LMFDB - Embedded newform 4029.2.a.j.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.71946 q^{2} +1.00000 q^{3} +0.956548 q^{4} -0.401705 q^{5} -1.71946 q^{6} +3.91285 q^{7} +1.79418 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.71946 q^{2} +1.00000 q^{3} +0.956548 q^{4} -0.401705 q^{5} -1.71946 q^{6} +3.91285 q^{7} +1.79418 q^{8} +1.00000 q^{9} +0.690716 q^{10} +4.47796 q^{11} +0.956548 q^{12} -0.579569 q^{13} -6.72800 q^{14} -0.401705 q^{15} -4.99811 q^{16} -1.00000 q^{17} -1.71946 q^{18} +7.65151 q^{19} -0.384250 q^{20} +3.91285 q^{21} -7.69969 q^{22} +6.49678 q^{23} +1.79418 q^{24} -4.83863 q^{25} +0.996547 q^{26} +1.00000 q^{27} +3.74283 q^{28} +3.77437 q^{29} +0.690716 q^{30} +6.46540 q^{31} +5.00571 q^{32} +4.47796 q^{33} +1.71946 q^{34} -1.57181 q^{35} +0.956548 q^{36} -7.41993 q^{37} -13.1565 q^{38} -0.579569 q^{39} -0.720729 q^{40} +6.32351 q^{41} -6.72800 q^{42} +0.998636 q^{43} +4.28339 q^{44} -0.401705 q^{45} -11.1710 q^{46} -3.71463 q^{47} -4.99811 q^{48} +8.31042 q^{49} +8.31984 q^{50} -1.00000 q^{51} -0.554386 q^{52} +5.98289 q^{53} -1.71946 q^{54} -1.79882 q^{55} +7.02035 q^{56} +7.65151 q^{57} -6.48989 q^{58} +7.09686 q^{59} -0.384250 q^{60} +3.16760 q^{61} -11.1170 q^{62} +3.91285 q^{63} +1.38910 q^{64} +0.232816 q^{65} -7.69969 q^{66} -12.5191 q^{67} -0.956548 q^{68} +6.49678 q^{69} +2.70267 q^{70} +1.28017 q^{71} +1.79418 q^{72} -12.3121 q^{73} +12.7583 q^{74} -4.83863 q^{75} +7.31903 q^{76} +17.5216 q^{77} +0.996547 q^{78} -1.00000 q^{79} +2.00777 q^{80} +1.00000 q^{81} -10.8730 q^{82} +1.34497 q^{83} +3.74283 q^{84} +0.401705 q^{85} -1.71712 q^{86} +3.77437 q^{87} +8.03425 q^{88} +2.62420 q^{89} +0.690716 q^{90} -2.26777 q^{91} +6.21448 q^{92} +6.46540 q^{93} +6.38716 q^{94} -3.07365 q^{95} +5.00571 q^{96} +0.773905 q^{97} -14.2894 q^{98} +4.47796 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * 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 $

$2$	−1.71946	−1.21584	−0.607921	−	0.793997i	$-0.707996\pi$
$2$	−1.71946	−1.21584	−0.607921	+	0.793997i	$0.707996\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.956548	0.478274
$5$	−0.401705	−0.179648	−0.0898239	−	0.995958i	$-0.528630\pi$
$5$	−0.401705	−0.179648	−0.0898239	+	0.995958i	$0.528630\pi$
$6$	−1.71946	−0.701967
$7$	3.91285	1.47892	0.739460	−	0.673201i	$-0.235081\pi$
$7$	3.91285	1.47892	0.739460	+	0.673201i	$0.235081\pi$
$8$	1.79418	0.634337
$9$	1.00000	0.333333
$10$	0.690716	0.218424
$11$	4.47796	1.35016	0.675078	−	0.737746i	$-0.264110\pi$
$11$	4.47796	1.35016	0.675078	+	0.737746i	$0.264110\pi$
$12$	0.956548	0.276132
$13$	−0.579569	−0.160744	−0.0803718	−	0.996765i	$-0.525611\pi$
$13$	−0.579569	−0.160744	−0.0803718	+	0.996765i	$0.525611\pi$
$14$	−6.72800	−1.79813
$15$	−0.401705	−0.103720
$16$	−4.99811	−1.24953
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.71946	−0.405281
$19$	7.65151	1.75538	0.877688	−	0.479233i	$-0.159085\pi$
$19$	7.65151	1.75538	0.877688	+	0.479233i	$0.159085\pi$
$20$	−0.384250	−0.0859209
$21$	3.91285	0.853855
$22$	−7.69969	−1.64158
$23$	6.49678	1.35467	0.677336	−	0.735673i	$-0.263134\pi$
$23$	6.49678	1.35467	0.677336	+	0.735673i	$0.263134\pi$
$24$	1.79418	0.366235
$25$	−4.83863	−0.967727
$26$	0.996547	0.195439
$27$	1.00000	0.192450
$28$	3.74283	0.707329
$29$	3.77437	0.700884	0.350442	−	0.936585i	$-0.386031\pi$
$29$	3.77437	0.700884	0.350442	+	0.936585i	$0.386031\pi$
$30$	0.690716	0.126107
$31$	6.46540	1.16122	0.580610	−	0.814182i	$-0.302814\pi$
$31$	6.46540	1.16122	0.580610	+	0.814182i	$0.302814\pi$
$32$	5.00571	0.884893
$33$	4.47796	0.779513
$34$	1.71946	0.294885
$35$	−1.57181	−0.265685
$36$	0.956548	0.159425
$37$	−7.41993	−1.21983	−0.609914	−	0.792467i	$-0.708796\pi$
$37$	−7.41993	−1.21983	−0.609914	+	0.792467i	$0.708796\pi$
$38$	−13.1565	−2.13426
$39$	−0.579569	−0.0928053
$40$	−0.720729	−0.113957
$41$	6.32351	0.987567	0.493783	−	0.869585i	$-0.335614\pi$
$41$	6.32351	0.987567	0.493783	+	0.869585i	$0.335614\pi$
$42$	−6.72800	−1.03815
$43$	0.998636	0.152291	0.0761453	−	0.997097i	$-0.475739\pi$
$43$	0.998636	0.152291	0.0761453	+	0.997097i	$0.475739\pi$
$44$	4.28339	0.645745
$45$	−0.401705	−0.0598826
$46$	−11.1710	−1.64707
$47$	−3.71463	−0.541834	−0.270917	−	0.962603i	$-0.587327\pi$
$47$	−3.71463	−0.541834	−0.270917	+	0.962603i	$0.587327\pi$
$48$	−4.99811	−0.721415
$49$	8.31042	1.18720
$50$	8.31984	1.17660
$51$	−1.00000	−0.140028
$52$	−0.554386	−0.0768794
$53$	5.98289	0.821813	0.410907	−	0.911677i	$-0.365212\pi$
$53$	5.98289	0.821813	0.410907	+	0.911677i	$0.365212\pi$
$54$	−1.71946	−0.233989
$55$	−1.79882	−0.242553
$56$	7.02035	0.938133
$57$	7.65151	1.01347
$58$	−6.48989	−0.852164
$59$	7.09686	0.923933	0.461967	−	0.886897i	$-0.347144\pi$
$59$	7.09686	0.923933	0.461967	+	0.886897i	$0.347144\pi$
$60$	−0.384250	−0.0496065
$61$	3.16760	0.405569	0.202785	−	0.979223i	$-0.435001\pi$
$61$	3.16760	0.405569	0.202785	+	0.979223i	$0.435001\pi$
$62$	−11.1170	−1.41186
$63$	3.91285	0.492973
$64$	1.38910	0.173637
$65$	0.232816	0.0288772
$66$	−7.69969	−0.947766
$67$	−12.5191	−1.52945	−0.764725	−	0.644357i	$-0.777125\pi$
$67$	−12.5191	−1.52945	−0.764725	+	0.644357i	$0.777125\pi$
$68$	−0.956548	−0.115998
$69$	6.49678	0.782121
$70$	2.70267	0.323031
$71$	1.28017	0.151928	0.0759642	−	0.997111i	$-0.475797\pi$
$71$	1.28017	0.151928	0.0759642	+	0.997111i	$0.475797\pi$
$72$	1.79418	0.211446
$73$	−12.3121	−1.44102	−0.720509	−	0.693446i	$-0.756092\pi$
$73$	−12.3121	−1.44102	−0.720509	+	0.693446i	$0.756092\pi$
$74$	12.7583	1.48312
$75$	−4.83863	−0.558717
$76$	7.31903	0.839550
$77$	17.5216	1.99677
$78$	0.996547	0.112837
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	2.00777	0.224475
$81$	1.00000	0.111111
$82$	−10.8730	−1.20073
$83$	1.34497	0.147630	0.0738148	−	0.997272i	$-0.476483\pi$
$83$	1.34497	0.147630	0.0738148	+	0.997272i	$0.476483\pi$
$84$	3.74283	0.408376
$85$	0.401705	0.0435710
$86$	−1.71712	−0.185161
$87$	3.77437	0.404655
$88$	8.03425	0.856454
$89$	2.62420	0.278165	0.139082	−	0.990281i	$-0.455585\pi$
$89$	2.62420	0.278165	0.139082	+	0.990281i	$0.455585\pi$
$90$	0.690716	0.0728079
$91$	−2.26777	−0.237727
$92$	6.21448	0.647905
$93$	6.46540	0.670431
$94$	6.38716	0.658785
$95$	−3.07365	−0.315350
$96$	5.00571	0.510893
$97$	0.773905	0.0785782	0.0392891	−	0.999228i	$-0.487491\pi$
$97$	0.773905	0.0785782	0.0392891	+	0.999228i	$0.487491\pi$
$98$	−14.2894	−1.44345
$99$	4.47796	0.450052
$100$	−4.62838	−0.462838
$101$	−9.57736	−0.952983	−0.476492	−	0.879179i	$-0.658092\pi$
$101$	−9.57736	−0.952983	−0.476492	+	0.879179i	$0.658092\pi$
$102$	1.71946	0.170252
$103$	−4.10093	−0.404077	−0.202039	−	0.979378i	$-0.564757\pi$
$103$	−4.10093	−0.404077	−0.202039	+	0.979378i	$0.564757\pi$
$104$	−1.03985	−0.101966
$105$	−1.57181	−0.153393
$106$	−10.2874	−0.999196
$107$	−18.1022	−1.75000	−0.875002	−	0.484120i	$-0.839140\pi$
$107$	−18.1022	−1.75000	−0.875002	+	0.484120i	$0.839140\pi$
$108$	0.956548	0.0920439
$109$	10.5680	1.01223	0.506113	−	0.862467i	$-0.331082\pi$
$109$	10.5680	1.01223	0.506113	+	0.862467i	$0.331082\pi$
$110$	3.09300	0.294906
$111$	−7.41993	−0.704268
$112$	−19.5569	−1.84795
$113$	−16.2710	−1.53064	−0.765322	−	0.643647i	$-0.777420\pi$
$113$	−16.2710	−1.53064	−0.765322	+	0.643647i	$0.777420\pi$
$114$	−13.1565	−1.23222
$115$	−2.60979	−0.243364
$116$	3.61037	0.335214
$117$	−0.579569	−0.0535812
$118$	−12.2028	−1.12336
$119$	−3.91285	−0.358691
$120$	−0.720729	−0.0657933
$121$	9.05216	0.822924
$122$	−5.44656	−0.493108
$123$	6.32351	0.570172
$124$	6.18447	0.555381
$125$	3.95223	0.353498
$126$	−6.72800	−0.599378
$127$	−5.69157	−0.505045	−0.252522	−	0.967591i	$-0.581260\pi$
$127$	−5.69157	−0.505045	−0.252522	+	0.967591i	$0.581260\pi$
$128$	−12.3999	−1.09601
$129$	0.998636	0.0879250
$130$	−0.400318	−0.0351102
$131$	0.414148	0.0361842	0.0180921	−	0.999836i	$-0.494241\pi$
$131$	0.414148	0.0361842	0.0180921	+	0.999836i	$0.494241\pi$
$132$	4.28339	0.372821
$133$	29.9392	2.59606
$134$	21.5261	1.85957
$135$	−0.401705	−0.0345733
$136$	−1.79418	−0.153849
$137$	7.27506	0.621551	0.310775	−	0.950483i	$-0.399411\pi$
$137$	7.27506	0.621551	0.310775	+	0.950483i	$0.399411\pi$
$138$	−11.1710	−0.950936
$139$	−13.4817	−1.14350	−0.571750	−	0.820428i	$-0.693735\pi$
$139$	−13.4817	−1.14350	−0.571750	+	0.820428i	$0.693735\pi$
$140$	−1.50351	−0.127070
$141$	−3.71463	−0.312828
$142$	−2.20121	−0.184721
$143$	−2.59529	−0.217029
$144$	−4.99811	−0.416509
$145$	−1.51618	−0.125912
$146$	21.1701	1.75205
$147$	8.31042	0.685432
$148$	−7.09751	−0.583412
$149$	−6.82719	−0.559305	−0.279653	−	0.960101i	$-0.590219\pi$
$149$	−6.82719	−0.559305	−0.279653	+	0.960101i	$0.590219\pi$
$150$	8.31984	0.679312
$151$	−20.8927	−1.70022	−0.850110	−	0.526605i	$-0.823465\pi$
$151$	−20.8927	−1.70022	−0.850110	+	0.526605i	$0.823465\pi$
$152$	13.7281	1.11350
$153$	−1.00000	−0.0808452
$154$	−30.1277	−2.42776
$155$	−2.59718	−0.208611
$156$	−0.554386	−0.0443864
$157$	−20.9066	−1.66852	−0.834262	−	0.551368i	$-0.814106\pi$
$157$	−20.9066	−1.66852	−0.834262	+	0.551368i	$0.814106\pi$
$158$	1.71946	0.136793
$159$	5.98289	0.474474
$160$	−2.01082	−0.158969
$161$	25.4210	2.00345
$162$	−1.71946	−0.135094
$163$	−6.97931	−0.546661	−0.273331	−	0.961920i	$-0.588125\pi$
$163$	−6.97931	−0.546661	−0.273331	+	0.961920i	$0.588125\pi$
$164$	6.04874	0.472327
$165$	−1.79882	−0.140038
$166$	−2.31262	−0.179494
$167$	14.1991	1.09876	0.549381	−	0.835572i	$-0.314864\pi$
$167$	14.1991	1.09876	0.549381	+	0.835572i	$0.314864\pi$
$168$	7.02035	0.541632
$169$	−12.6641	−0.974162
$170$	−0.690716	−0.0529755
$171$	7.65151	0.585125
$172$	0.955243	0.0728366
$173$	−5.65230	−0.429737	−0.214868	−	0.976643i	$-0.568932\pi$
$173$	−5.65230	−0.429737	−0.214868	+	0.976643i	$0.568932\pi$
$174$	−6.48989	−0.491997
$175$	−18.9329	−1.43119
$176$	−22.3814	−1.68706
$177$	7.09686	0.533433
$178$	−4.51221	−0.338205
$179$	6.75699	0.505041	0.252521	−	0.967591i	$-0.418740\pi$
$179$	6.75699	0.505041	0.252521	+	0.967591i	$0.418740\pi$
$180$	−0.384250	−0.0286403
$181$	−0.0835186	−0.00620789	−0.00310395	−	0.999995i	$-0.500988\pi$
$181$	−0.0835186	−0.00620789	−0.00310395	+	0.999995i	$0.500988\pi$
$182$	3.89934	0.289038
$183$	3.16760	0.234155
$184$	11.6564	0.859319
$185$	2.98062	0.219140
$186$	−11.1170	−0.815139
$187$	−4.47796	−0.327461
$188$	−3.55322	−0.259145
$189$	3.91285	0.284618
$190$	5.28502	0.383416
$191$	4.91758	0.355823	0.177912	−	0.984046i	$-0.443066\pi$
$191$	4.91758	0.355823	0.177912	+	0.984046i	$0.443066\pi$
$192$	1.38910	0.100250
$193$	24.4366	1.75898	0.879492	−	0.475914i	$-0.157883\pi$
$193$	24.4366	1.75898	0.879492	+	0.475914i	$0.157883\pi$
$194$	−1.33070	−0.0955387
$195$	0.232816	0.0166723
$196$	7.94932	0.567808
$197$	8.72310	0.621495	0.310747	−	0.950493i	$-0.399421\pi$
$197$	8.72310	0.621495	0.310747	+	0.950493i	$0.399421\pi$
$198$	−7.69969	−0.547193
$199$	−1.97242	−0.139821	−0.0699107	−	0.997553i	$-0.522271\pi$
$199$	−1.97242	−0.139821	−0.0699107	+	0.997553i	$0.522271\pi$
$200$	−8.68136	−0.613865
$201$	−12.5191	−0.883028
$202$	16.4679	1.15868
$203$	14.7686	1.03655
$204$	−0.956548	−0.0669717
$205$	−2.54019	−0.177414
$206$	7.05140	0.491294
$207$	6.49678	0.451558
$208$	2.89675	0.200854
$209$	34.2632	2.37003
$210$	2.70267	0.186502
$211$	−11.9251	−0.820958	−0.410479	−	0.911870i	$-0.634639\pi$
$211$	−11.9251	−0.820958	−0.410479	+	0.911870i	$0.634639\pi$
$212$	5.72292	0.393052
$213$	1.28017	0.0877159
$214$	31.1260	2.12773
$215$	−0.401157	−0.0273587
$216$	1.79418	0.122078
$217$	25.2982	1.71735
$218$	−18.1712	−1.23071
$219$	−12.3121	−0.831972
$220$	−1.72066	−0.116007
$221$	0.579569	0.0389860
$222$	12.7583	0.856280
$223$	−15.3501	−1.02792	−0.513960	−	0.857814i	$-0.671822\pi$
$223$	−15.3501	−1.02792	−0.513960	+	0.857814i	$0.671822\pi$
$224$	19.5866	1.30869
$225$	−4.83863	−0.322576
$226$	27.9773	1.86102
$227$	11.2564	0.747112	0.373556	−	0.927608i	$-0.378138\pi$
$227$	11.2564	0.747112	0.373556	+	0.927608i	$0.378138\pi$
$228$	7.31903	0.484715
$229$	9.42347	0.622720	0.311360	−	0.950292i	$-0.399215\pi$
$229$	9.42347	0.622720	0.311360	+	0.950292i	$0.399215\pi$
$230$	4.48743	0.295893
$231$	17.5216	1.15284
$232$	6.77189	0.444596
$233$	26.8113	1.75647	0.878234	−	0.478232i	$-0.158722\pi$
$233$	26.8113	1.75647	0.878234	+	0.478232i	$0.158722\pi$
$234$	0.996547	0.0651463
$235$	1.49218	0.0973394
$236$	6.78849	0.441893
$237$	−1.00000	−0.0649570
$238$	6.72800	0.436112
$239$	5.33257	0.344935	0.172468	−	0.985015i	$-0.444826\pi$
$239$	5.33257	0.344935	0.172468	+	0.985015i	$0.444826\pi$
$240$	2.00777	0.129601
$241$	12.3535	0.795757	0.397879	−	0.917438i	$-0.369747\pi$
$241$	12.3535	0.795757	0.397879	+	0.917438i	$0.369747\pi$
$242$	−15.5648	−1.00055
$243$	1.00000	0.0641500
$244$	3.02996	0.193973
$245$	−3.33834	−0.213279
$246$	−10.8730	−0.693239
$247$	−4.43458	−0.282165
$248$	11.6001	0.736605
$249$	1.34497	0.0852340
$250$	−6.79570	−0.429798
$251$	7.80965	0.492941	0.246470	−	0.969150i	$-0.420729\pi$
$251$	7.80965	0.492941	0.246470	+	0.969150i	$0.420729\pi$
$252$	3.74283	0.235776
$253$	29.0924	1.82902
$254$	9.78643	0.614055
$255$	0.401705	0.0251557
$256$	18.5430	1.15894
$257$	−14.8156	−0.924171	−0.462086	−	0.886835i	$-0.652899\pi$
$257$	−14.8156	−0.924171	−0.462086	+	0.886835i	$0.652899\pi$
$258$	−1.71712	−0.106903
$259$	−29.0331	−1.80403
$260$	0.222699	0.0138112
$261$	3.77437	0.233628
$262$	−0.712111	−0.0439943
$263$	−1.56029	−0.0962114	−0.0481057	−	0.998842i	$-0.515318\pi$
$263$	−1.56029	−0.0962114	−0.0481057	+	0.998842i	$0.515318\pi$
$264$	8.03425	0.494474
$265$	−2.40336	−0.147637
$266$	−51.4793	−3.15640
$267$	2.62420	0.160599
$268$	−11.9751	−0.731496
$269$	−7.63077	−0.465257	−0.232628	−	0.972566i	$-0.574733\pi$
$269$	−7.63077	−0.465257	−0.232628	+	0.972566i	$0.574733\pi$
$270$	0.690716	0.0420356
$271$	−10.9566	−0.665564	−0.332782	−	0.943004i	$-0.607987\pi$
$271$	−10.9566	−0.665564	−0.332782	+	0.943004i	$0.607987\pi$
$272$	4.99811	0.303055
$273$	−2.26777	−0.137252
$274$	−12.5092	−0.755708
$275$	−21.6672	−1.30658
$276$	6.21448	0.374068
$277$	10.3962	0.624649	0.312324	−	0.949976i	$-0.398892\pi$
$277$	10.3962	0.624649	0.312324	+	0.949976i	$0.398892\pi$
$278$	23.1812	1.39032
$279$	6.46540	0.387073
$280$	−2.82011	−0.168534
$281$	−22.2384	−1.32663	−0.663315	−	0.748340i	$-0.730851\pi$
$281$	−22.2384	−1.32663	−0.663315	+	0.748340i	$0.730851\pi$
$282$	6.38716	0.380350
$283$	−29.3827	−1.74662	−0.873310	−	0.487166i	$-0.838031\pi$
$283$	−29.3827	−1.74662	−0.873310	+	0.487166i	$0.838031\pi$
$284$	1.22454	0.0726634
$285$	−3.07365	−0.182067
$286$	4.46250	0.263873
$287$	24.7430	1.46053
$288$	5.00571	0.294964
$289$	1.00000	0.0588235
$290$	2.60702	0.153090
$291$	0.773905	0.0453671
$292$	−11.7771	−0.689201
$293$	−6.56491	−0.383526	−0.191763	−	0.981441i	$-0.561421\pi$
$293$	−6.56491	−0.383526	−0.191763	+	0.981441i	$0.561421\pi$
$294$	−14.2894	−0.833378
$295$	−2.85085	−0.165983
$296$	−13.3127	−0.773782
$297$	4.47796	0.259838
$298$	11.7391	0.680027
$299$	−3.76533	−0.217755
$300$	−4.62838	−0.267220
$301$	3.90752	0.225225
$302$	35.9241	2.06720
$303$	−9.57736	−0.550205
$304$	−38.2431	−2.19339
$305$	−1.27244	−0.0728596
$306$	1.71946	0.0982951
$307$	−0.171878	−0.00980960	−0.00490480	−	0.999988i	$-0.501561\pi$
$307$	−0.171878	−0.00980960	−0.00490480	+	0.999988i	$0.501561\pi$
$308$	16.7603	0.955005
$309$	−4.10093	−0.233294
$310$	4.46576	0.253638
$311$	−12.7672	−0.723961	−0.361980	−	0.932186i	$-0.617899\pi$
$311$	−12.7672	−0.723961	−0.361980	+	0.932186i	$0.617899\pi$
$312$	−1.03985	−0.0588699
$313$	24.6226	1.39175	0.695877	−	0.718161i	$-0.255016\pi$
$313$	24.6226	1.39175	0.695877	+	0.718161i	$0.255016\pi$
$314$	35.9480	2.02866
$315$	−1.57181	−0.0885616
$316$	−0.956548	−0.0538100
$317$	29.4751	1.65549	0.827744	−	0.561107i	$-0.189624\pi$
$317$	29.4751	1.65549	0.827744	+	0.561107i	$0.189624\pi$
$318$	−10.2874	−0.576886
$319$	16.9015	0.946303
$320$	−0.558008	−0.0311936
$321$	−18.1022	−1.01037
$322$	−43.7104	−2.43588
$323$	−7.65151	−0.425741
$324$	0.956548	0.0531415
$325$	2.80432	0.155556
$326$	12.0006	0.664654
$327$	10.5680	0.584409
$328$	11.3455	0.626450
$329$	−14.5348	−0.801329
$330$	3.09300	0.170264
$331$	18.8047	1.03360	0.516801	−	0.856106i	$-0.327123\pi$
$331$	18.8047	1.03360	0.516801	+	0.856106i	$0.327123\pi$
$332$	1.28653	0.0706074
$333$	−7.41993	−0.406609
$334$	−24.4149	−1.33592
$335$	5.02898	0.274762
$336$	−19.5569	−1.06692
$337$	−22.9222	−1.24865	−0.624326	−	0.781164i	$-0.714626\pi$
$337$	−22.9222	−1.24865	−0.624326	+	0.781164i	$0.714626\pi$
$338$	21.7754	1.18443
$339$	−16.2710	−0.883718
$340$	0.384250	0.0208389
$341$	28.9518	1.56783
$342$	−13.1565	−0.711420
$343$	5.12749	0.276858
$344$	1.79173	0.0966035
$345$	−2.60979	−0.140506
$346$	9.71892	0.522492
$347$	−9.74632	−0.523210	−0.261605	−	0.965175i	$-0.584252\pi$
$347$	−9.74632	−0.523210	−0.261605	+	0.965175i	$0.584252\pi$
$348$	3.61037	0.193536
$349$	1.61435	0.0864139	0.0432070	−	0.999066i	$-0.486243\pi$
$349$	1.61435	0.0864139	0.0432070	+	0.999066i	$0.486243\pi$
$350$	32.5543	1.74010
$351$	−0.579569	−0.0309351
$352$	22.4154	1.19474
$353$	−17.4957	−0.931202	−0.465601	−	0.884995i	$-0.654162\pi$
$353$	−17.4957	−0.931202	−0.465601	+	0.884995i	$0.654162\pi$
$354$	−12.2028	−0.648571
$355$	−0.514251	−0.0272936
$356$	2.51017	0.133039
$357$	−3.91285	−0.207090
$358$	−11.6184	−0.614051
$359$	−7.36609	−0.388768	−0.194384	−	0.980926i	$-0.562271\pi$
$359$	−7.36609	−0.388768	−0.194384	+	0.980926i	$0.562271\pi$
$360$	−0.720729	−0.0379858
$361$	39.5455	2.08134
$362$	0.143607	0.00754782
$363$	9.05216	0.475115
$364$	−2.16923	−0.113699
$365$	4.94582	0.258876
$366$	−5.44656	−0.284696
$367$	23.1116	1.20642	0.603208	−	0.797584i	$-0.293889\pi$
$367$	23.1116	1.20642	0.603208	+	0.797584i	$0.293889\pi$
$368$	−32.4716	−1.69270
$369$	6.32351	0.329189
$370$	−5.12506	−0.266439
$371$	23.4102	1.21540
$372$	6.18447	0.320650
$373$	−37.6358	−1.94871	−0.974354	−	0.225022i	$-0.927755\pi$
$373$	−37.6358	−1.94871	−0.974354	+	0.225022i	$0.927755\pi$
$374$	7.69969	0.398141
$375$	3.95223	0.204092
$376$	−6.66470	−0.343706
$377$	−2.18751	−0.112663
$378$	−6.72800	−0.346051
$379$	32.6631	1.67779	0.838895	−	0.544294i	$-0.183202\pi$
$379$	32.6631	1.67779	0.838895	+	0.544294i	$0.183202\pi$
$380$	−2.94009	−0.150823
$381$	−5.69157	−0.291588
$382$	−8.45558	−0.432625
$383$	6.74098	0.344448	0.172224	−	0.985058i	$-0.444905\pi$
$383$	6.74098	0.344448	0.172224	+	0.985058i	$0.444905\pi$
$384$	−12.3999	−0.632781
$385$	−7.03852	−0.358716
$386$	−42.0178	−2.13865
$387$	0.998636	0.0507635
$388$	0.740278	0.0375819
$389$	−12.2226	−0.619708	−0.309854	−	0.950784i	$-0.600280\pi$
$389$	−12.2226	−0.619708	−0.309854	+	0.950784i	$0.600280\pi$
$390$	−0.400318	−0.0202709
$391$	−6.49678	−0.328556
$392$	14.9104	0.753087
$393$	0.414148	0.0208910
$394$	−14.9990	−0.755640
$395$	0.401705	0.0202120
$396$	4.28339	0.215248
$397$	21.7953	1.09388	0.546938	−	0.837173i	$-0.315793\pi$
$397$	21.7953	1.09388	0.546938	+	0.837173i	$0.315793\pi$
$398$	3.39150	0.170001
$399$	29.9392	1.49884
$400$	24.1840	1.20920
$401$	−1.66950	−0.0833708	−0.0416854	−	0.999131i	$-0.513273\pi$
$401$	−1.66950	−0.0833708	−0.0416854	+	0.999131i	$0.513273\pi$
$402$	21.5261	1.07362
$403$	−3.74715	−0.186659
$404$	−9.16120	−0.455787
$405$	−0.401705	−0.0199609
$406$	−25.3940	−1.26028
$407$	−33.2262	−1.64696
$408$	−1.79418	−0.0888249
$409$	18.3247	0.906099	0.453050	−	0.891485i	$-0.350336\pi$
$409$	18.3247	0.906099	0.453050	+	0.891485i	$0.350336\pi$
$410$	4.36775	0.215708
$411$	7.27506	0.358852
$412$	−3.92274	−0.193259
$413$	27.7690	1.36642
$414$	−11.1710	−0.549023
$415$	−0.540281	−0.0265213
$416$	−2.90115	−0.142241
$417$	−13.4817	−0.660200
$418$	−58.9142	−2.88159
$419$	−11.1903	−0.546683	−0.273342	−	0.961917i	$-0.588129\pi$
$419$	−11.1903	−0.546683	−0.273342	+	0.961917i	$0.588129\pi$
$420$	−1.50351	−0.0733640
$421$	29.8669	1.45563	0.727813	−	0.685776i	$-0.240537\pi$
$421$	29.8669	1.45563	0.727813	+	0.685776i	$0.240537\pi$
$422$	20.5048	0.998156
$423$	−3.71463	−0.180611
$424$	10.7344	0.521307
$425$	4.83863	0.234708
$426$	−2.20121	−0.106649
$427$	12.3943	0.599804
$428$	−17.3156	−0.836981
$429$	−2.59529	−0.125302
$430$	0.689774	0.0332639
$431$	9.65685	0.465154	0.232577	−	0.972578i	$-0.425284\pi$
$431$	9.65685	0.465154	0.232577	+	0.972578i	$0.425284\pi$
$432$	−4.99811	−0.240472
$433$	−31.0268	−1.49105	−0.745527	−	0.666475i	$-0.767802\pi$
$433$	−31.0268	−1.49105	−0.745527	+	0.666475i	$0.767802\pi$
$434$	−43.4992	−2.08803
$435$	−1.51618	−0.0726955
$436$	10.1088	0.484122
$437$	49.7102	2.37796
$438$	21.1701	1.01155
$439$	−24.7433	−1.18093	−0.590467	−	0.807062i	$-0.701056\pi$
$439$	−24.7433	−1.18093	−0.590467	+	0.807062i	$0.701056\pi$
$440$	−3.22740	−0.153860
$441$	8.31042	0.395734
$442$	−0.996547	−0.0474009
$443$	4.89812	0.232717	0.116358	−	0.993207i	$-0.462878\pi$
$443$	4.89812	0.232717	0.116358	+	0.993207i	$0.462878\pi$
$444$	−7.09751	−0.336833
$445$	−1.05415	−0.0499717
$446$	26.3940	1.24979
$447$	−6.82719	−0.322915
$448$	5.43534	0.256796
$449$	34.0863	1.60863	0.804315	−	0.594203i	$-0.202532\pi$
$449$	34.0863	1.60863	0.804315	+	0.594203i	$0.202532\pi$
$450$	8.31984	0.392201
$451$	28.3165	1.33337
$452$	−15.5640	−0.732067
$453$	−20.8927	−0.981623
$454$	−19.3549	−0.908371
$455$	0.910974	0.0427071
$456$	13.7281	0.642879
$457$	−8.90149	−0.416394	−0.208197	−	0.978087i	$-0.566760\pi$
$457$	−8.90149	−0.416394	−0.208197	+	0.978087i	$0.566760\pi$
$458$	−16.2033	−0.757130
$459$	−1.00000	−0.0466760
$460$	−2.49639	−0.116395
$461$	−17.5609	−0.817895	−0.408947	−	0.912558i	$-0.634104\pi$
$461$	−17.5609	−0.817895	−0.408947	+	0.912558i	$0.634104\pi$
$462$	−30.1277	−1.40167
$463$	39.2156	1.82250	0.911251	−	0.411852i	$-0.135118\pi$
$463$	39.2156	1.82250	0.911251	+	0.411852i	$0.135118\pi$
$464$	−18.8647	−0.875774
$465$	−2.59718	−0.120441
$466$	−46.1010	−2.13559
$467$	30.9567	1.43250	0.716252	−	0.697842i	$-0.245856\pi$
$467$	30.9567	1.43250	0.716252	+	0.697842i	$0.245856\pi$
$468$	−0.554386	−0.0256265
$469$	−48.9853	−2.26193
$470$	−2.56575	−0.118349
$471$	−20.9066	−0.963323
$472$	12.7330	0.586085
$473$	4.47186	0.205616
$474$	1.71946	0.0789775
$475$	−37.0228	−1.69872
$476$	−3.74283	−0.171552
$477$	5.98289	0.273938
$478$	−9.16915	−0.419387
$479$	19.7041	0.900301	0.450151	−	0.892953i	$-0.351370\pi$
$479$	19.7041	0.900301	0.450151	+	0.892953i	$0.351370\pi$
$480$	−2.01082	−0.0917809
$481$	4.30036	0.196080
$482$	−21.2413	−0.967516
$483$	25.4210	1.15669
$484$	8.65882	0.393583
$485$	−0.310882	−0.0141164
$486$	−1.71946	−0.0779964
$487$	−30.4918	−1.38172	−0.690858	−	0.722990i	$-0.742767\pi$
$487$	−30.4918	−1.38172	−0.690858	+	0.722990i	$0.742767\pi$
$488$	5.68322	0.257267
$489$	−6.97931	−0.315615
$490$	5.74014	0.259313
$491$	−22.4784	−1.01443	−0.507217	−	0.861818i	$-0.669326\pi$
$491$	−22.4784	−1.01443	−0.507217	+	0.861818i	$0.669326\pi$
$492$	6.04874	0.272698
$493$	−3.77437	−0.169989
$494$	7.62508	0.343069
$495$	−1.79882	−0.0808509
$496$	−32.3148	−1.45098
$497$	5.00912	0.224690
$498$	−2.31262	−0.103631
$499$	18.2901	0.818776	0.409388	−	0.912360i	$-0.365742\pi$
$499$	18.2901	0.818776	0.409388	+	0.912360i	$0.365742\pi$
$500$	3.78049	0.169069
$501$	14.1991	0.634370
$502$	−13.4284	−0.599338
$503$	40.0445	1.78550	0.892748	−	0.450556i	$-0.148774\pi$
$503$	40.0445	1.78550	0.892748	+	0.450556i	$0.148774\pi$
$504$	7.02035	0.312711
$505$	3.84727	0.171201
$506$	−50.0232	−2.22380
$507$	−12.6641	−0.562432
$508$	−5.44426	−0.241550
$509$	8.07277	0.357819	0.178910	−	0.983866i	$-0.442743\pi$
$509$	8.07277	0.357819	0.178910	+	0.983866i	$0.442743\pi$
$510$	−0.690716	−0.0305854
$511$	−48.1753	−2.13115
$512$	−7.08411	−0.313076
$513$	7.65151	0.337822
$514$	25.4748	1.12365
$515$	1.64737	0.0725916
$516$	0.955243	0.0420522
$517$	−16.6340	−0.731561
$518$	49.9213	2.19341
$519$	−5.65230	−0.248109
$520$	0.417712	0.0183179
$521$	−25.0669	−1.09820	−0.549100	−	0.835757i	$-0.685029\pi$
$521$	−25.0669	−1.09820	−0.549100	+	0.835757i	$0.685029\pi$
$522$	−6.48989	−0.284055
$523$	28.5700	1.24928	0.624640	−	0.780913i	$-0.285246\pi$
$523$	28.5700	1.24928	0.624640	+	0.780913i	$0.285246\pi$
$524$	0.396152	0.0173060
$525$	−18.9329	−0.826298
$526$	2.68285	0.116978
$527$	−6.46540	−0.281637
$528$	−22.3814	−0.974024
$529$	19.2082	0.835138
$530$	4.13248	0.179503
$531$	7.09686	0.307978
$532$	28.6383	1.24163
$533$	−3.66491	−0.158745
$534$	−4.51221	−0.195263
$535$	7.27173	0.314384
$536$	−22.4614	−0.970186
$537$	6.75699	0.291586
$538$	13.1208	0.565679
$539$	37.2138	1.60291
$540$	−0.384250	−0.0165355
$541$	34.8780	1.49952	0.749761	−	0.661709i	$-0.230169\pi$
$541$	34.8780	1.49952	0.749761	+	0.661709i	$0.230169\pi$
$542$	18.8394	0.809222
$543$	−0.0835186	−0.00358413
$544$	−5.00571	−0.214618
$545$	−4.24520	−0.181844
$546$	3.89934	0.166876
$547$	−12.5643	−0.537209	−0.268605	−	0.963250i	$-0.586563\pi$
$547$	−12.5643	−0.537209	−0.268605	+	0.963250i	$0.586563\pi$
$548$	6.95895	0.297271
$549$	3.16760	0.135190
$550$	37.2560	1.58860
$551$	28.8796	1.23031
$552$	11.6564	0.496128
$553$	−3.91285	−0.166391
$554$	−17.8759	−0.759474
$555$	2.98062	0.126520
$556$	−12.8959	−0.546906
$557$	16.8903	0.715663	0.357832	−	0.933786i	$-0.383516\pi$
$557$	16.8903	0.715663	0.357832	+	0.933786i	$0.383516\pi$
$558$	−11.1170	−0.470621
$559$	−0.578779	−0.0244797
$560$	7.85609	0.331981
$561$	−4.47796	−0.189060
$562$	38.2380	1.61297
$563$	−31.6141	−1.33238	−0.666188	−	0.745784i	$-0.732075\pi$
$563$	−31.6141	−1.33238	−0.666188	+	0.745784i	$0.732075\pi$
$564$	−3.55322	−0.149618
$565$	6.53613	0.274977
$566$	50.5224	2.12361
$567$	3.91285	0.164324
$568$	2.29685	0.0963738
$569$	24.8541	1.04194	0.520970	−	0.853575i	$-0.325570\pi$
$569$	24.8541	1.04194	0.520970	+	0.853575i	$0.325570\pi$
$570$	5.28502	0.221365
$571$	32.9553	1.37914	0.689568	−	0.724221i	$-0.257801\pi$
$571$	32.9553	1.37914	0.689568	+	0.724221i	$0.257801\pi$
$572$	−2.48252	−0.103799
$573$	4.91758	0.205435
$574$	−42.5446	−1.77578
$575$	−31.4355	−1.31095
$576$	1.38910	0.0578792
$577$	−25.6614	−1.06830	−0.534149	−	0.845390i	$-0.679368\pi$
$577$	−25.6614	−1.06830	−0.534149	+	0.845390i	$0.679368\pi$
$578$	−1.71946	−0.0715202
$579$	24.4366	1.01555
$580$	−1.45030	−0.0602206
$581$	5.26267	0.218332
$582$	−1.33070	−0.0551593
$583$	26.7912	1.10958
$584$	−22.0900	−0.914091
$585$	0.232816	0.00962575
$586$	11.2881	0.466307
$587$	9.17711	0.378780	0.189390	−	0.981902i	$-0.439349\pi$
$587$	9.17711	0.378780	0.189390	+	0.981902i	$0.439349\pi$
$588$	7.94932	0.327824
$589$	49.4701	2.03838
$590$	4.90192	0.201809
$591$	8.72310	0.358820
$592$	37.0856	1.52421
$593$	17.0003	0.698117	0.349058	−	0.937101i	$-0.386501\pi$
$593$	17.0003	0.698117	0.349058	+	0.937101i	$0.386501\pi$
$594$	−7.69969	−0.315922
$595$	1.57181	0.0644380
$596$	−6.53054	−0.267501
$597$	−1.97242	−0.0807259
$598$	6.47435	0.264756
$599$	11.9714	0.489137	0.244568	−	0.969632i	$-0.421354\pi$
$599$	11.9714	0.489137	0.244568	+	0.969632i	$0.421354\pi$
$600$	−8.68136	−0.354415
$601$	−38.5955	−1.57434	−0.787172	−	0.616734i	$-0.788455\pi$
$601$	−38.5955	−1.57434	−0.787172	+	0.616734i	$0.788455\pi$
$602$	−6.71882	−0.273839
$603$	−12.5191	−0.509817
$604$	−19.9848	−0.813171
$605$	−3.63630	−0.147836
$606$	16.4679	0.668963
$607$	−19.6804	−0.798802	−0.399401	−	0.916776i	$-0.630782\pi$
$607$	−19.6804	−0.798802	−0.399401	+	0.916776i	$0.630782\pi$
$608$	38.3012	1.55332
$609$	14.7686	0.598453
$610$	2.18791	0.0885858
$611$	2.15288	0.0870964
$612$	−0.956548	−0.0386662
$613$	−33.2190	−1.34170	−0.670852	−	0.741591i	$-0.734071\pi$
$613$	−33.2190	−1.34170	−0.670852	+	0.741591i	$0.734071\pi$
$614$	0.295538	0.0119269
$615$	−2.54019	−0.102430
$616$	31.4369	1.26663
$617$	29.7255	1.19671	0.598353	−	0.801233i	$-0.295822\pi$
$617$	29.7255	1.19671	0.598353	+	0.801233i	$0.295822\pi$
$618$	7.05140	0.283649
$619$	−42.9924	−1.72801	−0.864006	−	0.503482i	$-0.832052\pi$
$619$	−42.9924	−1.72801	−0.864006	+	0.503482i	$0.832052\pi$
$620$	−2.48433	−0.0997731
$621$	6.49678	0.260707
$622$	21.9527	0.880223
$623$	10.2681	0.411383
$624$	2.89675	0.115963
$625$	22.6055	0.904221
$626$	−42.3377	−1.69215
$627$	34.2632	1.36834
$628$	−19.9981	−0.798012
$629$	7.41993	0.295852
$630$	2.70267	0.107677
$631$	25.4915	1.01480	0.507400	−	0.861711i	$-0.330607\pi$
$631$	25.4915	1.01480	0.507400	+	0.861711i	$0.330607\pi$
$632$	−1.79418	−0.0713685
$633$	−11.9251	−0.473981
$634$	−50.6813	−2.01281
$635$	2.28633	0.0907303
$636$	5.72292	0.226929
$637$	−4.81646	−0.190835
$638$	−29.0615	−1.15056
$639$	1.28017	0.0506428
$640$	4.98111	0.196896
$641$	−18.9382	−0.748014	−0.374007	−	0.927426i	$-0.622016\pi$
$641$	−18.9382	−0.748014	−0.374007	+	0.927426i	$0.622016\pi$
$642$	31.1260	1.22845
$643$	−2.78104	−0.109674	−0.0548368	−	0.998495i	$-0.517464\pi$
$643$	−2.78104	−0.109674	−0.0548368	+	0.998495i	$0.517464\pi$
$644$	24.3164	0.958199
$645$	−0.401157	−0.0157955
$646$	13.1565	0.517634
$647$	−28.9968	−1.13998	−0.569990	−	0.821652i	$-0.693053\pi$
$647$	−28.9968	−1.13998	−0.569990	+	0.821652i	$0.693053\pi$
$648$	1.79418	0.0704819
$649$	31.7795	1.24745
$650$	−4.82192	−0.189131
$651$	25.2982	0.991513
$652$	−6.67604	−0.261454
$653$	20.8629	0.816428	0.408214	−	0.912886i	$-0.366152\pi$
$653$	20.8629	0.816428	0.408214	+	0.912886i	$0.366152\pi$
$654$	−18.1712	−0.710550
$655$	−0.166365	−0.00650042
$656$	−31.6056	−1.23399
$657$	−12.3121	−0.480339
$658$	24.9920	0.974291
$659$	41.4572	1.61494	0.807471	−	0.589907i	$-0.200836\pi$
$659$	41.4572	1.61494	0.807471	+	0.589907i	$0.200836\pi$
$660$	−1.72066	−0.0669765
$661$	−44.3839	−1.72633	−0.863166	−	0.504920i	$-0.831522\pi$
$661$	−44.3839	−1.72633	−0.863166	+	0.504920i	$0.831522\pi$
$662$	−32.3340	−1.25670
$663$	0.579569	0.0225086
$664$	2.41311	0.0936469
$665$	−12.0267	−0.466377
$666$	12.7583	0.494373
$667$	24.5213	0.949468
$668$	13.5821	0.525509
$669$	−15.3501	−0.593470
$670$	−8.64713	−0.334068
$671$	14.1844	0.547582
$672$	19.5866	0.755570
$673$	27.1855	1.04793	0.523963	−	0.851741i	$-0.324453\pi$
$673$	27.1855	1.04793	0.523963	+	0.851741i	$0.324453\pi$
$674$	39.4138	1.51816
$675$	−4.83863	−0.186239
$676$	−12.1138	−0.465916
$677$	−16.8900	−0.649135	−0.324567	−	0.945863i	$-0.605219\pi$
$677$	−16.8900	−0.649135	−0.324567	+	0.945863i	$0.605219\pi$
$678$	27.9773	1.07446
$679$	3.02818	0.116211
$680$	0.720729	0.0276387
$681$	11.2564	0.431346
$682$	−49.7816	−1.90623
$683$	30.5400	1.16858	0.584291	−	0.811544i	$-0.301373\pi$
$683$	30.5400	1.16858	0.584291	+	0.811544i	$0.301373\pi$
$684$	7.31903	0.279850
$685$	−2.92243	−0.111660
$686$	−8.81652	−0.336616
$687$	9.42347	0.359528
$688$	−4.99129	−0.190291
$689$	−3.46750	−0.132101
$690$	4.48743	0.170834
$691$	−6.99551	−0.266122	−0.133061	−	0.991108i	$-0.542481\pi$
$691$	−6.99551	−0.266122	−0.133061	+	0.991108i	$0.542481\pi$
$692$	−5.40670	−0.205532
$693$	17.5216	0.665591
$694$	16.7584	0.636141
$695$	5.41565	0.205427
$696$	6.77189	0.256688
$697$	−6.32351	−0.239520
$698$	−2.77580	−0.105066
$699$	26.8113	1.01410
$700$	−18.1102	−0.684501
$701$	−47.7499	−1.80349	−0.901744	−	0.432270i	$-0.857713\pi$
$701$	−47.7499	−1.80349	−0.901744	+	0.432270i	$0.857713\pi$
$702$	0.996547	0.0376122
$703$	−56.7736	−2.14126
$704$	6.22034	0.234438
$705$	1.49218	0.0561989
$706$	30.0832	1.13220
$707$	−37.4748	−1.40939
$708$	6.78849	0.255127
$709$	34.8678	1.30949	0.654744	−	0.755851i	$-0.272777\pi$
$709$	34.8678	1.30949	0.654744	+	0.755851i	$0.272777\pi$
$710$	0.884235	0.0331847
$711$	−1.00000	−0.0375029
$712$	4.70828	0.176450
$713$	42.0043	1.57307
$714$	6.72800	0.251789
$715$	1.04254	0.0389888
$716$	6.46339	0.241548
$717$	5.33257	0.199149
$718$	12.6657	0.472680
$719$	−34.6853	−1.29354	−0.646772	−	0.762684i	$-0.723881\pi$
$719$	−34.6853	−1.29354	−0.646772	+	0.762684i	$0.723881\pi$
$720$	2.00777	0.0748250
$721$	−16.0464	−0.597597
$722$	−67.9970	−2.53059
$723$	12.3535	0.459431
$724$	−0.0798896	−0.00296907
$725$	−18.2628	−0.678264
$726$	−15.5648	−0.577665
$727$	10.7515	0.398751	0.199376	−	0.979923i	$-0.436109\pi$
$727$	10.7515	0.398751	0.199376	+	0.979923i	$0.436109\pi$
$728$	−4.06878	−0.150799
$729$	1.00000	0.0370370
$730$	−8.50414	−0.314752
$731$	−0.998636	−0.0369359
$732$	3.02996	0.111990
$733$	1.98075	0.0731606	0.0365803	−	0.999331i	$-0.488354\pi$
$733$	1.98075	0.0731606	0.0365803	+	0.999331i	$0.488354\pi$
$734$	−39.7395	−1.46681
$735$	−3.33834	−0.123136
$736$	32.5210	1.19874
$737$	−56.0600	−2.06500
$738$	−10.8730	−0.400242
$739$	−19.8622	−0.730644	−0.365322	−	0.930881i	$-0.619041\pi$
$739$	−19.8622	−0.730644	−0.365322	+	0.930881i	$0.619041\pi$
$740$	2.85111	0.104809
$741$	−4.43458	−0.162908
$742$	−40.2529	−1.47773
$743$	−2.13891	−0.0784690	−0.0392345	−	0.999230i	$-0.512492\pi$
$743$	−2.13891	−0.0784690	−0.0392345	+	0.999230i	$0.512492\pi$
$744$	11.6001	0.425279
$745$	2.74252	0.100478
$746$	64.7133	2.36932
$747$	1.34497	0.0492099
$748$	−4.28339	−0.156616
$749$	−70.8312	−2.58811
$750$	−6.79570	−0.248144
$751$	19.8565	0.724575	0.362288	−	0.932066i	$-0.381996\pi$
$751$	19.8565	0.724575	0.362288	+	0.932066i	$0.381996\pi$
$752$	18.5661	0.677037
$753$	7.80965	0.284599
$754$	3.76134	0.136980
$755$	8.39268	0.305441
$756$	3.74283	0.136125
$757$	−8.54644	−0.310626	−0.155313	−	0.987865i	$-0.549639\pi$
$757$	−8.54644	−0.310626	−0.155313	+	0.987865i	$0.549639\pi$
$758$	−56.1629	−2.03993
$759$	29.0924	1.05599
$760$	−5.51466	−0.200038
$761$	7.56809	0.274343	0.137172	−	0.990547i	$-0.456199\pi$
$761$	7.56809	0.274343	0.137172	+	0.990547i	$0.456199\pi$
$762$	9.78643	0.354525
$763$	41.3509	1.49700
$764$	4.70390	0.170181
$765$	0.401705	0.0145237
$766$	−11.5909	−0.418795
$767$	−4.11312	−0.148516
$768$	18.5430	0.669112
$769$	−38.1007	−1.37394	−0.686972	−	0.726683i	$-0.741061\pi$
$769$	−38.1007	−1.37394	−0.686972	+	0.726683i	$0.741061\pi$
$770$	12.1025	0.436142
$771$	−14.8156	−0.533571
$772$	23.3748	0.841276
$773$	−36.0295	−1.29589	−0.647945	−	0.761687i	$-0.724372\pi$
$773$	−36.0295	−1.29589	−0.647945	+	0.761687i	$0.724372\pi$
$774$	−1.71712	−0.0617205
$775$	−31.2837	−1.12374
$776$	1.38852	0.0498451
$777$	−29.0331	−1.04156
$778$	21.0162	0.753468
$779$	48.3844	1.73355
$780$	0.222699	0.00797392
$781$	5.73256	0.205127
$782$	11.1710	0.399473
$783$	3.77437	0.134885
$784$	−41.5364	−1.48344
$785$	8.39826	0.299747
$786$	−0.712111	−0.0254001
$787$	38.3216	1.36602	0.683009	−	0.730410i	$-0.260671\pi$
$787$	38.3216	1.36602	0.683009	+	0.730410i	$0.260671\pi$
$788$	8.34406	0.297245
$789$	−1.56029	−0.0555477
$790$	−0.690716	−0.0245746
$791$	−63.6659	−2.26370
$792$	8.03425	0.285485
$793$	−1.83584	−0.0651926
$794$	−37.4762	−1.32998
$795$	−2.40336	−0.0852383
$796$	−1.88672	−0.0668729
$797$	−28.9759	−1.02638	−0.513190	−	0.858275i	$-0.671536\pi$
$797$	−28.9759	−1.02638	−0.513190	+	0.858275i	$0.671536\pi$
$798$	−51.4793	−1.82235
$799$	3.71463	0.131414
$800$	−24.2208	−0.856334
$801$	2.62420	0.0927216
$802$	2.87064	0.101366
$803$	−55.1330	−1.94560
$804$	−11.9751	−0.422329
$805$	−10.2117	−0.359916
$806$	6.44308	0.226948
$807$	−7.63077	−0.268616
$808$	−17.1835	−0.604512
$809$	−31.3454	−1.10205	−0.551023	−	0.834490i	$-0.685762\pi$
$809$	−31.3454	−1.10205	−0.551023	+	0.834490i	$0.685762\pi$
$810$	0.690716	0.0242693
$811$	42.9428	1.50793	0.753963	−	0.656917i	$-0.228140\pi$
$811$	42.9428	1.50793	0.753963	+	0.656917i	$0.228140\pi$
$812$	14.1268	0.495755
$813$	−10.9566	−0.384264
$814$	57.1311	2.00244
$815$	2.80362	0.0982066
$816$	4.99811	0.174969
$817$	7.64107	0.267327
$818$	−31.5087	−1.10167
$819$	−2.26777	−0.0792423
$820$	−2.42981	−0.0848526
$821$	−26.6390	−0.929707	−0.464853	−	0.885388i	$-0.653893\pi$
$821$	−26.6390	−0.929707	−0.464853	+	0.885388i	$0.653893\pi$
$822$	−12.5092	−0.436308
$823$	−39.8235	−1.38816	−0.694080	−	0.719898i	$-0.744189\pi$
$823$	−39.8235	−1.38816	−0.694080	+	0.719898i	$0.744189\pi$
$824$	−7.35780	−0.256321
$825$	−21.6672	−0.754356
$826$	−47.7477	−1.66136
$827$	18.2622	0.635040	0.317520	−	0.948252i	$-0.397150\pi$
$827$	18.2622	0.635040	0.317520	+	0.948252i	$0.397150\pi$
$828$	6.21448	0.215968
$829$	−28.9088	−1.00404	−0.502022	−	0.864855i	$-0.667410\pi$
$829$	−28.9088	−1.00404	−0.502022	+	0.864855i	$0.667410\pi$
$830$	0.928992	0.0322458
$831$	10.3962	0.360641
$832$	−0.805079	−0.0279111
$833$	−8.31042	−0.287939
$834$	23.1812	0.802700
$835$	−5.70386	−0.197390
$836$	32.7744	1.13352
$837$	6.46540	0.223477
$838$	19.2413	0.664681
$839$	−17.4140	−0.601198	−0.300599	−	0.953751i	$-0.597187\pi$
$839$	−17.4140	−0.601198	−0.300599	+	0.953751i	$0.597187\pi$
$840$	−2.82011	−0.0973030
$841$	−14.7541	−0.508762
$842$	−51.3551	−1.76981
$843$	−22.2384	−0.765931
$844$	−11.4069	−0.392643
$845$	5.08723	0.175006
$846$	6.38716	0.219595
$847$	35.4198	1.21704
$848$	−29.9032	−1.02688
$849$	−29.3827	−1.00841
$850$	−8.31984	−0.285368
$851$	−48.2056	−1.65247
$852$	1.22454	0.0419522
$853$	34.7447	1.18964	0.594818	−	0.803860i	$-0.297224\pi$
$853$	34.7447	1.18964	0.594818	+	0.803860i	$0.297224\pi$
$854$	−21.3116	−0.729267
$855$	−3.07365	−0.105117
$856$	−32.4785	−1.11009
$857$	45.4498	1.55253	0.776267	−	0.630404i	$-0.217111\pi$
$857$	45.4498	1.55253	0.776267	+	0.630404i	$0.217111\pi$
$858$	4.46250	0.152347
$859$	−36.5369	−1.24662	−0.623312	−	0.781974i	$-0.714213\pi$
$859$	−36.5369	−1.24662	−0.623312	+	0.781974i	$0.714213\pi$
$860$	−0.383726	−0.0130849
$861$	24.7430	0.843238
$862$	−16.6046	−0.565554
$863$	−15.4826	−0.527033	−0.263516	−	0.964655i	$-0.584882\pi$
$863$	−15.4826	−0.527033	−0.263516	+	0.964655i	$0.584882\pi$
$864$	5.00571	0.170298
$865$	2.27056	0.0772013
$866$	53.3494	1.81289
$867$	1.00000	0.0339618
$868$	24.1989	0.821364
$869$	−4.47796	−0.151905
$870$	2.60702	0.0883863
$871$	7.25568	0.245849
$872$	18.9608	0.642093
$873$	0.773905	0.0261927
$874$	−85.4747	−2.89123
$875$	15.4645	0.522795
$876$	−11.7771	−0.397911
$877$	−42.4987	−1.43508	−0.717540	−	0.696517i	$-0.754732\pi$
$877$	−42.4987	−1.43508	−0.717540	+	0.696517i	$0.754732\pi$
$878$	42.5452	1.43583
$879$	−6.56491	−0.221429
$880$	8.99070	0.303077
$881$	45.4670	1.53182	0.765910	−	0.642947i	$-0.222289\pi$
$881$	45.4670	1.53182	0.765910	+	0.642947i	$0.222289\pi$
$882$	−14.2894	−0.481151
$883$	−19.3060	−0.649698	−0.324849	−	0.945766i	$-0.605313\pi$
$883$	−19.3060	−0.649698	−0.324849	+	0.945766i	$0.605313\pi$
$884$	0.554386	0.0186460
$885$	−2.85085	−0.0958301
$886$	−8.42213	−0.282947
$887$	−11.5850	−0.388986	−0.194493	−	0.980904i	$-0.562306\pi$
$887$	−11.5850	−0.388986	−0.194493	+	0.980904i	$0.562306\pi$
$888$	−13.3127	−0.446743
$889$	−22.2703	−0.746921
$890$	1.81258	0.0607578
$891$	4.47796	0.150017
$892$	−14.6831	−0.491628
$893$	−28.4225	−0.951123
$894$	11.7391	0.392614
$895$	−2.71432	−0.0907296
$896$	−48.5191	−1.62091
$897$	−3.76533	−0.125721
$898$	−58.6100	−1.95584
$899$	24.4028	0.813880
$900$	−4.62838	−0.154279
$901$	−5.98289	−0.199319
$902$	−48.6891	−1.62117
$903$	3.90752	0.130034
$904$	−29.1930	−0.970944
$905$	0.0335498	0.00111523
$906$	35.9241	1.19350
$907$	−36.3649	−1.20748	−0.603739	−	0.797182i	$-0.706323\pi$
$907$	−36.3649	−1.20748	−0.603739	+	0.797182i	$0.706323\pi$
$908$	10.7673	0.357324
$909$	−9.57736	−0.317661
$910$	−1.56638	−0.0519251
$911$	−22.0056	−0.729078	−0.364539	−	0.931188i	$-0.618773\pi$
$911$	−22.0056	−0.729078	−0.364539	+	0.931188i	$0.618773\pi$
$912$	−38.2431	−1.26635
$913$	6.02273	0.199323
$914$	15.3058	0.506270
$915$	−1.27244	−0.0420655
$916$	9.01400	0.297831
$917$	1.62050	0.0535136
$918$	1.71946	0.0567507
$919$	−2.35409	−0.0776542	−0.0388271	−	0.999246i	$-0.512362\pi$
$919$	−2.35409	−0.0776542	−0.0388271	+	0.999246i	$0.512362\pi$
$920$	−4.68242	−0.154375
$921$	−0.171878	−0.00566358
$922$	30.1954	0.994432
$923$	−0.741948	−0.0244215
$924$	16.7603	0.551372
$925$	35.9023	1.18046
$926$	−67.4296	−2.21588
$927$	−4.10093	−0.134692
$928$	18.8934	0.620207
$929$	51.6656	1.69509	0.847546	−	0.530722i	$-0.178079\pi$
$929$	51.6656	1.69509	0.847546	+	0.530722i	$0.178079\pi$
$930$	4.46576	0.146438
$931$	63.5872	2.08399
$932$	25.6463	0.840072
$933$	−12.7672	−0.417979
$934$	−53.2288	−1.74170
$935$	1.79882	0.0588277
$936$	−1.03985	−0.0339885
$937$	5.48636	0.179232	0.0896158	−	0.995976i	$-0.471436\pi$
$937$	5.48636	0.179232	0.0896158	+	0.995976i	$0.471436\pi$
$938$	84.2284	2.75016
$939$	24.6226	0.803529
$940$	1.42735	0.0465549
$941$	25.4846	0.830775	0.415388	−	0.909645i	$-0.363646\pi$
$941$	25.4846	0.830775	0.415388	+	0.909645i	$0.363646\pi$
$942$	35.9480	1.17125
$943$	41.0825	1.33783
$944$	−35.4709	−1.15448
$945$	−1.57181	−0.0511311
$946$	−7.68918	−0.249997
$947$	−3.00832	−0.0977573	−0.0488787	−	0.998805i	$-0.515565\pi$
$947$	−3.00832	−0.0977573	−0.0488787	+	0.998805i	$0.515565\pi$
$948$	−0.956548	−0.0310672
$949$	7.13569	0.231634
$950$	63.6593	2.06538
$951$	29.4751	0.955796
$952$	−7.02035	−0.227531
$953$	−8.56059	−0.277305	−0.138652	−	0.990341i	$-0.544277\pi$
$953$	−8.56059	−0.277305	−0.138652	+	0.990341i	$0.544277\pi$
$954$	−10.2874	−0.333065
$955$	−1.97541	−0.0639229
$956$	5.10086	0.164974
$957$	16.9015	0.546348
$958$	−33.8804	−1.09462
$959$	28.4663	0.919223
$960$	−0.558008	−0.0180096
$961$	10.8014	0.348433
$962$	−7.39430	−0.238402
$963$	−18.1022	−0.583335
$964$	11.8167	0.380590
$965$	−9.81629	−0.315998
$966$	−43.7104	−1.40636
$967$	−59.5803	−1.91597	−0.957987	−	0.286813i	$-0.907404\pi$
$967$	−59.5803	−1.91597	−0.957987	+	0.286813i	$0.907404\pi$
$968$	16.2412	0.522011
$969$	−7.65151	−0.245802
$970$	0.534549	0.0171633
$971$	−10.8154	−0.347082	−0.173541	−	0.984827i	$-0.555521\pi$
$971$	−10.8154	−0.347082	−0.173541	+	0.984827i	$0.555521\pi$
$972$	0.956548	0.0306813
$973$	−52.7518	−1.69115
$974$	52.4295	1.67995
$975$	2.80432	0.0898102
$976$	−15.8320	−0.506770
$977$	54.1632	1.73283	0.866416	−	0.499322i	$-0.166418\pi$
$977$	54.1632	1.73283	0.866416	+	0.499322i	$0.166418\pi$
$978$	12.0006	0.383738
$979$	11.7511	0.375566
$980$	−3.19328	−0.102006
$981$	10.5680	0.337409
$982$	38.6507	1.23339
$983$	32.5249	1.03738	0.518692	−	0.854961i	$-0.326419\pi$
$983$	32.5249	1.03738	0.518692	+	0.854961i	$0.326419\pi$
$984$	11.3455	0.361681
$985$	−3.50411	−0.111650
$986$	6.48989	0.206680
$987$	−14.5348	−0.462648
$988$	−4.24188	−0.134952
$989$	6.48792	0.206304
$990$	3.09300	0.0983020
$991$	16.4032	0.521064	0.260532	−	0.965465i	$-0.416102\pi$
$991$	16.4032	0.521064	0.260532	+	0.965465i	$0.416102\pi$
$992$	32.3639	1.02756
$993$	18.8047	0.596750
$994$	−8.61299	−0.273188
$995$	0.792332	0.0251186
$996$	1.28653	0.0407652
$997$	−16.0907	−0.509598	−0.254799	−	0.966994i	$-0.582009\pi$
$997$	−16.0907	−0.509598	−0.254799	+	0.966994i	$0.582009\pi$
$998$	−31.4491	−0.995502
$999$	−7.41993	−0.234756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.j.1.6	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.j.1.6	✓	25	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.71946 q^{2} +1.00000 q^{3} +0.956548 q^{4} -0.401705 q^{5} -1.71946 q^{6} +3.91285 q^{7} +1.79418 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.71946 q^{2} +1.00000 q^{3} +0.956548 q^{4} -0.401705 q^{5} -1.71946 q^{6} +3.91285 q^{7} +1.79418 q^{8} +1.00000 q^{9} +0.690716 q^{10} +4.47796 q^{11} +0.956548 q^{12} -0.579569 q^{13} -6.72800 q^{14} -0.401705 q^{15} -4.99811 q^{16} -1.00000 q^{17} -1.71946 q^{18} +7.65151 q^{19} -0.384250 q^{20} +3.91285 q^{21} -7.69969 q^{22} +6.49678 q^{23} +1.79418 q^{24} -4.83863 q^{25} +0.996547 q^{26} +1.00000 q^{27} +3.74283 q^{28} +3.77437 q^{29} +0.690716 q^{30} +6.46540 q^{31} +5.00571 q^{32} +4.47796 q^{33} +1.71946 q^{34} -1.57181 q^{35} +0.956548 q^{36} -7.41993 q^{37} -13.1565 q^{38} -0.579569 q^{39} -0.720729 q^{40} +6.32351 q^{41} -6.72800 q^{42} +0.998636 q^{43} +4.28339 q^{44} -0.401705 q^{45} -11.1710 q^{46} -3.71463 q^{47} -4.99811 q^{48} +8.31042 q^{49} +8.31984 q^{50} -1.00000 q^{51} -0.554386 q^{52} +5.98289 q^{53} -1.71946 q^{54} -1.79882 q^{55} +7.02035 q^{56} +7.65151 q^{57} -6.48989 q^{58} +7.09686 q^{59} -0.384250 q^{60} +3.16760 q^{61} -11.1170 q^{62} +3.91285 q^{63} +1.38910 q^{64} +0.232816 q^{65} -7.69969 q^{66} -12.5191 q^{67} -0.956548 q^{68} +6.49678 q^{69} +2.70267 q^{70} +1.28017 q^{71} +1.79418 q^{72} -12.3121 q^{73} +12.7583 q^{74} -4.83863 q^{75} +7.31903 q^{76} +17.5216 q^{77} +0.996547 q^{78} -1.00000 q^{79} +2.00777 q^{80} +1.00000 q^{81} -10.8730 q^{82} +1.34497 q^{83} +3.74283 q^{84} +0.401705 q^{85} -1.71712 q^{86} +3.77437 q^{87} +8.03425 q^{88} +2.62420 q^{89} +0.690716 q^{90} -2.26777 q^{91} +6.21448 q^{92} +6.46540 q^{93} +6.38716 q^{94} -3.07365 q^{95} +5.00571 q^{96} +0.773905 q^{97} -14.2894 q^{98} +4.47796 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * q^99

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