LMFDB - Embedded newform 8018.2.a.f.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.358038 q^{3} +1.00000 q^{4} +3.12453 q^{5} +0.358038 q^{6} -3.38298 q^{7} -1.00000 q^{8} -2.87181 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.358038 q^{3} +1.00000 q^{4} +3.12453 q^{5} +0.358038 q^{6} -3.38298 q^{7} -1.00000 q^{8} -2.87181 q^{9} -3.12453 q^{10} -3.00081 q^{11} -0.358038 q^{12} +5.58343 q^{13} +3.38298 q^{14} -1.11870 q^{15} +1.00000 q^{16} +0.615120 q^{17} +2.87181 q^{18} -1.00000 q^{19} +3.12453 q^{20} +1.21123 q^{21} +3.00081 q^{22} +7.17487 q^{23} +0.358038 q^{24} +4.76266 q^{25} -5.58343 q^{26} +2.10233 q^{27} -3.38298 q^{28} -1.35524 q^{29} +1.11870 q^{30} -6.18047 q^{31} -1.00000 q^{32} +1.07440 q^{33} -0.615120 q^{34} -10.5702 q^{35} -2.87181 q^{36} +4.34611 q^{37} +1.00000 q^{38} -1.99908 q^{39} -3.12453 q^{40} -4.36696 q^{41} -1.21123 q^{42} -1.24575 q^{43} -3.00081 q^{44} -8.97304 q^{45} -7.17487 q^{46} -6.56595 q^{47} -0.358038 q^{48} +4.44452 q^{49} -4.76266 q^{50} -0.220236 q^{51} +5.58343 q^{52} +2.38333 q^{53} -2.10233 q^{54} -9.37610 q^{55} +3.38298 q^{56} +0.358038 q^{57} +1.35524 q^{58} -0.0783359 q^{59} -1.11870 q^{60} -11.8770 q^{61} +6.18047 q^{62} +9.71526 q^{63} +1.00000 q^{64} +17.4456 q^{65} -1.07440 q^{66} +1.93235 q^{67} +0.615120 q^{68} -2.56887 q^{69} +10.5702 q^{70} -8.93518 q^{71} +2.87181 q^{72} +2.99156 q^{73} -4.34611 q^{74} -1.70521 q^{75} -1.00000 q^{76} +10.1517 q^{77} +1.99908 q^{78} +4.20610 q^{79} +3.12453 q^{80} +7.86271 q^{81} +4.36696 q^{82} +7.46260 q^{83} +1.21123 q^{84} +1.92196 q^{85} +1.24575 q^{86} +0.485227 q^{87} +3.00081 q^{88} +4.41557 q^{89} +8.97304 q^{90} -18.8886 q^{91} +7.17487 q^{92} +2.21284 q^{93} +6.56595 q^{94} -3.12453 q^{95} +0.358038 q^{96} +13.5539 q^{97} -4.44452 q^{98} +8.61775 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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
$3$	−0.358038	−0.206713	−0.103357	−	0.994644i	$-0.532958\pi$
$3$	−0.358038	−0.206713	−0.103357	+	0.994644i	$0.532958\pi$
$4$	1.00000	0.500000
$5$	3.12453	1.39733	0.698665	−	0.715449i	$-0.253778\pi$
$5$	3.12453	1.39733	0.698665	+	0.715449i	$0.253778\pi$
$6$	0.358038	0.146168
$7$	−3.38298	−1.27864	−0.639322	−	0.768939i	$-0.720785\pi$
$7$	−3.38298	−1.27864	−0.639322	+	0.768939i	$0.720785\pi$
$8$	−1.00000	−0.353553
$9$	−2.87181	−0.957270
$10$	−3.12453	−0.988062
$11$	−3.00081	−0.904778	−0.452389	−	0.891821i	$-0.649428\pi$
$11$	−3.00081	−0.904778	−0.452389	+	0.891821i	$0.649428\pi$
$12$	−0.358038	−0.103357
$13$	5.58343	1.54856	0.774282	−	0.632841i	$-0.218111\pi$
$13$	5.58343	1.54856	0.774282	+	0.632841i	$0.218111\pi$
$14$	3.38298	0.904138
$15$	−1.11870	−0.288847
$16$	1.00000	0.250000
$17$	0.615120	0.149188	0.0745942	−	0.997214i	$-0.476234\pi$
$17$	0.615120	0.149188	0.0745942	+	0.997214i	$0.476234\pi$
$18$	2.87181	0.676892
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.12453	0.698665
$21$	1.21123	0.264313
$22$	3.00081	0.639774
$23$	7.17487	1.49606	0.748032	−	0.663663i	$-0.230999\pi$
$23$	7.17487	1.49606	0.748032	+	0.663663i	$0.230999\pi$
$24$	0.358038	0.0730841
$25$	4.76266	0.952532
$26$	−5.58343	−1.09500
$27$	2.10233	0.404593
$28$	−3.38298	−0.639322
$29$	−1.35524	−0.251662	−0.125831	−	0.992052i	$-0.540160\pi$
$29$	−1.35524	−0.251662	−0.125831	+	0.992052i	$0.540160\pi$
$30$	1.11870	0.204245
$31$	−6.18047	−1.11004	−0.555022	−	0.831835i	$-0.687290\pi$
$31$	−6.18047	−1.11004	−0.555022	+	0.831835i	$0.687290\pi$
$32$	−1.00000	−0.176777
$33$	1.07440	0.187029
$34$	−0.615120	−0.105492
$35$	−10.5702	−1.78669
$36$	−2.87181	−0.478635
$37$	4.34611	0.714497	0.357248	−	0.934009i	$-0.383715\pi$
$37$	4.34611	0.714497	0.357248	+	0.934009i	$0.383715\pi$
$38$	1.00000	0.162221
$39$	−1.99908	−0.320109
$40$	−3.12453	−0.494031
$41$	−4.36696	−0.682005	−0.341002	−	0.940062i	$-0.610766\pi$
$41$	−4.36696	−0.682005	−0.341002	+	0.940062i	$0.610766\pi$
$42$	−1.21123	−0.186897
$43$	−1.24575	−0.189975	−0.0949876	−	0.995478i	$-0.530281\pi$
$43$	−1.24575	−0.189975	−0.0949876	+	0.995478i	$0.530281\pi$
$44$	−3.00081	−0.452389
$45$	−8.97304	−1.33762
$46$	−7.17487	−1.05788
$47$	−6.56595	−0.957742	−0.478871	−	0.877885i	$-0.658954\pi$
$47$	−6.56595	−0.957742	−0.478871	+	0.877885i	$0.658954\pi$
$48$	−0.358038	−0.0516783
$49$	4.44452	0.634932
$50$	−4.76266	−0.673542
$51$	−0.220236	−0.0308392
$52$	5.58343	0.774282
$53$	2.38333	0.327376	0.163688	−	0.986512i	$-0.447661\pi$
$53$	2.38333	0.327376	0.163688	+	0.986512i	$0.447661\pi$
$54$	−2.10233	−0.286091
$55$	−9.37610	−1.26427
$56$	3.38298	0.452069
$57$	0.358038	0.0474233
$58$	1.35524	0.177952
$59$	−0.0783359	−0.0101985	−0.00509923	−	0.999987i	$-0.501623\pi$
$59$	−0.0783359	−0.0101985	−0.00509923	+	0.999987i	$0.501623\pi$
$60$	−1.11870	−0.144423
$61$	−11.8770	−1.52069	−0.760346	−	0.649519i	$-0.774970\pi$
$61$	−11.8770	−1.52069	−0.760346	+	0.649519i	$0.774970\pi$
$62$	6.18047	0.784920
$63$	9.71526	1.22401
$64$	1.00000	0.125000
$65$	17.4456	2.16386
$66$	−1.07440	−0.132250
$67$	1.93235	0.236074	0.118037	−	0.993009i	$-0.462340\pi$
$67$	1.93235	0.236074	0.118037	+	0.993009i	$0.462340\pi$
$68$	0.615120	0.0745942
$69$	−2.56887	−0.309256
$70$	10.5702	1.26338
$71$	−8.93518	−1.06041	−0.530205	−	0.847869i	$-0.677885\pi$
$71$	−8.93518	−1.06041	−0.530205	+	0.847869i	$0.677885\pi$
$72$	2.87181	0.338446
$73$	2.99156	0.350136	0.175068	−	0.984556i	$-0.443986\pi$
$73$	2.99156	0.350136	0.175068	+	0.984556i	$0.443986\pi$
$74$	−4.34611	−0.505225
$75$	−1.70521	−0.196901
$76$	−1.00000	−0.114708
$77$	10.1517	1.15689
$78$	1.99908	0.226351
$79$	4.20610	0.473223	0.236611	−	0.971604i	$-0.423963\pi$
$79$	4.20610	0.473223	0.236611	+	0.971604i	$0.423963\pi$
$80$	3.12453	0.349333
$81$	7.86271	0.873635
$82$	4.36696	0.482250
$83$	7.46260	0.819127	0.409564	−	0.912282i	$-0.365681\pi$
$83$	7.46260	0.819127	0.409564	+	0.912282i	$0.365681\pi$
$84$	1.21123	0.132156
$85$	1.92196	0.208465
$86$	1.24575	0.134333
$87$	0.485227	0.0520218
$88$	3.00081	0.319887
$89$	4.41557	0.468050	0.234025	−	0.972231i	$-0.424810\pi$
$89$	4.41557	0.468050	0.234025	+	0.972231i	$0.424810\pi$
$90$	8.97304	0.945841
$91$	−18.8886	−1.98006
$92$	7.17487	0.748032
$93$	2.21284	0.229461
$94$	6.56595	0.677226
$95$	−3.12453	−0.320570
$96$	0.358038	0.0365421
$97$	13.5539	1.37619	0.688096	−	0.725620i	$-0.258447\pi$
$97$	13.5539	1.37619	0.688096	+	0.725620i	$0.258447\pi$
$98$	−4.44452	−0.448965
$99$	8.61775	0.866116
$100$	4.76266	0.476266
$101$	2.45726	0.244506	0.122253	−	0.992499i	$-0.460988\pi$
$101$	2.45726	0.244506	0.122253	+	0.992499i	$0.460988\pi$
$102$	0.220236	0.0218066
$103$	−7.74280	−0.762921	−0.381461	−	0.924385i	$-0.624579\pi$
$103$	−7.74280	−0.762921	−0.381461	+	0.924385i	$0.624579\pi$
$104$	−5.58343	−0.547500
$105$	3.78453	0.369332
$106$	−2.38333	−0.231490
$107$	9.74932	0.942502	0.471251	−	0.881999i	$-0.343803\pi$
$107$	9.74932	0.942502	0.471251	+	0.881999i	$0.343803\pi$
$108$	2.10233	0.202297
$109$	−1.84992	−0.177191	−0.0885953	−	0.996068i	$-0.528238\pi$
$109$	−1.84992	−0.177191	−0.0885953	+	0.996068i	$0.528238\pi$
$110$	9.37610	0.893976
$111$	−1.55607	−0.147696
$112$	−3.38298	−0.319661
$113$	−10.8551	−1.02117	−0.510583	−	0.859828i	$-0.670570\pi$
$113$	−10.8551	−1.02117	−0.510583	+	0.859828i	$0.670570\pi$
$114$	−0.358038	−0.0335333
$115$	22.4181	2.09049
$116$	−1.35524	−0.125831
$117$	−16.0345	−1.48239
$118$	0.0783359	0.00721140
$119$	−2.08093	−0.190759
$120$	1.11870	0.102123
$121$	−1.99515	−0.181377
$122$	11.8770	1.07529
$123$	1.56354	0.140979
$124$	−6.18047	−0.555022
$125$	−0.741577	−0.0663287
$126$	−9.71526	−0.865504
$127$	3.98375	0.353500	0.176750	−	0.984256i	$-0.443442\pi$
$127$	3.98375	0.353500	0.176750	+	0.984256i	$0.443442\pi$
$128$	−1.00000	−0.0883883
$129$	0.446026	0.0392704
$130$	−17.4456	−1.53008
$131$	−3.90039	−0.340779	−0.170389	−	0.985377i	$-0.554503\pi$
$131$	−3.90039	−0.340779	−0.170389	+	0.985377i	$0.554503\pi$
$132$	1.07440	0.0935147
$133$	3.38298	0.293341
$134$	−1.93235	−0.166929
$135$	6.56878	0.565351
$136$	−0.615120	−0.0527461
$137$	−4.07235	−0.347925	−0.173962	−	0.984752i	$-0.555657\pi$
$137$	−4.07235	−0.347925	−0.173962	+	0.984752i	$0.555657\pi$
$138$	2.56887	0.218677
$139$	−5.65075	−0.479290	−0.239645	−	0.970861i	$-0.577031\pi$
$139$	−5.65075	−0.479290	−0.239645	+	0.970861i	$0.577031\pi$
$140$	−10.5702	−0.893344
$141$	2.35086	0.197978
$142$	8.93518	0.749823
$143$	−16.7548	−1.40111
$144$	−2.87181	−0.239317
$145$	−4.23448	−0.351655
$146$	−2.99156	−0.247583
$147$	−1.59131	−0.131249
$148$	4.34611	0.357248
$149$	4.46885	0.366103	0.183051	−	0.983103i	$-0.441403\pi$
$149$	4.46885	0.366103	0.183051	+	0.983103i	$0.441403\pi$
$150$	1.70521	0.139230
$151$	−3.01879	−0.245665	−0.122833	−	0.992427i	$-0.539198\pi$
$151$	−3.01879	−0.245665	−0.122833	+	0.992427i	$0.539198\pi$
$152$	1.00000	0.0811107
$153$	−1.76651	−0.142814
$154$	−10.1517	−0.818044
$155$	−19.3110	−1.55110
$156$	−1.99908	−0.160054
$157$	14.3364	1.14417	0.572084	−	0.820195i	$-0.306135\pi$
$157$	14.3364	1.14417	0.572084	+	0.820195i	$0.306135\pi$
$158$	−4.20610	−0.334619
$159$	−0.853324	−0.0676730
$160$	−3.12453	−0.247015
$161$	−24.2724	−1.91293
$162$	−7.86271	−0.617753
$163$	−16.1862	−1.26780	−0.633902	−	0.773413i	$-0.718548\pi$
$163$	−16.1862	−1.26780	−0.633902	+	0.773413i	$0.718548\pi$
$164$	−4.36696	−0.341002
$165$	3.35700	0.261342
$166$	−7.46260	−0.579210
$167$	−16.2282	−1.25578	−0.627888	−	0.778304i	$-0.716080\pi$
$167$	−16.2282	−1.25578	−0.627888	+	0.778304i	$0.716080\pi$
$168$	−1.21123	−0.0934486
$169$	18.1747	1.39805
$170$	−1.92196	−0.147407
$171$	2.87181	0.219613
$172$	−1.24575	−0.0949876
$173$	12.7558	0.969804	0.484902	−	0.874568i	$-0.338855\pi$
$173$	12.7558	0.969804	0.484902	+	0.874568i	$0.338855\pi$
$174$	−0.485227	−0.0367850
$175$	−16.1120	−1.21795
$176$	−3.00081	−0.226194
$177$	0.0280472	0.00210816
$178$	−4.41557	−0.330961
$179$	−4.28228	−0.320073	−0.160036	−	0.987111i	$-0.551161\pi$
$179$	−4.28228	−0.320073	−0.160036	+	0.987111i	$0.551161\pi$
$180$	−8.97304	−0.668811
$181$	−0.0191058	−0.00142012	−0.000710061	−	1.00000i	$-0.500226\pi$
$181$	−0.0191058	−0.00142012	−0.000710061		1.00000i	$0.500226\pi$
$182$	18.8886	1.40012
$183$	4.25241	0.314347
$184$	−7.17487	−0.528938
$185$	13.5795	0.998388
$186$	−2.21284	−0.162253
$187$	−1.84586	−0.134982
$188$	−6.56595	−0.478871
$189$	−7.11213	−0.517331
$190$	3.12453	0.226677
$191$	−27.2759	−1.97361	−0.986807	−	0.161903i	$-0.948237\pi$
$191$	−27.2759	−1.97361	−0.986807	+	0.161903i	$0.948237\pi$
$192$	−0.358038	−0.0258391
$193$	−17.1033	−1.23113	−0.615563	−	0.788088i	$-0.711071\pi$
$193$	−17.1033	−1.23113	−0.615563	+	0.788088i	$0.711071\pi$
$194$	−13.5539	−0.973115
$195$	−6.24617	−0.447297
$196$	4.44452	0.317466
$197$	−6.67123	−0.475305	−0.237653	−	0.971350i	$-0.576378\pi$
$197$	−6.67123	−0.475305	−0.237653	+	0.971350i	$0.576378\pi$
$198$	−8.61775	−0.612437
$199$	−11.7554	−0.833321	−0.416661	−	0.909062i	$-0.636800\pi$
$199$	−11.7554	−0.833321	−0.416661	+	0.909062i	$0.636800\pi$
$200$	−4.76266	−0.336771
$201$	−0.691853	−0.0487996
$202$	−2.45726	−0.172892
$203$	4.58475	0.321786
$204$	−0.220236	−0.0154196
$205$	−13.6447	−0.952986
$206$	7.74280	0.539467
$207$	−20.6048	−1.43214
$208$	5.58343	0.387141
$209$	3.00081	0.207570
$210$	−3.78453	−0.261157
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	2.38333	0.163688
$213$	3.19913	0.219201
$214$	−9.74932	−0.666450
$215$	−3.89238	−0.265458
$216$	−2.10233	−0.143045
$217$	20.9084	1.41935
$218$	1.84992	0.125293
$219$	−1.07109	−0.0723776
$220$	−9.37610	−0.632137
$221$	3.43448	0.231028
$222$	1.55607	0.104437
$223$	4.71137	0.315497	0.157748	−	0.987479i	$-0.449577\pi$
$223$	4.71137	0.315497	0.157748	+	0.987479i	$0.449577\pi$
$224$	3.38298	0.226035
$225$	−13.6774	−0.911830
$226$	10.8551	0.722074
$227$	23.1619	1.53731	0.768655	−	0.639663i	$-0.220926\pi$
$227$	23.1619	1.53731	0.768655	+	0.639663i	$0.220926\pi$
$228$	0.358038	0.0237116
$229$	−12.7547	−0.842854	−0.421427	−	0.906862i	$-0.638471\pi$
$229$	−12.7547	−0.842854	−0.421427	+	0.906862i	$0.638471\pi$
$230$	−22.4181	−1.47820
$231$	−3.63468	−0.239144
$232$	1.35524	0.0889759
$233$	14.8648	0.973827	0.486914	−	0.873450i	$-0.338123\pi$
$233$	14.8648	0.973827	0.486914	+	0.873450i	$0.338123\pi$
$234$	16.0345	1.04821
$235$	−20.5155	−1.33828
$236$	−0.0783359	−0.00509923
$237$	−1.50594	−0.0978214
$238$	2.08093	0.134887
$239$	4.70178	0.304133	0.152066	−	0.988370i	$-0.451407\pi$
$239$	4.70178	0.304133	0.152066	+	0.988370i	$0.451407\pi$
$240$	−1.11870	−0.0722116
$241$	1.84635	0.118934	0.0594671	−	0.998230i	$-0.481060\pi$
$241$	1.84635	0.118934	0.0594671	+	0.998230i	$0.481060\pi$
$242$	1.99515	0.128253
$243$	−9.12214	−0.585185
$244$	−11.8770	−0.760346
$245$	13.8870	0.887209
$246$	−1.56354	−0.0996875
$247$	−5.58343	−0.355265
$248$	6.18047	0.392460
$249$	−2.67189	−0.169324
$250$	0.741577	0.0469015
$251$	−10.7902	−0.681069	−0.340534	−	0.940232i	$-0.610608\pi$
$251$	−10.7902	−0.681069	−0.340534	+	0.940232i	$0.610608\pi$
$252$	9.71526	0.612004
$253$	−21.5304	−1.35360
$254$	−3.98375	−0.249963
$255$	−0.688133	−0.0430926
$256$	1.00000	0.0625000
$257$	−8.57704	−0.535021	−0.267510	−	0.963555i	$-0.586201\pi$
$257$	−8.57704	−0.535021	−0.267510	+	0.963555i	$0.586201\pi$
$258$	−0.446026	−0.0277684
$259$	−14.7028	−0.913587
$260$	17.4456	1.08193
$261$	3.89199	0.240908
$262$	3.90039	0.240967
$263$	6.01493	0.370896	0.185448	−	0.982654i	$-0.440626\pi$
$263$	6.01493	0.370896	0.185448	+	0.982654i	$0.440626\pi$
$264$	−1.07440	−0.0661249
$265$	7.44679	0.457453
$266$	−3.38298	−0.207424
$267$	−1.58094	−0.0967521
$268$	1.93235	0.118037
$269$	−8.11925	−0.495039	−0.247520	−	0.968883i	$-0.579615\pi$
$269$	−8.11925	−0.495039	−0.247520	+	0.968883i	$0.579615\pi$
$270$	−6.56878	−0.399763
$271$	4.06018	0.246638	0.123319	−	0.992367i	$-0.460646\pi$
$271$	4.06018	0.246638	0.123319	+	0.992367i	$0.460646\pi$
$272$	0.615120	0.0372971
$273$	6.76283	0.409305
$274$	4.07235	0.246020
$275$	−14.2918	−0.861829
$276$	−2.56887	−0.154628
$277$	−8.51449	−0.511586	−0.255793	−	0.966732i	$-0.582337\pi$
$277$	−8.51449	−0.511586	−0.255793	+	0.966732i	$0.582337\pi$
$278$	5.65075	0.338909
$279$	17.7491	1.06261
$280$	10.5702	0.631690
$281$	3.50678	0.209197	0.104599	−	0.994515i	$-0.466644\pi$
$281$	3.50678	0.209197	0.104599	+	0.994515i	$0.466644\pi$
$282$	−2.35086	−0.139992
$283$	−16.1688	−0.961137	−0.480568	−	0.876957i	$-0.659570\pi$
$283$	−16.1688	−0.961137	−0.480568	+	0.876957i	$0.659570\pi$
$284$	−8.93518	−0.530205
$285$	1.11870	0.0662659
$286$	16.7548	0.990732
$287$	14.7733	0.872042
$288$	2.87181	0.169223
$289$	−16.6216	−0.977743
$290$	4.23448	0.248657
$291$	−4.85281	−0.284477
$292$	2.99156	0.175068
$293$	−10.2467	−0.598617	−0.299308	−	0.954156i	$-0.596756\pi$
$293$	−10.2467	−0.598617	−0.299308	+	0.954156i	$0.596756\pi$
$294$	1.59131	0.0928069
$295$	−0.244763	−0.0142506
$296$	−4.34611	−0.252613
$297$	−6.30869	−0.366067
$298$	−4.46885	−0.258874
$299$	40.0604	2.31675
$300$	−1.70521	−0.0984504
$301$	4.21434	0.242911
$302$	3.01879	0.173712
$303$	−0.879791	−0.0505426
$304$	−1.00000	−0.0573539
$305$	−37.1099	−2.12491
$306$	1.76651	0.100984
$307$	3.54653	0.202411	0.101206	−	0.994866i	$-0.467730\pi$
$307$	3.54653	0.202411	0.101206	+	0.994866i	$0.467730\pi$
$308$	10.1517	0.578444
$309$	2.77222	0.157706
$310$	19.3110	1.09679
$311$	−10.8457	−0.615003	−0.307501	−	0.951548i	$-0.599493\pi$
$311$	−10.8457	−0.615003	−0.307501	+	0.951548i	$0.599493\pi$
$312$	1.99908	0.113175
$313$	−4.14525	−0.234303	−0.117152	−	0.993114i	$-0.537376\pi$
$313$	−4.14525	−0.234303	−0.117152	+	0.993114i	$0.537376\pi$
$314$	−14.3364	−0.809050
$315$	30.3556	1.71034
$316$	4.20610	0.236611
$317$	20.3736	1.14430	0.572148	−	0.820150i	$-0.306110\pi$
$317$	20.3736	1.14430	0.572148	+	0.820150i	$0.306110\pi$
$318$	0.853324	0.0478520
$319$	4.06682	0.227698
$320$	3.12453	0.174666
$321$	−3.49062	−0.194828
$322$	24.2724	1.35265
$323$	−0.615120	−0.0342262
$324$	7.86271	0.436817
$325$	26.5920	1.47506
$326$	16.1862	0.896473
$327$	0.662343	0.0366276
$328$	4.36696	0.241125
$329$	22.2124	1.22461
$330$	−3.35700	−0.184797
$331$	−15.1441	−0.832394	−0.416197	−	0.909274i	$-0.636637\pi$
$331$	−15.1441	−0.832394	−0.416197	+	0.909274i	$0.636637\pi$
$332$	7.46260	0.409564
$333$	−12.4812	−0.683966
$334$	16.2282	0.887968
$335$	6.03767	0.329873
$336$	1.21123	0.0660782
$337$	−13.4583	−0.733122	−0.366561	−	0.930394i	$-0.619465\pi$
$337$	−13.4583	−0.733122	−0.366561	+	0.930394i	$0.619465\pi$
$338$	−18.1747	−0.988572
$339$	3.88655	0.211089
$340$	1.92196	0.104233
$341$	18.5464	1.00434
$342$	−2.87181	−0.155290
$343$	8.64512	0.466793
$344$	1.24575	0.0671664
$345$	−8.02651	−0.432133
$346$	−12.7558	−0.685755
$347$	−32.6416	−1.75229	−0.876147	−	0.482043i	$-0.839895\pi$
$347$	−32.6416	−1.75229	−0.876147	+	0.482043i	$0.839895\pi$
$348$	0.485227	0.0260109
$349$	−18.0042	−0.963742	−0.481871	−	0.876242i	$-0.660043\pi$
$349$	−18.0042	−0.963742	−0.481871	+	0.876242i	$0.660043\pi$
$350$	16.1120	0.861220
$351$	11.7382	0.626539
$352$	3.00081	0.159944
$353$	−29.7728	−1.58465	−0.792323	−	0.610102i	$-0.791128\pi$
$353$	−29.7728	−1.58465	−0.792323	+	0.610102i	$0.791128\pi$
$354$	−0.0280472	−0.00149069
$355$	−27.9182	−1.48174
$356$	4.41557	0.234025
$357$	0.745053	0.0394324
$358$	4.28228	0.226325
$359$	−32.1488	−1.69675	−0.848373	−	0.529398i	$-0.822418\pi$
$359$	−32.1488	−1.69675	−0.848373	+	0.529398i	$0.822418\pi$
$360$	8.97304	0.472921
$361$	1.00000	0.0526316
$362$	0.0191058	0.00100418
$363$	0.714340	0.0374931
$364$	−18.8886	−0.990032
$365$	9.34721	0.489255
$366$	−4.25241	−0.222277
$367$	24.4044	1.27390	0.636951	−	0.770905i	$-0.280196\pi$
$367$	24.4044	1.27390	0.636951	+	0.770905i	$0.280196\pi$
$368$	7.17487	0.374016
$369$	12.5411	0.652863
$370$	−13.5795	−0.705967
$371$	−8.06276	−0.418598
$372$	2.21284	0.114730
$373$	−24.2893	−1.25765	−0.628826	−	0.777546i	$-0.716464\pi$
$373$	−24.2893	−1.25765	−0.628826	+	0.777546i	$0.716464\pi$
$374$	1.84586	0.0954469
$375$	0.265513	0.0137110
$376$	6.56595	0.338613
$377$	−7.56689	−0.389715
$378$	7.11213	0.365808
$379$	10.7478	0.552077	0.276038	−	0.961147i	$-0.410978\pi$
$379$	10.7478	0.552077	0.276038	+	0.961147i	$0.410978\pi$
$380$	−3.12453	−0.160285
$381$	−1.42633	−0.0730732
$382$	27.2759	1.39556
$383$	−21.1458	−1.08050	−0.540249	−	0.841505i	$-0.681670\pi$
$383$	−21.1458	−1.08050	−0.540249	+	0.841505i	$0.681670\pi$
$384$	0.358038	0.0182710
$385$	31.7191	1.61656
$386$	17.1033	0.870537
$387$	3.57756	0.181858
$388$	13.5539	0.688096
$389$	10.0628	0.510206	0.255103	−	0.966914i	$-0.417891\pi$
$389$	10.0628	0.510206	0.255103	+	0.966914i	$0.417891\pi$
$390$	6.24617	0.316287
$391$	4.41340	0.223195
$392$	−4.44452	−0.224482
$393$	1.39649	0.0704434
$394$	6.67123	0.336091
$395$	13.1421	0.661248
$396$	8.61775	0.433058
$397$	16.9112	0.848748	0.424374	−	0.905487i	$-0.360494\pi$
$397$	16.9112	0.848748	0.424374	+	0.905487i	$0.360494\pi$
$398$	11.7554	0.589247
$399$	−1.21123	−0.0606375
$400$	4.76266	0.238133
$401$	26.5788	1.32728	0.663641	−	0.748051i	$-0.269010\pi$
$401$	26.5788	1.32728	0.663641	+	0.748051i	$0.269010\pi$
$402$	0.691853	0.0345065
$403$	−34.5082	−1.71898
$404$	2.45726	0.122253
$405$	24.5672	1.22076
$406$	−4.58475	−0.227537
$407$	−13.0419	−0.646461
$408$	0.220236	0.0109033
$409$	−8.32028	−0.411412	−0.205706	−	0.978614i	$-0.565949\pi$
$409$	−8.32028	−0.411412	−0.205706	+	0.978614i	$0.565949\pi$
$410$	13.6447	0.673863
$411$	1.45806	0.0719206
$412$	−7.74280	−0.381461
$413$	0.265008	0.0130402
$414$	20.6048	1.01267
$415$	23.3171	1.14459
$416$	−5.58343	−0.273750
$417$	2.02318	0.0990756
$418$	−3.00081	−0.146774
$419$	−32.8304	−1.60387	−0.801935	−	0.597411i	$-0.796196\pi$
$419$	−32.8304	−1.60387	−0.801935	+	0.597411i	$0.796196\pi$
$420$	3.78453	0.184666
$421$	2.12978	0.103799	0.0518994	−	0.998652i	$-0.483472\pi$
$421$	2.12978	0.103799	0.0518994	+	0.998652i	$0.483472\pi$
$422$	1.00000	0.0486792
$423$	18.8562	0.916817
$424$	−2.38333	−0.115745
$425$	2.92960	0.142107
$426$	−3.19913	−0.154998
$427$	40.1795	1.94442
$428$	9.74932	0.471251
$429$	5.99885	0.289627
$430$	3.89238	0.187707
$431$	−33.8992	−1.63286	−0.816432	−	0.577441i	$-0.804051\pi$
$431$	−33.8992	−1.63286	−0.816432	+	0.577441i	$0.804051\pi$
$432$	2.10233	0.101148
$433$	0.554211	0.0266337	0.0133168	−	0.999911i	$-0.495761\pi$
$433$	0.554211	0.0266337	0.0133168	+	0.999911i	$0.495761\pi$
$434$	−20.9084	−1.00363
$435$	1.51610	0.0726917
$436$	−1.84992	−0.0885953
$437$	−7.17487	−0.343220
$438$	1.07109	0.0511787
$439$	21.5358	1.02785	0.513923	−	0.857837i	$-0.328192\pi$
$439$	21.5358	1.02785	0.513923	+	0.857837i	$0.328192\pi$
$440$	9.37610	0.446988
$441$	−12.7638	−0.607801
$442$	−3.43448	−0.163361
$443$	−19.3598	−0.919812	−0.459906	−	0.887968i	$-0.652117\pi$
$443$	−19.3598	−0.919812	−0.459906	+	0.887968i	$0.652117\pi$
$444$	−1.55607	−0.0738479
$445$	13.7966	0.654020
$446$	−4.71137	−0.223090
$447$	−1.60002	−0.0756783
$448$	−3.38298	−0.159831
$449$	−28.3635	−1.33855	−0.669277	−	0.743013i	$-0.733396\pi$
$449$	−28.3635	−1.33855	−0.669277	+	0.743013i	$0.733396\pi$
$450$	13.6774	0.644761
$451$	13.1044	0.617063
$452$	−10.8551	−0.510583
$453$	1.08084	0.0507823
$454$	−23.1619	−1.08704
$455$	−59.0179	−2.76680
$456$	−0.358038	−0.0167667
$457$	−1.65460	−0.0773989	−0.0386994	−	0.999251i	$-0.512321\pi$
$457$	−1.65460	−0.0773989	−0.0386994	+	0.999251i	$0.512321\pi$
$458$	12.7547	0.595988
$459$	1.29318	0.0603606
$460$	22.4181	1.04525
$461$	39.2786	1.82939	0.914693	−	0.404149i	$-0.132432\pi$
$461$	39.2786	1.82939	0.914693	+	0.404149i	$0.132432\pi$
$462$	3.63468	0.169100
$463$	15.0384	0.698892	0.349446	−	0.936957i	$-0.386370\pi$
$463$	15.0384	0.698892	0.349446	+	0.936957i	$0.386370\pi$
$464$	−1.35524	−0.0629155
$465$	6.91408	0.320633
$466$	−14.8648	−0.688600
$467$	−13.5231	−0.625773	−0.312886	−	0.949791i	$-0.601296\pi$
$467$	−13.5231	−0.625773	−0.312886	+	0.949791i	$0.601296\pi$
$468$	−16.0345	−0.741197
$469$	−6.53709	−0.301855
$470$	20.5155	0.946308
$471$	−5.13297	−0.236515
$472$	0.0783359	0.00360570
$473$	3.73826	0.171885
$474$	1.50594	0.0691702
$475$	−4.76266	−0.218526
$476$	−2.08093	−0.0953795
$477$	−6.84448	−0.313387
$478$	−4.70178	−0.215054
$479$	−16.7659	−0.766055	−0.383027	−	0.923737i	$-0.625118\pi$
$479$	−16.7659	−0.766055	−0.383027	+	0.923737i	$0.625118\pi$
$480$	1.11870	0.0510613
$481$	24.2662	1.10644
$482$	−1.84635	−0.0840992
$483$	8.69043	0.395428
$484$	−1.99515	−0.0906887
$485$	42.3496	1.92299
$486$	9.12214	0.413788
$487$	−21.8167	−0.988611	−0.494305	−	0.869288i	$-0.664578\pi$
$487$	−21.8167	−0.988611	−0.494305	+	0.869288i	$0.664578\pi$
$488$	11.8770	0.537646
$489$	5.79529	0.262072
$490$	−13.8870	−0.627352
$491$	18.8936	0.852657	0.426329	−	0.904568i	$-0.359807\pi$
$491$	18.8936	0.852657	0.426329	+	0.904568i	$0.359807\pi$
$492$	1.56354	0.0704897
$493$	−0.833635	−0.0375450
$494$	5.58343	0.251210
$495$	26.9264	1.21025
$496$	−6.18047	−0.277511
$497$	30.2275	1.35589
$498$	2.67189	0.119730
$499$	−19.8282	−0.887634	−0.443817	−	0.896117i	$-0.646376\pi$
$499$	−19.8282	−0.887634	−0.443817	+	0.896117i	$0.646376\pi$
$500$	−0.741577	−0.0331643
$501$	5.81031	0.259586
$502$	10.7902	0.481588
$503$	−8.98579	−0.400657	−0.200328	−	0.979729i	$-0.564201\pi$
$503$	−8.98579	−0.400657	−0.200328	+	0.979729i	$0.564201\pi$
$504$	−9.71526	−0.432752
$505$	7.67776	0.341656
$506$	21.5304	0.957143
$507$	−6.50722	−0.288996
$508$	3.98375	0.176750
$509$	−12.9747	−0.575093	−0.287546	−	0.957767i	$-0.592840\pi$
$509$	−12.9747	−0.575093	−0.287546	+	0.957767i	$0.592840\pi$
$510$	0.688133	0.0304710
$511$	−10.1204	−0.447699
$512$	−1.00000	−0.0441942
$513$	−2.10233	−0.0928201
$514$	8.57704	0.378317
$515$	−24.1926	−1.06605
$516$	0.446026	0.0196352
$517$	19.7032	0.866544
$518$	14.7028	0.646004
$519$	−4.56705	−0.200471
$520$	−17.4456	−0.765039
$521$	−29.2714	−1.28240	−0.641201	−	0.767373i	$-0.721563\pi$
$521$	−29.2714	−1.28240	−0.641201	+	0.767373i	$0.721563\pi$
$522$	−3.89199	−0.170348
$523$	−3.09694	−0.135420	−0.0677099	−	0.997705i	$-0.521569\pi$
$523$	−3.09694	−0.135420	−0.0677099	+	0.997705i	$0.521569\pi$
$524$	−3.90039	−0.170389
$525$	5.76869	0.251766
$526$	−6.01493	−0.262263
$527$	−3.80173	−0.165606
$528$	1.07440	0.0467574
$529$	28.4787	1.23821
$530$	−7.44679	−0.323468
$531$	0.224966	0.00976268
$532$	3.38298	0.146671
$533$	−24.3826	−1.05613
$534$	1.58094	0.0684141
$535$	30.4620	1.31699
$536$	−1.93235	−0.0834647
$537$	1.53322	0.0661632
$538$	8.11925	0.350046
$539$	−13.3372	−0.574472
$540$	6.56878	0.282675
$541$	28.7730	1.23705	0.618524	−	0.785766i	$-0.287731\pi$
$541$	28.7730	1.23705	0.618524	+	0.785766i	$0.287731\pi$
$542$	−4.06018	−0.174400
$543$	0.00684059	0.000293558 0
$544$	−0.615120	−0.0263730
$545$	−5.78014	−0.247594
$546$	−6.76283	−0.289422
$547$	−36.6068	−1.56519	−0.782597	−	0.622529i	$-0.786105\pi$
$547$	−36.6068	−1.56519	−0.782597	+	0.622529i	$0.786105\pi$
$548$	−4.07235	−0.173962
$549$	34.1084	1.45571
$550$	14.2918	0.609405
$551$	1.35524	0.0577352
$552$	2.56887	0.109338
$553$	−14.2291	−0.605084
$554$	8.51449	0.361746
$555$	−4.86199	−0.206380
$556$	−5.65075	−0.239645
$557$	−0.621524	−0.0263348	−0.0131674	−	0.999913i	$-0.504191\pi$
$557$	−0.621524	−0.0263348	−0.0131674	+	0.999913i	$0.504191\pi$
$558$	−17.7491	−0.751380
$559$	−6.95556	−0.294189
$560$	−10.5702	−0.446672
$561$	0.660886	0.0279026
$562$	−3.50678	−0.147925
$563$	−27.1266	−1.14325	−0.571625	−	0.820515i	$-0.693687\pi$
$563$	−27.1266	−1.14325	−0.571625	+	0.820515i	$0.693687\pi$
$564$	2.35086	0.0989890
$565$	−33.9172	−1.42691
$566$	16.1688	0.679626
$567$	−26.5994	−1.11707
$568$	8.93518	0.374912
$569$	12.7725	0.535451	0.267726	−	0.963495i	$-0.413728\pi$
$569$	12.7725	0.535451	0.267726	+	0.963495i	$0.413728\pi$
$570$	−1.11870	−0.0468571
$571$	16.4930	0.690209	0.345104	−	0.938564i	$-0.387844\pi$
$571$	16.4930	0.690209	0.345104	+	0.938564i	$0.387844\pi$
$572$	−16.7548	−0.700553
$573$	9.76579	0.407972
$574$	−14.7733	−0.616627
$575$	34.1714	1.42505
$576$	−2.87181	−0.119659
$577$	16.2653	0.677132	0.338566	−	0.940943i	$-0.390058\pi$
$577$	16.2653	0.677132	0.338566	+	0.940943i	$0.390058\pi$
$578$	16.6216	0.691369
$579$	6.12364	0.254490
$580$	−4.23448	−0.175827
$581$	−25.2458	−1.04737
$582$	4.85281	0.201156
$583$	−7.15193	−0.296203
$584$	−2.99156	−0.123792
$585$	−50.1003	−2.07139
$586$	10.2467	0.423286
$587$	47.0653	1.94259	0.971296	−	0.237873i	$-0.0764501\pi$
$587$	47.0653	1.94259	0.971296	+	0.237873i	$0.0764501\pi$
$588$	−1.59131	−0.0656244
$589$	6.18047	0.254662
$590$	0.244763	0.0100767
$591$	2.38855	0.0982518
$592$	4.34611	0.178624
$593$	16.7663	0.688508	0.344254	−	0.938876i	$-0.388132\pi$
$593$	16.7663	0.688508	0.344254	+	0.938876i	$0.388132\pi$
$594$	6.30869	0.258849
$595$	−6.50193	−0.266553
$596$	4.46885	0.183051
$597$	4.20889	0.172258
$598$	−40.0604	−1.63819
$599$	−7.65934	−0.312952	−0.156476	−	0.987682i	$-0.550013\pi$
$599$	−7.65934	−0.312952	−0.156476	+	0.987682i	$0.550013\pi$
$600$	1.70521	0.0696150
$601$	−1.79716	−0.0733078	−0.0366539	−	0.999328i	$-0.511670\pi$
$601$	−1.79716	−0.0733078	−0.0366539	+	0.999328i	$0.511670\pi$
$602$	−4.21434	−0.171764
$603$	−5.54933	−0.225986
$604$	−3.01879	−0.122833
$605$	−6.23390	−0.253444
$606$	0.879791	0.0357390
$607$	3.69879	0.150129	0.0750647	−	0.997179i	$-0.476084\pi$
$607$	3.69879	0.150129	0.0750647	+	0.997179i	$0.476084\pi$
$608$	1.00000	0.0405554
$609$	−1.64151	−0.0665174
$610$	37.1099	1.50254
$611$	−36.6605	−1.48313
$612$	−1.76651	−0.0714068
$613$	12.5828	0.508216	0.254108	−	0.967176i	$-0.418218\pi$
$613$	12.5828	0.508216	0.254108	+	0.967176i	$0.418218\pi$
$614$	−3.54653	−0.143126
$615$	4.88531	0.196995
$616$	−10.1517	−0.409022
$617$	25.3603	1.02097	0.510484	−	0.859887i	$-0.329466\pi$
$617$	25.3603	1.02097	0.510484	+	0.859887i	$0.329466\pi$
$618$	−2.77222	−0.111515
$619$	−27.6129	−1.10986	−0.554928	−	0.831899i	$-0.687254\pi$
$619$	−27.6129	−1.10986	−0.554928	+	0.831899i	$0.687254\pi$
$620$	−19.3110	−0.775550
$621$	15.0839	0.605297
$622$	10.8457	0.434873
$623$	−14.9378	−0.598470
$624$	−1.99908	−0.0800272
$625$	−26.1304	−1.04521
$626$	4.14525	0.165678
$627$	−1.07440	−0.0429075
$628$	14.3364	0.572084
$629$	2.67338	0.106595
$630$	−30.3556	−1.20939
$631$	13.8660	0.551995	0.275998	−	0.961158i	$-0.410992\pi$
$631$	13.8660	0.551995	0.275998	+	0.961158i	$0.410992\pi$
$632$	−4.20610	−0.167310
$633$	0.358038	0.0142307
$634$	−20.3736	−0.809139
$635$	12.4473	0.493957
$636$	−0.853324	−0.0338365
$637$	24.8157	0.983233
$638$	−4.06682	−0.161007
$639$	25.6601	1.01510
$640$	−3.12453	−0.123508
$641$	−32.3492	−1.27772	−0.638858	−	0.769325i	$-0.720593\pi$
$641$	−32.3492	−1.27772	−0.638858	+	0.769325i	$0.720593\pi$
$642$	3.49062	0.137764
$643$	−39.6253	−1.56267	−0.781334	−	0.624113i	$-0.785461\pi$
$643$	−39.6253	−1.56267	−0.781334	+	0.624113i	$0.785461\pi$
$644$	−24.2724	−0.956466
$645$	1.39362	0.0548737
$646$	0.615120	0.0242016
$647$	22.3852	0.880052	0.440026	−	0.897985i	$-0.354969\pi$
$647$	22.3852	0.880052	0.440026	+	0.897985i	$0.354969\pi$
$648$	−7.86271	−0.308877
$649$	0.235071	0.00922734
$650$	−26.5920	−1.04302
$651$	−7.48599	−0.293399
$652$	−16.1862	−0.633902
$653$	−25.3919	−0.993662	−0.496831	−	0.867847i	$-0.665503\pi$
$653$	−25.3919	−0.993662	−0.496831	+	0.867847i	$0.665503\pi$
$654$	−0.662343	−0.0258997
$655$	−12.1869	−0.476180
$656$	−4.36696	−0.170501
$657$	−8.59119	−0.335174
$658$	−22.2124	−0.865931
$659$	0.0400543	0.00156030	0.000780148	−	1.00000i	$-0.499752\pi$
$659$	0.0400543	0.00156030	0.000780148		1.00000i	$0.499752\pi$
$660$	3.35700	0.130671
$661$	−43.2027	−1.68039	−0.840195	−	0.542284i	$-0.817560\pi$
$661$	−43.2027	−1.68039	−0.840195	+	0.542284i	$0.817560\pi$
$662$	15.1441	0.588592
$663$	−1.22967	−0.0477565
$664$	−7.46260	−0.289605
$665$	10.5702	0.409894
$666$	12.4812	0.483637
$667$	−9.72367	−0.376502
$668$	−16.2282	−0.627888
$669$	−1.68685	−0.0652173
$670$	−6.03767	−0.233256
$671$	35.6405	1.37589
$672$	−1.21123	−0.0467243
$673$	12.7442	0.491252	0.245626	−	0.969365i	$-0.421006\pi$
$673$	12.7442	0.491252	0.245626	+	0.969365i	$0.421006\pi$
$674$	13.4583	0.518396
$675$	10.0127	0.385388
$676$	18.1747	0.699026
$677$	−14.3958	−0.553274	−0.276637	−	0.960974i	$-0.589220\pi$
$677$	−14.3958	−0.553274	−0.276637	+	0.960974i	$0.589220\pi$
$678$	−3.88655	−0.149262
$679$	−45.8526	−1.75966
$680$	−1.92196	−0.0737037
$681$	−8.29284	−0.317782
$682$	−18.5464	−0.710178
$683$	−13.0006	−0.497455	−0.248727	−	0.968574i	$-0.580012\pi$
$683$	−13.0006	−0.497455	−0.248727	+	0.968574i	$0.580012\pi$
$684$	2.87181	0.109806
$685$	−12.7242	−0.486166
$686$	−8.64512	−0.330072
$687$	4.56666	0.174229
$688$	−1.24575	−0.0474938
$689$	13.3072	0.506963
$690$	8.02651	0.305564
$691$	0.218049	0.00829499	0.00414749	−	0.999991i	$-0.498680\pi$
$691$	0.218049	0.00829499	0.00414749	+	0.999991i	$0.498680\pi$
$692$	12.7558	0.484902
$693$	−29.1536	−1.10745
$694$	32.6416	1.23906
$695$	−17.6559	−0.669726
$696$	−0.485227	−0.0183925
$697$	−2.68620	−0.101747
$698$	18.0042	0.681468
$699$	−5.32217	−0.201303
$700$	−16.1120	−0.608975
$701$	25.2798	0.954806	0.477403	−	0.878684i	$-0.341578\pi$
$701$	25.2798	0.954806	0.477403	+	0.878684i	$0.341578\pi$
$702$	−11.7382	−0.443030
$703$	−4.34611	−0.163917
$704$	−3.00081	−0.113097
$705$	7.34531	0.276641
$706$	29.7728	1.12051
$707$	−8.31284	−0.312636
$708$	0.0280472	0.00105408
$709$	9.79497	0.367858	0.183929	−	0.982940i	$-0.441118\pi$
$709$	9.79497	0.367858	0.183929	+	0.982940i	$0.441118\pi$
$710$	27.9182	1.04775
$711$	−12.0791	−0.453002
$712$	−4.41557	−0.165481
$713$	−44.3440	−1.66070
$714$	−0.745053	−0.0278829
$715$	−52.3508	−1.95781
$716$	−4.28228	−0.160036
$717$	−1.68341	−0.0628682
$718$	32.1488	1.19978
$719$	38.7960	1.44685	0.723424	−	0.690404i	$-0.242567\pi$
$719$	38.7960	1.44685	0.723424	+	0.690404i	$0.242567\pi$
$720$	−8.97304	−0.334405
$721$	26.1937	0.975505
$722$	−1.00000	−0.0372161
$723$	−0.661065	−0.0245853
$724$	−0.0191058	−0.000710061 0
$725$	−6.45455	−0.239716
$726$	−0.714340	−0.0265116
$727$	−1.53700	−0.0570043	−0.0285021	−	0.999594i	$-0.509074\pi$
$727$	−1.53700	−0.0570043	−0.0285021	+	0.999594i	$0.509074\pi$
$728$	18.8886	0.700058
$729$	−20.3221	−0.752669
$730$	−9.34721	−0.345956
$731$	−0.766286	−0.0283421
$732$	4.25241	0.157173
$733$	50.8935	1.87980	0.939898	−	0.341455i	$-0.110920\pi$
$733$	50.8935	1.87980	0.939898	+	0.341455i	$0.110920\pi$
$734$	−24.4044	−0.900784
$735$	−4.97208	−0.183398
$736$	−7.17487	−0.264469
$737$	−5.79860	−0.213594
$738$	−12.5411	−0.461644
$739$	−5.83827	−0.214764	−0.107382	−	0.994218i	$-0.534247\pi$
$739$	−5.83827	−0.214764	−0.107382	+	0.994218i	$0.534247\pi$
$740$	13.5795	0.499194
$741$	1.99908	0.0734380
$742$	8.06276	0.295993
$743$	45.9366	1.68525	0.842625	−	0.538501i	$-0.181009\pi$
$743$	45.9366	1.68525	0.842625	+	0.538501i	$0.181009\pi$
$744$	−2.21284	−0.0811267
$745$	13.9630	0.511567
$746$	24.2893	0.889294
$747$	−21.4312	−0.784126
$748$	−1.84586	−0.0674912
$749$	−32.9817	−1.20513
$750$	−0.265513	−0.00969515
$751$	16.1899	0.590779	0.295390	−	0.955377i	$-0.404551\pi$
$751$	16.1899	0.590779	0.295390	+	0.955377i	$0.404551\pi$
$752$	−6.56595	−0.239436
$753$	3.86328	0.140786
$754$	7.56689	0.275570
$755$	−9.43228	−0.343276
$756$	−7.11213	−0.258666
$757$	−36.3310	−1.32047	−0.660236	−	0.751059i	$-0.729544\pi$
$757$	−36.3310	−1.32047	−0.660236	+	0.751059i	$0.729544\pi$
$758$	−10.7478	−0.390377
$759$	7.70869	0.279808
$760$	3.12453	0.113338
$761$	−6.83122	−0.247632	−0.123816	−	0.992305i	$-0.539513\pi$
$761$	−6.83122	−0.247632	−0.123816	+	0.992305i	$0.539513\pi$
$762$	1.42633	0.0516706
$763$	6.25825	0.226564
$764$	−27.2759	−0.986807
$765$	−5.51949	−0.199558
$766$	21.1458	0.764028
$767$	−0.437383	−0.0157930
$768$	−0.358038	−0.0129196
$769$	−10.3997	−0.375024	−0.187512	−	0.982262i	$-0.560042\pi$
$769$	−10.3997	−0.375024	−0.187512	+	0.982262i	$0.560042\pi$
$770$	−31.7191	−1.14308
$771$	3.07090	0.110596
$772$	−17.1033	−0.615563
$773$	−5.54935	−0.199596	−0.0997981	−	0.995008i	$-0.531820\pi$
$773$	−5.54935	−0.199596	−0.0997981	+	0.995008i	$0.531820\pi$
$774$	−3.57756	−0.128593
$775$	−29.4355	−1.05735
$776$	−13.5539	−0.486557
$777$	5.26415	0.188850
$778$	−10.0628	−0.360770
$779$	4.36696	0.156463
$780$	−6.24617	−0.223649
$781$	26.8127	0.959435
$782$	−4.41340	−0.157823
$783$	−2.84916	−0.101821
$784$	4.44452	0.158733
$785$	44.7944	1.59878
$786$	−1.39649	−0.0498110
$787$	−3.95969	−0.141148	−0.0705738	−	0.997507i	$-0.522483\pi$
$787$	−3.95969	−0.141148	−0.0705738	+	0.997507i	$0.522483\pi$
$788$	−6.67123	−0.237653
$789$	−2.15357	−0.0766692
$790$	−13.1421	−0.467573
$791$	36.7227	1.30571
$792$	−8.61775	−0.306218
$793$	−66.3143	−2.35489
$794$	−16.9112	−0.600155
$795$	−2.66623	−0.0945615
$796$	−11.7554	−0.416661
$797$	−0.820786	−0.0290737	−0.0145369	−	0.999894i	$-0.504627\pi$
$797$	−0.820786	−0.0290737	−0.0145369	+	0.999894i	$0.504627\pi$
$798$	1.21123	0.0428772
$799$	−4.03884	−0.142884
$800$	−4.76266	−0.168385
$801$	−12.6807	−0.448050
$802$	−26.5788	−0.938530
$803$	−8.97710	−0.316795
$804$	−0.691853	−0.0243998
$805$	−75.8397	−2.67300
$806$	34.5082	1.21550
$807$	2.90700	0.102331
$808$	−2.45726	−0.0864460
$809$	11.5408	0.405753	0.202876	−	0.979204i	$-0.434971\pi$
$809$	11.5408	0.405753	0.202876	+	0.979204i	$0.434971\pi$
$810$	−24.5672	−0.863205
$811$	−15.8151	−0.555342	−0.277671	−	0.960676i	$-0.589563\pi$
$811$	−15.8151	−0.555342	−0.277671	+	0.960676i	$0.589563\pi$
$812$	4.58475	0.160893
$813$	−1.45370	−0.0509834
$814$	13.0419	0.457117
$815$	−50.5743	−1.77154
$816$	−0.220236	−0.00770980
$817$	1.24575	0.0435833
$818$	8.32028	0.290912
$819$	54.2445	1.89545
$820$	−13.6447	−0.476493
$821$	7.13775	0.249109	0.124555	−	0.992213i	$-0.460250\pi$
$821$	7.13775	0.249109	0.124555	+	0.992213i	$0.460250\pi$
$822$	−1.45806	−0.0508555
$823$	22.3234	0.778145	0.389073	−	0.921207i	$-0.372796\pi$
$823$	22.3234	0.778145	0.389073	+	0.921207i	$0.372796\pi$
$824$	7.74280	0.269733
$825$	5.11701	0.178152
$826$	−0.265008	−0.00922082
$827$	−41.7018	−1.45011	−0.725057	−	0.688688i	$-0.758187\pi$
$827$	−41.7018	−1.45011	−0.725057	+	0.688688i	$0.758187\pi$
$828$	−20.6048	−0.716068
$829$	−49.0713	−1.70432	−0.852158	−	0.523285i	$-0.824706\pi$
$829$	−49.0713	−1.70432	−0.852158	+	0.523285i	$0.824706\pi$
$830$	−23.3171	−0.809348
$831$	3.04851	0.105752
$832$	5.58343	0.193571
$833$	2.73391	0.0947244
$834$	−2.02318	−0.0700570
$835$	−50.7054	−1.75473
$836$	3.00081	0.103785
$837$	−12.9934	−0.449117
$838$	32.8304	1.13411
$839$	19.1731	0.661928	0.330964	−	0.943643i	$-0.392626\pi$
$839$	19.1731	0.661928	0.330964	+	0.943643i	$0.392626\pi$
$840$	−3.78453	−0.130579
$841$	−27.1633	−0.936666
$842$	−2.12978	−0.0733969
$843$	−1.25556	−0.0432438
$844$	−1.00000	−0.0344214
$845$	56.7872	1.95354
$846$	−18.8562	−0.648288
$847$	6.74955	0.231917
$848$	2.38333	0.0818440
$849$	5.78905	0.198680
$850$	−2.92960	−0.100485
$851$	31.1828	1.06893
$852$	3.19913	0.109600
$853$	−20.3042	−0.695201	−0.347601	−	0.937643i	$-0.613003\pi$
$853$	−20.3042	−0.695201	−0.347601	+	0.937643i	$0.613003\pi$
$854$	−40.1795	−1.37491
$855$	8.97304	0.306872
$856$	−9.74932	−0.333225
$857$	8.86837	0.302938	0.151469	−	0.988462i	$-0.451600\pi$
$857$	8.86837	0.302938	0.151469	+	0.988462i	$0.451600\pi$
$858$	−5.99885	−0.204797
$859$	36.6955	1.25203	0.626017	−	0.779809i	$-0.284684\pi$
$859$	36.6955	1.25203	0.626017	+	0.779809i	$0.284684\pi$
$860$	−3.89238	−0.132729
$861$	−5.28941	−0.180263
$862$	33.8992	1.15461
$863$	28.8863	0.983302	0.491651	−	0.870792i	$-0.336394\pi$
$863$	28.8863	0.983302	0.491651	+	0.870792i	$0.336394\pi$
$864$	−2.10233	−0.0715227
$865$	39.8558	1.35514
$866$	−0.554211	−0.0188328
$867$	5.95117	0.202112
$868$	20.9084	0.709676
$869$	−12.6217	−0.428161
$870$	−1.51610	−0.0514008
$871$	10.7891	0.365576
$872$	1.84992	0.0626463
$873$	−38.9243	−1.31739
$874$	7.17487	0.242694
$875$	2.50874	0.0848108
$876$	−1.07109	−0.0361888
$877$	19.2468	0.649917	0.324958	−	0.945728i	$-0.394650\pi$
$877$	19.2468	0.649917	0.324958	+	0.945728i	$0.394650\pi$
$878$	−21.5358	−0.726796
$879$	3.66869	0.123742
$880$	−9.37610	−0.316068
$881$	32.7640	1.10385	0.551924	−	0.833895i	$-0.313894\pi$
$881$	32.7640	1.10385	0.551924	+	0.833895i	$0.313894\pi$
$882$	12.7638	0.429780
$883$	−39.0126	−1.31288	−0.656439	−	0.754379i	$-0.727938\pi$
$883$	−39.0126	−1.31288	−0.656439	+	0.754379i	$0.727938\pi$
$884$	3.43448	0.115514
$885$	0.0876342	0.00294579
$886$	19.3598	0.650405
$887$	−40.4343	−1.35765	−0.678825	−	0.734300i	$-0.737511\pi$
$887$	−40.4343	−1.35765	−0.678825	+	0.734300i	$0.737511\pi$
$888$	1.55607	0.0522184
$889$	−13.4769	−0.452001
$890$	−13.7966	−0.462462
$891$	−23.5945	−0.790445
$892$	4.71137	0.157748
$893$	6.56595	0.219721
$894$	1.60002	0.0535126
$895$	−13.3801	−0.447247
$896$	3.38298	0.113017
$897$	−14.3431	−0.478903
$898$	28.3635	0.946501
$899$	8.37602	0.279356
$900$	−13.6774	−0.455915
$901$	1.46604	0.0488407
$902$	−13.1044	−0.436329
$903$	−1.50889	−0.0502129
$904$	10.8551	0.361037
$905$	−0.0596965	−0.00198438
$906$	−1.08084	−0.0359085
$907$	−25.5757	−0.849229	−0.424614	−	0.905374i	$-0.639590\pi$
$907$	−25.5757	−0.849229	−0.424614	+	0.905374i	$0.639590\pi$
$908$	23.1619	0.768655
$909$	−7.05677	−0.234058
$910$	59.0179	1.95642
$911$	−45.4379	−1.50542	−0.752712	−	0.658350i	$-0.771255\pi$
$911$	−45.4379	−1.50542	−0.752712	+	0.658350i	$0.771255\pi$
$912$	0.358038	0.0118558
$913$	−22.3938	−0.741128
$914$	1.65460	0.0547293
$915$	13.2868	0.439246
$916$	−12.7547	−0.421427
$917$	13.1949	0.435735
$918$	−1.29318	−0.0426814
$919$	34.4806	1.13741	0.568706	−	0.822541i	$-0.307444\pi$
$919$	34.4806	1.13741	0.568706	+	0.822541i	$0.307444\pi$
$920$	−22.4181	−0.739101
$921$	−1.26979	−0.0418410
$922$	−39.2786	−1.29357
$923$	−49.8889	−1.64211
$924$	−3.63468	−0.119572
$925$	20.6991	0.680581
$926$	−15.0384	−0.494191
$927$	22.2358	0.730321
$928$	1.35524	0.0444880
$929$	58.4115	1.91642	0.958210	−	0.286065i	$-0.0923472\pi$
$929$	58.4115	1.91642	0.958210	+	0.286065i	$0.0923472\pi$
$930$	−6.91408	−0.226722
$931$	−4.44452	−0.145663
$932$	14.8648	0.486914
$933$	3.88317	0.127129
$934$	13.5231	0.442488
$935$	−5.76742	−0.188615
$936$	16.0345	0.524105
$937$	2.99786	0.0979357	0.0489678	−	0.998800i	$-0.484407\pi$
$937$	2.99786	0.0979357	0.0489678	+	0.998800i	$0.484407\pi$
$938$	6.53709	0.213443
$939$	1.48416	0.0484336
$940$	−20.5155	−0.669141
$941$	−48.7190	−1.58819	−0.794097	−	0.607791i	$-0.792056\pi$
$941$	−48.7190	−1.58819	−0.794097	+	0.607791i	$0.792056\pi$
$942$	5.13297	0.167241
$943$	−31.3324	−1.02032
$944$	−0.0783359	−0.00254962
$945$	−22.2220	−0.722882
$946$	−3.73826	−0.121541
$947$	30.5376	0.992338	0.496169	−	0.868226i	$-0.334740\pi$
$947$	30.5376	0.992338	0.496169	+	0.868226i	$0.334740\pi$
$948$	−1.50594	−0.0489107
$949$	16.7032	0.542208
$950$	4.76266	0.154521
$951$	−7.29452	−0.236541
$952$	2.08093	0.0674435
$953$	−18.2301	−0.590532	−0.295266	−	0.955415i	$-0.595408\pi$
$953$	−18.2301	−0.590532	−0.295266	+	0.955415i	$0.595408\pi$
$954$	6.84448	0.221598
$955$	−85.2242	−2.75779
$956$	4.70178	0.152066
$957$	−1.45607	−0.0470682
$958$	16.7659	0.541682
$959$	13.7767	0.444872
$960$	−1.11870	−0.0361058
$961$	7.19819	0.232200
$962$	−24.2662	−0.782374
$963$	−27.9982	−0.902229
$964$	1.84635	0.0594671
$965$	−53.4398	−1.72029
$966$	−8.69043	−0.279610
$967$	−48.3574	−1.55507	−0.777535	−	0.628840i	$-0.783530\pi$
$967$	−48.3574	−1.55507	−0.777535	+	0.628840i	$0.783530\pi$
$968$	1.99515	0.0641266
$969$	0.220236	0.00707500
$970$	−42.3496	−1.35976
$971$	−30.5748	−0.981191	−0.490595	−	0.871388i	$-0.663221\pi$
$971$	−30.5748	−0.981191	−0.490595	+	0.871388i	$0.663221\pi$
$972$	−9.12214	−0.292593
$973$	19.1163	0.612841
$974$	21.8167	0.699053
$975$	−9.52093	−0.304914
$976$	−11.8770	−0.380173
$977$	−24.8139	−0.793867	−0.396933	−	0.917847i	$-0.629926\pi$
$977$	−24.8139	−0.793867	−0.396933	+	0.917847i	$0.629926\pi$
$978$	−5.79529	−0.185313
$979$	−13.2503	−0.423481
$980$	13.8870	0.443605
$981$	5.31263	0.169619
$982$	−18.8936	−0.602920
$983$	22.4403	0.715734	0.357867	−	0.933773i	$-0.383504\pi$
$983$	22.4403	0.715734	0.357867	+	0.933773i	$0.383504\pi$
$984$	−1.56354	−0.0498437
$985$	−20.8444	−0.664158
$986$	0.833635	0.0265483
$987$	−7.95289	−0.253143
$988$	−5.58343	−0.177633
$989$	−8.93810	−0.284215
$990$	−26.9264	−0.855776
$991$	17.9030	0.568708	0.284354	−	0.958719i	$-0.408221\pi$
$991$	17.9030	0.568708	0.284354	+	0.958719i	$0.408221\pi$
$992$	6.18047	0.196230
$993$	5.42215	0.172067
$994$	−30.2275	−0.958757
$995$	−36.7302	−1.16442
$996$	−2.67189	−0.0846622
$997$	−37.7752	−1.19635	−0.598177	−	0.801364i	$-0.704108\pi$
$997$	−37.7752	−1.19635	−0.598177	+	0.801364i	$0.704108\pi$
$998$	19.8282	0.627652
$999$	9.13696	0.289081

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.18	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.18	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.358038 q^{3} +1.00000 q^{4} +3.12453 q^{5} +0.358038 q^{6} -3.38298 q^{7} -1.00000 q^{8} -2.87181 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.358038 q^{3} +1.00000 q^{4} +3.12453 q^{5} +0.358038 q^{6} -3.38298 q^{7} -1.00000 q^{8} -2.87181 q^{9} -3.12453 q^{10} -3.00081 q^{11} -0.358038 q^{12} +5.58343 q^{13} +3.38298 q^{14} -1.11870 q^{15} +1.00000 q^{16} +0.615120 q^{17} +2.87181 q^{18} -1.00000 q^{19} +3.12453 q^{20} +1.21123 q^{21} +3.00081 q^{22} +7.17487 q^{23} +0.358038 q^{24} +4.76266 q^{25} -5.58343 q^{26} +2.10233 q^{27} -3.38298 q^{28} -1.35524 q^{29} +1.11870 q^{30} -6.18047 q^{31} -1.00000 q^{32} +1.07440 q^{33} -0.615120 q^{34} -10.5702 q^{35} -2.87181 q^{36} +4.34611 q^{37} +1.00000 q^{38} -1.99908 q^{39} -3.12453 q^{40} -4.36696 q^{41} -1.21123 q^{42} -1.24575 q^{43} -3.00081 q^{44} -8.97304 q^{45} -7.17487 q^{46} -6.56595 q^{47} -0.358038 q^{48} +4.44452 q^{49} -4.76266 q^{50} -0.220236 q^{51} +5.58343 q^{52} +2.38333 q^{53} -2.10233 q^{54} -9.37610 q^{55} +3.38298 q^{56} +0.358038 q^{57} +1.35524 q^{58} -0.0783359 q^{59} -1.11870 q^{60} -11.8770 q^{61} +6.18047 q^{62} +9.71526 q^{63} +1.00000 q^{64} +17.4456 q^{65} -1.07440 q^{66} +1.93235 q^{67} +0.615120 q^{68} -2.56887 q^{69} +10.5702 q^{70} -8.93518 q^{71} +2.87181 q^{72} +2.99156 q^{73} -4.34611 q^{74} -1.70521 q^{75} -1.00000 q^{76} +10.1517 q^{77} +1.99908 q^{78} +4.20610 q^{79} +3.12453 q^{80} +7.86271 q^{81} +4.36696 q^{82} +7.46260 q^{83} +1.21123 q^{84} +1.92196 q^{85} +1.24575 q^{86} +0.485227 q^{87} +3.00081 q^{88} +4.41557 q^{89} +8.97304 q^{90} -18.8886 q^{91} +7.17487 q^{92} +2.21284 q^{93} +6.56595 q^{94} -3.12453 q^{95} +0.358038 q^{96} +13.5539 q^{97} -4.44452 q^{98} +8.61775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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