LMFDB - Embedded newform 6026.2.a.k.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.0851442 q^{3} +1.00000 q^{4} -0.378458 q^{5} +0.0851442 q^{6} +4.38766 q^{7} +1.00000 q^{8} -2.99275 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.0851442 q^{3} +1.00000 q^{4} -0.378458 q^{5} +0.0851442 q^{6} +4.38766 q^{7} +1.00000 q^{8} -2.99275 q^{9} -0.378458 q^{10} +0.576761 q^{11} +0.0851442 q^{12} +6.42203 q^{13} +4.38766 q^{14} -0.0322235 q^{15} +1.00000 q^{16} +2.26133 q^{17} -2.99275 q^{18} +0.566312 q^{19} -0.378458 q^{20} +0.373584 q^{21} +0.576761 q^{22} -1.00000 q^{23} +0.0851442 q^{24} -4.85677 q^{25} +6.42203 q^{26} -0.510248 q^{27} +4.38766 q^{28} +3.88019 q^{29} -0.0322235 q^{30} +1.97689 q^{31} +1.00000 q^{32} +0.0491078 q^{33} +2.26133 q^{34} -1.66054 q^{35} -2.99275 q^{36} -0.734306 q^{37} +0.566312 q^{38} +0.546798 q^{39} -0.378458 q^{40} +1.03112 q^{41} +0.373584 q^{42} +8.12129 q^{43} +0.576761 q^{44} +1.13263 q^{45} -1.00000 q^{46} +5.59040 q^{47} +0.0851442 q^{48} +12.2516 q^{49} -4.85677 q^{50} +0.192539 q^{51} +6.42203 q^{52} -13.5280 q^{53} -0.510248 q^{54} -0.218280 q^{55} +4.38766 q^{56} +0.0482182 q^{57} +3.88019 q^{58} -9.86060 q^{59} -0.0322235 q^{60} +7.35292 q^{61} +1.97689 q^{62} -13.1312 q^{63} +1.00000 q^{64} -2.43047 q^{65} +0.0491078 q^{66} -11.3177 q^{67} +2.26133 q^{68} -0.0851442 q^{69} -1.66054 q^{70} -0.336762 q^{71} -2.99275 q^{72} -8.53035 q^{73} -0.734306 q^{74} -0.413526 q^{75} +0.566312 q^{76} +2.53063 q^{77} +0.546798 q^{78} +10.8362 q^{79} -0.378458 q^{80} +8.93481 q^{81} +1.03112 q^{82} +1.38236 q^{83} +0.373584 q^{84} -0.855819 q^{85} +8.12129 q^{86} +0.330375 q^{87} +0.576761 q^{88} +4.53987 q^{89} +1.13263 q^{90} +28.1777 q^{91} -1.00000 q^{92} +0.168321 q^{93} +5.59040 q^{94} -0.214325 q^{95} +0.0851442 q^{96} +12.2852 q^{97} +12.2516 q^{98} -1.72610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) $ 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.0851442	0.0491580	0.0245790	−	0.999698i	$-0.492175\pi$
$3$	0.0851442	0.0491580	0.0245790	+	0.999698i	$0.492175\pi$
$4$	1.00000	0.500000
$5$	−0.378458	−0.169251	−0.0846257	−	0.996413i	$-0.526969\pi$
$5$	−0.378458	−0.169251	−0.0846257	+	0.996413i	$0.526969\pi$
$6$	0.0851442	0.0347600
$7$	4.38766	1.65838	0.829190	−	0.558966i	$-0.188802\pi$
$7$	4.38766	1.65838	0.829190	+	0.558966i	$0.188802\pi$
$8$	1.00000	0.353553
$9$	−2.99275	−0.997583
$10$	−0.378458	−0.119679
$11$	0.576761	0.173900	0.0869500	−	0.996213i	$-0.472288\pi$
$11$	0.576761	0.173900	0.0869500	+	0.996213i	$0.472288\pi$
$12$	0.0851442	0.0245790
$13$	6.42203	1.78115	0.890575	−	0.454837i	$-0.150302\pi$
$13$	6.42203	1.78115	0.890575	+	0.454837i	$0.150302\pi$
$14$	4.38766	1.17265
$15$	−0.0322235	−0.00832007
$16$	1.00000	0.250000
$17$	2.26133	0.548454	0.274227	−	0.961665i	$-0.411578\pi$
$17$	2.26133	0.548454	0.274227	+	0.961665i	$0.411578\pi$
$18$	−2.99275	−0.705398
$19$	0.566312	0.129921	0.0649605	−	0.997888i	$-0.479308\pi$
$19$	0.566312	0.129921	0.0649605	+	0.997888i	$0.479308\pi$
$20$	−0.378458	−0.0846257
$21$	0.373584	0.0815227
$22$	0.576761	0.122966
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.0851442	0.0173800
$25$	−4.85677	−0.971354
$26$	6.42203	1.25946
$27$	−0.510248	−0.0981973
$28$	4.38766	0.829190
$29$	3.88019	0.720533	0.360266	−	0.932850i	$-0.382686\pi$
$29$	3.88019	0.720533	0.360266	+	0.932850i	$0.382686\pi$
$30$	−0.0322235	−0.00588317
$31$	1.97689	0.355060	0.177530	−	0.984115i	$-0.443189\pi$
$31$	1.97689	0.355060	0.177530	+	0.984115i	$0.443189\pi$
$32$	1.00000	0.176777
$33$	0.0491078	0.00854858
$34$	2.26133	0.387816
$35$	−1.66054	−0.280683
$36$	−2.99275	−0.498792
$37$	−0.734306	−0.120719	−0.0603596	−	0.998177i	$-0.519225\pi$
$37$	−0.734306	−0.120719	−0.0603596	+	0.998177i	$0.519225\pi$
$38$	0.566312	0.0918680
$39$	0.546798	0.0875578
$40$	−0.378458	−0.0598394
$41$	1.03112	0.161033	0.0805167	−	0.996753i	$-0.474343\pi$
$41$	1.03112	0.161033	0.0805167	+	0.996753i	$0.474343\pi$
$42$	0.373584	0.0576453
$43$	8.12129	1.23848	0.619242	−	0.785200i	$-0.287440\pi$
$43$	8.12129	1.23848	0.619242	+	0.785200i	$0.287440\pi$
$44$	0.576761	0.0869500
$45$	1.13263	0.168842
$46$	−1.00000	−0.147442
$47$	5.59040	0.815444	0.407722	−	0.913106i	$-0.366323\pi$
$47$	5.59040	0.815444	0.407722	+	0.913106i	$0.366323\pi$
$48$	0.0851442	0.0122895
$49$	12.2516	1.75023
$50$	−4.85677	−0.686851
$51$	0.192539	0.0269609
$52$	6.42203	0.890575
$53$	−13.5280	−1.85821	−0.929106	−	0.369814i	$-0.879421\pi$
$53$	−13.5280	−1.85821	−0.929106	+	0.369814i	$0.879421\pi$
$54$	−0.510248	−0.0694359
$55$	−0.218280	−0.0294328
$56$	4.38766	0.586326
$57$	0.0482182	0.00638666
$58$	3.88019	0.509493
$59$	−9.86060	−1.28374	−0.641871	−	0.766813i	$-0.721841\pi$
$59$	−9.86060	−1.28374	−0.641871	+	0.766813i	$0.721841\pi$
$60$	−0.0322235	−0.00416003
$61$	7.35292	0.941445	0.470723	−	0.882281i	$-0.343993\pi$
$61$	7.35292	0.941445	0.470723	+	0.882281i	$0.343993\pi$
$62$	1.97689	0.251065
$63$	−13.1312	−1.65437
$64$	1.00000	0.125000
$65$	−2.43047	−0.301462
$66$	0.0491078	0.00604476
$67$	−11.3177	−1.38267	−0.691337	−	0.722532i	$-0.742978\pi$
$67$	−11.3177	−1.38267	−0.691337	+	0.722532i	$0.742978\pi$
$68$	2.26133	0.274227
$69$	−0.0851442	−0.0102502
$70$	−1.66054	−0.198473
$71$	−0.336762	−0.0399663	−0.0199831	−	0.999800i	$-0.506361\pi$
$71$	−0.336762	−0.0399663	−0.0199831	+	0.999800i	$0.506361\pi$
$72$	−2.99275	−0.352699
$73$	−8.53035	−0.998402	−0.499201	−	0.866486i	$-0.666373\pi$
$73$	−8.53035	−0.998402	−0.499201	+	0.866486i	$0.666373\pi$
$74$	−0.734306	−0.0853614
$75$	−0.413526	−0.0477498
$76$	0.566312	0.0649605
$77$	2.53063	0.288392
$78$	0.546798	0.0619127
$79$	10.8362	1.21917	0.609584	−	0.792721i	$-0.291336\pi$
$79$	10.8362	1.21917	0.609584	+	0.792721i	$0.291336\pi$
$80$	−0.378458	−0.0423129
$81$	8.93481	0.992756
$82$	1.03112	0.113868
$83$	1.38236	0.151733	0.0758667	−	0.997118i	$-0.475828\pi$
$83$	1.38236	0.151733	0.0758667	+	0.997118i	$0.475828\pi$
$84$	0.373584	0.0407614
$85$	−0.855819	−0.0928266
$86$	8.12129	0.875741
$87$	0.330375	0.0354200
$88$	0.576761	0.0614829
$89$	4.53987	0.481225	0.240613	−	0.970621i	$-0.422652\pi$
$89$	4.53987	0.481225	0.240613	+	0.970621i	$0.422652\pi$
$90$	1.13263	0.119390
$91$	28.1777	2.95382
$92$	−1.00000	−0.104257
$93$	0.168321	0.0174540
$94$	5.59040	0.576606
$95$	−0.214325	−0.0219893
$96$	0.0851442	0.00868999
$97$	12.2852	1.24737	0.623685	−	0.781676i	$-0.285635\pi$
$97$	12.2852	1.24737	0.623685	+	0.781676i	$0.285635\pi$
$98$	12.2516	1.23760
$99$	−1.72610	−0.173480
$100$	−4.85677	−0.485677
$101$	4.87224	0.484806	0.242403	−	0.970176i	$-0.422064\pi$
$101$	4.87224	0.484806	0.242403	+	0.970176i	$0.422064\pi$
$102$	0.192539	0.0190642
$103$	−4.39093	−0.432652	−0.216326	−	0.976321i	$-0.569407\pi$
$103$	−4.39093	−0.432652	−0.216326	+	0.976321i	$0.569407\pi$
$104$	6.42203	0.629732
$105$	−0.141386	−0.0137978
$106$	−13.5280	−1.31395
$107$	−0.762630	−0.0737262	−0.0368631	−	0.999320i	$-0.511737\pi$
$107$	−0.762630	−0.0737262	−0.0368631	+	0.999320i	$0.511737\pi$
$108$	−0.510248	−0.0490986
$109$	14.7086	1.40883	0.704415	−	0.709788i	$-0.251209\pi$
$109$	14.7086	1.40883	0.704415	+	0.709788i	$0.251209\pi$
$110$	−0.218280	−0.0208121
$111$	−0.0625219	−0.00593432
$112$	4.38766	0.414595
$113$	−19.5936	−1.84321	−0.921607	−	0.388125i	$-0.873123\pi$
$113$	−19.5936	−1.84321	−0.921607	+	0.388125i	$0.873123\pi$
$114$	0.0482182	0.00451605
$115$	0.378458	0.0352914
$116$	3.88019	0.360266
$117$	−19.2195	−1.77685
$118$	−9.86060	−0.907742
$119$	9.92197	0.909545
$120$	−0.0322235	−0.00294159
$121$	−10.6673	−0.969759
$122$	7.35292	0.665702
$123$	0.0877936	0.00791608
$124$	1.97689	0.177530
$125$	3.73037	0.333654
$126$	−13.1312	−1.16982
$127$	−9.53073	−0.845716	−0.422858	−	0.906196i	$-0.638973\pi$
$127$	−9.53073	−0.845716	−0.422858	+	0.906196i	$0.638973\pi$
$128$	1.00000	0.0883883
$129$	0.691480	0.0608815
$130$	−2.43047	−0.213166
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	0.0491078	0.00427429
$133$	2.48479	0.215458
$134$	−11.3177	−0.977699
$135$	0.193107	0.0166200
$136$	2.26133	0.193908
$137$	−9.19652	−0.785712	−0.392856	−	0.919600i	$-0.628513\pi$
$137$	−9.19652	−0.785712	−0.392856	+	0.919600i	$0.628513\pi$
$138$	−0.0851442	−0.00724796
$139$	21.0203	1.78292	0.891460	−	0.453099i	$-0.149682\pi$
$139$	21.0203	1.78292	0.891460	+	0.453099i	$0.149682\pi$
$140$	−1.66054	−0.140342
$141$	0.475990	0.0400856
$142$	−0.336762	−0.0282604
$143$	3.70397	0.309742
$144$	−2.99275	−0.249396
$145$	−1.46849	−0.121951
$146$	−8.53035	−0.705977
$147$	1.04315	0.0860377
$148$	−0.734306	−0.0603596
$149$	4.36633	0.357704	0.178852	−	0.983876i	$-0.442762\pi$
$149$	4.36633	0.357704	0.178852	+	0.983876i	$0.442762\pi$
$150$	−0.413526	−0.0337642
$151$	−13.3023	−1.08252	−0.541262	−	0.840854i	$-0.682053\pi$
$151$	−13.3023	−1.08252	−0.541262	+	0.840854i	$0.682053\pi$
$152$	0.566312	0.0459340
$153$	−6.76761	−0.547129
$154$	2.53063	0.203924
$155$	−0.748168	−0.0600943
$156$	0.546798	0.0437789
$157$	−13.4166	−1.07076	−0.535380	−	0.844611i	$-0.679832\pi$
$157$	−13.4166	−1.07076	−0.535380	+	0.844611i	$0.679832\pi$
$158$	10.8362	0.862082
$159$	−1.15183	−0.0913460
$160$	−0.378458	−0.0299197
$161$	−4.38766	−0.345796
$162$	8.93481	0.701985
$163$	−8.81229	−0.690232	−0.345116	−	0.938560i	$-0.612160\pi$
$163$	−8.81229	−0.690232	−0.345116	+	0.938560i	$0.612160\pi$
$164$	1.03112	0.0805167
$165$	−0.0185852	−0.00144686
$166$	1.38236	0.107292
$167$	7.28597	0.563805	0.281903	−	0.959443i	$-0.409034\pi$
$167$	7.28597	0.563805	0.281903	+	0.959443i	$0.409034\pi$
$168$	0.373584	0.0288226
$169$	28.2424	2.17249
$170$	−0.855819	−0.0656383
$171$	−1.69483	−0.129607
$172$	8.12129	0.619242
$173$	18.8478	1.43297	0.716484	−	0.697603i	$-0.245750\pi$
$173$	18.8478	1.43297	0.716484	+	0.697603i	$0.245750\pi$
$174$	0.330375	0.0250457
$175$	−21.3099	−1.61087
$176$	0.576761	0.0434750
$177$	−0.839573	−0.0631062
$178$	4.53987	0.340278
$179$	−4.27123	−0.319247	−0.159624	−	0.987178i	$-0.551028\pi$
$179$	−4.27123	−0.319247	−0.159624	+	0.987178i	$0.551028\pi$
$180$	1.13263	0.0844212
$181$	−16.7633	−1.24601	−0.623004	−	0.782218i	$-0.714088\pi$
$181$	−16.7633	−1.24601	−0.623004	+	0.782218i	$0.714088\pi$
$182$	28.1777	2.08867
$183$	0.626059	0.0462796
$184$	−1.00000	−0.0737210
$185$	0.277904	0.0204319
$186$	0.168321	0.0123419
$187$	1.30425	0.0953761
$188$	5.59040	0.407722
$189$	−2.23880	−0.162848
$190$	−0.214325	−0.0155488
$191$	−1.84167	−0.133259	−0.0666294	−	0.997778i	$-0.521225\pi$
$191$	−1.84167	−0.133259	−0.0666294	+	0.997778i	$0.521225\pi$
$192$	0.0851442	0.00614475
$193$	16.1688	1.16385	0.581926	−	0.813242i	$-0.302299\pi$
$193$	16.1688	1.16385	0.581926	+	0.813242i	$0.302299\pi$
$194$	12.2852	0.882023
$195$	−0.206940	−0.0148193
$196$	12.2516	0.875113
$197$	4.56554	0.325281	0.162641	−	0.986685i	$-0.447999\pi$
$197$	4.56554	0.325281	0.162641	+	0.986685i	$0.447999\pi$
$198$	−1.72610	−0.122669
$199$	19.6649	1.39400	0.697002	−	0.717069i	$-0.254517\pi$
$199$	19.6649	1.39400	0.697002	+	0.717069i	$0.254517\pi$
$200$	−4.85677	−0.343425
$201$	−0.963635	−0.0679696
$202$	4.87224	0.342810
$203$	17.0249	1.19492
$204$	0.192539	0.0134805
$205$	−0.390234	−0.0272551
$206$	−4.39093	−0.305931
$207$	2.99275	0.208011
$208$	6.42203	0.445287
$209$	0.326627	0.0225932
$210$	−0.141386	−0.00975654
$211$	23.1558	1.59411	0.797057	−	0.603904i	$-0.206389\pi$
$211$	23.1558	1.59411	0.797057	+	0.603904i	$0.206389\pi$
$212$	−13.5280	−0.929106
$213$	−0.0286733	−0.00196466
$214$	−0.762630	−0.0521323
$215$	−3.07356	−0.209615
$216$	−0.510248	−0.0347180
$217$	8.67392	0.588824
$218$	14.7086	0.996193
$219$	−0.726310	−0.0490795
$220$	−0.218280	−0.0147164
$221$	14.5223	0.976879
$222$	−0.0625219	−0.00419620
$223$	4.30774	0.288468	0.144234	−	0.989544i	$-0.453928\pi$
$223$	4.30774	0.288468	0.144234	+	0.989544i	$0.453928\pi$
$224$	4.38766	0.293163
$225$	14.5351	0.969007
$226$	−19.5936	−1.30335
$227$	12.7261	0.844659	0.422329	−	0.906442i	$-0.361213\pi$
$227$	12.7261	0.844659	0.422329	+	0.906442i	$0.361213\pi$
$228$	0.0482182	0.00319333
$229$	−26.3159	−1.73901	−0.869503	−	0.493928i	$-0.835560\pi$
$229$	−26.3159	−1.73901	−0.869503	+	0.493928i	$0.835560\pi$
$230$	0.378458	0.0249548
$231$	0.215469	0.0141768
$232$	3.88019	0.254747
$233$	−15.2579	−0.999581	−0.499791	−	0.866146i	$-0.666590\pi$
$233$	−15.2579	−0.999581	−0.499791	+	0.866146i	$0.666590\pi$
$234$	−19.2195	−1.25642
$235$	−2.11573	−0.138015
$236$	−9.86060	−0.641871
$237$	0.922640	0.0599319
$238$	9.92197	0.643146
$239$	9.92377	0.641915	0.320958	−	0.947094i	$-0.395995\pi$
$239$	9.92377	0.641915	0.320958	+	0.947094i	$0.395995\pi$
$240$	−0.0322235	−0.00208002
$241$	7.95975	0.512732	0.256366	−	0.966580i	$-0.417475\pi$
$241$	7.95975	0.512732	0.256366	+	0.966580i	$0.417475\pi$
$242$	−10.6673	−0.685723
$243$	2.29149	0.146999
$244$	7.35292	0.470723
$245$	−4.63670	−0.296228
$246$	0.0877936	0.00559752
$247$	3.63687	0.231409
$248$	1.97689	0.125533
$249$	0.117700	0.00745892
$250$	3.73037	0.235929
$251$	3.11061	0.196340	0.0981699	−	0.995170i	$-0.468701\pi$
$251$	3.11061	0.196340	0.0981699	+	0.995170i	$0.468701\pi$
$252$	−13.1312	−0.827187
$253$	−0.576761	−0.0362606
$254$	−9.53073	−0.598011
$255$	−0.0728680	−0.00456317
$256$	1.00000	0.0625000
$257$	2.44511	0.152522	0.0762609	−	0.997088i	$-0.475702\pi$
$257$	2.44511	0.152522	0.0762609	+	0.997088i	$0.475702\pi$
$258$	0.691480	0.0430497
$259$	−3.22189	−0.200198
$260$	−2.43047	−0.150731
$261$	−11.6124	−0.718791
$262$	−1.00000	−0.0617802
$263$	−9.48528	−0.584887	−0.292444	−	0.956283i	$-0.594468\pi$
$263$	−9.48528	−0.584887	−0.292444	+	0.956283i	$0.594468\pi$
$264$	0.0491078	0.00302238
$265$	5.11977	0.314505
$266$	2.48479	0.152352
$267$	0.386544	0.0236561
$268$	−11.3177	−0.691337
$269$	−20.2611	−1.23534	−0.617672	−	0.786436i	$-0.711924\pi$
$269$	−20.2611	−1.23534	−0.617672	+	0.786436i	$0.711924\pi$
$270$	0.193107	0.0117521
$271$	4.22026	0.256363	0.128181	−	0.991751i	$-0.459086\pi$
$271$	4.22026	0.256363	0.128181	+	0.991751i	$0.459086\pi$
$272$	2.26133	0.137114
$273$	2.39917	0.145204
$274$	−9.19652	−0.555582
$275$	−2.80119	−0.168918
$276$	−0.0851442	−0.00512508
$277$	−16.9891	−1.02078	−0.510388	−	0.859944i	$-0.670498\pi$
$277$	−16.9891	−1.02078	−0.510388	+	0.859944i	$0.670498\pi$
$278$	21.0203	1.26072
$279$	−5.91633	−0.354202
$280$	−1.66054	−0.0992365
$281$	−0.270221	−0.0161200	−0.00806001	−	0.999968i	$-0.502566\pi$
$281$	−0.270221	−0.0161200	−0.00806001	+	0.999968i	$0.502566\pi$
$282$	0.475990	0.0283448
$283$	28.1807	1.67517	0.837585	−	0.546307i	$-0.183967\pi$
$283$	28.1807	1.67517	0.837585	+	0.546307i	$0.183967\pi$
$284$	−0.336762	−0.0199831
$285$	−0.0182485	−0.00108095
$286$	3.70397	0.219021
$287$	4.52419	0.267055
$288$	−2.99275	−0.176350
$289$	−11.8864	−0.699198
$290$	−1.46849	−0.0862325
$291$	1.04601	0.0613182
$292$	−8.53035	−0.499201
$293$	15.3971	0.899507	0.449753	−	0.893153i	$-0.351512\pi$
$293$	15.3971	0.899507	0.449753	+	0.893153i	$0.351512\pi$
$294$	1.04315	0.0608378
$295$	3.73182	0.217275
$296$	−0.734306	−0.0426807
$297$	−0.294291	−0.0170765
$298$	4.36633	0.252935
$299$	−6.42203	−0.371395
$300$	−0.413526	−0.0238749
$301$	35.6335	2.05388
$302$	−13.3023	−0.765460
$303$	0.414843	0.0238321
$304$	0.566312	0.0324802
$305$	−2.78277	−0.159341
$306$	−6.76761	−0.386878
$307$	−1.73618	−0.0990888	−0.0495444	−	0.998772i	$-0.515777\pi$
$307$	−1.73618	−0.0990888	−0.0495444	+	0.998772i	$0.515777\pi$
$308$	2.53063	0.144196
$309$	−0.373863	−0.0212683
$310$	−0.748168	−0.0424931
$311$	28.0261	1.58922	0.794608	−	0.607123i	$-0.207676\pi$
$311$	28.0261	1.58922	0.794608	+	0.607123i	$0.207676\pi$
$312$	0.546798	0.0309564
$313$	8.24820	0.466216	0.233108	−	0.972451i	$-0.425110\pi$
$313$	8.24820	0.466216	0.233108	+	0.972451i	$0.425110\pi$
$314$	−13.4166	−0.757141
$315$	4.96960	0.280005
$316$	10.8362	0.609584
$317$	10.7835	0.605662	0.302831	−	0.953044i	$-0.402068\pi$
$317$	10.7835	0.605662	0.302831	+	0.953044i	$0.402068\pi$
$318$	−1.15183	−0.0645914
$319$	2.23794	0.125301
$320$	−0.378458	−0.0211564
$321$	−0.0649335	−0.00362424
$322$	−4.38766	−0.244515
$323$	1.28062	0.0712557
$324$	8.93481	0.496378
$325$	−31.1903	−1.73013
$326$	−8.81229	−0.488067
$327$	1.25235	0.0692553
$328$	1.03112	0.0569339
$329$	24.5288	1.35232
$330$	−0.0185852	−0.00102308
$331$	−14.3575	−0.789159	−0.394580	−	0.918862i	$-0.629110\pi$
$331$	−14.3575	−0.789159	−0.394580	+	0.918862i	$0.629110\pi$
$332$	1.38236	0.0758667
$333$	2.19760	0.120428
$334$	7.28597	0.398671
$335$	4.28326	0.234020
$336$	0.373584	0.0203807
$337$	14.7571	0.803869	0.401934	−	0.915668i	$-0.368338\pi$
$337$	14.7571	0.803869	0.401934	+	0.915668i	$0.368338\pi$
$338$	28.2424	1.53619
$339$	−1.66828	−0.0906087
$340$	−0.855819	−0.0464133
$341$	1.14019	0.0617448
$342$	−1.69483	−0.0916460
$343$	23.0422	1.24416
$344$	8.12129	0.437870
$345$	0.0322235	0.00173485
$346$	18.8478	1.01326
$347$	−1.05609	−0.0566938	−0.0283469	−	0.999598i	$-0.509024\pi$
$347$	−1.05609	−0.0566938	−0.0283469	+	0.999598i	$0.509024\pi$
$348$	0.330375	0.0177100
$349$	−6.57396	−0.351896	−0.175948	−	0.984399i	$-0.556299\pi$
$349$	−6.57396	−0.351896	−0.175948	+	0.984399i	$0.556299\pi$
$350$	−21.3099	−1.13906
$351$	−3.27683	−0.174904
$352$	0.576761	0.0307415
$353$	19.1251	1.01793	0.508963	−	0.860788i	$-0.330029\pi$
$353$	19.1251	1.01793	0.508963	+	0.860788i	$0.330029\pi$
$354$	−0.839573	−0.0446228
$355$	0.127450	0.00676435
$356$	4.53987	0.240613
$357$	0.844798	0.0447115
$358$	−4.27123	−0.225742
$359$	−11.7739	−0.621400	−0.310700	−	0.950508i	$-0.600563\pi$
$359$	−11.7739	−0.621400	−0.310700	+	0.950508i	$0.600563\pi$
$360$	1.13263	0.0596948
$361$	−18.6793	−0.983121
$362$	−16.7633	−0.881061
$363$	−0.908263	−0.0476714
$364$	28.1777	1.47691
$365$	3.22838	0.168981
$366$	0.626059	0.0327246
$367$	5.71525	0.298334	0.149167	−	0.988812i	$-0.452341\pi$
$367$	5.71525	0.298334	0.149167	+	0.988812i	$0.452341\pi$
$368$	−1.00000	−0.0521286
$369$	−3.08587	−0.160644
$370$	0.277904	0.0144475
$371$	−59.3562	−3.08162
$372$	0.168321	0.00872701
$373$	8.44258	0.437140	0.218570	−	0.975821i	$-0.429861\pi$
$373$	8.44258	0.437140	0.218570	+	0.975821i	$0.429861\pi$
$374$	1.30425	0.0674411
$375$	0.317619	0.0164018
$376$	5.59040	0.288303
$377$	24.9187	1.28338
$378$	−2.23880	−0.115151
$379$	−3.03983	−0.156146	−0.0780729	−	0.996948i	$-0.524877\pi$
$379$	−3.03983	−0.156146	−0.0780729	+	0.996948i	$0.524877\pi$
$380$	−0.214325	−0.0109947
$381$	−0.811487	−0.0415737
$382$	−1.84167	−0.0942283
$383$	−33.4675	−1.71011	−0.855054	−	0.518539i	$-0.826476\pi$
$383$	−33.4675	−1.71011	−0.855054	+	0.518539i	$0.826476\pi$
$384$	0.0851442	0.00434500
$385$	−0.957737	−0.0488108
$386$	16.1688	0.822968
$387$	−24.3050	−1.23549
$388$	12.2852	0.623685
$389$	−23.2147	−1.17703	−0.588517	−	0.808485i	$-0.700288\pi$
$389$	−23.2147	−1.17703	−0.588517	+	0.808485i	$0.700288\pi$
$390$	−0.206940	−0.0104788
$391$	−2.26133	−0.114361
$392$	12.2516	0.618798
$393$	−0.0851442	−0.00429496
$394$	4.56554	0.230009
$395$	−4.10105	−0.206346
$396$	−1.72610	−0.0867398
$397$	12.0610	0.605323	0.302661	−	0.953098i	$-0.402125\pi$
$397$	12.0610	0.605323	0.302661	+	0.953098i	$0.402125\pi$
$398$	19.6649	0.985710
$399$	0.211565	0.0105915
$400$	−4.85677	−0.242838
$401$	−36.2367	−1.80957	−0.904787	−	0.425864i	$-0.859970\pi$
$401$	−36.2367	−1.80957	−0.904787	+	0.425864i	$0.859970\pi$
$402$	−0.963635	−0.0480617
$403$	12.6956	0.632414
$404$	4.87224	0.242403
$405$	−3.38145	−0.168025
$406$	17.0249	0.844934
$407$	−0.423519	−0.0209931
$408$	0.192539	0.00953212
$409$	12.1745	0.601988	0.300994	−	0.953626i	$-0.402682\pi$
$409$	12.1745	0.601988	0.300994	+	0.953626i	$0.402682\pi$
$410$	−0.390234	−0.0192723
$411$	−0.783030	−0.0386240
$412$	−4.39093	−0.216326
$413$	−43.2650	−2.12893
$414$	2.99275	0.147086
$415$	−0.523164	−0.0256811
$416$	6.42203	0.314866
$417$	1.78976	0.0876448
$418$	0.326627	0.0159758
$419$	−22.6751	−1.10775	−0.553874	−	0.832600i	$-0.686851\pi$
$419$	−22.6751	−1.10775	−0.553874	+	0.832600i	$0.686851\pi$
$420$	−0.141386	−0.00689892
$421$	−10.2800	−0.501015	−0.250507	−	0.968115i	$-0.580597\pi$
$421$	−10.2800	−0.501015	−0.250507	+	0.968115i	$0.580597\pi$
$422$	23.1558	1.12721
$423$	−16.7307	−0.813474
$424$	−13.5280	−0.656977
$425$	−10.9828	−0.532743
$426$	−0.0286733	−0.00138923
$427$	32.2621	1.56127
$428$	−0.762630	−0.0368631
$429$	0.315372	0.0152263
$430$	−3.07356	−0.148220
$431$	−37.2125	−1.79246	−0.896232	−	0.443585i	$-0.853707\pi$
$431$	−37.2125	−1.79246	−0.896232	+	0.443585i	$0.853707\pi$
$432$	−0.510248	−0.0245493
$433$	21.9281	1.05380	0.526898	−	0.849929i	$-0.323355\pi$
$433$	21.9281	1.05380	0.526898	+	0.849929i	$0.323355\pi$
$434$	8.67392	0.416361
$435$	−0.125033	−0.00599488
$436$	14.7086	0.704415
$437$	−0.566312	−0.0270904
$438$	−0.726310	−0.0347044
$439$	−40.4123	−1.92877	−0.964387	−	0.264496i	$-0.914795\pi$
$439$	−40.4123	−1.92877	−0.964387	+	0.264496i	$0.914795\pi$
$440$	−0.218280	−0.0104061
$441$	−36.6659	−1.74600
$442$	14.5223	0.690758
$443$	−3.57666	−0.169932	−0.0849661	−	0.996384i	$-0.527078\pi$
$443$	−3.57666	−0.169932	−0.0849661	+	0.996384i	$0.527078\pi$
$444$	−0.0625219	−0.00296716
$445$	−1.71815	−0.0814481
$446$	4.30774	0.203978
$447$	0.371768	0.0175840
$448$	4.38766	0.207298
$449$	−17.9726	−0.848180	−0.424090	−	0.905620i	$-0.639406\pi$
$449$	−17.9726	−0.848180	−0.424090	+	0.905620i	$0.639406\pi$
$450$	14.5351	0.685191
$451$	0.594708	0.0280037
$452$	−19.5936	−0.921607
$453$	−1.13261	−0.0532147
$454$	12.7261	0.597264
$455$	−10.6641	−0.499939
$456$	0.0482182	0.00225802
$457$	24.7661	1.15851	0.579254	−	0.815147i	$-0.303344\pi$
$457$	24.7661	1.15851	0.579254	+	0.815147i	$0.303344\pi$
$458$	−26.3159	−1.22966
$459$	−1.15384	−0.0538567
$460$	0.378458	0.0176457
$461$	32.7713	1.52631	0.763156	−	0.646215i	$-0.223649\pi$
$461$	32.7713	1.52631	0.763156	+	0.646215i	$0.223649\pi$
$462$	0.215469	0.0100245
$463$	−39.7167	−1.84579	−0.922895	−	0.385051i	$-0.874184\pi$
$463$	−39.7167	−1.84579	−0.922895	+	0.385051i	$0.874184\pi$
$464$	3.88019	0.180133
$465$	−0.0637022	−0.00295412
$466$	−15.2579	−0.706811
$467$	41.3380	1.91289	0.956447	−	0.291906i	$-0.0942895\pi$
$467$	41.3380	1.91289	0.956447	+	0.291906i	$0.0942895\pi$
$468$	−19.2195	−0.888423
$469$	−49.6582	−2.29300
$470$	−2.11573	−0.0975914
$471$	−1.14234	−0.0526364
$472$	−9.86060	−0.453871
$473$	4.68404	0.215372
$474$	0.922640	0.0423783
$475$	−2.75045	−0.126199
$476$	9.92197	0.454773
$477$	40.4859	1.85372
$478$	9.92377	0.453903
$479$	23.5500	1.07603	0.538013	−	0.842936i	$-0.319175\pi$
$479$	23.5500	1.07603	0.538013	+	0.842936i	$0.319175\pi$
$480$	−0.0322235	−0.00147079
$481$	−4.71574	−0.215019
$482$	7.95975	0.362557
$483$	−0.373584	−0.0169987
$484$	−10.6673	−0.484879
$485$	−4.64941	−0.211119
$486$	2.29149	0.103944
$487$	34.1902	1.54931	0.774654	−	0.632385i	$-0.217924\pi$
$487$	34.1902	1.54931	0.774654	+	0.632385i	$0.217924\pi$
$488$	7.35292	0.332851
$489$	−0.750315	−0.0339304
$490$	−4.63670	−0.209465
$491$	−25.9804	−1.17248	−0.586240	−	0.810138i	$-0.699392\pi$
$491$	−25.9804	−1.17248	−0.586240	+	0.810138i	$0.699392\pi$
$492$	0.0877936	0.00395804
$493$	8.77440	0.395179
$494$	3.63687	0.163631
$495$	0.653256	0.0293617
$496$	1.97689	0.0887649
$497$	−1.47760	−0.0662793
$498$	0.117700	0.00527425
$499$	37.7462	1.68975	0.844875	−	0.534964i	$-0.179675\pi$
$499$	37.7462	1.68975	0.844875	+	0.534964i	$0.179675\pi$
$500$	3.73037	0.166827
$501$	0.620358	0.0277156
$502$	3.11061	0.138833
$503$	22.4759	1.00215	0.501076	−	0.865404i	$-0.332938\pi$
$503$	22.4759	1.00215	0.501076	+	0.865404i	$0.332938\pi$
$504$	−13.1312	−0.584909
$505$	−1.84394	−0.0820542
$506$	−0.576761	−0.0256401
$507$	2.40468	0.106796
$508$	−9.53073	−0.422858
$509$	−25.8203	−1.14446	−0.572231	−	0.820092i	$-0.693922\pi$
$509$	−25.8203	−1.14446	−0.572231	+	0.820092i	$0.693922\pi$
$510$	−0.0728680	−0.00322665
$511$	−37.4283	−1.65573
$512$	1.00000	0.0441942
$513$	−0.288960	−0.0127579
$514$	2.44511	0.107849
$515$	1.66178	0.0732269
$516$	0.691480	0.0304407
$517$	3.22433	0.141806
$518$	−3.22189	−0.141562
$519$	1.60478	0.0704419
$520$	−2.43047	−0.106583
$521$	−25.4996	−1.11716	−0.558579	−	0.829451i	$-0.688653\pi$
$521$	−25.4996	−1.11716	−0.558579	+	0.829451i	$0.688653\pi$
$522$	−11.6124	−0.508262
$523$	1.96241	0.0858102	0.0429051	−	0.999079i	$-0.486339\pi$
$523$	1.96241	0.0858102	0.0429051	+	0.999079i	$0.486339\pi$
$524$	−1.00000	−0.0436852
$525$	−1.81441	−0.0791874
$526$	−9.48528	−0.413578
$527$	4.47040	0.194734
$528$	0.0491078	0.00213714
$529$	1.00000	0.0434783
$530$	5.11977	0.222389
$531$	29.5103	1.28064
$532$	2.48479	0.107729
$533$	6.62186	0.286825
$534$	0.386544	0.0167274
$535$	0.288623	0.0124783
$536$	−11.3177	−0.488849
$537$	−0.363671	−0.0156936
$538$	−20.2611	−0.873520
$539$	7.06623	0.304364
$540$	0.193107	0.00831001
$541$	14.6566	0.630137	0.315068	−	0.949069i	$-0.397973\pi$
$541$	14.6566	0.630137	0.315068	+	0.949069i	$0.397973\pi$
$542$	4.22026	0.181276
$543$	−1.42730	−0.0612513
$544$	2.26133	0.0969539
$545$	−5.56659	−0.238446
$546$	2.39917	0.102675
$547$	0.123487	0.00527991	0.00263995	−	0.999997i	$-0.499160\pi$
$547$	0.123487	0.00527991	0.00263995	+	0.999997i	$0.499160\pi$
$548$	−9.19652	−0.392856
$549$	−22.0055	−0.939170
$550$	−2.80119	−0.119443
$551$	2.19740	0.0936123
$552$	−0.0851442	−0.00362398
$553$	47.5456	2.02185
$554$	−16.9891	−0.721798
$555$	0.0236619	0.00100439
$556$	21.0203	0.891460
$557$	−15.6222	−0.661935	−0.330967	−	0.943642i	$-0.607375\pi$
$557$	−15.6222	−0.661935	−0.330967	+	0.943642i	$0.607375\pi$
$558$	−5.91633	−0.250458
$559$	52.1551	2.20593
$560$	−1.66054	−0.0701708
$561$	0.111049	0.00468850
$562$	−0.270221	−0.0113986
$563$	−22.3732	−0.942920	−0.471460	−	0.881888i	$-0.656273\pi$
$563$	−22.3732	−0.942920	−0.471460	+	0.881888i	$0.656273\pi$
$564$	0.475990	0.0200428
$565$	7.41536	0.311967
$566$	28.1807	1.18452
$567$	39.2029	1.64637
$568$	−0.336762	−0.0141302
$569$	−13.4336	−0.563167	−0.281584	−	0.959537i	$-0.590860\pi$
$569$	−13.4336	−0.563167	−0.281584	+	0.959537i	$0.590860\pi$
$570$	−0.0182485	−0.000764348 0
$571$	24.7158	1.03432	0.517162	−	0.855887i	$-0.326988\pi$
$571$	24.7158	1.03432	0.517162	+	0.855887i	$0.326988\pi$
$572$	3.70397	0.154871
$573$	−0.156808	−0.00655074
$574$	4.52419	0.188836
$575$	4.85677	0.202541
$576$	−2.99275	−0.124698
$577$	−31.3975	−1.30709	−0.653547	−	0.756886i	$-0.726720\pi$
$577$	−31.3975	−1.30709	−0.653547	+	0.756886i	$0.726720\pi$
$578$	−11.8864	−0.494408
$579$	1.37668	0.0572127
$580$	−1.46849	−0.0609756
$581$	6.06532	0.251632
$582$	1.04601	0.0433585
$583$	−7.80241	−0.323143
$584$	−8.53035	−0.352988
$585$	7.27378	0.300734
$586$	15.3971	0.636047
$587$	−10.7260	−0.442709	−0.221354	−	0.975193i	$-0.571048\pi$
$587$	−10.7260	−0.442709	−0.221354	+	0.975193i	$0.571048\pi$
$588$	1.04315	0.0430188
$589$	1.11954	0.0461297
$590$	3.73182	0.153637
$591$	0.388730	0.0159902
$592$	−0.734306	−0.0301798
$593$	−15.7690	−0.647556	−0.323778	−	0.946133i	$-0.604953\pi$
$593$	−15.7690	−0.647556	−0.323778	+	0.946133i	$0.604953\pi$
$594$	−0.294291	−0.0120749
$595$	−3.75505	−0.153942
$596$	4.36633	0.178852
$597$	1.67435	0.0685265
$598$	−6.42203	−0.262616
$599$	−23.0658	−0.942444	−0.471222	−	0.882015i	$-0.656187\pi$
$599$	−23.0658	−0.942444	−0.471222	+	0.882015i	$0.656187\pi$
$600$	−0.413526	−0.0168821
$601$	−2.84360	−0.115993	−0.0579964	−	0.998317i	$-0.518471\pi$
$601$	−2.84360	−0.115993	−0.0579964	+	0.998317i	$0.518471\pi$
$602$	35.6335	1.45231
$603$	33.8710	1.37933
$604$	−13.3023	−0.541262
$605$	4.03714	0.164133
$606$	0.414843	0.0168519
$607$	−29.2311	−1.18645	−0.593227	−	0.805035i	$-0.702146\pi$
$607$	−29.2311	−1.18645	−0.593227	+	0.805035i	$0.702146\pi$
$608$	0.566312	0.0229670
$609$	1.44958	0.0587398
$610$	−2.78277	−0.112671
$611$	35.9017	1.45243
$612$	−6.76761	−0.273564
$613$	−2.11983	−0.0856191	−0.0428096	−	0.999083i	$-0.513631\pi$
$613$	−2.11983	−0.0856191	−0.0428096	+	0.999083i	$0.513631\pi$
$614$	−1.73618	−0.0700664
$615$	−0.0332262	−0.00133981
$616$	2.53063	0.101962
$617$	−29.4291	−1.18477	−0.592386	−	0.805654i	$-0.701814\pi$
$617$	−29.4291	−1.18477	−0.592386	+	0.805654i	$0.701814\pi$
$618$	−0.373863	−0.0150390
$619$	9.65775	0.388178	0.194089	−	0.980984i	$-0.437825\pi$
$619$	9.65775	0.388178	0.194089	+	0.980984i	$0.437825\pi$
$620$	−0.748168	−0.0300472
$621$	0.510248	0.0204755
$622$	28.0261	1.12375
$623$	19.9194	0.798055
$624$	0.546798	0.0218894
$625$	22.8721	0.914882
$626$	8.24820	0.329664
$627$	0.0278104	0.00111064
$628$	−13.4166	−0.535380
$629$	−1.66051	−0.0662090
$630$	4.96960	0.197993
$631$	−29.5969	−1.17823	−0.589116	−	0.808048i	$-0.700524\pi$
$631$	−29.5969	−1.17823	−0.589116	+	0.808048i	$0.700524\pi$
$632$	10.8362	0.431041
$633$	1.97159	0.0783635
$634$	10.7835	0.428268
$635$	3.60698	0.143139
$636$	−1.15183	−0.0456730
$637$	78.6800	3.11741
$638$	2.23794	0.0886009
$639$	1.00784	0.0398697
$640$	−0.378458	−0.0149599
$641$	12.7867	0.505044	0.252522	−	0.967591i	$-0.418740\pi$
$641$	12.7867	0.505044	0.252522	+	0.967591i	$0.418740\pi$
$642$	−0.0649335	−0.00256272
$643$	−35.3864	−1.39550	−0.697751	−	0.716340i	$-0.745816\pi$
$643$	−35.3864	−1.39550	−0.697751	+	0.716340i	$0.745816\pi$
$644$	−4.38766	−0.172898
$645$	−0.261696	−0.0103043
$646$	1.28062	0.0503854
$647$	−5.99641	−0.235743	−0.117872	−	0.993029i	$-0.537607\pi$
$647$	−5.99641	−0.235743	−0.117872	+	0.993029i	$0.537607\pi$
$648$	8.93481	0.350992
$649$	−5.68721	−0.223242
$650$	−31.1903	−1.22338
$651$	0.738534	0.0289454
$652$	−8.81229	−0.345116
$653$	−8.07161	−0.315866	−0.157933	−	0.987450i	$-0.550483\pi$
$653$	−8.07161	−0.315866	−0.157933	+	0.987450i	$0.550483\pi$
$654$	1.25235	0.0489709
$655$	0.378458	0.0147876
$656$	1.03112	0.0402583
$657$	25.5292	0.995989
$658$	24.5288	0.956232
$659$	34.9614	1.36190	0.680951	−	0.732329i	$-0.261567\pi$
$659$	34.9614	1.36190	0.680951	+	0.732329i	$0.261567\pi$
$660$	−0.0185852	−0.000723429 0
$661$	−0.0903181	−0.00351297	−0.00175648	−	0.999998i	$-0.500559\pi$
$661$	−0.0903181	−0.00351297	−0.00175648	+	0.999998i	$0.500559\pi$
$662$	−14.3575	−0.558020
$663$	1.23649	0.0480214
$664$	1.38236	0.0536459
$665$	−0.940387	−0.0364666
$666$	2.19760	0.0851551
$667$	−3.88019	−0.150241
$668$	7.28597	0.281903
$669$	0.366779	0.0141805
$670$	4.28326	0.165477
$671$	4.24088	0.163717
$672$	0.373584	0.0144113
$673$	12.4503	0.479924	0.239962	−	0.970782i	$-0.422865\pi$
$673$	12.4503	0.479924	0.239962	+	0.970782i	$0.422865\pi$
$674$	14.7571	0.568421
$675$	2.47816	0.0953843
$676$	28.2424	1.08625
$677$	−18.6413	−0.716444	−0.358222	−	0.933636i	$-0.616617\pi$
$677$	−18.6413	−0.716444	−0.358222	+	0.933636i	$0.616617\pi$
$678$	−1.66828	−0.0640701
$679$	53.9031	2.06861
$680$	−0.855819	−0.0328192
$681$	1.08355	0.0415218
$682$	1.14019	0.0436602
$683$	−26.0266	−0.995879	−0.497939	−	0.867212i	$-0.665910\pi$
$683$	−26.0266	−0.995879	−0.497939	+	0.867212i	$0.665910\pi$
$684$	−1.69483	−0.0648035
$685$	3.48049	0.132983
$686$	23.0422	0.879754
$687$	−2.24065	−0.0854861
$688$	8.12129	0.309621
$689$	−86.8771	−3.30975
$690$	0.0322235	0.00122673
$691$	15.4926	0.589364	0.294682	−	0.955595i	$-0.404786\pi$
$691$	15.4926	0.589364	0.294682	+	0.955595i	$0.404786\pi$
$692$	18.8478	0.716484
$693$	−7.57355	−0.287695
$694$	−1.05609	−0.0400885
$695$	−7.95530	−0.301762
$696$	0.330375	0.0125228
$697$	2.33170	0.0883194
$698$	−6.57396	−0.248828
$699$	−1.29913	−0.0491374
$700$	−21.3099	−0.805437
$701$	−42.9977	−1.62400	−0.812000	−	0.583657i	$-0.801621\pi$
$701$	−42.9977	−1.62400	−0.812000	+	0.583657i	$0.801621\pi$
$702$	−3.27683	−0.123676
$703$	−0.415847	−0.0156840
$704$	0.576761	0.0217375
$705$	−0.180142	−0.00678455
$706$	19.1251	0.719783
$707$	21.3778	0.803994
$708$	−0.839573	−0.0315531
$709$	29.4272	1.10516	0.552581	−	0.833459i	$-0.313643\pi$
$709$	29.4272	1.10516	0.552581	+	0.833459i	$0.313643\pi$
$710$	0.127450	0.00478312
$711$	−32.4301	−1.21622
$712$	4.53987	0.170139
$713$	−1.97689	−0.0740350
$714$	0.844798	0.0316158
$715$	−1.40180	−0.0524242
$716$	−4.27123	−0.159624
$717$	0.844951	0.0315553
$718$	−11.7739	−0.439396
$719$	7.70686	0.287417	0.143709	−	0.989620i	$-0.454097\pi$
$719$	7.70686	0.287417	0.143709	+	0.989620i	$0.454097\pi$
$720$	1.13263	0.0422106
$721$	−19.2659	−0.717501
$722$	−18.6793	−0.695171
$723$	0.677726	0.0252049
$724$	−16.7633	−0.623004
$725$	−18.8452	−0.699892
$726$	−0.908263	−0.0337088
$727$	−28.7619	−1.06672	−0.533360	−	0.845888i	$-0.679071\pi$
$727$	−28.7619	−1.06672	−0.533360	+	0.845888i	$0.679071\pi$
$728$	28.1777	1.04433
$729$	−26.6093	−0.985530
$730$	3.22838	0.119488
$731$	18.3649	0.679252
$732$	0.626059	0.0231398
$733$	−16.7233	−0.617690	−0.308845	−	0.951112i	$-0.599942\pi$
$733$	−16.7233	−0.617690	−0.308845	+	0.951112i	$0.599942\pi$
$734$	5.71525	0.210954
$735$	−0.394789	−0.0145620
$736$	−1.00000	−0.0368605
$737$	−6.52759	−0.240447
$738$	−3.08587	−0.113593
$739$	9.76737	0.359299	0.179649	−	0.983731i	$-0.442504\pi$
$739$	9.76737	0.359299	0.179649	+	0.983731i	$0.442504\pi$
$740$	0.277904	0.0102160
$741$	0.309659	0.0113756
$742$	−59.3562	−2.17904
$743$	27.4974	1.00878	0.504390	−	0.863476i	$-0.331717\pi$
$743$	27.4974	1.00878	0.504390	+	0.863476i	$0.331717\pi$
$744$	0.168321	0.00617093
$745$	−1.65247	−0.0605419
$746$	8.44258	0.309105
$747$	−4.13705	−0.151367
$748$	1.30425	0.0476881
$749$	−3.34616	−0.122266
$750$	0.317619	0.0115978
$751$	−14.2875	−0.521357	−0.260678	−	0.965426i	$-0.583946\pi$
$751$	−14.2875	−0.521357	−0.260678	+	0.965426i	$0.583946\pi$
$752$	5.59040	0.203861
$753$	0.264850	0.00965168
$754$	24.9187	0.907484
$755$	5.03435	0.183219
$756$	−2.23880	−0.0814242
$757$	−33.5070	−1.21783	−0.608917	−	0.793234i	$-0.708396\pi$
$757$	−33.5070	−1.21783	−0.608917	+	0.793234i	$0.708396\pi$
$758$	−3.03983	−0.110412
$759$	−0.0491078	−0.00178250
$760$	−0.214325	−0.00777439
$761$	20.4475	0.741222	0.370611	−	0.928788i	$-0.379148\pi$
$761$	20.4475	0.741222	0.370611	+	0.928788i	$0.379148\pi$
$762$	−0.811487	−0.0293971
$763$	64.5364	2.33638
$764$	−1.84167	−0.0666294
$765$	2.56125	0.0926023
$766$	−33.4675	−1.20923
$767$	−63.3251	−2.28654
$768$	0.0851442	0.00307238
$769$	40.8330	1.47248	0.736238	−	0.676723i	$-0.236601\pi$
$769$	40.8330	1.47248	0.736238	+	0.676723i	$0.236601\pi$
$770$	−0.957737	−0.0345144
$771$	0.208187	0.00749767
$772$	16.1688	0.581926
$773$	−16.7292	−0.601709	−0.300854	−	0.953670i	$-0.597272\pi$
$773$	−16.7292	−0.601709	−0.300854	+	0.953670i	$0.597272\pi$
$774$	−24.3050	−0.873625
$775$	−9.60129	−0.344888
$776$	12.2852	0.441012
$777$	−0.274325	−0.00984136
$778$	−23.2147	−0.832288
$779$	0.583934	0.0209216
$780$	−0.206940	−0.00740964
$781$	−0.194231	−0.00695013
$782$	−2.26133	−0.0808651
$783$	−1.97986	−0.0707543
$784$	12.2516	0.437556
$785$	5.07761	0.181228
$786$	−0.0851442	−0.00303699
$787$	−51.9576	−1.85209	−0.926045	−	0.377414i	$-0.876813\pi$
$787$	−51.9576	−1.85209	−0.926045	+	0.377414i	$0.876813\pi$
$788$	4.56554	0.162641
$789$	−0.807617	−0.0287519
$790$	−4.10105	−0.145909
$791$	−85.9702	−3.05675
$792$	−1.72610	−0.0613343
$793$	47.2207	1.67686
$794$	12.0610	0.428028
$795$	0.435919	0.0154604
$796$	19.6649	0.697002
$797$	−3.00795	−0.106547	−0.0532735	−	0.998580i	$-0.516966\pi$
$797$	−3.00795	−0.106547	−0.0532735	+	0.998580i	$0.516966\pi$
$798$	0.211565	0.00748933
$799$	12.6418	0.447234
$800$	−4.85677	−0.171713
$801$	−13.5867	−0.480063
$802$	−36.2367	−1.27956
$803$	−4.91997	−0.173622
$804$	−0.963635	−0.0339848
$805$	1.66054	0.0585265
$806$	12.6956	0.447184
$807$	−1.72512	−0.0607271
$808$	4.87224	0.171405
$809$	8.47028	0.297799	0.148900	−	0.988852i	$-0.452427\pi$
$809$	8.47028	0.297799	0.148900	+	0.988852i	$0.452427\pi$
$810$	−3.38145	−0.118812
$811$	−10.7767	−0.378419	−0.189210	−	0.981937i	$-0.560593\pi$
$811$	−10.7767	−0.378419	−0.189210	+	0.981937i	$0.560593\pi$
$812$	17.0249	0.597459
$813$	0.359331	0.0126023
$814$	−0.423519	−0.0148443
$815$	3.33508	0.116823
$816$	0.192539	0.00674023
$817$	4.59918	0.160905
$818$	12.1745	0.425670
$819$	−84.3288	−2.94669
$820$	−0.390234	−0.0136276
$821$	24.9297	0.870052	0.435026	−	0.900418i	$-0.356739\pi$
$821$	24.9297	0.870052	0.435026	+	0.900418i	$0.356739\pi$
$822$	−0.783030	−0.0273113
$823$	20.4015	0.711153	0.355576	−	0.934647i	$-0.384285\pi$
$823$	20.4015	0.711153	0.355576	+	0.934647i	$0.384285\pi$
$824$	−4.39093	−0.152965
$825$	−0.238505	−0.00830369
$826$	−43.2650	−1.50538
$827$	−0.765285	−0.0266116	−0.0133058	−	0.999911i	$-0.504235\pi$
$827$	−0.765285	−0.0266116	−0.0133058	+	0.999911i	$0.504235\pi$
$828$	2.99275	0.104005
$829$	23.9558	0.832019	0.416010	−	0.909360i	$-0.363428\pi$
$829$	23.9558	0.832019	0.416010	+	0.909360i	$0.363428\pi$
$830$	−0.523164	−0.0181593
$831$	−1.44652	−0.0501793
$832$	6.42203	0.222644
$833$	27.7049	0.959918
$834$	1.78976	0.0619743
$835$	−2.75743	−0.0954248
$836$	0.326627	0.0112966
$837$	−1.00870	−0.0348659
$838$	−22.6751	−0.783297
$839$	−11.1184	−0.383850	−0.191925	−	0.981410i	$-0.561473\pi$
$839$	−11.1184	−0.383850	−0.191925	+	0.981410i	$0.561473\pi$
$840$	−0.141386	−0.00487827
$841$	−13.9442	−0.480833
$842$	−10.2800	−0.354271
$843$	−0.0230077	−0.000792429 0
$844$	23.1558	0.797057
$845$	−10.6886	−0.367698
$846$	−16.7307	−0.575213
$847$	−46.8047	−1.60823
$848$	−13.5280	−0.464553
$849$	2.39942	0.0823481
$850$	−10.9828	−0.376706
$851$	0.734306	0.0251717
$852$	−0.0286733	−0.000982331 0
$853$	−35.7625	−1.22448	−0.612242	−	0.790670i	$-0.709732\pi$
$853$	−35.7625	−1.22448	−0.612242	+	0.790670i	$0.709732\pi$
$854$	32.2621	1.10399
$855$	0.641422	0.0219362
$856$	−0.762630	−0.0260662
$857$	−5.67298	−0.193785	−0.0968927	−	0.995295i	$-0.530890\pi$
$857$	−5.67298	−0.193785	−0.0968927	+	0.995295i	$0.530890\pi$
$858$	0.315372	0.0107666
$859$	−27.8604	−0.950586	−0.475293	−	0.879828i	$-0.657658\pi$
$859$	−27.8604	−0.950586	−0.475293	+	0.879828i	$0.657658\pi$
$860$	−3.07356	−0.104808
$861$	0.385209	0.0131279
$862$	−37.2125	−1.26746
$863$	−32.3707	−1.10191	−0.550956	−	0.834534i	$-0.685737\pi$
$863$	−32.3707	−1.10191	−0.550956	+	0.834534i	$0.685737\pi$
$864$	−0.510248	−0.0173590
$865$	−7.13308	−0.242532
$866$	21.9281	0.745146
$867$	−1.01206	−0.0343712
$868$	8.67392	0.294412
$869$	6.24990	0.212013
$870$	−0.125033	−0.00423902
$871$	−72.6825	−2.46275
$872$	14.7086	0.498097
$873$	−36.7664	−1.24435
$874$	−0.566312	−0.0191558
$875$	16.3676	0.553326
$876$	−0.726310	−0.0245397
$877$	−44.1140	−1.48962	−0.744812	−	0.667274i	$-0.767461\pi$
$877$	−44.1140	−1.48962	−0.744812	+	0.667274i	$0.767461\pi$
$878$	−40.4123	−1.36385
$879$	1.31097	0.0442180
$880$	−0.218280	−0.00735820
$881$	18.8691	0.635715	0.317857	−	0.948139i	$-0.397037\pi$
$881$	18.8691	0.635715	0.317857	+	0.948139i	$0.397037\pi$
$882$	−36.6659	−1.23461
$883$	−11.1489	−0.375191	−0.187596	−	0.982246i	$-0.560069\pi$
$883$	−11.1489	−0.375191	−0.187596	+	0.982246i	$0.560069\pi$
$884$	14.5223	0.488439
$885$	0.317743	0.0106808
$886$	−3.57666	−0.120160
$887$	−13.2737	−0.445688	−0.222844	−	0.974854i	$-0.571534\pi$
$887$	−13.2737	−0.445688	−0.222844	+	0.974854i	$0.571534\pi$
$888$	−0.0625219	−0.00209810
$889$	−41.8176	−1.40252
$890$	−1.71815	−0.0575925
$891$	5.15325	0.172640
$892$	4.30774	0.144234
$893$	3.16591	0.105943
$894$	0.371768	0.0124338
$895$	1.61648	0.0540330
$896$	4.38766	0.146582
$897$	−0.546798	−0.0182571
$898$	−17.9726	−0.599754
$899$	7.67069	0.255832
$900$	14.5351	0.484503
$901$	−30.5913	−1.01914
$902$	0.594708	0.0198016
$903$	3.03398	0.100965
$904$	−19.5936	−0.651674
$905$	6.34421	0.210889
$906$	−1.13261	−0.0376285
$907$	22.5566	0.748981	0.374490	−	0.927231i	$-0.377818\pi$
$907$	22.5566	0.748981	0.374490	+	0.927231i	$0.377818\pi$
$908$	12.7261	0.422329
$909$	−14.5814	−0.483635
$910$	−10.6641	−0.353510
$911$	42.7353	1.41588	0.707942	−	0.706271i	$-0.249624\pi$
$911$	42.7353	1.41588	0.707942	+	0.706271i	$0.249624\pi$
$912$	0.0482182	0.00159666
$913$	0.797290	0.0263864
$914$	24.7661	0.819189
$915$	−0.236937	−0.00783289
$916$	−26.3159	−0.869503
$917$	−4.38766	−0.144893
$918$	−1.15384	−0.0380824
$919$	20.4264	0.673805	0.336902	−	0.941540i	$-0.390621\pi$
$919$	20.4264	0.673805	0.336902	+	0.941540i	$0.390621\pi$
$920$	0.378458	0.0124774
$921$	−0.147825	−0.00487101
$922$	32.7713	1.07926
$923$	−2.16269	−0.0711859
$924$	0.215469	0.00708840
$925$	3.56636	0.117261
$926$	−39.7167	−1.30517
$927$	13.1410	0.431606
$928$	3.88019	0.127373
$929$	41.4068	1.35851	0.679257	−	0.733901i	$-0.262302\pi$
$929$	41.4068	1.35851	0.679257	+	0.733901i	$0.262302\pi$
$930$	−0.0637022	−0.00208888
$931$	6.93822	0.227391
$932$	−15.2579	−0.499791
$933$	2.38626	0.0781227
$934$	41.3380	1.35262
$935$	−0.493603	−0.0161425
$936$	−19.2195	−0.628210
$937$	−28.7824	−0.940280	−0.470140	−	0.882592i	$-0.655797\pi$
$937$	−28.7824	−0.940280	−0.470140	+	0.882592i	$0.655797\pi$
$938$	−49.6582	−1.62140
$939$	0.702286	0.0229183
$940$	−2.11573	−0.0690075
$941$	10.4560	0.340856	0.170428	−	0.985370i	$-0.445485\pi$
$941$	10.4560	0.340856	0.170428	+	0.985370i	$0.445485\pi$
$942$	−1.14234	−0.0372196
$943$	−1.03112	−0.0335778
$944$	−9.86060	−0.320935
$945$	0.847289	0.0275623
$946$	4.68404	0.152291
$947$	28.9992	0.942348	0.471174	−	0.882040i	$-0.343830\pi$
$947$	28.9992	0.942348	0.471174	+	0.882040i	$0.343830\pi$
$948$	0.922640	0.0299660
$949$	−54.7821	−1.77830
$950$	−2.75045	−0.0892363
$951$	0.918153	0.0297732
$952$	9.92197	0.321573
$953$	0.454225	0.0147138	0.00735689	−	0.999973i	$-0.497658\pi$
$953$	0.454225	0.0147138	0.00735689	+	0.999973i	$0.497658\pi$
$954$	40.4859	1.31078
$955$	0.696996	0.0225543
$956$	9.92377	0.320958
$957$	0.190548	0.00615953
$958$	23.5500	0.760865
$959$	−40.3512	−1.30301
$960$	−0.0322235	−0.00104001
$961$	−27.0919	−0.873933
$962$	−4.71574	−0.152041
$963$	2.28236	0.0735481
$964$	7.95975	0.256366
$965$	−6.11919	−0.196984
$966$	−0.373584	−0.0120199
$967$	−14.1878	−0.456250	−0.228125	−	0.973632i	$-0.573259\pi$
$967$	−14.1878	−0.456250	−0.228125	+	0.973632i	$0.573259\pi$
$968$	−10.6673	−0.342862
$969$	0.109037	0.00350279
$970$	−4.64941	−0.149284
$971$	−36.4390	−1.16938	−0.584691	−	0.811256i	$-0.698784\pi$
$971$	−36.4390	−1.16938	−0.584691	+	0.811256i	$0.698784\pi$
$972$	2.29149	0.0734996
$973$	92.2301	2.95676
$974$	34.1902	1.09553
$975$	−2.65567	−0.0850496
$976$	7.35292	0.235361
$977$	−33.8877	−1.08416	−0.542082	−	0.840326i	$-0.682364\pi$
$977$	−33.8877	−1.08416	−0.542082	+	0.840326i	$0.682364\pi$
$978$	−0.750315	−0.0239924
$979$	2.61842	0.0836851
$980$	−4.63670	−0.148114
$981$	−44.0192	−1.40543
$982$	−25.9804	−0.829068
$983$	−12.6803	−0.404437	−0.202219	−	0.979340i	$-0.564815\pi$
$983$	−12.6803	−0.404437	−0.202219	+	0.979340i	$0.564815\pi$
$984$	0.0877936	0.00279876
$985$	−1.72786	−0.0550544
$986$	8.77440	0.279434
$987$	2.08849	0.0664772
$988$	3.63687	0.115704
$989$	−8.12129	−0.258242
$990$	0.653256	0.0207618
$991$	−36.3967	−1.15618	−0.578090	−	0.815973i	$-0.696202\pi$
$991$	−36.3967	−1.15618	−0.578090	+	0.815973i	$0.696202\pi$
$992$	1.97689	0.0627663
$993$	−1.22246	−0.0387935
$994$	−1.47760	−0.0468665
$995$	−7.44231	−0.235937
$996$	0.117700	0.00372946
$997$	42.6495	1.35072	0.675361	−	0.737487i	$-0.263988\pi$
$997$	42.6495	1.35072	0.675361	+	0.737487i	$0.263988\pi$
$998$	37.7462	1.19483
$999$	0.374678	0.0118543

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.19	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.19	✓	35	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.0851442 q^{3} +1.00000 q^{4} -0.378458 q^{5} +0.0851442 q^{6} +4.38766 q^{7} +1.00000 q^{8} -2.99275 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.0851442 q^{3} +1.00000 q^{4} -0.378458 q^{5} +0.0851442 q^{6} +4.38766 q^{7} +1.00000 q^{8} -2.99275 q^{9} -0.378458 q^{10} +0.576761 q^{11} +0.0851442 q^{12} +6.42203 q^{13} +4.38766 q^{14} -0.0322235 q^{15} +1.00000 q^{16} +2.26133 q^{17} -2.99275 q^{18} +0.566312 q^{19} -0.378458 q^{20} +0.373584 q^{21} +0.576761 q^{22} -1.00000 q^{23} +0.0851442 q^{24} -4.85677 q^{25} +6.42203 q^{26} -0.510248 q^{27} +4.38766 q^{28} +3.88019 q^{29} -0.0322235 q^{30} +1.97689 q^{31} +1.00000 q^{32} +0.0491078 q^{33} +2.26133 q^{34} -1.66054 q^{35} -2.99275 q^{36} -0.734306 q^{37} +0.566312 q^{38} +0.546798 q^{39} -0.378458 q^{40} +1.03112 q^{41} +0.373584 q^{42} +8.12129 q^{43} +0.576761 q^{44} +1.13263 q^{45} -1.00000 q^{46} +5.59040 q^{47} +0.0851442 q^{48} +12.2516 q^{49} -4.85677 q^{50} +0.192539 q^{51} +6.42203 q^{52} -13.5280 q^{53} -0.510248 q^{54} -0.218280 q^{55} +4.38766 q^{56} +0.0482182 q^{57} +3.88019 q^{58} -9.86060 q^{59} -0.0322235 q^{60} +7.35292 q^{61} +1.97689 q^{62} -13.1312 q^{63} +1.00000 q^{64} -2.43047 q^{65} +0.0491078 q^{66} -11.3177 q^{67} +2.26133 q^{68} -0.0851442 q^{69} -1.66054 q^{70} -0.336762 q^{71} -2.99275 q^{72} -8.53035 q^{73} -0.734306 q^{74} -0.413526 q^{75} +0.566312 q^{76} +2.53063 q^{77} +0.546798 q^{78} +10.8362 q^{79} -0.378458 q^{80} +8.93481 q^{81} +1.03112 q^{82} +1.38236 q^{83} +0.373584 q^{84} -0.855819 q^{85} +8.12129 q^{86} +0.330375 q^{87} +0.576761 q^{88} +4.53987 q^{89} +1.13263 q^{90} +28.1777 q^{91} -1.00000 q^{92} +0.168321 q^{93} +5.59040 q^{94} -0.214325 q^{95} +0.0851442 q^{96} +12.2852 q^{97} +12.2516 q^{98} -1.72610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

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