LMFDB - Embedded newform 4027.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4027 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4027.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1557568940$
Analytic rank:	$1$
Dimension:	$159$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72666 q^{2} +0.318995 q^{3} +5.43469 q^{4} -1.22389 q^{5} -0.869792 q^{6} -4.59347 q^{7} -9.36524 q^{8} -2.89824 q^{9} +O(q^{10})$	\(q-2.72666 q^{2} +0.318995 q^{3} +5.43469 q^{4} -1.22389 q^{5} -0.869792 q^{6} -4.59347 q^{7} -9.36524 q^{8} -2.89824 q^{9} +3.33713 q^{10} +0.0767040 q^{11} +1.73364 q^{12} +4.43022 q^{13} +12.5249 q^{14} -0.390414 q^{15} +14.6665 q^{16} +2.02096 q^{17} +7.90253 q^{18} +3.34647 q^{19} -6.65145 q^{20} -1.46530 q^{21} -0.209146 q^{22} -4.38978 q^{23} -2.98747 q^{24} -3.50210 q^{25} -12.0797 q^{26} -1.88151 q^{27} -24.9641 q^{28} +2.45104 q^{29} +1.06453 q^{30} +7.34827 q^{31} -21.2601 q^{32} +0.0244682 q^{33} -5.51047 q^{34} +5.62190 q^{35} -15.7510 q^{36} -1.77871 q^{37} -9.12469 q^{38} +1.41322 q^{39} +11.4620 q^{40} -6.58524 q^{41} +3.99537 q^{42} -2.93248 q^{43} +0.416863 q^{44} +3.54712 q^{45} +11.9695 q^{46} +4.54751 q^{47} +4.67854 q^{48} +14.1000 q^{49} +9.54904 q^{50} +0.644675 q^{51} +24.0769 q^{52} -0.827981 q^{53} +5.13025 q^{54} -0.0938771 q^{55} +43.0190 q^{56} +1.06751 q^{57} -6.68315 q^{58} -7.88820 q^{59} -2.12178 q^{60} -4.03302 q^{61} -20.0363 q^{62} +13.3130 q^{63} +28.6361 q^{64} -5.42209 q^{65} -0.0667166 q^{66} +12.3270 q^{67} +10.9833 q^{68} -1.40032 q^{69} -15.3290 q^{70} +13.0860 q^{71} +27.1427 q^{72} +9.54468 q^{73} +4.84994 q^{74} -1.11715 q^{75} +18.1870 q^{76} -0.352338 q^{77} -3.85337 q^{78} +3.20637 q^{79} -17.9501 q^{80} +8.09453 q^{81} +17.9557 q^{82} -5.22405 q^{83} -7.96343 q^{84} -2.47342 q^{85} +7.99590 q^{86} +0.781869 q^{87} -0.718352 q^{88} +9.06651 q^{89} -9.67181 q^{90} -20.3501 q^{91} -23.8571 q^{92} +2.34406 q^{93} -12.3995 q^{94} -4.09570 q^{95} -6.78186 q^{96} +2.24441 q^{97} -38.4459 q^{98} -0.222307 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) $ 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9 - 23 * q^10 - 33 * q^11 - 57 * q^12 - 90 * q^13 - 28 * q^14 - 22 * q^15 + 130 * q^16 - 145 * q^17 - 50 * q^18 - 28 * q^19 - 121 * q^20 - 69 * q^21 - 26 * q^22 - 79 * q^23 - 62 * q^24 + 123 * q^25 - 40 * q^26 - 70 * q^27 - 43 * q^28 - 109 * q^29 - 43 * q^30 - 21 * q^31 - 139 * q^32 - 83 * q^33 - 93 * q^35 + 75 * q^36 - 65 * q^37 - 122 * q^38 - 18 * q^39 - 43 * q^40 - 71 * q^41 - 88 * q^42 - 72 * q^43 - 79 * q^44 - 181 * q^45 - 11 * q^46 - 114 * q^47 - 118 * q^48 + 118 * q^49 - 77 * q^50 - 29 * q^51 - 169 * q^52 - 220 * q^53 - 80 * q^54 - 37 * q^55 - 72 * q^56 - 90 * q^57 - 8 * q^58 - 60 * q^59 - 42 * q^60 - 108 * q^61 - 152 * q^62 - 65 * q^63 + 114 * q^64 - 81 * q^65 - 40 * q^66 - 50 * q^67 - 319 * q^68 - 103 * q^69 + 4 * q^70 - 7 * q^71 - 129 * q^72 - 94 * q^73 - 79 * q^74 - 59 * q^75 - 46 * q^76 - 329 * q^77 + 8 * q^78 - 18 * q^79 - 190 * q^80 + 59 * q^81 - 56 * q^82 - 201 * q^83 - 71 * q^84 - 26 * q^85 - 52 * q^86 - 126 * q^87 - 66 * q^88 - 114 * q^89 - 33 * q^90 - 30 * q^91 - 204 * q^92 - 125 * q^93 + 9 * q^94 - 84 * q^95 - 88 * q^96 - 56 * q^97 - 110 * q^98 - 46 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.72666	−1.92804	−0.964021	−	0.265826i	$-0.914355\pi$
$2$	−2.72666	−1.92804	−0.964021	+	0.265826i	$0.914355\pi$
$3$	0.318995	0.184172	0.0920860	−	0.995751i	$-0.470647\pi$
$3$	0.318995	0.184172	0.0920860	+	0.995751i	$0.470647\pi$
$4$	5.43469	2.71735
$5$	−1.22389	−0.547339	−0.273670	−	0.961824i	$-0.588238\pi$
$5$	−1.22389	−0.547339	−0.273670	+	0.961824i	$0.588238\pi$
$6$	−0.869792	−0.355091
$7$	−4.59347	−1.73617	−0.868085	−	0.496416i	$-0.834649\pi$
$7$	−4.59347	−1.73617	−0.868085	+	0.496416i	$0.834649\pi$
$8$	−9.36524	−3.31111
$9$	−2.89824	−0.966081
$10$	3.33713	1.05529
$11$	0.0767040	0.0231271	0.0115636	−	0.999933i	$-0.496319\pi$
$11$	0.0767040	0.0231271	0.0115636	+	0.999933i	$0.496319\pi$
$12$	1.73364	0.500459
$13$	4.43022	1.22872	0.614361	−	0.789025i	$-0.289414\pi$
$13$	4.43022	1.22872	0.614361	+	0.789025i	$0.289414\pi$
$14$	12.5249	3.34741
$15$	−0.390414	−0.100805
$16$	14.6665	3.66662
$17$	2.02096	0.490154	0.245077	−	0.969504i	$-0.421187\pi$
$17$	2.02096	0.490154	0.245077	+	0.969504i	$0.421187\pi$
$18$	7.90253	1.86264
$19$	3.34647	0.767732	0.383866	−	0.923389i	$-0.374592\pi$
$19$	3.34647	0.767732	0.383866	+	0.923389i	$0.374592\pi$
$20$	−6.65145	−1.48731
$21$	−1.46530	−0.319754
$22$	−0.209146	−0.0445901
$23$	−4.38978	−0.915333	−0.457666	−	0.889124i	$-0.651315\pi$
$23$	−4.38978	−0.915333	−0.457666	+	0.889124i	$0.651315\pi$
$24$	−2.98747	−0.609814
$25$	−3.50210	−0.700420
$26$	−12.0797	−2.36903
$27$	−1.88151	−0.362097
$28$	−24.9641	−4.71777
$29$	2.45104	0.455146	0.227573	−	0.973761i	$-0.426921\pi$
$29$	2.45104	0.455146	0.227573	+	0.973761i	$0.426921\pi$
$30$	1.06453	0.194355
$31$	7.34827	1.31979	0.659894	−	0.751359i	$-0.270601\pi$
$31$	7.34827	1.31979	0.659894	+	0.751359i	$0.270601\pi$
$32$	−21.2601	−3.75828
$33$	0.0244682	0.00425937
$34$	−5.51047	−0.945037
$35$	5.62190	0.950274
$36$	−15.7510	−2.62517
$37$	−1.77871	−0.292418	−0.146209	−	0.989254i	$-0.546707\pi$
$37$	−1.77871	−0.292418	−0.146209	+	0.989254i	$0.546707\pi$
$38$	−9.12469	−1.48022
$39$	1.41322	0.226296
$40$	11.4620	1.81230
$41$	−6.58524	−1.02844	−0.514221	−	0.857658i	$-0.671919\pi$
$41$	−6.58524	−1.02844	−0.514221	+	0.857658i	$0.671919\pi$
$42$	3.99537	0.616499
$43$	−2.93248	−0.447200	−0.223600	−	0.974681i	$-0.571781\pi$
$43$	−2.93248	−0.447200	−0.223600	+	0.974681i	$0.571781\pi$
$44$	0.416863	0.0628444
$45$	3.54712	0.528774
$46$	11.9695	1.76480
$47$	4.54751	0.663323	0.331662	−	0.943398i	$-0.392391\pi$
$47$	4.54751	0.663323	0.331662	+	0.943398i	$0.392391\pi$
$48$	4.67854	0.675289
$49$	14.1000	2.01428
$50$	9.54904	1.35044
$51$	0.644675	0.0902726
$52$	24.0769	3.33886
$53$	−0.827981	−0.113732	−0.0568660	−	0.998382i	$-0.518111\pi$
$53$	−0.827981	−0.113732	−0.0568660	+	0.998382i	$0.518111\pi$
$54$	5.13025	0.698138
$55$	−0.0938771	−0.0126584
$56$	43.0190	5.74865
$57$	1.06751	0.141395
$58$	−6.68315	−0.877540
$59$	−7.88820	−1.02696	−0.513478	−	0.858103i	$-0.671643\pi$
$59$	−7.88820	−1.02696	−0.513478	+	0.858103i	$0.671643\pi$
$60$	−2.12178	−0.273921
$61$	−4.03302	−0.516375	−0.258187	−	0.966095i	$-0.583125\pi$
$61$	−4.03302	−0.516375	−0.258187	+	0.966095i	$0.583125\pi$
$62$	−20.0363	−2.54461
$63$	13.3130	1.67728
$64$	28.6361	3.57951
$65$	−5.42209	−0.672528
$66$	−0.0667166	−0.00821224
$67$	12.3270	1.50598	0.752989	−	0.658034i	$-0.228611\pi$
$67$	12.3270	1.50598	0.752989	+	0.658034i	$0.228611\pi$
$68$	10.9833	1.33192
$69$	−1.40032	−0.168579
$70$	−15.3290	−1.83217
$71$	13.0860	1.55303	0.776513	−	0.630101i	$-0.216987\pi$
$71$	13.0860	1.55303	0.776513	+	0.630101i	$0.216987\pi$
$72$	27.1427	3.19880
$73$	9.54468	1.11712	0.558560	−	0.829464i	$-0.311354\pi$
$73$	9.54468	1.11712	0.558560	+	0.829464i	$0.311354\pi$
$74$	4.84994	0.563794
$75$	−1.11715	−0.128998
$76$	18.1870	2.08619
$77$	−0.352338	−0.0401526
$78$	−3.85337	−0.436308
$79$	3.20637	0.360745	0.180372	−	0.983598i	$-0.442270\pi$
$79$	3.20637	0.360745	0.180372	+	0.983598i	$0.442270\pi$
$80$	−17.9501	−2.00689
$81$	8.09453	0.899393
$82$	17.9557	1.98288
$83$	−5.22405	−0.573414	−0.286707	−	0.958018i	$-0.592561\pi$
$83$	−5.22405	−0.573414	−0.286707	+	0.958018i	$0.592561\pi$
$84$	−7.96343	−0.868881
$85$	−2.47342	−0.268281
$86$	7.99590	0.862220
$87$	0.781869	0.0838251
$88$	−0.718352	−0.0765765
$89$	9.06651	0.961048	0.480524	−	0.876982i	$-0.340447\pi$
$89$	9.06651	0.961048	0.480524	+	0.876982i	$0.340447\pi$
$90$	−9.67181	−1.01950
$91$	−20.3501	−2.13327
$92$	−23.8571	−2.48727
$93$	2.34406	0.243068
$94$	−12.3995	−1.27891
$95$	−4.09570	−0.420210
$96$	−6.78186	−0.692170
$97$	2.24441	0.227886	0.113943	−	0.993487i	$-0.463652\pi$
$97$	2.24441	0.227886	0.113943	+	0.993487i	$0.463652\pi$
$98$	−38.4459	−3.88362
$99$	−0.222307	−0.0223427
$100$	−19.0328	−1.90328
$101$	12.3306	1.22694	0.613472	−	0.789717i	$-0.289772\pi$
$101$	12.3306	1.22694	0.613472	+	0.789717i	$0.289772\pi$
$102$	−1.75781	−0.174049
$103$	−9.99808	−0.985140	−0.492570	−	0.870273i	$-0.663942\pi$
$103$	−9.99808	−0.985140	−0.492570	+	0.870273i	$0.663942\pi$
$104$	−41.4901	−4.06844
$105$	1.79336	0.175014
$106$	2.25762	0.219280
$107$	−4.07589	−0.394031	−0.197016	−	0.980400i	$-0.563125\pi$
$107$	−4.07589	−0.394031	−0.197016	+	0.980400i	$0.563125\pi$
$108$	−10.2254	−0.983942
$109$	6.77337	0.648771	0.324385	−	0.945925i	$-0.394843\pi$
$109$	6.77337	0.648771	0.324385	+	0.945925i	$0.394843\pi$
$110$	0.255971	0.0244059
$111$	−0.567399	−0.0538551
$112$	−67.3701	−6.36587
$113$	−12.4338	−1.16968	−0.584839	−	0.811150i	$-0.698842\pi$
$113$	−12.4338	−1.16968	−0.584839	+	0.811150i	$0.698842\pi$
$114$	−2.91073	−0.272615
$115$	5.37260	0.500998
$116$	13.3206	1.23679
$117$	−12.8399	−1.18704
$118$	21.5085	1.98001
$119$	−9.28321	−0.850990
$120$	3.65633	0.333775
$121$	−10.9941	−0.999465
$122$	10.9967	0.995592
$123$	−2.10066	−0.189410
$124$	39.9356	3.58632
$125$	10.4056	0.930707
$126$	−36.3001	−3.23387
$127$	14.7308	1.30715	0.653574	−	0.756862i	$-0.273269\pi$
$127$	14.7308	1.30715	0.653574	+	0.756862i	$0.273269\pi$
$128$	−35.5608	−3.14316
$129$	−0.935448	−0.0823616
$130$	14.7842	1.29666
$131$	−1.85378	−0.161965	−0.0809826	−	0.996716i	$-0.525806\pi$
$131$	−1.85378	−0.161965	−0.0809826	+	0.996716i	$0.525806\pi$
$132$	0.132977	0.0115742
$133$	−15.3719	−1.33291
$134$	−33.6115	−2.90359
$135$	2.30276	0.198190
$136$	−18.9267	−1.62296
$137$	−3.90189	−0.333361	−0.166680	−	0.986011i	$-0.553305\pi$
$137$	−3.90189	−0.333361	−0.166680	+	0.986011i	$0.553305\pi$
$138$	3.81820	0.325027
$139$	−12.0007	−1.01789	−0.508944	−	0.860800i	$-0.669964\pi$
$139$	−12.0007	−1.01789	−0.508944	+	0.860800i	$0.669964\pi$
$140$	30.5533	2.58222
$141$	1.45063	0.122165
$142$	−35.6812	−2.99430
$143$	0.339816	0.0284168
$144$	−42.5070	−3.54225
$145$	−2.99979	−0.249119
$146$	−26.0251	−2.15385
$147$	4.49783	0.370975
$148$	−9.66672	−0.794600
$149$	1.07760	0.0882806	0.0441403	−	0.999025i	$-0.485945\pi$
$149$	1.07760	0.0882806	0.0441403	+	0.999025i	$0.485945\pi$
$150$	3.04610	0.248713
$151$	0.0727389	0.00591941	0.00295971	−	0.999996i	$-0.499058\pi$
$151$	0.0727389	0.00591941	0.00295971	+	0.999996i	$0.499058\pi$
$152$	−31.3405	−2.54205
$153$	−5.85722	−0.473528
$154$	0.960706	0.0774159
$155$	−8.99346	−0.722372
$156$	7.68041	0.614925
$157$	−11.2655	−0.899083	−0.449542	−	0.893259i	$-0.648413\pi$
$157$	−11.2655	−0.899083	−0.449542	+	0.893259i	$0.648413\pi$
$158$	−8.74269	−0.695531
$159$	−0.264122	−0.0209462
$160$	26.0199	2.05706
$161$	20.1643	1.58917
$162$	−22.0711	−1.73407
$163$	7.08087	0.554616	0.277308	−	0.960781i	$-0.410558\pi$
$163$	7.08087	0.554616	0.277308	+	0.960781i	$0.410558\pi$
$164$	−35.7887	−2.79463
$165$	−0.0299463	−0.00233132
$166$	14.2442	1.10557
$167$	6.54491	0.506460	0.253230	−	0.967406i	$-0.418507\pi$
$167$	6.54491	0.506460	0.253230	+	0.967406i	$0.418507\pi$
$168$	13.7229	1.05874
$169$	6.62686	0.509758
$170$	6.74419	0.517256
$171$	−9.69887	−0.741691
$172$	−15.9371	−1.21520
$173$	−12.4608	−0.947374	−0.473687	−	0.880693i	$-0.657077\pi$
$173$	−12.4608	−0.947374	−0.473687	+	0.880693i	$0.657077\pi$
$174$	−2.13189	−0.161618
$175$	16.0868	1.21605
$176$	1.12498	0.0847984
$177$	−2.51630	−0.189136
$178$	−24.7213	−1.85294
$179$	−4.83883	−0.361671	−0.180836	−	0.983513i	$-0.557880\pi$
$179$	−4.83883	−0.361671	−0.180836	+	0.983513i	$0.557880\pi$
$180$	19.2775	1.43686
$181$	13.3777	0.994355	0.497177	−	0.867649i	$-0.334370\pi$
$181$	13.3777	0.994355	0.497177	+	0.867649i	$0.334370\pi$
$182$	55.4879	4.11303
$183$	−1.28651	−0.0951018
$184$	41.1114	3.03077
$185$	2.17694	0.160052
$186$	−6.39147	−0.468645
$187$	0.155015	0.0113359
$188$	24.7143	1.80248
$189$	8.64267	0.628662
$190$	11.1676	0.810183
$191$	−8.30249	−0.600747	−0.300373	−	0.953822i	$-0.597111\pi$
$191$	−8.30249	−0.600747	−0.300373	+	0.953822i	$0.597111\pi$
$192$	9.13477	0.659245
$193$	−10.9435	−0.787727	−0.393864	−	0.919169i	$-0.628862\pi$
$193$	−10.9435	−0.787727	−0.393864	+	0.919169i	$0.628862\pi$
$194$	−6.11976	−0.439373
$195$	−1.72962	−0.123861
$196$	76.6291	5.47351
$197$	−14.2043	−1.01202	−0.506008	−	0.862529i	$-0.668879\pi$
$197$	−14.2043	−1.01202	−0.506008	+	0.862529i	$0.668879\pi$
$198$	0.606156	0.0430776
$199$	19.3629	1.37260	0.686299	−	0.727319i	$-0.259234\pi$
$199$	19.3629	1.37260	0.686299	+	0.727319i	$0.259234\pi$
$200$	32.7980	2.31917
$201$	3.93224	0.277359
$202$	−33.6215	−2.36560
$203$	−11.2588	−0.790211
$204$	3.50361	0.245302
$205$	8.05959	0.562906
$206$	27.2614	1.89939
$207$	12.7226	0.884285
$208$	64.9757	4.50526
$209$	0.256687	0.0177554
$210$	−4.88988	−0.337434
$211$	8.18572	0.563528	0.281764	−	0.959484i	$-0.409080\pi$
$211$	8.18572	0.563528	0.281764	+	0.959484i	$0.409080\pi$
$212$	−4.49982	−0.309049
$213$	4.17438	0.286024
$214$	11.1136	0.759708
$215$	3.58903	0.244770
$216$	17.6208	1.19894
$217$	−33.7541	−2.29138
$218$	−18.4687	−1.25086
$219$	3.04471	0.205742
$220$	−0.510193	−0.0343972
$221$	8.95328	0.602263
$222$	1.54711	0.103835
$223$	−25.5227	−1.70913	−0.854563	−	0.519347i	$-0.826175\pi$
$223$	−25.5227	−1.70913	−0.854563	+	0.519347i	$0.826175\pi$
$224$	97.6575	6.52502
$225$	10.1499	0.676662
$226$	33.9029	2.25519
$227$	3.86109	0.256270	0.128135	−	0.991757i	$-0.459101\pi$
$227$	3.86109	0.256270	0.128135	+	0.991757i	$0.459101\pi$
$228$	5.80157	0.384218
$229$	1.01752	0.0672398	0.0336199	−	0.999435i	$-0.489296\pi$
$229$	1.01752	0.0672398	0.0336199	+	0.999435i	$0.489296\pi$
$230$	−14.6493	−0.965944
$231$	−0.112394	−0.00739499
$232$	−22.9545	−1.50704
$233$	3.37930	0.221385	0.110693	−	0.993855i	$-0.464693\pi$
$233$	3.37930	0.221385	0.110693	+	0.993855i	$0.464693\pi$
$234$	35.0099	2.28867
$235$	−5.56565	−0.363063
$236$	−42.8699	−2.79059
$237$	1.02282	0.0664391
$238$	25.3122	1.64074
$239$	−24.1570	−1.56259	−0.781293	−	0.624165i	$-0.785439\pi$
$239$	−24.1570	−1.56259	−0.781293	+	0.624165i	$0.785439\pi$
$240$	−5.72601	−0.369612
$241$	16.1189	1.03831	0.519156	−	0.854680i	$-0.326246\pi$
$241$	16.1189	1.03831	0.519156	+	0.854680i	$0.326246\pi$
$242$	29.9772	1.92701
$243$	8.22665	0.527740
$244$	−21.9182	−1.40317
$245$	−17.2568	−1.10250
$246$	5.72779	0.365190
$247$	14.8256	0.943330
$248$	−68.8183	−4.36997
$249$	−1.66645	−0.105607
$250$	−28.3726	−1.79444
$251$	−0.0555369	−0.00350546	−0.00175273	−	0.999998i	$-0.500558\pi$
$251$	−0.0555369	−0.00350546	−0.00175273	+	0.999998i	$0.500558\pi$
$252$	72.3520	4.55775
$253$	−0.336714	−0.0211690
$254$	−40.1660	−2.52024
$255$	−0.789010	−0.0494097
$256$	39.6901	2.48063
$257$	−20.7283	−1.29300	−0.646499	−	0.762915i	$-0.723768\pi$
$257$	−20.7283	−1.29300	−0.646499	+	0.762915i	$0.723768\pi$
$258$	2.55065	0.158797
$259$	8.17044	0.507687
$260$	−29.4674	−1.82749
$261$	−7.10370	−0.439708
$262$	5.05462	0.312276
$263$	−19.5611	−1.20619	−0.603095	−	0.797669i	$-0.706066\pi$
$263$	−19.5611	−1.20619	−0.603095	+	0.797669i	$0.706066\pi$
$264$	−0.229151	−0.0141033
$265$	1.01336	0.0622500
$266$	41.9140	2.56991
$267$	2.89217	0.176998
$268$	66.9932	4.09226
$269$	2.50727	0.152871	0.0764355	−	0.997075i	$-0.475646\pi$
$269$	2.50727	0.152871	0.0764355	+	0.997075i	$0.475646\pi$
$270$	−6.27885	−0.382118
$271$	−1.48586	−0.0902596	−0.0451298	−	0.998981i	$-0.514370\pi$
$271$	−1.48586	−0.0902596	−0.0451298	+	0.998981i	$0.514370\pi$
$272$	29.6403	1.79721
$273$	−6.49158	−0.392889
$274$	10.6391	0.642734
$275$	−0.268625	−0.0161987
$276$	−7.61030	−0.458086
$277$	−32.0357	−1.92484	−0.962421	−	0.271563i	$-0.912460\pi$
$277$	−32.0357	−1.92484	−0.962421	+	0.271563i	$0.912460\pi$
$278$	32.7219	1.96253
$279$	−21.2971	−1.27502
$280$	−52.6504	−3.14646
$281$	−22.4732	−1.34064	−0.670318	−	0.742074i	$-0.733842\pi$
$281$	−22.4732	−1.34064	−0.670318	+	0.742074i	$0.733842\pi$
$282$	−3.95539	−0.235540
$283$	30.8949	1.83651	0.918254	−	0.395991i	$-0.129599\pi$
$283$	30.8949	1.83651	0.918254	+	0.395991i	$0.129599\pi$
$284$	71.1185	4.22011
$285$	−1.30651	−0.0773909
$286$	−0.926563	−0.0547888
$287$	30.2491	1.78555
$288$	61.6168	3.63081
$289$	−12.9157	−0.759749
$290$	8.17943	0.480312
$291$	0.715957	0.0419701
$292$	51.8724	3.03560
$293$	−23.5664	−1.37676	−0.688382	−	0.725348i	$-0.741679\pi$
$293$	−23.5664	−1.37676	−0.688382	+	0.725348i	$0.741679\pi$
$294$	−12.2641	−0.715255
$295$	9.65427	0.562093
$296$	16.6580	0.968228
$297$	−0.144319	−0.00837426
$298$	−2.93826	−0.170209
$299$	−19.4477	−1.12469
$300$	−6.07138	−0.350531
$301$	13.4703	0.776414
$302$	−0.198335	−0.0114129
$303$	3.93341	0.225969
$304$	49.0809	2.81498
$305$	4.93596	0.282632
$306$	15.9707	0.912982
$307$	−24.5777	−1.40272	−0.701362	−	0.712805i	$-0.747424\pi$
$307$	−24.5777	−1.40272	−0.701362	+	0.712805i	$0.747424\pi$
$308$	−1.91485	−0.109109
$309$	−3.18934	−0.181435
$310$	24.5221	1.39276
$311$	−3.69329	−0.209428	−0.104714	−	0.994502i	$-0.533393\pi$
$311$	−3.69329	−0.209428	−0.104714	+	0.994502i	$0.533393\pi$
$312$	−13.2351	−0.749292
$313$	−17.5996	−0.994790	−0.497395	−	0.867524i	$-0.665710\pi$
$313$	−17.5996	−0.994790	−0.497395	+	0.867524i	$0.665710\pi$
$314$	30.7172	1.73347
$315$	−16.2936	−0.918041
$316$	17.4256	0.980268
$317$	−31.8892	−1.79108	−0.895539	−	0.444982i	$-0.853210\pi$
$317$	−31.8892	−1.79108	−0.895539	+	0.444982i	$0.853210\pi$
$318$	0.720171	0.0403852
$319$	0.188004	0.0105262
$320$	−35.0473	−1.95921
$321$	−1.30019	−0.0725695
$322$	−54.9814	−3.06399
$323$	6.76306	0.376307
$324$	43.9913	2.44396
$325$	−15.5151	−0.860621
$326$	−19.3071	−1.06932
$327$	2.16067	0.119485
$328$	61.6723	3.40529
$329$	−20.8889	−1.15164
$330$	0.0816536	0.00449488
$331$	27.9060	1.53385	0.766925	−	0.641736i	$-0.221786\pi$
$331$	27.9060	1.53385	0.766925	+	0.641736i	$0.221786\pi$
$332$	−28.3911	−1.55816
$333$	5.15512	0.282499
$334$	−17.8458	−0.976476
$335$	−15.0868	−0.824281
$336$	−21.4907	−1.17242
$337$	−28.6437	−1.56032	−0.780160	−	0.625580i	$-0.784862\pi$
$337$	−28.6437	−1.56032	−0.780160	+	0.625580i	$0.784862\pi$
$338$	−18.0692	−0.982835
$339$	−3.96633	−0.215422
$340$	−13.4423	−0.729011
$341$	0.563642	0.0305229
$342$	26.4456	1.43001
$343$	−32.6136	−1.76097
$344$	27.4634	1.48073
$345$	1.71383	0.0922697
$346$	33.9763	1.82658
$347$	16.1077	0.864705	0.432352	−	0.901705i	$-0.357684\pi$
$347$	16.1077	0.864705	0.432352	+	0.901705i	$0.357684\pi$
$348$	4.24921	0.227782
$349$	21.9370	1.17426	0.587131	−	0.809492i	$-0.300257\pi$
$349$	21.9370	1.17426	0.587131	+	0.809492i	$0.300257\pi$
$350$	−43.8633	−2.34459
$351$	−8.33551	−0.444917
$352$	−1.63073	−0.0869183
$353$	−0.615164	−0.0327419	−0.0163709	−	0.999866i	$-0.505211\pi$
$353$	−0.615164	−0.0327419	−0.0163709	+	0.999866i	$0.505211\pi$
$354$	6.86109	0.364663
$355$	−16.0158	−0.850032
$356$	49.2737	2.61150
$357$	−2.96130	−0.156729
$358$	13.1939	0.697318
$359$	−16.4492	−0.868156	−0.434078	−	0.900875i	$-0.642926\pi$
$359$	−16.4492	−0.868156	−0.434078	+	0.900875i	$0.642926\pi$
$360$	−33.2197	−1.75083
$361$	−7.80116	−0.410587
$362$	−36.4764	−1.91716
$363$	−3.50707	−0.184073
$364$	−110.596	−5.79683
$365$	−11.6816	−0.611444
$366$	3.50789	0.183360
$367$	−7.16610	−0.374068	−0.187034	−	0.982353i	$-0.559887\pi$
$367$	−7.16610	−0.374068	−0.187034	+	0.982353i	$0.559887\pi$
$368$	−64.3826	−3.35618
$369$	19.0856	0.993557
$370$	−5.93578	−0.308586
$371$	3.80331	0.197458
$372$	12.7393	0.660500
$373$	15.5375	0.804502	0.402251	−	0.915529i	$-0.368228\pi$
$373$	15.5375	0.804502	0.402251	+	0.915529i	$0.368228\pi$
$374$	−0.422675	−0.0218560
$375$	3.31934	0.171410
$376$	−42.5886	−2.19634
$377$	10.8586	0.559248
$378$	−23.5656	−1.21209
$379$	−12.2156	−0.627475	−0.313737	−	0.949510i	$-0.601581\pi$
$379$	−12.2156	−0.627475	−0.313737	+	0.949510i	$0.601581\pi$
$380$	−22.2589	−1.14186
$381$	4.69906	0.240740
$382$	22.6381	1.15827
$383$	−23.5244	−1.20204	−0.601020	−	0.799234i	$-0.705239\pi$
$383$	−23.5244	−1.20204	−0.601020	+	0.799234i	$0.705239\pi$
$384$	−11.3437	−0.578881
$385$	0.431222	0.0219771
$386$	29.8391	1.51877
$387$	8.49905	0.432031
$388$	12.1977	0.619244
$389$	−28.3970	−1.43979	−0.719893	−	0.694085i	$-0.755809\pi$
$389$	−28.3970	−1.43979	−0.719893	+	0.694085i	$0.755809\pi$
$390$	4.71610	0.238809
$391$	−8.87156	−0.448654
$392$	−132.050	−6.66952
$393$	−0.591345	−0.0298294
$394$	38.7304	1.95121
$395$	−3.92424	−0.197450
$396$	−1.20817	−0.0607128
$397$	3.05865	0.153509	0.0767546	−	0.997050i	$-0.475544\pi$
$397$	3.05865	0.153509	0.0767546	+	0.997050i	$0.475544\pi$
$398$	−52.7961	−2.64643
$399$	−4.90356	−0.245485
$400$	−51.3635	−2.56817
$401$	−8.36748	−0.417852	−0.208926	−	0.977931i	$-0.566997\pi$
$401$	−8.36748	−0.417852	−0.208926	+	0.977931i	$0.566997\pi$
$402$	−10.7219	−0.534759
$403$	32.5545	1.62165
$404$	67.0132	3.33403
$405$	−9.90680	−0.492273
$406$	30.6989	1.52356
$407$	−0.136434	−0.00676278
$408$	−6.03754	−0.298903
$409$	−3.16667	−0.156582	−0.0782908	−	0.996931i	$-0.524946\pi$
$409$	−3.16667	−0.156582	−0.0782908	+	0.996931i	$0.524946\pi$
$410$	−21.9758	−1.08531
$411$	−1.24468	−0.0613957
$412$	−54.3365	−2.67697
$413$	36.2342	1.78297
$414$	−34.6904	−1.70494
$415$	6.39365	0.313852
$416$	−94.1868	−4.61789
$417$	−3.82817	−0.187467
$418$	−0.699900	−0.0342332
$419$	26.2855	1.28413	0.642066	−	0.766650i	$-0.278078\pi$
$419$	26.2855	1.28413	0.642066	+	0.766650i	$0.278078\pi$
$420$	9.74635	0.475573
$421$	−27.4518	−1.33792	−0.668960	−	0.743299i	$-0.733260\pi$
$421$	−27.4518	−1.33792	−0.668960	+	0.743299i	$0.733260\pi$
$422$	−22.3197	−1.08651
$423$	−13.1798	−0.640824
$424$	7.75424	0.376579
$425$	−7.07759	−0.343313
$426$	−11.3821	−0.551466
$427$	18.5255	0.896514
$428$	−22.1512	−1.07072
$429$	0.108400	0.00523358
$430$	−9.78608	−0.471927
$431$	−24.1362	−1.16260	−0.581300	−	0.813689i	$-0.697456\pi$
$431$	−24.1362	−1.16260	−0.581300	+	0.813689i	$0.697456\pi$
$432$	−27.5951	−1.32767
$433$	26.4369	1.27048	0.635239	−	0.772316i	$-0.280902\pi$
$433$	26.4369	1.27048	0.635239	+	0.772316i	$0.280902\pi$
$434$	92.0360	4.41787
$435$	−0.956920	−0.0458808
$436$	36.8112	1.76293
$437$	−14.6903	−0.702730
$438$	−8.30189	−0.396680
$439$	−27.0574	−1.29138	−0.645690	−	0.763599i	$-0.723430\pi$
$439$	−27.0574	−1.29138	−0.645690	+	0.763599i	$0.723430\pi$
$440$	0.879182	0.0419134
$441$	−40.8652	−1.94596
$442$	−24.4126	−1.16119
$443$	21.3004	1.01201	0.506007	−	0.862530i	$-0.331121\pi$
$443$	21.3004	1.01201	0.506007	+	0.862530i	$0.331121\pi$
$444$	−3.08364	−0.146343
$445$	−11.0964	−0.526019
$446$	69.5918	3.29527
$447$	0.343750	0.0162588
$448$	−131.539	−6.21463
$449$	−5.60257	−0.264402	−0.132201	−	0.991223i	$-0.542204\pi$
$449$	−5.60257	−0.264402	−0.132201	+	0.991223i	$0.542204\pi$
$450$	−27.6754	−1.30463
$451$	−0.505114	−0.0237849
$452$	−67.5741	−3.17842
$453$	0.0232034	0.00109019
$454$	−10.5279	−0.494099
$455$	24.9062	1.16762
$456$	−9.99746	−0.468174
$457$	36.6697	1.71534	0.857668	−	0.514205i	$-0.171913\pi$
$457$	36.6697	1.71534	0.857668	+	0.514205i	$0.171913\pi$
$458$	−2.77444	−0.129641
$459$	−3.80245	−0.177483
$460$	29.1984	1.36138
$461$	−10.9470	−0.509852	−0.254926	−	0.966961i	$-0.582051\pi$
$461$	−10.9470	−0.509852	−0.254926	+	0.966961i	$0.582051\pi$
$462$	0.306461	0.0142578
$463$	5.10384	0.237196	0.118598	−	0.992942i	$-0.462160\pi$
$463$	5.10384	0.237196	0.118598	+	0.992942i	$0.462160\pi$
$464$	35.9481	1.66885
$465$	−2.86887	−0.133041
$466$	−9.21421	−0.426840
$467$	−3.65377	−0.169076	−0.0845382	−	0.996420i	$-0.526942\pi$
$467$	−3.65377	−0.169076	−0.0845382	+	0.996420i	$0.526942\pi$
$468$	−69.7806	−3.22561
$469$	−56.6235	−2.61463
$470$	15.1756	0.700000
$471$	−3.59363	−0.165586
$472$	73.8749	3.40037
$473$	−0.224933	−0.0103424
$474$	−2.78888	−0.128097
$475$	−11.7197	−0.537735
$476$	−50.4514	−2.31243
$477$	2.39969	0.109874
$478$	65.8679	3.01273
$479$	18.6569	0.852456	0.426228	−	0.904616i	$-0.359842\pi$
$479$	18.6569	0.852456	0.426228	+	0.904616i	$0.359842\pi$
$480$	8.30023	0.378852
$481$	−7.88007	−0.359300
$482$	−43.9509	−2.00191
$483$	6.43233	0.292681
$484$	−59.7496	−2.71589
$485$	−2.74691	−0.124731
$486$	−22.4313	−1.01750
$487$	37.6981	1.70826	0.854132	−	0.520057i	$-0.174089\pi$
$487$	37.6981	1.70826	0.854132	+	0.520057i	$0.174089\pi$
$488$	37.7702	1.70978
$489$	2.25876	0.102145
$490$	47.0535	2.12566
$491$	8.17571	0.368965	0.184482	−	0.982836i	$-0.440939\pi$
$491$	8.17571	0.368965	0.184482	+	0.982836i	$0.440939\pi$
$492$	−11.4164	−0.514692
$493$	4.95344	0.223092
$494$	−40.4244	−1.81878
$495$	0.272079	0.0122290
$496$	107.773	4.83916
$497$	−60.1103	−2.69632
$498$	4.54384	0.203614
$499$	−25.8366	−1.15661	−0.578303	−	0.815822i	$-0.696285\pi$
$499$	−25.8366	−1.15661	−0.578303	+	0.815822i	$0.696285\pi$
$500$	56.5513	2.52905
$501$	2.08779	0.0932758
$502$	0.151430	0.00675867
$503$	8.07997	0.360268	0.180134	−	0.983642i	$-0.442347\pi$
$503$	8.07997	0.360268	0.180134	+	0.983642i	$0.442347\pi$
$504$	−124.679	−5.55366
$505$	−15.0913	−0.671555
$506$	0.918105	0.0408147
$507$	2.11394	0.0938832
$508$	80.0574	3.55197
$509$	24.6675	1.09337	0.546685	−	0.837339i	$-0.315890\pi$
$509$	24.6675	1.09337	0.546685	+	0.837339i	$0.315890\pi$
$510$	2.15137	0.0952641
$511$	−43.8432	−1.93951
$512$	−37.1000	−1.63960
$513$	−6.29641	−0.277993
$514$	56.5192	2.49295
$515$	12.2365	0.539206
$516$	−5.08387	−0.223805
$517$	0.348813	0.0153408
$518$	−22.2780	−0.978841
$519$	−3.97492	−0.174480
$520$	50.7792	2.22682
$521$	36.6938	1.60758	0.803791	−	0.594911i	$-0.202813\pi$
$521$	36.6938	1.60758	0.803791	+	0.594911i	$0.202813\pi$
$522$	19.3694	0.847775
$523$	−15.1038	−0.660441	−0.330220	−	0.943904i	$-0.607123\pi$
$523$	−15.1038	−0.660441	−0.330220	+	0.943904i	$0.607123\pi$
$524$	−10.0747	−0.440115
$525$	5.13161	0.223962
$526$	53.3366	2.32558
$527$	14.8505	0.646899
$528$	0.358863	0.0156175
$529$	−3.72982	−0.162166
$530$	−2.76308	−0.120021
$531$	22.8619	0.992122
$532$	−83.5415	−3.62199
$533$	−29.1741	−1.26367
$534$	−7.88598	−0.341260
$535$	4.98843	0.215669
$536$	−115.445	−4.98646
$537$	−1.54356	−0.0666097
$538$	−6.83648	−0.294742
$539$	1.08153	0.0465846
$540$	12.5148	0.538550
$541$	12.4994	0.537392	0.268696	−	0.963225i	$-0.413407\pi$
$541$	12.4994	0.537392	0.268696	+	0.963225i	$0.413407\pi$
$542$	4.05144	0.174024
$543$	4.26741	0.183132
$544$	−42.9657	−1.84214
$545$	−8.28984	−0.355098
$546$	17.7004	0.757505
$547$	4.00457	0.171223	0.0856114	−	0.996329i	$-0.472716\pi$
$547$	4.00457	0.171223	0.0856114	+	0.996329i	$0.472716\pi$
$548$	−21.2056	−0.905856
$549$	11.6887	0.498860
$550$	0.732450	0.0312318
$551$	8.20231	0.349430
$552$	13.1143	0.558183
$553$	−14.7284	−0.626314
$554$	87.3507	3.71118
$555$	0.694433	0.0294770
$556$	−65.2202	−2.76595
$557$	5.59163	0.236925	0.118463	−	0.992959i	$-0.462203\pi$
$557$	5.59163	0.236925	0.118463	+	0.992959i	$0.462203\pi$
$558$	58.0699	2.45830
$559$	−12.9916	−0.549484
$560$	82.4534	3.48429
$561$	0.0494492	0.00208775
$562$	61.2767	2.58480
$563$	−9.95517	−0.419561	−0.209780	−	0.977749i	$-0.567275\pi$
$563$	−9.95517	−0.419561	−0.209780	+	0.977749i	$0.567275\pi$
$564$	7.88375	0.331966
$565$	15.2176	0.640210
$566$	−84.2399	−3.54087
$567$	−37.1820	−1.56150
$568$	−122.554	−5.14224
$569$	−36.0335	−1.51060	−0.755302	−	0.655377i	$-0.772510\pi$
$569$	−36.0335	−1.51060	−0.755302	+	0.655377i	$0.772510\pi$
$570$	3.56241	0.149213
$571$	−40.8566	−1.70980	−0.854898	−	0.518796i	$-0.826381\pi$
$571$	−40.8566	−1.70980	−0.854898	+	0.518796i	$0.826381\pi$
$572$	1.84679	0.0772183
$573$	−2.64845	−0.110641
$574$	−82.4791	−3.44261
$575$	15.3734	0.641117
$576$	−82.9942	−3.45809
$577$	28.9361	1.20463	0.602313	−	0.798260i	$-0.294246\pi$
$577$	28.9361	1.20463	0.602313	+	0.798260i	$0.294246\pi$
$578$	35.2169	1.46483
$579$	−3.49091	−0.145077
$580$	−16.3030	−0.676943
$581$	23.9965	0.995543
$582$	−1.95217	−0.0809202
$583$	−0.0635095	−0.00263029
$584$	−89.3883	−3.69891
$585$	15.7145	0.649716
$586$	64.2577	2.65446
$587$	43.3123	1.78769	0.893845	−	0.448375i	$-0.147997\pi$
$587$	43.3123	1.78769	0.893845	+	0.448375i	$0.147997\pi$
$588$	24.4443	1.00807
$589$	24.5907	1.01324
$590$	−26.3239	−1.08374
$591$	−4.53111	−0.186385
$592$	−26.0874	−1.07218
$593$	−11.0466	−0.453630	−0.226815	−	0.973938i	$-0.572831\pi$
$593$	−11.0466	−0.453630	−0.226815	+	0.973938i	$0.572831\pi$
$594$	0.393510	0.0161459
$595$	11.3616	0.465780
$596$	5.85644	0.239889
$597$	6.17667	0.252794
$598$	53.0273	2.16845
$599$	−9.75620	−0.398628	−0.199314	−	0.979936i	$-0.563871\pi$
$599$	−9.75620	−0.398628	−0.199314	+	0.979936i	$0.563871\pi$
$600$	10.4624	0.427126
$601$	−0.0259603	−0.00105894	−0.000529471	−	1.00000i	$-0.500169\pi$
$601$	−0.0259603	−0.00105894	−0.000529471		1.00000i	$0.500169\pi$
$602$	−36.7289	−1.49696
$603$	−35.7265	−1.45490
$604$	0.395314	0.0160851
$605$	13.4556	0.547047
$606$	−10.7251	−0.435677
$607$	−26.4476	−1.07348	−0.536738	−	0.843749i	$-0.680344\pi$
$607$	−26.4476	−1.07348	−0.536738	+	0.843749i	$0.680344\pi$
$608$	−71.1461	−2.88536
$609$	−3.59149	−0.145535
$610$	−13.4587	−0.544927
$611$	20.1465	0.815040
$612$	−31.8322	−1.28674
$613$	−32.1842	−1.29991	−0.649954	−	0.759974i	$-0.725212\pi$
$613$	−32.1842	−1.29991	−0.649954	+	0.759974i	$0.725212\pi$
$614$	67.0151	2.70451
$615$	2.57097	0.103672
$616$	3.29973	0.132950
$617$	−4.82633	−0.194301	−0.0971503	−	0.995270i	$-0.530973\pi$
$617$	−4.82633	−0.194301	−0.0971503	+	0.995270i	$0.530973\pi$
$618$	8.69625	0.349815
$619$	18.5542	0.745755	0.372877	−	0.927881i	$-0.378371\pi$
$619$	18.5542	0.745755	0.372877	+	0.927881i	$0.378371\pi$
$620$	−48.8767	−1.96293
$621$	8.25942	0.331439
$622$	10.0704	0.403785
$623$	−41.6467	−1.66854
$624$	20.7270	0.829742
$625$	4.77518	0.191007
$626$	47.9883	1.91800
$627$	0.0818821	0.00327005
$628$	−61.2244	−2.44312
$629$	−3.59469	−0.143330
$630$	44.4272	1.77002
$631$	1.30764	0.0520565	0.0260283	−	0.999661i	$-0.491714\pi$
$631$	1.30764	0.0520565	0.0260283	+	0.999661i	$0.491714\pi$
$632$	−30.0284	−1.19447
$633$	2.61121	0.103786
$634$	86.9512	3.45327
$635$	−18.0289	−0.715454
$636$	−1.43542	−0.0569181
$637$	62.4661	2.47500
$638$	−0.512624	−0.0202950
$639$	−37.9265	−1.50035
$640$	43.5224	1.72037
$641$	11.1746	0.441371	0.220686	−	0.975345i	$-0.429171\pi$
$641$	11.1746	0.441371	0.220686	+	0.975345i	$0.429171\pi$
$642$	3.54518	0.139917
$643$	8.14302	0.321129	0.160565	−	0.987025i	$-0.448668\pi$
$643$	8.14302	0.321129	0.160565	+	0.987025i	$0.448668\pi$
$644$	109.587	4.31833
$645$	1.14488	0.0450798
$646$	−18.4406	−0.725535
$647$	40.8536	1.60612	0.803059	−	0.595899i	$-0.203204\pi$
$647$	40.8536	1.60612	0.803059	+	0.595899i	$0.203204\pi$
$648$	−75.8073	−2.97799
$649$	−0.605056	−0.0237505
$650$	42.3044	1.65931
$651$	−10.7674	−0.422007
$652$	38.4823	1.50708
$653$	11.5515	0.452044	0.226022	−	0.974122i	$-0.427428\pi$
$653$	11.5515	0.452044	0.226022	+	0.974122i	$0.427428\pi$
$654$	−5.89142	−0.230373
$655$	2.26881	0.0886499
$656$	−96.5822	−3.77090
$657$	−27.6628	−1.07923
$658$	56.9569	2.22041
$659$	0.152464	0.00593915	0.00296958	−	0.999996i	$-0.499055\pi$
$659$	0.152464	0.00593915	0.00296958	+	0.999996i	$0.499055\pi$
$660$	−0.162749	−0.00633500
$661$	33.9517	1.32057	0.660285	−	0.751015i	$-0.270436\pi$
$661$	33.9517	1.32057	0.660285	+	0.751015i	$0.270436\pi$
$662$	−76.0902	−2.95733
$663$	2.85605	0.110920
$664$	48.9245	1.89864
$665$	18.8135	0.729556
$666$	−14.0563	−0.544670
$667$	−10.7595	−0.416610
$668$	35.5695	1.37623
$669$	−8.14162	−0.314773
$670$	41.1367	1.58925
$671$	−0.309348	−0.0119423
$672$	31.1523	1.20173
$673$	−40.0661	−1.54443	−0.772217	−	0.635359i	$-0.780852\pi$
$673$	−40.0661	−1.54443	−0.772217	+	0.635359i	$0.780852\pi$
$674$	78.1016	3.00836
$675$	6.58924	0.253620
$676$	36.0149	1.38519
$677$	−3.21447	−0.123542	−0.0617711	−	0.998090i	$-0.519675\pi$
$677$	−3.21447	−0.123542	−0.0617711	+	0.998090i	$0.519675\pi$
$678$	10.8149	0.415342
$679$	−10.3097	−0.395648
$680$	23.1642	0.888307
$681$	1.23167	0.0471977
$682$	−1.53686	−0.0588495
$683$	31.7268	1.21399	0.606995	−	0.794705i	$-0.292375\pi$
$683$	31.7268	1.21399	0.606995	+	0.794705i	$0.292375\pi$
$684$	−52.7104	−2.01543
$685$	4.77547	0.182461
$686$	88.9263	3.39522
$687$	0.324585	0.0123837
$688$	−43.0092	−1.63971
$689$	−3.66814	−0.139745
$690$	−4.67305	−0.177900
$691$	29.8667	1.13618	0.568092	−	0.822965i	$-0.307682\pi$
$691$	29.8667	1.13618	0.568092	+	0.822965i	$0.307682\pi$
$692$	−67.7204	−2.57434
$693$	1.02116	0.0387907
$694$	−43.9202	−1.66719
$695$	14.6875	0.557130
$696$	−7.32239	−0.277554
$697$	−13.3085	−0.504094
$698$	−59.8148	−2.26403
$699$	1.07798	0.0407730
$700$	87.4267	3.30442
$701$	−19.7788	−0.747036	−0.373518	−	0.927623i	$-0.621849\pi$
$701$	−19.7788	−0.747036	−0.373518	+	0.927623i	$0.621849\pi$
$702$	22.7281	0.857818
$703$	−5.95239	−0.224498
$704$	2.19650	0.0827837
$705$	−1.77541	−0.0668660
$706$	1.67735	0.0631278
$707$	−56.6404	−2.13018
$708$	−13.6753	−0.513949
$709$	−22.9207	−0.860805	−0.430402	−	0.902637i	$-0.641628\pi$
$709$	−22.9207	−0.860805	−0.430402	+	0.902637i	$0.641628\pi$
$710$	43.6698	1.63890
$711$	−9.29283	−0.348509
$712$	−84.9100	−3.18214
$713$	−32.2573	−1.20805
$714$	8.07446	0.302179
$715$	−0.415896	−0.0155536
$716$	−26.2976	−0.982786
$717$	−7.70596	−0.287784
$718$	44.8514	1.67384
$719$	−35.2955	−1.31630	−0.658150	−	0.752887i	$-0.728661\pi$
$719$	−35.2955	−1.31630	−0.658150	+	0.752887i	$0.728661\pi$
$720$	52.0238	1.93881
$721$	45.9259	1.71037
$722$	21.2711	0.791630
$723$	5.14186	0.191228
$724$	72.7035	2.70201
$725$	−8.58377	−0.318793
$726$	9.56260	0.354901
$727$	−43.0472	−1.59653	−0.798267	−	0.602304i	$-0.794249\pi$
$727$	−43.0472	−1.59653	−0.798267	+	0.602304i	$0.794249\pi$
$728$	190.584	7.06350
$729$	−21.6593	−0.802198
$730$	31.8518	1.17889
$731$	−5.92642	−0.219197
$732$	−6.99180	−0.258424
$733$	32.8989	1.21515	0.607574	−	0.794263i	$-0.292143\pi$
$733$	32.8989	1.21515	0.607574	+	0.794263i	$0.292143\pi$
$734$	19.5396	0.721218
$735$	−5.50484	−0.203049
$736$	93.3270	3.44008
$737$	0.945527	0.0348289
$738$	−52.0400	−1.91562
$739$	−2.69276	−0.0990549	−0.0495275	−	0.998773i	$-0.515772\pi$
$739$	−2.69276	−0.0990549	−0.0495275	+	0.998773i	$0.515772\pi$
$740$	11.8310	0.434916
$741$	4.72929	0.173735
$742$	−10.3703	−0.380707
$743$	−10.9860	−0.403039	−0.201519	−	0.979485i	$-0.564588\pi$
$743$	−10.9860	−0.403039	−0.201519	+	0.979485i	$0.564588\pi$
$744$	−21.9527	−0.804826
$745$	−1.31886	−0.0483195
$746$	−42.3656	−1.55111
$747$	15.1406	0.553964
$748$	0.842461	0.0308034
$749$	18.7225	0.684105
$750$	−9.05073	−0.330486
$751$	−43.7789	−1.59752	−0.798758	−	0.601652i	$-0.794509\pi$
$751$	−43.7789	−1.59752	−0.798758	+	0.601652i	$0.794509\pi$
$752$	66.6960	2.43215
$753$	−0.0177160	−0.000645607 0
$754$	−29.6078	−1.07825
$755$	−0.0890243	−0.00323993
$756$	46.9702	1.70829
$757$	19.5891	0.711977	0.355988	−	0.934490i	$-0.384144\pi$
$757$	19.5891	0.711977	0.355988	+	0.934490i	$0.384144\pi$
$758$	33.3079	1.20980
$759$	−0.107410	−0.00389874
$760$	38.3572	1.39136
$761$	51.4220	1.86405	0.932024	−	0.362397i	$-0.118042\pi$
$761$	51.4220	1.86405	0.932024	+	0.362397i	$0.118042\pi$
$762$	−12.8127	−0.464157
$763$	−31.1133	−1.12638
$764$	−45.1214	−1.63244
$765$	7.16858	0.259181
$766$	64.1431	2.31758
$767$	−34.9465	−1.26184
$768$	12.6609	0.456863
$769$	−18.7491	−0.676108	−0.338054	−	0.941127i	$-0.609769\pi$
$769$	−18.7491	−0.676108	−0.338054	+	0.941127i	$0.609769\pi$
$770$	−1.17580	−0.0423728
$771$	−6.61224	−0.238134
$772$	−59.4743	−2.14053
$773$	−6.47347	−0.232835	−0.116417	−	0.993200i	$-0.537141\pi$
$773$	−6.47347	−0.232835	−0.116417	+	0.993200i	$0.537141\pi$
$774$	−23.1740	−0.832974
$775$	−25.7344	−0.924406
$776$	−21.0195	−0.754555
$777$	2.60633	0.0935016
$778$	77.4291	2.77597
$779$	−22.0373	−0.789567
$780$	−9.39996	−0.336573
$781$	1.00375	0.0359170
$782$	24.1897	0.865023
$783$	−4.61165	−0.164807
$784$	206.797	7.38562
$785$	13.7877	0.492104
$786$	1.61240	0.0575124
$787$	−40.6887	−1.45039	−0.725197	−	0.688541i	$-0.758252\pi$
$787$	−40.6887	−1.45039	−0.725197	+	0.688541i	$0.758252\pi$
$788$	−77.1960	−2.74999
$789$	−6.23990	−0.222146
$790$	10.7001	0.380691
$791$	57.1145	2.03076
$792$	2.08196	0.0739791
$793$	−17.8672	−0.634481
$794$	−8.33991	−0.295972
$795$	0.323256	0.0114647
$796$	105.231	3.72982
$797$	−53.1516	−1.88273	−0.941363	−	0.337394i	$-0.890454\pi$
$797$	−53.1516	−1.88273	−0.941363	+	0.337394i	$0.890454\pi$
$798$	13.3704	0.473306
$799$	9.19033	0.325130
$800$	74.4548	2.63238
$801$	−26.2769	−0.928450
$802$	22.8153	0.805636
$803$	0.732115	0.0258358
$804$	21.3705	0.753680
$805$	−24.6789	−0.869817
$806$	−88.7650	−3.12662
$807$	0.799807	0.0281545
$808$	−115.479	−4.06255
$809$	−30.8686	−1.08528	−0.542641	−	0.839965i	$-0.682576\pi$
$809$	−30.8686	−1.08528	−0.542641	+	0.839965i	$0.682576\pi$
$810$	27.0125	0.949123
$811$	−15.3593	−0.539338	−0.269669	−	0.962953i	$-0.586914\pi$
$811$	−15.3593	−0.539338	−0.269669	+	0.962953i	$0.586914\pi$
$812$	−61.1879	−2.14727
$813$	−0.473982	−0.0166233
$814$	0.372009	0.0130389
$815$	−8.66619	−0.303563
$816$	9.45512	0.330995
$817$	−9.81346	−0.343330
$818$	8.63444	0.301896
$819$	58.9795	2.06091
$820$	43.8014	1.52961
$821$	−12.6276	−0.440705	−0.220352	−	0.975420i	$-0.570721\pi$
$821$	−12.6276	−0.440705	−0.220352	+	0.975420i	$0.570721\pi$
$822$	3.39383	0.118373
$823$	−39.5354	−1.37812	−0.689059	−	0.724705i	$-0.741976\pi$
$823$	−39.5354	−1.37812	−0.689059	+	0.724705i	$0.741976\pi$
$824$	93.6344	3.26191
$825$	−0.0856901	−0.00298335
$826$	−98.7985	−3.43764
$827$	57.1179	1.98619	0.993093	−	0.117332i	$-0.0374342\pi$
$827$	57.1179	1.98619	0.993093	+	0.117332i	$0.0374342\pi$
$828$	69.1437	2.40291
$829$	−7.98282	−0.277255	−0.138627	−	0.990345i	$-0.544269\pi$
$829$	−7.98282	−0.277255	−0.138627	+	0.990345i	$0.544269\pi$
$830$	−17.4333	−0.605120
$831$	−10.2192	−0.354502
$832$	126.864	4.39822
$833$	28.4955	0.987309
$834$	10.4381	0.361443
$835$	−8.01023	−0.277206
$836$	1.39502	0.0482477
$837$	−13.8259	−0.477891
$838$	−71.6717	−2.47586
$839$	12.6764	0.437639	0.218820	−	0.975765i	$-0.429779\pi$
$839$	12.6764	0.437639	0.218820	+	0.975765i	$0.429779\pi$
$840$	−16.7952	−0.579491
$841$	−22.9924	−0.792842
$842$	74.8518	2.57956
$843$	−7.16883	−0.246908
$844$	44.4869	1.53130
$845$	−8.11053	−0.279011
$846$	35.9369	1.23553
$847$	50.5012	1.73524
$848$	−12.1436	−0.417012
$849$	9.85531	0.338233
$850$	19.2982	0.661923
$851$	7.80814	0.267659
$852$	22.6865	0.777225
$853$	−33.9057	−1.16091	−0.580455	−	0.814292i	$-0.697125\pi$
$853$	−33.9057	−1.16091	−0.580455	+	0.814292i	$0.697125\pi$
$854$	−50.5129	−1.72852
$855$	11.8703	0.405957
$856$	38.1717	1.30468
$857$	−14.4864	−0.494846	−0.247423	−	0.968908i	$-0.579584\pi$
$857$	−14.4864	−0.494846	−0.247423	+	0.968908i	$0.579584\pi$
$858$	−0.295569	−0.0100906
$859$	35.4773	1.21047	0.605234	−	0.796047i	$-0.293079\pi$
$859$	35.4773	1.21047	0.605234	+	0.796047i	$0.293079\pi$
$860$	19.5053	0.665125
$861$	9.64932	0.328848
$862$	65.8113	2.24154
$863$	52.2838	1.77976	0.889880	−	0.456194i	$-0.150788\pi$
$863$	52.2838	1.77976	0.889880	+	0.456194i	$0.150788\pi$
$864$	40.0010	1.36086
$865$	15.2506	0.518535
$866$	−72.0846	−2.44953
$867$	−4.12006	−0.139924
$868$	−183.443	−6.22646
$869$	0.245941	0.00834299
$870$	2.60920	0.0884601
$871$	54.6111	1.85043
$872$	−63.4342	−2.14815
$873$	−6.50485	−0.220156
$874$	40.0554	1.35489
$875$	−47.7979	−1.61586
$876$	16.5470	0.559073
$877$	−40.7335	−1.37547	−0.687737	−	0.725960i	$-0.741396\pi$
$877$	−40.7335	−1.37547	−0.687737	+	0.725960i	$0.741396\pi$
$878$	73.7765	2.48984
$879$	−7.51757	−0.253561
$880$	−1.37685	−0.0464135
$881$	46.1935	1.55630	0.778149	−	0.628080i	$-0.216159\pi$
$881$	46.1935	1.55630	0.778149	+	0.628080i	$0.216159\pi$
$882$	111.426	3.75189
$883$	40.4421	1.36098	0.680492	−	0.732755i	$-0.261766\pi$
$883$	40.4421	1.36098	0.680492	+	0.732755i	$0.261766\pi$
$884$	48.6583	1.63656
$885$	3.07967	0.103522
$886$	−58.0791	−1.95120
$887$	−22.5117	−0.755869	−0.377934	−	0.925832i	$-0.623366\pi$
$887$	−22.5117	−0.755869	−0.377934	+	0.925832i	$0.623366\pi$
$888$	5.31383	0.178320
$889$	−67.6656	−2.26943
$890$	30.2561	1.01419
$891$	0.620883	0.0208004
$892$	−138.708	−4.64429
$893$	15.2181	0.509254
$894$	−0.937290	−0.0313477
$895$	5.92219	0.197957
$896$	163.347	5.45705
$897$	−6.20372	−0.207136
$898$	15.2763	0.509778
$899$	18.0109	0.600696
$900$	55.1617	1.83872
$901$	−1.67331	−0.0557461
$902$	1.37728	0.0458583
$903$	4.29696	0.142994
$904$	116.446	3.87293
$905$	−16.3728	−0.544250
$906$	−0.0632678	−0.00210193
$907$	−30.9617	−1.02807	−0.514033	−	0.857770i	$-0.671849\pi$
$907$	−30.9617	−1.02807	−0.514033	+	0.857770i	$0.671849\pi$
$908$	20.9839	0.696374
$909$	−35.7372	−1.18533
$910$	−67.9109	−2.25123
$911$	27.6858	0.917272	0.458636	−	0.888624i	$-0.348338\pi$
$911$	27.6858	0.917272	0.458636	+	0.888624i	$0.348338\pi$
$912$	15.6566	0.518441
$913$	−0.400705	−0.0132614
$914$	−99.9858	−3.30724
$915$	1.57455	0.0520529
$916$	5.52992	0.182714
$917$	8.51527	0.281199
$918$	10.3680	0.342195
$919$	−36.4237	−1.20151	−0.600753	−	0.799435i	$-0.705132\pi$
$919$	−36.4237	−1.20151	−0.600753	+	0.799435i	$0.705132\pi$
$920$	−50.3157	−1.65886
$921$	−7.84017	−0.258342
$922$	29.8487	0.983016
$923$	57.9740	1.90824
$924$	−0.610827	−0.0200947
$925$	6.22921	0.204815
$926$	−13.9164	−0.457323
$927$	28.9769	0.951725
$928$	−52.1092	−1.71057
$929$	27.3552	0.897496	0.448748	−	0.893658i	$-0.351870\pi$
$929$	27.3552	0.897496	0.448748	+	0.893658i	$0.351870\pi$
$930$	7.82244	0.256508
$931$	47.1852	1.54643
$932$	18.3655	0.601580
$933$	−1.17814	−0.0385707
$934$	9.96261	0.325987
$935$	−0.189722	−0.00620456
$936$	120.248	3.93044
$937$	29.3852	0.959972	0.479986	−	0.877276i	$-0.340642\pi$
$937$	29.3852	0.959972	0.479986	+	0.877276i	$0.340642\pi$
$938$	154.393	5.04112
$939$	−5.61420	−0.183212
$940$	−30.2476	−0.986567
$941$	−1.89243	−0.0616916	−0.0308458	−	0.999524i	$-0.509820\pi$
$941$	−1.89243	−0.0616916	−0.0308458	+	0.999524i	$0.509820\pi$
$942$	9.79863	0.319257
$943$	28.9077	0.941366
$944$	−115.692	−3.76546
$945$	−10.5777	−0.344091
$946$	0.613317	0.0199407
$947$	7.50635	0.243924	0.121962	−	0.992535i	$-0.461081\pi$
$947$	7.50635	0.243924	0.121962	+	0.992535i	$0.461081\pi$
$948$	5.55869	0.180538
$949$	42.2850	1.37263
$950$	31.9555	1.03677
$951$	−10.1725	−0.329866
$952$	86.9395	2.81773
$953$	13.7932	0.446806	0.223403	−	0.974726i	$-0.428283\pi$
$953$	13.7932	0.446806	0.223403	+	0.974726i	$0.428283\pi$
$954$	−6.54314	−0.211842
$955$	10.1613	0.328812
$956$	−131.286	−4.24608
$957$	0.0599725	0.00193863
$958$	−50.8711	−1.64357
$959$	17.9232	0.578771
$960$	−11.1799	−0.360831
$961$	22.9971	0.741841
$962$	21.4863	0.692746
$963$	11.8129	0.380666
$964$	87.6014	2.82145
$965$	13.3936	0.431154
$966$	−17.5388	−0.564301
$967$	16.9082	0.543731	0.271865	−	0.962335i	$-0.412359\pi$
$967$	16.9082	0.543731	0.271865	+	0.962335i	$0.412359\pi$
$968$	102.963	3.30934
$969$	2.15738	0.0693052
$970$	7.48990	0.240486
$971$	23.3544	0.749478	0.374739	−	0.927130i	$-0.377732\pi$
$971$	23.3544	0.749478	0.374739	+	0.927130i	$0.377732\pi$
$972$	44.7093	1.43405
$973$	55.1250	1.76723
$974$	−102.790	−3.29360
$975$	−4.94923	−0.158502
$976$	−59.1501	−1.89335
$977$	−27.1732	−0.869346	−0.434673	−	0.900588i	$-0.643136\pi$
$977$	−27.1732	−0.869346	−0.434673	+	0.900588i	$0.643136\pi$
$978$	−6.15888	−0.196939
$979$	0.695437	0.0222263
$980$	−93.7854	−2.99587
$981$	−19.6309	−0.626765
$982$	−22.2924	−0.711379
$983$	−46.2729	−1.47588	−0.737939	−	0.674868i	$-0.764201\pi$
$983$	−46.2729	−1.47588	−0.737939	+	0.674868i	$0.764201\pi$
$984$	19.6732	0.627158
$985$	17.3845	0.553916
$986$	−13.5064	−0.430130
$987$	−6.66345	−0.212100
$988$	80.5725	2.56335
$989$	12.8730	0.409336
$990$	−0.741867	−0.0235781
$991$	−7.81839	−0.248359	−0.124180	−	0.992260i	$-0.539630\pi$
$991$	−7.81839	−0.248359	−0.124180	+	0.992260i	$0.539630\pi$
$992$	−156.225	−4.96014
$993$	8.90187	0.282492
$994$	163.901	5.19861
$995$	−23.6980	−0.751277
$996$	−9.05662	−0.286970
$997$	19.0797	0.604261	0.302131	−	0.953267i	$-0.402302\pi$
$997$	19.0797	0.604261	0.302131	+	0.953267i	$0.402302\pi$
$998$	70.4478	2.22999
$999$	3.34666	0.105884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.b.1.5	✓	159

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.b.1.5	✓	159	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4027 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72666 q^{2} +0.318995 q^{3} +5.43469 q^{4} -1.22389 q^{5} -0.869792 q^{6} -4.59347 q^{7} -9.36524 q^{8} -2.89824 q^{9} +O(q^{10})\)	\(q-2.72666 q^{2} +0.318995 q^{3} +5.43469 q^{4} -1.22389 q^{5} -0.869792 q^{6} -4.59347 q^{7} -9.36524 q^{8} -2.89824 q^{9} +3.33713 q^{10} +0.0767040 q^{11} +1.73364 q^{12} +4.43022 q^{13} +12.5249 q^{14} -0.390414 q^{15} +14.6665 q^{16} +2.02096 q^{17} +7.90253 q^{18} +3.34647 q^{19} -6.65145 q^{20} -1.46530 q^{21} -0.209146 q^{22} -4.38978 q^{23} -2.98747 q^{24} -3.50210 q^{25} -12.0797 q^{26} -1.88151 q^{27} -24.9641 q^{28} +2.45104 q^{29} +1.06453 q^{30} +7.34827 q^{31} -21.2601 q^{32} +0.0244682 q^{33} -5.51047 q^{34} +5.62190 q^{35} -15.7510 q^{36} -1.77871 q^{37} -9.12469 q^{38} +1.41322 q^{39} +11.4620 q^{40} -6.58524 q^{41} +3.99537 q^{42} -2.93248 q^{43} +0.416863 q^{44} +3.54712 q^{45} +11.9695 q^{46} +4.54751 q^{47} +4.67854 q^{48} +14.1000 q^{49} +9.54904 q^{50} +0.644675 q^{51} +24.0769 q^{52} -0.827981 q^{53} +5.13025 q^{54} -0.0938771 q^{55} +43.0190 q^{56} +1.06751 q^{57} -6.68315 q^{58} -7.88820 q^{59} -2.12178 q^{60} -4.03302 q^{61} -20.0363 q^{62} +13.3130 q^{63} +28.6361 q^{64} -5.42209 q^{65} -0.0667166 q^{66} +12.3270 q^{67} +10.9833 q^{68} -1.40032 q^{69} -15.3290 q^{70} +13.0860 q^{71} +27.1427 q^{72} +9.54468 q^{73} +4.84994 q^{74} -1.11715 q^{75} +18.1870 q^{76} -0.352338 q^{77} -3.85337 q^{78} +3.20637 q^{79} -17.9501 q^{80} +8.09453 q^{81} +17.9557 q^{82} -5.22405 q^{83} -7.96343 q^{84} -2.47342 q^{85} +7.99590 q^{86} +0.781869 q^{87} -0.718352 q^{88} +9.06651 q^{89} -9.67181 q^{90} -20.3501 q^{91} -23.8571 q^{92} +2.34406 q^{93} -12.3995 q^{94} -4.09570 q^{95} -6.78186 q^{96} +2.24441 q^{97} -38.4459 q^{98} -0.222307 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9 - 23 * q^10 - 33 * q^11 - 57 * q^12 - 90 * q^13 - 28 * q^14 - 22 * q^15 + 130 * q^16 - 145 * q^17 - 50 * q^18 - 28 * q^19 - 121 * q^20 - 69 * q^21 - 26 * q^22 - 79 * q^23 - 62 * q^24 + 123 * q^25 - 40 * q^26 - 70 * q^27 - 43 * q^28 - 109 * q^29 - 43 * q^30 - 21 * q^31 - 139 * q^32 - 83 * q^33 - 93 * q^35 + 75 * q^36 - 65 * q^37 - 122 * q^38 - 18 * q^39 - 43 * q^40 - 71 * q^41 - 88 * q^42 - 72 * q^43 - 79 * q^44 - 181 * q^45 - 11 * q^46 - 114 * q^47 - 118 * q^48 + 118 * q^49 - 77 * q^50 - 29 * q^51 - 169 * q^52 - 220 * q^53 - 80 * q^54 - 37 * q^55 - 72 * q^56 - 90 * q^57 - 8 * q^58 - 60 * q^59 - 42 * q^60 - 108 * q^61 - 152 * q^62 - 65 * q^63 + 114 * q^64 - 81 * q^65 - 40 * q^66 - 50 * q^67 - 319 * q^68 - 103 * q^69 + 4 * q^70 - 7 * q^71 - 129 * q^72 - 94 * q^73 - 79 * q^74 - 59 * q^75 - 46 * q^76 - 329 * q^77 + 8 * q^78 - 18 * q^79 - 190 * q^80 + 59 * q^81 - 56 * q^82 - 201 * q^83 - 71 * q^84 - 26 * q^85 - 52 * q^86 - 126 * q^87 - 66 * q^88 - 114 * q^89 - 33 * q^90 - 30 * q^91 - 204 * q^92 - 125 * q^93 + 9 * q^94 - 84 * q^95 - 88 * q^96 - 56 * q^97 - 110 * q^98 - 46 * q^99

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