LMFDB - Embedded newform 8015.2.a.o.1.14

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:	$73$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-2.01224 q^{2} +2.54989 q^{3} +2.04911 q^{4} +1.00000 q^{5} -5.13098 q^{6} +1.00000 q^{7} -0.0988175 q^{8} +3.50192 q^{9} +O(q^{10})$	\(q-2.01224 q^{2} +2.54989 q^{3} +2.04911 q^{4} +1.00000 q^{5} -5.13098 q^{6} +1.00000 q^{7} -0.0988175 q^{8} +3.50192 q^{9} -2.01224 q^{10} +2.11418 q^{11} +5.22499 q^{12} +3.85388 q^{13} -2.01224 q^{14} +2.54989 q^{15} -3.89937 q^{16} +4.70442 q^{17} -7.04670 q^{18} -2.22297 q^{19} +2.04911 q^{20} +2.54989 q^{21} -4.25423 q^{22} +7.20831 q^{23} -0.251973 q^{24} +1.00000 q^{25} -7.75492 q^{26} +1.27984 q^{27} +2.04911 q^{28} +7.26498 q^{29} -5.13098 q^{30} -2.31929 q^{31} +8.04411 q^{32} +5.39091 q^{33} -9.46642 q^{34} +1.00000 q^{35} +7.17581 q^{36} -8.87502 q^{37} +4.47315 q^{38} +9.82694 q^{39} -0.0988175 q^{40} +5.55108 q^{41} -5.13098 q^{42} +3.08001 q^{43} +4.33218 q^{44} +3.50192 q^{45} -14.5048 q^{46} +10.2118 q^{47} -9.94296 q^{48} +1.00000 q^{49} -2.01224 q^{50} +11.9957 q^{51} +7.89701 q^{52} -13.3849 q^{53} -2.57534 q^{54} +2.11418 q^{55} -0.0988175 q^{56} -5.66832 q^{57} -14.6189 q^{58} +4.04193 q^{59} +5.22499 q^{60} -8.74093 q^{61} +4.66696 q^{62} +3.50192 q^{63} -8.38792 q^{64} +3.85388 q^{65} -10.8478 q^{66} +9.75974 q^{67} +9.63987 q^{68} +18.3804 q^{69} -2.01224 q^{70} -12.3182 q^{71} -0.346051 q^{72} +10.3918 q^{73} +17.8587 q^{74} +2.54989 q^{75} -4.55511 q^{76} +2.11418 q^{77} -19.7742 q^{78} -4.96208 q^{79} -3.89937 q^{80} -7.24232 q^{81} -11.1701 q^{82} +10.8656 q^{83} +5.22499 q^{84} +4.70442 q^{85} -6.19771 q^{86} +18.5249 q^{87} -0.208918 q^{88} -10.1387 q^{89} -7.04670 q^{90} +3.85388 q^{91} +14.7706 q^{92} -5.91392 q^{93} -20.5486 q^{94} -2.22297 q^{95} +20.5116 q^{96} -15.3125 q^{97} -2.01224 q^{98} +7.40368 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) $ 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * 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 $

$2$	−2.01224	−1.42287	−0.711434	−	0.702753i	$-0.751954\pi$
$2$	−2.01224	−1.42287	−0.711434	+	0.702753i	$0.751954\pi$
$3$	2.54989	1.47218	0.736089	−	0.676885i	$-0.236671\pi$
$3$	2.54989	1.47218	0.736089	+	0.676885i	$0.236671\pi$
$4$	2.04911	1.02455
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−5.13098	−2.09471
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.0988175	−0.0349373
$9$	3.50192	1.16731
$10$	−2.01224	−0.636326
$11$	2.11418	0.637448	0.318724	−	0.947848i	$-0.396746\pi$
$11$	2.11418	0.637448	0.318724	+	0.947848i	$0.396746\pi$
$12$	5.22499	1.50833
$13$	3.85388	1.06887	0.534436	−	0.845209i	$-0.320524\pi$
$13$	3.85388	1.06887	0.534436	+	0.845209i	$0.320524\pi$
$14$	−2.01224	−0.537794
$15$	2.54989	0.658378
$16$	−3.89937	−0.974843
$17$	4.70442	1.14099	0.570495	−	0.821301i	$-0.306751\pi$
$17$	4.70442	1.14099	0.570495	+	0.821301i	$0.306751\pi$
$18$	−7.04670	−1.66092
$19$	−2.22297	−0.509984	−0.254992	−	0.966943i	$-0.582073\pi$
$19$	−2.22297	−0.509984	−0.254992	+	0.966943i	$0.582073\pi$
$20$	2.04911	0.458195
$21$	2.54989	0.556431
$22$	−4.25423	−0.907005
$23$	7.20831	1.50304	0.751518	−	0.659712i	$-0.229322\pi$
$23$	7.20831	1.50304	0.751518	+	0.659712i	$0.229322\pi$
$24$	−0.251973	−0.0514339
$25$	1.00000	0.200000
$26$	−7.75492	−1.52087
$27$	1.27984	0.246305
$28$	2.04911	0.387245
$29$	7.26498	1.34907	0.674536	−	0.738242i	$-0.264344\pi$
$29$	7.26498	1.34907	0.674536	+	0.738242i	$0.264344\pi$
$30$	−5.13098	−0.936785
$31$	−2.31929	−0.416556	−0.208278	−	0.978070i	$-0.566786\pi$
$31$	−2.31929	−0.416556	−0.208278	+	0.978070i	$0.566786\pi$
$32$	8.04411	1.42201
$33$	5.39091	0.938437
$34$	−9.46642	−1.62348
$35$	1.00000	0.169031
$36$	7.17581	1.19597
$37$	−8.87502	−1.45904	−0.729522	−	0.683958i	$-0.760257\pi$
$37$	−8.87502	−1.45904	−0.729522	+	0.683958i	$0.760257\pi$
$38$	4.47315	0.725641
$39$	9.82694	1.57357
$40$	−0.0988175	−0.0156244
$41$	5.55108	0.866932	0.433466	−	0.901170i	$-0.357290\pi$
$41$	5.55108	0.866932	0.433466	+	0.901170i	$0.357290\pi$
$42$	−5.13098	−0.791728
$43$	3.08001	0.469697	0.234848	−	0.972032i	$-0.424541\pi$
$43$	3.08001	0.469697	0.234848	+	0.972032i	$0.424541\pi$
$44$	4.33218	0.653100
$45$	3.50192	0.522035
$46$	−14.5048	−2.13862
$47$	10.2118	1.48954	0.744772	−	0.667319i	$-0.232558\pi$
$47$	10.2118	1.48954	0.744772	+	0.667319i	$0.232558\pi$
$48$	−9.94296	−1.43514
$49$	1.00000	0.142857
$50$	−2.01224	−0.284574
$51$	11.9957	1.67974
$52$	7.89701	1.09512
$53$	−13.3849	−1.83856	−0.919281	−	0.393602i	$-0.871229\pi$
$53$	−13.3849	−1.83856	−0.919281	+	0.393602i	$0.871229\pi$
$54$	−2.57534	−0.350460
$55$	2.11418	0.285076
$56$	−0.0988175	−0.0132050
$57$	−5.66832	−0.750788
$58$	−14.6189	−1.91955
$59$	4.04193	0.526214	0.263107	−	0.964767i	$-0.415253\pi$
$59$	4.04193	0.526214	0.263107	+	0.964767i	$0.415253\pi$
$60$	5.22499	0.674544
$61$	−8.74093	−1.11916	−0.559581	−	0.828776i	$-0.689038\pi$
$61$	−8.74093	−1.11916	−0.559581	+	0.828776i	$0.689038\pi$
$62$	4.66696	0.592705
$63$	3.50192	0.441200
$64$	−8.38792	−1.04849
$65$	3.85388	0.478014
$66$	−10.8478	−1.33527
$67$	9.75974	1.19234	0.596171	−	0.802858i	$-0.296688\pi$
$67$	9.75974	1.19234	0.596171	+	0.802858i	$0.296688\pi$
$68$	9.63987	1.16901
$69$	18.3804	2.21274
$70$	−2.01224	−0.240509
$71$	−12.3182	−1.46190	−0.730948	−	0.682433i	$-0.760922\pi$
$71$	−12.3182	−1.46190	−0.730948	+	0.682433i	$0.760922\pi$
$72$	−0.346051	−0.0407825
$73$	10.3918	1.21626	0.608132	−	0.793836i	$-0.291919\pi$
$73$	10.3918	1.21626	0.608132	+	0.793836i	$0.291919\pi$
$74$	17.8587	2.07603
$75$	2.54989	0.294436
$76$	−4.55511	−0.522507
$77$	2.11418	0.240933
$78$	−19.7742	−2.23898
$79$	−4.96208	−0.558278	−0.279139	−	0.960251i	$-0.590049\pi$
$79$	−4.96208	−0.558278	−0.279139	+	0.960251i	$0.590049\pi$
$80$	−3.89937	−0.435963
$81$	−7.24232	−0.804702
$82$	−11.1701	−1.23353
$83$	10.8656	1.19265	0.596326	−	0.802742i	$-0.296627\pi$
$83$	10.8656	1.19265	0.596326	+	0.802742i	$0.296627\pi$
$84$	5.22499	0.570093
$85$	4.70442	0.510266
$86$	−6.19771	−0.668317
$87$	18.5249	1.98607
$88$	−0.208918	−0.0222707
$89$	−10.1387	−1.07470	−0.537350	−	0.843359i	$-0.680575\pi$
$89$	−10.1387	−1.07470	−0.537350	+	0.843359i	$0.680575\pi$
$90$	−7.04670	−0.742788
$91$	3.85388	0.403996
$92$	14.7706	1.53994
$93$	−5.91392	−0.613245
$94$	−20.5486	−2.11943
$95$	−2.22297	−0.228072
$96$	20.5116	2.09345
$97$	−15.3125	−1.55475	−0.777373	−	0.629039i	$-0.783448\pi$
$97$	−15.3125	−1.55475	−0.777373	+	0.629039i	$0.783448\pi$
$98$	−2.01224	−0.203267
$99$	7.40368	0.744098
$100$	2.04911	0.204911
$101$	−4.28689	−0.426562	−0.213281	−	0.976991i	$-0.568415\pi$
$101$	−4.28689	−0.426562	−0.213281	+	0.976991i	$0.568415\pi$
$102$	−24.1383	−2.39005
$103$	14.9681	1.47485	0.737424	−	0.675430i	$-0.236042\pi$
$103$	14.9681	1.47485	0.737424	+	0.675430i	$0.236042\pi$
$104$	−0.380830	−0.0373435
$105$	2.54989	0.248843
$106$	26.9337	2.61603
$107$	9.74645	0.942225	0.471112	−	0.882073i	$-0.343853\pi$
$107$	9.74645	0.942225	0.471112	+	0.882073i	$0.343853\pi$
$108$	2.62253	0.252353
$109$	−5.81412	−0.556891	−0.278446	−	0.960452i	$-0.589819\pi$
$109$	−5.81412	−0.556891	−0.278446	+	0.960452i	$0.589819\pi$
$110$	−4.25423	−0.405625
$111$	−22.6303	−2.14797
$112$	−3.89937	−0.368456
$113$	18.5966	1.74942	0.874709	−	0.484648i	$-0.161052\pi$
$113$	18.5966	1.74942	0.874709	+	0.484648i	$0.161052\pi$
$114$	11.4060	1.06827
$115$	7.20831	0.672178
$116$	14.8867	1.38220
$117$	13.4960	1.24770
$118$	−8.13333	−0.748734
$119$	4.70442	0.431254
$120$	−0.251973	−0.0230019
$121$	−6.53026	−0.593660
$122$	17.5889	1.59242
$123$	14.1546	1.27628
$124$	−4.75247	−0.426784
$125$	1.00000	0.0894427
$126$	−7.04670	−0.627770
$127$	−14.6489	−1.29988	−0.649938	−	0.759987i	$-0.725205\pi$
$127$	−14.6489	−1.29988	−0.649938	+	0.759987i	$0.725205\pi$
$128$	0.790302	0.0698535
$129$	7.85367	0.691477
$130$	−7.75492	−0.680152
$131$	−5.98200	−0.522649	−0.261325	−	0.965251i	$-0.584159\pi$
$131$	−5.98200	−0.522649	−0.261325	+	0.965251i	$0.584159\pi$
$132$	11.0466	0.961480
$133$	−2.22297	−0.192756
$134$	−19.6389	−1.69655
$135$	1.27984	0.110151
$136$	−0.464879	−0.0398631
$137$	−21.8702	−1.86850	−0.934250	−	0.356619i	$-0.883930\pi$
$137$	−21.8702	−1.86850	−0.934250	+	0.356619i	$0.883930\pi$
$138$	−36.9857	−3.14843
$139$	7.00725	0.594347	0.297174	−	0.954823i	$-0.403956\pi$
$139$	7.00725	0.594347	0.297174	+	0.954823i	$0.403956\pi$
$140$	2.04911	0.173181
$141$	26.0389	2.19287
$142$	24.7871	2.08009
$143$	8.14778	0.681351
$144$	−13.6553	−1.13794
$145$	7.26498	0.603323
$146$	−20.9107	−1.73058
$147$	2.54989	0.210311
$148$	−18.1859	−1.49487
$149$	−11.2437	−0.921120	−0.460560	−	0.887629i	$-0.652351\pi$
$149$	−11.2437	−0.921120	−0.460560	+	0.887629i	$0.652351\pi$
$150$	−5.13098	−0.418943
$151$	3.74916	0.305103	0.152551	−	0.988296i	$-0.451251\pi$
$151$	3.74916	0.305103	0.152551	+	0.988296i	$0.451251\pi$
$152$	0.219668	0.0178175
$153$	16.4745	1.33189
$154$	−4.25423	−0.342816
$155$	−2.31929	−0.186290
$156$	20.1365	1.61221
$157$	3.96646	0.316558	0.158279	−	0.987394i	$-0.449405\pi$
$157$	3.96646	0.316558	0.158279	+	0.987394i	$0.449405\pi$
$158$	9.98490	0.794356
$159$	−34.1301	−2.70669
$160$	8.04411	0.635942
$161$	7.20831	0.568094
$162$	14.5733	1.14498
$163$	13.2562	1.03830	0.519151	−	0.854682i	$-0.326248\pi$
$163$	13.2562	1.03830	0.519151	+	0.854682i	$0.326248\pi$
$164$	11.3748	0.888219
$165$	5.39091	0.419682
$166$	−21.8641	−1.69699
$167$	−11.4367	−0.884999	−0.442500	−	0.896769i	$-0.645908\pi$
$167$	−11.4367	−0.884999	−0.442500	+	0.896769i	$0.645908\pi$
$168$	−0.251973	−0.0194402
$169$	1.85236	0.142489
$170$	−9.46642	−0.726042
$171$	−7.78467	−0.595308
$172$	6.31127	0.481230
$173$	−9.77975	−0.743541	−0.371770	−	0.928325i	$-0.621249\pi$
$173$	−9.77975	−0.743541	−0.371770	+	0.928325i	$0.621249\pi$
$174$	−37.2765	−2.82592
$175$	1.00000	0.0755929
$176$	−8.24396	−0.621412
$177$	10.3065	0.774681
$178$	20.4015	1.52916
$179$	8.09286	0.604889	0.302444	−	0.953167i	$-0.402197\pi$
$179$	8.09286	0.604889	0.302444	+	0.953167i	$0.402197\pi$
$180$	7.17581	0.534854
$181$	10.7572	0.799574	0.399787	−	0.916608i	$-0.369084\pi$
$181$	10.7572	0.799574	0.399787	+	0.916608i	$0.369084\pi$
$182$	−7.75492	−0.574833
$183$	−22.2884	−1.64760
$184$	−0.712307	−0.0525120
$185$	−8.87502	−0.652504
$186$	11.9002	0.872566
$187$	9.94598	0.727322
$188$	20.9251	1.52612
$189$	1.27984	0.0930946
$190$	4.47315	0.324516
$191$	−23.5532	−1.70425	−0.852125	−	0.523338i	$-0.824686\pi$
$191$	−23.5532	−1.70425	−0.852125	+	0.523338i	$0.824686\pi$
$192$	−21.3883	−1.54356
$193$	−22.9736	−1.65367	−0.826837	−	0.562442i	$-0.809862\pi$
$193$	−22.9736	−1.65367	−0.826837	+	0.562442i	$0.809862\pi$
$194$	30.8124	2.21220
$195$	9.82694	0.703722
$196$	2.04911	0.146365
$197$	−1.01935	−0.0726257	−0.0363128	−	0.999340i	$-0.511561\pi$
$197$	−1.01935	−0.0726257	−0.0363128	+	0.999340i	$0.511561\pi$
$198$	−14.8980	−1.05875
$199$	−5.83958	−0.413957	−0.206978	−	0.978346i	$-0.566363\pi$
$199$	−5.83958	−0.413957	−0.206978	+	0.978346i	$0.566363\pi$
$200$	−0.0988175	−0.00698745
$201$	24.8862	1.75534
$202$	8.62625	0.606941
$203$	7.26498	0.509901
$204$	24.5806	1.72098
$205$	5.55108	0.387704
$206$	−30.1193	−2.09851
$207$	25.2429	1.75450
$208$	−15.0277	−1.04198
$209$	−4.69975	−0.325089
$210$	−5.13098	−0.354071
$211$	−0.933960	−0.0642965	−0.0321482	−	0.999483i	$-0.510235\pi$
$211$	−0.933960	−0.0642965	−0.0321482	+	0.999483i	$0.510235\pi$
$212$	−27.4272	−1.88371
$213$	−31.4099	−2.15217
$214$	−19.6122	−1.34066
$215$	3.08001	0.210055
$216$	−0.126471	−0.00860523
$217$	−2.31929	−0.157443
$218$	11.6994	0.792383
$219$	26.4978	1.79056
$220$	4.33218	0.292075
$221$	18.1303	1.21957
$222$	45.5375	3.05628
$223$	21.6991	1.45308	0.726540	−	0.687124i	$-0.241127\pi$
$223$	21.6991	1.45308	0.726540	+	0.687124i	$0.241127\pi$
$224$	8.04411	0.537469
$225$	3.50192	0.233461
$226$	−37.4208	−2.48919
$227$	24.4876	1.62530	0.812650	−	0.582752i	$-0.198024\pi$
$227$	24.4876	1.62530	0.812650	+	0.582752i	$0.198024\pi$
$228$	−11.6150	−0.769223
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−14.5048	−0.956421
$231$	5.39091	0.354696
$232$	−0.717907	−0.0471329
$233$	−18.6848	−1.22408	−0.612042	−	0.790825i	$-0.709652\pi$
$233$	−18.6848	−1.22408	−0.612042	+	0.790825i	$0.709652\pi$
$234$	−27.1571	−1.77532
$235$	10.2118	0.666144
$236$	8.28235	0.539135
$237$	−12.6527	−0.821884
$238$	−9.46642	−0.613617
$239$	17.2919	1.11852	0.559259	−	0.828993i	$-0.311086\pi$
$239$	17.2919	1.11852	0.559259	+	0.828993i	$0.311086\pi$
$240$	−9.94296	−0.641815
$241$	−0.186273	−0.0119989	−0.00599946	−	0.999982i	$-0.501910\pi$
$241$	−0.186273	−0.0119989	−0.00599946	+	0.999982i	$0.501910\pi$
$242$	13.1404	0.844699
$243$	−22.3066	−1.43097
$244$	−17.9111	−1.14664
$245$	1.00000	0.0638877
$246$	−28.4825	−1.81598
$247$	−8.56705	−0.545108
$248$	0.229186	0.0145533
$249$	27.7060	1.75580
$250$	−2.01224	−0.127265
$251$	−29.1197	−1.83802	−0.919008	−	0.394239i	$-0.871008\pi$
$251$	−29.1197	−1.83802	−0.919008	+	0.394239i	$0.871008\pi$
$252$	7.17581	0.452034
$253$	15.2396	0.958108
$254$	29.4770	1.84955
$255$	11.9957	0.751202
$256$	15.1856	0.949098
$257$	−4.36339	−0.272181	−0.136090	−	0.990696i	$-0.543454\pi$
$257$	−4.36339	−0.272181	−0.136090	+	0.990696i	$0.543454\pi$
$258$	−15.8035	−0.983881
$259$	−8.87502	−0.551467
$260$	7.89701	0.489752
$261$	25.4414	1.57478
$262$	12.0372	0.743661
$263$	−30.2659	−1.86627	−0.933136	−	0.359523i	$-0.882939\pi$
$263$	−30.2659	−1.86627	−0.933136	+	0.359523i	$0.882939\pi$
$264$	−0.532716	−0.0327864
$265$	−13.3849	−0.822230
$266$	4.47315	0.274266
$267$	−25.8525	−1.58215
$268$	19.9988	1.22162
$269$	−20.3259	−1.23929	−0.619645	−	0.784882i	$-0.712724\pi$
$269$	−20.3259	−1.23929	−0.619645	+	0.784882i	$0.712724\pi$
$270$	−2.57534	−0.156730
$271$	1.54896	0.0940927	0.0470464	−	0.998893i	$-0.485019\pi$
$271$	1.54896	0.0940927	0.0470464	+	0.998893i	$0.485019\pi$
$272$	−18.3443	−1.11229
$273$	9.82694	0.594754
$274$	44.0082	2.65863
$275$	2.11418	0.127490
$276$	37.6634	2.26707
$277$	23.3910	1.40543	0.702714	−	0.711473i	$-0.251971\pi$
$277$	23.3910	1.40543	0.702714	+	0.711473i	$0.251971\pi$
$278$	−14.1003	−0.845678
$279$	−8.12196	−0.486249
$280$	−0.0988175	−0.00590548
$281$	10.7502	0.641301	0.320650	−	0.947198i	$-0.396099\pi$
$281$	10.7502	0.641301	0.320650	+	0.947198i	$0.396099\pi$
$282$	−52.3966	−3.12017
$283$	14.6236	0.869282	0.434641	−	0.900604i	$-0.356875\pi$
$283$	14.6236	0.869282	0.434641	+	0.900604i	$0.356875\pi$
$284$	−25.2412	−1.49779
$285$	−5.66832	−0.335762
$286$	−16.3953	−0.969473
$287$	5.55108	0.327670
$288$	28.1698	1.65992
$289$	5.13158	0.301858
$290$	−14.6189	−0.858450
$291$	−39.0451	−2.28886
$292$	21.2938	1.24613
$293$	17.8274	1.04149	0.520744	−	0.853713i	$-0.325655\pi$
$293$	17.8274	1.04149	0.520744	+	0.853713i	$0.325655\pi$
$294$	−5.13098	−0.299245
$295$	4.04193	0.235330
$296$	0.877007	0.0509750
$297$	2.70581	0.157007
$298$	22.6250	1.31063
$299$	27.7799	1.60655
$300$	5.22499	0.301665
$301$	3.08001	0.177529
$302$	−7.54421	−0.434121
$303$	−10.9311	−0.627974
$304$	8.66819	0.497155
$305$	−8.74093	−0.500504
$306$	−33.1507	−1.89510
$307$	8.68360	0.495599	0.247800	−	0.968811i	$-0.420293\pi$
$307$	8.68360	0.495599	0.247800	+	0.968811i	$0.420293\pi$
$308$	4.33218	0.246849
$309$	38.1669	2.17124
$310$	4.66696	0.265066
$311$	8.62205	0.488912	0.244456	−	0.969660i	$-0.421391\pi$
$311$	8.62205	0.488912	0.244456	+	0.969660i	$0.421391\pi$
$312$	−0.971074	−0.0549763
$313$	−27.5018	−1.55449	−0.777245	−	0.629198i	$-0.783384\pi$
$313$	−27.5018	−1.55449	−0.777245	+	0.629198i	$0.783384\pi$
$314$	−7.98148	−0.450421
$315$	3.50192	0.197311
$316$	−10.1678	−0.571986
$317$	2.50044	0.140439	0.0702194	−	0.997532i	$-0.477630\pi$
$317$	2.50044	0.140439	0.0702194	+	0.997532i	$0.477630\pi$
$318$	68.6778	3.85126
$319$	15.3594	0.859964
$320$	−8.38792	−0.468899
$321$	24.8523	1.38712
$322$	−14.5048	−0.808323
$323$	−10.4578	−0.581887
$324$	−14.8403	−0.824460
$325$	3.85388	0.213775
$326$	−26.6746	−1.47737
$327$	−14.8253	−0.819843
$328$	−0.548544	−0.0302882
$329$	10.2118	0.562995
$330$	−10.8478	−0.597152
$331$	0.784176	0.0431022	0.0215511	−	0.999768i	$-0.493140\pi$
$331$	0.784176	0.0431022	0.0215511	+	0.999768i	$0.493140\pi$
$332$	22.2647	1.22194
$333$	−31.0796	−1.70315
$334$	23.0134	1.25924
$335$	9.75974	0.533231
$336$	−9.94296	−0.542433
$337$	9.23087	0.502837	0.251419	−	0.967878i	$-0.419103\pi$
$337$	9.23087	0.502837	0.251419	+	0.967878i	$0.419103\pi$
$338$	−3.72739	−0.202743
$339$	47.4191	2.57545
$340$	9.63987	0.522795
$341$	−4.90338	−0.265533
$342$	15.6646	0.847045
$343$	1.00000	0.0539949
$344$	−0.304359	−0.0164099
$345$	18.3804	0.989566
$346$	19.6792	1.05796
$347$	1.89919	0.101954	0.0509770	−	0.998700i	$-0.483766\pi$
$347$	1.89919	0.101954	0.0509770	+	0.998700i	$0.483766\pi$
$348$	37.9594	2.03484
$349$	18.7370	1.00297	0.501484	−	0.865167i	$-0.332788\pi$
$349$	18.7370	1.00297	0.501484	+	0.865167i	$0.332788\pi$
$350$	−2.01224	−0.107559
$351$	4.93234	0.263269
$352$	17.0067	0.906458
$353$	7.94204	0.422712	0.211356	−	0.977409i	$-0.432212\pi$
$353$	7.94204	0.422712	0.211356	+	0.977409i	$0.432212\pi$
$354$	−20.7391	−1.10227
$355$	−12.3182	−0.653780
$356$	−20.7753	−1.10109
$357$	11.9957	0.634882
$358$	−16.2848	−0.860677
$359$	1.18430	0.0625051	0.0312526	−	0.999512i	$-0.490050\pi$
$359$	1.18430	0.0625051	0.0312526	+	0.999512i	$0.490050\pi$
$360$	−0.346051	−0.0182385
$361$	−14.0584	−0.739916
$362$	−21.6460	−1.13769
$363$	−16.6514	−0.873972
$364$	7.89701	0.413916
$365$	10.3918	0.543929
$366$	44.8496	2.34432
$367$	32.5256	1.69782	0.848912	−	0.528534i	$-0.177258\pi$
$367$	32.5256	1.69782	0.848912	+	0.528534i	$0.177258\pi$
$368$	−28.1079	−1.46522
$369$	19.4394	1.01198
$370$	17.8587	0.928427
$371$	−13.3849	−0.694911
$372$	−12.1183	−0.628302
$373$	6.74892	0.349446	0.174723	−	0.984618i	$-0.444097\pi$
$373$	6.74892	0.349446	0.174723	+	0.984618i	$0.444097\pi$
$374$	−20.0137	−1.03488
$375$	2.54989	0.131676
$376$	−1.00910	−0.0520406
$377$	27.9983	1.44199
$378$	−2.57534	−0.132461
$379$	−26.1477	−1.34312	−0.671558	−	0.740952i	$-0.734374\pi$
$379$	−26.1477	−1.34312	−0.671558	+	0.740952i	$0.734374\pi$
$380$	−4.55511	−0.233672
$381$	−37.3529	−1.91365
$382$	47.3947	2.42492
$383$	−26.1987	−1.33869	−0.669346	−	0.742951i	$-0.733426\pi$
$383$	−26.1987	−1.33869	−0.669346	+	0.742951i	$0.733426\pi$
$384$	2.01518	0.102837
$385$	2.11418	0.107748
$386$	46.2283	2.35296
$387$	10.7859	0.548280
$388$	−31.3769	−1.59292
$389$	22.5563	1.14365	0.571826	−	0.820375i	$-0.306235\pi$
$389$	22.5563	1.14365	0.571826	+	0.820375i	$0.306235\pi$
$390$	−19.7742	−1.00130
$391$	33.9109	1.71495
$392$	−0.0988175	−0.00499104
$393$	−15.2534	−0.769433
$394$	2.05118	0.103337
$395$	−4.96208	−0.249669
$396$	15.1709	0.762368
$397$	−22.8162	−1.14511	−0.572557	−	0.819865i	$-0.694048\pi$
$397$	−22.8162	−1.14511	−0.572557	+	0.819865i	$0.694048\pi$
$398$	11.7506	0.589006
$399$	−5.66832	−0.283771
$400$	−3.89937	−0.194969
$401$	8.00259	0.399631	0.199815	−	0.979834i	$-0.435966\pi$
$401$	8.00259	0.399631	0.199815	+	0.979834i	$0.435966\pi$
$402$	−50.0770	−2.49762
$403$	−8.93824	−0.445246
$404$	−8.78430	−0.437035
$405$	−7.24232	−0.359874
$406$	−14.6189	−0.725522
$407$	−18.7634	−0.930065
$408$	−1.18539	−0.0586855
$409$	35.7046	1.76548	0.882740	−	0.469862i	$-0.155696\pi$
$409$	35.7046	1.76548	0.882740	+	0.469862i	$0.155696\pi$
$410$	−11.1701	−0.551652
$411$	−55.7666	−2.75076
$412$	30.6712	1.51106
$413$	4.04193	0.198890
$414$	−50.7948	−2.49643
$415$	10.8656	0.533370
$416$	31.0010	1.51995
$417$	17.8677	0.874985
$418$	9.45703	0.462558
$419$	−1.63098	−0.0796788	−0.0398394	−	0.999206i	$-0.512685\pi$
$419$	−1.63098	−0.0796788	−0.0398394	+	0.999206i	$0.512685\pi$
$420$	5.22499	0.254954
$421$	22.9536	1.11869	0.559346	−	0.828934i	$-0.311052\pi$
$421$	22.9536	1.11869	0.559346	+	0.828934i	$0.311052\pi$
$422$	1.87935	0.0914854
$423$	35.7609	1.73876
$424$	1.32267	0.0642343
$425$	4.70442	0.228198
$426$	63.2042	3.06226
$427$	−8.74093	−0.423003
$428$	19.9715	0.965360
$429$	20.7759	1.00307
$430$	−6.19771	−0.298880
$431$	−21.1220	−1.01741	−0.508706	−	0.860940i	$-0.669876\pi$
$431$	−21.1220	−1.01741	−0.508706	+	0.860940i	$0.669876\pi$
$432$	−4.99057	−0.240109
$433$	−22.9796	−1.10433	−0.552164	−	0.833735i	$-0.686198\pi$
$433$	−22.9796	−1.10433	−0.552164	+	0.833735i	$0.686198\pi$
$434$	4.66696	0.224021
$435$	18.5249	0.888199
$436$	−11.9138	−0.570565
$437$	−16.0239	−0.766525
$438$	−53.3199	−2.54772
$439$	−17.3350	−0.827353	−0.413677	−	0.910424i	$-0.635756\pi$
$439$	−17.3350	−0.827353	−0.413677	+	0.910424i	$0.635756\pi$
$440$	−0.208918	−0.00995976
$441$	3.50192	0.166758
$442$	−36.4824	−1.73529
$443$	−16.7649	−0.796525	−0.398263	−	0.917271i	$-0.630387\pi$
$443$	−16.7649	−0.796525	−0.398263	+	0.917271i	$0.630387\pi$
$444$	−46.3719	−2.20071
$445$	−10.1387	−0.480620
$446$	−43.6638	−2.06754
$447$	−28.6702	−1.35605
$448$	−8.38792	−0.396292
$449$	5.55543	0.262177	0.131089	−	0.991371i	$-0.458153\pi$
$449$	5.55543	0.262177	0.131089	+	0.991371i	$0.458153\pi$
$450$	−7.04670	−0.332185
$451$	11.7360	0.552625
$452$	38.1064	1.79237
$453$	9.55994	0.449165
$454$	−49.2750	−2.31259
$455$	3.85388	0.180672
$456$	0.560130	0.0262305
$457$	19.5505	0.914533	0.457267	−	0.889330i	$-0.348829\pi$
$457$	19.5505	0.914533	0.457267	+	0.889330i	$0.348829\pi$
$458$	−2.01224	−0.0940258
$459$	6.02090	0.281032
$460$	14.7706	0.688683
$461$	−31.8167	−1.48185	−0.740926	−	0.671587i	$-0.765613\pi$
$461$	−31.8167	−1.48185	−0.740926	+	0.671587i	$0.765613\pi$
$462$	−10.8478	−0.504686
$463$	−37.2868	−1.73287	−0.866433	−	0.499294i	$-0.833593\pi$
$463$	−37.2868	−1.73287	−0.866433	+	0.499294i	$0.833593\pi$
$464$	−28.3288	−1.31513
$465$	−5.91392	−0.274251
$466$	37.5984	1.74171
$467$	8.04299	0.372185	0.186093	−	0.982532i	$-0.440418\pi$
$467$	8.04299	0.372185	0.186093	+	0.982532i	$0.440418\pi$
$468$	27.6547	1.27834
$469$	9.75974	0.450663
$470$	−20.5486	−0.947836
$471$	10.1140	0.466030
$472$	−0.399413	−0.0183845
$473$	6.51168	0.299407
$474$	25.4604	1.16943
$475$	−2.22297	−0.101997
$476$	9.63987	0.441843
$477$	−46.8730	−2.14617
$478$	−34.7954	−1.59150
$479$	7.31320	0.334149	0.167074	−	0.985944i	$-0.446568\pi$
$479$	7.31320	0.334149	0.167074	+	0.985944i	$0.446568\pi$
$480$	20.5116	0.936220
$481$	−34.2032	−1.55953
$482$	0.374826	0.0170729
$483$	18.3804	0.836336
$484$	−13.3812	−0.608236
$485$	−15.3125	−0.695304
$486$	44.8862	2.03608
$487$	−7.06564	−0.320175	−0.160087	−	0.987103i	$-0.551178\pi$
$487$	−7.06564	−0.320175	−0.160087	+	0.987103i	$0.551178\pi$
$488$	0.863757	0.0391005
$489$	33.8017	1.52857
$490$	−2.01224	−0.0909037
$491$	38.0420	1.71681	0.858405	−	0.512973i	$-0.171456\pi$
$491$	38.0420	1.71681	0.858405	+	0.512973i	$0.171456\pi$
$492$	29.0043	1.30762
$493$	34.1775	1.53928
$494$	17.2390	0.775618
$495$	7.40368	0.332771
$496$	9.04376	0.406077
$497$	−12.3182	−0.552545
$498$	−55.7511	−2.49827
$499$	−33.2819	−1.48990	−0.744952	−	0.667118i	$-0.767528\pi$
$499$	−33.2819	−1.48990	−0.744952	+	0.667118i	$0.767528\pi$
$500$	2.04911	0.0916389
$501$	−29.1623	−1.30288
$502$	58.5957	2.61526
$503$	−29.5871	−1.31922	−0.659611	−	0.751607i	$-0.729279\pi$
$503$	−29.5871	−1.31922	−0.659611	+	0.751607i	$0.729279\pi$
$504$	−0.346051	−0.0154143
$505$	−4.28689	−0.190764
$506$	−30.6658	−1.36326
$507$	4.72330	0.209769
$508$	−30.0171	−1.33179
$509$	31.2944	1.38710	0.693551	−	0.720408i	$-0.256045\pi$
$509$	31.2944	1.38710	0.693551	+	0.720408i	$0.256045\pi$
$510$	−24.1383	−1.06886
$511$	10.3918	0.459704
$512$	−32.1376	−1.42030
$513$	−2.84504	−0.125612
$514$	8.78018	0.387277
$515$	14.9681	0.659572
$516$	16.0930	0.708456
$517$	21.5896	0.949508
$518$	17.8587	0.784664
$519$	−24.9373	−1.09462
$520$	−0.380830	−0.0167005
$521$	34.5348	1.51300	0.756499	−	0.653995i	$-0.226908\pi$
$521$	34.5348	1.51300	0.756499	+	0.653995i	$0.226908\pi$
$522$	−51.1941	−2.24071
$523$	−29.3356	−1.28275	−0.641377	−	0.767226i	$-0.721637\pi$
$523$	−29.3356	−1.28275	−0.641377	+	0.767226i	$0.721637\pi$
$524$	−12.2578	−0.535483
$525$	2.54989	0.111286
$526$	60.9021	2.65546
$527$	−10.9109	−0.475286
$528$	−21.0212	−0.914829
$529$	28.9597	1.25912
$530$	26.9337	1.16992
$531$	14.1545	0.614254
$532$	−4.55511	−0.197489
$533$	21.3932	0.926640
$534$	52.0215	2.25119
$535$	9.74645	0.421376
$536$	−0.964433	−0.0416572
$537$	20.6359	0.890503
$538$	40.9005	1.76335
$539$	2.11418	0.0910640
$540$	2.62253	0.112856
$541$	3.74540	0.161027	0.0805136	−	0.996754i	$-0.474344\pi$
$541$	3.74540	0.161027	0.0805136	+	0.996754i	$0.474344\pi$
$542$	−3.11688	−0.133882
$543$	27.4296	1.17712
$544$	37.8429	1.62250
$545$	−5.81412	−0.249049
$546$	−19.7742	−0.846256
$547$	−19.2641	−0.823673	−0.411836	−	0.911258i	$-0.635112\pi$
$547$	−19.2641	−0.823673	−0.411836	+	0.911258i	$0.635112\pi$
$548$	−44.8145	−1.91438
$549$	−30.6100	−1.30641
$550$	−4.25423	−0.181401
$551$	−16.1498	−0.688006
$552$	−1.81630	−0.0773070
$553$	−4.96208	−0.211009
$554$	−47.0683	−1.99974
$555$	−22.6303	−0.960602
$556$	14.3586	0.608941
$557$	12.3229	0.522138	0.261069	−	0.965320i	$-0.415925\pi$
$557$	12.3229	0.522138	0.261069	+	0.965320i	$0.415925\pi$
$558$	16.3433	0.691868
$559$	11.8700	0.502046
$560$	−3.89937	−0.164779
$561$	25.3611	1.07075
$562$	−21.6319	−0.912486
$563$	18.3532	0.773495	0.386748	−	0.922186i	$-0.373598\pi$
$563$	18.3532	0.773495	0.386748	+	0.922186i	$0.373598\pi$
$564$	53.3566	2.24672
$565$	18.5966	0.782364
$566$	−29.4262	−1.23687
$567$	−7.24232	−0.304149
$568$	1.21725	0.0510747
$569$	−36.2913	−1.52141	−0.760704	−	0.649098i	$-0.775146\pi$
$569$	−36.2913	−1.52141	−0.760704	+	0.649098i	$0.775146\pi$
$570$	11.4060	0.477746
$571$	15.6684	0.655703	0.327851	−	0.944729i	$-0.393675\pi$
$571$	15.6684	0.655703	0.327851	+	0.944729i	$0.393675\pi$
$572$	16.6957	0.698081
$573$	−60.0580	−2.50896
$574$	−11.1701	−0.466231
$575$	7.20831	0.300607
$576$	−29.3738	−1.22391
$577$	6.72267	0.279869	0.139934	−	0.990161i	$-0.455311\pi$
$577$	6.72267	0.279869	0.139934	+	0.990161i	$0.455311\pi$
$578$	−10.3260	−0.429504
$579$	−58.5800	−2.43450
$580$	14.8867	0.618137
$581$	10.8656	0.450780
$582$	78.5681	3.25675
$583$	−28.2981	−1.17199
$584$	−1.02689	−0.0424929
$585$	13.4960	0.557989
$586$	−35.8730	−1.48190
$587$	−16.1153	−0.665151	−0.332575	−	0.943077i	$-0.607918\pi$
$587$	−16.1153	−0.665151	−0.332575	+	0.943077i	$0.607918\pi$
$588$	5.22499	0.215475
$589$	5.15571	0.212437
$590$	−8.13333	−0.334844
$591$	−2.59923	−0.106918
$592$	34.6070	1.42234
$593$	−34.2111	−1.40488	−0.702440	−	0.711743i	$-0.747906\pi$
$593$	−34.2111	−1.40488	−0.702440	+	0.711743i	$0.747906\pi$
$594$	−5.44473	−0.223400
$595$	4.70442	0.192862
$596$	−23.0396	−0.943737
$597$	−14.8903	−0.609418
$598$	−55.8999	−2.28592
$599$	−19.7183	−0.805668	−0.402834	−	0.915273i	$-0.631975\pi$
$599$	−19.7183	−0.805668	−0.402834	+	0.915273i	$0.631975\pi$
$600$	−0.251973	−0.0102868
$601$	−16.2310	−0.662075	−0.331038	−	0.943618i	$-0.607399\pi$
$601$	−16.2310	−0.662075	−0.331038	+	0.943618i	$0.607399\pi$
$602$	−6.19771	−0.252600
$603$	34.1778	1.39183
$604$	7.68244	0.312594
$605$	−6.53026	−0.265493
$606$	21.9960	0.893525
$607$	−25.2112	−1.02329	−0.511646	−	0.859197i	$-0.670964\pi$
$607$	−25.2112	−1.02329	−0.511646	+	0.859197i	$0.670964\pi$
$608$	−17.8818	−0.725203
$609$	18.5249	0.750665
$610$	17.5889	0.712152
$611$	39.3550	1.59213
$612$	33.7581	1.36459
$613$	−5.86437	−0.236860	−0.118430	−	0.992962i	$-0.537786\pi$
$613$	−5.86437	−0.236860	−0.118430	+	0.992962i	$0.537786\pi$
$614$	−17.4735	−0.705173
$615$	14.1546	0.570769
$616$	−0.208918	−0.00841754
$617$	31.2607	1.25851	0.629253	−	0.777200i	$-0.283361\pi$
$617$	31.2607	1.25851	0.629253	+	0.777200i	$0.283361\pi$
$618$	−76.8009	−3.08938
$619$	2.39629	0.0963151	0.0481576	−	0.998840i	$-0.484665\pi$
$619$	2.39629	0.0963151	0.0481576	+	0.998840i	$0.484665\pi$
$620$	−4.75247	−0.190864
$621$	9.22548	0.370206
$622$	−17.3496	−0.695657
$623$	−10.1387	−0.406198
$624$	−38.3189	−1.53398
$625$	1.00000	0.0400000
$626$	55.3401	2.21184
$627$	−11.9838	−0.478588
$628$	8.12771	0.324331
$629$	−41.7518	−1.66475
$630$	−7.04670	−0.280747
$631$	37.5665	1.49550	0.747750	−	0.663980i	$-0.231134\pi$
$631$	37.5665	1.49550	0.747750	+	0.663980i	$0.231134\pi$
$632$	0.490341	0.0195047
$633$	−2.38149	−0.0946558
$634$	−5.03149	−0.199826
$635$	−14.6489	−0.581322
$636$	−69.9362	−2.77315
$637$	3.85388	0.152696
$638$	−30.9069	−1.22362
$639$	−43.1372	−1.70648
$640$	0.790302	0.0312394
$641$	15.1181	0.597129	0.298565	−	0.954389i	$-0.403492\pi$
$641$	15.1181	0.597129	0.298565	+	0.954389i	$0.403492\pi$
$642$	−50.0089	−1.97369
$643$	3.46282	0.136560	0.0682801	−	0.997666i	$-0.478249\pi$
$643$	3.46282	0.136560	0.0682801	+	0.997666i	$0.478249\pi$
$644$	14.7706	0.582043
$645$	7.85367	0.309238
$646$	21.0436	0.827949
$647$	3.25198	0.127848	0.0639242	−	0.997955i	$-0.479638\pi$
$647$	3.25198	0.127848	0.0639242	+	0.997955i	$0.479638\pi$
$648$	0.715668	0.0281141
$649$	8.54535	0.335434
$650$	−7.75492	−0.304173
$651$	−5.91392	−0.231785
$652$	27.1633	1.06380
$653$	9.66623	0.378269	0.189134	−	0.981951i	$-0.439432\pi$
$653$	9.66623	0.378269	0.189134	+	0.981951i	$0.439432\pi$
$654$	29.8321	1.16653
$655$	−5.98200	−0.233736
$656$	−21.6457	−0.845123
$657$	36.3911	1.41975
$658$	−20.5486	−0.801067
$659$	−6.52454	−0.254160	−0.127080	−	0.991892i	$-0.540560\pi$
$659$	−6.52454	−0.254160	−0.127080	+	0.991892i	$0.540560\pi$
$660$	11.0466	0.429987
$661$	−33.8847	−1.31796	−0.658982	−	0.752159i	$-0.729013\pi$
$661$	−33.8847	−1.31796	−0.658982	+	0.752159i	$0.729013\pi$
$662$	−1.57795	−0.0613288
$663$	46.2301	1.79543
$664$	−1.07371	−0.0416680
$665$	−2.22297	−0.0862031
$666$	62.5396	2.42336
$667$	52.3682	2.02770
$668$	−23.4351	−0.906729
$669$	55.3303	2.13919
$670$	−19.6389	−0.758718
$671$	−18.4799	−0.713408
$672$	20.5116	0.791250
$673$	−5.23960	−0.201972	−0.100986	−	0.994888i	$-0.532200\pi$
$673$	−5.23960	−0.201972	−0.100986	+	0.994888i	$0.532200\pi$
$674$	−18.5747	−0.715471
$675$	1.27984	0.0492610
$676$	3.79568	0.145988
$677$	−0.871198	−0.0334829	−0.0167414	−	0.999860i	$-0.505329\pi$
$677$	−0.871198	−0.0334829	−0.0167414	+	0.999860i	$0.505329\pi$
$678$	−95.4187	−3.66453
$679$	−15.3125	−0.587639
$680$	−0.464879	−0.0178273
$681$	62.4406	2.39273
$682$	9.86678	0.377819
$683$	−51.5001	−1.97060	−0.985298	−	0.170844i	$-0.945351\pi$
$683$	−51.5001	−1.97060	−0.985298	+	0.170844i	$0.945351\pi$
$684$	−15.9516	−0.609925
$685$	−21.8702	−0.835619
$686$	−2.01224	−0.0768277
$687$	2.54989	0.0972842
$688$	−12.0101	−0.457881
$689$	−51.5839	−1.96519
$690$	−36.9857	−1.40802
$691$	−0.588825	−0.0224000	−0.0112000	−	0.999937i	$-0.503565\pi$
$691$	−0.588825	−0.0224000	−0.0112000	+	0.999937i	$0.503565\pi$
$692$	−20.0398	−0.761798
$693$	7.40368	0.281243
$694$	−3.82163	−0.145067
$695$	7.00725	0.265800
$696$	−1.83058	−0.0693880
$697$	26.1146	0.989161
$698$	−37.7033	−1.42709
$699$	−47.6442	−1.80207
$700$	2.04911	0.0774490
$701$	−33.4863	−1.26476	−0.632379	−	0.774659i	$-0.717922\pi$
$701$	−33.4863	−1.26476	−0.632379	+	0.774659i	$0.717922\pi$
$702$	−9.92505	−0.374597
$703$	19.7289	0.744090
$704$	−17.7336	−0.668359
$705$	26.0389	0.980683
$706$	−15.9813	−0.601464
$707$	−4.28689	−0.161225
$708$	21.1191	0.793703
$709$	29.5992	1.11162	0.555811	−	0.831309i	$-0.312408\pi$
$709$	29.5992	1.11162	0.555811	+	0.831309i	$0.312408\pi$
$710$	24.7871	0.930243
$711$	−17.3768	−0.651681
$712$	1.00188	0.0375471
$713$	−16.7181	−0.626099
$714$	−24.1383	−0.903353
$715$	8.14778	0.304710
$716$	16.5831	0.619741
$717$	44.0923	1.64666
$718$	−2.38310	−0.0889365
$719$	3.29901	0.123032	0.0615162	−	0.998106i	$-0.480406\pi$
$719$	3.29901	0.123032	0.0615162	+	0.998106i	$0.480406\pi$
$720$	−13.6553	−0.508903
$721$	14.9681	0.557440
$722$	28.2889	1.05280
$723$	−0.474976	−0.0176645
$724$	22.0426	0.819207
$725$	7.26498	0.269814
$726$	33.5066	1.24355
$727$	29.2973	1.08658	0.543289	−	0.839546i	$-0.317179\pi$
$727$	29.2973	1.08658	0.543289	+	0.839546i	$0.317179\pi$
$728$	−0.380830	−0.0141145
$729$	−35.1523	−1.30194
$730$	−20.9107	−0.773940
$731$	14.4897	0.535919
$732$	−45.6713	−1.68806
$733$	41.6633	1.53887	0.769434	−	0.638726i	$-0.220538\pi$
$733$	41.6633	1.53887	0.769434	+	0.638726i	$0.220538\pi$
$734$	−65.4494	−2.41578
$735$	2.54989	0.0940540
$736$	57.9844	2.13733
$737$	20.6338	0.760056
$738$	−39.1168	−1.43991
$739$	−4.02943	−0.148225	−0.0741124	−	0.997250i	$-0.523612\pi$
$739$	−4.02943	−0.148225	−0.0741124	+	0.997250i	$0.523612\pi$
$740$	−18.1859	−0.668526
$741$	−21.8450	−0.802496
$742$	26.9337	0.988767
$743$	46.8760	1.71971	0.859856	−	0.510536i	$-0.170553\pi$
$743$	46.8760	1.71971	0.859856	+	0.510536i	$0.170553\pi$
$744$	0.584399	0.0214251
$745$	−11.2437	−0.411937
$746$	−13.5804	−0.497215
$747$	38.0504	1.39219
$748$	20.3804	0.745181
$749$	9.74645	0.356128
$750$	−5.13098	−0.187357
$751$	37.5764	1.37118	0.685591	−	0.727987i	$-0.259544\pi$
$751$	37.5764	1.37118	0.685591	+	0.727987i	$0.259544\pi$
$752$	−39.8196	−1.45207
$753$	−74.2518	−2.70589
$754$	−56.3393	−2.05176
$755$	3.74916	0.136446
$756$	2.62253	0.0953805
$757$	24.4989	0.890429	0.445215	−	0.895424i	$-0.353127\pi$
$757$	24.4989	0.890429	0.445215	+	0.895424i	$0.353127\pi$
$758$	52.6154	1.91108
$759$	38.8593	1.41051
$760$	0.219668	0.00796821
$761$	−19.7270	−0.715102	−0.357551	−	0.933894i	$-0.616388\pi$
$761$	−19.7270	−0.715102	−0.357551	+	0.933894i	$0.616388\pi$
$762$	75.1630	2.72287
$763$	−5.81412	−0.210485
$764$	−48.2631	−1.74610
$765$	16.4745	0.595637
$766$	52.7181	1.90478
$767$	15.5771	0.562456
$768$	38.7215	1.39724
$769$	5.04756	0.182020	0.0910098	−	0.995850i	$-0.470991\pi$
$769$	5.04756	0.182020	0.0910098	+	0.995850i	$0.470991\pi$
$770$	−4.25423	−0.153312
$771$	−11.1261	−0.400698
$772$	−47.0753	−1.69428
$773$	5.78574	0.208099	0.104049	−	0.994572i	$-0.466820\pi$
$773$	5.78574	0.208099	0.104049	+	0.994572i	$0.466820\pi$
$774$	−21.7039	−0.780131
$775$	−2.31929	−0.0833112
$776$	1.51314	0.0543186
$777$	−22.6303	−0.811857
$778$	−45.3888	−1.62727
$779$	−12.3399	−0.442122
$780$	20.1365	0.721001
$781$	−26.0428	−0.931883
$782$	−68.2369	−2.44015
$783$	9.29800	0.332283
$784$	−3.89937	−0.139263
$785$	3.96646	0.141569
$786$	30.6935	1.09480
$787$	−26.5758	−0.947324	−0.473662	−	0.880707i	$-0.657068\pi$
$787$	−26.5758	−0.947324	−0.473662	+	0.880707i	$0.657068\pi$
$788$	−2.08876	−0.0744090
$789$	−77.1745	−2.74748
$790$	9.98490	0.355247
$791$	18.5966	0.661218
$792$	−0.731613	−0.0259967
$793$	−33.6865	−1.19624
$794$	45.9117	1.62935
$795$	−34.1301	−1.21047
$796$	−11.9659	−0.424121
$797$	−18.0112	−0.637989	−0.318994	−	0.947757i	$-0.603345\pi$
$797$	−18.0112	−0.637989	−0.318994	+	0.947757i	$0.603345\pi$
$798$	11.4060	0.403769
$799$	48.0406	1.69955
$800$	8.04411	0.284402
$801$	−35.5049	−1.25450
$802$	−16.1031	−0.568622
$803$	21.9700	0.775305
$804$	50.9946	1.79844
$805$	7.20831	0.254059
$806$	17.9859	0.633526
$807$	−51.8287	−1.82446
$808$	0.423620	0.0149029
$809$	31.6960	1.11437	0.557186	−	0.830387i	$-0.311881\pi$
$809$	31.6960	1.11437	0.557186	+	0.830387i	$0.311881\pi$
$810$	14.5733	0.512053
$811$	−33.9235	−1.19121	−0.595607	−	0.803276i	$-0.703088\pi$
$811$	−33.9235	−1.19121	−0.595607	+	0.803276i	$0.703088\pi$
$812$	14.8867	0.522421
$813$	3.94968	0.138521
$814$	37.7564	1.32336
$815$	13.2562	0.464343
$816$	−46.7759	−1.63748
$817$	−6.84677	−0.239538
$818$	−71.8462	−2.51204
$819$	13.4960	0.471587
$820$	11.3748	0.397224
$821$	−21.8001	−0.760828	−0.380414	−	0.924816i	$-0.624219\pi$
$821$	−21.8001	−0.760828	−0.380414	+	0.924816i	$0.624219\pi$
$822$	112.216	3.91397
$823$	7.58602	0.264432	0.132216	−	0.991221i	$-0.457791\pi$
$823$	7.58602	0.264432	0.132216	+	0.991221i	$0.457791\pi$
$824$	−1.47911	−0.0515271
$825$	5.39091	0.187687
$826$	−8.13333	−0.282995
$827$	27.0268	0.939816	0.469908	−	0.882715i	$-0.344287\pi$
$827$	27.0268	0.939816	0.469908	+	0.882715i	$0.344287\pi$
$828$	51.7255	1.79758
$829$	1.89784	0.0659148	0.0329574	−	0.999457i	$-0.489507\pi$
$829$	1.89784	0.0659148	0.0329574	+	0.999457i	$0.489507\pi$
$830$	−21.8641	−0.758916
$831$	59.6443	2.06904
$832$	−32.3260	−1.12070
$833$	4.70442	0.162999
$834$	−35.9541	−1.24499
$835$	−11.4367	−0.395784
$836$	−9.63030	−0.333071
$837$	−2.96831	−0.102600
$838$	3.28193	0.113372
$839$	23.2795	0.803697	0.401848	−	0.915706i	$-0.368368\pi$
$839$	23.2795	0.803697	0.401848	+	0.915706i	$0.368368\pi$
$840$	−0.251973	−0.00869391
$841$	23.7799	0.819995
$842$	−46.1882	−1.59175
$843$	27.4117	0.944108
$844$	−1.91379	−0.0658752
$845$	1.85236	0.0637230
$846$	−71.9595	−2.47402
$847$	−6.53026	−0.224382
$848$	52.1928	1.79231
$849$	37.2885	1.27974
$850$	−9.46642	−0.324696
$851$	−63.9739	−2.19300
$852$	−64.3623	−2.20502
$853$	4.26467	0.146019	0.0730097	−	0.997331i	$-0.476740\pi$
$853$	4.26467	0.146019	0.0730097	+	0.997331i	$0.476740\pi$
$854$	17.5889	0.601878
$855$	−7.78467	−0.266230
$856$	−0.963120	−0.0329188
$857$	39.1361	1.33686	0.668432	−	0.743774i	$-0.266966\pi$
$857$	39.1361	1.33686	0.668432	+	0.743774i	$0.266966\pi$
$858$	−41.8061	−1.42724
$859$	7.14850	0.243904	0.121952	−	0.992536i	$-0.461085\pi$
$859$	7.14850	0.243904	0.121952	+	0.992536i	$0.461085\pi$
$860$	6.31127	0.215213
$861$	14.1546	0.482388
$862$	42.5026	1.44764
$863$	45.5893	1.55188	0.775939	−	0.630808i	$-0.217276\pi$
$863$	45.5893	1.55188	0.775939	+	0.630808i	$0.217276\pi$
$864$	10.2952	0.350249
$865$	−9.77975	−0.332522
$866$	46.2404	1.57131
$867$	13.0850	0.444388
$868$	−4.75247	−0.161309
$869$	−10.4907	−0.355873
$870$	−37.2765	−1.26379
$871$	37.6128	1.27446
$872$	0.574537	0.0194563
$873$	−53.6231	−1.81487
$874$	32.2438	1.09066
$875$	1.00000	0.0338062
$876$	54.2969	1.83452
$877$	−30.5544	−1.03175	−0.515875	−	0.856664i	$-0.672533\pi$
$877$	−30.5544	−1.03175	−0.515875	+	0.856664i	$0.672533\pi$
$878$	34.8821	1.17722
$879$	45.4579	1.53326
$880$	−8.24396	−0.277904
$881$	−28.3739	−0.955941	−0.477971	−	0.878376i	$-0.658627\pi$
$881$	−28.3739	−0.955941	−0.477971	+	0.878376i	$0.658627\pi$
$882$	−7.04670	−0.237275
$883$	−36.9535	−1.24358	−0.621792	−	0.783182i	$-0.713595\pi$
$883$	−36.9535	−1.24358	−0.621792	+	0.783182i	$0.713595\pi$
$884$	37.1509	1.24952
$885$	10.3065	0.346448
$886$	33.7350	1.13335
$887$	30.0642	1.00946	0.504728	−	0.863278i	$-0.331593\pi$
$887$	30.0642	1.00946	0.504728	+	0.863278i	$0.331593\pi$
$888$	2.23627	0.0750443
$889$	−14.6489	−0.491307
$890$	20.4015	0.683860
$891$	−15.3115	−0.512956
$892$	44.4638	1.48876
$893$	−22.7005	−0.759644
$894$	57.6912	1.92948
$895$	8.09286	0.270514
$896$	0.790302	0.0264021
$897$	70.8357	2.36513
$898$	−11.1789	−0.373044
$899$	−16.8496	−0.561964
$900$	7.17581	0.239194
$901$	−62.9684	−2.09778
$902$	−23.6156	−0.786312
$903$	7.85367	0.261354
$904$	−1.83767	−0.0611199
$905$	10.7572	0.357580
$906$	−19.2369	−0.639103
$907$	−25.5015	−0.846764	−0.423382	−	0.905951i	$-0.639157\pi$
$907$	−25.5015	−0.846764	−0.423382	+	0.905951i	$0.639157\pi$
$908$	50.1778	1.66521
$909$	−15.0123	−0.497928
$910$	−7.75492	−0.257073
$911$	−24.2087	−0.802071	−0.401036	−	0.916062i	$-0.631350\pi$
$911$	−24.2087	−0.802071	−0.401036	+	0.916062i	$0.631350\pi$
$912$	22.1029	0.731900
$913$	22.9718	0.760254
$914$	−39.3403	−1.30126
$915$	−22.2884	−0.736831
$916$	2.04911	0.0677044
$917$	−5.98200	−0.197543
$918$	−12.1155	−0.399871
$919$	25.5296	0.842144	0.421072	−	0.907027i	$-0.361654\pi$
$919$	25.5296	0.842144	0.421072	+	0.907027i	$0.361654\pi$
$920$	−0.712307	−0.0234841
$921$	22.1422	0.729610
$922$	64.0228	2.10848
$923$	−47.4726	−1.56258
$924$	11.0466	0.363405
$925$	−8.87502	−0.291809
$926$	75.0300	2.46564
$927$	52.4170	1.72160
$928$	58.4402	1.91839
$929$	39.9167	1.30962	0.654812	−	0.755792i	$-0.272748\pi$
$929$	39.9167	1.30962	0.654812	+	0.755792i	$0.272748\pi$
$930$	11.9002	0.390224
$931$	−2.22297	−0.0728549
$932$	−38.2872	−1.25414
$933$	21.9853	0.719765
$934$	−16.1844	−0.529571
$935$	9.94598	0.325268
$936$	−1.33364	−0.0435913
$937$	−45.9316	−1.50052	−0.750260	−	0.661143i	$-0.770072\pi$
$937$	−45.9316	−1.50052	−0.750260	+	0.661143i	$0.770072\pi$
$938$	−19.6389	−0.641234
$939$	−70.1263	−2.28849
$940$	20.9251	0.682501
$941$	−2.54443	−0.0829459	−0.0414730	−	0.999140i	$-0.513205\pi$
$941$	−2.54443	−0.0829459	−0.0414730	+	0.999140i	$0.513205\pi$
$942$	−20.3519	−0.663099
$943$	40.0139	1.30303
$944$	−15.7610	−0.512976
$945$	1.27984	0.0416332
$946$	−13.1031	−0.426017
$947$	20.0438	0.651337	0.325669	−	0.945484i	$-0.394411\pi$
$947$	20.0438	0.651337	0.325669	+	0.945484i	$0.394411\pi$
$948$	−25.9268	−0.842065
$949$	40.0485	1.30003
$950$	4.47315	0.145128
$951$	6.37585	0.206751
$952$	−0.464879	−0.0150668
$953$	30.8355	0.998861	0.499431	−	0.866354i	$-0.333543\pi$
$953$	30.8355	0.998861	0.499431	+	0.866354i	$0.333543\pi$
$954$	94.3196	3.05371
$955$	−23.5532	−0.762164
$956$	35.4329	1.14598
$957$	39.1648	1.26602
$958$	−14.7159	−0.475450
$959$	−21.8702	−0.706227
$960$	−21.3883	−0.690303
$961$	−25.6209	−0.826481
$962$	68.8251	2.21901
$963$	34.1313	1.09987
$964$	−0.381694	−0.0122935
$965$	−22.9736	−0.739545
$966$	−36.9857	−1.19000
$967$	−10.1337	−0.325879	−0.162940	−	0.986636i	$-0.552098\pi$
$967$	−10.1337	−0.325879	−0.162940	+	0.986636i	$0.552098\pi$
$968$	0.645304	0.0207408
$969$	−26.6662	−0.856641
$970$	30.8124	0.989326
$971$	44.9590	1.44280	0.721401	−	0.692518i	$-0.243499\pi$
$971$	44.9590	1.44280	0.721401	+	0.692518i	$0.243499\pi$
$972$	−45.7086	−1.46611
$973$	7.00725	0.224642
$974$	14.2178	0.455567
$975$	9.82694	0.314714
$976$	34.0841	1.09101
$977$	18.3667	0.587602	0.293801	−	0.955867i	$-0.405080\pi$
$977$	18.3667	0.587602	0.293801	+	0.955867i	$0.405080\pi$
$978$	−68.0171	−2.17495
$979$	−21.4350	−0.685066
$980$	2.04911	0.0654564
$981$	−20.3606	−0.650063
$982$	−76.5495	−2.44279
$983$	11.0428	0.352211	0.176105	−	0.984371i	$-0.443650\pi$
$983$	11.0428	0.352211	0.176105	+	0.984371i	$0.443650\pi$
$984$	−1.39872	−0.0445897
$985$	−1.01935	−0.0324792
$986$	−68.7733	−2.19019
$987$	26.0389	0.828828
$988$	−17.5548	−0.558493
$989$	22.2017	0.705971
$990$	−14.8980	−0.473489
$991$	52.8830	1.67988	0.839942	−	0.542676i	$-0.182589\pi$
$991$	52.8830	1.67988	0.839942	+	0.542676i	$0.182589\pi$
$992$	−18.6566	−0.592347
$993$	1.99956	0.0634541
$994$	24.7871	0.786198
$995$	−5.83958	−0.185127
$996$	56.7726	1.79891
$997$	26.0304	0.824391	0.412195	−	0.911096i	$-0.364762\pi$
$997$	26.0304	0.824391	0.412195	+	0.911096i	$0.364762\pi$
$998$	66.9713	2.11994
$999$	−11.3586	−0.359370

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.o.1.14	✓	73

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.o.1.14	✓	73	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)

\(f(q)\)	\(=\)	\(q-2.01224 q^{2} +2.54989 q^{3} +2.04911 q^{4} +1.00000 q^{5} -5.13098 q^{6} +1.00000 q^{7} -0.0988175 q^{8} +3.50192 q^{9} +O(q^{10})\)	\(q-2.01224 q^{2} +2.54989 q^{3} +2.04911 q^{4} +1.00000 q^{5} -5.13098 q^{6} +1.00000 q^{7} -0.0988175 q^{8} +3.50192 q^{9} -2.01224 q^{10} +2.11418 q^{11} +5.22499 q^{12} +3.85388 q^{13} -2.01224 q^{14} +2.54989 q^{15} -3.89937 q^{16} +4.70442 q^{17} -7.04670 q^{18} -2.22297 q^{19} +2.04911 q^{20} +2.54989 q^{21} -4.25423 q^{22} +7.20831 q^{23} -0.251973 q^{24} +1.00000 q^{25} -7.75492 q^{26} +1.27984 q^{27} +2.04911 q^{28} +7.26498 q^{29} -5.13098 q^{30} -2.31929 q^{31} +8.04411 q^{32} +5.39091 q^{33} -9.46642 q^{34} +1.00000 q^{35} +7.17581 q^{36} -8.87502 q^{37} +4.47315 q^{38} +9.82694 q^{39} -0.0988175 q^{40} +5.55108 q^{41} -5.13098 q^{42} +3.08001 q^{43} +4.33218 q^{44} +3.50192 q^{45} -14.5048 q^{46} +10.2118 q^{47} -9.94296 q^{48} +1.00000 q^{49} -2.01224 q^{50} +11.9957 q^{51} +7.89701 q^{52} -13.3849 q^{53} -2.57534 q^{54} +2.11418 q^{55} -0.0988175 q^{56} -5.66832 q^{57} -14.6189 q^{58} +4.04193 q^{59} +5.22499 q^{60} -8.74093 q^{61} +4.66696 q^{62} +3.50192 q^{63} -8.38792 q^{64} +3.85388 q^{65} -10.8478 q^{66} +9.75974 q^{67} +9.63987 q^{68} +18.3804 q^{69} -2.01224 q^{70} -12.3182 q^{71} -0.346051 q^{72} +10.3918 q^{73} +17.8587 q^{74} +2.54989 q^{75} -4.55511 q^{76} +2.11418 q^{77} -19.7742 q^{78} -4.96208 q^{79} -3.89937 q^{80} -7.24232 q^{81} -11.1701 q^{82} +10.8656 q^{83} +5.22499 q^{84} +4.70442 q^{85} -6.19771 q^{86} +18.5249 q^{87} -0.208918 q^{88} -10.1387 q^{89} -7.04670 q^{90} +3.85388 q^{91} +14.7706 q^{92} -5.91392 q^{93} -20.5486 q^{94} -2.22297 q^{95} +20.5116 q^{96} -15.3125 q^{97} -2.01224 q^{98} +7.40368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * q^99

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