LMFDB - Embedded newform 6047.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6047,2,Mod(1,6047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6047, 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("6047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6047 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6047.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:	$48.2855381023$
Analytic rank:	$0$
Dimension:	$287$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60365 q^{2} +1.57080 q^{3} +4.77897 q^{4} +2.08285 q^{5} -4.08981 q^{6} -3.47220 q^{7} -7.23545 q^{8} -0.532582 q^{9} +O(q^{10})$	\(q-2.60365 q^{2} +1.57080 q^{3} +4.77897 q^{4} +2.08285 q^{5} -4.08981 q^{6} -3.47220 q^{7} -7.23545 q^{8} -0.532582 q^{9} -5.42301 q^{10} +1.43844 q^{11} +7.50681 q^{12} +6.65417 q^{13} +9.04039 q^{14} +3.27175 q^{15} +9.28060 q^{16} -4.68582 q^{17} +1.38666 q^{18} -5.74973 q^{19} +9.95389 q^{20} -5.45415 q^{21} -3.74520 q^{22} -1.97032 q^{23} -11.3655 q^{24} -0.661720 q^{25} -17.3251 q^{26} -5.54899 q^{27} -16.5936 q^{28} +1.70936 q^{29} -8.51848 q^{30} -3.19486 q^{31} -9.69250 q^{32} +2.25951 q^{33} +12.2002 q^{34} -7.23210 q^{35} -2.54519 q^{36} +4.80361 q^{37} +14.9703 q^{38} +10.4524 q^{39} -15.0704 q^{40} -0.990926 q^{41} +14.2007 q^{42} +6.73807 q^{43} +6.87428 q^{44} -1.10929 q^{45} +5.13001 q^{46} -5.53543 q^{47} +14.5780 q^{48} +5.05621 q^{49} +1.72288 q^{50} -7.36050 q^{51} +31.8001 q^{52} +8.96308 q^{53} +14.4476 q^{54} +2.99607 q^{55} +25.1230 q^{56} -9.03169 q^{57} -4.45056 q^{58} +0.451925 q^{59} +15.6356 q^{60} +7.38421 q^{61} +8.31829 q^{62} +1.84924 q^{63} +6.67463 q^{64} +13.8597 q^{65} -5.88296 q^{66} -8.48124 q^{67} -22.3934 q^{68} -3.09498 q^{69} +18.8298 q^{70} +15.9848 q^{71} +3.85347 q^{72} +12.9878 q^{73} -12.5069 q^{74} -1.03943 q^{75} -27.4778 q^{76} -4.99457 q^{77} -27.2143 q^{78} -8.98180 q^{79} +19.3301 q^{80} -7.11861 q^{81} +2.58002 q^{82} -9.79575 q^{83} -26.0652 q^{84} -9.75988 q^{85} -17.5436 q^{86} +2.68506 q^{87} -10.4078 q^{88} +15.5091 q^{89} +2.88820 q^{90} -23.1046 q^{91} -9.41609 q^{92} -5.01850 q^{93} +14.4123 q^{94} -11.9758 q^{95} -15.2250 q^{96} +15.9720 q^{97} -13.1646 q^{98} -0.766090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) $ 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * 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 $

$2$	−2.60365	−1.84106	−0.920528	−	0.390678i	$-0.872241\pi$
$2$	−2.60365	−1.84106	−0.920528	+	0.390678i	$0.872241\pi$
$3$	1.57080	0.906903	0.453451	−	0.891281i	$-0.350193\pi$
$3$	1.57080	0.906903	0.453451	+	0.891281i	$0.350193\pi$
$4$	4.77897	2.38948
$5$	2.08285	0.931481	0.465740	−	0.884921i	$-0.345788\pi$
$5$	2.08285	0.931481	0.465740	+	0.884921i	$0.345788\pi$
$6$	−4.08981	−1.66966
$7$	−3.47220	−1.31237	−0.656185	−	0.754600i	$-0.727831\pi$
$7$	−3.47220	−1.31237	−0.656185	+	0.754600i	$0.727831\pi$
$8$	−7.23545	−2.55812
$9$	−0.532582	−0.177527
$10$	−5.42301	−1.71491
$11$	1.43844	0.433707	0.216854	−	0.976204i	$-0.430421\pi$
$11$	1.43844	0.433707	0.216854	+	0.976204i	$0.430421\pi$
$12$	7.50681	2.16703
$13$	6.65417	1.84553	0.922767	−	0.385359i	$-0.125922\pi$
$13$	6.65417	1.84553	0.922767	+	0.385359i	$0.125922\pi$
$14$	9.04039	2.41615
$15$	3.27175	0.844762
$16$	9.28060	2.32015
$17$	−4.68582	−1.13648	−0.568240	−	0.822863i	$-0.692375\pi$
$17$	−4.68582	−1.13648	−0.568240	+	0.822863i	$0.692375\pi$
$18$	1.38666	0.326838
$19$	−5.74973	−1.31908	−0.659539	−	0.751670i	$-0.729249\pi$
$19$	−5.74973	−1.31908	−0.659539	+	0.751670i	$0.729249\pi$
$20$	9.95389	2.22576
$21$	−5.45415	−1.19019
$22$	−3.74520	−0.798479
$23$	−1.97032	−0.410840	−0.205420	−	0.978674i	$-0.565856\pi$
$23$	−1.97032	−0.410840	−0.205420	+	0.978674i	$0.565856\pi$
$24$	−11.3655	−2.31996
$25$	−0.661720	−0.132344
$26$	−17.3251	−3.39773
$27$	−5.54899	−1.06790
$28$	−16.5936	−3.13589
$29$	1.70936	0.317420	0.158710	−	0.987325i	$-0.449267\pi$
$29$	1.70936	0.317420	0.158710	+	0.987325i	$0.449267\pi$
$30$	−8.51848	−1.55525
$31$	−3.19486	−0.573815	−0.286907	−	0.957958i	$-0.592627\pi$
$31$	−3.19486	−0.573815	−0.286907	+	0.957958i	$0.592627\pi$
$32$	−9.69250	−1.71341
$33$	2.25951	0.393330
$34$	12.2002	2.09232
$35$	−7.23210	−1.22245
$36$	−2.54519	−0.424199
$37$	4.80361	0.789709	0.394854	−	0.918744i	$-0.370795\pi$
$37$	4.80361	0.789709	0.394854	+	0.918744i	$0.370795\pi$
$38$	14.9703	2.42850
$39$	10.4524	1.67372
$40$	−15.0704	−2.38284
$41$	−0.990926	−0.154757	−0.0773783	−	0.997002i	$-0.524655\pi$
$41$	−0.990926	−0.154757	−0.0773783	+	0.997002i	$0.524655\pi$
$42$	14.2007	2.19121
$43$	6.73807	1.02755	0.513773	−	0.857926i	$-0.328247\pi$
$43$	6.73807	1.02755	0.513773	+	0.857926i	$0.328247\pi$
$44$	6.87428	1.03634
$45$	−1.10929	−0.165363
$46$	5.13001	0.756379
$47$	−5.53543	−0.807426	−0.403713	−	0.914886i	$-0.632281\pi$
$47$	−5.53543	−0.807426	−0.403713	+	0.914886i	$0.632281\pi$
$48$	14.5780	2.10415
$49$	5.05621	0.722315
$50$	1.72288	0.243653
$51$	−7.36050	−1.03068
$52$	31.8001	4.40987
$53$	8.96308	1.23117	0.615587	−	0.788069i	$-0.288919\pi$
$53$	8.96308	1.23117	0.615587	+	0.788069i	$0.288919\pi$
$54$	14.4476	1.96607
$55$	2.99607	0.403990
$56$	25.1230	3.35720
$57$	−9.03169	−1.19628
$58$	−4.45056	−0.584387
$59$	0.451925	0.0588356	0.0294178	−	0.999567i	$-0.490635\pi$
$59$	0.451925	0.0588356	0.0294178	+	0.999567i	$0.490635\pi$
$60$	15.6356	2.01855
$61$	7.38421	0.945451	0.472726	−	0.881210i	$-0.343270\pi$
$61$	7.38421	0.945451	0.472726	+	0.881210i	$0.343270\pi$
$62$	8.31829	1.05642
$63$	1.84924	0.232982
$64$	6.67463	0.834329
$65$	13.8597	1.71908
$66$	−5.88296	−0.724143
$67$	−8.48124	−1.03615	−0.518074	−	0.855336i	$-0.673351\pi$
$67$	−8.48124	−1.03615	−0.518074	+	0.855336i	$0.673351\pi$
$68$	−22.3934	−2.71560
$69$	−3.09498	−0.372592
$70$	18.8298	2.25059
$71$	15.9848	1.89704	0.948521	−	0.316715i	$-0.102580\pi$
$71$	15.9848	1.89704	0.948521	+	0.316715i	$0.102580\pi$
$72$	3.85347	0.454136
$73$	12.9878	1.52010	0.760051	−	0.649863i	$-0.225174\pi$
$73$	12.9878	1.52010	0.760051	+	0.649863i	$0.225174\pi$
$74$	−12.5069	−1.45390
$75$	−1.03943	−0.120023
$76$	−27.4778	−3.15192
$77$	−4.99457	−0.569184
$78$	−27.2143	−3.08141
$79$	−8.98180	−1.01053	−0.505265	−	0.862964i	$-0.668605\pi$
$79$	−8.98180	−1.01053	−0.505265	+	0.862964i	$0.668605\pi$
$80$	19.3301	2.16118
$81$	−7.11861	−0.790957
$82$	2.58002	0.284915
$83$	−9.79575	−1.07522	−0.537612	−	0.843192i	$-0.680673\pi$
$83$	−9.79575	−1.07522	−0.537612	+	0.843192i	$0.680673\pi$
$84$	−26.0652	−2.84395
$85$	−9.75988	−1.05861
$86$	−17.5436	−1.89177
$87$	2.68506	0.287869
$88$	−10.4078	−1.10947
$89$	15.5091	1.64396	0.821982	−	0.569514i	$-0.192868\pi$
$89$	15.5091	1.64396	0.821982	+	0.569514i	$0.192868\pi$
$90$	2.88820	0.304443
$91$	−23.1046	−2.42202
$92$	−9.41609	−0.981695
$93$	−5.01850	−0.520394
$94$	14.4123	1.48652
$95$	−11.9758	−1.22870
$96$	−15.2250	−1.55389
$97$	15.9720	1.62171	0.810857	−	0.585244i	$-0.199001\pi$
$97$	15.9720	1.62171	0.810857	+	0.585244i	$0.199001\pi$
$98$	−13.1646	−1.32982
$99$	−0.766090	−0.0769949
$100$	−3.16234	−0.316234
$101$	6.48270	0.645053	0.322527	−	0.946560i	$-0.395468\pi$
$101$	6.48270	0.645053	0.322527	+	0.946560i	$0.395468\pi$
$102$	19.1641	1.89753
$103$	18.5606	1.82883	0.914415	−	0.404778i	$-0.132651\pi$
$103$	18.5606	1.82883	0.914415	+	0.404778i	$0.132651\pi$
$104$	−48.1459	−4.72109
$105$	−11.3602	−1.10864
$106$	−23.3367	−2.26666
$107$	−2.79487	−0.270191	−0.135095	−	0.990833i	$-0.543134\pi$
$107$	−2.79487	−0.270191	−0.135095	+	0.990833i	$0.543134\pi$
$108$	−26.5184	−2.55174
$109$	20.1258	1.92771	0.963853	−	0.266433i	$-0.0858452\pi$
$109$	20.1258	1.92771	0.963853	+	0.266433i	$0.0858452\pi$
$110$	−7.80070	−0.743767
$111$	7.54552	0.716189
$112$	−32.2242	−3.04490
$113$	4.84067	0.455372	0.227686	−	0.973735i	$-0.426884\pi$
$113$	4.84067	0.455372	0.227686	+	0.973735i	$0.426884\pi$
$114$	23.5153	2.20241
$115$	−4.10388	−0.382689
$116$	8.16896	0.758469
$117$	−3.54389	−0.327633
$118$	−1.17665	−0.108320
$119$	16.2701	1.49148
$120$	−23.6726	−2.16100
$121$	−8.93088	−0.811898
$122$	−19.2259	−1.74063
$123$	−1.55655	−0.140349
$124$	−15.2682	−1.37112
$125$	−11.7925	−1.05476
$126$	−4.81475	−0.428932
$127$	−2.44186	−0.216680	−0.108340	−	0.994114i	$-0.534554\pi$
$127$	−2.44186	−0.216680	−0.108340	+	0.994114i	$0.534554\pi$
$128$	2.00664	0.177363
$129$	10.5842	0.931885
$130$	−36.0856	−3.16492
$131$	13.7480	1.20117	0.600585	−	0.799561i	$-0.294934\pi$
$131$	13.7480	1.20117	0.600585	+	0.799561i	$0.294934\pi$
$132$	10.7981	0.939856
$133$	19.9642	1.73112
$134$	22.0821	1.90761
$135$	−11.5577	−0.994731
$136$	33.9040	2.90725
$137$	−5.87241	−0.501714	−0.250857	−	0.968024i	$-0.580712\pi$
$137$	−5.87241	−0.501714	−0.250857	+	0.968024i	$0.580712\pi$
$138$	8.05823	0.685962
$139$	−13.5872	−1.15245	−0.576227	−	0.817290i	$-0.695476\pi$
$139$	−13.5872	−1.15245	−0.576227	+	0.817290i	$0.695476\pi$
$140$	−34.5620	−2.92102
$141$	−8.69506	−0.732257
$142$	−41.6186	−3.49256
$143$	9.57164	0.800421
$144$	−4.94269	−0.411890
$145$	3.56034	0.295670
$146$	−33.8155	−2.79859
$147$	7.94230	0.655070
$148$	22.9563	1.88700
$149$	−1.62472	−0.133102	−0.0665511	−	0.997783i	$-0.521200\pi$
$149$	−1.62472	−0.133102	−0.0665511	+	0.997783i	$0.521200\pi$
$150$	2.70631	0.220969
$151$	−4.50402	−0.366532	−0.183266	−	0.983063i	$-0.558667\pi$
$151$	−4.50402	−0.366532	−0.183266	+	0.983063i	$0.558667\pi$
$152$	41.6019	3.37436
$153$	2.49559	0.201756
$154$	13.0041	1.04790
$155$	−6.65444	−0.534497
$156$	49.9516	3.99933
$157$	15.5136	1.23812	0.619060	−	0.785343i	$-0.287514\pi$
$157$	15.5136	1.23812	0.619060	+	0.785343i	$0.287514\pi$
$158$	23.3854	1.86044
$159$	14.0792	1.11655
$160$	−20.1881	−1.59601
$161$	6.84135	0.539174
$162$	18.5343	1.45619
$163$	17.8164	1.39549	0.697743	−	0.716348i	$-0.254188\pi$
$163$	17.8164	1.39549	0.697743	+	0.716348i	$0.254188\pi$
$164$	−4.73560	−0.369788
$165$	4.70623	0.366379
$166$	25.5047	1.97955
$167$	−2.54406	−0.196866	−0.0984328	−	0.995144i	$-0.531383\pi$
$167$	−2.54406	−0.196866	−0.0984328	+	0.995144i	$0.531383\pi$
$168$	39.4632	3.04465
$169$	31.2779	2.40599
$170$	25.4113	1.94896
$171$	3.06221	0.234173
$172$	32.2010	2.45531
$173$	−13.7050	−1.04197	−0.520985	−	0.853566i	$-0.674435\pi$
$173$	−13.7050	−1.04197	−0.520985	+	0.853566i	$0.674435\pi$
$174$	−6.99094	−0.529982
$175$	2.29763	0.173684
$176$	13.3496	1.00627
$177$	0.709885	0.0533582
$178$	−40.3802	−3.02663
$179$	−13.8953	−1.03859	−0.519293	−	0.854596i	$-0.673805\pi$
$179$	−13.8953	−1.03859	−0.519293	+	0.854596i	$0.673805\pi$
$180$	−5.30127	−0.395133
$181$	9.90953	0.736569	0.368285	−	0.929713i	$-0.379945\pi$
$181$	9.90953	0.736569	0.368285	+	0.929713i	$0.379945\pi$
$182$	60.1563	4.45908
$183$	11.5991	0.857432
$184$	14.2561	1.05098
$185$	10.0052	0.735598
$186$	13.0664	0.958074
$187$	−6.74029	−0.492899
$188$	−26.4537	−1.92933
$189$	19.2672	1.40148
$190$	31.1809	2.26210
$191$	18.8918	1.36696	0.683481	−	0.729968i	$-0.260465\pi$
$191$	18.8918	1.36696	0.683481	+	0.729968i	$0.260465\pi$
$192$	10.4845	0.756655
$193$	1.64685	0.118543	0.0592713	−	0.998242i	$-0.481122\pi$
$193$	1.64685	0.118543	0.0592713	+	0.998242i	$0.481122\pi$
$194$	−41.5855	−2.98567
$195$	21.7708	1.55904
$196$	24.1635	1.72596
$197$	5.24965	0.374022	0.187011	−	0.982358i	$-0.440120\pi$
$197$	5.24965	0.374022	0.187011	+	0.982358i	$0.440120\pi$
$198$	1.99463	0.141752
$199$	28.0382	1.98758	0.993788	−	0.111291i	$-0.0354986\pi$
$199$	28.0382	1.98758	0.993788	+	0.111291i	$0.0354986\pi$
$200$	4.78784	0.338552
$201$	−13.3223	−0.939685
$202$	−16.8787	−1.18758
$203$	−5.93524	−0.416572
$204$	−35.1756	−2.46278
$205$	−2.06395	−0.144153
$206$	−48.3252	−3.36698
$207$	1.04936	0.0729353
$208$	61.7547	4.28192
$209$	−8.27067	−0.572094
$210$	29.5779	2.04107
$211$	−14.3109	−0.985201	−0.492601	−	0.870256i	$-0.663954\pi$
$211$	−14.3109	−0.985201	−0.492601	+	0.870256i	$0.663954\pi$
$212$	42.8343	2.94187
$213$	25.1089	1.72043
$214$	7.27686	0.497436
$215$	14.0344	0.957140
$216$	40.1494	2.73182
$217$	11.0932	0.753057
$218$	−52.4006	−3.54901
$219$	20.4012	1.37859
$220$	14.3181	0.965327
$221$	−31.1802	−2.09741
$222$	−19.6459	−1.31854
$223$	13.2150	0.884939	0.442470	−	0.896783i	$-0.354102\pi$
$223$	13.2150	0.884939	0.442470	+	0.896783i	$0.354102\pi$
$224$	33.6544	2.24863
$225$	0.352421	0.0234947
$226$	−12.6034	−0.838365
$227$	21.8379	1.44943	0.724716	−	0.689047i	$-0.241971\pi$
$227$	21.8379	1.44943	0.724716	+	0.689047i	$0.241971\pi$
$228$	−43.1621	−2.85848
$229$	21.8019	1.44071	0.720355	−	0.693605i	$-0.243979\pi$
$229$	21.8019	1.44071	0.720355	+	0.693605i	$0.243979\pi$
$230$	10.6851	0.704552
$231$	−7.84548	−0.516195
$232$	−12.3680	−0.811996
$233$	−12.3290	−0.807698	−0.403849	−	0.914826i	$-0.632328\pi$
$233$	−12.3290	−0.807698	−0.403849	+	0.914826i	$0.632328\pi$
$234$	9.22704	0.603190
$235$	−11.5295	−0.752101
$236$	2.15974	0.140587
$237$	−14.1086	−0.916453
$238$	−42.3617	−2.74590
$239$	−24.6188	−1.59246	−0.796228	−	0.604997i	$-0.793174\pi$
$239$	−24.6188	−1.59246	−0.796228	+	0.604997i	$0.793174\pi$
$240$	30.3638	1.95998
$241$	−12.5007	−0.805240	−0.402620	−	0.915367i	$-0.631900\pi$
$241$	−12.5007	−0.805240	−0.402620	+	0.915367i	$0.631900\pi$
$242$	23.2528	1.49475
$243$	5.46504	0.350582
$244$	35.2889	2.25914
$245$	10.5313	0.672823
$246$	4.05270	0.258391
$247$	−38.2597	−2.43440
$248$	23.1163	1.46789
$249$	−15.3872	−0.975123
$250$	30.7036	1.94186
$251$	11.7335	0.740614	0.370307	−	0.928909i	$-0.379253\pi$
$251$	11.7335	0.740614	0.370307	+	0.928909i	$0.379253\pi$
$252$	8.83744	0.556706
$253$	−2.83419	−0.178184
$254$	6.35774	0.398920
$255$	−15.3308	−0.960055
$256$	−18.5738	−1.16086
$257$	12.1550	0.758208	0.379104	−	0.925354i	$-0.376232\pi$
$257$	12.1550	0.758208	0.379104	+	0.925354i	$0.376232\pi$
$258$	−27.5574	−1.71565
$259$	−16.6791	−1.03639
$260$	66.2349	4.10771
$261$	−0.910373	−0.0563507
$262$	−35.7950	−2.21142
$263$	16.4294	1.01308	0.506540	−	0.862216i	$-0.330924\pi$
$263$	16.4294	1.01308	0.506540	+	0.862216i	$0.330924\pi$
$264$	−16.3486	−1.00618
$265$	18.6688	1.14681
$266$	−51.9798	−3.18709
$267$	24.3618	1.49091
$268$	−40.5316	−2.47586
$269$	−26.3384	−1.60588	−0.802941	−	0.596058i	$-0.796733\pi$
$269$	−26.3384	−1.60588	−0.802941	+	0.596058i	$0.796733\pi$
$270$	30.0922	1.83135
$271$	9.13044	0.554635	0.277317	−	0.960778i	$-0.410555\pi$
$271$	9.13044	0.554635	0.277317	+	0.960778i	$0.410555\pi$
$272$	−43.4873	−2.63680
$273$	−36.2928	−2.19654
$274$	15.2897	0.923683
$275$	−0.951847	−0.0573986
$276$	−14.7908	−0.890302
$277$	21.9200	1.31705	0.658523	−	0.752560i	$-0.271181\pi$
$277$	21.9200	1.31705	0.658523	+	0.752560i	$0.271181\pi$
$278$	35.3763	2.12173
$279$	1.70153	0.101868
$280$	52.3274	3.12716
$281$	−6.87435	−0.410090	−0.205045	−	0.978753i	$-0.565734\pi$
$281$	−6.87435	−0.410090	−0.205045	+	0.978753i	$0.565734\pi$
$282$	22.6389	1.34812
$283$	−24.9361	−1.48230	−0.741148	−	0.671341i	$-0.765718\pi$
$283$	−24.9361	−1.48230	−0.741148	+	0.671341i	$0.765718\pi$
$284$	76.3906	4.53295
$285$	−18.8117	−1.11431
$286$	−24.9212	−1.47362
$287$	3.44070	0.203098
$288$	5.16206	0.304177
$289$	4.95694	0.291585
$290$	−9.26986	−0.544345
$291$	25.0889	1.47074
$292$	62.0681	3.63226
$293$	−14.8989	−0.870406	−0.435203	−	0.900332i	$-0.643323\pi$
$293$	−14.8989	−0.870406	−0.435203	+	0.900332i	$0.643323\pi$
$294$	−20.6789	−1.20602
$295$	0.941294	0.0548042
$296$	−34.7563	−2.02017
$297$	−7.98190	−0.463157
$298$	4.23019	0.245048
$299$	−13.1108	−0.758219
$300$	−4.96741	−0.286794
$301$	−23.3960	−1.34852
$302$	11.7269	0.674805
$303$	10.1830	0.585001
$304$	−53.3610	−3.06046
$305$	15.3802	0.880669
$306$	−6.49762	−0.371444
$307$	−21.1100	−1.20481	−0.602406	−	0.798190i	$-0.705791\pi$
$307$	−21.1100	−1.20481	−0.602406	+	0.798190i	$0.705791\pi$
$308$	−23.8689	−1.36006
$309$	29.1550	1.65857
$310$	17.3258	0.984039
$311$	25.9749	1.47290	0.736450	−	0.676492i	$-0.236501\pi$
$311$	25.9749	1.47290	0.736450	+	0.676492i	$0.236501\pi$
$312$	−75.6276	−4.28157
$313$	6.67356	0.377212	0.188606	−	0.982053i	$-0.439603\pi$
$313$	6.67356	0.377212	0.188606	+	0.982053i	$0.439603\pi$
$314$	−40.3919	−2.27945
$315$	3.85169	0.217018
$316$	−42.9237	−2.41465
$317$	−0.0271176	−0.00152308	−0.000761538	−	1.00000i	$-0.500242\pi$
$317$	−0.0271176	−0.00152308	−0.000761538		1.00000i	$0.500242\pi$
$318$	−36.6573	−2.05564
$319$	2.45881	0.137667
$320$	13.9023	0.777161
$321$	−4.39019	−0.245037
$322$	−17.8124	−0.992649
$323$	26.9422	1.49911
$324$	−34.0196	−1.88998
$325$	−4.40320	−0.244245
$326$	−46.3875	−2.56917
$327$	31.6137	1.74824
$328$	7.16979	0.395886
$329$	19.2202	1.05964
$330$	−12.2533	−0.674525
$331$	−27.7913	−1.52755	−0.763773	−	0.645485i	$-0.776655\pi$
$331$	−27.7913	−1.52755	−0.763773	+	0.645485i	$0.776655\pi$
$332$	−46.8136	−2.56923
$333$	−2.55832	−0.140195
$334$	6.62384	0.362440
$335$	−17.6652	−0.965152
$336$	−50.6178	−2.76142
$337$	−21.6112	−1.17724	−0.588619	−	0.808410i	$-0.700328\pi$
$337$	−21.6112	−1.17724	−0.588619	+	0.808410i	$0.700328\pi$
$338$	−81.4366	−4.42957
$339$	7.60373	0.412978
$340$	−46.6422	−2.52953
$341$	−4.59563	−0.248867
$342$	−7.97290	−0.431125
$343$	6.74925	0.364425
$344$	−48.7530	−2.62858
$345$	−6.44639	−0.347062
$346$	35.6829	1.91832
$347$	−17.3124	−0.929377	−0.464688	−	0.885474i	$-0.653834\pi$
$347$	−17.3124	−0.929377	−0.464688	+	0.885474i	$0.653834\pi$
$348$	12.8318	0.687858
$349$	3.36411	0.180077	0.0900384	−	0.995938i	$-0.471301\pi$
$349$	3.36411	0.180077	0.0900384	+	0.995938i	$0.471301\pi$
$350$	−5.98221	−0.319763
$351$	−36.9239	−1.97085
$352$	−13.9421	−0.743117
$353$	26.4704	1.40887	0.704437	−	0.709766i	$-0.251199\pi$
$353$	26.4704	1.40887	0.704437	+	0.709766i	$0.251199\pi$
$354$	−1.84829	−0.0982354
$355$	33.2939	1.76706
$356$	74.1176	3.92822
$357$	25.5572	1.35263
$358$	36.1785	1.91209
$359$	−4.17359	−0.220274	−0.110137	−	0.993916i	$-0.535129\pi$
$359$	−4.17359	−0.220274	−0.110137	+	0.993916i	$0.535129\pi$
$360$	8.02622	0.423019
$361$	14.0594	0.739969
$362$	−25.8009	−1.35606
$363$	−14.0286	−0.736313
$364$	−110.416	−5.78739
$365$	27.0516	1.41595
$366$	−30.2000	−1.57858
$367$	−11.5125	−0.600947	−0.300474	−	0.953790i	$-0.597145\pi$
$367$	−11.5125	−0.600947	−0.300474	+	0.953790i	$0.597145\pi$
$368$	−18.2857	−0.953210
$369$	0.527750	0.0274735
$370$	−26.0500	−1.35428
$371$	−31.1217	−1.61576
$372$	−23.9832	−1.24347
$373$	10.4736	0.542305	0.271152	−	0.962536i	$-0.412595\pi$
$373$	10.4736	0.542305	0.271152	+	0.962536i	$0.412595\pi$
$374$	17.5493	0.907454
$375$	−18.5237	−0.956561
$376$	40.0513	2.06549
$377$	11.3743	0.585808
$378$	−50.1650	−2.58021
$379$	−19.3929	−0.996148	−0.498074	−	0.867134i	$-0.665959\pi$
$379$	−19.3929	−0.996148	−0.498074	+	0.867134i	$0.665959\pi$
$380$	−57.2322	−2.93595
$381$	−3.83568	−0.196508
$382$	−49.1875	−2.51665
$383$	30.9286	1.58038	0.790188	−	0.612865i	$-0.209983\pi$
$383$	30.9286	1.58038	0.790188	+	0.612865i	$0.209983\pi$
$384$	3.15203	0.160851
$385$	−10.4030	−0.530184
$386$	−4.28781	−0.218244
$387$	−3.58858	−0.182418
$388$	76.3299	3.87506
$389$	−14.4219	−0.731222	−0.365611	−	0.930768i	$-0.619140\pi$
$389$	−14.4219	−0.731222	−0.365611	+	0.930768i	$0.619140\pi$
$390$	−56.6834	−2.87027
$391$	9.23256	0.466911
$392$	−36.5839	−1.84777
$393$	21.5954	1.08934
$394$	−13.6682	−0.688595
$395$	−18.7078	−0.941290
$396$	−3.66112	−0.183978
$397$	19.4194	0.974632	0.487316	−	0.873226i	$-0.337976\pi$
$397$	19.4194	0.974632	0.487316	+	0.873226i	$0.337976\pi$
$398$	−73.0015	−3.65924
$399$	31.3599	1.56996
$400$	−6.14116	−0.307058
$401$	−17.0287	−0.850374	−0.425187	−	0.905106i	$-0.639792\pi$
$401$	−17.0287	−0.850374	−0.425187	+	0.905106i	$0.639792\pi$
$402$	34.6866	1.73001
$403$	−21.2592	−1.05899
$404$	30.9806	1.54134
$405$	−14.8270	−0.736761
$406$	15.4532	0.766932
$407$	6.90973	0.342502
$408$	53.2565	2.63659
$409$	11.0028	0.544053	0.272027	−	0.962290i	$-0.412306\pi$
$409$	11.0028	0.544053	0.272027	+	0.962290i	$0.412306\pi$
$410$	5.37380	0.265393
$411$	−9.22439	−0.455006
$412$	88.7005	4.36996
$413$	−1.56918	−0.0772141
$414$	−2.73215	−0.134278
$415$	−20.4031	−1.00155
$416$	−64.4955	−3.16215
$417$	−21.3429	−1.04516
$418$	21.5339	1.05326
$419$	−23.0006	−1.12365	−0.561827	−	0.827255i	$-0.689901\pi$
$419$	−23.0006	−1.12365	−0.561827	+	0.827255i	$0.689901\pi$
$420$	−54.2900	−2.64908
$421$	3.00580	0.146494	0.0732469	−	0.997314i	$-0.476664\pi$
$421$	3.00580	0.146494	0.0732469	+	0.997314i	$0.476664\pi$
$422$	37.2604	1.81381
$423$	2.94807	0.143340
$424$	−64.8519	−3.14949
$425$	3.10070	0.150406
$426$	−65.3746	−3.16741
$427$	−25.6395	−1.24078
$428$	−13.3566	−0.645616
$429$	15.0352	0.725904
$430$	−36.5407	−1.76215
$431$	−22.5269	−1.08508	−0.542540	−	0.840030i	$-0.682537\pi$
$431$	−22.5269	−1.08508	−0.542540	+	0.840030i	$0.682537\pi$
$432$	−51.4979	−2.47770
$433$	19.0595	0.915942	0.457971	−	0.888967i	$-0.348576\pi$
$433$	19.0595	0.915942	0.457971	+	0.888967i	$0.348576\pi$
$434$	−28.8828	−1.38642
$435$	5.59259	0.268144
$436$	96.1808	4.60622
$437$	11.3288	0.541930
$438$	−53.1175	−2.53805
$439$	25.7576	1.22934	0.614672	−	0.788783i	$-0.289288\pi$
$439$	25.7576	1.22934	0.614672	+	0.788783i	$0.289288\pi$
$440$	−21.6779	−1.03345
$441$	−2.69285	−0.128231
$442$	81.1823	3.86145
$443$	−25.7740	−1.22456	−0.612280	−	0.790641i	$-0.709747\pi$
$443$	−25.7740	−1.22456	−0.612280	+	0.790641i	$0.709747\pi$
$444$	36.0598	1.71132
$445$	32.3032	1.53132
$446$	−34.4071	−1.62922
$447$	−2.55211	−0.120711
$448$	−23.1757	−1.09495
$449$	−27.0667	−1.27735	−0.638677	−	0.769475i	$-0.720518\pi$
$449$	−27.0667	−1.27735	−0.638677	+	0.769475i	$0.720518\pi$
$450$	−0.917578	−0.0432550
$451$	−1.42539	−0.0671190
$452$	23.1334	1.08810
$453$	−7.07492	−0.332409
$454$	−56.8582	−2.66849
$455$	−48.1236	−2.25607
$456$	65.3483	3.06021
$457$	−13.7143	−0.641527	−0.320764	−	0.947159i	$-0.603939\pi$
$457$	−13.7143	−0.641527	−0.320764	+	0.947159i	$0.603939\pi$
$458$	−56.7644	−2.65243
$459$	26.0016	1.21365
$460$	−19.6123	−0.914430
$461$	−22.0642	−1.02763	−0.513816	−	0.857900i	$-0.671769\pi$
$461$	−22.0642	−1.02763	−0.513816	+	0.857900i	$0.671769\pi$
$462$	20.4268	0.950343
$463$	23.7536	1.10392	0.551962	−	0.833869i	$-0.313879\pi$
$463$	23.7536	1.10392	0.551962	+	0.833869i	$0.313879\pi$
$464$	15.8639	0.736461
$465$	−10.4528	−0.484737
$466$	32.1003	1.48702
$467$	−9.02641	−0.417693	−0.208846	−	0.977948i	$-0.566971\pi$
$467$	−9.02641	−0.417693	−0.208846	+	0.977948i	$0.566971\pi$
$468$	−16.9361	−0.782874
$469$	29.4486	1.35981
$470$	30.0187	1.38466
$471$	24.3688	1.12286
$472$	−3.26988	−0.150508
$473$	9.69234	0.445654
$474$	36.7338	1.68724
$475$	3.80471	0.174572
$476$	77.7545	3.56387
$477$	−4.77358	−0.218567
$478$	64.0985	2.93180
$479$	25.6131	1.17029	0.585147	−	0.810928i	$-0.301037\pi$
$479$	25.6131	1.17029	0.585147	+	0.810928i	$0.301037\pi$
$480$	−31.7114	−1.44742
$481$	31.9640	1.45743
$482$	32.5474	1.48249
$483$	10.7464	0.488978
$484$	−42.6804	−1.94002
$485$	33.2674	1.51060
$486$	−14.2290	−0.645441
$487$	5.69479	0.258056	0.129028	−	0.991641i	$-0.458814\pi$
$487$	5.69479	0.258056	0.129028	+	0.991641i	$0.458814\pi$
$488$	−53.4281	−2.41858
$489$	27.9860	1.26557
$490$	−27.4199	−1.23870
$491$	25.9738	1.17218	0.586090	−	0.810246i	$-0.300666\pi$
$491$	25.9738	1.17218	0.586090	+	0.810246i	$0.300666\pi$
$492$	−7.43869	−0.335362
$493$	−8.00974	−0.360741
$494$	99.6146	4.48187
$495$	−1.59565	−0.0717193
$496$	−29.6503	−1.33134
$497$	−55.5023	−2.48962
$498$	40.0628	1.79526
$499$	11.0816	0.496081	0.248041	−	0.968750i	$-0.420213\pi$
$499$	11.0816	0.496081	0.248041	+	0.968750i	$0.420213\pi$
$500$	−56.3562	−2.52032
$501$	−3.99622	−0.178538
$502$	−30.5499	−1.36351
$503$	32.1699	1.43439	0.717193	−	0.696875i	$-0.245427\pi$
$503$	32.1699	1.43439	0.717193	+	0.696875i	$0.245427\pi$
$504$	−13.3800	−0.595995
$505$	13.5025	0.600855
$506$	7.37923	0.328047
$507$	49.1314	2.18200
$508$	−11.6696	−0.517754
$509$	−27.6845	−1.22710	−0.613548	−	0.789657i	$-0.710258\pi$
$509$	−27.6845	−1.22710	−0.613548	+	0.789657i	$0.710258\pi$
$510$	39.9161	1.76751
$511$	−45.0962	−1.99494
$512$	44.3464	1.95985
$513$	31.9052	1.40865
$514$	−31.6473	−1.39590
$515$	38.6590	1.70352
$516$	50.5815	2.22672
$517$	−7.96241	−0.350186
$518$	43.4265	1.90805
$519$	−21.5278	−0.944965
$520$	−100.281	−4.39760
$521$	−17.4539	−0.764667	−0.382334	−	0.924024i	$-0.624880\pi$
$521$	−17.4539	−0.764667	−0.382334	+	0.924024i	$0.624880\pi$
$522$	2.37029	0.103745
$523$	12.5990	0.550914	0.275457	−	0.961313i	$-0.411171\pi$
$523$	12.5990	0.550914	0.275457	+	0.961313i	$0.411171\pi$
$524$	65.7013	2.87018
$525$	3.60912	0.157515
$526$	−42.7764	−1.86514
$527$	14.9706	0.652128
$528$	20.9696	0.912585
$529$	−19.1178	−0.831211
$530$	−48.6069	−2.11135
$531$	−0.240687	−0.0104449
$532$	95.4085	4.13648
$533$	−6.59379	−0.285609
$534$	−63.4294	−2.74486
$535$	−5.82131	−0.251677
$536$	61.3655	2.65059
$537$	−21.8268	−0.941896
$538$	68.5759	2.95652
$539$	7.27307	0.313273
$540$	−55.2340	−2.37689
$541$	4.99250	0.214644	0.107322	−	0.994224i	$-0.465772\pi$
$541$	4.99250	0.214644	0.107322	+	0.994224i	$0.465772\pi$
$542$	−23.7724	−1.02111
$543$	15.5659	0.667997
$544$	45.4173	1.94725
$545$	41.9192	1.79562
$546$	94.4935	4.04395
$547$	34.0535	1.45602	0.728012	−	0.685565i	$-0.240445\pi$
$547$	34.0535	1.45602	0.728012	+	0.685565i	$0.240445\pi$
$548$	−28.0641	−1.19884
$549$	−3.93270	−0.167844
$550$	2.47827	0.105674
$551$	−9.82834	−0.418701
$552$	22.3936	0.953133
$553$	31.1866	1.32619
$554$	−57.0720	−2.42476
$555$	15.7162	0.667116
$556$	−64.9330	−2.75377
$557$	37.0244	1.56877	0.784387	−	0.620272i	$-0.212978\pi$
$557$	37.0244	1.56877	0.784387	+	0.620272i	$0.212978\pi$
$558$	−4.43018	−0.187544
$559$	44.8363	1.89637
$560$	−67.1182	−2.83626
$561$	−10.5877	−0.447012
$562$	17.8984	0.754998
$563$	−4.88883	−0.206040	−0.103020	−	0.994679i	$-0.532851\pi$
$563$	−4.88883	−0.206040	−0.103020	+	0.994679i	$0.532851\pi$
$564$	−41.5534	−1.74972
$565$	10.0824	0.424170
$566$	64.9247	2.72899
$567$	24.7173	1.03803
$568$	−115.657	−4.85285
$569$	−21.8043	−0.914084	−0.457042	−	0.889445i	$-0.651091\pi$
$569$	−21.8043	−0.914084	−0.457042	+	0.889445i	$0.651091\pi$
$570$	48.9790	2.05150
$571$	16.8775	0.706299	0.353150	−	0.935567i	$-0.385111\pi$
$571$	16.8775	0.706299	0.353150	+	0.935567i	$0.385111\pi$
$572$	45.7426	1.91259
$573$	29.6753	1.23970
$574$	−8.95836	−0.373915
$575$	1.30380	0.0543722
$576$	−3.55479	−0.148116
$577$	3.84720	0.160161	0.0800805	−	0.996788i	$-0.474482\pi$
$577$	3.84720	0.160161	0.0800805	+	0.996788i	$0.474482\pi$
$578$	−12.9061	−0.536823
$579$	2.58687	0.107507
$580$	17.0148	0.706499
$581$	34.0129	1.41109
$582$	−65.3226	−2.70771
$583$	12.8929	0.533969
$584$	−93.9723	−3.88860
$585$	−7.38141	−0.305184
$586$	38.7916	1.60247
$587$	−38.1085	−1.57291	−0.786453	−	0.617650i	$-0.788085\pi$
$587$	−38.1085	−1.57291	−0.786453	+	0.617650i	$0.788085\pi$
$588$	37.9560	1.56528
$589$	18.3696	0.756907
$590$	−2.45080	−0.100898
$591$	8.24616	0.339202
$592$	44.5804	1.83224
$593$	12.2534	0.503187	0.251593	−	0.967833i	$-0.419045\pi$
$593$	12.2534	0.503187	0.251593	+	0.967833i	$0.419045\pi$
$594$	20.7820	0.852698
$595$	33.8883	1.38929
$596$	−7.76448	−0.318045
$597$	44.0425	1.80254
$598$	34.1359	1.39592
$599$	8.28350	0.338455	0.169227	−	0.985577i	$-0.445873\pi$
$599$	8.28350	0.338455	0.169227	+	0.985577i	$0.445873\pi$
$600$	7.52075	0.307033
$601$	−30.2162	−1.23254	−0.616272	−	0.787533i	$-0.711358\pi$
$601$	−30.2162	−1.23254	−0.616272	+	0.787533i	$0.711358\pi$
$602$	60.9148	2.48270
$603$	4.51696	0.183945
$604$	−21.5246	−0.875822
$605$	−18.6017	−0.756267
$606$	−26.5130	−1.07702
$607$	23.6558	0.960159	0.480079	−	0.877225i	$-0.340608\pi$
$607$	23.6558	0.960159	0.480079	+	0.877225i	$0.340608\pi$
$608$	55.7293	2.26012
$609$	−9.32308	−0.377790
$610$	−40.0447	−1.62136
$611$	−36.8337	−1.49013
$612$	11.9263	0.482093
$613$	−41.4375	−1.67365	−0.836823	−	0.547474i	$-0.815589\pi$
$613$	−41.4375	−1.67365	−0.836823	+	0.547474i	$0.815589\pi$
$614$	54.9630	2.21813
$615$	−3.24206	−0.130733
$616$	36.1380	1.45604
$617$	11.7774	0.474142	0.237071	−	0.971492i	$-0.423813\pi$
$617$	11.7774	0.474142	0.237071	+	0.971492i	$0.423813\pi$
$618$	−75.9093	−3.05352
$619$	−15.3147	−0.615549	−0.307774	−	0.951459i	$-0.599584\pi$
$619$	−15.3147	−0.615549	−0.307774	+	0.951459i	$0.599584\pi$
$620$	−31.8013	−1.27717
$621$	10.9333	0.438737
$622$	−67.6293	−2.71169
$623$	−53.8508	−2.15749
$624$	97.0043	3.88328
$625$	−21.2535	−0.850141
$626$	−17.3756	−0.694467
$627$	−12.9916	−0.518834
$628$	74.1390	2.95847
$629$	−22.5089	−0.897488
$630$	−10.0284	−0.399542
$631$	11.6604	0.464192	0.232096	−	0.972693i	$-0.425442\pi$
$631$	11.6604	0.464192	0.232096	+	0.972693i	$0.425442\pi$
$632$	64.9873	2.58506
$633$	−22.4795	−0.893481
$634$	0.0706046	0.00280407
$635$	−5.08604	−0.201833
$636$	67.2842	2.66799
$637$	33.6448	1.33306
$638$	−6.40188	−0.253453
$639$	−8.51320	−0.336777
$640$	4.17953	0.165210
$641$	−29.8459	−1.17884	−0.589421	−	0.807826i	$-0.700644\pi$
$641$	−29.8459	−1.17884	−0.589421	+	0.807826i	$0.700644\pi$
$642$	11.4305	0.451126
$643$	25.0348	0.987277	0.493639	−	0.869667i	$-0.335667\pi$
$643$	25.0348	0.987277	0.493639	+	0.869667i	$0.335667\pi$
$644$	32.6946	1.28835
$645$	22.0453	0.868033
$646$	−70.1480	−2.75994
$647$	−7.21188	−0.283528	−0.141764	−	0.989900i	$-0.545277\pi$
$647$	−7.21188	−0.283528	−0.141764	+	0.989900i	$0.545277\pi$
$648$	51.5063	2.02336
$649$	0.650069	0.0255174
$650$	11.4644	0.449669
$651$	17.4253	0.682950
$652$	85.1439	3.33449
$653$	−42.9983	−1.68266	−0.841328	−	0.540525i	$-0.818225\pi$
$653$	−42.9983	−1.68266	−0.841328	+	0.540525i	$0.818225\pi$
$654$	−82.3109	−3.21861
$655$	28.6351	1.11887
$656$	−9.19639	−0.359059
$657$	−6.91706	−0.269860
$658$	−50.0425	−1.95086
$659$	−42.8700	−1.66998	−0.834989	−	0.550267i	$-0.814526\pi$
$659$	−42.8700	−1.66998	−0.834989	+	0.550267i	$0.814526\pi$
$660$	22.4909	0.875458
$661$	44.1236	1.71621	0.858104	−	0.513477i	$-0.171643\pi$
$661$	44.1236	1.71621	0.858104	+	0.513477i	$0.171643\pi$
$662$	72.3586	2.81230
$663$	−48.9780	−1.90215
$664$	70.8767	2.75055
$665$	41.5826	1.61250
$666$	6.66096	0.258107
$667$	−3.36798	−0.130409
$668$	−12.1580	−0.470407
$669$	20.7581	0.802554
$670$	45.9938	1.77690
$671$	10.6218	0.410049
$672$	52.8643	2.03928
$673$	41.2621	1.59054	0.795268	−	0.606258i	$-0.207330\pi$
$673$	41.2621	1.59054	0.795268	+	0.606258i	$0.207330\pi$
$674$	56.2680	2.16736
$675$	3.67188	0.141331
$676$	149.476	5.74909
$677$	−30.6135	−1.17657	−0.588286	−	0.808653i	$-0.700197\pi$
$677$	−30.6135	−1.17657	−0.588286	+	0.808653i	$0.700197\pi$
$678$	−19.7974	−0.760315
$679$	−55.4582	−2.12829
$680$	70.6171	2.70804
$681$	34.3030	1.31449
$682$	11.9654	0.458179
$683$	−19.9633	−0.763875	−0.381938	−	0.924188i	$-0.624743\pi$
$683$	−19.9633	−0.763875	−0.381938	+	0.924188i	$0.624743\pi$
$684$	14.6342	0.559552
$685$	−12.2314	−0.467337
$686$	−17.5726	−0.670927
$687$	34.2465	1.30658
$688$	62.5334	2.38406
$689$	59.6418	2.27217
$690$	16.7841	0.638960
$691$	45.7835	1.74169	0.870843	−	0.491561i	$-0.163574\pi$
$691$	45.7835	1.74169	0.870843	+	0.491561i	$0.163574\pi$
$692$	−65.4956	−2.48977
$693$	2.66002	0.101046
$694$	45.0753	1.71103
$695$	−28.3002	−1.07349
$696$	−19.4276	−0.736402
$697$	4.64330	0.175878
$698$	−8.75896	−0.331531
$699$	−19.3664	−0.732504
$700$	10.9803	0.415016
$701$	26.1483	0.987609	0.493805	−	0.869573i	$-0.335606\pi$
$701$	26.1483	0.987609	0.493805	+	0.869573i	$0.335606\pi$
$702$	96.1367	3.62844
$703$	−27.6195	−1.04169
$704$	9.60108	0.361854
$705$	−18.1105	−0.682083
$706$	−68.9194	−2.59382
$707$	−22.5093	−0.846549
$708$	3.39252	0.127499
$709$	20.6445	0.775322	0.387661	−	0.921802i	$-0.373283\pi$
$709$	20.6445	0.775322	0.387661	+	0.921802i	$0.373283\pi$
$710$	−86.6855	−3.25325
$711$	4.78355	0.179397
$712$	−112.215	−4.20545
$713$	6.29490	0.235746
$714$	−66.5418	−2.49026
$715$	19.9363	0.745577
$716$	−66.4054	−2.48168
$717$	−38.6712	−1.44420
$718$	10.8666	0.405536
$719$	−42.6127	−1.58918	−0.794592	−	0.607144i	$-0.792315\pi$
$719$	−42.6127	−1.58918	−0.794592	+	0.607144i	$0.792315\pi$
$720$	−10.2949	−0.383668
$721$	−64.4462	−2.40010
$722$	−36.6057	−1.36232
$723$	−19.6361	−0.730275
$724$	47.3573	1.76002
$725$	−1.13112	−0.0420086
$726$	36.5256	1.35559
$727$	−20.4649	−0.759001	−0.379501	−	0.925191i	$-0.623904\pi$
$727$	−20.4649	−0.759001	−0.379501	+	0.925191i	$0.623904\pi$
$728$	167.172	6.19582
$729$	29.9403	1.10890
$730$	−70.4328	−2.60684
$731$	−31.5734	−1.16779
$732$	55.4319	2.04882
$733$	−8.29814	−0.306499	−0.153249	−	0.988188i	$-0.548974\pi$
$733$	−8.29814	−0.306499	−0.153249	+	0.988188i	$0.548974\pi$
$734$	29.9744	1.10638
$735$	16.5426	0.610185
$736$	19.0973	0.703936
$737$	−12.1998	−0.449385
$738$	−1.37407	−0.0505803
$739$	9.76996	0.359394	0.179697	−	0.983722i	$-0.442488\pi$
$739$	9.76996	0.359394	0.179697	+	0.983722i	$0.442488\pi$
$740$	47.8146	1.75770
$741$	−60.0983	−2.20777
$742$	81.0297	2.97470
$743$	−10.3070	−0.378128	−0.189064	−	0.981965i	$-0.560545\pi$
$743$	−10.3070	−0.378128	−0.189064	+	0.981965i	$0.560545\pi$
$744$	36.3111	1.33123
$745$	−3.38405	−0.123982
$746$	−27.2697	−0.998413
$747$	5.21705	0.190882
$748$	−32.2116	−1.17777
$749$	9.70438	0.354590
$750$	48.2292	1.76108
$751$	−21.4383	−0.782295	−0.391147	−	0.920328i	$-0.627922\pi$
$751$	−21.4383	−0.782295	−0.391147	+	0.920328i	$0.627922\pi$
$752$	−51.3721	−1.87335
$753$	18.4310	0.671665
$754$	−29.6148	−1.07851
$755$	−9.38121	−0.341417
$756$	92.0774	3.34882
$757$	−5.52797	−0.200918	−0.100459	−	0.994941i	$-0.532031\pi$
$757$	−5.52797	−0.200918	−0.100459	+	0.994941i	$0.532031\pi$
$758$	50.4923	1.83396
$759$	−4.45195	−0.161596
$760$	86.6506	3.14315
$761$	−22.5718	−0.818225	−0.409113	−	0.912484i	$-0.634162\pi$
$761$	−22.5718	−0.818225	−0.409113	+	0.912484i	$0.634162\pi$
$762$	9.98674	0.361782
$763$	−69.8811	−2.52986
$764$	90.2833	3.26634
$765$	5.19794	0.187932
$766$	−80.5270	−2.90956
$767$	3.00718	0.108583
$768$	−29.1758	−1.05279
$769$	14.9845	0.540355	0.270177	−	0.962811i	$-0.412918\pi$
$769$	14.9845	0.540355	0.270177	+	0.962811i	$0.412918\pi$
$770$	27.0856	0.976098
$771$	19.0931	0.687621
$772$	7.87023	0.283256
$773$	40.0686	1.44117	0.720583	−	0.693368i	$-0.243874\pi$
$773$	40.0686	1.44117	0.720583	+	0.693368i	$0.243874\pi$
$774$	9.34339	0.335841
$775$	2.11411	0.0759410
$776$	−115.565	−4.14854
$777$	−26.1996	−0.939905
$778$	37.5496	1.34622
$779$	5.69756	0.204136
$780$	104.042	3.72529
$781$	22.9932	0.822760
$782$	−24.0383	−0.859609
$783$	−9.48520	−0.338973
$784$	46.9247	1.67588
$785$	32.3126	1.15329
$786$	−56.2268	−2.00554
$787$	31.7995	1.13353	0.566764	−	0.823880i	$-0.308195\pi$
$787$	31.7995	1.13353	0.566764	+	0.823880i	$0.308195\pi$
$788$	25.0879	0.893720
$789$	25.8073	0.918766
$790$	48.7084	1.73297
$791$	−16.8078	−0.597617
$792$	5.54300	0.196962
$793$	49.1358	1.74486
$794$	−50.5613	−1.79435
$795$	29.3250	1.04005
$796$	133.994	4.74928
$797$	9.01735	0.319411	0.159705	−	0.987165i	$-0.448946\pi$
$797$	9.01735	0.319411	0.159705	+	0.987165i	$0.448946\pi$
$798$	−81.6500	−2.89038
$799$	25.9381	0.917622
$800$	6.41372	0.226759
$801$	−8.25988	−0.291849
$802$	44.3368	1.56559
$803$	18.6822	0.659279
$804$	−63.6670	−2.24536
$805$	14.2495	0.502230
$806$	55.3513	1.94967
$807$	−41.3724	−1.45638
$808$	−46.9053	−1.65012
$809$	0.473930	0.0166625	0.00833124	−	0.999965i	$-0.497348\pi$
$809$	0.473930	0.0166625	0.00833124	+	0.999965i	$0.497348\pi$
$810$	38.6043	1.35642
$811$	−42.6612	−1.49804	−0.749019	−	0.662548i	$-0.769475\pi$
$811$	−42.6612	−1.49804	−0.749019	+	0.662548i	$0.769475\pi$
$812$	−28.3643	−0.995392
$813$	14.3421	0.503000
$814$	−17.9905	−0.630566
$815$	37.1089	1.29987
$816$	−68.3099	−2.39132
$817$	−38.7421	−1.35542
$818$	−28.6474	−1.00163
$819$	12.3051	0.429976
$820$	−9.86357	−0.344451
$821$	−11.4421	−0.399330	−0.199665	−	0.979864i	$-0.563985\pi$
$821$	−11.4421	−0.399330	−0.199665	+	0.979864i	$0.563985\pi$
$822$	24.0170	0.837690
$823$	45.4806	1.58535	0.792676	−	0.609643i	$-0.208687\pi$
$823$	45.4806	1.58535	0.792676	+	0.609643i	$0.208687\pi$
$824$	−134.294	−4.67836
$825$	−1.49516	−0.0520549
$826$	4.08558	0.142155
$827$	27.7089	0.963533	0.481766	−	0.876300i	$-0.339995\pi$
$827$	27.7089	0.963533	0.481766	+	0.876300i	$0.339995\pi$
$828$	5.01484	0.174278
$829$	−4.75809	−0.165255	−0.0826277	−	0.996580i	$-0.526331\pi$
$829$	−4.75809	−0.165255	−0.0826277	+	0.996580i	$0.526331\pi$
$830$	53.1225	1.84391
$831$	34.4320	1.19443
$832$	44.4141	1.53978
$833$	−23.6925	−0.820896
$834$	55.5692	1.92420
$835$	−5.29891	−0.183376
$836$	−39.5253	−1.36701
$837$	17.7283	0.612778
$838$	59.8855	2.06871
$839$	7.74081	0.267242	0.133621	−	0.991032i	$-0.457339\pi$
$839$	7.74081	0.267242	0.133621	+	0.991032i	$0.457339\pi$
$840$	82.1960	2.83603
$841$	−26.0781	−0.899245
$842$	−7.82604	−0.269703
$843$	−10.7982	−0.371911
$844$	−68.3912	−2.35412
$845$	65.1474	2.24114
$846$	−7.67574	−0.263897
$847$	31.0098	1.06551
$848$	83.1828	2.85651
$849$	−39.1696	−1.34430
$850$	−8.07313	−0.276906
$851$	−9.46464	−0.324444
$852$	119.995	4.11095
$853$	−0.676715	−0.0231703	−0.0115851	−	0.999933i	$-0.503688\pi$
$853$	−0.676715	−0.0231703	−0.0115851	+	0.999933i	$0.503688\pi$
$854$	66.7561	2.28435
$855$	6.37813	0.218127
$856$	20.2222	0.691179
$857$	9.59860	0.327882	0.163941	−	0.986470i	$-0.447579\pi$
$857$	9.59860	0.327882	0.163941	+	0.986470i	$0.447579\pi$
$858$	−39.1462	−1.33643
$859$	2.29224	0.0782103	0.0391051	−	0.999235i	$-0.487549\pi$
$859$	2.29224	0.0782103	0.0391051	+	0.999235i	$0.487549\pi$
$860$	67.0701	2.28707
$861$	5.40465	0.184190
$862$	58.6519	1.99769
$863$	18.6596	0.635181	0.317591	−	0.948228i	$-0.397126\pi$
$863$	18.6596	0.635181	0.317591	+	0.948228i	$0.397126\pi$
$864$	53.7836	1.82975
$865$	−28.5455	−0.970575
$866$	−49.6242	−1.68630
$867$	7.78637	0.264439
$868$	53.0142	1.79942
$869$	−12.9198	−0.438275
$870$	−14.5611	−0.493668
$871$	−56.4356	−1.91225
$872$	−145.620	−4.93130
$873$	−8.50643	−0.287899
$874$	−29.4962	−0.997723
$875$	40.9461	1.38423
$876$	97.4967	3.29411
$877$	28.7736	0.971616	0.485808	−	0.874065i	$-0.338525\pi$
$877$	28.7736	0.971616	0.485808	+	0.874065i	$0.338525\pi$
$878$	−67.0637	−2.26329
$879$	−23.4033	−0.789373
$880$	27.8053	0.937317
$881$	3.68459	0.124137	0.0620684	−	0.998072i	$-0.480230\pi$
$881$	3.68459	0.124137	0.0620684	+	0.998072i	$0.480230\pi$
$882$	7.01122	0.236080
$883$	25.5615	0.860214	0.430107	−	0.902778i	$-0.358476\pi$
$883$	25.5615	0.860214	0.430107	+	0.902778i	$0.358476\pi$
$884$	−149.009	−5.01173
$885$	1.47859	0.0497021
$886$	67.1064	2.25448
$887$	−29.4590	−0.989137	−0.494569	−	0.869139i	$-0.664674\pi$
$887$	−29.4590	−0.989137	−0.494569	+	0.869139i	$0.664674\pi$
$888$	−54.5952	−1.83210
$889$	8.47864	0.284364
$890$	−84.1062	−2.81924
$891$	−10.2397	−0.343043
$892$	63.1539	2.11455
$893$	31.8272	1.06506
$894$	6.64479	0.222235
$895$	−28.9419	−0.967422
$896$	−6.96745	−0.232766
$897$	−20.5945	−0.687631
$898$	70.4720	2.35168
$899$	−5.46116	−0.182140
$900$	1.68421	0.0561402
$901$	−41.9994	−1.39920
$902$	3.71121	0.123570
$903$	−36.7504	−1.22298
$904$	−35.0244	−1.16489
$905$	20.6401	0.686100
$906$	18.4206	0.611983
$907$	11.0806	0.367927	0.183963	−	0.982933i	$-0.441107\pi$
$907$	11.0806	0.367927	0.183963	+	0.982933i	$0.441107\pi$
$908$	104.363	3.46340
$909$	−3.45257	−0.114515
$910$	125.297	4.15354
$911$	−36.8232	−1.22001	−0.610004	−	0.792398i	$-0.708832\pi$
$911$	−36.8232	−1.22001	−0.610004	+	0.792398i	$0.708832\pi$
$912$	−83.8195	−2.77554
$913$	−14.0906	−0.466332
$914$	35.7071	1.18109
$915$	24.1593	0.798681
$916$	104.191	3.44256
$917$	−47.7359	−1.57638
$918$	−67.6989	−2.23440
$919$	−22.9609	−0.757409	−0.378705	−	0.925518i	$-0.623630\pi$
$919$	−22.9609	−0.757409	−0.378705	+	0.925518i	$0.623630\pi$
$920$	29.6934	0.978964
$921$	−33.1597	−1.09265
$922$	57.4474	1.89193
$923$	106.365	3.50105
$924$	−37.4933	−1.23344
$925$	−3.17865	−0.104513
$926$	−61.8460	−2.03239
$927$	−9.88505	−0.324668
$928$	−16.5679	−0.543869
$929$	31.4008	1.03023	0.515114	−	0.857122i	$-0.327750\pi$
$929$	31.4008	1.03023	0.515114	+	0.857122i	$0.327750\pi$
$930$	27.2154	0.892427
$931$	−29.0718	−0.952791
$932$	−58.9198	−1.92998
$933$	40.8014	1.33578
$934$	23.5016	0.768995
$935$	−14.0390	−0.459126
$936$	25.6416	0.838123
$937$	0.667433	0.0218041	0.0109020	−	0.999941i	$-0.496530\pi$
$937$	0.667433	0.0218041	0.0109020	+	0.999941i	$0.496530\pi$
$938$	−76.6737	−2.50348
$939$	10.4828	0.342094
$940$	−55.0991	−1.79713
$941$	−7.87898	−0.256847	−0.128424	−	0.991719i	$-0.540992\pi$
$941$	−7.87898	−0.256847	−0.128424	+	0.991719i	$0.540992\pi$
$942$	−63.4477	−2.06724
$943$	1.95244	0.0635802
$944$	4.19414	0.136508
$945$	40.1308	1.30545
$946$	−25.2354	−0.820474
$947$	−38.5602	−1.25304	−0.626520	−	0.779406i	$-0.715521\pi$
$947$	−38.5602	−1.25304	−0.626520	+	0.779406i	$0.715521\pi$
$948$	−67.4246	−2.18985
$949$	86.4228	2.80540
$950$	−9.90613	−0.321397
$951$	−0.0425964	−0.00138128
$952$	−117.722	−3.81538
$953$	−33.3266	−1.07955	−0.539777	−	0.841808i	$-0.681491\pi$
$953$	−33.3266	−1.07955	−0.539777	+	0.841808i	$0.681491\pi$
$954$	12.4287	0.402394
$955$	39.3488	1.27330
$956$	−117.652	−3.80515
$957$	3.86231	0.124851
$958$	−66.6875	−2.15457
$959$	20.3902	0.658434
$960$	21.8377	0.704809
$961$	−20.7928	−0.670737
$962$	−83.2230	−2.68322
$963$	1.48850	0.0479663
$964$	−59.7404	−1.92411
$965$	3.43014	0.110420
$966$	−27.9798	−0.900236
$967$	60.0969	1.93259	0.966293	−	0.257445i	$-0.0828806\pi$
$967$	60.0969	1.93259	0.966293	+	0.257445i	$0.0828806\pi$
$968$	64.6189	2.07693
$969$	42.3209	1.35954
$970$	−86.6166	−2.78109
$971$	−9.19011	−0.294925	−0.147462	−	0.989068i	$-0.547111\pi$
$971$	−9.19011	−0.294925	−0.147462	+	0.989068i	$0.547111\pi$
$972$	26.1172	0.837711
$973$	47.1777	1.51245
$974$	−14.8272	−0.475095
$975$	−6.91655	−0.221507
$976$	68.5299	2.19359
$977$	−30.6352	−0.980106	−0.490053	−	0.871693i	$-0.663023\pi$
$977$	−30.6352	−0.980106	−0.490053	+	0.871693i	$0.663023\pi$
$978$	−72.8656	−2.32998
$979$	22.3090	0.712999
$980$	50.3289	1.60770
$981$	−10.7187	−0.342221
$982$	−67.6265	−2.15805
$983$	40.5709	1.29401	0.647005	−	0.762486i	$-0.276021\pi$
$983$	40.5709	1.29401	0.647005	+	0.762486i	$0.276021\pi$
$984$	11.2623	0.359030
$985$	10.9343	0.348394
$986$	20.8545	0.664143
$987$	30.1910	0.960992
$988$	−182.842	−5.81697
$989$	−13.2762	−0.422157
$990$	4.15451	0.132039
$991$	56.6501	1.79955	0.899775	−	0.436354i	$-0.143731\pi$
$991$	56.6501	1.79955	0.899775	+	0.436354i	$0.143731\pi$
$992$	30.9662	0.983179
$993$	−43.6546	−1.38534
$994$	144.508	4.58353
$995$	58.3995	1.85139
$996$	−73.5349	−2.33004
$997$	−37.6838	−1.19346	−0.596728	−	0.802443i	$-0.703533\pi$
$997$	−37.6838	−1.19346	−0.596728	+	0.802443i	$0.703533\pi$
$998$	−28.8526	−0.913313
$999$	−26.6552	−0.843332

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.b.1.12	✓	287

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.b.1.12	✓	287	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:	\( N \)	\(=\)	\( 6047 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60365 q^{2} +1.57080 q^{3} +4.77897 q^{4} +2.08285 q^{5} -4.08981 q^{6} -3.47220 q^{7} -7.23545 q^{8} -0.532582 q^{9} +O(q^{10})\)	\(q-2.60365 q^{2} +1.57080 q^{3} +4.77897 q^{4} +2.08285 q^{5} -4.08981 q^{6} -3.47220 q^{7} -7.23545 q^{8} -0.532582 q^{9} -5.42301 q^{10} +1.43844 q^{11} +7.50681 q^{12} +6.65417 q^{13} +9.04039 q^{14} +3.27175 q^{15} +9.28060 q^{16} -4.68582 q^{17} +1.38666 q^{18} -5.74973 q^{19} +9.95389 q^{20} -5.45415 q^{21} -3.74520 q^{22} -1.97032 q^{23} -11.3655 q^{24} -0.661720 q^{25} -17.3251 q^{26} -5.54899 q^{27} -16.5936 q^{28} +1.70936 q^{29} -8.51848 q^{30} -3.19486 q^{31} -9.69250 q^{32} +2.25951 q^{33} +12.2002 q^{34} -7.23210 q^{35} -2.54519 q^{36} +4.80361 q^{37} +14.9703 q^{38} +10.4524 q^{39} -15.0704 q^{40} -0.990926 q^{41} +14.2007 q^{42} +6.73807 q^{43} +6.87428 q^{44} -1.10929 q^{45} +5.13001 q^{46} -5.53543 q^{47} +14.5780 q^{48} +5.05621 q^{49} +1.72288 q^{50} -7.36050 q^{51} +31.8001 q^{52} +8.96308 q^{53} +14.4476 q^{54} +2.99607 q^{55} +25.1230 q^{56} -9.03169 q^{57} -4.45056 q^{58} +0.451925 q^{59} +15.6356 q^{60} +7.38421 q^{61} +8.31829 q^{62} +1.84924 q^{63} +6.67463 q^{64} +13.8597 q^{65} -5.88296 q^{66} -8.48124 q^{67} -22.3934 q^{68} -3.09498 q^{69} +18.8298 q^{70} +15.9848 q^{71} +3.85347 q^{72} +12.9878 q^{73} -12.5069 q^{74} -1.03943 q^{75} -27.4778 q^{76} -4.99457 q^{77} -27.2143 q^{78} -8.98180 q^{79} +19.3301 q^{80} -7.11861 q^{81} +2.58002 q^{82} -9.79575 q^{83} -26.0652 q^{84} -9.75988 q^{85} -17.5436 q^{86} +2.68506 q^{87} -10.4078 q^{88} +15.5091 q^{89} +2.88820 q^{90} -23.1046 q^{91} -9.41609 q^{92} -5.01850 q^{93} +14.4123 q^{94} -11.9758 q^{95} -15.2250 q^{96} +15.9720 q^{97} -13.1646 q^{98} -0.766090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * q^99

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