LMFDB - Embedded newform 6023.2.a.c.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22132 q^{2} +1.60897 q^{3} +2.93428 q^{4} +0.172135 q^{5} -3.57405 q^{6} -2.94325 q^{7} -2.07533 q^{8} -0.411206 q^{9} +O(q^{10})$	\(q-2.22132 q^{2} +1.60897 q^{3} +2.93428 q^{4} +0.172135 q^{5} -3.57405 q^{6} -2.94325 q^{7} -2.07533 q^{8} -0.411206 q^{9} -0.382368 q^{10} +3.78271 q^{11} +4.72117 q^{12} +1.78320 q^{13} +6.53792 q^{14} +0.276961 q^{15} -1.25858 q^{16} +7.14268 q^{17} +0.913420 q^{18} +1.00000 q^{19} +0.505092 q^{20} -4.73562 q^{21} -8.40262 q^{22} +5.99217 q^{23} -3.33915 q^{24} -4.97037 q^{25} -3.96106 q^{26} -5.48854 q^{27} -8.63632 q^{28} +8.26432 q^{29} -0.615219 q^{30} -5.11981 q^{31} +6.94636 q^{32} +6.08628 q^{33} -15.8662 q^{34} -0.506637 q^{35} -1.20659 q^{36} +1.99342 q^{37} -2.22132 q^{38} +2.86912 q^{39} -0.357237 q^{40} +8.29543 q^{41} +10.5193 q^{42} -6.94424 q^{43} +11.0995 q^{44} -0.0707829 q^{45} -13.3105 q^{46} +2.92053 q^{47} -2.02502 q^{48} +1.66274 q^{49} +11.0408 q^{50} +11.4924 q^{51} +5.23240 q^{52} -4.95183 q^{53} +12.1918 q^{54} +0.651138 q^{55} +6.10822 q^{56} +1.60897 q^{57} -18.3577 q^{58} +9.42408 q^{59} +0.812679 q^{60} +15.0896 q^{61} +11.3727 q^{62} +1.21028 q^{63} -12.9130 q^{64} +0.306951 q^{65} -13.5196 q^{66} -5.11529 q^{67} +20.9586 q^{68} +9.64124 q^{69} +1.12540 q^{70} -7.43922 q^{71} +0.853386 q^{72} +3.81614 q^{73} -4.42804 q^{74} -7.99719 q^{75} +2.93428 q^{76} -11.1335 q^{77} -6.37324 q^{78} -10.9185 q^{79} -0.216645 q^{80} -7.59729 q^{81} -18.4268 q^{82} -5.05630 q^{83} -13.8956 q^{84} +1.22951 q^{85} +15.4254 q^{86} +13.2971 q^{87} -7.85037 q^{88} -16.1761 q^{89} +0.157232 q^{90} -5.24841 q^{91} +17.5827 q^{92} -8.23763 q^{93} -6.48745 q^{94} +0.172135 q^{95} +11.1765 q^{96} +16.0271 q^{97} -3.69348 q^{98} -1.55547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * 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 $

$2$	−2.22132	−1.57071	−0.785356	−	0.619044i	$-0.787520\pi$
$2$	−2.22132	−1.57071	−0.785356	+	0.619044i	$0.787520\pi$
$3$	1.60897	0.928941	0.464471	−	0.885589i	$-0.346245\pi$
$3$	1.60897	0.928941	0.464471	+	0.885589i	$0.346245\pi$
$4$	2.93428	1.46714
$5$	0.172135	0.0769812	0.0384906	−	0.999259i	$-0.487745\pi$
$5$	0.172135	0.0769812	0.0384906	+	0.999259i	$0.487745\pi$
$6$	−3.57405	−1.45910
$7$	−2.94325	−1.11245	−0.556223	−	0.831033i	$-0.687750\pi$
$7$	−2.94325	−1.11245	−0.556223	+	0.831033i	$0.687750\pi$
$8$	−2.07533	−0.733739
$9$	−0.411206	−0.137069
$10$	−0.382368	−0.120915
$11$	3.78271	1.14053	0.570265	−	0.821461i	$-0.306840\pi$
$11$	3.78271	1.14053	0.570265	+	0.821461i	$0.306840\pi$
$12$	4.72117	1.36288
$13$	1.78320	0.494571	0.247285	−	0.968943i	$-0.420461\pi$
$13$	1.78320	0.494571	0.247285	+	0.968943i	$0.420461\pi$
$14$	6.53792	1.74733
$15$	0.276961	0.0715110
$16$	−1.25858	−0.314644
$17$	7.14268	1.73235	0.866177	−	0.499738i	$-0.166570\pi$
$17$	7.14268	1.73235	0.866177	+	0.499738i	$0.166570\pi$
$18$	0.913420	0.215295
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.505092	0.112942
$21$	−4.73562	−1.03340
$22$	−8.40262	−1.79145
$23$	5.99217	1.24945	0.624727	−	0.780843i	$-0.285210\pi$
$23$	5.99217	1.24945	0.624727	+	0.780843i	$0.285210\pi$
$24$	−3.33915	−0.681601
$25$	−4.97037	−0.994074
$26$	−3.96106	−0.776828
$27$	−5.48854	−1.05627
$28$	−8.63632	−1.63211
$29$	8.26432	1.53464	0.767322	−	0.641261i	$-0.221589\pi$
$29$	8.26432	1.53464	0.767322	+	0.641261i	$0.221589\pi$
$30$	−0.615219	−0.112323
$31$	−5.11981	−0.919544	−0.459772	−	0.888037i	$-0.652069\pi$
$31$	−5.11981	−0.919544	−0.459772	+	0.888037i	$0.652069\pi$
$32$	6.94636	1.22796
$33$	6.08628	1.05949
$34$	−15.8662	−2.72103
$35$	−0.506637	−0.0856373
$36$	−1.20659	−0.201098
$37$	1.99342	0.327717	0.163859	−	0.986484i	$-0.447606\pi$
$37$	1.99342	0.327717	0.163859	+	0.986484i	$0.447606\pi$
$38$	−2.22132	−0.360346
$39$	2.86912	0.459427
$40$	−0.357237	−0.0564841
$41$	8.29543	1.29553	0.647764	−	0.761841i	$-0.275704\pi$
$41$	8.29543	1.29553	0.647764	+	0.761841i	$0.275704\pi$
$42$	10.5193	1.62317
$43$	−6.94424	−1.05899	−0.529493	−	0.848314i	$-0.677618\pi$
$43$	−6.94424	−1.05899	−0.529493	+	0.848314i	$0.677618\pi$
$44$	11.0995	1.67332
$45$	−0.0707829	−0.0105517
$46$	−13.3105	−1.96253
$47$	2.92053	0.426004	0.213002	−	0.977052i	$-0.431676\pi$
$47$	2.92053	0.426004	0.213002	+	0.977052i	$0.431676\pi$
$48$	−2.02502	−0.292286
$49$	1.66274	0.237534
$50$	11.0408	1.56140
$51$	11.4924	1.60925
$52$	5.23240	0.725603
$53$	−4.95183	−0.680187	−0.340093	−	0.940392i	$-0.610459\pi$
$53$	−4.95183	−0.680187	−0.340093	+	0.940392i	$0.610459\pi$
$54$	12.1918	1.65910
$55$	0.651138	0.0877994
$56$	6.10822	0.816245
$57$	1.60897	0.213114
$58$	−18.3577	−2.41049
$59$	9.42408	1.22691	0.613456	−	0.789729i	$-0.289779\pi$
$59$	9.42408	1.22691	0.613456	+	0.789729i	$0.289779\pi$
$60$	0.812679	0.104916
$61$	15.0896	1.93203	0.966013	−	0.258494i	$-0.0832261\pi$
$61$	15.0896	1.93203	0.966013	+	0.258494i	$0.0832261\pi$
$62$	11.3727	1.44434
$63$	1.21028	0.152481
$64$	−12.9130	−1.61412
$65$	0.306951	0.0380726
$66$	−13.5196	−1.66415
$67$	−5.11529	−0.624932	−0.312466	−	0.949929i	$-0.601155\pi$
$67$	−5.11529	−0.624932	−0.312466	+	0.949929i	$0.601155\pi$
$68$	20.9586	2.54160
$69$	9.64124	1.16067
$70$	1.12540	0.134512
$71$	−7.43922	−0.882873	−0.441437	−	0.897292i	$-0.645531\pi$
$71$	−7.43922	−0.882873	−0.441437	+	0.897292i	$0.645531\pi$
$72$	0.853386	0.100573
$73$	3.81614	0.446646	0.223323	−	0.974745i	$-0.428310\pi$
$73$	3.81614	0.446646	0.223323	+	0.974745i	$0.428310\pi$
$74$	−4.42804	−0.514749
$75$	−7.99719	−0.923436
$76$	2.93428	0.336585
$77$	−11.1335	−1.26878
$78$	−6.37324	−0.721628
$79$	−10.9185	−1.22842	−0.614211	−	0.789142i	$-0.710526\pi$
$79$	−10.9185	−1.22842	−0.614211	+	0.789142i	$0.710526\pi$
$80$	−0.216645	−0.0242217
$81$	−7.59729	−0.844144
$82$	−18.4268	−2.03490
$83$	−5.05630	−0.555001	−0.277500	−	0.960726i	$-0.589506\pi$
$83$	−5.05630	−0.555001	−0.277500	+	0.960726i	$0.589506\pi$
$84$	−13.8956	−1.51613
$85$	1.22951	0.133359
$86$	15.4254	1.66336
$87$	13.2971	1.42559
$88$	−7.85037	−0.836852
$89$	−16.1761	−1.71466	−0.857330	−	0.514766i	$-0.827879\pi$
$89$	−16.1761	−1.71466	−0.857330	+	0.514766i	$0.827879\pi$
$90$	0.157232	0.0165737
$91$	−5.24841	−0.550183
$92$	17.5827	1.83312
$93$	−8.23763	−0.854202
$94$	−6.48745	−0.669129
$95$	0.172135	0.0176607
$96$	11.1765	1.14070
$97$	16.0271	1.62730	0.813652	−	0.581352i	$-0.197476\pi$
$97$	16.0271	1.62730	0.813652	+	0.581352i	$0.197476\pi$
$98$	−3.69348	−0.373098
$99$	−1.55547	−0.156331
$100$	−14.5844	−1.45844
$101$	−6.01088	−0.598105	−0.299053	−	0.954237i	$-0.596671\pi$
$101$	−6.01088	−0.598105	−0.299053	+	0.954237i	$0.596671\pi$
$102$	−25.5283	−2.52768
$103$	−5.01439	−0.494083	−0.247041	−	0.969005i	$-0.579458\pi$
$103$	−5.01439	−0.494083	−0.247041	+	0.969005i	$0.579458\pi$
$104$	−3.70073	−0.362886
$105$	−0.815166	−0.0795520
$106$	10.9996	1.06838
$107$	5.89121	0.569525	0.284763	−	0.958598i	$-0.408085\pi$
$107$	5.89121	0.569525	0.284763	+	0.958598i	$0.408085\pi$
$108$	−16.1049	−1.54969
$109$	16.4991	1.58033	0.790165	−	0.612894i	$-0.209995\pi$
$109$	16.4991	1.58033	0.790165	+	0.612894i	$0.209995\pi$
$110$	−1.44639	−0.137908
$111$	3.20737	0.304430
$112$	3.70431	0.350025
$113$	−5.11244	−0.480938	−0.240469	−	0.970657i	$-0.577301\pi$
$113$	−5.11244	−0.480938	−0.240469	+	0.970657i	$0.577301\pi$
$114$	−3.57405	−0.334740
$115$	1.03146	0.0961844
$116$	24.2498	2.25154
$117$	−0.733262	−0.0677901
$118$	−20.9339	−1.92712
$119$	−21.0227	−1.92715
$120$	−0.574784	−0.0524704
$121$	3.30891	0.300810
$122$	−33.5189	−3.03466
$123$	13.3471	1.20347
$124$	−15.0229	−1.34910
$125$	−1.71625	−0.153506
$126$	−2.68843	−0.239504
$127$	−1.84686	−0.163883	−0.0819413	−	0.996637i	$-0.526112\pi$
$127$	−1.84686	−0.163883	−0.0819413	+	0.996637i	$0.526112\pi$
$128$	14.7911	1.30736
$129$	−11.1731	−0.983736
$130$	−0.681838	−0.0598012
$131$	1.10755	0.0967672	0.0483836	−	0.998829i	$-0.484593\pi$
$131$	1.10755	0.0967672	0.0483836	+	0.998829i	$0.484593\pi$
$132$	17.8588	1.55441
$133$	−2.94325	−0.255212
$134$	11.3627	0.981589
$135$	−0.944770	−0.0813129
$136$	−14.8234	−1.27110
$137$	0.268473	0.0229372	0.0114686	−	0.999934i	$-0.496349\pi$
$137$	0.268473	0.0229372	0.0114686	+	0.999934i	$0.496349\pi$
$138$	−21.4163	−1.82308
$139$	−20.4942	−1.73829	−0.869147	−	0.494553i	$-0.835332\pi$
$139$	−20.4942	−1.73829	−0.869147	+	0.494553i	$0.835332\pi$
$140$	−1.48661	−0.125642
$141$	4.69906	0.395732
$142$	16.5249	1.38674
$143$	6.74533	0.564073
$144$	0.517534	0.0431278
$145$	1.42258	0.118139
$146$	−8.47689	−0.701552
$147$	2.67530	0.220655
$148$	5.84926	0.480806
$149$	−2.52710	−0.207028	−0.103514	−	0.994628i	$-0.533009\pi$
$149$	−2.52710	−0.207028	−0.103514	+	0.994628i	$0.533009\pi$
$150$	17.7643	1.45045
$151$	3.41334	0.277774	0.138887	−	0.990308i	$-0.455648\pi$
$151$	3.41334	0.277774	0.138887	+	0.990308i	$0.455648\pi$
$152$	−2.07533	−0.168331
$153$	−2.93711	−0.237451
$154$	24.7311	1.99289
$155$	−0.881298	−0.0707876
$156$	8.41879	0.674043
$157$	15.9696	1.27451	0.637256	−	0.770652i	$-0.280069\pi$
$157$	15.9696	1.27451	0.637256	+	0.770652i	$0.280069\pi$
$158$	24.2534	1.92950
$159$	−7.96737	−0.631853
$160$	1.19571	0.0945294
$161$	−17.6365	−1.38995
$162$	16.8760	1.32591
$163$	3.83832	0.300641	0.150320	−	0.988637i	$-0.451969\pi$
$163$	3.83832	0.300641	0.150320	+	0.988637i	$0.451969\pi$
$164$	24.3411	1.90072
$165$	1.04766	0.0815604
$166$	11.2317	0.871746
$167$	−0.0311260	−0.00240860	−0.00120430	−	0.999999i	$-0.500383\pi$
$167$	−0.0311260	−0.00240860	−0.00120430	+	0.999999i	$0.500383\pi$
$168$	9.82796	0.758243
$169$	−9.82020	−0.755400
$170$	−2.73113	−0.209468
$171$	−0.411206	−0.0314457
$172$	−20.3763	−1.55368
$173$	2.35681	0.179185	0.0895925	−	0.995979i	$-0.471444\pi$
$173$	2.35681	0.179185	0.0895925	+	0.995979i	$0.471444\pi$
$174$	−29.5371	−2.23920
$175$	14.6291	1.10585
$176$	−4.76084	−0.358862
$177$	15.1631	1.13973
$178$	35.9323	2.69324
$179$	24.0651	1.79871	0.899357	−	0.437216i	$-0.144035\pi$
$179$	24.0651	1.79871	0.899357	+	0.437216i	$0.144035\pi$
$180$	−0.207697	−0.0154808
$181$	11.6466	0.865682	0.432841	−	0.901470i	$-0.357511\pi$
$181$	11.6466	0.865682	0.432841	+	0.901470i	$0.357511\pi$
$182$	11.6584	0.864179
$183$	24.2788	1.79474
$184$	−12.4357	−0.916774
$185$	0.343138	0.0252280
$186$	18.2984	1.34171
$187$	27.0187	1.97580
$188$	8.56965	0.625006
$189$	16.1542	1.17504
$190$	−0.382368	−0.0277399
$191$	−2.12061	−0.153442	−0.0767209	−	0.997053i	$-0.524445\pi$
$191$	−2.12061	−0.153442	−0.0767209	+	0.997053i	$0.524445\pi$
$192$	−20.7766	−1.49942
$193$	6.81321	0.490425	0.245213	−	0.969469i	$-0.421142\pi$
$193$	6.81321	0.490425	0.245213	+	0.969469i	$0.421142\pi$
$194$	−35.6013	−2.55603
$195$	0.493877	0.0353672
$196$	4.87894	0.348496
$197$	21.4932	1.53133	0.765665	−	0.643239i	$-0.222410\pi$
$197$	21.4932	1.53133	0.765665	+	0.643239i	$0.222410\pi$
$198$	3.45521	0.245551
$199$	19.7473	1.39985	0.699925	−	0.714216i	$-0.253217\pi$
$199$	19.7473	1.39985	0.699925	+	0.714216i	$0.253217\pi$
$200$	10.3151	0.729391
$201$	−8.23036	−0.580525
$202$	13.3521	0.939451
$203$	−24.3240	−1.70721
$204$	33.7218	2.36100
$205$	1.42793	0.0997313
$206$	11.1386	0.776062
$207$	−2.46401	−0.171261
$208$	−2.24430	−0.155614
$209$	3.78271	0.261656
$210$	1.81075	0.124953
$211$	−13.0587	−0.898998	−0.449499	−	0.893281i	$-0.648397\pi$
$211$	−13.0587	−0.898998	−0.449499	+	0.893281i	$0.648397\pi$
$212$	−14.5300	−0.997927
$213$	−11.9695	−0.820137
$214$	−13.0863	−0.894560
$215$	−1.19535	−0.0815220
$216$	11.3905	0.775026
$217$	15.0689	1.02294
$218$	−36.6499	−2.48224
$219$	6.14007	0.414908
$220$	1.91062	0.128814
$221$	12.7368	0.856771
$222$	−7.12460	−0.478172
$223$	−22.0411	−1.47598	−0.737989	−	0.674813i	$-0.764224\pi$
$223$	−22.0411	−1.47598	−0.737989	+	0.674813i	$0.764224\pi$
$224$	−20.4449	−1.36603
$225$	2.04384	0.136256
$226$	11.3564	0.755415
$227$	7.98767	0.530161	0.265080	−	0.964226i	$-0.414602\pi$
$227$	7.98767	0.530161	0.265080	+	0.964226i	$0.414602\pi$
$228$	4.72117	0.312667
$229$	4.28973	0.283473	0.141737	−	0.989904i	$-0.454731\pi$
$229$	4.28973	0.283473	0.141737	+	0.989904i	$0.454731\pi$
$230$	−2.29121	−0.151078
$231$	−17.9135	−1.17862
$232$	−17.1512	−1.12603
$233$	26.3794	1.72817	0.864085	−	0.503346i	$-0.167898\pi$
$233$	26.3794	1.72817	0.864085	+	0.503346i	$0.167898\pi$
$234$	1.62881	0.106479
$235$	0.502727	0.0327943
$236$	27.6529	1.80005
$237$	−17.5675	−1.14113
$238$	46.6982	3.02700
$239$	−28.3527	−1.83398	−0.916992	−	0.398905i	$-0.869390\pi$
$239$	−28.3527	−1.83398	−0.916992	+	0.398905i	$0.869390\pi$
$240$	−0.348577	−0.0225005
$241$	20.8853	1.34534	0.672670	−	0.739943i	$-0.265147\pi$
$241$	20.8853	1.34534	0.672670	+	0.739943i	$0.265147\pi$
$242$	−7.35016	−0.472486
$243$	4.24177	0.272110
$244$	44.2771	2.83455
$245$	0.286216	0.0182857
$246$	−29.6483	−1.89030
$247$	1.78320	0.113462
$248$	10.6253	0.674706
$249$	−8.13545	−0.515563
$250$	3.81235	0.241114
$251$	16.3616	1.03274	0.516368	−	0.856367i	$-0.327284\pi$
$251$	16.3616	1.03274	0.516368	+	0.856367i	$0.327284\pi$
$252$	3.55130	0.223711
$253$	22.6667	1.42504
$254$	4.10248	0.257412
$255$	1.97824	0.123882
$256$	−7.02996	−0.439372
$257$	−14.6455	−0.913562	−0.456781	−	0.889579i	$-0.650998\pi$
$257$	−14.6455	−0.913562	−0.456781	+	0.889579i	$0.650998\pi$
$258$	24.8190	1.54517
$259$	−5.86715	−0.364567
$260$	0.900680	0.0558578
$261$	−3.39833	−0.210351
$262$	−2.46023	−0.151993
$263$	−6.34767	−0.391414	−0.195707	−	0.980662i	$-0.562700\pi$
$263$	−6.34767	−0.391414	−0.195707	+	0.980662i	$0.562700\pi$
$264$	−12.6310	−0.777386
$265$	−0.852384	−0.0523616
$266$	6.53792	0.400865
$267$	−26.0269	−1.59282
$268$	−15.0097	−0.916861
$269$	19.6604	1.19871	0.599357	−	0.800482i	$-0.295423\pi$
$269$	19.6604	1.19871	0.599357	+	0.800482i	$0.295423\pi$
$270$	2.09864	0.127719
$271$	7.24013	0.439807	0.219903	−	0.975522i	$-0.429426\pi$
$271$	7.24013	0.439807	0.219903	+	0.975522i	$0.429426\pi$
$272$	−8.98961	−0.545075
$273$	−8.44455	−0.511087
$274$	−0.596366	−0.0360278
$275$	−18.8015	−1.13377
$276$	28.2901	1.70286
$277$	−19.3941	−1.16528	−0.582641	−	0.812730i	$-0.697981\pi$
$277$	−19.3941	−1.16528	−0.582641	+	0.812730i	$0.697981\pi$
$278$	45.5242	2.73036
$279$	2.10529	0.126041
$280$	1.05144	0.0628355
$281$	27.0553	1.61398	0.806992	−	0.590563i	$-0.201094\pi$
$281$	27.0553	1.61398	0.806992	+	0.590563i	$0.201094\pi$
$282$	−10.4381	−0.621582
$283$	15.1188	0.898722	0.449361	−	0.893350i	$-0.351652\pi$
$283$	15.1188	0.898722	0.449361	+	0.893350i	$0.351652\pi$
$284$	−21.8287	−1.29530
$285$	0.276961	0.0164057
$286$	−14.9836	−0.885997
$287$	−24.4155	−1.44120
$288$	−2.85638	−0.168314
$289$	34.0178	2.00105
$290$	−3.16001	−0.185562
$291$	25.7871	1.51167
$292$	11.1976	0.655291
$293$	−32.1623	−1.87894	−0.939470	−	0.342631i	$-0.888682\pi$
$293$	−32.1623	−1.87894	−0.939470	+	0.342631i	$0.888682\pi$
$294$	−5.94272	−0.346586
$295$	1.62222	0.0944491
$296$	−4.13701	−0.240459
$297$	−20.7616	−1.20471
$298$	5.61350	0.325181
$299$	10.6852	0.617943
$300$	−23.4660	−1.35481
$301$	20.4387	1.17806
$302$	−7.58213	−0.436303
$303$	−9.67135	−0.555604
$304$	−1.25858	−0.0721844
$305$	2.59745	0.148730
$306$	6.52427	0.372967
$307$	2.98487	0.170355	0.0851776	−	0.996366i	$-0.472854\pi$
$307$	2.98487	0.170355	0.0851776	+	0.996366i	$0.472854\pi$
$308$	−32.6687	−1.86147
$309$	−8.06802	−0.458974
$310$	1.95765	0.111187
$311$	8.66976	0.491617	0.245809	−	0.969318i	$-0.420947\pi$
$311$	8.66976	0.491617	0.245809	+	0.969318i	$0.420947\pi$
$312$	−5.95437	−0.337100
$313$	21.3092	1.20447	0.602233	−	0.798320i	$-0.294278\pi$
$313$	21.3092	1.20447	0.602233	+	0.798320i	$0.294278\pi$
$314$	−35.4736	−2.00189
$315$	0.208332	0.0117382
$316$	−32.0378	−1.80226
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	17.6981	0.992460
$319$	31.2615	1.75031
$320$	−2.22277	−0.124257
$321$	9.47880	0.529055
$322$	39.1763	2.18321
$323$	7.14268	0.397429
$324$	−22.2926	−1.23848
$325$	−8.86316	−0.491640
$326$	−8.52616	−0.472220
$327$	26.5467	1.46803
$328$	−17.2157	−0.950580
$329$	−8.59587	−0.473906
$330$	−2.32720	−0.128108
$331$	−16.9019	−0.929013	−0.464507	−	0.885570i	$-0.653768\pi$
$331$	−16.9019	−0.929013	−0.464507	+	0.885570i	$0.653768\pi$
$332$	−14.8366	−0.814262
$333$	−0.819707	−0.0449197
$334$	0.0691408	0.00378322
$335$	−0.880521	−0.0481080
$336$	5.96014	0.325152
$337$	−22.8603	−1.24528	−0.622641	−	0.782507i	$-0.713940\pi$
$337$	−22.8603	−1.24528	−0.622641	+	0.782507i	$0.713940\pi$
$338$	21.8138	1.18652
$339$	−8.22578	−0.446763
$340$	3.60771	0.195655
$341$	−19.3667	−1.04877
$342$	0.913420	0.0493921
$343$	15.7089	0.848201
$344$	14.4116	0.777020
$345$	1.65960	0.0893497
$346$	−5.23524	−0.281448
$347$	13.5469	0.727236	0.363618	−	0.931548i	$-0.381541\pi$
$347$	13.5469	0.727236	0.363618	+	0.931548i	$0.381541\pi$
$348$	39.0172	2.09154
$349$	−14.2914	−0.764999	−0.382500	−	0.923956i	$-0.624937\pi$
$349$	−14.2914	−0.764999	−0.382500	+	0.923956i	$0.624937\pi$
$350$	−32.4959	−1.73698
$351$	−9.78716	−0.522400
$352$	26.2761	1.40052
$353$	14.5755	0.775778	0.387889	−	0.921706i	$-0.373204\pi$
$353$	14.5755	0.775778	0.387889	+	0.921706i	$0.373204\pi$
$354$	−33.6821	−1.79019
$355$	−1.28055	−0.0679646
$356$	−47.4651	−2.51564
$357$	−33.8250	−1.79021
$358$	−53.4565	−2.82526
$359$	25.7888	1.36108	0.680541	−	0.732710i	$-0.261745\pi$
$359$	25.7888	1.36108	0.680541	+	0.732710i	$0.261745\pi$
$360$	0.146898	0.00774219
$361$	1.00000	0.0526316
$362$	−25.8708	−1.35974
$363$	5.32395	0.279435
$364$	−15.4003	−0.807194
$365$	0.656892	0.0343833
$366$	−53.9310	−2.81902
$367$	−11.4556	−0.597979	−0.298990	−	0.954256i	$-0.596650\pi$
$367$	−11.4556	−0.597979	−0.298990	+	0.954256i	$0.596650\pi$
$368$	−7.54161	−0.393134
$369$	−3.41113	−0.177576
$370$	−0.762221	−0.0396260
$371$	14.5745	0.756670
$372$	−24.1715	−1.25323
$373$	33.1754	1.71776	0.858879	−	0.512178i	$-0.171161\pi$
$373$	33.1754	1.71776	0.858879	+	0.512178i	$0.171161\pi$
$374$	−60.0172	−3.10342
$375$	−2.76140	−0.142598
$376$	−6.06107	−0.312576
$377$	14.7369	0.758991
$378$	−35.8836	−1.84565
$379$	15.7625	0.809663	0.404831	−	0.914391i	$-0.367330\pi$
$379$	15.7625	0.809663	0.404831	+	0.914391i	$0.367330\pi$
$380$	0.505092	0.0259107
$381$	−2.97155	−0.152237
$382$	4.71056	0.241013
$383$	1.19349	0.0609847	0.0304923	−	0.999535i	$-0.490292\pi$
$383$	1.19349	0.0609847	0.0304923	+	0.999535i	$0.490292\pi$
$384$	23.7985	1.21446
$385$	−1.91646	−0.0976720
$386$	−15.1343	−0.770317
$387$	2.85551	0.145154
$388$	47.0279	2.38748
$389$	−26.5978	−1.34856	−0.674281	−	0.738475i	$-0.735546\pi$
$389$	−26.5978	−1.34856	−0.674281	+	0.738475i	$0.735546\pi$
$390$	−1.09706	−0.0555518
$391$	42.8001	2.16450
$392$	−3.45073	−0.174288
$393$	1.78202	0.0898910
$394$	−47.7434	−2.40528
$395$	−1.87945	−0.0945654
$396$	−4.56418	−0.229359
$397$	−15.8493	−0.795451	−0.397726	−	0.917504i	$-0.630200\pi$
$397$	−15.8493	−0.795451	−0.397726	+	0.917504i	$0.630200\pi$
$398$	−43.8652	−2.19876
$399$	−4.73562	−0.237077
$400$	6.25560	0.312780
$401$	−12.3910	−0.618775	−0.309388	−	0.950936i	$-0.600124\pi$
$401$	−12.3910	−0.618775	−0.309388	+	0.950936i	$0.600124\pi$
$402$	18.2823	0.911838
$403$	−9.12964	−0.454780
$404$	−17.6376	−0.877502
$405$	−1.30776	−0.0649832
$406$	54.0314	2.68153
$407$	7.54055	0.373771
$408$	−23.8504	−1.18077
$409$	−31.4641	−1.55580	−0.777900	−	0.628388i	$-0.783715\pi$
$409$	−31.4641	−1.55580	−0.777900	+	0.628388i	$0.783715\pi$
$410$	−3.17190	−0.156649
$411$	0.431967	0.0213073
$412$	−14.7136	−0.724887
$413$	−27.7375	−1.36487
$414$	5.47337	0.269002
$415$	−0.870366	−0.0427246
$416$	12.3868	0.607311
$417$	−32.9746	−1.61477
$418$	−8.40262	−0.410986
$419$	6.48563	0.316844	0.158422	−	0.987371i	$-0.449359\pi$
$419$	6.48563	0.316844	0.158422	+	0.987371i	$0.449359\pi$
$420$	−2.39192	−0.116714
$421$	−1.61767	−0.0788404	−0.0394202	−	0.999223i	$-0.512551\pi$
$421$	−1.61767	−0.0788404	−0.0394202	+	0.999223i	$0.512551\pi$
$422$	29.0076	1.41207
$423$	−1.20094	−0.0583917
$424$	10.2767	0.499080
$425$	−35.5017	−1.72209
$426$	26.5881	1.28820
$427$	−44.4125	−2.14927
$428$	17.2864	0.835572
$429$	10.8531	0.523991
$430$	2.65525	0.128048
$431$	11.1043	0.534876	0.267438	−	0.963575i	$-0.413823\pi$
$431$	11.1043	0.534876	0.267438	+	0.963575i	$0.413823\pi$
$432$	6.90775	0.332349
$433$	40.8951	1.96529	0.982647	−	0.185483i	$-0.0593850\pi$
$433$	40.8951	1.96529	0.982647	+	0.185483i	$0.0593850\pi$
$434$	−33.4729	−1.60675
$435$	2.28889	0.109744
$436$	48.4130	2.31856
$437$	5.99217	0.286644
$438$	−13.6391	−0.651701
$439$	−1.76437	−0.0842086	−0.0421043	−	0.999113i	$-0.513406\pi$
$439$	−1.76437	−0.0842086	−0.0421043	+	0.999113i	$0.513406\pi$
$440$	−1.35132	−0.0644218
$441$	−0.683728	−0.0325585
$442$	−28.2926	−1.34574
$443$	24.2861	1.15387	0.576933	−	0.816791i	$-0.304249\pi$
$443$	24.2861	1.15387	0.576933	+	0.816791i	$0.304249\pi$
$444$	9.41130	0.446640
$445$	−2.78447	−0.131997
$446$	48.9603	2.31834
$447$	−4.06603	−0.192317
$448$	38.0061	1.79562
$449$	−34.4592	−1.62623	−0.813115	−	0.582103i	$-0.802230\pi$
$449$	−34.4592	−1.62623	−0.813115	+	0.582103i	$0.802230\pi$
$450$	−4.54004	−0.214019
$451$	31.3792	1.47759
$452$	−15.0013	−0.705602
$453$	5.49197	0.258035
$454$	−17.7432	−0.832730
$455$	−0.903436	−0.0423537
$456$	−3.33915	−0.156370
$457$	−31.3480	−1.46640	−0.733200	−	0.680014i	$-0.761974\pi$
$457$	−31.3480	−1.46640	−0.733200	+	0.680014i	$0.761974\pi$
$458$	−9.52887	−0.445255
$459$	−39.2028	−1.82983
$460$	3.02660	0.141116
$461$	7.59035	0.353518	0.176759	−	0.984254i	$-0.443439\pi$
$461$	7.59035	0.353518	0.176759	+	0.984254i	$0.443439\pi$
$462$	39.7916	1.85127
$463$	−20.0417	−0.931415	−0.465708	−	0.884939i	$-0.654200\pi$
$463$	−20.0417	−0.931415	−0.465708	+	0.884939i	$0.654200\pi$
$464$	−10.4013	−0.482867
$465$	−1.41799	−0.0657575
$466$	−58.5971	−2.71446
$467$	27.9980	1.29559	0.647796	−	0.761814i	$-0.275691\pi$
$467$	27.9980	1.29559	0.647796	+	0.761814i	$0.275691\pi$
$468$	−2.15159	−0.0994574
$469$	15.0556	0.695203
$470$	−1.11672	−0.0515104
$471$	25.6946	1.18395
$472$	−19.5581	−0.900233
$473$	−26.2681	−1.20781
$474$	39.0231	1.79239
$475$	−4.97037	−0.228056
$476$	−61.6864	−2.82739
$477$	2.03622	0.0932322
$478$	62.9805	2.88066
$479$	1.83984	0.0840646	0.0420323	−	0.999116i	$-0.486617\pi$
$479$	1.83984	0.0840646	0.0420323	+	0.999116i	$0.486617\pi$
$480$	1.92387	0.0878123
$481$	3.55468	0.162079
$482$	−46.3930	−2.11314
$483$	−28.3766	−1.29118
$484$	9.70925	0.441330
$485$	2.75882	0.125272
$486$	−9.42235	−0.427406
$487$	−1.90029	−0.0861102	−0.0430551	−	0.999073i	$-0.513709\pi$
$487$	−1.90029	−0.0861102	−0.0430551	+	0.999073i	$0.513709\pi$
$488$	−31.3159	−1.41760
$489$	6.17576	0.279278
$490$	−0.635778	−0.0287215
$491$	17.2974	0.780621	0.390310	−	0.920683i	$-0.372368\pi$
$491$	17.2974	0.780621	0.390310	+	0.920683i	$0.372368\pi$
$492$	39.1641	1.76566
$493$	59.0293	2.65855
$494$	−3.96106	−0.178217
$495$	−0.267751	−0.0120345
$496$	6.44367	0.289329
$497$	21.8955	0.982148
$498$	18.0715	0.809801
$499$	−17.3143	−0.775096	−0.387548	−	0.921850i	$-0.626678\pi$
$499$	−17.3143	−0.775096	−0.387548	+	0.921850i	$0.626678\pi$
$500$	−5.03595	−0.225215
$501$	−0.0500808	−0.00223745
$502$	−36.3445	−1.62213
$503$	10.2438	0.456749	0.228375	−	0.973573i	$-0.426659\pi$
$503$	10.2438	0.456749	0.228375	+	0.973573i	$0.426659\pi$
$504$	−2.51173	−0.111881
$505$	−1.03468	−0.0460428
$506$	−50.3500	−2.23833
$507$	−15.8004	−0.701722
$508$	−5.41920	−0.240438
$509$	15.7808	0.699474	0.349737	−	0.936848i	$-0.386271\pi$
$509$	15.7808	0.699474	0.349737	+	0.936848i	$0.386271\pi$
$510$	−4.39431	−0.194583
$511$	−11.2319	−0.496869
$512$	−13.9665	−0.617236
$513$	−5.48854	−0.242325
$514$	32.5324	1.43494
$515$	−0.863153	−0.0380351
$516$	−32.7849	−1.44328
$517$	11.0475	0.485870
$518$	13.0328	0.572630
$519$	3.79204	0.166452
$520$	−0.637025	−0.0279354
$521$	21.4230	0.938561	0.469280	−	0.883049i	$-0.344513\pi$
$521$	21.4230	0.938561	0.469280	+	0.883049i	$0.344513\pi$
$522$	7.54879	0.330402
$523$	−26.0958	−1.14109	−0.570545	−	0.821266i	$-0.693268\pi$
$523$	−26.0958	−1.14109	−0.570545	+	0.821266i	$0.693268\pi$
$524$	3.24986	0.141971
$525$	23.5378	1.02727
$526$	14.1002	0.614799
$527$	−36.5691	−1.59298
$528$	−7.66006	−0.333361
$529$	12.9061	0.561136
$530$	1.89342	0.0822449
$531$	−3.87524	−0.168171
$532$	−8.63632	−0.374432
$533$	14.7924	0.640730
$534$	57.8141	2.50186
$535$	1.01408	0.0438427
$536$	10.6159	0.458537
$537$	38.7202	1.67090
$538$	−43.6720	−1.88283
$539$	6.28967	0.270915
$540$	−2.77222	−0.119297
$541$	−37.0166	−1.59147	−0.795733	−	0.605647i	$-0.792914\pi$
$541$	−37.0166	−1.59147	−0.795733	+	0.605647i	$0.792914\pi$
$542$	−16.0827	−0.690810
$543$	18.7390	0.804168
$544$	49.6156	2.12725
$545$	2.84008	0.121656
$546$	18.7581	0.802771
$547$	−0.565683	−0.0241868	−0.0120934	−	0.999927i	$-0.503850\pi$
$547$	−0.565683	−0.0241868	−0.0120934	+	0.999927i	$0.503850\pi$
$548$	0.787775	0.0336521
$549$	−6.20493	−0.264820
$550$	41.7642	1.78083
$551$	8.26432	0.352072
$552$	−20.0087	−0.851629
$553$	32.1358	1.36655
$554$	43.0807	1.83032
$555$	0.552100	0.0234354
$556$	−60.1356	−2.55032
$557$	−9.10323	−0.385716	−0.192858	−	0.981227i	$-0.561776\pi$
$557$	−9.10323	−0.385716	−0.192858	+	0.981227i	$0.561776\pi$
$558$	−4.67653	−0.197973
$559$	−12.3830	−0.523744
$560$	0.637642	0.0269453
$561$	43.4723	1.83540
$562$	−60.0985	−2.53510
$563$	−3.44698	−0.145273	−0.0726365	−	0.997358i	$-0.523141\pi$
$563$	−3.44698	−0.145273	−0.0726365	+	0.997358i	$0.523141\pi$
$564$	13.7883	0.580594
$565$	−0.880030	−0.0370231
$566$	−33.5838	−1.41163
$567$	22.3608	0.939064
$568$	15.4388	0.647799
$569$	33.8389	1.41860	0.709300	−	0.704907i	$-0.249011\pi$
$569$	33.8389	1.41860	0.709300	+	0.704907i	$0.249011\pi$
$570$	−0.615219	−0.0257687
$571$	−19.9656	−0.835534	−0.417767	−	0.908554i	$-0.637187\pi$
$571$	−19.9656	−0.835534	−0.417767	+	0.908554i	$0.637187\pi$
$572$	19.7927	0.827573
$573$	−3.41200	−0.142538
$574$	54.2348	2.26372
$575$	−29.7833	−1.24205
$576$	5.30988	0.221245
$577$	23.3743	0.973085	0.486542	−	0.873657i	$-0.338258\pi$
$577$	23.3743	0.973085	0.486542	+	0.873657i	$0.338258\pi$
$578$	−75.5646	−3.14307
$579$	10.9623	0.455576
$580$	4.17424	0.173326
$581$	14.8820	0.617408
$582$	−57.2816	−2.37440
$583$	−18.7314	−0.775774
$584$	−7.91975	−0.327722
$585$	−0.126220	−0.00521856
$586$	71.4428	2.95128
$587$	22.5909	0.932428	0.466214	−	0.884672i	$-0.345618\pi$
$587$	22.5909	0.932428	0.466214	+	0.884672i	$0.345618\pi$
$588$	7.85008	0.323732
$589$	−5.11981	−0.210958
$590$	−3.60347	−0.148352
$591$	34.5820	1.42252
$592$	−2.50888	−0.103114
$593$	31.8981	1.30990	0.654949	−	0.755673i	$-0.272690\pi$
$593$	31.8981	1.30990	0.654949	+	0.755673i	$0.272690\pi$
$594$	46.1181	1.89225
$595$	−3.61875	−0.148354
$596$	−7.41520	−0.303739
$597$	31.7729	1.30038
$598$	−23.7354	−0.970612
$599$	−15.1181	−0.617709	−0.308855	−	0.951109i	$-0.599946\pi$
$599$	−15.1181	−0.617709	−0.308855	+	0.951109i	$0.599946\pi$
$600$	16.5968	0.677561
$601$	12.8012	0.522173	0.261087	−	0.965315i	$-0.415919\pi$
$601$	12.8012	0.522173	0.261087	+	0.965315i	$0.415919\pi$
$602$	−45.4008	−1.85040
$603$	2.10344	0.0856585
$604$	10.0157	0.407532
$605$	0.569580	0.0231567
$606$	21.4832	0.872695
$607$	27.5204	1.11702	0.558510	−	0.829498i	$-0.311373\pi$
$607$	27.5204	1.11702	0.558510	+	0.829498i	$0.311373\pi$
$608$	6.94636	0.281712
$609$	−39.1366	−1.58590
$610$	−5.76978	−0.233611
$611$	5.20790	0.210689
$612$	−8.61828	−0.348373
$613$	−38.3412	−1.54858	−0.774292	−	0.632828i	$-0.781894\pi$
$613$	−38.3412	−1.54858	−0.774292	+	0.632828i	$0.781894\pi$
$614$	−6.63035	−0.267579
$615$	2.29751	0.0926445
$616$	23.1056	0.930952
$617$	32.2472	1.29822	0.649112	−	0.760693i	$-0.275140\pi$
$617$	32.2472	1.29822	0.649112	+	0.760693i	$0.275140\pi$
$618$	17.9217	0.720916
$619$	11.2271	0.451255	0.225628	−	0.974214i	$-0.427557\pi$
$619$	11.2271	0.451255	0.225628	+	0.974214i	$0.427557\pi$
$620$	−2.58597	−0.103855
$621$	−32.8883	−1.31976
$622$	−19.2583	−0.772189
$623$	47.6103	1.90747
$624$	−3.61101	−0.144556
$625$	24.5564	0.982257
$626$	−47.3346	−1.89187
$627$	6.08628	0.243063
$628$	46.8592	1.86989
$629$	14.2384	0.567722
$630$	−0.462773	−0.0184373
$631$	−15.1100	−0.601521	−0.300761	−	0.953700i	$-0.597241\pi$
$631$	−15.1100	−0.601521	−0.300761	+	0.953700i	$0.597241\pi$
$632$	22.6594	0.901342
$633$	−21.0111	−0.835116
$634$	2.22132	0.0882200
$635$	−0.317910	−0.0126159
$636$	−23.3784	−0.927016
$637$	2.96500	0.117478
$638$	−69.4419	−2.74923
$639$	3.05905	0.121014
$640$	2.54607	0.100642
$641$	10.1473	0.400796	0.200398	−	0.979715i	$-0.435777\pi$
$641$	10.1473	0.400796	0.200398	+	0.979715i	$0.435777\pi$
$642$	−21.0555	−0.830994
$643$	5.27644	0.208083	0.104041	−	0.994573i	$-0.466823\pi$
$643$	5.27644	0.208083	0.104041	+	0.994573i	$0.466823\pi$
$644$	−51.7503	−2.03925
$645$	−1.92328	−0.0757291
$646$	−15.8662	−0.624247
$647$	−10.5462	−0.414616	−0.207308	−	0.978276i	$-0.566470\pi$
$647$	−10.5462	−0.414616	−0.207308	+	0.978276i	$0.566470\pi$
$648$	15.7669	0.619381
$649$	35.6486	1.39933
$650$	19.6879	0.772225
$651$	24.2454	0.950253
$652$	11.2627	0.441081
$653$	4.45005	0.174144	0.0870720	−	0.996202i	$-0.472249\pi$
$653$	4.45005	0.174144	0.0870720	+	0.996202i	$0.472249\pi$
$654$	−58.9687	−2.30586
$655$	0.190648	0.00744925
$656$	−10.4404	−0.407631
$657$	−1.56922	−0.0612211
$658$	19.0942	0.744370
$659$	24.1032	0.938926	0.469463	−	0.882952i	$-0.344448\pi$
$659$	24.1032	0.938926	0.469463	+	0.882952i	$0.344448\pi$
$660$	3.07413	0.119660
$661$	41.0322	1.59597	0.797984	−	0.602679i	$-0.205900\pi$
$661$	41.0322	1.59597	0.797984	+	0.602679i	$0.205900\pi$
$662$	37.5446	1.45921
$663$	20.4932	0.795890
$664$	10.4935	0.407226
$665$	−0.506637	−0.0196466
$666$	1.82083	0.0705559
$667$	49.5212	1.91747
$668$	−0.0913321	−0.00353375
$669$	−35.4635	−1.37110
$670$	1.95592	0.0755638
$671$	57.0796	2.20353
$672$	−32.8953	−1.26896
$673$	−12.2830	−0.473477	−0.236738	−	0.971573i	$-0.576078\pi$
$673$	−12.2830	−0.473477	−0.236738	+	0.971573i	$0.576078\pi$
$674$	50.7802	1.95598
$675$	27.2801	1.05001
$676$	−28.8152	−1.10828
$677$	48.0212	1.84561	0.922803	−	0.385272i	$-0.125892\pi$
$677$	48.0212	1.84561	0.922803	+	0.385272i	$0.125892\pi$
$678$	18.2721	0.701736
$679$	−47.1718	−1.81029
$680$	−2.55163	−0.0978504
$681$	12.8520	0.492488
$682$	43.0198	1.64731
$683$	32.2274	1.23315	0.616574	−	0.787297i	$-0.288520\pi$
$683$	32.2274	1.23315	0.616574	+	0.787297i	$0.288520\pi$
$684$	−1.20659	−0.0461351
$685$	0.0462137	0.00176573
$686$	−34.8946	−1.33228
$687$	6.90206	0.263330
$688$	8.73986	0.333204
$689$	−8.83011	−0.336400
$690$	−3.68650	−0.140343
$691$	11.1345	0.423576	0.211788	−	0.977316i	$-0.432071\pi$
$691$	11.1345	0.423576	0.211788	+	0.977316i	$0.432071\pi$
$692$	6.91553	0.262889
$693$	4.57815	0.173909
$694$	−30.0921	−1.14228
$695$	−3.52777	−0.133816
$696$	−27.5958	−1.04601
$697$	59.2515	2.24431
$698$	31.7457	1.20159
$699$	42.4437	1.60537
$700$	42.9257	1.62244
$701$	18.5214	0.699543	0.349771	−	0.936835i	$-0.386259\pi$
$701$	18.5214	0.699543	0.349771	+	0.936835i	$0.386259\pi$
$702$	21.7404	0.820540
$703$	1.99342	0.0751834
$704$	−48.8460	−1.84095
$705$	0.808874	0.0304639
$706$	−32.3770	−1.21852
$707$	17.6915	0.665359
$708$	44.4927	1.67214
$709$	−5.68029	−0.213328	−0.106664	−	0.994295i	$-0.534017\pi$
$709$	−5.68029	−0.213328	−0.106664	+	0.994295i	$0.534017\pi$
$710$	2.84452	0.106753
$711$	4.48973	0.168378
$712$	33.5707	1.25811
$713$	−30.6788	−1.14893
$714$	75.1362	2.81190
$715$	1.16111	0.0434230
$716$	70.6138	2.63896
$717$	−45.6188	−1.70366
$718$	−57.2853	−2.13787
$719$	−34.8092	−1.29817	−0.649083	−	0.760718i	$-0.724847\pi$
$719$	−34.8092	−1.29817	−0.649083	+	0.760718i	$0.724847\pi$
$720$	0.0890858	0.00332003
$721$	14.7586	0.549640
$722$	−2.22132	−0.0826691
$723$	33.6039	1.24974
$724$	34.1742	1.27008
$725$	−41.0767	−1.52555
$726$	−11.8262	−0.438912
$727$	−5.21065	−0.193252	−0.0966261	−	0.995321i	$-0.530805\pi$
$727$	−5.21065	−0.193252	−0.0966261	+	0.995321i	$0.530805\pi$
$728$	10.8922	0.403691
$729$	29.6168	1.09692
$730$	−1.45917	−0.0540063
$731$	−49.6004	−1.83454
$732$	71.2406	2.63313
$733$	−25.2254	−0.931720	−0.465860	−	0.884858i	$-0.654255\pi$
$733$	−25.2254	−0.931720	−0.465860	+	0.884858i	$0.654255\pi$
$734$	25.4467	0.939253
$735$	0.460514	0.0169863
$736$	41.6238	1.53427
$737$	−19.3497	−0.712754
$738$	7.57721	0.278921
$739$	−4.36371	−0.160522	−0.0802609	−	0.996774i	$-0.525575\pi$
$739$	−4.36371	−0.160522	−0.0802609	+	0.996774i	$0.525575\pi$
$740$	1.00686	0.0370130
$741$	2.86912	0.105400
$742$	−32.3747	−1.18851
$743$	−37.7121	−1.38352	−0.691761	−	0.722126i	$-0.743165\pi$
$743$	−37.7121	−1.38352	−0.691761	+	0.722126i	$0.743165\pi$
$744$	17.0958	0.626762
$745$	−0.435002	−0.0159373
$746$	−73.6934	−2.69811
$747$	2.07918	0.0760731
$748$	79.2803	2.89877
$749$	−17.3393	−0.633566
$750$	6.13396	0.223981
$751$	−9.36684	−0.341801	−0.170900	−	0.985288i	$-0.554668\pi$
$751$	−9.36684	−0.341801	−0.170900	+	0.985288i	$0.554668\pi$
$752$	−3.67572	−0.134040
$753$	26.3254	0.959352
$754$	−32.7355	−1.19216
$755$	0.587556	0.0213833
$756$	47.4008	1.72395
$757$	−37.8041	−1.37401	−0.687007	−	0.726651i	$-0.741076\pi$
$757$	−37.8041	−1.37401	−0.687007	+	0.726651i	$0.741076\pi$
$758$	−35.0135	−1.27175
$759$	36.4700	1.32378
$760$	−0.357237	−0.0129583
$761$	−3.63729	−0.131852	−0.0659258	−	0.997825i	$-0.521000\pi$
$761$	−3.63729	−0.131852	−0.0659258	+	0.997825i	$0.521000\pi$
$762$	6.60078	0.239121
$763$	−48.5611	−1.75803
$764$	−6.22245	−0.225120
$765$	−0.505579	−0.0182793
$766$	−2.65114	−0.0957894
$767$	16.8050	0.606794
$768$	−11.3110	−0.408151
$769$	−43.2723	−1.56044	−0.780219	−	0.625507i	$-0.784892\pi$
$769$	−43.2723	−1.56044	−0.780219	+	0.625507i	$0.784892\pi$
$770$	4.25708	0.153415
$771$	−23.5642	−0.848645
$772$	19.9918	0.719522
$773$	0.884775	0.0318231	0.0159116	−	0.999873i	$-0.494935\pi$
$773$	0.884775	0.0318231	0.0159116	+	0.999873i	$0.494935\pi$
$774$	−6.34301	−0.227995
$775$	25.4473	0.914095
$776$	−33.2615	−1.19402
$777$	−9.44009	−0.338661
$778$	59.0823	2.11820
$779$	8.29543	0.297215
$780$	1.44917	0.0518886
$781$	−28.1404	−1.00694
$782$	−95.0729	−3.39980
$783$	−45.3590	−1.62100
$784$	−2.09269	−0.0747389
$785$	2.74893	0.0981134
$786$	−3.95844	−0.141193
$787$	−25.4155	−0.905966	−0.452983	−	0.891519i	$-0.649640\pi$
$787$	−25.4155	−0.905966	−0.452983	+	0.891519i	$0.649640\pi$
$788$	63.0671	2.24667
$789$	−10.2132	−0.363601
$790$	4.17486	0.148535
$791$	15.0472	0.535017
$792$	3.22811	0.114706
$793$	26.9078	0.955524
$794$	35.2063	1.24943
$795$	−1.37146	−0.0486408
$796$	57.9441	2.05377
$797$	32.2575	1.14262	0.571309	−	0.820735i	$-0.306436\pi$
$797$	32.2575	1.14262	0.571309	+	0.820735i	$0.306436\pi$
$798$	10.5193	0.372380
$799$	20.8604	0.737989
$800$	−34.5260	−1.22068
$801$	6.65169	0.235026
$802$	27.5243	0.971918
$803$	14.4354	0.509413
$804$	−24.1502	−0.851710
$805$	−3.03586	−0.107000
$806$	20.2799	0.714328
$807$	31.6330	1.11353
$808$	12.4745	0.438853
$809$	−37.1082	−1.30465	−0.652327	−	0.757937i	$-0.726207\pi$
$809$	−37.1082	−1.30465	−0.652327	+	0.757937i	$0.726207\pi$
$810$	2.90496	0.102070
$811$	3.16796	0.111242	0.0556211	−	0.998452i	$-0.482286\pi$
$811$	3.16796	0.111242	0.0556211	+	0.998452i	$0.482286\pi$
$812$	−71.3732	−2.50471
$813$	11.6492	0.408555
$814$	−16.7500	−0.587087
$815$	0.660710	0.0231437
$816$	−14.4640	−0.506343
$817$	−6.94424	−0.242948
$818$	69.8919	2.44371
$819$	2.15818	0.0754127
$820$	4.18995	0.146320
$821$	−27.7530	−0.968588	−0.484294	−	0.874905i	$-0.660923\pi$
$821$	−27.7530	−0.968588	−0.484294	+	0.874905i	$0.660923\pi$
$822$	−0.959537	−0.0334677
$823$	9.52784	0.332120	0.166060	−	0.986116i	$-0.446896\pi$
$823$	9.52784	0.332120	0.166060	+	0.986116i	$0.446896\pi$
$824$	10.4065	0.362528
$825$	−30.2511	−1.05321
$826$	61.6139	2.14382
$827$	11.4273	0.397366	0.198683	−	0.980064i	$-0.436334\pi$
$827$	11.4273	0.397366	0.198683	+	0.980064i	$0.436334\pi$
$828$	−7.23010	−0.251263
$829$	−10.0821	−0.350167	−0.175084	−	0.984554i	$-0.556020\pi$
$829$	−10.0821	−0.350167	−0.175084	+	0.984554i	$0.556020\pi$
$830$	1.93336	0.0671081
$831$	−31.2047	−1.08248
$832$	−23.0264	−0.798297
$833$	11.8764	0.411493
$834$	73.2472	2.53634
$835$	−0.00535787	−0.000185417 0
$836$	11.0995	0.383885
$837$	28.1002	0.971287
$838$	−14.4067	−0.497671
$839$	−17.1679	−0.592702	−0.296351	−	0.955079i	$-0.595770\pi$
$839$	−17.1679	−0.592702	−0.296351	+	0.955079i	$0.595770\pi$
$840$	1.69174	0.0583704
$841$	39.2989	1.35514
$842$	3.59337	0.123836
$843$	43.5312	1.49930
$844$	−38.3178	−1.31895
$845$	−1.69040	−0.0581516
$846$	2.66768	0.0917166
$847$	−9.73896	−0.334635
$848$	6.23227	0.214017
$849$	24.3258	0.834860
$850$	78.8608	2.70490
$851$	11.9449	0.409467
$852$	−35.1218	−1.20325
$853$	36.2164	1.24003	0.620013	−	0.784591i	$-0.287127\pi$
$853$	36.2164	1.24003	0.620013	+	0.784591i	$0.287127\pi$
$854$	98.6546	3.37589
$855$	−0.0707829	−0.00242072
$856$	−12.2262	−0.417883
$857$	−3.98959	−0.136282	−0.0681409	−	0.997676i	$-0.521707\pi$
$857$	−3.98959	−0.136282	−0.0681409	+	0.997676i	$0.521707\pi$
$858$	−24.1081	−0.823039
$859$	−0.0321813	−0.00109801	−0.000549006	−	1.00000i	$-0.500175\pi$
$859$	−0.0321813	−0.00109801	−0.000549006		1.00000i	$0.500175\pi$
$860$	−3.50748	−0.119604
$861$	−39.2840	−1.33879
$862$	−24.6662	−0.840136
$863$	2.61316	0.0889530	0.0444765	−	0.999010i	$-0.485838\pi$
$863$	2.61316	0.0889530	0.0444765	+	0.999010i	$0.485838\pi$
$864$	−38.1254	−1.29705
$865$	0.405690	0.0137939
$866$	−90.8413	−3.08691
$867$	54.7338	1.85886
$868$	44.2163	1.50080
$869$	−41.3014	−1.40105
$870$	−5.08437	−0.172376
$871$	−9.12158	−0.309073
$872$	−34.2411	−1.15955
$873$	−6.59043	−0.223052
$874$	−13.3105	−0.450236
$875$	5.05136	0.170767
$876$	18.0167	0.608727
$877$	42.0129	1.41868	0.709338	−	0.704869i	$-0.248994\pi$
$877$	42.0129	1.41868	0.709338	+	0.704869i	$0.248994\pi$
$878$	3.91923	0.132267
$879$	−51.7482	−1.74542
$880$	−0.819507	−0.0276256
$881$	47.1830	1.58964	0.794818	−	0.606848i	$-0.207566\pi$
$881$	47.1830	1.58964	0.794818	+	0.606848i	$0.207566\pi$
$882$	1.51878	0.0511400
$883$	23.6068	0.794432	0.397216	−	0.917725i	$-0.369976\pi$
$883$	23.6068	0.794432	0.397216	+	0.917725i	$0.369976\pi$
$884$	37.3733	1.25700
$885$	2.61010	0.0877376
$886$	−53.9473	−1.81239
$887$	55.0836	1.84953	0.924763	−	0.380544i	$-0.124263\pi$
$887$	55.0836	1.84953	0.924763	+	0.380544i	$0.124263\pi$
$888$	−6.65634	−0.223372
$889$	5.43578	0.182310
$890$	6.18521	0.207329
$891$	−28.7384	−0.962772
$892$	−64.6745	−2.16546
$893$	2.92053	0.0977320
$894$	9.03197	0.302074
$895$	4.14246	0.138467
$896$	−43.5340	−1.45437
$897$	17.1923	0.574033
$898$	76.5450	2.55434
$899$	−42.3117	−1.41117
$900$	5.99720	0.199907
$901$	−35.3693	−1.17832
$902$	−69.7034	−2.32087
$903$	32.8852	1.09435
$904$	10.6100	0.352883
$905$	2.00478	0.0666412
$906$	−12.1994	−0.405299
$907$	0.769154	0.0255393	0.0127697	−	0.999918i	$-0.495935\pi$
$907$	0.769154	0.0255393	0.0127697	+	0.999918i	$0.495935\pi$
$908$	23.4380	0.777819
$909$	2.47171	0.0819814
$910$	2.00682	0.0665255
$911$	−19.1003	−0.632822	−0.316411	−	0.948622i	$-0.602478\pi$
$911$	−19.1003	−0.632822	−0.316411	+	0.948622i	$0.602478\pi$
$912$	−2.02502	−0.0670550
$913$	−19.1265	−0.632995
$914$	69.6341	2.30329
$915$	4.17923	0.138161
$916$	12.5872	0.415894
$917$	−3.25980	−0.107648
$918$	87.0822	2.87414
$919$	23.4512	0.773584	0.386792	−	0.922167i	$-0.373583\pi$
$919$	23.4512	0.773584	0.386792	+	0.922167i	$0.373583\pi$
$920$	−2.14062	−0.0705743
$921$	4.80257	0.158250
$922$	−16.8606	−0.555275
$923$	−13.2656	−0.436643
$924$	−52.5631	−1.72920
$925$	−9.90806	−0.325775
$926$	44.5190	1.46299
$927$	2.06195	0.0677232
$928$	57.4069	1.88448
$929$	17.3504	0.569248	0.284624	−	0.958639i	$-0.408131\pi$
$929$	17.3504	0.569248	0.284624	+	0.958639i	$0.408131\pi$
$930$	3.14980	0.103286
$931$	1.66274	0.0544941
$932$	77.4044	2.53546
$933$	13.9494	0.456683
$934$	−62.1925	−2.03500
$935$	4.65086	0.152100
$936$	1.52176	0.0497402
$937$	18.4907	0.604066	0.302033	−	0.953297i	$-0.402335\pi$
$937$	18.4907	0.604066	0.302033	+	0.953297i	$0.402335\pi$
$938$	−33.4433	−1.09196
$939$	34.2859	1.11888
$940$	1.47514	0.0481137
$941$	−29.4694	−0.960676	−0.480338	−	0.877084i	$-0.659486\pi$
$941$	−29.4694	−0.960676	−0.480338	+	0.877084i	$0.659486\pi$
$942$	−57.0761	−1.85964
$943$	49.7076	1.61870
$944$	−11.8609	−0.386041
$945$	2.78070	0.0904561
$946$	58.3498	1.89712
$947$	9.27636	0.301441	0.150721	−	0.988576i	$-0.451841\pi$
$947$	9.27636	0.301441	0.150721	+	0.988576i	$0.451841\pi$
$948$	−51.5479	−1.67420
$949$	6.80495	0.220898
$950$	11.0408	0.358211
$951$	−1.60897	−0.0521745
$952$	43.6290	1.41402
$953$	56.2502	1.82212	0.911061	−	0.412271i	$-0.135264\pi$
$953$	56.2502	1.82212	0.911061	+	0.412271i	$0.135264\pi$
$954$	−4.52310	−0.146441
$955$	−0.365031	−0.0118121
$956$	−83.1947	−2.69071
$957$	50.2990	1.62593
$958$	−4.08689	−0.132041
$959$	−0.790185	−0.0255164
$960$	−3.57638	−0.115427
$961$	−4.78759	−0.154439
$962$	−7.89608	−0.254580
$963$	−2.42250	−0.0780640
$964$	61.2832	1.97380
$965$	1.17279	0.0377535
$966$	63.0336	2.02807
$967$	16.6763	0.536273	0.268136	−	0.963381i	$-0.413592\pi$
$967$	16.6763	0.536273	0.268136	+	0.963381i	$0.413592\pi$
$968$	−6.86707	−0.220716
$969$	11.4924	0.369188
$970$	−6.12824	−0.196766
$971$	−8.13371	−0.261023	−0.130512	−	0.991447i	$-0.541662\pi$
$971$	−8.13371	−0.261023	−0.130512	+	0.991447i	$0.541662\pi$
$972$	12.4465	0.399223
$973$	60.3196	1.93376
$974$	4.22115	0.135254
$975$	−14.2606	−0.456704
$976$	−18.9914	−0.607901
$977$	23.4639	0.750676	0.375338	−	0.926888i	$-0.377527\pi$
$977$	23.4639	0.750676	0.375338	+	0.926888i	$0.377527\pi$
$978$	−13.7184	−0.438665
$979$	−61.1894	−1.95562
$980$	0.839837	0.0268276
$981$	−6.78454	−0.216614
$982$	−38.4231	−1.22613
$983$	−17.6506	−0.562965	−0.281483	−	0.959566i	$-0.590826\pi$
$983$	−17.6506	−0.562965	−0.281483	+	0.959566i	$0.590826\pi$
$984$	−27.6997	−0.883033
$985$	3.69974	0.117884
$986$	−131.123	−4.17581
$987$	−13.8305	−0.440231
$988$	5.23240	0.166465
$989$	−41.6111	−1.32315
$990$	0.594762	0.0189028
$991$	−56.3913	−1.79133	−0.895665	−	0.444729i	$-0.853300\pi$
$991$	−56.3913	−1.79133	−0.895665	+	0.444729i	$0.853300\pi$
$992$	−35.5640	−1.12916
$993$	−27.1947	−0.862999
$994$	−48.6370	−1.54267
$995$	3.39921	0.107762
$996$	−23.8716	−0.756402
$997$	19.0337	0.602804	0.301402	−	0.953497i	$-0.402545\pi$
$997$	19.0337	0.602804	0.301402	+	0.953497i	$0.402545\pi$
$998$	38.4607	1.21745
$999$	−10.9410	−0.346158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.19	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.19	✓	138	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22132 q^{2} +1.60897 q^{3} +2.93428 q^{4} +0.172135 q^{5} -3.57405 q^{6} -2.94325 q^{7} -2.07533 q^{8} -0.411206 q^{9} +O(q^{10})\)	\(q-2.22132 q^{2} +1.60897 q^{3} +2.93428 q^{4} +0.172135 q^{5} -3.57405 q^{6} -2.94325 q^{7} -2.07533 q^{8} -0.411206 q^{9} -0.382368 q^{10} +3.78271 q^{11} +4.72117 q^{12} +1.78320 q^{13} +6.53792 q^{14} +0.276961 q^{15} -1.25858 q^{16} +7.14268 q^{17} +0.913420 q^{18} +1.00000 q^{19} +0.505092 q^{20} -4.73562 q^{21} -8.40262 q^{22} +5.99217 q^{23} -3.33915 q^{24} -4.97037 q^{25} -3.96106 q^{26} -5.48854 q^{27} -8.63632 q^{28} +8.26432 q^{29} -0.615219 q^{30} -5.11981 q^{31} +6.94636 q^{32} +6.08628 q^{33} -15.8662 q^{34} -0.506637 q^{35} -1.20659 q^{36} +1.99342 q^{37} -2.22132 q^{38} +2.86912 q^{39} -0.357237 q^{40} +8.29543 q^{41} +10.5193 q^{42} -6.94424 q^{43} +11.0995 q^{44} -0.0707829 q^{45} -13.3105 q^{46} +2.92053 q^{47} -2.02502 q^{48} +1.66274 q^{49} +11.0408 q^{50} +11.4924 q^{51} +5.23240 q^{52} -4.95183 q^{53} +12.1918 q^{54} +0.651138 q^{55} +6.10822 q^{56} +1.60897 q^{57} -18.3577 q^{58} +9.42408 q^{59} +0.812679 q^{60} +15.0896 q^{61} +11.3727 q^{62} +1.21028 q^{63} -12.9130 q^{64} +0.306951 q^{65} -13.5196 q^{66} -5.11529 q^{67} +20.9586 q^{68} +9.64124 q^{69} +1.12540 q^{70} -7.43922 q^{71} +0.853386 q^{72} +3.81614 q^{73} -4.42804 q^{74} -7.99719 q^{75} +2.93428 q^{76} -11.1335 q^{77} -6.37324 q^{78} -10.9185 q^{79} -0.216645 q^{80} -7.59729 q^{81} -18.4268 q^{82} -5.05630 q^{83} -13.8956 q^{84} +1.22951 q^{85} +15.4254 q^{86} +13.2971 q^{87} -7.85037 q^{88} -16.1761 q^{89} +0.157232 q^{90} -5.24841 q^{91} +17.5827 q^{92} -8.23763 q^{93} -6.48745 q^{94} +0.172135 q^{95} +11.1765 q^{96} +16.0271 q^{97} -3.69348 q^{98} -1.55547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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