LMFDB - Embedded newform 6019.2.a.c.1.8

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			1.8
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)

$f(q)$	$=$	$q-2.59599 q^{2} +1.19783 q^{3} +4.73919 q^{4} -2.90334 q^{5} -3.10956 q^{6} -3.26881 q^{7} -7.11092 q^{8} -1.56520 q^{9} +O(q^{10})$	\(q-2.59599 q^{2} +1.19783 q^{3} +4.73919 q^{4} -2.90334 q^{5} -3.10956 q^{6} -3.26881 q^{7} -7.11092 q^{8} -1.56520 q^{9} +7.53704 q^{10} -4.60151 q^{11} +5.67675 q^{12} -1.00000 q^{13} +8.48582 q^{14} -3.47771 q^{15} +8.98153 q^{16} -1.24562 q^{17} +4.06325 q^{18} +6.66984 q^{19} -13.7595 q^{20} -3.91549 q^{21} +11.9455 q^{22} +4.30073 q^{23} -8.51768 q^{24} +3.42936 q^{25} +2.59599 q^{26} -5.46834 q^{27} -15.4915 q^{28} +1.29367 q^{29} +9.02811 q^{30} +7.84670 q^{31} -9.09417 q^{32} -5.51183 q^{33} +3.23363 q^{34} +9.49046 q^{35} -7.41778 q^{36} +0.108301 q^{37} -17.3149 q^{38} -1.19783 q^{39} +20.6454 q^{40} -0.176638 q^{41} +10.1646 q^{42} +9.16147 q^{43} -21.8074 q^{44} +4.54430 q^{45} -11.1647 q^{46} -13.3444 q^{47} +10.7584 q^{48} +3.68514 q^{49} -8.90259 q^{50} -1.49205 q^{51} -4.73919 q^{52} +10.4074 q^{53} +14.1958 q^{54} +13.3597 q^{55} +23.2443 q^{56} +7.98935 q^{57} -3.35836 q^{58} -7.18999 q^{59} -16.4815 q^{60} -1.97518 q^{61} -20.3700 q^{62} +5.11635 q^{63} +5.64535 q^{64} +2.90334 q^{65} +14.3087 q^{66} +13.3805 q^{67} -5.90324 q^{68} +5.15155 q^{69} -24.6372 q^{70} -4.22652 q^{71} +11.1300 q^{72} -8.85875 q^{73} -0.281148 q^{74} +4.10779 q^{75} +31.6096 q^{76} +15.0415 q^{77} +3.10956 q^{78} +1.58575 q^{79} -26.0764 q^{80} -1.85455 q^{81} +0.458553 q^{82} +9.08708 q^{83} -18.5562 q^{84} +3.61646 q^{85} -23.7831 q^{86} +1.54960 q^{87} +32.7210 q^{88} -8.90530 q^{89} -11.7970 q^{90} +3.26881 q^{91} +20.3820 q^{92} +9.39903 q^{93} +34.6419 q^{94} -19.3648 q^{95} -10.8933 q^{96} +11.8648 q^{97} -9.56661 q^{98} +7.20228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.59599	−1.83565	−0.917823	−	0.396991i	$-0.870055\pi$
$2$	−2.59599	−1.83565	−0.917823	+	0.396991i	$0.870055\pi$
$3$	1.19783	0.691568	0.345784	−	0.938314i	$-0.387613\pi$
$3$	1.19783	0.691568	0.345784	+	0.938314i	$0.387613\pi$
$4$	4.73919	2.36959
$5$	−2.90334	−1.29841	−0.649206	−	0.760613i	$-0.724898\pi$
$5$	−2.90334	−1.29841	−0.649206	+	0.760613i	$0.724898\pi$
$6$	−3.10956	−1.26947
$7$	−3.26881	−1.23550	−0.617748	−	0.786376i	$-0.711955\pi$
$7$	−3.26881	−1.23550	−0.617748	+	0.786376i	$0.711955\pi$
$8$	−7.11092	−2.51409
$9$	−1.56520	−0.521733
$10$	7.53704	2.38342
$11$	−4.60151	−1.38741	−0.693704	−	0.720260i	$-0.744022\pi$
$11$	−4.60151	−1.38741	−0.693704	+	0.720260i	$0.744022\pi$
$12$	5.67675	1.63874
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	8.48582	2.26793
$15$	−3.47771	−0.897940
$16$	8.98153	2.24538
$17$	−1.24562	−0.302108	−0.151054	−	0.988526i	$-0.548267\pi$
$17$	−1.24562	−0.302108	−0.151054	+	0.988526i	$0.548267\pi$
$18$	4.06325	0.957717
$19$	6.66984	1.53017	0.765084	−	0.643931i	$-0.222698\pi$
$19$	6.66984	1.53017	0.765084	+	0.643931i	$0.222698\pi$
$20$	−13.7595	−3.07671
$21$	−3.91549	−0.854430
$22$	11.9455	2.54679
$23$	4.30073	0.896764	0.448382	−	0.893842i	$-0.352000\pi$
$23$	4.30073	0.896764	0.448382	+	0.893842i	$0.352000\pi$
$24$	−8.51768	−1.73866
$25$	3.42936	0.685871
$26$	2.59599	0.509116
$27$	−5.46834	−1.05238
$28$	−15.4915	−2.92762
$29$	1.29367	0.240228	0.120114	−	0.992760i	$-0.461674\pi$
$29$	1.29367	0.240228	0.120114	+	0.992760i	$0.461674\pi$
$30$	9.02811	1.64830
$31$	7.84670	1.40931	0.704655	−	0.709550i	$-0.251102\pi$
$31$	7.84670	1.40931	0.704655	+	0.709550i	$0.251102\pi$
$32$	−9.09417	−1.60764
$33$	−5.51183	−0.959487
$34$	3.23363	0.554563
$35$	9.49046	1.60418
$36$	−7.41778	−1.23630
$37$	0.108301	0.0178045	0.00890225	−	0.999960i	$-0.497166\pi$
$37$	0.108301	0.0178045	0.00890225	+	0.999960i	$0.497166\pi$
$38$	−17.3149	−2.80884
$39$	−1.19783	−0.191807
$40$	20.6454	3.26432
$41$	−0.176638	−0.0275863	−0.0137931	−	0.999905i	$-0.504391\pi$
$41$	−0.176638	−0.0275863	−0.0137931	+	0.999905i	$0.504391\pi$
$42$	10.1646	1.56843
$43$	9.16147	1.39711	0.698556	−	0.715556i	$-0.253826\pi$
$43$	9.16147	1.39711	0.698556	+	0.715556i	$0.253826\pi$
$44$	−21.8074	−3.28759
$45$	4.54430	0.677424
$46$	−11.1647	−1.64614
$47$	−13.3444	−1.94647	−0.973237	−	0.229803i	$-0.926192\pi$
$47$	−13.3444	−1.94647	−0.973237	+	0.229803i	$0.926192\pi$
$48$	10.7584	1.55284
$49$	3.68514	0.526449
$50$	−8.90259	−1.25902
$51$	−1.49205	−0.208928
$52$	−4.73919	−0.657207
$53$	10.4074	1.42957	0.714785	−	0.699344i	$-0.246524\pi$
$53$	10.4074	1.42957	0.714785	+	0.699344i	$0.246524\pi$
$54$	14.1958	1.93180
$55$	13.3597	1.80143
$56$	23.2443	3.10615
$57$	7.98935	1.05822
$58$	−3.35836	−0.440974
$59$	−7.18999	−0.936057	−0.468028	−	0.883713i	$-0.655036\pi$
$59$	−7.18999	−0.936057	−0.468028	+	0.883713i	$0.655036\pi$
$60$	−16.4815	−2.12775
$61$	−1.97518	−0.252896	−0.126448	−	0.991973i	$-0.540358\pi$
$61$	−1.97518	−0.252896	−0.126448	+	0.991973i	$0.540358\pi$
$62$	−20.3700	−2.58699
$63$	5.11635	0.644599
$64$	5.64535	0.705668
$65$	2.90334	0.360114
$66$	14.3087	1.76128
$67$	13.3805	1.63469	0.817347	−	0.576146i	$-0.195444\pi$
$67$	13.3805	1.63469	0.817347	+	0.576146i	$0.195444\pi$
$68$	−5.90324	−0.715873
$69$	5.15155	0.620174
$70$	−24.6372	−2.94471
$71$	−4.22652	−0.501596	−0.250798	−	0.968039i	$-0.580693\pi$
$71$	−4.22652	−0.501596	−0.250798	+	0.968039i	$0.580693\pi$
$72$	11.1300	1.31168
$73$	−8.85875	−1.03684	−0.518419	−	0.855127i	$-0.673479\pi$
$73$	−8.85875	−1.03684	−0.518419	+	0.855127i	$0.673479\pi$
$74$	−0.281148	−0.0326828
$75$	4.10779	0.474327
$76$	31.6096	3.62588
$77$	15.0415	1.71414
$78$	3.10956	0.352089
$79$	1.58575	0.178411	0.0892054	−	0.996013i	$-0.471567\pi$
$79$	1.58575	0.178411	0.0892054	+	0.996013i	$0.471567\pi$
$80$	−26.0764	−2.91543
$81$	−1.85455	−0.206061
$82$	0.458553	0.0506387
$83$	9.08708	0.997437	0.498718	−	0.866764i	$-0.333804\pi$
$83$	9.08708	0.997437	0.498718	+	0.866764i	$0.333804\pi$
$84$	−18.5562	−2.02465
$85$	3.61646	0.392260
$86$	−23.7831	−2.56460
$87$	1.54960	0.166134
$88$	32.7210	3.48807
$89$	−8.90530	−0.943960	−0.471980	−	0.881609i	$-0.656460\pi$
$89$	−8.90530	−0.943960	−0.471980	+	0.881609i	$0.656460\pi$
$90$	−11.7970	−1.24351
$91$	3.26881	0.342665
$92$	20.3820	2.12497
$93$	9.39903	0.974634
$94$	34.6419	3.57304
$95$	−19.3648	−1.98679
$96$	−10.8933	−1.11179
$97$	11.8648	1.20469	0.602345	−	0.798236i	$-0.294233\pi$
$97$	11.8648	1.20469	0.602345	+	0.798236i	$0.294233\pi$
$98$	−9.56661	−0.966373
$99$	7.20228	0.723857
$100$	16.2524	1.62524
$101$	5.10951	0.508415	0.254207	−	0.967150i	$-0.418185\pi$
$101$	5.10951	0.508415	0.254207	+	0.967150i	$0.418185\pi$
$102$	3.87334	0.383518
$103$	13.4851	1.32873	0.664363	−	0.747410i	$-0.268703\pi$
$103$	13.4851	1.32873	0.664363	+	0.747410i	$0.268703\pi$
$104$	7.11092	0.697283
$105$	11.3680	1.10940
$106$	−27.0176	−2.62418
$107$	15.9391	1.54089	0.770444	−	0.637508i	$-0.220035\pi$
$107$	15.9391	1.54089	0.770444	+	0.637508i	$0.220035\pi$
$108$	−25.9155	−2.49372
$109$	−7.42141	−0.710842	−0.355421	−	0.934706i	$-0.615662\pi$
$109$	−7.42141	−0.710842	−0.355421	+	0.934706i	$0.615662\pi$
$110$	−34.6818	−3.30678
$111$	0.129726	0.0123130
$112$	−29.3589	−2.77416
$113$	7.53667	0.708990	0.354495	−	0.935058i	$-0.384653\pi$
$113$	7.53667	0.708990	0.354495	+	0.935058i	$0.384653\pi$
$114$	−20.7403	−1.94251
$115$	−12.4865	−1.16437
$116$	6.13094	0.569244
$117$	1.56520	0.144703
$118$	18.6652	1.71827
$119$	4.07171	0.373253
$120$	24.7297	2.25750
$121$	10.1739	0.924900
$122$	5.12756	0.464227
$123$	−0.211583	−0.0190778
$124$	37.1870	3.33949
$125$	4.56011	0.407868
$126$	−13.2820	−1.18326
$127$	−21.4707	−1.90521	−0.952606	−	0.304207i	$-0.901609\pi$
$127$	−21.4707	−1.90521	−0.952606	+	0.304207i	$0.901609\pi$
$128$	3.53304	0.312280
$129$	10.9739	0.966198
$130$	−7.53704	−0.661042
$131$	−3.09293	−0.270231	−0.135115	−	0.990830i	$-0.543140\pi$
$131$	−3.09293	−0.270231	−0.135115	+	0.990830i	$0.543140\pi$
$132$	−26.1216	−2.27360
$133$	−21.8025	−1.89051
$134$	−34.7358	−3.00072
$135$	15.8764	1.36643
$136$	8.85752	0.759526
$137$	5.54114	0.473412	0.236706	−	0.971581i	$-0.423932\pi$
$137$	5.54114	0.473412	0.236706	+	0.971581i	$0.423932\pi$
$138$	−13.3734	−1.13842
$139$	−17.5232	−1.48630	−0.743149	−	0.669126i	$-0.766669\pi$
$139$	−17.5232	−1.48630	−0.743149	+	0.669126i	$0.766669\pi$
$140$	44.9771	3.80126
$141$	−15.9843	−1.34612
$142$	10.9720	0.920753
$143$	4.60151	0.384798
$144$	−14.0579	−1.17149
$145$	−3.75596	−0.311915
$146$	22.9973	1.90327
$147$	4.41418	0.364075
$148$	0.513257	0.0421895
$149$	20.3849	1.67000	0.834998	−	0.550254i	$-0.185469\pi$
$149$	20.3849	1.67000	0.834998	+	0.550254i	$0.185469\pi$
$150$	−10.6638	−0.870696
$151$	3.41286	0.277735	0.138867	−	0.990311i	$-0.455654\pi$
$151$	3.41286	0.277735	0.138867	+	0.990311i	$0.455654\pi$
$152$	−47.4287	−3.84698
$153$	1.94965	0.157620
$154$	−39.0476	−3.14655
$155$	−22.7816	−1.82986
$156$	−5.67675	−0.454504
$157$	4.87947	0.389424	0.194712	−	0.980860i	$-0.437623\pi$
$157$	4.87947	0.389424	0.194712	+	0.980860i	$0.437623\pi$
$158$	−4.11660	−0.327499
$159$	12.4663	0.988646
$160$	26.4034	2.08737
$161$	−14.0583	−1.10795
$162$	4.81441	0.378255
$163$	−19.6785	−1.54134	−0.770670	−	0.637234i	$-0.780078\pi$
$163$	−19.6785	−1.54134	−0.770670	+	0.637234i	$0.780078\pi$
$164$	−0.837123	−0.0653683
$165$	16.0027	1.24581
$166$	−23.5900	−1.83094
$167$	−8.13433	−0.629453	−0.314727	−	0.949182i	$-0.601913\pi$
$167$	−8.13433	−0.629453	−0.314727	+	0.949182i	$0.601913\pi$
$168$	27.8427	2.14811
$169$	1.00000	0.0769231
$170$	−9.38831	−0.720051
$171$	−10.4396	−0.798339
$172$	43.4179	3.31059
$173$	18.8623	1.43408	0.717039	−	0.697033i	$-0.245497\pi$
$173$	18.8623	1.43408	0.717039	+	0.697033i	$0.245497\pi$
$174$	−4.02275	−0.304964
$175$	−11.2099	−0.847391
$176$	−41.3286	−3.11526
$177$	−8.61240	−0.647347
$178$	23.1181	1.73278
$179$	−7.53282	−0.563030	−0.281515	−	0.959557i	$-0.590837\pi$
$179$	−7.53282	−0.563030	−0.281515	+	0.959557i	$0.590837\pi$
$180$	21.5363	1.60522
$181$	−20.3889	−1.51550	−0.757749	−	0.652546i	$-0.773701\pi$
$181$	−20.3889	−1.51550	−0.757749	+	0.652546i	$0.773701\pi$
$182$	−8.48582	−0.629011
$183$	−2.36593	−0.174895
$184$	−30.5821	−2.25454
$185$	−0.314433	−0.0231176
$186$	−24.3998	−1.78908
$187$	5.73175	0.419147
$188$	−63.2414	−4.61235
$189$	17.8750	1.30021
$190$	50.2709	3.64703
$191$	−20.9114	−1.51309	−0.756547	−	0.653939i	$-0.773115\pi$
$191$	−20.9114	−1.51309	−0.756547	+	0.653939i	$0.773115\pi$
$192$	6.76217	0.488018
$193$	−12.8488	−0.924876	−0.462438	−	0.886652i	$-0.653025\pi$
$193$	−12.8488	−0.924876	−0.462438	+	0.886652i	$0.653025\pi$
$194$	−30.8010	−2.21138
$195$	3.47771	0.249044
$196$	17.4646	1.24747
$197$	−0.469627	−0.0334595	−0.0167298	−	0.999860i	$-0.505325\pi$
$197$	−0.469627	−0.0334595	−0.0167298	+	0.999860i	$0.505325\pi$
$198$	−18.6971	−1.32874
$199$	5.12260	0.363131	0.181566	−	0.983379i	$-0.441883\pi$
$199$	5.12260	0.363131	0.181566	+	0.983379i	$0.441883\pi$
$200$	−24.3859	−1.72434
$201$	16.0276	1.13050
$202$	−13.2643	−0.933270
$203$	−4.22876	−0.296801
$204$	−7.07109	−0.495075
$205$	0.512841	0.0358184
$206$	−35.0072	−2.43907
$207$	−6.73150	−0.467872
$208$	−8.98153	−0.622757
$209$	−30.6914	−2.12297
$210$	−29.5112	−2.03647
$211$	6.48606	0.446519	0.223259	−	0.974759i	$-0.428330\pi$
$211$	6.48606	0.446519	0.223259	+	0.974759i	$0.428330\pi$
$212$	49.3228	3.38750
$213$	−5.06266	−0.346888
$214$	−41.3777	−2.82852
$215$	−26.5988	−1.81402
$216$	38.8849	2.64578
$217$	−25.6494	−1.74120
$218$	19.2659	1.30485
$219$	−10.6113	−0.717045
$220$	63.3143	4.26865
$221$	1.24562	0.0837897
$222$	−0.336768	−0.0226024
$223$	−3.13541	−0.209963	−0.104981	−	0.994474i	$-0.533478\pi$
$223$	−3.13541	−0.209963	−0.104981	+	0.994474i	$0.533478\pi$
$224$	29.7271	1.98623
$225$	−5.36763	−0.357842
$226$	−19.5651	−1.30145
$227$	10.7982	0.716703	0.358352	−	0.933587i	$-0.383339\pi$
$227$	10.7982	0.716703	0.358352	+	0.933587i	$0.383339\pi$
$228$	37.8630	2.50754
$229$	21.4214	1.41557	0.707784	−	0.706429i	$-0.249695\pi$
$229$	21.4214	1.41557	0.707784	+	0.706429i	$0.249695\pi$
$230$	32.4148	2.13737
$231$	18.0172	1.18544
$232$	−9.19918	−0.603956
$233$	−11.5668	−0.757766	−0.378883	−	0.925445i	$-0.623692\pi$
$233$	−11.5668	−0.757766	−0.378883	+	0.925445i	$0.623692\pi$
$234$	−4.06325	−0.265623
$235$	38.7431	2.52732
$236$	−34.0747	−2.21807
$237$	1.89946	0.123383
$238$	−10.5701	−0.685160
$239$	−14.4770	−0.936439	−0.468220	−	0.883612i	$-0.655104\pi$
$239$	−14.4770	−0.936439	−0.468220	+	0.883612i	$0.655104\pi$
$240$	−31.2351	−2.01622
$241$	0.0718574	0.00462874	0.00231437	−	0.999997i	$-0.499263\pi$
$241$	0.0718574	0.00462874	0.00231437	+	0.999997i	$0.499263\pi$
$242$	−26.4114	−1.69779
$243$	14.1836	0.909877
$244$	−9.36076	−0.599261
$245$	−10.6992	−0.683547
$246$	0.549269	0.0350201
$247$	−6.66984	−0.424392
$248$	−55.7973	−3.54313
$249$	10.8848	0.689796
$250$	−11.8380	−0.748702
$251$	−17.6859	−1.11632	−0.558161	−	0.829733i	$-0.688493\pi$
$251$	−17.6859	−1.11632	−0.558161	+	0.829733i	$0.688493\pi$
$252$	24.2473	1.52744
$253$	−19.7898	−1.24418
$254$	55.7377	3.49729
$255$	4.33191	0.271275
$256$	−20.4624	−1.27890
$257$	25.7299	1.60499	0.802493	−	0.596662i	$-0.203507\pi$
$257$	25.7299	1.60499	0.802493	+	0.596662i	$0.203507\pi$
$258$	−28.4882	−1.77360
$259$	−0.354014	−0.0219974
$260$	13.7595	0.853325
$261$	−2.02485	−0.125335
$262$	8.02923	0.496048
$263$	−17.1987	−1.06051	−0.530257	−	0.847837i	$-0.677905\pi$
$263$	−17.1987	−1.06051	−0.530257	+	0.847837i	$0.677905\pi$
$264$	39.1942	2.41224
$265$	−30.2163	−1.85617
$266$	56.5991	3.47031
$267$	−10.6670	−0.652813
$268$	63.4129	3.87356
$269$	−12.2811	−0.748791	−0.374396	−	0.927269i	$-0.622150\pi$
$269$	−12.2811	−0.748791	−0.374396	+	0.927269i	$0.622150\pi$
$270$	−41.2151	−2.50827
$271$	1.62404	0.0986537	0.0493269	−	0.998783i	$-0.484292\pi$
$271$	1.62404	0.0986537	0.0493269	+	0.998783i	$0.484292\pi$
$272$	−11.1876	−0.678348
$273$	3.91549	0.236976
$274$	−14.3848	−0.869016
$275$	−15.7802	−0.951583
$276$	24.4142	1.46956
$277$	3.36031	0.201902	0.100951	−	0.994891i	$-0.467812\pi$
$277$	3.36031	0.201902	0.100951	+	0.994891i	$0.467812\pi$
$278$	45.4901	2.72832
$279$	−12.2817	−0.735284
$280$	−67.4859	−4.03305
$281$	−2.10298	−0.125453	−0.0627267	−	0.998031i	$-0.519980\pi$
$281$	−2.10298	−0.125453	−0.0627267	+	0.998031i	$0.519980\pi$
$282$	41.4951	2.47100
$283$	−0.873881	−0.0519468	−0.0259734	−	0.999663i	$-0.508269\pi$
$283$	−0.873881	−0.0519468	−0.0259734	+	0.999663i	$0.508269\pi$
$284$	−20.0303	−1.18858
$285$	−23.1958	−1.37400
$286$	−11.9455	−0.706352
$287$	0.577398	0.0340827
$288$	14.2342	0.838757
$289$	−15.4484	−0.908731
$290$	9.75044	0.572566
$291$	14.2121	0.833126
$292$	−41.9833	−2.45689
$293$	−12.4057	−0.724749	−0.362374	−	0.932033i	$-0.618034\pi$
$293$	−12.4057	−0.724749	−0.362374	+	0.932033i	$0.618034\pi$
$294$	−11.4592	−0.668313
$295$	20.8749	1.21539
$296$	−0.770117	−0.0447621
$297$	25.1626	1.46008
$298$	−52.9191	−3.06552
$299$	−4.30073	−0.248718
$300$	19.4676	1.12396
$301$	−29.9471	−1.72612
$302$	−8.85977	−0.509823
$303$	6.12033	0.351604
$304$	59.9054	3.43581
$305$	5.73461	0.328363
$306$	−5.06128	−0.289334
$307$	−1.12674	−0.0643064	−0.0321532	−	0.999483i	$-0.510236\pi$
$307$	−1.12674	−0.0643064	−0.0321532	+	0.999483i	$0.510236\pi$
$308$	71.2844	4.06181
$309$	16.1529	0.918905
$310$	59.1409	3.35898
$311$	−12.5210	−0.710002	−0.355001	−	0.934866i	$-0.615520\pi$
$311$	−12.5210	−0.710002	−0.355001	+	0.934866i	$0.615520\pi$
$312$	8.51768	0.482219
$313$	16.2691	0.919585	0.459793	−	0.888026i	$-0.347924\pi$
$313$	16.2691	0.919585	0.459793	+	0.888026i	$0.347924\pi$
$314$	−12.6671	−0.714844
$315$	−14.8545	−0.836954
$316$	7.51516	0.422761
$317$	0.00967991	0.000543678 0	0.000271839	−	1.00000i	$-0.499913\pi$
$317$	0.00967991	0.000543678 0	0.000271839		1.00000i	$0.499913\pi$
$318$	−32.3626	−1.81480
$319$	−5.95283	−0.333295
$320$	−16.3903	−0.916248
$321$	19.0923	1.06563
$322$	36.4952	2.03380
$323$	−8.30811	−0.462276
$324$	−8.78907	−0.488282
$325$	−3.42936	−0.190226
$326$	51.0853	2.82935
$327$	−8.88960	−0.491596
$328$	1.25606	0.0693544
$329$	43.6202	2.40486
$330$	−41.5429	−2.28686
$331$	7.65841	0.420944	0.210472	−	0.977600i	$-0.432500\pi$
$331$	7.65841	0.420944	0.210472	+	0.977600i	$0.432500\pi$
$332$	43.0654	2.36352
$333$	−0.169512	−0.00928920
$334$	21.1167	1.15545
$335$	−38.8482	−2.12250
$336$	−35.1671	−1.91852
$337$	−23.0458	−1.25538	−0.627692	−	0.778462i	$-0.716000\pi$
$337$	−23.0458	−1.25538	−0.627692	+	0.778462i	$0.716000\pi$
$338$	−2.59599	−0.141203
$339$	9.02766	0.490315
$340$	17.1391	0.929498
$341$	−36.1067	−1.95529
$342$	27.1012	1.46547
$343$	10.8357	0.585070
$344$	−65.1465	−3.51246
$345$	−14.9567	−0.805240
$346$	−48.9666	−2.63246
$347$	−25.1132	−1.34815	−0.674073	−	0.738665i	$-0.735457\pi$
$347$	−25.1132	−1.34815	−0.674073	+	0.738665i	$0.735457\pi$
$348$	7.34384	0.393671
$349$	−1.29585	−0.0693652	−0.0346826	−	0.999398i	$-0.511042\pi$
$349$	−1.29585	−0.0693652	−0.0346826	+	0.999398i	$0.511042\pi$
$350$	29.1009	1.55551
$351$	5.46834	0.291878
$352$	41.8469	2.23045
$353$	−33.9466	−1.80679	−0.903397	−	0.428806i	$-0.858934\pi$
$353$	−33.9466	−1.80679	−0.903397	+	0.428806i	$0.858934\pi$
$354$	22.3577	1.18830
$355$	12.2710	0.651278
$356$	−42.2039	−2.23680
$357$	4.87722	0.258130
$358$	19.5552	1.03352
$359$	2.79617	0.147576	0.0737882	−	0.997274i	$-0.476491\pi$
$359$	2.79617	0.147576	0.0737882	+	0.997274i	$0.476491\pi$
$360$	−32.3141	−1.70310
$361$	25.4868	1.34141
$362$	52.9296	2.78192
$363$	12.1866	0.639632
$364$	15.4915	0.811976
$365$	25.7199	1.34624
$366$	6.14195	0.321045
$367$	34.9582	1.82480	0.912401	−	0.409297i	$-0.134226\pi$
$367$	34.9582	1.82480	0.912401	+	0.409297i	$0.134226\pi$
$368$	38.6271	2.01358
$369$	0.276475	0.0143927
$370$	0.816266	0.0424357
$371$	−34.0200	−1.76623
$372$	44.5438	2.30949
$373$	−9.69247	−0.501857	−0.250929	−	0.968006i	$-0.580736\pi$
$373$	−9.69247	−0.501857	−0.250929	+	0.968006i	$0.580736\pi$
$374$	−14.8796	−0.769405
$375$	5.46224	0.282069
$376$	94.8906	4.89361
$377$	−1.29367	−0.0666274
$378$	−46.4034	−2.38673
$379$	38.7486	1.99038	0.995191	−	0.0979547i	$-0.0312300\pi$
$379$	38.7486	1.99038	0.995191	+	0.0979547i	$0.0312300\pi$
$380$	−91.7734	−4.70788
$381$	−25.7182	−1.31758
$382$	54.2858	2.77750
$383$	−5.50089	−0.281083	−0.140541	−	0.990075i	$-0.544884\pi$
$383$	−5.50089	−0.281083	−0.140541	+	0.990075i	$0.544884\pi$
$384$	4.23199	0.215963
$385$	−43.6705	−2.22565
$386$	33.3554	1.69774
$387$	−14.3395	−0.728919
$388$	56.2296	2.85463
$389$	−31.3870	−1.59138	−0.795691	−	0.605703i	$-0.792892\pi$
$389$	−31.3870	−1.59138	−0.795691	+	0.605703i	$0.792892\pi$
$390$	−9.02811	−0.457156
$391$	−5.35709	−0.270919
$392$	−26.2047	−1.32354
$393$	−3.70481	−0.186883
$394$	1.21915	0.0614198
$395$	−4.60396	−0.231650
$396$	34.1330	1.71525
$397$	32.1944	1.61579	0.807896	−	0.589325i	$-0.200606\pi$
$397$	32.1944	1.61579	0.807896	+	0.589325i	$0.200606\pi$
$398$	−13.2982	−0.666581
$399$	−26.1157	−1.30742
$400$	30.8009	1.54004
$401$	−24.3503	−1.21600	−0.607998	−	0.793938i	$-0.708027\pi$
$401$	−24.3503	−1.21600	−0.607998	+	0.793938i	$0.708027\pi$
$402$	−41.6077	−2.07520
$403$	−7.84670	−0.390872
$404$	24.2149	1.20474
$405$	5.38438	0.267552
$406$	10.9778	0.544822
$407$	−0.498346	−0.0247021
$408$	10.6098	0.525264
$409$	39.3367	1.94507	0.972537	−	0.232748i	$-0.0747719\pi$
$409$	39.3367	1.94507	0.972537	+	0.232748i	$0.0747719\pi$
$410$	−1.33133	−0.0657498
$411$	6.63735	0.327396
$412$	63.9084	3.14854
$413$	23.5027	1.15649
$414$	17.4749	0.858846
$415$	−26.3828	−1.29508
$416$	9.09417	0.445878
$417$	−20.9898	−1.02788
$418$	79.6746	3.89701
$419$	21.7238	1.06128	0.530638	−	0.847599i	$-0.321952\pi$
$419$	21.7238	1.06128	0.530638	+	0.847599i	$0.321952\pi$
$420$	53.8750	2.62883
$421$	−12.0042	−0.585050	−0.292525	−	0.956258i	$-0.594496\pi$
$421$	−12.0042	−0.585050	−0.292525	+	0.956258i	$0.594496\pi$
$422$	−16.8378	−0.819650
$423$	20.8866	1.01554
$424$	−74.0064	−3.59407
$425$	−4.27168	−0.207207
$426$	13.1426	0.636763
$427$	6.45650	0.312452
$428$	75.5383	3.65128
$429$	5.51183	0.266114
$430$	69.0504	3.32991
$431$	−10.5962	−0.510403	−0.255202	−	0.966888i	$-0.582142\pi$
$431$	−10.5962	−0.510403	−0.255202	+	0.966888i	$0.582142\pi$
$432$	−49.1141	−2.36300
$433$	1.09459	0.0526025	0.0263012	−	0.999654i	$-0.491627\pi$
$433$	1.09459	0.0526025	0.0263012	+	0.999654i	$0.491627\pi$
$434$	66.5857	3.19622
$435$	−4.49900	−0.215711
$436$	−35.1714	−1.68441
$437$	28.6852	1.37220
$438$	27.5469	1.31624
$439$	0.612459	0.0292311	0.0146155	−	0.999893i	$-0.495348\pi$
$439$	0.612459	0.0292311	0.0146155	+	0.999893i	$0.495348\pi$
$440$	−94.9999	−4.52894
$441$	−5.76798	−0.274666
$442$	−3.23363	−0.153808
$443$	21.4424	1.01876	0.509378	−	0.860543i	$-0.329875\pi$
$443$	21.4424	1.01876	0.509378	+	0.860543i	$0.329875\pi$
$444$	0.614795	0.0291769
$445$	25.8551	1.22565
$446$	8.13951	0.385417
$447$	24.4177	1.15492
$448$	−18.4536	−0.871850
$449$	31.9339	1.50705	0.753527	−	0.657417i	$-0.228351\pi$
$449$	31.9339	1.50705	0.753527	+	0.657417i	$0.228351\pi$
$450$	13.9343	0.656871
$451$	0.812804	0.0382734
$452$	35.7177	1.68002
$453$	4.08803	0.192073
$454$	−28.0321	−1.31561
$455$	−9.49046	−0.444920
$456$	−56.8116	−2.66045
$457$	21.7988	1.01971	0.509853	−	0.860261i	$-0.329700\pi$
$457$	21.7988	1.01971	0.509853	+	0.860261i	$0.329700\pi$
$458$	−55.6099	−2.59848
$459$	6.81149	0.317933
$460$	−59.1757	−2.75908
$461$	−1.11998	−0.0521626	−0.0260813	−	0.999660i	$-0.508303\pi$
$461$	−1.11998	−0.0521626	−0.0260813	+	0.999660i	$0.508303\pi$
$462$	−46.7725	−2.17605
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	11.6191	0.539405
$465$	−27.2885	−1.26548
$466$	30.0273	1.39099
$467$	2.01749	0.0933583	0.0466791	−	0.998910i	$-0.485136\pi$
$467$	2.01749	0.0933583	0.0466791	+	0.998910i	$0.485136\pi$
$468$	7.41778	0.342887
$469$	−43.7385	−2.01966
$470$	−100.577	−4.63927
$471$	5.84478	0.269313
$472$	51.1274	2.35333
$473$	−42.1566	−1.93836
$474$	−4.93099	−0.226488
$475$	22.8733	1.04950
$476$	19.2966	0.884458
$477$	−16.2897	−0.745854
$478$	37.5822	1.71897
$479$	−4.31473	−0.197145	−0.0985726	−	0.995130i	$-0.531428\pi$
$479$	−4.31473	−0.197145	−0.0985726	+	0.995130i	$0.531428\pi$
$480$	31.6268	1.44356
$481$	−0.108301	−0.00493808
$482$	−0.186541	−0.00849673
$483$	−16.8395	−0.766222
$484$	48.2160	2.19164
$485$	−34.4476	−1.56418
$486$	−36.8205	−1.67021
$487$	−19.1205	−0.866434	−0.433217	−	0.901290i	$-0.642622\pi$
$487$	−19.1205	−0.866434	−0.433217	+	0.901290i	$0.642622\pi$
$488$	14.0454	0.635803
$489$	−23.5715	−1.06594
$490$	27.7751	1.25475
$491$	22.3271	1.00761	0.503805	−	0.863818i	$-0.331933\pi$
$491$	22.3271	1.00761	0.503805	+	0.863818i	$0.331933\pi$
$492$	−1.00273	−0.0452067
$493$	−1.61142	−0.0725749
$494$	17.3149	0.779033
$495$	−20.9106	−0.939863
$496$	70.4754	3.16444
$497$	13.8157	0.619720
$498$	−28.2569	−1.26622
$499$	−12.7580	−0.571128	−0.285564	−	0.958360i	$-0.592181\pi$
$499$	−12.7580	−0.571128	−0.285564	+	0.958360i	$0.592181\pi$
$500$	21.6112	0.966482
$501$	−9.74356	−0.435310
$502$	45.9124	2.04917
$503$	−5.67650	−0.253102	−0.126551	−	0.991960i	$-0.540391\pi$
$503$	−5.67650	−0.253102	−0.126551	+	0.991960i	$0.540391\pi$
$504$	−36.3819	−1.62058
$505$	−14.8346	−0.660132
$506$	51.3743	2.28387
$507$	1.19783	0.0531976
$508$	−101.753	−4.51458
$509$	−16.7761	−0.743589	−0.371795	−	0.928315i	$-0.621257\pi$
$509$	−16.7761	−0.743589	−0.371795	+	0.928315i	$0.621257\pi$
$510$	−11.2456	−0.497964
$511$	28.9576	1.28101
$512$	46.0543	2.03533
$513$	−36.4730	−1.61032
$514$	−66.7946	−2.94618
$515$	−39.1518	−1.72523
$516$	52.0074	2.28950
$517$	61.4042	2.70055
$518$	0.919020	0.0403794
$519$	22.5939	0.991763
$520$	−20.6454	−0.905360
$521$	−19.8684	−0.870448	−0.435224	−	0.900322i	$-0.643331\pi$
$521$	−19.8684	−0.870448	−0.435224	+	0.900322i	$0.643331\pi$
$522$	5.25650	0.230071
$523$	−24.6750	−1.07896	−0.539482	−	0.841997i	$-0.681380\pi$
$523$	−24.6750	−1.07896	−0.539482	+	0.841997i	$0.681380\pi$
$524$	−14.6580	−0.640337
$525$	−13.4276	−0.586029
$526$	44.6476	1.94673
$527$	−9.77403	−0.425764
$528$	−49.5047	−2.15442
$529$	−4.50373	−0.195814
$530$	78.4413	3.40727
$531$	11.2538	0.488372
$532$	−103.326	−4.47975
$533$	0.176638	0.00765106
$534$	27.6916	1.19833
$535$	−46.2765	−2.00071
$536$	−95.1480	−4.10977
$537$	−9.02306	−0.389374
$538$	31.8816	1.37451
$539$	−16.9572	−0.730399
$540$	75.2414	3.23787
$541$	37.1034	1.59520	0.797601	−	0.603186i	$-0.206102\pi$
$541$	37.1034	1.59520	0.797601	+	0.603186i	$0.206102\pi$
$542$	−4.21601	−0.181093
$543$	−24.4225	−1.04807
$544$	11.3279	0.485680
$545$	21.5468	0.922965
$546$	−10.1646	−0.435004
$547$	31.4731	1.34569	0.672847	−	0.739782i	$-0.265071\pi$
$547$	31.4731	1.34569	0.672847	+	0.739782i	$0.265071\pi$
$548$	26.2605	1.12179
$549$	3.09155	0.131944
$550$	40.9654	1.74677
$551$	8.62857	0.367590
$552$	−36.6322	−1.55917
$553$	−5.18352	−0.220426
$554$	−8.72335	−0.370620
$555$	−0.376638	−0.0159874
$556$	−83.0457	−3.52192
$557$	13.2351	0.560787	0.280394	−	0.959885i	$-0.409535\pi$
$557$	13.2351	0.560787	0.280394	+	0.959885i	$0.409535\pi$
$558$	31.8831	1.34972
$559$	−9.16147	−0.387489
$560$	85.2389	3.60200
$561$	6.86567	0.289869
$562$	5.45933	0.230288
$563$	6.59233	0.277834	0.138917	−	0.990304i	$-0.455638\pi$
$563$	6.59233	0.277834	0.138917	+	0.990304i	$0.455638\pi$
$564$	−75.7526	−3.18976
$565$	−21.8815	−0.920561
$566$	2.26859	0.0953560
$567$	6.06218	0.254588
$568$	30.0545	1.26106
$569$	34.8028	1.45901	0.729504	−	0.683977i	$-0.239751\pi$
$569$	34.8028	1.45901	0.729504	+	0.683977i	$0.239751\pi$
$570$	60.2161	2.52217
$571$	3.16335	0.132382	0.0661910	−	0.997807i	$-0.478915\pi$
$571$	3.16335	0.132382	0.0661910	+	0.997807i	$0.478915\pi$
$572$	21.8074	0.911814
$573$	−25.0483	−1.04641
$574$	−1.49892	−0.0625638
$575$	14.7487	0.615065
$576$	−8.83609	−0.368171
$577$	−26.6635	−1.11002	−0.555009	−	0.831844i	$-0.687285\pi$
$577$	−26.6635	−1.11002	−0.555009	+	0.831844i	$0.687285\pi$
$578$	40.1040	1.66811
$579$	−15.3907	−0.639615
$580$	−17.8002	−0.739112
$581$	−29.7040	−1.23233
$582$	−36.8944	−1.52932
$583$	−47.8899	−1.98340
$584$	62.9939	2.60670
$585$	−4.54430	−0.187884
$586$	32.2051	1.33038
$587$	0.0274605	0.00113342	0.000566708	−	1.00000i	$-0.499820\pi$
$587$	0.0274605	0.00113342	0.000566708		1.00000i	$0.499820\pi$
$588$	20.9196	0.862711
$589$	52.3363	2.15648
$590$	−54.1913	−2.23102
$591$	−0.562534	−0.0231395
$592$	0.972705	0.0399779
$593$	−33.2014	−1.36342	−0.681710	−	0.731623i	$-0.738763\pi$
$593$	−33.2014	−1.36342	−0.681710	+	0.731623i	$0.738763\pi$
$594$	−65.3220	−2.68020
$595$	−11.8215	−0.484636
$596$	96.6078	3.95721
$597$	6.13601	0.251130
$598$	11.1647	0.456557
$599$	−31.5585	−1.28944	−0.644722	−	0.764417i	$-0.723027\pi$
$599$	−31.5585	−1.28944	−0.644722	+	0.764417i	$0.723027\pi$
$600$	−29.2102	−1.19250
$601$	36.7472	1.49895	0.749475	−	0.662033i	$-0.230306\pi$
$601$	36.7472	1.49895	0.749475	+	0.662033i	$0.230306\pi$
$602$	77.7426	3.16855
$603$	−20.9432	−0.852874
$604$	16.1742	0.658119
$605$	−29.5382	−1.20090
$606$	−15.8883	−0.645420
$607$	−25.9084	−1.05159	−0.525794	−	0.850612i	$-0.676232\pi$
$607$	−25.9084	−1.05159	−0.525794	+	0.850612i	$0.676232\pi$
$608$	−60.6567	−2.45995
$609$	−5.06535	−0.205258
$610$	−14.8870	−0.602758
$611$	13.3444	0.539855
$612$	9.23975	0.373495
$613$	−21.9901	−0.888172	−0.444086	−	0.895984i	$-0.646472\pi$
$613$	−21.9901	−0.888172	−0.444086	+	0.895984i	$0.646472\pi$
$614$	2.92501	0.118044
$615$	0.614297	0.0247708
$616$	−106.959	−4.30949
$617$	11.6709	0.469853	0.234927	−	0.972013i	$-0.424515\pi$
$617$	11.6709	0.469853	0.234927	+	0.972013i	$0.424515\pi$
$618$	−41.9328	−1.68678
$619$	1.95607	0.0786211	0.0393106	−	0.999227i	$-0.487484\pi$
$619$	1.95607	0.0786211	0.0393106	+	0.999227i	$0.487484\pi$
$620$	−107.966	−4.33603
$621$	−23.5178	−0.943739
$622$	32.5045	1.30331
$623$	29.1098	1.16626
$624$	−10.7584	−0.430679
$625$	−30.3863	−1.21545
$626$	−42.2346	−1.68803
$627$	−36.7631	−1.46818
$628$	23.1247	0.922777
$629$	−0.134902	−0.00537888
$630$	38.5621	1.53635
$631$	−37.9288	−1.50992	−0.754961	−	0.655769i	$-0.772344\pi$
$631$	−37.9288	−1.50992	−0.754961	+	0.655769i	$0.772344\pi$
$632$	−11.2761	−0.448541
$633$	7.76921	0.308798
$634$	−0.0251290	−0.000997999 0
$635$	62.3365	2.47375
$636$	59.0804	2.34269
$637$	−3.68514	−0.146011
$638$	15.4535	0.611811
$639$	6.61535	0.261699
$640$	−10.2576	−0.405467
$641$	−10.6835	−0.421971	−0.210986	−	0.977489i	$-0.567667\pi$
$641$	−10.6835	−0.421971	−0.210986	+	0.977489i	$0.567667\pi$
$642$	−49.5636	−1.95612
$643$	−35.1803	−1.38738	−0.693688	−	0.720276i	$-0.744015\pi$
$643$	−35.1803	−1.38738	−0.693688	+	0.720276i	$0.744015\pi$
$644$	−66.6248	−2.62539
$645$	−31.8609	−1.25452
$646$	21.5678	0.848574
$647$	−37.6032	−1.47833	−0.739166	−	0.673523i	$-0.764780\pi$
$647$	−37.6032	−1.47833	−0.739166	+	0.673523i	$0.764780\pi$
$648$	13.1876	0.518056
$649$	33.0848	1.29869
$650$	8.90259	0.349188
$651$	−30.7237	−1.20416
$652$	−93.2602	−3.65235
$653$	−4.58942	−0.179598	−0.0897989	−	0.995960i	$-0.528622\pi$
$653$	−4.58942	−0.179598	−0.0897989	+	0.995960i	$0.528622\pi$
$654$	23.0773	0.902396
$655$	8.97982	0.350870
$656$	−1.58648	−0.0619418
$657$	13.8657	0.540953
$658$	−113.238	−4.41447
$659$	3.63735	0.141691	0.0708456	−	0.997487i	$-0.477430\pi$
$659$	3.63735	0.141691	0.0708456	+	0.997487i	$0.477430\pi$
$660$	75.8398	2.95206
$661$	−18.6143	−0.724011	−0.362006	−	0.932176i	$-0.617908\pi$
$661$	−18.6143	−0.724011	−0.362006	+	0.932176i	$0.617908\pi$
$662$	−19.8812	−0.772704
$663$	1.49205	0.0579463
$664$	−64.6175	−2.50765
$665$	63.2999	2.45466
$666$	0.440052	0.0170517
$667$	5.56372	0.215428
$668$	−38.5501	−1.49155
$669$	−3.75569	−0.145203
$670$	100.850	3.89617
$671$	9.08882	0.350870
$672$	35.6081	1.37361
$673$	−28.2604	−1.08936	−0.544678	−	0.838645i	$-0.683348\pi$
$673$	−28.2604	−1.08936	−0.544678	+	0.838645i	$0.683348\pi$
$674$	59.8267	2.30444
$675$	−18.7529	−0.721799
$676$	4.73919	0.182276
$677$	18.1421	0.697257	0.348628	−	0.937261i	$-0.386648\pi$
$677$	18.1421	0.697257	0.348628	+	0.937261i	$0.386648\pi$
$678$	−23.4358	−0.900045
$679$	−38.7839	−1.48839
$680$	−25.7164	−0.986177
$681$	12.9345	0.495649
$682$	93.7328	3.58921
$683$	−21.8870	−0.837482	−0.418741	−	0.908106i	$-0.637528\pi$
$683$	−21.8870	−0.837482	−0.418741	+	0.908106i	$0.637528\pi$
$684$	−49.4754	−1.89174
$685$	−16.0878	−0.614683
$686$	−28.1293	−1.07398
$687$	25.6593	0.978961
$688$	82.2840	3.13705
$689$	−10.4074	−0.396492
$690$	38.8274	1.47814
$691$	26.4461	1.00606	0.503029	−	0.864269i	$-0.332219\pi$
$691$	26.4461	1.00606	0.503029	+	0.864269i	$0.332219\pi$
$692$	89.3922	3.39818
$693$	−23.5429	−0.894322
$694$	65.1936	2.47472
$695$	50.8757	1.92983
$696$	−11.0191	−0.417677
$697$	0.220025	0.00833404
$698$	3.36402	0.127330
$699$	−13.8551	−0.524047
$700$	−53.1259	−2.00797
$701$	−8.16197	−0.308273	−0.154137	−	0.988050i	$-0.549260\pi$
$701$	−8.16197	−0.308273	−0.154137	+	0.988050i	$0.549260\pi$
$702$	−14.1958	−0.535785
$703$	0.722348	0.0272439
$704$	−25.9771	−0.979050
$705$	46.4078	1.74782
$706$	88.1251	3.31663
$707$	−16.7020	−0.628144
$708$	−40.8158	−1.53395
$709$	−28.4035	−1.06672	−0.533358	−	0.845890i	$-0.679070\pi$
$709$	−28.4035	−1.06672	−0.533358	+	0.845890i	$0.679070\pi$
$710$	−31.8555	−1.19552
$711$	−2.48201	−0.0930828
$712$	63.3248	2.37320
$713$	33.7465	1.26382
$714$	−12.6612	−0.473835
$715$	−13.3597	−0.499626
$716$	−35.6995	−1.33415
$717$	−17.3410	−0.647612
$718$	−7.25885	−0.270898
$719$	−0.0521446	−0.00194467	−0.000972333	−	1.00000i	$-0.500310\pi$
$719$	−0.0521446	−0.00194467	−0.000972333		1.00000i	$0.500310\pi$
$720$	40.8148	1.52108
$721$	−44.0803	−1.64163
$722$	−66.1636	−2.46236
$723$	0.0860730	0.00320109
$724$	−96.6270	−3.59112
$725$	4.43645	0.164766
$726$	−31.6364	−1.17414
$727$	−26.5609	−0.985091	−0.492545	−	0.870287i	$-0.663933\pi$
$727$	−26.5609	−0.985091	−0.492545	+	0.870287i	$0.663933\pi$
$728$	−23.2443	−0.861490
$729$	22.5532	0.835303
$730$	−66.7688	−2.47122
$731$	−11.4117	−0.422078
$732$	−11.2126	−0.414430
$733$	−18.3348	−0.677213	−0.338606	−	0.940928i	$-0.609955\pi$
$733$	−18.3348	−0.677213	−0.338606	+	0.940928i	$0.609955\pi$
$734$	−90.7512	−3.34969
$735$	−12.8158	−0.472719
$736$	−39.1115	−1.44167
$737$	−61.5707	−2.26799
$738$	−0.717726	−0.0264199
$739$	38.9057	1.43117	0.715584	−	0.698527i	$-0.246161\pi$
$739$	38.9057	1.43117	0.715584	+	0.698527i	$0.246161\pi$
$740$	−1.49016	−0.0547793
$741$	−7.98935	−0.293496
$742$	88.3156	3.24217
$743$	18.4919	0.678403	0.339202	−	0.940714i	$-0.389843\pi$
$743$	18.4919	0.678403	0.339202	+	0.940714i	$0.389843\pi$
$744$	−66.8357	−2.45032
$745$	−59.1842	−2.16834
$746$	25.1616	0.921232
$747$	−14.2231	−0.520396
$748$	27.1638	0.993208
$749$	−52.1018	−1.90376
$750$	−14.1799	−0.517778
$751$	−12.4821	−0.455478	−0.227739	−	0.973722i	$-0.573133\pi$
$751$	−12.4821	−0.455478	−0.227739	+	0.973722i	$0.573133\pi$
$752$	−119.853	−4.37058
$753$	−21.1847	−0.772013
$754$	3.35836	0.122304
$755$	−9.90868	−0.360614
$756$	84.7129	3.08098
$757$	24.4333	0.888042	0.444021	−	0.896016i	$-0.353552\pi$
$757$	24.4333	0.888042	0.444021	+	0.896016i	$0.353552\pi$
$758$	−100.591	−3.65364
$759$	−23.7049	−0.860434
$760$	137.701	4.99496
$761$	−7.10635	−0.257605	−0.128803	−	0.991670i	$-0.541113\pi$
$761$	−7.10635	−0.257605	−0.128803	+	0.991670i	$0.541113\pi$
$762$	66.7644	2.41862
$763$	24.2592	0.878242
$764$	−99.1029	−3.58542
$765$	−5.66048	−0.204655
$766$	14.2803	0.515968
$767$	7.18999	0.259615
$768$	−24.5106	−0.884449
$769$	−10.1591	−0.366345	−0.183172	−	0.983081i	$-0.558637\pi$
$769$	−10.1591	−0.366345	−0.183172	+	0.983081i	$0.558637\pi$
$770$	113.368	4.08551
$771$	30.8201	1.10996
$772$	−60.8928	−2.19158
$773$	34.6072	1.24474	0.622368	−	0.782725i	$-0.286171\pi$
$773$	34.6072	1.24474	0.622368	+	0.782725i	$0.286171\pi$
$774$	37.2253	1.33804
$775$	26.9091	0.966605
$776$	−84.3698	−3.02870
$777$	−0.424050	−0.0152127
$778$	81.4804	2.92121
$779$	−1.17815	−0.0422116
$780$	16.4815	0.590133
$781$	19.4484	0.695918
$782$	13.9070	0.497312
$783$	−7.07422	−0.252812
$784$	33.0982	1.18208
$785$	−14.1667	−0.505632
$786$	9.61767	0.343051
$787$	16.8127	0.599308	0.299654	−	0.954048i	$-0.403129\pi$
$787$	16.8127	0.599308	0.299654	+	0.954048i	$0.403129\pi$
$788$	−2.22565	−0.0792855
$789$	−20.6011	−0.733419
$790$	11.9519	0.425228
$791$	−24.6360	−0.875954
$792$	−51.2148	−1.81984
$793$	1.97518	0.0701407
$794$	−83.5766	−2.96602
$795$	−36.1940	−1.28367
$796$	24.2770	0.860474
$797$	−35.4398	−1.25534	−0.627671	−	0.778479i	$-0.715992\pi$
$797$	−35.4398	−1.25534	−0.627671	+	0.778479i	$0.715992\pi$
$798$	67.7962	2.39996
$799$	16.6220	0.588045
$800$	−31.1871	−1.10263
$801$	13.9386	0.492495
$802$	63.2133	2.23214
$803$	40.7636	1.43852
$804$	75.9580	2.67883
$805$	40.8159	1.43857
$806$	20.3700	0.717503
$807$	−14.7107	−0.517840
$808$	−36.3333	−1.27820
$809$	10.2835	0.361548	0.180774	−	0.983525i	$-0.442140\pi$
$809$	10.2835	0.361548	0.180774	+	0.983525i	$0.442140\pi$
$810$	−13.9778	−0.491131
$811$	−24.0961	−0.846130	−0.423065	−	0.906099i	$-0.639046\pi$
$811$	−24.0961	−0.846130	−0.423065	+	0.906099i	$0.639046\pi$
$812$	−20.0409	−0.703298
$813$	1.94533	0.0682258
$814$	1.29370	0.0453443
$815$	57.1333	2.00129
$816$	−13.4009	−0.469124
$817$	61.1056	2.13781
$818$	−102.118	−3.57047
$819$	−5.11635	−0.178780
$820$	2.43045	0.0848750
$821$	−34.8312	−1.21562	−0.607809	−	0.794083i	$-0.707951\pi$
$821$	−34.8312	−1.21562	−0.607809	+	0.794083i	$0.707951\pi$
$822$	−17.2305	−0.600984
$823$	5.04681	0.175921	0.0879603	−	0.996124i	$-0.471965\pi$
$823$	5.04681	0.175921	0.0879603	+	0.996124i	$0.471965\pi$
$824$	−95.8914	−3.34054
$825$	−18.9020	−0.658085
$826$	−61.0130	−2.12291
$827$	49.3935	1.71758	0.858790	−	0.512328i	$-0.171217\pi$
$827$	49.3935	1.71758	0.858790	+	0.512328i	$0.171217\pi$
$828$	−31.9018	−1.10867
$829$	−51.4141	−1.78569	−0.892843	−	0.450368i	$-0.851293\pi$
$829$	−51.4141	−1.78569	−0.892843	+	0.450368i	$0.851293\pi$
$830$	68.4897	2.37731
$831$	4.02509	0.139629
$832$	−5.64535	−0.195717
$833$	−4.59030	−0.159044
$834$	54.4895	1.88682
$835$	23.6167	0.817289
$836$	−145.452	−5.03057
$837$	−42.9084	−1.48313
$838$	−56.3948	−1.94813
$839$	−32.8652	−1.13463	−0.567316	−	0.823500i	$-0.692018\pi$
$839$	−32.8652	−1.13463	−0.567316	+	0.823500i	$0.692018\pi$
$840$	−80.8367	−2.78913
$841$	−27.3264	−0.942290
$842$	31.1629	1.07395
$843$	−2.51902	−0.0867596
$844$	30.7387	1.05807
$845$	−2.90334	−0.0998778
$846$	−54.2215	−1.86417
$847$	−33.2566	−1.14271
$848$	93.4747	3.20993
$849$	−1.04676	−0.0359248
$850$	11.0893	0.380359
$851$	0.465771	0.0159664
$852$	−23.9929	−0.821984
$853$	28.6955	0.982517	0.491258	−	0.871014i	$-0.336537\pi$
$853$	28.6955	0.982517	0.491258	+	0.871014i	$0.336537\pi$
$854$	−16.7610	−0.573551
$855$	30.3098	1.03657
$856$	−113.341	−3.87393
$857$	30.4299	1.03947	0.519733	−	0.854329i	$-0.326031\pi$
$857$	30.4299	1.03947	0.519733	+	0.854329i	$0.326031\pi$
$858$	−14.3087	−0.488491
$859$	−8.60599	−0.293632	−0.146816	−	0.989164i	$-0.546903\pi$
$859$	−8.60599	−0.293632	−0.146816	+	0.989164i	$0.546903\pi$
$860$	−126.057	−4.29850
$861$	0.691626	0.0235705
$862$	27.5078	0.936919
$863$	30.3056	1.03161	0.515807	−	0.856705i	$-0.327492\pi$
$863$	30.3056	1.03161	0.515807	+	0.856705i	$0.327492\pi$
$864$	49.7300	1.69185
$865$	−54.7637	−1.86202
$866$	−2.84154	−0.0965595
$867$	−18.5046	−0.628449
$868$	−121.557	−4.12593
$869$	−7.29684	−0.247528
$870$	11.6794	0.395968
$871$	−13.3805	−0.453383
$872$	52.7730	1.78712
$873$	−18.5708	−0.628527
$874$	−74.4666	−2.51887
$875$	−14.9061	−0.503919
$876$	−50.2889	−1.69910
$877$	−39.1307	−1.32135	−0.660676	−	0.750671i	$-0.729730\pi$
$877$	−39.1307	−1.32135	−0.660676	+	0.750671i	$0.729730\pi$
$878$	−1.58994	−0.0536579
$879$	−14.8599	−0.501213
$880$	119.991	4.04489
$881$	58.3121	1.96458	0.982291	−	0.187359i	$-0.0599929\pi$
$881$	58.3121	1.96458	0.982291	+	0.187359i	$0.0599929\pi$
$882$	14.9737	0.504189
$883$	−44.5609	−1.49959	−0.749797	−	0.661668i	$-0.769849\pi$
$883$	−44.5609	−1.49959	−0.749797	+	0.661668i	$0.769849\pi$
$884$	5.90324	0.198548
$885$	25.0047	0.840523
$886$	−55.6642	−1.87008
$887$	22.5831	0.758265	0.379133	−	0.925342i	$-0.376222\pi$
$887$	22.5831	0.758265	0.379133	+	0.925342i	$0.376222\pi$
$888$	−0.922470	−0.0309561
$889$	70.1836	2.35388
$890$	−67.1196	−2.24985
$891$	8.53374	0.285891
$892$	−14.8593	−0.497526
$893$	−89.0048	−2.97843
$894$	−63.3881	−2.12002
$895$	21.8703	0.731044
$896$	−11.5489	−0.385820
$897$	−5.15155	−0.172005
$898$	−82.9002	−2.76642
$899$	10.1510	0.338556
$900$	−25.4382	−0.847940
$901$	−12.9637	−0.431885
$902$	−2.11003	−0.0702565
$903$	−35.8716	−1.19373
$904$	−53.5926	−1.78246
$905$	59.1959	1.96774
$906$	−10.6125	−0.352577
$907$	−10.2604	−0.340689	−0.170345	−	0.985385i	$-0.554488\pi$
$907$	−10.2604	−0.340689	−0.170345	+	0.985385i	$0.554488\pi$
$908$	51.1748	1.69830
$909$	−7.99740	−0.265257
$910$	24.6372	0.816715
$911$	1.36032	0.0450694	0.0225347	−	0.999746i	$-0.492826\pi$
$911$	1.36032	0.0450694	0.0225347	+	0.999746i	$0.492826\pi$
$912$	71.7566	2.37610
$913$	−41.8143	−1.38385
$914$	−56.5897	−1.87182
$915$	6.86910	0.227085
$916$	101.520	3.35432
$917$	10.1102	0.333869
$918$	−17.6826	−0.583612
$919$	32.9722	1.08765	0.543826	−	0.839198i	$-0.316975\pi$
$919$	32.9722	1.08765	0.543826	+	0.839198i	$0.316975\pi$
$920$	88.7902	2.92733
$921$	−1.34964	−0.0444723
$922$	2.90746	0.0957520
$923$	4.22652	0.139118
$924$	85.3867	2.80902
$925$	0.371401	0.0122116
$926$	2.59599	0.0853097
$927$	−21.1069	−0.693240
$928$	−11.7648	−0.386200
$929$	12.6825	0.416098	0.208049	−	0.978118i	$-0.433289\pi$
$929$	12.6825	0.416098	0.208049	+	0.978118i	$0.433289\pi$
$930$	70.8409	2.32296
$931$	24.5793	0.805555
$932$	−54.8172	−1.79560
$933$	−14.9981	−0.491015
$934$	−5.23739	−0.171373
$935$	−16.6412	−0.544225
$936$	−11.1300	−0.363796
$937$	−0.329127	−0.0107521	−0.00537605	−	0.999986i	$-0.501711\pi$
$937$	−0.329127	−0.0107521	−0.00537605	+	0.999986i	$0.501711\pi$
$938$	113.545	3.70737
$939$	19.4877	0.635956
$940$	183.611	5.98873
$941$	17.6086	0.574025	0.287013	−	0.957927i	$-0.407338\pi$
$941$	17.6086	0.574025	0.287013	+	0.957927i	$0.407338\pi$
$942$	−15.1730	−0.494364
$943$	−0.759674	−0.0247384
$944$	−64.5771	−2.10181
$945$	−51.8971	−1.68821
$946$	109.438	3.55815
$947$	36.8187	1.19645	0.598223	−	0.801330i	$-0.295874\pi$
$947$	36.8187	1.19645	0.598223	+	0.801330i	$0.295874\pi$
$948$	9.00190	0.292368
$949$	8.85875	0.287567
$950$	−59.3789	−1.92651
$951$	0.0115949	0.000375990 0
$952$	−28.9536	−0.938391
$953$	10.5860	0.342914	0.171457	−	0.985192i	$-0.445153\pi$
$953$	10.5860	0.342914	0.171457	+	0.985192i	$0.445153\pi$
$954$	42.2880	1.36912
$955$	60.7127	1.96462
$956$	−68.6092	−2.21898
$957$	−7.13049	−0.230496
$958$	11.2010	0.361889
$959$	−18.1130	−0.584898
$960$	−19.6329	−0.633648
$961$	30.5708	0.986154
$962$	0.281148	0.00906457
$963$	−24.9478	−0.803932
$964$	0.340546	0.0109682
$965$	37.3043	1.20087
$966$	43.7151	1.40651
$967$	46.7024	1.50185	0.750924	−	0.660389i	$-0.229609\pi$
$967$	46.7024	1.50185	0.750924	+	0.660389i	$0.229609\pi$
$968$	−72.3458	−2.32528
$969$	−9.95172	−0.319695
$970$	89.4257	2.87129
$971$	−50.4489	−1.61898	−0.809491	−	0.587132i	$-0.800257\pi$
$971$	−50.4489	−1.61898	−0.809491	+	0.587132i	$0.800257\pi$
$972$	67.2187	2.15604
$973$	57.2801	1.83631
$974$	49.6368	1.59046
$975$	−4.10779	−0.131555
$976$	−17.7401	−0.567848
$977$	−29.3294	−0.938330	−0.469165	−	0.883111i	$-0.655445\pi$
$977$	−29.3294	−0.938330	−0.469165	+	0.883111i	$0.655445\pi$
$978$	61.1916	1.95669
$979$	40.9778	1.30966
$980$	−50.7055	−1.61973
$981$	11.6160	0.370870
$982$	−57.9611	−1.84961
$983$	11.4122	0.363992	0.181996	−	0.983299i	$-0.441744\pi$
$983$	11.4122	0.363992	0.181996	+	0.983299i	$0.441744\pi$
$984$	1.50455	0.0479633
$985$	1.36348	0.0434442
$986$	4.18325	0.133222
$987$	52.2497	1.66313
$988$	−31.6096	−1.00564
$989$	39.4010	1.25288
$990$	54.2839	1.72526
$991$	−14.9053	−0.473483	−0.236742	−	0.971573i	$-0.576079\pi$
$991$	−14.9053	−0.473483	−0.236742	+	0.971573i	$0.576079\pi$
$992$	−71.3592	−2.26566
$993$	9.17348	0.291112
$994$	−35.8655	−1.13759
$995$	−14.8726	−0.471494
$996$	51.5851	1.63454
$997$	−3.76399	−0.119207	−0.0596034	−	0.998222i	$-0.518984\pi$
$997$	−3.76399	−0.119207	−0.0596034	+	0.998222i	$0.518984\pi$
$998$	33.1198	1.04839
$999$	−0.592224	−0.0187372

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.8	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-2.59599 q^{2} +1.19783 q^{3} +4.73919 q^{4} -2.90334 q^{5} -3.10956 q^{6} -3.26881 q^{7} -7.11092 q^{8} -1.56520 q^{9} +O(q^{10})\)	\(q-2.59599 q^{2} +1.19783 q^{3} +4.73919 q^{4} -2.90334 q^{5} -3.10956 q^{6} -3.26881 q^{7} -7.11092 q^{8} -1.56520 q^{9} +7.53704 q^{10} -4.60151 q^{11} +5.67675 q^{12} -1.00000 q^{13} +8.48582 q^{14} -3.47771 q^{15} +8.98153 q^{16} -1.24562 q^{17} +4.06325 q^{18} +6.66984 q^{19} -13.7595 q^{20} -3.91549 q^{21} +11.9455 q^{22} +4.30073 q^{23} -8.51768 q^{24} +3.42936 q^{25} +2.59599 q^{26} -5.46834 q^{27} -15.4915 q^{28} +1.29367 q^{29} +9.02811 q^{30} +7.84670 q^{31} -9.09417 q^{32} -5.51183 q^{33} +3.23363 q^{34} +9.49046 q^{35} -7.41778 q^{36} +0.108301 q^{37} -17.3149 q^{38} -1.19783 q^{39} +20.6454 q^{40} -0.176638 q^{41} +10.1646 q^{42} +9.16147 q^{43} -21.8074 q^{44} +4.54430 q^{45} -11.1647 q^{46} -13.3444 q^{47} +10.7584 q^{48} +3.68514 q^{49} -8.90259 q^{50} -1.49205 q^{51} -4.73919 q^{52} +10.4074 q^{53} +14.1958 q^{54} +13.3597 q^{55} +23.2443 q^{56} +7.98935 q^{57} -3.35836 q^{58} -7.18999 q^{59} -16.4815 q^{60} -1.97518 q^{61} -20.3700 q^{62} +5.11635 q^{63} +5.64535 q^{64} +2.90334 q^{65} +14.3087 q^{66} +13.3805 q^{67} -5.90324 q^{68} +5.15155 q^{69} -24.6372 q^{70} -4.22652 q^{71} +11.1300 q^{72} -8.85875 q^{73} -0.281148 q^{74} +4.10779 q^{75} +31.6096 q^{76} +15.0415 q^{77} +3.10956 q^{78} +1.58575 q^{79} -26.0764 q^{80} -1.85455 q^{81} +0.458553 q^{82} +9.08708 q^{83} -18.5562 q^{84} +3.61646 q^{85} -23.7831 q^{86} +1.54960 q^{87} +32.7210 q^{88} -8.90530 q^{89} -11.7970 q^{90} +3.26881 q^{91} +20.3820 q^{92} +9.39903 q^{93} +34.6419 q^{94} -19.3648 q^{95} -10.8933 q^{96} +11.8648 q^{97} -9.56661 q^{98} +7.20228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 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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