LMFDB - Embedded newform 6015.2.a.g.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73556 q^{2} -1.00000 q^{3} +1.01218 q^{4} +1.00000 q^{5} +1.73556 q^{6} -3.79849 q^{7} +1.71442 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.73556 q^{2} -1.00000 q^{3} +1.01218 q^{4} +1.00000 q^{5} +1.73556 q^{6} -3.79849 q^{7} +1.71442 q^{8} +1.00000 q^{9} -1.73556 q^{10} -0.963301 q^{11} -1.01218 q^{12} -3.39904 q^{13} +6.59253 q^{14} -1.00000 q^{15} -4.99985 q^{16} -6.17770 q^{17} -1.73556 q^{18} +1.05533 q^{19} +1.01218 q^{20} +3.79849 q^{21} +1.67187 q^{22} -1.21075 q^{23} -1.71442 q^{24} +1.00000 q^{25} +5.89925 q^{26} -1.00000 q^{27} -3.84478 q^{28} -5.75563 q^{29} +1.73556 q^{30} -4.28613 q^{31} +5.24873 q^{32} +0.963301 q^{33} +10.7218 q^{34} -3.79849 q^{35} +1.01218 q^{36} +4.40120 q^{37} -1.83159 q^{38} +3.39904 q^{39} +1.71442 q^{40} -7.32447 q^{41} -6.59253 q^{42} -6.93997 q^{43} -0.975038 q^{44} +1.00000 q^{45} +2.10134 q^{46} -5.62594 q^{47} +4.99985 q^{48} +7.42856 q^{49} -1.73556 q^{50} +6.17770 q^{51} -3.44046 q^{52} -11.9535 q^{53} +1.73556 q^{54} -0.963301 q^{55} -6.51220 q^{56} -1.05533 q^{57} +9.98926 q^{58} -0.574166 q^{59} -1.01218 q^{60} +7.36238 q^{61} +7.43885 q^{62} -3.79849 q^{63} +0.890189 q^{64} -3.39904 q^{65} -1.67187 q^{66} -2.50245 q^{67} -6.25297 q^{68} +1.21075 q^{69} +6.59253 q^{70} +1.21463 q^{71} +1.71442 q^{72} -4.37654 q^{73} -7.63857 q^{74} -1.00000 q^{75} +1.06819 q^{76} +3.65909 q^{77} -5.89925 q^{78} -6.49619 q^{79} -4.99985 q^{80} +1.00000 q^{81} +12.7121 q^{82} +3.39712 q^{83} +3.84478 q^{84} -6.17770 q^{85} +12.0448 q^{86} +5.75563 q^{87} -1.65150 q^{88} +10.7276 q^{89} -1.73556 q^{90} +12.9112 q^{91} -1.22550 q^{92} +4.28613 q^{93} +9.76418 q^{94} +1.05533 q^{95} -5.24873 q^{96} +6.80754 q^{97} -12.8927 q^{98} -0.963301 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9} + 15 q^{11} - 36 q^{12} + 8 q^{13} + 10 q^{14} - 36 q^{15} + 36 q^{16} + 32 q^{17} + 5 q^{19} + 36 q^{20} + 4 q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + 36 q^{25} + 22 q^{26} - 36 q^{27} + 61 q^{29} + 15 q^{31} - q^{32} - 15 q^{33} + 26 q^{34} - 4 q^{35} + 36 q^{36} + 16 q^{37} + 20 q^{38} - 8 q^{39} - 3 q^{40} + 61 q^{41} - 10 q^{42} - 35 q^{43} + 39 q^{44} + 36 q^{45} + 11 q^{46} - 28 q^{47} - 36 q^{48} + 68 q^{49} - 32 q^{51} + 4 q^{52} + 33 q^{53} + 15 q^{55} + 23 q^{56} - 5 q^{57} + 6 q^{58} + 35 q^{59} - 36 q^{60} + 55 q^{61} + q^{62} - 4 q^{63} + 15 q^{64} + 8 q^{65} - q^{66} - 34 q^{67} + 60 q^{68} + 10 q^{69} + 10 q^{70} + 42 q^{71} - 3 q^{72} + 53 q^{73} + 54 q^{74} - 36 q^{75} + 20 q^{76} + 20 q^{77} - 22 q^{78} + 25 q^{79} + 36 q^{80} + 36 q^{81} - 15 q^{82} - 11 q^{83} + 32 q^{85} + 53 q^{86} - 61 q^{87} + 27 q^{88} + 81 q^{89} + 15 q^{91} - 7 q^{92} - 15 q^{93} + 56 q^{94} + 5 q^{95} + q^{96} + 47 q^{97} - 3 q^{98} + 15 q^{99}+O(q^{100}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9 + 15 * q^11 - 36 * q^12 + 8 * q^13 + 10 * q^14 - 36 * q^15 + 36 * q^16 + 32 * q^17 + 5 * q^19 + 36 * q^20 + 4 * q^21 + q^22 - 10 * q^23 + 3 * q^24 + 36 * q^25 + 22 * q^26 - 36 * q^27 + 61 * q^29 + 15 * q^31 - q^32 - 15 * q^33 + 26 * q^34 - 4 * q^35 + 36 * q^36 + 16 * q^37 + 20 * q^38 - 8 * q^39 - 3 * q^40 + 61 * q^41 - 10 * q^42 - 35 * q^43 + 39 * q^44 + 36 * q^45 + 11 * q^46 - 28 * q^47 - 36 * q^48 + 68 * q^49 - 32 * q^51 + 4 * q^52 + 33 * q^53 + 15 * q^55 + 23 * q^56 - 5 * q^57 + 6 * q^58 + 35 * q^59 - 36 * q^60 + 55 * q^61 + q^62 - 4 * q^63 + 15 * q^64 + 8 * q^65 - q^66 - 34 * q^67 + 60 * q^68 + 10 * q^69 + 10 * q^70 + 42 * q^71 - 3 * q^72 + 53 * q^73 + 54 * q^74 - 36 * q^75 + 20 * q^76 + 20 * q^77 - 22 * q^78 + 25 * q^79 + 36 * q^80 + 36 * q^81 - 15 * q^82 - 11 * q^83 + 32 * q^85 + 53 * q^86 - 61 * q^87 + 27 * q^88 + 81 * q^89 + 15 * q^91 - 7 * q^92 - 15 * q^93 + 56 * q^94 + 5 * q^95 + q^96 + 47 * q^97 - 3 * q^98 + 15 * 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 $

$2$	−1.73556	−1.22723	−0.613615	−	0.789606i	$-0.710285\pi$
$2$	−1.73556	−1.22723	−0.613615	+	0.789606i	$0.710285\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.01218	0.506092
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.73556	0.708541
$7$	−3.79849	−1.43570	−0.717848	−	0.696200i	$-0.754873\pi$
$7$	−3.79849	−1.43570	−0.717848	+	0.696200i	$0.754873\pi$
$8$	1.71442	0.606138
$9$	1.00000	0.333333
$10$	−1.73556	−0.548834
$11$	−0.963301	−0.290446	−0.145223	−	0.989399i	$-0.546390\pi$
$11$	−0.963301	−0.290446	−0.145223	+	0.989399i	$0.546390\pi$
$12$	−1.01218	−0.292193
$13$	−3.39904	−0.942724	−0.471362	−	0.881940i	$-0.656237\pi$
$13$	−3.39904	−0.942724	−0.471362	+	0.881940i	$0.656237\pi$
$14$	6.59253	1.76193
$15$	−1.00000	−0.258199
$16$	−4.99985	−1.24996
$17$	−6.17770	−1.49831	−0.749156	−	0.662394i	$-0.769541\pi$
$17$	−6.17770	−1.49831	−0.749156	+	0.662394i	$0.769541\pi$
$18$	−1.73556	−0.409077
$19$	1.05533	0.242109	0.121055	−	0.992646i	$-0.461372\pi$
$19$	1.05533	0.242109	0.121055	+	0.992646i	$0.461372\pi$
$20$	1.01218	0.226331
$21$	3.79849	0.828899
$22$	1.67187	0.356444
$23$	−1.21075	−0.252459	−0.126230	−	0.992001i	$-0.540288\pi$
$23$	−1.21075	−0.252459	−0.126230	+	0.992001i	$0.540288\pi$
$24$	−1.71442	−0.349954
$25$	1.00000	0.200000
$26$	5.89925	1.15694
$27$	−1.00000	−0.192450
$28$	−3.84478	−0.726595
$29$	−5.75563	−1.06879	−0.534397	−	0.845234i	$-0.679461\pi$
$29$	−5.75563	−1.06879	−0.534397	+	0.845234i	$0.679461\pi$
$30$	1.73556	0.316869
$31$	−4.28613	−0.769811	−0.384906	−	0.922956i	$-0.625766\pi$
$31$	−4.28613	−0.769811	−0.384906	+	0.922956i	$0.625766\pi$
$32$	5.24873	0.927854
$33$	0.963301	0.167689
$34$	10.7218	1.83877
$35$	−3.79849	−0.642063
$36$	1.01218	0.168697
$37$	4.40120	0.723553	0.361776	−	0.932265i	$-0.382170\pi$
$37$	4.40120	0.723553	0.361776	+	0.932265i	$0.382170\pi$
$38$	−1.83159	−0.297124
$39$	3.39904	0.544282
$40$	1.71442	0.271073
$41$	−7.32447	−1.14389	−0.571945	−	0.820292i	$-0.693811\pi$
$41$	−7.32447	−1.14389	−0.571945	+	0.820292i	$0.693811\pi$
$42$	−6.59253	−1.01725
$43$	−6.93997	−1.05834	−0.529168	−	0.848517i	$-0.677496\pi$
$43$	−6.93997	−1.05834	−0.529168	+	0.848517i	$0.677496\pi$
$44$	−0.975038	−0.146993
$45$	1.00000	0.149071
$46$	2.10134	0.309825
$47$	−5.62594	−0.820628	−0.410314	−	0.911944i	$-0.634581\pi$
$47$	−5.62594	−0.820628	−0.410314	+	0.911944i	$0.634581\pi$
$48$	4.99985	0.721666
$49$	7.42856	1.06122
$50$	−1.73556	−0.245446
$51$	6.17770	0.865050
$52$	−3.44046	−0.477106
$53$	−11.9535	−1.64194	−0.820971	−	0.570970i	$-0.806567\pi$
$53$	−11.9535	−1.64194	−0.820971	+	0.570970i	$0.806567\pi$
$54$	1.73556	0.236180
$55$	−0.963301	−0.129891
$56$	−6.51220	−0.870230
$57$	−1.05533	−0.139782
$58$	9.98926	1.31165
$59$	−0.574166	−0.0747500	−0.0373750	−	0.999301i	$-0.511900\pi$
$59$	−0.574166	−0.0747500	−0.0373750	+	0.999301i	$0.511900\pi$
$60$	−1.01218	−0.130673
$61$	7.36238	0.942656	0.471328	−	0.881958i	$-0.343775\pi$
$61$	7.36238	0.942656	0.471328	+	0.881958i	$0.343775\pi$
$62$	7.43885	0.944735
$63$	−3.79849	−0.478565
$64$	0.890189	0.111274
$65$	−3.39904	−0.421599
$66$	−1.67187	−0.205793
$67$	−2.50245	−0.305722	−0.152861	−	0.988248i	$-0.548849\pi$
$67$	−2.50245	−0.305722	−0.152861	+	0.988248i	$0.548849\pi$
$68$	−6.25297	−0.758284
$69$	1.21075	0.145757
$70$	6.59253	0.787958
$71$	1.21463	0.144150	0.0720749	−	0.997399i	$-0.477038\pi$
$71$	1.21463	0.144150	0.0720749	+	0.997399i	$0.477038\pi$
$72$	1.71442	0.202046
$73$	−4.37654	−0.512235	−0.256118	−	0.966646i	$-0.582443\pi$
$73$	−4.37654	−0.512235	−0.256118	+	0.966646i	$0.582443\pi$
$74$	−7.63857	−0.887965
$75$	−1.00000	−0.115470
$76$	1.06819	0.122530
$77$	3.65909	0.416992
$78$	−5.89925	−0.667959
$79$	−6.49619	−0.730879	−0.365439	−	0.930835i	$-0.619081\pi$
$79$	−6.49619	−0.730879	−0.365439	+	0.930835i	$0.619081\pi$
$80$	−4.99985	−0.559000
$81$	1.00000	0.111111
$82$	12.7121	1.40382
$83$	3.39712	0.372882	0.186441	−	0.982466i	$-0.440305\pi$
$83$	3.39712	0.372882	0.186441	+	0.982466i	$0.440305\pi$
$84$	3.84478	0.419500
$85$	−6.17770	−0.670065
$86$	12.0448	1.29882
$87$	5.75563	0.617068
$88$	−1.65150	−0.176050
$89$	10.7276	1.13713	0.568563	−	0.822639i	$-0.307499\pi$
$89$	10.7276	1.13713	0.568563	+	0.822639i	$0.307499\pi$
$90$	−1.73556	−0.182945
$91$	12.9112	1.35346
$92$	−1.22550	−0.127768
$93$	4.28613	0.444451
$94$	9.76418	1.00710
$95$	1.05533	0.108275
$96$	−5.24873	−0.535696
$97$	6.80754	0.691201	0.345601	−	0.938382i	$-0.387675\pi$
$97$	6.80754	0.691201	0.345601	+	0.938382i	$0.387675\pi$
$98$	−12.8927	−1.30236
$99$	−0.963301	−0.0968153
$100$	1.01218	0.101218
$101$	−1.82235	−0.181331	−0.0906653	−	0.995881i	$-0.528899\pi$
$101$	−1.82235	−0.181331	−0.0906653	+	0.995881i	$0.528899\pi$
$102$	−10.7218	−1.06162
$103$	−19.6921	−1.94032	−0.970161	−	0.242462i	$-0.922045\pi$
$103$	−19.6921	−1.94032	−0.970161	+	0.242462i	$0.922045\pi$
$104$	−5.82737	−0.571421
$105$	3.79849	0.370695
$106$	20.7461	2.01504
$107$	8.06655	0.779823	0.389912	−	0.920852i	$-0.372506\pi$
$107$	8.06655	0.779823	0.389912	+	0.920852i	$0.372506\pi$
$108$	−1.01218	−0.0973975
$109$	−2.54482	−0.243750	−0.121875	−	0.992545i	$-0.538891\pi$
$109$	−2.54482	−0.243750	−0.121875	+	0.992545i	$0.538891\pi$
$110$	1.67187	0.159407
$111$	−4.40120	−0.417743
$112$	18.9919	1.79457
$113$	−3.22476	−0.303360	−0.151680	−	0.988430i	$-0.548468\pi$
$113$	−3.22476	−0.303360	−0.151680	+	0.988430i	$0.548468\pi$
$114$	1.83159	0.171544
$115$	−1.21075	−0.112903
$116$	−5.82576	−0.540908
$117$	−3.39904	−0.314241
$118$	0.996502	0.0917354
$119$	23.4659	2.15112
$120$	−1.71442	−0.156504
$121$	−10.0721	−0.915641
$122$	−12.7779	−1.15686
$123$	7.32447	0.660426
$124$	−4.33835	−0.389596
$125$	1.00000	0.0894427
$126$	6.59253	0.587309
$127$	−6.84251	−0.607175	−0.303587	−	0.952804i	$-0.598184\pi$
$127$	−6.84251	−0.607175	−0.303587	+	0.952804i	$0.598184\pi$
$128$	−12.0424	−1.06441
$129$	6.93997	0.611030
$130$	5.89925	0.517399
$131$	17.1930	1.50216	0.751080	−	0.660212i	$-0.229533\pi$
$131$	17.1930	1.50216	0.751080	+	0.660212i	$0.229533\pi$
$132$	0.975038	0.0848662
$133$	−4.00866	−0.347595
$134$	4.34316	0.375192
$135$	−1.00000	−0.0860663
$136$	−10.5911	−0.908183
$137$	−16.4789	−1.40789	−0.703944	−	0.710256i	$-0.748579\pi$
$137$	−16.4789	−1.40789	−0.703944	+	0.710256i	$0.748579\pi$
$138$	−2.10134	−0.178878
$139$	−11.7497	−0.996598	−0.498299	−	0.867005i	$-0.666042\pi$
$139$	−11.7497	−0.996598	−0.498299	+	0.867005i	$0.666042\pi$
$140$	−3.84478	−0.324943
$141$	5.62594	0.473790
$142$	−2.10807	−0.176905
$143$	3.27430	0.273810
$144$	−4.99985	−0.416654
$145$	−5.75563	−0.477979
$146$	7.59577	0.628630
$147$	−7.42856	−0.612697
$148$	4.45483	0.366185
$149$	19.4101	1.59014	0.795069	−	0.606518i	$-0.207434\pi$
$149$	19.4101	1.59014	0.795069	+	0.606518i	$0.207434\pi$
$150$	1.73556	0.141708
$151$	1.33180	0.108380	0.0541901	−	0.998531i	$-0.482742\pi$
$151$	1.33180	0.108380	0.0541901	+	0.998531i	$0.482742\pi$
$152$	1.80928	0.146752
$153$	−6.17770	−0.499437
$154$	−6.35059	−0.511745
$155$	−4.28613	−0.344270
$156$	3.44046	0.275457
$157$	4.83787	0.386104	0.193052	−	0.981189i	$-0.438161\pi$
$157$	4.83787	0.386104	0.193052	+	0.981189i	$0.438161\pi$
$158$	11.2746	0.896956
$159$	11.9535	0.947976
$160$	5.24873	0.414949
$161$	4.59903	0.362455
$162$	−1.73556	−0.136359
$163$	−19.8150	−1.55203	−0.776017	−	0.630712i	$-0.782763\pi$
$163$	−19.8150	−1.55203	−0.776017	+	0.630712i	$0.782763\pi$
$164$	−7.41372	−0.578914
$165$	0.963301	0.0749928
$166$	−5.89592	−0.457612
$167$	−5.15406	−0.398833	−0.199417	−	0.979915i	$-0.563905\pi$
$167$	−5.15406	−0.398833	−0.199417	+	0.979915i	$0.563905\pi$
$168$	6.51220	0.502427
$169$	−1.44653	−0.111271
$170$	10.7218	0.822324
$171$	1.05533	0.0807031
$172$	−7.02453	−0.535616
$173$	−10.9319	−0.831140	−0.415570	−	0.909561i	$-0.636418\pi$
$173$	−10.9319	−0.831140	−0.415570	+	0.909561i	$0.636418\pi$
$174$	−9.98926	−0.757284
$175$	−3.79849	−0.287139
$176$	4.81636	0.363047
$177$	0.574166	0.0431569
$178$	−18.6185	−1.39552
$179$	8.15041	0.609190	0.304595	−	0.952482i	$-0.401479\pi$
$179$	8.15041	0.609190	0.304595	+	0.952482i	$0.401479\pi$
$180$	1.01218	0.0754438
$181$	0.905365	0.0672952	0.0336476	−	0.999434i	$-0.489288\pi$
$181$	0.905365	0.0672952	0.0336476	+	0.999434i	$0.489288\pi$
$182$	−22.4083	−1.66101
$183$	−7.36238	−0.544243
$184$	−2.07573	−0.153025
$185$	4.40120	0.323583
$186$	−7.43885	−0.545443
$187$	5.95098	0.435179
$188$	−5.69449	−0.415314
$189$	3.79849	0.276300
$190$	−1.83159	−0.132878
$191$	−14.0926	−1.01970	−0.509851	−	0.860263i	$-0.670299\pi$
$191$	−14.0926	−1.01970	−0.509851	+	0.860263i	$0.670299\pi$
$192$	−0.890189	−0.0642438
$193$	16.3107	1.17407	0.587036	−	0.809561i	$-0.300295\pi$
$193$	16.3107	1.17407	0.587036	+	0.809561i	$0.300295\pi$
$194$	−11.8149	−0.848262
$195$	3.39904	0.243410
$196$	7.51907	0.537077
$197$	7.16667	0.510604	0.255302	−	0.966861i	$-0.417825\pi$
$197$	7.16667	0.510604	0.255302	+	0.966861i	$0.417825\pi$
$198$	1.67187	0.118815
$199$	−14.1829	−1.00540	−0.502701	−	0.864460i	$-0.667660\pi$
$199$	−14.1829	−1.00540	−0.502701	+	0.864460i	$0.667660\pi$
$200$	1.71442	0.121228
$201$	2.50245	0.176509
$202$	3.16281	0.222534
$203$	21.8627	1.53446
$204$	6.25297	0.437796
$205$	−7.32447	−0.511563
$206$	34.1769	2.38122
$207$	−1.21075	−0.0841531
$208$	16.9947	1.17837
$209$	−1.01660	−0.0703197
$210$	−6.59253	−0.454928
$211$	−21.4191	−1.47455	−0.737276	−	0.675591i	$-0.763888\pi$
$211$	−21.4191	−1.47455	−0.737276	+	0.675591i	$0.763888\pi$
$212$	−12.0992	−0.830975
$213$	−1.21463	−0.0832249
$214$	−14.0000	−0.957022
$215$	−6.93997	−0.473302
$216$	−1.71442	−0.116651
$217$	16.2808	1.10521
$218$	4.41670	0.299137
$219$	4.37654	0.295739
$220$	−0.975038	−0.0657371
$221$	20.9982	1.41249
$222$	7.63857	0.512667
$223$	−21.9525	−1.47005	−0.735023	−	0.678042i	$-0.762829\pi$
$223$	−21.9525	−1.47005	−0.735023	+	0.678042i	$0.762829\pi$
$224$	−19.9373	−1.33212
$225$	1.00000	0.0666667
$226$	5.59678	0.372292
$227$	7.75582	0.514772	0.257386	−	0.966309i	$-0.417139\pi$
$227$	7.75582	0.514772	0.257386	+	0.966309i	$0.417139\pi$
$228$	−1.06819	−0.0707425
$229$	3.80913	0.251714	0.125857	−	0.992048i	$-0.459832\pi$
$229$	3.80913	0.251714	0.125857	+	0.992048i	$0.459832\pi$
$230$	2.10134	0.138558
$231$	−3.65909	−0.240751
$232$	−9.86755	−0.647836
$233$	9.91586	0.649609	0.324805	−	0.945781i	$-0.394701\pi$
$233$	9.91586	0.649609	0.324805	+	0.945781i	$0.394701\pi$
$234$	5.89925	0.385646
$235$	−5.62594	−0.366996
$236$	−0.581162	−0.0378304
$237$	6.49619	0.421973
$238$	−40.7267	−2.63992
$239$	−14.8323	−0.959422	−0.479711	−	0.877427i	$-0.659258\pi$
$239$	−14.8323	−0.959422	−0.479711	+	0.877427i	$0.659258\pi$
$240$	4.99985	0.322739
$241$	−9.66460	−0.622552	−0.311276	−	0.950320i	$-0.600756\pi$
$241$	−9.66460	−0.622552	−0.311276	+	0.950320i	$0.600756\pi$
$242$	17.4807	1.12370
$243$	−1.00000	−0.0641500
$244$	7.45209	0.477071
$245$	7.42856	0.474593
$246$	−12.7121	−0.810494
$247$	−3.58711	−0.228242
$248$	−7.34821	−0.466612
$249$	−3.39712	−0.215284
$250$	−1.73556	−0.109767
$251$	−0.620935	−0.0391931	−0.0195965	−	0.999808i	$-0.506238\pi$
$251$	−0.620935	−0.0391931	−0.0195965	+	0.999808i	$0.506238\pi$
$252$	−3.84478	−0.242198
$253$	1.16632	0.0733258
$254$	11.8756	0.745143
$255$	6.17770	0.386862
$256$	19.1201	1.19500
$257$	2.96673	0.185059	0.0925297	−	0.995710i	$-0.470505\pi$
$257$	2.96673	0.185059	0.0925297	+	0.995710i	$0.470505\pi$
$258$	−12.0448	−0.749874
$259$	−16.7179	−1.03880
$260$	−3.44046	−0.213368
$261$	−5.75563	−0.356264
$262$	−29.8396	−1.84349
$263$	−1.15805	−0.0714082	−0.0357041	−	0.999362i	$-0.511367\pi$
$263$	−1.15805	−0.0714082	−0.0357041	+	0.999362i	$0.511367\pi$
$264$	1.65150	0.101643
$265$	−11.9535	−0.734299
$266$	6.95729	0.426579
$267$	−10.7276	−0.656520
$268$	−2.53294	−0.154724
$269$	−21.2522	−1.29577	−0.647884	−	0.761739i	$-0.724346\pi$
$269$	−21.2522	−1.29577	−0.647884	+	0.761739i	$0.724346\pi$
$270$	1.73556	0.105623
$271$	18.6744	1.13439	0.567195	−	0.823584i	$-0.308029\pi$
$271$	18.6744	1.13439	0.567195	+	0.823584i	$0.308029\pi$
$272$	30.8876	1.87283
$273$	−12.9112	−0.781423
$274$	28.6002	1.72780
$275$	−0.963301	−0.0580892
$276$	1.22550	0.0737667
$277$	−1.85487	−0.111448	−0.0557241	−	0.998446i	$-0.517747\pi$
$277$	−1.85487	−0.111448	−0.0557241	+	0.998446i	$0.517747\pi$
$278$	20.3924	1.22305
$279$	−4.28613	−0.256604
$280$	−6.51220	−0.389179
$281$	27.2502	1.62561	0.812805	−	0.582536i	$-0.197940\pi$
$281$	27.2502	1.62561	0.812805	+	0.582536i	$0.197940\pi$
$282$	−9.76418	−0.581449
$283$	−13.3380	−0.792862	−0.396431	−	0.918064i	$-0.629751\pi$
$283$	−13.3380	−0.792862	−0.396431	+	0.918064i	$0.629751\pi$
$284$	1.22943	0.0729531
$285$	−1.05533	−0.0625123
$286$	−5.68275	−0.336028
$287$	27.8220	1.64228
$288$	5.24873	0.309285
$289$	21.1639	1.24494
$290$	9.98926	0.586590
$291$	−6.80754	−0.399065
$292$	−4.42987	−0.259238
$293$	7.68057	0.448704	0.224352	−	0.974508i	$-0.427974\pi$
$293$	7.68057	0.448704	0.224352	+	0.974508i	$0.427974\pi$
$294$	12.8927	0.751920
$295$	−0.574166	−0.0334292
$296$	7.54549	0.438573
$297$	0.963301	0.0558964
$298$	−33.6875	−1.95147
$299$	4.11539	0.237999
$300$	−1.01218	−0.0584385
$301$	26.3614	1.51945
$302$	−2.31142	−0.133007
$303$	1.82235	0.104691
$304$	−5.27649	−0.302628
$305$	7.36238	0.421569
$306$	10.7218	0.612924
$307$	15.5060	0.884976	0.442488	−	0.896775i	$-0.354096\pi$
$307$	15.5060	0.884976	0.442488	+	0.896775i	$0.354096\pi$
$308$	3.70368	0.211037
$309$	19.6921	1.12025
$310$	7.43885	0.422498
$311$	−23.8827	−1.35426	−0.677132	−	0.735862i	$-0.736777\pi$
$311$	−23.8827	−1.35426	−0.677132	+	0.735862i	$0.736777\pi$
$312$	5.82737	0.329910
$313$	0.964888	0.0545387	0.0272693	−	0.999628i	$-0.491319\pi$
$313$	0.964888	0.0545387	0.0272693	+	0.999628i	$0.491319\pi$
$314$	−8.39643	−0.473838
$315$	−3.79849	−0.214021
$316$	−6.57535	−0.369892
$317$	−11.5684	−0.649748	−0.324874	−	0.945757i	$-0.605322\pi$
$317$	−11.5684	−0.649748	−0.324874	+	0.945757i	$0.605322\pi$
$318$	−20.7461	−1.16338
$319$	5.54440	0.310427
$320$	0.890189	0.0497631
$321$	−8.06655	−0.450231
$322$	−7.98192	−0.444815
$323$	−6.51951	−0.362755
$324$	1.01218	0.0562325
$325$	−3.39904	−0.188545
$326$	34.3903	1.90470
$327$	2.54482	0.140729
$328$	−12.5572	−0.693356
$329$	21.3701	1.17817
$330$	−1.67187	−0.0920334
$331$	17.1347	0.941810	0.470905	−	0.882184i	$-0.343927\pi$
$331$	17.1347	0.941810	0.470905	+	0.882184i	$0.343927\pi$
$332$	3.43851	0.188713
$333$	4.40120	0.241184
$334$	8.94521	0.489460
$335$	−2.50245	−0.136723
$336$	−18.9919	−1.03609
$337$	12.0927	0.658729	0.329364	−	0.944203i	$-0.393166\pi$
$337$	12.0927	0.658729	0.329364	+	0.944203i	$0.393166\pi$
$338$	2.51054	0.136556
$339$	3.22476	0.175145
$340$	−6.25297	−0.339115
$341$	4.12883	0.223589
$342$	−1.83159	−0.0990412
$343$	−1.62787	−0.0878965
$344$	−11.8980	−0.641497
$345$	1.21075	0.0651847
$346$	18.9731	1.02000
$347$	3.30841	0.177605	0.0888023	−	0.996049i	$-0.471696\pi$
$347$	3.30841	0.177605	0.0888023	+	0.996049i	$0.471696\pi$
$348$	5.82576	0.312293
$349$	−10.1240	−0.541926	−0.270963	−	0.962590i	$-0.587342\pi$
$349$	−10.1240	−0.541926	−0.270963	+	0.962590i	$0.587342\pi$
$350$	6.59253	0.352386
$351$	3.39904	0.181427
$352$	−5.05611	−0.269491
$353$	−35.4434	−1.88646	−0.943231	−	0.332138i	$-0.892230\pi$
$353$	−35.4434	−1.88646	−0.943231	+	0.332138i	$0.892230\pi$
$354$	−0.996502	−0.0529635
$355$	1.21463	0.0644658
$356$	10.8583	0.575491
$357$	−23.4659	−1.24195
$358$	−14.1456	−0.747617
$359$	5.46956	0.288672	0.144336	−	0.989529i	$-0.453895\pi$
$359$	5.46956	0.288672	0.144336	+	0.989529i	$0.453895\pi$
$360$	1.71442	0.0903577
$361$	−17.8863	−0.941383
$362$	−1.57132	−0.0825867
$363$	10.0721	0.528646
$364$	13.0686	0.684978
$365$	−4.37654	−0.229078
$366$	12.7779	0.667911
$367$	9.22951	0.481777	0.240888	−	0.970553i	$-0.422561\pi$
$367$	9.22951	0.481777	0.240888	+	0.970553i	$0.422561\pi$
$368$	6.05358	0.315565
$369$	−7.32447	−0.381297
$370$	−7.63857	−0.397110
$371$	45.4054	2.35733
$372$	4.33835	0.224933
$373$	21.3471	1.10531	0.552655	−	0.833410i	$-0.313615\pi$
$373$	21.3471	1.10531	0.552655	+	0.833410i	$0.313615\pi$
$374$	−10.3283	−0.534064
$375$	−1.00000	−0.0516398
$376$	−9.64521	−0.497414
$377$	19.5636	1.00758
$378$	−6.59253	−0.339083
$379$	12.5891	0.646657	0.323328	−	0.946287i	$-0.395198\pi$
$379$	12.5891	0.646657	0.323328	+	0.946287i	$0.395198\pi$
$380$	1.06819	0.0547969
$381$	6.84251	0.350553
$382$	24.4585	1.25141
$383$	21.9881	1.12354	0.561770	−	0.827293i	$-0.310121\pi$
$383$	21.9881	1.12354	0.561770	+	0.827293i	$0.310121\pi$
$384$	12.0424	0.614538
$385$	3.65909	0.186485
$386$	−28.3083	−1.44086
$387$	−6.93997	−0.352779
$388$	6.89049	0.349812
$389$	−25.9751	−1.31699	−0.658495	−	0.752585i	$-0.728807\pi$
$389$	−25.9751	−1.31699	−0.658495	+	0.752585i	$0.728807\pi$
$390$	−5.89925	−0.298720
$391$	7.47966	0.378263
$392$	12.7356	0.643247
$393$	−17.1930	−0.867272
$394$	−12.4382	−0.626629
$395$	−6.49619	−0.326859
$396$	−0.975038	−0.0489975
$397$	−14.8274	−0.744165	−0.372083	−	0.928200i	$-0.621356\pi$
$397$	−14.8274	−0.744165	−0.372083	+	0.928200i	$0.621356\pi$
$398$	24.6154	1.23386
$399$	4.00866	0.200684
$400$	−4.99985	−0.249993
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−4.34316	−0.216617
$403$	14.5687	0.725719
$404$	−1.84456	−0.0917701
$405$	1.00000	0.0496904
$406$	−37.9442	−1.88314
$407$	−4.23968	−0.210153
$408$	10.5911	0.524340
$409$	14.7227	0.727989	0.363995	−	0.931401i	$-0.381413\pi$
$409$	14.7227	0.727989	0.363995	+	0.931401i	$0.381413\pi$
$410$	12.7121	0.627806
$411$	16.4789	0.812844
$412$	−19.9321	−0.981982
$413$	2.18097	0.107318
$414$	2.10134	0.103275
$415$	3.39712	0.166758
$416$	−17.8406	−0.874710
$417$	11.7497	0.575386
$418$	1.76437	0.0862984
$419$	18.4967	0.903624	0.451812	−	0.892113i	$-0.350778\pi$
$419$	18.4967	0.903624	0.451812	+	0.892113i	$0.350778\pi$
$420$	3.84478	0.187606
$421$	−11.0718	−0.539608	−0.269804	−	0.962915i	$-0.586959\pi$
$421$	−11.0718	−0.539608	−0.269804	+	0.962915i	$0.586959\pi$
$422$	37.1743	1.80962
$423$	−5.62594	−0.273543
$424$	−20.4933	−0.995243
$425$	−6.17770	−0.299662
$426$	2.10807	0.102136
$427$	−27.9660	−1.35337
$428$	8.16484	0.394663
$429$	−3.27430	−0.158085
$430$	12.0448	0.580850
$431$	23.9241	1.15238	0.576191	−	0.817315i	$-0.304539\pi$
$431$	23.9241	1.15238	0.576191	+	0.817315i	$0.304539\pi$
$432$	4.99985	0.240555
$433$	3.92764	0.188750	0.0943752	−	0.995537i	$-0.469915\pi$
$433$	3.92764	0.188750	0.0943752	+	0.995537i	$0.469915\pi$
$434$	−28.2564	−1.35635
$435$	5.75563	0.275961
$436$	−2.57583	−0.123360
$437$	−1.27774	−0.0611227
$438$	−7.59577	−0.362940
$439$	18.1030	0.864009	0.432004	−	0.901871i	$-0.357806\pi$
$439$	18.1030	0.864009	0.432004	+	0.901871i	$0.357806\pi$
$440$	−1.65150	−0.0787321
$441$	7.42856	0.353741
$442$	−36.4438	−1.73345
$443$	−20.2285	−0.961084	−0.480542	−	0.876972i	$-0.659560\pi$
$443$	−20.2285	−0.961084	−0.480542	+	0.876972i	$0.659560\pi$
$444$	−4.45483	−0.211417
$445$	10.7276	0.508539
$446$	38.0999	1.80408
$447$	−19.4101	−0.918067
$448$	−3.38138	−0.159755
$449$	−3.73621	−0.176323	−0.0881614	−	0.996106i	$-0.528099\pi$
$449$	−3.73621	−0.176323	−0.0881614	+	0.996106i	$0.528099\pi$
$450$	−1.73556	−0.0818153
$451$	7.05567	0.332239
$452$	−3.26405	−0.153528
$453$	−1.33180	−0.0625733
$454$	−13.4607	−0.631743
$455$	12.9112	0.605288
$456$	−1.80928	−0.0847271
$457$	8.54797	0.399857	0.199928	−	0.979810i	$-0.435929\pi$
$457$	8.54797	0.399857	0.199928	+	0.979810i	$0.435929\pi$
$458$	−6.61099	−0.308911
$459$	6.17770	0.288350
$460$	−1.22550	−0.0571395
$461$	17.1387	0.798229	0.399114	−	0.916901i	$-0.369318\pi$
$461$	17.1387	0.798229	0.399114	+	0.916901i	$0.369318\pi$
$462$	6.35059	0.295456
$463$	−12.7486	−0.592479	−0.296240	−	0.955114i	$-0.595733\pi$
$463$	−12.7486	−0.592479	−0.296240	+	0.955114i	$0.595733\pi$
$464$	28.7773	1.33595
$465$	4.28613	0.198764
$466$	−17.2096	−0.797220
$467$	−15.5836	−0.721124	−0.360562	−	0.932735i	$-0.617415\pi$
$467$	−15.5836	−0.721124	−0.360562	+	0.932735i	$0.617415\pi$
$468$	−3.44046	−0.159035
$469$	9.50552	0.438924
$470$	9.76418	0.450388
$471$	−4.83787	−0.222917
$472$	−0.984360	−0.0453088
$473$	6.68528	0.307389
$474$	−11.2746	−0.517858
$475$	1.05533	0.0484218
$476$	23.7519	1.08867
$477$	−11.9535	−0.547314
$478$	25.7424	1.17743
$479$	−12.1983	−0.557355	−0.278677	−	0.960385i	$-0.589896\pi$
$479$	−12.1983	−0.557355	−0.278677	+	0.960385i	$0.589896\pi$
$480$	−5.24873	−0.239571
$481$	−14.9598	−0.682110
$482$	16.7735	0.764014
$483$	−4.59903	−0.209263
$484$	−10.1948	−0.463399
$485$	6.80754	0.309115
$486$	1.73556	0.0787268
$487$	−24.1182	−1.09290	−0.546450	−	0.837491i	$-0.684021\pi$
$487$	−24.1182	−1.09290	−0.546450	+	0.837491i	$0.684021\pi$
$488$	12.6222	0.571380
$489$	19.8150	0.896067
$490$	−12.8927	−0.582435
$491$	16.4954	0.744426	0.372213	−	0.928147i	$-0.378599\pi$
$491$	16.4954	0.744426	0.372213	+	0.928147i	$0.378599\pi$
$492$	7.41372	0.334236
$493$	35.5565	1.60138
$494$	6.22566	0.280106
$495$	−0.963301	−0.0432971
$496$	21.4300	0.962235
$497$	−4.61376	−0.206955
$498$	5.89592	0.264202
$499$	−8.32440	−0.372651	−0.186326	−	0.982488i	$-0.559658\pi$
$499$	−8.32440	−0.372651	−0.186326	+	0.982488i	$0.559658\pi$
$500$	1.01218	0.0452663
$501$	5.15406	0.230266
$502$	1.07767	0.0480989
$503$	34.2661	1.52785	0.763925	−	0.645305i	$-0.223270\pi$
$503$	34.2661	1.52785	0.763925	+	0.645305i	$0.223270\pi$
$504$	−6.51220	−0.290077
$505$	−1.82235	−0.0810935
$506$	−2.02422	−0.0899876
$507$	1.44653	0.0642426
$508$	−6.92589	−0.307287
$509$	30.7402	1.36254	0.681269	−	0.732034i	$-0.261429\pi$
$509$	30.7402	1.36254	0.681269	+	0.732034i	$0.261429\pi$
$510$	−10.7218	−0.474769
$511$	16.6243	0.735414
$512$	−9.09922	−0.402133
$513$	−1.05533	−0.0465939
$514$	−5.14895	−0.227110
$515$	−19.6921	−0.867738
$516$	7.02453	0.309238
$517$	5.41947	0.238348
$518$	29.0150	1.27485
$519$	10.9319	0.479859
$520$	−5.82737	−0.255547
$521$	26.5432	1.16288	0.581438	−	0.813590i	$-0.302490\pi$
$521$	26.5432	1.16288	0.581438	+	0.813590i	$0.302490\pi$
$522$	9.98926	0.437218
$523$	−17.6389	−0.771296	−0.385648	−	0.922646i	$-0.626022\pi$
$523$	−17.6389	−0.771296	−0.385648	+	0.922646i	$0.626022\pi$
$524$	17.4025	0.760232
$525$	3.79849	0.165780
$526$	2.00986	0.0876343
$527$	26.4784	1.15342
$528$	−4.81636	−0.209605
$529$	−21.5341	−0.936264
$530$	20.7461	0.901153
$531$	−0.574166	−0.0249167
$532$	−4.05751	−0.175915
$533$	24.8962	1.07837
$534$	18.6185	0.805701
$535$	8.06655	0.348748
$536$	−4.29024	−0.185310
$537$	−8.15041	−0.351716
$538$	36.8846	1.59021
$539$	−7.15593	−0.308228
$540$	−1.01218	−0.0435575
$541$	3.47151	0.149252	0.0746259	−	0.997212i	$-0.476224\pi$
$541$	3.47151	0.149252	0.0746259	+	0.997212i	$0.476224\pi$
$542$	−32.4106	−1.39216
$543$	−0.905365	−0.0388529
$544$	−32.4251	−1.39021
$545$	−2.54482	−0.109008
$546$	22.4083	0.958986
$547$	18.2318	0.779536	0.389768	−	0.920913i	$-0.372555\pi$
$547$	18.2318	0.779536	0.389768	+	0.920913i	$0.372555\pi$
$548$	−16.6797	−0.712521
$549$	7.36238	0.314219
$550$	1.67187	0.0712888
$551$	−6.07408	−0.258765
$552$	2.07573	0.0883491
$553$	24.6758	1.04932
$554$	3.21924	0.136772
$555$	−4.40120	−0.186820
$556$	−11.8929	−0.504371
$557$	40.4157	1.71247	0.856234	−	0.516588i	$-0.172798\pi$
$557$	40.4157	1.71247	0.856234	+	0.516588i	$0.172798\pi$
$558$	7.43885	0.314912
$559$	23.5892	0.997718
$560$	18.9919	0.802554
$561$	−5.95098	−0.251250
$562$	−47.2945	−1.99500
$563$	−19.0884	−0.804481	−0.402241	−	0.915534i	$-0.631768\pi$
$563$	−19.0884	−0.804481	−0.402241	+	0.915534i	$0.631768\pi$
$564$	5.69449	0.239781
$565$	−3.22476	−0.135667
$566$	23.1490	0.973024
$567$	−3.79849	−0.159522
$568$	2.08238	0.0873747
$569$	11.6995	0.490468	0.245234	−	0.969464i	$-0.421135\pi$
$569$	11.6995	0.490468	0.245234	+	0.969464i	$0.421135\pi$
$570$	1.83159	0.0767170
$571$	2.32571	0.0973278	0.0486639	−	0.998815i	$-0.484504\pi$
$571$	2.32571	0.0973278	0.0486639	+	0.998815i	$0.484504\pi$
$572$	3.31419	0.138573
$573$	14.0926	0.588725
$574$	−48.2868	−2.01545
$575$	−1.21075	−0.0504918
$576$	0.890189	0.0370912
$577$	19.4474	0.809606	0.404803	−	0.914404i	$-0.367340\pi$
$577$	19.4474	0.809606	0.404803	+	0.914404i	$0.367340\pi$
$578$	−36.7314	−1.52782
$579$	−16.3107	−0.677851
$580$	−5.82576	−0.241901
$581$	−12.9039	−0.535345
$582$	11.8149	0.489745
$583$	11.5148	0.476896
$584$	−7.50321	−0.310485
$585$	−3.39904	−0.140533
$586$	−13.3301	−0.550662
$587$	−13.3092	−0.549328	−0.274664	−	0.961540i	$-0.588567\pi$
$587$	−13.3092	−0.549328	−0.274664	+	0.961540i	$0.588567\pi$
$588$	−7.51907	−0.310081
$589$	−4.52328	−0.186378
$590$	0.996502	0.0410253
$591$	−7.16667	−0.294798
$592$	−22.0053	−0.904414
$593$	30.5702	1.25537	0.627683	−	0.778469i	$-0.284003\pi$
$593$	30.5702	1.25537	0.627683	+	0.778469i	$0.284003\pi$
$594$	−1.67187	−0.0685977
$595$	23.4659	0.962010
$596$	19.6466	0.804757
$597$	14.1829	0.580469
$598$	−7.14253	−0.292080
$599$	7.73303	0.315963	0.157982	−	0.987442i	$-0.449501\pi$
$599$	7.73303	0.315963	0.157982	+	0.987442i	$0.449501\pi$
$600$	−1.71442	−0.0699908
$601$	9.01147	0.367586	0.183793	−	0.982965i	$-0.441162\pi$
$601$	9.01147	0.367586	0.183793	+	0.982965i	$0.441162\pi$
$602$	−45.7520	−1.86471
$603$	−2.50245	−0.101907
$604$	1.34803	0.0548504
$605$	−10.0721	−0.409487
$606$	−3.16281	−0.128480
$607$	−43.0590	−1.74771	−0.873855	−	0.486187i	$-0.838387\pi$
$607$	−43.0590	−1.74771	−0.873855	+	0.486187i	$0.838387\pi$
$608$	5.53914	0.224642
$609$	−21.8627	−0.885922
$610$	−12.7779	−0.517361
$611$	19.1228	0.773626
$612$	−6.25297	−0.252761
$613$	39.5017	1.59546	0.797730	−	0.603014i	$-0.206034\pi$
$613$	39.5017	1.59546	0.797730	+	0.603014i	$0.206034\pi$
$614$	−26.9117	−1.08607
$615$	7.32447	0.295351
$616$	6.27321	0.252755
$617$	−30.6074	−1.23221	−0.616104	−	0.787665i	$-0.711290\pi$
$617$	−30.6074	−1.23221	−0.616104	+	0.787665i	$0.711290\pi$
$618$	−34.1769	−1.37480
$619$	−30.1545	−1.21201	−0.606006	−	0.795460i	$-0.707229\pi$
$619$	−30.1545	−1.21201	−0.606006	+	0.795460i	$0.707229\pi$
$620$	−4.33835	−0.174232
$621$	1.21075	0.0485858
$622$	41.4500	1.66199
$623$	−40.7488	−1.63257
$624$	−16.9947	−0.680332
$625$	1.00000	0.0400000
$626$	−1.67463	−0.0669315
$627$	1.01660	0.0405991
$628$	4.89682	0.195404
$629$	−27.1893	−1.08411
$630$	6.59253	0.262653
$631$	−18.9680	−0.755105	−0.377553	−	0.925988i	$-0.623234\pi$
$631$	−18.9680	−0.755105	−0.377553	+	0.925988i	$0.623234\pi$
$632$	−11.1372	−0.443013
$633$	21.4191	0.851334
$634$	20.0778	0.797390
$635$	−6.84251	−0.271537
$636$	12.0992	0.479763
$637$	−25.2500	−1.00044
$638$	−9.62266	−0.380965
$639$	1.21463	0.0480499
$640$	−12.0424	−0.476019
$641$	27.8194	1.09880	0.549400	−	0.835560i	$-0.314856\pi$
$641$	27.8194	1.09880	0.549400	+	0.835560i	$0.314856\pi$
$642$	14.0000	0.552537
$643$	24.5533	0.968287	0.484144	−	0.874988i	$-0.339131\pi$
$643$	24.5533	0.968287	0.484144	+	0.874988i	$0.339131\pi$
$644$	4.65507	0.183436
$645$	6.93997	0.273261
$646$	11.3150	0.445184
$647$	49.9588	1.96408	0.982041	−	0.188669i	$-0.0604175\pi$
$647$	49.9588	1.96408	0.982041	+	0.188669i	$0.0604175\pi$
$648$	1.71442	0.0673487
$649$	0.553094	0.0217108
$650$	5.89925	0.231388
$651$	−16.2808	−0.638096
$652$	−20.0565	−0.785473
$653$	36.0422	1.41044	0.705221	−	0.708988i	$-0.250848\pi$
$653$	36.0422	1.41044	0.705221	+	0.708988i	$0.250848\pi$
$654$	−4.41670	−0.172707
$655$	17.1930	0.671786
$656$	36.6213	1.42982
$657$	−4.37654	−0.170745
$658$	−37.0892	−1.44589
$659$	18.8988	0.736194	0.368097	−	0.929787i	$-0.380009\pi$
$659$	18.8988	0.736194	0.368097	+	0.929787i	$0.380009\pi$
$660$	0.975038	0.0379533
$661$	22.4967	0.875019	0.437509	−	0.899214i	$-0.355861\pi$
$661$	22.4967	0.875019	0.437509	+	0.899214i	$0.355861\pi$
$662$	−29.7384	−1.15582
$663$	−20.9982	−0.815504
$664$	5.82408	0.226018
$665$	−4.00866	−0.155449
$666$	−7.63857	−0.295988
$667$	6.96864	0.269827
$668$	−5.21686	−0.201846
$669$	21.9525	0.848731
$670$	4.34316	0.167791
$671$	−7.09218	−0.273791
$672$	19.9373	0.769097
$673$	−17.6890	−0.681860	−0.340930	−	0.940089i	$-0.610742\pi$
$673$	−17.6890	−0.681860	−0.340930	+	0.940089i	$0.610742\pi$
$674$	−20.9876	−0.808412
$675$	−1.00000	−0.0384900
$676$	−1.46415	−0.0563136
$677$	5.87456	0.225778	0.112889	−	0.993608i	$-0.463990\pi$
$677$	5.87456	0.225778	0.112889	+	0.993608i	$0.463990\pi$
$678$	−5.59678	−0.214943
$679$	−25.8584	−0.992355
$680$	−10.5911	−0.406152
$681$	−7.75582	−0.297204
$682$	−7.16585	−0.274395
$683$	42.2596	1.61702	0.808510	−	0.588483i	$-0.200274\pi$
$683$	42.2596	1.61702	0.808510	+	0.588483i	$0.200274\pi$
$684$	1.06819	0.0408432
$685$	−16.4789	−0.629626
$686$	2.82527	0.107869
$687$	−3.80913	−0.145327
$688$	34.6988	1.32288
$689$	40.6305	1.54790
$690$	−2.10134	−0.0799966
$691$	−7.45155	−0.283470	−0.141735	−	0.989905i	$-0.545268\pi$
$691$	−7.45155	−0.283470	−0.141735	+	0.989905i	$0.545268\pi$
$692$	−11.0652	−0.420634
$693$	3.65909	0.138997
$694$	−5.74195	−0.217962
$695$	−11.7497	−0.445692
$696$	9.86755	0.374028
$697$	45.2484	1.71390
$698$	17.5709	0.665067
$699$	−9.91586	−0.375052
$700$	−3.84478	−0.145319
$701$	−24.6338	−0.930407	−0.465204	−	0.885204i	$-0.654019\pi$
$701$	−24.6338	−0.930407	−0.465204	+	0.885204i	$0.654019\pi$
$702$	−5.89925	−0.222653
$703$	4.64472	0.175179
$704$	−0.857519	−0.0323190
$705$	5.62594	0.211885
$706$	61.5143	2.31512
$707$	6.92219	0.260336
$708$	0.581162	0.0218414
$709$	−1.53109	−0.0575013	−0.0287506	−	0.999587i	$-0.509153\pi$
$709$	−1.53109	−0.0575013	−0.0287506	+	0.999587i	$0.509153\pi$
$710$	−2.10807	−0.0791143
$711$	−6.49619	−0.243626
$712$	18.3916	0.689256
$713$	5.18944	0.194346
$714$	40.7267	1.52416
$715$	3.27430	0.122452
$716$	8.24973	0.308307
$717$	14.8323	0.553922
$718$	−9.49278	−0.354267
$719$	23.3326	0.870158	0.435079	−	0.900392i	$-0.356720\pi$
$719$	23.3326	0.870158	0.435079	+	0.900392i	$0.356720\pi$
$720$	−4.99985	−0.186333
$721$	74.8004	2.78571
$722$	31.0428	1.15529
$723$	9.66460	0.359430
$724$	0.916396	0.0340576
$725$	−5.75563	−0.213759
$726$	−17.4807	−0.648770
$727$	−11.9029	−0.441456	−0.220728	−	0.975335i	$-0.570843\pi$
$727$	−11.9029	−0.441456	−0.220728	+	0.975335i	$0.570843\pi$
$728$	22.1352	0.820386
$729$	1.00000	0.0370370
$730$	7.59577	0.281132
$731$	42.8730	1.58572
$732$	−7.45209	−0.275437
$733$	−33.9906	−1.25547	−0.627736	−	0.778427i	$-0.716018\pi$
$733$	−33.9906	−1.25547	−0.627736	+	0.778427i	$0.716018\pi$
$734$	−16.0184	−0.591250
$735$	−7.42856	−0.274006
$736$	−6.35491	−0.234245
$737$	2.41061	0.0887959
$738$	12.7121	0.467939
$739$	4.82065	0.177330	0.0886652	−	0.996061i	$-0.471740\pi$
$739$	4.82065	0.177330	0.0886652	+	0.996061i	$0.471740\pi$
$740$	4.45483	0.163763
$741$	3.58711	0.131776
$742$	−78.8040	−2.89298
$743$	−41.0753	−1.50691	−0.753454	−	0.657501i	$-0.771614\pi$
$743$	−41.0753	−1.50691	−0.753454	+	0.657501i	$0.771614\pi$
$744$	7.34821	0.269398
$745$	19.4101	0.711132
$746$	−37.0493	−1.35647
$747$	3.39712	0.124294
$748$	6.02349	0.220241
$749$	−30.6408	−1.11959
$750$	1.73556	0.0633739
$751$	11.0890	0.404643	0.202322	−	0.979319i	$-0.435151\pi$
$751$	11.0890	0.404643	0.202322	+	0.979319i	$0.435151\pi$
$752$	28.1289	1.02575
$753$	0.620935	0.0226281
$754$	−33.9539	−1.23653
$755$	1.33180	0.0484691
$756$	3.84478	0.139833
$757$	−22.0512	−0.801463	−0.400732	−	0.916195i	$-0.631244\pi$
$757$	−22.0512	−0.801463	−0.400732	+	0.916195i	$0.631244\pi$
$758$	−21.8491	−0.793596
$759$	−1.16632	−0.0423347
$760$	1.80928	0.0656293
$761$	28.6497	1.03855	0.519275	−	0.854607i	$-0.326202\pi$
$761$	28.6497	1.03855	0.519275	+	0.854607i	$0.326202\pi$
$762$	−11.8756	−0.430208
$763$	9.66649	0.349950
$764$	−14.2643	−0.516063
$765$	−6.17770	−0.223355
$766$	−38.1618	−1.37884
$767$	1.95161	0.0704686
$768$	−19.1201	−0.689936
$769$	16.8056	0.606026	0.303013	−	0.952986i	$-0.402007\pi$
$769$	16.8056	0.606026	0.303013	+	0.952986i	$0.402007\pi$
$770$	−6.35059	−0.228859
$771$	−2.96673	−0.106844
$772$	16.5095	0.594189
$773$	−20.5892	−0.740544	−0.370272	−	0.928923i	$-0.620735\pi$
$773$	−20.5892	−0.740544	−0.370272	+	0.928923i	$0.620735\pi$
$774$	12.0448	0.432940
$775$	−4.28613	−0.153962
$776$	11.6710	0.418963
$777$	16.7179	0.599752
$778$	45.0815	1.61625
$779$	−7.72973	−0.276946
$780$	3.44046	0.123188
$781$	−1.17005	−0.0418677
$782$	−12.9814	−0.464215
$783$	5.75563	0.205689
$784$	−37.1417	−1.32649
$785$	4.83787	0.172671
$786$	29.8396	1.06434
$787$	27.5674	0.982673	0.491336	−	0.870970i	$-0.336509\pi$
$787$	27.5674	0.982673	0.491336	+	0.870970i	$0.336509\pi$
$788$	7.25400	0.258413
$789$	1.15805	0.0412275
$790$	11.2746	0.401131
$791$	12.2492	0.435533
$792$	−1.65150	−0.0586835
$793$	−25.0250	−0.888664
$794$	25.7339	0.913262
$795$	11.9535	0.423948
$796$	−14.3558	−0.508826
$797$	14.9339	0.528985	0.264493	−	0.964388i	$-0.414795\pi$
$797$	14.9339	0.528985	0.264493	+	0.964388i	$0.414795\pi$
$798$	−6.95729	−0.246286
$799$	34.7554	1.22956
$800$	5.24873	0.185571
$801$	10.7276	0.379042
$802$	1.73556	0.0612849
$803$	4.21592	0.148777
$804$	2.53294	0.0893298
$805$	4.59903	0.162095
$806$	−25.2849	−0.890624
$807$	21.2522	0.748113
$808$	−3.12427	−0.109911
$809$	49.8249	1.75175	0.875876	−	0.482537i	$-0.160285\pi$
$809$	49.8249	1.75175	0.875876	+	0.482537i	$0.160285\pi$
$810$	−1.73556	−0.0609815
$811$	−45.7344	−1.60595	−0.802976	−	0.596012i	$-0.796751\pi$
$811$	−45.7344	−1.60595	−0.802976	+	0.596012i	$0.796751\pi$
$812$	22.1291	0.776580
$813$	−18.6744	−0.654940
$814$	7.35823	0.257906
$815$	−19.8150	−0.694091
$816$	−30.8876	−1.08128
$817$	−7.32396	−0.256233
$818$	−25.5521	−0.893410
$819$	12.9112	0.451155
$820$	−7.41372	−0.258898
$821$	50.7052	1.76962	0.884812	−	0.465949i	$-0.154287\pi$
$821$	50.7052	1.76962	0.884812	+	0.465949i	$0.154287\pi$
$822$	−28.6002	−0.997546
$823$	39.0155	1.35999	0.679997	−	0.733215i	$-0.261981\pi$
$823$	39.0155	1.35999	0.679997	+	0.733215i	$0.261981\pi$
$824$	−33.7605	−1.17610
$825$	0.963301	0.0335378
$826$	−3.78521	−0.131704
$827$	3.62978	0.126220	0.0631098	−	0.998007i	$-0.479898\pi$
$827$	3.62978	0.126220	0.0631098	+	0.998007i	$0.479898\pi$
$828$	−1.22550	−0.0425892
$829$	43.6700	1.51672	0.758361	−	0.651835i	$-0.226001\pi$
$829$	43.6700	1.51672	0.758361	+	0.651835i	$0.226001\pi$
$830$	−5.89592	−0.204650
$831$	1.85487	0.0643446
$832$	−3.02579	−0.104900
$833$	−45.8914	−1.59004
$834$	−20.3924	−0.706131
$835$	−5.15406	−0.178364
$836$	−1.02899	−0.0355883
$837$	4.28613	0.148150
$838$	−32.1023	−1.10895
$839$	−31.3476	−1.08224	−0.541120	−	0.840946i	$-0.681999\pi$
$839$	−31.3476	−1.08224	−0.541120	+	0.840946i	$0.681999\pi$
$840$	6.51220	0.224692
$841$	4.12725	0.142319
$842$	19.2159	0.662223
$843$	−27.2502	−0.938546
$844$	−21.6801	−0.746260
$845$	−1.44653	−0.0497621
$846$	9.76418	0.335700
$847$	38.2586	1.31458
$848$	59.7658	2.05237
$849$	13.3380	0.457759
$850$	10.7218	0.367754
$851$	−5.32876	−0.182668
$852$	−1.22943	−0.0421195
$853$	49.3852	1.69092	0.845458	−	0.534042i	$-0.179328\pi$
$853$	49.3852	1.69092	0.845458	+	0.534042i	$0.179328\pi$
$854$	48.5367	1.66089
$855$	1.05533	0.0360915
$856$	13.8294	0.472680
$857$	9.71790	0.331957	0.165979	−	0.986129i	$-0.446922\pi$
$857$	9.71790	0.331957	0.165979	+	0.986129i	$0.446922\pi$
$858$	5.68275	0.194006
$859$	4.05097	0.138217	0.0691086	−	0.997609i	$-0.477985\pi$
$859$	4.05097	0.138217	0.0691086	+	0.997609i	$0.477985\pi$
$860$	−7.02453	−0.239535
$861$	−27.8220	−0.948170
$862$	−41.5217	−1.41424
$863$	2.02180	0.0688229	0.0344115	−	0.999408i	$-0.489044\pi$
$863$	2.02180	0.0688229	0.0344115	+	0.999408i	$0.489044\pi$
$864$	−5.24873	−0.178565
$865$	−10.9319	−0.371697
$866$	−6.81668	−0.231640
$867$	−21.1639	−0.718765
$868$	16.4792	0.559341
$869$	6.25779	0.212281
$870$	−9.98926	−0.338668
$871$	8.50591	0.288212
$872$	−4.36289	−0.147746
$873$	6.80754	0.230400
$874$	2.21760	0.0750116
$875$	−3.79849	−0.128413
$876$	4.42987	0.149671
$877$	−34.8063	−1.17533	−0.587663	−	0.809106i	$-0.699952\pi$
$877$	−34.8063	−1.17533	−0.587663	+	0.809106i	$0.699952\pi$
$878$	−31.4189	−1.06034
$879$	−7.68057	−0.259059
$880$	4.81636	0.162359
$881$	24.0903	0.811622	0.405811	−	0.913957i	$-0.366989\pi$
$881$	24.0903	0.811622	0.405811	+	0.913957i	$0.366989\pi$
$882$	−12.8927	−0.434121
$883$	−34.6190	−1.16502	−0.582510	−	0.812823i	$-0.697929\pi$
$883$	−34.6190	−1.16502	−0.582510	+	0.812823i	$0.697929\pi$
$884$	21.2541	0.714853
$885$	0.574166	0.0193004
$886$	35.1078	1.17947
$887$	−31.0676	−1.04315	−0.521573	−	0.853207i	$-0.674655\pi$
$887$	−31.0676	−1.04315	−0.521573	+	0.853207i	$0.674655\pi$
$888$	−7.54549	−0.253210
$889$	25.9912	0.871718
$890$	−18.6185	−0.624094
$891$	−0.963301	−0.0322718
$892$	−22.2200	−0.743979
$893$	−5.93722	−0.198682
$894$	33.6875	1.12668
$895$	8.15041	0.272438
$896$	45.7432	1.52817
$897$	−4.11539	−0.137409
$898$	6.48444	0.216388
$899$	24.6693	0.822769
$900$	1.01218	0.0337395
$901$	73.8452	2.46014
$902$	−12.2456	−0.407733
$903$	−26.3614	−0.877254
$904$	−5.52858	−0.183878
$905$	0.905365	0.0300953
$906$	2.31142	0.0767918
$907$	8.02026	0.266308	0.133154	−	0.991095i	$-0.457489\pi$
$907$	8.02026	0.266308	0.133154	+	0.991095i	$0.457489\pi$
$908$	7.85032	0.260522
$909$	−1.82235	−0.0604436
$910$	−22.4083	−0.742827
$911$	−37.9492	−1.25731	−0.628656	−	0.777683i	$-0.716395\pi$
$911$	−37.9492	−1.25731	−0.628656	+	0.777683i	$0.716395\pi$
$912$	5.27649	0.174722
$913$	−3.27244	−0.108302
$914$	−14.8355	−0.490716
$915$	−7.36238	−0.243393
$916$	3.85554	0.127391
$917$	−65.3075	−2.15664
$918$	−10.7218	−0.353872
$919$	−33.6667	−1.11056	−0.555281	−	0.831662i	$-0.687389\pi$
$919$	−33.6667	−1.11056	−0.555281	+	0.831662i	$0.687389\pi$
$920$	−2.07573	−0.0684349
$921$	−15.5060	−0.510941
$922$	−29.7453	−0.979610
$923$	−4.12857	−0.135893
$924$	−3.70368	−0.121842
$925$	4.40120	0.144711
$926$	22.1261	0.727108
$927$	−19.6921	−0.646774
$928$	−30.2097	−0.991684
$929$	−13.4719	−0.441998	−0.220999	−	0.975274i	$-0.570932\pi$
$929$	−13.4719	−0.441998	−0.220999	+	0.975274i	$0.570932\pi$
$930$	−7.43885	−0.243930
$931$	7.83957	0.256932
$932$	10.0367	0.328762
$933$	23.8827	0.781884
$934$	27.0464	0.884984
$935$	5.95098	0.194618
$936$	−5.82737	−0.190474
$937$	6.46212	0.211108	0.105554	−	0.994414i	$-0.466338\pi$
$937$	6.46212	0.211108	0.105554	+	0.994414i	$0.466338\pi$
$938$	−16.4975	−0.538661
$939$	−0.964888	−0.0314879
$940$	−5.69449	−0.185734
$941$	58.3103	1.90086	0.950430	−	0.310937i	$-0.100643\pi$
$941$	58.3103	1.90086	0.950430	+	0.310937i	$0.100643\pi$
$942$	8.39643	0.273571
$943$	8.86812	0.288786
$944$	2.87074	0.0934348
$945$	3.79849	0.123565
$946$	−11.6027	−0.377237
$947$	15.7991	0.513402	0.256701	−	0.966491i	$-0.417364\pi$
$947$	15.7991	0.513402	0.256701	+	0.966491i	$0.417364\pi$
$948$	6.57535	0.213557
$949$	14.8760	0.482896
$950$	−1.83159	−0.0594247
$951$	11.5684	0.375132
$952$	40.2304	1.30387
$953$	−59.1385	−1.91568	−0.957842	−	0.287295i	$-0.907244\pi$
$953$	−59.1385	−1.91568	−0.957842	+	0.287295i	$0.907244\pi$
$954$	20.7461	0.671680
$955$	−14.0926	−0.456024
$956$	−15.0130	−0.485556
$957$	−5.54440	−0.179225
$958$	21.1709	0.684002
$959$	62.5950	2.02130
$960$	−0.890189	−0.0287307
$961$	−12.6291	−0.407391
$962$	25.9638	0.837106
$963$	8.06655	0.259941
$964$	−9.78236	−0.315069
$965$	16.3107	0.525061
$966$	7.98192	0.256814
$967$	26.0501	0.837714	0.418857	−	0.908052i	$-0.362431\pi$
$967$	26.0501	0.837714	0.418857	+	0.908052i	$0.362431\pi$
$968$	−17.2677	−0.555005
$969$	6.51951	0.209437
$970$	−11.8149	−0.379355
$971$	0.665049	0.0213424	0.0106712	−	0.999943i	$-0.496603\pi$
$971$	0.665049	0.0213424	0.0106712	+	0.999943i	$0.496603\pi$
$972$	−1.01218	−0.0324658
$973$	44.6312	1.43081
$974$	41.8587	1.34124
$975$	3.39904	0.108856
$976$	−36.8108	−1.17829
$977$	24.2921	0.777173	0.388586	−	0.921412i	$-0.372964\pi$
$977$	24.2921	0.777173	0.388586	+	0.921412i	$0.372964\pi$
$978$	−34.3903	−1.09968
$979$	−10.3339	−0.330274
$980$	7.51907	0.240188
$981$	−2.54482	−0.0812499
$982$	−28.6288	−0.913581
$983$	−25.8652	−0.824973	−0.412486	−	0.910964i	$-0.635340\pi$
$983$	−25.8652	−0.824973	−0.412486	+	0.910964i	$0.635340\pi$
$984$	12.5572	0.400309
$985$	7.16667	0.228349
$986$	−61.7106	−1.96527
$987$	−21.3701	−0.680218
$988$	−3.63082	−0.115512
$989$	8.40258	0.267187
$990$	1.67187	0.0531355
$991$	−49.9428	−1.58648	−0.793242	−	0.608907i	$-0.791608\pi$
$991$	−49.9428	−1.58648	−0.793242	+	0.608907i	$0.791608\pi$
$992$	−22.4967	−0.714272
$993$	−17.1347	−0.543754
$994$	8.00747	0.253982
$995$	−14.1829	−0.449630
$996$	−3.43851	−0.108953
$997$	7.82323	0.247764	0.123882	−	0.992297i	$-0.460466\pi$
$997$	7.82323	0.247764	0.123882	+	0.992297i	$0.460466\pi$
$998$	14.4475	0.457329
$999$	−4.40120	−0.139248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.g.1.9	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.g.1.9	✓	36	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.73556 q^{2} -1.00000 q^{3} +1.01218 q^{4} +1.00000 q^{5} +1.73556 q^{6} -3.79849 q^{7} +1.71442 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.73556 q^{2} -1.00000 q^{3} +1.01218 q^{4} +1.00000 q^{5} +1.73556 q^{6} -3.79849 q^{7} +1.71442 q^{8} +1.00000 q^{9} -1.73556 q^{10} -0.963301 q^{11} -1.01218 q^{12} -3.39904 q^{13} +6.59253 q^{14} -1.00000 q^{15} -4.99985 q^{16} -6.17770 q^{17} -1.73556 q^{18} +1.05533 q^{19} +1.01218 q^{20} +3.79849 q^{21} +1.67187 q^{22} -1.21075 q^{23} -1.71442 q^{24} +1.00000 q^{25} +5.89925 q^{26} -1.00000 q^{27} -3.84478 q^{28} -5.75563 q^{29} +1.73556 q^{30} -4.28613 q^{31} +5.24873 q^{32} +0.963301 q^{33} +10.7218 q^{34} -3.79849 q^{35} +1.01218 q^{36} +4.40120 q^{37} -1.83159 q^{38} +3.39904 q^{39} +1.71442 q^{40} -7.32447 q^{41} -6.59253 q^{42} -6.93997 q^{43} -0.975038 q^{44} +1.00000 q^{45} +2.10134 q^{46} -5.62594 q^{47} +4.99985 q^{48} +7.42856 q^{49} -1.73556 q^{50} +6.17770 q^{51} -3.44046 q^{52} -11.9535 q^{53} +1.73556 q^{54} -0.963301 q^{55} -6.51220 q^{56} -1.05533 q^{57} +9.98926 q^{58} -0.574166 q^{59} -1.01218 q^{60} +7.36238 q^{61} +7.43885 q^{62} -3.79849 q^{63} +0.890189 q^{64} -3.39904 q^{65} -1.67187 q^{66} -2.50245 q^{67} -6.25297 q^{68} +1.21075 q^{69} +6.59253 q^{70} +1.21463 q^{71} +1.71442 q^{72} -4.37654 q^{73} -7.63857 q^{74} -1.00000 q^{75} +1.06819 q^{76} +3.65909 q^{77} -5.89925 q^{78} -6.49619 q^{79} -4.99985 q^{80} +1.00000 q^{81} +12.7121 q^{82} +3.39712 q^{83} +3.84478 q^{84} -6.17770 q^{85} +12.0448 q^{86} +5.75563 q^{87} -1.65150 q^{88} +10.7276 q^{89} -1.73556 q^{90} +12.9112 q^{91} -1.22550 q^{92} +4.28613 q^{93} +9.76418 q^{94} +1.05533 q^{95} -5.24873 q^{96} +6.80754 q^{97} -12.8927 q^{98} -0.963301 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9} + 15 q^{11} - 36 q^{12} + 8 q^{13} + 10 q^{14} - 36 q^{15} + 36 q^{16} + 32 q^{17} + 5 q^{19} + 36 q^{20} + 4 q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + 36 q^{25} + 22 q^{26} - 36 q^{27} + 61 q^{29} + 15 q^{31} - q^{32} - 15 q^{33} + 26 q^{34} - 4 q^{35} + 36 q^{36} + 16 q^{37} + 20 q^{38} - 8 q^{39} - 3 q^{40} + 61 q^{41} - 10 q^{42} - 35 q^{43} + 39 q^{44} + 36 q^{45} + 11 q^{46} - 28 q^{47} - 36 q^{48} + 68 q^{49} - 32 q^{51} + 4 q^{52} + 33 q^{53} + 15 q^{55} + 23 q^{56} - 5 q^{57} + 6 q^{58} + 35 q^{59} - 36 q^{60} + 55 q^{61} + q^{62} - 4 q^{63} + 15 q^{64} + 8 q^{65} - q^{66} - 34 q^{67} + 60 q^{68} + 10 q^{69} + 10 q^{70} + 42 q^{71} - 3 q^{72} + 53 q^{73} + 54 q^{74} - 36 q^{75} + 20 q^{76} + 20 q^{77} - 22 q^{78} + 25 q^{79} + 36 q^{80} + 36 q^{81} - 15 q^{82} - 11 q^{83} + 32 q^{85} + 53 q^{86} - 61 q^{87} + 27 q^{88} + 81 q^{89} + 15 q^{91} - 7 q^{92} - 15 q^{93} + 56 q^{94} + 5 q^{95} + q^{96} + 47 q^{97} - 3 q^{98} + 15 q^{99}+O(q^{100}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9 + 15 * q^11 - 36 * q^12 + 8 * q^13 + 10 * q^14 - 36 * q^15 + 36 * q^16 + 32 * q^17 + 5 * q^19 + 36 * q^20 + 4 * q^21 + q^22 - 10 * q^23 + 3 * q^24 + 36 * q^25 + 22 * q^26 - 36 * q^27 + 61 * q^29 + 15 * q^31 - q^32 - 15 * q^33 + 26 * q^34 - 4 * q^35 + 36 * q^36 + 16 * q^37 + 20 * q^38 - 8 * q^39 - 3 * q^40 + 61 * q^41 - 10 * q^42 - 35 * q^43 + 39 * q^44 + 36 * q^45 + 11 * q^46 - 28 * q^47 - 36 * q^48 + 68 * q^49 - 32 * q^51 + 4 * q^52 + 33 * q^53 + 15 * q^55 + 23 * q^56 - 5 * q^57 + 6 * q^58 + 35 * q^59 - 36 * q^60 + 55 * q^61 + q^62 - 4 * q^63 + 15 * q^64 + 8 * q^65 - q^66 - 34 * q^67 + 60 * q^68 + 10 * q^69 + 10 * q^70 + 42 * q^71 - 3 * q^72 + 53 * q^73 + 54 * q^74 - 36 * q^75 + 20 * q^76 + 20 * q^77 - 22 * q^78 + 25 * q^79 + 36 * q^80 + 36 * q^81 - 15 * q^82 - 11 * q^83 + 32 * q^85 + 53 * q^86 - 61 * q^87 + 27 * q^88 + 81 * q^89 + 15 * q^91 - 7 * q^92 - 15 * q^93 + 56 * q^94 + 5 * q^95 + q^96 + 47 * q^97 - 3 * q^98 + 15 * q^99

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