LMFDB - Embedded newform 6013.2.a.e.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23377 q^{2} -0.900406 q^{3} +2.98971 q^{4} +4.46215 q^{5} +2.01130 q^{6} +1.00000 q^{7} -2.21077 q^{8} -2.18927 q^{9} +O(q^{10})$	\(q-2.23377 q^{2} -0.900406 q^{3} +2.98971 q^{4} +4.46215 q^{5} +2.01130 q^{6} +1.00000 q^{7} -2.21077 q^{8} -2.18927 q^{9} -9.96739 q^{10} -0.526347 q^{11} -2.69195 q^{12} -6.37545 q^{13} -2.23377 q^{14} -4.01775 q^{15} -1.04107 q^{16} +6.97364 q^{17} +4.89031 q^{18} +5.09549 q^{19} +13.3405 q^{20} -0.900406 q^{21} +1.17573 q^{22} -0.455611 q^{23} +1.99059 q^{24} +14.9108 q^{25} +14.2413 q^{26} +4.67245 q^{27} +2.98971 q^{28} -9.94990 q^{29} +8.97470 q^{30} +1.30521 q^{31} +6.74704 q^{32} +0.473926 q^{33} -15.5775 q^{34} +4.46215 q^{35} -6.54527 q^{36} +1.57662 q^{37} -11.3821 q^{38} +5.74050 q^{39} -9.86479 q^{40} +3.19420 q^{41} +2.01130 q^{42} -8.41675 q^{43} -1.57362 q^{44} -9.76884 q^{45} +1.01773 q^{46} -9.20136 q^{47} +0.937383 q^{48} +1.00000 q^{49} -33.3071 q^{50} -6.27911 q^{51} -19.0607 q^{52} +0.888546 q^{53} -10.4372 q^{54} -2.34864 q^{55} -2.21077 q^{56} -4.58801 q^{57} +22.2258 q^{58} +7.52327 q^{59} -12.0119 q^{60} +4.92384 q^{61} -2.91554 q^{62} -2.18927 q^{63} -12.9892 q^{64} -28.4482 q^{65} -1.05864 q^{66} +13.5970 q^{67} +20.8491 q^{68} +0.410235 q^{69} -9.96739 q^{70} -0.849215 q^{71} +4.83997 q^{72} -4.88653 q^{73} -3.52181 q^{74} -13.4257 q^{75} +15.2340 q^{76} -0.526347 q^{77} -12.8229 q^{78} +6.03715 q^{79} -4.64539 q^{80} +2.36070 q^{81} -7.13509 q^{82} -12.1878 q^{83} -2.69195 q^{84} +31.1174 q^{85} +18.8010 q^{86} +8.95896 q^{87} +1.16363 q^{88} +9.45755 q^{89} +21.8213 q^{90} -6.37545 q^{91} -1.36214 q^{92} -1.17522 q^{93} +20.5537 q^{94} +22.7368 q^{95} -6.07508 q^{96} +8.91376 q^{97} -2.23377 q^{98} +1.15231 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9}+O(q^{10}) $ 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9} + 15 q^{10} + 48 q^{11} + 72 q^{12} + 29 q^{13} + 19 q^{14} + 29 q^{15} + 115 q^{16} + 72 q^{17} + 33 q^{18} + 58 q^{19} + 88 q^{20} + 38 q^{21} + 4 q^{22} + 65 q^{23} + 46 q^{24} + 124 q^{25} + 49 q^{26} + 131 q^{27} + 111 q^{28} + 25 q^{29} + 2 q^{30} + 41 q^{31} + 75 q^{32} + 54 q^{33} + 23 q^{34} + 43 q^{35} + 111 q^{36} + 25 q^{37} + 54 q^{38} + 27 q^{39} + 30 q^{40} + 109 q^{41} + 14 q^{42} + 38 q^{43} + 68 q^{44} + 84 q^{45} - 9 q^{46} + 121 q^{47} + 106 q^{48} + 109 q^{49} + 14 q^{50} + 36 q^{51} + 38 q^{52} + 61 q^{53} + 31 q^{54} + 50 q^{55} + 48 q^{56} + 5 q^{57} - 20 q^{58} + 181 q^{59} + 25 q^{60} + 34 q^{61} + 75 q^{62} + 119 q^{63} + 96 q^{64} + 12 q^{65} + 19 q^{66} + 87 q^{67} + 150 q^{68} + 89 q^{69} + 15 q^{70} + 83 q^{71} + 65 q^{72} + 32 q^{73} - 19 q^{74} + 112 q^{75} + 84 q^{76} + 48 q^{77} - 34 q^{78} - 9 q^{79} + 137 q^{80} + 109 q^{81} - 19 q^{82} + 136 q^{83} + 72 q^{84} - 32 q^{85} - 24 q^{86} + 28 q^{87} - 24 q^{88} + 142 q^{89} + 19 q^{90} + 29 q^{91} + 96 q^{92} + 29 q^{93} + 9 q^{94} + 52 q^{95} + 88 q^{96} + 75 q^{97} + 19 q^{98} + 84 q^{99}+O(q^{100}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9 + 15 * q^10 + 48 * q^11 + 72 * q^12 + 29 * q^13 + 19 * q^14 + 29 * q^15 + 115 * q^16 + 72 * q^17 + 33 * q^18 + 58 * q^19 + 88 * q^20 + 38 * q^21 + 4 * q^22 + 65 * q^23 + 46 * q^24 + 124 * q^25 + 49 * q^26 + 131 * q^27 + 111 * q^28 + 25 * q^29 + 2 * q^30 + 41 * q^31 + 75 * q^32 + 54 * q^33 + 23 * q^34 + 43 * q^35 + 111 * q^36 + 25 * q^37 + 54 * q^38 + 27 * q^39 + 30 * q^40 + 109 * q^41 + 14 * q^42 + 38 * q^43 + 68 * q^44 + 84 * q^45 - 9 * q^46 + 121 * q^47 + 106 * q^48 + 109 * q^49 + 14 * q^50 + 36 * q^51 + 38 * q^52 + 61 * q^53 + 31 * q^54 + 50 * q^55 + 48 * q^56 + 5 * q^57 - 20 * q^58 + 181 * q^59 + 25 * q^60 + 34 * q^61 + 75 * q^62 + 119 * q^63 + 96 * q^64 + 12 * q^65 + 19 * q^66 + 87 * q^67 + 150 * q^68 + 89 * q^69 + 15 * q^70 + 83 * q^71 + 65 * q^72 + 32 * q^73 - 19 * q^74 + 112 * q^75 + 84 * q^76 + 48 * q^77 - 34 * q^78 - 9 * q^79 + 137 * q^80 + 109 * q^81 - 19 * q^82 + 136 * q^83 + 72 * q^84 - 32 * q^85 - 24 * q^86 + 28 * q^87 - 24 * q^88 + 142 * q^89 + 19 * q^90 + 29 * q^91 + 96 * q^92 + 29 * q^93 + 9 * q^94 + 52 * q^95 + 88 * q^96 + 75 * q^97 + 19 * q^98 + 84 * 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 $

$2$	−2.23377	−1.57951	−0.789755	−	0.613422i	$-0.789792\pi$
$2$	−2.23377	−1.57951	−0.789755	+	0.613422i	$0.789792\pi$
$3$	−0.900406	−0.519850	−0.259925	−	0.965629i	$-0.583698\pi$
$3$	−0.900406	−0.519850	−0.259925	+	0.965629i	$0.583698\pi$
$4$	2.98971	1.49485
$5$	4.46215	1.99553	0.997766	−	0.0667999i	$-0.0212789\pi$
$5$	4.46215	1.99553	0.997766	+	0.0667999i	$0.0212789\pi$
$6$	2.01130	0.821108
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.21077	−0.781626
$9$	−2.18927	−0.729756
$10$	−9.96739	−3.15196
$11$	−0.526347	−0.158699	−0.0793497	−	0.996847i	$-0.525284\pi$
$11$	−0.526347	−0.158699	−0.0793497	+	0.996847i	$0.525284\pi$
$12$	−2.69195	−0.777099
$13$	−6.37545	−1.76823	−0.884116	−	0.467267i	$-0.845239\pi$
$13$	−6.37545	−1.76823	−0.884116	+	0.467267i	$0.845239\pi$
$14$	−2.23377	−0.596999
$15$	−4.01775	−1.03738
$16$	−1.04107	−0.260267
$17$	6.97364	1.69136	0.845678	−	0.533693i	$-0.179196\pi$
$17$	6.97364	1.69136	0.845678	+	0.533693i	$0.179196\pi$
$18$	4.89031	1.15266
$19$	5.09549	1.16899	0.584493	−	0.811399i	$-0.301293\pi$
$19$	5.09549	1.16899	0.584493	+	0.811399i	$0.301293\pi$
$20$	13.3405	2.98303
$21$	−0.900406	−0.196485
$22$	1.17573	0.250668
$23$	−0.455611	−0.0950016	−0.0475008	−	0.998871i	$-0.515126\pi$
$23$	−0.455611	−0.0950016	−0.0475008	+	0.998871i	$0.515126\pi$
$24$	1.99059	0.406328
$25$	14.9108	2.98215
$26$	14.2413	2.79294
$27$	4.67245	0.899213
$28$	2.98971	0.565001
$29$	−9.94990	−1.84765	−0.923825	−	0.382814i	$-0.874955\pi$
$29$	−9.94990	−1.84765	−0.923825	+	0.382814i	$0.874955\pi$
$30$	8.97470	1.63855
$31$	1.30521	0.234423	0.117212	−	0.993107i	$-0.462604\pi$
$31$	1.30521	0.234423	0.117212	+	0.993107i	$0.462604\pi$
$32$	6.74704	1.19272
$33$	0.473926	0.0824999
$34$	−15.5775	−2.67151
$35$	4.46215	0.754240
$36$	−6.54527	−1.09088
$37$	1.57662	0.259195	0.129598	−	0.991567i	$-0.458631\pi$
$37$	1.57662	0.259195	0.129598	+	0.991567i	$0.458631\pi$
$38$	−11.3821	−1.84643
$39$	5.74050	0.919216
$40$	−9.86479	−1.55976
$41$	3.19420	0.498850	0.249425	−	0.968394i	$-0.419758\pi$
$41$	3.19420	0.498850	0.249425	+	0.968394i	$0.419758\pi$
$42$	2.01130	0.310350
$43$	−8.41675	−1.28354	−0.641771	−	0.766896i	$-0.721800\pi$
$43$	−8.41675	−1.28354	−0.641771	+	0.766896i	$0.721800\pi$
$44$	−1.57362	−0.237232
$45$	−9.76884	−1.45625
$46$	1.01773	0.150056
$47$	−9.20136	−1.34216	−0.671078	−	0.741387i	$-0.734168\pi$
$47$	−9.20136	−1.34216	−0.671078	+	0.741387i	$0.734168\pi$
$48$	0.937383	0.135300
$49$	1.00000	0.142857
$50$	−33.3071	−4.71034
$51$	−6.27911	−0.879251
$52$	−19.0607	−2.64325
$53$	0.888546	0.122051	0.0610256	−	0.998136i	$-0.480563\pi$
$53$	0.888546	0.122051	0.0610256	+	0.998136i	$0.480563\pi$
$54$	−10.4372	−1.42032
$55$	−2.34864	−0.316690
$56$	−2.21077	−0.295427
$57$	−4.58801	−0.607697
$58$	22.2258	2.91838
$59$	7.52327	0.979446	0.489723	−	0.871878i	$-0.337098\pi$
$59$	7.52327	0.979446	0.489723	+	0.871878i	$0.337098\pi$
$60$	−12.0119	−1.55073
$61$	4.92384	0.630433	0.315216	−	0.949020i	$-0.397923\pi$
$61$	4.92384	0.630433	0.315216	+	0.949020i	$0.397923\pi$
$62$	−2.91554	−0.370274
$63$	−2.18927	−0.275822
$64$	−12.9892	−1.62365
$65$	−28.4482	−3.52857
$66$	−1.05864	−0.130309
$67$	13.5970	1.66114	0.830569	−	0.556916i	$-0.188015\pi$
$67$	13.5970	1.66114	0.830569	+	0.556916i	$0.188015\pi$
$68$	20.8491	2.52833
$69$	0.410235	0.0493865
$70$	−9.96739	−1.19133
$71$	−0.849215	−0.100783	−0.0503917	−	0.998730i	$-0.516047\pi$
$71$	−0.849215	−0.100783	−0.0503917	+	0.998730i	$0.516047\pi$
$72$	4.83997	0.570396
$73$	−4.88653	−0.571925	−0.285963	−	0.958241i	$-0.592313\pi$
$73$	−4.88653	−0.571925	−0.285963	+	0.958241i	$0.592313\pi$
$74$	−3.52181	−0.409402
$75$	−13.4257	−1.55027
$76$	15.2340	1.74746
$77$	−0.526347	−0.0599828
$78$	−12.8229	−1.45191
$79$	6.03715	0.679232	0.339616	−	0.940564i	$-0.389703\pi$
$79$	6.03715	0.679232	0.339616	+	0.940564i	$0.389703\pi$
$80$	−4.64539	−0.519371
$81$	2.36070	0.262300
$82$	−7.13509	−0.787939
$83$	−12.1878	−1.33778	−0.668890	−	0.743362i	$-0.733230\pi$
$83$	−12.1878	−1.33778	−0.668890	+	0.743362i	$0.733230\pi$
$84$	−2.69195	−0.293716
$85$	31.1174	3.37516
$86$	18.8010	2.02737
$87$	8.95896	0.960501
$88$	1.16363	0.124044
$89$	9.45755	1.00250	0.501249	−	0.865303i	$-0.332874\pi$
$89$	9.45755	1.00250	0.501249	+	0.865303i	$0.332874\pi$
$90$	21.8213	2.30017
$91$	−6.37545	−0.668329
$92$	−1.36214	−0.142013
$93$	−1.17522	−0.121865
$94$	20.5537	2.11995
$95$	22.7368	2.33275
$96$	−6.07508	−0.620035
$97$	8.91376	0.905055	0.452527	−	0.891750i	$-0.350522\pi$
$97$	8.91376	0.905055	0.452527	+	0.891750i	$0.350522\pi$
$98$	−2.23377	−0.225644
$99$	1.15231	0.115812
$100$	44.5788	4.45788
$101$	−9.63298	−0.958517	−0.479259	−	0.877674i	$-0.659094\pi$
$101$	−9.63298	−0.958517	−0.479259	+	0.877674i	$0.659094\pi$
$102$	14.0261	1.38879
$103$	16.1299	1.58932	0.794661	−	0.607053i	$-0.207649\pi$
$103$	16.1299	1.58932	0.794661	+	0.607053i	$0.207649\pi$
$104$	14.0947	1.38210
$105$	−4.01775	−0.392092
$106$	−1.98480	−0.192781
$107$	−1.76141	−0.170282	−0.0851410	−	0.996369i	$-0.527134\pi$
$107$	−1.76141	−0.170282	−0.0851410	+	0.996369i	$0.527134\pi$
$108$	13.9693	1.34419
$109$	2.29729	0.220040	0.110020	−	0.993929i	$-0.464908\pi$
$109$	2.29729	0.220040	0.110020	+	0.993929i	$0.464908\pi$
$110$	5.24630	0.500215
$111$	−1.41960	−0.134743
$112$	−1.04107	−0.0983716
$113$	13.1293	1.23510	0.617551	−	0.786531i	$-0.288125\pi$
$113$	13.1293	1.23510	0.617551	+	0.786531i	$0.288125\pi$
$114$	10.2485	0.959864
$115$	−2.03301	−0.189579
$116$	−29.7473	−2.76197
$117$	13.9576	1.29038
$118$	−16.8052	−1.54705
$119$	6.97364	0.639272
$120$	8.88232	0.810841
$121$	−10.7230	−0.974814
$122$	−10.9987	−0.995775
$123$	−2.87608	−0.259327
$124$	3.90221	0.350428
$125$	44.2232	3.95545
$126$	4.89031	0.435664
$127$	10.4781	0.929777	0.464888	−	0.885369i	$-0.346094\pi$
$127$	10.4781	0.929777	0.464888	+	0.885369i	$0.346094\pi$
$128$	15.5207	1.37185
$129$	7.57849	0.667249
$130$	63.5466	5.57341
$131$	−10.0724	−0.880029	−0.440015	−	0.897991i	$-0.645027\pi$
$131$	−10.0724	−0.880029	−0.440015	+	0.897991i	$0.645027\pi$
$132$	1.41690	0.123325
$133$	5.09549	0.441835
$134$	−30.3725	−2.62378
$135$	20.8492	1.79441
$136$	−15.4171	−1.32201
$137$	−18.5714	−1.58667	−0.793333	−	0.608788i	$-0.791656\pi$
$137$	−18.5714	−1.58667	−0.793333	+	0.608788i	$0.791656\pi$
$138$	−0.916370	−0.0780066
$139$	3.15554	0.267649	0.133825	−	0.991005i	$-0.457274\pi$
$139$	3.15554	0.267649	0.133825	+	0.991005i	$0.457274\pi$
$140$	13.3405	1.12748
$141$	8.28496	0.697719
$142$	1.89695	0.159188
$143$	3.35570	0.280618
$144$	2.27918	0.189931
$145$	−44.3979	−3.68705
$146$	10.9154	0.903362
$147$	−0.900406	−0.0742643
$148$	4.71364	0.387459
$149$	15.7270	1.28840	0.644202	−	0.764855i	$-0.277190\pi$
$149$	15.7270	1.28840	0.644202	+	0.764855i	$0.277190\pi$
$150$	29.9899	2.44867
$151$	−13.6738	−1.11276	−0.556379	−	0.830929i	$-0.687810\pi$
$151$	−13.6738	−1.11276	−0.556379	+	0.830929i	$0.687810\pi$
$152$	−11.2650	−0.913710
$153$	−15.2672	−1.23428
$154$	1.17573	0.0947434
$155$	5.82405	0.467799
$156$	17.1624	1.37409
$157$	−7.00587	−0.559129	−0.279565	−	0.960127i	$-0.590190\pi$
$157$	−7.00587	−0.559129	−0.279565	+	0.960127i	$0.590190\pi$
$158$	−13.4856	−1.07285
$159$	−0.800052	−0.0634483
$160$	30.1063	2.38011
$161$	−0.455611	−0.0359072
$162$	−5.27325	−0.414306
$163$	−8.16891	−0.639838	−0.319919	−	0.947445i	$-0.603656\pi$
$163$	−8.16891	−0.639838	−0.319919	+	0.947445i	$0.603656\pi$
$164$	9.54972	0.745708
$165$	2.11473	0.164631
$166$	27.2246	2.11304
$167$	21.0185	1.62646	0.813230	−	0.581942i	$-0.197707\pi$
$167$	21.0185	1.62646	0.813230	+	0.581942i	$0.197707\pi$
$168$	1.99059	0.153578
$169$	27.6464	2.12665
$170$	−69.5090	−5.33109
$171$	−11.1554	−0.853075
$172$	−25.1636	−1.91871
$173$	3.92999	0.298792	0.149396	−	0.988777i	$-0.452267\pi$
$173$	3.92999	0.298792	0.149396	+	0.988777i	$0.452267\pi$
$174$	−20.0122	−1.51712
$175$	14.9108	1.12715
$176$	0.547962	0.0413042
$177$	−6.77400	−0.509165
$178$	−21.1260	−1.58346
$179$	16.3309	1.22063	0.610313	−	0.792160i	$-0.291044\pi$
$179$	16.3309	1.22063	0.610313	+	0.792160i	$0.291044\pi$
$180$	−29.2060	−2.17688
$181$	−18.4709	−1.37293	−0.686464	−	0.727164i	$-0.740838\pi$
$181$	−18.4709	−1.37293	−0.686464	+	0.727164i	$0.740838\pi$
$182$	14.2413	1.05563
$183$	−4.43345	−0.327730
$184$	1.00725	0.0742557
$185$	7.03512	0.517233
$186$	2.62517	0.192487
$187$	−3.67055	−0.268417
$188$	−27.5094	−2.00633
$189$	4.67245	0.339871
$190$	−50.7888	−3.68460
$191$	9.46168	0.684623	0.342312	−	0.939587i	$-0.388790\pi$
$191$	9.46168	0.684623	0.342312	+	0.939587i	$0.388790\pi$
$192$	11.6955	0.844053
$193$	12.7772	0.919727	0.459863	−	0.887990i	$-0.347898\pi$
$193$	12.7772	0.919727	0.459863	+	0.887990i	$0.347898\pi$
$194$	−19.9112	−1.42954
$195$	25.6150	1.83432
$196$	2.98971	0.213550
$197$	8.71604	0.620992	0.310496	−	0.950575i	$-0.399505\pi$
$197$	8.71604	0.620992	0.310496	+	0.950575i	$0.399505\pi$
$198$	−2.57400	−0.182926
$199$	6.26668	0.444233	0.222117	−	0.975020i	$-0.428703\pi$
$199$	6.26668	0.444233	0.222117	+	0.975020i	$0.428703\pi$
$200$	−32.9643	−2.33093
$201$	−12.2428	−0.863542
$202$	21.5178	1.51399
$203$	−9.94990	−0.698346
$204$	−18.7727	−1.31435
$205$	14.2530	0.995472
$206$	−36.0303	−2.51035
$207$	0.997456	0.0693280
$208$	6.63728	0.460212
$209$	−2.68200	−0.185518
$210$	8.97470	0.619313
$211$	14.3154	0.985510	0.492755	−	0.870168i	$-0.335990\pi$
$211$	14.3154	0.985510	0.492755	+	0.870168i	$0.335990\pi$
$212$	2.65649	0.182449
$213$	0.764639	0.0523922
$214$	3.93458	0.268962
$215$	−37.5568	−2.56135
$216$	−10.3297	−0.702849
$217$	1.30521	0.0886037
$218$	−5.13160	−0.347556
$219$	4.39987	0.297315
$220$	−7.02173	−0.473405
$221$	−44.4601	−2.99071
$222$	3.17106	0.212827
$223$	−12.0828	−0.809126	−0.404563	−	0.914510i	$-0.632576\pi$
$223$	−12.0828	−0.809126	−0.404563	+	0.914510i	$0.632576\pi$
$224$	6.74704	0.450806
$225$	−32.6436	−2.17624
$226$	−29.3278	−1.95086
$227$	29.3129	1.94557	0.972784	−	0.231714i	$-0.0744335\pi$
$227$	29.3129	1.94557	0.972784	+	0.231714i	$0.0744335\pi$
$228$	−13.7168	−0.908418
$229$	20.2013	1.33494	0.667468	−	0.744638i	$-0.267378\pi$
$229$	20.2013	1.33494	0.667468	+	0.744638i	$0.267378\pi$
$230$	4.54126	0.299442
$231$	0.473926	0.0311820
$232$	21.9970	1.44417
$233$	−20.2075	−1.32384	−0.661918	−	0.749576i	$-0.730257\pi$
$233$	−20.2075	−1.32384	−0.661918	+	0.749576i	$0.730257\pi$
$234$	−31.1780	−2.03817
$235$	−41.0578	−2.67832
$236$	22.4924	1.46413
$237$	−5.43589	−0.353099
$238$	−15.5775	−1.00974
$239$	8.10770	0.524444	0.262222	−	0.965008i	$-0.415545\pi$
$239$	8.10770	0.524444	0.262222	+	0.965008i	$0.415545\pi$
$240$	4.18274	0.269995
$241$	−21.9686	−1.41513	−0.707563	−	0.706651i	$-0.750205\pi$
$241$	−21.9686	−1.41513	−0.707563	+	0.706651i	$0.750205\pi$
$242$	23.9526	1.53973
$243$	−16.1429	−1.03557
$244$	14.7208	0.942404
$245$	4.46215	0.285076
$246$	6.42448	0.409610
$247$	−32.4861	−2.06704
$248$	−2.88553	−0.183231
$249$	10.9739	0.695444
$250$	−98.7843	−6.24767
$251$	−7.79820	−0.492218	−0.246109	−	0.969242i	$-0.579152\pi$
$251$	−7.79820	−0.492218	−0.246109	+	0.969242i	$0.579152\pi$
$252$	−6.54527	−0.412313
$253$	0.239810	0.0150767
$254$	−23.4055	−1.46859
$255$	−28.0183	−1.75457
$256$	−8.69121	−0.543201
$257$	−12.6254	−0.787548	−0.393774	−	0.919207i	$-0.628831\pi$
$257$	−12.6254	−0.787548	−0.393774	+	0.919207i	$0.628831\pi$
$258$	−16.9286	−1.05393
$259$	1.57662	0.0979666
$260$	−85.0518	−5.27469
$261$	21.7830	1.34833
$262$	22.4994	1.39002
$263$	6.50505	0.401118	0.200559	−	0.979682i	$-0.435724\pi$
$263$	6.50505	0.401118	0.200559	+	0.979682i	$0.435724\pi$
$264$	−1.04774	−0.0644841
$265$	3.96482	0.243557
$266$	−11.3821	−0.697883
$267$	−8.51564	−0.521149
$268$	40.6510	2.48316
$269$	−11.7000	−0.713359	−0.356679	−	0.934227i	$-0.616091\pi$
$269$	−11.7000	−0.713359	−0.356679	+	0.934227i	$0.616091\pi$
$270$	−46.5721	−2.83429
$271$	5.26637	0.319909	0.159955	−	0.987124i	$-0.448865\pi$
$271$	5.26637	0.319909	0.159955	+	0.987124i	$0.448865\pi$
$272$	−7.26003	−0.440204
$273$	5.74050	0.347431
$274$	41.4842	2.50615
$275$	−7.84823	−0.473266
$276$	1.22648	0.0738256
$277$	24.3261	1.46161	0.730806	−	0.682585i	$-0.239144\pi$
$277$	24.3261	1.46161	0.730806	+	0.682585i	$0.239144\pi$
$278$	−7.04872	−0.422754
$279$	−2.85746	−0.171072
$280$	−9.86479	−0.589534
$281$	−4.64862	−0.277313	−0.138657	−	0.990341i	$-0.544278\pi$
$281$	−4.64862	−0.277313	−0.138657	+	0.990341i	$0.544278\pi$
$282$	−18.5067	−1.10206
$283$	−0.0973309	−0.00578572	−0.00289286	−	0.999996i	$-0.500921\pi$
$283$	−0.0973309	−0.00578572	−0.00289286	+	0.999996i	$0.500921\pi$
$284$	−2.53890	−0.150656
$285$	−20.4724	−1.21268
$286$	−7.49584	−0.443239
$287$	3.19420	0.188548
$288$	−14.7711	−0.870395
$289$	31.6316	1.86069
$290$	99.1746	5.82373
$291$	−8.02600	−0.470493
$292$	−14.6093	−0.854945
$293$	23.2352	1.35742	0.678708	−	0.734408i	$-0.262540\pi$
$293$	23.2352	1.35742	0.678708	+	0.734408i	$0.262540\pi$
$294$	2.01130	0.117301
$295$	33.5699	1.95452
$296$	−3.48555	−0.202594
$297$	−2.45933	−0.142705
$298$	−35.1304	−2.03505
$299$	2.90473	0.167985
$300$	−40.1390	−2.31743
$301$	−8.41675	−0.485133
$302$	30.5441	1.75761
$303$	8.67359	0.498285
$304$	−5.30475	−0.304248
$305$	21.9709	1.25805
$306$	34.1033	1.94955
$307$	−8.13559	−0.464322	−0.232161	−	0.972677i	$-0.574580\pi$
$307$	−8.13559	−0.464322	−0.232161	+	0.972677i	$0.574580\pi$
$308$	−1.57362	−0.0896654
$309$	−14.5234	−0.826209
$310$	−13.0096	−0.738894
$311$	−10.3055	−0.584372	−0.292186	−	0.956361i	$-0.594383\pi$
$311$	−10.3055	−0.584372	−0.292186	+	0.956361i	$0.594383\pi$
$312$	−12.6909	−0.718483
$313$	2.90599	0.164256	0.0821280	−	0.996622i	$-0.473828\pi$
$313$	2.90599	0.164256	0.0821280	+	0.996622i	$0.473828\pi$
$314$	15.6495	0.883150
$315$	−9.76884	−0.550412
$316$	18.0493	1.01535
$317$	19.9611	1.12113	0.560564	−	0.828111i	$-0.310584\pi$
$317$	19.9611	1.12113	0.560564	+	0.828111i	$0.310584\pi$
$318$	1.78713	0.100217
$319$	5.23710	0.293221
$320$	−57.9596	−3.24004
$321$	1.58599	0.0885211
$322$	1.01773	0.0567158
$323$	35.5341	1.97717
$324$	7.05781	0.392100
$325$	−95.0628	−5.27314
$326$	18.2474	1.01063
$327$	−2.06849	−0.114388
$328$	−7.06165	−0.389914
$329$	−9.20136	−0.507287
$330$	−4.72380	−0.260037
$331$	20.9048	1.14903	0.574515	−	0.818494i	$-0.305191\pi$
$331$	20.9048	1.14903	0.574515	+	0.818494i	$0.305191\pi$
$332$	−36.4378	−1.99978
$333$	−3.45165	−0.189149
$334$	−46.9504	−2.56901
$335$	60.6718	3.31486
$336$	0.937383	0.0511385
$337$	−10.9159	−0.594627	−0.297313	−	0.954780i	$-0.596091\pi$
$337$	−10.9159	−0.594627	−0.297313	+	0.954780i	$0.596091\pi$
$338$	−61.7556	−3.35906
$339$	−11.8217	−0.642068
$340$	93.0319	5.04536
$341$	−0.686995	−0.0372029
$342$	24.9185	1.34744
$343$	1.00000	0.0539949
$344$	18.6075	1.00325
$345$	1.83053	0.0985525
$346$	−8.77867	−0.471944
$347$	2.97742	0.159836	0.0799181	−	0.996801i	$-0.474534\pi$
$347$	2.97742	0.159836	0.0799181	+	0.996801i	$0.474534\pi$
$348$	26.7847	1.43581
$349$	−23.7661	−1.27217	−0.636085	−	0.771619i	$-0.719447\pi$
$349$	−23.7661	−1.27217	−0.636085	+	0.771619i	$0.719447\pi$
$350$	−33.3071	−1.78034
$351$	−29.7890	−1.59002
$352$	−3.55128	−0.189284
$353$	17.6298	0.938342	0.469171	−	0.883107i	$-0.344553\pi$
$353$	17.6298	0.938342	0.469171	+	0.883107i	$0.344553\pi$
$354$	15.1315	0.804231
$355$	−3.78932	−0.201116
$356$	28.2753	1.49859
$357$	−6.27911	−0.332326
$358$	−36.4793	−1.92799
$359$	6.94661	0.366628	0.183314	−	0.983054i	$-0.441317\pi$
$359$	6.94661	0.366628	0.183314	+	0.983054i	$0.441317\pi$
$360$	21.5967	1.13824
$361$	6.96404	0.366529
$362$	41.2595	2.16855
$363$	9.65502	0.506757
$364$	−19.0607	−0.999054
$365$	−21.8044	−1.14130
$366$	9.90329	0.517653
$367$	1.10669	0.0577685	0.0288843	−	0.999583i	$-0.490805\pi$
$367$	1.10669	0.0577685	0.0288843	+	0.999583i	$0.490805\pi$
$368$	0.474322	0.0247257
$369$	−6.99296	−0.364039
$370$	−15.7148	−0.816974
$371$	0.888546	0.0461310
$372$	−3.51357	−0.182170
$373$	27.2695	1.41196	0.705981	−	0.708230i	$-0.250506\pi$
$373$	27.2695	1.41196	0.705981	+	0.708230i	$0.250506\pi$
$374$	8.19915	0.423968
$375$	−39.8189	−2.05624
$376$	20.3421	1.04906
$377$	63.4352	3.26708
$378$	−10.4372	−0.536829
$379$	30.2000	1.55127	0.775635	−	0.631181i	$-0.217430\pi$
$379$	30.2000	1.55127	0.775635	+	0.631181i	$0.217430\pi$
$380$	67.9765	3.48712
$381$	−9.43450	−0.483344
$382$	−21.1352	−1.08137
$383$	14.8636	0.759497	0.379749	−	0.925090i	$-0.376011\pi$
$383$	14.8636	0.759497	0.379749	+	0.925090i	$0.376011\pi$
$384$	−13.9749	−0.713155
$385$	−2.34864	−0.119698
$386$	−28.5414	−1.45272
$387$	18.4265	0.936673
$388$	26.6495	1.35292
$389$	−10.5505	−0.534930	−0.267465	−	0.963568i	$-0.586186\pi$
$389$	−10.5505	−0.534930	−0.267465	+	0.963568i	$0.586186\pi$
$390$	−57.2178	−2.89734
$391$	−3.17727	−0.160681
$392$	−2.21077	−0.111661
$393$	9.06925	0.457483
$394$	−19.4696	−0.980863
$395$	26.9386	1.35543
$396$	3.44508	0.173122
$397$	4.74814	0.238302	0.119151	−	0.992876i	$-0.461983\pi$
$397$	4.74814	0.238302	0.119151	+	0.992876i	$0.461983\pi$
$398$	−13.9983	−0.701671
$399$	−4.58801	−0.229688
$400$	−15.5231	−0.776155
$401$	−5.06567	−0.252968	−0.126484	−	0.991969i	$-0.540369\pi$
$401$	−5.06567	−0.252968	−0.126484	+	0.991969i	$0.540369\pi$
$402$	27.3476	1.36397
$403$	−8.32133	−0.414515
$404$	−28.7998	−1.43284
$405$	10.5338	0.523429
$406$	22.2258	1.10305
$407$	−0.829850	−0.0411341
$408$	13.8817	0.687246
$409$	−27.4733	−1.35847	−0.679234	−	0.733922i	$-0.737688\pi$
$409$	−27.4733	−1.35847	−0.679234	+	0.733922i	$0.737688\pi$
$410$	−31.8378	−1.57236
$411$	16.7218	0.824828
$412$	48.2236	2.37580
$413$	7.52327	0.370196
$414$	−2.22808	−0.109504
$415$	−54.3835	−2.66958
$416$	−43.0155	−2.10901
$417$	−2.84126	−0.139137
$418$	5.99095	0.293027
$419$	15.3996	0.752318	0.376159	−	0.926555i	$-0.377245\pi$
$419$	15.3996	0.752318	0.376159	+	0.926555i	$0.377245\pi$
$420$	−12.0119	−0.586120
$421$	−17.1872	−0.837654	−0.418827	−	0.908066i	$-0.637559\pi$
$421$	−17.1872	−0.837654	−0.418827	+	0.908066i	$0.637559\pi$
$422$	−31.9772	−1.55662
$423$	20.1442	0.979446
$424$	−1.96437	−0.0953984
$425$	103.982	5.04388
$426$	−1.70802	−0.0827540
$427$	4.92384	0.238281
$428$	−5.26610	−0.254547
$429$	−3.02149	−0.145879
$430$	83.8930	4.04568
$431$	−7.39071	−0.355998	−0.177999	−	0.984031i	$-0.556962\pi$
$431$	−7.39071	−0.355998	−0.177999	+	0.984031i	$0.556962\pi$
$432$	−4.86433	−0.234035
$433$	11.3784	0.546809	0.273404	−	0.961899i	$-0.411850\pi$
$433$	11.3784	0.546809	0.273404	+	0.961899i	$0.411850\pi$
$434$	−2.91554	−0.139950
$435$	39.9762	1.91671
$436$	6.86822	0.328928
$437$	−2.32156	−0.111055
$438$	−9.82827	−0.469613
$439$	−28.1959	−1.34572	−0.672860	−	0.739770i	$-0.734934\pi$
$439$	−28.1959	−1.34572	−0.672860	+	0.739770i	$0.734934\pi$
$440$	5.19230	0.247533
$441$	−2.18927	−0.104251
$442$	99.3135	4.72386
$443$	7.45278	0.354092	0.177046	−	0.984203i	$-0.443346\pi$
$443$	7.45278	0.354092	0.177046	+	0.984203i	$0.443346\pi$
$444$	−4.24419	−0.201420
$445$	42.2010	2.00052
$446$	26.9902	1.27802
$447$	−14.1607	−0.669777
$448$	−12.9892	−0.613681
$449$	−26.3820	−1.24505	−0.622523	−	0.782602i	$-0.713892\pi$
$449$	−26.3820	−1.24505	−0.622523	+	0.782602i	$0.713892\pi$
$450$	72.9182	3.43740
$451$	−1.68126	−0.0791673
$452$	39.2528	1.84630
$453$	12.3120	0.578467
$454$	−65.4782	−3.07304
$455$	−28.4482	−1.33367
$456$	10.1431	0.474992
$457$	−23.9595	−1.12078	−0.560388	−	0.828230i	$-0.689348\pi$
$457$	−23.9595	−1.12078	−0.560388	+	0.828230i	$0.689348\pi$
$458$	−45.1249	−2.10855
$459$	32.5840	1.52089
$460$	−6.07809	−0.283392
$461$	4.60432	0.214445	0.107222	−	0.994235i	$-0.465804\pi$
$461$	4.60432	0.214445	0.107222	+	0.994235i	$0.465804\pi$
$462$	−1.05864	−0.0492524
$463$	−1.08285	−0.0503244	−0.0251622	−	0.999683i	$-0.508010\pi$
$463$	−1.08285	−0.0503244	−0.0251622	+	0.999683i	$0.508010\pi$
$464$	10.3585	0.480882
$465$	−5.24402	−0.243185
$466$	45.1388	2.09101
$467$	27.2429	1.26065	0.630324	−	0.776332i	$-0.282922\pi$
$467$	27.2429	1.26065	0.630324	+	0.776332i	$0.282922\pi$
$468$	41.7291	1.92893
$469$	13.5970	0.627851
$470$	91.7135	4.23043
$471$	6.30813	0.290663
$472$	−16.6322	−0.765561
$473$	4.43013	0.203697
$474$	12.1425	0.557723
$475$	75.9776	3.48609
$476$	20.8491	0.955619
$477$	−1.94527	−0.0890676
$478$	−18.1107	−0.828364
$479$	30.6303	1.39953	0.699766	−	0.714372i	$-0.253287\pi$
$479$	30.6303	1.39953	0.699766	+	0.714372i	$0.253287\pi$
$480$	−27.1079	−1.23730
$481$	−10.0517	−0.458317
$482$	49.0728	2.23520
$483$	0.410235	0.0186664
$484$	−32.0585	−1.45720
$485$	39.7745	1.80607
$486$	36.0595	1.63569
$487$	−41.0110	−1.85838	−0.929192	−	0.369598i	$-0.879496\pi$
$487$	−41.0110	−1.85838	−0.929192	+	0.369598i	$0.879496\pi$
$488$	−10.8855	−0.492763
$489$	7.35534	0.332620
$490$	−9.96739	−0.450281
$491$	−1.40166	−0.0632559	−0.0316279	−	0.999500i	$-0.510069\pi$
$491$	−1.40166	−0.0632559	−0.0316279	+	0.999500i	$0.510069\pi$
$492$	−8.59863	−0.387656
$493$	−69.3871	−3.12504
$494$	72.5663	3.26491
$495$	5.14180	0.231107
$496$	−1.35881	−0.0610126
$497$	−0.849215	−0.0380925
$498$	−24.5132	−1.09846
$499$	−13.3476	−0.597519	−0.298759	−	0.954328i	$-0.596573\pi$
$499$	−13.3476	−0.597519	−0.298759	+	0.954328i	$0.596573\pi$
$500$	132.215	5.91281
$501$	−18.9252	−0.845515
$502$	17.4194	0.777464
$503$	−29.2391	−1.30371	−0.651853	−	0.758346i	$-0.726008\pi$
$503$	−29.2391	−1.30371	−0.651853	+	0.758346i	$0.726008\pi$
$504$	4.83997	0.215590
$505$	−42.9838	−1.91275
$506$	−0.535678	−0.0238138
$507$	−24.8930	−1.10554
$508$	31.3263	1.38988
$509$	−43.9838	−1.94955	−0.974773	−	0.223199i	$-0.928350\pi$
$509$	−43.9838	−1.94955	−0.974773	+	0.223199i	$0.928350\pi$
$510$	62.5863	2.77137
$511$	−4.88653	−0.216167
$512$	−11.6273	−0.513857
$513$	23.8084	1.05117
$514$	28.2021	1.24394
$515$	71.9738	3.17155
$516$	22.6575	0.997439
$517$	4.84310	0.212999
$518$	−3.52181	−0.154739
$519$	−3.53859	−0.155327
$520$	62.8925	2.75802
$521$	0.145470	0.00637317	0.00318658	−	0.999995i	$-0.498986\pi$
$521$	0.145470	0.00637317	0.00318658	+	0.999995i	$0.498986\pi$
$522$	−48.6581	−2.12971
$523$	20.5747	0.899671	0.449835	−	0.893112i	$-0.351483\pi$
$523$	20.5747	0.899671	0.449835	+	0.893112i	$0.351483\pi$
$524$	−30.1135	−1.31551
$525$	−13.4257	−0.585947
$526$	−14.5307	−0.633571
$527$	9.10209	0.396493
$528$	−0.493389	−0.0214720
$529$	−22.7924	−0.990975
$530$	−8.85648	−0.384701
$531$	−16.4705	−0.714757
$532$	15.2340	0.660479
$533$	−20.3645	−0.882083
$534$	19.0219	0.823160
$535$	−7.85967	−0.339803
$536$	−30.0599	−1.29839
$537$	−14.7044	−0.634543
$538$	26.1350	1.12676
$539$	−0.526347	−0.0226714
$540$	62.3329	2.68238
$541$	−14.0739	−0.605086	−0.302543	−	0.953136i	$-0.597836\pi$
$541$	−14.0739	−0.605086	−0.302543	+	0.953136i	$0.597836\pi$
$542$	−11.7638	−0.505300
$543$	16.6313	0.713716
$544$	47.0515	2.01731
$545$	10.2508	0.439098
$546$	−12.8229	−0.548771
$547$	−3.28065	−0.140271	−0.0701353	−	0.997537i	$-0.522343\pi$
$547$	−3.28065	−0.140271	−0.0701353	+	0.997537i	$0.522343\pi$
$548$	−55.5232	−2.37183
$549$	−10.7796	−0.460062
$550$	17.5311	0.747528
$551$	−50.6997	−2.15988
$552$	−0.906937	−0.0386018
$553$	6.03715	0.256726
$554$	−54.3387	−2.30863
$555$	−6.33447	−0.268883
$556$	9.43413	0.400096
$557$	14.1173	0.598170	0.299085	−	0.954227i	$-0.403319\pi$
$557$	14.1173	0.598170	0.299085	+	0.954227i	$0.403319\pi$
$558$	6.38290	0.270210
$559$	53.6606	2.26960
$560$	−4.64539	−0.196304
$561$	3.30499	0.139537
$562$	10.3839	0.438019
$563$	28.2079	1.18882	0.594410	−	0.804162i	$-0.297385\pi$
$563$	28.2079	1.18882	0.594410	+	0.804162i	$0.297385\pi$
$564$	24.7696	1.04299
$565$	58.5849	2.46469
$566$	0.217414	0.00913861
$567$	2.36070	0.0991401
$568$	1.87742	0.0787749
$569$	−25.8420	−1.08335	−0.541677	−	0.840586i	$-0.682211\pi$
$569$	−25.8420	−1.08335	−0.541677	+	0.840586i	$0.682211\pi$
$570$	45.7305	1.91544
$571$	20.8890	0.874178	0.437089	−	0.899418i	$-0.356010\pi$
$571$	20.8890	0.874178	0.437089	+	0.899418i	$0.356010\pi$
$572$	10.0326	0.419482
$573$	−8.51936	−0.355901
$574$	−7.13509	−0.297813
$575$	−6.79351	−0.283309
$576$	28.4368	1.18487
$577$	−1.39398	−0.0580323	−0.0290162	−	0.999579i	$-0.509237\pi$
$577$	−1.39398	−0.0580323	−0.0290162	+	0.999579i	$0.509237\pi$
$578$	−70.6577	−2.93897
$579$	−11.5047	−0.478120
$580$	−132.737	−5.51160
$581$	−12.1878	−0.505633
$582$	17.9282	0.743148
$583$	−0.467683	−0.0193695
$584$	10.8030	0.447032
$585$	62.2808	2.57499
$586$	−51.9021	−2.14405
$587$	27.0529	1.11659	0.558297	−	0.829641i	$-0.311455\pi$
$587$	27.0529	1.11659	0.558297	+	0.829641i	$0.311455\pi$
$588$	−2.69195	−0.111014
$589$	6.65071	0.274038
$590$	−74.9873	−3.08718
$591$	−7.84798	−0.322823
$592$	−1.64137	−0.0674599
$593$	3.23856	0.132992	0.0664958	−	0.997787i	$-0.478818\pi$
$593$	3.23856	0.132992	0.0664958	+	0.997787i	$0.478818\pi$
$594$	5.49356	0.225404
$595$	31.1174	1.27569
$596$	47.0191	1.92598
$597$	−5.64256	−0.230935
$598$	−6.48848	−0.265334
$599$	17.5819	0.718378	0.359189	−	0.933265i	$-0.383053\pi$
$599$	17.5819	0.718378	0.359189	+	0.933265i	$0.383053\pi$
$600$	29.6813	1.21173
$601$	−16.9088	−0.689724	−0.344862	−	0.938653i	$-0.612074\pi$
$601$	−16.9088	−0.689724	−0.344862	+	0.938653i	$0.612074\pi$
$602$	18.8010	0.766273
$603$	−29.7675	−1.21223
$604$	−40.8807	−1.66341
$605$	−47.8474	−1.94527
$606$	−19.3748	−0.787046
$607$	−12.4774	−0.506442	−0.253221	−	0.967408i	$-0.581490\pi$
$607$	−12.4774	−0.506442	−0.253221	+	0.967408i	$0.581490\pi$
$608$	34.3795	1.39427
$609$	8.95896	0.363035
$610$	−49.0778	−1.98710
$611$	58.6628	2.37324
$612$	−45.6444	−1.84506
$613$	4.18629	0.169083	0.0845414	−	0.996420i	$-0.473057\pi$
$613$	4.18629	0.169083	0.0845414	+	0.996420i	$0.473057\pi$
$614$	18.1730	0.733402
$615$	−12.8335	−0.517496
$616$	1.16363	0.0468841
$617$	−27.7996	−1.11917	−0.559584	−	0.828774i	$-0.689039\pi$
$617$	−27.7996	−1.11917	−0.559584	+	0.828774i	$0.689039\pi$
$618$	32.4419	1.30501
$619$	−13.6357	−0.548066	−0.274033	−	0.961720i	$-0.588358\pi$
$619$	−13.6357	−0.548066	−0.274033	+	0.961720i	$0.588358\pi$
$620$	17.4122	0.699291
$621$	−2.12882	−0.0854267
$622$	23.0201	0.923022
$623$	9.45755	0.378909
$624$	−5.97625	−0.239241
$625$	122.777	4.91107
$626$	−6.49129	−0.259444
$627$	2.41489	0.0964412
$628$	−20.9455	−0.835816
$629$	10.9948	0.438391
$630$	21.8213	0.869381
$631$	40.0848	1.59575	0.797875	−	0.602823i	$-0.205958\pi$
$631$	40.0848	1.59575	0.797875	+	0.602823i	$0.205958\pi$
$632$	−13.3468	−0.530906
$633$	−12.8896	−0.512317
$634$	−44.5885	−1.77083
$635$	46.7546	1.85540
$636$	−2.39192	−0.0948459
$637$	−6.37545	−0.252605
$638$	−11.6985	−0.463146
$639$	1.85916	0.0735472
$640$	69.2556	2.73757
$641$	7.01529	0.277087	0.138544	−	0.990356i	$-0.455758\pi$
$641$	7.01529	0.277087	0.138544	+	0.990356i	$0.455758\pi$
$642$	−3.54272	−0.139820
$643$	3.16092	0.124655	0.0623273	−	0.998056i	$-0.480148\pi$
$643$	3.16092	0.124655	0.0623273	+	0.998056i	$0.480148\pi$
$644$	−1.36214	−0.0536760
$645$	33.8163	1.33152
$646$	−79.3749	−3.12296
$647$	−16.1403	−0.634541	−0.317270	−	0.948335i	$-0.602766\pi$
$647$	−16.1403	−0.634541	−0.317270	+	0.948335i	$0.602766\pi$
$648$	−5.21897	−0.205021
$649$	−3.95985	−0.155438
$650$	212.348	8.32898
$651$	−1.17522	−0.0460606
$652$	−24.4226	−0.956464
$653$	19.5090	0.763445	0.381723	−	0.924277i	$-0.375331\pi$
$653$	19.5090	0.763445	0.381723	+	0.924277i	$0.375331\pi$
$654$	4.62053	0.180677
$655$	−44.9445	−1.75613
$656$	−3.32538	−0.129834
$657$	10.6979	0.417366
$658$	20.5537	0.801265
$659$	−37.8607	−1.47485	−0.737423	−	0.675432i	$-0.763957\pi$
$659$	−37.8607	−1.47485	−0.737423	+	0.675432i	$0.763957\pi$
$660$	6.32241	0.246100
$661$	−7.06400	−0.274758	−0.137379	−	0.990519i	$-0.543868\pi$
$661$	−7.06400	−0.274758	−0.137379	+	0.990519i	$0.543868\pi$
$662$	−46.6964	−1.81491
$663$	40.0322	1.55472
$664$	26.9443	1.04564
$665$	22.7368	0.881697
$666$	7.71018	0.298763
$667$	4.53329	0.175530
$668$	62.8392	2.43132
$669$	10.8795	0.420624
$670$	−135.527	−5.23585
$671$	−2.59165	−0.100049
$672$	−6.07508	−0.234351
$673$	12.9456	0.499015	0.249507	−	0.968373i	$-0.419731\pi$
$673$	12.9456	0.499015	0.249507	+	0.968373i	$0.419731\pi$
$674$	24.3836	0.939220
$675$	69.6698	2.68159
$676$	82.6547	3.17903
$677$	25.9069	0.995681	0.497841	−	0.867269i	$-0.334126\pi$
$677$	25.9069	0.995681	0.497841	+	0.867269i	$0.334126\pi$
$678$	26.4069	1.01415
$679$	8.91376	0.342079
$680$	−68.7935	−2.63811
$681$	−26.3936	−1.01140
$682$	1.53458	0.0587623
$683$	32.0846	1.22768	0.613842	−	0.789429i	$-0.289623\pi$
$683$	32.0846	1.22768	0.613842	+	0.789429i	$0.289623\pi$
$684$	−33.3514	−1.27522
$685$	−82.8685	−3.16624
$686$	−2.23377	−0.0852855
$687$	−18.1893	−0.693967
$688$	8.76240	0.334063
$689$	−5.66488	−0.215815
$690$	−4.08898	−0.155665
$691$	25.3423	0.964068	0.482034	−	0.876153i	$-0.339898\pi$
$691$	25.3423	0.964068	0.482034	+	0.876153i	$0.339898\pi$
$692$	11.7495	0.446650
$693$	1.15231	0.0437728
$694$	−6.65085	−0.252463
$695$	14.0805	0.534102
$696$	−19.8062	−0.750753
$697$	22.2752	0.843733
$698$	53.0879	2.00941
$699$	18.1949	0.688196
$700$	44.5788	1.68492
$701$	50.6849	1.91434	0.957170	−	0.289525i	$-0.0934974\pi$
$701$	50.6849	1.91434	0.957170	+	0.289525i	$0.0934974\pi$
$702$	66.5416	2.51145
$703$	8.03367	0.302996
$704$	6.83681	0.257672
$705$	36.9687	1.39232
$706$	−39.3809	−1.48212
$707$	−9.63298	−0.362285
$708$	−20.2523	−0.761127
$709$	−3.08392	−0.115819	−0.0579096	−	0.998322i	$-0.518444\pi$
$709$	−3.08392	−0.115819	−0.0579096	+	0.998322i	$0.518444\pi$
$710$	8.46446	0.317665
$711$	−13.2169	−0.495674
$712$	−20.9085	−0.783579
$713$	−0.594670	−0.0222706
$714$	14.0261	0.524912
$715$	14.9736	0.559982
$716$	48.8245	1.82466
$717$	−7.30022	−0.272632
$718$	−15.5171	−0.579093
$719$	31.9019	1.18974	0.594871	−	0.803821i	$-0.297203\pi$
$719$	31.9019	1.18974	0.594871	+	0.803821i	$0.297203\pi$
$720$	10.1700	0.379014
$721$	16.1299	0.600707
$722$	−15.5560	−0.578936
$723$	19.7807	0.735653
$724$	−55.2224	−2.05233
$725$	−148.361	−5.50997
$726$	−21.5670	−0.800428
$727$	−40.0122	−1.48397	−0.741985	−	0.670416i	$-0.766116\pi$
$727$	−40.0122	−1.48397	−0.741985	+	0.670416i	$0.766116\pi$
$728$	14.0947	0.522384
$729$	7.45310	0.276041
$730$	48.7060	1.80269
$731$	−58.6954	−2.17093
$732$	−13.2547	−0.489909
$733$	−26.3432	−0.973009	−0.486505	−	0.873678i	$-0.661728\pi$
$733$	−26.3432	−0.973009	−0.486505	+	0.873678i	$0.661728\pi$
$734$	−2.47208	−0.0912460
$735$	−4.01775	−0.148197
$736$	−3.07403	−0.113310
$737$	−7.15674	−0.263622
$738$	15.6206	0.575003
$739$	−19.4173	−0.714277	−0.357139	−	0.934051i	$-0.616248\pi$
$739$	−19.4173	−0.714277	−0.357139	+	0.934051i	$0.616248\pi$
$740$	21.0330	0.773187
$741$	29.2507	1.07455
$742$	−1.98480	−0.0728644
$743$	28.7863	1.05607	0.528033	−	0.849224i	$-0.322930\pi$
$743$	28.7863	1.05607	0.528033	+	0.849224i	$0.322930\pi$
$744$	2.59815	0.0952528
$745$	70.1761	2.57105
$746$	−60.9137	−2.23021
$747$	26.6823	0.976253
$748$	−10.9739	−0.401245
$749$	−1.76141	−0.0643605
$750$	88.9461	3.24785
$751$	18.3207	0.668531	0.334265	−	0.942479i	$-0.391512\pi$
$751$	18.3207	0.668531	0.334265	+	0.942479i	$0.391512\pi$
$752$	9.57923	0.349319
$753$	7.02155	0.255880
$754$	−141.699	−5.16038
$755$	−61.0145	−2.22055
$756$	13.9693	0.508057
$757$	11.1744	0.406141	0.203071	−	0.979164i	$-0.434908\pi$
$757$	11.1744	0.406141	0.203071	+	0.979164i	$0.434908\pi$
$758$	−67.4597	−2.45025
$759$	−0.215926	−0.00783762
$760$	−50.2660	−1.82334
$761$	−14.4258	−0.522934	−0.261467	−	0.965212i	$-0.584206\pi$
$761$	−14.4258	−0.522934	−0.261467	+	0.965212i	$0.584206\pi$
$762$	21.0745	0.763447
$763$	2.29729	0.0831674
$764$	28.2876	1.02341
$765$	−68.1244	−2.46304
$766$	−33.2019	−1.19963
$767$	−47.9643	−1.73189
$768$	7.82562	0.282383
$769$	−1.82075	−0.0656581	−0.0328290	−	0.999461i	$-0.510452\pi$
$769$	−1.82075	−0.0656581	−0.0328290	+	0.999461i	$0.510452\pi$
$770$	5.24630	0.189064
$771$	11.3679	0.409407
$772$	38.2002	1.37486
$773$	13.9081	0.500240	0.250120	−	0.968215i	$-0.419530\pi$
$773$	13.9081	0.500240	0.250120	+	0.968215i	$0.419530\pi$
$774$	−41.1605	−1.47948
$775$	19.4617	0.699086
$776$	−19.7063	−0.707414
$777$	−1.41960	−0.0509279
$778$	23.5673	0.844927
$779$	16.2760	0.583149
$780$	76.5812	2.74205
$781$	0.446982	0.0159943
$782$	7.09727	0.253798
$783$	−46.4904	−1.66143
$784$	−1.04107	−0.0371810
$785$	−31.2612	−1.11576
$786$	−20.2586	−0.722599
$787$	12.5241	0.446437	0.223219	−	0.974768i	$-0.428344\pi$
$787$	12.5241	0.446437	0.223219	+	0.974768i	$0.428344\pi$
$788$	26.0584	0.928292
$789$	−5.85719	−0.208521
$790$	−60.1746	−2.14092
$791$	13.1293	0.466825
$792$	−2.54750	−0.0905216
$793$	−31.3917	−1.11475
$794$	−10.6062	−0.376401
$795$	−3.56995	−0.126613
$796$	18.7355	0.664064
$797$	15.3340	0.543157	0.271579	−	0.962416i	$-0.412454\pi$
$797$	15.3340	0.543157	0.271579	+	0.962416i	$0.412454\pi$
$798$	10.2485	0.362795
$799$	−64.1669	−2.27006
$800$	100.604	3.55687
$801$	−20.7051	−0.731580
$802$	11.3155	0.399565
$803$	2.57201	0.0907643
$804$	−36.6025	−1.29087
$805$	−2.03301	−0.0716540
$806$	18.5879	0.654731
$807$	10.5347	0.370840
$808$	21.2963	0.749202
$809$	−30.7417	−1.08082	−0.540410	−	0.841402i	$-0.681731\pi$
$809$	−30.7417	−1.08082	−0.540410	+	0.841402i	$0.681731\pi$
$810$	−23.5300	−0.826761
$811$	10.3123	0.362114	0.181057	−	0.983473i	$-0.442048\pi$
$811$	10.3123	0.362114	0.181057	+	0.983473i	$0.442048\pi$
$812$	−29.7473	−1.04393
$813$	−4.74187	−0.166305
$814$	1.85369	0.0649718
$815$	−36.4509	−1.27682
$816$	6.53697	0.228840
$817$	−42.8875	−1.50044
$818$	61.3689	2.14571
$819$	13.9576	0.487717
$820$	42.6122	1.48808
$821$	33.6972	1.17604	0.588020	−	0.808846i	$-0.299908\pi$
$821$	33.6972	1.17604	0.588020	+	0.808846i	$0.299908\pi$
$822$	−37.3527	−1.30282
$823$	−7.52834	−0.262421	−0.131211	−	0.991354i	$-0.541886\pi$
$823$	−7.52834	−0.262421	−0.131211	+	0.991354i	$0.541886\pi$
$824$	−35.6595	−1.24226
$825$	7.06659	0.246027
$826$	−16.8052	−0.584728
$827$	−9.02053	−0.313674	−0.156837	−	0.987624i	$-0.550130\pi$
$827$	−9.02053	−0.313674	−0.156837	+	0.987624i	$0.550130\pi$
$828$	2.98210	0.103635
$829$	20.3771	0.707727	0.353863	−	0.935297i	$-0.384868\pi$
$829$	20.3771	0.707727	0.353863	+	0.935297i	$0.384868\pi$
$830$	121.480	4.21663
$831$	−21.9033	−0.759819
$832$	82.8119	2.87099
$833$	6.97364	0.241622
$834$	6.34672	0.219769
$835$	93.7877	3.24566
$836$	−8.01838	−0.277321
$837$	6.09854	0.210797
$838$	−34.3990	−1.18829
$839$	−16.6884	−0.576149	−0.288074	−	0.957608i	$-0.593015\pi$
$839$	−16.6884	−0.576149	−0.288074	+	0.957608i	$0.593015\pi$
$840$	8.88232	0.306469
$841$	70.0006	2.41381
$842$	38.3922	1.32308
$843$	4.18564	0.144161
$844$	42.7987	1.47319
$845$	123.362	4.24379
$846$	−44.9975	−1.54705
$847$	−10.7230	−0.368445
$848$	−0.925036	−0.0317659
$849$	0.0876373	0.00300771
$850$	−232.272	−7.96686
$851$	−0.718327	−0.0246239
$852$	2.28605	0.0783186
$853$	−44.1223	−1.51072	−0.755360	−	0.655310i	$-0.772538\pi$
$853$	−44.1223	−1.51072	−0.755360	+	0.655310i	$0.772538\pi$
$854$	−10.9987	−0.376368
$855$	−49.7770	−1.70234
$856$	3.89408	0.133097
$857$	25.5337	0.872215	0.436107	−	0.899895i	$-0.356357\pi$
$857$	25.5337	0.872215	0.436107	+	0.899895i	$0.356357\pi$
$858$	6.74931	0.230417
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	−112.284	−3.82884
$861$	−2.87608	−0.0980164
$862$	16.5091	0.562303
$863$	34.9600	1.19005	0.595026	−	0.803707i	$-0.297142\pi$
$863$	34.9600	1.19005	0.595026	+	0.803707i	$0.297142\pi$
$864$	31.5252	1.07251
$865$	17.5362	0.596248
$866$	−25.4166	−0.863690
$867$	−28.4813	−0.967277
$868$	3.90221	0.132449
$869$	−3.17763	−0.107794
$870$	−89.2974	−3.02747
$871$	−86.6870	−2.93728
$872$	−5.07878	−0.171989
$873$	−19.5146	−0.660469
$874$	5.18583	0.175413
$875$	44.2232	1.49502
$876$	13.1543	0.444443
$877$	25.5168	0.861642	0.430821	−	0.902437i	$-0.358224\pi$
$877$	25.5168	0.861642	0.430821	+	0.902437i	$0.358224\pi$
$878$	62.9831	2.12558
$879$	−20.9212	−0.705653
$880$	2.44509	0.0824239
$881$	39.9157	1.34479	0.672397	−	0.740191i	$-0.265265\pi$
$881$	39.9157	1.34479	0.672397	+	0.740191i	$0.265265\pi$
$882$	4.89031	0.164665
$883$	6.50507	0.218913	0.109456	−	0.993992i	$-0.465089\pi$
$883$	6.50507	0.218913	0.109456	+	0.993992i	$0.465089\pi$
$884$	−132.923	−4.47067
$885$	−30.2266	−1.01606
$886$	−16.6478	−0.559293
$887$	−46.4962	−1.56119	−0.780595	−	0.625037i	$-0.785084\pi$
$887$	−46.4962	−1.56119	−0.780595	+	0.625037i	$0.785084\pi$
$888$	3.13842	0.105318
$889$	10.4781	0.351423
$890$	−94.2671	−3.15984
$891$	−1.24255	−0.0416269
$892$	−36.1241	−1.20952
$893$	−46.8854	−1.56896
$894$	31.6316	1.05792
$895$	72.8707	2.43580
$896$	15.5207	0.518510
$897$	−2.61544	−0.0873269
$898$	58.9313	1.96656
$899$	−12.9867	−0.433132
$900$	−97.5949	−3.25316
$901$	6.19640	0.206432
$902$	3.75553	0.125046
$903$	7.57849	0.252196
$904$	−29.0259	−0.965388
$905$	−82.4197	−2.73972
$906$	−27.5021	−0.913695
$907$	16.1269	0.535485	0.267743	−	0.963490i	$-0.413722\pi$
$907$	16.1269	0.535485	0.267743	+	0.963490i	$0.413722\pi$
$908$	87.6371	2.90834
$909$	21.0892	0.699484
$910$	63.5466	2.10655
$911$	6.97312	0.231030	0.115515	−	0.993306i	$-0.463148\pi$
$911$	6.97312	0.231030	0.115515	+	0.993306i	$0.463148\pi$
$912$	4.77643	0.158163
$913$	6.41498	0.212305
$914$	53.5198	1.77028
$915$	−19.7827	−0.653997
$916$	60.3958	1.99553
$917$	−10.0724	−0.332620
$918$	−72.7850	−2.40226
$919$	−21.7103	−0.716157	−0.358079	−	0.933691i	$-0.616568\pi$
$919$	−21.7103	−0.716157	−0.358079	+	0.933691i	$0.616568\pi$
$920$	4.49451	0.148180
$921$	7.32533	0.241378
$922$	−10.2850	−0.338718
$923$	5.41413	0.178208
$924$	1.41690	0.0466126
$925$	23.5086	0.772959
$926$	2.41884	0.0794879
$927$	−35.3126	−1.15982
$928$	−67.1324	−2.20373
$929$	−23.1620	−0.759919	−0.379960	−	0.925003i	$-0.624062\pi$
$929$	−23.1620	−0.759919	−0.379960	+	0.925003i	$0.624062\pi$
$930$	11.7139	0.384114
$931$	5.09549	0.166998
$932$	−60.4144	−1.97894
$933$	9.27916	0.303786
$934$	−60.8541	−1.99121
$935$	−16.3785	−0.535636
$936$	−30.8570	−1.00859
$937$	24.3243	0.794639	0.397319	−	0.917680i	$-0.369941\pi$
$937$	24.3243	0.794639	0.397319	+	0.917680i	$0.369941\pi$
$938$	−30.3725	−0.991697
$939$	−2.61657	−0.0853885
$940$	−122.751	−4.00369
$941$	15.3427	0.500158	0.250079	−	0.968225i	$-0.419543\pi$
$941$	15.3427	0.500158	0.250079	+	0.968225i	$0.419543\pi$
$942$	−14.0909	−0.459106
$943$	−1.45531	−0.0473915
$944$	−7.83223	−0.254917
$945$	20.8492	0.678223
$946$	−9.89586	−0.321742
$947$	53.0561	1.72409	0.862046	−	0.506830i	$-0.169183\pi$
$947$	53.0561	1.72409	0.862046	+	0.506830i	$0.169183\pi$
$948$	−16.2517	−0.527831
$949$	31.1539	1.01130
$950$	−169.716	−5.50632
$951$	−17.9731	−0.582819
$952$	−15.4171	−0.499672
$953$	57.3018	1.85619	0.928093	−	0.372348i	$-0.121447\pi$
$953$	57.3018	1.85619	0.928093	+	0.372348i	$0.121447\pi$
$954$	4.34527	0.140683
$955$	42.2194	1.36619
$956$	24.2396	0.783966
$957$	−4.71552	−0.152431
$958$	−68.4208	−2.21058
$959$	−18.5714	−0.599703
$960$	52.1872	1.68433
$961$	−29.2964	−0.945046
$962$	22.4531	0.723917
$963$	3.85620	0.124264
$964$	−65.6798	−2.11540
$965$	57.0140	1.83534
$966$	−0.916370	−0.0294837
$967$	6.52011	0.209673	0.104836	−	0.994489i	$-0.466568\pi$
$967$	6.52011	0.209673	0.104836	+	0.994489i	$0.466568\pi$
$968$	23.7060	0.761940
$969$	−31.9952	−1.02783
$970$	−88.8469	−2.85270
$971$	3.39692	0.109012	0.0545062	−	0.998513i	$-0.482642\pi$
$971$	3.39692	0.109012	0.0545062	+	0.998513i	$0.482642\pi$
$972$	−48.2627	−1.54803
$973$	3.15554	0.101162
$974$	91.6088	2.93534
$975$	85.5952	2.74124
$976$	−5.12604	−0.164081
$977$	42.8930	1.37227	0.686134	−	0.727475i	$-0.259306\pi$
$977$	42.8930	1.37227	0.686134	+	0.727475i	$0.259306\pi$
$978$	−16.4301	−0.525376
$979$	−4.97795	−0.159096
$980$	13.3405	0.426147
$981$	−5.02938	−0.160576
$982$	3.13097	0.0999133
$983$	19.1984	0.612333	0.306166	−	0.951978i	$-0.400954\pi$
$983$	19.1984	0.612333	0.306166	+	0.951978i	$0.400954\pi$
$984$	6.35835	0.202697
$985$	38.8922	1.23921
$986$	154.994	4.93603
$987$	8.28496	0.263713
$988$	−97.1238	−3.08992
$989$	3.83477	0.121938
$990$	−11.4856	−0.365035
$991$	1.65063	0.0524341	0.0262171	−	0.999656i	$-0.491654\pi$
$991$	1.65063	0.0524341	0.0262171	+	0.999656i	$0.491654\pi$
$992$	8.80633	0.279601
$993$	−18.8228	−0.597324
$994$	1.89695	0.0601675
$995$	27.9629	0.886482
$996$	32.8088	1.03959
$997$	47.2251	1.49563	0.747817	−	0.663905i	$-0.231102\pi$
$997$	47.2251	1.49563	0.747817	+	0.663905i	$0.231102\pi$
$998$	29.8153	0.943787
$999$	7.36669	0.233072

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.e.1.12	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.e.1.12	✓	109	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23377 q^{2} -0.900406 q^{3} +2.98971 q^{4} +4.46215 q^{5} +2.01130 q^{6} +1.00000 q^{7} -2.21077 q^{8} -2.18927 q^{9} +O(q^{10})\)	\(q-2.23377 q^{2} -0.900406 q^{3} +2.98971 q^{4} +4.46215 q^{5} +2.01130 q^{6} +1.00000 q^{7} -2.21077 q^{8} -2.18927 q^{9} -9.96739 q^{10} -0.526347 q^{11} -2.69195 q^{12} -6.37545 q^{13} -2.23377 q^{14} -4.01775 q^{15} -1.04107 q^{16} +6.97364 q^{17} +4.89031 q^{18} +5.09549 q^{19} +13.3405 q^{20} -0.900406 q^{21} +1.17573 q^{22} -0.455611 q^{23} +1.99059 q^{24} +14.9108 q^{25} +14.2413 q^{26} +4.67245 q^{27} +2.98971 q^{28} -9.94990 q^{29} +8.97470 q^{30} +1.30521 q^{31} +6.74704 q^{32} +0.473926 q^{33} -15.5775 q^{34} +4.46215 q^{35} -6.54527 q^{36} +1.57662 q^{37} -11.3821 q^{38} +5.74050 q^{39} -9.86479 q^{40} +3.19420 q^{41} +2.01130 q^{42} -8.41675 q^{43} -1.57362 q^{44} -9.76884 q^{45} +1.01773 q^{46} -9.20136 q^{47} +0.937383 q^{48} +1.00000 q^{49} -33.3071 q^{50} -6.27911 q^{51} -19.0607 q^{52} +0.888546 q^{53} -10.4372 q^{54} -2.34864 q^{55} -2.21077 q^{56} -4.58801 q^{57} +22.2258 q^{58} +7.52327 q^{59} -12.0119 q^{60} +4.92384 q^{61} -2.91554 q^{62} -2.18927 q^{63} -12.9892 q^{64} -28.4482 q^{65} -1.05864 q^{66} +13.5970 q^{67} +20.8491 q^{68} +0.410235 q^{69} -9.96739 q^{70} -0.849215 q^{71} +4.83997 q^{72} -4.88653 q^{73} -3.52181 q^{74} -13.4257 q^{75} +15.2340 q^{76} -0.526347 q^{77} -12.8229 q^{78} +6.03715 q^{79} -4.64539 q^{80} +2.36070 q^{81} -7.13509 q^{82} -12.1878 q^{83} -2.69195 q^{84} +31.1174 q^{85} +18.8010 q^{86} +8.95896 q^{87} +1.16363 q^{88} +9.45755 q^{89} +21.8213 q^{90} -6.37545 q^{91} -1.36214 q^{92} -1.17522 q^{93} +20.5537 q^{94} +22.7368 q^{95} -6.07508 q^{96} +8.91376 q^{97} -2.23377 q^{98} +1.15231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9}+O(q^{10}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9} + 15 q^{10} + 48 q^{11} + 72 q^{12} + 29 q^{13} + 19 q^{14} + 29 q^{15} + 115 q^{16} + 72 q^{17} + 33 q^{18} + 58 q^{19} + 88 q^{20} + 38 q^{21} + 4 q^{22} + 65 q^{23} + 46 q^{24} + 124 q^{25} + 49 q^{26} + 131 q^{27} + 111 q^{28} + 25 q^{29} + 2 q^{30} + 41 q^{31} + 75 q^{32} + 54 q^{33} + 23 q^{34} + 43 q^{35} + 111 q^{36} + 25 q^{37} + 54 q^{38} + 27 q^{39} + 30 q^{40} + 109 q^{41} + 14 q^{42} + 38 q^{43} + 68 q^{44} + 84 q^{45} - 9 q^{46} + 121 q^{47} + 106 q^{48} + 109 q^{49} + 14 q^{50} + 36 q^{51} + 38 q^{52} + 61 q^{53} + 31 q^{54} + 50 q^{55} + 48 q^{56} + 5 q^{57} - 20 q^{58} + 181 q^{59} + 25 q^{60} + 34 q^{61} + 75 q^{62} + 119 q^{63} + 96 q^{64} + 12 q^{65} + 19 q^{66} + 87 q^{67} + 150 q^{68} + 89 q^{69} + 15 q^{70} + 83 q^{71} + 65 q^{72} + 32 q^{73} - 19 q^{74} + 112 q^{75} + 84 q^{76} + 48 q^{77} - 34 q^{78} - 9 q^{79} + 137 q^{80} + 109 q^{81} - 19 q^{82} + 136 q^{83} + 72 q^{84} - 32 q^{85} - 24 q^{86} + 28 q^{87} - 24 q^{88} + 142 q^{89} + 19 q^{90} + 29 q^{91} + 96 q^{92} + 29 q^{93} + 9 q^{94} + 52 q^{95} + 88 q^{96} + 75 q^{97} + 19 q^{98} + 84 q^{99}+O(q^{100}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9 + 15 * q^10 + 48 * q^11 + 72 * q^12 + 29 * q^13 + 19 * q^14 + 29 * q^15 + 115 * q^16 + 72 * q^17 + 33 * q^18 + 58 * q^19 + 88 * q^20 + 38 * q^21 + 4 * q^22 + 65 * q^23 + 46 * q^24 + 124 * q^25 + 49 * q^26 + 131 * q^27 + 111 * q^28 + 25 * q^29 + 2 * q^30 + 41 * q^31 + 75 * q^32 + 54 * q^33 + 23 * q^34 + 43 * q^35 + 111 * q^36 + 25 * q^37 + 54 * q^38 + 27 * q^39 + 30 * q^40 + 109 * q^41 + 14 * q^42 + 38 * q^43 + 68 * q^44 + 84 * q^45 - 9 * q^46 + 121 * q^47 + 106 * q^48 + 109 * q^49 + 14 * q^50 + 36 * q^51 + 38 * q^52 + 61 * q^53 + 31 * q^54 + 50 * q^55 + 48 * q^56 + 5 * q^57 - 20 * q^58 + 181 * q^59 + 25 * q^60 + 34 * q^61 + 75 * q^62 + 119 * q^63 + 96 * q^64 + 12 * q^65 + 19 * q^66 + 87 * q^67 + 150 * q^68 + 89 * q^69 + 15 * q^70 + 83 * q^71 + 65 * q^72 + 32 * q^73 - 19 * q^74 + 112 * q^75 + 84 * q^76 + 48 * q^77 - 34 * q^78 - 9 * q^79 + 137 * q^80 + 109 * q^81 - 19 * q^82 + 136 * q^83 + 72 * q^84 - 32 * q^85 - 24 * q^86 + 28 * q^87 - 24 * q^88 + 142 * q^89 + 19 * q^90 + 29 * q^91 + 96 * q^92 + 29 * q^93 + 9 * q^94 + 52 * q^95 + 88 * q^96 + 75 * q^97 + 19 * q^98 + 84 * q^99

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