LMFDB - Embedded newform 25.38.a.f.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,38,Mod(1,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 38, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 38);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 38 $
Character orbit:	$[\chi]$	$=$	25.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:	$216.785095312$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 481549068639 x^{16} + \cdots - 94\!\cdots\!56 $ x^18 - 481549068639x^16 + 93985965632669777852076x^14 - 9628368566809387473030890752468224x^12 + 560141172354070767376864400274123366345670656x^10 - 18546934724816320070044693242782989845297920321809022976x^8 + 324939831814575640345464640472992367787298129881716003189098020864x^6 - 2370422361889416509431397077280114217555992479156444172822242462880734642176x^4 + 1228913418955626210538188759121588894935204618869926387774623804097150250958584807424x^2 - 94567986416239745059180217502439958544533873348778114712636267676791575291958859488355680256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	multiple of $ 2^{103}\cdot 3^{40}\cdot 5^{86}\cdot 7^{4}\cdot 11\cdot 29 $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$348173.$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+696347. q^{2} +1.07237e9 q^{3} +3.47460e11 q^{4} +7.46739e14 q^{6} -3.76344e15 q^{7} +1.46247e17 q^{8} +6.99686e17 q^{9} +O(q^{10})$	\(q+696347. q^{2} +1.07237e9 q^{3} +3.47460e11 q^{4} +7.46739e14 q^{6} -3.76344e15 q^{7} +1.46247e17 q^{8} +6.99686e17 q^{9} +2.53166e19 q^{11} +3.72604e20 q^{12} +6.57721e19 q^{13} -2.62066e21 q^{14} +5.40844e22 q^{16} -7.51516e21 q^{17} +4.87224e23 q^{18} -1.78356e23 q^{19} -4.03579e24 q^{21} +1.76291e25 q^{22} +2.64970e25 q^{23} +1.56831e26 q^{24} +4.58002e25 q^{26} +2.67450e26 q^{27} -1.30764e27 q^{28} +8.23288e26 q^{29} -9.92016e26 q^{31} +1.75614e28 q^{32} +2.71487e28 q^{33} -5.23315e27 q^{34} +2.43113e29 q^{36} -4.09638e28 q^{37} -1.24198e29 q^{38} +7.05318e28 q^{39} +8.49376e28 q^{41} -2.81031e30 q^{42} -2.56457e30 q^{43} +8.79650e30 q^{44} +1.84511e31 q^{46} -4.27002e30 q^{47} +5.79983e31 q^{48} -4.39865e30 q^{49} -8.05900e30 q^{51} +2.28532e31 q^{52} -8.57703e31 q^{53} +1.86238e32 q^{54} -5.50393e32 q^{56} -1.91263e32 q^{57} +5.73294e32 q^{58} +1.01436e33 q^{59} -9.47537e30 q^{61} -6.90787e32 q^{62} -2.63322e33 q^{63} +4.79551e33 q^{64} +1.89049e34 q^{66} +6.38156e33 q^{67} -2.61121e33 q^{68} +2.84145e34 q^{69} +7.93378e33 q^{71} +1.02327e35 q^{72} +4.03964e34 q^{73} -2.85250e34 q^{74} -6.19716e34 q^{76} -9.52775e34 q^{77} +4.91146e34 q^{78} -2.28886e33 q^{79} -2.82526e34 q^{81} +5.91460e34 q^{82} -2.53820e35 q^{83} -1.40227e36 q^{84} -1.78583e36 q^{86} +8.82866e35 q^{87} +3.70249e36 q^{88} +5.47125e35 q^{89} -2.47529e35 q^{91} +9.20664e36 q^{92} -1.06380e36 q^{93} -2.97342e36 q^{94} +1.88322e37 q^{96} -8.40088e36 q^{97} -3.06298e36 q^{98} +1.77137e37 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 1378491386616 q^{4} + 235050070586136 q^{6} + 26\!\cdots\!74 q^{9}+O(q^{10}) $ 18 * q + 1378491386616 * q^4 + 235050070586136 * q^6 + 2687284960012241874 * q^9	$ 18 q + 1378491386616 q^{4} + 235050070586136 q^{6} + 26\!\cdots\!74 q^{9}+ \cdots + 56\!\cdots\!28 q^{99}+O(q^{100}) $ 18 * q + 1378491386616 * q^4 + 235050070586136 * q^6 + 2687284960012241874 * q^9 + 33986627223034798296 * q^11 + 1891478635206760615032 * q^14 + 156966361562724410096928 * q^16 + 302760323265144477867480 * q^19 - 4075600057180968977719704 * q^21 + 149013794188298144591103840 * q^24 + 740755125071253494506988496 * q^26 + 4979198281142680608411084420 * q^29 - 6151542350452781958579360384 * q^31 - 4353870657762813132282760128 * q^34 + 106785265488844195864724376888 * q^36 - 862865339998466438248367480112 * q^39 - 855196121794787398902389240124 * q^41 + 13806087517221679193940877688352 * q^44 + 21104472252831571358912888976456 * q^46 + 70801883273781655273950124330026 * q^49 - 23706017526907962630925223712384 * q^51 + 523190901027760133510234826308880 * q^54 + 600728793662143364055878849971680 * q^56 + 3947688162499809731531683814232840 * q^59 + 1757475029942100801736311637166796 * q^61 + 35293446897899611856499858227515776 * q^64 + 32483717310049996392729278134533792 * q^66 + 29536156423306266276087371479398168 * q^69 - 15852144098617191882453852538452144 * q^71 - 35174192734582932814586482689499248 * q^74 - 8033980639764558547374281250927840 * q^76 + 81628804120848018323973892688639520 * q^79 - 51387579768336601107744192991686822 * q^81 - 3799290048936464645757894225695060448 * q^84 - 3995229770967016576777180478600492424 * q^86 - 5941001429647591369362270403151043540 * q^89 + 2681006692210129770276250954718747856 * q^91 - 2447341171808746326507906787285919208 * q^94 - 2375166431920457136532866502177021824 * q^96 + 56285732505135601101448147731191891928 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	696347.	1.87832	0.939162	−	0.343474i	$-0.111604\pi$
$2$	696347.	1.87832	0.939162	+	0.343474i	$0.111604\pi$
$3$	1.07237e9	1.59809	0.799043	−	0.601274i	$-0.205340\pi$
$3$	1.07237e9	1.59809	0.799043	+	0.601274i	$0.205340\pi$
$4$	3.47460e11	2.52810
$5$	0	0
$5$	0	0
$6$	7.46739e14	3.00172
$7$	−3.76344e15	−0.873516	−0.436758	−	0.899579i	$-0.643873\pi$
$7$	−3.76344e15	−0.873516	−0.436758	+	0.899579i	$0.643873\pi$
$8$	1.46247e17	2.87027
$9$	6.99686e17	1.55388
$10$	0	0
$11$	2.53166e19	1.37291	0.686453	−	0.727174i	$-0.259167\pi$
$11$	2.53166e19	1.37291	0.686453	+	0.727174i	$0.259167\pi$
$12$	3.72604e20	4.04012
$13$	6.57721e19	0.162214	0.0811072	−	0.996705i	$-0.474154\pi$
$13$	6.57721e19	0.162214	0.0811072	+	0.996705i	$0.474154\pi$
$14$	−2.62066e21	−1.64075
$15$	0	0
$16$	5.40844e22	2.86320
$17$	−7.51516e21	−0.129608	−0.0648042	−	0.997898i	$-0.520642\pi$
$17$	−7.51516e21	−0.129608	−0.0648042	+	0.997898i	$0.520642\pi$
$18$	4.87224e23	2.91869
$19$	−1.78356e23	−0.392959	−0.196479	−	0.980508i	$-0.562951\pi$
$19$	−1.78356e23	−0.392959	−0.196479	+	0.980508i	$0.562951\pi$
$20$	0	0
$21$	−4.03579e24	−1.39595
$22$	1.76291e25	2.57876
$23$	2.64970e25	1.70307	0.851533	−	0.524301i	$-0.175673\pi$
$23$	2.64970e25	1.70307	0.851533	+	0.524301i	$0.175673\pi$
$24$	1.56831e26	4.58694
$25$	0	0
$26$	4.58002e25	0.304691
$27$	2.67450e26	0.885143
$28$	−1.30764e27	−2.20834
$29$	8.23288e26	0.726421	0.363211	−	0.931707i	$-0.381681\pi$
$29$	8.23288e26	0.726421	0.363211	+	0.931707i	$0.381681\pi$
$30$	0	0
$31$	−9.92016e26	−0.254875	−0.127438	−	0.991847i	$-0.540675\pi$
$31$	−9.92016e26	−0.254875	−0.127438	+	0.991847i	$0.540675\pi$
$32$	1.75614e28	2.50775
$33$	2.71487e28	2.19402
$34$	−5.23315e27	−0.243447
$35$	0	0
$36$	2.43113e29	3.92836
$37$	−4.09638e28	−0.398720	−0.199360	−	0.979926i	$-0.563886\pi$
$37$	−4.09638e28	−0.398720	−0.199360	+	0.979926i	$0.563886\pi$
$38$	−1.24198e29	−0.738104
$39$	7.05318e28	0.259233
$40$	0	0
$41$	8.49376e28	0.123765	0.0618826	−	0.998083i	$-0.480290\pi$
$41$	8.49376e28	0.123765	0.0618826	+	0.998083i	$0.480290\pi$
$42$	−2.81031e30	−2.62205
$43$	−2.56457e30	−1.54828	−0.774138	−	0.633016i	$-0.781817\pi$
$43$	−2.56457e30	−1.54828	−0.774138	+	0.633016i	$0.781817\pi$
$44$	8.79650e30	3.47085
$45$	0	0
$46$	1.84511e31	3.19891
$47$	−4.27002e30	−0.497302	−0.248651	−	0.968593i	$-0.579987\pi$
$47$	−4.27002e30	−0.497302	−0.248651	+	0.968593i	$0.579987\pi$
$48$	5.79983e31	4.57564
$49$	−4.39865e30	−0.236969
$50$	0	0
$51$	−8.05900e30	−0.207125
$52$	2.28532e31	0.410095
$53$	−8.57703e31	−1.08201	−0.541007	−	0.841018i	$-0.681957\pi$
$53$	−8.57703e31	−1.08201	−0.541007	+	0.841018i	$0.681957\pi$
$54$	1.86238e32	1.66259
$55$	0	0
$56$	−5.50393e32	−2.50723
$57$	−1.91263e32	−0.627981
$58$	5.73294e32	1.36446
$59$	1.01436e33	1.75967	0.879834	−	0.475282i	$-0.157654\pi$
$59$	1.01436e33	1.75967	0.879834	+	0.475282i	$0.157654\pi$
$60$	0	0
$61$	−9.47537e30	−0.00887145	−0.00443572	−	0.999990i	$-0.501412\pi$
$61$	−9.47537e30	−0.00887145	−0.00443572	+	0.999990i	$0.501412\pi$
$62$	−6.90787e32	−0.478738
$63$	−2.63322e33	−1.35734
$64$	4.79551e33	1.84717
$65$	0	0
$66$	1.89049e34	4.12108
$67$	6.38156e33	1.05328	0.526639	−	0.850089i	$-0.323452\pi$
$67$	6.38156e33	1.05328	0.526639	+	0.850089i	$0.323452\pi$
$68$	−2.61121e33	−0.327663
$69$	2.84145e34	2.72165
$70$	0	0
$71$	7.93378e33	0.447920	0.223960	−	0.974598i	$-0.428101\pi$
$71$	7.93378e33	0.447920	0.223960	+	0.974598i	$0.428101\pi$
$72$	1.02327e35	4.46005
$73$	4.03964e34	1.36417	0.682087	−	0.731271i	$-0.261073\pi$
$73$	4.03964e34	1.36417	0.682087	+	0.731271i	$0.261073\pi$
$74$	−2.85250e34	−0.748926
$75$	0	0
$76$	−6.19716e34	−0.993440
$77$	−9.52775e34	−1.19926
$78$	4.91146e34	0.486923
$79$	−2.28886e33	−0.0179274	−0.00896370	−	0.999960i	$-0.502853\pi$
$79$	−2.28886e33	−0.0179274	−0.00896370	+	0.999960i	$0.502853\pi$
$80$	0	0
$81$	−2.82526e34	−0.139343
$82$	5.91460e34	0.232471
$83$	−2.53820e35	−0.797225	−0.398613	−	0.917119i	$-0.630508\pi$
$83$	−2.53820e35	−0.797225	−0.398613	+	0.917119i	$0.630508\pi$
$84$	−1.40227e36	−3.52912
$85$	0	0
$86$	−1.78583e36	−2.90817
$87$	8.82866e35	1.16088
$88$	3.70249e36	3.94061
$89$	5.47125e35	0.472467	0.236233	−	0.971696i	$-0.424087\pi$
$89$	5.47125e35	0.472467	0.236233	+	0.971696i	$0.424087\pi$
$90$	0	0
$91$	−2.47529e35	−0.141697
$92$	9.20664e36	4.30553
$93$	−1.06380e36	−0.407312
$94$	−2.97342e36	−0.934094
$95$	0	0
$96$	1.88322e37	4.00760
$97$	−8.40088e36	−1.47587	−0.737934	−	0.674872i	$-0.764199\pi$
$97$	−8.40088e36	−1.47587	−0.737934	+	0.674872i	$0.764199\pi$
$98$	−3.06298e36	−0.445105
$99$	1.77137e37	2.13333
$100$	0	0
$101$	−3.87883e36	−0.322668	−0.161334	−	0.986900i	$-0.551580\pi$
$101$	−3.87883e36	−0.322668	−0.161334	+	0.986900i	$0.551580\pi$
$102$	−5.61186e36	−0.389048
$103$	2.20919e36	0.127863	0.0639313	−	0.997954i	$-0.479636\pi$
$103$	2.20919e36	0.127863	0.0639313	+	0.997954i	$0.479636\pi$
$104$	9.61900e36	0.465600
$105$	0	0
$106$	−5.97259e37	−2.03238
$107$	5.74887e37	1.64430	0.822152	−	0.569268i	$-0.192773\pi$
$107$	5.74887e37	1.64430	0.822152	+	0.569268i	$0.192773\pi$
$108$	9.29282e37	2.23773
$109$	5.73062e37	1.16362	0.581811	−	0.813324i	$-0.302344\pi$
$109$	5.73062e37	1.16362	0.581811	+	0.813324i	$0.302344\pi$
$110$	0	0
$111$	−4.39282e37	−0.637189
$112$	−2.03543e38	−2.50105
$113$	2.04481e37	0.213158	0.106579	−	0.994304i	$-0.466010\pi$
$113$	2.04481e37	0.213158	0.106579	+	0.994304i	$0.466010\pi$
$114$	−1.33186e38	−1.17955
$115$	0	0
$116$	2.86059e38	1.83647
$117$	4.60198e37	0.252061
$118$	7.06347e38	3.30523
$119$	2.82828e37	0.113215
$120$	0	0
$121$	3.00891e38	0.884870
$122$	−6.59815e36	−0.0166635
$123$	9.10843e37	0.197787
$124$	−3.44686e38	−0.644351
$125$	0	0
$126$	−1.83364e39	−2.54952
$127$	−7.13876e38	−0.857539	−0.428770	−	0.903414i	$-0.641053\pi$
$127$	−7.13876e38	−0.857539	−0.428770	+	0.903414i	$0.641053\pi$
$128$	9.25723e38	0.961826
$129$	−2.75016e39	−2.47428
$130$	0	0
$131$	1.46420e39	0.991017	0.495509	−	0.868603i	$-0.334982\pi$
$131$	1.46420e39	0.991017	0.495509	+	0.868603i	$0.334982\pi$
$132$	9.43307e39	5.54671
$133$	6.71233e38	0.343256
$134$	4.44378e39	1.97840
$135$	0	0
$136$	−1.09907e39	−0.372011
$137$	−1.80697e39	−0.534096	−0.267048	−	0.963683i	$-0.586048\pi$
$137$	−1.80697e39	−0.534096	−0.267048	+	0.963683i	$0.586048\pi$
$138$	1.97863e40	5.11213
$139$	−5.94115e39	−1.34306	−0.671532	−	0.740975i	$-0.734364\pi$
$139$	−5.94115e39	−1.34306	−0.671532	+	0.740975i	$0.734364\pi$
$140$	0	0
$141$	−4.57903e39	−0.794731
$142$	5.52466e39	0.841339
$143$	1.66513e39	0.222705
$144$	3.78421e40	4.44906
$145$	0	0
$146$	2.81299e40	2.56236
$147$	−4.71696e39	−0.378697
$148$	−1.42333e40	−1.00801
$149$	2.61168e39	0.163295	0.0816477	−	0.996661i	$-0.473982\pi$
$149$	2.61168e39	0.163295	0.0816477	+	0.996661i	$0.473982\pi$
$150$	0	0
$151$	−1.02439e40	−0.500487	−0.250244	−	0.968183i	$-0.580511\pi$
$151$	−1.02439e40	−0.500487	−0.250244	+	0.968183i	$0.580511\pi$
$152$	−2.60841e40	−1.12790
$153$	−5.25825e39	−0.201395
$154$	−6.63462e40	−2.25259
$155$	0	0
$156$	2.45070e40	0.655367
$157$	4.76347e40	1.13183	0.565913	−	0.824465i	$-0.308524\pi$
$157$	4.76347e40	1.13183	0.565913	+	0.824465i	$0.308524\pi$
$158$	−1.59384e39	−0.0336735
$159$	−9.19772e40	−1.72915
$160$	0	0
$161$	−9.97198e40	−1.48766
$162$	−1.96736e40	−0.261732
$163$	−1.39467e41	−1.65577	−0.827884	−	0.560899i	$-0.810456\pi$
$163$	−1.39467e41	−1.65577	−0.827884	+	0.560899i	$0.810456\pi$
$164$	2.95124e40	0.312891
$165$	0	0
$166$	−1.76747e41	−1.49745
$167$	−2.48524e41	−1.88414	−0.942072	−	0.335409i	$-0.891125\pi$
$167$	−2.48524e41	−1.88414	−0.942072	+	0.335409i	$0.891125\pi$
$168$	−5.90223e41	−4.00677
$169$	−1.60075e41	−0.973686
$170$	0	0
$171$	−1.24793e41	−0.610609
$172$	−8.91086e41	−3.91420
$173$	−7.82431e39	−0.0308740	−0.0154370	−	0.999881i	$-0.504914\pi$
$173$	−7.82431e39	−0.0308740	−0.0154370	+	0.999881i	$0.504914\pi$
$174$	6.14781e41	2.18052
$175$	0	0
$176$	1.36923e42	3.93091
$177$	1.08777e42	2.81210
$178$	3.80988e41	0.887446
$179$	−7.16818e41	−1.50532	−0.752658	−	0.658412i	$-0.771229\pi$
$179$	−7.16818e41	−1.50532	−0.752658	+	0.658412i	$0.771229\pi$
$180$	0	0
$181$	4.98187e41	0.851802	0.425901	−	0.904770i	$-0.359957\pi$
$181$	4.98187e41	0.851802	0.425901	+	0.904770i	$0.359957\pi$
$182$	−1.72366e41	−0.266153
$183$	−1.01611e40	−0.0141773
$184$	3.87512e42	4.88827
$185$	0	0
$186$	−7.40777e41	−0.765065
$187$	−1.90258e41	−0.177940
$188$	−1.48366e42	−1.25723
$189$	−1.00653e42	−0.773187
$190$	0	0
$191$	−1.76598e42	−1.11652	−0.558262	−	0.829664i	$-0.688532\pi$
$191$	−1.76598e42	−1.11652	−0.558262	+	0.829664i	$0.688532\pi$
$192$	5.14255e42	2.95193
$193$	−1.50945e42	−0.787063	−0.393532	−	0.919311i	$-0.628747\pi$
$193$	−1.50945e42	−0.787063	−0.393532	+	0.919311i	$0.628747\pi$
$194$	−5.84993e42	−2.77216
$195$	0	0
$196$	−1.52835e42	−0.599082
$197$	−2.10157e42	−0.749754	−0.374877	−	0.927075i	$-0.622315\pi$
$197$	−2.10157e42	−0.749754	−0.374877	+	0.927075i	$0.622315\pi$
$198$	1.23349e43	4.00708
$199$	−1.51830e42	−0.449341	−0.224670	−	0.974435i	$-0.572131\pi$
$199$	−1.51830e42	−0.449341	−0.224670	+	0.974435i	$0.572131\pi$
$200$	0	0
$201$	6.84337e42	1.68323
$202$	−2.70101e42	−0.606075
$203$	−3.09839e42	−0.634541
$204$	−2.80018e42	−0.523634
$205$	0	0
$206$	1.53836e42	0.240167
$207$	1.85396e43	2.64636
$208$	3.55724e42	0.464453
$209$	−4.51537e42	−0.539495
$210$	0	0
$211$	1.22287e42	0.122505	0.0612525	−	0.998122i	$-0.480491\pi$
$211$	1.22287e42	0.122505	0.0612525	+	0.998122i	$0.480491\pi$
$212$	−2.98017e43	−2.73545
$213$	8.50792e42	0.715815
$214$	4.00320e43	3.08854
$215$	0	0
$216$	3.91139e43	2.54060
$217$	3.73339e42	0.222638
$218$	3.99050e43	2.18566
$219$	4.33197e43	2.18007
$220$	0	0
$221$	−4.94287e41	−0.0210243
$222$	−3.05893e43	−1.19685
$223$	3.82214e42	0.137615	0.0688076	−	0.997630i	$-0.478081\pi$
$223$	3.82214e42	0.137615	0.0688076	+	0.997630i	$0.478081\pi$
$224$	−6.60912e43	−2.19056
$225$	0	0
$226$	1.42390e43	0.400380
$227$	−1.26313e43	−0.327317	−0.163659	−	0.986517i	$-0.552330\pi$
$227$	−1.26313e43	−0.327317	−0.163659	+	0.986517i	$0.552330\pi$
$228$	−6.64563e43	−1.58760
$229$	1.83892e43	0.405142	0.202571	−	0.979268i	$-0.435070\pi$
$229$	1.83892e43	0.405142	0.202571	+	0.979268i	$0.435070\pi$
$230$	0	0
$231$	−1.02172e44	−1.91651
$232$	1.20404e44	2.08503
$233$	−8.49920e43	−1.35923	−0.679616	−	0.733568i	$-0.737853\pi$
$233$	−8.49920e43	−1.35923	−0.679616	+	0.733568i	$0.737853\pi$
$234$	3.20457e43	0.473453
$235$	0	0
$236$	3.52450e44	4.44862
$237$	−2.45449e42	−0.0286495
$238$	1.96947e43	0.212655
$239$	1.19777e44	1.19677	0.598386	−	0.801208i	$-0.295809\pi$
$239$	1.19777e44	1.19677	0.598386	+	0.801208i	$0.295809\pi$
$240$	0	0
$241$	5.80986e43	0.497566	0.248783	−	0.968559i	$-0.419969\pi$
$241$	5.80986e43	0.497566	0.248783	+	0.968559i	$0.419969\pi$
$242$	2.09524e44	1.66207
$243$	−1.50726e44	−1.10783
$244$	−3.29231e42	−0.0224279
$245$	0	0
$246$	6.34262e43	0.371509
$247$	−1.17309e43	−0.0637436
$248$	−1.45080e44	−0.731561
$249$	−2.72188e44	−1.27403
$250$	0	0
$251$	2.32079e44	0.936852	0.468426	−	0.883503i	$-0.344821\pi$
$251$	2.32079e44	0.936852	0.468426	+	0.883503i	$0.344821\pi$
$252$	−9.14940e44	−3.43149
$253$	6.70814e44	2.33815
$254$	−4.97105e44	−1.61074
$255$	0	0
$256$	−1.44664e43	−0.0405435
$257$	−4.93996e44	−1.28813	−0.644067	−	0.764969i	$-0.722754\pi$
$257$	−4.93996e44	−1.28813	−0.644067	+	0.764969i	$0.722754\pi$
$258$	−1.91507e45	−4.64750
$259$	1.54165e44	0.348289
$260$	0	0
$261$	5.76043e44	1.12877
$262$	1.01959e45	1.86145
$263$	3.82610e44	0.650990	0.325495	−	0.945544i	$-0.394469\pi$
$263$	3.82610e44	0.650990	0.325495	+	0.945544i	$0.394469\pi$
$264$	3.97042e45	6.29744
$265$	0	0
$266$	4.67411e44	0.644746
$267$	5.86718e44	0.755042
$268$	2.21734e45	2.66279
$269$	−9.36758e44	−1.05005	−0.525025	−	0.851087i	$-0.675944\pi$
$269$	−9.36758e44	−1.05005	−0.525025	+	0.851087i	$0.675944\pi$
$270$	0	0
$271$	−1.60550e45	−1.56920	−0.784601	−	0.620001i	$-0.787132\pi$
$271$	−1.60550e45	−1.56920	−0.784601	+	0.620001i	$0.787132\pi$
$272$	−4.06452e44	−0.371095
$273$	−2.65442e44	−0.226444
$274$	−1.25827e45	−1.00321
$275$	0	0
$276$	9.87289e45	6.88060
$277$	−1.74154e44	−0.113516	−0.0567580	−	0.998388i	$-0.518076\pi$
$277$	−1.74154e44	−0.113516	−0.0567580	+	0.998388i	$0.518076\pi$
$278$	−4.13710e45	−2.52271
$279$	−6.94100e44	−0.396045
$280$	0	0
$281$	−2.65793e45	−1.32885	−0.664425	−	0.747355i	$-0.731324\pi$
$281$	−2.65793e45	−1.32885	−0.664425	+	0.747355i	$0.731324\pi$
$282$	−3.18859e45	−1.49276
$283$	3.79920e45	1.66588	0.832940	−	0.553364i	$-0.186656\pi$
$283$	3.79920e45	1.66588	0.832940	+	0.553364i	$0.186656\pi$
$284$	2.75667e45	1.13239
$285$	0	0
$286$	1.15950e45	0.418313
$287$	−3.19658e44	−0.108111
$288$	1.22875e46	3.89673
$289$	−3.30562e45	−0.983202
$290$	0	0
$291$	−9.00882e45	−2.35856
$292$	1.40361e46	3.44877
$293$	4.32979e45	0.998657	0.499328	−	0.866413i	$-0.333580\pi$
$293$	4.32979e45	0.998657	0.499328	+	0.866413i	$0.333580\pi$
$294$	−3.28464e45	−0.711315
$295$	0	0
$296$	−5.99085e45	−1.14444
$297$	6.77093e45	1.21522
$298$	1.81863e45	0.306722
$299$	1.74276e45	0.276262
$300$	0	0
$301$	9.65161e45	1.35245
$302$	−7.13332e45	−0.940077
$303$	−4.15953e45	−0.515651
$304$	−9.64629e45	−1.12512
$305$	0	0
$306$	−3.66156e45	−0.378286
$307$	−6.14213e45	−0.597392	−0.298696	−	0.954348i	$-0.596552\pi$
$307$	−6.14213e45	−0.597392	−0.298696	+	0.954348i	$0.596552\pi$
$308$	−3.31051e46	−3.03184
$309$	2.36906e45	0.204335
$310$	0	0
$311$	7.80237e45	0.597254	0.298627	−	0.954370i	$-0.403471\pi$
$311$	7.80237e45	0.597254	0.298627	+	0.954370i	$0.403471\pi$
$312$	1.03151e46	0.744068
$313$	1.95443e46	1.32877	0.664384	−	0.747391i	$-0.268694\pi$
$313$	1.95443e46	1.32877	0.664384	+	0.747391i	$0.268694\pi$
$314$	3.31703e46	2.12594
$315$	0	0
$316$	−7.95286e44	−0.0453223
$317$	−1.71779e46	−0.923367	−0.461683	−	0.887045i	$-0.652754\pi$
$317$	−1.71779e46	−0.923367	−0.461683	+	0.887045i	$0.652754\pi$
$318$	−6.40480e46	−3.24791
$319$	2.08428e46	0.997308
$320$	0	0
$321$	6.16489e46	2.62774
$322$	−6.94396e46	−2.79430
$323$	1.34038e45	0.0509307
$324$	−9.81665e45	−0.352274
$325$	0	0
$326$	−9.71171e46	−3.11007
$327$	6.14533e46	1.85957
$328$	1.24219e46	0.355240
$329$	1.60700e46	0.434401
$330$	0	0
$331$	−2.03580e46	−0.491946	−0.245973	−	0.969277i	$-0.579108\pi$
$331$	−2.03580e46	−0.491946	−0.245973	+	0.969277i	$0.579108\pi$
$332$	−8.81922e46	−2.01547
$333$	−2.86618e46	−0.619562
$334$	−1.73059e47	−3.53904
$335$	0	0
$336$	−2.18273e47	−3.99690
$337$	2.93928e46	0.509435	0.254717	−	0.967016i	$-0.418018\pi$
$337$	2.93928e46	0.509435	0.254717	+	0.967016i	$0.418018\pi$
$338$	−1.11468e47	−1.82890
$339$	2.19279e46	0.340645
$340$	0	0
$341$	−2.51145e46	−0.349919
$342$	−8.68994e46	−1.14692
$343$	8.64114e46	1.08051
$344$	−3.75062e47	−4.44398
$345$	0	0
$346$	−5.44843e45	−0.0579914
$347$	−3.88555e46	−0.392064	−0.196032	−	0.980597i	$-0.562806\pi$
$347$	−3.88555e46	−0.392064	−0.196032	+	0.980597i	$0.562806\pi$
$348$	3.06760e47	2.93483
$349$	1.07951e47	0.979396	0.489698	−	0.871892i	$-0.337107\pi$
$349$	1.07951e47	0.979396	0.489698	+	0.871892i	$0.337107\pi$
$350$	0	0
$351$	1.75908e46	0.143583
$352$	4.44595e47	3.44290
$353$	5.27241e46	0.387416	0.193708	−	0.981059i	$-0.437949\pi$
$353$	5.27241e46	0.387416	0.193708	+	0.981059i	$0.437949\pi$
$354$	7.57463e47	5.28203
$355$	0	0
$356$	1.90104e47	1.19444
$357$	3.03296e46	0.180927
$358$	−4.99154e47	−2.82747
$359$	−3.08785e47	−1.66115	−0.830574	−	0.556908i	$-0.811988\pi$
$359$	−3.08785e47	−1.66115	−0.830574	+	0.556908i	$0.811988\pi$
$360$	0	0
$361$	−1.74197e47	−0.845584
$362$	3.46911e47	1.59996
$363$	3.22665e47	1.41410
$364$	−8.60065e46	−0.358225
$365$	0	0
$366$	−7.07563e45	−0.0266296
$367$	3.10224e47	1.11008	0.555038	−	0.831825i	$-0.312704\pi$
$367$	3.10224e47	1.11008	0.555038	+	0.831825i	$0.312704\pi$
$368$	1.43307e48	4.87622
$369$	5.94296e46	0.192316
$370$	0	0
$371$	3.22791e47	0.945158
$372$	−3.69629e47	−1.02973
$373$	−5.32911e46	−0.141267	−0.0706336	−	0.997502i	$-0.522502\pi$
$373$	−5.32911e46	−0.141267	−0.0706336	+	0.997502i	$0.522502\pi$
$374$	−1.32486e47	−0.334229
$375$	0	0
$376$	−6.24480e47	−1.42739
$377$	5.41493e46	0.117836
$378$	−7.00896e47	−1.45230
$379$	−3.49485e47	−0.689610	−0.344805	−	0.938674i	$-0.612055\pi$
$379$	−3.49485e47	−0.689610	−0.344805	+	0.938674i	$0.612055\pi$
$380$	0	0
$381$	−7.65537e47	−1.37042
$382$	−1.22973e48	−2.09720
$383$	1.32247e46	0.0214886	0.0107443	−	0.999942i	$-0.496580\pi$
$383$	1.32247e46	0.0214886	0.0107443	+	0.999942i	$0.496580\pi$
$384$	9.92714e47	1.53708
$385$	0	0
$386$	−1.05110e48	−1.47836
$387$	−1.79440e48	−2.40583
$388$	−2.91897e48	−3.73115
$389$	−7.66711e47	−0.934467	−0.467233	−	0.884134i	$-0.654749\pi$
$389$	−7.66711e47	−0.934467	−0.467233	+	0.884134i	$0.654749\pi$
$390$	0	0
$391$	−1.99129e47	−0.220732
$392$	−6.43290e47	−0.680166
$393$	1.57016e48	1.58373
$394$	−1.46342e48	−1.40828
$395$	0	0
$396$	6.15479e48	5.39327
$397$	7.06434e47	0.590809	0.295404	−	0.955372i	$-0.404546\pi$
$397$	7.06434e47	0.590809	0.295404	+	0.955372i	$0.404546\pi$
$398$	−1.05726e48	−0.844008
$399$	7.19808e47	0.548552
$400$	0	0
$401$	2.24416e48	1.55913	0.779567	−	0.626319i	$-0.215439\pi$
$401$	2.24416e48	1.55913	0.779567	+	0.626319i	$0.215439\pi$
$402$	4.76536e48	3.16165
$403$	−6.52470e46	−0.0413444
$404$	−1.34774e48	−0.815738
$405$	0	0
$406$	−2.15756e48	−1.19187
$407$	−1.03706e48	−0.547405
$408$	−1.17861e48	−0.594506
$409$	−1.58596e48	−0.764561	−0.382281	−	0.924046i	$-0.624861\pi$
$409$	−1.58596e48	−0.764561	−0.382281	+	0.924046i	$0.624861\pi$
$410$	0	0
$411$	−1.93773e48	−0.853531
$412$	7.67603e47	0.323250
$413$	−3.81749e48	−1.53710
$414$	1.29100e49	4.97071
$415$	0	0
$416$	1.15505e48	0.406793
$417$	−6.37109e48	−2.14633
$418$	−3.14427e48	−1.01335
$419$	5.76828e48	1.77863	0.889317	−	0.457290i	$-0.151180\pi$
$419$	5.76828e48	1.77863	0.889317	+	0.457290i	$0.151180\pi$
$420$	0	0
$421$	2.06195e48	0.582183	0.291091	−	0.956695i	$-0.405982\pi$
$421$	2.06195e48	0.582183	0.291091	+	0.956695i	$0.405982\pi$
$422$	8.51539e47	0.230104
$423$	−2.98768e48	−0.772746
$424$	−1.25437e49	−3.10568
$425$	0	0
$426$	5.92446e48	1.34453
$427$	3.56600e46	0.00774935
$428$	1.99750e49	4.15697
$429$	1.78562e48	0.355902
$430$	0	0
$431$	−6.25009e48	−1.14303	−0.571513	−	0.820593i	$-0.693643\pi$
$431$	−6.25009e48	−1.14303	−0.571513	+	0.820593i	$0.693643\pi$
$432$	1.44649e49	2.53434
$433$	−1.21431e48	−0.203846	−0.101923	−	0.994792i	$-0.532500\pi$
$433$	−1.21431e48	−0.203846	−0.101923	+	0.994792i	$0.532500\pi$
$434$	2.59974e48	0.418186
$435$	0	0
$436$	1.99116e49	2.94176
$437$	−4.72590e48	−0.669235
$438$	3.01656e49	4.09487
$439$	1.08258e49	1.40885	0.704427	−	0.709776i	$-0.251204\pi$
$439$	1.08258e49	1.40885	0.704427	+	0.709776i	$0.251204\pi$
$440$	0	0
$441$	−3.07767e48	−0.368221
$442$	−3.44195e47	−0.0394905
$443$	−1.45455e49	−1.60052	−0.800258	−	0.599656i	$-0.795304\pi$
$443$	−1.45455e49	−1.60052	−0.800258	+	0.599656i	$0.795304\pi$
$444$	−1.52633e49	−1.61088
$445$	0	0
$446$	2.66153e48	0.258486
$447$	2.80068e48	0.260960
$448$	−1.80476e49	−1.61353
$449$	−1.72851e49	−1.48291	−0.741455	−	0.671002i	$-0.765864\pi$
$449$	−1.72851e49	−1.48291	−0.741455	+	0.671002i	$0.765864\pi$
$450$	0	0
$451$	2.15033e48	0.169918
$452$	7.10489e48	0.538886
$453$	−1.09852e49	−0.799821
$454$	−8.79575e48	−0.614808
$455$	0	0
$456$	−2.79718e49	−1.80248
$457$	−3.35731e48	−0.207750	−0.103875	−	0.994590i	$-0.533124\pi$
$457$	−3.35731e48	−0.207750	−0.103875	+	0.994590i	$0.533124\pi$
$458$	1.28053e49	0.760988
$459$	−2.00993e48	−0.114722
$460$	0	0
$461$	3.40483e48	0.179320	0.0896599	−	0.995972i	$-0.471422\pi$
$461$	3.40483e48	0.179320	0.0896599	+	0.995972i	$0.471422\pi$
$462$	−7.11474e49	−3.59983
$463$	2.35508e49	1.14487	0.572436	−	0.819949i	$-0.305999\pi$
$463$	2.35508e49	1.14487	0.572436	+	0.819949i	$0.305999\pi$
$464$	4.45270e49	2.07989
$465$	0	0
$466$	−5.91839e49	−2.55308
$467$	−2.02654e49	−0.840220	−0.420110	−	0.907473i	$-0.638009\pi$
$467$	−2.02654e49	−0.840220	−0.420110	+	0.907473i	$0.638009\pi$
$468$	1.59900e49	0.637237
$469$	−2.40166e49	−0.920056
$470$	0	0
$471$	5.10818e49	1.80875
$472$	1.48348e50	5.05073
$473$	−6.49263e49	−2.12564
$474$	−1.70918e48	−0.0538131
$475$	0	0
$476$	9.82715e48	0.286219
$477$	−6.00122e49	−1.68132
$478$	8.34061e49	2.24793
$479$	4.20382e49	1.09003	0.545013	−	0.838427i	$-0.316525\pi$
$479$	4.20382e49	1.09003	0.545013	+	0.838427i	$0.316525\pi$
$480$	0	0
$481$	−2.69428e48	−0.0646782
$482$	4.04568e49	0.934590
$483$	−1.06936e50	−2.37740
$484$	1.04547e50	2.23704
$485$	0	0
$486$	−1.04957e50	−2.08086
$487$	−7.68862e49	−1.46745	−0.733724	−	0.679447i	$-0.762220\pi$
$487$	−7.68862e49	−1.46745	−0.733724	+	0.679447i	$0.762220\pi$
$488$	−1.38575e48	−0.0254635
$489$	−1.49559e50	−2.64606
$490$	0	0
$491$	6.11710e49	1.00355	0.501774	−	0.864999i	$-0.332681\pi$
$491$	6.11710e49	1.00355	0.501774	+	0.864999i	$0.332681\pi$
$492$	3.16481e49	0.500027
$493$	−6.18713e48	−0.0941503
$494$	−8.16875e48	−0.119731
$495$	0	0
$496$	−5.36526e49	−0.729759
$497$	−2.98583e49	−0.391266
$498$	−1.89537e50	−2.39305
$499$	5.74578e49	0.699019	0.349510	−	0.936933i	$-0.386348\pi$
$499$	5.74578e49	0.699019	0.349510	+	0.936933i	$0.386348\pi$
$500$	0	0
$501$	−2.66509e50	−3.01102
$502$	1.61607e50	1.75971
$503$	1.69228e50	1.77609	0.888043	−	0.459761i	$-0.152065\pi$
$503$	1.69228e50	1.77609	0.888043	+	0.459761i	$0.152065\pi$
$504$	−3.85102e50	−3.89593
$505$	0	0
$506$	4.67119e50	4.39180
$507$	−1.71659e50	−1.55603
$508$	−2.48043e50	−2.16795
$509$	9.61224e49	0.810113	0.405056	−	0.914292i	$-0.367252\pi$
$509$	9.61224e49	0.810113	0.405056	+	0.914292i	$0.367252\pi$
$510$	0	0
$511$	−1.52029e50	−1.19163
$512$	−1.37304e50	−1.03798
$513$	−4.77014e49	−0.347824
$514$	−3.43993e50	−2.41953
$515$	0	0
$516$	−9.55571e50	−6.25523
$517$	−1.08103e50	−0.682748
$518$	1.07352e50	0.654199
$519$	−8.39053e48	−0.0493393
$520$	0	0
$521$	1.20953e49	0.0662396	0.0331198	−	0.999451i	$-0.489456\pi$
$521$	1.20953e49	0.0662396	0.0331198	+	0.999451i	$0.489456\pi$
$522$	4.01125e50	2.12020
$523$	−1.32297e50	−0.674948	−0.337474	−	0.941335i	$-0.609573\pi$
$523$	−1.32297e50	−0.674948	−0.337474	+	0.941335i	$0.609573\pi$
$524$	5.08750e50	2.50539
$525$	0	0
$526$	2.66429e50	1.22277
$527$	7.45516e48	0.0330339
$528$	1.46832e51	6.28192
$529$	4.60027e50	1.90044
$530$	0	0
$531$	7.09734e50	2.73431
$532$	2.33226e50	0.867786
$533$	5.58652e48	0.0200765
$534$	4.08559e50	1.41821
$535$	0	0
$536$	9.33286e50	3.02320
$537$	−7.68691e50	−2.40562
$538$	−6.52308e50	−1.97234
$539$	−1.11359e50	−0.325336
$540$	0	0
$541$	3.44799e50	0.940626	0.470313	−	0.882500i	$-0.344141\pi$
$541$	3.44799e50	0.940626	0.470313	+	0.882500i	$0.344141\pi$
$542$	−1.11799e51	−2.94747
$543$	5.34239e50	1.36125
$544$	−1.31977e50	−0.325025
$545$	0	0
$546$	−1.84840e50	−0.425335
$547$	−2.55038e50	−0.567334	−0.283667	−	0.958923i	$-0.591551\pi$
$547$	−2.55038e50	−0.567334	−0.283667	+	0.958923i	$0.591551\pi$
$548$	−6.27848e50	−1.35025
$549$	−6.62978e48	−0.0137851
$550$	0	0
$551$	−1.46839e50	−0.285454
$552$	4.15554e51	7.81187
$553$	8.61397e48	0.0156599
$554$	−1.21271e50	−0.213220
$555$	0	0
$556$	−2.06431e51	−3.39541
$557$	9.33880e50	1.48583	0.742916	−	0.669384i	$-0.233442\pi$
$557$	9.33880e50	1.48583	0.742916	+	0.669384i	$0.233442\pi$
$558$	−4.83334e50	−0.743900
$559$	−1.68677e50	−0.251153
$560$	0	0
$561$	−2.04026e50	−0.284363
$562$	−1.85084e51	−2.49601
$563$	1.28314e51	1.67444	0.837221	−	0.546865i	$-0.184179\pi$
$563$	1.28314e51	1.67444	0.837221	+	0.546865i	$0.184179\pi$
$564$	−1.59103e51	−2.00916
$565$	0	0
$566$	2.64556e51	3.12906
$567$	1.06327e50	0.121719
$568$	1.16029e51	1.28565
$569$	1.56139e50	0.167469	0.0837343	−	0.996488i	$-0.473315\pi$
$569$	1.56139e50	0.167469	0.0837343	+	0.996488i	$0.473315\pi$
$570$	0	0
$571$	−1.69665e51	−1.70539	−0.852696	−	0.522408i	$-0.825034\pi$
$571$	−1.69665e51	−1.70539	−0.852696	+	0.522408i	$0.825034\pi$
$572$	5.78564e50	0.563022
$573$	−1.89378e51	−1.78430
$574$	−2.22592e50	−0.203068
$575$	0	0
$576$	3.35535e51	2.87027
$577$	−2.27367e50	−0.188354	−0.0941770	−	0.995555i	$-0.530022\pi$
$577$	−2.27367e50	−0.188354	−0.0941770	+	0.995555i	$0.530022\pi$
$578$	−2.30186e51	−1.84677
$579$	−1.61869e51	−1.25779
$580$	0	0
$581$	9.55236e50	0.696389
$582$	−6.27327e51	−4.43015
$583$	−2.17141e51	−1.48550
$584$	5.90787e51	3.91555
$585$	0	0
$586$	3.01504e51	1.87580
$587$	−3.99196e50	−0.240648	−0.120324	−	0.992735i	$-0.538393\pi$
$587$	−3.99196e50	−0.240648	−0.120324	+	0.992735i	$0.538393\pi$
$588$	−1.63895e51	−0.957384
$589$	1.76932e50	0.100155
$590$	0	0
$591$	−2.25365e51	−1.19817
$592$	−2.21550e51	−1.14162
$593$	−2.04714e50	−0.102244	−0.0511218	−	0.998692i	$-0.516280\pi$
$593$	−2.04714e50	−0.102244	−0.0511218	+	0.998692i	$0.516280\pi$
$594$	4.71492e51	2.28257
$595$	0	0
$596$	9.07453e50	0.412827
$597$	−1.62817e51	−0.718085
$598$	1.21357e51	0.518910
$599$	6.86053e50	0.284421	0.142210	−	0.989836i	$-0.454579\pi$
$599$	6.86053e50	0.284421	0.142210	+	0.989836i	$0.454579\pi$
$600$	0	0
$601$	5.57554e50	0.217325	0.108662	−	0.994079i	$-0.465343\pi$
$601$	5.57554e50	0.217325	0.108662	+	0.994079i	$0.465343\pi$
$602$	6.72087e51	2.54033
$603$	4.46509e51	1.63666
$604$	−3.55935e51	−1.26528
$605$	0	0
$606$	−2.89648e51	−0.968560
$607$	3.99784e51	1.29669	0.648343	−	0.761348i	$-0.275462\pi$
$607$	3.99784e51	1.29669	0.648343	+	0.761348i	$0.275462\pi$
$608$	−3.13218e51	−0.985442
$609$	−3.32261e51	−1.01405
$610$	0	0
$611$	−2.80848e50	−0.0806696
$612$	−1.82703e51	−0.509148
$613$	−2.99219e50	−0.0809041	−0.0404521	−	0.999181i	$-0.512880\pi$
$613$	−2.99219e50	−0.0809041	−0.0404521	+	0.999181i	$0.512880\pi$
$614$	−4.27705e51	−1.12210
$615$	0	0
$616$	−1.39341e52	−3.44219
$617$	3.88319e50	0.0930923	0.0465461	−	0.998916i	$-0.485179\pi$
$617$	3.88319e50	0.0930923	0.0465461	+	0.998916i	$0.485179\pi$
$618$	1.64968e51	0.383808
$619$	−2.43299e51	−0.549369	−0.274684	−	0.961534i	$-0.588573\pi$
$619$	−2.43299e51	−0.549369	−0.274684	+	0.961534i	$0.588573\pi$
$620$	0	0
$621$	7.08663e51	1.50746
$622$	5.43316e51	1.12184
$623$	−2.05907e51	−0.412707
$624$	3.81467e51	0.742235
$625$	0	0
$626$	1.36096e52	2.49586
$627$	−4.84214e51	−0.862159
$628$	1.65511e52	2.86137
$629$	3.07849e50	0.0516775
$630$	0	0
$631$	−5.54962e51	−0.878456	−0.439228	−	0.898376i	$-0.644748\pi$
$631$	−5.54962e51	−0.878456	−0.439228	+	0.898376i	$0.644748\pi$
$632$	−3.34739e50	−0.0514565
$633$	1.31136e51	0.195773
$634$	−1.19618e52	−1.73438
$635$	0	0
$636$	−3.19584e52	−4.37147
$637$	−2.89308e50	−0.0384398
$638$	1.45138e52	1.87327
$639$	5.55115e51	0.696013
$640$	0	0
$641$	5.54549e51	0.656246	0.328123	−	0.944635i	$-0.393584\pi$
$641$	5.54549e51	0.656246	0.328123	+	0.944635i	$0.393584\pi$
$642$	4.29290e52	4.93575
$643$	6.41403e51	0.716520	0.358260	−	0.933622i	$-0.383370\pi$
$643$	6.41403e51	0.716520	0.358260	+	0.933622i	$0.383370\pi$
$644$	−3.46486e52	−3.76095
$645$	0	0
$646$	9.33366e50	0.0956644
$647$	−1.05432e52	−1.05013	−0.525065	−	0.851062i	$-0.675959\pi$
$647$	−1.05432e52	−1.05013	−0.525065	+	0.851062i	$0.675959\pi$
$648$	−4.13187e51	−0.399953
$649$	2.56802e52	2.41586
$650$	0	0
$651$	4.00356e51	0.355794
$652$	−4.84590e52	−4.18595
$653$	−1.64891e52	−1.38453	−0.692266	−	0.721642i	$-0.743388\pi$
$653$	−1.64891e52	−1.38453	−0.692266	+	0.721642i	$0.743388\pi$
$654$	4.27928e52	3.49287
$655$	0	0
$656$	4.59380e51	0.354365
$657$	2.82648e52	2.11976
$658$	1.11903e52	0.815947
$659$	−6.94083e51	−0.492075	−0.246038	−	0.969260i	$-0.579129\pi$
$659$	−6.94083e51	−0.492075	−0.246038	+	0.969260i	$0.579129\pi$
$660$	0	0
$661$	1.11097e51	0.0744690	0.0372345	−	0.999307i	$-0.488145\pi$
$661$	1.11097e51	0.0744690	0.0372345	+	0.999307i	$0.488145\pi$
$662$	−1.41762e52	−0.924035
$663$	−5.30057e50	−0.0335987
$664$	−3.71205e52	−2.28825
$665$	0	0
$666$	−1.99585e52	−1.16374
$667$	2.18146e52	1.23714
$668$	−8.63522e52	−4.76331
$669$	4.09873e51	0.219921
$670$	0	0
$671$	−2.39884e50	−0.0121797
$672$	−7.08740e52	−3.50070
$673$	1.04310e52	0.501242	0.250621	−	0.968085i	$-0.419365\pi$
$673$	1.04310e52	0.501242	0.250621	+	0.968085i	$0.419365\pi$
$674$	2.04676e52	0.956884
$675$	0	0
$676$	−5.56196e52	−2.46158
$677$	3.15527e51	0.135877	0.0679386	−	0.997690i	$-0.478358\pi$
$677$	3.15527e51	0.135877	0.0679386	+	0.997690i	$0.478358\pi$
$678$	1.52694e52	0.639842
$679$	3.16162e52	1.28920
$680$	0	0
$681$	−1.35454e52	−0.523081
$682$	−1.74884e52	−0.657262
$683$	3.25248e52	1.18969	0.594843	−	0.803842i	$-0.297214\pi$
$683$	3.25248e52	1.18969	0.594843	+	0.803842i	$0.297214\pi$
$684$	−4.33607e52	−1.54368
$685$	0	0
$686$	6.01723e52	2.02955
$687$	1.97200e52	0.647452
$688$	−1.38703e53	−4.43303
$689$	−5.64129e51	−0.175518
$690$	0	0
$691$	3.77463e52	1.11309	0.556545	−	0.830817i	$-0.312127\pi$
$691$	3.77463e52	1.11309	0.556545	+	0.830817i	$0.312127\pi$
$692$	−2.71863e51	−0.0780527
$693$	−6.66643e52	−1.86350
$694$	−2.70569e52	−0.736424
$695$	0	0
$696$	1.29117e53	3.33205
$697$	−6.38319e50	−0.0160410
$698$	7.51717e52	1.83962
$699$	−9.11425e52	−2.17217
$700$	0	0
$701$	−6.99498e52	−1.58126	−0.790630	−	0.612295i	$-0.790247\pi$
$701$	−6.99498e52	−1.58126	−0.790630	+	0.612295i	$0.790247\pi$
$702$	1.22493e52	0.269695
$703$	7.30615e51	0.156681
$704$	1.21406e53	2.53598
$705$	0	0
$706$	3.67143e52	0.727692
$707$	1.45978e52	0.281856
$708$	3.77955e53	7.10928
$709$	−4.10995e52	−0.753149	−0.376574	−	0.926386i	$-0.622898\pi$
$709$	−4.10995e52	−0.753149	−0.376574	+	0.926386i	$0.622898\pi$
$710$	0	0
$711$	−1.60148e51	−0.0278570
$712$	8.00155e52	1.35611
$713$	−2.62854e52	−0.434069
$714$	2.11199e52	0.339840
$715$	0	0
$716$	−2.49065e53	−3.80559
$717$	1.28445e53	1.91254
$718$	−2.15021e53	−3.12018
$719$	2.22282e52	0.314354	0.157177	−	0.987570i	$-0.449761\pi$
$719$	2.22282e52	0.314354	0.157177	+	0.987570i	$0.449761\pi$
$720$	0	0
$721$	−8.31413e51	−0.111690
$722$	−1.21301e53	−1.58828
$723$	6.23030e52	0.795153
$724$	1.73100e53	2.15344
$725$	0	0
$726$	2.24687e53	2.65613
$727$	−3.40663e52	−0.392589	−0.196295	−	0.980545i	$-0.562891\pi$
$727$	−3.40663e52	−0.392589	−0.196295	+	0.980545i	$0.562891\pi$
$728$	−3.62005e52	−0.406709
$729$	−1.48911e53	−1.63106
$730$	0	0
$731$	1.92732e52	0.200670
$732$	−3.53056e51	−0.0358417
$733$	9.49209e52	0.939589	0.469795	−	0.882776i	$-0.344328\pi$
$733$	9.49209e52	0.939589	0.469795	+	0.882776i	$0.344328\pi$
$734$	2.16023e53	2.08508
$735$	0	0
$736$	4.65324e53	4.27086
$737$	1.61559e53	1.44605
$738$	4.13836e52	0.361232
$739$	1.44126e53	1.22693	0.613467	−	0.789721i	$-0.289774\pi$
$739$	1.44126e53	1.22693	0.613467	+	0.789721i	$0.289774\pi$
$740$	0	0
$741$	−1.25798e52	−0.101868
$742$	2.24775e53	1.77531
$743$	9.79782e52	0.754808	0.377404	−	0.926049i	$-0.376817\pi$
$743$	9.79782e52	0.754808	0.377404	+	0.926049i	$0.376817\pi$
$744$	−1.55579e53	−1.16910
$745$	0	0
$746$	−3.71091e52	−0.265346
$747$	−1.77594e53	−1.23879
$748$	−6.61071e52	−0.449851
$749$	−2.16355e53	−1.43633
$750$	0	0
$751$	2.08036e53	1.31462	0.657310	−	0.753621i	$-0.271694\pi$
$751$	2.08036e53	1.31462	0.657310	+	0.753621i	$0.271694\pi$
$752$	−2.30942e53	−1.42388
$753$	2.48873e53	1.49717
$754$	3.77067e52	0.221334
$755$	0	0
$756$	−3.49730e53	−1.95470
$757$	1.09334e53	0.596322	0.298161	−	0.954516i	$-0.403627\pi$
$757$	1.09334e53	0.596322	0.298161	+	0.954516i	$0.403627\pi$
$758$	−2.43363e53	−1.29531
$759$	7.19358e53	3.73656
$760$	0	0
$761$	1.14985e53	0.568886	0.284443	−	0.958693i	$-0.408191\pi$
$761$	1.14985e53	0.568886	0.284443	+	0.958693i	$0.408191\pi$
$762$	−5.33079e53	−2.57409
$763$	−2.15669e53	−1.01644
$764$	−6.13607e53	−2.82269
$765$	0	0
$766$	9.20898e51	0.0403626
$767$	6.67167e52	0.285444
$768$	−1.55133e52	−0.0647920
$769$	1.85767e53	0.757410	0.378705	−	0.925517i	$-0.376369\pi$
$769$	1.85767e53	0.757410	0.378705	+	0.925517i	$0.376369\pi$
$770$	0	0
$771$	−5.29745e53	−2.05855
$772$	−5.24475e53	−1.98978
$773$	−9.34822e52	−0.346265	−0.173132	−	0.984899i	$-0.555389\pi$
$773$	−9.34822e52	−0.346265	−0.173132	+	0.984899i	$0.555389\pi$
$774$	−1.24952e54	−4.51893
$775$	0	0
$776$	−1.22861e54	−4.23615
$777$	1.65321e53	0.556595
$778$	−5.33897e53	−1.75523
$779$	−1.51492e52	−0.0486346
$780$	0	0
$781$	2.00856e53	0.614952
$782$	−1.38663e53	−0.414606
$783$	2.20188e53	0.642987
$784$	−2.37898e53	−0.678490
$785$	0	0
$786$	1.09337e54	2.97476
$787$	−4.23158e53	−1.12453	−0.562264	−	0.826958i	$-0.690070\pi$
$787$	−4.23158e53	−1.12453	−0.562264	+	0.826958i	$0.690070\pi$
$788$	−7.30211e53	−1.89546
$789$	4.10298e53	1.04034
$790$	0	0
$791$	−7.69552e52	−0.186197
$792$	2.59058e54	6.12323
$793$	−6.23215e50	−0.00143908
$794$	4.91923e53	1.10973
$795$	0	0
$796$	−5.27548e53	−1.13598
$797$	−6.48251e53	−1.36384	−0.681922	−	0.731425i	$-0.738856\pi$
$797$	−6.48251e53	−1.36384	−0.681922	+	0.731425i	$0.738856\pi$
$798$	5.01236e53	1.03036
$799$	3.20899e52	0.0644545
$800$	0	0
$801$	3.82815e53	0.734155
$802$	1.56271e54	2.92856
$803$	1.02270e54	1.87288
$804$	2.37780e54	4.25537
$805$	0	0
$806$	−4.54345e52	−0.0776583
$807$	−1.00455e54	−1.67807
$808$	−5.67269e53	−0.926145
$809$	−7.72275e53	−1.23232	−0.616161	−	0.787620i	$-0.711313\pi$
$809$	−7.72275e53	−1.23232	−0.616161	+	0.787620i	$0.711313\pi$
$810$	0	0
$811$	2.21495e52	0.0337659	0.0168830	−	0.999857i	$-0.494626\pi$
$811$	2.21495e52	0.0337659	0.0168830	+	0.999857i	$0.494626\pi$
$812$	−1.07657e54	−1.60419
$813$	−1.72169e54	−2.50772
$814$	−7.22156e53	−1.02821
$815$	0	0
$816$	−4.35866e53	−0.593041
$817$	4.57408e53	0.608409
$818$	−1.10438e54	−1.43609
$819$	−1.73193e53	−0.220180
$820$	0	0
$821$	1.17174e54	1.42391	0.711957	−	0.702223i	$-0.247809\pi$
$821$	1.17174e54	1.42391	0.711957	+	0.702223i	$0.247809\pi$
$822$	−1.34933e54	−1.60321
$823$	2.38356e53	0.276904	0.138452	−	0.990369i	$-0.455787\pi$
$823$	2.38356e53	0.276904	0.138452	+	0.990369i	$0.455787\pi$
$824$	3.23088e53	0.367001
$825$	0	0
$826$	−2.65830e54	−2.88717
$827$	−7.47921e53	−0.794336	−0.397168	−	0.917746i	$-0.630007\pi$
$827$	−7.47921e53	−0.794336	−0.397168	+	0.917746i	$0.630007\pi$
$828$	6.44176e54	6.69026
$829$	−1.23210e53	−0.125138	−0.0625688	−	0.998041i	$-0.519929\pi$
$829$	−1.23210e53	−0.125138	−0.0625688	+	0.998041i	$0.519929\pi$
$830$	0	0
$831$	−1.86757e53	−0.181408
$832$	3.15411e53	0.299637
$833$	3.30565e52	0.0307132
$834$	−4.43649e54	−4.03151
$835$	0	0
$836$	−1.56891e54	−1.36390
$837$	−2.65315e53	−0.225601
$838$	4.01672e54	3.34085
$839$	−2.18835e54	−1.78041	−0.890205	−	0.455559i	$-0.849439\pi$
$839$	−2.18835e54	−1.78041	−0.890205	+	0.455559i	$0.849439\pi$
$840$	0	0
$841$	−6.06673e53	−0.472312
$842$	1.43583e54	1.09353
$843$	−2.85027e54	−2.12362
$844$	4.24897e53	0.309705
$845$	0	0
$846$	−2.08046e54	−1.45147
$847$	−1.13238e54	−0.772948
$848$	−4.63883e54	−3.09803
$849$	4.07414e54	2.66222
$850$	0	0
$851$	−1.08542e54	−0.679047
$852$	2.95616e54	1.80965
$853$	−1.64231e53	−0.0983783	−0.0491891	−	0.998789i	$-0.515664\pi$
$853$	−1.64231e53	−0.0983783	−0.0491891	+	0.998789i	$0.515664\pi$
$854$	2.48317e52	0.0145558
$855$	0	0
$856$	8.40756e54	4.71960
$857$	1.29393e54	0.710831	0.355415	−	0.934708i	$-0.384339\pi$
$857$	1.29393e54	0.710831	0.355415	+	0.934708i	$0.384339\pi$
$858$	1.24341e54	0.668499
$859$	−4.66068e53	−0.245231	−0.122616	−	0.992454i	$-0.539128\pi$
$859$	−4.66068e53	−0.245231	−0.122616	+	0.992454i	$0.539128\pi$
$860$	0	0
$861$	−3.42790e53	−0.172771
$862$	−4.35223e54	−2.14698
$863$	−1.09405e54	−0.528249	−0.264124	−	0.964489i	$-0.585083\pi$
$863$	−1.09405e54	−0.528249	−0.264124	+	0.964489i	$0.585083\pi$
$864$	4.69680e54	2.21972
$865$	0	0
$866$	−8.45580e53	−0.382890
$867$	−3.54483e54	−1.57124
$868$	1.29720e54	0.562851
$869$	−5.79461e52	−0.0246126
$870$	0	0
$871$	4.19728e53	0.170857
$872$	8.38089e54	3.33991
$873$	−5.87798e54	−2.29332
$874$	−3.29087e54	−1.25704
$875$	0	0
$876$	1.50519e55	5.51143
$877$	2.08722e54	0.748299	0.374149	−	0.927368i	$-0.377935\pi$
$877$	2.08722e54	0.748299	0.374149	+	0.927368i	$0.377935\pi$
$878$	7.53851e54	2.64629
$879$	4.64313e54	1.59594
$880$	0	0
$881$	1.91734e54	0.631895	0.315948	−	0.948777i	$-0.397678\pi$
$881$	1.91734e54	0.631895	0.315948	+	0.948777i	$0.397678\pi$
$882$	−2.14313e54	−0.691638
$883$	9.08223e53	0.287025	0.143512	−	0.989649i	$-0.454160\pi$
$883$	9.08223e53	0.287025	0.143512	+	0.989649i	$0.454160\pi$
$884$	−1.71745e53	−0.0531517
$885$	0	0
$886$	−1.01287e55	−3.00629
$887$	−5.94849e54	−1.72910	−0.864549	−	0.502548i	$-0.832396\pi$
$887$	−5.94849e54	−1.72910	−0.864549	+	0.502548i	$0.832396\pi$
$888$	−6.42438e54	−1.82891
$889$	2.68663e54	0.749074
$890$	0	0
$891$	−7.15260e53	−0.191305
$892$	1.32804e54	0.347906
$893$	7.61586e53	0.195419
$894$	1.95024e54	0.490167
$895$	0	0
$896$	−3.48390e54	−0.840171
$897$	1.86888e54	0.441490
$898$	−1.20364e55	−2.78539
$899$	−8.16715e53	−0.185147
$900$	0	0
$901$	6.44577e53	0.140238
$902$	1.49738e54	0.319161
$903$	1.03501e55	2.16132
$904$	2.99048e54	0.611822
$905$	0	0
$906$	−7.64954e54	−1.50232
$907$	5.62159e54	1.08174	0.540872	−	0.841105i	$-0.318094\pi$
$907$	5.62159e54	1.08174	0.540872	+	0.841105i	$0.318094\pi$
$908$	−4.38886e54	−0.827492
$909$	−2.71397e54	−0.501386
$910$	0	0
$911$	9.31208e54	1.65180	0.825899	−	0.563818i	$-0.190668\pi$
$911$	9.31208e54	1.65180	0.825899	+	0.563818i	$0.190668\pi$
$912$	−1.03444e55	−1.79804
$913$	−6.42586e54	−1.09452
$914$	−2.33785e54	−0.390223
$915$	0	0
$916$	6.38952e54	1.02424
$917$	−5.51042e54	−0.865670
$918$	−1.39961e54	−0.215485
$919$	3.17778e53	0.0479498	0.0239749	−	0.999713i	$-0.492368\pi$
$919$	3.17778e53	0.0479498	0.0239749	+	0.999713i	$0.492368\pi$
$920$	0	0
$921$	−6.58662e54	−0.954683
$922$	2.37094e54	0.336821
$923$	5.21821e53	0.0726591
$924$	−3.55008e55	−4.84514
$925$	0	0
$926$	1.63995e55	2.15044
$927$	1.54574e54	0.198683
$928$	1.44581e55	1.82168
$929$	9.76242e54	1.20578	0.602888	−	0.797826i	$-0.294016\pi$
$929$	9.76242e54	1.20578	0.602888	+	0.797826i	$0.294016\pi$
$930$	0	0
$931$	7.84526e53	0.0931190
$932$	−2.95313e55	−3.43628
$933$	8.36700e54	0.954464
$934$	−1.41118e55	−1.57821
$935$	0	0
$936$	6.73027e54	0.723485
$937$	−2.90595e54	−0.306271	−0.153135	−	0.988205i	$-0.548937\pi$
$937$	−2.90595e54	−0.306271	−0.153135	+	0.988205i	$0.548937\pi$
$938$	−1.67239e55	−1.72816
$939$	2.09586e55	2.12349
$940$	0	0
$941$	1.41536e55	1.37867	0.689333	−	0.724444i	$-0.257904\pi$
$941$	1.41536e55	1.37867	0.689333	+	0.724444i	$0.257904\pi$
$942$	3.55707e55	3.39743
$943$	2.25059e54	0.210780
$944$	5.48611e55	5.03828
$945$	0	0
$946$	−4.52112e55	−3.99264
$947$	1.10102e55	0.953498	0.476749	−	0.879040i	$-0.341815\pi$
$947$	1.10102e55	0.953498	0.476749	+	0.879040i	$0.341815\pi$
$948$	−8.52837e53	−0.0724289
$949$	2.65696e54	0.221289
$950$	0	0
$951$	−1.84210e55	−1.47562
$952$	4.13629e54	0.324958
$953$	7.28364e53	0.0561216	0.0280608	−	0.999606i	$-0.491067\pi$
$953$	7.28364e53	0.0561216	0.0280608	+	0.999606i	$0.491067\pi$
$954$	−4.17893e55	−3.15806
$955$	0	0
$956$	4.16176e55	3.02556
$957$	2.23512e55	1.59378
$958$	2.92732e55	2.04742
$959$	6.80040e54	0.466542
$960$	0	0
$961$	−1.41649e55	−0.935039
$962$	−1.87615e54	−0.121487
$963$	4.02240e55	2.55505
$964$	2.01869e55	1.25790
$965$	0	0
$966$	−7.44646e55	−4.46553
$967$	3.12160e53	0.0183648	0.00918241	−	0.999958i	$-0.497077\pi$
$967$	3.12160e53	0.0183648	0.00918241	+	0.999958i	$0.497077\pi$
$968$	4.40045e55	2.53982
$969$	1.43737e54	0.0813916
$970$	0	0
$971$	1.39269e55	0.759099	0.379550	−	0.925171i	$-0.376079\pi$
$971$	1.39269e55	0.759099	0.379550	+	0.925171i	$0.376079\pi$
$972$	−5.23711e55	−2.80070
$973$	2.23592e55	1.17319
$974$	−5.35395e55	−2.75634
$975$	0	0
$976$	−5.12470e53	−0.0254007
$977$	1.96974e54	0.0957986	0.0478993	−	0.998852i	$-0.484747\pi$
$977$	1.96974e54	0.0957986	0.0478993	+	0.998852i	$0.484747\pi$
$978$	−1.04145e56	−4.97016
$979$	1.38513e55	0.648652
$980$	0	0
$981$	4.00964e55	1.80812
$982$	4.25963e55	1.88499
$983$	−3.18701e55	−1.38402	−0.692011	−	0.721887i	$-0.743275\pi$
$983$	−3.18701e55	−1.38402	−0.692011	+	0.721887i	$0.743275\pi$
$984$	1.33208e55	0.567704
$985$	0	0
$986$	−4.30839e54	−0.176845
$987$	1.72329e55	0.694210
$988$	−4.07600e54	−0.161150
$989$	−6.79535e55	−2.63682
$990$	0	0
$991$	−4.07995e54	−0.152508	−0.0762540	−	0.997088i	$-0.524296\pi$
$991$	−4.07995e54	−0.152508	−0.0762540	+	0.997088i	$0.524296\pi$
$992$	−1.74212e55	−0.639163
$993$	−2.18313e55	−0.786172
$994$	−2.07917e55	−0.734924
$995$	0	0
$996$	−9.45744e55	−3.22089
$997$	4.43930e55	1.48407	0.742035	−	0.670361i	$-0.233861\pi$
$997$	4.43930e55	1.48407	0.742035	+	0.670361i	$0.233861\pi$
$998$	4.00106e55	1.31299
$999$	−1.09558e55	−0.352924

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.38.a.f.1.17		18
5.2	odd	4		5.38.b.a.4.17	yes	18
5.3	odd	4		5.38.b.a.4.2	✓	18
5.4	even	2	inner	25.38.a.f.1.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.38.b.a.4.2	✓	18	5.3	odd	4
5.38.b.a.4.17	yes	18	5.2	odd	4
25.38.a.f.1.2		18	5.4	even	2	inner
25.38.a.f.1.17		18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+696347. q^{2} +1.07237e9 q^{3} +3.47460e11 q^{4} +7.46739e14 q^{6} -3.76344e15 q^{7} +1.46247e17 q^{8} +6.99686e17 q^{9} +O(q^{10})\)	\(q+696347. q^{2} +1.07237e9 q^{3} +3.47460e11 q^{4} +7.46739e14 q^{6} -3.76344e15 q^{7} +1.46247e17 q^{8} +6.99686e17 q^{9} +2.53166e19 q^{11} +3.72604e20 q^{12} +6.57721e19 q^{13} -2.62066e21 q^{14} +5.40844e22 q^{16} -7.51516e21 q^{17} +4.87224e23 q^{18} -1.78356e23 q^{19} -4.03579e24 q^{21} +1.76291e25 q^{22} +2.64970e25 q^{23} +1.56831e26 q^{24} +4.58002e25 q^{26} +2.67450e26 q^{27} -1.30764e27 q^{28} +8.23288e26 q^{29} -9.92016e26 q^{31} +1.75614e28 q^{32} +2.71487e28 q^{33} -5.23315e27 q^{34} +2.43113e29 q^{36} -4.09638e28 q^{37} -1.24198e29 q^{38} +7.05318e28 q^{39} +8.49376e28 q^{41} -2.81031e30 q^{42} -2.56457e30 q^{43} +8.79650e30 q^{44} +1.84511e31 q^{46} -4.27002e30 q^{47} +5.79983e31 q^{48} -4.39865e30 q^{49} -8.05900e30 q^{51} +2.28532e31 q^{52} -8.57703e31 q^{53} +1.86238e32 q^{54} -5.50393e32 q^{56} -1.91263e32 q^{57} +5.73294e32 q^{58} +1.01436e33 q^{59} -9.47537e30 q^{61} -6.90787e32 q^{62} -2.63322e33 q^{63} +4.79551e33 q^{64} +1.89049e34 q^{66} +6.38156e33 q^{67} -2.61121e33 q^{68} +2.84145e34 q^{69} +7.93378e33 q^{71} +1.02327e35 q^{72} +4.03964e34 q^{73} -2.85250e34 q^{74} -6.19716e34 q^{76} -9.52775e34 q^{77} +4.91146e34 q^{78} -2.28886e33 q^{79} -2.82526e34 q^{81} +5.91460e34 q^{82} -2.53820e35 q^{83} -1.40227e36 q^{84} -1.78583e36 q^{86} +8.82866e35 q^{87} +3.70249e36 q^{88} +5.47125e35 q^{89} -2.47529e35 q^{91} +9.20664e36 q^{92} -1.06380e36 q^{93} -2.97342e36 q^{94} +1.88322e37 q^{96} -8.40088e36 q^{97} -3.06298e36 q^{98} +1.77137e37 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 1378491386616 q^{4} + 235050070586136 q^{6} + 26\!\cdots\!74 q^{9}+O(q^{10}) \) 18 * q + 1378491386616 * q^4 + 235050070586136 * q^6 + 2687284960012241874 * q^9	\( 18 q + 1378491386616 q^{4} + 235050070586136 q^{6} + 26\!\cdots\!74 q^{9}+ \cdots + 56\!\cdots\!28 q^{99}+O(q^{100}) \) 18 * q + 1378491386616 * q^4 + 235050070586136 * q^6 + 2687284960012241874 * q^9 + 33986627223034798296 * q^11 + 1891478635206760615032 * q^14 + 156966361562724410096928 * q^16 + 302760323265144477867480 * q^19 - 4075600057180968977719704 * q^21 + 149013794188298144591103840 * q^24 + 740755125071253494506988496 * q^26 + 4979198281142680608411084420 * q^29 - 6151542350452781958579360384 * q^31 - 4353870657762813132282760128 * q^34 + 106785265488844195864724376888 * q^36 - 862865339998466438248367480112 * q^39 - 855196121794787398902389240124 * q^41 + 13806087517221679193940877688352 * q^44 + 21104472252831571358912888976456 * q^46 + 70801883273781655273950124330026 * q^49 - 23706017526907962630925223712384 * q^51 + 523190901027760133510234826308880 * q^54 + 600728793662143364055878849971680 * q^56 + 3947688162499809731531683814232840 * q^59 + 1757475029942100801736311637166796 * q^61 + 35293446897899611856499858227515776 * q^64 + 32483717310049996392729278134533792 * q^66 + 29536156423306266276087371479398168 * q^69 - 15852144098617191882453852538452144 * q^71 - 35174192734582932814586482689499248 * q^74 - 8033980639764558547374281250927840 * q^76 + 81628804120848018323973892688639520 * q^79 - 51387579768336601107744192991686822 * q^81 - 3799290048936464645757894225695060448 * q^84 - 3995229770967016576777180478600492424 * q^86 - 5941001429647591369362270403151043540 * q^89 + 2681006692210129770276250954718747856 * q^91 - 2447341171808746326507906787285919208 * q^94 - 2375166431920457136532866502177021824 * q^96 + 56285732505135601101448147731191891928 * q^99

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