LMFDB - Embedded newform 6017.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.43520 q^{2} -0.763891 q^{3} +3.93019 q^{4} +1.56797 q^{5} +1.86023 q^{6} +2.19104 q^{7} -4.70040 q^{8} -2.41647 q^{9} +O(q^{10})$	\(q-2.43520 q^{2} -0.763891 q^{3} +3.93019 q^{4} +1.56797 q^{5} +1.86023 q^{6} +2.19104 q^{7} -4.70040 q^{8} -2.41647 q^{9} -3.81832 q^{10} +1.00000 q^{11} -3.00224 q^{12} +2.36121 q^{13} -5.33563 q^{14} -1.19776 q^{15} +3.58603 q^{16} -7.19121 q^{17} +5.88459 q^{18} -5.00968 q^{19} +6.16243 q^{20} -1.67372 q^{21} -2.43520 q^{22} +5.48829 q^{23} +3.59060 q^{24} -2.54147 q^{25} -5.75002 q^{26} +4.13759 q^{27} +8.61122 q^{28} +3.08689 q^{29} +2.91678 q^{30} +0.979432 q^{31} +0.668107 q^{32} -0.763891 q^{33} +17.5120 q^{34} +3.43549 q^{35} -9.49720 q^{36} -10.5213 q^{37} +12.1996 q^{38} -1.80371 q^{39} -7.37010 q^{40} -6.32400 q^{41} +4.07584 q^{42} +12.6521 q^{43} +3.93019 q^{44} -3.78896 q^{45} -13.3651 q^{46} +8.78320 q^{47} -2.73934 q^{48} -2.19933 q^{49} +6.18898 q^{50} +5.49330 q^{51} +9.28002 q^{52} -0.712147 q^{53} -10.0759 q^{54} +1.56797 q^{55} -10.2988 q^{56} +3.82685 q^{57} -7.51719 q^{58} +5.94876 q^{59} -4.70742 q^{60} -8.95486 q^{61} -2.38511 q^{62} -5.29459 q^{63} -8.79904 q^{64} +3.70231 q^{65} +1.86023 q^{66} +15.3258 q^{67} -28.2628 q^{68} -4.19245 q^{69} -8.36611 q^{70} +10.1508 q^{71} +11.3584 q^{72} +5.23097 q^{73} +25.6214 q^{74} +1.94140 q^{75} -19.6890 q^{76} +2.19104 q^{77} +4.39239 q^{78} -2.02337 q^{79} +5.62280 q^{80} +4.08874 q^{81} +15.4002 q^{82} -10.2756 q^{83} -6.57803 q^{84} -11.2756 q^{85} -30.8105 q^{86} -2.35805 q^{87} -4.70040 q^{88} -9.97324 q^{89} +9.22686 q^{90} +5.17352 q^{91} +21.5700 q^{92} -0.748179 q^{93} -21.3888 q^{94} -7.85503 q^{95} -0.510361 q^{96} -9.49463 q^{97} +5.35580 q^{98} -2.41647 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * 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 $

$2$	−2.43520	−1.72195	−0.860973	−	0.508651i	$-0.830144\pi$
$2$	−2.43520	−1.72195	−0.860973	+	0.508651i	$0.830144\pi$
$3$	−0.763891	−0.441033	−0.220516	−	0.975383i	$-0.570774\pi$
$3$	−0.763891	−0.441033	−0.220516	+	0.975383i	$0.570774\pi$
$4$	3.93019	1.96510
$5$	1.56797	0.701218	0.350609	−	0.936522i	$-0.385975\pi$
$5$	1.56797	0.701218	0.350609	+	0.936522i	$0.385975\pi$
$6$	1.86023	0.759434
$7$	2.19104	0.828136	0.414068	−	0.910246i	$-0.364107\pi$
$7$	2.19104	0.828136	0.414068	+	0.910246i	$0.364107\pi$
$8$	−4.70040	−1.66184
$9$	−2.41647	−0.805490
$10$	−3.81832	−1.20746
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.00224	−0.866672
$13$	2.36121	0.654883	0.327441	−	0.944872i	$-0.393814\pi$
$13$	2.36121	0.654883	0.327441	+	0.944872i	$0.393814\pi$
$14$	−5.33563	−1.42601
$15$	−1.19776	−0.309260
$16$	3.58603	0.896508
$17$	−7.19121	−1.74412	−0.872062	−	0.489395i	$-0.837218\pi$
$17$	−7.19121	−1.74412	−0.872062	+	0.489395i	$0.837218\pi$
$18$	5.88459	1.38701
$19$	−5.00968	−1.14930	−0.574650	−	0.818400i	$-0.694862\pi$
$19$	−5.00968	−1.14930	−0.574650	+	0.818400i	$0.694862\pi$
$20$	6.16243	1.37796
$21$	−1.67372	−0.365235
$22$	−2.43520	−0.519186
$23$	5.48829	1.14439	0.572194	−	0.820119i	$-0.306093\pi$
$23$	5.48829	1.14439	0.572194	+	0.820119i	$0.306093\pi$
$24$	3.59060	0.732927
$25$	−2.54147	−0.508293
$26$	−5.75002	−1.12767
$27$	4.13759	0.796280
$28$	8.61122	1.62737
$29$	3.08689	0.573221	0.286610	−	0.958047i	$-0.407471\pi$
$29$	3.08689	0.573221	0.286610	+	0.958047i	$0.407471\pi$
$30$	2.91678	0.532529
$31$	0.979432	0.175911	0.0879556	−	0.996124i	$-0.471967\pi$
$31$	0.979432	0.175911	0.0879556	+	0.996124i	$0.471967\pi$
$32$	0.668107	0.118106
$33$	−0.763891	−0.132976
$34$	17.5120	3.00329
$35$	3.43549	0.580704
$36$	−9.49720	−1.58287
$37$	−10.5213	−1.72968	−0.864842	−	0.502043i	$-0.832582\pi$
$37$	−10.5213	−1.72968	−0.864842	+	0.502043i	$0.832582\pi$
$38$	12.1996	1.97903
$39$	−1.80371	−0.288825
$40$	−7.37010	−1.16531
$41$	−6.32400	−0.987643	−0.493821	−	0.869563i	$-0.664400\pi$
$41$	−6.32400	−0.987643	−0.493821	+	0.869563i	$0.664400\pi$
$42$	4.07584	0.628915
$43$	12.6521	1.92943	0.964717	−	0.263289i	$-0.0848072\pi$
$43$	12.6521	1.92943	0.964717	+	0.263289i	$0.0848072\pi$
$44$	3.93019	0.592499
$45$	−3.78896	−0.564824
$46$	−13.3651	−1.97057
$47$	8.78320	1.28116	0.640580	−	0.767891i	$-0.278694\pi$
$47$	8.78320	1.28116	0.640580	+	0.767891i	$0.278694\pi$
$48$	−2.73934	−0.395389
$49$	−2.19933	−0.314190
$50$	6.18898	0.875253
$51$	5.49330	0.769216
$52$	9.28002	1.28691
$53$	−0.712147	−0.0978209	−0.0489105	−	0.998803i	$-0.515575\pi$
$53$	−0.712147	−0.0978209	−0.0489105	+	0.998803i	$0.515575\pi$
$54$	−10.0759	−1.37115
$55$	1.56797	0.211425
$56$	−10.2988	−1.37623
$57$	3.82685	0.506878
$58$	−7.51719	−0.987055
$59$	5.94876	0.774462	0.387231	−	0.921983i	$-0.373432\pi$
$59$	5.94876	0.774462	0.387231	+	0.921983i	$0.373432\pi$
$60$	−4.70742	−0.607726
$61$	−8.95486	−1.14655	−0.573276	−	0.819362i	$-0.694328\pi$
$61$	−8.95486	−1.14655	−0.573276	+	0.819362i	$0.694328\pi$
$62$	−2.38511	−0.302910
$63$	−5.29459	−0.667056
$64$	−8.79904	−1.09988
$65$	3.70231	0.459215
$66$	1.86023	0.228978
$67$	15.3258	1.87234	0.936172	−	0.351544i	$-0.114343\pi$
$67$	15.3258	1.87234	0.936172	+	0.351544i	$0.114343\pi$
$68$	−28.2628	−3.42737
$69$	−4.19245	−0.504712
$70$	−8.36611	−0.999941
$71$	10.1508	1.20468	0.602340	−	0.798240i	$-0.294235\pi$
$71$	10.1508	1.20468	0.602340	+	0.798240i	$0.294235\pi$
$72$	11.3584	1.33860
$73$	5.23097	0.612238	0.306119	−	0.951993i	$-0.400969\pi$
$73$	5.23097	0.612238	0.306119	+	0.951993i	$0.400969\pi$
$74$	25.6214	2.97842
$75$	1.94140	0.224174
$76$	−19.6890	−2.25848
$77$	2.19104	0.249693
$78$	4.39239	0.497340
$79$	−2.02337	−0.227647	−0.113824	−	0.993501i	$-0.536310\pi$
$79$	−2.02337	−0.227647	−0.113824	+	0.993501i	$0.536310\pi$
$80$	5.62280	0.628648
$81$	4.08874	0.454305
$82$	15.4002	1.70067
$83$	−10.2756	−1.12789	−0.563946	−	0.825812i	$-0.690717\pi$
$83$	−10.2756	−1.12789	−0.563946	+	0.825812i	$0.690717\pi$
$84$	−6.57803	−0.717722
$85$	−11.2756	−1.22301
$86$	−30.8105	−3.32238
$87$	−2.35805	−0.252809
$88$	−4.70040	−0.501065
$89$	−9.97324	−1.05716	−0.528581	−	0.848883i	$-0.677276\pi$
$89$	−9.97324	−1.05716	−0.528581	+	0.848883i	$0.677276\pi$
$90$	9.22686	0.972597
$91$	5.17352	0.542332
$92$	21.5700	2.24883
$93$	−0.748179	−0.0775826
$94$	−21.3888	−2.20609
$95$	−7.85503	−0.805909
$96$	−0.510361	−0.0520885
$97$	−9.49463	−0.964034	−0.482017	−	0.876162i	$-0.660096\pi$
$97$	−9.49463	−0.964034	−0.482017	+	0.876162i	$0.660096\pi$
$98$	5.35580	0.541018
$99$	−2.41647	−0.242864
$100$	−9.98845	−0.998845
$101$	−5.22934	−0.520339	−0.260169	−	0.965563i	$-0.583778\pi$
$101$	−5.22934	−0.520339	−0.260169	+	0.965563i	$0.583778\pi$
$102$	−13.3773	−1.32455
$103$	−14.4770	−1.42646	−0.713231	−	0.700929i	$-0.752769\pi$
$103$	−14.4770	−1.42646	−0.713231	+	0.700929i	$0.752769\pi$
$104$	−11.0987	−1.08831
$105$	−2.62434	−0.256109
$106$	1.73422	0.168442
$107$	−5.54375	−0.535935	−0.267967	−	0.963428i	$-0.586352\pi$
$107$	−5.54375	−0.535935	−0.267967	+	0.963428i	$0.586352\pi$
$108$	16.2615	1.56477
$109$	3.82204	0.366085	0.183043	−	0.983105i	$-0.441405\pi$
$109$	3.82204	0.366085	0.183043	+	0.983105i	$0.441405\pi$
$110$	−3.81832	−0.364063
$111$	8.03710	0.762847
$112$	7.85715	0.742431
$113$	−4.62935	−0.435493	−0.217746	−	0.976005i	$-0.569871\pi$
$113$	−4.62935	−0.435493	−0.217746	+	0.976005i	$0.569871\pi$
$114$	−9.31914	−0.872817
$115$	8.60548	0.802465
$116$	12.1321	1.12643
$117$	−5.70580	−0.527501
$118$	−14.4864	−1.33358
$119$	−15.7563	−1.44437
$120$	5.62995	0.513942
$121$	1.00000	0.0909091
$122$	21.8069	1.97430
$123$	4.83084	0.435583
$124$	3.84936	0.345683
$125$	−11.8248	−1.05764
$126$	12.8934	1.14863
$127$	−14.0517	−1.24689	−0.623446	−	0.781867i	$-0.714268\pi$
$127$	−14.0517	−1.24689	−0.623446	+	0.781867i	$0.714268\pi$
$128$	20.0912	1.77583
$129$	−9.66486	−0.850943
$130$	−9.01587	−0.790744
$131$	12.8505	1.12276	0.561378	−	0.827560i	$-0.310272\pi$
$131$	12.8505	1.12276	0.561378	+	0.827560i	$0.310272\pi$
$132$	−3.00224	−0.261311
$133$	−10.9764	−0.951777
$134$	−37.3213	−3.22407
$135$	6.48763	0.558366
$136$	33.8016	2.89846
$137$	11.4305	0.976576	0.488288	−	0.872683i	$-0.337622\pi$
$137$	11.4305	0.976576	0.488288	+	0.872683i	$0.337622\pi$
$138$	10.2095	0.869087
$139$	−16.1763	−1.37206	−0.686028	−	0.727575i	$-0.740647\pi$
$139$	−16.1763	−1.37206	−0.686028	+	0.727575i	$0.740647\pi$
$140$	13.5021	1.14114
$141$	−6.70940	−0.565034
$142$	−24.7192	−2.07439
$143$	2.36121	0.197455
$144$	−8.66554	−0.722129
$145$	4.84015	0.401953
$146$	−12.7384	−1.05424
$147$	1.68005	0.138568
$148$	−41.3506	−3.39900
$149$	7.67056	0.628396	0.314198	−	0.949357i	$-0.398264\pi$
$149$	7.67056	0.628396	0.314198	+	0.949357i	$0.398264\pi$
$150$	−4.72770	−0.386015
$151$	12.8964	1.04950	0.524748	−	0.851258i	$-0.324160\pi$
$151$	12.8964	1.04950	0.524748	+	0.851258i	$0.324160\pi$
$152$	23.5475	1.90996
$153$	17.3774	1.40488
$154$	−5.33563	−0.429957
$155$	1.53572	0.123352
$156$	−7.08892	−0.567568
$157$	−20.5437	−1.63956	−0.819782	−	0.572676i	$-0.805905\pi$
$157$	−20.5437	−1.63956	−0.819782	+	0.572676i	$0.805905\pi$
$158$	4.92731	0.391996
$159$	0.544003	0.0431422
$160$	1.04757	0.0828179
$161$	12.0251	0.947709
$162$	−9.95690	−0.782288
$163$	−16.4075	−1.28514	−0.642569	−	0.766228i	$-0.722131\pi$
$163$	−16.4075	−1.28514	−0.642569	+	0.766228i	$0.722131\pi$
$164$	−24.8545	−1.94081
$165$	−1.19776	−0.0932454
$166$	25.0231	1.94217
$167$	−16.4271	−1.27117	−0.635584	−	0.772032i	$-0.719240\pi$
$167$	−16.4271	−1.27117	−0.635584	+	0.772032i	$0.719240\pi$
$168$	7.86715	0.606964
$169$	−7.42468	−0.571129
$170$	27.4584	2.10596
$171$	12.1057	0.925749
$172$	49.7254	3.79152
$173$	15.9620	1.21357	0.606783	−	0.794867i	$-0.292460\pi$
$173$	15.9620	1.21357	0.606783	+	0.794867i	$0.292460\pi$
$174$	5.74231	0.435323
$175$	−5.56846	−0.420936
$176$	3.58603	0.270307
$177$	−4.54420	−0.341563
$178$	24.2868	1.82037
$179$	6.85535	0.512393	0.256197	−	0.966625i	$-0.417531\pi$
$179$	6.85535	0.512393	0.256197	+	0.966625i	$0.417531\pi$
$180$	−14.8913	−1.10993
$181$	−8.42470	−0.626203	−0.313101	−	0.949720i	$-0.601368\pi$
$181$	−8.42470	−0.626203	−0.313101	+	0.949720i	$0.601368\pi$
$182$	−12.5985	−0.933866
$183$	6.84054	0.505667
$184$	−25.7972	−1.90179
$185$	−16.4970	−1.21289
$186$	1.82197	0.133593
$187$	−7.19121	−0.525873
$188$	34.5197	2.51761
$189$	9.06564	0.659429
$190$	19.1286	1.38773
$191$	25.0042	1.80924	0.904621	−	0.426217i	$-0.140154\pi$
$191$	25.0042	1.80924	0.904621	+	0.426217i	$0.140154\pi$
$192$	6.72150	0.485083
$193$	−4.22340	−0.304007	−0.152003	−	0.988380i	$-0.548572\pi$
$193$	−4.22340	−0.304007	−0.152003	+	0.988380i	$0.548572\pi$
$194$	23.1213	1.66001
$195$	−2.82816	−0.202529
$196$	−8.64379	−0.617414
$197$	−10.9462	−0.779881	−0.389941	−	0.920840i	$-0.627504\pi$
$197$	−10.9462	−0.779881	−0.389941	+	0.920840i	$0.627504\pi$
$198$	5.88459	0.418199
$199$	11.5026	0.815397	0.407698	−	0.913117i	$-0.366332\pi$
$199$	11.5026	0.815397	0.407698	+	0.913117i	$0.366332\pi$
$200$	11.9459	0.844704
$201$	−11.7072	−0.825764
$202$	12.7345	0.895995
$203$	6.76350	0.474705
$204$	21.5897	1.51158
$205$	−9.91585	−0.692553
$206$	35.2544	2.45629
$207$	−13.2623	−0.921793
$208$	8.46738	0.587107
$209$	−5.00968	−0.346527
$210$	6.39079	0.441007
$211$	−10.5438	−0.725868	−0.362934	−	0.931815i	$-0.618225\pi$
$211$	−10.5438	−0.725868	−0.362934	+	0.931815i	$0.618225\pi$
$212$	−2.79888	−0.192228
$213$	−7.75411	−0.531303
$214$	13.5001	0.922851
$215$	19.8382	1.35295
$216$	−19.4484	−1.32329
$217$	2.14598	0.145679
$218$	−9.30743	−0.630379
$219$	−3.99589	−0.270017
$220$	6.16243	0.415471
$221$	−16.9800	−1.14220
$222$	−19.5719	−1.31358
$223$	−2.22968	−0.149310	−0.0746552	−	0.997209i	$-0.523786\pi$
$223$	−2.22968	−0.149310	−0.0746552	+	0.997209i	$0.523786\pi$
$224$	1.46385	0.0978077
$225$	6.14138	0.409425
$226$	11.2734	0.749895
$227$	−20.4542	−1.35759	−0.678797	−	0.734326i	$-0.737498\pi$
$227$	−20.4542	−1.35759	−0.678797	+	0.734326i	$0.737498\pi$
$228$	15.0403	0.996065
$229$	0.879388	0.0581116	0.0290558	−	0.999578i	$-0.490750\pi$
$229$	0.879388	0.0581116	0.0290558	+	0.999578i	$0.490750\pi$
$230$	−20.9561	−1.38180
$231$	−1.67372	−0.110123
$232$	−14.5096	−0.952603
$233$	−15.6972	−1.02836	−0.514179	−	0.857683i	$-0.671903\pi$
$233$	−15.6972	−1.02836	−0.514179	+	0.857683i	$0.671903\pi$
$234$	13.8948	0.908329
$235$	13.7718	0.898373
$236$	23.3798	1.52189
$237$	1.54564	0.100400
$238$	38.3696	2.48713
$239$	−25.8453	−1.67179	−0.835897	−	0.548887i	$-0.815052\pi$
$239$	−25.8453	−1.67179	−0.835897	+	0.548887i	$0.815052\pi$
$240$	−4.29520	−0.277254
$241$	−7.20437	−0.464074	−0.232037	−	0.972707i	$-0.574539\pi$
$241$	−7.20437	−0.464074	−0.232037	+	0.972707i	$0.574539\pi$
$242$	−2.43520	−0.156541
$243$	−15.5361	−0.996643
$244$	−35.1943	−2.25309
$245$	−3.44849	−0.220316
$246$	−11.7641	−0.750050
$247$	−11.8289	−0.752656
$248$	−4.60373	−0.292337
$249$	7.84943	0.497437
$250$	28.7957	1.82120
$251$	17.5250	1.10617	0.553083	−	0.833126i	$-0.313451\pi$
$251$	17.5250	1.10617	0.553083	+	0.833126i	$0.313451\pi$
$252$	−20.8088	−1.31083
$253$	5.48829	0.345046
$254$	34.2188	2.14708
$255$	8.61334	0.539388
$256$	−31.3280	−1.95800
$257$	10.3216	0.643842	0.321921	−	0.946766i	$-0.395671\pi$
$257$	10.3216	0.643842	0.321921	+	0.946766i	$0.395671\pi$
$258$	23.5359	1.46528
$259$	−23.0525	−1.43242
$260$	14.5508	0.902403
$261$	−7.45937	−0.461724
$262$	−31.2936	−1.93332
$263$	24.7141	1.52394	0.761970	−	0.647612i	$-0.224232\pi$
$263$	24.7141	1.52394	0.761970	+	0.647612i	$0.224232\pi$
$264$	3.59060	0.220986
$265$	−1.11663	−0.0685938
$266$	26.7298	1.63891
$267$	7.61846	0.466242
$268$	60.2333	3.67933
$269$	−15.2288	−0.928518	−0.464259	−	0.885700i	$-0.653679\pi$
$269$	−15.2288	−0.928518	−0.464259	+	0.885700i	$0.653679\pi$
$270$	−15.7987	−0.961476
$271$	9.43014	0.572840	0.286420	−	0.958104i	$-0.407535\pi$
$271$	9.43014	0.572840	0.286420	+	0.958104i	$0.407535\pi$
$272$	−25.7879	−1.56362
$273$	−3.95200	−0.239186
$274$	−27.8356	−1.68161
$275$	−2.54147	−0.153256
$276$	−16.4772	−0.991808
$277$	−7.19599	−0.432365	−0.216183	−	0.976353i	$-0.569361\pi$
$277$	−7.19599	−0.432365	−0.216183	+	0.976353i	$0.569361\pi$
$278$	39.3925	2.36260
$279$	−2.36677	−0.141695
$280$	−16.1482	−0.965040
$281$	20.3404	1.21341	0.606703	−	0.794929i	$-0.292492\pi$
$281$	20.3404	1.21341	0.606703	+	0.794929i	$0.292492\pi$
$282$	16.3387	0.972957
$283$	7.22134	0.429264	0.214632	−	0.976695i	$-0.431145\pi$
$283$	7.22134	0.429264	0.214632	+	0.976695i	$0.431145\pi$
$284$	39.8947	2.36731
$285$	6.00039	0.355432
$286$	−5.75002	−0.340006
$287$	−13.8562	−0.817903
$288$	−1.61446	−0.0951330
$289$	34.7135	2.04197
$290$	−11.7867	−0.692141
$291$	7.25286	0.425170
$292$	20.5587	1.20311
$293$	−17.8132	−1.04066	−0.520330	−	0.853965i	$-0.674191\pi$
$293$	−17.8132	−1.04066	−0.520330	+	0.853965i	$0.674191\pi$
$294$	−4.09125	−0.238607
$295$	9.32748	0.543067
$296$	49.4542	2.87447
$297$	4.13759	0.240087
$298$	−18.6793	−1.08206
$299$	12.9590	0.749439
$300$	7.63009	0.440523
$301$	27.7214	1.59783
$302$	−31.4053	−1.80717
$303$	3.99464	0.229486
$304$	−17.9649	−1.03036
$305$	−14.0410	−0.803983
$306$	−42.3173	−2.41912
$307$	−10.3194	−0.588960	−0.294480	−	0.955658i	$-0.595146\pi$
$307$	−10.3194	−0.588960	−0.294480	+	0.955658i	$0.595146\pi$
$308$	8.61122	0.490670
$309$	11.0588	0.629116
$310$	−3.73979	−0.212406
$311$	−21.5717	−1.22322	−0.611609	−	0.791160i	$-0.709477\pi$
$311$	−21.5717	−1.22322	−0.611609	+	0.791160i	$0.709477\pi$
$312$	8.47816	0.479981
$313$	1.96689	0.111175	0.0555877	−	0.998454i	$-0.482297\pi$
$313$	1.96689	0.111175	0.0555877	+	0.998454i	$0.482297\pi$
$314$	50.0279	2.82324
$315$	−8.30177	−0.467752
$316$	−7.95224	−0.447349
$317$	27.5855	1.54936	0.774679	−	0.632355i	$-0.217911\pi$
$317$	27.5855	1.54936	0.774679	+	0.632355i	$0.217911\pi$
$318$	−1.32475	−0.0742885
$319$	3.08689	0.172833
$320$	−13.7966	−0.771255
$321$	4.23482	0.236365
$322$	−29.2835	−1.63190
$323$	36.0257	2.00452
$324$	16.0695	0.892753
$325$	−6.00094	−0.332872
$326$	39.9556	2.21294
$327$	−2.91962	−0.161456
$328$	29.7253	1.64131
$329$	19.2444	1.06098
$330$	2.91678	0.160564
$331$	−0.589243	−0.0323877	−0.0161939	−	0.999869i	$-0.505155\pi$
$331$	−0.589243	−0.0323877	−0.0161939	+	0.999869i	$0.505155\pi$
$332$	−40.3850	−2.21642
$333$	25.4243	1.39324
$334$	40.0033	2.18888
$335$	24.0304	1.31292
$336$	−6.00201	−0.327436
$337$	−26.7165	−1.45534	−0.727669	−	0.685928i	$-0.759396\pi$
$337$	−26.7165	−1.45534	−0.727669	+	0.685928i	$0.759396\pi$
$338$	18.0806	0.983453
$339$	3.53632	0.192066
$340$	−44.3153	−2.40334
$341$	0.979432	0.0530392
$342$	−29.4799	−1.59409
$343$	−20.1561	−1.08833
$344$	−59.4702	−3.20642
$345$	−6.57365	−0.353913
$346$	−38.8706	−2.08970
$347$	−15.0308	−0.806893	−0.403447	−	0.915003i	$-0.632188\pi$
$347$	−15.0308	−0.806893	−0.403447	+	0.915003i	$0.632188\pi$
$348$	−9.26757	−0.496794
$349$	−21.4996	−1.15085	−0.575423	−	0.817856i	$-0.695162\pi$
$349$	−21.4996	−1.15085	−0.575423	+	0.817856i	$0.695162\pi$
$350$	13.5603	0.724829
$351$	9.76974	0.521470
$352$	0.668107	0.0356102
$353$	−4.39168	−0.233746	−0.116873	−	0.993147i	$-0.537287\pi$
$353$	−4.39168	−0.233746	−0.116873	+	0.993147i	$0.537287\pi$
$354$	11.0660	0.588153
$355$	15.9162	0.844743
$356$	−39.1967	−2.07742
$357$	12.0361	0.637016
$358$	−16.6941	−0.882313
$359$	−26.7658	−1.41265	−0.706323	−	0.707889i	$-0.749648\pi$
$359$	−26.7658	−1.41265	−0.706323	+	0.707889i	$0.749648\pi$
$360$	17.8096	0.938650
$361$	6.09689	0.320889
$362$	20.5158	1.07829
$363$	−0.763891	−0.0400939
$364$	20.3329	1.06574
$365$	8.20201	0.429313
$366$	−16.6581	−0.870731
$367$	4.48215	0.233966	0.116983	−	0.993134i	$-0.462678\pi$
$367$	4.48215	0.233966	0.116983	+	0.993134i	$0.462678\pi$
$368$	19.6812	1.02595
$369$	15.2818	0.795536
$370$	40.1736	2.08852
$371$	−1.56034	−0.0810091
$372$	−2.94049	−0.152457
$373$	21.9987	1.13905	0.569524	−	0.821975i	$-0.307128\pi$
$373$	21.9987	1.13905	0.569524	+	0.821975i	$0.307128\pi$
$374$	17.5120	0.905525
$375$	9.03286	0.466455
$376$	−41.2846	−2.12909
$377$	7.28880	0.375392
$378$	−22.0766	−1.13550
$379$	−3.88775	−0.199700	−0.0998502	−	0.995002i	$-0.531836\pi$
$379$	−3.88775	−0.199700	−0.0998502	+	0.995002i	$0.531836\pi$
$380$	−30.8718	−1.58369
$381$	10.7340	0.549920
$382$	−60.8903	−3.11542
$383$	6.79431	0.347173	0.173587	−	0.984819i	$-0.444464\pi$
$383$	6.79431	0.347173	0.173587	+	0.984819i	$0.444464\pi$
$384$	−15.3475	−0.783198
$385$	3.43549	0.175089
$386$	10.2848	0.523483
$387$	−30.5735	−1.55414
$388$	−37.3157	−1.89442
$389$	24.9260	1.26380	0.631899	−	0.775051i	$-0.282276\pi$
$389$	24.9260	1.26380	0.631899	+	0.775051i	$0.282276\pi$
$390$	6.88714	0.348744
$391$	−39.4674	−1.99595
$392$	10.3377	0.522135
$393$	−9.81640	−0.495172
$394$	26.6561	1.34291
$395$	−3.17259	−0.159630
$396$	−9.49720	−0.477252
$397$	7.15999	0.359349	0.179675	−	0.983726i	$-0.442495\pi$
$397$	7.15999	0.359349	0.179675	+	0.983726i	$0.442495\pi$
$398$	−28.0111	−1.40407
$399$	8.38479	0.419765
$400$	−9.11378	−0.455689
$401$	3.12648	0.156129	0.0780645	−	0.996948i	$-0.475126\pi$
$401$	3.12648	0.156129	0.0780645	+	0.996948i	$0.475126\pi$
$402$	28.5094	1.42192
$403$	2.31265	0.115201
$404$	−20.5523	−1.02252
$405$	6.41103	0.318567
$406$	−16.4705	−0.817416
$407$	−10.5213	−0.521520
$408$	−25.8207	−1.27832
$409$	27.6544	1.36742	0.683711	−	0.729753i	$-0.260365\pi$
$409$	27.6544	1.36742	0.683711	+	0.729753i	$0.260365\pi$
$410$	24.1471	1.19254
$411$	−8.73167	−0.430702
$412$	−56.8974	−2.80313
$413$	13.0340	0.641360
$414$	32.2963	1.58728
$415$	−16.1118	−0.790898
$416$	1.57754	0.0773454
$417$	12.3569	0.605121
$418$	12.1996	0.596700
$419$	7.58206	0.370408	0.185204	−	0.982700i	$-0.440705\pi$
$419$	7.58206	0.370408	0.185204	+	0.982700i	$0.440705\pi$
$420$	−10.3142	−0.503280
$421$	0.627076	0.0305618	0.0152809	−	0.999883i	$-0.495136\pi$
$421$	0.627076	0.0305618	0.0152809	+	0.999883i	$0.495136\pi$
$422$	25.6763	1.24990
$423$	−21.2243	−1.03196
$424$	3.34738	0.162563
$425$	18.2762	0.886527
$426$	18.8828	0.914875
$427$	−19.6205	−0.949502
$428$	−21.7880	−1.05316
$429$	−1.80371	−0.0870839
$430$	−48.3100	−2.32971
$431$	38.8000	1.86893	0.934465	−	0.356054i	$-0.115878\pi$
$431$	38.8000	1.86893	0.934465	+	0.356054i	$0.115878\pi$
$432$	14.8375	0.713872
$433$	−13.6308	−0.655056	−0.327528	−	0.944842i	$-0.606216\pi$
$433$	−13.6308	−0.655056	−0.327528	+	0.944842i	$0.606216\pi$
$434$	−5.22588	−0.250850
$435$	−3.69735	−0.177274
$436$	15.0214	0.719393
$437$	−27.4946	−1.31524
$438$	9.73078	0.464955
$439$	−17.9114	−0.854867	−0.427433	−	0.904047i	$-0.640582\pi$
$439$	−17.9114	−0.854867	−0.427433	+	0.904047i	$0.640582\pi$
$440$	−7.37010	−0.351356
$441$	5.31462	0.253077
$442$	41.3496	1.96680
$443$	−7.11797	−0.338185	−0.169093	−	0.985600i	$-0.554084\pi$
$443$	−7.11797	−0.338185	−0.169093	+	0.985600i	$0.554084\pi$
$444$	31.5873	1.49907
$445$	−15.6377	−0.741300
$446$	5.42971	0.257104
$447$	−5.85947	−0.277143
$448$	−19.2791	−0.910851
$449$	24.1884	1.14152	0.570761	−	0.821116i	$-0.306648\pi$
$449$	24.1884	1.14152	0.570761	+	0.821116i	$0.306648\pi$
$450$	−14.9555	−0.705008
$451$	−6.32400	−0.297785
$452$	−18.1942	−0.855785
$453$	−9.85145	−0.462862
$454$	49.8100	2.33770
$455$	8.11193	0.380293
$456$	−17.9877	−0.842353
$457$	−7.74850	−0.362459	−0.181230	−	0.983441i	$-0.558008\pi$
$457$	−7.74850	−0.362459	−0.181230	+	0.983441i	$0.558008\pi$
$458$	−2.14148	−0.100065
$459$	−29.7543	−1.38881
$460$	33.8212	1.57692
$461$	−11.6350	−0.541898	−0.270949	−	0.962594i	$-0.587337\pi$
$461$	−11.6350	−0.541898	−0.270949	+	0.962594i	$0.587337\pi$
$462$	4.07584	0.189625
$463$	27.3291	1.27009	0.635046	−	0.772474i	$-0.280981\pi$
$463$	27.3291	1.27009	0.635046	+	0.772474i	$0.280981\pi$
$464$	11.0697	0.513897
$465$	−1.17312	−0.0544023
$466$	38.2258	1.77077
$467$	−9.16785	−0.424238	−0.212119	−	0.977244i	$-0.568036\pi$
$467$	−9.16785	−0.424238	−0.212119	+	0.977244i	$0.568036\pi$
$468$	−22.4249	−1.03659
$469$	33.5795	1.55056
$470$	−33.5371	−1.54695
$471$	15.6931	0.723101
$472$	−27.9616	−1.28704
$473$	12.6521	0.581746
$474$	−3.76393	−0.172883
$475$	12.7319	0.584181
$476$	−61.9251	−2.83833
$477$	1.72088	0.0787938
$478$	62.9384	2.87874
$479$	−32.8967	−1.50309	−0.751545	−	0.659681i	$-0.770691\pi$
$479$	−32.8967	−1.50309	−0.751545	+	0.659681i	$0.770691\pi$
$480$	−0.800231	−0.0365254
$481$	−24.8429	−1.13274
$482$	17.5441	0.799111
$483$	−9.18585	−0.417971
$484$	3.93019	0.178645
$485$	−14.8873	−0.675998
$486$	37.8336	1.71617
$487$	9.10966	0.412798	0.206399	−	0.978468i	$-0.433825\pi$
$487$	9.10966	0.412798	0.206399	+	0.978468i	$0.433825\pi$
$488$	42.0915	1.90539
$489$	12.5336	0.566788
$490$	8.39775	0.379372
$491$	−26.9215	−1.21495	−0.607475	−	0.794339i	$-0.707817\pi$
$491$	−26.9215	−1.21495	−0.607475	+	0.794339i	$0.707817\pi$
$492$	18.9862	0.855962
$493$	−22.1985	−0.999768
$494$	28.8058	1.29603
$495$	−3.78896	−0.170301
$496$	3.51228	0.157706
$497$	22.2409	0.997639
$498$	−19.1149	−0.856560
$499$	−2.27222	−0.101718	−0.0508592	−	0.998706i	$-0.516196\pi$
$499$	−2.27222	−0.101718	−0.0508592	+	0.998706i	$0.516196\pi$
$500$	−46.4738	−2.07837
$501$	12.5485	0.560626
$502$	−42.6768	−1.90476
$503$	−2.44008	−0.108798	−0.0543990	−	0.998519i	$-0.517324\pi$
$503$	−2.44008	−0.108798	−0.0543990	+	0.998519i	$0.517324\pi$
$504$	24.8867	1.10854
$505$	−8.19945	−0.364871
$506$	−13.3651	−0.594150
$507$	5.67164	0.251886
$508$	−55.2261	−2.45026
$509$	−39.0193	−1.72950	−0.864751	−	0.502201i	$-0.832524\pi$
$509$	−39.0193	−1.72950	−0.864751	+	0.502201i	$0.832524\pi$
$510$	−20.9752	−0.928797
$511$	11.4613	0.507017
$512$	36.1075	1.59574
$513$	−20.7280	−0.915164
$514$	−25.1351	−1.10866
$515$	−22.6995	−1.00026
$516$	−37.9848	−1.67219
$517$	8.78320	0.386285
$518$	56.1375	2.46654
$519$	−12.1932	−0.535223
$520$	−17.4024	−0.763144
$521$	−15.1687	−0.664552	−0.332276	−	0.943182i	$-0.607817\pi$
$521$	−15.1687	−0.664552	−0.332276	+	0.943182i	$0.607817\pi$
$522$	18.1651	0.795063
$523$	−18.0898	−0.791011	−0.395506	−	0.918464i	$-0.629431\pi$
$523$	−18.0898	−0.791011	−0.395506	+	0.918464i	$0.629431\pi$
$524$	50.5050	2.20632
$525$	4.25370	0.185647
$526$	−60.1839	−2.62414
$527$	−7.04331	−0.306811
$528$	−2.73934	−0.119214
$529$	7.12132	0.309622
$530$	2.71921	0.118115
$531$	−14.3750	−0.623822
$532$	−43.1395	−1.87033
$533$	−14.9323	−0.646790
$534$	−18.5525	−0.802844
$535$	−8.69245	−0.375807
$536$	−72.0374	−3.11154
$537$	−5.23674	−0.225982
$538$	37.0852	1.59886
$539$	−2.19933	−0.0947318
$540$	25.4976	1.09724
$541$	−14.2429	−0.612350	−0.306175	−	0.951975i	$-0.599049\pi$
$541$	−14.2429	−0.612350	−0.306175	+	0.951975i	$0.599049\pi$
$542$	−22.9643	−0.986400
$543$	6.43555	0.276176
$544$	−4.80450	−0.205991
$545$	5.99285	0.256706
$546$	9.62392	0.411866
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	44.9242	1.91907
$549$	21.6392	0.923537
$550$	6.18898	0.263899
$551$	−15.4643	−0.658802
$552$	19.7062	0.838753
$553$	−4.43330	−0.188523
$554$	17.5237	0.744510
$555$	12.6019	0.534922
$556$	−63.5760	−2.69622
$557$	32.2993	1.36857	0.684283	−	0.729217i	$-0.260115\pi$
$557$	32.2993	1.36857	0.684283	+	0.729217i	$0.260115\pi$
$558$	5.76355	0.243991
$559$	29.8744	1.26355
$560$	12.3198	0.520606
$561$	5.49330	0.231927
$562$	−49.5329	−2.08942
$563$	−34.4539	−1.45206	−0.726030	−	0.687663i	$-0.758637\pi$
$563$	−34.4539	−1.45206	−0.726030	+	0.687663i	$0.758637\pi$
$564$	−26.3693	−1.11035
$565$	−7.25869	−0.305375
$566$	−17.5854	−0.739169
$567$	8.95861	0.376226
$568$	−47.7129	−2.00199
$569$	−6.32001	−0.264948	−0.132474	−	0.991186i	$-0.542292\pi$
$569$	−6.32001	−0.264948	−0.132474	+	0.991186i	$0.542292\pi$
$570$	−14.6121	−0.612035
$571$	7.02090	0.293816	0.146908	−	0.989150i	$-0.453068\pi$
$571$	7.02090	0.293816	0.146908	+	0.989150i	$0.453068\pi$
$572$	9.28002	0.388017
$573$	−19.1005	−0.797935
$574$	33.7425	1.40838
$575$	−13.9483	−0.581684
$576$	21.2626	0.885942
$577$	−13.5808	−0.565376	−0.282688	−	0.959212i	$-0.591226\pi$
$577$	−13.5808	−0.565376	−0.282688	+	0.959212i	$0.591226\pi$
$578$	−84.5343	−3.51616
$579$	3.22622	0.134077
$580$	19.0227	0.789876
$581$	−22.5142	−0.934048
$582$	−17.6622	−0.732120
$583$	−0.712147	−0.0294941
$584$	−24.5877	−1.01744
$585$	−8.94653	−0.369894
$586$	43.3788	1.79196
$587$	−33.2500	−1.37237	−0.686186	−	0.727426i	$-0.740717\pi$
$587$	−33.2500	−1.37237	−0.686186	+	0.727426i	$0.740717\pi$
$588$	6.60291	0.272300
$589$	−4.90664	−0.202175
$590$	−22.7143	−0.935131
$591$	8.36167	0.343953
$592$	−37.7296	−1.55068
$593$	−48.5792	−1.99491	−0.997454	−	0.0713146i	$-0.977281\pi$
$593$	−48.5792	−1.99491	−0.997454	+	0.0713146i	$0.977281\pi$
$594$	−10.0759	−0.413418
$595$	−24.7054	−1.01282
$596$	30.1468	1.23486
$597$	−8.78672	−0.359616
$598$	−31.5578	−1.29049
$599$	35.9532	1.46901	0.734504	−	0.678604i	$-0.237415\pi$
$599$	35.9532	1.46901	0.734504	+	0.678604i	$0.237415\pi$
$600$	−9.12538	−0.372542
$601$	1.55862	0.0635775	0.0317888	−	0.999495i	$-0.489880\pi$
$601$	1.55862	0.0635775	0.0317888	+	0.999495i	$0.489880\pi$
$602$	−67.5071	−2.75138
$603$	−37.0343	−1.50815
$604$	50.6854	2.06236
$605$	1.56797	0.0637471
$606$	−9.72775	−0.395163
$607$	−32.4058	−1.31531	−0.657655	−	0.753319i	$-0.728452\pi$
$607$	−32.4058	−1.31531	−0.657655	+	0.753319i	$0.728452\pi$
$608$	−3.34700	−0.135739
$609$	−5.16658	−0.209360
$610$	34.1925	1.38442
$611$	20.7390	0.839010
$612$	68.2963	2.76072
$613$	−38.1965	−1.54274	−0.771370	−	0.636387i	$-0.780428\pi$
$613$	−38.1965	−1.54274	−0.771370	+	0.636387i	$0.780428\pi$
$614$	25.1298	1.01416
$615$	7.57462	0.305438
$616$	−10.2988	−0.414950
$617$	−25.4434	−1.02431	−0.512156	−	0.858892i	$-0.671153\pi$
$617$	−25.4434	−1.02431	−0.512156	+	0.858892i	$0.671153\pi$
$618$	−26.9305	−1.08330
$619$	−15.9094	−0.639451	−0.319726	−	0.947510i	$-0.603591\pi$
$619$	−15.9094	−0.639451	−0.319726	+	0.947510i	$0.603591\pi$
$620$	6.03568	0.242399
$621$	22.7083	0.911253
$622$	52.5313	2.10631
$623$	−21.8518	−0.875474
$624$	−6.46816	−0.258934
$625$	−5.83361	−0.233345
$626$	−4.78978	−0.191438
$627$	3.82685	0.152830
$628$	−80.7406	−3.22190
$629$	75.6606	3.01679
$630$	20.2165	0.805443
$631$	−16.5748	−0.659832	−0.329916	−	0.944010i	$-0.607020\pi$
$631$	−16.5748	−0.659832	−0.329916	+	0.944010i	$0.607020\pi$
$632$	9.51067	0.378314
$633$	8.05434	0.320131
$634$	−67.1763	−2.66791
$635$	−22.0327	−0.874342
$636$	2.13804	0.0847786
$637$	−5.19308	−0.205758
$638$	−7.51719	−0.297608
$639$	−24.5291	−0.970358
$640$	31.5024	1.24524
$641$	4.80188	0.189663	0.0948314	−	0.995493i	$-0.469769\pi$
$641$	4.80188	0.189663	0.0948314	+	0.995493i	$0.469769\pi$
$642$	−10.3126	−0.407007
$643$	−3.25443	−0.128342	−0.0641711	−	0.997939i	$-0.520440\pi$
$643$	−3.25443	−0.128342	−0.0641711	+	0.997939i	$0.520440\pi$
$644$	47.2609	1.86234
$645$	−15.1542	−0.596697
$646$	−87.7297	−3.45168
$647$	−18.8073	−0.739390	−0.369695	−	0.929153i	$-0.620538\pi$
$647$	−18.8073	−0.739390	−0.369695	+	0.929153i	$0.620538\pi$
$648$	−19.2187	−0.754984
$649$	5.94876	0.233509
$650$	14.6135	0.573188
$651$	−1.63929	−0.0642490
$652$	−64.4848	−2.52542
$653$	23.5446	0.921373	0.460686	−	0.887563i	$-0.347603\pi$
$653$	23.5446	0.921373	0.460686	+	0.887563i	$0.347603\pi$
$654$	7.10986	0.278018
$655$	20.1492	0.787296
$656$	−22.6781	−0.885430
$657$	−12.6405	−0.493152
$658$	−46.8639	−1.82694
$659$	−34.9931	−1.36314	−0.681569	−	0.731753i	$-0.738702\pi$
$659$	−34.9931	−1.36314	−0.681569	+	0.731753i	$0.738702\pi$
$660$	−4.70742	−0.183236
$661$	10.3438	0.402327	0.201163	−	0.979558i	$-0.435528\pi$
$661$	10.3438	0.402327	0.201163	+	0.979558i	$0.435528\pi$
$662$	1.43492	0.0557699
$663$	12.9709	0.503746
$664$	48.2994	1.87438
$665$	−17.2107	−0.667403
$666$	−61.9133	−2.39909
$667$	16.9417	0.655986
$668$	−64.5617	−2.49797
$669$	1.70323	0.0658507
$670$	−58.5188	−2.26078
$671$	−8.95486	−0.345699
$672$	−1.11822	−0.0431364
$673$	22.2648	0.858245	0.429123	−	0.903246i	$-0.358823\pi$
$673$	22.2648	0.858245	0.429123	+	0.903246i	$0.358823\pi$
$674$	65.0599	2.50601
$675$	−10.5156	−0.404744
$676$	−29.1804	−1.12232
$677$	−51.4181	−1.97616	−0.988078	−	0.153953i	$-0.950800\pi$
$677$	−51.4181	−1.97616	−0.988078	+	0.153953i	$0.950800\pi$
$678$	−8.61164	−0.330728
$679$	−20.8032	−0.798352
$680$	52.9999	2.03245
$681$	15.6248	0.598743
$682$	−2.38511	−0.0913307
$683$	−4.18932	−0.160300	−0.0801500	−	0.996783i	$-0.525540\pi$
$683$	−4.18932	−0.160300	−0.0801500	+	0.996783i	$0.525540\pi$
$684$	47.5779	1.81919
$685$	17.9227	0.684792
$686$	49.0842	1.87404
$687$	−0.671757	−0.0256291
$688$	45.3710	1.72975
$689$	−1.68153	−0.0640612
$690$	16.0081	0.609419
$691$	32.3996	1.23254	0.616270	−	0.787535i	$-0.288643\pi$
$691$	32.3996	1.23254	0.616270	+	0.787535i	$0.288643\pi$
$692$	62.7337	2.38478
$693$	−5.29459	−0.201125
$694$	36.6029	1.38943
$695$	−25.3640	−0.962110
$696$	11.0838	0.420129
$697$	45.4772	1.72257
$698$	52.3557	1.98169
$699$	11.9909	0.453539
$700$	−21.8851	−0.827180
$701$	−11.5464	−0.436102	−0.218051	−	0.975937i	$-0.569970\pi$
$701$	−11.5464	−0.436102	−0.218051	+	0.975937i	$0.569970\pi$
$702$	−23.7912	−0.897943
$703$	52.7081	1.98793
$704$	−8.79904	−0.331626
$705$	−10.5202	−0.396212
$706$	10.6946	0.402497
$707$	−11.4577	−0.430911
$708$	−17.8596	−0.671204
$709$	−22.4188	−0.841957	−0.420978	−	0.907071i	$-0.638313\pi$
$709$	−22.4188	−0.841957	−0.420978	+	0.907071i	$0.638313\pi$
$710$	−38.7591	−1.45460
$711$	4.88942	0.183368
$712$	46.8782	1.75684
$713$	5.37541	0.201311
$714$	−29.3102	−1.09691
$715$	3.70231	0.138459
$716$	26.9429	1.00690
$717$	19.7430	0.737316
$718$	65.1801	2.43250
$719$	11.1796	0.416928	0.208464	−	0.978030i	$-0.433154\pi$
$719$	11.1796	0.416928	0.208464	+	0.978030i	$0.433154\pi$
$720$	−13.5873	−0.506370
$721$	−31.7197	−1.18130
$722$	−14.8471	−0.552553
$723$	5.50335	0.204672
$724$	−33.1107	−1.23055
$725$	−7.84522	−0.291364
$726$	1.86023	0.0690395
$727$	−28.4724	−1.05598	−0.527992	−	0.849249i	$-0.677055\pi$
$727$	−28.4724	−1.05598	−0.527992	+	0.849249i	$0.677055\pi$
$728$	−24.3176	−0.901271
$729$	−0.398319	−0.0147526
$730$	−19.9735	−0.739253
$731$	−90.9843	−3.36517
$732$	26.8846	0.993685
$733$	−14.9133	−0.550837	−0.275418	−	0.961324i	$-0.588816\pi$
$733$	−14.9133	−0.550837	−0.275418	+	0.961324i	$0.588816\pi$
$734$	−10.9149	−0.402877
$735$	2.63427	0.0971664
$736$	3.66676	0.135159
$737$	15.3258	0.564533
$738$	−37.2141	−1.36987
$739$	−16.3153	−0.600167	−0.300084	−	0.953913i	$-0.597015\pi$
$739$	−16.3153	−0.600167	−0.300084	+	0.953913i	$0.597015\pi$
$740$	−64.8365	−2.38344
$741$	9.03600	0.331946
$742$	3.79975	0.139493
$743$	21.0138	0.770921	0.385460	−	0.922724i	$-0.374043\pi$
$743$	21.0138	0.770921	0.385460	+	0.922724i	$0.374043\pi$
$744$	3.51675	0.128930
$745$	12.0272	0.440643
$746$	−53.5711	−1.96138
$747$	24.8306	0.908506
$748$	−28.2628	−1.03339
$749$	−12.1466	−0.443827
$750$	−21.9968	−0.803210
$751$	33.4990	1.22239	0.611197	−	0.791478i	$-0.290688\pi$
$751$	33.4990	1.22239	0.611197	+	0.791478i	$0.290688\pi$
$752$	31.4968	1.14857
$753$	−13.3872	−0.487856
$754$	−17.7497	−0.646405
$755$	20.2212	0.735925
$756$	35.6297	1.29584
$757$	−27.7614	−1.00900	−0.504502	−	0.863410i	$-0.668324\pi$
$757$	−27.7614	−1.00900	−0.504502	+	0.863410i	$0.668324\pi$
$758$	9.46745	0.343873
$759$	−4.19245	−0.152176
$760$	36.9218	1.33930
$761$	5.16706	0.187306	0.0936529	−	0.995605i	$-0.470146\pi$
$761$	5.16706	0.187306	0.0936529	+	0.995605i	$0.470146\pi$
$762$	−26.1394	−0.946932
$763$	8.37426	0.303169
$764$	98.2714	3.55534
$765$	27.2472	0.985124
$766$	−16.5455	−0.597813
$767$	14.0463	0.507182
$768$	23.9312	0.863541
$769$	−23.3969	−0.843713	−0.421856	−	0.906663i	$-0.638621\pi$
$769$	−23.3969	−0.843713	−0.421856	+	0.906663i	$0.638621\pi$
$770$	−8.36611	−0.301494
$771$	−7.88456	−0.283956
$772$	−16.5988	−0.597403
$773$	38.8786	1.39837	0.699184	−	0.714942i	$-0.253547\pi$
$773$	38.8786	1.39837	0.699184	+	0.714942i	$0.253547\pi$
$774$	74.4526	2.67615
$775$	−2.48919	−0.0894145
$776$	44.6286	1.60207
$777$	17.6096	0.631742
$778$	−60.6997	−2.17619
$779$	31.6812	1.13510
$780$	−11.1152	−0.397989
$781$	10.1508	0.363225
$782$	96.1111	3.43693
$783$	12.7723	0.456444
$784$	−7.88687	−0.281674
$785$	−32.2119	−1.14969
$786$	23.9049	0.852659
$787$	27.5709	0.982795	0.491397	−	0.870936i	$-0.336486\pi$
$787$	27.5709	0.982795	0.491397	+	0.870936i	$0.336486\pi$
$788$	−43.0205	−1.53254
$789$	−18.8789	−0.672107
$790$	7.72589	0.274875
$791$	−10.1431	−0.360647
$792$	11.3584	0.403603
$793$	−21.1443	−0.750857
$794$	−17.4360	−0.618780
$795$	0.852980	0.0302521
$796$	45.2074	1.60233
$797$	−5.25809	−0.186251	−0.0931255	−	0.995654i	$-0.529686\pi$
$797$	−5.25809	−0.186251	−0.0931255	+	0.995654i	$0.529686\pi$
$798$	−20.4186	−0.722812
$799$	−63.1618	−2.23450
$800$	−1.69797	−0.0600323
$801$	24.1000	0.851533
$802$	−7.61360	−0.268846
$803$	5.23097	0.184597
$804$	−46.0117	−1.62271
$805$	18.8550	0.664551
$806$	−5.63176	−0.198370
$807$	11.6332	0.409507
$808$	24.5800	0.864722
$809$	8.87182	0.311917	0.155958	−	0.987764i	$-0.450153\pi$
$809$	8.87182	0.311917	0.155958	+	0.987764i	$0.450153\pi$
$810$	−15.6121	−0.548554
$811$	−38.8083	−1.36274	−0.681372	−	0.731938i	$-0.738616\pi$
$811$	−38.8083	−1.36274	−0.681372	+	0.731938i	$0.738616\pi$
$812$	26.5819	0.932841
$813$	−7.20360	−0.252641
$814$	25.6214	0.898028
$815$	−25.7265	−0.901162
$816$	19.6992	0.689608
$817$	−63.3832	−2.21750
$818$	−67.3440	−2.35463
$819$	−12.5017	−0.436843
$820$	−38.9712	−1.36093
$821$	−16.7312	−0.583922	−0.291961	−	0.956430i	$-0.594308\pi$
$821$	−16.7312	−0.583922	−0.291961	+	0.956430i	$0.594308\pi$
$822$	21.2634	0.741645
$823$	−41.0599	−1.43126	−0.715630	−	0.698480i	$-0.753860\pi$
$823$	−41.0599	−1.43126	−0.715630	+	0.698480i	$0.753860\pi$
$824$	68.0478	2.37056
$825$	1.94140	0.0675910
$826$	−31.7403	−1.10439
$827$	−18.6710	−0.649255	−0.324627	−	0.945842i	$-0.605239\pi$
$827$	−18.6710	−0.649255	−0.324627	+	0.945842i	$0.605239\pi$
$828$	−52.1234	−1.81141
$829$	1.24073	0.0430923	0.0215462	−	0.999768i	$-0.493141\pi$
$829$	1.24073	0.0430923	0.0215462	+	0.999768i	$0.493141\pi$
$830$	39.2355	1.36188
$831$	5.49695	0.190687
$832$	−20.7764	−0.720292
$833$	15.8158	0.547987
$834$	−30.0916	−1.04199
$835$	−25.7572	−0.891365
$836$	−19.6890	−0.680959
$837$	4.05249	0.140075
$838$	−18.4638	−0.637823
$839$	36.9217	1.27468	0.637340	−	0.770583i	$-0.280035\pi$
$839$	36.9217	1.27468	0.637340	+	0.770583i	$0.280035\pi$
$840$	12.3355	0.425614
$841$	−19.4711	−0.671418
$842$	−1.52705	−0.0526258
$843$	−15.5378	−0.535152
$844$	−41.4393	−1.42640
$845$	−11.6417	−0.400486
$846$	51.6855	1.77698
$847$	2.19104	0.0752851
$848$	−2.55378	−0.0876972
$849$	−5.51631	−0.189319
$850$	−44.5062	−1.52655
$851$	−57.7437	−1.97943
$852$	−30.4752	−1.04406
$853$	47.8695	1.63902	0.819510	−	0.573065i	$-0.194246\pi$
$853$	47.8695	1.63902	0.819510	+	0.573065i	$0.194246\pi$
$854$	47.7798	1.63499
$855$	18.9815	0.649152
$856$	26.0579	0.890640
$857$	−24.0450	−0.821361	−0.410681	−	0.911779i	$-0.634709\pi$
$857$	−24.0450	−0.821361	−0.410681	+	0.911779i	$0.634709\pi$
$858$	4.39239	0.149954
$859$	−23.7542	−0.810483	−0.405242	−	0.914210i	$-0.632813\pi$
$859$	−23.7542	−0.810483	−0.405242	+	0.914210i	$0.632813\pi$
$860$	77.9680	2.65869
$861$	10.5846	0.360722
$862$	−94.4857	−3.21820
$863$	55.6395	1.89399	0.946995	−	0.321250i	$-0.104103\pi$
$863$	55.6395	1.89399	0.946995	+	0.321250i	$0.104103\pi$
$864$	2.76435	0.0940452
$865$	25.0279	0.850975
$866$	33.1938	1.12797
$867$	−26.5173	−0.900576
$868$	8.43411	0.286272
$869$	−2.02337	−0.0686382
$870$	9.00378	0.305257
$871$	36.1874	1.22616
$872$	−17.9651	−0.608376
$873$	22.9435	0.776520
$874$	66.9547	2.26478
$875$	−25.9087	−0.875872
$876$	−15.7046	−0.530610
$877$	13.8784	0.468640	0.234320	−	0.972160i	$-0.424714\pi$
$877$	13.8784	0.468640	0.234320	+	0.972160i	$0.424714\pi$
$878$	43.6179	1.47203
$879$	13.6074	0.458965
$880$	5.62280	0.189544
$881$	28.4446	0.958322	0.479161	−	0.877727i	$-0.340941\pi$
$881$	28.4446	0.958322	0.479161	+	0.877727i	$0.340941\pi$
$882$	−12.9421	−0.435785
$883$	6.14593	0.206827	0.103413	−	0.994638i	$-0.467024\pi$
$883$	6.14593	0.206827	0.103413	+	0.994638i	$0.467024\pi$
$884$	−66.7346	−2.24453
$885$	−7.12518	−0.239510
$886$	17.3337	0.582336
$887$	−1.54466	−0.0518645	−0.0259322	−	0.999664i	$-0.508255\pi$
$887$	−1.54466	−0.0518645	−0.0259322	+	0.999664i	$0.508255\pi$
$888$	−37.7776	−1.26773
$889$	−30.7880	−1.03260
$890$	38.0810	1.27648
$891$	4.08874	0.136978
$892$	−8.76307	−0.293409
$893$	−44.0010	−1.47244
$894$	14.2690	0.477226
$895$	10.7490	0.359299
$896$	44.0207	1.47063
$897$	−9.89927	−0.330527
$898$	−58.9037	−1.96564
$899$	3.02340	0.100836
$900$	24.1368	0.804560
$901$	5.12120	0.170612
$902$	15.4002	0.512770
$903$	−21.1761	−0.704697
$904$	21.7598	0.723721
$905$	−13.2097	−0.439105
$906$	23.9902	0.797023
$907$	36.6993	1.21858	0.609290	−	0.792948i	$-0.291455\pi$
$907$	36.6993	1.21858	0.609290	+	0.792948i	$0.291455\pi$
$908$	−80.3890	−2.66780
$909$	12.6365	0.419128
$910$	−19.7542	−0.654844
$911$	−30.1967	−1.00046	−0.500230	−	0.865893i	$-0.666751\pi$
$911$	−30.1967	−1.00046	−0.500230	+	0.865893i	$0.666751\pi$
$912$	13.7232	0.454421
$913$	−10.2756	−0.340072
$914$	18.8691	0.624135
$915$	10.7258	0.354583
$916$	3.45616	0.114195
$917$	28.1560	0.929795
$918$	72.4576	2.39146
$919$	22.7262	0.749667	0.374833	−	0.927092i	$-0.377700\pi$
$919$	22.7262	0.749667	0.374833	+	0.927092i	$0.377700\pi$
$920$	−40.4492	−1.33357
$921$	7.88291	0.259751
$922$	28.3336	0.933119
$923$	23.9682	0.788924
$924$	−6.57803	−0.216401
$925$	26.7394	0.879187
$926$	−66.5519	−2.18703
$927$	34.9832	1.14900
$928$	2.06237	0.0677006
$929$	−8.05096	−0.264143	−0.132072	−	0.991240i	$-0.542163\pi$
$929$	−8.05096	−0.264143	−0.132072	+	0.991240i	$0.542163\pi$
$930$	2.85679	0.0936778
$931$	11.0179	0.361098
$932$	−61.6930	−2.02082
$933$	16.4784	0.539479
$934$	22.3255	0.730514
$935$	−11.2756	−0.368752
$936$	26.8196	0.876625
$937$	1.10645	0.0361461	0.0180731	−	0.999837i	$-0.494247\pi$
$937$	1.10645	0.0361461	0.0180731	+	0.999837i	$0.494247\pi$
$938$	−81.7727	−2.66997
$939$	−1.50249	−0.0490320
$940$	54.1258	1.76539
$941$	35.6500	1.16216	0.581079	−	0.813847i	$-0.302631\pi$
$941$	35.6500	1.16216	0.581079	+	0.813847i	$0.302631\pi$
$942$	−38.2159	−1.24514
$943$	−34.7079	−1.13025
$944$	21.3324	0.694312
$945$	14.2147	0.462403
$946$	−30.8105	−1.00174
$947$	26.4446	0.859333	0.429666	−	0.902988i	$-0.358631\pi$
$947$	26.4446	0.859333	0.429666	+	0.902988i	$0.358631\pi$
$948$	6.07465	0.197295
$949$	12.3514	0.400944
$950$	−31.0048	−1.00593
$951$	−21.0723	−0.683317
$952$	74.0608	2.40032
$953$	−28.9222	−0.936883	−0.468441	−	0.883495i	$-0.655184\pi$
$953$	−28.9222	−0.936883	−0.468441	+	0.883495i	$0.655184\pi$
$954$	−4.19069	−0.135679
$955$	39.2059	1.26867
$956$	−101.577	−3.28524
$957$	−2.35805	−0.0762248
$958$	80.1101	2.58824
$959$	25.0448	0.808738
$960$	10.5391	0.340149
$961$	−30.0407	−0.969055
$962$	60.4975	1.95052
$963$	13.3963	0.431690
$964$	−28.3146	−0.911951
$965$	−6.62217	−0.213175
$966$	22.3694	0.719723
$967$	−22.1638	−0.712740	−0.356370	−	0.934345i	$-0.615986\pi$
$967$	−22.1638	−0.712740	−0.356370	+	0.934345i	$0.615986\pi$
$968$	−4.70040	−0.151077
$969$	−27.5197	−0.884059
$970$	36.2536	1.16403
$971$	6.91747	0.221992	0.110996	−	0.993821i	$-0.464596\pi$
$971$	6.91747	0.221992	0.110996	+	0.993821i	$0.464596\pi$
$972$	−61.0600	−1.95850
$973$	−35.4430	−1.13625
$974$	−22.1838	−0.710816
$975$	4.58407	0.146808
$976$	−32.1124	−1.02789
$977$	−12.9607	−0.414650	−0.207325	−	0.978272i	$-0.566476\pi$
$977$	−12.9607	−0.414650	−0.207325	+	0.978272i	$0.566476\pi$
$978$	−30.5217	−0.975978
$979$	−9.97324	−0.318746
$980$	−13.5532	−0.432942
$981$	−9.23585	−0.294878
$982$	65.5591	2.09208
$983$	23.6571	0.754545	0.377272	−	0.926102i	$-0.376862\pi$
$983$	23.6571	0.754545	0.377272	+	0.926102i	$0.376862\pi$
$984$	−22.7069	−0.723870
$985$	−17.1633	−0.546867
$986$	54.0577	1.72155
$987$	−14.7006	−0.467925
$988$	−46.4899	−1.47904
$989$	69.4386	2.20802
$990$	9.22686	0.293249
$991$	30.7144	0.975674	0.487837	−	0.872935i	$-0.337786\pi$
$991$	30.7144	0.975674	0.487837	+	0.872935i	$0.337786\pi$
$992$	0.654365	0.0207761
$993$	0.450117	0.0142840
$994$	−54.1609	−1.71788
$995$	18.0357	0.571771
$996$	30.8498	0.977512
$997$	−19.1273	−0.605768	−0.302884	−	0.953028i	$-0.597949\pi$
$997$	−19.1273	−0.605768	−0.302884	+	0.953028i	$0.597949\pi$
$998$	5.53330	0.175153
$999$	−43.5327	−1.37731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.10	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.10	✓	106	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.43520 q^{2} -0.763891 q^{3} +3.93019 q^{4} +1.56797 q^{5} +1.86023 q^{6} +2.19104 q^{7} -4.70040 q^{8} -2.41647 q^{9} +O(q^{10})\)	\(q-2.43520 q^{2} -0.763891 q^{3} +3.93019 q^{4} +1.56797 q^{5} +1.86023 q^{6} +2.19104 q^{7} -4.70040 q^{8} -2.41647 q^{9} -3.81832 q^{10} +1.00000 q^{11} -3.00224 q^{12} +2.36121 q^{13} -5.33563 q^{14} -1.19776 q^{15} +3.58603 q^{16} -7.19121 q^{17} +5.88459 q^{18} -5.00968 q^{19} +6.16243 q^{20} -1.67372 q^{21} -2.43520 q^{22} +5.48829 q^{23} +3.59060 q^{24} -2.54147 q^{25} -5.75002 q^{26} +4.13759 q^{27} +8.61122 q^{28} +3.08689 q^{29} +2.91678 q^{30} +0.979432 q^{31} +0.668107 q^{32} -0.763891 q^{33} +17.5120 q^{34} +3.43549 q^{35} -9.49720 q^{36} -10.5213 q^{37} +12.1996 q^{38} -1.80371 q^{39} -7.37010 q^{40} -6.32400 q^{41} +4.07584 q^{42} +12.6521 q^{43} +3.93019 q^{44} -3.78896 q^{45} -13.3651 q^{46} +8.78320 q^{47} -2.73934 q^{48} -2.19933 q^{49} +6.18898 q^{50} +5.49330 q^{51} +9.28002 q^{52} -0.712147 q^{53} -10.0759 q^{54} +1.56797 q^{55} -10.2988 q^{56} +3.82685 q^{57} -7.51719 q^{58} +5.94876 q^{59} -4.70742 q^{60} -8.95486 q^{61} -2.38511 q^{62} -5.29459 q^{63} -8.79904 q^{64} +3.70231 q^{65} +1.86023 q^{66} +15.3258 q^{67} -28.2628 q^{68} -4.19245 q^{69} -8.36611 q^{70} +10.1508 q^{71} +11.3584 q^{72} +5.23097 q^{73} +25.6214 q^{74} +1.94140 q^{75} -19.6890 q^{76} +2.19104 q^{77} +4.39239 q^{78} -2.02337 q^{79} +5.62280 q^{80} +4.08874 q^{81} +15.4002 q^{82} -10.2756 q^{83} -6.57803 q^{84} -11.2756 q^{85} -30.8105 q^{86} -2.35805 q^{87} -4.70040 q^{88} -9.97324 q^{89} +9.22686 q^{90} +5.17352 q^{91} +21.5700 q^{92} -0.748179 q^{93} -21.3888 q^{94} -7.85503 q^{95} -0.510361 q^{96} -9.49463 q^{97} +5.35580 q^{98} -2.41647 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

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