LMFDB - Embedded newform 8021.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35872 q^{2} +2.44520 q^{3} +3.56358 q^{4} +2.52211 q^{5} -5.76755 q^{6} +2.39189 q^{7} -3.68804 q^{8} +2.97900 q^{9} +O(q^{10})$	\(q-2.35872 q^{2} +2.44520 q^{3} +3.56358 q^{4} +2.52211 q^{5} -5.76755 q^{6} +2.39189 q^{7} -3.68804 q^{8} +2.97900 q^{9} -5.94896 q^{10} +1.62491 q^{11} +8.71366 q^{12} -1.00000 q^{13} -5.64180 q^{14} +6.16706 q^{15} +1.57192 q^{16} -6.79793 q^{17} -7.02665 q^{18} -6.09289 q^{19} +8.98773 q^{20} +5.84864 q^{21} -3.83271 q^{22} -5.55907 q^{23} -9.01801 q^{24} +1.36104 q^{25} +2.35872 q^{26} -0.0513388 q^{27} +8.52367 q^{28} -9.47169 q^{29} -14.5464 q^{30} -2.22553 q^{31} +3.66836 q^{32} +3.97323 q^{33} +16.0344 q^{34} +6.03260 q^{35} +10.6159 q^{36} -7.29740 q^{37} +14.3714 q^{38} -2.44520 q^{39} -9.30165 q^{40} +1.41867 q^{41} -13.7953 q^{42} -0.618567 q^{43} +5.79049 q^{44} +7.51338 q^{45} +13.1123 q^{46} -1.95788 q^{47} +3.84367 q^{48} -1.27889 q^{49} -3.21031 q^{50} -16.6223 q^{51} -3.56358 q^{52} -2.90795 q^{53} +0.121094 q^{54} +4.09820 q^{55} -8.82138 q^{56} -14.8983 q^{57} +22.3411 q^{58} +5.66037 q^{59} +21.9768 q^{60} +0.395004 q^{61} +5.24941 q^{62} +7.12544 q^{63} -11.7965 q^{64} -2.52211 q^{65} -9.37174 q^{66} -0.946751 q^{67} -24.2250 q^{68} -13.5930 q^{69} -14.2292 q^{70} +9.09488 q^{71} -10.9867 q^{72} -0.345920 q^{73} +17.2125 q^{74} +3.32801 q^{75} -21.7125 q^{76} +3.88659 q^{77} +5.76755 q^{78} +13.4667 q^{79} +3.96456 q^{80} -9.06255 q^{81} -3.34625 q^{82} +11.5890 q^{83} +20.8421 q^{84} -17.1451 q^{85} +1.45903 q^{86} -23.1602 q^{87} -5.99273 q^{88} -14.7194 q^{89} -17.7220 q^{90} -2.39189 q^{91} -19.8102 q^{92} -5.44187 q^{93} +4.61811 q^{94} -15.3669 q^{95} +8.96986 q^{96} -9.52147 q^{97} +3.01654 q^{98} +4.84061 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) $ 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * 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 $

$2$	−2.35872	−1.66787	−0.833935	−	0.551863i	$-0.813917\pi$
$2$	−2.35872	−1.66787	−0.833935	+	0.551863i	$0.813917\pi$
$3$	2.44520	1.41174	0.705869	−	0.708343i	$-0.250557\pi$
$3$	2.44520	1.41174	0.705869	+	0.708343i	$0.250557\pi$
$4$	3.56358	1.78179
$5$	2.52211	1.12792	0.563961	−	0.825802i	$-0.309277\pi$
$5$	2.52211	1.12792	0.563961	+	0.825802i	$0.309277\pi$
$6$	−5.76755	−2.35459
$7$	2.39189	0.904048	0.452024	−	0.892006i	$-0.350702\pi$
$7$	2.39189	0.904048	0.452024	+	0.892006i	$0.350702\pi$
$8$	−3.68804	−1.30392
$9$	2.97900	0.993001
$10$	−5.94896	−1.88123
$11$	1.62491	0.489928	0.244964	−	0.969532i	$-0.421224\pi$
$11$	1.62491	0.489928	0.244964	+	0.969532i	$0.421224\pi$
$12$	8.71366	2.51542
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−5.64180	−1.50783
$15$	6.16706	1.59233
$16$	1.57192	0.392981
$17$	−6.79793	−1.64874	−0.824370	−	0.566051i	$-0.808471\pi$
$17$	−6.79793	−1.64874	−0.824370	+	0.566051i	$0.808471\pi$
$18$	−7.02665	−1.65620
$19$	−6.09289	−1.39780	−0.698902	−	0.715217i	$-0.746328\pi$
$19$	−6.09289	−1.39780	−0.698902	+	0.715217i	$0.746328\pi$
$20$	8.98773	2.00972
$21$	5.84864	1.27628
$22$	−3.83271	−0.817137
$23$	−5.55907	−1.15915	−0.579573	−	0.814920i	$-0.696781\pi$
$23$	−5.55907	−1.15915	−0.579573	+	0.814920i	$0.696781\pi$
$24$	−9.01801	−1.84079
$25$	1.36104	0.272207
$26$	2.35872	0.462584
$27$	−0.0513388	−0.00988016
$28$	8.52367	1.61082
$29$	−9.47169	−1.75885	−0.879424	−	0.476039i	$-0.842072\pi$
$29$	−9.47169	−1.75885	−0.879424	+	0.476039i	$0.842072\pi$
$30$	−14.5464	−2.65580
$31$	−2.22553	−0.399717	−0.199859	−	0.979825i	$-0.564048\pi$
$31$	−2.22553	−0.399717	−0.199859	+	0.979825i	$0.564048\pi$
$32$	3.66836	0.648480
$33$	3.97323	0.691650
$34$	16.0344	2.74988
$35$	6.03260	1.01969
$36$	10.6159	1.76932
$37$	−7.29740	−1.19968	−0.599842	−	0.800118i	$-0.704770\pi$
$37$	−7.29740	−1.19968	−0.599842	+	0.800118i	$0.704770\pi$
$38$	14.3714	2.33135
$39$	−2.44520	−0.391545
$40$	−9.30165	−1.47072
$41$	1.41867	0.221559	0.110780	−	0.993845i	$-0.464665\pi$
$41$	1.41867	0.221559	0.110780	+	0.993845i	$0.464665\pi$
$42$	−13.7953	−2.12866
$43$	−0.618567	−0.0943306	−0.0471653	−	0.998887i	$-0.515019\pi$
$43$	−0.618567	−0.0943306	−0.0471653	+	0.998887i	$0.515019\pi$
$44$	5.79049	0.872949
$45$	7.51338	1.12003
$46$	13.1123	1.93330
$47$	−1.95788	−0.285587	−0.142793	−	0.989753i	$-0.545608\pi$
$47$	−1.95788	−0.285587	−0.142793	+	0.989753i	$0.545608\pi$
$48$	3.84367	0.554786
$49$	−1.27889	−0.182698
$50$	−3.21031	−0.454007
$51$	−16.6223	−2.32759
$52$	−3.56358	−0.494179
$53$	−2.90795	−0.399438	−0.199719	−	0.979853i	$-0.564003\pi$
$53$	−2.90795	−0.399438	−0.199719	+	0.979853i	$0.564003\pi$
$54$	0.121094	0.0164788
$55$	4.09820	0.552601
$56$	−8.82138	−1.17881
$57$	−14.8983	−1.97333
$58$	22.3411	2.93353
$59$	5.66037	0.736917	0.368459	−	0.929644i	$-0.379886\pi$
$59$	5.66037	0.736917	0.368459	+	0.929644i	$0.379886\pi$
$60$	21.9768	2.83719
$61$	0.395004	0.0505751	0.0252876	−	0.999680i	$-0.491950\pi$
$61$	0.395004	0.0505751	0.0252876	+	0.999680i	$0.491950\pi$
$62$	5.24941	0.666676
$63$	7.12544	0.897721
$64$	−11.7965	−1.47456
$65$	−2.52211	−0.312829
$66$	−9.37174	−1.15358
$67$	−0.946751	−0.115664	−0.0578320	−	0.998326i	$-0.518419\pi$
$67$	−0.946751	−0.115664	−0.0578320	+	0.998326i	$0.518419\pi$
$68$	−24.2250	−2.93771
$69$	−13.5930	−1.63641
$70$	−14.2292	−1.70072
$71$	9.09488	1.07936	0.539682	−	0.841869i	$-0.318545\pi$
$71$	9.09488	1.07936	0.539682	+	0.841869i	$0.318545\pi$
$72$	−10.9867	−1.29479
$73$	−0.345920	−0.0404868	−0.0202434	−	0.999795i	$-0.506444\pi$
$73$	−0.345920	−0.0404868	−0.0202434	+	0.999795i	$0.506444\pi$
$74$	17.2125	2.00092
$75$	3.32801	0.384285
$76$	−21.7125	−2.49059
$77$	3.88659	0.442919
$78$	5.76755	0.653047
$79$	13.4667	1.51512	0.757560	−	0.652766i	$-0.226391\pi$
$79$	13.4667	1.51512	0.757560	+	0.652766i	$0.226391\pi$
$80$	3.96456	0.443252
$81$	−9.06255	−1.00695
$82$	−3.34625	−0.369532
$83$	11.5890	1.27205	0.636026	−	0.771667i	$-0.280577\pi$
$83$	11.5890	1.27205	0.636026	+	0.771667i	$0.280577\pi$
$84$	20.8421	2.27406
$85$	−17.1451	−1.85965
$86$	1.45903	0.157331
$87$	−23.1602	−2.48303
$88$	−5.99273	−0.638828
$89$	−14.7194	−1.56026	−0.780129	−	0.625619i	$-0.784846\pi$
$89$	−14.7194	−1.56026	−0.780129	+	0.625619i	$0.784846\pi$
$90$	−17.7220	−1.86806
$91$	−2.39189	−0.250738
$92$	−19.8102	−2.06535
$93$	−5.44187	−0.564295
$94$	4.61811	0.476321
$95$	−15.3669	−1.57661
$96$	8.96986	0.915483
$97$	−9.52147	−0.966759	−0.483379	−	0.875411i	$-0.660591\pi$
$97$	−9.52147	−0.966759	−0.483379	+	0.875411i	$0.660591\pi$
$98$	3.01654	0.304716
$99$	4.84061	0.486500
$100$	4.85016	0.485016
$101$	−6.54849	−0.651600	−0.325800	−	0.945439i	$-0.605634\pi$
$101$	−6.54849	−0.651600	−0.325800	+	0.945439i	$0.605634\pi$
$102$	39.2074	3.88211
$103$	−3.71132	−0.365687	−0.182844	−	0.983142i	$-0.558530\pi$
$103$	−3.71132	−0.365687	−0.182844	+	0.983142i	$0.558530\pi$
$104$	3.68804	0.361642
$105$	14.7509	1.43954
$106$	6.85905	0.666210
$107$	17.1065	1.65374	0.826872	−	0.562390i	$-0.190118\pi$
$107$	17.1065	1.65374	0.826872	+	0.562390i	$0.190118\pi$
$108$	−0.182950	−0.0176044
$109$	−14.3500	−1.37448	−0.687238	−	0.726432i	$-0.741177\pi$
$109$	−14.3500	−1.37448	−0.687238	+	0.726432i	$0.741177\pi$
$110$	−9.66652	−0.921666
$111$	−17.8436	−1.69364
$112$	3.75986	0.355273
$113$	0.875822	0.0823904	0.0411952	−	0.999151i	$-0.486883\pi$
$113$	0.875822	0.0823904	0.0411952	+	0.999151i	$0.486883\pi$
$114$	35.1410	3.29126
$115$	−14.0206	−1.30743
$116$	−33.7531	−3.13390
$117$	−2.97900	−0.275409
$118$	−13.3512	−1.22908
$119$	−16.2599	−1.49054
$120$	−22.7444	−2.07627
$121$	−8.35967	−0.759970
$122$	−0.931706	−0.0843527
$123$	3.46894	0.312783
$124$	−7.93085	−0.712211
$125$	−9.17786	−0.820893
$126$	−16.8069	−1.49728
$127$	13.5021	1.19812	0.599059	−	0.800705i	$-0.295542\pi$
$127$	13.5021	1.19812	0.599059	+	0.800705i	$0.295542\pi$
$128$	20.4879	1.81089
$129$	−1.51252	−0.133170
$130$	5.94896	0.521758
$131$	16.9970	1.48504	0.742518	−	0.669826i	$-0.233631\pi$
$131$	16.9970	1.48504	0.742518	+	0.669826i	$0.233631\pi$
$132$	14.1589	1.23237
$133$	−14.5735	−1.26368
$134$	2.23312	0.192913
$135$	−0.129482	−0.0111440
$136$	25.0711	2.14983
$137$	−9.66481	−0.825721	−0.412860	−	0.910794i	$-0.635470\pi$
$137$	−9.66481	−0.825721	−0.412860	+	0.910794i	$0.635470\pi$
$138$	32.0622	2.72932
$139$	14.2129	1.20552	0.602762	−	0.797921i	$-0.294067\pi$
$139$	14.2129	1.20552	0.602762	+	0.797921i	$0.294067\pi$
$140$	21.4976	1.81688
$141$	−4.78742	−0.403173
$142$	−21.4523	−1.80024
$143$	−1.62491	−0.135882
$144$	4.68277	0.390231
$145$	−23.8886	−1.98384
$146$	0.815929	0.0675268
$147$	−3.12713	−0.257921
$148$	−26.0048	−2.13758
$149$	15.0516	1.23308	0.616539	−	0.787324i	$-0.288534\pi$
$149$	15.0516	1.23308	0.616539	+	0.787324i	$0.288534\pi$
$150$	−7.84985	−0.640938
$151$	−8.27940	−0.673768	−0.336884	−	0.941546i	$-0.609373\pi$
$151$	−8.27940	−0.673768	−0.336884	+	0.941546i	$0.609373\pi$
$152$	22.4708	1.82263
$153$	−20.2511	−1.63720
$154$	−9.16740	−0.738730
$155$	−5.61303	−0.450850
$156$	−8.71366	−0.697651
$157$	20.5568	1.64061	0.820305	−	0.571927i	$-0.193804\pi$
$157$	20.5568	1.64061	0.820305	+	0.571927i	$0.193804\pi$
$158$	−31.7642	−2.52702
$159$	−7.11052	−0.563901
$160$	9.25200	0.731434
$161$	−13.2967	−1.04792
$162$	21.3760	1.67946
$163$	4.14376	0.324564	0.162282	−	0.986744i	$-0.448115\pi$
$163$	4.14376	0.324564	0.162282	+	0.986744i	$0.448115\pi$
$164$	5.05554	0.394772
$165$	10.0209	0.780127
$166$	−27.3351	−2.12162
$167$	−11.7362	−0.908175	−0.454088	−	0.890957i	$-0.650035\pi$
$167$	−11.7362	−0.908175	−0.454088	+	0.890957i	$0.650035\pi$
$168$	−21.5700	−1.66416
$169$	1.00000	0.0769231
$170$	40.4406	3.10165
$171$	−18.1507	−1.38802
$172$	−2.20431	−0.168077
$173$	8.74923	0.665192	0.332596	−	0.943069i	$-0.392076\pi$
$173$	8.74923	0.665192	0.332596	+	0.943069i	$0.392076\pi$
$174$	54.6285	4.14137
$175$	3.25545	0.246089
$176$	2.55423	0.192532
$177$	13.8407	1.04033
$178$	34.7191	2.60231
$179$	0.886688	0.0662742	0.0331371	−	0.999451i	$-0.489450\pi$
$179$	0.886688	0.0662742	0.0331371	+	0.999451i	$0.489450\pi$
$180$	26.7745	1.99565
$181$	7.18543	0.534088	0.267044	−	0.963684i	$-0.413953\pi$
$181$	7.18543	0.534088	0.267044	+	0.963684i	$0.413953\pi$
$182$	5.64180	0.418198
$183$	0.965865	0.0713988
$184$	20.5021	1.51143
$185$	−18.4048	−1.35315
$186$	12.8359	0.941171
$187$	−11.0460	−0.807765
$188$	−6.97707	−0.508855
$189$	−0.122797	−0.00893214
$190$	36.2463	2.62959
$191$	−6.18802	−0.447749	−0.223875	−	0.974618i	$-0.571871\pi$
$191$	−6.18802	−0.447749	−0.223875	+	0.974618i	$0.571871\pi$
$192$	−28.8448	−2.08169
$193$	−11.8839	−0.855424	−0.427712	−	0.903915i	$-0.640680\pi$
$193$	−11.8839	−0.855424	−0.427712	+	0.903915i	$0.640680\pi$
$194$	22.4585	1.61243
$195$	−6.16706	−0.441633
$196$	−4.55741	−0.325529
$197$	2.61669	0.186432	0.0932158	−	0.995646i	$-0.470285\pi$
$197$	2.61669	0.186432	0.0932158	+	0.995646i	$0.470285\pi$
$198$	−11.4177	−0.811418
$199$	−2.83272	−0.200806	−0.100403	−	0.994947i	$-0.532013\pi$
$199$	−2.83272	−0.200806	−0.100403	+	0.994947i	$0.532013\pi$
$200$	−5.01957	−0.354937
$201$	−2.31500	−0.163287
$202$	15.4461	1.08678
$203$	−22.6552	−1.59008
$204$	−59.2349	−4.14727
$205$	3.57804	0.249901
$206$	8.75398	0.609919
$207$	−16.5605	−1.15103
$208$	−1.57192	−0.108993
$209$	−9.90039	−0.684824
$210$	−34.7933	−2.40097
$211$	−10.3279	−0.711003	−0.355502	−	0.934676i	$-0.615690\pi$
$211$	−10.3279	−0.711003	−0.355502	+	0.934676i	$0.615690\pi$
$212$	−10.3627	−0.711713
$213$	22.2388	1.52378
$214$	−40.3494	−2.75823
$215$	−1.56009	−0.106398
$216$	0.189340	0.0128829
$217$	−5.32321	−0.361363
$218$	33.8476	2.29245
$219$	−0.845843	−0.0571568
$220$	14.6042	0.984618
$221$	6.79793	0.457278
$222$	42.0881	2.82477
$223$	−8.78970	−0.588602	−0.294301	−	0.955713i	$-0.595087\pi$
$223$	−8.78970	−0.588602	−0.294301	+	0.955713i	$0.595087\pi$
$224$	8.77429	0.586257
$225$	4.05454	0.270302
$226$	−2.06582	−0.137416
$227$	16.4463	1.09158	0.545789	−	0.837922i	$-0.316230\pi$
$227$	16.4463	1.09158	0.545789	+	0.837922i	$0.316230\pi$
$228$	−53.0913	−3.51606
$229$	−15.4024	−1.01782	−0.508909	−	0.860820i	$-0.669951\pi$
$229$	−15.4024	−1.01782	−0.508909	+	0.860820i	$0.669951\pi$
$230$	33.0707	2.18062
$231$	9.50350	0.625285
$232$	34.9320	2.29340
$233$	−28.1905	−1.84682	−0.923410	−	0.383815i	$-0.874610\pi$
$233$	−28.1905	−1.84682	−0.923410	+	0.383815i	$0.874610\pi$
$234$	7.02665	0.459346
$235$	−4.93800	−0.322119
$236$	20.1712	1.31303
$237$	32.9287	2.13895
$238$	38.3525	2.48603
$239$	7.07675	0.457757	0.228878	−	0.973455i	$-0.426494\pi$
$239$	7.07675	0.457757	0.228878	+	0.973455i	$0.426494\pi$
$240$	9.69415	0.625755
$241$	0.144456	0.00930520	0.00465260	−	0.999989i	$-0.498519\pi$
$241$	0.144456	0.00930520	0.00465260	+	0.999989i	$0.498519\pi$
$242$	19.7182	1.26753
$243$	−22.0057	−1.41167
$244$	1.40763	0.0901142
$245$	−3.22549	−0.206069
$246$	−8.18226	−0.521682
$247$	6.09289	0.387681
$248$	8.20785	0.521199
$249$	28.3373	1.79580
$250$	21.6480	1.36914
$251$	−17.5388	−1.10704	−0.553521	−	0.832836i	$-0.686716\pi$
$251$	−17.5388	−1.10704	−0.553521	+	0.832836i	$0.686716\pi$
$252$	25.3920	1.59955
$253$	−9.03298	−0.567898
$254$	−31.8477	−1.99830
$255$	−41.9233	−2.62534
$256$	−24.7324	−1.54577
$257$	−5.46123	−0.340662	−0.170331	−	0.985387i	$-0.554484\pi$
$257$	−5.46123	−0.340662	−0.170331	+	0.985387i	$0.554484\pi$
$258$	3.56762	0.222110
$259$	−17.4545	−1.08457
$260$	−8.98773	−0.557395
$261$	−28.2162	−1.74654
$262$	−40.0912	−2.47685
$263$	−0.416546	−0.0256853	−0.0128427	−	0.999918i	$-0.504088\pi$
$263$	−0.416546	−0.0256853	−0.0128427	+	0.999918i	$0.504088\pi$
$264$	−14.6534	−0.901857
$265$	−7.33417	−0.450534
$266$	34.3748	2.10766
$267$	−35.9920	−2.20267
$268$	−3.37382	−0.206089
$269$	20.0040	1.21966	0.609831	−	0.792531i	$-0.291237\pi$
$269$	20.0040	1.21966	0.609831	+	0.792531i	$0.291237\pi$
$270$	0.305413	0.0185868
$271$	3.90325	0.237106	0.118553	−	0.992948i	$-0.462174\pi$
$271$	3.90325	0.237106	0.118553	+	0.992948i	$0.462174\pi$
$272$	−10.6858	−0.647924
$273$	−5.84864	−0.353976
$274$	22.7966	1.37719
$275$	2.21156	0.133362
$276$	−48.4398	−2.91573
$277$	4.31089	0.259016	0.129508	−	0.991578i	$-0.458660\pi$
$277$	4.31089	0.259016	0.129508	+	0.991578i	$0.458660\pi$
$278$	−33.5243	−2.01066
$279$	−6.62986	−0.396920
$280$	−22.2485	−1.32960
$281$	−17.6519	−1.05302	−0.526512	−	0.850168i	$-0.676500\pi$
$281$	−17.6519	−1.05302	−0.526512	+	0.850168i	$0.676500\pi$
$282$	11.2922	0.672440
$283$	3.31027	0.196775	0.0983875	−	0.995148i	$-0.468632\pi$
$283$	3.31027	0.196775	0.0983875	+	0.995148i	$0.468632\pi$
$284$	32.4103	1.92320
$285$	−37.5752	−2.22576
$286$	3.83271	0.226633
$287$	3.39330	0.200300
$288$	10.9280	0.643941
$289$	29.2119	1.71835
$290$	56.3467	3.30879
$291$	−23.2819	−1.36481
$292$	−1.23271	−0.0721390
$293$	29.4317	1.71942	0.859710	−	0.510782i	$-0.170644\pi$
$293$	29.4317	1.71942	0.859710	+	0.510782i	$0.170644\pi$
$294$	7.37604	0.430179
$295$	14.2761	0.831185
$296$	26.9131	1.56429
$297$	−0.0834209	−0.00484057
$298$	−35.5026	−2.05661
$299$	5.55907	0.321489
$300$	11.8596	0.684715
$301$	−1.47954	−0.0852794
$302$	19.5288	1.12376
$303$	−16.0124	−0.919887
$304$	−9.57755	−0.549310
$305$	0.996244	0.0570448
$306$	47.7667	2.73064
$307$	9.12626	0.520863	0.260431	−	0.965492i	$-0.416135\pi$
$307$	9.12626	0.520863	0.260431	+	0.965492i	$0.416135\pi$
$308$	13.8502	0.789187
$309$	−9.07492	−0.516254
$310$	13.2396	0.751958
$311$	−4.43381	−0.251418	−0.125709	−	0.992067i	$-0.540121\pi$
$311$	−4.43381	−0.251418	−0.125709	+	0.992067i	$0.540121\pi$
$312$	9.01801	0.510544
$313$	−23.4567	−1.32585	−0.662924	−	0.748687i	$-0.730685\pi$
$313$	−23.4567	−1.32585	−0.662924	+	0.748687i	$0.730685\pi$
$314$	−48.4877	−2.73632
$315$	17.9711	1.01256
$316$	47.9895	2.69962
$317$	3.42174	0.192184	0.0960921	−	0.995372i	$-0.469366\pi$
$317$	3.42174	0.192184	0.0960921	+	0.995372i	$0.469366\pi$
$318$	16.7717	0.940513
$319$	−15.3906	−0.861710
$320$	−29.7520	−1.66319
$321$	41.8287	2.33465
$322$	31.3631	1.74780
$323$	41.4190	2.30462
$324$	−32.2951	−1.79417
$325$	−1.36104	−0.0754968
$326$	−9.77399	−0.541331
$327$	−35.0885	−1.94040
$328$	−5.23212	−0.288896
$329$	−4.68303	−0.258184
$330$	−23.6366	−1.30115
$331$	−25.3816	−1.39510	−0.697550	−	0.716536i	$-0.745726\pi$
$331$	−25.3816	−1.39510	−0.697550	+	0.716536i	$0.745726\pi$
$332$	41.2981	2.26653
$333$	−21.7390	−1.19129
$334$	27.6825	1.51472
$335$	−2.38781	−0.130460
$336$	9.19361	0.501553
$337$	−19.4107	−1.05737	−0.528685	−	0.848818i	$-0.677315\pi$
$337$	−19.4107	−1.05737	−0.528685	+	0.848818i	$0.677315\pi$
$338$	−2.35872	−0.128298
$339$	2.14156	0.116314
$340$	−61.0980	−3.31350
$341$	−3.61628	−0.195833
$342$	42.8126	2.31504
$343$	−19.8021	−1.06922
$344$	2.28130	0.123000
$345$	−34.2831	−1.84574
$346$	−20.6370	−1.10945
$347$	5.39902	0.289834	0.144917	−	0.989444i	$-0.453708\pi$
$347$	5.39902	0.289834	0.144917	+	0.989444i	$0.453708\pi$
$348$	−82.5331	−4.42424
$349$	9.81668	0.525475	0.262737	−	0.964867i	$-0.415375\pi$
$349$	9.81668	0.525475	0.262737	+	0.964867i	$0.415375\pi$
$350$	−7.67869	−0.410444
$351$	0.0513388	0.00274026
$352$	5.96074	0.317709
$353$	2.06101	0.109697	0.0548483	−	0.998495i	$-0.482532\pi$
$353$	2.06101	0.109697	0.0548483	+	0.998495i	$0.482532\pi$
$354$	−32.6465	−1.73514
$355$	22.9383	1.21744
$356$	−52.4538	−2.78005
$357$	−39.7586	−2.10425
$358$	−2.09145	−0.110537
$359$	9.27768	0.489657	0.244829	−	0.969566i	$-0.421268\pi$
$359$	9.27768	0.489657	0.244829	+	0.969566i	$0.421268\pi$
$360$	−27.7097	−1.46043
$361$	18.1233	0.953857
$362$	−16.9484	−0.890790
$363$	−20.4411	−1.07288
$364$	−8.52367	−0.446761
$365$	−0.872447	−0.0456660
$366$	−2.27821	−0.119084
$367$	−7.04850	−0.367929	−0.183964	−	0.982933i	$-0.558893\pi$
$367$	−7.04850	−0.367929	−0.183964	+	0.982933i	$0.558893\pi$
$368$	−8.73843	−0.455522
$369$	4.22623	0.220009
$370$	43.4119	2.25688
$371$	−6.95548	−0.361111
$372$	−19.3925	−1.00545
$373$	5.40280	0.279746	0.139873	−	0.990169i	$-0.455331\pi$
$373$	5.40280	0.279746	0.139873	+	0.990169i	$0.455331\pi$
$374$	26.0545	1.34725
$375$	−22.4417	−1.15889
$376$	7.22076	0.372382
$377$	9.47169	0.487817
$378$	0.289643	0.0148976
$379$	25.4397	1.30675	0.653375	−	0.757034i	$-0.273353\pi$
$379$	25.4397	1.30675	0.653375	+	0.757034i	$0.273353\pi$
$380$	−54.7612	−2.80919
$381$	33.0153	1.69143
$382$	14.5958	0.746787
$383$	−20.5425	−1.04967	−0.524837	−	0.851203i	$-0.675874\pi$
$383$	−20.5425	−1.04967	−0.524837	+	0.851203i	$0.675874\pi$
$384$	50.0971	2.55651
$385$	9.80242	0.499577
$386$	28.0309	1.42674
$387$	−1.84271	−0.0936705
$388$	−33.9305	−1.72256
$389$	−9.95921	−0.504952	−0.252476	−	0.967603i	$-0.581245\pi$
$389$	−9.95921	−0.504952	−0.252476	+	0.967603i	$0.581245\pi$
$390$	14.5464	0.736585
$391$	37.7902	1.91113
$392$	4.71659	0.238224
$393$	41.5611	2.09648
$394$	−6.17205	−0.310943
$395$	33.9644	1.70894
$396$	17.2499	0.866839
$397$	9.13986	0.458716	0.229358	−	0.973342i	$-0.426337\pi$
$397$	9.13986	0.458716	0.229358	+	0.973342i	$0.426337\pi$
$398$	6.68160	0.334918
$399$	−35.6351	−1.78399
$400$	2.13945	0.106972
$401$	18.2091	0.909318	0.454659	−	0.890666i	$-0.349761\pi$
$401$	18.2091	0.909318	0.454659	+	0.890666i	$0.349761\pi$
$402$	5.46044	0.272342
$403$	2.22553	0.110862
$404$	−23.3361	−1.16101
$405$	−22.8567	−1.13576
$406$	53.4373	2.65205
$407$	−11.8576	−0.587760
$408$	61.3038	3.03499
$409$	16.0847	0.795336	0.397668	−	0.917529i	$-0.369820\pi$
$409$	16.0847	0.795336	0.397668	+	0.917529i	$0.369820\pi$
$410$	−8.43962	−0.416803
$411$	−23.6324	−1.16570
$412$	−13.2256	−0.651577
$413$	13.5389	0.666208
$414$	39.0616	1.91977
$415$	29.2286	1.43478
$416$	−3.66836	−0.179856
$417$	34.7534	1.70188
$418$	23.3523	1.14220
$419$	−23.4211	−1.14420	−0.572098	−	0.820185i	$-0.693870\pi$
$419$	−23.4211	−1.14420	−0.572098	+	0.820185i	$0.693870\pi$
$420$	52.5660	2.56496
$421$	−36.6398	−1.78571	−0.892857	−	0.450341i	$-0.851303\pi$
$421$	−36.6398	−1.78571	−0.892857	+	0.450341i	$0.851303\pi$
$422$	24.3607	1.18586
$423$	−5.83254	−0.283588
$424$	10.7246	0.520835
$425$	−9.25224	−0.448800
$426$	−52.4552	−2.54146
$427$	0.944805	0.0457223
$428$	60.9602	2.94662
$429$	−3.97323	−0.191829
$430$	3.67983	0.177457
$431$	−3.62948	−0.174826	−0.0874130	−	0.996172i	$-0.527860\pi$
$431$	−3.62948	−0.174826	−0.0874130	+	0.996172i	$0.527860\pi$
$432$	−0.0807007	−0.00388271
$433$	29.8209	1.43310	0.716550	−	0.697536i	$-0.245720\pi$
$433$	29.8209	1.43310	0.716550	+	0.697536i	$0.245720\pi$
$434$	12.5560	0.602707
$435$	−58.4125	−2.80067
$436$	−51.1372	−2.44903
$437$	33.8708	1.62026
$438$	1.99511	0.0953300
$439$	−16.8134	−0.802461	−0.401230	−	0.915977i	$-0.631417\pi$
$439$	−16.8134	−0.802461	−0.401230	+	0.915977i	$0.631417\pi$
$440$	−15.1143	−0.720548
$441$	−3.80980	−0.181419
$442$	−16.0344	−0.762681
$443$	20.2201	0.960686	0.480343	−	0.877081i	$-0.340512\pi$
$443$	20.2201	0.960686	0.480343	+	0.877081i	$0.340512\pi$
$444$	−63.5870	−3.01771
$445$	−37.1240	−1.75985
$446$	20.7325	0.981711
$447$	36.8043	1.74078
$448$	−28.2158	−1.33307
$449$	−6.96110	−0.328515	−0.164257	−	0.986418i	$-0.552523\pi$
$449$	−6.96110	−0.328515	−0.164257	+	0.986418i	$0.552523\pi$
$450$	−9.56353	−0.450829
$451$	2.30521	0.108548
$452$	3.12106	0.146802
$453$	−20.2448	−0.951183
$454$	−38.7923	−1.82061
$455$	−6.03260	−0.282813
$456$	54.9457	2.57307
$457$	5.79399	0.271032	0.135516	−	0.990775i	$-0.456731\pi$
$457$	5.79399	0.271032	0.135516	+	0.990775i	$0.456731\pi$
$458$	36.3300	1.69759
$459$	0.348998	0.0162898
$460$	−49.9634	−2.32956
$461$	−2.78967	−0.129928	−0.0649640	−	0.997888i	$-0.520693\pi$
$461$	−2.78967	−0.129928	−0.0649640	+	0.997888i	$0.520693\pi$
$462$	−22.4161	−1.04289
$463$	10.2261	0.475248	0.237624	−	0.971357i	$-0.423631\pi$
$463$	10.2261	0.475248	0.237624	+	0.971357i	$0.423631\pi$
$464$	−14.8888	−0.691194
$465$	−13.7250	−0.636481
$466$	66.4936	3.08025
$467$	31.0570	1.43714	0.718572	−	0.695452i	$-0.244796\pi$
$467$	31.0570	1.43714	0.718572	+	0.695452i	$0.244796\pi$
$468$	−10.6159	−0.490721
$469$	−2.26452	−0.104566
$470$	11.6474	0.537253
$471$	50.2654	2.31611
$472$	−20.8757	−0.960881
$473$	−1.00512	−0.0462153
$474$	−77.6698	−3.56749
$475$	−8.29265	−0.380493
$476$	−57.9433	−2.65583
$477$	−8.66279	−0.396642
$478$	−16.6921	−0.763479
$479$	26.0770	1.19149	0.595744	−	0.803174i	$-0.296857\pi$
$479$	26.0770	1.19149	0.595744	+	0.803174i	$0.296857\pi$
$480$	22.6230	1.03259
$481$	7.29740	0.332733
$482$	−0.340731	−0.0155199
$483$	−32.5130	−1.47939
$484$	−29.7903	−1.35411
$485$	−24.0142	−1.09043
$486$	51.9054	2.35448
$487$	−17.6502	−0.799806	−0.399903	−	0.916557i	$-0.630956\pi$
$487$	−17.6502	−0.799806	−0.399903	+	0.916557i	$0.630956\pi$
$488$	−1.45679	−0.0659459
$489$	10.1323	0.458200
$490$	7.60804	0.343696
$491$	20.6293	0.930985	0.465493	−	0.885052i	$-0.345877\pi$
$491$	20.6293	0.930985	0.465493	+	0.885052i	$0.345877\pi$
$492$	12.3618	0.557314
$493$	64.3879	2.89989
$494$	−14.3714	−0.646602
$495$	12.2085	0.548733
$496$	−3.49836	−0.157081
$497$	21.7539	0.975796
$498$	−66.8399	−2.99517
$499$	9.83613	0.440326	0.220163	−	0.975463i	$-0.429341\pi$
$499$	9.83613	0.440326	0.220163	+	0.975463i	$0.429341\pi$
$500$	−32.7060	−1.46266
$501$	−28.6974	−1.28210
$502$	41.3692	1.84640
$503$	21.5253	0.959765	0.479882	−	0.877333i	$-0.340679\pi$
$503$	21.5253	0.959765	0.479882	+	0.877333i	$0.340679\pi$
$504$	−26.2789	−1.17056
$505$	−16.5160	−0.734953
$506$	21.3063	0.947180
$507$	2.44520	0.108595
$508$	48.1158	2.13479
$509$	28.9751	1.28430	0.642149	−	0.766580i	$-0.278043\pi$
$509$	28.9751	1.28430	0.642149	+	0.766580i	$0.278043\pi$
$510$	98.8854	4.37872
$511$	−0.827400	−0.0366020
$512$	17.3610	0.767256
$513$	0.312802	0.0138105
$514$	12.8815	0.568180
$515$	−9.36036	−0.412467
$516$	−5.38998	−0.237281
$517$	−3.18138	−0.139917
$518$	41.1704	1.80892
$519$	21.3936	0.939076
$520$	9.30165	0.407904
$521$	8.68000	0.380278	0.190139	−	0.981757i	$-0.439106\pi$
$521$	8.68000	0.380278	0.190139	+	0.981757i	$0.439106\pi$
$522$	66.5542	2.91300
$523$	20.7793	0.908615	0.454307	−	0.890845i	$-0.349887\pi$
$523$	20.7793	0.908615	0.454307	+	0.890845i	$0.349887\pi$
$524$	60.5701	2.64602
$525$	7.96022	0.347412
$526$	0.982517	0.0428398
$527$	15.1290	0.659030
$528$	6.24561	0.271805
$529$	7.90324	0.343619
$530$	17.2993	0.751432
$531$	16.8623	0.731760
$532$	−51.9337	−2.25161
$533$	−1.41867	−0.0614495
$534$	84.8951	3.67377
$535$	43.1444	1.86529
$536$	3.49166	0.150817
$537$	2.16813	0.0935618
$538$	−47.1838	−2.03424
$539$	−2.07807	−0.0895089
$540$	−0.461420	−0.0198563
$541$	−2.90646	−0.124958	−0.0624792	−	0.998046i	$-0.519901\pi$
$541$	−2.90646	−0.124958	−0.0624792	+	0.998046i	$0.519901\pi$
$542$	−9.20670	−0.395461
$543$	17.5698	0.753992
$544$	−24.9372	−1.06918
$545$	−36.1922	−1.55030
$546$	13.7953	0.590385
$547$	7.45363	0.318694	0.159347	−	0.987223i	$-0.449061\pi$
$547$	7.45363	0.318694	0.159347	+	0.987223i	$0.449061\pi$
$548$	−34.4413	−1.47126
$549$	1.17672	0.0502212
$550$	−5.21646	−0.222431
$551$	57.7099	2.45853
$552$	50.1317	2.13375
$553$	32.2108	1.36974
$554$	−10.1682	−0.432006
$555$	−45.0035	−1.91029
$556$	50.6488	2.14799
$557$	−32.5153	−1.37772	−0.688859	−	0.724895i	$-0.741888\pi$
$557$	−32.5153	−1.37772	−0.688859	+	0.724895i	$0.741888\pi$
$558$	15.6380	0.662010
$559$	0.618567	0.0261626
$560$	9.48278	0.400721
$561$	−27.0097	−1.14035
$562$	41.6360	1.75631
$563$	22.1849	0.934981	0.467490	−	0.883998i	$-0.345158\pi$
$563$	22.1849	0.934981	0.467490	+	0.883998i	$0.345158\pi$
$564$	−17.0603	−0.718369
$565$	2.20892	0.0929299
$566$	−7.80801	−0.328195
$567$	−21.6766	−0.910330
$568$	−33.5423	−1.40740
$569$	40.2856	1.68886	0.844430	−	0.535666i	$-0.179939\pi$
$569$	40.2856	1.68886	0.844430	+	0.535666i	$0.179939\pi$
$570$	88.6296	3.71228
$571$	16.4799	0.689661	0.344831	−	0.938665i	$-0.387936\pi$
$571$	16.4799	0.689661	0.344831	+	0.938665i	$0.387936\pi$
$572$	−5.79049	−0.242112
$573$	−15.1309	−0.632104
$574$	−8.00385	−0.334074
$575$	−7.56610	−0.315528
$576$	−35.1418	−1.46424
$577$	−21.0971	−0.878284	−0.439142	−	0.898418i	$-0.644717\pi$
$577$	−21.0971	−0.878284	−0.439142	+	0.898418i	$0.644717\pi$
$578$	−68.9028	−2.86598
$579$	−29.0586	−1.20763
$580$	−85.1290	−3.53479
$581$	27.7194	1.15000
$582$	54.9156	2.27632
$583$	−4.72515	−0.195696
$584$	1.27577	0.0527916
$585$	−7.51338	−0.310640
$586$	−69.4213	−2.86777
$587$	−27.0905	−1.11814	−0.559072	−	0.829119i	$-0.688842\pi$
$587$	−27.0905	−1.11814	−0.559072	+	0.829119i	$0.688842\pi$
$588$	−11.1438	−0.459561
$589$	13.5599	0.558726
$590$	−33.6733	−1.38631
$591$	6.39833	0.263192
$592$	−11.4710	−0.471453
$593$	7.35434	0.302007	0.151003	−	0.988533i	$-0.451750\pi$
$593$	7.35434	0.302007	0.151003	+	0.988533i	$0.451750\pi$
$594$	0.196767	0.00807344
$595$	−41.0092	−1.68121
$596$	53.6377	2.19708
$597$	−6.92657	−0.283486
$598$	−13.1123	−0.536202
$599$	28.5195	1.16528	0.582638	−	0.812732i	$-0.302020\pi$
$599$	28.5195	1.16528	0.582638	+	0.812732i	$0.302020\pi$
$600$	−12.2738	−0.501078
$601$	−13.0175	−0.530995	−0.265497	−	0.964112i	$-0.585536\pi$
$601$	−13.0175	−0.530995	−0.265497	+	0.964112i	$0.585536\pi$
$602$	3.48983	0.142235
$603$	−2.82038	−0.114855
$604$	−29.5043	−1.20051
$605$	−21.0840	−0.857187
$606$	37.7688	1.53425
$607$	−31.2351	−1.26780	−0.633898	−	0.773417i	$-0.718546\pi$
$607$	−31.2351	−1.26780	−0.633898	+	0.773417i	$0.718546\pi$
$608$	−22.3509	−0.906448
$609$	−55.3965	−2.24478
$610$	−2.34987	−0.0951433
$611$	1.95788	0.0792075
$612$	−72.1662	−2.91715
$613$	4.53372	0.183115	0.0915576	−	0.995800i	$-0.470815\pi$
$613$	4.53372	0.183115	0.0915576	+	0.995800i	$0.470815\pi$
$614$	−21.5263	−0.868731
$615$	8.74903	0.352795
$616$	−14.3339	−0.577531
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	21.4052	0.861045
$619$	−20.9044	−0.840218	−0.420109	−	0.907474i	$-0.638008\pi$
$619$	−20.9044	−0.840218	−0.420109	+	0.907474i	$0.638008\pi$
$620$	−20.0025	−0.803318
$621$	0.285396	0.0114525
$622$	10.4581	0.419333
$623$	−35.2072	−1.41055
$624$	−3.84367	−0.153870
$625$	−29.9528	−1.19811
$626$	55.3278	2.21134
$627$	−24.2084	−0.966791
$628$	73.2556	2.92322
$629$	49.6072	1.97797
$630$	−42.3889	−1.68882
$631$	10.4160	0.414655	0.207328	−	0.978272i	$-0.433523\pi$
$631$	10.4160	0.414655	0.207328	+	0.978272i	$0.433523\pi$
$632$	−49.6657	−1.97560
$633$	−25.2538	−1.00375
$634$	−8.07094	−0.320538
$635$	34.0538	1.35138
$636$	−25.3389	−1.00475
$637$	1.27889	0.0506713
$638$	36.3022	1.43722
$639$	27.0937	1.07181
$640$	51.6728	2.04255
$641$	7.55733	0.298496	0.149248	−	0.988800i	$-0.452315\pi$
$641$	7.55733	0.298496	0.149248	+	0.988800i	$0.452315\pi$
$642$	−98.6624	−3.89390
$643$	−6.86497	−0.270728	−0.135364	−	0.990796i	$-0.543220\pi$
$643$	−6.86497	−0.270728	−0.135364	+	0.990796i	$0.543220\pi$
$644$	−47.3836	−1.86718
$645$	−3.81474	−0.150205
$646$	−97.6961	−3.84380
$647$	−23.1637	−0.910659	−0.455330	−	0.890323i	$-0.650479\pi$
$647$	−23.1637	−0.910659	−0.455330	+	0.890323i	$0.650479\pi$
$648$	33.4231	1.31298
$649$	9.19758	0.361037
$650$	3.21031	0.125919
$651$	−13.0163	−0.510150
$652$	14.7666	0.578305
$653$	20.2724	0.793322	0.396661	−	0.917965i	$-0.370169\pi$
$653$	20.2724	0.793322	0.396661	+	0.917965i	$0.370169\pi$
$654$	82.7641	3.23633
$655$	42.8683	1.67500
$656$	2.23004	0.0870685
$657$	−1.03050	−0.0402035
$658$	11.0460	0.430617
$659$	−8.02302	−0.312533	−0.156266	−	0.987715i	$-0.549946\pi$
$659$	−8.02302	−0.312533	−0.156266	+	0.987715i	$0.549946\pi$
$660$	35.7103	1.39002
$661$	−10.2123	−0.397213	−0.198607	−	0.980079i	$-0.563642\pi$
$661$	−10.2123	−0.397213	−0.198607	+	0.980079i	$0.563642\pi$
$662$	59.8682	2.32684
$663$	16.6223	0.645557
$664$	−42.7406	−1.65866
$665$	−36.7559	−1.42533
$666$	51.2762	1.98691
$667$	52.6538	2.03876
$668$	−41.8229	−1.61818
$669$	−21.4926	−0.830951
$670$	5.63219	0.217590
$671$	0.641846	0.0247782
$672$	21.4549	0.827640
$673$	−15.5790	−0.600525	−0.300263	−	0.953857i	$-0.597074\pi$
$673$	−15.5790	−0.600525	−0.300263	+	0.953857i	$0.597074\pi$
$674$	45.7846	1.76356
$675$	−0.0698741	−0.00268945
$676$	3.56358	0.137061
$677$	−33.8489	−1.30092	−0.650460	−	0.759540i	$-0.725424\pi$
$677$	−33.8489	−1.30092	−0.650460	+	0.759540i	$0.725424\pi$
$678$	−5.05135	−0.193996
$679$	−22.7743	−0.873996
$680$	63.2320	2.42484
$681$	40.2145	1.54102
$682$	8.52981	0.326623
$683$	2.68902	0.102893	0.0514463	−	0.998676i	$-0.483617\pi$
$683$	2.68902	0.102893	0.0514463	+	0.998676i	$0.483617\pi$
$684$	−64.6815	−2.47316
$685$	−24.3757	−0.931348
$686$	46.7078	1.78331
$687$	−37.6619	−1.43689
$688$	−0.972341	−0.0370701
$689$	2.90795	0.110784
$690$	80.8644	3.07846
$691$	−19.1583	−0.728817	−0.364408	−	0.931239i	$-0.618729\pi$
$691$	−19.1583	−0.728817	−0.364408	+	0.931239i	$0.618729\pi$
$692$	31.1785	1.18523
$693$	11.5782	0.439819
$694$	−12.7348	−0.483406
$695$	35.8465	1.35974
$696$	85.4158	3.23768
$697$	−9.64403	−0.365294
$698$	−23.1548	−0.876423
$699$	−68.9314	−2.60722
$700$	11.6010	0.438478
$701$	−8.28783	−0.313027	−0.156513	−	0.987676i	$-0.550025\pi$
$701$	−8.28783	−0.313027	−0.156513	+	0.987676i	$0.550025\pi$
$702$	−0.121094	−0.00457040
$703$	44.4622	1.67692
$704$	−19.1682	−0.722429
$705$	−12.0744	−0.454748
$706$	−4.86136	−0.182960
$707$	−15.6632	−0.589077
$708$	49.3225	1.85365
$709$	−38.9567	−1.46305	−0.731525	−	0.681814i	$-0.761191\pi$
$709$	−38.9567	−1.46305	−0.731525	+	0.681814i	$0.761191\pi$
$710$	−54.1051	−2.03053
$711$	40.1173	1.50452
$712$	54.2859	2.03445
$713$	12.3719	0.463330
$714$	93.7797	3.50962
$715$	−4.09820	−0.153264
$716$	3.15978	0.118087
$717$	17.3041	0.646232
$718$	−21.8835	−0.816685
$719$	10.2888	0.383708	0.191854	−	0.981424i	$-0.438550\pi$
$719$	10.2888	0.383708	0.191854	+	0.981424i	$0.438550\pi$
$720$	11.8105	0.440149
$721$	−8.87705	−0.330599
$722$	−42.7478	−1.59091
$723$	0.353223	0.0131365
$724$	25.6058	0.951632
$725$	−12.8913	−0.478772
$726$	48.2148	1.78942
$727$	−39.0274	−1.44745	−0.723724	−	0.690090i	$-0.757571\pi$
$727$	−39.0274	−1.44745	−0.723724	+	0.690090i	$0.757571\pi$
$728$	8.82138	0.326942
$729$	−26.6208	−0.985954
$730$	2.05786	0.0761649
$731$	4.20498	0.155527
$732$	3.44193	0.127218
$733$	−3.39091	−0.125246	−0.0626230	−	0.998037i	$-0.519947\pi$
$733$	−3.39091	−0.125246	−0.0626230	+	0.998037i	$0.519947\pi$
$734$	16.6255	0.613657
$735$	−7.88697	−0.290915
$736$	−20.3926	−0.751683
$737$	−1.53838	−0.0566671
$738$	−9.96850	−0.366946
$739$	−12.8949	−0.474347	−0.237174	−	0.971467i	$-0.576221\pi$
$739$	−12.8949	−0.474347	−0.237174	+	0.971467i	$0.576221\pi$
$740$	−65.5870	−2.41103
$741$	14.8983	0.547304
$742$	16.4061	0.602285
$743$	30.8685	1.13246	0.566228	−	0.824249i	$-0.308402\pi$
$743$	30.8685	1.13246	0.566228	+	0.824249i	$0.308402\pi$
$744$	20.0698	0.735796
$745$	37.9619	1.39082
$746$	−12.7437	−0.466580
$747$	34.5235	1.26315
$748$	−39.3633	−1.43927
$749$	40.9167	1.49506
$750$	52.9338	1.93287
$751$	−33.8625	−1.23566	−0.617829	−	0.786312i	$-0.711988\pi$
$751$	−33.8625	−1.23566	−0.617829	+	0.786312i	$0.711988\pi$
$752$	−3.07764	−0.112230
$753$	−42.8859	−1.56285
$754$	−22.3411	−0.813615
$755$	−20.8815	−0.759957
$756$	−0.437595	−0.0159152
$757$	−18.6259	−0.676969	−0.338485	−	0.940972i	$-0.609914\pi$
$757$	−18.6259	−0.676969	−0.338485	+	0.940972i	$0.609914\pi$
$758$	−60.0052	−2.17949
$759$	−22.0874	−0.801723
$760$	56.6739	2.05578
$761$	−14.7812	−0.535820	−0.267910	−	0.963444i	$-0.586333\pi$
$761$	−14.7812	−0.535820	−0.267910	+	0.963444i	$0.586333\pi$
$762$	−77.8740	−2.82108
$763$	−34.3235	−1.24259
$764$	−22.0515	−0.797794
$765$	−51.0754	−1.84664
$766$	48.4542	1.75072
$767$	−5.66037	−0.204384
$768$	−60.4757	−2.18223
$769$	−37.4828	−1.35167	−0.675833	−	0.737055i	$-0.736216\pi$
$769$	−37.4828	−1.35167	−0.675833	+	0.737055i	$0.736216\pi$
$770$	−23.1212	−0.833230
$771$	−13.3538	−0.480925
$772$	−42.3493	−1.52418
$773$	−8.85901	−0.318637	−0.159318	−	0.987227i	$-0.550930\pi$
$773$	−8.85901	−0.318637	−0.159318	+	0.987227i	$0.550930\pi$
$774$	4.34646	0.156230
$775$	−3.02903	−0.108806
$776$	35.1156	1.26058
$777$	−42.6798	−1.53113
$778$	23.4910	0.842194
$779$	−8.64380	−0.309696
$780$	−21.9768	−0.786896
$781$	14.7783	0.528811
$782$	−89.1366	−3.18752
$783$	0.486265	0.0173777
$784$	−2.01031	−0.0717968
$785$	51.8464	1.85048
$786$	−98.0311	−3.49665
$787$	26.3881	0.940634	0.470317	−	0.882497i	$-0.344140\pi$
$787$	26.3881	0.940634	0.470317	+	0.882497i	$0.344140\pi$
$788$	9.32478	0.332181
$789$	−1.01854	−0.0362609
$790$	−80.1127	−2.85028
$791$	2.09487	0.0744848
$792$	−17.8524	−0.634357
$793$	−0.395004	−0.0140270
$794$	−21.5584	−0.765079
$795$	−17.9335	−0.636036
$796$	−10.0946	−0.357794
$797$	−20.3308	−0.720153	−0.360076	−	0.932923i	$-0.617249\pi$
$797$	−20.3308	−0.720153	−0.360076	+	0.932923i	$0.617249\pi$
$798$	84.0533	2.97546
$799$	13.3096	0.470858
$800$	4.99277	0.176521
$801$	−43.8493	−1.54934
$802$	−42.9502	−1.51662
$803$	−0.562088	−0.0198356
$804$	−8.24967	−0.290943
$805$	−33.5356	−1.18198
$806$	−5.24941	−0.184903
$807$	48.9137	1.72184
$808$	24.1511	0.849634
$809$	18.8644	0.663238	0.331619	−	0.943413i	$-0.392405\pi$
$809$	18.8644	0.663238	0.331619	+	0.943413i	$0.392405\pi$
$810$	53.9127	1.89430
$811$	20.1343	0.707011	0.353506	−	0.935432i	$-0.384990\pi$
$811$	20.1343	0.707011	0.353506	+	0.935432i	$0.384990\pi$
$812$	−80.7335	−2.83319
$813$	9.54424	0.334731
$814$	27.9688	0.980306
$815$	10.4510	0.366083
$816$	−26.1290	−0.914698
$817$	3.76886	0.131856
$818$	−37.9393	−1.32652
$819$	−7.12544	−0.248983
$820$	12.7506	0.445271
$821$	−7.16565	−0.250083	−0.125041	−	0.992152i	$-0.539906\pi$
$821$	−7.16565	−0.250083	−0.125041	+	0.992152i	$0.539906\pi$
$822$	55.7423	1.94424
$823$	41.1981	1.43607	0.718037	−	0.696005i	$-0.245041\pi$
$823$	41.1981	1.43607	0.718037	+	0.696005i	$0.245041\pi$
$824$	13.6875	0.476827
$825$	5.40771	0.188272
$826$	−31.9346	−1.11115
$827$	47.4729	1.65079	0.825397	−	0.564553i	$-0.190951\pi$
$827$	47.4729	1.65079	0.825397	+	0.564553i	$0.190951\pi$
$828$	−59.0146	−2.05090
$829$	−46.2456	−1.60618	−0.803088	−	0.595860i	$-0.796811\pi$
$829$	−46.2456	−1.60618	−0.803088	+	0.595860i	$0.796811\pi$
$830$	−68.9422	−2.39302
$831$	10.5410	0.365663
$832$	11.7965	0.408969
$833$	8.69378	0.301221
$834$	−81.9737	−2.83852
$835$	−29.6000	−1.02435
$836$	−35.2808	−1.22021
$837$	0.114256	0.00394927
$838$	55.2439	1.90837
$839$	−32.3448	−1.11667	−0.558333	−	0.829617i	$-0.688559\pi$
$839$	−32.3448	−1.11667	−0.558333	+	0.829617i	$0.688559\pi$
$840$	−54.4020	−1.87705
$841$	60.7129	2.09355
$842$	86.4231	2.97834
$843$	−43.1624	−1.48659
$844$	−36.8043	−1.26686
$845$	2.52211	0.0867632
$846$	13.7574	0.472988
$847$	−19.9954	−0.687049
$848$	−4.57107	−0.156971
$849$	8.09427	0.277795
$850$	21.8235	0.748539
$851$	40.5667	1.39061
$852$	79.2497	2.71505
$853$	28.3158	0.969516	0.484758	−	0.874648i	$-0.338908\pi$
$853$	28.3158	0.969516	0.484758	+	0.874648i	$0.338908\pi$
$854$	−2.22853	−0.0762589
$855$	−45.7782	−1.56558
$856$	−63.0894	−2.15635
$857$	−40.5887	−1.38648	−0.693241	−	0.720706i	$-0.743818\pi$
$857$	−40.5887	−1.38648	−0.693241	+	0.720706i	$0.743818\pi$
$858$	9.37174	0.319946
$859$	9.84248	0.335821	0.167911	−	0.985802i	$-0.446298\pi$
$859$	9.84248	0.335821	0.167911	+	0.985802i	$0.446298\pi$
$860$	−5.55952	−0.189578
$861$	8.29729	0.282771
$862$	8.56095	0.291587
$863$	24.5555	0.835880	0.417940	−	0.908475i	$-0.362752\pi$
$863$	24.5555	0.835880	0.417940	+	0.908475i	$0.362752\pi$
$864$	−0.188329	−0.00640709
$865$	22.0665	0.750284
$866$	−70.3392	−2.39022
$867$	71.4289	2.42585
$868$	−18.9697	−0.643873
$869$	21.8821	0.742300
$870$	137.779	4.67114
$871$	0.946751	0.0320794
$872$	52.9233	1.79221
$873$	−28.3645	−0.959993
$874$	−79.8918	−2.70238
$875$	−21.9524	−0.742126
$876$	−3.01423	−0.101841
$877$	−19.3162	−0.652261	−0.326130	−	0.945325i	$-0.605745\pi$
$877$	−19.3162	−0.652261	−0.326130	+	0.945325i	$0.605745\pi$
$878$	39.6582	1.33840
$879$	71.9665	2.42737
$880$	6.44205	0.217162
$881$	5.61015	0.189011	0.0945054	−	0.995524i	$-0.469873\pi$
$881$	5.61015	0.189011	0.0945054	+	0.995524i	$0.469873\pi$
$882$	8.98628	0.302584
$883$	44.5972	1.50081	0.750407	−	0.660976i	$-0.229858\pi$
$883$	44.5972	1.50081	0.750407	+	0.660976i	$0.229858\pi$
$884$	24.2250	0.814773
$885$	34.9078	1.17341
$886$	−47.6937	−1.60230
$887$	−44.1195	−1.48139	−0.740694	−	0.671842i	$-0.765503\pi$
$887$	−44.1195	−1.48139	−0.740694	+	0.671842i	$0.765503\pi$
$888$	65.8080	2.20837
$889$	32.2955	1.08316
$890$	87.5654	2.93520
$891$	−14.7258	−0.493333
$892$	−31.3228	−1.04876
$893$	11.9292	0.399194
$894$	−86.8111	−2.90340
$895$	2.23633	0.0747521
$896$	49.0048	1.63713
$897$	13.5930	0.453858
$898$	16.4193	0.547920
$899$	21.0795	0.703042
$900$	14.4486	0.481622
$901$	19.7680	0.658569
$902$	−5.43736	−0.181044
$903$	−3.61778	−0.120392
$904$	−3.23007	−0.107431
$905$	18.1224	0.602410
$906$	47.7518	1.58645
$907$	−39.3726	−1.30734	−0.653672	−	0.756778i	$-0.726773\pi$
$907$	−39.3726	−1.30734	−0.653672	+	0.756778i	$0.726773\pi$
$908$	58.6076	1.94496
$909$	−19.5080	−0.647039
$910$	14.2292	0.471694
$911$	16.3560	0.541900	0.270950	−	0.962593i	$-0.412662\pi$
$911$	16.3560	0.541900	0.270950	+	0.962593i	$0.412662\pi$
$912$	−23.4190	−0.775482
$913$	18.8310	0.623215
$914$	−13.6664	−0.452045
$915$	2.43602	0.0805322
$916$	−54.8876	−1.81354
$917$	40.6549	1.34254
$918$	−0.823189	−0.0271693
$919$	−1.52269	−0.0502290	−0.0251145	−	0.999685i	$-0.507995\pi$
$919$	−1.52269	−0.0502290	−0.0251145	+	0.999685i	$0.507995\pi$
$920$	51.7085	1.70478
$921$	22.3155	0.735322
$922$	6.58006	0.216703
$923$	−9.09488	−0.299362
$924$	33.8665	1.11412
$925$	−9.93203	−0.326563
$926$	−24.1206	−0.792651
$927$	−11.0560	−0.363128
$928$	−34.7455	−1.14058
$929$	−2.69016	−0.0882613	−0.0441307	−	0.999026i	$-0.514052\pi$
$929$	−2.69016	−0.0882613	−0.0441307	+	0.999026i	$0.514052\pi$
$930$	32.3735	1.06157
$931$	7.79210	0.255376
$932$	−100.459	−3.29064
$933$	−10.8416	−0.354937
$934$	−73.2548	−2.39697
$935$	−27.8593	−0.911096
$936$	10.9867	0.359111
$937$	−42.4647	−1.38726	−0.693630	−	0.720332i	$-0.743990\pi$
$937$	−42.4647	−1.38726	−0.693630	+	0.720332i	$0.743990\pi$
$938$	5.34138	0.174402
$939$	−57.3562	−1.87175
$940$	−17.5969	−0.573949
$941$	−4.77372	−0.155619	−0.0778095	−	0.996968i	$-0.524793\pi$
$941$	−4.77372	−0.155619	−0.0778095	+	0.996968i	$0.524793\pi$
$942$	−118.562	−3.86297
$943$	−7.88649	−0.256819
$944$	8.89766	0.289594
$945$	−0.309706	−0.0100748
$946$	2.37079	0.0770810
$947$	19.3215	0.627864	0.313932	−	0.949445i	$-0.398354\pi$
$947$	19.3215	0.627864	0.313932	+	0.949445i	$0.398354\pi$
$948$	117.344	3.81116
$949$	0.345920	0.0112290
$950$	19.5601	0.634612
$951$	8.36684	0.271313
$952$	59.9671	1.94355
$953$	1.63619	0.0530013	0.0265007	−	0.999649i	$-0.491564\pi$
$953$	1.63619	0.0530013	0.0265007	+	0.999649i	$0.491564\pi$
$954$	20.4331	0.661547
$955$	−15.6069	−0.505026
$956$	25.2185	0.815626
$957$	−37.6332	−1.21651
$958$	−61.5084	−1.98725
$959$	−23.1171	−0.746491
$960$	−72.7497	−2.34799
$961$	−26.0470	−0.840226
$962$	−17.2125	−0.554955
$963$	50.9602	1.64217
$964$	0.514779	0.0165799
$965$	−29.9726	−0.964852
$966$	76.6891	2.46743
$967$	−36.1438	−1.16231	−0.581153	−	0.813794i	$-0.697398\pi$
$967$	−36.1438	−1.16231	−0.581153	+	0.813794i	$0.697398\pi$
$968$	30.8308	0.990941
$969$	101.278	3.25351
$970$	56.6428	1.81869
$971$	43.8243	1.40639	0.703195	−	0.710997i	$-0.251756\pi$
$971$	43.8243	1.40639	0.703195	+	0.710997i	$0.251756\pi$
$972$	−78.4191	−2.51529
$973$	33.9957	1.08985
$974$	41.6319	1.33397
$975$	−3.32801	−0.106582
$976$	0.620917	0.0198751
$977$	34.8944	1.11637	0.558185	−	0.829717i	$-0.311498\pi$
$977$	34.8944	1.11637	0.558185	+	0.829717i	$0.311498\pi$
$978$	−23.8994	−0.764217
$979$	−23.9177	−0.764414
$980$	−11.4943	−0.367171
$981$	−42.7486	−1.36486
$982$	−48.6587	−1.55276
$983$	3.85867	0.123072	0.0615362	−	0.998105i	$-0.480400\pi$
$983$	3.85867	0.123072	0.0615362	+	0.998105i	$0.480400\pi$
$984$	−12.7936	−0.407845
$985$	6.59958	0.210280
$986$	−151.873	−4.83663
$987$	−11.4510	−0.364488
$988$	21.7125	0.690766
$989$	3.43866	0.109343
$990$	−28.7966	−0.915216
$991$	14.8937	0.473115	0.236557	−	0.971618i	$-0.423981\pi$
$991$	14.8937	0.473115	0.236557	+	0.971618i	$0.423981\pi$
$992$	−8.16404	−0.259208
$993$	−62.0631	−1.96951
$994$	−51.3115	−1.62750
$995$	−7.14443	−0.226494
$996$	100.982	3.19974
$997$	−55.8582	−1.76905	−0.884523	−	0.466497i	$-0.845516\pi$
$997$	−55.8582	−1.76905	−0.884523	+	0.466497i	$0.845516\pi$
$998$	−23.2007	−0.734405
$999$	0.374640	0.0118531

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.b.1.15	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.b.1.15	✓	140	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.35872 q^{2} +2.44520 q^{3} +3.56358 q^{4} +2.52211 q^{5} -5.76755 q^{6} +2.39189 q^{7} -3.68804 q^{8} +2.97900 q^{9} +O(q^{10})\)	\(q-2.35872 q^{2} +2.44520 q^{3} +3.56358 q^{4} +2.52211 q^{5} -5.76755 q^{6} +2.39189 q^{7} -3.68804 q^{8} +2.97900 q^{9} -5.94896 q^{10} +1.62491 q^{11} +8.71366 q^{12} -1.00000 q^{13} -5.64180 q^{14} +6.16706 q^{15} +1.57192 q^{16} -6.79793 q^{17} -7.02665 q^{18} -6.09289 q^{19} +8.98773 q^{20} +5.84864 q^{21} -3.83271 q^{22} -5.55907 q^{23} -9.01801 q^{24} +1.36104 q^{25} +2.35872 q^{26} -0.0513388 q^{27} +8.52367 q^{28} -9.47169 q^{29} -14.5464 q^{30} -2.22553 q^{31} +3.66836 q^{32} +3.97323 q^{33} +16.0344 q^{34} +6.03260 q^{35} +10.6159 q^{36} -7.29740 q^{37} +14.3714 q^{38} -2.44520 q^{39} -9.30165 q^{40} +1.41867 q^{41} -13.7953 q^{42} -0.618567 q^{43} +5.79049 q^{44} +7.51338 q^{45} +13.1123 q^{46} -1.95788 q^{47} +3.84367 q^{48} -1.27889 q^{49} -3.21031 q^{50} -16.6223 q^{51} -3.56358 q^{52} -2.90795 q^{53} +0.121094 q^{54} +4.09820 q^{55} -8.82138 q^{56} -14.8983 q^{57} +22.3411 q^{58} +5.66037 q^{59} +21.9768 q^{60} +0.395004 q^{61} +5.24941 q^{62} +7.12544 q^{63} -11.7965 q^{64} -2.52211 q^{65} -9.37174 q^{66} -0.946751 q^{67} -24.2250 q^{68} -13.5930 q^{69} -14.2292 q^{70} +9.09488 q^{71} -10.9867 q^{72} -0.345920 q^{73} +17.2125 q^{74} +3.32801 q^{75} -21.7125 q^{76} +3.88659 q^{77} +5.76755 q^{78} +13.4667 q^{79} +3.96456 q^{80} -9.06255 q^{81} -3.34625 q^{82} +11.5890 q^{83} +20.8421 q^{84} -17.1451 q^{85} +1.45903 q^{86} -23.1602 q^{87} -5.99273 q^{88} -14.7194 q^{89} -17.7220 q^{90} -2.39189 q^{91} -19.8102 q^{92} -5.44187 q^{93} +4.61811 q^{94} -15.3669 q^{95} +8.96986 q^{96} -9.52147 q^{97} +3.01654 q^{98} +4.84061 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * q^99

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