LMFDB - Embedded newform 4027.2.a.b.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4027,2,Mod(1,4027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4027 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4027.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:	$32.1557568940$
Analytic rank:	$1$
Dimension:	$159$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48250 q^{2} -1.21941 q^{3} +4.16279 q^{4} +0.264971 q^{5} +3.02717 q^{6} -2.37151 q^{7} -5.36913 q^{8} -1.51305 q^{9} +O(q^{10})$	\(q-2.48250 q^{2} -1.21941 q^{3} +4.16279 q^{4} +0.264971 q^{5} +3.02717 q^{6} -2.37151 q^{7} -5.36913 q^{8} -1.51305 q^{9} -0.657790 q^{10} +6.00450 q^{11} -5.07614 q^{12} -1.83620 q^{13} +5.88726 q^{14} -0.323108 q^{15} +5.00327 q^{16} +5.24105 q^{17} +3.75614 q^{18} +3.52827 q^{19} +1.10302 q^{20} +2.89183 q^{21} -14.9062 q^{22} -8.26025 q^{23} +6.54716 q^{24} -4.92979 q^{25} +4.55837 q^{26} +5.50324 q^{27} -9.87210 q^{28} -7.17908 q^{29} +0.802114 q^{30} +0.326356 q^{31} -1.68234 q^{32} -7.32193 q^{33} -13.0109 q^{34} -0.628381 q^{35} -6.29850 q^{36} -1.62800 q^{37} -8.75892 q^{38} +2.23908 q^{39} -1.42267 q^{40} +8.47028 q^{41} -7.17896 q^{42} +6.35210 q^{43} +24.9955 q^{44} -0.400914 q^{45} +20.5061 q^{46} -9.71840 q^{47} -6.10102 q^{48} -1.37596 q^{49} +12.2382 q^{50} -6.39097 q^{51} -7.64373 q^{52} +9.38787 q^{53} -13.6618 q^{54} +1.59102 q^{55} +12.7329 q^{56} -4.30240 q^{57} +17.8221 q^{58} +8.80566 q^{59} -1.34503 q^{60} -0.781021 q^{61} -0.810179 q^{62} +3.58820 q^{63} -5.83013 q^{64} -0.486541 q^{65} +18.1767 q^{66} -14.4187 q^{67} +21.8174 q^{68} +10.0726 q^{69} +1.55995 q^{70} -13.6638 q^{71} +8.12375 q^{72} +7.48284 q^{73} +4.04150 q^{74} +6.01142 q^{75} +14.6875 q^{76} -14.2397 q^{77} -5.55850 q^{78} +10.0509 q^{79} +1.32572 q^{80} -2.17155 q^{81} -21.0274 q^{82} -4.93575 q^{83} +12.0381 q^{84} +1.38873 q^{85} -15.7691 q^{86} +8.75422 q^{87} -32.2390 q^{88} +12.6440 q^{89} +0.995268 q^{90} +4.35456 q^{91} -34.3857 q^{92} -0.397961 q^{93} +24.1259 q^{94} +0.934890 q^{95} +2.05146 q^{96} -8.09283 q^{97} +3.41581 q^{98} -9.08509 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) $ 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9 - 23 * q^10 - 33 * q^11 - 57 * q^12 - 90 * q^13 - 28 * q^14 - 22 * q^15 + 130 * q^16 - 145 * q^17 - 50 * q^18 - 28 * q^19 - 121 * q^20 - 69 * q^21 - 26 * q^22 - 79 * q^23 - 62 * q^24 + 123 * q^25 - 40 * q^26 - 70 * q^27 - 43 * q^28 - 109 * q^29 - 43 * q^30 - 21 * q^31 - 139 * q^32 - 83 * q^33 - 93 * q^35 + 75 * q^36 - 65 * q^37 - 122 * q^38 - 18 * q^39 - 43 * q^40 - 71 * q^41 - 88 * q^42 - 72 * q^43 - 79 * q^44 - 181 * q^45 - 11 * q^46 - 114 * q^47 - 118 * q^48 + 118 * q^49 - 77 * q^50 - 29 * q^51 - 169 * q^52 - 220 * q^53 - 80 * q^54 - 37 * q^55 - 72 * q^56 - 90 * q^57 - 8 * q^58 - 60 * q^59 - 42 * q^60 - 108 * q^61 - 152 * q^62 - 65 * q^63 + 114 * q^64 - 81 * q^65 - 40 * q^66 - 50 * q^67 - 319 * q^68 - 103 * q^69 + 4 * q^70 - 7 * q^71 - 129 * q^72 - 94 * q^73 - 79 * q^74 - 59 * q^75 - 46 * q^76 - 329 * q^77 + 8 * q^78 - 18 * q^79 - 190 * q^80 + 59 * q^81 - 56 * q^82 - 201 * q^83 - 71 * q^84 - 26 * q^85 - 52 * q^86 - 126 * q^87 - 66 * q^88 - 114 * q^89 - 33 * q^90 - 30 * q^91 - 204 * q^92 - 125 * q^93 + 9 * q^94 - 84 * q^95 - 88 * q^96 - 56 * q^97 - 110 * q^98 - 46 * 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 $

$2$	−2.48250	−1.75539	−0.877695	−	0.479219i	$-0.840920\pi$
$2$	−2.48250	−1.75539	−0.877695	+	0.479219i	$0.840920\pi$
$3$	−1.21941	−0.704025	−0.352012	−	0.935995i	$-0.614503\pi$
$3$	−1.21941	−0.704025	−0.352012	+	0.935995i	$0.614503\pi$
$4$	4.16279	2.08140
$5$	0.264971	0.118499	0.0592494	−	0.998243i	$-0.481129\pi$
$5$	0.264971	0.118499	0.0592494	+	0.998243i	$0.481129\pi$
$6$	3.02717	1.23584
$7$	−2.37151	−0.896345	−0.448173	−	0.893947i	$-0.647925\pi$
$7$	−2.37151	−0.896345	−0.448173	+	0.893947i	$0.647925\pi$
$8$	−5.36913	−1.89828
$9$	−1.51305	−0.504349
$10$	−0.657790	−0.208012
$11$	6.00450	1.81042	0.905212	−	0.424960i	$-0.139712\pi$
$11$	6.00450	1.81042	0.905212	+	0.424960i	$0.139712\pi$
$12$	−5.07614	−1.46536
$13$	−1.83620	−0.509271	−0.254635	−	0.967037i	$-0.581955\pi$
$13$	−1.83620	−0.509271	−0.254635	+	0.967037i	$0.581955\pi$
$14$	5.88726	1.57344
$15$	−0.323108	−0.0834260
$16$	5.00327	1.25082
$17$	5.24105	1.27114	0.635571	−	0.772043i	$-0.280765\pi$
$17$	5.24105	1.27114	0.635571	+	0.772043i	$0.280765\pi$
$18$	3.75614	0.885330
$19$	3.52827	0.809441	0.404720	−	0.914440i	$-0.367369\pi$
$19$	3.52827	0.809441	0.404720	+	0.914440i	$0.367369\pi$
$20$	1.10302	0.246643
$21$	2.89183	0.631049
$22$	−14.9062	−3.17800
$23$	−8.26025	−1.72238	−0.861191	−	0.508282i	$-0.830281\pi$
$23$	−8.26025	−1.72238	−0.861191	+	0.508282i	$0.830281\pi$
$24$	6.54716	1.33643
$25$	−4.92979	−0.985958
$26$	4.55837	0.893969
$27$	5.50324	1.05910
$28$	−9.87210	−1.86565
$29$	−7.17908	−1.33312	−0.666561	−	0.745451i	$-0.732234\pi$
$29$	−7.17908	−1.33312	−0.666561	+	0.745451i	$0.732234\pi$
$30$	0.802114	0.146445
$31$	0.326356	0.0586154	0.0293077	−	0.999570i	$-0.490670\pi$
$31$	0.326356	0.0586154	0.0293077	+	0.999570i	$0.490670\pi$
$32$	−1.68234	−0.297399
$33$	−7.32193	−1.27458
$34$	−13.0109	−2.23135
$35$	−0.628381	−0.106216
$36$	−6.29850	−1.04975
$37$	−1.62800	−0.267641	−0.133821	−	0.991006i	$-0.542725\pi$
$37$	−1.62800	−0.267641	−0.133821	+	0.991006i	$0.542725\pi$
$38$	−8.75892	−1.42089
$39$	2.23908	0.358539
$40$	−1.42267	−0.224943
$41$	8.47028	1.32284	0.661418	−	0.750018i	$-0.269955\pi$
$41$	8.47028	1.32284	0.661418	+	0.750018i	$0.269955\pi$
$42$	−7.17896	−1.10774
$43$	6.35210	0.968686	0.484343	−	0.874878i	$-0.339059\pi$
$43$	6.35210	0.968686	0.484343	+	0.874878i	$0.339059\pi$
$44$	24.9955	3.76821
$45$	−0.400914	−0.0597647
$46$	20.5061	3.02345
$47$	−9.71840	−1.41757	−0.708787	−	0.705423i	$-0.750757\pi$
$47$	−9.71840	−1.41757	−0.708787	+	0.705423i	$0.750757\pi$
$48$	−6.10102	−0.880607
$49$	−1.37596	−0.196565
$50$	12.2382	1.73074
$51$	−6.39097	−0.894915
$52$	−7.64373	−1.05999
$53$	9.38787	1.28952	0.644762	−	0.764384i	$-0.276957\pi$
$53$	9.38787	1.28952	0.644762	+	0.764384i	$0.276957\pi$
$54$	−13.6618	−1.85913
$55$	1.59102	0.214533
$56$	12.7329	1.70151
$57$	−4.30240	−0.569866
$58$	17.8221	2.34015
$59$	8.80566	1.14640	0.573200	−	0.819416i	$-0.305702\pi$
$59$	8.80566	1.14640	0.573200	+	0.819416i	$0.305702\pi$
$60$	−1.34503	−0.173643
$61$	−0.781021	−0.0999995	−0.0499997	−	0.998749i	$-0.515922\pi$
$61$	−0.781021	−0.0999995	−0.0499997	+	0.998749i	$0.515922\pi$
$62$	−0.810179	−0.102893
$63$	3.58820	0.452071
$64$	−5.83013	−0.728766
$65$	−0.486541	−0.0603479
$66$	18.1767	2.23739
$67$	−14.4187	−1.76153	−0.880764	−	0.473556i	$-0.842970\pi$
$67$	−14.4187	−1.76153	−0.880764	+	0.473556i	$0.842970\pi$
$68$	21.8174	2.64575
$69$	10.0726	1.21260
$70$	1.55995	0.186450
$71$	−13.6638	−1.62159	−0.810795	−	0.585331i	$-0.800965\pi$
$71$	−13.6638	−1.62159	−0.810795	+	0.585331i	$0.800965\pi$
$72$	8.12375	0.957393
$73$	7.48284	0.875800	0.437900	−	0.899024i	$-0.355722\pi$
$73$	7.48284	0.875800	0.437900	+	0.899024i	$0.355722\pi$
$74$	4.04150	0.469815
$75$	6.01142	0.694139
$76$	14.6875	1.68477
$77$	−14.2397	−1.62277
$78$	−5.55850	−0.629377
$79$	10.0509	1.13081	0.565407	−	0.824812i	$-0.308719\pi$
$79$	10.0509	1.13081	0.565407	+	0.824812i	$0.308719\pi$
$80$	1.32572	0.148220
$81$	−2.17155	−0.241283
$82$	−21.0274	−2.32209
$83$	−4.93575	−0.541769	−0.270885	−	0.962612i	$-0.587316\pi$
$83$	−4.93575	−0.541769	−0.270885	+	0.962612i	$0.587316\pi$
$84$	12.0381	1.31346
$85$	1.38873	0.150629
$86$	−15.7691	−1.70042
$87$	8.75422	0.938551
$88$	−32.2390	−3.43668
$89$	12.6440	1.34026	0.670132	−	0.742242i	$-0.266237\pi$
$89$	12.6440	1.34026	0.670132	+	0.742242i	$0.266237\pi$
$90$	0.995268	0.104910
$91$	4.35456	0.456482
$92$	−34.3857	−3.58496
$93$	−0.397961	−0.0412667
$94$	24.1259	2.48840
$95$	0.934890	0.0959177
$96$	2.05146	0.209376
$97$	−8.09283	−0.821703	−0.410851	−	0.911702i	$-0.634768\pi$
$97$	−8.09283	−0.821703	−0.410851	+	0.911702i	$0.634768\pi$
$98$	3.41581	0.345049
$99$	−9.08509	−0.913086
$100$	−20.5217	−2.05217
$101$	−4.36608	−0.434441	−0.217221	−	0.976123i	$-0.569699\pi$
$101$	−4.36608	−0.434441	−0.217221	+	0.976123i	$0.569699\pi$
$102$	15.8656	1.57093
$103$	16.8145	1.65678	0.828392	−	0.560149i	$-0.189256\pi$
$103$	16.8145	1.65678	0.828392	+	0.560149i	$0.189256\pi$
$104$	9.85881	0.966736
$105$	0.766252	0.0747785
$106$	−23.3054	−2.26362
$107$	−16.8224	−1.62629	−0.813143	−	0.582065i	$-0.802245\pi$
$107$	−16.8224	−1.62629	−0.813143	+	0.582065i	$0.802245\pi$
$108$	22.9089	2.20441
$109$	−4.06081	−0.388955	−0.194478	−	0.980907i	$-0.562301\pi$
$109$	−4.06081	−0.388955	−0.194478	+	0.980907i	$0.562301\pi$
$110$	−3.94970	−0.376589
$111$	1.98519	0.188426
$112$	−11.8653	−1.12116
$113$	−9.46979	−0.890843	−0.445421	−	0.895321i	$-0.646946\pi$
$113$	−9.46979	−0.890843	−0.445421	+	0.895321i	$0.646946\pi$
$114$	10.6807	1.00034
$115$	−2.18873	−0.204100
$116$	−29.8850	−2.77476
$117$	2.77826	0.256850
$118$	−21.8600	−2.01238
$119$	−12.4292	−1.13938
$120$	1.73481	0.158366
$121$	25.0540	2.27764
$122$	1.93888	0.175538
$123$	−10.3287	−0.931309
$124$	1.35856	0.122002
$125$	−2.63111	−0.235333
$126$	−8.90770	−0.793561
$127$	−0.887955	−0.0787933	−0.0393966	−	0.999224i	$-0.512544\pi$
$127$	−0.887955	−0.0787933	−0.0393966	+	0.999224i	$0.512544\pi$
$128$	17.8380	1.57667
$129$	−7.74579	−0.681979
$130$	1.20784	0.105934
$131$	−5.00037	−0.436884	−0.218442	−	0.975850i	$-0.570097\pi$
$131$	−5.00037	−0.436884	−0.218442	+	0.975850i	$0.570097\pi$
$132$	−30.4797	−2.65292
$133$	−8.36732	−0.725538
$134$	35.7945	3.09217
$135$	1.45820	0.125502
$136$	−28.1399	−2.41298
$137$	−3.93808	−0.336453	−0.168226	−	0.985748i	$-0.553804\pi$
$137$	−3.93808	−0.336453	−0.168226	+	0.985748i	$0.553804\pi$
$138$	−25.0052	−2.12859
$139$	20.0298	1.69890	0.849451	−	0.527667i	$-0.176933\pi$
$139$	20.0298	1.69890	0.849451	+	0.527667i	$0.176933\pi$
$140$	−2.61582	−0.221077
$141$	11.8507	0.998007
$142$	33.9202	2.84652
$143$	−11.0255	−0.921996
$144$	−7.57019	−0.630849
$145$	−1.90225	−0.157973
$146$	−18.5761	−1.53737
$147$	1.67785	0.138387
$148$	−6.77702	−0.557068
$149$	22.2667	1.82416	0.912081	−	0.410011i	$-0.134475\pi$
$149$	22.2667	1.82416	0.912081	+	0.410011i	$0.134475\pi$
$150$	−14.9233	−1.21849
$151$	−3.33649	−0.271519	−0.135760	−	0.990742i	$-0.543348\pi$
$151$	−3.33649	−0.271519	−0.135760	+	0.990742i	$0.543348\pi$
$152$	−18.9438	−1.53654
$153$	−7.92995	−0.641099
$154$	35.3500	2.84859
$155$	0.0864751	0.00694584
$156$	9.32082	0.746263
$157$	22.8269	1.82178	0.910891	−	0.412647i	$-0.135396\pi$
$157$	22.8269	1.82178	0.910891	+	0.412647i	$0.135396\pi$
$158$	−24.9513	−1.98502
$159$	−11.4476	−0.907857
$160$	−0.445773	−0.0352414
$161$	19.5892	1.54385
$162$	5.39086	0.423546
$163$	6.57738	0.515180	0.257590	−	0.966254i	$-0.417072\pi$
$163$	6.57738	0.515180	0.257590	+	0.966254i	$0.417072\pi$
$164$	35.2600	2.75335
$165$	−1.94010	−0.151037
$166$	12.2530	0.951017
$167$	−7.56768	−0.585605	−0.292802	−	0.956173i	$-0.594588\pi$
$167$	−7.56768	−0.585605	−0.292802	+	0.956173i	$0.594588\pi$
$168$	−15.5266	−1.19791
$169$	−9.62836	−0.740643
$170$	−3.44751	−0.264412
$171$	−5.33844	−0.408241
$172$	26.4425	2.01622
$173$	9.00406	0.684566	0.342283	−	0.939597i	$-0.388800\pi$
$173$	9.00406	0.684566	0.342283	+	0.939597i	$0.388800\pi$
$174$	−21.7323	−1.64752
$175$	11.6910	0.883759
$176$	30.0421	2.26451
$177$	−10.7377	−0.807094
$178$	−31.3888	−2.35269
$179$	−5.19012	−0.387928	−0.193964	−	0.981009i	$-0.562134\pi$
$179$	−5.19012	−0.387928	−0.193964	+	0.981009i	$0.562134\pi$
$180$	−1.66892	−0.124394
$181$	10.5159	0.781637	0.390819	−	0.920468i	$-0.372192\pi$
$181$	10.5159	0.781637	0.390819	+	0.920468i	$0.372192\pi$
$182$	−10.8102	−0.801305
$183$	0.952382	0.0704021
$184$	44.3504	3.26955
$185$	−0.431373	−0.0317151
$186$	0.987938	0.0724391
$187$	31.4699	2.30131
$188$	−40.4557	−2.95054
$189$	−13.0510	−0.949318
$190$	−2.32086	−0.168373
$191$	−2.17097	−0.157086	−0.0785429	−	0.996911i	$-0.525027\pi$
$191$	−2.17097	−0.157086	−0.0785429	+	0.996911i	$0.525027\pi$
$192$	7.10930	0.513069
$193$	−16.3330	−1.17567	−0.587837	−	0.808979i	$-0.700020\pi$
$193$	−16.3330	−1.17567	−0.587837	+	0.808979i	$0.700020\pi$
$194$	20.0904	1.44241
$195$	0.593291	0.0424864
$196$	−5.72782	−0.409130
$197$	−9.69574	−0.690793	−0.345396	−	0.938457i	$-0.612256\pi$
$197$	−9.69574	−0.690793	−0.345396	+	0.938457i	$0.612256\pi$
$198$	22.5537	1.60282
$199$	−13.7039	−0.971444	−0.485722	−	0.874113i	$-0.661443\pi$
$199$	−13.7039	−0.971444	−0.485722	+	0.874113i	$0.661443\pi$
$200$	26.4687	1.87162
$201$	17.5823	1.24016
$202$	10.8388	0.762614
$203$	17.0252	1.19494
$204$	−26.6043	−1.86267
$205$	2.24438	0.156754
$206$	−41.7420	−2.90830
$207$	12.4981	0.868681
$208$	−9.18702	−0.637005
$209$	21.1855	1.46543
$210$	−1.90222	−0.131266
$211$	9.50573	0.654401	0.327201	−	0.944955i	$-0.393895\pi$
$211$	9.50573	0.654401	0.327201	+	0.944955i	$0.393895\pi$
$212$	39.0798	2.68401
$213$	16.6617	1.14164
$214$	41.7616	2.85477
$215$	1.68312	0.114788
$216$	−29.5476	−2.01046
$217$	−0.773957	−0.0525396
$218$	10.0810	0.682768
$219$	−9.12462	−0.616585
$220$	6.62309	0.446528
$221$	−9.62362	−0.647355
$222$	−4.92823	−0.330761
$223$	15.4460	1.03434	0.517171	−	0.855882i	$-0.326985\pi$
$223$	15.4460	1.03434	0.517171	+	0.855882i	$0.326985\pi$
$224$	3.98969	0.266572
$225$	7.45900	0.497267
$226$	23.5087	1.56378
$227$	17.9896	1.19401	0.597005	−	0.802238i	$-0.296357\pi$
$227$	17.9896	1.19401	0.597005	+	0.802238i	$0.296357\pi$
$228$	−17.9100	−1.18612
$229$	7.42490	0.490651	0.245326	−	0.969441i	$-0.421105\pi$
$229$	7.42490	0.490651	0.245326	+	0.969441i	$0.421105\pi$
$230$	5.43351	0.358275
$231$	17.3640	1.14247
$232$	38.5454	2.53063
$233$	−5.49326	−0.359876	−0.179938	−	0.983678i	$-0.557590\pi$
$233$	−5.49326	−0.359876	−0.179938	+	0.983678i	$0.557590\pi$
$234$	−6.89702	−0.450873
$235$	−2.57510	−0.167981
$236$	36.6562	2.38611
$237$	−12.2561	−0.796122
$238$	30.8554	2.00006
$239$	−6.33907	−0.410040	−0.205020	−	0.978758i	$-0.565726\pi$
$239$	−6.33907	−0.410040	−0.205020	+	0.978758i	$0.565726\pi$
$240$	−1.61660	−0.104351
$241$	−15.3575	−0.989261	−0.494631	−	0.869103i	$-0.664697\pi$
$241$	−15.3575	−0.989261	−0.494631	+	0.869103i	$0.664697\pi$
$242$	−62.1965	−3.99814
$243$	−13.8617	−0.889230
$244$	−3.25123	−0.208139
$245$	−0.364589	−0.0232927
$246$	25.6410	1.63481
$247$	−6.47862	−0.412225
$248$	−1.75225	−0.111268
$249$	6.01869	0.381419
$250$	6.53172	0.413102
$251$	−7.76111	−0.489877	−0.244938	−	0.969539i	$-0.578768\pi$
$251$	−7.76111	−0.489877	−0.244938	+	0.969539i	$0.578768\pi$
$252$	14.9369	0.940939
$253$	−49.5987	−3.11824
$254$	2.20435	0.138313
$255$	−1.69342	−0.106046
$256$	−32.6225	−2.03890
$257$	−25.4349	−1.58659	−0.793293	−	0.608841i	$-0.791635\pi$
$257$	−25.4349	−1.58659	−0.793293	+	0.608841i	$0.791635\pi$
$258$	19.2289	1.19714
$259$	3.86081	0.239899
$260$	−2.02537	−0.125608
$261$	10.8623	0.672359
$262$	12.4134	0.766902
$263$	−16.6127	−1.02438	−0.512191	−	0.858871i	$-0.671166\pi$
$263$	−16.6127	−1.02438	−0.512191	+	0.858871i	$0.671166\pi$
$264$	39.3124	2.41951
$265$	2.48752	0.152807
$266$	20.7718	1.27360
$267$	−15.4182	−0.943580
$268$	−60.0222	−3.66644
$269$	13.9887	0.852907	0.426454	−	0.904509i	$-0.359763\pi$
$269$	13.9887	0.852907	0.426454	+	0.904509i	$0.359763\pi$
$270$	−3.61998	−0.220305
$271$	−10.1675	−0.617630	−0.308815	−	0.951122i	$-0.599932\pi$
$271$	−10.1675	−0.617630	−0.308815	+	0.951122i	$0.599932\pi$
$272$	26.2224	1.58997
$273$	−5.30999	−0.321375
$274$	9.77627	0.590606
$275$	−29.6009	−1.78500
$276$	41.9302	2.52390
$277$	−4.91106	−0.295077	−0.147539	−	0.989056i	$-0.547135\pi$
$277$	−4.91106	−0.295077	−0.147539	+	0.989056i	$0.547135\pi$
$278$	−49.7238	−2.98224
$279$	−0.493793	−0.0295626
$280$	3.37386	0.201627
$281$	−15.9906	−0.953922	−0.476961	−	0.878924i	$-0.658262\pi$
$281$	−15.9906	−0.953922	−0.476961	+	0.878924i	$0.658262\pi$
$282$	−29.4193	−1.75189
$283$	28.5193	1.69530	0.847648	−	0.530558i	$-0.178018\pi$
$283$	28.5193	1.69530	0.847648	+	0.530558i	$0.178018\pi$
$284$	−56.8794	−3.37517
$285$	−1.14001	−0.0675284
$286$	27.3707	1.61846
$287$	−20.0873	−1.18572
$288$	2.54547	0.149993
$289$	10.4686	0.615800
$290$	4.72233	0.277305
$291$	9.86845	0.578499
$292$	31.1495	1.82289
$293$	−25.7391	−1.50370	−0.751848	−	0.659337i	$-0.770837\pi$
$293$	−25.7391	−1.50370	−0.751848	+	0.659337i	$0.770837\pi$
$294$	−4.16526	−0.242923
$295$	2.33325	0.135847
$296$	8.74094	0.508057
$297$	33.0442	1.91742
$298$	−55.2771	−3.20212
$299$	15.1675	0.877158
$300$	25.0243	1.44478
$301$	−15.0640	−0.868277
$302$	8.28282	0.476623
$303$	5.32403	0.305858
$304$	17.6529	1.01246
$305$	−0.206948	−0.0118498
$306$	19.6861	1.12538
$307$	−0.541119	−0.0308833	−0.0154416	−	0.999881i	$-0.504915\pi$
$307$	−0.541119	−0.0308833	−0.0154416	+	0.999881i	$0.504915\pi$
$308$	−59.2770	−3.37762
$309$	−20.5037	−1.16642
$310$	−0.214674	−0.0121927
$311$	−3.22763	−0.183022	−0.0915111	−	0.995804i	$-0.529170\pi$
$311$	−3.22763	−0.183022	−0.0915111	+	0.995804i	$0.529170\pi$
$312$	−12.0219	−0.680606
$313$	−14.7400	−0.833152	−0.416576	−	0.909101i	$-0.636770\pi$
$313$	−14.7400	−0.833152	−0.416576	+	0.909101i	$0.636770\pi$
$314$	−56.6676	−3.19794
$315$	0.950770	0.0535698
$316$	41.8398	2.35368
$317$	−10.2062	−0.573239	−0.286620	−	0.958044i	$-0.592532\pi$
$317$	−10.2062	−0.573239	−0.286620	+	0.958044i	$0.592532\pi$
$318$	28.4187	1.59364
$319$	−43.1068	−2.41352
$320$	−1.54482	−0.0863578
$321$	20.5134	1.14495
$322$	−48.6302	−2.71006
$323$	18.4918	1.02891
$324$	−9.03971	−0.502206
$325$	9.05209	0.502120
$326$	−16.3283	−0.904342
$327$	4.95178	0.273834
$328$	−45.4781	−2.51111
$329$	23.0472	1.27064
$330$	4.81629	0.265128
$331$	2.67916	0.147260	0.0736299	−	0.997286i	$-0.476542\pi$
$331$	2.67916	0.147260	0.0736299	+	0.997286i	$0.476542\pi$
$332$	−20.5465	−1.12764
$333$	2.46324	0.134985
$334$	18.7868	1.02797
$335$	−3.82055	−0.208739
$336$	14.4686	0.789328
$337$	−9.91763	−0.540248	−0.270124	−	0.962826i	$-0.587065\pi$
$337$	−9.91763	−0.540248	−0.270124	+	0.962826i	$0.587065\pi$
$338$	23.9024	1.30012
$339$	11.5475	0.627176
$340$	5.78099	0.313518
$341$	1.95961	0.106119
$342$	13.2527	0.716622
$343$	19.8636	1.07254
$344$	−34.1053	−1.83883
$345$	2.66895	0.143691
$346$	−22.3526	−1.20168
$347$	21.8183	1.17127	0.585634	−	0.810575i	$-0.300845\pi$
$347$	21.8183	1.17127	0.585634	+	0.810575i	$0.300845\pi$
$348$	36.4420	1.95350
$349$	6.11082	0.327105	0.163552	−	0.986535i	$-0.447705\pi$
$349$	6.11082	0.327105	0.163552	+	0.986535i	$0.447705\pi$
$350$	−29.0230	−1.55134
$351$	−10.1051	−0.539368
$352$	−10.1016	−0.538419
$353$	−12.6946	−0.675666	−0.337833	−	0.941206i	$-0.609694\pi$
$353$	−12.6946	−0.675666	−0.337833	+	0.941206i	$0.609694\pi$
$354$	26.6563	1.41676
$355$	−3.62050	−0.192156
$356$	52.6345	2.78962
$357$	15.1562	0.802153
$358$	12.8845	0.680965
$359$	−2.43139	−0.128324	−0.0641619	−	0.997940i	$-0.520437\pi$
$359$	−2.43139	−0.128324	−0.0641619	+	0.997940i	$0.520437\pi$
$360$	2.15256	0.113450
$361$	−6.55131	−0.344806
$362$	−26.1056	−1.37208
$363$	−30.5510	−1.60351
$364$	18.1272	0.950121
$365$	1.98274	0.103781
$366$	−2.36429	−0.123583
$367$	−14.3644	−0.749813	−0.374907	−	0.927063i	$-0.622325\pi$
$367$	−14.3644	−0.749813	−0.374907	+	0.927063i	$0.622325\pi$
$368$	−41.3283	−2.15439
$369$	−12.8159	−0.667171
$370$	1.07088	0.0556725
$371$	−22.2634	−1.15586
$372$	−1.65663	−0.0858923
$373$	−21.3886	−1.10746	−0.553730	−	0.832697i	$-0.686796\pi$
$373$	−21.3886	−1.10746	−0.553730	+	0.832697i	$0.686796\pi$
$374$	−78.1239	−4.03969
$375$	3.20839	0.165681
$376$	52.1794	2.69095
$377$	13.1822	0.678920
$378$	32.3990	1.66643
$379$	18.4420	0.947300	0.473650	−	0.880713i	$-0.342936\pi$
$379$	18.4420	0.947300	0.473650	+	0.880713i	$0.342936\pi$
$380$	3.89176	0.199643
$381$	1.08278	0.0554724
$382$	5.38942	0.275747
$383$	−11.7768	−0.601764	−0.300882	−	0.953661i	$-0.597281\pi$
$383$	−11.7768	−0.601764	−0.300882	+	0.953661i	$0.597281\pi$
$384$	−21.7517	−1.11001
$385$	−3.77311	−0.192296
$386$	40.5466	2.06377
$387$	−9.61103	−0.488556
$388$	−33.6888	−1.71029
$389$	−28.4961	−1.44481	−0.722404	−	0.691472i	$-0.756963\pi$
$389$	−28.4961	−1.44481	−0.722404	+	0.691472i	$0.756963\pi$
$390$	−1.47284	−0.0745803
$391$	−43.2924	−2.18939
$392$	7.38769	0.373135
$393$	6.09748	0.307577
$394$	24.0696	1.21261
$395$	2.66320	0.134000
$396$	−37.8194	−1.90049
$397$	−4.74194	−0.237991	−0.118996	−	0.992895i	$-0.537967\pi$
$397$	−4.74194	−0.237991	−0.118996	+	0.992895i	$0.537967\pi$
$398$	34.0199	1.70526
$399$	10.2032	0.510797
$400$	−24.6651	−1.23325
$401$	−30.1137	−1.50380	−0.751902	−	0.659274i	$-0.770864\pi$
$401$	−30.1137	−1.50380	−0.751902	+	0.659274i	$0.770864\pi$
$402$	−43.6480	−2.17696
$403$	−0.599256	−0.0298511
$404$	−18.1751	−0.904245
$405$	−0.575398	−0.0285917
$406$	−42.2651	−2.09758
$407$	−9.77531	−0.484544
$408$	34.3140	1.69880
$409$	9.02321	0.446169	0.223084	−	0.974799i	$-0.428387\pi$
$409$	9.02321	0.446169	0.223084	+	0.974799i	$0.428387\pi$
$410$	−5.57167	−0.275165
$411$	4.80212	0.236871
$412$	69.9954	3.44843
$413$	−20.8827	−1.02757
$414$	−31.0266	−1.52488
$415$	−1.30783	−0.0641990
$416$	3.08912	0.151457
$417$	−24.4244	−1.19607
$418$	−52.5929	−2.57241
$419$	−19.1627	−0.936158	−0.468079	−	0.883687i	$-0.655054\pi$
$419$	−19.1627	−0.936158	−0.468079	+	0.883687i	$0.655054\pi$
$420$	3.18975	0.155644
$421$	4.88450	0.238056	0.119028	−	0.992891i	$-0.462022\pi$
$421$	4.88450	0.238056	0.119028	+	0.992891i	$0.462022\pi$
$422$	−23.5979	−1.14873
$423$	14.7044	0.714952
$424$	−50.4047	−2.44787
$425$	−25.8373	−1.25329
$426$	−41.3626	−2.00402
$427$	1.85220	0.0896341
$428$	−70.0283	−3.38495
$429$	13.4445	0.649108
$430$	−4.17835	−0.201498
$431$	20.1375	0.969989	0.484995	−	0.874517i	$-0.338822\pi$
$431$	20.1375	0.969989	0.484995	+	0.874517i	$0.338822\pi$
$432$	27.5342	1.32474
$433$	−15.2084	−0.730870	−0.365435	−	0.930837i	$-0.619080\pi$
$433$	−15.2084	−0.730870	−0.365435	+	0.930837i	$0.619080\pi$
$434$	1.92135	0.0922275
$435$	2.31962	0.111217
$436$	−16.9043	−0.809570
$437$	−29.1444	−1.39417
$438$	22.6518	1.08235
$439$	9.02803	0.430884	0.215442	−	0.976517i	$-0.430881\pi$
$439$	9.02803	0.430884	0.215442	+	0.976517i	$0.430881\pi$
$440$	−8.54239	−0.407243
$441$	2.08189	0.0991374
$442$	23.8906	1.13636
$443$	31.2572	1.48507	0.742537	−	0.669805i	$-0.233622\pi$
$443$	31.2572	1.48507	0.742537	+	0.669805i	$0.233622\pi$
$444$	8.26395	0.392190
$445$	3.35030	0.158820
$446$	−38.3447	−1.81567
$447$	−27.1522	−1.28425
$448$	13.8262	0.653226
$449$	−25.7636	−1.21586	−0.607930	−	0.793991i	$-0.708000\pi$
$449$	−25.7636	−1.21586	−0.607930	+	0.793991i	$0.708000\pi$
$450$	−18.5170	−0.872898
$451$	50.8598	2.39489
$452$	−39.4208	−1.85420
$453$	4.06853	0.191156
$454$	−44.6591	−2.09595
$455$	1.15383	0.0540926
$456$	23.1001	1.08176
$457$	−19.6752	−0.920367	−0.460184	−	0.887824i	$-0.652216\pi$
$457$	−19.6752	−0.920367	−0.460184	+	0.887824i	$0.652216\pi$
$458$	−18.4323	−0.861285
$459$	28.8428	1.34626
$460$	−9.11123	−0.424813
$461$	16.1792	0.753541	0.376771	−	0.926307i	$-0.377034\pi$
$461$	16.1792	0.753541	0.376771	+	0.926307i	$0.377034\pi$
$462$	−43.1061	−2.00548
$463$	−26.5226	−1.23261	−0.616304	−	0.787508i	$-0.711371\pi$
$463$	−26.5226	−1.23261	−0.616304	+	0.787508i	$0.711371\pi$
$464$	−35.9189	−1.66749
$465$	−0.105448	−0.00489005
$466$	13.6370	0.631722
$467$	−21.3131	−0.986251	−0.493125	−	0.869958i	$-0.664146\pi$
$467$	−21.3131	−0.986251	−0.493125	+	0.869958i	$0.664146\pi$
$468$	11.5653	0.534607
$469$	34.1941	1.57894
$470$	6.39267	0.294872
$471$	−27.8352	−1.28258
$472$	−47.2788	−2.17618
$473$	38.1412	1.75373
$474$	30.4258	1.39751
$475$	−17.3936	−0.798075
$476$	−51.7401	−2.37151
$477$	−14.2043	−0.650370
$478$	15.7367	0.719781
$479$	−20.0615	−0.916632	−0.458316	−	0.888789i	$-0.651547\pi$
$479$	−20.0615	−0.916632	−0.458316	+	0.888789i	$0.651547\pi$
$480$	0.543578	0.0248108
$481$	2.98933	0.136302
$482$	38.1249	1.73654
$483$	−23.8872	−1.08691
$484$	104.295	4.74067
$485$	−2.14437	−0.0973707
$486$	34.4117	1.56095
$487$	−21.9050	−0.992611	−0.496305	−	0.868148i	$-0.665310\pi$
$487$	−21.9050	−0.992611	−0.496305	+	0.868148i	$0.665310\pi$
$488$	4.19341	0.189827
$489$	−8.02050	−0.362699
$490$	0.905091	0.0408878
$491$	−23.9843	−1.08240	−0.541198	−	0.840895i	$-0.682029\pi$
$491$	−23.9843	−1.08240	−0.541198	+	0.840895i	$0.682029\pi$
$492$	−42.9963	−1.93842
$493$	−37.6259	−1.69459
$494$	16.0832	0.723615
$495$	−2.40729	−0.108199
$496$	1.63285	0.0733171
$497$	32.4037	1.45350
$498$	−14.9414	−0.669540
$499$	8.86921	0.397040	0.198520	−	0.980097i	$-0.436386\pi$
$499$	8.86921	0.397040	0.198520	+	0.980097i	$0.436386\pi$
$500$	−10.9528	−0.489823
$501$	9.22809	0.412280
$502$	19.2669	0.859925
$503$	−19.4076	−0.865343	−0.432671	−	0.901552i	$-0.642429\pi$
$503$	−19.4076	−0.865343	−0.432671	+	0.901552i	$0.642429\pi$
$504$	−19.2655	−0.858155
$505$	−1.15689	−0.0514807
$506$	123.129	5.47373
$507$	11.7409	0.521431
$508$	−3.69638	−0.164000
$509$	16.8751	0.747976	0.373988	−	0.927434i	$-0.377990\pi$
$509$	16.8751	0.747976	0.373988	+	0.927434i	$0.377990\pi$
$510$	4.20392	0.186153
$511$	−17.7456	−0.785019
$512$	45.3092	2.00240
$513$	19.4169	0.857278
$514$	63.1421	2.78508
$515$	4.45536	0.196327
$516$	−32.2442	−1.41947
$517$	−58.3541	−2.56641
$518$	−9.58445	−0.421116
$519$	−10.9796	−0.481952
$520$	2.61230	0.114557
$521$	−33.8774	−1.48420	−0.742098	−	0.670291i	$-0.766169\pi$
$521$	−33.8774	−1.48420	−0.742098	+	0.670291i	$0.766169\pi$
$522$	−26.9656	−1.18025
$523$	19.0930	0.834878	0.417439	−	0.908705i	$-0.362928\pi$
$523$	19.0930	0.834878	0.417439	+	0.908705i	$0.362928\pi$
$524$	−20.8155	−0.909329
$525$	−14.2561	−0.622188
$526$	41.2410	1.79819
$527$	1.71045	0.0745084
$528$	−36.6336	−1.59427
$529$	45.2317	1.96660
$530$	−6.17525	−0.268236
$531$	−13.3234	−0.578185
$532$	−34.8314	−1.51013
$533$	−15.5531	−0.673681
$534$	38.2757	1.65635
$535$	−4.45746	−0.192713
$536$	77.4161	3.34386
$537$	6.32887	0.273111
$538$	−34.7270	−1.49719
$539$	−8.26193	−0.355866
$540$	6.07019	0.261219
$541$	−36.2281	−1.55757	−0.778783	−	0.627294i	$-0.784163\pi$
$541$	−36.2281	−1.55757	−0.778783	+	0.627294i	$0.784163\pi$
$542$	25.2407	1.08418
$543$	−12.8231	−0.550292
$544$	−8.81725	−0.378036
$545$	−1.07600	−0.0460907
$546$	13.1820	0.564139
$547$	−15.9910	−0.683727	−0.341864	−	0.939750i	$-0.611058\pi$
$547$	−15.9910	−0.683727	−0.341864	+	0.939750i	$0.611058\pi$
$548$	−16.3934	−0.700292
$549$	1.18172	0.0504346
$550$	73.4842	3.13338
$551$	−25.3297	−1.07908
$552$	−54.0812	−2.30185
$553$	−23.8358	−1.01360
$554$	12.1917	0.517976
$555$	0.526019	0.0223282
$556$	83.3798	3.53609
$557$	−1.22214	−0.0517836	−0.0258918	−	0.999665i	$-0.508243\pi$
$557$	−1.22214	−0.0517836	−0.0258918	+	0.999665i	$0.508243\pi$
$558$	1.22584	0.0518939
$559$	−11.6637	−0.493324
$560$	−3.14396	−0.132857
$561$	−38.3746	−1.62018
$562$	39.6968	1.67451
$563$	33.9167	1.42942	0.714709	−	0.699421i	$-0.246559\pi$
$563$	33.9167	1.42942	0.714709	+	0.699421i	$0.246559\pi$
$564$	49.3320	2.07725
$565$	−2.50922	−0.105564
$566$	−70.7991	−2.97591
$567$	5.14984	0.216273
$568$	73.3625	3.07822
$569$	−12.5611	−0.526588	−0.263294	−	0.964716i	$-0.584809\pi$
$569$	−12.5611	−0.526588	−0.263294	+	0.964716i	$0.584809\pi$
$570$	2.83008	0.118539
$571$	44.8390	1.87645	0.938227	−	0.346019i	$-0.112467\pi$
$571$	44.8390	1.87645	0.938227	+	0.346019i	$0.112467\pi$
$572$	−45.8968	−1.91904
$573$	2.64729	0.110592
$574$	49.8667	2.08140
$575$	40.7213	1.69820
$576$	8.82126	0.367552
$577$	−24.1099	−1.00371	−0.501853	−	0.864953i	$-0.667348\pi$
$577$	−24.1099	−1.00371	−0.501853	+	0.864953i	$0.667348\pi$
$578$	−25.9883	−1.08097
$579$	19.9166	0.827704
$580$	−7.91868	−0.328805
$581$	11.7052	0.485612
$582$	−24.4984	−1.01549
$583$	56.3695	2.33458
$584$	−40.1763	−1.66251
$585$	0.736159	0.0304364
$586$	63.8973	2.63957
$587$	−2.66685	−0.110073	−0.0550363	−	0.998484i	$-0.517527\pi$
$587$	−2.66685	−0.110073	−0.0550363	+	0.998484i	$0.517527\pi$
$588$	6.98455	0.288038
$589$	1.15147	0.0474457
$590$	−5.79228	−0.238464
$591$	11.8230	0.486335
$592$	−8.14532	−0.334770
$593$	−7.19207	−0.295343	−0.147672	−	0.989036i	$-0.547178\pi$
$593$	−7.19207	−0.295343	−0.147672	+	0.989036i	$0.547178\pi$
$594$	−82.0321	−3.36582
$595$	−3.29338	−0.135015
$596$	92.6918	3.79680
$597$	16.7106	0.683921
$598$	−37.6532	−1.53976
$599$	−43.1837	−1.76444	−0.882218	−	0.470841i	$-0.843951\pi$
$599$	−43.1837	−1.76444	−0.882218	+	0.470841i	$0.843951\pi$
$600$	−32.2761	−1.31767
$601$	−23.9680	−0.977676	−0.488838	−	0.872375i	$-0.662579\pi$
$601$	−23.9680	−0.977676	−0.488838	+	0.872375i	$0.662579\pi$
$602$	37.3965	1.52417
$603$	21.8162	0.888425
$604$	−13.8891	−0.565140
$605$	6.63859	0.269897
$606$	−13.2169	−0.536900
$607$	13.9887	0.567782	0.283891	−	0.958856i	$-0.408375\pi$
$607$	13.9887	0.567782	0.283891	+	0.958856i	$0.408375\pi$
$608$	−5.93576	−0.240727
$609$	−20.7607	−0.841266
$610$	0.513748	0.0208011
$611$	17.8449	0.721929
$612$	−33.0108	−1.33438
$613$	−42.4272	−1.71362	−0.856810	−	0.515632i	$-0.827557\pi$
$613$	−42.4272	−1.71362	−0.856810	+	0.515632i	$0.827557\pi$
$614$	1.34333	0.0542122
$615$	−2.73681	−0.110359
$616$	76.4549	3.08046
$617$	−43.5957	−1.75510	−0.877548	−	0.479489i	$-0.840822\pi$
$617$	−43.5957	−1.75510	−0.877548	+	0.479489i	$0.840822\pi$
$618$	50.9005	2.04752
$619$	38.5008	1.54748	0.773739	−	0.633504i	$-0.218384\pi$
$619$	38.5008	1.54748	0.773739	+	0.633504i	$0.218384\pi$
$620$	0.359978	0.0144571
$621$	−45.4581	−1.82417
$622$	8.01259	0.321276
$623$	−29.9854	−1.20134
$624$	11.2027	0.448467
$625$	23.9518	0.958071
$626$	36.5919	1.46251
$627$	−25.8337	−1.03170
$628$	95.0236	3.79185
$629$	−8.53242	−0.340210
$630$	−2.36028	−0.0940360
$631$	−10.2390	−0.407609	−0.203804	−	0.979012i	$-0.565331\pi$
$631$	−10.2390	−0.407609	−0.203804	+	0.979012i	$0.565331\pi$
$632$	−53.9646	−2.14660
$633$	−11.5913	−0.460715
$634$	25.3369	1.00626
$635$	−0.235283	−0.00933690
$636$	−47.6542	−1.88961
$637$	2.52653	0.100105
$638$	107.012	4.23667
$639$	20.6739	0.817847
$640$	4.72655	0.186833
$641$	−21.8330	−0.862353	−0.431177	−	0.902268i	$-0.641901\pi$
$641$	−21.8330	−0.862353	−0.431177	+	0.902268i	$0.641901\pi$
$642$	−50.9244	−2.00983
$643$	20.0091	0.789083	0.394542	−	0.918878i	$-0.370903\pi$
$643$	20.0091	0.789083	0.394542	+	0.918878i	$0.370903\pi$
$644$	81.5460	3.21336
$645$	−2.05241	−0.0808137
$646$	−45.9060	−1.80615
$647$	−15.7883	−0.620701	−0.310350	−	0.950622i	$-0.600446\pi$
$647$	−15.7883	−0.620701	−0.310350	+	0.950622i	$0.600446\pi$
$648$	11.6593	0.458022
$649$	52.8736	2.07547
$650$	−22.4718	−0.881416
$651$	0.943768	0.0369892
$652$	27.3803	1.07229
$653$	34.3250	1.34324	0.671620	−	0.740896i	$-0.265599\pi$
$653$	34.3250	1.34324	0.671620	+	0.740896i	$0.265599\pi$
$654$	−12.2928	−0.480686
$655$	−1.32495	−0.0517702
$656$	42.3791	1.65463
$657$	−11.3219	−0.441709
$658$	−57.2147	−2.23046
$659$	−38.4005	−1.49587	−0.747935	−	0.663772i	$-0.768954\pi$
$659$	−38.4005	−1.49587	−0.747935	+	0.663772i	$0.768954\pi$
$660$	−8.07624	−0.314367
$661$	−21.8838	−0.851180	−0.425590	−	0.904916i	$-0.639933\pi$
$661$	−21.8838	−0.851180	−0.425590	+	0.904916i	$0.639933\pi$
$662$	−6.65100	−0.258499
$663$	11.7351	0.455754
$664$	26.5007	1.02843
$665$	−2.21710	−0.0859754
$666$	−6.11498	−0.236951
$667$	59.3010	2.29614
$668$	−31.5027	−1.21888
$669$	−18.8350	−0.728202
$670$	9.48450	0.366418
$671$	−4.68964	−0.181042
$672$	−4.86505	−0.187674
$673$	17.9544	0.692090	0.346045	−	0.938218i	$-0.387524\pi$
$673$	17.9544	0.692090	0.346045	+	0.938218i	$0.387524\pi$
$674$	24.6205	0.948346
$675$	−27.1298	−1.04423
$676$	−40.0809	−1.54157
$677$	−49.5603	−1.90476	−0.952379	−	0.304917i	$-0.901371\pi$
$677$	−49.5603	−1.90476	−0.952379	+	0.304917i	$0.901371\pi$
$678$	−28.6667	−1.10094
$679$	19.1922	0.736529
$680$	−7.45626	−0.285935
$681$	−21.9366	−0.840612
$682$	−4.86472	−0.186280
$683$	6.60277	0.252648	0.126324	−	0.991989i	$-0.459682\pi$
$683$	6.60277	0.252648	0.126324	+	0.991989i	$0.459682\pi$
$684$	−22.2228	−0.849711
$685$	−1.04348	−0.0398692
$686$	−49.3114	−1.88272
$687$	−9.05397	−0.345431
$688$	31.7813	1.21165
$689$	−17.2380	−0.656717
$690$	−6.62566	−0.252235
$691$	−26.4393	−1.00580	−0.502898	−	0.864346i	$-0.667733\pi$
$691$	−26.4393	−1.00580	−0.502898	+	0.864346i	$0.667733\pi$
$692$	37.4821	1.42485
$693$	21.5453	0.818440
$694$	−54.1639	−2.05603
$695$	5.30731	0.201318
$696$	−47.0026	−1.78163
$697$	44.3931	1.68151
$698$	−15.1701	−0.574197
$699$	6.69852	0.253361
$700$	48.6674	1.83945
$701$	−28.4769	−1.07556	−0.537779	−	0.843086i	$-0.680737\pi$
$701$	−28.4769	−1.07556	−0.537779	+	0.843086i	$0.680737\pi$
$702$	25.0858	0.946802
$703$	−5.74402	−0.216640
$704$	−35.0070	−1.31938
$705$	3.14009	0.118263
$706$	31.5143	1.18606
$707$	10.3542	0.389409
$708$	−44.6988	−1.67988
$709$	−4.21519	−0.158305	−0.0791524	−	0.996863i	$-0.525221\pi$
$709$	−4.21519	−0.158305	−0.0791524	+	0.996863i	$0.525221\pi$
$710$	8.98789	0.337309
$711$	−15.2075	−0.570325
$712$	−67.8875	−2.54419
$713$	−2.69579	−0.100958
$714$	−37.6253	−1.40809
$715$	−2.92143	−0.109255
$716$	−21.6054	−0.807432
$717$	7.72990	0.288678
$718$	6.03591	0.225258
$719$	−12.1077	−0.451542	−0.225771	−	0.974180i	$-0.572490\pi$
$719$	−12.1077	−0.451542	−0.225771	+	0.974180i	$0.572490\pi$
$720$	−2.00588	−0.0747548
$721$	−39.8758	−1.48505
$722$	16.2636	0.605269
$723$	18.7270	0.696465
$724$	43.7753	1.62690
$725$	35.3914	1.31440
$726$	75.8428	2.81479
$727$	−13.0624	−0.484459	−0.242230	−	0.970219i	$-0.577879\pi$
$727$	−13.0624	−0.484459	−0.242230	+	0.970219i	$0.577879\pi$
$728$	−23.3802	−0.866529
$729$	23.4177	0.867323
$730$	−4.92214	−0.182176
$731$	33.2917	1.23134
$732$	3.96457	0.146535
$733$	−25.7839	−0.952352	−0.476176	−	0.879350i	$-0.657977\pi$
$733$	−25.7839	−0.952352	−0.476176	+	0.879350i	$0.657977\pi$
$734$	35.6595	1.31622
$735$	0.444582	0.0163987
$736$	13.8966	0.512235
$737$	−86.5772	−3.18911
$738$	31.8155	1.17115
$739$	−46.9760	−1.72804	−0.864019	−	0.503458i	$-0.832061\pi$
$739$	−46.9760	−1.72804	−0.864019	+	0.503458i	$0.832061\pi$
$740$	−1.79572	−0.0660118
$741$	7.90007	0.290216
$742$	55.2688	2.02898
$743$	−18.0135	−0.660852	−0.330426	−	0.943832i	$-0.607192\pi$
$743$	−18.0135	−0.660852	−0.330426	+	0.943832i	$0.607192\pi$
$744$	2.13671	0.0783355
$745$	5.90004	0.216161
$746$	53.0971	1.94402
$747$	7.46803	0.273241
$748$	131.003	4.78993
$749$	39.8945	1.45771
$750$	−7.96482	−0.290834
$751$	23.5472	0.859248	0.429624	−	0.903008i	$-0.358646\pi$
$751$	23.5472	0.859248	0.429624	+	0.903008i	$0.358646\pi$
$752$	−48.6238	−1.77313
$753$	9.46395	0.344885
$754$	−32.7249	−1.19177
$755$	−0.884073	−0.0321747
$756$	−54.3285	−1.97591
$757$	20.8393	0.757416	0.378708	−	0.925516i	$-0.376368\pi$
$757$	20.8393	0.757416	0.378708	+	0.925516i	$0.376368\pi$
$758$	−45.7821	−1.66288
$759$	60.4809	2.19532
$760$	−5.01955	−0.182078
$761$	−0.0647869	−0.00234852	−0.00117426	−	0.999999i	$-0.500374\pi$
$761$	−0.0647869	−0.00234852	−0.00117426	+	0.999999i	$0.500374\pi$
$762$	−2.68800	−0.0973758
$763$	9.63024	0.348638
$764$	−9.03730	−0.326958
$765$	−2.10121	−0.0759694
$766$	29.2358	1.05633
$767$	−16.1690	−0.583828
$768$	39.7801	1.43544
$769$	−23.7707	−0.857192	−0.428596	−	0.903496i	$-0.640992\pi$
$769$	−23.7707	−0.857192	−0.428596	+	0.903496i	$0.640992\pi$
$770$	9.36674	0.337554
$771$	31.0155	1.11700
$772$	−67.9909	−2.44705
$773$	28.8855	1.03894	0.519469	−	0.854489i	$-0.326130\pi$
$773$	28.8855	1.03894	0.519469	+	0.854489i	$0.326130\pi$
$774$	23.8594	0.857607
$775$	−1.60887	−0.0577923
$776$	43.4515	1.55982
$777$	−4.70790	−0.168895
$778$	70.7414	2.53620
$779$	29.8854	1.07076
$780$	2.46975	0.0884312
$781$	−82.0440	−2.93576
$782$	107.473	3.84323
$783$	−39.5082	−1.41191
$784$	−6.88428	−0.245867
$785$	6.04846	0.215879
$786$	−15.1370	−0.539918
$787$	−2.84239	−0.101320	−0.0506602	−	0.998716i	$-0.516133\pi$
$787$	−2.84239	−0.101320	−0.0506602	+	0.998716i	$0.516133\pi$
$788$	−40.3614	−1.43781
$789$	20.2576	0.721191
$790$	−6.61139	−0.235223
$791$	22.4577	0.798503
$792$	48.7791	1.73329
$793$	1.43411	0.0509268
$794$	11.7719	0.417768
$795$	−3.03329	−0.107580
$796$	−57.0466	−2.02196
$797$	8.63802	0.305974	0.152987	−	0.988228i	$-0.451111\pi$
$797$	8.63802	0.305974	0.152987	+	0.988228i	$0.451111\pi$
$798$	−25.3293	−0.896649
$799$	−50.9346	−1.80194
$800$	8.29360	0.293223
$801$	−19.1310	−0.675961
$802$	74.7571	2.63977
$803$	44.9307	1.58557
$804$	73.1915	2.58126
$805$	5.19058	0.182944
$806$	1.48765	0.0524003
$807$	−17.0579	−0.600468
$808$	23.4421	0.824689
$809$	45.1019	1.58570	0.792850	−	0.609417i	$-0.208597\pi$
$809$	45.1019	1.58570	0.792850	+	0.609417i	$0.208597\pi$
$810$	1.42842	0.0501897
$811$	6.00101	0.210724	0.105362	−	0.994434i	$-0.466400\pi$
$811$	6.00101	0.210724	0.105362	+	0.994434i	$0.466400\pi$
$812$	70.8726	2.48714
$813$	12.3983	0.434827
$814$	24.2672	0.850565
$815$	1.74281	0.0610481
$816$	−31.9758	−1.11938
$817$	22.4119	0.784094
$818$	−22.4001	−0.783201
$819$	−6.58866	−0.230226
$820$	9.34289	0.326268
$821$	−22.3234	−0.779093	−0.389547	−	0.921007i	$-0.627368\pi$
$821$	−22.3234	−0.779093	−0.389547	+	0.921007i	$0.627368\pi$
$822$	−11.9212	−0.415801
$823$	−47.5203	−1.65645	−0.828226	−	0.560394i	$-0.810650\pi$
$823$	−47.5203	−1.65645	−0.828226	+	0.560394i	$0.810650\pi$
$824$	−90.2794	−3.14503
$825$	36.0956	1.25669
$826$	51.8412	1.80379
$827$	7.41373	0.257801	0.128900	−	0.991658i	$-0.458855\pi$
$827$	7.41373	0.257801	0.128900	+	0.991658i	$0.458855\pi$
$828$	52.0272	1.80807
$829$	44.7893	1.55560	0.777798	−	0.628514i	$-0.216337\pi$
$829$	44.7893	1.55560	0.777798	+	0.628514i	$0.216337\pi$
$830$	3.24669	0.112694
$831$	5.98858	0.207742
$832$	10.7053	0.371139
$833$	−7.21145	−0.249862
$834$	60.6336	2.09957
$835$	−2.00522	−0.0693934
$836$	88.1909	3.05015
$837$	1.79602	0.0620795
$838$	47.5713	1.64332
$839$	18.3082	0.632071	0.316035	−	0.948747i	$-0.397648\pi$
$839$	18.3082	0.632071	0.316035	+	0.948747i	$0.397648\pi$
$840$	−4.11411	−0.141950
$841$	22.5392	0.777214
$842$	−12.1258	−0.417881
$843$	19.4991	0.671585
$844$	39.5704	1.36207
$845$	−2.55124	−0.0877653
$846$	−36.5036	−1.25502
$847$	−59.4157	−2.04155
$848$	46.9701	1.61296
$849$	−34.7766	−1.19353
$850$	64.1410	2.20002
$851$	13.4477	0.460980
$852$	69.3591	2.37620
$853$	39.4987	1.35241	0.676205	−	0.736713i	$-0.263623\pi$
$853$	39.4987	1.35241	0.676205	+	0.736713i	$0.263623\pi$
$854$	−4.59807	−0.157343
$855$	−1.41453	−0.0483760
$856$	90.3218	3.08714
$857$	5.44390	0.185960	0.0929801	−	0.995668i	$-0.470361\pi$
$857$	5.44390	0.185960	0.0929801	+	0.995668i	$0.470361\pi$
$858$	−33.3760	−1.13944
$859$	13.3333	0.454926	0.227463	−	0.973787i	$-0.426957\pi$
$859$	13.3333	0.454926	0.227463	+	0.973787i	$0.426957\pi$
$860$	7.00650	0.238920
$861$	24.4946	0.834774
$862$	−49.9913	−1.70271
$863$	25.8321	0.879334	0.439667	−	0.898161i	$-0.355096\pi$
$863$	25.8321	0.879334	0.439667	+	0.898161i	$0.355096\pi$
$864$	−9.25834	−0.314975
$865$	2.38582	0.0811202
$866$	37.7549	1.28296
$867$	−12.7655	−0.433538
$868$	−3.22182	−0.109356
$869$	60.3506	2.04726
$870$	−5.75844	−0.195229
$871$	26.4757	0.897094
$872$	21.8030	0.738344
$873$	12.2448	0.414425
$874$	72.3509	2.44731
$875$	6.23969	0.210940
$876$	−37.9839	−1.28336
$877$	−39.9734	−1.34981	−0.674903	−	0.737907i	$-0.735814\pi$
$877$	−39.9734	−1.34981	−0.674903	+	0.737907i	$0.735814\pi$
$878$	−22.4121	−0.756371
$879$	31.3865	1.05864
$880$	7.96030	0.268342
$881$	1.08796	0.0366542	0.0183271	−	0.999832i	$-0.494166\pi$
$881$	1.08796	0.0366542	0.0183271	+	0.999832i	$0.494166\pi$
$882$	−5.16828	−0.174025
$883$	3.54749	0.119383	0.0596913	−	0.998217i	$-0.480988\pi$
$883$	3.54749	0.119383	0.0596913	+	0.998217i	$0.480988\pi$
$884$	−40.0612	−1.34740
$885$	−2.84518	−0.0956396
$886$	−77.5959	−2.60689
$887$	33.1529	1.11317	0.556583	−	0.830792i	$-0.312112\pi$
$887$	33.1529	1.11317	0.556583	+	0.830792i	$0.312112\pi$
$888$	−10.6588	−0.357685
$889$	2.10579	0.0706260
$890$	−8.31712	−0.278791
$891$	−13.0391	−0.436825
$892$	64.2986	2.15288
$893$	−34.2891	−1.14744
$894$	67.4053	2.25437
$895$	−1.37523	−0.0459690
$896$	−42.3029	−1.41324
$897$	−18.4953	−0.617541
$898$	63.9581	2.13431
$899$	−2.34294	−0.0781414
$900$	31.0503	1.03501
$901$	49.2023	1.63917
$902$	−126.259	−4.20397
$903$	18.3692	0.611289
$904$	50.8446	1.69107
$905$	2.78640	0.0926230
$906$	−10.1001	−0.335554
$907$	−33.3094	−1.10602	−0.553009	−	0.833175i	$-0.686521\pi$
$907$	−33.3094	−1.10602	−0.553009	+	0.833175i	$0.686521\pi$
$908$	74.8869	2.48521
$909$	6.60609	0.219110
$910$	−2.86439	−0.0949536
$911$	−13.4263	−0.444832	−0.222416	−	0.974952i	$-0.571394\pi$
$911$	−13.4263	−0.444832	−0.222416	+	0.974952i	$0.571394\pi$
$912$	−21.5261	−0.712799
$913$	−29.6367	−0.980832
$914$	48.8437	1.61560
$915$	0.252354	0.00834256
$916$	30.9083	1.02124
$917$	11.8584	0.391599
$918$	−71.6021	−2.36322
$919$	−26.9017	−0.887405	−0.443703	−	0.896174i	$-0.646335\pi$
$919$	−26.9017	−0.887405	−0.443703	+	0.896174i	$0.646335\pi$
$920$	11.7516	0.387438
$921$	0.659844	0.0217426
$922$	−40.1649	−1.32276
$923$	25.0894	0.825828
$924$	72.2828	2.37793
$925$	8.02569	0.263883
$926$	65.8422	2.16371
$927$	−25.4412	−0.835598
$928$	12.0777	0.396469
$929$	−30.6354	−1.00512	−0.502558	−	0.864543i	$-0.667608\pi$
$929$	−30.6354	−1.00512	−0.502558	+	0.864543i	$0.667608\pi$
$930$	0.261775	0.00858394
$931$	−4.85475	−0.159108
$932$	−22.8673	−0.749044
$933$	3.93580	0.128852
$934$	52.9096	1.73126
$935$	8.33861	0.272702
$936$	−14.9168	−0.487572
$937$	31.5800	1.03167	0.515837	−	0.856686i	$-0.327481\pi$
$937$	31.5800	1.03167	0.515837	+	0.856686i	$0.327481\pi$
$938$	−84.8868	−2.77165
$939$	17.9740	0.586559
$940$	−10.7196	−0.349635
$941$	−9.97044	−0.325027	−0.162513	−	0.986706i	$-0.551960\pi$
$941$	−9.97044	−0.325027	−0.162513	+	0.986706i	$0.551960\pi$
$942$	69.1009	2.25143
$943$	−69.9666	−2.27843
$944$	44.0571	1.43394
$945$	−3.45813	−0.112493
$946$	−94.6854	−3.07849
$947$	45.3892	1.47495	0.737476	−	0.675373i	$-0.236017\pi$
$947$	45.3892	1.47495	0.737476	+	0.675373i	$0.236017\pi$
$948$	−51.0198	−1.65705
$949$	−13.7400	−0.446019
$950$	43.1797	1.40093
$951$	12.4455	0.403575
$952$	66.7339	2.16286
$953$	−41.2142	−1.33506	−0.667529	−	0.744584i	$-0.732648\pi$
$953$	−41.2142	−1.33506	−0.667529	+	0.744584i	$0.732648\pi$
$954$	35.2621	1.14165
$955$	−0.575244	−0.0186145
$956$	−26.3882	−0.853456
$957$	52.5647	1.69918
$958$	49.8026	1.60905
$959$	9.33917	0.301578
$960$	1.88376	0.0607981
$961$	−30.8935	−0.996564
$962$	−7.42101	−0.239263
$963$	25.4531	0.820215
$964$	−63.9300	−2.05905
$965$	−4.32777	−0.139316
$966$	59.3000	1.90795
$967$	−13.0625	−0.420060	−0.210030	−	0.977695i	$-0.567356\pi$
$967$	−13.0625	−0.420060	−0.210030	+	0.977695i	$0.567356\pi$
$968$	−134.518	−4.32358
$969$	−22.5491	−0.724381
$970$	5.32339	0.170924
$971$	−12.3999	−0.397933	−0.198966	−	0.980006i	$-0.563758\pi$
$971$	−12.3999	−0.397933	−0.198966	+	0.980006i	$0.563758\pi$
$972$	−57.7035	−1.85084
$973$	−47.5007	−1.52280
$974$	54.3791	1.74242
$975$	−11.0382	−0.353505
$976$	−3.90766	−0.125081
$977$	45.0656	1.44178	0.720889	−	0.693051i	$-0.243734\pi$
$977$	45.0656	1.44178	0.720889	+	0.693051i	$0.243734\pi$
$978$	19.9109	0.636679
$979$	75.9211	2.42645
$980$	−1.51771	−0.0484814
$981$	6.14420	0.196169
$982$	59.5409	1.90003
$983$	48.2994	1.54051	0.770256	−	0.637735i	$-0.220129\pi$
$983$	48.2994	1.54051	0.770256	+	0.637735i	$0.220129\pi$
$984$	55.4563	1.76788
$985$	−2.56909	−0.0818580
$986$	93.4063	2.97466
$987$	−28.1040	−0.894559
$988$	−26.9692	−0.858003
$989$	−52.4699	−1.66845
$990$	5.97608	0.189932
$991$	−12.0213	−0.381868	−0.190934	−	0.981603i	$-0.561152\pi$
$991$	−12.0213	−0.381868	−0.190934	+	0.981603i	$0.561152\pi$
$992$	−0.549044	−0.0174322
$993$	−3.26698	−0.103675
$994$	−80.4421	−2.55147
$995$	−3.63114	−0.115115
$996$	25.0546	0.793885
$997$	−14.1684	−0.448717	−0.224359	−	0.974507i	$-0.572029\pi$
$997$	−14.1684	−0.448717	−0.224359	+	0.974507i	$0.572029\pi$
$998$	−22.0178	−0.696961
$999$	−8.95926	−0.283459

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.b.1.16	✓	159

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.b.1.16	✓	159	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:	\( N \)	\(=\)	\( 4027 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48250 q^{2} -1.21941 q^{3} +4.16279 q^{4} +0.264971 q^{5} +3.02717 q^{6} -2.37151 q^{7} -5.36913 q^{8} -1.51305 q^{9} +O(q^{10})\)	\(q-2.48250 q^{2} -1.21941 q^{3} +4.16279 q^{4} +0.264971 q^{5} +3.02717 q^{6} -2.37151 q^{7} -5.36913 q^{8} -1.51305 q^{9} -0.657790 q^{10} +6.00450 q^{11} -5.07614 q^{12} -1.83620 q^{13} +5.88726 q^{14} -0.323108 q^{15} +5.00327 q^{16} +5.24105 q^{17} +3.75614 q^{18} +3.52827 q^{19} +1.10302 q^{20} +2.89183 q^{21} -14.9062 q^{22} -8.26025 q^{23} +6.54716 q^{24} -4.92979 q^{25} +4.55837 q^{26} +5.50324 q^{27} -9.87210 q^{28} -7.17908 q^{29} +0.802114 q^{30} +0.326356 q^{31} -1.68234 q^{32} -7.32193 q^{33} -13.0109 q^{34} -0.628381 q^{35} -6.29850 q^{36} -1.62800 q^{37} -8.75892 q^{38} +2.23908 q^{39} -1.42267 q^{40} +8.47028 q^{41} -7.17896 q^{42} +6.35210 q^{43} +24.9955 q^{44} -0.400914 q^{45} +20.5061 q^{46} -9.71840 q^{47} -6.10102 q^{48} -1.37596 q^{49} +12.2382 q^{50} -6.39097 q^{51} -7.64373 q^{52} +9.38787 q^{53} -13.6618 q^{54} +1.59102 q^{55} +12.7329 q^{56} -4.30240 q^{57} +17.8221 q^{58} +8.80566 q^{59} -1.34503 q^{60} -0.781021 q^{61} -0.810179 q^{62} +3.58820 q^{63} -5.83013 q^{64} -0.486541 q^{65} +18.1767 q^{66} -14.4187 q^{67} +21.8174 q^{68} +10.0726 q^{69} +1.55995 q^{70} -13.6638 q^{71} +8.12375 q^{72} +7.48284 q^{73} +4.04150 q^{74} +6.01142 q^{75} +14.6875 q^{76} -14.2397 q^{77} -5.55850 q^{78} +10.0509 q^{79} +1.32572 q^{80} -2.17155 q^{81} -21.0274 q^{82} -4.93575 q^{83} +12.0381 q^{84} +1.38873 q^{85} -15.7691 q^{86} +8.75422 q^{87} -32.2390 q^{88} +12.6440 q^{89} +0.995268 q^{90} +4.35456 q^{91} -34.3857 q^{92} -0.397961 q^{93} +24.1259 q^{94} +0.934890 q^{95} +2.05146 q^{96} -8.09283 q^{97} +3.41581 q^{98} -9.08509 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9 - 23 * q^10 - 33 * q^11 - 57 * q^12 - 90 * q^13 - 28 * q^14 - 22 * q^15 + 130 * q^16 - 145 * q^17 - 50 * q^18 - 28 * q^19 - 121 * q^20 - 69 * q^21 - 26 * q^22 - 79 * q^23 - 62 * q^24 + 123 * q^25 - 40 * q^26 - 70 * q^27 - 43 * q^28 - 109 * q^29 - 43 * q^30 - 21 * q^31 - 139 * q^32 - 83 * q^33 - 93 * q^35 + 75 * q^36 - 65 * q^37 - 122 * q^38 - 18 * q^39 - 43 * q^40 - 71 * q^41 - 88 * q^42 - 72 * q^43 - 79 * q^44 - 181 * q^45 - 11 * q^46 - 114 * q^47 - 118 * q^48 + 118 * q^49 - 77 * q^50 - 29 * q^51 - 169 * q^52 - 220 * q^53 - 80 * q^54 - 37 * q^55 - 72 * q^56 - 90 * q^57 - 8 * q^58 - 60 * q^59 - 42 * q^60 - 108 * q^61 - 152 * q^62 - 65 * q^63 + 114 * q^64 - 81 * q^65 - 40 * q^66 - 50 * q^67 - 319 * q^68 - 103 * q^69 + 4 * q^70 - 7 * q^71 - 129 * q^72 - 94 * q^73 - 79 * q^74 - 59 * q^75 - 46 * q^76 - 329 * q^77 + 8 * q^78 - 18 * q^79 - 190 * q^80 + 59 * q^81 - 56 * q^82 - 201 * q^83 - 71 * q^84 - 26 * q^85 - 52 * q^86 - 126 * q^87 - 66 * q^88 - 114 * q^89 - 33 * q^90 - 30 * q^91 - 204 * q^92 - 125 * q^93 + 9 * q^94 - 84 * q^95 - 88 * q^96 - 56 * q^97 - 110 * q^98 - 46 * q^99

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