LMFDB - Embedded newform 4015.2.a.f.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.754723 q^{2} -0.390285 q^{3} -1.43039 q^{4} -1.00000 q^{5} +0.294557 q^{6} +1.05438 q^{7} +2.58900 q^{8} -2.84768 q^{9} +O(q^{10})$	\(q-0.754723 q^{2} -0.390285 q^{3} -1.43039 q^{4} -1.00000 q^{5} +0.294557 q^{6} +1.05438 q^{7} +2.58900 q^{8} -2.84768 q^{9} +0.754723 q^{10} +1.00000 q^{11} +0.558261 q^{12} -2.40281 q^{13} -0.795767 q^{14} +0.390285 q^{15} +0.906810 q^{16} +3.66972 q^{17} +2.14921 q^{18} -6.12380 q^{19} +1.43039 q^{20} -0.411510 q^{21} -0.754723 q^{22} +8.20612 q^{23} -1.01045 q^{24} +1.00000 q^{25} +1.81346 q^{26} +2.28226 q^{27} -1.50818 q^{28} +0.129962 q^{29} -0.294557 q^{30} -9.62281 q^{31} -5.86238 q^{32} -0.390285 q^{33} -2.76963 q^{34} -1.05438 q^{35} +4.07330 q^{36} +3.15257 q^{37} +4.62177 q^{38} +0.937781 q^{39} -2.58900 q^{40} -2.61328 q^{41} +0.310576 q^{42} +1.73597 q^{43} -1.43039 q^{44} +2.84768 q^{45} -6.19335 q^{46} +6.15011 q^{47} -0.353915 q^{48} -5.88828 q^{49} -0.754723 q^{50} -1.43224 q^{51} +3.43696 q^{52} +6.86449 q^{53} -1.72248 q^{54} -1.00000 q^{55} +2.72979 q^{56} +2.39003 q^{57} -0.0980851 q^{58} +10.3841 q^{59} -0.558261 q^{60} +12.2775 q^{61} +7.26256 q^{62} -3.00254 q^{63} +2.61086 q^{64} +2.40281 q^{65} +0.294557 q^{66} -5.40210 q^{67} -5.24915 q^{68} -3.20272 q^{69} +0.795767 q^{70} +6.30972 q^{71} -7.37263 q^{72} +1.00000 q^{73} -2.37931 q^{74} -0.390285 q^{75} +8.75944 q^{76} +1.05438 q^{77} -0.707765 q^{78} -5.89919 q^{79} -0.906810 q^{80} +7.65230 q^{81} +1.97230 q^{82} -1.52632 q^{83} +0.588621 q^{84} -3.66972 q^{85} -1.31017 q^{86} -0.0507221 q^{87} +2.58900 q^{88} -13.3115 q^{89} -2.14921 q^{90} -2.53348 q^{91} -11.7380 q^{92} +3.75564 q^{93} -4.64163 q^{94} +6.12380 q^{95} +2.28800 q^{96} -2.84880 q^{97} +4.44402 q^{98} -2.84768 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * 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 $

$2$	−0.754723	−0.533670	−0.266835	−	0.963742i	$-0.585978\pi$
$2$	−0.754723	−0.533670	−0.266835	+	0.963742i	$0.585978\pi$
$3$	−0.390285	−0.225331	−0.112666	−	0.993633i	$-0.535939\pi$
$3$	−0.390285	−0.225331	−0.112666	+	0.993633i	$0.535939\pi$
$4$	−1.43039	−0.715197
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.294557	0.120252
$7$	1.05438	0.398519	0.199260	−	0.979947i	$-0.436146\pi$
$7$	1.05438	0.398519	0.199260	+	0.979947i	$0.436146\pi$
$8$	2.58900	0.915349
$9$	−2.84768	−0.949226
$10$	0.754723	0.238664
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.558261	0.161156
$13$	−2.40281	−0.666419	−0.333210	−	0.942853i	$-0.608132\pi$
$13$	−2.40281	−0.666419	−0.333210	+	0.942853i	$0.608132\pi$
$14$	−0.795767	−0.212678
$15$	0.390285	0.100771
$16$	0.906810	0.226703
$17$	3.66972	0.890039	0.445019	−	0.895521i	$-0.353197\pi$
$17$	3.66972	0.890039	0.445019	+	0.895521i	$0.353197\pi$
$18$	2.14921	0.506573
$19$	−6.12380	−1.40490	−0.702448	−	0.711735i	$-0.747909\pi$
$19$	−6.12380	−1.40490	−0.702448	+	0.711735i	$0.747909\pi$
$20$	1.43039	0.319846
$21$	−0.411510	−0.0897988
$22$	−0.754723	−0.160908
$23$	8.20612	1.71109	0.855547	−	0.517726i	$-0.173221\pi$
$23$	8.20612	1.71109	0.855547	+	0.517726i	$0.173221\pi$
$24$	−1.01045	−0.206257
$25$	1.00000	0.200000
$26$	1.81346	0.355648
$27$	2.28226	0.439221
$28$	−1.50818	−0.285020
$29$	0.129962	0.0241333	0.0120666	−	0.999927i	$-0.496159\pi$
$29$	0.129962	0.0241333	0.0120666	+	0.999927i	$0.496159\pi$
$30$	−0.294557	−0.0537785
$31$	−9.62281	−1.72831	−0.864154	−	0.503227i	$-0.832146\pi$
$31$	−9.62281	−1.72831	−0.864154	+	0.503227i	$0.832146\pi$
$32$	−5.86238	−1.03633
$33$	−0.390285	−0.0679399
$34$	−2.76963	−0.474987
$35$	−1.05438	−0.178223
$36$	4.07330	0.678883
$37$	3.15257	0.518279	0.259139	−	0.965840i	$-0.416561\pi$
$37$	3.15257	0.518279	0.259139	+	0.965840i	$0.416561\pi$
$38$	4.62177	0.749750
$39$	0.937781	0.150165
$40$	−2.58900	−0.409356
$41$	−2.61328	−0.408125	−0.204063	−	0.978958i	$-0.565415\pi$
$41$	−2.61328	−0.408125	−0.204063	+	0.978958i	$0.565415\pi$
$42$	0.310576	0.0479229
$43$	1.73597	0.264732	0.132366	−	0.991201i	$-0.457743\pi$
$43$	1.73597	0.264732	0.132366	+	0.991201i	$0.457743\pi$
$44$	−1.43039	−0.215640
$45$	2.84768	0.424507
$46$	−6.19335	−0.913159
$47$	6.15011	0.897085	0.448543	−	0.893761i	$-0.351943\pi$
$47$	6.15011	0.897085	0.448543	+	0.893761i	$0.351943\pi$
$48$	−0.353915	−0.0510832
$49$	−5.88828	−0.841182
$50$	−0.754723	−0.106734
$51$	−1.43224	−0.200554
$52$	3.43696	0.476621
$53$	6.86449	0.942910	0.471455	−	0.881890i	$-0.343729\pi$
$53$	6.86449	0.942910	0.471455	+	0.881890i	$0.343729\pi$
$54$	−1.72248	−0.234399
$55$	−1.00000	−0.134840
$56$	2.72979	0.364784
$57$	2.39003	0.316567
$58$	−0.0980851	−0.0128792
$59$	10.3841	1.35189	0.675947	−	0.736950i	$-0.263735\pi$
$59$	10.3841	1.35189	0.675947	+	0.736950i	$0.263735\pi$
$60$	−0.558261	−0.0720712
$61$	12.2775	1.57197	0.785984	−	0.618247i	$-0.212157\pi$
$61$	12.2775	1.57197	0.785984	+	0.618247i	$0.212157\pi$
$62$	7.26256	0.922346
$63$	−3.00254	−0.378285
$64$	2.61086	0.326357
$65$	2.40281	0.298032
$66$	0.294557	0.0362575
$67$	−5.40210	−0.659972	−0.329986	−	0.943986i	$-0.607044\pi$
$67$	−5.40210	−0.659972	−0.329986	+	0.943986i	$0.607044\pi$
$68$	−5.24915	−0.636553
$69$	−3.20272	−0.385563
$70$	0.795767	0.0951123
$71$	6.30972	0.748826	0.374413	−	0.927262i	$-0.377844\pi$
$71$	6.30972	0.748826	0.374413	+	0.927262i	$0.377844\pi$
$72$	−7.37263	−0.868873
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−2.37931	−0.276590
$75$	−0.390285	−0.0450662
$76$	8.75944	1.00478
$77$	1.05438	0.120158
$78$	−0.707765	−0.0801386
$79$	−5.89919	−0.663711	−0.331855	−	0.943330i	$-0.607675\pi$
$79$	−5.89919	−0.663711	−0.331855	+	0.943330i	$0.607675\pi$
$80$	−0.906810	−0.101384
$81$	7.65230	0.850256
$82$	1.97230	0.217804
$83$	−1.52632	−0.167535	−0.0837674	−	0.996485i	$-0.526695\pi$
$83$	−1.52632	−0.167535	−0.0837674	+	0.996485i	$0.526695\pi$
$84$	0.588621	0.0642238
$85$	−3.66972	−0.398037
$86$	−1.31017	−0.141280
$87$	−0.0507221	−0.00543798
$88$	2.58900	0.275988
$89$	−13.3115	−1.41102	−0.705508	−	0.708702i	$-0.749281\pi$
$89$	−13.3115	−1.41102	−0.705508	+	0.708702i	$0.749281\pi$
$90$	−2.14921	−0.226546
$91$	−2.53348	−0.265581
$92$	−11.7380	−1.22377
$93$	3.75564	0.389442
$94$	−4.64163	−0.478747
$95$	6.12380	0.628288
$96$	2.28800	0.233518
$97$	−2.84880	−0.289252	−0.144626	−	0.989486i	$-0.546198\pi$
$97$	−2.84880	−0.289252	−0.144626	+	0.989486i	$0.546198\pi$
$98$	4.44402	0.448914
$99$	−2.84768	−0.286202
$100$	−1.43039	−0.143039
$101$	−10.7361	−1.06828	−0.534141	−	0.845396i	$-0.679365\pi$
$101$	−10.7361	−1.06828	−0.534141	+	0.845396i	$0.679365\pi$
$102$	1.08094	0.107029
$103$	−1.93367	−0.190530	−0.0952649	−	0.995452i	$-0.530370\pi$
$103$	−1.93367	−0.190530	−0.0952649	+	0.995452i	$0.530370\pi$
$104$	−6.22087	−0.610006
$105$	0.411510	0.0401593
$106$	−5.18079	−0.503202
$107$	−4.85777	−0.469619	−0.234809	−	0.972041i	$-0.575447\pi$
$107$	−4.85777	−0.469619	−0.234809	+	0.972041i	$0.575447\pi$
$108$	−3.26453	−0.314130
$109$	−15.2074	−1.45660	−0.728301	−	0.685258i	$-0.759690\pi$
$109$	−15.2074	−1.45660	−0.728301	+	0.685258i	$0.759690\pi$
$110$	0.754723	0.0719600
$111$	−1.23040	−0.116784
$112$	0.956125	0.0903453
$113$	14.9222	1.40376	0.701882	−	0.712293i	$-0.252343\pi$
$113$	14.9222	1.40376	0.701882	+	0.712293i	$0.252343\pi$
$114$	−1.80381	−0.168942
$115$	−8.20612	−0.765224
$116$	−0.185896	−0.0172600
$117$	6.84243	0.632582
$118$	−7.83711	−0.721465
$119$	3.86929	0.354698
$120$	1.01045	0.0922408
$121$	1.00000	0.0909091
$122$	−9.26608	−0.838911
$123$	1.01992	0.0919633
$124$	13.7644	1.23608
$125$	−1.00000	−0.0894427
$126$	2.26609	0.201879
$127$	8.21181	0.728680	0.364340	−	0.931266i	$-0.381295\pi$
$127$	8.21181	0.728680	0.364340	+	0.931266i	$0.381295\pi$
$128$	9.75430	0.862166
$129$	−0.677521	−0.0596524
$130$	−1.81346	−0.159051
$131$	19.5192	1.70540	0.852702	−	0.522398i	$-0.174963\pi$
$131$	19.5192	1.70540	0.852702	+	0.522398i	$0.174963\pi$
$132$	0.558261	0.0485904
$133$	−6.45682	−0.559878
$134$	4.07709	0.352207
$135$	−2.28226	−0.196426
$136$	9.50090	0.814696
$137$	−10.7354	−0.917186	−0.458593	−	0.888647i	$-0.651646\pi$
$137$	−10.7354	−0.917186	−0.458593	+	0.888647i	$0.651646\pi$
$138$	2.41717	0.205763
$139$	−5.47195	−0.464125	−0.232062	−	0.972701i	$-0.574547\pi$
$139$	−5.47195	−0.464125	−0.232062	+	0.972701i	$0.574547\pi$
$140$	1.50818	0.127465
$141$	−2.40030	−0.202141
$142$	−4.76209	−0.399626
$143$	−2.40281	−0.200933
$144$	−2.58230	−0.215192
$145$	−0.129962	−0.0107927
$146$	−0.754723	−0.0624613
$147$	2.29811	0.189545
$148$	−4.50941	−0.370671
$149$	−5.33343	−0.436932	−0.218466	−	0.975845i	$-0.570105\pi$
$149$	−5.33343	−0.436932	−0.218466	+	0.975845i	$0.570105\pi$
$150$	0.294557	0.0240505
$151$	−2.88780	−0.235006	−0.117503	−	0.993073i	$-0.537489\pi$
$151$	−2.88780	−0.235006	−0.117503	+	0.993073i	$0.537489\pi$
$152$	−15.8545	−1.28597
$153$	−10.4502	−0.844848
$154$	−0.795767	−0.0641247
$155$	9.62281	0.772923
$156$	−1.34139	−0.107398
$157$	−2.30301	−0.183800	−0.0919002	−	0.995768i	$-0.529294\pi$
$157$	−2.30301	−0.183800	−0.0919002	+	0.995768i	$0.529294\pi$
$158$	4.45225	0.354202
$159$	−2.67911	−0.212467
$160$	5.86238	0.463462
$161$	8.65239	0.681904
$162$	−5.77537	−0.453756
$163$	−13.2629	−1.03883	−0.519413	−	0.854523i	$-0.673850\pi$
$163$	−13.2629	−1.03883	−0.519413	+	0.854523i	$0.673850\pi$
$164$	3.73801	0.291890
$165$	0.390285	0.0303837
$166$	1.15195	0.0894083
$167$	−9.62177	−0.744555	−0.372277	−	0.928122i	$-0.621423\pi$
$167$	−9.62177	−0.744555	−0.372277	+	0.928122i	$0.621423\pi$
$168$	−1.06540	−0.0821972
$169$	−7.22651	−0.555885
$170$	2.76963	0.212421
$171$	17.4386	1.33356
$172$	−2.48311	−0.189336
$173$	−12.2044	−0.927884	−0.463942	−	0.885866i	$-0.653565\pi$
$173$	−12.2044	−0.927884	−0.463942	+	0.885866i	$0.653565\pi$
$174$	0.0382811	0.00290209
$175$	1.05438	0.0797038
$176$	0.906810	0.0683534
$177$	−4.05276	−0.304624
$178$	10.0465	0.753016
$179$	1.71636	0.128287	0.0641435	−	0.997941i	$-0.479568\pi$
$179$	1.71636	0.128287	0.0641435	+	0.997941i	$0.479568\pi$
$180$	−4.07330	−0.303606
$181$	4.62329	0.343647	0.171823	−	0.985128i	$-0.445034\pi$
$181$	4.62329	0.343647	0.171823	+	0.985128i	$0.445034\pi$
$182$	1.91208	0.141733
$183$	−4.79171	−0.354213
$184$	21.2456	1.56625
$185$	−3.15257	−0.231781
$186$	−2.83447	−0.207833
$187$	3.66972	0.268357
$188$	−8.79707	−0.641592
$189$	2.40638	0.175038
$190$	−4.62177	−0.335298
$191$	−12.1686	−0.880488	−0.440244	−	0.897878i	$-0.645108\pi$
$191$	−12.1686	−0.880488	−0.440244	+	0.897878i	$0.645108\pi$
$192$	−1.01898	−0.0735384
$193$	20.0057	1.44004	0.720021	−	0.693952i	$-0.244132\pi$
$193$	20.0057	1.44004	0.720021	+	0.693952i	$0.244132\pi$
$194$	2.15005	0.154365
$195$	−0.937781	−0.0671559
$196$	8.42255	0.601611
$197$	−11.1108	−0.791609	−0.395805	−	0.918335i	$-0.629534\pi$
$197$	−11.1108	−0.791609	−0.395805	+	0.918335i	$0.629534\pi$
$198$	2.14921	0.152738
$199$	−7.24723	−0.513742	−0.256871	−	0.966446i	$-0.582692\pi$
$199$	−7.24723	−0.513742	−0.256871	+	0.966446i	$0.582692\pi$
$200$	2.58900	0.183070
$201$	2.10836	0.148712
$202$	8.10278	0.570109
$203$	0.137029	0.00961757
$204$	2.04866	0.143435
$205$	2.61328	0.182519
$206$	1.45938	0.101680
$207$	−23.3684	−1.62421
$208$	−2.17889	−0.151079
$209$	−6.12380	−0.423592
$210$	−0.310576	−0.0214318
$211$	−13.4910	−0.928758	−0.464379	−	0.885637i	$-0.653722\pi$
$211$	−13.4910	−0.928758	−0.464379	+	0.885637i	$0.653722\pi$
$212$	−9.81891	−0.674366
$213$	−2.46259	−0.168734
$214$	3.66627	0.250621
$215$	−1.73597	−0.118392
$216$	5.90877	0.402041
$217$	−10.1461	−0.688764
$218$	11.4773	0.777344
$219$	−0.390285	−0.0263730
$220$	1.43039	0.0964371
$221$	−8.81765	−0.593139
$222$	0.928611	0.0623243
$223$	−25.7365	−1.72345	−0.861723	−	0.507378i	$-0.830615\pi$
$223$	−25.7365	−1.72345	−0.861723	+	0.507378i	$0.830615\pi$
$224$	−6.18120	−0.412999
$225$	−2.84768	−0.189845
$226$	−11.2621	−0.749146
$227$	−3.30561	−0.219401	−0.109700	−	0.993965i	$-0.534989\pi$
$227$	−3.30561	−0.219401	−0.109700	+	0.993965i	$0.534989\pi$
$228$	−3.41868	−0.226407
$229$	20.1783	1.33342	0.666709	−	0.745318i	$-0.267702\pi$
$229$	20.1783	1.33342	0.666709	+	0.745318i	$0.267702\pi$
$230$	6.19335	0.408377
$231$	−0.411510	−0.0270754
$232$	0.336470	0.0220904
$233$	15.6252	1.02364	0.511821	−	0.859092i	$-0.328971\pi$
$233$	15.6252	1.02364	0.511821	+	0.859092i	$0.328971\pi$
$234$	−5.16414	−0.337590
$235$	−6.15011	−0.401189
$236$	−14.8533	−0.966870
$237$	2.30237	0.149555
$238$	−2.92025	−0.189291
$239$	−16.5553	−1.07087	−0.535437	−	0.844575i	$-0.679853\pi$
$239$	−16.5553	−1.07087	−0.535437	+	0.844575i	$0.679853\pi$
$240$	0.353915	0.0228451
$241$	7.63855	0.492042	0.246021	−	0.969264i	$-0.420877\pi$
$241$	7.63855	0.492042	0.246021	+	0.969264i	$0.420877\pi$
$242$	−0.754723	−0.0485154
$243$	−9.83336	−0.630811
$244$	−17.5616	−1.12427
$245$	5.88828	0.376188
$246$	−0.769759	−0.0490781
$247$	14.7143	0.936249
$248$	−24.9134	−1.58200
$249$	0.595698	0.0377508
$250$	0.754723	0.0477329
$251$	−16.0969	−1.01603	−0.508015	−	0.861348i	$-0.669621\pi$
$251$	−16.0969	−1.01603	−0.508015	+	0.861348i	$0.669621\pi$
$252$	4.29482	0.270548
$253$	8.20612	0.515914
$254$	−6.19764	−0.388875
$255$	1.43224	0.0896903
$256$	−12.5835	−0.786469
$257$	16.9632	1.05813	0.529067	−	0.848580i	$-0.322542\pi$
$257$	16.9632	1.05813	0.529067	+	0.848580i	$0.322542\pi$
$258$	0.511341	0.0318347
$259$	3.32401	0.206544
$260$	−3.43696	−0.213151
$261$	−0.370089	−0.0229079
$262$	−14.7316	−0.910122
$263$	−26.4907	−1.63349	−0.816745	−	0.576999i	$-0.804224\pi$
$263$	−26.4907	−1.63349	−0.816745	+	0.576999i	$0.804224\pi$
$264$	−1.01045	−0.0621887
$265$	−6.86449	−0.421682
$266$	4.87311	0.298790
$267$	5.19528	0.317946
$268$	7.72713	0.472010
$269$	−25.2676	−1.54059	−0.770295	−	0.637687i	$-0.779891\pi$
$269$	−25.2676	−1.54059	−0.770295	+	0.637687i	$0.779891\pi$
$270$	1.72248	0.104827
$271$	−17.8688	−1.08545	−0.542725	−	0.839911i	$-0.682607\pi$
$271$	−17.8688	−1.08545	−0.542725	+	0.839911i	$0.682607\pi$
$272$	3.32774	0.201774
$273$	0.988780	0.0598437
$274$	8.10224	0.489474
$275$	1.00000	0.0603023
$276$	4.58116	0.275753
$277$	29.4088	1.76700	0.883500	−	0.468430i	$-0.155180\pi$
$277$	29.4088	1.76700	0.883500	+	0.468430i	$0.155180\pi$
$278$	4.12981	0.247689
$279$	27.4027	1.64055
$280$	−2.72979	−0.163136
$281$	−1.17474	−0.0700792	−0.0350396	−	0.999386i	$-0.511156\pi$
$281$	−1.17474	−0.0700792	−0.0350396	+	0.999386i	$0.511156\pi$
$282$	1.81156	0.107877
$283$	13.4919	0.802010	0.401005	−	0.916076i	$-0.368661\pi$
$283$	13.4919	0.802010	0.401005	+	0.916076i	$0.368661\pi$
$284$	−9.02537	−0.535557
$285$	−2.39003	−0.141573
$286$	1.81346	0.107232
$287$	−2.75539	−0.162646
$288$	16.6942	0.983714
$289$	−3.53312	−0.207831
$290$	0.0980851	0.00575975
$291$	1.11184	0.0651775
$292$	−1.43039	−0.0837074
$293$	−31.0364	−1.81317	−0.906583	−	0.422027i	$-0.861319\pi$
$293$	−31.0364	−1.81317	−0.906583	+	0.422027i	$0.861319\pi$
$294$	−1.73443	−0.101154
$295$	−10.3841	−0.604585
$296$	8.16198	0.474406
$297$	2.28226	0.132430
$298$	4.02527	0.233177
$299$	−19.7177	−1.14031
$300$	0.558261	0.0322312
$301$	1.83037	0.105501
$302$	2.17949	0.125416
$303$	4.19014	0.240717
$304$	−5.55312	−0.318493
$305$	−12.2775	−0.703005
$306$	7.88700	0.450870
$307$	−17.4604	−0.996517	−0.498258	−	0.867029i	$-0.666027\pi$
$307$	−17.4604	−0.996517	−0.498258	+	0.867029i	$0.666027\pi$
$308$	−1.50818	−0.0859366
$309$	0.754681	0.0429323
$310$	−7.26256	−0.412486
$311$	−22.8161	−1.29378	−0.646892	−	0.762581i	$-0.723932\pi$
$311$	−22.8161	−1.29378	−0.646892	+	0.762581i	$0.723932\pi$
$312$	2.42791	0.137453
$313$	−31.1336	−1.75977	−0.879886	−	0.475185i	$-0.842381\pi$
$313$	−31.1336	−1.75977	−0.879886	+	0.475185i	$0.842381\pi$
$314$	1.73814	0.0980887
$315$	3.00254	0.169174
$316$	8.43816	0.474684
$317$	−20.1493	−1.13170	−0.565850	−	0.824508i	$-0.691452\pi$
$317$	−20.1493	−1.13170	−0.565850	+	0.824508i	$0.691452\pi$
$318$	2.02198	0.113387
$319$	0.129962	0.00727646
$320$	−2.61086	−0.145951
$321$	1.89592	0.105820
$322$	−6.53016	−0.363911
$323$	−22.4726	−1.25041
$324$	−10.9458	−0.608100
$325$	−2.40281	−0.133284
$326$	10.0098	0.554391
$327$	5.93521	0.328218
$328$	−6.76576	−0.373577
$329$	6.48457	0.357506
$330$	−0.294557	−0.0162148
$331$	1.67093	0.0918424	0.0459212	−	0.998945i	$-0.485378\pi$
$331$	1.67093	0.0918424	0.0459212	+	0.998945i	$0.485378\pi$
$332$	2.18323	0.119820
$333$	−8.97749	−0.491964
$334$	7.26177	0.397346
$335$	5.40210	0.295149
$336$	−0.373161	−0.0203576
$337$	2.25667	0.122929	0.0614644	−	0.998109i	$-0.480423\pi$
$337$	2.25667	0.122929	0.0614644	+	0.998109i	$0.480423\pi$
$338$	5.45401	0.296659
$339$	−5.82392	−0.316312
$340$	5.24915	0.284675
$341$	−9.62281	−0.521105
$342$	−13.1613	−0.711682
$343$	−13.5892	−0.733747
$344$	4.49441	0.242322
$345$	3.20272	0.172429
$346$	9.21095	0.495184
$347$	34.4718	1.85055	0.925273	−	0.379302i	$-0.123836\pi$
$347$	34.4718	1.85055	0.925273	+	0.379302i	$0.123836\pi$
$348$	0.0725525	0.00388922
$349$	13.5767	0.726744	0.363372	−	0.931644i	$-0.381625\pi$
$349$	13.5767	0.726744	0.363372	+	0.931644i	$0.381625\pi$
$350$	−0.795767	−0.0425355
$351$	−5.48384	−0.292706
$352$	−5.86238	−0.312466
$353$	−17.8692	−0.951081	−0.475541	−	0.879694i	$-0.657747\pi$
$353$	−17.8692	−0.951081	−0.475541	+	0.879694i	$0.657747\pi$
$354$	3.05871	0.162569
$355$	−6.30972	−0.334885
$356$	19.0407	1.00915
$357$	−1.51013	−0.0799244
$358$	−1.29538	−0.0684629
$359$	−16.3815	−0.864584	−0.432292	−	0.901734i	$-0.642295\pi$
$359$	−16.3815	−0.864584	−0.432292	+	0.901734i	$0.642295\pi$
$360$	7.37263	0.388572
$361$	18.5009	0.973731
$362$	−3.48931	−0.183394
$363$	−0.390285	−0.0204847
$364$	3.62387	0.189943
$365$	−1.00000	−0.0523424
$366$	3.61641	0.189033
$367$	−1.11005	−0.0579439	−0.0289720	−	0.999580i	$-0.509223\pi$
$367$	−1.11005	−0.0579439	−0.0289720	+	0.999580i	$0.509223\pi$
$368$	7.44139	0.387909
$369$	7.44177	0.387403
$370$	2.37931	0.123695
$371$	7.23780	0.375768
$372$	−5.37204	−0.278527
$373$	20.4867	1.06076	0.530381	−	0.847760i	$-0.322049\pi$
$373$	20.4867	1.06076	0.530381	+	0.847760i	$0.322049\pi$
$374$	−2.76963	−0.143214
$375$	0.390285	0.0201542
$376$	15.9226	0.821146
$377$	−0.312273	−0.0160829
$378$	−1.81615	−0.0934126
$379$	−33.7183	−1.73199	−0.865997	−	0.500049i	$-0.833315\pi$
$379$	−33.7183	−1.73199	−0.865997	+	0.500049i	$0.833315\pi$
$380$	−8.75944	−0.449350
$381$	−3.20495	−0.164194
$382$	9.18391	0.469890
$383$	17.9095	0.915133	0.457566	−	0.889175i	$-0.348721\pi$
$383$	17.9095	0.915133	0.457566	+	0.889175i	$0.348721\pi$
$384$	−3.80696	−0.194273
$385$	−1.05438	−0.0537363
$386$	−15.0988	−0.768507
$387$	−4.94347	−0.251291
$388$	4.07490	0.206872
$389$	9.04949	0.458828	0.229414	−	0.973329i	$-0.426319\pi$
$389$	9.04949	0.458828	0.229414	+	0.973329i	$0.426319\pi$
$390$	0.707765	0.0358391
$391$	30.1142	1.52294
$392$	−15.2447	−0.769975
$393$	−7.61807	−0.384281
$394$	8.38555	0.422458
$395$	5.89919	0.296820
$396$	4.07330	0.204691
$397$	−13.2363	−0.664310	−0.332155	−	0.943225i	$-0.607776\pi$
$397$	−13.2363	−0.664310	−0.332155	+	0.943225i	$0.607776\pi$
$398$	5.46965	0.274169
$399$	2.52000	0.126158
$400$	0.906810	0.0453405
$401$	17.5305	0.875433	0.437717	−	0.899113i	$-0.355787\pi$
$401$	17.5305	0.875433	0.437717	+	0.899113i	$0.355787\pi$
$402$	−1.59123	−0.0793633
$403$	23.1218	1.15178
$404$	15.3568	0.764031
$405$	−7.65230	−0.380246
$406$	−0.103419	−0.00513261
$407$	3.15257	0.156267
$408$	−3.70806	−0.183576
$409$	−29.7021	−1.46867	−0.734336	−	0.678786i	$-0.762506\pi$
$409$	−29.7021	−1.46867	−0.734336	+	0.678786i	$0.762506\pi$
$410$	−1.97230	−0.0974049
$411$	4.18986	0.206671
$412$	2.76590	0.136266
$413$	10.9488	0.538756
$414$	17.6366	0.866794
$415$	1.52632	0.0749239
$416$	14.0862	0.690632
$417$	2.13562	0.104582
$418$	4.62177	0.226058
$419$	11.3375	0.553872	0.276936	−	0.960888i	$-0.410681\pi$
$419$	11.3375	0.553872	0.276936	+	0.960888i	$0.410681\pi$
$420$	−0.588621	−0.0287218
$421$	23.5083	1.14572	0.572861	−	0.819652i	$-0.305833\pi$
$421$	23.5083	1.14572	0.572861	+	0.819652i	$0.305833\pi$
$422$	10.1820	0.495650
$423$	−17.5135	−0.851537
$424$	17.7721	0.863091
$425$	3.66972	0.178008
$426$	1.85857	0.0900481
$427$	12.9451	0.626459
$428$	6.94853	0.335870
$429$	0.937781	0.0452765
$430$	1.31017	0.0631822
$431$	−11.3406	−0.546258	−0.273129	−	0.961977i	$-0.588059\pi$
$431$	−11.3406	−0.546258	−0.273129	+	0.961977i	$0.588059\pi$
$432$	2.06958	0.0995726
$433$	−36.7247	−1.76487	−0.882437	−	0.470430i	$-0.844099\pi$
$433$	−36.7247	−1.76487	−0.882437	+	0.470430i	$0.844099\pi$
$434$	7.65752	0.367573
$435$	0.0507221	0.00243194
$436$	21.7525	1.04176
$437$	−50.2526	−2.40391
$438$	0.294557	0.0140745
$439$	−2.17048	−0.103591	−0.0517956	−	0.998658i	$-0.516494\pi$
$439$	−2.17048	−0.103591	−0.0517956	+	0.998658i	$0.516494\pi$
$440$	−2.58900	−0.123426
$441$	16.7679	0.798472
$442$	6.65488	0.316540
$443$	−18.2573	−0.867432	−0.433716	−	0.901050i	$-0.642798\pi$
$443$	−18.2573	−0.867432	−0.433716	+	0.901050i	$0.642798\pi$
$444$	1.75996	0.0835238
$445$	13.3115	0.631025
$446$	19.4240	0.919752
$447$	2.08156	0.0984544
$448$	2.75284	0.130060
$449$	10.0197	0.472857	0.236428	−	0.971649i	$-0.424023\pi$
$449$	10.0197	0.472857	0.236428	+	0.971649i	$0.424023\pi$
$450$	2.14921	0.101315
$451$	−2.61328	−0.123054
$452$	−21.3446	−1.00397
$453$	1.12707	0.0529542
$454$	2.49482	0.117088
$455$	2.53348	0.118771
$456$	6.18777	0.289769
$457$	−31.6046	−1.47840	−0.739201	−	0.673485i	$-0.764797\pi$
$457$	−31.6046	−1.47840	−0.739201	+	0.673485i	$0.764797\pi$
$458$	−15.2290	−0.711605
$459$	8.37527	0.390924
$460$	11.7380	0.547286
$461$	−30.8136	−1.43513	−0.717566	−	0.696490i	$-0.754744\pi$
$461$	−30.8136	−1.43513	−0.717566	+	0.696490i	$0.754744\pi$
$462$	0.310576	0.0144493
$463$	−25.6780	−1.19336	−0.596678	−	0.802481i	$-0.703513\pi$
$463$	−25.6780	−1.19336	−0.596678	+	0.802481i	$0.703513\pi$
$464$	0.117851	0.00547108
$465$	−3.75564	−0.174164
$466$	−11.7927	−0.546286
$467$	17.5230	0.810869	0.405435	−	0.914124i	$-0.367120\pi$
$467$	17.5230	0.810869	0.405435	+	0.914124i	$0.367120\pi$
$468$	−9.78736	−0.452421
$469$	−5.69589	−0.263012
$470$	4.64163	0.214102
$471$	0.898832	0.0414160
$472$	26.8844	1.23745
$473$	1.73597	0.0798198
$474$	−1.73765	−0.0798129
$475$	−6.12380	−0.280979
$476$	−5.53461	−0.253678
$477$	−19.5478	−0.895034
$478$	12.4947	0.571493
$479$	24.3336	1.11183	0.555915	−	0.831239i	$-0.312368\pi$
$479$	24.3336	1.11183	0.555915	+	0.831239i	$0.312368\pi$
$480$	−2.28800	−0.104432
$481$	−7.57502	−0.345391
$482$	−5.76499	−0.262588
$483$	−3.37690	−0.153654
$484$	−1.43039	−0.0650179
$485$	2.84880	0.129357
$486$	7.42147	0.336645
$487$	−14.0831	−0.638168	−0.319084	−	0.947726i	$-0.603375\pi$
$487$	−14.0831	−0.638168	−0.319084	+	0.947726i	$0.603375\pi$
$488$	31.7863	1.43890
$489$	5.17629	0.234080
$490$	−4.44402	−0.200760
$491$	26.0749	1.17674	0.588372	−	0.808590i	$-0.299769\pi$
$491$	26.0749	1.17674	0.588372	+	0.808590i	$0.299769\pi$
$492$	−1.45889	−0.0657719
$493$	0.476923	0.0214796
$494$	−11.1052	−0.499648
$495$	2.84768	0.127994
$496$	−8.72607	−0.391812
$497$	6.65286	0.298421
$498$	−0.449587	−0.0201465
$499$	−18.9578	−0.848666	−0.424333	−	0.905506i	$-0.639491\pi$
$499$	−18.9578	−0.848666	−0.424333	+	0.905506i	$0.639491\pi$
$500$	1.43039	0.0639691
$501$	3.75523	0.167771
$502$	12.1487	0.542224
$503$	−24.4015	−1.08801	−0.544004	−	0.839083i	$-0.683092\pi$
$503$	−24.4015	−1.08801	−0.544004	+	0.839083i	$0.683092\pi$
$504$	−7.77357	−0.346262
$505$	10.7361	0.477750
$506$	−6.19335	−0.275328
$507$	2.82040	0.125258
$508$	−11.7461	−0.521150
$509$	8.06309	0.357390	0.178695	−	0.983904i	$-0.442812\pi$
$509$	8.06309	0.357390	0.178695	+	0.983904i	$0.442812\pi$
$510$	−1.08094	−0.0478650
$511$	1.05438	0.0466431
$512$	−10.0115	−0.442451
$513$	−13.9761	−0.617060
$514$	−12.8025	−0.564694
$515$	1.93367	0.0852075
$516$	0.969122	0.0426632
$517$	6.15011	0.270481
$518$	−2.50871	−0.110226
$519$	4.76320	0.209081
$520$	6.22087	0.272803
$521$	13.1579	0.576458	0.288229	−	0.957562i	$-0.406934\pi$
$521$	13.1579	0.576458	0.288229	+	0.957562i	$0.406934\pi$
$522$	0.279315	0.0122253
$523$	8.23078	0.359907	0.179953	−	0.983675i	$-0.442405\pi$
$523$	8.23078	0.359907	0.179953	+	0.983675i	$0.442405\pi$
$524$	−27.9202	−1.21970
$525$	−0.411510	−0.0179598
$526$	19.9932	0.871744
$527$	−35.3131	−1.53826
$528$	−0.353915	−0.0154022
$529$	44.3403	1.92784
$530$	5.18079	0.225039
$531$	−29.5705	−1.28325
$532$	9.23580	0.400423
$533$	6.27920	0.271983
$534$	−3.92100	−0.169678
$535$	4.85777	0.210020
$536$	−13.9860	−0.604105
$537$	−0.669871	−0.0289071
$538$	19.0700	0.822167
$539$	−5.88828	−0.253626
$540$	3.26453	0.140483
$541$	22.3336	0.960196	0.480098	−	0.877215i	$-0.340601\pi$
$541$	22.3336	0.960196	0.480098	+	0.877215i	$0.340601\pi$
$542$	13.4860	0.579272
$543$	−1.80440	−0.0774343
$544$	−21.5133	−0.922377
$545$	15.2074	0.651412
$546$	−0.746255	−0.0319368
$547$	40.1023	1.71465	0.857325	−	0.514776i	$-0.172125\pi$
$547$	40.1023	1.71465	0.857325	+	0.514776i	$0.172125\pi$
$548$	15.3558	0.655968
$549$	−34.9622	−1.49215
$550$	−0.754723	−0.0321815
$551$	−0.795859	−0.0339047
$552$	−8.29184	−0.352924
$553$	−6.22000	−0.264501
$554$	−22.1955	−0.942995
$555$	1.23040	0.0522276
$556$	7.82704	0.331940
$557$	−41.5500	−1.76053	−0.880265	−	0.474482i	$-0.842636\pi$
$557$	−41.5500	−1.76053	−0.880265	+	0.474482i	$0.842636\pi$
$558$	−20.6814	−0.875515
$559$	−4.17119	−0.176423
$560$	−0.956125	−0.0404037
$561$	−1.43224	−0.0604692
$562$	0.886604	0.0373991
$563$	27.3259	1.15165	0.575824	−	0.817574i	$-0.304681\pi$
$563$	27.3259	1.15165	0.575824	+	0.817574i	$0.304681\pi$
$564$	3.43337	0.144571
$565$	−14.9222	−0.627782
$566$	−10.1826	−0.428009
$567$	8.06845	0.338843
$568$	16.3358	0.685436
$569$	−2.02410	−0.0848546	−0.0424273	−	0.999100i	$-0.513509\pi$
$569$	−2.02410	−0.0848546	−0.0424273	+	0.999100i	$0.513509\pi$
$570$	1.80381	0.0755532
$571$	−27.4668	−1.14945	−0.574725	−	0.818346i	$-0.694891\pi$
$571$	−27.4668	−1.14945	−0.574725	+	0.818346i	$0.694891\pi$
$572$	3.43696	0.143707
$573$	4.74922	0.198401
$574$	2.07956	0.0867991
$575$	8.20612	0.342219
$576$	−7.43488	−0.309787
$577$	19.5659	0.814540	0.407270	−	0.913308i	$-0.366481\pi$
$577$	19.5659	0.814540	0.407270	+	0.913308i	$0.366481\pi$
$578$	2.66653	0.110913
$579$	−7.80793	−0.324487
$580$	0.185896	0.00771892
$581$	−1.60932	−0.0667659
$582$	−0.839134	−0.0347832
$583$	6.86449	0.284298
$584$	2.58900	0.107133
$585$	−6.84243	−0.282899
$586$	23.4239	0.967632
$587$	17.2842	0.713394	0.356697	−	0.934220i	$-0.383903\pi$
$587$	17.2842	0.713394	0.356697	+	0.934220i	$0.383903\pi$
$588$	−3.28720	−0.135562
$589$	58.9282	2.42809
$590$	7.83711	0.322649
$591$	4.33637	0.178374
$592$	2.85878	0.117495
$593$	22.7842	0.935635	0.467818	−	0.883825i	$-0.345040\pi$
$593$	22.7842	0.935635	0.467818	+	0.883825i	$0.345040\pi$
$594$	−1.72248	−0.0706740
$595$	−3.86929	−0.158626
$596$	7.62891	0.312492
$597$	2.82849	0.115762
$598$	14.8814	0.608547
$599$	45.3129	1.85144	0.925718	−	0.378216i	$-0.123462\pi$
$599$	45.3129	1.85144	0.925718	+	0.378216i	$0.123462\pi$
$600$	−1.01045	−0.0412513
$601$	−1.76576	−0.0720269	−0.0360134	−	0.999351i	$-0.511466\pi$
$601$	−1.76576	−0.0720269	−0.0360134	+	0.999351i	$0.511466\pi$
$602$	−1.38142	−0.0563026
$603$	15.3835	0.626463
$604$	4.13069	0.168075
$605$	−1.00000	−0.0406558
$606$	−3.16239	−0.128463
$607$	9.74802	0.395660	0.197830	−	0.980236i	$-0.436611\pi$
$607$	9.74802	0.395660	0.197830	+	0.980236i	$0.436611\pi$
$608$	35.9000	1.45594
$609$	−0.0534805	−0.00216714
$610$	9.26608	0.375173
$611$	−14.7775	−0.597835
$612$	14.9479	0.604232
$613$	11.1032	0.448454	0.224227	−	0.974537i	$-0.428014\pi$
$613$	11.1032	0.448454	0.224227	+	0.974537i	$0.428014\pi$
$614$	13.1778	0.531811
$615$	−1.01992	−0.0411273
$616$	2.72979	0.109987
$617$	−28.6901	−1.15502	−0.577509	−	0.816384i	$-0.695975\pi$
$617$	−28.6901	−1.15502	−0.577509	+	0.816384i	$0.695975\pi$
$618$	−0.569575	−0.0229117
$619$	17.6884	0.710959	0.355479	−	0.934684i	$-0.384318\pi$
$619$	17.6884	0.710959	0.355479	+	0.934684i	$0.384318\pi$
$620$	−13.7644	−0.552792
$621$	18.7285	0.751549
$622$	17.2199	0.690454
$623$	−14.0354	−0.562317
$624$	0.850389	0.0340428
$625$	1.00000	0.0400000
$626$	23.4972	0.939137
$627$	2.39003	0.0954485
$628$	3.29421	0.131453
$629$	11.5690	0.461288
$630$	−2.26609	−0.0902831
$631$	24.6823	0.982588	0.491294	−	0.870994i	$-0.336524\pi$
$631$	24.6823	0.982588	0.491294	+	0.870994i	$0.336524\pi$
$632$	−15.2730	−0.607527
$633$	5.26533	0.209278
$634$	15.2072	0.603954
$635$	−8.21181	−0.325876
$636$	3.83218	0.151956
$637$	14.1484	0.560580
$638$	−0.0980851	−0.00388322
$639$	−17.9680	−0.710805
$640$	−9.75430	−0.385572
$641$	8.06779	0.318658	0.159329	−	0.987226i	$-0.449067\pi$
$641$	8.06779	0.318658	0.159329	+	0.987226i	$0.449067\pi$
$642$	−1.43089	−0.0564728
$643$	−24.1719	−0.953245	−0.476623	−	0.879108i	$-0.658139\pi$
$643$	−24.1719	−0.953245	−0.476623	+	0.879108i	$0.658139\pi$
$644$	−12.3763	−0.487695
$645$	0.677521	0.0266774
$646$	16.9606	0.667307
$647$	−19.7968	−0.778294	−0.389147	−	0.921176i	$-0.627230\pi$
$647$	−19.7968	−0.778294	−0.389147	+	0.921176i	$0.627230\pi$
$648$	19.8118	0.778280
$649$	10.3841	0.407611
$650$	1.81346	0.0711296
$651$	3.95988	0.155200
$652$	18.9711	0.742965
$653$	40.1962	1.57300	0.786499	−	0.617591i	$-0.211891\pi$
$653$	40.1962	1.57300	0.786499	+	0.617591i	$0.211891\pi$
$654$	−4.47944	−0.175160
$655$	−19.5192	−0.762680
$656$	−2.36975	−0.0925230
$657$	−2.84768	−0.111098
$658$	−4.89405	−0.190790
$659$	−18.2446	−0.710709	−0.355355	−	0.934732i	$-0.615640\pi$
$659$	−18.2446	−0.710709	−0.355355	+	0.934732i	$0.615640\pi$
$660$	−0.558261	−0.0217303
$661$	−2.93163	−0.114027	−0.0570137	−	0.998373i	$-0.518158\pi$
$661$	−2.93163	−0.114027	−0.0570137	+	0.998373i	$0.518158\pi$
$662$	−1.26109	−0.0490135
$663$	3.44140	0.133653
$664$	−3.95163	−0.153353
$665$	6.45682	0.250385
$666$	6.77552	0.262546
$667$	1.06648	0.0412943
$668$	13.7629	0.532503
$669$	10.0446	0.388346
$670$	−4.07709	−0.157512
$671$	12.2775	0.473966
$672$	2.41243	0.0930615
$673$	10.3949	0.400694	0.200347	−	0.979725i	$-0.435793\pi$
$673$	10.3949	0.400694	0.200347	+	0.979725i	$0.435793\pi$
$674$	−1.70316	−0.0656034
$675$	2.28226	0.0878443
$676$	10.3367	0.397567
$677$	−15.3816	−0.591164	−0.295582	−	0.955317i	$-0.595514\pi$
$677$	−15.3816	−0.591164	−0.295582	+	0.955317i	$0.595514\pi$
$678$	4.39545	0.168806
$679$	−3.00373	−0.115272
$680$	−9.50090	−0.364343
$681$	1.29013	0.0494379
$682$	7.26256	0.278098
$683$	−25.6002	−0.979563	−0.489782	−	0.871845i	$-0.662923\pi$
$683$	−25.6002	−0.979563	−0.489782	+	0.871845i	$0.662923\pi$
$684$	−24.9440	−0.953760
$685$	10.7354	0.410178
$686$	10.2561	0.391578
$687$	−7.87528	−0.300461
$688$	1.57419	0.0600155
$689$	−16.4941	−0.628373
$690$	−2.41717	−0.0920201
$691$	17.6858	0.672801	0.336401	−	0.941719i	$-0.390790\pi$
$691$	17.6858	0.672801	0.336401	+	0.941719i	$0.390790\pi$
$692$	17.4571	0.663619
$693$	−3.00254	−0.114057
$694$	−26.0167	−0.987580
$695$	5.47195	0.207563
$696$	−0.131319	−0.00497765
$697$	−9.59000	−0.363247
$698$	−10.2467	−0.387842
$699$	−6.09828	−0.230658
$700$	−1.50818	−0.0570039
$701$	−5.93590	−0.224196	−0.112098	−	0.993697i	$-0.535757\pi$
$701$	−5.93590	−0.224196	−0.112098	+	0.993697i	$0.535757\pi$
$702$	4.13878	0.156208
$703$	−19.3057	−0.728127
$704$	2.61086	0.0984003
$705$	2.40030	0.0904004
$706$	13.4863	0.507563
$707$	−11.3199	−0.425731
$708$	5.79704	0.217866
$709$	34.7824	1.30628	0.653140	−	0.757237i	$-0.273451\pi$
$709$	34.7824	1.30628	0.653140	+	0.757237i	$0.273451\pi$
$710$	4.76209	0.178718
$711$	16.7990	0.630011
$712$	−34.4634	−1.29157
$713$	−78.9659	−2.95730
$714$	1.13973	0.0426533
$715$	2.40281	0.0898600
$716$	−2.45507	−0.0917504
$717$	6.46129	0.241301
$718$	12.3635	0.461402
$719$	−9.87632	−0.368324	−0.184162	−	0.982896i	$-0.558957\pi$
$719$	−9.87632	−0.368324	−0.184162	+	0.982896i	$0.558957\pi$
$720$	2.58230	0.0962368
$721$	−2.03882	−0.0759298
$722$	−13.9630	−0.519651
$723$	−2.98121	−0.110872
$724$	−6.61313	−0.245775
$725$	0.129962	0.00482665
$726$	0.294557	0.0109320
$727$	22.6805	0.841173	0.420586	−	0.907252i	$-0.361824\pi$
$727$	22.6805	0.841173	0.420586	+	0.907252i	$0.361824\pi$
$728$	−6.55917	−0.243099
$729$	−19.1191	−0.708114
$730$	0.754723	0.0279336
$731$	6.37051	0.235622
$732$	6.85403	0.253332
$733$	−19.4483	−0.718338	−0.359169	−	0.933273i	$-0.616940\pi$
$733$	−19.4483	−0.718338	−0.359169	+	0.933273i	$0.616940\pi$
$734$	0.837777	0.0309229
$735$	−2.29811	−0.0847670
$736$	−48.1074	−1.77326
$737$	−5.40210	−0.198989
$738$	−5.61647	−0.206745
$739$	−13.8789	−0.510543	−0.255272	−	0.966869i	$-0.582165\pi$
$739$	−13.8789	−0.510543	−0.255272	+	0.966869i	$0.582165\pi$
$740$	4.50941	0.165769
$741$	−5.74278	−0.210966
$742$	−5.46253	−0.200536
$743$	8.33756	0.305875	0.152938	−	0.988236i	$-0.451127\pi$
$743$	8.33756	0.305875	0.152938	+	0.988236i	$0.451127\pi$
$744$	9.72334	0.356475
$745$	5.33343	0.195402
$746$	−15.4618	−0.566096
$747$	4.34645	0.159028
$748$	−5.24915	−0.191928
$749$	−5.12195	−0.187152
$750$	−0.294557	−0.0107557
$751$	47.4908	1.73296	0.866482	−	0.499208i	$-0.166376\pi$
$751$	47.4908	1.73296	0.866482	+	0.499208i	$0.166376\pi$
$752$	5.57698	0.203372
$753$	6.28240	0.228943
$754$	0.235680	0.00858295
$755$	2.88780	0.105098
$756$	−3.44207	−0.125187
$757$	0.489642	0.0177963	0.00889816	−	0.999960i	$-0.497168\pi$
$757$	0.489642	0.0177963	0.00889816	+	0.999960i	$0.497168\pi$
$758$	25.4480	0.924313
$759$	−3.20272	−0.116252
$760$	15.8545	0.575103
$761$	−15.5850	−0.564955	−0.282478	−	0.959274i	$-0.591156\pi$
$761$	−15.5850	−0.564955	−0.282478	+	0.959274i	$0.591156\pi$
$762$	2.41885	0.0876256
$763$	−16.0344	−0.580484
$764$	17.4059	0.629722
$765$	10.4502	0.377827
$766$	−13.5167	−0.488379
$767$	−24.9510	−0.900928
$768$	4.91115	0.177216
$769$	−6.02711	−0.217343	−0.108671	−	0.994078i	$-0.534660\pi$
$769$	−6.02711	−0.217343	−0.108671	+	0.994078i	$0.534660\pi$
$770$	0.795767	0.0286775
$771$	−6.62047	−0.238431
$772$	−28.6160	−1.02991
$773$	11.2865	0.405947	0.202973	−	0.979184i	$-0.434939\pi$
$773$	11.2865	0.405947	0.202973	+	0.979184i	$0.434939\pi$
$774$	3.73095	0.134106
$775$	−9.62281	−0.345662
$776$	−7.37553	−0.264766
$777$	−1.29731	−0.0465408
$778$	−6.82986	−0.244862
$779$	16.0032	0.573373
$780$	1.34139	0.0480296
$781$	6.30972	0.225779
$782$	−22.7279	−0.812747
$783$	0.296606	0.0105999
$784$	−5.33955	−0.190698
$785$	2.30301	0.0821980
$786$	5.74953	0.205079
$787$	−44.6724	−1.59240	−0.796200	−	0.605034i	$-0.793160\pi$
$787$	−44.6724	−1.59240	−0.796200	+	0.605034i	$0.793160\pi$
$788$	15.8928	0.566156
$789$	10.3389	0.368076
$790$	−4.45225	−0.158404
$791$	15.7337	0.559427
$792$	−7.37263	−0.261975
$793$	−29.5004	−1.04759
$794$	9.98973	0.354522
$795$	2.67911	0.0950181
$796$	10.3664	0.367427
$797$	23.7903	0.842695	0.421347	−	0.906899i	$-0.361557\pi$
$797$	23.7903	0.842695	0.421347	+	0.906899i	$0.361557\pi$
$798$	−1.90190	−0.0673267
$799$	22.5692	0.798441
$800$	−5.86238	−0.207267
$801$	37.9068	1.33937
$802$	−13.2307	−0.467192
$803$	1.00000	0.0352892
$804$	−3.01578	−0.106359
$805$	−8.65239	−0.304957
$806$	−17.4505	−0.614669
$807$	9.86155	0.347143
$808$	−27.7957	−0.977850
$809$	12.7179	0.447139	0.223569	−	0.974688i	$-0.428229\pi$
$809$	12.7179	0.447139	0.223569	+	0.974688i	$0.428229\pi$
$810$	5.77537	0.202926
$811$	−2.70405	−0.0949522	−0.0474761	−	0.998872i	$-0.515118\pi$
$811$	−2.70405	−0.0949522	−0.0474761	+	0.998872i	$0.515118\pi$
$812$	−0.196006	−0.00687845
$813$	6.97391	0.244586
$814$	−2.37931	−0.0833949
$815$	13.2629	0.464578
$816$	−1.29877	−0.0454660
$817$	−10.6307	−0.371921
$818$	22.4168	0.783786
$819$	7.21454	0.252096
$820$	−3.73801	−0.130537
$821$	41.3790	1.44414	0.722068	−	0.691822i	$-0.243192\pi$
$821$	41.3790	1.44414	0.722068	+	0.691822i	$0.243192\pi$
$822$	−3.16218	−0.110294
$823$	5.19637	0.181134	0.0905671	−	0.995890i	$-0.471132\pi$
$823$	5.19637	0.181134	0.0905671	+	0.995890i	$0.471132\pi$
$824$	−5.00626	−0.174401
$825$	−0.390285	−0.0135880
$826$	−8.26332	−0.287518
$827$	−13.4299	−0.467002	−0.233501	−	0.972357i	$-0.575018\pi$
$827$	−13.4299	−0.467002	−0.233501	+	0.972357i	$0.575018\pi$
$828$	33.4260	1.16163
$829$	2.38986	0.0830034	0.0415017	−	0.999138i	$-0.486786\pi$
$829$	2.38986	0.0830034	0.0415017	+	0.999138i	$0.486786\pi$
$830$	−1.15195	−0.0399846
$831$	−11.4778	−0.398160
$832$	−6.27339	−0.217491
$833$	−21.6084	−0.748685
$834$	−1.61180	−0.0558122
$835$	9.62177	0.332975
$836$	8.75944	0.302951
$837$	−21.9618	−0.759110
$838$	−8.55665	−0.295585
$839$	23.7560	0.820148	0.410074	−	0.912052i	$-0.365503\pi$
$839$	23.7560	0.820148	0.410074	+	0.912052i	$0.365503\pi$
$840$	1.06540	0.0367597
$841$	−28.9831	−0.999418
$842$	−17.7422	−0.611437
$843$	0.458484	0.0157910
$844$	19.2974	0.664244
$845$	7.22651	0.248599
$846$	13.2179	0.454439
$847$	1.05438	0.0362290
$848$	6.22479	0.213760
$849$	−5.26569	−0.180718
$850$	−2.76963	−0.0949974
$851$	25.8703	0.886823
$852$	3.52247	0.120678
$853$	−38.9392	−1.33325	−0.666626	−	0.745392i	$-0.732262\pi$
$853$	−38.9392	−1.33325	−0.666626	+	0.745392i	$0.732262\pi$
$854$	−9.76999	−0.334322
$855$	−17.4386	−0.596387
$856$	−12.5768	−0.429865
$857$	−25.3886	−0.867257	−0.433628	−	0.901092i	$-0.642767\pi$
$857$	−25.3886	−0.867257	−0.433628	+	0.901092i	$0.642767\pi$
$858$	−0.707765	−0.0241627
$859$	6.16288	0.210275	0.105137	−	0.994458i	$-0.466472\pi$
$859$	6.16288	0.210275	0.105137	+	0.994458i	$0.466472\pi$
$860$	2.48311	0.0846734
$861$	1.07539	0.0366492
$862$	8.55902	0.291521
$863$	−4.20771	−0.143232	−0.0716161	−	0.997432i	$-0.522816\pi$
$863$	−4.20771	−0.143232	−0.0716161	+	0.997432i	$0.522816\pi$
$864$	−13.3795	−0.455180
$865$	12.2044	0.414962
$866$	27.7170	0.941861
$867$	1.37893	0.0468308
$868$	14.5130	0.492602
$869$	−5.89919	−0.200116
$870$	−0.0382811	−0.00129785
$871$	12.9802	0.439818
$872$	−39.3718	−1.33330
$873$	8.11246	0.274565
$874$	37.9268	1.28289
$875$	−1.05438	−0.0356446
$876$	0.558261	0.0188619
$877$	−49.3904	−1.66780	−0.833898	−	0.551919i	$-0.813896\pi$
$877$	−49.3904	−1.66780	−0.833898	+	0.551919i	$0.813896\pi$
$878$	1.63811	0.0552835
$879$	12.1131	0.408563
$880$	−0.906810	−0.0305686
$881$	−20.0532	−0.675610	−0.337805	−	0.941216i	$-0.609684\pi$
$881$	−20.0532	−0.675610	−0.337805	+	0.941216i	$0.609684\pi$
$882$	−12.6551	−0.426120
$883$	28.1195	0.946298	0.473149	−	0.880982i	$-0.343117\pi$
$883$	28.1195	0.946298	0.473149	+	0.880982i	$0.343117\pi$
$884$	12.6127	0.424211
$885$	4.05276	0.136232
$886$	13.7792	0.462922
$887$	18.7085	0.628169	0.314085	−	0.949395i	$-0.398302\pi$
$887$	18.7085	0.628169	0.314085	+	0.949395i	$0.398302\pi$
$888$	−3.18550	−0.106898
$889$	8.65839	0.290393
$890$	−10.0465	−0.336759
$891$	7.65230	0.256362
$892$	36.8134	1.23260
$893$	−37.6620	−1.26031
$894$	−1.57100	−0.0525422
$895$	−1.71636	−0.0573717
$896$	10.2848	0.343590
$897$	7.69554	0.256946
$898$	−7.56206	−0.252349
$899$	−1.25060	−0.0417097
$900$	4.07330	0.135777
$901$	25.1908	0.839226
$902$	1.97230	0.0656704
$903$	−0.714367	−0.0237726
$904$	38.6336	1.28493
$905$	−4.62329	−0.153683
$906$	−0.850623	−0.0282600
$907$	−2.39576	−0.0795499	−0.0397749	−	0.999209i	$-0.512664\pi$
$907$	−2.39576	−0.0795499	−0.0397749	+	0.999209i	$0.512664\pi$
$908$	4.72832	0.156915
$909$	30.5729	1.01404
$910$	−1.91208	−0.0633847
$911$	−20.5562	−0.681056	−0.340528	−	0.940234i	$-0.610606\pi$
$911$	−20.5562	−0.681056	−0.340528	+	0.940234i	$0.610606\pi$
$912$	2.16730	0.0717665
$913$	−1.52632	−0.0505137
$914$	23.8527	0.788978
$915$	4.79171	0.158409
$916$	−28.8629	−0.953656
$917$	20.5807	0.679636
$918$	−6.32101	−0.208624
$919$	−16.1491	−0.532709	−0.266354	−	0.963875i	$-0.585819\pi$
$919$	−16.1491	−0.532709	−0.266354	+	0.963875i	$0.585819\pi$
$920$	−21.2456	−0.700447
$921$	6.81453	0.224546
$922$	23.2557	0.765887
$923$	−15.1610	−0.499032
$924$	0.588621	0.0193642
$925$	3.15257	0.103656
$926$	19.3798	0.636858
$927$	5.50646	0.180856
$928$	−0.761885	−0.0250101
$929$	−53.4248	−1.75281	−0.876406	−	0.481574i	$-0.840065\pi$
$929$	−53.4248	−1.75281	−0.876406	+	0.481574i	$0.840065\pi$
$930$	2.83447	0.0929459
$931$	36.0586	1.18177
$932$	−22.3502	−0.732105
$933$	8.90480	0.291530
$934$	−13.2250	−0.432736
$935$	−3.66972	−0.120013
$936$	17.7150	0.579033
$937$	−33.1489	−1.08293	−0.541464	−	0.840724i	$-0.682130\pi$
$937$	−33.1489	−1.08293	−0.541464	+	0.840724i	$0.682130\pi$
$938$	4.29882	0.140361
$939$	12.1510	0.396532
$940$	8.79707	0.286929
$941$	−40.6274	−1.32442	−0.662208	−	0.749320i	$-0.730381\pi$
$941$	−40.6274	−1.32442	−0.662208	+	0.749320i	$0.730381\pi$
$942$	−0.678369	−0.0221025
$943$	−21.4448	−0.698340
$944$	9.41640	0.306478
$945$	−2.40638	−0.0782795
$946$	−1.31017	−0.0425974
$947$	50.8929	1.65380	0.826899	−	0.562350i	$-0.190103\pi$
$947$	50.8929	1.65380	0.826899	+	0.562350i	$0.190103\pi$
$948$	−3.29329	−0.106961
$949$	−2.40281	−0.0779985
$950$	4.62177	0.149950
$951$	7.86399	0.255007
$952$	10.0176	0.324672
$953$	−10.2158	−0.330921	−0.165461	−	0.986216i	$-0.552911\pi$
$953$	−10.2158	−0.330921	−0.165461	+	0.986216i	$0.552911\pi$
$954$	14.7532	0.477653
$955$	12.1686	0.393766
$956$	23.6806	0.765885
$957$	−0.0507221	−0.00163961
$958$	−18.3651	−0.593350
$959$	−11.3192	−0.365516
$960$	1.01898	0.0328874
$961$	61.5985	1.98705
$962$	5.71704	0.184325
$963$	13.8334	0.445774
$964$	−10.9261	−0.351907
$965$	−20.0057	−0.644007
$966$	2.54862	0.0820006
$967$	13.0488	0.419623	0.209811	−	0.977742i	$-0.432715\pi$
$967$	13.0488	0.419623	0.209811	+	0.977742i	$0.432715\pi$
$968$	2.58900	0.0832135
$969$	8.77074	0.281757
$970$	−2.15005	−0.0690341
$971$	−36.8464	−1.18246	−0.591228	−	0.806505i	$-0.701357\pi$
$971$	−36.8464	−1.18246	−0.591228	+	0.806505i	$0.701357\pi$
$972$	14.0656	0.451154
$973$	−5.76953	−0.184963
$974$	10.6289	0.340571
$975$	0.937781	0.0300330
$976$	11.1333	0.356369
$977$	14.2404	0.455591	0.227796	−	0.973709i	$-0.426848\pi$
$977$	14.2404	0.455591	0.227796	+	0.973709i	$0.426848\pi$
$978$	−3.90667	−0.124922
$979$	−13.3115	−0.425437
$980$	−8.42255	−0.269049
$981$	43.3057	1.38264
$982$	−19.6793	−0.627993
$983$	41.1843	1.31358	0.656788	−	0.754075i	$-0.271915\pi$
$983$	41.1843	1.31358	0.656788	+	0.754075i	$0.271915\pi$
$984$	2.64058	0.0841785
$985$	11.1108	0.354018
$986$	−0.359945	−0.0114630
$987$	−2.53083	−0.0805572
$988$	−21.0473	−0.669602
$989$	14.2455	0.452982
$990$	−2.14921	−0.0683063
$991$	−36.6406	−1.16393	−0.581964	−	0.813215i	$-0.697715\pi$
$991$	−36.6406	−1.16393	−0.581964	+	0.813215i	$0.697715\pi$
$992$	56.4126	1.79110
$993$	−0.652138	−0.0206950
$994$	−5.02106	−0.159258
$995$	7.24723	0.229753
$996$	−0.852083	−0.0269993
$997$	30.3789	0.962109	0.481054	−	0.876691i	$-0.340254\pi$
$997$	30.3789	0.962109	0.481054	+	0.876691i	$0.340254\pi$
$998$	14.3079	0.452907
$999$	7.19498	0.227639

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.f.1.13	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.f.1.13	✓	31	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.754723 q^{2} -0.390285 q^{3} -1.43039 q^{4} -1.00000 q^{5} +0.294557 q^{6} +1.05438 q^{7} +2.58900 q^{8} -2.84768 q^{9} +O(q^{10})\)	\(q-0.754723 q^{2} -0.390285 q^{3} -1.43039 q^{4} -1.00000 q^{5} +0.294557 q^{6} +1.05438 q^{7} +2.58900 q^{8} -2.84768 q^{9} +0.754723 q^{10} +1.00000 q^{11} +0.558261 q^{12} -2.40281 q^{13} -0.795767 q^{14} +0.390285 q^{15} +0.906810 q^{16} +3.66972 q^{17} +2.14921 q^{18} -6.12380 q^{19} +1.43039 q^{20} -0.411510 q^{21} -0.754723 q^{22} +8.20612 q^{23} -1.01045 q^{24} +1.00000 q^{25} +1.81346 q^{26} +2.28226 q^{27} -1.50818 q^{28} +0.129962 q^{29} -0.294557 q^{30} -9.62281 q^{31} -5.86238 q^{32} -0.390285 q^{33} -2.76963 q^{34} -1.05438 q^{35} +4.07330 q^{36} +3.15257 q^{37} +4.62177 q^{38} +0.937781 q^{39} -2.58900 q^{40} -2.61328 q^{41} +0.310576 q^{42} +1.73597 q^{43} -1.43039 q^{44} +2.84768 q^{45} -6.19335 q^{46} +6.15011 q^{47} -0.353915 q^{48} -5.88828 q^{49} -0.754723 q^{50} -1.43224 q^{51} +3.43696 q^{52} +6.86449 q^{53} -1.72248 q^{54} -1.00000 q^{55} +2.72979 q^{56} +2.39003 q^{57} -0.0980851 q^{58} +10.3841 q^{59} -0.558261 q^{60} +12.2775 q^{61} +7.26256 q^{62} -3.00254 q^{63} +2.61086 q^{64} +2.40281 q^{65} +0.294557 q^{66} -5.40210 q^{67} -5.24915 q^{68} -3.20272 q^{69} +0.795767 q^{70} +6.30972 q^{71} -7.37263 q^{72} +1.00000 q^{73} -2.37931 q^{74} -0.390285 q^{75} +8.75944 q^{76} +1.05438 q^{77} -0.707765 q^{78} -5.89919 q^{79} -0.906810 q^{80} +7.65230 q^{81} +1.97230 q^{82} -1.52632 q^{83} +0.588621 q^{84} -3.66972 q^{85} -1.31017 q^{86} -0.0507221 q^{87} +2.58900 q^{88} -13.3115 q^{89} -2.14921 q^{90} -2.53348 q^{91} -11.7380 q^{92} +3.75564 q^{93} -4.64163 q^{94} +6.12380 q^{95} +2.28800 q^{96} -2.84880 q^{97} +4.44402 q^{98} -2.84768 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * q^99

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