LMFDB - Embedded newform 6026.2.a.g.1.5

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:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.74967 q^{3} +1.00000 q^{4} +2.79997 q^{5} -1.74967 q^{6} +0.229508 q^{7} +1.00000 q^{8} +0.0613311 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.74967 q^{3} +1.00000 q^{4} +2.79997 q^{5} -1.74967 q^{6} +0.229508 q^{7} +1.00000 q^{8} +0.0613311 q^{9} +2.79997 q^{10} -4.72406 q^{11} -1.74967 q^{12} +0.543430 q^{13} +0.229508 q^{14} -4.89901 q^{15} +1.00000 q^{16} -1.47141 q^{17} +0.0613311 q^{18} -0.554213 q^{19} +2.79997 q^{20} -0.401563 q^{21} -4.72406 q^{22} -1.00000 q^{23} -1.74967 q^{24} +2.83982 q^{25} +0.543430 q^{26} +5.14169 q^{27} +0.229508 q^{28} -3.35816 q^{29} -4.89901 q^{30} +7.40566 q^{31} +1.00000 q^{32} +8.26552 q^{33} -1.47141 q^{34} +0.642615 q^{35} +0.0613311 q^{36} -5.86974 q^{37} -0.554213 q^{38} -0.950820 q^{39} +2.79997 q^{40} -3.90577 q^{41} -0.401563 q^{42} +9.53038 q^{43} -4.72406 q^{44} +0.171725 q^{45} -1.00000 q^{46} +1.28431 q^{47} -1.74967 q^{48} -6.94733 q^{49} +2.83982 q^{50} +2.57448 q^{51} +0.543430 q^{52} -6.17584 q^{53} +5.14169 q^{54} -13.2272 q^{55} +0.229508 q^{56} +0.969688 q^{57} -3.35816 q^{58} -12.0452 q^{59} -4.89901 q^{60} +2.44251 q^{61} +7.40566 q^{62} +0.0140760 q^{63} +1.00000 q^{64} +1.52159 q^{65} +8.26552 q^{66} -7.79461 q^{67} -1.47141 q^{68} +1.74967 q^{69} +0.642615 q^{70} +9.38996 q^{71} +0.0613311 q^{72} -13.3820 q^{73} -5.86974 q^{74} -4.96874 q^{75} -0.554213 q^{76} -1.08421 q^{77} -0.950820 q^{78} -3.82662 q^{79} +2.79997 q^{80} -9.18023 q^{81} -3.90577 q^{82} -0.949460 q^{83} -0.401563 q^{84} -4.11991 q^{85} +9.53038 q^{86} +5.87566 q^{87} -4.72406 q^{88} +7.74194 q^{89} +0.171725 q^{90} +0.124722 q^{91} -1.00000 q^{92} -12.9574 q^{93} +1.28431 q^{94} -1.55178 q^{95} -1.74967 q^{96} -11.8028 q^{97} -6.94733 q^{98} -0.289732 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * 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
$3$	−1.74967	−1.01017	−0.505085	−	0.863070i	$-0.668539\pi$
$3$	−1.74967	−1.01017	−0.505085	+	0.863070i	$0.668539\pi$
$4$	1.00000	0.500000
$5$	2.79997	1.25218	0.626092	−	0.779749i	$-0.284653\pi$
$5$	2.79997	1.25218	0.626092	+	0.779749i	$0.284653\pi$
$6$	−1.74967	−0.714298
$7$	0.229508	0.0867459	0.0433730	−	0.999059i	$-0.486190\pi$
$7$	0.229508	0.0867459	0.0433730	+	0.999059i	$0.486190\pi$
$8$	1.00000	0.353553
$9$	0.0613311	0.0204437
$10$	2.79997	0.885428
$11$	−4.72406	−1.42436	−0.712178	−	0.701999i	$-0.752291\pi$
$11$	−4.72406	−1.42436	−0.712178	+	0.701999i	$0.752291\pi$
$12$	−1.74967	−0.505085
$13$	0.543430	0.150720	0.0753601	−	0.997156i	$-0.475989\pi$
$13$	0.543430	0.150720	0.0753601	+	0.997156i	$0.475989\pi$
$14$	0.229508	0.0613386
$15$	−4.89901	−1.26492
$16$	1.00000	0.250000
$17$	−1.47141	−0.356870	−0.178435	−	0.983952i	$-0.557103\pi$
$17$	−1.47141	−0.356870	−0.178435	+	0.983952i	$0.557103\pi$
$18$	0.0613311	0.0144559
$19$	−0.554213	−0.127145	−0.0635726	−	0.997977i	$-0.520249\pi$
$19$	−0.554213	−0.127145	−0.0635726	+	0.997977i	$0.520249\pi$
$20$	2.79997	0.626092
$21$	−0.401563	−0.0876281
$22$	−4.72406	−1.00717
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.74967	−0.357149
$25$	2.83982	0.567965
$26$	0.543430	0.106575
$27$	5.14169	0.989519
$28$	0.229508	0.0433730
$29$	−3.35816	−0.623595	−0.311797	−	0.950149i	$-0.600931\pi$
$29$	−3.35816	−0.623595	−0.311797	+	0.950149i	$0.600931\pi$
$30$	−4.89901	−0.894433
$31$	7.40566	1.33010	0.665048	−	0.746801i	$-0.268411\pi$
$31$	7.40566	1.33010	0.665048	+	0.746801i	$0.268411\pi$
$32$	1.00000	0.176777
$33$	8.26552	1.43884
$34$	−1.47141	−0.252346
$35$	0.642615	0.108622
$36$	0.0613311	0.0102219
$37$	−5.86974	−0.964980	−0.482490	−	0.875902i	$-0.660267\pi$
$37$	−5.86974	−0.964980	−0.482490	+	0.875902i	$0.660267\pi$
$38$	−0.554213	−0.0899052
$39$	−0.950820	−0.152253
$40$	2.79997	0.442714
$41$	−3.90577	−0.609979	−0.304989	−	0.952356i	$-0.598653\pi$
$41$	−3.90577	−0.609979	−0.304989	+	0.952356i	$0.598653\pi$
$42$	−0.401563	−0.0619624
$43$	9.53038	1.45337	0.726684	−	0.686971i	$-0.241060\pi$
$43$	9.53038	1.45337	0.726684	+	0.686971i	$0.241060\pi$
$44$	−4.72406	−0.712178
$45$	0.171725	0.0255993
$46$	−1.00000	−0.147442
$47$	1.28431	0.187336	0.0936682	−	0.995603i	$-0.470141\pi$
$47$	1.28431	0.187336	0.0936682	+	0.995603i	$0.470141\pi$
$48$	−1.74967	−0.252543
$49$	−6.94733	−0.992475
$50$	2.83982	0.401612
$51$	2.57448	0.360500
$52$	0.543430	0.0753601
$53$	−6.17584	−0.848317	−0.424158	−	0.905588i	$-0.639430\pi$
$53$	−6.17584	−0.848317	−0.424158	+	0.905588i	$0.639430\pi$
$54$	5.14169	0.699695
$55$	−13.2272	−1.78356
$56$	0.229508	0.0306693
$57$	0.969688	0.128438
$58$	−3.35816	−0.440948
$59$	−12.0452	−1.56816	−0.784078	−	0.620662i	$-0.786864\pi$
$59$	−12.0452	−1.56816	−0.784078	+	0.620662i	$0.786864\pi$
$60$	−4.89901	−0.632459
$61$	2.44251	0.312732	0.156366	−	0.987699i	$-0.450022\pi$
$61$	2.44251	0.312732	0.156366	+	0.987699i	$0.450022\pi$
$62$	7.40566	0.940519
$63$	0.0140760	0.00177341
$64$	1.00000	0.125000
$65$	1.52159	0.188730
$66$	8.26552	1.01742
$67$	−7.79461	−0.952263	−0.476132	−	0.879374i	$-0.657961\pi$
$67$	−7.79461	−0.952263	−0.476132	+	0.879374i	$0.657961\pi$
$68$	−1.47141	−0.178435
$69$	1.74967	0.210635
$70$	0.642615	0.0768072
$71$	9.38996	1.11438	0.557191	−	0.830384i	$-0.311879\pi$
$71$	9.38996	1.11438	0.557191	+	0.830384i	$0.311879\pi$
$72$	0.0613311	0.00722794
$73$	−13.3820	−1.56625	−0.783124	−	0.621866i	$-0.786375\pi$
$73$	−13.3820	−1.56625	−0.783124	+	0.621866i	$0.786375\pi$
$74$	−5.86974	−0.682344
$75$	−4.96874	−0.573741
$76$	−0.554213	−0.0635726
$77$	−1.08421	−0.123557
$78$	−0.950820	−0.107659
$79$	−3.82662	−0.430529	−0.215264	−	0.976556i	$-0.569061\pi$
$79$	−3.82662	−0.430529	−0.215264	+	0.976556i	$0.569061\pi$
$80$	2.79997	0.313046
$81$	−9.18023	−1.02003
$82$	−3.90577	−0.431320
$83$	−0.949460	−0.104217	−0.0521084	−	0.998641i	$-0.516594\pi$
$83$	−0.949460	−0.104217	−0.0521084	+	0.998641i	$0.516594\pi$
$84$	−0.401563	−0.0438141
$85$	−4.11991	−0.446867
$86$	9.53038	1.02769
$87$	5.87566	0.629937
$88$	−4.72406	−0.503586
$89$	7.74194	0.820644	0.410322	−	0.911941i	$-0.365416\pi$
$89$	7.74194	0.820644	0.410322	+	0.911941i	$0.365416\pi$
$90$	0.171725	0.0181014
$91$	0.124722	0.0130744
$92$	−1.00000	−0.104257
$93$	−12.9574	−1.34362
$94$	1.28431	0.132467
$95$	−1.55178	−0.159209
$96$	−1.74967	−0.178575
$97$	−11.8028	−1.19840	−0.599198	−	0.800601i	$-0.704514\pi$
$97$	−11.8028	−1.19840	−0.599198	+	0.800601i	$0.704514\pi$
$98$	−6.94733	−0.701786
$99$	−0.289732	−0.0291191
$100$	2.83982	0.283982
$101$	−4.49821	−0.447589	−0.223795	−	0.974636i	$-0.571844\pi$
$101$	−4.49821	−0.447589	−0.223795	+	0.974636i	$0.571844\pi$
$102$	2.57448	0.254912
$103$	−4.06411	−0.400449	−0.200224	−	0.979750i	$-0.564167\pi$
$103$	−4.06411	−0.400449	−0.200224	+	0.979750i	$0.564167\pi$
$104$	0.543430	0.0532877
$105$	−1.12436	−0.109727
$106$	−6.17584	−0.599851
$107$	2.71971	0.262925	0.131462	−	0.991321i	$-0.458033\pi$
$107$	2.71971	0.262925	0.131462	+	0.991321i	$0.458033\pi$
$108$	5.14169	0.494759
$109$	−3.53704	−0.338787	−0.169393	−	0.985549i	$-0.554181\pi$
$109$	−3.53704	−0.338787	−0.169393	+	0.985549i	$0.554181\pi$
$110$	−13.2272	−1.26116
$111$	10.2701	0.974794
$112$	0.229508	0.0216865
$113$	−7.14774	−0.672403	−0.336202	−	0.941790i	$-0.609142\pi$
$113$	−7.14774	−0.672403	−0.336202	+	0.941790i	$0.609142\pi$
$114$	0.969688	0.0908196
$115$	−2.79997	−0.261098
$116$	−3.35816	−0.311797
$117$	0.0333292	0.00308128
$118$	−12.0452	−1.10885
$119$	−0.337702	−0.0309571
$120$	−4.89901	−0.447216
$121$	11.3167	1.02879
$122$	2.44251	0.221135
$123$	6.83379	0.616182
$124$	7.40566	0.665048
$125$	−6.04843	−0.540988
$126$	0.0140760	0.00125399
$127$	−9.77050	−0.866992	−0.433496	−	0.901156i	$-0.642720\pi$
$127$	−9.77050	−0.866992	−0.433496	+	0.901156i	$0.642720\pi$
$128$	1.00000	0.0883883
$129$	−16.6750	−1.46815
$130$	1.52159	0.133452
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	8.26552	0.719421
$133$	−0.127196	−0.0110293
$134$	−7.79461	−0.673352
$135$	14.3966	1.23906
$136$	−1.47141	−0.126173
$137$	−8.76297	−0.748671	−0.374336	−	0.927293i	$-0.622129\pi$
$137$	−8.76297	−0.748671	−0.374336	+	0.927293i	$0.622129\pi$
$138$	1.74967	0.148941
$139$	−10.6309	−0.901702	−0.450851	−	0.892599i	$-0.648879\pi$
$139$	−10.6309	−0.901702	−0.450851	+	0.892599i	$0.648879\pi$
$140$	0.642615	0.0543109
$141$	−2.24712	−0.189242
$142$	9.38996	0.787988
$143$	−2.56719	−0.214679
$144$	0.0613311	0.00511093
$145$	−9.40274	−0.780855
$146$	−13.3820	−1.10750
$147$	12.1555	1.00257
$148$	−5.86974	−0.482490
$149$	19.6942	1.61341	0.806705	−	0.590955i	$-0.201249\pi$
$149$	19.6942	1.61341	0.806705	+	0.590955i	$0.201249\pi$
$150$	−4.96874	−0.405696
$151$	−0.961897	−0.0782781	−0.0391390	−	0.999234i	$-0.512462\pi$
$151$	−0.961897	−0.0782781	−0.0391390	+	0.999234i	$0.512462\pi$
$152$	−0.554213	−0.0449526
$153$	−0.0902435	−0.00729576
$154$	−1.08421	−0.0873681
$155$	20.7356	1.66552
$156$	−0.950820	−0.0761266
$157$	2.94226	0.234818	0.117409	−	0.993084i	$-0.462541\pi$
$157$	2.94226	0.234818	0.117409	+	0.993084i	$0.462541\pi$
$158$	−3.82662	−0.304430
$159$	10.8057	0.856944
$160$	2.79997	0.221357
$161$	−0.229508	−0.0180878
$162$	−9.18023	−0.721267
$163$	1.57110	0.123058	0.0615289	−	0.998105i	$-0.480402\pi$
$163$	1.57110	0.123058	0.0615289	+	0.998105i	$0.480402\pi$
$164$	−3.90577	−0.304989
$165$	23.1432	1.80170
$166$	−0.949460	−0.0736924
$167$	11.9708	0.926332	0.463166	−	0.886272i	$-0.346713\pi$
$167$	11.9708	0.926332	0.463166	+	0.886272i	$0.346713\pi$
$168$	−0.401563	−0.0309812
$169$	−12.7047	−0.977283
$170$	−4.11991	−0.315983
$171$	−0.0339905	−0.00259932
$172$	9.53038	0.726684
$173$	−8.61885	−0.655279	−0.327640	−	0.944803i	$-0.606253\pi$
$173$	−8.61885	−0.655279	−0.327640	+	0.944803i	$0.606253\pi$
$174$	5.87566	0.445432
$175$	0.651762	0.0492686
$176$	−4.72406	−0.356089
$177$	21.0751	1.58411
$178$	7.74194	0.580283
$179$	10.0324	0.749860	0.374930	−	0.927053i	$-0.377667\pi$
$179$	10.0324	0.749860	0.374930	+	0.927053i	$0.377667\pi$
$180$	0.171725	0.0127996
$181$	−18.0117	−1.33880	−0.669401	−	0.742901i	$-0.733449\pi$
$181$	−18.0117	−1.33880	−0.669401	+	0.742901i	$0.733449\pi$
$182$	0.124722	0.00924497
$183$	−4.27358	−0.315912
$184$	−1.00000	−0.0737210
$185$	−16.4351	−1.20833
$186$	−12.9574	−0.950085
$187$	6.95105	0.508311
$188$	1.28431	0.0936682
$189$	1.18006	0.0858367
$190$	−1.55178	−0.112578
$191$	−8.78412	−0.635597	−0.317798	−	0.948158i	$-0.602944\pi$
$191$	−8.78412	−0.635597	−0.317798	+	0.948158i	$0.602944\pi$
$192$	−1.74967	−0.126271
$193$	13.9982	1.00762	0.503808	−	0.863816i	$-0.331932\pi$
$193$	13.9982	1.00762	0.503808	+	0.863816i	$0.331932\pi$
$194$	−11.8028	−0.847394
$195$	−2.66227	−0.190649
$196$	−6.94733	−0.496238
$197$	21.1740	1.50858	0.754291	−	0.656540i	$-0.227981\pi$
$197$	21.1740	1.50858	0.754291	+	0.656540i	$0.227981\pi$
$198$	−0.289732	−0.0205903
$199$	−17.3625	−1.23080	−0.615398	−	0.788216i	$-0.711005\pi$
$199$	−17.3625	−1.23080	−0.615398	+	0.788216i	$0.711005\pi$
$200$	2.83982	0.200806
$201$	13.6380	0.961948
$202$	−4.49821	−0.316493
$203$	−0.770725	−0.0540943
$204$	2.57448	0.180250
$205$	−10.9360	−0.763806
$206$	−4.06411	−0.283160
$207$	−0.0613311	−0.00426281
$208$	0.543430	0.0376801
$209$	2.61813	0.181100
$210$	−1.12436	−0.0775884
$211$	−1.15486	−0.0795038	−0.0397519	−	0.999210i	$-0.512657\pi$
$211$	−1.15486	−0.0795038	−0.0397519	+	0.999210i	$0.512657\pi$
$212$	−6.17584	−0.424158
$213$	−16.4293	−1.12572
$214$	2.71971	0.185916
$215$	26.6848	1.81989
$216$	5.14169	0.349848
$217$	1.69966	0.115380
$218$	−3.53704	−0.239558
$219$	23.4141	1.58218
$220$	−13.2272	−0.891778
$221$	−0.799610	−0.0537876
$222$	10.2701	0.689283
$223$	1.33737	0.0895567	0.0447784	−	0.998997i	$-0.485742\pi$
$223$	1.33737	0.0895567	0.0447784	+	0.998997i	$0.485742\pi$
$224$	0.229508	0.0153347
$225$	0.174170	0.0116113
$226$	−7.14774	−0.475461
$227$	22.3446	1.48306	0.741531	−	0.670918i	$-0.234100\pi$
$227$	22.3446	1.48306	0.741531	+	0.670918i	$0.234100\pi$
$228$	0.969688	0.0642192
$229$	−8.40283	−0.555275	−0.277637	−	0.960686i	$-0.589551\pi$
$229$	−8.40283	−0.555275	−0.277637	+	0.960686i	$0.589551\pi$
$230$	−2.79997	−0.184624
$231$	1.89700	0.124814
$232$	−3.35816	−0.220474
$233$	3.64576	0.238842	0.119421	−	0.992844i	$-0.461896\pi$
$233$	3.64576	0.238842	0.119421	+	0.992844i	$0.461896\pi$
$234$	0.0333292	0.00217880
$235$	3.59604	0.234580
$236$	−12.0452	−0.784078
$237$	6.69531	0.434907
$238$	−0.337702	−0.0218899
$239$	19.7338	1.27647	0.638236	−	0.769841i	$-0.279664\pi$
$239$	19.7338	1.27647	0.638236	+	0.769841i	$0.279664\pi$
$240$	−4.89901	−0.316230
$241$	−14.1570	−0.911935	−0.455968	−	0.889996i	$-0.650707\pi$
$241$	−14.1570	−0.911935	−0.455968	+	0.889996i	$0.650707\pi$
$242$	11.3167	0.727466
$243$	0.637273	0.0408811
$244$	2.44251	0.156366
$245$	−19.4523	−1.24276
$246$	6.83379	0.435707
$247$	−0.301176	−0.0191634
$248$	7.40566	0.470260
$249$	1.66124	0.105277
$250$	−6.04843	−0.382536
$251$	−16.4965	−1.04125	−0.520625	−	0.853785i	$-0.674301\pi$
$251$	−16.4965	−1.04125	−0.520625	+	0.853785i	$0.674301\pi$
$252$	0.0140760	0.000886704 0
$253$	4.72406	0.296999
$254$	−9.77050	−0.613056
$255$	7.20847	0.451412
$256$	1.00000	0.0625000
$257$	−28.5305	−1.77968	−0.889842	−	0.456268i	$-0.849186\pi$
$257$	−28.5305	−1.77968	−0.889842	+	0.456268i	$0.849186\pi$
$258$	−16.6750	−1.03814
$259$	−1.34715	−0.0837081
$260$	1.52159	0.0943648
$261$	−0.205960	−0.0127486
$262$	1.00000	0.0617802
$263$	−11.7502	−0.724546	−0.362273	−	0.932072i	$-0.617999\pi$
$263$	−11.7502	−0.724546	−0.362273	+	0.932072i	$0.617999\pi$
$264$	8.26552	0.508708
$265$	−17.2922	−1.06225
$266$	−0.127196	−0.00779891
$267$	−13.5458	−0.828990
$268$	−7.79461	−0.476132
$269$	13.3575	0.814419	0.407210	−	0.913335i	$-0.366502\pi$
$269$	13.3575	0.814419	0.407210	+	0.913335i	$0.366502\pi$
$270$	14.3966	0.876147
$271$	23.4352	1.42359	0.711794	−	0.702388i	$-0.247883\pi$
$271$	23.4352	1.42359	0.711794	+	0.702388i	$0.247883\pi$
$272$	−1.47141	−0.0892176
$273$	−0.218221	−0.0132073
$274$	−8.76297	−0.529391
$275$	−13.4155	−0.808984
$276$	1.74967	0.105318
$277$	−9.40263	−0.564949	−0.282475	−	0.959275i	$-0.591155\pi$
$277$	−9.40263	−0.564949	−0.282475	+	0.959275i	$0.591155\pi$
$278$	−10.6309	−0.637600
$279$	0.454197	0.0271921
$280$	0.642615	0.0384036
$281$	17.7885	1.06117	0.530586	−	0.847631i	$-0.321972\pi$
$281$	17.7885	1.06117	0.530586	+	0.847631i	$0.321972\pi$
$282$	−2.24712	−0.133814
$283$	21.9421	1.30432	0.652162	−	0.758079i	$-0.273862\pi$
$283$	21.9421	1.30432	0.652162	+	0.758079i	$0.273862\pi$
$284$	9.38996	0.557191
$285$	2.71510	0.160828
$286$	−2.56719	−0.151801
$287$	−0.896406	−0.0529132
$288$	0.0613311	0.00361397
$289$	−14.8349	−0.872643
$290$	−9.40274	−0.552148
$291$	20.6510	1.21058
$292$	−13.3820	−0.783124
$293$	−10.0251	−0.585670	−0.292835	−	0.956163i	$-0.594599\pi$
$293$	−10.0251	−0.585670	−0.292835	+	0.956163i	$0.594599\pi$
$294$	12.1555	0.708923
$295$	−33.7263	−1.96362
$296$	−5.86974	−0.341172
$297$	−24.2896	−1.40943
$298$	19.6942	1.14085
$299$	−0.543430	−0.0314273
$300$	−4.96874	−0.286870
$301$	2.18730	0.126074
$302$	−0.961897	−0.0553509
$303$	7.87037	0.452141
$304$	−0.554213	−0.0317863
$305$	6.83896	0.391597
$306$	−0.0902435	−0.00515888
$307$	−10.4824	−0.598262	−0.299131	−	0.954212i	$-0.596697\pi$
$307$	−10.4824	−0.598262	−0.299131	+	0.954212i	$0.596697\pi$
$308$	−1.08421	−0.0617786
$309$	7.11083	0.404521
$310$	20.7356	1.17770
$311$	−33.8626	−1.92017	−0.960086	−	0.279704i	$-0.909764\pi$
$311$	−33.8626	−1.92017	−0.960086	+	0.279704i	$0.909764\pi$
$312$	−0.950820	−0.0538296
$313$	0.286893	0.0162162	0.00810808	−	0.999967i	$-0.497419\pi$
$313$	0.286893	0.0162162	0.00810808	+	0.999967i	$0.497419\pi$
$314$	2.94226	0.166041
$315$	0.0394123	0.00222063
$316$	−3.82662	−0.215264
$317$	−22.6361	−1.27137	−0.635684	−	0.771949i	$-0.719282\pi$
$317$	−22.6361	−1.27137	−0.635684	+	0.771949i	$0.719282\pi$
$318$	10.8057	0.605951
$319$	15.8641	0.888221
$320$	2.79997	0.156523
$321$	−4.75859	−0.265599
$322$	−0.229508	−0.0127900
$323$	0.815477	0.0453744
$324$	−9.18023	−0.510013
$325$	1.54324	0.0856038
$326$	1.57110	0.0870150
$327$	6.18863	0.342232
$328$	−3.90577	−0.215660
$329$	0.294760	0.0162507
$330$	23.1432	1.27399
$331$	26.9839	1.48317	0.741586	−	0.670858i	$-0.234074\pi$
$331$	26.9839	1.48317	0.741586	+	0.670858i	$0.234074\pi$
$332$	−0.949460	−0.0521084
$333$	−0.359998	−0.0197278
$334$	11.9708	0.655015
$335$	−21.8247	−1.19241
$336$	−0.401563	−0.0219070
$337$	4.95950	0.270161	0.135081	−	0.990835i	$-0.456871\pi$
$337$	4.95950	0.270161	0.135081	+	0.990835i	$0.456871\pi$
$338$	−12.7047	−0.691044
$339$	12.5062	0.679242
$340$	−4.11991	−0.223434
$341$	−34.9847	−1.89453
$342$	−0.0339905	−0.00183800
$343$	−3.20102	−0.172839
$344$	9.53038	0.513843
$345$	4.89901	0.263754
$346$	−8.61885	−0.463352
$347$	3.03429	0.162889	0.0814446	−	0.996678i	$-0.474047\pi$
$347$	3.03429	0.162889	0.0814446	+	0.996678i	$0.474047\pi$
$348$	5.87566	0.314968
$349$	8.02878	0.429771	0.214885	−	0.976639i	$-0.431062\pi$
$349$	8.02878	0.429771	0.214885	+	0.976639i	$0.431062\pi$
$350$	0.651762	0.0348382
$351$	2.79415	0.149141
$352$	−4.72406	−0.251793
$353$	9.08138	0.483353	0.241677	−	0.970357i	$-0.422303\pi$
$353$	9.08138	0.483353	0.241677	+	0.970357i	$0.422303\pi$
$354$	21.0751	1.12013
$355$	26.2916	1.39541
$356$	7.74194	0.410322
$357$	0.590865	0.0312719
$358$	10.0324	0.530231
$359$	8.02576	0.423583	0.211792	−	0.977315i	$-0.432070\pi$
$359$	8.02576	0.423583	0.211792	+	0.977315i	$0.432070\pi$
$360$	0.171725	0.00905072
$361$	−18.6928	−0.983834
$362$	−18.0117	−0.946676
$363$	−19.8005	−1.03925
$364$	0.124722	0.00653718
$365$	−37.4692	−1.96123
$366$	−4.27358	−0.223384
$367$	−14.0536	−0.733592	−0.366796	−	0.930301i	$-0.619545\pi$
$367$	−14.0536	−0.733592	−0.366796	+	0.930301i	$0.619545\pi$
$368$	−1.00000	−0.0521286
$369$	−0.239545	−0.0124702
$370$	−16.4351	−0.854420
$371$	−1.41741	−0.0735880
$372$	−12.9574	−0.671811
$373$	−29.4771	−1.52626	−0.763132	−	0.646242i	$-0.776339\pi$
$373$	−29.4771	−1.52626	−0.763132	+	0.646242i	$0.776339\pi$
$374$	6.95105	0.359430
$375$	10.5827	0.546490
$376$	1.28431	0.0662334
$377$	−1.82492	−0.0939883
$378$	1.18006	0.0606957
$379$	8.10696	0.416426	0.208213	−	0.978083i	$-0.433235\pi$
$379$	8.10696	0.416426	0.208213	+	0.978083i	$0.433235\pi$
$380$	−1.55178	−0.0796046
$381$	17.0951	0.875809
$382$	−8.78412	−0.449435
$383$	8.05853	0.411772	0.205886	−	0.978576i	$-0.433992\pi$
$383$	8.05853	0.411772	0.205886	+	0.978576i	$0.433992\pi$
$384$	−1.74967	−0.0892873
$385$	−3.03575	−0.154716
$386$	13.9982	0.712492
$387$	0.584509	0.0297123
$388$	−11.8028	−0.599198
$389$	−34.4103	−1.74467	−0.872336	−	0.488908i	$-0.837395\pi$
$389$	−34.4103	−1.74467	−0.872336	+	0.488908i	$0.837395\pi$
$390$	−2.66227	−0.134809
$391$	1.47141	0.0744126
$392$	−6.94733	−0.350893
$393$	−1.74967	−0.0882590
$394$	21.1740	1.06673
$395$	−10.7144	−0.539101
$396$	−0.289732	−0.0145596
$397$	−11.1833	−0.561274	−0.280637	−	0.959814i	$-0.590546\pi$
$397$	−11.1833	−0.561274	−0.280637	+	0.959814i	$0.590546\pi$
$398$	−17.3625	−0.870305
$399$	0.222551	0.0111415
$400$	2.83982	0.141991
$401$	6.13666	0.306450	0.153225	−	0.988191i	$-0.451034\pi$
$401$	6.13666	0.306450	0.153225	+	0.988191i	$0.451034\pi$
$402$	13.6380	0.680200
$403$	4.02445	0.200472
$404$	−4.49821	−0.223795
$405$	−25.7044	−1.27726
$406$	−0.770725	−0.0382504
$407$	27.7290	1.37448
$408$	2.57448	0.127456
$409$	−18.4453	−0.912062	−0.456031	−	0.889964i	$-0.650729\pi$
$409$	−18.4453	−0.912062	−0.456031	+	0.889964i	$0.650729\pi$
$410$	−10.9360	−0.540092
$411$	15.3323	0.756285
$412$	−4.06411	−0.200224
$413$	−2.76448	−0.136031
$414$	−0.0613311	−0.00301426
$415$	−2.65846	−0.130499
$416$	0.543430	0.0266438
$417$	18.6005	0.910873
$418$	2.61813	0.128057
$419$	9.21453	0.450159	0.225080	−	0.974340i	$-0.427736\pi$
$419$	9.21453	0.450159	0.225080	+	0.974340i	$0.427736\pi$
$420$	−1.12436	−0.0548633
$421$	1.26204	0.0615081	0.0307540	−	0.999527i	$-0.490209\pi$
$421$	1.26204	0.0615081	0.0307540	+	0.999527i	$0.490209\pi$
$422$	−1.15486	−0.0562177
$423$	0.0787684	0.00382985
$424$	−6.17584	−0.299925
$425$	−4.17856	−0.202690
$426$	−16.4293	−0.796002
$427$	0.560576	0.0271282
$428$	2.71971	0.131462
$429$	4.49173	0.216863
$430$	26.6848	1.28685
$431$	−5.01604	−0.241614	−0.120807	−	0.992676i	$-0.538548\pi$
$431$	−5.01604	−0.241614	−0.120807	+	0.992676i	$0.538548\pi$
$432$	5.14169	0.247380
$433$	−2.42539	−0.116557	−0.0582784	−	0.998300i	$-0.518561\pi$
$433$	−2.42539	−0.116557	−0.0582784	+	0.998300i	$0.518561\pi$
$434$	1.69966	0.0815862
$435$	16.4517	0.788796
$436$	−3.53704	−0.169393
$437$	0.554213	0.0265116
$438$	23.4141	1.11877
$439$	−10.2666	−0.489999	−0.245000	−	0.969523i	$-0.578788\pi$
$439$	−10.2666	−0.489999	−0.245000	+	0.969523i	$0.578788\pi$
$440$	−13.2272	−0.630582
$441$	−0.426087	−0.0202899
$442$	−0.799610	−0.0380336
$443$	−27.9110	−1.32609	−0.663045	−	0.748580i	$-0.730736\pi$
$443$	−27.9110	−1.32609	−0.663045	+	0.748580i	$0.730736\pi$
$444$	10.2701	0.487397
$445$	21.6772	1.02760
$446$	1.33737	0.0633262
$447$	−34.4582	−1.62982
$448$	0.229508	0.0108432
$449$	23.8361	1.12490	0.562448	−	0.826833i	$-0.309860\pi$
$449$	23.8361	1.12490	0.562448	+	0.826833i	$0.309860\pi$
$450$	0.174170	0.00821043
$451$	18.4511	0.868827
$452$	−7.14774	−0.336202
$453$	1.68300	0.0790741
$454$	22.3446	1.04868
$455$	0.349216	0.0163715
$456$	0.969688	0.0454098
$457$	−32.8930	−1.53867	−0.769335	−	0.638846i	$-0.779412\pi$
$457$	−32.8930	−1.53867	−0.769335	+	0.638846i	$0.779412\pi$
$458$	−8.40283	−0.392639
$459$	−7.56556	−0.353130
$460$	−2.79997	−0.130549
$461$	27.7467	1.29229	0.646146	−	0.763214i	$-0.276380\pi$
$461$	27.7467	1.29229	0.646146	+	0.763214i	$0.276380\pi$
$462$	1.89700	0.0882566
$463$	26.4989	1.23151	0.615754	−	0.787939i	$-0.288852\pi$
$463$	26.4989	1.23151	0.615754	+	0.787939i	$0.288852\pi$
$464$	−3.35816	−0.155899
$465$	−36.2804	−1.68246
$466$	3.64576	0.168887
$467$	−24.0208	−1.11155	−0.555774	−	0.831333i	$-0.687578\pi$
$467$	−24.0208	−1.11155	−0.555774	+	0.831333i	$0.687578\pi$
$468$	0.0333292	0.00154064
$469$	−1.78893	−0.0826049
$470$	3.59604	0.165873
$471$	−5.14796	−0.237206
$472$	−12.0452	−0.554427
$473$	−45.0220	−2.07012
$474$	6.69531	0.307526
$475$	−1.57387	−0.0722140
$476$	−0.337702	−0.0154785
$477$	−0.378771	−0.0173427
$478$	19.7338	0.902602
$479$	−21.6839	−0.990763	−0.495381	−	0.868676i	$-0.664972\pi$
$479$	−21.6839	−0.990763	−0.495381	+	0.868676i	$0.664972\pi$
$480$	−4.89901	−0.223608
$481$	−3.18979	−0.145442
$482$	−14.1570	−0.644836
$483$	0.401563	0.0182717
$484$	11.3167	0.514396
$485$	−33.0475	−1.50061
$486$	0.637273	0.0289073
$487$	6.52263	0.295569	0.147784	−	0.989020i	$-0.452786\pi$
$487$	6.52263	0.295569	0.147784	+	0.989020i	$0.452786\pi$
$488$	2.44251	0.110567
$489$	−2.74889	−0.124309
$490$	−19.4523	−0.878765
$491$	35.2804	1.59218	0.796092	−	0.605176i	$-0.206897\pi$
$491$	35.2804	1.59218	0.796092	+	0.605176i	$0.206897\pi$
$492$	6.83379	0.308091
$493$	4.94124	0.222542
$494$	−0.301176	−0.0135505
$495$	−0.811240	−0.0364625
$496$	7.40566	0.332524
$497$	2.15507	0.0966682
$498$	1.66124	0.0744418
$499$	−27.9402	−1.25077	−0.625387	−	0.780315i	$-0.715059\pi$
$499$	−27.9402	−1.25077	−0.625387	+	0.780315i	$0.715059\pi$
$500$	−6.04843	−0.270494
$501$	−20.9450	−0.935753
$502$	−16.4965	−0.736276
$503$	33.0892	1.47537	0.737687	−	0.675143i	$-0.235918\pi$
$503$	33.0892	1.47537	0.737687	+	0.675143i	$0.235918\pi$
$504$	0.0140760	0.000626995 0
$505$	−12.5949	−0.560464
$506$	4.72406	0.210010
$507$	22.2290	0.987223
$508$	−9.77050	−0.433496
$509$	33.6070	1.48960	0.744801	−	0.667287i	$-0.232544\pi$
$509$	33.6070	1.48960	0.744801	+	0.667287i	$0.232544\pi$
$510$	7.20847	0.319197
$511$	−3.07128	−0.135866
$512$	1.00000	0.0441942
$513$	−2.84959	−0.125813
$514$	−28.5305	−1.25843
$515$	−11.3794	−0.501435
$516$	−16.6750	−0.734075
$517$	−6.06717	−0.266834
$518$	−1.34715	−0.0591905
$519$	15.0801	0.661944
$520$	1.52159	0.0667260
$521$	31.6373	1.38606	0.693028	−	0.720910i	$-0.256276\pi$
$521$	31.6373	1.38606	0.693028	+	0.720910i	$0.256276\pi$
$522$	−0.205960	−0.00901461
$523$	−12.6170	−0.551701	−0.275851	−	0.961201i	$-0.588959\pi$
$523$	−12.6170	−0.551701	−0.275851	+	0.961201i	$0.588959\pi$
$524$	1.00000	0.0436852
$525$	−1.14037	−0.0497697
$526$	−11.7502	−0.512332
$527$	−10.8968	−0.474672
$528$	8.26552	0.359711
$529$	1.00000	0.0434783
$530$	−17.2922	−0.751123
$531$	−0.738748	−0.0320589
$532$	−0.127196	−0.00551466
$533$	−2.12251	−0.0919362
$534$	−13.5458	−0.586184
$535$	7.61511	0.329230
$536$	−7.79461	−0.336676
$537$	−17.5534	−0.757486
$538$	13.3575	0.575881
$539$	32.8196	1.41364
$540$	14.3966	0.619530
$541$	32.4360	1.39453	0.697266	−	0.716813i	$-0.254400\pi$
$541$	32.4360	1.39453	0.697266	+	0.716813i	$0.254400\pi$
$542$	23.4352	1.00663
$543$	31.5145	1.35242
$544$	−1.47141	−0.0630864
$545$	−9.90359	−0.424223
$546$	−0.218221	−0.00933900
$547$	−29.1856	−1.24789	−0.623943	−	0.781470i	$-0.714470\pi$
$547$	−29.1856	−1.24789	−0.623943	+	0.781470i	$0.714470\pi$
$548$	−8.76297	−0.374336
$549$	0.149802	0.00639340
$550$	−13.4155	−0.572038
$551$	1.86114	0.0792871
$552$	1.74967	0.0744707
$553$	−0.878241	−0.0373466
$554$	−9.40263	−0.399479
$555$	28.7559	1.22062
$556$	−10.6309	−0.450851
$557$	−4.26190	−0.180582	−0.0902912	−	0.995915i	$-0.528780\pi$
$557$	−4.26190	−0.180582	−0.0902912	+	0.995915i	$0.528780\pi$
$558$	0.454197	0.0192277
$559$	5.17909	0.219052
$560$	0.642615	0.0271555
$561$	−12.1620	−0.513480
$562$	17.7885	0.750361
$563$	−11.8749	−0.500468	−0.250234	−	0.968185i	$-0.580507\pi$
$563$	−11.8749	−0.500468	−0.250234	+	0.968185i	$0.580507\pi$
$564$	−2.24712	−0.0946208
$565$	−20.0135	−0.841973
$566$	21.9421	0.922297
$567$	−2.10694	−0.0884831
$568$	9.38996	0.393994
$569$	26.9618	1.13030	0.565148	−	0.824989i	$-0.308819\pi$
$569$	26.9618	1.13030	0.565148	+	0.824989i	$0.308819\pi$
$570$	2.71510	0.113723
$571$	−16.3748	−0.685262	−0.342631	−	0.939470i	$-0.611318\pi$
$571$	−16.3748	−0.685262	−0.342631	+	0.939470i	$0.611318\pi$
$572$	−2.56719	−0.107340
$573$	15.3693	0.642061
$574$	−0.896406	−0.0374153
$575$	−2.83982	−0.118429
$576$	0.0613311	0.00255546
$577$	11.2862	0.469849	0.234925	−	0.972014i	$-0.424516\pi$
$577$	11.2862	0.469849	0.234925	+	0.972014i	$0.424516\pi$
$578$	−14.8349	−0.617052
$579$	−24.4923	−1.01786
$580$	−9.40274	−0.390428
$581$	−0.217909	−0.00904038
$582$	20.6510	0.856012
$583$	29.1750	1.20831
$584$	−13.3820	−0.553752
$585$	0.0933206	0.00385833
$586$	−10.0251	−0.414131
$587$	−14.0160	−0.578501	−0.289251	−	0.957253i	$-0.593406\pi$
$587$	−14.0160	−0.578501	−0.289251	+	0.957253i	$0.593406\pi$
$588$	12.1555	0.501284
$589$	−4.10431	−0.169115
$590$	−33.7263	−1.38849
$591$	−37.0474	−1.52393
$592$	−5.86974	−0.241245
$593$	37.6251	1.54508	0.772539	−	0.634968i	$-0.218987\pi$
$593$	37.6251	1.54508	0.772539	+	0.634968i	$0.218987\pi$
$594$	−24.2896	−0.996616
$595$	−0.945554	−0.0387639
$596$	19.6942	0.806705
$597$	30.3786	1.24331
$598$	−0.543430	−0.0222225
$599$	−7.34978	−0.300304	−0.150152	−	0.988663i	$-0.547976\pi$
$599$	−7.34978	−0.300304	−0.150152	+	0.988663i	$0.547976\pi$
$600$	−4.96874	−0.202848
$601$	−21.9428	−0.895065	−0.447533	−	0.894268i	$-0.647697\pi$
$601$	−21.9428	−0.895065	−0.447533	+	0.894268i	$0.647697\pi$
$602$	2.18730	0.0891476
$603$	−0.478052	−0.0194678
$604$	−0.961897	−0.0391390
$605$	31.6864	1.28824
$606$	7.87037	0.319712
$607$	23.6163	0.958557	0.479279	−	0.877663i	$-0.340898\pi$
$607$	23.6163	0.958557	0.479279	+	0.877663i	$0.340898\pi$
$608$	−0.554213	−0.0224763
$609$	1.34851	0.0546444
$610$	6.83896	0.276901
$611$	0.697934	0.0282354
$612$	−0.0902435	−0.00364788
$613$	5.12360	0.206940	0.103470	−	0.994633i	$-0.467005\pi$
$613$	5.12360	0.206940	0.103470	+	0.994633i	$0.467005\pi$
$614$	−10.4824	−0.423035
$615$	19.1344	0.771574
$616$	−1.08421	−0.0436840
$617$	23.6900	0.953723	0.476861	−	0.878978i	$-0.341774\pi$
$617$	23.6900	0.953723	0.476861	+	0.878978i	$0.341774\pi$
$618$	7.11083	0.286040
$619$	−16.9681	−0.682007	−0.341003	−	0.940062i	$-0.610767\pi$
$619$	−16.9681	−0.682007	−0.341003	+	0.940062i	$0.610767\pi$
$620$	20.7356	0.832762
$621$	−5.14169	−0.206329
$622$	−33.8626	−1.35777
$623$	1.77684	0.0711875
$624$	−0.950820	−0.0380633
$625$	−31.1345	−1.24538
$626$	0.286893	0.0114666
$627$	−4.58086	−0.182942
$628$	2.94226	0.117409
$629$	8.63682	0.344373
$630$	0.0394123	0.00157023
$631$	0.169126	0.00673279	0.00336639	−	0.999994i	$-0.498928\pi$
$631$	0.169126	0.00673279	0.00336639	+	0.999994i	$0.498928\pi$
$632$	−3.82662	−0.152215
$633$	2.02062	0.0803124
$634$	−22.6361	−0.898994
$635$	−27.3571	−1.08563
$636$	10.8057	0.428472
$637$	−3.77538	−0.149586
$638$	15.8641	0.628067
$639$	0.575897	0.0227821
$640$	2.79997	0.110678
$641$	−4.91026	−0.193944	−0.0969718	−	0.995287i	$-0.530916\pi$
$641$	−4.91026	−0.193944	−0.0969718	+	0.995287i	$0.530916\pi$
$642$	−4.75859	−0.187807
$643$	15.7477	0.621031	0.310515	−	0.950568i	$-0.399498\pi$
$643$	15.7477	0.621031	0.310515	+	0.950568i	$0.399498\pi$
$644$	−0.229508	−0.00904389
$645$	−46.6894	−1.83839
$646$	0.815477	0.0320845
$647$	−40.4714	−1.59109	−0.795547	−	0.605893i	$-0.792816\pi$
$647$	−40.4714	−1.59109	−0.795547	+	0.605893i	$0.792816\pi$
$648$	−9.18023	−0.360634
$649$	56.9024	2.23361
$650$	1.54324	0.0605310
$651$	−2.97383	−0.116554
$652$	1.57110	0.0615289
$653$	16.5225	0.646576	0.323288	−	0.946301i	$-0.395212\pi$
$653$	16.5225	0.646576	0.323288	+	0.946301i	$0.395212\pi$
$654$	6.18863	0.241995
$655$	2.79997	0.109404
$656$	−3.90577	−0.152495
$657$	−0.820735	−0.0320199
$658$	0.294760	0.0114910
$659$	13.3654	0.520643	0.260322	−	0.965522i	$-0.416171\pi$
$659$	13.3654	0.520643	0.260322	+	0.965522i	$0.416171\pi$
$660$	23.1432	0.900848
$661$	50.7921	1.97558	0.987791	−	0.155784i	$-0.0497905\pi$
$661$	50.7921	1.97558	0.987791	+	0.155784i	$0.0497905\pi$
$662$	26.9839	1.04876
$663$	1.39905	0.0543346
$664$	−0.949460	−0.0368462
$665$	−0.356146	−0.0138107
$666$	−0.359998	−0.0139496
$667$	3.35816	0.130028
$668$	11.9708	0.463166
$669$	−2.33995	−0.0904675
$670$	−21.8247	−0.843160
$671$	−11.5386	−0.445441
$672$	−0.401563	−0.0154906
$673$	−5.33403	−0.205612	−0.102806	−	0.994701i	$-0.532782\pi$
$673$	−5.33403	−0.205612	−0.102806	+	0.994701i	$0.532782\pi$
$674$	4.95950	0.191033
$675$	14.6015	0.562011
$676$	−12.7047	−0.488642
$677$	−12.2923	−0.472431	−0.236215	−	0.971701i	$-0.575907\pi$
$677$	−12.2923	−0.472431	−0.236215	+	0.971701i	$0.575907\pi$
$678$	12.5062	0.480296
$679$	−2.70885	−0.103956
$680$	−4.11991	−0.157992
$681$	−39.0956	−1.49815
$682$	−34.9847	−1.33963
$683$	−16.9844	−0.649892	−0.324946	−	0.945733i	$-0.605346\pi$
$683$	−16.9844	−0.649892	−0.324946	+	0.945733i	$0.605346\pi$
$684$	−0.0339905	−0.00129966
$685$	−24.5361	−0.937474
$686$	−3.20102	−0.122216
$687$	14.7022	0.560922
$688$	9.53038	0.363342
$689$	−3.35613	−0.127859
$690$	4.89901	0.186502
$691$	−28.8303	−1.09676	−0.548378	−	0.836231i	$-0.684754\pi$
$691$	−28.8303	−1.09676	−0.548378	+	0.836231i	$0.684754\pi$
$692$	−8.61885	−0.327640
$693$	−0.0664958	−0.00252597
$694$	3.03429	0.115180
$695$	−29.7662	−1.12910
$696$	5.87566	0.222716
$697$	5.74701	0.217683
$698$	8.02878	0.303894
$699$	−6.37887	−0.241271
$700$	0.651762	0.0246343
$701$	−28.3251	−1.06982	−0.534911	−	0.844908i	$-0.679655\pi$
$701$	−28.3251	−1.06982	−0.534911	+	0.844908i	$0.679655\pi$
$702$	2.79415	0.105458
$703$	3.25309	0.122693
$704$	−4.72406	−0.178045
$705$	−6.29186	−0.236965
$706$	9.08138	0.341782
$707$	−1.03238	−0.0388265
$708$	21.0751	0.792053
$709$	40.1575	1.50815	0.754074	−	0.656790i	$-0.228086\pi$
$709$	40.1575	1.50815	0.754074	+	0.656790i	$0.228086\pi$
$710$	26.2916	0.986706
$711$	−0.234691	−0.00880161
$712$	7.74194	0.290141
$713$	−7.40566	−0.277344
$714$	0.590865	0.0221126
$715$	−7.18806	−0.268818
$716$	10.0324	0.374930
$717$	−34.5275	−1.28945
$718$	8.02576	0.299519
$719$	36.0573	1.34471	0.672355	−	0.740229i	$-0.265283\pi$
$719$	36.0573	1.34471	0.672355	+	0.740229i	$0.265283\pi$
$720$	0.171725	0.00639982
$721$	−0.932746	−0.0347373
$722$	−18.6928	−0.695676
$723$	24.7701	0.921210
$724$	−18.0117	−0.669401
$725$	−9.53658	−0.354180
$726$	−19.8005	−0.734864
$727$	29.3000	1.08668	0.543338	−	0.839514i	$-0.317160\pi$
$727$	29.3000	1.08668	0.543338	+	0.839514i	$0.317160\pi$
$728$	0.124722	0.00462249
$729$	26.4257	0.978729
$730$	−37.4692	−1.38680
$731$	−14.0231	−0.518664
$732$	−4.27358	−0.157956
$733$	1.71650	0.0634004	0.0317002	−	0.999497i	$-0.489908\pi$
$733$	1.71650	0.0634004	0.0317002	+	0.999497i	$0.489908\pi$
$734$	−14.0536	−0.518728
$735$	34.0350	1.25540
$736$	−1.00000	−0.0368605
$737$	36.8222	1.35636
$738$	−0.239545	−0.00881779
$739$	−6.08160	−0.223715	−0.111858	−	0.993724i	$-0.535680\pi$
$739$	−6.08160	−0.223715	−0.111858	+	0.993724i	$0.535680\pi$
$740$	−16.4351	−0.604166
$741$	0.526957	0.0193583
$742$	−1.41741	−0.0520346
$743$	−8.49315	−0.311583	−0.155792	−	0.987790i	$-0.549793\pi$
$743$	−8.49315	−0.311583	−0.155792	+	0.987790i	$0.549793\pi$
$744$	−12.9574	−0.475042
$745$	55.1431	2.02029
$746$	−29.4771	−1.07923
$747$	−0.0582315	−0.00213058
$748$	6.95105	0.254155
$749$	0.624196	0.0228076
$750$	10.5827	0.386427
$751$	−2.41960	−0.0882923	−0.0441461	−	0.999025i	$-0.514057\pi$
$751$	−2.41960	−0.0882923	−0.0441461	+	0.999025i	$0.514057\pi$
$752$	1.28431	0.0468341
$753$	28.8634	1.05184
$754$	−1.82492	−0.0664598
$755$	−2.69328	−0.0980185
$756$	1.18006	0.0429183
$757$	21.1105	0.767273	0.383637	−	0.923484i	$-0.374672\pi$
$757$	21.1105	0.767273	0.383637	+	0.923484i	$0.374672\pi$
$758$	8.10696	0.294458
$759$	−8.26552	−0.300019
$760$	−1.55178	−0.0562890
$761$	42.2582	1.53186	0.765930	−	0.642924i	$-0.222279\pi$
$761$	42.2582	1.53186	0.765930	+	0.642924i	$0.222279\pi$
$762$	17.0951	0.619291
$763$	−0.811778	−0.0293884
$764$	−8.78412	−0.317798
$765$	−0.252679	−0.00913563
$766$	8.05853	0.291167
$767$	−6.54574	−0.236353
$768$	−1.74967	−0.0631356
$769$	−18.2867	−0.659434	−0.329717	−	0.944080i	$-0.606953\pi$
$769$	−18.2867	−0.659434	−0.329717	+	0.944080i	$0.606953\pi$
$770$	−3.03575	−0.109401
$771$	49.9189	1.79778
$772$	13.9982	0.503808
$773$	43.3885	1.56058	0.780288	−	0.625420i	$-0.215072\pi$
$773$	43.3885	1.56058	0.780288	+	0.625420i	$0.215072\pi$
$774$	0.584509	0.0210097
$775$	21.0308	0.755447
$776$	−11.8028	−0.423697
$777$	2.35707	0.0845594
$778$	−34.4103	−1.23367
$779$	2.16463	0.0775559
$780$	−2.66227	−0.0953245
$781$	−44.3587	−1.58728
$782$	1.47141	0.0526177
$783$	−17.2666	−0.617058
$784$	−6.94733	−0.248119
$785$	8.23822	0.294035
$786$	−1.74967	−0.0624085
$787$	49.5830	1.76744	0.883722	−	0.468013i	$-0.155030\pi$
$787$	49.5830	1.76744	0.883722	+	0.468013i	$0.155030\pi$
$788$	21.1740	0.754291
$789$	20.5589	0.731915
$790$	−10.7144	−0.381202
$791$	−1.64047	−0.0583282
$792$	−0.289732	−0.0102952
$793$	1.32733	0.0471350
$794$	−11.1833	−0.396881
$795$	30.2555	1.07305
$796$	−17.3625	−0.615398
$797$	29.5569	1.04696	0.523480	−	0.852038i	$-0.324634\pi$
$797$	29.5569	1.04696	0.523480	+	0.852038i	$0.324634\pi$
$798$	0.222551	0.00787823
$799$	−1.88976	−0.0668548
$800$	2.83982	0.100403
$801$	0.474822	0.0167770
$802$	6.13666	0.216693
$803$	63.2174	2.23089
$804$	13.6380	0.480974
$805$	−0.642615	−0.0226492
$806$	4.02445	0.141755
$807$	−23.3711	−0.822702
$808$	−4.49821	−0.158247
$809$	−20.8493	−0.733022	−0.366511	−	0.930414i	$-0.619448\pi$
$809$	−20.8493	−0.733022	−0.366511	+	0.930414i	$0.619448\pi$
$810$	−25.7044	−0.903159
$811$	15.4366	0.542054	0.271027	−	0.962572i	$-0.412637\pi$
$811$	15.4366	0.542054	0.271027	+	0.962572i	$0.412637\pi$
$812$	−0.770725	−0.0270471
$813$	−41.0038	−1.43807
$814$	27.7290	0.971901
$815$	4.39902	0.154091
$816$	2.57448	0.0901250
$817$	−5.28186	−0.184789
$818$	−18.4453	−0.644925
$819$	0.00764931	0.000267289 0
$820$	−10.9360	−0.381903
$821$	30.1638	1.05272	0.526362	−	0.850261i	$-0.323556\pi$
$821$	30.1638	1.05272	0.526362	+	0.850261i	$0.323556\pi$
$822$	15.3323	0.534775
$823$	13.7395	0.478930	0.239465	−	0.970905i	$-0.423028\pi$
$823$	13.7395	0.478930	0.239465	+	0.970905i	$0.423028\pi$
$824$	−4.06411	−0.141580
$825$	23.4726	0.817212
$826$	−2.76448	−0.0961886
$827$	−15.7007	−0.545965	−0.272983	−	0.962019i	$-0.588010\pi$
$827$	−15.7007	−0.545965	−0.272983	+	0.962019i	$0.588010\pi$
$828$	−0.0613311	−0.00213140
$829$	−8.56332	−0.297416	−0.148708	−	0.988881i	$-0.547512\pi$
$829$	−8.56332	−0.297416	−0.148708	+	0.988881i	$0.547512\pi$
$830$	−2.65846	−0.0922764
$831$	16.4515	0.570695
$832$	0.543430	0.0188400
$833$	10.2224	0.354185
$834$	18.6005	0.644084
$835$	33.5180	1.15994
$836$	2.61813	0.0905501
$837$	38.0776	1.31615
$838$	9.21453	0.318311
$839$	37.5163	1.29521	0.647604	−	0.761977i	$-0.275771\pi$
$839$	37.5163	1.29521	0.647604	+	0.761977i	$0.275771\pi$
$840$	−1.12436	−0.0387942
$841$	−17.7228	−0.611130
$842$	1.26204	0.0434928
$843$	−31.1239	−1.07196
$844$	−1.15486	−0.0397519
$845$	−35.5727	−1.22374
$846$	0.0787684	0.00270811
$847$	2.59728	0.0892435
$848$	−6.17584	−0.212079
$849$	−38.3914	−1.31759
$850$	−4.17856	−0.143323
$851$	5.86974	0.201212
$852$	−16.4293	−0.562858
$853$	19.8272	0.678869	0.339435	−	0.940630i	$-0.389764\pi$
$853$	19.8272	0.678869	0.339435	+	0.940630i	$0.389764\pi$
$854$	0.560576	0.0191825
$855$	−0.0951724	−0.00325483
$856$	2.71971	0.0929579
$857$	−5.75936	−0.196736	−0.0983680	−	0.995150i	$-0.531362\pi$
$857$	−5.75936	−0.196736	−0.0983680	+	0.995150i	$0.531362\pi$
$858$	4.49173	0.153345
$859$	−47.3341	−1.61502	−0.807509	−	0.589855i	$-0.799185\pi$
$859$	−47.3341	−1.61502	−0.807509	+	0.589855i	$0.799185\pi$
$860$	26.6848	0.909943
$861$	1.56841	0.0534513
$862$	−5.01604	−0.170847
$863$	2.40298	0.0817985	0.0408993	−	0.999163i	$-0.486978\pi$
$863$	2.40298	0.0817985	0.0408993	+	0.999163i	$0.486978\pi$
$864$	5.14169	0.174924
$865$	−24.1325	−0.820530
$866$	−2.42539	−0.0824181
$867$	25.9562	0.881518
$868$	1.69966	0.0576902
$869$	18.0772	0.613227
$870$	16.4517	0.557763
$871$	−4.23582	−0.143525
$872$	−3.53704	−0.119779
$873$	−0.723881	−0.0244997
$874$	0.554213	0.0187465
$875$	−1.38816	−0.0469285
$876$	23.4141	0.791088
$877$	28.1434	0.950335	0.475168	−	0.879895i	$-0.342387\pi$
$877$	28.1434	0.950335	0.475168	+	0.879895i	$0.342387\pi$
$878$	−10.2666	−0.346482
$879$	17.5405	0.591626
$880$	−13.2272	−0.445889
$881$	−38.5135	−1.29755	−0.648777	−	0.760979i	$-0.724719\pi$
$881$	−38.5135	−1.29755	−0.648777	+	0.760979i	$0.724719\pi$
$882$	−0.426087	−0.0143471
$883$	3.91217	0.131655	0.0658275	−	0.997831i	$-0.479031\pi$
$883$	3.91217	0.131655	0.0658275	+	0.997831i	$0.479031\pi$
$884$	−0.799610	−0.0268938
$885$	59.0097	1.98359
$886$	−27.9110	−0.937687
$887$	−23.7978	−0.799051	−0.399525	−	0.916722i	$-0.630825\pi$
$887$	−23.7978	−0.799051	−0.399525	+	0.916722i	$0.630825\pi$
$888$	10.2701	0.344642
$889$	−2.24241	−0.0752080
$890$	21.6772	0.726621
$891$	43.3679	1.45288
$892$	1.33737	0.0447784
$893$	−0.711783	−0.0238189
$894$	−34.4582	−1.15246
$895$	28.0905	0.938962
$896$	0.229508	0.00766733
$897$	0.950820	0.0317470
$898$	23.8361	0.795422
$899$	−24.8694	−0.829440
$900$	0.174170	0.00580565
$901$	9.08722	0.302739
$902$	18.4511	0.614354
$903$	−3.82704	−0.127356
$904$	−7.14774	−0.237730
$905$	−50.4323	−1.67643
$906$	1.68300	0.0559139
$907$	−2.62759	−0.0872476	−0.0436238	−	0.999048i	$-0.513890\pi$
$907$	−2.62759	−0.0872476	−0.0436238	+	0.999048i	$0.513890\pi$
$908$	22.3446	0.741531
$909$	−0.275881	−0.00915038
$910$	0.349216	0.0115764
$911$	−49.1657	−1.62893	−0.814466	−	0.580211i	$-0.802970\pi$
$911$	−49.1657	−1.62893	−0.814466	+	0.580211i	$0.802970\pi$
$912$	0.969688	0.0321096
$913$	4.48530	0.148442
$914$	−32.8930	−1.08800
$915$	−11.9659	−0.395580
$916$	−8.40283	−0.277637
$917$	0.229508	0.00757903
$918$	−7.56556	−0.249701
$919$	−15.1930	−0.501170	−0.250585	−	0.968095i	$-0.580623\pi$
$919$	−15.1930	−0.501170	−0.250585	+	0.968095i	$0.580623\pi$
$920$	−2.79997	−0.0923122
$921$	18.3407	0.604346
$922$	27.7467	0.913788
$923$	5.10278	0.167960
$924$	1.89700	0.0624069
$925$	−16.6690	−0.548074
$926$	26.4989	0.870807
$927$	−0.249257	−0.00818666
$928$	−3.35816	−0.110237
$929$	−0.504495	−0.0165519	−0.00827596	−	0.999966i	$-0.502634\pi$
$929$	−0.504495	−0.0165519	−0.00827596	+	0.999966i	$0.502634\pi$
$930$	−36.2804	−1.18968
$931$	3.85030	0.126188
$932$	3.64576	0.119421
$933$	59.2483	1.93970
$934$	−24.0208	−0.785984
$935$	19.4627	0.636499
$936$	0.0333292	0.00108940
$937$	−20.7479	−0.677804	−0.338902	−	0.940822i	$-0.610055\pi$
$937$	−20.7479	−0.677804	−0.338902	+	0.940822i	$0.610055\pi$
$938$	−1.78893	−0.0584105
$939$	−0.501967	−0.0163811
$940$	3.59604	0.117290
$941$	−19.8032	−0.645564	−0.322782	−	0.946473i	$-0.604618\pi$
$941$	−19.8032	−0.645564	−0.322782	+	0.946473i	$0.604618\pi$
$942$	−5.14796	−0.167730
$943$	3.90577	0.127189
$944$	−12.0452	−0.392039
$945$	3.30413	0.107483
$946$	−45.0220	−1.46379
$947$	−40.6925	−1.32233	−0.661165	−	0.750240i	$-0.729938\pi$
$947$	−40.6925	−1.32233	−0.661165	+	0.750240i	$0.729938\pi$
$948$	6.69531	0.217454
$949$	−7.27219	−0.236065
$950$	−1.57387	−0.0510630
$951$	39.6056	1.28430
$952$	−0.337702	−0.0109450
$953$	15.1965	0.492262	0.246131	−	0.969237i	$-0.420841\pi$
$953$	15.1965	0.492262	0.246131	+	0.969237i	$0.420841\pi$
$954$	−0.378771	−0.0122632
$955$	−24.5953	−0.795884
$956$	19.7338	0.638236
$957$	−27.7569	−0.897254
$958$	−21.6839	−0.700575
$959$	−2.01117	−0.0649442
$960$	−4.89901	−0.158115
$961$	23.8438	0.769153
$962$	−3.18979	−0.102843
$963$	0.166803	0.00537516
$964$	−14.1570	−0.455968
$965$	39.1946	1.26172
$966$	0.401563	0.0129201
$967$	−7.47802	−0.240477	−0.120238	−	0.992745i	$-0.538366\pi$
$967$	−7.47802	−0.240477	−0.120238	+	0.992745i	$0.538366\pi$
$968$	11.3167	0.363733
$969$	−1.42681	−0.0458358
$970$	−33.0475	−1.06109
$971$	−10.1238	−0.324887	−0.162443	−	0.986718i	$-0.551938\pi$
$971$	−10.1238	−0.324887	−0.162443	+	0.986718i	$0.551938\pi$
$972$	0.637273	0.0204405
$973$	−2.43988	−0.0782190
$974$	6.52263	0.208999
$975$	−2.70016	−0.0864744
$976$	2.44251	0.0781829
$977$	−27.5003	−0.879812	−0.439906	−	0.898044i	$-0.644988\pi$
$977$	−27.5003	−0.879812	−0.439906	+	0.898044i	$0.644988\pi$
$978$	−2.74889	−0.0879000
$979$	−36.5734	−1.16889
$980$	−19.4523	−0.621381
$981$	−0.216930	−0.00692606
$982$	35.2804	1.12584
$983$	31.0867	0.991512	0.495756	−	0.868462i	$-0.334891\pi$
$983$	31.0867	0.991512	0.495756	+	0.868462i	$0.334891\pi$
$984$	6.83379	0.217853
$985$	59.2864	1.88902
$986$	4.94124	0.157361
$987$	−0.515732	−0.0164159
$988$	−0.301176	−0.00958168
$989$	−9.53038	−0.303048
$990$	−0.811240	−0.0257829
$991$	30.7674	0.977358	0.488679	−	0.872464i	$-0.337479\pi$
$991$	30.7674	0.977358	0.488679	+	0.872464i	$0.337479\pi$
$992$	7.40566	0.235130
$993$	−47.2129	−1.49826
$994$	2.15507	0.0683547
$995$	−48.6145	−1.54118
$996$	1.66124	0.0526383
$997$	−0.0142736	−0.000452049 0	−0.000226025	−	1.00000i	$-0.500072\pi$
$997$	−0.0142736	−0.000452049 0	−0.000226025		1.00000i	$0.500072\pi$
$998$	−27.9402	−0.884430
$999$	−30.1804	−0.954865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.g.1.5	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.g.1.5	✓	21	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.74967 q^{3} +1.00000 q^{4} +2.79997 q^{5} -1.74967 q^{6} +0.229508 q^{7} +1.00000 q^{8} +0.0613311 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.74967 q^{3} +1.00000 q^{4} +2.79997 q^{5} -1.74967 q^{6} +0.229508 q^{7} +1.00000 q^{8} +0.0613311 q^{9} +2.79997 q^{10} -4.72406 q^{11} -1.74967 q^{12} +0.543430 q^{13} +0.229508 q^{14} -4.89901 q^{15} +1.00000 q^{16} -1.47141 q^{17} +0.0613311 q^{18} -0.554213 q^{19} +2.79997 q^{20} -0.401563 q^{21} -4.72406 q^{22} -1.00000 q^{23} -1.74967 q^{24} +2.83982 q^{25} +0.543430 q^{26} +5.14169 q^{27} +0.229508 q^{28} -3.35816 q^{29} -4.89901 q^{30} +7.40566 q^{31} +1.00000 q^{32} +8.26552 q^{33} -1.47141 q^{34} +0.642615 q^{35} +0.0613311 q^{36} -5.86974 q^{37} -0.554213 q^{38} -0.950820 q^{39} +2.79997 q^{40} -3.90577 q^{41} -0.401563 q^{42} +9.53038 q^{43} -4.72406 q^{44} +0.171725 q^{45} -1.00000 q^{46} +1.28431 q^{47} -1.74967 q^{48} -6.94733 q^{49} +2.83982 q^{50} +2.57448 q^{51} +0.543430 q^{52} -6.17584 q^{53} +5.14169 q^{54} -13.2272 q^{55} +0.229508 q^{56} +0.969688 q^{57} -3.35816 q^{58} -12.0452 q^{59} -4.89901 q^{60} +2.44251 q^{61} +7.40566 q^{62} +0.0140760 q^{63} +1.00000 q^{64} +1.52159 q^{65} +8.26552 q^{66} -7.79461 q^{67} -1.47141 q^{68} +1.74967 q^{69} +0.642615 q^{70} +9.38996 q^{71} +0.0613311 q^{72} -13.3820 q^{73} -5.86974 q^{74} -4.96874 q^{75} -0.554213 q^{76} -1.08421 q^{77} -0.950820 q^{78} -3.82662 q^{79} +2.79997 q^{80} -9.18023 q^{81} -3.90577 q^{82} -0.949460 q^{83} -0.401563 q^{84} -4.11991 q^{85} +9.53038 q^{86} +5.87566 q^{87} -4.72406 q^{88} +7.74194 q^{89} +0.171725 q^{90} +0.124722 q^{91} -1.00000 q^{92} -12.9574 q^{93} +1.28431 q^{94} -1.55178 q^{95} -1.74967 q^{96} -11.8028 q^{97} -6.94733 q^{98} -0.289732 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * q^99

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