LMFDB - Embedded newform 6022.2.a.e.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.15100 q^{3} +1.00000 q^{4} +1.71186 q^{5} -1.15100 q^{6} +3.72563 q^{7} +1.00000 q^{8} -1.67520 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.15100 q^{3} +1.00000 q^{4} +1.71186 q^{5} -1.15100 q^{6} +3.72563 q^{7} +1.00000 q^{8} -1.67520 q^{9} +1.71186 q^{10} -6.17862 q^{11} -1.15100 q^{12} +2.42728 q^{13} +3.72563 q^{14} -1.97035 q^{15} +1.00000 q^{16} +4.92231 q^{17} -1.67520 q^{18} -4.33677 q^{19} +1.71186 q^{20} -4.28820 q^{21} -6.17862 q^{22} -0.461292 q^{23} -1.15100 q^{24} -2.06954 q^{25} +2.42728 q^{26} +5.38115 q^{27} +3.72563 q^{28} +0.165157 q^{29} -1.97035 q^{30} +0.0741034 q^{31} +1.00000 q^{32} +7.11159 q^{33} +4.92231 q^{34} +6.37775 q^{35} -1.67520 q^{36} +3.11616 q^{37} -4.33677 q^{38} -2.79379 q^{39} +1.71186 q^{40} +4.66151 q^{41} -4.28820 q^{42} +4.76881 q^{43} -6.17862 q^{44} -2.86771 q^{45} -0.461292 q^{46} +12.1145 q^{47} -1.15100 q^{48} +6.88031 q^{49} -2.06954 q^{50} -5.66558 q^{51} +2.42728 q^{52} -1.40562 q^{53} +5.38115 q^{54} -10.5769 q^{55} +3.72563 q^{56} +4.99162 q^{57} +0.165157 q^{58} +2.18717 q^{59} -1.97035 q^{60} -13.4779 q^{61} +0.0741034 q^{62} -6.24117 q^{63} +1.00000 q^{64} +4.15516 q^{65} +7.11159 q^{66} +8.85100 q^{67} +4.92231 q^{68} +0.530946 q^{69} +6.37775 q^{70} +13.8710 q^{71} -1.67520 q^{72} +0.166468 q^{73} +3.11616 q^{74} +2.38204 q^{75} -4.33677 q^{76} -23.0192 q^{77} -2.79379 q^{78} +10.1561 q^{79} +1.71186 q^{80} -1.16810 q^{81} +4.66151 q^{82} +9.77815 q^{83} -4.28820 q^{84} +8.42630 q^{85} +4.76881 q^{86} -0.190095 q^{87} -6.17862 q^{88} +16.7617 q^{89} -2.86771 q^{90} +9.04313 q^{91} -0.461292 q^{92} -0.0852929 q^{93} +12.1145 q^{94} -7.42394 q^{95} -1.15100 q^{96} +5.95560 q^{97} +6.88031 q^{98} +10.3504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) $ 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9 + 20 * q^10 + 46 * q^11 + 25 * q^12 + 30 * q^13 + 29 * q^14 + 13 * q^15 + 68 * q^16 + 73 * q^17 + 87 * q^18 + 56 * q^19 + 20 * q^20 - 5 * q^21 + 46 * q^22 + 63 * q^23 + 25 * q^24 + 88 * q^25 + 30 * q^26 + 67 * q^27 + 29 * q^28 + 43 * q^29 + 13 * q^30 + 68 * q^31 + 68 * q^32 + 26 * q^33 + 73 * q^34 + 50 * q^35 + 87 * q^36 + 8 * q^37 + 56 * q^38 + 6 * q^39 + 20 * q^40 + 64 * q^41 - 5 * q^42 + 52 * q^43 + 46 * q^44 + 7 * q^45 + 63 * q^46 + 94 * q^47 + 25 * q^48 + 91 * q^49 + 88 * q^50 + 20 * q^51 + 30 * q^52 + 38 * q^53 + 67 * q^54 + 37 * q^55 + 29 * q^56 + 4 * q^57 + 43 * q^58 + 84 * q^59 + 13 * q^60 + 26 * q^61 + 68 * q^62 + 22 * q^63 + 68 * q^64 - 20 * q^65 + 26 * q^66 + 54 * q^67 + 73 * q^68 - 11 * q^69 + 50 * q^70 + 46 * q^71 + 87 * q^72 + 62 * q^73 + 8 * q^74 + 54 * q^75 + 56 * q^76 + 67 * q^77 + 6 * q^78 + 67 * q^79 + 20 * q^80 + 120 * q^81 + 64 * q^82 + 130 * q^83 - 5 * q^84 - 24 * q^85 + 52 * q^86 + 72 * q^87 + 46 * q^88 + 61 * q^89 + 7 * q^90 + 43 * q^91 + 63 * q^92 + 40 * q^93 + 94 * q^94 + 55 * q^95 + 25 * q^96 + 41 * q^97 + 91 * q^98 + 106 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.15100	−0.664530	−0.332265	−	0.943186i	$-0.607813\pi$
$3$	−1.15100	−0.664530	−0.332265	+	0.943186i	$0.607813\pi$
$4$	1.00000	0.500000
$5$	1.71186	0.765567	0.382783	−	0.923838i	$-0.374966\pi$
$5$	1.71186	0.765567	0.382783	+	0.923838i	$0.374966\pi$
$6$	−1.15100	−0.469894
$7$	3.72563	1.40816	0.704078	−	0.710123i	$-0.251361\pi$
$7$	3.72563	1.40816	0.704078	+	0.710123i	$0.251361\pi$
$8$	1.00000	0.353553
$9$	−1.67520	−0.558400
$10$	1.71186	0.541337
$11$	−6.17862	−1.86292	−0.931462	−	0.363838i	$-0.881466\pi$
$11$	−6.17862	−1.86292	−0.931462	+	0.363838i	$0.881466\pi$
$12$	−1.15100	−0.332265
$13$	2.42728	0.673205	0.336603	−	0.941647i	$-0.390722\pi$
$13$	2.42728	0.673205	0.336603	+	0.941647i	$0.390722\pi$
$14$	3.72563	0.995716
$15$	−1.97035	−0.508742
$16$	1.00000	0.250000
$17$	4.92231	1.19384	0.596918	−	0.802302i	$-0.296392\pi$
$17$	4.92231	1.19384	0.596918	+	0.802302i	$0.296392\pi$
$18$	−1.67520	−0.394849
$19$	−4.33677	−0.994923	−0.497462	−	0.867486i	$-0.665735\pi$
$19$	−4.33677	−0.994923	−0.497462	+	0.867486i	$0.665735\pi$
$20$	1.71186	0.382783
$21$	−4.28820	−0.935761
$22$	−6.17862	−1.31729
$23$	−0.461292	−0.0961859	−0.0480930	−	0.998843i	$-0.515314\pi$
$23$	−0.461292	−0.0961859	−0.0480930	+	0.998843i	$0.515314\pi$
$24$	−1.15100	−0.234947
$25$	−2.06954	−0.413908
$26$	2.42728	0.476028
$27$	5.38115	1.03560
$28$	3.72563	0.704078
$29$	0.165157	0.0306688	0.0153344	−	0.999882i	$-0.495119\pi$
$29$	0.165157	0.0306688	0.0153344	+	0.999882i	$0.495119\pi$
$30$	−1.97035	−0.359735
$31$	0.0741034	0.0133094	0.00665468	−	0.999978i	$-0.497882\pi$
$31$	0.0741034	0.0133094	0.00665468	+	0.999978i	$0.497882\pi$
$32$	1.00000	0.176777
$33$	7.11159	1.23797
$34$	4.92231	0.844169
$35$	6.37775	1.07804
$36$	−1.67520	−0.279200
$37$	3.11616	0.512294	0.256147	−	0.966638i	$-0.417547\pi$
$37$	3.11616	0.512294	0.256147	+	0.966638i	$0.417547\pi$
$38$	−4.33677	−0.703517
$39$	−2.79379	−0.447365
$40$	1.71186	0.270669
$41$	4.66151	0.728005	0.364002	−	0.931398i	$-0.381410\pi$
$41$	4.66151	0.728005	0.364002	+	0.931398i	$0.381410\pi$
$42$	−4.28820	−0.661683
$43$	4.76881	0.727237	0.363619	−	0.931548i	$-0.381541\pi$
$43$	4.76881	0.727237	0.363619	+	0.931548i	$0.381541\pi$
$44$	−6.17862	−0.931462
$45$	−2.86771	−0.427493
$46$	−0.461292	−0.0680137
$47$	12.1145	1.76708	0.883540	−	0.468356i	$-0.155153\pi$
$47$	12.1145	1.76708	0.883540	+	0.468356i	$0.155153\pi$
$48$	−1.15100	−0.166132
$49$	6.88031	0.982901
$50$	−2.06954	−0.292677
$51$	−5.66558	−0.793339
$52$	2.42728	0.336603
$53$	−1.40562	−0.193077	−0.0965386	−	0.995329i	$-0.530777\pi$
$53$	−1.40562	−0.193077	−0.0965386	+	0.995329i	$0.530777\pi$
$54$	5.38115	0.732282
$55$	−10.5769	−1.42619
$56$	3.72563	0.497858
$57$	4.99162	0.661156
$58$	0.165157	0.0216861
$59$	2.18717	0.284745	0.142372	−	0.989813i	$-0.454527\pi$
$59$	2.18717	0.284745	0.142372	+	0.989813i	$0.454527\pi$
$60$	−1.97035	−0.254371
$61$	−13.4779	−1.72567	−0.862837	−	0.505482i	$-0.831315\pi$
$61$	−13.4779	−1.72567	−0.862837	+	0.505482i	$0.831315\pi$
$62$	0.0741034	0.00941113
$63$	−6.24117	−0.786314
$64$	1.00000	0.125000
$65$	4.15516	0.515384
$66$	7.11159	0.875376
$67$	8.85100	1.08132	0.540661	−	0.841240i	$-0.318174\pi$
$67$	8.85100	1.08132	0.540661	+	0.841240i	$0.318174\pi$
$68$	4.92231	0.596918
$69$	0.530946	0.0639184
$70$	6.37775	0.762287
$71$	13.8710	1.64619	0.823094	−	0.567905i	$-0.192246\pi$
$71$	13.8710	1.64619	0.823094	+	0.567905i	$0.192246\pi$
$72$	−1.67520	−0.197424
$73$	0.166468	0.0194836	0.00974182	−	0.999953i	$-0.496899\pi$
$73$	0.166468	0.0194836	0.00974182	+	0.999953i	$0.496899\pi$
$74$	3.11616	0.362246
$75$	2.38204	0.275054
$76$	−4.33677	−0.497462
$77$	−23.0192	−2.62329
$78$	−2.79379	−0.316335
$79$	10.1561	1.14265	0.571327	−	0.820723i	$-0.306429\pi$
$79$	10.1561	1.14265	0.571327	+	0.820723i	$0.306429\pi$
$80$	1.71186	0.191392
$81$	−1.16810	−0.129789
$82$	4.66151	0.514777
$83$	9.77815	1.07329	0.536646	−	0.843808i	$-0.319691\pi$
$83$	9.77815	1.07329	0.536646	+	0.843808i	$0.319691\pi$
$84$	−4.28820	−0.467881
$85$	8.42630	0.913961
$86$	4.76881	0.514235
$87$	−0.190095	−0.0203803
$88$	−6.17862	−0.658643
$89$	16.7617	1.77674	0.888371	−	0.459127i	$-0.151838\pi$
$89$	16.7617	1.77674	0.888371	+	0.459127i	$0.151838\pi$
$90$	−2.86771	−0.302283
$91$	9.04313	0.947978
$92$	−0.461292	−0.0480930
$93$	−0.0852929	−0.00884446
$94$	12.1145	1.24951
$95$	−7.42394	−0.761680
$96$	−1.15100	−0.117473
$97$	5.95560	0.604700	0.302350	−	0.953197i	$-0.402229\pi$
$97$	5.95560	0.604700	0.302350	+	0.953197i	$0.402229\pi$
$98$	6.88031	0.695016
$99$	10.3504	1.04026
$100$	−2.06954	−0.206954
$101$	−14.2332	−1.41625	−0.708126	−	0.706086i	$-0.750459\pi$
$101$	−14.2332	−1.41625	−0.708126	+	0.706086i	$0.750459\pi$
$102$	−5.66558	−0.560976
$103$	9.34764	0.921050	0.460525	−	0.887647i	$-0.347661\pi$
$103$	9.34764	0.921050	0.460525	+	0.887647i	$0.347661\pi$
$104$	2.42728	0.238014
$105$	−7.34079	−0.716388
$106$	−1.40562	−0.136526
$107$	4.66760	0.451234	0.225617	−	0.974216i	$-0.427560\pi$
$107$	4.66760	0.451234	0.225617	+	0.974216i	$0.427560\pi$
$108$	5.38115	0.517802
$109$	−0.539501	−0.0516748	−0.0258374	−	0.999666i	$-0.508225\pi$
$109$	−0.539501	−0.0516748	−0.0258374	+	0.999666i	$0.508225\pi$
$110$	−10.5769	−1.00847
$111$	−3.58670	−0.340434
$112$	3.72563	0.352039
$113$	−13.3027	−1.25141	−0.625706	−	0.780059i	$-0.715189\pi$
$113$	−13.3027	−1.25141	−0.625706	+	0.780059i	$0.715189\pi$
$114$	4.99162	0.467508
$115$	−0.789666	−0.0736368
$116$	0.165157	0.0153344
$117$	−4.06617	−0.375918
$118$	2.18717	0.201345
$119$	18.3387	1.68111
$120$	−1.97035	−0.179867
$121$	27.1754	2.47049
$122$	−13.4779	−1.22024
$123$	−5.36539	−0.483781
$124$	0.0741034	0.00665468
$125$	−12.1021	−1.08244
$126$	−6.24117	−0.556008
$127$	20.9872	1.86231	0.931157	−	0.364619i	$-0.118801\pi$
$127$	20.9872	1.86231	0.931157	+	0.364619i	$0.118801\pi$
$128$	1.00000	0.0883883
$129$	−5.48890	−0.483271
$130$	4.15516	0.364431
$131$	−0.746215	−0.0651971	−0.0325986	−	0.999469i	$-0.510378\pi$
$131$	−0.746215	−0.0651971	−0.0325986	+	0.999469i	$0.510378\pi$
$132$	7.11159	0.618984
$133$	−16.1572	−1.40101
$134$	8.85100	0.764610
$135$	9.21178	0.792824
$136$	4.92231	0.422085
$137$	−2.28338	−0.195082	−0.0975410	−	0.995232i	$-0.531098\pi$
$137$	−2.28338	−0.195082	−0.0975410	+	0.995232i	$0.531098\pi$
$138$	0.530946	0.0451971
$139$	10.1166	0.858081	0.429040	−	0.903285i	$-0.358852\pi$
$139$	10.1166	0.858081	0.429040	+	0.903285i	$0.358852\pi$
$140$	6.37775	0.539018
$141$	−13.9438	−1.17428
$142$	13.8710	1.16403
$143$	−14.9972	−1.25413
$144$	−1.67520	−0.139600
$145$	0.282725	0.0234790
$146$	0.166468	0.0137770
$147$	−7.91923	−0.653167
$148$	3.11616	0.256147
$149$	−11.0187	−0.902686	−0.451343	−	0.892351i	$-0.649055\pi$
$149$	−11.0187	−0.902686	−0.451343	+	0.892351i	$0.649055\pi$
$150$	2.38204	0.194492
$151$	0.884605	0.0719881	0.0359941	−	0.999352i	$-0.488540\pi$
$151$	0.884605	0.0719881	0.0359941	+	0.999352i	$0.488540\pi$
$152$	−4.33677	−0.351759
$153$	−8.24586	−0.666638
$154$	−23.0192	−1.85494
$155$	0.126855	0.0101892
$156$	−2.79379	−0.223682
$157$	−13.9723	−1.11511	−0.557557	−	0.830139i	$-0.688261\pi$
$157$	−13.9723	−1.11511	−0.557557	+	0.830139i	$0.688261\pi$
$158$	10.1561	0.807978
$159$	1.61787	0.128306
$160$	1.71186	0.135334
$161$	−1.71860	−0.135445
$162$	−1.16810	−0.0917747
$163$	−9.98149	−0.781810	−0.390905	−	0.920431i	$-0.627838\pi$
$163$	−9.98149	−0.781810	−0.390905	+	0.920431i	$0.627838\pi$
$164$	4.66151	0.364002
$165$	12.1740	0.947748
$166$	9.77815	0.758932
$167$	−20.3660	−1.57597	−0.787984	−	0.615695i	$-0.788875\pi$
$167$	−20.3660	−1.57597	−0.787984	+	0.615695i	$0.788875\pi$
$168$	−4.28820	−0.330841
$169$	−7.10833	−0.546795
$170$	8.42630	0.646268
$171$	7.26496	0.555565
$172$	4.76881	0.363619
$173$	6.24076	0.474476	0.237238	−	0.971452i	$-0.423758\pi$
$173$	6.24076	0.474476	0.237238	+	0.971452i	$0.423758\pi$
$174$	−0.190095	−0.0144111
$175$	−7.71033	−0.582846
$176$	−6.17862	−0.465731
$177$	−2.51743	−0.189221
$178$	16.7617	1.25635
$179$	1.03017	0.0769982	0.0384991	−	0.999259i	$-0.487742\pi$
$179$	1.03017	0.0769982	0.0384991	+	0.999259i	$0.487742\pi$
$180$	−2.86771	−0.213746
$181$	−17.4380	−1.29616	−0.648078	−	0.761574i	$-0.724427\pi$
$181$	−17.4380	−1.29616	−0.648078	+	0.761574i	$0.724427\pi$
$182$	9.04313	0.670321
$183$	15.5131	1.14676
$184$	−0.461292	−0.0340069
$185$	5.33443	0.392195
$186$	−0.0852929	−0.00625398
$187$	−30.4131	−2.22403
$188$	12.1145	0.883540
$189$	20.0482	1.45829
$190$	−7.42394	−0.538589
$191$	−10.1494	−0.734386	−0.367193	−	0.930145i	$-0.619681\pi$
$191$	−10.1494	−0.734386	−0.367193	+	0.930145i	$0.619681\pi$
$192$	−1.15100	−0.0830662
$193$	−11.4682	−0.825499	−0.412750	−	0.910845i	$-0.635432\pi$
$193$	−11.4682	−0.825499	−0.412750	+	0.910845i	$0.635432\pi$
$194$	5.95560	0.427587
$195$	−4.78258	−0.342488
$196$	6.88031	0.491450
$197$	0.485388	0.0345825	0.0172912	−	0.999850i	$-0.494496\pi$
$197$	0.485388	0.0345825	0.0172912	+	0.999850i	$0.494496\pi$
$198$	10.3504	0.735573
$199$	−11.5753	−0.820550	−0.410275	−	0.911962i	$-0.634567\pi$
$199$	−11.5753	−0.820550	−0.410275	+	0.911962i	$0.634567\pi$
$200$	−2.06954	−0.146338
$201$	−10.1875	−0.718571
$202$	−14.2332	−1.00144
$203$	0.615312	0.0431864
$204$	−5.66558	−0.396670
$205$	7.97984	0.557336
$206$	9.34764	0.651281
$207$	0.772756	0.0537102
$208$	2.42728	0.168301
$209$	26.7953	1.85347
$210$	−7.34079	−0.506563
$211$	3.01285	0.207413	0.103707	−	0.994608i	$-0.466930\pi$
$211$	3.01285	0.207413	0.103707	+	0.994608i	$0.466930\pi$
$212$	−1.40562	−0.0965386
$213$	−15.9655	−1.09394
$214$	4.66760	0.319070
$215$	8.16354	0.556749
$216$	5.38115	0.366141
$217$	0.276082	0.0187416
$218$	−0.539501	−0.0365396
$219$	−0.191605	−0.0129475
$220$	−10.5769	−0.713097
$221$	11.9478	0.803696
$222$	−3.58670	−0.240723
$223$	−4.55180	−0.304811	−0.152405	−	0.988318i	$-0.548702\pi$
$223$	−4.55180	−0.304811	−0.152405	+	0.988318i	$0.548702\pi$
$224$	3.72563	0.248929
$225$	3.46689	0.231126
$226$	−13.3027	−0.884882
$227$	13.1790	0.874722	0.437361	−	0.899286i	$-0.355913\pi$
$227$	13.1790	0.874722	0.437361	+	0.899286i	$0.355913\pi$
$228$	4.99162	0.330578
$229$	−3.37501	−0.223027	−0.111514	−	0.993763i	$-0.535570\pi$
$229$	−3.37501	−0.223027	−0.111514	+	0.993763i	$0.535570\pi$
$230$	−0.789666	−0.0520691
$231$	26.4951	1.74325
$232$	0.165157	0.0108431
$233$	25.4279	1.66583	0.832917	−	0.553398i	$-0.186669\pi$
$233$	25.4279	1.66583	0.832917	+	0.553398i	$0.186669\pi$
$234$	−4.06617	−0.265814
$235$	20.7383	1.35282
$236$	2.18717	0.142372
$237$	−11.6897	−0.759328
$238$	18.3387	1.18872
$239$	0.350098	0.0226460	0.0113230	−	0.999936i	$-0.496396\pi$
$239$	0.350098	0.0226460	0.0113230	+	0.999936i	$0.496396\pi$
$240$	−1.97035	−0.127185
$241$	4.16379	0.268213	0.134107	−	0.990967i	$-0.457184\pi$
$241$	4.16379	0.268213	0.134107	+	0.990967i	$0.457184\pi$
$242$	27.1754	1.74690
$243$	−14.7990	−0.949355
$244$	−13.4779	−0.862837
$245$	11.7781	0.752476
$246$	−5.36539	−0.342085
$247$	−10.5265	−0.669788
$248$	0.0741034	0.00470557
$249$	−11.2546	−0.713234
$250$	−12.1021	−0.765401
$251$	4.73591	0.298928	0.149464	−	0.988767i	$-0.452245\pi$
$251$	4.73591	0.298928	0.149464	+	0.988767i	$0.452245\pi$
$252$	−6.24117	−0.393157
$253$	2.85015	0.179187
$254$	20.9872	1.31685
$255$	−9.69867	−0.607354
$256$	1.00000	0.0625000
$257$	−3.09162	−0.192850	−0.0964249	−	0.995340i	$-0.530741\pi$
$257$	−3.09162	−0.192850	−0.0964249	+	0.995340i	$0.530741\pi$
$258$	−5.48890	−0.341724
$259$	11.6097	0.721389
$260$	4.15516	0.257692
$261$	−0.276670	−0.0171255
$262$	−0.746215	−0.0461013
$263$	−17.1976	−1.06045	−0.530223	−	0.847858i	$-0.677892\pi$
$263$	−17.1976	−1.06045	−0.530223	+	0.847858i	$0.677892\pi$
$264$	7.11159	0.437688
$265$	−2.40623	−0.147814
$266$	−16.1572	−0.990661
$267$	−19.2928	−1.18070
$268$	8.85100	0.540661
$269$	16.6640	1.01602	0.508012	−	0.861350i	$-0.330381\pi$
$269$	16.6640	1.01602	0.508012	+	0.861350i	$0.330381\pi$
$270$	9.21178	0.560611
$271$	5.33061	0.323812	0.161906	−	0.986806i	$-0.448236\pi$
$271$	5.33061	0.323812	0.161906	+	0.986806i	$0.448236\pi$
$272$	4.92231	0.298459
$273$	−10.4086	−0.629959
$274$	−2.28338	−0.137944
$275$	12.7869	0.771078
$276$	0.530946	0.0319592
$277$	13.8007	0.829206	0.414603	−	0.910002i	$-0.363920\pi$
$277$	13.8007	0.829206	0.414603	+	0.910002i	$0.363920\pi$
$278$	10.1166	0.606755
$279$	−0.124138	−0.00743195
$280$	6.37775	0.381144
$281$	25.4000	1.51523	0.757617	−	0.652699i	$-0.226363\pi$
$281$	25.4000	1.51523	0.757617	+	0.652699i	$0.226363\pi$
$282$	−13.9438	−0.830339
$283$	−1.25038	−0.0743272	−0.0371636	−	0.999309i	$-0.511832\pi$
$283$	−1.25038	−0.0743272	−0.0371636	+	0.999309i	$0.511832\pi$
$284$	13.8710	0.823094
$285$	8.54495	0.506159
$286$	−14.9972	−0.886804
$287$	17.3670	1.02514
$288$	−1.67520	−0.0987121
$289$	7.22914	0.425243
$290$	0.282725	0.0166022
$291$	−6.85489	−0.401841
$292$	0.166468	0.00974182
$293$	−15.2137	−0.888794	−0.444397	−	0.895830i	$-0.646582\pi$
$293$	−15.2137	−0.888794	−0.444397	+	0.895830i	$0.646582\pi$
$294$	−7.91923	−0.461859
$295$	3.74412	0.217991
$296$	3.11616	0.181123
$297$	−33.2481	−1.92925
$298$	−11.0187	−0.638295
$299$	−1.11968	−0.0647529
$300$	2.38204	0.137527
$301$	17.7668	1.02406
$302$	0.884605	0.0509033
$303$	16.3823	0.941141
$304$	−4.33677	−0.248731
$305$	−23.0723	−1.32112
$306$	−8.24586	−0.471384
$307$	25.0011	1.42689	0.713445	−	0.700711i	$-0.247134\pi$
$307$	25.0011	1.42689	0.713445	+	0.700711i	$0.247134\pi$
$308$	−23.0192	−1.31164
$309$	−10.7591	−0.612065
$310$	0.126855	0.00720485
$311$	15.7069	0.890656	0.445328	−	0.895368i	$-0.353087\pi$
$311$	15.7069	0.890656	0.445328	+	0.895368i	$0.353087\pi$
$312$	−2.79379	−0.158167
$313$	−15.4706	−0.874450	−0.437225	−	0.899352i	$-0.644039\pi$
$313$	−15.4706	−0.874450	−0.437225	+	0.899352i	$0.644039\pi$
$314$	−13.9723	−0.788505
$315$	−10.6840	−0.601976
$316$	10.1561	0.571327
$317$	25.0538	1.40716	0.703580	−	0.710616i	$-0.251584\pi$
$317$	25.0538	1.40716	0.703580	+	0.710616i	$0.251584\pi$
$318$	1.61787	0.0907257
$319$	−1.02044	−0.0571337
$320$	1.71186	0.0956958
$321$	−5.37240	−0.299858
$322$	−1.71860	−0.0957739
$323$	−21.3469	−1.18778
$324$	−1.16810	−0.0648945
$325$	−5.02334	−0.278645
$326$	−9.98149	−0.552823
$327$	0.620965	0.0343395
$328$	4.66151	0.257389
$329$	45.1341	2.48832
$330$	12.1740	0.670159
$331$	33.1505	1.82212	0.911058	−	0.412279i	$-0.135267\pi$
$331$	33.1505	1.82212	0.911058	+	0.412279i	$0.135267\pi$
$332$	9.77815	0.536646
$333$	−5.22019	−0.286065
$334$	−20.3660	−1.11438
$335$	15.1517	0.827824
$336$	−4.28820	−0.233940
$337$	−9.94696	−0.541846	−0.270923	−	0.962601i	$-0.587329\pi$
$337$	−9.94696	−0.541846	−0.270923	+	0.962601i	$0.587329\pi$
$338$	−7.10833	−0.386642
$339$	15.3114	0.831600
$340$	8.42630	0.456980
$341$	−0.457857	−0.0247943
$342$	7.26496	0.392844
$343$	−0.445934	−0.0240782
$344$	4.76881	0.257117
$345$	0.908905	0.0489338
$346$	6.24076	0.335505
$347$	−25.0820	−1.34647	−0.673236	−	0.739428i	$-0.735096\pi$
$347$	−25.0820	−1.34647	−0.673236	+	0.739428i	$0.735096\pi$
$348$	−0.190095	−0.0101902
$349$	−5.28966	−0.283149	−0.141574	−	0.989928i	$-0.545216\pi$
$349$	−5.28966	−0.283149	−0.141574	+	0.989928i	$0.545216\pi$
$350$	−7.71033	−0.412134
$351$	13.0615	0.697174
$352$	−6.17862	−0.329322
$353$	14.7988	0.787663	0.393831	−	0.919183i	$-0.371149\pi$
$353$	14.7988	0.787663	0.393831	+	0.919183i	$0.371149\pi$
$354$	−2.51743	−0.133800
$355$	23.7453	1.26027
$356$	16.7617	0.888371
$357$	−21.1078	−1.11714
$358$	1.03017	0.0544459
$359$	11.4980	0.606842	0.303421	−	0.952857i	$-0.401871\pi$
$359$	11.4980	0.606842	0.303421	+	0.952857i	$0.401871\pi$
$360$	−2.86771	−0.151141
$361$	−0.192417	−0.0101272
$362$	−17.4380	−0.916520
$363$	−31.2788	−1.64171
$364$	9.04313	0.473989
$365$	0.284970	0.0149160
$366$	15.5131	0.810883
$367$	−17.6994	−0.923901	−0.461950	−	0.886906i	$-0.652850\pi$
$367$	−17.6994	−0.923901	−0.461950	+	0.886906i	$0.652850\pi$
$368$	−0.461292	−0.0240465
$369$	−7.80896	−0.406518
$370$	5.33443	0.277324
$371$	−5.23683	−0.271883
$372$	−0.0852929	−0.00442223
$373$	−2.49714	−0.129297	−0.0646486	−	0.997908i	$-0.520593\pi$
$373$	−2.49714	−0.129297	−0.0646486	+	0.997908i	$0.520593\pi$
$374$	−30.4131	−1.57262
$375$	13.9295	0.719314
$376$	12.1145	0.624757
$377$	0.400881	0.0206464
$378$	20.0482	1.03117
$379$	10.0944	0.518514	0.259257	−	0.965808i	$-0.416522\pi$
$379$	10.0944	0.518514	0.259257	+	0.965808i	$0.416522\pi$
$380$	−7.42394	−0.380840
$381$	−24.1563	−1.23756
$382$	−10.1494	−0.519289
$383$	23.7508	1.21361	0.606804	−	0.794852i	$-0.292451\pi$
$383$	23.7508	1.21361	0.606804	+	0.794852i	$0.292451\pi$
$384$	−1.15100	−0.0587367
$385$	−39.4057	−2.00830
$386$	−11.4682	−0.583716
$387$	−7.98872	−0.406090
$388$	5.95560	0.302350
$389$	−20.0980	−1.01901	−0.509505	−	0.860468i	$-0.670171\pi$
$389$	−20.0980	−1.01901	−0.509505	+	0.860468i	$0.670171\pi$
$390$	−4.78258	−0.242175
$391$	−2.27062	−0.114830
$392$	6.88031	0.347508
$393$	0.858893	0.0433254
$394$	0.485388	0.0244535
$395$	17.3859	0.874778
$396$	10.3504	0.520129
$397$	13.9134	0.698293	0.349147	−	0.937068i	$-0.386472\pi$
$397$	13.9134	0.698293	0.349147	+	0.937068i	$0.386472\pi$
$398$	−11.5753	−0.580216
$399$	18.5969	0.931011
$400$	−2.06954	−0.103477
$401$	3.96105	0.197805	0.0989027	−	0.995097i	$-0.468467\pi$
$401$	3.96105	0.197805	0.0989027	+	0.995097i	$0.468467\pi$
$402$	−10.1875	−0.508106
$403$	0.179869	0.00895993
$404$	−14.2332	−0.708126
$405$	−1.99963	−0.0993622
$406$	0.615312	0.0305374
$407$	−19.2536	−0.954365
$408$	−5.66558	−0.280488
$409$	−4.42632	−0.218867	−0.109434	−	0.993994i	$-0.534904\pi$
$409$	−4.42632	−0.218867	−0.109434	+	0.993994i	$0.534904\pi$
$410$	7.97984	0.394096
$411$	2.62816	0.129638
$412$	9.34764	0.460525
$413$	8.14856	0.400965
$414$	0.772756	0.0379789
$415$	16.7388	0.821677
$416$	2.42728	0.119007
$417$	−11.6442	−0.570220
$418$	26.7953	1.31060
$419$	−4.57690	−0.223596	−0.111798	−	0.993731i	$-0.535661\pi$
$419$	−4.57690	−0.223596	−0.111798	+	0.993731i	$0.535661\pi$
$420$	−7.34079	−0.358194
$421$	33.8521	1.64985	0.824925	−	0.565242i	$-0.191217\pi$
$421$	33.8521	1.64985	0.824925	+	0.565242i	$0.191217\pi$
$422$	3.01285	0.146663
$423$	−20.2942	−0.986738
$424$	−1.40562	−0.0682631
$425$	−10.1869	−0.494138
$426$	−15.9655	−0.773533
$427$	−50.2138	−2.43002
$428$	4.66760	0.225617
$429$	17.2618	0.833407
$430$	8.16354	0.393681
$431$	−29.2158	−1.40727	−0.703637	−	0.710560i	$-0.748442\pi$
$431$	−29.2158	−1.40727	−0.703637	+	0.710560i	$0.748442\pi$
$432$	5.38115	0.258901
$433$	−38.2051	−1.83602	−0.918009	−	0.396559i	$-0.870204\pi$
$433$	−38.2051	−1.83602	−0.918009	+	0.396559i	$0.870204\pi$
$434$	0.276082	0.0132523
$435$	−0.325416	−0.0156025
$436$	−0.539501	−0.0258374
$437$	2.00052	0.0956976
$438$	−0.191605	−0.00915524
$439$	−40.6329	−1.93930	−0.969650	−	0.244497i	$-0.921377\pi$
$439$	−40.6329	−1.93930	−0.969650	+	0.244497i	$0.921377\pi$
$440$	−10.5769	−0.504235
$441$	−11.5259	−0.548852
$442$	11.9478	0.568299
$443$	−28.1709	−1.33844	−0.669221	−	0.743064i	$-0.733372\pi$
$443$	−28.1709	−1.33844	−0.669221	+	0.743064i	$0.733372\pi$
$444$	−3.58670	−0.170217
$445$	28.6937	1.36021
$446$	−4.55180	−0.215534
$447$	12.6825	0.599862
$448$	3.72563	0.176019
$449$	30.8772	1.45718	0.728592	−	0.684948i	$-0.240175\pi$
$449$	30.8772	1.45718	0.728592	+	0.684948i	$0.240175\pi$
$450$	3.46689	0.163431
$451$	−28.8017	−1.35622
$452$	−13.3027	−0.625706
$453$	−1.01818	−0.0478383
$454$	13.1790	0.618522
$455$	15.4806	0.725740
$456$	4.99162	0.233754
$457$	5.76202	0.269536	0.134768	−	0.990877i	$-0.456971\pi$
$457$	5.76202	0.269536	0.134768	+	0.990877i	$0.456971\pi$
$458$	−3.37501	−0.157704
$459$	26.4877	1.23634
$460$	−0.789666	−0.0368184
$461$	−38.4917	−1.79274	−0.896369	−	0.443308i	$-0.853805\pi$
$461$	−38.4917	−1.79274	−0.896369	+	0.443308i	$0.853805\pi$
$462$	26.4951	1.23267
$463$	0.899932	0.0418234	0.0209117	−	0.999781i	$-0.493343\pi$
$463$	0.899932	0.0418234	0.0209117	+	0.999781i	$0.493343\pi$
$464$	0.165157	0.00766720
$465$	−0.146009	−0.00677103
$466$	25.4279	1.17792
$467$	29.4544	1.36299	0.681494	−	0.731824i	$-0.261331\pi$
$467$	29.4544	1.36299	0.681494	+	0.731824i	$0.261331\pi$
$468$	−4.06617	−0.187959
$469$	32.9756	1.52267
$470$	20.7383	0.956587
$471$	16.0822	0.741027
$472$	2.18717	0.100672
$473$	−29.4647	−1.35479
$474$	−11.6897	−0.536926
$475$	8.97511	0.411806
$476$	18.3387	0.840553
$477$	2.35470	0.107814
$478$	0.350098	0.0160131
$479$	39.7116	1.81447	0.907235	−	0.420624i	$-0.138189\pi$
$479$	39.7116	1.81447	0.907235	+	0.420624i	$0.138189\pi$
$480$	−1.97035	−0.0899337
$481$	7.56378	0.344879
$482$	4.16379	0.189655
$483$	1.97811	0.0900071
$484$	27.1754	1.23524
$485$	10.1952	0.462938
$486$	−14.7990	−0.671295
$487$	−11.5056	−0.521366	−0.260683	−	0.965424i	$-0.583948\pi$
$487$	−11.5056	−0.521366	−0.260683	+	0.965424i	$0.583948\pi$
$488$	−13.4779	−0.610118
$489$	11.4887	0.519536
$490$	11.7781	0.532081
$491$	23.4248	1.05715	0.528573	−	0.848888i	$-0.322727\pi$
$491$	23.4248	1.05715	0.528573	+	0.848888i	$0.322727\pi$
$492$	−5.36539	−0.241890
$493$	0.812952	0.0366135
$494$	−10.5265	−0.473611
$495$	17.7185	0.796386
$496$	0.0741034	0.00332734
$497$	51.6783	2.31809
$498$	−11.2546	−0.504333
$499$	23.3698	1.04617	0.523087	−	0.852279i	$-0.324780\pi$
$499$	23.3698	1.04617	0.523087	+	0.852279i	$0.324780\pi$
$500$	−12.1021	−0.541220
$501$	23.4413	1.04728
$502$	4.73591	0.211374
$503$	3.50033	0.156072	0.0780360	−	0.996951i	$-0.475135\pi$
$503$	3.50033	0.156072	0.0780360	+	0.996951i	$0.475135\pi$
$504$	−6.24117	−0.278004
$505$	−24.3652	−1.08424
$506$	2.85015	0.126704
$507$	8.18168	0.363361
$508$	20.9872	0.931157
$509$	12.5088	0.554445	0.277222	−	0.960806i	$-0.410586\pi$
$509$	12.5088	0.554445	0.277222	+	0.960806i	$0.410586\pi$
$510$	−9.69867	−0.429464
$511$	0.620199	0.0274360
$512$	1.00000	0.0441942
$513$	−23.3368	−1.03035
$514$	−3.09162	−0.136365
$515$	16.0018	0.705125
$516$	−5.48890	−0.241635
$517$	−74.8509	−3.29194
$518$	11.6097	0.510099
$519$	−7.18311	−0.315303
$520$	4.15516	0.182216
$521$	−15.6799	−0.686949	−0.343475	−	0.939162i	$-0.611604\pi$
$521$	−15.6799	−0.686949	−0.343475	+	0.939162i	$0.611604\pi$
$522$	−0.276670	−0.0121095
$523$	−3.79481	−0.165936	−0.0829678	−	0.996552i	$-0.526440\pi$
$523$	−3.79481	−0.165936	−0.0829678	+	0.996552i	$0.526440\pi$
$524$	−0.746215	−0.0325986
$525$	8.87458	0.387319
$526$	−17.1976	−0.749849
$527$	0.364760	0.0158892
$528$	7.11159	0.309492
$529$	−22.7872	−0.990748
$530$	−2.40623	−0.104520
$531$	−3.66394	−0.159001
$532$	−16.1572	−0.700503
$533$	11.3148	0.490097
$534$	−19.2928	−0.834879
$535$	7.99027	0.345450
$536$	8.85100	0.382305
$537$	−1.18572	−0.0511676
$538$	16.6640	0.718438
$539$	−42.5108	−1.83107
$540$	9.21178	0.396412
$541$	−31.5420	−1.35610	−0.678049	−	0.735017i	$-0.737174\pi$
$541$	−31.5420	−1.35610	−0.678049	+	0.735017i	$0.737174\pi$
$542$	5.33061	0.228969
$543$	20.0711	0.861334
$544$	4.92231	0.211042
$545$	−0.923550	−0.0395605
$546$	−10.4086	−0.445449
$547$	−36.4859	−1.56003	−0.780013	−	0.625763i	$-0.784788\pi$
$547$	−36.4859	−1.56003	−0.780013	+	0.625763i	$0.784788\pi$
$548$	−2.28338	−0.0975410
$549$	22.5783	0.963617
$550$	12.7869	0.545235
$551$	−0.716246	−0.0305131
$552$	0.530946	0.0225986
$553$	37.8380	1.60903
$554$	13.8007	0.586337
$555$	−6.13992	−0.260625
$556$	10.1166	0.429040
$557$	18.5736	0.786989	0.393494	−	0.919327i	$-0.371266\pi$
$557$	18.5736	0.786989	0.393494	+	0.919327i	$0.371266\pi$
$558$	−0.124138	−0.00525518
$559$	11.5752	0.489580
$560$	6.37775	0.269509
$561$	35.0055	1.47793
$562$	25.4000	1.07143
$563$	−34.0709	−1.43592	−0.717959	−	0.696085i	$-0.754924\pi$
$563$	−34.0709	−1.43592	−0.717959	+	0.696085i	$0.754924\pi$
$564$	−13.9438	−0.587139
$565$	−22.7723	−0.958039
$566$	−1.25038	−0.0525573
$567$	−4.35191	−0.182763
$568$	13.8710	0.582016
$569$	12.3556	0.517974	0.258987	−	0.965881i	$-0.416611\pi$
$569$	12.3556	0.517974	0.258987	+	0.965881i	$0.416611\pi$
$570$	8.54495	0.357909
$571$	−1.12353	−0.0470185	−0.0235092	−	0.999724i	$-0.507484\pi$
$571$	−1.12353	−0.0470185	−0.0235092	+	0.999724i	$0.507484\pi$
$572$	−14.9972	−0.627065
$573$	11.6820	0.488021
$574$	17.3670	0.724886
$575$	0.954660	0.0398121
$576$	−1.67520	−0.0698000
$577$	0.169714	0.00706530	0.00353265	−	0.999994i	$-0.498876\pi$
$577$	0.169714	0.00706530	0.00353265	+	0.999994i	$0.498876\pi$
$578$	7.22914	0.300693
$579$	13.1999	0.548569
$580$	0.282725	0.0117395
$581$	36.4298	1.51136
$582$	−6.85489	−0.284144
$583$	8.68482	0.359688
$584$	0.166468	0.00688851
$585$	−6.96072	−0.287790
$586$	−15.2137	−0.628473
$587$	25.2335	1.04150	0.520749	−	0.853710i	$-0.325653\pi$
$587$	25.2335	1.04150	0.520749	+	0.853710i	$0.325653\pi$
$588$	−7.91923	−0.326583
$589$	−0.321369	−0.0132418
$590$	3.74412	0.154143
$591$	−0.558681	−0.0229811
$592$	3.11616	0.128073
$593$	−16.3111	−0.669819	−0.334909	−	0.942250i	$-0.608706\pi$
$593$	−16.3111	−0.669819	−0.334909	+	0.942250i	$0.608706\pi$
$594$	−33.2481	−1.36419
$595$	31.3933	1.28700
$596$	−11.0187	−0.451343
$597$	13.3231	0.545280
$598$	−1.11968	−0.0457872
$599$	44.2462	1.80785	0.903925	−	0.427691i	$-0.140673\pi$
$599$	44.2462	1.80785	0.903925	+	0.427691i	$0.140673\pi$
$600$	2.38204	0.0972462
$601$	−19.8520	−0.809779	−0.404889	−	0.914366i	$-0.632690\pi$
$601$	−19.8520	−0.809779	−0.404889	+	0.914366i	$0.632690\pi$
$602$	17.7668	0.724122
$603$	−14.8272	−0.603811
$604$	0.884605	0.0359941
$605$	46.5204	1.89132
$606$	16.3823	0.665487
$607$	41.3443	1.67811	0.839057	−	0.544044i	$-0.183108\pi$
$607$	41.3443	1.67811	0.839057	+	0.544044i	$0.183108\pi$
$608$	−4.33677	−0.175879
$609$	−0.708224	−0.0286987
$610$	−23.0723	−0.934172
$611$	29.4052	1.18961
$612$	−8.24586	−0.333319
$613$	35.1706	1.42053	0.710263	−	0.703937i	$-0.248576\pi$
$613$	35.1706	1.42053	0.710263	+	0.703937i	$0.248576\pi$
$614$	25.0011	1.00896
$615$	−9.18479	−0.370367
$616$	−23.0192	−0.927472
$617$	−18.5409	−0.746429	−0.373215	−	0.927745i	$-0.621744\pi$
$617$	−18.5409	−0.746429	−0.373215	+	0.927745i	$0.621744\pi$
$618$	−10.7591	−0.432795
$619$	−29.6242	−1.19070	−0.595349	−	0.803467i	$-0.702986\pi$
$619$	−29.6242	−1.19070	−0.595349	+	0.803467i	$0.702986\pi$
$620$	0.126855	0.00509460
$621$	−2.48228	−0.0996105
$622$	15.7069	0.629789
$623$	62.4480	2.50193
$624$	−2.79379	−0.111841
$625$	−10.3693	−0.414773
$626$	−15.4706	−0.618330
$627$	−30.8413	−1.23168
$628$	−13.9723	−0.557557
$629$	15.3387	0.611594
$630$	−10.6840	−0.425661
$631$	−22.6606	−0.902105	−0.451052	−	0.892497i	$-0.648951\pi$
$631$	−22.6606	−0.902105	−0.451052	+	0.892497i	$0.648951\pi$
$632$	10.1561	0.403989
$633$	−3.46779	−0.137832
$634$	25.0538	0.995012
$635$	35.9271	1.42573
$636$	1.61787	0.0641528
$637$	16.7004	0.661694
$638$	−1.02044	−0.0403996
$639$	−23.2368	−0.919232
$640$	1.71186	0.0676672
$641$	45.0842	1.78072	0.890360	−	0.455258i	$-0.150453\pi$
$641$	45.0842	1.78072	0.890360	+	0.455258i	$0.150453\pi$
$642$	−5.37240	−0.212032
$643$	−37.2929	−1.47069	−0.735344	−	0.677695i	$-0.762979\pi$
$643$	−37.2929	−1.47069	−0.735344	+	0.677695i	$0.762979\pi$
$644$	−1.71860	−0.0677224
$645$	−9.39623	−0.369976
$646$	−21.3469	−0.839884
$647$	−31.4921	−1.23808	−0.619042	−	0.785358i	$-0.712479\pi$
$647$	−31.4921	−1.23808	−0.619042	+	0.785358i	$0.712479\pi$
$648$	−1.16810	−0.0458874
$649$	−13.5137	−0.530458
$650$	−5.02334	−0.197032
$651$	−0.317770	−0.0124544
$652$	−9.98149	−0.390905
$653$	−28.9582	−1.13322	−0.566611	−	0.823985i	$-0.691746\pi$
$653$	−28.9582	−1.13322	−0.566611	+	0.823985i	$0.691746\pi$
$654$	0.620965	0.0242817
$655$	−1.27742	−0.0499128
$656$	4.66151	0.182001
$657$	−0.278868	−0.0108797
$658$	45.1341	1.75951
$659$	24.6643	0.960786	0.480393	−	0.877053i	$-0.340494\pi$
$659$	24.6643	0.960786	0.480393	+	0.877053i	$0.340494\pi$
$660$	12.1740	0.473874
$661$	−11.1115	−0.432187	−0.216093	−	0.976373i	$-0.569332\pi$
$661$	−11.1115	−0.432187	−0.216093	+	0.976373i	$0.569332\pi$
$662$	33.1505	1.28843
$663$	−13.7519	−0.534080
$664$	9.77815	0.379466
$665$	−27.6588	−1.07256
$666$	−5.22019	−0.202278
$667$	−0.0761853	−0.00294991
$668$	−20.3660	−0.787984
$669$	5.23912	0.202556
$670$	15.1517	0.585360
$671$	83.2751	3.21480
$672$	−4.28820	−0.165421
$673$	43.4749	1.67583	0.837917	−	0.545798i	$-0.183773\pi$
$673$	43.4749	1.67583	0.837917	+	0.545798i	$0.183773\pi$
$674$	−9.94696	−0.383143
$675$	−11.1365	−0.428644
$676$	−7.10833	−0.273397
$677$	−33.0810	−1.27141	−0.635703	−	0.771934i	$-0.719290\pi$
$677$	−33.0810	−1.27141	−0.635703	+	0.771934i	$0.719290\pi$
$678$	15.3114	0.588030
$679$	22.1884	0.851511
$680$	8.42630	0.323134
$681$	−15.1690	−0.581279
$682$	−0.457857	−0.0175322
$683$	9.73368	0.372449	0.186224	−	0.982507i	$-0.440375\pi$
$683$	9.73368	0.372449	0.186224	+	0.982507i	$0.440375\pi$
$684$	7.26496	0.277783
$685$	−3.90882	−0.149348
$686$	−0.445934	−0.0170258
$687$	3.88464	0.148208
$688$	4.76881	0.181809
$689$	−3.41184	−0.129981
$690$	0.908905	0.0346014
$691$	−25.3263	−0.963458	−0.481729	−	0.876320i	$-0.659991\pi$
$691$	−25.3263	−0.963458	−0.481729	+	0.876320i	$0.659991\pi$
$692$	6.24076	0.237238
$693$	38.5619	1.46484
$694$	−25.0820	−0.952099
$695$	17.3182	0.656918
$696$	−0.190095	−0.00720554
$697$	22.9454	0.869118
$698$	−5.28966	−0.200216
$699$	−29.2674	−1.10700
$700$	−7.71033	−0.291423
$701$	−44.3237	−1.67408	−0.837041	−	0.547140i	$-0.815716\pi$
$701$	−44.3237	−1.67408	−0.837041	+	0.547140i	$0.815716\pi$
$702$	13.0615	0.492976
$703$	−13.5141	−0.509693
$704$	−6.17862	−0.232866
$705$	−23.8698	−0.898988
$706$	14.7988	0.556962
$707$	−53.0274	−1.99430
$708$	−2.51743	−0.0946106
$709$	−26.6974	−1.00264	−0.501320	−	0.865262i	$-0.667152\pi$
$709$	−26.6974	−1.00264	−0.501320	+	0.865262i	$0.667152\pi$
$710$	23.7453	0.891143
$711$	−17.0136	−0.638058
$712$	16.7617	0.628173
$713$	−0.0341832	−0.00128017
$714$	−21.1078	−0.789941
$715$	−25.6731	−0.960121
$716$	1.03017	0.0384991
$717$	−0.402963	−0.0150489
$718$	11.4980	0.429102
$719$	−32.3273	−1.20561	−0.602803	−	0.797890i	$-0.705949\pi$
$719$	−32.3273	−1.20561	−0.602803	+	0.797890i	$0.705949\pi$
$720$	−2.86771	−0.106873
$721$	34.8258	1.29698
$722$	−0.192417	−0.00716104
$723$	−4.79252	−0.178236
$724$	−17.4380	−0.648078
$725$	−0.341798	−0.0126940
$726$	−31.2788	−1.16087
$727$	−17.0058	−0.630711	−0.315355	−	0.948974i	$-0.602124\pi$
$727$	−17.0058	−0.630711	−0.315355	+	0.948974i	$0.602124\pi$
$728$	9.04313	0.335161
$729$	20.5379	0.760664
$730$	0.284970	0.0105472
$731$	23.4736	0.868202
$732$	15.5131	0.573381
$733$	−9.23384	−0.341060	−0.170530	−	0.985353i	$-0.554548\pi$
$733$	−9.23384	−0.341060	−0.170530	+	0.985353i	$0.554548\pi$
$734$	−17.6994	−0.653296
$735$	−13.5566	−0.500043
$736$	−0.461292	−0.0170034
$737$	−54.6870	−2.01442
$738$	−7.80896	−0.287452
$739$	6.15967	0.226587	0.113294	−	0.993562i	$-0.463860\pi$
$739$	6.15967	0.226587	0.113294	+	0.993562i	$0.463860\pi$
$740$	5.33443	0.196098
$741$	12.1160	0.445094
$742$	−5.23683	−0.192250
$743$	10.7569	0.394632	0.197316	−	0.980340i	$-0.436778\pi$
$743$	10.7569	0.394632	0.197316	+	0.980340i	$0.436778\pi$
$744$	−0.0852929	−0.00312699
$745$	−18.8624	−0.691066
$746$	−2.49714	−0.0914269
$747$	−16.3804	−0.599326
$748$	−30.4131	−1.11201
$749$	17.3897	0.635407
$750$	13.9295	0.508632
$751$	−51.0431	−1.86259	−0.931294	−	0.364268i	$-0.881319\pi$
$751$	−51.0431	−1.86259	−0.931294	+	0.364268i	$0.881319\pi$
$752$	12.1145	0.441770
$753$	−5.45103	−0.198646
$754$	0.400881	0.0145992
$755$	1.51432	0.0551117
$756$	20.0482	0.729145
$757$	−13.8941	−0.504990	−0.252495	−	0.967598i	$-0.581251\pi$
$757$	−13.8941	−0.504990	−0.252495	+	0.967598i	$0.581251\pi$
$758$	10.0944	0.366645
$759$	−3.28052	−0.119075
$760$	−7.42394	−0.269295
$761$	−29.3075	−1.06240	−0.531198	−	0.847248i	$-0.678258\pi$
$761$	−29.3075	−1.06240	−0.531198	+	0.847248i	$0.678258\pi$
$762$	−24.1563	−0.875089
$763$	−2.00998	−0.0727662
$764$	−10.1494	−0.367193
$765$	−14.1157	−0.510356
$766$	23.7508	0.858150
$767$	5.30885	0.191692
$768$	−1.15100	−0.0415331
$769$	1.33308	0.0480722	0.0240361	−	0.999711i	$-0.492348\pi$
$769$	1.33308	0.0480722	0.0240361	+	0.999711i	$0.492348\pi$
$770$	−39.4057	−1.42008
$771$	3.55845	0.128154
$772$	−11.4682	−0.412750
$773$	13.0612	0.469778	0.234889	−	0.972022i	$-0.424527\pi$
$773$	13.0612	0.469778	0.234889	+	0.972022i	$0.424527\pi$
$774$	−7.98872	−0.287149
$775$	−0.153360	−0.00550884
$776$	5.95560	0.213794
$777$	−13.3627	−0.479384
$778$	−20.0980	−0.720548
$779$	−20.2159	−0.724309
$780$	−4.78258	−0.171244
$781$	−85.7039	−3.06672
$782$	−2.27062	−0.0811972
$783$	0.888733	0.0317607
$784$	6.88031	0.245725
$785$	−23.9187	−0.853695
$786$	0.858893	0.0306357
$787$	−45.9765	−1.63888	−0.819442	−	0.573162i	$-0.805717\pi$
$787$	−45.9765	−1.63888	−0.819442	+	0.573162i	$0.805717\pi$
$788$	0.485388	0.0172912
$789$	19.7944	0.704698
$790$	17.3859	0.618561
$791$	−49.5609	−1.76218
$792$	10.3504	0.367787
$793$	−32.7147	−1.16173
$794$	13.9134	0.493768
$795$	2.76957	0.0982265
$796$	−11.5753	−0.410275
$797$	13.9206	0.493094	0.246547	−	0.969131i	$-0.420704\pi$
$797$	13.9206	0.493094	0.246547	+	0.969131i	$0.420704\pi$
$798$	18.5969	0.658324
$799$	59.6313	2.10960
$800$	−2.06954	−0.0731692
$801$	−28.0793	−0.992133
$802$	3.96105	0.139870
$803$	−1.02854	−0.0362966
$804$	−10.1875	−0.359285
$805$	−2.94200	−0.103692
$806$	0.179869	0.00633563
$807$	−19.1803	−0.675178
$808$	−14.2332	−0.500721
$809$	−32.8523	−1.15502	−0.577512	−	0.816382i	$-0.695976\pi$
$809$	−32.8523	−1.15502	−0.577512	+	0.816382i	$0.695976\pi$
$810$	−1.99963	−0.0702597
$811$	−21.1333	−0.742089	−0.371045	−	0.928615i	$-0.621000\pi$
$811$	−21.1333	−0.742089	−0.371045	+	0.928615i	$0.621000\pi$
$812$	0.615312	0.0215932
$813$	−6.13553	−0.215182
$814$	−19.2536	−0.674838
$815$	−17.0869	−0.598528
$816$	−5.66558	−0.198335
$817$	−20.6813	−0.723546
$818$	−4.42632	−0.154763
$819$	−15.1491	−0.529351
$820$	7.97984	0.278668
$821$	−8.73097	−0.304713	−0.152356	−	0.988326i	$-0.548686\pi$
$821$	−8.73097	−0.304713	−0.152356	+	0.988326i	$0.548686\pi$
$822$	2.62816	0.0916678
$823$	−7.91719	−0.275976	−0.137988	−	0.990434i	$-0.544064\pi$
$823$	−7.91719	−0.275976	−0.137988	+	0.990434i	$0.544064\pi$
$824$	9.34764	0.325640
$825$	−14.7177	−0.512405
$826$	8.14856	0.283525
$827$	0.720329	0.0250483	0.0125242	−	0.999922i	$-0.496013\pi$
$827$	0.720329	0.0250483	0.0125242	+	0.999922i	$0.496013\pi$
$828$	0.772756	0.0268551
$829$	37.7284	1.31036	0.655181	−	0.755472i	$-0.272592\pi$
$829$	37.7284	1.31036	0.655181	+	0.755472i	$0.272592\pi$
$830$	16.7388	0.581013
$831$	−15.8846	−0.551032
$832$	2.42728	0.0841507
$833$	33.8670	1.17342
$834$	−11.6442	−0.403207
$835$	−34.8637	−1.20651
$836$	26.7953	0.926734
$837$	0.398761	0.0137832
$838$	−4.57690	−0.158106
$839$	34.9963	1.20821	0.604104	−	0.796906i	$-0.293531\pi$
$839$	34.9963	1.20821	0.604104	+	0.796906i	$0.293531\pi$
$840$	−7.34079	−0.253281
$841$	−28.9727	−0.999059
$842$	33.8521	1.16662
$843$	−29.2353	−1.00692
$844$	3.01285	0.103707
$845$	−12.1685	−0.418608
$846$	−20.2942	−0.697729
$847$	101.245	3.47883
$848$	−1.40562	−0.0482693
$849$	1.43918	0.0493926
$850$	−10.1869	−0.349408
$851$	−1.43746	−0.0492755
$852$	−15.9655	−0.546971
$853$	4.01796	0.137572	0.0687861	−	0.997631i	$-0.478087\pi$
$853$	4.01796	0.137572	0.0687861	+	0.997631i	$0.478087\pi$
$854$	−50.2138	−1.71828
$855$	12.4366	0.425322
$856$	4.66760	0.159535
$857$	−7.24275	−0.247408	−0.123704	−	0.992319i	$-0.539477\pi$
$857$	−7.24275	−0.247408	−0.123704	+	0.992319i	$0.539477\pi$
$858$	17.2618	0.589308
$859$	17.2959	0.590128	0.295064	−	0.955477i	$-0.404659\pi$
$859$	17.2959	0.590128	0.295064	+	0.955477i	$0.404659\pi$
$860$	8.16354	0.278374
$861$	−19.9894	−0.681239
$862$	−29.2158	−0.995093
$863$	−13.1084	−0.446213	−0.223107	−	0.974794i	$-0.571620\pi$
$863$	−13.1084	−0.446213	−0.223107	+	0.974794i	$0.571620\pi$
$864$	5.38115	0.183071
$865$	10.6833	0.363243
$866$	−38.2051	−1.29826
$867$	−8.32073	−0.282587
$868$	0.276082	0.00937082
$869$	−62.7509	−2.12868
$870$	−0.325416	−0.0110326
$871$	21.4838	0.727952
$872$	−0.539501	−0.0182698
$873$	−9.97683	−0.337664
$874$	2.00052	0.0676685
$875$	−45.0878	−1.52424
$876$	−0.191605	−0.00647373
$877$	24.1574	0.815738	0.407869	−	0.913040i	$-0.366272\pi$
$877$	24.1574	0.815738	0.407869	+	0.913040i	$0.366272\pi$
$878$	−40.6329	−1.37129
$879$	17.5110	0.590630
$880$	−10.5769	−0.356548
$881$	8.09648	0.272777	0.136389	−	0.990655i	$-0.456450\pi$
$881$	8.09648	0.272777	0.136389	+	0.990655i	$0.456450\pi$
$882$	−11.5259	−0.388097
$883$	2.77360	0.0933391	0.0466696	−	0.998910i	$-0.485139\pi$
$883$	2.77360	0.0933391	0.0466696	+	0.998910i	$0.485139\pi$
$884$	11.9478	0.401848
$885$	−4.30948	−0.144862
$886$	−28.1709	−0.946421
$887$	19.2160	0.645209	0.322604	−	0.946534i	$-0.395442\pi$
$887$	19.2160	0.645209	0.322604	+	0.946534i	$0.395442\pi$
$888$	−3.58670	−0.120362
$889$	78.1905	2.62243
$890$	28.6937	0.961817
$891$	7.21726	0.241787
$892$	−4.55180	−0.152405
$893$	−52.5378	−1.75811
$894$	12.6825	0.424166
$895$	1.76350	0.0589472
$896$	3.72563	0.124465
$897$	1.28875	0.0430302
$898$	30.8772	1.03038
$899$	0.0122387	0.000408182 0
$900$	3.46689	0.115563
$901$	−6.91892	−0.230502
$902$	−28.8017	−0.958991
$903$	−20.4496	−0.680520
$904$	−13.3027	−0.442441
$905$	−29.8514	−0.992294
$906$	−1.01818	−0.0338268
$907$	−34.2488	−1.13721	−0.568606	−	0.822610i	$-0.692517\pi$
$907$	−34.2488	−1.13721	−0.568606	+	0.822610i	$0.692517\pi$
$908$	13.1790	0.437361
$909$	23.8434	0.790835
$910$	15.4806	0.513176
$911$	27.0582	0.896477	0.448239	−	0.893914i	$-0.352051\pi$
$911$	27.0582	0.896477	0.448239	+	0.893914i	$0.352051\pi$
$912$	4.99162	0.165289
$913$	−60.4155	−1.99946
$914$	5.76202	0.190591
$915$	26.5563	0.877923
$916$	−3.37501	−0.111514
$917$	−2.78012	−0.0918077
$918$	26.4877	0.874224
$919$	−32.4629	−1.07085	−0.535426	−	0.844582i	$-0.679849\pi$
$919$	−32.4629	−1.07085	−0.535426	+	0.844582i	$0.679849\pi$
$920$	−0.789666	−0.0260345
$921$	−28.7763	−0.948211
$922$	−38.4917	−1.26766
$923$	33.6688	1.10822
$924$	26.4951	0.871626
$925$	−6.44901	−0.212042
$926$	0.899932	0.0295736
$927$	−15.6592	−0.514314
$928$	0.165157	0.00542153
$929$	35.3238	1.15893	0.579467	−	0.814995i	$-0.303261\pi$
$929$	35.3238	1.15893	0.579467	+	0.814995i	$0.303261\pi$
$930$	−0.146009	−0.00478784
$931$	−29.8383	−0.977911
$932$	25.4279	0.832917
$933$	−18.0786	−0.591867
$934$	29.4544	0.963778
$935$	−52.0629	−1.70264
$936$	−4.06617	−0.132907
$937$	7.27906	0.237796	0.118898	−	0.992906i	$-0.462064\pi$
$937$	7.27906	0.237796	0.118898	+	0.992906i	$0.462064\pi$
$938$	32.9756	1.07669
$939$	17.8067	0.581098
$940$	20.7383	0.676409
$941$	36.4243	1.18740	0.593699	−	0.804687i	$-0.297667\pi$
$941$	36.4243	1.18740	0.593699	+	0.804687i	$0.297667\pi$
$942$	16.0822	0.523985
$943$	−2.15031	−0.0700238
$944$	2.18717	0.0711862
$945$	34.3197	1.11642
$946$	−29.4647	−0.957980
$947$	11.2663	0.366105	0.183053	−	0.983103i	$-0.441402\pi$
$947$	11.2663	0.366105	0.183053	+	0.983103i	$0.441402\pi$
$948$	−11.6897	−0.379664
$949$	0.404065	0.0131165
$950$	8.97511	0.291191
$951$	−28.8369	−0.935099
$952$	18.3387	0.594361
$953$	20.5982	0.667240	0.333620	−	0.942708i	$-0.391730\pi$
$953$	20.5982	0.667240	0.333620	+	0.942708i	$0.391730\pi$
$954$	2.35470	0.0762363
$955$	−17.3744	−0.562222
$956$	0.350098	0.0113230
$957$	1.17453	0.0379670
$958$	39.7116	1.28302
$959$	−8.50701	−0.274706
$960$	−1.97035	−0.0635927
$961$	−30.9945	−0.999823
$962$	7.56378	0.243866
$963$	−7.81916	−0.251969
$964$	4.16379	0.134107
$965$	−19.6319	−0.631975
$966$	1.97811	0.0636446
$967$	−1.53130	−0.0492433	−0.0246217	−	0.999697i	$-0.507838\pi$
$967$	−1.53130	−0.0492433	−0.0246217	+	0.999697i	$0.507838\pi$
$968$	27.1754	0.873449
$969$	24.5703	0.789312
$970$	10.1952	0.327347
$971$	−31.4030	−1.00777	−0.503885	−	0.863771i	$-0.668097\pi$
$971$	−31.4030	−1.00777	−0.503885	+	0.863771i	$0.668097\pi$
$972$	−14.7990	−0.474677
$973$	37.6908	1.20831
$974$	−11.5056	−0.368662
$975$	5.78186	0.185168
$976$	−13.4779	−0.431419
$977$	10.8856	0.348261	0.174130	−	0.984723i	$-0.444289\pi$
$977$	10.8856	0.348261	0.174130	+	0.984723i	$0.444289\pi$
$978$	11.4887	0.367368
$979$	−103.564	−3.30993
$980$	11.7781	0.376238
$981$	0.903772	0.0288552
$982$	23.4248	0.747514
$983$	−11.3266	−0.361261	−0.180631	−	0.983551i	$-0.557814\pi$
$983$	−11.3266	−0.361261	−0.180631	+	0.983551i	$0.557814\pi$
$984$	−5.36539	−0.171042
$985$	0.830916	0.0264752
$986$	0.812952	0.0258897
$987$	−51.9493	−1.65356
$988$	−10.5265	−0.334894
$989$	−2.19981	−0.0699500
$990$	17.7185	0.563130
$991$	42.4461	1.34834	0.674172	−	0.738575i	$-0.264501\pi$
$991$	42.4461	1.34834	0.674172	+	0.738575i	$0.264501\pi$
$992$	0.0741034	0.00235278
$993$	−38.1562	−1.21085
$994$	51.6783	1.63914
$995$	−19.8152	−0.628185
$996$	−11.2546	−0.356617
$997$	38.3028	1.21306	0.606530	−	0.795060i	$-0.292561\pi$
$997$	38.3028	1.21306	0.606530	+	0.795060i	$0.292561\pi$
$998$	23.3698	0.739757
$999$	16.7685	0.530533

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.e.1.18	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.e.1.18	✓	68	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.15100 q^{3} +1.00000 q^{4} +1.71186 q^{5} -1.15100 q^{6} +3.72563 q^{7} +1.00000 q^{8} -1.67520 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.15100 q^{3} +1.00000 q^{4} +1.71186 q^{5} -1.15100 q^{6} +3.72563 q^{7} +1.00000 q^{8} -1.67520 q^{9} +1.71186 q^{10} -6.17862 q^{11} -1.15100 q^{12} +2.42728 q^{13} +3.72563 q^{14} -1.97035 q^{15} +1.00000 q^{16} +4.92231 q^{17} -1.67520 q^{18} -4.33677 q^{19} +1.71186 q^{20} -4.28820 q^{21} -6.17862 q^{22} -0.461292 q^{23} -1.15100 q^{24} -2.06954 q^{25} +2.42728 q^{26} +5.38115 q^{27} +3.72563 q^{28} +0.165157 q^{29} -1.97035 q^{30} +0.0741034 q^{31} +1.00000 q^{32} +7.11159 q^{33} +4.92231 q^{34} +6.37775 q^{35} -1.67520 q^{36} +3.11616 q^{37} -4.33677 q^{38} -2.79379 q^{39} +1.71186 q^{40} +4.66151 q^{41} -4.28820 q^{42} +4.76881 q^{43} -6.17862 q^{44} -2.86771 q^{45} -0.461292 q^{46} +12.1145 q^{47} -1.15100 q^{48} +6.88031 q^{49} -2.06954 q^{50} -5.66558 q^{51} +2.42728 q^{52} -1.40562 q^{53} +5.38115 q^{54} -10.5769 q^{55} +3.72563 q^{56} +4.99162 q^{57} +0.165157 q^{58} +2.18717 q^{59} -1.97035 q^{60} -13.4779 q^{61} +0.0741034 q^{62} -6.24117 q^{63} +1.00000 q^{64} +4.15516 q^{65} +7.11159 q^{66} +8.85100 q^{67} +4.92231 q^{68} +0.530946 q^{69} +6.37775 q^{70} +13.8710 q^{71} -1.67520 q^{72} +0.166468 q^{73} +3.11616 q^{74} +2.38204 q^{75} -4.33677 q^{76} -23.0192 q^{77} -2.79379 q^{78} +10.1561 q^{79} +1.71186 q^{80} -1.16810 q^{81} +4.66151 q^{82} +9.77815 q^{83} -4.28820 q^{84} +8.42630 q^{85} +4.76881 q^{86} -0.190095 q^{87} -6.17862 q^{88} +16.7617 q^{89} -2.86771 q^{90} +9.04313 q^{91} -0.461292 q^{92} -0.0852929 q^{93} +12.1145 q^{94} -7.42394 q^{95} -1.15100 q^{96} +5.95560 q^{97} +6.88031 q^{98} +10.3504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9 + 20 * q^10 + 46 * q^11 + 25 * q^12 + 30 * q^13 + 29 * q^14 + 13 * q^15 + 68 * q^16 + 73 * q^17 + 87 * q^18 + 56 * q^19 + 20 * q^20 - 5 * q^21 + 46 * q^22 + 63 * q^23 + 25 * q^24 + 88 * q^25 + 30 * q^26 + 67 * q^27 + 29 * q^28 + 43 * q^29 + 13 * q^30 + 68 * q^31 + 68 * q^32 + 26 * q^33 + 73 * q^34 + 50 * q^35 + 87 * q^36 + 8 * q^37 + 56 * q^38 + 6 * q^39 + 20 * q^40 + 64 * q^41 - 5 * q^42 + 52 * q^43 + 46 * q^44 + 7 * q^45 + 63 * q^46 + 94 * q^47 + 25 * q^48 + 91 * q^49 + 88 * q^50 + 20 * q^51 + 30 * q^52 + 38 * q^53 + 67 * q^54 + 37 * q^55 + 29 * q^56 + 4 * q^57 + 43 * q^58 + 84 * q^59 + 13 * q^60 + 26 * q^61 + 68 * q^62 + 22 * q^63 + 68 * q^64 - 20 * q^65 + 26 * q^66 + 54 * q^67 + 73 * q^68 - 11 * q^69 + 50 * q^70 + 46 * q^71 + 87 * q^72 + 62 * q^73 + 8 * q^74 + 54 * q^75 + 56 * q^76 + 67 * q^77 + 6 * q^78 + 67 * q^79 + 20 * q^80 + 120 * q^81 + 64 * q^82 + 130 * q^83 - 5 * q^84 - 24 * q^85 + 52 * q^86 + 72 * q^87 + 46 * q^88 + 61 * q^89 + 7 * q^90 + 43 * q^91 + 63 * q^92 + 40 * q^93 + 94 * q^94 + 55 * q^95 + 25 * q^96 + 41 * q^97 + 91 * q^98 + 106 * q^99

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