0.662354
$243$	6.39606e29	0.967907
$244$	1.99838e29	0.287281
$245$	0	0
$246$	1.77914e29	0.230951
$247$	−1.23235e30	−1.52063
$248$	9.78347e27	0.0114775
$249$	2.82169e29	0.314788
$250$	0	0
$251$	9.82414e29	0.991684	0.495842	−	0.868413i	$-0.334860\pi$
$251$	9.82414e29	0.991684	0.495842	+	0.868413i	$0.334860\pi$
$252$	−1.19556e29	−0.114833
$253$	−2.42949e28	−0.0222080
$254$	5.83909e29	0.508070
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	−1.90279e30	−1.42964	−0.714821	−	0.699308i	$-0.753492\pi$
$257$	−1.90279e30	−1.42964	−0.714821	+	0.699308i	$0.753492\pi$
$258$	7.65681e29	0.548026
$259$	7.82563e29	0.533669
$260$	0	0
$261$	−6.82263e29	−0.422615
$262$	−2.19327e30	−1.29517
$263$	2.16480e30	1.21891	0.609454	−	0.792821i	$-0.291389\pi$
$263$	2.16480e30	1.21891	0.609454	+	0.792821i	$0.291389\pi$
$264$	1.07614e29	0.0577858
$265$	0	0
$266$	4.83410e29	0.236208
$267$	−1.98930e30	−0.927493
$268$	1.97642e30	0.879418
$269$	2.85539e30	1.21272	0.606362	−	0.795189i	$-0.292628\pi$
$269$	2.85539e30	1.21272	0.606362	+	0.795189i	$0.292628\pi$
$270$	0	0
$271$	3.91860e30	1.51710	0.758551	−	0.651614i	$-0.225908\pi$
$271$	3.91860e30	1.51710	0.758551	+	0.651614i	$0.225908\pi$
$272$	8.87951e29	0.328305
$273$	1.32252e30	0.467058
$274$	−1.18430e30	−0.399557
$275$	0	0
$276$	9.30835e28	0.0286754
$277$	4.65569e30	1.37084	0.685421	−	0.728147i	$-0.259618\pi$
$277$	4.65569e30	1.37084	0.685421	+	0.728147i	$0.259618\pi$
$278$	−2.37196e30	−0.667646
$279$	6.97126e28	0.0187611
$280$	0	0
$281$	1.40228e30	0.345148	0.172574	−	0.984997i	$-0.444792\pi$
$281$	1.40228e30	0.345148	0.172574	+	0.984997i	$0.444792\pi$
$282$	−6.02123e28	−0.0141766
$283$	5.44976e30	1.22757	0.613785	−	0.789473i	$-0.289646\pi$
$283$	5.44976e30	1.22757	0.613785	+	0.789473i	$0.289646\pi$
$284$	2.15362e30	0.464184
$285$	0	0
$286$	1.62994e30	0.321807
$287$	−1.05704e30	−0.199787
$288$	5.64544e29	0.102162
$289$	4.18111e30	0.724550
$290$	0	0
$291$	−1.30172e30	−0.206945
$292$	3.57186e29	0.0544013
$293$	−1.13376e30	−0.165454	−0.0827268	−	0.996572i	$-0.526363\pi$
$293$	−1.13376e30	−0.165454	−0.0827268	+	0.996572i	$0.526363\pi$
$294$	2.76614e30	0.386841
$295$	0	0
$296$	−3.69525e30	−0.474786
$297$	2.09366e30	0.257900
$298$	6.71555e30	0.793191
$299$	1.40985e30	0.159692
$300$	0	0
$301$	−4.54914e30	−0.474076
$302$	−3.57896e30	−0.357824
$303$	5.68043e29	0.0544940
$304$	−2.28266e30	−0.210146
$305$	0	0
$306$	6.32714e30	0.536648
$307$	1.74515e31	1.42103	0.710515	−	0.703682i	$-0.248462\pi$
$307$	1.74515e31	1.42103	0.710515	+	0.703682i	$0.248462\pi$
$308$	−6.39368e29	−0.0499882
$309$	−9.46358e30	−0.710517
$310$	0	0
$311$	1.83900e31	1.27373	0.636865	−	0.770975i	$-0.280231\pi$
$311$	1.83900e31	1.27373	0.636865	+	0.770975i	$0.280231\pi$
$312$	−6.24495e30	−0.415524
$313$	−5.22205e30	−0.333839	−0.166919	−	0.985971i	$-0.553382\pi$
$313$	−5.22205e30	−0.333839	−0.166919	+	0.985971i	$0.553382\pi$
$314$	−2.09499e31	−1.28695
$315$	0	0
$316$	−4.10295e30	−0.232813
$317$	−1.02145e31	−0.557158	−0.278579	−	0.960413i	$-0.589863\pi$
$317$	−1.02145e31	−0.557158	−0.278579	+	0.960413i	$0.589863\pi$
$318$	−1.69414e30	−0.0888405
$319$	−3.64863e30	−0.183970
$320$	0	0
$321$	3.33142e30	0.155352
$322$	−5.53036e29	−0.0248059
$323$	−2.55829e31	−1.10387
$324$	−1.06101e30	−0.0440461
$325$	0	0
$326$	−3.64945e31	−1.40284
$327$	−3.67920e30	−0.136115
$328$	4.99132e30	0.177743
$329$	3.57739e29	0.0122636
$330$	0	0
$331$	−4.70386e31	−1.49487	−0.747436	−	0.664334i	$-0.768715\pi$
$331$	−4.70386e31	−1.49487	−0.747436	+	0.664334i	$0.768715\pi$
$332$	7.91618e30	0.242264
$333$	−2.63307e31	−0.776085
$334$	1.84808e31	0.524675
$335$	0	0
$336$	2.44968e30	0.0645458
$337$	6.26572e30	0.159073	0.0795367	−	0.996832i	$-0.474656\pi$
$337$	6.26572e30	0.159073	0.0795367	+	0.996832i	$0.474656\pi$
$338$	−6.56836e31	−1.60693
$339$	−4.50763e31	−1.06280
$340$	0	0
$341$	3.72812e29	0.00816695
$342$	−1.62652e31	−0.343504
$343$	−3.59511e31	−0.732042
$344$	2.14810e31	0.421768
$345$	0	0
$346$	1.94056e31	0.354386
$347$	5.96085e31	1.05000	0.525000	−	0.851102i	$-0.324065\pi$
$347$	5.96085e31	1.05000	0.525000	+	0.851102i	$0.324065\pi$
$348$	1.39794e31	0.237546
$349$	−4.14342e31	−0.679268	−0.339634	−	0.940558i	$-0.610303\pi$
$349$	−4.14342e31	−0.679268	−0.339634	+	0.940558i	$0.610303\pi$
$350$	0	0
$351$	−1.21497e32	−1.85450
$352$	3.01909e30	0.0444726
$353$	6.99904e30	0.0995073	0.0497536	−	0.998762i	$-0.484156\pi$
$353$	6.99904e30	0.0995073	0.0497536	+	0.998762i	$0.484156\pi$
$354$	−2.25620e31	−0.309626
$355$	0	0
$356$	−5.58094e31	−0.713810
$357$	2.74548e31	0.339051
$358$	−6.59640e31	−0.786627
$359$	−1.15020e31	−0.132462	−0.0662312	−	0.997804i	$-0.521097\pi$
$359$	−1.15020e31	−0.132462	−0.0662312	+	0.997804i	$0.521097\pi$
$360$	0	0
$361$	−2.73104e31	−0.293419
$362$	−7.52277e30	−0.0780766
$363$	−6.06927e31	−0.608560
$364$	3.71031e31	0.359453
$365$	0	0
$366$	−2.91765e31	−0.263949
$367$	8.40201e31	0.734611	0.367306	−	0.930100i	$-0.380280\pi$
$367$	8.40201e31	0.734611	0.367306	+	0.930100i	$0.380280\pi$
$368$	2.61143e30	0.0220689
$369$	3.55659e31	0.290539
$370$	0	0
$371$	1.00654e31	0.0768524
$372$	−1.42839e30	−0.0105453
$373$	−9.28607e31	−0.662936	−0.331468	−	0.943466i	$-0.607544\pi$
$373$	−9.28607e31	−0.662936	−0.331468	+	0.943466i	$0.607544\pi$
$374$	3.38365e31	0.233610
$375$	0	0
$376$	−1.68924e30	−0.0109105
$377$	2.11733e32	1.32288
$378$	4.76590e31	0.288069
$379$	−2.04933e32	−1.19845	−0.599226	−	0.800580i	$-0.704525\pi$
$379$	−2.04933e32	−1.19845	−0.599226	+	0.800580i	$0.704525\pi$
$380$	0	0
$381$	−8.52510e31	−0.466807
$382$	3.61613e31	0.191625
$383$	2.43020e32	1.24640	0.623200	−	0.782063i	$-0.285832\pi$
$383$	2.43020e32	1.24640	0.623200	+	0.782063i	$0.285832\pi$
$384$	−1.15673e31	−0.0574240
$385$	0	0
$386$	−1.99082e32	−0.926171
$387$	1.53064e32	0.689421
$388$	−3.65194e31	−0.159268
$389$	−1.98585e32	−0.838640	−0.419320	−	0.907838i	$-0.637732\pi$
$389$	−1.98585e32	−0.838640	−0.419320	+	0.907838i	$0.637732\pi$
$390$	0	0
$391$	2.92677e31	0.115925
$392$	7.76033e31	0.297717
$393$	3.20219e32	1.18998
$394$	3.32022e32	1.19526
$395$	0	0
$396$	2.15127e31	0.0726949
$397$	9.28363e31	0.303974	0.151987	−	0.988382i	$-0.451433\pi$
$397$	9.28363e31	0.303974	0.151987	+	0.988382i	$0.451433\pi$
$398$	−9.00098e31	−0.285595
$399$	−7.05781e31	−0.217024
$400$	0	0
$401$	−4.87975e32	−1.40959	−0.704796	−	0.709410i	$-0.748961\pi$
$401$	−4.87975e32	−1.40959	−0.704796	+	0.709410i	$0.748961\pi$
$402$	−2.88559e32	−0.807995
$403$	−2.16346e31	−0.0587266
$404$	1.59363e31	0.0419392
$405$	0	0
$406$	−8.30555e31	−0.205491
$407$	−1.40812e32	−0.337840
$408$	−1.29641e32	−0.301642
$409$	−3.05167e32	−0.688646	−0.344323	−	0.938851i	$-0.611892\pi$
$409$	−3.05167e32	−0.688646	−0.344323	+	0.938851i	$0.611892\pi$
$410$	0	0
$411$	1.72908e32	0.367107
$412$	−2.65498e32	−0.546822
$413$	1.34048e32	0.267845
$414$	1.86079e31	0.0360738
$415$	0	0
$416$	−1.75200e32	−0.319792
$417$	3.46306e32	0.613423
$418$	−8.69835e31	−0.149532
$419$	1.13245e33	1.88949	0.944743	−	0.327811i	$-0.106311\pi$
$419$	1.13245e33	1.88949	0.944743	+	0.327811i	$0.106311\pi$
$420$	0	0
$421$	1.20520e33	1.89466	0.947331	−	0.320257i	$-0.103769\pi$
$421$	1.20520e33	1.89466	0.947331	+	0.320257i	$0.103769\pi$
$422$	−4.79057e32	−0.731108
$423$	−1.20368e31	−0.0178342
$424$	−4.75287e31	−0.0683727
$425$	0	0
$426$	−3.14429e32	−0.426484
$427$	1.73346e32	0.228331
$428$	9.34621e31	0.119561
$429$	−2.37972e32	−0.295671
$430$	0	0
$431$	1.58506e33	1.85814	0.929071	−	0.369901i	$-0.120608\pi$
$431$	1.58506e33	1.85814	0.929071	+	0.369901i	$0.120608\pi$
$432$	−2.25045e32	−0.256285
$433$	2.62028e32	0.289900	0.144950	−	0.989439i	$-0.453698\pi$
$433$	2.62028e32	0.289900	0.144950	+	0.989439i	$0.453698\pi$
$434$	8.48649e30	0.00912235
$435$	0	0
$436$	−1.03219e32	−0.104756
$437$	−7.52384e31	−0.0742030
$438$	−5.21494e31	−0.0499830
$439$	6.01248e32	0.560076	0.280038	−	0.959989i	$-0.409653\pi$
$439$	6.01248e32	0.560076	0.280038	+	0.959989i	$0.409653\pi$
$440$	0	0
$441$	5.52966e32	0.486649
$442$	−1.96356e33	−1.67983
$443$	−1.09376e33	−0.909656	−0.454828	−	0.890579i	$-0.650299\pi$
$443$	−1.09376e33	−0.909656	−0.454828	+	0.890579i	$0.650299\pi$
$444$	5.39508e32	0.436225
$445$	0	0
$446$	7.43655e32	0.568442
$447$	−9.80472e32	−0.728771
$448$	6.87250e31	0.0496752
$449$	−7.47845e32	−0.525693	−0.262846	−	0.964838i	$-0.584661\pi$
$449$	−7.47845e32	−0.525693	−0.262846	+	0.964838i	$0.584661\pi$
$450$	0	0
$451$	1.90201e32	0.126475
$452$	−1.26460e33	−0.817945
$453$	5.22529e32	0.328763
$454$	1.15621e33	0.707681
$455$	0	0
$456$	3.33269e32	0.193079
$457$	−4.45068e32	−0.250885	−0.125442	−	0.992101i	$-0.540035\pi$
$457$	−4.45068e32	−0.250885	−0.125442	+	0.992101i	$0.540035\pi$
$458$	2.62129e32	0.143779
$459$	−2.52220e33	−1.34623
$460$	0	0
$461$	3.01850e33	1.52591	0.762957	−	0.646449i	$-0.223747\pi$
$461$	3.01850e33	1.52591	0.762957	+	0.646449i	$0.223747\pi$
$462$	9.33480e31	0.0459283
$463$	3.41535e33	1.63559	0.817793	−	0.575513i	$-0.195198\pi$
$463$	3.41535e33	1.63559	0.817793	+	0.575513i	$0.195198\pi$
$464$	3.92187e32	0.182818
$465$	0	0
$466$	−2.08685e33	−0.921864
$467$	4.56176e33	1.96187	0.980937	−	0.194326i	$-0.0622518\pi$
$467$	4.56176e33	1.96187	0.980937	+	0.194326i	$0.0622518\pi$
$468$	−1.24840e33	−0.522732
$469$	1.71441e33	0.698964
$470$	0	0
$471$	3.05870e33	1.18243
$472$	−6.32971e32	−0.238292
$473$	8.18559e32	0.300114
$474$	5.99032e32	0.213905
$475$	0	0
$476$	7.70237e32	0.260938
$477$	−3.38668e32	−0.111762
$478$	1.14170e33	0.367031
$479$	−5.85782e33	−1.83460	−0.917301	−	0.398194i	$-0.869637\pi$
$479$	−5.85782e33	−1.83460	−0.917301	+	0.398194i	$0.869637\pi$
$480$	0	0
$481$	8.17145e33	2.42933
$482$	−4.77136e33	−1.38215
$483$	8.07435e31	0.0227913
$484$	−1.70272e33	−0.468355
$485$	0	0
$486$	−2.61982e33	−0.684414
$487$	−4.33198e32	−0.110300	−0.0551499	−	0.998478i	$-0.517564\pi$
$487$	−4.33198e32	−0.110300	−0.0551499	+	0.998478i	$0.517564\pi$
$488$	−8.18538e32	−0.203138
$489$	5.32821e33	1.28890
$490$	0	0
$491$	−3.36826e33	−0.774261	−0.387131	−	0.922025i	$-0.626534\pi$
$491$	−3.36826e33	−0.774261	−0.387131	+	0.922025i	$0.626534\pi$
$492$	−7.28735e32	−0.163307
$493$	4.39545e33	0.960321
$494$	5.04773e33	1.07525
$495$	0	0
$496$	−4.00731e31	−0.00811581
$497$	1.86812e33	0.368935
$498$	−1.15577e33	−0.222589
$499$	2.86948e33	0.538947	0.269474	−	0.963008i	$-0.413150\pi$
$499$	2.86948e33	0.538947	0.269474	+	0.963008i	$0.413150\pi$
$500$	0	0
$501$	−2.69820e33	−0.482062
$502$	−4.02397e33	−0.701226
$503$	5.60647e33	0.952994	0.476497	−	0.879176i	$-0.341906\pi$
$503$	5.60647e33	0.952994	0.476497	+	0.879176i	$0.341906\pi$
$504$	4.89703e32	0.0811990
$505$	0	0
$506$	9.95119e31	0.0157034
$507$	9.58983e33	1.47643
$508$	−2.39169e33	−0.359260
$509$	−5.45018e33	−0.798802	−0.399401	−	0.916776i	$-0.630782\pi$
$509$	−5.45018e33	−0.798802	−0.399401	+	0.916776i	$0.630782\pi$
$510$	0	0
$511$	3.09835e32	0.0432383
$512$	−3.24519e32	−0.0441942
$513$	6.48382e33	0.861715
$514$	7.79384e33	1.01091
$515$	0	0
$516$	−3.13623e33	−0.387513
$517$	−6.43706e31	−0.00776347
$518$	−3.20538e33	−0.377361
$519$	−2.83323e33	−0.325604
$520$	0	0
$521$	−6.07119e33	−0.664970	−0.332485	−	0.943108i	$-0.607887\pi$
$521$	−6.07119e33	−0.664970	−0.332485	+	0.943108i	$0.607887\pi$
$522$	2.79455e33	0.298834
$523$	−5.31876e33	−0.555315	−0.277657	−	0.960680i	$-0.589558\pi$
$523$	−5.31876e33	−0.555315	−0.277657	+	0.960680i	$0.589558\pi$
$524$	8.98364e33	0.915823
$525$	0	0
$526$	−8.86702e33	−0.861898
$527$	−4.49120e32	−0.0426314
$528$	−4.40788e32	−0.0408607
$529$	−1.09597e34	−0.992207
$530$	0	0
$531$	−4.51027e33	−0.389512
$532$	−1.98005e33	−0.167025
$533$	−1.10375e34	−0.909453
$534$	8.14819e33	0.655837
$535$	0	0
$536$	−8.09544e33	−0.621842
$537$	9.63077e33	0.722740
$538$	−1.16957e34	−0.857525
$539$	2.95717e33	0.211844
$540$	0	0
$541$	−4.32128e33	−0.295561	−0.147780	−	0.989020i	$-0.547213\pi$
$541$	−4.32128e33	−0.295561	−0.147780	+	0.989020i	$0.547213\pi$
$542$	−1.60506e34	−1.07275
$543$	1.09833e33	0.0717355
$544$	−3.63705e33	−0.232147
$545$	0	0
$546$	−5.41706e33	−0.330260
$547$	1.33475e34	0.795350	0.397675	−	0.917526i	$-0.369817\pi$
$547$	1.33475e34	0.795350	0.397675	+	0.917526i	$0.369817\pi$
$548$	4.85089e33	0.282530
$549$	−5.83253e33	−0.332049
$550$	0	0
$551$	−1.12994e34	−0.614695
$552$	−3.81270e32	−0.0202766
$553$	−3.55903e33	−0.185041
$554$	−1.90697e34	−0.969332
$555$	0	0
$556$	9.71553e33	0.472097
$557$	3.10182e34	1.47376	0.736879	−	0.676025i	$-0.236299\pi$
$557$	3.10182e34	1.47376	0.736879	+	0.676025i	$0.236299\pi$
$558$	−2.85543e32	−0.0132661
$559$	−4.75017e34	−2.15805
$560$	0	0
$561$	−4.94014e33	−0.214637
$562$	−5.74373e33	−0.244056
$563$	−2.24681e34	−0.933707	−0.466853	−	0.884335i	$-0.654612\pi$
$563$	−2.24681e34	−0.933707	−0.466853	+	0.884335i	$0.654612\pi$
$564$	2.46630e32	0.0100244
$565$	0	0
$566$	−2.23222e34	−0.868024
$567$	−9.20354e32	−0.0350080
$568$	−8.82123e33	−0.328227
$569$	−1.20893e34	−0.440047	−0.220024	−	0.975495i	$-0.570613\pi$
$569$	−1.20893e34	−0.440047	−0.220024	+	0.975495i	$0.570613\pi$
$570$	0	0
$571$	1.23143e34	0.429003	0.214501	−	0.976724i	$-0.431187\pi$
$571$	1.23143e34	0.429003	0.214501	+	0.976724i	$0.431187\pi$
$572$	−6.67623e33	−0.227552
$573$	−5.27957e33	−0.176062
$574$	4.32963e33	0.141271
$575$	0	0
$576$	−2.31237e33	−0.0722398
$577$	5.40970e33	0.165377	0.0826886	−	0.996575i	$-0.473649\pi$
$577$	5.40970e33	0.165377	0.0826886	+	0.996575i	$0.473649\pi$
$578$	−1.71258e34	−0.512334
$579$	2.90661e34	0.850950
$580$	0	0
$581$	6.86674e33	0.192552
$582$	5.33185e33	0.146332
$583$	−1.81114e33	−0.0486514
$584$	−1.46304e33	−0.0384675
$585$	0	0
$586$	4.64388e33	0.116993
$587$	3.54869e34	0.875168	0.437584	−	0.899178i	$-0.355834\pi$
$587$	3.54869e34	0.875168	0.437584	+	0.899178i	$0.355834\pi$
$588$	−1.13301e34	−0.273538
$589$	1.15455e33	0.0272881
$590$	0	0
$591$	−4.84753e34	−1.09819
$592$	1.51358e34	0.335724
$593$	−2.30822e34	−0.501294	−0.250647	−	0.968079i	$-0.580643\pi$
$593$	−2.30822e34	−0.501294	−0.250647	+	0.968079i	$0.580643\pi$
$594$	−8.57563e33	−0.182362
$595$	0	0
$596$	−2.75069e34	−0.560871
$597$	1.31415e34	0.262400
$598$	−5.77476e33	−0.112919
$599$	−5.42443e34	−1.03877	−0.519384	−	0.854541i	$-0.673839\pi$
$599$	−5.42443e34	−1.03877	−0.519384	+	0.854541i	$0.673839\pi$
$600$	0	0
$601$	6.07959e34	1.11672	0.558358	−	0.829600i	$-0.311431\pi$
$601$	6.07959e34	1.11672	0.558358	+	0.829600i	$0.311431\pi$
$602$	1.86333e34	0.335222
$603$	−5.76844e34	−1.01646
$604$	1.46594e34	0.253020
$605$	0	0
$606$	−2.32670e33	−0.0385330
$607$	2.92200e34	0.474047	0.237023	−	0.971504i	$-0.423828\pi$
$607$	2.92200e34	0.474047	0.237023	+	0.971504i	$0.423828\pi$
$608$	9.34976e33	0.148596
$609$	1.21261e34	0.188802
$610$	0	0
$611$	3.73548e33	0.0558253
$612$	−2.59159e34	−0.379467
$613$	5.85284e34	0.839674	0.419837	−	0.907600i	$-0.362087\pi$
$613$	5.85284e34	0.839674	0.419837	+	0.907600i	$0.362087\pi$
$614$	−7.14814e34	−1.00482
$615$	0	0
$616$	2.61885e33	0.0353470
$617$	−6.82025e34	−0.902061	−0.451030	−	0.892509i	$-0.648943\pi$
$617$	−6.82025e34	−0.902061	−0.451030	+	0.892509i	$0.648943\pi$
$618$	3.87628e34	0.502411
$619$	9.49546e34	1.20610	0.603049	−	0.797704i	$-0.293952\pi$
$619$	9.49546e34	1.20610	0.603049	+	0.797704i	$0.293952\pi$
$620$	0	0
$621$	−7.41769e33	−0.0904948
$622$	−7.53256e34	−0.900664
$623$	−4.84108e34	−0.567338
$624$	2.55793e34	0.293820
$625$	0	0
$626$	2.13895e34	0.236059
$627$	1.26996e34	0.137387
$628$	8.58109e34	0.910011
$629$	1.69634e35	1.76352
$630$	0	0
$631$	−1.61402e35	−1.61265	−0.806327	−	0.591471i	$-0.798548\pi$
$631$	−1.61402e35	−1.61265	−0.806327	+	0.591471i	$0.798548\pi$
$632$	1.68057e34	0.164624
$633$	6.99425e34	0.671730
$634$	4.18388e34	0.393970
$635$	0	0
$636$	6.93921e33	0.0628197
$637$	−1.71607e35	−1.52332
$638$	1.49448e34	0.130086
$639$	−6.28560e34	−0.536520
$640$	0	0
$641$	1.81108e35	1.48666	0.743331	−	0.668924i	$-0.233245\pi$
$641$	1.81108e35	1.48666	0.743331	+	0.668924i	$0.233245\pi$
$642$	−1.36455e34	−0.109850
$643$	4.05766e34	0.320360	0.160180	−	0.987088i	$-0.448793\pi$
$643$	4.05766e34	0.320360	0.160180	+	0.987088i	$0.448793\pi$
$644$	2.26524e33	0.0175404
$645$	0	0
$646$	1.04788e35	0.780555
$647$	−1.36523e35	−0.997473	−0.498737	−	0.866754i	$-0.666202\pi$
$647$	−1.36523e35	−0.997473	−0.498737	+	0.866754i	$0.666202\pi$
$648$	4.34590e33	0.0311453
$649$	−2.41202e34	−0.169559
$650$	0	0
$651$	−1.23903e33	−0.00838146
$652$	1.49481e35	0.991955
$653$	2.42856e35	1.58101	0.790506	−	0.612455i	$-0.209818\pi$
$653$	2.42856e35	1.58101	0.790506	+	0.612455i	$0.209818\pi$
$654$	1.50700e34	0.0962480
$655$	0	0
$656$	−2.04444e34	−0.125683
$657$	−1.04249e34	−0.0628790
$658$	−1.46530e33	−0.00867167
$659$	1.97195e35	1.14506	0.572529	−	0.819884i	$-0.305962\pi$
$659$	1.97195e35	1.14506	0.572529	+	0.819884i	$0.305962\pi$
$660$	0	0
$661$	1.13646e35	0.635384	0.317692	−	0.948194i	$-0.397092\pi$
$661$	1.13646e35	0.635384	0.317692	+	0.948194i	$0.397092\pi$
$662$	1.92670e35	1.05703
$663$	2.86681e35	1.54340
$664$	−3.24247e34	−0.171307
$665$	0	0
$666$	1.07850e35	0.548775
$667$	1.29268e34	0.0645535
$668$	−7.56974e34	−0.371001
$669$	−1.08574e35	−0.522275
$670$	0	0
$671$	−3.11914e34	−0.144545
$672$	−1.00339e34	−0.0456408
$673$	−6.16466e34	−0.275246	−0.137623	−	0.990485i	$-0.543946\pi$
$673$	−6.16466e34	−0.275246	−0.137623	+	0.990485i	$0.543946\pi$
$674$	−2.56644e34	−0.112482
$675$	0	0
$676$	2.69040e35	1.13627
$677$	−3.87398e35	−1.60620	−0.803099	−	0.595845i	$-0.796817\pi$
$677$	−3.87398e35	−1.60620	−0.803099	+	0.595845i	$0.796817\pi$
$678$	1.84633e35	0.751514
$679$	−3.16781e34	−0.126586
$680$	0	0
$681$	−1.68807e35	−0.650206
$682$	−1.52704e33	−0.00577490
$683$	−2.57159e35	−0.954866	−0.477433	−	0.878668i	$-0.658433\pi$
$683$	−2.57159e35	−0.954866	−0.477433	+	0.878668i	$0.658433\pi$
$684$	6.66221e34	0.242894
$685$	0	0
$686$	1.47256e35	0.517632
$687$	−3.82709e34	−0.132102
$688$	−8.79860e34	−0.298235
$689$	1.05102e35	0.349841
$690$	0	0
$691$	5.38796e35	1.72961	0.864806	−	0.502107i	$-0.167442\pi$
$691$	5.38796e35	1.72961	0.864806	+	0.502107i	$0.167442\pi$
$692$	−7.94854e34	−0.250588
$693$	1.86608e34	0.0577782
$694$	−2.44156e35	−0.742463
$695$	0	0
$696$	−5.72595e34	−0.167970
$697$	−2.29132e35	−0.660200
$698$	1.69714e35	0.480315
$699$	3.04681e35	0.846994
$700$	0	0
$701$	2.98227e35	0.799966	0.399983	−	0.916522i	$-0.369016\pi$
$701$	2.98227e35	0.799966	0.399983	+	0.916522i	$0.369016\pi$
$702$	4.97651e35	1.31133
$703$	−4.36079e35	−1.12882
$704$	−1.23662e34	−0.0314469
$705$	0	0
$706$	−2.86681e34	−0.0703623
$707$	1.38236e34	0.0333334
$708$	9.24141e34	0.218939
$709$	1.71720e35	0.399709	0.199854	−	0.979826i	$-0.435953\pi$
$709$	1.71720e35	0.399709	0.199854	+	0.979826i	$0.435953\pi$
$710$	0	0
$711$	1.19750e35	0.269094
$712$	2.28595e35	0.504740
$713$	−1.32085e33	−0.00286571
$714$	−1.12455e35	−0.239746
$715$	0	0
$716$	2.70189e35	0.556230
$717$	−1.66688e35	−0.337222
$718$	4.71122e34	0.0936650
$719$	−5.06044e35	−0.988728	−0.494364	−	0.869255i	$-0.664599\pi$
$719$	−5.06044e35	−0.988728	−0.494364	+	0.869255i	$0.664599\pi$
$720$	0	0
$721$	−2.30301e35	−0.434616
$722$	1.11864e35	0.207479
$723$	6.96621e35	1.26989
$724$	3.08133e34	0.0552085
$725$	0	0
$726$	2.48597e35	0.430317
$727$	−9.39720e35	−1.59889	−0.799445	−	0.600739i	$-0.794873\pi$
$727$	−9.39720e35	−1.59889	−0.799445	+	0.600739i	$0.794873\pi$
$728$	−1.51974e35	−0.254172
$729$	4.36079e35	0.716921
$730$	0	0
$731$	−9.86105e35	−1.56659
$732$	1.19507e35	0.186640
$733$	−1.16413e36	−1.78732	−0.893659	−	0.448747i	$-0.851870\pi$
$733$	−1.16413e36	−1.78732	−0.893659	+	0.448747i	$0.851870\pi$
$734$	−3.44146e35	−0.519449
$735$	0	0
$736$	−1.06964e34	−0.0156051
$737$	−3.08487e35	−0.442479
$738$	−1.45678e35	−0.205442
$739$	−3.05798e35	−0.424012	−0.212006	−	0.977268i	$-0.568000\pi$
$739$	−3.05798e35	−0.424012	−0.212006	+	0.977268i	$0.568000\pi$
$740$	0	0
$741$	−7.36970e35	−0.987921
$742$	−4.12279e34	−0.0543428
$743$	−1.03102e36	−1.33630	−0.668152	−	0.744025i	$-0.732914\pi$
$743$	−1.03102e36	−1.33630	−0.668152	+	0.744025i	$0.732914\pi$
$744$	5.85069e33	0.00745668
$745$	0	0
$746$	3.80357e35	0.468767
$747$	−2.31043e35	−0.280018
$748$	−1.38594e35	−0.165187
$749$	8.10720e34	0.0950272
$750$	0	0
$751$	−1.09969e36	−1.24672	−0.623362	−	0.781933i	$-0.714234\pi$
$751$	−1.09969e36	−1.24672	−0.623362	+	0.781933i	$0.714234\pi$
$752$	6.91913e33	0.00771486
$753$	5.87501e35	0.644275
$754$	−8.67259e35	−0.935420
$755$	0	0
$756$	−1.95211e35	−0.203696
$757$	7.01440e35	0.719933	0.359967	−	0.932965i	$-0.382788\pi$
$757$	7.01440e35	0.719933	0.359967	+	0.932965i	$0.382788\pi$
$758$	8.39404e35	0.847434
$759$	−1.45288e34	−0.0144280
$760$	0	0
$761$	−5.24100e34	−0.0503624	−0.0251812	−	0.999683i	$-0.508016\pi$
$761$	−5.24100e34	−0.0503624	−0.0251812	+	0.999683i	$0.508016\pi$
$762$	3.49188e35	0.330082
$763$	−8.95354e34	−0.0832603
$764$	−1.48117e35	−0.135499
$765$	0	0
$766$	−9.95410e35	−0.881337
$767$	1.39971e36	1.21926
$768$	4.73798e34	0.0406049
$769$	9.50588e35	0.801517	0.400759	−	0.916184i	$-0.368747\pi$
$769$	9.50588e35	0.801517	0.400759	+	0.916184i	$0.368747\pi$
$770$	0	0
$771$	−1.13790e36	−0.928807
$772$	8.15440e35	0.654901
$773$	−1.18680e36	−0.937852	−0.468926	−	0.883238i	$-0.655359\pi$
$773$	−1.18680e36	−0.937852	−0.468926	+	0.883238i	$0.655359\pi$
$774$	−6.26948e35	−0.487494
$775$	0	0
$776$	1.49584e35	0.112619
$777$	4.67986e35	0.346713
$778$	8.13403e35	0.593008
$779$	5.89029e35	0.422589
$780$	0	0
$781$	−3.36144e35	−0.233554
$782$	−1.19880e35	−0.0819717
$783$	−1.11400e36	−0.749655
$784$	−3.17863e35	−0.210518
$785$	0	0
$786$	−1.31162e36	−0.841443
$787$	9.20091e35	0.580961	0.290480	−	0.956881i	$-0.406185\pi$
$787$	9.20091e35	0.580961	0.290480	+	0.956881i	$0.406185\pi$
$788$	−1.35996e36	−0.845179
$789$	1.29459e36	0.791898
$790$	0	0
$791$	−1.09696e36	−0.650105
$792$	−8.81158e34	−0.0514031
$793$	1.81006e36	1.03939
$794$	−3.80257e35	−0.214942
$795$	0	0
$796$	3.68680e35	0.201946
$797$	−4.72101e35	−0.254569	−0.127285	−	0.991866i	$-0.540626\pi$
$797$	−4.72101e35	−0.254569	−0.127285	+	0.991866i	$0.540626\pi$
$798$	2.89088e35	0.153459
$799$	7.75463e34	0.0405253
$800$	0	0
$801$	1.62887e36	0.825047
$802$	1.99875e36	0.996732
$803$	−5.57508e34	−0.0273720
$804$	1.18194e36	0.571339
$805$	0	0
$806$	8.86152e34	0.0415260
$807$	1.70757e36	0.787880
$808$	−6.52750e34	−0.0296555
$809$	−3.41733e36	−1.52873	−0.764364	−	0.644785i	$-0.776947\pi$
$809$	−3.41733e36	−1.52873	−0.764364	+	0.644785i	$0.776947\pi$
$810$	0	0
$811$	−2.85674e36	−1.23911	−0.619555	−	0.784953i	$-0.712687\pi$
$811$	−2.85674e36	−1.23911	−0.619555	+	0.784953i	$0.712687\pi$
$812$	3.40196e35	0.145304
$813$	2.34339e36	0.985627
$814$	5.76767e35	0.238889
$815$	0	0
$816$	5.31011e35	0.213293
$817$	2.53498e36	1.00276
$818$	1.24996e36	0.486946
$819$	−1.08290e36	−0.415469
$820$	0	0
$821$	−6.54545e35	−0.243585	−0.121792	−	0.992556i	$-0.538864\pi$
$821$	−6.54545e35	−0.243585	−0.121792	+	0.992556i	$0.538864\pi$
$822$	−7.08231e35	−0.259584
$823$	−1.62716e36	−0.587399	−0.293700	−	0.955898i	$-0.594887\pi$
$823$	−1.62716e36	−0.587399	−0.293700	+	0.955898i	$0.594887\pi$
$824$	1.08748e36	0.386662
$825$	0	0
$826$	−5.49059e35	−0.189395
$827$	−2.75985e36	−0.937707	−0.468853	−	0.883276i	$-0.655333\pi$
$827$	−2.75985e36	−0.937707	−0.468853	+	0.883276i	$0.655333\pi$
$828$	−7.62178e34	−0.0255081
$829$	−4.58088e36	−1.51014	−0.755070	−	0.655644i	$-0.772397\pi$
$829$	−4.58088e36	−1.51014	−0.755070	+	0.655644i	$0.772397\pi$
$830$	0	0
$831$	2.78419e36	0.890606
$832$	7.17620e35	0.226127
$833$	−3.56246e36	−1.10583
$834$	−1.41847e36	−0.433755
$835$	0	0
$836$	3.56285e35	0.105735
$837$	1.13826e35	0.0332794
$838$	−4.63852e36	−1.33607
$839$	5.08460e36	1.44289	0.721444	−	0.692473i	$-0.243479\pi$
$839$	5.08460e36	1.44289	0.721444	+	0.692473i	$0.243479\pi$
$840$	0	0
$841$	−1.68900e36	−0.465242
$842$	−4.93648e36	−1.33973
$843$	8.38586e35	0.224235
$844$	1.96222e36	0.516971
$845$	0	0
$846$	4.93025e34	0.0126107
$847$	−1.47699e36	−0.372250
$848$	1.94678e35	0.0483468
$849$	3.25905e36	0.797526
$850$	0	0
$851$	4.98888e35	0.118545
$852$	1.28790e36	0.301570
$853$	−1.45784e36	−0.336394	−0.168197	−	0.985753i	$-0.553794\pi$
$853$	−1.45784e36	−0.336394	−0.168197	+	0.985753i	$0.553794\pi$
$854$	−7.10026e35	−0.161455
$855$	0	0
$856$	−3.82821e35	−0.0845422
$857$	−4.83711e36	−1.05275	−0.526375	−	0.850252i	$-0.676449\pi$
$857$	−4.83711e36	−1.05275	−0.526375	+	0.850252i	$0.676449\pi$
$858$	9.74732e35	0.209071
$859$	−7.94888e36	−1.68032	−0.840159	−	0.542341i	$-0.817538\pi$
$859$	−7.94888e36	−1.68032	−0.840159	+	0.542341i	$0.817538\pi$
$860$	0	0
$861$	−6.32127e35	−0.129797
$862$	−6.49239e36	−1.31391
$863$	6.70455e36	1.33732	0.668659	−	0.743569i	$-0.266869\pi$
$863$	6.70455e36	1.33732	0.668659	+	0.743569i	$0.266869\pi$
$864$	9.21785e35	0.181221
$865$	0	0
$866$	−1.07327e36	−0.204990
$867$	2.50038e36	0.470724
$868$	−3.47607e34	−0.00645047
$869$	6.40402e35	0.117140
$870$	0	0
$871$	1.79017e37	3.18177
$872$	4.22785e35	0.0740736
$873$	1.06586e36	0.184087
$874$	3.08177e35	0.0524695
$875$	0	0
$876$	2.13604e35	0.0353433
$877$	1.44057e36	0.234984	0.117492	−	0.993074i	$-0.462515\pi$
$877$	1.44057e36	0.234984	0.117492	+	0.993074i	$0.462515\pi$
$878$	−2.46271e36	−0.396034
$879$	−6.78009e35	−0.107492
$880$	0	0
$881$	2.54210e36	0.391736	0.195868	−	0.980630i	$-0.437248\pi$
$881$	2.54210e36	0.391736	0.195868	+	0.980630i	$0.437248\pi$
$882$	−2.26495e36	−0.344113
$883$	5.66424e36	0.848463	0.424232	−	0.905554i	$-0.360544\pi$
$883$	5.66424e36	0.848463	0.424232	+	0.905554i	$0.360544\pi$
$884$	8.04274e36	1.18782
$885$	0	0
$886$	4.48006e36	0.643224
$887$	−5.48781e36	−0.776879	−0.388440	−	0.921474i	$-0.626986\pi$
$887$	−5.48781e36	−0.776879	−0.388440	+	0.921474i	$0.626986\pi$
$888$	−2.20983e36	−0.308458
$889$	−2.07463e36	−0.285541
$890$	0	0
$891$	1.65606e35	0.0221618
$892$	−3.04601e36	−0.401949
$893$	−1.99348e35	−0.0259399
$894$	4.01601e36	0.515319
$895$	0	0
$896$	−2.81498e35	−0.0351257
$897$	8.43117e35	0.103749
$898$	3.06317e36	0.371721
$899$	−1.98366e35	−0.0237395
$900$	0	0
$901$	2.18185e36	0.253960
$902$	−7.79062e35	−0.0894314
$903$	−2.72046e36	−0.307997
$904$	5.17981e36	0.578374
$905$	0	0
$906$	−2.14028e36	−0.232471
$907$	−1.51562e36	−0.162367	−0.0811836	−	0.996699i	$-0.525870\pi$
$907$	−1.51562e36	−0.162367	−0.0811836	+	0.996699i	$0.525870\pi$
$908$	−4.73583e36	−0.500406
$909$	−4.65120e35	−0.0484749
$910$	0	0
$911$	1.29981e37	1.31796	0.658978	−	0.752162i	$-0.270989\pi$
$911$	1.29981e37	1.31796	0.658978	+	0.752162i	$0.270989\pi$
$912$	−1.36507e36	−0.136527
$913$	−1.23558e36	−0.121895
$914$	1.82300e36	0.177402
$915$	0	0
$916$	−1.07368e36	−0.101667
$917$	7.79269e36	0.727899
$918$	1.03309e37	0.951931
$919$	1.24307e37	1.12993	0.564965	−	0.825115i	$-0.308890\pi$
$919$	1.24307e37	1.12993	0.564965	+	0.825115i	$0.308890\pi$
$920$	0	0
$921$	1.04363e37	0.923212
$922$	−1.23638e37	−1.07898
$923$	1.95067e37	1.67943
$924$	−3.82354e35	−0.0324762
$925$	0	0
$926$	−1.39893e37	−1.15653
$927$	7.74889e36	0.632037
$928$	−1.60640e36	−0.129272
$929$	−3.66569e36	−0.291044	−0.145522	−	0.989355i	$-0.546486\pi$
$929$	−3.66569e36	−0.291044	−0.145522	+	0.989355i	$0.546486\pi$
$930$	0	0
$931$	9.15801e36	0.707832
$932$	8.54773e36	0.651856
$933$	1.09976e37	0.827515
$934$	−1.86850e37	−1.38725
$935$	0	0
$936$	5.11343e36	0.369628
$937$	2.02379e37	1.44351	0.721756	−	0.692147i	$-0.243335\pi$
$937$	2.02379e37	1.44351	0.721756	+	0.692147i	$0.243335\pi$
$938$	−7.02224e36	−0.494242
$939$	−3.12288e36	−0.216888
$940$	0	0
$941$	1.25574e36	0.0849241	0.0424621	−	0.999098i	$-0.486480\pi$
$941$	1.25574e36	0.0849241	0.0424621	+	0.999098i	$0.486480\pi$
$942$	−1.25284e37	−0.836104
$943$	−6.73867e35	−0.0443791
$944$	2.59265e36	0.168498
$945$	0	0
$946$	−3.35282e36	−0.212212
$947$	6.83841e36	0.427150	0.213575	−	0.976927i	$-0.431489\pi$
$947$	6.83841e36	0.427150	0.213575	+	0.976927i	$0.431489\pi$
$948$	−2.45364e36	−0.151254
$949$	3.23527e36	0.196826
$950$	0	0
$951$	−6.10847e36	−0.361973
$952$	−3.15489e36	−0.184511
$953$	1.56146e37	0.901301	0.450650	−	0.892701i	$-0.351192\pi$
$953$	1.56146e37	0.901301	0.450650	+	0.892701i	$0.351192\pi$
$954$	1.38718e36	0.0790277
$955$	0	0
$956$	−4.67639e36	−0.259530
$957$	−2.18195e36	−0.119521
$958$	2.39936e37	1.29726
$959$	4.20781e36	0.224555
$960$	0	0
$961$	−1.92125e37	−0.998946
$962$	−3.34703e37	−1.71779
$963$	−2.72781e36	−0.138193
$964$	1.95435e37	0.977326
$965$	0	0
$966$	−3.30726e35	−0.0161159
$967$	2.05955e37	0.990699	0.495349	−	0.868694i	$-0.335040\pi$
$967$	2.05955e37	0.990699	0.495349	+	0.868694i	$0.335040\pi$
$968$	6.97432e36	0.331177
$969$	−1.52990e37	−0.717162
$970$	0	0
$971$	−1.82125e37	−0.832012	−0.416006	−	0.909362i	$-0.636570\pi$
$971$	−1.82125e37	−0.832012	−0.416006	+	0.909362i	$0.636570\pi$
$972$	1.07308e37	0.483954
$973$	8.42755e36	0.375224
$974$	1.77438e36	0.0779938
$975$	0	0
$976$	3.35273e36	0.143640
$977$	−3.37630e37	−1.42810	−0.714051	−	0.700094i	$-0.753141\pi$
$977$	−3.37630e37	−1.42810	−0.714051	+	0.700094i	$0.753141\pi$
$978$	−2.18243e37	−0.911392
$979$	8.71091e36	0.359153
$980$	0	0
$981$	3.01257e36	0.121081
$982$	1.37964e37	0.547485
$983$	−4.70453e37	−1.84331	−0.921653	−	0.388014i	$-0.873161\pi$
$983$	−4.70453e37	−1.84331	−0.921653	+	0.388014i	$0.873161\pi$
$984$	2.98490e36	0.115476
$985$	0	0
$986$	−1.80038e37	−0.679050
$987$	2.13934e35	0.00796739
$988$	−2.06755e37	−0.760316
$989$	−2.90010e36	−0.105307
$990$	0	0
$991$	6.93324e35	0.0245480	0.0122740	−	0.999925i	$-0.496093\pi$
$991$	6.93324e35	0.0245480	0.0122740	+	0.999925i	$0.496093\pi$
$992$	1.64139e35	0.00573875
$993$	−2.81299e37	−0.971186
$994$	−7.65181e36	−0.260876
$995$	0	0
$996$	4.73401e36	0.157394
$997$	2.90656e37	0.954310	0.477155	−	0.878819i	$-0.341668\pi$
$997$	2.90656e37	0.954310	0.477155	+	0.878819i	$0.341668\pi$
$998$	−1.17534e37	−0.381093
$999$	−4.29926e37	−1.37666

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.a.i.1.4	✓	5
5.2	odd	4		50.26.b.h.49.2		10
5.3	odd	4		50.26.b.h.49.9		10
5.4	even	2		50.26.a.j.1.2	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.26.a.i.1.4	✓	5	1.1	even	1	trivial
50.26.a.j.1.2	yes	5	5.4	even	2
50.26.b.h.49.2		10	5.2	odd	4
50.26.b.h.49.9		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)

\(f(q)\)	\(=\)	\(q-4096.00 q^{2} +598018. q^{3} +1.67772e7 q^{4} -2.44948e9 q^{6} +1.45531e10 q^{7} -6.87195e10 q^{8} -4.89664e11 q^{9} -2.61864e12 q^{11} +1.00331e13 q^{12} +1.51962e14 q^{13} -5.96094e13 q^{14} +2.81475e14 q^{16} +3.15464e15 q^{17} +2.00566e15 q^{18} -8.10963e15 q^{19} +8.70300e15 q^{21} +1.07260e16 q^{22} +9.27767e15 q^{23} -4.10955e16 q^{24} -6.22436e17 q^{26} -7.99521e17 q^{27} +2.44160e17 q^{28} +1.39333e18 q^{29} -1.42368e17 q^{31} -1.15292e18 q^{32} -1.56599e18 q^{33} -1.29214e19 q^{34} -8.21519e18 q^{36} +5.37730e19 q^{37} +3.32170e19 q^{38} +9.08759e19 q^{39} -7.26333e19 q^{41} -3.56475e19 q^{42} -3.12589e20 q^{43} -4.39335e19 q^{44} -3.80013e19 q^{46} +2.45817e19 q^{47} +1.68327e20 q^{48} -1.12928e21 q^{49} +1.88653e21 q^{51} +2.54950e21 q^{52} +6.91634e20 q^{53} +3.27484e21 q^{54} -1.00008e21 q^{56} -4.84970e21 q^{57} -5.70708e21 q^{58} +9.21095e21 q^{59} +1.19113e22 q^{61} +5.83140e20 q^{62} -7.12611e21 q^{63} +4.72237e21 q^{64} +6.41431e21 q^{66} +1.17804e23 q^{67} +5.29260e22 q^{68} +5.54821e21 q^{69} +1.28366e23 q^{71} +3.36494e22 q^{72} +2.12900e22 q^{73} -2.20254e23 q^{74} -1.36057e23 q^{76} -3.81093e22 q^{77} -3.72228e23 q^{78} -2.44555e23 q^{79} -6.32412e22 q^{81} +2.97506e23 q^{82} +4.71841e23 q^{83} +1.46012e23 q^{84} +1.28037e24 q^{86} +8.33235e23 q^{87} +1.79952e23 q^{88} -3.32650e24 q^{89} +2.21152e24 q^{91} +1.55653e23 q^{92} -8.51387e22 q^{93} -1.00687e23 q^{94} -6.89467e23 q^{96} -2.17673e24 q^{97} +4.62552e24 q^{98} +1.28225e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20480 q^{2} - 723995 q^{3} + 83886080 q^{4} + 2965483520 q^{6} - 49218886190 q^{7} - 343597383680 q^{8} + 975375361390 q^{9} - 8837033983815 q^{11} - 12146620497920 q^{12} - 67609989586220 q^{13}+ \cdots - 23\!\cdots\!70 q^{99}+O(q^{100}) \) 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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