LMFDB - Embedded newform 6018.2.a.ba.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
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} - 4 x^{11} - 31 x^{10} + 111 x^{9} + 381 x^{8} - 1101 x^{7} - 2301 x^{6} + 4690 x^{5} + \cdots + 5653 $ x^12 - 4x^11 - 31x^10 + 111x^9 + 381x^8 - 1101x^7 - 2301x^6 + 4690x^5 + 6915x^4 - 8325x^3 - 10082x^2 + 5149*x + 5653
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.06946$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.06946 q^{5} +1.00000 q^{6} -4.76338 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.06946 q^{5} +1.00000 q^{6} -4.76338 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.06946 q^{10} -0.237118 q^{11} +1.00000 q^{12} -2.53153 q^{13} -4.76338 q^{14} -2.06946 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +1.61274 q^{19} -2.06946 q^{20} -4.76338 q^{21} -0.237118 q^{22} +8.81683 q^{23} +1.00000 q^{24} -0.717316 q^{25} -2.53153 q^{26} +1.00000 q^{27} -4.76338 q^{28} -5.43652 q^{29} -2.06946 q^{30} -1.93765 q^{31} +1.00000 q^{32} -0.237118 q^{33} -1.00000 q^{34} +9.85764 q^{35} +1.00000 q^{36} +3.55256 q^{37} +1.61274 q^{38} -2.53153 q^{39} -2.06946 q^{40} +7.26844 q^{41} -4.76338 q^{42} +7.92557 q^{43} -0.237118 q^{44} -2.06946 q^{45} +8.81683 q^{46} -12.5997 q^{47} +1.00000 q^{48} +15.6898 q^{49} -0.717316 q^{50} -1.00000 q^{51} -2.53153 q^{52} +0.0982197 q^{53} +1.00000 q^{54} +0.490708 q^{55} -4.76338 q^{56} +1.61274 q^{57} -5.43652 q^{58} +1.00000 q^{59} -2.06946 q^{60} -6.13889 q^{61} -1.93765 q^{62} -4.76338 q^{63} +1.00000 q^{64} +5.23890 q^{65} -0.237118 q^{66} +10.2924 q^{67} -1.00000 q^{68} +8.81683 q^{69} +9.85764 q^{70} +10.7735 q^{71} +1.00000 q^{72} +8.08854 q^{73} +3.55256 q^{74} -0.717316 q^{75} +1.61274 q^{76} +1.12948 q^{77} -2.53153 q^{78} +15.3578 q^{79} -2.06946 q^{80} +1.00000 q^{81} +7.26844 q^{82} -16.3429 q^{83} -4.76338 q^{84} +2.06946 q^{85} +7.92557 q^{86} -5.43652 q^{87} -0.237118 q^{88} -6.74693 q^{89} -2.06946 q^{90} +12.0586 q^{91} +8.81683 q^{92} -1.93765 q^{93} -12.5997 q^{94} -3.33750 q^{95} +1.00000 q^{96} -2.58294 q^{97} +15.6898 q^{98} -0.237118 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 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 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * 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
$5$	−2.06946	−0.925493	−0.462746	−	0.886491i	$-0.653136\pi$
$5$	−2.06946	−0.925493	−0.462746	+	0.886491i	$0.653136\pi$
$6$	1.00000	0.408248
$7$	−4.76338	−1.80039	−0.900194	−	0.435490i	$-0.856575\pi$
$7$	−4.76338	−1.80039	−0.900194	+	0.435490i	$0.856575\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.06946	−0.654422
$11$	−0.237118	−0.0714939	−0.0357469	−	0.999361i	$-0.511381\pi$
$11$	−0.237118	−0.0714939	−0.0357469	+	0.999361i	$0.511381\pi$
$12$	1.00000	0.288675
$13$	−2.53153	−0.702119	−0.351059	−	0.936353i	$-0.614178\pi$
$13$	−2.53153	−0.702119	−0.351059	+	0.936353i	$0.614178\pi$
$14$	−4.76338	−1.27307
$15$	−2.06946	−0.534334
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	1.61274	0.369987	0.184994	−	0.982740i	$-0.440774\pi$
$19$	1.61274	0.369987	0.184994	+	0.982740i	$0.440774\pi$
$20$	−2.06946	−0.462746
$21$	−4.76338	−1.03945
$22$	−0.237118	−0.0505538
$23$	8.81683	1.83844	0.919218	−	0.393749i	$-0.128822\pi$
$23$	8.81683	1.83844	0.919218	+	0.393749i	$0.128822\pi$
$24$	1.00000	0.204124
$25$	−0.717316	−0.143463
$26$	−2.53153	−0.496473
$27$	1.00000	0.192450
$28$	−4.76338	−0.900194
$29$	−5.43652	−1.00954	−0.504768	−	0.863255i	$-0.668422\pi$
$29$	−5.43652	−1.00954	−0.504768	+	0.863255i	$0.668422\pi$
$30$	−2.06946	−0.377831
$31$	−1.93765	−0.348013	−0.174006	−	0.984745i	$-0.555671\pi$
$31$	−1.93765	−0.348013	−0.174006	+	0.984745i	$0.555671\pi$
$32$	1.00000	0.176777
$33$	−0.237118	−0.0412770
$34$	−1.00000	−0.171499
$35$	9.85764	1.66625
$36$	1.00000	0.166667
$37$	3.55256	0.584037	0.292019	−	0.956413i	$-0.405673\pi$
$37$	3.55256	0.584037	0.292019	+	0.956413i	$0.405673\pi$
$38$	1.61274	0.261620
$39$	−2.53153	−0.405368
$40$	−2.06946	−0.327211
$41$	7.26844	1.13514	0.567570	−	0.823325i	$-0.307884\pi$
$41$	7.26844	1.13514	0.567570	+	0.823325i	$0.307884\pi$
$42$	−4.76338	−0.735005
$43$	7.92557	1.20864	0.604319	−	0.796743i	$-0.293445\pi$
$43$	7.92557	1.20864	0.604319	+	0.796743i	$0.293445\pi$
$44$	−0.237118	−0.0357469
$45$	−2.06946	−0.308498
$46$	8.81683	1.29997
$47$	−12.5997	−1.83786	−0.918930	−	0.394420i	$-0.870945\pi$
$47$	−12.5997	−1.83786	−0.918930	+	0.394420i	$0.870945\pi$
$48$	1.00000	0.144338
$49$	15.6898	2.24139
$50$	−0.717316	−0.101444
$51$	−1.00000	−0.140028
$52$	−2.53153	−0.351059
$53$	0.0982197	0.0134915	0.00674576	−	0.999977i	$-0.497853\pi$
$53$	0.0982197	0.0134915	0.00674576	+	0.999977i	$0.497853\pi$
$54$	1.00000	0.136083
$55$	0.490708	0.0661671
$56$	−4.76338	−0.636533
$57$	1.61274	0.213612
$58$	−5.43652	−0.713850
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−2.06946	−0.267167
$61$	−6.13889	−0.786004	−0.393002	−	0.919538i	$-0.628563\pi$
$61$	−6.13889	−0.786004	−0.393002	+	0.919538i	$0.628563\pi$
$62$	−1.93765	−0.246082
$63$	−4.76338	−0.600129
$64$	1.00000	0.125000
$65$	5.23890	0.649806
$66$	−0.237118	−0.0291873
$67$	10.2924	1.25742	0.628709	−	0.777641i	$-0.283584\pi$
$67$	10.2924	1.25742	0.628709	+	0.777641i	$0.283584\pi$
$68$	−1.00000	−0.121268
$69$	8.81683	1.06142
$70$	9.85764	1.17821
$71$	10.7735	1.27858	0.639290	−	0.768966i	$-0.279229\pi$
$71$	10.7735	1.27858	0.639290	+	0.768966i	$0.279229\pi$
$72$	1.00000	0.117851
$73$	8.08854	0.946692	0.473346	−	0.880877i	$-0.343046\pi$
$73$	8.08854	0.946692	0.473346	+	0.880877i	$0.343046\pi$
$74$	3.55256	0.412977
$75$	−0.717316	−0.0828285
$76$	1.61274	0.184994
$77$	1.12948	0.128717
$78$	−2.53153	−0.286639
$79$	15.3578	1.72789	0.863943	−	0.503589i	$-0.167987\pi$
$79$	15.3578	1.72789	0.863943	+	0.503589i	$0.167987\pi$
$80$	−2.06946	−0.231373
$81$	1.00000	0.111111
$82$	7.26844	0.802665
$83$	−16.3429	−1.79386	−0.896931	−	0.442171i	$-0.854208\pi$
$83$	−16.3429	−1.79386	−0.896931	+	0.442171i	$0.854208\pi$
$84$	−4.76338	−0.519727
$85$	2.06946	0.224465
$86$	7.92557	0.854636
$87$	−5.43652	−0.582856
$88$	−0.237118	−0.0252769
$89$	−6.74693	−0.715173	−0.357586	−	0.933880i	$-0.616400\pi$
$89$	−6.74693	−0.715173	−0.357586	+	0.933880i	$0.616400\pi$
$90$	−2.06946	−0.218141
$91$	12.0586	1.26409
$92$	8.81683	0.919218
$93$	−1.93765	−0.200925
$94$	−12.5997	−1.29956
$95$	−3.33750	−0.342420
$96$	1.00000	0.102062
$97$	−2.58294	−0.262258	−0.131129	−	0.991365i	$-0.541860\pi$
$97$	−2.58294	−0.262258	−0.131129	+	0.991365i	$0.541860\pi$
$98$	15.6898	1.58490
$99$	−0.237118	−0.0238313
$100$	−0.717316	−0.0717316
$101$	5.53730	0.550982	0.275491	−	0.961304i	$-0.411160\pi$
$101$	5.53730	0.550982	0.275491	+	0.961304i	$0.411160\pi$
$102$	−1.00000	−0.0990148
$103$	13.8047	1.36022	0.680108	−	0.733112i	$-0.261933\pi$
$103$	13.8047	1.36022	0.680108	+	0.733112i	$0.261933\pi$
$104$	−2.53153	−0.248236
$105$	9.85764	0.962007
$106$	0.0982197	0.00953994
$107$	7.16902	0.693056	0.346528	−	0.938040i	$-0.387361\pi$
$107$	7.16902	0.693056	0.346528	+	0.938040i	$0.387361\pi$
$108$	1.00000	0.0962250
$109$	−2.00145	−0.191704	−0.0958520	−	0.995396i	$-0.530558\pi$
$109$	−2.00145	−0.191704	−0.0958520	+	0.995396i	$0.530558\pi$
$110$	0.490708	0.0467872
$111$	3.55256	0.337194
$112$	−4.76338	−0.450097
$113$	10.4918	0.986986	0.493493	−	0.869750i	$-0.335720\pi$
$113$	10.4918	0.986986	0.493493	+	0.869750i	$0.335720\pi$
$114$	1.61274	0.151047
$115$	−18.2461	−1.70146
$116$	−5.43652	−0.504768
$117$	−2.53153	−0.234040
$118$	1.00000	0.0920575
$119$	4.76338	0.436658
$120$	−2.06946	−0.188915
$121$	−10.9438	−0.994889
$122$	−6.13889	−0.555789
$123$	7.26844	0.655373
$124$	−1.93765	−0.174006
$125$	11.8318	1.05827
$126$	−4.76338	−0.424355
$127$	14.9220	1.32412	0.662059	−	0.749452i	$-0.269683\pi$
$127$	14.9220	1.32412	0.662059	+	0.749452i	$0.269683\pi$
$128$	1.00000	0.0883883
$129$	7.92557	0.697807
$130$	5.23890	0.459482
$131$	20.9569	1.83101	0.915506	−	0.402305i	$-0.131791\pi$
$131$	20.9569	1.83101	0.915506	+	0.402305i	$0.131791\pi$
$132$	−0.237118	−0.0206385
$133$	−7.68207	−0.666120
$134$	10.2924	0.889129
$135$	−2.06946	−0.178111
$136$	−1.00000	−0.0857493
$137$	−1.73136	−0.147920	−0.0739600	−	0.997261i	$-0.523564\pi$
$137$	−1.73136	−0.147920	−0.0739600	+	0.997261i	$0.523564\pi$
$138$	8.81683	0.750538
$139$	11.8431	1.00452	0.502259	−	0.864717i	$-0.332502\pi$
$139$	11.8431	1.00452	0.502259	+	0.864717i	$0.332502\pi$
$140$	9.85764	0.833123
$141$	−12.5997	−1.06109
$142$	10.7735	0.904092
$143$	0.600271	0.0501972
$144$	1.00000	0.0833333
$145$	11.2507	0.934319
$146$	8.08854	0.669412
$147$	15.6898	1.29407
$148$	3.55256	0.292019
$149$	1.30119	0.106598	0.0532988	−	0.998579i	$-0.483026\pi$
$149$	1.30119	0.106598	0.0532988	+	0.998579i	$0.483026\pi$
$150$	−0.717316	−0.0585686
$151$	−14.5744	−1.18605	−0.593024	−	0.805185i	$-0.702066\pi$
$151$	−14.5744	−1.18605	−0.593024	+	0.805185i	$0.702066\pi$
$152$	1.61274	0.130810
$153$	−1.00000	−0.0808452
$154$	1.12948	0.0910164
$155$	4.00990	0.322083
$156$	−2.53153	−0.202684
$157$	3.59065	0.286565	0.143282	−	0.989682i	$-0.454234\pi$
$157$	3.59065	0.286565	0.143282	+	0.989682i	$0.454234\pi$
$158$	15.3578	1.22180
$159$	0.0982197	0.00778933
$160$	−2.06946	−0.163606
$161$	−41.9979	−3.30990
$162$	1.00000	0.0785674
$163$	−5.24793	−0.411050	−0.205525	−	0.978652i	$-0.565890\pi$
$163$	−5.24793	−0.411050	−0.205525	+	0.978652i	$0.565890\pi$
$164$	7.26844	0.567570
$165$	0.490708	0.0382016
$166$	−16.3429	−1.26845
$167$	−21.8489	−1.69072	−0.845361	−	0.534195i	$-0.820615\pi$
$167$	−21.8489	−1.69072	−0.845361	+	0.534195i	$0.820615\pi$
$168$	−4.76338	−0.367502
$169$	−6.59138	−0.507029
$170$	2.06946	0.158721
$171$	1.61274	0.123329
$172$	7.92557	0.604319
$173$	17.3598	1.31984	0.659920	−	0.751336i	$-0.270590\pi$
$173$	17.3598	1.31984	0.659920	+	0.751336i	$0.270590\pi$
$174$	−5.43652	−0.412142
$175$	3.41684	0.258289
$176$	−0.237118	−0.0178735
$177$	1.00000	0.0751646
$178$	−6.74693	−0.505704
$179$	−4.88226	−0.364917	−0.182458	−	0.983214i	$-0.558406\pi$
$179$	−4.88226	−0.364917	−0.182458	+	0.983214i	$0.558406\pi$
$180$	−2.06946	−0.154249
$181$	−15.0779	−1.12073	−0.560364	−	0.828246i	$-0.689339\pi$
$181$	−15.0779	−1.12073	−0.560364	+	0.828246i	$0.689339\pi$
$182$	12.0586	0.893843
$183$	−6.13889	−0.453800
$184$	8.81683	0.649985
$185$	−7.35190	−0.540522
$186$	−1.93765	−0.142076
$187$	0.237118	0.0173398
$188$	−12.5997	−0.918930
$189$	−4.76338	−0.346485
$190$	−3.33750	−0.242128
$191$	13.2949	0.961987	0.480994	−	0.876724i	$-0.340276\pi$
$191$	13.2949	0.961987	0.480994	+	0.876724i	$0.340276\pi$
$192$	1.00000	0.0721688
$193$	15.8804	1.14310	0.571549	−	0.820568i	$-0.306343\pi$
$193$	15.8804	1.14310	0.571549	+	0.820568i	$0.306343\pi$
$194$	−2.58294	−0.185445
$195$	5.23890	0.375166
$196$	15.6898	1.12070
$197$	19.3505	1.37866	0.689332	−	0.724446i	$-0.257904\pi$
$197$	19.3505	1.37866	0.689332	+	0.724446i	$0.257904\pi$
$198$	−0.237118	−0.0168513
$199$	−9.04009	−0.640835	−0.320417	−	0.947276i	$-0.603823\pi$
$199$	−9.04009	−0.640835	−0.320417	+	0.947276i	$0.603823\pi$
$200$	−0.717316	−0.0507219
$201$	10.2924	0.725970
$202$	5.53730	0.389603
$203$	25.8962	1.81756
$204$	−1.00000	−0.0700140
$205$	−15.0418	−1.05056
$206$	13.8047	0.961818
$207$	8.81683	0.612812
$208$	−2.53153	−0.175530
$209$	−0.382409	−0.0264518
$210$	9.85764	0.680242
$211$	14.7679	1.01667	0.508333	−	0.861161i	$-0.330262\pi$
$211$	14.7679	1.01667	0.508333	+	0.861161i	$0.330262\pi$
$212$	0.0982197	0.00674576
$213$	10.7735	0.738188
$214$	7.16902	0.490064
$215$	−16.4017	−1.11859
$216$	1.00000	0.0680414
$217$	9.22977	0.626557
$218$	−2.00145	−0.135555
$219$	8.08854	0.546573
$220$	0.490708	0.0330835
$221$	2.53153	0.170289
$222$	3.55256	0.238432
$223$	−11.8623	−0.794359	−0.397180	−	0.917741i	$-0.630011\pi$
$223$	−11.8623	−0.794359	−0.397180	+	0.917741i	$0.630011\pi$
$224$	−4.76338	−0.318266
$225$	−0.717316	−0.0478210
$226$	10.4918	0.697905
$227$	6.17822	0.410063	0.205032	−	0.978755i	$-0.434270\pi$
$227$	6.17822	0.410063	0.205032	+	0.978755i	$0.434270\pi$
$228$	1.61274	0.106806
$229$	10.1007	0.667476	0.333738	−	0.942666i	$-0.391690\pi$
$229$	10.1007	0.667476	0.333738	+	0.942666i	$0.391690\pi$
$230$	−18.2461	−1.20311
$231$	1.12948	0.0743146
$232$	−5.43652	−0.356925
$233$	29.1530	1.90988	0.954939	−	0.296801i	$-0.0959197\pi$
$233$	29.1530	1.90988	0.954939	+	0.296801i	$0.0959197\pi$
$234$	−2.53153	−0.165491
$235$	26.0747	1.70093
$236$	1.00000	0.0650945
$237$	15.3578	0.997596
$238$	4.76338	0.308764
$239$	−0.873991	−0.0565338	−0.0282669	−	0.999600i	$-0.508999\pi$
$239$	−0.873991	−0.0565338	−0.0282669	+	0.999600i	$0.508999\pi$
$240$	−2.06946	−0.133583
$241$	−5.09567	−0.328241	−0.164121	−	0.986440i	$-0.552479\pi$
$241$	−5.09567	−0.328241	−0.164121	+	0.986440i	$0.552479\pi$
$242$	−10.9438	−0.703492
$243$	1.00000	0.0641500
$244$	−6.13889	−0.393002
$245$	−32.4694	−2.07439
$246$	7.26844	0.463419
$247$	−4.08268	−0.259775
$248$	−1.93765	−0.123041
$249$	−16.3429	−1.03569
$250$	11.8318	0.748308
$251$	0.468526	0.0295731	0.0147866	−	0.999891i	$-0.495293\pi$
$251$	0.468526	0.0295731	0.0147866	+	0.999891i	$0.495293\pi$
$252$	−4.76338	−0.300065
$253$	−2.09063	−0.131437
$254$	14.9220	0.936292
$255$	2.06946	0.129595
$256$	1.00000	0.0625000
$257$	−9.62074	−0.600125	−0.300063	−	0.953919i	$-0.597008\pi$
$257$	−9.62074	−0.600125	−0.300063	+	0.953919i	$0.597008\pi$
$258$	7.92557	0.493424
$259$	−16.9222	−1.05149
$260$	5.23890	0.324903
$261$	−5.43652	−0.336512
$262$	20.9569	1.29472
$263$	−7.59944	−0.468601	−0.234301	−	0.972164i	$-0.575280\pi$
$263$	−7.59944	−0.468601	−0.234301	+	0.972164i	$0.575280\pi$
$264$	−0.237118	−0.0145936
$265$	−0.203262	−0.0124863
$266$	−7.68207	−0.471018
$267$	−6.74693	−0.412905
$268$	10.2924	0.628709
$269$	11.2807	0.687795	0.343897	−	0.939007i	$-0.388253\pi$
$269$	11.2807	0.687795	0.343897	+	0.939007i	$0.388253\pi$
$270$	−2.06946	−0.125944
$271$	−16.3194	−0.991331	−0.495665	−	0.868514i	$-0.665076\pi$
$271$	−16.3194	−0.991331	−0.495665	+	0.868514i	$0.665076\pi$
$272$	−1.00000	−0.0606339
$273$	12.0586	0.729820
$274$	−1.73136	−0.104595
$275$	0.170089	0.0102567
$276$	8.81683	0.530711
$277$	−22.2266	−1.33546	−0.667732	−	0.744402i	$-0.732735\pi$
$277$	−22.2266	−1.33546	−0.667732	+	0.744402i	$0.732735\pi$
$278$	11.8431	0.710302
$279$	−1.93765	−0.116004
$280$	9.85764	0.589107
$281$	−13.1891	−0.786794	−0.393397	−	0.919369i	$-0.628700\pi$
$281$	−13.1891	−0.786794	−0.393397	+	0.919369i	$0.628700\pi$
$282$	−12.5997	−0.750303
$283$	−10.3099	−0.612859	−0.306430	−	0.951893i	$-0.599134\pi$
$283$	−10.3099	−0.612859	−0.306430	+	0.951893i	$0.599134\pi$
$284$	10.7735	0.639290
$285$	−3.33750	−0.197696
$286$	0.600271	0.0354948
$287$	−34.6223	−2.04369
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	11.2507	0.660663
$291$	−2.58294	−0.151415
$292$	8.08854	0.473346
$293$	10.4325	0.609472	0.304736	−	0.952437i	$-0.401432\pi$
$293$	10.4325	0.609472	0.304736	+	0.952437i	$0.401432\pi$
$294$	15.6898	0.915045
$295$	−2.06946	−0.120489
$296$	3.55256	0.206488
$297$	−0.237118	−0.0137590
$298$	1.30119	0.0753759
$299$	−22.3200	−1.29080
$300$	−0.717316	−0.0414142
$301$	−37.7525	−2.17602
$302$	−14.5744	−0.838663
$303$	5.53730	0.318110
$304$	1.61274	0.0924968
$305$	12.7042	0.727441
$306$	−1.00000	−0.0571662
$307$	19.0243	1.08578	0.542888	−	0.839805i	$-0.317331\pi$
$307$	19.0243	1.08578	0.542888	+	0.839805i	$0.317331\pi$
$308$	1.12948	0.0643583
$309$	13.8047	0.785321
$310$	4.00990	0.227747
$311$	−16.7795	−0.951478	−0.475739	−	0.879586i	$-0.657819\pi$
$311$	−16.7795	−0.951478	−0.475739	+	0.879586i	$0.657819\pi$
$312$	−2.53153	−0.143319
$313$	12.1179	0.684942	0.342471	−	0.939528i	$-0.388736\pi$
$313$	12.1179	0.684942	0.342471	+	0.939528i	$0.388736\pi$
$314$	3.59065	0.202632
$315$	9.85764	0.555415
$316$	15.3578	0.863943
$317$	−8.25737	−0.463780	−0.231890	−	0.972742i	$-0.574491\pi$
$317$	−8.25737	−0.463780	−0.231890	+	0.972742i	$0.574491\pi$
$318$	0.0982197	0.00550789
$319$	1.28910	0.0721757
$320$	−2.06946	−0.115687
$321$	7.16902	0.400136
$322$	−41.9979	−2.34045
$323$	−1.61274	−0.0897350
$324$	1.00000	0.0555556
$325$	1.81590	0.100728
$326$	−5.24793	−0.290656
$327$	−2.00145	−0.110680
$328$	7.26844	0.401332
$329$	60.0173	3.30886
$330$	0.490708	0.0270126
$331$	23.8712	1.31208	0.656040	−	0.754726i	$-0.272230\pi$
$331$	23.8712	1.31208	0.656040	+	0.754726i	$0.272230\pi$
$332$	−16.3429	−0.896931
$333$	3.55256	0.194679
$334$	−21.8489	−1.19552
$335$	−21.2998	−1.16373
$336$	−4.76338	−0.259863
$337$	−29.7184	−1.61886	−0.809432	−	0.587213i	$-0.800225\pi$
$337$	−29.7184	−1.61886	−0.809432	+	0.587213i	$0.800225\pi$
$338$	−6.59138	−0.358524
$339$	10.4918	0.569837
$340$	2.06946	0.112232
$341$	0.459453	0.0248808
$342$	1.61274	0.0872068
$343$	−41.3926	−2.23499
$344$	7.92557	0.427318
$345$	−18.2461	−0.982338
$346$	17.3598	0.933268
$347$	−6.90861	−0.370873	−0.185437	−	0.982656i	$-0.559370\pi$
$347$	−6.90861	−0.370873	−0.185437	+	0.982656i	$0.559370\pi$
$348$	−5.43652	−0.291428
$349$	−9.01910	−0.482781	−0.241391	−	0.970428i	$-0.577604\pi$
$349$	−9.01910	−0.482781	−0.241391	+	0.970428i	$0.577604\pi$
$350$	3.41684	0.182638
$351$	−2.53153	−0.135123
$352$	−0.237118	−0.0126385
$353$	21.9912	1.17047	0.585237	−	0.810862i	$-0.301002\pi$
$353$	21.9912	1.17047	0.585237	+	0.810862i	$0.301002\pi$
$354$	1.00000	0.0531494
$355$	−22.2954	−1.18332
$356$	−6.74693	−0.357586
$357$	4.76338	0.252105
$358$	−4.88226	−0.258035
$359$	16.2161	0.855853	0.427927	−	0.903813i	$-0.359244\pi$
$359$	16.2161	0.855853	0.427927	+	0.903813i	$0.359244\pi$
$360$	−2.06946	−0.109070
$361$	−16.3991	−0.863110
$362$	−15.0779	−0.792475
$363$	−10.9438	−0.574399
$364$	12.0586	0.632043
$365$	−16.7389	−0.876156
$366$	−6.13889	−0.320885
$367$	9.77227	0.510109	0.255054	−	0.966927i	$-0.417907\pi$
$367$	9.77227	0.510109	0.255054	+	0.966927i	$0.417907\pi$
$368$	8.81683	0.459609
$369$	7.26844	0.378380
$370$	−7.35190	−0.382207
$371$	−0.467858	−0.0242900
$372$	−1.93765	−0.100463
$373$	12.6665	0.655846	0.327923	−	0.944704i	$-0.393651\pi$
$373$	12.6665	0.655846	0.327923	+	0.944704i	$0.393651\pi$
$374$	0.237118	0.0122611
$375$	11.8318	0.610991
$376$	−12.5997	−0.649782
$377$	13.7627	0.708815
$378$	−4.76338	−0.245002
$379$	−18.9194	−0.971826	−0.485913	−	0.874007i	$-0.661513\pi$
$379$	−18.9194	−0.971826	−0.485913	+	0.874007i	$0.661513\pi$
$380$	−3.33750	−0.171210
$381$	14.9220	0.764480
$382$	13.2949	0.680228
$383$	−26.4289	−1.35045	−0.675226	−	0.737611i	$-0.735954\pi$
$383$	−26.4289	−1.35045	−0.675226	+	0.737611i	$0.735954\pi$
$384$	1.00000	0.0510310
$385$	−2.33743	−0.119126
$386$	15.8804	0.808292
$387$	7.92557	0.402879
$388$	−2.58294	−0.131129
$389$	4.81419	0.244089	0.122045	−	0.992525i	$-0.461055\pi$
$389$	4.81419	0.244089	0.122045	+	0.992525i	$0.461055\pi$
$390$	5.23890	0.265282
$391$	−8.81683	−0.445886
$392$	15.6898	0.792452
$393$	20.9569	1.05713
$394$	19.3505	0.974862
$395$	−31.7824	−1.59915
$396$	−0.237118	−0.0119156
$397$	−30.8557	−1.54860	−0.774302	−	0.632816i	$-0.781899\pi$
$397$	−30.8557	−1.54860	−0.774302	+	0.632816i	$0.781899\pi$
$398$	−9.04009	−0.453139
$399$	−7.68207	−0.384585
$400$	−0.717316	−0.0358658
$401$	35.9482	1.79517	0.897584	−	0.440844i	$-0.145321\pi$
$401$	35.9482	1.79517	0.897584	+	0.440844i	$0.145321\pi$
$402$	10.2924	0.513339
$403$	4.90522	0.244346
$404$	5.53730	0.275491
$405$	−2.06946	−0.102833
$406$	25.8962	1.28521
$407$	−0.842377	−0.0417551
$408$	−1.00000	−0.0495074
$409$	−6.05573	−0.299437	−0.149718	−	0.988729i	$-0.547837\pi$
$409$	−6.05573	−0.299437	−0.149718	+	0.988729i	$0.547837\pi$
$410$	−15.0418	−0.742860
$411$	−1.73136	−0.0854017
$412$	13.8047	0.680108
$413$	−4.76338	−0.234390
$414$	8.81683	0.433324
$415$	33.8210	1.66021
$416$	−2.53153	−0.124118
$417$	11.8431	0.579959
$418$	−0.382409	−0.0187043
$419$	−2.94420	−0.143833	−0.0719167	−	0.997411i	$-0.522912\pi$
$419$	−2.94420	−0.143833	−0.0719167	+	0.997411i	$0.522912\pi$
$420$	9.85764	0.481004
$421$	−4.87014	−0.237356	−0.118678	−	0.992933i	$-0.537866\pi$
$421$	−4.87014	−0.237356	−0.118678	+	0.992933i	$0.537866\pi$
$422$	14.7679	0.718891
$423$	−12.5997	−0.612620
$424$	0.0982197	0.00476997
$425$	0.717316	0.0347949
$426$	10.7735	0.521978
$427$	29.2418	1.41511
$428$	7.16902	0.346528
$429$	0.600271	0.0289814
$430$	−16.4017	−0.790959
$431$	−9.12447	−0.439510	−0.219755	−	0.975555i	$-0.570526\pi$
$431$	−9.12447	−0.439510	−0.219755	+	0.975555i	$0.570526\pi$
$432$	1.00000	0.0481125
$433$	10.9209	0.524826	0.262413	−	0.964956i	$-0.415482\pi$
$433$	10.9209	0.524826	0.262413	+	0.964956i	$0.415482\pi$
$434$	9.22977	0.443043
$435$	11.2507	0.539429
$436$	−2.00145	−0.0958520
$437$	14.2192	0.680198
$438$	8.08854	0.386485
$439$	9.23386	0.440708	0.220354	−	0.975420i	$-0.429279\pi$
$439$	9.23386	0.440708	0.220354	+	0.975420i	$0.429279\pi$
$440$	0.490708	0.0233936
$441$	15.6898	0.747131
$442$	2.53153	0.120412
$443$	12.5997	0.598628	0.299314	−	0.954155i	$-0.403242\pi$
$443$	12.5997	0.598628	0.299314	+	0.954155i	$0.403242\pi$
$444$	3.55256	0.168597
$445$	13.9625	0.661887
$446$	−11.8623	−0.561697
$447$	1.30119	0.0615442
$448$	−4.76338	−0.225048
$449$	38.0101	1.79381	0.896903	−	0.442227i	$-0.145811\pi$
$449$	38.0101	1.79381	0.896903	+	0.442227i	$0.145811\pi$
$450$	−0.717316	−0.0338146
$451$	−1.72348	−0.0811555
$452$	10.4918	0.493493
$453$	−14.5744	−0.684765
$454$	6.17822	0.289958
$455$	−24.9549	−1.16990
$456$	1.61274	0.0755233
$457$	16.0628	0.751385	0.375693	−	0.926744i	$-0.377405\pi$
$457$	16.0628	0.751385	0.375693	+	0.926744i	$0.377405\pi$
$458$	10.1007	0.471977
$459$	−1.00000	−0.0466760
$460$	−18.2461	−0.850730
$461$	12.4385	0.579320	0.289660	−	0.957130i	$-0.406458\pi$
$461$	12.4385	0.579320	0.289660	+	0.957130i	$0.406458\pi$
$462$	1.12948	0.0525484
$463$	−37.0374	−1.72127	−0.860636	−	0.509220i	$-0.829934\pi$
$463$	−37.0374	−1.72127	−0.860636	+	0.509220i	$0.829934\pi$
$464$	−5.43652	−0.252384
$465$	4.00990	0.185955
$466$	29.1530	1.35049
$467$	−35.2092	−1.62929	−0.814643	−	0.579963i	$-0.803067\pi$
$467$	−35.2092	−1.62929	−0.814643	+	0.579963i	$0.803067\pi$
$468$	−2.53153	−0.117020
$469$	−49.0266	−2.26384
$470$	26.0747	1.20274
$471$	3.59065	0.165448
$472$	1.00000	0.0460287
$473$	−1.87930	−0.0864102
$474$	15.3578	0.705407
$475$	−1.15684	−0.0530795
$476$	4.76338	0.218329
$477$	0.0982197	0.00449717
$478$	−0.873991	−0.0399754
$479$	14.4978	0.662419	0.331210	−	0.943557i	$-0.392543\pi$
$479$	14.4978	0.662419	0.331210	+	0.943557i	$0.392543\pi$
$480$	−2.06946	−0.0944577
$481$	−8.99339	−0.410063
$482$	−5.09567	−0.232102
$483$	−41.9979	−1.91097
$484$	−10.9438	−0.497444
$485$	5.34531	0.242718
$486$	1.00000	0.0453609
$487$	−12.5931	−0.570649	−0.285325	−	0.958431i	$-0.592101\pi$
$487$	−12.5931	−0.570649	−0.285325	+	0.958431i	$0.592101\pi$
$488$	−6.13889	−0.277894
$489$	−5.24793	−0.237320
$490$	−32.4694	−1.46682
$491$	6.09255	0.274953	0.137476	−	0.990505i	$-0.456101\pi$
$491$	6.09255	0.274953	0.137476	+	0.990505i	$0.456101\pi$
$492$	7.26844	0.327687
$493$	5.43652	0.244849
$494$	−4.08268	−0.183689
$495$	0.490708	0.0220557
$496$	−1.93765	−0.0870032
$497$	−51.3182	−2.30194
$498$	−16.3429	−0.732341
$499$	−4.20125	−0.188074	−0.0940369	−	0.995569i	$-0.529977\pi$
$499$	−4.20125	−0.188074	−0.0940369	+	0.995569i	$0.529977\pi$
$500$	11.8318	0.529133
$501$	−21.8489	−0.976139
$502$	0.468526	0.0209113
$503$	18.0687	0.805643	0.402821	−	0.915279i	$-0.368030\pi$
$503$	18.0687	0.805643	0.402821	+	0.915279i	$0.368030\pi$
$504$	−4.76338	−0.212178
$505$	−11.4593	−0.509930
$506$	−2.09063	−0.0929400
$507$	−6.59138	−0.292733
$508$	14.9220	0.662059
$509$	−30.8628	−1.36797	−0.683984	−	0.729497i	$-0.739754\pi$
$509$	−30.8628	−1.36797	−0.683984	+	0.729497i	$0.739754\pi$
$510$	2.06946	0.0916374
$511$	−38.5287	−1.70441
$512$	1.00000	0.0441942
$513$	1.61274	0.0712040
$514$	−9.62074	−0.424353
$515$	−28.5683	−1.25887
$516$	7.92557	0.348904
$517$	2.98763	0.131396
$518$	−16.9222	−0.743518
$519$	17.3598	0.762010
$520$	5.23890	0.229741
$521$	13.5083	0.591810	0.295905	−	0.955217i	$-0.404379\pi$
$521$	13.5083	0.591810	0.295905	+	0.955217i	$0.404379\pi$
$522$	−5.43652	−0.237950
$523$	−21.0658	−0.921143	−0.460571	−	0.887623i	$-0.652355\pi$
$523$	−21.0658	−0.921143	−0.460571	+	0.887623i	$0.652355\pi$
$524$	20.9569	0.915506
$525$	3.41684	0.149123
$526$	−7.59944	−0.331351
$527$	1.93765	0.0844055
$528$	−0.237118	−0.0103193
$529$	54.7365	2.37985
$530$	−0.203262	−0.00882915
$531$	1.00000	0.0433963
$532$	−7.68207	−0.333060
$533$	−18.4002	−0.797003
$534$	−6.74693	−0.291968
$535$	−14.8360	−0.641418
$536$	10.2924	0.444564
$537$	−4.88226	−0.210685
$538$	11.2807	0.486344
$539$	−3.72033	−0.160246
$540$	−2.06946	−0.0890556
$541$	−21.6708	−0.931701	−0.465850	−	0.884863i	$-0.654252\pi$
$541$	−21.6708	−0.931701	−0.465850	+	0.884863i	$0.654252\pi$
$542$	−16.3194	−0.700977
$543$	−15.0779	−0.647053
$544$	−1.00000	−0.0428746
$545$	4.14193	0.177421
$546$	12.0586	0.516061
$547$	11.6885	0.499765	0.249882	−	0.968276i	$-0.419608\pi$
$547$	11.6885	0.499765	0.249882	+	0.968276i	$0.419608\pi$
$548$	−1.73136	−0.0739600
$549$	−6.13889	−0.262001
$550$	0.170089	0.00725261
$551$	−8.76768	−0.373516
$552$	8.81683	0.375269
$553$	−73.1549	−3.11086
$554$	−22.2266	−0.944316
$555$	−7.35190	−0.312071
$556$	11.8431	0.502259
$557$	12.1800	0.516081	0.258041	−	0.966134i	$-0.416923\pi$
$557$	12.1800	0.516081	0.258041	+	0.966134i	$0.416923\pi$
$558$	−1.93765	−0.0820274
$559$	−20.0638	−0.848607
$560$	9.85764	0.416561
$561$	0.237118	0.0100111
$562$	−13.1891	−0.556347
$563$	−2.13990	−0.0901859	−0.0450929	−	0.998983i	$-0.514358\pi$
$563$	−2.13990	−0.0901859	−0.0450929	+	0.998983i	$0.514358\pi$
$564$	−12.5997	−0.530545
$565$	−21.7124	−0.913449
$566$	−10.3099	−0.433357
$567$	−4.76338	−0.200043
$568$	10.7735	0.452046
$569$	−20.0210	−0.839325	−0.419662	−	0.907680i	$-0.637852\pi$
$569$	−20.0210	−0.839325	−0.419662	+	0.907680i	$0.637852\pi$
$570$	−3.33750	−0.139793
$571$	−31.1001	−1.30150	−0.650749	−	0.759293i	$-0.725545\pi$
$571$	−31.1001	−1.30150	−0.650749	+	0.759293i	$0.725545\pi$
$572$	0.600271	0.0250986
$573$	13.2949	0.555404
$574$	−34.6223	−1.44511
$575$	−6.32445	−0.263748
$576$	1.00000	0.0416667
$577$	−26.4234	−1.10002	−0.550011	−	0.835158i	$-0.685376\pi$
$577$	−26.4234	−1.10002	−0.550011	+	0.835158i	$0.685376\pi$
$578$	1.00000	0.0415945
$579$	15.8804	0.659968
$580$	11.2507	0.467159
$581$	77.8472	3.22964
$582$	−2.58294	−0.107066
$583$	−0.0232897	−0.000964561 0
$584$	8.08854	0.334706
$585$	5.23890	0.216602
$586$	10.4325	0.430962
$587$	6.46119	0.266682	0.133341	−	0.991070i	$-0.457429\pi$
$587$	6.46119	0.266682	0.133341	+	0.991070i	$0.457429\pi$
$588$	15.6898	0.647035
$589$	−3.12492	−0.128760
$590$	−2.06946	−0.0851985
$591$	19.3505	0.795972
$592$	3.55256	0.146009
$593$	40.1795	1.64998	0.824988	−	0.565151i	$-0.191182\pi$
$593$	40.1795	1.64998	0.824988	+	0.565151i	$0.191182\pi$
$594$	−0.237118	−0.00972909
$595$	−9.85764	−0.404124
$596$	1.30119	0.0532988
$597$	−9.04009	−0.369986
$598$	−22.3200	−0.912734
$599$	11.0046	0.449636	0.224818	−	0.974401i	$-0.427821\pi$
$599$	11.0046	0.449636	0.224818	+	0.974401i	$0.427821\pi$
$600$	−0.717316	−0.0292843
$601$	−2.44226	−0.0996219	−0.0498110	−	0.998759i	$-0.515862\pi$
$601$	−2.44226	−0.0996219	−0.0498110	+	0.998759i	$0.515862\pi$
$602$	−37.7525	−1.53868
$603$	10.2924	0.419139
$604$	−14.5744	−0.593024
$605$	22.6478	0.920762
$606$	5.53730	0.224938
$607$	10.2884	0.417595	0.208797	−	0.977959i	$-0.433045\pi$
$607$	10.2884	0.417595	0.208797	+	0.977959i	$0.433045\pi$
$608$	1.61274	0.0654051
$609$	25.8962	1.04937
$610$	12.7042	0.514378
$611$	31.8966	1.29040
$612$	−1.00000	−0.0404226
$613$	−13.5545	−0.547462	−0.273731	−	0.961806i	$-0.588258\pi$
$613$	−13.5545	−0.547462	−0.273731	+	0.961806i	$0.588258\pi$
$614$	19.0243	0.767760
$615$	−15.0418	−0.606543
$616$	1.12948	0.0455082
$617$	24.7725	0.997302	0.498651	−	0.866803i	$-0.333829\pi$
$617$	24.7725	0.997302	0.498651	+	0.866803i	$0.333829\pi$
$618$	13.8047	0.555306
$619$	−16.4456	−0.661005	−0.330502	−	0.943805i	$-0.607218\pi$
$619$	−16.4456	−0.661005	−0.330502	+	0.943805i	$0.607218\pi$
$620$	4.00990	0.161042
$621$	8.81683	0.353807
$622$	−16.7795	−0.672797
$623$	32.1382	1.28759
$624$	−2.53153	−0.101342
$625$	−20.8989	−0.835955
$626$	12.1179	0.484327
$627$	−0.382409	−0.0152720
$628$	3.59065	0.143282
$629$	−3.55256	−0.141650
$630$	9.85764	0.392738
$631$	−47.9430	−1.90858	−0.954290	−	0.298883i	$-0.903386\pi$
$631$	−47.9430	−1.90858	−0.954290	+	0.298883i	$0.903386\pi$
$632$	15.3578	0.610900
$633$	14.7679	0.586972
$634$	−8.25737	−0.327942
$635$	−30.8806	−1.22546
$636$	0.0982197	0.00389467
$637$	−39.7190	−1.57372
$638$	1.28910	0.0510359
$639$	10.7735	0.426193
$640$	−2.06946	−0.0818028
$641$	−41.6797	−1.64625	−0.823124	−	0.567861i	$-0.807771\pi$
$641$	−41.6797	−1.64625	−0.823124	+	0.567861i	$0.807771\pi$
$642$	7.16902	0.282939
$643$	36.6824	1.44661	0.723306	−	0.690528i	$-0.242622\pi$
$643$	36.6824	1.44661	0.723306	+	0.690528i	$0.242622\pi$
$644$	−41.9979	−1.65495
$645$	−16.4017	−0.645816
$646$	−1.61274	−0.0634523
$647$	−1.54251	−0.0606424	−0.0303212	−	0.999540i	$-0.509653\pi$
$647$	−1.54251	−0.0606424	−0.0303212	+	0.999540i	$0.509653\pi$
$648$	1.00000	0.0392837
$649$	−0.237118	−0.00930771
$650$	1.81590	0.0712256
$651$	9.22977	0.361743
$652$	−5.24793	−0.205525
$653$	−34.4345	−1.34752	−0.673762	−	0.738948i	$-0.735323\pi$
$653$	−34.4345	−1.34752	−0.673762	+	0.738948i	$0.735323\pi$
$654$	−2.00145	−0.0782629
$655$	−43.3695	−1.69459
$656$	7.26844	0.283785
$657$	8.08854	0.315564
$658$	60.0173	2.33972
$659$	23.7511	0.925213	0.462606	−	0.886564i	$-0.346914\pi$
$659$	23.7511	0.925213	0.462606	+	0.886564i	$0.346914\pi$
$660$	0.490708	0.0191008
$661$	34.2662	1.33280	0.666401	−	0.745594i	$-0.267834\pi$
$661$	34.2662	1.33280	0.666401	+	0.745594i	$0.267834\pi$
$662$	23.8712	0.927781
$663$	2.53153	0.0983163
$664$	−16.3429	−0.634226
$665$	15.8978	0.616489
$666$	3.55256	0.137659
$667$	−47.9329	−1.85597
$668$	−21.8489	−0.845361
$669$	−11.8623	−0.458624
$670$	−21.2998	−0.822882
$671$	1.45564	0.0561945
$672$	−4.76338	−0.183751
$673$	37.0990	1.43006	0.715030	−	0.699094i	$-0.246413\pi$
$673$	37.0990	1.43006	0.715030	+	0.699094i	$0.246413\pi$
$674$	−29.7184	−1.14471
$675$	−0.717316	−0.0276095
$676$	−6.59138	−0.253515
$677$	7.10870	0.273209	0.136605	−	0.990626i	$-0.456381\pi$
$677$	7.10870	0.273209	0.136605	+	0.990626i	$0.456381\pi$
$678$	10.4918	0.402936
$679$	12.3035	0.472166
$680$	2.06946	0.0793604
$681$	6.17822	0.236750
$682$	0.459453	0.0175934
$683$	−36.9915	−1.41544	−0.707720	−	0.706493i	$-0.750276\pi$
$683$	−36.9915	−1.41544	−0.707720	+	0.706493i	$0.750276\pi$
$684$	1.61274	0.0616645
$685$	3.58299	0.136899
$686$	−41.3926	−1.58038
$687$	10.1007	0.385367
$688$	7.92557	0.302159
$689$	−0.248646	−0.00947265
$690$	−18.2461	−0.694618
$691$	−16.8260	−0.640089	−0.320045	−	0.947402i	$-0.603698\pi$
$691$	−16.8260	−0.640089	−0.320045	+	0.947402i	$0.603698\pi$
$692$	17.3598	0.659920
$693$	1.12948	0.0429056
$694$	−6.90861	−0.262247
$695$	−24.5089	−0.929675
$696$	−5.43652	−0.206071
$697$	−7.26844	−0.275312
$698$	−9.01910	−0.341378
$699$	29.1530	1.10267
$700$	3.41684	0.129145
$701$	−40.8034	−1.54112	−0.770561	−	0.637367i	$-0.780024\pi$
$701$	−40.8034	−1.54112	−0.770561	+	0.637367i	$0.780024\pi$
$702$	−2.53153	−0.0955463
$703$	5.72934	0.216086
$704$	−0.237118	−0.00893674
$705$	26.0747	0.982030
$706$	21.9912	0.827650
$707$	−26.3763	−0.991981
$708$	1.00000	0.0375823
$709$	9.40949	0.353381	0.176690	−	0.984266i	$-0.443461\pi$
$709$	9.40949	0.353381	0.176690	+	0.984266i	$0.443461\pi$
$710$	−22.2954	−0.836731
$711$	15.3578	0.575962
$712$	−6.74693	−0.252852
$713$	−17.0839	−0.639799
$714$	4.76338	0.178265
$715$	−1.24224	−0.0464571
$716$	−4.88226	−0.182458
$717$	−0.873991	−0.0326398
$718$	16.2161	0.605180
$719$	48.5536	1.81074	0.905372	−	0.424619i	$-0.139592\pi$
$719$	48.5536	1.81074	0.905372	+	0.424619i	$0.139592\pi$
$720$	−2.06946	−0.0771244
$721$	−65.7569	−2.44891
$722$	−16.3991	−0.610311
$723$	−5.09567	−0.189510
$724$	−15.0779	−0.560364
$725$	3.89970	0.144831
$726$	−10.9438	−0.406162
$727$	−2.14906	−0.0797043	−0.0398521	−	0.999206i	$-0.512689\pi$
$727$	−2.14906	−0.0797043	−0.0398521	+	0.999206i	$0.512689\pi$
$728$	12.0586	0.446922
$729$	1.00000	0.0370370
$730$	−16.7389	−0.619536
$731$	−7.92557	−0.293138
$732$	−6.13889	−0.226900
$733$	−26.1572	−0.966138	−0.483069	−	0.875582i	$-0.660478\pi$
$733$	−26.1572	−0.966138	−0.483069	+	0.875582i	$0.660478\pi$
$734$	9.77227	0.360701
$735$	−32.4694	−1.19765
$736$	8.81683	0.324993
$737$	−2.44052	−0.0898977
$738$	7.26844	0.267555
$739$	25.9266	0.953724	0.476862	−	0.878978i	$-0.341774\pi$
$739$	25.9266	0.953724	0.476862	+	0.878978i	$0.341774\pi$
$740$	−7.35190	−0.270261
$741$	−4.08268	−0.149981
$742$	−0.467858	−0.0171756
$743$	33.7982	1.23994	0.619968	−	0.784627i	$-0.287145\pi$
$743$	33.7982	1.23994	0.619968	+	0.784627i	$0.287145\pi$
$744$	−1.93765	−0.0710378
$745$	−2.69277	−0.0986553
$746$	12.6665	0.463753
$747$	−16.3429	−0.597954
$748$	0.237118	0.00866991
$749$	−34.1488	−1.24777
$750$	11.8318	0.432036
$751$	−3.22490	−0.117678	−0.0588392	−	0.998267i	$-0.518740\pi$
$751$	−3.22490	−0.117678	−0.0588392	+	0.998267i	$0.518740\pi$
$752$	−12.5997	−0.459465
$753$	0.468526	0.0170740
$754$	13.7627	0.501208
$755$	30.1612	1.09768
$756$	−4.76338	−0.173242
$757$	16.4251	0.596979	0.298489	−	0.954413i	$-0.403517\pi$
$757$	16.4251	0.596979	0.298489	+	0.954413i	$0.403517\pi$
$758$	−18.9194	−0.687185
$759$	−2.09063	−0.0758852
$760$	−3.33750	−0.121064
$761$	37.2793	1.35137	0.675687	−	0.737189i	$-0.263847\pi$
$761$	37.2793	1.35137	0.675687	+	0.737189i	$0.263847\pi$
$762$	14.9220	0.540569
$763$	9.53366	0.345142
$764$	13.2949	0.480994
$765$	2.06946	0.0748217
$766$	−26.4289	−0.954914
$767$	−2.53153	−0.0914081
$768$	1.00000	0.0360844
$769$	2.13385	0.0769485	0.0384743	−	0.999260i	$-0.487750\pi$
$769$	2.13385	0.0769485	0.0384743	+	0.999260i	$0.487750\pi$
$770$	−2.33743	−0.0842350
$771$	−9.62074	−0.346483
$772$	15.8804	0.571549
$773$	39.0959	1.40618	0.703090	−	0.711100i	$-0.251803\pi$
$773$	39.0959	1.40618	0.703090	+	0.711100i	$0.251803\pi$
$774$	7.92557	0.284879
$775$	1.38991	0.0499270
$776$	−2.58294	−0.0927223
$777$	−16.9222	−0.607080
$778$	4.81419	0.172597
$779$	11.7221	0.419987
$780$	5.23890	0.187583
$781$	−2.55459	−0.0914106
$782$	−8.81683	−0.315289
$783$	−5.43652	−0.194285
$784$	15.6898	0.560348
$785$	−7.43072	−0.265214
$786$	20.9569	0.747507
$787$	20.1694	0.718962	0.359481	−	0.933152i	$-0.382954\pi$
$787$	20.1694	0.718962	0.359481	+	0.933152i	$0.382954\pi$
$788$	19.3505	0.689332
$789$	−7.59944	−0.270547
$790$	−31.7824	−1.13077
$791$	−49.9764	−1.77696
$792$	−0.237118	−0.00842564
$793$	15.5407	0.551868
$794$	−30.8557	−1.09503
$795$	−0.203262	−0.00720897
$796$	−9.04009	−0.320417
$797$	−25.7880	−0.913458	−0.456729	−	0.889606i	$-0.650979\pi$
$797$	−25.7880	−0.913458	−0.456729	+	0.889606i	$0.650979\pi$
$798$	−7.68207	−0.271942
$799$	12.5997	0.445747
$800$	−0.717316	−0.0253609
$801$	−6.74693	−0.238391
$802$	35.9482	1.26938
$803$	−1.91794	−0.0676827
$804$	10.2924	0.362985
$805$	86.9131	3.06329
$806$	4.90522	0.172779
$807$	11.2807	0.397098
$808$	5.53730	0.194802
$809$	−46.9091	−1.64924	−0.824619	−	0.565689i	$-0.808610\pi$
$809$	−46.9091	−1.64924	−0.824619	+	0.565689i	$0.808610\pi$
$810$	−2.06946	−0.0727136
$811$	−18.1612	−0.637726	−0.318863	−	0.947801i	$-0.603301\pi$
$811$	−18.1612	−0.637726	−0.318863	+	0.947801i	$0.603301\pi$
$812$	25.8962	0.908778
$813$	−16.3194	−0.572345
$814$	−0.842377	−0.0295253
$815$	10.8604	0.380424
$816$	−1.00000	−0.0350070
$817$	12.7819	0.447180
$818$	−6.05573	−0.211734
$819$	12.0586	0.421362
$820$	−15.0418	−0.525282
$821$	16.3964	0.572238	0.286119	−	0.958194i	$-0.407635\pi$
$821$	16.3964	0.572238	0.286119	+	0.958194i	$0.407635\pi$
$822$	−1.73136	−0.0603881
$823$	−14.2311	−0.496064	−0.248032	−	0.968752i	$-0.579784\pi$
$823$	−14.2311	−0.496064	−0.248032	+	0.968752i	$0.579784\pi$
$824$	13.8047	0.480909
$825$	0.170089	0.00592173
$826$	−4.76338	−0.165739
$827$	−10.8426	−0.377034	−0.188517	−	0.982070i	$-0.560368\pi$
$827$	−10.8426	−0.377034	−0.188517	+	0.982070i	$0.560368\pi$
$828$	8.81683	0.306406
$829$	51.4749	1.78780	0.893899	−	0.448268i	$-0.147959\pi$
$829$	51.4749	1.78780	0.893899	+	0.448268i	$0.147959\pi$
$830$	33.8210	1.17394
$831$	−22.2266	−0.771031
$832$	−2.53153	−0.0877649
$833$	−15.6898	−0.543618
$834$	11.8431	0.410093
$835$	45.2156	1.56475
$836$	−0.382409	−0.0132259
$837$	−1.93765	−0.0669751
$838$	−2.94420	−0.101706
$839$	12.8597	0.443968	0.221984	−	0.975050i	$-0.428747\pi$
$839$	12.8597	0.443968	0.221984	+	0.975050i	$0.428747\pi$
$840$	9.85764	0.340121
$841$	0.555770	0.0191645
$842$	−4.87014	−0.167836
$843$	−13.1891	−0.454256
$844$	14.7679	0.508333
$845$	13.6406	0.469252
$846$	−12.5997	−0.433188
$847$	52.1293	1.79118
$848$	0.0982197	0.00337288
$849$	−10.3099	−0.353834
$850$	0.717316	0.0246037
$851$	31.3223	1.07371
$852$	10.7735	0.369094
$853$	33.4082	1.14388	0.571938	−	0.820297i	$-0.306192\pi$
$853$	33.4082	1.14388	0.571938	+	0.820297i	$0.306192\pi$
$854$	29.2418	1.00063
$855$	−3.33750	−0.114140
$856$	7.16902	0.245032
$857$	49.2477	1.68227	0.841135	−	0.540826i	$-0.181888\pi$
$857$	49.2477	1.68227	0.841135	+	0.540826i	$0.181888\pi$
$858$	0.600271	0.0204929
$859$	46.5988	1.58993	0.794965	−	0.606655i	$-0.207489\pi$
$859$	46.5988	1.58993	0.794965	+	0.606655i	$0.207489\pi$
$860$	−16.4017	−0.559293
$861$	−34.6223	−1.17993
$862$	−9.12447	−0.310781
$863$	−6.00737	−0.204493	−0.102247	−	0.994759i	$-0.532603\pi$
$863$	−6.00737	−0.204493	−0.102247	+	0.994759i	$0.532603\pi$
$864$	1.00000	0.0340207
$865$	−35.9255	−1.22150
$866$	10.9209	0.371108
$867$	1.00000	0.0339618
$868$	9.22977	0.313279
$869$	−3.64162	−0.123533
$870$	11.2507	0.381434
$871$	−26.0555	−0.882857
$872$	−2.00145	−0.0677776
$873$	−2.58294	−0.0874194
$874$	14.2192	0.480972
$875$	−56.3592	−1.90529
$876$	8.08854	0.273286
$877$	39.9482	1.34895	0.674477	−	0.738296i	$-0.264369\pi$
$877$	39.9482	1.34895	0.674477	+	0.738296i	$0.264369\pi$
$878$	9.23386	0.311628
$879$	10.4325	0.351879
$880$	0.490708	0.0165418
$881$	−16.4971	−0.555801	−0.277900	−	0.960610i	$-0.589639\pi$
$881$	−16.4971	−0.555801	−0.277900	+	0.960610i	$0.589639\pi$
$882$	15.6898	0.528301
$883$	48.7281	1.63983	0.819915	−	0.572485i	$-0.194020\pi$
$883$	48.7281	1.63983	0.819915	+	0.572485i	$0.194020\pi$
$884$	2.53153	0.0851444
$885$	−2.06946	−0.0695643
$886$	12.5997	0.423294
$887$	7.87819	0.264524	0.132262	−	0.991215i	$-0.457776\pi$
$887$	7.87819	0.264524	0.132262	+	0.991215i	$0.457776\pi$
$888$	3.55256	0.119216
$889$	−71.0793	−2.38392
$890$	13.9625	0.468025
$891$	−0.237118	−0.00794377
$892$	−11.8623	−0.397180
$893$	−20.3201	−0.679985
$894$	1.30119	0.0435183
$895$	10.1037	0.337728
$896$	−4.76338	−0.159133
$897$	−22.3200	−0.745244
$898$	38.0101	1.26841
$899$	10.5341	0.351332
$900$	−0.717316	−0.0239105
$901$	−0.0982197	−0.00327217
$902$	−1.72348	−0.0573856
$903$	−37.7525	−1.25632
$904$	10.4918	0.348952
$905$	31.2031	1.03723
$906$	−14.5744	−0.484202
$907$	29.2652	0.971735	0.485867	−	0.874033i	$-0.338504\pi$
$907$	29.2652	0.971735	0.485867	+	0.874033i	$0.338504\pi$
$908$	6.17822	0.205032
$909$	5.53730	0.183661
$910$	−24.9549	−0.827246
$911$	28.3366	0.938834	0.469417	−	0.882977i	$-0.344464\pi$
$911$	28.3366	0.938834	0.469417	+	0.882977i	$0.344464\pi$
$912$	1.61274	0.0534030
$913$	3.87519	0.128250
$914$	16.0628	0.531309
$915$	12.7042	0.419988
$916$	10.1007	0.333738
$917$	−99.8255	−3.29653
$918$	−1.00000	−0.0330049
$919$	−30.9237	−1.02008	−0.510039	−	0.860151i	$-0.670369\pi$
$919$	−30.9237	−1.02008	−0.510039	+	0.860151i	$0.670369\pi$
$920$	−18.2461	−0.601557
$921$	19.0243	0.626873
$922$	12.4385	0.409641
$923$	−27.2734	−0.897714
$924$	1.12948	0.0371573
$925$	−2.54831	−0.0837878
$926$	−37.0374	−1.21712
$927$	13.8047	0.453405
$928$	−5.43652	−0.178463
$929$	−59.4882	−1.95175	−0.975873	−	0.218340i	$-0.929936\pi$
$929$	−59.4882	−1.95175	−0.975873	+	0.218340i	$0.929936\pi$
$930$	4.00990	0.131490
$931$	25.3034	0.829287
$932$	29.1530	0.954939
$933$	−16.7795	−0.549336
$934$	−35.2092	−1.15208
$935$	−0.490708	−0.0160479
$936$	−2.53153	−0.0827455
$937$	28.4505	0.929437	0.464718	−	0.885459i	$-0.346156\pi$
$937$	28.4505	0.929437	0.464718	+	0.885459i	$0.346156\pi$
$938$	−49.0266	−1.60078
$939$	12.1179	0.395451
$940$	26.0747	0.850463
$941$	36.5192	1.19049	0.595247	−	0.803543i	$-0.297054\pi$
$941$	36.5192	1.19049	0.595247	+	0.803543i	$0.297054\pi$
$942$	3.59065	0.116990
$943$	64.0846	2.08688
$944$	1.00000	0.0325472
$945$	9.85764	0.320669
$946$	−1.87930	−0.0611012
$947$	−3.72110	−0.120920	−0.0604598	−	0.998171i	$-0.519257\pi$
$947$	−3.72110	−0.120920	−0.0604598	+	0.998171i	$0.519257\pi$
$948$	15.3578	0.498798
$949$	−20.4763	−0.664690
$950$	−1.15684	−0.0375329
$951$	−8.25737	−0.267764
$952$	4.76338	0.154382
$953$	41.1465	1.33287	0.666434	−	0.745564i	$-0.267820\pi$
$953$	41.1465	1.33287	0.666434	+	0.745564i	$0.267820\pi$
$954$	0.0982197	0.00317998
$955$	−27.5134	−0.890312
$956$	−0.873991	−0.0282669
$957$	1.28910	0.0416707
$958$	14.4978	0.468401
$959$	8.24712	0.266313
$960$	−2.06946	−0.0667917
$961$	−27.2455	−0.878887
$962$	−8.99339	−0.289959
$963$	7.16902	0.231019
$964$	−5.09567	−0.164121
$965$	−32.8640	−1.05793
$966$	−41.9979	−1.35126
$967$	47.1365	1.51581	0.757903	−	0.652367i	$-0.226224\pi$
$967$	47.1365	1.51581	0.757903	+	0.652367i	$0.226224\pi$
$968$	−10.9438	−0.351746
$969$	−1.61274	−0.0518086
$970$	5.34531	0.171628
$971$	−6.25873	−0.200852	−0.100426	−	0.994945i	$-0.532021\pi$
$971$	−6.25873	−0.200852	−0.100426	+	0.994945i	$0.532021\pi$
$972$	1.00000	0.0320750
$973$	−56.4131	−1.80852
$974$	−12.5931	−0.403510
$975$	1.81590	0.0581554
$976$	−6.13889	−0.196501
$977$	−5.22589	−0.167191	−0.0835955	−	0.996500i	$-0.526640\pi$
$977$	−5.22589	−0.167191	−0.0835955	+	0.996500i	$0.526640\pi$
$978$	−5.24793	−0.167810
$979$	1.59982	0.0511305
$980$	−32.4694	−1.03720
$981$	−2.00145	−0.0639014
$982$	6.09255	0.194421
$983$	34.7957	1.10981	0.554906	−	0.831913i	$-0.312754\pi$
$983$	34.7957	1.10981	0.554906	+	0.831913i	$0.312754\pi$
$984$	7.26844	0.231709
$985$	−40.0451	−1.27594
$986$	5.43652	0.173134
$987$	60.0173	1.91037
$988$	−4.08268	−0.129887
$989$	69.8784	2.22200
$990$	0.490708	0.0155957
$991$	35.4620	1.12649	0.563244	−	0.826291i	$-0.309553\pi$
$991$	35.4620	1.12649	0.563244	+	0.826291i	$0.309553\pi$
$992$	−1.93765	−0.0615205
$993$	23.8712	0.757530
$994$	−51.3182	−1.62772
$995$	18.7081	0.593088
$996$	−16.3429	−0.517843
$997$	41.6760	1.31989	0.659945	−	0.751314i	$-0.270579\pi$
$997$	41.6760	1.31989	0.659945	+	0.751314i	$0.270579\pi$
$998$	−4.20125	−0.132988
$999$	3.55256	0.112398

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.ba.1.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.ba.1.3	✓	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.06946 q^{5} +1.00000 q^{6} -4.76338 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.06946 q^{5} +1.00000 q^{6} -4.76338 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.06946 q^{10} -0.237118 q^{11} +1.00000 q^{12} -2.53153 q^{13} -4.76338 q^{14} -2.06946 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +1.61274 q^{19} -2.06946 q^{20} -4.76338 q^{21} -0.237118 q^{22} +8.81683 q^{23} +1.00000 q^{24} -0.717316 q^{25} -2.53153 q^{26} +1.00000 q^{27} -4.76338 q^{28} -5.43652 q^{29} -2.06946 q^{30} -1.93765 q^{31} +1.00000 q^{32} -0.237118 q^{33} -1.00000 q^{34} +9.85764 q^{35} +1.00000 q^{36} +3.55256 q^{37} +1.61274 q^{38} -2.53153 q^{39} -2.06946 q^{40} +7.26844 q^{41} -4.76338 q^{42} +7.92557 q^{43} -0.237118 q^{44} -2.06946 q^{45} +8.81683 q^{46} -12.5997 q^{47} +1.00000 q^{48} +15.6898 q^{49} -0.717316 q^{50} -1.00000 q^{51} -2.53153 q^{52} +0.0982197 q^{53} +1.00000 q^{54} +0.490708 q^{55} -4.76338 q^{56} +1.61274 q^{57} -5.43652 q^{58} +1.00000 q^{59} -2.06946 q^{60} -6.13889 q^{61} -1.93765 q^{62} -4.76338 q^{63} +1.00000 q^{64} +5.23890 q^{65} -0.237118 q^{66} +10.2924 q^{67} -1.00000 q^{68} +8.81683 q^{69} +9.85764 q^{70} +10.7735 q^{71} +1.00000 q^{72} +8.08854 q^{73} +3.55256 q^{74} -0.717316 q^{75} +1.61274 q^{76} +1.12948 q^{77} -2.53153 q^{78} +15.3578 q^{79} -2.06946 q^{80} +1.00000 q^{81} +7.26844 q^{82} -16.3429 q^{83} -4.76338 q^{84} +2.06946 q^{85} +7.92557 q^{86} -5.43652 q^{87} -0.237118 q^{88} -6.74693 q^{89} -2.06946 q^{90} +12.0586 q^{91} +8.81683 q^{92} -1.93765 q^{93} -12.5997 q^{94} -3.33750 q^{95} +1.00000 q^{96} -2.58294 q^{97} +15.6898 q^{98} -0.237118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * q^99

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