LMFDB - Embedded newform 8038.2.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8038,2,Mod(1,8038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8038, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8038 = 2 \cdot 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8038.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:	$64.1837531447$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.90955 q^{3} +1.00000 q^{4} +4.18412 q^{5} -1.90955 q^{6} -2.40151 q^{7} +1.00000 q^{8} +0.646387 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.90955 q^{3} +1.00000 q^{4} +4.18412 q^{5} -1.90955 q^{6} -2.40151 q^{7} +1.00000 q^{8} +0.646387 q^{9} +4.18412 q^{10} +2.50162 q^{11} -1.90955 q^{12} +2.98262 q^{13} -2.40151 q^{14} -7.98979 q^{15} +1.00000 q^{16} +0.884354 q^{17} +0.646387 q^{18} +5.55658 q^{19} +4.18412 q^{20} +4.58582 q^{21} +2.50162 q^{22} +3.12740 q^{23} -1.90955 q^{24} +12.5068 q^{25} +2.98262 q^{26} +4.49434 q^{27} -2.40151 q^{28} -1.42879 q^{29} -7.98979 q^{30} +6.72338 q^{31} +1.00000 q^{32} -4.77697 q^{33} +0.884354 q^{34} -10.0482 q^{35} +0.646387 q^{36} -6.16651 q^{37} +5.55658 q^{38} -5.69547 q^{39} +4.18412 q^{40} -5.22484 q^{41} +4.58582 q^{42} +7.73403 q^{43} +2.50162 q^{44} +2.70456 q^{45} +3.12740 q^{46} +5.28424 q^{47} -1.90955 q^{48} -1.23273 q^{49} +12.5068 q^{50} -1.68872 q^{51} +2.98262 q^{52} -3.24857 q^{53} +4.49434 q^{54} +10.4671 q^{55} -2.40151 q^{56} -10.6106 q^{57} -1.42879 q^{58} -13.2348 q^{59} -7.98979 q^{60} -9.14313 q^{61} +6.72338 q^{62} -1.55231 q^{63} +1.00000 q^{64} +12.4796 q^{65} -4.77697 q^{66} -8.98251 q^{67} +0.884354 q^{68} -5.97193 q^{69} -10.0482 q^{70} +9.04629 q^{71} +0.646387 q^{72} -14.4933 q^{73} -6.16651 q^{74} -23.8824 q^{75} +5.55658 q^{76} -6.00768 q^{77} -5.69547 q^{78} -3.80569 q^{79} +4.18412 q^{80} -10.5213 q^{81} -5.22484 q^{82} +7.48160 q^{83} +4.58582 q^{84} +3.70024 q^{85} +7.73403 q^{86} +2.72835 q^{87} +2.50162 q^{88} +13.2480 q^{89} +2.70456 q^{90} -7.16281 q^{91} +3.12740 q^{92} -12.8386 q^{93} +5.28424 q^{94} +23.2494 q^{95} -1.90955 q^{96} -7.48325 q^{97} -1.23273 q^{98} +1.61702 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9}+O(q^{10}) $ 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9	\( 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9} + 28 q^{10} + 37 q^{11} + 31 q^{12} + 20 q^{13} + 29 q^{14} + 30 q^{15} + 92 q^{16} + 52 q^{17} + 113 q^{18} + 61 q^{19} + 28 q^{20} + 5 q^{21} + 37 q^{22} + 71 q^{23} + 31 q^{24} + 118 q^{25} + 20 q^{26} + 112 q^{27} + 29 q^{28} + 30 q^{29} + 30 q^{30} + 89 q^{31} + 92 q^{32} + 52 q^{33} + 52 q^{34} + 58 q^{35} + 113 q^{36} + 15 q^{37} + 61 q^{38} + 43 q^{39} + 28 q^{40} + 75 q^{41} + 5 q^{42} + 46 q^{43} + 37 q^{44} + 63 q^{45} + 71 q^{46} + 92 q^{47} + 31 q^{48} + 131 q^{49} + 118 q^{50} + 45 q^{51} + 20 q^{52} + 72 q^{53} + 112 q^{54} + 86 q^{55} + 29 q^{56} + 44 q^{57} + 30 q^{58} + 95 q^{59} + 30 q^{60} - 4 q^{61} + 89 q^{62} + 67 q^{63} + 92 q^{64} + 55 q^{65} + 52 q^{66} + 40 q^{67} + 52 q^{68} + 25 q^{69} + 58 q^{70} + 84 q^{71} + 113 q^{72} + 87 q^{73} + 15 q^{74} + 132 q^{75} + 61 q^{76} + 96 q^{77} + 43 q^{78} + 68 q^{79} + 28 q^{80} + 156 q^{81} + 75 q^{82} + 120 q^{83} + 5 q^{84} - 14 q^{85} + 46 q^{86} + 73 q^{87} + 37 q^{88} + 86 q^{89} + 63 q^{90} + 93 q^{91} + 71 q^{92} + 29 q^{93} + 92 q^{94} + 67 q^{95} + 31 q^{96} + 65 q^{97} + 131 q^{98} + 94 q^{99}+O(q^{100}) \) 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9 + 28 * q^10 + 37 * q^11 + 31 * q^12 + 20 * q^13 + 29 * q^14 + 30 * q^15 + 92 * q^16 + 52 * q^17 + 113 * q^18 + 61 * q^19 + 28 * q^20 + 5 * q^21 + 37 * q^22 + 71 * q^23 + 31 * q^24 + 118 * q^25 + 20 * q^26 + 112 * q^27 + 29 * q^28 + 30 * q^29 + 30 * q^30 + 89 * q^31 + 92 * q^32 + 52 * q^33 + 52 * q^34 + 58 * q^35 + 113 * q^36 + 15 * q^37 + 61 * q^38 + 43 * q^39 + 28 * q^40 + 75 * q^41 + 5 * q^42 + 46 * q^43 + 37 * q^44 + 63 * q^45 + 71 * q^46 + 92 * q^47 + 31 * q^48 + 131 * q^49 + 118 * q^50 + 45 * q^51 + 20 * q^52 + 72 * q^53 + 112 * q^54 + 86 * q^55 + 29 * q^56 + 44 * q^57 + 30 * q^58 + 95 * q^59 + 30 * q^60 - 4 * q^61 + 89 * q^62 + 67 * q^63 + 92 * q^64 + 55 * q^65 + 52 * q^66 + 40 * q^67 + 52 * q^68 + 25 * q^69 + 58 * q^70 + 84 * q^71 + 113 * q^72 + 87 * q^73 + 15 * q^74 + 132 * q^75 + 61 * q^76 + 96 * q^77 + 43 * q^78 + 68 * q^79 + 28 * q^80 + 156 * q^81 + 75 * q^82 + 120 * q^83 + 5 * q^84 - 14 * q^85 + 46 * q^86 + 73 * q^87 + 37 * q^88 + 86 * q^89 + 63 * q^90 + 93 * q^91 + 71 * q^92 + 29 * q^93 + 92 * q^94 + 67 * q^95 + 31 * q^96 + 65 * q^97 + 131 * q^98 + 94 * 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
$3$	−1.90955	−1.10248	−0.551240	−	0.834347i	$-0.685845\pi$
$3$	−1.90955	−1.10248	−0.551240	+	0.834347i	$0.685845\pi$
$4$	1.00000	0.500000
$5$	4.18412	1.87119	0.935597	−	0.353070i	$-0.114862\pi$
$5$	4.18412	1.87119	0.935597	+	0.353070i	$0.114862\pi$
$6$	−1.90955	−0.779571
$7$	−2.40151	−0.907687	−0.453844	−	0.891081i	$-0.649948\pi$
$7$	−2.40151	−0.907687	−0.453844	+	0.891081i	$0.649948\pi$
$8$	1.00000	0.353553
$9$	0.646387	0.215462
$10$	4.18412	1.32313
$11$	2.50162	0.754267	0.377133	−	0.926159i	$-0.376910\pi$
$11$	2.50162	0.754267	0.377133	+	0.926159i	$0.376910\pi$
$12$	−1.90955	−0.551240
$13$	2.98262	0.827231	0.413615	−	0.910452i	$-0.364266\pi$
$13$	2.98262	0.827231	0.413615	+	0.910452i	$0.364266\pi$
$14$	−2.40151	−0.641832
$15$	−7.98979	−2.06295
$16$	1.00000	0.250000
$17$	0.884354	0.214487	0.107244	−	0.994233i	$-0.465797\pi$
$17$	0.884354	0.214487	0.107244	+	0.994233i	$0.465797\pi$
$18$	0.646387	0.152355
$19$	5.55658	1.27477	0.637384	−	0.770546i	$-0.280017\pi$
$19$	5.55658	1.27477	0.637384	+	0.770546i	$0.280017\pi$
$20$	4.18412	0.935597
$21$	4.58582	1.00071
$22$	2.50162	0.533347
$23$	3.12740	0.652107	0.326054	−	0.945351i	$-0.394281\pi$
$23$	3.12740	0.652107	0.326054	+	0.945351i	$0.394281\pi$
$24$	−1.90955	−0.389786
$25$	12.5068	2.50137
$26$	2.98262	0.584940
$27$	4.49434	0.864937
$28$	−2.40151	−0.453844
$29$	−1.42879	−0.265319	−0.132660	−	0.991162i	$-0.542352\pi$
$29$	−1.42879	−0.265319	−0.132660	+	0.991162i	$0.542352\pi$
$30$	−7.98979	−1.45873
$31$	6.72338	1.20755	0.603777	−	0.797153i	$-0.293662\pi$
$31$	6.72338	1.20755	0.603777	+	0.797153i	$0.293662\pi$
$32$	1.00000	0.176777
$33$	−4.77697	−0.831564
$34$	0.884354	0.151665
$35$	−10.0482	−1.69846
$36$	0.646387	0.107731
$37$	−6.16651	−1.01377	−0.506884	−	0.862014i	$-0.669203\pi$
$37$	−6.16651	−1.01377	−0.506884	+	0.862014i	$0.669203\pi$
$38$	5.55658	0.901397
$39$	−5.69547	−0.912005
$40$	4.18412	0.661567
$41$	−5.22484	−0.815983	−0.407991	−	0.912986i	$-0.633771\pi$
$41$	−5.22484	−0.815983	−0.407991	+	0.912986i	$0.633771\pi$
$42$	4.58582	0.707607
$43$	7.73403	1.17943	0.589714	−	0.807612i	$-0.299240\pi$
$43$	7.73403	1.17943	0.589714	+	0.807612i	$0.299240\pi$
$44$	2.50162	0.377133
$45$	2.70456	0.403172
$46$	3.12740	0.461109
$47$	5.28424	0.770786	0.385393	−	0.922753i	$-0.374066\pi$
$47$	5.28424	0.770786	0.385393	+	0.922753i	$0.374066\pi$
$48$	−1.90955	−0.275620
$49$	−1.23273	−0.176104
$50$	12.5068	1.76873
$51$	−1.68872	−0.236468
$52$	2.98262	0.413615
$53$	−3.24857	−0.446226	−0.223113	−	0.974793i	$-0.571622\pi$
$53$	−3.24857	−0.446226	−0.223113	+	0.974793i	$0.571622\pi$
$54$	4.49434	0.611603
$55$	10.4671	1.41138
$56$	−2.40151	−0.320916
$57$	−10.6106	−1.40541
$58$	−1.42879	−0.187609
$59$	−13.2348	−1.72303	−0.861515	−	0.507732i	$-0.830484\pi$
$59$	−13.2348	−1.72303	−0.861515	+	0.507732i	$0.830484\pi$
$60$	−7.98979	−1.03148
$61$	−9.14313	−1.17066	−0.585329	−	0.810796i	$-0.699035\pi$
$61$	−9.14313	−1.17066	−0.585329	+	0.810796i	$0.699035\pi$
$62$	6.72338	0.853870
$63$	−1.55231	−0.195573
$64$	1.00000	0.125000
$65$	12.4796	1.54791
$66$	−4.77697	−0.588005
$67$	−8.98251	−1.09739	−0.548694	−	0.836023i	$-0.684875\pi$
$67$	−8.98251	−1.09739	−0.548694	+	0.836023i	$0.684875\pi$
$68$	0.884354	0.107244
$69$	−5.97193	−0.718935
$70$	−10.0482	−1.20099
$71$	9.04629	1.07360	0.536798	−	0.843711i	$-0.319634\pi$
$71$	9.04629	1.07360	0.536798	+	0.843711i	$0.319634\pi$
$72$	0.646387	0.0761775
$73$	−14.4933	−1.69631	−0.848155	−	0.529749i	$-0.822286\pi$
$73$	−14.4933	−1.69631	−0.848155	+	0.529749i	$0.822286\pi$
$74$	−6.16651	−0.716842
$75$	−23.8824	−2.75771
$76$	5.55658	0.637384
$77$	−6.00768	−0.684638
$78$	−5.69547	−0.644885
$79$	−3.80569	−0.428174	−0.214087	−	0.976815i	$-0.568678\pi$
$79$	−3.80569	−0.428174	−0.214087	+	0.976815i	$0.568678\pi$
$80$	4.18412	0.467798
$81$	−10.5213	−1.16904
$82$	−5.22484	−0.576987
$83$	7.48160	0.821212	0.410606	−	0.911813i	$-0.365317\pi$
$83$	7.48160	0.821212	0.410606	+	0.911813i	$0.365317\pi$
$84$	4.58582	0.500354
$85$	3.70024	0.401347
$86$	7.73403	0.833982
$87$	2.72835	0.292509
$88$	2.50162	0.266674
$89$	13.2480	1.40428	0.702140	−	0.712039i	$-0.252228\pi$
$89$	13.2480	1.40428	0.702140	+	0.712039i	$0.252228\pi$
$90$	2.70456	0.285086
$91$	−7.16281	−0.750867
$92$	3.12740	0.326054
$93$	−12.8386	−1.33130
$94$	5.28424	0.545028
$95$	23.2494	2.38534
$96$	−1.90955	−0.194893
$97$	−7.48325	−0.759809	−0.379905	−	0.925026i	$-0.624043\pi$
$97$	−7.48325	−0.759809	−0.379905	+	0.925026i	$0.624043\pi$
$98$	−1.23273	−0.124524
$99$	1.61702	0.162516
$100$	12.5068	1.25068
$101$	4.16336	0.414269	0.207135	−	0.978312i	$-0.433586\pi$
$101$	4.16336	0.414269	0.207135	+	0.978312i	$0.433586\pi$
$102$	−1.68872	−0.167208
$103$	14.5813	1.43674	0.718370	−	0.695661i	$-0.244889\pi$
$103$	14.5813	1.43674	0.718370	+	0.695661i	$0.244889\pi$
$104$	2.98262	0.292470
$105$	19.1876	1.87252
$106$	−3.24857	−0.315529
$107$	1.98503	0.191900	0.0959500	−	0.995386i	$-0.469411\pi$
$107$	1.98503	0.191900	0.0959500	+	0.995386i	$0.469411\pi$
$108$	4.49434	0.432469
$109$	18.4145	1.76379	0.881895	−	0.471446i	$-0.156268\pi$
$109$	18.4145	1.76379	0.881895	+	0.471446i	$0.156268\pi$
$110$	10.4671	0.997996
$111$	11.7753	1.11766
$112$	−2.40151	−0.226922
$113$	−8.00788	−0.753318	−0.376659	−	0.926352i	$-0.622927\pi$
$113$	−8.00788	−0.753318	−0.376659	+	0.926352i	$0.622927\pi$
$114$	−10.6106	−0.993772
$115$	13.0854	1.22022
$116$	−1.42879	−0.132660
$117$	1.92793	0.178237
$118$	−13.2348	−1.21837
$119$	−2.12379	−0.194687
$120$	−7.98979	−0.729364
$121$	−4.74190	−0.431082
$122$	−9.14313	−0.827780
$123$	9.97710	0.899605
$124$	6.72338	0.603777
$125$	31.4095	2.80935
$126$	−1.55231	−0.138291
$127$	21.0081	1.86417	0.932083	−	0.362244i	$-0.117989\pi$
$127$	21.0081	1.86417	0.932083	+	0.362244i	$0.117989\pi$
$128$	1.00000	0.0883883
$129$	−14.7685	−1.30030
$130$	12.4796	1.09454
$131$	−16.2076	−1.41606	−0.708031	−	0.706181i	$-0.750417\pi$
$131$	−16.2076	−1.41606	−0.708031	+	0.706181i	$0.750417\pi$
$132$	−4.77697	−0.415782
$133$	−13.3442	−1.15709
$134$	−8.98251	−0.775971
$135$	18.8049	1.61846
$136$	0.884354	0.0758327
$137$	−18.6512	−1.59348	−0.796741	−	0.604320i	$-0.793445\pi$
$137$	−18.6512	−1.59348	−0.796741	+	0.604320i	$0.793445\pi$
$138$	−5.97193	−0.508364
$139$	0.421150	0.0357215	0.0178608	−	0.999840i	$-0.494314\pi$
$139$	0.421150	0.0357215	0.0178608	+	0.999840i	$0.494314\pi$
$140$	−10.0482	−0.849229
$141$	−10.0905	−0.849776
$142$	9.04629	0.759148
$143$	7.46139	0.623953
$144$	0.646387	0.0538656
$145$	−5.97822	−0.496464
$146$	−14.4933	−1.19947
$147$	2.35396	0.194151
$148$	−6.16651	−0.506884
$149$	16.6023	1.36011	0.680056	−	0.733161i	$-0.261956\pi$
$149$	16.6023	1.36011	0.680056	+	0.733161i	$0.261956\pi$
$150$	−23.8824	−1.94999
$151$	10.1237	0.823856	0.411928	−	0.911216i	$-0.364856\pi$
$151$	10.1237	0.823856	0.411928	+	0.911216i	$0.364856\pi$
$152$	5.55658	0.450699
$153$	0.571635	0.0462140
$154$	−6.00768	−0.484112
$155$	28.1314	2.25957
$156$	−5.69547	−0.456003
$157$	14.2665	1.13859	0.569295	−	0.822133i	$-0.307216\pi$
$157$	14.2665	1.13859	0.569295	+	0.822133i	$0.307216\pi$
$158$	−3.80569	−0.302764
$159$	6.20331	0.491955
$160$	4.18412	0.330783
$161$	−7.51049	−0.591909
$162$	−10.5213	−0.826635
$163$	−21.7211	−1.70133	−0.850664	−	0.525710i	$-0.823800\pi$
$163$	−21.7211	−1.70133	−0.850664	+	0.525710i	$0.823800\pi$
$164$	−5.22484	−0.407991
$165$	−19.9874	−1.55602
$166$	7.48160	0.580685
$167$	14.1052	1.09149	0.545745	−	0.837951i	$-0.316247\pi$
$167$	14.1052	1.09149	0.545745	+	0.837951i	$0.316247\pi$
$168$	4.58582	0.353803
$169$	−4.10396	−0.315689
$170$	3.70024	0.283796
$171$	3.59171	0.274665
$172$	7.73403	0.589714
$173$	4.32404	0.328750	0.164375	−	0.986398i	$-0.447439\pi$
$173$	4.32404	0.328750	0.164375	+	0.986398i	$0.447439\pi$
$174$	2.72835	0.206835
$175$	−30.0353	−2.27046
$176$	2.50162	0.188567
$177$	25.2726	1.89961
$178$	13.2480	0.992976
$179$	−8.28301	−0.619101	−0.309550	−	0.950883i	$-0.600179\pi$
$179$	−8.28301	−0.619101	−0.309550	+	0.950883i	$0.600179\pi$
$180$	2.70456	0.201586
$181$	−12.7503	−0.947720	−0.473860	−	0.880600i	$-0.657140\pi$
$181$	−12.7503	−0.947720	−0.473860	+	0.880600i	$0.657140\pi$
$182$	−7.16281	−0.530943
$183$	17.4593	1.29063
$184$	3.12740	0.230555
$185$	−25.8014	−1.89696
$186$	−12.8386	−0.941375
$187$	2.21232	0.161781
$188$	5.28424	0.385393
$189$	−10.7932	−0.785092
$190$	23.2494	1.68669
$191$	0.730899	0.0528860	0.0264430	−	0.999650i	$-0.491582\pi$
$191$	0.730899	0.0528860	0.0264430	+	0.999650i	$0.491582\pi$
$192$	−1.90955	−0.137810
$193$	15.1344	1.08940	0.544699	−	0.838631i	$-0.316644\pi$
$193$	15.1344	1.08940	0.544699	+	0.838631i	$0.316644\pi$
$194$	−7.48325	−0.537266
$195$	−23.8305	−1.70654
$196$	−1.23273	−0.0880519
$197$	−6.73556	−0.479889	−0.239945	−	0.970787i	$-0.577129\pi$
$197$	−6.73556	−0.479889	−0.239945	+	0.970787i	$0.577129\pi$
$198$	1.61702	0.114916
$199$	1.28291	0.0909431	0.0454715	−	0.998966i	$-0.485521\pi$
$199$	1.28291	0.0909431	0.0454715	+	0.998966i	$0.485521\pi$
$200$	12.5068	0.884367
$201$	17.1526	1.20985
$202$	4.16336	0.292933
$203$	3.43126	0.240827
$204$	−1.68872	−0.118234
$205$	−21.8613	−1.52686
$206$	14.5813	1.01593
$207$	2.02151	0.140505
$208$	2.98262	0.206808
$209$	13.9005	0.961515
$210$	19.1876	1.32407
$211$	−13.3854	−0.921492	−0.460746	−	0.887532i	$-0.652418\pi$
$211$	−13.3854	−0.921492	−0.460746	+	0.887532i	$0.652418\pi$
$212$	−3.24857	−0.223113
$213$	−17.2744	−1.18362
$214$	1.98503	0.135694
$215$	32.3601	2.20694
$216$	4.49434	0.305801
$217$	−16.1463	−1.09608
$218$	18.4145	1.24719
$219$	27.6756	1.87015
$220$	10.4671	0.705690
$221$	2.63769	0.177431
$222$	11.7753	0.790304
$223$	−9.18533	−0.615095	−0.307548	−	0.951533i	$-0.599508\pi$
$223$	−9.18533	−0.615095	−0.307548	+	0.951533i	$0.599508\pi$
$224$	−2.40151	−0.160458
$225$	8.08426	0.538950
$226$	−8.00788	−0.532676
$227$	5.80689	0.385417	0.192708	−	0.981256i	$-0.438273\pi$
$227$	5.80689	0.385417	0.192708	+	0.981256i	$0.438273\pi$
$228$	−10.6106	−0.702703
$229$	−7.50662	−0.496051	−0.248026	−	0.968753i	$-0.579782\pi$
$229$	−7.50662	−0.496051	−0.248026	+	0.968753i	$0.579782\pi$
$230$	13.0854	0.862825
$231$	11.4720	0.754800
$232$	−1.42879	−0.0938046
$233$	23.2747	1.52478	0.762389	−	0.647119i	$-0.224026\pi$
$233$	23.2747	1.52478	0.762389	+	0.647119i	$0.224026\pi$
$234$	1.92793	0.126033
$235$	22.1099	1.44229
$236$	−13.2348	−0.861515
$237$	7.26716	0.472053
$238$	−2.12379	−0.137665
$239$	11.8307	0.765267	0.382634	−	0.923900i	$-0.375017\pi$
$239$	11.8307	0.765267	0.382634	+	0.923900i	$0.375017\pi$
$240$	−7.98979	−0.515739
$241$	22.3529	1.43988	0.719938	−	0.694038i	$-0.244170\pi$
$241$	22.3529	1.43988	0.719938	+	0.694038i	$0.244170\pi$
$242$	−4.74190	−0.304821
$243$	6.60802	0.423905
$244$	−9.14313	−0.585329
$245$	−5.15787	−0.329524
$246$	9.97710	0.636117
$247$	16.5732	1.05453
$248$	6.72338	0.426935
$249$	−14.2865	−0.905370
$250$	31.4095	1.98651
$251$	−3.05605	−0.192896	−0.0964481	−	0.995338i	$-0.530748\pi$
$251$	−3.05605	−0.192896	−0.0964481	+	0.995338i	$0.530748\pi$
$252$	−1.55231	−0.0977863
$253$	7.82356	0.491863
$254$	21.0081	1.31817
$255$	−7.06580	−0.442478
$256$	1.00000	0.0625000
$257$	8.09995	0.505261	0.252631	−	0.967563i	$-0.418704\pi$
$257$	8.09995	0.505261	0.252631	+	0.967563i	$0.418704\pi$
$258$	−14.7685	−0.919448
$259$	14.8090	0.920184
$260$	12.4796	0.773954
$261$	−0.923551	−0.0571664
$262$	−16.2076	−1.00131
$263$	25.0648	1.54556	0.772780	−	0.634674i	$-0.218865\pi$
$263$	25.0648	1.54556	0.772780	+	0.634674i	$0.218865\pi$
$264$	−4.77697	−0.294002
$265$	−13.5924	−0.834974
$266$	−13.3442	−0.818187
$267$	−25.2977	−1.54819
$268$	−8.98251	−0.548694
$269$	26.5281	1.61745	0.808724	−	0.588189i	$-0.200159\pi$
$269$	26.5281	1.61745	0.808724	+	0.588189i	$0.200159\pi$
$270$	18.8049	1.14443
$271$	−13.4892	−0.819412	−0.409706	−	0.912218i	$-0.634369\pi$
$271$	−13.4892	−0.819412	−0.409706	+	0.912218i	$0.634369\pi$
$272$	0.884354	0.0536218
$273$	13.6778	0.827816
$274$	−18.6512	−1.12676
$275$	31.2873	1.88670
$276$	−5.97193	−0.359468
$277$	28.2163	1.69535	0.847676	−	0.530514i	$-0.178001\pi$
$277$	28.2163	1.69535	0.847676	+	0.530514i	$0.178001\pi$
$278$	0.421150	0.0252589
$279$	4.34591	0.260183
$280$	−10.0482	−0.600496
$281$	−27.3556	−1.63190	−0.815948	−	0.578126i	$-0.803784\pi$
$281$	−27.3556	−1.63190	−0.815948	+	0.578126i	$0.803784\pi$
$282$	−10.0905	−0.600882
$283$	1.02284	0.0608014	0.0304007	−	0.999538i	$-0.490322\pi$
$283$	1.02284	0.0608014	0.0304007	+	0.999538i	$0.490322\pi$
$284$	9.04629	0.536798
$285$	−44.3959	−2.62979
$286$	7.46139	0.441201
$287$	12.5475	0.740657
$288$	0.646387	0.0380887
$289$	−16.2179	−0.953995
$290$	−5.97822	−0.351053
$291$	14.2897	0.837675
$292$	−14.4933	−0.848155
$293$	−32.7414	−1.91277	−0.956387	−	0.292103i	$-0.905645\pi$
$293$	−32.7414	−1.91277	−0.956387	+	0.292103i	$0.905645\pi$
$294$	2.35396	0.137285
$295$	−55.3761	−3.22412
$296$	−6.16651	−0.358421
$297$	11.2431	0.652393
$298$	16.6023	0.961744
$299$	9.32784	0.539443
$300$	−23.8824	−1.37885
$301$	−18.5734	−1.07055
$302$	10.1237	0.582554
$303$	−7.95014	−0.456724
$304$	5.55658	0.318692
$305$	−38.2559	−2.19053
$306$	0.571635	0.0326782
$307$	−4.10900	−0.234513	−0.117257	−	0.993102i	$-0.537410\pi$
$307$	−4.10900	−0.234513	−0.117257	+	0.993102i	$0.537410\pi$
$308$	−6.00768	−0.342319
$309$	−27.8438	−1.58398
$310$	28.1314	1.59776
$311$	−5.64110	−0.319878	−0.159939	−	0.987127i	$-0.551130\pi$
$311$	−5.64110	−0.319878	−0.159939	+	0.987127i	$0.551130\pi$
$312$	−5.69547	−0.322443
$313$	−27.9117	−1.57766	−0.788832	−	0.614609i	$-0.789314\pi$
$313$	−27.9117	−1.57766	−0.788832	+	0.614609i	$0.789314\pi$
$314$	14.2665	0.805105
$315$	−6.49504	−0.365954
$316$	−3.80569	−0.214087
$317$	20.3317	1.14194	0.570972	−	0.820969i	$-0.306566\pi$
$317$	20.3317	1.14194	0.570972	+	0.820969i	$0.306566\pi$
$318$	6.20331	0.347865
$319$	−3.57429	−0.200122
$320$	4.18412	0.233899
$321$	−3.79052	−0.211566
$322$	−7.51049	−0.418543
$323$	4.91399	0.273422
$324$	−10.5213	−0.584519
$325$	37.3032	2.06921
$326$	−21.7211	−1.20302
$327$	−35.1635	−1.94454
$328$	−5.22484	−0.288494
$329$	−12.6902	−0.699633
$330$	−19.9874	−1.10027
$331$	−12.1064	−0.665427	−0.332714	−	0.943028i	$-0.607964\pi$
$331$	−12.1064	−0.665427	−0.332714	+	0.943028i	$0.607964\pi$
$332$	7.48160	0.410606
$333$	−3.98595	−0.218429
$334$	14.1052	0.771800
$335$	−37.5839	−2.05343
$336$	4.58582	0.250177
$337$	0.101822	0.00554661	0.00277330	−	0.999996i	$-0.499117\pi$
$337$	0.101822	0.00554661	0.00277330	+	0.999996i	$0.499117\pi$
$338$	−4.10396	−0.223226
$339$	15.2915	0.830518
$340$	3.70024	0.200674
$341$	16.8193	0.910818
$342$	3.59171	0.194217
$343$	19.7710	1.06753
$344$	7.73403	0.416991
$345$	−24.9872	−1.34527
$346$	4.32404	0.232462
$347$	16.6688	0.894830	0.447415	−	0.894326i	$-0.352345\pi$
$347$	16.6688	0.894830	0.447415	+	0.894326i	$0.352345\pi$
$348$	2.72835	0.146255
$349$	20.0174	1.07151	0.535753	−	0.844375i	$-0.320028\pi$
$349$	20.0174	1.07151	0.535753	+	0.844375i	$0.320028\pi$
$350$	−30.0353	−1.60546
$351$	13.4049	0.715502
$352$	2.50162	0.133337
$353$	−25.9079	−1.37894	−0.689468	−	0.724316i	$-0.742156\pi$
$353$	−25.9079	−1.37894	−0.689468	+	0.724316i	$0.742156\pi$
$354$	25.2726	1.34322
$355$	37.8507	2.00891
$356$	13.2480	0.702140
$357$	4.05549	0.214639
$358$	−8.28301	−0.437770
$359$	−20.9581	−1.10613	−0.553064	−	0.833139i	$-0.686542\pi$
$359$	−20.9581	−1.10613	−0.553064	+	0.833139i	$0.686542\pi$
$360$	2.70456	0.142543
$361$	11.8756	0.625033
$362$	−12.7503	−0.670139
$363$	9.05490	0.475259
$364$	−7.16281	−0.375433
$365$	−60.6415	−3.17412
$366$	17.4593	0.912611
$367$	−2.85611	−0.149088	−0.0745440	−	0.997218i	$-0.523750\pi$
$367$	−2.85611	−0.149088	−0.0745440	+	0.997218i	$0.523750\pi$
$368$	3.12740	0.163027
$369$	−3.37727	−0.175814
$370$	−25.8014	−1.34135
$371$	7.80149	0.405033
$372$	−12.8386	−0.665652
$373$	−3.66631	−0.189834	−0.0949171	−	0.995485i	$-0.530259\pi$
$373$	−3.66631	−0.189834	−0.0949171	+	0.995485i	$0.530259\pi$
$374$	2.21232	0.114396
$375$	−59.9780	−3.09725
$376$	5.28424	0.272514
$377$	−4.26154	−0.219480
$378$	−10.7932	−0.555144
$379$	10.9098	0.560397	0.280199	−	0.959942i	$-0.409600\pi$
$379$	10.9098	0.560397	0.280199	+	0.959942i	$0.409600\pi$
$380$	23.2494	1.19267
$381$	−40.1160	−2.05521
$382$	0.730899	0.0373961
$383$	13.0910	0.668917	0.334459	−	0.942410i	$-0.391447\pi$
$383$	13.0910	0.668917	0.334459	+	0.942410i	$0.391447\pi$
$384$	−1.90955	−0.0974464
$385$	−25.1368	−1.28109
$386$	15.1344	0.770321
$387$	4.99918	0.254122
$388$	−7.48325	−0.379905
$389$	1.00019	0.0507115	0.0253557	−	0.999678i	$-0.491928\pi$
$389$	1.00019	0.0507115	0.0253557	+	0.999678i	$0.491928\pi$
$390$	−23.8305	−1.20671
$391$	2.76573	0.139869
$392$	−1.23273	−0.0622621
$393$	30.9492	1.56118
$394$	−6.73556	−0.339333
$395$	−15.9235	−0.801196
$396$	1.61702	0.0812581
$397$	39.4229	1.97858	0.989289	−	0.145973i	$-0.0466311\pi$
$397$	39.4229	1.97858	0.989289	+	0.145973i	$0.0466311\pi$
$398$	1.28291	0.0643065
$399$	25.4815	1.27567
$400$	12.5068	0.625342
$401$	−15.8812	−0.793070	−0.396535	−	0.918020i	$-0.629787\pi$
$401$	−15.8812	−0.793070	−0.396535	+	0.918020i	$0.629787\pi$
$402$	17.1526	0.855492
$403$	20.0533	0.998926
$404$	4.16336	0.207135
$405$	−44.0225	−2.18750
$406$	3.43126	0.170290
$407$	−15.4263	−0.764651
$408$	−1.68872	−0.0836041
$409$	−12.3229	−0.609329	−0.304665	−	0.952460i	$-0.598544\pi$
$409$	−12.3229	−0.609329	−0.304665	+	0.952460i	$0.598544\pi$
$410$	−21.8613	−1.07965
$411$	35.6155	1.75678
$412$	14.5813	0.718370
$413$	31.7837	1.56397
$414$	2.02151	0.0993518
$415$	31.3039	1.53665
$416$	2.98262	0.146235
$417$	−0.804208	−0.0393822
$418$	13.9005	0.679894
$419$	17.1732	0.838968	0.419484	−	0.907763i	$-0.362211\pi$
$419$	17.1732	0.838968	0.419484	+	0.907763i	$0.362211\pi$
$420$	19.1876	0.936259
$421$	8.33481	0.406214	0.203107	−	0.979157i	$-0.434896\pi$
$421$	8.33481	0.406214	0.203107	+	0.979157i	$0.434896\pi$
$422$	−13.3854	−0.651593
$423$	3.41567	0.166075
$424$	−3.24857	−0.157765
$425$	11.0605	0.536512
$426$	−17.2744	−0.836945
$427$	21.9574	1.06259
$428$	1.98503	0.0959500
$429$	−14.2479	−0.687895
$430$	32.3601	1.56054
$431$	29.1557	1.40438	0.702189	−	0.711990i	$-0.252206\pi$
$431$	29.1557	1.40438	0.702189	+	0.711990i	$0.252206\pi$
$432$	4.49434	0.216234
$433$	−23.0701	−1.10868	−0.554338	−	0.832291i	$-0.687029\pi$
$433$	−23.0701	−1.10868	−0.554338	+	0.832291i	$0.687029\pi$
$434$	−16.1463	−0.775047
$435$	11.4157	0.547342
$436$	18.4145	0.881895
$437$	17.3776	0.831285
$438$	27.6756	1.32239
$439$	−3.62553	−0.173037	−0.0865184	−	0.996250i	$-0.527574\pi$
$439$	−3.62553	−0.173037	−0.0865184	+	0.996250i	$0.527574\pi$
$440$	10.4671	0.498998
$441$	−0.796819	−0.0379438
$442$	2.63769	0.125462
$443$	−20.4972	−0.973853	−0.486927	−	0.873443i	$-0.661882\pi$
$443$	−20.4972	−0.973853	−0.486927	+	0.873443i	$0.661882\pi$
$444$	11.7753	0.558829
$445$	55.4310	2.62768
$446$	−9.18533	−0.434938
$447$	−31.7029	−1.49950
$448$	−2.40151	−0.113461
$449$	7.29843	0.344434	0.172217	−	0.985059i	$-0.444907\pi$
$449$	7.29843	0.344434	0.172217	+	0.985059i	$0.444907\pi$
$450$	8.08426	0.381096
$451$	−13.0706	−0.615469
$452$	−8.00788	−0.376659
$453$	−19.3317	−0.908284
$454$	5.80689	0.272531
$455$	−29.9700	−1.40502
$456$	−10.6106	−0.496886
$457$	26.6076	1.24465	0.622324	−	0.782759i	$-0.286188\pi$
$457$	26.6076	1.24465	0.622324	+	0.782759i	$0.286188\pi$
$458$	−7.50662	−0.350761
$459$	3.97459	0.185518
$460$	13.0854	0.610110
$461$	−35.2133	−1.64005	−0.820023	−	0.572331i	$-0.806039\pi$
$461$	−35.2133	−1.64005	−0.820023	+	0.572331i	$0.806039\pi$
$462$	11.4720	0.533724
$463$	−6.97059	−0.323951	−0.161975	−	0.986795i	$-0.551786\pi$
$463$	−6.97059	−0.323951	−0.161975	+	0.986795i	$0.551786\pi$
$464$	−1.42879	−0.0663298
$465$	−53.7184	−2.49113
$466$	23.2747	1.07818
$467$	3.27635	0.151611	0.0758057	−	0.997123i	$-0.475847\pi$
$467$	3.27635	0.151611	0.0758057	+	0.997123i	$0.475847\pi$
$468$	1.92793	0.0891186
$469$	21.5716	0.996085
$470$	22.1099	1.01985
$471$	−27.2426	−1.25527
$472$	−13.2348	−0.609183
$473$	19.3476	0.889603
$474$	7.26716	0.333792
$475$	69.4953	3.18866
$476$	−2.12379	−0.0973437
$477$	−2.09983	−0.0961448
$478$	11.8307	0.541126
$479$	1.64953	0.0753691	0.0376846	−	0.999290i	$-0.488002\pi$
$479$	1.64953	0.0753691	0.0376846	+	0.999290i	$0.488002\pi$
$480$	−7.98979	−0.364682
$481$	−18.3924	−0.838620
$482$	22.3529	1.01815
$483$	14.3417	0.652568
$484$	−4.74190	−0.215541
$485$	−31.3108	−1.42175
$486$	6.60802	0.299746
$487$	−10.1379	−0.459391	−0.229695	−	0.973263i	$-0.573773\pi$
$487$	−10.1379	−0.459391	−0.229695	+	0.973263i	$0.573773\pi$
$488$	−9.14313	−0.413890
$489$	41.4776	1.87568
$490$	−5.15787	−0.233009
$491$	8.32053	0.375500	0.187750	−	0.982217i	$-0.439881\pi$
$491$	8.32053	0.375500	0.187750	+	0.982217i	$0.439881\pi$
$492$	9.97710	0.449802
$493$	−1.26356	−0.0569077
$494$	16.5732	0.745663
$495$	6.76578	0.304099
$496$	6.72338	0.301889
$497$	−21.7248	−0.974490
$498$	−14.2865	−0.640193
$499$	35.7962	1.60246	0.801230	−	0.598357i	$-0.204179\pi$
$499$	35.7962	1.60246	0.801230	+	0.598357i	$0.204179\pi$
$500$	31.4095	1.40467
$501$	−26.9345	−1.20335
$502$	−3.05605	−0.136398
$503$	18.6502	0.831573	0.415787	−	0.909462i	$-0.363506\pi$
$503$	18.6502	0.831573	0.415787	+	0.909462i	$0.363506\pi$
$504$	−1.55231	−0.0691453
$505$	17.4200	0.775178
$506$	7.82356	0.347800
$507$	7.83673	0.348041
$508$	21.0081	0.932083
$509$	−18.2547	−0.809125	−0.404562	−	0.914510i	$-0.632576\pi$
$509$	−18.2547	−0.809125	−0.404562	+	0.914510i	$0.632576\pi$
$510$	−7.06580	−0.312879
$511$	34.8058	1.53972
$512$	1.00000	0.0441942
$513$	24.9732	1.10259
$514$	8.09995	0.357273
$515$	61.0099	2.68842
$516$	−14.7685	−0.650148
$517$	13.2192	0.581378
$518$	14.8090	0.650668
$519$	−8.25697	−0.362441
$520$	12.4796	0.547268
$521$	−16.5138	−0.723483	−0.361742	−	0.932278i	$-0.617818\pi$
$521$	−16.5138	−0.723483	−0.361742	+	0.932278i	$0.617818\pi$
$522$	−0.923551	−0.0404227
$523$	−32.0532	−1.40159	−0.700795	−	0.713363i	$-0.747171\pi$
$523$	−32.0532	−1.40159	−0.700795	+	0.713363i	$0.747171\pi$
$524$	−16.2076	−0.708031
$525$	57.3540	2.50314
$526$	25.0648	1.09288
$527$	5.94585	0.259005
$528$	−4.77697	−0.207891
$529$	−13.2194	−0.574756
$530$	−13.5924	−0.590416
$531$	−8.55483	−0.371248
$532$	−13.3442	−0.578545
$533$	−15.5837	−0.675006
$534$	−25.2977	−1.09474
$535$	8.30560	0.359082
$536$	−8.98251	−0.387985
$537$	15.8168	0.682546
$538$	26.5281	1.14371
$539$	−3.08381	−0.132829
$540$	18.8049	0.809232
$541$	−3.60227	−0.154874	−0.0774369	−	0.996997i	$-0.524674\pi$
$541$	−3.60227	−0.154874	−0.0774369	+	0.996997i	$0.524674\pi$
$542$	−13.4892	−0.579412
$543$	24.3473	1.04484
$544$	0.884354	0.0379164
$545$	77.0485	3.30039
$546$	13.6778	0.585354
$547$	7.42184	0.317335	0.158668	−	0.987332i	$-0.449280\pi$
$547$	7.42184	0.317335	0.158668	+	0.987332i	$0.449280\pi$
$548$	−18.6512	−0.796741
$549$	−5.91000	−0.252233
$550$	31.2873	1.33410
$551$	−7.93918	−0.338221
$552$	−5.97193	−0.254182
$553$	9.13942	0.388648
$554$	28.2163	1.19880
$555$	49.2691	2.09136
$556$	0.421150	0.0178608
$557$	−20.8675	−0.884183	−0.442091	−	0.896970i	$-0.645763\pi$
$557$	−20.8675	−0.884183	−0.442091	+	0.896970i	$0.645763\pi$
$558$	4.34591	0.183977
$559$	23.0677	0.975659
$560$	−10.0482	−0.424615
$561$	−4.22454	−0.178360
$562$	−27.3556	−1.15392
$563$	−42.3953	−1.78675	−0.893374	−	0.449314i	$-0.851668\pi$
$563$	−42.3953	−1.78675	−0.893374	+	0.449314i	$0.851668\pi$
$564$	−10.0905	−0.424888
$565$	−33.5059	−1.40960
$566$	1.02284	0.0429931
$567$	25.2672	1.06112
$568$	9.04629	0.379574
$569$	−23.0187	−0.964996	−0.482498	−	0.875897i	$-0.660270\pi$
$569$	−23.0187	−0.964996	−0.482498	+	0.875897i	$0.660270\pi$
$570$	−44.3959	−1.85954
$571$	5.71208	0.239043	0.119521	−	0.992832i	$-0.461864\pi$
$571$	5.71208	0.239043	0.119521	+	0.992832i	$0.461864\pi$
$572$	7.46139	0.311976
$573$	−1.39569	−0.0583058
$574$	12.5475	0.523724
$575$	39.1138	1.63116
$576$	0.646387	0.0269328
$577$	35.5093	1.47827	0.739135	−	0.673557i	$-0.235234\pi$
$577$	35.5093	1.47827	0.739135	+	0.673557i	$0.235234\pi$
$578$	−16.2179	−0.674576
$579$	−28.8999	−1.20104
$580$	−5.97822	−0.248232
$581$	−17.9672	−0.745404
$582$	14.2897	0.592325
$583$	−8.12669	−0.336573
$584$	−14.4933	−0.599736
$585$	8.06668	0.333516
$586$	−32.7414	−1.35254
$587$	−9.52455	−0.393120	−0.196560	−	0.980492i	$-0.562977\pi$
$587$	−9.52455	−0.393120	−0.196560	+	0.980492i	$0.562977\pi$
$588$	2.35396	0.0970755
$589$	37.3590	1.53935
$590$	−55.3761	−2.27980
$591$	12.8619	0.529068
$592$	−6.16651	−0.253442
$593$	−11.2719	−0.462882	−0.231441	−	0.972849i	$-0.574344\pi$
$593$	−11.2719	−0.462882	−0.231441	+	0.972849i	$0.574344\pi$
$594$	11.2431	0.461312
$595$	−8.88618	−0.364298
$596$	16.6023	0.680056
$597$	−2.44978	−0.100263
$598$	9.32784	0.381444
$599$	8.72255	0.356394	0.178197	−	0.983995i	$-0.442974\pi$
$599$	8.72255	0.356394	0.178197	+	0.983995i	$0.442974\pi$
$600$	−23.8824	−0.974997
$601$	37.6707	1.53662	0.768310	−	0.640078i	$-0.221098\pi$
$601$	37.6707	1.53662	0.768310	+	0.640078i	$0.221098\pi$
$602$	−18.5734	−0.756994
$603$	−5.80618	−0.236446
$604$	10.1237	0.411928
$605$	−19.8407	−0.806637
$606$	−7.95014	−0.322953
$607$	−40.9992	−1.66411	−0.832053	−	0.554697i	$-0.812834\pi$
$607$	−40.9992	−1.66411	−0.832053	+	0.554697i	$0.812834\pi$
$608$	5.55658	0.225349
$609$	−6.55216	−0.265507
$610$	−38.2559	−1.54894
$611$	15.7609	0.637618
$612$	0.571635	0.0231070
$613$	−15.2670	−0.616627	−0.308314	−	0.951285i	$-0.599765\pi$
$613$	−15.2670	−0.616627	−0.308314	+	0.951285i	$0.599765\pi$
$614$	−4.10900	−0.165826
$615$	41.7454	1.68334
$616$	−6.00768	−0.242056
$617$	6.15300	0.247710	0.123855	−	0.992300i	$-0.460474\pi$
$617$	6.15300	0.247710	0.123855	+	0.992300i	$0.460474\pi$
$618$	−27.8438	−1.12004
$619$	15.3158	0.615595	0.307798	−	0.951452i	$-0.400408\pi$
$619$	15.3158	0.615595	0.307798	+	0.951452i	$0.400408\pi$
$620$	28.1314	1.12978
$621$	14.0556	0.564032
$622$	−5.64110	−0.226188
$623$	−31.8152	−1.27465
$624$	−5.69547	−0.228001
$625$	68.8867	2.75547
$626$	−27.9117	−1.11558
$627$	−26.5437	−1.06005
$628$	14.2665	0.569295
$629$	−5.45338	−0.217440
$630$	−6.49504	−0.258769
$631$	0.196197	0.00781046	0.00390523	−	0.999992i	$-0.498757\pi$
$631$	0.196197	0.00781046	0.00390523	+	0.999992i	$0.498757\pi$
$632$	−3.80569	−0.151382
$633$	25.5602	1.01593
$634$	20.3317	0.807477
$635$	87.9003	3.48822
$636$	6.20331	0.245977
$637$	−3.67676	−0.145678
$638$	−3.57429	−0.141507
$639$	5.84741	0.231320
$640$	4.18412	0.165392
$641$	−13.7052	−0.541321	−0.270660	−	0.962675i	$-0.587242\pi$
$641$	−13.7052	−0.541321	−0.270660	+	0.962675i	$0.587242\pi$
$642$	−3.79052	−0.149600
$643$	37.5077	1.47916	0.739580	−	0.673068i	$-0.235024\pi$
$643$	37.5077	1.47916	0.739580	+	0.673068i	$0.235024\pi$
$644$	−7.51049	−0.295955
$645$	−61.7932	−2.43311
$646$	4.91399	0.193338
$647$	−13.5709	−0.533527	−0.266763	−	0.963762i	$-0.585954\pi$
$647$	−13.5709	−0.533527	−0.266763	+	0.963762i	$0.585954\pi$
$648$	−10.5213	−0.413317
$649$	−33.1085	−1.29962
$650$	37.3032	1.46315
$651$	30.8322	1.20841
$652$	−21.7211	−0.850664
$653$	49.3592	1.93157	0.965787	−	0.259337i	$-0.0835041\pi$
$653$	49.3592	1.93157	0.965787	+	0.259337i	$0.0835041\pi$
$654$	−35.1635	−1.37500
$655$	−67.8144	−2.64973
$656$	−5.22484	−0.203996
$657$	−9.36827	−0.365491
$658$	−12.6902	−0.494715
$659$	−12.8489	−0.500522	−0.250261	−	0.968178i	$-0.580516\pi$
$659$	−12.8489	−0.500522	−0.250261	+	0.968178i	$0.580516\pi$
$660$	−19.9874	−0.778009
$661$	44.5833	1.73409	0.867045	−	0.498231i	$-0.166017\pi$
$661$	44.5833	1.73409	0.867045	+	0.498231i	$0.166017\pi$
$662$	−12.1064	−0.470528
$663$	−5.03681	−0.195614
$664$	7.48160	0.290342
$665$	−55.8338	−2.16514
$666$	−3.98595	−0.154453
$667$	−4.46839	−0.173017
$668$	14.1052	0.545745
$669$	17.5399	0.678130
$670$	−37.5839	−1.45199
$671$	−22.8726	−0.882989
$672$	4.58582	0.176902
$673$	−15.9513	−0.614876	−0.307438	−	0.951568i	$-0.599472\pi$
$673$	−15.9513	−0.614876	−0.307438	+	0.951568i	$0.599472\pi$
$674$	0.101822	0.00392204
$675$	56.2100	2.16352
$676$	−4.10396	−0.157845
$677$	29.3785	1.12911	0.564554	−	0.825396i	$-0.309048\pi$
$677$	29.3785	1.12911	0.564554	+	0.825396i	$0.309048\pi$
$678$	15.2915	0.587265
$679$	17.9711	0.689669
$680$	3.70024	0.141898
$681$	−11.0886	−0.424914
$682$	16.8193	0.644046
$683$	−49.4106	−1.89064	−0.945321	−	0.326141i	$-0.894252\pi$
$683$	−49.4106	−1.89064	−0.945321	+	0.326141i	$0.894252\pi$
$684$	3.59171	0.137332
$685$	−78.0390	−2.98172
$686$	19.7710	0.754861
$687$	14.3343	0.546887
$688$	7.73403	0.294857
$689$	−9.68926	−0.369131
$690$	−24.9872	−0.951248
$691$	−38.1748	−1.45224	−0.726119	−	0.687569i	$-0.758678\pi$
$691$	−38.1748	−1.45224	−0.726119	+	0.687569i	$0.758678\pi$
$692$	4.32404	0.164375
$693$	−3.88329	−0.147514
$694$	16.6688	0.632741
$695$	1.76214	0.0668419
$696$	2.72835	0.103418
$697$	−4.62061	−0.175018
$698$	20.0174	0.757669
$699$	−44.4443	−1.68104
$700$	−30.0353	−1.13523
$701$	31.0142	1.17139	0.585695	−	0.810532i	$-0.300822\pi$
$701$	31.0142	1.17139	0.585695	+	0.810532i	$0.300822\pi$
$702$	13.4049	0.505937
$703$	−34.2647	−1.29232
$704$	2.50162	0.0942834
$705$	−42.2200	−1.59010
$706$	−25.9079	−0.975055
$707$	−9.99836	−0.376027
$708$	25.2726	0.949803
$709$	12.8143	0.481251	0.240625	−	0.970618i	$-0.422647\pi$
$709$	12.8143	0.481251	0.240625	+	0.970618i	$0.422647\pi$
$710$	37.8507	1.42051
$711$	−2.45995	−0.0922553
$712$	13.2480	0.496488
$713$	21.0267	0.787455
$714$	4.05549	0.151773
$715$	31.2193	1.16754
$716$	−8.28301	−0.309550
$717$	−22.5914	−0.843692
$718$	−20.9581	−0.782151
$719$	−39.2273	−1.46293	−0.731467	−	0.681877i	$-0.761164\pi$
$719$	−39.2273	−1.46293	−0.731467	+	0.681877i	$0.761164\pi$
$720$	2.70456	0.100793
$721$	−35.0172	−1.30411
$722$	11.8756	0.441965
$723$	−42.6840	−1.58743
$724$	−12.7503	−0.473860
$725$	−17.8696	−0.663661
$726$	9.05490	0.336059
$727$	0.00653734	0.000242456 0	0.000121228	−	1.00000i	$-0.499961\pi$
$727$	0.00653734	0.000242456 0	0.000121228		1.00000i	$0.499961\pi$
$728$	−7.16281	−0.265471
$729$	18.9457	0.701692
$730$	−60.6415	−2.24444
$731$	6.83962	0.252972
$732$	17.4593	0.645314
$733$	−7.64266	−0.282288	−0.141144	−	0.989989i	$-0.545078\pi$
$733$	−7.64266	−0.282288	−0.141144	+	0.989989i	$0.545078\pi$
$734$	−2.85611	−0.105421
$735$	9.84922	0.363294
$736$	3.12740	0.115277
$737$	−22.4708	−0.827723
$738$	−3.37727	−0.124319
$739$	25.7658	0.947809	0.473905	−	0.880576i	$-0.342844\pi$
$739$	25.7658	0.947809	0.473905	+	0.880576i	$0.342844\pi$
$740$	−25.8014	−0.948478
$741$	−31.6474	−1.16260
$742$	7.80149	0.286402
$743$	−4.33908	−0.159185	−0.0795927	−	0.996827i	$-0.525362\pi$
$743$	−4.33908	−0.159185	−0.0795927	+	0.996827i	$0.525362\pi$
$744$	−12.8386	−0.470687
$745$	69.4658	2.54503
$746$	−3.66631	−0.134233
$747$	4.83601	0.176940
$748$	2.21232	0.0808904
$749$	−4.76708	−0.174185
$750$	−59.9780	−2.19009
$751$	8.78375	0.320524	0.160262	−	0.987075i	$-0.448766\pi$
$751$	8.78375	0.320524	0.160262	+	0.987075i	$0.448766\pi$
$752$	5.28424	0.192696
$753$	5.83569	0.212664
$754$	−4.26154	−0.155196
$755$	42.3588	1.54159
$756$	−10.7932	−0.392546
$757$	37.2438	1.35365	0.676825	−	0.736144i	$-0.263355\pi$
$757$	37.2438	1.35365	0.676825	+	0.736144i	$0.263355\pi$
$758$	10.9098	0.396261
$759$	−14.9395	−0.542269
$760$	23.2494	0.843344
$761$	16.3439	0.592466	0.296233	−	0.955116i	$-0.404269\pi$
$761$	16.3439	0.592466	0.296233	+	0.955116i	$0.404269\pi$
$762$	−40.1160	−1.45325
$763$	−44.2227	−1.60097
$764$	0.730899	0.0264430
$765$	2.39179	0.0864753
$766$	13.0910	0.472996
$767$	−39.4745	−1.42534
$768$	−1.90955	−0.0689050
$769$	6.56279	0.236660	0.118330	−	0.992974i	$-0.462246\pi$
$769$	6.56279	0.236660	0.118330	+	0.992974i	$0.462246\pi$
$770$	−25.1368	−0.905868
$771$	−15.4673	−0.557040
$772$	15.1344	0.544699
$773$	−44.8943	−1.61474	−0.807368	−	0.590048i	$-0.799109\pi$
$773$	−44.8943	−1.61474	−0.807368	+	0.590048i	$0.799109\pi$
$774$	4.99918	0.179692
$775$	84.0882	3.02054
$776$	−7.48325	−0.268633
$777$	−28.2785	−1.01448
$778$	1.00019	0.0358584
$779$	−29.0323	−1.04019
$780$	−23.8305	−0.853269
$781$	22.6304	0.809778
$782$	2.76573	0.0989022
$783$	−6.42147	−0.229485
$784$	−1.23273	−0.0440260
$785$	59.6927	2.13052
$786$	30.9492	1.10392
$787$	−41.0052	−1.46168	−0.730838	−	0.682551i	$-0.760871\pi$
$787$	−41.0052	−1.46168	−0.730838	+	0.682551i	$0.760871\pi$
$788$	−6.73556	−0.239945
$789$	−47.8625	−1.70395
$790$	−15.9235	−0.566531
$791$	19.2310	0.683777
$792$	1.61702	0.0574581
$793$	−27.2705	−0.968404
$794$	39.4229	1.39907
$795$	25.9554	0.920543
$796$	1.28291	0.0454715
$797$	20.1860	0.715026	0.357513	−	0.933908i	$-0.383625\pi$
$797$	20.1860	0.715026	0.357513	+	0.933908i	$0.383625\pi$
$798$	25.4815	0.902034
$799$	4.67314	0.165324
$800$	12.5068	0.442183
$801$	8.56331	0.302570
$802$	−15.8812	−0.560785
$803$	−36.2567	−1.27947
$804$	17.1526	0.604924
$805$	−31.4248	−1.10758
$806$	20.0533	0.706347
$807$	−50.6568	−1.78320
$808$	4.16336	0.146466
$809$	−38.8504	−1.36591	−0.682953	−	0.730462i	$-0.739305\pi$
$809$	−38.8504	−1.36591	−0.682953	+	0.730462i	$0.739305\pi$
$810$	−44.0225	−1.54679
$811$	12.6782	0.445193	0.222597	−	0.974911i	$-0.428547\pi$
$811$	12.6782	0.445193	0.222597	+	0.974911i	$0.428547\pi$
$812$	3.43126	0.120414
$813$	25.7584	0.903386
$814$	−15.4263	−0.540690
$815$	−90.8836	−3.18351
$816$	−1.68872	−0.0591170
$817$	42.9748	1.50350
$818$	−12.3229	−0.430861
$819$	−4.62995	−0.161784
$820$	−21.8613	−0.763431
$821$	−40.9015	−1.42747	−0.713736	−	0.700415i	$-0.752998\pi$
$821$	−40.9015	−1.42747	−0.713736	+	0.700415i	$0.752998\pi$
$822$	35.6155	1.24223
$823$	−1.51490	−0.0528062	−0.0264031	−	0.999651i	$-0.508405\pi$
$823$	−1.51490	−0.0528062	−0.0264031	+	0.999651i	$0.508405\pi$
$824$	14.5813	0.507964
$825$	−59.7448	−2.08005
$826$	31.7837	1.10590
$827$	9.64661	0.335445	0.167723	−	0.985834i	$-0.446359\pi$
$827$	9.64661	0.335445	0.167723	+	0.985834i	$0.446359\pi$
$828$	2.02151	0.0702523
$829$	−21.6288	−0.751200	−0.375600	−	0.926782i	$-0.622563\pi$
$829$	−21.6288	−0.751200	−0.375600	+	0.926782i	$0.622563\pi$
$830$	31.3039	1.08657
$831$	−53.8805	−1.86909
$832$	2.98262	0.103404
$833$	−1.09017	−0.0377720
$834$	−0.804208	−0.0278475
$835$	59.0177	2.04239
$836$	13.9005	0.480758
$837$	30.2172	1.04446
$838$	17.1732	0.593240
$839$	−27.3424	−0.943966	−0.471983	−	0.881608i	$-0.656462\pi$
$839$	−27.3424	−0.943966	−0.471983	+	0.881608i	$0.656462\pi$
$840$	19.1876	0.662035
$841$	−26.9586	−0.929606
$842$	8.33481	0.287237
$843$	52.2368	1.79913
$844$	−13.3854	−0.460746
$845$	−17.1715	−0.590716
$846$	3.41567	0.117433
$847$	11.3877	0.391287
$848$	−3.24857	−0.111556
$849$	−1.95316	−0.0670323
$850$	11.0605	0.379371
$851$	−19.2851	−0.661085
$852$	−17.2744	−0.591810
$853$	15.1368	0.518275	0.259137	−	0.965840i	$-0.416562\pi$
$853$	15.1368	0.518275	0.259137	+	0.965840i	$0.416562\pi$
$854$	21.9574	0.751366
$855$	15.0281	0.513951
$856$	1.98503	0.0678469
$857$	25.9309	0.885784	0.442892	−	0.896575i	$-0.353953\pi$
$857$	25.9309	0.885784	0.442892	+	0.896575i	$0.353953\pi$
$858$	−14.2479	−0.486416
$859$	−35.5922	−1.21439	−0.607194	−	0.794553i	$-0.707705\pi$
$859$	−35.5922	−1.21439	−0.607194	+	0.794553i	$0.707705\pi$
$860$	32.3601	1.10347
$861$	−23.9602	−0.816560
$862$	29.1557	0.993046
$863$	43.1491	1.46881	0.734407	−	0.678709i	$-0.237460\pi$
$863$	43.1491	1.46881	0.734407	+	0.678709i	$0.237460\pi$
$864$	4.49434	0.152901
$865$	18.0923	0.615156
$866$	−23.0701	−0.783953
$867$	30.9690	1.05176
$868$	−16.1463	−0.548041
$869$	−9.52039	−0.322957
$870$	11.4157	0.387029
$871$	−26.7914	−0.907793
$872$	18.4145	0.623594
$873$	−4.83708	−0.163710
$874$	17.3776	0.587808
$875$	−75.4303	−2.55001
$876$	27.6756	0.935074
$877$	19.1650	0.647155	0.323577	−	0.946202i	$-0.395114\pi$
$877$	19.1650	0.647155	0.323577	+	0.946202i	$0.395114\pi$
$878$	−3.62553	−0.122356
$879$	62.5214	2.10879
$880$	10.4671	0.352845
$881$	3.63793	0.122565	0.0612824	−	0.998120i	$-0.480481\pi$
$881$	3.63793	0.122565	0.0612824	+	0.998120i	$0.480481\pi$
$882$	−0.796819	−0.0268303
$883$	0.569926	0.0191795	0.00958976	−	0.999954i	$-0.496947\pi$
$883$	0.569926	0.0191795	0.00958976	+	0.999954i	$0.496947\pi$
$884$	2.63769	0.0887153
$885$	105.744	3.55453
$886$	−20.4972	−0.688618
$887$	25.7804	0.865620	0.432810	−	0.901485i	$-0.357522\pi$
$887$	25.7804	0.865620	0.432810	+	0.901485i	$0.357522\pi$
$888$	11.7753	0.395152
$889$	−50.4512	−1.69208
$890$	55.4310	1.85805
$891$	−26.3204	−0.881767
$892$	−9.18533	−0.307548
$893$	29.3623	0.982573
$894$	−31.7029	−1.06030
$895$	−34.6571	−1.15846
$896$	−2.40151	−0.0802290
$897$	−17.8120	−0.594725
$898$	7.29843	0.243552
$899$	−9.60629	−0.320388
$900$	8.08426	0.269475
$901$	−2.87289	−0.0957097
$902$	−13.0706	−0.435202
$903$	35.4668	1.18026
$904$	−8.00788	−0.266338
$905$	−53.3486	−1.77337
$906$	−19.3317	−0.642254
$907$	18.5504	0.615955	0.307978	−	0.951394i	$-0.400348\pi$
$907$	18.5504	0.615955	0.307978	+	0.951394i	$0.400348\pi$
$908$	5.80689	0.192708
$909$	2.69114	0.0892595
$910$	−29.9700	−0.993497
$911$	−8.87970	−0.294197	−0.147099	−	0.989122i	$-0.546994\pi$
$911$	−8.87970	−0.294197	−0.147099	+	0.989122i	$0.546994\pi$
$912$	−10.6106	−0.351352
$913$	18.7161	0.619413
$914$	26.6076	0.880100
$915$	73.0517	2.41501
$916$	−7.50662	−0.248026
$917$	38.9227	1.28534
$918$	3.97459	0.131181
$919$	−11.5492	−0.380972	−0.190486	−	0.981690i	$-0.561006\pi$
$919$	−11.5492	−0.380972	−0.190486	+	0.981690i	$0.561006\pi$
$920$	13.0854	0.431413
$921$	7.84635	0.258546
$922$	−35.2133	−1.15969
$923$	26.9817	0.888112
$924$	11.4720	0.377400
$925$	−77.1235	−2.53580
$926$	−6.97059	−0.229068
$927$	9.42518	0.309563
$928$	−1.42879	−0.0469023
$929$	−47.1155	−1.54581	−0.772905	−	0.634522i	$-0.781197\pi$
$929$	−47.1155	−1.54581	−0.772905	+	0.634522i	$0.781197\pi$
$930$	−53.7184	−1.76149
$931$	−6.84975	−0.224491
$932$	23.2747	0.762389
$933$	10.7720	0.352659
$934$	3.27635	0.107205
$935$	9.25660	0.302723
$936$	1.92793	0.0630163
$937$	15.0528	0.491752	0.245876	−	0.969301i	$-0.420924\pi$
$937$	15.0528	0.491752	0.245876	+	0.969301i	$0.420924\pi$
$938$	21.5716	0.704339
$939$	53.2989	1.73934
$940$	22.1099	0.721145
$941$	4.65124	0.151626	0.0758130	−	0.997122i	$-0.475845\pi$
$941$	4.65124	0.151626	0.0758130	+	0.997122i	$0.475845\pi$
$942$	−27.2426	−0.887612
$943$	−16.3401	−0.532108
$944$	−13.2348	−0.430757
$945$	−45.1602	−1.46906
$946$	19.3476	0.629045
$947$	37.4496	1.21695	0.608474	−	0.793574i	$-0.291782\pi$
$947$	37.4496	1.21695	0.608474	+	0.793574i	$0.291782\pi$
$948$	7.26716	0.236026
$949$	−43.2280	−1.40324
$950$	69.4953	2.25472
$951$	−38.8245	−1.25897
$952$	−2.12379	−0.0688324
$953$	−34.0702	−1.10364	−0.551820	−	0.833963i	$-0.686067\pi$
$953$	−34.0702	−1.10364	−0.551820	+	0.833963i	$0.686067\pi$
$954$	−2.09983	−0.0679847
$955$	3.05817	0.0989600
$956$	11.8307	0.382634
$957$	6.82528	0.220630
$958$	1.64953	0.0532940
$959$	44.7912	1.44638
$960$	−7.98979	−0.257869
$961$	14.2038	0.458188
$962$	−18.3924	−0.592994
$963$	1.28310	0.0413473
$964$	22.3529	0.719938
$965$	63.3242	2.03848
$966$	14.3417	0.461436
$967$	−7.42469	−0.238762	−0.119381	−	0.992849i	$-0.538091\pi$
$967$	−7.42469	−0.238762	−0.119381	+	0.992849i	$0.538091\pi$
$968$	−4.74190	−0.152410
$969$	−9.38351	−0.301442
$970$	−31.3108	−1.00533
$971$	14.7242	0.472520	0.236260	−	0.971690i	$-0.424078\pi$
$971$	14.7242	0.472520	0.236260	+	0.971690i	$0.424078\pi$
$972$	6.60802	0.211952
$973$	−1.01140	−0.0324240
$974$	−10.1379	−0.324838
$975$	−71.2323	−2.28126
$976$	−9.14313	−0.292665
$977$	−10.6961	−0.342200	−0.171100	−	0.985254i	$-0.554732\pi$
$977$	−10.6961	−0.342200	−0.171100	+	0.985254i	$0.554732\pi$
$978$	41.4776	1.32631
$979$	33.1414	1.05920
$980$	−5.15787	−0.164762
$981$	11.9029	0.380031
$982$	8.32053	0.265519
$983$	−17.2623	−0.550583	−0.275291	−	0.961361i	$-0.588774\pi$
$983$	−17.2623	−0.550583	−0.275291	+	0.961361i	$0.588774\pi$
$984$	9.97710	0.318058
$985$	−28.1824	−0.897966
$986$	−1.26356	−0.0402398
$987$	24.2326	0.771331
$988$	16.5732	0.527264
$989$	24.1874	0.769114
$990$	6.76578	0.215031
$991$	−20.0984	−0.638446	−0.319223	−	0.947680i	$-0.603422\pi$
$991$	−20.0984	−0.638446	−0.319223	+	0.947680i	$0.603422\pi$
$992$	6.72338	0.213467
$993$	23.1178	0.733620
$994$	−21.7248	−0.689069
$995$	5.36784	0.170172
$996$	−14.2865	−0.452685
$997$	−31.7569	−1.00575	−0.502875	−	0.864359i	$-0.667724\pi$
$997$	−31.7569	−1.00575	−0.502875	+	0.864359i	$0.667724\pi$
$998$	35.7962	1.13311
$999$	−27.7144	−0.876845

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8038.2.a.d.1.18	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8038.2.a.d.1.18	✓	92	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:	\( N \)	\(=\)	\( 8038 = 2 \cdot 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.90955 q^{3} +1.00000 q^{4} +4.18412 q^{5} -1.90955 q^{6} -2.40151 q^{7} +1.00000 q^{8} +0.646387 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.90955 q^{3} +1.00000 q^{4} +4.18412 q^{5} -1.90955 q^{6} -2.40151 q^{7} +1.00000 q^{8} +0.646387 q^{9} +4.18412 q^{10} +2.50162 q^{11} -1.90955 q^{12} +2.98262 q^{13} -2.40151 q^{14} -7.98979 q^{15} +1.00000 q^{16} +0.884354 q^{17} +0.646387 q^{18} +5.55658 q^{19} +4.18412 q^{20} +4.58582 q^{21} +2.50162 q^{22} +3.12740 q^{23} -1.90955 q^{24} +12.5068 q^{25} +2.98262 q^{26} +4.49434 q^{27} -2.40151 q^{28} -1.42879 q^{29} -7.98979 q^{30} +6.72338 q^{31} +1.00000 q^{32} -4.77697 q^{33} +0.884354 q^{34} -10.0482 q^{35} +0.646387 q^{36} -6.16651 q^{37} +5.55658 q^{38} -5.69547 q^{39} +4.18412 q^{40} -5.22484 q^{41} +4.58582 q^{42} +7.73403 q^{43} +2.50162 q^{44} +2.70456 q^{45} +3.12740 q^{46} +5.28424 q^{47} -1.90955 q^{48} -1.23273 q^{49} +12.5068 q^{50} -1.68872 q^{51} +2.98262 q^{52} -3.24857 q^{53} +4.49434 q^{54} +10.4671 q^{55} -2.40151 q^{56} -10.6106 q^{57} -1.42879 q^{58} -13.2348 q^{59} -7.98979 q^{60} -9.14313 q^{61} +6.72338 q^{62} -1.55231 q^{63} +1.00000 q^{64} +12.4796 q^{65} -4.77697 q^{66} -8.98251 q^{67} +0.884354 q^{68} -5.97193 q^{69} -10.0482 q^{70} +9.04629 q^{71} +0.646387 q^{72} -14.4933 q^{73} -6.16651 q^{74} -23.8824 q^{75} +5.55658 q^{76} -6.00768 q^{77} -5.69547 q^{78} -3.80569 q^{79} +4.18412 q^{80} -10.5213 q^{81} -5.22484 q^{82} +7.48160 q^{83} +4.58582 q^{84} +3.70024 q^{85} +7.73403 q^{86} +2.72835 q^{87} +2.50162 q^{88} +13.2480 q^{89} +2.70456 q^{90} -7.16281 q^{91} +3.12740 q^{92} -12.8386 q^{93} +5.28424 q^{94} +23.2494 q^{95} -1.90955 q^{96} -7.48325 q^{97} -1.23273 q^{98} +1.61702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9}+O(q^{10}) \) 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9	\( 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9} + 28 q^{10} + 37 q^{11} + 31 q^{12} + 20 q^{13} + 29 q^{14} + 30 q^{15} + 92 q^{16} + 52 q^{17} + 113 q^{18} + 61 q^{19} + 28 q^{20} + 5 q^{21} + 37 q^{22} + 71 q^{23} + 31 q^{24} + 118 q^{25} + 20 q^{26} + 112 q^{27} + 29 q^{28} + 30 q^{29} + 30 q^{30} + 89 q^{31} + 92 q^{32} + 52 q^{33} + 52 q^{34} + 58 q^{35} + 113 q^{36} + 15 q^{37} + 61 q^{38} + 43 q^{39} + 28 q^{40} + 75 q^{41} + 5 q^{42} + 46 q^{43} + 37 q^{44} + 63 q^{45} + 71 q^{46} + 92 q^{47} + 31 q^{48} + 131 q^{49} + 118 q^{50} + 45 q^{51} + 20 q^{52} + 72 q^{53} + 112 q^{54} + 86 q^{55} + 29 q^{56} + 44 q^{57} + 30 q^{58} + 95 q^{59} + 30 q^{60} - 4 q^{61} + 89 q^{62} + 67 q^{63} + 92 q^{64} + 55 q^{65} + 52 q^{66} + 40 q^{67} + 52 q^{68} + 25 q^{69} + 58 q^{70} + 84 q^{71} + 113 q^{72} + 87 q^{73} + 15 q^{74} + 132 q^{75} + 61 q^{76} + 96 q^{77} + 43 q^{78} + 68 q^{79} + 28 q^{80} + 156 q^{81} + 75 q^{82} + 120 q^{83} + 5 q^{84} - 14 q^{85} + 46 q^{86} + 73 q^{87} + 37 q^{88} + 86 q^{89} + 63 q^{90} + 93 q^{91} + 71 q^{92} + 29 q^{93} + 92 q^{94} + 67 q^{95} + 31 q^{96} + 65 q^{97} + 131 q^{98} + 94 q^{99}+O(q^{100}) \) 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9 + 28 * q^10 + 37 * q^11 + 31 * q^12 + 20 * q^13 + 29 * q^14 + 30 * q^15 + 92 * q^16 + 52 * q^17 + 113 * q^18 + 61 * q^19 + 28 * q^20 + 5 * q^21 + 37 * q^22 + 71 * q^23 + 31 * q^24 + 118 * q^25 + 20 * q^26 + 112 * q^27 + 29 * q^28 + 30 * q^29 + 30 * q^30 + 89 * q^31 + 92 * q^32 + 52 * q^33 + 52 * q^34 + 58 * q^35 + 113 * q^36 + 15 * q^37 + 61 * q^38 + 43 * q^39 + 28 * q^40 + 75 * q^41 + 5 * q^42 + 46 * q^43 + 37 * q^44 + 63 * q^45 + 71 * q^46 + 92 * q^47 + 31 * q^48 + 131 * q^49 + 118 * q^50 + 45 * q^51 + 20 * q^52 + 72 * q^53 + 112 * q^54 + 86 * q^55 + 29 * q^56 + 44 * q^57 + 30 * q^58 + 95 * q^59 + 30 * q^60 - 4 * q^61 + 89 * q^62 + 67 * q^63 + 92 * q^64 + 55 * q^65 + 52 * q^66 + 40 * q^67 + 52 * q^68 + 25 * q^69 + 58 * q^70 + 84 * q^71 + 113 * q^72 + 87 * q^73 + 15 * q^74 + 132 * q^75 + 61 * q^76 + 96 * q^77 + 43 * q^78 + 68 * q^79 + 28 * q^80 + 156 * q^81 + 75 * q^82 + 120 * q^83 + 5 * q^84 - 14 * q^85 + 46 * q^86 + 73 * q^87 + 37 * q^88 + 86 * q^89 + 63 * q^90 + 93 * q^91 + 71 * q^92 + 29 * q^93 + 92 * q^94 + 67 * q^95 + 31 * q^96 + 65 * q^97 + 131 * q^98 + 94 * q^99

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