LMFDB - Embedded newform 6038.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6038,2,Mod(1,6038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6038, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6038 = 2 \cdot 3019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6038.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:	$48.2136727404$
Analytic rank:	$1$
Dimension:	$57$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.40132 q^{3} +1.00000 q^{4} -0.259244 q^{5} +3.40132 q^{6} +0.796720 q^{7} -1.00000 q^{8} +8.56895 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.40132 q^{3} +1.00000 q^{4} -0.259244 q^{5} +3.40132 q^{6} +0.796720 q^{7} -1.00000 q^{8} +8.56895 q^{9} +0.259244 q^{10} +1.51902 q^{11} -3.40132 q^{12} -4.61363 q^{13} -0.796720 q^{14} +0.881772 q^{15} +1.00000 q^{16} +3.94985 q^{17} -8.56895 q^{18} +3.36409 q^{19} -0.259244 q^{20} -2.70990 q^{21} -1.51902 q^{22} +0.314269 q^{23} +3.40132 q^{24} -4.93279 q^{25} +4.61363 q^{26} -18.9418 q^{27} +0.796720 q^{28} +1.20517 q^{29} -0.881772 q^{30} +9.51992 q^{31} -1.00000 q^{32} -5.16667 q^{33} -3.94985 q^{34} -0.206545 q^{35} +8.56895 q^{36} +2.93646 q^{37} -3.36409 q^{38} +15.6924 q^{39} +0.259244 q^{40} -3.43668 q^{41} +2.70990 q^{42} -8.47808 q^{43} +1.51902 q^{44} -2.22145 q^{45} -0.314269 q^{46} -12.0536 q^{47} -3.40132 q^{48} -6.36524 q^{49} +4.93279 q^{50} -13.4347 q^{51} -4.61363 q^{52} -3.69151 q^{53} +18.9418 q^{54} -0.393798 q^{55} -0.796720 q^{56} -11.4423 q^{57} -1.20517 q^{58} +11.2993 q^{59} +0.881772 q^{60} -7.53205 q^{61} -9.51992 q^{62} +6.82706 q^{63} +1.00000 q^{64} +1.19606 q^{65} +5.16667 q^{66} -2.89748 q^{67} +3.94985 q^{68} -1.06893 q^{69} +0.206545 q^{70} -2.35855 q^{71} -8.56895 q^{72} +15.8124 q^{73} -2.93646 q^{74} +16.7780 q^{75} +3.36409 q^{76} +1.21024 q^{77} -15.6924 q^{78} +6.38305 q^{79} -0.259244 q^{80} +38.7201 q^{81} +3.43668 q^{82} -15.3731 q^{83} -2.70990 q^{84} -1.02398 q^{85} +8.47808 q^{86} -4.09917 q^{87} -1.51902 q^{88} -11.8530 q^{89} +2.22145 q^{90} -3.67577 q^{91} +0.314269 q^{92} -32.3802 q^{93} +12.0536 q^{94} -0.872121 q^{95} +3.40132 q^{96} +2.36845 q^{97} +6.36524 q^{98} +13.0164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9}+O(q^{10}) $ 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9	\( 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9} + 15 q^{10} + 13 q^{11} - 5 q^{12} - 43 q^{13} + 28 q^{14} - 10 q^{15} + 57 q^{16} - 50 q^{18} - 6 q^{19} - 15 q^{20} - 23 q^{21} - 13 q^{22} - q^{23} + 5 q^{24} + 20 q^{25} + 43 q^{26} - 20 q^{27} - 28 q^{28} - 4 q^{29} + 10 q^{30} - 34 q^{31} - 57 q^{32} - 43 q^{33} + 26 q^{35} + 50 q^{36} - 64 q^{37} + 6 q^{38} + 8 q^{39} + 15 q^{40} + 27 q^{41} + 23 q^{42} - 29 q^{43} + 13 q^{44} - 76 q^{45} + q^{46} - 25 q^{47} - 5 q^{48} + 7 q^{49} - 20 q^{50} + 27 q^{51} - 43 q^{52} - 34 q^{53} + 20 q^{54} - 36 q^{55} + 28 q^{56} - 33 q^{57} + 4 q^{58} + 19 q^{59} - 10 q^{60} - 58 q^{61} + 34 q^{62} - 65 q^{63} + 57 q^{64} + 17 q^{65} + 43 q^{66} - 84 q^{67} - 33 q^{69} - 26 q^{70} + 22 q^{71} - 50 q^{72} - 82 q^{73} + 64 q^{74} + 8 q^{75} - 6 q^{76} - 41 q^{77} - 8 q^{78} + 8 q^{79} - 15 q^{80} + 25 q^{81} - 27 q^{82} - 23 q^{83} - 23 q^{84} - 58 q^{85} + 29 q^{86} - 17 q^{87} - 13 q^{88} + 18 q^{89} + 76 q^{90} - 4 q^{91} - q^{92} - 60 q^{93} + 25 q^{94} + 36 q^{95} + 5 q^{96} - 156 q^{97} - 7 q^{98} + 25 q^{99}+O(q^{100}) \) 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9 + 15 * q^10 + 13 * q^11 - 5 * q^12 - 43 * q^13 + 28 * q^14 - 10 * q^15 + 57 * q^16 - 50 * q^18 - 6 * q^19 - 15 * q^20 - 23 * q^21 - 13 * q^22 - q^23 + 5 * q^24 + 20 * q^25 + 43 * q^26 - 20 * q^27 - 28 * q^28 - 4 * q^29 + 10 * q^30 - 34 * q^31 - 57 * q^32 - 43 * q^33 + 26 * q^35 + 50 * q^36 - 64 * q^37 + 6 * q^38 + 8 * q^39 + 15 * q^40 + 27 * q^41 + 23 * q^42 - 29 * q^43 + 13 * q^44 - 76 * q^45 + q^46 - 25 * q^47 - 5 * q^48 + 7 * q^49 - 20 * q^50 + 27 * q^51 - 43 * q^52 - 34 * q^53 + 20 * q^54 - 36 * q^55 + 28 * q^56 - 33 * q^57 + 4 * q^58 + 19 * q^59 - 10 * q^60 - 58 * q^61 + 34 * q^62 - 65 * q^63 + 57 * q^64 + 17 * q^65 + 43 * q^66 - 84 * q^67 - 33 * q^69 - 26 * q^70 + 22 * q^71 - 50 * q^72 - 82 * q^73 + 64 * q^74 + 8 * q^75 - 6 * q^76 - 41 * q^77 - 8 * q^78 + 8 * q^79 - 15 * q^80 + 25 * q^81 - 27 * q^82 - 23 * q^83 - 23 * q^84 - 58 * q^85 + 29 * q^86 - 17 * q^87 - 13 * q^88 + 18 * q^89 + 76 * q^90 - 4 * q^91 - q^92 - 60 * q^93 + 25 * q^94 + 36 * q^95 + 5 * q^96 - 156 * q^97 - 7 * q^98 + 25 * 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
$3$	−3.40132	−1.96375	−0.981875	−	0.189528i	$-0.939304\pi$
$3$	−3.40132	−1.96375	−0.981875	+	0.189528i	$0.939304\pi$
$4$	1.00000	0.500000
$5$	−0.259244	−0.115938	−0.0579688	−	0.998318i	$-0.518462\pi$
$5$	−0.259244	−0.115938	−0.0579688	+	0.998318i	$0.518462\pi$
$6$	3.40132	1.38858
$7$	0.796720	0.301132	0.150566	−	0.988600i	$-0.451890\pi$
$7$	0.796720	0.301132	0.150566	+	0.988600i	$0.451890\pi$
$8$	−1.00000	−0.353553
$9$	8.56895	2.85632
$10$	0.259244	0.0819803
$11$	1.51902	0.458002	0.229001	−	0.973426i	$-0.426454\pi$
$11$	1.51902	0.458002	0.229001	+	0.973426i	$0.426454\pi$
$12$	−3.40132	−0.981875
$13$	−4.61363	−1.27959	−0.639795	−	0.768545i	$-0.720981\pi$
$13$	−4.61363	−1.27959	−0.639795	+	0.768545i	$0.720981\pi$
$14$	−0.796720	−0.212932
$15$	0.881772	0.227673
$16$	1.00000	0.250000
$17$	3.94985	0.957980	0.478990	−	0.877820i	$-0.341003\pi$
$17$	3.94985	0.957980	0.478990	+	0.877820i	$0.341003\pi$
$18$	−8.56895	−2.01972
$19$	3.36409	0.771775	0.385887	−	0.922546i	$-0.373895\pi$
$19$	3.36409	0.771775	0.385887	+	0.922546i	$0.373895\pi$
$20$	−0.259244	−0.0579688
$21$	−2.70990	−0.591348
$22$	−1.51902	−0.323857
$23$	0.314269	0.0655297	0.0327649	−	0.999463i	$-0.489569\pi$
$23$	0.314269	0.0655297	0.0327649	+	0.999463i	$0.489569\pi$
$24$	3.40132	0.694291
$25$	−4.93279	−0.986558
$26$	4.61363	0.904807
$27$	−18.9418	−3.64534
$28$	0.796720	0.150566
$29$	1.20517	0.223795	0.111897	−	0.993720i	$-0.464307\pi$
$29$	1.20517	0.223795	0.111897	+	0.993720i	$0.464307\pi$
$30$	−0.881772	−0.160989
$31$	9.51992	1.70983	0.854914	−	0.518770i	$-0.173610\pi$
$31$	9.51992	1.70983	0.854914	+	0.518770i	$0.173610\pi$
$32$	−1.00000	−0.176777
$33$	−5.16667	−0.899402
$34$	−3.94985	−0.677394
$35$	−0.206545	−0.0349125
$36$	8.56895	1.42816
$37$	2.93646	0.482751	0.241376	−	0.970432i	$-0.422401\pi$
$37$	2.93646	0.482751	0.241376	+	0.970432i	$0.422401\pi$
$38$	−3.36409	−0.545727
$39$	15.6924	2.51280
$40$	0.259244	0.0409901
$41$	−3.43668	−0.536720	−0.268360	−	0.963319i	$-0.586482\pi$
$41$	−3.43668	−0.536720	−0.268360	+	0.963319i	$0.586482\pi$
$42$	2.70990	0.418146
$43$	−8.47808	−1.29290	−0.646448	−	0.762958i	$-0.723746\pi$
$43$	−8.47808	−1.29290	−0.646448	+	0.762958i	$0.723746\pi$
$44$	1.51902	0.229001
$45$	−2.22145	−0.331155
$46$	−0.314269	−0.0463365
$47$	−12.0536	−1.75820	−0.879099	−	0.476639i	$-0.841855\pi$
$47$	−12.0536	−1.75820	−0.879099	+	0.476639i	$0.841855\pi$
$48$	−3.40132	−0.490938
$49$	−6.36524	−0.909320
$50$	4.93279	0.697602
$51$	−13.4347	−1.88123
$52$	−4.61363	−0.639795
$53$	−3.69151	−0.507068	−0.253534	−	0.967326i	$-0.581593\pi$
$53$	−3.69151	−0.507068	−0.253534	+	0.967326i	$0.581593\pi$
$54$	18.9418	2.57765
$55$	−0.393798	−0.0530997
$56$	−0.796720	−0.106466
$57$	−11.4423	−1.51557
$58$	−1.20517	−0.158247
$59$	11.2993	1.47105	0.735523	−	0.677500i	$-0.236937\pi$
$59$	11.2993	1.47105	0.735523	+	0.677500i	$0.236937\pi$
$60$	0.881772	0.113836
$61$	−7.53205	−0.964380	−0.482190	−	0.876067i	$-0.660159\pi$
$61$	−7.53205	−0.964380	−0.482190	+	0.876067i	$0.660159\pi$
$62$	−9.51992	−1.20903
$63$	6.82706	0.860128
$64$	1.00000	0.125000
$65$	1.19606	0.148353
$66$	5.16667	0.635973
$67$	−2.89748	−0.353984	−0.176992	−	0.984212i	$-0.556637\pi$
$67$	−2.89748	−0.353984	−0.176992	+	0.984212i	$0.556637\pi$
$68$	3.94985	0.478990
$69$	−1.06893	−0.128684
$70$	0.206545	0.0246869
$71$	−2.35855	−0.279908	−0.139954	−	0.990158i	$-0.544696\pi$
$71$	−2.35855	−0.279908	−0.139954	+	0.990158i	$0.544696\pi$
$72$	−8.56895	−1.00986
$73$	15.8124	1.85070	0.925352	−	0.379108i	$-0.123769\pi$
$73$	15.8124	1.85070	0.925352	+	0.379108i	$0.123769\pi$
$74$	−2.93646	−0.341357
$75$	16.7780	1.93735
$76$	3.36409	0.385887
$77$	1.21024	0.137919
$78$	−15.6924	−1.77682
$79$	6.38305	0.718149	0.359075	−	0.933309i	$-0.383092\pi$
$79$	6.38305	0.718149	0.359075	+	0.933309i	$0.383092\pi$
$80$	−0.259244	−0.0289844
$81$	38.7201	4.30223
$82$	3.43668	0.379518
$83$	−15.3731	−1.68741	−0.843707	−	0.536804i	$-0.819631\pi$
$83$	−15.3731	−1.68741	−0.843707	+	0.536804i	$0.819631\pi$
$84$	−2.70990	−0.295674
$85$	−1.02398	−0.111066
$86$	8.47808	0.914215
$87$	−4.09917	−0.439477
$88$	−1.51902	−0.161928
$89$	−11.8530	−1.25641	−0.628206	−	0.778047i	$-0.716211\pi$
$89$	−11.8530	−1.25641	−0.628206	+	0.778047i	$0.716211\pi$
$90$	2.22145	0.234162
$91$	−3.67577	−0.385326
$92$	0.314269	0.0327649
$93$	−32.3802	−3.35768
$94$	12.0536	1.24323
$95$	−0.872121	−0.0894777
$96$	3.40132	0.347145
$97$	2.36845	0.240480	0.120240	−	0.992745i	$-0.461634\pi$
$97$	2.36845	0.240480	0.120240	+	0.992745i	$0.461634\pi$
$98$	6.36524	0.642986
$99$	13.0164	1.30820
$100$	−4.93279	−0.493279
$101$	2.79945	0.278555	0.139278	−	0.990253i	$-0.455522\pi$
$101$	2.79945	0.278555	0.139278	+	0.990253i	$0.455522\pi$
$102$	13.4347	1.33023
$103$	−4.94992	−0.487730	−0.243865	−	0.969809i	$-0.578415\pi$
$103$	−4.94992	−0.487730	−0.243865	+	0.969809i	$0.578415\pi$
$104$	4.61363	0.452404
$105$	0.702525	0.0685595
$106$	3.69151	0.358551
$107$	10.8433	1.04826	0.524129	−	0.851639i	$-0.324391\pi$
$107$	10.8433	1.04826	0.524129	+	0.851639i	$0.324391\pi$
$108$	−18.9418	−1.82267
$109$	−3.53684	−0.338768	−0.169384	−	0.985550i	$-0.554178\pi$
$109$	−3.53684	−0.338768	−0.169384	+	0.985550i	$0.554178\pi$
$110$	0.393798	0.0375471
$111$	−9.98783	−0.948003
$112$	0.796720	0.0752830
$113$	1.86055	0.175026	0.0875131	−	0.996163i	$-0.472108\pi$
$113$	1.86055	0.175026	0.0875131	+	0.996163i	$0.472108\pi$
$114$	11.4423	1.07167
$115$	−0.0814726	−0.00759736
$116$	1.20517	0.111897
$117$	−39.5340	−3.65492
$118$	−11.2993	−1.04019
$119$	3.14693	0.288478
$120$	−0.881772	−0.0804944
$121$	−8.69257	−0.790234
$122$	7.53205	0.681920
$123$	11.6892	1.05398
$124$	9.51992	0.854914
$125$	2.57502	0.230317
$126$	−6.82706	−0.608202
$127$	13.8765	1.23134	0.615669	−	0.788005i	$-0.288886\pi$
$127$	13.8765	1.23134	0.615669	+	0.788005i	$0.288886\pi$
$128$	−1.00000	−0.0883883
$129$	28.8366	2.53892
$130$	−1.19606	−0.104901
$131$	−17.3840	−1.51885	−0.759425	−	0.650595i	$-0.774520\pi$
$131$	−17.3840	−1.51885	−0.759425	+	0.650595i	$0.774520\pi$
$132$	−5.16667	−0.449701
$133$	2.68024	0.232406
$134$	2.89748	0.250305
$135$	4.91054	0.422632
$136$	−3.94985	−0.338697
$137$	7.83469	0.669363	0.334682	−	0.942331i	$-0.391371\pi$
$137$	7.83469	0.669363	0.334682	+	0.942331i	$0.391371\pi$
$138$	1.06893	0.0909933
$139$	−3.21240	−0.272472	−0.136236	−	0.990676i	$-0.543501\pi$
$139$	−3.21240	−0.272472	−0.136236	+	0.990676i	$0.543501\pi$
$140$	−0.206545	−0.0174563
$141$	40.9981	3.45266
$142$	2.35855	0.197925
$143$	−7.00820	−0.586055
$144$	8.56895	0.714079
$145$	−0.312434	−0.0259462
$146$	−15.8124	−1.30865
$147$	21.6502	1.78568
$148$	2.93646	0.241376
$149$	18.2557	1.49557	0.747784	−	0.663942i	$-0.231118\pi$
$149$	18.2557	1.49557	0.747784	+	0.663942i	$0.231118\pi$
$150$	−16.7780	−1.36992
$151$	−3.46978	−0.282366	−0.141183	−	0.989983i	$-0.545091\pi$
$151$	−3.46978	−0.282366	−0.141183	+	0.989983i	$0.545091\pi$
$152$	−3.36409	−0.272864
$153$	33.8461	2.73630
$154$	−1.21024	−0.0975235
$155$	−2.46798	−0.198233
$156$	15.6924	1.25640
$157$	−14.9843	−1.19587	−0.597937	−	0.801543i	$-0.704013\pi$
$157$	−14.9843	−1.19587	−0.597937	+	0.801543i	$0.704013\pi$
$158$	−6.38305	−0.507808
$159$	12.5560	0.995755
$160$	0.259244	0.0204951
$161$	0.250385	0.0197331
$162$	−38.7201	−3.04214
$163$	16.9216	1.32540	0.662699	−	0.748886i	$-0.269411\pi$
$163$	16.9216	1.32540	0.662699	+	0.748886i	$0.269411\pi$
$164$	−3.43668	−0.268360
$165$	1.33943	0.104275
$166$	15.3731	1.19318
$167$	20.1374	1.55828	0.779139	−	0.626851i	$-0.215657\pi$
$167$	20.1374	1.55828	0.779139	+	0.626851i	$0.215657\pi$
$168$	2.70990	0.209073
$169$	8.28558	0.637352
$170$	1.02398	0.0785355
$171$	28.8267	2.20443
$172$	−8.47808	−0.646448
$173$	−6.23288	−0.473877	−0.236939	−	0.971525i	$-0.576144\pi$
$173$	−6.23288	−0.473877	−0.236939	+	0.971525i	$0.576144\pi$
$174$	4.09917	0.310757
$175$	−3.93005	−0.297084
$176$	1.51902	0.114501
$177$	−38.4325	−2.88877
$178$	11.8530	0.888418
$179$	9.67564	0.723191	0.361595	−	0.932335i	$-0.382232\pi$
$179$	9.67564	0.723191	0.361595	+	0.932335i	$0.382232\pi$
$180$	−2.22145	−0.165577
$181$	10.3472	0.769103	0.384551	−	0.923104i	$-0.374356\pi$
$181$	10.3472	0.769103	0.384551	+	0.923104i	$0.374356\pi$
$182$	3.67577	0.272466
$183$	25.6189	1.89380
$184$	−0.314269	−0.0231683
$185$	−0.761261	−0.0559690
$186$	32.3802	2.37424
$187$	5.99991	0.438757
$188$	−12.0536	−0.879099
$189$	−15.0913	−1.09773
$190$	0.872121	0.0632703
$191$	10.1664	0.735617	0.367809	−	0.929901i	$-0.380108\pi$
$191$	10.1664	0.735617	0.367809	+	0.929901i	$0.380108\pi$
$192$	−3.40132	−0.245469
$193$	−20.1719	−1.45200	−0.726002	−	0.687692i	$-0.758624\pi$
$193$	−20.1719	−1.45200	−0.726002	+	0.687692i	$0.758624\pi$
$194$	−2.36845	−0.170045
$195$	−4.06817	−0.291328
$196$	−6.36524	−0.454660
$197$	12.3330	0.878691	0.439345	−	0.898318i	$-0.355210\pi$
$197$	12.3330	0.878691	0.439345	+	0.898318i	$0.355210\pi$
$198$	−13.0164	−0.925037
$199$	27.6502	1.96007	0.980035	−	0.198825i	$-0.0637124\pi$
$199$	27.6502	1.96007	0.980035	+	0.198825i	$0.0637124\pi$
$200$	4.93279	0.348801
$201$	9.85526	0.695137
$202$	−2.79945	−0.196968
$203$	0.960184	0.0673917
$204$	−13.4347	−0.940617
$205$	0.890941	0.0622260
$206$	4.94992	0.344877
$207$	2.69296	0.187174
$208$	−4.61363	−0.319898
$209$	5.11012	0.353475
$210$	−0.702525	−0.0484789
$211$	5.85476	0.403059	0.201529	−	0.979482i	$-0.435409\pi$
$211$	5.85476	0.403059	0.201529	+	0.979482i	$0.435409\pi$
$212$	−3.69151	−0.253534
$213$	8.02218	0.549671
$214$	−10.8433	−0.741230
$215$	2.19789	0.149895
$216$	18.9418	1.28882
$217$	7.58471	0.514884
$218$	3.53684	0.239545
$219$	−53.7831	−3.63432
$220$	−0.393798	−0.0265498
$221$	−18.2232	−1.22582
$222$	9.98783	0.670339
$223$	1.09507	0.0733314	0.0366657	−	0.999328i	$-0.488326\pi$
$223$	1.09507	0.0733314	0.0366657	+	0.999328i	$0.488326\pi$
$224$	−0.796720	−0.0532331
$225$	−42.2689	−2.81792
$226$	−1.86055	−0.123762
$227$	6.41541	0.425806	0.212903	−	0.977073i	$-0.431708\pi$
$227$	6.41541	0.425806	0.212903	+	0.977073i	$0.431708\pi$
$228$	−11.4423	−0.757787
$229$	−9.15864	−0.605220	−0.302610	−	0.953114i	$-0.597858\pi$
$229$	−9.15864	−0.605220	−0.302610	+	0.953114i	$0.597858\pi$
$230$	0.0814726	0.00537214
$231$	−4.11639	−0.270839
$232$	−1.20517	−0.0791234
$233$	−5.80356	−0.380204	−0.190102	−	0.981764i	$-0.560882\pi$
$233$	−5.80356	−0.380204	−0.190102	+	0.981764i	$0.560882\pi$
$234$	39.5340	2.58442
$235$	3.12483	0.203841
$236$	11.2993	0.735523
$237$	−21.7108	−1.41027
$238$	−3.14693	−0.203985
$239$	13.0554	0.844485	0.422243	−	0.906483i	$-0.361243\pi$
$239$	13.0554	0.844485	0.422243	+	0.906483i	$0.361243\pi$
$240$	0.881772	0.0569181
$241$	−15.9342	−1.02641	−0.513207	−	0.858265i	$-0.671543\pi$
$241$	−15.9342	−1.02641	−0.513207	+	0.858265i	$0.671543\pi$
$242$	8.69257	0.558780
$243$	−74.8739	−4.80316
$244$	−7.53205	−0.482190
$245$	1.65015	0.105424
$246$	−11.6892	−0.745279
$247$	−15.5207	−0.987556
$248$	−9.51992	−0.604515
$249$	52.2887	3.31366
$250$	−2.57502	−0.162859
$251$	−20.6111	−1.30096	−0.650480	−	0.759524i	$-0.725432\pi$
$251$	−20.6111	−1.30096	−0.650480	+	0.759524i	$0.725432\pi$
$252$	6.82706	0.430064
$253$	0.477382	0.0300128
$254$	−13.8765	−0.870687
$255$	3.48287	0.218106
$256$	1.00000	0.0625000
$257$	1.89019	0.117907	0.0589535	−	0.998261i	$-0.481224\pi$
$257$	1.89019	0.117907	0.0589535	+	0.998261i	$0.481224\pi$
$258$	−28.8366	−1.79529
$259$	2.33954	0.145372
$260$	1.19606	0.0741763
$261$	10.3271	0.639229
$262$	17.3840	1.07399
$263$	6.01784	0.371076	0.185538	−	0.982637i	$-0.440597\pi$
$263$	6.01784	0.371076	0.185538	+	0.982637i	$0.440597\pi$
$264$	5.16667	0.317987
$265$	0.957003	0.0587882
$266$	−2.68024	−0.164336
$267$	40.3157	2.46728
$268$	−2.89748	−0.176992
$269$	−29.3528	−1.78967	−0.894836	−	0.446394i	$-0.852708\pi$
$269$	−29.3528	−1.78967	−0.894836	+	0.446394i	$0.852708\pi$
$270$	−4.91054	−0.298846
$271$	−13.0760	−0.794312	−0.397156	−	0.917751i	$-0.630003\pi$
$271$	−13.0760	−0.794312	−0.397156	+	0.917751i	$0.630003\pi$
$272$	3.94985	0.239495
$273$	12.5025	0.756683
$274$	−7.83469	−0.473311
$275$	−7.49302	−0.451846
$276$	−1.06893	−0.0643420
$277$	−26.4736	−1.59064	−0.795322	−	0.606187i	$-0.792698\pi$
$277$	−26.4736	−1.59064	−0.795322	+	0.606187i	$0.792698\pi$
$278$	3.21240	0.192667
$279$	81.5757	4.88381
$280$	0.206545	0.0123434
$281$	−1.08791	−0.0648991	−0.0324495	−	0.999473i	$-0.510331\pi$
$281$	−1.08791	−0.0648991	−0.0324495	+	0.999473i	$0.510331\pi$
$282$	−40.9981	−2.44140
$283$	5.21507	0.310004	0.155002	−	0.987914i	$-0.450462\pi$
$283$	5.21507	0.310004	0.155002	+	0.987914i	$0.450462\pi$
$284$	−2.35855	−0.139954
$285$	2.96636	0.175712
$286$	7.00820	0.414404
$287$	−2.73808	−0.161623
$288$	−8.56895	−0.504930
$289$	−1.39866	−0.0822740
$290$	0.312434	0.0183468
$291$	−8.05586	−0.472243
$292$	15.8124	0.925352
$293$	1.73936	0.101615	0.0508073	−	0.998708i	$-0.483821\pi$
$293$	1.73936	0.101615	0.0508073	+	0.998708i	$0.483821\pi$
$294$	−21.6502	−1.26266
$295$	−2.92928	−0.170549
$296$	−2.93646	−0.170678
$297$	−28.7729	−1.66958
$298$	−18.2557	−1.05753
$299$	−1.44992	−0.0838512
$300$	16.7780	0.968677
$301$	−6.75466	−0.389332
$302$	3.46978	0.199663
$303$	−9.52180	−0.547013
$304$	3.36409	0.192944
$305$	1.95264	0.111808
$306$	−33.8461	−1.93485
$307$	−19.8814	−1.13469	−0.567347	−	0.823479i	$-0.692030\pi$
$307$	−19.8814	−1.13469	−0.567347	+	0.823479i	$0.692030\pi$
$308$	1.21024	0.0689595
$309$	16.8362	0.957781
$310$	2.46798	0.140172
$311$	14.1279	0.801121	0.400561	−	0.916270i	$-0.368815\pi$
$311$	14.1279	0.801121	0.400561	+	0.916270i	$0.368815\pi$
$312$	−15.6924	−0.888408
$313$	−32.1177	−1.81540	−0.907699	−	0.419621i	$-0.862163\pi$
$313$	−32.1177	−1.81540	−0.907699	+	0.419621i	$0.862163\pi$
$314$	14.9843	0.845611
$315$	−1.76988	−0.0997212
$316$	6.38305	0.359075
$317$	−8.23689	−0.462630	−0.231315	−	0.972879i	$-0.574303\pi$
$317$	−8.23689	−0.462630	−0.231315	+	0.972879i	$0.574303\pi$
$318$	−12.5560	−0.704105
$319$	1.83068	0.102499
$320$	−0.259244	−0.0144922
$321$	−36.8814	−2.05852
$322$	−0.250385	−0.0139534
$323$	13.2877	0.739345
$324$	38.7201	2.15112
$325$	22.7581	1.26239
$326$	−16.9216	−0.937198
$327$	12.0299	0.665256
$328$	3.43668	0.189759
$329$	−9.60335	−0.529450
$330$	−1.33943	−0.0737332
$331$	−8.32468	−0.457566	−0.228783	−	0.973477i	$-0.573475\pi$
$331$	−8.32468	−0.457566	−0.228783	+	0.973477i	$0.573475\pi$
$332$	−15.3731	−0.843707
$333$	25.1624	1.37889
$334$	−20.1374	−1.10187
$335$	0.751156	0.0410401
$336$	−2.70990	−0.147837
$337$	0.0564264	0.00307374	0.00153687	−	0.999999i	$-0.499511\pi$
$337$	0.0564264	0.00307374	0.00153687	+	0.999999i	$0.499511\pi$
$338$	−8.28558	−0.450676
$339$	−6.32833	−0.343708
$340$	−1.02398	−0.0555330
$341$	14.4610	0.783105
$342$	−28.8267	−1.55877
$343$	−10.6484	−0.574957
$344$	8.47808	0.457108
$345$	0.277114	0.0149193
$346$	6.23288	0.335082
$347$	8.41457	0.451718	0.225859	−	0.974160i	$-0.427481\pi$
$347$	8.41457	0.451718	0.225859	+	0.974160i	$0.427481\pi$
$348$	−4.09917	−0.219739
$349$	−26.1797	−1.40137	−0.700683	−	0.713473i	$-0.747121\pi$
$349$	−26.1797	−1.40137	−0.700683	+	0.713473i	$0.747121\pi$
$350$	3.93005	0.210070
$351$	87.3903	4.66455
$352$	−1.51902	−0.0809641
$353$	1.56593	0.0833461	0.0416731	−	0.999131i	$-0.486731\pi$
$353$	1.56593	0.0833461	0.0416731	+	0.999131i	$0.486731\pi$
$354$	38.4325	2.04267
$355$	0.611441	0.0324519
$356$	−11.8530	−0.628206
$357$	−10.7037	−0.566500
$358$	−9.67564	−0.511373
$359$	−10.0103	−0.528322	−0.264161	−	0.964479i	$-0.585095\pi$
$359$	−10.0103	−0.528322	−0.264161	+	0.964479i	$0.585095\pi$
$360$	2.22145	0.117081
$361$	−7.68291	−0.404364
$362$	−10.3472	−0.543838
$363$	29.5662	1.55182
$364$	−3.67577	−0.192663
$365$	−4.09928	−0.214566
$366$	−25.6189	−1.33912
$367$	23.9000	1.24757	0.623784	−	0.781597i	$-0.285595\pi$
$367$	23.9000	1.24757	0.623784	+	0.781597i	$0.285595\pi$
$368$	0.314269	0.0163824
$369$	−29.4488	−1.53304
$370$	0.761261	0.0395761
$371$	−2.94110	−0.152694
$372$	−32.3802	−1.67884
$373$	10.9184	0.565332	0.282666	−	0.959218i	$-0.408781\pi$
$373$	10.9184	0.565332	0.282666	+	0.959218i	$0.408781\pi$
$374$	−5.99991	−0.310248
$375$	−8.75846	−0.452285
$376$	12.0536	0.621617
$377$	−5.56022	−0.286366
$378$	15.0913	0.776212
$379$	23.9410	1.22977	0.614883	−	0.788618i	$-0.289203\pi$
$379$	23.9410	1.22977	0.614883	+	0.788618i	$0.289203\pi$
$380$	−0.872121	−0.0447389
$381$	−47.1982	−2.41804
$382$	−10.1664	−0.520160
$383$	20.5144	1.04824	0.524118	−	0.851646i	$-0.324395\pi$
$383$	20.5144	1.04824	0.524118	+	0.851646i	$0.324395\pi$
$384$	3.40132	0.173573
$385$	−0.313747	−0.0159900
$386$	20.1719	1.02672
$387$	−72.6483	−3.69292
$388$	2.36845	0.120240
$389$	−11.4980	−0.582973	−0.291487	−	0.956575i	$-0.594150\pi$
$389$	−11.4980	−0.582973	−0.291487	+	0.956575i	$0.594150\pi$
$390$	4.06817	0.206000
$391$	1.24132	0.0627762
$392$	6.36524	0.321493
$393$	59.1286	2.98264
$394$	−12.3330	−0.621328
$395$	−1.65477	−0.0832605
$396$	13.0164	0.654100
$397$	−36.1281	−1.81322	−0.906608	−	0.421974i	$-0.861337\pi$
$397$	−36.1281	−1.81322	−0.906608	+	0.421974i	$0.861337\pi$
$398$	−27.6502	−1.38598
$399$	−9.11633	−0.456387
$400$	−4.93279	−0.246640
$401$	38.8202	1.93859	0.969294	−	0.245905i	$-0.0790850\pi$
$401$	38.8202	1.93859	0.969294	+	0.245905i	$0.0790850\pi$
$402$	−9.85526	−0.491536
$403$	−43.9214	−2.18788
$404$	2.79945	0.139278
$405$	−10.0380	−0.498790
$406$	−0.960184	−0.0476532
$407$	4.46055	0.221101
$408$	13.4347	0.665117
$409$	−13.2498	−0.655161	−0.327580	−	0.944823i	$-0.606233\pi$
$409$	−13.2498	−0.655161	−0.327580	+	0.944823i	$0.606233\pi$
$410$	−0.890941	−0.0440004
$411$	−26.6483	−1.31446
$412$	−4.94992	−0.243865
$413$	9.00239	0.442979
$414$	−2.69296	−0.132352
$415$	3.98538	0.195635
$416$	4.61363	0.226202
$417$	10.9264	0.535067
$418$	−5.11012	−0.249944
$419$	−9.20006	−0.449452	−0.224726	−	0.974422i	$-0.572149\pi$
$419$	−9.20006	−0.449452	−0.224726	+	0.974422i	$0.572149\pi$
$420$	0.702525	0.0342797
$421$	−25.9493	−1.26469	−0.632346	−	0.774686i	$-0.717908\pi$
$421$	−25.9493	−1.26469	−0.632346	+	0.774686i	$0.717908\pi$
$422$	−5.85476	−0.285005
$423$	−103.287	−5.02197
$424$	3.69151	0.179276
$425$	−19.4838	−0.945103
$426$	−8.02218	−0.388676
$427$	−6.00094	−0.290406
$428$	10.8433	0.524129
$429$	23.8371	1.15087
$430$	−2.19789	−0.105992
$431$	4.95957	0.238894	0.119447	−	0.992841i	$-0.461888\pi$
$431$	4.95957	0.238894	0.119447	+	0.992841i	$0.461888\pi$
$432$	−18.9418	−0.911336
$433$	6.97590	0.335240	0.167620	−	0.985852i	$-0.446392\pi$
$433$	6.97590	0.335240	0.167620	+	0.985852i	$0.446392\pi$
$434$	−7.58471	−0.364078
$435$	1.06269	0.0509519
$436$	−3.53684	−0.169384
$437$	1.05723	0.0505742
$438$	53.7831	2.56985
$439$	18.1831	0.867833	0.433917	−	0.900953i	$-0.357131\pi$
$439$	18.1831	0.867833	0.433917	+	0.900953i	$0.357131\pi$
$440$	0.393798	0.0187736
$441$	−54.5434	−2.59731
$442$	18.2232	0.866787
$443$	−15.1415	−0.719396	−0.359698	−	0.933069i	$-0.617120\pi$
$443$	−15.1415	−0.719396	−0.359698	+	0.933069i	$0.617120\pi$
$444$	−9.98783	−0.474002
$445$	3.07282	0.145665
$446$	−1.09507	−0.0518531
$447$	−62.0936	−2.93692
$448$	0.796720	0.0376415
$449$	−6.84112	−0.322853	−0.161426	−	0.986885i	$-0.551609\pi$
$449$	−6.84112	−0.322853	−0.161426	+	0.986885i	$0.551609\pi$
$450$	42.2689	1.99257
$451$	−5.22040	−0.245819
$452$	1.86055	0.0875131
$453$	11.8018	0.554497
$454$	−6.41541	−0.301090
$455$	0.952923	0.0446737
$456$	11.4423	0.535836
$457$	−39.1674	−1.83218	−0.916088	−	0.400978i	$-0.868670\pi$
$457$	−39.1674	−1.83218	−0.916088	+	0.400978i	$0.868670\pi$
$458$	9.15864	0.427955
$459$	−74.8172	−3.49217
$460$	−0.0814726	−0.00379868
$461$	−18.9865	−0.884288	−0.442144	−	0.896944i	$-0.645782\pi$
$461$	−18.9865	−0.884288	−0.442144	+	0.896944i	$0.645782\pi$
$462$	4.11639	0.191512
$463$	−18.8233	−0.874793	−0.437396	−	0.899269i	$-0.644099\pi$
$463$	−18.8233	−0.874793	−0.437396	+	0.899269i	$0.644099\pi$
$464$	1.20517	0.0559487
$465$	8.39440	0.389281
$466$	5.80356	0.268845
$467$	−9.03639	−0.418154	−0.209077	−	0.977899i	$-0.567046\pi$
$467$	−9.03639	−0.418154	−0.209077	+	0.977899i	$0.567046\pi$
$468$	−39.5340	−1.82746
$469$	−2.30848	−0.106596
$470$	−3.12483	−0.144138
$471$	50.9662	2.34840
$472$	−11.2993	−0.520093
$473$	−12.8784	−0.592149
$474$	21.7108	0.997209
$475$	−16.5943	−0.761401
$476$	3.14693	0.144239
$477$	−31.6324	−1.44835
$478$	−13.0554	−0.597141
$479$	−12.8377	−0.586569	−0.293285	−	0.956025i	$-0.594748\pi$
$479$	−12.8377	−0.586569	−0.293285	+	0.956025i	$0.594748\pi$
$480$	−0.881772	−0.0402472
$481$	−13.5477	−0.617724
$482$	15.9342	0.725784
$483$	−0.851638	−0.0387509
$484$	−8.69257	−0.395117
$485$	−0.614008	−0.0278807
$486$	74.8739	3.39635
$487$	−9.38696	−0.425364	−0.212682	−	0.977121i	$-0.568220\pi$
$487$	−9.38696	−0.425364	−0.212682	+	0.977121i	$0.568220\pi$
$488$	7.53205	0.340960
$489$	−57.5556	−2.60275
$490$	−1.65015	−0.0745463
$491$	−18.1695	−0.819977	−0.409988	−	0.912091i	$-0.634467\pi$
$491$	−18.1695	−0.819977	−0.409988	+	0.912091i	$0.634467\pi$
$492$	11.6892	0.526992
$493$	4.76025	0.214391
$494$	15.5207	0.698307
$495$	−3.37443	−0.151670
$496$	9.51992	0.427457
$497$	−1.87910	−0.0842894
$498$	−52.2887	−2.34311
$499$	−20.0166	−0.896065	−0.448032	−	0.894017i	$-0.647875\pi$
$499$	−20.0166	−0.896065	−0.448032	+	0.894017i	$0.647875\pi$
$500$	2.57502	0.115158
$501$	−68.4936	−3.06007
$502$	20.6111	0.919917
$503$	25.1297	1.12048	0.560240	−	0.828330i	$-0.310709\pi$
$503$	25.1297	1.12048	0.560240	+	0.828330i	$0.310709\pi$
$504$	−6.82706	−0.304101
$505$	−0.725740	−0.0322950
$506$	−0.477382	−0.0212222
$507$	−28.1819	−1.25160
$508$	13.8765	0.615669
$509$	10.9773	0.486560	0.243280	−	0.969956i	$-0.421777\pi$
$509$	10.9773	0.486560	0.243280	+	0.969956i	$0.421777\pi$
$510$	−3.48287	−0.154224
$511$	12.5981	0.557306
$512$	−1.00000	−0.0441942
$513$	−63.7218	−2.81338
$514$	−1.89019	−0.0833728
$515$	1.28324	0.0565463
$516$	28.8366	1.26946
$517$	−18.3097	−0.805259
$518$	−2.33954	−0.102793
$519$	21.2000	0.930577
$520$	−1.19606	−0.0524506
$521$	21.3040	0.933347	0.466673	−	0.884430i	$-0.345452\pi$
$521$	21.3040	0.933347	0.466673	+	0.884430i	$0.345452\pi$
$522$	−10.3271	−0.452003
$523$	24.6083	1.07605	0.538024	−	0.842930i	$-0.319171\pi$
$523$	24.6083	1.07605	0.538024	+	0.842930i	$0.319171\pi$
$524$	−17.3840	−0.759425
$525$	13.3674	0.583399
$526$	−6.01784	−0.262390
$527$	37.6023	1.63798
$528$	−5.16667	−0.224851
$529$	−22.9012	−0.995706
$530$	−0.957003	−0.0415696
$531$	96.8233	4.20177
$532$	2.68024	0.116203
$533$	15.8556	0.686782
$534$	−40.3157	−1.74463
$535$	−2.81105	−0.121532
$536$	2.89748	0.125152
$537$	−32.9099	−1.42017
$538$	29.3528	1.26549
$539$	−9.66893	−0.416470
$540$	4.91054	0.211316
$541$	−13.4225	−0.577077	−0.288539	−	0.957468i	$-0.593169\pi$
$541$	−13.4225	−0.577077	−0.288539	+	0.957468i	$0.593169\pi$
$542$	13.0760	0.561663
$543$	−35.1942	−1.51033
$544$	−3.94985	−0.169349
$545$	0.916907	0.0392760
$546$	−12.5025	−0.535056
$547$	9.42570	0.403014	0.201507	−	0.979487i	$-0.435416\pi$
$547$	9.42570	0.403014	0.201507	+	0.979487i	$0.435416\pi$
$548$	7.83469	0.334682
$549$	−64.5418	−2.75458
$550$	7.49302	0.319503
$551$	4.05430	0.172719
$552$	1.06893	0.0454967
$553$	5.08551	0.216258
$554$	26.4736	1.12476
$555$	2.58929	0.109909
$556$	−3.21240	−0.136236
$557$	19.7998	0.838946	0.419473	−	0.907768i	$-0.362215\pi$
$557$	19.7998	0.838946	0.419473	+	0.907768i	$0.362215\pi$
$558$	−81.5757	−3.45338
$559$	39.1147	1.65438
$560$	−0.206545	−0.00872813
$561$	−20.4076	−0.861610
$562$	1.08791	0.0458906
$563$	6.14160	0.258838	0.129419	−	0.991590i	$-0.458689\pi$
$563$	6.14160	0.258838	0.129419	+	0.991590i	$0.458689\pi$
$564$	40.9981	1.72633
$565$	−0.482338	−0.0202921
$566$	−5.21507	−0.219206
$567$	30.8491	1.29554
$568$	2.35855	0.0989626
$569$	−0.927698	−0.0388911	−0.0194456	−	0.999811i	$-0.506190\pi$
$569$	−0.927698	−0.0388911	−0.0194456	+	0.999811i	$0.506190\pi$
$570$	−2.96636	−0.124247
$571$	−28.5392	−1.19433	−0.597164	−	0.802119i	$-0.703706\pi$
$571$	−28.5392	−1.19433	−0.597164	+	0.802119i	$0.703706\pi$
$572$	−7.00820	−0.293028
$573$	−34.5793	−1.44457
$574$	2.73808	0.114285
$575$	−1.55023	−0.0646489
$576$	8.56895	0.357040
$577$	32.0087	1.33254	0.666270	−	0.745711i	$-0.267890\pi$
$577$	32.0087	1.33254	0.666270	+	0.745711i	$0.267890\pi$
$578$	1.39866	0.0581765
$579$	68.6110	2.85138
$580$	−0.312434	−0.0129731
$581$	−12.2480	−0.508134
$582$	8.05586	0.333926
$583$	−5.60748	−0.232238
$584$	−15.8124	−0.654323
$585$	10.2490	0.423742
$586$	−1.73936	−0.0718523
$587$	−32.9266	−1.35903	−0.679514	−	0.733663i	$-0.737809\pi$
$587$	−32.9266	−1.35903	−0.679514	+	0.733663i	$0.737809\pi$
$588$	21.6502	0.892839
$589$	32.0258	1.31960
$590$	2.92928	0.120597
$591$	−41.9485	−1.72553
$592$	2.93646	0.120688
$593$	29.4629	1.20990	0.604948	−	0.796265i	$-0.293194\pi$
$593$	29.4629	1.20990	0.604948	+	0.796265i	$0.293194\pi$
$594$	28.7729	1.18057
$595$	−0.815823	−0.0334455
$596$	18.2557	0.747784
$597$	−94.0470	−3.84909
$598$	1.44992	0.0592918
$599$	−20.2817	−0.828689	−0.414344	−	0.910120i	$-0.635989\pi$
$599$	−20.2817	−0.828689	−0.414344	+	0.910120i	$0.635989\pi$
$600$	−16.7780	−0.684958
$601$	−46.1566	−1.88277	−0.941384	−	0.337338i	$-0.890474\pi$
$601$	−46.1566	−1.88277	−0.941384	+	0.337338i	$0.890474\pi$
$602$	6.75466	0.275299
$603$	−24.8284	−1.01109
$604$	−3.46978	−0.141183
$605$	2.25350	0.0916178
$606$	9.52180	0.386797
$607$	10.0276	0.407006	0.203503	−	0.979074i	$-0.434767\pi$
$607$	10.0276	0.407006	0.203503	+	0.979074i	$0.434767\pi$
$608$	−3.36409	−0.136432
$609$	−3.26589	−0.132341
$610$	−1.95264	−0.0790601
$611$	55.6109	2.24977
$612$	33.8461	1.36815
$613$	0.431778	0.0174394	0.00871968	−	0.999962i	$-0.497224\pi$
$613$	0.431778	0.0174394	0.00871968	+	0.999962i	$0.497224\pi$
$614$	19.8814	0.802349
$615$	−3.03037	−0.122196
$616$	−1.21024	−0.0487618
$617$	−18.5851	−0.748210	−0.374105	−	0.927386i	$-0.622050\pi$
$617$	−18.5851	−0.748210	−0.374105	+	0.927386i	$0.622050\pi$
$618$	−16.8362	−0.677253
$619$	13.6830	0.549965	0.274983	−	0.961449i	$-0.411328\pi$
$619$	13.6830	0.549965	0.274983	+	0.961449i	$0.411328\pi$
$620$	−2.46798	−0.0991166
$621$	−5.95282	−0.238878
$622$	−14.1279	−0.566478
$623$	−9.44350	−0.378346
$624$	15.6924	0.628199
$625$	23.9964	0.959856
$626$	32.1177	1.28368
$627$	−17.3811	−0.694136
$628$	−14.9843	−0.597937
$629$	11.5986	0.462466
$630$	1.76988	0.0705135
$631$	−24.2243	−0.964355	−0.482178	−	0.876074i	$-0.660154\pi$
$631$	−24.2243	−0.964355	−0.482178	+	0.876074i	$0.660154\pi$
$632$	−6.38305	−0.253904
$633$	−19.9139	−0.791507
$634$	8.23689	0.327129
$635$	−3.59739	−0.142758
$636$	12.5560	0.497877
$637$	29.3668	1.16356
$638$	−1.83068	−0.0724774
$639$	−20.2103	−0.799507
$640$	0.259244	0.0102475
$641$	32.7458	1.29338	0.646690	−	0.762753i	$-0.276153\pi$
$641$	32.7458	1.29338	0.646690	+	0.762753i	$0.276153\pi$
$642$	36.8814	1.45559
$643$	13.4301	0.529633	0.264816	−	0.964299i	$-0.414689\pi$
$643$	13.4301	0.529633	0.264816	+	0.964299i	$0.414689\pi$
$644$	0.250385	0.00986654
$645$	−7.47574	−0.294357
$646$	−13.2877	−0.522796
$647$	−13.6259	−0.535691	−0.267845	−	0.963462i	$-0.586312\pi$
$647$	−13.6259	−0.535691	−0.267845	+	0.963462i	$0.586312\pi$
$648$	−38.7201	−1.52107
$649$	17.1639	0.673742
$650$	−22.7581	−0.892645
$651$	−25.7980	−1.01110
$652$	16.9216	0.662699
$653$	31.5221	1.23355	0.616777	−	0.787138i	$-0.288438\pi$
$653$	31.5221	1.23355	0.616777	+	0.787138i	$0.288438\pi$
$654$	−12.0299	−0.470407
$655$	4.50671	0.176092
$656$	−3.43668	−0.134180
$657$	135.496	5.28620
$658$	9.60335	0.374377
$659$	−20.8182	−0.810964	−0.405482	−	0.914103i	$-0.632896\pi$
$659$	−20.8182	−0.810964	−0.405482	+	0.914103i	$0.632896\pi$
$660$	1.33943	0.0521373
$661$	8.82169	0.343124	0.171562	−	0.985173i	$-0.445119\pi$
$661$	8.82169	0.343124	0.171562	+	0.985173i	$0.445119\pi$
$662$	8.32468	0.323548
$663$	61.9827	2.40721
$664$	15.3731	0.596591
$665$	−0.694836	−0.0269446
$666$	−25.1624	−0.975023
$667$	0.378749	0.0146652
$668$	20.1374	0.779139
$669$	−3.72468	−0.144005
$670$	−0.751156	−0.0290197
$671$	−11.4413	−0.441688
$672$	2.70990	0.104537
$673$	−45.0225	−1.73549	−0.867744	−	0.497011i	$-0.834431\pi$
$673$	−45.0225	−1.73549	−0.867744	+	0.497011i	$0.834431\pi$
$674$	−0.0564264	−0.00217346
$675$	93.4358	3.59635
$676$	8.28558	0.318676
$677$	18.3256	0.704310	0.352155	−	0.935942i	$-0.385449\pi$
$677$	18.3256	0.704310	0.352155	+	0.935942i	$0.385449\pi$
$678$	6.32833	0.243038
$679$	1.88700	0.0724162
$680$	1.02398	0.0392677
$681$	−21.8208	−0.836176
$682$	−14.4610	−0.553739
$683$	14.5160	0.555440	0.277720	−	0.960662i	$-0.410421\pi$
$683$	14.5160	0.555440	0.277720	+	0.960662i	$0.410421\pi$
$684$	28.8267	1.10222
$685$	−2.03110	−0.0776043
$686$	10.6484	0.406556
$687$	31.1514	1.18850
$688$	−8.47808	−0.323224
$689$	17.0313	0.648839
$690$	−0.277114	−0.0105495
$691$	4.62150	0.175810	0.0879050	−	0.996129i	$-0.471983\pi$
$691$	4.62150	0.175810	0.0879050	+	0.996129i	$0.471983\pi$
$692$	−6.23288	−0.236939
$693$	10.3704	0.393941
$694$	−8.41457	−0.319413
$695$	0.832796	0.0315897
$696$	4.09917	0.155379
$697$	−13.5744	−0.514167
$698$	26.1797	0.990916
$699$	19.7398	0.746626
$700$	−3.93005	−0.148542
$701$	−24.3667	−0.920317	−0.460159	−	0.887837i	$-0.652207\pi$
$701$	−24.3667	−0.920317	−0.460159	+	0.887837i	$0.652207\pi$
$702$	−87.3903	−3.29833
$703$	9.87852	0.372575
$704$	1.51902	0.0572503
$705$	−10.6285	−0.400294
$706$	−1.56593	−0.0589346
$707$	2.23037	0.0838819
$708$	−38.4325	−1.44438
$709$	16.1935	0.608159	0.304080	−	0.952647i	$-0.401651\pi$
$709$	16.1935	0.608159	0.304080	+	0.952647i	$0.401651\pi$
$710$	−0.611441	−0.0229470
$711$	54.6961	2.05126
$712$	11.8530	0.444209
$713$	2.99182	0.112045
$714$	10.7037	0.400576
$715$	1.81684	0.0679459
$716$	9.67564	0.361595
$717$	−44.4056	−1.65836
$718$	10.0103	0.373580
$719$	13.2096	0.492636	0.246318	−	0.969189i	$-0.420779\pi$
$719$	13.2096	0.492636	0.246318	+	0.969189i	$0.420779\pi$
$720$	−2.22145	−0.0827886
$721$	−3.94370	−0.146871
$722$	7.68291	0.285928
$723$	54.1973	2.01562
$724$	10.3472	0.384551
$725$	−5.94486	−0.220787
$726$	−29.5662	−1.09730
$727$	−50.0321	−1.85559	−0.927794	−	0.373093i	$-0.878297\pi$
$727$	−50.0321	−1.85559	−0.927794	+	0.373093i	$0.878297\pi$
$728$	3.67577	0.136233
$729$	138.510	5.12999
$730$	4.09928	0.151721
$731$	−33.4872	−1.23857
$732$	25.6189	0.946901
$733$	35.6875	1.31815	0.659073	−	0.752079i	$-0.270949\pi$
$733$	35.6875	1.31815	0.659073	+	0.752079i	$0.270949\pi$
$734$	−23.9000	−0.882163
$735$	−5.61269	−0.207027
$736$	−0.314269	−0.0115841
$737$	−4.40134	−0.162126
$738$	29.4488	1.08402
$739$	31.9926	1.17687	0.588433	−	0.808546i	$-0.299745\pi$
$739$	31.9926	1.17687	0.588433	+	0.808546i	$0.299745\pi$
$740$	−0.761261	−0.0279845
$741$	52.7907	1.93931
$742$	2.94110	0.107971
$743$	−12.0698	−0.442799	−0.221399	−	0.975183i	$-0.571062\pi$
$743$	−12.0698	−0.442799	−0.221399	+	0.975183i	$0.571062\pi$
$744$	32.3802	1.18712
$745$	−4.73270	−0.173393
$746$	−10.9184	−0.399750
$747$	−131.731	−4.81979
$748$	5.99991	0.219379
$749$	8.63904	0.315664
$750$	8.75846	0.319814
$751$	−41.5571	−1.51644	−0.758219	−	0.652000i	$-0.773930\pi$
$751$	−41.5571	−1.51644	−0.758219	+	0.652000i	$0.773930\pi$
$752$	−12.0536	−0.439550
$753$	70.1048	2.55476
$754$	5.56022	0.202491
$755$	0.899520	0.0327369
$756$	−15.0913	−0.548865
$757$	−36.2765	−1.31849	−0.659245	−	0.751928i	$-0.729124\pi$
$757$	−36.2765	−1.31849	−0.659245	+	0.751928i	$0.729124\pi$
$758$	−23.9410	−0.869576
$759$	−1.62373	−0.0589376
$760$	0.872121	0.0316351
$761$	10.1466	0.367813	0.183906	−	0.982944i	$-0.441126\pi$
$761$	10.1466	0.367813	0.183906	+	0.982944i	$0.441126\pi$
$762$	47.1982	1.70981
$763$	−2.81787	−0.102014
$764$	10.1664	0.367809
$765$	−8.77441	−0.317239
$766$	−20.5144	−0.741215
$767$	−52.1309	−1.88234
$768$	−3.40132	−0.122734
$769$	19.3375	0.697326	0.348663	−	0.937248i	$-0.386636\pi$
$769$	19.3375	0.697326	0.348663	+	0.937248i	$0.386636\pi$
$770$	0.313747	0.0113066
$771$	−6.42914	−0.231540
$772$	−20.1719	−0.726002
$773$	−36.2364	−1.30333	−0.651666	−	0.758506i	$-0.725929\pi$
$773$	−36.2364	−1.30333	−0.651666	+	0.758506i	$0.725929\pi$
$774$	72.6483	2.61129
$775$	−46.9598	−1.68684
$776$	−2.36845	−0.0850226
$777$	−7.95751	−0.285474
$778$	11.4980	0.412224
$779$	−11.5613	−0.414227
$780$	−4.06817	−0.145664
$781$	−3.58269	−0.128199
$782$	−1.24132	−0.0443895
$783$	−22.8281	−0.815809
$784$	−6.36524	−0.227330
$785$	3.88459	0.138647
$786$	−59.1286	−2.10905
$787$	−9.15907	−0.326486	−0.163243	−	0.986586i	$-0.552195\pi$
$787$	−9.15907	−0.326486	−0.163243	+	0.986586i	$0.552195\pi$
$788$	12.3330	0.439345
$789$	−20.4686	−0.728701
$790$	1.65477	0.0588741
$791$	1.48234	0.0527060
$792$	−13.0164	−0.462518
$793$	34.7501	1.23401
$794$	36.1281	1.28214
$795$	−3.25507	−0.115445
$796$	27.6502	0.980035
$797$	−39.5296	−1.40021	−0.700106	−	0.714039i	$-0.746864\pi$
$797$	−39.5296	−1.40021	−0.700106	+	0.714039i	$0.746864\pi$
$798$	9.11633	0.322715
$799$	−47.6100	−1.68432
$800$	4.93279	0.174401
$801$	−101.568	−3.58871
$802$	−38.8202	−1.37079
$803$	24.0194	0.847627
$804$	9.85526	0.347568
$805$	−0.0649108	−0.00228781
$806$	43.9214	1.54706
$807$	99.8382	3.51447
$808$	−2.79945	−0.0984842
$809$	11.3428	0.398792	0.199396	−	0.979919i	$-0.436102\pi$
$809$	11.3428	0.398792	0.199396	+	0.979919i	$0.436102\pi$
$810$	10.0380	0.352698
$811$	−43.8753	−1.54067	−0.770335	−	0.637639i	$-0.779911\pi$
$811$	−43.8753	−1.54067	−0.770335	+	0.637639i	$0.779911\pi$
$812$	0.960184	0.0336959
$813$	44.4757	1.55983
$814$	−4.46055	−0.156342
$815$	−4.38682	−0.153664
$816$	−13.4347	−0.470309
$817$	−28.5210	−0.997824
$818$	13.2498	0.463269
$819$	−31.4975	−1.10061
$820$	0.890941	0.0311130
$821$	−46.1070	−1.60914	−0.804572	−	0.593855i	$-0.797605\pi$
$821$	−46.1070	−1.60914	−0.804572	+	0.593855i	$0.797605\pi$
$822$	26.6483	0.929465
$823$	−16.7375	−0.583432	−0.291716	−	0.956505i	$-0.594226\pi$
$823$	−16.7375	−0.583432	−0.291716	+	0.956505i	$0.594226\pi$
$824$	4.94992	0.172439
$825$	25.4861	0.887313
$826$	−9.00239	−0.313233
$827$	47.3662	1.64708	0.823542	−	0.567255i	$-0.191995\pi$
$827$	47.3662	1.64708	0.823542	+	0.567255i	$0.191995\pi$
$828$	2.69296	0.0935868
$829$	−50.2332	−1.74467	−0.872336	−	0.488908i	$-0.837395\pi$
$829$	−50.2332	−1.74467	−0.872336	+	0.488908i	$0.837395\pi$
$830$	−3.98538	−0.138335
$831$	90.0450	3.12363
$832$	−4.61363	−0.159949
$833$	−25.1418	−0.871110
$834$	−10.9264	−0.378350
$835$	−5.22050	−0.180663
$836$	5.11012	0.176737
$837$	−180.324	−6.23291
$838$	9.20006	0.317811
$839$	4.44277	0.153381	0.0766907	−	0.997055i	$-0.475565\pi$
$839$	4.44277	0.153381	0.0766907	+	0.997055i	$0.475565\pi$
$840$	−0.702525	−0.0242394
$841$	−27.5476	−0.949916
$842$	25.9493	0.894272
$843$	3.70031	0.127446
$844$	5.85476	0.201529
$845$	−2.14799	−0.0738931
$846$	103.287	3.55107
$847$	−6.92555	−0.237965
$848$	−3.69151	−0.126767
$849$	−17.7381	−0.608770
$850$	19.4838	0.668289
$851$	0.922840	0.0316346
$852$	8.02218	0.274835
$853$	8.17746	0.279991	0.139995	−	0.990152i	$-0.455291\pi$
$853$	8.17746	0.279991	0.139995	+	0.990152i	$0.455291\pi$
$854$	6.00094	0.205348
$855$	−7.47316	−0.255577
$856$	−10.8433	−0.370615
$857$	−23.6246	−0.807001	−0.403501	−	0.914979i	$-0.632207\pi$
$857$	−23.6246	−0.807001	−0.403501	+	0.914979i	$0.632207\pi$
$858$	−23.8371	−0.813786
$859$	−29.8704	−1.01916	−0.509582	−	0.860422i	$-0.670200\pi$
$859$	−29.8704	−1.01916	−0.509582	+	0.860422i	$0.670200\pi$
$860$	2.19789	0.0749476
$861$	9.31306	0.317388
$862$	−4.95957	−0.168924
$863$	13.7975	0.469674	0.234837	−	0.972035i	$-0.424544\pi$
$863$	13.7975	0.469674	0.234837	+	0.972035i	$0.424544\pi$
$864$	18.9418	0.644412
$865$	1.61584	0.0549402
$866$	−6.97590	−0.237051
$867$	4.75728	0.161566
$868$	7.58471	0.257442
$869$	9.69599	0.328914
$870$	−1.06269	−0.0360284
$871$	13.3679	0.452955
$872$	3.53684	0.119773
$873$	20.2952	0.686887
$874$	−1.05723	−0.0357613
$875$	2.05157	0.0693557
$876$	−53.7831	−1.81716
$877$	19.4803	0.657804	0.328902	−	0.944364i	$-0.393321\pi$
$877$	19.4803	0.657804	0.328902	+	0.944364i	$0.393321\pi$
$878$	−18.1831	−0.613651
$879$	−5.91611	−0.199546
$880$	−0.393798	−0.0132749
$881$	−7.35782	−0.247891	−0.123946	−	0.992289i	$-0.539555\pi$
$881$	−7.35782	−0.247891	−0.123946	+	0.992289i	$0.539555\pi$
$882$	54.5434	1.83657
$883$	23.4767	0.790055	0.395028	−	0.918669i	$-0.370735\pi$
$883$	23.4767	0.790055	0.395028	+	0.918669i	$0.370735\pi$
$884$	−18.2232	−0.612911
$885$	9.96342	0.334917
$886$	15.1415	0.508690
$887$	−46.3692	−1.55692	−0.778462	−	0.627691i	$-0.784000\pi$
$887$	−46.3692	−1.55692	−0.778462	+	0.627691i	$0.784000\pi$
$888$	9.98783	0.335170
$889$	11.0557	0.370795
$890$	−3.07282	−0.103001
$891$	58.8166	1.97043
$892$	1.09507	0.0366657
$893$	−40.5494	−1.35693
$894$	62.0936	2.07672
$895$	−2.50835	−0.0838450
$896$	−0.796720	−0.0266166
$897$	4.93165	0.164663
$898$	6.84112	0.228291
$899$	11.4731	0.382650
$900$	−42.2689	−1.40896
$901$	−14.5809	−0.485761
$902$	5.22040	0.173820
$903$	22.9747	0.764551
$904$	−1.86055	−0.0618811
$905$	−2.68246	−0.0891679
$906$	−11.8018	−0.392089
$907$	51.3339	1.70451	0.852257	−	0.523124i	$-0.175233\pi$
$907$	51.3339	1.70451	0.852257	+	0.523124i	$0.175233\pi$
$908$	6.41541	0.212903
$909$	23.9883	0.795642
$910$	−0.952923	−0.0315891
$911$	57.0256	1.88934	0.944670	−	0.328021i	$-0.106382\pi$
$911$	57.0256	1.88934	0.944670	+	0.328021i	$0.106382\pi$
$912$	−11.4423	−0.378893
$913$	−23.3520	−0.772839
$914$	39.1674	1.29554
$915$	−6.64155	−0.219563
$916$	−9.15864	−0.302610
$917$	−13.8502	−0.457374
$918$	74.8172	2.46934
$919$	−18.4850	−0.609763	−0.304881	−	0.952390i	$-0.598617\pi$
$919$	−18.4850	−0.609763	−0.304881	+	0.952390i	$0.598617\pi$
$920$	0.0814726	0.00268607
$921$	67.6231	2.22826
$922$	18.9865	0.625286
$923$	10.8815	0.358168
$924$	−4.11639	−0.135419
$925$	−14.4850	−0.476262
$926$	18.8233	0.618572
$927$	−42.4156	−1.39311
$928$	−1.20517	−0.0395617
$929$	51.3684	1.68534	0.842671	−	0.538429i	$-0.180982\pi$
$929$	51.3684	1.68534	0.842671	+	0.538429i	$0.180982\pi$
$930$	−8.39440	−0.275263
$931$	−21.4132	−0.701790
$932$	−5.80356	−0.190102
$933$	−48.0535	−1.57320
$934$	9.03639	0.295680
$935$	−1.55544	−0.0508684
$936$	39.5340	1.29221
$937$	−50.5945	−1.65285	−0.826425	−	0.563047i	$-0.809629\pi$
$937$	−50.5945	−1.65285	−0.826425	+	0.563047i	$0.809629\pi$
$938$	2.30848	0.0753747
$939$	109.242	3.56499
$940$	3.12483	0.101921
$941$	−2.13540	−0.0696119	−0.0348059	−	0.999394i	$-0.511081\pi$
$941$	−2.13540	−0.0696119	−0.0348059	+	0.999394i	$0.511081\pi$
$942$	−50.9662	−1.66057
$943$	−1.08004	−0.0351711
$944$	11.2993	0.367761
$945$	3.91233	0.127268
$946$	12.8784	0.418713
$947$	−25.5112	−0.829003	−0.414502	−	0.910049i	$-0.636044\pi$
$947$	−25.5112	−0.829003	−0.414502	+	0.910049i	$0.636044\pi$
$948$	−21.7108	−0.705133
$949$	−72.9527	−2.36814
$950$	16.5943	0.538392
$951$	28.0163	0.908490
$952$	−3.14693	−0.101993
$953$	50.9222	1.64953	0.824766	−	0.565474i	$-0.191307\pi$
$953$	50.9222	1.64953	0.824766	+	0.565474i	$0.191307\pi$
$954$	31.6324	1.02414
$955$	−2.63559	−0.0852857
$956$	13.0554	0.422243
$957$	−6.22673	−0.201282
$958$	12.8377	0.414767
$959$	6.24206	0.201567
$960$	0.881772	0.0284591
$961$	59.6288	1.92351
$962$	13.5477	0.436797
$963$	92.9154	2.99416
$964$	−15.9342	−0.513207
$965$	5.22945	0.168342
$966$	0.851638	0.0274010
$967$	−2.67590	−0.0860510	−0.0430255	−	0.999074i	$-0.513700\pi$
$967$	−2.67590	−0.0860510	−0.0430255	+	0.999074i	$0.513700\pi$
$968$	8.69257	0.279390
$969$	−45.1955	−1.45189
$970$	0.614008	0.0197146
$971$	30.2389	0.970414	0.485207	−	0.874399i	$-0.338744\pi$
$971$	30.2389	0.970414	0.485207	+	0.874399i	$0.338744\pi$
$972$	−74.8739	−2.40158
$973$	−2.55938	−0.0820500
$974$	9.38696	0.300778
$975$	−77.4074	−2.47902
$976$	−7.53205	−0.241095
$977$	54.2751	1.73641	0.868207	−	0.496202i	$-0.165272\pi$
$977$	54.2751	1.73641	0.868207	+	0.496202i	$0.165272\pi$
$978$	57.5556	1.84042
$979$	−18.0049	−0.575440
$980$	1.65015	0.0527122
$981$	−30.3070	−0.967629
$982$	18.1695	0.579811
$983$	4.88253	0.155729	0.0778643	−	0.996964i	$-0.475190\pi$
$983$	4.88253	0.155729	0.0778643	+	0.996964i	$0.475190\pi$
$984$	−11.6892	−0.372640
$985$	−3.19726	−0.101873
$986$	−4.76025	−0.151597
$987$	32.6640	1.03971
$988$	−15.5207	−0.493778
$989$	−2.66440	−0.0847231
$990$	3.37443	0.107247
$991$	−32.5617	−1.03436	−0.517179	−	0.855877i	$-0.673018\pi$
$991$	−32.5617	−1.03436	−0.517179	+	0.855877i	$0.673018\pi$
$992$	−9.51992	−0.302258
$993$	28.3149	0.898545
$994$	1.87910	0.0596016
$995$	−7.16816	−0.227246
$996$	52.2887	1.65683
$997$	−12.2258	−0.387193	−0.193597	−	0.981081i	$-0.562015\pi$
$997$	−12.2258	−0.387193	−0.193597	+	0.981081i	$0.562015\pi$
$998$	20.0166	0.633613
$999$	−55.6218	−1.75979

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.c.1.1	✓	57

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.c.1.1	✓	57	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:	\( N \)	\(=\)	\( 6038 = 2 \cdot 3019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6038.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.40132 q^{3} +1.00000 q^{4} -0.259244 q^{5} +3.40132 q^{6} +0.796720 q^{7} -1.00000 q^{8} +8.56895 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.40132 q^{3} +1.00000 q^{4} -0.259244 q^{5} +3.40132 q^{6} +0.796720 q^{7} -1.00000 q^{8} +8.56895 q^{9} +0.259244 q^{10} +1.51902 q^{11} -3.40132 q^{12} -4.61363 q^{13} -0.796720 q^{14} +0.881772 q^{15} +1.00000 q^{16} +3.94985 q^{17} -8.56895 q^{18} +3.36409 q^{19} -0.259244 q^{20} -2.70990 q^{21} -1.51902 q^{22} +0.314269 q^{23} +3.40132 q^{24} -4.93279 q^{25} +4.61363 q^{26} -18.9418 q^{27} +0.796720 q^{28} +1.20517 q^{29} -0.881772 q^{30} +9.51992 q^{31} -1.00000 q^{32} -5.16667 q^{33} -3.94985 q^{34} -0.206545 q^{35} +8.56895 q^{36} +2.93646 q^{37} -3.36409 q^{38} +15.6924 q^{39} +0.259244 q^{40} -3.43668 q^{41} +2.70990 q^{42} -8.47808 q^{43} +1.51902 q^{44} -2.22145 q^{45} -0.314269 q^{46} -12.0536 q^{47} -3.40132 q^{48} -6.36524 q^{49} +4.93279 q^{50} -13.4347 q^{51} -4.61363 q^{52} -3.69151 q^{53} +18.9418 q^{54} -0.393798 q^{55} -0.796720 q^{56} -11.4423 q^{57} -1.20517 q^{58} +11.2993 q^{59} +0.881772 q^{60} -7.53205 q^{61} -9.51992 q^{62} +6.82706 q^{63} +1.00000 q^{64} +1.19606 q^{65} +5.16667 q^{66} -2.89748 q^{67} +3.94985 q^{68} -1.06893 q^{69} +0.206545 q^{70} -2.35855 q^{71} -8.56895 q^{72} +15.8124 q^{73} -2.93646 q^{74} +16.7780 q^{75} +3.36409 q^{76} +1.21024 q^{77} -15.6924 q^{78} +6.38305 q^{79} -0.259244 q^{80} +38.7201 q^{81} +3.43668 q^{82} -15.3731 q^{83} -2.70990 q^{84} -1.02398 q^{85} +8.47808 q^{86} -4.09917 q^{87} -1.51902 q^{88} -11.8530 q^{89} +2.22145 q^{90} -3.67577 q^{91} +0.314269 q^{92} -32.3802 q^{93} +12.0536 q^{94} -0.872121 q^{95} +3.40132 q^{96} +2.36845 q^{97} +6.36524 q^{98} +13.0164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9}+O(q^{10}) \) 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9	\( 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9} + 15 q^{10} + 13 q^{11} - 5 q^{12} - 43 q^{13} + 28 q^{14} - 10 q^{15} + 57 q^{16} - 50 q^{18} - 6 q^{19} - 15 q^{20} - 23 q^{21} - 13 q^{22} - q^{23} + 5 q^{24} + 20 q^{25} + 43 q^{26} - 20 q^{27} - 28 q^{28} - 4 q^{29} + 10 q^{30} - 34 q^{31} - 57 q^{32} - 43 q^{33} + 26 q^{35} + 50 q^{36} - 64 q^{37} + 6 q^{38} + 8 q^{39} + 15 q^{40} + 27 q^{41} + 23 q^{42} - 29 q^{43} + 13 q^{44} - 76 q^{45} + q^{46} - 25 q^{47} - 5 q^{48} + 7 q^{49} - 20 q^{50} + 27 q^{51} - 43 q^{52} - 34 q^{53} + 20 q^{54} - 36 q^{55} + 28 q^{56} - 33 q^{57} + 4 q^{58} + 19 q^{59} - 10 q^{60} - 58 q^{61} + 34 q^{62} - 65 q^{63} + 57 q^{64} + 17 q^{65} + 43 q^{66} - 84 q^{67} - 33 q^{69} - 26 q^{70} + 22 q^{71} - 50 q^{72} - 82 q^{73} + 64 q^{74} + 8 q^{75} - 6 q^{76} - 41 q^{77} - 8 q^{78} + 8 q^{79} - 15 q^{80} + 25 q^{81} - 27 q^{82} - 23 q^{83} - 23 q^{84} - 58 q^{85} + 29 q^{86} - 17 q^{87} - 13 q^{88} + 18 q^{89} + 76 q^{90} - 4 q^{91} - q^{92} - 60 q^{93} + 25 q^{94} + 36 q^{95} + 5 q^{96} - 156 q^{97} - 7 q^{98} + 25 q^{99}+O(q^{100}) \) 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9 + 15 * q^10 + 13 * q^11 - 5 * q^12 - 43 * q^13 + 28 * q^14 - 10 * q^15 + 57 * q^16 - 50 * q^18 - 6 * q^19 - 15 * q^20 - 23 * q^21 - 13 * q^22 - q^23 + 5 * q^24 + 20 * q^25 + 43 * q^26 - 20 * q^27 - 28 * q^28 - 4 * q^29 + 10 * q^30 - 34 * q^31 - 57 * q^32 - 43 * q^33 + 26 * q^35 + 50 * q^36 - 64 * q^37 + 6 * q^38 + 8 * q^39 + 15 * q^40 + 27 * q^41 + 23 * q^42 - 29 * q^43 + 13 * q^44 - 76 * q^45 + q^46 - 25 * q^47 - 5 * q^48 + 7 * q^49 - 20 * q^50 + 27 * q^51 - 43 * q^52 - 34 * q^53 + 20 * q^54 - 36 * q^55 + 28 * q^56 - 33 * q^57 + 4 * q^58 + 19 * q^59 - 10 * q^60 - 58 * q^61 + 34 * q^62 - 65 * q^63 + 57 * q^64 + 17 * q^65 + 43 * q^66 - 84 * q^67 - 33 * q^69 - 26 * q^70 + 22 * q^71 - 50 * q^72 - 82 * q^73 + 64 * q^74 + 8 * q^75 - 6 * q^76 - 41 * q^77 - 8 * q^78 + 8 * q^79 - 15 * q^80 + 25 * q^81 - 27 * q^82 - 23 * q^83 - 23 * q^84 - 58 * q^85 + 29 * q^86 - 17 * q^87 - 13 * q^88 + 18 * q^89 + 76 * q^90 - 4 * q^91 - q^92 - 60 * q^93 + 25 * q^94 + 36 * q^95 + 5 * q^96 - 156 * q^97 - 7 * q^98 + 25 * q^99

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