LMFDB - Embedded newform 8015.2.a.h.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.520713 q^{2} -3.35310 q^{3} -1.72886 q^{4} +1.00000 q^{5} +1.74600 q^{6} +1.00000 q^{7} +1.94166 q^{8} +8.24329 q^{9} +O(q^{10})$	\(q-0.520713 q^{2} -3.35310 q^{3} -1.72886 q^{4} +1.00000 q^{5} +1.74600 q^{6} +1.00000 q^{7} +1.94166 q^{8} +8.24329 q^{9} -0.520713 q^{10} +0.0909571 q^{11} +5.79704 q^{12} +3.30881 q^{13} -0.520713 q^{14} -3.35310 q^{15} +2.44667 q^{16} +1.15426 q^{17} -4.29239 q^{18} +4.14519 q^{19} -1.72886 q^{20} -3.35310 q^{21} -0.0473625 q^{22} +6.21965 q^{23} -6.51060 q^{24} +1.00000 q^{25} -1.72294 q^{26} -17.5813 q^{27} -1.72886 q^{28} -2.56284 q^{29} +1.74600 q^{30} +1.72587 q^{31} -5.15734 q^{32} -0.304988 q^{33} -0.601040 q^{34} +1.00000 q^{35} -14.2515 q^{36} -4.36923 q^{37} -2.15846 q^{38} -11.0948 q^{39} +1.94166 q^{40} -7.98228 q^{41} +1.74600 q^{42} -8.73716 q^{43} -0.157252 q^{44} +8.24329 q^{45} -3.23865 q^{46} +5.90882 q^{47} -8.20392 q^{48} +1.00000 q^{49} -0.520713 q^{50} -3.87037 q^{51} -5.72047 q^{52} -3.00706 q^{53} +9.15480 q^{54} +0.0909571 q^{55} +1.94166 q^{56} -13.8993 q^{57} +1.33450 q^{58} -5.95499 q^{59} +5.79704 q^{60} -4.63627 q^{61} -0.898685 q^{62} +8.24329 q^{63} -2.20784 q^{64} +3.30881 q^{65} +0.158811 q^{66} +4.50115 q^{67} -1.99556 q^{68} -20.8551 q^{69} -0.520713 q^{70} -3.82503 q^{71} +16.0057 q^{72} -3.56851 q^{73} +2.27511 q^{74} -3.35310 q^{75} -7.16645 q^{76} +0.0909571 q^{77} +5.77720 q^{78} -4.66440 q^{79} +2.44667 q^{80} +34.2219 q^{81} +4.15647 q^{82} +5.74349 q^{83} +5.79704 q^{84} +1.15426 q^{85} +4.54955 q^{86} +8.59347 q^{87} +0.176608 q^{88} -17.2873 q^{89} -4.29239 q^{90} +3.30881 q^{91} -10.7529 q^{92} -5.78703 q^{93} -3.07680 q^{94} +4.14519 q^{95} +17.2931 q^{96} -3.41470 q^{97} -0.520713 q^{98} +0.749786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) $ 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.520713	−0.368200	−0.184100	−	0.982908i	$-0.558937\pi$
$2$	−0.520713	−0.368200	−0.184100	+	0.982908i	$0.558937\pi$
$3$	−3.35310	−1.93591	−0.967957	−	0.251116i	$-0.919202\pi$
$3$	−3.35310	−1.93591	−0.967957	+	0.251116i	$0.919202\pi$
$4$	−1.72886	−0.864429
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.74600	0.712803
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.94166	0.686482
$9$	8.24329	2.74776
$10$	−0.520713	−0.164664
$11$	0.0909571	0.0274246	0.0137123	−	0.999906i	$-0.495635\pi$
$11$	0.0909571	0.0274246	0.0137123	+	0.999906i	$0.495635\pi$
$12$	5.79704	1.67346
$13$	3.30881	0.917700	0.458850	−	0.888514i	$-0.348262\pi$
$13$	3.30881	0.917700	0.458850	+	0.888514i	$0.348262\pi$
$14$	−0.520713	−0.139166
$15$	−3.35310	−0.865767
$16$	2.44667	0.611667
$17$	1.15426	0.279950	0.139975	−	0.990155i	$-0.455298\pi$
$17$	1.15426	0.279950	0.139975	+	0.990155i	$0.455298\pi$
$18$	−4.29239	−1.01173
$19$	4.14519	0.950972	0.475486	−	0.879723i	$-0.342272\pi$
$19$	4.14519	0.950972	0.475486	+	0.879723i	$0.342272\pi$
$20$	−1.72886	−0.386584
$21$	−3.35310	−0.731707
$22$	−0.0473625	−0.0100977
$23$	6.21965	1.29689	0.648444	−	0.761263i	$-0.275420\pi$
$23$	6.21965	1.29689	0.648444	+	0.761263i	$0.275420\pi$
$24$	−6.51060	−1.32897
$25$	1.00000	0.200000
$26$	−1.72294	−0.337897
$27$	−17.5813	−3.38352
$28$	−1.72886	−0.326723
$29$	−2.56284	−0.475908	−0.237954	−	0.971276i	$-0.576477\pi$
$29$	−2.56284	−0.475908	−0.237954	+	0.971276i	$0.576477\pi$
$30$	1.74600	0.318775
$31$	1.72587	0.309976	0.154988	−	0.987916i	$-0.450466\pi$
$31$	1.72587	0.309976	0.154988	+	0.987916i	$0.450466\pi$
$32$	−5.15734	−0.911697
$33$	−0.304988	−0.0530917
$34$	−0.601040	−0.103078
$35$	1.00000	0.169031
$36$	−14.2515	−2.37525
$37$	−4.36923	−0.718297	−0.359149	−	0.933280i	$-0.616933\pi$
$37$	−4.36923	−0.718297	−0.359149	+	0.933280i	$0.616933\pi$
$38$	−2.15846	−0.350148
$39$	−11.0948	−1.77659
$40$	1.94166	0.307004
$41$	−7.98228	−1.24662	−0.623311	−	0.781974i	$-0.714213\pi$
$41$	−7.98228	−1.24662	−0.623311	+	0.781974i	$0.714213\pi$
$42$	1.74600	0.269414
$43$	−8.73716	−1.33240	−0.666202	−	0.745771i	$-0.732081\pi$
$43$	−8.73716	−1.33240	−0.666202	+	0.745771i	$0.732081\pi$
$44$	−0.157252	−0.0237066
$45$	8.24329	1.22884
$46$	−3.23865	−0.477513
$47$	5.90882	0.861890	0.430945	−	0.902378i	$-0.358180\pi$
$47$	5.90882	0.861890	0.430945	+	0.902378i	$0.358180\pi$
$48$	−8.20392	−1.18413
$49$	1.00000	0.142857
$50$	−0.520713	−0.0736399
$51$	−3.87037	−0.541960
$52$	−5.72047	−0.793286
$53$	−3.00706	−0.413052	−0.206526	−	0.978441i	$-0.566216\pi$
$53$	−3.00706	−0.413052	−0.206526	+	0.978441i	$0.566216\pi$
$54$	9.15480	1.24581
$55$	0.0909571	0.0122647
$56$	1.94166	0.259466
$57$	−13.8993	−1.84100
$58$	1.33450	0.175229
$59$	−5.95499	−0.775274	−0.387637	−	0.921812i	$-0.626709\pi$
$59$	−5.95499	−0.775274	−0.387637	+	0.921812i	$0.626709\pi$
$60$	5.79704	0.748394
$61$	−4.63627	−0.593613	−0.296807	−	0.954938i	$-0.595922\pi$
$61$	−4.63627	−0.593613	−0.296807	+	0.954938i	$0.595922\pi$
$62$	−0.898685	−0.114133
$63$	8.24329	1.03856
$64$	−2.20784	−0.275980
$65$	3.30881	0.410408
$66$	0.158811	0.0195483
$67$	4.50115	0.549903	0.274952	−	0.961458i	$-0.411338\pi$
$67$	4.50115	0.549903	0.274952	+	0.961458i	$0.411338\pi$
$68$	−1.99556	−0.241997
$69$	−20.8551	−2.51066
$70$	−0.520713	−0.0622371
$71$	−3.82503	−0.453947	−0.226974	−	0.973901i	$-0.572883\pi$
$71$	−3.82503	−0.453947	−0.226974	+	0.973901i	$0.572883\pi$
$72$	16.0057	1.88629
$73$	−3.56851	−0.417662	−0.208831	−	0.977952i	$-0.566966\pi$
$73$	−3.56851	−0.417662	−0.208831	+	0.977952i	$0.566966\pi$
$74$	2.27511	0.264477
$75$	−3.35310	−0.387183
$76$	−7.16645	−0.822048
$77$	0.0909571	0.0103655
$78$	5.77720	0.654139
$79$	−4.66440	−0.524786	−0.262393	−	0.964961i	$-0.584512\pi$
$79$	−4.66440	−0.524786	−0.262393	+	0.964961i	$0.584512\pi$
$80$	2.44667	0.273546
$81$	34.2219	3.80244
$82$	4.15647	0.459006
$83$	5.74349	0.630430	0.315215	−	0.949020i	$-0.397923\pi$
$83$	5.74349	0.630430	0.315215	+	0.949020i	$0.397923\pi$
$84$	5.79704	0.632509
$85$	1.15426	0.125198
$86$	4.54955	0.490590
$87$	8.59347	0.921316
$88$	0.176608	0.0188265
$89$	−17.2873	−1.83245	−0.916225	−	0.400664i	$-0.868779\pi$
$89$	−17.2873	−1.83245	−0.916225	+	0.400664i	$0.868779\pi$
$90$	−4.29239	−0.452457
$91$	3.30881	0.346858
$92$	−10.7529	−1.12107
$93$	−5.78703	−0.600087
$94$	−3.07680	−0.317348
$95$	4.14519	0.425288
$96$	17.2931	1.76497
$97$	−3.41470	−0.346710	−0.173355	−	0.984859i	$-0.555461\pi$
$97$	−3.41470	−0.346710	−0.173355	+	0.984859i	$0.555461\pi$
$98$	−0.520713	−0.0525999
$99$	0.749786	0.0753563
$100$	−1.72886	−0.172886
$101$	3.64745	0.362935	0.181467	−	0.983397i	$-0.441915\pi$
$101$	3.64745	0.362935	0.181467	+	0.983397i	$0.441915\pi$
$102$	2.01535	0.199549
$103$	−6.85234	−0.675181	−0.337591	−	0.941293i	$-0.609612\pi$
$103$	−6.85234	−0.675181	−0.337591	+	0.941293i	$0.609612\pi$
$104$	6.42461	0.629984
$105$	−3.35310	−0.327229
$106$	1.56582	0.152086
$107$	7.18405	0.694509	0.347254	−	0.937771i	$-0.387114\pi$
$107$	7.18405	0.694509	0.347254	+	0.937771i	$0.387114\pi$
$108$	30.3955	2.92481
$109$	−9.46064	−0.906165	−0.453082	−	0.891469i	$-0.649676\pi$
$109$	−9.46064	−0.906165	−0.453082	+	0.891469i	$0.649676\pi$
$110$	−0.0473625	−0.00451584
$111$	14.6505	1.39056
$112$	2.44667	0.231188
$113$	−13.2903	−1.25024	−0.625122	−	0.780527i	$-0.714951\pi$
$113$	−13.2903	−1.25024	−0.625122	+	0.780527i	$0.714951\pi$
$114$	7.23752	0.677856
$115$	6.21965	0.579986
$116$	4.43079	0.411388
$117$	27.2755	2.52162
$118$	3.10084	0.285456
$119$	1.15426	0.105811
$120$	−6.51060	−0.594334
$121$	−10.9917	−0.999248
$122$	2.41416	0.218568
$123$	26.7654	2.41335
$124$	−2.98379	−0.267952
$125$	1.00000	0.0894427
$126$	−4.29239	−0.382396
$127$	4.34082	0.385186	0.192593	−	0.981279i	$-0.438310\pi$
$127$	4.34082	0.385186	0.192593	+	0.981279i	$0.438310\pi$
$128$	11.4643	1.01331
$129$	29.2966	2.57942
$130$	−1.72294	−0.151112
$131$	−4.34583	−0.379697	−0.189849	−	0.981813i	$-0.560800\pi$
$131$	−4.34583	−0.379697	−0.189849	+	0.981813i	$0.560800\pi$
$132$	0.527282	0.0458940
$133$	4.14519	0.359434
$134$	−2.34381	−0.202474
$135$	−17.5813	−1.51316
$136$	2.24119	0.192181
$137$	−11.6918	−0.998901	−0.499451	−	0.866342i	$-0.666465\pi$
$137$	−11.6918	−0.998901	−0.499451	+	0.866342i	$0.666465\pi$
$138$	10.8595	0.924425
$139$	3.53450	0.299793	0.149896	−	0.988702i	$-0.452106\pi$
$139$	3.53450	0.299793	0.149896	+	0.988702i	$0.452106\pi$
$140$	−1.72886	−0.146115
$141$	−19.8129	−1.66855
$142$	1.99174	0.167143
$143$	0.300960	0.0251676
$144$	20.1686	1.68071
$145$	−2.56284	−0.212832
$146$	1.85817	0.153783
$147$	−3.35310	−0.276559
$148$	7.55378	0.620917
$149$	0.497456	0.0407532	0.0203766	−	0.999792i	$-0.493513\pi$
$149$	0.497456	0.0407532	0.0203766	+	0.999792i	$0.493513\pi$
$150$	1.74600	0.142561
$151$	−6.09695	−0.496163	−0.248081	−	0.968739i	$-0.579800\pi$
$151$	−6.09695	−0.496163	−0.248081	+	0.968739i	$0.579800\pi$
$152$	8.04857	0.652825
$153$	9.51494	0.769237
$154$	−0.0473625	−0.00381658
$155$	1.72587	0.138626
$156$	19.1813	1.53573
$157$	−0.325555	−0.0259821	−0.0129910	−	0.999916i	$-0.504135\pi$
$157$	−0.325555	−0.0259821	−0.0129910	+	0.999916i	$0.504135\pi$
$158$	2.42881	0.193226
$159$	10.0830	0.799633
$160$	−5.15734	−0.407723
$161$	6.21965	0.490177
$162$	−17.8198	−1.40006
$163$	11.3141	0.886188	0.443094	−	0.896475i	$-0.353881\pi$
$163$	11.3141	0.886188	0.443094	+	0.896475i	$0.353881\pi$
$164$	13.8002	1.07762
$165$	−0.304988	−0.0237433
$166$	−2.99071	−0.232124
$167$	−4.76972	−0.369092	−0.184546	−	0.982824i	$-0.559081\pi$
$167$	−4.76972	−0.369092	−0.184546	+	0.982824i	$0.559081\pi$
$168$	−6.51060	−0.502304
$169$	−2.05175	−0.157827
$170$	−0.601040	−0.0460977
$171$	34.1700	2.61305
$172$	15.1053	1.15177
$173$	2.56762	0.195212	0.0976061	−	0.995225i	$-0.468881\pi$
$173$	2.56762	0.195212	0.0976061	+	0.995225i	$0.468881\pi$
$174$	−4.47473	−0.339228
$175$	1.00000	0.0755929
$176$	0.222542	0.0167747
$177$	19.9677	1.50086
$178$	9.00172	0.674707
$179$	−0.197229	−0.0147416	−0.00737078	−	0.999973i	$-0.502346\pi$
$179$	−0.197229	−0.0147416	−0.00737078	+	0.999973i	$0.502346\pi$
$180$	−14.2515	−1.06224
$181$	9.20081	0.683891	0.341946	−	0.939720i	$-0.388914\pi$
$181$	9.20081	0.683891	0.341946	+	0.939720i	$0.388914\pi$
$182$	−1.72294	−0.127713
$183$	15.5459	1.14918
$184$	12.0765	0.890290
$185$	−4.36923	−0.321232
$186$	3.01338	0.220952
$187$	0.104989	0.00767752
$188$	−10.2155	−0.745043
$189$	−17.5813	−1.27885
$190$	−2.15846	−0.156591
$191$	−10.2742	−0.743415	−0.371708	−	0.928350i	$-0.621228\pi$
$191$	−10.2742	−0.743415	−0.371708	+	0.928350i	$0.621228\pi$
$192$	7.40311	0.534274
$193$	−23.8312	−1.71541	−0.857705	−	0.514143i	$-0.828110\pi$
$193$	−23.8312	−1.71541	−0.857705	+	0.514143i	$0.828110\pi$
$194$	1.77808	0.127658
$195$	−11.0948	−0.794514
$196$	−1.72886	−0.123490
$197$	15.3170	1.09129	0.545647	−	0.838015i	$-0.316284\pi$
$197$	15.3170	1.09129	0.545647	+	0.838015i	$0.316284\pi$
$198$	−0.390423	−0.0277462
$199$	−19.8701	−1.40855	−0.704276	−	0.709927i	$-0.748728\pi$
$199$	−19.8701	−1.40855	−0.704276	+	0.709927i	$0.748728\pi$
$200$	1.94166	0.137296
$201$	−15.0928	−1.06457
$202$	−1.89927	−0.133632
$203$	−2.56284	−0.179876
$204$	6.69131	0.468486
$205$	−7.98228	−0.557506
$206$	3.56810	0.248601
$207$	51.2704	3.56354
$208$	8.09556	0.561326
$209$	0.377035	0.0260800
$210$	1.74600	0.120486
$211$	4.85307	0.334099	0.167050	−	0.985948i	$-0.446576\pi$
$211$	4.85307	0.334099	0.167050	+	0.985948i	$0.446576\pi$
$212$	5.19879	0.357054
$213$	12.8257	0.878803
$214$	−3.74083	−0.255718
$215$	−8.73716	−0.595869
$216$	−34.1369	−2.32272
$217$	1.72587	0.117160
$218$	4.92628	0.333650
$219$	11.9656	0.808558
$220$	−0.157252	−0.0106019
$221$	3.81925	0.256910
$222$	−7.62869	−0.512004
$223$	−12.8161	−0.858233	−0.429116	−	0.903249i	$-0.641175\pi$
$223$	−12.8161	−0.858233	−0.429116	+	0.903249i	$0.641175\pi$
$224$	−5.15734	−0.344589
$225$	8.24329	0.549553
$226$	6.92041	0.460339
$227$	7.26286	0.482053	0.241026	−	0.970519i	$-0.422516\pi$
$227$	7.26286	0.482053	0.241026	+	0.970519i	$0.422516\pi$
$228$	24.0298	1.59141
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−3.23865	−0.213550
$231$	−0.304988	−0.0200668
$232$	−4.97618	−0.326702
$233$	−28.2316	−1.84952	−0.924758	−	0.380555i	$-0.875733\pi$
$233$	−28.2316	−1.84952	−0.924758	+	0.380555i	$0.875733\pi$
$234$	−14.2027	−0.928460
$235$	5.90882	0.385449
$236$	10.2953	0.670169
$237$	15.6402	1.01594
$238$	−0.601040	−0.0389597
$239$	12.9597	0.838292	0.419146	−	0.907919i	$-0.362330\pi$
$239$	12.9597	0.838292	0.419146	+	0.907919i	$0.362330\pi$
$240$	−8.20392	−0.529561
$241$	4.91422	0.316553	0.158276	−	0.987395i	$-0.449406\pi$
$241$	4.91422	0.316553	0.158276	+	0.987395i	$0.449406\pi$
$242$	5.72353	0.367923
$243$	−62.0058	−3.97767
$244$	8.01545	0.513136
$245$	1.00000	0.0638877
$246$	−13.9371	−0.888596
$247$	13.7157	0.872707
$248$	3.35107	0.212793
$249$	−19.2585	−1.22046
$250$	−0.520713	−0.0329328
$251$	2.27103	0.143346	0.0716731	−	0.997428i	$-0.477166\pi$
$251$	2.27103	0.143346	0.0716731	+	0.997428i	$0.477166\pi$
$252$	−14.2515	−0.897759
$253$	0.565722	0.0355666
$254$	−2.26032	−0.141825
$255$	−3.87037	−0.242372
$256$	−1.55394	−0.0971215
$257$	31.6379	1.97352	0.986758	−	0.162201i	$-0.0518592\pi$
$257$	31.6379	1.97352	0.986758	+	0.162201i	$0.0518592\pi$
$258$	−15.2551	−0.949741
$259$	−4.36923	−0.271491
$260$	−5.72047	−0.354768
$261$	−21.1262	−1.30768
$262$	2.26293	0.139804
$263$	16.2627	1.00280	0.501402	−	0.865214i	$-0.332818\pi$
$263$	16.2627	1.00280	0.501402	+	0.865214i	$0.332818\pi$
$264$	−0.592185	−0.0364465
$265$	−3.00706	−0.184723
$266$	−2.15846	−0.132343
$267$	57.9661	3.54747
$268$	−7.78185	−0.475352
$269$	7.28676	0.444282	0.222141	−	0.975015i	$-0.428695\pi$
$269$	7.28676	0.444282	0.222141	+	0.975015i	$0.428695\pi$
$270$	9.15480	0.557143
$271$	−8.65736	−0.525897	−0.262949	−	0.964810i	$-0.584695\pi$
$271$	−8.65736	−0.525897	−0.262949	+	0.964810i	$0.584695\pi$
$272$	2.82410	0.171236
$273$	−11.0948	−0.671487
$274$	6.08809	0.367795
$275$	0.0909571	0.00548492
$276$	36.0556	2.17029
$277$	−17.9050	−1.07580	−0.537902	−	0.843007i	$-0.680783\pi$
$277$	−17.9050	−1.07580	−0.537902	+	0.843007i	$0.680783\pi$
$278$	−1.84046	−0.110384
$279$	14.2269	0.851741
$280$	1.94166	0.116037
$281$	−28.2502	−1.68526	−0.842632	−	0.538489i	$-0.818995\pi$
$281$	−28.2502	−1.68526	−0.842632	+	0.538489i	$0.818995\pi$
$282$	10.3168	0.614358
$283$	−21.0030	−1.24850	−0.624249	−	0.781226i	$-0.714595\pi$
$283$	−21.0030	−1.24850	−0.624249	+	0.781226i	$0.714595\pi$
$284$	6.61293	0.392405
$285$	−13.8993	−0.823321
$286$	−0.156714	−0.00926668
$287$	−7.98228	−0.471179
$288$	−42.5134	−2.50513
$289$	−15.6677	−0.921628
$290$	1.33450	0.0783648
$291$	11.4498	0.671200
$292$	6.16944	0.361039
$293$	16.7360	0.977727	0.488863	−	0.872360i	$-0.337412\pi$
$293$	16.7360	0.977727	0.488863	+	0.872360i	$0.337412\pi$
$294$	1.74600	0.101829
$295$	−5.95499	−0.346713
$296$	−8.48358	−0.493098
$297$	−1.59914	−0.0927917
$298$	−0.259032	−0.0150053
$299$	20.5797	1.19015
$300$	5.79704	0.334692
$301$	−8.73716	−0.503601
$302$	3.17476	0.182687
$303$	−12.2303	−0.702611
$304$	10.1419	0.581678
$305$	−4.63627	−0.265472
$306$	−4.95455	−0.283233
$307$	−22.6194	−1.29096	−0.645478	−	0.763779i	$-0.723342\pi$
$307$	−22.6194	−1.29096	−0.645478	+	0.763779i	$0.723342\pi$
$308$	−0.157252	−0.00896026
$309$	22.9766	1.30709
$310$	−0.898685	−0.0510419
$311$	−12.8630	−0.729392	−0.364696	−	0.931127i	$-0.618827\pi$
$311$	−12.8630	−0.729392	−0.364696	+	0.931127i	$0.618827\pi$
$312$	−21.5424	−1.21960
$313$	17.8793	1.01060	0.505298	−	0.862945i	$-0.331383\pi$
$313$	17.8793	1.01060	0.505298	+	0.862945i	$0.331383\pi$
$314$	0.169520	0.00956659
$315$	8.24329	0.464457
$316$	8.06409	0.453640
$317$	−12.8958	−0.724301	−0.362150	−	0.932120i	$-0.617957\pi$
$317$	−12.8958	−0.724301	−0.362150	+	0.932120i	$0.617957\pi$
$318$	−5.25034	−0.294425
$319$	−0.233109	−0.0130516
$320$	−2.20784	−0.123422
$321$	−24.0889	−1.34451
$322$	−3.23865	−0.180483
$323$	4.78465	0.266225
$324$	−59.1649	−3.28694
$325$	3.30881	0.183540
$326$	−5.89139	−0.326294
$327$	31.7225	1.75426
$328$	−15.4989	−0.855784
$329$	5.90882	0.325764
$330$	0.158811	0.00874228
$331$	30.2454	1.66244	0.831220	−	0.555944i	$-0.187643\pi$
$331$	30.2454	1.66244	0.831220	+	0.555944i	$0.187643\pi$
$332$	−9.92968	−0.544962
$333$	−36.0168	−1.97371
$334$	2.48365	0.135899
$335$	4.50115	0.245924
$336$	−8.20392	−0.447561
$337$	2.49195	0.135745	0.0678725	−	0.997694i	$-0.478379\pi$
$337$	2.49195	0.135745	0.0678725	+	0.997694i	$0.478379\pi$
$338$	1.06837	0.0581118
$339$	44.5636	2.42036
$340$	−1.99556	−0.108224
$341$	0.156981	0.00850097
$342$	−17.7928	−0.962123
$343$	1.00000	0.0539949
$344$	−16.9646	−0.914671
$345$	−20.8551	−1.12280
$346$	−1.33699	−0.0718771
$347$	25.2169	1.35371	0.676856	−	0.736115i	$-0.263342\pi$
$347$	25.2169	1.35371	0.676856	+	0.736115i	$0.263342\pi$
$348$	−14.8569	−0.796413
$349$	2.82463	0.151199	0.0755996	−	0.997138i	$-0.475913\pi$
$349$	2.82463	0.151199	0.0755996	+	0.997138i	$0.475913\pi$
$350$	−0.520713	−0.0278333
$351$	−58.1732	−3.10505
$352$	−0.469097	−0.0250029
$353$	−1.91283	−0.101810	−0.0509049	−	0.998704i	$-0.516211\pi$
$353$	−1.91283	−0.101810	−0.0509049	+	0.998704i	$0.516211\pi$
$354$	−10.3974	−0.552617
$355$	−3.82503	−0.203011
$356$	29.8873	1.58402
$357$	−3.87037	−0.204841
$358$	0.102700	0.00542784
$359$	−26.0234	−1.37346	−0.686730	−	0.726913i	$-0.740955\pi$
$359$	−26.0234	−1.37346	−0.686730	+	0.726913i	$0.740955\pi$
$360$	16.0057	0.843574
$361$	−1.81738	−0.0956514
$362$	−4.79098	−0.251808
$363$	36.8564	1.93446
$364$	−5.72047	−0.299834
$365$	−3.56851	−0.186784
$366$	−8.09494	−0.423129
$367$	28.8906	1.50808	0.754038	−	0.656831i	$-0.228103\pi$
$367$	28.8906	1.50808	0.754038	+	0.656831i	$0.228103\pi$
$368$	15.2174	0.793263
$369$	−65.8002	−3.42542
$370$	2.27511	0.118278
$371$	−3.00706	−0.156119
$372$	10.0050	0.518733
$373$	−15.7874	−0.817442	−0.408721	−	0.912659i	$-0.634025\pi$
$373$	−15.7874	−0.817442	−0.408721	+	0.912659i	$0.634025\pi$
$374$	−0.0546689	−0.00282686
$375$	−3.35310	−0.173153
$376$	11.4730	0.591672
$377$	−8.47997	−0.436740
$378$	9.15480	0.470872
$379$	15.9374	0.818650	0.409325	−	0.912389i	$-0.365764\pi$
$379$	15.9374	0.818650	0.409325	+	0.912389i	$0.365764\pi$
$380$	−7.16645	−0.367631
$381$	−14.5552	−0.745687
$382$	5.34991	0.273725
$383$	−13.6316	−0.696541	−0.348270	−	0.937394i	$-0.613231\pi$
$383$	−13.6316	−0.696541	−0.348270	+	0.937394i	$0.613231\pi$
$384$	−38.4411	−1.96169
$385$	0.0909571	0.00463560
$386$	12.4092	0.631613
$387$	−72.0229	−3.66113
$388$	5.90352	0.299706
$389$	−15.0814	−0.764656	−0.382328	−	0.924027i	$-0.624878\pi$
$389$	−15.0814	−0.764656	−0.382328	+	0.924027i	$0.624878\pi$
$390$	5.77720	0.292540
$391$	7.17912	0.363064
$392$	1.94166	0.0980689
$393$	14.5720	0.735061
$394$	−7.97578	−0.401814
$395$	−4.66440	−0.234691
$396$	−1.29627	−0.0651402
$397$	39.0099	1.95785	0.978925	−	0.204219i	$-0.0654656\pi$
$397$	39.0099	1.95785	0.978925	+	0.204219i	$0.0654656\pi$
$398$	10.3466	0.518628
$399$	−13.8993	−0.695833
$400$	2.44667	0.122333
$401$	−17.1696	−0.857408	−0.428704	−	0.903445i	$-0.641030\pi$
$401$	−17.1696	−0.857408	−0.428704	+	0.903445i	$0.641030\pi$
$402$	7.85902	0.391973
$403$	5.71060	0.284465
$404$	−6.30593	−0.313731
$405$	34.2219	1.70050
$406$	1.33450	0.0662304
$407$	−0.397413	−0.0196990
$408$	−7.51495	−0.372046
$409$	−29.5411	−1.46071	−0.730356	−	0.683067i	$-0.760646\pi$
$409$	−29.5411	−1.46071	−0.730356	+	0.683067i	$0.760646\pi$
$410$	4.15647	0.205274
$411$	39.2039	1.93379
$412$	11.8467	0.583646
$413$	−5.95499	−0.293026
$414$	−26.6972	−1.31209
$415$	5.74349	0.281937
$416$	−17.0647	−0.836665
$417$	−11.8516	−0.580373
$418$	−0.196327	−0.00960266
$419$	3.64515	0.178077	0.0890386	−	0.996028i	$-0.471621\pi$
$419$	3.64515	0.178077	0.0890386	+	0.996028i	$0.471621\pi$
$420$	5.79704	0.282866
$421$	−27.5696	−1.34366	−0.671831	−	0.740705i	$-0.734492\pi$
$421$	−27.5696	−1.34366	−0.671831	+	0.740705i	$0.734492\pi$
$422$	−2.52706	−0.123015
$423$	48.7081	2.36827
$424$	−5.83871	−0.283553
$425$	1.15426	0.0559901
$426$	−6.67851	−0.323575
$427$	−4.63627	−0.224365
$428$	−12.4202	−0.600354
$429$	−1.00915	−0.0487222
$430$	4.54955	0.219399
$431$	−28.4697	−1.37134	−0.685668	−	0.727914i	$-0.740490\pi$
$431$	−28.4697	−1.37134	−0.685668	+	0.727914i	$0.740490\pi$
$432$	−43.0155	−2.06959
$433$	−18.2340	−0.876271	−0.438136	−	0.898909i	$-0.644361\pi$
$433$	−18.2340	−0.876271	−0.438136	+	0.898909i	$0.644361\pi$
$434$	−0.898685	−0.0431383
$435$	8.59347	0.412025
$436$	16.3561	0.783315
$437$	25.7817	1.23330
$438$	−6.23062	−0.297711
$439$	21.2766	1.01548	0.507739	−	0.861511i	$-0.330481\pi$
$439$	21.2766	1.01548	0.507739	+	0.861511i	$0.330481\pi$
$440$	0.176608	0.00841947
$441$	8.24329	0.392538
$442$	−1.98873	−0.0945943
$443$	7.20596	0.342366	0.171183	−	0.985239i	$-0.445241\pi$
$443$	7.20596	0.342366	0.171183	+	0.985239i	$0.445241\pi$
$444$	−25.3286	−1.20204
$445$	−17.2873	−0.819497
$446$	6.67353	0.316001
$447$	−1.66802	−0.0788946
$448$	−2.20784	−0.104311
$449$	1.92000	0.0906103	0.0453051	−	0.998973i	$-0.485574\pi$
$449$	1.92000	0.0906103	0.0453051	+	0.998973i	$0.485574\pi$
$450$	−4.29239	−0.202345
$451$	−0.726045	−0.0341881
$452$	22.9770	1.08075
$453$	20.4437	0.960529
$454$	−3.78186	−0.177492
$455$	3.30881	0.155120
$456$	−26.9877	−1.26381
$457$	−18.3542	−0.858571	−0.429286	−	0.903169i	$-0.641235\pi$
$457$	−18.3542	−0.858571	−0.429286	+	0.903169i	$0.641235\pi$
$458$	0.520713	0.0243313
$459$	−20.2934	−0.947217
$460$	−10.7529	−0.501356
$461$	−3.08257	−0.143570	−0.0717848	−	0.997420i	$-0.522869\pi$
$461$	−3.08257	−0.143570	−0.0717848	+	0.997420i	$0.522869\pi$
$462$	0.158811	0.00738857
$463$	−21.5252	−1.00036	−0.500180	−	0.865922i	$-0.666733\pi$
$463$	−21.5252	−1.00036	−0.500180	+	0.865922i	$0.666733\pi$
$464$	−6.27042	−0.291097
$465$	−5.78703	−0.268367
$466$	14.7006	0.680991
$467$	0.213827	0.00989475	0.00494737	−	0.999988i	$-0.498425\pi$
$467$	0.213827	0.00989475	0.00494737	+	0.999988i	$0.498425\pi$
$468$	−47.1555	−2.17976
$469$	4.50115	0.207844
$470$	−3.07680	−0.141922
$471$	1.09162	0.0502991
$472$	−11.5626	−0.532212
$473$	−0.794706	−0.0365406
$474$	−8.14406	−0.374069
$475$	4.14519	0.190194
$476$	−1.99556	−0.0914663
$477$	−24.7881	−1.13497
$478$	−6.74827	−0.308659
$479$	−26.7120	−1.22050	−0.610252	−	0.792207i	$-0.708932\pi$
$479$	−26.7120	−1.22050	−0.610252	+	0.792207i	$0.708932\pi$
$480$	17.2931	0.789318
$481$	−14.4570	−0.659181
$482$	−2.55890	−0.116555
$483$	−20.8551	−0.948941
$484$	19.0031	0.863779
$485$	−3.41470	−0.155053
$486$	32.2872	1.46458
$487$	−5.97092	−0.270568	−0.135284	−	0.990807i	$-0.543195\pi$
$487$	−5.97092	−0.270568	−0.135284	+	0.990807i	$0.543195\pi$
$488$	−9.00207	−0.407505
$489$	−37.9373	−1.71558
$490$	−0.520713	−0.0235234
$491$	−40.8520	−1.84363	−0.921813	−	0.387636i	$-0.873292\pi$
$491$	−40.8520	−1.84363	−0.921813	+	0.387636i	$0.873292\pi$
$492$	−46.2735	−2.08617
$493$	−2.95820	−0.133230
$494$	−7.14193	−0.321330
$495$	0.749786	0.0337004
$496$	4.22264	0.189602
$497$	−3.82503	−0.171576
$498$	10.0282	0.449372
$499$	11.2236	0.502439	0.251219	−	0.967930i	$-0.419168\pi$
$499$	11.2236	0.502439	0.251219	+	0.967930i	$0.419168\pi$
$500$	−1.72886	−0.0773169
$501$	15.9933	0.714530
$502$	−1.18256	−0.0527800
$503$	16.5861	0.739539	0.369769	−	0.929124i	$-0.379437\pi$
$503$	16.5861	0.739539	0.369769	+	0.929124i	$0.379437\pi$
$504$	16.0057	0.712951
$505$	3.64745	0.162309
$506$	−0.294579	−0.0130956
$507$	6.87973	0.305539
$508$	−7.50467	−0.332966
$509$	−19.0876	−0.846042	−0.423021	−	0.906120i	$-0.639030\pi$
$509$	−19.0876	−0.846042	−0.423021	+	0.906120i	$0.639030\pi$
$510$	2.01535	0.0892412
$511$	−3.56851	−0.157861
$512$	−22.1195	−0.977553
$513$	−72.8778	−3.21763
$514$	−16.4742	−0.726648
$515$	−6.85234	−0.301950
$516$	−50.6496	−2.22972
$517$	0.537449	0.0236370
$518$	2.27511	0.0999628
$519$	−8.60948	−0.377914
$520$	6.42461	0.281738
$521$	6.66350	0.291933	0.145967	−	0.989290i	$-0.453371\pi$
$521$	6.66350	0.291933	0.145967	+	0.989290i	$0.453371\pi$
$522$	11.0007	0.481488
$523$	−33.5642	−1.46766	−0.733831	−	0.679332i	$-0.762270\pi$
$523$	−33.5642	−1.46766	−0.733831	+	0.679332i	$0.762270\pi$
$524$	7.51333	0.328221
$525$	−3.35310	−0.146341
$526$	−8.46822	−0.369232
$527$	1.99212	0.0867779
$528$	−0.746205	−0.0324744
$529$	15.6841	0.681917
$530$	1.56582	0.0680148
$531$	−49.0887	−2.13027
$532$	−7.16645	−0.310705
$533$	−26.4119	−1.14402
$534$	−30.1837	−1.30618
$535$	7.18405	0.310594
$536$	8.73973	0.377499
$537$	0.661328	0.0285384
$538$	−3.79431	−0.163584
$539$	0.0909571	0.00391780
$540$	30.3955	1.30802
$541$	13.3244	0.572862	0.286431	−	0.958101i	$-0.407531\pi$
$541$	13.3244	0.572862	0.286431	+	0.958101i	$0.407531\pi$
$542$	4.50800	0.193635
$543$	−30.8513	−1.32395
$544$	−5.95293	−0.255230
$545$	−9.46064	−0.405249
$546$	5.77720	0.247241
$547$	4.22977	0.180852	0.0904260	−	0.995903i	$-0.471177\pi$
$547$	4.22977	0.180852	0.0904260	+	0.995903i	$0.471177\pi$
$548$	20.2135	0.863479
$549$	−38.2181	−1.63111
$550$	−0.0473625	−0.00201955
$551$	−10.6235	−0.452575
$552$	−40.4937	−1.72352
$553$	−4.66440	−0.198351
$554$	9.32334	0.396111
$555$	14.6505	0.621878
$556$	−6.11066	−0.259150
$557$	−1.87247	−0.0793392	−0.0396696	−	0.999213i	$-0.512631\pi$
$557$	−1.87247	−0.0793392	−0.0396696	+	0.999213i	$0.512631\pi$
$558$	−7.40812	−0.313611
$559$	−28.9096	−1.22275
$560$	2.44667	0.103391
$561$	−0.352037	−0.0148630
$562$	14.7102	0.620514
$563$	−0.869478	−0.0366441	−0.0183221	−	0.999832i	$-0.505832\pi$
$563$	−0.869478	−0.0366441	−0.0183221	+	0.999832i	$0.505832\pi$
$564$	34.2537	1.44234
$565$	−13.2903	−0.559126
$566$	10.9365	0.459696
$567$	34.2219	1.43719
$568$	−7.42692	−0.311627
$569$	−5.22993	−0.219250	−0.109625	−	0.993973i	$-0.534965\pi$
$569$	−5.22993	−0.219250	−0.109625	+	0.993973i	$0.534965\pi$
$570$	7.23752	0.303146
$571$	19.5245	0.817074	0.408537	−	0.912742i	$-0.366039\pi$
$571$	19.5245	0.817074	0.408537	+	0.912742i	$0.366039\pi$
$572$	−0.520317	−0.0217556
$573$	34.4504	1.43919
$574$	4.15647	0.173488
$575$	6.21965	0.259377
$576$	−18.1999	−0.758328
$577$	21.6405	0.900908	0.450454	−	0.892800i	$-0.351262\pi$
$577$	21.6405	0.900908	0.450454	+	0.892800i	$0.351262\pi$
$578$	8.15836	0.339343
$579$	79.9085	3.32088
$580$	4.43079	0.183979
$581$	5.74349	0.238280
$582$	−5.96207	−0.247136
$583$	−0.273514	−0.0113278
$584$	−6.92884	−0.286718
$585$	27.2755	1.12770
$586$	−8.71464	−0.359999
$587$	−14.0663	−0.580580	−0.290290	−	0.956939i	$-0.593752\pi$
$587$	−14.0663	−0.580580	−0.290290	+	0.956939i	$0.593752\pi$
$588$	5.79704	0.239066
$589$	7.15408	0.294779
$590$	3.10084	0.127660
$591$	−51.3596	−2.11265
$592$	−10.6901	−0.439358
$593$	13.9828	0.574205	0.287102	−	0.957900i	$-0.407308\pi$
$593$	13.9828	0.574205	0.287102	+	0.957900i	$0.407308\pi$
$594$	0.832694	0.0341659
$595$	1.15426	0.0473202
$596$	−0.860031	−0.0352282
$597$	66.6263	2.72683
$598$	−10.7161	−0.438214
$599$	−0.928623	−0.0379425	−0.0189712	−	0.999820i	$-0.506039\pi$
$599$	−0.928623	−0.0379425	−0.0189712	+	0.999820i	$0.506039\pi$
$600$	−6.51060	−0.265794
$601$	−41.2669	−1.68331	−0.841657	−	0.540013i	$-0.818419\pi$
$601$	−41.2669	−1.68331	−0.841657	+	0.540013i	$0.818419\pi$
$602$	4.54955	0.185426
$603$	37.1043	1.51100
$604$	10.5408	0.428898
$605$	−10.9917	−0.446877
$606$	6.36846	0.258701
$607$	26.1792	1.06258	0.531291	−	0.847190i	$-0.321707\pi$
$607$	26.1792	1.06258	0.531291	+	0.847190i	$0.321707\pi$
$608$	−21.3782	−0.866999
$609$	8.59347	0.348225
$610$	2.41416	0.0977466
$611$	19.5512	0.790957
$612$	−16.4500	−0.664951
$613$	−4.10202	−0.165679	−0.0828396	−	0.996563i	$-0.526399\pi$
$613$	−4.10202	−0.165679	−0.0828396	+	0.996563i	$0.526399\pi$
$614$	11.7782	0.475329
$615$	26.7654	1.07928
$616$	0.176608	0.00711575
$617$	41.5398	1.67233	0.836164	−	0.548480i	$-0.184793\pi$
$617$	41.5398	1.67233	0.836164	+	0.548480i	$0.184793\pi$
$618$	−11.9642	−0.481271
$619$	40.4950	1.62763	0.813815	−	0.581124i	$-0.197387\pi$
$619$	40.4950	1.62763	0.813815	+	0.581124i	$0.197387\pi$
$620$	−2.98379	−0.119832
$621$	−109.349	−4.38804
$622$	6.69791	0.268562
$623$	−17.2873	−0.692601
$624$	−27.1452	−1.08668
$625$	1.00000	0.0400000
$626$	−9.30996	−0.372101
$627$	−1.26424	−0.0504887
$628$	0.562838	0.0224597
$629$	−5.04325	−0.201087
$630$	−4.29239	−0.171013
$631$	−18.8238	−0.749364	−0.374682	−	0.927153i	$-0.622248\pi$
$631$	−18.8238	−0.749364	−0.374682	+	0.927153i	$0.622248\pi$
$632$	−9.05670	−0.360256
$633$	−16.2728	−0.646787
$634$	6.71501	0.266687
$635$	4.34082	0.172260
$636$	−17.4321	−0.691226
$637$	3.30881	0.131100
$638$	0.121383	0.00480559
$639$	−31.5308	−1.24734
$640$	11.4643	0.453167
$641$	−23.7452	−0.937881	−0.468940	−	0.883230i	$-0.655364\pi$
$641$	−23.7452	−0.937881	−0.468940	+	0.883230i	$0.655364\pi$
$642$	12.5434	0.495048
$643$	−19.5192	−0.769762	−0.384881	−	0.922966i	$-0.625757\pi$
$643$	−19.5192	−0.769762	−0.384881	+	0.922966i	$0.625757\pi$
$644$	−10.7529	−0.423724
$645$	29.2966	1.15355
$646$	−2.49143	−0.0980239
$647$	34.3815	1.35168	0.675838	−	0.737050i	$-0.263782\pi$
$647$	34.3815	1.35168	0.675838	+	0.737050i	$0.263782\pi$
$648$	66.4475	2.61031
$649$	−0.541649	−0.0212616
$650$	−1.72294	−0.0675793
$651$	−5.78703	−0.226812
$652$	−19.5605	−0.766047
$653$	−27.9987	−1.09567	−0.547837	−	0.836585i	$-0.684549\pi$
$653$	−27.9987	−1.09567	−0.547837	+	0.836585i	$0.684549\pi$
$654$	−16.5183	−0.645917
$655$	−4.34583	−0.169806
$656$	−19.5300	−0.762517
$657$	−29.4162	−1.14764
$658$	−3.07680	−0.119946
$659$	−17.0870	−0.665616	−0.332808	−	0.942995i	$-0.607996\pi$
$659$	−17.0870	−0.665616	−0.332808	+	0.942995i	$0.607996\pi$
$660$	0.527282	0.0205244
$661$	4.11890	0.160207	0.0801033	−	0.996787i	$-0.474475\pi$
$661$	4.11890	0.160207	0.0801033	+	0.996787i	$0.474475\pi$
$662$	−15.7492	−0.612110
$663$	−12.8063	−0.497356
$664$	11.1519	0.432779
$665$	4.14519	0.160744
$666$	18.7544	0.726719
$667$	−15.9400	−0.617199
$668$	8.24616	0.319054
$669$	42.9738	1.66146
$670$	−2.34381	−0.0905492
$671$	−0.421701	−0.0162796
$672$	17.2931	0.667095
$673$	40.5182	1.56186	0.780932	−	0.624616i	$-0.214745\pi$
$673$	40.5182	1.56186	0.780932	+	0.624616i	$0.214745\pi$
$674$	−1.29759	−0.0499812
$675$	−17.5813	−0.676704
$676$	3.54718	0.136430
$677$	22.9081	0.880431	0.440216	−	0.897892i	$-0.354902\pi$
$677$	22.9081	0.880431	0.440216	+	0.897892i	$0.354902\pi$
$678$	−23.2049	−0.891177
$679$	−3.41470	−0.131044
$680$	2.24119	0.0859459
$681$	−24.3531	−0.933212
$682$	−0.0817418	−0.00313006
$683$	45.9175	1.75699	0.878493	−	0.477755i	$-0.158550\pi$
$683$	45.9175	1.75699	0.878493	+	0.477755i	$0.158550\pi$
$684$	−59.0751	−2.25879
$685$	−11.6918	−0.446722
$686$	−0.520713	−0.0198809
$687$	3.35310	0.127929
$688$	−21.3769	−0.814987
$689$	−9.94982	−0.379058
$690$	10.8595	0.413415
$691$	−4.56432	−0.173635	−0.0868175	−	0.996224i	$-0.527670\pi$
$691$	−4.56432	−0.173635	−0.0868175	+	0.996224i	$0.527670\pi$
$692$	−4.43905	−0.168747
$693$	0.749786	0.0284820
$694$	−13.1308	−0.498436
$695$	3.53450	0.134071
$696$	16.6856	0.632467
$697$	−9.21366	−0.348992
$698$	−1.47082	−0.0556715
$699$	94.6636	3.58050
$700$	−1.72886	−0.0653447
$701$	−51.4991	−1.94509	−0.972547	−	0.232707i	$-0.925242\pi$
$701$	−51.4991	−1.94509	−0.972547	+	0.232707i	$0.925242\pi$
$702$	30.2915	1.14328
$703$	−18.1113	−0.683081
$704$	−0.200819	−0.00756864
$705$	−19.8129	−0.746196
$706$	0.996036	0.0374863
$707$	3.64745	0.137177
$708$	−34.5213	−1.29739
$709$	−25.4722	−0.956627	−0.478313	−	0.878189i	$-0.658752\pi$
$709$	−25.4722	−0.956627	−0.478313	+	0.878189i	$0.658752\pi$
$710$	1.99174	0.0747487
$711$	−38.4500	−1.44199
$712$	−33.5661	−1.25794
$713$	10.7343	0.402004
$714$	2.01535	0.0754226
$715$	0.300960	0.0112553
$716$	0.340980	0.0127430
$717$	−43.4551	−1.62286
$718$	13.5507	0.505707
$719$	−32.9354	−1.22828	−0.614141	−	0.789197i	$-0.710497\pi$
$719$	−32.9354	−1.22828	−0.614141	+	0.789197i	$0.710497\pi$
$720$	20.1686	0.751639
$721$	−6.85234	−0.255194
$722$	0.946331	0.0352188
$723$	−16.4779	−0.612819
$724$	−15.9069	−0.591175
$725$	−2.56284	−0.0951815
$726$	−19.1916	−0.712267
$727$	−4.25079	−0.157653	−0.0788266	−	0.996888i	$-0.525117\pi$
$727$	−4.25079	−0.157653	−0.0788266	+	0.996888i	$0.525117\pi$
$728$	6.42461	0.238112
$729$	105.246	3.89800
$730$	1.85817	0.0687739
$731$	−10.0850	−0.373007
$732$	−26.8766	−0.993388
$733$	−17.6614	−0.652340	−0.326170	−	0.945311i	$-0.605758\pi$
$733$	−17.6614	−0.652340	−0.326170	+	0.945311i	$0.605758\pi$
$734$	−15.0437	−0.555273
$735$	−3.35310	−0.123681
$736$	−32.0769	−1.18237
$737$	0.409412	0.0150809
$738$	34.2630	1.26124
$739$	23.3031	0.857218	0.428609	−	0.903490i	$-0.359004\pi$
$739$	23.3031	0.857218	0.428609	+	0.903490i	$0.359004\pi$
$740$	7.55378	0.277683
$741$	−45.9900	−1.68949
$742$	1.56582	0.0574830
$743$	−7.11463	−0.261010	−0.130505	−	0.991448i	$-0.541660\pi$
$743$	−7.11463	−0.261010	−0.130505	+	0.991448i	$0.541660\pi$
$744$	−11.2365	−0.411949
$745$	0.497456	0.0182254
$746$	8.22071	0.300982
$747$	47.3453	1.73227
$748$	−0.181510	−0.00663668
$749$	7.18405	0.262500
$750$	1.74600	0.0637550
$751$	4.20933	0.153601	0.0768004	−	0.997046i	$-0.475530\pi$
$751$	4.20933	0.153601	0.0768004	+	0.997046i	$0.475530\pi$
$752$	14.4569	0.527190
$753$	−7.61500	−0.277506
$754$	4.41563	0.160808
$755$	−6.09695	−0.221891
$756$	30.3955	1.10547
$757$	50.3410	1.82967	0.914837	−	0.403823i	$-0.132319\pi$
$757$	50.3410	1.82967	0.914837	+	0.403823i	$0.132319\pi$
$758$	−8.29882	−0.301427
$759$	−1.89692	−0.0688539
$760$	8.04857	0.291952
$761$	42.4834	1.54002	0.770011	−	0.638030i	$-0.220250\pi$
$761$	42.4834	1.54002	0.770011	+	0.638030i	$0.220250\pi$
$762$	7.57909	0.274561
$763$	−9.46064	−0.342498
$764$	17.7626	0.642630
$765$	9.51494	0.344013
$766$	7.09813	0.256466
$767$	−19.7040	−0.711469
$768$	5.21053	0.188019
$769$	49.9958	1.80289	0.901447	−	0.432889i	$-0.142506\pi$
$769$	49.9958	1.80289	0.901447	+	0.432889i	$0.142506\pi$
$770$	−0.0473625	−0.00170683
$771$	−106.085	−3.82056
$772$	41.2008	1.48285
$773$	−32.9819	−1.18628	−0.593139	−	0.805100i	$-0.702111\pi$
$773$	−32.9819	−1.18628	−0.593139	+	0.805100i	$0.702111\pi$
$774$	37.5032	1.34803
$775$	1.72587	0.0619952
$776$	−6.63019	−0.238010
$777$	14.6505	0.525583
$778$	7.85307	0.281546
$779$	−33.0881	−1.18550
$780$	19.1813	0.686801
$781$	−0.347914	−0.0124493
$782$	−3.73826	−0.133680
$783$	45.0580	1.61024
$784$	2.44667	0.0873809
$785$	−0.325555	−0.0116195
$786$	−7.58784	−0.270649
$787$	21.5306	0.767485	0.383742	−	0.923440i	$-0.374635\pi$
$787$	21.5306	0.767485	0.383742	+	0.923440i	$0.374635\pi$
$788$	−26.4810	−0.943346
$789$	−54.5306	−1.94134
$790$	2.42881	0.0864133
$791$	−13.2903	−0.472548
$792$	1.45583	0.0517307
$793$	−15.3405	−0.544759
$794$	−20.3130	−0.720880
$795$	10.0830	0.357607
$796$	34.3525	1.21759
$797$	−7.46757	−0.264515	−0.132258	−	0.991215i	$-0.542223\pi$
$797$	−7.46757	−0.264515	−0.132258	+	0.991215i	$0.542223\pi$
$798$	7.23752	0.256205
$799$	6.82034	0.241286
$800$	−5.15734	−0.182339
$801$	−142.504	−5.03514
$802$	8.94042	0.315697
$803$	−0.324581	−0.0114542
$804$	26.0933	0.920241
$805$	6.21965	0.219214
$806$	−2.97358	−0.104740
$807$	−24.4333	−0.860091
$808$	7.08213	0.249148
$809$	28.1337	0.989128	0.494564	−	0.869141i	$-0.335328\pi$
$809$	28.1337	0.989128	0.494564	+	0.869141i	$0.335328\pi$
$810$	−17.8198	−0.626124
$811$	30.4874	1.07056	0.535279	−	0.844676i	$-0.320207\pi$
$811$	30.4874	1.07056	0.535279	+	0.844676i	$0.320207\pi$
$812$	4.43079	0.155490
$813$	29.0290	1.01809
$814$	0.206938	0.00725317
$815$	11.3141	0.396315
$816$	−9.46949	−0.331499
$817$	−36.2172	−1.26708
$818$	15.3824	0.537834
$819$	27.2755	0.953083
$820$	13.8002	0.481925
$821$	12.9162	0.450780	0.225390	−	0.974269i	$-0.427634\pi$
$821$	12.9162	0.450780	0.225390	+	0.974269i	$0.427634\pi$
$822$	−20.4140	−0.712020
$823$	42.5988	1.48490	0.742450	−	0.669902i	$-0.233664\pi$
$823$	42.5988	1.48490	0.742450	+	0.669902i	$0.233664\pi$
$824$	−13.3049	−0.463500
$825$	−0.304988	−0.0106183
$826$	3.10084	0.107892
$827$	−0.0457268	−0.00159008	−0.000795038	−	1.00000i	$-0.500253\pi$
$827$	−0.0457268	−0.00159008	−0.000795038		1.00000i	$0.500253\pi$
$828$	−88.6392	−3.08043
$829$	−36.9490	−1.28329	−0.641646	−	0.767001i	$-0.721748\pi$
$829$	−36.9490	−1.28329	−0.641646	+	0.767001i	$0.721748\pi$
$830$	−2.99071	−0.103809
$831$	60.0372	2.08267
$832$	−7.30533	−0.253267
$833$	1.15426	0.0399929
$834$	6.17125	0.213693
$835$	−4.76972	−0.165063
$836$	−0.651840	−0.0225443
$837$	−30.3431	−1.04881
$838$	−1.89808	−0.0655680
$839$	−16.0926	−0.555580	−0.277790	−	0.960642i	$-0.589602\pi$
$839$	−16.0926	−0.555580	−0.277790	+	0.960642i	$0.589602\pi$
$840$	−6.51060	−0.224637
$841$	−22.4318	−0.773512
$842$	14.3559	0.494736
$843$	94.7257	3.26253
$844$	−8.39027	−0.288805
$845$	−2.05175	−0.0705823
$846$	−25.3630	−0.871996
$847$	−10.9917	−0.377680
$848$	−7.35728	−0.252650
$849$	70.4251	2.41698
$850$	−0.601040	−0.0206155
$851$	−27.1751	−0.931550
$852$	−22.1738	−0.759663
$853$	−0.619205	−0.0212012	−0.0106006	−	0.999944i	$-0.503374\pi$
$853$	−0.619205	−0.0212012	−0.0106006	+	0.999944i	$0.503374\pi$
$854$	2.41416	0.0826110
$855$	34.1700	1.16859
$856$	13.9490	0.476768
$857$	7.40403	0.252917	0.126458	−	0.991972i	$-0.459639\pi$
$857$	7.40403	0.252917	0.126458	+	0.991972i	$0.459639\pi$
$858$	0.525477	0.0179395
$859$	24.4176	0.833116	0.416558	−	0.909109i	$-0.363236\pi$
$859$	24.4176	0.833116	0.416558	+	0.909109i	$0.363236\pi$
$860$	15.1053	0.515087
$861$	26.7654	0.912162
$862$	14.8245	0.504926
$863$	14.7316	0.501470	0.250735	−	0.968056i	$-0.419328\pi$
$863$	14.7316	0.501470	0.250735	+	0.968056i	$0.419328\pi$
$864$	90.6726	3.08475
$865$	2.56762	0.0873016
$866$	9.49469	0.322643
$867$	52.5353	1.78419
$868$	−2.98379	−0.101276
$869$	−0.424260	−0.0143921
$870$	−4.47473	−0.151708
$871$	14.8935	0.504646
$872$	−18.3694	−0.622066
$873$	−28.1483	−0.952676
$874$	−13.4248	−0.454102
$875$	1.00000	0.0338062
$876$	−20.6868	−0.698941
$877$	−11.4629	−0.387075	−0.193537	−	0.981093i	$-0.561996\pi$
$877$	−11.4629	−0.387075	−0.193537	+	0.981093i	$0.561996\pi$
$878$	−11.0790	−0.373899
$879$	−56.1175	−1.89279
$880$	0.222542	0.00750188
$881$	28.5629	0.962309	0.481154	−	0.876636i	$-0.340218\pi$
$881$	28.5629	0.962309	0.481154	+	0.876636i	$0.340218\pi$
$882$	−4.29239	−0.144532
$883$	−3.18765	−0.107273	−0.0536365	−	0.998561i	$-0.517081\pi$
$883$	−3.18765	−0.107273	−0.0536365	+	0.998561i	$0.517081\pi$
$884$	−6.60294	−0.222081
$885$	19.9677	0.671207
$886$	−3.75224	−0.126059
$887$	15.5175	0.521027	0.260513	−	0.965470i	$-0.416108\pi$
$887$	15.5175	0.521027	0.260513	+	0.965470i	$0.416108\pi$
$888$	28.4463	0.954596
$889$	4.34082	0.145587
$890$	9.00172	0.301738
$891$	3.11273	0.104280
$892$	22.1573	0.741881
$893$	24.4932	0.819634
$894$	0.868560	0.0290490
$895$	−0.197229	−0.00659263
$896$	11.4643	0.382996
$897$	−69.0057	−2.30403
$898$	−0.999767	−0.0333627
$899$	−4.42314	−0.147520
$900$	−14.2515	−0.475049
$901$	−3.47095	−0.115634
$902$	0.378061	0.0125880
$903$	29.2966	0.974929
$904$	−25.8052	−0.858270
$905$	9.20081	0.305845
$906$	−10.6453	−0.353666
$907$	22.9699	0.762704	0.381352	−	0.924430i	$-0.375459\pi$
$907$	22.9699	0.762704	0.381352	+	0.924430i	$0.375459\pi$
$908$	−12.5564	−0.416700
$909$	30.0670	0.997259
$910$	−1.72294	−0.0571150
$911$	0.858403	0.0284402	0.0142201	−	0.999899i	$-0.495473\pi$
$911$	0.858403	0.0284402	0.0142201	+	0.999899i	$0.495473\pi$
$912$	−34.0068	−1.12608
$913$	0.522412	0.0172893
$914$	9.55724	0.316126
$915$	15.5459	0.513931
$916$	1.72886	0.0571231
$917$	−4.34583	−0.143512
$918$	10.5671	0.348765
$919$	43.3041	1.42847	0.714236	−	0.699905i	$-0.246775\pi$
$919$	43.3041	1.42847	0.714236	+	0.699905i	$0.246775\pi$
$920$	12.0765	0.398150
$921$	75.8451	2.49918
$922$	1.60513	0.0528622
$923$	−12.6563	−0.416588
$924$	0.527282	0.0173463
$925$	−4.36923	−0.143659
$926$	11.2084	0.368332
$927$	−56.4858	−1.85524
$928$	13.2174	0.433884
$929$	6.78197	0.222509	0.111255	−	0.993792i	$-0.464513\pi$
$929$	6.78197	0.222509	0.111255	+	0.993792i	$0.464513\pi$
$930$	3.01338	0.0988127
$931$	4.14519	0.135853
$932$	48.8085	1.59878
$933$	43.1308	1.41204
$934$	−0.111343	−0.00364324
$935$	0.104989	0.00343349
$936$	52.9599	1.73105
$937$	5.41322	0.176842	0.0884210	−	0.996083i	$-0.471818\pi$
$937$	5.41322	0.176842	0.0884210	+	0.996083i	$0.471818\pi$
$938$	−2.34381	−0.0765280
$939$	−59.9510	−1.95643
$940$	−10.2155	−0.333193
$941$	37.9753	1.23796	0.618980	−	0.785407i	$-0.287546\pi$
$941$	37.9753	1.23796	0.618980	+	0.785407i	$0.287546\pi$
$942$	−0.568419	−0.0185201
$943$	−49.6470	−1.61673
$944$	−14.5699	−0.474209
$945$	−17.5813	−0.571919
$946$	0.413814	0.0134542
$947$	11.9950	0.389786	0.194893	−	0.980825i	$-0.437564\pi$
$947$	11.9950	0.389786	0.194893	+	0.980825i	$0.437564\pi$
$948$	−27.0397	−0.878209
$949$	−11.8075	−0.383288
$950$	−2.15846	−0.0700295
$951$	43.2410	1.40218
$952$	2.24119	0.0726375
$953$	35.7300	1.15741	0.578705	−	0.815537i	$-0.303558\pi$
$953$	35.7300	1.15741	0.578705	+	0.815537i	$0.303558\pi$
$954$	12.9075	0.417895
$955$	−10.2742	−0.332465
$956$	−22.4054	−0.724644
$957$	0.781637	0.0252667
$958$	13.9093	0.449389
$959$	−11.6918	−0.377549
$960$	7.40311	0.238934
$961$	−28.0214	−0.903915
$962$	7.52793	0.242710
$963$	59.2202	1.90835
$964$	−8.49599	−0.273637
$965$	−23.8312	−0.767154
$966$	10.8595	0.349400
$967$	−15.4304	−0.496208	−0.248104	−	0.968733i	$-0.579808\pi$
$967$	−15.4304	−0.496208	−0.248104	+	0.968733i	$0.579808\pi$
$968$	−21.3422	−0.685966
$969$	−16.0434	−0.515389
$970$	1.77808	0.0570906
$971$	4.57003	0.146659	0.0733296	−	0.997308i	$-0.476637\pi$
$971$	4.57003	0.146659	0.0733296	+	0.997308i	$0.476637\pi$
$972$	107.199	3.43842
$973$	3.53450	0.113311
$974$	3.10913	0.0996231
$975$	−11.0948	−0.355318
$976$	−11.3434	−0.363093
$977$	−2.20390	−0.0705090	−0.0352545	−	0.999378i	$-0.511224\pi$
$977$	−2.20390	−0.0705090	−0.0352545	+	0.999378i	$0.511224\pi$
$978$	19.7544	0.631677
$979$	−1.57240	−0.0502542
$980$	−1.72886	−0.0552263
$981$	−77.9868	−2.48993
$982$	21.2722	0.678822
$983$	9.81775	0.313138	0.156569	−	0.987667i	$-0.449957\pi$
$983$	9.81775	0.313138	0.156569	+	0.987667i	$0.449957\pi$
$984$	51.9694	1.65672
$985$	15.3170	0.488042
$986$	1.54037	0.0490554
$987$	−19.8129	−0.630651
$988$	−23.7125	−0.754394
$989$	−54.3421	−1.72798
$990$	−0.390423	−0.0124085
$991$	−52.1818	−1.65761	−0.828805	−	0.559538i	$-0.810979\pi$
$991$	−52.1818	−1.65761	−0.828805	+	0.559538i	$0.810979\pi$
$992$	−8.90092	−0.282605
$993$	−101.416	−3.21834
$994$	1.99174	0.0631742
$995$	−19.8701	−0.629923
$996$	33.2952	1.05500
$997$	1.21486	0.0384751	0.0192376	−	0.999815i	$-0.493876\pi$
$997$	1.21486	0.0384751	0.0192376	+	0.999815i	$0.493876\pi$
$998$	−5.84429	−0.184998
$999$	76.8167	2.43037

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.h.1.17	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.h.1.17	✓	38	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.520713 q^{2} -3.35310 q^{3} -1.72886 q^{4} +1.00000 q^{5} +1.74600 q^{6} +1.00000 q^{7} +1.94166 q^{8} +8.24329 q^{9} +O(q^{10})\)	\(q-0.520713 q^{2} -3.35310 q^{3} -1.72886 q^{4} +1.00000 q^{5} +1.74600 q^{6} +1.00000 q^{7} +1.94166 q^{8} +8.24329 q^{9} -0.520713 q^{10} +0.0909571 q^{11} +5.79704 q^{12} +3.30881 q^{13} -0.520713 q^{14} -3.35310 q^{15} +2.44667 q^{16} +1.15426 q^{17} -4.29239 q^{18} +4.14519 q^{19} -1.72886 q^{20} -3.35310 q^{21} -0.0473625 q^{22} +6.21965 q^{23} -6.51060 q^{24} +1.00000 q^{25} -1.72294 q^{26} -17.5813 q^{27} -1.72886 q^{28} -2.56284 q^{29} +1.74600 q^{30} +1.72587 q^{31} -5.15734 q^{32} -0.304988 q^{33} -0.601040 q^{34} +1.00000 q^{35} -14.2515 q^{36} -4.36923 q^{37} -2.15846 q^{38} -11.0948 q^{39} +1.94166 q^{40} -7.98228 q^{41} +1.74600 q^{42} -8.73716 q^{43} -0.157252 q^{44} +8.24329 q^{45} -3.23865 q^{46} +5.90882 q^{47} -8.20392 q^{48} +1.00000 q^{49} -0.520713 q^{50} -3.87037 q^{51} -5.72047 q^{52} -3.00706 q^{53} +9.15480 q^{54} +0.0909571 q^{55} +1.94166 q^{56} -13.8993 q^{57} +1.33450 q^{58} -5.95499 q^{59} +5.79704 q^{60} -4.63627 q^{61} -0.898685 q^{62} +8.24329 q^{63} -2.20784 q^{64} +3.30881 q^{65} +0.158811 q^{66} +4.50115 q^{67} -1.99556 q^{68} -20.8551 q^{69} -0.520713 q^{70} -3.82503 q^{71} +16.0057 q^{72} -3.56851 q^{73} +2.27511 q^{74} -3.35310 q^{75} -7.16645 q^{76} +0.0909571 q^{77} +5.77720 q^{78} -4.66440 q^{79} +2.44667 q^{80} +34.2219 q^{81} +4.15647 q^{82} +5.74349 q^{83} +5.79704 q^{84} +1.15426 q^{85} +4.54955 q^{86} +8.59347 q^{87} +0.176608 q^{88} -17.2873 q^{89} -4.29239 q^{90} +3.30881 q^{91} -10.7529 q^{92} -5.78703 q^{93} -3.07680 q^{94} +4.14519 q^{95} +17.2931 q^{96} -3.41470 q^{97} -0.520713 q^{98} +0.749786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * q^99

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