LMFDB - Embedded newform 6015.2.a.i.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.83425 q^{2} +1.00000 q^{3} +1.36446 q^{4} +1.00000 q^{5} -1.83425 q^{6} +0.959721 q^{7} +1.16574 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.83425 q^{2} +1.00000 q^{3} +1.36446 q^{4} +1.00000 q^{5} -1.83425 q^{6} +0.959721 q^{7} +1.16574 q^{8} +1.00000 q^{9} -1.83425 q^{10} -0.930855 q^{11} +1.36446 q^{12} +6.87239 q^{13} -1.76036 q^{14} +1.00000 q^{15} -4.86717 q^{16} +7.27108 q^{17} -1.83425 q^{18} -6.06263 q^{19} +1.36446 q^{20} +0.959721 q^{21} +1.70742 q^{22} -2.05052 q^{23} +1.16574 q^{24} +1.00000 q^{25} -12.6057 q^{26} +1.00000 q^{27} +1.30950 q^{28} +8.89957 q^{29} -1.83425 q^{30} +3.39998 q^{31} +6.59610 q^{32} -0.930855 q^{33} -13.3370 q^{34} +0.959721 q^{35} +1.36446 q^{36} +3.06334 q^{37} +11.1203 q^{38} +6.87239 q^{39} +1.16574 q^{40} -6.29435 q^{41} -1.76036 q^{42} +5.27988 q^{43} -1.27011 q^{44} +1.00000 q^{45} +3.76115 q^{46} -3.83774 q^{47} -4.86717 q^{48} -6.07894 q^{49} -1.83425 q^{50} +7.27108 q^{51} +9.37708 q^{52} +6.27212 q^{53} -1.83425 q^{54} -0.930855 q^{55} +1.11879 q^{56} -6.06263 q^{57} -16.3240 q^{58} -3.14386 q^{59} +1.36446 q^{60} -3.48000 q^{61} -6.23641 q^{62} +0.959721 q^{63} -2.36453 q^{64} +6.87239 q^{65} +1.70742 q^{66} +7.11967 q^{67} +9.92108 q^{68} -2.05052 q^{69} -1.76036 q^{70} +1.18395 q^{71} +1.16574 q^{72} +16.9597 q^{73} -5.61893 q^{74} +1.00000 q^{75} -8.27219 q^{76} -0.893361 q^{77} -12.6057 q^{78} +14.0593 q^{79} -4.86717 q^{80} +1.00000 q^{81} +11.5454 q^{82} -9.25149 q^{83} +1.30950 q^{84} +7.27108 q^{85} -9.68459 q^{86} +8.89957 q^{87} -1.08514 q^{88} -5.69383 q^{89} -1.83425 q^{90} +6.59558 q^{91} -2.79784 q^{92} +3.39998 q^{93} +7.03936 q^{94} -6.06263 q^{95} +6.59610 q^{96} +17.8087 q^{97} +11.1503 q^{98} -0.930855 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) $ 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * 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 $

$2$	−1.83425	−1.29701	−0.648504	−	0.761211i	$-0.724605\pi$
$2$	−1.83425	−1.29701	−0.648504	+	0.761211i	$0.724605\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.36446	0.682229
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.83425	−0.748828
$7$	0.959721	0.362740	0.181370	−	0.983415i	$-0.441947\pi$
$7$	0.959721	0.362740	0.181370	+	0.983415i	$0.441947\pi$
$8$	1.16574	0.412152
$9$	1.00000	0.333333
$10$	−1.83425	−0.580039
$11$	−0.930855	−0.280663	−0.140332	−	0.990105i	$-0.544817\pi$
$11$	−0.930855	−0.280663	−0.140332	+	0.990105i	$0.544817\pi$
$12$	1.36446	0.393885
$13$	6.87239	1.90606	0.953029	−	0.302878i	$-0.0979474\pi$
$13$	6.87239	1.90606	0.953029	+	0.302878i	$0.0979474\pi$
$14$	−1.76036	−0.470477
$15$	1.00000	0.258199
$16$	−4.86717	−1.21679
$17$	7.27108	1.76350	0.881749	−	0.471720i	$-0.156367\pi$
$17$	7.27108	1.76350	0.881749	+	0.471720i	$0.156367\pi$
$18$	−1.83425	−0.432336
$19$	−6.06263	−1.39086	−0.695431	−	0.718593i	$-0.744787\pi$
$19$	−6.06263	−1.39086	−0.695431	+	0.718593i	$0.744787\pi$
$20$	1.36446	0.305102
$21$	0.959721	0.209428
$22$	1.70742	0.364023
$23$	−2.05052	−0.427563	−0.213781	−	0.976882i	$-0.568578\pi$
$23$	−2.05052	−0.427563	−0.213781	+	0.976882i	$0.568578\pi$
$24$	1.16574	0.237956
$25$	1.00000	0.200000
$26$	−12.6057	−2.47217
$27$	1.00000	0.192450
$28$	1.30950	0.247472
$29$	8.89957	1.65261	0.826305	−	0.563224i	$-0.190439\pi$
$29$	8.89957	1.65261	0.826305	+	0.563224i	$0.190439\pi$
$30$	−1.83425	−0.334886
$31$	3.39998	0.610655	0.305328	−	0.952247i	$-0.401234\pi$
$31$	3.39998	0.610655	0.305328	+	0.952247i	$0.401234\pi$
$32$	6.59610	1.16604
$33$	−0.930855	−0.162041
$34$	−13.3370	−2.28727
$35$	0.959721	0.162222
$36$	1.36446	0.227410
$37$	3.06334	0.503611	0.251805	−	0.967778i	$-0.418976\pi$
$37$	3.06334	0.503611	0.251805	+	0.967778i	$0.418976\pi$
$38$	11.1203	1.80396
$39$	6.87239	1.10046
$40$	1.16574	0.184320
$41$	−6.29435	−0.983013	−0.491506	−	0.870874i	$-0.663554\pi$
$41$	−6.29435	−0.983013	−0.491506	+	0.870874i	$0.663554\pi$
$42$	−1.76036	−0.271630
$43$	5.27988	0.805173	0.402587	−	0.915382i	$-0.368111\pi$
$43$	5.27988	0.805173	0.402587	+	0.915382i	$0.368111\pi$
$44$	−1.27011	−0.191477
$45$	1.00000	0.149071
$46$	3.76115	0.554552
$47$	−3.83774	−0.559792	−0.279896	−	0.960030i	$-0.590300\pi$
$47$	−3.83774	−0.559792	−0.279896	+	0.960030i	$0.590300\pi$
$48$	−4.86717	−0.702516
$49$	−6.07894	−0.868419
$50$	−1.83425	−0.259402
$51$	7.27108	1.01816
$52$	9.37708	1.30037
$53$	6.27212	0.861542	0.430771	−	0.902461i	$-0.358242\pi$
$53$	6.27212	0.861542	0.430771	+	0.902461i	$0.358242\pi$
$54$	−1.83425	−0.249609
$55$	−0.930855	−0.125516
$56$	1.11879	0.149504
$57$	−6.06263	−0.803015
$58$	−16.3240	−2.14345
$59$	−3.14386	−0.409296	−0.204648	−	0.978836i	$-0.565605\pi$
$59$	−3.14386	−0.409296	−0.204648	+	0.978836i	$0.565605\pi$
$60$	1.36446	0.176151
$61$	−3.48000	−0.445568	−0.222784	−	0.974868i	$-0.571515\pi$
$61$	−3.48000	−0.445568	−0.222784	+	0.974868i	$0.571515\pi$
$62$	−6.23641	−0.792024
$63$	0.959721	0.120913
$64$	−2.36453	−0.295566
$65$	6.87239	0.852415
$66$	1.70742	0.210168
$67$	7.11967	0.869806	0.434903	−	0.900477i	$-0.356783\pi$
$67$	7.11967	0.869806	0.434903	+	0.900477i	$0.356783\pi$
$68$	9.92108	1.20311
$69$	−2.05052	−0.246853
$70$	−1.76036	−0.210404
$71$	1.18395	0.140510	0.0702548	−	0.997529i	$-0.477619\pi$
$71$	1.18395	0.140510	0.0702548	+	0.997529i	$0.477619\pi$
$72$	1.16574	0.137384
$73$	16.9597	1.98498	0.992492	−	0.122308i	$-0.0390295\pi$
$73$	16.9597	1.98498	0.992492	+	0.122308i	$0.0390295\pi$
$74$	−5.61893	−0.653187
$75$	1.00000	0.115470
$76$	−8.27219	−0.948886
$77$	−0.893361	−0.101808
$78$	−12.6057	−1.42731
$79$	14.0593	1.58180	0.790898	−	0.611948i	$-0.209614\pi$
$79$	14.0593	1.58180	0.790898	+	0.611948i	$0.209614\pi$
$80$	−4.86717	−0.544166
$81$	1.00000	0.111111
$82$	11.5454	1.27497
$83$	−9.25149	−1.01548	−0.507742	−	0.861509i	$-0.669520\pi$
$83$	−9.25149	−1.01548	−0.507742	+	0.861509i	$0.669520\pi$
$84$	1.30950	0.142878
$85$	7.27108	0.788660
$86$	−9.68459	−1.04432
$87$	8.89957	0.954134
$88$	−1.08514	−0.115676
$89$	−5.69383	−0.603545	−0.301772	−	0.953380i	$-0.597578\pi$
$89$	−5.69383	−0.603545	−0.301772	+	0.953380i	$0.597578\pi$
$90$	−1.83425	−0.193346
$91$	6.59558	0.691405
$92$	−2.79784	−0.291695
$93$	3.39998	0.352562
$94$	7.03936	0.726055
$95$	−6.06263	−0.622012
$96$	6.59610	0.673212
$97$	17.8087	1.80820	0.904101	−	0.427320i	$-0.140542\pi$
$97$	17.8087	1.80820	0.904101	+	0.427320i	$0.140542\pi$
$98$	11.1503	1.12635
$99$	−0.930855	−0.0935545
$100$	1.36446	0.136446
$101$	−16.7737	−1.66905	−0.834524	−	0.550971i	$-0.814257\pi$
$101$	−16.7737	−1.66905	−0.834524	+	0.550971i	$0.814257\pi$
$102$	−13.3370	−1.32056
$103$	−8.22538	−0.810471	−0.405235	−	0.914212i	$-0.632810\pi$
$103$	−8.22538	−0.810471	−0.405235	+	0.914212i	$0.632810\pi$
$104$	8.01144	0.785586
$105$	0.959721	0.0936592
$106$	−11.5046	−1.11743
$107$	1.22166	0.118103	0.0590513	−	0.998255i	$-0.481192\pi$
$107$	1.22166	0.118103	0.0590513	+	0.998255i	$0.481192\pi$
$108$	1.36446	0.131295
$109$	−16.2366	−1.55518	−0.777592	−	0.628769i	$-0.783559\pi$
$109$	−16.2366	−1.55518	−0.777592	+	0.628769i	$0.783559\pi$
$110$	1.70742	0.162796
$111$	3.06334	0.290760
$112$	−4.67113	−0.441380
$113$	5.41701	0.509589	0.254795	−	0.966995i	$-0.417992\pi$
$113$	5.41701	0.509589	0.254795	+	0.966995i	$0.417992\pi$
$114$	11.1203	1.04152
$115$	−2.05052	−0.191212
$116$	12.1431	1.12746
$117$	6.87239	0.635353
$118$	5.76661	0.530860
$119$	6.97821	0.639692
$120$	1.16574	0.106417
$121$	−10.1335	−0.921228
$122$	6.38318	0.577906
$123$	−6.29435	−0.567543
$124$	4.63913	0.416606
$125$	1.00000	0.0894427
$126$	−1.76036	−0.156826
$127$	3.08713	0.273939	0.136969	−	0.990575i	$-0.456264\pi$
$127$	3.08713	0.273939	0.136969	+	0.990575i	$0.456264\pi$
$128$	−8.85507	−0.782685
$129$	5.27988	0.464867
$130$	−12.6057	−1.10559
$131$	−12.8651	−1.12403	−0.562013	−	0.827129i	$-0.689973\pi$
$131$	−12.8651	−1.12403	−0.562013	+	0.827129i	$0.689973\pi$
$132$	−1.27011	−0.110549
$133$	−5.81843	−0.504522
$134$	−13.0592	−1.12814
$135$	1.00000	0.0860663
$136$	8.47621	0.726829
$137$	−5.07594	−0.433667	−0.216833	−	0.976209i	$-0.569573\pi$
$137$	−5.07594	−0.433667	−0.216833	+	0.976209i	$0.569573\pi$
$138$	3.76115	0.320171
$139$	−3.92863	−0.333222	−0.166611	−	0.986023i	$-0.553282\pi$
$139$	−3.92863	−0.333222	−0.166611	+	0.986023i	$0.553282\pi$
$140$	1.30950	0.110673
$141$	−3.83774	−0.323196
$142$	−2.17166	−0.182242
$143$	−6.39720	−0.534961
$144$	−4.86717	−0.405598
$145$	8.89957	0.739069
$146$	−31.1083	−2.57454
$147$	−6.07894	−0.501382
$148$	4.17980	0.343578
$149$	8.99155	0.736616	0.368308	−	0.929704i	$-0.379937\pi$
$149$	8.99155	0.736616	0.368308	+	0.929704i	$0.379937\pi$
$150$	−1.83425	−0.149766
$151$	−7.82895	−0.637111	−0.318556	−	0.947904i	$-0.603198\pi$
$151$	−7.82895	−0.637111	−0.318556	+	0.947904i	$0.603198\pi$
$152$	−7.06746	−0.573247
$153$	7.27108	0.587832
$154$	1.63864	0.132046
$155$	3.39998	0.273093
$156$	9.37708	0.750768
$157$	23.5489	1.87941	0.939705	−	0.341985i	$-0.111099\pi$
$157$	23.5489	1.87941	0.939705	+	0.341985i	$0.111099\pi$
$158$	−25.7882	−2.05160
$159$	6.27212	0.497412
$160$	6.59610	0.521468
$161$	−1.96793	−0.155094
$162$	−1.83425	−0.144112
$163$	−14.2579	−1.11676	−0.558381	−	0.829584i	$-0.688577\pi$
$163$	−14.2579	−1.11676	−0.558381	+	0.829584i	$0.688577\pi$
$164$	−8.58837	−0.670639
$165$	−0.930855	−0.0724670
$166$	16.9695	1.31709
$167$	5.82370	0.450651	0.225326	−	0.974284i	$-0.427655\pi$
$167$	5.82370	0.450651	0.225326	+	0.974284i	$0.427655\pi$
$168$	1.11879	0.0863163
$169$	34.2298	2.63306
$170$	−13.3370	−1.02290
$171$	−6.06263	−0.463621
$172$	7.20416	0.549312
$173$	0.587873	0.0446951	0.0223476	−	0.999750i	$-0.492886\pi$
$173$	0.587873	0.0446951	0.0223476	+	0.999750i	$0.492886\pi$
$174$	−16.3240	−1.23752
$175$	0.959721	0.0725481
$176$	4.53063	0.341509
$177$	−3.14386	−0.236307
$178$	10.4439	0.782802
$179$	2.77049	0.207076	0.103538	−	0.994625i	$-0.466984\pi$
$179$	2.77049	0.207076	0.103538	+	0.994625i	$0.466984\pi$
$180$	1.36446	0.101701
$181$	7.47273	0.555443	0.277722	−	0.960662i	$-0.410421\pi$
$181$	7.47273	0.555443	0.277722	+	0.960662i	$0.410421\pi$
$182$	−12.0979	−0.896757
$183$	−3.48000	−0.257249
$184$	−2.39037	−0.176221
$185$	3.06334	0.225222
$186$	−6.23641	−0.457275
$187$	−6.76833	−0.494949
$188$	−5.23643	−0.381906
$189$	0.959721	0.0698094
$190$	11.1203	0.806755
$191$	8.05313	0.582704	0.291352	−	0.956616i	$-0.405895\pi$
$191$	8.05313	0.582704	0.291352	+	0.956616i	$0.405895\pi$
$192$	−2.36453	−0.170645
$193$	−14.6716	−1.05608	−0.528041	−	0.849219i	$-0.677073\pi$
$193$	−14.6716	−1.05608	−0.528041	+	0.849219i	$0.677073\pi$
$194$	−32.6656	−2.34525
$195$	6.87239	0.492142
$196$	−8.29445	−0.592460
$197$	−2.28530	−0.162821	−0.0814105	−	0.996681i	$-0.525942\pi$
$197$	−2.28530	−0.162821	−0.0814105	+	0.996681i	$0.525942\pi$
$198$	1.70742	0.121341
$199$	−19.9089	−1.41130	−0.705652	−	0.708559i	$-0.749346\pi$
$199$	−19.9089	−1.41130	−0.705652	+	0.708559i	$0.749346\pi$
$200$	1.16574	0.0824304
$201$	7.11967	0.502183
$202$	30.7671	2.16477
$203$	8.54111	0.599468
$204$	9.92108	0.694615
$205$	−6.29435	−0.439617
$206$	15.0874	1.05119
$207$	−2.05052	−0.142521
$208$	−33.4491	−2.31928
$209$	5.64343	0.390364
$210$	−1.76036	−0.121477
$211$	6.49798	0.447339	0.223670	−	0.974665i	$-0.428196\pi$
$211$	6.49798	0.447339	0.223670	+	0.974665i	$0.428196\pi$
$212$	8.55804	0.587769
$213$	1.18395	0.0811232
$214$	−2.24083	−0.153180
$215$	5.27988	0.360085
$216$	1.16574	0.0793187
$217$	3.26304	0.221509
$218$	29.7819	2.01709
$219$	16.9597	1.14603
$220$	−1.27011	−0.0856309
$221$	49.9697	3.36133
$222$	−5.61893	−0.377118
$223$	16.2300	1.08684	0.543422	−	0.839460i	$-0.317128\pi$
$223$	16.2300	1.08684	0.543422	+	0.839460i	$0.317128\pi$
$224$	6.33042	0.422969
$225$	1.00000	0.0666667
$226$	−9.93613	−0.660941
$227$	−24.1232	−1.60111	−0.800556	−	0.599258i	$-0.795462\pi$
$227$	−24.1232	−1.60111	−0.800556	+	0.599258i	$0.795462\pi$
$228$	−8.27219	−0.547839
$229$	−11.1625	−0.737640	−0.368820	−	0.929501i	$-0.620238\pi$
$229$	−11.1625	−0.737640	−0.368820	+	0.929501i	$0.620238\pi$
$230$	3.76115	0.248003
$231$	−0.893361	−0.0587789
$232$	10.3746	0.681126
$233$	−19.9312	−1.30573	−0.652867	−	0.757472i	$-0.726434\pi$
$233$	−19.9312	−1.30573	−0.652867	+	0.757472i	$0.726434\pi$
$234$	−12.6057	−0.824058
$235$	−3.83774	−0.250347
$236$	−4.28966	−0.279233
$237$	14.0593	0.913250
$238$	−12.7998	−0.829685
$239$	23.5671	1.52443	0.762213	−	0.647326i	$-0.224113\pi$
$239$	23.5671	1.52443	0.762213	+	0.647326i	$0.224113\pi$
$240$	−4.86717	−0.314175
$241$	7.15245	0.460730	0.230365	−	0.973104i	$-0.426008\pi$
$241$	7.15245	0.460730	0.230365	+	0.973104i	$0.426008\pi$
$242$	18.5873	1.19484
$243$	1.00000	0.0641500
$244$	−4.74831	−0.303979
$245$	−6.07894	−0.388369
$246$	11.5454	0.736107
$247$	−41.6648	−2.65106
$248$	3.96350	0.251683
$249$	−9.25149	−0.586290
$250$	−1.83425	−0.116008
$251$	−0.194608	−0.0122835	−0.00614176	−	0.999981i	$-0.501955\pi$
$251$	−0.194608	−0.0122835	−0.00614176	+	0.999981i	$0.501955\pi$
$252$	1.30950	0.0824906
$253$	1.90873	0.120001
$254$	−5.66256	−0.355300
$255$	7.27108	0.455333
$256$	20.9714	1.31072
$257$	−1.14598	−0.0714843	−0.0357422	−	0.999361i	$-0.511380\pi$
$257$	−1.14598	−0.0714843	−0.0357422	+	0.999361i	$0.511380\pi$
$258$	−9.68459	−0.602936
$259$	2.93996	0.182680
$260$	9.37708	0.581542
$261$	8.89957	0.550870
$262$	23.5977	1.45787
$263$	11.6020	0.715407	0.357704	−	0.933835i	$-0.383560\pi$
$263$	11.6020	0.715407	0.357704	+	0.933835i	$0.383560\pi$
$264$	−1.08514	−0.0667856
$265$	6.27212	0.385293
$266$	10.6724	0.654369
$267$	−5.69383	−0.348457
$268$	9.71448	0.593406
$269$	−0.296371	−0.0180700	−0.00903502	−	0.999959i	$-0.502876\pi$
$269$	−0.296371	−0.0180700	−0.00903502	+	0.999959i	$0.502876\pi$
$270$	−1.83425	−0.111629
$271$	−4.14368	−0.251710	−0.125855	−	0.992049i	$-0.540167\pi$
$271$	−4.14368	−0.251710	−0.125855	+	0.992049i	$0.540167\pi$
$272$	−35.3896	−2.14581
$273$	6.59558	0.399183
$274$	9.31052	0.562469
$275$	−0.930855	−0.0561327
$276$	−2.79784	−0.168410
$277$	8.92913	0.536500	0.268250	−	0.963349i	$-0.413555\pi$
$277$	8.92913	0.536500	0.268250	+	0.963349i	$0.413555\pi$
$278$	7.20607	0.432191
$279$	3.39998	0.203552
$280$	1.11879	0.0668603
$281$	−25.8791	−1.54382	−0.771908	−	0.635734i	$-0.780697\pi$
$281$	−25.8791	−1.54382	−0.771908	+	0.635734i	$0.780697\pi$
$282$	7.03936	0.419188
$283$	8.96553	0.532946	0.266473	−	0.963842i	$-0.414142\pi$
$283$	8.96553	0.532946	0.266473	+	0.963842i	$0.414142\pi$
$284$	1.61545	0.0958596
$285$	−6.06263	−0.359119
$286$	11.7340	0.693848
$287$	−6.04082	−0.356578
$288$	6.59610	0.388679
$289$	35.8687	2.10992
$290$	−16.3240	−0.958578
$291$	17.8087	1.04397
$292$	23.1408	1.35421
$293$	−22.5999	−1.32030	−0.660151	−	0.751133i	$-0.729508\pi$
$293$	−22.5999	−1.32030	−0.660151	+	0.751133i	$0.729508\pi$
$294$	11.1503	0.650296
$295$	−3.14386	−0.183043
$296$	3.57107	0.207564
$297$	−0.930855	−0.0540137
$298$	−16.4927	−0.955397
$299$	−14.0920	−0.814959
$300$	1.36446	0.0787770
$301$	5.06721	0.292069
$302$	14.3602	0.826338
$303$	−16.7737	−0.963626
$304$	29.5078	1.69239
$305$	−3.48000	−0.199264
$306$	−13.3370	−0.762423
$307$	−24.5617	−1.40181	−0.700906	−	0.713254i	$-0.747221\pi$
$307$	−24.5617	−1.40181	−0.700906	+	0.713254i	$0.747221\pi$
$308$	−1.21895	−0.0694563
$309$	−8.22538	−0.467926
$310$	−6.23641	−0.354204
$311$	6.67825	0.378689	0.189344	−	0.981911i	$-0.439364\pi$
$311$	6.67825	0.378689	0.189344	+	0.981911i	$0.439364\pi$
$312$	8.01144	0.453558
$313$	−12.2975	−0.695094	−0.347547	−	0.937663i	$-0.612985\pi$
$313$	−12.2975	−0.695094	−0.347547	+	0.937663i	$0.612985\pi$
$314$	−43.1946	−2.43761
$315$	0.959721	0.0540742
$316$	19.1833	1.07915
$317$	−3.94752	−0.221715	−0.110857	−	0.993836i	$-0.535360\pi$
$317$	−3.94752	−0.221715	−0.110857	+	0.993836i	$0.535360\pi$
$318$	−11.5046	−0.645147
$319$	−8.28421	−0.463827
$320$	−2.36453	−0.132181
$321$	1.22166	0.0681866
$322$	3.60966	0.201158
$323$	−44.0819	−2.45278
$324$	1.36446	0.0758032
$325$	6.87239	0.381212
$326$	26.1524	1.44845
$327$	−16.2366	−0.897886
$328$	−7.33759	−0.405151
$329$	−3.68316	−0.203059
$330$	1.70742	0.0939902
$331$	9.04676	0.497255	0.248627	−	0.968599i	$-0.420021\pi$
$331$	9.04676	0.497255	0.248627	+	0.968599i	$0.420021\pi$
$332$	−12.6233	−0.692792
$333$	3.06334	0.167870
$334$	−10.6821	−0.584498
$335$	7.11967	0.388989
$336$	−4.67113	−0.254831
$337$	27.9906	1.52475	0.762374	−	0.647137i	$-0.224034\pi$
$337$	27.9906	1.52475	0.762374	+	0.647137i	$0.224034\pi$
$338$	−62.7858	−3.41510
$339$	5.41701	0.294212
$340$	9.92108	0.538046
$341$	−3.16489	−0.171389
$342$	11.1203	0.601320
$343$	−12.5521	−0.677751
$344$	6.15497	0.331854
$345$	−2.05052	−0.110396
$346$	−1.07830	−0.0579699
$347$	−34.2893	−1.84075	−0.920374	−	0.391040i	$-0.872115\pi$
$347$	−34.2893	−1.84075	−0.920374	+	0.391040i	$0.872115\pi$
$348$	12.1431	0.650938
$349$	36.2745	1.94173	0.970864	−	0.239629i	$-0.0770259\pi$
$349$	36.2745	1.94173	0.970864	+	0.239629i	$0.0770259\pi$
$350$	−1.76036	−0.0940954
$351$	6.87239	0.366821
$352$	−6.14002	−0.327264
$353$	3.60315	0.191776	0.0958882	−	0.995392i	$-0.469431\pi$
$353$	3.60315	0.191776	0.0958882	+	0.995392i	$0.469431\pi$
$354$	5.76661	0.306492
$355$	1.18395	0.0628378
$356$	−7.76898	−0.411755
$357$	6.97821	0.369326
$358$	−5.08176	−0.268579
$359$	−35.4882	−1.87300	−0.936499	−	0.350671i	$-0.885954\pi$
$359$	−35.4882	−1.87300	−0.936499	+	0.350671i	$0.885954\pi$
$360$	1.16574	0.0614400
$361$	17.7555	0.934498
$362$	−13.7068	−0.720414
$363$	−10.1335	−0.531871
$364$	8.99939	0.471696
$365$	16.9597	0.887712
$366$	6.38318	0.333654
$367$	26.5982	1.38841	0.694207	−	0.719775i	$-0.255755\pi$
$367$	26.5982	1.38841	0.694207	+	0.719775i	$0.255755\pi$
$368$	9.98022	0.520255
$369$	−6.29435	−0.327671
$370$	−5.61893	−0.292114
$371$	6.01949	0.312516
$372$	4.63913	0.240528
$373$	−5.00448	−0.259122	−0.129561	−	0.991571i	$-0.541357\pi$
$373$	−5.00448	−0.259122	−0.129561	+	0.991571i	$0.541357\pi$
$374$	12.4148	0.641953
$375$	1.00000	0.0516398
$376$	−4.47382	−0.230720
$377$	61.1614	3.14997
$378$	−1.76036	−0.0905434
$379$	−32.4380	−1.66623	−0.833114	−	0.553101i	$-0.813444\pi$
$379$	−32.4380	−1.66623	−0.833114	+	0.553101i	$0.813444\pi$
$380$	−8.27219	−0.424355
$381$	3.08713	0.158159
$382$	−14.7714	−0.755771
$383$	−12.0713	−0.616816	−0.308408	−	0.951254i	$-0.599796\pi$
$383$	−12.0713	−0.616816	−0.308408	+	0.951254i	$0.599796\pi$
$384$	−8.85507	−0.451884
$385$	−0.893361	−0.0455299
$386$	26.9112	1.36975
$387$	5.27988	0.268391
$388$	24.2992	1.23361
$389$	2.61507	0.132589	0.0662947	−	0.997800i	$-0.478882\pi$
$389$	2.61507	0.132589	0.0662947	+	0.997800i	$0.478882\pi$
$390$	−12.6057	−0.638312
$391$	−14.9095	−0.754005
$392$	−7.08647	−0.357921
$393$	−12.8651	−0.648956
$394$	4.19180	0.211180
$395$	14.0593	0.707400
$396$	−1.27011	−0.0638255
$397$	30.2384	1.51762	0.758811	−	0.651311i	$-0.225780\pi$
$397$	30.2384	1.51762	0.758811	+	0.651311i	$0.225780\pi$
$398$	36.5178	1.83047
$399$	−5.81843	−0.291286
$400$	−4.86717	−0.243359
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−13.0592	−0.651335
$403$	23.3660	1.16394
$404$	−22.8870	−1.13867
$405$	1.00000	0.0496904
$406$	−15.6665	−0.777515
$407$	−2.85153	−0.141345
$408$	8.47621	0.419635
$409$	−1.85354	−0.0916515	−0.0458257	−	0.998949i	$-0.514592\pi$
$409$	−1.85354	−0.0916515	−0.0458257	+	0.998949i	$0.514592\pi$
$410$	11.5454	0.570186
$411$	−5.07594	−0.250378
$412$	−11.2232	−0.552926
$413$	−3.01723	−0.148468
$414$	3.76115	0.184851
$415$	−9.25149	−0.454138
$416$	45.3310	2.22254
$417$	−3.92863	−0.192386
$418$	−10.3514	−0.506305
$419$	31.6462	1.54602	0.773010	−	0.634394i	$-0.218750\pi$
$419$	31.6462	1.54602	0.773010	+	0.634394i	$0.218750\pi$
$420$	1.30950	0.0638970
$421$	12.5066	0.609537	0.304768	−	0.952427i	$-0.401421\pi$
$421$	12.5066	0.609537	0.304768	+	0.952427i	$0.401421\pi$
$422$	−11.9189	−0.580203
$423$	−3.83774	−0.186597
$424$	7.31168	0.355086
$425$	7.27108	0.352699
$426$	−2.17166	−0.105217
$427$	−3.33983	−0.161626
$428$	1.66691	0.0805730
$429$	−6.39720	−0.308860
$430$	−9.68459	−0.467032
$431$	−11.9884	−0.577462	−0.288731	−	0.957410i	$-0.593233\pi$
$431$	−11.9884	−0.577462	−0.288731	+	0.957410i	$0.593233\pi$
$432$	−4.86717	−0.234172
$433$	−22.7958	−1.09550	−0.547748	−	0.836643i	$-0.684515\pi$
$433$	−22.7958	−1.09550	−0.547748	+	0.836643i	$0.684515\pi$
$434$	−5.98521	−0.287299
$435$	8.89957	0.426702
$436$	−22.1541	−1.06099
$437$	12.4315	0.594681
$438$	−31.1083	−1.48641
$439$	20.0996	0.959301	0.479650	−	0.877460i	$-0.340763\pi$
$439$	20.0996	0.959301	0.479650	+	0.877460i	$0.340763\pi$
$440$	−1.08514	−0.0517319
$441$	−6.07894	−0.289473
$442$	−91.6568	−4.35967
$443$	−36.5749	−1.73772	−0.868862	−	0.495055i	$-0.835148\pi$
$443$	−36.5749	−1.73772	−0.868862	+	0.495055i	$0.835148\pi$
$444$	4.17980	0.198365
$445$	−5.69383	−0.269913
$446$	−29.7699	−1.40965
$447$	8.99155	0.425286
$448$	−2.26929	−0.107214
$449$	−17.4235	−0.822265	−0.411133	−	0.911576i	$-0.634867\pi$
$449$	−17.4235	−0.822265	−0.411133	+	0.911576i	$0.634867\pi$
$450$	−1.83425	−0.0864672
$451$	5.85913	0.275896
$452$	7.39128	0.347656
$453$	−7.82895	−0.367836
$454$	44.2478	2.07665
$455$	6.59558	0.309206
$456$	−7.06746	−0.330964
$457$	37.2983	1.74474	0.872369	−	0.488847i	$-0.162583\pi$
$457$	37.2983	1.74474	0.872369	+	0.488847i	$0.162583\pi$
$458$	20.4748	0.956725
$459$	7.27108	0.339385
$460$	−2.79784	−0.130450
$461$	23.9871	1.11719	0.558596	−	0.829440i	$-0.311340\pi$
$461$	23.9871	1.11719	0.558596	+	0.829440i	$0.311340\pi$
$462$	1.63864	0.0762366
$463$	−10.2931	−0.478362	−0.239181	−	0.970975i	$-0.576879\pi$
$463$	−10.2931	−0.478362	−0.239181	+	0.970975i	$0.576879\pi$
$464$	−43.3157	−2.01088
$465$	3.39998	0.157670
$466$	36.5587	1.69355
$467$	−12.6038	−0.583235	−0.291617	−	0.956535i	$-0.594193\pi$
$467$	−12.6038	−0.583235	−0.291617	+	0.956535i	$0.594193\pi$
$468$	9.37708	0.433456
$469$	6.83289	0.315514
$470$	7.03936	0.324702
$471$	23.5489	1.08508
$472$	−3.66493	−0.168692
$473$	−4.91480	−0.225983
$474$	−25.7882	−1.18449
$475$	−6.06263	−0.278172
$476$	9.52147	0.436416
$477$	6.27212	0.287181
$478$	−43.2278	−1.97719
$479$	39.2714	1.79436	0.897179	−	0.441668i	$-0.145613\pi$
$479$	39.2714	1.79436	0.897179	+	0.441668i	$0.145613\pi$
$480$	6.59610	0.301070
$481$	21.0525	0.959912
$482$	−13.1194	−0.597570
$483$	−1.96793	−0.0895437
$484$	−13.8267	−0.628488
$485$	17.8087	0.808652
$486$	−1.83425	−0.0832031
$487$	−21.2694	−0.963806	−0.481903	−	0.876224i	$-0.660054\pi$
$487$	−21.2694	−0.963806	−0.481903	+	0.876224i	$0.660054\pi$
$488$	−4.05678	−0.183642
$489$	−14.2579	−0.644763
$490$	11.1503	0.503717
$491$	29.9233	1.35042	0.675211	−	0.737625i	$-0.264053\pi$
$491$	29.9233	1.35042	0.675211	+	0.737625i	$0.264053\pi$
$492$	−8.58837	−0.387194
$493$	64.7095	2.91437
$494$	76.4234	3.43845
$495$	−0.930855	−0.0418388
$496$	−16.5483	−0.743041
$497$	1.13627	0.0509685
$498$	16.9695	0.760422
$499$	−3.01344	−0.134900	−0.0674501	−	0.997723i	$-0.521486\pi$
$499$	−3.01344	−0.134900	−0.0674501	+	0.997723i	$0.521486\pi$
$500$	1.36446	0.0610204
$501$	5.82370	0.260184
$502$	0.356958	0.0159318
$503$	−10.4217	−0.464683	−0.232341	−	0.972634i	$-0.574639\pi$
$503$	−10.4217	−0.464683	−0.232341	+	0.972634i	$0.574639\pi$
$504$	1.11879	0.0498347
$505$	−16.7737	−0.746421
$506$	−3.50109	−0.155642
$507$	34.2298	1.52020
$508$	4.21226	0.186889
$509$	7.89620	0.349993	0.174996	−	0.984569i	$-0.444009\pi$
$509$	7.89620	0.349993	0.174996	+	0.984569i	$0.444009\pi$
$510$	−13.3370	−0.590570
$511$	16.2766	0.720034
$512$	−20.7566	−0.917322
$513$	−6.06263	−0.267672
$514$	2.10201	0.0927157
$515$	−8.22538	−0.362454
$516$	7.20416	0.317146
$517$	3.57238	0.157113
$518$	−5.39260	−0.236937
$519$	0.587873	0.0258047
$520$	8.01144	0.351325
$521$	−8.35041	−0.365838	−0.182919	−	0.983128i	$-0.558555\pi$
$521$	−8.35041	−0.365838	−0.182919	+	0.983128i	$0.558555\pi$
$522$	−16.3240	−0.714482
$523$	19.1464	0.837213	0.418607	−	0.908168i	$-0.362519\pi$
$523$	19.1464	0.837213	0.418607	+	0.908168i	$0.362519\pi$
$524$	−17.5538	−0.766842
$525$	0.959721	0.0418857
$526$	−21.2808	−0.927889
$527$	24.7216	1.07689
$528$	4.53063	0.197170
$529$	−18.7954	−0.817190
$530$	−11.5046	−0.499728
$531$	−3.14386	−0.136432
$532$	−7.93900	−0.344199
$533$	−43.2573	−1.87368
$534$	10.4439	0.451951
$535$	1.22166	0.0528171
$536$	8.29969	0.358492
$537$	2.77049	0.119555
$538$	0.543617	0.0234370
$539$	5.65861	0.243734
$540$	1.36446	0.0587169
$541$	−14.7230	−0.632991	−0.316495	−	0.948594i	$-0.602506\pi$
$541$	−14.7230	−0.632991	−0.316495	+	0.948594i	$0.602506\pi$
$542$	7.60052	0.326470
$543$	7.47273	0.320685
$544$	47.9608	2.05630
$545$	−16.2366	−0.695500
$546$	−12.0979	−0.517743
$547$	33.4237	1.42909	0.714547	−	0.699587i	$-0.246633\pi$
$547$	33.4237	1.42909	0.714547	+	0.699587i	$0.246633\pi$
$548$	−6.92590	−0.295860
$549$	−3.48000	−0.148523
$550$	1.70742	0.0728045
$551$	−53.9548	−2.29855
$552$	−2.39037	−0.101741
$553$	13.4930	0.573781
$554$	−16.3782	−0.695844
$555$	3.06334	0.130032
$556$	−5.36044	−0.227333
$557$	23.0899	0.978352	0.489176	−	0.872185i	$-0.337298\pi$
$557$	23.0899	0.978352	0.489176	+	0.872185i	$0.337298\pi$
$558$	−6.23641	−0.264008
$559$	36.2854	1.53471
$560$	−4.67113	−0.197391
$561$	−6.76833	−0.285759
$562$	47.4686	2.00234
$563$	9.31172	0.392442	0.196221	−	0.980560i	$-0.437133\pi$
$563$	9.31172	0.392442	0.196221	+	0.980560i	$0.437133\pi$
$564$	−5.23643	−0.220494
$565$	5.41701	0.227895
$566$	−16.4450	−0.691235
$567$	0.959721	0.0403045
$568$	1.38019	0.0579113
$569$	8.37066	0.350916	0.175458	−	0.984487i	$-0.443859\pi$
$569$	8.37066	0.350916	0.175458	+	0.984487i	$0.443859\pi$
$570$	11.1203	0.465780
$571$	0.811676	0.0339676	0.0169838	−	0.999856i	$-0.494594\pi$
$571$	0.811676	0.0339676	0.0169838	+	0.999856i	$0.494594\pi$
$572$	−8.72871	−0.364966
$573$	8.05313	0.336424
$574$	11.0804	0.462485
$575$	−2.05052	−0.0855125
$576$	−2.36453	−0.0985222
$577$	−4.51698	−0.188045	−0.0940223	−	0.995570i	$-0.529972\pi$
$577$	−4.51698	−0.188045	−0.0940223	+	0.995570i	$0.529972\pi$
$578$	−65.7920	−2.73658
$579$	−14.6716	−0.609729
$580$	12.1431	0.504214
$581$	−8.87885	−0.368357
$582$	−32.6656	−1.35403
$583$	−5.83844	−0.241803
$584$	19.7707	0.818115
$585$	6.87239	0.284138
$586$	41.4538	1.71244
$587$	31.6101	1.30469	0.652345	−	0.757922i	$-0.273785\pi$
$587$	31.6101	1.30469	0.652345	+	0.757922i	$0.273785\pi$
$588$	−8.29445	−0.342057
$589$	−20.6128	−0.849337
$590$	5.76661	0.237408
$591$	−2.28530	−0.0940047
$592$	−14.9098	−0.612790
$593$	−5.00047	−0.205345	−0.102672	−	0.994715i	$-0.532739\pi$
$593$	−5.00047	−0.205345	−0.102672	+	0.994715i	$0.532739\pi$
$594$	1.70742	0.0700562
$595$	6.97821	0.286079
$596$	12.2686	0.502541
$597$	−19.9089	−0.814816
$598$	25.8481	1.05701
$599$	−18.6778	−0.763155	−0.381578	−	0.924337i	$-0.624619\pi$
$599$	−18.6778	−0.763155	−0.381578	+	0.924337i	$0.624619\pi$
$600$	1.16574	0.0475912
$601$	−2.23807	−0.0912927	−0.0456464	−	0.998958i	$-0.514535\pi$
$601$	−2.23807	−0.0912927	−0.0456464	+	0.998958i	$0.514535\pi$
$602$	−9.29450	−0.378816
$603$	7.11967	0.289935
$604$	−10.6823	−0.434655
$605$	−10.1335	−0.411986
$606$	30.7671	1.24983
$607$	−17.3061	−0.702434	−0.351217	−	0.936294i	$-0.614232\pi$
$607$	−17.3061	−0.702434	−0.351217	+	0.936294i	$0.614232\pi$
$608$	−39.9897	−1.62180
$609$	8.54111	0.346103
$610$	6.38318	0.258447
$611$	−26.3745	−1.06700
$612$	9.92108	0.401036
$613$	26.5713	1.07320	0.536602	−	0.843836i	$-0.319708\pi$
$613$	26.5713	1.07320	0.536602	+	0.843836i	$0.319708\pi$
$614$	45.0522	1.81816
$615$	−6.29435	−0.253813
$616$	−1.04143	−0.0419604
$617$	5.54269	0.223140	0.111570	−	0.993757i	$-0.464412\pi$
$617$	5.54269	0.223140	0.111570	+	0.993757i	$0.464412\pi$
$618$	15.0874	0.606903
$619$	−0.264727	−0.0106403	−0.00532014	−	0.999986i	$-0.501693\pi$
$619$	−0.264727	−0.0106403	−0.00532014	+	0.999986i	$0.501693\pi$
$620$	4.63913	0.186312
$621$	−2.05052	−0.0822844
$622$	−12.2495	−0.491162
$623$	−5.46449	−0.218930
$624$	−33.4491	−1.33904
$625$	1.00000	0.0400000
$626$	22.5566	0.901543
$627$	5.64343	0.225377
$628$	32.1315	1.28219
$629$	22.2738	0.888116
$630$	−1.76036	−0.0701346
$631$	−7.18166	−0.285897	−0.142949	−	0.989730i	$-0.545658\pi$
$631$	−7.18166	−0.285897	−0.142949	+	0.989730i	$0.545658\pi$
$632$	16.3895	0.651940
$633$	6.49798	0.258272
$634$	7.24073	0.287566
$635$	3.08713	0.122509
$636$	8.55804	0.339348
$637$	−41.7768	−1.65526
$638$	15.1953	0.601587
$639$	1.18395	0.0468365
$640$	−8.85507	−0.350028
$641$	−0.353718	−0.0139710	−0.00698552	−	0.999976i	$-0.502224\pi$
$641$	−0.353718	−0.0139710	−0.00698552	+	0.999976i	$0.502224\pi$
$642$	−2.24083	−0.0884385
$643$	40.6615	1.60353	0.801766	−	0.597638i	$-0.203894\pi$
$643$	40.6615	1.60353	0.801766	+	0.597638i	$0.203894\pi$
$644$	−2.68515	−0.105810
$645$	5.27988	0.207895
$646$	80.8570	3.18128
$647$	40.1185	1.57722	0.788610	−	0.614893i	$-0.210801\pi$
$647$	40.1185	1.57722	0.788610	+	0.614893i	$0.210801\pi$
$648$	1.16574	0.0457947
$649$	2.92648	0.114874
$650$	−12.6057	−0.494435
$651$	3.26304	0.127888
$652$	−19.4543	−0.761887
$653$	−18.2947	−0.715925	−0.357963	−	0.933736i	$-0.616529\pi$
$653$	−18.2947	−0.715925	−0.357963	+	0.933736i	$0.616529\pi$
$654$	29.7819	1.16457
$655$	−12.8651	−0.502679
$656$	30.6357	1.19612
$657$	16.9597	0.661661
$658$	6.75582	0.263369
$659$	−15.6976	−0.611492	−0.305746	−	0.952113i	$-0.598906\pi$
$659$	−15.6976	−0.611492	−0.305746	+	0.952113i	$0.598906\pi$
$660$	−1.27011	−0.0494390
$661$	12.1044	0.470806	0.235403	−	0.971898i	$-0.424359\pi$
$661$	12.1044	0.470806	0.235403	+	0.971898i	$0.424359\pi$
$662$	−16.5940	−0.644943
$663$	49.9697	1.94066
$664$	−10.7849	−0.418533
$665$	−5.81843	−0.225629
$666$	−5.61893	−0.217729
$667$	−18.2487	−0.706594
$668$	7.94619	0.307447
$669$	16.2300	0.627490
$670$	−13.0592	−0.504522
$671$	3.23938	0.125055
$672$	6.33042	0.244201
$673$	−5.57738	−0.214992	−0.107496	−	0.994206i	$-0.534283\pi$
$673$	−5.57738	−0.214992	−0.107496	+	0.994206i	$0.534283\pi$
$674$	−51.3417	−1.97761
$675$	1.00000	0.0384900
$676$	46.7051	1.79635
$677$	22.1440	0.851061	0.425531	−	0.904944i	$-0.360087\pi$
$677$	22.1440	0.851061	0.425531	+	0.904944i	$0.360087\pi$
$678$	−9.93613	−0.381595
$679$	17.0914	0.655908
$680$	8.47621	0.325048
$681$	−24.1232	−0.924402
$682$	5.80519	0.222292
$683$	−27.6646	−1.05856	−0.529279	−	0.848448i	$-0.677537\pi$
$683$	−27.6646	−1.05856	−0.529279	+	0.848448i	$0.677537\pi$
$684$	−8.27219	−0.316295
$685$	−5.07594	−0.193942
$686$	23.0237	0.879049
$687$	−11.1625	−0.425877
$688$	−25.6981	−0.979729
$689$	43.1045	1.64215
$690$	3.76115	0.143185
$691$	26.9733	1.02611	0.513056	−	0.858355i	$-0.328513\pi$
$691$	26.9733	1.02611	0.513056	+	0.858355i	$0.328513\pi$
$692$	0.802127	0.0304923
$693$	−0.893361	−0.0339360
$694$	62.8950	2.38746
$695$	−3.92863	−0.149021
$696$	10.3746	0.393248
$697$	−45.7668	−1.73354
$698$	−66.5363	−2.51844
$699$	−19.9312	−0.753866
$700$	1.30950	0.0494944
$701$	−34.7188	−1.31131	−0.655655	−	0.755060i	$-0.727608\pi$
$701$	−34.7188	−1.31131	−0.655655	+	0.755060i	$0.727608\pi$
$702$	−12.6057	−0.475770
$703$	−18.5719	−0.700453
$704$	2.20104	0.0829547
$705$	−3.83774	−0.144538
$706$	−6.60906	−0.248735
$707$	−16.0981	−0.605432
$708$	−4.28966	−0.161215
$709$	40.0555	1.50431	0.752157	−	0.658984i	$-0.229013\pi$
$709$	40.0555	1.50431	0.752157	+	0.658984i	$0.229013\pi$
$710$	−2.17166	−0.0815011
$711$	14.0593	0.527265
$712$	−6.63753	−0.248752
$713$	−6.97173	−0.261093
$714$	−12.7998	−0.479019
$715$	−6.39720	−0.239242
$716$	3.78021	0.141273
$717$	23.5671	0.880128
$718$	65.0941	2.42929
$719$	49.2100	1.83522	0.917611	−	0.397480i	$-0.130115\pi$
$719$	49.2100	1.83522	0.917611	+	0.397480i	$0.130115\pi$
$720$	−4.86717	−0.181389
$721$	−7.89407	−0.293991
$722$	−32.5679	−1.21205
$723$	7.15245	0.266003
$724$	10.1962	0.378939
$725$	8.89957	0.330522
$726$	18.5873	0.689841
$727$	48.8386	1.81132	0.905661	−	0.424003i	$-0.139375\pi$
$727$	48.8386	1.81132	0.905661	+	0.424003i	$0.139375\pi$
$728$	7.68874	0.284964
$729$	1.00000	0.0370370
$730$	−31.1083	−1.15137
$731$	38.3904	1.41992
$732$	−4.74831	−0.175503
$733$	29.8409	1.10220	0.551099	−	0.834440i	$-0.314209\pi$
$733$	29.8409	1.10220	0.551099	+	0.834440i	$0.314209\pi$
$734$	−48.7876	−1.80078
$735$	−6.07894	−0.224225
$736$	−13.5254	−0.498554
$737$	−6.62738	−0.244123
$738$	11.5454	0.424992
$739$	−7.02005	−0.258237	−0.129118	−	0.991629i	$-0.541215\pi$
$739$	−7.02005	−0.258237	−0.129118	+	0.991629i	$0.541215\pi$
$740$	4.17980	0.153653
$741$	−41.6648	−1.53059
$742$	−11.0412	−0.405336
$743$	−33.0028	−1.21076	−0.605378	−	0.795938i	$-0.706978\pi$
$743$	−33.0028	−1.21076	−0.605378	+	0.795938i	$0.706978\pi$
$744$	3.96350	0.145309
$745$	8.99155	0.329425
$746$	9.17945	0.336083
$747$	−9.25149	−0.338494
$748$	−9.23509	−0.337668
$749$	1.17246	0.0428406
$750$	−1.83425	−0.0669772
$751$	14.8514	0.541935	0.270967	−	0.962589i	$-0.412656\pi$
$751$	14.8514	0.541935	0.270967	+	0.962589i	$0.412656\pi$
$752$	18.6789	0.681151
$753$	−0.194608	−0.00709189
$754$	−112.185	−4.08553
$755$	−7.82895	−0.284925
$756$	1.30950	0.0476260
$757$	33.3487	1.21208	0.606039	−	0.795435i	$-0.292758\pi$
$757$	33.3487	1.21208	0.606039	+	0.795435i	$0.292758\pi$
$758$	59.4993	2.16111
$759$	1.90873	0.0692827
$760$	−7.06746	−0.256364
$761$	−6.17538	−0.223857	−0.111929	−	0.993716i	$-0.535703\pi$
$761$	−6.17538	−0.223857	−0.111929	+	0.993716i	$0.535703\pi$
$762$	−5.66256	−0.205133
$763$	−15.5826	−0.564128
$764$	10.9881	0.397537
$765$	7.27108	0.262887
$766$	22.1418	0.800015
$767$	−21.6058	−0.780142
$768$	20.9714	0.756742
$769$	−38.0600	−1.37248	−0.686240	−	0.727375i	$-0.740740\pi$
$769$	−38.0600	−1.37248	−0.686240	+	0.727375i	$0.740740\pi$
$770$	1.63864	0.0590526
$771$	−1.14598	−0.0412715
$772$	−20.0187	−0.720489
$773$	5.29322	0.190384	0.0951920	−	0.995459i	$-0.469653\pi$
$773$	5.29322	0.190384	0.0951920	+	0.995459i	$0.469653\pi$
$774$	−9.68459	−0.348105
$775$	3.39998	0.122131
$776$	20.7604	0.745254
$777$	2.93996	0.105470
$778$	−4.79669	−0.171970
$779$	38.1603	1.36723
$780$	9.37708	0.335753
$781$	−1.10209	−0.0394359
$782$	27.3477	0.977950
$783$	8.89957	0.318045
$784$	29.5872	1.05669
$785$	23.5489	0.840498
$786$	23.5977	0.841701
$787$	−51.1098	−1.82187	−0.910934	−	0.412552i	$-0.864638\pi$
$787$	−51.1098	−1.82187	−0.910934	+	0.412552i	$0.864638\pi$
$788$	−3.11819	−0.111081
$789$	11.6020	0.413041
$790$	−25.7882	−0.917504
$791$	5.19882	0.184849
$792$	−1.08514	−0.0385587
$793$	−23.9159	−0.849280
$794$	−55.4647	−1.96837
$795$	6.27212	0.222449
$796$	−27.1648	−0.962831
$797$	47.4927	1.68228	0.841139	−	0.540819i	$-0.181886\pi$
$797$	47.4927	1.68228	0.841139	+	0.540819i	$0.181886\pi$
$798$	10.6724	0.377800
$799$	−27.9046	−0.987192
$800$	6.59610	0.233207
$801$	−5.69383	−0.201182
$802$	−1.83425	−0.0647695
$803$	−15.7870	−0.557112
$804$	9.71448	0.342603
$805$	−1.96793	−0.0693603
$806$	−42.8590	−1.50964
$807$	−0.296371	−0.0104327
$808$	−19.5538	−0.687902
$809$	21.3033	0.748985	0.374493	−	0.927230i	$-0.377817\pi$
$809$	21.3033	0.748985	0.374493	+	0.927230i	$0.377817\pi$
$810$	−1.83425	−0.0644488
$811$	8.01649	0.281497	0.140748	−	0.990045i	$-0.455049\pi$
$811$	8.01649	0.281497	0.140748	+	0.990045i	$0.455049\pi$
$812$	11.6540	0.408974
$813$	−4.14368	−0.145325
$814$	5.23041	0.183326
$815$	−14.2579	−0.499431
$816$	−35.3896	−1.23888
$817$	−32.0099	−1.11989
$818$	3.39984	0.118873
$819$	6.59558	0.230468
$820$	−8.58837	−0.299919
$821$	56.6500	1.97710	0.988550	−	0.150894i	$-0.0482151\pi$
$821$	56.6500	1.97710	0.988550	+	0.150894i	$0.0482151\pi$
$822$	9.31052	0.324742
$823$	38.1347	1.32929	0.664645	−	0.747159i	$-0.268583\pi$
$823$	38.1347	1.32929	0.664645	+	0.747159i	$0.268583\pi$
$824$	−9.58867	−0.334037
$825$	−0.930855	−0.0324082
$826$	5.53434	0.192564
$827$	−8.88278	−0.308885	−0.154442	−	0.988002i	$-0.549358\pi$
$827$	−8.88278	−0.308885	−0.154442	+	0.988002i	$0.549358\pi$
$828$	−2.79784	−0.0972318
$829$	−21.2359	−0.737553	−0.368777	−	0.929518i	$-0.620223\pi$
$829$	−21.2359	−0.737553	−0.368777	+	0.929518i	$0.620223\pi$
$830$	16.9695	0.589020
$831$	8.92913	0.309748
$832$	−16.2500	−0.563367
$833$	−44.2005	−1.53145
$834$	7.20607	0.249526
$835$	5.82370	0.201537
$836$	7.70021	0.266318
$837$	3.39998	0.117521
$838$	−58.0469	−2.00520
$839$	−48.1639	−1.66280	−0.831401	−	0.555673i	$-0.812461\pi$
$839$	−48.1639	−1.66280	−0.831401	+	0.555673i	$0.812461\pi$
$840$	1.11879	0.0386018
$841$	50.2024	1.73112
$842$	−22.9403	−0.790574
$843$	−25.8791	−0.891323
$844$	8.86622	0.305188
$845$	34.2298	1.17754
$846$	7.03936	0.242018
$847$	−9.72534	−0.334167
$848$	−30.5275	−1.04832
$849$	8.96553	0.307696
$850$	−13.3370	−0.457454
$851$	−6.28144	−0.215325
$852$	1.61545	0.0553446
$853$	28.9757	0.992108	0.496054	−	0.868292i	$-0.334782\pi$
$853$	28.9757	0.992108	0.496054	+	0.868292i	$0.334782\pi$
$854$	6.12607	0.209630
$855$	−6.06263	−0.207337
$856$	1.42414	0.0486763
$857$	16.6205	0.567746	0.283873	−	0.958862i	$-0.408381\pi$
$857$	16.6205	0.567746	0.283873	+	0.958862i	$0.408381\pi$
$858$	11.7340	0.400593
$859$	−46.9487	−1.60187	−0.800934	−	0.598752i	$-0.795664\pi$
$859$	−46.9487	−1.60187	−0.800934	+	0.598752i	$0.795664\pi$
$860$	7.20416	0.245660
$861$	−6.04082	−0.205871
$862$	21.9897	0.748972
$863$	49.8882	1.69821	0.849107	−	0.528221i	$-0.177141\pi$
$863$	49.8882	1.69821	0.849107	+	0.528221i	$0.177141\pi$
$864$	6.59610	0.224404
$865$	0.587873	0.0199883
$866$	41.8131	1.42087
$867$	35.8687	1.21816
$868$	4.45227	0.151120
$869$	−13.0872	−0.443952
$870$	−16.3240	−0.553435
$871$	48.9291	1.65790
$872$	−18.9277	−0.640972
$873$	17.8087	0.602734
$874$	−22.8025	−0.771305
$875$	0.959721	0.0324445
$876$	23.1408	0.781855
$877$	−35.3512	−1.19372	−0.596862	−	0.802344i	$-0.703586\pi$
$877$	−35.3512	−1.19372	−0.596862	+	0.802344i	$0.703586\pi$
$878$	−36.8676	−1.24422
$879$	−22.5999	−0.762276
$880$	4.53063	0.152728
$881$	−55.1407	−1.85774	−0.928868	−	0.370411i	$-0.879217\pi$
$881$	−55.1407	−1.85774	−0.928868	+	0.370411i	$0.879217\pi$
$882$	11.1503	0.375449
$883$	5.38581	0.181247	0.0906234	−	0.995885i	$-0.471114\pi$
$883$	5.38581	0.181247	0.0906234	+	0.995885i	$0.471114\pi$
$884$	68.1816	2.29319
$885$	−3.14386	−0.105680
$886$	67.0873	2.25384
$887$	45.2404	1.51902	0.759511	−	0.650494i	$-0.225438\pi$
$887$	45.2404	1.51902	0.759511	+	0.650494i	$0.225438\pi$
$888$	3.57107	0.119837
$889$	2.96278	0.0993686
$890$	10.4439	0.350080
$891$	−0.930855	−0.0311848
$892$	22.1452	0.741476
$893$	23.2668	0.778594
$894$	−16.4927	−0.551599
$895$	2.77049	0.0926072
$896$	−8.49840	−0.283912
$897$	−14.0920	−0.470517
$898$	31.9589	1.06648
$899$	30.2584	1.00917
$900$	1.36446	0.0454819
$901$	45.6051	1.51933
$902$	−10.7471	−0.357839
$903$	5.06721	0.168626
$904$	6.31484	0.210028
$905$	7.47273	0.248402
$906$	14.3602	0.477086
$907$	37.3810	1.24122	0.620608	−	0.784121i	$-0.286886\pi$
$907$	37.3810	1.24122	0.620608	+	0.784121i	$0.286886\pi$
$908$	−32.9150	−1.09232
$909$	−16.7737	−0.556350
$910$	−12.0979	−0.401042
$911$	28.1205	0.931673	0.465837	−	0.884871i	$-0.345753\pi$
$911$	28.1205	0.931673	0.465837	+	0.884871i	$0.345753\pi$
$912$	29.5078	0.977102
$913$	8.61180	0.285009
$914$	−68.4142	−2.26294
$915$	−3.48000	−0.115045
$916$	−15.2308	−0.503239
$917$	−12.3469	−0.407729
$918$	−13.3370	−0.440185
$919$	−2.63577	−0.0869461	−0.0434730	−	0.999055i	$-0.513842\pi$
$919$	−2.63577	−0.0869461	−0.0434730	+	0.999055i	$0.513842\pi$
$920$	−2.39037	−0.0788083
$921$	−24.5617	−0.809336
$922$	−43.9983	−1.44901
$923$	8.13660	0.267819
$924$	−1.21895	−0.0401006
$925$	3.06334	0.100722
$926$	18.8801	0.620440
$927$	−8.22538	−0.270157
$928$	58.7025	1.92700
$929$	34.7563	1.14032	0.570158	−	0.821535i	$-0.306882\pi$
$929$	34.7563	1.14032	0.570158	+	0.821535i	$0.306882\pi$
$930$	−6.23641	−0.204500
$931$	36.8543	1.20785
$932$	−27.1952	−0.890810
$933$	6.67825	0.218636
$934$	23.1185	0.756460
$935$	−6.76833	−0.221348
$936$	8.01144	0.261862
$937$	−29.2315	−0.954953	−0.477477	−	0.878645i	$-0.658448\pi$
$937$	−29.2315	−0.954953	−0.477477	+	0.878645i	$0.658448\pi$
$938$	−12.5332	−0.409224
$939$	−12.2975	−0.401313
$940$	−5.23643	−0.170794
$941$	−37.1442	−1.21087	−0.605434	−	0.795896i	$-0.707000\pi$
$941$	−37.1442	−1.21087	−0.605434	+	0.795896i	$0.707000\pi$
$942$	−43.1946	−1.40735
$943$	12.9067	0.420299
$944$	15.3017	0.498028
$945$	0.959721	0.0312197
$946$	9.01495	0.293101
$947$	−11.3843	−0.369940	−0.184970	−	0.982744i	$-0.559219\pi$
$947$	−11.3843	−0.369940	−0.184970	+	0.982744i	$0.559219\pi$
$948$	19.1833	0.623045
$949$	116.554	3.78350
$950$	11.1203	0.360792
$951$	−3.94752	−0.128007
$952$	8.13480	0.263650
$953$	37.7218	1.22193	0.610964	−	0.791658i	$-0.290782\pi$
$953$	37.7218	1.22193	0.610964	+	0.791658i	$0.290782\pi$
$954$	−11.5046	−0.372476
$955$	8.05313	0.260593
$956$	32.1562	1.04001
$957$	−8.28421	−0.267791
$958$	−72.0334	−2.32729
$959$	−4.87149	−0.157309
$960$	−2.36453	−0.0763149
$961$	−19.4401	−0.627100
$962$	−38.6155	−1.24501
$963$	1.22166	0.0393676
$964$	9.75921	0.314323
$965$	−14.6716	−0.472294
$966$	3.60966	0.116139
$967$	36.7094	1.18049	0.590247	−	0.807223i	$-0.299030\pi$
$967$	36.7094	1.18049	0.590247	+	0.807223i	$0.299030\pi$
$968$	−11.8131	−0.379686
$969$	−44.0819	−1.41611
$970$	−32.6656	−1.04883
$971$	4.45364	0.142924	0.0714620	−	0.997443i	$-0.477234\pi$
$971$	4.45364	0.142924	0.0714620	+	0.997443i	$0.477234\pi$
$972$	1.36446	0.0437650
$973$	−3.77039	−0.120873
$974$	39.0132	1.25006
$975$	6.87239	0.220093
$976$	16.9378	0.542164
$977$	−18.4518	−0.590325	−0.295162	−	0.955447i	$-0.595374\pi$
$977$	−18.4518	−0.590325	−0.295162	+	0.955447i	$0.595374\pi$
$978$	26.1524	0.836263
$979$	5.30013	0.169393
$980$	−8.29445	−0.264956
$981$	−16.2366	−0.518395
$982$	−54.8868	−1.75151
$983$	−2.77583	−0.0885351	−0.0442675	−	0.999020i	$-0.514095\pi$
$983$	−2.77583	−0.0885351	−0.0442675	+	0.999020i	$0.514095\pi$
$984$	−7.33759	−0.233914
$985$	−2.28530	−0.0728157
$986$	−118.693	−3.77996
$987$	−3.68316	−0.117236
$988$	−56.8498	−1.80863
$989$	−10.8265	−0.344262
$990$	1.70742	0.0542653
$991$	27.3915	0.870120	0.435060	−	0.900401i	$-0.356727\pi$
$991$	27.3915	0.870120	0.435060	+	0.900401i	$0.356727\pi$
$992$	22.4266	0.712047
$993$	9.04676	0.287090
$994$	−2.08419	−0.0661065
$995$	−19.9089	−0.631154
$996$	−12.6233	−0.399983
$997$	−32.7871	−1.03838	−0.519190	−	0.854659i	$-0.673766\pi$
$997$	−32.7871	−1.03838	−0.519190	+	0.854659i	$0.673766\pi$
$998$	5.52739	0.174967
$999$	3.06334	0.0969199

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.i.1.10	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.i.1.10	✓	43	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.83425 q^{2} +1.00000 q^{3} +1.36446 q^{4} +1.00000 q^{5} -1.83425 q^{6} +0.959721 q^{7} +1.16574 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.83425 q^{2} +1.00000 q^{3} +1.36446 q^{4} +1.00000 q^{5} -1.83425 q^{6} +0.959721 q^{7} +1.16574 q^{8} +1.00000 q^{9} -1.83425 q^{10} -0.930855 q^{11} +1.36446 q^{12} +6.87239 q^{13} -1.76036 q^{14} +1.00000 q^{15} -4.86717 q^{16} +7.27108 q^{17} -1.83425 q^{18} -6.06263 q^{19} +1.36446 q^{20} +0.959721 q^{21} +1.70742 q^{22} -2.05052 q^{23} +1.16574 q^{24} +1.00000 q^{25} -12.6057 q^{26} +1.00000 q^{27} +1.30950 q^{28} +8.89957 q^{29} -1.83425 q^{30} +3.39998 q^{31} +6.59610 q^{32} -0.930855 q^{33} -13.3370 q^{34} +0.959721 q^{35} +1.36446 q^{36} +3.06334 q^{37} +11.1203 q^{38} +6.87239 q^{39} +1.16574 q^{40} -6.29435 q^{41} -1.76036 q^{42} +5.27988 q^{43} -1.27011 q^{44} +1.00000 q^{45} +3.76115 q^{46} -3.83774 q^{47} -4.86717 q^{48} -6.07894 q^{49} -1.83425 q^{50} +7.27108 q^{51} +9.37708 q^{52} +6.27212 q^{53} -1.83425 q^{54} -0.930855 q^{55} +1.11879 q^{56} -6.06263 q^{57} -16.3240 q^{58} -3.14386 q^{59} +1.36446 q^{60} -3.48000 q^{61} -6.23641 q^{62} +0.959721 q^{63} -2.36453 q^{64} +6.87239 q^{65} +1.70742 q^{66} +7.11967 q^{67} +9.92108 q^{68} -2.05052 q^{69} -1.76036 q^{70} +1.18395 q^{71} +1.16574 q^{72} +16.9597 q^{73} -5.61893 q^{74} +1.00000 q^{75} -8.27219 q^{76} -0.893361 q^{77} -12.6057 q^{78} +14.0593 q^{79} -4.86717 q^{80} +1.00000 q^{81} +11.5454 q^{82} -9.25149 q^{83} +1.30950 q^{84} +7.27108 q^{85} -9.68459 q^{86} +8.89957 q^{87} -1.08514 q^{88} -5.69383 q^{89} -1.83425 q^{90} +6.59558 q^{91} -2.79784 q^{92} +3.39998 q^{93} +7.03936 q^{94} -6.06263 q^{95} +6.59610 q^{96} +17.8087 q^{97} +11.1503 q^{98} -0.930855 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * q^99

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