LMFDB - Embedded newform 8015.2.a.l.1.21

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:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
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)

$f(q)$	$=$	$q-1.05535 q^{2} +0.176354 q^{3} -0.886237 q^{4} -1.00000 q^{5} -0.186115 q^{6} -1.00000 q^{7} +3.04599 q^{8} -2.96890 q^{9} +O(q^{10})$	\(q-1.05535 q^{2} +0.176354 q^{3} -0.886237 q^{4} -1.00000 q^{5} -0.186115 q^{6} -1.00000 q^{7} +3.04599 q^{8} -2.96890 q^{9} +1.05535 q^{10} +3.44108 q^{11} -0.156292 q^{12} +6.99973 q^{13} +1.05535 q^{14} -0.176354 q^{15} -1.44211 q^{16} -1.17778 q^{17} +3.13323 q^{18} +1.90054 q^{19} +0.886237 q^{20} -0.176354 q^{21} -3.63154 q^{22} +7.72001 q^{23} +0.537173 q^{24} +1.00000 q^{25} -7.38716 q^{26} -1.05264 q^{27} +0.886237 q^{28} +9.32486 q^{29} +0.186115 q^{30} -5.28696 q^{31} -4.57005 q^{32} +0.606848 q^{33} +1.24297 q^{34} +1.00000 q^{35} +2.63115 q^{36} -8.69853 q^{37} -2.00574 q^{38} +1.23443 q^{39} -3.04599 q^{40} +7.81091 q^{41} +0.186115 q^{42} +2.29810 q^{43} -3.04961 q^{44} +2.96890 q^{45} -8.14731 q^{46} +8.63688 q^{47} -0.254322 q^{48} +1.00000 q^{49} -1.05535 q^{50} -0.207706 q^{51} -6.20342 q^{52} +5.56374 q^{53} +1.11090 q^{54} -3.44108 q^{55} -3.04599 q^{56} +0.335169 q^{57} -9.84099 q^{58} +1.85923 q^{59} +0.156292 q^{60} +0.0439074 q^{61} +5.57960 q^{62} +2.96890 q^{63} +7.70722 q^{64} -6.99973 q^{65} -0.640437 q^{66} -2.23381 q^{67} +1.04379 q^{68} +1.36145 q^{69} -1.05535 q^{70} +15.3936 q^{71} -9.04324 q^{72} +8.20243 q^{73} +9.17999 q^{74} +0.176354 q^{75} -1.68433 q^{76} -3.44108 q^{77} -1.30276 q^{78} -4.53514 q^{79} +1.44211 q^{80} +8.72106 q^{81} -8.24324 q^{82} -7.32652 q^{83} +0.156292 q^{84} +1.17778 q^{85} -2.42530 q^{86} +1.64448 q^{87} +10.4815 q^{88} -14.6526 q^{89} -3.13323 q^{90} -6.99973 q^{91} -6.84176 q^{92} -0.932378 q^{93} -9.11492 q^{94} -1.90054 q^{95} -0.805947 q^{96} -8.10190 q^{97} -1.05535 q^{98} -10.2162 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.05535	−0.746245	−0.373122	−	0.927782i	$-0.621713\pi$
$2$	−1.05535	−0.746245	−0.373122	+	0.927782i	$0.621713\pi$
$3$	0.176354	0.101818	0.0509090	−	0.998703i	$-0.483788\pi$
$3$	0.176354	0.101818	0.0509090	+	0.998703i	$0.483788\pi$
$4$	−0.886237	−0.443119
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.186115	−0.0759812
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.04599	1.07692
$9$	−2.96890	−0.989633
$10$	1.05535	0.333731
$11$	3.44108	1.03752	0.518762	−	0.854919i	$-0.326393\pi$
$11$	3.44108	1.03752	0.518762	+	0.854919i	$0.326393\pi$
$12$	−0.156292	−0.0451175
$13$	6.99973	1.94137	0.970687	−	0.240346i	$-0.0772609\pi$
$13$	6.99973	1.94137	0.970687	+	0.240346i	$0.0772609\pi$
$14$	1.05535	0.282054
$15$	−0.176354	−0.0455344
$16$	−1.44211	−0.360527
$17$	−1.17778	−0.285654	−0.142827	−	0.989748i	$-0.545619\pi$
$17$	−1.17778	−0.285654	−0.142827	+	0.989748i	$0.545619\pi$
$18$	3.13323	0.738509
$19$	1.90054	0.436015	0.218007	−	0.975947i	$-0.430044\pi$
$19$	1.90054	0.436015	0.218007	+	0.975947i	$0.430044\pi$
$20$	0.886237	0.198169
$21$	−0.176354	−0.0384836
$22$	−3.63154	−0.774246
$23$	7.72001	1.60973	0.804866	−	0.593456i	$-0.202237\pi$
$23$	7.72001	1.60973	0.804866	+	0.593456i	$0.202237\pi$
$24$	0.537173	0.109650
$25$	1.00000	0.200000
$26$	−7.38716	−1.44874
$27$	−1.05264	−0.202581
$28$	0.886237	0.167483
$29$	9.32486	1.73158	0.865791	−	0.500405i	$-0.166816\pi$
$29$	9.32486	1.73158	0.865791	+	0.500405i	$0.166816\pi$
$30$	0.186115	0.0339798
$31$	−5.28696	−0.949567	−0.474783	−	0.880103i	$-0.657474\pi$
$31$	−5.28696	−0.949567	−0.474783	+	0.880103i	$0.657474\pi$
$32$	−4.57005	−0.807878
$33$	0.606848	0.105639
$34$	1.24297	0.213167
$35$	1.00000	0.169031
$36$	2.63115	0.438525
$37$	−8.69853	−1.43003	−0.715015	−	0.699109i	$-0.753580\pi$
$37$	−8.69853	−1.43003	−0.715015	+	0.699109i	$0.753580\pi$
$38$	−2.00574	−0.325374
$39$	1.23443	0.197667
$40$	−3.04599	−0.481613
$41$	7.81091	1.21986	0.609930	−	0.792456i	$-0.291198\pi$
$41$	7.81091	1.21986	0.609930	+	0.792456i	$0.291198\pi$
$42$	0.186115	0.0287182
$43$	2.29810	0.350458	0.175229	−	0.984528i	$-0.443933\pi$
$43$	2.29810	0.350458	0.175229	+	0.984528i	$0.443933\pi$
$44$	−3.04961	−0.459746
$45$	2.96890	0.442577
$46$	−8.14731	−1.20125
$47$	8.63688	1.25982	0.629909	−	0.776669i	$-0.283092\pi$
$47$	8.63688	1.25982	0.629909	+	0.776669i	$0.283092\pi$
$48$	−0.254322	−0.0367082
$49$	1.00000	0.142857
$50$	−1.05535	−0.149249
$51$	−0.207706	−0.0290847
$52$	−6.20342	−0.860259
$53$	5.56374	0.764238	0.382119	−	0.924113i	$-0.375194\pi$
$53$	5.56374	0.764238	0.382119	+	0.924113i	$0.375194\pi$
$54$	1.11090	0.151175
$55$	−3.44108	−0.463995
$56$	−3.04599	−0.407037
$57$	0.335169	0.0443942
$58$	−9.84099	−1.29218
$59$	1.85923	0.242051	0.121026	−	0.992649i	$-0.461382\pi$
$59$	1.85923	0.242051	0.121026	+	0.992649i	$0.461382\pi$
$60$	0.156292	0.0201772
$61$	0.0439074	0.00562177	0.00281088	−	0.999996i	$-0.499105\pi$
$61$	0.0439074	0.00562177	0.00281088	+	0.999996i	$0.499105\pi$
$62$	5.57960	0.708609
$63$	2.96890	0.374046
$64$	7.70722	0.963402
$65$	−6.99973	−0.868209
$66$	−0.640437	−0.0788323
$67$	−2.23381	−0.272903	−0.136452	−	0.990647i	$-0.543570\pi$
$67$	−2.23381	−0.272903	−0.136452	+	0.990647i	$0.543570\pi$
$68$	1.04379	0.126578
$69$	1.36145	0.163900
$70$	−1.05535	−0.126138
$71$	15.3936	1.82688	0.913440	−	0.406972i	$-0.133415\pi$
$71$	15.3936	1.82688	0.913440	+	0.406972i	$0.133415\pi$
$72$	−9.04324	−1.06576
$73$	8.20243	0.960022	0.480011	−	0.877262i	$-0.340633\pi$
$73$	8.20243	0.960022	0.480011	+	0.877262i	$0.340633\pi$
$74$	9.17999	1.06715
$75$	0.176354	0.0203636
$76$	−1.68433	−0.193206
$77$	−3.44108	−0.392147
$78$	−1.30276	−0.147508
$79$	−4.53514	−0.510243	−0.255121	−	0.966909i	$-0.582115\pi$
$79$	−4.53514	−0.510243	−0.255121	+	0.966909i	$0.582115\pi$
$80$	1.44211	0.161233
$81$	8.72106	0.969007
$82$	−8.24324	−0.910314
$83$	−7.32652	−0.804190	−0.402095	−	0.915598i	$-0.631718\pi$
$83$	−7.32652	−0.804190	−0.402095	+	0.915598i	$0.631718\pi$
$84$	0.156292	0.0170528
$85$	1.17778	0.127748
$86$	−2.42530	−0.261527
$87$	1.64448	0.176306
$88$	10.4815	1.11733
$89$	−14.6526	−1.55317	−0.776587	−	0.630010i	$-0.783051\pi$
$89$	−14.6526	−1.55317	−0.776587	+	0.630010i	$0.783051\pi$
$90$	−3.13323	−0.330271
$91$	−6.99973	−0.733771
$92$	−6.84176	−0.713303
$93$	−0.932378	−0.0966831
$94$	−9.11492	−0.940133
$95$	−1.90054	−0.194992
$96$	−0.805947	−0.0822566
$97$	−8.10190	−0.822624	−0.411312	−	0.911495i	$-0.634929\pi$
$97$	−8.10190	−0.822624	−0.411312	+	0.911495i	$0.634929\pi$
$98$	−1.05535	−0.106606
$99$	−10.2162	−1.02677
$100$	−0.886237	−0.0886237
$101$	6.83585	0.680193	0.340096	−	0.940391i	$-0.389540\pi$
$101$	6.83585	0.680193	0.340096	+	0.940391i	$0.389540\pi$
$102$	0.219203	0.0217043
$103$	12.1047	1.19271	0.596354	−	0.802722i	$-0.296616\pi$
$103$	12.1047	1.19271	0.596354	+	0.802722i	$0.296616\pi$
$104$	21.3211	2.09070
$105$	0.176354	0.0172104
$106$	−5.87169	−0.570309
$107$	−3.99447	−0.386160	−0.193080	−	0.981183i	$-0.561848\pi$
$107$	−3.99447	−0.386160	−0.193080	+	0.981183i	$0.561848\pi$
$108$	0.932888	0.0897672
$109$	−8.18543	−0.784022	−0.392011	−	0.919960i	$-0.628221\pi$
$109$	−8.18543	−0.784022	−0.392011	+	0.919960i	$0.628221\pi$
$110$	3.63154	0.346254
$111$	−1.53402	−0.145603
$112$	1.44211	0.136267
$113$	−16.8701	−1.58701	−0.793504	−	0.608566i	$-0.791745\pi$
$113$	−16.8701	−1.58701	−0.793504	+	0.608566i	$0.791745\pi$
$114$	−0.353720	−0.0331289
$115$	−7.72001	−0.719894
$116$	−8.26404	−0.767296
$117$	−20.7815	−1.92125
$118$	−1.96214	−0.180629
$119$	1.17778	0.107967
$120$	−0.537173	−0.0490369
$121$	0.841001	0.0764546
$122$	−0.0463377	−0.00419522
$123$	1.37749	0.124204
$124$	4.68550	0.420771
$125$	−1.00000	−0.0894427
$126$	−3.13323	−0.279130
$127$	−14.1236	−1.25327	−0.626634	−	0.779313i	$-0.715568\pi$
$127$	−14.1236	−1.25327	−0.626634	+	0.779313i	$0.715568\pi$
$128$	1.00629	0.0889441
$129$	0.405280	0.0356829
$130$	7.38716	0.647897
$131$	−12.0149	−1.04975	−0.524874	−	0.851180i	$-0.675887\pi$
$131$	−12.0149	−1.04975	−0.524874	+	0.851180i	$0.675887\pi$
$132$	−0.537811	−0.0468104
$133$	−1.90054	−0.164798
$134$	2.35745	0.203653
$135$	1.05264	0.0905968
$136$	−3.58750	−0.307626
$137$	8.09677	0.691754	0.345877	−	0.938280i	$-0.387581\pi$
$137$	8.09677	0.691754	0.345877	+	0.938280i	$0.387581\pi$
$138$	−1.43681	−0.122309
$139$	4.28815	0.363716	0.181858	−	0.983325i	$-0.441789\pi$
$139$	4.28815	0.363716	0.181858	+	0.983325i	$0.441789\pi$
$140$	−0.886237	−0.0749007
$141$	1.52315	0.128272
$142$	−16.2456	−1.36330
$143$	24.0866	2.01422
$144$	4.28148	0.356790
$145$	−9.32486	−0.774387
$146$	−8.65643	−0.716412
$147$	0.176354	0.0145454
$148$	7.70896	0.633673
$149$	6.63875	0.543867	0.271934	−	0.962316i	$-0.412337\pi$
$149$	6.63875	0.543867	0.271934	+	0.962316i	$0.412337\pi$
$150$	−0.186115	−0.0151962
$151$	−0.535768	−0.0436002	−0.0218001	−	0.999762i	$-0.506940\pi$
$151$	−0.535768	−0.0436002	−0.0218001	+	0.999762i	$0.506940\pi$
$152$	5.78903	0.469553
$153$	3.49671	0.282692
$154$	3.63154	0.292638
$155$	5.28696	0.424659
$156$	−1.09400	−0.0875899
$157$	8.74303	0.697769	0.348885	−	0.937166i	$-0.386560\pi$
$157$	8.74303	0.697769	0.348885	+	0.937166i	$0.386560\pi$
$158$	4.78615	0.380766
$159$	0.981188	0.0778132
$160$	4.57005	0.361294
$161$	−7.72001	−0.608422
$162$	−9.20377	−0.723116
$163$	−17.0760	−1.33749	−0.668747	−	0.743490i	$-0.733169\pi$
$163$	−17.0760	−1.33749	−0.668747	+	0.743490i	$0.733169\pi$
$164$	−6.92232	−0.540542
$165$	−0.606848	−0.0472430
$166$	7.73204	0.600122
$167$	6.63610	0.513517	0.256758	−	0.966476i	$-0.417346\pi$
$167$	6.63610	0.513517	0.256758	+	0.966476i	$0.417346\pi$
$168$	−0.537173	−0.0414438
$169$	35.9962	2.76894
$170$	−1.24297	−0.0953314
$171$	−5.64252	−0.431494
$172$	−2.03667	−0.155294
$173$	−10.7189	−0.814939	−0.407470	−	0.913219i	$-0.633589\pi$
$173$	−10.7189	−0.814939	−0.407470	+	0.913219i	$0.633589\pi$
$174$	−1.73550	−0.131568
$175$	−1.00000	−0.0755929
$176$	−4.96241	−0.374056
$177$	0.327883	0.0246452
$178$	15.4636	1.15905
$179$	−18.7926	−1.40462	−0.702312	−	0.711870i	$-0.747849\pi$
$179$	−18.7926	−1.40462	−0.702312	+	0.711870i	$0.747849\pi$
$180$	−2.63115	−0.196114
$181$	0.679653	0.0505182	0.0252591	−	0.999681i	$-0.491959\pi$
$181$	0.679653	0.0505182	0.0252591	+	0.999681i	$0.491959\pi$
$182$	7.38716	0.547573
$183$	0.00774325	0.000572398 0
$184$	23.5151	1.73355
$185$	8.69853	0.639529
$186$	0.983985	0.0721492
$187$	−4.05283	−0.296372
$188$	−7.65432	−0.558249
$189$	1.05264	0.0765683
$190$	2.00574	0.145512
$191$	9.78238	0.707828	0.353914	−	0.935278i	$-0.384850\pi$
$191$	9.78238	0.707828	0.353914	+	0.935278i	$0.384850\pi$
$192$	1.35920	0.0980918
$193$	−11.3460	−0.816706	−0.408353	−	0.912824i	$-0.633897\pi$
$193$	−11.3460	−0.816706	−0.408353	+	0.912824i	$0.633897\pi$
$194$	8.55034	0.613879
$195$	−1.23443	−0.0883994
$196$	−0.886237	−0.0633027
$197$	−13.0279	−0.928201	−0.464100	−	0.885783i	$-0.653622\pi$
$197$	−13.0279	−0.928201	−0.464100	+	0.885783i	$0.653622\pi$
$198$	10.7817	0.766220
$199$	6.11713	0.433632	0.216816	−	0.976212i	$-0.430433\pi$
$199$	6.11713	0.433632	0.216816	+	0.976212i	$0.430433\pi$
$200$	3.04599	0.215384
$201$	−0.393942	−0.0277865
$202$	−7.21422	−0.507590
$203$	−9.32486	−0.654477
$204$	0.184077	0.0128880
$205$	−7.81091	−0.545538
$206$	−12.7747	−0.890052
$207$	−22.9199	−1.59304
$208$	−10.0944	−0.699919
$209$	6.53991	0.452375
$210$	−0.186115	−0.0128432
$211$	5.38574	0.370770	0.185385	−	0.982666i	$-0.440647\pi$
$211$	5.38574	0.370770	0.185385	+	0.982666i	$0.440647\pi$
$212$	−4.93079	−0.338648
$213$	2.71472	0.186010
$214$	4.21556	0.288170
$215$	−2.29810	−0.156729
$216$	−3.20633	−0.218163
$217$	5.28696	0.358903
$218$	8.63849	0.585073
$219$	1.44653	0.0977476
$220$	3.04961	0.205605
$221$	−8.24413	−0.554560
$222$	1.61893	0.108655
$223$	2.53650	0.169857	0.0849284	−	0.996387i	$-0.472934\pi$
$223$	2.53650	0.169857	0.0849284	+	0.996387i	$0.472934\pi$
$224$	4.57005	0.305349
$225$	−2.96890	−0.197927
$226$	17.8039	1.18430
$227$	−14.8731	−0.987164	−0.493582	−	0.869699i	$-0.664313\pi$
$227$	−14.8731	−0.987164	−0.493582	+	0.869699i	$0.664313\pi$
$228$	−0.297039	−0.0196719
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	8.14731	0.537218
$231$	−0.606848	−0.0399277
$232$	28.4034	1.86478
$233$	−6.46901	−0.423799	−0.211899	−	0.977292i	$-0.567965\pi$
$233$	−6.46901	−0.423799	−0.211899	+	0.977292i	$0.567965\pi$
$234$	21.9317	1.43372
$235$	−8.63688	−0.563408
$236$	−1.64772	−0.107257
$237$	−0.799790	−0.0519519
$238$	−1.24297	−0.0805697
$239$	10.3407	0.668882	0.334441	−	0.942417i	$-0.391452\pi$
$239$	10.3407	0.668882	0.334441	+	0.942417i	$0.391452\pi$
$240$	0.254322	0.0164164
$241$	−11.1851	−0.720497	−0.360249	−	0.932856i	$-0.617308\pi$
$241$	−11.1851	−0.720497	−0.360249	+	0.932856i	$0.617308\pi$
$242$	−0.887550	−0.0570539
$243$	4.69591	0.301243
$244$	−0.0389124	−0.00249111
$245$	−1.00000	−0.0638877
$246$	−1.45373	−0.0926864
$247$	13.3033	0.846468
$248$	−16.1040	−1.02261
$249$	−1.29206	−0.0818810
$250$	1.05535	0.0667462
$251$	14.7123	0.928633	0.464316	−	0.885669i	$-0.346300\pi$
$251$	14.7123	0.928633	0.464316	+	0.885669i	$0.346300\pi$
$252$	−2.63115	−0.165747
$253$	26.5651	1.67014
$254$	14.9054	0.935245
$255$	0.207706	0.0130071
$256$	−16.4764	−1.02978
$257$	31.0456	1.93657	0.968286	−	0.249845i	$-0.0803796\pi$
$257$	31.0456	1.93657	0.968286	+	0.249845i	$0.0803796\pi$
$258$	−0.427712	−0.0266282
$259$	8.69853	0.540501
$260$	6.20342	0.384720
$261$	−27.6846	−1.71363
$262$	12.6799	0.783369
$263$	13.4504	0.829384	0.414692	−	0.909962i	$-0.363889\pi$
$263$	13.4504	0.829384	0.414692	+	0.909962i	$0.363889\pi$
$264$	1.84845	0.113764
$265$	−5.56374	−0.341778
$266$	2.00574	0.122980
$267$	−2.58405	−0.158141
$268$	1.97969	0.120929
$269$	−2.69957	−0.164596	−0.0822980	−	0.996608i	$-0.526226\pi$
$269$	−2.69957	−0.164596	−0.0822980	+	0.996608i	$0.526226\pi$
$270$	−1.11090	−0.0676074
$271$	3.68602	0.223910	0.111955	−	0.993713i	$-0.464289\pi$
$271$	3.68602	0.223910	0.111955	+	0.993713i	$0.464289\pi$
$272$	1.69849	0.102986
$273$	−1.23443	−0.0747111
$274$	−8.54493	−0.516218
$275$	3.44108	0.207505
$276$	−1.20657	−0.0726271
$277$	25.9698	1.56037	0.780187	−	0.625547i	$-0.215124\pi$
$277$	25.9698	1.56037	0.780187	+	0.625547i	$0.215124\pi$
$278$	−4.52550	−0.271421
$279$	15.6965	0.939723
$280$	3.04599	0.182033
$281$	3.83290	0.228652	0.114326	−	0.993443i	$-0.463529\pi$
$281$	3.83290	0.228652	0.114326	+	0.993443i	$0.463529\pi$
$282$	−1.60745	−0.0957225
$283$	−24.3622	−1.44818	−0.724092	−	0.689704i	$-0.757741\pi$
$283$	−24.3622	−1.44818	−0.724092	+	0.689704i	$0.757741\pi$
$284$	−13.6424	−0.809525
$285$	−0.335169	−0.0198537
$286$	−25.4198	−1.50310
$287$	−7.81091	−0.461064
$288$	13.5680	0.799503
$289$	−15.6128	−0.918402
$290$	9.84099	0.577883
$291$	−1.42880	−0.0837580
$292$	−7.26930	−0.425404
$293$	−11.2255	−0.655804	−0.327902	−	0.944712i	$-0.606342\pi$
$293$	−11.2255	−0.655804	−0.327902	+	0.944712i	$0.606342\pi$
$294$	−0.186115	−0.0108545
$295$	−1.85923	−0.108249
$296$	−26.4956	−1.54003
$297$	−3.62221	−0.210182
$298$	−7.00620	−0.405858
$299$	54.0379	3.12509
$300$	−0.156292	−0.00902350
$301$	−2.29810	−0.132461
$302$	0.565423	0.0325364
$303$	1.20553	0.0692559
$304$	−2.74079	−0.157195
$305$	−0.0439074	−0.00251413
$306$	−3.69025	−0.210958
$307$	34.5744	1.97326	0.986631	−	0.162967i	$-0.0521065\pi$
$307$	34.5744	1.97326	0.986631	+	0.162967i	$0.0521065\pi$
$308$	3.04961	0.173768
$309$	2.13471	0.121439
$310$	−5.57960	−0.316900
$311$	−18.8728	−1.07018	−0.535090	−	0.844795i	$-0.679722\pi$
$311$	−18.8728	−1.07018	−0.535090	+	0.844795i	$0.679722\pi$
$312$	3.76006	0.212872
$313$	22.2370	1.25691	0.628455	−	0.777846i	$-0.283688\pi$
$313$	22.2370	1.25691	0.628455	+	0.777846i	$0.283688\pi$
$314$	−9.22695	−0.520707
$315$	−2.96890	−0.167279
$316$	4.01921	0.226098
$317$	14.7211	0.826822	0.413411	−	0.910545i	$-0.364337\pi$
$317$	14.7211	0.826822	0.413411	+	0.910545i	$0.364337\pi$
$318$	−1.03550	−0.0580677
$319$	32.0875	1.79656
$320$	−7.70722	−0.430847
$321$	−0.704441	−0.0393181
$322$	8.14731	0.454032
$323$	−2.23842	−0.124549
$324$	−7.72893	−0.429385
$325$	6.99973	0.388275
$326$	18.0211	0.998098
$327$	−1.44353	−0.0798276
$328$	23.7920	1.31369
$329$	−8.63688	−0.476166
$330$	0.640437	0.0352549
$331$	29.4760	1.62015	0.810074	−	0.586327i	$-0.199427\pi$
$331$	29.4760	1.62015	0.810074	+	0.586327i	$0.199427\pi$
$332$	6.49303	0.356351
$333$	25.8251	1.41521
$334$	−7.00340	−0.383209
$335$	2.23381	0.122046
$336$	0.254322	0.0138744
$337$	20.5174	1.11765	0.558827	−	0.829284i	$-0.311252\pi$
$337$	20.5174	1.11765	0.558827	+	0.829284i	$0.311252\pi$
$338$	−37.9885	−2.06630
$339$	−2.97511	−0.161586
$340$	−1.04379	−0.0566076
$341$	−18.1928	−0.985198
$342$	5.95483	0.322001
$343$	−1.00000	−0.0539949
$344$	7.00000	0.377415
$345$	−1.36145	−0.0732983
$346$	11.3121	0.608144
$347$	15.9899	0.858384	0.429192	−	0.903213i	$-0.358798\pi$
$347$	15.9899	0.858384	0.429192	+	0.903213i	$0.358798\pi$
$348$	−1.45740	−0.0781246
$349$	15.5304	0.831326	0.415663	−	0.909519i	$-0.363550\pi$
$349$	15.5304	0.831326	0.415663	+	0.909519i	$0.363550\pi$
$350$	1.05535	0.0564108
$351$	−7.36819	−0.393285
$352$	−15.7259	−0.838192
$353$	−16.1927	−0.861852	−0.430926	−	0.902387i	$-0.641813\pi$
$353$	−16.1927	−0.861852	−0.430926	+	0.902387i	$0.641813\pi$
$354$	−0.346031	−0.0183913
$355$	−15.3936	−0.817006
$356$	12.9857	0.688240
$357$	0.207706	0.0109930
$358$	19.8327	1.04819
$359$	29.1666	1.53935	0.769677	−	0.638434i	$-0.220417\pi$
$359$	29.1666	1.53935	0.769677	+	0.638434i	$0.220417\pi$
$360$	9.04324	0.476620
$361$	−15.3879	−0.809891
$362$	−0.717271	−0.0376989
$363$	0.148314	0.00778446
$364$	6.20342	0.325147
$365$	−8.20243	−0.429335
$366$	−0.00817184	−0.000427149 0
$367$	−5.07904	−0.265124	−0.132562	−	0.991175i	$-0.542320\pi$
$367$	−5.07904	−0.265124	−0.132562	+	0.991175i	$0.542320\pi$
$368$	−11.1331	−0.580353
$369$	−23.1898	−1.20721
$370$	−9.17999	−0.477245
$371$	−5.56374	−0.288855
$372$	0.826308	0.0428421
$373$	21.3097	1.10338	0.551688	−	0.834050i	$-0.313984\pi$
$373$	21.3097	1.10338	0.551688	+	0.834050i	$0.313984\pi$
$374$	4.27715	0.221166
$375$	−0.176354	−0.00910689
$376$	26.3078	1.35672
$377$	65.2714	3.36165
$378$	−1.11090	−0.0571387
$379$	−36.5100	−1.87539	−0.937697	−	0.347455i	$-0.887046\pi$
$379$	−36.5100	−1.87539	−0.937697	+	0.347455i	$0.887046\pi$
$380$	1.68433	0.0864044
$381$	−2.49076	−0.127605
$382$	−10.3238	−0.528213
$383$	4.21828	0.215544	0.107772	−	0.994176i	$-0.465628\pi$
$383$	4.21828	0.215544	0.107772	+	0.994176i	$0.465628\pi$
$384$	0.177463	0.00905612
$385$	3.44108	0.175373
$386$	11.9740	0.609462
$387$	−6.82284	−0.346824
$388$	7.18021	0.364520
$389$	−2.43112	−0.123263	−0.0616313	−	0.998099i	$-0.519630\pi$
$389$	−2.43112	−0.123263	−0.0616313	+	0.998099i	$0.519630\pi$
$390$	1.30276	0.0659676
$391$	−9.09247	−0.459826
$392$	3.04599	0.153846
$393$	−2.11888	−0.106883
$394$	13.7490	0.692665
$395$	4.53514	0.228187
$396$	9.05398	0.454980
$397$	3.62747	0.182057	0.0910287	−	0.995848i	$-0.470984\pi$
$397$	3.62747	0.182057	0.0910287	+	0.995848i	$0.470984\pi$
$398$	−6.45571	−0.323596
$399$	−0.335169	−0.0167794
$400$	−1.44211	−0.0721055
$401$	17.3416	0.866000	0.433000	−	0.901394i	$-0.357455\pi$
$401$	17.3416	0.866000	0.433000	+	0.901394i	$0.357455\pi$
$402$	0.415746	0.0207355
$403$	−37.0073	−1.84346
$404$	−6.05819	−0.301406
$405$	−8.72106	−0.433353
$406$	9.84099	0.488400
$407$	−29.9323	−1.48369
$408$	−0.632671	−0.0313219
$409$	2.41659	0.119493	0.0597465	−	0.998214i	$-0.480971\pi$
$409$	2.41659	0.119493	0.0597465	+	0.998214i	$0.480971\pi$
$410$	8.24324	0.407105
$411$	1.42790	0.0704331
$412$	−10.7276	−0.528511
$413$	−1.85923	−0.0914868
$414$	24.1885	1.18880
$415$	7.32652	0.359644
$416$	−31.9891	−1.56839
$417$	0.756233	0.0370329
$418$	−6.90190	−0.337583
$419$	7.35049	0.359095	0.179548	−	0.983749i	$-0.442537\pi$
$419$	7.35049	0.359095	0.179548	+	0.983749i	$0.442537\pi$
$420$	−0.156292	−0.00762625
$421$	8.66867	0.422485	0.211243	−	0.977434i	$-0.432249\pi$
$421$	8.66867	0.422485	0.211243	+	0.977434i	$0.432249\pi$
$422$	−5.68384	−0.276685
$423$	−25.6420	−1.24676
$424$	16.9471	0.823023
$425$	−1.17778	−0.0571307
$426$	−2.86498	−0.138809
$427$	−0.0439074	−0.00212483
$428$	3.54005	0.171115
$429$	4.24777	0.205084
$430$	2.42530	0.116959
$431$	18.9096	0.910842	0.455421	−	0.890276i	$-0.349489\pi$
$431$	18.9096	0.910842	0.455421	+	0.890276i	$0.349489\pi$
$432$	1.51802	0.0730359
$433$	30.7692	1.47867	0.739337	−	0.673335i	$-0.235139\pi$
$433$	30.7692	1.47867	0.739337	+	0.673335i	$0.235139\pi$
$434$	−5.57960	−0.267829
$435$	−1.64448	−0.0788466
$436$	7.25423	0.347415
$437$	14.6722	0.701867
$438$	−1.52660	−0.0729437
$439$	−25.3465	−1.20972	−0.604861	−	0.796331i	$-0.706771\pi$
$439$	−25.3465	−1.20972	−0.604861	+	0.796331i	$0.706771\pi$
$440$	−10.4815	−0.499685
$441$	−2.96890	−0.141376
$442$	8.70044	0.413838
$443$	−16.2193	−0.770604	−0.385302	−	0.922790i	$-0.625903\pi$
$443$	−16.2193	−0.770604	−0.385302	+	0.922790i	$0.625903\pi$
$444$	1.35951	0.0645194
$445$	14.6526	0.694601
$446$	−2.67690	−0.126755
$447$	1.17077	0.0553755
$448$	−7.70722	−0.364132
$449$	−33.2507	−1.56920	−0.784599	−	0.620003i	$-0.787131\pi$
$449$	−33.2507	−1.56920	−0.784599	+	0.620003i	$0.787131\pi$
$450$	3.13323	0.147702
$451$	26.8779	1.26563
$452$	14.9509	0.703232
$453$	−0.0944849	−0.00443929
$454$	15.6963	0.736666
$455$	6.99973	0.328152
$456$	1.02092	0.0478090
$457$	−14.7416	−0.689583	−0.344792	−	0.938679i	$-0.612050\pi$
$457$	−14.7416	−0.689583	−0.344792	+	0.938679i	$0.612050\pi$
$458$	−1.05535	−0.0493132
$459$	1.23978	0.0578679
$460$	6.84176	0.318999
$461$	20.2338	0.942382	0.471191	−	0.882031i	$-0.343824\pi$
$461$	20.2338	0.942382	0.471191	+	0.882031i	$0.343824\pi$
$462$	0.640437	0.0297958
$463$	9.79492	0.455209	0.227604	−	0.973754i	$-0.426911\pi$
$463$	9.79492	0.455209	0.227604	+	0.973754i	$0.426911\pi$
$464$	−13.4475	−0.624283
$465$	0.932378	0.0432380
$466$	6.82706	0.316258
$467$	−0.857035	−0.0396589	−0.0198294	−	0.999803i	$-0.506312\pi$
$467$	−0.857035	−0.0396589	−0.0198294	+	0.999803i	$0.506312\pi$
$468$	18.4173	0.851341
$469$	2.23381	0.103148
$470$	9.11492	0.420440
$471$	1.54187	0.0710456
$472$	5.66320	0.260670
$473$	7.90795	0.363608
$474$	0.844058	0.0387689
$475$	1.90054	0.0872029
$476$	−1.04379	−0.0478421
$477$	−16.5182	−0.756315
$478$	−10.9130	−0.499150
$479$	−27.9193	−1.27567	−0.637834	−	0.770174i	$-0.720169\pi$
$479$	−27.9193	−1.27567	−0.637834	+	0.770174i	$0.720169\pi$
$480$	0.805947	0.0367863
$481$	−60.8873	−2.77622
$482$	11.8042	0.537668
$483$	−1.36145	−0.0619483
$484$	−0.745326	−0.0338785
$485$	8.10190	0.367888
$486$	−4.95583	−0.224801
$487$	30.3011	1.37307	0.686537	−	0.727095i	$-0.259130\pi$
$487$	30.3011	1.37307	0.686537	+	0.727095i	$0.259130\pi$
$488$	0.133742	0.00605419
$489$	−3.01142	−0.136181
$490$	1.05535	0.0476758
$491$	−8.69063	−0.392203	−0.196101	−	0.980584i	$-0.562828\pi$
$491$	−8.69063	−0.392203	−0.196101	+	0.980584i	$0.562828\pi$
$492$	−1.22078	−0.0550370
$493$	−10.9826	−0.494633
$494$	−14.0396	−0.631672
$495$	10.2162	0.459184
$496$	7.62438	0.342345
$497$	−15.3936	−0.690496
$498$	1.36358	0.0611033
$499$	11.1086	0.497290	0.248645	−	0.968595i	$-0.420015\pi$
$499$	11.1086	0.497290	0.248645	+	0.968595i	$0.420015\pi$
$500$	0.886237	0.0396337
$501$	1.17030	0.0522853
$502$	−15.5266	−0.692987
$503$	1.81849	0.0810823	0.0405412	−	0.999178i	$-0.487092\pi$
$503$	1.81849	0.0810823	0.0405412	+	0.999178i	$0.487092\pi$
$504$	9.04324	0.402818
$505$	−6.83585	−0.304192
$506$	−28.0355	−1.24633
$507$	6.34807	0.281928
$508$	12.5169	0.555347
$509$	23.4429	1.03909	0.519544	−	0.854443i	$-0.326102\pi$
$509$	23.4429	1.03909	0.519544	+	0.854443i	$0.326102\pi$
$510$	−0.219203	−0.00970646
$511$	−8.20243	−0.362854
$512$	15.3758	0.679521
$513$	−2.00059	−0.0883281
$514$	−32.7640	−1.44516
$515$	−12.1047	−0.533395
$516$	−0.359174	−0.0158118
$517$	29.7201	1.30709
$518$	−9.17999	−0.403346
$519$	−1.89031	−0.0829756
$520$	−21.3211	−0.934992
$521$	−25.8648	−1.13316	−0.566579	−	0.824007i	$-0.691733\pi$
$521$	−25.8648	−1.13316	−0.566579	+	0.824007i	$0.691733\pi$
$522$	29.2169	1.27879
$523$	−1.38587	−0.0605997	−0.0302999	−	0.999541i	$-0.509646\pi$
$523$	−1.38587	−0.0605997	−0.0302999	+	0.999541i	$0.509646\pi$
$524$	10.6481	0.465163
$525$	−0.176354	−0.00769672
$526$	−14.1948	−0.618924
$527$	6.22688	0.271247
$528$	−0.875141	−0.0380856
$529$	36.5985	1.59124
$530$	5.87169	0.255050
$531$	−5.51987	−0.239542
$532$	1.68433	0.0730251
$533$	54.6742	2.36820
$534$	2.72707	0.118012
$535$	3.99447	0.172696
$536$	−6.80416	−0.293895
$537$	−3.31415	−0.143016
$538$	2.84900	0.122829
$539$	3.44108	0.148218
$540$	−0.932888	−0.0401451
$541$	0.469849	0.0202004	0.0101002	−	0.999949i	$-0.496785\pi$
$541$	0.469849	0.0202004	0.0101002	+	0.999949i	$0.496785\pi$
$542$	−3.89004	−0.167092
$543$	0.119860	0.00514367
$544$	5.38251	0.230773
$545$	8.18543	0.350625
$546$	1.30276	0.0557528
$547$	22.5965	0.966156	0.483078	−	0.875577i	$-0.339519\pi$
$547$	22.5965	0.966156	0.483078	+	0.875577i	$0.339519\pi$
$548$	−7.17566	−0.306529
$549$	−0.130357	−0.00556349
$550$	−3.63154	−0.154849
$551$	17.7223	0.754995
$552$	4.14698	0.176507
$553$	4.53514	0.192854
$554$	−27.4072	−1.16442
$555$	1.53402	0.0651156
$556$	−3.80032	−0.161169
$557$	−11.2564	−0.476949	−0.238474	−	0.971149i	$-0.576647\pi$
$557$	−11.2564	−0.476949	−0.238474	+	0.971149i	$0.576647\pi$
$558$	−16.5653	−0.701263
$559$	16.0861	0.680369
$560$	−1.44211	−0.0609402
$561$	−0.714733	−0.0301760
$562$	−4.04505	−0.170630
$563$	−16.8583	−0.710493	−0.355246	−	0.934773i	$-0.615603\pi$
$563$	−16.8583	−0.710493	−0.355246	+	0.934773i	$0.615603\pi$
$564$	−1.34987	−0.0568398
$565$	16.8701	0.709731
$566$	25.7107	1.08070
$567$	−8.72106	−0.366250
$568$	46.8887	1.96740
$569$	−21.2557	−0.891084	−0.445542	−	0.895261i	$-0.646989\pi$
$569$	−21.2557	−0.891084	−0.445542	+	0.895261i	$0.646989\pi$
$570$	0.353720	0.0148157
$571$	32.7283	1.36964	0.684819	−	0.728713i	$-0.259881\pi$
$571$	32.7283	1.36964	0.684819	+	0.728713i	$0.259881\pi$
$572$	−21.3464	−0.892539
$573$	1.72516	0.0720697
$574$	8.24324	0.344066
$575$	7.72001	0.321947
$576$	−22.8820	−0.953415
$577$	−4.36463	−0.181702	−0.0908510	−	0.995864i	$-0.528959\pi$
$577$	−4.36463	−0.181702	−0.0908510	+	0.995864i	$0.528959\pi$
$578$	16.4770	0.685353
$579$	−2.00092	−0.0831554
$580$	8.26404	0.343145
$581$	7.32652	0.303955
$582$	1.50789	0.0625039
$583$	19.1452	0.792915
$584$	24.9845	1.03387
$585$	20.7815	0.859208
$586$	11.8469	0.489390
$587$	25.0269	1.03297	0.516485	−	0.856296i	$-0.327240\pi$
$587$	25.0269	1.03297	0.516485	+	0.856296i	$0.327240\pi$
$588$	−0.156292	−0.00644535
$589$	−10.0481	−0.414025
$590$	1.96214	0.0807800
$591$	−2.29753	−0.0945076
$592$	12.5442	0.515565
$593$	21.3000	0.874685	0.437342	−	0.899295i	$-0.355920\pi$
$593$	21.3000	0.874685	0.437342	+	0.899295i	$0.355920\pi$
$594$	3.82270	0.156847
$595$	−1.17778	−0.0482843
$596$	−5.88351	−0.240998
$597$	1.07878	0.0441516
$598$	−57.0289	−2.33209
$599$	10.6826	0.436478	0.218239	−	0.975895i	$-0.429969\pi$
$599$	10.6826	0.436478	0.218239	+	0.975895i	$0.429969\pi$
$600$	0.537173	0.0219300
$601$	−32.1515	−1.31149	−0.655744	−	0.754984i	$-0.727645\pi$
$601$	−32.1515	−1.31149	−0.655744	+	0.754984i	$0.727645\pi$
$602$	2.42530	0.0988480
$603$	6.63196	0.270074
$604$	0.474818	0.0193201
$605$	−0.841001	−0.0341915
$606$	−1.27226	−0.0516819
$607$	−7.63372	−0.309843	−0.154922	−	0.987927i	$-0.549512\pi$
$607$	−7.63372	−0.309843	−0.154922	+	0.987927i	$0.549512\pi$
$608$	−8.68558	−0.352247
$609$	−1.64448	−0.0666376
$610$	0.0463377	0.00187616
$611$	60.4558	2.44578
$612$	−3.09891	−0.125266
$613$	41.3140	1.66866	0.834329	−	0.551267i	$-0.185856\pi$
$613$	41.3140	1.66866	0.834329	+	0.551267i	$0.185856\pi$
$614$	−36.4880	−1.47254
$615$	−1.37749	−0.0555456
$616$	−10.4815	−0.422311
$617$	−37.6139	−1.51428	−0.757140	−	0.653252i	$-0.773404\pi$
$617$	−37.6139	−1.51428	−0.757140	+	0.653252i	$0.773404\pi$
$618$	−2.25286	−0.0906234
$619$	8.96197	0.360212	0.180106	−	0.983647i	$-0.442356\pi$
$619$	8.96197	0.360212	0.180106	+	0.983647i	$0.442356\pi$
$620$	−4.68550	−0.188174
$621$	−8.12639	−0.326101
$622$	19.9174	0.798617
$623$	14.6526	0.587045
$624$	−1.78018	−0.0712644
$625$	1.00000	0.0400000
$626$	−23.4678	−0.937962
$627$	1.15334	0.0460600
$628$	−7.74839	−0.309195
$629$	10.2450	0.408493
$630$	3.13323	0.124831
$631$	−23.8093	−0.947835	−0.473917	−	0.880569i	$-0.657160\pi$
$631$	−23.8093	−0.947835	−0.473917	+	0.880569i	$0.657160\pi$
$632$	−13.8140	−0.549490
$633$	0.949797	0.0377510
$634$	−15.5360	−0.617011
$635$	14.1236	0.560479
$636$	−0.869565	−0.0344805
$637$	6.99973	0.277339
$638$	−33.8636	−1.34067
$639$	−45.7020	−1.80794
$640$	−1.00629	−0.0397770
$641$	−39.3068	−1.55252	−0.776262	−	0.630411i	$-0.782887\pi$
$641$	−39.3068	−1.55252	−0.776262	+	0.630411i	$0.782887\pi$
$642$	0.743432	0.0293409
$643$	−30.3638	−1.19743	−0.598715	−	0.800962i	$-0.704322\pi$
$643$	−30.3638	−1.19743	−0.598715	+	0.800962i	$0.704322\pi$
$644$	6.84176	0.269603
$645$	−0.405280	−0.0159579
$646$	2.36232	0.0929441
$647$	19.4049	0.762884	0.381442	−	0.924393i	$-0.375428\pi$
$647$	19.4049	0.762884	0.381442	+	0.924393i	$0.375428\pi$
$648$	26.5643	1.04354
$649$	6.39775	0.251134
$650$	−7.38716	−0.289748
$651$	0.932378	0.0365428
$652$	15.1334	0.592668
$653$	−37.5277	−1.46857	−0.734285	−	0.678841i	$-0.762483\pi$
$653$	−37.5277	−1.46857	−0.734285	+	0.678841i	$0.762483\pi$
$654$	1.52343	0.0595710
$655$	12.0149	0.469461
$656$	−11.2642	−0.439793
$657$	−24.3522	−0.950070
$658$	9.11492	0.355337
$659$	−7.91358	−0.308269	−0.154135	−	0.988050i	$-0.549259\pi$
$659$	−7.91358	−0.308269	−0.154135	+	0.988050i	$0.549259\pi$
$660$	0.537811	0.0209343
$661$	−9.73139	−0.378507	−0.189254	−	0.981928i	$-0.560607\pi$
$661$	−9.73139	−0.378507	−0.189254	+	0.981928i	$0.560607\pi$
$662$	−31.1075	−1.20903
$663$	−1.45389	−0.0564643
$664$	−22.3165	−0.866048
$665$	1.90054	0.0736999
$666$	−27.2545	−1.05609
$667$	71.9880	2.78739
$668$	−5.88116	−0.227549
$669$	0.447323	0.0172945
$670$	−2.35745	−0.0910763
$671$	0.151089	0.00583272
$672$	0.805947	0.0310901
$673$	13.7602	0.530417	0.265208	−	0.964191i	$-0.414559\pi$
$673$	13.7602	0.530417	0.265208	+	0.964191i	$0.414559\pi$
$674$	−21.6530	−0.834044
$675$	−1.05264	−0.0405161
$676$	−31.9011	−1.22697
$677$	−36.7348	−1.41183	−0.705917	−	0.708295i	$-0.749465\pi$
$677$	−36.7348	−1.41183	−0.705917	+	0.708295i	$0.749465\pi$
$678$	3.13979	0.120583
$679$	8.10190	0.310922
$680$	3.58750	0.137575
$681$	−2.62294	−0.100511
$682$	19.1998	0.735199
$683$	39.9800	1.52979	0.764895	−	0.644155i	$-0.222791\pi$
$683$	39.9800	1.52979	0.764895	+	0.644155i	$0.222791\pi$
$684$	5.00061	0.191203
$685$	−8.09677	−0.309362
$686$	1.05535	0.0402934
$687$	0.176354	0.00672833
$688$	−3.31412	−0.126350
$689$	38.9446	1.48367
$690$	1.43681	0.0546985
$691$	−21.4525	−0.816092	−0.408046	−	0.912961i	$-0.633790\pi$
$691$	−21.4525	−0.816092	−0.408046	+	0.912961i	$0.633790\pi$
$692$	9.49945	0.361115
$693$	10.2162	0.388082
$694$	−16.8750	−0.640565
$695$	−4.28815	−0.162659
$696$	5.00906	0.189868
$697$	−9.19953	−0.348457
$698$	−16.3900	−0.620373
$699$	−1.14084	−0.0431504
$700$	0.886237	0.0334966
$701$	13.2233	0.499439	0.249720	−	0.968318i	$-0.419662\pi$
$701$	13.2233	0.499439	0.249720	+	0.968318i	$0.419662\pi$
$702$	7.77602	0.293487
$703$	−16.5319	−0.623514
$704$	26.5211	0.999552
$705$	−1.52315	−0.0573651
$706$	17.0890	0.643152
$707$	−6.83585	−0.257089
$708$	−0.290582	−0.0109207
$709$	−22.7931	−0.856014	−0.428007	−	0.903775i	$-0.640784\pi$
$709$	−22.7931	−0.856014	−0.428007	+	0.903775i	$0.640784\pi$
$710$	16.2456	0.609687
$711$	13.4644	0.504953
$712$	−44.6317	−1.67264
$713$	−40.8154	−1.52855
$714$	−0.219203	−0.00820346
$715$	−24.0866	−0.900787
$716$	16.6547	0.622415
$717$	1.82362	0.0681043
$718$	−30.7810	−1.14873
$719$	−23.9806	−0.894325	−0.447163	−	0.894453i	$-0.647565\pi$
$719$	−23.9806	−0.894325	−0.447163	+	0.894453i	$0.647565\pi$
$720$	−4.28148	−0.159561
$721$	−12.1047	−0.450801
$722$	16.2397	0.604377
$723$	−1.97254	−0.0733597
$724$	−0.602334	−0.0223856
$725$	9.32486	0.346317
$726$	−0.156523	−0.00580911
$727$	−14.9127	−0.553080	−0.276540	−	0.961002i	$-0.589188\pi$
$727$	−14.9127	−0.553080	−0.276540	+	0.961002i	$0.589188\pi$
$728$	−21.3211	−0.790212
$729$	−25.3350	−0.938335
$730$	8.65643	0.320389
$731$	−2.70666	−0.100109
$732$	−0.00686236	−0.000253640 0
$733$	41.8848	1.54705	0.773526	−	0.633764i	$-0.218491\pi$
$733$	41.8848	1.54705	0.773526	+	0.633764i	$0.218491\pi$
$734$	5.36016	0.197847
$735$	−0.176354	−0.00650492
$736$	−35.2808	−1.30047
$737$	−7.68671	−0.283144
$738$	24.4734	0.900877
$739$	23.6216	0.868933	0.434467	−	0.900688i	$-0.356937\pi$
$739$	23.6216	0.868933	0.434467	+	0.900688i	$0.356937\pi$
$740$	−7.70896	−0.283387
$741$	2.34609	0.0861857
$742$	5.87169	0.215556
$743$	36.0578	1.32283	0.661416	−	0.750020i	$-0.269956\pi$
$743$	36.0578	1.32283	0.661416	+	0.750020i	$0.269956\pi$
$744$	−2.84001	−0.104120
$745$	−6.63875	−0.243225
$746$	−22.4892	−0.823389
$747$	21.7517	0.795853
$748$	3.59177	0.131328
$749$	3.99447	0.145955
$750$	0.186115	0.00679597
$751$	−9.26373	−0.338038	−0.169019	−	0.985613i	$-0.554060\pi$
$751$	−9.26373	−0.338038	−0.169019	+	0.985613i	$0.554060\pi$
$752$	−12.4553	−0.454199
$753$	2.59458	0.0945516
$754$	−68.8842	−2.50861
$755$	0.535768	0.0194986
$756$	−0.932888	−0.0339288
$757$	−33.0741	−1.20210	−0.601050	−	0.799212i	$-0.705251\pi$
$757$	−33.0741	−1.20210	−0.601050	+	0.799212i	$0.705251\pi$
$758$	38.5308	1.39950
$759$	4.68487	0.170050
$760$	−5.78903	−0.209990
$761$	10.4377	0.378368	0.189184	−	0.981942i	$-0.439416\pi$
$761$	10.4377	0.378368	0.189184	+	0.981942i	$0.439416\pi$
$762$	2.62862	0.0952249
$763$	8.18543	0.296333
$764$	−8.66951	−0.313652
$765$	−3.49671	−0.126424
$766$	−4.45176	−0.160849
$767$	13.0141	0.469912
$768$	−2.90568	−0.104850
$769$	6.24782	0.225302	0.112651	−	0.993635i	$-0.464066\pi$
$769$	6.24782	0.225302	0.112651	+	0.993635i	$0.464066\pi$
$770$	−3.63154	−0.130872
$771$	5.47502	0.197178
$772$	10.0553	0.361897
$773$	37.3719	1.34417	0.672087	−	0.740473i	$-0.265398\pi$
$773$	37.3719	1.34417	0.672087	+	0.740473i	$0.265398\pi$
$774$	7.20048	0.258816
$775$	−5.28696	−0.189913
$776$	−24.6783	−0.885900
$777$	1.53402	0.0550327
$778$	2.56568	0.0919841
$779$	14.8450	0.531876
$780$	1.09400	0.0391714
$781$	52.9704	1.89543
$782$	9.59573	0.343143
$783$	−9.81572	−0.350785
$784$	−1.44211	−0.0515039
$785$	−8.74303	−0.312052
$786$	2.23616	0.0797611
$787$	10.6026	0.377940	0.188970	−	0.981983i	$-0.439485\pi$
$787$	10.6026	0.377940	0.188970	+	0.981983i	$0.439485\pi$
$788$	11.5458	0.411303
$789$	2.37202	0.0844463
$790$	−4.78615	−0.170284
$791$	16.8701	0.599832
$792$	−31.1185	−1.10575
$793$	0.307340	0.0109140
$794$	−3.82825	−0.135859
$795$	−0.981188	−0.0347991
$796$	−5.42123	−0.192150
$797$	4.88587	0.173066	0.0865332	−	0.996249i	$-0.472421\pi$
$797$	4.88587	0.173066	0.0865332	+	0.996249i	$0.472421\pi$
$798$	0.353720	0.0125216
$799$	−10.1723	−0.359871
$800$	−4.57005	−0.161576
$801$	43.5021	1.53707
$802$	−18.3015	−0.646248
$803$	28.2252	0.996045
$804$	0.349126	0.0123127
$805$	7.72001	0.272095
$806$	39.0556	1.37568
$807$	−0.476081	−0.0167588
$808$	20.8219	0.732513
$809$	8.15712	0.286789	0.143395	−	0.989666i	$-0.454198\pi$
$809$	8.15712	0.286789	0.143395	+	0.989666i	$0.454198\pi$
$810$	9.20377	0.323387
$811$	20.0066	0.702527	0.351264	−	0.936277i	$-0.385752\pi$
$811$	20.0066	0.702527	0.351264	+	0.936277i	$0.385752\pi$
$812$	8.26404	0.290011
$813$	0.650045	0.0227981
$814$	31.5891	1.10720
$815$	17.0760	0.598145
$816$	0.299535	0.0104858
$817$	4.36765	0.152805
$818$	−2.55035	−0.0891710
$819$	20.7815	0.726164
$820$	6.92232	0.241738
$821$	−21.3976	−0.746783	−0.373391	−	0.927674i	$-0.621805\pi$
$821$	−21.3976	−0.746783	−0.373391	+	0.927674i	$0.621805\pi$
$822$	−1.50693	−0.0525603
$823$	−49.0475	−1.70969	−0.854844	−	0.518885i	$-0.826347\pi$
$823$	−49.0475	−1.70969	−0.854844	+	0.518885i	$0.826347\pi$
$824$	36.8707	1.28445
$825$	0.606848	0.0211277
$826$	1.96214	0.0682715
$827$	6.48400	0.225471	0.112735	−	0.993625i	$-0.464039\pi$
$827$	6.48400	0.225471	0.112735	+	0.993625i	$0.464039\pi$
$828$	20.3125	0.705908
$829$	−5.09284	−0.176882	−0.0884408	−	0.996081i	$-0.528188\pi$
$829$	−5.09284	−0.176882	−0.0884408	+	0.996081i	$0.528188\pi$
$830$	−7.73204	−0.268383
$831$	4.57988	0.158874
$832$	53.9484	1.87032
$833$	−1.17778	−0.0408076
$834$	−0.798090	−0.0276356
$835$	−6.63610	−0.229652
$836$	−5.79591	−0.200456
$837$	5.56527	0.192364
$838$	−7.75734	−0.267973
$839$	−0.820289	−0.0283195	−0.0141598	−	0.999900i	$-0.504507\pi$
$839$	−0.820289	−0.0283195	−0.0141598	+	0.999900i	$0.504507\pi$
$840$	0.537173	0.0185342
$841$	57.9530	1.99838
$842$	−9.14848	−0.315277
$843$	0.675948	0.0232809
$844$	−4.77304	−0.164295
$845$	−35.9962	−1.23831
$846$	27.0613	0.930386
$847$	−0.841001	−0.0288971
$848$	−8.02352	−0.275529
$849$	−4.29638	−0.147451
$850$	1.24297	0.0426335
$851$	−67.1527	−2.30197
$852$	−2.40589	−0.0824243
$853$	−40.9686	−1.40274	−0.701370	−	0.712798i	$-0.747428\pi$
$853$	−40.9686	−1.40274	−0.701370	+	0.712798i	$0.747428\pi$
$854$	0.0463377	0.00158564
$855$	5.64252	0.192970
$856$	−12.1671	−0.415863
$857$	54.4420	1.85970	0.929852	−	0.367935i	$-0.119935\pi$
$857$	54.4420	1.85970	0.929852	+	0.367935i	$0.119935\pi$
$858$	−4.48288	−0.153043
$859$	−39.6992	−1.35452	−0.677260	−	0.735744i	$-0.736833\pi$
$859$	−39.6992	−1.35452	−0.677260	+	0.735744i	$0.736833\pi$
$860$	2.03667	0.0694497
$861$	−1.37749	−0.0469446
$862$	−19.9562	−0.679711
$863$	14.8822	0.506595	0.253298	−	0.967388i	$-0.418485\pi$
$863$	14.8822	0.506595	0.253298	+	0.967388i	$0.418485\pi$
$864$	4.81062	0.163660
$865$	10.7189	0.364452
$866$	−32.4723	−1.10345
$867$	−2.75339	−0.0935099
$868$	−4.68550	−0.159036
$869$	−15.6057	−0.529389
$870$	1.73550	0.0588389
$871$	−15.6361	−0.529808
$872$	−24.9327	−0.844329
$873$	24.0537	0.814095
$874$	−15.4843	−0.523765
$875$	1.00000	0.0338062
$876$	−1.28197	−0.0433138
$877$	−37.4492	−1.26457	−0.632284	−	0.774736i	$-0.717883\pi$
$877$	−37.4492	−1.26457	−0.632284	+	0.774736i	$0.717883\pi$
$878$	26.7494	0.902748
$879$	−1.97967	−0.0667727
$880$	4.96241	0.167283
$881$	11.0613	0.372664	0.186332	−	0.982487i	$-0.440340\pi$
$881$	11.0613	0.372664	0.186332	+	0.982487i	$0.440340\pi$
$882$	3.13323	0.105501
$883$	4.25775	0.143285	0.0716423	−	0.997430i	$-0.477176\pi$
$883$	4.25775	0.143285	0.0716423	+	0.997430i	$0.477176\pi$
$884$	7.30626	0.245736
$885$	−0.327883	−0.0110217
$886$	17.1171	0.575060
$887$	8.24772	0.276931	0.138466	−	0.990367i	$-0.455783\pi$
$887$	8.24772	0.276931	0.138466	+	0.990367i	$0.455783\pi$
$888$	−4.67261	−0.156803
$889$	14.1236	0.473691
$890$	−15.4636	−0.518342
$891$	30.0098	1.00537
$892$	−2.24794	−0.0752667
$893$	16.4148	0.549299
$894$	−1.23557	−0.0413237
$895$	18.7926	0.628167
$896$	−1.00629	−0.0336177
$897$	9.52981	0.318191
$898$	35.0911	1.17101
$899$	−49.3002	−1.64425
$900$	2.63115	0.0877050
$901$	−6.55286	−0.218307
$902$	−28.3656	−0.944472
$903$	−0.405280	−0.0134869
$904$	−51.3862	−1.70908
$905$	−0.679653	−0.0225924
$906$	0.0997147	0.00331280
$907$	37.9050	1.25862	0.629308	−	0.777156i	$-0.283338\pi$
$907$	37.9050	1.25862	0.629308	+	0.777156i	$0.283338\pi$
$908$	13.1811	0.437431
$909$	−20.2950	−0.673141
$910$	−7.38716	−0.244882
$911$	0.389540	0.0129060	0.00645302	−	0.999979i	$-0.497946\pi$
$911$	0.389540	0.0129060	0.00645302	+	0.999979i	$0.497946\pi$
$912$	−0.483350	−0.0160053
$913$	−25.2111	−0.834365
$914$	15.5576	0.514598
$915$	−0.00774325	−0.000255984 0
$916$	−0.886237	−0.0292821
$917$	12.0149	0.396767
$918$	−1.30840	−0.0431836
$919$	−22.0521	−0.727431	−0.363715	−	0.931510i	$-0.618492\pi$
$919$	−22.0521	−0.727431	−0.363715	+	0.931510i	$0.618492\pi$
$920$	−23.5151	−0.775269
$921$	6.09733	0.200914
$922$	−21.3537	−0.703248
$923$	107.751	3.54666
$924$	0.537811	0.0176927
$925$	−8.69853	−0.286006
$926$	−10.3371	−0.339697
$927$	−35.9375	−1.18034
$928$	−42.6151	−1.39891
$929$	23.2441	0.762614	0.381307	−	0.924449i	$-0.375474\pi$
$929$	23.2441	0.762614	0.381307	+	0.924449i	$0.375474\pi$
$930$	−0.983985	−0.0322661
$931$	1.90054	0.0622878
$932$	5.73307	0.187793
$933$	−3.32830	−0.108964
$934$	0.904472	0.0295952
$935$	4.05283	0.132542
$936$	−63.3002	−2.06903
$937$	28.3995	0.927771	0.463885	−	0.885895i	$-0.346455\pi$
$937$	28.3995	0.927771	0.463885	+	0.885895i	$0.346455\pi$
$938$	−2.35745	−0.0769735
$939$	3.92159	0.127976
$940$	7.65432	0.249656
$941$	−8.65126	−0.282023	−0.141012	−	0.990008i	$-0.545035\pi$
$941$	−8.65126	−0.282023	−0.141012	+	0.990008i	$0.545035\pi$
$942$	−1.62721	−0.0530174
$943$	60.3003	1.96365
$944$	−2.68121	−0.0872661
$945$	−1.05264	−0.0342424
$946$	−8.34565	−0.271341
$947$	−57.0061	−1.85245	−0.926224	−	0.376974i	$-0.876965\pi$
$947$	−57.0061	−1.85245	−0.926224	+	0.376974i	$0.876965\pi$
$948$	0.708803	0.0230209
$949$	57.4148	1.86376
$950$	−2.00574	−0.0650747
$951$	2.59613	0.0841854
$952$	3.58750	0.116272
$953$	−18.9213	−0.612921	−0.306461	−	0.951883i	$-0.599145\pi$
$953$	−18.9213	−0.612921	−0.306461	+	0.951883i	$0.599145\pi$
$954$	17.4324	0.564396
$955$	−9.78238	−0.316550
$956$	−9.16428	−0.296394
$957$	5.65877	0.182922
$958$	29.4647	0.951960
$959$	−8.09677	−0.261458
$960$	−1.35920	−0.0438680
$961$	−3.04801	−0.0983228
$962$	64.2574	2.07174
$963$	11.8592	0.382157
$964$	9.91268	0.319266
$965$	11.3460	0.365242
$966$	1.43681	0.0462286
$967$	6.72890	0.216387	0.108193	−	0.994130i	$-0.465493\pi$
$967$	6.72890	0.216387	0.108193	+	0.994130i	$0.465493\pi$
$968$	2.56168	0.0823355
$969$	−0.394755	−0.0126814
$970$	−8.55034	−0.274535
$971$	20.8492	0.669083	0.334541	−	0.942381i	$-0.391419\pi$
$971$	20.8492	0.669083	0.334541	+	0.942381i	$0.391419\pi$
$972$	−4.16169	−0.133486
$973$	−4.28815	−0.137472
$974$	−31.9783	−1.02465
$975$	1.23443	0.0395334
$976$	−0.0633193	−0.00202680
$977$	−47.1315	−1.50787	−0.753935	−	0.656949i	$-0.771847\pi$
$977$	−47.1315	−1.50787	−0.753935	+	0.656949i	$0.771847\pi$
$978$	3.17810	0.101624
$979$	−50.4208	−1.61145
$980$	0.886237	0.0283098
$981$	24.3017	0.775894
$982$	9.17165	0.292679
$983$	42.2594	1.34787	0.673933	−	0.738793i	$-0.264604\pi$
$983$	42.2594	1.34787	0.673933	+	0.738793i	$0.264604\pi$
$984$	4.19581	0.133757
$985$	13.0279	0.415104
$986$	11.5905	0.369117
$987$	−1.52315	−0.0484823
$988$	−11.7899	−0.375086
$989$	17.7414	0.564143
$990$	−10.7817	−0.342664
$991$	−39.1637	−1.24408	−0.622038	−	0.782987i	$-0.713695\pi$
$991$	−39.1637	−1.24408	−0.622038	+	0.782987i	$0.713695\pi$
$992$	24.1617	0.767134
$993$	5.19822	0.164960
$994$	16.2456	0.515279
$995$	−6.11713	−0.193926
$996$	1.14507	0.0362830
$997$	11.3276	0.358749	0.179375	−	0.983781i	$-0.442593\pi$
$997$	11.3276	0.358749	0.179375	+	0.983781i	$0.442593\pi$
$998$	−11.7235	−0.371100
$999$	9.15642	0.289696

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.21	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.21	✓	62	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)

\(f(q)\)	\(=\)	\(q-1.05535 q^{2} +0.176354 q^{3} -0.886237 q^{4} -1.00000 q^{5} -0.186115 q^{6} -1.00000 q^{7} +3.04599 q^{8} -2.96890 q^{9} +O(q^{10})\)	\(q-1.05535 q^{2} +0.176354 q^{3} -0.886237 q^{4} -1.00000 q^{5} -0.186115 q^{6} -1.00000 q^{7} +3.04599 q^{8} -2.96890 q^{9} +1.05535 q^{10} +3.44108 q^{11} -0.156292 q^{12} +6.99973 q^{13} +1.05535 q^{14} -0.176354 q^{15} -1.44211 q^{16} -1.17778 q^{17} +3.13323 q^{18} +1.90054 q^{19} +0.886237 q^{20} -0.176354 q^{21} -3.63154 q^{22} +7.72001 q^{23} +0.537173 q^{24} +1.00000 q^{25} -7.38716 q^{26} -1.05264 q^{27} +0.886237 q^{28} +9.32486 q^{29} +0.186115 q^{30} -5.28696 q^{31} -4.57005 q^{32} +0.606848 q^{33} +1.24297 q^{34} +1.00000 q^{35} +2.63115 q^{36} -8.69853 q^{37} -2.00574 q^{38} +1.23443 q^{39} -3.04599 q^{40} +7.81091 q^{41} +0.186115 q^{42} +2.29810 q^{43} -3.04961 q^{44} +2.96890 q^{45} -8.14731 q^{46} +8.63688 q^{47} -0.254322 q^{48} +1.00000 q^{49} -1.05535 q^{50} -0.207706 q^{51} -6.20342 q^{52} +5.56374 q^{53} +1.11090 q^{54} -3.44108 q^{55} -3.04599 q^{56} +0.335169 q^{57} -9.84099 q^{58} +1.85923 q^{59} +0.156292 q^{60} +0.0439074 q^{61} +5.57960 q^{62} +2.96890 q^{63} +7.70722 q^{64} -6.99973 q^{65} -0.640437 q^{66} -2.23381 q^{67} +1.04379 q^{68} +1.36145 q^{69} -1.05535 q^{70} +15.3936 q^{71} -9.04324 q^{72} +8.20243 q^{73} +9.17999 q^{74} +0.176354 q^{75} -1.68433 q^{76} -3.44108 q^{77} -1.30276 q^{78} -4.53514 q^{79} +1.44211 q^{80} +8.72106 q^{81} -8.24324 q^{82} -7.32652 q^{83} +0.156292 q^{84} +1.17778 q^{85} -2.42530 q^{86} +1.64448 q^{87} +10.4815 q^{88} -14.6526 q^{89} -3.13323 q^{90} -6.99973 q^{91} -6.84176 q^{92} -0.932378 q^{93} -9.11492 q^{94} -1.90054 q^{95} -0.805947 q^{96} -8.10190 q^{97} -1.05535 q^{98} -10.2162 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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