LMFDB - Embedded newform 6042.2.a.bb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 16x^{7} + 76x^{6} + 30x^{5} - 366x^{4} + 300x^{3} + 101x^{2} - 106x + 16 $ x^9 - 4x^8 - 16x^7 + 76x^6 + 30x^5 - 366x^4 + 300x^3 + 101x^2 - 106x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.91020$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.16096 q^{5} -1.00000 q^{6} +0.910204 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.16096 q^{5} -1.00000 q^{6} +0.910204 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.16096 q^{10} -1.61368 q^{11} -1.00000 q^{12} +5.05812 q^{13} +0.910204 q^{14} +4.16096 q^{15} +1.00000 q^{16} -5.02844 q^{17} +1.00000 q^{18} -1.00000 q^{19} -4.16096 q^{20} -0.910204 q^{21} -1.61368 q^{22} -6.18022 q^{23} -1.00000 q^{24} +12.3136 q^{25} +5.05812 q^{26} -1.00000 q^{27} +0.910204 q^{28} +6.09944 q^{29} +4.16096 q^{30} +10.3692 q^{31} +1.00000 q^{32} +1.61368 q^{33} -5.02844 q^{34} -3.78732 q^{35} +1.00000 q^{36} -1.16053 q^{37} -1.00000 q^{38} -5.05812 q^{39} -4.16096 q^{40} -3.25217 q^{41} -0.910204 q^{42} -9.91571 q^{43} -1.61368 q^{44} -4.16096 q^{45} -6.18022 q^{46} +10.4541 q^{47} -1.00000 q^{48} -6.17153 q^{49} +12.3136 q^{50} +5.02844 q^{51} +5.05812 q^{52} +1.00000 q^{53} -1.00000 q^{54} +6.71446 q^{55} +0.910204 q^{56} +1.00000 q^{57} +6.09944 q^{58} -0.621122 q^{59} +4.16096 q^{60} +6.45584 q^{61} +10.3692 q^{62} +0.910204 q^{63} +1.00000 q^{64} -21.0466 q^{65} +1.61368 q^{66} +8.64129 q^{67} -5.02844 q^{68} +6.18022 q^{69} -3.78732 q^{70} -6.55454 q^{71} +1.00000 q^{72} -2.69703 q^{73} -1.16053 q^{74} -12.3136 q^{75} -1.00000 q^{76} -1.46878 q^{77} -5.05812 q^{78} +8.95893 q^{79} -4.16096 q^{80} +1.00000 q^{81} -3.25217 q^{82} -4.45871 q^{83} -0.910204 q^{84} +20.9232 q^{85} -9.91571 q^{86} -6.09944 q^{87} -1.61368 q^{88} -18.0502 q^{89} -4.16096 q^{90} +4.60392 q^{91} -6.18022 q^{92} -10.3692 q^{93} +10.4541 q^{94} +4.16096 q^{95} -1.00000 q^{96} -14.5442 q^{97} -6.17153 q^{98} -1.61368 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 5 q^{5} - 9 q^{6} - 5 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 5 * q^5 - 9 * q^6 - 5 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 5 q^{5} - 9 q^{6} - 5 q^{7} + 9 q^{8} + 9 q^{9} - 5 q^{10} + 3 q^{11} - 9 q^{12} - 4 q^{13} - 5 q^{14} + 5 q^{15} + 9 q^{16} - 16 q^{17} + 9 q^{18} - 9 q^{19} - 5 q^{20} + 5 q^{21} + 3 q^{22} - 9 q^{24} + 8 q^{25} - 4 q^{26} - 9 q^{27} - 5 q^{28} - 2 q^{29} + 5 q^{30} - 10 q^{31} + 9 q^{32} - 3 q^{33} - 16 q^{34} - q^{35} + 9 q^{36} - 14 q^{37} - 9 q^{38} + 4 q^{39} - 5 q^{40} - 21 q^{41} + 5 q^{42} - 4 q^{43} + 3 q^{44} - 5 q^{45} - 8 q^{47} - 9 q^{48} - 14 q^{49} + 8 q^{50} + 16 q^{51} - 4 q^{52} + 9 q^{53} - 9 q^{54} - 14 q^{55} - 5 q^{56} + 9 q^{57} - 2 q^{58} - 12 q^{59} + 5 q^{60} - 13 q^{61} - 10 q^{62} - 5 q^{63} + 9 q^{64} - 13 q^{65} - 3 q^{66} + 22 q^{67} - 16 q^{68} - q^{70} - 13 q^{71} + 9 q^{72} - 17 q^{73} - 14 q^{74} - 8 q^{75} - 9 q^{76} - 25 q^{77} + 4 q^{78} - 5 q^{80} + 9 q^{81} - 21 q^{82} - 24 q^{83} + 5 q^{84} - 16 q^{85} - 4 q^{86} + 2 q^{87} + 3 q^{88} - 23 q^{89} - 5 q^{90} - 11 q^{91} + 10 q^{93} - 8 q^{94} + 5 q^{95} - 9 q^{96} - 29 q^{97} - 14 q^{98} + 3 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 5 * q^5 - 9 * q^6 - 5 * q^7 + 9 * q^8 + 9 * q^9 - 5 * q^10 + 3 * q^11 - 9 * q^12 - 4 * q^13 - 5 * q^14 + 5 * q^15 + 9 * q^16 - 16 * q^17 + 9 * q^18 - 9 * q^19 - 5 * q^20 + 5 * q^21 + 3 * q^22 - 9 * q^24 + 8 * q^25 - 4 * q^26 - 9 * q^27 - 5 * q^28 - 2 * q^29 + 5 * q^30 - 10 * q^31 + 9 * q^32 - 3 * q^33 - 16 * q^34 - q^35 + 9 * q^36 - 14 * q^37 - 9 * q^38 + 4 * q^39 - 5 * q^40 - 21 * q^41 + 5 * q^42 - 4 * q^43 + 3 * q^44 - 5 * q^45 - 8 * q^47 - 9 * q^48 - 14 * q^49 + 8 * q^50 + 16 * q^51 - 4 * q^52 + 9 * q^53 - 9 * q^54 - 14 * q^55 - 5 * q^56 + 9 * q^57 - 2 * q^58 - 12 * q^59 + 5 * q^60 - 13 * q^61 - 10 * q^62 - 5 * q^63 + 9 * q^64 - 13 * q^65 - 3 * q^66 + 22 * q^67 - 16 * q^68 - q^70 - 13 * q^71 + 9 * q^72 - 17 * q^73 - 14 * q^74 - 8 * q^75 - 9 * q^76 - 25 * q^77 + 4 * q^78 - 5 * q^80 + 9 * q^81 - 21 * q^82 - 24 * q^83 + 5 * q^84 - 16 * q^85 - 4 * q^86 + 2 * q^87 + 3 * q^88 - 23 * q^89 - 5 * q^90 - 11 * q^91 + 10 * q^93 - 8 * q^94 + 5 * q^95 - 9 * q^96 - 29 * q^97 - 14 * q^98 + 3 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−4.16096	−1.86084	−0.930419	−	0.366498i	$-0.880557\pi$
$5$	−4.16096	−1.86084	−0.930419	+	0.366498i	$0.880557\pi$
$6$	−1.00000	−0.408248
$7$	0.910204	0.344025	0.172012	−	0.985095i	$-0.444973\pi$
$7$	0.910204	0.344025	0.172012	+	0.985095i	$0.444973\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−4.16096	−1.31581
$11$	−1.61368	−0.486543	−0.243271	−	0.969958i	$-0.578221\pi$
$11$	−1.61368	−0.486543	−0.243271	+	0.969958i	$0.578221\pi$
$12$	−1.00000	−0.288675
$13$	5.05812	1.40287	0.701435	−	0.712734i	$-0.252543\pi$
$13$	5.05812	1.40287	0.701435	+	0.712734i	$0.252543\pi$
$14$	0.910204	0.243262
$15$	4.16096	1.07436
$16$	1.00000	0.250000
$17$	−5.02844	−1.21958	−0.609788	−	0.792564i	$-0.708746\pi$
$17$	−5.02844	−1.21958	−0.609788	+	0.792564i	$0.708746\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−4.16096	−0.930419
$21$	−0.910204	−0.198623
$22$	−1.61368	−0.344038
$23$	−6.18022	−1.28867	−0.644333	−	0.764745i	$-0.722865\pi$
$23$	−6.18022	−1.28867	−0.644333	+	0.764745i	$0.722865\pi$
$24$	−1.00000	−0.204124
$25$	12.3136	2.46272
$26$	5.05812	0.991978
$27$	−1.00000	−0.192450
$28$	0.910204	0.172012
$29$	6.09944	1.13264	0.566319	−	0.824186i	$-0.308367\pi$
$29$	6.09944	1.13264	0.566319	+	0.824186i	$0.308367\pi$
$30$	4.16096	0.759684
$31$	10.3692	1.86236	0.931180	−	0.364561i	$-0.118781\pi$
$31$	10.3692	1.86236	0.931180	+	0.364561i	$0.118781\pi$
$32$	1.00000	0.176777
$33$	1.61368	0.280906
$34$	−5.02844	−0.862371
$35$	−3.78732	−0.640174
$36$	1.00000	0.166667
$37$	−1.16053	−0.190790	−0.0953948	−	0.995440i	$-0.530411\pi$
$37$	−1.16053	−0.190790	−0.0953948	+	0.995440i	$0.530411\pi$
$38$	−1.00000	−0.162221
$39$	−5.05812	−0.809947
$40$	−4.16096	−0.657906
$41$	−3.25217	−0.507903	−0.253952	−	0.967217i	$-0.581730\pi$
$41$	−3.25217	−0.507903	−0.253952	+	0.967217i	$0.581730\pi$
$42$	−0.910204	−0.140448
$43$	−9.91571	−1.51213	−0.756066	−	0.654495i	$-0.772881\pi$
$43$	−9.91571	−1.51213	−0.756066	+	0.654495i	$0.772881\pi$
$44$	−1.61368	−0.243271
$45$	−4.16096	−0.620279
$46$	−6.18022	−0.911224
$47$	10.4541	1.52488	0.762442	−	0.647057i	$-0.224000\pi$
$47$	10.4541	1.52488	0.762442	+	0.647057i	$0.224000\pi$
$48$	−1.00000	−0.144338
$49$	−6.17153	−0.881647
$50$	12.3136	1.74140
$51$	5.02844	0.704123
$52$	5.05812	0.701435
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−1.00000	−0.136083
$55$	6.71446	0.905377
$56$	0.910204	0.121631
$57$	1.00000	0.132453
$58$	6.09944	0.800895
$59$	−0.621122	−0.0808632	−0.0404316	−	0.999182i	$-0.512873\pi$
$59$	−0.621122	−0.0808632	−0.0404316	+	0.999182i	$0.512873\pi$
$60$	4.16096	0.537178
$61$	6.45584	0.826585	0.413293	−	0.910598i	$-0.364379\pi$
$61$	6.45584	0.826585	0.413293	+	0.910598i	$0.364379\pi$
$62$	10.3692	1.31689
$63$	0.910204	0.114675
$64$	1.00000	0.125000
$65$	−21.0466	−2.61051
$66$	1.61368	0.198630
$67$	8.64129	1.05570	0.527851	−	0.849337i	$-0.322998\pi$
$67$	8.64129	1.05570	0.527851	+	0.849337i	$0.322998\pi$
$68$	−5.02844	−0.609788
$69$	6.18022	0.744011
$70$	−3.78732	−0.452672
$71$	−6.55454	−0.777881	−0.388940	−	0.921263i	$-0.627159\pi$
$71$	−6.55454	−0.777881	−0.388940	+	0.921263i	$0.627159\pi$
$72$	1.00000	0.117851
$73$	−2.69703	−0.315664	−0.157832	−	0.987466i	$-0.550450\pi$
$73$	−2.69703	−0.315664	−0.157832	+	0.987466i	$0.550450\pi$
$74$	−1.16053	−0.134909
$75$	−12.3136	−1.42185
$76$	−1.00000	−0.114708
$77$	−1.46878	−0.167383
$78$	−5.05812	−0.572719
$79$	8.95893	1.00796	0.503979	−	0.863716i	$-0.331869\pi$
$79$	8.95893	1.00796	0.503979	+	0.863716i	$0.331869\pi$
$80$	−4.16096	−0.465209
$81$	1.00000	0.111111
$82$	−3.25217	−0.359142
$83$	−4.45871	−0.489407	−0.244704	−	0.969598i	$-0.578691\pi$
$83$	−4.45871	−0.489407	−0.244704	+	0.969598i	$0.578691\pi$
$84$	−0.910204	−0.0993114
$85$	20.9232	2.26943
$86$	−9.91571	−1.06924
$87$	−6.09944	−0.653928
$88$	−1.61368	−0.172019
$89$	−18.0502	−1.91332	−0.956659	−	0.291211i	$-0.905942\pi$
$89$	−18.0502	−1.91332	−0.956659	+	0.291211i	$0.905942\pi$
$90$	−4.16096	−0.438604
$91$	4.60392	0.482622
$92$	−6.18022	−0.644333
$93$	−10.3692	−1.07523
$94$	10.4541	1.07826
$95$	4.16096	0.426905
$96$	−1.00000	−0.102062
$97$	−14.5442	−1.47674	−0.738369	−	0.674397i	$-0.764403\pi$
$97$	−14.5442	−1.47674	−0.738369	+	0.674397i	$0.764403\pi$
$98$	−6.17153	−0.623419
$99$	−1.61368	−0.162181
$100$	12.3136	1.23136
$101$	11.9847	1.19253	0.596263	−	0.802789i	$-0.296651\pi$
$101$	11.9847	1.19253	0.596263	+	0.802789i	$0.296651\pi$
$102$	5.02844	0.497890
$103$	−2.42966	−0.239401	−0.119701	−	0.992810i	$-0.538193\pi$
$103$	−2.42966	−0.239401	−0.119701	+	0.992810i	$0.538193\pi$
$104$	5.05812	0.495989
$105$	3.78732	0.369605
$106$	1.00000	0.0971286
$107$	−2.97287	−0.287398	−0.143699	−	0.989621i	$-0.545900\pi$
$107$	−2.97287	−0.287398	−0.143699	+	0.989621i	$0.545900\pi$
$108$	−1.00000	−0.0962250
$109$	−7.87159	−0.753962	−0.376981	−	0.926221i	$-0.623038\pi$
$109$	−7.87159	−0.753962	−0.376981	+	0.926221i	$0.623038\pi$
$110$	6.71446	0.640198
$111$	1.16053	0.110152
$112$	0.910204	0.0860062
$113$	−1.29686	−0.121998	−0.0609991	−	0.998138i	$-0.519429\pi$
$113$	−1.29686	−0.121998	−0.0609991	+	0.998138i	$0.519429\pi$
$114$	1.00000	0.0936586
$115$	25.7157	2.39800
$116$	6.09944	0.566319
$117$	5.05812	0.467623
$118$	−0.621122	−0.0571789
$119$	−4.57691	−0.419565
$120$	4.16096	0.379842
$121$	−8.39604	−0.763276
$122$	6.45584	0.584484
$123$	3.25217	0.293238
$124$	10.3692	0.931180
$125$	−30.4315	−2.72188
$126$	0.910204	0.0810874
$127$	−6.26588	−0.556007	−0.278004	−	0.960580i	$-0.589673\pi$
$127$	−6.26588	−0.556007	−0.278004	+	0.960580i	$0.589673\pi$
$128$	1.00000	0.0883883
$129$	9.91571	0.873030
$130$	−21.0466	−1.84591
$131$	−19.1155	−1.67013	−0.835064	−	0.550153i	$-0.814570\pi$
$131$	−19.1155	−1.67013	−0.835064	+	0.550153i	$0.814570\pi$
$132$	1.61368	0.140453
$133$	−0.910204	−0.0789247
$134$	8.64129	0.746494
$135$	4.16096	0.358118
$136$	−5.02844	−0.431186
$137$	−7.87996	−0.673231	−0.336615	−	0.941642i	$-0.609282\pi$
$137$	−7.87996	−0.673231	−0.336615	+	0.941642i	$0.609282\pi$
$138$	6.18022	0.526095
$139$	−1.49053	−0.126425	−0.0632126	−	0.998000i	$-0.520135\pi$
$139$	−1.49053	−0.126425	−0.0632126	+	0.998000i	$0.520135\pi$
$140$	−3.78732	−0.320087
$141$	−10.4541	−0.880392
$142$	−6.55454	−0.550045
$143$	−8.16218	−0.682556
$144$	1.00000	0.0833333
$145$	−25.3795	−2.10765
$146$	−2.69703	−0.223208
$147$	6.17153	0.509019
$148$	−1.16053	−0.0953948
$149$	17.3330	1.41998	0.709988	−	0.704213i	$-0.248700\pi$
$149$	17.3330	1.41998	0.709988	+	0.704213i	$0.248700\pi$
$150$	−12.3136	−1.00540
$151$	5.15079	0.419165	0.209583	−	0.977791i	$-0.432789\pi$
$151$	5.15079	0.419165	0.209583	+	0.977791i	$0.432789\pi$
$152$	−1.00000	−0.0811107
$153$	−5.02844	−0.406526
$154$	−1.46878	−0.118357
$155$	−43.1457	−3.46555
$156$	−5.05812	−0.404973
$157$	−15.6397	−1.24818	−0.624090	−	0.781352i	$-0.714530\pi$
$157$	−15.6397	−1.24818	−0.624090	+	0.781352i	$0.714530\pi$
$158$	8.95893	0.712734
$159$	−1.00000	−0.0793052
$160$	−4.16096	−0.328953
$161$	−5.62526	−0.443333
$162$	1.00000	0.0785674
$163$	−18.3469	−1.43704	−0.718521	−	0.695506i	$-0.755180\pi$
$163$	−18.3469	−1.43704	−0.718521	+	0.695506i	$0.755180\pi$
$164$	−3.25217	−0.253952
$165$	−6.71446	−0.522720
$166$	−4.45871	−0.346063
$167$	−1.01535	−0.0785705	−0.0392852	−	0.999228i	$-0.512508\pi$
$167$	−1.01535	−0.0785705	−0.0392852	+	0.999228i	$0.512508\pi$
$168$	−0.910204	−0.0702238
$169$	12.5845	0.968042
$170$	20.9232	1.60473
$171$	−1.00000	−0.0764719
$172$	−9.91571	−0.756066
$173$	−9.31160	−0.707948	−0.353974	−	0.935255i	$-0.615170\pi$
$173$	−9.31160	−0.707948	−0.353974	+	0.935255i	$0.615170\pi$
$174$	−6.09944	−0.462397
$175$	11.2079	0.847236
$176$	−1.61368	−0.121636
$177$	0.621122	0.0466864
$178$	−18.0502	−1.35292
$179$	2.25692	0.168690	0.0843451	−	0.996437i	$-0.473120\pi$
$179$	2.25692	0.168690	0.0843451	+	0.996437i	$0.473120\pi$
$180$	−4.16096	−0.310140
$181$	10.5293	0.782640	0.391320	−	0.920255i	$-0.372019\pi$
$181$	10.5293	0.782640	0.391320	+	0.920255i	$0.372019\pi$
$182$	4.60392	0.341265
$183$	−6.45584	−0.477229
$184$	−6.18022	−0.455612
$185$	4.82891	0.355029
$186$	−10.3692	−0.760305
$187$	8.11430	0.593376
$188$	10.4541	0.762442
$189$	−0.910204	−0.0662076
$190$	4.16096	0.301868
$191$	26.1574	1.89268	0.946341	−	0.323171i	$-0.104749\pi$
$191$	26.1574	1.89268	0.946341	+	0.323171i	$0.104749\pi$
$192$	−1.00000	−0.0721688
$193$	22.9441	1.65155	0.825775	−	0.563999i	$-0.190738\pi$
$193$	22.9441	1.65155	0.825775	+	0.563999i	$0.190738\pi$
$194$	−14.5442	−1.04421
$195$	21.0466	1.50718
$196$	−6.17153	−0.440823
$197$	10.7254	0.764150	0.382075	−	0.924131i	$-0.375210\pi$
$197$	10.7254	0.764150	0.382075	+	0.924131i	$0.375210\pi$
$198$	−1.61368	−0.114679
$199$	−23.1006	−1.63756	−0.818778	−	0.574111i	$-0.805348\pi$
$199$	−23.1006	−1.63756	−0.818778	+	0.574111i	$0.805348\pi$
$200$	12.3136	0.870702
$201$	−8.64129	−0.609510
$202$	11.9847	0.843243
$203$	5.55173	0.389655
$204$	5.02844	0.352062
$205$	13.5321	0.945125
$206$	−2.42966	−0.169282
$207$	−6.18022	−0.429555
$208$	5.05812	0.350717
$209$	1.61368	0.111621
$210$	3.78732	0.261350
$211$	−6.07426	−0.418169	−0.209085	−	0.977898i	$-0.567048\pi$
$211$	−6.07426	−0.418169	−0.209085	+	0.977898i	$0.567048\pi$
$212$	1.00000	0.0686803
$213$	6.55454	0.449110
$214$	−2.97287	−0.203221
$215$	41.2589	2.81383
$216$	−1.00000	−0.0680414
$217$	9.43807	0.640698
$218$	−7.87159	−0.533131
$219$	2.69703	0.182248
$220$	6.71446	0.452689
$221$	−25.4345	−1.71091
$222$	1.16053	0.0778895
$223$	−23.3219	−1.56175	−0.780876	−	0.624686i	$-0.785227\pi$
$223$	−23.3219	−1.56175	−0.780876	+	0.624686i	$0.785227\pi$
$224$	0.910204	0.0608156
$225$	12.3136	0.820906
$226$	−1.29686	−0.0862657
$227$	3.49187	0.231764	0.115882	−	0.993263i	$-0.463031\pi$
$227$	3.49187	0.231764	0.115882	+	0.993263i	$0.463031\pi$
$228$	1.00000	0.0662266
$229$	−10.5890	−0.699744	−0.349872	−	0.936798i	$-0.613775\pi$
$229$	−10.5890	−0.699744	−0.349872	+	0.936798i	$0.613775\pi$
$230$	25.7157	1.69564
$231$	1.46878	0.0966385
$232$	6.09944	0.400448
$233$	−16.7887	−1.09986	−0.549932	−	0.835209i	$-0.685346\pi$
$233$	−16.7887	−1.09986	−0.549932	+	0.835209i	$0.685346\pi$
$234$	5.05812	0.330659
$235$	−43.4990	−2.83756
$236$	−0.621122	−0.0404316
$237$	−8.95893	−0.581945
$238$	−4.57691	−0.296677
$239$	3.99510	0.258421	0.129211	−	0.991617i	$-0.458756\pi$
$239$	3.99510	0.258421	0.129211	+	0.991617i	$0.458756\pi$
$240$	4.16096	0.268589
$241$	−15.9855	−1.02971	−0.514857	−	0.857276i	$-0.672155\pi$
$241$	−15.9855	−1.02971	−0.514857	+	0.857276i	$0.672155\pi$
$242$	−8.39604	−0.539718
$243$	−1.00000	−0.0641500
$244$	6.45584	0.413293
$245$	25.6795	1.64060
$246$	3.25217	0.207351
$247$	−5.05812	−0.321840
$248$	10.3692	0.658443
$249$	4.45871	0.282559
$250$	−30.4315	−1.92466
$251$	15.1250	0.954679	0.477340	−	0.878719i	$-0.341601\pi$
$251$	15.1250	0.954679	0.477340	+	0.878719i	$0.341601\pi$
$252$	0.910204	0.0573375
$253$	9.97290	0.626991
$254$	−6.26588	−0.393156
$255$	−20.9232	−1.31026
$256$	1.00000	0.0625000
$257$	−24.6253	−1.53609	−0.768043	−	0.640398i	$-0.778769\pi$
$257$	−24.6253	−1.53609	−0.768043	+	0.640398i	$0.778769\pi$
$258$	9.91571	0.617325
$259$	−1.05632	−0.0656364
$260$	−21.0466	−1.30526
$261$	6.09944	0.377546
$262$	−19.1155	−1.18096
$263$	−5.53601	−0.341365	−0.170683	−	0.985326i	$-0.554597\pi$
$263$	−5.53601	−0.341365	−0.170683	+	0.985326i	$0.554597\pi$
$264$	1.61368	0.0993151
$265$	−4.16096	−0.255606
$266$	−0.910204	−0.0558082
$267$	18.0502	1.10465
$268$	8.64129	0.527851
$269$	−10.0140	−0.610565	−0.305283	−	0.952262i	$-0.598751\pi$
$269$	−10.0140	−0.610565	−0.305283	+	0.952262i	$0.598751\pi$
$270$	4.16096	0.253228
$271$	−3.31327	−0.201267	−0.100633	−	0.994924i	$-0.532087\pi$
$271$	−3.31327	−0.201267	−0.100633	+	0.994924i	$0.532087\pi$
$272$	−5.02844	−0.304894
$273$	−4.60392	−0.278642
$274$	−7.87996	−0.476046
$275$	−19.8702	−1.19822
$276$	6.18022	0.372006
$277$	7.11413	0.427446	0.213723	−	0.976894i	$-0.431441\pi$
$277$	7.11413	0.427446	0.213723	+	0.976894i	$0.431441\pi$
$278$	−1.49053	−0.0893961
$279$	10.3692	0.620786
$280$	−3.78732	−0.226336
$281$	−22.5858	−1.34735	−0.673677	−	0.739026i	$-0.735286\pi$
$281$	−22.5858	−1.34735	−0.673677	+	0.739026i	$0.735286\pi$
$282$	−10.4541	−0.622531
$283$	−13.0749	−0.777222	−0.388611	−	0.921402i	$-0.627045\pi$
$283$	−13.0749	−0.777222	−0.388611	+	0.921402i	$0.627045\pi$
$284$	−6.55454	−0.388940
$285$	−4.16096	−0.246474
$286$	−8.16218	−0.482640
$287$	−2.96014	−0.174731
$288$	1.00000	0.0589256
$289$	8.28525	0.487368
$290$	−25.3795	−1.49034
$291$	14.5442	0.852595
$292$	−2.69703	−0.157832
$293$	−21.5672	−1.25997	−0.629983	−	0.776609i	$-0.716938\pi$
$293$	−21.5672	−1.25997	−0.629983	+	0.776609i	$0.716938\pi$
$294$	6.17153	0.359931
$295$	2.58446	0.150473
$296$	−1.16053	−0.0674543
$297$	1.61368	0.0936352
$298$	17.3330	1.00408
$299$	−31.2603	−1.80783
$300$	−12.3136	−0.710925
$301$	−9.02532	−0.520211
$302$	5.15079	0.296395
$303$	−11.9847	−0.688505
$304$	−1.00000	−0.0573539
$305$	−26.8625	−1.53814
$306$	−5.02844	−0.287457
$307$	−10.0912	−0.575937	−0.287969	−	0.957640i	$-0.592980\pi$
$307$	−10.0912	−0.575937	−0.287969	+	0.957640i	$0.592980\pi$
$308$	−1.46878	−0.0836914
$309$	2.42966	0.138218
$310$	−43.1457	−2.45051
$311$	−26.2552	−1.48880	−0.744399	−	0.667735i	$-0.767264\pi$
$311$	−26.2552	−1.48880	−0.744399	+	0.667735i	$0.767264\pi$
$312$	−5.05812	−0.286359
$313$	10.9391	0.618312	0.309156	−	0.951011i	$-0.399953\pi$
$313$	10.9391	0.618312	0.309156	+	0.951011i	$0.399953\pi$
$314$	−15.6397	−0.882597
$315$	−3.78732	−0.213391
$316$	8.95893	0.503979
$317$	−6.73489	−0.378269	−0.189135	−	0.981951i	$-0.560568\pi$
$317$	−6.73489	−0.378269	−0.189135	+	0.981951i	$0.560568\pi$
$318$	−1.00000	−0.0560772
$319$	−9.84254	−0.551076
$320$	−4.16096	−0.232605
$321$	2.97287	0.165930
$322$	−5.62526	−0.313484
$323$	5.02844	0.279790
$324$	1.00000	0.0555556
$325$	62.2836	3.45487
$326$	−18.3469	−1.01614
$327$	7.87159	0.435300
$328$	−3.25217	−0.179571
$329$	9.51534	0.524598
$330$	−6.71446	−0.369619
$331$	−18.3594	−1.00913	−0.504563	−	0.863375i	$-0.668346\pi$
$331$	−18.3594	−1.00913	−0.504563	+	0.863375i	$0.668346\pi$
$332$	−4.45871	−0.244704
$333$	−1.16053	−0.0635965
$334$	−1.01535	−0.0555577
$335$	−35.9561	−1.96449
$336$	−0.910204	−0.0496557
$337$	−4.99587	−0.272142	−0.136071	−	0.990699i	$-0.543448\pi$
$337$	−4.99587	−0.272142	−0.136071	+	0.990699i	$0.543448\pi$
$338$	12.5845	0.684509
$339$	1.29686	0.0704357
$340$	20.9232	1.13472
$341$	−16.7325	−0.906117
$342$	−1.00000	−0.0540738
$343$	−11.9888	−0.647333
$344$	−9.91571	−0.534619
$345$	−25.7157	−1.38448
$346$	−9.31160	−0.500595
$347$	12.1689	0.653260	0.326630	−	0.945152i	$-0.394087\pi$
$347$	12.1689	0.653260	0.326630	+	0.945152i	$0.394087\pi$
$348$	−6.09944	−0.326964
$349$	20.5247	1.09866	0.549331	−	0.835605i	$-0.314883\pi$
$349$	20.5247	1.09866	0.549331	+	0.835605i	$0.314883\pi$
$350$	11.2079	0.599086
$351$	−5.05812	−0.269982
$352$	−1.61368	−0.0860094
$353$	−7.85025	−0.417827	−0.208913	−	0.977934i	$-0.566993\pi$
$353$	−7.85025	−0.417827	−0.208913	+	0.977934i	$0.566993\pi$
$354$	0.621122	0.0330123
$355$	27.2732	1.44751
$356$	−18.0502	−0.956659
$357$	4.57691	0.242236
$358$	2.25692	0.119282
$359$	−2.58986	−0.136688	−0.0683439	−	0.997662i	$-0.521772\pi$
$359$	−2.58986	−0.136688	−0.0683439	+	0.997662i	$0.521772\pi$
$360$	−4.16096	−0.219302
$361$	1.00000	0.0526316
$362$	10.5293	0.553410
$363$	8.39604	0.440678
$364$	4.60392	0.241311
$365$	11.2222	0.587399
$366$	−6.45584	−0.337452
$367$	−33.6418	−1.75609	−0.878045	−	0.478578i	$-0.841152\pi$
$367$	−33.6418	−1.75609	−0.878045	+	0.478578i	$0.841152\pi$
$368$	−6.18022	−0.322166
$369$	−3.25217	−0.169301
$370$	4.82891	0.251043
$371$	0.910204	0.0472554
$372$	−10.3692	−0.537617
$373$	−5.85429	−0.303123	−0.151562	−	0.988448i	$-0.548430\pi$
$373$	−5.85429	−0.303123	−0.151562	+	0.988448i	$0.548430\pi$
$374$	8.11430	0.419580
$375$	30.4315	1.57148
$376$	10.4541	0.539128
$377$	30.8517	1.58894
$378$	−0.910204	−0.0468158
$379$	−34.9381	−1.79465	−0.897325	−	0.441371i	$-0.854492\pi$
$379$	−34.9381	−1.79465	−0.897325	+	0.441371i	$0.854492\pi$
$380$	4.16096	0.213453
$381$	6.26588	0.321011
$382$	26.1574	1.33833
$383$	−5.63771	−0.288074	−0.144037	−	0.989572i	$-0.546008\pi$
$383$	−5.63771	−0.288074	−0.144037	+	0.989572i	$0.546008\pi$
$384$	−1.00000	−0.0510310
$385$	6.11152	0.311472
$386$	22.9441	1.16782
$387$	−9.91571	−0.504044
$388$	−14.5442	−0.738369
$389$	9.15935	0.464398	0.232199	−	0.972668i	$-0.425408\pi$
$389$	9.15935	0.464398	0.232199	+	0.972668i	$0.425408\pi$
$390$	21.0466	1.06574
$391$	31.0769	1.57163
$392$	−6.17153	−0.311709
$393$	19.1155	0.964249
$394$	10.7254	0.540336
$395$	−37.2778	−1.87565
$396$	−1.61368	−0.0810904
$397$	−22.0761	−1.10797	−0.553985	−	0.832527i	$-0.686894\pi$
$397$	−22.0761	−1.10797	−0.553985	+	0.832527i	$0.686894\pi$
$398$	−23.1006	−1.15793
$399$	0.910204	0.0455672
$400$	12.3136	0.615679
$401$	−26.1359	−1.30516	−0.652581	−	0.757719i	$-0.726314\pi$
$401$	−26.1359	−1.30516	−0.652581	+	0.757719i	$0.726314\pi$
$402$	−8.64129	−0.430989
$403$	52.4485	2.61265
$404$	11.9847	0.596263
$405$	−4.16096	−0.206760
$406$	5.55173	0.275528
$407$	1.87272	0.0928273
$408$	5.02844	0.248945
$409$	16.9913	0.840164	0.420082	−	0.907486i	$-0.362001\pi$
$409$	16.9913	0.840164	0.420082	+	0.907486i	$0.362001\pi$
$410$	13.5321	0.668305
$411$	7.87996	0.388690
$412$	−2.42966	−0.119701
$413$	−0.565348	−0.0278189
$414$	−6.18022	−0.303741
$415$	18.5525	0.910707
$416$	5.05812	0.247995
$417$	1.49053	0.0729916
$418$	1.61368	0.0789276
$419$	31.1088	1.51977	0.759883	−	0.650059i	$-0.225256\pi$
$419$	31.1088	1.51977	0.759883	+	0.650059i	$0.225256\pi$
$420$	3.78732	0.184802
$421$	−14.0374	−0.684139	−0.342070	−	0.939675i	$-0.611128\pi$
$421$	−14.0374	−0.684139	−0.342070	+	0.939675i	$0.611128\pi$
$422$	−6.07426	−0.295690
$423$	10.4541	0.508295
$424$	1.00000	0.0485643
$425$	−61.9182	−3.00347
$426$	6.55454	0.317568
$427$	5.87613	0.284366
$428$	−2.97287	−0.143699
$429$	8.16218	0.394074
$430$	41.2589	1.98968
$431$	14.8695	0.716237	0.358119	−	0.933676i	$-0.383418\pi$
$431$	14.8695	0.716237	0.358119	+	0.933676i	$0.383418\pi$
$432$	−1.00000	−0.0481125
$433$	−1.93675	−0.0930741	−0.0465370	−	0.998917i	$-0.514819\pi$
$433$	−1.93675	−0.0930741	−0.0465370	+	0.998917i	$0.514819\pi$
$434$	9.43807	0.453042
$435$	25.3795	1.21685
$436$	−7.87159	−0.376981
$437$	6.18022	0.295640
$438$	2.69703	0.128869
$439$	−19.2634	−0.919392	−0.459696	−	0.888076i	$-0.652042\pi$
$439$	−19.2634	−0.919392	−0.459696	+	0.888076i	$0.652042\pi$
$440$	6.71446	0.320099
$441$	−6.17153	−0.293882
$442$	−25.4345	−1.20979
$443$	19.0657	0.905840	0.452920	−	0.891551i	$-0.350382\pi$
$443$	19.0657	0.905840	0.452920	+	0.891551i	$0.350382\pi$
$444$	1.16053	0.0550762
$445$	75.1062	3.56037
$446$	−23.3219	−1.10433
$447$	−17.3330	−0.819824
$448$	0.910204	0.0430031
$449$	23.1735	1.09362	0.546812	−	0.837255i	$-0.315841\pi$
$449$	23.1735	1.09362	0.546812	+	0.837255i	$0.315841\pi$
$450$	12.3136	0.580468
$451$	5.24795	0.247117
$452$	−1.29686	−0.0609991
$453$	−5.15079	−0.242005
$454$	3.49187	0.163882
$455$	−19.1567	−0.898081
$456$	1.00000	0.0468293
$457$	27.8790	1.30413	0.652063	−	0.758165i	$-0.273904\pi$
$457$	27.8790	1.30413	0.652063	+	0.758165i	$0.273904\pi$
$458$	−10.5890	−0.494793
$459$	5.02844	0.234708
$460$	25.7157	1.19900
$461$	37.6707	1.75450	0.877251	−	0.480033i	$-0.159375\pi$
$461$	37.6707	1.75450	0.877251	+	0.480033i	$0.159375\pi$
$462$	1.46878	0.0683337
$463$	27.8503	1.29431	0.647156	−	0.762357i	$-0.275958\pi$
$463$	27.8503	1.29431	0.647156	+	0.762357i	$0.275958\pi$
$464$	6.09944	0.283159
$465$	43.1457	2.00084
$466$	−16.7887	−0.777722
$467$	11.4575	0.530188	0.265094	−	0.964223i	$-0.414597\pi$
$467$	11.4575	0.530188	0.265094	+	0.964223i	$0.414597\pi$
$468$	5.05812	0.233812
$469$	7.86534	0.363188
$470$	−43.4990	−2.00646
$471$	15.6397	0.720638
$472$	−0.621122	−0.0285895
$473$	16.0008	0.735717
$474$	−8.95893	−0.411497
$475$	−12.3136	−0.564986
$476$	−4.57691	−0.209782
$477$	1.00000	0.0457869
$478$	3.99510	0.182731
$479$	−1.77576	−0.0811364	−0.0405682	−	0.999177i	$-0.512917\pi$
$479$	−1.77576	−0.0811364	−0.0405682	+	0.999177i	$0.512917\pi$
$480$	4.16096	0.189921
$481$	−5.87009	−0.267653
$482$	−15.9855	−0.728118
$483$	5.62526	0.255958
$484$	−8.39604	−0.381638
$485$	60.5177	2.74797
$486$	−1.00000	−0.0453609
$487$	−16.5506	−0.749978	−0.374989	−	0.927029i	$-0.622353\pi$
$487$	−16.5506	−0.749978	−0.374989	+	0.927029i	$0.622353\pi$
$488$	6.45584	0.292242
$489$	18.3469	0.829676
$490$	25.6795	1.16008
$491$	30.1979	1.36281	0.681406	−	0.731906i	$-0.261369\pi$
$491$	30.1979	1.36281	0.681406	+	0.731906i	$0.261369\pi$
$492$	3.25217	0.146619
$493$	−30.6707	−1.38134
$494$	−5.05812	−0.227575
$495$	6.71446	0.301792
$496$	10.3692	0.465590
$497$	−5.96597	−0.267610
$498$	4.45871	0.199800
$499$	−4.67663	−0.209355	−0.104677	−	0.994506i	$-0.533381\pi$
$499$	−4.67663	−0.209355	−0.104677	+	0.994506i	$0.533381\pi$
$500$	−30.4315	−1.36094
$501$	1.01535	0.0453627
$502$	15.1250	0.675060
$503$	1.46978	0.0655344	0.0327672	−	0.999463i	$-0.489568\pi$
$503$	1.46978	0.0655344	0.0327672	+	0.999463i	$0.489568\pi$
$504$	0.910204	0.0405437
$505$	−49.8680	−2.21910
$506$	9.97290	0.443349
$507$	−12.5845	−0.558899
$508$	−6.26588	−0.278004
$509$	−8.80858	−0.390433	−0.195217	−	0.980760i	$-0.562541\pi$
$509$	−8.80858	−0.390433	−0.195217	+	0.980760i	$0.562541\pi$
$510$	−20.9232	−0.926493
$511$	−2.45485	−0.108596
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	−24.6253	−1.08618
$515$	10.1097	0.445487
$516$	9.91571	0.436515
$517$	−16.8695	−0.741921
$518$	−1.05632	−0.0464119
$519$	9.31160	0.408734
$520$	−21.0466	−0.922955
$521$	34.7718	1.52338	0.761690	−	0.647942i	$-0.224370\pi$
$521$	34.7718	1.52338	0.761690	+	0.647942i	$0.224370\pi$
$522$	6.09944	0.266965
$523$	12.1233	0.530116	0.265058	−	0.964232i	$-0.414609\pi$
$523$	12.1233	0.530116	0.265058	+	0.964232i	$0.414609\pi$
$524$	−19.1155	−0.835064
$525$	−11.2079	−0.489152
$526$	−5.53601	−0.241382
$527$	−52.1408	−2.27129
$528$	1.61368	0.0702264
$529$	15.1951	0.660659
$530$	−4.16096	−0.180741
$531$	−0.621122	−0.0269544
$532$	−0.910204	−0.0394624
$533$	−16.4498	−0.712522
$534$	18.0502	0.781109
$535$	12.3700	0.534802
$536$	8.64129	0.373247
$537$	−2.25692	−0.0973934
$538$	−10.0140	−0.431735
$539$	9.95887	0.428959
$540$	4.16096	0.179059
$541$	−2.62483	−0.112850	−0.0564251	−	0.998407i	$-0.517970\pi$
$541$	−2.62483	−0.112850	−0.0564251	+	0.998407i	$0.517970\pi$
$542$	−3.31327	−0.142317
$543$	−10.5293	−0.451857
$544$	−5.02844	−0.215593
$545$	32.7534	1.40300
$546$	−4.60392	−0.197030
$547$	−1.11369	−0.0476180	−0.0238090	−	0.999717i	$-0.507579\pi$
$547$	−1.11369	−0.0476180	−0.0238090	+	0.999717i	$0.507579\pi$
$548$	−7.87996	−0.336615
$549$	6.45584	0.275528
$550$	−19.8702	−0.847268
$551$	−6.09944	−0.259845
$552$	6.18022	0.263048
$553$	8.15446	0.346763
$554$	7.11413	0.302250
$555$	−4.82891	−0.204976
$556$	−1.49053	−0.0632126
$557$	38.8043	1.64419	0.822094	−	0.569351i	$-0.192805\pi$
$557$	38.8043	1.64419	0.822094	+	0.569351i	$0.192805\pi$
$558$	10.3692	0.438962
$559$	−50.1548	−2.12132
$560$	−3.78732	−0.160044
$561$	−8.11430	−0.342586
$562$	−22.5858	−0.952722
$563$	36.1728	1.52450	0.762251	−	0.647282i	$-0.224094\pi$
$563$	36.1728	1.52450	0.762251	+	0.647282i	$0.224094\pi$
$564$	−10.4541	−0.440196
$565$	5.39618	0.227019
$566$	−13.0749	−0.549579
$567$	0.910204	0.0382250
$568$	−6.55454	−0.275022
$569$	−4.90941	−0.205813	−0.102907	−	0.994691i	$-0.532814\pi$
$569$	−4.90941	−0.205813	−0.102907	+	0.994691i	$0.532814\pi$
$570$	−4.16096	−0.174283
$571$	4.49481	0.188102	0.0940509	−	0.995567i	$-0.470018\pi$
$571$	4.49481	0.188102	0.0940509	+	0.995567i	$0.470018\pi$
$572$	−8.16218	−0.341278
$573$	−26.1574	−1.09274
$574$	−2.96014	−0.123554
$575$	−76.1007	−3.17362
$576$	1.00000	0.0416667
$577$	−36.1004	−1.50288	−0.751439	−	0.659802i	$-0.770640\pi$
$577$	−36.1004	−1.50288	−0.751439	+	0.659802i	$0.770640\pi$
$578$	8.28525	0.344621
$579$	−22.9441	−0.953523
$580$	−25.3795	−1.05383
$581$	−4.05834	−0.168368
$582$	14.5442	0.602875
$583$	−1.61368	−0.0668318
$584$	−2.69703	−0.111604
$585$	−21.0466	−0.870171
$586$	−21.5672	−0.890931
$587$	−14.0847	−0.581338	−0.290669	−	0.956824i	$-0.593878\pi$
$587$	−14.0847	−0.581338	−0.290669	+	0.956824i	$0.593878\pi$
$588$	6.17153	0.254510
$589$	−10.3692	−0.427254
$590$	2.58446	0.106401
$591$	−10.7254	−0.441182
$592$	−1.16053	−0.0476974
$593$	5.96280	0.244863	0.122431	−	0.992477i	$-0.460931\pi$
$593$	5.96280	0.244863	0.122431	+	0.992477i	$0.460931\pi$
$594$	1.61368	0.0662101
$595$	19.0443	0.780742
$596$	17.3330	0.709988
$597$	23.1006	0.945443
$598$	−31.2603	−1.27833
$599$	−8.77987	−0.358736	−0.179368	−	0.983782i	$-0.557405\pi$
$599$	−8.77987	−0.358736	−0.179368	+	0.983782i	$0.557405\pi$
$600$	−12.3136	−0.502700
$601$	22.3516	0.911739	0.455870	−	0.890047i	$-0.349328\pi$
$601$	22.3516	0.911739	0.455870	+	0.890047i	$0.349328\pi$
$602$	−9.02532	−0.367845
$603$	8.64129	0.351901
$604$	5.15079	0.209583
$605$	34.9356	1.42033
$606$	−11.9847	−0.486847
$607$	11.8159	0.479593	0.239796	−	0.970823i	$-0.422919\pi$
$607$	11.8159	0.479593	0.239796	+	0.970823i	$0.422919\pi$
$608$	−1.00000	−0.0405554
$609$	−5.55173	−0.224968
$610$	−26.8625	−1.08763
$611$	52.8779	2.13921
$612$	−5.02844	−0.203263
$613$	35.8379	1.44748	0.723740	−	0.690073i	$-0.242422\pi$
$613$	35.8379	1.44748	0.723740	+	0.690073i	$0.242422\pi$
$614$	−10.0912	−0.407249
$615$	−13.5321	−0.545668
$616$	−1.46878	−0.0591787
$617$	−33.4780	−1.34777	−0.673887	−	0.738835i	$-0.735376\pi$
$617$	−33.4780	−1.34777	−0.673887	+	0.738835i	$0.735376\pi$
$618$	2.42966	0.0977352
$619$	−4.91912	−0.197716	−0.0988581	−	0.995102i	$-0.531519\pi$
$619$	−4.91912	−0.197716	−0.0988581	+	0.995102i	$0.531519\pi$
$620$	−43.1457	−1.73277
$621$	6.18022	0.248004
$622$	−26.2552	−1.05274
$623$	−16.4294	−0.658229
$624$	−5.05812	−0.202487
$625$	65.0565	2.60226
$626$	10.9391	0.437213
$627$	−1.61368	−0.0644441
$628$	−15.6397	−0.624090
$629$	5.83565	0.232683
$630$	−3.78732	−0.150891
$631$	−6.01314	−0.239379	−0.119690	−	0.992811i	$-0.538190\pi$
$631$	−6.01314	−0.239379	−0.119690	+	0.992811i	$0.538190\pi$
$632$	8.95893	0.356367
$633$	6.07426	0.241430
$634$	−6.73489	−0.267477
$635$	26.0721	1.03464
$636$	−1.00000	−0.0396526
$637$	−31.2163	−1.23684
$638$	−9.84254	−0.389670
$639$	−6.55454	−0.259294
$640$	−4.16096	−0.164476
$641$	−2.63126	−0.103928	−0.0519642	−	0.998649i	$-0.516548\pi$
$641$	−2.63126	−0.103928	−0.0519642	+	0.998649i	$0.516548\pi$
$642$	2.97287	0.117330
$643$	42.8498	1.68983	0.844916	−	0.534899i	$-0.179650\pi$
$643$	42.8498	1.68983	0.844916	+	0.534899i	$0.179650\pi$
$644$	−5.62526	−0.221666
$645$	−41.2589	−1.62457
$646$	5.02844	0.197841
$647$	−9.24031	−0.363274	−0.181637	−	0.983366i	$-0.558140\pi$
$647$	−9.24031	−0.363274	−0.181637	+	0.983366i	$0.558140\pi$
$648$	1.00000	0.0392837
$649$	1.00229	0.0393434
$650$	62.2836	2.44296
$651$	−9.43807	−0.369907
$652$	−18.3469	−0.718521
$653$	−15.5914	−0.610138	−0.305069	−	0.952330i	$-0.598680\pi$
$653$	−15.5914	−0.610138	−0.305069	+	0.952330i	$0.598680\pi$
$654$	7.87159	0.307804
$655$	79.5388	3.10784
$656$	−3.25217	−0.126976
$657$	−2.69703	−0.105221
$658$	9.51534	0.370947
$659$	14.5209	0.565655	0.282828	−	0.959171i	$-0.408728\pi$
$659$	14.5209	0.565655	0.282828	+	0.959171i	$0.408728\pi$
$660$	−6.71446	−0.261360
$661$	21.6598	0.842468	0.421234	−	0.906952i	$-0.361597\pi$
$661$	21.6598	0.842468	0.421234	+	0.906952i	$0.361597\pi$
$662$	−18.3594	−0.713559
$663$	25.4345	0.987792
$664$	−4.45871	−0.173032
$665$	3.78732	0.146866
$666$	−1.16053	−0.0449695
$667$	−37.6959	−1.45959
$668$	−1.01535	−0.0392852
$669$	23.3219	0.901678
$670$	−35.9561	−1.38910
$671$	−10.4177	−0.402169
$672$	−0.910204	−0.0351119
$673$	13.5554	0.522521	0.261260	−	0.965268i	$-0.415862\pi$
$673$	13.5554	0.522521	0.261260	+	0.965268i	$0.415862\pi$
$674$	−4.99587	−0.192434
$675$	−12.3136	−0.473950
$676$	12.5845	0.484021
$677$	15.3094	0.588386	0.294193	−	0.955746i	$-0.404949\pi$
$677$	15.3094	0.588386	0.294193	+	0.955746i	$0.404949\pi$
$678$	1.29686	0.0498055
$679$	−13.2382	−0.508034
$680$	20.9232	0.802366
$681$	−3.49187	−0.133809
$682$	−16.7325	−0.640722
$683$	29.4186	1.12567	0.562836	−	0.826569i	$-0.309710\pi$
$683$	29.4186	1.12567	0.562836	+	0.826569i	$0.309710\pi$
$684$	−1.00000	−0.0382360
$685$	32.7882	1.25277
$686$	−11.9888	−0.457734
$687$	10.5890	0.403997
$688$	−9.91571	−0.378033
$689$	5.05812	0.192699
$690$	−25.7157	−0.978978
$691$	−8.48623	−0.322831	−0.161416	−	0.986887i	$-0.551606\pi$
$691$	−8.48623	−0.322831	−0.161416	+	0.986887i	$0.551606\pi$
$692$	−9.31160	−0.353974
$693$	−1.46878	−0.0557942
$694$	12.1689	0.461925
$695$	6.20204	0.235257
$696$	−6.09944	−0.231199
$697$	16.3533	0.619427
$698$	20.5247	0.776872
$699$	16.7887	0.635007
$700$	11.2079	0.423618
$701$	−19.0710	−0.720302	−0.360151	−	0.932894i	$-0.617275\pi$
$701$	−19.0710	−0.720302	−0.360151	+	0.932894i	$0.617275\pi$
$702$	−5.05812	−0.190906
$703$	1.16053	0.0437701
$704$	−1.61368	−0.0608178
$705$	43.4990	1.63827
$706$	−7.85025	−0.295448
$707$	10.9086	0.410259
$708$	0.621122	0.0233432
$709$	−17.6920	−0.664436	−0.332218	−	0.943203i	$-0.607797\pi$
$709$	−17.6920	−0.664436	−0.332218	+	0.943203i	$0.607797\pi$
$710$	27.2732	1.02354
$711$	8.95893	0.335986
$712$	−18.0502	−0.676460
$713$	−64.0838	−2.39996
$714$	4.57691	0.171287
$715$	33.9625	1.27013
$716$	2.25692	0.0843451
$717$	−3.99510	−0.149200
$718$	−2.58986	−0.0966528
$719$	17.6324	0.657576	0.328788	−	0.944404i	$-0.393360\pi$
$719$	17.6324	0.657576	0.328788	+	0.944404i	$0.393360\pi$
$720$	−4.16096	−0.155070
$721$	−2.21148	−0.0823600
$722$	1.00000	0.0372161
$723$	15.9855	0.594506
$724$	10.5293	0.391320
$725$	75.1060	2.78937
$726$	8.39604	0.311606
$727$	−26.0740	−0.967030	−0.483515	−	0.875336i	$-0.660640\pi$
$727$	−26.0740	−0.967030	−0.483515	+	0.875336i	$0.660640\pi$
$728$	4.60392	0.170633
$729$	1.00000	0.0370370
$730$	11.2222	0.415354
$731$	49.8606	1.84416
$732$	−6.45584	−0.238615
$733$	13.1972	0.487451	0.243726	−	0.969844i	$-0.421630\pi$
$733$	13.1972	0.487451	0.243726	+	0.969844i	$0.421630\pi$
$734$	−33.6418	−1.24174
$735$	−25.6795	−0.947202
$736$	−6.18022	−0.227806
$737$	−13.9443	−0.513644
$738$	−3.25217	−0.119714
$739$	28.1993	1.03733	0.518663	−	0.854979i	$-0.326430\pi$
$739$	28.1993	1.03733	0.518663	+	0.854979i	$0.326430\pi$
$740$	4.82891	0.177514
$741$	5.05812	0.185815
$742$	0.910204	0.0334146
$743$	4.32188	0.158554	0.0792772	−	0.996853i	$-0.474739\pi$
$743$	4.32188	0.158554	0.0792772	+	0.996853i	$0.474739\pi$
$744$	−10.3692	−0.380152
$745$	−72.1220	−2.64235
$746$	−5.85429	−0.214341
$747$	−4.45871	−0.163136
$748$	8.11430	0.296688
$749$	−2.70592	−0.0988722
$750$	30.4315	1.11120
$751$	23.9688	0.874633	0.437316	−	0.899308i	$-0.355929\pi$
$751$	23.9688	0.874633	0.437316	+	0.899308i	$0.355929\pi$
$752$	10.4541	0.381221
$753$	−15.1250	−0.551184
$754$	30.8517	1.12355
$755$	−21.4322	−0.779999
$756$	−0.910204	−0.0331038
$757$	−32.0450	−1.16470	−0.582348	−	0.812940i	$-0.697866\pi$
$757$	−32.0450	−1.16470	−0.582348	+	0.812940i	$0.697866\pi$
$758$	−34.9381	−1.26901
$759$	−9.97290	−0.361993
$760$	4.16096	0.150934
$761$	−38.3947	−1.39181	−0.695904	−	0.718135i	$-0.744996\pi$
$761$	−38.3947	−1.39181	−0.695904	+	0.718135i	$0.744996\pi$
$762$	6.26588	0.226989
$763$	−7.16475	−0.259382
$764$	26.1574	0.946341
$765$	20.9232	0.756478
$766$	−5.63771	−0.203699
$767$	−3.14171	−0.113440
$768$	−1.00000	−0.0360844
$769$	−31.1948	−1.12491	−0.562457	−	0.826827i	$-0.690144\pi$
$769$	−31.1948	−1.12491	−0.562457	+	0.826827i	$0.690144\pi$
$770$	6.11152	0.220244
$771$	24.6253	0.886860
$772$	22.9441	0.825775
$773$	−33.3932	−1.20107	−0.600535	−	0.799598i	$-0.705046\pi$
$773$	−33.3932	−1.20107	−0.600535	+	0.799598i	$0.705046\pi$
$774$	−9.91571	−0.356413
$775$	127.682	4.58646
$776$	−14.5442	−0.522105
$777$	1.05632	0.0378952
$778$	9.15935	0.328379
$779$	3.25217	0.116521
$780$	21.0466	0.753590
$781$	10.5769	0.378472
$782$	31.0769	1.11131
$783$	−6.09944	−0.217976
$784$	−6.17153	−0.220412
$785$	65.0760	2.32266
$786$	19.1155	0.681827
$787$	29.6663	1.05749	0.528745	−	0.848781i	$-0.322663\pi$
$787$	29.6663	1.05749	0.528745	+	0.848781i	$0.322663\pi$
$788$	10.7254	0.382075
$789$	5.53601	0.197087
$790$	−37.2778	−1.32628
$791$	−1.18041	−0.0419704
$792$	−1.61368	−0.0573396
$793$	32.6544	1.15959
$794$	−22.0761	−0.783453
$795$	4.16096	0.147574
$796$	−23.1006	−0.818778
$797$	−14.9315	−0.528902	−0.264451	−	0.964399i	$-0.585191\pi$
$797$	−14.9315	−0.528902	−0.264451	+	0.964399i	$0.585191\pi$
$798$	0.910204	0.0322209
$799$	−52.5678	−1.85971
$800$	12.3136	0.435351
$801$	−18.0502	−0.637773
$802$	−26.1359	−0.922889
$803$	4.35214	0.153584
$804$	−8.64129	−0.304755
$805$	23.4065	0.824971
$806$	52.4485	1.84742
$807$	10.0140	0.352510
$808$	11.9847	0.421622
$809$	−35.5249	−1.24899	−0.624495	−	0.781029i	$-0.714695\pi$
$809$	−35.5249	−1.24899	−0.624495	+	0.781029i	$0.714695\pi$
$810$	−4.16096	−0.146201
$811$	−53.2092	−1.86843	−0.934213	−	0.356716i	$-0.883897\pi$
$811$	−53.2092	−1.86843	−0.934213	+	0.356716i	$0.883897\pi$
$812$	5.55173	0.194828
$813$	3.31327	0.116201
$814$	1.87272	0.0656388
$815$	76.3408	2.67410
$816$	5.02844	0.176031
$817$	9.91571	0.346907
$818$	16.9913	0.594086
$819$	4.60392	0.160874
$820$	13.5321	0.472563
$821$	−18.0390	−0.629564	−0.314782	−	0.949164i	$-0.601931\pi$
$821$	−18.0390	−0.629564	−0.314782	+	0.949164i	$0.601931\pi$
$822$	7.87996	0.274845
$823$	−34.7364	−1.21083	−0.605417	−	0.795909i	$-0.706993\pi$
$823$	−34.7364	−1.21083	−0.605417	+	0.795909i	$0.706993\pi$
$824$	−2.42966	−0.0846411
$825$	19.8702	0.691791
$826$	−0.565348	−0.0196710
$827$	−4.59219	−0.159686	−0.0798431	−	0.996807i	$-0.525442\pi$
$827$	−4.59219	−0.159686	−0.0798431	+	0.996807i	$0.525442\pi$
$828$	−6.18022	−0.214778
$829$	45.5883	1.58335	0.791673	−	0.610945i	$-0.209210\pi$
$829$	45.5883	1.58335	0.791673	+	0.610945i	$0.209210\pi$
$830$	18.5525	0.643967
$831$	−7.11413	−0.246786
$832$	5.05812	0.175359
$833$	31.0332	1.07524
$834$	1.49053	0.0516129
$835$	4.22485	0.146207
$836$	1.61368	0.0558103
$837$	−10.3692	−0.358411
$838$	31.1088	1.07464
$839$	1.49784	0.0517112	0.0258556	−	0.999666i	$-0.491769\pi$
$839$	1.49784	0.0517112	0.0258556	+	0.999666i	$0.491769\pi$
$840$	3.78732	0.130675
$841$	8.20313	0.282867
$842$	−14.0374	−0.483760
$843$	22.5858	0.777895
$844$	−6.07426	−0.209085
$845$	−52.3638	−1.80137
$846$	10.4541	0.359419
$847$	−7.64211	−0.262586
$848$	1.00000	0.0343401
$849$	13.0749	0.448729
$850$	−61.9182	−2.12378
$851$	7.17232	0.245864
$852$	6.55454	0.224555
$853$	−35.6800	−1.22166	−0.610829	−	0.791762i	$-0.709164\pi$
$853$	−35.6800	−1.22166	−0.610829	+	0.791762i	$0.709164\pi$
$854$	5.87613	0.201077
$855$	4.16096	0.142302
$856$	−2.97287	−0.101611
$857$	33.3192	1.13816	0.569082	−	0.822281i	$-0.307299\pi$
$857$	33.3192	1.13816	0.569082	+	0.822281i	$0.307299\pi$
$858$	8.16218	0.278652
$859$	45.3926	1.54877	0.774387	−	0.632712i	$-0.218058\pi$
$859$	45.3926	1.54877	0.774387	+	0.632712i	$0.218058\pi$
$860$	41.2589	1.40692
$861$	2.96014	0.100881
$862$	14.8695	0.506456
$863$	25.2032	0.857927	0.428963	−	0.903322i	$-0.358879\pi$
$863$	25.2032	0.857927	0.428963	+	0.903322i	$0.358879\pi$
$864$	−1.00000	−0.0340207
$865$	38.7452	1.31738
$866$	−1.93675	−0.0658133
$867$	−8.28525	−0.281382
$868$	9.43807	0.320349
$869$	−14.4568	−0.490415
$870$	25.3795	0.860446
$871$	43.7087	1.48101
$872$	−7.87159	−0.266566
$873$	−14.5442	−0.492246
$874$	6.18022	0.209049
$875$	−27.6989	−0.936394
$876$	2.69703	0.0911242
$877$	11.4882	0.387930	0.193965	−	0.981008i	$-0.437865\pi$
$877$	11.4882	0.387930	0.193965	+	0.981008i	$0.437865\pi$
$878$	−19.2634	−0.650108
$879$	21.5672	0.727442
$880$	6.71446	0.226344
$881$	−23.5299	−0.792744	−0.396372	−	0.918090i	$-0.629731\pi$
$881$	−23.5299	−0.792744	−0.396372	+	0.918090i	$0.629731\pi$
$882$	−6.17153	−0.207806
$883$	−23.4254	−0.788328	−0.394164	−	0.919040i	$-0.628966\pi$
$883$	−23.4254	−0.788328	−0.394164	+	0.919040i	$0.628966\pi$
$884$	−25.4345	−0.855453
$885$	−2.58446	−0.0868758
$886$	19.0657	0.640525
$887$	18.6608	0.626570	0.313285	−	0.949659i	$-0.398571\pi$
$887$	18.6608	0.626570	0.313285	+	0.949659i	$0.398571\pi$
$888$	1.16053	0.0389448
$889$	−5.70323	−0.191280
$890$	75.1062	2.51756
$891$	−1.61368	−0.0540603
$892$	−23.3219	−0.780876
$893$	−10.4541	−0.349832
$894$	−17.3330	−0.579703
$895$	−9.39096	−0.313905
$896$	0.910204	0.0304078
$897$	31.2603	1.04375
$898$	23.1735	0.773309
$899$	63.2461	2.10938
$900$	12.3136	0.410453
$901$	−5.02844	−0.167522
$902$	5.24795	0.174738
$903$	9.02532	0.300344
$904$	−1.29686	−0.0431329
$905$	−43.8122	−1.45637
$906$	−5.15079	−0.171124
$907$	−13.2781	−0.440891	−0.220445	−	0.975399i	$-0.570751\pi$
$907$	−13.2781	−0.440891	−0.220445	+	0.975399i	$0.570751\pi$
$908$	3.49187	0.115882
$909$	11.9847	0.397509
$910$	−19.1567	−0.635039
$911$	40.7887	1.35139	0.675695	−	0.737182i	$-0.263844\pi$
$911$	40.7887	1.35139	0.675695	+	0.737182i	$0.263844\pi$
$912$	1.00000	0.0331133
$913$	7.19493	0.238117
$914$	27.8790	0.922156
$915$	26.8625	0.888046
$916$	−10.5890	−0.349872
$917$	−17.3990	−0.574566
$918$	5.02844	0.165963
$919$	2.14942	0.0709029	0.0354514	−	0.999371i	$-0.488713\pi$
$919$	2.14942	0.0709029	0.0354514	+	0.999371i	$0.488713\pi$
$920$	25.7157	0.847820
$921$	10.0912	0.332518
$922$	37.6707	1.24062
$923$	−33.1536	−1.09126
$924$	1.46878	0.0483192
$925$	−14.2903	−0.469861
$926$	27.8503	0.915217
$927$	−2.42966	−0.0798004
$928$	6.09944	0.200224
$929$	−36.2371	−1.18890	−0.594451	−	0.804132i	$-0.702631\pi$
$929$	−36.2371	−1.18890	−0.594451	+	0.804132i	$0.702631\pi$
$930$	43.1457	1.41480
$931$	6.17153	0.202264
$932$	−16.7887	−0.549932
$933$	26.2552	0.859558
$934$	11.4575	0.374899
$935$	−33.7633	−1.10418
$936$	5.05812	0.165330
$937$	−8.09827	−0.264559	−0.132279	−	0.991212i	$-0.542230\pi$
$937$	−8.09827	−0.264559	−0.132279	+	0.991212i	$0.542230\pi$
$938$	7.86534	0.256812
$939$	−10.9391	−0.356983
$940$	−43.4990	−1.41878
$941$	−60.8663	−1.98419	−0.992093	−	0.125505i	$-0.959945\pi$
$941$	−60.8663	−1.98419	−0.992093	+	0.125505i	$0.959945\pi$
$942$	15.6397	0.509568
$943$	20.0991	0.654517
$944$	−0.621122	−0.0202158
$945$	3.78732	0.123202
$946$	16.0008	0.520230
$947$	11.0210	0.358133	0.179067	−	0.983837i	$-0.442692\pi$
$947$	11.0210	0.358133	0.179067	+	0.983837i	$0.442692\pi$
$948$	−8.95893	−0.290973
$949$	−13.6419	−0.442835
$950$	−12.3136	−0.399506
$951$	6.73489	0.218394
$952$	−4.57691	−0.148339
$953$	−34.7925	−1.12704	−0.563520	−	0.826102i	$-0.690553\pi$
$953$	−34.7925	−1.12704	−0.563520	+	0.826102i	$0.690553\pi$
$954$	1.00000	0.0323762
$955$	−108.840	−3.52197
$956$	3.99510	0.129211
$957$	9.84254	0.318164
$958$	−1.77576	−0.0573721
$959$	−7.17238	−0.231608
$960$	4.16096	0.134294
$961$	76.5198	2.46838
$962$	−5.87009	−0.189259
$963$	−2.97287	−0.0957995
$964$	−15.9855	−0.514857
$965$	−95.4694	−3.07327
$966$	5.62526	0.180990
$967$	−0.685903	−0.0220572	−0.0110286	−	0.999939i	$-0.503511\pi$
$967$	−0.685903	−0.0220572	−0.0110286	+	0.999939i	$0.503511\pi$
$968$	−8.39604	−0.269859
$969$	−5.02844	−0.161537
$970$	60.5177	1.94311
$971$	−0.285022	−0.00914678	−0.00457339	−	0.999990i	$-0.501456\pi$
$971$	−0.285022	−0.00914678	−0.00457339	+	0.999990i	$0.501456\pi$
$972$	−1.00000	−0.0320750
$973$	−1.35669	−0.0434934
$974$	−16.5506	−0.530314
$975$	−62.2836	−1.99467
$976$	6.45584	0.206646
$977$	46.9276	1.50135	0.750673	−	0.660674i	$-0.229730\pi$
$977$	46.9276	1.50135	0.750673	+	0.660674i	$0.229730\pi$
$978$	18.3469	0.586670
$979$	29.1272	0.930911
$980$	25.6795	0.820301
$981$	−7.87159	−0.251321
$982$	30.1979	0.963653
$983$	−18.0858	−0.576849	−0.288424	−	0.957503i	$-0.593131\pi$
$983$	−18.0858	−0.576849	−0.288424	+	0.957503i	$0.593131\pi$
$984$	3.25217	0.103675
$985$	−44.6278	−1.42196
$986$	−30.6707	−0.976753
$987$	−9.51534	−0.302877
$988$	−5.05812	−0.160920
$989$	61.2813	1.94863
$990$	6.71446	0.213399
$991$	−12.9040	−0.409908	−0.204954	−	0.978772i	$-0.565705\pi$
$991$	−12.9040	−0.409908	−0.204954	+	0.978772i	$0.565705\pi$
$992$	10.3692	0.329222
$993$	18.3594	0.582619
$994$	−5.96597	−0.189229
$995$	96.1205	3.04722
$996$	4.45871	0.141280
$997$	−47.4698	−1.50338	−0.751691	−	0.659515i	$-0.770762\pi$
$997$	−47.4698	−1.50338	−0.751691	+	0.659515i	$0.770762\pi$
$998$	−4.67663	−0.148036
$999$	1.16053	0.0367175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bb.1.1	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bb.1.1	✓	9	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.16096 q^{5} -1.00000 q^{6} +0.910204 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.16096 q^{5} -1.00000 q^{6} +0.910204 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.16096 q^{10} -1.61368 q^{11} -1.00000 q^{12} +5.05812 q^{13} +0.910204 q^{14} +4.16096 q^{15} +1.00000 q^{16} -5.02844 q^{17} +1.00000 q^{18} -1.00000 q^{19} -4.16096 q^{20} -0.910204 q^{21} -1.61368 q^{22} -6.18022 q^{23} -1.00000 q^{24} +12.3136 q^{25} +5.05812 q^{26} -1.00000 q^{27} +0.910204 q^{28} +6.09944 q^{29} +4.16096 q^{30} +10.3692 q^{31} +1.00000 q^{32} +1.61368 q^{33} -5.02844 q^{34} -3.78732 q^{35} +1.00000 q^{36} -1.16053 q^{37} -1.00000 q^{38} -5.05812 q^{39} -4.16096 q^{40} -3.25217 q^{41} -0.910204 q^{42} -9.91571 q^{43} -1.61368 q^{44} -4.16096 q^{45} -6.18022 q^{46} +10.4541 q^{47} -1.00000 q^{48} -6.17153 q^{49} +12.3136 q^{50} +5.02844 q^{51} +5.05812 q^{52} +1.00000 q^{53} -1.00000 q^{54} +6.71446 q^{55} +0.910204 q^{56} +1.00000 q^{57} +6.09944 q^{58} -0.621122 q^{59} +4.16096 q^{60} +6.45584 q^{61} +10.3692 q^{62} +0.910204 q^{63} +1.00000 q^{64} -21.0466 q^{65} +1.61368 q^{66} +8.64129 q^{67} -5.02844 q^{68} +6.18022 q^{69} -3.78732 q^{70} -6.55454 q^{71} +1.00000 q^{72} -2.69703 q^{73} -1.16053 q^{74} -12.3136 q^{75} -1.00000 q^{76} -1.46878 q^{77} -5.05812 q^{78} +8.95893 q^{79} -4.16096 q^{80} +1.00000 q^{81} -3.25217 q^{82} -4.45871 q^{83} -0.910204 q^{84} +20.9232 q^{85} -9.91571 q^{86} -6.09944 q^{87} -1.61368 q^{88} -18.0502 q^{89} -4.16096 q^{90} +4.60392 q^{91} -6.18022 q^{92} -10.3692 q^{93} +10.4541 q^{94} +4.16096 q^{95} -1.00000 q^{96} -14.5442 q^{97} -6.17153 q^{98} -1.61368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 5 q^{5} - 9 q^{6} - 5 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 5 * q^5 - 9 * q^6 - 5 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 5 q^{5} - 9 q^{6} - 5 q^{7} + 9 q^{8} + 9 q^{9} - 5 q^{10} + 3 q^{11} - 9 q^{12} - 4 q^{13} - 5 q^{14} + 5 q^{15} + 9 q^{16} - 16 q^{17} + 9 q^{18} - 9 q^{19} - 5 q^{20} + 5 q^{21} + 3 q^{22} - 9 q^{24} + 8 q^{25} - 4 q^{26} - 9 q^{27} - 5 q^{28} - 2 q^{29} + 5 q^{30} - 10 q^{31} + 9 q^{32} - 3 q^{33} - 16 q^{34} - q^{35} + 9 q^{36} - 14 q^{37} - 9 q^{38} + 4 q^{39} - 5 q^{40} - 21 q^{41} + 5 q^{42} - 4 q^{43} + 3 q^{44} - 5 q^{45} - 8 q^{47} - 9 q^{48} - 14 q^{49} + 8 q^{50} + 16 q^{51} - 4 q^{52} + 9 q^{53} - 9 q^{54} - 14 q^{55} - 5 q^{56} + 9 q^{57} - 2 q^{58} - 12 q^{59} + 5 q^{60} - 13 q^{61} - 10 q^{62} - 5 q^{63} + 9 q^{64} - 13 q^{65} - 3 q^{66} + 22 q^{67} - 16 q^{68} - q^{70} - 13 q^{71} + 9 q^{72} - 17 q^{73} - 14 q^{74} - 8 q^{75} - 9 q^{76} - 25 q^{77} + 4 q^{78} - 5 q^{80} + 9 q^{81} - 21 q^{82} - 24 q^{83} + 5 q^{84} - 16 q^{85} - 4 q^{86} + 2 q^{87} + 3 q^{88} - 23 q^{89} - 5 q^{90} - 11 q^{91} + 10 q^{93} - 8 q^{94} + 5 q^{95} - 9 q^{96} - 29 q^{97} - 14 q^{98} + 3 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 5 * q^5 - 9 * q^6 - 5 * q^7 + 9 * q^8 + 9 * q^9 - 5 * q^10 + 3 * q^11 - 9 * q^12 - 4 * q^13 - 5 * q^14 + 5 * q^15 + 9 * q^16 - 16 * q^17 + 9 * q^18 - 9 * q^19 - 5 * q^20 + 5 * q^21 + 3 * q^22 - 9 * q^24 + 8 * q^25 - 4 * q^26 - 9 * q^27 - 5 * q^28 - 2 * q^29 + 5 * q^30 - 10 * q^31 + 9 * q^32 - 3 * q^33 - 16 * q^34 - q^35 + 9 * q^36 - 14 * q^37 - 9 * q^38 + 4 * q^39 - 5 * q^40 - 21 * q^41 + 5 * q^42 - 4 * q^43 + 3 * q^44 - 5 * q^45 - 8 * q^47 - 9 * q^48 - 14 * q^49 + 8 * q^50 + 16 * q^51 - 4 * q^52 + 9 * q^53 - 9 * q^54 - 14 * q^55 - 5 * q^56 + 9 * q^57 - 2 * q^58 - 12 * q^59 + 5 * q^60 - 13 * q^61 - 10 * q^62 - 5 * q^63 + 9 * q^64 - 13 * q^65 - 3 * q^66 + 22 * q^67 - 16 * q^68 - q^70 - 13 * q^71 + 9 * q^72 - 17 * q^73 - 14 * q^74 - 8 * q^75 - 9 * q^76 - 25 * q^77 + 4 * q^78 - 5 * q^80 + 9 * q^81 - 21 * q^82 - 24 * q^83 + 5 * q^84 - 16 * q^85 - 4 * q^86 + 2 * q^87 + 3 * q^88 - 23 * q^89 - 5 * q^90 - 11 * q^91 + 10 * q^93 - 8 * q^94 + 5 * q^95 - 9 * q^96 - 29 * q^97 - 14 * q^98 + 3 * q^99

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