LMFDB - Embedded newform 5239.2.a.m.1.9

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:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 4 x^{16} - 19 x^{15} + 90 x^{14} + 116 x^{13} - 776 x^{12} - 146 x^{11} + 3232 x^{10} + \cdots - 1 $ x^17 - 4x^16 - 19x^15 + 90x^14 + 116x^13 - 776x^12 - 146x^11 + 3232x^10 - 995x^9 - 6763x^8 + 3668x^7 + 6782x^6 - 4160x^5 - 2876x^4 + 1449x^3 + 392x^2 + 6x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			1.9
Root			$0.0410842$ 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)

$f(q)$	$=$	$q-0.0410842 q^{2} +2.09330 q^{3} -1.99831 q^{4} +1.98920 q^{5} -0.0860016 q^{6} -2.68785 q^{7} +0.164267 q^{8} +1.38192 q^{9} +O(q^{10})$	\(q-0.0410842 q^{2} +2.09330 q^{3} -1.99831 q^{4} +1.98920 q^{5} -0.0860016 q^{6} -2.68785 q^{7} +0.164267 q^{8} +1.38192 q^{9} -0.0817244 q^{10} -3.60861 q^{11} -4.18307 q^{12} +0.110428 q^{14} +4.16399 q^{15} +3.98988 q^{16} +7.00846 q^{17} -0.0567750 q^{18} -0.0340014 q^{19} -3.97503 q^{20} -5.62648 q^{21} +0.148257 q^{22} +2.76669 q^{23} +0.343861 q^{24} -1.04310 q^{25} -3.38713 q^{27} +5.37116 q^{28} -6.00691 q^{29} -0.171074 q^{30} -1.00000 q^{31} -0.492455 q^{32} -7.55391 q^{33} -0.287937 q^{34} -5.34666 q^{35} -2.76150 q^{36} -0.859950 q^{37} +0.00139692 q^{38} +0.326760 q^{40} -0.0789012 q^{41} +0.231159 q^{42} -1.25846 q^{43} +7.21112 q^{44} +2.74891 q^{45} -0.113667 q^{46} -6.99256 q^{47} +8.35202 q^{48} +0.224536 q^{49} +0.0428550 q^{50} +14.6708 q^{51} -3.93927 q^{53} +0.139158 q^{54} -7.17822 q^{55} -0.441526 q^{56} -0.0711753 q^{57} +0.246789 q^{58} -3.52882 q^{59} -8.32095 q^{60} +4.71208 q^{61} +0.0410842 q^{62} -3.71439 q^{63} -7.95952 q^{64} +0.310346 q^{66} -9.71755 q^{67} -14.0051 q^{68} +5.79151 q^{69} +0.219663 q^{70} +4.53944 q^{71} +0.227004 q^{72} -0.0228577 q^{73} +0.0353303 q^{74} -2.18353 q^{75} +0.0679454 q^{76} +9.69939 q^{77} +12.1483 q^{79} +7.93664 q^{80} -11.2361 q^{81} +0.00324159 q^{82} +5.82781 q^{83} +11.2435 q^{84} +13.9412 q^{85} +0.0517026 q^{86} -12.5743 q^{87} -0.592776 q^{88} -2.38047 q^{89} -0.112936 q^{90} -5.52870 q^{92} -2.09330 q^{93} +0.287283 q^{94} -0.0676354 q^{95} -1.03086 q^{96} -3.13580 q^{97} -0.00922489 q^{98} -4.98680 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9	$ 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9} + 6 q^{10} - 13 q^{11} + 4 q^{12} - 4 q^{15} + 34 q^{16} - 6 q^{17} + 12 q^{18} - 4 q^{19} - 28 q^{20} - 18 q^{21} - 34 q^{22} - 8 q^{23} - 40 q^{24} + 8 q^{25} - 3 q^{27} - 21 q^{28} - 6 q^{29} + 19 q^{30} - 17 q^{31} - 6 q^{32} - 7 q^{33} - 24 q^{34} - 9 q^{35} - 14 q^{37} + 11 q^{38} - 10 q^{40} - 43 q^{41} + 33 q^{42} + 18 q^{43} - 28 q^{44} - 26 q^{45} - 7 q^{46} - 6 q^{47} - 95 q^{48} - q^{49} - 44 q^{50} + 26 q^{51} - 5 q^{53} - 27 q^{54} + 39 q^{55} + 39 q^{56} - 46 q^{57} - 8 q^{58} + q^{59} - 21 q^{60} - 19 q^{61} + 4 q^{62} - 5 q^{63} + 42 q^{64} + 26 q^{66} - 10 q^{67} + 34 q^{68} + 32 q^{69} + 24 q^{70} - 35 q^{71} + 26 q^{72} - 11 q^{73} - 68 q^{74} - 62 q^{75} - 2 q^{76} + 21 q^{77} + q^{79} - 49 q^{80} + 37 q^{81} + 35 q^{82} - 24 q^{83} + 34 q^{84} + 13 q^{85} - 76 q^{86} - 22 q^{87} - 37 q^{88} - 42 q^{89} + 15 q^{90} + 15 q^{92} + 42 q^{94} + 34 q^{95} - 33 q^{96} + 38 q^{97} - 8 q^{98} - 17 q^{99}+O(q^{100}) $ 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9 + 6 * q^10 - 13 * q^11 + 4 * q^12 - 4 * q^15 + 34 * q^16 - 6 * q^17 + 12 * q^18 - 4 * q^19 - 28 * q^20 - 18 * q^21 - 34 * q^22 - 8 * q^23 - 40 * q^24 + 8 * q^25 - 3 * q^27 - 21 * q^28 - 6 * q^29 + 19 * q^30 - 17 * q^31 - 6 * q^32 - 7 * q^33 - 24 * q^34 - 9 * q^35 - 14 * q^37 + 11 * q^38 - 10 * q^40 - 43 * q^41 + 33 * q^42 + 18 * q^43 - 28 * q^44 - 26 * q^45 - 7 * q^46 - 6 * q^47 - 95 * q^48 - q^49 - 44 * q^50 + 26 * q^51 - 5 * q^53 - 27 * q^54 + 39 * q^55 + 39 * q^56 - 46 * q^57 - 8 * q^58 + q^59 - 21 * q^60 - 19 * q^61 + 4 * q^62 - 5 * q^63 + 42 * q^64 + 26 * q^66 - 10 * q^67 + 34 * q^68 + 32 * q^69 + 24 * q^70 - 35 * q^71 + 26 * q^72 - 11 * q^73 - 68 * q^74 - 62 * q^75 - 2 * q^76 + 21 * q^77 + q^79 - 49 * q^80 + 37 * q^81 + 35 * q^82 - 24 * q^83 + 34 * q^84 + 13 * q^85 - 76 * q^86 - 22 * q^87 - 37 * q^88 - 42 * q^89 + 15 * q^90 + 15 * q^92 + 42 * q^94 + 34 * q^95 - 33 * q^96 + 38 * q^97 - 8 * q^98 - 17 * 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 $

$2$	−0.0410842	−0.0290509	−0.0145254	−	0.999895i	$-0.504624\pi$
$2$	−0.0410842	−0.0290509	−0.0145254	+	0.999895i	$0.504624\pi$
$3$	2.09330	1.20857	0.604285	−	0.796769i	$-0.293459\pi$
$3$	2.09330	1.20857	0.604285	+	0.796769i	$0.293459\pi$
$4$	−1.99831	−0.999156
$5$	1.98920	0.889595	0.444798	−	0.895631i	$-0.353276\pi$
$5$	1.98920	0.889595	0.444798	+	0.895631i	$0.353276\pi$
$6$	−0.0860016	−0.0351100
$7$	−2.68785	−1.01591	−0.507956	−	0.861383i	$-0.669599\pi$
$7$	−2.68785	−1.01591	−0.507956	+	0.861383i	$0.669599\pi$
$8$	0.164267	0.0580772
$9$	1.38192	0.460640
$10$	−0.0817244	−0.0258435
$11$	−3.60861	−1.08804	−0.544018	−	0.839074i	$-0.683098\pi$
$11$	−3.60861	−1.08804	−0.544018	+	0.839074i	$0.683098\pi$
$12$	−4.18307	−1.20755
$13$	0	0
$13$	0	0
$14$	0.110428	0.0295131
$15$	4.16399	1.07514
$16$	3.98988	0.997469
$17$	7.00846	1.69980	0.849901	−	0.526943i	$-0.176662\pi$
$17$	7.00846	1.69980	0.849901	+	0.526943i	$0.176662\pi$
$18$	−0.0567750	−0.0133820
$19$	−0.0340014	−0.00780046	−0.00390023	−	0.999992i	$-0.501241\pi$
$19$	−0.0340014	−0.00780046	−0.00390023	+	0.999992i	$0.501241\pi$
$20$	−3.97503	−0.888844
$21$	−5.62648	−1.22780
$22$	0.148257	0.0316084
$23$	2.76669	0.576894	0.288447	−	0.957496i	$-0.406861\pi$
$23$	2.76669	0.576894	0.288447	+	0.957496i	$0.406861\pi$
$24$	0.343861	0.0701904
$25$	−1.04310	−0.208620
$26$	0	0
$27$	−3.38713	−0.651854
$28$	5.37116	1.01505
$29$	−6.00691	−1.11545	−0.557727	−	0.830024i	$-0.688326\pi$
$29$	−6.00691	−1.11545	−0.557727	+	0.830024i	$0.688326\pi$
$30$	−0.171074	−0.0312337
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−0.492455	−0.0870546
$33$	−7.55391	−1.31497
$34$	−0.287937	−0.0493807
$35$	−5.34666	−0.903750
$36$	−2.76150	−0.460251
$37$	−0.859950	−0.141375	−0.0706874	−	0.997499i	$-0.522519\pi$
$37$	−0.859950	−0.141375	−0.0706874	+	0.997499i	$0.522519\pi$
$38$	0.00139692	0.000226610 0
$39$	0	0
$40$	0.326760	0.0516652
$41$	−0.0789012	−0.0123223	−0.00616115	−	0.999981i	$-0.501961\pi$
$41$	−0.0789012	−0.0123223	−0.00616115	+	0.999981i	$0.501961\pi$
$42$	0.231159	0.0356687
$43$	−1.25846	−0.191913	−0.0959564	−	0.995386i	$-0.530591\pi$
$43$	−1.25846	−0.191913	−0.0959564	+	0.995386i	$0.530591\pi$
$44$	7.21112	1.08712
$45$	2.74891	0.409783
$46$	−0.113667	−0.0167593
$47$	−6.99256	−1.01997	−0.509985	−	0.860183i	$-0.670349\pi$
$47$	−6.99256	−1.01997	−0.509985	+	0.860183i	$0.670349\pi$
$48$	8.35202	1.20551
$49$	0.224536	0.0320766
$50$	0.0428550	0.00606061
$51$	14.6708	2.05433
$52$	0	0
$53$	−3.93927	−0.541101	−0.270550	−	0.962706i	$-0.587206\pi$
$53$	−3.93927	−0.541101	−0.270550	+	0.962706i	$0.587206\pi$
$54$	0.139158	0.0189369
$55$	−7.17822	−0.967912
$56$	−0.441526	−0.0590014
$57$	−0.0711753	−0.00942739
$58$	0.246789	0.0324049
$59$	−3.52882	−0.459413	−0.229707	−	0.973260i	$-0.573777\pi$
$59$	−3.52882	−0.459413	−0.229707	+	0.973260i	$0.573777\pi$
$60$	−8.32095	−1.07423
$61$	4.71208	0.603320	0.301660	−	0.953416i	$-0.402459\pi$
$61$	4.71208	0.603320	0.301660	+	0.953416i	$0.402459\pi$
$62$	0.0410842	0.00521769
$63$	−3.71439	−0.467969
$64$	−7.95952	−0.994940
$65$	0	0
$66$	0.310346	0.0382009
$67$	−9.71755	−1.18719	−0.593594	−	0.804765i	$-0.702291\pi$
$67$	−9.71755	−1.18719	−0.593594	+	0.804765i	$0.702291\pi$
$68$	−14.0051	−1.69837
$69$	5.79151	0.697216
$70$	0.219663	0.0262547
$71$	4.53944	0.538732	0.269366	−	0.963038i	$-0.413186\pi$
$71$	4.53944	0.538732	0.269366	+	0.963038i	$0.413186\pi$
$72$	0.227004	0.0267527
$73$	−0.0228577	−0.00267530	−0.00133765	−	0.999999i	$-0.500426\pi$
$73$	−0.0228577	−0.00267530	−0.00133765	+	0.999999i	$0.500426\pi$
$74$	0.0353303	0.00410706
$75$	−2.18353	−0.252132
$76$	0.0679454	0.00779387
$77$	9.69939	1.10535
$78$	0	0
$79$	12.1483	1.36680	0.683398	−	0.730046i	$-0.260501\pi$
$79$	12.1483	1.36680	0.683398	+	0.730046i	$0.260501\pi$
$80$	7.93664	0.887343
$81$	−11.2361	−1.24845
$82$	0.00324159	0.000357974 0
$83$	5.82781	0.639685	0.319842	−	0.947471i	$-0.396370\pi$
$83$	5.82781	0.639685	0.319842	+	0.947471i	$0.396370\pi$
$84$	11.2435	1.22676
$85$	13.9412	1.51214
$86$	0.0517026	0.00557523
$87$	−12.5743	−1.34810
$88$	−0.592776	−0.0631901
$89$	−2.38047	−0.252330	−0.126165	−	0.992009i	$-0.540267\pi$
$89$	−2.38047	−0.252330	−0.126165	+	0.992009i	$0.540267\pi$
$90$	−0.112936	−0.0119046
$91$	0	0
$92$	−5.52870	−0.576407
$93$	−2.09330	−0.217065
$94$	0.287283	0.0296310
$95$	−0.0676354	−0.00693925
$96$	−1.03086	−0.105212
$97$	−3.13580	−0.318392	−0.159196	−	0.987247i	$-0.550890\pi$
$97$	−3.13580	−0.318392	−0.159196	+	0.987247i	$0.550890\pi$
$98$	−0.00922489	−0.000931854 0
$99$	−4.98680	−0.501192
$100$	2.08444	0.208444
$101$	−17.9976	−1.79083	−0.895416	−	0.445231i	$-0.853122\pi$
$101$	−17.9976	−1.79083	−0.895416	+	0.445231i	$0.853122\pi$
$102$	−0.602739	−0.0596800
$103$	−6.56844	−0.647208	−0.323604	−	0.946193i	$-0.604895\pi$
$103$	−6.56844	−0.647208	−0.323604	+	0.946193i	$0.604895\pi$
$104$	0	0
$105$	−11.1922	−1.09224
$106$	0.161842	0.0157195
$107$	15.9322	1.54023	0.770113	−	0.637908i	$-0.220200\pi$
$107$	15.9322	1.54023	0.770113	+	0.637908i	$0.220200\pi$
$108$	6.76855	0.651304
$109$	−20.3376	−1.94799	−0.973995	−	0.226568i	$-0.927249\pi$
$109$	−20.3376	−1.94799	−0.973995	+	0.226568i	$0.927249\pi$
$110$	0.294911	0.0281187
$111$	−1.80014	−0.170861
$112$	−10.7242	−1.01334
$113$	−0.528851	−0.0497501	−0.0248750	−	0.999691i	$-0.507919\pi$
$113$	−0.528851	−0.0497501	−0.0248750	+	0.999691i	$0.507919\pi$
$114$	0.00292417	0.000273874 0
$115$	5.50348	0.513202
$116$	12.0037	1.11451
$117$	0	0
$118$	0.144979	0.0133464
$119$	−18.8377	−1.72685
$120$	0.684007	0.0624410
$121$	2.02205	0.183822
$122$	−0.193592	−0.0175270
$123$	−0.165164	−0.0148923
$124$	1.99831	0.179454
$125$	−12.0209	−1.07518
$126$	0.152603	0.0135949
$127$	10.0282	0.889860	0.444930	−	0.895565i	$-0.353229\pi$
$127$	10.0282	0.889860	0.444930	+	0.895565i	$0.353229\pi$
$128$	1.31192	0.115958
$129$	−2.63433	−0.231940
$130$	0	0
$131$	12.3846	1.08205	0.541023	−	0.841008i	$-0.318037\pi$
$131$	12.3846	1.08205	0.541023	+	0.841008i	$0.318037\pi$
$132$	15.0951	1.31386
$133$	0.0913907	0.00792458
$134$	0.399237	0.0344889
$135$	−6.73767	−0.579887
$136$	1.15126	0.0987198
$137$	−16.2962	−1.39228	−0.696140	−	0.717906i	$-0.745101\pi$
$137$	−16.2962	−1.39228	−0.696140	+	0.717906i	$0.745101\pi$
$138$	−0.237939	−0.0202547
$139$	−19.2360	−1.63158	−0.815789	−	0.578349i	$-0.803697\pi$
$139$	−19.2360	−1.63158	−0.815789	+	0.578349i	$0.803697\pi$
$140$	10.6843	0.902987
$141$	−14.6376	−1.23270
$142$	−0.186499	−0.0156506
$143$	0	0
$144$	5.51368	0.459474
$145$	−11.9489	−0.992303
$146$	0.000939091 0	7.77197e−5 0
$147$	0.470023	0.0387668
$148$	1.71845	0.141256
$149$	−12.8775	−1.05497	−0.527483	−	0.849566i	$-0.676864\pi$
$149$	−12.8775	−1.05497	−0.527483	+	0.849566i	$0.676864\pi$
$150$	0.0897085	0.00732467
$151$	−5.70708	−0.464435	−0.232218	−	0.972664i	$-0.574598\pi$
$151$	−5.70708	−0.464435	−0.232218	+	0.972664i	$0.574598\pi$
$152$	−0.00558532	−0.000453029 0
$153$	9.68512	0.782996
$154$	−0.398491	−0.0321114
$155$	−1.98920	−0.159776
$156$	0	0
$157$	0.897113	0.0715974	0.0357987	−	0.999359i	$-0.488602\pi$
$157$	0.897113	0.0715974	0.0357987	+	0.999359i	$0.488602\pi$
$158$	−0.499104	−0.0397066
$159$	−8.24609	−0.653958
$160$	−0.979590	−0.0774434
$161$	−7.43643	−0.586073
$162$	0.461624	0.0362686
$163$	−19.1537	−1.50023	−0.750116	−	0.661307i	$-0.770002\pi$
$163$	−19.1537	−1.50023	−0.750116	+	0.661307i	$0.770002\pi$
$164$	0.157669	0.0123119
$165$	−15.0262	−1.16979
$166$	−0.239430	−0.0185834
$167$	7.61434	0.589215	0.294607	−	0.955618i	$-0.404811\pi$
$167$	7.61434	0.589215	0.294607	+	0.955618i	$0.404811\pi$
$168$	−0.924247	−0.0713072
$169$	0	0
$170$	−0.572762	−0.0439289
$171$	−0.0469872	−0.00359320
$172$	2.51479	0.191751
$173$	3.17621	0.241483	0.120741	−	0.992684i	$-0.461473\pi$
$173$	3.17621	0.241483	0.120741	+	0.992684i	$0.461473\pi$
$174$	0.516603	0.0391636
$175$	2.80370	0.211940
$176$	−14.3979	−1.08528
$177$	−7.38689	−0.555233
$178$	0.0977997	0.00733040
$179$	−25.7064	−1.92138	−0.960692	−	0.277615i	$-0.910456\pi$
$179$	−25.7064	−1.92138	−0.960692	+	0.277615i	$0.910456\pi$
$180$	−5.49317	−0.409437
$181$	−1.20564	−0.0896148	−0.0448074	−	0.998996i	$-0.514267\pi$
$181$	−1.20564	−0.0896148	−0.0448074	+	0.998996i	$0.514267\pi$
$182$	0	0
$183$	9.86381	0.729154
$184$	0.454476	0.0335044
$185$	−1.71061	−0.125766
$186$	0.0860016	0.00630594
$187$	−25.2908	−1.84945
$188$	13.9733	1.01911
$189$	9.10411	0.662227
$190$	0.00277874	0.000201591 0
$191$	−19.9232	−1.44159	−0.720795	−	0.693148i	$-0.756223\pi$
$191$	−19.9232	−1.44159	−0.720795	+	0.693148i	$0.756223\pi$
$192$	−16.6617	−1.20245
$193$	−25.8672	−1.86196	−0.930980	−	0.365070i	$-0.881045\pi$
$193$	−25.8672	−1.86196	−0.930980	+	0.365070i	$0.881045\pi$
$194$	0.128832	0.00924957
$195$	0	0
$196$	−0.448694	−0.0320496
$197$	12.0857	0.861070	0.430535	−	0.902574i	$-0.358325\pi$
$197$	12.0857	0.861070	0.430535	+	0.902574i	$0.358325\pi$
$198$	0.204879	0.0145601
$199$	17.1571	1.21623	0.608116	−	0.793849i	$-0.291926\pi$
$199$	17.1571	1.21623	0.608116	+	0.793849i	$0.291926\pi$
$200$	−0.171348	−0.0121161
$201$	−20.3418	−1.43480
$202$	0.739418	0.0520252
$203$	16.1457	1.13320
$204$	−29.3169	−2.05259
$205$	−0.156950	−0.0109619
$206$	0.269859	0.0188020
$207$	3.82333	0.265740
$208$	0	0
$209$	0.122698	0.00848718
$210$	0.459821	0.0317307
$211$	18.3437	1.26283	0.631415	−	0.775445i	$-0.282474\pi$
$211$	18.3437	1.26283	0.631415	+	0.775445i	$0.282474\pi$
$212$	7.87190	0.540644
$213$	9.50242	0.651095
$214$	−0.654562	−0.0447449
$215$	−2.50331	−0.170725
$216$	−0.556395	−0.0378579
$217$	2.68785	0.182463
$218$	0.835554	0.0565909
$219$	−0.0478482	−0.00323328
$220$	14.3443	0.967095
$221$	0	0
$222$	0.0739570	0.00496367
$223$	6.62586	0.443701	0.221850	−	0.975081i	$-0.428790\pi$
$223$	6.62586	0.443701	0.221850	+	0.975081i	$0.428790\pi$
$224$	1.32365	0.0884398
$225$	−1.44148	−0.0960988
$226$	0.0217274	0.00144528
$227$	−4.39204	−0.291510	−0.145755	−	0.989321i	$-0.546561\pi$
$227$	−4.39204	−0.291510	−0.145755	+	0.989321i	$0.546561\pi$
$228$	0.142230	0.00941944
$229$	−16.5022	−1.09049	−0.545247	−	0.838275i	$-0.683564\pi$
$229$	−16.5022	−1.09049	−0.545247	+	0.838275i	$0.683564\pi$
$230$	−0.226106	−0.0149090
$231$	20.3038	1.33589
$232$	−0.986738	−0.0647825
$233$	0.112192	0.00734994	0.00367497	−	0.999993i	$-0.498830\pi$
$233$	0.112192	0.00734994	0.00367497	+	0.999993i	$0.498830\pi$
$234$	0	0
$235$	−13.9096	−0.907360
$236$	7.05169	0.459026
$237$	25.4302	1.65187
$238$	0.773930	0.0501665
$239$	−0.152681	−0.00987612	−0.00493806	−	0.999988i	$-0.501572\pi$
$239$	−0.152681	−0.00987612	−0.00493806	+	0.999988i	$0.501572\pi$
$240$	16.6138	1.07242
$241$	28.1714	1.81468	0.907339	−	0.420401i	$-0.138110\pi$
$241$	28.1714	1.81468	0.907339	+	0.420401i	$0.138110\pi$
$242$	−0.0830741	−0.00534020
$243$	−13.3591	−0.856985
$244$	−9.41620	−0.602811
$245$	0.446647	0.0285352
$246$	0.00678563	0.000432636 0
$247$	0	0
$248$	−0.164267	−0.0104310
$249$	12.1994	0.773103
$250$	0.493869	0.0312350
$251$	27.4095	1.73007	0.865036	−	0.501709i	$-0.167295\pi$
$251$	27.4095	1.73007	0.865036	+	0.501709i	$0.167295\pi$
$252$	7.42251	0.467574
$253$	−9.98388	−0.627681
$254$	−0.412000	−0.0258512
$255$	29.1832	1.82752
$256$	15.8651	0.991571
$257$	13.7652	0.858648	0.429324	−	0.903151i	$-0.358752\pi$
$257$	13.7652	0.858648	0.429324	+	0.903151i	$0.358752\pi$
$258$	0.108229	0.00673806
$259$	2.31142	0.143624
$260$	0	0
$261$	−8.30105	−0.513822
$262$	−0.508810	−0.0314344
$263$	21.6566	1.33541	0.667703	−	0.744428i	$-0.267278\pi$
$263$	21.6566	1.33541	0.667703	+	0.744428i	$0.267278\pi$
$264$	−1.24086	−0.0763697
$265$	−7.83598	−0.481361
$266$	−0.00375471	−0.000230216 0
$267$	−4.98305	−0.304958
$268$	19.4187	1.18619
$269$	1.46273	0.0891844	0.0445922	−	0.999005i	$-0.485801\pi$
$269$	1.46273	0.0891844	0.0445922	+	0.999005i	$0.485801\pi$
$270$	0.276812	0.0168462
$271$	−9.30267	−0.565097	−0.282548	−	0.959253i	$-0.591180\pi$
$271$	−9.30267	−0.565097	−0.282548	+	0.959253i	$0.591180\pi$
$272$	27.9629	1.69550
$273$	0	0
$274$	0.669516	0.0404469
$275$	3.76415	0.226987
$276$	−11.5732	−0.696628
$277$	−19.9424	−1.19822	−0.599111	−	0.800666i	$-0.704479\pi$
$277$	−19.9424	−1.19822	−0.599111	+	0.800666i	$0.704479\pi$
$278$	0.790296	0.0473988
$279$	−1.38192	−0.0827333
$280$	−0.878281	−0.0524873
$281$	3.44422	0.205465	0.102732	−	0.994709i	$-0.467241\pi$
$281$	3.44422	0.205465	0.102732	+	0.994709i	$0.467241\pi$
$282$	0.601371	0.0358111
$283$	−19.9930	−1.18846	−0.594231	−	0.804294i	$-0.702544\pi$
$283$	−19.9930	−1.18846	−0.594231	+	0.804294i	$0.702544\pi$
$284$	−9.07121	−0.538277
$285$	−0.141581	−0.00838656
$286$	0	0
$287$	0.212075	0.0125184
$288$	−0.680533	−0.0401008
$289$	32.1185	1.88932
$290$	0.490911	0.0288273
$291$	−6.56417	−0.384799
$292$	0.0456769	0.00267304
$293$	9.49932	0.554956	0.277478	−	0.960732i	$-0.410501\pi$
$293$	9.49932	0.554956	0.277478	+	0.960732i	$0.410501\pi$
$294$	−0.0193105	−0.00112621
$295$	−7.01951	−0.408692
$296$	−0.141262	−0.00821066
$297$	12.2228	0.709241
$298$	0.529061	0.0306477
$299$	0	0
$300$	4.36337	0.251919
$301$	3.38254	0.194966
$302$	0.234470	0.0134923
$303$	−37.6745	−2.16434
$304$	−0.135661	−0.00778071
$305$	9.37324	0.536710
$306$	−0.397905	−0.0227467
$307$	−25.8098	−1.47304	−0.736522	−	0.676413i	$-0.763533\pi$
$307$	−25.8098	−1.47304	−0.736522	+	0.676413i	$0.763533\pi$
$308$	−19.3824	−1.10442
$309$	−13.7497	−0.782195
$310$	0.0817244	0.00464163
$311$	7.38471	0.418749	0.209374	−	0.977836i	$-0.432857\pi$
$311$	7.38471	0.418749	0.209374	+	0.977836i	$0.432857\pi$
$312$	0	0
$313$	−16.9040	−0.955468	−0.477734	−	0.878505i	$-0.658542\pi$
$313$	−16.9040	−0.955468	−0.477734	+	0.878505i	$0.658542\pi$
$314$	−0.0368571	−0.00207997
$315$	−7.38865	−0.416303
$316$	−24.2762	−1.36564
$317$	−17.7091	−0.994643	−0.497321	−	0.867566i	$-0.665683\pi$
$317$	−17.7091	−0.994643	−0.497321	+	0.867566i	$0.665683\pi$
$318$	0.338784	0.0189980
$319$	21.6766	1.21365
$320$	−15.8330	−0.885094
$321$	33.3510	1.86147
$322$	0.305520	0.0170259
$323$	−0.238297	−0.0132592
$324$	22.4531	1.24740
$325$	0	0
$326$	0.786912	0.0435830
$327$	−42.5728	−2.35428
$328$	−0.0129609	−0.000715645 0
$329$	18.7950	1.03620
$330$	0.617339	0.0339834
$331$	18.6679	1.02608	0.513042	−	0.858364i	$-0.328519\pi$
$331$	18.6679	1.02608	0.513042	+	0.858364i	$0.328519\pi$
$332$	−11.6458	−0.639145
$333$	−1.18838	−0.0651228
$334$	−0.312829	−0.0171172
$335$	−19.3301	−1.05612
$336$	−22.4490	−1.22469
$337$	−1.90926	−0.104004	−0.0520021	−	0.998647i	$-0.516560\pi$
$337$	−1.90926	−0.104004	−0.0520021	+	0.998647i	$0.516560\pi$
$338$	0	0
$339$	−1.10704	−0.0601264
$340$	−27.8589	−1.51086
$341$	3.60861	0.195417
$342$	0.00193043	0.000104386 0
$343$	18.2114	0.983325
$344$	−0.206723	−0.0111458
$345$	11.5204	0.620240
$346$	−0.130492	−0.00701529
$347$	26.8548	1.44164	0.720821	−	0.693122i	$-0.243765\pi$
$347$	26.8548	1.44164	0.720821	+	0.693122i	$0.243765\pi$
$348$	25.1273	1.34697
$349$	4.31750	0.231110	0.115555	−	0.993301i	$-0.463135\pi$
$349$	4.31750	0.231110	0.115555	+	0.993301i	$0.463135\pi$
$350$	−0.115188	−0.00615704
$351$	0	0
$352$	1.77708	0.0947185
$353$	−32.3786	−1.72334	−0.861668	−	0.507472i	$-0.830580\pi$
$353$	−32.3786	−1.72334	−0.861668	+	0.507472i	$0.830580\pi$
$354$	0.303484	0.0161300
$355$	9.02983	0.479253
$356$	4.75693	0.252117
$357$	−39.4330	−2.08702
$358$	1.05612	0.0558179
$359$	−16.4956	−0.870604	−0.435302	−	0.900284i	$-0.643358\pi$
$359$	−16.4956	−0.870604	−0.435302	+	0.900284i	$0.643358\pi$
$360$	0.451555	0.0237991
$361$	−18.9988	−0.999939
$362$	0.0495329	0.00260339
$363$	4.23276	0.222162
$364$	0	0
$365$	−0.0454685	−0.00237993
$366$	−0.405246	−0.0211826
$367$	3.41259	0.178136	0.0890680	−	0.996026i	$-0.471611\pi$
$367$	3.41259	0.178136	0.0890680	+	0.996026i	$0.471611\pi$
$368$	11.0387	0.575434
$369$	−0.109035	−0.00567614
$370$	0.0702789	0.00365362
$371$	10.5882	0.549711
$372$	4.18307	0.216882
$373$	−28.5314	−1.47730	−0.738649	−	0.674090i	$-0.764536\pi$
$373$	−28.5314	−1.47730	−0.738649	+	0.674090i	$0.764536\pi$
$374$	1.03905	0.0537280
$375$	−25.1634	−1.29943
$376$	−1.14865	−0.0592371
$377$	0	0
$378$	−0.374035	−0.0192383
$379$	28.6815	1.47327	0.736636	−	0.676290i	$-0.236413\pi$
$379$	28.6815	1.47327	0.736636	+	0.676290i	$0.236413\pi$
$380$	0.135157	0.00693339
$381$	20.9921	1.07546
$382$	0.818527	0.0418795
$383$	34.3523	1.75532	0.877661	−	0.479283i	$-0.159103\pi$
$383$	34.3523	1.75532	0.877661	+	0.479283i	$0.159103\pi$
$384$	2.74625	0.140144
$385$	19.2940	0.983313
$386$	1.06273	0.0540916
$387$	−1.73908	−0.0884026
$388$	6.26630	0.318123
$389$	−6.09669	−0.309114	−0.154557	−	0.987984i	$-0.549395\pi$
$389$	−6.09669	−0.309114	−0.154557	+	0.987984i	$0.549395\pi$
$390$	0	0
$391$	19.3902	0.980605
$392$	0.0368840	0.00186292
$393$	25.9247	1.30773
$394$	−0.496530	−0.0250148
$395$	24.1654	1.21589
$396$	9.96519	0.500769
$397$	−7.20294	−0.361505	−0.180753	−	0.983529i	$-0.557853\pi$
$397$	−7.20294	−0.361505	−0.180753	+	0.983529i	$0.557853\pi$
$398$	−0.704883	−0.0353326
$399$	0.191308	0.00957740
$400$	−4.16185	−0.208092
$401$	14.0693	0.702589	0.351295	−	0.936265i	$-0.385742\pi$
$401$	14.0693	0.702589	0.351295	+	0.936265i	$0.385742\pi$
$402$	0.835725	0.0416822
$403$	0	0
$404$	35.9649	1.78932
$405$	−22.3507	−1.11062
$406$	−0.663331	−0.0329206
$407$	3.10322	0.153821
$408$	2.40994	0.119310
$409$	−13.9801	−0.691270	−0.345635	−	0.938369i	$-0.612336\pi$
$409$	−13.9801	−0.691270	−0.345635	+	0.938369i	$0.612336\pi$
$410$	0.00644815	0.000318452 0
$411$	−34.1129	−1.68267
$412$	13.1258	0.646662
$413$	9.48494	0.466723
$414$	−0.157078	−0.00771998
$415$	11.5926	0.569061
$416$	0	0
$417$	−40.2668	−1.97188
$418$	−0.00504093	−0.000246560 0
$419$	30.1818	1.47448	0.737239	−	0.675632i	$-0.236129\pi$
$419$	30.1818	1.47448	0.737239	+	0.675632i	$0.236129\pi$
$420$	22.3655	1.09132
$421$	37.8526	1.84482	0.922412	−	0.386207i	$-0.126215\pi$
$421$	37.8526	1.84482	0.922412	+	0.386207i	$0.126215\pi$
$422$	−0.753634	−0.0366863
$423$	−9.66315	−0.469839
$424$	−0.647094	−0.0314256
$425$	−7.31054	−0.354613
$426$	−0.390399	−0.0189149
$427$	−12.6654	−0.612920
$428$	−31.8375	−1.53893
$429$	0	0
$430$	0.102847	0.00495970
$431$	−30.0265	−1.44633	−0.723163	−	0.690678i	$-0.757312\pi$
$431$	−30.0265	−1.44633	−0.723163	+	0.690678i	$0.757312\pi$
$432$	−13.5142	−0.650204
$433$	−18.5867	−0.893220	−0.446610	−	0.894729i	$-0.647369\pi$
$433$	−18.5867	−0.893220	−0.446610	+	0.894729i	$0.647369\pi$
$434$	−0.110428	−0.00530072
$435$	−25.0127	−1.19927
$436$	40.6409	1.94635
$437$	−0.0940712	−0.00450003
$438$	0.00196580	9.39297e−5 0
$439$	−31.1113	−1.48486	−0.742430	−	0.669923i	$-0.766327\pi$
$439$	−31.1113	−1.48486	−0.742430	+	0.669923i	$0.766327\pi$
$440$	−1.17915	−0.0562136
$441$	0.310291	0.0147758
$442$	0	0
$443$	14.2242	0.675811	0.337906	−	0.941180i	$-0.390282\pi$
$443$	14.2242	0.675811	0.337906	+	0.941180i	$0.390282\pi$
$444$	3.59723	0.170717
$445$	−4.73523	−0.224471
$446$	−0.272218	−0.0128899
$447$	−26.9565	−1.27500
$448$	21.3940	1.01077
$449$	6.86763	0.324104	0.162052	−	0.986782i	$-0.448189\pi$
$449$	6.86763	0.324104	0.162052	+	0.986782i	$0.448189\pi$
$450$	0.0592221	0.00279176
$451$	0.284723	0.0134071
$452$	1.05681	0.0497081
$453$	−11.9466	−0.561302
$454$	0.180443	0.00846862
$455$	0	0
$456$	−0.0116918	−0.000547517 0
$457$	−17.3834	−0.813161	−0.406581	−	0.913615i	$-0.633279\pi$
$457$	−17.3834	−0.813161	−0.406581	+	0.913615i	$0.633279\pi$
$458$	0.677978	0.0316798
$459$	−23.7386	−1.10802
$460$	−10.9977	−0.512769
$461$	−6.01492	−0.280143	−0.140071	−	0.990141i	$-0.544733\pi$
$461$	−6.01492	−0.280143	−0.140071	+	0.990141i	$0.544733\pi$
$462$	−0.834163	−0.0388088
$463$	21.3532	0.992369	0.496184	−	0.868217i	$-0.334734\pi$
$463$	21.3532	0.992369	0.496184	+	0.868217i	$0.334734\pi$
$464$	−23.9668	−1.11263
$465$	−4.16399	−0.193100
$466$	−0.00460931	−0.000213522 0
$467$	6.16489	0.285277	0.142639	−	0.989775i	$-0.454441\pi$
$467$	6.16489	0.285277	0.142639	+	0.989775i	$0.454441\pi$
$468$	0	0
$469$	26.1193	1.20608
$470$	0.571463	0.0263596
$471$	1.87793	0.0865304
$472$	−0.579670	−0.0266815
$473$	4.54127	0.208808
$474$	−1.04478	−0.0479882
$475$	0.0354669	0.00162733
$476$	37.6436	1.72539
$477$	−5.44375	−0.249252
$478$	0.00627277	0.000286910 0
$479$	22.0734	1.00856	0.504280	−	0.863540i	$-0.331758\pi$
$479$	22.0734	1.00856	0.504280	+	0.863540i	$0.331758\pi$
$480$	−2.05058	−0.0935957
$481$	0	0
$482$	−1.15740	−0.0527180
$483$	−15.5667	−0.708310
$484$	−4.04068	−0.183667
$485$	−6.23771	−0.283240
$486$	0.548846	0.0248962
$487$	−5.37891	−0.243742	−0.121871	−	0.992546i	$-0.538889\pi$
$487$	−5.37891	−0.243742	−0.121871	+	0.992546i	$0.538889\pi$
$488$	0.774040	0.0350391
$489$	−40.0944	−1.81313
$490$	−0.0183501	−0.000828973 0
$491$	9.59943	0.433216	0.216608	−	0.976259i	$-0.430501\pi$
$491$	9.59943	0.433216	0.216608	+	0.976259i	$0.430501\pi$
$492$	0.330050	0.0148798
$493$	−42.0992	−1.89605
$494$	0	0
$495$	−9.91972	−0.445858
$496$	−3.98988	−0.179151
$497$	−12.2013	−0.547304
$498$	−0.501201	−0.0224593
$499$	−39.3295	−1.76063	−0.880315	−	0.474389i	$-0.842669\pi$
$499$	−39.3295	−1.76063	−0.880315	+	0.474389i	$0.842669\pi$
$500$	24.0215	1.07428
$501$	15.9391	0.712107
$502$	−1.12610	−0.0502601
$503$	13.1928	0.588240	0.294120	−	0.955769i	$-0.404973\pi$
$503$	13.1928	0.588240	0.294120	+	0.955769i	$0.404973\pi$
$504$	−0.610153	−0.0271784
$505$	−35.8008	−1.59312
$506$	0.410179	0.0182347
$507$	0	0
$508$	−20.0395	−0.889109
$509$	26.9664	1.19527	0.597633	−	0.801770i	$-0.296108\pi$
$509$	26.9664	1.19527	0.597633	+	0.801770i	$0.296108\pi$
$510$	−1.19897	−0.0530911
$511$	0.0614382	0.00271786
$512$	−3.27565	−0.144765
$513$	0.115167	0.00508476
$514$	−0.565531	−0.0249445
$515$	−13.0659	−0.575753
$516$	5.26421	0.231744
$517$	25.2334	1.10976
$518$	−0.0949625	−0.00417241
$519$	6.64877	0.291849
$520$	0	0
$521$	2.93885	0.128753	0.0643767	−	0.997926i	$-0.479494\pi$
$521$	2.93885	0.128753	0.0643767	+	0.997926i	$0.479494\pi$
$522$	0.341042	0.0149270
$523$	16.3181	0.713542	0.356771	−	0.934192i	$-0.383878\pi$
$523$	16.3181	0.713542	0.356771	+	0.934192i	$0.383878\pi$
$524$	−24.7483	−1.08113
$525$	5.86900	0.256144
$526$	−0.889745	−0.0387947
$527$	−7.00846	−0.305293
$528$	−30.1392	−1.31164
$529$	−15.3455	−0.667194
$530$	0.321935	0.0139839
$531$	−4.87654	−0.211624
$532$	−0.182627	−0.00791789
$533$	0	0
$534$	0.204724	0.00885929
$535$	31.6923	1.37018
$536$	−1.59628	−0.0689486
$537$	−53.8112	−2.32213
$538$	−0.0600952	−0.00259089
$539$	−0.810264	−0.0349005
$540$	13.4640	0.579397
$541$	46.1372	1.98359	0.991797	−	0.127824i	$-0.0407992\pi$
$541$	46.1372	1.98359	0.991797	+	0.127824i	$0.0407992\pi$
$542$	0.382192	0.0164166
$543$	−2.52378	−0.108306
$544$	−3.45135	−0.147976
$545$	−40.4555	−1.73292
$546$	0	0
$547$	−20.6177	−0.881549	−0.440774	−	0.897618i	$-0.645296\pi$
$547$	−20.6177	−0.881549	−0.440774	+	0.897618i	$0.645296\pi$
$548$	32.5649	1.39110
$549$	6.51171	0.277913
$550$	−0.154647	−0.00659416
$551$	0.204243	0.00870105
$552$	0.951356	0.0404924
$553$	−32.6529	−1.38854
$554$	0.819316	0.0348094
$555$	−3.58082	−0.151997
$556$	38.4396	1.63020
$557$	44.7853	1.89761	0.948807	−	0.315858i	$-0.102292\pi$
$557$	44.7853	1.89761	0.948807	+	0.315858i	$0.102292\pi$
$558$	0.0567750	0.00240348
$559$	0	0
$560$	−21.3325	−0.901463
$561$	−52.9413	−2.23518
$562$	−0.141503	−0.00596893
$563$	34.2000	1.44136	0.720679	−	0.693269i	$-0.243830\pi$
$563$	34.2000	1.44136	0.720679	+	0.693269i	$0.243830\pi$
$564$	29.2504	1.23166
$565$	−1.05199	−0.0442574
$566$	0.821397	0.0345259
$567$	30.2008	1.26832
$568$	0.745681	0.0312881
$569$	−46.2223	−1.93774	−0.968870	−	0.247569i	$-0.920368\pi$
$569$	−46.2223	−1.93774	−0.968870	+	0.247569i	$0.920368\pi$
$570$	0.00581675	0.000243637 0
$571$	8.09392	0.338720	0.169360	−	0.985554i	$-0.445830\pi$
$571$	8.09392	0.338720	0.169360	+	0.985554i	$0.445830\pi$
$572$	0	0
$573$	−41.7053	−1.74226
$574$	−0.00871290	−0.000363670 0
$575$	−2.88594	−0.120352
$576$	−10.9994	−0.458309
$577$	16.6135	0.691628	0.345814	−	0.938303i	$-0.387603\pi$
$577$	16.6135	0.691628	0.345814	+	0.938303i	$0.387603\pi$
$578$	−1.31956	−0.0548865
$579$	−54.1478	−2.25031
$580$	23.8776	0.991465
$581$	−15.6643	−0.649863
$582$	0.269683	0.0111787
$583$	14.2153	0.588737
$584$	−0.00375478	−0.000155374 0
$585$	0	0
$586$	−0.390271	−0.0161220
$587$	43.3479	1.78916	0.894579	−	0.446910i	$-0.147476\pi$
$587$	43.3479	1.78916	0.894579	+	0.446910i	$0.147476\pi$
$588$	−0.939252	−0.0387341
$589$	0.0340014	0.00140100
$590$	0.288391	0.0118729
$591$	25.2990	1.04066
$592$	−3.43109	−0.141017
$593$	−26.2397	−1.07754	−0.538768	−	0.842454i	$-0.681110\pi$
$593$	−26.2397	−1.07754	−0.538768	+	0.842454i	$0.681110\pi$
$594$	−0.502165	−0.0206041
$595$	−37.4718	−1.53620
$596$	25.7333	1.05408
$597$	35.9149	1.46990
$598$	0	0
$599$	24.4417	0.998661	0.499330	−	0.866412i	$-0.333579\pi$
$599$	24.4417	0.998661	0.499330	+	0.866412i	$0.333579\pi$
$600$	−0.358682	−0.0146431
$601$	−43.6012	−1.77853	−0.889265	−	0.457392i	$-0.848784\pi$
$601$	−43.6012	−1.77853	−0.889265	+	0.457392i	$0.848784\pi$
$602$	−0.138969	−0.00566395
$603$	−13.4289	−0.546866
$604$	11.4045	0.464043
$605$	4.02225	0.163528
$606$	1.54783	0.0628761
$607$	3.77334	0.153155	0.0765776	−	0.997064i	$-0.475601\pi$
$607$	3.77334	0.153155	0.0765776	+	0.997064i	$0.475601\pi$
$608$	0.0167442	0.000679066 0
$609$	33.7978	1.36955
$610$	−0.385092	−0.0155919
$611$	0	0
$612$	−19.3539	−0.782335
$613$	43.5614	1.75943	0.879714	−	0.475503i	$-0.157734\pi$
$613$	43.5614	1.75943	0.879714	+	0.475503i	$0.157734\pi$
$614$	1.06037	0.0427932
$615$	−0.328544	−0.0132482
$616$	1.59329	0.0641956
$617$	−9.97680	−0.401651	−0.200825	−	0.979627i	$-0.564362\pi$
$617$	−9.97680	−0.401651	−0.200825	+	0.979627i	$0.564362\pi$
$618$	0.564896	0.0227235
$619$	14.5672	0.585506	0.292753	−	0.956188i	$-0.405429\pi$
$619$	14.5672	0.585506	0.292753	+	0.956188i	$0.405429\pi$
$620$	3.97503	0.159641
$621$	−9.37114	−0.376051
$622$	−0.303395	−0.0121650
$623$	6.39835	0.256345
$624$	0	0
$625$	−18.6964	−0.747857
$626$	0.694485	0.0277572
$627$	0.256844	0.0102573
$628$	−1.79271	−0.0715370
$629$	−6.02692	−0.240309
$630$	0.303556	0.0120940
$631$	−44.9944	−1.79120	−0.895600	−	0.444861i	$-0.853253\pi$
$631$	−44.9944	−1.79120	−0.895600	+	0.444861i	$0.853253\pi$
$632$	1.99558	0.0793797
$633$	38.3989	1.52622
$634$	0.727564	0.0288952
$635$	19.9481	0.791615
$636$	16.4783	0.653406
$637$	0	0
$638$	−0.890563	−0.0352577
$639$	6.27313	0.248161
$640$	2.60967	0.103156
$641$	27.6007	1.09016	0.545080	−	0.838384i	$-0.316499\pi$
$641$	27.6007	1.09016	0.545080	+	0.838384i	$0.316499\pi$
$642$	−1.37020	−0.0540773
$643$	38.2437	1.50818	0.754092	−	0.656768i	$-0.228077\pi$
$643$	38.2437	1.50818	0.754092	+	0.656768i	$0.228077\pi$
$644$	14.8603	0.585578
$645$	−5.24020	−0.206333
$646$	0.00979025	0.000385192 0
$647$	−12.6092	−0.495719	−0.247860	−	0.968796i	$-0.579727\pi$
$647$	−12.6092	−0.495719	−0.247860	+	0.968796i	$0.579727\pi$
$648$	−1.84572	−0.0725066
$649$	12.7341	0.499858
$650$	0	0
$651$	5.62648	0.220519
$652$	38.2750	1.49897
$653$	−33.0984	−1.29524	−0.647621	−	0.761963i	$-0.724236\pi$
$653$	−33.0984	−1.29524	−0.647621	+	0.761963i	$0.724236\pi$
$654$	1.74907	0.0683940
$655$	24.6354	0.962584
$656$	−0.314806	−0.0122911
$657$	−0.0315875	−0.00123235
$658$	−0.772175	−0.0301025
$659$	6.77675	0.263985	0.131992	−	0.991251i	$-0.457863\pi$
$659$	6.77675	0.263985	0.131992	+	0.991251i	$0.457863\pi$
$660$	30.0270	1.16880
$661$	34.9481	1.35932	0.679661	−	0.733526i	$-0.262127\pi$
$661$	34.9481	1.35932	0.679661	+	0.733526i	$0.262127\pi$
$662$	−0.766957	−0.0298086
$663$	0	0
$664$	0.957318	0.0371511
$665$	0.181794	0.00704966
$666$	0.0488236	0.00189188
$667$	−16.6192	−0.643499
$668$	−15.2158	−0.588718
$669$	13.8699	0.536243
$670$	0.794161	0.0306811
$671$	−17.0040	−0.656434
$672$	2.77079	0.106886
$673$	−12.8510	−0.495368	−0.247684	−	0.968841i	$-0.579670\pi$
$673$	−12.8510	−0.495368	−0.247684	+	0.968841i	$0.579670\pi$
$674$	0.0784405	0.00302142
$675$	3.53313	0.135990
$676$	0	0
$677$	5.23104	0.201045	0.100523	−	0.994935i	$-0.467949\pi$
$677$	5.23104	0.201045	0.100523	+	0.994935i	$0.467949\pi$
$678$	0.0454820	0.00174673
$679$	8.42855	0.323458
$680$	2.29008	0.0878206
$681$	−9.19387	−0.352310
$682$	−0.148257	−0.00567704
$683$	−24.8006	−0.948970	−0.474485	−	0.880264i	$-0.657366\pi$
$683$	−24.8006	−0.948970	−0.474485	+	0.880264i	$0.657366\pi$
$684$	0.0938950	0.00359017
$685$	−32.4163	−1.23856
$686$	−0.748201	−0.0285665
$687$	−34.5441	−1.31794
$688$	−5.02108	−0.191427
$689$	0	0
$690$	−0.473308	−0.0180185
$691$	13.3444	0.507647	0.253823	−	0.967251i	$-0.418312\pi$
$691$	13.3444	0.507647	0.253823	+	0.967251i	$0.418312\pi$
$692$	−6.34706	−0.241279
$693$	13.4038	0.509167
$694$	−1.10331	−0.0418810
$695$	−38.2642	−1.45144
$696$	−2.06554	−0.0782942
$697$	−0.552976	−0.0209455
$698$	−0.177381	−0.00671396
$699$	0.234852	0.00888291
$700$	−5.60267	−0.211761
$701$	−14.1263	−0.533544	−0.266772	−	0.963760i	$-0.585957\pi$
$701$	−14.1263	−0.533544	−0.266772	+	0.963760i	$0.585957\pi$
$702$	0	0
$703$	0.0292395	0.00110279
$704$	28.7228	1.08253
$705$	−29.1170	−1.09661
$706$	1.33025	0.0500645
$707$	48.3749	1.81933
$708$	14.7613	0.554764
$709$	13.2739	0.498513	0.249256	−	0.968438i	$-0.419814\pi$
$709$	13.2739	0.498513	0.249256	+	0.968438i	$0.419814\pi$
$710$	−0.370983	−0.0139227
$711$	16.7880	0.629600
$712$	−0.391034	−0.0146546
$713$	−2.76669	−0.103613
$714$	1.62007	0.0606296
$715$	0	0
$716$	51.3694	1.91976
$717$	−0.319608	−0.0119360
$718$	0.677708	0.0252918
$719$	22.5096	0.839468	0.419734	−	0.907647i	$-0.362123\pi$
$719$	22.5096	0.839468	0.419734	+	0.907647i	$0.362123\pi$
$720$	10.9678	0.408745
$721$	17.6550	0.657506
$722$	0.780551	0.0290491
$723$	58.9712	2.19316
$724$	2.40925	0.0895392
$725$	6.26582	0.232707
$726$	−0.173899	−0.00645401
$727$	19.7975	0.734248	0.367124	−	0.930172i	$-0.380342\pi$
$727$	19.7975	0.734248	0.367124	+	0.930172i	$0.380342\pi$
$728$	0	0
$729$	5.74359	0.212725
$730$	0.00186804	6.91391e−5 0
$731$	−8.81984	−0.326213
$732$	−19.7110	−0.728538
$733$	−44.0398	−1.62665	−0.813323	−	0.581813i	$-0.802344\pi$
$733$	−44.0398	−1.62665	−0.813323	+	0.581813i	$0.802344\pi$
$734$	−0.140204	−0.00517501
$735$	0.934967	0.0344868
$736$	−1.36247	−0.0502213
$737$	35.0668	1.29170
$738$	0.00447961	0.000164897 0
$739$	32.8735	1.20927	0.604636	−	0.796502i	$-0.293319\pi$
$739$	32.8735	1.20927	0.604636	+	0.796502i	$0.293319\pi$
$740$	3.41833	0.125660
$741$	0	0
$742$	−0.435006	−0.0159696
$743$	−6.62782	−0.243151	−0.121576	−	0.992582i	$-0.538795\pi$
$743$	−6.62782	−0.243151	−0.121576	+	0.992582i	$0.538795\pi$
$744$	−0.343861	−0.0126066
$745$	−25.6159	−0.938492
$746$	1.17219	0.0429168
$747$	8.05355	0.294664
$748$	50.5389	1.84788
$749$	−42.8234	−1.56473
$750$	1.03382	0.0377497
$751$	19.8405	0.723991	0.361996	−	0.932180i	$-0.382096\pi$
$751$	19.8405	0.723991	0.361996	+	0.932180i	$0.382096\pi$
$752$	−27.8995	−1.01739
$753$	57.3764	2.09091
$754$	0	0
$755$	−11.3525	−0.413159
$756$	−18.1929	−0.661668
$757$	−30.5511	−1.11040	−0.555200	−	0.831717i	$-0.687358\pi$
$757$	−30.5511	−1.11040	−0.555200	+	0.831717i	$0.687358\pi$
$758$	−1.17836	−0.0427998
$759$	−20.8993	−0.758596
$760$	−0.0111103	−0.000403012 0
$761$	−42.5749	−1.54334	−0.771669	−	0.636024i	$-0.780578\pi$
$761$	−42.5749	−1.54334	−0.771669	+	0.636024i	$0.780578\pi$
$762$	−0.862442	−0.0312430
$763$	54.6645	1.97899
$764$	39.8127	1.44037
$765$	19.2656	0.696549
$766$	−1.41134	−0.0509936
$767$	0	0
$768$	33.2105	1.19838
$769$	−26.9857	−0.973130	−0.486565	−	0.873644i	$-0.661750\pi$
$769$	−26.9857	−0.973130	−0.486565	+	0.873644i	$0.661750\pi$
$770$	−0.792677	−0.0285661
$771$	28.8147	1.03774
$772$	51.6907	1.86039
$773$	−7.57372	−0.272408	−0.136204	−	0.990681i	$-0.543490\pi$
$773$	−7.57372	−0.272408	−0.136204	+	0.990681i	$0.543490\pi$
$774$	0.0714488	0.00256817
$775$	1.04310	0.0374693
$776$	−0.515109	−0.0184913
$777$	4.83849	0.173580
$778$	0.250477	0.00898004
$779$	0.00268275	9.61196e−5 0
$780$	0	0
$781$	−16.3810	−0.586160
$782$	−0.796630	−0.0284874
$783$	20.3462	0.727114
$784$	0.895872	0.0319954
$785$	1.78453	0.0636927
$786$	−1.06509	−0.0379907
$787$	2.94328	0.104917	0.0524583	−	0.998623i	$-0.483294\pi$
$787$	2.94328	0.104917	0.0524583	+	0.998623i	$0.483294\pi$
$788$	−24.1510	−0.860343
$789$	45.3339	1.61393
$790$	−0.992816	−0.0353228
$791$	1.42147	0.0505417
$792$	−0.819168	−0.0291079
$793$	0	0
$794$	0.295927	0.0105020
$795$	−16.4031	−0.581758
$796$	−34.2851	−1.21520
$797$	7.34675	0.260235	0.130118	−	0.991499i	$-0.458465\pi$
$797$	7.34675	0.260235	0.130118	+	0.991499i	$0.458465\pi$
$798$	−0.00785974	−0.000278232 0
$799$	−49.0071	−1.73375
$800$	0.513681	0.0181614
$801$	−3.28962	−0.116233
$802$	−0.578027	−0.0204108
$803$	0.0824846	0.00291082
$804$	40.6492	1.43359
$805$	−14.7925	−0.521368
$806$	0	0
$807$	3.06194	0.107786
$808$	−2.95642	−0.104007
$809$	8.40746	0.295590	0.147795	−	0.989018i	$-0.452782\pi$
$809$	8.40746	0.295590	0.147795	+	0.989018i	$0.452782\pi$
$810$	0.918260	0.0322644
$811$	−15.7063	−0.551524	−0.275762	−	0.961226i	$-0.588930\pi$
$811$	−15.7063	−0.551524	−0.275762	+	0.961226i	$0.588930\pi$
$812$	−32.2641	−1.13225
$813$	−19.4733	−0.682959
$814$	−0.127493	−0.00446863
$815$	−38.1004	−1.33460
$816$	58.5348	2.04913
$817$	0.0427893	0.00149701
$818$	0.574360	0.0200820
$819$	0	0
$820$	0.313635	0.0109526
$821$	49.4942	1.72736	0.863680	−	0.504040i	$-0.168154\pi$
$821$	49.4942	1.72736	0.863680	+	0.504040i	$0.168154\pi$
$822$	1.40150	0.0488829
$823$	38.6112	1.34590	0.672952	−	0.739687i	$-0.265026\pi$
$823$	38.6112	1.34590	0.672952	+	0.739687i	$0.265026\pi$
$824$	−1.07898	−0.0375880
$825$	7.87950	0.274329
$826$	−0.389681	−0.0135587
$827$	−7.87477	−0.273833	−0.136916	−	0.990583i	$-0.543719\pi$
$827$	−7.87477	−0.273833	−0.136916	+	0.990583i	$0.543719\pi$
$828$	−7.64021	−0.265516
$829$	−22.8000	−0.791877	−0.395939	−	0.918277i	$-0.629581\pi$
$829$	−22.8000	−0.791877	−0.395939	+	0.918277i	$0.629581\pi$
$830$	−0.476274	−0.0165317
$831$	−41.7455	−1.44813
$832$	0	0
$833$	1.57365	0.0545239
$834$	1.65433	0.0572847
$835$	15.1464	0.524163
$836$	−0.245188	−0.00848002
$837$	3.38713	0.117077
$838$	−1.23999	−0.0428349
$839$	17.8247	0.615376	0.307688	−	0.951487i	$-0.400445\pi$
$839$	17.8247	0.615376	0.307688	+	0.951487i	$0.400445\pi$
$840$	−1.83851	−0.0634346
$841$	7.08291	0.244238
$842$	−1.55514	−0.0535938
$843$	7.20979	0.248318
$844$	−36.6564	−1.26176
$845$	0	0
$846$	0.397002	0.0136492
$847$	−5.43496	−0.186747
$848$	−15.7172	−0.539731
$849$	−41.8515	−1.43634
$850$	0.300347	0.0103018
$851$	−2.37921	−0.0815583
$852$	−18.9888	−0.650545
$853$	10.3020	0.352733	0.176367	−	0.984325i	$-0.443566\pi$
$853$	10.3020	0.352733	0.176367	+	0.984325i	$0.443566\pi$
$854$	0.520345	0.0178059
$855$	−0.0934667	−0.00319649
$856$	2.61714	0.0894521
$857$	−23.0595	−0.787696	−0.393848	−	0.919176i	$-0.628856\pi$
$857$	−23.0595	−0.787696	−0.393848	+	0.919176i	$0.628856\pi$
$858$	0	0
$859$	44.7548	1.52701	0.763507	−	0.645799i	$-0.223476\pi$
$859$	44.7548	1.52701	0.763507	+	0.645799i	$0.223476\pi$
$860$	5.00240	0.170581
$861$	0.443936	0.0151293
$862$	1.23361	0.0420170
$863$	−19.6422	−0.668630	−0.334315	−	0.942461i	$-0.608505\pi$
$863$	−19.6422	−0.668630	−0.334315	+	0.942461i	$0.608505\pi$
$864$	1.66801	0.0567469
$865$	6.31810	0.214822
$866$	0.763619	0.0259488
$867$	67.2338	2.28338
$868$	−5.37116	−0.182309
$869$	−43.8386	−1.48712
$870$	1.02763	0.0348398
$871$	0	0
$872$	−3.34081	−0.113134
$873$	−4.33342	−0.146664
$874$	0.00386483	0.000130730 0
$875$	32.3104	1.09229
$876$	0.0956156	0.00323055
$877$	9.69906	0.327514	0.163757	−	0.986501i	$-0.447639\pi$
$877$	9.69906	0.327514	0.163757	+	0.986501i	$0.447639\pi$
$878$	1.27818	0.0431365
$879$	19.8849	0.670703
$880$	−28.6402	−0.965462
$881$	27.7683	0.935538	0.467769	−	0.883851i	$-0.345058\pi$
$881$	27.7683	0.935538	0.467769	+	0.883851i	$0.345058\pi$
$882$	−0.0127480	−0.000429249 0
$883$	32.9099	1.10751	0.553754	−	0.832681i	$-0.313195\pi$
$883$	32.9099	1.10751	0.553754	+	0.832681i	$0.313195\pi$
$884$	0	0
$885$	−14.6940	−0.493932
$886$	−0.584388	−0.0196329
$887$	−24.3048	−0.816076	−0.408038	−	0.912965i	$-0.633787\pi$
$887$	−24.3048	−0.816076	−0.408038	+	0.912965i	$0.633787\pi$
$888$	−0.295703	−0.00992315
$889$	−26.9543	−0.904019
$890$	0.194543	0.00652109
$891$	40.5465	1.35836
$892$	−13.2405	−0.443326
$893$	0.237757	0.00795623
$894$	1.10749	0.0370398
$895$	−51.1350	−1.70925
$896$	−3.52625	−0.117804
$897$	0	0
$898$	−0.282151	−0.00941550
$899$	6.00691	0.200342
$900$	2.88053	0.0960177
$901$	−27.6082	−0.919764
$902$	−0.0116976	−0.000389488 0
$903$	7.08068	0.235630
$904$	−0.0868729	−0.00288935
$905$	−2.39826	−0.0797209
$906$	0.490818	0.0163063
$907$	−34.8677	−1.15776	−0.578881	−	0.815412i	$-0.696510\pi$
$907$	−34.8677	−1.15776	−0.578881	+	0.815412i	$0.696510\pi$
$908$	8.77667	0.291264
$909$	−24.8713	−0.824928
$910$	0	0
$911$	−47.0964	−1.56037	−0.780186	−	0.625547i	$-0.784876\pi$
$911$	−47.0964	−1.56037	−0.780186	+	0.625547i	$0.784876\pi$
$912$	−0.283980	−0.00940353
$913$	−21.0303	−0.696000
$914$	0.714182	0.0236231
$915$	19.6210	0.648652
$916$	32.9765	1.08957
$917$	−33.2879	−1.09926
$918$	0.975280	0.0321890
$919$	−31.5239	−1.03988	−0.519939	−	0.854203i	$-0.674045\pi$
$919$	−31.5239	−1.03988	−0.519939	+	0.854203i	$0.674045\pi$
$920$	0.904041	0.0298054
$921$	−54.0278	−1.78028
$922$	0.247118	0.00813840
$923$	0	0
$924$	−40.5733	−1.33476
$925$	0.897015	0.0294937
$926$	−0.877280	−0.0288292
$927$	−9.07705	−0.298129
$928$	2.95813	0.0971054
$929$	−1.66884	−0.0547528	−0.0273764	−	0.999625i	$-0.508715\pi$
$929$	−1.66884	−0.0547528	−0.0273764	+	0.999625i	$0.508715\pi$
$930$	0.171074	0.00560974
$931$	−0.00763455	−0.000250212 0
$932$	−0.224195	−0.00734374
$933$	15.4584	0.506087
$934$	−0.253279	−0.00828756
$935$	−50.3083	−1.64526
$936$	0	0
$937$	40.6727	1.32872	0.664359	−	0.747414i	$-0.268705\pi$
$937$	40.6727	1.32872	0.664359	+	0.747414i	$0.268705\pi$
$938$	−1.07309	−0.0350376
$939$	−35.3851	−1.15475
$940$	27.7957	0.906595
$941$	−3.23019	−0.105301	−0.0526505	−	0.998613i	$-0.516767\pi$
$941$	−3.23019	−0.105301	−0.0526505	+	0.998613i	$0.516767\pi$
$942$	−0.0771531	−0.00251379
$943$	−0.218295	−0.00710866
$944$	−14.0796	−0.458250
$945$	18.1099	0.589114
$946$	−0.186574	−0.00606606
$947$	−13.7592	−0.447114	−0.223557	−	0.974691i	$-0.571767\pi$
$947$	−13.7592	−0.447114	−0.223557	+	0.974691i	$0.571767\pi$
$948$	−50.8174	−1.65047
$949$	0	0
$950$	−0.00145713	−4.72755e−5 0
$951$	−37.0705	−1.20209
$952$	−3.09442	−0.100291
$953$	−12.4481	−0.403232	−0.201616	−	0.979465i	$-0.564619\pi$
$953$	−12.4481	−0.403232	−0.201616	+	0.979465i	$0.564619\pi$
$954$	0.223652	0.00724100
$955$	−39.6311	−1.28243
$956$	0.305104	0.00986778
$957$	45.3756	1.46679
$958$	−0.906867	−0.0292995
$959$	43.8018	1.41443
$960$	−33.1433	−1.06970
$961$	1.00000	0.0322581
$962$	0	0
$963$	22.0170	0.709489
$964$	−56.2952	−1.81315
$965$	−51.4549	−1.65639
$966$	0.639545	0.0205770
$967$	−39.6282	−1.27436	−0.637179	−	0.770716i	$-0.719899\pi$
$967$	−39.6282	−1.27436	−0.637179	+	0.770716i	$0.719899\pi$
$968$	0.332156	0.0106759
$969$	−0.498829	−0.0160247
$970$	0.256271	0.00822837
$971$	22.1096	0.709531	0.354766	−	0.934955i	$-0.384561\pi$
$971$	22.1096	0.709531	0.354766	+	0.934955i	$0.384561\pi$
$972$	26.6956	0.856261
$973$	51.7036	1.65754
$974$	0.220988	0.00708091
$975$	0	0
$976$	18.8006	0.601793
$977$	9.50456	0.304078	0.152039	−	0.988375i	$-0.451416\pi$
$977$	9.50456	0.304078	0.152039	+	0.988375i	$0.451416\pi$
$978$	1.64725	0.0526731
$979$	8.59019	0.274544
$980$	−0.892539	−0.0285111
$981$	−28.1049	−0.897322
$982$	−0.394384	−0.0125853
$983$	34.7301	1.10772	0.553860	−	0.832610i	$-0.313154\pi$
$983$	34.7301	1.10772	0.553860	+	0.832610i	$0.313154\pi$
$984$	−0.0271311	−0.000864907 0
$985$	24.0408	0.766004
$986$	1.72961	0.0550820
$987$	39.3435	1.25232
$988$	0	0
$989$	−3.48175	−0.110713
$990$	0.407543	0.0129526
$991$	2.61715	0.0831365	0.0415682	−	0.999136i	$-0.486765\pi$
$991$	2.61715	0.0831365	0.0415682	+	0.999136i	$0.486765\pi$
$992$	0.492455	0.0156355
$993$	39.0777	1.24009
$994$	0.501281	0.0158997
$995$	34.1287	1.08195
$996$	−24.3781	−0.772451
$997$	−35.4696	−1.12333	−0.561667	−	0.827363i	$-0.689840\pi$
$997$	−35.4696	−1.12333	−0.561667	+	0.827363i	$0.689840\pi$
$998$	1.61582	0.0511479
$999$	2.91277	0.0921558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.m.1.9		17
13.3	even	3		403.2.f.b.373.9	yes	34
13.9	even	3		403.2.f.b.94.9	✓	34
13.12	even	2		5239.2.a.n.1.9		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.b.94.9	✓	34	13.9	even	3
403.2.f.b.373.9	yes	34	13.3	even	3
5239.2.a.m.1.9		17	1.1	even	1	trivial
5239.2.a.n.1.9		17	13.12	even	2

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)

\(f(q)\)	\(=\)	\(q-0.0410842 q^{2} +2.09330 q^{3} -1.99831 q^{4} +1.98920 q^{5} -0.0860016 q^{6} -2.68785 q^{7} +0.164267 q^{8} +1.38192 q^{9} +O(q^{10})\)	\(q-0.0410842 q^{2} +2.09330 q^{3} -1.99831 q^{4} +1.98920 q^{5} -0.0860016 q^{6} -2.68785 q^{7} +0.164267 q^{8} +1.38192 q^{9} -0.0817244 q^{10} -3.60861 q^{11} -4.18307 q^{12} +0.110428 q^{14} +4.16399 q^{15} +3.98988 q^{16} +7.00846 q^{17} -0.0567750 q^{18} -0.0340014 q^{19} -3.97503 q^{20} -5.62648 q^{21} +0.148257 q^{22} +2.76669 q^{23} +0.343861 q^{24} -1.04310 q^{25} -3.38713 q^{27} +5.37116 q^{28} -6.00691 q^{29} -0.171074 q^{30} -1.00000 q^{31} -0.492455 q^{32} -7.55391 q^{33} -0.287937 q^{34} -5.34666 q^{35} -2.76150 q^{36} -0.859950 q^{37} +0.00139692 q^{38} +0.326760 q^{40} -0.0789012 q^{41} +0.231159 q^{42} -1.25846 q^{43} +7.21112 q^{44} +2.74891 q^{45} -0.113667 q^{46} -6.99256 q^{47} +8.35202 q^{48} +0.224536 q^{49} +0.0428550 q^{50} +14.6708 q^{51} -3.93927 q^{53} +0.139158 q^{54} -7.17822 q^{55} -0.441526 q^{56} -0.0711753 q^{57} +0.246789 q^{58} -3.52882 q^{59} -8.32095 q^{60} +4.71208 q^{61} +0.0410842 q^{62} -3.71439 q^{63} -7.95952 q^{64} +0.310346 q^{66} -9.71755 q^{67} -14.0051 q^{68} +5.79151 q^{69} +0.219663 q^{70} +4.53944 q^{71} +0.227004 q^{72} -0.0228577 q^{73} +0.0353303 q^{74} -2.18353 q^{75} +0.0679454 q^{76} +9.69939 q^{77} +12.1483 q^{79} +7.93664 q^{80} -11.2361 q^{81} +0.00324159 q^{82} +5.82781 q^{83} +11.2435 q^{84} +13.9412 q^{85} +0.0517026 q^{86} -12.5743 q^{87} -0.592776 q^{88} -2.38047 q^{89} -0.112936 q^{90} -5.52870 q^{92} -2.09330 q^{93} +0.287283 q^{94} -0.0676354 q^{95} -1.03086 q^{96} -3.13580 q^{97} -0.00922489 q^{98} -4.98680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9	\( 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9} + 6 q^{10} - 13 q^{11} + 4 q^{12} - 4 q^{15} + 34 q^{16} - 6 q^{17} + 12 q^{18} - 4 q^{19} - 28 q^{20} - 18 q^{21} - 34 q^{22} - 8 q^{23} - 40 q^{24} + 8 q^{25} - 3 q^{27} - 21 q^{28} - 6 q^{29} + 19 q^{30} - 17 q^{31} - 6 q^{32} - 7 q^{33} - 24 q^{34} - 9 q^{35} - 14 q^{37} + 11 q^{38} - 10 q^{40} - 43 q^{41} + 33 q^{42} + 18 q^{43} - 28 q^{44} - 26 q^{45} - 7 q^{46} - 6 q^{47} - 95 q^{48} - q^{49} - 44 q^{50} + 26 q^{51} - 5 q^{53} - 27 q^{54} + 39 q^{55} + 39 q^{56} - 46 q^{57} - 8 q^{58} + q^{59} - 21 q^{60} - 19 q^{61} + 4 q^{62} - 5 q^{63} + 42 q^{64} + 26 q^{66} - 10 q^{67} + 34 q^{68} + 32 q^{69} + 24 q^{70} - 35 q^{71} + 26 q^{72} - 11 q^{73} - 68 q^{74} - 62 q^{75} - 2 q^{76} + 21 q^{77} + q^{79} - 49 q^{80} + 37 q^{81} + 35 q^{82} - 24 q^{83} + 34 q^{84} + 13 q^{85} - 76 q^{86} - 22 q^{87} - 37 q^{88} - 42 q^{89} + 15 q^{90} + 15 q^{92} + 42 q^{94} + 34 q^{95} - 33 q^{96} + 38 q^{97} - 8 q^{98} - 17 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9 + 6 * q^10 - 13 * q^11 + 4 * q^12 - 4 * q^15 + 34 * q^16 - 6 * q^17 + 12 * q^18 - 4 * q^19 - 28 * q^20 - 18 * q^21 - 34 * q^22 - 8 * q^23 - 40 * q^24 + 8 * q^25 - 3 * q^27 - 21 * q^28 - 6 * q^29 + 19 * q^30 - 17 * q^31 - 6 * q^32 - 7 * q^33 - 24 * q^34 - 9 * q^35 - 14 * q^37 + 11 * q^38 - 10 * q^40 - 43 * q^41 + 33 * q^42 + 18 * q^43 - 28 * q^44 - 26 * q^45 - 7 * q^46 - 6 * q^47 - 95 * q^48 - q^49 - 44 * q^50 + 26 * q^51 - 5 * q^53 - 27 * q^54 + 39 * q^55 + 39 * q^56 - 46 * q^57 - 8 * q^58 + q^59 - 21 * q^60 - 19 * q^61 + 4 * q^62 - 5 * q^63 + 42 * q^64 + 26 * q^66 - 10 * q^67 + 34 * q^68 + 32 * q^69 + 24 * q^70 - 35 * q^71 + 26 * q^72 - 11 * q^73 - 68 * q^74 - 62 * q^75 - 2 * q^76 + 21 * q^77 + q^79 - 49 * q^80 + 37 * q^81 + 35 * q^82 - 24 * q^83 + 34 * q^84 + 13 * q^85 - 76 * q^86 - 22 * q^87 - 37 * q^88 - 42 * q^89 + 15 * q^90 + 15 * q^92 + 42 * q^94 + 34 * q^95 - 33 * q^96 + 38 * q^97 - 8 * q^98 - 17 * q^99

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