LMFDB - Embedded newform 6034.2.a.p.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.222181 q^{3} +1.00000 q^{4} +0.181430 q^{5} +0.222181 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.95064 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.222181 q^{3} +1.00000 q^{4} +0.181430 q^{5} +0.222181 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.95064 q^{9} -0.181430 q^{10} -1.69115 q^{11} -0.222181 q^{12} -0.764574 q^{13} -1.00000 q^{14} -0.0403104 q^{15} +1.00000 q^{16} -3.26296 q^{17} +2.95064 q^{18} -0.180812 q^{19} +0.181430 q^{20} -0.222181 q^{21} +1.69115 q^{22} -9.07368 q^{23} +0.222181 q^{24} -4.96708 q^{25} +0.764574 q^{26} +1.32212 q^{27} +1.00000 q^{28} +2.26843 q^{29} +0.0403104 q^{30} +6.23761 q^{31} -1.00000 q^{32} +0.375742 q^{33} +3.26296 q^{34} +0.181430 q^{35} -2.95064 q^{36} -6.61975 q^{37} +0.180812 q^{38} +0.169874 q^{39} -0.181430 q^{40} +9.18400 q^{41} +0.222181 q^{42} -10.7521 q^{43} -1.69115 q^{44} -0.535335 q^{45} +9.07368 q^{46} +0.872479 q^{47} -0.222181 q^{48} +1.00000 q^{49} +4.96708 q^{50} +0.724968 q^{51} -0.764574 q^{52} +4.44835 q^{53} -1.32212 q^{54} -0.306826 q^{55} -1.00000 q^{56} +0.0401730 q^{57} -2.26843 q^{58} +8.43820 q^{59} -0.0403104 q^{60} -1.44890 q^{61} -6.23761 q^{62} -2.95064 q^{63} +1.00000 q^{64} -0.138717 q^{65} -0.375742 q^{66} -6.30903 q^{67} -3.26296 q^{68} +2.01600 q^{69} -0.181430 q^{70} +3.51206 q^{71} +2.95064 q^{72} -0.619658 q^{73} +6.61975 q^{74} +1.10359 q^{75} -0.180812 q^{76} -1.69115 q^{77} -0.169874 q^{78} +8.64934 q^{79} +0.181430 q^{80} +8.55816 q^{81} -9.18400 q^{82} +12.5383 q^{83} -0.222181 q^{84} -0.591999 q^{85} +10.7521 q^{86} -0.504003 q^{87} +1.69115 q^{88} -0.954562 q^{89} +0.535335 q^{90} -0.764574 q^{91} -9.07368 q^{92} -1.38588 q^{93} -0.872479 q^{94} -0.0328047 q^{95} +0.222181 q^{96} +11.6487 q^{97} -1.00000 q^{98} +4.98997 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * 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
$3$	−0.222181	−0.128276	−0.0641382	−	0.997941i	$-0.520430\pi$
$3$	−0.222181	−0.128276	−0.0641382	+	0.997941i	$0.520430\pi$
$4$	1.00000	0.500000
$5$	0.181430	0.0811381	0.0405690	−	0.999177i	$-0.487083\pi$
$5$	0.181430	0.0811381	0.0405690	+	0.999177i	$0.487083\pi$
$6$	0.222181	0.0907050
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.95064	−0.983545
$10$	−0.181430	−0.0573733
$11$	−1.69115	−0.509901	−0.254951	−	0.966954i	$-0.582059\pi$
$11$	−1.69115	−0.509901	−0.254951	+	0.966954i	$0.582059\pi$
$12$	−0.222181	−0.0641382
$13$	−0.764574	−0.212055	−0.106027	−	0.994363i	$-0.533813\pi$
$13$	−0.764574	−0.212055	−0.106027	+	0.994363i	$0.533813\pi$
$14$	−1.00000	−0.267261
$15$	−0.0403104	−0.0104081
$16$	1.00000	0.250000
$17$	−3.26296	−0.791384	−0.395692	−	0.918383i	$-0.629495\pi$
$17$	−3.26296	−0.791384	−0.395692	+	0.918383i	$0.629495\pi$
$18$	2.95064	0.695471
$19$	−0.180812	−0.0414811	−0.0207405	−	0.999785i	$-0.506602\pi$
$19$	−0.180812	−0.0414811	−0.0207405	+	0.999785i	$0.506602\pi$
$20$	0.181430	0.0405690
$21$	−0.222181	−0.0484839
$22$	1.69115	0.360555
$23$	−9.07368	−1.89199	−0.945996	−	0.324178i	$-0.894912\pi$
$23$	−9.07368	−1.89199	−0.945996	+	0.324178i	$0.894912\pi$
$24$	0.222181	0.0453525
$25$	−4.96708	−0.993417
$26$	0.764574	0.149945
$27$	1.32212	0.254442
$28$	1.00000	0.188982
$29$	2.26843	0.421238	0.210619	−	0.977568i	$-0.432452\pi$
$29$	2.26843	0.421238	0.210619	+	0.977568i	$0.432452\pi$
$30$	0.0403104	0.00735963
$31$	6.23761	1.12031	0.560154	−	0.828389i	$-0.310742\pi$
$31$	6.23761	1.12031	0.560154	+	0.828389i	$0.310742\pi$
$32$	−1.00000	−0.176777
$33$	0.375742	0.0654083
$34$	3.26296	0.559593
$35$	0.181430	0.0306673
$36$	−2.95064	−0.491773
$37$	−6.61975	−1.08828	−0.544140	−	0.838994i	$-0.683144\pi$
$37$	−6.61975	−1.08828	−0.544140	+	0.838994i	$0.683144\pi$
$38$	0.180812	0.0293316
$39$	0.169874	0.0272016
$40$	−0.181430	−0.0286866
$41$	9.18400	1.43430	0.717150	−	0.696919i	$-0.245446\pi$
$41$	9.18400	1.43430	0.717150	+	0.696919i	$0.245446\pi$
$42$	0.222181	0.0342833
$43$	−10.7521	−1.63968	−0.819842	−	0.572590i	$-0.805939\pi$
$43$	−10.7521	−1.63968	−0.819842	+	0.572590i	$0.805939\pi$
$44$	−1.69115	−0.254951
$45$	−0.535335	−0.0798030
$46$	9.07368	1.33784
$47$	0.872479	0.127264	0.0636321	−	0.997973i	$-0.479732\pi$
$47$	0.872479	0.127264	0.0636321	+	0.997973i	$0.479732\pi$
$48$	−0.222181	−0.0320691
$49$	1.00000	0.142857
$50$	4.96708	0.702452
$51$	0.724968	0.101516
$52$	−0.764574	−0.106027
$53$	4.44835	0.611028	0.305514	−	0.952188i	$-0.401172\pi$
$53$	4.44835	0.611028	0.305514	+	0.952188i	$0.401172\pi$
$54$	−1.32212	−0.179918
$55$	−0.306826	−0.0413724
$56$	−1.00000	−0.133631
$57$	0.0401730	0.00532104
$58$	−2.26843	−0.297860
$59$	8.43820	1.09856	0.549280	−	0.835638i	$-0.314902\pi$
$59$	8.43820	1.09856	0.549280	+	0.835638i	$0.314902\pi$
$60$	−0.0403104	−0.00520405
$61$	−1.44890	−0.185513	−0.0927564	−	0.995689i	$-0.529568\pi$
$61$	−1.44890	−0.185513	−0.0927564	+	0.995689i	$0.529568\pi$
$62$	−6.23761	−0.792177
$63$	−2.95064	−0.371745
$64$	1.00000	0.125000
$65$	−0.138717	−0.0172057
$66$	−0.375742	−0.0462506
$67$	−6.30903	−0.770771	−0.385385	−	0.922756i	$-0.625931\pi$
$67$	−6.30903	−0.770771	−0.385385	+	0.922756i	$0.625931\pi$
$68$	−3.26296	−0.395692
$69$	2.01600	0.242698
$70$	−0.181430	−0.0216851
$71$	3.51206	0.416805	0.208402	−	0.978043i	$-0.433174\pi$
$71$	3.51206	0.416805	0.208402	+	0.978043i	$0.433174\pi$
$72$	2.95064	0.347736
$73$	−0.619658	−0.0725255	−0.0362628	−	0.999342i	$-0.511545\pi$
$73$	−0.619658	−0.0725255	−0.0362628	+	0.999342i	$0.511545\pi$
$74$	6.61975	0.769530
$75$	1.10359	0.127432
$76$	−0.180812	−0.0207405
$77$	−1.69115	−0.192725
$78$	−0.169874	−0.0192344
$79$	8.64934	0.973127	0.486563	−	0.873645i	$-0.338250\pi$
$79$	8.64934	0.973127	0.486563	+	0.873645i	$0.338250\pi$
$80$	0.181430	0.0202845
$81$	8.55816	0.950906
$82$	−9.18400	−1.01420
$83$	12.5383	1.37625	0.688126	−	0.725591i	$-0.258434\pi$
$83$	12.5383	1.37625	0.688126	+	0.725591i	$0.258434\pi$
$84$	−0.222181	−0.0242419
$85$	−0.591999	−0.0642114
$86$	10.7521	1.15943
$87$	−0.504003	−0.0540348
$88$	1.69115	0.180277
$89$	−0.954562	−0.101183	−0.0505917	−	0.998719i	$-0.516111\pi$
$89$	−0.954562	−0.101183	−0.0505917	+	0.998719i	$0.516111\pi$
$90$	0.535335	0.0564292
$91$	−0.764574	−0.0801492
$92$	−9.07368	−0.945996
$93$	−1.38588	−0.143709
$94$	−0.872479	−0.0899893
$95$	−0.0328047	−0.00336570
$96$	0.222181	0.0226763
$97$	11.6487	1.18274	0.591372	−	0.806399i	$-0.298586\pi$
$97$	11.6487	1.18274	0.591372	+	0.806399i	$0.298586\pi$
$98$	−1.00000	−0.101015
$99$	4.98997	0.501511
$100$	−4.96708	−0.496708
$101$	7.60806	0.757030	0.378515	−	0.925595i	$-0.376435\pi$
$101$	7.60806	0.757030	0.378515	+	0.925595i	$0.376435\pi$
$102$	−0.724968	−0.0717825
$103$	−2.29684	−0.226315	−0.113157	−	0.993577i	$-0.536096\pi$
$103$	−2.29684	−0.226315	−0.113157	+	0.993577i	$0.536096\pi$
$104$	0.764574	0.0749727
$105$	−0.0403104	−0.00393389
$106$	−4.44835	−0.432062
$107$	3.11241	0.300888	0.150444	−	0.988619i	$-0.451930\pi$
$107$	3.11241	0.300888	0.150444	+	0.988619i	$0.451930\pi$
$108$	1.32212	0.127221
$109$	7.52106	0.720387	0.360193	−	0.932878i	$-0.382711\pi$
$109$	7.52106	0.720387	0.360193	+	0.932878i	$0.382711\pi$
$110$	0.306826	0.0292547
$111$	1.47078	0.139601
$112$	1.00000	0.0944911
$113$	−12.4522	−1.17141	−0.585703	−	0.810526i	$-0.699182\pi$
$113$	−12.4522	−1.17141	−0.585703	+	0.810526i	$0.699182\pi$
$114$	−0.0401730	−0.00376254
$115$	−1.64624	−0.153513
$116$	2.26843	0.210619
$117$	2.25598	0.208565
$118$	−8.43820	−0.776800
$119$	−3.26296	−0.299115
$120$	0.0403104	0.00367982
$121$	−8.14001	−0.740001
$122$	1.44890	0.131177
$123$	−2.04051	−0.183987
$124$	6.23761	0.560154
$125$	−1.80833	−0.161742
$126$	2.95064	0.262864
$127$	−7.59123	−0.673613	−0.336807	−	0.941574i	$-0.609347\pi$
$127$	−7.59123	−0.673613	−0.336807	+	0.941574i	$0.609347\pi$
$128$	−1.00000	−0.0883883
$129$	2.38892	0.210333
$130$	0.138717	0.0121663
$131$	14.5569	1.27184	0.635921	−	0.771754i	$-0.280620\pi$
$131$	14.5569	1.27184	0.635921	+	0.771754i	$0.280620\pi$
$132$	0.375742	0.0327041
$133$	−0.180812	−0.0156784
$134$	6.30903	0.545017
$135$	0.239872	0.0206449
$136$	3.26296	0.279796
$137$	17.6146	1.50491	0.752457	−	0.658642i	$-0.228869\pi$
$137$	17.6146	1.50491	0.752457	+	0.658642i	$0.228869\pi$
$138$	−2.01600	−0.171613
$139$	12.9671	1.09986	0.549929	−	0.835212i	$-0.314655\pi$
$139$	12.9671	1.09986	0.549929	+	0.835212i	$0.314655\pi$
$140$	0.181430	0.0153337
$141$	−0.193848	−0.0163250
$142$	−3.51206	−0.294725
$143$	1.29301	0.108127
$144$	−2.95064	−0.245886
$145$	0.411563	0.0341784
$146$	0.619658	0.0512833
$147$	−0.222181	−0.0183252
$148$	−6.61975	−0.544140
$149$	8.65495	0.709041	0.354521	−	0.935048i	$-0.384644\pi$
$149$	8.65495	0.709041	0.354521	+	0.935048i	$0.384644\pi$
$150$	−1.10359	−0.0901079
$151$	0.864486	0.0703509	0.0351755	−	0.999381i	$-0.488801\pi$
$151$	0.864486	0.0703509	0.0351755	+	0.999381i	$0.488801\pi$
$152$	0.180812	0.0146658
$153$	9.62780	0.778362
$154$	1.69115	0.136277
$155$	1.13169	0.0908996
$156$	0.169874	0.0136008
$157$	−10.4682	−0.835455	−0.417727	−	0.908572i	$-0.637173\pi$
$157$	−10.4682	−0.835455	−0.417727	+	0.908572i	$0.637173\pi$
$158$	−8.64934	−0.688104
$159$	−0.988340	−0.0783804
$160$	−0.181430	−0.0143433
$161$	−9.07368	−0.715106
$162$	−8.55816	−0.672392
$163$	−21.5570	−1.68847	−0.844237	−	0.535970i	$-0.819946\pi$
$163$	−21.5570	−1.68847	−0.844237	+	0.535970i	$0.819946\pi$
$164$	9.18400	0.717150
$165$	0.0681710	0.00530710
$166$	−12.5383	−0.973157
$167$	11.1046	0.859302	0.429651	−	0.902995i	$-0.358637\pi$
$167$	11.1046	0.859302	0.429651	+	0.902995i	$0.358637\pi$
$168$	0.222181	0.0171416
$169$	−12.4154	−0.955033
$170$	0.591999	0.0454043
$171$	0.533510	0.0407985
$172$	−10.7521	−0.819842
$173$	15.8285	1.20342	0.601709	−	0.798715i	$-0.294487\pi$
$173$	15.8285	1.20342	0.601709	+	0.798715i	$0.294487\pi$
$174$	0.504003	0.0382084
$175$	−4.96708	−0.375476
$176$	−1.69115	−0.127475
$177$	−1.87481	−0.140919
$178$	0.954562	0.0715474
$179$	−15.6984	−1.17336	−0.586678	−	0.809820i	$-0.699565\pi$
$179$	−15.6984	−1.17336	−0.586678	+	0.809820i	$0.699565\pi$
$180$	−0.535335	−0.0399015
$181$	2.21669	0.164765	0.0823827	−	0.996601i	$-0.473747\pi$
$181$	2.21669	0.164765	0.0823827	+	0.996601i	$0.473747\pi$
$182$	0.764574	0.0566740
$183$	0.321919	0.0237969
$184$	9.07368	0.668920
$185$	−1.20102	−0.0883010
$186$	1.38588	0.101618
$187$	5.51816	0.403528
$188$	0.872479	0.0636321
$189$	1.32212	0.0961700
$190$	0.0328047	0.00237991
$191$	9.50153	0.687507	0.343753	−	0.939060i	$-0.388302\pi$
$191$	9.50153	0.687507	0.343753	+	0.939060i	$0.388302\pi$
$192$	−0.222181	−0.0160345
$193$	14.9199	1.07396	0.536980	−	0.843595i	$-0.319565\pi$
$193$	14.9199	1.07396	0.536980	+	0.843595i	$0.319565\pi$
$194$	−11.6487	−0.836327
$195$	0.0308203	0.00220709
$196$	1.00000	0.0714286
$197$	10.0386	0.715224	0.357612	−	0.933870i	$-0.383591\pi$
$197$	10.0386	0.715224	0.357612	+	0.933870i	$0.383591\pi$
$198$	−4.98997	−0.354622
$199$	12.6335	0.895562	0.447781	−	0.894143i	$-0.352214\pi$
$199$	12.6335	0.895562	0.447781	+	0.894143i	$0.352214\pi$
$200$	4.96708	0.351226
$201$	1.40175	0.0988716
$202$	−7.60806	−0.535301
$203$	2.26843	0.159213
$204$	0.724968	0.0507579
$205$	1.66626	0.116376
$206$	2.29684	0.160029
$207$	26.7731	1.86086
$208$	−0.764574	−0.0530137
$209$	0.305780	0.0211513
$210$	0.0403104	0.00278168
$211$	10.0923	0.694780	0.347390	−	0.937721i	$-0.387068\pi$
$211$	10.0923	0.694780	0.347390	+	0.937721i	$0.387068\pi$
$212$	4.44835	0.305514
$213$	−0.780313	−0.0534661
$214$	−3.11241	−0.212760
$215$	−1.95076	−0.133041
$216$	−1.32212	−0.0899588
$217$	6.23761	0.423436
$218$	−7.52106	−0.509390
$219$	0.137676	0.00930330
$220$	−0.306826	−0.0206862
$221$	2.49477	0.167817
$222$	−1.47078	−0.0987125
$223$	−22.5213	−1.50814	−0.754070	−	0.656795i	$-0.771912\pi$
$223$	−22.5213	−1.50814	−0.754070	+	0.656795i	$0.771912\pi$
$224$	−1.00000	−0.0668153
$225$	14.6561	0.977070
$226$	12.4522	0.828309
$227$	−18.5599	−1.23186	−0.615930	−	0.787801i	$-0.711220\pi$
$227$	−18.5599	−1.23186	−0.615930	+	0.787801i	$0.711220\pi$
$228$	0.0401730	0.00266052
$229$	−14.5860	−0.963868	−0.481934	−	0.876207i	$-0.660066\pi$
$229$	−14.5860	−0.963868	−0.481934	+	0.876207i	$0.660066\pi$
$230$	1.64624	0.108550
$231$	0.375742	0.0247220
$232$	−2.26843	−0.148930
$233$	12.5957	0.825171	0.412586	−	0.910919i	$-0.364626\pi$
$233$	12.5957	0.825171	0.412586	+	0.910919i	$0.364626\pi$
$234$	−2.25598	−0.147478
$235$	0.158294	0.0103260
$236$	8.43820	0.549280
$237$	−1.92172	−0.124829
$238$	3.26296	0.211506
$239$	8.42651	0.545066	0.272533	−	0.962146i	$-0.412139\pi$
$239$	8.42651	0.545066	0.272533	+	0.962146i	$0.412139\pi$
$240$	−0.0403104	−0.00260202
$241$	−13.6211	−0.877411	−0.438705	−	0.898631i	$-0.644563\pi$
$241$	−13.6211	−0.877411	−0.438705	+	0.898631i	$0.644563\pi$
$242$	8.14001	0.523259
$243$	−5.86782	−0.376421
$244$	−1.44890	−0.0927564
$245$	0.181430	0.0115912
$246$	2.04051	0.130098
$247$	0.138244	0.00879626
$248$	−6.23761	−0.396088
$249$	−2.78576	−0.176541
$250$	1.80833	0.114369
$251$	16.2758	1.02732	0.513661	−	0.857993i	$-0.328289\pi$
$251$	16.2758	1.02732	0.513661	+	0.857993i	$0.328289\pi$
$252$	−2.95064	−0.185873
$253$	15.3450	0.964730
$254$	7.59123	0.476316
$255$	0.131531	0.00823680
$256$	1.00000	0.0625000
$257$	−0.687165	−0.0428642	−0.0214321	−	0.999770i	$-0.506823\pi$
$257$	−0.687165	−0.0428642	−0.0214321	+	0.999770i	$0.506823\pi$
$258$	−2.38892	−0.148728
$259$	−6.61975	−0.411331
$260$	−0.138717	−0.00860286
$261$	−6.69332	−0.414306
$262$	−14.5569	−0.899328
$263$	−7.31477	−0.451048	−0.225524	−	0.974238i	$-0.572409\pi$
$263$	−7.31477	−0.451048	−0.225524	+	0.974238i	$0.572409\pi$
$264$	−0.375742	−0.0231253
$265$	0.807066	0.0495776
$266$	0.180812	0.0110863
$267$	0.212086	0.0129794
$268$	−6.30903	−0.385385
$269$	1.01353	0.0617958	0.0308979	−	0.999523i	$-0.490163\pi$
$269$	1.01353	0.0617958	0.0308979	+	0.999523i	$0.490163\pi$
$270$	−0.239872	−0.0145982
$271$	−11.3333	−0.688451	−0.344225	−	0.938887i	$-0.611858\pi$
$271$	−11.3333	−0.688451	−0.344225	+	0.938887i	$0.611858\pi$
$272$	−3.26296	−0.197846
$273$	0.169874	0.0102812
$274$	−17.6146	−1.06413
$275$	8.40009	0.506545
$276$	2.01600	0.121349
$277$	10.1251	0.608358	0.304179	−	0.952615i	$-0.401618\pi$
$277$	10.1251	0.608358	0.304179	+	0.952615i	$0.401618\pi$
$278$	−12.9671	−0.777717
$279$	−18.4049	−1.10187
$280$	−0.181430	−0.0108425
$281$	−10.4542	−0.623645	−0.311823	−	0.950140i	$-0.600939\pi$
$281$	−10.4542	−0.623645	−0.311823	+	0.950140i	$0.600939\pi$
$282$	0.193848	0.0115435
$283$	−4.85289	−0.288475	−0.144237	−	0.989543i	$-0.546073\pi$
$283$	−4.85289	−0.288475	−0.144237	+	0.989543i	$0.546073\pi$
$284$	3.51206	0.208402
$285$	0.00728859	0.000431739 0
$286$	−1.29301	−0.0764574
$287$	9.18400	0.542115
$288$	2.95064	0.173868
$289$	−6.35310	−0.373712
$290$	−0.411563	−0.0241678
$291$	−2.58812	−0.151718
$292$	−0.619658	−0.0362628
$293$	−16.7739	−0.979939	−0.489970	−	0.871740i	$-0.662992\pi$
$293$	−16.7739	−0.979939	−0.489970	+	0.871740i	$0.662992\pi$
$294$	0.222181	0.0129579
$295$	1.53095	0.0891351
$296$	6.61975	0.384765
$297$	−2.23590	−0.129740
$298$	−8.65495	−0.501368
$299$	6.93750	0.401206
$300$	1.10359	0.0637159
$301$	−10.7521	−0.619742
$302$	−0.864486	−0.0497456
$303$	−1.69037	−0.0971090
$304$	−0.180812	−0.0103703
$305$	−0.262875	−0.0150522
$306$	−9.62780	−0.550385
$307$	2.02016	0.115296	0.0576482	−	0.998337i	$-0.481640\pi$
$307$	2.02016	0.115296	0.0576482	+	0.998337i	$0.481640\pi$
$308$	−1.69115	−0.0963623
$309$	0.510315	0.0290308
$310$	−1.13169	−0.0642757
$311$	22.6040	1.28176	0.640878	−	0.767643i	$-0.278570\pi$
$311$	22.6040	1.28176	0.640878	+	0.767643i	$0.278570\pi$
$312$	−0.169874	−0.00961722
$313$	27.6395	1.56228	0.781140	−	0.624356i	$-0.214639\pi$
$313$	27.6395	1.56228	0.781140	+	0.624356i	$0.214639\pi$
$314$	10.4682	0.590756
$315$	−0.535335	−0.0301627
$316$	8.64934	0.486563
$317$	2.82069	0.158426	0.0792129	−	0.996858i	$-0.474759\pi$
$317$	2.82069	0.158426	0.0792129	+	0.996858i	$0.474759\pi$
$318$	0.988340	0.0554233
$319$	−3.83627	−0.214790
$320$	0.181430	0.0101423
$321$	−0.691518	−0.0385968
$322$	9.07368	0.505656
$323$	0.589982	0.0328275
$324$	8.55816	0.475453
$325$	3.79770	0.210659
$326$	21.5570	1.19393
$327$	−1.67104	−0.0924086
$328$	−9.18400	−0.507102
$329$	0.872479	0.0481013
$330$	−0.0681710	−0.00375269
$331$	2.57504	0.141537	0.0707684	−	0.997493i	$-0.477455\pi$
$331$	2.57504	0.141537	0.0707684	+	0.997493i	$0.477455\pi$
$332$	12.5383	0.688126
$333$	19.5325	1.07037
$334$	−11.1046	−0.607618
$335$	−1.14465	−0.0625389
$336$	−0.222181	−0.0121210
$337$	25.6528	1.39740	0.698700	−	0.715415i	$-0.253762\pi$
$337$	25.6528	1.39740	0.698700	+	0.715415i	$0.253762\pi$
$338$	12.4154	0.675310
$339$	2.76665	0.150264
$340$	−0.591999	−0.0321057
$341$	−10.5487	−0.571246
$342$	−0.533510	−0.0288489
$343$	1.00000	0.0539949
$344$	10.7521	0.579716
$345$	0.365763	0.0196920
$346$	−15.8285	−0.850945
$347$	7.27047	0.390299	0.195150	−	0.980773i	$-0.437481\pi$
$347$	7.27047	0.390299	0.195150	+	0.980773i	$0.437481\pi$
$348$	−0.504003	−0.0270174
$349$	−2.62662	−0.140600	−0.0702998	−	0.997526i	$-0.522396\pi$
$349$	−2.62662	−0.140600	−0.0702998	+	0.997526i	$0.522396\pi$
$350$	4.96708	0.265502
$351$	−1.01086	−0.0539556
$352$	1.69115	0.0901387
$353$	3.01229	0.160328	0.0801641	−	0.996782i	$-0.474456\pi$
$353$	3.01229	0.160328	0.0801641	+	0.996782i	$0.474456\pi$
$354$	1.87481	0.0996450
$355$	0.637194	0.0338187
$356$	−0.954562	−0.0505917
$357$	0.724968	0.0383694
$358$	15.6984	0.829688
$359$	−22.6329	−1.19452	−0.597260	−	0.802048i	$-0.703744\pi$
$359$	−22.6329	−1.19452	−0.597260	+	0.802048i	$0.703744\pi$
$360$	0.535335	0.0282146
$361$	−18.9673	−0.998279
$362$	−2.21669	−0.116507
$363$	1.80856	0.0949245
$364$	−0.764574	−0.0400746
$365$	−0.112425	−0.00588458
$366$	−0.321919	−0.0168270
$367$	−21.7500	−1.13534	−0.567670	−	0.823256i	$-0.692155\pi$
$367$	−21.7500	−1.13534	−0.567670	+	0.823256i	$0.692155\pi$
$368$	−9.07368	−0.472998
$369$	−27.0986	−1.41070
$370$	1.20102	0.0624382
$371$	4.44835	0.230947
$372$	−1.38588	−0.0718544
$373$	−19.4177	−1.00541	−0.502706	−	0.864457i	$-0.667662\pi$
$373$	−19.4177	−1.00541	−0.502706	+	0.864457i	$0.667662\pi$
$374$	−5.51816	−0.285337
$375$	0.401777	0.0207477
$376$	−0.872479	−0.0449947
$377$	−1.73439	−0.0893254
$378$	−1.32212	−0.0680024
$379$	−7.48114	−0.384280	−0.192140	−	0.981367i	$-0.561543\pi$
$379$	−7.48114	−0.384280	−0.192140	+	0.981367i	$0.561543\pi$
$380$	−0.0328047	−0.00168285
$381$	1.68663	0.0864086
$382$	−9.50153	−0.486141
$383$	−20.9325	−1.06960	−0.534800	−	0.844978i	$-0.679613\pi$
$383$	−20.9325	−1.06960	−0.534800	+	0.844978i	$0.679613\pi$
$384$	0.222181	0.0113381
$385$	−0.306826	−0.0156373
$386$	−14.9199	−0.759404
$387$	31.7256	1.61270
$388$	11.6487	0.591372
$389$	21.6585	1.09813	0.549066	−	0.835779i	$-0.314984\pi$
$389$	21.6585	1.09813	0.549066	+	0.835779i	$0.314984\pi$
$390$	−0.0308203	−0.00156065
$391$	29.6070	1.49729
$392$	−1.00000	−0.0505076
$393$	−3.23427	−0.163147
$394$	−10.0386	−0.505740
$395$	1.56925	0.0789576
$396$	4.98997	0.250756
$397$	−7.88730	−0.395852	−0.197926	−	0.980217i	$-0.563421\pi$
$397$	−7.88730	−0.395852	−0.197926	+	0.980217i	$0.563421\pi$
$398$	−12.6335	−0.633258
$399$	0.0401730	0.00201116
$400$	−4.96708	−0.248354
$401$	4.85539	0.242466	0.121233	−	0.992624i	$-0.461315\pi$
$401$	4.85539	0.242466	0.121233	+	0.992624i	$0.461315\pi$
$402$	−1.40175	−0.0699128
$403$	−4.76911	−0.237566
$404$	7.60806	0.378515
$405$	1.55271	0.0771547
$406$	−2.26843	−0.112580
$407$	11.1950	0.554916
$408$	−0.724968	−0.0358912
$409$	8.40627	0.415663	0.207832	−	0.978165i	$-0.433359\pi$
$409$	8.40627	0.415663	0.207832	+	0.978165i	$0.433359\pi$
$410$	−1.66626	−0.0822905
$411$	−3.91362	−0.193045
$412$	−2.29684	−0.113157
$413$	8.43820	0.415217
$414$	−26.7731	−1.31583
$415$	2.27482	0.111666
$416$	0.764574	0.0374863
$417$	−2.88105	−0.141086
$418$	−0.305780	−0.0149562
$419$	28.7383	1.40396	0.701979	−	0.712197i	$-0.252300\pi$
$419$	28.7383	1.40396	0.701979	+	0.712197i	$0.252300\pi$
$420$	−0.0403104	−0.00196694
$421$	13.7606	0.670652	0.335326	−	0.942102i	$-0.391153\pi$
$421$	13.7606	0.670652	0.335326	+	0.942102i	$0.391153\pi$
$422$	−10.0923	−0.491284
$423$	−2.57437	−0.125170
$424$	−4.44835	−0.216031
$425$	16.2074	0.786174
$426$	0.780313	0.0378063
$427$	−1.44890	−0.0701173
$428$	3.11241	0.150444
$429$	−0.287283	−0.0138701
$430$	1.95076	0.0940740
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	1.32212	0.0636105
$433$	26.5821	1.27745	0.638726	−	0.769434i	$-0.279462\pi$
$433$	26.5821	1.27745	0.638726	+	0.769434i	$0.279462\pi$
$434$	−6.23761	−0.299415
$435$	−0.0914414	−0.00438428
$436$	7.52106	0.360193
$437$	1.64063	0.0784819
$438$	−0.137676	−0.00657843
$439$	29.1398	1.39077	0.695383	−	0.718639i	$-0.255235\pi$
$439$	29.1398	1.39077	0.695383	+	0.718639i	$0.255235\pi$
$440$	0.306826	0.0146274
$441$	−2.95064	−0.140506
$442$	−2.49477	−0.118664
$443$	−3.97756	−0.188980	−0.0944898	−	0.995526i	$-0.530122\pi$
$443$	−3.97756	−0.188980	−0.0944898	+	0.995526i	$0.530122\pi$
$444$	1.47078	0.0698003
$445$	−0.173186	−0.00820982
$446$	22.5213	1.06642
$447$	−1.92297	−0.0909532
$448$	1.00000	0.0472456
$449$	−37.6928	−1.77883	−0.889416	−	0.457098i	$-0.848889\pi$
$449$	−37.6928	−1.77883	−0.889416	+	0.457098i	$0.848889\pi$
$450$	−14.6561	−0.690893
$451$	−15.5315	−0.731352
$452$	−12.4522	−0.585703
$453$	−0.192073	−0.00902435
$454$	18.5599	0.871057
$455$	−0.138717	−0.00650315
$456$	−0.0401730	−0.00188127
$457$	−15.5137	−0.725701	−0.362850	−	0.931847i	$-0.618196\pi$
$457$	−15.5137	−0.725701	−0.362850	+	0.931847i	$0.618196\pi$
$458$	14.5860	0.681558
$459$	−4.31402	−0.201361
$460$	−1.64624	−0.0767563
$461$	−8.71695	−0.405989	−0.202995	−	0.979180i	$-0.565067\pi$
$461$	−8.71695	−0.405989	−0.202995	+	0.979180i	$0.565067\pi$
$462$	−0.375742	−0.0174811
$463$	2.18324	0.101464	0.0507319	−	0.998712i	$-0.483845\pi$
$463$	2.18324	0.101464	0.0507319	+	0.998712i	$0.483845\pi$
$464$	2.26843	0.105309
$465$	−0.251440	−0.0116603
$466$	−12.5957	−0.583484
$467$	10.4903	0.485434	0.242717	−	0.970097i	$-0.421961\pi$
$467$	10.4903	0.485434	0.242717	+	0.970097i	$0.421961\pi$
$468$	2.25598	0.104283
$469$	−6.30903	−0.291324
$470$	−0.158294	−0.00730156
$471$	2.32584	0.107169
$472$	−8.43820	−0.388400
$473$	18.1835	0.836077
$474$	1.92172	0.0882675
$475$	0.898108	0.0412080
$476$	−3.26296	−0.149557
$477$	−13.1255	−0.600974
$478$	−8.42651	−0.385420
$479$	−15.1276	−0.691199	−0.345600	−	0.938382i	$-0.612324\pi$
$479$	−15.1276	−0.691199	−0.345600	+	0.938382i	$0.612324\pi$
$480$	0.0403104	0.00183991
$481$	5.06129	0.230775
$482$	13.6211	0.620423
$483$	2.01600	0.0917311
$484$	−8.14001	−0.370000
$485$	2.11342	0.0959656
$486$	5.86782	0.266170
$487$	38.1697	1.72963	0.864816	−	0.502089i	$-0.167435\pi$
$487$	38.1697	1.72963	0.864816	+	0.502089i	$0.167435\pi$
$488$	1.44890	0.0655887
$489$	4.78956	0.216591
$490$	−0.181430	−0.00819618
$491$	23.6915	1.06918	0.534592	−	0.845110i	$-0.320465\pi$
$491$	23.6915	1.06918	0.534592	+	0.845110i	$0.320465\pi$
$492$	−2.04051	−0.0919934
$493$	−7.40180	−0.333361
$494$	−0.138244	−0.00621990
$495$	0.905332	0.0406917
$496$	6.23761	0.280077
$497$	3.51206	0.157537
$498$	2.78576	0.124833
$499$	−4.81388	−0.215499	−0.107749	−	0.994178i	$-0.534364\pi$
$499$	−4.81388	−0.215499	−0.107749	+	0.994178i	$0.534364\pi$
$500$	−1.80833	−0.0808710
$501$	−2.46724	−0.110228
$502$	−16.2758	−0.726426
$503$	17.9650	0.801022	0.400511	−	0.916292i	$-0.368833\pi$
$503$	17.9650	0.801022	0.400511	+	0.916292i	$0.368833\pi$
$504$	2.95064	0.131432
$505$	1.38033	0.0614239
$506$	−15.3450	−0.682167
$507$	2.75847	0.122508
$508$	−7.59123	−0.336807
$509$	−39.3976	−1.74627	−0.873133	−	0.487481i	$-0.837916\pi$
$509$	−39.3976	−1.74627	−0.873133	+	0.487481i	$0.837916\pi$
$510$	−0.131531	−0.00582429
$511$	−0.619658	−0.0274121
$512$	−1.00000	−0.0441942
$513$	−0.239055	−0.0105545
$514$	0.687165	0.0303095
$515$	−0.416717	−0.0183627
$516$	2.38892	0.105166
$517$	−1.47549	−0.0648922
$518$	6.61975	0.290855
$519$	−3.51679	−0.154370
$520$	0.138717	0.00608314
$521$	0.589027	0.0258057	0.0129029	−	0.999917i	$-0.495893\pi$
$521$	0.589027	0.0258057	0.0129029	+	0.999917i	$0.495893\pi$
$522$	6.69332	0.292959
$523$	31.0425	1.35739	0.678697	−	0.734419i	$-0.262545\pi$
$523$	31.0425	1.35739	0.678697	+	0.734419i	$0.262545\pi$
$524$	14.5569	0.635921
$525$	1.10359	0.0481647
$526$	7.31477	0.318939
$527$	−20.3531	−0.886593
$528$	0.375742	0.0163521
$529$	59.3316	2.57963
$530$	−0.807066	−0.0350567
$531$	−24.8981	−1.08048
$532$	−0.180812	−0.00783919
$533$	−7.02185	−0.304150
$534$	−0.212086	−0.00917784
$535$	0.564685	0.0244135
$536$	6.30903	0.272509
$537$	3.48790	0.150514
$538$	−1.01353	−0.0436962
$539$	−1.69115	−0.0728431
$540$	0.239872	0.0103225
$541$	22.1239	0.951182	0.475591	−	0.879667i	$-0.342234\pi$
$541$	22.1239	0.951182	0.475591	+	0.879667i	$0.342234\pi$
$542$	11.3333	0.486808
$543$	−0.492507	−0.0211355
$544$	3.26296	0.139898
$545$	1.36455	0.0584508
$546$	−0.169874	−0.00726993
$547$	25.6048	1.09478	0.547391	−	0.836877i	$-0.315621\pi$
$547$	25.6048	1.09478	0.547391	+	0.836877i	$0.315621\pi$
$548$	17.6146	0.752457
$549$	4.27518	0.182460
$550$	−8.40009	−0.358181
$551$	−0.410160	−0.0174734
$552$	−2.01600	−0.0858066
$553$	8.64934	0.367807
$554$	−10.1251	−0.430174
$555$	0.266845	0.0113269
$556$	12.9671	0.549929
$557$	−1.26146	−0.0534496	−0.0267248	−	0.999643i	$-0.508508\pi$
$557$	−1.26146	−0.0534496	−0.0267248	+	0.999643i	$0.508508\pi$
$558$	18.4049	0.779142
$559$	8.22080	0.347703
$560$	0.181430	0.00766683
$561$	−1.22603	−0.0517630
$562$	10.4542	0.440984
$563$	−3.61481	−0.152346	−0.0761731	−	0.997095i	$-0.524270\pi$
$563$	−3.61481	−0.152346	−0.0761731	+	0.997095i	$0.524270\pi$
$564$	−0.193848	−0.00816249
$565$	−2.25921	−0.0950457
$566$	4.85289	0.203982
$567$	8.55816	0.359409
$568$	−3.51206	−0.147363
$569$	32.5639	1.36515	0.682574	−	0.730816i	$-0.260860\pi$
$569$	32.5639	1.36515	0.682574	+	0.730816i	$0.260860\pi$
$570$	−0.00728859	−0.000305286 0
$571$	−8.32894	−0.348555	−0.174278	−	0.984697i	$-0.555759\pi$
$571$	−8.32894	−0.348555	−0.174278	+	0.984697i	$0.555759\pi$
$572$	1.29301	0.0540635
$573$	−2.11106	−0.0881908
$574$	−9.18400	−0.383333
$575$	45.0697	1.87954
$576$	−2.95064	−0.122943
$577$	35.0961	1.46107	0.730535	−	0.682876i	$-0.239271\pi$
$577$	35.0961	1.46107	0.730535	+	0.682876i	$0.239271\pi$
$578$	6.35310	0.264254
$579$	−3.31492	−0.137764
$580$	0.411563	0.0170892
$581$	12.5383	0.520174
$582$	2.58812	0.107281
$583$	−7.52284	−0.311564
$584$	0.619658	0.0256416
$585$	0.409303	0.0169226
$586$	16.7739	0.692922
$587$	35.6815	1.47273	0.736367	−	0.676583i	$-0.236540\pi$
$587$	35.6815	1.47273	0.736367	+	0.676583i	$0.236540\pi$
$588$	−0.222181	−0.00916259
$589$	−1.12783	−0.0464716
$590$	−1.53095	−0.0630280
$591$	−2.23040	−0.0917463
$592$	−6.61975	−0.272070
$593$	−37.6621	−1.54660	−0.773299	−	0.634042i	$-0.781395\pi$
$593$	−37.6621	−1.54660	−0.773299	+	0.634042i	$0.781395\pi$
$594$	2.23590	0.0917402
$595$	−0.591999	−0.0242696
$596$	8.65495	0.354521
$597$	−2.80692	−0.114879
$598$	−6.93750	−0.283695
$599$	18.4917	0.755551	0.377776	−	0.925897i	$-0.376689\pi$
$599$	18.4917	0.755551	0.377776	+	0.925897i	$0.376689\pi$
$600$	−1.10359	−0.0450540
$601$	24.1633	0.985640	0.492820	−	0.870131i	$-0.335966\pi$
$601$	24.1633	0.985640	0.492820	+	0.870131i	$0.335966\pi$
$602$	10.7521	0.438224
$603$	18.6156	0.758088
$604$	0.864486	0.0351755
$605$	−1.47684	−0.0600422
$606$	1.69037	0.0686664
$607$	−5.29316	−0.214843	−0.107421	−	0.994214i	$-0.534259\pi$
$607$	−5.29316	−0.214843	−0.107421	+	0.994214i	$0.534259\pi$
$608$	0.180812	0.00733289
$609$	−0.504003	−0.0204232
$610$	0.262875	0.0106435
$611$	−0.667075	−0.0269870
$612$	9.62780	0.389181
$613$	26.4744	1.06929	0.534646	−	0.845076i	$-0.320445\pi$
$613$	26.4744	1.06929	0.534646	+	0.845076i	$0.320445\pi$
$614$	−2.02016	−0.0815269
$615$	−0.370211	−0.0149283
$616$	1.69115	0.0681384
$617$	−14.3109	−0.576136	−0.288068	−	0.957610i	$-0.593013\pi$
$617$	−14.3109	−0.576136	−0.288068	+	0.957610i	$0.593013\pi$
$618$	−0.510315	−0.0205279
$619$	43.7445	1.75824	0.879120	−	0.476600i	$-0.158131\pi$
$619$	43.7445	1.75824	0.879120	+	0.476600i	$0.158131\pi$
$620$	1.13169	0.0454498
$621$	−11.9965	−0.481402
$622$	−22.6040	−0.906338
$623$	−0.954562	−0.0382437
$624$	0.169874	0.00680040
$625$	24.5073	0.980293
$626$	−27.6395	−1.10470
$627$	−0.0679386	−0.00271321
$628$	−10.4682	−0.417727
$629$	21.6000	0.861247
$630$	0.535335	0.0213282
$631$	26.5405	1.05656	0.528280	−	0.849070i	$-0.322837\pi$
$631$	26.5405	1.05656	0.528280	+	0.849070i	$0.322837\pi$
$632$	−8.64934	−0.344052
$633$	−2.24231	−0.0891239
$634$	−2.82069	−0.112024
$635$	−1.37728	−0.0546557
$636$	−0.988340	−0.0391902
$637$	−0.764574	−0.0302935
$638$	3.83627	0.151879
$639$	−10.3628	−0.409946
$640$	−0.181430	−0.00717166
$641$	3.66224	0.144650	0.0723249	−	0.997381i	$-0.476958\pi$
$641$	3.66224	0.144650	0.0723249	+	0.997381i	$0.476958\pi$
$642$	0.691518	0.0272920
$643$	49.6520	1.95808	0.979041	−	0.203662i	$-0.0652842\pi$
$643$	49.6520	1.95808	0.979041	+	0.203662i	$0.0652842\pi$
$644$	−9.07368	−0.357553
$645$	0.433422	0.0170660
$646$	−0.589982	−0.0232125
$647$	9.81980	0.386056	0.193028	−	0.981193i	$-0.438169\pi$
$647$	9.81980	0.386056	0.193028	+	0.981193i	$0.438169\pi$
$648$	−8.55816	−0.336196
$649$	−14.2703	−0.560158
$650$	−3.79770	−0.148958
$651$	−1.38588	−0.0543168
$652$	−21.5570	−0.844237
$653$	−9.80228	−0.383593	−0.191796	−	0.981435i	$-0.561431\pi$
$653$	−9.80228	−0.383593	−0.191796	+	0.981435i	$0.561431\pi$
$654$	1.67104	0.0653427
$655$	2.64106	0.103195
$656$	9.18400	0.358575
$657$	1.82839	0.0713321
$658$	−0.872479	−0.0340128
$659$	−0.605696	−0.0235946	−0.0117973	−	0.999930i	$-0.503755\pi$
$659$	−0.605696	−0.0235946	−0.0117973	+	0.999930i	$0.503755\pi$
$660$	0.0681710	0.00265355
$661$	−23.2628	−0.904817	−0.452409	−	0.891811i	$-0.649435\pi$
$661$	−23.2628	−0.904817	−0.452409	+	0.891811i	$0.649435\pi$
$662$	−2.57504	−0.100082
$663$	−0.554292	−0.0215269
$664$	−12.5383	−0.486579
$665$	−0.0328047	−0.00127211
$666$	−19.5325	−0.756868
$667$	−20.5830	−0.796978
$668$	11.1046	0.429651
$669$	5.00381	0.193459
$670$	1.14465	0.0442216
$671$	2.45031	0.0945933
$672$	0.222181	0.00857082
$673$	−26.8544	−1.03516	−0.517581	−	0.855634i	$-0.673167\pi$
$673$	−26.8544	−1.03516	−0.517581	+	0.855634i	$0.673167\pi$
$674$	−25.6528	−0.988111
$675$	−6.56707	−0.252767
$676$	−12.4154	−0.477516
$677$	41.6367	1.60023	0.800113	−	0.599849i	$-0.204773\pi$
$677$	41.6367	1.60023	0.800113	+	0.599849i	$0.204773\pi$
$678$	−2.76665	−0.106252
$679$	11.6487	0.447035
$680$	0.591999	0.0227021
$681$	4.12365	0.158019
$682$	10.5487	0.403932
$683$	39.0735	1.49511	0.747553	−	0.664202i	$-0.231228\pi$
$683$	39.0735	1.49511	0.747553	+	0.664202i	$0.231228\pi$
$684$	0.533510	0.0203993
$685$	3.19581	0.122106
$686$	−1.00000	−0.0381802
$687$	3.24073	0.123641
$688$	−10.7521	−0.409921
$689$	−3.40109	−0.129571
$690$	−0.365763	−0.0139244
$691$	9.88876	0.376186	0.188093	−	0.982151i	$-0.439769\pi$
$691$	9.88876	0.376186	0.188093	+	0.982151i	$0.439769\pi$
$692$	15.8285	0.601709
$693$	4.98997	0.189553
$694$	−7.27047	−0.275983
$695$	2.35263	0.0892403
$696$	0.504003	0.0191042
$697$	−29.9670	−1.13508
$698$	2.62662	0.0994190
$699$	−2.79852	−0.105850
$700$	−4.96708	−0.187738
$701$	−45.2366	−1.70856	−0.854281	−	0.519812i	$-0.826002\pi$
$701$	−45.2366	−1.70856	−0.854281	+	0.519812i	$0.826002\pi$
$702$	1.01086	0.0381524
$703$	1.19693	0.0451430
$704$	−1.69115	−0.0637377
$705$	−0.0351700	−0.00132458
$706$	−3.01229	−0.113369
$707$	7.60806	0.286130
$708$	−1.87481	−0.0704596
$709$	−41.0990	−1.54351	−0.771753	−	0.635923i	$-0.780620\pi$
$709$	−41.0990	−1.54351	−0.771753	+	0.635923i	$0.780620\pi$
$710$	−0.637194	−0.0239134
$711$	−25.5210	−0.957114
$712$	0.954562	0.0357737
$713$	−56.5980	−2.11961
$714$	−0.724968	−0.0271312
$715$	0.234591	0.00877322
$716$	−15.6984	−0.586678
$717$	−1.87221	−0.0699190
$718$	22.6329	0.844653
$719$	−8.88811	−0.331470	−0.165735	−	0.986170i	$-0.553000\pi$
$719$	−8.88811	−0.331470	−0.165735	+	0.986170i	$0.553000\pi$
$720$	−0.535335	−0.0199507
$721$	−2.29684	−0.0855389
$722$	18.9673	0.705890
$723$	3.02635	0.112551
$724$	2.21669	0.0823827
$725$	−11.2675	−0.418464
$726$	−1.80856	−0.0671218
$727$	−49.4887	−1.83543	−0.917717	−	0.397235i	$-0.869970\pi$
$727$	−49.4887	−1.83543	−0.917717	+	0.397235i	$0.869970\pi$
$728$	0.764574	0.0283370
$729$	−24.3708	−0.902620
$730$	0.112425	0.00416103
$731$	35.0837	1.29762
$732$	0.321919	0.0118985
$733$	11.3903	0.420709	0.210354	−	0.977625i	$-0.432538\pi$
$733$	11.3903	0.420709	0.210354	+	0.977625i	$0.432538\pi$
$734$	21.7500	0.802806
$735$	−0.0403104	−0.00148687
$736$	9.07368	0.334460
$737$	10.6695	0.393017
$738$	27.0986	0.997515
$739$	−42.6236	−1.56793	−0.783966	−	0.620803i	$-0.786807\pi$
$739$	−42.6236	−1.56793	−0.783966	+	0.620803i	$0.786807\pi$
$740$	−1.20102	−0.0441505
$741$	−0.0307152	−0.00112835
$742$	−4.44835	−0.163304
$743$	−32.8497	−1.20514	−0.602570	−	0.798066i	$-0.705857\pi$
$743$	−32.8497	−1.20514	−0.602570	+	0.798066i	$0.705857\pi$
$744$	1.38588	0.0508088
$745$	1.57027	0.0575302
$746$	19.4177	0.710934
$747$	−36.9958	−1.35361
$748$	5.51816	0.201764
$749$	3.11241	0.113725
$750$	−0.401777	−0.0146708
$751$	−21.8231	−0.796336	−0.398168	−	0.917313i	$-0.630354\pi$
$751$	−21.8231	−0.796336	−0.398168	+	0.917313i	$0.630354\pi$
$752$	0.872479	0.0318160
$753$	−3.61618	−0.131781
$754$	1.73439	0.0631626
$755$	0.156844	0.00570814
$756$	1.32212	0.0480850
$757$	41.5711	1.51093	0.755464	−	0.655190i	$-0.227412\pi$
$757$	41.5711	1.51093	0.755464	+	0.655190i	$0.227412\pi$
$758$	7.48114	0.271727
$759$	−3.40936	−0.123752
$760$	0.0328047	0.00118995
$761$	12.4935	0.452890	0.226445	−	0.974024i	$-0.427290\pi$
$761$	12.4935	0.452890	0.226445	+	0.974024i	$0.427290\pi$
$762$	−1.68663	−0.0611001
$763$	7.52106	0.272281
$764$	9.50153	0.343753
$765$	1.74677	0.0631548
$766$	20.9325	0.756322
$767$	−6.45163	−0.232955
$768$	−0.222181	−0.00801727
$769$	−27.3982	−0.988005	−0.494002	−	0.869461i	$-0.664467\pi$
$769$	−27.3982	−0.988005	−0.494002	+	0.869461i	$0.664467\pi$
$770$	0.306826	0.0110572
$771$	0.152675	0.00549846
$772$	14.9199	0.536980
$773$	50.8343	1.82838	0.914192	−	0.405282i	$-0.132827\pi$
$773$	50.8343	1.82838	0.914192	+	0.405282i	$0.132827\pi$
$774$	−31.7256	−1.14035
$775$	−30.9827	−1.11293
$776$	−11.6487	−0.418163
$777$	1.47078	0.0527641
$778$	−21.6585	−0.776496
$779$	−1.66058	−0.0594963
$780$	0.0308203	0.00110354
$781$	−5.93942	−0.212529
$782$	−29.6070	−1.05875
$783$	2.99914	0.107180
$784$	1.00000	0.0357143
$785$	−1.89925	−0.0677872
$786$	3.23427	0.115363
$787$	0.493542	0.0175929	0.00879644	−	0.999961i	$-0.497200\pi$
$787$	0.493542	0.0175929	0.00879644	+	0.999961i	$0.497200\pi$
$788$	10.0386	0.357612
$789$	1.62520	0.0578588
$790$	−1.56925	−0.0558315
$791$	−12.4522	−0.442750
$792$	−4.98997	−0.177311
$793$	1.10779	0.0393389
$794$	7.88730	0.279910
$795$	−0.179315	−0.00635964
$796$	12.6335	0.447781
$797$	−36.3198	−1.28651	−0.643256	−	0.765651i	$-0.722417\pi$
$797$	−36.3198	−1.28651	−0.643256	+	0.765651i	$0.722417\pi$
$798$	−0.0401730	−0.00142211
$799$	−2.84686	−0.100715
$800$	4.96708	0.175613
$801$	2.81656	0.0995184
$802$	−4.85539	−0.171450
$803$	1.04794	0.0369809
$804$	1.40175	0.0494358
$805$	−1.64624	−0.0580223
$806$	4.76911	0.167985
$807$	−0.225186	−0.00792694
$808$	−7.60806	−0.267650
$809$	49.1509	1.72805	0.864027	−	0.503446i	$-0.167935\pi$
$809$	49.1509	1.72805	0.864027	+	0.503446i	$0.167935\pi$
$810$	−1.55271	−0.0545566
$811$	33.7687	1.18578	0.592890	−	0.805284i	$-0.297987\pi$
$811$	33.7687	1.18578	0.592890	+	0.805284i	$0.297987\pi$
$812$	2.26843	0.0796064
$813$	2.51805	0.0883119
$814$	−11.1950	−0.392385
$815$	−3.91109	−0.137000
$816$	0.724968	0.0253789
$817$	1.94411	0.0680159
$818$	−8.40627	−0.293918
$819$	2.25598	0.0788303
$820$	1.66626	0.0581882
$821$	13.9867	0.488141	0.244070	−	0.969758i	$-0.421517\pi$
$821$	13.9867	0.488141	0.244070	+	0.969758i	$0.421517\pi$
$822$	3.91362	0.136503
$823$	5.27876	0.184006	0.0920029	−	0.995759i	$-0.470673\pi$
$823$	5.27876	0.184006	0.0920029	+	0.995759i	$0.470673\pi$
$824$	2.29684	0.0800144
$825$	−1.86634	−0.0649777
$826$	−8.43820	−0.293603
$827$	−29.9732	−1.04227	−0.521135	−	0.853474i	$-0.674491\pi$
$827$	−29.9732	−1.04227	−0.521135	+	0.853474i	$0.674491\pi$
$828$	26.7731	0.930430
$829$	23.1779	0.805001	0.402501	−	0.915420i	$-0.368141\pi$
$829$	23.1779	0.805001	0.402501	+	0.915420i	$0.368141\pi$
$830$	−2.27482	−0.0789601
$831$	−2.24960	−0.0780379
$832$	−0.764574	−0.0265068
$833$	−3.26296	−0.113055
$834$	2.88105	0.0997626
$835$	2.01472	0.0697221
$836$	0.305780	0.0105756
$837$	8.24686	0.285053
$838$	−28.7383	−0.992749
$839$	31.7932	1.09762	0.548811	−	0.835946i	$-0.315081\pi$
$839$	31.7932	1.09762	0.548811	+	0.835946i	$0.315081\pi$
$840$	0.0403104	0.00139084
$841$	−23.8542	−0.822559
$842$	−13.7606	−0.474223
$843$	2.32272	0.0799989
$844$	10.0923	0.347390
$845$	−2.25253	−0.0774895
$846$	2.57437	0.0885086
$847$	−8.14001	−0.279694
$848$	4.44835	0.152757
$849$	1.07822	0.0370045
$850$	−16.2074	−0.555909
$851$	60.0655	2.05902
$852$	−0.780313	−0.0267331
$853$	−23.9796	−0.821045	−0.410523	−	0.911850i	$-0.634654\pi$
$853$	−23.9796	−0.821045	−0.410523	+	0.911850i	$0.634654\pi$
$854$	1.44890	0.0495804
$855$	0.0967948	0.00331031
$856$	−3.11241	−0.106380
$857$	−32.3002	−1.10335	−0.551676	−	0.834058i	$-0.686012\pi$
$857$	−32.3002	−1.10335	−0.551676	+	0.834058i	$0.686012\pi$
$858$	0.287283	0.00980767
$859$	−13.4031	−0.457309	−0.228655	−	0.973508i	$-0.573433\pi$
$859$	−13.4031	−0.457309	−0.228655	+	0.973508i	$0.573433\pi$
$860$	−1.95076	−0.0665204
$861$	−2.04051	−0.0695405
$862$	1.00000	0.0340601
$863$	35.8740	1.22116	0.610582	−	0.791953i	$-0.290936\pi$
$863$	35.8740	1.22116	0.610582	+	0.791953i	$0.290936\pi$
$864$	−1.32212	−0.0449794
$865$	2.87177	0.0976431
$866$	−26.5821	−0.903295
$867$	1.41154	0.0479384
$868$	6.23761	0.211718
$869$	−14.6273	−0.496199
$870$	0.0914414	0.00310015
$871$	4.82372	0.163446
$872$	−7.52106	−0.254695
$873$	−34.3710	−1.16328
$874$	−1.64063	−0.0554951
$875$	−1.80833	−0.0611327
$876$	0.137676	0.00465165
$877$	−33.2518	−1.12283	−0.561416	−	0.827533i	$-0.689743\pi$
$877$	−33.2518	−1.12283	−0.561416	+	0.827533i	$0.689743\pi$
$878$	−29.1398	−0.983420
$879$	3.72683	0.125703
$880$	−0.306826	−0.0103431
$881$	−54.7340	−1.84404	−0.922018	−	0.387146i	$-0.873461\pi$
$881$	−54.7340	−1.84404	−0.922018	+	0.387146i	$0.873461\pi$
$882$	2.95064	0.0993531
$883$	−32.4511	−1.09207	−0.546033	−	0.837763i	$-0.683863\pi$
$883$	−32.4511	−1.09207	−0.546033	+	0.837763i	$0.683863\pi$
$884$	2.49477	0.0839083
$885$	−0.340147	−0.0114339
$886$	3.97756	0.133629
$887$	30.6836	1.03026	0.515128	−	0.857113i	$-0.327744\pi$
$887$	30.6836	1.03026	0.515128	+	0.857113i	$0.327744\pi$
$888$	−1.47078	−0.0493563
$889$	−7.59123	−0.254602
$890$	0.173186	0.00580522
$891$	−14.4731	−0.484869
$892$	−22.5213	−0.754070
$893$	−0.157755	−0.00527906
$894$	1.92297	0.0643136
$895$	−2.84817	−0.0952039
$896$	−1.00000	−0.0334077
$897$	−1.54138	−0.0514652
$898$	37.6928	1.25782
$899$	14.1496	0.471915
$900$	14.6561	0.488535
$901$	−14.5148	−0.483558
$902$	15.5315	0.517144
$903$	2.38892	0.0794982
$904$	12.4522	0.414155
$905$	0.402175	0.0133688
$906$	0.192073	0.00638118
$907$	44.6104	1.48126	0.740632	−	0.671910i	$-0.234526\pi$
$907$	44.6104	1.48126	0.740632	+	0.671910i	$0.234526\pi$
$908$	−18.5599	−0.615930
$909$	−22.4486	−0.744573
$910$	0.138717	0.00459842
$911$	−28.3826	−0.940358	−0.470179	−	0.882571i	$-0.655811\pi$
$911$	−28.3826	−0.940358	−0.470179	+	0.882571i	$0.655811\pi$
$912$	0.0401730	0.00133026
$913$	−21.2041	−0.701753
$914$	15.5137	0.513148
$915$	0.0584058	0.00193084
$916$	−14.5860	−0.481934
$917$	14.5569	0.480711
$918$	4.31402	0.142384
$919$	0.869292	0.0286753	0.0143376	−	0.999897i	$-0.495436\pi$
$919$	0.869292	0.0286753	0.0143376	+	0.999897i	$0.495436\pi$
$920$	1.64624	0.0542749
$921$	−0.448841	−0.0147898
$922$	8.71695	0.287078
$923$	−2.68523	−0.0883854
$924$	0.375742	0.0123610
$925$	32.8808	1.08112
$926$	−2.18324	−0.0717458
$927$	6.77715	0.222591
$928$	−2.26843	−0.0744650
$929$	−21.3795	−0.701438	−0.350719	−	0.936481i	$-0.614063\pi$
$929$	−21.3795	−0.701438	−0.350719	+	0.936481i	$0.614063\pi$
$930$	0.251440	0.00824505
$931$	−0.180812	−0.00592587
$932$	12.5957	0.412586
$933$	−5.02218	−0.164419
$934$	−10.4903	−0.343253
$935$	1.00116	0.0327415
$936$	−2.25598	−0.0737390
$937$	50.2248	1.64077	0.820386	−	0.571810i	$-0.193759\pi$
$937$	50.2248	1.64077	0.820386	+	0.571810i	$0.193759\pi$
$938$	6.30903	0.205997
$939$	−6.14098	−0.200403
$940$	0.158294	0.00516298
$941$	43.8993	1.43108	0.715539	−	0.698573i	$-0.246181\pi$
$941$	43.8993	1.43108	0.715539	+	0.698573i	$0.246181\pi$
$942$	−2.32584	−0.0757800
$943$	−83.3327	−2.71368
$944$	8.43820	0.274640
$945$	0.239872	0.00780305
$946$	−18.1835	−0.591196
$947$	50.4144	1.63825	0.819124	−	0.573617i	$-0.194460\pi$
$947$	50.4144	1.63825	0.819124	+	0.573617i	$0.194460\pi$
$948$	−1.92172	−0.0624145
$949$	0.473775	0.0153794
$950$	−0.898108	−0.0291385
$951$	−0.626704	−0.0203223
$952$	3.26296	0.105753
$953$	−13.2352	−0.428729	−0.214364	−	0.976754i	$-0.568768\pi$
$953$	−13.2352	−0.428729	−0.214364	+	0.976754i	$0.568768\pi$
$954$	13.1255	0.424953
$955$	1.72387	0.0557830
$956$	8.42651	0.272533
$957$	0.852346	0.0275524
$958$	15.1276	0.488752
$959$	17.6146	0.568804
$960$	−0.0403104	−0.00130101
$961$	7.90773	0.255088
$962$	−5.06129	−0.163183
$963$	−9.18358	−0.295937
$964$	−13.6211	−0.438705
$965$	2.70693	0.0871390
$966$	−2.01600	−0.0648637
$967$	23.2874	0.748871	0.374435	−	0.927253i	$-0.377837\pi$
$967$	23.2874	0.748871	0.374435	+	0.927253i	$0.377837\pi$
$968$	8.14001	0.261630
$969$	−0.131083	−0.00421098
$970$	−2.11342	−0.0678579
$971$	−25.5910	−0.821253	−0.410627	−	0.911804i	$-0.634690\pi$
$971$	−25.5910	−0.821253	−0.410627	+	0.911804i	$0.634690\pi$
$972$	−5.86782	−0.188210
$973$	12.9671	0.415707
$974$	−38.1697	−1.22303
$975$	−0.843778	−0.0270225
$976$	−1.44890	−0.0463782
$977$	−12.0856	−0.386653	−0.193326	−	0.981134i	$-0.561928\pi$
$977$	−12.0856	−0.386653	−0.193326	+	0.981134i	$0.561928\pi$
$978$	−4.78956	−0.153153
$979$	1.61431	0.0515935
$980$	0.181430	0.00579558
$981$	−22.1919	−0.708533
$982$	−23.6915	−0.756027
$983$	−19.7032	−0.628434	−0.314217	−	0.949351i	$-0.601742\pi$
$983$	−19.7032	−0.628434	−0.314217	+	0.949351i	$0.601742\pi$
$984$	2.04051	0.0650491
$985$	1.82131	0.0580319
$986$	7.40180	0.235721
$987$	−0.193848	−0.00617026
$988$	0.138244	0.00439813
$989$	97.5613	3.10227
$990$	−0.905332	−0.0287733
$991$	−23.2132	−0.737390	−0.368695	−	0.929550i	$-0.620195\pi$
$991$	−23.2132	−0.737390	−0.368695	+	0.929550i	$0.620195\pi$
$992$	−6.23761	−0.198044
$993$	−0.572125	−0.0181558
$994$	−3.51206	−0.111396
$995$	2.29209	0.0726642
$996$	−2.78576	−0.0882703
$997$	11.1354	0.352662	0.176331	−	0.984331i	$-0.443577\pi$
$997$	11.1354	0.352662	0.176331	+	0.984331i	$0.443577\pi$
$998$	4.81388	0.152381
$999$	−8.75210	−0.276904

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.p.1.14	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.p.1.14	✓	27	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.222181 q^{3} +1.00000 q^{4} +0.181430 q^{5} +0.222181 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.95064 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.222181 q^{3} +1.00000 q^{4} +0.181430 q^{5} +0.222181 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.95064 q^{9} -0.181430 q^{10} -1.69115 q^{11} -0.222181 q^{12} -0.764574 q^{13} -1.00000 q^{14} -0.0403104 q^{15} +1.00000 q^{16} -3.26296 q^{17} +2.95064 q^{18} -0.180812 q^{19} +0.181430 q^{20} -0.222181 q^{21} +1.69115 q^{22} -9.07368 q^{23} +0.222181 q^{24} -4.96708 q^{25} +0.764574 q^{26} +1.32212 q^{27} +1.00000 q^{28} +2.26843 q^{29} +0.0403104 q^{30} +6.23761 q^{31} -1.00000 q^{32} +0.375742 q^{33} +3.26296 q^{34} +0.181430 q^{35} -2.95064 q^{36} -6.61975 q^{37} +0.180812 q^{38} +0.169874 q^{39} -0.181430 q^{40} +9.18400 q^{41} +0.222181 q^{42} -10.7521 q^{43} -1.69115 q^{44} -0.535335 q^{45} +9.07368 q^{46} +0.872479 q^{47} -0.222181 q^{48} +1.00000 q^{49} +4.96708 q^{50} +0.724968 q^{51} -0.764574 q^{52} +4.44835 q^{53} -1.32212 q^{54} -0.306826 q^{55} -1.00000 q^{56} +0.0401730 q^{57} -2.26843 q^{58} +8.43820 q^{59} -0.0403104 q^{60} -1.44890 q^{61} -6.23761 q^{62} -2.95064 q^{63} +1.00000 q^{64} -0.138717 q^{65} -0.375742 q^{66} -6.30903 q^{67} -3.26296 q^{68} +2.01600 q^{69} -0.181430 q^{70} +3.51206 q^{71} +2.95064 q^{72} -0.619658 q^{73} +6.61975 q^{74} +1.10359 q^{75} -0.180812 q^{76} -1.69115 q^{77} -0.169874 q^{78} +8.64934 q^{79} +0.181430 q^{80} +8.55816 q^{81} -9.18400 q^{82} +12.5383 q^{83} -0.222181 q^{84} -0.591999 q^{85} +10.7521 q^{86} -0.504003 q^{87} +1.69115 q^{88} -0.954562 q^{89} +0.535335 q^{90} -0.764574 q^{91} -9.07368 q^{92} -1.38588 q^{93} -0.872479 q^{94} -0.0328047 q^{95} +0.222181 q^{96} +11.6487 q^{97} -1.00000 q^{98} +4.98997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * q^99

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