LMFDB - Embedded newform 4030.2.a.l.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 14x^{6} - 6x^{5} + 54x^{4} + 46x^{3} - 32x^{2} - 43x - 11 $ x^8 - 14x^6 - 6x^5 + 54x^4 + 46x^3 - 32x^2 - 43x - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.839784$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.08982 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.08982 q^{6} +4.96118 q^{7} -1.00000 q^{8} -1.81229 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.08982 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.08982 q^{6} +4.96118 q^{7} -1.00000 q^{8} -1.81229 q^{9} -1.00000 q^{10} -1.00148 q^{11} +1.08982 q^{12} -1.00000 q^{13} -4.96118 q^{14} +1.08982 q^{15} +1.00000 q^{16} +5.06695 q^{17} +1.81229 q^{18} -4.28772 q^{19} +1.00000 q^{20} +5.40681 q^{21} +1.00148 q^{22} -8.20272 q^{23} -1.08982 q^{24} +1.00000 q^{25} +1.00000 q^{26} -5.24454 q^{27} +4.96118 q^{28} +8.17389 q^{29} -1.08982 q^{30} -1.00000 q^{31} -1.00000 q^{32} -1.09144 q^{33} -5.06695 q^{34} +4.96118 q^{35} -1.81229 q^{36} +5.01252 q^{37} +4.28772 q^{38} -1.08982 q^{39} -1.00000 q^{40} +7.64099 q^{41} -5.40681 q^{42} -5.56149 q^{43} -1.00148 q^{44} -1.81229 q^{45} +8.20272 q^{46} +7.05423 q^{47} +1.08982 q^{48} +17.6133 q^{49} -1.00000 q^{50} +5.52208 q^{51} -1.00000 q^{52} +9.44650 q^{53} +5.24454 q^{54} -1.00148 q^{55} -4.96118 q^{56} -4.67285 q^{57} -8.17389 q^{58} -6.34691 q^{59} +1.08982 q^{60} +14.0128 q^{61} +1.00000 q^{62} -8.99109 q^{63} +1.00000 q^{64} -1.00000 q^{65} +1.09144 q^{66} -8.15928 q^{67} +5.06695 q^{68} -8.93951 q^{69} -4.96118 q^{70} +16.2437 q^{71} +1.81229 q^{72} +0.894410 q^{73} -5.01252 q^{74} +1.08982 q^{75} -4.28772 q^{76} -4.96853 q^{77} +1.08982 q^{78} +0.562425 q^{79} +1.00000 q^{80} -0.278758 q^{81} -7.64099 q^{82} +7.03718 q^{83} +5.40681 q^{84} +5.06695 q^{85} +5.56149 q^{86} +8.90809 q^{87} +1.00148 q^{88} +5.09468 q^{89} +1.81229 q^{90} -4.96118 q^{91} -8.20272 q^{92} -1.08982 q^{93} -7.05423 q^{94} -4.28772 q^{95} -1.08982 q^{96} +6.54677 q^{97} -17.6133 q^{98} +1.81497 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + q^{3} + 8 q^{4} + 8 q^{5} - q^{6} + 11 q^{7} - 8 q^{8} + 9 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + q^3 + 8 * q^4 + 8 * q^5 - q^6 + 11 * q^7 - 8 * q^8 + 9 * q^9	$ 8 q - 8 q^{2} + q^{3} + 8 q^{4} + 8 q^{5} - q^{6} + 11 q^{7} - 8 q^{8} + 9 q^{9} - 8 q^{10} + q^{12} - 8 q^{13} - 11 q^{14} + q^{15} + 8 q^{16} + 7 q^{17} - 9 q^{18} - 2 q^{19} + 8 q^{20} + q^{21} + 8 q^{23} - q^{24} + 8 q^{25} + 8 q^{26} + 7 q^{27} + 11 q^{28} - q^{29} - q^{30} - 8 q^{31} - 8 q^{32} + 14 q^{33} - 7 q^{34} + 11 q^{35} + 9 q^{36} + q^{37} + 2 q^{38} - q^{39} - 8 q^{40} + 16 q^{41} - q^{42} + 3 q^{43} + 9 q^{45} - 8 q^{46} + 29 q^{47} + q^{48} + 11 q^{49} - 8 q^{50} + 11 q^{51} - 8 q^{52} + 22 q^{53} - 7 q^{54} - 11 q^{56} + 33 q^{57} + q^{58} - 8 q^{59} + q^{60} + 4 q^{61} + 8 q^{62} + 38 q^{63} + 8 q^{64} - 8 q^{65} - 14 q^{66} + 28 q^{67} + 7 q^{68} - 42 q^{69} - 11 q^{70} + 4 q^{71} - 9 q^{72} + 39 q^{73} - q^{74} + q^{75} - 2 q^{76} + 11 q^{77} + q^{78} - 16 q^{79} + 8 q^{80} + 32 q^{81} - 16 q^{82} + 25 q^{83} + q^{84} + 7 q^{85} - 3 q^{86} + 13 q^{87} + 21 q^{89} - 9 q^{90} - 11 q^{91} + 8 q^{92} - q^{93} - 29 q^{94} - 2 q^{95} - q^{96} + 28 q^{97} - 11 q^{98} + 23 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + q^3 + 8 * q^4 + 8 * q^5 - q^6 + 11 * q^7 - 8 * q^8 + 9 * q^9 - 8 * q^10 + q^12 - 8 * q^13 - 11 * q^14 + q^15 + 8 * q^16 + 7 * q^17 - 9 * q^18 - 2 * q^19 + 8 * q^20 + q^21 + 8 * q^23 - q^24 + 8 * q^25 + 8 * q^26 + 7 * q^27 + 11 * q^28 - q^29 - q^30 - 8 * q^31 - 8 * q^32 + 14 * q^33 - 7 * q^34 + 11 * q^35 + 9 * q^36 + q^37 + 2 * q^38 - q^39 - 8 * q^40 + 16 * q^41 - q^42 + 3 * q^43 + 9 * q^45 - 8 * q^46 + 29 * q^47 + q^48 + 11 * q^49 - 8 * q^50 + 11 * q^51 - 8 * q^52 + 22 * q^53 - 7 * q^54 - 11 * q^56 + 33 * q^57 + q^58 - 8 * q^59 + q^60 + 4 * q^61 + 8 * q^62 + 38 * q^63 + 8 * q^64 - 8 * q^65 - 14 * q^66 + 28 * q^67 + 7 * q^68 - 42 * q^69 - 11 * q^70 + 4 * q^71 - 9 * q^72 + 39 * q^73 - q^74 + q^75 - 2 * q^76 + 11 * q^77 + q^78 - 16 * q^79 + 8 * q^80 + 32 * q^81 - 16 * q^82 + 25 * q^83 + q^84 + 7 * q^85 - 3 * q^86 + 13 * q^87 + 21 * q^89 - 9 * q^90 - 11 * q^91 + 8 * q^92 - q^93 - 29 * q^94 - 2 * q^95 - q^96 + 28 * q^97 - 11 * q^98 + 23 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.08982	0.629209	0.314605	−	0.949223i	$-0.398128\pi$
$3$	1.08982	0.629209	0.314605	+	0.949223i	$0.398128\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.08982	−0.444918
$7$	4.96118	1.87515	0.937576	−	0.347782i	$-0.113065\pi$
$7$	4.96118	1.87515	0.937576	+	0.347782i	$0.113065\pi$
$8$	−1.00000	−0.353553
$9$	−1.81229	−0.604095
$10$	−1.00000	−0.316228
$11$	−1.00148	−0.301958	−0.150979	−	0.988537i	$-0.548243\pi$
$11$	−1.00148	−0.301958	−0.150979	+	0.988537i	$0.548243\pi$
$12$	1.08982	0.314605
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.96118	−1.32593
$15$	1.08982	0.281391
$16$	1.00000	0.250000
$17$	5.06695	1.22892	0.614458	−	0.788950i	$-0.289375\pi$
$17$	5.06695	1.22892	0.614458	+	0.788950i	$0.289375\pi$
$18$	1.81229	0.427160
$19$	−4.28772	−0.983670	−0.491835	−	0.870688i	$-0.663674\pi$
$19$	−4.28772	−0.983670	−0.491835	+	0.870688i	$0.663674\pi$
$20$	1.00000	0.223607
$21$	5.40681	1.17986
$22$	1.00148	0.213516
$23$	−8.20272	−1.71038	−0.855192	−	0.518311i	$-0.826561\pi$
$23$	−8.20272	−1.71038	−0.855192	+	0.518311i	$0.826561\pi$
$24$	−1.08982	−0.222459
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−5.24454	−1.00931
$28$	4.96118	0.937576
$29$	8.17389	1.51785	0.758926	−	0.651176i	$-0.225724\pi$
$29$	8.17389	1.51785	0.758926	+	0.651176i	$0.225724\pi$
$30$	−1.08982	−0.198973
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	−1.09144	−0.189995
$34$	−5.06695	−0.868974
$35$	4.96118	0.838593
$36$	−1.81229	−0.302048
$37$	5.01252	0.824053	0.412026	−	0.911172i	$-0.364821\pi$
$37$	5.01252	0.824053	0.412026	+	0.911172i	$0.364821\pi$
$38$	4.28772	0.695560
$39$	−1.08982	−0.174511
$40$	−1.00000	−0.158114
$41$	7.64099	1.19332	0.596661	−	0.802493i	$-0.296494\pi$
$41$	7.64099	1.19332	0.596661	+	0.802493i	$0.296494\pi$
$42$	−5.40681	−0.834289
$43$	−5.56149	−0.848119	−0.424059	−	0.905634i	$-0.639395\pi$
$43$	−5.56149	−0.848119	−0.424059	+	0.905634i	$0.639395\pi$
$44$	−1.00148	−0.150979
$45$	−1.81229	−0.270160
$46$	8.20272	1.20942
$47$	7.05423	1.02897	0.514483	−	0.857501i	$-0.327984\pi$
$47$	7.05423	1.02897	0.514483	+	0.857501i	$0.327984\pi$
$48$	1.08982	0.157302
$49$	17.6133	2.51619
$50$	−1.00000	−0.141421
$51$	5.52208	0.773245
$52$	−1.00000	−0.138675
$53$	9.44650	1.29758	0.648788	−	0.760969i	$-0.275276\pi$
$53$	9.44650	1.29758	0.648788	+	0.760969i	$0.275276\pi$
$54$	5.24454	0.713691
$55$	−1.00148	−0.135040
$56$	−4.96118	−0.662966
$57$	−4.67285	−0.618935
$58$	−8.17389	−1.07328
$59$	−6.34691	−0.826297	−0.413148	−	0.910664i	$-0.635571\pi$
$59$	−6.34691	−0.826297	−0.413148	+	0.910664i	$0.635571\pi$
$60$	1.08982	0.140696
$61$	14.0128	1.79415	0.897076	−	0.441875i	$-0.145687\pi$
$61$	14.0128	1.79415	0.897076	+	0.441875i	$0.145687\pi$
$62$	1.00000	0.127000
$63$	−8.99109	−1.13277
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	1.09144	0.134347
$67$	−8.15928	−0.996815	−0.498407	−	0.866943i	$-0.666082\pi$
$67$	−8.15928	−0.996815	−0.498407	+	0.866943i	$0.666082\pi$
$68$	5.06695	0.614458
$69$	−8.93951	−1.07619
$70$	−4.96118	−0.592975
$71$	16.2437	1.92777	0.963885	−	0.266320i	$-0.0858079\pi$
$71$	16.2437	1.92777	0.963885	+	0.266320i	$0.0858079\pi$
$72$	1.81229	0.213580
$73$	0.894410	0.104683	0.0523414	−	0.998629i	$-0.483332\pi$
$73$	0.894410	0.104683	0.0523414	+	0.998629i	$0.483332\pi$
$74$	−5.01252	−0.582693
$75$	1.08982	0.125842
$76$	−4.28772	−0.491835
$77$	−4.96853	−0.566217
$78$	1.08982	0.123398
$79$	0.562425	0.0632778	0.0316389	−	0.999499i	$-0.489927\pi$
$79$	0.562425	0.0632778	0.0316389	+	0.999499i	$0.489927\pi$
$80$	1.00000	0.111803
$81$	−0.278758	−0.0309731
$82$	−7.64099	−0.843806
$83$	7.03718	0.772431	0.386216	−	0.922408i	$-0.373782\pi$
$83$	7.03718	0.772431	0.386216	+	0.922408i	$0.373782\pi$
$84$	5.40681	0.589931
$85$	5.06695	0.549588
$86$	5.56149	0.599710
$87$	8.90809	0.955047
$88$	1.00148	0.106758
$89$	5.09468	0.540035	0.270018	−	0.962855i	$-0.412970\pi$
$89$	5.09468	0.540035	0.270018	+	0.962855i	$0.412970\pi$
$90$	1.81229	0.191032
$91$	−4.96118	−0.520073
$92$	−8.20272	−0.855192
$93$	−1.08982	−0.113009
$94$	−7.05423	−0.727589
$95$	−4.28772	−0.439911
$96$	−1.08982	−0.111230
$97$	6.54677	0.664723	0.332362	−	0.943152i	$-0.392155\pi$
$97$	6.54677	0.664723	0.332362	+	0.943152i	$0.392155\pi$
$98$	−17.6133	−1.77922
$99$	1.81497	0.182411
$100$	1.00000	0.100000
$101$	12.9479	1.28836	0.644181	−	0.764873i	$-0.277198\pi$
$101$	12.9479	1.28836	0.644181	+	0.764873i	$0.277198\pi$
$102$	−5.52208	−0.546767
$103$	11.2190	1.10544	0.552721	−	0.833367i	$-0.313590\pi$
$103$	11.2190	1.10544	0.552721	+	0.833367i	$0.313590\pi$
$104$	1.00000	0.0980581
$105$	5.40681	0.527651
$106$	−9.44650	−0.917525
$107$	6.36253	0.615089	0.307545	−	0.951534i	$-0.400493\pi$
$107$	6.36253	0.615089	0.307545	+	0.951534i	$0.400493\pi$
$108$	−5.24454	−0.504656
$109$	−16.6946	−1.59906	−0.799529	−	0.600628i	$-0.794917\pi$
$109$	−16.6946	−1.59906	−0.799529	+	0.600628i	$0.794917\pi$
$110$	1.00148	0.0954875
$111$	5.46276	0.518502
$112$	4.96118	0.468788
$113$	−4.07352	−0.383205	−0.191602	−	0.981473i	$-0.561368\pi$
$113$	−4.07352	−0.383205	−0.191602	+	0.981473i	$0.561368\pi$
$114$	4.67285	0.437653
$115$	−8.20272	−0.764907
$116$	8.17389	0.758926
$117$	1.81229	0.167546
$118$	6.34691	0.584280
$119$	25.1381	2.30440
$120$	−1.08982	−0.0994867
$121$	−9.99704	−0.908821
$122$	−14.0128	−1.26866
$123$	8.32732	0.750849
$124$	−1.00000	−0.0898027
$125$	1.00000	0.0894427
$126$	8.99109	0.800990
$127$	−9.23699	−0.819651	−0.409825	−	0.912164i	$-0.634410\pi$
$127$	−9.23699	−0.819651	−0.409825	+	0.912164i	$0.634410\pi$
$128$	−1.00000	−0.0883883
$129$	−6.06103	−0.533644
$130$	1.00000	0.0877058
$131$	7.80605	0.682018	0.341009	−	0.940060i	$-0.389231\pi$
$131$	7.80605	0.682018	0.341009	+	0.940060i	$0.389231\pi$
$132$	−1.09144	−0.0949974
$133$	−21.2722	−1.84453
$134$	8.15928	0.704854
$135$	−5.24454	−0.451378
$136$	−5.06695	−0.434487
$137$	17.0346	1.45536	0.727681	−	0.685916i	$-0.240598\pi$
$137$	17.0346	1.45536	0.727681	+	0.685916i	$0.240598\pi$
$138$	8.93951	0.760981
$139$	0.627740	0.0532442	0.0266221	−	0.999646i	$-0.491525\pi$
$139$	0.627740	0.0532442	0.0266221	+	0.999646i	$0.491525\pi$
$140$	4.96118	0.419297
$141$	7.68786	0.647435
$142$	−16.2437	−1.36314
$143$	1.00148	0.0837480
$144$	−1.81229	−0.151024
$145$	8.17389	0.678804
$146$	−0.894410	−0.0740219
$147$	19.1954	1.58321
$148$	5.01252	0.412026
$149$	−2.02628	−0.165999	−0.0829997	−	0.996550i	$-0.526450\pi$
$149$	−2.02628	−0.165999	−0.0829997	+	0.996550i	$0.526450\pi$
$150$	−1.08982	−0.0889837
$151$	0.943012	0.0767412	0.0383706	−	0.999264i	$-0.487783\pi$
$151$	0.943012	0.0767412	0.0383706	+	0.999264i	$0.487783\pi$
$152$	4.28772	0.347780
$153$	−9.18276	−0.742382
$154$	4.96853	0.400376
$155$	−1.00000	−0.0803219
$156$	−1.08982	−0.0872556
$157$	17.7313	1.41511	0.707557	−	0.706657i	$-0.249797\pi$
$157$	17.7313	1.41511	0.707557	+	0.706657i	$0.249797\pi$
$158$	−0.562425	−0.0447442
$159$	10.2950	0.816447
$160$	−1.00000	−0.0790569
$161$	−40.6952	−3.20723
$162$	0.278758	0.0219013
$163$	−20.2660	−1.58735	−0.793677	−	0.608339i	$-0.791836\pi$
$163$	−20.2660	−1.58735	−0.793677	+	0.608339i	$0.791836\pi$
$164$	7.64099	0.596661
$165$	−1.09144	−0.0849682
$166$	−7.03718	−0.546191
$167$	−8.62073	−0.667092	−0.333546	−	0.942734i	$-0.608245\pi$
$167$	−8.62073	−0.667092	−0.333546	+	0.942734i	$0.608245\pi$
$168$	−5.40681	−0.417144
$169$	1.00000	0.0769231
$170$	−5.06695	−0.388617
$171$	7.77058	0.594231
$172$	−5.56149	−0.424059
$173$	−15.9140	−1.20992	−0.604961	−	0.796255i	$-0.706811\pi$
$173$	−15.9140	−1.20992	−0.604961	+	0.796255i	$0.706811\pi$
$174$	−8.90809	−0.675320
$175$	4.96118	0.375030
$176$	−1.00148	−0.0754895
$177$	−6.91700	−0.519914
$178$	−5.09468	−0.381863
$179$	−23.6769	−1.76970	−0.884848	−	0.465879i	$-0.845738\pi$
$179$	−23.6769	−1.76970	−0.884848	+	0.465879i	$0.845738\pi$
$180$	−1.81229	−0.135080
$181$	12.1217	0.900999	0.450499	−	0.892777i	$-0.351246\pi$
$181$	12.1217	0.900999	0.450499	+	0.892777i	$0.351246\pi$
$182$	4.96118	0.367747
$183$	15.2714	1.12890
$184$	8.20272	0.604712
$185$	5.01252	0.368528
$186$	1.08982	0.0799097
$187$	−5.07445	−0.371081
$188$	7.05423	0.514483
$189$	−26.0191	−1.89261
$190$	4.28772	0.311064
$191$	−14.9164	−1.07931	−0.539655	−	0.841886i	$-0.681445\pi$
$191$	−14.9164	−1.07931	−0.539655	+	0.841886i	$0.681445\pi$
$192$	1.08982	0.0786512
$193$	−6.37449	−0.458846	−0.229423	−	0.973327i	$-0.573684\pi$
$193$	−6.37449	−0.458846	−0.229423	+	0.973327i	$0.573684\pi$
$194$	−6.54677	−0.470030
$195$	−1.08982	−0.0780438
$196$	17.6133	1.25810
$197$	−22.5372	−1.60571	−0.802853	−	0.596177i	$-0.796686\pi$
$197$	−22.5372	−1.60571	−0.802853	+	0.596177i	$0.796686\pi$
$198$	−1.81497	−0.128984
$199$	−8.95366	−0.634708	−0.317354	−	0.948307i	$-0.602794\pi$
$199$	−8.95366	−0.634708	−0.317354	+	0.948307i	$0.602794\pi$
$200$	−1.00000	−0.0707107
$201$	−8.89217	−0.627205
$202$	−12.9479	−0.911010
$203$	40.5521	2.84620
$204$	5.52208	0.386623
$205$	7.64099	0.533670
$206$	−11.2190	−0.781665
$207$	14.8657	1.03324
$208$	−1.00000	−0.0693375
$209$	4.29407	0.297027
$210$	−5.40681	−0.373105
$211$	−0.236207	−0.0162611	−0.00813057	−	0.999967i	$-0.502588\pi$
$211$	−0.236207	−0.0162611	−0.00813057	+	0.999967i	$0.502588\pi$
$212$	9.44650	0.648788
$213$	17.7027	1.21297
$214$	−6.36253	−0.434934
$215$	−5.56149	−0.379290
$216$	5.24454	0.356846
$217$	−4.96118	−0.336787
$218$	16.6946	1.13070
$219$	0.974748	0.0658674
$220$	−1.00148	−0.0675198
$221$	−5.06695	−0.340840
$222$	−5.46276	−0.366636
$223$	8.29157	0.555245	0.277622	−	0.960690i	$-0.410454\pi$
$223$	8.29157	0.555245	0.277622	+	0.960690i	$0.410454\pi$
$224$	−4.96118	−0.331483
$225$	−1.81229	−0.120819
$226$	4.07352	0.270967
$227$	4.50067	0.298720	0.149360	−	0.988783i	$-0.452279\pi$
$227$	4.50067	0.298720	0.149360	+	0.988783i	$0.452279\pi$
$228$	−4.67285	−0.309467
$229$	−1.07309	−0.0709120	−0.0354560	−	0.999371i	$-0.511288\pi$
$229$	−1.07309	−0.0709120	−0.0354560	+	0.999371i	$0.511288\pi$
$230$	8.20272	0.540871
$231$	−5.41482	−0.356269
$232$	−8.17389	−0.536642
$233$	−13.2135	−0.865646	−0.432823	−	0.901479i	$-0.642482\pi$
$233$	−13.2135	−0.865646	−0.432823	+	0.901479i	$0.642482\pi$
$234$	−1.81229	−0.118473
$235$	7.05423	0.460168
$236$	−6.34691	−0.413148
$237$	0.612944	0.0398150
$238$	−25.1381	−1.62946
$239$	14.3290	0.926867	0.463433	−	0.886132i	$-0.346617\pi$
$239$	14.3290	0.926867	0.463433	+	0.886132i	$0.346617\pi$
$240$	1.08982	0.0703478
$241$	−24.6609	−1.58855	−0.794273	−	0.607560i	$-0.792148\pi$
$241$	−24.6609	−1.58855	−0.794273	+	0.607560i	$0.792148\pi$
$242$	9.99704	0.642634
$243$	15.4298	0.989823
$244$	14.0128	0.897076
$245$	17.6133	1.12527
$246$	−8.32732	−0.530931
$247$	4.28772	0.272821
$248$	1.00000	0.0635001
$249$	7.66928	0.486021
$250$	−1.00000	−0.0632456
$251$	−17.7446	−1.12003	−0.560013	−	0.828484i	$-0.689204\pi$
$251$	−17.7446	−1.12003	−0.560013	+	0.828484i	$0.689204\pi$
$252$	−8.99109	−0.566385
$253$	8.21487	0.516464
$254$	9.23699	0.579580
$255$	5.52208	0.345806
$256$	1.00000	0.0625000
$257$	12.1517	0.758004	0.379002	−	0.925396i	$-0.376267\pi$
$257$	12.1517	0.758004	0.379002	+	0.925396i	$0.376267\pi$
$258$	6.06103	0.377343
$259$	24.8680	1.54522
$260$	−1.00000	−0.0620174
$261$	−14.8134	−0.916928
$262$	−7.80605	−0.482259
$263$	28.8007	1.77592	0.887962	−	0.459916i	$-0.152121\pi$
$263$	28.8007	1.77592	0.887962	+	0.459916i	$0.152121\pi$
$264$	1.09144	0.0671733
$265$	9.44650	0.580294
$266$	21.2722	1.30428
$267$	5.55230	0.339795
$268$	−8.15928	−0.498407
$269$	4.02916	0.245662	0.122831	−	0.992428i	$-0.460803\pi$
$269$	4.02916	0.245662	0.122831	+	0.992428i	$0.460803\pi$
$270$	5.24454	0.319172
$271$	−25.5887	−1.55441	−0.777203	−	0.629250i	$-0.783362\pi$
$271$	−25.5887	−1.55441	−0.777203	+	0.629250i	$0.783362\pi$
$272$	5.06695	0.307229
$273$	−5.40681	−0.327235
$274$	−17.0346	−1.02910
$275$	−1.00148	−0.0603916
$276$	−8.93951	−0.538095
$277$	−12.9495	−0.778062	−0.389031	−	0.921225i	$-0.627190\pi$
$277$	−12.9495	−0.778062	−0.389031	+	0.921225i	$0.627190\pi$
$278$	−0.627740	−0.0376494
$279$	1.81229	0.108499
$280$	−4.96118	−0.296487
$281$	23.7020	1.41394	0.706972	−	0.707241i	$-0.250060\pi$
$281$	23.7020	1.41394	0.706972	+	0.707241i	$0.250060\pi$
$282$	−7.68786	−0.457806
$283$	−14.8319	−0.881664	−0.440832	−	0.897590i	$-0.645317\pi$
$283$	−14.8319	−0.881664	−0.440832	+	0.897590i	$0.645317\pi$
$284$	16.2437	0.963885
$285$	−4.67285	−0.276796
$286$	−1.00148	−0.0592188
$287$	37.9083	2.23766
$288$	1.81229	0.106790
$289$	8.67396	0.510233
$290$	−8.17389	−0.479987
$291$	7.13481	0.418250
$292$	0.894410	0.0523414
$293$	16.0797	0.939388	0.469694	−	0.882829i	$-0.344364\pi$
$293$	16.0797	0.939388	0.469694	+	0.882829i	$0.344364\pi$
$294$	−19.1954	−1.11950
$295$	−6.34691	−0.369531
$296$	−5.01252	−0.291347
$297$	5.25231	0.304770
$298$	2.02628	0.117379
$299$	8.20272	0.474375
$300$	1.08982	0.0629209
$301$	−27.5915	−1.59035
$302$	−0.943012	−0.0542643
$303$	14.1109	0.810650
$304$	−4.28772	−0.245918
$305$	14.0128	0.802370
$306$	9.18276	0.524944
$307$	5.66173	0.323132	0.161566	−	0.986862i	$-0.448346\pi$
$307$	5.66173	0.323132	0.161566	+	0.986862i	$0.448346\pi$
$308$	−4.96853	−0.283108
$309$	12.2267	0.695554
$310$	1.00000	0.0567962
$311$	−27.8342	−1.57833	−0.789166	−	0.614180i	$-0.789487\pi$
$311$	−27.8342	−1.57833	−0.789166	+	0.614180i	$0.789487\pi$
$312$	1.08982	0.0616991
$313$	−31.5433	−1.78293	−0.891466	−	0.453087i	$-0.850323\pi$
$313$	−31.5433	−1.78293	−0.891466	+	0.453087i	$0.850323\pi$
$314$	−17.7313	−1.00064
$315$	−8.99109	−0.506590
$316$	0.562425	0.0316389
$317$	14.0655	0.789998	0.394999	−	0.918682i	$-0.370745\pi$
$317$	14.0655	0.789998	0.394999	+	0.918682i	$0.370745\pi$
$318$	−10.2950	−0.577315
$319$	−8.18599	−0.458328
$320$	1.00000	0.0559017
$321$	6.93403	0.387020
$322$	40.6952	2.26785
$323$	−21.7257	−1.20885
$324$	−0.278758	−0.0154866
$325$	−1.00000	−0.0554700
$326$	20.2660	1.12243
$327$	−18.1942	−1.00614
$328$	−7.64099	−0.421903
$329$	34.9973	1.92947
$330$	1.09144	0.0600816
$331$	−28.4021	−1.56112	−0.780561	−	0.625080i	$-0.785066\pi$
$331$	−28.4021	−1.56112	−0.780561	+	0.625080i	$0.785066\pi$
$332$	7.03718	0.386216
$333$	−9.08412	−0.497807
$334$	8.62073	0.471705
$335$	−8.15928	−0.445789
$336$	5.40681	0.294966
$337$	−18.9101	−1.03010	−0.515050	−	0.857160i	$-0.672227\pi$
$337$	−18.9101	−1.03010	−0.515050	+	0.857160i	$0.672227\pi$
$338$	−1.00000	−0.0543928
$339$	−4.43941	−0.241116
$340$	5.06695	0.274794
$341$	1.00148	0.0542332
$342$	−7.77058	−0.420185
$343$	52.6547	2.84309
$344$	5.56149	0.299855
$345$	−8.93951	−0.481287
$346$	15.9140	0.855544
$347$	5.06775	0.272051	0.136026	−	0.990705i	$-0.456567\pi$
$347$	5.06775	0.272051	0.136026	+	0.990705i	$0.456567\pi$
$348$	8.90809	0.477524
$349$	−12.4602	−0.666981	−0.333491	−	0.942753i	$-0.608227\pi$
$349$	−12.4602	−0.666981	−0.333491	+	0.942753i	$0.608227\pi$
$350$	−4.96118	−0.265186
$351$	5.24454	0.279933
$352$	1.00148	0.0533791
$353$	−1.74851	−0.0930636	−0.0465318	−	0.998917i	$-0.514817\pi$
$353$	−1.74851	−0.0930636	−0.0465318	+	0.998917i	$0.514817\pi$
$354$	6.91700	0.367634
$355$	16.2437	0.862125
$356$	5.09468	0.270018
$357$	27.3960	1.44995
$358$	23.6769	1.25136
$359$	4.17615	0.220409	0.110204	−	0.993909i	$-0.464849\pi$
$359$	4.17615	0.220409	0.110204	+	0.993909i	$0.464849\pi$
$360$	1.81229	0.0955159
$361$	−0.615459	−0.0323926
$362$	−12.1217	−0.637102
$363$	−10.8950	−0.571839
$364$	−4.96118	−0.260037
$365$	0.894410	0.0468155
$366$	−15.2714	−0.798251
$367$	20.9729	1.09478	0.547388	−	0.836879i	$-0.315622\pi$
$367$	20.9729	1.09478	0.547388	+	0.836879i	$0.315622\pi$
$368$	−8.20272	−0.427596
$369$	−13.8477	−0.720880
$370$	−5.01252	−0.260588
$371$	46.8658	2.43315
$372$	−1.08982	−0.0565047
$373$	12.9552	0.670796	0.335398	−	0.942076i	$-0.391129\pi$
$373$	12.9552	0.670796	0.335398	+	0.942076i	$0.391129\pi$
$374$	5.07445	0.262394
$375$	1.08982	0.0562782
$376$	−7.05423	−0.363794
$377$	−8.17389	−0.420977
$378$	26.0191	1.33828
$379$	15.0547	0.773310	0.386655	−	0.922224i	$-0.373630\pi$
$379$	15.0547	0.773310	0.386655	+	0.922224i	$0.373630\pi$
$380$	−4.28772	−0.219955
$381$	−10.0667	−0.515732
$382$	14.9164	0.763188
$383$	31.2022	1.59436	0.797179	−	0.603743i	$-0.206325\pi$
$383$	31.2022	1.59436	0.797179	+	0.603743i	$0.206325\pi$
$384$	−1.08982	−0.0556148
$385$	−4.96853	−0.253220
$386$	6.37449	0.324453
$387$	10.0790	0.512345
$388$	6.54677	0.332362
$389$	33.3544	1.69113	0.845567	−	0.533870i	$-0.179263\pi$
$389$	33.3544	1.69113	0.845567	+	0.533870i	$0.179263\pi$
$390$	1.08982	0.0551853
$391$	−41.5627	−2.10192
$392$	−17.6133	−0.889608
$393$	8.50721	0.429132
$394$	22.5372	1.13541
$395$	0.562425	0.0282987
$396$	1.81497	0.0912057
$397$	3.23022	0.162120	0.0810602	−	0.996709i	$-0.474169\pi$
$397$	3.23022	0.162120	0.0810602	+	0.996709i	$0.474169\pi$
$398$	8.95366	0.448806
$399$	−23.1829	−1.16060
$400$	1.00000	0.0500000
$401$	−8.48325	−0.423633	−0.211817	−	0.977309i	$-0.567938\pi$
$401$	−8.48325	−0.423633	−0.211817	+	0.977309i	$0.567938\pi$
$402$	8.89217	0.443501
$403$	1.00000	0.0498135
$404$	12.9479	0.644181
$405$	−0.278758	−0.0138516
$406$	−40.5521	−2.01257
$407$	−5.01994	−0.248829
$408$	−5.52208	−0.273383
$409$	14.4448	0.714250	0.357125	−	0.934057i	$-0.383757\pi$
$409$	14.4448	0.714250	0.357125	+	0.934057i	$0.383757\pi$
$410$	−7.64099	−0.377361
$411$	18.5647	0.915727
$412$	11.2190	0.552721
$413$	−31.4882	−1.54943
$414$	−14.8657	−0.730608
$415$	7.03718	0.345442
$416$	1.00000	0.0490290
$417$	0.684125	0.0335018
$418$	−4.29407	−0.210030
$419$	−3.89338	−0.190204	−0.0951020	−	0.995468i	$-0.530318\pi$
$419$	−3.89338	−0.190204	−0.0951020	+	0.995468i	$0.530318\pi$
$420$	5.40681	0.263825
$421$	25.4068	1.23825	0.619125	−	0.785292i	$-0.287487\pi$
$421$	25.4068	1.23825	0.619125	+	0.785292i	$0.287487\pi$
$422$	0.236207	0.0114984
$423$	−12.7843	−0.621594
$424$	−9.44650	−0.458762
$425$	5.06695	0.245783
$426$	−17.7027	−0.857700
$427$	69.5200	3.36431
$428$	6.36253	0.307545
$429$	1.09144	0.0526951
$430$	5.56149	0.268199
$431$	−11.4261	−0.550376	−0.275188	−	0.961390i	$-0.588740\pi$
$431$	−11.4261	−0.550376	−0.275188	+	0.961390i	$0.588740\pi$
$432$	−5.24454	−0.252328
$433$	−1.39452	−0.0670162	−0.0335081	−	0.999438i	$-0.510668\pi$
$433$	−1.39452	−0.0670162	−0.0335081	+	0.999438i	$0.510668\pi$
$434$	4.96118	0.238144
$435$	8.90809	0.427110
$436$	−16.6946	−0.799529
$437$	35.1710	1.68245
$438$	−0.974748	−0.0465753
$439$	7.77600	0.371128	0.185564	−	0.982632i	$-0.440589\pi$
$439$	7.77600	0.371128	0.185564	+	0.982632i	$0.440589\pi$
$440$	1.00148	0.0477437
$441$	−31.9204	−1.52002
$442$	5.06695	0.241010
$443$	−39.7302	−1.88764	−0.943819	−	0.330463i	$-0.892795\pi$
$443$	−39.7302	−1.88764	−0.943819	+	0.330463i	$0.892795\pi$
$444$	5.46276	0.259251
$445$	5.09468	0.241511
$446$	−8.29157	−0.392617
$447$	−2.20829	−0.104448
$448$	4.96118	0.234394
$449$	−25.8375	−1.21935	−0.609674	−	0.792652i	$-0.708700\pi$
$449$	−25.8375	−1.21935	−0.609674	+	0.792652i	$0.708700\pi$
$450$	1.81229	0.0854320
$451$	−7.65230	−0.360333
$452$	−4.07352	−0.191602
$453$	1.02772	0.0482863
$454$	−4.50067	−0.211227
$455$	−4.96118	−0.232584
$456$	4.67285	0.218826
$457$	−16.8215	−0.786878	−0.393439	−	0.919351i	$-0.628715\pi$
$457$	−16.8215	−0.786878	−0.393439	+	0.919351i	$0.628715\pi$
$458$	1.07309	0.0501424
$459$	−26.5738	−1.24036
$460$	−8.20272	−0.382454
$461$	−3.89528	−0.181421	−0.0907106	−	0.995877i	$-0.528914\pi$
$461$	−3.89528	−0.181421	−0.0907106	+	0.995877i	$0.528914\pi$
$462$	5.41482	0.251920
$463$	17.3349	0.805619	0.402810	−	0.915284i	$-0.368034\pi$
$463$	17.3349	0.805619	0.402810	+	0.915284i	$0.368034\pi$
$464$	8.17389	0.379463
$465$	−1.08982	−0.0505393
$466$	13.2135	0.612104
$467$	−8.73678	−0.404290	−0.202145	−	0.979356i	$-0.564791\pi$
$467$	−8.73678	−0.404290	−0.202145	+	0.979356i	$0.564791\pi$
$468$	1.81229	0.0837730
$469$	−40.4797	−1.86918
$470$	−7.05423	−0.325388
$471$	19.3240	0.890403
$472$	6.34691	0.292140
$473$	5.56972	0.256096
$474$	−0.612944	−0.0281534
$475$	−4.28772	−0.196734
$476$	25.1381	1.15220
$477$	−17.1198	−0.783860
$478$	−14.3290	−0.655394
$479$	31.7288	1.44972	0.724862	−	0.688894i	$-0.241903\pi$
$479$	31.7288	1.44972	0.724862	+	0.688894i	$0.241903\pi$
$480$	−1.08982	−0.0497434
$481$	−5.01252	−0.228551
$482$	24.6609	1.12327
$483$	−44.3505	−2.01802
$484$	−9.99704	−0.454411
$485$	6.54677	0.297273
$486$	−15.4298	−0.699911
$487$	−0.277886	−0.0125922	−0.00629610	−	0.999980i	$-0.502004\pi$
$487$	−0.277886	−0.0125922	−0.00629610	+	0.999980i	$0.502004\pi$
$488$	−14.0128	−0.634329
$489$	−22.0863	−0.998778
$490$	−17.6133	−0.795690
$491$	−34.6793	−1.56506	−0.782528	−	0.622615i	$-0.786070\pi$
$491$	−34.6793	−1.56506	−0.782528	+	0.622615i	$0.786070\pi$
$492$	8.32732	0.375425
$493$	41.4167	1.86531
$494$	−4.28772	−0.192914
$495$	1.81497	0.0815769
$496$	−1.00000	−0.0449013
$497$	80.5878	3.61486
$498$	−7.66928	−0.343669
$499$	15.1437	0.677925	0.338963	−	0.940800i	$-0.389924\pi$
$499$	15.1437	0.677925	0.338963	+	0.940800i	$0.389924\pi$
$500$	1.00000	0.0447214
$501$	−9.39507	−0.419741
$502$	17.7446	0.791978
$503$	−27.9571	−1.24655	−0.623273	−	0.782004i	$-0.714197\pi$
$503$	−27.9571	−1.24655	−0.623273	+	0.782004i	$0.714197\pi$
$504$	8.99109	0.400495
$505$	12.9479	0.576173
$506$	−8.21487	−0.365195
$507$	1.08982	0.0484007
$508$	−9.23699	−0.409825
$509$	−26.9055	−1.19256	−0.596282	−	0.802775i	$-0.703356\pi$
$509$	−26.9055	−1.19256	−0.596282	+	0.802775i	$0.703356\pi$
$510$	−5.52208	−0.244522
$511$	4.43733	0.196296
$512$	−1.00000	−0.0441942
$513$	22.4871	0.992830
$514$	−12.1517	−0.535989
$515$	11.2190	0.494368
$516$	−6.06103	−0.266822
$517$	−7.06468	−0.310704
$518$	−24.8680	−1.09264
$519$	−17.3435	−0.761294
$520$	1.00000	0.0438529
$521$	0.763066	0.0334305	0.0167153	−	0.999860i	$-0.494679\pi$
$521$	0.763066	0.0334305	0.0167153	+	0.999860i	$0.494679\pi$
$522$	14.8134	0.648366
$523$	−36.4706	−1.59475	−0.797373	−	0.603487i	$-0.793778\pi$
$523$	−36.4706	−1.59475	−0.797373	+	0.603487i	$0.793778\pi$
$524$	7.80605	0.341009
$525$	5.40681	0.235973
$526$	−28.8007	−1.25577
$527$	−5.06695	−0.220720
$528$	−1.09144	−0.0474987
$529$	44.2846	1.92542
$530$	−9.44650	−0.410330
$531$	11.5024	0.499162
$532$	−21.2722	−0.922265
$533$	−7.64099	−0.330968
$534$	−5.55230	−0.240272
$535$	6.36253	0.275076
$536$	8.15928	0.352427
$537$	−25.8037	−1.11351
$538$	−4.02916	−0.173709
$539$	−17.6394	−0.759784
$540$	−5.24454	−0.225689
$541$	−22.9897	−0.988403	−0.494202	−	0.869347i	$-0.664540\pi$
$541$	−22.9897	−0.988403	−0.494202	+	0.869347i	$0.664540\pi$
$542$	25.5887	1.09913
$543$	13.2105	0.566917
$544$	−5.06695	−0.217244
$545$	−16.6946	−0.715120
$546$	5.40681	0.231390
$547$	−10.3106	−0.440849	−0.220424	−	0.975404i	$-0.570744\pi$
$547$	−10.3106	−0.440849	−0.220424	+	0.975404i	$0.570744\pi$
$548$	17.0346	0.727681
$549$	−25.3952	−1.08384
$550$	1.00148	0.0427033
$551$	−35.0473	−1.49307
$552$	8.93951	0.380491
$553$	2.79029	0.118655
$554$	12.9495	0.550173
$555$	5.46276	0.231881
$556$	0.627740	0.0266221
$557$	38.2589	1.62108	0.810540	−	0.585683i	$-0.199174\pi$
$557$	38.2589	1.62108	0.810540	+	0.585683i	$0.199174\pi$
$558$	−1.81229	−0.0767202
$559$	5.56149	0.235226
$560$	4.96118	0.209648
$561$	−5.53025	−0.233487
$562$	−23.7020	−0.999810
$563$	−4.31541	−0.181873	−0.0909364	−	0.995857i	$-0.528986\pi$
$563$	−4.31541	−0.181873	−0.0909364	+	0.995857i	$0.528986\pi$
$564$	7.68786	0.323717
$565$	−4.07352	−0.171374
$566$	14.8319	0.623431
$567$	−1.38297	−0.0580793
$568$	−16.2437	−0.681569
$569$	−32.6862	−1.37027	−0.685137	−	0.728414i	$-0.740258\pi$
$569$	−32.6862	−1.37027	−0.685137	+	0.728414i	$0.740258\pi$
$570$	4.67285	0.195724
$571$	−12.5775	−0.526354	−0.263177	−	0.964748i	$-0.584770\pi$
$571$	−12.5775	−0.526354	−0.263177	+	0.964748i	$0.584770\pi$
$572$	1.00148	0.0418740
$573$	−16.2562	−0.679112
$574$	−37.9083	−1.58226
$575$	−8.20272	−0.342077
$576$	−1.81229	−0.0755119
$577$	0.673768	0.0280493	0.0140247	−	0.999902i	$-0.495536\pi$
$577$	0.673768	0.0280493	0.0140247	+	0.999902i	$0.495536\pi$
$578$	−8.67396	−0.360789
$579$	−6.94706	−0.288710
$580$	8.17389	0.339402
$581$	34.9128	1.44843
$582$	−7.13481	−0.295748
$583$	−9.46049	−0.391813
$584$	−0.894410	−0.0370109
$585$	1.81229	0.0749288
$586$	−16.0797	−0.664247
$587$	29.3088	1.20970	0.604851	−	0.796338i	$-0.293232\pi$
$587$	29.3088	1.20970	0.604851	+	0.796338i	$0.293232\pi$
$588$	19.1954	0.791606
$589$	4.28772	0.176672
$590$	6.34691	0.261298
$591$	−24.5615	−1.01033
$592$	5.01252	0.206013
$593$	29.3566	1.20553	0.602766	−	0.797918i	$-0.294065\pi$
$593$	29.3566	1.20553	0.602766	+	0.797918i	$0.294065\pi$
$594$	−5.25231	−0.215505
$595$	25.1381	1.03056
$596$	−2.02628	−0.0829997
$597$	−9.75790	−0.399364
$598$	−8.20272	−0.335434
$599$	−6.42194	−0.262393	−0.131197	−	0.991356i	$-0.541882\pi$
$599$	−6.42194	−0.262393	−0.131197	+	0.991356i	$0.541882\pi$
$600$	−1.08982	−0.0444918
$601$	11.3679	0.463708	0.231854	−	0.972751i	$-0.425521\pi$
$601$	11.3679	0.463708	0.231854	+	0.972751i	$0.425521\pi$
$602$	27.5915	1.12455
$603$	14.7870	0.602171
$604$	0.943012	0.0383706
$605$	−9.99704	−0.406437
$606$	−14.1109	−0.573216
$607$	23.0843	0.936963	0.468482	−	0.883473i	$-0.344801\pi$
$607$	23.0843	0.936963	0.468482	+	0.883473i	$0.344801\pi$
$608$	4.28772	0.173890
$609$	44.1947	1.79086
$610$	−14.0128	−0.567361
$611$	−7.05423	−0.285384
$612$	−9.18276	−0.371191
$613$	28.5507	1.15315	0.576577	−	0.817043i	$-0.304388\pi$
$613$	28.5507	1.15315	0.576577	+	0.817043i	$0.304388\pi$
$614$	−5.66173	−0.228489
$615$	8.32732	0.335790
$616$	4.96853	0.200188
$617$	−3.15771	−0.127125	−0.0635624	−	0.997978i	$-0.520246\pi$
$617$	−3.15771	−0.127125	−0.0635624	+	0.997978i	$0.520246\pi$
$618$	−12.2267	−0.491831
$619$	−14.4072	−0.579073	−0.289537	−	0.957167i	$-0.593501\pi$
$619$	−14.4072	−0.579073	−0.289537	+	0.957167i	$0.593501\pi$
$620$	−1.00000	−0.0401610
$621$	43.0195	1.72631
$622$	27.8342	1.11605
$623$	25.2757	1.01265
$624$	−1.08982	−0.0436278
$625$	1.00000	0.0400000
$626$	31.5433	1.26072
$627$	4.67977	0.186892
$628$	17.7313	0.707557
$629$	25.3982	1.01269
$630$	8.99109	0.358213
$631$	43.9783	1.75075	0.875374	−	0.483447i	$-0.160615\pi$
$631$	43.9783	1.75075	0.875374	+	0.483447i	$0.160615\pi$
$632$	−0.562425	−0.0223721
$633$	−0.257423	−0.0102317
$634$	−14.0655	−0.558613
$635$	−9.23699	−0.366559
$636$	10.2950	0.408224
$637$	−17.6133	−0.697866
$638$	8.18599	0.324087
$639$	−29.4382	−1.16456
$640$	−1.00000	−0.0395285
$641$	−5.37831	−0.212431	−0.106215	−	0.994343i	$-0.533873\pi$
$641$	−5.37831	−0.212431	−0.106215	+	0.994343i	$0.533873\pi$
$642$	−6.93403	−0.273664
$643$	−8.48433	−0.334589	−0.167295	−	0.985907i	$-0.553503\pi$
$643$	−8.48433	−0.334589	−0.167295	+	0.985907i	$0.553503\pi$
$644$	−40.6952	−1.60361
$645$	−6.06103	−0.238653
$646$	21.7257	0.854784
$647$	−12.8371	−0.504680	−0.252340	−	0.967639i	$-0.581200\pi$
$647$	−12.8371	−0.504680	−0.252340	+	0.967639i	$0.581200\pi$
$648$	0.278758	0.0109507
$649$	6.35631	0.249507
$650$	1.00000	0.0392232
$651$	−5.40681	−0.211910
$652$	−20.2660	−0.793677
$653$	16.1634	0.632524	0.316262	−	0.948672i	$-0.397572\pi$
$653$	16.1634	0.632524	0.316262	+	0.948672i	$0.397572\pi$
$654$	18.1942	0.711450
$655$	7.80605	0.305008
$656$	7.64099	0.298330
$657$	−1.62093	−0.0632384
$658$	−34.9973	−1.36434
$659$	−15.7809	−0.614738	−0.307369	−	0.951590i	$-0.599449\pi$
$659$	−15.7809	−0.614738	−0.307369	+	0.951590i	$0.599449\pi$
$660$	−1.09144	−0.0424841
$661$	−18.5100	−0.719957	−0.359978	−	0.932961i	$-0.617216\pi$
$661$	−18.5100	−0.719957	−0.359978	+	0.932961i	$0.617216\pi$
$662$	28.4021	1.10388
$663$	−5.52208	−0.214460
$664$	−7.03718	−0.273096
$665$	−21.2722	−0.824899
$666$	9.08412	0.352002
$667$	−67.0481	−2.59611
$668$	−8.62073	−0.333546
$669$	9.03634	0.349365
$670$	8.15928	0.315220
$671$	−14.0335	−0.541759
$672$	−5.40681	−0.208572
$673$	−18.0990	−0.697666	−0.348833	−	0.937185i	$-0.613422\pi$
$673$	−18.0990	−0.697666	−0.348833	+	0.937185i	$0.613422\pi$
$674$	18.9101	0.728391
$675$	−5.24454	−0.201862
$676$	1.00000	0.0384615
$677$	−23.8620	−0.917089	−0.458545	−	0.888671i	$-0.651629\pi$
$677$	−23.8620	−0.917089	−0.458545	+	0.888671i	$0.651629\pi$
$678$	4.43941	0.170495
$679$	32.4797	1.24646
$680$	−5.06695	−0.194309
$681$	4.90493	0.187958
$682$	−1.00148	−0.0383487
$683$	6.01414	0.230125	0.115062	−	0.993358i	$-0.463293\pi$
$683$	6.01414	0.230125	0.115062	+	0.993358i	$0.463293\pi$
$684$	7.77058	0.297115
$685$	17.0346	0.650857
$686$	−52.6547	−2.01037
$687$	−1.16948	−0.0446185
$688$	−5.56149	−0.212030
$689$	−9.44650	−0.359883
$690$	8.93951	0.340321
$691$	−13.4451	−0.511475	−0.255737	−	0.966746i	$-0.582318\pi$
$691$	−13.4451	−0.511475	−0.255737	+	0.966746i	$0.582318\pi$
$692$	−15.9140	−0.604961
$693$	9.00440	0.342049
$694$	−5.06775	−0.192369
$695$	0.627740	0.0238115
$696$	−8.90809	−0.337660
$697$	38.7165	1.46649
$698$	12.4602	0.471627
$699$	−14.4004	−0.544673
$700$	4.96118	0.187515
$701$	−3.58314	−0.135333	−0.0676667	−	0.997708i	$-0.521555\pi$
$701$	−3.58314	−0.135333	−0.0676667	+	0.997708i	$0.521555\pi$
$702$	−5.24454	−0.197942
$703$	−21.4923	−0.810596
$704$	−1.00148	−0.0377447
$705$	7.68786	0.289542
$706$	1.74851	0.0658059
$707$	64.2368	2.41587
$708$	−6.91700	−0.259957
$709$	−13.9515	−0.523958	−0.261979	−	0.965074i	$-0.584375\pi$
$709$	−13.9515	−0.523958	−0.261979	+	0.965074i	$0.584375\pi$
$710$	−16.2437	−0.609614
$711$	−1.01928	−0.0382258
$712$	−5.09468	−0.190931
$713$	8.20272	0.307194
$714$	−27.3960	−1.02527
$715$	1.00148	0.0374533
$716$	−23.6769	−0.884848
$717$	15.6161	0.583193
$718$	−4.17615	−0.155853
$719$	−2.36101	−0.0880509	−0.0440254	−	0.999030i	$-0.514018\pi$
$719$	−2.36101	−0.0880509	−0.0440254	+	0.999030i	$0.514018\pi$
$720$	−1.81229	−0.0675399
$721$	55.6595	2.07287
$722$	0.615459	0.0229050
$723$	−26.8760	−0.999529
$724$	12.1217	0.450499
$725$	8.17389	0.303571
$726$	10.8950	0.404351
$727$	52.5890	1.95042	0.975210	−	0.221283i	$-0.0710243\pi$
$727$	52.5890	1.95042	0.975210	+	0.221283i	$0.0710243\pi$
$728$	4.96118	0.183874
$729$	17.6520	0.653779
$730$	−0.894410	−0.0331036
$731$	−28.1798	−1.04227
$732$	15.2714	0.564449
$733$	−34.8481	−1.28714	−0.643572	−	0.765386i	$-0.722548\pi$
$733$	−34.8481	−1.28714	−0.643572	+	0.765386i	$0.722548\pi$
$734$	−20.9729	−0.774124
$735$	19.1954	0.708034
$736$	8.20272	0.302356
$737$	8.17136	0.300996
$738$	13.8477	0.509739
$739$	−0.532165	−0.0195760	−0.00978800	−	0.999952i	$-0.503116\pi$
$739$	−0.532165	−0.0195760	−0.00978800	+	0.999952i	$0.503116\pi$
$740$	5.01252	0.184264
$741$	4.67285	0.171662
$742$	−46.8658	−1.72050
$743$	−50.7271	−1.86100	−0.930498	−	0.366298i	$-0.880625\pi$
$743$	−50.7271	−1.86100	−0.930498	+	0.366298i	$0.880625\pi$
$744$	1.08982	0.0399548
$745$	−2.02628	−0.0742372
$746$	−12.9552	−0.474325
$747$	−12.7534	−0.466622
$748$	−5.07445	−0.185540
$749$	31.5657	1.15339
$750$	−1.08982	−0.0397947
$751$	28.8265	1.05189	0.525947	−	0.850517i	$-0.323711\pi$
$751$	28.8265	1.05189	0.525947	+	0.850517i	$0.323711\pi$
$752$	7.05423	0.257241
$753$	−19.3384	−0.704731
$754$	8.17389	0.297675
$755$	0.943012	0.0343197
$756$	−26.0191	−0.946306
$757$	−24.6801	−0.897014	−0.448507	−	0.893779i	$-0.648044\pi$
$757$	−24.6801	−0.897014	−0.448507	+	0.893779i	$0.648044\pi$
$758$	−15.0547	−0.546813
$759$	8.95275	0.324964
$760$	4.28772	0.155532
$761$	35.3365	1.28095	0.640473	−	0.767981i	$-0.278738\pi$
$761$	35.3365	1.28095	0.640473	+	0.767981i	$0.278738\pi$
$762$	10.0667	0.364677
$763$	−82.8252	−2.99847
$764$	−14.9164	−0.539655
$765$	−9.18276	−0.332003
$766$	−31.2022	−1.12738
$767$	6.34691	0.229173
$768$	1.08982	0.0393256
$769$	30.5500	1.10166	0.550831	−	0.834617i	$-0.314311\pi$
$769$	30.5500	1.10166	0.550831	+	0.834617i	$0.314311\pi$
$770$	4.96853	0.179053
$771$	13.2432	0.476943
$772$	−6.37449	−0.229423
$773$	7.93216	0.285300	0.142650	−	0.989773i	$-0.454438\pi$
$773$	7.93216	0.285300	0.142650	+	0.989773i	$0.454438\pi$
$774$	−10.0790	−0.362282
$775$	−1.00000	−0.0359211
$776$	−6.54677	−0.235015
$777$	27.1017	0.972269
$778$	−33.3544	−1.19581
$779$	−32.7624	−1.17384
$780$	−1.08982	−0.0390219
$781$	−16.2677	−0.582105
$782$	41.5627	1.48628
$783$	−42.8683	−1.53199
$784$	17.6133	0.629048
$785$	17.7313	0.632858
$786$	−8.50721	−0.303442
$787$	43.4619	1.54925	0.774624	−	0.632422i	$-0.217939\pi$
$787$	43.4619	1.54925	0.774624	+	0.632422i	$0.217939\pi$
$788$	−22.5372	−0.802853
$789$	31.3876	1.11743
$790$	−0.562425	−0.0200102
$791$	−20.2095	−0.718566
$792$	−1.81497	−0.0644922
$793$	−14.0128	−0.497608
$794$	−3.23022	−0.114636
$795$	10.2950	0.365126
$796$	−8.95366	−0.317354
$797$	7.77853	0.275530	0.137765	−	0.990465i	$-0.456008\pi$
$797$	7.77853	0.275530	0.137765	+	0.990465i	$0.456008\pi$
$798$	23.1829	0.820665
$799$	35.7434	1.26451
$800$	−1.00000	−0.0353553
$801$	−9.23302	−0.326233
$802$	8.48325	0.299554
$803$	−0.895734	−0.0316098
$804$	−8.89217	−0.313603
$805$	−40.6952	−1.43432
$806$	−1.00000	−0.0352235
$807$	4.39107	0.154573
$808$	−12.9479	−0.455505
$809$	−25.0235	−0.879778	−0.439889	−	0.898052i	$-0.644982\pi$
$809$	−25.0235	−0.879778	−0.439889	+	0.898052i	$0.644982\pi$
$810$	0.278758	0.00979456
$811$	−46.4134	−1.62980	−0.814898	−	0.579604i	$-0.803207\pi$
$811$	−46.4134	−1.62980	−0.814898	+	0.579604i	$0.803207\pi$
$812$	40.5521	1.42310
$813$	−27.8872	−0.978047
$814$	5.01994	0.175949
$815$	−20.2660	−0.709886
$816$	5.52208	0.193311
$817$	23.8461	0.834269
$818$	−14.4448	−0.505051
$819$	8.99109	0.314174
$820$	7.64099	0.266835
$821$	−23.1492	−0.807914	−0.403957	−	0.914778i	$-0.632365\pi$
$821$	−23.1492	−0.807914	−0.403957	+	0.914778i	$0.632365\pi$
$822$	−18.5647	−0.647517
$823$	19.7169	0.687289	0.343645	−	0.939100i	$-0.388338\pi$
$823$	19.7169	0.687289	0.343645	+	0.939100i	$0.388338\pi$
$824$	−11.2190	−0.390833
$825$	−1.09144	−0.0379989
$826$	31.4882	1.09561
$827$	11.9521	0.415615	0.207808	−	0.978170i	$-0.433367\pi$
$827$	11.9521	0.415615	0.207808	+	0.978170i	$0.433367\pi$
$828$	14.8657	0.516618
$829$	41.4206	1.43860	0.719298	−	0.694702i	$-0.244464\pi$
$829$	41.4206	1.43860	0.719298	+	0.694702i	$0.244464\pi$
$830$	−7.03718	−0.244264
$831$	−14.1127	−0.489564
$832$	−1.00000	−0.0346688
$833$	89.2459	3.09219
$834$	−0.684125	−0.0236893
$835$	−8.62073	−0.298333
$836$	4.29407	0.148514
$837$	5.24454	0.181278
$838$	3.89338	0.134495
$839$	−1.86292	−0.0643150	−0.0321575	−	0.999483i	$-0.510238\pi$
$839$	−1.86292	−0.0643150	−0.0321575	+	0.999483i	$0.510238\pi$
$840$	−5.40681	−0.186553
$841$	37.8124	1.30388
$842$	−25.4068	−0.875575
$843$	25.8310	0.889667
$844$	−0.236207	−0.00813057
$845$	1.00000	0.0344010
$846$	12.7843	0.439533
$847$	−49.5971	−1.70418
$848$	9.44650	0.324394
$849$	−16.1641	−0.554751
$850$	−5.06695	−0.173795
$851$	−41.1163	−1.40945
$852$	17.7027	0.606485
$853$	22.8763	0.783270	0.391635	−	0.920121i	$-0.371910\pi$
$853$	22.8763	0.783270	0.391635	+	0.920121i	$0.371910\pi$
$854$	−69.5200	−2.37892
$855$	7.77058	0.265748
$856$	−6.36253	−0.217467
$857$	−28.2032	−0.963403	−0.481701	−	0.876335i	$-0.659981\pi$
$857$	−28.2032	−0.963403	−0.481701	+	0.876335i	$0.659981\pi$
$858$	−1.09144	−0.0372610
$859$	0.657263	0.0224255	0.0112128	−	0.999937i	$-0.496431\pi$
$859$	0.657263	0.0224255	0.0112128	+	0.999937i	$0.496431\pi$
$860$	−5.56149	−0.189645
$861$	41.3134	1.40796
$862$	11.4261	0.389174
$863$	−4.28084	−0.145722	−0.0728608	−	0.997342i	$-0.523213\pi$
$863$	−4.28084	−0.145722	−0.0728608	+	0.997342i	$0.523213\pi$
$864$	5.24454	0.178423
$865$	−15.9140	−0.541093
$866$	1.39452	0.0473876
$867$	9.45308	0.321044
$868$	−4.96118	−0.168394
$869$	−0.563258	−0.0191072
$870$	−8.90809	−0.302012
$871$	8.15928	0.276467
$872$	16.6946	0.565352
$873$	−11.8646	−0.401556
$874$	−35.1710	−1.18968
$875$	4.96118	0.167719
$876$	0.974748	0.0329337
$877$	−17.5589	−0.592923	−0.296462	−	0.955045i	$-0.595807\pi$
$877$	−17.5589	−0.592923	−0.296462	+	0.955045i	$0.595807\pi$
$878$	−7.77600	−0.262427
$879$	17.5241	0.591072
$880$	−1.00148	−0.0337599
$881$	38.4635	1.29587	0.647934	−	0.761696i	$-0.275633\pi$
$881$	38.4635	1.29587	0.647934	+	0.761696i	$0.275633\pi$
$882$	31.9204	1.07482
$883$	−3.39721	−0.114325	−0.0571626	−	0.998365i	$-0.518205\pi$
$883$	−3.39721	−0.114325	−0.0571626	+	0.998365i	$0.518205\pi$
$884$	−5.06695	−0.170420
$885$	−6.91700	−0.232512
$886$	39.7302	1.33476
$887$	−33.6580	−1.13012	−0.565062	−	0.825048i	$-0.691148\pi$
$887$	−33.6580	−1.13012	−0.565062	+	0.825048i	$0.691148\pi$
$888$	−5.46276	−0.183318
$889$	−45.8264	−1.53697
$890$	−5.09468	−0.170774
$891$	0.279171	0.00935258
$892$	8.29157	0.277622
$893$	−30.2466	−1.01216
$894$	2.20829	0.0738561
$895$	−23.6769	−0.791433
$896$	−4.96118	−0.165742
$897$	8.93951	0.298481
$898$	25.8375	0.862209
$899$	−8.17389	−0.272614
$900$	−1.81229	−0.0604095
$901$	47.8649	1.59461
$902$	7.65230	0.254794
$903$	−30.0699	−1.00066
$904$	4.07352	0.135483
$905$	12.1217	0.402939
$906$	−1.02772	−0.0341436
$907$	−39.5622	−1.31364	−0.656821	−	0.754047i	$-0.728099\pi$
$907$	−39.5622	−1.31364	−0.656821	+	0.754047i	$0.728099\pi$
$908$	4.50067	0.149360
$909$	−23.4653	−0.778294
$910$	4.96118	0.164462
$911$	−53.9715	−1.78815	−0.894077	−	0.447912i	$-0.852168\pi$
$911$	−53.9715	−1.78815	−0.894077	+	0.447912i	$0.852168\pi$
$912$	−4.67285	−0.154734
$913$	−7.04761	−0.233242
$914$	16.8215	0.556407
$915$	15.2714	0.504859
$916$	−1.07309	−0.0354560
$917$	38.7272	1.27889
$918$	26.5738	0.877066
$919$	16.0971	0.530993	0.265497	−	0.964112i	$-0.414464\pi$
$919$	16.0971	0.530993	0.265497	+	0.964112i	$0.414464\pi$
$920$	8.20272	0.270436
$921$	6.17028	0.203318
$922$	3.89528	0.128284
$923$	−16.2437	−0.534667
$924$	−5.41482	−0.178134
$925$	5.01252	0.164811
$926$	−17.3349	−0.569659
$927$	−20.3321	−0.667792
$928$	−8.17389	−0.268321
$929$	−27.8318	−0.913131	−0.456565	−	0.889690i	$-0.650921\pi$
$929$	−27.8318	−0.913131	−0.456565	+	0.889690i	$0.650921\pi$
$930$	1.08982	0.0357367
$931$	−75.5211	−2.47510
$932$	−13.2135	−0.432823
$933$	−30.3343	−0.993101
$934$	8.73678	0.285876
$935$	−5.07445	−0.165952
$936$	−1.81229	−0.0592364
$937$	−34.9493	−1.14175	−0.570873	−	0.821039i	$-0.693395\pi$
$937$	−34.9493	−1.14175	−0.570873	+	0.821039i	$0.693395\pi$
$938$	40.4797	1.32171
$939$	−34.3766	−1.12184
$940$	7.05423	0.230084
$941$	−22.9463	−0.748028	−0.374014	−	0.927423i	$-0.622019\pi$
$941$	−22.9463	−0.748028	−0.374014	+	0.927423i	$0.622019\pi$
$942$	−19.3240	−0.629610
$943$	−62.6769	−2.04104
$944$	−6.34691	−0.206574
$945$	−26.0191	−0.846402
$946$	−5.56972	−0.181087
$947$	−15.0579	−0.489315	−0.244658	−	0.969610i	$-0.578676\pi$
$947$	−15.0579	−0.489315	−0.244658	+	0.969610i	$0.578676\pi$
$948$	0.612944	0.0199075
$949$	−0.894410	−0.0290338
$950$	4.28772	0.139112
$951$	15.3289	0.497074
$952$	−25.1381	−0.814729
$953$	−22.1382	−0.717125	−0.358563	−	0.933506i	$-0.616733\pi$
$953$	−22.1382	−0.717125	−0.358563	+	0.933506i	$0.616733\pi$
$954$	17.1198	0.554273
$955$	−14.9164	−0.482682
$956$	14.3290	0.463433
$957$	−8.92128	−0.288384
$958$	−31.7288	−1.02511
$959$	84.5116	2.72902
$960$	1.08982	0.0351739
$961$	1.00000	0.0322581
$962$	5.01252	0.161610
$963$	−11.5307	−0.371573
$964$	−24.6609	−0.794273
$965$	−6.37449	−0.205202
$966$	44.3505	1.42696
$967$	−29.1054	−0.935967	−0.467983	−	0.883737i	$-0.655019\pi$
$967$	−29.1054	−0.935967	−0.467983	+	0.883737i	$0.655019\pi$
$968$	9.99704	0.321317
$969$	−23.6771	−0.760618
$970$	−6.54677	−0.210204
$971$	−29.9994	−0.962727	−0.481364	−	0.876521i	$-0.659858\pi$
$971$	−29.9994	−0.962727	−0.481364	+	0.876521i	$0.659858\pi$
$972$	15.4298	0.494912
$973$	3.11433	0.0998410
$974$	0.277886	0.00890404
$975$	−1.08982	−0.0349023
$976$	14.0128	0.448538
$977$	−55.8943	−1.78822	−0.894108	−	0.447851i	$-0.852189\pi$
$977$	−55.8943	−1.78822	−0.894108	+	0.447851i	$0.852189\pi$
$978$	22.0863	0.706243
$979$	−5.10223	−0.163068
$980$	17.6133	0.562637
$981$	30.2555	0.965983
$982$	34.6793	1.10666
$983$	19.2540	0.614107	0.307054	−	0.951692i	$-0.400657\pi$
$983$	19.2540	0.614107	0.307054	+	0.951692i	$0.400657\pi$
$984$	−8.32732	−0.265465
$985$	−22.5372	−0.718094
$986$	−41.4167	−1.31898
$987$	38.1409	1.21404
$988$	4.28772	0.136411
$989$	45.6193	1.45061
$990$	−1.81497	−0.0576835
$991$	−7.64124	−0.242732	−0.121366	−	0.992608i	$-0.538727\pi$
$991$	−7.64124	−0.242732	−0.121366	+	0.992608i	$0.538727\pi$
$992$	1.00000	0.0317500
$993$	−30.9533	−0.982272
$994$	−80.5878	−2.55609
$995$	−8.95366	−0.283850
$996$	7.66928	0.243011
$997$	5.55484	0.175924	0.0879618	−	0.996124i	$-0.471965\pi$
$997$	5.55484	0.175924	0.0879618	+	0.996124i	$0.471965\pi$
$998$	−15.1437	−0.479366
$999$	−26.2883	−0.831726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.l.1.6	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.l.1.6	✓	8	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.08982 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.08982 q^{6} +4.96118 q^{7} -1.00000 q^{8} -1.81229 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.08982 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.08982 q^{6} +4.96118 q^{7} -1.00000 q^{8} -1.81229 q^{9} -1.00000 q^{10} -1.00148 q^{11} +1.08982 q^{12} -1.00000 q^{13} -4.96118 q^{14} +1.08982 q^{15} +1.00000 q^{16} +5.06695 q^{17} +1.81229 q^{18} -4.28772 q^{19} +1.00000 q^{20} +5.40681 q^{21} +1.00148 q^{22} -8.20272 q^{23} -1.08982 q^{24} +1.00000 q^{25} +1.00000 q^{26} -5.24454 q^{27} +4.96118 q^{28} +8.17389 q^{29} -1.08982 q^{30} -1.00000 q^{31} -1.00000 q^{32} -1.09144 q^{33} -5.06695 q^{34} +4.96118 q^{35} -1.81229 q^{36} +5.01252 q^{37} +4.28772 q^{38} -1.08982 q^{39} -1.00000 q^{40} +7.64099 q^{41} -5.40681 q^{42} -5.56149 q^{43} -1.00148 q^{44} -1.81229 q^{45} +8.20272 q^{46} +7.05423 q^{47} +1.08982 q^{48} +17.6133 q^{49} -1.00000 q^{50} +5.52208 q^{51} -1.00000 q^{52} +9.44650 q^{53} +5.24454 q^{54} -1.00148 q^{55} -4.96118 q^{56} -4.67285 q^{57} -8.17389 q^{58} -6.34691 q^{59} +1.08982 q^{60} +14.0128 q^{61} +1.00000 q^{62} -8.99109 q^{63} +1.00000 q^{64} -1.00000 q^{65} +1.09144 q^{66} -8.15928 q^{67} +5.06695 q^{68} -8.93951 q^{69} -4.96118 q^{70} +16.2437 q^{71} +1.81229 q^{72} +0.894410 q^{73} -5.01252 q^{74} +1.08982 q^{75} -4.28772 q^{76} -4.96853 q^{77} +1.08982 q^{78} +0.562425 q^{79} +1.00000 q^{80} -0.278758 q^{81} -7.64099 q^{82} +7.03718 q^{83} +5.40681 q^{84} +5.06695 q^{85} +5.56149 q^{86} +8.90809 q^{87} +1.00148 q^{88} +5.09468 q^{89} +1.81229 q^{90} -4.96118 q^{91} -8.20272 q^{92} -1.08982 q^{93} -7.05423 q^{94} -4.28772 q^{95} -1.08982 q^{96} +6.54677 q^{97} -17.6133 q^{98} +1.81497 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + q^{3} + 8 q^{4} + 8 q^{5} - q^{6} + 11 q^{7} - 8 q^{8} + 9 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + q^3 + 8 * q^4 + 8 * q^5 - q^6 + 11 * q^7 - 8 * q^8 + 9 * q^9	\( 8 q - 8 q^{2} + q^{3} + 8 q^{4} + 8 q^{5} - q^{6} + 11 q^{7} - 8 q^{8} + 9 q^{9} - 8 q^{10} + q^{12} - 8 q^{13} - 11 q^{14} + q^{15} + 8 q^{16} + 7 q^{17} - 9 q^{18} - 2 q^{19} + 8 q^{20} + q^{21} + 8 q^{23} - q^{24} + 8 q^{25} + 8 q^{26} + 7 q^{27} + 11 q^{28} - q^{29} - q^{30} - 8 q^{31} - 8 q^{32} + 14 q^{33} - 7 q^{34} + 11 q^{35} + 9 q^{36} + q^{37} + 2 q^{38} - q^{39} - 8 q^{40} + 16 q^{41} - q^{42} + 3 q^{43} + 9 q^{45} - 8 q^{46} + 29 q^{47} + q^{48} + 11 q^{49} - 8 q^{50} + 11 q^{51} - 8 q^{52} + 22 q^{53} - 7 q^{54} - 11 q^{56} + 33 q^{57} + q^{58} - 8 q^{59} + q^{60} + 4 q^{61} + 8 q^{62} + 38 q^{63} + 8 q^{64} - 8 q^{65} - 14 q^{66} + 28 q^{67} + 7 q^{68} - 42 q^{69} - 11 q^{70} + 4 q^{71} - 9 q^{72} + 39 q^{73} - q^{74} + q^{75} - 2 q^{76} + 11 q^{77} + q^{78} - 16 q^{79} + 8 q^{80} + 32 q^{81} - 16 q^{82} + 25 q^{83} + q^{84} + 7 q^{85} - 3 q^{86} + 13 q^{87} + 21 q^{89} - 9 q^{90} - 11 q^{91} + 8 q^{92} - q^{93} - 29 q^{94} - 2 q^{95} - q^{96} + 28 q^{97} - 11 q^{98} + 23 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + q^3 + 8 * q^4 + 8 * q^5 - q^6 + 11 * q^7 - 8 * q^8 + 9 * q^9 - 8 * q^10 + q^12 - 8 * q^13 - 11 * q^14 + q^15 + 8 * q^16 + 7 * q^17 - 9 * q^18 - 2 * q^19 + 8 * q^20 + q^21 + 8 * q^23 - q^24 + 8 * q^25 + 8 * q^26 + 7 * q^27 + 11 * q^28 - q^29 - q^30 - 8 * q^31 - 8 * q^32 + 14 * q^33 - 7 * q^34 + 11 * q^35 + 9 * q^36 + q^37 + 2 * q^38 - q^39 - 8 * q^40 + 16 * q^41 - q^42 + 3 * q^43 + 9 * q^45 - 8 * q^46 + 29 * q^47 + q^48 + 11 * q^49 - 8 * q^50 + 11 * q^51 - 8 * q^52 + 22 * q^53 - 7 * q^54 - 11 * q^56 + 33 * q^57 + q^58 - 8 * q^59 + q^60 + 4 * q^61 + 8 * q^62 + 38 * q^63 + 8 * q^64 - 8 * q^65 - 14 * q^66 + 28 * q^67 + 7 * q^68 - 42 * q^69 - 11 * q^70 + 4 * q^71 - 9 * q^72 + 39 * q^73 - q^74 + q^75 - 2 * q^76 + 11 * q^77 + q^78 - 16 * q^79 + 8 * q^80 + 32 * q^81 - 16 * q^82 + 25 * q^83 + q^84 + 7 * q^85 - 3 * q^86 + 13 * q^87 + 21 * q^89 - 9 * q^90 - 11 * q^91 + 8 * q^92 - q^93 - 29 * q^94 - 2 * q^95 - q^96 + 28 * q^97 - 11 * q^98 + 23 * q^99

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