LMFDB - Embedded newform 6014.2.a.l.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.06494 q^{3} +1.00000 q^{4} -3.85153 q^{5} +3.06494 q^{6} +4.92968 q^{7} -1.00000 q^{8} +6.39384 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.06494 q^{3} +1.00000 q^{4} -3.85153 q^{5} +3.06494 q^{6} +4.92968 q^{7} -1.00000 q^{8} +6.39384 q^{9} +3.85153 q^{10} -3.45164 q^{11} -3.06494 q^{12} -6.10249 q^{13} -4.92968 q^{14} +11.8047 q^{15} +1.00000 q^{16} +6.53932 q^{17} -6.39384 q^{18} +8.49768 q^{19} -3.85153 q^{20} -15.1092 q^{21} +3.45164 q^{22} -3.16538 q^{23} +3.06494 q^{24} +9.83425 q^{25} +6.10249 q^{26} -10.4019 q^{27} +4.92968 q^{28} +5.69058 q^{29} -11.8047 q^{30} +1.00000 q^{31} -1.00000 q^{32} +10.5791 q^{33} -6.53932 q^{34} -18.9868 q^{35} +6.39384 q^{36} -5.47905 q^{37} -8.49768 q^{38} +18.7037 q^{39} +3.85153 q^{40} +1.11717 q^{41} +15.1092 q^{42} +9.85208 q^{43} -3.45164 q^{44} -24.6260 q^{45} +3.16538 q^{46} -0.756954 q^{47} -3.06494 q^{48} +17.3018 q^{49} -9.83425 q^{50} -20.0426 q^{51} -6.10249 q^{52} -2.41949 q^{53} +10.4019 q^{54} +13.2941 q^{55} -4.92968 q^{56} -26.0449 q^{57} -5.69058 q^{58} +7.49004 q^{59} +11.8047 q^{60} +7.73982 q^{61} -1.00000 q^{62} +31.5196 q^{63} +1.00000 q^{64} +23.5039 q^{65} -10.5791 q^{66} +8.05727 q^{67} +6.53932 q^{68} +9.70170 q^{69} +18.9868 q^{70} -2.20214 q^{71} -6.39384 q^{72} +0.461049 q^{73} +5.47905 q^{74} -30.1413 q^{75} +8.49768 q^{76} -17.0155 q^{77} -18.7037 q^{78} +2.70659 q^{79} -3.85153 q^{80} +12.6996 q^{81} -1.11717 q^{82} -9.44859 q^{83} -15.1092 q^{84} -25.1864 q^{85} -9.85208 q^{86} -17.4413 q^{87} +3.45164 q^{88} -9.78906 q^{89} +24.6260 q^{90} -30.0833 q^{91} -3.16538 q^{92} -3.06494 q^{93} +0.756954 q^{94} -32.7290 q^{95} +3.06494 q^{96} -1.00000 q^{97} -17.3018 q^{98} -22.0692 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) $ 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * 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
$3$	−3.06494	−1.76954	−0.884771	−	0.466026i	$-0.845685\pi$
$3$	−3.06494	−1.76954	−0.884771	+	0.466026i	$0.845685\pi$
$4$	1.00000	0.500000
$5$	−3.85153	−1.72245	−0.861227	−	0.508220i	$-0.830304\pi$
$5$	−3.85153	−1.72245	−0.861227	+	0.508220i	$0.830304\pi$
$6$	3.06494	1.25126
$7$	4.92968	1.86325	0.931623	−	0.363427i	$-0.118393\pi$
$7$	4.92968	1.86325	0.931623	+	0.363427i	$0.118393\pi$
$8$	−1.00000	−0.353553
$9$	6.39384	2.13128
$10$	3.85153	1.21796
$11$	−3.45164	−1.04071	−0.520355	−	0.853950i	$-0.674200\pi$
$11$	−3.45164	−1.04071	−0.520355	+	0.853950i	$0.674200\pi$
$12$	−3.06494	−0.884771
$13$	−6.10249	−1.69253	−0.846263	−	0.532766i	$-0.821153\pi$
$13$	−6.10249	−1.69253	−0.846263	+	0.532766i	$0.821153\pi$
$14$	−4.92968	−1.31751
$15$	11.8047	3.04796
$16$	1.00000	0.250000
$17$	6.53932	1.58602	0.793009	−	0.609210i	$-0.208513\pi$
$17$	6.53932	1.58602	0.793009	+	0.609210i	$0.208513\pi$
$18$	−6.39384	−1.50704
$19$	8.49768	1.94950	0.974751	−	0.223293i	$-0.0716808\pi$
$19$	8.49768	1.94950	0.974751	+	0.223293i	$0.0716808\pi$
$20$	−3.85153	−0.861227
$21$	−15.1092	−3.29709
$22$	3.45164	0.735893
$23$	−3.16538	−0.660028	−0.330014	−	0.943976i	$-0.607054\pi$
$23$	−3.16538	−0.660028	−0.330014	+	0.943976i	$0.607054\pi$
$24$	3.06494	0.625628
$25$	9.83425	1.96685
$26$	6.10249	1.19680
$27$	−10.4019	−2.00185
$28$	4.92968	0.931623
$29$	5.69058	1.05671	0.528357	−	0.849022i	$-0.322808\pi$
$29$	5.69058	1.05671	0.528357	+	0.849022i	$0.322808\pi$
$30$	−11.8047	−2.15523
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	10.5791	1.84158
$34$	−6.53932	−1.12148
$35$	−18.9868	−3.20936
$36$	6.39384	1.06564
$37$	−5.47905	−0.900750	−0.450375	−	0.892840i	$-0.648710\pi$
$37$	−5.47905	−0.900750	−0.450375	+	0.892840i	$0.648710\pi$
$38$	−8.49768	−1.37851
$39$	18.7037	2.99499
$40$	3.85153	0.608980
$41$	1.11717	0.174472	0.0872362	−	0.996188i	$-0.472197\pi$
$41$	1.11717	0.174472	0.0872362	+	0.996188i	$0.472197\pi$
$42$	15.1092	2.33140
$43$	9.85208	1.50243	0.751214	−	0.660058i	$-0.229468\pi$
$43$	9.85208	1.50243	0.751214	+	0.660058i	$0.229468\pi$
$44$	−3.45164	−0.520355
$45$	−24.6260	−3.67103
$46$	3.16538	0.466710
$47$	−0.756954	−0.110413	−0.0552065	−	0.998475i	$-0.517582\pi$
$47$	−0.756954	−0.110413	−0.0552065	+	0.998475i	$0.517582\pi$
$48$	−3.06494	−0.442385
$49$	17.3018	2.47168
$50$	−9.83425	−1.39077
$51$	−20.0426	−2.80653
$52$	−6.10249	−0.846263
$53$	−2.41949	−0.332342	−0.166171	−	0.986097i	$-0.553140\pi$
$53$	−2.41949	−0.332342	−0.166171	+	0.986097i	$0.553140\pi$
$54$	10.4019	1.41552
$55$	13.2941	1.79257
$56$	−4.92968	−0.658757
$57$	−26.0449	−3.44973
$58$	−5.69058	−0.747210
$59$	7.49004	0.975120	0.487560	−	0.873089i	$-0.337887\pi$
$59$	7.49004	0.975120	0.487560	+	0.873089i	$0.337887\pi$
$60$	11.8047	1.52398
$61$	7.73982	0.990982	0.495491	−	0.868613i	$-0.334988\pi$
$61$	7.73982	0.990982	0.495491	+	0.868613i	$0.334988\pi$
$62$	−1.00000	−0.127000
$63$	31.5196	3.97110
$64$	1.00000	0.125000
$65$	23.5039	2.91530
$66$	−10.5791	−1.30219
$67$	8.05727	0.984353	0.492176	−	0.870496i	$-0.336202\pi$
$67$	8.05727	0.984353	0.492176	+	0.870496i	$0.336202\pi$
$68$	6.53932	0.793009
$69$	9.70170	1.16795
$70$	18.9868	2.26936
$71$	−2.20214	−0.261346	−0.130673	−	0.991426i	$-0.541714\pi$
$71$	−2.20214	−0.261346	−0.130673	+	0.991426i	$0.541714\pi$
$72$	−6.39384	−0.753521
$73$	0.461049	0.0539617	0.0269809	−	0.999636i	$-0.491411\pi$
$73$	0.461049	0.0539617	0.0269809	+	0.999636i	$0.491411\pi$
$74$	5.47905	0.636926
$75$	−30.1413	−3.48042
$76$	8.49768	0.974751
$77$	−17.0155	−1.93910
$78$	−18.7037	−2.11778
$79$	2.70659	0.304515	0.152258	−	0.988341i	$-0.451346\pi$
$79$	2.70659	0.304515	0.152258	+	0.988341i	$0.451346\pi$
$80$	−3.85153	−0.430614
$81$	12.6996	1.41107
$82$	−1.11717	−0.123371
$83$	−9.44859	−1.03712	−0.518559	−	0.855042i	$-0.673531\pi$
$83$	−9.44859	−1.03712	−0.518559	+	0.855042i	$0.673531\pi$
$84$	−15.1092	−1.64855
$85$	−25.1864	−2.73184
$86$	−9.85208	−1.06238
$87$	−17.4413	−1.86990
$88$	3.45164	0.367946
$89$	−9.78906	−1.03764	−0.518819	−	0.854884i	$-0.673628\pi$
$89$	−9.78906	−1.03764	−0.518819	+	0.854884i	$0.673628\pi$
$90$	24.6260	2.59581
$91$	−30.0833	−3.15359
$92$	−3.16538	−0.330014
$93$	−3.06494	−0.317819
$94$	0.756954	0.0780738
$95$	−32.7290	−3.35793
$96$	3.06494	0.312814
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−17.3018	−1.74774
$99$	−22.0692	−2.21804
$100$	9.83425	0.983425
$101$	7.11467	0.707936	0.353968	−	0.935257i	$-0.384832\pi$
$101$	7.11467	0.707936	0.353968	+	0.935257i	$0.384832\pi$
$102$	20.0426	1.98451
$103$	9.84037	0.969600	0.484800	−	0.874625i	$-0.338892\pi$
$103$	9.84037	0.969600	0.484800	+	0.874625i	$0.338892\pi$
$104$	6.10249	0.598398
$105$	58.1934	5.67909
$106$	2.41949	0.235002
$107$	11.8579	1.14635	0.573174	−	0.819434i	$-0.305712\pi$
$107$	11.8579	1.14635	0.573174	+	0.819434i	$0.305712\pi$
$108$	−10.4019	−1.00092
$109$	−8.87244	−0.849826	−0.424913	−	0.905234i	$-0.639695\pi$
$109$	−8.87244	−0.849826	−0.424913	+	0.905234i	$0.639695\pi$
$110$	−13.2941	−1.26754
$111$	16.7929	1.59391
$112$	4.92968	0.465811
$113$	−13.7167	−1.29036	−0.645179	−	0.764031i	$-0.723217\pi$
$113$	−13.7167	−1.29036	−0.645179	+	0.764031i	$0.723217\pi$
$114$	26.0449	2.43933
$115$	12.1916	1.13687
$116$	5.69058	0.528357
$117$	−39.0183	−3.60724
$118$	−7.49004	−0.689514
$119$	32.2368	2.95514
$120$	−11.8047	−1.07762
$121$	0.913839	0.0830763
$122$	−7.73982	−0.700730
$123$	−3.42405	−0.308736
$124$	1.00000	0.0898027
$125$	−18.6192	−1.66535
$126$	−31.5196	−2.80799
$127$	−14.0273	−1.24472	−0.622361	−	0.782730i	$-0.713826\pi$
$127$	−14.0273	−1.24472	−0.622361	+	0.782730i	$0.713826\pi$
$128$	−1.00000	−0.0883883
$129$	−30.1960	−2.65861
$130$	−23.5039	−2.06143
$131$	13.0631	1.14133	0.570663	−	0.821185i	$-0.306686\pi$
$131$	13.0631	1.14133	0.570663	+	0.821185i	$0.306686\pi$
$132$	10.5791	0.920790
$133$	41.8909	3.63240
$134$	−8.05727	−0.696042
$135$	40.0632	3.44809
$136$	−6.53932	−0.560742
$137$	−0.688229	−0.0587993	−0.0293997	−	0.999568i	$-0.509360\pi$
$137$	−0.688229	−0.0587993	−0.0293997	+	0.999568i	$0.509360\pi$
$138$	−9.70170	−0.825864
$139$	−1.00585	−0.0853151	−0.0426575	−	0.999090i	$-0.513582\pi$
$139$	−1.00585	−0.0853151	−0.0426575	+	0.999090i	$0.513582\pi$
$140$	−18.9868	−1.60468
$141$	2.32001	0.195380
$142$	2.20214	0.184799
$143$	21.0636	1.76143
$144$	6.39384	0.532820
$145$	−21.9174	−1.82014
$146$	−0.461049	−0.0381567
$147$	−53.0289	−4.37375
$148$	−5.47905	−0.450375
$149$	−21.4806	−1.75976	−0.879880	−	0.475196i	$-0.842377\pi$
$149$	−21.4806	−1.75976	−0.879880	+	0.475196i	$0.842377\pi$
$150$	30.1413	2.46103
$151$	4.74422	0.386080	0.193040	−	0.981191i	$-0.438165\pi$
$151$	4.74422	0.386080	0.193040	+	0.981191i	$0.438165\pi$
$152$	−8.49768	−0.689253
$153$	41.8113	3.38025
$154$	17.0155	1.37115
$155$	−3.85153	−0.309362
$156$	18.7037	1.49750
$157$	1.28853	0.102836	0.0514181	−	0.998677i	$-0.483626\pi$
$157$	1.28853	0.102836	0.0514181	+	0.998677i	$0.483626\pi$
$158$	−2.70659	−0.215325
$159$	7.41558	0.588094
$160$	3.85153	0.304490
$161$	−15.6043	−1.22979
$162$	−12.6996	−0.997778
$163$	−1.07987	−0.0845822	−0.0422911	−	0.999105i	$-0.513466\pi$
$163$	−1.07987	−0.0845822	−0.0422911	+	0.999105i	$0.513466\pi$
$164$	1.11717	0.0872362
$165$	−40.7455	−3.17204
$166$	9.44859	0.733353
$167$	−11.9576	−0.925310	−0.462655	−	0.886539i	$-0.653103\pi$
$167$	−11.9576	−0.925310	−0.462655	+	0.886539i	$0.653103\pi$
$168$	15.1092	1.16570
$169$	24.2403	1.86464
$170$	25.1864	1.93171
$171$	54.3328	4.15493
$172$	9.85208	0.751214
$173$	−5.76464	−0.438278	−0.219139	−	0.975694i	$-0.570325\pi$
$173$	−5.76464	−0.438278	−0.219139	+	0.975694i	$0.570325\pi$
$174$	17.4413	1.32222
$175$	48.4797	3.66472
$176$	−3.45164	−0.260177
$177$	−22.9565	−1.72552
$178$	9.78906	0.733721
$179$	−4.16277	−0.311140	−0.155570	−	0.987825i	$-0.549721\pi$
$179$	−4.16277	−0.311140	−0.155570	+	0.987825i	$0.549721\pi$
$180$	−24.6260	−1.83552
$181$	−24.3420	−1.80933	−0.904665	−	0.426124i	$-0.859879\pi$
$181$	−24.3420	−1.80933	−0.904665	+	0.426124i	$0.859879\pi$
$182$	30.0833	2.22992
$183$	−23.7220	−1.75358
$184$	3.16538	0.233355
$185$	21.1027	1.55150
$186$	3.06494	0.224732
$187$	−22.5714	−1.65058
$188$	−0.756954	−0.0552065
$189$	−51.2781	−3.72993
$190$	32.7290	2.37441
$191$	−9.56085	−0.691798	−0.345899	−	0.938272i	$-0.612426\pi$
$191$	−9.56085	−0.691798	−0.345899	+	0.938272i	$0.612426\pi$
$192$	−3.06494	−0.221193
$193$	−25.8174	−1.85838	−0.929188	−	0.369608i	$-0.879492\pi$
$193$	−25.8174	−1.85838	−0.929188	+	0.369608i	$0.879492\pi$
$194$	1.00000	0.0717958
$195$	−72.0379	−5.15874
$196$	17.3018	1.23584
$197$	24.7423	1.76282	0.881409	−	0.472353i	$-0.156595\pi$
$197$	24.7423	1.76282	0.881409	+	0.472353i	$0.156595\pi$
$198$	22.0692	1.56839
$199$	−13.2276	−0.937680	−0.468840	−	0.883283i	$-0.655328\pi$
$199$	−13.2276	−0.937680	−0.468840	+	0.883283i	$0.655328\pi$
$200$	−9.83425	−0.695386
$201$	−24.6950	−1.74185
$202$	−7.11467	−0.500587
$203$	28.0528	1.96892
$204$	−20.0426	−1.40326
$205$	−4.30280	−0.300521
$206$	−9.84037	−0.685611
$207$	−20.2390	−1.40670
$208$	−6.10249	−0.423131
$209$	−29.3310	−2.02887
$210$	−58.1934	−4.01572
$211$	−17.6484	−1.21496	−0.607482	−	0.794333i	$-0.707820\pi$
$211$	−17.6484	−1.21496	−0.607482	+	0.794333i	$0.707820\pi$
$212$	−2.41949	−0.166171
$213$	6.74942	0.462463
$214$	−11.8579	−0.810590
$215$	−37.9456	−2.58787
$216$	10.4019	0.707759
$217$	4.92968	0.334649
$218$	8.87244	0.600918
$219$	−1.41309	−0.0954875
$220$	13.2941	0.896287
$221$	−39.9061	−2.68438
$222$	−16.7929	−1.12707
$223$	15.7759	1.05643	0.528217	−	0.849109i	$-0.322861\pi$
$223$	15.7759	1.05643	0.528217	+	0.849109i	$0.322861\pi$
$224$	−4.92968	−0.329378
$225$	62.8786	4.19190
$226$	13.7167	0.912421
$227$	−11.4409	−0.759357	−0.379678	−	0.925119i	$-0.623965\pi$
$227$	−11.4409	−0.759357	−0.379678	+	0.925119i	$0.623965\pi$
$228$	−26.0449	−1.72486
$229$	0.784603	0.0518480	0.0259240	−	0.999664i	$-0.491747\pi$
$229$	0.784603	0.0518480	0.0259240	+	0.999664i	$0.491747\pi$
$230$	−12.1916	−0.803888
$231$	52.1515	3.43131
$232$	−5.69058	−0.373605
$233$	−4.50097	−0.294869	−0.147434	−	0.989072i	$-0.547101\pi$
$233$	−4.50097	−0.294869	−0.147434	+	0.989072i	$0.547101\pi$
$234$	39.0183	2.55071
$235$	2.91543	0.190181
$236$	7.49004	0.487560
$237$	−8.29552	−0.538852
$238$	−32.2368	−2.08960
$239$	16.3573	1.05807	0.529033	−	0.848601i	$-0.322555\pi$
$239$	16.3573	1.05807	0.529033	+	0.848601i	$0.322555\pi$
$240$	11.8047	0.761989
$241$	25.9433	1.67115	0.835577	−	0.549374i	$-0.185134\pi$
$241$	25.9433	1.67115	0.835577	+	0.549374i	$0.185134\pi$
$242$	−0.913839	−0.0587438
$243$	−7.71790	−0.495104
$244$	7.73982	0.495491
$245$	−66.6383	−4.25736
$246$	3.42405	0.218309
$247$	−51.8570	−3.29958
$248$	−1.00000	−0.0635001
$249$	28.9593	1.83522
$250$	18.6192	1.17758
$251$	21.7668	1.37391	0.686954	−	0.726701i	$-0.258947\pi$
$251$	21.7668	1.37391	0.686954	+	0.726701i	$0.258947\pi$
$252$	31.5196	1.98555
$253$	10.9258	0.686898
$254$	14.0273	0.880152
$255$	77.1946	4.83411
$256$	1.00000	0.0625000
$257$	5.92558	0.369627	0.184814	−	0.982774i	$-0.440832\pi$
$257$	5.92558	0.369627	0.184814	+	0.982774i	$0.440832\pi$
$258$	30.1960	1.87992
$259$	−27.0100	−1.67832
$260$	23.5039	1.45765
$261$	36.3847	2.25215
$262$	−13.0631	−0.807039
$263$	3.78360	0.233307	0.116653	−	0.993173i	$-0.462783\pi$
$263$	3.78360	0.233307	0.116653	+	0.993173i	$0.462783\pi$
$264$	−10.5791	−0.651097
$265$	9.31872	0.572445
$266$	−41.8909	−2.56850
$267$	30.0029	1.83615
$268$	8.05727	0.492176
$269$	16.9075	1.03087	0.515433	−	0.856930i	$-0.327631\pi$
$269$	16.9075	1.03087	0.515433	+	0.856930i	$0.327631\pi$
$270$	−40.0632	−2.43817
$271$	−25.7727	−1.56558	−0.782791	−	0.622285i	$-0.786204\pi$
$271$	−25.7727	−1.56558	−0.782791	+	0.622285i	$0.786204\pi$
$272$	6.53932	0.396505
$273$	92.2035	5.58041
$274$	0.688229	0.0415774
$275$	−33.9443	−2.04692
$276$	9.70170	0.583974
$277$	−12.0538	−0.724240	−0.362120	−	0.932132i	$-0.617947\pi$
$277$	−12.0538	−0.724240	−0.362120	+	0.932132i	$0.617947\pi$
$278$	1.00585	0.0603269
$279$	6.39384	0.382789
$280$	18.9868	1.13468
$281$	31.9518	1.90609	0.953043	−	0.302836i	$-0.0979335\pi$
$281$	31.9518	1.90609	0.953043	+	0.302836i	$0.0979335\pi$
$282$	−2.32001	−0.138155
$283$	0.514410	0.0305785	0.0152893	−	0.999883i	$-0.495133\pi$
$283$	0.514410	0.0305785	0.0152893	+	0.999883i	$0.495133\pi$
$284$	−2.20214	−0.130673
$285$	100.312	5.94200
$286$	−21.0636	−1.24552
$287$	5.50729	0.325085
$288$	−6.39384	−0.376760
$289$	25.7627	1.51545
$290$	21.9174	1.28704
$291$	3.06494	0.179670
$292$	0.461049	0.0269809
$293$	13.1595	0.768784	0.384392	−	0.923170i	$-0.374411\pi$
$293$	13.1595	0.768784	0.384392	+	0.923170i	$0.374411\pi$
$294$	53.0289	3.09271
$295$	−28.8481	−1.67960
$296$	5.47905	0.318463
$297$	35.9036	2.08334
$298$	21.4806	1.24434
$299$	19.3167	1.11711
$300$	−30.1413	−1.74021
$301$	48.5677	2.79939
$302$	−4.74422	−0.272999
$303$	−21.8060	−1.25272
$304$	8.49768	0.487376
$305$	−29.8101	−1.70692
$306$	−41.8113	−2.39020
$307$	11.3044	0.645178	0.322589	−	0.946539i	$-0.395447\pi$
$307$	11.3044	0.645178	0.322589	+	0.946539i	$0.395447\pi$
$308$	−17.0155	−0.969549
$309$	−30.1601	−1.71575
$310$	3.85153	0.218752
$311$	12.3209	0.698653	0.349326	−	0.937001i	$-0.386410\pi$
$311$	12.3209	0.698653	0.349326	+	0.937001i	$0.386410\pi$
$312$	−18.7037	−1.05889
$313$	−12.3292	−0.696887	−0.348444	−	0.937330i	$-0.613290\pi$
$313$	−12.3292	−0.696887	−0.348444	+	0.937330i	$0.613290\pi$
$314$	−1.28853	−0.0727161
$315$	−121.399	−6.84003
$316$	2.70659	0.152258
$317$	16.0172	0.899614	0.449807	−	0.893126i	$-0.351493\pi$
$317$	16.0172	0.899614	0.449807	+	0.893126i	$0.351493\pi$
$318$	−7.41558	−0.415845
$319$	−19.6419	−1.09973
$320$	−3.85153	−0.215307
$321$	−36.3437	−2.02851
$322$	15.6043	0.869596
$323$	55.5691	3.09195
$324$	12.6996	0.705535
$325$	−60.0134	−3.32894
$326$	1.07987	0.0598086
$327$	27.1935	1.50380
$328$	−1.11717	−0.0616853
$329$	−3.73154	−0.205727
$330$	40.7455	2.24297
$331$	6.36856	0.350048	0.175024	−	0.984564i	$-0.444000\pi$
$331$	6.36856	0.350048	0.175024	+	0.984564i	$0.444000\pi$
$332$	−9.44859	−0.518559
$333$	−35.0321	−1.91975
$334$	11.9576	0.654293
$335$	−31.0328	−1.69550
$336$	−15.1092	−0.824273
$337$	0.958455	0.0522104	0.0261052	−	0.999659i	$-0.491690\pi$
$337$	0.958455	0.0522104	0.0261052	+	0.999659i	$0.491690\pi$
$338$	−24.2403	−1.31850
$339$	42.0408	2.28334
$340$	−25.1864	−1.36592
$341$	−3.45164	−0.186917
$342$	−54.3328	−2.93798
$343$	50.7846	2.74211
$344$	−9.85208	−0.531189
$345$	−37.3664	−2.01174
$346$	5.76464	0.309909
$347$	−10.6459	−0.571502	−0.285751	−	0.958304i	$-0.592243\pi$
$347$	−10.6459	−0.571502	−0.285751	+	0.958304i	$0.592243\pi$
$348$	−17.4413	−0.934951
$349$	19.2901	1.03257	0.516287	−	0.856416i	$-0.327314\pi$
$349$	19.2901	1.03257	0.516287	+	0.856416i	$0.327314\pi$
$350$	−48.4797	−2.59135
$351$	63.4774	3.38817
$352$	3.45164	0.183973
$353$	13.7474	0.731700	0.365850	−	0.930674i	$-0.380778\pi$
$353$	13.7474	0.731700	0.365850	+	0.930674i	$0.380778\pi$
$354$	22.9565	1.22012
$355$	8.48160	0.450156
$356$	−9.78906	−0.518819
$357$	−98.8037	−5.22925
$358$	4.16277	0.220009
$359$	11.5214	0.608074	0.304037	−	0.952660i	$-0.401665\pi$
$359$	11.5214	0.608074	0.304037	+	0.952660i	$0.401665\pi$
$360$	24.6260	1.29791
$361$	53.2106	2.80056
$362$	24.3420	1.27939
$363$	−2.80086	−0.147007
$364$	−30.0833	−1.57679
$365$	−1.77574	−0.0929466
$366$	23.7220	1.23997
$367$	5.66668	0.295798	0.147899	−	0.989002i	$-0.452749\pi$
$367$	5.66668	0.295798	0.147899	+	0.989002i	$0.452749\pi$
$368$	−3.16538	−0.165007
$369$	7.14299	0.371849
$370$	−21.1027	−1.09708
$371$	−11.9273	−0.619235
$372$	−3.06494	−0.158910
$373$	4.30399	0.222852	0.111426	−	0.993773i	$-0.464458\pi$
$373$	4.30399	0.222852	0.111426	+	0.993773i	$0.464458\pi$
$374$	22.5714	1.16714
$375$	57.0667	2.94691
$376$	0.756954	0.0390369
$377$	−34.7267	−1.78852
$378$	51.2781	2.63746
$379$	−13.2956	−0.682951	−0.341476	−	0.939891i	$-0.610927\pi$
$379$	−13.2956	−0.682951	−0.341476	+	0.939891i	$0.610927\pi$
$380$	−32.7290	−1.67896
$381$	42.9928	2.20259
$382$	9.56085	0.489175
$383$	7.54467	0.385515	0.192757	−	0.981246i	$-0.438257\pi$
$383$	7.54467	0.385515	0.192757	+	0.981246i	$0.438257\pi$
$384$	3.06494	0.156407
$385$	65.5357	3.34001
$386$	25.8174	1.31407
$387$	62.9926	3.20209
$388$	−1.00000	−0.0507673
$389$	−4.71412	−0.239015	−0.119508	−	0.992833i	$-0.538132\pi$
$389$	−4.71412	−0.239015	−0.119508	+	0.992833i	$0.538132\pi$
$390$	72.0379	3.64778
$391$	−20.6995	−1.04682
$392$	−17.3018	−0.873872
$393$	−40.0375	−2.01962
$394$	−24.7423	−1.24650
$395$	−10.4245	−0.524513
$396$	−22.0692	−1.10902
$397$	23.2947	1.16913	0.584563	−	0.811348i	$-0.301266\pi$
$397$	23.2947	1.16913	0.584563	+	0.811348i	$0.301266\pi$
$398$	13.2276	0.663040
$399$	−128.393	−6.42769
$400$	9.83425	0.491712
$401$	−0.729241	−0.0364166	−0.0182083	−	0.999834i	$-0.505796\pi$
$401$	−0.729241	−0.0364166	−0.0182083	+	0.999834i	$0.505796\pi$
$402$	24.6950	1.23168
$403$	−6.10249	−0.303986
$404$	7.11467	0.353968
$405$	−48.9130	−2.43051
$406$	−28.0528	−1.39224
$407$	18.9117	0.937419
$408$	20.0426	0.992257
$409$	−14.5498	−0.719444	−0.359722	−	0.933060i	$-0.617128\pi$
$409$	−14.5498	−0.719444	−0.359722	+	0.933060i	$0.617128\pi$
$410$	4.30280	0.212500
$411$	2.10938	0.104048
$412$	9.84037	0.484800
$413$	36.9235	1.81689
$414$	20.2390	0.994690
$415$	36.3915	1.78639
$416$	6.10249	0.299199
$417$	3.08287	0.150969
$418$	29.3310	1.43462
$419$	4.06168	0.198426	0.0992131	−	0.995066i	$-0.468367\pi$
$419$	4.06168	0.198426	0.0992131	+	0.995066i	$0.468367\pi$
$420$	58.1934	2.83954
$421$	−2.07225	−0.100995	−0.0504976	−	0.998724i	$-0.516081\pi$
$421$	−2.07225	−0.100995	−0.0504976	+	0.998724i	$0.516081\pi$
$422$	17.6484	0.859110
$423$	−4.83984	−0.235321
$424$	2.41949	0.117501
$425$	64.3093	3.11946
$426$	−6.74942	−0.327010
$427$	38.1549	1.84644
$428$	11.8579	0.573174
$429$	−64.5586	−3.11692
$430$	37.9456	1.82990
$431$	9.82153	0.473086	0.236543	−	0.971621i	$-0.423986\pi$
$431$	9.82153	0.473086	0.236543	+	0.971621i	$0.423986\pi$
$432$	−10.4019	−0.500461
$433$	27.5060	1.32185	0.660927	−	0.750451i	$-0.270163\pi$
$433$	27.5060	1.32185	0.660927	+	0.750451i	$0.270163\pi$
$434$	−4.92968	−0.236632
$435$	67.1755	3.22082
$436$	−8.87244	−0.424913
$437$	−26.8984	−1.28673
$438$	1.41309	0.0675199
$439$	−5.01310	−0.239262	−0.119631	−	0.992818i	$-0.538171\pi$
$439$	−5.01310	−0.239262	−0.119631	+	0.992818i	$0.538171\pi$
$440$	−13.2941	−0.633771
$441$	110.625	5.26785
$442$	39.9061	1.89814
$443$	−21.7732	−1.03448	−0.517239	−	0.855841i	$-0.673040\pi$
$443$	−21.7732	−1.03448	−0.517239	+	0.855841i	$0.673040\pi$
$444$	16.7929	0.796957
$445$	37.7028	1.78729
$446$	−15.7759	−0.747012
$447$	65.8367	3.11397
$448$	4.92968	0.232906
$449$	24.5277	1.15753	0.578767	−	0.815493i	$-0.303534\pi$
$449$	24.5277	1.15753	0.578767	+	0.815493i	$0.303534\pi$
$450$	−62.8786	−2.96412
$451$	−3.85607	−0.181575
$452$	−13.7167	−0.645179
$453$	−14.5407	−0.683184
$454$	11.4409	0.536946
$455$	115.867	5.43191
$456$	26.0449	1.21966
$457$	6.44513	0.301490	0.150745	−	0.988573i	$-0.451833\pi$
$457$	6.44513	0.301490	0.150745	+	0.988573i	$0.451833\pi$
$458$	−0.784603	−0.0366621
$459$	−68.0213	−3.17496
$460$	12.1916	0.568434
$461$	2.73416	0.127343	0.0636713	−	0.997971i	$-0.479719\pi$
$461$	2.73416	0.127343	0.0636713	+	0.997971i	$0.479719\pi$
$462$	−52.1515	−2.42631
$463$	−33.1599	−1.54107	−0.770536	−	0.637397i	$-0.780011\pi$
$463$	−33.1599	−1.54107	−0.770536	+	0.637397i	$0.780011\pi$
$464$	5.69058	0.264179
$465$	11.8047	0.547429
$466$	4.50097	0.208504
$467$	6.23132	0.288351	0.144176	−	0.989552i	$-0.453947\pi$
$467$	6.23132	0.288351	0.144176	+	0.989552i	$0.453947\pi$
$468$	−39.0183	−1.80362
$469$	39.7198	1.83409
$470$	−2.91543	−0.134479
$471$	−3.94927	−0.181973
$472$	−7.49004	−0.344757
$473$	−34.0059	−1.56359
$474$	8.29552	0.381026
$475$	83.5683	3.83438
$476$	32.2368	1.47757
$477$	−15.4698	−0.708314
$478$	−16.3573	−0.748165
$479$	41.7125	1.90589	0.952947	−	0.303138i	$-0.0980343\pi$
$479$	41.7125	1.90589	0.952947	+	0.303138i	$0.0980343\pi$
$480$	−11.8047	−0.538808
$481$	33.4358	1.52454
$482$	−25.9433	−1.18168
$483$	47.8263	2.17617
$484$	0.913839	0.0415382
$485$	3.85153	0.174889
$486$	7.71790	0.350091
$487$	−15.0217	−0.680697	−0.340349	−	0.940299i	$-0.610545\pi$
$487$	−15.0217	−0.680697	−0.340349	+	0.940299i	$0.610545\pi$
$488$	−7.73982	−0.350365
$489$	3.30974	0.149672
$490$	66.6383	3.01041
$491$	−15.8436	−0.715011	−0.357506	−	0.933911i	$-0.616373\pi$
$491$	−15.8436	−0.715011	−0.357506	+	0.933911i	$0.616373\pi$
$492$	−3.42405	−0.154368
$493$	37.2125	1.67597
$494$	51.8570	2.33316
$495$	85.0002	3.82048
$496$	1.00000	0.0449013
$497$	−10.8559	−0.486952
$498$	−28.9593	−1.29770
$499$	29.8519	1.33635	0.668177	−	0.744003i	$-0.267075\pi$
$499$	29.8519	1.33635	0.668177	+	0.744003i	$0.267075\pi$
$500$	−18.6192	−0.832677
$501$	36.6494	1.63737
$502$	−21.7668	−0.971499
$503$	−44.4572	−1.98225	−0.991124	−	0.132938i	$-0.957559\pi$
$503$	−44.4572	−1.98225	−0.991124	+	0.132938i	$0.957559\pi$
$504$	−31.5196	−1.40399
$505$	−27.4023	−1.21939
$506$	−10.9258	−0.485710
$507$	−74.2951	−3.29956
$508$	−14.0273	−0.622361
$509$	−19.0738	−0.845432	−0.422716	−	0.906262i	$-0.638923\pi$
$509$	−19.0738	−0.845432	−0.422716	+	0.906262i	$0.638923\pi$
$510$	−77.1946	−3.41823
$511$	2.27283	0.100544
$512$	−1.00000	−0.0441942
$513$	−88.3920	−3.90260
$514$	−5.92558	−0.261366
$515$	−37.9004	−1.67009
$516$	−30.1960	−1.32931
$517$	2.61273	0.114908
$518$	27.0100	1.18675
$519$	17.6683	0.775551
$520$	−23.5039	−1.03071
$521$	−7.84383	−0.343644	−0.171822	−	0.985128i	$-0.554965\pi$
$521$	−7.84383	−0.343644	−0.171822	+	0.985128i	$0.554965\pi$
$522$	−36.3847	−1.59251
$523$	4.79400	0.209627	0.104814	−	0.994492i	$-0.466575\pi$
$523$	4.79400	0.209627	0.104814	+	0.994492i	$0.466575\pi$
$524$	13.0631	0.570663
$525$	−148.587	−6.48488
$526$	−3.78360	−0.164973
$527$	6.53932	0.284857
$528$	10.5791	0.460395
$529$	−12.9803	−0.564363
$530$	−9.31872	−0.404779
$531$	47.8901	2.07825
$532$	41.8909	1.81620
$533$	−6.81750	−0.295299
$534$	−30.0029	−1.29835
$535$	−45.6710	−1.97453
$536$	−8.05727	−0.348021
$537$	12.7586	0.550575
$538$	−16.9075	−0.728932
$539$	−59.7196	−2.57231
$540$	40.0632	1.72404
$541$	1.51103	0.0649641	0.0324821	−	0.999472i	$-0.489659\pi$
$541$	1.51103	0.0649641	0.0324821	+	0.999472i	$0.489659\pi$
$542$	25.7727	1.10703
$543$	74.6068	3.20169
$544$	−6.53932	−0.280371
$545$	34.1724	1.46379
$546$	−92.2035	−3.94595
$547$	22.4491	0.959856	0.479928	−	0.877308i	$-0.340663\pi$
$547$	22.4491	0.959856	0.479928	+	0.877308i	$0.340663\pi$
$548$	−0.688229	−0.0293997
$549$	49.4871	2.11206
$550$	33.9443	1.44739
$551$	48.3568	2.06007
$552$	−9.70170	−0.412932
$553$	13.3426	0.567386
$554$	12.0538	0.512115
$555$	−64.6784	−2.74544
$556$	−1.00585	−0.0426575
$557$	2.05183	0.0869390	0.0434695	−	0.999055i	$-0.486159\pi$
$557$	2.05183	0.0869390	0.0434695	+	0.999055i	$0.486159\pi$
$558$	−6.39384	−0.270673
$559$	−60.1222	−2.54290
$560$	−18.9868	−0.802339
$561$	69.1799	2.92078
$562$	−31.9518	−1.34781
$563$	−6.47015	−0.272684	−0.136342	−	0.990662i	$-0.543535\pi$
$563$	−6.47015	−0.272684	−0.136342	+	0.990662i	$0.543535\pi$
$564$	2.32001	0.0976902
$565$	52.8302	2.22258
$566$	−0.514410	−0.0216223
$567$	62.6052	2.62917
$568$	2.20214	0.0923997
$569$	8.92701	0.374240	0.187120	−	0.982337i	$-0.440085\pi$
$569$	8.92701	0.374240	0.187120	+	0.982337i	$0.440085\pi$
$570$	−100.312	−4.20163
$571$	37.2968	1.56082	0.780411	−	0.625267i	$-0.215010\pi$
$571$	37.2968	1.56082	0.780411	+	0.625267i	$0.215010\pi$
$572$	21.0636	0.880713
$573$	29.3034	1.22417
$574$	−5.50729	−0.229870
$575$	−31.1292	−1.29818
$576$	6.39384	0.266410
$577$	29.5410	1.22981	0.614904	−	0.788602i	$-0.289195\pi$
$577$	29.5410	1.22981	0.614904	+	0.788602i	$0.289195\pi$
$578$	−25.7627	−1.07159
$579$	79.1286	3.28847
$580$	−21.9174	−0.910072
$581$	−46.5786	−1.93240
$582$	−3.06494	−0.127046
$583$	8.35121	0.345872
$584$	−0.461049	−0.0190784
$585$	150.280	6.21331
$586$	−13.1595	−0.543613
$587$	−13.4671	−0.555848	−0.277924	−	0.960603i	$-0.589646\pi$
$587$	−13.4671	−0.555848	−0.277924	+	0.960603i	$0.589646\pi$
$588$	−53.0289	−2.18687
$589$	8.49768	0.350141
$590$	28.8481	1.18766
$591$	−75.8337	−3.11938
$592$	−5.47905	−0.225187
$593$	10.3903	0.426678	0.213339	−	0.976978i	$-0.431566\pi$
$593$	10.3903	0.426678	0.213339	+	0.976978i	$0.431566\pi$
$594$	−35.9036	−1.47314
$595$	−124.161	−5.09010
$596$	−21.4806	−0.879880
$597$	40.5417	1.65926
$598$	−19.3167	−0.789919
$599$	−41.8874	−1.71147	−0.855737	−	0.517411i	$-0.826896\pi$
$599$	−41.8874	−1.71147	−0.855737	+	0.517411i	$0.826896\pi$
$600$	30.1413	1.23052
$601$	18.0075	0.734541	0.367270	−	0.930114i	$-0.380292\pi$
$601$	18.0075	0.734541	0.367270	+	0.930114i	$0.380292\pi$
$602$	−48.5677	−1.97947
$603$	51.5169	2.09793
$604$	4.74422	0.193040
$605$	−3.51968	−0.143095
$606$	21.8060	0.885809
$607$	−36.3832	−1.47675	−0.738373	−	0.674392i	$-0.764406\pi$
$607$	−36.3832	−1.47675	−0.738373	+	0.674392i	$0.764406\pi$
$608$	−8.49768	−0.344627
$609$	−85.9800	−3.48409
$610$	29.8101	1.20698
$611$	4.61930	0.186877
$612$	41.8113	1.69012
$613$	−8.03632	−0.324584	−0.162292	−	0.986743i	$-0.551889\pi$
$613$	−8.03632	−0.324584	−0.162292	+	0.986743i	$0.551889\pi$
$614$	−11.3044	−0.456210
$615$	13.1878	0.531784
$616$	17.0155	0.685574
$617$	21.8111	0.878080	0.439040	−	0.898467i	$-0.355319\pi$
$617$	21.8111	0.878080	0.439040	+	0.898467i	$0.355319\pi$
$618$	30.1601	1.21322
$619$	−21.2779	−0.855230	−0.427615	−	0.903961i	$-0.640646\pi$
$619$	−21.2779	−0.855230	−0.427615	+	0.903961i	$0.640646\pi$
$620$	−3.85153	−0.154681
$621$	32.9260	1.32127
$622$	−12.3209	−0.494022
$623$	−48.2570	−1.93338
$624$	18.7037	0.748749
$625$	22.5412	0.901647
$626$	12.3292	0.492774
$627$	89.8976	3.59016
$628$	1.28853	0.0514181
$629$	−35.8292	−1.42861
$630$	121.399	4.83663
$631$	32.7789	1.30491	0.652454	−	0.757828i	$-0.273739\pi$
$631$	32.7789	1.30491	0.652454	+	0.757828i	$0.273739\pi$
$632$	−2.70659	−0.107662
$633$	54.0912	2.14993
$634$	−16.0172	−0.636123
$635$	54.0265	2.14398
$636$	7.41558	0.294047
$637$	−105.584	−4.18339
$638$	19.6419	0.777629
$639$	−14.0801	−0.557001
$640$	3.85153	0.152245
$641$	−29.3567	−1.15952	−0.579761	−	0.814787i	$-0.696854\pi$
$641$	−29.3567	−1.15952	−0.579761	+	0.814787i	$0.696854\pi$
$642$	36.3437	1.43437
$643$	5.35967	0.211365	0.105682	−	0.994400i	$-0.466297\pi$
$643$	5.35967	0.211365	0.105682	+	0.994400i	$0.466297\pi$
$644$	−15.6043	−0.614897
$645$	116.301	4.57934
$646$	−55.5691	−2.18634
$647$	−36.8941	−1.45046	−0.725228	−	0.688509i	$-0.758266\pi$
$647$	−36.8941	−1.45046	−0.725228	+	0.688509i	$0.758266\pi$
$648$	−12.6996	−0.498889
$649$	−25.8529	−1.01482
$650$	60.0134	2.35392
$651$	−15.1092	−0.592175
$652$	−1.07987	−0.0422911
$653$	−30.5364	−1.19498	−0.597490	−	0.801876i	$-0.703835\pi$
$653$	−30.5364	−1.19498	−0.597490	+	0.801876i	$0.703835\pi$
$654$	−27.1935	−1.06335
$655$	−50.3127	−1.96588
$656$	1.11717	0.0436181
$657$	2.94787	0.115007
$658$	3.73154	0.145471
$659$	−13.6494	−0.531706	−0.265853	−	0.964014i	$-0.585654\pi$
$659$	−13.6494	−0.531706	−0.265853	+	0.964014i	$0.585654\pi$
$660$	−40.7455	−1.58602
$661$	11.2389	0.437142	0.218571	−	0.975821i	$-0.429860\pi$
$661$	11.2389	0.437142	0.218571	+	0.975821i	$0.429860\pi$
$662$	−6.36856	−0.247521
$663$	122.310	4.75012
$664$	9.44859	0.366676
$665$	−161.344	−6.25665
$666$	35.0321	1.35747
$667$	−18.0129	−0.697462
$668$	−11.9576	−0.462655
$669$	−48.3522	−1.86941
$670$	31.0328	1.19890
$671$	−26.7151	−1.03132
$672$	15.1092	0.582849
$673$	34.2904	1.32180	0.660898	−	0.750476i	$-0.270176\pi$
$673$	34.2904	1.32180	0.660898	+	0.750476i	$0.270176\pi$
$674$	−0.958455	−0.0369183
$675$	−102.295	−3.93733
$676$	24.2403	0.932320
$677$	−15.2058	−0.584407	−0.292204	−	0.956356i	$-0.594389\pi$
$677$	−15.2058	−0.584407	−0.292204	+	0.956356i	$0.594389\pi$
$678$	−42.0408	−1.61457
$679$	−4.92968	−0.189184
$680$	25.1864	0.965853
$681$	35.0655	1.34371
$682$	3.45164	0.132170
$683$	8.80456	0.336897	0.168449	−	0.985710i	$-0.446124\pi$
$683$	8.80456	0.336897	0.168449	+	0.985710i	$0.446124\pi$
$684$	54.3328	2.07747
$685$	2.65073	0.101279
$686$	−50.7846	−1.93896
$687$	−2.40476	−0.0917472
$688$	9.85208	0.375607
$689$	14.7649	0.562498
$690$	37.3664	1.42251
$691$	31.3645	1.19316	0.596581	−	0.802553i	$-0.296525\pi$
$691$	31.3645	1.19316	0.596581	+	0.802553i	$0.296525\pi$
$692$	−5.76464	−0.219139
$693$	−108.794	−4.13276
$694$	10.6459	0.404113
$695$	3.87406	0.146951
$696$	17.4413	0.661110
$697$	7.30552	0.276716
$698$	−19.2901	−0.730140
$699$	13.7952	0.521782
$700$	48.4797	1.83236
$701$	−20.9775	−0.792310	−0.396155	−	0.918184i	$-0.629656\pi$
$701$	−20.9775	−0.792310	−0.396155	+	0.918184i	$0.629656\pi$
$702$	−63.4774	−2.39580
$703$	−46.5592	−1.75601
$704$	−3.45164	−0.130089
$705$	−8.93560	−0.336534
$706$	−13.7474	−0.517390
$707$	35.0731	1.31906
$708$	−22.9565	−0.862758
$709$	4.57551	0.171837	0.0859184	−	0.996302i	$-0.472618\pi$
$709$	4.57551	0.171837	0.0859184	+	0.996302i	$0.472618\pi$
$710$	−8.48160	−0.318309
$711$	17.3055	0.649006
$712$	9.78906	0.366861
$713$	−3.16538	−0.118545
$714$	98.8037	3.69764
$715$	−81.1270	−3.03398
$716$	−4.16277	−0.155570
$717$	−50.1341	−1.87229
$718$	−11.5214	−0.429973
$719$	4.67915	0.174503	0.0872515	−	0.996186i	$-0.472192\pi$
$719$	4.67915	0.174503	0.0872515	+	0.996186i	$0.472192\pi$
$720$	−24.6260	−0.917758
$721$	48.5099	1.80660
$722$	−53.2106	−1.98030
$723$	−79.5145	−2.95718
$724$	−24.3420	−0.904665
$725$	55.9626	2.07840
$726$	2.80086	0.103950
$727$	−40.4336	−1.49960	−0.749799	−	0.661665i	$-0.769850\pi$
$727$	−40.4336	−1.49960	−0.749799	+	0.661665i	$0.769850\pi$
$728$	30.0833	1.11496
$729$	−14.4440	−0.534964
$730$	1.77574	0.0657232
$731$	64.4259	2.38288
$732$	−23.7220	−0.876792
$733$	39.2728	1.45058	0.725288	−	0.688446i	$-0.241707\pi$
$733$	39.2728	1.45058	0.725288	+	0.688446i	$0.241707\pi$
$734$	−5.66668	−0.209161
$735$	204.242	7.53358
$736$	3.16538	0.116678
$737$	−27.8108	−1.02443
$738$	−7.14299	−0.262937
$739$	−23.2769	−0.856256	−0.428128	−	0.903718i	$-0.640827\pi$
$739$	−23.2769	−0.856256	−0.428128	+	0.903718i	$0.640827\pi$
$740$	21.1027	0.775750
$741$	158.938	5.83875
$742$	11.9273	0.437866
$743$	−13.3609	−0.490166	−0.245083	−	0.969502i	$-0.578815\pi$
$743$	−13.3609	−0.490166	−0.245083	+	0.969502i	$0.578815\pi$
$744$	3.06494	0.112366
$745$	82.7331	3.03111
$746$	−4.30399	−0.157580
$747$	−60.4127	−2.21039
$748$	−22.5714	−0.825292
$749$	58.4558	2.13593
$750$	−57.0667	−2.08378
$751$	20.1213	0.734238	0.367119	−	0.930174i	$-0.380344\pi$
$751$	20.1213	0.734238	0.367119	+	0.930174i	$0.380344\pi$
$752$	−0.756954	−0.0276033
$753$	−66.7138	−2.43119
$754$	34.7267	1.26467
$755$	−18.2725	−0.665004
$756$	−51.2781	−1.86496
$757$	−7.40415	−0.269108	−0.134554	−	0.990906i	$-0.542960\pi$
$757$	−7.40415	−0.269108	−0.134554	+	0.990906i	$0.542960\pi$
$758$	13.2956	0.482919
$759$	−33.4868	−1.21549
$760$	32.7290	1.18721
$761$	49.4935	1.79414	0.897068	−	0.441892i	$-0.145693\pi$
$761$	49.4935	1.79414	0.897068	+	0.441892i	$0.145693\pi$
$762$	−42.9928	−1.55747
$763$	−43.7384	−1.58343
$764$	−9.56085	−0.345899
$765$	−161.037	−5.82232
$766$	−7.54467	−0.272600
$767$	−45.7079	−1.65042
$768$	−3.06494	−0.110596
$769$	32.7532	1.18111	0.590555	−	0.806997i	$-0.298909\pi$
$769$	32.7532	1.18111	0.590555	+	0.806997i	$0.298909\pi$
$770$	−65.5357	−2.36174
$771$	−18.1615	−0.654071
$772$	−25.8174	−0.929188
$773$	29.5440	1.06262	0.531312	−	0.847176i	$-0.321699\pi$
$773$	29.5440	1.06262	0.531312	+	0.847176i	$0.321699\pi$
$774$	−62.9926	−2.26422
$775$	9.83425	0.353257
$776$	1.00000	0.0358979
$777$	82.7838	2.96985
$778$	4.71412	0.169009
$779$	9.49334	0.340134
$780$	−72.0379	−2.57937
$781$	7.60100	0.271985
$782$	20.6995	0.740211
$783$	−59.1929	−2.11538
$784$	17.3018	0.617921
$785$	−4.96282	−0.177131
$786$	40.0375	1.42809
$787$	−20.4713	−0.729722	−0.364861	−	0.931062i	$-0.618884\pi$
$787$	−20.4713	−0.729722	−0.364861	+	0.931062i	$0.618884\pi$
$788$	24.7423	0.881409
$789$	−11.5965	−0.412846
$790$	10.4245	0.370887
$791$	−67.6190	−2.40426
$792$	22.0692	0.784196
$793$	−47.2321	−1.67726
$794$	−23.2947	−0.826697
$795$	−28.5613	−1.01296
$796$	−13.2276	−0.468840
$797$	−25.7837	−0.913306	−0.456653	−	0.889645i	$-0.650952\pi$
$797$	−25.7837	−0.913306	−0.456653	+	0.889645i	$0.650952\pi$
$798$	128.393	4.54506
$799$	−4.94996	−0.175117
$800$	−9.83425	−0.347693
$801$	−62.5897	−2.21150
$802$	0.729241	0.0257504
$803$	−1.59138	−0.0561585
$804$	−24.6950	−0.870927
$805$	60.1005	2.11827
$806$	6.10249	0.214951
$807$	−51.8203	−1.82416
$808$	−7.11467	−0.250293
$809$	−31.9718	−1.12407	−0.562035	−	0.827113i	$-0.689981\pi$
$809$	−31.9718	−1.12407	−0.562035	+	0.827113i	$0.689981\pi$
$810$	48.9130	1.71863
$811$	−26.8633	−0.943298	−0.471649	−	0.881786i	$-0.656341\pi$
$811$	−26.8633	−0.943298	−0.471649	+	0.881786i	$0.656341\pi$
$812$	28.0528	0.984460
$813$	78.9917	2.77036
$814$	−18.9117	−0.662855
$815$	4.15916	0.145689
$816$	−20.0426	−0.701631
$817$	83.7199	2.92899
$818$	14.5498	0.508723
$819$	−192.348	−6.72118
$820$	−4.30280	−0.150260
$821$	22.6682	0.791126	0.395563	−	0.918439i	$-0.370550\pi$
$821$	22.6682	0.791126	0.395563	+	0.918439i	$0.370550\pi$
$822$	−2.10938	−0.0735730
$823$	7.53022	0.262487	0.131243	−	0.991350i	$-0.458103\pi$
$823$	7.53022	0.262487	0.131243	+	0.991350i	$0.458103\pi$
$824$	−9.84037	−0.342806
$825$	104.037	3.62211
$826$	−36.9235	−1.28473
$827$	−32.3407	−1.12460	−0.562298	−	0.826935i	$-0.690082\pi$
$827$	−32.3407	−1.12460	−0.562298	+	0.826935i	$0.690082\pi$
$828$	−20.2390	−0.703352
$829$	30.0634	1.04414	0.522072	−	0.852902i	$-0.325159\pi$
$829$	30.0634	1.04414	0.522072	+	0.852902i	$0.325159\pi$
$830$	−36.3915	−1.26317
$831$	36.9440	1.28157
$832$	−6.10249	−0.211566
$833$	113.142	3.92014
$834$	−3.08287	−0.106751
$835$	46.0551	1.59380
$836$	−29.3310	−1.01443
$837$	−10.4019	−0.359542
$838$	−4.06168	−0.140309
$839$	23.7109	0.818590	0.409295	−	0.912402i	$-0.365775\pi$
$839$	23.7109	0.818590	0.409295	+	0.912402i	$0.365775\pi$
$840$	−58.1934	−2.00786
$841$	3.38274	0.116646
$842$	2.07225	0.0714144
$843$	−97.9303	−3.37290
$844$	−17.6484	−0.607482
$845$	−93.3623	−3.21176
$846$	4.83984	0.166397
$847$	4.50494	0.154792
$848$	−2.41949	−0.0830856
$849$	−1.57664	−0.0541100
$850$	−64.3093	−2.20579
$851$	17.3433	0.594520
$852$	6.74942	0.231231
$853$	54.5881	1.86906	0.934531	−	0.355881i	$-0.115819\pi$
$853$	54.5881	1.86906	0.934531	+	0.355881i	$0.115819\pi$
$854$	−38.1549	−1.30563
$855$	−209.264	−7.15668
$856$	−11.8579	−0.405295
$857$	−24.9172	−0.851154	−0.425577	−	0.904922i	$-0.639929\pi$
$857$	−24.9172	−0.851154	−0.425577	+	0.904922i	$0.639929\pi$
$858$	64.5586	2.20399
$859$	32.4115	1.10587	0.552933	−	0.833226i	$-0.313508\pi$
$859$	32.4115	1.10587	0.552933	+	0.833226i	$0.313508\pi$
$860$	−37.9456	−1.29393
$861$	−16.8795	−0.575251
$862$	−9.82153	−0.334523
$863$	24.2122	0.824192	0.412096	−	0.911140i	$-0.364797\pi$
$863$	24.2122	0.824192	0.412096	+	0.911140i	$0.364797\pi$
$864$	10.4019	0.353880
$865$	22.2027	0.754913
$866$	−27.5060	−0.934691
$867$	−78.9611	−2.68166
$868$	4.92968	0.167324
$869$	−9.34218	−0.316912
$870$	−67.1755	−2.27746
$871$	−49.1694	−1.66604
$872$	8.87244	0.300459
$873$	−6.39384	−0.216399
$874$	26.8984	0.909853
$875$	−91.7869	−3.10296
$876$	−1.41309	−0.0477438
$877$	−31.3672	−1.05920	−0.529598	−	0.848249i	$-0.677657\pi$
$877$	−31.3672	−1.05920	−0.529598	+	0.848249i	$0.677657\pi$
$878$	5.01310	0.169184
$879$	−40.3329	−1.36040
$880$	13.2941	0.448144
$881$	12.2149	0.411531	0.205765	−	0.978601i	$-0.434032\pi$
$881$	12.2149	0.411531	0.205765	+	0.978601i	$0.434032\pi$
$882$	−110.625	−3.72493
$883$	−30.9959	−1.04309	−0.521547	−	0.853222i	$-0.674645\pi$
$883$	−30.9959	−1.04309	−0.521547	+	0.853222i	$0.674645\pi$
$884$	−39.9061	−1.34219
$885$	88.4175	2.97212
$886$	21.7732	0.731487
$887$	12.7701	0.428778	0.214389	−	0.976748i	$-0.431224\pi$
$887$	12.7701	0.428778	0.214389	+	0.976748i	$0.431224\pi$
$888$	−16.7929	−0.563534
$889$	−69.1502	−2.31922
$890$	−37.7028	−1.26380
$891$	−43.8346	−1.46851
$892$	15.7759	0.528217
$893$	−6.43235	−0.215250
$894$	−65.8367	−2.20191
$895$	16.0330	0.535925
$896$	−4.92968	−0.164689
$897$	−59.2045	−1.97678
$898$	−24.5277	−0.818501
$899$	5.69058	0.189792
$900$	62.8786	2.09595
$901$	−15.8218	−0.527101
$902$	3.85607	0.128393
$903$	−148.857	−4.95364
$904$	13.7167	0.456211
$905$	93.7540	3.11649
$906$	14.5407	0.483084
$907$	−22.7671	−0.755969	−0.377985	−	0.925812i	$-0.623383\pi$
$907$	−22.7671	−0.755969	−0.377985	+	0.925812i	$0.623383\pi$
$908$	−11.4409	−0.379678
$909$	45.4901	1.50881
$910$	−115.867	−3.84094
$911$	−40.7619	−1.35050	−0.675251	−	0.737588i	$-0.735965\pi$
$911$	−40.7619	−1.35050	−0.675251	+	0.737588i	$0.735965\pi$
$912$	−26.0449	−0.862432
$913$	32.6132	1.07934
$914$	−6.44513	−0.213186
$915$	91.3661	3.02047
$916$	0.784603	0.0259240
$917$	64.3968	2.12657
$918$	68.0213	2.24504
$919$	−52.2486	−1.72352	−0.861761	−	0.507314i	$-0.830638\pi$
$919$	−52.2486	−1.72352	−0.861761	+	0.507314i	$0.830638\pi$
$920$	−12.1916	−0.401944
$921$	−34.6474	−1.14167
$922$	−2.73416	−0.0900449
$923$	13.4385	0.442335
$924$	52.1515	1.71566
$925$	−53.8823	−1.77164
$926$	33.1599	1.08970
$927$	62.9177	2.06649
$928$	−5.69058	−0.186803
$929$	35.1136	1.15204	0.576021	−	0.817435i	$-0.304605\pi$
$929$	35.1136	1.15204	0.576021	+	0.817435i	$0.304605\pi$
$930$	−11.8047	−0.387091
$931$	147.025	4.81856
$932$	−4.50097	−0.147434
$933$	−37.7627	−1.23630
$934$	−6.23132	−0.203895
$935$	86.9343	2.84306
$936$	39.0183	1.27535
$937$	25.4220	0.830501	0.415251	−	0.909707i	$-0.363694\pi$
$937$	25.4220	0.830501	0.415251	+	0.909707i	$0.363694\pi$
$938$	−39.7198	−1.29690
$939$	37.7882	1.23317
$940$	2.91543	0.0950907
$941$	−30.8244	−1.00485	−0.502423	−	0.864622i	$-0.667558\pi$
$941$	−30.8244	−1.00485	−0.502423	+	0.864622i	$0.667558\pi$
$942$	3.94927	0.128674
$943$	−3.53627	−0.115157
$944$	7.49004	0.243780
$945$	197.499	6.42463
$946$	34.0059	1.10563
$947$	−12.7920	−0.415685	−0.207842	−	0.978162i	$-0.566644\pi$
$947$	−12.7920	−0.415685	−0.207842	+	0.978162i	$0.566644\pi$
$948$	−8.29552	−0.269426
$949$	−2.81355	−0.0913316
$950$	−83.5683	−2.71131
$951$	−49.0916	−1.59190
$952$	−32.2368	−1.04480
$953$	43.9278	1.42296	0.711480	−	0.702706i	$-0.248025\pi$
$953$	43.9278	1.42296	0.711480	+	0.702706i	$0.248025\pi$
$954$	15.4698	0.500854
$955$	36.8238	1.19159
$956$	16.3573	0.529033
$957$	60.2011	1.94602
$958$	−41.7125	−1.34767
$959$	−3.39275	−0.109558
$960$	11.8047	0.380994
$961$	1.00000	0.0322581
$962$	−33.4358	−1.07801
$963$	75.8175	2.44319
$964$	25.9433	0.835577
$965$	99.4363	3.20097
$966$	−47.8263	−1.53879
$967$	31.7200	1.02004	0.510022	−	0.860161i	$-0.329637\pi$
$967$	31.7200	1.02004	0.510022	+	0.860161i	$0.329637\pi$
$968$	−0.913839	−0.0293719
$969$	−170.316	−5.47133
$970$	−3.85153	−0.123665
$971$	31.3881	1.00729	0.503646	−	0.863910i	$-0.331992\pi$
$971$	31.3881	1.00729	0.503646	+	0.863910i	$0.331992\pi$
$972$	−7.71790	−0.247552
$973$	−4.95852	−0.158963
$974$	15.0217	0.481326
$975$	183.937	5.89070
$976$	7.73982	0.247746
$977$	−5.61256	−0.179562	−0.0897808	−	0.995962i	$-0.528617\pi$
$977$	−5.61256	−0.179562	−0.0897808	+	0.995962i	$0.528617\pi$
$978$	−3.30974	−0.105834
$979$	33.7884	1.07988
$980$	−66.6383	−2.12868
$981$	−56.7290	−1.81122
$982$	15.8436	0.505589
$983$	−24.6529	−0.786307	−0.393153	−	0.919473i	$-0.628616\pi$
$983$	−24.6529	−0.786307	−0.393153	+	0.919473i	$0.628616\pi$
$984$	3.42405	0.109155
$985$	−95.2958	−3.03638
$986$	−37.2125	−1.18509
$987$	11.4369	0.364042
$988$	−51.8570	−1.64979
$989$	−31.1856	−0.991645
$990$	−85.0002	−2.70148
$991$	−40.9673	−1.30137	−0.650685	−	0.759348i	$-0.725518\pi$
$991$	−40.9673	−1.30137	−0.650685	+	0.759348i	$0.725518\pi$
$992$	−1.00000	−0.0317500
$993$	−19.5192	−0.619424
$994$	10.8559	0.344327
$995$	50.9464	1.61511
$996$	28.9593	0.917612
$997$	26.8612	0.850703	0.425351	−	0.905028i	$-0.360151\pi$
$997$	26.8612	0.850703	0.425351	+	0.905028i	$0.360151\pi$
$998$	−29.8519	−0.944944
$999$	56.9925	1.80316

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.l.1.4	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.l.1.4	✓	38	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.06494 q^{3} +1.00000 q^{4} -3.85153 q^{5} +3.06494 q^{6} +4.92968 q^{7} -1.00000 q^{8} +6.39384 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.06494 q^{3} +1.00000 q^{4} -3.85153 q^{5} +3.06494 q^{6} +4.92968 q^{7} -1.00000 q^{8} +6.39384 q^{9} +3.85153 q^{10} -3.45164 q^{11} -3.06494 q^{12} -6.10249 q^{13} -4.92968 q^{14} +11.8047 q^{15} +1.00000 q^{16} +6.53932 q^{17} -6.39384 q^{18} +8.49768 q^{19} -3.85153 q^{20} -15.1092 q^{21} +3.45164 q^{22} -3.16538 q^{23} +3.06494 q^{24} +9.83425 q^{25} +6.10249 q^{26} -10.4019 q^{27} +4.92968 q^{28} +5.69058 q^{29} -11.8047 q^{30} +1.00000 q^{31} -1.00000 q^{32} +10.5791 q^{33} -6.53932 q^{34} -18.9868 q^{35} +6.39384 q^{36} -5.47905 q^{37} -8.49768 q^{38} +18.7037 q^{39} +3.85153 q^{40} +1.11717 q^{41} +15.1092 q^{42} +9.85208 q^{43} -3.45164 q^{44} -24.6260 q^{45} +3.16538 q^{46} -0.756954 q^{47} -3.06494 q^{48} +17.3018 q^{49} -9.83425 q^{50} -20.0426 q^{51} -6.10249 q^{52} -2.41949 q^{53} +10.4019 q^{54} +13.2941 q^{55} -4.92968 q^{56} -26.0449 q^{57} -5.69058 q^{58} +7.49004 q^{59} +11.8047 q^{60} +7.73982 q^{61} -1.00000 q^{62} +31.5196 q^{63} +1.00000 q^{64} +23.5039 q^{65} -10.5791 q^{66} +8.05727 q^{67} +6.53932 q^{68} +9.70170 q^{69} +18.9868 q^{70} -2.20214 q^{71} -6.39384 q^{72} +0.461049 q^{73} +5.47905 q^{74} -30.1413 q^{75} +8.49768 q^{76} -17.0155 q^{77} -18.7037 q^{78} +2.70659 q^{79} -3.85153 q^{80} +12.6996 q^{81} -1.11717 q^{82} -9.44859 q^{83} -15.1092 q^{84} -25.1864 q^{85} -9.85208 q^{86} -17.4413 q^{87} +3.45164 q^{88} -9.78906 q^{89} +24.6260 q^{90} -30.0833 q^{91} -3.16538 q^{92} -3.06494 q^{93} +0.756954 q^{94} -32.7290 q^{95} +3.06494 q^{96} -1.00000 q^{97} -17.3018 q^{98} -22.0692 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * q^99

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