LMFDB - Embedded newform 4029.2.a.j.1.12

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			1.12
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)

$f(q)$	$=$	$q+0.367511 q^{2} +1.00000 q^{3} -1.86494 q^{4} -0.382809 q^{5} +0.367511 q^{6} +2.18053 q^{7} -1.42041 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.367511 q^{2} +1.00000 q^{3} -1.86494 q^{4} -0.382809 q^{5} +0.367511 q^{6} +2.18053 q^{7} -1.42041 q^{8} +1.00000 q^{9} -0.140687 q^{10} -5.51754 q^{11} -1.86494 q^{12} -2.93055 q^{13} +0.801369 q^{14} -0.382809 q^{15} +3.20785 q^{16} -1.00000 q^{17} +0.367511 q^{18} +5.52998 q^{19} +0.713914 q^{20} +2.18053 q^{21} -2.02776 q^{22} -0.477048 q^{23} -1.42041 q^{24} -4.85346 q^{25} -1.07701 q^{26} +1.00000 q^{27} -4.06654 q^{28} +3.54641 q^{29} -0.140687 q^{30} +0.807994 q^{31} +4.01974 q^{32} -5.51754 q^{33} -0.367511 q^{34} -0.834725 q^{35} -1.86494 q^{36} +1.01666 q^{37} +2.03233 q^{38} -2.93055 q^{39} +0.543745 q^{40} +9.86112 q^{41} +0.801369 q^{42} -0.423848 q^{43} +10.2899 q^{44} -0.382809 q^{45} -0.175321 q^{46} +4.89484 q^{47} +3.20785 q^{48} -2.24530 q^{49} -1.78370 q^{50} -1.00000 q^{51} +5.46529 q^{52} +9.10953 q^{53} +0.367511 q^{54} +2.11216 q^{55} -3.09724 q^{56} +5.52998 q^{57} +1.30335 q^{58} +2.89285 q^{59} +0.713914 q^{60} -5.87415 q^{61} +0.296947 q^{62} +2.18053 q^{63} -4.93841 q^{64} +1.12184 q^{65} -2.02776 q^{66} -4.06274 q^{67} +1.86494 q^{68} -0.477048 q^{69} -0.306771 q^{70} +16.3620 q^{71} -1.42041 q^{72} +1.50889 q^{73} +0.373635 q^{74} -4.85346 q^{75} -10.3131 q^{76} -12.0312 q^{77} -1.07701 q^{78} -1.00000 q^{79} -1.22799 q^{80} +1.00000 q^{81} +3.62408 q^{82} +2.84844 q^{83} -4.06654 q^{84} +0.382809 q^{85} -0.155769 q^{86} +3.54641 q^{87} +7.83716 q^{88} +2.36222 q^{89} -0.140687 q^{90} -6.39015 q^{91} +0.889664 q^{92} +0.807994 q^{93} +1.79891 q^{94} -2.11693 q^{95} +4.01974 q^{96} -2.24444 q^{97} -0.825174 q^{98} -5.51754 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.367511	0.259870	0.129935	−	0.991523i	$-0.458523\pi$
$2$	0.367511	0.259870	0.129935	+	0.991523i	$0.458523\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.86494	−0.932468
$5$	−0.382809	−0.171197	−0.0855986	−	0.996330i	$-0.527280\pi$
$5$	−0.382809	−0.171197	−0.0855986	+	0.996330i	$0.527280\pi$
$6$	0.367511	0.150036
$7$	2.18053	0.824162	0.412081	−	0.911147i	$-0.364802\pi$
$7$	2.18053	0.824162	0.412081	+	0.911147i	$0.364802\pi$
$8$	−1.42041	−0.502190
$9$	1.00000	0.333333
$10$	−0.140687	−0.0444890
$11$	−5.51754	−1.66360	−0.831801	−	0.555074i	$-0.812690\pi$
$11$	−5.51754	−1.66360	−0.831801	+	0.555074i	$0.812690\pi$
$12$	−1.86494	−0.538360
$13$	−2.93055	−0.812789	−0.406394	−	0.913698i	$-0.633214\pi$
$13$	−2.93055	−0.812789	−0.406394	+	0.913698i	$0.633214\pi$
$14$	0.801369	0.214175
$15$	−0.382809	−0.0988408
$16$	3.20785	0.801964
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.367511	0.0866233
$19$	5.52998	1.26866	0.634332	−	0.773060i	$-0.281275\pi$
$19$	5.52998	1.26866	0.634332	+	0.773060i	$0.281275\pi$
$20$	0.713914	0.159636
$21$	2.18053	0.475830
$22$	−2.02776	−0.432320
$23$	−0.477048	−0.0994715	−0.0497357	−	0.998762i	$-0.515838\pi$
$23$	−0.477048	−0.0994715	−0.0497357	+	0.998762i	$0.515838\pi$
$24$	−1.42041	−0.289940
$25$	−4.85346	−0.970691
$26$	−1.07701	−0.211219
$27$	1.00000	0.192450
$28$	−4.06654	−0.768504
$29$	3.54641	0.658552	0.329276	−	0.944234i	$-0.393195\pi$
$29$	3.54641	0.658552	0.329276	+	0.944234i	$0.393195\pi$
$30$	−0.140687	−0.0256857
$31$	0.807994	0.145120	0.0725600	−	0.997364i	$-0.476883\pi$
$31$	0.807994	0.145120	0.0725600	+	0.997364i	$0.476883\pi$
$32$	4.01974	0.710596
$33$	−5.51754	−0.960481
$34$	−0.367511	−0.0630277
$35$	−0.834725	−0.141094
$36$	−1.86494	−0.310823
$37$	1.01666	0.167138	0.0835692	−	0.996502i	$-0.473368\pi$
$37$	1.01666	0.167138	0.0835692	+	0.996502i	$0.473368\pi$
$38$	2.03233	0.329688
$39$	−2.93055	−0.469264
$40$	0.543745	0.0859736
$41$	9.86112	1.54005	0.770024	−	0.638014i	$-0.220244\pi$
$41$	9.86112	1.54005	0.770024	+	0.638014i	$0.220244\pi$
$42$	0.801369	0.123654
$43$	−0.423848	−0.0646362	−0.0323181	−	0.999478i	$-0.510289\pi$
$43$	−0.423848	−0.0646362	−0.0323181	+	0.999478i	$0.510289\pi$
$44$	10.2899	1.55125
$45$	−0.382809	−0.0570658
$46$	−0.175321	−0.0258496
$47$	4.89484	0.713985	0.356993	−	0.934107i	$-0.383802\pi$
$47$	4.89484	0.713985	0.356993	+	0.934107i	$0.383802\pi$
$48$	3.20785	0.463014
$49$	−2.24530	−0.320757
$50$	−1.78370	−0.252253
$51$	−1.00000	−0.140028
$52$	5.46529	0.757899
$53$	9.10953	1.25129	0.625645	−	0.780108i	$-0.284836\pi$
$53$	9.10953	1.25129	0.625645	+	0.780108i	$0.284836\pi$
$54$	0.367511	0.0500120
$55$	2.11216	0.284804
$56$	−3.09724	−0.413886
$57$	5.52998	0.732464
$58$	1.30335	0.171138
$59$	2.89285	0.376617	0.188309	−	0.982110i	$-0.439699\pi$
$59$	2.89285	0.376617	0.188309	+	0.982110i	$0.439699\pi$
$60$	0.713914	0.0921659
$61$	−5.87415	−0.752108	−0.376054	−	0.926598i	$-0.622719\pi$
$61$	−5.87415	−0.752108	−0.376054	+	0.926598i	$0.622719\pi$
$62$	0.296947	0.0377123
$63$	2.18053	0.274721
$64$	−4.93841	−0.617301
$65$	1.12184	0.139147
$66$	−2.02776	−0.249600
$67$	−4.06274	−0.496342	−0.248171	−	0.968716i	$-0.579830\pi$
$67$	−4.06274	−0.496342	−0.248171	+	0.968716i	$0.579830\pi$
$68$	1.86494	0.226157
$69$	−0.477048	−0.0574299
$70$	−0.306771	−0.0366661
$71$	16.3620	1.94181	0.970904	−	0.239470i	$-0.0769737\pi$
$71$	16.3620	1.94181	0.970904	+	0.239470i	$0.0769737\pi$
$72$	−1.42041	−0.167397
$73$	1.50889	0.176602	0.0883010	−	0.996094i	$-0.471856\pi$
$73$	1.50889	0.176602	0.0883010	+	0.996094i	$0.471856\pi$
$74$	0.373635	0.0434342
$75$	−4.85346	−0.560429
$76$	−10.3131	−1.18299
$77$	−12.0312	−1.37108
$78$	−1.07701	−0.121948
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−1.22799	−0.137294
$81$	1.00000	0.111111
$82$	3.62408	0.400212
$83$	2.84844	0.312657	0.156328	−	0.987705i	$-0.450034\pi$
$83$	2.84844	0.312657	0.156328	+	0.987705i	$0.450034\pi$
$84$	−4.06654	−0.443696
$85$	0.382809	0.0415214
$86$	−0.155769	−0.0167970
$87$	3.54641	0.380215
$88$	7.83716	0.835444
$89$	2.36222	0.250395	0.125197	−	0.992132i	$-0.460044\pi$
$89$	2.36222	0.250395	0.125197	+	0.992132i	$0.460044\pi$
$90$	−0.140687	−0.0148297
$91$	−6.39015	−0.669869
$92$	0.889664	0.0927539
$93$	0.807994	0.0837851
$94$	1.79891	0.185543
$95$	−2.11693	−0.217192
$96$	4.01974	0.410263
$97$	−2.24444	−0.227889	−0.113944	−	0.993487i	$-0.536349\pi$
$97$	−2.24444	−0.227889	−0.113944	+	0.993487i	$0.536349\pi$
$98$	−0.825174	−0.0833552
$99$	−5.51754	−0.554534
$100$	9.05138	0.905138
$101$	16.2005	1.61201	0.806006	−	0.591908i	$-0.201625\pi$
$101$	16.2005	1.61201	0.806006	+	0.591908i	$0.201625\pi$
$102$	−0.367511	−0.0363891
$103$	11.2347	1.10699	0.553494	−	0.832853i	$-0.313294\pi$
$103$	11.2347	1.10699	0.553494	+	0.832853i	$0.313294\pi$
$104$	4.16258	0.408174
$105$	−0.834725	−0.0814608
$106$	3.34786	0.325172
$107$	−1.72468	−0.166731	−0.0833654	−	0.996519i	$-0.526567\pi$
$107$	−1.72468	−0.166731	−0.0833654	+	0.996519i	$0.526567\pi$
$108$	−1.86494	−0.179453
$109$	14.9255	1.42961	0.714803	−	0.699325i	$-0.246516\pi$
$109$	14.9255	1.42961	0.714803	+	0.699325i	$0.246516\pi$
$110$	0.776244	0.0740120
$111$	1.01666	0.0964973
$112$	6.99481	0.660948
$113$	7.65867	0.720467	0.360233	−	0.932862i	$-0.382697\pi$
$113$	7.65867	0.720467	0.360233	+	0.932862i	$0.382697\pi$
$114$	2.03233	0.190345
$115$	0.182618	0.0170292
$116$	−6.61383	−0.614079
$117$	−2.93055	−0.270930
$118$	1.06316	0.0978715
$119$	−2.18053	−0.199889
$120$	0.543745	0.0496369
$121$	19.4433	1.76757
$122$	−2.15882	−0.195450
$123$	9.86112	0.889148
$124$	−1.50686	−0.135320
$125$	3.77199	0.337377
$126$	0.801369	0.0713916
$127$	−9.99913	−0.887279	−0.443640	−	0.896205i	$-0.646313\pi$
$127$	−9.99913	−0.887279	−0.443640	+	0.896205i	$0.646313\pi$
$128$	−9.85440	−0.871014
$129$	−0.423848	−0.0373177
$130$	0.412289	0.0361602
$131$	6.51967	0.569627	0.284813	−	0.958583i	$-0.408068\pi$
$131$	6.51967	0.569627	0.284813	+	0.958583i	$0.408068\pi$
$132$	10.2899	0.895617
$133$	12.0583	1.04558
$134$	−1.49310	−0.128984
$135$	−0.382809	−0.0329469
$136$	1.42041	0.121799
$137$	−14.1882	−1.21218	−0.606091	−	0.795395i	$-0.707263\pi$
$137$	−14.1882	−1.21218	−0.606091	+	0.795395i	$0.707263\pi$
$138$	−0.175321	−0.0149243
$139$	−13.3202	−1.12980	−0.564902	−	0.825158i	$-0.691086\pi$
$139$	−13.3202	−1.12980	−0.564902	+	0.825158i	$0.691086\pi$
$140$	1.55671	0.131566
$141$	4.89484	0.412220
$142$	6.01321	0.504617
$143$	16.1694	1.35216
$144$	3.20785	0.267321
$145$	−1.35760	−0.112742
$146$	0.554534	0.0458935
$147$	−2.24530	−0.185189
$148$	−1.89601	−0.155851
$149$	13.7565	1.12698	0.563490	−	0.826123i	$-0.309458\pi$
$149$	13.7565	1.12698	0.563490	+	0.826123i	$0.309458\pi$
$150$	−1.78370	−0.145639
$151$	−10.0070	−0.814359	−0.407179	−	0.913348i	$-0.633488\pi$
$151$	−10.0070	−0.814359	−0.407179	+	0.913348i	$0.633488\pi$
$152$	−7.85483	−0.637111
$153$	−1.00000	−0.0808452
$154$	−4.42159	−0.356302
$155$	−0.309307	−0.0248441
$156$	5.46529	0.437573
$157$	6.90172	0.550818	0.275409	−	0.961327i	$-0.411187\pi$
$157$	6.90172	0.550818	0.275409	+	0.961327i	$0.411187\pi$
$158$	−0.367511	−0.0292376
$159$	9.10953	0.722433
$160$	−1.53879	−0.121652
$161$	−1.04022	−0.0819806
$162$	0.367511	0.0288744
$163$	−11.2953	−0.884713	−0.442356	−	0.896839i	$-0.645857\pi$
$163$	−11.2953	−0.884713	−0.442356	+	0.896839i	$0.645857\pi$
$164$	−18.3904	−1.43605
$165$	2.11216	0.164432
$166$	1.04683	0.0812500
$167$	−5.21843	−0.403814	−0.201907	−	0.979405i	$-0.564714\pi$
$167$	−5.21843	−0.403814	−0.201907	+	0.979405i	$0.564714\pi$
$168$	−3.09724	−0.238957
$169$	−4.41187	−0.339374
$170$	0.140687	0.0107902
$171$	5.52998	0.422888
$172$	0.790449	0.0602711
$173$	−10.3873	−0.789730	−0.394865	−	0.918739i	$-0.629209\pi$
$173$	−10.3873	−0.789730	−0.394865	+	0.918739i	$0.629209\pi$
$174$	1.30335	0.0988065
$175$	−10.5831	−0.800007
$176$	−17.6995	−1.33415
$177$	2.89285	0.217440
$178$	0.868143	0.0650701
$179$	21.8647	1.63424	0.817121	−	0.576467i	$-0.195569\pi$
$179$	21.8647	1.63424	0.817121	+	0.576467i	$0.195569\pi$
$180$	0.713914	0.0532120
$181$	2.04874	0.152282	0.0761410	−	0.997097i	$-0.475740\pi$
$181$	2.04874	0.152282	0.0761410	+	0.997097i	$0.475740\pi$
$182$	−2.34845	−0.174079
$183$	−5.87415	−0.434230
$184$	0.677603	0.0499536
$185$	−0.389187	−0.0286136
$186$	0.296947	0.0217732
$187$	5.51754	0.403483
$188$	−9.12855	−0.665768
$189$	2.18053	0.158610
$190$	−0.777994	−0.0564416
$191$	4.08753	0.295763	0.147882	−	0.989005i	$-0.452754\pi$
$191$	4.08753	0.295763	0.147882	+	0.989005i	$0.452754\pi$
$192$	−4.93841	−0.356399
$193$	3.11423	0.224168	0.112084	−	0.993699i	$-0.464248\pi$
$193$	3.11423	0.224168	0.112084	+	0.993699i	$0.464248\pi$
$194$	−0.824859	−0.0592214
$195$	1.12184	0.0803367
$196$	4.18734	0.299096
$197$	−3.80437	−0.271050	−0.135525	−	0.990774i	$-0.543272\pi$
$197$	−3.80437	−0.271050	−0.135525	+	0.990774i	$0.543272\pi$
$198$	−2.02776	−0.144107
$199$	−0.0810948	−0.00574866	−0.00287433	−	0.999996i	$-0.500915\pi$
$199$	−0.0810948	−0.00574866	−0.00287433	+	0.999996i	$0.500915\pi$
$200$	6.89389	0.487472
$201$	−4.06274	−0.286563
$202$	5.95387	0.418913
$203$	7.73305	0.542754
$204$	1.86494	0.130572
$205$	−3.77493	−0.263652
$206$	4.12888	0.287673
$207$	−0.477048	−0.0331572
$208$	−9.40078	−0.651827
$209$	−30.5119	−2.11055
$210$	−0.306771	−0.0211692
$211$	16.2555	1.11908	0.559538	−	0.828805i	$-0.310979\pi$
$211$	16.2555	1.11908	0.559538	+	0.828805i	$0.310979\pi$
$212$	−16.9887	−1.16679
$213$	16.3620	1.12110
$214$	−0.633839	−0.0433283
$215$	0.162253	0.0110655
$216$	−1.42041	−0.0966465
$217$	1.76185	0.119602
$218$	5.48530	0.371512
$219$	1.50889	0.101961
$220$	−3.93905	−0.265571
$221$	2.93055	0.197130
$222$	0.373635	0.0250767
$223$	10.4061	0.696841	0.348421	−	0.937338i	$-0.386718\pi$
$223$	10.4061	0.696841	0.348421	+	0.937338i	$0.386718\pi$
$224$	8.76515	0.585646
$225$	−4.85346	−0.323564
$226$	2.81465	0.187228
$227$	−1.79134	−0.118895	−0.0594476	−	0.998231i	$-0.518934\pi$
$227$	−1.79134	−0.118895	−0.0594476	+	0.998231i	$0.518934\pi$
$228$	−10.3131	−0.682999
$229$	−5.62851	−0.371942	−0.185971	−	0.982555i	$-0.559543\pi$
$229$	−5.62851	−0.371942	−0.185971	+	0.982555i	$0.559543\pi$
$230$	0.0671143	0.00442539
$231$	−12.0312	−0.791592
$232$	−5.03735	−0.330718
$233$	2.53202	0.165878	0.0829391	−	0.996555i	$-0.473569\pi$
$233$	2.53202	0.165878	0.0829391	+	0.996555i	$0.473569\pi$
$234$	−1.07701	−0.0704064
$235$	−1.87379	−0.122232
$236$	−5.39498	−0.351183
$237$	−1.00000	−0.0649570
$238$	−0.801369	−0.0519450
$239$	−1.47449	−0.0953770	−0.0476885	−	0.998862i	$-0.515185\pi$
$239$	−1.47449	−0.0953770	−0.0476885	+	0.998862i	$0.515185\pi$
$240$	−1.22799	−0.0792667
$241$	18.4668	1.18955	0.594775	−	0.803892i	$-0.297241\pi$
$241$	18.4668	1.18955	0.594775	+	0.803892i	$0.297241\pi$
$242$	7.14563	0.459338
$243$	1.00000	0.0641500
$244$	10.9549	0.701316
$245$	0.859521	0.0549128
$246$	3.62408	0.231063
$247$	−16.2059	−1.03116
$248$	−1.14768	−0.0728778
$249$	2.84844	0.180512
$250$	1.38625	0.0876741
$251$	16.0362	1.01220	0.506099	−	0.862475i	$-0.331087\pi$
$251$	16.0362	1.01220	0.506099	+	0.862475i	$0.331087\pi$
$252$	−4.06654	−0.256168
$253$	2.63214	0.165481
$254$	−3.67479	−0.230577
$255$	0.382809	0.0239724
$256$	6.25521	0.390951
$257$	−4.02376	−0.250995	−0.125498	−	0.992094i	$-0.540053\pi$
$257$	−4.02376	−0.250995	−0.125498	+	0.992094i	$0.540053\pi$
$258$	−0.155769	−0.00969775
$259$	2.21686	0.137749
$260$	−2.09216	−0.129750
$261$	3.54641	0.219517
$262$	2.39605	0.148029
$263$	−13.8579	−0.854512	−0.427256	−	0.904131i	$-0.640520\pi$
$263$	−13.8579	−0.854512	−0.427256	+	0.904131i	$0.640520\pi$
$264$	7.83716	0.482344
$265$	−3.48721	−0.214217
$266$	4.43155	0.271716
$267$	2.36222	0.144566
$268$	7.57674	0.462823
$269$	−5.80134	−0.353714	−0.176857	−	0.984237i	$-0.556593\pi$
$269$	−5.80134	−0.353714	−0.176857	+	0.984237i	$0.556593\pi$
$270$	−0.140687	−0.00856191
$271$	3.87971	0.235676	0.117838	−	0.993033i	$-0.462404\pi$
$271$	3.87971	0.235676	0.117838	+	0.993033i	$0.462404\pi$
$272$	−3.20785	−0.194505
$273$	−6.39015	−0.386749
$274$	−5.21434	−0.315010
$275$	26.7792	1.61484
$276$	0.889664	0.0535515
$277$	24.0750	1.44653	0.723264	−	0.690571i	$-0.242641\pi$
$277$	24.0750	1.44653	0.723264	+	0.690571i	$0.242641\pi$
$278$	−4.89533	−0.293602
$279$	0.807994	0.0483733
$280$	1.18565	0.0708561
$281$	11.1519	0.665269	0.332635	−	0.943056i	$-0.392062\pi$
$281$	11.1519	0.665269	0.332635	+	0.943056i	$0.392062\pi$
$282$	1.79891	0.107123
$283$	12.9211	0.768081	0.384041	−	0.923316i	$-0.374532\pi$
$283$	12.9211	0.768081	0.384041	+	0.923316i	$0.374532\pi$
$284$	−30.5140	−1.81067
$285$	−2.11693	−0.125396
$286$	5.94246	0.351385
$287$	21.5024	1.26925
$288$	4.01974	0.236865
$289$	1.00000	0.0588235
$290$	−0.498933	−0.0292983
$291$	−2.24444	−0.131572
$292$	−2.81398	−0.164676
$293$	25.7788	1.50602	0.753008	−	0.658011i	$-0.228602\pi$
$293$	25.7788	1.50602	0.753008	+	0.658011i	$0.228602\pi$
$294$	−0.825174	−0.0481251
$295$	−1.10741	−0.0644759
$296$	−1.44408	−0.0839352
$297$	−5.51754	−0.320160
$298$	5.05569	0.292868
$299$	1.39802	0.0808493
$300$	9.05138	0.522582
$301$	−0.924212	−0.0532707
$302$	−3.67769	−0.211627
$303$	16.2005	0.930695
$304$	17.7394	1.01742
$305$	2.24868	0.128759
$306$	−0.367511	−0.0210092
$307$	−13.0731	−0.746123	−0.373061	−	0.927807i	$-0.621692\pi$
$307$	−13.0731	−0.746123	−0.373061	+	0.927807i	$0.621692\pi$
$308$	22.4373	1.27849
$309$	11.2347	0.639120
$310$	−0.113674	−0.00645624
$311$	28.3349	1.60673	0.803363	−	0.595490i	$-0.203042\pi$
$311$	28.3349	1.60673	0.803363	+	0.595490i	$0.203042\pi$
$312$	4.16258	0.235660
$313$	−25.9935	−1.46924	−0.734619	−	0.678480i	$-0.762639\pi$
$313$	−25.9935	−1.46924	−0.734619	+	0.678480i	$0.762639\pi$
$314$	2.53646	0.143141
$315$	−0.834725	−0.0470314
$316$	1.86494	0.104911
$317$	−11.9578	−0.671619	−0.335809	−	0.941930i	$-0.609010\pi$
$317$	−11.9578	−0.671619	−0.335809	+	0.941930i	$0.609010\pi$
$318$	3.34786	0.187738
$319$	−19.5675	−1.09557
$320$	1.89047	0.105680
$321$	−1.72468	−0.0962621
$322$	−0.382292	−0.0213043
$323$	−5.52998	−0.307696
$324$	−1.86494	−0.103608
$325$	14.2233	0.788967
$326$	−4.15114	−0.229910
$327$	14.9255	0.825384
$328$	−14.0068	−0.773397
$329$	10.6733	0.588439
$330$	0.776244	0.0427309
$331$	3.22026	0.177001	0.0885007	−	0.996076i	$-0.471792\pi$
$331$	3.22026	0.177001	0.0885007	+	0.996076i	$0.471792\pi$
$332$	−5.31215	−0.291542
$333$	1.01666	0.0557128
$334$	−1.91783	−0.104939
$335$	1.55525	0.0849724
$336$	6.99481	0.381598
$337$	−8.80463	−0.479619	−0.239809	−	0.970820i	$-0.577085\pi$
$337$	−8.80463	−0.479619	−0.239809	+	0.970820i	$0.577085\pi$
$338$	−1.62141	−0.0881932
$339$	7.65867	0.415962
$340$	−0.713914	−0.0387174
$341$	−4.45814	−0.241422
$342$	2.03233	0.109896
$343$	−20.1596	−1.08852
$344$	0.602037	0.0324596
$345$	0.182618	0.00983184
$346$	−3.81744	−0.205227
$347$	11.6763	0.626817	0.313408	−	0.949618i	$-0.398529\pi$
$347$	11.6763	0.626817	0.313408	+	0.949618i	$0.398529\pi$
$348$	−6.61383	−0.354538
$349$	0.664019	0.0355441	0.0177721	−	0.999842i	$-0.494343\pi$
$349$	0.664019	0.0355441	0.0177721	+	0.999842i	$0.494343\pi$
$350$	−3.88941	−0.207898
$351$	−2.93055	−0.156421
$352$	−22.1791	−1.18215
$353$	7.27430	0.387172	0.193586	−	0.981083i	$-0.437988\pi$
$353$	7.27430	0.387172	0.193586	+	0.981083i	$0.437988\pi$
$354$	1.06316	0.0565061
$355$	−6.26350	−0.332432
$356$	−4.40539	−0.233485
$357$	−2.18053	−0.115406
$358$	8.03551	0.424690
$359$	22.3202	1.17801	0.589007	−	0.808128i	$-0.299519\pi$
$359$	22.3202	1.17801	0.589007	+	0.808128i	$0.299519\pi$
$360$	0.543745	0.0286579
$361$	11.5807	0.609510
$362$	0.752937	0.0395735
$363$	19.4433	1.02051
$364$	11.9172	0.624632
$365$	−0.577616	−0.0302338
$366$	−2.15882	−0.112843
$367$	0.817655	0.0426812	0.0213406	−	0.999772i	$-0.493207\pi$
$367$	0.817655	0.0426812	0.0213406	+	0.999772i	$0.493207\pi$
$368$	−1.53030	−0.0797725
$369$	9.86112	0.513350
$370$	−0.143031	−0.00743582
$371$	19.8636	1.03127
$372$	−1.50686	−0.0781269
$373$	34.3484	1.77849	0.889246	−	0.457428i	$-0.151229\pi$
$373$	34.3484	1.77849	0.889246	+	0.457428i	$0.151229\pi$
$374$	2.02776	0.104853
$375$	3.77199	0.194785
$376$	−6.95266	−0.358556
$377$	−10.3929	−0.535264
$378$	0.801369	0.0412180
$379$	−12.3175	−0.632706	−0.316353	−	0.948642i	$-0.602458\pi$
$379$	−12.3175	−0.632706	−0.316353	+	0.948642i	$0.602458\pi$
$380$	3.94793	0.202524
$381$	−9.99913	−0.512271
$382$	1.50222	0.0768600
$383$	−37.6081	−1.92168	−0.960842	−	0.277097i	$-0.910628\pi$
$383$	−37.6081	−1.92168	−0.960842	+	0.277097i	$0.910628\pi$
$384$	−9.85440	−0.502880
$385$	4.60563	0.234725
$386$	1.14452	0.0582544
$387$	−0.423848	−0.0215454
$388$	4.18574	0.212499
$389$	−0.524470	−0.0265917	−0.0132959	−	0.999912i	$-0.504232\pi$
$389$	−0.524470	−0.0265917	−0.0132959	+	0.999912i	$0.504232\pi$
$390$	0.412289	0.0208771
$391$	0.477048	0.0241254
$392$	3.18924	0.161081
$393$	6.51967	0.328874
$394$	−1.39815	−0.0704378
$395$	0.382809	0.0192612
$396$	10.2899	0.517085
$397$	−8.41612	−0.422393	−0.211197	−	0.977444i	$-0.567736\pi$
$397$	−8.41612	−0.422393	−0.211197	+	0.977444i	$0.567736\pi$
$398$	−0.0298033	−0.00149390
$399$	12.0583	0.603669
$400$	−15.5692	−0.778459
$401$	−19.8174	−0.989634	−0.494817	−	0.868997i	$-0.664765\pi$
$401$	−19.8174	−0.989634	−0.494817	+	0.868997i	$0.664765\pi$
$402$	−1.49310	−0.0744691
$403$	−2.36787	−0.117952
$404$	−30.2129	−1.50315
$405$	−0.382809	−0.0190219
$406$	2.84198	0.141045
$407$	−5.60948	−0.278052
$408$	1.42041	0.0703207
$409$	27.1771	1.34382	0.671910	−	0.740632i	$-0.265474\pi$
$409$	27.1771	1.34382	0.671910	+	0.740632i	$0.265474\pi$
$410$	−1.38733	−0.0685153
$411$	−14.1882	−0.699854
$412$	−20.9520	−1.03223
$413$	6.30794	0.310394
$414$	−0.175321	−0.00861655
$415$	−1.09041	−0.0535260
$416$	−11.7801	−0.577565
$417$	−13.3202	−0.652293
$418$	−11.2135	−0.548469
$419$	19.5123	0.953240	0.476620	−	0.879109i	$-0.341862\pi$
$419$	19.5123	0.953240	0.476620	+	0.879109i	$0.341862\pi$
$420$	1.55671	0.0759596
$421$	23.5366	1.14711	0.573553	−	0.819169i	$-0.305565\pi$
$421$	23.5366	1.14711	0.573553	+	0.819169i	$0.305565\pi$
$422$	5.97408	0.290814
$423$	4.89484	0.237995
$424$	−12.9392	−0.628385
$425$	4.85346	0.235427
$426$	6.01321	0.291341
$427$	−12.8087	−0.619858
$428$	3.21641	0.155471
$429$	16.1694	0.780668
$430$	0.0596297	0.00287560
$431$	26.2862	1.26616	0.633081	−	0.774086i	$-0.281790\pi$
$431$	26.2862	1.26616	0.633081	+	0.774086i	$0.281790\pi$
$432$	3.20785	0.154338
$433$	−32.1300	−1.54407	−0.772034	−	0.635581i	$-0.780761\pi$
$433$	−32.1300	−1.54407	−0.772034	+	0.635581i	$0.780761\pi$
$434$	0.647501	0.0310810
$435$	−1.35760	−0.0650918
$436$	−27.8352	−1.33306
$437$	−2.63807	−0.126196
$438$	0.554534	0.0264966
$439$	3.61175	0.172379	0.0861897	−	0.996279i	$-0.472531\pi$
$439$	3.61175	0.172379	0.0861897	+	0.996279i	$0.472531\pi$
$440$	−3.00013	−0.143026
$441$	−2.24530	−0.106919
$442$	1.07701	0.0512282
$443$	−30.0106	−1.42585	−0.712923	−	0.701243i	$-0.752629\pi$
$443$	−30.0106	−1.42585	−0.712923	+	0.701243i	$0.752629\pi$
$444$	−1.89601	−0.0899807
$445$	−0.904279	−0.0428669
$446$	3.82435	0.181088
$447$	13.7565	0.650662
$448$	−10.7683	−0.508756
$449$	19.6124	0.925567	0.462784	−	0.886471i	$-0.346851\pi$
$449$	19.6124	0.925567	0.462784	+	0.886471i	$0.346851\pi$
$450$	−1.78370	−0.0840845
$451$	−54.4092	−2.56203
$452$	−14.2829	−0.671812
$453$	−10.0070	−0.470170
$454$	−0.658336	−0.0308973
$455$	2.44620	0.114680
$456$	−7.85483	−0.367836
$457$	28.7552	1.34511	0.672555	−	0.740048i	$-0.265197\pi$
$457$	28.7552	1.34511	0.672555	+	0.740048i	$0.265197\pi$
$458$	−2.06854	−0.0966566
$459$	−1.00000	−0.0466760
$460$	−0.340571	−0.0158792
$461$	−33.0707	−1.54026	−0.770129	−	0.637888i	$-0.779808\pi$
$461$	−33.0707	−1.54026	−0.770129	+	0.637888i	$0.779808\pi$
$462$	−4.42159	−0.205711
$463$	−19.9068	−0.925147	−0.462573	−	0.886581i	$-0.653074\pi$
$463$	−19.9068	−0.925147	−0.462573	+	0.886581i	$0.653074\pi$
$464$	11.3764	0.528135
$465$	−0.309307	−0.0143438
$466$	0.930547	0.0431067
$467$	−2.71169	−0.125482	−0.0627411	−	0.998030i	$-0.519984\pi$
$467$	−2.71169	−0.125482	−0.0627411	+	0.998030i	$0.519984\pi$
$468$	5.46529	0.252633
$469$	−8.85890	−0.409066
$470$	−0.688638	−0.0317645
$471$	6.90172	0.318015
$472$	−4.10903	−0.189133
$473$	2.33860	0.107529
$474$	−0.367511	−0.0168804
$475$	−26.8395	−1.23148
$476$	4.06654	0.186390
$477$	9.10953	0.417097
$478$	−0.541893	−0.0247856
$479$	−32.1239	−1.46778	−0.733888	−	0.679270i	$-0.762297\pi$
$479$	−32.1239	−1.46778	−0.733888	+	0.679270i	$0.762297\pi$
$480$	−1.53879	−0.0702359
$481$	−2.97938	−0.135848
$482$	6.78676	0.309128
$483$	−1.04022	−0.0473315
$484$	−36.2605	−1.64820
$485$	0.859193	0.0390139
$486$	0.367511	0.0166707
$487$	23.4070	1.06067	0.530337	−	0.847787i	$-0.322065\pi$
$487$	23.4070	1.06067	0.530337	+	0.847787i	$0.322065\pi$
$488$	8.34369	0.377701
$489$	−11.2953	−0.510789
$490$	0.315884	0.0142702
$491$	−9.20820	−0.415560	−0.207780	−	0.978176i	$-0.566624\pi$
$491$	−9.20820	−0.415560	−0.207780	+	0.978176i	$0.566624\pi$
$492$	−18.3904	−0.829101
$493$	−3.54641	−0.159722
$494$	−5.95585	−0.267966
$495$	2.11216	0.0949347
$496$	2.59193	0.116381
$497$	35.6777	1.60036
$498$	1.04683	0.0469097
$499$	35.3873	1.58415	0.792076	−	0.610423i	$-0.209001\pi$
$499$	35.3873	1.58415	0.792076	+	0.610423i	$0.209001\pi$
$500$	−7.03452	−0.314593
$501$	−5.21843	−0.233142
$502$	5.89350	0.263040
$503$	−39.5185	−1.76204	−0.881020	−	0.473078i	$-0.843143\pi$
$503$	−39.5185	−1.76204	−0.881020	+	0.473078i	$0.843143\pi$
$504$	−3.09724	−0.137962
$505$	−6.20170	−0.275972
$506$	0.967340	0.0430035
$507$	−4.41187	−0.195938
$508$	18.6477	0.827359
$509$	−35.6009	−1.57798	−0.788990	−	0.614406i	$-0.789396\pi$
$509$	−35.6009	−1.57798	−0.788990	+	0.614406i	$0.789396\pi$
$510$	0.140687	0.00622971
$511$	3.29017	0.145549
$512$	22.0077	0.972610
$513$	5.52998	0.244155
$514$	−1.47878	−0.0652260
$515$	−4.30074	−0.189513
$516$	0.790449	0.0347976
$517$	−27.0075	−1.18779
$518$	0.814722	0.0357968
$519$	−10.3873	−0.455951
$520$	−1.59347	−0.0698784
$521$	−10.4625	−0.458369	−0.229184	−	0.973383i	$-0.573606\pi$
$521$	−10.4625	−0.458369	−0.229184	+	0.973383i	$0.573606\pi$
$522$	1.30335	0.0570460
$523$	−27.7555	−1.21366	−0.606832	−	0.794830i	$-0.707560\pi$
$523$	−27.7555	−1.21366	−0.606832	+	0.794830i	$0.707560\pi$
$524$	−12.1588	−0.531158
$525$	−10.5831	−0.461884
$526$	−5.09292	−0.222062
$527$	−0.807994	−0.0351968
$528$	−17.6995	−0.770271
$529$	−22.7724	−0.990105
$530$	−1.28159	−0.0556686
$531$	2.89285	0.125539
$532$	−22.4879	−0.974974
$533$	−28.8985	−1.25173
$534$	0.868143	0.0375682
$535$	0.660222	0.0285439
$536$	5.77074	0.249258
$537$	21.8647	0.943530
$538$	−2.13206	−0.0919196
$539$	12.3885	0.533613
$540$	0.713914	0.0307220
$541$	−42.5422	−1.82903	−0.914516	−	0.404550i	$-0.867428\pi$
$541$	−42.5422	−1.82903	−0.914516	+	0.404550i	$0.867428\pi$
$542$	1.42584	0.0612450
$543$	2.04874	0.0879200
$544$	−4.01974	−0.172345
$545$	−5.71363	−0.244745
$546$	−2.34845	−0.100504
$547$	−24.0202	−1.02703	−0.513516	−	0.858080i	$-0.671657\pi$
$547$	−24.0202	−1.02703	−0.513516	+	0.858080i	$0.671657\pi$
$548$	26.4601	1.13032
$549$	−5.87415	−0.250703
$550$	9.84165	0.419649
$551$	19.6116	0.835482
$552$	0.677603	0.0288407
$553$	−2.18053	−0.0927254
$554$	8.84785	0.375909
$555$	−0.389187	−0.0165201
$556$	24.8413	1.05351
$557$	−3.59297	−0.152239	−0.0761195	−	0.997099i	$-0.524253\pi$
$557$	−3.59297	−0.152239	−0.0761195	+	0.997099i	$0.524253\pi$
$558$	0.296947	0.0125708
$559$	1.24211	0.0525356
$560$	−2.67768	−0.113152
$561$	5.51754	0.232951
$562$	4.09847	0.172883
$563$	16.0931	0.678242	0.339121	−	0.940743i	$-0.389870\pi$
$563$	16.0931	0.678242	0.339121	+	0.940743i	$0.389870\pi$
$564$	−9.12855	−0.384381
$565$	−2.93181	−0.123342
$566$	4.74866	0.199601
$567$	2.18053	0.0915735
$568$	−23.2407	−0.975156
$569$	−33.9340	−1.42259	−0.711293	−	0.702895i	$-0.751890\pi$
$569$	−33.9340	−1.42259	−0.711293	+	0.702895i	$0.751890\pi$
$570$	−0.777994	−0.0325866
$571$	−30.1460	−1.26157	−0.630785	−	0.775957i	$-0.717267\pi$
$571$	−30.1460	−1.26157	−0.630785	+	0.775957i	$0.717267\pi$
$572$	−30.1550	−1.26084
$573$	4.08753	0.170759
$574$	7.90240	0.329840
$575$	2.31533	0.0965561
$576$	−4.93841	−0.205767
$577$	34.8036	1.44889	0.724447	−	0.689331i	$-0.242095\pi$
$577$	34.8036	1.44889	0.724447	+	0.689331i	$0.242095\pi$
$578$	0.367511	0.0152865
$579$	3.11423	0.129423
$580$	2.53183	0.105129
$581$	6.21109	0.257680
$582$	−0.824859	−0.0341915
$583$	−50.2622	−2.08165
$584$	−2.14324	−0.0886878
$585$	1.12184	0.0463824
$586$	9.47402	0.391368
$587$	14.8599	0.613332	0.306666	−	0.951817i	$-0.400787\pi$
$587$	14.8599	0.613332	0.306666	+	0.951817i	$0.400787\pi$
$588$	4.18734	0.172683
$589$	4.46819	0.184109
$590$	−0.406986	−0.0167553
$591$	−3.80437	−0.156491
$592$	3.26131	0.134039
$593$	36.3660	1.49337	0.746687	−	0.665175i	$-0.231643\pi$
$593$	36.3660	1.49337	0.746687	+	0.665175i	$0.231643\pi$
$594$	−2.02776	−0.0832000
$595$	0.834725	0.0342204
$596$	−25.6551	−1.05087
$597$	−0.0810948	−0.00331899
$598$	0.513787	0.0210103
$599$	−22.8277	−0.932716	−0.466358	−	0.884596i	$-0.654434\pi$
$599$	−22.8277	−0.932716	−0.466358	+	0.884596i	$0.654434\pi$
$600$	6.89389	0.281442
$601$	−24.5927	−1.00316	−0.501578	−	0.865112i	$-0.667247\pi$
$601$	−24.5927	−1.00316	−0.501578	+	0.865112i	$0.667247\pi$
$602$	−0.339658	−0.0138434
$603$	−4.06274	−0.165447
$604$	18.6624	0.759363
$605$	−7.44306	−0.302603
$606$	5.95387	0.241860
$607$	−2.25042	−0.0913416	−0.0456708	−	0.998957i	$-0.514543\pi$
$607$	−2.25042	−0.0913416	−0.0456708	+	0.998957i	$0.514543\pi$
$608$	22.2291	0.901508
$609$	7.73305	0.313359
$610$	0.826414	0.0334605
$611$	−14.3446	−0.580319
$612$	1.86494	0.0753855
$613$	−5.07989	−0.205175	−0.102587	−	0.994724i	$-0.532712\pi$
$613$	−5.07989	−0.205175	−0.102587	+	0.994724i	$0.532712\pi$
$614$	−4.80452	−0.193895
$615$	−3.77493	−0.152220
$616$	17.0891	0.688541
$617$	15.1684	0.610659	0.305329	−	0.952247i	$-0.401233\pi$
$617$	15.1684	0.610659	0.305329	+	0.952247i	$0.401233\pi$
$618$	4.12888	0.166088
$619$	37.2562	1.49745	0.748726	−	0.662880i	$-0.230666\pi$
$619$	37.2562	1.49745	0.748726	+	0.662880i	$0.230666\pi$
$620$	0.576838	0.0231664
$621$	−0.477048	−0.0191433
$622$	10.4134	0.417540
$623$	5.15089	0.206366
$624$	−9.40078	−0.376333
$625$	22.8233	0.912933
$626$	−9.55290	−0.381811
$627$	−30.5119	−1.21853
$628$	−12.8713	−0.513620
$629$	−1.01666	−0.0405370
$630$	−0.306771	−0.0122220
$631$	−10.6040	−0.422139	−0.211070	−	0.977471i	$-0.567695\pi$
$631$	−10.6040	−0.422139	−0.211070	+	0.977471i	$0.567695\pi$
$632$	1.42041	0.0565008
$633$	16.2555	0.646098
$634$	−4.39464	−0.174533
$635$	3.82775	0.151900
$636$	−16.9887	−0.673645
$637$	6.57997	0.260708
$638$	−7.19127	−0.284705
$639$	16.3620	0.647269
$640$	3.77235	0.149115
$641$	5.04172	0.199136	0.0995681	−	0.995031i	$-0.468254\pi$
$641$	5.04172	0.199136	0.0995681	+	0.995031i	$0.468254\pi$
$642$	−0.633839	−0.0250156
$643$	−27.1403	−1.07031	−0.535154	−	0.844755i	$-0.679746\pi$
$643$	−27.1403	−1.07031	−0.535154	+	0.844755i	$0.679746\pi$
$644$	1.93994	0.0764442
$645$	0.162253	0.00638869
$646$	−2.03233	−0.0799610
$647$	28.0870	1.10421	0.552106	−	0.833774i	$-0.313824\pi$
$647$	28.0870	1.10421	0.552106	+	0.833774i	$0.313824\pi$
$648$	−1.42041	−0.0557989
$649$	−15.9614	−0.626541
$650$	5.22723	0.205029
$651$	1.76185	0.0690524
$652$	21.0649	0.824966
$653$	46.0035	1.80026	0.900128	−	0.435627i	$-0.143473\pi$
$653$	46.0035	1.80026	0.900128	+	0.435627i	$0.143473\pi$
$654$	5.48530	0.214492
$655$	−2.49579	−0.0975185
$656$	31.6331	1.23506
$657$	1.50889	0.0588673
$658$	3.92257	0.152918
$659$	−27.7134	−1.07956	−0.539781	−	0.841806i	$-0.681493\pi$
$659$	−27.7134	−1.07956	−0.539781	+	0.841806i	$0.681493\pi$
$660$	−3.93905	−0.153327
$661$	−26.0556	−1.01345	−0.506723	−	0.862109i	$-0.669143\pi$
$661$	−26.0556	−1.01345	−0.506723	+	0.862109i	$0.669143\pi$
$662$	1.18348	0.0459973
$663$	2.93055	0.113813
$664$	−4.04594	−0.157013
$665$	−4.61601	−0.179001
$666$	0.373635	0.0144781
$667$	−1.69181	−0.0655072
$668$	9.73203	0.376544
$669$	10.4061	0.402321
$670$	0.571572	0.0220818
$671$	32.4109	1.25121
$672$	8.76515	0.338123
$673$	−43.9954	−1.69590	−0.847948	−	0.530079i	$-0.822162\pi$
$673$	−43.9954	−1.69590	−0.847948	+	0.530079i	$0.822162\pi$
$674$	−3.23580	−0.124638
$675$	−4.85346	−0.186810
$676$	8.22785	0.316456
$677$	−7.72962	−0.297073	−0.148537	−	0.988907i	$-0.547456\pi$
$677$	−7.72962	−0.297073	−0.148537	+	0.988907i	$0.547456\pi$
$678$	2.81465	0.108096
$679$	−4.89407	−0.187817
$680$	−0.543745	−0.0208517
$681$	−1.79134	−0.0686441
$682$	−1.63842	−0.0627383
$683$	32.2698	1.23477	0.617384	−	0.786662i	$-0.288192\pi$
$683$	32.2698	1.23477	0.617384	+	0.786662i	$0.288192\pi$
$684$	−10.3131	−0.394330
$685$	5.43138	0.207522
$686$	−7.40890	−0.282873
$687$	−5.62851	−0.214741
$688$	−1.35964	−0.0518359
$689$	−26.6959	−1.01703
$690$	0.0671143	0.00255500
$691$	44.2577	1.68364	0.841821	−	0.539756i	$-0.181484\pi$
$691$	44.2577	1.68364	0.841821	+	0.539756i	$0.181484\pi$
$692$	19.3716	0.736398
$693$	−12.0312	−0.457026
$694$	4.29117	0.162891
$695$	5.09909	0.193420
$696$	−5.03735	−0.190940
$697$	−9.86112	−0.373517
$698$	0.244034	0.00923684
$699$	2.53202	0.0957698
$700$	19.7368	0.745980
$701$	−9.72138	−0.367171	−0.183586	−	0.983004i	$-0.558770\pi$
$701$	−9.72138	−0.367171	−0.183586	+	0.983004i	$0.558770\pi$
$702$	−1.07701	−0.0406492
$703$	5.62213	0.212042
$704$	27.2479	1.02694
$705$	−1.87379	−0.0705709
$706$	2.67339	0.100614
$707$	35.3257	1.32856
$708$	−5.39498	−0.202756
$709$	9.27187	0.348213	0.174106	−	0.984727i	$-0.444296\pi$
$709$	9.27187	0.348213	0.174106	+	0.984727i	$0.444296\pi$
$710$	−2.30191	−0.0863891
$711$	−1.00000	−0.0375029
$712$	−3.35532	−0.125746
$713$	−0.385452	−0.0144353
$714$	−0.801369	−0.0299905
$715$	−6.18981	−0.231486
$716$	−40.7762	−1.52388
$717$	−1.47449	−0.0550659
$718$	8.20292	0.306130
$719$	10.7975	0.402679	0.201339	−	0.979522i	$-0.435471\pi$
$719$	10.7975	0.402679	0.201339	+	0.979522i	$0.435471\pi$
$720$	−1.22799	−0.0457647
$721$	24.4976	0.912337
$722$	4.25604	0.158393
$723$	18.4668	0.686787
$724$	−3.82077	−0.141998
$725$	−17.2124	−0.639251
$726$	7.14563	0.265199
$727$	−41.4398	−1.53692	−0.768459	−	0.639899i	$-0.778976\pi$
$727$	−41.4398	−1.53692	−0.768459	+	0.639899i	$0.778976\pi$
$728$	9.07662	0.336402
$729$	1.00000	0.0370370
$730$	−0.212280	−0.00785685
$731$	0.423848	0.0156766
$732$	10.9549	0.404905
$733$	−39.2812	−1.45088	−0.725442	−	0.688283i	$-0.758365\pi$
$733$	−39.2812	−1.45088	−0.725442	+	0.688283i	$0.758365\pi$
$734$	0.300498	0.0110916
$735$	0.859521	0.0317039
$736$	−1.91761	−0.0706841
$737$	22.4163	0.825716
$738$	3.62408	0.133404
$739$	33.6985	1.23962	0.619810	−	0.784752i	$-0.287210\pi$
$739$	33.6985	1.23962	0.619810	+	0.784752i	$0.287210\pi$
$740$	0.725809	0.0266813
$741$	−16.2059	−0.595338
$742$	7.30009	0.267995
$743$	17.3620	0.636948	0.318474	−	0.947932i	$-0.396830\pi$
$743$	17.3620	0.636948	0.318474	+	0.947932i	$0.396830\pi$
$744$	−1.14768	−0.0420760
$745$	−5.26613	−0.192936
$746$	12.6234	0.462177
$747$	2.84844	0.104219
$748$	−10.2899	−0.376235
$749$	−3.76071	−0.137413
$750$	1.38625	0.0506187
$751$	14.6725	0.535405	0.267703	−	0.963502i	$-0.413735\pi$
$751$	14.6725	0.535405	0.267703	+	0.963502i	$0.413735\pi$
$752$	15.7019	0.572590
$753$	16.0362	0.584393
$754$	−3.81953	−0.139099
$755$	3.83077	0.139416
$756$	−4.06654	−0.147899
$757$	7.13679	0.259391	0.129695	−	0.991554i	$-0.458600\pi$
$757$	7.13679	0.259391	0.129695	+	0.991554i	$0.458600\pi$
$758$	−4.52681	−0.164421
$759$	2.63214	0.0955405
$760$	3.00690	0.109072
$761$	−26.4623	−0.959257	−0.479629	−	0.877472i	$-0.659229\pi$
$761$	−26.4623	−0.959257	−0.479629	+	0.877472i	$0.659229\pi$
$762$	−3.67479	−0.133124
$763$	32.5455	1.17823
$764$	−7.62298	−0.275790
$765$	0.382809	0.0138405
$766$	−13.8214	−0.499388
$767$	−8.47765	−0.306110
$768$	6.25521	0.225716
$769$	−26.8773	−0.969221	−0.484610	−	0.874730i	$-0.661039\pi$
$769$	−26.8773	−0.969221	−0.484610	+	0.874730i	$0.661039\pi$
$770$	1.69262	0.0609979
$771$	−4.02376	−0.144912
$772$	−5.80785	−0.209029
$773$	6.32001	0.227315	0.113658	−	0.993520i	$-0.463743\pi$
$773$	6.32001	0.227315	0.113658	+	0.993520i	$0.463743\pi$
$774$	−0.155769	−0.00559900
$775$	−3.92156	−0.140867
$776$	3.18803	0.114443
$777$	2.21686	0.0795294
$778$	−0.192749	−0.00691038
$779$	54.5318	1.95381
$780$	−2.09216	−0.0749114
$781$	−90.2778	−3.23039
$782$	0.175321	0.00626946
$783$	3.54641	0.126738
$784$	−7.20260	−0.257236
$785$	−2.64204	−0.0942985
$786$	2.39605	0.0854645
$787$	−15.5193	−0.553205	−0.276602	−	0.960984i	$-0.589208\pi$
$787$	−15.5193	−0.553205	−0.276602	+	0.960984i	$0.589208\pi$
$788$	7.09491	0.252746
$789$	−13.8579	−0.493353
$790$	0.140687	0.00500541
$791$	16.6999	0.593781
$792$	7.83716	0.278481
$793$	17.2145	0.611305
$794$	−3.09302	−0.109767
$795$	−3.48721	−0.123678
$796$	0.151237	0.00536044
$797$	37.8584	1.34101	0.670507	−	0.741903i	$-0.266076\pi$
$797$	37.8584	1.34101	0.670507	+	0.741903i	$0.266076\pi$
$798$	4.43155	0.156875
$799$	−4.89484	−0.173167
$800$	−19.5096	−0.689770
$801$	2.36222	0.0834650
$802$	−7.28313	−0.257176
$803$	−8.32535	−0.293795
$804$	7.57674	0.267211
$805$	0.398204	0.0140349
$806$	−0.870218	−0.0306521
$807$	−5.80134	−0.204217
$808$	−23.0113	−0.809536
$809$	−29.4251	−1.03453	−0.517267	−	0.855824i	$-0.673050\pi$
$809$	−29.4251	−1.03453	−0.517267	+	0.855824i	$0.673050\pi$
$810$	−0.140687	−0.00494322
$811$	12.0016	0.421434	0.210717	−	0.977547i	$-0.432420\pi$
$811$	12.0016	0.421434	0.210717	+	0.977547i	$0.432420\pi$
$812$	−14.4216	−0.506100
$813$	3.87971	0.136067
$814$	−2.06155	−0.0722572
$815$	4.32392	0.151460
$816$	−3.20785	−0.112297
$817$	−2.34387	−0.0820016
$818$	9.98789	0.349219
$819$	−6.39015	−0.223290
$820$	7.03999	0.245847
$821$	−19.1920	−0.669805	−0.334902	−	0.942253i	$-0.608703\pi$
$821$	−19.1920	−0.669805	−0.334902	+	0.942253i	$0.608703\pi$
$822$	−5.21434	−0.181871
$823$	20.4192	0.711770	0.355885	−	0.934530i	$-0.384179\pi$
$823$	20.4192	0.711770	0.355885	+	0.934530i	$0.384179\pi$
$824$	−15.9579	−0.555918
$825$	26.7792	0.932331
$826$	2.31824	0.0806619
$827$	−29.6077	−1.02956	−0.514781	−	0.857322i	$-0.672127\pi$
$827$	−29.6077	−1.02956	−0.514781	+	0.857322i	$0.672127\pi$
$828$	0.889664	0.0309180
$829$	37.1245	1.28939	0.644693	−	0.764441i	$-0.276985\pi$
$829$	37.1245	1.28939	0.644693	+	0.764441i	$0.276985\pi$
$830$	−0.400737	−0.0139098
$831$	24.0750	0.835154
$832$	14.4723	0.501735
$833$	2.24530	0.0777951
$834$	−4.89533	−0.169511
$835$	1.99766	0.0691319
$836$	56.9027	1.96802
$837$	0.807994	0.0279284
$838$	7.17101	0.247718
$839$	−37.9046	−1.30861	−0.654306	−	0.756230i	$-0.727039\pi$
$839$	−37.9046	−1.30861	−0.654306	+	0.756230i	$0.727039\pi$
$840$	1.18565	0.0409088
$841$	−16.4230	−0.566309
$842$	8.64998	0.298098
$843$	11.1519	0.384093
$844$	−30.3155	−1.04350
$845$	1.68890	0.0581000
$846$	1.79891	0.0618477
$847$	42.3966	1.45676
$848$	29.2220	1.00349
$849$	12.9211	0.443452
$850$	1.78370	0.0611804
$851$	−0.484997	−0.0166255
$852$	−30.5140	−1.04539
$853$	−40.3406	−1.38124	−0.690618	−	0.723219i	$-0.742662\pi$
$853$	−40.3406	−1.38124	−0.690618	+	0.723219i	$0.742662\pi$
$854$	−4.70736	−0.161082
$855$	−2.11693	−0.0723973
$856$	2.44975	0.0837306
$857$	−21.6263	−0.738740	−0.369370	−	0.929282i	$-0.620426\pi$
$857$	−21.6263	−0.738740	−0.369370	+	0.929282i	$0.620426\pi$
$858$	5.94246	0.202872
$859$	−35.3715	−1.20686	−0.603430	−	0.797416i	$-0.706200\pi$
$859$	−35.3715	−1.20686	−0.603430	+	0.797416i	$0.706200\pi$
$860$	−0.302591	−0.0103183
$861$	21.5024	0.732802
$862$	9.66048	0.329037
$863$	−16.0016	−0.544700	−0.272350	−	0.962198i	$-0.587801\pi$
$863$	−16.0016	−0.544700	−0.272350	+	0.962198i	$0.587801\pi$
$864$	4.01974	0.136754
$865$	3.97634	0.135200
$866$	−11.8081	−0.401257
$867$	1.00000	0.0339618
$868$	−3.28574	−0.111525
$869$	5.51754	0.187170
$870$	−0.498933	−0.0169154
$871$	11.9061	0.403421
$872$	−21.2003	−0.717934
$873$	−2.24444	−0.0759629
$874$	−0.969520	−0.0327945
$875$	8.22493	0.278053
$876$	−2.81398	−0.0950755
$877$	21.7138	0.733222	0.366611	−	0.930374i	$-0.380518\pi$
$877$	21.7138	0.733222	0.366611	+	0.930374i	$0.380518\pi$
$878$	1.32736	0.0447962
$879$	25.7788	0.869499
$880$	6.77551	0.228403
$881$	−22.7939	−0.767947	−0.383974	−	0.923344i	$-0.625445\pi$
$881$	−22.7939	−0.767947	−0.383974	+	0.923344i	$0.625445\pi$
$882$	−0.825174	−0.0277851
$883$	−56.3908	−1.89770	−0.948850	−	0.315726i	$-0.897752\pi$
$883$	−56.3908	−1.89770	−0.948850	+	0.315726i	$0.897752\pi$
$884$	−5.46529	−0.183818
$885$	−1.10741	−0.0372252
$886$	−11.0292	−0.370534
$887$	−10.1354	−0.340314	−0.170157	−	0.985417i	$-0.554428\pi$
$887$	−10.1354	−0.340314	−0.170157	+	0.985417i	$0.554428\pi$
$888$	−1.44408	−0.0484600
$889$	−21.8034	−0.731261
$890$	−0.332333	−0.0111398
$891$	−5.51754	−0.184845
$892$	−19.4066	−0.649782
$893$	27.0684	0.905808
$894$	5.05569	0.169088
$895$	−8.36998	−0.279778
$896$	−21.4878	−0.717857
$897$	1.39802	0.0466784
$898$	7.20779	0.240527
$899$	2.86548	0.0955691
$900$	9.05138	0.301713
$901$	−9.10953	−0.303482
$902$	−19.9960	−0.665794
$903$	−0.924212	−0.0307558
$904$	−10.8784	−0.361811
$905$	−0.784277	−0.0260703
$906$	−3.67769	−0.122183
$907$	14.8880	0.494347	0.247174	−	0.968971i	$-0.420498\pi$
$907$	14.8880	0.494347	0.247174	+	0.968971i	$0.420498\pi$
$908$	3.34073	0.110866
$909$	16.2005	0.537337
$910$	0.899008	0.0298018
$911$	−27.7938	−0.920849	−0.460424	−	0.887699i	$-0.652303\pi$
$911$	−27.7938	−0.920849	−0.460424	+	0.887699i	$0.652303\pi$
$912$	17.7394	0.587409
$913$	−15.7164	−0.520136
$914$	10.5678	0.349553
$915$	2.24868	0.0743389
$916$	10.4968	0.346824
$917$	14.2163	0.469464
$918$	−0.367511	−0.0121297
$919$	19.9894	0.659391	0.329696	−	0.944087i	$-0.393054\pi$
$919$	19.9894	0.659391	0.329696	+	0.944087i	$0.393054\pi$
$920$	−0.259393	−0.00855192
$921$	−13.0731	−0.430774
$922$	−12.1539	−0.400267
$923$	−47.9496	−1.57828
$924$	22.4373	0.738134
$925$	−4.93433	−0.162240
$926$	−7.31597	−0.240418
$927$	11.2347	0.368996
$928$	14.2557	0.467965
$929$	−28.3026	−0.928578	−0.464289	−	0.885684i	$-0.653690\pi$
$929$	−28.3026	−0.928578	−0.464289	+	0.885684i	$0.653690\pi$
$930$	−0.113674	−0.00372751
$931$	−12.4165	−0.406934
$932$	−4.72206	−0.154676
$933$	28.3349	0.927643
$934$	−0.996578	−0.0326090
$935$	−2.11216	−0.0690752
$936$	4.16258	0.136058
$937$	25.9914	0.849102	0.424551	−	0.905404i	$-0.360432\pi$
$937$	25.9914	0.849102	0.424551	+	0.905404i	$0.360432\pi$
$938$	−3.25575	−0.106304
$939$	−25.9935	−0.848265
$940$	3.49449	0.113978
$941$	21.5004	0.700892	0.350446	−	0.936583i	$-0.386030\pi$
$941$	21.5004	0.700892	0.350446	+	0.936583i	$0.386030\pi$
$942$	2.53646	0.0826424
$943$	−4.70423	−0.153191
$944$	9.27985	0.302033
$945$	−0.834725	−0.0271536
$946$	0.859462	0.0279435
$947$	45.2249	1.46961	0.734807	−	0.678277i	$-0.237273\pi$
$947$	45.2249	1.46961	0.734807	+	0.678277i	$0.237273\pi$
$948$	1.86494	0.0605703
$949$	−4.42187	−0.143540
$950$	−9.86383	−0.320025
$951$	−11.9578	−0.387759
$952$	3.09724	0.100382
$953$	8.05585	0.260955	0.130477	−	0.991451i	$-0.458349\pi$
$953$	8.05585	0.260955	0.130477	+	0.991451i	$0.458349\pi$
$954$	3.34786	0.108391
$955$	−1.56474	−0.0506339
$956$	2.74983	0.0889359
$957$	−19.5675	−0.632527
$958$	−11.8059	−0.381431
$959$	−30.9378	−0.999034
$960$	1.89047	0.0610145
$961$	−30.3471	−0.978940
$962$	−1.09496	−0.0353028
$963$	−1.72468	−0.0555770
$964$	−34.4394	−1.10922
$965$	−1.19216	−0.0383769
$966$	−0.382292	−0.0123000
$967$	4.53396	0.145802	0.0729012	−	0.997339i	$-0.476774\pi$
$967$	4.53396	0.145802	0.0729012	+	0.997339i	$0.476774\pi$
$968$	−27.6174	−0.887657
$969$	−5.52998	−0.177649
$970$	0.315763	0.0101385
$971$	38.9963	1.25145	0.625725	−	0.780043i	$-0.284803\pi$
$971$	38.9963	1.25145	0.625725	+	0.780043i	$0.284803\pi$
$972$	−1.86494	−0.0598178
$973$	−29.0451	−0.931142
$974$	8.60235	0.275637
$975$	14.2233	0.455510
$976$	−18.8434	−0.603163
$977$	52.5314	1.68063	0.840314	−	0.542100i	$-0.182370\pi$
$977$	52.5314	1.68063	0.840314	+	0.542100i	$0.182370\pi$
$978$	−4.15114	−0.132739
$979$	−13.0337	−0.416557
$980$	−1.60295	−0.0512044
$981$	14.9255	0.476536
$982$	−3.38412	−0.107992
$983$	51.7501	1.65057	0.825286	−	0.564715i	$-0.191014\pi$
$983$	51.7501	1.65057	0.825286	+	0.564715i	$0.191014\pi$
$984$	−14.0068	−0.446521
$985$	1.45635	0.0464031
$986$	−1.30335	−0.0415070
$987$	10.6733	0.339736
$988$	30.2229	0.961520
$989$	0.202196	0.00642946
$990$	0.776244	0.0246707
$991$	−1.33225	−0.0423204	−0.0211602	−	0.999776i	$-0.506736\pi$
$991$	−1.33225	−0.0423204	−0.0211602	+	0.999776i	$0.506736\pi$
$992$	3.24792	0.103122
$993$	3.22026	0.102192
$994$	13.1120	0.415886
$995$	0.0310438	0.000984155 0
$996$	−5.31215	−0.168322
$997$	17.4760	0.553470	0.276735	−	0.960946i	$-0.410748\pi$
$997$	17.4760	0.553470	0.276735	+	0.960946i	$0.410748\pi$
$998$	13.0052	0.411673
$999$	1.01666	0.0321658

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.j.1.12	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.j.1.12	✓	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)

\(f(q)\)	\(=\)	\(q+0.367511 q^{2} +1.00000 q^{3} -1.86494 q^{4} -0.382809 q^{5} +0.367511 q^{6} +2.18053 q^{7} -1.42041 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.367511 q^{2} +1.00000 q^{3} -1.86494 q^{4} -0.382809 q^{5} +0.367511 q^{6} +2.18053 q^{7} -1.42041 q^{8} +1.00000 q^{9} -0.140687 q^{10} -5.51754 q^{11} -1.86494 q^{12} -2.93055 q^{13} +0.801369 q^{14} -0.382809 q^{15} +3.20785 q^{16} -1.00000 q^{17} +0.367511 q^{18} +5.52998 q^{19} +0.713914 q^{20} +2.18053 q^{21} -2.02776 q^{22} -0.477048 q^{23} -1.42041 q^{24} -4.85346 q^{25} -1.07701 q^{26} +1.00000 q^{27} -4.06654 q^{28} +3.54641 q^{29} -0.140687 q^{30} +0.807994 q^{31} +4.01974 q^{32} -5.51754 q^{33} -0.367511 q^{34} -0.834725 q^{35} -1.86494 q^{36} +1.01666 q^{37} +2.03233 q^{38} -2.93055 q^{39} +0.543745 q^{40} +9.86112 q^{41} +0.801369 q^{42} -0.423848 q^{43} +10.2899 q^{44} -0.382809 q^{45} -0.175321 q^{46} +4.89484 q^{47} +3.20785 q^{48} -2.24530 q^{49} -1.78370 q^{50} -1.00000 q^{51} +5.46529 q^{52} +9.10953 q^{53} +0.367511 q^{54} +2.11216 q^{55} -3.09724 q^{56} +5.52998 q^{57} +1.30335 q^{58} +2.89285 q^{59} +0.713914 q^{60} -5.87415 q^{61} +0.296947 q^{62} +2.18053 q^{63} -4.93841 q^{64} +1.12184 q^{65} -2.02776 q^{66} -4.06274 q^{67} +1.86494 q^{68} -0.477048 q^{69} -0.306771 q^{70} +16.3620 q^{71} -1.42041 q^{72} +1.50889 q^{73} +0.373635 q^{74} -4.85346 q^{75} -10.3131 q^{76} -12.0312 q^{77} -1.07701 q^{78} -1.00000 q^{79} -1.22799 q^{80} +1.00000 q^{81} +3.62408 q^{82} +2.84844 q^{83} -4.06654 q^{84} +0.382809 q^{85} -0.155769 q^{86} +3.54641 q^{87} +7.83716 q^{88} +2.36222 q^{89} -0.140687 q^{90} -6.39015 q^{91} +0.889664 q^{92} +0.807994 q^{93} +1.79891 q^{94} -2.11693 q^{95} +4.01974 q^{96} -2.24444 q^{97} -0.825174 q^{98} -5.51754 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) \) 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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