LMFDB - Embedded newform 6017.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.39877 q^{2} +0.712166 q^{3} +3.75408 q^{4} +0.976168 q^{5} -1.70832 q^{6} -3.65167 q^{7} -4.20764 q^{8} -2.49282 q^{9} +O(q^{10})$	\(q-2.39877 q^{2} +0.712166 q^{3} +3.75408 q^{4} +0.976168 q^{5} -1.70832 q^{6} -3.65167 q^{7} -4.20764 q^{8} -2.49282 q^{9} -2.34160 q^{10} +1.00000 q^{11} +2.67353 q^{12} +6.01255 q^{13} +8.75950 q^{14} +0.695193 q^{15} +2.58498 q^{16} -5.87343 q^{17} +5.97969 q^{18} +3.25716 q^{19} +3.66462 q^{20} -2.60059 q^{21} -2.39877 q^{22} +3.77285 q^{23} -2.99654 q^{24} -4.04710 q^{25} -14.4227 q^{26} -3.91180 q^{27} -13.7087 q^{28} -3.29803 q^{29} -1.66761 q^{30} -5.66835 q^{31} +2.21451 q^{32} +0.712166 q^{33} +14.0890 q^{34} -3.56464 q^{35} -9.35826 q^{36} +6.24312 q^{37} -7.81316 q^{38} +4.28193 q^{39} -4.10736 q^{40} +8.92708 q^{41} +6.23822 q^{42} +8.96313 q^{43} +3.75408 q^{44} -2.43341 q^{45} -9.05018 q^{46} -5.47059 q^{47} +1.84094 q^{48} +6.33468 q^{49} +9.70804 q^{50} -4.18285 q^{51} +22.5716 q^{52} -5.81005 q^{53} +9.38350 q^{54} +0.976168 q^{55} +15.3649 q^{56} +2.31964 q^{57} +7.91121 q^{58} +2.41058 q^{59} +2.60981 q^{60} +2.35196 q^{61} +13.5970 q^{62} +9.10295 q^{63} -10.4821 q^{64} +5.86926 q^{65} -1.70832 q^{66} -9.74527 q^{67} -22.0493 q^{68} +2.68689 q^{69} +8.55074 q^{70} +1.20411 q^{71} +10.4889 q^{72} -0.538879 q^{73} -14.9758 q^{74} -2.88220 q^{75} +12.2276 q^{76} -3.65167 q^{77} -10.2714 q^{78} -1.87471 q^{79} +2.52338 q^{80} +4.69261 q^{81} -21.4140 q^{82} -9.33130 q^{83} -9.76285 q^{84} -5.73345 q^{85} -21.5005 q^{86} -2.34875 q^{87} -4.20764 q^{88} -8.85064 q^{89} +5.83718 q^{90} -21.9558 q^{91} +14.1636 q^{92} -4.03680 q^{93} +13.1227 q^{94} +3.17953 q^{95} +1.57710 q^{96} -2.90476 q^{97} -15.1954 q^{98} -2.49282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) $ 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * 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 $

$2$	−2.39877	−1.69618	−0.848092	−	0.529848i	$-0.822249\pi$
$2$	−2.39877	−1.69618	−0.848092	+	0.529848i	$0.822249\pi$
$3$	0.712166	0.411169	0.205585	−	0.978639i	$-0.434090\pi$
$3$	0.712166	0.411169	0.205585	+	0.978639i	$0.434090\pi$
$4$	3.75408	1.87704
$5$	0.976168	0.436555	0.218278	−	0.975887i	$-0.429956\pi$
$5$	0.976168	0.436555	0.218278	+	0.975887i	$0.429956\pi$
$6$	−1.70832	−0.697419
$7$	−3.65167	−1.38020	−0.690100	−	0.723714i	$-0.742434\pi$
$7$	−3.65167	−1.38020	−0.690100	+	0.723714i	$0.742434\pi$
$8$	−4.20764	−1.48763
$9$	−2.49282	−0.830940
$10$	−2.34160	−0.740479
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.67353	0.771782
$13$	6.01255	1.66758	0.833791	−	0.552081i	$-0.186166\pi$
$13$	6.01255	1.66758	0.833791	+	0.552081i	$0.186166\pi$
$14$	8.75950	2.34108
$15$	0.695193	0.179498
$16$	2.58498	0.646246
$17$	−5.87343	−1.42451	−0.712257	−	0.701918i	$-0.752327\pi$
$17$	−5.87343	−1.42451	−0.712257	+	0.701918i	$0.752327\pi$
$18$	5.97969	1.40943
$19$	3.25716	0.747243	0.373622	−	0.927581i	$-0.378116\pi$
$19$	3.25716	0.747243	0.373622	+	0.927581i	$0.378116\pi$
$20$	3.66462	0.819433
$21$	−2.60059	−0.567496
$22$	−2.39877	−0.511419
$23$	3.77285	0.786693	0.393346	−	0.919390i	$-0.371317\pi$
$23$	3.77285	0.786693	0.393346	+	0.919390i	$0.371317\pi$
$24$	−2.99654	−0.611666
$25$	−4.04710	−0.809419
$26$	−14.4227	−2.82853
$27$	−3.91180	−0.752826
$28$	−13.7087	−2.59070
$29$	−3.29803	−0.612429	−0.306214	−	0.951963i	$-0.599062\pi$
$29$	−3.29803	−0.612429	−0.306214	+	0.951963i	$0.599062\pi$
$30$	−1.66761	−0.304462
$31$	−5.66835	−1.01807	−0.509033	−	0.860747i	$-0.669997\pi$
$31$	−5.66835	−1.01807	−0.509033	+	0.860747i	$0.669997\pi$
$32$	2.21451	0.391474
$33$	0.712166	0.123972
$34$	14.0890	2.41624
$35$	−3.56464	−0.602534
$36$	−9.35826	−1.55971
$37$	6.24312	1.02636	0.513181	−	0.858280i	$-0.328467\pi$
$37$	6.24312	1.02636	0.513181	+	0.858280i	$0.328467\pi$
$38$	−7.81316	−1.26746
$39$	4.28193	0.685658
$40$	−4.10736	−0.649431
$41$	8.92708	1.39418	0.697088	−	0.716986i	$-0.254479\pi$
$41$	8.92708	1.39418	0.697088	+	0.716986i	$0.254479\pi$
$42$	6.23822	0.962578
$43$	8.96313	1.36687	0.683433	−	0.730014i	$-0.260486\pi$
$43$	8.96313	1.36687	0.683433	+	0.730014i	$0.260486\pi$
$44$	3.75408	0.565950
$45$	−2.43341	−0.362751
$46$	−9.05018	−1.33438
$47$	−5.47059	−0.797967	−0.398984	−	0.916958i	$-0.630637\pi$
$47$	−5.47059	−0.797967	−0.398984	+	0.916958i	$0.630637\pi$
$48$	1.84094	0.265716
$49$	6.33468	0.904955
$50$	9.70804	1.37292
$51$	−4.18285	−0.585717
$52$	22.5716	3.13012
$53$	−5.81005	−0.798072	−0.399036	−	0.916935i	$-0.630655\pi$
$53$	−5.81005	−0.798072	−0.399036	+	0.916935i	$0.630655\pi$
$54$	9.38350	1.27693
$55$	0.976168	0.131626
$56$	15.3649	2.05322
$57$	2.31964	0.307243
$58$	7.91121	1.03879
$59$	2.41058	0.313831	0.156915	−	0.987612i	$-0.449845\pi$
$59$	2.41058	0.313831	0.156915	+	0.987612i	$0.449845\pi$
$60$	2.60981	0.336926
$61$	2.35196	0.301138	0.150569	−	0.988599i	$-0.451889\pi$
$61$	2.35196	0.301138	0.150569	+	0.988599i	$0.451889\pi$
$62$	13.5970	1.72683
$63$	9.10295	1.14686
$64$	−10.4821	−1.31026
$65$	5.86926	0.727992
$66$	−1.70832	−0.210280
$67$	−9.74527	−1.19057	−0.595287	−	0.803513i	$-0.702962\pi$
$67$	−9.74527	−1.19057	−0.595287	+	0.803513i	$0.702962\pi$
$68$	−22.0493	−2.67387
$69$	2.68689	0.323464
$70$	8.55074	1.02201
$71$	1.20411	0.142901	0.0714505	−	0.997444i	$-0.477237\pi$
$71$	1.20411	0.142901	0.0714505	+	0.997444i	$0.477237\pi$
$72$	10.4889	1.23613
$73$	−0.538879	−0.0630710	−0.0315355	−	0.999503i	$-0.510040\pi$
$73$	−0.538879	−0.0630710	−0.0315355	+	0.999503i	$0.510040\pi$
$74$	−14.9758	−1.74090
$75$	−2.88220	−0.332808
$76$	12.2276	1.40261
$77$	−3.65167	−0.416146
$78$	−10.2714	−1.16300
$79$	−1.87471	−0.210922	−0.105461	−	0.994423i	$-0.533632\pi$
$79$	−1.87471	−0.210922	−0.105461	+	0.994423i	$0.533632\pi$
$80$	2.52338	0.282122
$81$	4.69261	0.521401
$82$	−21.4140	−2.36478
$83$	−9.33130	−1.02424	−0.512122	−	0.858913i	$-0.671140\pi$
$83$	−9.33130	−1.02424	−0.512122	+	0.858913i	$0.671140\pi$
$84$	−9.76285	−1.06521
$85$	−5.73345	−0.621880
$86$	−21.5005	−2.31846
$87$	−2.34875	−0.251812
$88$	−4.20764	−0.448536
$89$	−8.85064	−0.938166	−0.469083	−	0.883154i	$-0.655416\pi$
$89$	−8.85064	−0.938166	−0.469083	+	0.883154i	$0.655416\pi$
$90$	5.83718	0.615293
$91$	−21.9558	−2.30160
$92$	14.1636	1.47666
$93$	−4.03680	−0.418597
$94$	13.1227	1.35350
$95$	3.17953	0.326213
$96$	1.57710	0.160962
$97$	−2.90476	−0.294934	−0.147467	−	0.989067i	$-0.547112\pi$
$97$	−2.90476	−0.294934	−0.147467	+	0.989067i	$0.547112\pi$
$98$	−15.1954	−1.53497
$99$	−2.49282	−0.250538
$100$	−15.1931	−1.51931
$101$	0.386594	0.0384675	0.0192338	−	0.999815i	$-0.493877\pi$
$101$	0.386594	0.0384675	0.0192338	+	0.999815i	$0.493877\pi$
$102$	10.0337	0.993484
$103$	15.4536	1.52269	0.761345	−	0.648347i	$-0.224540\pi$
$103$	15.4536	1.52269	0.761345	+	0.648347i	$0.224540\pi$
$104$	−25.2987	−2.48074
$105$	−2.53862	−0.247744
$106$	13.9370	1.35368
$107$	−8.43226	−0.815177	−0.407588	−	0.913166i	$-0.633630\pi$
$107$	−8.43226	−0.815177	−0.407588	+	0.913166i	$0.633630\pi$
$108$	−14.6852	−1.41309
$109$	−9.42858	−0.903094	−0.451547	−	0.892247i	$-0.649128\pi$
$109$	−9.42858	−0.903094	−0.451547	+	0.892247i	$0.649128\pi$
$110$	−2.34160	−0.223263
$111$	4.44613	0.422008
$112$	−9.43950	−0.891949
$113$	15.0472	1.41552	0.707761	−	0.706452i	$-0.249705\pi$
$113$	15.0472	1.41552	0.707761	+	0.706452i	$0.249705\pi$
$114$	−5.56427	−0.521142
$115$	3.68293	0.343435
$116$	−12.3811	−1.14956
$117$	−14.9882	−1.38566
$118$	−5.78242	−0.532315
$119$	21.4478	1.96612
$120$	−2.92512	−0.267026
$121$	1.00000	0.0909091
$122$	−5.64182	−0.510786
$123$	6.35756	0.573242
$124$	−21.2795	−1.91095
$125$	−8.83148	−0.789912
$126$	−21.8359	−1.94529
$127$	10.1778	0.903134	0.451567	−	0.892237i	$-0.350865\pi$
$127$	10.1778	0.903134	0.451567	+	0.892237i	$0.350865\pi$
$128$	20.7150	1.83096
$129$	6.38324	0.562013
$130$	−14.0790	−1.23481
$131$	15.3471	1.34088	0.670439	−	0.741964i	$-0.266106\pi$
$131$	15.3471	1.34088	0.670439	+	0.741964i	$0.266106\pi$
$132$	2.67353	0.232701
$133$	−11.8941	−1.03135
$134$	23.3766	2.01943
$135$	−3.81857	−0.328650
$136$	24.7133	2.11914
$137$	−5.64673	−0.482433	−0.241216	−	0.970471i	$-0.577546\pi$
$137$	−5.64673	−0.482433	−0.241216	+	0.970471i	$0.577546\pi$
$138$	−6.44523	−0.548655
$139$	5.97506	0.506798	0.253399	−	0.967362i	$-0.418452\pi$
$139$	5.97506	0.506798	0.253399	+	0.967362i	$0.418452\pi$
$140$	−13.3820	−1.13098
$141$	−3.89597	−0.328100
$142$	−2.88837	−0.242386
$143$	6.01255	0.502795
$144$	−6.44390	−0.536991
$145$	−3.21943	−0.267359
$146$	1.29264	0.106980
$147$	4.51135	0.372090
$148$	23.4372	1.92652
$149$	5.43082	0.444910	0.222455	−	0.974943i	$-0.428593\pi$
$149$	5.43082	0.444910	0.222455	+	0.974943i	$0.428593\pi$
$150$	6.91374	0.564504
$151$	3.95861	0.322147	0.161074	−	0.986942i	$-0.448504\pi$
$151$	3.95861	0.322147	0.161074	+	0.986942i	$0.448504\pi$
$152$	−13.7049	−1.11162
$153$	14.6414	1.18369
$154$	8.75950	0.705861
$155$	−5.53326	−0.444442
$156$	16.0747	1.28701
$157$	6.24073	0.498064	0.249032	−	0.968495i	$-0.419887\pi$
$157$	6.24073	0.498064	0.249032	+	0.968495i	$0.419887\pi$
$158$	4.49700	0.357762
$159$	−4.13772	−0.328143
$160$	2.16173	0.170900
$161$	−13.7772	−1.08579
$162$	−11.2565	−0.884392
$163$	2.68301	0.210150	0.105075	−	0.994464i	$-0.466492\pi$
$163$	2.68301	0.210150	0.105075	+	0.994464i	$0.466492\pi$
$164$	33.5130	2.61693
$165$	0.695193	0.0541207
$166$	22.3836	1.73731
$167$	12.2773	0.950048	0.475024	−	0.879973i	$-0.342439\pi$
$167$	12.2773	0.950048	0.475024	+	0.879973i	$0.342439\pi$
$168$	10.9424	0.844222
$169$	23.1508	1.78083
$170$	13.7532	1.05482
$171$	−8.11951	−0.620914
$172$	33.6484	2.56566
$173$	6.46319	0.491387	0.245694	−	0.969348i	$-0.420984\pi$
$173$	6.46319	0.491387	0.245694	+	0.969348i	$0.420984\pi$
$174$	5.63409	0.427120
$175$	14.7787	1.11716
$176$	2.58498	0.194850
$177$	1.71673	0.129038
$178$	21.2306	1.59130
$179$	−3.19309	−0.238662	−0.119331	−	0.992854i	$-0.538075\pi$
$179$	−3.19309	−0.238662	−0.119331	+	0.992854i	$0.538075\pi$
$180$	−9.13523	−0.680900
$181$	−18.1132	−1.34634	−0.673171	−	0.739487i	$-0.735068\pi$
$181$	−18.1132	−1.34634	−0.673171	+	0.739487i	$0.735068\pi$
$182$	52.6670	3.90393
$183$	1.67499	0.123819
$184$	−15.8748	−1.17030
$185$	6.09433	0.448064
$186$	9.68336	0.710018
$187$	−5.87343	−0.429507
$188$	−20.5371	−1.49782
$189$	14.2846	1.03905
$190$	−7.62696	−0.553318
$191$	−22.4754	−1.62626	−0.813132	−	0.582079i	$-0.802239\pi$
$191$	−22.4754	−1.62626	−0.813132	+	0.582079i	$0.802239\pi$
$192$	−7.46497	−0.538738
$193$	7.75848	0.558468	0.279234	−	0.960223i	$-0.409920\pi$
$193$	7.75848	0.558468	0.279234	+	0.960223i	$0.409920\pi$
$194$	6.96785	0.500263
$195$	4.17988	0.299328
$196$	23.7809	1.69864
$197$	16.4697	1.17342	0.586710	−	0.809797i	$-0.300423\pi$
$197$	16.4697	1.17342	0.586710	+	0.809797i	$0.300423\pi$
$198$	5.97969	0.424958
$199$	17.1919	1.21870	0.609349	−	0.792902i	$-0.291431\pi$
$199$	17.1919	1.21870	0.609349	+	0.792902i	$0.291431\pi$
$200$	17.0287	1.20411
$201$	−6.94025	−0.489527
$202$	−0.927348	−0.0652480
$203$	12.0433	0.845275
$204$	−15.7028	−1.09941
$205$	8.71432	0.608635
$206$	−37.0696	−2.58276
$207$	−9.40503	−0.653695
$208$	15.5423	1.07767
$209$	3.25716	0.225302
$210$	6.08955	0.420219
$211$	5.18087	0.356666	0.178333	−	0.983970i	$-0.442930\pi$
$211$	5.18087	0.356666	0.178333	+	0.983970i	$0.442930\pi$
$212$	−21.8114	−1.49802
$213$	0.857523	0.0587565
$214$	20.2270	1.38269
$215$	8.74952	0.596712
$216$	16.4594	1.11992
$217$	20.6989	1.40513
$218$	22.6170	1.53181
$219$	−0.383771	−0.0259329
$220$	3.66462	0.247068
$221$	−35.3143	−2.37549
$222$	−10.6652	−0.715804
$223$	−12.9054	−0.864208	−0.432104	−	0.901824i	$-0.642229\pi$
$223$	−12.9054	−0.864208	−0.432104	+	0.901824i	$0.642229\pi$
$224$	−8.08666	−0.540313
$225$	10.0887	0.672579
$226$	−36.0947	−2.40099
$227$	−5.96860	−0.396150	−0.198075	−	0.980187i	$-0.563469\pi$
$227$	−5.96860	−0.396150	−0.198075	+	0.980187i	$0.563469\pi$
$228$	8.70811	0.576709
$229$	−6.52477	−0.431169	−0.215584	−	0.976485i	$-0.569166\pi$
$229$	−6.52477	−0.431169	−0.215584	+	0.976485i	$0.569166\pi$
$230$	−8.83449	−0.582529
$231$	−2.60059	−0.171107
$232$	13.8769	0.911065
$233$	−2.59313	−0.169882	−0.0849409	−	0.996386i	$-0.527070\pi$
$233$	−2.59313	−0.169882	−0.0849409	+	0.996386i	$0.527070\pi$
$234$	35.9532	2.35034
$235$	−5.34021	−0.348357
$236$	9.04953	0.589074
$237$	−1.33511	−0.0867246
$238$	−51.4483	−3.33490
$239$	7.12549	0.460910	0.230455	−	0.973083i	$-0.425979\pi$
$239$	7.12549	0.460910	0.230455	+	0.973083i	$0.425979\pi$
$240$	1.79706	0.116000
$241$	8.47608	0.545992	0.272996	−	0.962015i	$-0.411985\pi$
$241$	8.47608	0.545992	0.272996	+	0.962015i	$0.411985\pi$
$242$	−2.39877	−0.154199
$243$	15.0773	0.967210
$244$	8.82947	0.565249
$245$	6.18371	0.395063
$246$	−15.2503	−0.972324
$247$	19.5838	1.24609
$248$	23.8504	1.51450
$249$	−6.64543	−0.421137
$250$	21.1847	1.33984
$251$	−2.39773	−0.151343	−0.0756716	−	0.997133i	$-0.524110\pi$
$251$	−2.39773	−0.151343	−0.0756716	+	0.997133i	$0.524110\pi$
$252$	34.1732	2.15271
$253$	3.77285	0.237197
$254$	−24.4142	−1.53188
$255$	−4.08317	−0.255698
$256$	−28.7264	−1.79540
$257$	3.43745	0.214422	0.107211	−	0.994236i	$-0.465808\pi$
$257$	3.43745	0.214422	0.107211	+	0.994236i	$0.465808\pi$
$258$	−15.3119	−0.953277
$259$	−22.7978	−1.41659
$260$	22.0337	1.36647
$261$	8.22140	0.508892
$262$	−36.8140	−2.27438
$263$	0.194037	0.0119649	0.00598243	−	0.999982i	$-0.498096\pi$
$263$	0.194037	0.0119649	0.00598243	+	0.999982i	$0.498096\pi$
$264$	−2.99654	−0.184424
$265$	−5.67159	−0.348403
$266$	28.5311	1.74935
$267$	−6.30313	−0.385745
$268$	−36.5846	−2.23476
$269$	27.4941	1.67635	0.838174	−	0.545404i	$-0.183624\pi$
$269$	27.4941	1.67635	0.838174	+	0.545404i	$0.183624\pi$
$270$	9.15986	0.557452
$271$	−2.76528	−0.167979	−0.0839895	−	0.996467i	$-0.526766\pi$
$271$	−2.76528	−0.167979	−0.0839895	+	0.996467i	$0.526766\pi$
$272$	−15.1827	−0.920586
$273$	−15.6362	−0.946346
$274$	13.5452	0.818295
$275$	−4.04710	−0.244049
$276$	10.0868	0.607155
$277$	6.92430	0.416041	0.208021	−	0.978124i	$-0.433298\pi$
$277$	6.92430	0.416041	0.208021	+	0.978124i	$0.433298\pi$
$278$	−14.3328	−0.859622
$279$	14.1302	0.845951
$280$	14.9987	0.896345
$281$	−5.86512	−0.349884	−0.174942	−	0.984579i	$-0.555974\pi$
$281$	−5.86512	−0.349884	−0.174942	+	0.984579i	$0.555974\pi$
$282$	9.34552	0.556518
$283$	22.0915	1.31321	0.656603	−	0.754237i	$-0.271993\pi$
$283$	22.0915	1.31321	0.656603	+	0.754237i	$0.271993\pi$
$284$	4.52031	0.268231
$285$	2.26435	0.134129
$286$	−14.4227	−0.852833
$287$	−32.5987	−1.92424
$288$	−5.52038	−0.325291
$289$	17.4971	1.02924
$290$	7.72266	0.453491
$291$	−2.06867	−0.121268
$292$	−2.02300	−0.118387
$293$	−18.9272	−1.10574	−0.552870	−	0.833268i	$-0.686467\pi$
$293$	−18.9272	−1.10574	−0.552870	+	0.833268i	$0.686467\pi$
$294$	−10.8217	−0.631133
$295$	2.35313	0.137005
$296$	−26.2688	−1.52684
$297$	−3.91180	−0.226986
$298$	−13.0273	−0.754649
$299$	22.6844	1.31187
$300$	−10.8200	−0.624695
$301$	−32.7304	−1.88655
$302$	−9.49579	−0.546421
$303$	0.275319	0.0158167
$304$	8.41969	0.482903
$305$	2.29591	0.131463
$306$	−35.1213	−2.00775
$307$	6.88857	0.393151	0.196576	−	0.980489i	$-0.437018\pi$
$307$	6.88857	0.393151	0.196576	+	0.980489i	$0.437018\pi$
$308$	−13.7087	−0.781124
$309$	11.0055	0.626083
$310$	13.2730	0.753856
$311$	7.34742	0.416634	0.208317	−	0.978061i	$-0.433201\pi$
$311$	7.34742	0.416634	0.208317	+	0.978061i	$0.433201\pi$
$312$	−18.0168	−1.02000
$313$	−12.9177	−0.730152	−0.365076	−	0.930978i	$-0.618957\pi$
$313$	−12.9177	−0.730152	−0.365076	+	0.930978i	$0.618957\pi$
$314$	−14.9701	−0.844809
$315$	8.88601	0.500670
$316$	−7.03784	−0.395909
$317$	31.2130	1.75310	0.876549	−	0.481313i	$-0.159840\pi$
$317$	31.2130	1.75310	0.876549	+	0.481313i	$0.159840\pi$
$318$	9.92543	0.556591
$319$	−3.29803	−0.184654
$320$	−10.2322	−0.572000
$321$	−6.00517	−0.335176
$322$	33.0483	1.84171
$323$	−19.1307	−1.06446
$324$	17.6165	0.978692
$325$	−24.3334	−1.34977
$326$	−6.43592	−0.356453
$327$	−6.71471	−0.371325
$328$	−37.5619	−2.07401
$329$	19.9768	1.10136
$330$	−1.66761	−0.0917987
$331$	25.3209	1.39176	0.695880	−	0.718158i	$-0.255014\pi$
$331$	25.3209	1.39176	0.695880	+	0.718158i	$0.255014\pi$
$332$	−35.0305	−1.92255
$333$	−15.5630	−0.852845
$334$	−29.4504	−1.61146
$335$	−9.51301	−0.519751
$336$	−6.72249	−0.366742
$337$	25.1326	1.36906	0.684531	−	0.728984i	$-0.260007\pi$
$337$	25.1326	1.36906	0.684531	+	0.728984i	$0.260007\pi$
$338$	−55.5333	−3.02061
$339$	10.7161	0.582019
$340$	−21.5238	−1.16729
$341$	−5.66835	−0.306958
$342$	19.4768	1.05319
$343$	2.42952	0.131182
$344$	−37.7136	−2.03338
$345$	2.62286	0.141210
$346$	−15.5037	−0.833483
$347$	17.0682	0.916267	0.458134	−	0.888883i	$-0.348518\pi$
$347$	17.0682	0.916267	0.458134	+	0.888883i	$0.348518\pi$
$348$	−8.81739	−0.472662
$349$	12.6121	0.675110	0.337555	−	0.941306i	$-0.390400\pi$
$349$	12.6121	0.675110	0.337555	+	0.941306i	$0.390400\pi$
$350$	−35.4506	−1.89491
$351$	−23.5199	−1.25540
$352$	2.21451	0.118034
$353$	20.9389	1.11447	0.557234	−	0.830356i	$-0.311863\pi$
$353$	20.9389	1.11447	0.557234	+	0.830356i	$0.311863\pi$
$354$	−4.11804	−0.218872
$355$	1.17541	0.0623842
$356$	−33.2261	−1.76098
$357$	15.2744	0.808407
$358$	7.65947	0.404816
$359$	−22.2133	−1.17237	−0.586187	−	0.810176i	$-0.699372\pi$
$359$	−22.2133	−1.17237	−0.586187	+	0.810176i	$0.699372\pi$
$360$	10.2389	0.539638
$361$	−8.39093	−0.441628
$362$	43.4493	2.28365
$363$	0.712166	0.0373790
$364$	−82.4241	−4.32020
$365$	−0.526036	−0.0275340
$366$	−4.01791	−0.210019
$367$	−8.71763	−0.455057	−0.227528	−	0.973771i	$-0.573064\pi$
$367$	−8.71763	−0.455057	−0.227528	+	0.973771i	$0.573064\pi$
$368$	9.75274	0.508397
$369$	−22.2536	−1.15848
$370$	−14.6189	−0.759999
$371$	21.2164	1.10150
$372$	−15.1545	−0.785725
$373$	9.66595	0.500484	0.250242	−	0.968183i	$-0.419490\pi$
$373$	9.66595	0.500484	0.250242	+	0.968183i	$0.419490\pi$
$374$	14.0890	0.728524
$375$	−6.28948	−0.324787
$376$	23.0183	1.18708
$377$	−19.8296	−1.02128
$378$	−34.2654	−1.76242
$379$	20.2973	1.04260	0.521302	−	0.853372i	$-0.325447\pi$
$379$	20.2973	1.04260	0.521302	+	0.853372i	$0.325447\pi$
$380$	11.9362	0.612316
$381$	7.24829	0.371341
$382$	53.9133	2.75844
$383$	−16.6299	−0.849750	−0.424875	−	0.905252i	$-0.639682\pi$
$383$	−16.6299	−0.849750	−0.424875	+	0.905252i	$0.639682\pi$
$384$	14.7525	0.752836
$385$	−3.56464	−0.181671
$386$	−18.6108	−0.947265
$387$	−22.3435	−1.13578
$388$	−10.9047	−0.553604
$389$	−35.5789	−1.80392	−0.901962	−	0.431816i	$-0.857873\pi$
$389$	−35.5789	−1.80392	−0.901962	+	0.431816i	$0.857873\pi$
$390$	−10.0266	−0.507715
$391$	−22.1595	−1.12066
$392$	−26.6541	−1.34623
$393$	10.9297	0.551328
$394$	−39.5071	−1.99034
$395$	−1.83003	−0.0920791
$396$	−9.35826	−0.470270
$397$	2.48840	0.124889	0.0624446	−	0.998048i	$-0.480110\pi$
$397$	2.48840	0.124889	0.0624446	+	0.998048i	$0.480110\pi$
$398$	−41.2393	−2.06714
$399$	−8.47054	−0.424058
$400$	−10.4617	−0.523084
$401$	25.7373	1.28526	0.642629	−	0.766177i	$-0.277844\pi$
$401$	25.7373	1.28526	0.642629	+	0.766177i	$0.277844\pi$
$402$	16.6480	0.830329
$403$	−34.0812	−1.69771
$404$	1.45131	0.0722052
$405$	4.58077	0.227620
$406$	−28.8891	−1.43374
$407$	6.24312	0.309460
$408$	17.5999	0.871327
$409$	22.1324	1.09438	0.547188	−	0.837010i	$-0.315698\pi$
$409$	22.1324	1.09438	0.547188	+	0.837010i	$0.315698\pi$
$410$	−20.9036	−1.03236
$411$	−4.02141	−0.198361
$412$	58.0142	2.85815
$413$	−8.80264	−0.433150
$414$	22.5605	1.10879
$415$	−9.10891	−0.447139
$416$	13.3149	0.652815
$417$	4.25523	0.208380
$418$	−7.81316	−0.382154
$419$	−28.4267	−1.38873	−0.694367	−	0.719621i	$-0.744315\pi$
$419$	−28.4267	−1.38873	−0.694367	+	0.719621i	$0.744315\pi$
$420$	−9.53018	−0.465025
$421$	4.24891	0.207079	0.103540	−	0.994625i	$-0.466983\pi$
$421$	4.24891	0.207079	0.103540	+	0.994625i	$0.466983\pi$
$422$	−12.4277	−0.604971
$423$	13.6372	0.663063
$424$	24.4466	1.18723
$425$	23.7703	1.15303
$426$	−2.05700	−0.0996618
$427$	−8.58859	−0.415631
$428$	−31.6554	−1.53012
$429$	4.28193	0.206734
$430$	−20.9881	−1.01213
$431$	−29.3165	−1.41213	−0.706063	−	0.708149i	$-0.749530\pi$
$431$	−29.3165	−1.41213	−0.706063	+	0.708149i	$0.749530\pi$
$432$	−10.1119	−0.486511
$433$	−3.57087	−0.171605	−0.0858025	−	0.996312i	$-0.527345\pi$
$433$	−3.57087	−0.171605	−0.0858025	+	0.996312i	$0.527345\pi$
$434$	−49.6519	−2.38337
$435$	−2.29277	−0.109930
$436$	−35.3957	−1.69515
$437$	12.2888	0.587851
$438$	0.920578	0.0439869
$439$	38.5524	1.84000	0.920002	−	0.391914i	$-0.128187\pi$
$439$	38.5524	1.84000	0.920002	+	0.391914i	$0.128187\pi$
$440$	−4.10736	−0.195811
$441$	−15.7912	−0.751963
$442$	84.7107	4.02928
$443$	−20.8761	−0.991852	−0.495926	−	0.868365i	$-0.665171\pi$
$443$	−20.8761	−0.991852	−0.495926	+	0.868365i	$0.665171\pi$
$444$	16.6912	0.792128
$445$	−8.63971	−0.409562
$446$	30.9570	1.46586
$447$	3.86764	0.182933
$448$	38.2770	1.80842
$449$	−15.6489	−0.738515	−0.369258	−	0.929327i	$-0.620388\pi$
$449$	−15.6489	−0.738515	−0.369258	+	0.929327i	$0.620388\pi$
$450$	−24.2004	−1.14082
$451$	8.92708	0.420360
$452$	56.4885	2.65699
$453$	2.81919	0.132457
$454$	14.3173	0.671943
$455$	−21.4326	−1.00477
$456$	−9.76020	−0.457063
$457$	5.28770	0.247348	0.123674	−	0.992323i	$-0.460532\pi$
$457$	5.28770	0.247348	0.123674	+	0.992323i	$0.460532\pi$
$458$	15.6514	0.731342
$459$	22.9757	1.07241
$460$	13.8260	0.644642
$461$	−31.1714	−1.45180	−0.725899	−	0.687801i	$-0.758576\pi$
$461$	−31.1714	−1.45180	−0.725899	+	0.687801i	$0.758576\pi$
$462$	6.23822	0.290228
$463$	33.2723	1.54629	0.773147	−	0.634227i	$-0.218682\pi$
$463$	33.2723	1.54629	0.773147	+	0.634227i	$0.218682\pi$
$464$	−8.52535	−0.395780
$465$	−3.94060	−0.182741
$466$	6.22032	0.288151
$467$	−5.51673	−0.255284	−0.127642	−	0.991820i	$-0.540741\pi$
$467$	−5.51673	−0.255284	−0.127642	+	0.991820i	$0.540741\pi$
$468$	−56.2670	−2.60094
$469$	35.5865	1.64323
$470$	12.8099	0.590878
$471$	4.44443	0.204789
$472$	−10.1429	−0.466863
$473$	8.96313	0.412125
$474$	3.20261	0.147101
$475$	−13.1820	−0.604833
$476$	80.5169	3.69048
$477$	14.4834	0.663150
$478$	−17.0924	−0.781788
$479$	−30.5923	−1.39780	−0.698899	−	0.715220i	$-0.746326\pi$
$479$	−30.5923	−1.39780	−0.698899	+	0.715220i	$0.746326\pi$
$480$	1.53951	0.0702688
$481$	37.5371	1.71154
$482$	−20.3321	−0.926103
$483$	−9.81164	−0.446445
$484$	3.75408	0.170640
$485$	−2.83554	−0.128755
$486$	−36.1670	−1.64057
$487$	23.5607	1.06764	0.533818	−	0.845599i	$-0.320757\pi$
$487$	23.5607	1.06764	0.533818	+	0.845599i	$0.320757\pi$
$488$	−9.89622	−0.447981
$489$	1.91075	0.0864071
$490$	−14.8333	−0.670100
$491$	21.9979	0.992750	0.496375	−	0.868108i	$-0.334664\pi$
$491$	21.9979	0.992750	0.496375	+	0.868108i	$0.334664\pi$
$492$	23.8668	1.07600
$493$	19.3707	0.872414
$494$	−46.9770	−2.11360
$495$	−2.43341	−0.109374
$496$	−14.6526	−0.657920
$497$	−4.39699	−0.197232
$498$	15.9408	0.714326
$499$	38.7673	1.73546	0.867730	−	0.497035i	$-0.165578\pi$
$499$	38.7673	1.73546	0.867730	+	0.497035i	$0.165578\pi$
$500$	−33.1541	−1.48270
$501$	8.74349	0.390630
$502$	5.75159	0.256706
$503$	34.1622	1.52322	0.761608	−	0.648038i	$-0.224410\pi$
$503$	34.1622	1.52322	0.761608	+	0.648038i	$0.224410\pi$
$504$	−38.3020	−1.70610
$505$	0.377380	0.0167932
$506$	−9.05018	−0.402330
$507$	16.4872	0.732222
$508$	38.2083	1.69522
$509$	35.9579	1.59381	0.796903	−	0.604108i	$-0.206470\pi$
$509$	35.9579	1.59381	0.796903	+	0.604108i	$0.206470\pi$
$510$	9.79456	0.433711
$511$	1.96781	0.0870507
$512$	27.4778	1.21436
$513$	−12.7413	−0.562544
$514$	−8.24564	−0.363700
$515$	15.0853	0.664738
$516$	23.9632	1.05492
$517$	−5.47059	−0.240596
$518$	54.6866	2.40279
$519$	4.60286	0.202043
$520$	−24.6957	−1.08298
$521$	−0.927576	−0.0406378	−0.0203189	−	0.999794i	$-0.506468\pi$
$521$	−0.927576	−0.0406378	−0.0203189	+	0.999794i	$0.506468\pi$
$522$	−19.7212	−0.863174
$523$	20.4375	0.893668	0.446834	−	0.894617i	$-0.352551\pi$
$523$	20.4375	0.893668	0.446834	+	0.894617i	$0.352551\pi$
$524$	57.6141	2.51689
$525$	10.5249	0.459342
$526$	−0.465451	−0.0202946
$527$	33.2926	1.45025
$528$	1.84094	0.0801165
$529$	−8.76563	−0.381114
$530$	13.6048	0.590955
$531$	−6.00914	−0.260775
$532$	−44.6513	−1.93588
$533$	53.6745	2.32490
$534$	15.1197	0.654295
$535$	−8.23129	−0.355870
$536$	41.0046	1.77113
$537$	−2.27401	−0.0981307
$538$	−65.9520	−2.84339
$539$	6.33468	0.272854
$540$	−14.3352	−0.616891
$541$	25.5366	1.09790	0.548952	−	0.835854i	$-0.315027\pi$
$541$	25.5366	1.09790	0.548952	+	0.835854i	$0.315027\pi$
$542$	6.63327	0.284923
$543$	−12.8996	−0.553575
$544$	−13.0068	−0.557660
$545$	−9.20388	−0.394251
$546$	37.5076	1.60518
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−21.1983	−0.905547
$549$	−5.86302	−0.250228
$550$	9.70804	0.413952
$551$	−10.7422	−0.457633
$552$	−11.3055	−0.481193
$553$	6.84583	0.291114
$554$	−16.6098	−0.705682
$555$	4.34017	0.184230
$556$	22.4309	0.951281
$557$	12.2104	0.517371	0.258685	−	0.965962i	$-0.416711\pi$
$557$	12.2104	0.517371	0.258685	+	0.965962i	$0.416711\pi$
$558$	−33.8950	−1.43489
$559$	53.8913	2.27936
$560$	−9.21453	−0.389385
$561$	−4.18285	−0.176600
$562$	14.0691	0.593468
$563$	−24.9210	−1.05029	−0.525147	−	0.851011i	$-0.675990\pi$
$563$	−24.9210	−1.05029	−0.525147	+	0.851011i	$0.675990\pi$
$564$	−14.6258	−0.615857
$565$	14.6886	0.617954
$566$	−52.9924	−2.22744
$567$	−17.1359	−0.719638
$568$	−5.06644	−0.212583
$569$	−26.2317	−1.09969	−0.549844	−	0.835267i	$-0.685313\pi$
$569$	−26.2317	−1.09969	−0.549844	+	0.835267i	$0.685313\pi$
$570$	−5.43166	−0.227507
$571$	10.9879	0.459829	0.229914	−	0.973211i	$-0.426155\pi$
$571$	10.9879	0.459829	0.229914	+	0.973211i	$0.426155\pi$
$572$	22.5716	0.943767
$573$	−16.0062	−0.668670
$574$	78.1968	3.26387
$575$	−15.2691	−0.636765
$576$	26.1299	1.08875
$577$	−21.2869	−0.886186	−0.443093	−	0.896476i	$-0.646119\pi$
$577$	−21.2869	−0.886186	−0.443093	+	0.896476i	$0.646119\pi$
$578$	−41.9715	−1.74579
$579$	5.52533	0.229625
$580$	−12.0860	−0.501844
$581$	34.0748	1.41366
$582$	4.96227	0.205693
$583$	−5.81005	−0.240628
$584$	2.26741	0.0938260
$585$	−14.6310	−0.604917
$586$	45.4020	1.87554
$587$	21.9962	0.907882	0.453941	−	0.891032i	$-0.350018\pi$
$587$	21.9962	0.907882	0.453941	+	0.891032i	$0.350018\pi$
$588$	16.9360	0.698428
$589$	−18.4627	−0.760742
$590$	−5.64461	−0.232385
$591$	11.7292	0.482474
$592$	16.1383	0.663282
$593$	−27.3624	−1.12364	−0.561819	−	0.827260i	$-0.689898\pi$
$593$	−27.3624	−1.12364	−0.561819	+	0.827260i	$0.689898\pi$
$594$	9.38350	0.385010
$595$	20.9366	0.858319
$596$	20.3877	0.835114
$597$	12.2435	0.501091
$598$	−54.4147	−2.22518
$599$	−4.86327	−0.198708	−0.0993539	−	0.995052i	$-0.531678\pi$
$599$	−4.86327	−0.198708	−0.0993539	+	0.995052i	$0.531678\pi$
$600$	12.1273	0.495094
$601$	−10.3693	−0.422973	−0.211486	−	0.977381i	$-0.567830\pi$
$601$	−10.3693	−0.422973	−0.211486	+	0.977381i	$0.567830\pi$
$602$	78.5126	3.19993
$603$	24.2932	0.989295
$604$	14.8610	0.604684
$605$	0.976168	0.0396869
$606$	−0.660426	−0.0268280
$607$	5.06076	0.205410	0.102705	−	0.994712i	$-0.467250\pi$
$607$	5.06076	0.205410	0.102705	+	0.994712i	$0.467250\pi$
$608$	7.21301	0.292526
$609$	8.57684	0.347551
$610$	−5.50736	−0.222986
$611$	−32.8922	−1.33068
$612$	54.9650	2.22183
$613$	40.2190	1.62443	0.812216	−	0.583357i	$-0.198261\pi$
$613$	40.2190	1.62443	0.812216	+	0.583357i	$0.198261\pi$
$614$	−16.5241	−0.666857
$615$	6.20604	0.250252
$616$	15.3649	0.619070
$617$	−5.58616	−0.224890	−0.112445	−	0.993658i	$-0.535868\pi$
$617$	−5.58616	−0.224890	−0.112445	+	0.993658i	$0.535868\pi$
$618$	−26.3997	−1.06195
$619$	26.4619	1.06359	0.531796	−	0.846872i	$-0.321517\pi$
$619$	26.4619	1.06359	0.531796	+	0.846872i	$0.321517\pi$
$620$	−20.7723	−0.834236
$621$	−14.7586	−0.592243
$622$	−17.6248	−0.706688
$623$	32.3196	1.29486
$624$	11.0687	0.443104
$625$	11.6145	0.464579
$626$	30.9866	1.23847
$627$	2.31964	0.0926374
$628$	23.4282	0.934888
$629$	−36.6685	−1.46207
$630$	−21.3155	−0.849228
$631$	−22.2480	−0.885678	−0.442839	−	0.896601i	$-0.646029\pi$
$631$	−22.2480	−0.885678	−0.442839	+	0.896601i	$0.646029\pi$
$632$	7.88812	0.313773
$633$	3.68964	0.146650
$634$	−74.8728	−2.97358
$635$	9.93524	0.394268
$636$	−15.5334	−0.615938
$637$	38.0876	1.50909
$638$	7.91121	0.313208
$639$	−3.00162	−0.118742
$640$	20.2213	0.799318
$641$	14.5984	0.576602	0.288301	−	0.957540i	$-0.406910\pi$
$641$	14.5984	0.576602	0.288301	+	0.957540i	$0.406910\pi$
$642$	14.4050	0.568520
$643$	41.9119	1.65284	0.826422	−	0.563051i	$-0.190373\pi$
$643$	41.9119	1.65284	0.826422	+	0.563051i	$0.190373\pi$
$644$	−51.7207	−2.03808
$645$	6.23111	0.245350
$646$	45.8900	1.80552
$647$	−22.0839	−0.868207	−0.434104	−	0.900863i	$-0.642935\pi$
$647$	−22.0839	−0.868207	−0.434104	+	0.900863i	$0.642935\pi$
$648$	−19.7448	−0.775649
$649$	2.41058	0.0946236
$650$	58.3701	2.28946
$651$	14.7411	0.577748
$652$	10.0723	0.394460
$653$	7.49978	0.293489	0.146745	−	0.989174i	$-0.453120\pi$
$653$	7.49978	0.293489	0.146745	+	0.989174i	$0.453120\pi$
$654$	16.1070	0.629835
$655$	14.9813	0.585368
$656$	23.0763	0.900980
$657$	1.34333	0.0524082
$658$	−47.9196	−1.86810
$659$	−16.4539	−0.640951	−0.320476	−	0.947257i	$-0.603843\pi$
$659$	−16.4539	−0.640951	−0.320476	+	0.947257i	$0.603843\pi$
$660$	2.60981	0.101587
$661$	−25.2981	−0.983981	−0.491991	−	0.870601i	$-0.663731\pi$
$661$	−25.2981	−0.983981	−0.491991	+	0.870601i	$0.663731\pi$
$662$	−60.7389	−2.36068
$663$	−25.1496	−0.976730
$664$	39.2628	1.52369
$665$	−11.6106	−0.450240
$666$	37.3319	1.44658
$667$	−12.4430	−0.481794
$668$	46.0901	1.78328
$669$	−9.19077	−0.355336
$670$	22.8195	0.881595
$671$	2.35196	0.0907966
$672$	−5.75904	−0.222160
$673$	−4.76089	−0.183519	−0.0917594	−	0.995781i	$-0.529249\pi$
$673$	−4.76089	−0.183519	−0.0917594	+	0.995781i	$0.529249\pi$
$674$	−60.2873	−2.32218
$675$	15.8314	0.609352
$676$	86.9099	3.34269
$677$	28.7356	1.10440	0.552199	−	0.833712i	$-0.313789\pi$
$677$	28.7356	1.10440	0.552199	+	0.833712i	$0.313789\pi$
$678$	−25.7054	−0.987212
$679$	10.6072	0.407068
$680$	24.1243	0.925124
$681$	−4.25063	−0.162885
$682$	13.5970	0.520658
$683$	48.5655	1.85831	0.929153	−	0.369696i	$-0.120538\pi$
$683$	48.5655	1.85831	0.929153	+	0.369696i	$0.120538\pi$
$684$	−30.4813	−1.16548
$685$	−5.51215	−0.210609
$686$	−5.82784	−0.222508
$687$	−4.64672	−0.177283
$688$	23.1695	0.883331
$689$	−34.9332	−1.33085
$690$	−6.29163	−0.239518
$691$	−22.4279	−0.853198	−0.426599	−	0.904441i	$-0.640288\pi$
$691$	−22.4279	−0.853198	−0.426599	+	0.904441i	$0.640288\pi$
$692$	24.2634	0.922355
$693$	9.10295	0.345793
$694$	−40.9426	−1.55416
$695$	5.83266	0.221245
$696$	9.88268	0.374602
$697$	−52.4325	−1.98602
$698$	−30.2535	−1.14511
$699$	−1.84674	−0.0698502
$700$	55.4803	2.09696
$701$	−20.1092	−0.759512	−0.379756	−	0.925087i	$-0.623992\pi$
$701$	−20.1092	−0.759512	−0.379756	+	0.925087i	$0.623992\pi$
$702$	56.4187	2.12939
$703$	20.3348	0.766942
$704$	−10.4821	−0.395058
$705$	−3.80312	−0.143234
$706$	−50.2276	−1.89034
$707$	−1.41171	−0.0530929
$708$	6.44476	0.242209
$709$	−34.4983	−1.29561	−0.647806	−	0.761806i	$-0.724313\pi$
$709$	−34.4983	−1.29561	−0.647806	+	0.761806i	$0.724313\pi$
$710$	−2.81953	−0.105815
$711$	4.67332	0.175263
$712$	37.2403	1.39564
$713$	−21.3858	−0.800905
$714$	−36.6397	−1.37121
$715$	5.86926	0.219498
$716$	−11.9871	−0.447980
$717$	5.07453	0.189512
$718$	53.2846	1.98856
$719$	48.1205	1.79459	0.897295	−	0.441430i	$-0.145529\pi$
$719$	48.1205	1.79459	0.897295	+	0.441430i	$0.145529\pi$
$720$	−6.29032	−0.234426
$721$	−56.4315	−2.10162
$722$	20.1279	0.749082
$723$	6.03637	0.224495
$724$	−67.9984	−2.52714
$725$	13.3475	0.495712
$726$	−1.70832	−0.0634017
$727$	38.7453	1.43698	0.718492	−	0.695535i	$-0.244833\pi$
$727$	38.7453	1.43698	0.718492	+	0.695535i	$0.244833\pi$
$728$	92.3823	3.42392
$729$	−3.34028	−0.123714
$730$	1.26184	0.0467027
$731$	−52.6443	−1.94712
$732$	6.28805	0.232413
$733$	−41.3948	−1.52895	−0.764476	−	0.644652i	$-0.777002\pi$
$733$	−41.3948	−1.52895	−0.764476	+	0.644652i	$0.777002\pi$
$734$	20.9116	0.771860
$735$	4.40383	0.162438
$736$	8.35501	0.307970
$737$	−9.74527	−0.358972
$738$	53.3812	1.96499
$739$	−1.45206	−0.0534147	−0.0267074	−	0.999643i	$-0.508502\pi$
$739$	−1.45206	−0.0534147	−0.0267074	+	0.999643i	$0.508502\pi$
$740$	22.8786	0.841035
$741$	13.9469	0.512353
$742$	−50.8932	−1.86835
$743$	13.3935	0.491359	0.245679	−	0.969351i	$-0.420989\pi$
$743$	13.3935	0.491359	0.245679	+	0.969351i	$0.420989\pi$
$744$	16.9854	0.622716
$745$	5.30139	0.194228
$746$	−23.1864	−0.848913
$747$	23.2612	0.851084
$748$	−22.0493	−0.806204
$749$	30.7918	1.12511
$750$	15.0870	0.550899
$751$	−49.9400	−1.82234	−0.911169	−	0.412034i	$-0.864819\pi$
$751$	−49.9400	−1.82234	−0.911169	+	0.412034i	$0.864819\pi$
$752$	−14.1414	−0.515683
$753$	−1.70758	−0.0622276
$754$	47.5665	1.73227
$755$	3.86427	0.140635
$756$	53.6256	1.95034
$757$	−8.92405	−0.324350	−0.162175	−	0.986762i	$-0.551851\pi$
$757$	−8.92405	−0.324350	−0.162175	+	0.986762i	$0.551851\pi$
$758$	−48.6885	−1.76845
$759$	2.68689	0.0975280
$760$	−13.3783	−0.485283
$761$	−22.6320	−0.820409	−0.410204	−	0.911994i	$-0.634543\pi$
$761$	−22.6320	−0.820409	−0.410204	+	0.911994i	$0.634543\pi$
$762$	−17.3870	−0.629863
$763$	34.4301	1.24645
$764$	−84.3746	−3.05257
$765$	14.2924	0.516745
$766$	39.8914	1.44133
$767$	14.4937	0.523339
$768$	−20.4579	−0.738212
$769$	−6.88293	−0.248205	−0.124102	−	0.992269i	$-0.539605\pi$
$769$	−6.88293	−0.248205	−0.124102	+	0.992269i	$0.539605\pi$
$770$	8.55074	0.308147
$771$	2.44803	0.0881638
$772$	29.1260	1.04827
$773$	−3.95960	−0.142417	−0.0712084	−	0.997461i	$-0.522686\pi$
$773$	−3.95960	−0.142417	−0.0712084	+	0.997461i	$0.522686\pi$
$774$	53.5968	1.92650
$775$	22.9404	0.824042
$776$	12.2222	0.438752
$777$	−16.2358	−0.582456
$778$	85.3456	3.05979
$779$	29.0769	1.04179
$780$	15.6916	0.561851
$781$	1.20411	0.0430863
$782$	53.1556	1.90084
$783$	12.9012	0.461053
$784$	16.3750	0.584823
$785$	6.09200	0.217433
$786$	−26.2177	−0.935154
$787$	45.8453	1.63421	0.817104	−	0.576491i	$-0.195578\pi$
$787$	45.8453	1.63421	0.817104	+	0.576491i	$0.195578\pi$
$788$	61.8288	2.20256
$789$	0.138187	0.00491958
$790$	4.38983	0.156183
$791$	−54.9474	−1.95370
$792$	10.4889	0.372706
$793$	14.1413	0.502172
$794$	−5.96909	−0.211835
$795$	−4.03911	−0.143252
$796$	64.5397	2.28755
$797$	10.2225	0.362099	0.181049	−	0.983474i	$-0.442051\pi$
$797$	10.2225	0.362099	0.181049	+	0.983474i	$0.442051\pi$
$798$	20.3189	0.719280
$799$	32.1311	1.13672
$800$	−8.96234	−0.316867
$801$	22.0631	0.779560
$802$	−61.7378	−2.18004
$803$	−0.538879	−0.0190166
$804$	−26.0543	−0.918864
$805$	−13.4488	−0.474009
$806$	81.7529	2.87962
$807$	19.5804	0.689262
$808$	−1.62665	−0.0572253
$809$	−16.0923	−0.565776	−0.282888	−	0.959153i	$-0.591293\pi$
$809$	−16.0923	−0.565776	−0.282888	+	0.959153i	$0.591293\pi$
$810$	−10.9882	−0.386086
$811$	31.6005	1.10964	0.554821	−	0.831970i	$-0.312787\pi$
$811$	31.6005	1.10964	0.554821	+	0.831970i	$0.312787\pi$
$812$	45.2116	1.58662
$813$	−1.96934	−0.0690678
$814$	−14.9758	−0.524901
$815$	2.61907	0.0917420
$816$	−10.8126	−0.378517
$817$	29.1943	1.02138
$818$	−53.0905	−1.85626
$819$	54.7320	1.91249
$820$	32.7143	1.14243
$821$	−30.9874	−1.08147	−0.540734	−	0.841194i	$-0.681853\pi$
$821$	−30.9874	−1.08147	−0.540734	+	0.841194i	$0.681853\pi$
$822$	9.64642	0.336458
$823$	19.4490	0.677948	0.338974	−	0.940796i	$-0.389920\pi$
$823$	19.4490	0.677948	0.338974	+	0.940796i	$0.389920\pi$
$824$	−65.0232	−2.26519
$825$	−2.88220	−0.100345
$826$	21.1155	0.734702
$827$	24.5998	0.855418	0.427709	−	0.903917i	$-0.359321\pi$
$827$	24.5998	0.855418	0.427709	+	0.903917i	$0.359321\pi$
$828$	−35.3073	−1.22701
$829$	54.7323	1.90093	0.950466	−	0.310829i	$-0.100607\pi$
$829$	54.7323	1.90093	0.950466	+	0.310829i	$0.100607\pi$
$830$	21.8502	0.758430
$831$	4.93125	0.171063
$832$	−63.0239	−2.18496
$833$	−37.2063	−1.28912
$834$	−10.2073	−0.353450
$835$	11.9847	0.414749
$836$	12.2276	0.422902
$837$	22.1734	0.766426
$838$	68.1890	2.35555
$839$	−11.1746	−0.385791	−0.192895	−	0.981219i	$-0.561788\pi$
$839$	−11.1746	−0.385791	−0.192895	+	0.981219i	$0.561788\pi$
$840$	10.6816	0.368550
$841$	−18.1230	−0.624931
$842$	−10.1922	−0.351245
$843$	−4.17694	−0.143862
$844$	19.4494	0.669476
$845$	22.5990	0.777430
$846$	−32.7125	−1.12468
$847$	−3.65167	−0.125473
$848$	−15.0189	−0.515751
$849$	15.7328	0.539950
$850$	−57.0195	−1.95575
$851$	23.5543	0.807432
$852$	3.21921	0.110288
$853$	51.3123	1.75690	0.878451	−	0.477833i	$-0.158578\pi$
$853$	51.3123	1.75690	0.878451	+	0.477833i	$0.158578\pi$
$854$	20.6020	0.704987
$855$	−7.92600	−0.271063
$856$	35.4799	1.21268
$857$	34.2787	1.17094	0.585468	−	0.810695i	$-0.300911\pi$
$857$	34.2787	1.17094	0.585468	+	0.810695i	$0.300911\pi$
$858$	−10.2714	−0.350659
$859$	−7.28584	−0.248590	−0.124295	−	0.992245i	$-0.539667\pi$
$859$	−7.28584	−0.248590	−0.124295	+	0.992245i	$0.539667\pi$
$860$	32.8464	1.12005
$861$	−23.2157	−0.791189
$862$	70.3234	2.39523
$863$	5.89083	0.200526	0.100263	−	0.994961i	$-0.468032\pi$
$863$	5.89083	0.200526	0.100263	+	0.994961i	$0.468032\pi$
$864$	−8.66272	−0.294712
$865$	6.30916	0.214518
$866$	8.56569	0.291074
$867$	12.4609	0.423193
$868$	77.7055	2.63750
$869$	−1.87471	−0.0635953
$870$	5.49982	0.186461
$871$	−58.5939	−1.98538
$872$	39.6721	1.34347
$873$	7.24105	0.245072
$874$	−29.4779	−0.997104
$875$	32.2496	1.09024
$876$	−1.44071	−0.0486771
$877$	40.3604	1.36288	0.681438	−	0.731876i	$-0.261355\pi$
$877$	40.3604	1.36288	0.681438	+	0.731876i	$0.261355\pi$
$878$	−92.4781	−3.12099
$879$	−13.4793	−0.454646
$880$	2.52338	0.0850630
$881$	0.235924	0.00794847	0.00397423	−	0.999992i	$-0.498735\pi$
$881$	0.235924	0.00794847	0.00397423	+	0.999992i	$0.498735\pi$
$882$	37.8795	1.27547
$883$	4.85529	0.163393	0.0816967	−	0.996657i	$-0.473966\pi$
$883$	4.85529	0.163393	0.0816967	+	0.996657i	$0.473966\pi$
$884$	−132.573	−4.45890
$885$	1.67582	0.0563321
$886$	50.0768	1.68236
$887$	−9.54027	−0.320331	−0.160165	−	0.987090i	$-0.551203\pi$
$887$	−9.54027	−0.320331	−0.160165	+	0.987090i	$0.551203\pi$
$888$	−18.7077	−0.627791
$889$	−37.1660	−1.24651
$890$	20.7247	0.694692
$891$	4.69261	0.157208
$892$	−48.4479	−1.62216
$893$	−17.8186	−0.596276
$894$	−9.27757	−0.310288
$895$	−3.11699	−0.104189
$896$	−75.6443	−2.52710
$897$	16.1551	0.539402
$898$	37.5380	1.25266
$899$	18.6944	0.623493
$900$	37.8738	1.26246
$901$	34.1249	1.13687
$902$	−21.4140	−0.713008
$903$	−23.3095	−0.775691
$904$	−63.3132	−2.10577
$905$	−17.6815	−0.587753
$906$	−6.76258	−0.224672
$907$	34.8979	1.15877	0.579383	−	0.815055i	$-0.303294\pi$
$907$	34.8979	1.15877	0.579383	+	0.815055i	$0.303294\pi$
$908$	−22.4066	−0.743590
$909$	−0.963708	−0.0319642
$910$	51.4118	1.70428
$911$	18.8272	0.623774	0.311887	−	0.950119i	$-0.399039\pi$
$911$	18.8272	0.623774	0.311887	+	0.950119i	$0.399039\pi$
$912$	5.99622	0.198555
$913$	−9.33130	−0.308821
$914$	−12.6840	−0.419548
$915$	1.63507	0.0540537
$916$	−24.4945	−0.809322
$917$	−56.0424	−1.85068
$918$	−55.1133	−1.81901
$919$	−34.1204	−1.12553	−0.562764	−	0.826618i	$-0.690262\pi$
$919$	−34.1204	−1.12553	−0.562764	+	0.826618i	$0.690262\pi$
$920$	−15.4965	−0.510903
$921$	4.90580	0.161652
$922$	74.7730	2.46252
$923$	7.23974	0.238299
$924$	−9.76285	−0.321174
$925$	−25.2665	−0.830757
$926$	−79.8124	−2.62280
$927$	−38.5231	−1.26526
$928$	−7.30352	−0.239750
$929$	15.4209	0.505943	0.252972	−	0.967474i	$-0.418592\pi$
$929$	15.4209	0.505943	0.252972	+	0.967474i	$0.418592\pi$
$930$	9.45258	0.309962
$931$	20.6331	0.676221
$932$	−9.73484	−0.318875
$933$	5.23258	0.171307
$934$	13.2334	0.433009
$935$	−5.73345	−0.187504
$936$	63.0650	2.06134
$937$	−19.2755	−0.629705	−0.314852	−	0.949141i	$-0.601955\pi$
$937$	−19.2755	−0.629705	−0.314852	+	0.949141i	$0.601955\pi$
$938$	−85.3637	−2.78722
$939$	−9.19955	−0.300216
$940$	−20.0476	−0.653881
$941$	33.5809	1.09471	0.547354	−	0.836901i	$-0.315635\pi$
$941$	33.5809	1.09471	0.547354	+	0.836901i	$0.315635\pi$
$942$	−10.6612	−0.347360
$943$	33.6805	1.09679
$944$	6.23131	0.202812
$945$	13.9442	0.453603
$946$	−21.5005	−0.699041
$947$	40.2761	1.30880	0.654398	−	0.756150i	$-0.272922\pi$
$947$	40.2761	1.30880	0.654398	+	0.756150i	$0.272922\pi$
$948$	−5.01211	−0.162786
$949$	−3.24004	−0.105176
$950$	31.6206	1.02591
$951$	22.2289	0.720820
$952$	−90.2447	−2.92485
$953$	−2.55027	−0.0826112	−0.0413056	−	0.999147i	$-0.513152\pi$
$953$	−2.55027	−0.0826112	−0.0413056	+	0.999147i	$0.513152\pi$
$954$	−34.7423	−1.12482
$955$	−21.9398	−0.709954
$956$	26.7497	0.865147
$957$	−2.34875	−0.0759242
$958$	73.3838	2.37092
$959$	20.6200	0.665854
$960$	−7.28706	−0.235189
$961$	1.13017	0.0364572
$962$	−90.0427	−2.90309
$963$	21.0201	0.677363
$964$	31.8199	1.02485
$965$	7.57358	0.243802
$966$	23.5358	0.757254
$967$	−42.7396	−1.37441	−0.687207	−	0.726462i	$-0.741163\pi$
$967$	−42.7396	−1.37441	−0.687207	+	0.726462i	$0.741163\pi$
$968$	−4.20764	−0.135239
$969$	−13.6242	−0.437673
$970$	6.80179	0.218392
$971$	39.5789	1.27015	0.635073	−	0.772452i	$-0.280970\pi$
$971$	39.5789	1.27015	0.635073	+	0.772452i	$0.280970\pi$
$972$	56.6015	1.81549
$973$	−21.8189	−0.699483
$974$	−56.5166	−1.81091
$975$	−17.3294	−0.554985
$976$	6.07979	0.194609
$977$	33.9475	1.08608	0.543038	−	0.839708i	$-0.317274\pi$
$977$	33.9475	1.08608	0.543038	+	0.839708i	$0.317274\pi$
$978$	−4.58344	−0.146562
$979$	−8.85064	−0.282868
$980$	23.2142	0.741550
$981$	23.5038	0.750417
$982$	−52.7678	−1.68389
$983$	−19.7724	−0.630642	−0.315321	−	0.948985i	$-0.602112\pi$
$983$	−19.7724	−0.630642	−0.315321	+	0.948985i	$0.602112\pi$
$984$	−26.7503	−0.852769
$985$	16.0772	0.512263
$986$	−46.4659	−1.47978
$987$	14.2268	0.452843
$988$	73.5193	2.33896
$989$	33.8165	1.07530
$990$	5.83718	0.185518
$991$	13.4205	0.426315	0.213158	−	0.977018i	$-0.431625\pi$
$991$	13.4205	0.426315	0.213158	+	0.977018i	$0.431625\pi$
$992$	−12.5526	−0.398546
$993$	18.0327	0.572249
$994$	10.5474	0.334542
$995$	16.7821	0.532029
$996$	−24.9475	−0.790492
$997$	−11.4825	−0.363654	−0.181827	−	0.983331i	$-0.558201\pi$
$997$	−11.4825	−0.363654	−0.181827	+	0.983331i	$0.558201\pi$
$998$	−92.9936	−2.94366
$999$	−24.4218	−0.772672

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.e.1.10	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.e.1.10	✓	119	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.39877 q^{2} +0.712166 q^{3} +3.75408 q^{4} +0.976168 q^{5} -1.70832 q^{6} -3.65167 q^{7} -4.20764 q^{8} -2.49282 q^{9} +O(q^{10})\)	\(q-2.39877 q^{2} +0.712166 q^{3} +3.75408 q^{4} +0.976168 q^{5} -1.70832 q^{6} -3.65167 q^{7} -4.20764 q^{8} -2.49282 q^{9} -2.34160 q^{10} +1.00000 q^{11} +2.67353 q^{12} +6.01255 q^{13} +8.75950 q^{14} +0.695193 q^{15} +2.58498 q^{16} -5.87343 q^{17} +5.97969 q^{18} +3.25716 q^{19} +3.66462 q^{20} -2.60059 q^{21} -2.39877 q^{22} +3.77285 q^{23} -2.99654 q^{24} -4.04710 q^{25} -14.4227 q^{26} -3.91180 q^{27} -13.7087 q^{28} -3.29803 q^{29} -1.66761 q^{30} -5.66835 q^{31} +2.21451 q^{32} +0.712166 q^{33} +14.0890 q^{34} -3.56464 q^{35} -9.35826 q^{36} +6.24312 q^{37} -7.81316 q^{38} +4.28193 q^{39} -4.10736 q^{40} +8.92708 q^{41} +6.23822 q^{42} +8.96313 q^{43} +3.75408 q^{44} -2.43341 q^{45} -9.05018 q^{46} -5.47059 q^{47} +1.84094 q^{48} +6.33468 q^{49} +9.70804 q^{50} -4.18285 q^{51} +22.5716 q^{52} -5.81005 q^{53} +9.38350 q^{54} +0.976168 q^{55} +15.3649 q^{56} +2.31964 q^{57} +7.91121 q^{58} +2.41058 q^{59} +2.60981 q^{60} +2.35196 q^{61} +13.5970 q^{62} +9.10295 q^{63} -10.4821 q^{64} +5.86926 q^{65} -1.70832 q^{66} -9.74527 q^{67} -22.0493 q^{68} +2.68689 q^{69} +8.55074 q^{70} +1.20411 q^{71} +10.4889 q^{72} -0.538879 q^{73} -14.9758 q^{74} -2.88220 q^{75} +12.2276 q^{76} -3.65167 q^{77} -10.2714 q^{78} -1.87471 q^{79} +2.52338 q^{80} +4.69261 q^{81} -21.4140 q^{82} -9.33130 q^{83} -9.76285 q^{84} -5.73345 q^{85} -21.5005 q^{86} -2.34875 q^{87} -4.20764 q^{88} -8.85064 q^{89} +5.83718 q^{90} -21.9558 q^{91} +14.1636 q^{92} -4.03680 q^{93} +13.1227 q^{94} +3.17953 q^{95} +1.57710 q^{96} -2.90476 q^{97} -15.1954 q^{98} -2.49282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * q^99

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