LMFDB - Embedded newform 6017.2.a.c.1.1

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:	$1$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.78235 q^{2} -0.369906 q^{3} +5.74149 q^{4} -3.02150 q^{5} +1.02921 q^{6} -3.23246 q^{7} -10.4101 q^{8} -2.86317 q^{9} +O(q^{10})$	\(q-2.78235 q^{2} -0.369906 q^{3} +5.74149 q^{4} -3.02150 q^{5} +1.02921 q^{6} -3.23246 q^{7} -10.4101 q^{8} -2.86317 q^{9} +8.40687 q^{10} +1.00000 q^{11} -2.12381 q^{12} -1.60091 q^{13} +8.99385 q^{14} +1.11767 q^{15} +17.4817 q^{16} -5.40853 q^{17} +7.96635 q^{18} -8.12643 q^{19} -17.3479 q^{20} +1.19571 q^{21} -2.78235 q^{22} +7.83182 q^{23} +3.85077 q^{24} +4.12945 q^{25} +4.45431 q^{26} +2.16882 q^{27} -18.5591 q^{28} +8.88985 q^{29} -3.10975 q^{30} -4.53381 q^{31} -27.8200 q^{32} -0.369906 q^{33} +15.0484 q^{34} +9.76687 q^{35} -16.4389 q^{36} +4.86447 q^{37} +22.6106 q^{38} +0.592188 q^{39} +31.4542 q^{40} -4.18181 q^{41} -3.32688 q^{42} -10.7011 q^{43} +5.74149 q^{44} +8.65106 q^{45} -21.7909 q^{46} +3.41901 q^{47} -6.46659 q^{48} +3.44880 q^{49} -11.4896 q^{50} +2.00065 q^{51} -9.19164 q^{52} -1.59181 q^{53} -6.03443 q^{54} -3.02150 q^{55} +33.6504 q^{56} +3.00602 q^{57} -24.7347 q^{58} +3.95433 q^{59} +6.41709 q^{60} +8.90823 q^{61} +12.6147 q^{62} +9.25508 q^{63} +42.4417 q^{64} +4.83716 q^{65} +1.02921 q^{66} -6.11719 q^{67} -31.0530 q^{68} -2.89703 q^{69} -27.1749 q^{70} +10.6733 q^{71} +29.8060 q^{72} -9.38126 q^{73} -13.5347 q^{74} -1.52751 q^{75} -46.6578 q^{76} -3.23246 q^{77} -1.64768 q^{78} +14.4939 q^{79} -52.8210 q^{80} +7.78725 q^{81} +11.6353 q^{82} +12.8185 q^{83} +6.86513 q^{84} +16.3419 q^{85} +29.7743 q^{86} -3.28841 q^{87} -10.4101 q^{88} +1.63937 q^{89} -24.0703 q^{90} +5.17489 q^{91} +44.9663 q^{92} +1.67708 q^{93} -9.51290 q^{94} +24.5540 q^{95} +10.2908 q^{96} -10.9231 q^{97} -9.59577 q^{98} -2.86317 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * 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 $

$2$	−2.78235	−1.96742	−0.983710	−	0.179760i	$-0.942468\pi$
$2$	−2.78235	−1.96742	−0.983710	+	0.179760i	$0.942468\pi$
$3$	−0.369906	−0.213565	−0.106783	−	0.994282i	$-0.534055\pi$
$3$	−0.369906	−0.213565	−0.106783	+	0.994282i	$0.534055\pi$
$4$	5.74149	2.87074
$5$	−3.02150	−1.35125	−0.675627	−	0.737243i	$-0.736127\pi$
$5$	−3.02150	−1.35125	−0.675627	+	0.737243i	$0.736127\pi$
$6$	1.02921	0.420173
$7$	−3.23246	−1.22176	−0.610878	−	0.791725i	$-0.709183\pi$
$7$	−3.23246	−1.22176	−0.610878	+	0.791725i	$0.709183\pi$
$8$	−10.4101	−3.68054
$9$	−2.86317	−0.954390
$10$	8.40687	2.65849
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.12381	−0.613091
$13$	−1.60091	−0.444014	−0.222007	−	0.975045i	$-0.571261\pi$
$13$	−1.60091	−0.444014	−0.222007	+	0.975045i	$0.571261\pi$
$14$	8.99385	2.40371
$15$	1.11767	0.288581
$16$	17.4817	4.37043
$17$	−5.40853	−1.31176	−0.655881	−	0.754865i	$-0.727703\pi$
$17$	−5.40853	−1.31176	−0.655881	+	0.754865i	$0.727703\pi$
$18$	7.96635	1.87769
$19$	−8.12643	−1.86433	−0.932166	−	0.362031i	$-0.882083\pi$
$19$	−8.12643	−1.86433	−0.932166	+	0.362031i	$0.882083\pi$
$20$	−17.3479	−3.87911
$21$	1.19571	0.260924
$22$	−2.78235	−0.593200
$23$	7.83182	1.63305	0.816523	−	0.577313i	$-0.195899\pi$
$23$	7.83182	1.63305	0.816523	+	0.577313i	$0.195899\pi$
$24$	3.85077	0.786036
$25$	4.12945	0.825889
$26$	4.45431	0.873562
$27$	2.16882	0.417390
$28$	−18.5591	−3.50735
$29$	8.88985	1.65080	0.825402	−	0.564545i	$-0.190948\pi$
$29$	8.88985	1.65080	0.825402	+	0.564545i	$0.190948\pi$
$30$	−3.10975	−0.567760
$31$	−4.53381	−0.814297	−0.407148	−	0.913362i	$-0.633477\pi$
$31$	−4.53381	−0.814297	−0.407148	+	0.913362i	$0.633477\pi$
$32$	−27.8200	−4.91794
$33$	−0.369906	−0.0643923
$34$	15.0484	2.58079
$35$	9.76687	1.65090
$36$	−16.4389	−2.73981
$37$	4.86447	0.799715	0.399857	−	0.916577i	$-0.369060\pi$
$37$	4.86447	0.799715	0.399857	+	0.916577i	$0.369060\pi$
$38$	22.6106	3.66793
$39$	0.592188	0.0948259
$40$	31.4542	4.97335
$41$	−4.18181	−0.653089	−0.326545	−	0.945182i	$-0.605884\pi$
$41$	−4.18181	−0.653089	−0.326545	+	0.945182i	$0.605884\pi$
$42$	−3.32688	−0.513348
$43$	−10.7011	−1.63190	−0.815952	−	0.578120i	$-0.803787\pi$
$43$	−10.7011	−1.63190	−0.815952	+	0.578120i	$0.803787\pi$
$44$	5.74149	0.865562
$45$	8.65106	1.28962
$46$	−21.7909	−3.21289
$47$	3.41901	0.498714	0.249357	−	0.968412i	$-0.419781\pi$
$47$	3.41901	0.498714	0.249357	+	0.968412i	$0.419781\pi$
$48$	−6.46659	−0.933372
$49$	3.44880	0.492685
$50$	−11.4896	−1.62487
$51$	2.00065	0.280147
$52$	−9.19164	−1.27465
$53$	−1.59181	−0.218652	−0.109326	−	0.994006i	$-0.534869\pi$
$53$	−1.59181	−0.218652	−0.109326	+	0.994006i	$0.534869\pi$
$54$	−6.03443	−0.821181
$55$	−3.02150	−0.407419
$56$	33.6504	4.49672
$57$	3.00602	0.398156
$58$	−24.7347	−3.24783
$59$	3.95433	0.514811	0.257405	−	0.966304i	$-0.417132\pi$
$59$	3.95433	0.514811	0.257405	+	0.966304i	$0.417132\pi$
$60$	6.41709	0.828443
$61$	8.90823	1.14058	0.570291	−	0.821443i	$-0.306830\pi$
$61$	8.90823	1.14058	0.570291	+	0.821443i	$0.306830\pi$
$62$	12.6147	1.60206
$63$	9.25508	1.16603
$64$	42.4417	5.30522
$65$	4.83716	0.599976
$66$	1.02921	0.126687
$67$	−6.11719	−0.747333	−0.373667	−	0.927563i	$-0.621900\pi$
$67$	−6.11719	−0.747333	−0.373667	+	0.927563i	$0.621900\pi$
$68$	−31.0530	−3.76573
$69$	−2.89703	−0.348762
$70$	−27.1749	−3.24802
$71$	10.6733	1.26669	0.633343	−	0.773872i	$-0.281682\pi$
$71$	10.6733	1.26669	0.633343	+	0.773872i	$0.281682\pi$
$72$	29.8060	3.51267
$73$	−9.38126	−1.09799	−0.548997	−	0.835824i	$-0.684990\pi$
$73$	−9.38126	−1.09799	−0.548997	+	0.835824i	$0.684990\pi$
$74$	−13.5347	−1.57338
$75$	−1.52751	−0.176381
$76$	−46.6578	−5.35202
$77$	−3.23246	−0.368373
$78$	−1.64768	−0.186563
$79$	14.4939	1.63069	0.815347	−	0.578972i	$-0.196546\pi$
$79$	14.4939	1.63069	0.815347	+	0.578972i	$0.196546\pi$
$80$	−52.8210	−5.90557
$81$	7.78725	0.865250
$82$	11.6353	1.28490
$83$	12.8185	1.40701	0.703507	−	0.710688i	$-0.251616\pi$
$83$	12.8185	1.40701	0.703507	+	0.710688i	$0.251616\pi$
$84$	6.86513	0.749047
$85$	16.3419	1.77252
$86$	29.7743	3.21064
$87$	−3.28841	−0.352554
$88$	−10.4101	−1.10973
$89$	1.63937	0.173773	0.0868865	−	0.996218i	$-0.472308\pi$
$89$	1.63937	0.173773	0.0868865	+	0.996218i	$0.472308\pi$
$90$	−24.0703	−2.53723
$91$	5.17489	0.542476
$92$	44.9663	4.68806
$93$	1.67708	0.173905
$94$	−9.51290	−0.981181
$95$	24.5540	2.51919
$96$	10.2908	1.05030
$97$	−10.9231	−1.10907	−0.554536	−	0.832159i	$-0.687104\pi$
$97$	−10.9231	−1.10907	−0.554536	+	0.832159i	$0.687104\pi$
$98$	−9.59577	−0.969320
$99$	−2.86317	−0.287759
$100$	23.7092	2.37092
$101$	14.8175	1.47440	0.737201	−	0.675674i	$-0.236147\pi$
$101$	14.8175	1.47440	0.737201	+	0.675674i	$0.236147\pi$
$102$	−5.56651	−0.551166
$103$	−0.149015	−0.0146828	−0.00734142	−	0.999973i	$-0.502337\pi$
$103$	−0.149015	−0.0146828	−0.00734142	+	0.999973i	$0.502337\pi$
$104$	16.6658	1.63421
$105$	−3.61282	−0.352575
$106$	4.42898	0.430180
$107$	0.761562	0.0736230	0.0368115	−	0.999322i	$-0.488280\pi$
$107$	0.761562	0.0736230	0.0368115	+	0.999322i	$0.488280\pi$
$108$	12.4523	1.19822
$109$	−7.34630	−0.703648	−0.351824	−	0.936066i	$-0.614438\pi$
$109$	−7.34630	−0.703648	−0.351824	+	0.936066i	$0.614438\pi$
$110$	8.40687	0.801564
$111$	−1.79940	−0.170791
$112$	−56.5090	−5.33960
$113$	12.5236	1.17812	0.589060	−	0.808089i	$-0.299498\pi$
$113$	12.5236	1.17812	0.589060	+	0.808089i	$0.299498\pi$
$114$	−8.36380	−0.783341
$115$	−23.6638	−2.20666
$116$	51.0410	4.73904
$117$	4.58369	0.423762
$118$	−11.0024	−1.01285
$119$	17.4829	1.60265
$120$	−11.6351	−1.06213
$121$	1.00000	0.0909091
$122$	−24.7859	−2.24401
$123$	1.54688	0.139477
$124$	−26.0308	−2.33764
$125$	2.63037	0.235268
$126$	−25.7509	−2.29407
$127$	−8.02483	−0.712088	−0.356044	−	0.934469i	$-0.615875\pi$
$127$	−8.02483	−0.712088	−0.356044	+	0.934469i	$0.615875\pi$
$128$	−62.4478	−5.51966
$129$	3.95840	0.348518
$130$	−13.4587	−1.18041
$131$	−3.50424	−0.306167	−0.153083	−	0.988213i	$-0.548920\pi$
$131$	−3.50424	−0.306167	−0.153083	+	0.988213i	$0.548920\pi$
$132$	−2.12381	−0.184854
$133$	26.2684	2.27776
$134$	17.0202	1.47032
$135$	−6.55309	−0.564000
$136$	56.3036	4.82799
$137$	5.60118	0.478541	0.239271	−	0.970953i	$-0.423092\pi$
$137$	5.60118	0.478541	0.239271	+	0.970953i	$0.423092\pi$
$138$	8.06057	0.686162
$139$	1.03733	0.0879850	0.0439925	−	0.999032i	$-0.485992\pi$
$139$	1.03733	0.0879850	0.0439925	+	0.999032i	$0.485992\pi$
$140$	56.0764	4.73932
$141$	−1.26471	−0.106508
$142$	−29.6968	−2.49210
$143$	−1.60091	−0.133875
$144$	−50.0531	−4.17110
$145$	−26.8607	−2.23066
$146$	26.1020	2.16022
$147$	−1.27573	−0.105220
$148$	27.9293	2.29578
$149$	−16.2552	−1.33168	−0.665840	−	0.746095i	$-0.731927\pi$
$149$	−16.2552	−1.33168	−0.665840	+	0.746095i	$0.731927\pi$
$150$	4.25006	0.347016
$151$	13.3041	1.08267	0.541337	−	0.840805i	$-0.317918\pi$
$151$	13.3041	1.08267	0.541337	+	0.840805i	$0.317918\pi$
$152$	84.5974	6.86175
$153$	15.4855	1.25193
$154$	8.99385	0.724745
$155$	13.6989	1.10032
$156$	3.40004	0.272221
$157$	19.3566	1.54482	0.772412	−	0.635122i	$-0.219050\pi$
$157$	19.3566	1.54482	0.772412	+	0.635122i	$0.219050\pi$
$158$	−40.3272	−3.20826
$159$	0.588820	0.0466964
$160$	84.0582	6.64538
$161$	−25.3160	−1.99518
$162$	−21.6669	−1.70231
$163$	−10.1512	−0.795106	−0.397553	−	0.917579i	$-0.630140\pi$
$163$	−10.1512	−0.795106	−0.397553	+	0.917579i	$0.630140\pi$
$164$	−24.0098	−1.87485
$165$	1.11767	0.0870105
$166$	−35.6656	−2.76819
$167$	−6.56475	−0.507996	−0.253998	−	0.967205i	$-0.581746\pi$
$167$	−6.56475	−0.507996	−0.253998	+	0.967205i	$0.581746\pi$
$168$	−12.4475	−0.960343
$169$	−10.4371	−0.802852
$170$	−45.4688	−3.48730
$171$	23.2674	1.77930
$172$	−61.4403	−4.68478
$173$	−7.38958	−0.561819	−0.280910	−	0.959734i	$-0.590636\pi$
$173$	−7.38958	−0.561819	−0.280910	+	0.959734i	$0.590636\pi$
$174$	9.14952	0.693623
$175$	−13.3483	−1.00903
$176$	17.4817	1.31773
$177$	−1.46273	−0.109946
$178$	−4.56131	−0.341884
$179$	−24.4864	−1.83020	−0.915098	−	0.403230i	$-0.867887\pi$
$179$	−24.4864	−1.83020	−0.915098	+	0.403230i	$0.867887\pi$
$180$	49.6700	3.70218
$181$	8.74888	0.650299	0.325149	−	0.945663i	$-0.394585\pi$
$181$	8.74888	0.650299	0.325149	+	0.945663i	$0.394585\pi$
$182$	−14.3984	−1.06728
$183$	−3.29521	−0.243589
$184$	−81.5304	−6.01050
$185$	−14.6980	−1.08062
$186$	−4.66624	−0.342145
$187$	−5.40853	−0.395511
$188$	19.6302	1.43168
$189$	−7.01063	−0.509948
$190$	−68.3179	−4.95630
$191$	−9.71590	−0.703018	−0.351509	−	0.936185i	$-0.614331\pi$
$191$	−9.71590	−0.703018	−0.351509	+	0.936185i	$0.614331\pi$
$192$	−15.6994	−1.13301
$193$	2.94363	0.211887	0.105944	−	0.994372i	$-0.466214\pi$
$193$	2.94363	0.211887	0.105944	+	0.994372i	$0.466214\pi$
$194$	30.3919	2.18201
$195$	−1.78929	−0.128134
$196$	19.8012	1.41437
$197$	3.85864	0.274917	0.137458	−	0.990508i	$-0.456107\pi$
$197$	3.85864	0.274917	0.137458	+	0.990508i	$0.456107\pi$
$198$	7.96635	0.566144
$199$	11.0852	0.785809	0.392904	−	0.919579i	$-0.371470\pi$
$199$	11.0852	0.785809	0.392904	+	0.919579i	$0.371470\pi$
$200$	−42.9882	−3.03972
$201$	2.26278	0.159604
$202$	−41.2277	−2.90077
$203$	−28.7361	−2.01688
$204$	11.4867	0.804229
$205$	12.6353	0.882490
$206$	0.414611	0.0288873
$207$	−22.4238	−1.55856
$208$	−27.9868	−1.94053
$209$	−8.12643	−0.562117
$210$	10.0521	0.693664
$211$	18.7079	1.28790	0.643951	−	0.765067i	$-0.277294\pi$
$211$	18.7079	1.28790	0.643951	+	0.765067i	$0.277294\pi$
$212$	−9.13936	−0.627694
$213$	−3.94811	−0.270520
$214$	−2.11894	−0.144847
$215$	32.3334	2.20512
$216$	−22.5777	−1.53622
$217$	14.6554	0.994871
$218$	20.4400	1.38437
$219$	3.47018	0.234493
$220$	−17.3479	−1.16960
$221$	8.65859	0.582440
$222$	5.00656	0.336018
$223$	0.533409	0.0357197	0.0178598	−	0.999841i	$-0.494315\pi$
$223$	0.533409	0.0357197	0.0178598	+	0.999841i	$0.494315\pi$
$224$	89.9272	6.00851
$225$	−11.8233	−0.788221
$226$	−34.8451	−2.31786
$227$	−6.99185	−0.464065	−0.232033	−	0.972708i	$-0.574538\pi$
$227$	−6.99185	−0.464065	−0.232033	+	0.972708i	$0.574538\pi$
$228$	17.2590	1.14301
$229$	2.12478	0.140410	0.0702048	−	0.997533i	$-0.477635\pi$
$229$	2.12478	0.140410	0.0702048	+	0.997533i	$0.477635\pi$
$230$	65.8411	4.34143
$231$	1.19571	0.0786717
$232$	−92.5447	−6.07586
$233$	−19.0126	−1.24556	−0.622778	−	0.782399i	$-0.713996\pi$
$233$	−19.0126	−1.24556	−0.622778	+	0.782399i	$0.713996\pi$
$234$	−12.7534	−0.833719
$235$	−10.3305	−0.673890
$236$	22.7038	1.47789
$237$	−5.36139	−0.348260
$238$	−48.6435	−3.15309
$239$	3.58014	0.231580	0.115790	−	0.993274i	$-0.463060\pi$
$239$	3.58014	0.231580	0.115790	+	0.993274i	$0.463060\pi$
$240$	19.5388	1.26122
$241$	15.0887	0.971950	0.485975	−	0.873973i	$-0.338465\pi$
$241$	15.0887	0.971950	0.485975	+	0.873973i	$0.338465\pi$
$242$	−2.78235	−0.178856
$243$	−9.38701	−0.602177
$244$	51.1465	3.27432
$245$	−10.4205	−0.665743
$246$	−4.30396	−0.274410
$247$	13.0097	0.827789
$248$	47.1976	2.99705
$249$	−4.74164	−0.300489
$250$	−7.31863	−0.462871
$251$	−9.64924	−0.609055	−0.304527	−	0.952504i	$-0.598498\pi$
$251$	−9.64924	−0.609055	−0.304527	+	0.952504i	$0.598498\pi$
$252$	53.1380	3.34738
$253$	7.83182	0.492382
$254$	22.3279	1.40098
$255$	−6.04495	−0.378549
$256$	88.8685	5.55428
$257$	−15.1105	−0.942568	−0.471284	−	0.881982i	$-0.656209\pi$
$257$	−15.1105	−0.942568	−0.471284	+	0.881982i	$0.656209\pi$
$258$	−11.0137	−0.685681
$259$	−15.7242	−0.977055
$260$	27.7725	1.72238
$261$	−25.4532	−1.57551
$262$	9.75003	0.602359
$263$	28.1168	1.73376	0.866879	−	0.498519i	$-0.166123\pi$
$263$	28.1168	1.73376	0.866879	+	0.498519i	$0.166123\pi$
$264$	3.85077	0.236999
$265$	4.80965	0.295454
$266$	−73.0879	−4.48131
$267$	−0.606413	−0.0371119
$268$	−35.1218	−2.14540
$269$	−14.6323	−0.892148	−0.446074	−	0.894996i	$-0.647178\pi$
$269$	−14.6323	−0.892148	−0.446074	+	0.894996i	$0.647178\pi$
$270$	18.2330	1.10963
$271$	14.2099	0.863190	0.431595	−	0.902068i	$-0.357951\pi$
$271$	14.2099	0.863190	0.431595	+	0.902068i	$0.357951\pi$
$272$	−94.5504	−5.73296
$273$	−1.91422	−0.115854
$274$	−15.5845	−0.941492
$275$	4.12945	0.249015
$276$	−16.6333	−1.00121
$277$	−10.3365	−0.621063	−0.310531	−	0.950563i	$-0.600507\pi$
$277$	−10.3365	−0.621063	−0.310531	+	0.950563i	$0.600507\pi$
$278$	−2.88621	−0.173103
$279$	12.9811	0.777156
$280$	−101.675	−6.07622
$281$	29.9564	1.78705	0.893526	−	0.449012i	$-0.148224\pi$
$281$	29.9564	1.78705	0.893526	+	0.449012i	$0.148224\pi$
$282$	3.51888	0.209546
$283$	−19.4708	−1.15742	−0.578711	−	0.815533i	$-0.696444\pi$
$283$	−19.4708	−1.15742	−0.578711	+	0.815533i	$0.696444\pi$
$284$	61.2805	3.63633
$285$	−9.08267	−0.538011
$286$	4.45431	0.263389
$287$	13.5175	0.797915
$288$	79.6535	4.69363
$289$	12.2522	0.720717
$290$	74.7359	4.38864
$291$	4.04052	0.236859
$292$	−53.8624	−3.15206
$293$	−0.306046	−0.0178794	−0.00893969	−	0.999960i	$-0.502846\pi$
$293$	−0.306046	−0.0178794	−0.00893969	+	0.999960i	$0.502846\pi$
$294$	3.54953	0.207013
$295$	−11.9480	−0.695640
$296$	−50.6399	−2.94338
$297$	2.16882	0.125848
$298$	45.2278	2.61997
$299$	−12.5381	−0.725095
$300$	−8.77016	−0.506346
$301$	34.5909	1.99379
$302$	−37.0168	−2.13008
$303$	−5.48110	−0.314881
$304$	−142.064	−8.14793
$305$	−26.9162	−1.54122
$306$	−43.0862	−2.46308
$307$	33.1585	1.89245	0.946226	−	0.323505i	$-0.104861\pi$
$307$	33.1585	1.89245	0.946226	+	0.323505i	$0.104861\pi$
$308$	−18.5591	−1.05750
$309$	0.0551214	0.00313574
$310$	−38.1152	−2.16480
$311$	−10.5200	−0.596533	−0.298267	−	0.954483i	$-0.596408\pi$
$311$	−10.5200	−0.596533	−0.298267	+	0.954483i	$0.596408\pi$
$312$	−6.16476	−0.349011
$313$	−16.6291	−0.939932	−0.469966	−	0.882685i	$-0.655734\pi$
$313$	−16.6291	−0.939932	−0.469966	+	0.882685i	$0.655734\pi$
$314$	−53.8569	−3.03932
$315$	−27.9642	−1.57560
$316$	83.2168	4.68131
$317$	10.6028	0.595515	0.297758	−	0.954641i	$-0.403761\pi$
$317$	10.6028	0.595515	0.297758	+	0.954641i	$0.403761\pi$
$318$	−1.63830	−0.0918715
$319$	8.88985	0.497736
$320$	−128.238	−7.16870
$321$	−0.281706	−0.0157233
$322$	70.4381	3.92536
$323$	43.9521	2.44556
$324$	44.7104	2.48391
$325$	−6.61089	−0.366706
$326$	28.2443	1.56431
$327$	2.71744	0.150275
$328$	43.5333	2.40372
$329$	−11.0518	−0.609307
$330$	−3.10975	−0.171186
$331$	−16.7418	−0.920214	−0.460107	−	0.887863i	$-0.652189\pi$
$331$	−16.7418	−0.920214	−0.460107	+	0.887863i	$0.652189\pi$
$332$	73.5973	4.03918
$333$	−13.9278	−0.763240
$334$	18.2655	0.999442
$335$	18.4831	1.00984
$336$	20.9030	1.14035
$337$	−0.917724	−0.0499916	−0.0249958	−	0.999688i	$-0.507957\pi$
$337$	−0.917724	−0.0499916	−0.0249958	+	0.999688i	$0.507957\pi$
$338$	29.0396	1.57955
$339$	−4.63255	−0.251606
$340$	93.8266	5.08846
$341$	−4.53381	−0.245520
$342$	−64.7380	−3.50063
$343$	11.4791	0.619814
$344$	111.400	6.00629
$345$	8.75338	0.471266
$346$	20.5604	1.10533
$347$	2.27193	0.121963	0.0609817	−	0.998139i	$-0.480577\pi$
$347$	2.27193	0.121963	0.0609817	+	0.998139i	$0.480577\pi$
$348$	−18.8804	−1.01209
$349$	−4.03550	−0.216015	−0.108008	−	0.994150i	$-0.534447\pi$
$349$	−4.03550	−0.216015	−0.108008	+	0.994150i	$0.534447\pi$
$350$	37.1396	1.98520
$351$	−3.47210	−0.185327
$352$	−27.8200	−1.48281
$353$	26.8131	1.42712	0.713559	−	0.700596i	$-0.247082\pi$
$353$	26.8131	1.42712	0.713559	+	0.700596i	$0.247082\pi$
$354$	4.06984	0.216309
$355$	−32.2493	−1.71161
$356$	9.41243	0.498858
$357$	−6.46701	−0.342270
$358$	68.1297	3.60077
$359$	−27.5883	−1.45606	−0.728029	−	0.685547i	$-0.759563\pi$
$359$	−27.5883	−1.45606	−0.728029	+	0.685547i	$0.759563\pi$
$360$	−90.0588	−4.74652
$361$	47.0389	2.47573
$362$	−24.3425	−1.27941
$363$	−0.369906	−0.0194150
$364$	29.7116	1.55731
$365$	28.3455	1.48367
$366$	9.16843	0.479242
$367$	4.42264	0.230860	0.115430	−	0.993316i	$-0.463175\pi$
$367$	4.42264	0.230860	0.115430	+	0.993316i	$0.463175\pi$
$368$	136.914	7.13712
$369$	11.9732	0.623302
$370$	40.8950	2.12603
$371$	5.14546	0.267139
$372$	9.62896	0.499238
$373$	18.8035	0.973611	0.486805	−	0.873510i	$-0.338162\pi$
$373$	18.8035	0.973611	0.486805	+	0.873510i	$0.338162\pi$
$374$	15.0484	0.778136
$375$	−0.972990	−0.0502450
$376$	−35.5924	−1.83554
$377$	−14.2319	−0.732980
$378$	19.5060	1.00328
$379$	15.1435	0.777869	0.388935	−	0.921265i	$-0.372843\pi$
$379$	15.1435	0.777869	0.388935	+	0.921265i	$0.372843\pi$
$380$	140.977	7.23194
$381$	2.96843	0.152077
$382$	27.0331	1.38313
$383$	−23.6585	−1.20889	−0.604445	−	0.796647i	$-0.706605\pi$
$383$	−23.6585	−1.20889	−0.604445	+	0.796647i	$0.706605\pi$
$384$	23.0998	1.17881
$385$	9.76687	0.497766
$386$	−8.19022	−0.416871
$387$	30.6391	1.55747
$388$	−62.7149	−3.18386
$389$	−5.21352	−0.264336	−0.132168	−	0.991227i	$-0.542194\pi$
$389$	−5.21352	−0.264336	−0.132168	+	0.991227i	$0.542194\pi$
$390$	4.97845	0.252093
$391$	−42.3586	−2.14217
$392$	−35.9025	−1.81335
$393$	1.29624	0.0653866
$394$	−10.7361	−0.540877
$395$	−43.7934	−2.20348
$396$	−16.4389	−0.826084
$397$	5.59129	0.280619	0.140310	−	0.990108i	$-0.455190\pi$
$397$	5.59129	0.280619	0.140310	+	0.990108i	$0.455190\pi$
$398$	−30.8429	−1.54602
$399$	−9.71682	−0.486450
$400$	72.1899	3.60949
$401$	9.67610	0.483201	0.241601	−	0.970376i	$-0.422328\pi$
$401$	9.67610	0.483201	0.241601	+	0.970376i	$0.422328\pi$
$402$	−6.29586	−0.314009
$403$	7.25825	0.361559
$404$	85.0748	4.23263
$405$	−23.5292	−1.16917
$406$	79.9540	3.96805
$407$	4.86447	0.241123
$408$	−20.8270	−1.03109
$409$	−13.6318	−0.674050	−0.337025	−	0.941496i	$-0.609421\pi$
$409$	−13.6318	−0.674050	−0.337025	+	0.941496i	$0.609421\pi$
$410$	−35.1560	−1.73623
$411$	−2.07191	−0.102200
$412$	−0.855566	−0.0421507
$413$	−12.7822	−0.628972
$414$	62.3910	3.06635
$415$	−38.7311	−1.90123
$416$	44.5375	2.18363
$417$	−0.383714	−0.0187905
$418$	22.6106	1.10592
$419$	24.0912	1.17693	0.588465	−	0.808523i	$-0.299732\pi$
$419$	24.0912	1.17693	0.588465	+	0.808523i	$0.299732\pi$
$420$	−20.7430	−1.01215
$421$	−15.2927	−0.745322	−0.372661	−	0.927967i	$-0.621555\pi$
$421$	−15.2927	−0.745322	−0.372661	+	0.927967i	$0.621555\pi$
$422$	−52.0519	−2.53385
$423$	−9.78922	−0.475968
$424$	16.5710	0.804757
$425$	−22.3342	−1.08337
$426$	10.9850	0.532226
$427$	−28.7955	−1.39351
$428$	4.37250	0.211353
$429$	0.592188	0.0285911
$430$	−89.9629	−4.33839
$431$	27.7104	1.33476	0.667382	−	0.744716i	$-0.267415\pi$
$431$	27.7104	1.33476	0.667382	+	0.744716i	$0.267415\pi$
$432$	37.9147	1.82417
$433$	1.25243	0.0601879	0.0300939	−	0.999547i	$-0.490419\pi$
$433$	1.25243	0.0601879	0.0300939	+	0.999547i	$0.490419\pi$
$434$	−40.7764	−1.95733
$435$	9.93592	0.476391
$436$	−42.1787	−2.01999
$437$	−63.6447	−3.04454
$438$	−9.65528	−0.461347
$439$	29.1559	1.39154	0.695768	−	0.718266i	$-0.255064\pi$
$439$	29.1559	1.39154	0.695768	+	0.718266i	$0.255064\pi$
$440$	31.4542	1.49952
$441$	−9.87449	−0.470214
$442$	−24.0913	−1.14590
$443$	6.65121	0.316009	0.158004	−	0.987438i	$-0.449494\pi$
$443$	6.65121	0.316009	0.158004	+	0.987438i	$0.449494\pi$
$444$	−10.3312	−0.490298
$445$	−4.95335	−0.234811
$446$	−1.48413	−0.0702757
$447$	6.01290	0.284401
$448$	−137.191	−6.48168
$449$	−31.4116	−1.48240	−0.741202	−	0.671282i	$-0.765744\pi$
$449$	−31.4116	−1.48240	−0.741202	+	0.671282i	$0.765744\pi$
$450$	32.8966	1.55076
$451$	−4.18181	−0.196914
$452$	71.9041	3.38208
$453$	−4.92128	−0.231222
$454$	19.4538	0.913012
$455$	−15.6359	−0.733024
$456$	−31.2931	−1.46543
$457$	−13.1643	−0.615799	−0.307900	−	0.951419i	$-0.599626\pi$
$457$	−13.1643	−0.615799	−0.307900	+	0.951419i	$0.599626\pi$
$458$	−5.91190	−0.276245
$459$	−11.7301	−0.547516
$460$	−135.866	−6.33476
$461$	−17.5224	−0.816098	−0.408049	−	0.912960i	$-0.633791\pi$
$461$	−17.5224	−0.816098	−0.408049	+	0.912960i	$0.633791\pi$
$462$	−3.32688	−0.154780
$463$	−26.2381	−1.21939	−0.609694	−	0.792637i	$-0.708708\pi$
$463$	−26.2381	−1.21939	−0.609694	+	0.792637i	$0.708708\pi$
$464$	155.410	7.21473
$465$	−5.06730	−0.234991
$466$	52.8997	2.45053
$467$	40.8247	1.88914	0.944571	−	0.328307i	$-0.106478\pi$
$467$	40.8247	1.88914	0.944571	+	0.328307i	$0.106478\pi$
$468$	26.3172	1.21651
$469$	19.7736	0.913058
$470$	28.7432	1.32583
$471$	−7.16012	−0.329921
$472$	−41.1652	−1.89478
$473$	−10.7011	−0.492037
$474$	14.9173	0.685173
$475$	−33.5577	−1.53973
$476$	100.378	4.60080
$477$	4.55762	0.208679
$478$	−9.96121	−0.455615
$479$	42.5468	1.94401	0.972007	−	0.234951i	$-0.0754929\pi$
$479$	42.5468	1.94401	0.972007	+	0.234951i	$0.0754929\pi$
$480$	−31.0936	−1.41922
$481$	−7.78761	−0.355084
$482$	−41.9821	−1.91223
$483$	9.36455	0.426102
$484$	5.74149	0.260977
$485$	33.0041	1.49864
$486$	26.1180	1.18474
$487$	−19.8231	−0.898272	−0.449136	−	0.893463i	$-0.648268\pi$
$487$	−19.8231	−0.898272	−0.449136	+	0.893463i	$0.648268\pi$
$488$	−92.7360	−4.19796
$489$	3.75500	0.169807
$490$	28.9936	1.30980
$491$	−13.1086	−0.591581	−0.295790	−	0.955253i	$-0.595583\pi$
$491$	−13.1086	−0.591581	−0.295790	+	0.955253i	$0.595583\pi$
$492$	8.88138	0.400403
$493$	−48.0810	−2.16546
$494$	−36.1977	−1.62861
$495$	8.65106	0.388836
$496$	−79.2589	−3.55883
$497$	−34.5009	−1.54758
$498$	13.1929	0.591189
$499$	−8.04610	−0.360193	−0.180097	−	0.983649i	$-0.557641\pi$
$499$	−8.04610	−0.360193	−0.180097	+	0.983649i	$0.557641\pi$
$500$	15.1023	0.675394
$501$	2.42834	0.108490
$502$	26.8476	1.19827
$503$	−12.6910	−0.565862	−0.282931	−	0.959140i	$-0.591307\pi$
$503$	−12.6910	−0.565862	−0.282931	+	0.959140i	$0.591307\pi$
$504$	−96.3468	−4.29163
$505$	−44.7712	−1.99229
$506$	−21.7909	−0.968723
$507$	3.86073	0.171461
$508$	−46.0745	−2.04422
$509$	21.8502	0.968492	0.484246	−	0.874932i	$-0.339094\pi$
$509$	21.8502	0.968492	0.484246	+	0.874932i	$0.339094\pi$
$510$	16.8192	0.744766
$511$	30.3245	1.34148
$512$	−122.368	−5.40794
$513$	−17.6248	−0.778153
$514$	42.0428	1.85443
$515$	0.450247	0.0198403
$516$	22.7271	1.00051
$517$	3.41901	0.150368
$518$	43.7503	1.92228
$519$	2.73345	0.119985
$520$	−50.3555	−2.20824
$521$	−4.52379	−0.198191	−0.0990955	−	0.995078i	$-0.531595\pi$
$521$	−4.52379	−0.198191	−0.0990955	+	0.995078i	$0.531595\pi$
$522$	70.8197	3.09969
$523$	−21.0835	−0.921918	−0.460959	−	0.887422i	$-0.652494\pi$
$523$	−21.0835	−0.921918	−0.460959	+	0.887422i	$0.652494\pi$
$524$	−20.1196	−0.878927
$525$	4.93760	0.215495
$526$	−78.2309	−3.41103
$527$	24.5213	1.06816
$528$	−6.46659	−0.281422
$529$	38.3373	1.66684
$530$	−13.3821	−0.581283
$531$	−11.3219	−0.491330
$532$	150.820	6.53886
$533$	6.69473	0.289981
$534$	1.68725	0.0730146
$535$	−2.30106	−0.0994835
$536$	63.6808	2.75059
$537$	9.05765	0.390866
$538$	40.7123	1.75523
$539$	3.44880	0.148550
$540$	−37.6245	−1.61910
$541$	2.02550	0.0870831	0.0435416	−	0.999052i	$-0.486136\pi$
$541$	2.02550	0.0870831	0.0435416	+	0.999052i	$0.486136\pi$
$542$	−39.5369	−1.69826
$543$	−3.23626	−0.138881
$544$	150.466	6.45116
$545$	22.1968	0.950807
$546$	5.32605	0.227934
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	32.1591	1.37377
$549$	−25.5058	−1.08856
$550$	−11.4896	−0.489917
$551$	−72.2428	−3.07765
$552$	30.1586	1.28363
$553$	−46.8511	−1.99231
$554$	28.7599	1.22189
$555$	5.43688	0.230783
$556$	5.95581	0.252582
$557$	−32.1446	−1.36201	−0.681005	−	0.732278i	$-0.738457\pi$
$557$	−32.1446	−1.36201	−0.681005	+	0.732278i	$0.738457\pi$
$558$	−36.1179	−1.52899
$559$	17.1316	0.724588
$560$	170.742	7.21516
$561$	2.00065	0.0844674
$562$	−83.3494	−3.51588
$563$	17.2461	0.726838	0.363419	−	0.931626i	$-0.381609\pi$
$563$	17.2461	0.726838	0.363419	+	0.931626i	$0.381609\pi$
$564$	−7.26134	−0.305757
$565$	−37.8400	−1.59194
$566$	54.1748	2.27713
$567$	−25.1720	−1.05712
$568$	−111.110	−4.66209
$569$	33.9742	1.42427	0.712137	−	0.702040i	$-0.247727\pi$
$569$	33.9742	1.42427	0.712137	+	0.702040i	$0.247727\pi$
$570$	25.2712	1.05849
$571$	6.72731	0.281529	0.140765	−	0.990043i	$-0.455044\pi$
$571$	6.72731	0.281529	0.140765	+	0.990043i	$0.455044\pi$
$572$	−9.19164	−0.384322
$573$	3.59397	0.150140
$574$	−37.6106	−1.56984
$575$	32.3411	1.34872
$576$	−121.518	−5.06325
$577$	−29.0145	−1.20789	−0.603944	−	0.797027i	$-0.706405\pi$
$577$	−29.0145	−1.20789	−0.603944	+	0.797027i	$0.706405\pi$
$578$	−34.0899	−1.41795
$579$	−1.08887	−0.0452518
$580$	−154.220	−6.40365
$581$	−41.4353	−1.71903
$582$	−11.2421	−0.466002
$583$	−1.59181	−0.0659260
$584$	97.6603	4.04121
$585$	−13.8496	−0.572611
$586$	0.851527	0.0351763
$587$	8.41581	0.347358	0.173679	−	0.984802i	$-0.444435\pi$
$587$	8.41581	0.347358	0.173679	+	0.984802i	$0.444435\pi$
$588$	−7.32459	−0.302061
$589$	36.8437	1.51812
$590$	33.2436	1.36862
$591$	−1.42733	−0.0587126
$592$	85.0394	3.49510
$593$	−8.04906	−0.330535	−0.165268	−	0.986249i	$-0.552849\pi$
$593$	−8.04906	−0.330535	−0.165268	+	0.986249i	$0.552849\pi$
$594$	−6.03443	−0.247595
$595$	−52.8244	−2.16559
$596$	−93.3292	−3.82291
$597$	−4.10048	−0.167821
$598$	34.8853	1.42657
$599$	−31.2227	−1.27572	−0.637862	−	0.770151i	$-0.720181\pi$
$599$	−31.2227	−1.27572	−0.637862	+	0.770151i	$0.720181\pi$
$600$	15.9016	0.649179
$601$	−29.4266	−1.20033	−0.600167	−	0.799874i	$-0.704899\pi$
$601$	−29.4266	−1.20033	−0.600167	+	0.799874i	$0.704899\pi$
$602$	−96.2441	−3.92262
$603$	17.5145	0.713247
$604$	76.3855	3.10808
$605$	−3.02150	−0.122841
$606$	15.2503	0.619503
$607$	−40.6510	−1.64997	−0.824987	−	0.565151i	$-0.808818\pi$
$607$	−40.6510	−1.64997	−0.824987	+	0.565151i	$0.808818\pi$
$608$	226.078	9.16866
$609$	10.6297	0.430735
$610$	74.8904	3.03222
$611$	−5.47355	−0.221436
$612$	88.9101	3.59398
$613$	26.1867	1.05767	0.528836	−	0.848724i	$-0.322629\pi$
$613$	26.1867	1.05767	0.528836	+	0.848724i	$0.322629\pi$
$614$	−92.2585	−3.72325
$615$	−4.67389	−0.188469
$616$	33.6504	1.35581
$617$	11.0233	0.443781	0.221890	−	0.975072i	$-0.428777\pi$
$617$	11.0233	0.443781	0.221890	+	0.975072i	$0.428777\pi$
$618$	−0.153367	−0.00616933
$619$	22.1315	0.889542	0.444771	−	0.895644i	$-0.353285\pi$
$619$	22.1315	0.889542	0.444771	+	0.895644i	$0.353285\pi$
$620$	78.6521	3.15874
$621$	16.9858	0.681617
$622$	29.2703	1.17363
$623$	−5.29920	−0.212308
$624$	10.3525	0.414430
$625$	−28.5949	−1.14380
$626$	46.2680	1.84924
$627$	3.00602	0.120049
$628$	111.136	4.43480
$629$	−26.3097	−1.04903
$630$	77.8063	3.09988
$631$	42.4264	1.68897	0.844484	−	0.535581i	$-0.179907\pi$
$631$	42.4264	1.68897	0.844484	+	0.535581i	$0.179907\pi$
$632$	−150.884	−6.00184
$633$	−6.92015	−0.275051
$634$	−29.5009	−1.17163
$635$	24.2470	0.962212
$636$	3.38070	0.134054
$637$	−5.52123	−0.218759
$638$	−24.7347	−0.979257
$639$	−30.5594	−1.20891
$640$	188.686	7.45847
$641$	−0.856853	−0.0338437	−0.0169218	−	0.999857i	$-0.505387\pi$
$641$	−0.856853	−0.0338437	−0.0169218	+	0.999857i	$0.505387\pi$
$642$	0.783807	0.0309344
$643$	−42.6715	−1.68280	−0.841400	−	0.540413i	$-0.818268\pi$
$643$	−42.6715	−1.68280	−0.841400	+	0.540413i	$0.818268\pi$
$644$	−145.352	−5.72766
$645$	−11.9603	−0.470936
$646$	−122.290	−4.81144
$647$	−2.60122	−0.102265	−0.0511323	−	0.998692i	$-0.516283\pi$
$647$	−2.60122	−0.102265	−0.0511323	+	0.998692i	$0.516283\pi$
$648$	−81.0664	−3.18459
$649$	3.95433	0.155221
$650$	18.3938	0.721466
$651$	−5.42110	−0.212470
$652$	−58.2832	−2.28255
$653$	−19.9689	−0.781443	−0.390721	−	0.920509i	$-0.627774\pi$
$653$	−19.9689	−0.781443	−0.390721	+	0.920509i	$0.627774\pi$
$654$	−7.56087	−0.295654
$655$	10.5881	0.413709
$656$	−73.1053	−2.85428
$657$	26.8601	1.04791
$658$	30.7501	1.19876
$659$	−42.1816	−1.64316	−0.821581	−	0.570091i	$-0.806908\pi$
$659$	−42.1816	−1.64316	−0.821581	+	0.570091i	$0.806908\pi$
$660$	6.41709	0.249785
$661$	−33.4395	−1.30065	−0.650324	−	0.759657i	$-0.725367\pi$
$661$	−33.4395	−1.30065	−0.650324	+	0.759657i	$0.725367\pi$
$662$	46.5817	1.81045
$663$	−3.20286	−0.124389
$664$	−133.443	−5.17857
$665$	−79.3698	−3.07783
$666$	38.7521	1.50161
$667$	69.6237	2.69584
$668$	−37.6915	−1.45833
$669$	−0.197311	−0.00762848
$670$	−51.4264	−1.98678
$671$	8.90823	0.343899
$672$	−33.2646	−1.28321
$673$	−31.6600	−1.22040	−0.610201	−	0.792246i	$-0.708912\pi$
$673$	−31.6600	−1.22040	−0.610201	+	0.792246i	$0.708912\pi$
$674$	2.55343	0.0983546
$675$	8.95603	0.344718
$676$	−59.9243	−2.30478
$677$	−16.5866	−0.637474	−0.318737	−	0.947843i	$-0.603259\pi$
$677$	−16.5866	−0.637474	−0.318737	+	0.947843i	$0.603259\pi$
$678$	12.8894	0.495014
$679$	35.3085	1.35502
$680$	−170.121	−6.52385
$681$	2.58633	0.0991082
$682$	12.6147	0.483041
$683$	20.4749	0.783449	0.391724	−	0.920083i	$-0.371879\pi$
$683$	20.4749	0.783449	0.391724	+	0.920083i	$0.371879\pi$
$684$	133.589	5.10791
$685$	−16.9240	−0.646631
$686$	−31.9390	−1.21944
$687$	−0.785969	−0.0299866
$688$	−187.074	−7.13212
$689$	2.54835	0.0970844
$690$	−24.3550	−0.927179
$691$	15.1715	0.577151	0.288576	−	0.957457i	$-0.406818\pi$
$691$	15.1715	0.577151	0.288576	+	0.957457i	$0.406818\pi$
$692$	−42.4272	−1.61284
$693$	9.25508	0.351571
$694$	−6.32130	−0.239953
$695$	−3.13428	−0.118890
$696$	34.2328	1.29759
$697$	22.6175	0.856697
$698$	11.2282	0.424993
$699$	7.03287	0.266008
$700$	−76.6390	−2.89668
$701$	−13.4535	−0.508133	−0.254067	−	0.967187i	$-0.581768\pi$
$701$	−13.4535	−0.508133	−0.254067	+	0.967187i	$0.581768\pi$
$702$	9.66060	0.364616
$703$	−39.5308	−1.49093
$704$	42.4417	1.59958
$705$	3.82133	0.143920
$706$	−74.6035	−2.80774
$707$	−47.8971	−1.80136
$708$	−8.39826	−0.315626
$709$	−37.6205	−1.41287	−0.706433	−	0.707780i	$-0.749697\pi$
$709$	−37.6205	−1.41287	−0.706433	+	0.707780i	$0.749697\pi$
$710$	89.7289	3.36747
$711$	−41.4986	−1.55632
$712$	−17.0661	−0.639579
$713$	−35.5080	−1.32978
$714$	17.9935	0.673390
$715$	4.83716	0.180900
$716$	−140.588	−5.25403
$717$	−1.32431	−0.0494574
$718$	76.7605	2.86468
$719$	16.9198	0.631000	0.315500	−	0.948926i	$-0.397828\pi$
$719$	16.9198	0.631000	0.315500	+	0.948926i	$0.397828\pi$
$720$	151.235	5.63621
$721$	0.481684	0.0179388
$722$	−130.879	−4.87081
$723$	−5.58140	−0.207575
$724$	50.2316	1.86684
$725$	36.7102	1.36338
$726$	1.02921	0.0381975
$727$	11.4690	0.425362	0.212681	−	0.977122i	$-0.431781\pi$
$727$	11.4690	0.425362	0.212681	+	0.977122i	$0.431781\pi$
$728$	−53.8714	−1.99661
$729$	−19.8894	−0.736646
$730$	−78.8671	−2.91900
$731$	57.8773	2.14067
$732$	−18.9194	−0.699281
$733$	−17.4214	−0.643473	−0.321736	−	0.946829i	$-0.604266\pi$
$733$	−17.4214	−0.643473	−0.321736	+	0.946829i	$0.604266\pi$
$734$	−12.3053	−0.454198
$735$	3.85462	0.142180
$736$	−217.881	−8.03122
$737$	−6.11719	−0.225329
$738$	−33.3138	−1.22630
$739$	−12.3820	−0.455479	−0.227740	−	0.973722i	$-0.573134\pi$
$739$	−12.3820	−0.455479	−0.227740	+	0.973722i	$0.573134\pi$
$740$	−84.3884	−3.10218
$741$	−4.81237	−0.176787
$742$	−14.3165	−0.525575
$743$	−7.06478	−0.259182	−0.129591	−	0.991568i	$-0.541366\pi$
$743$	−7.06478	−0.259182	−0.129591	+	0.991568i	$0.541366\pi$
$744$	−17.4587	−0.640066
$745$	49.1151	1.79944
$746$	−52.3181	−1.91550
$747$	−36.7016	−1.34284
$748$	−31.0530	−1.13541
$749$	−2.46172	−0.0899493
$750$	2.70720	0.0988531
$751$	−23.6430	−0.862746	−0.431373	−	0.902174i	$-0.641971\pi$
$751$	−23.6430	−0.862746	−0.431373	+	0.902174i	$0.641971\pi$
$752$	59.7703	2.17960
$753$	3.56931	0.130073
$754$	39.5982	1.44208
$755$	−40.1984	−1.46297
$756$	−40.2514	−1.46393
$757$	38.9078	1.41413	0.707064	−	0.707150i	$-0.250019\pi$
$757$	38.9078	1.41413	0.707064	+	0.707150i	$0.250019\pi$
$758$	−42.1346	−1.53040
$759$	−2.89703	−0.105156
$760$	−255.611	−9.27198
$761$	−8.90114	−0.322666	−0.161333	−	0.986900i	$-0.551579\pi$
$761$	−8.90114	−0.322666	−0.161333	+	0.986900i	$0.551579\pi$
$762$	−8.25922	−0.299200
$763$	23.7466	0.859685
$764$	−55.7837	−2.01818
$765$	−46.7895	−1.69168
$766$	65.8262	2.37840
$767$	−6.33055	−0.228583
$768$	−32.8730	−1.18620
$769$	28.1138	1.01381	0.506905	−	0.862002i	$-0.330789\pi$
$769$	28.1138	1.01381	0.506905	+	0.862002i	$0.330789\pi$
$770$	−27.1749	−0.979315
$771$	5.58947	0.201300
$772$	16.9008	0.608274
$773$	30.9353	1.11267	0.556333	−	0.830959i	$-0.312208\pi$
$773$	30.9353	1.11267	0.556333	+	0.830959i	$0.312208\pi$
$774$	−85.2488	−3.06420
$775$	−18.7221	−0.672519
$776$	113.711	4.08199
$777$	5.81648	0.208665
$778$	14.5059	0.520060
$779$	33.9832	1.21758
$780$	−10.2732	−0.367840
$781$	10.6733	0.381920
$782$	117.857	4.21454
$783$	19.2805	0.689029
$784$	60.2909	2.15325
$785$	−58.4859	−2.08745
$786$	−3.60659	−0.128643
$787$	−28.3099	−1.00914	−0.504570	−	0.863371i	$-0.668349\pi$
$787$	−28.3099	−1.00914	−0.504570	+	0.863371i	$0.668349\pi$
$788$	22.1543	0.789215
$789$	−10.4006	−0.370270
$790$	121.849	4.33518
$791$	−40.4820	−1.43937
$792$	29.8060	1.05911
$793$	−14.2613	−0.506434
$794$	−15.5570	−0.552096
$795$	−1.77912	−0.0630988
$796$	63.6456	2.25586
$797$	−4.89838	−0.173509	−0.0867547	−	0.996230i	$-0.527650\pi$
$797$	−4.89838	−0.173509	−0.0867547	+	0.996230i	$0.527650\pi$
$798$	27.0356	0.957051
$799$	−18.4918	−0.654194
$800$	−114.881	−4.06167
$801$	−4.69380	−0.165847
$802$	−26.9223	−0.950660
$803$	−9.38126	−0.331057
$804$	12.9917	0.458183
$805$	76.4923	2.69600
$806$	−20.1950	−0.711339
$807$	5.41258	0.190532
$808$	−154.253	−5.42660
$809$	−36.9797	−1.30014	−0.650068	−	0.759876i	$-0.725260\pi$
$809$	−36.9797	−1.30014	−0.650068	+	0.759876i	$0.725260\pi$
$810$	65.4664	2.30026
$811$	−20.5398	−0.721250	−0.360625	−	0.932711i	$-0.617437\pi$
$811$	−20.5398	−0.721250	−0.360625	+	0.932711i	$0.617437\pi$
$812$	−164.988	−5.78994
$813$	−5.25632	−0.184347
$814$	−13.5347	−0.474391
$815$	30.6719	1.07439
$816$	34.9748	1.22436
$817$	86.9618	3.04241
$818$	37.9285	1.32614
$819$	−14.8166	−0.517734
$820$	72.5457	2.53340
$821$	38.5094	1.34399	0.671993	−	0.740557i	$-0.265438\pi$
$821$	38.5094	1.34399	0.671993	+	0.740557i	$0.265438\pi$
$822$	5.76479	0.201070
$823$	54.4941	1.89955	0.949773	−	0.312939i	$-0.101314\pi$
$823$	54.4941	1.89955	0.949773	+	0.312939i	$0.101314\pi$
$824$	1.55126	0.0540408
$825$	−1.52751	−0.0531810
$826$	35.5647	1.23745
$827$	−0.725418	−0.0252253	−0.0126126	−	0.999920i	$-0.504015\pi$
$827$	−0.725418	−0.0252253	−0.0126126	+	0.999920i	$0.504015\pi$
$828$	−128.746	−4.47424
$829$	27.6414	0.960026	0.480013	−	0.877261i	$-0.340632\pi$
$829$	27.6414	0.960026	0.480013	+	0.877261i	$0.340632\pi$
$830$	107.764	3.74053
$831$	3.82355	0.132637
$832$	−67.9456	−2.35559
$833$	−18.6529	−0.646286
$834$	1.06763	0.0369689
$835$	19.8354	0.686432
$836$	−46.6578	−1.61370
$837$	−9.83302	−0.339879
$838$	−67.0301	−2.31552
$839$	−40.7885	−1.40818	−0.704088	−	0.710112i	$-0.748644\pi$
$839$	−40.7885	−1.40818	−0.704088	+	0.710112i	$0.748644\pi$
$840$	37.6100	1.29767
$841$	50.0295	1.72516
$842$	42.5498	1.46636
$843$	−11.0811	−0.381652
$844$	107.411	3.69724
$845$	31.5356	1.08486
$846$	27.2371	0.936429
$847$	−3.23246	−0.111069
$848$	−27.8276	−0.955603
$849$	7.20238	0.247185
$850$	62.1417	2.13144
$851$	38.0977	1.30597
$852$	−22.6680	−0.776594
$853$	−4.53519	−0.155282	−0.0776409	−	0.996981i	$-0.524739\pi$
$853$	−4.53519	−0.155282	−0.0776409	+	0.996981i	$0.524739\pi$
$854$	80.1193	2.74163
$855$	−70.3023	−2.40429
$856$	−7.92798	−0.270973
$857$	−16.1709	−0.552386	−0.276193	−	0.961102i	$-0.589073\pi$
$857$	−16.1709	−0.552386	−0.276193	+	0.961102i	$0.589073\pi$
$858$	−1.64768	−0.0562507
$859$	−29.1048	−0.993043	−0.496521	−	0.868024i	$-0.665390\pi$
$859$	−29.1048	−0.993043	−0.496521	+	0.868024i	$0.665390\pi$
$860$	185.642	6.33033
$861$	−5.00022	−0.170407
$862$	−77.1002	−2.62604
$863$	40.5085	1.37892	0.689462	−	0.724322i	$-0.257847\pi$
$863$	40.5085	1.37892	0.689462	+	0.724322i	$0.257847\pi$
$864$	−60.3367	−2.05270
$865$	22.3276	0.759161
$866$	−3.48470	−0.118415
$867$	−4.53216	−0.153920
$868$	84.1436	2.85602
$869$	14.4939	0.491673
$870$	−27.6452	−0.937261
$871$	9.79309	0.331826
$872$	76.4760	2.58981
$873$	31.2747	1.05849
$874$	177.082	5.98989
$875$	−8.50258	−0.287440
$876$	19.9240	0.673170
$877$	−50.0943	−1.69156	−0.845782	−	0.533528i	$-0.820866\pi$
$877$	−50.0943	−1.69156	−0.845782	+	0.533528i	$0.820866\pi$
$878$	−81.1221	−2.73774
$879$	0.113208	0.00381842
$880$	−52.8210	−1.78060
$881$	24.5202	0.826106	0.413053	−	0.910707i	$-0.364462\pi$
$881$	24.5202	0.826106	0.413053	+	0.910707i	$0.364462\pi$
$882$	27.4743	0.925109
$883$	8.22067	0.276648	0.138324	−	0.990387i	$-0.455829\pi$
$883$	8.22067	0.276648	0.138324	+	0.990387i	$0.455829\pi$
$884$	49.7132	1.67204
$885$	4.41964	0.148565
$886$	−18.5060	−0.621722
$887$	−26.9097	−0.903539	−0.451769	−	0.892135i	$-0.649207\pi$
$887$	−26.9097	−0.903539	−0.451769	+	0.892135i	$0.649207\pi$
$888$	18.7320	0.628605
$889$	25.9399	0.869997
$890$	13.7820	0.461973
$891$	7.78725	0.260883
$892$	3.06256	0.102542
$893$	−27.7844	−0.929769
$894$	−16.7300	−0.559536
$895$	73.9855	2.47306
$896$	201.860	6.74367
$897$	4.63791	0.154855
$898$	87.3981	2.91651
$899$	−40.3049	−1.34424
$900$	−67.8834	−2.26278
$901$	8.60935	0.286819
$902$	11.6353	0.387412
$903$	−12.7954	−0.425804
$904$	−130.372	−4.33612
$905$	−26.4347	−0.878720
$906$	13.6927	0.454910
$907$	−0.368288	−0.0122288	−0.00611441	−	0.999981i	$-0.501946\pi$
$907$	−0.368288	−0.0122288	−0.00611441	+	0.999981i	$0.501946\pi$
$908$	−40.1436	−1.33221
$909$	−42.4252	−1.40715
$910$	43.5047	1.44217
$911$	50.0968	1.65978	0.829890	−	0.557927i	$-0.188403\pi$
$911$	50.0968	1.65978	0.829890	+	0.557927i	$0.188403\pi$
$912$	52.5503	1.74012
$913$	12.8185	0.424231
$914$	36.6277	1.21154
$915$	9.95646	0.329150
$916$	12.1994	0.403080
$917$	11.3273	0.374061
$918$	32.6374	1.07719
$919$	−3.32382	−0.109643	−0.0548213	−	0.998496i	$-0.517459\pi$
$919$	−3.32382	−0.109643	−0.0548213	+	0.998496i	$0.517459\pi$
$920$	246.344	8.12171
$921$	−12.2655	−0.404162
$922$	48.7534	1.60561
$923$	−17.0870	−0.562426
$924$	6.86513	0.225846
$925$	20.0876	0.660476
$926$	73.0037	2.39905
$927$	0.426654	0.0140132
$928$	−247.316	−8.11855
$929$	−22.0958	−0.724941	−0.362471	−	0.931995i	$-0.618067\pi$
$929$	−22.0958	−0.724941	−0.362471	+	0.931995i	$0.618067\pi$
$930$	14.0990	0.462325
$931$	−28.0264	−0.918529
$932$	−109.161	−3.57567
$933$	3.89140	0.127399
$934$	−113.589	−3.71674
$935$	16.3419	0.534436
$936$	−47.7169	−1.55968
$937$	12.1518	0.396983	0.198492	−	0.980103i	$-0.436396\pi$
$937$	12.1518	0.396983	0.198492	+	0.980103i	$0.436396\pi$
$938$	−55.0170	−1.79637
$939$	6.15120	0.200737
$940$	−59.3127	−1.93457
$941$	30.7389	1.00206	0.501030	−	0.865430i	$-0.332955\pi$
$941$	30.7389	1.00206	0.501030	+	0.865430i	$0.332955\pi$
$942$	19.9220	0.649093
$943$	−32.7512	−1.06653
$944$	69.1286	2.24994
$945$	21.1826	0.689070
$946$	29.7743	0.968045
$947$	32.9084	1.06938	0.534690	−	0.845049i	$-0.320429\pi$
$947$	32.9084	1.06938	0.534690	+	0.845049i	$0.320429\pi$
$948$	−30.7824	−0.999765
$949$	15.0186	0.487524
$950$	93.3693	3.02930
$951$	−3.92206	−0.127181
$952$	−181.999	−5.89862
$953$	−8.92071	−0.288970	−0.144485	−	0.989507i	$-0.546153\pi$
$953$	−8.92071	−0.288970	−0.144485	+	0.989507i	$0.546153\pi$
$954$	−12.6809	−0.410560
$955$	29.3566	0.949956
$956$	20.5553	0.664807
$957$	−3.28841	−0.106299
$958$	−118.380	−3.82469
$959$	−18.1056	−0.584660
$960$	47.4358	1.53099
$961$	−10.4446	−0.336921
$962$	21.6679	0.698600
$963$	−2.18048	−0.0702651
$964$	86.6317	2.79022
$965$	−8.89418	−0.286314
$966$	−26.0555	−0.838321
$967$	43.8786	1.41104	0.705520	−	0.708690i	$-0.250714\pi$
$967$	43.8786	1.41104	0.705520	+	0.708690i	$0.250714\pi$
$968$	−10.4101	−0.334595
$969$	−16.2581	−0.522286
$970$	−91.8291	−2.94846
$971$	−2.58510	−0.0829597	−0.0414798	−	0.999139i	$-0.513207\pi$
$971$	−2.58510	−0.0829597	−0.0414798	+	0.999139i	$0.513207\pi$
$972$	−53.8954	−1.72870
$973$	−3.35312	−0.107496
$974$	55.1550	1.76728
$975$	2.44541	0.0783157
$976$	155.731	4.98484
$977$	40.0582	1.28158	0.640788	−	0.767718i	$-0.278608\pi$
$977$	40.0582	1.28158	0.640788	+	0.767718i	$0.278608\pi$
$978$	−10.4477	−0.334082
$979$	1.63937	0.0523945
$980$	−59.8294	−1.91118
$981$	21.0337	0.671554
$982$	36.4726	1.16389
$983$	−46.8066	−1.49290	−0.746449	−	0.665443i	$-0.768243\pi$
$983$	−46.8066	−1.49290	−0.746449	+	0.665443i	$0.768243\pi$
$984$	−16.1032	−0.513352
$985$	−11.6589	−0.371482
$986$	133.778	4.26037
$987$	4.08813	0.130127
$988$	74.6952	2.37637
$989$	−83.8091	−2.66497
$990$	−24.0703	−0.765005
$991$	8.10580	0.257489	0.128745	−	0.991678i	$-0.458905\pi$
$991$	8.10580	0.257489	0.128745	+	0.991678i	$0.458905\pi$
$992$	126.131	4.00466
$993$	6.19290	0.196526
$994$	95.9938	3.04474
$995$	−33.4939	−1.06183
$996$	−27.2241	−0.862628
$997$	−45.1827	−1.43095	−0.715475	−	0.698638i	$-0.753790\pi$
$997$	−45.1827	−1.43095	−0.715475	+	0.698638i	$0.753790\pi$
$998$	22.3871	0.708651
$999$	10.5502	0.333793

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.1	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.1	✓	106	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)

\(f(q)\)	\(=\)	\(q-2.78235 q^{2} -0.369906 q^{3} +5.74149 q^{4} -3.02150 q^{5} +1.02921 q^{6} -3.23246 q^{7} -10.4101 q^{8} -2.86317 q^{9} +O(q^{10})\)	\(q-2.78235 q^{2} -0.369906 q^{3} +5.74149 q^{4} -3.02150 q^{5} +1.02921 q^{6} -3.23246 q^{7} -10.4101 q^{8} -2.86317 q^{9} +8.40687 q^{10} +1.00000 q^{11} -2.12381 q^{12} -1.60091 q^{13} +8.99385 q^{14} +1.11767 q^{15} +17.4817 q^{16} -5.40853 q^{17} +7.96635 q^{18} -8.12643 q^{19} -17.3479 q^{20} +1.19571 q^{21} -2.78235 q^{22} +7.83182 q^{23} +3.85077 q^{24} +4.12945 q^{25} +4.45431 q^{26} +2.16882 q^{27} -18.5591 q^{28} +8.88985 q^{29} -3.10975 q^{30} -4.53381 q^{31} -27.8200 q^{32} -0.369906 q^{33} +15.0484 q^{34} +9.76687 q^{35} -16.4389 q^{36} +4.86447 q^{37} +22.6106 q^{38} +0.592188 q^{39} +31.4542 q^{40} -4.18181 q^{41} -3.32688 q^{42} -10.7011 q^{43} +5.74149 q^{44} +8.65106 q^{45} -21.7909 q^{46} +3.41901 q^{47} -6.46659 q^{48} +3.44880 q^{49} -11.4896 q^{50} +2.00065 q^{51} -9.19164 q^{52} -1.59181 q^{53} -6.03443 q^{54} -3.02150 q^{55} +33.6504 q^{56} +3.00602 q^{57} -24.7347 q^{58} +3.95433 q^{59} +6.41709 q^{60} +8.90823 q^{61} +12.6147 q^{62} +9.25508 q^{63} +42.4417 q^{64} +4.83716 q^{65} +1.02921 q^{66} -6.11719 q^{67} -31.0530 q^{68} -2.89703 q^{69} -27.1749 q^{70} +10.6733 q^{71} +29.8060 q^{72} -9.38126 q^{73} -13.5347 q^{74} -1.52751 q^{75} -46.6578 q^{76} -3.23246 q^{77} -1.64768 q^{78} +14.4939 q^{79} -52.8210 q^{80} +7.78725 q^{81} +11.6353 q^{82} +12.8185 q^{83} +6.86513 q^{84} +16.3419 q^{85} +29.7743 q^{86} -3.28841 q^{87} -10.4101 q^{88} +1.63937 q^{89} -24.0703 q^{90} +5.17489 q^{91} +44.9663 q^{92} +1.67708 q^{93} -9.51290 q^{94} +24.5540 q^{95} +10.2908 q^{96} -10.9231 q^{97} -9.59577 q^{98} -2.86317 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

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