LMFDB - Embedded newform 6019.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$108$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25939 q^{2} +2.42736 q^{3} +3.10485 q^{4} -0.500622 q^{5} -5.48435 q^{6} +4.41326 q^{7} -2.49629 q^{8} +2.89206 q^{9} +O(q^{10})$	\(q-2.25939 q^{2} +2.42736 q^{3} +3.10485 q^{4} -0.500622 q^{5} -5.48435 q^{6} +4.41326 q^{7} -2.49629 q^{8} +2.89206 q^{9} +1.13110 q^{10} -1.42556 q^{11} +7.53659 q^{12} -1.00000 q^{13} -9.97128 q^{14} -1.21519 q^{15} -0.569596 q^{16} +3.13782 q^{17} -6.53430 q^{18} -7.27226 q^{19} -1.55436 q^{20} +10.7126 q^{21} +3.22091 q^{22} -8.26540 q^{23} -6.05940 q^{24} -4.74938 q^{25} +2.25939 q^{26} -0.262003 q^{27} +13.7025 q^{28} -1.90070 q^{29} +2.74559 q^{30} +5.25956 q^{31} +6.27953 q^{32} -3.46035 q^{33} -7.08957 q^{34} -2.20937 q^{35} +8.97943 q^{36} +6.75569 q^{37} +16.4309 q^{38} -2.42736 q^{39} +1.24970 q^{40} -10.9114 q^{41} -24.2039 q^{42} -6.84316 q^{43} -4.42616 q^{44} -1.44783 q^{45} +18.6748 q^{46} -4.39465 q^{47} -1.38261 q^{48} +12.4769 q^{49} +10.7307 q^{50} +7.61661 q^{51} -3.10485 q^{52} +3.05136 q^{53} +0.591968 q^{54} +0.713668 q^{55} -11.0168 q^{56} -17.6524 q^{57} +4.29444 q^{58} -11.4178 q^{59} -3.77298 q^{60} +12.7964 q^{61} -11.8834 q^{62} +12.7634 q^{63} -13.0487 q^{64} +0.500622 q^{65} +7.81829 q^{66} +1.26329 q^{67} +9.74247 q^{68} -20.0631 q^{69} +4.99184 q^{70} -9.87557 q^{71} -7.21944 q^{72} -7.90176 q^{73} -15.2638 q^{74} -11.5284 q^{75} -22.5793 q^{76} -6.29138 q^{77} +5.48435 q^{78} -6.88388 q^{79} +0.285152 q^{80} -9.31216 q^{81} +24.6532 q^{82} -2.36869 q^{83} +33.2609 q^{84} -1.57086 q^{85} +15.4614 q^{86} -4.61369 q^{87} +3.55863 q^{88} -3.70599 q^{89} +3.27121 q^{90} -4.41326 q^{91} -25.6628 q^{92} +12.7668 q^{93} +9.92924 q^{94} +3.64065 q^{95} +15.2427 q^{96} -15.1692 q^{97} -28.1901 q^{98} -4.12282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) $ 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * 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 $

$2$	−2.25939	−1.59763	−0.798816	−	0.601576i	$-0.794540\pi$
$2$	−2.25939	−1.59763	−0.798816	+	0.601576i	$0.794540\pi$
$3$	2.42736	1.40144	0.700718	−	0.713439i	$-0.252863\pi$
$3$	2.42736	1.40144	0.700718	+	0.713439i	$0.252863\pi$
$4$	3.10485	1.55243
$5$	−0.500622	−0.223885	−0.111942	−	0.993715i	$-0.535707\pi$
$5$	−0.500622	−0.223885	−0.111942	+	0.993715i	$0.535707\pi$
$6$	−5.48435	−2.23898
$7$	4.41326	1.66806	0.834028	−	0.551723i	$-0.186029\pi$
$7$	4.41326	1.66806	0.834028	+	0.551723i	$0.186029\pi$
$8$	−2.49629	−0.882574
$9$	2.89206	0.964021
$10$	1.13110	0.357686
$11$	−1.42556	−0.429823	−0.214912	−	0.976633i	$-0.568946\pi$
$11$	−1.42556	−0.429823	−0.214912	+	0.976633i	$0.568946\pi$
$12$	7.53659	2.17562
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−9.97128	−2.66494
$15$	−1.21519	−0.313760
$16$	−0.569596	−0.142399
$17$	3.13782	0.761033	0.380517	−	0.924774i	$-0.375746\pi$
$17$	3.13782	0.761033	0.380517	+	0.924774i	$0.375746\pi$
$18$	−6.53430	−1.54015
$19$	−7.27226	−1.66837	−0.834186	−	0.551484i	$-0.814062\pi$
$19$	−7.27226	−1.66837	−0.834186	+	0.551484i	$0.814062\pi$
$20$	−1.55436	−0.347565
$21$	10.7126	2.33767
$22$	3.22091	0.686700
$23$	−8.26540	−1.72345	−0.861727	−	0.507372i	$-0.830617\pi$
$23$	−8.26540	−1.72345	−0.861727	+	0.507372i	$0.830617\pi$
$24$	−6.05940	−1.23687
$25$	−4.74938	−0.949876
$26$	2.25939	0.443103
$27$	−0.262003	−0.0504225
$28$	13.7025	2.58953
$29$	−1.90070	−0.352952	−0.176476	−	0.984305i	$-0.556470\pi$
$29$	−1.90070	−0.352952	−0.176476	+	0.984305i	$0.556470\pi$
$30$	2.74559	0.501273
$31$	5.25956	0.944645	0.472322	−	0.881426i	$-0.343416\pi$
$31$	5.25956	0.944645	0.472322	+	0.881426i	$0.343416\pi$
$32$	6.27953	1.11007
$33$	−3.46035	−0.602370
$34$	−7.08957	−1.21585
$35$	−2.20937	−0.373452
$36$	8.97943	1.49657
$37$	6.75569	1.11063	0.555315	−	0.831640i	$-0.312598\pi$
$37$	6.75569	1.11063	0.555315	+	0.831640i	$0.312598\pi$
$38$	16.4309	2.66544
$39$	−2.42736	−0.388688
$40$	1.24970	0.197595
$41$	−10.9114	−1.70408	−0.852041	−	0.523475i	$-0.824635\pi$
$41$	−10.9114	−1.70408	−0.852041	+	0.523475i	$0.824635\pi$
$42$	−24.2039	−3.73474
$43$	−6.84316	−1.04357	−0.521786	−	0.853076i	$-0.674734\pi$
$43$	−6.84316	−1.04357	−0.521786	+	0.853076i	$0.674734\pi$
$44$	−4.42616	−0.667269
$45$	−1.44783	−0.215830
$46$	18.6748	2.75345
$47$	−4.39465	−0.641026	−0.320513	−	0.947244i	$-0.603855\pi$
$47$	−4.39465	−0.641026	−0.320513	+	0.947244i	$0.603855\pi$
$48$	−1.38261	−0.199563
$49$	12.4769	1.78241
$50$	10.7307	1.51755
$51$	7.61661	1.06654
$52$	−3.10485	−0.430566
$53$	3.05136	0.419136	0.209568	−	0.977794i	$-0.432794\pi$
$53$	3.05136	0.419136	0.209568	+	0.977794i	$0.432794\pi$
$54$	0.591968	0.0805566
$55$	0.713668	0.0962310
$56$	−11.0168	−1.47218
$57$	−17.6524	−2.33811
$58$	4.29444	0.563887
$59$	−11.4178	−1.48647	−0.743237	−	0.669028i	$-0.766710\pi$
$59$	−11.4178	−1.48647	−0.743237	+	0.669028i	$0.766710\pi$
$60$	−3.77298	−0.487090
$61$	12.7964	1.63841	0.819205	−	0.573501i	$-0.194415\pi$
$61$	12.7964	1.63841	0.819205	+	0.573501i	$0.194415\pi$
$62$	−11.8834	−1.50919
$63$	12.7634	1.60804
$64$	−13.0487	−1.63109
$65$	0.500622	0.0620945
$66$	7.81829	0.962365
$67$	1.26329	0.154336	0.0771679	−	0.997018i	$-0.475412\pi$
$67$	1.26329	0.154336	0.0771679	+	0.997018i	$0.475412\pi$
$68$	9.74247	1.18145
$69$	−20.0631	−2.41531
$70$	4.99184	0.596639
$71$	−9.87557	−1.17201	−0.586007	−	0.810306i	$-0.699301\pi$
$71$	−9.87557	−1.17201	−0.586007	+	0.810306i	$0.699301\pi$
$72$	−7.21944	−0.850819
$73$	−7.90176	−0.924831	−0.462416	−	0.886663i	$-0.653017\pi$
$73$	−7.90176	−0.924831	−0.462416	+	0.886663i	$0.653017\pi$
$74$	−15.2638	−1.77438
$75$	−11.5284	−1.33119
$76$	−22.5793	−2.59002
$77$	−6.29138	−0.716969
$78$	5.48435	0.620981
$79$	−6.88388	−0.774497	−0.387249	−	0.921975i	$-0.626574\pi$
$79$	−6.88388	−0.774497	−0.387249	+	0.921975i	$0.626574\pi$
$80$	0.285152	0.0318810
$81$	−9.31216	−1.03468
$82$	24.6532	2.72250
$83$	−2.36869	−0.259997	−0.129999	−	0.991514i	$-0.541497\pi$
$83$	−2.36869	−0.259997	−0.129999	+	0.991514i	$0.541497\pi$
$84$	33.2609	3.62906
$85$	−1.57086	−0.170384
$86$	15.4614	1.66724
$87$	−4.61369	−0.494639
$88$	3.55863	0.379351
$89$	−3.70599	−0.392834	−0.196417	−	0.980520i	$-0.562931\pi$
$89$	−3.70599	−0.392834	−0.196417	+	0.980520i	$0.562931\pi$
$90$	3.27121	0.344816
$91$	−4.41326	−0.462635
$92$	−25.6628	−2.67554
$93$	12.7668	1.32386
$94$	9.92924	1.02412
$95$	3.64065	0.373523
$96$	15.2427	1.55570
$97$	−15.1692	−1.54020	−0.770100	−	0.637923i	$-0.779794\pi$
$97$	−15.1692	−1.54020	−0.770100	+	0.637923i	$0.779794\pi$
$98$	−28.1901	−2.84763
$99$	−4.12282	−0.414359
$100$	−14.7461	−1.47461
$101$	8.31300	0.827175	0.413587	−	0.910464i	$-0.364276\pi$
$101$	8.31300	0.827175	0.413587	+	0.910464i	$0.364276\pi$
$102$	−17.2089	−1.70394
$103$	17.1535	1.69019	0.845095	−	0.534617i	$-0.179544\pi$
$103$	17.1535	1.69019	0.845095	+	0.534617i	$0.179544\pi$
$104$	2.49629	0.244782
$105$	−5.36294	−0.523369
$106$	−6.89422	−0.669625
$107$	−17.1940	−1.66221	−0.831105	−	0.556116i	$-0.812291\pi$
$107$	−17.1940	−1.66221	−0.831105	+	0.556116i	$0.812291\pi$
$108$	−0.813481	−0.0782773
$109$	−17.0135	−1.62959	−0.814797	−	0.579746i	$-0.803152\pi$
$109$	−17.0135	−1.62959	−0.814797	+	0.579746i	$0.803152\pi$
$110$	−1.61246	−0.153742
$111$	16.3985	1.55647
$112$	−2.51378	−0.237529
$113$	4.53839	0.426936	0.213468	−	0.976950i	$-0.431524\pi$
$113$	4.53839	0.426936	0.213468	+	0.976950i	$0.431524\pi$
$114$	39.8836	3.73545
$115$	4.13784	0.385855
$116$	−5.90141	−0.547932
$117$	−2.89206	−0.267371
$118$	25.7973	2.37484
$119$	13.8480	1.26945
$120$	3.03347	0.276916
$121$	−8.96777	−0.815252
$122$	−28.9121	−2.61757
$123$	−26.4860	−2.38816
$124$	16.3302	1.46649
$125$	4.88075	0.436548
$126$	−28.8376	−2.56905
$127$	11.3985	1.01145	0.505726	−	0.862694i	$-0.331225\pi$
$127$	11.3985	1.01145	0.505726	+	0.862694i	$0.331225\pi$
$128$	16.9231	1.49581
$129$	−16.6108	−1.46250
$130$	−1.13110	−0.0992041
$131$	8.05120	0.703437	0.351719	−	0.936106i	$-0.385597\pi$
$131$	8.05120	0.703437	0.351719	+	0.936106i	$0.385597\pi$
$132$	−10.7439	−0.935135
$133$	−32.0944	−2.78294
$134$	−2.85428	−0.246572
$135$	0.131165	0.0112888
$136$	−7.83293	−0.671668
$137$	−10.4214	−0.890361	−0.445181	−	0.895441i	$-0.646861\pi$
$137$	−10.4214	−0.890361	−0.445181	+	0.895441i	$0.646861\pi$
$138$	45.3303	3.85877
$139$	−8.35576	−0.708727	−0.354363	−	0.935108i	$-0.615302\pi$
$139$	−8.35576	−0.708727	−0.354363	+	0.935108i	$0.615302\pi$
$140$	−6.85978	−0.579757
$141$	−10.6674	−0.898356
$142$	22.3128	1.87245
$143$	1.42556	0.119212
$144$	−1.64731	−0.137276
$145$	0.951534	0.0790206
$146$	17.8532	1.47754
$147$	30.2858	2.49793
$148$	20.9754	1.72417
$149$	3.81003	0.312130	0.156065	−	0.987747i	$-0.450119\pi$
$149$	3.81003	0.312130	0.156065	+	0.987747i	$0.450119\pi$
$150$	26.0473	2.12675
$151$	14.3357	1.16663	0.583313	−	0.812247i	$-0.301756\pi$
$151$	14.3357	1.16663	0.583313	+	0.812247i	$0.301756\pi$
$152$	18.1537	1.47246
$153$	9.07477	0.733652
$154$	14.2147	1.14545
$155$	−2.63305	−0.211492
$156$	−7.53659	−0.603410
$157$	2.13284	0.170219	0.0851094	−	0.996372i	$-0.472876\pi$
$157$	2.13284	0.170219	0.0851094	+	0.996372i	$0.472876\pi$
$158$	15.5534	1.23736
$159$	7.40674	0.587393
$160$	−3.14367	−0.248529
$161$	−36.4773	−2.87482
$162$	21.0398	1.65304
$163$	−0.398816	−0.0312377	−0.0156188	−	0.999878i	$-0.504972\pi$
$163$	−0.398816	−0.0312377	−0.0156188	+	0.999878i	$0.504972\pi$
$164$	−33.8784	−2.64546
$165$	1.73233	0.134861
$166$	5.35180	0.415380
$167$	−2.36092	−0.182693	−0.0913467	−	0.995819i	$-0.529117\pi$
$167$	−2.36092	−0.182693	−0.0913467	+	0.995819i	$0.529117\pi$
$168$	−26.7417	−2.06317
$169$	1.00000	0.0769231
$170$	3.54919	0.272211
$171$	−21.0318	−1.60834
$172$	−21.2470	−1.62007
$173$	−0.260989	−0.0198426	−0.00992132	−	0.999951i	$-0.503158\pi$
$173$	−0.260989	−0.0198426	−0.00992132	+	0.999951i	$0.503158\pi$
$174$	10.4241	0.790251
$175$	−20.9602	−1.58444
$176$	0.811995	0.0612064
$177$	−27.7151	−2.08320
$178$	8.37329	0.627604
$179$	22.3568	1.67102	0.835512	−	0.549473i	$-0.185171\pi$
$179$	22.3568	1.67102	0.835512	+	0.549473i	$0.185171\pi$
$180$	−4.49530	−0.335060
$181$	13.5208	1.00499	0.502496	−	0.864580i	$-0.332415\pi$
$181$	13.5208	1.00499	0.502496	+	0.864580i	$0.332415\pi$
$182$	9.97128	0.739121
$183$	31.0614	2.29613
$184$	20.6329	1.52108
$185$	−3.38205	−0.248653
$186$	−28.8453	−2.11504
$187$	−4.47316	−0.327110
$188$	−13.6447	−0.995146
$189$	−1.15629	−0.0841076
$190$	−8.22566	−0.596752
$191$	9.04166	0.654231	0.327116	−	0.944984i	$-0.393923\pi$
$191$	9.04166	0.654231	0.327116	+	0.944984i	$0.393923\pi$
$192$	−31.6739	−2.28587
$193$	−5.67409	−0.408430	−0.204215	−	0.978926i	$-0.565464\pi$
$193$	−5.67409	−0.408430	−0.204215	+	0.978926i	$0.565464\pi$
$194$	34.2732	2.46067
$195$	1.21519	0.0870214
$196$	38.7388	2.76706
$197$	−3.63596	−0.259051	−0.129526	−	0.991576i	$-0.541345\pi$
$197$	−3.63596	−0.259051	−0.129526	+	0.991576i	$0.541345\pi$
$198$	9.31506	0.661993
$199$	−8.68652	−0.615771	−0.307886	−	0.951423i	$-0.599621\pi$
$199$	−8.68652	−0.615771	−0.307886	+	0.951423i	$0.599621\pi$
$200$	11.8558	0.838335
$201$	3.06646	0.216292
$202$	−18.7823	−1.32152
$203$	−8.38830	−0.588743
$204$	23.6485	1.65572
$205$	5.46251	0.381518
$206$	−38.7566	−2.70030
$207$	−23.9040	−1.66145
$208$	0.569596	0.0394944
$209$	10.3671	0.717105
$210$	12.1170	0.836151
$211$	13.1202	0.903230	0.451615	−	0.892213i	$-0.350848\pi$
$211$	13.1202	0.903230	0.451615	+	0.892213i	$0.350848\pi$
$212$	9.47402	0.650678
$213$	−23.9715	−1.64250
$214$	38.8481	2.65560
$215$	3.42583	0.233640
$216$	0.654037	0.0445016
$217$	23.2118	1.57572
$218$	38.4401	2.60349
$219$	−19.1804	−1.29609
$220$	2.21583	0.149392
$221$	−3.13782	−0.211073
$222$	−37.0506	−2.48667
$223$	7.26442	0.486461	0.243231	−	0.969968i	$-0.421793\pi$
$223$	7.26442	0.486461	0.243231	+	0.969968i	$0.421793\pi$
$224$	27.7132	1.85167
$225$	−13.7355	−0.915700
$226$	−10.2540	−0.682086
$227$	−17.1791	−1.14022	−0.570108	−	0.821570i	$-0.693098\pi$
$227$	−17.1791	−1.14022	−0.570108	+	0.821570i	$0.693098\pi$
$228$	−54.8080	−3.62975
$229$	13.1285	0.867553	0.433776	−	0.901021i	$-0.357181\pi$
$229$	13.1285	0.867553	0.433776	+	0.901021i	$0.357181\pi$
$230$	−9.34900	−0.616455
$231$	−15.2714	−1.00479
$232$	4.74472	0.311506
$233$	8.50600	0.557247	0.278623	−	0.960400i	$-0.410122\pi$
$233$	8.50600	0.557247	0.278623	+	0.960400i	$0.410122\pi$
$234$	6.53430	0.427161
$235$	2.20006	0.143516
$236$	−35.4506	−2.30764
$237$	−16.7096	−1.08541
$238$	−31.2881	−2.02811
$239$	−16.1972	−1.04771	−0.523854	−	0.851808i	$-0.675506\pi$
$239$	−16.1972	−1.04771	−0.523854	+	0.851808i	$0.675506\pi$
$240$	0.692166	0.0446791
$241$	−12.8332	−0.826657	−0.413328	−	0.910582i	$-0.635634\pi$
$241$	−12.8332	−0.826657	−0.413328	+	0.910582i	$0.635634\pi$
$242$	20.2617	1.30247
$243$	−21.8179	−1.39962
$244$	39.7309	2.54351
$245$	−6.24619	−0.399054
$246$	59.8422	3.81540
$247$	7.27226	0.462723
$248$	−13.1294	−0.833719
$249$	−5.74965	−0.364370
$250$	−11.0275	−0.697442
$251$	−0.126202	−0.00796582	−0.00398291	−	0.999992i	$-0.501268\pi$
$251$	−0.126202	−0.00796582	−0.00398291	+	0.999992i	$0.501268\pi$
$252$	39.6285	2.49636
$253$	11.7828	0.740781
$254$	−25.7536	−1.61593
$255$	−3.81304	−0.238782
$256$	−12.1385	−0.758659
$257$	8.29401	0.517366	0.258683	−	0.965962i	$-0.416711\pi$
$257$	8.29401	0.517366	0.258683	+	0.965962i	$0.416711\pi$
$258$	37.5303	2.33653
$259$	29.8146	1.85259
$260$	1.55436	0.0963971
$261$	−5.49696	−0.340253
$262$	−18.1908	−1.12383
$263$	16.7730	1.03427	0.517133	−	0.855905i	$-0.326999\pi$
$263$	16.7730	1.03427	0.517133	+	0.855905i	$0.326999\pi$
$264$	8.63806	0.531636
$265$	−1.52758	−0.0938383
$266$	72.5138	4.44611
$267$	−8.99576	−0.550532
$268$	3.92234	0.239595
$269$	−20.5132	−1.25071	−0.625355	−	0.780341i	$-0.715046\pi$
$269$	−20.5132	−1.25071	−0.625355	+	0.780341i	$0.715046\pi$
$270$	−0.296352	−0.0180354
$271$	24.7716	1.50477	0.752385	−	0.658723i	$-0.228903\pi$
$271$	24.7716	1.50477	0.752385	+	0.658723i	$0.228903\pi$
$272$	−1.78729	−0.108370
$273$	−10.7126	−0.648353
$274$	23.5461	1.42247
$275$	6.77054	0.408279
$276$	−62.2929	−3.74959
$277$	18.8033	1.12978	0.564890	−	0.825166i	$-0.308918\pi$
$277$	18.8033	1.12978	0.564890	+	0.825166i	$0.308918\pi$
$278$	18.8789	1.13228
$279$	15.2110	0.910657
$280$	5.51525	0.329599
$281$	29.7889	1.77705	0.888527	−	0.458824i	$-0.151729\pi$
$281$	29.7889	1.77705	0.888527	+	0.458824i	$0.151729\pi$
$282$	24.1018	1.43524
$283$	19.0897	1.13476	0.567381	−	0.823455i	$-0.307957\pi$
$283$	19.0897	1.13476	0.567381	+	0.823455i	$0.307957\pi$
$284$	−30.6622	−1.81947
$285$	8.83717	0.523469
$286$	−3.22091	−0.190456
$287$	−48.1551	−2.84250
$288$	18.1608	1.07014
$289$	−7.15408	−0.420828
$290$	−2.14989	−0.126246
$291$	−36.8211	−2.15849
$292$	−24.5338	−1.43573
$293$	−20.1293	−1.17597	−0.587983	−	0.808873i	$-0.700078\pi$
$293$	−20.1293	−1.17597	−0.587983	+	0.808873i	$0.700078\pi$
$294$	−68.4275	−3.99077
$295$	5.71601	0.332799
$296$	−16.8642	−0.980212
$297$	0.373502	0.0216728
$298$	−8.60836	−0.498669
$299$	8.26540	0.478000
$300$	−35.7941	−2.06657
$301$	−30.2006	−1.74074
$302$	−32.3901	−1.86384
$303$	20.1786	1.15923
$304$	4.14225	0.237574
$305$	−6.40615	−0.366815
$306$	−20.5035	−1.17211
$307$	−21.2467	−1.21261	−0.606307	−	0.795231i	$-0.707350\pi$
$307$	−21.2467	−1.21261	−0.606307	+	0.795231i	$0.707350\pi$
$308$	−19.5338	−1.11304
$309$	41.6378	2.36869
$310$	5.94909	0.337886
$311$	−10.1016	−0.572808	−0.286404	−	0.958109i	$-0.592460\pi$
$311$	−10.1016	−0.572808	−0.286404	+	0.958109i	$0.592460\pi$
$312$	6.05940	0.343046
$313$	−21.9204	−1.23901	−0.619507	−	0.784991i	$-0.712667\pi$
$313$	−21.9204	−1.23901	−0.619507	+	0.784991i	$0.712667\pi$
$314$	−4.81891	−0.271947
$315$	−6.38965	−0.360016
$316$	−21.3734	−1.20235
$317$	−24.1933	−1.35883	−0.679416	−	0.733753i	$-0.737767\pi$
$317$	−24.1933	−1.35883	−0.679416	+	0.733753i	$0.737767\pi$
$318$	−16.7347	−0.938437
$319$	2.70957	0.151707
$320$	6.53248	0.365177
$321$	−41.7361	−2.32948
$322$	82.4166	4.59290
$323$	−22.8191	−1.26969
$324$	−28.9129	−1.60627
$325$	4.74938	0.263448
$326$	0.901081	0.0499063
$327$	−41.2978	−2.28377
$328$	27.2382	1.50398
$329$	−19.3947	−1.06927
$330$	−3.91401	−0.215459
$331$	9.01493	0.495505	0.247753	−	0.968823i	$-0.420308\pi$
$331$	9.01493	0.495505	0.247753	+	0.968823i	$0.420308\pi$
$332$	−7.35443	−0.403627
$333$	19.5379	1.07067
$334$	5.33424	0.291877
$335$	−0.632432	−0.0345535
$336$	−6.10183	−0.332882
$337$	−21.9916	−1.19796	−0.598980	−	0.800764i	$-0.704427\pi$
$337$	−21.9916	−1.19796	−0.598980	+	0.800764i	$0.704427\pi$
$338$	−2.25939	−0.122895
$339$	11.0163	0.598323
$340$	−4.87729	−0.264508
$341$	−7.49784	−0.406031
$342$	47.5192	2.56954
$343$	24.1708	1.30510
$344$	17.0825	0.921029
$345$	10.0440	0.540751
$346$	0.589677	0.0317012
$347$	−13.8394	−0.742939	−0.371469	−	0.928445i	$-0.621146\pi$
$347$	−13.8394	−0.742939	−0.371469	+	0.928445i	$0.621146\pi$
$348$	−14.3248	−0.767891
$349$	3.59936	0.192669	0.0963347	−	0.995349i	$-0.469288\pi$
$349$	3.59936	0.192669	0.0963347	+	0.995349i	$0.469288\pi$
$350$	47.3574	2.53136
$351$	0.262003	0.0139847
$352$	−8.95187	−0.477136
$353$	−3.85925	−0.205407	−0.102704	−	0.994712i	$-0.532749\pi$
$353$	−3.85925	−0.205407	−0.102704	+	0.994712i	$0.532749\pi$
$354$	62.6193	3.32818
$355$	4.94393	0.262396
$356$	−11.5066	−0.609846
$357$	33.6141	1.77905
$358$	−50.5127	−2.66968
$359$	8.30954	0.438561	0.219280	−	0.975662i	$-0.429629\pi$
$359$	8.30954	0.438561	0.219280	+	0.975662i	$0.429629\pi$
$360$	3.61421	0.190486
$361$	33.8858	1.78346
$362$	−30.5488	−1.60561
$363$	−21.7680	−1.14252
$364$	−13.7025	−0.718207
$365$	3.95580	0.207056
$366$	−70.1799	−3.66836
$367$	18.5090	0.966162	0.483081	−	0.875576i	$-0.339518\pi$
$367$	18.5090	0.966162	0.483081	+	0.875576i	$0.339518\pi$
$368$	4.70794	0.245418
$369$	−31.5566	−1.64277
$370$	7.64137	0.397256
$371$	13.4664	0.699143
$372$	39.6391	2.05519
$373$	−8.31567	−0.430569	−0.215284	−	0.976551i	$-0.569068\pi$
$373$	−8.31567	−0.430569	−0.215284	+	0.976551i	$0.569068\pi$
$374$	10.1066	0.522601
$375$	11.8473	0.611793
$376$	10.9703	0.565753
$377$	1.90070	0.0978913
$378$	2.61251	0.134373
$379$	25.1001	1.28930	0.644652	−	0.764476i	$-0.277002\pi$
$379$	25.1001	1.28930	0.644652	+	0.764476i	$0.277002\pi$
$380$	11.3037	0.579867
$381$	27.6682	1.41748
$382$	−20.4286	−1.04522
$383$	19.9566	1.01973	0.509867	−	0.860253i	$-0.329694\pi$
$383$	19.9566	1.01973	0.509867	+	0.860253i	$0.329694\pi$
$384$	41.0785	2.09628
$385$	3.14960	0.160519
$386$	12.8200	0.652521
$387$	−19.7908	−1.00603
$388$	−47.0982	−2.39105
$389$	−2.93457	−0.148788	−0.0743942	−	0.997229i	$-0.523702\pi$
$389$	−2.93457	−0.148788	−0.0743942	+	0.997229i	$0.523702\pi$
$390$	−2.74559	−0.139028
$391$	−25.9353	−1.31161
$392$	−31.1459	−1.57311
$393$	19.5431	0.985821
$394$	8.21505	0.413868
$395$	3.44622	0.173398
$396$	−12.8007	−0.643261
$397$	9.31463	0.467488	0.233744	−	0.972298i	$-0.424902\pi$
$397$	9.31463	0.467488	0.233744	+	0.972298i	$0.424902\pi$
$398$	19.6263	0.983776
$399$	−77.9045	−3.90010
$400$	2.70523	0.135261
$401$	3.11165	0.155389	0.0776943	−	0.996977i	$-0.475244\pi$
$401$	3.11165	0.155389	0.0776943	+	0.996977i	$0.475244\pi$
$402$	−6.92835	−0.345554
$403$	−5.25956	−0.261997
$404$	25.8106	1.28413
$405$	4.66187	0.231650
$406$	18.9525	0.940595
$407$	−9.63067	−0.477374
$408$	−19.0133	−0.941299
$409$	3.93964	0.194802	0.0974012	−	0.995245i	$-0.468947\pi$
$409$	3.93964	0.194802	0.0974012	+	0.995245i	$0.468947\pi$
$410$	−12.3420	−0.609526
$411$	−25.2965	−1.24778
$412$	53.2592	2.62389
$413$	−50.3898	−2.47952
$414$	54.0086	2.65438
$415$	1.18582	0.0582095
$416$	−6.27953	−0.307879
$417$	−20.2824	−0.993234
$418$	−23.4233	−1.14567
$419$	13.7535	0.671905	0.335952	−	0.941879i	$-0.390942\pi$
$419$	13.7535	0.671905	0.335952	+	0.941879i	$0.390942\pi$
$420$	−16.6511	−0.812492
$421$	28.7304	1.40024	0.700118	−	0.714028i	$-0.253131\pi$
$421$	28.7304	1.40024	0.700118	+	0.714028i	$0.253131\pi$
$422$	−29.6436	−1.44303
$423$	−12.7096	−0.617962
$424$	−7.61709	−0.369919
$425$	−14.9027	−0.722887
$426$	54.1611	2.62411
$427$	56.4738	2.73296
$428$	−53.3849	−2.58046
$429$	3.46035	0.167067
$430$	−7.74030	−0.373271
$431$	−4.37709	−0.210837	−0.105419	−	0.994428i	$-0.533618\pi$
$431$	−4.37709	−0.210837	−0.105419	+	0.994428i	$0.533618\pi$
$432$	0.149236	0.00718012
$433$	29.8842	1.43614	0.718071	−	0.695970i	$-0.245025\pi$
$433$	29.8842	1.43614	0.718071	+	0.695970i	$0.245025\pi$
$434$	−52.4446	−2.51742
$435$	2.30971	0.110742
$436$	−52.8243	−2.52983
$437$	60.1081	2.87536
$438$	43.3360	2.07068
$439$	15.6911	0.748896	0.374448	−	0.927248i	$-0.377832\pi$
$439$	15.6911	0.748896	0.374448	+	0.927248i	$0.377832\pi$
$440$	−1.78153	−0.0849309
$441$	36.0838	1.71828
$442$	7.08957	0.337216
$443$	−22.0329	−1.04682	−0.523408	−	0.852082i	$-0.675340\pi$
$443$	−22.0329	−1.04682	−0.523408	+	0.852082i	$0.675340\pi$
$444$	50.9149	2.41631
$445$	1.85530	0.0879497
$446$	−16.4132	−0.777186
$447$	9.24831	0.437430
$448$	−57.5874	−2.72075
$449$	12.5016	0.589985	0.294992	−	0.955500i	$-0.404683\pi$
$449$	12.5016	0.589985	0.294992	+	0.955500i	$0.404683\pi$
$450$	31.0339	1.46295
$451$	15.5550	0.732455
$452$	14.0910	0.662787
$453$	34.7980	1.63495
$454$	38.8143	1.82164
$455$	2.20937	0.103577
$456$	44.0655	2.06356
$457$	31.6221	1.47922	0.739611	−	0.673035i	$-0.235010\pi$
$457$	31.6221	1.47922	0.739611	+	0.673035i	$0.235010\pi$
$458$	−29.6623	−1.38603
$459$	−0.822119	−0.0383732
$460$	12.8474	0.599012
$461$	15.7316	0.732695	0.366348	−	0.930478i	$-0.380608\pi$
$461$	15.7316	0.732695	0.366348	+	0.930478i	$0.380608\pi$
$462$	34.5041	1.60528
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	1.08263	0.0502600
$465$	−6.39135	−0.296392
$466$	−19.2184	−0.890275
$467$	35.0632	1.62253	0.811265	−	0.584679i	$-0.198779\pi$
$467$	35.0632	1.62253	0.811265	+	0.584679i	$0.198779\pi$
$468$	−8.97943	−0.415074
$469$	5.57524	0.257441
$470$	−4.97080	−0.229286
$471$	5.17716	0.238551
$472$	28.5022	1.31192
$473$	9.75536	0.448552
$474$	37.7536	1.73408
$475$	34.5387	1.58475
$476$	42.9960	1.97072
$477$	8.82472	0.404056
$478$	36.5957	1.67385
$479$	12.9719	0.592701	0.296350	−	0.955079i	$-0.404230\pi$
$479$	12.9719	0.592701	0.296350	+	0.955079i	$0.404230\pi$
$480$	−7.63081	−0.348297
$481$	−6.75569	−0.308033
$482$	28.9952	1.32069
$483$	−88.5435	−4.02887
$484$	−27.8436	−1.26562
$485$	7.59404	0.344828
$486$	49.2953	2.23608
$487$	15.8936	0.720207	0.360103	−	0.932912i	$-0.382741\pi$
$487$	15.8936	0.720207	0.360103	+	0.932912i	$0.382741\pi$
$488$	−31.9436	−1.44602
$489$	−0.968068	−0.0437776
$490$	14.1126	0.637542
$491$	−2.49045	−0.112392	−0.0561962	−	0.998420i	$-0.517897\pi$
$491$	−2.49045	−0.112392	−0.0561962	+	0.998420i	$0.517897\pi$
$492$	−82.2351	−3.70744
$493$	−5.96407	−0.268608
$494$	−16.4309	−0.739261
$495$	2.06397	0.0927687
$496$	−2.99583	−0.134517
$497$	−43.5834	−1.95498
$498$	12.9907	0.582128
$499$	−14.9183	−0.667837	−0.333918	−	0.942602i	$-0.608371\pi$
$499$	−14.9183	−0.667837	−0.333918	+	0.942602i	$0.608371\pi$
$500$	15.1540	0.677708
$501$	−5.73079	−0.256033
$502$	0.285141	0.0127265
$503$	4.68926	0.209084	0.104542	−	0.994520i	$-0.466662\pi$
$503$	4.68926	0.209084	0.104542	+	0.994520i	$0.466662\pi$
$504$	−31.8613	−1.41921
$505$	−4.16167	−0.185192
$506$	−26.6221	−1.18350
$507$	2.42736	0.107803
$508$	35.3906	1.57020
$509$	−1.28176	−0.0568131	−0.0284065	−	0.999596i	$-0.509043\pi$
$509$	−1.28176	−0.0568131	−0.0284065	+	0.999596i	$0.509043\pi$
$510$	8.61516	0.381486
$511$	−34.8725	−1.54267
$512$	−6.42056	−0.283751
$513$	1.90536	0.0841235
$514$	−18.7394	−0.826560
$515$	−8.58744	−0.378408
$516$	−51.5741	−2.27042
$517$	6.26486	0.275528
$518$	−67.3629	−2.95976
$519$	−0.633514	−0.0278082
$520$	−1.24970	−0.0548030
$521$	9.27993	0.406561	0.203281	−	0.979121i	$-0.434840\pi$
$521$	9.27993	0.406561	0.203281	+	0.979121i	$0.434840\pi$
$522$	12.4198	0.543599
$523$	42.2067	1.84557	0.922786	−	0.385313i	$-0.125907\pi$
$523$	42.2067	1.84557	0.922786	+	0.385313i	$0.125907\pi$
$524$	24.9978	1.09203
$525$	−50.8780	−2.22050
$526$	−37.8967	−1.65237
$527$	16.5036	0.718906
$528$	1.97100	0.0857769
$529$	45.3168	1.97030
$530$	3.45140	0.149919
$531$	−33.0210	−1.43299
$532$	−99.6483	−4.32030
$533$	10.9114	0.472627
$534$	20.3250	0.879547
$535$	8.60771	0.372144
$536$	−3.15355	−0.136213
$537$	54.2679	2.34183
$538$	46.3473	1.99817
$539$	−17.7865	−0.766121
$540$	0.407247	0.0175251
$541$	−42.4956	−1.82703	−0.913514	−	0.406807i	$-0.866642\pi$
$541$	−42.4956	−1.82703	−0.913514	+	0.406807i	$0.866642\pi$
$542$	−55.9689	−2.40407
$543$	32.8198	1.40843
$544$	19.7040	0.844804
$545$	8.51731	0.364842
$546$	24.2039	1.03583
$547$	23.0202	0.984273	0.492136	−	0.870518i	$-0.336216\pi$
$547$	23.0202	0.984273	0.492136	+	0.870518i	$0.336216\pi$
$548$	−32.3569	−1.38222
$549$	37.0080	1.57946
$550$	−15.2973	−0.652279
$551$	13.8224	0.588855
$552$	50.0833	2.13169
$553$	−30.3804	−1.29190
$554$	−42.4840	−1.80497
$555$	−8.20944	−0.348471
$556$	−25.9434	−1.10025
$557$	−33.1487	−1.40456	−0.702279	−	0.711902i	$-0.747834\pi$
$557$	−33.1487	−1.40456	−0.702279	+	0.711902i	$0.747834\pi$
$558$	−34.3676	−1.45489
$559$	6.84316	0.289435
$560$	1.25845	0.0531793
$561$	−10.8580	−0.458423
$562$	−67.3047	−2.83908
$563$	−32.9532	−1.38881	−0.694406	−	0.719583i	$-0.744333\pi$
$563$	−32.9532	−1.38881	−0.694406	+	0.719583i	$0.744333\pi$
$564$	−33.1207	−1.39463
$565$	−2.27202	−0.0955845
$566$	−43.1310	−1.81293
$567$	−41.0970	−1.72591
$568$	24.6523	1.03439
$569$	−3.53665	−0.148264	−0.0741320	−	0.997248i	$-0.523619\pi$
$569$	−3.53665	−0.148264	−0.0741320	+	0.997248i	$0.523619\pi$
$570$	−19.9666	−0.836310
$571$	−9.42884	−0.394585	−0.197292	−	0.980345i	$-0.563215\pi$
$571$	−9.42884	−0.394585	−0.197292	+	0.980345i	$0.563215\pi$
$572$	4.42616	0.185067
$573$	21.9473	0.916863
$574$	108.801	4.54127
$575$	39.2555	1.63707
$576$	−37.7377	−1.57241
$577$	−44.3051	−1.84445	−0.922223	−	0.386659i	$-0.873629\pi$
$577$	−44.3051	−1.84445	−0.922223	+	0.386659i	$0.873629\pi$
$578$	16.1639	0.672329
$579$	−13.7730	−0.572388
$580$	2.95437	0.122674
$581$	−10.4536	−0.433690
$582$	83.1933	3.44847
$583$	−4.34991	−0.180155
$584$	19.7251	0.816232
$585$	1.44783	0.0598604
$586$	45.4800	1.87876
$587$	−4.45810	−0.184006	−0.0920028	−	0.995759i	$-0.529327\pi$
$587$	−4.45810	−0.184006	−0.0920028	+	0.995759i	$0.529327\pi$
$588$	94.0329	3.87785
$589$	−38.2489	−1.57602
$590$	−12.9147	−0.531690
$591$	−8.82577	−0.363044
$592$	−3.84802	−0.158152
$593$	−34.5096	−1.41714	−0.708571	−	0.705640i	$-0.750660\pi$
$593$	−34.5096	−1.41714	−0.708571	+	0.705640i	$0.750660\pi$
$594$	−0.843888	−0.0346251
$595$	−6.93262	−0.284210
$596$	11.8296	0.484559
$597$	−21.0853	−0.862964
$598$	−18.6748	−0.763668
$599$	−41.1084	−1.67965	−0.839823	−	0.542861i	$-0.817341\pi$
$599$	−41.1084	−1.67965	−0.839823	+	0.542861i	$0.817341\pi$
$600$	28.7784	1.17487
$601$	−12.3698	−0.504573	−0.252286	−	0.967653i	$-0.581182\pi$
$601$	−12.3698	−0.504573	−0.252286	+	0.967653i	$0.581182\pi$
$602$	68.2351	2.78105
$603$	3.65352	0.148783
$604$	44.5104	1.81110
$605$	4.48946	0.182523
$606$	−45.5914	−1.85203
$607$	−17.4467	−0.708139	−0.354070	−	0.935219i	$-0.615202\pi$
$607$	−17.4467	−0.708139	−0.354070	+	0.935219i	$0.615202\pi$
$608$	−45.6664	−1.85202
$609$	−20.3614	−0.825086
$610$	14.4740	0.586035
$611$	4.39465	0.177789
$612$	28.1758	1.13894
$613$	−21.9841	−0.887931	−0.443966	−	0.896044i	$-0.646429\pi$
$613$	−21.9841	−0.887931	−0.443966	+	0.896044i	$0.646429\pi$
$614$	48.0046	1.93731
$615$	13.2595	0.534673
$616$	15.7051	0.632778
$617$	−17.1761	−0.691485	−0.345743	−	0.938329i	$-0.612373\pi$
$617$	−17.1761	−0.691485	−0.345743	+	0.938329i	$0.612373\pi$
$618$	−94.0761	−3.78430
$619$	12.1978	0.490273	0.245136	−	0.969489i	$-0.421167\pi$
$619$	12.1978	0.490273	0.245136	+	0.969489i	$0.421167\pi$
$620$	−8.17523	−0.328325
$621$	2.16556	0.0869010
$622$	22.8234	0.915136
$623$	−16.3555	−0.655269
$624$	1.38261	0.0553488
$625$	21.3035	0.852139
$626$	49.5267	1.97949
$627$	25.1646	1.00498
$628$	6.62214	0.264252
$629$	21.1981	0.845226
$630$	14.4367	0.575173
$631$	24.4143	0.971918	0.485959	−	0.873982i	$-0.338470\pi$
$631$	24.4143	0.971918	0.485959	+	0.873982i	$0.338470\pi$
$632$	17.1842	0.683551
$633$	31.8473	1.26582
$634$	54.6622	2.17091
$635$	−5.70633	−0.226449
$636$	22.9968	0.911884
$637$	−12.4769	−0.494351
$638$	−6.12199	−0.242372
$639$	−28.5608	−1.12985
$640$	−8.47209	−0.334889
$641$	−37.7005	−1.48908	−0.744540	−	0.667578i	$-0.767331\pi$
$641$	−37.7005	−1.48908	−0.744540	+	0.667578i	$0.767331\pi$
$642$	94.2981	3.72165
$643$	−47.1181	−1.85816	−0.929079	−	0.369882i	$-0.879398\pi$
$643$	−47.1181	−1.85816	−0.929079	+	0.369882i	$0.879398\pi$
$644$	−113.257	−4.46294
$645$	8.31572	0.327431
$646$	51.5572	2.02849
$647$	−19.8341	−0.779760	−0.389880	−	0.920866i	$-0.627483\pi$
$647$	−19.8341	−0.779760	−0.389880	+	0.920866i	$0.627483\pi$
$648$	23.2459	0.913185
$649$	16.2768	0.638921
$650$	−10.7307	−0.420893
$651$	56.3433	2.20827
$652$	−1.23826	−0.0484942
$653$	17.5247	0.685796	0.342898	−	0.939373i	$-0.388592\pi$
$653$	17.5247	0.685796	0.342898	+	0.939373i	$0.388592\pi$
$654$	93.3078	3.64863
$655$	−4.03061	−0.157489
$656$	6.21512	0.242660
$657$	−22.8524	−0.891557
$658$	43.8203	1.70829
$659$	19.2598	0.750254	0.375127	−	0.926973i	$-0.377599\pi$
$659$	19.2598	0.750254	0.375127	+	0.926973i	$0.377599\pi$
$660$	5.37862	0.209363
$661$	33.1412	1.28904	0.644521	−	0.764586i	$-0.277057\pi$
$661$	33.1412	1.28904	0.644521	+	0.764586i	$0.277057\pi$
$662$	−20.3683	−0.791635
$663$	−7.61661	−0.295805
$664$	5.91295	0.229467
$665$	16.0671	0.623057
$666$	−44.1437	−1.71054
$667$	15.7101	0.608297
$668$	−7.33030	−0.283618
$669$	17.6333	0.681744
$670$	1.42891	0.0552037
$671$	−18.2421	−0.704227
$672$	67.2698	2.59499
$673$	−41.3761	−1.59493	−0.797466	−	0.603363i	$-0.793827\pi$
$673$	−41.3761	−1.59493	−0.797466	+	0.603363i	$0.793827\pi$
$674$	49.6877	1.91390
$675$	1.24435	0.0478951
$676$	3.10485	0.119417
$677$	−0.406026	−0.0156048	−0.00780242	−	0.999970i	$-0.502484\pi$
$677$	−0.406026	−0.0156048	−0.00780242	+	0.999970i	$0.502484\pi$
$678$	−24.8901	−0.955900
$679$	−66.9457	−2.56914
$680$	3.92133	0.150376
$681$	−41.6997	−1.59794
$682$	16.9406	0.648687
$683$	−21.2673	−0.813771	−0.406885	−	0.913479i	$-0.633385\pi$
$683$	−21.2673	−0.813771	−0.406885	+	0.913479i	$0.633385\pi$
$684$	−65.3008	−2.49684
$685$	5.21719	0.199338
$686$	−54.6113	−2.08507
$687$	31.8675	1.21582
$688$	3.89784	0.148604
$689$	−3.05136	−0.116248
$690$	−22.6934	−0.863921
$691$	−25.6566	−0.976023	−0.488011	−	0.872837i	$-0.662278\pi$
$691$	−25.6566	−0.976023	−0.488011	+	0.872837i	$0.662278\pi$
$692$	−0.810333	−0.0308042
$693$	−18.1951	−0.691173
$694$	31.2687	1.18694
$695$	4.18308	0.158673
$696$	11.5171	0.436556
$697$	−34.2382	−1.29686
$698$	−8.13237	−0.307815
$699$	20.6471	0.780945
$700$	−65.0784	−2.45973
$701$	−20.3870	−0.770007	−0.385003	−	0.922915i	$-0.625800\pi$
$701$	−20.3870	−0.770007	−0.385003	+	0.922915i	$0.625800\pi$
$702$	−0.591968	−0.0223424
$703$	−49.1292	−1.85294
$704$	18.6018	0.701081
$705$	5.34033	0.201128
$706$	8.71956	0.328165
$707$	36.6874	1.37977
$708$	−86.0514	−3.23401
$709$	−14.8967	−0.559456	−0.279728	−	0.960079i	$-0.590244\pi$
$709$	−14.8967	−0.559456	−0.279728	+	0.960079i	$0.590244\pi$
$710$	−11.1703	−0.419213
$711$	−19.9086	−0.746631
$712$	9.25125	0.346705
$713$	−43.4724	−1.62805
$714$	−75.9474	−2.84226
$715$	−0.713668	−0.0266897
$716$	69.4145	2.59414
$717$	−39.3163	−1.46829
$718$	−18.7745	−0.700658
$719$	−15.0128	−0.559881	−0.279941	−	0.960017i	$-0.590315\pi$
$719$	−15.0128	−0.559881	−0.279941	+	0.960017i	$0.590315\pi$
$720$	0.824678	0.0307339
$721$	75.7031	2.81933
$722$	−76.5613	−2.84932
$723$	−31.1507	−1.15851
$724$	41.9800	1.56018
$725$	9.02717	0.335261
$726$	49.1824	1.82533
$727$	−6.05656	−0.224625	−0.112313	−	0.993673i	$-0.535826\pi$
$727$	−6.05656	−0.224625	−0.112313	+	0.993673i	$0.535826\pi$
$728$	11.0168	0.408310
$729$	−25.0234	−0.926794
$730$	−8.93769	−0.330799
$731$	−21.4726	−0.794193
$732$	96.4411	3.56456
$733$	3.08414	0.113915	0.0569577	−	0.998377i	$-0.481860\pi$
$733$	3.08414	0.113915	0.0569577	+	0.998377i	$0.481860\pi$
$734$	−41.8191	−1.54357
$735$	−15.1617	−0.559249
$736$	−51.9028	−1.91316
$737$	−1.80090	−0.0663372
$738$	71.2987	2.62454
$739$	20.5392	0.755548	0.377774	−	0.925898i	$-0.376690\pi$
$739$	20.5392	0.755548	0.377774	+	0.925898i	$0.376690\pi$
$740$	−10.5008	−0.386016
$741$	17.6524	0.648476
$742$	−30.4260	−1.11697
$743$	8.00492	0.293672	0.146836	−	0.989161i	$-0.453091\pi$
$743$	8.00492	0.293672	0.146836	+	0.989161i	$0.453091\pi$
$744$	−31.8698	−1.16840
$745$	−1.90739	−0.0698812
$746$	18.7884	0.687890
$747$	−6.85040	−0.250643
$748$	−13.8885	−0.507814
$749$	−75.8817	−2.77266
$750$	−26.7678	−0.977420
$751$	8.36300	0.305170	0.152585	−	0.988290i	$-0.451240\pi$
$751$	8.36300	0.305170	0.152585	+	0.988290i	$0.451240\pi$
$752$	2.50318	0.0912815
$753$	−0.306338	−0.0111636
$754$	−4.29444	−0.156394
$755$	−7.17679	−0.261190
$756$	−3.59010	−0.130571
$757$	−33.9896	−1.23537	−0.617686	−	0.786425i	$-0.711930\pi$
$757$	−33.9896	−1.23537	−0.617686	+	0.786425i	$0.711930\pi$
$758$	−56.7109	−2.05983
$759$	28.6012	1.03816
$760$	−9.08815	−0.329662
$761$	44.7848	1.62345	0.811724	−	0.584041i	$-0.198529\pi$
$761$	44.7848	1.62345	0.811724	+	0.584041i	$0.198529\pi$
$762$	−62.5133	−2.26462
$763$	−75.0849	−2.71825
$764$	28.0730	1.01565
$765$	−4.54303	−0.164254
$766$	−45.0898	−1.62916
$767$	11.4178	0.412274
$768$	−29.4646	−1.06321
$769$	−55.0355	−1.98463	−0.992315	−	0.123734i	$-0.960513\pi$
$769$	−55.0355	−1.98463	−0.992315	+	0.123734i	$0.960513\pi$
$770$	−7.11619	−0.256450
$771$	20.1325	0.725055
$772$	−17.6172	−0.634058
$773$	−26.2196	−0.943052	−0.471526	−	0.881852i	$-0.656297\pi$
$773$	−26.2196	−0.943052	−0.471526	+	0.881852i	$0.656297\pi$
$774$	44.7153	1.60726
$775$	−24.9796	−0.897295
$776$	37.8668	1.35934
$777$	72.3707	2.59629
$778$	6.63033	0.237709
$779$	79.3509	2.84304
$780$	3.77298	0.135094
$781$	14.0782	0.503759
$782$	58.5981	2.09546
$783$	0.497991	0.0177967
$784$	−7.10677	−0.253813
$785$	−1.06774	−0.0381094
$786$	−44.1556	−1.57498
$787$	−11.8062	−0.420845	−0.210423	−	0.977610i	$-0.567484\pi$
$787$	−11.8062	−0.420845	−0.210423	+	0.977610i	$0.567484\pi$
$788$	−11.2891	−0.402158
$789$	40.7140	1.44946
$790$	−7.78637	−0.277026
$791$	20.0291	0.712153
$792$	10.2918	0.365702
$793$	−12.7964	−0.454413
$794$	−21.0454	−0.746873
$795$	−3.70797	−0.131508
$796$	−26.9704	−0.955940
$797$	−23.6726	−0.838528	−0.419264	−	0.907864i	$-0.637712\pi$
$797$	−23.6726	−0.838528	−0.419264	+	0.907864i	$0.637712\pi$
$798$	176.017	6.23093
$799$	−13.7896	−0.487842
$800$	−29.8239	−1.05443
$801$	−10.7180	−0.378700
$802$	−7.03045	−0.248254
$803$	11.2645	0.397514
$804$	9.52092	0.335777
$805$	18.2614	0.643628
$806$	11.8834	0.418575
$807$	−49.7928	−1.75279
$808$	−20.7517	−0.730042
$809$	12.4371	0.437265	0.218633	−	0.975807i	$-0.429840\pi$
$809$	12.4371	0.437265	0.218633	+	0.975807i	$0.429840\pi$
$810$	−10.5330	−0.370092
$811$	28.5505	1.00254	0.501271	−	0.865290i	$-0.332866\pi$
$811$	28.5505	1.00254	0.501271	+	0.865290i	$0.332866\pi$
$812$	−26.0444	−0.913981
$813$	60.1296	2.10884
$814$	21.7595	0.762668
$815$	0.199656	0.00699364
$816$	−4.33839	−0.151874
$817$	49.7653	1.74107
$818$	−8.90118	−0.311223
$819$	−12.7634	−0.445990
$820$	16.9603	0.592279
$821$	28.5283	0.995643	0.497822	−	0.867279i	$-0.334133\pi$
$821$	28.5283	0.995643	0.497822	+	0.867279i	$0.334133\pi$
$822$	57.1547	1.99350
$823$	0.611865	0.0213283	0.0106641	−	0.999943i	$-0.496605\pi$
$823$	0.611865	0.0213283	0.0106641	+	0.999943i	$0.496605\pi$
$824$	−42.8203	−1.49172
$825$	16.4345	0.572176
$826$	113.850	3.96136
$827$	−1.39672	−0.0485688	−0.0242844	−	0.999705i	$-0.507731\pi$
$827$	−1.39672	−0.0485688	−0.0242844	+	0.999705i	$0.507731\pi$
$828$	−74.2185	−2.57927
$829$	19.8978	0.691079	0.345540	−	0.938404i	$-0.387696\pi$
$829$	19.8978	0.691079	0.345540	+	0.938404i	$0.387696\pi$
$830$	−2.67923	−0.0929973
$831$	45.6423	1.58331
$832$	13.0487	0.452383
$833$	39.1501	1.35647
$834$	45.8259	1.58682
$835$	1.18193	0.0409023
$836$	32.1882	1.11325
$837$	−1.37802	−0.0476314
$838$	−31.0747	−1.07346
$839$	−46.8515	−1.61749	−0.808747	−	0.588156i	$-0.799854\pi$
$839$	−46.8515	−1.61749	−0.808747	+	0.588156i	$0.799854\pi$
$840$	13.3875	0.461912
$841$	−25.3873	−0.875425
$842$	−64.9133	−2.23706
$843$	72.3082	2.49043
$844$	40.7362	1.40220
$845$	−0.500622	−0.0172219
$846$	28.7160	0.987276
$847$	−39.5771	−1.35988
$848$	−1.73804	−0.0596846
$849$	46.3374	1.59030
$850$	33.6710	1.15491
$851$	−55.8385	−1.91412
$852$	−74.4281	−2.54986
$853$	−2.82819	−0.0968352	−0.0484176	−	0.998827i	$-0.515418\pi$
$853$	−2.82819	−0.0968352	−0.0484176	+	0.998827i	$0.515418\pi$
$854$	−127.596	−4.36626
$855$	10.5290	0.360084
$856$	42.9214	1.46702
$857$	47.7385	1.63072	0.815358	−	0.578958i	$-0.196540\pi$
$857$	47.7385	1.63072	0.815358	+	0.578958i	$0.196540\pi$
$858$	−7.81829	−0.266912
$859$	−22.4413	−0.765689	−0.382844	−	0.923813i	$-0.625055\pi$
$859$	−22.4413	−0.765689	−0.382844	+	0.923813i	$0.625055\pi$
$860$	10.6367	0.362709
$861$	−116.890	−3.98358
$862$	9.88956	0.336840
$863$	−26.3657	−0.897498	−0.448749	−	0.893658i	$-0.648130\pi$
$863$	−26.3657	−0.897498	−0.448749	+	0.893658i	$0.648130\pi$
$864$	−1.64526	−0.0559728
$865$	0.130657	0.00444247
$866$	−67.5200	−2.29442
$867$	−17.3655	−0.589764
$868$	72.0692	2.44619
$869$	9.81341	0.332897
$870$	−5.21855	−0.176925
$871$	−1.26329	−0.0428051
$872$	42.4706	1.43824
$873$	−43.8703	−1.48479
$874$	−135.808	−4.59377
$875$	21.5400	0.728186
$876$	−59.5523	−2.01209
$877$	20.4596	0.690872	0.345436	−	0.938442i	$-0.387731\pi$
$877$	20.4596	0.690872	0.345436	+	0.938442i	$0.387731\pi$
$878$	−35.4524	−1.19646
$879$	−48.8610	−1.64804
$880$	−0.406503	−0.0137032
$881$	−44.1552	−1.48763	−0.743813	−	0.668388i	$-0.766985\pi$
$881$	−44.1552	−1.48763	−0.743813	+	0.668388i	$0.766985\pi$
$882$	−81.5276	−2.74518
$883$	−20.4976	−0.689800	−0.344900	−	0.938640i	$-0.612087\pi$
$883$	−20.4976	−0.689800	−0.344900	+	0.938640i	$0.612087\pi$
$884$	−9.74247	−0.327675
$885$	13.8748	0.466396
$886$	49.7811	1.67243
$887$	−51.8347	−1.74044	−0.870219	−	0.492665i	$-0.836023\pi$
$887$	−51.8347	−1.74044	−0.870219	+	0.492665i	$0.836023\pi$
$888$	−40.9354	−1.37370
$889$	50.3044	1.68716
$890$	−4.19185	−0.140511
$891$	13.2751	0.444732
$892$	22.5549	0.755195
$893$	31.9591	1.06947
$894$	−20.8956	−0.698852
$895$	−11.1923	−0.374117
$896$	74.6862	2.49509
$897$	20.0631	0.669886
$898$	−28.2459	−0.942578
$899$	−9.99687	−0.333414
$900$	−42.6467	−1.42156
$901$	9.57462	0.318977
$902$	−35.1448	−1.17019
$903$	−73.3077	−2.43953
$904$	−11.3292	−0.376802
$905$	−6.76880	−0.225003
$906$	−78.6223	−2.61205
$907$	−6.46458	−0.214653	−0.107326	−	0.994224i	$-0.534229\pi$
$907$	−6.46458	−0.214653	−0.107326	+	0.994224i	$0.534229\pi$
$908$	−53.3385	−1.77010
$909$	24.0417	0.797414
$910$	−4.99184	−0.165478
$911$	9.59642	0.317943	0.158972	−	0.987283i	$-0.449182\pi$
$911$	9.59642	0.317943	0.158972	+	0.987283i	$0.449182\pi$
$912$	10.0547	0.332945
$913$	3.37672	0.111753
$914$	−71.4468	−2.36325
$915$	−15.5500	−0.514068
$916$	40.7619	1.34681
$917$	35.5321	1.17337
$918$	1.85749	0.0613063
$919$	−6.55296	−0.216162	−0.108081	−	0.994142i	$-0.534471\pi$
$919$	−6.55296	−0.216162	−0.108081	+	0.994142i	$0.534471\pi$
$920$	−10.3293	−0.340546
$921$	−51.5734	−1.69940
$922$	−35.5439	−1.17058
$923$	9.87557	0.325058
$924$	−47.4155	−1.55986
$925$	−32.0853	−1.05496
$926$	2.25939	0.0742482
$927$	49.6091	1.62938
$928$	−11.9355	−0.391803
$929$	−3.94686	−0.129492	−0.0647462	−	0.997902i	$-0.520624\pi$
$929$	−3.94686	−0.129492	−0.0647462	+	0.997902i	$0.520624\pi$
$930$	14.4406	0.473525
$931$	−90.7350	−2.97372
$932$	26.4099	0.865084
$933$	−24.5201	−0.802753
$934$	−79.2214	−2.59220
$935$	2.23936	0.0732350
$936$	7.21944	0.235975
$937$	−21.9296	−0.716408	−0.358204	−	0.933643i	$-0.616611\pi$
$937$	−21.9296	−0.716408	−0.358204	+	0.933643i	$0.616611\pi$
$938$	−12.5967	−0.411295
$939$	−53.2086	−1.73640
$940$	6.83086	0.222798
$941$	13.0132	0.424219	0.212109	−	0.977246i	$-0.431967\pi$
$941$	13.0132	0.424219	0.212109	+	0.977246i	$0.431967\pi$
$942$	−11.6972	−0.381116
$943$	90.1875	2.93691
$944$	6.50355	0.211672
$945$	0.578863	0.0188304
$946$	−22.0412	−0.716620
$947$	−21.2379	−0.690139	−0.345070	−	0.938577i	$-0.612145\pi$
$947$	−21.2379	−0.690139	−0.345070	+	0.938577i	$0.612145\pi$
$948$	−51.8810	−1.68502
$949$	7.90176	0.256502
$950$	−78.0365	−2.53184
$951$	−58.7258	−1.90431
$952$	−34.5687	−1.12038
$953$	47.9556	1.55343	0.776717	−	0.629850i	$-0.216883\pi$
$953$	47.9556	1.55343	0.776717	+	0.629850i	$0.216883\pi$
$954$	−19.9385	−0.645533
$955$	−4.52645	−0.146473
$956$	−50.2898	−1.62649
$957$	6.57711	0.212608
$958$	−29.3086	−0.946917
$959$	−45.9924	−1.48517
$960$	15.8567	0.511771
$961$	−3.33702	−0.107646
$962$	15.2638	0.492123
$963$	−49.7262	−1.60240
$964$	−39.8451	−1.28332
$965$	2.84057	0.0914413
$966$	200.055	6.43665
$967$	29.2656	0.941119	0.470560	−	0.882368i	$-0.344052\pi$
$967$	29.2656	0.941119	0.470560	+	0.882368i	$0.344052\pi$
$968$	22.3862	0.719520
$969$	−55.3900	−1.77938
$970$	−17.1579	−0.550908
$971$	4.15655	0.133390	0.0666951	−	0.997773i	$-0.478755\pi$
$971$	4.15655	0.133390	0.0666951	+	0.997773i	$0.478755\pi$
$972$	−67.7415	−2.17281
$973$	−36.8761	−1.18220
$974$	−35.9098	−1.15062
$975$	11.5284	0.369205
$976$	−7.28877	−0.233308
$977$	27.3819	0.876025	0.438012	−	0.898969i	$-0.355683\pi$
$977$	27.3819	0.876025	0.438012	+	0.898969i	$0.355683\pi$
$978$	2.18725	0.0699404
$979$	5.28312	0.168849
$980$	−19.3935	−0.619502
$981$	−49.2040	−1.57096
$982$	5.62691	0.179562
$983$	37.8216	1.20632	0.603161	−	0.797620i	$-0.293908\pi$
$983$	37.8216	1.20632	0.603161	+	0.797620i	$0.293908\pi$
$984$	66.1168	2.10773
$985$	1.82024	0.0579977
$986$	13.4752	0.429137
$987$	−47.0780	−1.49851
$988$	22.5793	0.718343
$989$	56.5614	1.79855
$990$	−4.66332	−0.148210
$991$	21.0434	0.668466	0.334233	−	0.942491i	$-0.391523\pi$
$991$	21.0434	0.668466	0.334233	+	0.942491i	$0.391523\pi$
$992$	33.0276	1.04863
$993$	21.8824	0.694419
$994$	98.4721	3.12335
$995$	4.34866	0.137862
$996$	−17.8518	−0.565657
$997$	12.1203	0.383853	0.191927	−	0.981409i	$-0.438526\pi$
$997$	12.1203	0.383853	0.191927	+	0.981409i	$0.438526\pi$
$998$	33.7064	1.06696
$999$	−1.77001	−0.0560007

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.15	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.15	✓	108	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25939 q^{2} +2.42736 q^{3} +3.10485 q^{4} -0.500622 q^{5} -5.48435 q^{6} +4.41326 q^{7} -2.49629 q^{8} +2.89206 q^{9} +O(q^{10})\)	\(q-2.25939 q^{2} +2.42736 q^{3} +3.10485 q^{4} -0.500622 q^{5} -5.48435 q^{6} +4.41326 q^{7} -2.49629 q^{8} +2.89206 q^{9} +1.13110 q^{10} -1.42556 q^{11} +7.53659 q^{12} -1.00000 q^{13} -9.97128 q^{14} -1.21519 q^{15} -0.569596 q^{16} +3.13782 q^{17} -6.53430 q^{18} -7.27226 q^{19} -1.55436 q^{20} +10.7126 q^{21} +3.22091 q^{22} -8.26540 q^{23} -6.05940 q^{24} -4.74938 q^{25} +2.25939 q^{26} -0.262003 q^{27} +13.7025 q^{28} -1.90070 q^{29} +2.74559 q^{30} +5.25956 q^{31} +6.27953 q^{32} -3.46035 q^{33} -7.08957 q^{34} -2.20937 q^{35} +8.97943 q^{36} +6.75569 q^{37} +16.4309 q^{38} -2.42736 q^{39} +1.24970 q^{40} -10.9114 q^{41} -24.2039 q^{42} -6.84316 q^{43} -4.42616 q^{44} -1.44783 q^{45} +18.6748 q^{46} -4.39465 q^{47} -1.38261 q^{48} +12.4769 q^{49} +10.7307 q^{50} +7.61661 q^{51} -3.10485 q^{52} +3.05136 q^{53} +0.591968 q^{54} +0.713668 q^{55} -11.0168 q^{56} -17.6524 q^{57} +4.29444 q^{58} -11.4178 q^{59} -3.77298 q^{60} +12.7964 q^{61} -11.8834 q^{62} +12.7634 q^{63} -13.0487 q^{64} +0.500622 q^{65} +7.81829 q^{66} +1.26329 q^{67} +9.74247 q^{68} -20.0631 q^{69} +4.99184 q^{70} -9.87557 q^{71} -7.21944 q^{72} -7.90176 q^{73} -15.2638 q^{74} -11.5284 q^{75} -22.5793 q^{76} -6.29138 q^{77} +5.48435 q^{78} -6.88388 q^{79} +0.285152 q^{80} -9.31216 q^{81} +24.6532 q^{82} -2.36869 q^{83} +33.2609 q^{84} -1.57086 q^{85} +15.4614 q^{86} -4.61369 q^{87} +3.55863 q^{88} -3.70599 q^{89} +3.27121 q^{90} -4.41326 q^{91} -25.6628 q^{92} +12.7668 q^{93} +9.92924 q^{94} +3.64065 q^{95} +15.2427 q^{96} -15.1692 q^{97} -28.1901 q^{98} -4.12282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * q^99

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