LMFDB - Embedded newform 6042.2.a.bf.1.5

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:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 27 x^{10} + 134 x^{9} + 294 x^{8} - 1313 x^{7} - 1685 x^{6} + 5910 x^{5} + \cdots + 4048 $ x^12 - 5x^11 - 27x^10 + 134x^9 + 294x^8 - 1313x^7 - 1685x^6 + 5910x^5 + 5237x^4 - 12206x^3 - 7876x^2 + 9264*x + 4048
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.60709$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.60709 q^{5} -1.00000 q^{6} -4.26018 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.60709 q^{5} -1.00000 q^{6} -4.26018 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.60709 q^{10} +3.88296 q^{11} +1.00000 q^{12} +1.17061 q^{13} +4.26018 q^{14} -2.60709 q^{15} +1.00000 q^{16} +7.34248 q^{17} -1.00000 q^{18} +1.00000 q^{19} -2.60709 q^{20} -4.26018 q^{21} -3.88296 q^{22} -3.84659 q^{23} -1.00000 q^{24} +1.79692 q^{25} -1.17061 q^{26} +1.00000 q^{27} -4.26018 q^{28} +6.30281 q^{29} +2.60709 q^{30} -6.13083 q^{31} -1.00000 q^{32} +3.88296 q^{33} -7.34248 q^{34} +11.1067 q^{35} +1.00000 q^{36} -7.87979 q^{37} -1.00000 q^{38} +1.17061 q^{39} +2.60709 q^{40} -12.7037 q^{41} +4.26018 q^{42} +5.84659 q^{43} +3.88296 q^{44} -2.60709 q^{45} +3.84659 q^{46} -10.0617 q^{47} +1.00000 q^{48} +11.1491 q^{49} -1.79692 q^{50} +7.34248 q^{51} +1.17061 q^{52} +1.00000 q^{53} -1.00000 q^{54} -10.1232 q^{55} +4.26018 q^{56} +1.00000 q^{57} -6.30281 q^{58} +4.82836 q^{59} -2.60709 q^{60} +5.71459 q^{61} +6.13083 q^{62} -4.26018 q^{63} +1.00000 q^{64} -3.05188 q^{65} -3.88296 q^{66} +4.23256 q^{67} +7.34248 q^{68} -3.84659 q^{69} -11.1067 q^{70} +4.20318 q^{71} -1.00000 q^{72} +1.42526 q^{73} +7.87979 q^{74} +1.79692 q^{75} +1.00000 q^{76} -16.5421 q^{77} -1.17061 q^{78} -0.672153 q^{79} -2.60709 q^{80} +1.00000 q^{81} +12.7037 q^{82} -1.22315 q^{83} -4.26018 q^{84} -19.1425 q^{85} -5.84659 q^{86} +6.30281 q^{87} -3.88296 q^{88} -3.71532 q^{89} +2.60709 q^{90} -4.98700 q^{91} -3.84659 q^{92} -6.13083 q^{93} +10.0617 q^{94} -2.60709 q^{95} -1.00000 q^{96} +14.4211 q^{97} -11.1491 q^{98} +3.88296 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9} + 7 q^{10} - 5 q^{11} + 12 q^{12} + 10 q^{13} - 5 q^{14} - 7 q^{15} + 12 q^{16} + 6 q^{17} - 12 q^{18} + 12 q^{19} - 7 q^{20} + 5 q^{21} + 5 q^{22} - 12 q^{24} + 21 q^{25} - 10 q^{26} + 12 q^{27} + 5 q^{28} + 7 q^{30} + 2 q^{31} - 12 q^{32} - 5 q^{33} - 6 q^{34} - 17 q^{35} + 12 q^{36} + 16 q^{37} - 12 q^{38} + 10 q^{39} + 7 q^{40} + 7 q^{41} - 5 q^{42} + 24 q^{43} - 5 q^{44} - 7 q^{45} + 4 q^{47} + 12 q^{48} + 29 q^{49} - 21 q^{50} + 6 q^{51} + 10 q^{52} + 12 q^{53} - 12 q^{54} - 2 q^{55} - 5 q^{56} + 12 q^{57} + 2 q^{59} - 7 q^{60} + 29 q^{61} - 2 q^{62} + 5 q^{63} + 12 q^{64} - 17 q^{65} + 5 q^{66} + 36 q^{67} + 6 q^{68} + 17 q^{70} - 3 q^{71} - 12 q^{72} + 7 q^{73} - 16 q^{74} + 21 q^{75} + 12 q^{76} - 35 q^{77} - 10 q^{78} + 40 q^{79} - 7 q^{80} + 12 q^{81} - 7 q^{82} + 24 q^{83} + 5 q^{84} - 22 q^{85} - 24 q^{86} + 5 q^{88} - 45 q^{89} + 7 q^{90} + 71 q^{91} + 2 q^{93} - 4 q^{94} - 7 q^{95} - 12 q^{96} + q^{97} - 29 q^{98} - 5 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9 + 7 * q^10 - 5 * q^11 + 12 * q^12 + 10 * q^13 - 5 * q^14 - 7 * q^15 + 12 * q^16 + 6 * q^17 - 12 * q^18 + 12 * q^19 - 7 * q^20 + 5 * q^21 + 5 * q^22 - 12 * q^24 + 21 * q^25 - 10 * q^26 + 12 * q^27 + 5 * q^28 + 7 * q^30 + 2 * q^31 - 12 * q^32 - 5 * q^33 - 6 * q^34 - 17 * q^35 + 12 * q^36 + 16 * q^37 - 12 * q^38 + 10 * q^39 + 7 * q^40 + 7 * q^41 - 5 * q^42 + 24 * q^43 - 5 * q^44 - 7 * q^45 + 4 * q^47 + 12 * q^48 + 29 * q^49 - 21 * q^50 + 6 * q^51 + 10 * q^52 + 12 * q^53 - 12 * q^54 - 2 * q^55 - 5 * q^56 + 12 * q^57 + 2 * q^59 - 7 * q^60 + 29 * q^61 - 2 * q^62 + 5 * q^63 + 12 * q^64 - 17 * q^65 + 5 * q^66 + 36 * q^67 + 6 * q^68 + 17 * q^70 - 3 * q^71 - 12 * q^72 + 7 * q^73 - 16 * q^74 + 21 * q^75 + 12 * q^76 - 35 * q^77 - 10 * q^78 + 40 * q^79 - 7 * q^80 + 12 * q^81 - 7 * q^82 + 24 * q^83 + 5 * q^84 - 22 * q^85 - 24 * q^86 + 5 * q^88 - 45 * q^89 + 7 * q^90 + 71 * q^91 + 2 * q^93 - 4 * q^94 - 7 * q^95 - 12 * q^96 + q^97 - 29 * q^98 - 5 * 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
$5$	−2.60709	−1.16593	−0.582963	−	0.812499i	$-0.698107\pi$
$5$	−2.60709	−1.16593	−0.582963	+	0.812499i	$0.698107\pi$
$6$	−1.00000	−0.408248
$7$	−4.26018	−1.61019	−0.805097	−	0.593143i	$-0.797887\pi$
$7$	−4.26018	−1.61019	−0.805097	+	0.593143i	$0.797887\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.60709	0.824434
$11$	3.88296	1.17076	0.585378	−	0.810760i	$-0.300946\pi$
$11$	3.88296	1.17076	0.585378	+	0.810760i	$0.300946\pi$
$12$	1.00000	0.288675
$13$	1.17061	0.324669	0.162334	−	0.986736i	$-0.448098\pi$
$13$	1.17061	0.324669	0.162334	+	0.986736i	$0.448098\pi$
$14$	4.26018	1.13858
$15$	−2.60709	−0.673148
$16$	1.00000	0.250000
$17$	7.34248	1.78081	0.890407	−	0.455165i	$-0.150420\pi$
$17$	7.34248	1.78081	0.890407	+	0.455165i	$0.150420\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.60709	−0.582963
$21$	−4.26018	−0.929646
$22$	−3.88296	−0.827850
$23$	−3.84659	−0.802068	−0.401034	−	0.916063i	$-0.631349\pi$
$23$	−3.84659	−0.802068	−0.401034	+	0.916063i	$0.631349\pi$
$24$	−1.00000	−0.204124
$25$	1.79692	0.359384
$26$	−1.17061	−0.229575
$27$	1.00000	0.192450
$28$	−4.26018	−0.805097
$29$	6.30281	1.17040	0.585201	−	0.810888i	$-0.301016\pi$
$29$	6.30281	1.17040	0.585201	+	0.810888i	$0.301016\pi$
$30$	2.60709	0.475987
$31$	−6.13083	−1.10113	−0.550565	−	0.834792i	$-0.685588\pi$
$31$	−6.13083	−1.10113	−0.550565	+	0.834792i	$0.685588\pi$
$32$	−1.00000	−0.176777
$33$	3.88296	0.675937
$34$	−7.34248	−1.25923
$35$	11.1067	1.87737
$36$	1.00000	0.166667
$37$	−7.87979	−1.29543	−0.647715	−	0.761883i	$-0.724275\pi$
$37$	−7.87979	−1.29543	−0.647715	+	0.761883i	$0.724275\pi$
$38$	−1.00000	−0.162221
$39$	1.17061	0.187448
$40$	2.60709	0.412217
$41$	−12.7037	−1.98398	−0.991991	−	0.126305i	$-0.959688\pi$
$41$	−12.7037	−1.98398	−0.991991	+	0.126305i	$0.959688\pi$
$42$	4.26018	0.657359
$43$	5.84659	0.891596	0.445798	−	0.895134i	$-0.352920\pi$
$43$	5.84659	0.891596	0.445798	+	0.895134i	$0.352920\pi$
$44$	3.88296	0.585378
$45$	−2.60709	−0.388642
$46$	3.84659	0.567148
$47$	−10.0617	−1.46764	−0.733822	−	0.679341i	$-0.762266\pi$
$47$	−10.0617	−1.46764	−0.733822	+	0.679341i	$0.762266\pi$
$48$	1.00000	0.144338
$49$	11.1491	1.59273
$50$	−1.79692	−0.254123
$51$	7.34248	1.02815
$52$	1.17061	0.162334
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−1.00000	−0.136083
$55$	−10.1232	−1.36502
$56$	4.26018	0.569290
$57$	1.00000	0.132453
$58$	−6.30281	−0.827599
$59$	4.82836	0.628599	0.314299	−	0.949324i	$-0.398230\pi$
$59$	4.82836	0.628599	0.314299	+	0.949324i	$0.398230\pi$
$60$	−2.60709	−0.336574
$61$	5.71459	0.731678	0.365839	−	0.930678i	$-0.380782\pi$
$61$	5.71459	0.731678	0.365839	+	0.930678i	$0.380782\pi$
$62$	6.13083	0.778617
$63$	−4.26018	−0.536732
$64$	1.00000	0.125000
$65$	−3.05188	−0.378540
$66$	−3.88296	−0.477960
$67$	4.23256	0.517089	0.258545	−	0.965999i	$-0.416757\pi$
$67$	4.23256	0.517089	0.258545	+	0.965999i	$0.416757\pi$
$68$	7.34248	0.890407
$69$	−3.84659	−0.463074
$70$	−11.1067	−1.32750
$71$	4.20318	0.498826	0.249413	−	0.968397i	$-0.419762\pi$
$71$	4.20318	0.498826	0.249413	+	0.968397i	$0.419762\pi$
$72$	−1.00000	−0.117851
$73$	1.42526	0.166814	0.0834069	−	0.996516i	$-0.473420\pi$
$73$	1.42526	0.166814	0.0834069	+	0.996516i	$0.473420\pi$
$74$	7.87979	0.916008
$75$	1.79692	0.207491
$76$	1.00000	0.114708
$77$	−16.5421	−1.88515
$78$	−1.17061	−0.132545
$79$	−0.672153	−0.0756231	−0.0378115	−	0.999285i	$-0.512039\pi$
$79$	−0.672153	−0.0756231	−0.0378115	+	0.999285i	$0.512039\pi$
$80$	−2.60709	−0.291482
$81$	1.00000	0.111111
$82$	12.7037	1.40289
$83$	−1.22315	−0.134259	−0.0671293	−	0.997744i	$-0.521384\pi$
$83$	−1.22315	−0.134259	−0.0671293	+	0.997744i	$0.521384\pi$
$84$	−4.26018	−0.464823
$85$	−19.1425	−2.07630
$86$	−5.84659	−0.630453
$87$	6.30281	0.675732
$88$	−3.88296	−0.413925
$89$	−3.71532	−0.393823	−0.196911	−	0.980421i	$-0.563091\pi$
$89$	−3.71532	−0.393823	−0.196911	+	0.980421i	$0.563091\pi$
$90$	2.60709	0.274811
$91$	−4.98700	−0.522780
$92$	−3.84659	−0.401034
$93$	−6.13083	−0.635738
$94$	10.0617	1.03778
$95$	−2.60709	−0.267482
$96$	−1.00000	−0.102062
$97$	14.4211	1.46424	0.732121	−	0.681174i	$-0.238530\pi$
$97$	14.4211	1.46424	0.732121	+	0.681174i	$0.238530\pi$
$98$	−11.1491	−1.12623
$99$	3.88296	0.390252
$100$	1.79692	0.179692
$101$	−16.8598	−1.67762	−0.838808	−	0.544427i	$-0.816747\pi$
$101$	−16.8598	−1.67762	−0.838808	+	0.544427i	$0.816747\pi$
$102$	−7.34248	−0.727014
$103$	16.3170	1.60776	0.803880	−	0.594791i	$-0.202765\pi$
$103$	16.3170	1.60776	0.803880	+	0.594791i	$0.202765\pi$
$104$	−1.17061	−0.114788
$105$	11.1067	1.08390
$106$	−1.00000	−0.0971286
$107$	−12.2600	−1.18521	−0.592607	−	0.805491i	$-0.701901\pi$
$107$	−12.2600	−1.18521	−0.592607	+	0.805491i	$0.701901\pi$
$108$	1.00000	0.0962250
$109$	−10.3397	−0.990367	−0.495184	−	0.868788i	$-0.664899\pi$
$109$	−10.3397	−0.990367	−0.495184	+	0.868788i	$0.664899\pi$
$110$	10.1232	0.965212
$111$	−7.87979	−0.747917
$112$	−4.26018	−0.402549
$113$	14.3225	1.34734	0.673672	−	0.739031i	$-0.264716\pi$
$113$	14.3225	1.34734	0.673672	+	0.739031i	$0.264716\pi$
$114$	−1.00000	−0.0936586
$115$	10.0284	0.935153
$116$	6.30281	0.585201
$117$	1.17061	0.108223
$118$	−4.82836	−0.444486
$119$	−31.2803	−2.86746
$120$	2.60709	0.237994
$121$	4.07739	0.370672
$122$	−5.71459	−0.517375
$123$	−12.7037	−1.14545
$124$	−6.13083	−0.550565
$125$	8.35072	0.746911
$126$	4.26018	0.379527
$127$	21.6644	1.92240	0.961201	−	0.275850i	$-0.0889594\pi$
$127$	21.6644	1.92240	0.961201	+	0.275850i	$0.0889594\pi$
$128$	−1.00000	−0.0883883
$129$	5.84659	0.514763
$130$	3.05188	0.267668
$131$	−10.2166	−0.892633	−0.446316	−	0.894875i	$-0.647264\pi$
$131$	−10.2166	−0.892633	−0.446316	+	0.894875i	$0.647264\pi$
$132$	3.88296	0.337968
$133$	−4.26018	−0.369404
$134$	−4.23256	−0.365637
$135$	−2.60709	−0.224383
$136$	−7.34248	−0.629613
$137$	−7.37045	−0.629700	−0.314850	−	0.949141i	$-0.601954\pi$
$137$	−7.37045	−0.629700	−0.314850	+	0.949141i	$0.601954\pi$
$138$	3.84659	0.327443
$139$	3.20239	0.271623	0.135812	−	0.990735i	$-0.456636\pi$
$139$	3.20239	0.271623	0.135812	+	0.990735i	$0.456636\pi$
$140$	11.1067	0.938684
$141$	−10.0617	−0.847345
$142$	−4.20318	−0.352723
$143$	4.54543	0.380108
$144$	1.00000	0.0833333
$145$	−16.4320	−1.36460
$146$	−1.42526	−0.117955
$147$	11.1491	0.919562
$148$	−7.87979	−0.647715
$149$	−15.3255	−1.25552	−0.627758	−	0.778409i	$-0.716027\pi$
$149$	−15.3255	−1.25552	−0.627758	+	0.778409i	$0.716027\pi$
$150$	−1.79692	−0.146718
$151$	8.03932	0.654230	0.327115	−	0.944984i	$-0.393924\pi$
$151$	8.03932	0.654230	0.327115	+	0.944984i	$0.393924\pi$
$152$	−1.00000	−0.0811107
$153$	7.34248	0.593605
$154$	16.5421	1.33300
$155$	15.9836	1.28384
$156$	1.17061	0.0937238
$157$	11.1834	0.892535	0.446267	−	0.894900i	$-0.352753\pi$
$157$	11.1834	0.892535	0.446267	+	0.894900i	$0.352753\pi$
$158$	0.672153	0.0534736
$159$	1.00000	0.0793052
$160$	2.60709	0.206109
$161$	16.3871	1.29149
$162$	−1.00000	−0.0785674
$163$	24.4244	1.91307	0.956534	−	0.291619i	$-0.0941941\pi$
$163$	24.4244	1.91307	0.956534	+	0.291619i	$0.0941941\pi$
$164$	−12.7037	−0.991991
$165$	−10.1232	−0.788093
$166$	1.22315	0.0949352
$167$	7.20664	0.557666	0.278833	−	0.960340i	$-0.410052\pi$
$167$	7.20664	0.557666	0.278833	+	0.960340i	$0.410052\pi$
$168$	4.26018	0.328680
$169$	−11.6297	−0.894590
$170$	19.1425	1.46816
$171$	1.00000	0.0764719
$172$	5.84659	0.445798
$173$	−0.0148678	−0.00113038	−0.000565189	−	1.00000i	$-0.500180\pi$
$173$	−0.0148678	−0.00113038	−0.000565189		1.00000i	$0.500180\pi$
$174$	−6.30281	−0.477815
$175$	−7.65520	−0.578679
$176$	3.88296	0.292689
$177$	4.82836	0.362922
$178$	3.71532	0.278475
$179$	18.5617	1.38737	0.693684	−	0.720280i	$-0.255987\pi$
$179$	18.5617	1.38737	0.693684	+	0.720280i	$0.255987\pi$
$180$	−2.60709	−0.194321
$181$	−19.8251	−1.47359	−0.736794	−	0.676117i	$-0.763661\pi$
$181$	−19.8251	−1.47359	−0.736794	+	0.676117i	$0.763661\pi$
$182$	4.98700	0.369661
$183$	5.71459	0.422435
$184$	3.84659	0.283574
$185$	20.5433	1.51038
$186$	6.13083	0.449535
$187$	28.5106	2.08490
$188$	−10.0617	−0.733822
$189$	−4.26018	−0.309882
$190$	2.60709	0.189138
$191$	−7.07364	−0.511830	−0.255915	−	0.966699i	$-0.582377\pi$
$191$	−7.07364	−0.511830	−0.255915	+	0.966699i	$0.582377\pi$
$192$	1.00000	0.0721688
$193$	−22.3742	−1.61053	−0.805266	−	0.592914i	$-0.797977\pi$
$193$	−22.3742	−1.61053	−0.805266	+	0.592914i	$0.797977\pi$
$194$	−14.4211	−1.03538
$195$	−3.05188	−0.218550
$196$	11.1491	0.796364
$197$	26.7301	1.90444	0.952222	−	0.305407i	$-0.0987925\pi$
$197$	26.7301	1.90444	0.952222	+	0.305407i	$0.0987925\pi$
$198$	−3.88296	−0.275950
$199$	5.10401	0.361814	0.180907	−	0.983500i	$-0.442097\pi$
$199$	5.10401	0.361814	0.180907	+	0.983500i	$0.442097\pi$
$200$	−1.79692	−0.127062
$201$	4.23256	0.298542
$202$	16.8598	1.18625
$203$	−26.8511	−1.88457
$204$	7.34248	0.514077
$205$	33.1197	2.31318
$206$	−16.3170	−1.13686
$207$	−3.84659	−0.267356
$208$	1.17061	0.0811672
$209$	3.88296	0.268590
$210$	−11.1067	−0.766433
$211$	−1.25499	−0.0863972	−0.0431986	−	0.999067i	$-0.513755\pi$
$211$	−1.25499	−0.0863972	−0.0431986	+	0.999067i	$0.513755\pi$
$212$	1.00000	0.0686803
$213$	4.20318	0.287997
$214$	12.2600	0.838073
$215$	−15.2426	−1.03954
$216$	−1.00000	−0.0680414
$217$	26.1184	1.77303
$218$	10.3397	0.700295
$219$	1.42526	0.0963100
$220$	−10.1232	−0.682508
$221$	8.59518	0.578174
$222$	7.87979	0.528857
$223$	24.9080	1.66796	0.833981	−	0.551793i	$-0.186056\pi$
$223$	24.9080	1.66796	0.833981	+	0.551793i	$0.186056\pi$
$224$	4.26018	0.284645
$225$	1.79692	0.119795
$226$	−14.3225	−0.952716
$227$	4.76884	0.316519	0.158259	−	0.987398i	$-0.449412\pi$
$227$	4.76884	0.316519	0.158259	+	0.987398i	$0.449412\pi$
$228$	1.00000	0.0662266
$229$	21.2367	1.40336	0.701679	−	0.712493i	$-0.252434\pi$
$229$	21.2367	1.40336	0.701679	+	0.712493i	$0.252434\pi$
$230$	−10.0284	−0.661253
$231$	−16.5421	−1.08839
$232$	−6.30281	−0.413800
$233$	2.72417	0.178466	0.0892331	−	0.996011i	$-0.471558\pi$
$233$	2.72417	0.178466	0.0892331	+	0.996011i	$0.471558\pi$
$234$	−1.17061	−0.0765251
$235$	26.2317	1.71117
$236$	4.82836	0.314299
$237$	−0.672153	−0.0436610
$238$	31.2803	2.02760
$239$	4.07034	0.263288	0.131644	−	0.991297i	$-0.457974\pi$
$239$	4.07034	0.263288	0.131644	+	0.991297i	$0.457974\pi$
$240$	−2.60709	−0.168287
$241$	11.3570	0.731571	0.365785	−	0.930699i	$-0.380800\pi$
$241$	11.3570	0.731571	0.365785	+	0.930699i	$0.380800\pi$
$242$	−4.07739	−0.262105
$243$	1.00000	0.0641500
$244$	5.71459	0.365839
$245$	−29.0667	−1.85700
$246$	12.7037	0.809958
$247$	1.17061	0.0744841
$248$	6.13083	0.389308
$249$	−1.22315	−0.0775143
$250$	−8.35072	−0.528146
$251$	−14.6644	−0.925607	−0.462803	−	0.886461i	$-0.653156\pi$
$251$	−14.6644	−0.925607	−0.462803	+	0.886461i	$0.653156\pi$
$252$	−4.26018	−0.268366
$253$	−14.9361	−0.939027
$254$	−21.6644	−1.35934
$255$	−19.1425	−1.19875
$256$	1.00000	0.0625000
$257$	25.7206	1.60441	0.802204	−	0.597050i	$-0.203661\pi$
$257$	25.7206	1.60441	0.802204	+	0.597050i	$0.203661\pi$
$258$	−5.84659	−0.363992
$259$	33.5693	2.08590
$260$	−3.05188	−0.189270
$261$	6.30281	0.390134
$262$	10.2166	0.631187
$263$	12.0474	0.742876	0.371438	−	0.928458i	$-0.378865\pi$
$263$	12.0474	0.742876	0.371438	+	0.928458i	$0.378865\pi$
$264$	−3.88296	−0.238980
$265$	−2.60709	−0.160152
$266$	4.26018	0.261208
$267$	−3.71532	−0.227374
$268$	4.23256	0.258545
$269$	22.4276	1.36744	0.683718	−	0.729747i	$-0.260362\pi$
$269$	22.4276	1.36744	0.683718	+	0.729747i	$0.260362\pi$
$270$	2.60709	0.158662
$271$	23.2258	1.41087	0.705435	−	0.708775i	$-0.250752\pi$
$271$	23.2258	1.41087	0.705435	+	0.708775i	$0.250752\pi$
$272$	7.34248	0.445204
$273$	−4.98700	−0.301827
$274$	7.37045	0.445265
$275$	6.97738	0.420752
$276$	−3.84659	−0.231537
$277$	−7.51423	−0.451486	−0.225743	−	0.974187i	$-0.572481\pi$
$277$	−7.51423	−0.451486	−0.225743	+	0.974187i	$0.572481\pi$
$278$	−3.20239	−0.192066
$279$	−6.13083	−0.367043
$280$	−11.1067	−0.663750
$281$	11.3139	0.674930	0.337465	−	0.941338i	$-0.390431\pi$
$281$	11.3139	0.674930	0.337465	+	0.941338i	$0.390431\pi$
$282$	10.0617	0.599163
$283$	22.9678	1.36529	0.682647	−	0.730749i	$-0.260829\pi$
$283$	22.9678	1.36529	0.682647	+	0.730749i	$0.260829\pi$
$284$	4.20318	0.249413
$285$	−2.60709	−0.154431
$286$	−4.54543	−0.268777
$287$	54.1199	3.19460
$288$	−1.00000	−0.0589256
$289$	36.9121	2.17130
$290$	16.4320	0.964920
$291$	14.4211	0.845381
$292$	1.42526	0.0834069
$293$	−26.2476	−1.53340	−0.766700	−	0.642005i	$-0.778103\pi$
$293$	−26.2476	−1.53340	−0.766700	+	0.642005i	$0.778103\pi$
$294$	−11.1491	−0.650228
$295$	−12.5880	−0.732900
$296$	7.87979	0.458004
$297$	3.88296	0.225312
$298$	15.3255	0.887784
$299$	−4.50285	−0.260406
$300$	1.79692	0.103745
$301$	−24.9075	−1.43564
$302$	−8.03932	−0.462611
$303$	−16.8598	−0.968572
$304$	1.00000	0.0573539
$305$	−14.8985	−0.853083
$306$	−7.34248	−0.419742
$307$	1.75290	0.100043	0.0500215	−	0.998748i	$-0.484071\pi$
$307$	1.75290	0.100043	0.0500215	+	0.998748i	$0.484071\pi$
$308$	−16.5421	−0.942573
$309$	16.3170	0.928241
$310$	−15.9836	−0.907810
$311$	−3.41258	−0.193509	−0.0967547	−	0.995308i	$-0.530846\pi$
$311$	−3.41258	−0.193509	−0.0967547	+	0.995308i	$0.530846\pi$
$312$	−1.17061	−0.0662727
$313$	27.5975	1.55990	0.779951	−	0.625840i	$-0.215244\pi$
$313$	27.5975	1.55990	0.779951	+	0.625840i	$0.215244\pi$
$314$	−11.1834	−0.631118
$315$	11.1067	0.625790
$316$	−0.672153	−0.0378115
$317$	−17.3098	−0.972214	−0.486107	−	0.873899i	$-0.661583\pi$
$317$	−17.3098	−0.972214	−0.486107	+	0.873899i	$0.661583\pi$
$318$	−1.00000	−0.0560772
$319$	24.4736	1.37026
$320$	−2.60709	−0.145741
$321$	−12.2600	−0.684284
$322$	−16.3871	−0.913219
$323$	7.34248	0.408547
$324$	1.00000	0.0555556
$325$	2.10349	0.116681
$326$	−24.4244	−1.35274
$327$	−10.3397	−0.571789
$328$	12.7037	0.701444
$329$	42.8645	2.36319
$330$	10.1232	0.557266
$331$	−9.42481	−0.518035	−0.259017	−	0.965873i	$-0.583399\pi$
$331$	−9.42481	−0.518035	−0.259017	+	0.965873i	$0.583399\pi$
$332$	−1.22315	−0.0671293
$333$	−7.87979	−0.431810
$334$	−7.20664	−0.394330
$335$	−11.0347	−0.602888
$336$	−4.26018	−0.232412
$337$	−8.84832	−0.481999	−0.240999	−	0.970525i	$-0.577475\pi$
$337$	−8.84832	−0.481999	−0.240999	+	0.970525i	$0.577475\pi$
$338$	11.6297	0.632571
$339$	14.3225	0.777889
$340$	−19.1425	−1.03815
$341$	−23.8058	−1.28916
$342$	−1.00000	−0.0540738
$343$	−17.6759	−0.954406
$344$	−5.84659	−0.315227
$345$	10.0284	0.539911
$346$	0.0148678	0.000799297 0
$347$	5.41090	0.290472	0.145236	−	0.989397i	$-0.453606\pi$
$347$	5.41090	0.290472	0.145236	+	0.989397i	$0.453606\pi$
$348$	6.30281	0.337866
$349$	−26.3195	−1.40885	−0.704424	−	0.709779i	$-0.748795\pi$
$349$	−26.3195	−1.40885	−0.704424	+	0.709779i	$0.748795\pi$
$350$	7.65520	0.409188
$351$	1.17061	0.0624825
$352$	−3.88296	−0.206963
$353$	31.5456	1.67900	0.839501	−	0.543358i	$-0.182848\pi$
$353$	31.5456	1.67900	0.839501	+	0.543358i	$0.182848\pi$
$354$	−4.82836	−0.256624
$355$	−10.9581	−0.581595
$356$	−3.71532	−0.196911
$357$	−31.2803	−1.65553
$358$	−18.5617	−0.981017
$359$	8.10868	0.427960	0.213980	−	0.976838i	$-0.431357\pi$
$359$	8.10868	0.427960	0.213980	+	0.976838i	$0.431357\pi$
$360$	2.60709	0.137406
$361$	1.00000	0.0526316
$362$	19.8251	1.04198
$363$	4.07739	0.214007
$364$	−4.98700	−0.261390
$365$	−3.71578	−0.194493
$366$	−5.71459	−0.298706
$367$	−1.17150	−0.0611517	−0.0305758	−	0.999532i	$-0.509734\pi$
$367$	−1.17150	−0.0611517	−0.0305758	+	0.999532i	$0.509734\pi$
$368$	−3.84659	−0.200517
$369$	−12.7037	−0.661328
$370$	−20.5433	−1.06800
$371$	−4.26018	−0.221177
$372$	−6.13083	−0.317869
$373$	27.7793	1.43836	0.719179	−	0.694824i	$-0.244518\pi$
$373$	27.7793	1.43836	0.719179	+	0.694824i	$0.244518\pi$
$374$	−28.5106	−1.47425
$375$	8.35072	0.431229
$376$	10.0617	0.518891
$377$	7.37812	0.379993
$378$	4.26018	0.219120
$379$	−15.1717	−0.779318	−0.389659	−	0.920959i	$-0.627407\pi$
$379$	−15.1717	−0.779318	−0.389659	+	0.920959i	$0.627407\pi$
$380$	−2.60709	−0.133741
$381$	21.6644	1.10990
$382$	7.07364	0.361919
$383$	11.4268	0.583881	0.291941	−	0.956436i	$-0.405699\pi$
$383$	11.4268	0.583881	0.291941	+	0.956436i	$0.405699\pi$
$384$	−1.00000	−0.0510310
$385$	43.1267	2.19794
$386$	22.3742	1.13882
$387$	5.84659	0.297199
$388$	14.4211	0.732121
$389$	−10.0477	−0.509440	−0.254720	−	0.967015i	$-0.581983\pi$
$389$	−10.0477	−0.509440	−0.254720	+	0.967015i	$0.581983\pi$
$390$	3.05188	0.154538
$391$	−28.2435	−1.42833
$392$	−11.1491	−0.563114
$393$	−10.2166	−0.515362
$394$	−26.7301	−1.34665
$395$	1.75236	0.0881709
$396$	3.88296	0.195126
$397$	18.7483	0.940949	0.470474	−	0.882414i	$-0.344083\pi$
$397$	18.7483	0.940949	0.470474	+	0.882414i	$0.344083\pi$
$398$	−5.10401	−0.255841
$399$	−4.26018	−0.213276
$400$	1.79692	0.0898461
$401$	−5.96139	−0.297697	−0.148849	−	0.988860i	$-0.547557\pi$
$401$	−5.96139	−0.297697	−0.148849	+	0.988860i	$0.547557\pi$
$402$	−4.23256	−0.211101
$403$	−7.17681	−0.357502
$404$	−16.8598	−0.838808
$405$	−2.60709	−0.129547
$406$	26.8511	1.33260
$407$	−30.5969	−1.51663
$408$	−7.34248	−0.363507
$409$	−8.65264	−0.427846	−0.213923	−	0.976851i	$-0.568624\pi$
$409$	−8.65264	−0.427846	−0.213923	+	0.976851i	$0.568624\pi$
$410$	−33.1197	−1.63566
$411$	−7.37045	−0.363557
$412$	16.3170	0.803880
$413$	−20.5697	−1.01217
$414$	3.84659	0.189049
$415$	3.18887	0.156536
$416$	−1.17061	−0.0573938
$417$	3.20239	0.156822
$418$	−3.88296	−0.189922
$419$	−15.7715	−0.770486	−0.385243	−	0.922815i	$-0.625882\pi$
$419$	−15.7715	−0.770486	−0.385243	+	0.922815i	$0.625882\pi$
$420$	11.1067	0.541950
$421$	−34.2284	−1.66819	−0.834095	−	0.551621i	$-0.814009\pi$
$421$	−34.2284	−1.66819	−0.834095	+	0.551621i	$0.814009\pi$
$422$	1.25499	0.0610920
$423$	−10.0617	−0.489215
$424$	−1.00000	−0.0485643
$425$	13.1939	0.639997
$426$	−4.20318	−0.203645
$427$	−24.3452	−1.17814
$428$	−12.2600	−0.592607
$429$	4.54543	0.219455
$430$	15.2426	0.735062
$431$	29.3608	1.41426	0.707131	−	0.707083i	$-0.249989\pi$
$431$	29.3608	1.41426	0.707131	+	0.707083i	$0.249989\pi$
$432$	1.00000	0.0481125
$433$	14.2049	0.682645	0.341323	−	0.939946i	$-0.389125\pi$
$433$	14.2049	0.682645	0.341323	+	0.939946i	$0.389125\pi$
$434$	−26.1184	−1.25372
$435$	−16.4320	−0.787854
$436$	−10.3397	−0.495184
$437$	−3.84659	−0.184007
$438$	−1.42526	−0.0681015
$439$	28.4873	1.35963	0.679813	−	0.733385i	$-0.262061\pi$
$439$	28.4873	1.35963	0.679813	+	0.733385i	$0.262061\pi$
$440$	10.1232	0.482606
$441$	11.1491	0.530909
$442$	−8.59518	−0.408831
$443$	−3.63464	−0.172687	−0.0863435	−	0.996265i	$-0.527518\pi$
$443$	−3.63464	−0.172687	−0.0863435	+	0.996265i	$0.527518\pi$
$444$	−7.87979	−0.373959
$445$	9.68617	0.459169
$446$	−24.9080	−1.17943
$447$	−15.3255	−0.724872
$448$	−4.26018	−0.201274
$449$	−14.1986	−0.670076	−0.335038	−	0.942205i	$-0.608749\pi$
$449$	−14.1986	−0.670076	−0.335038	+	0.942205i	$0.608749\pi$
$450$	−1.79692	−0.0847077
$451$	−49.3279	−2.32276
$452$	14.3225	0.673672
$453$	8.03932	0.377720
$454$	−4.76884	−0.223813
$455$	13.0016	0.609523
$456$	−1.00000	−0.0468293
$457$	−40.4663	−1.89293	−0.946467	−	0.322800i	$-0.895376\pi$
$457$	−40.4663	−1.89293	−0.946467	+	0.322800i	$0.895376\pi$
$458$	−21.2367	−0.992324
$459$	7.34248	0.342718
$460$	10.0284	0.467576
$461$	7.63953	0.355808	0.177904	−	0.984048i	$-0.443068\pi$
$461$	7.63953	0.355808	0.177904	+	0.984048i	$0.443068\pi$
$462$	16.5421	0.769608
$463$	−27.9478	−1.29885	−0.649423	−	0.760427i	$-0.724990\pi$
$463$	−27.9478	−1.29885	−0.649423	+	0.760427i	$0.724990\pi$
$464$	6.30281	0.292600
$465$	15.9836	0.741224
$466$	−2.72417	−0.126195
$467$	−6.78135	−0.313804	−0.156902	−	0.987614i	$-0.550151\pi$
$467$	−6.78135	−0.313804	−0.156902	+	0.987614i	$0.550151\pi$
$468$	1.17061	0.0541114
$469$	−18.0314	−0.832614
$470$	−26.2317	−1.20998
$471$	11.1834	0.515305
$472$	−4.82836	−0.222243
$473$	22.7021	1.04384
$474$	0.672153	0.0308730
$475$	1.79692	0.0824484
$476$	−31.2803	−1.43373
$477$	1.00000	0.0457869
$478$	−4.07034	−0.186173
$479$	19.6374	0.897256	0.448628	−	0.893719i	$-0.351913\pi$
$479$	19.6374	0.897256	0.448628	+	0.893719i	$0.351913\pi$
$480$	2.60709	0.118997
$481$	−9.22416	−0.420586
$482$	−11.3570	−0.517299
$483$	16.3871	0.745640
$484$	4.07739	0.185336
$485$	−37.5972	−1.70720
$486$	−1.00000	−0.0453609
$487$	11.4417	0.518471	0.259236	−	0.965814i	$-0.416529\pi$
$487$	11.4417	0.518471	0.259236	+	0.965814i	$0.416529\pi$
$488$	−5.71459	−0.258687
$489$	24.4244	1.10451
$490$	29.0667	1.31310
$491$	−7.15466	−0.322885	−0.161443	−	0.986882i	$-0.551615\pi$
$491$	−7.15466	−0.322885	−0.161443	+	0.986882i	$0.551615\pi$
$492$	−12.7037	−0.572727
$493$	46.2783	2.08427
$494$	−1.17061	−0.0526682
$495$	−10.1232	−0.455005
$496$	−6.13083	−0.275283
$497$	−17.9063	−0.803207
$498$	1.22315	0.0548109
$499$	−0.842658	−0.0377225	−0.0188613	−	0.999822i	$-0.506004\pi$
$499$	−0.842658	−0.0377225	−0.0188613	+	0.999822i	$0.506004\pi$
$500$	8.35072	0.373455
$501$	7.20664	0.321969
$502$	14.6644	0.654503
$503$	−13.5378	−0.603620	−0.301810	−	0.953368i	$-0.597591\pi$
$503$	−13.5378	−0.603620	−0.301810	+	0.953368i	$0.597591\pi$
$504$	4.26018	0.189763
$505$	43.9551	1.95598
$506$	14.9361	0.663992
$507$	−11.6297	−0.516492
$508$	21.6644	0.961201
$509$	4.74666	0.210392	0.105196	−	0.994452i	$-0.466453\pi$
$509$	4.74666	0.210392	0.105196	+	0.994452i	$0.466453\pi$
$510$	19.1425	0.847645
$511$	−6.07185	−0.268603
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	−25.7206	−1.13449
$515$	−42.5399	−1.87453
$516$	5.84659	0.257382
$517$	−39.0691	−1.71826
$518$	−33.5693	−1.47495
$519$	−0.0148678	−0.000652624 0
$520$	3.05188	0.133834
$521$	−1.62081	−0.0710088	−0.0355044	−	0.999370i	$-0.511304\pi$
$521$	−1.62081	−0.0710088	−0.0355044	+	0.999370i	$0.511304\pi$
$522$	−6.30281	−0.275866
$523$	−25.2416	−1.10374	−0.551869	−	0.833931i	$-0.686085\pi$
$523$	−25.2416	−1.10374	−0.551869	+	0.833931i	$0.686085\pi$
$524$	−10.2166	−0.446316
$525$	−7.65520	−0.334100
$526$	−12.0474	−0.525293
$527$	−45.0156	−1.96091
$528$	3.88296	0.168984
$529$	−8.20378	−0.356686
$530$	2.60709	0.113245
$531$	4.82836	0.209533
$532$	−4.26018	−0.184702
$533$	−14.8711	−0.644137
$534$	3.71532	0.160778
$535$	31.9628	1.38187
$536$	−4.23256	−0.182819
$537$	18.5617	0.800997
$538$	−22.4276	−0.966923
$539$	43.2915	1.86470
$540$	−2.60709	−0.112191
$541$	43.1712	1.85608	0.928038	−	0.372486i	$-0.121494\pi$
$541$	43.1712	1.85608	0.928038	+	0.372486i	$0.121494\pi$
$542$	−23.2258	−0.997635
$543$	−19.8251	−0.850777
$544$	−7.34248	−0.314806
$545$	26.9566	1.15470
$546$	4.98700	0.213424
$547$	14.1901	0.606727	0.303363	−	0.952875i	$-0.401890\pi$
$547$	14.1901	0.606727	0.303363	+	0.952875i	$0.401890\pi$
$548$	−7.37045	−0.314850
$549$	5.71459	0.243893
$550$	−6.97738	−0.297516
$551$	6.30281	0.268509
$552$	3.84659	0.163722
$553$	2.86349	0.121768
$554$	7.51423	0.319249
$555$	20.5433	0.872016
$556$	3.20239	0.135812
$557$	37.0018	1.56782	0.783909	−	0.620876i	$-0.213223\pi$
$557$	37.0018	1.56782	0.783909	+	0.620876i	$0.213223\pi$
$558$	6.13083	0.259539
$559$	6.84407	0.289473
$560$	11.1067	0.469342
$561$	28.5106	1.20372
$562$	−11.3139	−0.477247
$563$	−19.0090	−0.801134	−0.400567	−	0.916268i	$-0.631187\pi$
$563$	−19.0090	−0.801134	−0.400567	+	0.916268i	$0.631187\pi$
$564$	−10.0617	−0.423672
$565$	−37.3399	−1.57090
$566$	−22.9678	−0.965408
$567$	−4.26018	−0.178911
$568$	−4.20318	−0.176362
$569$	−22.3277	−0.936025	−0.468013	−	0.883722i	$-0.655030\pi$
$569$	−22.3277	−0.936025	−0.468013	+	0.883722i	$0.655030\pi$
$570$	2.60709	0.109199
$571$	26.0616	1.09064	0.545322	−	0.838227i	$-0.316407\pi$
$571$	26.0616	1.09064	0.545322	+	0.838227i	$0.316407\pi$
$572$	4.54543	0.190054
$573$	−7.07364	−0.295505
$574$	−54.1199	−2.25892
$575$	−6.91201	−0.288251
$576$	1.00000	0.0416667
$577$	20.4422	0.851018	0.425509	−	0.904954i	$-0.360095\pi$
$577$	20.4422	0.851018	0.425509	+	0.904954i	$0.360095\pi$
$578$	−36.9121	−1.53534
$579$	−22.3742	−0.929841
$580$	−16.4320	−0.682301
$581$	5.21085	0.216183
$582$	−14.4211	−0.597774
$583$	3.88296	0.160816
$584$	−1.42526	−0.0589776
$585$	−3.05188	−0.126180
$586$	26.2476	1.08428
$587$	22.4631	0.927153	0.463576	−	0.886057i	$-0.346566\pi$
$587$	22.4631	0.927153	0.463576	+	0.886057i	$0.346566\pi$
$588$	11.1491	0.459781
$589$	−6.13083	−0.252617
$590$	12.5880	0.518238
$591$	26.7301	1.09953
$592$	−7.87979	−0.323858
$593$	9.27332	0.380809	0.190405	−	0.981706i	$-0.439020\pi$
$593$	9.27332	0.380809	0.190405	+	0.981706i	$0.439020\pi$
$594$	−3.88296	−0.159320
$595$	81.5505	3.34324
$596$	−15.3255	−0.627758
$597$	5.10401	0.208893
$598$	4.50285	0.184135
$599$	9.00467	0.367921	0.183960	−	0.982934i	$-0.441108\pi$
$599$	9.00467	0.367921	0.183960	+	0.982934i	$0.441108\pi$
$600$	−1.79692	−0.0733590
$601$	26.8239	1.09417	0.547084	−	0.837078i	$-0.315738\pi$
$601$	26.8239	1.09417	0.547084	+	0.837078i	$0.315738\pi$
$602$	24.9075	1.01515
$603$	4.23256	0.172363
$604$	8.03932	0.327115
$605$	−10.6301	−0.432176
$606$	16.8598	0.684884
$607$	36.4313	1.47870	0.739350	−	0.673322i	$-0.235133\pi$
$607$	36.4313	1.47870	0.739350	+	0.673322i	$0.235133\pi$
$608$	−1.00000	−0.0405554
$609$	−26.8511	−1.08806
$610$	14.8985	0.603221
$611$	−11.7783	−0.476498
$612$	7.34248	0.296802
$613$	23.8755	0.964324	0.482162	−	0.876082i	$-0.339852\pi$
$613$	23.8755	0.964324	0.482162	+	0.876082i	$0.339852\pi$
$614$	−1.75290	−0.0707411
$615$	33.1197	1.33551
$616$	16.5421	0.666500
$617$	−33.0942	−1.33232	−0.666160	−	0.745808i	$-0.732063\pi$
$617$	−33.0942	−1.33232	−0.666160	+	0.745808i	$0.732063\pi$
$618$	−16.3170	−0.656366
$619$	43.3889	1.74395	0.871973	−	0.489554i	$-0.162840\pi$
$619$	43.3889	1.74395	0.871973	+	0.489554i	$0.162840\pi$
$620$	15.9836	0.641919
$621$	−3.84659	−0.154358
$622$	3.41258	0.136832
$623$	15.8279	0.634132
$624$	1.17061	0.0468619
$625$	−30.7557	−1.23023
$626$	−27.5975	−1.10302
$627$	3.88296	0.155071
$628$	11.1834	0.446267
$629$	−57.8573	−2.30692
$630$	−11.1067	−0.442500
$631$	7.01066	0.279090	0.139545	−	0.990216i	$-0.455436\pi$
$631$	7.01066	0.279090	0.139545	+	0.990216i	$0.455436\pi$
$632$	0.672153	0.0267368
$633$	−1.25499	−0.0498814
$634$	17.3098	0.687459
$635$	−56.4810	−2.24138
$636$	1.00000	0.0396526
$637$	13.0512	0.517109
$638$	−24.4736	−0.968917
$639$	4.20318	0.166275
$640$	2.60709	0.103054
$641$	21.4606	0.847641	0.423820	−	0.905746i	$-0.360689\pi$
$641$	21.4606	0.847641	0.423820	+	0.905746i	$0.360689\pi$
$642$	12.2600	0.483862
$643$	−3.43026	−0.135276	−0.0676380	−	0.997710i	$-0.521546\pi$
$643$	−3.43026	−0.135276	−0.0676380	+	0.997710i	$0.521546\pi$
$644$	16.3871	0.645743
$645$	−15.2426	−0.600176
$646$	−7.34248	−0.288886
$647$	−12.9793	−0.510268	−0.255134	−	0.966906i	$-0.582120\pi$
$647$	−12.9793	−0.510268	−0.255134	+	0.966906i	$0.582120\pi$
$648$	−1.00000	−0.0392837
$649$	18.7483	0.735936
$650$	−2.10349	−0.0825058
$651$	26.1184	1.02366
$652$	24.4244	0.956534
$653$	−5.66984	−0.221878	−0.110939	−	0.993827i	$-0.535386\pi$
$653$	−5.66984	−0.221878	−0.110939	+	0.993827i	$0.535386\pi$
$654$	10.3397	0.404316
$655$	26.6357	1.04074
$656$	−12.7037	−0.495996
$657$	1.42526	0.0556046
$658$	−42.8645	−1.67103
$659$	−32.1319	−1.25168	−0.625841	−	0.779951i	$-0.715244\pi$
$659$	−32.1319	−1.25168	−0.625841	+	0.779951i	$0.715244\pi$
$660$	−10.1232	−0.394046
$661$	7.34894	0.285841	0.142920	−	0.989734i	$-0.454351\pi$
$661$	7.34894	0.285841	0.142920	+	0.989734i	$0.454351\pi$
$662$	9.42481	0.366306
$663$	8.59518	0.333809
$664$	1.22315	0.0474676
$665$	11.1067	0.430698
$666$	7.87979	0.305336
$667$	−24.2443	−0.938742
$668$	7.20664	0.278833
$669$	24.9080	0.962998
$670$	11.0347	0.426306
$671$	22.1895	0.856617
$672$	4.26018	0.164340
$673$	−0.111888	−0.00431297	−0.00215648	−	0.999998i	$-0.500686\pi$
$673$	−0.111888	−0.00431297	−0.00215648	+	0.999998i	$0.500686\pi$
$674$	8.84832	0.340825
$675$	1.79692	0.0691635
$676$	−11.6297	−0.447295
$677$	39.4175	1.51494	0.757469	−	0.652871i	$-0.226436\pi$
$677$	39.4175	1.51494	0.757469	+	0.652871i	$0.226436\pi$
$678$	−14.3225	−0.550051
$679$	−61.4365	−2.35772
$680$	19.1425	0.734082
$681$	4.76884	0.182742
$682$	23.8058	0.911571
$683$	−7.27525	−0.278380	−0.139190	−	0.990266i	$-0.544450\pi$
$683$	−7.27525	−0.278380	−0.139190	+	0.990266i	$0.544450\pi$
$684$	1.00000	0.0382360
$685$	19.2154	0.734183
$686$	17.6759	0.674867
$687$	21.2367	0.810229
$688$	5.84659	0.222899
$689$	1.17061	0.0445967
$690$	−10.0284	−0.381775
$691$	24.6619	0.938183	0.469091	−	0.883150i	$-0.344582\pi$
$691$	24.6619	0.938183	0.469091	+	0.883150i	$0.344582\pi$
$692$	−0.0148678	−0.000565189 0
$693$	−16.5421	−0.628382
$694$	−5.41090	−0.205395
$695$	−8.34892	−0.316692
$696$	−6.30281	−0.238907
$697$	−93.2766	−3.53310
$698$	26.3195	0.996206
$699$	2.72417	0.103037
$700$	−7.65520	−0.289339
$701$	−38.1986	−1.44274	−0.721371	−	0.692549i	$-0.756488\pi$
$701$	−38.1986	−1.44274	−0.721371	+	0.692549i	$0.756488\pi$
$702$	−1.17061	−0.0441818
$703$	−7.87979	−0.297192
$704$	3.88296	0.146345
$705$	26.2317	0.987942
$706$	−31.5456	−1.18723
$707$	71.8259	2.70129
$708$	4.82836	0.181461
$709$	19.1468	0.719073	0.359537	−	0.933131i	$-0.382935\pi$
$709$	19.1468	0.719073	0.359537	+	0.933131i	$0.382935\pi$
$710$	10.9581	0.411249
$711$	−0.672153	−0.0252077
$712$	3.71532	0.139237
$713$	23.5828	0.883182
$714$	31.2803	1.17063
$715$	−11.8504	−0.443178
$716$	18.5617	0.693684
$717$	4.07034	0.152010
$718$	−8.10868	−0.302613
$719$	31.9634	1.19203	0.596016	−	0.802972i	$-0.296749\pi$
$719$	31.9634	1.19203	0.596016	+	0.802972i	$0.296749\pi$
$720$	−2.60709	−0.0971605
$721$	−69.5132	−2.58881
$722$	−1.00000	−0.0372161
$723$	11.3570	0.422372
$724$	−19.8251	−0.736794
$725$	11.3256	0.420624
$726$	−4.07739	−0.151326
$727$	−26.3474	−0.977169	−0.488585	−	0.872517i	$-0.662487\pi$
$727$	−26.3474	−0.977169	−0.488585	+	0.872517i	$0.662487\pi$
$728$	4.98700	0.184831
$729$	1.00000	0.0370370
$730$	3.71578	0.137527
$731$	42.9285	1.58777
$732$	5.71459	0.211217
$733$	9.83003	0.363080	0.181540	−	0.983384i	$-0.441892\pi$
$733$	9.83003	0.363080	0.181540	+	0.983384i	$0.441892\pi$
$734$	1.17150	0.0432408
$735$	−29.0667	−1.07214
$736$	3.84659	0.141787
$737$	16.4349	0.605386
$738$	12.7037	0.467629
$739$	−39.7120	−1.46083	−0.730414	−	0.683004i	$-0.760673\pi$
$739$	−39.7120	−1.46083	−0.730414	+	0.683004i	$0.760673\pi$
$740$	20.5433	0.755188
$741$	1.17061	0.0430034
$742$	4.26018	0.156396
$743$	−1.69197	−0.0620723	−0.0310362	−	0.999518i	$-0.509881\pi$
$743$	−1.69197	−0.0620723	−0.0310362	+	0.999518i	$0.509881\pi$
$744$	6.13083	0.224767
$745$	39.9550	1.46384
$746$	−27.7793	−1.01707
$747$	−1.22315	−0.0447529
$748$	28.5106	1.04245
$749$	52.2296	1.90843
$750$	−8.35072	−0.304925
$751$	−20.1120	−0.733896	−0.366948	−	0.930241i	$-0.619597\pi$
$751$	−20.1120	−0.733896	−0.366948	+	0.930241i	$0.619597\pi$
$752$	−10.0617	−0.366911
$753$	−14.6644	−0.534399
$754$	−7.37812	−0.268695
$755$	−20.9592	−0.762784
$756$	−4.26018	−0.154941
$757$	−19.5988	−0.712332	−0.356166	−	0.934423i	$-0.615916\pi$
$757$	−19.5988	−0.712332	−0.356166	+	0.934423i	$0.615916\pi$
$758$	15.1717	0.551061
$759$	−14.9361	−0.542148
$760$	2.60709	0.0945691
$761$	−44.4731	−1.61215	−0.806074	−	0.591815i	$-0.798412\pi$
$761$	−44.4731	−1.61215	−0.806074	+	0.591815i	$0.798412\pi$
$762$	−21.6644	−0.784817
$763$	44.0491	1.59468
$764$	−7.07364	−0.255915
$765$	−19.1425	−0.692099
$766$	−11.4268	−0.412866
$767$	5.65212	0.204086
$768$	1.00000	0.0360844
$769$	−10.0797	−0.363483	−0.181741	−	0.983346i	$-0.558173\pi$
$769$	−10.0797	−0.363483	−0.181741	+	0.983346i	$0.558173\pi$
$770$	−43.1267	−1.55418
$771$	25.7206	0.926306
$772$	−22.3742	−0.805266
$773$	−38.4834	−1.38415	−0.692075	−	0.721825i	$-0.743303\pi$
$773$	−38.4834	−1.38415	−0.692075	+	0.721825i	$0.743303\pi$
$774$	−5.84659	−0.210151
$775$	−11.0166	−0.395729
$776$	−14.4211	−0.517688
$777$	33.5693	1.20429
$778$	10.0477	0.360228
$779$	−12.7037	−0.455157
$780$	−3.05188	−0.109275
$781$	16.3208	0.584004
$782$	28.2435	1.00999
$783$	6.30281	0.225244
$784$	11.1491	0.398182
$785$	−29.1562	−1.04063
$786$	10.2166	0.364416
$787$	−52.1075	−1.85743	−0.928715	−	0.370794i	$-0.879086\pi$
$787$	−52.1075	−1.85743	−0.928715	+	0.370794i	$0.879086\pi$
$788$	26.7301	0.952222
$789$	12.0474	0.428900
$790$	−1.75236	−0.0623463
$791$	−61.0162	−2.16949
$792$	−3.88296	−0.137975
$793$	6.68955	0.237553
$794$	−18.7483	−0.665351
$795$	−2.60709	−0.0924640
$796$	5.10401	0.180907
$797$	20.2905	0.718725	0.359363	−	0.933198i	$-0.382994\pi$
$797$	20.2905	0.718725	0.359363	+	0.933198i	$0.382994\pi$
$798$	4.26018	0.150809
$799$	−73.8776	−2.61360
$800$	−1.79692	−0.0635308
$801$	−3.71532	−0.131274
$802$	5.96139	0.210504
$803$	5.53422	0.195298
$804$	4.23256	0.149271
$805$	−42.7227	−1.50578
$806$	7.17681	0.252792
$807$	22.4276	0.789489
$808$	16.8598	0.593127
$809$	51.3497	1.80536	0.902680	−	0.430312i	$-0.141596\pi$
$809$	51.3497	1.80536	0.902680	+	0.430312i	$0.141596\pi$
$810$	2.60709	0.0916038
$811$	41.3386	1.45159	0.725797	−	0.687909i	$-0.241471\pi$
$811$	41.3386	1.45159	0.725797	+	0.687909i	$0.241471\pi$
$812$	−26.8511	−0.942287
$813$	23.2258	0.814566
$814$	30.5969	1.07242
$815$	−63.6767	−2.23050
$816$	7.34248	0.257038
$817$	5.84659	0.204546
$818$	8.65264	0.302533
$819$	−4.98700	−0.174260
$820$	33.1197	1.15659
$821$	−2.88543	−0.100702	−0.0503510	−	0.998732i	$-0.516034\pi$
$821$	−2.88543	−0.100702	−0.0503510	+	0.998732i	$0.516034\pi$
$822$	7.37045	0.257074
$823$	−50.1525	−1.74821	−0.874104	−	0.485739i	$-0.838551\pi$
$823$	−50.1525	−1.74821	−0.874104	+	0.485739i	$0.838551\pi$
$824$	−16.3170	−0.568429
$825$	6.97738	0.242921
$826$	20.5697	0.715710
$827$	42.3150	1.47144	0.735718	−	0.677288i	$-0.236845\pi$
$827$	42.3150	1.47144	0.735718	+	0.677288i	$0.236845\pi$
$828$	−3.84659	−0.133678
$829$	28.4585	0.988404	0.494202	−	0.869347i	$-0.335460\pi$
$829$	28.4585	0.988404	0.494202	+	0.869347i	$0.335460\pi$
$830$	−3.18887	−0.110687
$831$	−7.51423	−0.260666
$832$	1.17061	0.0405836
$833$	81.8620	2.83635
$834$	−3.20239	−0.110890
$835$	−18.7884	−0.650198
$836$	3.88296	0.134295
$837$	−6.13083	−0.211913
$838$	15.7715	0.544816
$839$	24.5988	0.849246	0.424623	−	0.905370i	$-0.360407\pi$
$839$	24.5988	0.849246	0.424623	+	0.905370i	$0.360407\pi$
$840$	−11.1067	−0.383216
$841$	10.7254	0.369840
$842$	34.2284	1.17959
$843$	11.3139	0.389671
$844$	−1.25499	−0.0431986
$845$	30.3196	1.04303
$846$	10.0617	0.345927
$847$	−17.3704	−0.596854
$848$	1.00000	0.0343401
$849$	22.9678	0.788252
$850$	−13.1939	−0.452546
$851$	30.3103	1.03902
$852$	4.20318	0.143999
$853$	24.0745	0.824295	0.412147	−	0.911117i	$-0.364779\pi$
$853$	24.0745	0.824295	0.412147	+	0.911117i	$0.364779\pi$
$854$	24.3452	0.833074
$855$	−2.60709	−0.0891606
$856$	12.2600	0.419037
$857$	41.3750	1.41334	0.706671	−	0.707542i	$-0.250196\pi$
$857$	41.3750	1.41334	0.706671	+	0.707542i	$0.250196\pi$
$858$	−4.54543	−0.155178
$859$	−38.0743	−1.29908	−0.649539	−	0.760328i	$-0.725038\pi$
$859$	−38.0743	−1.29908	−0.649539	+	0.760328i	$0.725038\pi$
$860$	−15.2426	−0.519768
$861$	54.1199	1.84440
$862$	−29.3608	−1.00003
$863$	12.9173	0.439709	0.219854	−	0.975533i	$-0.429442\pi$
$863$	12.9173	0.439709	0.219854	+	0.975533i	$0.429442\pi$
$864$	−1.00000	−0.0340207
$865$	0.0387617	0.00131794
$866$	−14.2049	−0.482703
$867$	36.9121	1.25360
$868$	26.1184	0.886517
$869$	−2.60994	−0.0885362
$870$	16.4320	0.557097
$871$	4.95467	0.167883
$872$	10.3397	0.350148
$873$	14.4211	0.488081
$874$	3.84659	0.130113
$875$	−35.5755	−1.20267
$876$	1.42526	0.0481550
$877$	−38.7830	−1.30961	−0.654804	−	0.755799i	$-0.727249\pi$
$877$	−38.7830	−1.30961	−0.654804	+	0.755799i	$0.727249\pi$
$878$	−28.4873	−0.961401
$879$	−26.2476	−0.885309
$880$	−10.1232	−0.341254
$881$	−31.7163	−1.06855	−0.534275	−	0.845311i	$-0.679415\pi$
$881$	−31.7163	−1.06855	−0.534275	+	0.845311i	$0.679415\pi$
$882$	−11.1491	−0.375409
$883$	−26.1045	−0.878487	−0.439244	−	0.898368i	$-0.644753\pi$
$883$	−26.1045	−0.878487	−0.439244	+	0.898368i	$0.644753\pi$
$884$	8.59518	0.289087
$885$	−12.5880	−0.423140
$886$	3.63464	0.122108
$887$	−8.32931	−0.279671	−0.139835	−	0.990175i	$-0.544657\pi$
$887$	−8.32931	−0.279671	−0.139835	+	0.990175i	$0.544657\pi$
$888$	7.87979	0.264429
$889$	−92.2940	−3.09544
$890$	−9.68617	−0.324681
$891$	3.88296	0.130084
$892$	24.9080	0.833981
$893$	−10.0617	−0.336701
$894$	15.3255	0.512562
$895$	−48.3921	−1.61757
$896$	4.26018	0.142322
$897$	−4.50285	−0.150346
$898$	14.1986	0.473815
$899$	−38.6415	−1.28877
$900$	1.79692	0.0598974
$901$	7.34248	0.244614
$902$	49.3279	1.64244
$903$	−24.9075	−0.828869
$904$	−14.3225	−0.476358
$905$	51.6858	1.71810
$906$	−8.03932	−0.267088
$907$	58.4166	1.93969	0.969846	−	0.243720i	$-0.0783677\pi$
$907$	58.4166	1.93969	0.969846	+	0.243720i	$0.0783677\pi$
$908$	4.76884	0.158259
$909$	−16.8598	−0.559205
$910$	−13.0016	−0.430998
$911$	−32.3587	−1.07209	−0.536046	−	0.844189i	$-0.680083\pi$
$911$	−32.3587	−1.07209	−0.536046	+	0.844189i	$0.680083\pi$
$912$	1.00000	0.0331133
$913$	−4.74946	−0.157184
$914$	40.4663	1.33851
$915$	−14.8985	−0.492528
$916$	21.2367	0.701679
$917$	43.5247	1.43731
$918$	−7.34248	−0.242338
$919$	−3.05618	−0.100814	−0.0504070	−	0.998729i	$-0.516052\pi$
$919$	−3.05618	−0.100814	−0.0504070	+	0.998729i	$0.516052\pi$
$920$	−10.0284	−0.330626
$921$	1.75290	0.0577599
$922$	−7.63953	−0.251594
$923$	4.92029	0.161953
$924$	−16.5421	−0.544195
$925$	−14.1594	−0.465557
$926$	27.9478	0.918423
$927$	16.3170	0.535920
$928$	−6.30281	−0.206900
$929$	54.4919	1.78782	0.893910	−	0.448246i	$-0.147951\pi$
$929$	54.4919	1.78782	0.893910	+	0.448246i	$0.147951\pi$
$930$	−15.9836	−0.524124
$931$	11.1491	0.365397
$932$	2.72417	0.0892331
$933$	−3.41258	−0.111723
$934$	6.78135	0.221893
$935$	−74.3297	−2.43084
$936$	−1.17061	−0.0382626
$937$	−11.8130	−0.385915	−0.192957	−	0.981207i	$-0.561808\pi$
$937$	−11.8130	−0.385915	−0.192957	+	0.981207i	$0.561808\pi$
$938$	18.0314	0.588747
$939$	27.5975	0.900610
$940$	26.2317	0.855583
$941$	11.6897	0.381072	0.190536	−	0.981680i	$-0.438977\pi$
$941$	11.6897	0.381072	0.190536	+	0.981680i	$0.438977\pi$
$942$	−11.1834	−0.364376
$943$	48.8658	1.59129
$944$	4.82836	0.157150
$945$	11.1067	0.361300
$946$	−22.7021	−0.738108
$947$	30.9538	1.00586	0.502932	−	0.864326i	$-0.332255\pi$
$947$	30.9538	1.00586	0.502932	+	0.864326i	$0.332255\pi$
$948$	−0.672153	−0.0218305
$949$	1.66842	0.0541592
$950$	−1.79692	−0.0582998
$951$	−17.3098	−0.561308
$952$	31.2803	1.01380
$953$	−49.2236	−1.59451	−0.797255	−	0.603643i	$-0.793715\pi$
$953$	−49.2236	−1.59451	−0.797255	+	0.603643i	$0.793715\pi$
$954$	−1.00000	−0.0323762
$955$	18.4416	0.596757
$956$	4.07034	0.131644
$957$	24.4736	0.791118
$958$	−19.6374	−0.634455
$959$	31.3994	1.01394
$960$	−2.60709	−0.0841435
$961$	6.58713	0.212488
$962$	9.22416	0.297399
$963$	−12.2600	−0.395072
$964$	11.3570	0.365785
$965$	58.3316	1.87776
$966$	−16.3871	−0.527247
$967$	30.3680	0.976570	0.488285	−	0.872684i	$-0.337623\pi$
$967$	30.3680	0.976570	0.488285	+	0.872684i	$0.337623\pi$
$968$	−4.07739	−0.131052
$969$	7.34248	0.235875
$970$	37.5972	1.20717
$971$	−54.7799	−1.75797	−0.878985	−	0.476849i	$-0.841779\pi$
$971$	−54.7799	−1.75797	−0.878985	+	0.476849i	$0.841779\pi$
$972$	1.00000	0.0320750
$973$	−13.6427	−0.437366
$974$	−11.4417	−0.366615
$975$	2.10349	0.0673657
$976$	5.71459	0.182920
$977$	11.7767	0.376771	0.188386	−	0.982095i	$-0.439675\pi$
$977$	11.7767	0.376771	0.188386	+	0.982095i	$0.439675\pi$
$978$	−24.4244	−0.781007
$979$	−14.4264	−0.461071
$980$	−29.0667	−0.928501
$981$	−10.3397	−0.330122
$982$	7.15466	0.228314
$983$	−2.36113	−0.0753083	−0.0376541	−	0.999291i	$-0.511989\pi$
$983$	−2.36113	−0.0753083	−0.0376541	+	0.999291i	$0.511989\pi$
$984$	12.7037	0.404979
$985$	−69.6879	−2.22044
$986$	−46.2783	−1.47380
$987$	42.8645	1.36439
$988$	1.17061	0.0372420
$989$	−22.4894	−0.715121
$990$	10.1232	0.321737
$991$	36.8956	1.17203	0.586014	−	0.810301i	$-0.300697\pi$
$991$	36.8956	1.17203	0.586014	+	0.810301i	$0.300697\pi$
$992$	6.13083	0.194654
$993$	−9.42481	−0.299087
$994$	17.9063	0.567953
$995$	−13.3066	−0.421848
$996$	−1.22315	−0.0387571
$997$	−34.1886	−1.08276	−0.541382	−	0.840777i	$-0.682099\pi$
$997$	−34.1886	−1.08276	−0.541382	+	0.840777i	$0.682099\pi$
$998$	0.842658	0.0266739
$999$	−7.87979	−0.249306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bf.1.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bf.1.5	✓	12	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.60709 q^{5} -1.00000 q^{6} -4.26018 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.60709 q^{5} -1.00000 q^{6} -4.26018 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.60709 q^{10} +3.88296 q^{11} +1.00000 q^{12} +1.17061 q^{13} +4.26018 q^{14} -2.60709 q^{15} +1.00000 q^{16} +7.34248 q^{17} -1.00000 q^{18} +1.00000 q^{19} -2.60709 q^{20} -4.26018 q^{21} -3.88296 q^{22} -3.84659 q^{23} -1.00000 q^{24} +1.79692 q^{25} -1.17061 q^{26} +1.00000 q^{27} -4.26018 q^{28} +6.30281 q^{29} +2.60709 q^{30} -6.13083 q^{31} -1.00000 q^{32} +3.88296 q^{33} -7.34248 q^{34} +11.1067 q^{35} +1.00000 q^{36} -7.87979 q^{37} -1.00000 q^{38} +1.17061 q^{39} +2.60709 q^{40} -12.7037 q^{41} +4.26018 q^{42} +5.84659 q^{43} +3.88296 q^{44} -2.60709 q^{45} +3.84659 q^{46} -10.0617 q^{47} +1.00000 q^{48} +11.1491 q^{49} -1.79692 q^{50} +7.34248 q^{51} +1.17061 q^{52} +1.00000 q^{53} -1.00000 q^{54} -10.1232 q^{55} +4.26018 q^{56} +1.00000 q^{57} -6.30281 q^{58} +4.82836 q^{59} -2.60709 q^{60} +5.71459 q^{61} +6.13083 q^{62} -4.26018 q^{63} +1.00000 q^{64} -3.05188 q^{65} -3.88296 q^{66} +4.23256 q^{67} +7.34248 q^{68} -3.84659 q^{69} -11.1067 q^{70} +4.20318 q^{71} -1.00000 q^{72} +1.42526 q^{73} +7.87979 q^{74} +1.79692 q^{75} +1.00000 q^{76} -16.5421 q^{77} -1.17061 q^{78} -0.672153 q^{79} -2.60709 q^{80} +1.00000 q^{81} +12.7037 q^{82} -1.22315 q^{83} -4.26018 q^{84} -19.1425 q^{85} -5.84659 q^{86} +6.30281 q^{87} -3.88296 q^{88} -3.71532 q^{89} +2.60709 q^{90} -4.98700 q^{91} -3.84659 q^{92} -6.13083 q^{93} +10.0617 q^{94} -2.60709 q^{95} -1.00000 q^{96} +14.4211 q^{97} -11.1491 q^{98} +3.88296 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9} + 7 q^{10} - 5 q^{11} + 12 q^{12} + 10 q^{13} - 5 q^{14} - 7 q^{15} + 12 q^{16} + 6 q^{17} - 12 q^{18} + 12 q^{19} - 7 q^{20} + 5 q^{21} + 5 q^{22} - 12 q^{24} + 21 q^{25} - 10 q^{26} + 12 q^{27} + 5 q^{28} + 7 q^{30} + 2 q^{31} - 12 q^{32} - 5 q^{33} - 6 q^{34} - 17 q^{35} + 12 q^{36} + 16 q^{37} - 12 q^{38} + 10 q^{39} + 7 q^{40} + 7 q^{41} - 5 q^{42} + 24 q^{43} - 5 q^{44} - 7 q^{45} + 4 q^{47} + 12 q^{48} + 29 q^{49} - 21 q^{50} + 6 q^{51} + 10 q^{52} + 12 q^{53} - 12 q^{54} - 2 q^{55} - 5 q^{56} + 12 q^{57} + 2 q^{59} - 7 q^{60} + 29 q^{61} - 2 q^{62} + 5 q^{63} + 12 q^{64} - 17 q^{65} + 5 q^{66} + 36 q^{67} + 6 q^{68} + 17 q^{70} - 3 q^{71} - 12 q^{72} + 7 q^{73} - 16 q^{74} + 21 q^{75} + 12 q^{76} - 35 q^{77} - 10 q^{78} + 40 q^{79} - 7 q^{80} + 12 q^{81} - 7 q^{82} + 24 q^{83} + 5 q^{84} - 22 q^{85} - 24 q^{86} + 5 q^{88} - 45 q^{89} + 7 q^{90} + 71 q^{91} + 2 q^{93} - 4 q^{94} - 7 q^{95} - 12 q^{96} + q^{97} - 29 q^{98} - 5 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9 + 7 * q^10 - 5 * q^11 + 12 * q^12 + 10 * q^13 - 5 * q^14 - 7 * q^15 + 12 * q^16 + 6 * q^17 - 12 * q^18 + 12 * q^19 - 7 * q^20 + 5 * q^21 + 5 * q^22 - 12 * q^24 + 21 * q^25 - 10 * q^26 + 12 * q^27 + 5 * q^28 + 7 * q^30 + 2 * q^31 - 12 * q^32 - 5 * q^33 - 6 * q^34 - 17 * q^35 + 12 * q^36 + 16 * q^37 - 12 * q^38 + 10 * q^39 + 7 * q^40 + 7 * q^41 - 5 * q^42 + 24 * q^43 - 5 * q^44 - 7 * q^45 + 4 * q^47 + 12 * q^48 + 29 * q^49 - 21 * q^50 + 6 * q^51 + 10 * q^52 + 12 * q^53 - 12 * q^54 - 2 * q^55 - 5 * q^56 + 12 * q^57 + 2 * q^59 - 7 * q^60 + 29 * q^61 - 2 * q^62 + 5 * q^63 + 12 * q^64 - 17 * q^65 + 5 * q^66 + 36 * q^67 + 6 * q^68 + 17 * q^70 - 3 * q^71 - 12 * q^72 + 7 * q^73 - 16 * q^74 + 21 * q^75 + 12 * q^76 - 35 * q^77 - 10 * q^78 + 40 * q^79 - 7 * q^80 + 12 * q^81 - 7 * q^82 + 24 * q^83 + 5 * q^84 - 22 * q^85 - 24 * q^86 + 5 * q^88 - 45 * q^89 + 7 * q^90 + 71 * q^91 + 2 * q^93 - 4 * q^94 - 7 * q^95 - 12 * q^96 + q^97 - 29 * q^98 - 5 * q^99

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