LMFDB - Embedded newform 5239.2.a.l.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5239,2,Mod(1,5239)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5239, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("5239.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.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:	$41.8336256189$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 17 x^{14} + 80 x^{13} + 98 x^{12} - 628 x^{11} - 158 x^{10} + 2458 x^{9} + \cdots - 147 $ x^16 - 4x^15 - 17x^14 + 80x^13 + 98x^12 - 628x^11 - 158x^10 + 2458x^9 - 510x^8 - 5030x^7 + 2318x^6 + 5112x^5 - 3154x^4 - 2086x^3 + 1542x^2 + 124*x - 147
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 403)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.40506$ of defining polynomial
Character	$\chi$	$=$	5239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.40506 q^{2} +1.52886 q^{3} -0.0258025 q^{4} -1.01618 q^{5} -2.14814 q^{6} +2.90958 q^{7} +2.84638 q^{8} -0.662589 q^{9} +O(q^{10})$	\(q-1.40506 q^{2} +1.52886 q^{3} -0.0258025 q^{4} -1.01618 q^{5} -2.14814 q^{6} +2.90958 q^{7} +2.84638 q^{8} -0.662589 q^{9} +1.42779 q^{10} -2.94134 q^{11} -0.0394484 q^{12} -4.08813 q^{14} -1.55359 q^{15} -3.94773 q^{16} +5.52858 q^{17} +0.930978 q^{18} +3.13639 q^{19} +0.0262199 q^{20} +4.44833 q^{21} +4.13277 q^{22} -3.87847 q^{23} +4.35171 q^{24} -3.96739 q^{25} -5.59958 q^{27} -0.0750744 q^{28} +5.59296 q^{29} +2.18289 q^{30} -1.00000 q^{31} -0.145952 q^{32} -4.49690 q^{33} -7.76799 q^{34} -2.95664 q^{35} +0.0170965 q^{36} +3.92962 q^{37} -4.40682 q^{38} -2.89242 q^{40} +12.1899 q^{41} -6.25018 q^{42} -3.52296 q^{43} +0.0758940 q^{44} +0.673307 q^{45} +5.44949 q^{46} +9.64114 q^{47} -6.03552 q^{48} +1.46564 q^{49} +5.57442 q^{50} +8.45242 q^{51} -11.3388 q^{53} +7.86776 q^{54} +2.98892 q^{55} +8.28175 q^{56} +4.79510 q^{57} -7.85846 q^{58} -12.4904 q^{59} +0.0400865 q^{60} +5.57570 q^{61} +1.40506 q^{62} -1.92785 q^{63} +8.10053 q^{64} +6.31842 q^{66} +4.26478 q^{67} -0.142651 q^{68} -5.92963 q^{69} +4.15426 q^{70} +9.44757 q^{71} -1.88598 q^{72} -0.784520 q^{73} -5.52136 q^{74} -6.06558 q^{75} -0.0809267 q^{76} -8.55806 q^{77} +6.11817 q^{79} +4.01159 q^{80} -6.57321 q^{81} -17.1275 q^{82} -8.81342 q^{83} -0.114778 q^{84} -5.61801 q^{85} +4.94997 q^{86} +8.55086 q^{87} -8.37217 q^{88} +6.58407 q^{89} -0.946037 q^{90} +0.100074 q^{92} -1.52886 q^{93} -13.5464 q^{94} -3.18712 q^{95} -0.223140 q^{96} +6.44332 q^{97} -2.05931 q^{98} +1.94890 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 2 q^{3} + 18 q^{4} + 4 q^{5} + 6 q^{6} + 2 q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 2 * q^3 + 18 * q^4 + 4 * q^5 + 6 * q^6 + 2 * q^7 + 12 * q^8 + 10 * q^9	$ 16 q + 4 q^{2} - 2 q^{3} + 18 q^{4} + 4 q^{5} + 6 q^{6} + 2 q^{7} + 12 q^{8} + 10 q^{9} - 2 q^{10} + 14 q^{11} + 8 q^{12} - 8 q^{14} + 14 q^{16} + 4 q^{17} - 28 q^{18} + 22 q^{19} + 28 q^{20} + 12 q^{21} - 8 q^{22} + 4 q^{23} - 8 q^{24} - 2 q^{25} + 10 q^{27} + 16 q^{28} - 8 q^{29} - 20 q^{30} - 16 q^{31} + 48 q^{32} + 10 q^{33} + 8 q^{34} - 2 q^{35} + 22 q^{36} + 16 q^{37} - 6 q^{38} + 14 q^{40} + 44 q^{41} + 14 q^{42} + 16 q^{43} + 4 q^{44} + 56 q^{45} + 10 q^{47} + 32 q^{49} + 2 q^{50} - 6 q^{53} + 24 q^{54} + 22 q^{55} - 4 q^{56} - 8 q^{57} + 74 q^{58} + 2 q^{59} + 40 q^{60} + 8 q^{61} - 4 q^{62} + 56 q^{63} + 38 q^{64} - 34 q^{66} - 8 q^{67} + 32 q^{68} - 10 q^{69} - 108 q^{70} + 50 q^{71} - 44 q^{72} + 14 q^{73} + 8 q^{74} + 44 q^{76} + 16 q^{77} + 32 q^{79} + 68 q^{80} - 8 q^{81} - 6 q^{82} - 20 q^{83} + 136 q^{84} - 32 q^{85} + 8 q^{86} - 36 q^{87} - 40 q^{88} + 52 q^{89} - 34 q^{90} + 14 q^{92} + 2 q^{93} + 44 q^{94} - 2 q^{95} - 80 q^{96} + 18 q^{97} + 12 q^{98} + 38 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 2 * q^3 + 18 * q^4 + 4 * q^5 + 6 * q^6 + 2 * q^7 + 12 * q^8 + 10 * q^9 - 2 * q^10 + 14 * q^11 + 8 * q^12 - 8 * q^14 + 14 * q^16 + 4 * q^17 - 28 * q^18 + 22 * q^19 + 28 * q^20 + 12 * q^21 - 8 * q^22 + 4 * q^23 - 8 * q^24 - 2 * q^25 + 10 * q^27 + 16 * q^28 - 8 * q^29 - 20 * q^30 - 16 * q^31 + 48 * q^32 + 10 * q^33 + 8 * q^34 - 2 * q^35 + 22 * q^36 + 16 * q^37 - 6 * q^38 + 14 * q^40 + 44 * q^41 + 14 * q^42 + 16 * q^43 + 4 * q^44 + 56 * q^45 + 10 * q^47 + 32 * q^49 + 2 * q^50 - 6 * q^53 + 24 * q^54 + 22 * q^55 - 4 * q^56 - 8 * q^57 + 74 * q^58 + 2 * q^59 + 40 * q^60 + 8 * q^61 - 4 * q^62 + 56 * q^63 + 38 * q^64 - 34 * q^66 - 8 * q^67 + 32 * q^68 - 10 * q^69 - 108 * q^70 + 50 * q^71 - 44 * q^72 + 14 * q^73 + 8 * q^74 + 44 * q^76 + 16 * q^77 + 32 * q^79 + 68 * q^80 - 8 * q^81 - 6 * q^82 - 20 * q^83 + 136 * q^84 - 32 * q^85 + 8 * q^86 - 36 * q^87 - 40 * q^88 + 52 * q^89 - 34 * q^90 + 14 * q^92 + 2 * q^93 + 44 * q^94 - 2 * q^95 - 80 * q^96 + 18 * q^97 + 12 * q^98 + 38 * 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 $

$2$	−1.40506	−0.993528	−0.496764	−	0.867886i	$-0.665479\pi$
$2$	−1.40506	−0.993528	−0.496764	+	0.867886i	$0.665479\pi$
$3$	1.52886	0.882687	0.441344	−	0.897338i	$-0.354502\pi$
$3$	1.52886	0.882687	0.441344	+	0.897338i	$0.354502\pi$
$4$	−0.0258025	−0.0129013
$5$	−1.01618	−0.454448	−0.227224	−	0.973843i	$-0.572965\pi$
$5$	−1.01618	−0.454448	−0.227224	+	0.973843i	$0.572965\pi$
$6$	−2.14814	−0.876975
$7$	2.90958	1.09972	0.549858	−	0.835258i	$-0.314682\pi$
$7$	2.90958	1.09972	0.549858	+	0.835258i	$0.314682\pi$
$8$	2.84638	1.00635
$9$	−0.662589	−0.220863
$10$	1.42779	0.451507
$11$	−2.94134	−0.886848	−0.443424	−	0.896312i	$-0.646236\pi$
$11$	−2.94134	−0.886848	−0.443424	+	0.896312i	$0.646236\pi$
$12$	−0.0394484	−0.0113878
$13$	0	0
$13$	0	0
$14$	−4.08813	−1.09260
$15$	−1.55359	−0.401135
$16$	−3.94773	−0.986932
$17$	5.52858	1.34088	0.670438	−	0.741965i	$-0.266106\pi$
$17$	5.52858	1.34088	0.670438	+	0.741965i	$0.266106\pi$
$18$	0.930978	0.219434
$19$	3.13639	0.719537	0.359768	−	0.933042i	$-0.382856\pi$
$19$	3.13639	0.719537	0.359768	+	0.933042i	$0.382856\pi$
$20$	0.0262199	0.00586295
$21$	4.44833	0.970706
$22$	4.13277	0.881109
$23$	−3.87847	−0.808717	−0.404358	−	0.914601i	$-0.632505\pi$
$23$	−3.87847	−0.808717	−0.404358	+	0.914601i	$0.632505\pi$
$24$	4.35171	0.888289
$25$	−3.96739	−0.793477
$26$	0	0
$27$	−5.59958	−1.07764
$28$	−0.0750744	−0.0141877
$29$	5.59296	1.03859	0.519294	−	0.854596i	$-0.326195\pi$
$29$	5.59296	1.03859	0.519294	+	0.854596i	$0.326195\pi$
$30$	2.18289	0.398539
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−0.145952	−0.0258009
$33$	−4.49690	−0.782810
$34$	−7.76799	−1.33220
$35$	−2.95664	−0.499764
$36$	0.0170965	0.00284941
$37$	3.92962	0.646025	0.323013	−	0.946395i	$-0.395304\pi$
$37$	3.92962	0.646025	0.323013	+	0.946395i	$0.395304\pi$
$38$	−4.40682	−0.714880
$39$	0	0
$40$	−2.89242	−0.457332
$41$	12.1899	1.90374	0.951868	−	0.306509i	$-0.0991608\pi$
$41$	12.1899	1.90374	0.951868	+	0.306509i	$0.0991608\pi$
$42$	−6.25018	−0.964424
$43$	−3.52296	−0.537246	−0.268623	−	0.963245i	$-0.586569\pi$
$43$	−3.52296	−0.537246	−0.268623	+	0.963245i	$0.586569\pi$
$44$	0.0758940	0.0114415
$45$	0.673307	0.100371
$46$	5.44949	0.803483
$47$	9.64114	1.40630	0.703152	−	0.711040i	$-0.251775\pi$
$47$	9.64114	1.40630	0.703152	+	0.711040i	$0.251775\pi$
$48$	−6.03552	−0.871153
$49$	1.46564	0.209377
$50$	5.57442	0.788342
$51$	8.45242	1.18358
$52$	0	0
$53$	−11.3388	−1.55751	−0.778753	−	0.627330i	$-0.784148\pi$
$53$	−11.3388	−1.55751	−0.778753	+	0.627330i	$0.784148\pi$
$54$	7.86776	1.07067
$55$	2.98892	0.403026
$56$	8.28175	1.10670
$57$	4.79510	0.635126
$58$	−7.85846	−1.03187
$59$	−12.4904	−1.62611	−0.813053	−	0.582190i	$-0.802196\pi$
$59$	−12.4904	−1.62611	−0.813053	+	0.582190i	$0.802196\pi$
$60$	0.0400865	0.00517515
$61$	5.57570	0.713895	0.356947	−	0.934125i	$-0.383818\pi$
$61$	5.57570	0.713895	0.356947	+	0.934125i	$0.383818\pi$
$62$	1.40506	0.178443
$63$	−1.92785	−0.242887
$64$	8.10053	1.01257
$65$	0	0
$66$	6.31842	0.777744
$67$	4.26478	0.521026	0.260513	−	0.965470i	$-0.416108\pi$
$67$	4.26478	0.521026	0.260513	+	0.965470i	$0.416108\pi$
$68$	−0.142651	−0.0172990
$69$	−5.92963	−0.713844
$70$	4.15426	0.496530
$71$	9.44757	1.12122	0.560610	−	0.828080i	$-0.310567\pi$
$71$	9.44757	1.12122	0.560610	+	0.828080i	$0.310567\pi$
$72$	−1.88598	−0.222265
$73$	−0.784520	−0.0918211	−0.0459106	−	0.998946i	$-0.514619\pi$
$73$	−0.784520	−0.0918211	−0.0459106	+	0.998946i	$0.514619\pi$
$74$	−5.52136	−0.641845
$75$	−6.06558	−0.700392
$76$	−0.0809267	−0.00928293
$77$	−8.55806	−0.975282
$78$	0	0
$79$	6.11817	0.688348	0.344174	−	0.938906i	$-0.388159\pi$
$79$	6.11817	0.688348	0.344174	+	0.938906i	$0.388159\pi$
$80$	4.01159	0.448509
$81$	−6.57321	−0.730357
$82$	−17.1275	−1.89142
$83$	−8.81342	−0.967399	−0.483699	−	0.875234i	$-0.660707\pi$
$83$	−8.81342	−0.967399	−0.483699	+	0.875234i	$0.660707\pi$
$84$	−0.114778	−0.0125233
$85$	−5.61801	−0.609358
$86$	4.94997	0.533769
$87$	8.55086	0.916748
$88$	−8.37217	−0.892476
$89$	6.58407	0.697910	0.348955	−	0.937140i	$-0.386537\pi$
$89$	6.58407	0.697910	0.348955	+	0.937140i	$0.386537\pi$
$90$	−0.946037	−0.0997211
$91$	0	0
$92$	0.100074	0.0104335
$93$	−1.52886	−0.158535
$94$	−13.5464	−1.39720
$95$	−3.18712	−0.326992
$96$	−0.223140	−0.0227741
$97$	6.44332	0.654220	0.327110	−	0.944986i	$-0.393925\pi$
$97$	6.44332	0.654220	0.327110	+	0.944986i	$0.393925\pi$
$98$	−2.05931	−0.208022
$99$	1.94890	0.195872
$100$	0.102369	0.0102369
$101$	18.1325	1.80425	0.902123	−	0.431478i	$-0.142008\pi$
$101$	18.1325	1.80425	0.902123	+	0.431478i	$0.142008\pi$
$102$	−11.8762	−1.17592
$103$	−17.3257	−1.70715	−0.853575	−	0.520970i	$-0.825570\pi$
$103$	−17.3257	−1.70715	−0.853575	+	0.520970i	$0.825570\pi$
$104$	0	0
$105$	−4.52029	−0.441135
$106$	15.9317	1.54743
$107$	−7.73734	−0.747997	−0.373998	−	0.927429i	$-0.622013\pi$
$107$	−7.73734	−0.747997	−0.373998	+	0.927429i	$0.622013\pi$
$108$	0.144483	0.0139029
$109$	11.1918	1.07198	0.535991	−	0.844224i	$-0.319938\pi$
$109$	11.1918	1.07198	0.535991	+	0.844224i	$0.319938\pi$
$110$	−4.19962	−0.400418
$111$	6.00784	0.570238
$112$	−11.4862	−1.08535
$113$	14.3095	1.34612	0.673061	−	0.739587i	$-0.264979\pi$
$113$	14.3095	1.34612	0.673061	+	0.739587i	$0.264979\pi$
$114$	−6.73741	−0.631016
$115$	3.94121	0.367519
$116$	−0.144313	−0.0133991
$117$	0	0
$118$	17.5497	1.61558
$119$	16.0858	1.47458
$120$	−4.42210	−0.403681
$121$	−2.34851	−0.213501
$122$	−7.83419	−0.709275
$123$	18.6366	1.68040
$124$	0.0258025	0.00231713
$125$	9.11244	0.815042
$126$	2.70875	0.241315
$127$	17.9788	1.59536	0.797682	−	0.603079i	$-0.206060\pi$
$127$	17.9788	1.59536	0.797682	+	0.603079i	$0.206060\pi$
$128$	−11.0898	−0.980212
$129$	−5.38611	−0.474220
$130$	0	0
$131$	−8.60202	−0.751562	−0.375781	−	0.926708i	$-0.622626\pi$
$131$	−8.60202	−0.751562	−0.375781	+	0.926708i	$0.622626\pi$
$132$	0.116031	0.0100992
$133$	9.12556	0.791287
$134$	−5.99228	−0.517654
$135$	5.69016	0.489731
$136$	15.7364	1.34939
$137$	13.4868	1.15226	0.576128	−	0.817360i	$-0.304563\pi$
$137$	13.4868	1.15226	0.576128	+	0.817360i	$0.304563\pi$
$138$	8.33150	0.709224
$139$	−8.93572	−0.757918	−0.378959	−	0.925414i	$-0.623718\pi$
$139$	−8.93572	−0.757918	−0.378959	+	0.925414i	$0.623718\pi$
$140$	0.0762888	0.00644758
$141$	14.7399	1.24133
$142$	−13.2744	−1.11396
$143$	0	0
$144$	2.61572	0.217977
$145$	−5.68344	−0.471984
$146$	1.10230	0.0912269
$147$	2.24076	0.184814
$148$	−0.101394	−0.00833454
$149$	−2.58006	−0.211367	−0.105683	−	0.994400i	$-0.533703\pi$
$149$	−2.58006	−0.211367	−0.105683	+	0.994400i	$0.533703\pi$
$150$	8.52251	0.695860
$151$	−1.75601	−0.142902	−0.0714510	−	0.997444i	$-0.522763\pi$
$151$	−1.75601	−0.142902	−0.0714510	+	0.997444i	$0.522763\pi$
$152$	8.92734	0.724103
$153$	−3.66317	−0.296150
$154$	12.0246	0.968970
$155$	1.01618	0.0816212
$156$	0	0
$157$	−19.0327	−1.51898	−0.759489	−	0.650520i	$-0.774551\pi$
$157$	−19.0327	−1.51898	−0.759489	+	0.650520i	$0.774551\pi$
$158$	−8.59640	−0.683893
$159$	−17.3355	−1.37479
$160$	0.148313	0.0117252
$161$	−11.2847	−0.889359
$162$	9.23576	0.725630
$163$	−7.89713	−0.618551	−0.309275	−	0.950973i	$-0.600086\pi$
$163$	−7.89713	−0.618551	−0.309275	+	0.950973i	$0.600086\pi$
$164$	−0.314529	−0.0245606
$165$	4.56964	0.355746
$166$	12.3834	0.961138
$167$	−6.55351	−0.507126	−0.253563	−	0.967319i	$-0.581602\pi$
$167$	−6.55351	−0.507126	−0.253563	+	0.967319i	$0.581602\pi$
$168$	12.6616	0.976866
$169$	0	0
$170$	7.89364	0.605415
$171$	−2.07814	−0.158919
$172$	0.0909012	0.00693115
$173$	21.5664	1.63966	0.819832	−	0.572604i	$-0.194067\pi$
$173$	21.5664	1.63966	0.819832	+	0.572604i	$0.194067\pi$
$174$	−12.0145	−0.910815
$175$	−11.5434	−0.872600
$176$	11.6116	0.875259
$177$	−19.0960	−1.43534
$178$	−9.25102	−0.693393
$179$	5.03686	0.376472	0.188236	−	0.982124i	$-0.439723\pi$
$179$	5.03686	0.376472	0.188236	+	0.982124i	$0.439723\pi$
$180$	−0.0173730	−0.00129491
$181$	−9.32320	−0.692988	−0.346494	−	0.938052i	$-0.612628\pi$
$181$	−9.32320	−0.692988	−0.346494	+	0.938052i	$0.612628\pi$
$182$	0	0
$183$	8.52445	0.630146
$184$	−11.0396	−0.813849
$185$	−3.99318	−0.293585
$186$	2.14814	0.157509
$187$	−16.2614	−1.18915
$188$	−0.248766	−0.0181431
$189$	−16.2924	−1.18510
$190$	4.47810	0.324876
$191$	10.5572	0.763892	0.381946	−	0.924185i	$-0.375254\pi$
$191$	10.5572	0.763892	0.381946	+	0.924185i	$0.375254\pi$
$192$	12.3846	0.893779
$193$	16.1267	1.16082	0.580411	−	0.814324i	$-0.302892\pi$
$193$	16.1267	1.16082	0.580411	+	0.814324i	$0.302892\pi$
$194$	−9.05326	−0.649986
$195$	0	0
$196$	−0.0378172	−0.00270123
$197$	4.22408	0.300953	0.150477	−	0.988614i	$-0.451919\pi$
$197$	4.22408	0.300953	0.150477	+	0.988614i	$0.451919\pi$
$198$	−2.73832	−0.194604
$199$	−2.01987	−0.143185	−0.0715923	−	0.997434i	$-0.522808\pi$
$199$	−2.01987	−0.143185	−0.0715923	+	0.997434i	$0.522808\pi$
$200$	−11.2927	−0.798513
$201$	6.52025	0.459903
$202$	−25.4772	−1.79257
$203$	16.2732	1.14215
$204$	−0.218094	−0.0152696
$205$	−12.3870	−0.865148
$206$	24.3436	1.69610
$207$	2.56983	0.178615
$208$	0	0
$209$	−9.22519	−0.638120
$210$	6.35129	0.438280
$211$	−24.2401	−1.66876	−0.834379	−	0.551191i	$-0.814174\pi$
$211$	−24.2401	−1.66876	−0.834379	+	0.551191i	$0.814174\pi$
$212$	0.292570	0.0200938
$213$	14.4440	0.989687
$214$	10.8714	0.743156
$215$	3.57995	0.244150
$216$	−15.9385	−1.08448
$217$	−2.90958	−0.197515
$218$	−15.7252	−1.06504
$219$	−1.19942	−0.0810494
$220$	−0.0771217	−0.00519954
$221$	0	0
$222$	−8.44138	−0.566548
$223$	5.61510	0.376015	0.188008	−	0.982168i	$-0.439797\pi$
$223$	5.61510	0.376015	0.188008	+	0.982168i	$0.439797\pi$
$224$	−0.424658	−0.0283737
$225$	2.62875	0.175250
$226$	−20.1057	−1.33741
$227$	−8.69104	−0.576845	−0.288422	−	0.957503i	$-0.593131\pi$
$227$	−8.69104	−0.576845	−0.288422	+	0.957503i	$0.593131\pi$
$228$	−0.123726	−0.00819393
$229$	27.5444	1.82018	0.910092	−	0.414407i	$-0.136011\pi$
$229$	27.5444	1.82018	0.910092	+	0.414407i	$0.136011\pi$
$230$	−5.53764	−0.365141
$231$	−13.0841	−0.860869
$232$	15.9197	1.04518
$233$	13.7931	0.903615	0.451808	−	0.892115i	$-0.350779\pi$
$233$	13.7931	0.903615	0.451808	+	0.892115i	$0.350779\pi$
$234$	0	0
$235$	−9.79709	−0.639092
$236$	0.322283	0.0209788
$237$	9.35382	0.607596
$238$	−22.6016	−1.46504
$239$	−1.37922	−0.0892146	−0.0446073	−	0.999005i	$-0.514204\pi$
$239$	−1.37922	−0.0892146	−0.0446073	+	0.999005i	$0.514204\pi$
$240$	6.13315	0.395893
$241$	27.8626	1.79479	0.897394	−	0.441231i	$-0.145458\pi$
$241$	27.8626	1.79479	0.897394	+	0.441231i	$0.145458\pi$
$242$	3.29980	0.212119
$243$	6.74924	0.432964
$244$	−0.143867	−0.00921014
$245$	−1.48935	−0.0951509
$246$	−26.1855	−1.66953
$247$	0	0
$248$	−2.84638	−0.180745
$249$	−13.4745	−0.853911
$250$	−12.8035	−0.809767
$251$	−5.04891	−0.318685	−0.159342	−	0.987223i	$-0.550937\pi$
$251$	−5.04891	−0.318685	−0.159342	+	0.987223i	$0.550937\pi$
$252$	0.0497435	0.00313354
$253$	11.4079	0.717209
$254$	−25.2614	−1.58504
$255$	−8.58914	−0.537873
$256$	−0.619157	−0.0386973
$257$	21.7141	1.35449	0.677243	−	0.735759i	$-0.263175\pi$
$257$	21.7141	1.35449	0.677243	+	0.735759i	$0.263175\pi$
$258$	7.56781	0.471151
$259$	11.4335	0.710445
$260$	0	0
$261$	−3.70584	−0.229385
$262$	12.0864	0.746698
$263$	21.0672	1.29906	0.649529	−	0.760337i	$-0.274966\pi$
$263$	21.0672	1.29906	0.649529	+	0.760337i	$0.274966\pi$
$264$	−12.7999	−0.787777
$265$	11.5222	0.707805
$266$	−12.8220	−0.786166
$267$	10.0661	0.616036
$268$	−0.110042	−0.00672189
$269$	11.1314	0.678696	0.339348	−	0.940661i	$-0.389794\pi$
$269$	11.1314	0.678696	0.339348	+	0.940661i	$0.389794\pi$
$270$	−7.99503	−0.486562
$271$	−17.2105	−1.04546	−0.522731	−	0.852498i	$-0.675087\pi$
$271$	−17.2105	−1.04546	−0.522731	+	0.852498i	$0.675087\pi$
$272$	−21.8253	−1.32335
$273$	0	0
$274$	−18.9498	−1.14480
$275$	11.6694	0.703694
$276$	0.152999	0.00920949
$277$	−1.64549	−0.0988681	−0.0494340	−	0.998777i	$-0.515742\pi$
$277$	−1.64549	−0.0988681	−0.0494340	+	0.998777i	$0.515742\pi$
$278$	12.5552	0.753013
$279$	0.662589	0.0396681
$280$	−8.41572	−0.502935
$281$	21.4692	1.28075	0.640374	−	0.768064i	$-0.278780\pi$
$281$	21.4692	1.28075	0.640374	+	0.768064i	$0.278780\pi$
$282$	−20.7105	−1.23329
$283$	2.52897	0.150332	0.0751660	−	0.997171i	$-0.476051\pi$
$283$	2.52897	0.150332	0.0751660	+	0.997171i	$0.476051\pi$
$284$	−0.243771	−0.0144652
$285$	−4.87266	−0.288632
$286$	0	0
$287$	35.4673	2.09357
$288$	0.0967061	0.00569846
$289$	13.5652	0.797950
$290$	7.98558	0.468929
$291$	9.85093	0.577472
$292$	0.0202426	0.00118461
$293$	−8.49502	−0.496284	−0.248142	−	0.968724i	$-0.579820\pi$
$293$	−8.49502	−0.496284	−0.248142	+	0.968724i	$0.579820\pi$
$294$	−3.14840	−0.183618
$295$	12.6924	0.738980
$296$	11.1852	0.650125
$297$	16.4703	0.955703
$298$	3.62514	0.209999
$299$	0	0
$300$	0.156507	0.00903594
$301$	−10.2503	−0.590819
$302$	2.46730	0.141977
$303$	27.7220	1.59259
$304$	−12.3816	−0.710134
$305$	−5.66589	−0.324428
$306$	5.14698	0.294233
$307$	−24.6040	−1.40423	−0.702113	−	0.712065i	$-0.747760\pi$
$307$	−24.6040	−1.40423	−0.702113	+	0.712065i	$0.747760\pi$
$308$	0.220820	0.0125824
$309$	−26.4885	−1.50688
$310$	−1.42779	−0.0810930
$311$	8.07331	0.457795	0.228898	−	0.973451i	$-0.426488\pi$
$311$	8.07331	0.457795	0.228898	+	0.973451i	$0.426488\pi$
$312$	0	0
$313$	−14.6297	−0.826922	−0.413461	−	0.910522i	$-0.635680\pi$
$313$	−14.6297	−0.826922	−0.413461	+	0.910522i	$0.635680\pi$
$314$	26.7422	1.50915
$315$	1.95904	0.110379
$316$	−0.157864	−0.00888055
$317$	−6.32778	−0.355403	−0.177702	−	0.984084i	$-0.556866\pi$
$317$	−6.32778	−0.355403	−0.177702	+	0.984084i	$0.556866\pi$
$318$	24.3574	1.36589
$319$	−16.4508	−0.921069
$320$	−8.23156	−0.460158
$321$	−11.8293	−0.660247
$322$	15.8557	0.883604
$323$	17.3398	0.964810
$324$	0.169605	0.00942252
$325$	0	0
$326$	11.0959	0.614548
$327$	17.1107	0.946224
$328$	34.6969	1.91582
$329$	28.0516	1.54654
$330$	−6.42063	−0.353444
$331$	8.95949	0.492458	0.246229	−	0.969212i	$-0.420808\pi$
$331$	8.95949	0.492458	0.246229	+	0.969212i	$0.420808\pi$
$332$	0.227408	0.0124807
$333$	−2.60372	−0.142683
$334$	9.20808	0.503844
$335$	−4.33377	−0.236779
$336$	−17.5608	−0.958021
$337$	19.7375	1.07517	0.537586	−	0.843209i	$-0.319336\pi$
$337$	19.7375	1.07517	0.537586	+	0.843209i	$0.319336\pi$
$338$	0	0
$339$	21.8772	1.18820
$340$	0.144959	0.00786149
$341$	2.94134	0.159283
$342$	2.91991	0.157891
$343$	−16.1027	−0.869461
$344$	−10.0277	−0.540656
$345$	6.02555	0.324405
$346$	−30.3021	−1.62905
$347$	13.0978	0.703127	0.351563	−	0.936164i	$-0.385650\pi$
$347$	13.0978	0.703127	0.351563	+	0.936164i	$0.385650\pi$
$348$	−0.220634	−0.0118272
$349$	7.30002	0.390761	0.195381	−	0.980728i	$-0.437406\pi$
$349$	7.30002	0.390761	0.195381	+	0.980728i	$0.437406\pi$
$350$	16.2192	0.866953
$351$	0	0
$352$	0.429295	0.0228815
$353$	−34.9174	−1.85846	−0.929232	−	0.369497i	$-0.879530\pi$
$353$	−34.9174	−1.85846	−0.929232	+	0.369497i	$0.879530\pi$
$354$	26.8310	1.42605
$355$	−9.60039	−0.509536
$356$	−0.169885	−0.00900391
$357$	24.5930	1.30160
$358$	−7.07709	−0.374036
$359$	−11.6905	−0.617002	−0.308501	−	0.951224i	$-0.599827\pi$
$359$	−11.6905	−0.617002	−0.308501	+	0.951224i	$0.599827\pi$
$360$	1.91648	0.101008
$361$	−9.16307	−0.482267
$362$	13.0997	0.688503
$363$	−3.59054	−0.188454
$364$	0	0
$365$	0.797211	0.0417279
$366$	−11.9774	−0.626068
$367$	19.0286	0.993286	0.496643	−	0.867955i	$-0.334566\pi$
$367$	19.0286	0.993286	0.496643	+	0.867955i	$0.334566\pi$
$368$	15.3111	0.798149
$369$	−8.07686	−0.420465
$370$	5.61067	0.291685
$371$	−32.9912	−1.71282
$372$	0.0394484	0.00204531
$373$	8.09393	0.419088	0.209544	−	0.977799i	$-0.432802\pi$
$373$	8.09393	0.419088	0.209544	+	0.977799i	$0.432802\pi$
$374$	22.8483	1.18146
$375$	13.9316	0.719427
$376$	27.4423	1.41523
$377$	0	0
$378$	22.8918	1.17743
$379$	8.82330	0.453222	0.226611	−	0.973985i	$-0.427235\pi$
$379$	8.82330	0.453222	0.226611	+	0.973985i	$0.427235\pi$
$380$	0.0822358	0.00421861
$381$	27.4871	1.40821
$382$	−14.8335	−0.758948
$383$	36.6362	1.87202	0.936010	−	0.351973i	$-0.114489\pi$
$383$	36.6362	1.87202	0.936010	+	0.351973i	$0.114489\pi$
$384$	−16.9548	−0.865221
$385$	8.69650	0.443215
$386$	−22.6589	−1.15331
$387$	2.33427	0.118658
$388$	−0.166254	−0.00844026
$389$	7.70656	0.390738	0.195369	−	0.980730i	$-0.437410\pi$
$389$	7.70656	0.390738	0.195369	+	0.980730i	$0.437410\pi$
$390$	0	0
$391$	−21.4424	−1.08439
$392$	4.17176	0.210706
$393$	−13.1513	−0.663394
$394$	−5.93509	−0.299006
$395$	−6.21714	−0.312818
$396$	−0.0502865	−0.00252699
$397$	8.55515	0.429371	0.214685	−	0.976683i	$-0.431127\pi$
$397$	8.55515	0.429371	0.214685	+	0.976683i	$0.431127\pi$
$398$	2.83804	0.142258
$399$	13.9517	0.698459
$400$	15.6622	0.783108
$401$	2.11758	0.105747	0.0528734	−	0.998601i	$-0.483162\pi$
$401$	2.11758	0.105747	0.0528734	+	0.998601i	$0.483162\pi$
$402$	−9.16135	−0.456926
$403$	0	0
$404$	−0.467863	−0.0232771
$405$	6.67954	0.331909
$406$	−22.8648	−1.13476
$407$	−11.5584	−0.572926
$408$	24.0588	1.19109
$409$	4.47719	0.221383	0.110691	−	0.993855i	$-0.464694\pi$
$409$	4.47719	0.221383	0.110691	+	0.993855i	$0.464694\pi$
$410$	17.4046	0.859550
$411$	20.6194	1.01708
$412$	0.447046	0.0220244
$413$	−36.3416	−1.78826
$414$	−3.61077	−0.177460
$415$	8.95599	0.439632
$416$	0	0
$417$	−13.6615	−0.669004
$418$	12.9620	0.633990
$419$	34.4369	1.68235	0.841176	−	0.540761i	$-0.181864\pi$
$419$	34.4369	1.68235	0.841176	+	0.540761i	$0.181864\pi$
$420$	0.116635	0.00569120
$421$	−33.7742	−1.64605	−0.823027	−	0.568002i	$-0.807717\pi$
$421$	−33.7742	−1.64605	−0.823027	+	0.568002i	$0.807717\pi$
$422$	34.0589	1.65796
$423$	−6.38811	−0.310600
$424$	−32.2745	−1.56739
$425$	−21.9340	−1.06396
$426$	−20.2947	−0.983282
$427$	16.2229	0.785082
$428$	0.199643	0.00965010
$429$	0	0
$430$	−5.03004	−0.242570
$431$	−17.7153	−0.853318	−0.426659	−	0.904413i	$-0.640310\pi$
$431$	−17.7153	−0.853318	−0.426659	+	0.904413i	$0.640310\pi$
$432$	22.1056	1.06356
$433$	4.59958	0.221042	0.110521	−	0.993874i	$-0.464748\pi$
$433$	4.59958	0.221042	0.110521	+	0.993874i	$0.464748\pi$
$434$	4.08813	0.196237
$435$	−8.68918	−0.416614
$436$	−0.288777	−0.0138299
$437$	−12.1644	−0.581901
$438$	1.68526	0.0805249
$439$	25.5577	1.21980	0.609900	−	0.792478i	$-0.291209\pi$
$439$	25.5577	1.21980	0.609900	+	0.792478i	$0.291209\pi$
$440$	8.50760	0.405584
$441$	−0.971115	−0.0462436
$442$	0	0
$443$	24.7736	1.17703	0.588515	−	0.808486i	$-0.299713\pi$
$443$	24.7736	1.17703	0.588515	+	0.808486i	$0.299713\pi$
$444$	−0.155017	−0.00735679
$445$	−6.69057	−0.317163
$446$	−7.88956	−0.373582
$447$	−3.94455	−0.186571
$448$	23.5691	1.11354
$449$	38.0058	1.79360	0.896801	−	0.442433i	$-0.145885\pi$
$449$	38.0058	1.79360	0.896801	+	0.442433i	$0.145885\pi$
$450$	−3.69355	−0.174116
$451$	−35.8545	−1.68832
$452$	−0.369220	−0.0173667
$453$	−2.68469	−0.126138
$454$	12.2114	0.573111
$455$	0	0
$456$	13.6487	0.639157
$457$	−0.690146	−0.0322837	−0.0161418	−	0.999870i	$-0.505138\pi$
$457$	−0.690146	−0.0322837	−0.0161418	+	0.999870i	$0.505138\pi$
$458$	−38.7015	−1.80840
$459$	−30.9577	−1.44498
$460$	−0.101693	−0.00474146
$461$	3.50495	0.163242	0.0816210	−	0.996663i	$-0.473990\pi$
$461$	3.50495	0.163242	0.0816210	+	0.996663i	$0.473990\pi$
$462$	18.3839	0.855298
$463$	11.0533	0.513691	0.256845	−	0.966453i	$-0.417317\pi$
$463$	11.0533	0.513691	0.256845	+	0.966453i	$0.417317\pi$
$464$	−22.0795	−1.02502
$465$	1.55359	0.0720460
$466$	−19.3801	−0.897768
$467$	13.4125	0.620655	0.310328	−	0.950630i	$-0.399561\pi$
$467$	13.4125	0.620655	0.310328	+	0.950630i	$0.399561\pi$
$468$	0	0
$469$	12.4087	0.572981
$470$	13.7655	0.634956
$471$	−29.0984	−1.34078
$472$	−35.5523	−1.63643
$473$	10.3622	0.476456
$474$	−13.1427	−0.603664
$475$	−12.4433	−0.570936
$476$	−0.415055	−0.0190240
$477$	7.51297	0.343995
$478$	1.93790	0.0886373
$479$	−9.11526	−0.416487	−0.208243	−	0.978077i	$-0.566775\pi$
$479$	−9.11526	−0.416487	−0.208243	+	0.978077i	$0.566775\pi$
$480$	0.226750	0.0103497
$481$	0	0
$482$	−39.1487	−1.78317
$483$	−17.2527	−0.785026
$484$	0.0605974	0.00275443
$485$	−6.54755	−0.297309
$486$	−9.48309	−0.430162
$487$	7.68894	0.348419	0.174210	−	0.984709i	$-0.444263\pi$
$487$	7.68894	0.348419	0.174210	+	0.984709i	$0.444263\pi$
$488$	15.8705	0.718425
$489$	−12.0736	−0.545987
$490$	2.09262	0.0945351
$491$	−2.30951	−0.104227	−0.0521134	−	0.998641i	$-0.516596\pi$
$491$	−2.30951	−0.104227	−0.0521134	+	0.998641i	$0.516596\pi$
$492$	−0.480871	−0.0216793
$493$	30.9211	1.39262
$494$	0	0
$495$	−1.98043	−0.0890135
$496$	3.94773	0.177258
$497$	27.4884	1.23302
$498$	18.9325	0.848384
$499$	−16.9769	−0.759992	−0.379996	−	0.924988i	$-0.624075\pi$
$499$	−16.9769	−0.759992	−0.379996	+	0.924988i	$0.624075\pi$
$500$	−0.235124	−0.0105151
$501$	−10.0194	−0.447633
$502$	7.09403	0.316622
$503$	9.24502	0.412215	0.206108	−	0.978529i	$-0.433920\pi$
$503$	9.24502	0.412215	0.206108	+	0.978529i	$0.433920\pi$
$504$	−5.48740	−0.244428
$505$	−18.4258	−0.819936
$506$	−16.0288	−0.712567
$507$	0	0
$508$	−0.463899	−0.0205822
$509$	1.38544	0.0614086	0.0307043	−	0.999529i	$-0.490225\pi$
$509$	1.38544	0.0614086	0.0307043	+	0.999529i	$0.490225\pi$
$510$	12.0683	0.534392
$511$	−2.28262	−0.100977
$512$	23.0496	1.01866
$513$	−17.5625	−0.775402
$514$	−30.5096	−1.34572
$515$	17.6059	0.775810
$516$	0.138975	0.00611804
$517$	−28.3579	−1.24718
$518$	−16.0648	−0.705847
$519$	32.9720	1.44731
$520$	0	0
$521$	5.80992	0.254537	0.127268	−	0.991868i	$-0.459379\pi$
$521$	5.80992	0.254537	0.127268	+	0.991868i	$0.459379\pi$
$522$	5.20693	0.227901
$523$	−2.01451	−0.0880885	−0.0440443	−	0.999030i	$-0.514024\pi$
$523$	−2.01451	−0.0880885	−0.0440443	+	0.999030i	$0.514024\pi$
$524$	0.221954	0.00969610
$525$	−17.6483	−0.770233
$526$	−29.6007	−1.29065
$527$	−5.52858	−0.240829
$528$	17.7525	0.772580
$529$	−7.95748	−0.345977
$530$	−16.1894	−0.703225
$531$	8.27597	0.359146
$532$	−0.235463	−0.0102086
$533$	0	0
$534$	−14.1435	−0.612049
$535$	7.86250	0.339926
$536$	12.1392	0.524332
$537$	7.70065	0.332307
$538$	−15.6404	−0.674304
$539$	−4.31094	−0.185685
$540$	−0.146821	−0.00631815
$541$	21.4836	0.923652	0.461826	−	0.886971i	$-0.347194\pi$
$541$	21.4836	0.923652	0.461826	+	0.886971i	$0.347194\pi$
$542$	24.1818	1.03870
$543$	−14.2539	−0.611692
$544$	−0.806906	−0.0345958
$545$	−11.3729	−0.487160
$546$	0	0
$547$	7.77420	0.332401	0.166200	−	0.986092i	$-0.446850\pi$
$547$	7.77420	0.332401	0.166200	+	0.986092i	$0.446850\pi$
$548$	−0.347993	−0.0148655
$549$	−3.69439	−0.157673
$550$	−16.3963	−0.699140
$551$	17.5417	0.747302
$552$	−16.8780	−0.718374
$553$	17.8013	0.756987
$554$	2.31202	0.0982282
$555$	−6.10502	−0.259144
$556$	0.230564	0.00977809
$557$	−8.44764	−0.357938	−0.178969	−	0.983855i	$-0.557276\pi$
$557$	−8.44764	−0.357938	−0.178969	+	0.983855i	$0.557276\pi$
$558$	−0.930978	−0.0394114
$559$	0	0
$560$	11.6720	0.493233
$561$	−24.8614	−1.04965
$562$	−30.1656	−1.27246
$563$	35.3836	1.49124	0.745620	−	0.666371i	$-0.232153\pi$
$563$	35.3836	1.49124	0.745620	+	0.666371i	$0.232153\pi$
$564$	−0.380328	−0.0160147
$565$	−14.5409	−0.611742
$566$	−3.55336	−0.149359
$567$	−19.1253	−0.803185
$568$	26.8913	1.12834
$569$	20.3682	0.853881	0.426940	−	0.904280i	$-0.359591\pi$
$569$	20.3682	0.853881	0.426940	+	0.904280i	$0.359591\pi$
$570$	6.84639	0.286764
$571$	−18.7808	−0.785951	−0.392976	−	0.919549i	$-0.628554\pi$
$571$	−18.7808	−0.785951	−0.392976	+	0.919549i	$0.628554\pi$
$572$	0	0
$573$	16.1405	0.674278
$574$	−49.8338	−2.08002
$575$	15.3874	0.641698
$576$	−5.36732	−0.223638
$577$	33.7171	1.40366	0.701830	−	0.712345i	$-0.252367\pi$
$577$	33.7171	1.40366	0.701830	+	0.712345i	$0.252367\pi$
$578$	−19.0599	−0.792786
$579$	24.6554	1.02464
$580$	0.146647	0.00608918
$581$	−25.6433	−1.06386
$582$	−13.8412	−0.573735
$583$	33.3513	1.38127
$584$	−2.23304	−0.0924039
$585$	0	0
$586$	11.9360	0.493072
$587$	33.1106	1.36662	0.683310	−	0.730129i	$-0.260540\pi$
$587$	33.1106	1.36662	0.683310	+	0.730129i	$0.260540\pi$
$588$	−0.0578171	−0.00238434
$589$	−3.13639	−0.129233
$590$	−17.8336	−0.734198
$591$	6.45803	0.265648
$592$	−15.5131	−0.637583
$593$	−30.7925	−1.26449	−0.632247	−	0.774767i	$-0.717867\pi$
$593$	−30.7925	−1.26449	−0.632247	+	0.774767i	$0.717867\pi$
$594$	−23.1418	−0.949518
$595$	−16.3460	−0.670122
$596$	0.0665721	0.00272690
$597$	−3.08809	−0.126387
$598$	0	0
$599$	3.80719	0.155558	0.0777788	−	0.996971i	$-0.475217\pi$
$599$	3.80719	0.155558	0.0777788	+	0.996971i	$0.475217\pi$
$600$	−17.2649	−0.704837
$601$	7.77021	0.316954	0.158477	−	0.987363i	$-0.449342\pi$
$601$	7.77021	0.316954	0.158477	+	0.987363i	$0.449342\pi$
$602$	14.4023	0.586995
$603$	−2.82579	−0.115075
$604$	0.0453094	0.00184361
$605$	2.38650	0.0970249
$606$	−38.9511	−1.58228
$607$	−15.3747	−0.624042	−0.312021	−	0.950075i	$-0.601006\pi$
$607$	−15.3747	−0.624042	−0.312021	+	0.950075i	$0.601006\pi$
$608$	−0.457762	−0.0185647
$609$	24.8794	1.00816
$610$	7.96092	0.322328
$611$	0	0
$612$	0.0945191	0.00382071
$613$	−37.2449	−1.50431	−0.752154	−	0.658987i	$-0.770985\pi$
$613$	−37.2449	−1.50431	−0.752154	+	0.658987i	$0.770985\pi$
$614$	34.5702	1.39514
$615$	−18.9380	−0.763656
$616$	−24.3595	−0.981471
$617$	−12.2249	−0.492154	−0.246077	−	0.969250i	$-0.579142\pi$
$617$	−12.2249	−0.492154	−0.246077	+	0.969250i	$0.579142\pi$
$618$	37.2180	1.49713
$619$	35.0566	1.40904	0.704521	−	0.709683i	$-0.251162\pi$
$619$	35.0566	1.40904	0.704521	+	0.709683i	$0.251162\pi$
$620$	−0.0262199	−0.00105302
$621$	21.7178	0.871506
$622$	−11.3435	−0.454832
$623$	19.1568	0.767503
$624$	0	0
$625$	10.5771	0.423083
$626$	20.5557	0.821571
$627$	−14.1040	−0.563260
$628$	0.491093	0.0195967
$629$	21.7252	0.866240
$630$	−2.75257	−0.109665
$631$	7.46467	0.297164	0.148582	−	0.988900i	$-0.452529\pi$
$631$	7.46467	0.297164	0.148582	+	0.988900i	$0.452529\pi$
$632$	17.4146	0.692716
$633$	−37.0597	−1.47299
$634$	8.89092	0.353103
$635$	−18.2697	−0.725009
$636$	0.447298	0.0177365
$637$	0	0
$638$	23.1144	0.915108
$639$	−6.25985	−0.247636
$640$	11.2692	0.445455
$641$	−35.1991	−1.39028	−0.695141	−	0.718873i	$-0.744658\pi$
$641$	−35.1991	−1.39028	−0.695141	+	0.718873i	$0.744658\pi$
$642$	16.6209	0.655975
$643$	20.9264	0.825257	0.412628	−	0.910899i	$-0.364611\pi$
$643$	20.9264	0.825257	0.412628	+	0.910899i	$0.364611\pi$
$644$	0.291174	0.0114739
$645$	5.47323	0.215508
$646$	−24.3634	−0.958567
$647$	−48.3523	−1.90092	−0.950462	−	0.310841i	$-0.899389\pi$
$647$	−48.3523	−1.90092	−0.950462	+	0.310841i	$0.899389\pi$
$648$	−18.7098	−0.734992
$649$	36.7384	1.44211
$650$	0	0
$651$	−4.44833	−0.174344
$652$	0.203766	0.00798008
$653$	−13.8535	−0.542127	−0.271064	−	0.962561i	$-0.587375\pi$
$653$	−13.8535	−0.542127	−0.271064	+	0.962561i	$0.587375\pi$
$654$	−24.0416	−0.940101
$655$	8.74117	0.341546
$656$	−48.1223	−1.87886
$657$	0.519814	0.0202799
$658$	−39.4143	−1.53653
$659$	24.2242	0.943639	0.471820	−	0.881695i	$-0.343597\pi$
$659$	24.2242	0.943639	0.471820	+	0.881695i	$0.343597\pi$
$660$	−0.117908	−0.00458957
$661$	−22.2852	−0.866795	−0.433397	−	0.901203i	$-0.642685\pi$
$661$	−22.2852	−0.866795	−0.433397	+	0.901203i	$0.642685\pi$
$662$	−12.5886	−0.489271
$663$	0	0
$664$	−25.0863	−0.973538
$665$	−9.27318	−0.359599
$666$	3.65839	0.141760
$667$	−21.6921	−0.839923
$668$	0.169097	0.00654256
$669$	8.58470	0.331904
$670$	6.08921	0.235247
$671$	−16.4000	−0.633116
$672$	−0.649243	−0.0250451
$673$	−20.4711	−0.789103	−0.394552	−	0.918874i	$-0.629100\pi$
$673$	−20.4711	−0.789103	−0.394552	+	0.918874i	$0.629100\pi$
$674$	−27.7325	−1.06821
$675$	22.2157	0.855083
$676$	0	0
$677$	−2.15024	−0.0826404	−0.0413202	−	0.999146i	$-0.513156\pi$
$677$	−2.15024	−0.0826404	−0.0413202	+	0.999146i	$0.513156\pi$
$678$	−30.7388	−1.18052
$679$	18.7473	0.719457
$680$	−15.9910	−0.613226
$681$	−13.2874	−0.509173
$682$	−4.13277	−0.158252
$683$	−38.4682	−1.47194	−0.735971	−	0.677013i	$-0.763274\pi$
$683$	−38.4682	−1.47194	−0.735971	+	0.677013i	$0.763274\pi$
$684$	0.0536211	0.00205026
$685$	−13.7050	−0.523640
$686$	22.6252	0.863835
$687$	42.1115	1.60665
$688$	13.9077	0.530226
$689$	0	0
$690$	−8.46627	−0.322305
$691$	17.9832	0.684112	0.342056	−	0.939679i	$-0.388877\pi$
$691$	17.9832	0.684112	0.342056	+	0.939679i	$0.388877\pi$
$692$	−0.556468	−0.0211537
$693$	5.67047	0.215404
$694$	−18.4032	−0.698576
$695$	9.08026	0.344434
$696$	24.3390	0.922566
$697$	67.3926	2.55267
$698$	−10.2570	−0.388232
$699$	21.0877	0.797610
$700$	0.297849	0.0112576
$701$	−23.3608	−0.882327	−0.441164	−	0.897427i	$-0.645434\pi$
$701$	−23.3608	−0.882327	−0.441164	+	0.897427i	$0.645434\pi$
$702$	0	0
$703$	12.3248	0.464839
$704$	−23.8264	−0.897992
$705$	−14.9784	−0.564118
$706$	49.0610	1.84644
$707$	52.7578	1.98416
$708$	0.492725	0.0185177
$709$	−33.1442	−1.24476	−0.622378	−	0.782717i	$-0.713833\pi$
$709$	−33.1442	−1.24476	−0.622378	+	0.782717i	$0.713833\pi$
$710$	13.4891	0.506239
$711$	−4.05383	−0.152030
$712$	18.7407	0.702339
$713$	3.87847	0.145250
$714$	−34.5546	−1.29317
$715$	0	0
$716$	−0.129964	−0.00485697
$717$	−2.10864	−0.0787486
$718$	16.4259	0.613009
$719$	16.8313	0.627700	0.313850	−	0.949473i	$-0.398381\pi$
$719$	16.8313	0.627700	0.313850	+	0.949473i	$0.398381\pi$
$720$	−2.65803	−0.0990590
$721$	−50.4104	−1.87738
$722$	12.8747	0.479146
$723$	42.5980	1.58424
$724$	0.240562	0.00894042
$725$	−22.1895	−0.824096
$726$	5.04493	0.187235
$727$	−14.8322	−0.550095	−0.275047	−	0.961431i	$-0.588694\pi$
$727$	−14.8322	−0.550095	−0.275047	+	0.961431i	$0.588694\pi$
$728$	0	0
$729$	30.0383	1.11253
$730$	−1.12013	−0.0414579
$731$	−19.4769	−0.720381
$732$	−0.219952	−0.00812967
$733$	31.6000	1.16717	0.583587	−	0.812050i	$-0.301649\pi$
$733$	31.6000	1.16717	0.583587	+	0.812050i	$0.301649\pi$
$734$	−26.7364	−0.986858
$735$	−2.27700	−0.0839885
$736$	0.566070	0.0208656
$737$	−12.5442	−0.462070
$738$	11.3485	0.417744
$739$	−18.2260	−0.670453	−0.335226	−	0.942138i	$-0.608813\pi$
$739$	−18.2260	−0.670453	−0.335226	+	0.942138i	$0.608813\pi$
$740$	0.103034	0.00378761
$741$	0	0
$742$	46.3546	1.70173
$743$	36.3278	1.33274	0.666369	−	0.745622i	$-0.267848\pi$
$743$	36.3278	1.33274	0.666369	+	0.745622i	$0.267848\pi$
$744$	−4.35171	−0.159541
$745$	2.62180	0.0960552
$746$	−11.3725	−0.416375
$747$	5.83967	0.213662
$748$	0.419586	0.0153416
$749$	−22.5124	−0.822585
$750$	−19.5748	−0.714771
$751$	−14.5974	−0.532667	−0.266333	−	0.963881i	$-0.585812\pi$
$751$	−14.5974	−0.532667	−0.266333	+	0.963881i	$0.585812\pi$
$752$	−38.0606	−1.38793
$753$	−7.71908	−0.281299
$754$	0	0
$755$	1.78441	0.0649415
$756$	0.420385	0.0152893
$757$	21.1706	0.769457	0.384728	−	0.923030i	$-0.374295\pi$
$757$	21.1706	0.769457	0.384728	+	0.923030i	$0.374295\pi$
$758$	−12.3973	−0.450289
$759$	17.4411	0.633071
$760$	−9.07175	−0.329067
$761$	−11.2052	−0.406188	−0.203094	−	0.979159i	$-0.565100\pi$
$761$	−11.2052	−0.406188	−0.203094	+	0.979159i	$0.565100\pi$
$762$	−38.6211	−1.39909
$763$	32.5634	1.17888
$764$	−0.272402	−0.00985516
$765$	3.72243	0.134585
$766$	−51.4760	−1.85991
$767$	0	0
$768$	−0.946604	−0.0341576
$769$	31.9705	1.15289	0.576444	−	0.817137i	$-0.304440\pi$
$769$	31.9705	1.15289	0.576444	+	0.817137i	$0.304440\pi$
$770$	−12.2191	−0.440346
$771$	33.1978	1.19559
$772$	−0.416108	−0.0149761
$773$	11.6707	0.419767	0.209884	−	0.977726i	$-0.432691\pi$
$773$	11.6707	0.419767	0.209884	+	0.977726i	$0.432691\pi$
$774$	−3.27980	−0.117890
$775$	3.96739	0.142513
$776$	18.3401	0.658372
$777$	17.4803	0.627101
$778$	−10.8282	−0.388210
$779$	38.2321	1.36981
$780$	0	0
$781$	−27.7885	−0.994352
$782$	30.1279	1.07737
$783$	−31.3183	−1.11922
$784$	−5.78594	−0.206641
$785$	19.3406	0.690296
$786$	18.4784	0.659101
$787$	9.35234	0.333375	0.166687	−	0.986010i	$-0.446693\pi$
$787$	9.35234	0.333375	0.166687	+	0.986010i	$0.446693\pi$
$788$	−0.108992	−0.00388268
$789$	32.2088	1.14666
$790$	8.73546	0.310794
$791$	41.6345	1.48035
$792$	5.54730	0.197115
$793$	0	0
$794$	−12.0205	−0.426592
$795$	17.6159	0.624771
$796$	0.0521177	0.00184726
$797$	3.91090	0.138531	0.0692656	−	0.997598i	$-0.477934\pi$
$797$	3.91090	0.138531	0.0692656	+	0.997598i	$0.477934\pi$
$798$	−19.6030	−0.693939
$799$	53.3018	1.88568
$800$	0.579048	0.0204724
$801$	−4.36253	−0.154142
$802$	−2.97533	−0.105063
$803$	2.30754	0.0814314
$804$	−0.168239	−0.00593332
$805$	11.4672	0.404167
$806$	0	0
$807$	17.0184	0.599077
$808$	51.6118	1.81570
$809$	−23.7735	−0.835833	−0.417917	−	0.908485i	$-0.637240\pi$
$809$	−23.7735	−0.835833	−0.417917	+	0.908485i	$0.637240\pi$
$810$	−9.38516	−0.329761
$811$	42.9117	1.50683	0.753417	−	0.657543i	$-0.228404\pi$
$811$	42.9117	1.50683	0.753417	+	0.657543i	$0.228404\pi$
$812$	−0.419889	−0.0147352
$813$	−26.3124	−0.922816
$814$	16.2402	0.569219
$815$	8.02487	0.281099
$816$	−33.3679	−1.16811
$817$	−11.0494	−0.386568
$818$	−6.29072	−0.219950
$819$	0	0
$820$	0.319617	0.0111615
$821$	26.4026	0.921455	0.460728	−	0.887542i	$-0.347588\pi$
$821$	26.4026	0.921455	0.460728	+	0.887542i	$0.347588\pi$
$822$	−28.9716	−1.01050
$823$	40.1436	1.39932	0.699660	−	0.714476i	$-0.253335\pi$
$823$	40.1436	1.39932	0.699660	+	0.714476i	$0.253335\pi$
$824$	−49.3154	−1.71798
$825$	17.8409	0.621142
$826$	51.0622	1.77668
$827$	3.59807	0.125117	0.0625585	−	0.998041i	$-0.480074\pi$
$827$	3.59807	0.125117	0.0625585	+	0.998041i	$0.480074\pi$
$828$	−0.0663081	−0.00230436
$829$	37.0408	1.28648	0.643240	−	0.765665i	$-0.277590\pi$
$829$	37.0408	1.28648	0.643240	+	0.765665i	$0.277590\pi$
$830$	−12.5837	−0.436787
$831$	−2.51573	−0.0872696
$832$	0	0
$833$	8.10289	0.280749
$834$	19.1952	0.664675
$835$	6.65952	0.230462
$836$	0.238033	0.00823255
$837$	5.59958	0.193550
$838$	−48.3860	−1.67146
$839$	5.11651	0.176641	0.0883207	−	0.996092i	$-0.471850\pi$
$839$	5.11651	0.176641	0.0883207	+	0.996092i	$0.471850\pi$
$840$	−12.8665	−0.443935
$841$	2.28125	0.0786639
$842$	47.4549	1.63540
$843$	32.8234	1.13050
$844$	0.625456	0.0215291
$845$	0	0
$846$	8.97568	0.308590
$847$	−6.83316	−0.234790
$848$	44.7626	1.53715
$849$	3.86645	0.132696
$850$	30.8186	1.05707
$851$	−15.2409	−0.522451
$852$	−0.372692	−0.0127682
$853$	18.5310	0.634489	0.317244	−	0.948344i	$-0.397242\pi$
$853$	18.5310	0.634489	0.317244	+	0.948344i	$0.397242\pi$
$854$	−22.7942	−0.780001
$855$	2.11175	0.0722204
$856$	−22.0234	−0.752744
$857$	−29.0052	−0.990799	−0.495399	−	0.868665i	$-0.664978\pi$
$857$	−29.0052	−0.990799	−0.495399	+	0.868665i	$0.664978\pi$
$858$	0	0
$859$	−37.6122	−1.28331	−0.641656	−	0.766993i	$-0.721752\pi$
$859$	−37.6122	−1.28331	−0.641656	+	0.766993i	$0.721752\pi$
$860$	−0.0923716	−0.00314985
$861$	54.2246	1.84797
$862$	24.8911	0.847796
$863$	6.95953	0.236905	0.118453	−	0.992960i	$-0.462207\pi$
$863$	6.95953	0.236905	0.118453	+	0.992960i	$0.462207\pi$
$864$	0.817270	0.0278041
$865$	−21.9153	−0.745142
$866$	−6.46269	−0.219611
$867$	20.7392	0.704341
$868$	0.0750744	0.00254819
$869$	−17.9956	−0.610460
$870$	12.2088	0.413918
$871$	0	0
$872$	31.8561	1.07878
$873$	−4.26927	−0.144493
$874$	17.0917	0.578136
$875$	26.5134	0.896315
$876$	0.0309481	0.00104564
$877$	−16.1474	−0.545259	−0.272629	−	0.962119i	$-0.587893\pi$
$877$	−16.1474	−0.545259	−0.272629	+	0.962119i	$0.587893\pi$
$878$	−35.9101	−1.21191
$879$	−12.9877	−0.438064
$880$	−11.7995	−0.397759
$881$	−57.8312	−1.94838	−0.974191	−	0.225723i	$-0.927525\pi$
$881$	−57.8312	−1.94838	−0.974191	+	0.225723i	$0.927525\pi$
$882$	1.36448	0.0459443
$883$	−35.2033	−1.18468	−0.592342	−	0.805686i	$-0.701797\pi$
$883$	−35.2033	−1.18468	−0.592342	+	0.805686i	$0.701797\pi$
$884$	0	0
$885$	19.4049	0.652288
$886$	−34.8085	−1.16941
$887$	−9.93969	−0.333742	−0.166871	−	0.985979i	$-0.553366\pi$
$887$	−9.93969	−0.333742	−0.166871	+	0.985979i	$0.553366\pi$
$888$	17.1006	0.573857
$889$	52.3108	1.75445
$890$	9.40066	0.315111
$891$	19.3341	0.647715
$892$	−0.144884	−0.00485107
$893$	30.2383	1.01189
$894$	5.54233	0.185363
$895$	−5.11833	−0.171087
$896$	−32.2667	−1.07796
$897$	0	0
$898$	−53.4004	−1.78200
$899$	−5.59296	−0.186536
$900$	−0.0678282	−0.00226094
$901$	−62.6875	−2.08842
$902$	50.3778	1.67740
$903$	−15.6713	−0.521508
$904$	40.7302	1.35466
$905$	9.47401	0.314927
$906$	3.77215	0.125321
$907$	−38.5077	−1.27863	−0.639314	−	0.768946i	$-0.720782\pi$
$907$	−38.5077	−1.27863	−0.639314	+	0.768946i	$0.720782\pi$
$908$	0.224251	0.00744202
$909$	−12.0144	−0.398491
$910$	0	0
$911$	26.1703	0.867061	0.433531	−	0.901139i	$-0.357268\pi$
$911$	26.1703	0.867061	0.433531	+	0.901139i	$0.357268\pi$
$912$	−18.9297	−0.626827
$913$	25.9233	0.857935
$914$	0.969697	0.0320747
$915$	−8.66235	−0.286368
$916$	−0.710714	−0.0234827
$917$	−25.0282	−0.826505
$918$	43.4975	1.43563
$919$	−41.2705	−1.36139	−0.680694	−	0.732568i	$-0.738321\pi$
$919$	−41.2705	−1.36139	−0.680694	+	0.732568i	$0.738321\pi$
$920$	11.2182	0.369852
$921$	−37.6161	−1.23949
$922$	−4.92467	−0.162185
$923$	0	0
$924$	0.337602	0.0111063
$925$	−15.5903	−0.512606
$926$	−15.5306	−0.510366
$927$	11.4798	0.377046
$928$	−0.816304	−0.0267965
$929$	−8.54363	−0.280307	−0.140154	−	0.990130i	$-0.544760\pi$
$929$	−8.54363	−0.280307	−0.140154	+	0.990130i	$0.544760\pi$
$930$	−2.18289	−0.0715798
$931$	4.59681	0.150654
$932$	−0.355896	−0.0116578
$933$	12.3429	0.404090
$934$	−18.8454	−0.616639
$935$	16.5245	0.540408
$936$	0	0
$937$	−9.82051	−0.320822	−0.160411	−	0.987050i	$-0.551282\pi$
$937$	−9.82051	−0.320822	−0.160411	+	0.987050i	$0.551282\pi$
$938$	−17.4350	−0.569272
$939$	−22.3668	−0.729914
$940$	0.252790	0.00824509
$941$	6.99443	0.228012	0.114006	−	0.993480i	$-0.463632\pi$
$941$	6.99443	0.228012	0.114006	+	0.993480i	$0.463632\pi$
$942$	40.8850	1.33211
$943$	−47.2780	−1.53958
$944$	49.3085	1.60486
$945$	16.5560	0.538566
$946$	−14.5596	−0.473372
$947$	2.07373	0.0673872	0.0336936	−	0.999432i	$-0.489273\pi$
$947$	2.07373	0.0673872	0.0336936	+	0.999432i	$0.489273\pi$
$948$	−0.241352	−0.00783875
$949$	0	0
$950$	17.4836	0.567241
$951$	−9.67428	−0.313710
$952$	45.7863	1.48394
$953$	−5.68472	−0.184146	−0.0920730	−	0.995752i	$-0.529349\pi$
$953$	−5.68472	−0.184146	−0.0920730	+	0.995752i	$0.529349\pi$
$954$	−10.5562	−0.341769
$955$	−10.7280	−0.347149
$956$	0.0355875	0.00115098
$957$	−25.1510	−0.813016
$958$	12.8075	0.413791
$959$	39.2409	1.26715
$960$	−12.5849	−0.406176
$961$	1.00000	0.0322581
$962$	0	0
$963$	5.12667	0.165205
$964$	−0.718925	−0.0231550
$965$	−16.3875	−0.527533
$966$	24.2411	0.779946
$967$	−60.0678	−1.93165	−0.965826	−	0.259193i	$-0.916543\pi$
$967$	−60.0678	−1.93165	−0.965826	+	0.259193i	$0.916543\pi$
$968$	−6.68474	−0.214856
$969$	26.5101	0.851626
$970$	9.19971	0.295385
$971$	15.2770	0.490263	0.245132	−	0.969490i	$-0.421169\pi$
$971$	15.2770	0.490263	0.245132	+	0.969490i	$0.421169\pi$
$972$	−0.174147	−0.00558578
$973$	−25.9992	−0.833495
$974$	−10.8034	−0.346164
$975$	0	0
$976$	−22.0113	−0.704566
$977$	−18.3389	−0.586715	−0.293357	−	0.956003i	$-0.594773\pi$
$977$	−18.3389	−0.586715	−0.293357	+	0.956003i	$0.594773\pi$
$978$	16.9641	0.542454
$979$	−19.3660	−0.618940
$980$	0.0384289	0.00122757
$981$	−7.41557	−0.236761
$982$	3.24501	0.103552
$983$	11.3039	0.360538	0.180269	−	0.983617i	$-0.442303\pi$
$983$	11.3039	0.360538	0.180269	+	0.983617i	$0.442303\pi$
$984$	53.0467	1.69107
$985$	−4.29241	−0.136768
$986$	−43.4461	−1.38361
$987$	42.8870	1.36511
$988$	0	0
$989$	13.6637	0.434480
$990$	2.78262	0.0884375
$991$	−9.29869	−0.295383	−0.147691	−	0.989033i	$-0.547184\pi$
$991$	−9.29869	−0.295383	−0.147691	+	0.989033i	$0.547184\pi$
$992$	0.145952	0.00463398
$993$	13.6978	0.434686
$994$	−38.6229	−1.22505
$995$	2.05254	0.0650699
$996$	0.347676	0.0110165
$997$	−14.4171	−0.456594	−0.228297	−	0.973592i	$-0.573316\pi$
$997$	−14.4171	−0.456594	−0.228297	+	0.973592i	$0.573316\pi$
$998$	23.8536	0.755073
$999$	−22.0042	−0.696183

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.l.1.5		16
13.5	odd	4		403.2.c.b.311.22	yes	32
13.8	odd	4		403.2.c.b.311.11	✓	32
13.12	even	2		5239.2.a.k.1.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.c.b.311.11	✓	32	13.8	odd	4
403.2.c.b.311.22	yes	32	13.5	odd	4
5239.2.a.k.1.12		16	13.12	even	2
5239.2.a.l.1.5		16	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:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q-1.40506 q^{2} +1.52886 q^{3} -0.0258025 q^{4} -1.01618 q^{5} -2.14814 q^{6} +2.90958 q^{7} +2.84638 q^{8} -0.662589 q^{9} +O(q^{10})\)	\(q-1.40506 q^{2} +1.52886 q^{3} -0.0258025 q^{4} -1.01618 q^{5} -2.14814 q^{6} +2.90958 q^{7} +2.84638 q^{8} -0.662589 q^{9} +1.42779 q^{10} -2.94134 q^{11} -0.0394484 q^{12} -4.08813 q^{14} -1.55359 q^{15} -3.94773 q^{16} +5.52858 q^{17} +0.930978 q^{18} +3.13639 q^{19} +0.0262199 q^{20} +4.44833 q^{21} +4.13277 q^{22} -3.87847 q^{23} +4.35171 q^{24} -3.96739 q^{25} -5.59958 q^{27} -0.0750744 q^{28} +5.59296 q^{29} +2.18289 q^{30} -1.00000 q^{31} -0.145952 q^{32} -4.49690 q^{33} -7.76799 q^{34} -2.95664 q^{35} +0.0170965 q^{36} +3.92962 q^{37} -4.40682 q^{38} -2.89242 q^{40} +12.1899 q^{41} -6.25018 q^{42} -3.52296 q^{43} +0.0758940 q^{44} +0.673307 q^{45} +5.44949 q^{46} +9.64114 q^{47} -6.03552 q^{48} +1.46564 q^{49} +5.57442 q^{50} +8.45242 q^{51} -11.3388 q^{53} +7.86776 q^{54} +2.98892 q^{55} +8.28175 q^{56} +4.79510 q^{57} -7.85846 q^{58} -12.4904 q^{59} +0.0400865 q^{60} +5.57570 q^{61} +1.40506 q^{62} -1.92785 q^{63} +8.10053 q^{64} +6.31842 q^{66} +4.26478 q^{67} -0.142651 q^{68} -5.92963 q^{69} +4.15426 q^{70} +9.44757 q^{71} -1.88598 q^{72} -0.784520 q^{73} -5.52136 q^{74} -6.06558 q^{75} -0.0809267 q^{76} -8.55806 q^{77} +6.11817 q^{79} +4.01159 q^{80} -6.57321 q^{81} -17.1275 q^{82} -8.81342 q^{83} -0.114778 q^{84} -5.61801 q^{85} +4.94997 q^{86} +8.55086 q^{87} -8.37217 q^{88} +6.58407 q^{89} -0.946037 q^{90} +0.100074 q^{92} -1.52886 q^{93} -13.5464 q^{94} -3.18712 q^{95} -0.223140 q^{96} +6.44332 q^{97} -2.05931 q^{98} +1.94890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} + 18 q^{4} + 4 q^{5} + 6 q^{6} + 2 q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 2 * q^3 + 18 * q^4 + 4 * q^5 + 6 * q^6 + 2 * q^7 + 12 * q^8 + 10 * q^9	\( 16 q + 4 q^{2} - 2 q^{3} + 18 q^{4} + 4 q^{5} + 6 q^{6} + 2 q^{7} + 12 q^{8} + 10 q^{9} - 2 q^{10} + 14 q^{11} + 8 q^{12} - 8 q^{14} + 14 q^{16} + 4 q^{17} - 28 q^{18} + 22 q^{19} + 28 q^{20} + 12 q^{21} - 8 q^{22} + 4 q^{23} - 8 q^{24} - 2 q^{25} + 10 q^{27} + 16 q^{28} - 8 q^{29} - 20 q^{30} - 16 q^{31} + 48 q^{32} + 10 q^{33} + 8 q^{34} - 2 q^{35} + 22 q^{36} + 16 q^{37} - 6 q^{38} + 14 q^{40} + 44 q^{41} + 14 q^{42} + 16 q^{43} + 4 q^{44} + 56 q^{45} + 10 q^{47} + 32 q^{49} + 2 q^{50} - 6 q^{53} + 24 q^{54} + 22 q^{55} - 4 q^{56} - 8 q^{57} + 74 q^{58} + 2 q^{59} + 40 q^{60} + 8 q^{61} - 4 q^{62} + 56 q^{63} + 38 q^{64} - 34 q^{66} - 8 q^{67} + 32 q^{68} - 10 q^{69} - 108 q^{70} + 50 q^{71} - 44 q^{72} + 14 q^{73} + 8 q^{74} + 44 q^{76} + 16 q^{77} + 32 q^{79} + 68 q^{80} - 8 q^{81} - 6 q^{82} - 20 q^{83} + 136 q^{84} - 32 q^{85} + 8 q^{86} - 36 q^{87} - 40 q^{88} + 52 q^{89} - 34 q^{90} + 14 q^{92} + 2 q^{93} + 44 q^{94} - 2 q^{95} - 80 q^{96} + 18 q^{97} + 12 q^{98} + 38 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 + 18 * q^4 + 4 * q^5 + 6 * q^6 + 2 * q^7 + 12 * q^8 + 10 * q^9 - 2 * q^10 + 14 * q^11 + 8 * q^12 - 8 * q^14 + 14 * q^16 + 4 * q^17 - 28 * q^18 + 22 * q^19 + 28 * q^20 + 12 * q^21 - 8 * q^22 + 4 * q^23 - 8 * q^24 - 2 * q^25 + 10 * q^27 + 16 * q^28 - 8 * q^29 - 20 * q^30 - 16 * q^31 + 48 * q^32 + 10 * q^33 + 8 * q^34 - 2 * q^35 + 22 * q^36 + 16 * q^37 - 6 * q^38 + 14 * q^40 + 44 * q^41 + 14 * q^42 + 16 * q^43 + 4 * q^44 + 56 * q^45 + 10 * q^47 + 32 * q^49 + 2 * q^50 - 6 * q^53 + 24 * q^54 + 22 * q^55 - 4 * q^56 - 8 * q^57 + 74 * q^58 + 2 * q^59 + 40 * q^60 + 8 * q^61 - 4 * q^62 + 56 * q^63 + 38 * q^64 - 34 * q^66 - 8 * q^67 + 32 * q^68 - 10 * q^69 - 108 * q^70 + 50 * q^71 - 44 * q^72 + 14 * q^73 + 8 * q^74 + 44 * q^76 + 16 * q^77 + 32 * q^79 + 68 * q^80 - 8 * q^81 - 6 * q^82 - 20 * q^83 + 136 * q^84 - 32 * q^85 + 8 * q^86 - 36 * q^87 - 40 * q^88 + 52 * q^89 - 34 * q^90 + 14 * q^92 + 2 * q^93 + 44 * q^94 - 2 * q^95 - 80 * q^96 + 18 * q^97 + 12 * q^98 + 38 * q^99

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