LMFDB - Embedded newform 6037.2.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, 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("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$1$
Dimension:	$243$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63616 q^{2} +2.26078 q^{3} +4.94932 q^{4} -3.62229 q^{5} -5.95976 q^{6} +1.87932 q^{7} -7.77485 q^{8} +2.11112 q^{9} +O(q^{10})$	\(q-2.63616 q^{2} +2.26078 q^{3} +4.94932 q^{4} -3.62229 q^{5} -5.95976 q^{6} +1.87932 q^{7} -7.77485 q^{8} +2.11112 q^{9} +9.54892 q^{10} +5.65974 q^{11} +11.1893 q^{12} -3.90835 q^{13} -4.95418 q^{14} -8.18920 q^{15} +10.5971 q^{16} -6.51206 q^{17} -5.56523 q^{18} +2.29268 q^{19} -17.9279 q^{20} +4.24873 q^{21} -14.9200 q^{22} -4.01981 q^{23} -17.5772 q^{24} +8.12099 q^{25} +10.3030 q^{26} -2.00957 q^{27} +9.30136 q^{28} -8.27055 q^{29} +21.5880 q^{30} +6.34469 q^{31} -12.3859 q^{32} +12.7954 q^{33} +17.1668 q^{34} -6.80745 q^{35} +10.4486 q^{36} +4.92743 q^{37} -6.04387 q^{38} -8.83591 q^{39} +28.1628 q^{40} +4.52556 q^{41} -11.2003 q^{42} +5.35348 q^{43} +28.0118 q^{44} -7.64708 q^{45} +10.5968 q^{46} +8.64243 q^{47} +23.9577 q^{48} -3.46815 q^{49} -21.4082 q^{50} -14.7223 q^{51} -19.3437 q^{52} +12.7504 q^{53} +5.29753 q^{54} -20.5012 q^{55} -14.6115 q^{56} +5.18324 q^{57} +21.8025 q^{58} -4.11361 q^{59} -40.5309 q^{60} +12.5991 q^{61} -16.7256 q^{62} +3.96747 q^{63} +11.4569 q^{64} +14.1572 q^{65} -33.7307 q^{66} -12.2384 q^{67} -32.2302 q^{68} -9.08789 q^{69} +17.9455 q^{70} +0.0173576 q^{71} -16.4136 q^{72} -8.68355 q^{73} -12.9895 q^{74} +18.3598 q^{75} +11.3472 q^{76} +10.6365 q^{77} +23.2928 q^{78} -15.7173 q^{79} -38.3857 q^{80} -10.8765 q^{81} -11.9301 q^{82} -8.21983 q^{83} +21.0283 q^{84} +23.5886 q^{85} -14.1126 q^{86} -18.6979 q^{87} -44.0037 q^{88} -13.3585 q^{89} +20.1589 q^{90} -7.34505 q^{91} -19.8953 q^{92} +14.3439 q^{93} -22.7828 q^{94} -8.30476 q^{95} -28.0017 q^{96} -7.74671 q^{97} +9.14258 q^{98} +11.9484 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) $ 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.63616	−1.86404	−0.932022	−	0.362403i	$-0.881957\pi$
$2$	−2.63616	−1.86404	−0.932022	+	0.362403i	$0.881957\pi$
$3$	2.26078	1.30526	0.652630	−	0.757676i	$-0.273665\pi$
$3$	2.26078	1.30526	0.652630	+	0.757676i	$0.273665\pi$
$4$	4.94932	2.47466
$5$	−3.62229	−1.61994	−0.809969	−	0.586473i	$-0.800516\pi$
$5$	−3.62229	−1.61994	−0.809969	+	0.586473i	$0.800516\pi$
$6$	−5.95976	−2.43306
$7$	1.87932	0.710317	0.355158	−	0.934806i	$-0.384427\pi$
$7$	1.87932	0.710317	0.355158	+	0.934806i	$0.384427\pi$
$8$	−7.77485	−2.74883
$9$	2.11112	0.703705
$10$	9.54892	3.01963
$11$	5.65974	1.70648	0.853238	−	0.521522i	$-0.174635\pi$
$11$	5.65974	1.70648	0.853238	+	0.521522i	$0.174635\pi$
$12$	11.1893	3.23007
$13$	−3.90835	−1.08398	−0.541991	−	0.840385i	$-0.682329\pi$
$13$	−3.90835	−1.08398	−0.541991	+	0.840385i	$0.682329\pi$
$14$	−4.95418	−1.32406
$15$	−8.18920	−2.11444
$16$	10.5971	2.64927
$17$	−6.51206	−1.57941	−0.789703	−	0.613490i	$-0.789765\pi$
$17$	−6.51206	−1.57941	−0.789703	+	0.613490i	$0.789765\pi$
$18$	−5.56523	−1.31174
$19$	2.29268	0.525977	0.262989	−	0.964799i	$-0.415292\pi$
$19$	2.29268	0.525977	0.262989	+	0.964799i	$0.415292\pi$
$20$	−17.9279	−4.00879
$21$	4.24873	0.927149
$22$	−14.9200	−3.18095
$23$	−4.01981	−0.838188	−0.419094	−	0.907943i	$-0.637652\pi$
$23$	−4.01981	−0.838188	−0.419094	+	0.907943i	$0.637652\pi$
$24$	−17.5772	−3.58793
$25$	8.12099	1.62420
$26$	10.3030	2.02059
$27$	−2.00957	−0.386742
$28$	9.30136	1.75779
$29$	−8.27055	−1.53580	−0.767902	−	0.640568i	$-0.778699\pi$
$29$	−8.27055	−1.53580	−0.767902	+	0.640568i	$0.778699\pi$
$30$	21.5880	3.94141
$31$	6.34469	1.13954	0.569770	−	0.821804i	$-0.307032\pi$
$31$	6.34469	1.13954	0.569770	+	0.821804i	$0.307032\pi$
$32$	−12.3859	−2.18953
$33$	12.7954	2.22740
$34$	17.1668	2.94408
$35$	−6.80745	−1.15067
$36$	10.4486	1.74143
$37$	4.92743	0.810065	0.405032	−	0.914302i	$-0.367260\pi$
$37$	4.92743	0.810065	0.405032	+	0.914302i	$0.367260\pi$
$38$	−6.04387	−0.980445
$39$	−8.83591	−1.41488
$40$	28.1628	4.45293
$41$	4.52556	0.706774	0.353387	−	0.935477i	$-0.385030\pi$
$41$	4.52556	0.706774	0.353387	+	0.935477i	$0.385030\pi$
$42$	−11.2003	−1.72825
$43$	5.35348	0.816398	0.408199	−	0.912893i	$-0.366157\pi$
$43$	5.35348	0.816398	0.408199	+	0.912893i	$0.366157\pi$
$44$	28.0118	4.22294
$45$	−7.64708	−1.13996
$46$	10.5968	1.56242
$47$	8.64243	1.26063	0.630314	−	0.776340i	$-0.282926\pi$
$47$	8.64243	1.26063	0.630314	+	0.776340i	$0.282926\pi$
$48$	23.9577	3.45799
$49$	−3.46815	−0.495450
$50$	−21.4082	−3.02758
$51$	−14.7223	−2.06154
$52$	−19.3437	−2.68248
$53$	12.7504	1.75140	0.875702	−	0.482852i	$-0.160399\pi$
$53$	12.7504	1.75140	0.875702	+	0.482852i	$0.160399\pi$
$54$	5.29753	0.720903
$55$	−20.5012	−2.76439
$56$	−14.6115	−1.95254
$57$	5.18324	0.686538
$58$	21.8025	2.86280
$59$	−4.11361	−0.535547	−0.267773	−	0.963482i	$-0.586288\pi$
$59$	−4.11361	−0.535547	−0.267773	+	0.963482i	$0.586288\pi$
$60$	−40.5309	−5.23252
$61$	12.5991	1.61314	0.806572	−	0.591136i	$-0.201320\pi$
$61$	12.5991	1.61314	0.806572	+	0.591136i	$0.201320\pi$
$62$	−16.7256	−2.12415
$63$	3.96747	0.499854
$64$	11.4569	1.43211
$65$	14.1572	1.75598
$66$	−33.7307	−4.15196
$67$	−12.2384	−1.49515	−0.747577	−	0.664175i	$-0.768783\pi$
$67$	−12.2384	−1.49515	−0.747577	+	0.664175i	$0.768783\pi$
$68$	−32.2302	−3.90849
$69$	−9.08789	−1.09405
$70$	17.9455	2.14490
$71$	0.0173576	0.00205997	0.00102998	−	0.999999i	$-0.499672\pi$
$71$	0.0173576	0.00205997	0.00102998	+	0.999999i	$0.499672\pi$
$72$	−16.4136	−1.93436
$73$	−8.68355	−1.01633	−0.508166	−	0.861259i	$-0.669676\pi$
$73$	−8.68355	−1.01633	−0.508166	+	0.861259i	$0.669676\pi$
$74$	−12.9895	−1.51000
$75$	18.3598	2.12000
$76$	11.3472	1.30161
$77$	10.6365	1.21214
$78$	23.2928	2.63739
$79$	−15.7173	−1.76834	−0.884169	−	0.467167i	$-0.845275\pi$
$79$	−15.7173	−1.76834	−0.884169	+	0.467167i	$0.845275\pi$
$80$	−38.3857	−4.29166
$81$	−10.8765	−1.20850
$82$	−11.9301	−1.31746
$83$	−8.21983	−0.902243	−0.451122	−	0.892463i	$-0.648976\pi$
$83$	−8.21983	−0.902243	−0.451122	+	0.892463i	$0.648976\pi$
$84$	21.0283	2.29438
$85$	23.5886	2.55854
$86$	−14.1126	−1.52180
$87$	−18.6979	−2.00462
$88$	−44.0037	−4.69081
$89$	−13.3585	−1.41599	−0.707997	−	0.706215i	$-0.750401\pi$
$89$	−13.3585	−1.41599	−0.707997	+	0.706215i	$0.750401\pi$
$90$	20.1589	2.12493
$91$	−7.34505	−0.769970
$92$	−19.8953	−2.07423
$93$	14.3439	1.48740
$94$	−22.7828	−2.34987
$95$	−8.30476	−0.852051
$96$	−28.0017	−2.85791
$97$	−7.74671	−0.786560	−0.393280	−	0.919419i	$-0.628660\pi$
$97$	−7.74671	−0.786560	−0.393280	+	0.919419i	$0.628660\pi$
$98$	9.14258	0.923540
$99$	11.9484	1.20086
$100$	40.1934	4.01934
$101$	6.78423	0.675056	0.337528	−	0.941315i	$-0.390409\pi$
$101$	6.78423	0.675056	0.337528	+	0.941315i	$0.390409\pi$
$102$	38.8103	3.84279
$103$	3.04045	0.299584	0.149792	−	0.988718i	$-0.452140\pi$
$103$	3.04045	0.299584	0.149792	+	0.988718i	$0.452140\pi$
$104$	30.3868	2.97968
$105$	−15.3901	−1.50192
$106$	−33.6121	−3.26469
$107$	−16.9705	−1.64060	−0.820299	−	0.571934i	$-0.806193\pi$
$107$	−16.9705	−1.64060	−0.820299	+	0.571934i	$0.806193\pi$
$108$	−9.94599	−0.957053
$109$	3.61896	0.346634	0.173317	−	0.984866i	$-0.444552\pi$
$109$	3.61896	0.346634	0.173317	+	0.984866i	$0.444552\pi$
$110$	54.0444	5.15293
$111$	11.1398	1.05735
$112$	19.9153	1.88182
$113$	8.73777	0.821980	0.410990	−	0.911640i	$-0.365183\pi$
$113$	8.73777	0.821980	0.410990	+	0.911640i	$0.365183\pi$
$114$	−13.6638	−1.27974
$115$	14.5609	1.35781
$116$	−40.9336	−3.80059
$117$	−8.25098	−0.762803
$118$	10.8441	0.998282
$119$	−12.2382	−1.12188
$120$	63.6698	5.81223
$121$	21.0327	1.91206
$122$	−33.2131	−3.00697
$123$	10.2313	0.922524
$124$	31.4019	2.81997
$125$	−11.3052	−1.01116
$126$	−10.4589	−0.931749
$127$	14.1920	1.25933	0.629667	−	0.776865i	$-0.283191\pi$
$127$	14.1920	1.25933	0.629667	+	0.776865i	$0.283191\pi$
$128$	−5.43042	−0.479986
$129$	12.1030	1.06561
$130$	−37.3205	−3.27323
$131$	2.34418	0.204812	0.102406	−	0.994743i	$-0.467346\pi$
$131$	2.34418	0.204812	0.102406	+	0.994743i	$0.467346\pi$
$132$	63.3286	5.51204
$133$	4.30869	0.373611
$134$	32.2622	2.78703
$135$	7.27924	0.626497
$136$	50.6303	4.34151
$137$	−16.4051	−1.40158	−0.700790	−	0.713368i	$-0.747169\pi$
$137$	−16.4051	−1.40158	−0.700790	+	0.713368i	$0.747169\pi$
$138$	23.9571	2.03936
$139$	−11.1497	−0.945705	−0.472853	−	0.881142i	$-0.656776\pi$
$139$	−11.1497	−0.945705	−0.472853	+	0.881142i	$0.656776\pi$
$140$	−33.6922	−2.84751
$141$	19.5386	1.64545
$142$	−0.0457574	−0.00383987
$143$	−22.1202	−1.84979
$144$	22.3717	1.86431
$145$	29.9584	2.48791
$146$	22.8912	1.89449
$147$	−7.84072	−0.646691
$148$	24.3874	2.00463
$149$	−14.4811	−1.18634	−0.593171	−	0.805077i	$-0.702124\pi$
$149$	−14.4811	−1.18634	−0.593171	+	0.805077i	$0.702124\pi$
$150$	−48.3992	−3.95178
$151$	−6.64659	−0.540892	−0.270446	−	0.962735i	$-0.587171\pi$
$151$	−6.64659	−0.540892	−0.270446	+	0.962735i	$0.587171\pi$
$152$	−17.8253	−1.44582
$153$	−13.7477	−1.11144
$154$	−28.0394	−2.25948
$155$	−22.9823	−1.84598
$156$	−43.7317	−3.50134
$157$	−14.3312	−1.14376	−0.571879	−	0.820338i	$-0.693785\pi$
$157$	−14.3312	−1.14376	−0.571879	+	0.820338i	$0.693785\pi$
$158$	41.4333	3.29626
$159$	28.8259	2.28604
$160$	44.8652	3.54691
$161$	−7.55451	−0.595379
$162$	28.6722	2.25270
$163$	10.7801	0.844360	0.422180	−	0.906512i	$-0.361265\pi$
$163$	10.7801	0.844360	0.422180	+	0.906512i	$0.361265\pi$
$164$	22.3984	1.74902
$165$	−46.3487	−3.60824
$166$	21.6687	1.68182
$167$	−14.8919	−1.15237	−0.576184	−	0.817320i	$-0.695459\pi$
$167$	−14.8919	−1.15237	−0.576184	+	0.817320i	$0.695459\pi$
$168$	−33.0332	−2.54857
$169$	2.27520	0.175015
$170$	−62.1831	−4.76923
$171$	4.84012	0.370133
$172$	26.4961	2.02031
$173$	−11.7849	−0.895987	−0.447994	−	0.894037i	$-0.647861\pi$
$173$	−11.7849	−0.895987	−0.447994	+	0.894037i	$0.647861\pi$
$174$	49.2905	3.73670
$175$	15.2620	1.15370
$176$	59.9768	4.52092
$177$	−9.29996	−0.699028
$178$	35.2150	2.63948
$179$	25.5644	1.91077	0.955386	−	0.295362i	$-0.0954401\pi$
$179$	25.5644	1.91077	0.955386	+	0.295362i	$0.0954401\pi$
$180$	−37.8478	−2.82101
$181$	14.6238	1.08698	0.543490	−	0.839415i	$-0.317102\pi$
$181$	14.6238	1.08698	0.543490	+	0.839415i	$0.317102\pi$
$182$	19.3627	1.43526
$183$	28.4837	2.10557
$184$	31.2534	2.30403
$185$	−17.8486	−1.31225
$186$	−37.8128	−2.77257
$187$	−36.8566	−2.69522
$188$	42.7741	3.11962
$189$	−3.77663	−0.274709
$190$	21.8926	1.58826
$191$	−16.1504	−1.16860	−0.584299	−	0.811538i	$-0.698631\pi$
$191$	−16.1504	−1.16860	−0.584299	+	0.811538i	$0.698631\pi$
$192$	25.9015	1.86928
$193$	−23.4379	−1.68710	−0.843550	−	0.537051i	$-0.819538\pi$
$193$	−23.4379	−1.68710	−0.843550	+	0.537051i	$0.819538\pi$
$194$	20.4215	1.46618
$195$	32.0062	2.29201
$196$	−17.1650	−1.22607
$197$	5.42090	0.386223	0.193112	−	0.981177i	$-0.438142\pi$
$197$	5.42090	0.386223	0.193112	+	0.981177i	$0.438142\pi$
$198$	−31.4978	−2.23845
$199$	11.1628	0.791308	0.395654	−	0.918400i	$-0.370518\pi$
$199$	11.1628	0.791308	0.395654	+	0.918400i	$0.370518\pi$
$200$	−63.1395	−4.46464
$201$	−27.6682	−1.95157
$202$	−17.8843	−1.25833
$203$	−15.5430	−1.09091
$204$	−72.8654	−5.10160
$205$	−16.3929	−1.14493
$206$	−8.01509	−0.558438
$207$	−8.48628	−0.589837
$208$	−41.4171	−2.87176
$209$	12.9760	0.897568
$210$	40.5708	2.79965
$211$	14.3700	0.989269	0.494635	−	0.869101i	$-0.335302\pi$
$211$	14.3700	0.989269	0.494635	+	0.869101i	$0.335302\pi$
$212$	63.1058	4.33412
$213$	0.0392417	0.00268880
$214$	44.7368	3.05815
$215$	−19.3919	−1.32251
$216$	15.6241	1.06309
$217$	11.9237	0.809434
$218$	−9.54015	−0.646140
$219$	−19.6316	−1.32658
$220$	−101.467	−6.84091
$221$	25.4514	1.71205
$222$	−29.3663	−1.97094
$223$	−25.3394	−1.69685	−0.848425	−	0.529316i	$-0.822449\pi$
$223$	−25.3394	−1.69685	−0.848425	+	0.529316i	$0.822449\pi$
$224$	−23.2770	−1.55526
$225$	17.1444	1.14296
$226$	−23.0341	−1.53221
$227$	7.42527	0.492832	0.246416	−	0.969164i	$-0.420747\pi$
$227$	7.42527	0.492832	0.246416	+	0.969164i	$0.420747\pi$
$228$	25.6535	1.69895
$229$	14.3786	0.950161	0.475081	−	0.879942i	$-0.342419\pi$
$229$	14.3786	0.950161	0.475081	+	0.879942i	$0.342419\pi$
$230$	−38.3848	−2.53102
$231$	24.0467	1.58216
$232$	64.3023	4.22165
$233$	−4.51579	−0.295839	−0.147920	−	0.988999i	$-0.547258\pi$
$233$	−4.51579	−0.295839	−0.147920	+	0.988999i	$0.547258\pi$
$234$	21.7509	1.42190
$235$	−31.3054	−2.04214
$236$	−20.3596	−1.32529
$237$	−35.5334	−2.30814
$238$	32.2619	2.09123
$239$	−3.53675	−0.228774	−0.114387	−	0.993436i	$-0.536490\pi$
$239$	−3.53675	−0.228774	−0.114387	+	0.993436i	$0.536490\pi$
$240$	−86.7816	−5.60173
$241$	−1.11636	−0.0719113	−0.0359557	−	0.999353i	$-0.511448\pi$
$241$	−1.11636	−0.0719113	−0.0359557	+	0.999353i	$0.511448\pi$
$242$	−55.4454	−3.56416
$243$	−18.5607	−1.19067
$244$	62.3567	3.99198
$245$	12.5626	0.802598
$246$	−26.9713	−1.71963
$247$	−8.96060	−0.570149
$248$	−49.3290	−3.13240
$249$	−18.5832	−1.17766
$250$	29.8021	1.88485
$251$	2.15528	0.136040	0.0680200	−	0.997684i	$-0.478332\pi$
$251$	2.15528	0.136040	0.0680200	+	0.997684i	$0.478332\pi$
$252$	19.6362	1.23697
$253$	−22.7511	−1.43035
$254$	−37.4122	−2.34745
$255$	53.3285	3.33956
$256$	−8.59836	−0.537397
$257$	−29.2570	−1.82500	−0.912500	−	0.409078i	$-0.865850\pi$
$257$	−29.2570	−1.82500	−0.912500	+	0.409078i	$0.865850\pi$
$258$	−31.9055	−1.98635
$259$	9.26023	0.575402
$260$	70.0683	4.34545
$261$	−17.4601	−1.08075
$262$	−6.17963	−0.381779
$263$	−11.5637	−0.713050	−0.356525	−	0.934286i	$-0.616038\pi$
$263$	−11.5637	−0.713050	−0.356525	+	0.934286i	$0.616038\pi$
$264$	−99.4825	−6.12272
$265$	−46.1857	−2.83717
$266$	−11.3584	−0.696426
$267$	−30.2005	−1.84824
$268$	−60.5715	−3.69999
$269$	6.71699	0.409542	0.204771	−	0.978810i	$-0.434355\pi$
$269$	6.71699	0.409542	0.204771	+	0.978810i	$0.434355\pi$
$270$	−19.1892	−1.16782
$271$	10.2717	0.623963	0.311981	−	0.950088i	$-0.399007\pi$
$271$	10.2717	0.623963	0.311981	+	0.950088i	$0.399007\pi$
$272$	−69.0088	−4.18428
$273$	−16.6055	−1.00501
$274$	43.2463	2.61261
$275$	45.9627	2.77166
$276$	−44.9788	−2.70741
$277$	−7.62663	−0.458240	−0.229120	−	0.973398i	$-0.573585\pi$
$277$	−7.62663	−0.458240	−0.229120	+	0.973398i	$0.573585\pi$
$278$	29.3923	1.76284
$279$	13.3944	0.801901
$280$	52.9269	3.16299
$281$	12.9909	0.774974	0.387487	−	0.921875i	$-0.373343\pi$
$281$	12.9909	0.774974	0.387487	+	0.921875i	$0.373343\pi$
$282$	−51.5068	−3.06719
$283$	−5.55961	−0.330484	−0.165242	−	0.986253i	$-0.552841\pi$
$283$	−5.55961	−0.330484	−0.165242	+	0.986253i	$0.552841\pi$
$284$	0.0859083	0.00509772
$285$	−18.7752	−1.11215
$286$	58.3124	3.44808
$287$	8.50499	0.502033
$288$	−26.1480	−1.54079
$289$	25.4069	1.49452
$290$	−78.9749	−4.63756
$291$	−17.5136	−1.02667
$292$	−42.9776	−2.51507
$293$	9.24805	0.540277	0.270138	−	0.962821i	$-0.412931\pi$
$293$	9.24805	0.540277	0.270138	+	0.962821i	$0.412931\pi$
$294$	20.6693	1.20546
$295$	14.9007	0.867553
$296$	−38.3100	−2.22673
$297$	−11.3736	−0.659965
$298$	38.1745	2.21139
$299$	15.7108	0.908580
$300$	90.8683	5.24628
$301$	10.0609	0.579902
$302$	17.5215	1.00825
$303$	15.3376	0.881124
$304$	24.2958	1.39346
$305$	−45.6375	−2.61319
$306$	36.2411	2.07177
$307$	15.4216	0.880159	0.440079	−	0.897959i	$-0.354950\pi$
$307$	15.4216	0.880159	0.440079	+	0.897959i	$0.354950\pi$
$308$	52.6433	2.99963
$309$	6.87377	0.391035
$310$	60.5850	3.44099
$311$	−0.454415	−0.0257675	−0.0128837	−	0.999917i	$-0.504101\pi$
$311$	−0.454415	−0.0257675	−0.0128837	+	0.999917i	$0.504101\pi$
$312$	68.6979	3.88925
$313$	9.15234	0.517321	0.258661	−	0.965968i	$-0.416719\pi$
$313$	9.15234	0.517321	0.258661	+	0.965968i	$0.416719\pi$
$314$	37.7794	2.13201
$315$	−14.3713	−0.809732
$316$	−77.7900	−4.37603
$317$	14.3870	0.808052	0.404026	−	0.914747i	$-0.367610\pi$
$317$	14.3870	0.808052	0.404026	+	0.914747i	$0.367610\pi$
$318$	−75.9894	−4.26128
$319$	−46.8092	−2.62081
$320$	−41.5002	−2.31993
$321$	−38.3665	−2.14141
$322$	19.9149	1.10981
$323$	−14.9301	−0.830732
$324$	−53.8314	−2.99063
$325$	−31.7397	−1.76060
$326$	−28.4179	−1.57392
$327$	8.18167	0.452447
$328$	−35.1856	−1.94280
$329$	16.2419	0.895445
$330$	122.182	6.72592
$331$	−18.3304	−1.00753	−0.503765	−	0.863841i	$-0.668052\pi$
$331$	−18.3304	−1.00753	−0.503765	+	0.863841i	$0.668052\pi$
$332$	−40.6825	−2.23274
$333$	10.4024	0.570047
$334$	39.2573	2.14806
$335$	44.3309	2.42206
$336$	45.0242	2.45627
$337$	−18.6584	−1.01639	−0.508194	−	0.861243i	$-0.669687\pi$
$337$	−18.6584	−1.01639	−0.508194	+	0.861243i	$0.669687\pi$
$338$	−5.99777	−0.326236
$339$	19.7542	1.07290
$340$	116.747	6.33151
$341$	35.9093	1.94460
$342$	−12.7593	−0.689944
$343$	−19.6730	−1.06224
$344$	−41.6225	−2.24414
$345$	32.9190	1.77230
$346$	31.0668	1.67016
$347$	−23.3493	−1.25345	−0.626727	−	0.779239i	$-0.715606\pi$
$347$	−23.3493	−1.25345	−0.626727	+	0.779239i	$0.715606\pi$
$348$	−92.5417	−4.96076
$349$	−29.3355	−1.57029	−0.785146	−	0.619310i	$-0.787412\pi$
$349$	−29.3355	−1.57029	−0.785146	+	0.619310i	$0.787412\pi$
$350$	−40.2329	−2.15054
$351$	7.85410	0.419221
$352$	−70.1008	−3.73639
$353$	31.1397	1.65740	0.828701	−	0.559692i	$-0.189081\pi$
$353$	31.1397	1.65740	0.828701	+	0.559692i	$0.189081\pi$
$354$	24.5162	1.30302
$355$	−0.0628743	−0.00333702
$356$	−66.1153	−3.50410
$357$	−27.6680	−1.46434
$358$	−67.3917	−3.56176
$359$	10.0063	0.528114	0.264057	−	0.964507i	$-0.414939\pi$
$359$	10.0063	0.528114	0.264057	+	0.964507i	$0.414939\pi$
$360$	59.4549	3.13355
$361$	−13.7436	−0.723348
$362$	−38.5507	−2.02618
$363$	47.5502	2.49574
$364$	−36.3529	−1.90541
$365$	31.4543	1.64640
$366$	−75.0874	−3.92488
$367$	25.4067	1.32622	0.663108	−	0.748523i	$-0.269237\pi$
$367$	25.4067	1.32622	0.663108	+	0.748523i	$0.269237\pi$
$368$	−42.5983	−2.22059
$369$	9.55399	0.497361
$370$	47.0517	2.44610
$371$	23.9621	1.24405
$372$	70.9927	3.68080
$373$	−36.0526	−1.86673	−0.933367	−	0.358924i	$-0.883144\pi$
$373$	−36.0526	−1.86673	−0.933367	+	0.358924i	$0.883144\pi$
$374$	97.1596	5.02400
$375$	−25.5584	−1.31983
$376$	−67.1936	−3.46525
$377$	32.3242	1.66478
$378$	9.95577	0.512070
$379$	17.7345	0.910960	0.455480	−	0.890246i	$-0.349468\pi$
$379$	17.7345	0.910960	0.455480	+	0.890246i	$0.349468\pi$
$380$	−41.1029	−2.10853
$381$	32.0849	1.64376
$382$	42.5748	2.17832
$383$	11.2834	0.576552	0.288276	−	0.957547i	$-0.406918\pi$
$383$	11.2834	0.576552	0.288276	+	0.957547i	$0.406918\pi$
$384$	−12.2770	−0.626507
$385$	−38.5284	−1.96359
$386$	61.7861	3.14483
$387$	11.3018	0.574504
$388$	−38.3409	−1.94647
$389$	−16.0830	−0.815440	−0.407720	−	0.913107i	$-0.633676\pi$
$389$	−16.0830	−0.815440	−0.407720	+	0.913107i	$0.633676\pi$
$390$	−84.3734	−4.27241
$391$	26.1772	1.32384
$392$	26.9644	1.36191
$393$	5.29967	0.267333
$394$	−14.2903	−0.719937
$395$	56.9328	2.86460
$396$	59.1363	2.97171
$397$	2.14160	0.107484	0.0537419	−	0.998555i	$-0.482885\pi$
$397$	2.14160	0.107484	0.0537419	+	0.998555i	$0.482885\pi$
$398$	−29.4268	−1.47503
$399$	9.74098	0.487659
$400$	86.0589	4.30295
$401$	−21.8289	−1.09009	−0.545043	−	0.838408i	$-0.683487\pi$
$401$	−21.8289	−1.09009	−0.545043	+	0.838408i	$0.683487\pi$
$402$	72.9377	3.63780
$403$	−24.7973	−1.23524
$404$	33.5773	1.67053
$405$	39.3980	1.95770
$406$	40.9738	2.03350
$407$	27.8880	1.38236
$408$	114.464	5.66680
$409$	−32.5747	−1.61071	−0.805357	−	0.592790i	$-0.798026\pi$
$409$	−32.5747	−1.61071	−0.805357	+	0.592790i	$0.798026\pi$
$410$	43.2142	2.13420
$411$	−37.0882	−1.82943
$412$	15.0481	0.741368
$413$	−7.73080	−0.380408
$414$	22.3712	1.09948
$415$	29.7746	1.46158
$416$	48.4083	2.37341
$417$	−25.2070	−1.23439
$418$	−34.2067	−1.67311
$419$	−16.6825	−0.814992	−0.407496	−	0.913207i	$-0.633598\pi$
$419$	−16.6825	−0.814992	−0.407496	+	0.913207i	$0.633598\pi$
$420$	−76.1706	−3.71675
$421$	19.1114	0.931433	0.465717	−	0.884934i	$-0.345797\pi$
$421$	19.1114	0.931433	0.465717	+	0.884934i	$0.345797\pi$
$422$	−37.8815	−1.84404
$423$	18.2452	0.887111
$424$	−99.1326	−4.81430
$425$	−52.8844	−2.56527
$426$	−0.103447	−0.00501203
$427$	23.6777	1.14584
$428$	−83.9923	−4.05992
$429$	−50.0090	−2.41446
$430$	51.1200	2.46523
$431$	1.73546	0.0835943	0.0417971	−	0.999126i	$-0.486692\pi$
$431$	1.73546	0.0835943	0.0417971	+	0.999126i	$0.486692\pi$
$432$	−21.2956	−1.02458
$433$	−1.97257	−0.0947955	−0.0473978	−	0.998876i	$-0.515093\pi$
$433$	−1.97257	−0.0947955	−0.0473978	+	0.998876i	$0.515093\pi$
$434$	−31.4328	−1.50882
$435$	67.7292	3.24737
$436$	17.9114	0.857800
$437$	−9.21614	−0.440868
$438$	51.7519	2.47280
$439$	23.5443	1.12371	0.561854	−	0.827237i	$-0.310088\pi$
$439$	23.5443	1.12371	0.561854	+	0.827237i	$0.310088\pi$
$440$	159.394	7.59881
$441$	−7.32167	−0.348651
$442$	−67.0938	−3.19133
$443$	−15.6000	−0.741179	−0.370589	−	0.928797i	$-0.620844\pi$
$443$	−15.6000	−0.741179	−0.370589	+	0.928797i	$0.620844\pi$
$444$	55.1345	2.61657
$445$	48.3883	2.29382
$446$	66.7985	3.16300
$447$	−32.7387	−1.54849
$448$	21.5312	1.01725
$449$	−11.2249	−0.529734	−0.264867	−	0.964285i	$-0.585328\pi$
$449$	−11.2249	−0.529734	−0.264867	+	0.964285i	$0.585328\pi$
$450$	−45.1952	−2.13052
$451$	25.6135	1.20609
$452$	43.2460	2.03412
$453$	−15.0265	−0.706005
$454$	−19.5742	−0.918661
$455$	26.6059	1.24730
$456$	−40.2990	−1.88717
$457$	−18.7227	−0.875811	−0.437906	−	0.899021i	$-0.644280\pi$
$457$	−18.7227	−0.875811	−0.437906	+	0.899021i	$0.644280\pi$
$458$	−37.9041	−1.77114
$459$	13.0864	0.610822
$460$	72.0665	3.36012
$461$	−18.5401	−0.863501	−0.431750	−	0.901993i	$-0.642104\pi$
$461$	−18.5401	−0.863501	−0.431750	+	0.901993i	$0.642104\pi$
$462$	−63.3909	−2.94921
$463$	−24.3339	−1.13089	−0.565446	−	0.824785i	$-0.691296\pi$
$463$	−24.3339	−1.13089	−0.565446	+	0.824785i	$0.691296\pi$
$464$	−87.6438	−4.06876
$465$	−51.9579	−2.40949
$466$	11.9043	0.551457
$467$	20.5636	0.951568	0.475784	−	0.879562i	$-0.342164\pi$
$467$	20.5636	0.951568	0.475784	+	0.879562i	$0.342164\pi$
$468$	−40.8367	−1.88768
$469$	−22.9998	−1.06203
$470$	82.5259	3.80664
$471$	−32.3997	−1.49290
$472$	31.9827	1.47212
$473$	30.2993	1.39316
$474$	93.6716	4.30248
$475$	18.6189	0.854292
$476$	−60.5710	−2.77627
$477$	26.9176	1.23247
$478$	9.32344	0.426444
$479$	−33.0900	−1.51192	−0.755961	−	0.654617i	$-0.772830\pi$
$479$	−33.0900	−1.51192	−0.755961	+	0.654617i	$0.772830\pi$
$480$	101.430	4.62964
$481$	−19.2581	−0.878095
$482$	2.94291	0.134046
$483$	−17.0791	−0.777125
$484$	104.097	4.73170
$485$	28.0609	1.27418
$486$	48.9290	2.21946
$487$	−6.40332	−0.290162	−0.145081	−	0.989420i	$-0.546344\pi$
$487$	−6.40332	−0.290162	−0.145081	+	0.989420i	$0.546344\pi$
$488$	−97.9559	−4.43425
$489$	24.3713	1.10211
$490$	−33.1171	−1.49608
$491$	−17.1152	−0.772400	−0.386200	−	0.922415i	$-0.626212\pi$
$491$	−17.1152	−0.772400	−0.386200	+	0.922415i	$0.626212\pi$
$492$	50.6379	2.28293
$493$	53.8583	2.42566
$494$	23.6215	1.06278
$495$	−43.2805	−1.94531
$496$	67.2353	3.01895
$497$	0.0326205	0.00146323
$498$	48.9882	2.19521
$499$	−7.33629	−0.328417	−0.164209	−	0.986426i	$-0.552507\pi$
$499$	−7.33629	−0.328417	−0.164209	+	0.986426i	$0.552507\pi$
$500$	−55.9528	−2.50228
$501$	−33.6672	−1.50414
$502$	−5.68165	−0.253585
$503$	−1.73650	−0.0774268	−0.0387134	−	0.999250i	$-0.512326\pi$
$503$	−1.73650	−0.0774268	−0.0387134	+	0.999250i	$0.512326\pi$
$504$	−30.8465	−1.37401
$505$	−24.5745	−1.09355
$506$	59.9753	2.66623
$507$	5.14371	0.228440
$508$	70.2405	3.11642
$509$	−17.2500	−0.764592	−0.382296	−	0.924040i	$-0.624866\pi$
$509$	−17.2500	−0.764592	−0.382296	+	0.924040i	$0.624866\pi$
$510$	−140.582	−6.22509
$511$	−16.3192	−0.721918
$512$	33.5275	1.48172
$513$	−4.60730	−0.203417
$514$	77.1259	3.40188
$515$	−11.0134	−0.485308
$516$	59.9017	2.63703
$517$	48.9139	2.15123
$518$	−24.4114	−1.07258
$519$	−26.6430	−1.16950
$520$	−110.070	−4.82689
$521$	27.7826	1.21718	0.608589	−	0.793486i	$-0.291736\pi$
$521$	27.7826	1.21718	0.608589	+	0.793486i	$0.291736\pi$
$522$	46.0275	2.01457
$523$	15.6264	0.683296	0.341648	−	0.939828i	$-0.389015\pi$
$523$	15.6264	0.683296	0.341648	+	0.939828i	$0.389015\pi$
$524$	11.6021	0.506840
$525$	34.5039	1.50587
$526$	30.4838	1.32916
$527$	−41.3170	−1.79980
$528$	135.594	5.90098
$529$	−6.84115	−0.297441
$530$	121.753	5.28860
$531$	−8.68432	−0.376867
$532$	21.3251	0.924558
$533$	−17.6875	−0.766130
$534$	79.6133	3.44520
$535$	61.4721	2.65767
$536$	95.1514	4.10992
$537$	57.7954	2.49405
$538$	−17.7070	−0.763404
$539$	−19.6288	−0.845474
$540$	36.0273	1.55037
$541$	−39.0241	−1.67778	−0.838888	−	0.544305i	$-0.816794\pi$
$541$	−39.0241	−1.67778	−0.838888	+	0.544305i	$0.816794\pi$
$542$	−27.0779	−1.16309
$543$	33.0612	1.41879
$544$	80.6575	3.45816
$545$	−13.1089	−0.561525
$546$	43.7747	1.87339
$547$	8.70518	0.372207	0.186103	−	0.982530i	$-0.440414\pi$
$547$	8.70518	0.372207	0.186103	+	0.982530i	$0.440414\pi$
$548$	−81.1939	−3.46843
$549$	26.5981	1.13518
$550$	−121.165	−5.16649
$551$	−18.9617	−0.807798
$552$	70.6570	3.00736
$553$	−29.5379	−1.25608
$554$	20.1050	0.854179
$555$	−40.3517	−1.71283
$556$	−55.1834	−2.34030
$557$	26.7761	1.13454	0.567269	−	0.823533i	$-0.308000\pi$
$557$	26.7761	1.13454	0.567269	+	0.823533i	$0.308000\pi$
$558$	−35.3097	−1.49478
$559$	−20.9233	−0.884961
$560$	−72.1392	−3.04844
$561$	−83.3245	−3.51796
$562$	−34.2461	−1.44459
$563$	−22.5502	−0.950380	−0.475190	−	0.879883i	$-0.657621\pi$
$563$	−22.5502	−0.950380	−0.475190	+	0.879883i	$0.657621\pi$
$564$	96.7028	4.07192
$565$	−31.6507	−1.33156
$566$	14.6560	0.616037
$567$	−20.4405	−0.858421
$568$	−0.134953	−0.00566250
$569$	32.4585	1.36073	0.680365	−	0.732873i	$-0.261821\pi$
$569$	32.4585	1.36073	0.680365	+	0.732873i	$0.261821\pi$
$570$	49.4944	2.07309
$571$	−45.3518	−1.89791	−0.948956	−	0.315407i	$-0.897859\pi$
$571$	−45.3518	−1.89791	−0.948956	+	0.315407i	$0.897859\pi$
$572$	−109.480	−4.57759
$573$	−36.5124	−1.52533
$574$	−22.4205	−0.935812
$575$	−32.6448	−1.36138
$576$	24.1868	1.00779
$577$	−16.5870	−0.690526	−0.345263	−	0.938506i	$-0.612210\pi$
$577$	−16.5870	−0.690526	−0.345263	+	0.938506i	$0.612210\pi$
$578$	−66.9765	−2.78585
$579$	−52.9880	−2.20211
$580$	148.273	6.15671
$581$	−15.4477	−0.640878
$582$	46.1686	1.91375
$583$	72.1640	2.98873
$584$	67.5133	2.79372
$585$	29.8875	1.23569
$586$	−24.3793	−1.00710
$587$	−19.2160	−0.793129	−0.396564	−	0.918007i	$-0.629798\pi$
$587$	−19.2160	−0.793129	−0.396564	+	0.918007i	$0.629798\pi$
$588$	−38.8062	−1.60034
$589$	14.5464	0.599372
$590$	−39.2806	−1.61716
$591$	12.2555	0.504122
$592$	52.2164	2.14608
$593$	20.7827	0.853443	0.426722	−	0.904383i	$-0.359668\pi$
$593$	20.7827	0.853443	0.426722	+	0.904383i	$0.359668\pi$
$594$	29.9827	1.23020
$595$	44.3305	1.81737
$596$	−71.6717	−2.93579
$597$	25.2365	1.03286
$598$	−41.4161	−1.69363
$599$	−31.3712	−1.28179	−0.640897	−	0.767627i	$-0.721437\pi$
$599$	−31.3712	−1.28179	−0.640897	+	0.767627i	$0.721437\pi$
$600$	−142.744	−5.82752
$601$	5.03189	0.205255	0.102627	−	0.994720i	$-0.467275\pi$
$601$	5.03189	0.205255	0.102627	+	0.994720i	$0.467275\pi$
$602$	−26.5221	−1.08096
$603$	−25.8366	−1.05215
$604$	−32.8961	−1.33852
$605$	−76.1865	−3.09742
$606$	−40.4324	−1.64245
$607$	25.3974	1.03085	0.515424	−	0.856935i	$-0.327634\pi$
$607$	25.3974	1.03085	0.515424	+	0.856935i	$0.327634\pi$
$608$	−28.3969	−1.15164
$609$	−35.1393	−1.42392
$610$	120.307	4.87111
$611$	−33.7776	−1.36650
$612$	−68.0417	−2.75042
$613$	19.5551	0.789823	0.394911	−	0.918719i	$-0.370775\pi$
$613$	19.5551	0.789823	0.394911	+	0.918719i	$0.370775\pi$
$614$	−40.6538	−1.64065
$615$	−37.0607	−1.49443
$616$	−82.6970	−3.33196
$617$	−34.0953	−1.37262	−0.686312	−	0.727308i	$-0.740771\pi$
$617$	−34.0953	−1.37262	−0.686312	+	0.727308i	$0.740771\pi$
$618$	−18.1203	−0.728907
$619$	−31.8931	−1.28189	−0.640946	−	0.767586i	$-0.721458\pi$
$619$	−31.8931	−1.28189	−0.640946	+	0.767586i	$0.721458\pi$
$620$	−113.747	−4.56818
$621$	8.07808	0.324162
$622$	1.19791	0.0480317
$623$	−25.1049	−1.00580
$624$	−93.6349	−3.74840
$625$	0.345580	0.0138232
$626$	−24.1270	−0.964309
$627$	29.3358	1.17156
$628$	−70.9298	−2.83041
$629$	−32.0877	−1.27942
$630$	37.8850	1.50938
$631$	−16.1086	−0.641274	−0.320637	−	0.947202i	$-0.603897\pi$
$631$	−16.1086	−0.641274	−0.320637	+	0.947202i	$0.603897\pi$
$632$	122.200	4.86085
$633$	32.4873	1.29125
$634$	−37.9263	−1.50624
$635$	−51.4075	−2.04004
$636$	142.668	5.65716
$637$	13.5547	0.537058
$638$	123.396	4.88531
$639$	0.0366439	0.00144961
$640$	19.6706	0.777548
$641$	0.696605	0.0275143	0.0137571	−	0.999905i	$-0.495621\pi$
$641$	0.696605	0.0275143	0.0137571	+	0.999905i	$0.495621\pi$
$642$	101.140	3.99168
$643$	−31.0841	−1.22584	−0.612918	−	0.790146i	$-0.710005\pi$
$643$	−31.0841	−1.22584	−0.612918	+	0.790146i	$0.710005\pi$
$644$	−37.3897	−1.47336
$645$	−43.8407	−1.72623
$646$	39.3580	1.54852
$647$	18.4732	0.726257	0.363129	−	0.931739i	$-0.381709\pi$
$647$	18.4732	0.726257	0.363129	+	0.931739i	$0.381709\pi$
$648$	84.5635	3.32197
$649$	−23.2820	−0.913898
$650$	83.6707	3.28184
$651$	26.9569	1.05652
$652$	53.3540	2.08950
$653$	−48.1859	−1.88566	−0.942830	−	0.333274i	$-0.891846\pi$
$653$	−48.1859	−1.88566	−0.942830	+	0.333274i	$0.891846\pi$
$654$	−21.5682	−0.843382
$655$	−8.49131	−0.331783
$656$	47.9578	1.87244
$657$	−18.3320	−0.715199
$658$	−42.8162	−1.66915
$659$	21.4031	0.833748	0.416874	−	0.908964i	$-0.363126\pi$
$659$	21.4031	0.833748	0.416874	+	0.908964i	$0.363126\pi$
$660$	−229.394	−8.92917
$661$	−28.3101	−1.10114	−0.550568	−	0.834790i	$-0.685589\pi$
$661$	−28.3101	−1.10114	−0.550568	+	0.834790i	$0.685589\pi$
$662$	48.3218	1.87808
$663$	57.5399	2.23467
$664$	63.9079	2.48011
$665$	−15.6073	−0.605226
$666$	−27.4223	−1.06259
$667$	33.2460	1.28729
$668$	−73.7045	−2.85171
$669$	−57.2867	−2.21483
$670$	−116.863	−4.51482
$671$	71.3074	2.75279
$672$	−52.6242	−2.03002
$673$	−12.0807	−0.465677	−0.232838	−	0.972515i	$-0.574801\pi$
$673$	−12.0807	−0.465677	−0.232838	+	0.972515i	$0.574801\pi$
$674$	49.1864	1.89459
$675$	−16.3197	−0.628145
$676$	11.2607	0.433102
$677$	−19.2366	−0.739322	−0.369661	−	0.929167i	$-0.620526\pi$
$677$	−19.2366	−0.739322	−0.369661	+	0.929167i	$0.620526\pi$
$678$	−52.0750	−1.99993
$679$	−14.5586	−0.558707
$680$	−183.398	−7.03298
$681$	16.7869	0.643275
$682$	−94.6625	−3.62481
$683$	−27.5789	−1.05528	−0.527638	−	0.849469i	$-0.676922\pi$
$683$	−27.5789	−1.05528	−0.527638	+	0.849469i	$0.676922\pi$
$684$	23.9553	0.915953
$685$	59.4239	2.27047
$686$	51.8611	1.98007
$687$	32.5067	1.24021
$688$	56.7313	2.16286
$689$	−49.8331	−1.89849
$690$	−86.7796	−3.30364
$691$	4.12930	0.157086	0.0785431	−	0.996911i	$-0.474973\pi$
$691$	4.12930	0.157086	0.0785431	+	0.996911i	$0.474973\pi$
$692$	−58.3270	−2.21726
$693$	22.4548	0.852989
$694$	61.5523	2.33649
$695$	40.3875	1.53198
$696$	145.373	5.51036
$697$	−29.4707	−1.11628
$698$	77.3329	2.92709
$699$	−10.2092	−0.386147
$700$	75.5363	2.85500
$701$	31.5539	1.19177	0.595887	−	0.803068i	$-0.296801\pi$
$701$	31.5539	1.19177	0.595887	+	0.803068i	$0.296801\pi$
$702$	−20.7046	−0.781445
$703$	11.2970	0.426076
$704$	64.8431	2.44387
$705$	−70.7745	−2.66552
$706$	−82.0892	−3.08947
$707$	12.7498	0.479504
$708$	−46.0285	−1.72986
$709$	−9.07511	−0.340823	−0.170411	−	0.985373i	$-0.554510\pi$
$709$	−9.07511	−0.340823	−0.170411	+	0.985373i	$0.554510\pi$
$710$	0.165747	0.00622036
$711$	−33.1811	−1.24439
$712$	103.860	3.89232
$713$	−25.5044	−0.955148
$714$	72.9370	2.72960
$715$	80.1260	2.99654
$716$	126.526	4.72850
$717$	−7.99582	−0.298609
$718$	−26.3783	−0.984428
$719$	38.2747	1.42741	0.713703	−	0.700448i	$-0.247016\pi$
$719$	38.2747	1.42741	0.713703	+	0.700448i	$0.247016\pi$
$720$	−81.0368	−3.02006
$721$	5.71398	0.212800
$722$	36.2303	1.34835
$723$	−2.52385	−0.0938630
$724$	72.3779	2.68991
$725$	−67.1651	−2.49445
$726$	−125.350	−4.65216
$727$	−18.9948	−0.704477	−0.352238	−	0.935910i	$-0.614579\pi$
$727$	−18.9948	−0.704477	−0.352238	+	0.935910i	$0.614579\pi$
$728$	57.1067	2.11651
$729$	−9.33207	−0.345632
$730$	−82.9185	−3.06895
$731$	−34.8622	−1.28942
$732$	140.975	5.21057
$733$	−11.0680	−0.408806	−0.204403	−	0.978887i	$-0.565525\pi$
$733$	−11.0680	−0.408806	−0.204403	+	0.978887i	$0.565525\pi$
$734$	−66.9759	−2.47213
$735$	28.4014	1.04760
$736$	49.7888	1.83524
$737$	−69.2659	−2.55144
$738$	−25.1858	−0.927102
$739$	−14.0017	−0.515060	−0.257530	−	0.966270i	$-0.582909\pi$
$739$	−14.0017	−0.515060	−0.257530	+	0.966270i	$0.582909\pi$
$740$	−88.3383	−3.24738
$741$	−20.2579	−0.744194
$742$	−63.1679	−2.31897
$743$	0.580564	0.0212988	0.0106494	−	0.999943i	$-0.496610\pi$
$743$	0.580564	0.0212988	0.0106494	+	0.999943i	$0.496610\pi$
$744$	−111.522	−4.08859
$745$	52.4549	1.92180
$746$	95.0403	3.47967
$747$	−17.3530	−0.634913
$748$	−182.415	−6.66974
$749$	−31.8930	−1.16535
$750$	67.3760	2.46022
$751$	40.6483	1.48328	0.741639	−	0.670800i	$-0.234049\pi$
$751$	40.6483	1.48328	0.741639	+	0.670800i	$0.234049\pi$
$752$	91.5846	3.33975
$753$	4.87261	0.177568
$754$	−85.2116	−3.10322
$755$	24.0759	0.876212
$756$	−18.6917	−0.679811
$757$	9.13565	0.332041	0.166020	−	0.986122i	$-0.446908\pi$
$757$	9.13565	0.332041	0.166020	+	0.986122i	$0.446908\pi$
$758$	−46.7509	−1.69807
$759$	−51.4351	−1.86698
$760$	64.5683	2.34214
$761$	46.3031	1.67849	0.839243	−	0.543756i	$-0.182998\pi$
$761$	46.3031	1.67849	0.839243	+	0.543756i	$0.182998\pi$
$762$	−84.5808	−3.06404
$763$	6.80120	0.246220
$764$	−79.9332	−2.89188
$765$	49.7982	1.80046
$766$	−29.7447	−1.07472
$767$	16.0774	0.580523
$768$	−19.4390	−0.701444
$769$	24.0027	0.865558	0.432779	−	0.901500i	$-0.357533\pi$
$769$	24.0027	0.865558	0.432779	+	0.901500i	$0.357533\pi$
$770$	101.567	3.66022
$771$	−66.1435	−2.38210
$772$	−116.002	−4.17499
$773$	6.36333	0.228873	0.114437	−	0.993431i	$-0.463494\pi$
$773$	6.36333	0.228873	0.114437	+	0.993431i	$0.463494\pi$
$774$	−29.7934	−1.07090
$775$	51.5252	1.85084
$776$	60.2296	2.16212
$777$	20.9353	0.751050
$778$	42.3972	1.52001
$779$	10.3757	0.371747
$780$	158.409	5.67195
$781$	0.0982396	0.00351529
$782$	−69.0072	−2.46769
$783$	16.6202	0.593959
$784$	−36.7523	−1.31258
$785$	51.9119	1.85282
$786$	−13.9708	−0.498321
$787$	−24.8236	−0.884867	−0.442433	−	0.896801i	$-0.645885\pi$
$787$	−24.8236	−0.884867	−0.442433	+	0.896801i	$0.645885\pi$
$788$	26.8297	0.955770
$789$	−26.1430	−0.930716
$790$	−150.084	−5.33973
$791$	16.4211	0.583866
$792$	−92.8968	−3.30095
$793$	−49.2415	−1.74862
$794$	−5.64559	−0.200355
$795$	−104.416	−3.70324
$796$	55.2481	1.95822
$797$	22.6917	0.803782	0.401891	−	0.915688i	$-0.368353\pi$
$797$	22.6917	0.803782	0.401891	+	0.915688i	$0.368353\pi$
$798$	−25.6787	−0.909018
$799$	−56.2800	−1.99104
$800$	−100.586	−3.55624
$801$	−28.2013	−0.996443
$802$	57.5445	2.03197
$803$	−49.1466	−1.73435
$804$	−136.939	−4.82946
$805$	27.3646	0.964477
$806$	65.3694	2.30254
$807$	15.1856	0.534559
$808$	−52.7464	−1.85561
$809$	−24.5496	−0.863118	−0.431559	−	0.902085i	$-0.642036\pi$
$809$	−24.5496	−0.863118	−0.431559	+	0.902085i	$0.642036\pi$
$810$	−103.859	−3.64924
$811$	32.2191	1.13137	0.565683	−	0.824623i	$-0.308613\pi$
$811$	32.2191	1.13137	0.565683	+	0.824623i	$0.308613\pi$
$812$	−76.9273	−2.69962
$813$	23.2221	0.814434
$814$	−73.5170	−2.57677
$815$	−39.0485	−1.36781
$816$	−156.014	−5.46157
$817$	12.2738	0.429407
$818$	85.8719	3.00244
$819$	−15.5062	−0.541832
$820$	−81.1336	−2.83331
$821$	18.7264	0.653556	0.326778	−	0.945101i	$-0.394037\pi$
$821$	18.7264	0.653556	0.326778	+	0.945101i	$0.394037\pi$
$822$	97.7703	3.41013
$823$	18.0706	0.629901	0.314950	−	0.949108i	$-0.398012\pi$
$823$	18.0706	0.629901	0.314950	+	0.949108i	$0.398012\pi$
$824$	−23.6390	−0.823505
$825$	103.912	3.61773
$826$	20.3796	0.709097
$827$	8.98012	0.312269	0.156135	−	0.987736i	$-0.450097\pi$
$827$	8.98012	0.312269	0.156135	+	0.987736i	$0.450097\pi$
$828$	−42.0013	−1.45965
$829$	17.2083	0.597668	0.298834	−	0.954305i	$-0.403402\pi$
$829$	17.2083	0.597668	0.298834	+	0.954305i	$0.403402\pi$
$830$	−78.4905	−2.72444
$831$	−17.2421	−0.598122
$832$	−44.7776	−1.55238
$833$	22.5848	0.782517
$834$	66.4495	2.30096
$835$	53.9427	1.86676
$836$	64.2223	2.22117
$837$	−12.7501	−0.440708
$838$	43.9776	1.51918
$839$	18.8624	0.651203	0.325601	−	0.945507i	$-0.394433\pi$
$839$	18.8624	0.651203	0.325601	+	0.945507i	$0.394433\pi$
$840$	119.656	4.12853
$841$	39.4020	1.35869
$842$	−50.3806	−1.73623
$843$	29.3696	1.01154
$844$	71.1215	2.44810
$845$	−8.24142	−0.283513
$846$	−48.0971	−1.65361
$847$	39.5272	1.35817
$848$	135.117	4.63995
$849$	−12.5690	−0.431368
$850$	139.411	4.78177
$851$	−19.8073	−0.678986
$852$	0.194220	0.00665385
$853$	−16.1285	−0.552229	−0.276115	−	0.961125i	$-0.589047\pi$
$853$	−16.1285	−0.552229	−0.276115	+	0.961125i	$0.589047\pi$
$854$	−62.4181	−2.13590
$855$	−17.5323	−0.599593
$856$	131.943	4.50972
$857$	11.8324	0.404188	0.202094	−	0.979366i	$-0.435225\pi$
$857$	11.8324	0.404188	0.202094	+	0.979366i	$0.435225\pi$
$858$	131.831	4.50065
$859$	3.54913	0.121095	0.0605473	−	0.998165i	$-0.480715\pi$
$859$	3.54913	0.121095	0.0605473	+	0.998165i	$0.480715\pi$
$860$	−95.9765	−3.27277
$861$	19.2279	0.655285
$862$	−4.57495	−0.155823
$863$	13.5205	0.460242	0.230121	−	0.973162i	$-0.426088\pi$
$863$	13.5205	0.460242	0.230121	+	0.973162i	$0.426088\pi$
$864$	24.8903	0.846784
$865$	42.6882	1.45144
$866$	5.19999	0.176703
$867$	57.4393	1.95074
$868$	59.0142	2.00307
$869$	−88.9560	−3.01763
$870$	−178.545	−6.05323
$871$	47.8318	1.62072
$872$	−28.1369	−0.952836
$873$	−16.3542	−0.553506
$874$	24.2952	0.821797
$875$	−21.2460	−0.718246
$876$	−97.1628	−3.28283
$877$	−40.3413	−1.36223	−0.681115	−	0.732177i	$-0.738505\pi$
$877$	−40.3413	−1.36223	−0.681115	+	0.732177i	$0.738505\pi$
$878$	−62.0664	−2.09464
$879$	20.9078	0.705202
$880$	−217.253	−7.32361
$881$	8.21663	0.276825	0.138413	−	0.990375i	$-0.455800\pi$
$881$	8.21663	0.276825	0.138413	+	0.990375i	$0.455800\pi$
$882$	19.3011	0.649900
$883$	−11.3747	−0.382789	−0.191395	−	0.981513i	$-0.561301\pi$
$883$	−11.3747	−0.382789	−0.191395	+	0.981513i	$0.561301\pi$
$884$	125.967	4.23673
$885$	33.6872	1.13238
$886$	41.1240	1.38159
$887$	20.7635	0.697170	0.348585	−	0.937277i	$-0.386662\pi$
$887$	20.7635	0.697170	0.348585	+	0.937277i	$0.386662\pi$
$888$	−86.6105	−2.90646
$889$	26.6713	0.894526
$890$	−127.559	−4.27579
$891$	−61.5584	−2.06228
$892$	−125.413	−4.19912
$893$	19.8143	0.663062
$894$	86.3042	2.88644
$895$	−92.6016	−3.09533
$896$	−10.2055	−0.340942
$897$	35.5186	1.18593
$898$	29.5905	0.987447
$899$	−52.4741	−1.75011
$900$	84.8529	2.82843
$901$	−83.0314	−2.76618
$902$	−67.5212	−2.24821
$903$	22.7455	0.756923
$904$	−67.9349	−2.25948
$905$	−52.9718	−1.76084
$906$	39.6121	1.31602
$907$	−4.82059	−0.160065	−0.0800325	−	0.996792i	$-0.525502\pi$
$907$	−4.82059	−0.160065	−0.0800325	+	0.996792i	$0.525502\pi$
$908$	36.7500	1.21959
$909$	14.3223	0.475041
$910$	−70.1373	−2.32503
$911$	−32.5713	−1.07914	−0.539568	−	0.841942i	$-0.681412\pi$
$911$	−32.5713	−1.07914	−0.539568	+	0.841942i	$0.681412\pi$
$912$	54.9273	1.81883
$913$	−46.5221	−1.53966
$914$	49.3560	1.63255
$915$	−103.176	−3.41090
$916$	71.1640	2.35132
$917$	4.40547	0.145481
$918$	−34.4978	−1.13860
$919$	−16.5653	−0.546440	−0.273220	−	0.961952i	$-0.588089\pi$
$919$	−16.5653	−0.546440	−0.273220	+	0.961952i	$0.588089\pi$
$920$	−113.209	−3.73239
$921$	34.8649	1.14884
$922$	48.8747	1.60960
$923$	−0.0678396	−0.00223297
$924$	119.015	3.91530
$925$	40.0156	1.31571
$926$	64.1480	2.10803
$927$	6.41874	0.210819
$928$	102.438	3.36269
$929$	13.3972	0.439547	0.219774	−	0.975551i	$-0.429468\pi$
$929$	13.3972	0.439547	0.219774	+	0.975551i	$0.429468\pi$
$930$	136.969	4.49139
$931$	−7.95137	−0.260595
$932$	−22.3501	−0.732100
$933$	−1.02733	−0.0336333
$934$	−54.2088	−1.77376
$935$	133.505	4.36609
$936$	64.1502	2.09681
$937$	14.8426	0.484885	0.242443	−	0.970166i	$-0.422051\pi$
$937$	14.8426	0.484885	0.242443	+	0.970166i	$0.422051\pi$
$938$	60.6311	1.97968
$939$	20.6914	0.675239
$940$	−154.940	−5.05359
$941$	−52.3156	−1.70544	−0.852719	−	0.522369i	$-0.825048\pi$
$941$	−52.3156	−1.70544	−0.852719	+	0.522369i	$0.825048\pi$
$942$	85.4107	2.78283
$943$	−18.1919	−0.592409
$944$	−43.5923	−1.41881
$945$	13.6800	0.445012
$946$	−79.8737	−2.59692
$947$	37.1252	1.20641	0.603204	−	0.797587i	$-0.293890\pi$
$947$	37.1252	1.20641	0.603204	+	0.797587i	$0.293890\pi$
$948$	−175.866	−5.71186
$949$	33.9383	1.10169
$950$	−49.0822	−1.59244
$951$	32.5257	1.05472
$952$	95.1506	3.08385
$953$	−24.3215	−0.787851	−0.393926	−	0.919142i	$-0.628883\pi$
$953$	−24.3215	−0.787851	−0.393926	+	0.919142i	$0.628883\pi$
$954$	−70.9590	−2.29738
$955$	58.5013	1.89306
$956$	−17.5045	−0.566136
$957$	−105.825	−3.42084
$958$	87.2304	2.81829
$959$	−30.8304	−0.995566
$960$	−93.8228	−3.02812
$961$	9.25510	0.298551
$962$	50.7674	1.63681
$963$	−35.8267	−1.15450
$964$	−5.52524	−0.177956
$965$	84.8991	2.73300
$966$	45.0231	1.44859
$967$	14.4070	0.463297	0.231649	−	0.972800i	$-0.425588\pi$
$967$	14.4070	0.463297	0.231649	+	0.972800i	$0.425588\pi$
$968$	−163.526	−5.25592
$969$	−33.7536	−1.08432
$970$	−73.9728	−2.37512
$971$	−7.10457	−0.227996	−0.113998	−	0.993481i	$-0.536366\pi$
$971$	−7.10457	−0.227996	−0.113998	+	0.993481i	$0.536366\pi$
$972$	−91.8629	−2.94650
$973$	−20.9539	−0.671750
$974$	16.8801	0.540875
$975$	−71.7564	−2.29804
$976$	133.513	4.27366
$977$	−6.44172	−0.206089	−0.103044	−	0.994677i	$-0.532858\pi$
$977$	−6.44172	−0.206089	−0.103044	+	0.994677i	$0.532858\pi$
$978$	−64.2466	−2.05438
$979$	−75.6055	−2.41636
$980$	62.1765	1.98616
$981$	7.64005	0.243928
$982$	45.1184	1.43979
$983$	−36.7902	−1.17343	−0.586713	−	0.809795i	$-0.699578\pi$
$983$	−36.7902	−1.17343	−0.586713	+	0.809795i	$0.699578\pi$
$984$	−79.5468	−2.53586
$985$	−19.6361	−0.625658
$986$	−141.979	−4.52153
$987$	36.7193	1.16879
$988$	−44.3488	−1.41092
$989$	−21.5200	−0.684295
$990$	114.094	3.62615
$991$	9.15927	0.290954	0.145477	−	0.989362i	$-0.453528\pi$
$991$	9.15927	0.290954	0.145477	+	0.989362i	$0.453528\pi$
$992$	−78.5845	−2.49506
$993$	−41.4410	−1.31509
$994$	−0.0859928	−0.00272753
$995$	−40.4348	−1.28187
$996$	−91.9741	−2.91431
$997$	−32.3907	−1.02583	−0.512913	−	0.858441i	$-0.671433\pi$
$997$	−32.3907	−1.02583	−0.512913	+	0.858441i	$0.671433\pi$
$998$	19.3396	0.612184
$999$	−9.90201	−0.313286

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.a.1.15	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.15	✓	243	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63616 q^{2} +2.26078 q^{3} +4.94932 q^{4} -3.62229 q^{5} -5.95976 q^{6} +1.87932 q^{7} -7.77485 q^{8} +2.11112 q^{9} +O(q^{10})\)	\(q-2.63616 q^{2} +2.26078 q^{3} +4.94932 q^{4} -3.62229 q^{5} -5.95976 q^{6} +1.87932 q^{7} -7.77485 q^{8} +2.11112 q^{9} +9.54892 q^{10} +5.65974 q^{11} +11.1893 q^{12} -3.90835 q^{13} -4.95418 q^{14} -8.18920 q^{15} +10.5971 q^{16} -6.51206 q^{17} -5.56523 q^{18} +2.29268 q^{19} -17.9279 q^{20} +4.24873 q^{21} -14.9200 q^{22} -4.01981 q^{23} -17.5772 q^{24} +8.12099 q^{25} +10.3030 q^{26} -2.00957 q^{27} +9.30136 q^{28} -8.27055 q^{29} +21.5880 q^{30} +6.34469 q^{31} -12.3859 q^{32} +12.7954 q^{33} +17.1668 q^{34} -6.80745 q^{35} +10.4486 q^{36} +4.92743 q^{37} -6.04387 q^{38} -8.83591 q^{39} +28.1628 q^{40} +4.52556 q^{41} -11.2003 q^{42} +5.35348 q^{43} +28.0118 q^{44} -7.64708 q^{45} +10.5968 q^{46} +8.64243 q^{47} +23.9577 q^{48} -3.46815 q^{49} -21.4082 q^{50} -14.7223 q^{51} -19.3437 q^{52} +12.7504 q^{53} +5.29753 q^{54} -20.5012 q^{55} -14.6115 q^{56} +5.18324 q^{57} +21.8025 q^{58} -4.11361 q^{59} -40.5309 q^{60} +12.5991 q^{61} -16.7256 q^{62} +3.96747 q^{63} +11.4569 q^{64} +14.1572 q^{65} -33.7307 q^{66} -12.2384 q^{67} -32.2302 q^{68} -9.08789 q^{69} +17.9455 q^{70} +0.0173576 q^{71} -16.4136 q^{72} -8.68355 q^{73} -12.9895 q^{74} +18.3598 q^{75} +11.3472 q^{76} +10.6365 q^{77} +23.2928 q^{78} -15.7173 q^{79} -38.3857 q^{80} -10.8765 q^{81} -11.9301 q^{82} -8.21983 q^{83} +21.0283 q^{84} +23.5886 q^{85} -14.1126 q^{86} -18.6979 q^{87} -44.0037 q^{88} -13.3585 q^{89} +20.1589 q^{90} -7.34505 q^{91} -19.8953 q^{92} +14.3439 q^{93} -22.7828 q^{94} -8.30476 q^{95} -28.0017 q^{96} -7.74671 q^{97} +9.14258 q^{98} +11.9484 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * q^99

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