LMFDB - Embedded newform 6042.2.a.bb.1.6

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			1.6
Root			$0.217879$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.926601 q^{5} -1.00000 q^{6} -0.782121 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.926601 q^{5} -1.00000 q^{6} -0.782121 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.926601 q^{10} -4.19823 q^{11} -1.00000 q^{12} +1.67596 q^{13} -0.782121 q^{14} -0.926601 q^{15} +1.00000 q^{16} +0.331752 q^{17} +1.00000 q^{18} -1.00000 q^{19} +0.926601 q^{20} +0.782121 q^{21} -4.19823 q^{22} +0.149937 q^{23} -1.00000 q^{24} -4.14141 q^{25} +1.67596 q^{26} -1.00000 q^{27} -0.782121 q^{28} +3.09255 q^{29} -0.926601 q^{30} +4.21227 q^{31} +1.00000 q^{32} +4.19823 q^{33} +0.331752 q^{34} -0.724714 q^{35} +1.00000 q^{36} -10.0253 q^{37} -1.00000 q^{38} -1.67596 q^{39} +0.926601 q^{40} -5.83159 q^{41} +0.782121 q^{42} +6.59799 q^{43} -4.19823 q^{44} +0.926601 q^{45} +0.149937 q^{46} -0.211837 q^{47} -1.00000 q^{48} -6.38829 q^{49} -4.14141 q^{50} -0.331752 q^{51} +1.67596 q^{52} +1.00000 q^{53} -1.00000 q^{54} -3.89008 q^{55} -0.782121 q^{56} +1.00000 q^{57} +3.09255 q^{58} -9.04676 q^{59} -0.926601 q^{60} -0.848763 q^{61} +4.21227 q^{62} -0.782121 q^{63} +1.00000 q^{64} +1.55295 q^{65} +4.19823 q^{66} +1.44469 q^{67} +0.331752 q^{68} -0.149937 q^{69} -0.724714 q^{70} -8.46784 q^{71} +1.00000 q^{72} -8.41498 q^{73} -10.0253 q^{74} +4.14141 q^{75} -1.00000 q^{76} +3.28353 q^{77} -1.67596 q^{78} +16.4095 q^{79} +0.926601 q^{80} +1.00000 q^{81} -5.83159 q^{82} +11.2084 q^{83} +0.782121 q^{84} +0.307402 q^{85} +6.59799 q^{86} -3.09255 q^{87} -4.19823 q^{88} +13.8033 q^{89} +0.926601 q^{90} -1.31081 q^{91} +0.149937 q^{92} -4.21227 q^{93} -0.211837 q^{94} -0.926601 q^{95} -1.00000 q^{96} -13.9685 q^{97} -6.38829 q^{98} -4.19823 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.926601	0.414388	0.207194	−	0.978300i	$-0.433567\pi$
$5$	0.926601	0.414388	0.207194	+	0.978300i	$0.433567\pi$
$6$	−1.00000	−0.408248
$7$	−0.782121	−0.295614	−0.147807	−	0.989016i	$-0.547221\pi$
$7$	−0.782121	−0.295614	−0.147807	+	0.989016i	$0.547221\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.926601	0.293017
$11$	−4.19823	−1.26581	−0.632907	−	0.774228i	$-0.718139\pi$
$11$	−4.19823	−1.26581	−0.632907	+	0.774228i	$0.718139\pi$
$12$	−1.00000	−0.288675
$13$	1.67596	0.464828	0.232414	−	0.972617i	$-0.425337\pi$
$13$	1.67596	0.464828	0.232414	+	0.972617i	$0.425337\pi$
$14$	−0.782121	−0.209031
$15$	−0.926601	−0.239247
$16$	1.00000	0.250000
$17$	0.331752	0.0804618	0.0402309	−	0.999190i	$-0.487191\pi$
$17$	0.331752	0.0804618	0.0402309	+	0.999190i	$0.487191\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.926601	0.207194
$21$	0.782121	0.170673
$22$	−4.19823	−0.895066
$23$	0.149937	0.0312639	0.0156320	−	0.999878i	$-0.495024\pi$
$23$	0.149937	0.0312639	0.0156320	+	0.999878i	$0.495024\pi$
$24$	−1.00000	−0.204124
$25$	−4.14141	−0.828282
$26$	1.67596	0.328683
$27$	−1.00000	−0.192450
$28$	−0.782121	−0.147807
$29$	3.09255	0.574273	0.287136	−	0.957890i	$-0.407297\pi$
$29$	3.09255	0.574273	0.287136	+	0.957890i	$0.407297\pi$
$30$	−0.926601	−0.169173
$31$	4.21227	0.756545	0.378273	−	0.925694i	$-0.376518\pi$
$31$	4.21227	0.756545	0.378273	+	0.925694i	$0.376518\pi$
$32$	1.00000	0.176777
$33$	4.19823	0.730818
$34$	0.331752	0.0568951
$35$	−0.724714	−0.122499
$36$	1.00000	0.166667
$37$	−10.0253	−1.64815	−0.824075	−	0.566481i	$-0.808304\pi$
$37$	−10.0253	−1.64815	−0.824075	+	0.566481i	$0.808304\pi$
$38$	−1.00000	−0.162221
$39$	−1.67596	−0.268369
$40$	0.926601	0.146508
$41$	−5.83159	−0.910742	−0.455371	−	0.890302i	$-0.650493\pi$
$41$	−5.83159	−0.910742	−0.455371	+	0.890302i	$0.650493\pi$
$42$	0.782121	0.120684
$43$	6.59799	1.00618	0.503092	−	0.864233i	$-0.332196\pi$
$43$	6.59799	1.00618	0.503092	+	0.864233i	$0.332196\pi$
$44$	−4.19823	−0.632907
$45$	0.926601	0.138129
$46$	0.149937	0.0221069
$47$	−0.211837	−0.0308996	−0.0154498	−	0.999881i	$-0.504918\pi$
$47$	−0.211837	−0.0308996	−0.0154498	+	0.999881i	$0.504918\pi$
$48$	−1.00000	−0.144338
$49$	−6.38829	−0.912612
$50$	−4.14141	−0.585684
$51$	−0.331752	−0.0464546
$52$	1.67596	0.232414
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−1.00000	−0.136083
$55$	−3.89008	−0.524539
$56$	−0.782121	−0.104515
$57$	1.00000	0.132453
$58$	3.09255	0.406072
$59$	−9.04676	−1.17779	−0.588894	−	0.808211i	$-0.700436\pi$
$59$	−9.04676	−1.17779	−0.588894	+	0.808211i	$0.700436\pi$
$60$	−0.926601	−0.119624
$61$	−0.848763	−0.108673	−0.0543365	−	0.998523i	$-0.517304\pi$
$61$	−0.848763	−0.108673	−0.0543365	+	0.998523i	$0.517304\pi$
$62$	4.21227	0.534958
$63$	−0.782121	−0.0985380
$64$	1.00000	0.125000
$65$	1.55295	0.192620
$66$	4.19823	0.516767
$67$	1.44469	0.176497	0.0882484	−	0.996099i	$-0.471873\pi$
$67$	1.44469	0.176497	0.0882484	+	0.996099i	$0.471873\pi$
$68$	0.331752	0.0402309
$69$	−0.149937	−0.0180502
$70$	−0.724714	−0.0866199
$71$	−8.46784	−1.00495	−0.502474	−	0.864593i	$-0.667577\pi$
$71$	−8.46784	−1.00495	−0.502474	+	0.864593i	$0.667577\pi$
$72$	1.00000	0.117851
$73$	−8.41498	−0.984899	−0.492450	−	0.870341i	$-0.663898\pi$
$73$	−8.41498	−0.984899	−0.492450	+	0.870341i	$0.663898\pi$
$74$	−10.0253	−1.16542
$75$	4.14141	0.478209
$76$	−1.00000	−0.114708
$77$	3.28353	0.374192
$78$	−1.67596	−0.189765
$79$	16.4095	1.84621	0.923104	−	0.384551i	$-0.125644\pi$
$79$	16.4095	1.84621	0.923104	+	0.384551i	$0.125644\pi$
$80$	0.926601	0.103597
$81$	1.00000	0.111111
$82$	−5.83159	−0.643992
$83$	11.2084	1.23029	0.615143	−	0.788415i	$-0.289098\pi$
$83$	11.2084	1.23029	0.615143	+	0.788415i	$0.289098\pi$
$84$	0.782121	0.0853364
$85$	0.307402	0.0333424
$86$	6.59799	0.711480
$87$	−3.09255	−0.331557
$88$	−4.19823	−0.447533
$89$	13.8033	1.46315	0.731573	−	0.681763i	$-0.238786\pi$
$89$	13.8033	1.46315	0.731573	+	0.681763i	$0.238786\pi$
$90$	0.926601	0.0976723
$91$	−1.31081	−0.137410
$92$	0.149937	0.0156320
$93$	−4.21227	−0.436792
$94$	−0.211837	−0.0218493
$95$	−0.926601	−0.0950672
$96$	−1.00000	−0.102062
$97$	−13.9685	−1.41828	−0.709142	−	0.705066i	$-0.750917\pi$
$97$	−13.9685	−1.41828	−0.709142	+	0.705066i	$0.750917\pi$
$98$	−6.38829	−0.645314
$99$	−4.19823	−0.421938
$100$	−4.14141	−0.414141
$101$	−18.3409	−1.82499	−0.912496	−	0.409085i	$-0.865848\pi$
$101$	−18.3409	−1.82499	−0.912496	+	0.409085i	$0.865848\pi$
$102$	−0.331752	−0.0328484
$103$	3.24954	0.320187	0.160093	−	0.987102i	$-0.448820\pi$
$103$	3.24954	0.320187	0.160093	+	0.987102i	$0.448820\pi$
$104$	1.67596	0.164342
$105$	0.724714	0.0707248
$106$	1.00000	0.0971286
$107$	−9.19467	−0.888883	−0.444441	−	0.895808i	$-0.646598\pi$
$107$	−9.19467	−0.888883	−0.444441	+	0.895808i	$0.646598\pi$
$108$	−1.00000	−0.0962250
$109$	−14.6653	−1.40468	−0.702341	−	0.711841i	$-0.747862\pi$
$109$	−14.6653	−1.40468	−0.702341	+	0.711841i	$0.747862\pi$
$110$	−3.89008	−0.370905
$111$	10.0253	0.951560
$112$	−0.782121	−0.0739035
$113$	−19.8904	−1.87113	−0.935566	−	0.353153i	$-0.885110\pi$
$113$	−19.8904	−1.87113	−0.935566	+	0.353153i	$0.885110\pi$
$114$	1.00000	0.0936586
$115$	0.138931	0.0129554
$116$	3.09255	0.287136
$117$	1.67596	0.154943
$118$	−9.04676	−0.832821
$119$	−0.259470	−0.0237856
$120$	−0.926601	−0.0845867
$121$	6.62515	0.602286
$122$	−0.848763	−0.0768434
$123$	5.83159	0.525817
$124$	4.21227	0.378273
$125$	−8.47044	−0.757619
$126$	−0.782121	−0.0696769
$127$	3.58632	0.318235	0.159117	−	0.987260i	$-0.449135\pi$
$127$	3.58632	0.318235	0.159117	+	0.987260i	$0.449135\pi$
$128$	1.00000	0.0883883
$129$	−6.59799	−0.580921
$130$	1.55295	0.136203
$131$	−14.6250	−1.27780	−0.638898	−	0.769292i	$-0.720609\pi$
$131$	−14.6250	−1.27780	−0.638898	+	0.769292i	$0.720609\pi$
$132$	4.19823	0.365409
$133$	0.782121	0.0678185
$134$	1.44469	0.124802
$135$	−0.926601	−0.0797491
$136$	0.331752	0.0284475
$137$	−3.01463	−0.257558	−0.128779	−	0.991673i	$-0.541106\pi$
$137$	−3.01463	−0.257558	−0.128779	+	0.991673i	$0.541106\pi$
$138$	−0.149937	−0.0127634
$139$	6.69751	0.568075	0.284038	−	0.958813i	$-0.408326\pi$
$139$	6.69751	0.568075	0.284038	+	0.958813i	$0.408326\pi$
$140$	−0.724714	−0.0612495
$141$	0.211837	0.0178399
$142$	−8.46784	−0.710605
$143$	−7.03608	−0.588387
$144$	1.00000	0.0833333
$145$	2.86556	0.237972
$146$	−8.41498	−0.696429
$147$	6.38829	0.526897
$148$	−10.0253	−0.824075
$149$	8.53603	0.699299	0.349649	−	0.936881i	$-0.386301\pi$
$149$	8.53603	0.699299	0.349649	+	0.936881i	$0.386301\pi$
$150$	4.14141	0.338145
$151$	−14.2099	−1.15639	−0.578195	−	0.815899i	$-0.696243\pi$
$151$	−14.2099	−1.15639	−0.578195	+	0.815899i	$0.696243\pi$
$152$	−1.00000	−0.0811107
$153$	0.331752	0.0268206
$154$	3.28353	0.264594
$155$	3.90309	0.313504
$156$	−1.67596	−0.134184
$157$	−3.89737	−0.311044	−0.155522	−	0.987832i	$-0.549706\pi$
$157$	−3.89737	−0.311044	−0.155522	+	0.987832i	$0.549706\pi$
$158$	16.4095	1.30547
$159$	−1.00000	−0.0793052
$160$	0.926601	0.0732542
$161$	−0.117268	−0.00924205
$162$	1.00000	0.0785674
$163$	13.0131	1.01927	0.509634	−	0.860391i	$-0.329781\pi$
$163$	13.0131	1.01927	0.509634	+	0.860391i	$0.329781\pi$
$164$	−5.83159	−0.455371
$165$	3.89008	0.302843
$166$	11.2084	0.869944
$167$	7.49380	0.579888	0.289944	−	0.957044i	$-0.406363\pi$
$167$	7.49380	0.579888	0.289944	+	0.957044i	$0.406363\pi$
$168$	0.782121	0.0603419
$169$	−10.1911	−0.783934
$170$	0.307402	0.0235767
$171$	−1.00000	−0.0764719
$172$	6.59799	0.503092
$173$	−2.08193	−0.158286	−0.0791432	−	0.996863i	$-0.525218\pi$
$173$	−2.08193	−0.158286	−0.0791432	+	0.996863i	$0.525218\pi$
$174$	−3.09255	−0.234446
$175$	3.23908	0.244852
$176$	−4.19823	−0.316454
$177$	9.04676	0.679996
$178$	13.8033	1.03460
$179$	5.99501	0.448088	0.224044	−	0.974579i	$-0.428074\pi$
$179$	5.99501	0.448088	0.224044	+	0.974579i	$0.428074\pi$
$180$	0.926601	0.0690647
$181$	−10.6345	−0.790458	−0.395229	−	0.918583i	$-0.629335\pi$
$181$	−10.6345	−0.790458	−0.395229	+	0.918583i	$0.629335\pi$
$182$	−1.31081	−0.0971634
$183$	0.848763	0.0627423
$184$	0.149937	0.0110535
$185$	−9.28945	−0.682974
$186$	−4.21227	−0.308858
$187$	−1.39277	−0.101850
$188$	−0.211837	−0.0154498
$189$	0.782121	0.0568909
$190$	−0.926601	−0.0672227
$191$	−14.0937	−1.01978	−0.509891	−	0.860239i	$-0.670314\pi$
$191$	−14.0937	−1.01978	−0.509891	+	0.860239i	$0.670314\pi$
$192$	−1.00000	−0.0721688
$193$	−4.26766	−0.307193	−0.153597	−	0.988134i	$-0.549086\pi$
$193$	−4.26766	−0.307193	−0.153597	+	0.988134i	$0.549086\pi$
$194$	−13.9685	−1.00288
$195$	−1.55295	−0.111209
$196$	−6.38829	−0.456306
$197$	−7.60094	−0.541544	−0.270772	−	0.962643i	$-0.587279\pi$
$197$	−7.60094	−0.541544	−0.270772	+	0.962643i	$0.587279\pi$
$198$	−4.19823	−0.298355
$199$	15.5322	1.10105	0.550524	−	0.834819i	$-0.314428\pi$
$199$	15.5322	1.10105	0.550524	+	0.834819i	$0.314428\pi$
$200$	−4.14141	−0.292842
$201$	−1.44469	−0.101900
$202$	−18.3409	−1.29046
$203$	−2.41875	−0.169763
$204$	−0.331752	−0.0232273
$205$	−5.40356	−0.377401
$206$	3.24954	0.226406
$207$	0.149937	0.0104213
$208$	1.67596	0.116207
$209$	4.19823	0.290398
$210$	0.724714	0.0500100
$211$	17.5152	1.20579	0.602897	−	0.797819i	$-0.294013\pi$
$211$	17.5152	1.20579	0.602897	+	0.797819i	$0.294013\pi$
$212$	1.00000	0.0686803
$213$	8.46784	0.580207
$214$	−9.19467	−0.628535
$215$	6.11371	0.416951
$216$	−1.00000	−0.0680414
$217$	−3.29450	−0.223645
$218$	−14.6653	−0.993260
$219$	8.41498	0.568632
$220$	−3.89008	−0.262269
$221$	0.556005	0.0374009
$222$	10.0253	0.672854
$223$	6.25847	0.419098	0.209549	−	0.977798i	$-0.432800\pi$
$223$	6.25847	0.419098	0.209549	+	0.977798i	$0.432800\pi$
$224$	−0.782121	−0.0522577
$225$	−4.14141	−0.276094
$226$	−19.8904	−1.32309
$227$	−0.619197	−0.0410975	−0.0205488	−	0.999789i	$-0.506541\pi$
$227$	−0.619197	−0.0410975	−0.0205488	+	0.999789i	$0.506541\pi$
$228$	1.00000	0.0662266
$229$	25.8321	1.70703	0.853517	−	0.521065i	$-0.174465\pi$
$229$	25.8321	1.70703	0.853517	+	0.521065i	$0.174465\pi$
$230$	0.138931	0.00916086
$231$	−3.28353	−0.216040
$232$	3.09255	0.203036
$233$	−8.13029	−0.532633	−0.266317	−	0.963886i	$-0.585807\pi$
$233$	−8.13029	−0.532633	−0.266317	+	0.963886i	$0.585807\pi$
$234$	1.67596	0.109561
$235$	−0.196288	−0.0128044
$236$	−9.04676	−0.588894
$237$	−16.4095	−1.06591
$238$	−0.259470	−0.0168190
$239$	−7.75661	−0.501733	−0.250867	−	0.968022i	$-0.580716\pi$
$239$	−7.75661	−0.501733	−0.250867	+	0.968022i	$0.580716\pi$
$240$	−0.926601	−0.0598118
$241$	−5.37695	−0.346359	−0.173180	−	0.984890i	$-0.555404\pi$
$241$	−5.37695	−0.346359	−0.173180	+	0.984890i	$0.555404\pi$
$242$	6.62515	0.425881
$243$	−1.00000	−0.0641500
$244$	−0.848763	−0.0543365
$245$	−5.91939	−0.378176
$246$	5.83159	0.371809
$247$	−1.67596	−0.106639
$248$	4.21227	0.267479
$249$	−11.2084	−0.710306
$250$	−8.47044	−0.535718
$251$	−12.5236	−0.790484	−0.395242	−	0.918577i	$-0.629339\pi$
$251$	−12.5236	−0.790484	−0.395242	+	0.918577i	$0.629339\pi$
$252$	−0.782121	−0.0492690
$253$	−0.629468	−0.0395743
$254$	3.58632	0.225026
$255$	−0.307402	−0.0192503
$256$	1.00000	0.0625000
$257$	−3.06979	−0.191489	−0.0957443	−	0.995406i	$-0.530523\pi$
$257$	−3.06979	−0.191489	−0.0957443	+	0.995406i	$0.530523\pi$
$258$	−6.59799	−0.410773
$259$	7.84100	0.487216
$260$	1.55295	0.0963098
$261$	3.09255	0.191424
$262$	−14.6250	−0.903538
$263$	16.9553	1.04551	0.522755	−	0.852483i	$-0.324904\pi$
$263$	16.9553	1.04551	0.522755	+	0.852483i	$0.324904\pi$
$264$	4.19823	0.258383
$265$	0.926601	0.0569206
$266$	0.782121	0.0479549
$267$	−13.8033	−0.844748
$268$	1.44469	0.0882484
$269$	5.93047	0.361587	0.180794	−	0.983521i	$-0.442133\pi$
$269$	5.93047	0.361587	0.180794	+	0.983521i	$0.442133\pi$
$270$	−0.926601	−0.0563911
$271$	−2.26289	−0.137461	−0.0687303	−	0.997635i	$-0.521895\pi$
$271$	−2.26289	−0.137461	−0.0687303	+	0.997635i	$0.521895\pi$
$272$	0.331752	0.0201154
$273$	1.31081	0.0793336
$274$	−3.01463	−0.182121
$275$	17.3866	1.04845
$276$	−0.149937	−0.00902512
$277$	11.2497	0.675930	0.337965	−	0.941159i	$-0.390261\pi$
$277$	11.2497	0.675930	0.337965	+	0.941159i	$0.390261\pi$
$278$	6.69751	0.401690
$279$	4.21227	0.252182
$280$	−0.724714	−0.0433099
$281$	−21.8386	−1.30278	−0.651392	−	0.758741i	$-0.725815\pi$
$281$	−21.8386	−1.30278	−0.651392	+	0.758741i	$0.725815\pi$
$282$	0.211837	0.0126147
$283$	−9.22107	−0.548136	−0.274068	−	0.961710i	$-0.588369\pi$
$283$	−9.22107	−0.548136	−0.274068	+	0.961710i	$0.588369\pi$
$284$	−8.46784	−0.502474
$285$	0.926601	0.0548871
$286$	−7.03608	−0.416052
$287$	4.56101	0.269228
$288$	1.00000	0.0589256
$289$	−16.8899	−0.993526
$290$	2.86556	0.168272
$291$	13.9685	0.818846
$292$	−8.41498	−0.492450
$293$	20.5377	1.19983	0.599913	−	0.800065i	$-0.295202\pi$
$293$	20.5377	1.19983	0.599913	+	0.800065i	$0.295202\pi$
$294$	6.38829	0.372572
$295$	−8.38273	−0.488061
$296$	−10.0253	−0.582709
$297$	4.19823	0.243606
$298$	8.53603	0.494479
$299$	0.251288	0.0145324
$300$	4.14141	0.239104
$301$	−5.16043	−0.297442
$302$	−14.2099	−0.817691
$303$	18.3409	1.05366
$304$	−1.00000	−0.0573539
$305$	−0.786464	−0.0450328
$306$	0.331752	0.0189650
$307$	−27.6440	−1.57773	−0.788863	−	0.614569i	$-0.789330\pi$
$307$	−27.6440	−1.57773	−0.788863	+	0.614569i	$0.789330\pi$
$308$	3.28353	0.187096
$309$	−3.24954	−0.184860
$310$	3.90309	0.221681
$311$	14.0486	0.796622	0.398311	−	0.917250i	$-0.369596\pi$
$311$	14.0486	0.796622	0.398311	+	0.917250i	$0.369596\pi$
$312$	−1.67596	−0.0948827
$313$	−18.3113	−1.03502	−0.517508	−	0.855678i	$-0.673140\pi$
$313$	−18.3113	−1.03502	−0.517508	+	0.855678i	$0.673140\pi$
$314$	−3.89737	−0.219941
$315$	−0.724714	−0.0408330
$316$	16.4095	0.923104
$317$	11.3498	0.637466	0.318733	−	0.947844i	$-0.396743\pi$
$317$	11.3498	0.637466	0.318733	+	0.947844i	$0.396743\pi$
$318$	−1.00000	−0.0560772
$319$	−12.9833	−0.726923
$320$	0.926601	0.0517986
$321$	9.19467	0.513197
$322$	−0.117268	−0.00653512
$323$	−0.331752	−0.0184592
$324$	1.00000	0.0555556
$325$	−6.94085	−0.385009
$326$	13.0131	0.720731
$327$	14.6653	0.810994
$328$	−5.83159	−0.321996
$329$	0.165682	0.00913434
$330$	3.89008	0.214142
$331$	−1.52973	−0.0840817	−0.0420408	−	0.999116i	$-0.513386\pi$
$331$	−1.52973	−0.0840817	−0.0420408	+	0.999116i	$0.513386\pi$
$332$	11.2084	0.615143
$333$	−10.0253	−0.549383
$334$	7.49380	0.410043
$335$	1.33865	0.0731382
$336$	0.782121	0.0426682
$337$	−30.0246	−1.63555	−0.817773	−	0.575540i	$-0.804792\pi$
$337$	−30.0246	−1.63555	−0.817773	+	0.575540i	$0.804792\pi$
$338$	−10.1911	−0.554325
$339$	19.8904	1.08030
$340$	0.307402	0.0166712
$341$	−17.6841	−0.957646
$342$	−1.00000	−0.0540738
$343$	10.4713	0.565395
$344$	6.59799	0.355740
$345$	−0.138931	−0.00747981
$346$	−2.08193	−0.111925
$347$	−19.7549	−1.06050	−0.530248	−	0.847842i	$-0.677901\pi$
$347$	−19.7549	−1.06050	−0.530248	+	0.847842i	$0.677901\pi$
$348$	−3.09255	−0.165778
$349$	−26.5106	−1.41908	−0.709541	−	0.704664i	$-0.751098\pi$
$349$	−26.5106	−1.41908	−0.709541	+	0.704664i	$0.751098\pi$
$350$	3.23908	0.173136
$351$	−1.67596	−0.0894563
$352$	−4.19823	−0.223767
$353$	13.0469	0.694415	0.347207	−	0.937788i	$-0.387130\pi$
$353$	13.0469	0.694415	0.347207	+	0.937788i	$0.387130\pi$
$354$	9.04676	0.480830
$355$	−7.84630	−0.416438
$356$	13.8033	0.731573
$357$	0.259470	0.0137326
$358$	5.99501	0.316846
$359$	1.34879	0.0711863	0.0355932	−	0.999366i	$-0.488668\pi$
$359$	1.34879	0.0711863	0.0355932	+	0.999366i	$0.488668\pi$
$360$	0.926601	0.0488361
$361$	1.00000	0.0526316
$362$	−10.6345	−0.558938
$363$	−6.62515	−0.347730
$364$	−1.31081	−0.0687049
$365$	−7.79733	−0.408131
$366$	0.848763	0.0443655
$367$	7.04736	0.367869	0.183935	−	0.982938i	$-0.441117\pi$
$367$	7.04736	0.367869	0.183935	+	0.982938i	$0.441117\pi$
$368$	0.149937	0.00781598
$369$	−5.83159	−0.303581
$370$	−9.28945	−0.482936
$371$	−0.782121	−0.0406057
$372$	−4.21227	−0.218396
$373$	−4.63270	−0.239872	−0.119936	−	0.992782i	$-0.538269\pi$
$373$	−4.63270	−0.239872	−0.119936	+	0.992782i	$0.538269\pi$
$374$	−1.39277	−0.0720186
$375$	8.47044	0.437412
$376$	−0.211837	−0.0109246
$377$	5.18300	0.266938
$378$	0.782121	0.0402280
$379$	−1.15152	−0.0591498	−0.0295749	−	0.999563i	$-0.509415\pi$
$379$	−1.15152	−0.0591498	−0.0295749	+	0.999563i	$0.509415\pi$
$380$	−0.926601	−0.0475336
$381$	−3.58632	−0.183733
$382$	−14.0937	−0.721095
$383$	−21.9422	−1.12119	−0.560596	−	0.828089i	$-0.689428\pi$
$383$	−21.9422	−1.12119	−0.560596	+	0.828089i	$0.689428\pi$
$384$	−1.00000	−0.0510310
$385$	3.04252	0.155061
$386$	−4.26766	−0.217218
$387$	6.59799	0.335395
$388$	−13.9685	−0.709142
$389$	−36.2915	−1.84005	−0.920026	−	0.391858i	$-0.871832\pi$
$389$	−36.2915	−1.84005	−0.920026	+	0.391858i	$0.871832\pi$
$390$	−1.55295	−0.0786366
$391$	0.0497418	0.00251555
$392$	−6.38829	−0.322657
$393$	14.6250	0.737735
$394$	−7.60094	−0.382930
$395$	15.2050	0.765047
$396$	−4.19823	−0.210969
$397$	0.247673	0.0124304	0.00621518	−	0.999981i	$-0.498022\pi$
$397$	0.247673	0.0124304	0.00621518	+	0.999981i	$0.498022\pi$
$398$	15.5322	0.778559
$399$	−0.782121	−0.0391550
$400$	−4.14141	−0.207071
$401$	7.65273	0.382159	0.191080	−	0.981575i	$-0.438801\pi$
$401$	7.65273	0.382159	0.191080	+	0.981575i	$0.438801\pi$
$402$	−1.44469	−0.0720545
$403$	7.05960	0.351664
$404$	−18.3409	−0.912496
$405$	0.926601	0.0460432
$406$	−2.41875	−0.120041
$407$	42.0885	2.08625
$408$	−0.331752	−0.0164242
$409$	2.60227	0.128674	0.0643369	−	0.997928i	$-0.479507\pi$
$409$	2.60227	0.128674	0.0643369	+	0.997928i	$0.479507\pi$
$410$	−5.40356	−0.266863
$411$	3.01463	0.148701
$412$	3.24954	0.160093
$413$	7.07566	0.348170
$414$	0.149937	0.00736898
$415$	10.3858	0.509816
$416$	1.67596	0.0821708
$417$	−6.69751	−0.327978
$418$	4.19823	0.205342
$419$	19.4884	0.952070	0.476035	−	0.879426i	$-0.342073\pi$
$419$	19.4884	0.952070	0.476035	+	0.879426i	$0.342073\pi$
$420$	0.724714	0.0353624
$421$	13.4744	0.656703	0.328352	−	0.944556i	$-0.393507\pi$
$421$	13.4744	0.656703	0.328352	+	0.944556i	$0.393507\pi$
$422$	17.5152	0.852626
$423$	−0.211837	−0.0102999
$424$	1.00000	0.0485643
$425$	−1.37392	−0.0666450
$426$	8.46784	0.410268
$427$	0.663835	0.0321252
$428$	−9.19467	−0.444441
$429$	7.03608	0.339705
$430$	6.11371	0.294829
$431$	−5.56985	−0.268290	−0.134145	−	0.990962i	$-0.542829\pi$
$431$	−5.56985	−0.268290	−0.134145	+	0.990962i	$0.542829\pi$
$432$	−1.00000	−0.0481125
$433$	39.4783	1.89721	0.948603	−	0.316467i	$-0.102497\pi$
$433$	39.4783	1.89721	0.948603	+	0.316467i	$0.102497\pi$
$434$	−3.29450	−0.158141
$435$	−2.86556	−0.137393
$436$	−14.6653	−0.702341
$437$	−0.149937	−0.00717244
$438$	8.41498	0.402083
$439$	25.2570	1.20545	0.602725	−	0.797949i	$-0.294082\pi$
$439$	25.2570	1.20545	0.602725	+	0.797949i	$0.294082\pi$
$440$	−3.89008	−0.185452
$441$	−6.38829	−0.304204
$442$	0.556005	0.0264464
$443$	−8.17156	−0.388243	−0.194121	−	0.980978i	$-0.562186\pi$
$443$	−8.17156	−0.388243	−0.194121	+	0.980978i	$0.562186\pi$
$444$	10.0253	0.475780
$445$	12.7901	0.606311
$446$	6.25847	0.296347
$447$	−8.53603	−0.403740
$448$	−0.782121	−0.0369517
$449$	−27.2199	−1.28459	−0.642294	−	0.766458i	$-0.722017\pi$
$449$	−27.2199	−1.28459	−0.642294	+	0.766458i	$0.722017\pi$
$450$	−4.14141	−0.195228
$451$	24.4824	1.15283
$452$	−19.8904	−0.935566
$453$	14.2099	0.667642
$454$	−0.619197	−0.0290603
$455$	−1.21459	−0.0569410
$456$	1.00000	0.0468293
$457$	21.0437	0.984385	0.492192	−	0.870486i	$-0.336196\pi$
$457$	21.0437	0.984385	0.492192	+	0.870486i	$0.336196\pi$
$458$	25.8321	1.20706
$459$	−0.331752	−0.0154849
$460$	0.138931	0.00647770
$461$	21.6102	1.00649	0.503244	−	0.864144i	$-0.332140\pi$
$461$	21.6102	1.00649	0.503244	+	0.864144i	$0.332140\pi$
$462$	−3.28353	−0.152763
$463$	−5.20944	−0.242103	−0.121052	−	0.992646i	$-0.538627\pi$
$463$	−5.20944	−0.242103	−0.121052	+	0.992646i	$0.538627\pi$
$464$	3.09255	0.143568
$465$	−3.90309	−0.181001
$466$	−8.13029	−0.376629
$467$	3.52818	0.163265	0.0816324	−	0.996663i	$-0.473987\pi$
$467$	3.52818	0.163265	0.0816324	+	0.996663i	$0.473987\pi$
$468$	1.67596	0.0774714
$469$	−1.12992	−0.0521749
$470$	−0.196288	−0.00905409
$471$	3.89737	0.179581
$472$	−9.04676	−0.416411
$473$	−27.6999	−1.27364
$474$	−16.4095	−0.753711
$475$	4.14141	0.190021
$476$	−0.259470	−0.0118928
$477$	1.00000	0.0457869
$478$	−7.75661	−0.354779
$479$	7.53696	0.344372	0.172186	−	0.985064i	$-0.444917\pi$
$479$	7.53696	0.344372	0.172186	+	0.985064i	$0.444917\pi$
$480$	−0.926601	−0.0422933
$481$	−16.8020	−0.766107
$482$	−5.37695	−0.244913
$483$	0.117268	0.00533590
$484$	6.62515	0.301143
$485$	−12.9432	−0.587720
$486$	−1.00000	−0.0453609
$487$	−10.5849	−0.479648	−0.239824	−	0.970816i	$-0.577090\pi$
$487$	−10.5849	−0.479648	−0.239824	+	0.970816i	$0.577090\pi$
$488$	−0.848763	−0.0384217
$489$	−13.0131	−0.588475
$490$	−5.91939	−0.267411
$491$	−15.6741	−0.707364	−0.353682	−	0.935366i	$-0.615071\pi$
$491$	−15.6741	−0.707364	−0.353682	+	0.935366i	$0.615071\pi$
$492$	5.83159	0.262909
$493$	1.02596	0.0462070
$494$	−1.67596	−0.0754051
$495$	−3.89008	−0.174846
$496$	4.21227	0.189136
$497$	6.62287	0.297076
$498$	−11.2084	−0.502262
$499$	−24.7962	−1.11003	−0.555015	−	0.831840i	$-0.687288\pi$
$499$	−24.7962	−1.11003	−0.555015	+	0.831840i	$0.687288\pi$
$500$	−8.47044	−0.378809
$501$	−7.49380	−0.334798
$502$	−12.5236	−0.558957
$503$	−16.5036	−0.735857	−0.367929	−	0.929854i	$-0.619933\pi$
$503$	−16.5036	−0.735857	−0.367929	+	0.929854i	$0.619933\pi$
$504$	−0.782121	−0.0348384
$505$	−16.9947	−0.756256
$506$	−0.629468	−0.0279833
$507$	10.1911	0.452605
$508$	3.58632	0.159117
$509$	−10.1343	−0.449193	−0.224597	−	0.974452i	$-0.572106\pi$
$509$	−10.1343	−0.449193	−0.224597	+	0.974452i	$0.572106\pi$
$510$	−0.307402	−0.0136120
$511$	6.58154	0.291150
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	−3.06979	−0.135403
$515$	3.01103	0.132682
$516$	−6.59799	−0.290460
$517$	0.889340	0.0391131
$518$	7.84100	0.344514
$519$	2.08193	0.0913867
$520$	1.55295	0.0681013
$521$	−43.7732	−1.91774	−0.958869	−	0.283849i	$-0.908389\pi$
$521$	−43.7732	−1.91774	−0.958869	+	0.283849i	$0.908389\pi$
$522$	3.09255	0.135357
$523$	−1.72443	−0.0754040	−0.0377020	−	0.999289i	$-0.512004\pi$
$523$	−1.72443	−0.0754040	−0.0377020	+	0.999289i	$0.512004\pi$
$524$	−14.6250	−0.638898
$525$	−3.23908	−0.141365
$526$	16.9553	0.739287
$527$	1.39743	0.0608730
$528$	4.19823	0.182705
$529$	−22.9775	−0.999023
$530$	0.926601	0.0402490
$531$	−9.04676	−0.392596
$532$	0.782121	0.0339092
$533$	−9.77353	−0.423339
$534$	−13.8033	−0.597327
$535$	−8.51979	−0.368343
$536$	1.44469	0.0624010
$537$	−5.99501	−0.258704
$538$	5.93047	0.255681
$539$	26.8195	1.15520
$540$	−0.926601	−0.0398745
$541$	6.52896	0.280702	0.140351	−	0.990102i	$-0.455177\pi$
$541$	6.52896	0.280702	0.140351	+	0.990102i	$0.455177\pi$
$542$	−2.26289	−0.0971993
$543$	10.6345	0.456371
$544$	0.331752	0.0142238
$545$	−13.5889	−0.582084
$546$	1.31081	0.0560973
$547$	13.6643	0.584242	0.292121	−	0.956381i	$-0.405639\pi$
$547$	13.6643	0.584242	0.292121	+	0.956381i	$0.405639\pi$
$548$	−3.01463	−0.128779
$549$	−0.848763	−0.0362243
$550$	17.3866	0.741367
$551$	−3.09255	−0.131747
$552$	−0.149937	−0.00638172
$553$	−12.8342	−0.545765
$554$	11.2497	0.477955
$555$	9.28945	0.394315
$556$	6.69751	0.284038
$557$	24.8490	1.05289	0.526443	−	0.850210i	$-0.323525\pi$
$557$	24.8490	1.05289	0.526443	+	0.850210i	$0.323525\pi$
$558$	4.21227	0.178319
$559$	11.0580	0.467703
$560$	−0.724714	−0.0306247
$561$	1.39277	0.0588029
$562$	−21.8386	−0.921208
$563$	−28.5775	−1.20440	−0.602200	−	0.798346i	$-0.705709\pi$
$563$	−28.5775	−1.20440	−0.602200	+	0.798346i	$0.705709\pi$
$564$	0.211837	0.00891993
$565$	−18.4305	−0.775375
$566$	−9.22107	−0.387590
$567$	−0.782121	−0.0328460
$568$	−8.46784	−0.355302
$569$	12.4014	0.519894	0.259947	−	0.965623i	$-0.416295\pi$
$569$	12.4014	0.519894	0.259947	+	0.965623i	$0.416295\pi$
$570$	0.926601	0.0388110
$571$	−1.84998	−0.0774194	−0.0387097	−	0.999250i	$-0.512325\pi$
$571$	−1.84998	−0.0774194	−0.0387097	+	0.999250i	$0.512325\pi$
$572$	−7.03608	−0.294193
$573$	14.0937	0.588771
$574$	4.56101	0.190373
$575$	−0.620949	−0.0258954
$576$	1.00000	0.0416667
$577$	24.6027	1.02423	0.512113	−	0.858918i	$-0.328863\pi$
$577$	24.6027	1.02423	0.512113	+	0.858918i	$0.328863\pi$
$578$	−16.8899	−0.702529
$579$	4.26766	0.177358
$580$	2.86556	0.118986
$581$	−8.76636	−0.363690
$582$	13.9685	0.579012
$583$	−4.19823	−0.173873
$584$	−8.41498	−0.348215
$585$	1.55295	0.0642065
$586$	20.5377	0.848406
$587$	−16.4405	−0.678572	−0.339286	−	0.940683i	$-0.610186\pi$
$587$	−16.4405	−0.678572	−0.339286	+	0.940683i	$0.610186\pi$
$588$	6.38829	0.263449
$589$	−4.21227	−0.173563
$590$	−8.38273	−0.345112
$591$	7.60094	0.312661
$592$	−10.0253	−0.412037
$593$	35.4418	1.45542	0.727710	−	0.685885i	$-0.240585\pi$
$593$	35.4418	1.45542	0.727710	+	0.685885i	$0.240585\pi$
$594$	4.19823	0.172256
$595$	−0.240426	−0.00985649
$596$	8.53603	0.349649
$597$	−15.5322	−0.635691
$598$	0.251288	0.0102759
$599$	39.6790	1.62124	0.810619	−	0.585574i	$-0.199131\pi$
$599$	39.6790	1.62124	0.810619	+	0.585574i	$0.199131\pi$
$600$	4.14141	0.169072
$601$	38.0169	1.55074	0.775370	−	0.631507i	$-0.217563\pi$
$601$	38.0169	1.55074	0.775370	+	0.631507i	$0.217563\pi$
$602$	−5.16043	−0.210323
$603$	1.44469	0.0588322
$604$	−14.2099	−0.578195
$605$	6.13887	0.249581
$606$	18.3409	0.745050
$607$	−34.2258	−1.38918	−0.694590	−	0.719406i	$-0.744414\pi$
$607$	−34.2258	−1.38918	−0.694590	+	0.719406i	$0.744414\pi$
$608$	−1.00000	−0.0405554
$609$	2.41875	0.0980127
$610$	−0.786464	−0.0318430
$611$	−0.355030	−0.0143630
$612$	0.331752	0.0134103
$613$	−10.5287	−0.425248	−0.212624	−	0.977134i	$-0.568201\pi$
$613$	−10.5287	−0.425248	−0.212624	+	0.977134i	$0.568201\pi$
$614$	−27.6440	−1.11562
$615$	5.40356	0.217892
$616$	3.28353	0.132297
$617$	−4.29010	−0.172713	−0.0863564	−	0.996264i	$-0.527522\pi$
$617$	−4.29010	−0.172713	−0.0863564	+	0.996264i	$0.527522\pi$
$618$	−3.24954	−0.130716
$619$	−27.7701	−1.11617	−0.558087	−	0.829782i	$-0.688465\pi$
$619$	−27.7701	−1.11617	−0.558087	+	0.829782i	$0.688465\pi$
$620$	3.90309	0.156752
$621$	−0.149937	−0.00601674
$622$	14.0486	0.563297
$623$	−10.7958	−0.432527
$624$	−1.67596	−0.0670922
$625$	12.8583	0.514334
$626$	−18.3113	−0.731867
$627$	−4.19823	−0.167661
$628$	−3.89737	−0.155522
$629$	−3.32592	−0.132613
$630$	−0.724714	−0.0288733
$631$	25.3230	1.00809	0.504046	−	0.863677i	$-0.331844\pi$
$631$	25.3230	1.00809	0.504046	+	0.863677i	$0.331844\pi$
$632$	16.4095	0.652733
$633$	−17.5152	−0.696166
$634$	11.3498	0.450757
$635$	3.32309	0.131873
$636$	−1.00000	−0.0396526
$637$	−10.7065	−0.424208
$638$	−12.9833	−0.514012
$639$	−8.46784	−0.334982
$640$	0.926601	0.0366271
$641$	1.63996	0.0647747	0.0323874	−	0.999475i	$-0.489689\pi$
$641$	1.63996	0.0647747	0.0323874	+	0.999475i	$0.489689\pi$
$642$	9.19467	0.362885
$643$	−26.6621	−1.05145	−0.525724	−	0.850655i	$-0.676206\pi$
$643$	−26.6621	−1.05145	−0.525724	+	0.850655i	$0.676206\pi$
$644$	−0.117268	−0.00462103
$645$	−6.11371	−0.240727
$646$	−0.331752	−0.0130526
$647$	2.42564	0.0953617	0.0476808	−	0.998863i	$-0.484817\pi$
$647$	2.42564	0.0953617	0.0476808	+	0.998863i	$0.484817\pi$
$648$	1.00000	0.0392837
$649$	37.9804	1.49086
$650$	−6.94085	−0.272243
$651$	3.29450	0.129122
$652$	13.0131	0.509634
$653$	29.1302	1.13995	0.569976	−	0.821661i	$-0.306953\pi$
$653$	29.1302	1.13995	0.569976	+	0.821661i	$0.306953\pi$
$654$	14.6653	0.573459
$655$	−13.5516	−0.529504
$656$	−5.83159	−0.227685
$657$	−8.41498	−0.328300
$658$	0.165682	0.00645895
$659$	16.5266	0.643786	0.321893	−	0.946776i	$-0.395681\pi$
$659$	16.5266	0.643786	0.321893	+	0.946776i	$0.395681\pi$
$660$	3.89008	0.151421
$661$	18.3133	0.712304	0.356152	−	0.934428i	$-0.384088\pi$
$661$	18.3133	0.712304	0.356152	+	0.934428i	$0.384088\pi$
$662$	−1.52973	−0.0594547
$663$	−0.556005	−0.0215934
$664$	11.2084	0.434972
$665$	0.724714	0.0281032
$666$	−10.0253	−0.388473
$667$	0.463687	0.0179540
$668$	7.49380	0.289944
$669$	−6.25847	−0.241967
$670$	1.33865	0.0517165
$671$	3.56330	0.137560
$672$	0.782121	0.0301710
$673$	43.7839	1.68775	0.843873	−	0.536543i	$-0.180270\pi$
$673$	43.7839	1.68775	0.843873	+	0.536543i	$0.180270\pi$
$674$	−30.0246	−1.15651
$675$	4.14141	0.159403
$676$	−10.1911	−0.391967
$677$	−8.25364	−0.317213	−0.158607	−	0.987342i	$-0.550700\pi$
$677$	−8.25364	−0.317213	−0.158607	+	0.987342i	$0.550700\pi$
$678$	19.8904	0.763886
$679$	10.9250	0.419264
$680$	0.307402	0.0117883
$681$	0.619197	0.0237277
$682$	−17.6841	−0.677158
$683$	−50.0861	−1.91649	−0.958245	−	0.285948i	$-0.907692\pi$
$683$	−50.0861	−1.91649	−0.958245	+	0.285948i	$0.907692\pi$
$684$	−1.00000	−0.0382360
$685$	−2.79336	−0.106729
$686$	10.4713	0.399795
$687$	−25.8321	−0.985557
$688$	6.59799	0.251546
$689$	1.67596	0.0638491
$690$	−0.138931	−0.00528902
$691$	34.6500	1.31815	0.659074	−	0.752078i	$-0.270948\pi$
$691$	34.6500	1.31815	0.659074	+	0.752078i	$0.270948\pi$
$692$	−2.08193	−0.0791432
$693$	3.28353	0.124731
$694$	−19.7549	−0.749884
$695$	6.20591	0.235404
$696$	−3.09255	−0.117223
$697$	−1.93464	−0.0732799
$698$	−26.5106	−1.00344
$699$	8.13029	0.307516
$700$	3.23908	0.122426
$701$	28.7541	1.08603	0.543013	−	0.839724i	$-0.317283\pi$
$701$	28.7541	1.08603	0.543013	+	0.839724i	$0.317283\pi$
$702$	−1.67596	−0.0632551
$703$	10.0253	0.378111
$704$	−4.19823	−0.158227
$705$	0.196288	0.00739263
$706$	13.0469	0.491026
$707$	14.3448	0.539493
$708$	9.04676	0.339998
$709$	48.1115	1.80687	0.903433	−	0.428729i	$-0.141038\pi$
$709$	48.1115	1.80687	0.903433	+	0.428729i	$0.141038\pi$
$710$	−7.84630	−0.294466
$711$	16.4095	0.615403
$712$	13.8033	0.517300
$713$	0.631572	0.0236526
$714$	0.259470	0.00971044
$715$	−6.51964	−0.243821
$716$	5.99501	0.224044
$717$	7.75661	0.289676
$718$	1.34879	0.0503363
$719$	−29.8717	−1.11403	−0.557013	−	0.830504i	$-0.688052\pi$
$719$	−29.8717	−1.11403	−0.557013	+	0.830504i	$0.688052\pi$
$720$	0.926601	0.0345324
$721$	−2.54153	−0.0946517
$722$	1.00000	0.0372161
$723$	5.37695	0.199971
$724$	−10.6345	−0.395229
$725$	−12.8075	−0.475660
$726$	−6.62515	−0.245882
$727$	3.06414	0.113643	0.0568214	−	0.998384i	$-0.481903\pi$
$727$	3.06414	0.113643	0.0568214	+	0.998384i	$0.481903\pi$
$728$	−1.31081	−0.0485817
$729$	1.00000	0.0370370
$730$	−7.79733	−0.288592
$731$	2.18890	0.0809594
$732$	0.848763	0.0313712
$733$	−3.18666	−0.117702	−0.0588510	−	0.998267i	$-0.518744\pi$
$733$	−3.18666	−0.117702	−0.0588510	+	0.998267i	$0.518744\pi$
$734$	7.04736	0.260123
$735$	5.91939	0.218340
$736$	0.149937	0.00552673
$737$	−6.06514	−0.223412
$738$	−5.83159	−0.214664
$739$	35.9719	1.32325	0.661625	−	0.749835i	$-0.269867\pi$
$739$	35.9719	1.32325	0.661625	+	0.749835i	$0.269867\pi$
$740$	−9.28945	−0.341487
$741$	1.67596	0.0615680
$742$	−0.782121	−0.0287126
$743$	−47.8091	−1.75395	−0.876973	−	0.480540i	$-0.840441\pi$
$743$	−47.8091	−1.75395	−0.876973	+	0.480540i	$0.840441\pi$
$744$	−4.21227	−0.154429
$745$	7.90949	0.289781
$746$	−4.63270	−0.169615
$747$	11.2084	0.410096
$748$	−1.39277	−0.0509248
$749$	7.19135	0.262766
$750$	8.47044	0.309297
$751$	9.04037	0.329888	0.164944	−	0.986303i	$-0.447256\pi$
$751$	9.04037	0.329888	0.164944	+	0.986303i	$0.447256\pi$
$752$	−0.211837	−0.00772489
$753$	12.5236	0.456386
$754$	5.18300	0.188754
$755$	−13.1669	−0.479194
$756$	0.782121	0.0284455
$757$	36.9450	1.34279	0.671395	−	0.741100i	$-0.265696\pi$
$757$	36.9450	1.34279	0.671395	+	0.741100i	$0.265696\pi$
$758$	−1.15152	−0.0418252
$759$	0.629468	0.0228482
$760$	−0.926601	−0.0336113
$761$	−19.4165	−0.703849	−0.351925	−	0.936028i	$-0.614473\pi$
$761$	−19.4165	−0.703849	−0.351925	+	0.936028i	$0.614473\pi$
$762$	−3.58632	−0.129919
$763$	11.4700	0.415244
$764$	−14.0937	−0.509891
$765$	0.307402	0.0111141
$766$	−21.9422	−0.792802
$767$	−15.1620	−0.547469
$768$	−1.00000	−0.0360844
$769$	47.0334	1.69607	0.848033	−	0.529943i	$-0.177787\pi$
$769$	47.0334	1.69607	0.848033	+	0.529943i	$0.177787\pi$
$770$	3.04252	0.109645
$771$	3.06979	0.110556
$772$	−4.26766	−0.153597
$773$	5.93932	0.213622	0.106811	−	0.994279i	$-0.465936\pi$
$773$	5.93932	0.213622	0.106811	+	0.994279i	$0.465936\pi$
$774$	6.59799	0.237160
$775$	−17.4447	−0.626633
$776$	−13.9685	−0.501439
$777$	−7.84100	−0.281294
$778$	−36.2915	−1.30111
$779$	5.83159	0.208939
$780$	−1.55295	−0.0556045
$781$	35.5499	1.27208
$782$	0.0497418	0.00177876
$783$	−3.09255	−0.110519
$784$	−6.38829	−0.228153
$785$	−3.61131	−0.128893
$786$	14.6250	0.521658
$787$	15.4545	0.550894	0.275447	−	0.961316i	$-0.411174\pi$
$787$	15.4545	0.550894	0.275447	+	0.961316i	$0.411174\pi$
$788$	−7.60094	−0.270772
$789$	−16.9553	−0.603625
$790$	15.2050	0.540970
$791$	15.5567	0.553133
$792$	−4.19823	−0.149178
$793$	−1.42249	−0.0505143
$794$	0.247673	0.00878959
$795$	−0.926601	−0.0328631
$796$	15.5322	0.550524
$797$	3.49048	0.123639	0.0618195	−	0.998087i	$-0.480310\pi$
$797$	3.49048	0.123639	0.0618195	+	0.998087i	$0.480310\pi$
$798$	−0.782121	−0.0276868
$799$	−0.0702773	−0.00248623
$800$	−4.14141	−0.146421
$801$	13.8033	0.487716
$802$	7.65273	0.270227
$803$	35.3281	1.24670
$804$	−1.44469	−0.0509502
$805$	−0.108661	−0.00382980
$806$	7.05960	0.248664
$807$	−5.93047	−0.208762
$808$	−18.3409	−0.645232
$809$	31.3872	1.10351	0.551757	−	0.834005i	$-0.313958\pi$
$809$	31.3872	1.10351	0.551757	+	0.834005i	$0.313958\pi$
$810$	0.926601	0.0325574
$811$	55.4180	1.94599	0.972995	−	0.230825i	$-0.0741424\pi$
$811$	55.4180	1.94599	0.972995	+	0.230825i	$0.0741424\pi$
$812$	−2.41875	−0.0848815
$813$	2.26289	0.0793629
$814$	42.0885	1.47520
$815$	12.0580	0.422373
$816$	−0.331752	−0.0116137
$817$	−6.59799	−0.230835
$818$	2.60227	0.0909861
$819$	−1.31081	−0.0458033
$820$	−5.40356	−0.188700
$821$	22.9887	0.802311	0.401156	−	0.916010i	$-0.368609\pi$
$821$	22.9887	0.802311	0.401156	+	0.916010i	$0.368609\pi$
$822$	3.01463	0.105147
$823$	−5.69726	−0.198594	−0.0992969	−	0.995058i	$-0.531659\pi$
$823$	−5.69726	−0.198594	−0.0992969	+	0.995058i	$0.531659\pi$
$824$	3.24954	0.113203
$825$	−17.3866	−0.605324
$826$	7.07566	0.246194
$827$	17.8996	0.622429	0.311214	−	0.950340i	$-0.399264\pi$
$827$	17.8996	0.622429	0.311214	+	0.950340i	$0.399264\pi$
$828$	0.149937	0.00521065
$829$	12.9390	0.449389	0.224695	−	0.974429i	$-0.427862\pi$
$829$	12.9390	0.449389	0.224695	+	0.974429i	$0.427862\pi$
$830$	10.3858	0.360495
$831$	−11.2497	−0.390248
$832$	1.67596	0.0581036
$833$	−2.11933	−0.0734304
$834$	−6.69751	−0.231916
$835$	6.94376	0.240299
$836$	4.19823	0.145199
$837$	−4.21227	−0.145597
$838$	19.4884	0.673215
$839$	0.700273	0.0241761	0.0120880	−	0.999927i	$-0.496152\pi$
$839$	0.700273	0.0241761	0.0120880	+	0.999927i	$0.496152\pi$
$840$	0.724714	0.0250050
$841$	−19.4361	−0.670211
$842$	13.4744	0.464359
$843$	21.8386	0.752163
$844$	17.5152	0.602897
$845$	−9.44312	−0.324853
$846$	−0.211837	−0.00728310
$847$	−5.18167	−0.178044
$848$	1.00000	0.0343401
$849$	9.22107	0.316466
$850$	−1.37392	−0.0471252
$851$	−1.50316	−0.0515276
$852$	8.46784	0.290103
$853$	45.8864	1.57112	0.785560	−	0.618785i	$-0.212375\pi$
$853$	45.8864	1.57112	0.785560	+	0.618785i	$0.212375\pi$
$854$	0.663835	0.0227160
$855$	−0.926601	−0.0316891
$856$	−9.19467	−0.314268
$857$	−12.3197	−0.420835	−0.210417	−	0.977612i	$-0.567482\pi$
$857$	−12.3197	−0.420835	−0.210417	+	0.977612i	$0.567482\pi$
$858$	7.03608	0.240208
$859$	−42.5135	−1.45054	−0.725271	−	0.688464i	$-0.758285\pi$
$859$	−42.5135	−1.45054	−0.725271	+	0.688464i	$0.758285\pi$
$860$	6.11371	0.208476
$861$	−4.56101	−0.155439
$862$	−5.56985	−0.189710
$863$	39.0220	1.32833	0.664163	−	0.747588i	$-0.268788\pi$
$863$	39.0220	1.32833	0.664163	+	0.747588i	$0.268788\pi$
$864$	−1.00000	−0.0340207
$865$	−1.92912	−0.0655920
$866$	39.4783	1.34153
$867$	16.8899	0.573612
$868$	−3.29450	−0.111823
$869$	−68.8907	−2.33696
$870$	−2.86556	−0.0971516
$871$	2.42124	0.0820407
$872$	−14.6653	−0.496630
$873$	−13.9685	−0.472761
$874$	−0.149937	−0.00507168
$875$	6.62491	0.223963
$876$	8.41498	0.284316
$877$	40.2448	1.35897	0.679486	−	0.733689i	$-0.262203\pi$
$877$	40.2448	1.35897	0.679486	+	0.733689i	$0.262203\pi$
$878$	25.2570	0.852382
$879$	−20.5377	−0.692720
$880$	−3.89008	−0.131135
$881$	−31.3607	−1.05657	−0.528284	−	0.849068i	$-0.677164\pi$
$881$	−31.3607	−1.05657	−0.528284	+	0.849068i	$0.677164\pi$
$882$	−6.38829	−0.215105
$883$	14.3976	0.484516	0.242258	−	0.970212i	$-0.422112\pi$
$883$	14.3976	0.484516	0.242258	+	0.970212i	$0.422112\pi$
$884$	0.556005	0.0187005
$885$	8.38273	0.281782
$886$	−8.17156	−0.274529
$887$	−39.1132	−1.31329	−0.656646	−	0.754199i	$-0.728026\pi$
$887$	−39.1132	−1.31329	−0.656646	+	0.754199i	$0.728026\pi$
$888$	10.0253	0.336427
$889$	−2.80494	−0.0940746
$890$	12.7901	0.428727
$891$	−4.19823	−0.140646
$892$	6.25847	0.209549
$893$	0.211837	0.00708884
$894$	−8.53603	−0.285488
$895$	5.55498	0.185683
$896$	−0.782121	−0.0261288
$897$	−0.251288	−0.00839026
$898$	−27.2199	−0.908341
$899$	13.0267	0.434463
$900$	−4.14141	−0.138047
$901$	0.331752	0.0110523
$902$	24.4824	0.815174
$903$	5.16043	0.171728
$904$	−19.8904	−0.661545
$905$	−9.85395	−0.327556
$906$	14.2099	0.472094
$907$	11.1385	0.369849	0.184924	−	0.982753i	$-0.440796\pi$
$907$	11.1385	0.369849	0.184924	+	0.982753i	$0.440796\pi$
$908$	−0.619197	−0.0205488
$909$	−18.3409	−0.608331
$910$	−1.21459	−0.0402634
$911$	10.1461	0.336155	0.168077	−	0.985774i	$-0.446244\pi$
$911$	10.1461	0.336155	0.168077	+	0.985774i	$0.446244\pi$
$912$	1.00000	0.0331133
$913$	−47.0556	−1.55731
$914$	21.0437	0.696065
$915$	0.786464	0.0259997
$916$	25.8321	0.853517
$917$	11.4385	0.377734
$918$	−0.331752	−0.0109495
$919$	−11.3027	−0.372842	−0.186421	−	0.982470i	$-0.559689\pi$
$919$	−11.3027	−0.372842	−0.186421	+	0.982470i	$0.559689\pi$
$920$	0.138931	0.00458043
$921$	27.6440	0.910901
$922$	21.6102	0.711694
$923$	−14.1918	−0.467128
$924$	−3.28353	−0.108020
$925$	41.5189	1.36513
$926$	−5.20944	−0.171193
$927$	3.24954	0.106729
$928$	3.09255	0.101518
$929$	−26.9442	−0.884011	−0.442005	−	0.897012i	$-0.645733\pi$
$929$	−26.9442	−0.884011	−0.442005	+	0.897012i	$0.645733\pi$
$930$	−3.90309	−0.127987
$931$	6.38829	0.209368
$932$	−8.13029	−0.266317
$933$	−14.0486	−0.459930
$934$	3.52818	0.115446
$935$	−1.29054	−0.0422053
$936$	1.67596	0.0547806
$937$	−37.6440	−1.22978	−0.614889	−	0.788614i	$-0.710799\pi$
$937$	−37.6440	−1.22978	−0.614889	+	0.788614i	$0.710799\pi$
$938$	−1.12992	−0.0368932
$939$	18.3113	0.597567
$940$	−0.196288	−0.00640221
$941$	38.6897	1.26125	0.630625	−	0.776088i	$-0.282799\pi$
$941$	38.6897	1.26125	0.630625	+	0.776088i	$0.282799\pi$
$942$	3.89737	0.126983
$943$	−0.874369	−0.0284734
$944$	−9.04676	−0.294447
$945$	0.724714	0.0235749
$946$	−27.6999	−0.900602
$947$	−36.5240	−1.18687	−0.593436	−	0.804881i	$-0.702229\pi$
$947$	−36.5240	−1.18687	−0.593436	+	0.804881i	$0.702229\pi$
$948$	−16.4095	−0.532954
$949$	−14.1032	−0.457809
$950$	4.14141	0.134365
$951$	−11.3498	−0.368041
$952$	−0.259470	−0.00840949
$953$	−0.0467423	−0.00151413	−0.000757065	−	1.00000i	$-0.500241\pi$
$953$	−0.0467423	−0.00151413	−0.000757065		1.00000i	$0.500241\pi$
$954$	1.00000	0.0323762
$955$	−13.0592	−0.422586
$956$	−7.75661	−0.250867
$957$	12.9833	0.419689
$958$	7.53696	0.243508
$959$	2.35781	0.0761376
$960$	−0.926601	−0.0299059
$961$	−13.2568	−0.427639
$962$	−16.8020	−0.541719
$963$	−9.19467	−0.296294
$964$	−5.37695	−0.173180
$965$	−3.95442	−0.127297
$966$	0.117268	0.00377305
$967$	29.6933	0.954872	0.477436	−	0.878667i	$-0.341566\pi$
$967$	29.6933	0.954872	0.477436	+	0.878667i	$0.341566\pi$
$968$	6.62515	0.212940
$969$	0.331752	0.0106574
$970$	−12.9432	−0.415581
$971$	−20.8945	−0.670538	−0.335269	−	0.942123i	$-0.608827\pi$
$971$	−20.8945	−0.670538	−0.335269	+	0.942123i	$0.608827\pi$
$972$	−1.00000	−0.0320750
$973$	−5.23826	−0.167931
$974$	−10.5849	−0.339162
$975$	6.94085	0.222285
$976$	−0.848763	−0.0271682
$977$	−1.90091	−0.0608156	−0.0304078	−	0.999538i	$-0.509681\pi$
$977$	−1.90091	−0.0608156	−0.0304078	+	0.999538i	$0.509681\pi$
$978$	−13.0131	−0.416114
$979$	−57.9494	−1.85207
$980$	−5.91939	−0.189088
$981$	−14.6653	−0.468227
$982$	−15.6741	−0.500182
$983$	27.6214	0.880986	0.440493	−	0.897756i	$-0.354804\pi$
$983$	27.6214	0.880986	0.440493	+	0.897756i	$0.354804\pi$
$984$	5.83159	0.185904
$985$	−7.04303	−0.224410
$986$	1.02596	0.0326733
$987$	−0.165682	−0.00527371
$988$	−1.67596	−0.0533195
$989$	0.989280	0.0314573
$990$	−3.89008	−0.123635
$991$	−2.75269	−0.0874419	−0.0437210	−	0.999044i	$-0.513921\pi$
$991$	−2.75269	−0.0874419	−0.0437210	+	0.999044i	$0.513921\pi$
$992$	4.21227	0.133740
$993$	1.52973	0.0485446
$994$	6.62287	0.210065
$995$	14.3921	0.456262
$996$	−11.2084	−0.355153
$997$	−22.2864	−0.705818	−0.352909	−	0.935658i	$-0.614808\pi$
$997$	−22.2864	−0.705818	−0.352909	+	0.935658i	$0.614808\pi$
$998$	−24.7962	−0.784910
$999$	10.0253	0.317187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bb.1.6	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bb.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.926601 q^{5} -1.00000 q^{6} -0.782121 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.926601 q^{5} -1.00000 q^{6} -0.782121 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.926601 q^{10} -4.19823 q^{11} -1.00000 q^{12} +1.67596 q^{13} -0.782121 q^{14} -0.926601 q^{15} +1.00000 q^{16} +0.331752 q^{17} +1.00000 q^{18} -1.00000 q^{19} +0.926601 q^{20} +0.782121 q^{21} -4.19823 q^{22} +0.149937 q^{23} -1.00000 q^{24} -4.14141 q^{25} +1.67596 q^{26} -1.00000 q^{27} -0.782121 q^{28} +3.09255 q^{29} -0.926601 q^{30} +4.21227 q^{31} +1.00000 q^{32} +4.19823 q^{33} +0.331752 q^{34} -0.724714 q^{35} +1.00000 q^{36} -10.0253 q^{37} -1.00000 q^{38} -1.67596 q^{39} +0.926601 q^{40} -5.83159 q^{41} +0.782121 q^{42} +6.59799 q^{43} -4.19823 q^{44} +0.926601 q^{45} +0.149937 q^{46} -0.211837 q^{47} -1.00000 q^{48} -6.38829 q^{49} -4.14141 q^{50} -0.331752 q^{51} +1.67596 q^{52} +1.00000 q^{53} -1.00000 q^{54} -3.89008 q^{55} -0.782121 q^{56} +1.00000 q^{57} +3.09255 q^{58} -9.04676 q^{59} -0.926601 q^{60} -0.848763 q^{61} +4.21227 q^{62} -0.782121 q^{63} +1.00000 q^{64} +1.55295 q^{65} +4.19823 q^{66} +1.44469 q^{67} +0.331752 q^{68} -0.149937 q^{69} -0.724714 q^{70} -8.46784 q^{71} +1.00000 q^{72} -8.41498 q^{73} -10.0253 q^{74} +4.14141 q^{75} -1.00000 q^{76} +3.28353 q^{77} -1.67596 q^{78} +16.4095 q^{79} +0.926601 q^{80} +1.00000 q^{81} -5.83159 q^{82} +11.2084 q^{83} +0.782121 q^{84} +0.307402 q^{85} +6.59799 q^{86} -3.09255 q^{87} -4.19823 q^{88} +13.8033 q^{89} +0.926601 q^{90} -1.31081 q^{91} +0.149937 q^{92} -4.21227 q^{93} -0.211837 q^{94} -0.926601 q^{95} -1.00000 q^{96} -13.9685 q^{97} -6.38829 q^{98} -4.19823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 5 q^{5} - 9 q^{6} - 5 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 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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