LMFDB - Embedded newform 6037.2.a.a.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.81439 q^{2} +2.72661 q^{3} +5.92080 q^{4} +4.37726 q^{5} -7.67375 q^{6} -1.67878 q^{7} -11.0347 q^{8} +4.43441 q^{9} +O(q^{10})$	\(q-2.81439 q^{2} +2.72661 q^{3} +5.92080 q^{4} +4.37726 q^{5} -7.67375 q^{6} -1.67878 q^{7} -11.0347 q^{8} +4.43441 q^{9} -12.3193 q^{10} -4.62107 q^{11} +16.1437 q^{12} -3.74200 q^{13} +4.72474 q^{14} +11.9351 q^{15} +19.2143 q^{16} -4.30426 q^{17} -12.4802 q^{18} +1.86232 q^{19} +25.9169 q^{20} -4.57737 q^{21} +13.0055 q^{22} -2.10458 q^{23} -30.0873 q^{24} +14.1604 q^{25} +10.5315 q^{26} +3.91108 q^{27} -9.93971 q^{28} -6.63530 q^{29} -33.5900 q^{30} -1.46430 q^{31} -32.0073 q^{32} -12.5999 q^{33} +12.1139 q^{34} -7.34844 q^{35} +26.2553 q^{36} -10.6215 q^{37} -5.24130 q^{38} -10.2030 q^{39} -48.3016 q^{40} +4.23874 q^{41} +12.8825 q^{42} +7.99027 q^{43} -27.3604 q^{44} +19.4106 q^{45} +5.92311 q^{46} -8.16691 q^{47} +52.3900 q^{48} -4.18171 q^{49} -39.8529 q^{50} -11.7360 q^{51} -22.1556 q^{52} -3.00048 q^{53} -11.0073 q^{54} -20.2276 q^{55} +18.5248 q^{56} +5.07783 q^{57} +18.6743 q^{58} -4.76521 q^{59} +70.6653 q^{60} -9.57537 q^{61} +4.12110 q^{62} -7.44439 q^{63} +51.6524 q^{64} -16.3797 q^{65} +35.4609 q^{66} -5.38481 q^{67} -25.4847 q^{68} -5.73837 q^{69} +20.6814 q^{70} +0.0228056 q^{71} -48.9323 q^{72} +8.08027 q^{73} +29.8931 q^{74} +38.6099 q^{75} +11.0264 q^{76} +7.75774 q^{77} +28.7152 q^{78} +9.62004 q^{79} +84.1060 q^{80} -2.63924 q^{81} -11.9295 q^{82} -17.5861 q^{83} -27.1017 q^{84} -18.8409 q^{85} -22.4878 q^{86} -18.0919 q^{87} +50.9920 q^{88} +11.5858 q^{89} -54.6289 q^{90} +6.28198 q^{91} -12.4608 q^{92} -3.99257 q^{93} +22.9849 q^{94} +8.15186 q^{95} -87.2714 q^{96} -13.2417 q^{97} +11.7690 q^{98} -20.4917 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.81439	−1.99008	−0.995038	−	0.0994960i	$-0.968277\pi$
$2$	−2.81439	−1.99008	−0.995038	+	0.0994960i	$0.968277\pi$
$3$	2.72661	1.57421	0.787105	−	0.616819i	$-0.211579\pi$
$3$	2.72661	1.57421	0.787105	+	0.616819i	$0.211579\pi$
$4$	5.92080	2.96040
$5$	4.37726	1.95757	0.978785	−	0.204892i	$-0.0656843\pi$
$5$	4.37726	1.95757	0.978785	+	0.204892i	$0.0656843\pi$
$6$	−7.67375	−3.13280
$7$	−1.67878	−0.634518	−0.317259	−	0.948339i	$-0.602762\pi$
$7$	−1.67878	−0.634518	−0.317259	+	0.948339i	$0.602762\pi$
$8$	−11.0347	−3.90135
$9$	4.43441	1.47814
$10$	−12.3193	−3.89571
$11$	−4.62107	−1.39330	−0.696652	−	0.717409i	$-0.745328\pi$
$11$	−4.62107	−1.39330	−0.696652	+	0.717409i	$0.745328\pi$
$12$	16.1437	4.66029
$13$	−3.74200	−1.03784	−0.518922	−	0.854822i	$-0.673666\pi$
$13$	−3.74200	−1.03784	−0.518922	+	0.854822i	$0.673666\pi$
$14$	4.72474	1.26274
$15$	11.9351	3.08162
$16$	19.2143	4.80358
$17$	−4.30426	−1.04394	−0.521968	−	0.852965i	$-0.674802\pi$
$17$	−4.30426	−1.04394	−0.521968	+	0.852965i	$0.674802\pi$
$18$	−12.4802	−2.94160
$19$	1.86232	0.427246	0.213623	−	0.976916i	$-0.431474\pi$
$19$	1.86232	0.427246	0.213623	+	0.976916i	$0.431474\pi$
$20$	25.9169	5.79519
$21$	−4.57737	−0.998865
$22$	13.0055	2.77278
$23$	−2.10458	−0.438835	−0.219418	−	0.975631i	$-0.570416\pi$
$23$	−2.10458	−0.438835	−0.219418	+	0.975631i	$0.570416\pi$
$24$	−30.0873	−6.14154
$25$	14.1604	2.83208
$26$	10.5315	2.06539
$27$	3.91108	0.752688
$28$	−9.93971	−1.87843
$29$	−6.63530	−1.23214	−0.616072	−	0.787690i	$-0.711277\pi$
$29$	−6.63530	−1.23214	−0.616072	+	0.787690i	$0.711277\pi$
$30$	−33.5900	−6.13267
$31$	−1.46430	−0.262995	−0.131498	−	0.991316i	$-0.541979\pi$
$31$	−1.46430	−0.262995	−0.131498	+	0.991316i	$0.541979\pi$
$32$	−32.0073	−5.65814
$33$	−12.5999	−2.19335
$34$	12.1139	2.07751
$35$	−7.34844	−1.24211
$36$	26.2553	4.37588
$37$	−10.6215	−1.74616	−0.873082	−	0.487574i	$-0.837882\pi$
$37$	−10.6215	−1.74616	−0.873082	+	0.487574i	$0.837882\pi$
$38$	−5.24130	−0.850252
$39$	−10.2030	−1.63378
$40$	−48.3016	−7.63716
$41$	4.23874	0.661980	0.330990	−	0.943634i	$-0.392617\pi$
$41$	4.23874	0.661980	0.330990	+	0.943634i	$0.392617\pi$
$42$	12.8825	1.98782
$43$	7.99027	1.21851	0.609253	−	0.792976i	$-0.291470\pi$
$43$	7.99027	1.21851	0.609253	+	0.792976i	$0.291470\pi$
$44$	−27.3604	−4.12474
$45$	19.4106	2.89356
$46$	5.92311	0.873315
$47$	−8.16691	−1.19127	−0.595633	−	0.803256i	$-0.703099\pi$
$47$	−8.16691	−1.19127	−0.595633	+	0.803256i	$0.703099\pi$
$48$	52.3900	7.56184
$49$	−4.18171	−0.597387
$50$	−39.8529	−5.63605
$51$	−11.7360	−1.64337
$52$	−22.1556	−3.07244
$53$	−3.00048	−0.412147	−0.206074	−	0.978537i	$-0.566069\pi$
$53$	−3.00048	−0.412147	−0.206074	+	0.978537i	$0.566069\pi$
$54$	−11.0073	−1.49791
$55$	−20.2276	−2.72749
$56$	18.5248	2.47548
$57$	5.07783	0.672575
$58$	18.6743	2.45206
$59$	−4.76521	−0.620378	−0.310189	−	0.950675i	$-0.600392\pi$
$59$	−4.76521	−0.620378	−0.310189	+	0.950675i	$0.600392\pi$
$60$	70.6653	9.12285
$61$	−9.57537	−1.22600	−0.613000	−	0.790083i	$-0.710038\pi$
$61$	−9.57537	−1.22600	−0.613000	+	0.790083i	$0.710038\pi$
$62$	4.12110	0.523381
$63$	−7.44439	−0.937904
$64$	51.6524	6.45654
$65$	−16.3797	−2.03165
$66$	35.4609	4.36494
$67$	−5.38481	−0.657859	−0.328929	−	0.944355i	$-0.606688\pi$
$67$	−5.38481	−0.657859	−0.328929	+	0.944355i	$0.606688\pi$
$68$	−25.4847	−3.09047
$69$	−5.73837	−0.690819
$70$	20.6814	2.47190
$71$	0.0228056	0.00270653	0.00135326	−	0.999999i	$-0.499569\pi$
$71$	0.0228056	0.00270653	0.00135326	+	0.999999i	$0.499569\pi$
$72$	−48.9323	−5.76673
$73$	8.08027	0.945724	0.472862	−	0.881137i	$-0.343221\pi$
$73$	8.08027	0.945724	0.472862	+	0.881137i	$0.343221\pi$
$74$	29.8931	3.47500
$75$	38.6099	4.45828
$76$	11.0264	1.26482
$77$	7.75774	0.884076
$78$	28.7152	3.25135
$79$	9.62004	1.08234	0.541169	−	0.840914i	$-0.317982\pi$
$79$	9.62004	1.08234	0.541169	+	0.840914i	$0.317982\pi$
$80$	84.1060	9.40334
$81$	−2.63924	−0.293248
$82$	−11.9295	−1.31739
$83$	−17.5861	−1.93032	−0.965161	−	0.261658i	$-0.915731\pi$
$83$	−17.5861	−1.93032	−0.965161	+	0.261658i	$0.915731\pi$
$84$	−27.1017	−2.95704
$85$	−18.8409	−2.04358
$86$	−22.4878	−2.42492
$87$	−18.0919	−1.93965
$88$	50.9920	5.43576
$89$	11.5858	1.22809	0.614044	−	0.789272i	$-0.289542\pi$
$89$	11.5858	1.22809	0.614044	+	0.789272i	$0.289542\pi$
$90$	−54.6289	−5.75839
$91$	6.28198	0.658531
$92$	−12.4608	−1.29913
$93$	−3.99257	−0.414010
$94$	22.9849	2.37071
$95$	8.15186	0.836363
$96$	−87.2714	−8.90710
$97$	−13.2417	−1.34449	−0.672247	−	0.740327i	$-0.734671\pi$
$97$	−13.2417	−1.34449	−0.672247	+	0.740327i	$0.734671\pi$
$98$	11.7690	1.18885
$99$	−20.4917	−2.05949
$100$	83.8409	8.38409
$101$	15.0472	1.49725	0.748624	−	0.662995i	$-0.230715\pi$
$101$	15.0472	1.49725	0.748624	+	0.662995i	$0.230715\pi$
$102$	33.0298	3.27044
$103$	−0.787234	−0.0775684	−0.0387842	−	0.999248i	$-0.512348\pi$
$103$	−0.787234	−0.0775684	−0.0387842	+	0.999248i	$0.512348\pi$
$104$	41.2918	4.04899
$105$	−20.0363	−1.95535
$106$	8.44452	0.820204
$107$	4.26632	0.412441	0.206220	−	0.978506i	$-0.433884\pi$
$107$	4.26632	0.412441	0.206220	+	0.978506i	$0.433884\pi$
$108$	23.1567	2.22826
$109$	2.21999	0.212636	0.106318	−	0.994332i	$-0.466094\pi$
$109$	2.21999	0.212636	0.106318	+	0.994332i	$0.466094\pi$
$110$	56.9284	5.42791
$111$	−28.9607	−2.74883
$112$	−32.2566	−3.04796
$113$	12.1880	1.14655	0.573275	−	0.819363i	$-0.305673\pi$
$113$	12.1880	1.14655	0.573275	+	0.819363i	$0.305673\pi$
$114$	−14.2910	−1.33847
$115$	−9.21229	−0.859050
$116$	−39.2863	−3.64764
$117$	−16.5936	−1.53408
$118$	13.4112	1.23460
$119$	7.22589	0.662396
$120$	−131.700	−12.0225
$121$	10.3542	0.941295
$122$	26.9489	2.43983
$123$	11.5574	1.04210
$124$	−8.66981	−0.778572
$125$	40.0974	3.58642
$126$	20.9514	1.86650
$127$	11.1254	0.987216	0.493608	−	0.869685i	$-0.335678\pi$
$127$	11.1254	0.987216	0.493608	+	0.869685i	$0.335678\pi$
$128$	−81.3555	−7.19088
$129$	21.7864	1.91818
$130$	46.0989	4.04314
$131$	−16.1464	−1.41072	−0.705359	−	0.708851i	$-0.749214\pi$
$131$	−16.1464	−1.41072	−0.705359	+	0.708851i	$0.749214\pi$
$132$	−74.6012	−6.49321
$133$	−3.12642	−0.271095
$134$	15.1550	1.30919
$135$	17.1198	1.47344
$136$	47.4961	4.07276
$137$	−11.8428	−1.01180	−0.505901	−	0.862591i	$-0.668840\pi$
$137$	−11.8428	−1.01180	−0.505901	+	0.862591i	$0.668840\pi$
$138$	16.1500	1.37478
$139$	−20.4528	−1.73478	−0.867390	−	0.497629i	$-0.834204\pi$
$139$	−20.4528	−1.73478	−0.867390	+	0.497629i	$0.834204\pi$
$140$	−43.5087	−3.67715
$141$	−22.2680	−1.87530
$142$	−0.0641839	−0.00538620
$143$	17.2920	1.44603
$144$	85.2042	7.10035
$145$	−29.0444	−2.41201
$146$	−22.7410	−1.88206
$147$	−11.4019	−0.940412
$148$	−62.8878	−5.16935
$149$	−6.91204	−0.566256	−0.283128	−	0.959082i	$-0.591372\pi$
$149$	−6.91204	−0.566256	−0.283128	+	0.959082i	$0.591372\pi$
$150$	−108.663	−8.87232
$151$	0.128381	0.0104475	0.00522375	−	0.999986i	$-0.498337\pi$
$151$	0.128381	0.0104475	0.00522375	+	0.999986i	$0.498337\pi$
$152$	−20.5501	−1.66683
$153$	−19.0869	−1.54308
$154$	−21.8333	−1.75938
$155$	−6.40960	−0.514831
$156$	−60.4098	−4.83666
$157$	11.8215	0.943462	0.471731	−	0.881742i	$-0.343629\pi$
$157$	11.8215	0.943462	0.471731	+	0.881742i	$0.343629\pi$
$158$	−27.0746	−2.15394
$159$	−8.18113	−0.648806
$160$	−140.104	−11.0762
$161$	3.53312	0.278449
$162$	7.42785	0.583587
$163$	−17.9551	−1.40635	−0.703177	−	0.711015i	$-0.748236\pi$
$163$	−17.9551	−1.40635	−0.703177	+	0.711015i	$0.748236\pi$
$164$	25.0968	1.95973
$165$	−55.1528	−4.29364
$166$	49.4941	3.84149
$167$	4.34235	0.336022	0.168011	−	0.985785i	$-0.446266\pi$
$167$	4.34235	0.336022	0.168011	+	0.985785i	$0.446266\pi$
$168$	50.5099	3.89692
$169$	1.00256	0.0771198
$170$	53.0256	4.06687
$171$	8.25830	0.631528
$172$	47.3089	3.60727
$173$	−2.63906	−0.200644	−0.100322	−	0.994955i	$-0.531987\pi$
$173$	−2.63906	−0.200644	−0.100322	+	0.994955i	$0.531987\pi$
$174$	50.9176	3.86006
$175$	−23.7721	−1.79700
$176$	−88.7906	−6.69284
$177$	−12.9929	−0.976605
$178$	−32.6069	−2.44399
$179$	10.4356	0.779995	0.389997	−	0.920816i	$-0.372476\pi$
$179$	10.4356	0.779995	0.389997	+	0.920816i	$0.372476\pi$
$180$	114.926	8.56609
$181$	2.02539	0.150546	0.0752732	−	0.997163i	$-0.476017\pi$
$181$	2.02539	0.150546	0.0752732	+	0.997163i	$0.476017\pi$
$182$	−17.6800	−1.31053
$183$	−26.1083	−1.92998
$184$	23.2234	1.71205
$185$	−46.4930	−3.41824
$186$	11.2366	0.823911
$187$	19.8903	1.45452
$188$	−48.3547	−3.52663
$189$	−6.56583	−0.477594
$190$	−22.9425	−1.66443
$191$	7.83950	0.567246	0.283623	−	0.958936i	$-0.408464\pi$
$191$	7.83950	0.567246	0.283623	+	0.958936i	$0.408464\pi$
$192$	140.836	10.1640
$193$	5.48790	0.395028	0.197514	−	0.980300i	$-0.436713\pi$
$193$	5.48790	0.395028	0.197514	+	0.980300i	$0.436713\pi$
$194$	37.2674	2.67565
$195$	−44.6611	−3.19825
$196$	−24.7591	−1.76851
$197$	17.1805	1.22406	0.612032	−	0.790833i	$-0.290353\pi$
$197$	17.1805	1.22406	0.612032	+	0.790833i	$0.290353\pi$
$198$	57.6717	4.09855
$199$	7.82646	0.554803	0.277402	−	0.960754i	$-0.410527\pi$
$199$	7.82646	0.554803	0.277402	+	0.960754i	$0.410527\pi$
$200$	−156.255	−11.0489
$201$	−14.6823	−1.03561
$202$	−42.3486	−2.97964
$203$	11.1392	0.781817
$204$	−69.4868	−4.86505
$205$	18.5541	1.29587
$206$	2.21558	0.154367
$207$	−9.33257	−0.648658
$208$	−71.9000	−4.98536
$209$	−8.60591	−0.595283
$210$	56.3901	3.89129
$211$	14.6758	1.01032	0.505161	−	0.863025i	$-0.331433\pi$
$211$	14.6758	1.01032	0.505161	+	0.863025i	$0.331433\pi$
$212$	−17.7652	−1.22012
$213$	0.0621820	0.00426064
$214$	−12.0071	−0.820789
$215$	34.9755	2.38531
$216$	−43.1575	−2.93650
$217$	2.45823	0.166875
$218$	−6.24792	−0.423163
$219$	22.0317	1.48877
$220$	−119.764	−8.07446
$221$	16.1065	1.08344
$222$	81.5068	5.47038
$223$	−9.21878	−0.617335	−0.308668	−	0.951170i	$-0.599883\pi$
$223$	−9.21878	−0.617335	−0.308668	+	0.951170i	$0.599883\pi$
$224$	53.7331	3.59019
$225$	62.7930	4.18620
$226$	−34.3018	−2.28172
$227$	−16.2561	−1.07896	−0.539478	−	0.842000i	$-0.681378\pi$
$227$	−16.2561	−1.07896	−0.539478	+	0.842000i	$0.681378\pi$
$228$	30.0648	1.99109
$229$	14.9263	0.986357	0.493179	−	0.869928i	$-0.335835\pi$
$229$	14.9263	0.986357	0.493179	+	0.869928i	$0.335835\pi$
$230$	25.9270	1.70958
$231$	21.1523	1.39172
$232$	73.2184	4.80702
$233$	−4.62373	−0.302911	−0.151455	−	0.988464i	$-0.548396\pi$
$233$	−4.62373	−0.302911	−0.151455	+	0.988464i	$0.548396\pi$
$234$	46.7008	3.05293
$235$	−35.7487	−2.33199
$236$	−28.2139	−1.83657
$237$	26.2301	1.70383
$238$	−20.3365	−1.31822
$239$	−2.29741	−0.148607	−0.0743036	−	0.997236i	$-0.523673\pi$
$239$	−2.29741	−0.148607	−0.0743036	+	0.997236i	$0.523673\pi$
$240$	229.324	14.8028
$241$	13.1638	0.847953	0.423977	−	0.905673i	$-0.360634\pi$
$241$	13.1638	0.847953	0.423977	+	0.905673i	$0.360634\pi$
$242$	−29.1409	−1.87325
$243$	−18.9294	−1.21432
$244$	−56.6939	−3.62945
$245$	−18.3044	−1.16943
$246$	−32.5271	−2.07385
$247$	−6.96880	−0.443414
$248$	16.1580	1.02604
$249$	−47.9504	−3.03873
$250$	−112.850	−7.13724
$251$	2.72461	0.171976	0.0859881	−	0.996296i	$-0.472595\pi$
$251$	2.72461	0.171976	0.0859881	+	0.996296i	$0.472595\pi$
$252$	−44.0768	−2.77657
$253$	9.72540	0.611431
$254$	−31.3111	−1.96463
$255$	−51.3717	−3.21702
$256$	125.662	7.85384
$257$	2.31511	0.144413	0.0722064	−	0.997390i	$-0.476996\pi$
$257$	2.31511	0.144413	0.0722064	+	0.997390i	$0.476996\pi$
$258$	−61.3154	−3.81733
$259$	17.8311	1.10797
$260$	−96.9810	−6.01450
$261$	−29.4236	−1.82128
$262$	45.4423	2.80743
$263$	4.60486	0.283948	0.141974	−	0.989870i	$-0.454655\pi$
$263$	4.60486	0.283948	0.141974	+	0.989870i	$0.454655\pi$
$264$	139.035	8.55703
$265$	−13.1339	−0.806806
$266$	8.79898	0.539500
$267$	31.5899	1.93327
$268$	−31.8824	−1.94753
$269$	−21.2762	−1.29723	−0.648617	−	0.761115i	$-0.724652\pi$
$269$	−21.2762	−1.29723	−0.648617	+	0.761115i	$0.724652\pi$
$270$	−48.1818	−2.93225
$271$	7.01944	0.426401	0.213200	−	0.977009i	$-0.431611\pi$
$271$	7.01944	0.426401	0.213200	+	0.977009i	$0.431611\pi$
$272$	−82.7034	−5.01463
$273$	17.1285	1.03667
$274$	33.3304	2.01356
$275$	−65.4361	−3.94594
$276$	−33.9758	−2.04510
$277$	−1.03548	−0.0622160	−0.0311080	−	0.999516i	$-0.509904\pi$
$277$	−1.03548	−0.0622160	−0.0311080	+	0.999516i	$0.509904\pi$
$278$	57.5621	3.45234
$279$	−6.49329	−0.388743
$280$	81.0877	4.84592
$281$	−11.9875	−0.715114	−0.357557	−	0.933891i	$-0.616390\pi$
$281$	−11.9875	−0.715114	−0.357557	+	0.933891i	$0.616390\pi$
$282$	62.6709	3.73200
$283$	−27.4101	−1.62936	−0.814681	−	0.579910i	$-0.803088\pi$
$283$	−27.4101	−1.62936	−0.814681	+	0.579910i	$0.803088\pi$
$284$	0.135028	0.00801241
$285$	22.2270	1.31661
$286$	−48.6665	−2.87771
$287$	−7.11590	−0.420038
$288$	−141.933	−8.36350
$289$	1.52665	0.0898028
$290$	81.7423	4.80007
$291$	−36.1051	−2.11652
$292$	47.8417	2.79972
$293$	10.2229	0.597227	0.298613	−	0.954374i	$-0.403476\pi$
$293$	10.2229	0.597227	0.298613	+	0.954374i	$0.403476\pi$
$294$	32.0894	1.87149
$295$	−20.8586	−1.21443
$296$	117.205	6.81239
$297$	−18.0734	−1.04872
$298$	19.4532	1.12689
$299$	7.87534	0.455442
$300$	228.602	13.1983
$301$	−13.4139	−0.773164
$302$	−0.361315	−0.0207913
$303$	41.0278	2.35698
$304$	35.7832	2.05231
$305$	−41.9139	−2.39998
$306$	53.7179	3.07085
$307$	22.6245	1.29125	0.645625	−	0.763654i	$-0.276597\pi$
$307$	22.6245	1.29125	0.645625	+	0.763654i	$0.276597\pi$
$308$	45.9321	2.61722
$309$	−2.14648	−0.122109
$310$	18.0391	1.02455
$311$	−5.40506	−0.306493	−0.153246	−	0.988188i	$-0.548973\pi$
$311$	−5.40506	−0.306493	−0.153246	+	0.988188i	$0.548973\pi$
$312$	112.587	6.37396
$313$	13.5746	0.767280	0.383640	−	0.923483i	$-0.374670\pi$
$313$	13.5746	0.767280	0.383640	+	0.923483i	$0.374670\pi$
$314$	−33.2705	−1.87756
$315$	−32.5860	−1.83601
$316$	56.9584	3.20416
$317$	−11.2380	−0.631189	−0.315595	−	0.948894i	$-0.602204\pi$
$317$	−11.2380	−0.631189	−0.315595	+	0.948894i	$0.602204\pi$
$318$	23.0249	1.29117
$319$	30.6621	1.71675
$320$	226.096	12.6391
$321$	11.6326	0.649269
$322$	−9.94359	−0.554134
$323$	−8.01591	−0.446017
$324$	−15.6264	−0.868133
$325$	−52.9882	−2.93925
$326$	50.5328	2.79875
$327$	6.05305	0.334734
$328$	−46.7732	−2.58262
$329$	13.7104	0.755880
$330$	155.222	8.54467
$331$	23.7342	1.30455	0.652276	−	0.757982i	$-0.273814\pi$
$331$	23.7342	1.30455	0.652276	+	0.757982i	$0.273814\pi$
$332$	−104.124	−5.71453
$333$	−47.1001	−2.58107
$334$	−12.2211	−0.668708
$335$	−23.5707	−1.28780
$336$	−87.9511	−4.79812
$337$	11.0560	0.602259	0.301129	−	0.953583i	$-0.402636\pi$
$337$	11.0560	0.602259	0.301129	+	0.953583i	$0.402636\pi$
$338$	−2.82159	−0.153474
$339$	33.2319	1.80491
$340$	−111.553	−6.04981
$341$	6.76661	0.366432
$342$	−23.2421	−1.25679
$343$	18.7716	1.01357
$344$	−88.1701	−4.75382
$345$	−25.1183	−1.35233
$346$	7.42734	0.399296
$347$	−5.89849	−0.316647	−0.158324	−	0.987387i	$-0.550609\pi$
$347$	−5.89849	−0.316647	−0.158324	+	0.987387i	$0.550609\pi$
$348$	−107.118	−5.74215
$349$	5.57534	0.298441	0.149221	−	0.988804i	$-0.452324\pi$
$349$	5.57534	0.298441	0.149221	+	0.988804i	$0.452324\pi$
$350$	66.9041	3.57617
$351$	−14.6353	−0.781172
$352$	147.908	7.88350
$353$	−21.7681	−1.15860	−0.579298	−	0.815116i	$-0.696673\pi$
$353$	−21.7681	−1.15860	−0.579298	+	0.815116i	$0.696673\pi$
$354$	36.5671	1.94352
$355$	0.0998260	0.00529822
$356$	68.5970	3.63564
$357$	19.7022	1.04275
$358$	−29.3699	−1.55225
$359$	−24.5217	−1.29421	−0.647103	−	0.762403i	$-0.724020\pi$
$359$	−24.5217	−1.29421	−0.647103	+	0.762403i	$0.724020\pi$
$360$	−214.189	−11.2888
$361$	−15.5318	−0.817461
$362$	−5.70026	−0.299599
$363$	28.2320	1.48180
$364$	37.1944	1.94952
$365$	35.3694	1.85132
$366$	73.4790	3.84081
$367$	6.31487	0.329633	0.164817	−	0.986324i	$-0.447297\pi$
$367$	6.31487	0.329633	0.164817	+	0.986324i	$0.447297\pi$
$368$	−40.4381	−2.10798
$369$	18.7963	0.978497
$370$	130.850	6.80255
$371$	5.03713	0.261515
$372$	−23.6392	−1.22564
$373$	−21.7751	−1.12747	−0.563736	−	0.825955i	$-0.690637\pi$
$373$	−21.7751	−1.12747	−0.563736	+	0.825955i	$0.690637\pi$
$374$	−55.9790	−2.89461
$375$	109.330	5.64577
$376$	90.1193	4.64755
$377$	24.8293	1.27877
$378$	18.4788	0.950448
$379$	5.68193	0.291861	0.145930	−	0.989295i	$-0.453382\pi$
$379$	5.68193	0.291861	0.145930	+	0.989295i	$0.453382\pi$
$380$	48.2656	2.47597
$381$	30.3345	1.55409
$382$	−22.0634	−1.12886
$383$	−6.04745	−0.309010	−0.154505	−	0.987992i	$-0.549378\pi$
$383$	−6.04745	−0.309010	−0.154505	+	0.987992i	$0.549378\pi$
$384$	−221.825	−11.3199
$385$	33.9576	1.73064
$386$	−15.4451	−0.786135
$387$	35.4322	1.80112
$388$	−78.4017	−3.98024
$389$	−15.2008	−0.770712	−0.385356	−	0.922768i	$-0.625921\pi$
$389$	−15.2008	−0.770712	−0.385356	+	0.922768i	$0.625921\pi$
$390$	125.694	6.36475
$391$	9.05866	0.458116
$392$	46.1438	2.33061
$393$	−44.0249	−2.22076
$394$	−48.3528	−2.43598
$395$	42.1094	2.11875
$396$	−121.327	−6.09693
$397$	5.58675	0.280391	0.140196	−	0.990124i	$-0.455227\pi$
$397$	5.58675	0.280391	0.140196	+	0.990124i	$0.455227\pi$
$398$	−22.0267	−1.10410
$399$	−8.52454	−0.426761
$400$	272.082	13.6041
$401$	−7.54723	−0.376891	−0.188445	−	0.982084i	$-0.560345\pi$
$401$	−7.54723	−0.376891	−0.188445	+	0.982084i	$0.560345\pi$
$402$	41.3217	2.06094
$403$	5.47939	0.272948
$404$	89.0913	4.43246
$405$	−11.5526	−0.574054
$406$	−31.3500	−1.55588
$407$	49.0826	2.43294
$408$	129.504	6.41138
$409$	15.9452	0.788438	0.394219	−	0.919016i	$-0.371015\pi$
$409$	15.9452	0.788438	0.394219	+	0.919016i	$0.371015\pi$
$410$	−52.2184	−2.57888
$411$	−32.2909	−1.59279
$412$	−4.66106	−0.229634
$413$	7.99973	0.393641
$414$	26.2655	1.29088
$415$	−76.9787	−3.77874
$416$	119.771	5.87226
$417$	−55.7667	−2.73091
$418$	24.2204	1.18466
$419$	−18.9516	−0.925845	−0.462923	−	0.886399i	$-0.653199\pi$
$419$	−18.9516	−0.925845	−0.462923	+	0.886399i	$0.653199\pi$
$420$	−118.631	−5.78861
$421$	21.3195	1.03905	0.519525	−	0.854455i	$-0.326109\pi$
$421$	21.3195	1.03905	0.519525	+	0.854455i	$0.326109\pi$
$422$	−41.3034	−2.01062
$423$	−36.2154	−1.76086
$424$	33.1093	1.60793
$425$	−60.9500	−2.95651
$426$	−0.175005	−0.00847900
$427$	16.0749	0.777920
$428$	25.2601	1.22099
$429$	47.1486	2.27636
$430$	−98.4348	−4.74695
$431$	28.7501	1.38484	0.692422	−	0.721493i	$-0.256544\pi$
$431$	28.7501	1.38484	0.692422	+	0.721493i	$0.256544\pi$
$432$	75.1487	3.61559
$433$	8.31032	0.399369	0.199684	−	0.979860i	$-0.436008\pi$
$433$	8.31032	0.399369	0.199684	+	0.979860i	$0.436008\pi$
$434$	−6.91841	−0.332094
$435$	−79.1928	−3.79700
$436$	13.1441	0.629489
$437$	−3.91940	−0.187490
$438$	−62.0060	−2.96276
$439$	15.0835	0.719894	0.359947	−	0.932973i	$-0.382795\pi$
$439$	15.0835	0.719894	0.359947	+	0.932973i	$0.382795\pi$
$440$	223.205	10.6409
$441$	−18.5434	−0.883019
$442$	−45.3301	−2.15613
$443$	−23.0316	−1.09426	−0.547131	−	0.837047i	$-0.684280\pi$
$443$	−23.0316	−1.09426	−0.547131	+	0.837047i	$0.684280\pi$
$444$	−171.471	−8.13763
$445$	50.7139	2.40407
$446$	25.9453	1.22854
$447$	−18.8465	−0.891407
$448$	−86.7128	−4.09679
$449$	−1.53646	−0.0725102	−0.0362551	−	0.999343i	$-0.511543\pi$
$449$	−1.53646	−0.0725102	−0.0362551	+	0.999343i	$0.511543\pi$
$450$	−176.724	−8.33085
$451$	−19.5875	−0.922339
$452$	72.1627	3.39425
$453$	0.350045	0.0164466
$454$	45.7511	2.14720
$455$	27.4979	1.28912
$456$	−56.0322	−2.62395
$457$	30.9725	1.44883	0.724417	−	0.689362i	$-0.242109\pi$
$457$	30.9725	1.44883	0.724417	+	0.689362i	$0.242109\pi$
$458$	−42.0084	−1.96293
$459$	−16.8343	−0.785758
$460$	−54.5442	−2.54313
$461$	−11.4800	−0.534679	−0.267339	−	0.963602i	$-0.586144\pi$
$461$	−11.4800	−0.534679	−0.267339	+	0.963602i	$0.586144\pi$
$462$	−59.5310	−2.76963
$463$	−21.3420	−0.991849	−0.495924	−	0.868366i	$-0.665171\pi$
$463$	−21.3420	−0.991849	−0.495924	+	0.868366i	$0.665171\pi$
$464$	−127.493	−5.91870
$465$	−17.4765	−0.810453
$466$	13.0130	0.602815
$467$	−0.371382	−0.0171855	−0.00859277	−	0.999963i	$-0.502735\pi$
$467$	−0.371382	−0.0171855	−0.00859277	+	0.999963i	$0.502735\pi$
$468$	−98.2472	−4.54148
$469$	9.03989	0.417423
$470$	100.611	4.64083
$471$	32.2328	1.48521
$472$	52.5826	2.42031
$473$	−36.9236	−1.69775
$474$	−73.8218	−3.39075
$475$	26.3712	1.20999
$476$	42.7831	1.96096
$477$	−13.3053	−0.609210
$478$	6.46582	0.295740
$479$	−21.1415	−0.965980	−0.482990	−	0.875626i	$-0.660449\pi$
$479$	−21.1415	−0.965980	−0.482990	+	0.875626i	$0.660449\pi$
$480$	−382.009	−17.4363
$481$	39.7456	1.81224
$482$	−37.0480	−1.68749
$483$	9.63345	0.438337
$484$	61.3055	2.78661
$485$	−57.9625	−2.63194
$486$	53.2748	2.41659
$487$	36.4101	1.64990	0.824949	−	0.565207i	$-0.191204\pi$
$487$	36.4101	1.64990	0.824949	+	0.565207i	$0.191204\pi$
$488$	105.661	4.78306
$489$	−48.9566	−2.21390
$490$	51.5158	2.32725
$491$	8.94765	0.403802	0.201901	−	0.979406i	$-0.435288\pi$
$491$	8.94765	0.403802	0.201901	+	0.979406i	$0.435288\pi$
$492$	68.4291	3.08502
$493$	28.5600	1.28628
$494$	19.6129	0.882428
$495$	−89.6975	−4.03160
$496$	−28.1354	−1.26332
$497$	−0.0382855	−0.00171734
$498$	134.951	6.04730
$499$	1.22770	0.0549593	0.0274796	−	0.999622i	$-0.491252\pi$
$499$	1.22770	0.0549593	0.0274796	+	0.999622i	$0.491252\pi$
$500$	237.409	10.6172
$501$	11.8399	0.528968
$502$	−7.66813	−0.342246
$503$	7.19403	0.320766	0.160383	−	0.987055i	$-0.448727\pi$
$503$	7.19403	0.320766	0.160383	+	0.987055i	$0.448727\pi$
$504$	82.1464	3.65909
$505$	65.8653	2.93097
$506$	−27.3711	−1.21679
$507$	2.73358	0.121403
$508$	65.8711	2.92256
$509$	5.02816	0.222869	0.111435	−	0.993772i	$-0.464455\pi$
$509$	5.02816	0.222869	0.111435	+	0.993772i	$0.464455\pi$
$510$	144.580	6.40211
$511$	−13.5650	−0.600079
$512$	−190.950	−8.43887
$513$	7.28369	0.321583
$514$	−6.51564	−0.287393
$515$	−3.44592	−0.151846
$516$	128.993	5.67859
$517$	37.7398	1.65980
$518$	−50.1838	−2.20495
$519$	−7.19568	−0.315855
$520$	180.745	7.92618
$521$	−17.1934	−0.753259	−0.376629	−	0.926364i	$-0.622917\pi$
$521$	−17.1934	−0.753259	−0.376629	+	0.926364i	$0.622917\pi$
$522$	82.8096	3.62448
$523$	19.7198	0.862287	0.431144	−	0.902283i	$-0.358110\pi$
$523$	19.7198	0.862287	0.431144	+	0.902283i	$0.358110\pi$
$524$	−95.5996	−4.17629
$525$	−64.8174	−2.82886
$526$	−12.9599	−0.565078
$527$	6.30271	0.274550
$528$	−242.098	−10.5359
$529$	−18.5707	−0.807424
$530$	36.9638	1.60561
$531$	−21.1309	−0.917004
$532$	−18.5109	−0.802551
$533$	−15.8614	−0.687032
$534$	−88.9063	−3.84735
$535$	18.6748	0.807382
$536$	59.4196	2.56654
$537$	28.4539	1.22788
$538$	59.8796	2.58159
$539$	19.3239	0.832341
$540$	101.363	4.36197
$541$	−23.1380	−0.994778	−0.497389	−	0.867528i	$-0.665708\pi$
$541$	−23.1380	−0.994778	−0.497389	+	0.867528i	$0.665708\pi$
$542$	−19.7555	−0.848570
$543$	5.52247	0.236992
$544$	137.768	5.90673
$545$	9.71746	0.416250
$546$	−48.2064	−2.06304
$547$	−29.3754	−1.25600	−0.628000	−	0.778213i	$-0.716126\pi$
$547$	−29.3754	−1.25600	−0.628000	+	0.778213i	$0.716126\pi$
$548$	−70.1192	−2.99534
$549$	−42.4611	−1.81220
$550$	184.163	7.85273
$551$	−12.3571	−0.526428
$552$	63.3211	2.69513
$553$	−16.1499	−0.686763
$554$	2.91425	0.123815
$555$	−126.768	−5.38102
$556$	−121.097	−5.13565
$557$	−25.0393	−1.06095	−0.530475	−	0.847701i	$-0.677986\pi$
$557$	−25.0393	−1.06095	−0.530475	+	0.847701i	$0.677986\pi$
$558$	18.2747	0.773628
$559$	−29.8996	−1.26462
$560$	−141.195	−5.96659
$561$	54.2330	2.28972
$562$	33.7375	1.42313
$563$	−12.4659	−0.525373	−0.262687	−	0.964881i	$-0.584608\pi$
$563$	−12.4659	−0.525373	−0.262687	+	0.964881i	$0.584608\pi$
$564$	−131.844	−5.55165
$565$	53.3500	2.24445
$566$	77.1428	3.24255
$567$	4.43069	0.186071
$568$	−0.251653	−0.0105591
$569$	40.3185	1.69024	0.845121	−	0.534576i	$-0.179529\pi$
$569$	40.3185	1.69024	0.845121	+	0.534576i	$0.179529\pi$
$570$	−62.5554	−2.62016
$571$	23.7185	0.992587	0.496293	−	0.868155i	$-0.334694\pi$
$571$	23.7185	0.992587	0.496293	+	0.868155i	$0.334694\pi$
$572$	102.383	4.28084
$573$	21.3753	0.892965
$574$	20.0269	0.835908
$575$	−29.8017	−1.24282
$576$	229.048	9.54366
$577$	−7.32081	−0.304769	−0.152385	−	0.988321i	$-0.548695\pi$
$577$	−7.32081	−0.304769	−0.152385	+	0.988321i	$0.548695\pi$
$578$	−4.29659	−0.178714
$579$	14.9634	0.621856
$580$	−171.966	−7.14051
$581$	29.5231	1.22482
$582$	101.614	4.21203
$583$	13.8654	0.574246
$584$	−89.1632	−3.68960
$585$	−72.6343	−3.00306
$586$	−28.7712	−1.18853
$587$	−23.2800	−0.960868	−0.480434	−	0.877031i	$-0.659521\pi$
$587$	−23.2800	−0.960868	−0.480434	+	0.877031i	$0.659521\pi$
$588$	−67.5084	−2.78400
$589$	−2.72699	−0.112364
$590$	58.7042	2.41681
$591$	46.8447	1.92693
$592$	−204.085	−8.38783
$593$	−21.1155	−0.867111	−0.433555	−	0.901127i	$-0.642741\pi$
$593$	−21.1155	−0.867111	−0.433555	+	0.901127i	$0.642741\pi$
$594$	50.8655	2.08704
$595$	31.6296	1.29669
$596$	−40.9248	−1.67635
$597$	21.3397	0.873377
$598$	−22.1643	−0.906365
$599$	44.4417	1.81584	0.907918	−	0.419147i	$-0.137671\pi$
$599$	44.4417	1.81584	0.907918	+	0.419147i	$0.137671\pi$
$600$	−426.048	−17.3933
$601$	−22.2845	−0.909005	−0.454503	−	0.890745i	$-0.650183\pi$
$601$	−22.2845	−0.909005	−0.454503	+	0.890745i	$0.650183\pi$
$602$	37.7519	1.53865
$603$	−23.8784	−0.972405
$604$	0.760119	0.0309288
$605$	45.3232	1.84265
$606$	−115.468	−4.69057
$607$	−12.7974	−0.519431	−0.259716	−	0.965685i	$-0.583629\pi$
$607$	−12.7974	−0.519431	−0.259716	+	0.965685i	$0.583629\pi$
$608$	−59.6078	−2.41742
$609$	30.3722	1.23074
$610$	117.962	4.77614
$611$	30.5606	1.23635
$612$	−113.010	−4.56814
$613$	−33.6629	−1.35963	−0.679817	−	0.733382i	$-0.737941\pi$
$613$	−33.6629	−1.35963	−0.679817	+	0.733382i	$0.737941\pi$
$614$	−63.6743	−2.56969
$615$	50.5897	2.03997
$616$	−85.6042	−3.44909
$617$	41.9301	1.68804	0.844022	−	0.536309i	$-0.180182\pi$
$617$	41.9301	1.68804	0.844022	+	0.536309i	$0.180182\pi$
$618$	6.04104	0.243006
$619$	−3.45519	−0.138876	−0.0694380	−	0.997586i	$-0.522121\pi$
$619$	−3.45519	−0.138876	−0.0694380	+	0.997586i	$0.522121\pi$
$620$	−37.9500	−1.52411
$621$	−8.23118	−0.330306
$622$	15.2119	0.609944
$623$	−19.4499	−0.779244
$624$	−196.043	−7.84801
$625$	104.715	4.18858
$626$	−38.2042	−1.52695
$627$	−23.4650	−0.937101
$628$	69.9931	2.79303
$629$	45.7177	1.82288
$630$	91.7098	3.65381
$631$	−24.8279	−0.988383	−0.494191	−	0.869353i	$-0.664536\pi$
$631$	−24.8279	−0.988383	−0.494191	+	0.869353i	$0.664536\pi$
$632$	−106.154	−4.22258
$633$	40.0152	1.59046
$634$	31.6281	1.25611
$635$	48.6986	1.93254
$636$	−48.4389	−1.92073
$637$	15.6479	0.619994
$638$	−86.2953	−3.41646
$639$	0.101129	0.00400062
$640$	−356.114	−14.0766
$641$	−28.3795	−1.12092	−0.560461	−	0.828181i	$-0.689376\pi$
$641$	−28.3795	−1.12092	−0.560461	+	0.828181i	$0.689376\pi$
$642$	−32.7387	−1.29209
$643$	−48.8692	−1.92721	−0.963606	−	0.267328i	$-0.913859\pi$
$643$	−48.8692	−1.92721	−0.963606	+	0.267328i	$0.913859\pi$
$644$	20.9189	0.824321
$645$	95.3646	3.75498
$646$	22.5599	0.887608
$647$	38.6001	1.51753	0.758763	−	0.651366i	$-0.225804\pi$
$647$	38.6001	1.51753	0.758763	+	0.651366i	$0.225804\pi$
$648$	29.1231	1.14406
$649$	22.0204	0.864375
$650$	149.129	5.84934
$651$	6.70263	0.262697
$652$	−106.309	−4.16337
$653$	17.0402	0.666835	0.333418	−	0.942779i	$-0.391798\pi$
$653$	17.0402	0.666835	0.333418	+	0.942779i	$0.391798\pi$
$654$	−17.0357	−0.666147
$655$	−70.6769	−2.76158
$656$	81.4445	3.17987
$657$	35.8312	1.39791
$658$	−38.5865	−1.50426
$659$	−33.0239	−1.28643	−0.643214	−	0.765686i	$-0.722399\pi$
$659$	−33.0239	−1.28643	−0.643214	+	0.765686i	$0.722399\pi$
$660$	−326.549	−12.7109
$661$	1.56108	0.0607190	0.0303595	−	0.999539i	$-0.490335\pi$
$661$	1.56108	0.0607190	0.0303595	+	0.999539i	$0.490335\pi$
$662$	−66.7974	−2.59616
$663$	43.9163	1.70557
$664$	194.057	7.53086
$665$	−13.6852	−0.530688
$666$	132.558	5.13652
$667$	13.9645	0.540708
$668$	25.7102	0.994759
$669$	−25.1360	−0.971816
$670$	66.3372	2.56283
$671$	44.2484	1.70819
$672$	146.509	5.65171
$673$	38.1422	1.47027	0.735137	−	0.677918i	$-0.237118\pi$
$673$	38.1422	1.47027	0.735137	+	0.677918i	$0.237118\pi$
$674$	−31.1159	−1.19854
$675$	55.3824	2.13167
$676$	5.93594	0.228305
$677$	13.5056	0.519062	0.259531	−	0.965735i	$-0.416432\pi$
$677$	13.5056	0.519062	0.259531	+	0.965735i	$0.416432\pi$
$678$	−93.5276	−3.59191
$679$	22.2299	0.853106
$680$	207.903	7.97271
$681$	−44.3241	−1.69850
$682$	−19.0439	−0.729228
$683$	−40.7298	−1.55848	−0.779242	−	0.626724i	$-0.784396\pi$
$683$	−40.7298	−1.55848	−0.779242	+	0.626724i	$0.784396\pi$
$684$	48.8958	1.86958
$685$	−51.8392	−1.98067
$686$	−52.8306	−2.01708
$687$	40.6982	1.55273
$688$	153.528	5.85319
$689$	11.2278	0.427744
$690$	70.6928	2.69123
$691$	9.09711	0.346070	0.173035	−	0.984916i	$-0.444643\pi$
$691$	9.09711	0.346070	0.173035	+	0.984916i	$0.444643\pi$
$692$	−15.6253	−0.593986
$693$	34.4010	1.30679
$694$	16.6007	0.630152
$695$	−89.5270	−3.39595
$696$	199.638	7.56726
$697$	−18.2446	−0.691065
$698$	−15.6912	−0.593921
$699$	−12.6071	−0.476845
$700$	−140.750	−5.31986
$701$	−5.44691	−0.205727	−0.102863	−	0.994695i	$-0.532800\pi$
$701$	−5.44691	−0.205727	−0.102863	+	0.994695i	$0.532800\pi$
$702$	41.1894	1.55459
$703$	−19.7806	−0.746041
$704$	−238.689	−8.99593
$705$	−97.4728	−3.67104
$706$	61.2639	2.30570
$707$	−25.2608	−0.950031
$708$	−76.9283	−2.89114
$709$	19.9278	0.748404	0.374202	−	0.927347i	$-0.377917\pi$
$709$	19.9278	0.748404	0.374202	+	0.927347i	$0.377917\pi$
$710$	−0.280950	−0.0105439
$711$	42.6592	1.59984
$712$	−127.845	−4.79120
$713$	3.08173	0.115412
$714$	−55.4497	−2.07515
$715$	75.6916	2.83071
$716$	61.7872	2.30910
$717$	−6.26415	−0.233939
$718$	69.0137	2.57557
$719$	−32.3346	−1.20588	−0.602939	−	0.797787i	$-0.706004\pi$
$719$	−32.3346	−1.20588	−0.602939	+	0.797787i	$0.706004\pi$
$720$	372.961	13.8994
$721$	1.32159	0.0492186
$722$	43.7125	1.62681
$723$	35.8925	1.33486
$724$	11.9920	0.445678
$725$	−93.9583	−3.48953
$726$	−79.4559	−2.94889
$727$	−41.1311	−1.52547	−0.762735	−	0.646712i	$-0.776144\pi$
$727$	−41.1311	−1.52547	−0.762735	+	0.646712i	$0.776144\pi$
$728$	−69.3197	−2.56916
$729$	−43.6954	−1.61835
$730$	−99.5434	−3.68427
$731$	−34.3922	−1.27204
$732$	−154.582	−5.71352
$733$	−36.4256	−1.34541	−0.672705	−	0.739911i	$-0.734868\pi$
$733$	−36.4256	−1.34541	−0.672705	+	0.739911i	$0.734868\pi$
$734$	−17.7725	−0.655996
$735$	−49.9090	−1.84092
$736$	67.3618	2.48299
$737$	24.8835	0.916597
$738$	−52.9002	−1.94728
$739$	10.7956	0.397122	0.198561	−	0.980088i	$-0.436373\pi$
$739$	10.7956	0.397122	0.198561	+	0.980088i	$0.436373\pi$
$740$	−275.276	−10.1194
$741$	−19.0012	−0.698027
$742$	−14.1765	−0.520434
$743$	38.3008	1.40512	0.702560	−	0.711624i	$-0.252040\pi$
$743$	38.3008	1.40512	0.702560	+	0.711624i	$0.252040\pi$
$744$	44.0567	1.61520
$745$	−30.2558	−1.10849
$746$	61.2837	2.24376
$747$	−77.9838	−2.85328
$748$	117.766	4.30596
$749$	−7.16220	−0.261701
$750$	−307.697	−11.2355
$751$	22.1201	0.807175	0.403588	−	0.914941i	$-0.367763\pi$
$751$	22.1201	0.807175	0.403588	+	0.914941i	$0.367763\pi$
$752$	−156.922	−5.72234
$753$	7.42897	0.270727
$754$	−69.8793	−2.54485
$755$	0.561957	0.0204517
$756$	−38.8750	−1.41387
$757$	37.9802	1.38041	0.690207	−	0.723612i	$-0.257520\pi$
$757$	37.9802	1.38041	0.690207	+	0.723612i	$0.257520\pi$
$758$	−15.9912	−0.580825
$759$	26.5174	0.962520
$760$	−89.9532	−3.26294
$761$	−29.1310	−1.05600	−0.527999	−	0.849245i	$-0.677057\pi$
$761$	−29.1310	−1.05600	−0.527999	+	0.849245i	$0.677057\pi$
$762$	−85.3733	−3.09275
$763$	−3.72687	−0.134922
$764$	46.4162	1.67928
$765$	−83.5481	−3.02069
$766$	17.0199	0.614954
$767$	17.8314	0.643855
$768$	342.630	12.3636
$769$	−48.7749	−1.75887	−0.879434	−	0.476021i	$-0.842078\pi$
$769$	−48.7749	−1.75887	−0.879434	+	0.476021i	$0.842078\pi$
$770$	−95.5701	−3.44411
$771$	6.31242	0.227336
$772$	32.4928	1.16944
$773$	10.6896	0.384477	0.192239	−	0.981348i	$-0.438425\pi$
$773$	10.6896	0.384477	0.192239	+	0.981348i	$0.438425\pi$
$774$	−99.7200	−3.58436
$775$	−20.7350	−0.744823
$776$	146.118	5.24534
$777$	48.6185	1.74418
$778$	42.7810	1.53377
$779$	7.89390	0.282828
$780$	−264.429	−9.46809
$781$	−0.105386	−0.00377102
$782$	−25.4946	−0.911686
$783$	−25.9512	−0.927419
$784$	−80.3487	−2.86959
$785$	51.7460	1.84689
$786$	123.903	4.41949
$787$	−14.2535	−0.508082	−0.254041	−	0.967193i	$-0.581760\pi$
$787$	−14.2535	−0.508082	−0.254041	+	0.967193i	$0.581760\pi$
$788$	101.723	3.62372
$789$	12.5557	0.446994
$790$	−118.512	−4.21648
$791$	−20.4609	−0.727506
$792$	226.119	8.03480
$793$	35.8310	1.27240
$794$	−15.7233	−0.558000
$795$	−35.8109	−1.27008
$796$	46.3389	1.64244
$797$	−13.7187	−0.485940	−0.242970	−	0.970034i	$-0.578122\pi$
$797$	−13.7187	−0.485940	−0.242970	+	0.970034i	$0.578122\pi$
$798$	23.9914	0.849286
$799$	35.1525	1.24361
$800$	−453.235	−16.0243
$801$	51.3760	1.81528
$802$	21.2409	0.750041
$803$	−37.3394	−1.31768
$804$	−86.9309	−3.06582
$805$	15.4654	0.545083
$806$	−15.4212	−0.543187
$807$	−58.0120	−2.04212
$808$	−166.041	−5.84129
$809$	29.0707	1.02207	0.511036	−	0.859559i	$-0.329262\pi$
$809$	29.0707	1.02207	0.511036	+	0.859559i	$0.329262\pi$
$810$	32.5136	1.14241
$811$	−25.0731	−0.880435	−0.440217	−	0.897891i	$-0.645099\pi$
$811$	−25.0731	−0.880435	−0.440217	+	0.897891i	$0.645099\pi$
$812$	65.9529	2.31449
$813$	19.1393	0.671244
$814$	−138.138	−4.84173
$815$	−78.5942	−2.75303
$816$	−225.500	−7.89408
$817$	14.8805	0.520601
$818$	−44.8760	−1.56905
$819$	27.8569	0.973398
$820$	109.855	3.83630
$821$	14.6424	0.511023	0.255512	−	0.966806i	$-0.417756\pi$
$821$	14.6424	0.511023	0.255512	+	0.966806i	$0.417756\pi$
$822$	90.8791	3.16977
$823$	−7.49120	−0.261127	−0.130563	−	0.991440i	$-0.541679\pi$
$823$	−7.49120	−0.261127	−0.130563	+	0.991440i	$0.541679\pi$
$824$	8.68687	0.302622
$825$	−178.419	−6.21174
$826$	−22.5144	−0.783376
$827$	−23.3622	−0.812383	−0.406191	−	0.913788i	$-0.633143\pi$
$827$	−23.3622	−0.812383	−0.406191	+	0.913788i	$0.633143\pi$
$828$	−55.2563	−1.92029
$829$	11.1613	0.387649	0.193824	−	0.981036i	$-0.437911\pi$
$829$	11.1613	0.387649	0.193824	+	0.981036i	$0.437911\pi$
$830$	216.648	7.51997
$831$	−2.82335	−0.0979411
$832$	−193.283	−6.70088
$833$	17.9992	0.623634
$834$	156.949	5.43471
$835$	19.0076	0.657785
$836$	−50.9539	−1.76228
$837$	−5.72698	−0.197953
$838$	53.3372	1.84250
$839$	52.1729	1.80121	0.900605	−	0.434638i	$-0.143124\pi$
$839$	52.1729	1.80121	0.900605	+	0.434638i	$0.143124\pi$
$840$	221.095	7.62849
$841$	15.0271	0.518177
$842$	−60.0015	−2.06779
$843$	−32.6853	−1.12574
$844$	86.8925	2.99096
$845$	4.38845	0.150967
$846$	101.924	3.50424
$847$	−17.3825	−0.597269
$848$	−57.6521	−1.97978
$849$	−74.7367	−2.56496
$850$	171.537	5.88368
$851$	22.3538	0.766278
$852$	0.368168	0.0126132
$853$	33.7960	1.15715	0.578577	−	0.815628i	$-0.303608\pi$
$853$	33.7960	1.15715	0.578577	+	0.815628i	$0.303608\pi$
$854$	−45.2411	−1.54812
$855$	36.1487	1.23626
$856$	−47.0775	−1.60908
$857$	−5.70220	−0.194783	−0.0973917	−	0.995246i	$-0.531050\pi$
$857$	−5.70220	−0.194783	−0.0973917	+	0.995246i	$0.531050\pi$
$858$	−132.695	−4.53012
$859$	35.8341	1.22265	0.611323	−	0.791381i	$-0.290638\pi$
$859$	35.8341	1.22265	0.611323	+	0.791381i	$0.290638\pi$
$860$	207.083	7.06147
$861$	−19.4023	−0.661228
$862$	−80.9141	−2.75594
$863$	8.05376	0.274153	0.137077	−	0.990560i	$-0.456229\pi$
$863$	8.05376	0.274153	0.137077	+	0.990560i	$0.456229\pi$
$864$	−125.183	−4.25881
$865$	−11.5518	−0.392774
$866$	−23.3885	−0.794774
$867$	4.16258	0.141369
$868$	14.5547	0.494018
$869$	−44.4548	−1.50803
$870$	222.880	7.55633
$871$	20.1499	0.682755
$872$	−24.4969	−0.829569
$873$	−58.7193	−1.98735
$874$	11.0307	0.373120
$875$	−67.3145	−2.27565
$876$	130.446	4.40735
$877$	16.6628	0.562664	0.281332	−	0.959610i	$-0.409224\pi$
$877$	16.6628	0.562664	0.281332	+	0.959610i	$0.409224\pi$
$878$	−42.4508	−1.43264
$879$	27.8738	0.940161
$880$	−388.659	−13.1017
$881$	26.7608	0.901593	0.450797	−	0.892627i	$-0.351140\pi$
$881$	26.7608	0.901593	0.450797	+	0.892627i	$0.351140\pi$
$882$	52.1884	1.75728
$883$	−11.0379	−0.371456	−0.185728	−	0.982601i	$-0.559464\pi$
$883$	−11.0379	−0.371456	−0.185728	+	0.982601i	$0.559464\pi$
$884$	95.3636	3.20743
$885$	−56.8732	−1.91177
$886$	64.8198	2.17766
$887$	51.7903	1.73895	0.869474	−	0.493979i	$-0.164458\pi$
$887$	51.7903	1.73895	0.869474	+	0.493979i	$0.164458\pi$
$888$	319.572	10.7241
$889$	−18.6770	−0.626406
$890$	−142.729	−4.78428
$891$	12.1961	0.408584
$892$	−54.5826	−1.82756
$893$	−15.2094	−0.508964
$894$	53.0413	1.77397
$895$	45.6794	1.52689
$896$	136.578	4.56274
$897$	21.4730	0.716962
$898$	4.32421	0.144301
$899$	9.71603	0.324048
$900$	371.785	12.3928
$901$	12.9148	0.430255
$902$	55.1269	1.83553
$903$	−36.5745	−1.21712
$904$	−134.491	−4.47309
$905$	8.86568	0.294705
$906$	−0.985165	−0.0327299
$907$	−20.1919	−0.670460	−0.335230	−	0.942136i	$-0.608814\pi$
$907$	−20.1919	−0.670460	−0.335230	+	0.942136i	$0.608814\pi$
$908$	−96.2492	−3.19414
$909$	66.7253	2.21314
$910$	−77.3898	−2.56545
$911$	−1.04665	−0.0346771	−0.0173386	−	0.999850i	$-0.505519\pi$
$911$	−1.04665	−0.0346771	−0.0173386	+	0.999850i	$0.505519\pi$
$912$	97.5670	3.23076
$913$	81.2663	2.68952
$914$	−87.1688	−2.88329
$915$	−114.283	−3.77807
$916$	88.3756	2.92001
$917$	27.1062	0.895125
$918$	47.3783	1.56372
$919$	−31.7088	−1.04598	−0.522988	−	0.852340i	$-0.675183\pi$
$919$	−31.7088	−1.04598	−0.522988	+	0.852340i	$0.675183\pi$
$920$	101.655	3.35146
$921$	61.6883	2.03270
$922$	32.3093	1.06405
$923$	−0.0853386	−0.00280895
$924$	125.239	4.12006
$925$	−150.404	−4.94527
$926$	60.0649	1.97385
$927$	−3.49092	−0.114657
$928$	212.378	6.97164
$929$	11.8315	0.388177	0.194089	−	0.980984i	$-0.437825\pi$
$929$	11.8315	0.388177	0.194089	+	0.980984i	$0.437825\pi$
$930$	49.1857	1.61286
$931$	−7.78768	−0.255231
$932$	−27.3762	−0.896738
$933$	−14.7375	−0.482484
$934$	1.04522	0.0342005
$935$	87.0648	2.84732
$936$	183.105	5.98496
$937$	18.2122	0.594965	0.297483	−	0.954727i	$-0.403853\pi$
$937$	18.2122	0.594965	0.297483	+	0.954727i	$0.403853\pi$
$938$	−25.4418	−0.830704
$939$	37.0126	1.20786
$940$	−211.661	−6.90362
$941$	27.8457	0.907743	0.453872	−	0.891067i	$-0.350042\pi$
$941$	27.8457	0.907743	0.453872	+	0.891067i	$0.350042\pi$
$942$	−90.7156	−2.95568
$943$	−8.92077	−0.290500
$944$	−91.5603	−2.98003
$945$	−28.7403	−0.934923
$946$	103.917	3.37865
$947$	28.8367	0.937067	0.468534	−	0.883446i	$-0.344783\pi$
$947$	28.8367	0.937067	0.468534	+	0.883446i	$0.344783\pi$
$948$	155.303	5.04402
$949$	−30.2364	−0.981514
$950$	−74.2189	−2.40798
$951$	−30.6417	−0.993624
$952$	−79.7354	−2.58424
$953$	15.8680	0.514015	0.257008	−	0.966409i	$-0.417263\pi$
$953$	15.8680	0.514015	0.257008	+	0.966409i	$0.417263\pi$
$954$	37.4465	1.21237
$955$	34.3155	1.11042
$956$	−13.6025	−0.439937
$957$	83.6037	2.70252
$958$	59.5005	1.92237
$959$	19.8815	0.642007
$960$	616.475	19.8966
$961$	−28.8558	−0.930833
$962$	−111.860	−3.60650
$963$	18.9186	0.609644
$964$	77.9401	2.51028
$965$	24.0220	0.773294
$966$	−27.1123	−0.872324
$967$	−2.86183	−0.0920303	−0.0460151	−	0.998941i	$-0.514652\pi$
$967$	−2.86183	−0.0920303	−0.0460151	+	0.998941i	$0.514652\pi$
$968$	−114.256	−3.67232
$969$	−21.8563	−0.702125
$970$	163.129	5.23776
$971$	12.4538	0.399660	0.199830	−	0.979831i	$-0.435961\pi$
$971$	12.4538	0.399660	0.199830	+	0.979831i	$0.435961\pi$
$972$	−112.077	−3.59488
$973$	34.3356	1.10075
$974$	−102.472	−3.28342
$975$	−144.478	−4.62700
$976$	−183.984	−5.88919
$977$	−14.2559	−0.456085	−0.228043	−	0.973651i	$-0.573233\pi$
$977$	−14.2559	−0.456085	−0.228043	+	0.973651i	$0.573233\pi$
$978$	137.783	4.40582
$979$	−53.5386	−1.71110
$980$	−108.377	−3.46197
$981$	9.84434	0.314306
$982$	−25.1822	−0.803596
$983$	−24.4028	−0.778327	−0.389164	−	0.921169i	$-0.627236\pi$
$983$	−24.4028	−0.778327	−0.389164	+	0.921169i	$0.627236\pi$
$984$	−127.532	−4.06558
$985$	75.2037	2.39619
$986$	−80.3791	−2.55979
$987$	37.3830	1.18991
$988$	−41.2609	−1.31268
$989$	−16.8162	−0.534723
$990$	252.444	8.02319
$991$	−26.0748	−0.828292	−0.414146	−	0.910210i	$-0.635920\pi$
$991$	−26.0748	−0.828292	−0.414146	+	0.910210i	$0.635920\pi$
$992$	46.8681	1.48806
$993$	64.7140	2.05364
$994$	0.107751	0.00341764
$995$	34.2584	1.08607
$996$	−283.905	−8.99586
$997$	15.7965	0.500280	0.250140	−	0.968210i	$-0.419523\pi$
$997$	15.7965	0.500280	0.250140	+	0.968210i	$0.419523\pi$
$998$	−3.45522	−0.109373
$999$	−41.5415	−1.31432

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.81439 q^{2} +2.72661 q^{3} +5.92080 q^{4} +4.37726 q^{5} -7.67375 q^{6} -1.67878 q^{7} -11.0347 q^{8} +4.43441 q^{9} +O(q^{10})\)	\(q-2.81439 q^{2} +2.72661 q^{3} +5.92080 q^{4} +4.37726 q^{5} -7.67375 q^{6} -1.67878 q^{7} -11.0347 q^{8} +4.43441 q^{9} -12.3193 q^{10} -4.62107 q^{11} +16.1437 q^{12} -3.74200 q^{13} +4.72474 q^{14} +11.9351 q^{15} +19.2143 q^{16} -4.30426 q^{17} -12.4802 q^{18} +1.86232 q^{19} +25.9169 q^{20} -4.57737 q^{21} +13.0055 q^{22} -2.10458 q^{23} -30.0873 q^{24} +14.1604 q^{25} +10.5315 q^{26} +3.91108 q^{27} -9.93971 q^{28} -6.63530 q^{29} -33.5900 q^{30} -1.46430 q^{31} -32.0073 q^{32} -12.5999 q^{33} +12.1139 q^{34} -7.34844 q^{35} +26.2553 q^{36} -10.6215 q^{37} -5.24130 q^{38} -10.2030 q^{39} -48.3016 q^{40} +4.23874 q^{41} +12.8825 q^{42} +7.99027 q^{43} -27.3604 q^{44} +19.4106 q^{45} +5.92311 q^{46} -8.16691 q^{47} +52.3900 q^{48} -4.18171 q^{49} -39.8529 q^{50} -11.7360 q^{51} -22.1556 q^{52} -3.00048 q^{53} -11.0073 q^{54} -20.2276 q^{55} +18.5248 q^{56} +5.07783 q^{57} +18.6743 q^{58} -4.76521 q^{59} +70.6653 q^{60} -9.57537 q^{61} +4.12110 q^{62} -7.44439 q^{63} +51.6524 q^{64} -16.3797 q^{65} +35.4609 q^{66} -5.38481 q^{67} -25.4847 q^{68} -5.73837 q^{69} +20.6814 q^{70} +0.0228056 q^{71} -48.9323 q^{72} +8.08027 q^{73} +29.8931 q^{74} +38.6099 q^{75} +11.0264 q^{76} +7.75774 q^{77} +28.7152 q^{78} +9.62004 q^{79} +84.1060 q^{80} -2.63924 q^{81} -11.9295 q^{82} -17.5861 q^{83} -27.1017 q^{84} -18.8409 q^{85} -22.4878 q^{86} -18.0919 q^{87} +50.9920 q^{88} +11.5858 q^{89} -54.6289 q^{90} +6.28198 q^{91} -12.4608 q^{92} -3.99257 q^{93} +22.9849 q^{94} +8.15186 q^{95} -87.2714 q^{96} -13.2417 q^{97} +11.7690 q^{98} -20.4917 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 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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