LMFDB - Embedded newform 6013.2.a.e.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.65451 q^{2} -2.36774 q^{3} +5.04644 q^{4} -0.160322 q^{5} +6.28521 q^{6} +1.00000 q^{7} -8.08683 q^{8} +2.60621 q^{9} +O(q^{10})$	\(q-2.65451 q^{2} -2.36774 q^{3} +5.04644 q^{4} -0.160322 q^{5} +6.28521 q^{6} +1.00000 q^{7} -8.08683 q^{8} +2.60621 q^{9} +0.425577 q^{10} -0.871782 q^{11} -11.9487 q^{12} +0.818140 q^{13} -2.65451 q^{14} +0.379601 q^{15} +11.3737 q^{16} +4.11170 q^{17} -6.91823 q^{18} -0.545295 q^{19} -0.809056 q^{20} -2.36774 q^{21} +2.31416 q^{22} +8.22459 q^{23} +19.1475 q^{24} -4.97430 q^{25} -2.17176 q^{26} +0.932389 q^{27} +5.04644 q^{28} +5.19127 q^{29} -1.00766 q^{30} -1.28470 q^{31} -14.0180 q^{32} +2.06416 q^{33} -10.9146 q^{34} -0.160322 q^{35} +13.1521 q^{36} -2.04257 q^{37} +1.44749 q^{38} -1.93715 q^{39} +1.29650 q^{40} +7.99035 q^{41} +6.28521 q^{42} -1.08034 q^{43} -4.39940 q^{44} -0.417833 q^{45} -21.8323 q^{46} +1.54043 q^{47} -26.9300 q^{48} +1.00000 q^{49} +13.2043 q^{50} -9.73545 q^{51} +4.12870 q^{52} -0.678971 q^{53} -2.47504 q^{54} +0.139766 q^{55} -8.08683 q^{56} +1.29112 q^{57} -13.7803 q^{58} -3.03261 q^{59} +1.91564 q^{60} +4.28301 q^{61} +3.41026 q^{62} +2.60621 q^{63} +14.4636 q^{64} -0.131166 q^{65} -5.47933 q^{66} +13.0086 q^{67} +20.7495 q^{68} -19.4737 q^{69} +0.425577 q^{70} +0.359103 q^{71} -21.0760 q^{72} +8.05664 q^{73} +5.42204 q^{74} +11.7779 q^{75} -2.75180 q^{76} -0.871782 q^{77} +5.14218 q^{78} -6.47312 q^{79} -1.82346 q^{80} -10.0263 q^{81} -21.2105 q^{82} +1.74046 q^{83} -11.9487 q^{84} -0.659196 q^{85} +2.86779 q^{86} -12.2916 q^{87} +7.04995 q^{88} +4.18555 q^{89} +1.10914 q^{90} +0.818140 q^{91} +41.5049 q^{92} +3.04185 q^{93} -4.08910 q^{94} +0.0874228 q^{95} +33.1911 q^{96} -14.0397 q^{97} -2.65451 q^{98} -2.27205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65451	−1.87702	−0.938512	−	0.345246i	$-0.887796\pi$
$2$	−2.65451	−1.87702	−0.938512	+	0.345246i	$0.887796\pi$
$3$	−2.36774	−1.36702	−0.683509	−	0.729942i	$-0.739547\pi$
$3$	−2.36774	−1.36702	−0.683509	+	0.729942i	$0.739547\pi$
$4$	5.04644	2.52322
$5$	−0.160322	−0.0716982	−0.0358491	−	0.999357i	$-0.511414\pi$
$5$	−0.160322	−0.0716982	−0.0358491	+	0.999357i	$0.511414\pi$
$6$	6.28521	2.56593
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−8.08683	−2.85913
$9$	2.60621	0.868737
$10$	0.425577	0.134579
$11$	−0.871782	−0.262852	−0.131426	−	0.991326i	$-0.541956\pi$
$11$	−0.871782	−0.262852	−0.131426	+	0.991326i	$0.541956\pi$
$12$	−11.9487	−3.44929
$13$	0.818140	0.226911	0.113456	−	0.993543i	$-0.463808\pi$
$13$	0.818140	0.226911	0.113456	+	0.993543i	$0.463808\pi$
$14$	−2.65451	−0.709449
$15$	0.379601	0.0980127
$16$	11.3737	2.84343
$17$	4.11170	0.997234	0.498617	−	0.866823i	$-0.333841\pi$
$17$	4.11170	0.997234	0.498617	+	0.866823i	$0.333841\pi$
$18$	−6.91823	−1.63064
$19$	−0.545295	−0.125099	−0.0625497	−	0.998042i	$-0.519923\pi$
$19$	−0.545295	−0.125099	−0.0625497	+	0.998042i	$0.519923\pi$
$20$	−0.809056	−0.180910
$21$	−2.36774	−0.516684
$22$	2.31416	0.493380
$23$	8.22459	1.71495	0.857473	−	0.514529i	$-0.172033\pi$
$23$	8.22459	1.71495	0.857473	+	0.514529i	$0.172033\pi$
$24$	19.1475	3.90847
$25$	−4.97430	−0.994859
$26$	−2.17176	−0.425918
$27$	0.932389	0.179438
$28$	5.04644	0.953688
$29$	5.19127	0.963994	0.481997	−	0.876173i	$-0.339912\pi$
$29$	5.19127	0.963994	0.481997	+	0.876173i	$0.339912\pi$
$30$	−1.00766	−0.183972
$31$	−1.28470	−0.230739	−0.115370	−	0.993323i	$-0.536805\pi$
$31$	−1.28470	−0.230739	−0.115370	+	0.993323i	$0.536805\pi$
$32$	−14.0180	−2.47806
$33$	2.06416	0.359323
$34$	−10.9146	−1.87183
$35$	−0.160322	−0.0270994
$36$	13.1521	2.19202
$37$	−2.04257	−0.335797	−0.167898	−	0.985804i	$-0.553698\pi$
$37$	−2.04257	−0.335797	−0.167898	+	0.985804i	$0.553698\pi$
$38$	1.44749	0.234814
$39$	−1.93715	−0.310192
$40$	1.29650	0.204994
$41$	7.99035	1.24788	0.623942	−	0.781471i	$-0.285530\pi$
$41$	7.99035	1.24788	0.623942	+	0.781471i	$0.285530\pi$
$42$	6.28521	0.969829
$43$	−1.08034	−0.164751	−0.0823755	−	0.996601i	$-0.526251\pi$
$43$	−1.08034	−0.164751	−0.0823755	+	0.996601i	$0.526251\pi$
$44$	−4.39940	−0.663234
$45$	−0.417833	−0.0622869
$46$	−21.8323	−3.21900
$47$	1.54043	0.224695	0.112348	−	0.993669i	$-0.464163\pi$
$47$	1.54043	0.224695	0.112348	+	0.993669i	$0.464163\pi$
$48$	−26.9300	−3.88701
$49$	1.00000	0.142857
$50$	13.2043	1.86738
$51$	−9.73545	−1.36324
$52$	4.12870	0.572548
$53$	−0.678971	−0.0932638	−0.0466319	−	0.998912i	$-0.514849\pi$
$53$	−0.678971	−0.0932638	−0.0466319	+	0.998912i	$0.514849\pi$
$54$	−2.47504	−0.336810
$55$	0.139766	0.0188460
$56$	−8.08683	−1.08065
$57$	1.29112	0.171013
$58$	−13.7803	−1.80944
$59$	−3.03261	−0.394812	−0.197406	−	0.980322i	$-0.563252\pi$
$59$	−3.03261	−0.394812	−0.197406	+	0.980322i	$0.563252\pi$
$60$	1.91564	0.247308
$61$	4.28301	0.548383	0.274191	−	0.961675i	$-0.411590\pi$
$61$	4.28301	0.548383	0.274191	+	0.961675i	$0.411590\pi$
$62$	3.41026	0.433104
$63$	2.60621	0.328352
$64$	14.4636	1.80795
$65$	−0.131166	−0.0162691
$66$	−5.47933	−0.674459
$67$	13.0086	1.58925	0.794625	−	0.607100i	$-0.207667\pi$
$67$	13.0086	1.58925	0.794625	+	0.607100i	$0.207667\pi$
$68$	20.7495	2.51624
$69$	−19.4737	−2.34436
$70$	0.425577	0.0508662
$71$	0.359103	0.0426177	0.0213088	−	0.999773i	$-0.493217\pi$
$71$	0.359103	0.0426177	0.0213088	+	0.999773i	$0.493217\pi$
$72$	−21.0760	−2.48383
$73$	8.05664	0.942959	0.471479	−	0.881877i	$-0.343720\pi$
$73$	8.05664	0.942959	0.471479	+	0.881877i	$0.343720\pi$
$74$	5.42204	0.630299
$75$	11.7779	1.35999
$76$	−2.75180	−0.315653
$77$	−0.871782	−0.0993487
$78$	5.14218	0.582238
$79$	−6.47312	−0.728283	−0.364141	−	0.931344i	$-0.618638\pi$
$79$	−6.47312	−0.728283	−0.364141	+	0.931344i	$0.618638\pi$
$80$	−1.82346	−0.203869
$81$	−10.0263	−1.11403
$82$	−21.2105	−2.34231
$83$	1.74046	0.191040	0.0955201	−	0.995427i	$-0.469549\pi$
$83$	1.74046	0.191040	0.0955201	+	0.995427i	$0.469549\pi$
$84$	−11.9487	−1.30371
$85$	−0.659196	−0.0714998
$86$	2.86779	0.309242
$87$	−12.2916	−1.31780
$88$	7.04995	0.751527
$89$	4.18555	0.443668	0.221834	−	0.975084i	$-0.428796\pi$
$89$	4.18555	0.443668	0.221834	+	0.975084i	$0.428796\pi$
$90$	1.10914	0.116914
$91$	0.818140	0.0857644
$92$	41.5049	4.32719
$93$	3.04185	0.315425
$94$	−4.08910	−0.421759
$95$	0.0874228	0.00896939
$96$	33.1911	3.38755
$97$	−14.0397	−1.42551	−0.712755	−	0.701413i	$-0.752553\pi$
$97$	−14.0397	−1.42551	−0.712755	+	0.701413i	$0.752553\pi$
$98$	−2.65451	−0.268146
$99$	−2.27205	−0.228349
$100$	−25.1025	−2.51025
$101$	−9.56933	−0.952184	−0.476092	−	0.879395i	$-0.657947\pi$
$101$	−9.56933	−0.952184	−0.476092	+	0.879395i	$0.657947\pi$
$102$	25.8429	2.55883
$103$	14.4000	1.41888	0.709439	−	0.704767i	$-0.248948\pi$
$103$	14.4000	1.41888	0.709439	+	0.704767i	$0.248948\pi$
$104$	−6.61616	−0.648768
$105$	0.379601	0.0370453
$106$	1.80234	0.175058
$107$	12.6857	1.22637	0.613184	−	0.789940i	$-0.289888\pi$
$107$	12.6857	1.22637	0.613184	+	0.789940i	$0.289888\pi$
$108$	4.70525	0.452763
$109$	18.5314	1.77498	0.887491	−	0.460825i	$-0.152446\pi$
$109$	18.5314	1.77498	0.887491	+	0.460825i	$0.152446\pi$
$110$	−0.371010	−0.0353744
$111$	4.83629	0.459040
$112$	11.3737	1.07471
$113$	4.78955	0.450563	0.225282	−	0.974294i	$-0.427670\pi$
$113$	4.78955	0.450563	0.225282	+	0.974294i	$0.427670\pi$
$114$	−3.42729	−0.320996
$115$	−1.31858	−0.122958
$116$	26.1974	2.43237
$117$	2.13225	0.197126
$118$	8.05011	0.741073
$119$	4.11170	0.376919
$120$	−3.06977	−0.280230
$121$	−10.2400	−0.930909
$122$	−11.3693	−1.02933
$123$	−18.9191	−1.70588
$124$	−6.48318	−0.582207
$125$	1.59910	0.143028
$126$	−6.91823	−0.616325
$127$	15.4385	1.36995	0.684974	−	0.728567i	$-0.259814\pi$
$127$	15.4385	1.36995	0.684974	+	0.728567i	$0.259814\pi$
$128$	−10.3578	−0.915506
$129$	2.55798	0.225217
$130$	0.348182	0.0305375
$131$	21.7764	1.90261	0.951305	−	0.308250i	$-0.0997434\pi$
$131$	21.7764	1.90261	0.951305	+	0.308250i	$0.0997434\pi$
$132$	10.4166	0.906653
$133$	−0.545295	−0.0472831
$134$	−34.5315	−2.98306
$135$	−0.149482	−0.0128654
$136$	−33.2506	−2.85122
$137$	−0.154988	−0.0132415	−0.00662075	−	0.999978i	$-0.502107\pi$
$137$	−0.154988	−0.0132415	−0.00662075	+	0.999978i	$0.502107\pi$
$138$	51.6933	4.40042
$139$	−17.9616	−1.52348	−0.761740	−	0.647883i	$-0.775655\pi$
$139$	−17.9616	−1.52348	−0.761740	+	0.647883i	$0.775655\pi$
$140$	−0.809056	−0.0683777
$141$	−3.64735	−0.307163
$142$	−0.953244	−0.0799945
$143$	−0.713240	−0.0596441
$144$	29.6423	2.47019
$145$	−0.832274	−0.0691166
$146$	−21.3865	−1.76996
$147$	−2.36774	−0.195288
$148$	−10.3077	−0.847290
$149$	16.2665	1.33261	0.666303	−	0.745681i	$-0.267876\pi$
$149$	16.2665	1.33261	0.666303	+	0.745681i	$0.267876\pi$
$150$	−31.2645	−2.55274
$151$	−7.39737	−0.601990	−0.300995	−	0.953626i	$-0.597319\pi$
$151$	−7.39737	−0.601990	−0.300995	+	0.953626i	$0.597319\pi$
$152$	4.40971	0.357675
$153$	10.7160	0.866334
$154$	2.31416	0.186480
$155$	0.205966	0.0165436
$156$	−9.77570	−0.782683
$157$	−2.67073	−0.213147	−0.106574	−	0.994305i	$-0.533988\pi$
$157$	−2.67073	−0.213147	−0.106574	+	0.994305i	$0.533988\pi$
$158$	17.1830	1.36701
$159$	1.60763	0.127493
$160$	2.24740	0.177672
$161$	8.22459	0.648189
$162$	26.6149	2.09107
$163$	3.34208	0.261772	0.130886	−	0.991397i	$-0.458218\pi$
$163$	3.34208	0.261772	0.130886	+	0.991397i	$0.458218\pi$
$164$	40.3229	3.14869
$165$	−0.330930	−0.0257628
$166$	−4.62007	−0.358587
$167$	−4.08377	−0.316011	−0.158006	−	0.987438i	$-0.550506\pi$
$167$	−4.08377	−0.316011	−0.158006	+	0.987438i	$0.550506\pi$
$168$	19.1475	1.47726
$169$	−12.3306	−0.948511
$170$	1.74984	0.134207
$171$	−1.42116	−0.108678
$172$	−5.45190	−0.415703
$173$	1.93253	0.146928	0.0734639	−	0.997298i	$-0.476595\pi$
$173$	1.93253	0.146928	0.0734639	+	0.997298i	$0.476595\pi$
$174$	32.6282	2.47354
$175$	−4.97430	−0.376021
$176$	−9.91539	−0.747401
$177$	7.18045	0.539716
$178$	−11.1106	−0.832775
$179$	−10.8453	−0.810613	−0.405306	−	0.914181i	$-0.632835\pi$
$179$	−10.8453	−0.810613	−0.405306	+	0.914181i	$0.632835\pi$
$180$	−2.10857	−0.157164
$181$	−12.7640	−0.948743	−0.474372	−	0.880325i	$-0.657325\pi$
$181$	−12.7640	−0.948743	−0.474372	+	0.880325i	$0.657325\pi$
$182$	−2.17176	−0.160982
$183$	−10.1411	−0.749649
$184$	−66.5108	−4.90324
$185$	0.327469	0.0240760
$186$	−8.07463	−0.592060
$187$	−3.58450	−0.262125
$188$	7.77371	0.566956
$189$	0.932389	0.0678213
$190$	−0.232065	−0.0168358
$191$	3.49998	0.253250	0.126625	−	0.991951i	$-0.459586\pi$
$191$	3.49998	0.253250	0.126625	+	0.991951i	$0.459586\pi$
$192$	−34.2461	−2.47150
$193$	−16.8862	−1.21550	−0.607748	−	0.794130i	$-0.707927\pi$
$193$	−16.8862	−1.21550	−0.607748	+	0.794130i	$0.707927\pi$
$194$	37.2684	2.67572
$195$	0.310567	0.0222402
$196$	5.04644	0.360460
$197$	−3.12436	−0.222601	−0.111301	−	0.993787i	$-0.535502\pi$
$197$	−3.12436	−0.222601	−0.111301	+	0.993787i	$0.535502\pi$
$198$	6.03118	0.428618
$199$	−13.4626	−0.954340	−0.477170	−	0.878811i	$-0.658337\pi$
$199$	−13.4626	−0.954340	−0.477170	+	0.878811i	$0.658337\pi$
$200$	40.2263	2.84443
$201$	−30.8010	−2.17253
$202$	25.4019	1.78727
$203$	5.19127	0.364355
$204$	−49.1294	−3.43975
$205$	−1.28103	−0.0894710
$206$	−38.2251	−2.66327
$207$	21.4350	1.48984
$208$	9.30529	0.645206
$209$	0.475378	0.0328826
$210$	−1.00766	−0.0695350
$211$	17.9534	1.23596	0.617980	−	0.786194i	$-0.287951\pi$
$211$	17.9534	1.23596	0.617980	+	0.786194i	$0.287951\pi$
$212$	−3.42639	−0.235325
$213$	−0.850264	−0.0582591
$214$	−33.6742	−2.30192
$215$	0.173203	0.0118123
$216$	−7.54007	−0.513037
$217$	−1.28470	−0.0872113
$218$	−49.1917	−3.33169
$219$	−19.0761	−1.28904
$220$	0.705320	0.0475527
$221$	3.36395	0.226284
$222$	−12.8380	−0.861630
$223$	−3.55002	−0.237727	−0.118864	−	0.992911i	$-0.537925\pi$
$223$	−3.55002	−0.237727	−0.118864	+	0.992911i	$0.537925\pi$
$224$	−14.0180	−0.936618
$225$	−12.9641	−0.864272
$226$	−12.7139	−0.845719
$227$	3.51755	0.233468	0.116734	−	0.993163i	$-0.462758\pi$
$227$	3.51755	0.233468	0.116734	+	0.993163i	$0.462758\pi$
$228$	6.51556	0.431504
$229$	−12.4487	−0.822631	−0.411316	−	0.911493i	$-0.634931\pi$
$229$	−12.4487	−0.822631	−0.411316	+	0.911493i	$0.634931\pi$
$230$	3.50020	0.230796
$231$	2.06416	0.135811
$232$	−41.9809	−2.75618
$233$	−8.88291	−0.581938	−0.290969	−	0.956732i	$-0.593978\pi$
$233$	−8.88291	−0.581938	−0.290969	+	0.956732i	$0.593978\pi$
$234$	−5.66008	−0.370011
$235$	−0.246965	−0.0161102
$236$	−15.3039	−0.996199
$237$	15.3267	0.995576
$238$	−10.9146	−0.707486
$239$	−19.4018	−1.25500	−0.627498	−	0.778618i	$-0.715921\pi$
$239$	−19.4018	−1.25500	−0.627498	+	0.778618i	$0.715921\pi$
$240$	4.31748	0.278692
$241$	−18.0921	−1.16542	−0.582708	−	0.812682i	$-0.698007\pi$
$241$	−18.0921	−1.16542	−0.582708	+	0.812682i	$0.698007\pi$
$242$	27.1822	1.74734
$243$	20.9425	1.34346
$244$	21.6140	1.38369
$245$	−0.160322	−0.0102426
$246$	50.2211	3.20198
$247$	−0.446128	−0.0283864
$248$	10.3892	0.659713
$249$	−4.12096	−0.261155
$250$	−4.24483	−0.268467
$251$	3.95043	0.249349	0.124674	−	0.992198i	$-0.460211\pi$
$251$	3.95043	0.249349	0.124674	+	0.992198i	$0.460211\pi$
$252$	13.1521	0.828505
$253$	−7.17005	−0.450777
$254$	−40.9818	−2.57143
$255$	1.56081	0.0977415
$256$	−1.43233	−0.0895204
$257$	2.91380	0.181758	0.0908788	−	0.995862i	$-0.471032\pi$
$257$	2.91380	0.181758	0.0908788	+	0.995862i	$0.471032\pi$
$258$	−6.79019	−0.422739
$259$	−2.04257	−0.126919
$260$	−0.661921	−0.0410506
$261$	13.5295	0.837458
$262$	−57.8057	−3.57125
$263$	−11.3419	−0.699373	−0.349686	−	0.936867i	$-0.613712\pi$
$263$	−11.3419	−0.699373	−0.349686	+	0.936867i	$0.613712\pi$
$264$	−16.6925	−1.02735
$265$	0.108854	0.00668684
$266$	1.44749	0.0887515
$267$	−9.91032	−0.606501
$268$	65.6471	4.01003
$269$	2.54216	0.154998	0.0774992	−	0.996992i	$-0.475306\pi$
$269$	2.54216	0.154998	0.0774992	+	0.996992i	$0.475306\pi$
$270$	0.396803	0.0241487
$271$	−3.70597	−0.225122	−0.112561	−	0.993645i	$-0.535905\pi$
$271$	−3.70597	−0.225122	−0.112561	+	0.993645i	$0.535905\pi$
$272$	46.7653	2.83556
$273$	−1.93715	−0.117241
$274$	0.411417	0.0248546
$275$	4.33650	0.261501
$276$	−98.2731	−5.91534
$277$	−16.1960	−0.973124	−0.486562	−	0.873646i	$-0.661749\pi$
$277$	−16.1960	−0.973124	−0.486562	+	0.873646i	$0.661749\pi$
$278$	47.6792	2.85961
$279$	−3.34821	−0.200452
$280$	1.29650	0.0774805
$281$	−13.5976	−0.811165	−0.405583	−	0.914058i	$-0.632931\pi$
$281$	−13.5976	−0.811165	−0.405583	+	0.914058i	$0.632931\pi$
$282$	9.68195	0.576552
$283$	−9.17040	−0.545123	−0.272562	−	0.962138i	$-0.587871\pi$
$283$	−9.17040	−0.545123	−0.272562	+	0.962138i	$0.587871\pi$
$284$	1.81219	0.107534
$285$	−0.206995	−0.0122613
$286$	1.89330	0.111953
$287$	7.99035	0.471656
$288$	−36.5339	−2.15278
$289$	−0.0939266	−0.00552510
$290$	2.20928	0.129734
$291$	33.2423	1.94870
$292$	40.6574	2.37929
$293$	29.0939	1.69969	0.849843	−	0.527036i	$-0.176697\pi$
$293$	29.0939	1.69969	0.849843	+	0.527036i	$0.176697\pi$
$294$	6.28521	0.366561
$295$	0.486194	0.0283073
$296$	16.5179	0.960085
$297$	−0.812839	−0.0471657
$298$	−43.1797	−2.50133
$299$	6.72887	0.389141
$300$	59.4363	3.43156
$301$	−1.08034	−0.0622700
$302$	19.6364	1.12995
$303$	22.6577	1.30165
$304$	−6.20203	−0.355711
$305$	−0.686660	−0.0393181
$306$	−28.4457	−1.62613
$307$	31.5622	1.80135	0.900675	−	0.434494i	$-0.143073\pi$
$307$	31.5622	1.80135	0.900675	+	0.434494i	$0.143073\pi$
$308$	−4.39940	−0.250679
$309$	−34.0956	−1.93963
$310$	−0.546740	−0.0310527
$311$	−1.77430	−0.100611	−0.0503056	−	0.998734i	$-0.516020\pi$
$311$	−1.77430	−0.100611	−0.0503056	+	0.998734i	$0.516020\pi$
$312$	15.6654	0.886877
$313$	−5.14132	−0.290604	−0.145302	−	0.989387i	$-0.546415\pi$
$313$	−5.14132	−0.290604	−0.145302	+	0.989387i	$0.546415\pi$
$314$	7.08948	0.400082
$315$	−0.417833	−0.0235422
$316$	−32.6662	−1.83762
$317$	18.0776	1.01534	0.507670	−	0.861552i	$-0.330507\pi$
$317$	18.0776	1.01534	0.507670	+	0.861552i	$0.330507\pi$
$318$	−4.26747	−0.239308
$319$	−4.52565	−0.253388
$320$	−2.31883	−0.129627
$321$	−30.0364	−1.67647
$322$	−21.8323	−1.21667
$323$	−2.24209	−0.124753
$324$	−50.5971	−2.81095
$325$	−4.06967	−0.225745
$326$	−8.87159	−0.491352
$327$	−43.8775	−2.42643
$328$	−64.6166	−3.56786
$329$	1.54043	0.0849269
$330$	0.878457	0.0483575
$331$	−17.3737	−0.954943	−0.477472	−	0.878647i	$-0.658447\pi$
$331$	−17.3737	−0.954943	−0.477472	+	0.878647i	$0.658447\pi$
$332$	8.78313	0.482037
$333$	−5.32338	−0.291719
$334$	10.8404	0.593161
$335$	−2.08556	−0.113946
$336$	−26.9300	−1.46915
$337$	−1.95690	−0.106599	−0.0532995	−	0.998579i	$-0.516974\pi$
$337$	−1.95690	−0.106599	−0.0532995	+	0.998579i	$0.516974\pi$
$338$	32.7319	1.78038
$339$	−11.3404	−0.615928
$340$	−3.32659	−0.180410
$341$	1.11998	0.0606504
$342$	3.77248	0.203992
$343$	1.00000	0.0539949
$344$	8.73656	0.471043
$345$	3.12207	0.168086
$346$	−5.12994	−0.275787
$347$	−16.0927	−0.863904	−0.431952	−	0.901897i	$-0.642175\pi$
$347$	−16.0927	−0.863904	−0.431952	+	0.901897i	$0.642175\pi$
$348$	−62.0288	−3.32509
$349$	5.96157	0.319116	0.159558	−	0.987189i	$-0.448993\pi$
$349$	5.96157	0.319116	0.159558	+	0.987189i	$0.448993\pi$
$350$	13.2043	0.705802
$351$	0.762825	0.0407166
$352$	12.2206	0.651363
$353$	13.0092	0.692411	0.346206	−	0.938159i	$-0.387470\pi$
$353$	13.0092	0.692411	0.346206	+	0.938159i	$0.387470\pi$
$354$	−19.0606	−1.01306
$355$	−0.0575721	−0.00305561
$356$	21.1222	1.11947
$357$	−9.73545	−0.515255
$358$	28.7889	1.52154
$359$	−6.18525	−0.326445	−0.163222	−	0.986589i	$-0.552189\pi$
$359$	−6.18525	−0.326445	−0.163222	+	0.986589i	$0.552189\pi$
$360$	3.37894	0.178086
$361$	−18.7027	−0.984350
$362$	33.8823	1.78081
$363$	24.2457	1.27257
$364$	4.12870	0.216403
$365$	−1.29166	−0.0676084
$366$	26.9196	1.40711
$367$	−30.2767	−1.58043	−0.790215	−	0.612830i	$-0.790031\pi$
$367$	−30.2767	−1.58043	−0.790215	+	0.612830i	$0.790031\pi$
$368$	93.5441	4.87632
$369$	20.8246	1.08408
$370$	−0.869272	−0.0451913
$371$	−0.678971	−0.0352504
$372$	15.3505	0.795887
$373$	−6.60106	−0.341790	−0.170895	−	0.985289i	$-0.554666\pi$
$373$	−6.60106	−0.341790	−0.170895	+	0.985289i	$0.554666\pi$
$374$	9.51512	0.492015
$375$	−3.78626	−0.195521
$376$	−12.4572	−0.642432
$377$	4.24718	0.218741
$378$	−2.47504	−0.127302
$379$	29.7626	1.52880	0.764401	−	0.644741i	$-0.223035\pi$
$379$	29.7626	1.52880	0.764401	+	0.644741i	$0.223035\pi$
$380$	0.441174	0.0226318
$381$	−36.5545	−1.87274
$382$	−9.29074	−0.475356
$383$	−8.62935	−0.440939	−0.220470	−	0.975394i	$-0.570759\pi$
$383$	−8.62935	−0.440939	−0.220470	+	0.975394i	$0.570759\pi$
$384$	24.5246	1.25151
$385$	0.139766	0.00712312
$386$	44.8247	2.28152
$387$	−2.81561	−0.143125
$388$	−70.8503	−3.59688
$389$	−36.6144	−1.85643	−0.928213	−	0.372050i	$-0.878655\pi$
$389$	−36.6144	−1.85643	−0.928213	+	0.372050i	$0.878655\pi$
$390$	−0.824405	−0.0417454
$391$	33.8170	1.71020
$392$	−8.08683	−0.408446
$393$	−51.5609	−2.60090
$394$	8.29366	0.417828
$395$	1.03778	0.0522166
$396$	−11.4658	−0.576176
$397$	15.3182	0.768798	0.384399	−	0.923167i	$-0.374409\pi$
$397$	15.3182	0.768798	0.384399	+	0.923167i	$0.374409\pi$
$398$	35.7367	1.79132
$399$	1.29112	0.0646368
$400$	−56.5762	−2.82881
$401$	0.244011	0.0121853	0.00609266	−	0.999981i	$-0.498061\pi$
$401$	0.244011	0.0121853	0.00609266	+	0.999981i	$0.498061\pi$
$402$	81.7616	4.07790
$403$	−1.05107	−0.0523574
$404$	−48.2911	−2.40257
$405$	1.60744	0.0798741
$406$	−13.7803	−0.683904
$407$	1.78068	0.0882649
$408$	78.7289	3.89766
$409$	17.4133	0.861031	0.430516	−	0.902583i	$-0.358332\pi$
$409$	17.4133	0.861031	0.430516	+	0.902583i	$0.358332\pi$
$410$	3.40051	0.167939
$411$	0.366971	0.0181014
$412$	72.6690	3.58015
$413$	−3.03261	−0.149225
$414$	−56.8996	−2.79646
$415$	−0.279034	−0.0136972
$416$	−11.4687	−0.562299
$417$	42.5284	2.08262
$418$	−1.26190	−0.0617215
$419$	24.3426	1.18921	0.594606	−	0.804017i	$-0.297308\pi$
$419$	24.3426	1.18921	0.594606	+	0.804017i	$0.297308\pi$
$420$	1.91564	0.0934735
$421$	12.2674	0.597878	0.298939	−	0.954272i	$-0.403367\pi$
$421$	12.2674	0.597878	0.298939	+	0.954272i	$0.403367\pi$
$422$	−47.6574	−2.31993
$423$	4.01470	0.195201
$424$	5.49072	0.266653
$425$	−20.4528	−0.992107
$426$	2.25704	0.109354
$427$	4.28301	0.207269
$428$	64.0174	3.09440
$429$	1.68877	0.0815345
$430$	−0.459769	−0.0221721
$431$	11.3563	0.547014	0.273507	−	0.961870i	$-0.411816\pi$
$431$	11.3563	0.547014	0.273507	+	0.961870i	$0.411816\pi$
$432$	10.6047	0.510220
$433$	26.0576	1.25225	0.626124	−	0.779724i	$-0.284641\pi$
$433$	26.0576	1.25225	0.626124	+	0.779724i	$0.284641\pi$
$434$	3.41026	0.163698
$435$	1.97061	0.0944836
$436$	93.5175	4.47867
$437$	−4.48483	−0.214539
$438$	50.6377	2.41956
$439$	−5.70087	−0.272088	−0.136044	−	0.990703i	$-0.543439\pi$
$439$	−5.70087	−0.272088	−0.136044	+	0.990703i	$0.543439\pi$
$440$	−1.13026	−0.0538831
$441$	2.60621	0.124105
$442$	−8.92964	−0.424740
$443$	−16.8267	−0.799460	−0.399730	−	0.916633i	$-0.630896\pi$
$443$	−16.8267	−0.799460	−0.399730	+	0.916633i	$0.630896\pi$
$444$	24.4061	1.15826
$445$	−0.671036	−0.0318102
$446$	9.42358	0.446220
$447$	−38.5150	−1.82170
$448$	14.4636	0.683340
$449$	−9.93629	−0.468922	−0.234461	−	0.972125i	$-0.575333\pi$
$449$	−9.93629	−0.468922	−0.234461	+	0.972125i	$0.575333\pi$
$450$	34.4133	1.62226
$451$	−6.96584	−0.328009
$452$	24.1702	1.13687
$453$	17.5151	0.822931
$454$	−9.33738	−0.438225
$455$	−0.131166	−0.00614915
$456$	−10.4411	−0.488947
$457$	−7.80932	−0.365305	−0.182652	−	0.983178i	$-0.558468\pi$
$457$	−7.80932	−0.365305	−0.182652	+	0.983178i	$0.558468\pi$
$458$	33.0452	1.54410
$459$	3.83370	0.178942
$460$	−6.65415	−0.310252
$461$	20.2544	0.943342	0.471671	−	0.881775i	$-0.343651\pi$
$461$	20.2544	0.943342	0.471671	+	0.881775i	$0.343651\pi$
$462$	−5.47933	−0.254922
$463$	7.66482	0.356214	0.178107	−	0.984011i	$-0.443003\pi$
$463$	7.66482	0.356214	0.178107	+	0.984011i	$0.443003\pi$
$464$	59.0439	2.74105
$465$	−0.487675	−0.0226154
$466$	23.5798	1.09231
$467$	32.2178	1.49086	0.745431	−	0.666583i	$-0.232244\pi$
$467$	32.2178	1.49086	0.745431	+	0.666583i	$0.232244\pi$
$468$	10.7603	0.497393
$469$	13.0086	0.600680
$470$	0.655573	0.0302393
$471$	6.32359	0.291376
$472$	24.5242	1.12882
$473$	0.941824	0.0433051
$474$	−40.6849	−1.86872
$475$	2.71246	0.124456
$476$	20.7495	0.951050
$477$	−1.76954	−0.0810217
$478$	51.5023	2.35566
$479$	9.24461	0.422397	0.211199	−	0.977443i	$-0.432263\pi$
$479$	9.24461	0.422397	0.211199	+	0.977443i	$0.432263\pi$
$480$	−5.32126	−0.242881
$481$	−1.67111	−0.0761961
$482$	48.0258	2.18752
$483$	−19.4737	−0.886085
$484$	−51.6756	−2.34889
$485$	2.25086	0.102206
$486$	−55.5922	−2.52172
$487$	−7.44636	−0.337427	−0.168713	−	0.985665i	$-0.553961\pi$
$487$	−7.44636	−0.337427	−0.168713	+	0.985665i	$0.553961\pi$
$488$	−34.6359	−1.56790
$489$	−7.91318	−0.357846
$490$	0.425577	0.0192256
$491$	−26.1677	−1.18093	−0.590466	−	0.807063i	$-0.701056\pi$
$491$	−26.1677	−1.18093	−0.590466	+	0.807063i	$0.701056\pi$
$492$	−95.4743	−4.30431
$493$	21.3449	0.961327
$494$	1.18425	0.0532821
$495$	0.364259	0.0163722
$496$	−14.6118	−0.656091
$497$	0.359103	0.0161080
$498$	10.9392	0.490195
$499$	15.8236	0.708360	0.354180	−	0.935177i	$-0.384760\pi$
$499$	15.8236	0.708360	0.354180	+	0.935177i	$0.384760\pi$
$500$	8.06976	0.360891
$501$	9.66932	0.431993
$502$	−10.4865	−0.468034
$503$	11.2296	0.500702	0.250351	−	0.968155i	$-0.419454\pi$
$503$	11.2296	0.500702	0.250351	+	0.968155i	$0.419454\pi$
$504$	−21.0760	−0.938799
$505$	1.53417	0.0682698
$506$	19.0330	0.846120
$507$	29.1958	1.29663
$508$	77.9097	3.45668
$509$	−0.0613138	−0.00271769	−0.00135884	−	0.999999i	$-0.500433\pi$
$509$	−0.0613138	−0.00271769	−0.00135884	+	0.999999i	$0.500433\pi$
$510$	−4.14318	−0.183463
$511$	8.05664	0.356405
$512$	24.5177	1.08354
$513$	−0.508427	−0.0224476
$514$	−7.73471	−0.341163
$515$	−2.30864	−0.101731
$516$	12.9087	0.568274
$517$	−1.34292	−0.0590617
$518$	5.42204	0.238231
$519$	−4.57575	−0.200853
$520$	1.06072	0.0465155
$521$	−30.5822	−1.33983	−0.669915	−	0.742438i	$-0.733669\pi$
$521$	−30.5822	−1.33983	−0.669915	+	0.742438i	$0.733669\pi$
$522$	−35.9144	−1.57193
$523$	42.6032	1.86291	0.931453	−	0.363861i	$-0.118542\pi$
$523$	42.6032	1.86291	0.931453	+	0.363861i	$0.118542\pi$
$524$	109.893	4.80071
$525$	11.7779	0.514028
$526$	30.1073	1.31274
$527$	−5.28231	−0.230101
$528$	23.4771	1.02171
$529$	44.6439	1.94104
$530$	−0.288954	−0.0125514
$531$	−7.90363	−0.342988
$532$	−2.75180	−0.119306
$533$	6.53723	0.283159
$534$	26.3071	1.13842
$535$	−2.03379	−0.0879284
$536$	−105.198	−4.54387
$537$	25.6788	1.10812
$538$	−6.74820	−0.290936
$539$	−0.871782	−0.0375503
$540$	−0.754355	−0.0324623
$541$	−32.0468	−1.37780	−0.688900	−	0.724856i	$-0.741906\pi$
$541$	−32.0468	−1.37780	−0.688900	+	0.724856i	$0.741906\pi$
$542$	9.83755	0.422559
$543$	30.2220	1.29695
$544$	−57.6378	−2.47120
$545$	−2.97098	−0.127263
$546$	5.14218	0.220065
$547$	2.73729	0.117038	0.0585190	−	0.998286i	$-0.481362\pi$
$547$	2.73729	0.117038	0.0585190	+	0.998286i	$0.481362\pi$
$548$	−0.782137	−0.0334112
$549$	11.1624	0.476401
$550$	−11.5113	−0.490844
$551$	−2.83077	−0.120595
$552$	157.481	6.70282
$553$	−6.47312	−0.275265
$554$	42.9926	1.82658
$555$	−0.775363	−0.0329123
$556$	−90.6420	−3.84408
$557$	24.8221	1.05175	0.525873	−	0.850563i	$-0.323739\pi$
$557$	24.8221	1.05175	0.525873	+	0.850563i	$0.323739\pi$
$558$	8.88787	0.376253
$559$	−0.883873	−0.0373838
$560$	−1.82346	−0.0770551
$561$	8.48719	0.358329
$562$	36.0950	1.52258
$563$	21.6853	0.913926	0.456963	−	0.889486i	$-0.348937\pi$
$563$	21.6853	0.913926	0.456963	+	0.889486i	$0.348937\pi$
$564$	−18.4062	−0.775039
$565$	−0.767871	−0.0323046
$566$	24.3429	1.02321
$567$	−10.0263	−0.421065
$568$	−2.90400	−0.121849
$569$	4.39910	0.184420	0.0922099	−	0.995740i	$-0.470607\pi$
$569$	4.39910	0.184420	0.0922099	+	0.995740i	$0.470607\pi$
$570$	0.549471	0.0230148
$571$	−25.3632	−1.06142	−0.530708	−	0.847555i	$-0.678074\pi$
$571$	−25.3632	−1.06142	−0.530708	+	0.847555i	$0.678074\pi$
$572$	−3.59932	−0.150495
$573$	−8.28705	−0.346197
$574$	−21.2105	−0.885309
$575$	−40.9116	−1.70613
$576$	37.6952	1.57063
$577$	9.61388	0.400231	0.200115	−	0.979772i	$-0.435868\pi$
$577$	9.61388	0.400231	0.200115	+	0.979772i	$0.435868\pi$
$578$	0.249330	0.0103707
$579$	39.9823	1.66161
$580$	−4.20002	−0.174397
$581$	1.74046	0.0722064
$582$	−88.2421	−3.65775
$583$	0.591914	0.0245146
$584$	−65.1527	−2.69604
$585$	−0.341846	−0.0141336
$586$	−77.2302	−3.19035
$587$	4.30109	0.177525	0.0887625	−	0.996053i	$-0.471709\pi$
$587$	4.30109	0.177525	0.0887625	+	0.996053i	$0.471709\pi$
$588$	−11.9487	−0.492756
$589$	0.700542	0.0288654
$590$	−1.29061	−0.0531336
$591$	7.39769	0.304300
$592$	−23.2316	−0.954814
$593$	1.93282	0.0793715	0.0396857	−	0.999212i	$-0.487364\pi$
$593$	1.93282	0.0793715	0.0396857	+	0.999212i	$0.487364\pi$
$594$	2.15769	0.0885312
$595$	−0.659196	−0.0270244
$596$	82.0881	3.36246
$597$	31.8760	1.30460
$598$	−17.8619	−0.730426
$599$	3.89070	0.158970	0.0794848	−	0.996836i	$-0.474672\pi$
$599$	3.89070	0.158970	0.0794848	+	0.996836i	$0.474672\pi$
$600$	−95.2455	−3.88838
$601$	24.2303	0.988373	0.494186	−	0.869356i	$-0.335466\pi$
$601$	24.2303	0.988373	0.494186	+	0.869356i	$0.335466\pi$
$602$	2.86779	0.116882
$603$	33.9031	1.38064
$604$	−37.3304	−1.51895
$605$	1.64170	0.0667445
$606$	−60.1452	−2.44323
$607$	−9.10323	−0.369489	−0.184744	−	0.982787i	$-0.559146\pi$
$607$	−9.10323	−0.369489	−0.184744	+	0.982787i	$0.559146\pi$
$608$	7.64395	0.310003
$609$	−12.2916	−0.498080
$610$	1.82275	0.0738010
$611$	1.26029	0.0509859
$612$	54.0775	2.18595
$613$	−3.55619	−0.143633	−0.0718165	−	0.997418i	$-0.522880\pi$
$613$	−3.55619	−0.143633	−0.0718165	+	0.997418i	$0.522880\pi$
$614$	−83.7823	−3.38118
$615$	3.03315	0.122308
$616$	7.04995	0.284050
$617$	−18.4776	−0.743879	−0.371940	−	0.928257i	$-0.621307\pi$
$617$	−18.4776	−0.743879	−0.371940	+	0.928257i	$0.621307\pi$
$618$	90.5073	3.64074
$619$	−25.4725	−1.02383	−0.511913	−	0.859037i	$-0.671063\pi$
$619$	−25.4725	−1.02383	−0.511913	+	0.859037i	$0.671063\pi$
$620$	1.03940	0.0417432
$621$	7.66852	0.307727
$622$	4.70990	0.188850
$623$	4.18555	0.167691
$624$	−22.0325	−0.882008
$625$	24.6151	0.984605
$626$	13.6477	0.545472
$627$	−1.12557	−0.0449511
$628$	−13.4777	−0.537817
$629$	−8.39844	−0.334868
$630$	1.10914	0.0441893
$631$	48.9831	1.94999	0.974993	−	0.222234i	$-0.0713349\pi$
$631$	48.9831	1.94999	0.974993	+	0.222234i	$0.0713349\pi$
$632$	52.3470	2.08225
$633$	−42.5090	−1.68958
$634$	−47.9873	−1.90582
$635$	−2.47514	−0.0982228
$636$	8.11281	0.321694
$637$	0.818140	0.0324159
$638$	12.0134	0.475615
$639$	0.935899	0.0370236
$640$	1.66058	0.0656401
$641$	10.7418	0.424276	0.212138	−	0.977240i	$-0.431957\pi$
$641$	10.7418	0.424276	0.212138	+	0.977240i	$0.431957\pi$
$642$	79.7320	3.14677
$643$	−18.7523	−0.739517	−0.369758	−	0.929128i	$-0.620560\pi$
$643$	−18.7523	−0.739517	−0.369758	+	0.929128i	$0.620560\pi$
$644$	41.5049	1.63552
$645$	−0.410100	−0.0161477
$646$	5.95166	0.234165
$647$	21.1648	0.832073	0.416037	−	0.909348i	$-0.363419\pi$
$647$	21.1648	0.832073	0.416037	+	0.909348i	$0.363419\pi$
$648$	81.0809	3.18516
$649$	2.64378	0.103777
$650$	10.8030	0.423729
$651$	3.04185	0.119219
$652$	16.8656	0.660508
$653$	27.7865	1.08737	0.543685	−	0.839290i	$-0.317029\pi$
$653$	27.7865	1.08737	0.543685	+	0.839290i	$0.317029\pi$
$654$	116.473	4.55447
$655$	−3.49123	−0.136414
$656$	90.8800	3.54827
$657$	20.9973	0.819183
$658$	−4.08910	−0.159410
$659$	−31.5549	−1.22920	−0.614602	−	0.788838i	$-0.710683\pi$
$659$	−31.5549	−1.22920	−0.614602	+	0.788838i	$0.710683\pi$
$660$	−1.67002	−0.0650053
$661$	27.3255	1.06284	0.531420	−	0.847108i	$-0.321659\pi$
$661$	27.3255	1.06284	0.531420	+	0.847108i	$0.321659\pi$
$662$	46.1187	1.79245
$663$	−7.96497	−0.309334
$664$	−14.0748	−0.546208
$665$	0.0874228	0.00339011
$666$	14.1310	0.547564
$667$	42.6960	1.65320
$668$	−20.6085	−0.797367
$669$	8.40554	0.324977
$670$	5.53615	0.213880
$671$	−3.73385	−0.144144
$672$	33.1911	1.28037
$673$	−30.4742	−1.17469	−0.587347	−	0.809335i	$-0.699828\pi$
$673$	−30.4742	−1.17469	−0.587347	+	0.809335i	$0.699828\pi$
$674$	5.19461	0.200089
$675$	−4.63798	−0.178516
$676$	−62.2259	−2.39330
$677$	−5.51373	−0.211910	−0.105955	−	0.994371i	$-0.533790\pi$
$677$	−5.51373	−0.211910	−0.105955	+	0.994371i	$0.533790\pi$
$678$	30.1034	1.15611
$679$	−14.0397	−0.538792
$680$	5.33080	0.204427
$681$	−8.32865	−0.319155
$682$	−2.97300	−0.113842
$683$	−18.9400	−0.724720	−0.362360	−	0.932038i	$-0.618029\pi$
$683$	−18.9400	−0.724720	−0.362360	+	0.932038i	$0.618029\pi$
$684$	−7.17178	−0.274220
$685$	0.0248479	0.000949391 0
$686$	−2.65451	−0.101350
$687$	29.4753	1.12455
$688$	−12.2875	−0.468457
$689$	−0.555493	−0.0211626
$690$	−8.28757	−0.315502
$691$	26.8931	1.02306	0.511532	−	0.859264i	$-0.329078\pi$
$691$	26.8931	1.02306	0.511532	+	0.859264i	$0.329078\pi$
$692$	9.75242	0.370732
$693$	−2.27205	−0.0863080
$694$	42.7184	1.62157
$695$	2.87963	0.109231
$696$	99.4000	3.76775
$697$	32.8539	1.24443
$698$	−15.8251	−0.598988
$699$	21.0324	0.795520
$700$	−25.1025	−0.948786
$701$	−36.3110	−1.37145	−0.685724	−	0.727862i	$-0.740514\pi$
$701$	−36.3110	−1.37145	−0.685724	+	0.727862i	$0.740514\pi$
$702$	−2.02493	−0.0764260
$703$	1.11380	0.0420080
$704$	−12.6091	−0.475223
$705$	0.584751	0.0220230
$706$	−34.5332	−1.29967
$707$	−9.56933	−0.359892
$708$	36.2357	1.36182
$709$	16.3740	0.614940	0.307470	−	0.951558i	$-0.400518\pi$
$709$	16.3740	0.614940	0.307470	+	0.951558i	$0.400518\pi$
$710$	0.152826	0.00573546
$711$	−16.8703	−0.632687
$712$	−33.8478	−1.26850
$713$	−10.5662	−0.395706
$714$	25.8429	0.967146
$715$	0.114348	0.00427637
$716$	−54.7300	−2.04536
$717$	45.9384	1.71560
$718$	16.4188	0.612745
$719$	33.2297	1.23926	0.619630	−	0.784894i	$-0.287283\pi$
$719$	33.2297	1.23926	0.619630	+	0.784894i	$0.287283\pi$
$720$	−4.75231	−0.177108
$721$	14.4000	0.536286
$722$	49.6465	1.84765
$723$	42.8375	1.59314
$724$	−64.4130	−2.39389
$725$	−25.8229	−0.959038
$726$	−64.3605	−2.38864
$727$	−7.03577	−0.260942	−0.130471	−	0.991452i	$-0.541649\pi$
$727$	−7.03577	−0.260942	−0.130471	+	0.991452i	$0.541649\pi$
$728$	−6.61616	−0.245211
$729$	−19.5077	−0.722507
$730$	3.42872	0.126903
$731$	−4.44205	−0.164295
$732$	−51.1763	−1.89153
$733$	6.62622	0.244745	0.122372	−	0.992484i	$-0.460950\pi$
$733$	6.62622	0.244745	0.122372	+	0.992484i	$0.460950\pi$
$734$	80.3699	2.96651
$735$	0.379601	0.0140018
$736$	−115.292	−4.24973
$737$	−11.3406	−0.417738
$738$	−55.2791	−2.03485
$739$	44.0172	1.61920	0.809600	−	0.586982i	$-0.199684\pi$
$739$	44.0172	1.61920	0.809600	+	0.586982i	$0.199684\pi$
$740$	1.65256	0.0607491
$741$	1.05632	0.0388048
$742$	1.80234	0.0661659
$743$	−7.95982	−0.292017	−0.146009	−	0.989283i	$-0.546643\pi$
$743$	−7.95982	−0.292017	−0.146009	+	0.989283i	$0.546643\pi$
$744$	−24.5989	−0.901839
$745$	−2.60788	−0.0955454
$746$	17.5226	0.641548
$747$	4.53601	0.165964
$748$	−18.0890	−0.661399
$749$	12.6857	0.463524
$750$	10.0507	0.366999
$751$	−22.0631	−0.805094	−0.402547	−	0.915399i	$-0.631875\pi$
$751$	−22.0631	−0.805094	−0.402547	+	0.915399i	$0.631875\pi$
$752$	17.5204	0.638905
$753$	−9.35360	−0.340864
$754$	−11.2742	−0.410582
$755$	1.18596	0.0431616
$756$	4.70525	0.171128
$757$	51.8506	1.88454	0.942271	−	0.334850i	$-0.108686\pi$
$757$	51.8506	1.88454	0.942271	+	0.334850i	$0.108686\pi$
$758$	−79.0052	−2.86960
$759$	16.9768	0.616220
$760$	−0.706973	−0.0256446
$761$	5.39729	0.195652	0.0978258	−	0.995204i	$-0.468811\pi$
$761$	5.39729	0.195652	0.0978258	+	0.995204i	$0.468811\pi$
$762$	97.0344	3.51519
$763$	18.5314	0.670880
$764$	17.6624	0.639005
$765$	−1.71800	−0.0621146
$766$	22.9067	0.827654
$767$	−2.48110	−0.0895874
$768$	3.39138	0.122376
$769$	41.5476	1.49824	0.749122	−	0.662432i	$-0.230476\pi$
$769$	41.5476	1.49824	0.749122	+	0.662432i	$0.230476\pi$
$770$	−0.371010	−0.0133703
$771$	−6.89912	−0.248466
$772$	−85.2154	−3.06697
$773$	−46.4125	−1.66934	−0.834671	−	0.550749i	$-0.814342\pi$
$773$	−46.4125	−1.66934	−0.834671	+	0.550749i	$0.814342\pi$
$774$	7.47406	0.268650
$775$	6.39049	0.229553
$776$	113.536	4.07571
$777$	4.83629	0.173501
$778$	97.1935	3.48456
$779$	−4.35710	−0.156109
$780$	1.56726	0.0561169
$781$	−0.313059	−0.0112021
$782$	−89.7678	−3.21009
$783$	4.84028	0.172977
$784$	11.3737	0.406204
$785$	0.428176	0.0152823
$786$	136.869	4.88196
$787$	16.8877	0.601980	0.300990	−	0.953627i	$-0.402683\pi$
$787$	16.8877	0.601980	0.300990	+	0.953627i	$0.402683\pi$
$788$	−15.7669	−0.561673
$789$	26.8548	0.956055
$790$	−2.75481	−0.0980118
$791$	4.78955	0.170297
$792$	18.3737	0.652880
$793$	3.50410	0.124434
$794$	−40.6623	−1.44305
$795$	−0.257738	−0.00914103
$796$	−67.9384	−2.40801
$797$	−2.82269	−0.0999848	−0.0499924	−	0.998750i	$-0.515920\pi$
$797$	−2.82269	−0.0999848	−0.0499924	+	0.998750i	$0.515920\pi$
$798$	−3.42729	−0.121325
$799$	6.33380	0.224074
$800$	69.7297	2.46532
$801$	10.9084	0.385431
$802$	−0.647731	−0.0228722
$803$	−7.02363	−0.247859
$804$	−155.435	−5.48179
$805$	−1.31858	−0.0464739
$806$	2.79007	0.0982761
$807$	−6.01919	−0.211886
$808$	77.3855	2.72241
$809$	25.1135	0.882942	0.441471	−	0.897276i	$-0.354457\pi$
$809$	25.1135	0.882942	0.441471	+	0.897276i	$0.354457\pi$
$810$	−4.26696	−0.149926
$811$	4.49743	0.157926	0.0789631	−	0.996878i	$-0.474839\pi$
$811$	4.49743	0.157926	0.0789631	+	0.996878i	$0.474839\pi$
$812$	26.1974	0.919350
$813$	8.77479	0.307745
$814$	−4.72683	−0.165675
$815$	−0.535808	−0.0187685
$816$	−110.728	−3.87626
$817$	0.589106	0.0206102
$818$	−46.2238	−1.61618
$819$	2.13225	0.0745067
$820$	−6.46464	−0.225755
$821$	−23.7925	−0.830364	−0.415182	−	0.909738i	$-0.636282\pi$
$821$	−23.7925	−0.830364	−0.415182	+	0.909738i	$0.636282\pi$
$822$	−0.974130	−0.0339767
$823$	19.9148	0.694186	0.347093	−	0.937831i	$-0.387169\pi$
$823$	19.9148	0.694186	0.347093	+	0.937831i	$0.387169\pi$
$824$	−116.451	−4.05675
$825$	−10.2677	−0.357476
$826$	8.05011	0.280099
$827$	45.3978	1.57863	0.789317	−	0.613985i	$-0.210435\pi$
$827$	45.3978	1.57863	0.789317	+	0.613985i	$0.210435\pi$
$828$	108.171	3.75919
$829$	−33.5410	−1.16493	−0.582464	−	0.812857i	$-0.697911\pi$
$829$	−33.5410	−1.16493	−0.582464	+	0.812857i	$0.697911\pi$
$830$	0.740699	0.0257101
$831$	38.3480	1.33028
$832$	11.8332	0.410244
$833$	4.11170	0.142462
$834$	−112.892	−3.90914
$835$	0.654718	0.0226574
$836$	2.39897	0.0829701
$837$	−1.19784	−0.0414035
$838$	−64.6177	−2.23218
$839$	38.9873	1.34599	0.672996	−	0.739646i	$-0.265007\pi$
$839$	38.9873	1.34599	0.672996	+	0.739646i	$0.265007\pi$
$840$	−3.06977	−0.105917
$841$	−2.05076	−0.0707157
$842$	−32.5641	−1.12223
$843$	32.1957	1.10888
$844$	90.6006	3.11860
$845$	1.97687	0.0680065
$846$	−10.6571	−0.366398
$847$	−10.2400	−0.351850
$848$	−7.72241	−0.265189
$849$	21.7132	0.745193
$850$	54.2923	1.86221
$851$	−16.7993	−0.575873
$852$	−4.29081	−0.147001
$853$	−7.23337	−0.247666	−0.123833	−	0.992303i	$-0.539519\pi$
$853$	−7.23337	−0.247666	−0.123833	+	0.992303i	$0.539519\pi$
$854$	−11.3693	−0.389050
$855$	0.227842	0.00779205
$856$	−102.587	−3.50634
$857$	−37.1725	−1.26979	−0.634894	−	0.772599i	$-0.718956\pi$
$857$	−37.1725	−1.26979	−0.634894	+	0.772599i	$0.718956\pi$
$858$	−4.48286	−0.153042
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	0.874059	0.0298052
$861$	−18.9191	−0.644762
$862$	−30.1455	−1.02676
$863$	14.7733	0.502889	0.251444	−	0.967872i	$-0.419094\pi$
$863$	14.7733	0.502889	0.251444	+	0.967872i	$0.419094\pi$
$864$	−13.0702	−0.444658
$865$	−0.309828	−0.0105345
$866$	−69.1702	−2.35050
$867$	0.222394	0.00755290
$868$	−6.48318	−0.220054
$869$	5.64315	0.191431
$870$	−5.23102	−0.177348
$871$	10.6428	0.360619
$872$	−149.860	−5.07490
$873$	−36.5903	−1.23839
$874$	11.9050	0.402694
$875$	1.59910	0.0540594
$876$	−96.2663	−3.25254
$877$	42.6673	1.44077	0.720387	−	0.693572i	$-0.243964\pi$
$877$	42.6673	1.44077	0.720387	+	0.693572i	$0.243964\pi$
$878$	15.1330	0.510715
$879$	−68.8870	−2.32350
$880$	1.58965	0.0535873
$881$	22.1657	0.746782	0.373391	−	0.927674i	$-0.378195\pi$
$881$	22.1657	0.746782	0.373391	+	0.927674i	$0.378195\pi$
$882$	−6.91823	−0.232949
$883$	−5.95627	−0.200444	−0.100222	−	0.994965i	$-0.531955\pi$
$883$	−5.95627	−0.200444	−0.100222	+	0.994965i	$0.531955\pi$
$884$	16.9760	0.570964
$885$	−1.15118	−0.0386966
$886$	44.6667	1.50061
$887$	45.9360	1.54238	0.771190	−	0.636604i	$-0.219662\pi$
$887$	45.9360	1.54238	0.771190	+	0.636604i	$0.219662\pi$
$888$	−39.1102	−1.31245
$889$	15.4385	0.517792
$890$	1.78127	0.0597084
$891$	8.74074	0.292826
$892$	−17.9150	−0.599838
$893$	−0.839991	−0.0281092
$894$	102.239	3.41937
$895$	1.73873	0.0581195
$896$	−10.3578	−0.346029
$897$	−15.9322	−0.531962
$898$	26.3760	0.880179
$899$	−6.66924	−0.222431
$900$	−65.4225	−2.18075
$901$	−2.79172	−0.0930058
$902$	18.4909	0.615681
$903$	2.55798	0.0851242
$904$	−38.7323	−1.28822
$905$	2.04635	0.0680231
$906$	−46.4940	−1.54466
$907$	9.54805	0.317038	0.158519	−	0.987356i	$-0.449328\pi$
$907$	9.54805	0.317038	0.158519	+	0.987356i	$0.449328\pi$
$908$	17.7511	0.589091
$909$	−24.9397	−0.827198
$910$	0.348182	0.0115421
$911$	7.71705	0.255677	0.127839	−	0.991795i	$-0.459196\pi$
$911$	7.71705	0.255677	0.127839	+	0.991795i	$0.459196\pi$
$912$	14.6848	0.486263
$913$	−1.51730	−0.0502153
$914$	20.7299	0.685686
$915$	1.62584	0.0537485
$916$	−62.8215	−2.07568
$917$	21.7764	0.719119
$918$	−10.1766	−0.335878
$919$	46.0963	1.52058	0.760289	−	0.649585i	$-0.225057\pi$
$919$	46.0963	1.52058	0.760289	+	0.649585i	$0.225057\pi$
$920$	10.6632	0.351554
$921$	−74.7312	−2.46248
$922$	−53.7656	−1.77068
$923$	0.293797	0.00967044
$924$	10.4166	0.342683
$925$	10.1604	0.334071
$926$	−20.3464	−0.668623
$927$	37.5296	1.23263
$928$	−72.7712	−2.38883
$929$	34.2048	1.12222	0.561111	−	0.827740i	$-0.310374\pi$
$929$	34.2048	1.12222	0.561111	+	0.827740i	$0.310374\pi$
$930$	1.29454	0.0424497
$931$	−0.545295	−0.0178713
$932$	−44.8271	−1.46836
$933$	4.20108	0.137537
$934$	−85.5226	−2.79839
$935$	0.574675	0.0187939
$936$	−17.2431	−0.563609
$937$	−38.8829	−1.27025	−0.635125	−	0.772410i	$-0.719051\pi$
$937$	−38.8829	−1.27025	−0.635125	+	0.772410i	$0.719051\pi$
$938$	−34.5315	−1.12749
$939$	12.1733	0.397261
$940$	−1.24630	−0.0406497
$941$	−24.5173	−0.799241	−0.399620	−	0.916681i	$-0.630858\pi$
$941$	−24.5173	−0.799241	−0.399620	+	0.916681i	$0.630858\pi$
$942$	−16.7861	−0.546920
$943$	65.7174	2.14005
$944$	−34.4920	−1.12262
$945$	−0.149482	−0.00486266
$946$	−2.50009	−0.0812848
$947$	−44.4261	−1.44366	−0.721828	−	0.692073i	$-0.756698\pi$
$947$	−44.4261	−1.44366	−0.721828	+	0.692073i	$0.756698\pi$
$948$	77.3453	2.51206
$949$	6.59146	0.213968
$950$	−7.20026	−0.233607
$951$	−42.8031	−1.38799
$952$	−33.2506	−1.07766
$953$	−32.8599	−1.06444	−0.532218	−	0.846608i	$-0.678641\pi$
$953$	−32.8599	−1.06444	−0.532218	+	0.846608i	$0.678641\pi$
$954$	4.69727	0.152080
$955$	−0.561123	−0.0181575
$956$	−97.9100	−3.16664
$957$	10.7156	0.346386
$958$	−24.5400	−0.792850
$959$	−0.154988	−0.00500481
$960$	5.49040	0.177202
$961$	−29.3495	−0.946759
$962$	4.43599	0.143022
$963$	33.0615	1.06539
$964$	−91.3009	−2.94060
$965$	2.70723	0.0871489
$966$	51.6933	1.66320
$967$	30.7949	0.990297	0.495149	−	0.868808i	$-0.335114\pi$
$967$	30.7949	0.990297	0.495149	+	0.868808i	$0.335114\pi$
$968$	82.8091	2.66158
$969$	5.30870	0.170540
$970$	−5.97495	−0.191844
$971$	28.7419	0.922373	0.461186	−	0.887303i	$-0.347424\pi$
$971$	28.7419	0.922373	0.461186	+	0.887303i	$0.347424\pi$
$972$	105.685	3.38986
$973$	−17.9616	−0.575821
$974$	19.7665	0.633358
$975$	9.63594	0.308597
$976$	48.7137	1.55929
$977$	−42.6844	−1.36560	−0.682798	−	0.730607i	$-0.739237\pi$
$977$	−42.6844	−1.36560	−0.682798	+	0.730607i	$0.739237\pi$
$978$	21.0056	0.671687
$979$	−3.64889	−0.116619
$980$	−0.809056	−0.0258443
$981$	48.2966	1.54199
$982$	69.4625	2.21664
$983$	−9.12448	−0.291026	−0.145513	−	0.989356i	$-0.546483\pi$
$983$	−9.12448	−0.291026	−0.145513	+	0.989356i	$0.546483\pi$
$984$	152.996	4.87732
$985$	0.500904	0.0159601
$986$	−56.6604	−1.80443
$987$	−3.64735	−0.116097
$988$	−2.25136	−0.0716253
$989$	−8.88539	−0.282539
$990$	−0.966931	−0.0307311
$991$	25.9732	0.825067	0.412533	−	0.910943i	$-0.364644\pi$
$991$	25.9732	0.825067	0.412533	+	0.910943i	$0.364644\pi$
$992$	18.0090	0.571786
$993$	41.1364	1.30542
$994$	−0.953244	−0.0302351
$995$	2.15835	0.0684244
$996$	−20.7962	−0.658953
$997$	−33.7048	−1.06744	−0.533721	−	0.845661i	$-0.679207\pi$
$997$	−33.7048	−1.06744	−0.533721	+	0.845661i	$0.679207\pi$
$998$	−42.0039	−1.32961
$999$	−1.90447	−0.0602548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.e.1.3	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.e.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.65451 q^{2} -2.36774 q^{3} +5.04644 q^{4} -0.160322 q^{5} +6.28521 q^{6} +1.00000 q^{7} -8.08683 q^{8} +2.60621 q^{9} +O(q^{10})\)	\(q-2.65451 q^{2} -2.36774 q^{3} +5.04644 q^{4} -0.160322 q^{5} +6.28521 q^{6} +1.00000 q^{7} -8.08683 q^{8} +2.60621 q^{9} +0.425577 q^{10} -0.871782 q^{11} -11.9487 q^{12} +0.818140 q^{13} -2.65451 q^{14} +0.379601 q^{15} +11.3737 q^{16} +4.11170 q^{17} -6.91823 q^{18} -0.545295 q^{19} -0.809056 q^{20} -2.36774 q^{21} +2.31416 q^{22} +8.22459 q^{23} +19.1475 q^{24} -4.97430 q^{25} -2.17176 q^{26} +0.932389 q^{27} +5.04644 q^{28} +5.19127 q^{29} -1.00766 q^{30} -1.28470 q^{31} -14.0180 q^{32} +2.06416 q^{33} -10.9146 q^{34} -0.160322 q^{35} +13.1521 q^{36} -2.04257 q^{37} +1.44749 q^{38} -1.93715 q^{39} +1.29650 q^{40} +7.99035 q^{41} +6.28521 q^{42} -1.08034 q^{43} -4.39940 q^{44} -0.417833 q^{45} -21.8323 q^{46} +1.54043 q^{47} -26.9300 q^{48} +1.00000 q^{49} +13.2043 q^{50} -9.73545 q^{51} +4.12870 q^{52} -0.678971 q^{53} -2.47504 q^{54} +0.139766 q^{55} -8.08683 q^{56} +1.29112 q^{57} -13.7803 q^{58} -3.03261 q^{59} +1.91564 q^{60} +4.28301 q^{61} +3.41026 q^{62} +2.60621 q^{63} +14.4636 q^{64} -0.131166 q^{65} -5.47933 q^{66} +13.0086 q^{67} +20.7495 q^{68} -19.4737 q^{69} +0.425577 q^{70} +0.359103 q^{71} -21.0760 q^{72} +8.05664 q^{73} +5.42204 q^{74} +11.7779 q^{75} -2.75180 q^{76} -0.871782 q^{77} +5.14218 q^{78} -6.47312 q^{79} -1.82346 q^{80} -10.0263 q^{81} -21.2105 q^{82} +1.74046 q^{83} -11.9487 q^{84} -0.659196 q^{85} +2.86779 q^{86} -12.2916 q^{87} +7.04995 q^{88} +4.18555 q^{89} +1.10914 q^{90} +0.818140 q^{91} +41.5049 q^{92} +3.04185 q^{93} -4.08910 q^{94} +0.0874228 q^{95} +33.1911 q^{96} -14.0397 q^{97} -2.65451 q^{98} -2.27205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9}+O(q^{10}) \) 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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