LMFDB - Embedded newform 6019.2.a.c.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.64969 q^{2} -0.413927 q^{3} +5.02086 q^{4} -1.95969 q^{5} +1.09678 q^{6} -0.899778 q^{7} -8.00435 q^{8} -2.82866 q^{9} +O(q^{10})$	\(q-2.64969 q^{2} -0.413927 q^{3} +5.02086 q^{4} -1.95969 q^{5} +1.09678 q^{6} -0.899778 q^{7} -8.00435 q^{8} -2.82866 q^{9} +5.19257 q^{10} +4.83103 q^{11} -2.07827 q^{12} -1.00000 q^{13} +2.38413 q^{14} +0.811168 q^{15} +11.1673 q^{16} +2.65234 q^{17} +7.49509 q^{18} -3.64749 q^{19} -9.83933 q^{20} +0.372442 q^{21} -12.8007 q^{22} +5.87423 q^{23} +3.31322 q^{24} -1.15962 q^{25} +2.64969 q^{26} +2.41264 q^{27} -4.51766 q^{28} -4.43883 q^{29} -2.14935 q^{30} +5.22174 q^{31} -13.5813 q^{32} -1.99969 q^{33} -7.02788 q^{34} +1.76329 q^{35} -14.2023 q^{36} +3.29448 q^{37} +9.66472 q^{38} +0.413927 q^{39} +15.6860 q^{40} -10.9911 q^{41} -0.986857 q^{42} -3.92099 q^{43} +24.2559 q^{44} +5.54330 q^{45} -15.5649 q^{46} -3.93450 q^{47} -4.62246 q^{48} -6.19040 q^{49} +3.07263 q^{50} -1.09788 q^{51} -5.02086 q^{52} +2.69311 q^{53} -6.39276 q^{54} -9.46732 q^{55} +7.20214 q^{56} +1.50980 q^{57} +11.7615 q^{58} -14.7234 q^{59} +4.07276 q^{60} +11.8266 q^{61} -13.8360 q^{62} +2.54517 q^{63} +13.6515 q^{64} +1.95969 q^{65} +5.29857 q^{66} +2.89289 q^{67} +13.3170 q^{68} -2.43150 q^{69} -4.67216 q^{70} +4.80128 q^{71} +22.6416 q^{72} +14.0811 q^{73} -8.72935 q^{74} +0.479998 q^{75} -18.3135 q^{76} -4.34686 q^{77} -1.09678 q^{78} +15.3643 q^{79} -21.8845 q^{80} +7.48734 q^{81} +29.1229 q^{82} -14.6641 q^{83} +1.86998 q^{84} -5.19776 q^{85} +10.3894 q^{86} +1.83735 q^{87} -38.6693 q^{88} +1.94412 q^{89} -14.6880 q^{90} +0.899778 q^{91} +29.4937 q^{92} -2.16142 q^{93} +10.4252 q^{94} +7.14795 q^{95} +5.62166 q^{96} +12.1069 q^{97} +16.4026 q^{98} -13.6654 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.64969	−1.87361	−0.936807	−	0.349846i	$-0.886234\pi$
$2$	−2.64969	−1.87361	−0.936807	+	0.349846i	$0.886234\pi$
$3$	−0.413927	−0.238981	−0.119490	−	0.992835i	$-0.538126\pi$
$3$	−0.413927	−0.238981	−0.119490	+	0.992835i	$0.538126\pi$
$4$	5.02086	2.51043
$5$	−1.95969	−0.876400	−0.438200	−	0.898878i	$-0.644384\pi$
$5$	−1.95969	−0.876400	−0.438200	+	0.898878i	$0.644384\pi$
$6$	1.09678	0.447758
$7$	−0.899778	−0.340084	−0.170042	−	0.985437i	$-0.554390\pi$
$7$	−0.899778	−0.340084	−0.170042	+	0.985437i	$0.554390\pi$
$8$	−8.00435	−2.82997
$9$	−2.82866	−0.942888
$10$	5.19257	1.64203
$11$	4.83103	1.45661	0.728305	−	0.685253i	$-0.240308\pi$
$11$	4.83103	1.45661	0.728305	+	0.685253i	$0.240308\pi$
$12$	−2.07827	−0.599945
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.38413	0.637187
$15$	0.811168	0.209443
$16$	11.1673	2.79183
$17$	2.65234	0.643287	0.321644	−	0.946861i	$-0.395765\pi$
$17$	2.65234	0.643287	0.321644	+	0.946861i	$0.395765\pi$
$18$	7.49509	1.76661
$19$	−3.64749	−0.836792	−0.418396	−	0.908265i	$-0.637408\pi$
$19$	−3.64749	−0.836792	−0.418396	+	0.908265i	$0.637408\pi$
$20$	−9.83933	−2.20014
$21$	0.372442	0.0812736
$22$	−12.8007	−2.72913
$23$	5.87423	1.22486	0.612431	−	0.790524i	$-0.290192\pi$
$23$	5.87423	1.22486	0.612431	+	0.790524i	$0.290192\pi$
$24$	3.31322	0.676308
$25$	−1.15962	−0.231924
$26$	2.64969	0.519647
$27$	2.41264	0.464313
$28$	−4.51766	−0.853758
$29$	−4.43883	−0.824271	−0.412135	−	0.911123i	$-0.635217\pi$
$29$	−4.43883	−0.824271	−0.412135	+	0.911123i	$0.635217\pi$
$30$	−2.14935	−0.392415
$31$	5.22174	0.937851	0.468926	−	0.883238i	$-0.344641\pi$
$31$	5.22174	0.937851	0.468926	+	0.883238i	$0.344641\pi$
$32$	−13.5813	−2.40085
$33$	−1.99969	−0.348102
$34$	−7.02788	−1.20527
$35$	1.76329	0.298050
$36$	−14.2023	−2.36706
$37$	3.29448	0.541609	0.270804	−	0.962634i	$-0.412710\pi$
$37$	3.29448	0.541609	0.270804	+	0.962634i	$0.412710\pi$
$38$	9.66472	1.56783
$39$	0.413927	0.0662814
$40$	15.6860	2.48018
$41$	−10.9911	−1.71651	−0.858257	−	0.513219i	$-0.828453\pi$
$41$	−10.9911	−1.71651	−0.858257	+	0.513219i	$0.828453\pi$
$42$	−0.986857	−0.152275
$43$	−3.92099	−0.597945	−0.298973	−	0.954262i	$-0.596644\pi$
$43$	−3.92099	−0.597945	−0.298973	+	0.954262i	$0.596644\pi$
$44$	24.2559	3.65672
$45$	5.54330	0.826347
$46$	−15.5649	−2.29492
$47$	−3.93450	−0.573906	−0.286953	−	0.957945i	$-0.592642\pi$
$47$	−3.93450	−0.573906	−0.286953	+	0.957945i	$0.592642\pi$
$48$	−4.62246	−0.667195
$49$	−6.19040	−0.884343
$50$	3.07263	0.434536
$51$	−1.09788	−0.153733
$52$	−5.02086	−0.696268
$53$	2.69311	0.369927	0.184963	−	0.982745i	$-0.440783\pi$
$53$	2.69311	0.369927	0.184963	+	0.982745i	$0.440783\pi$
$54$	−6.39276	−0.869944
$55$	−9.46732	−1.27657
$56$	7.20214	0.962426
$57$	1.50980	0.199977
$58$	11.7615	1.54437
$59$	−14.7234	−1.91682	−0.958409	−	0.285398i	$-0.907874\pi$
$59$	−14.7234	−1.91682	−0.958409	+	0.285398i	$0.907874\pi$
$60$	4.07276	0.525792
$61$	11.8266	1.51424	0.757122	−	0.653274i	$-0.226605\pi$
$61$	11.8266	1.51424	0.757122	+	0.653274i	$0.226605\pi$
$62$	−13.8360	−1.75717
$63$	2.54517	0.320661
$64$	13.6515	1.70644
$65$	1.95969	0.243070
$66$	5.29857	0.652209
$67$	2.89289	0.353422	0.176711	−	0.984263i	$-0.443454\pi$
$67$	2.89289	0.353422	0.176711	+	0.984263i	$0.443454\pi$
$68$	13.3170	1.61493
$69$	−2.43150	−0.292719
$70$	−4.67216	−0.558430
$71$	4.80128	0.569807	0.284904	−	0.958556i	$-0.408038\pi$
$71$	4.80128	0.569807	0.284904	+	0.958556i	$0.408038\pi$
$72$	22.6416	2.66834
$73$	14.0811	1.64807	0.824037	−	0.566536i	$-0.191717\pi$
$73$	14.0811	1.64807	0.824037	+	0.566536i	$0.191717\pi$
$74$	−8.72935	−1.01477
$75$	0.479998	0.0554254
$76$	−18.3135	−2.10071
$77$	−4.34686	−0.495370
$78$	−1.09678	−0.124186
$79$	15.3643	1.72862	0.864310	−	0.502960i	$-0.167756\pi$
$79$	15.3643	1.72862	0.864310	+	0.502960i	$0.167756\pi$
$80$	−21.8845	−2.44676
$81$	7.48734	0.831926
$82$	29.1229	3.21609
$83$	−14.6641	−1.60959	−0.804797	−	0.593551i	$-0.797726\pi$
$83$	−14.6641	−1.60959	−0.804797	+	0.593551i	$0.797726\pi$
$84$	1.86998	0.204032
$85$	−5.19776	−0.563777
$86$	10.3894	1.12032
$87$	1.83735	0.196985
$88$	−38.6693	−4.12216
$89$	1.94412	0.206076	0.103038	−	0.994677i	$-0.467144\pi$
$89$	1.94412	0.206076	0.103038	+	0.994677i	$0.467144\pi$
$90$	−14.6880	−1.54826
$91$	0.899778	0.0943224
$92$	29.4937	3.07493
$93$	−2.16142	−0.224129
$94$	10.4252	1.07528
$95$	7.14795	0.733364
$96$	5.62166	0.573758
$97$	12.1069	1.22927	0.614636	−	0.788811i	$-0.289303\pi$
$97$	12.1069	1.22927	0.614636	+	0.788811i	$0.289303\pi$
$98$	16.4026	1.65692
$99$	−13.6654	−1.37342
$100$	−5.82229	−0.582229
$101$	−1.89217	−0.188278	−0.0941389	−	0.995559i	$-0.530010\pi$
$101$	−1.89217	−0.188278	−0.0941389	+	0.995559i	$0.530010\pi$
$102$	2.90903	0.288037
$103$	3.41117	0.336113	0.168056	−	0.985777i	$-0.446251\pi$
$103$	3.41117	0.336113	0.168056	+	0.985777i	$0.446251\pi$
$104$	8.00435	0.784891
$105$	−0.729871	−0.0712282
$106$	−7.13590	−0.693100
$107$	−5.91694	−0.572013	−0.286006	−	0.958228i	$-0.592328\pi$
$107$	−5.91694	−0.572013	−0.286006	+	0.958228i	$0.592328\pi$
$108$	12.1135	1.16563
$109$	−7.22686	−0.692208	−0.346104	−	0.938196i	$-0.612496\pi$
$109$	−7.22686	−0.692208	−0.346104	+	0.938196i	$0.612496\pi$
$110$	25.0855	2.39181
$111$	−1.36367	−0.129434
$112$	−10.0481	−0.949458
$113$	−12.0550	−1.13404	−0.567018	−	0.823705i	$-0.691903\pi$
$113$	−12.0550	−1.13404	−0.567018	+	0.823705i	$0.691903\pi$
$114$	−4.00049	−0.374680
$115$	−11.5117	−1.07347
$116$	−22.2868	−2.06927
$117$	2.82866	0.261510
$118$	39.0124	3.59138
$119$	−2.38652	−0.218772
$120$	−6.49288	−0.592716
$121$	12.3389	1.12172
$122$	−31.3369	−2.83711
$123$	4.54950	0.410214
$124$	26.2176	2.35441
$125$	12.0709	1.07966
$126$	−6.74391	−0.600796
$127$	5.79873	0.514554	0.257277	−	0.966338i	$-0.417175\pi$
$127$	5.79873	0.514554	0.257277	+	0.966338i	$0.417175\pi$
$128$	−9.00976	−0.796358
$129$	1.62300	0.142897
$130$	−5.19257	−0.455419
$131$	16.7921	1.46714	0.733568	−	0.679616i	$-0.237853\pi$
$131$	16.7921	1.46714	0.733568	+	0.679616i	$0.237853\pi$
$132$	−10.0402	−0.873887
$133$	3.28193	0.284580
$134$	−7.66525	−0.662177
$135$	−4.72803	−0.406924
$136$	−21.2303	−1.82048
$137$	14.8934	1.27243	0.636214	−	0.771512i	$-0.280499\pi$
$137$	14.8934	1.27243	0.636214	+	0.771512i	$0.280499\pi$
$138$	6.44273	0.548442
$139$	21.3712	1.81268	0.906342	−	0.422545i	$-0.138863\pi$
$139$	21.3712	1.81268	0.906342	+	0.422545i	$0.138863\pi$
$140$	8.85321	0.748233
$141$	1.62860	0.137153
$142$	−12.7219	−1.06760
$143$	−4.83103	−0.403991
$144$	−31.5886	−2.63239
$145$	8.69873	0.722390
$146$	−37.3107	−3.08785
$147$	2.56237	0.211341
$148$	16.5411	1.35967
$149$	−20.2929	−1.66246	−0.831231	−	0.555927i	$-0.812363\pi$
$149$	−20.2929	−1.66246	−0.831231	+	0.555927i	$0.812363\pi$
$150$	−1.27185	−0.103846
$151$	1.51776	0.123513	0.0617566	−	0.998091i	$-0.480330\pi$
$151$	1.51776	0.123513	0.0617566	+	0.998091i	$0.480330\pi$
$152$	29.1958	2.36809
$153$	−7.50258	−0.606548
$154$	11.5178	0.928133
$155$	−10.2330	−0.821933
$156$	2.07827	0.166395
$157$	−14.7567	−1.17771	−0.588855	−	0.808238i	$-0.700421\pi$
$157$	−14.7567	−1.17771	−0.588855	+	0.808238i	$0.700421\pi$
$158$	−40.7107	−3.23877
$159$	−1.11475	−0.0884054
$160$	26.6151	2.10411
$161$	−5.28551	−0.416556
$162$	−19.8391	−1.55871
$163$	−16.6154	−1.30142	−0.650710	−	0.759327i	$-0.725528\pi$
$163$	−16.6154	−1.30142	−0.650710	+	0.759327i	$0.725528\pi$
$164$	−55.1846	−4.30919
$165$	3.91878	0.305077
$166$	38.8553	3.01576
$167$	−4.98367	−0.385648	−0.192824	−	0.981233i	$-0.561765\pi$
$167$	−4.98367	−0.385648	−0.192824	+	0.981233i	$0.561765\pi$
$168$	−2.98116	−0.230001
$169$	1.00000	0.0769231
$170$	13.7725	1.05630
$171$	10.3175	0.789001
$172$	−19.6867	−1.50110
$173$	21.2173	1.61312	0.806562	−	0.591150i	$-0.201326\pi$
$173$	21.2173	1.61312	0.806562	+	0.591150i	$0.201326\pi$
$174$	−4.86842	−0.369074
$175$	1.04340	0.0788736
$176$	53.9497	4.06661
$177$	6.09440	0.458083
$178$	−5.15132	−0.386108
$179$	4.40911	0.329553	0.164776	−	0.986331i	$-0.447310\pi$
$179$	4.40911	0.329553	0.164776	+	0.986331i	$0.447310\pi$
$180$	27.8322	2.07449
$181$	12.0691	0.897089	0.448545	−	0.893760i	$-0.351942\pi$
$181$	12.0691	0.897089	0.448545	+	0.893760i	$0.351942\pi$
$182$	−2.38413	−0.176724
$183$	−4.89536	−0.361875
$184$	−47.0194	−3.46632
$185$	−6.45615	−0.474666
$186$	5.72709	0.419931
$187$	12.8135	0.937019
$188$	−19.7546	−1.44075
$189$	−2.17084	−0.157906
$190$	−18.9399	−1.37404
$191$	−7.01101	−0.507299	−0.253650	−	0.967296i	$-0.581631\pi$
$191$	−7.01101	−0.507299	−0.253650	+	0.967296i	$0.581631\pi$
$192$	−5.65073	−0.407807
$193$	−2.96284	−0.213270	−0.106635	−	0.994298i	$-0.534008\pi$
$193$	−2.96284	−0.213270	−0.106635	+	0.994298i	$0.534008\pi$
$194$	−32.0796	−2.30318
$195$	−0.811168	−0.0580890
$196$	−31.0811	−2.22008
$197$	0.242144	0.0172520	0.00862601	−	0.999963i	$-0.497254\pi$
$197$	0.242144	0.0172520	0.00862601	+	0.999963i	$0.497254\pi$
$198$	36.2090	2.57326
$199$	−21.8303	−1.54751	−0.773754	−	0.633487i	$-0.781623\pi$
$199$	−21.8303	−1.54751	−0.773754	+	0.633487i	$0.781623\pi$
$200$	9.28200	0.656336
$201$	−1.19744	−0.0844611
$202$	5.01366	0.352760
$203$	3.99396	0.280321
$204$	−5.51228	−0.385937
$205$	21.5391	1.50435
$206$	−9.03856	−0.629746
$207$	−16.6162	−1.15491
$208$	−11.1673	−0.774315
$209$	−17.6211	−1.21888
$210$	1.93393	0.133454
$211$	11.9531	0.822888	0.411444	−	0.911435i	$-0.365024\pi$
$211$	11.9531	0.822888	0.411444	+	0.911435i	$0.365024\pi$
$212$	13.5217	0.928676
$213$	−1.98738	−0.136173
$214$	15.6781	1.07173
$215$	7.68392	0.524039
$216$	−19.3116	−1.31399
$217$	−4.69840	−0.318948
$218$	19.1490	1.29693
$219$	−5.82857	−0.393858
$220$	−47.5341	−3.20475
$221$	−2.65234	−0.178416
$222$	3.61331	0.242510
$223$	4.58527	0.307052	0.153526	−	0.988145i	$-0.450937\pi$
$223$	4.58527	0.307052	0.153526	+	0.988145i	$0.450937\pi$
$224$	12.2201	0.816492
$225$	3.28017	0.218678
$226$	31.9420	2.12475
$227$	−20.5188	−1.36188	−0.680941	−	0.732338i	$-0.738429\pi$
$227$	−20.5188	−1.36188	−0.680941	+	0.732338i	$0.738429\pi$
$228$	7.58047	0.502029
$229$	−28.0049	−1.85061	−0.925307	−	0.379219i	$-0.876193\pi$
$229$	−28.0049	−1.85061	−0.925307	+	0.379219i	$0.876193\pi$
$230$	30.5024	2.01127
$231$	1.79928	0.118384
$232$	35.5300	2.33266
$233$	−2.40928	−0.157837	−0.0789186	−	0.996881i	$-0.525147\pi$
$233$	−2.40928	−0.157837	−0.0789186	+	0.996881i	$0.525147\pi$
$234$	−7.49509	−0.489969
$235$	7.71040	0.502971
$236$	−73.9240	−4.81204
$237$	−6.35970	−0.413107
$238$	6.32354	0.409894
$239$	−18.7938	−1.21567	−0.607834	−	0.794064i	$-0.707961\pi$
$239$	−18.7938	−1.21567	−0.607834	+	0.794064i	$0.707961\pi$
$240$	9.05859	0.584729
$241$	22.7407	1.46486	0.732428	−	0.680844i	$-0.238387\pi$
$241$	22.7407	1.46486	0.732428	+	0.680844i	$0.238387\pi$
$242$	−32.6942	−2.10166
$243$	−10.3371	−0.663128
$244$	59.3798	3.80140
$245$	12.1313	0.775038
$246$	−12.0548	−0.768583
$247$	3.64749	0.232084
$248$	−41.7966	−2.65409
$249$	6.06986	0.384662
$250$	−31.9843	−2.02286
$251$	−17.9850	−1.13520	−0.567602	−	0.823303i	$-0.692129\pi$
$251$	−17.9850	−1.13520	−0.567602	+	0.823303i	$0.692129\pi$
$252$	12.7789	0.804998
$253$	28.3786	1.78415
$254$	−15.3648	−0.964076
$255$	2.15150	0.134732
$256$	−3.42997	−0.214373
$257$	9.96098	0.621349	0.310674	−	0.950516i	$-0.399445\pi$
$257$	9.96098	0.621349	0.310674	+	0.950516i	$0.399445\pi$
$258$	−4.30046	−0.267735
$259$	−2.96430	−0.184193
$260$	9.83933	0.610209
$261$	12.5560	0.777195
$262$	−44.4940	−2.74885
$263$	4.29805	0.265029	0.132515	−	0.991181i	$-0.457695\pi$
$263$	4.29805	0.265029	0.132515	+	0.991181i	$0.457695\pi$
$264$	16.0063	0.985117
$265$	−5.27765	−0.324204
$266$	−8.69611	−0.533192
$267$	−0.804724	−0.0492483
$268$	14.5248	0.887242
$269$	−8.98038	−0.547544	−0.273772	−	0.961795i	$-0.588271\pi$
$269$	−8.98038	−0.547544	−0.273772	+	0.961795i	$0.588271\pi$
$270$	12.5278	0.762418
$271$	−4.78584	−0.290719	−0.145359	−	0.989379i	$-0.546434\pi$
$271$	−4.78584	−0.290719	−0.145359	+	0.989379i	$0.546434\pi$
$272$	29.6196	1.79595
$273$	−0.372442	−0.0225412
$274$	−39.4629	−2.38404
$275$	−5.60216	−0.337823
$276$	−12.2082	−0.734850
$277$	18.4811	1.11042	0.555209	−	0.831711i	$-0.312638\pi$
$277$	18.4811	1.11042	0.555209	+	0.831711i	$0.312638\pi$
$278$	−56.6272	−3.39627
$279$	−14.7705	−0.884289
$280$	−14.1140	−0.843470
$281$	−11.4528	−0.683214	−0.341607	−	0.939843i	$-0.610971\pi$
$281$	−11.4528	−0.683214	−0.341607	+	0.939843i	$0.610971\pi$
$282$	−4.31528	−0.256971
$283$	−7.32082	−0.435177	−0.217589	−	0.976041i	$-0.569819\pi$
$283$	−7.32082	−0.435177	−0.217589	+	0.976041i	$0.569819\pi$
$284$	24.1066	1.43046
$285$	−2.95873	−0.175260
$286$	12.8007	0.756924
$287$	9.88951	0.583759
$288$	38.4169	2.26374
$289$	−9.96509	−0.586182
$290$	−23.0490	−1.35348
$291$	−5.01138	−0.293773
$292$	70.6995	4.13738
$293$	12.3922	0.723961	0.361981	−	0.932186i	$-0.382101\pi$
$293$	12.3922	0.723961	0.361981	+	0.932186i	$0.382101\pi$
$294$	−6.78950	−0.395972
$295$	28.8532	1.67990
$296$	−26.3702	−1.53273
$297$	11.6556	0.676324
$298$	53.7700	3.11481
$299$	−5.87423	−0.339716
$300$	2.41000	0.139142
$301$	3.52802	0.203352
$302$	−4.02158	−0.231416
$303$	0.783220	0.0449948
$304$	−40.7327	−2.33618
$305$	−23.1765	−1.32708
$306$	19.8795	1.13644
$307$	19.0913	1.08960	0.544799	−	0.838566i	$-0.316606\pi$
$307$	19.0913	1.08960	0.544799	+	0.838566i	$0.316606\pi$
$308$	−21.8250	−1.24359
$309$	−1.41198	−0.0803246
$310$	27.1142	1.53998
$311$	−7.14971	−0.405423	−0.202712	−	0.979238i	$-0.564975\pi$
$311$	−7.14971	−0.405423	−0.202712	+	0.979238i	$0.564975\pi$
$312$	−3.31322	−0.187574
$313$	28.6971	1.62206	0.811028	−	0.585007i	$-0.198908\pi$
$313$	28.6971	1.62206	0.811028	+	0.585007i	$0.198908\pi$
$314$	39.1006	2.20658
$315$	−4.98774	−0.281027
$316$	77.1421	4.33958
$317$	2.50653	0.140781	0.0703903	−	0.997520i	$-0.477576\pi$
$317$	2.50653	0.140781	0.0703903	+	0.997520i	$0.477576\pi$
$318$	2.95374	0.165638
$319$	−21.4441	−1.20064
$320$	−26.7527	−1.49552
$321$	2.44918	0.136700
$322$	14.0050	0.780466
$323$	−9.67439	−0.538298
$324$	37.5929	2.08849
$325$	1.15962	0.0643241
$326$	44.0257	2.43836
$327$	2.99139	0.165424
$328$	87.9763	4.85768
$329$	3.54018	0.195176
$330$	−10.3836	−0.571596
$331$	−28.4339	−1.56287	−0.781433	−	0.623989i	$-0.785511\pi$
$331$	−28.4339	−1.56287	−0.781433	+	0.623989i	$0.785511\pi$
$332$	−73.6264	−4.04077
$333$	−9.31897	−0.510677
$334$	13.2052	0.722556
$335$	−5.66916	−0.309739
$336$	4.15919	0.226902
$337$	8.77352	0.477924	0.238962	−	0.971029i	$-0.423193\pi$
$337$	8.77352	0.477924	0.238962	+	0.971029i	$0.423193\pi$
$338$	−2.64969	−0.144124
$339$	4.98988	0.271013
$340$	−26.0973	−1.41532
$341$	25.2264	1.36608
$342$	−27.3383	−1.47828
$343$	11.8684	0.640835
$344$	31.3850	1.69216
$345$	4.76499	0.256539
$346$	−56.2194	−3.02237
$347$	30.3148	1.62738	0.813691	−	0.581297i	$-0.197455\pi$
$347$	30.3148	1.62738	0.813691	+	0.581297i	$0.197455\pi$
$348$	9.22510	0.494517
$349$	26.6175	1.42480	0.712402	−	0.701771i	$-0.247607\pi$
$349$	26.6175	1.42480	0.712402	+	0.701771i	$0.247607\pi$
$350$	−2.76469	−0.147779
$351$	−2.41264	−0.128777
$352$	−65.6116	−3.49711
$353$	21.9385	1.16767	0.583835	−	0.811872i	$-0.301551\pi$
$353$	21.9385	1.16767	0.583835	+	0.811872i	$0.301551\pi$
$354$	−16.1483	−0.858271
$355$	−9.40902	−0.499379
$356$	9.76116	0.517341
$357$	0.987844	0.0522823
$358$	−11.6828	−0.617455
$359$	31.3915	1.65678	0.828391	−	0.560150i	$-0.189256\pi$
$359$	31.3915	1.65678	0.828391	+	0.560150i	$0.189256\pi$
$360$	−44.3705	−2.33853
$361$	−5.69581	−0.299779
$362$	−31.9794	−1.68080
$363$	−5.10739	−0.268069
$364$	4.51766	0.236790
$365$	−27.5947	−1.44437
$366$	12.9712	0.678015
$367$	24.8320	1.29622	0.648111	−	0.761546i	$-0.275559\pi$
$367$	24.8320	1.29622	0.648111	+	0.761546i	$0.275559\pi$
$368$	65.5995	3.41961
$369$	31.0900	1.61848
$370$	17.1068	0.889341
$371$	−2.42320	−0.125806
$372$	−10.8522	−0.562659
$373$	37.6810	1.95105	0.975524	−	0.219893i	$-0.0705708\pi$
$373$	37.6810	1.95105	0.975524	+	0.219893i	$0.0705708\pi$
$374$	−33.9519	−1.75561
$375$	−4.99649	−0.258018
$376$	31.4931	1.62413
$377$	4.43883	0.228612
$378$	5.75206	0.295854
$379$	−31.6292	−1.62469	−0.812343	−	0.583181i	$-0.801808\pi$
$379$	−31.6292	−1.62469	−0.812343	+	0.583181i	$0.801808\pi$
$380$	35.8889	1.84106
$381$	−2.40025	−0.122969
$382$	18.5770	0.950483
$383$	−2.72712	−0.139350	−0.0696748	−	0.997570i	$-0.522196\pi$
$383$	−2.72712	−0.139350	−0.0696748	+	0.997570i	$0.522196\pi$
$384$	3.72938	0.190314
$385$	8.51849	0.434142
$386$	7.85062	0.399586
$387$	11.0912	0.563795
$388$	60.7872	3.08600
$389$	−15.4717	−0.784446	−0.392223	−	0.919870i	$-0.628294\pi$
$389$	−15.4717	−0.784446	−0.392223	+	0.919870i	$0.628294\pi$
$390$	2.14935	0.108836
$391$	15.5805	0.787938
$392$	49.5501	2.50266
$393$	−6.95072	−0.350618
$394$	−0.641606	−0.0323236
$395$	−30.1093	−1.51496
$396$	−68.6119	−3.44788
$397$	−8.31160	−0.417147	−0.208574	−	0.978007i	$-0.566882\pi$
$397$	−8.31160	−0.417147	−0.208574	+	0.978007i	$0.566882\pi$
$398$	57.8435	2.89943
$399$	−1.35848	−0.0680091
$400$	−12.9499	−0.647493
$401$	3.81218	0.190371	0.0951856	−	0.995460i	$-0.469656\pi$
$401$	3.81218	0.190371	0.0951856	+	0.995460i	$0.469656\pi$
$402$	3.17286	0.158248
$403$	−5.22174	−0.260113
$404$	−9.50032	−0.472659
$405$	−14.6728	−0.729100
$406$	−10.5828	−0.525214
$407$	15.9157	0.788914
$408$	8.78778	0.435060
$409$	−22.0866	−1.09211	−0.546056	−	0.837748i	$-0.683872\pi$
$409$	−22.0866	−1.09211	−0.546056	+	0.837748i	$0.683872\pi$
$410$	−57.0718	−2.81858
$411$	−6.16478	−0.304086
$412$	17.1270	0.843788
$413$	13.2478	0.651879
$414$	44.0279	2.16385
$415$	28.7371	1.41065
$416$	13.5813	0.665877
$417$	−8.84613	−0.433197
$418$	46.6906	2.28371
$419$	9.13359	0.446205	0.223102	−	0.974795i	$-0.428382\pi$
$419$	9.13359	0.446205	0.223102	+	0.974795i	$0.428382\pi$
$420$	−3.66458	−0.178813
$421$	−21.9095	−1.06780	−0.533901	−	0.845547i	$-0.679274\pi$
$421$	−21.9095	−1.06780	−0.533901	+	0.845547i	$0.679274\pi$
$422$	−31.6721	−1.54178
$423$	11.1294	0.541129
$424$	−21.5566	−1.04688
$425$	−3.07571	−0.149194
$426$	5.26594	0.255136
$427$	−10.6413	−0.514970
$428$	−29.7082	−1.43600
$429$	1.99969	0.0965462
$430$	−20.3600	−0.981847
$431$	−18.9657	−0.913547	−0.456773	−	0.889583i	$-0.650995\pi$
$431$	−18.9657	−0.913547	−0.456773	+	0.889583i	$0.650995\pi$
$432$	26.9428	1.29628
$433$	−25.0396	−1.20333	−0.601664	−	0.798749i	$-0.705496\pi$
$433$	−25.0396	−1.20333	−0.601664	+	0.798749i	$0.705496\pi$
$434$	12.4493	0.597586
$435$	−3.60064	−0.172637
$436$	−36.2851	−1.73774
$437$	−21.4262	−1.02495
$438$	15.4439	0.737938
$439$	−26.7623	−1.27730	−0.638648	−	0.769499i	$-0.720506\pi$
$439$	−26.7623	−1.27730	−0.638648	+	0.769499i	$0.720506\pi$
$440$	75.7798	3.61266
$441$	17.5106	0.833836
$442$	7.02788	0.334282
$443$	−25.9016	−1.23062	−0.615312	−	0.788283i	$-0.710970\pi$
$443$	−25.9016	−1.23062	−0.615312	+	0.788283i	$0.710970\pi$
$444$	−6.84682	−0.324936
$445$	−3.80987	−0.180605
$446$	−12.1495	−0.575298
$447$	8.39979	0.397297
$448$	−12.2833	−0.580333
$449$	13.1287	0.619582	0.309791	−	0.950805i	$-0.399741\pi$
$449$	13.1287	0.619582	0.309791	+	0.950805i	$0.399741\pi$
$450$	−8.69145	−0.409719
$451$	−53.0982	−2.50029
$452$	−60.5264	−2.84692
$453$	−0.628240	−0.0295173
$454$	54.3686	2.55164
$455$	−1.76329	−0.0826641
$456$	−12.0849	−0.565929
$457$	−23.8514	−1.11572	−0.557860	−	0.829935i	$-0.688377\pi$
$457$	−23.8514	−1.11572	−0.557860	+	0.829935i	$0.688377\pi$
$458$	74.2042	3.46734
$459$	6.39915	0.298687
$460$	−57.7985	−2.69487
$461$	−31.8061	−1.48136	−0.740680	−	0.671858i	$-0.765496\pi$
$461$	−31.8061	−1.48136	−0.740680	+	0.671858i	$0.765496\pi$
$462$	−4.76754	−0.221806
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−49.5699	−2.30123
$465$	4.23571	0.196426
$466$	6.38384	0.295726
$467$	−28.0531	−1.29814	−0.649071	−	0.760728i	$-0.724842\pi$
$467$	−28.0531	−1.29814	−0.649071	+	0.760728i	$0.724842\pi$
$468$	14.2023	0.656503
$469$	−2.60295	−0.120193
$470$	−20.4302	−0.942374
$471$	6.10819	0.281450
$472$	117.851	5.42453
$473$	−18.9424	−0.870973
$474$	16.8512	0.774003
$475$	4.22970	0.194072
$476$	−11.9824	−0.549211
$477$	−7.61790	−0.348800
$478$	49.7977	2.27769
$479$	−38.2009	−1.74544	−0.872722	−	0.488217i	$-0.837647\pi$
$479$	−38.2009	−1.74544	−0.872722	+	0.488217i	$0.837647\pi$
$480$	−11.0167	−0.502841
$481$	−3.29448	−0.150215
$482$	−60.2558	−2.74458
$483$	2.18781	0.0995490
$484$	61.9518	2.81599
$485$	−23.7258	−1.07733
$486$	27.3902	1.24245
$487$	−17.0616	−0.773134	−0.386567	−	0.922261i	$-0.626339\pi$
$487$	−17.0616	−0.773134	−0.386567	+	0.922261i	$0.626339\pi$
$488$	−94.6644	−4.28526
$489$	6.87757	0.311014
$490$	−32.1441	−1.45212
$491$	−18.6717	−0.842641	−0.421321	−	0.906912i	$-0.638433\pi$
$491$	−18.6717	−0.842641	−0.421321	+	0.906912i	$0.638433\pi$
$492$	22.8424	1.02981
$493$	−11.7733	−0.530243
$494$	−9.66472	−0.434836
$495$	26.7799	1.20367
$496$	58.3129	2.61832
$497$	−4.32009	−0.193782
$498$	−16.0833	−0.720708
$499$	−42.9725	−1.92371	−0.961857	−	0.273554i	$-0.911801\pi$
$499$	−42.9725	−1.92371	−0.961857	+	0.273554i	$0.911801\pi$
$500$	60.6065	2.71041
$501$	2.06288	0.0921626
$502$	47.6548	2.12694
$503$	−28.0379	−1.25015	−0.625073	−	0.780566i	$-0.714931\pi$
$503$	−28.0379	−1.25015	−0.625073	+	0.780566i	$0.714931\pi$
$504$	−20.3724	−0.907460
$505$	3.70806	0.165007
$506$	−75.1946	−3.34281
$507$	−0.413927	−0.0183831
$508$	29.1146	1.29175
$509$	7.33703	0.325208	0.162604	−	0.986691i	$-0.448011\pi$
$509$	7.33703	0.325208	0.162604	+	0.986691i	$0.448011\pi$
$510$	−5.70080	−0.252436
$511$	−12.6699	−0.560484
$512$	27.1079	1.19801
$513$	−8.80009	−0.388533
$514$	−26.3935	−1.16417
$515$	−6.68484	−0.294569
$516$	8.14887	0.358734
$517$	−19.0077	−0.835958
$518$	7.85448	0.345106
$519$	−8.78242	−0.385506
$520$	−15.6860	−0.687878
$521$	−8.67880	−0.380225	−0.190113	−	0.981762i	$-0.560885\pi$
$521$	−8.67880	−0.380225	−0.190113	+	0.981762i	$0.560885\pi$
$522$	−33.2694	−1.45616
$523$	28.4641	1.24465	0.622323	−	0.782760i	$-0.286189\pi$
$523$	28.4641	1.24465	0.622323	+	0.782760i	$0.286189\pi$
$524$	84.3110	3.68314
$525$	−0.431891	−0.0188493
$526$	−11.3885	−0.496562
$527$	13.8498	0.603308
$528$	−22.3313	−0.971843
$529$	11.5066	0.500288
$530$	13.9842	0.607433
$531$	41.6474	1.80735
$532$	16.4781	0.714417
$533$	10.9911	0.476076
$534$	2.13227	0.0922724
$535$	11.5954	0.501312
$536$	−23.1557	−1.00017
$537$	−1.82505	−0.0787568
$538$	23.7952	1.02589
$539$	−29.9060	−1.28814
$540$	−23.7388	−1.02155
$541$	8.04305	0.345798	0.172899	−	0.984940i	$-0.444687\pi$
$541$	8.04305	0.345798	0.172899	+	0.984940i	$0.444687\pi$
$542$	12.6810	0.544695
$543$	−4.99573	−0.214387
$544$	−36.0222	−1.54444
$545$	14.1624	0.606651
$546$	0.986857	0.0422336
$547$	−5.87315	−0.251118	−0.125559	−	0.992086i	$-0.540072\pi$
$547$	−5.87315	−0.251118	−0.125559	+	0.992086i	$0.540072\pi$
$548$	74.7777	3.19434
$549$	−33.4535	−1.42776
$550$	14.8440	0.632950
$551$	16.1906	0.689743
$552$	19.4626	0.828384
$553$	−13.8245	−0.587876
$554$	−48.9691	−2.08050
$555$	2.67238	0.113436
$556$	107.302	4.55062
$557$	−3.33356	−0.141248	−0.0706238	−	0.997503i	$-0.522499\pi$
$557$	−3.33356	−0.141248	−0.0706238	+	0.997503i	$0.522499\pi$
$558$	39.1374	1.65682
$559$	3.92099	0.165840
$560$	19.6912	0.832105
$561$	−5.30387	−0.223930
$562$	30.3463	1.28008
$563$	25.1499	1.05994	0.529971	−	0.848016i	$-0.322203\pi$
$563$	25.1499	1.05994	0.529971	+	0.848016i	$0.322203\pi$
$564$	8.17696	0.344312
$565$	23.6240	0.993869
$566$	19.3979	0.815355
$567$	−6.73694	−0.282925
$568$	−38.4311	−1.61253
$569$	−26.7075	−1.11964	−0.559819	−	0.828615i	$-0.689129\pi$
$569$	−26.7075	−1.11964	−0.559819	+	0.828615i	$0.689129\pi$
$570$	7.83972	0.328370
$571$	−38.5799	−1.61452	−0.807259	−	0.590198i	$-0.799050\pi$
$571$	−38.5799	−1.61452	−0.807259	+	0.590198i	$0.799050\pi$
$572$	−24.2559	−1.01419
$573$	2.90205	0.121235
$574$	−26.2042	−1.09374
$575$	−6.81187	−0.284075
$576$	−38.6156	−1.60898
$577$	35.1345	1.46267	0.731334	−	0.682019i	$-0.238898\pi$
$577$	35.1345	1.46267	0.731334	+	0.682019i	$0.238898\pi$
$578$	26.4044	1.09828
$579$	1.22640	0.0509675
$580$	43.6751	1.81351
$581$	13.1944	0.547397
$582$	13.2786	0.550417
$583$	13.0105	0.538839
$584$	−112.710	−4.66399
$585$	−5.54330	−0.229187
$586$	−32.8356	−1.35642
$587$	6.89899	0.284752	0.142376	−	0.989813i	$-0.454526\pi$
$587$	6.89899	0.284752	0.142376	+	0.989813i	$0.454526\pi$
$588$	12.8653	0.530557
$589$	−19.0462	−0.784786
$590$	−76.4521	−3.14748
$591$	−0.100230	−0.00412290
$592$	36.7905	1.51208
$593$	−20.5518	−0.843963	−0.421981	−	0.906605i	$-0.638665\pi$
$593$	−20.5518	−0.843963	−0.421981	+	0.906605i	$0.638665\pi$
$594$	−30.8836	−1.26717
$595$	4.67683	0.191731
$596$	−101.888	−4.17350
$597$	9.03614	0.369825
$598$	15.5649	0.636496
$599$	27.9786	1.14318	0.571588	−	0.820541i	$-0.306328\pi$
$599$	27.9786	1.14318	0.571588	+	0.820541i	$0.306328\pi$
$600$	−3.84207	−0.156852
$601$	−26.9961	−1.10120	−0.550598	−	0.834771i	$-0.685600\pi$
$601$	−26.9961	−1.10120	−0.550598	+	0.834771i	$0.685600\pi$
$602$	−9.34816	−0.381003
$603$	−8.18300	−0.333238
$604$	7.62044	0.310071
$605$	−24.1803	−0.983071
$606$	−2.07529	−0.0843029
$607$	13.0038	0.527810	0.263905	−	0.964549i	$-0.414989\pi$
$607$	13.0038	0.527810	0.263905	+	0.964549i	$0.414989\pi$
$608$	49.5376	2.00901
$609$	−1.65321	−0.0669914
$610$	61.4106	2.48644
$611$	3.93450	0.159173
$612$	−37.6694	−1.52270
$613$	−19.9874	−0.807282	−0.403641	−	0.914917i	$-0.632256\pi$
$613$	−19.9874	−0.807282	−0.403641	+	0.914917i	$0.632256\pi$
$614$	−50.5861	−2.04149
$615$	−8.91560	−0.359512
$616$	34.7938	1.40188
$617$	−46.3160	−1.86461	−0.932306	−	0.361670i	$-0.882207\pi$
$617$	−46.3160	−1.86461	−0.932306	+	0.361670i	$0.882207\pi$
$618$	3.74130	0.150497
$619$	20.0857	0.807311	0.403655	−	0.914911i	$-0.367739\pi$
$619$	20.0857	0.807311	0.403655	+	0.914911i	$0.367739\pi$
$620$	−51.3784	−2.06341
$621$	14.1724	0.568720
$622$	18.9445	0.759607
$623$	−1.74928	−0.0700833
$624$	4.62246	0.185047
$625$	−17.8572	−0.714288
$626$	−76.0385	−3.03911
$627$	7.29387	0.291289
$628$	−74.0912	−2.95656
$629$	8.73808	0.348410
$630$	13.2160	0.526537
$631$	−34.0299	−1.35471	−0.677355	−	0.735656i	$-0.736874\pi$
$631$	−34.0299	−1.35471	−0.677355	+	0.735656i	$0.736874\pi$
$632$	−122.981	−4.89193
$633$	−4.94773	−0.196655
$634$	−6.64152	−0.263769
$635$	−11.3637	−0.450955
$636$	−5.59701	−0.221936
$637$	6.19040	0.245273
$638$	56.8204	2.24954
$639$	−13.5812	−0.537264
$640$	17.6563	0.697927
$641$	−14.0803	−0.556139	−0.278069	−	0.960561i	$-0.589694\pi$
$641$	−14.0803	−0.556139	−0.278069	+	0.960561i	$0.589694\pi$
$642$	−6.48958	−0.256123
$643$	−23.3635	−0.921367	−0.460683	−	0.887565i	$-0.652396\pi$
$643$	−23.3635	−0.921367	−0.460683	+	0.887565i	$0.652396\pi$
$644$	−26.5378	−1.04574
$645$	−3.18058	−0.125235
$646$	25.6341	1.00856
$647$	43.0423	1.69217	0.846083	−	0.533051i	$-0.178955\pi$
$647$	43.0423	1.69217	0.846083	+	0.533051i	$0.178955\pi$
$648$	−59.9313	−2.35432
$649$	−71.1290	−2.79206
$650$	−3.07263	−0.120519
$651$	1.94480	0.0762226
$652$	−83.4237	−3.26712
$653$	11.9834	0.468949	0.234474	−	0.972122i	$-0.424663\pi$
$653$	11.9834	0.468949	0.234474	+	0.972122i	$0.424663\pi$
$654$	−7.92627	−0.309942
$655$	−32.9074	−1.28580
$656$	−122.741	−4.79222
$657$	−39.8308	−1.55395
$658$	−9.38038	−0.365685
$659$	−18.3732	−0.715720	−0.357860	−	0.933775i	$-0.616493\pi$
$659$	−18.3732	−0.715720	−0.357860	+	0.933775i	$0.616493\pi$
$660$	19.6757	0.765874
$661$	44.6304	1.73592	0.867961	−	0.496632i	$-0.165430\pi$
$661$	44.6304	1.73592	0.867961	+	0.496632i	$0.165430\pi$
$662$	75.3410	2.92821
$663$	1.09788	0.0426380
$664$	117.377	4.55509
$665$	−6.43157	−0.249405
$666$	24.6924	0.956811
$667$	−26.0747	−1.00962
$668$	−25.0223	−0.968144
$669$	−1.89797	−0.0733797
$670$	15.0215	0.580332
$671$	57.1348	2.20566
$672$	−5.05824	−0.195126
$673$	−28.8970	−1.11390	−0.556950	−	0.830546i	$-0.688028\pi$
$673$	−28.8970	−1.11390	−0.556950	+	0.830546i	$0.688028\pi$
$674$	−23.2471	−0.895445
$675$	−2.79775	−0.107685
$676$	5.02086	0.193110
$677$	−49.1585	−1.88931	−0.944657	−	0.328061i	$-0.893605\pi$
$677$	−49.1585	−1.88931	−0.944657	+	0.328061i	$0.893605\pi$
$678$	−13.2216	−0.507774
$679$	−10.8935	−0.418056
$680$	41.6047	1.59547
$681$	8.49330	0.325464
$682$	−66.8421	−2.55952
$683$	40.8138	1.56170	0.780848	−	0.624720i	$-0.214787\pi$
$683$	40.8138	1.56170	0.780848	+	0.624720i	$0.214787\pi$
$684$	51.8029	1.98073
$685$	−29.1864	−1.11516
$686$	−31.4477	−1.20068
$687$	11.5920	0.442261
$688$	−43.7870	−1.66936
$689$	−2.69311	−0.102599
$690$	−12.6258	−0.480654
$691$	7.27353	0.276698	0.138349	−	0.990384i	$-0.455820\pi$
$691$	7.27353	0.276698	0.138349	+	0.990384i	$0.455820\pi$
$692$	106.529	4.04963
$693$	12.2958	0.467079
$694$	−80.3248	−3.04909
$695$	−41.8810	−1.58864
$696$	−14.7068	−0.557460
$697$	−29.1520	−1.10421
$698$	−70.5283	−2.66953
$699$	0.997266	0.0377201
$700$	5.23877	0.198007
$701$	48.1641	1.81913	0.909567	−	0.415557i	$-0.136413\pi$
$701$	48.1641	1.81913	0.909567	+	0.415557i	$0.136413\pi$
$702$	6.39276	0.241279
$703$	−12.0166	−0.453214
$704$	65.9509	2.48562
$705$	−3.19154	−0.120200
$706$	−58.1303	−2.18776
$707$	1.70253	0.0640303
$708$	30.5991	1.14999
$709$	−36.6537	−1.37656	−0.688280	−	0.725445i	$-0.741634\pi$
$709$	−36.6537	−1.37656	−0.688280	+	0.725445i	$0.741634\pi$
$710$	24.9310	0.935643
$711$	−43.4605	−1.62990
$712$	−15.5614	−0.583189
$713$	30.6737	1.14874
$714$	−2.61748	−0.0979568
$715$	9.46732	0.354058
$716$	22.1376	0.827319
$717$	7.77925	0.290521
$718$	−83.1779	−3.10417
$719$	−50.4954	−1.88316	−0.941580	−	0.336790i	$-0.890659\pi$
$719$	−50.4954	−1.88316	−0.941580	+	0.336790i	$0.890659\pi$
$720$	61.9039	2.30702
$721$	−3.06930	−0.114307
$722$	15.0921	0.561671
$723$	−9.41299	−0.350073
$724$	60.5973	2.25208
$725$	5.14736	0.191168
$726$	13.5330	0.502257
$727$	−2.96134	−0.109830	−0.0549150	−	0.998491i	$-0.517489\pi$
$727$	−2.96134	−0.109830	−0.0549150	+	0.998491i	$0.517489\pi$
$728$	−7.20214	−0.266929
$729$	−18.1832	−0.673451
$730$	73.1174	2.70619
$731$	−10.3998	−0.384650
$732$	−24.5789	−0.908463
$733$	−23.6914	−0.875063	−0.437531	−	0.899203i	$-0.644147\pi$
$733$	−23.6914	−0.875063	−0.437531	+	0.899203i	$0.644147\pi$
$734$	−65.7972	−2.42862
$735$	−5.02146	−0.185219
$736$	−79.7796	−2.94071
$737$	13.9756	0.514799
$738$	−82.3789	−3.03241
$739$	−6.25918	−0.230248	−0.115124	−	0.993351i	$-0.536727\pi$
$739$	−6.25918	−0.230248	−0.115124	+	0.993351i	$0.536727\pi$
$740$	−32.4155	−1.19162
$741$	−1.50980	−0.0554637
$742$	6.42073	0.235712
$743$	6.71458	0.246334	0.123167	−	0.992386i	$-0.460695\pi$
$743$	6.71458	0.246334	0.123167	+	0.992386i	$0.460695\pi$
$744$	17.3007	0.634276
$745$	39.7678	1.45698
$746$	−99.8430	−3.65551
$747$	41.4798	1.51767
$748$	64.3350	2.35232
$749$	5.32394	0.194532
$750$	13.2391	0.483425
$751$	−24.6319	−0.898829	−0.449415	−	0.893323i	$-0.648367\pi$
$751$	−24.6319	−0.898829	−0.449415	+	0.893323i	$0.648367\pi$
$752$	−43.9379	−1.60225
$753$	7.44449	0.271292
$754$	−11.7615	−0.428330
$755$	−2.97433	−0.108247
$756$	−10.8995	−0.396411
$757$	−1.56738	−0.0569674	−0.0284837	−	0.999594i	$-0.509068\pi$
$757$	−1.56738	−0.0569674	−0.0284837	+	0.999594i	$0.509068\pi$
$758$	83.8077	3.04403
$759$	−11.7467	−0.426377
$760$	−57.2147	−2.07539
$761$	10.6864	0.387383	0.193692	−	0.981062i	$-0.437954\pi$
$761$	10.6864	0.387383	0.193692	+	0.981062i	$0.437954\pi$
$762$	6.35993	0.230396
$763$	6.50257	0.235409
$764$	−35.2013	−1.27354
$765$	14.7027	0.531578
$766$	7.22604	0.261087
$767$	14.7234	0.531630
$768$	1.41976	0.0512310
$769$	42.5838	1.53561	0.767805	−	0.640684i	$-0.221349\pi$
$769$	42.5838	1.53561	0.767805	+	0.640684i	$0.221349\pi$
$770$	−22.5714	−0.813415
$771$	−4.12312	−0.148491
$772$	−14.8760	−0.535400
$773$	−23.3805	−0.840938	−0.420469	−	0.907307i	$-0.638134\pi$
$773$	−23.3805	−0.840938	−0.420469	+	0.907307i	$0.638134\pi$
$774$	−29.3881	−1.05634
$775$	−6.05522	−0.217510
$776$	−96.9081	−3.47880
$777$	1.22700	0.0440185
$778$	40.9952	1.46975
$779$	40.0898	1.43637
$780$	−4.07276	−0.145828
$781$	23.1951	0.829987
$782$	−41.2834	−1.47629
$783$	−10.7093	−0.382720
$784$	−69.1302	−2.46894
$785$	28.9185	1.03214
$786$	18.4173	0.656922
$787$	−13.6241	−0.485647	−0.242824	−	0.970070i	$-0.578074\pi$
$787$	−13.6241	−0.485647	−0.242824	+	0.970070i	$0.578074\pi$
$788$	1.21577	0.0433100
$789$	−1.77908	−0.0633369
$790$	79.7802	2.83845
$791$	10.8468	0.385668
$792$	109.382	3.88673
$793$	−11.8266	−0.419976
$794$	22.0232	0.781573
$795$	2.18456	0.0774785
$796$	−109.607	−3.88491
$797$	−22.5701	−0.799473	−0.399736	−	0.916630i	$-0.630898\pi$
$797$	−22.5701	−0.799473	−0.399736	+	0.916630i	$0.630898\pi$
$798$	3.59955	0.127423
$799$	−10.4356	−0.369187
$800$	15.7491	0.556815
$801$	−5.49926	−0.194307
$802$	−10.1011	−0.356682
$803$	68.0265	2.40060
$804$	−6.01220	−0.212034
$805$	10.3579	0.365070
$806$	13.8360	0.487352
$807$	3.71722	0.130852
$808$	15.1456	0.532820
$809$	−1.17991	−0.0414833	−0.0207416	−	0.999785i	$-0.506603\pi$
$809$	−1.17991	−0.0414833	−0.0207416	+	0.999785i	$0.506603\pi$
$810$	38.8785	1.36605
$811$	−6.85550	−0.240729	−0.120365	−	0.992730i	$-0.538406\pi$
$811$	−6.85550	−0.240729	−0.120365	+	0.992730i	$0.538406\pi$
$812$	20.0531	0.703727
$813$	1.98099	0.0694763
$814$	−42.1718	−1.47812
$815$	32.5610	1.14056
$816$	−12.2603	−0.429198
$817$	14.3018	0.500356
$818$	58.5227	2.04620
$819$	−2.54517	−0.0889354
$820$	108.145	3.77657
$821$	−40.1981	−1.40292	−0.701462	−	0.712707i	$-0.747469\pi$
$821$	−40.1981	−1.40292	−0.701462	+	0.712707i	$0.747469\pi$
$822$	16.3348	0.569740
$823$	14.0483	0.489694	0.244847	−	0.969562i	$-0.421262\pi$
$823$	14.0483	0.489694	0.244847	+	0.969562i	$0.421262\pi$
$824$	−27.3042	−0.951188
$825$	2.31888	0.0807332
$826$	−35.1025	−1.22137
$827$	−17.4584	−0.607089	−0.303544	−	0.952817i	$-0.598170\pi$
$827$	−17.4584	−0.607089	−0.303544	+	0.952817i	$0.598170\pi$
$828$	−83.4278	−2.89932
$829$	7.07316	0.245661	0.122831	−	0.992428i	$-0.460803\pi$
$829$	7.07316	0.245661	0.122831	+	0.992428i	$0.460803\pi$
$830$	−76.1443	−2.64301
$831$	−7.64981	−0.265369
$832$	−13.6515	−0.473281
$833$	−16.4191	−0.568886
$834$	23.4395	0.811644
$835$	9.76645	0.337982
$836$	−88.4733	−3.05991
$837$	12.5982	0.435457
$838$	−24.2012	−0.836016
$839$	25.1413	0.867975	0.433987	−	0.900919i	$-0.357106\pi$
$839$	25.1413	0.867975	0.433987	+	0.900919i	$0.357106\pi$
$840$	5.84215	0.201573
$841$	−9.29676	−0.320578
$842$	58.0533	2.00065
$843$	4.74061	0.163275
$844$	60.0151	2.06580
$845$	−1.95969	−0.0674154
$846$	−29.4894	−1.01387
$847$	−11.1022	−0.381478
$848$	30.0748	1.03277
$849$	3.03028	0.103999
$850$	8.14967	0.279531
$851$	19.3525	0.663396
$852$	−9.97836	−0.341853
$853$	−17.2532	−0.590738	−0.295369	−	0.955383i	$-0.595443\pi$
$853$	−17.2532	−0.590738	−0.295369	+	0.955383i	$0.595443\pi$
$854$	28.1962	0.964856
$855$	−20.2191	−0.691480
$856$	47.3613	1.61878
$857$	11.1396	0.380521	0.190260	−	0.981734i	$-0.439067\pi$
$857$	11.1396	0.380521	0.190260	+	0.981734i	$0.439067\pi$
$858$	−5.29857	−0.180890
$859$	21.3998	0.730151	0.365076	−	0.930978i	$-0.381043\pi$
$859$	21.3998	0.730151	0.365076	+	0.930978i	$0.381043\pi$
$860$	38.5799	1.31556
$861$	−4.09354	−0.139507
$862$	50.2533	1.71163
$863$	7.13563	0.242900	0.121450	−	0.992598i	$-0.461246\pi$
$863$	7.13563	0.242900	0.121450	+	0.992598i	$0.461246\pi$
$864$	−32.7668	−1.11475
$865$	−41.5794	−1.41374
$866$	66.3473	2.25457
$867$	4.12482	0.140086
$868$	−23.5900	−0.800698
$869$	74.2255	2.51793
$870$	9.54058	0.323456
$871$	−2.89289	−0.0980217
$872$	57.8463	1.95892
$873$	−34.2464	−1.15907
$874$	56.7729	1.92037
$875$	−10.8612	−0.367174
$876$	−29.2644	−0.988754
$877$	1.03423	0.0349233	0.0174617	−	0.999848i	$-0.494441\pi$
$877$	1.03423	0.0349233	0.0174617	+	0.999848i	$0.494441\pi$
$878$	70.9119	2.39316
$879$	−5.12948	−0.173013
$880$	−105.725	−3.56398
$881$	−32.5509	−1.09667	−0.548334	−	0.836260i	$-0.684738\pi$
$881$	−32.5509	−1.09667	−0.548334	+	0.836260i	$0.684738\pi$
$882$	−46.3976	−1.56229
$883$	−17.5679	−0.591208	−0.295604	−	0.955311i	$-0.595521\pi$
$883$	−17.5679	−0.591208	−0.295604	+	0.955311i	$0.595521\pi$
$884$	−13.3170	−0.447901
$885$	−11.9431	−0.401464
$886$	68.6314	2.30572
$887$	3.01691	0.101298	0.0506490	−	0.998717i	$-0.483871\pi$
$887$	3.01691	0.101298	0.0506490	+	0.998717i	$0.483871\pi$
$888$	10.9153	0.366294
$889$	−5.21757	−0.174992
$890$	10.0950	0.338385
$891$	36.1716	1.21179
$892$	23.0220	0.770834
$893$	14.3511	0.480240
$894$	−22.2569	−0.744381
$895$	−8.64049	−0.288820
$896$	8.10678	0.270829
$897$	2.43150	0.0811856
$898$	−34.7870	−1.16086
$899$	−23.1784	−0.773043
$900$	16.4693	0.548977
$901$	7.14304	0.237969
$902$	140.694	4.68459
$903$	−1.46034	−0.0485972
$904$	96.4922	3.20928
$905$	−23.6517	−0.786209
$906$	1.66464	0.0553040
$907$	−27.7579	−0.921687	−0.460843	−	0.887481i	$-0.652453\pi$
$907$	−27.7579	−0.921687	−0.460843	+	0.887481i	$0.652453\pi$
$908$	−103.022	−3.41891
$909$	5.35231	0.177525
$910$	4.67216	0.154881
$911$	8.57527	0.284111	0.142056	−	0.989859i	$-0.454629\pi$
$911$	8.57527	0.284111	0.142056	+	0.989859i	$0.454629\pi$
$912$	16.8604	0.558303
$913$	−70.8427	−2.34455
$914$	63.1987	2.09043
$915$	9.59338	0.317147
$916$	−140.609	−4.64584
$917$	−15.1092	−0.498950
$918$	−16.9558	−0.559624
$919$	20.0421	0.661129	0.330564	−	0.943783i	$-0.392761\pi$
$919$	20.0421	0.661129	0.330564	+	0.943783i	$0.392761\pi$
$920$	92.1435	3.03788
$921$	−7.90241	−0.260393
$922$	84.2764	2.77550
$923$	−4.80128	−0.158036
$924$	9.03394	0.297195
$925$	−3.82034	−0.125612
$926$	2.64969	0.0870742
$927$	−9.64907	−0.316917
$928$	60.2850	1.97895
$929$	2.18252	0.0716062	0.0358031	−	0.999359i	$-0.488601\pi$
$929$	2.18252	0.0716062	0.0358031	+	0.999359i	$0.488601\pi$
$930$	−11.2233	−0.368027
$931$	22.5794	0.740011
$932$	−12.0967	−0.396239
$933$	2.95946	0.0968884
$934$	74.3320	2.43222
$935$	−25.1106	−0.821203
$936$	−22.6416	−0.740065
$937$	−58.2317	−1.90235	−0.951173	−	0.308659i	$-0.900120\pi$
$937$	−58.2317	−1.90235	−0.951173	+	0.308659i	$0.900120\pi$
$938$	6.89702	0.225196
$939$	−11.8785	−0.387641
$940$	38.7129	1.26267
$941$	−23.4047	−0.762971	−0.381485	−	0.924375i	$-0.624587\pi$
$941$	−23.4047	−0.762971	−0.381485	+	0.924375i	$0.624587\pi$
$942$	−16.1848	−0.527329
$943$	−64.5641	−2.10249
$944$	−164.421	−5.35144
$945$	4.25418	0.138388
$946$	50.1916	1.63187
$947$	−47.9018	−1.55660	−0.778300	−	0.627892i	$-0.783918\pi$
$947$	−47.9018	−1.55660	−0.778300	+	0.627892i	$0.783918\pi$
$948$	−31.9312	−1.03708
$949$	−14.0811	−0.457093
$950$	−11.2074	−0.363616
$951$	−1.03752	−0.0336439
$952$	19.1025	0.619117
$953$	−48.9451	−1.58549	−0.792744	−	0.609555i	$-0.791348\pi$
$953$	−48.9451	−1.58549	−0.792744	+	0.609555i	$0.791348\pi$
$954$	20.1851	0.653516
$955$	13.7394	0.444597
$956$	−94.3609	−3.05185
$957$	8.87631	0.286930
$958$	101.221	3.27029
$959$	−13.4007	−0.432733
$960$	11.0737	0.357401
$961$	−3.73347	−0.120435
$962$	8.72935	0.281446
$963$	16.7370	0.539344
$964$	114.178	3.67742
$965$	5.80625	0.186910
$966$	−5.79703	−0.186516
$967$	4.96610	0.159699	0.0798494	−	0.996807i	$-0.474556\pi$
$967$	4.96610	0.159699	0.0798494	+	0.996807i	$0.474556\pi$
$968$	−98.7647	−3.17442
$969$	4.00449	0.128643
$970$	62.8661	2.01851
$971$	40.4627	1.29851	0.649254	−	0.760571i	$-0.275081\pi$
$971$	40.4627	1.29851	0.649254	+	0.760571i	$0.275081\pi$
$972$	−51.9013	−1.66474
$973$	−19.2294	−0.616465
$974$	45.2079	1.44856
$975$	−0.479998	−0.0153722
$976$	132.072	4.22752
$977$	9.12482	0.291929	0.145964	−	0.989290i	$-0.453371\pi$
$977$	9.12482	0.291929	0.145964	+	0.989290i	$0.453371\pi$
$978$	−18.2234	−0.582721
$979$	9.39211	0.300173
$980$	60.9094	1.94568
$981$	20.4424	0.652675
$982$	49.4742	1.57879
$983$	26.3868	0.841609	0.420804	−	0.907151i	$-0.361748\pi$
$983$	26.3868	0.841609	0.420804	+	0.907151i	$0.361748\pi$
$984$	−36.4158	−1.16089
$985$	−0.474526	−0.0151197
$986$	31.1956	0.993470
$987$	−1.46538	−0.0466434
$988$	18.3135	0.582632
$989$	−23.0328	−0.732400
$990$	−70.9584	−2.25521
$991$	−44.7317	−1.42095	−0.710475	−	0.703723i	$-0.751520\pi$
$991$	−44.7317	−1.42095	−0.710475	+	0.703723i	$0.751520\pi$
$992$	−70.9178	−2.25164
$993$	11.7695	0.373495
$994$	11.4469	0.363073
$995$	42.7806	1.35623
$996$	30.4760	0.965668
$997$	14.5865	0.461960	0.230980	−	0.972958i	$-0.425807\pi$
$997$	14.5865	0.461960	0.230980	+	0.972958i	$0.425807\pi$
$998$	113.864	3.60430
$999$	7.94840	0.251476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.3	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.64969 q^{2} -0.413927 q^{3} +5.02086 q^{4} -1.95969 q^{5} +1.09678 q^{6} -0.899778 q^{7} -8.00435 q^{8} -2.82866 q^{9} +O(q^{10})\)	\(q-2.64969 q^{2} -0.413927 q^{3} +5.02086 q^{4} -1.95969 q^{5} +1.09678 q^{6} -0.899778 q^{7} -8.00435 q^{8} -2.82866 q^{9} +5.19257 q^{10} +4.83103 q^{11} -2.07827 q^{12} -1.00000 q^{13} +2.38413 q^{14} +0.811168 q^{15} +11.1673 q^{16} +2.65234 q^{17} +7.49509 q^{18} -3.64749 q^{19} -9.83933 q^{20} +0.372442 q^{21} -12.8007 q^{22} +5.87423 q^{23} +3.31322 q^{24} -1.15962 q^{25} +2.64969 q^{26} +2.41264 q^{27} -4.51766 q^{28} -4.43883 q^{29} -2.14935 q^{30} +5.22174 q^{31} -13.5813 q^{32} -1.99969 q^{33} -7.02788 q^{34} +1.76329 q^{35} -14.2023 q^{36} +3.29448 q^{37} +9.66472 q^{38} +0.413927 q^{39} +15.6860 q^{40} -10.9911 q^{41} -0.986857 q^{42} -3.92099 q^{43} +24.2559 q^{44} +5.54330 q^{45} -15.5649 q^{46} -3.93450 q^{47} -4.62246 q^{48} -6.19040 q^{49} +3.07263 q^{50} -1.09788 q^{51} -5.02086 q^{52} +2.69311 q^{53} -6.39276 q^{54} -9.46732 q^{55} +7.20214 q^{56} +1.50980 q^{57} +11.7615 q^{58} -14.7234 q^{59} +4.07276 q^{60} +11.8266 q^{61} -13.8360 q^{62} +2.54517 q^{63} +13.6515 q^{64} +1.95969 q^{65} +5.29857 q^{66} +2.89289 q^{67} +13.3170 q^{68} -2.43150 q^{69} -4.67216 q^{70} +4.80128 q^{71} +22.6416 q^{72} +14.0811 q^{73} -8.72935 q^{74} +0.479998 q^{75} -18.3135 q^{76} -4.34686 q^{77} -1.09678 q^{78} +15.3643 q^{79} -21.8845 q^{80} +7.48734 q^{81} +29.1229 q^{82} -14.6641 q^{83} +1.86998 q^{84} -5.19776 q^{85} +10.3894 q^{86} +1.83735 q^{87} -38.6693 q^{88} +1.94412 q^{89} -14.6880 q^{90} +0.899778 q^{91} +29.4937 q^{92} -2.16142 q^{93} +10.4252 q^{94} +7.14795 q^{95} +5.62166 q^{96} +12.1069 q^{97} +16.4026 q^{98} -13.6654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 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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