LMFDB - Embedded newform 6042.2.a.bh.1.2

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:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 40 x^{11} + 123 x^{10} + 537 x^{9} - 1707 x^{8} - 2914 x^{7} + 9639 x^{6} + \cdots + 1200 $ x^13 - 3x^12 - 40x^11 + 123x^10 + 537x^9 - 1707x^8 - 2914x^7 + 9639x^6 + 6938x^5 - 22200x^4 - 9466x^3 + 16812x^2 + 9304x + 1200
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			1.2
Root			$-3.54278$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.54278 q^{5} +1.00000 q^{6} -0.903867 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.54278 q^{5} +1.00000 q^{6} -0.903867 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.54278 q^{10} +3.40249 q^{11} +1.00000 q^{12} +5.79690 q^{13} -0.903867 q^{14} -3.54278 q^{15} +1.00000 q^{16} -3.54105 q^{17} +1.00000 q^{18} +1.00000 q^{19} -3.54278 q^{20} -0.903867 q^{21} +3.40249 q^{22} +0.263610 q^{23} +1.00000 q^{24} +7.55132 q^{25} +5.79690 q^{26} +1.00000 q^{27} -0.903867 q^{28} -2.23217 q^{29} -3.54278 q^{30} +0.984967 q^{31} +1.00000 q^{32} +3.40249 q^{33} -3.54105 q^{34} +3.20221 q^{35} +1.00000 q^{36} +4.62976 q^{37} +1.00000 q^{38} +5.79690 q^{39} -3.54278 q^{40} -8.44464 q^{41} -0.903867 q^{42} -1.67278 q^{43} +3.40249 q^{44} -3.54278 q^{45} +0.263610 q^{46} -1.15206 q^{47} +1.00000 q^{48} -6.18302 q^{49} +7.55132 q^{50} -3.54105 q^{51} +5.79690 q^{52} -1.00000 q^{53} +1.00000 q^{54} -12.0543 q^{55} -0.903867 q^{56} +1.00000 q^{57} -2.23217 q^{58} +2.89337 q^{59} -3.54278 q^{60} +4.29599 q^{61} +0.984967 q^{62} -0.903867 q^{63} +1.00000 q^{64} -20.5372 q^{65} +3.40249 q^{66} +13.7907 q^{67} -3.54105 q^{68} +0.263610 q^{69} +3.20221 q^{70} +9.89099 q^{71} +1.00000 q^{72} +2.42558 q^{73} +4.62976 q^{74} +7.55132 q^{75} +1.00000 q^{76} -3.07540 q^{77} +5.79690 q^{78} -8.43325 q^{79} -3.54278 q^{80} +1.00000 q^{81} -8.44464 q^{82} +2.41831 q^{83} -0.903867 q^{84} +12.5452 q^{85} -1.67278 q^{86} -2.23217 q^{87} +3.40249 q^{88} -4.26049 q^{89} -3.54278 q^{90} -5.23963 q^{91} +0.263610 q^{92} +0.984967 q^{93} -1.15206 q^{94} -3.54278 q^{95} +1.00000 q^{96} +18.5661 q^{97} -6.18302 q^{98} +3.40249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 4 q^{11} + 13 q^{12} + 18 q^{13} + 12 q^{14} + 3 q^{15} + 13 q^{16} + 3 q^{17} + 13 q^{18} + 13 q^{19} + 3 q^{20} + 12 q^{21} + 4 q^{22} + 8 q^{23} + 13 q^{24} + 24 q^{25} + 18 q^{26} + 13 q^{27} + 12 q^{28} + 11 q^{29} + 3 q^{30} + 2 q^{31} + 13 q^{32} + 4 q^{33} + 3 q^{34} - 6 q^{35} + 13 q^{36} + 26 q^{37} + 13 q^{38} + 18 q^{39} + 3 q^{40} + 3 q^{41} + 12 q^{42} + 24 q^{43} + 4 q^{44} + 3 q^{45} + 8 q^{46} + 4 q^{47} + 13 q^{48} + 41 q^{49} + 24 q^{50} + 3 q^{51} + 18 q^{52} - 13 q^{53} + 13 q^{54} + 23 q^{55} + 12 q^{56} + 13 q^{57} + 11 q^{58} + 8 q^{59} + 3 q^{60} + 29 q^{61} + 2 q^{62} + 12 q^{63} + 13 q^{64} + 13 q^{65} + 4 q^{66} - 5 q^{67} + 3 q^{68} + 8 q^{69} - 6 q^{70} + 29 q^{71} + 13 q^{72} + 15 q^{73} + 26 q^{74} + 24 q^{75} + 13 q^{76} + 3 q^{77} + 18 q^{78} + 15 q^{79} + 3 q^{80} + 13 q^{81} + 3 q^{82} + 4 q^{83} + 12 q^{84} - q^{85} + 24 q^{86} + 11 q^{87} + 4 q^{88} + 3 q^{89} + 3 q^{90} - 29 q^{91} + 8 q^{92} + 2 q^{93} + 4 q^{94} + 3 q^{95} + 13 q^{96} + 50 q^{97} + 41 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 4 * q^11 + 13 * q^12 + 18 * q^13 + 12 * q^14 + 3 * q^15 + 13 * q^16 + 3 * q^17 + 13 * q^18 + 13 * q^19 + 3 * q^20 + 12 * q^21 + 4 * q^22 + 8 * q^23 + 13 * q^24 + 24 * q^25 + 18 * q^26 + 13 * q^27 + 12 * q^28 + 11 * q^29 + 3 * q^30 + 2 * q^31 + 13 * q^32 + 4 * q^33 + 3 * q^34 - 6 * q^35 + 13 * q^36 + 26 * q^37 + 13 * q^38 + 18 * q^39 + 3 * q^40 + 3 * q^41 + 12 * q^42 + 24 * q^43 + 4 * q^44 + 3 * q^45 + 8 * q^46 + 4 * q^47 + 13 * q^48 + 41 * q^49 + 24 * q^50 + 3 * q^51 + 18 * q^52 - 13 * q^53 + 13 * q^54 + 23 * q^55 + 12 * q^56 + 13 * q^57 + 11 * q^58 + 8 * q^59 + 3 * q^60 + 29 * q^61 + 2 * q^62 + 12 * q^63 + 13 * q^64 + 13 * q^65 + 4 * q^66 - 5 * q^67 + 3 * q^68 + 8 * q^69 - 6 * q^70 + 29 * q^71 + 13 * q^72 + 15 * q^73 + 26 * q^74 + 24 * q^75 + 13 * q^76 + 3 * q^77 + 18 * q^78 + 15 * q^79 + 3 * q^80 + 13 * q^81 + 3 * q^82 + 4 * q^83 + 12 * q^84 - q^85 + 24 * q^86 + 11 * q^87 + 4 * q^88 + 3 * q^89 + 3 * q^90 - 29 * q^91 + 8 * q^92 + 2 * q^93 + 4 * q^94 + 3 * q^95 + 13 * q^96 + 50 * q^97 + 41 * q^98 + 4 * 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
$5$	−3.54278	−1.58438	−0.792191	−	0.610274i	$-0.791059\pi$
$5$	−3.54278	−1.58438	−0.792191	+	0.610274i	$0.791059\pi$
$6$	1.00000	0.408248
$7$	−0.903867	−0.341630	−0.170815	−	0.985303i	$-0.554640\pi$
$7$	−0.903867	−0.341630	−0.170815	+	0.985303i	$0.554640\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.54278	−1.12033
$11$	3.40249	1.02589	0.512945	−	0.858422i	$-0.328555\pi$
$11$	3.40249	1.02589	0.512945	+	0.858422i	$0.328555\pi$
$12$	1.00000	0.288675
$13$	5.79690	1.60777	0.803885	−	0.594784i	$-0.202762\pi$
$13$	5.79690	1.60777	0.803885	+	0.594784i	$0.202762\pi$
$14$	−0.903867	−0.241569
$15$	−3.54278	−0.914743
$16$	1.00000	0.250000
$17$	−3.54105	−0.858832	−0.429416	−	0.903107i	$-0.641281\pi$
$17$	−3.54105	−0.858832	−0.429416	+	0.903107i	$0.641281\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.54278	−0.792191
$21$	−0.903867	−0.197240
$22$	3.40249	0.725413
$23$	0.263610	0.0549665	0.0274833	−	0.999622i	$-0.491251\pi$
$23$	0.263610	0.0549665	0.0274833	+	0.999622i	$0.491251\pi$
$24$	1.00000	0.204124
$25$	7.55132	1.51026
$26$	5.79690	1.13687
$27$	1.00000	0.192450
$28$	−0.903867	−0.170815
$29$	−2.23217	−0.414503	−0.207252	−	0.978288i	$-0.566452\pi$
$29$	−2.23217	−0.414503	−0.207252	+	0.978288i	$0.566452\pi$
$30$	−3.54278	−0.646821
$31$	0.984967	0.176905	0.0884527	−	0.996080i	$-0.471808\pi$
$31$	0.984967	0.176905	0.0884527	+	0.996080i	$0.471808\pi$
$32$	1.00000	0.176777
$33$	3.40249	0.592298
$34$	−3.54105	−0.607286
$35$	3.20221	0.541272
$36$	1.00000	0.166667
$37$	4.62976	0.761127	0.380564	−	0.924755i	$-0.375730\pi$
$37$	4.62976	0.761127	0.380564	+	0.924755i	$0.375730\pi$
$38$	1.00000	0.162221
$39$	5.79690	0.928247
$40$	−3.54278	−0.560163
$41$	−8.44464	−1.31883	−0.659415	−	0.751779i	$-0.729196\pi$
$41$	−8.44464	−1.31883	−0.659415	+	0.751779i	$0.729196\pi$
$42$	−0.903867	−0.139470
$43$	−1.67278	−0.255097	−0.127548	−	0.991832i	$-0.540711\pi$
$43$	−1.67278	−0.255097	−0.127548	+	0.991832i	$0.540711\pi$
$44$	3.40249	0.512945
$45$	−3.54278	−0.528127
$46$	0.263610	0.0388672
$47$	−1.15206	−0.168045	−0.0840226	−	0.996464i	$-0.526777\pi$
$47$	−1.15206	−0.168045	−0.0840226	+	0.996464i	$0.526777\pi$
$48$	1.00000	0.144338
$49$	−6.18302	−0.883289
$50$	7.55132	1.06792
$51$	−3.54105	−0.495847
$52$	5.79690	0.803885
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	1.00000	0.136083
$55$	−12.0543	−1.62540
$56$	−0.903867	−0.120784
$57$	1.00000	0.132453
$58$	−2.23217	−0.293098
$59$	2.89337	0.376684	0.188342	−	0.982103i	$-0.439689\pi$
$59$	2.89337	0.376684	0.188342	+	0.982103i	$0.439689\pi$
$60$	−3.54278	−0.457371
$61$	4.29599	0.550045	0.275022	−	0.961438i	$-0.411315\pi$
$61$	4.29599	0.550045	0.275022	+	0.961438i	$0.411315\pi$
$62$	0.984967	0.125091
$63$	−0.903867	−0.113877
$64$	1.00000	0.125000
$65$	−20.5372	−2.54732
$66$	3.40249	0.418818
$67$	13.7907	1.68480	0.842400	−	0.538853i	$-0.181142\pi$
$67$	13.7907	1.68480	0.842400	+	0.538853i	$0.181142\pi$
$68$	−3.54105	−0.429416
$69$	0.263610	0.0317350
$70$	3.20221	0.382737
$71$	9.89099	1.17384	0.586922	−	0.809643i	$-0.300339\pi$
$71$	9.89099	1.17384	0.586922	+	0.809643i	$0.300339\pi$
$72$	1.00000	0.117851
$73$	2.42558	0.283893	0.141946	−	0.989874i	$-0.454664\pi$
$73$	2.42558	0.283893	0.141946	+	0.989874i	$0.454664\pi$
$74$	4.62976	0.538198
$75$	7.55132	0.871951
$76$	1.00000	0.114708
$77$	−3.07540	−0.350474
$78$	5.79690	0.656370
$79$	−8.43325	−0.948815	−0.474407	−	0.880305i	$-0.657338\pi$
$79$	−8.43325	−0.948815	−0.474407	+	0.880305i	$0.657338\pi$
$80$	−3.54278	−0.396095
$81$	1.00000	0.111111
$82$	−8.44464	−0.932554
$83$	2.41831	0.265444	0.132722	−	0.991153i	$-0.457628\pi$
$83$	2.41831	0.265444	0.132722	+	0.991153i	$0.457628\pi$
$84$	−0.903867	−0.0986200
$85$	12.5452	1.36072
$86$	−1.67278	−0.180381
$87$	−2.23217	−0.239314
$88$	3.40249	0.362707
$89$	−4.26049	−0.451611	−0.225806	−	0.974172i	$-0.572501\pi$
$89$	−4.26049	−0.451611	−0.225806	+	0.974172i	$0.572501\pi$
$90$	−3.54278	−0.373442
$91$	−5.23963	−0.549262
$92$	0.263610	0.0274833
$93$	0.984967	0.102136
$94$	−1.15206	−0.118826
$95$	−3.54278	−0.363482
$96$	1.00000	0.102062
$97$	18.5661	1.88510	0.942550	−	0.334065i	$-0.108421\pi$
$97$	18.5661	1.88510	0.942550	+	0.334065i	$0.108421\pi$
$98$	−6.18302	−0.624580
$99$	3.40249	0.341963
$100$	7.55132	0.755132
$101$	19.8244	1.97260	0.986301	−	0.164954i	$-0.0527475\pi$
$101$	19.8244	1.97260	0.986301	+	0.164954i	$0.0527475\pi$
$102$	−3.54105	−0.350617
$103$	19.9128	1.96206	0.981032	−	0.193846i	$-0.0620961\pi$
$103$	19.9128	1.96206	0.981032	+	0.193846i	$0.0620961\pi$
$104$	5.79690	0.568433
$105$	3.20221	0.312503
$106$	−1.00000	−0.0971286
$107$	2.66757	0.257884	0.128942	−	0.991652i	$-0.458842\pi$
$107$	2.66757	0.257884	0.128942	+	0.991652i	$0.458842\pi$
$108$	1.00000	0.0962250
$109$	14.2645	1.36630	0.683148	−	0.730280i	$-0.260610\pi$
$109$	14.2645	1.36630	0.683148	+	0.730280i	$0.260610\pi$
$110$	−12.0543	−1.14933
$111$	4.62976	0.439437
$112$	−0.903867	−0.0854074
$113$	−5.22389	−0.491423	−0.245711	−	0.969343i	$-0.579022\pi$
$113$	−5.22389	−0.491423	−0.245711	+	0.969343i	$0.579022\pi$
$114$	1.00000	0.0936586
$115$	−0.933914	−0.0870880
$116$	−2.23217	−0.207252
$117$	5.79690	0.535924
$118$	2.89337	0.266356
$119$	3.20064	0.293402
$120$	−3.54278	−0.323410
$121$	0.576943	0.0524494
$122$	4.29599	0.388940
$123$	−8.44464	−0.761427
$124$	0.984967	0.0884527
$125$	−9.03876	−0.808451
$126$	−0.903867	−0.0805229
$127$	−14.0777	−1.24920	−0.624598	−	0.780946i	$-0.714737\pi$
$127$	−14.0777	−1.24920	−0.624598	+	0.780946i	$0.714737\pi$
$128$	1.00000	0.0883883
$129$	−1.67278	−0.147280
$130$	−20.5372	−1.80123
$131$	13.7318	1.19975	0.599876	−	0.800093i	$-0.295216\pi$
$131$	13.7318	1.19975	0.599876	+	0.800093i	$0.295216\pi$
$132$	3.40249	0.296149
$133$	−0.903867	−0.0783752
$134$	13.7907	1.19133
$135$	−3.54278	−0.304914
$136$	−3.54105	−0.303643
$137$	−2.24585	−0.191876	−0.0959379	−	0.995387i	$-0.530585\pi$
$137$	−2.24585	−0.191876	−0.0959379	+	0.995387i	$0.530585\pi$
$138$	0.263610	0.0224400
$139$	18.0065	1.52729	0.763645	−	0.645637i	$-0.223408\pi$
$139$	18.0065	1.52729	0.763645	+	0.645637i	$0.223408\pi$
$140$	3.20221	0.270636
$141$	−1.15206	−0.0970209
$142$	9.89099	0.830034
$143$	19.7239	1.64940
$144$	1.00000	0.0833333
$145$	7.90809	0.656731
$146$	2.42558	0.200742
$147$	−6.18302	−0.509967
$148$	4.62976	0.380564
$149$	0.245347	0.0200996	0.0100498	−	0.999949i	$-0.496801\pi$
$149$	0.245347	0.0200996	0.0100498	+	0.999949i	$0.496801\pi$
$150$	7.55132	0.616562
$151$	−1.59670	−0.129937	−0.0649687	−	0.997887i	$-0.520695\pi$
$151$	−1.59670	−0.129937	−0.0649687	+	0.997887i	$0.520695\pi$
$152$	1.00000	0.0811107
$153$	−3.54105	−0.286277
$154$	−3.07540	−0.247823
$155$	−3.48953	−0.280285
$156$	5.79690	0.464123
$157$	3.27375	0.261273	0.130637	−	0.991430i	$-0.458298\pi$
$157$	3.27375	0.261273	0.130637	+	0.991430i	$0.458298\pi$
$158$	−8.43325	−0.670913
$159$	−1.00000	−0.0793052
$160$	−3.54278	−0.280082
$161$	−0.238269	−0.0187782
$162$	1.00000	0.0785674
$163$	−1.76604	−0.138327	−0.0691634	−	0.997605i	$-0.522033\pi$
$163$	−1.76604	−0.138327	−0.0691634	+	0.997605i	$0.522033\pi$
$164$	−8.44464	−0.659415
$165$	−12.0543	−0.938425
$166$	2.41831	0.187697
$167$	−5.88705	−0.455554	−0.227777	−	0.973713i	$-0.573146\pi$
$167$	−5.88705	−0.455554	−0.227777	+	0.973713i	$0.573146\pi$
$168$	−0.903867	−0.0697349
$169$	20.6041	1.58493
$170$	12.5452	0.962172
$171$	1.00000	0.0764719
$172$	−1.67278	−0.127548
$173$	21.8396	1.66044	0.830218	−	0.557438i	$-0.188216\pi$
$173$	21.8396	1.66044	0.830218	+	0.557438i	$0.188216\pi$
$174$	−2.23217	−0.169220
$175$	−6.82539	−0.515951
$176$	3.40249	0.256472
$177$	2.89337	0.217479
$178$	−4.26049	−0.319337
$179$	−0.919039	−0.0686922	−0.0343461	−	0.999410i	$-0.510935\pi$
$179$	−0.919039	−0.0686922	−0.0343461	+	0.999410i	$0.510935\pi$
$180$	−3.54278	−0.264064
$181$	−11.5691	−0.859922	−0.429961	−	0.902847i	$-0.641473\pi$
$181$	−11.5691	−0.859922	−0.429961	+	0.902847i	$0.641473\pi$
$182$	−5.23963	−0.388387
$183$	4.29599	0.317569
$184$	0.263610	0.0194336
$185$	−16.4022	−1.20592
$186$	0.984967	0.0722213
$187$	−12.0484	−0.881066
$188$	−1.15206	−0.0840226
$189$	−0.903867	−0.0657467
$190$	−3.54278	−0.257021
$191$	14.6006	1.05646	0.528230	−	0.849101i	$-0.322856\pi$
$191$	14.6006	1.05646	0.528230	+	0.849101i	$0.322856\pi$
$192$	1.00000	0.0721688
$193$	−11.7966	−0.849135	−0.424567	−	0.905396i	$-0.639574\pi$
$193$	−11.7966	−0.849135	−0.424567	+	0.905396i	$0.639574\pi$
$194$	18.5661	1.33297
$195$	−20.5372	−1.47070
$196$	−6.18302	−0.441645
$197$	1.28148	0.0913018	0.0456509	−	0.998957i	$-0.485464\pi$
$197$	1.28148	0.0913018	0.0456509	+	0.998957i	$0.485464\pi$
$198$	3.40249	0.241804
$199$	−17.1405	−1.21506	−0.607529	−	0.794297i	$-0.707839\pi$
$199$	−17.1405	−1.21506	−0.607529	+	0.794297i	$0.707839\pi$
$200$	7.55132	0.533959
$201$	13.7907	0.972719
$202$	19.8244	1.39484
$203$	2.01758	0.141607
$204$	−3.54105	−0.247923
$205$	29.9175	2.08953
$206$	19.9128	1.38739
$207$	0.263610	0.0183222
$208$	5.79690	0.401943
$209$	3.40249	0.235355
$210$	3.20221	0.220973
$211$	12.6213	0.868889	0.434444	−	0.900699i	$-0.356945\pi$
$211$	12.6213	0.868889	0.434444	+	0.900699i	$0.356945\pi$
$212$	−1.00000	−0.0686803
$213$	9.89099	0.677720
$214$	2.66757	0.182351
$215$	5.92630	0.404170
$216$	1.00000	0.0680414
$217$	−0.890280	−0.0604361
$218$	14.2645	0.966117
$219$	2.42558	0.163905
$220$	−12.0543	−0.812700
$221$	−20.5271	−1.38080
$222$	4.62976	0.310729
$223$	−15.9386	−1.06732	−0.533662	−	0.845698i	$-0.679185\pi$
$223$	−15.9386	−1.06732	−0.533662	+	0.845698i	$0.679185\pi$
$224$	−0.903867	−0.0603922
$225$	7.55132	0.503421
$226$	−5.22389	−0.347488
$227$	−7.50788	−0.498316	−0.249158	−	0.968463i	$-0.580154\pi$
$227$	−7.50788	−0.498316	−0.249158	+	0.968463i	$0.580154\pi$
$228$	1.00000	0.0662266
$229$	−7.61475	−0.503197	−0.251599	−	0.967832i	$-0.580956\pi$
$229$	−7.61475	−0.503197	−0.251599	+	0.967832i	$0.580956\pi$
$230$	−0.933914	−0.0615805
$231$	−3.07540	−0.202346
$232$	−2.23217	−0.146549
$233$	−26.4084	−1.73007	−0.865035	−	0.501712i	$-0.832704\pi$
$233$	−26.4084	−1.73007	−0.865035	+	0.501712i	$0.832704\pi$
$234$	5.79690	0.378955
$235$	4.08150	0.266248
$236$	2.89337	0.188342
$237$	−8.43325	−0.547798
$238$	3.20064	0.207467
$239$	−6.65750	−0.430638	−0.215319	−	0.976544i	$-0.569079\pi$
$239$	−6.65750	−0.430638	−0.215319	+	0.976544i	$0.569079\pi$
$240$	−3.54278	−0.228686
$241$	15.4489	0.995150	0.497575	−	0.867421i	$-0.334224\pi$
$241$	15.4489	0.995150	0.497575	+	0.867421i	$0.334224\pi$
$242$	0.576943	0.0370873
$243$	1.00000	0.0641500
$244$	4.29599	0.275022
$245$	21.9051	1.39947
$246$	−8.44464	−0.538410
$247$	5.79690	0.368848
$248$	0.984967	0.0625455
$249$	2.41831	0.153254
$250$	−9.03876	−0.571661
$251$	21.7248	1.37126	0.685630	−	0.727950i	$-0.259527\pi$
$251$	21.7248	1.37126	0.685630	+	0.727950i	$0.259527\pi$
$252$	−0.903867	−0.0569383
$253$	0.896932	0.0563896
$254$	−14.0777	−0.883315
$255$	12.5452	0.785610
$256$	1.00000	0.0625000
$257$	4.48222	0.279593	0.139797	−	0.990180i	$-0.455355\pi$
$257$	4.48222	0.279593	0.139797	+	0.990180i	$0.455355\pi$
$258$	−1.67278	−0.104143
$259$	−4.18469	−0.260024
$260$	−20.5372	−1.27366
$261$	−2.23217	−0.138168
$262$	13.7318	0.848353
$263$	−17.6364	−1.08751	−0.543754	−	0.839245i	$-0.682997\pi$
$263$	−17.6364	−1.08751	−0.543754	+	0.839245i	$0.682997\pi$
$264$	3.40249	0.209409
$265$	3.54278	0.217631
$266$	−0.903867	−0.0554197
$267$	−4.26049	−0.260738
$268$	13.7907	0.842400
$269$	14.7204	0.897518	0.448759	−	0.893653i	$-0.351866\pi$
$269$	14.7204	0.897518	0.448759	+	0.893653i	$0.351866\pi$
$270$	−3.54278	−0.215607
$271$	26.0130	1.58018	0.790088	−	0.612993i	$-0.210035\pi$
$271$	26.0130	1.58018	0.790088	+	0.612993i	$0.210035\pi$
$272$	−3.54105	−0.214708
$273$	−5.23963	−0.317117
$274$	−2.24585	−0.135677
$275$	25.6933	1.54936
$276$	0.263610	0.0158675
$277$	−16.4991	−0.991333	−0.495666	−	0.868513i	$-0.665076\pi$
$277$	−16.4991	−0.991333	−0.495666	+	0.868513i	$0.665076\pi$
$278$	18.0065	1.07996
$279$	0.984967	0.0589684
$280$	3.20221	0.191368
$281$	1.30812	0.0780356	0.0390178	−	0.999239i	$-0.487577\pi$
$281$	1.30812	0.0780356	0.0390178	+	0.999239i	$0.487577\pi$
$282$	−1.15206	−0.0686042
$283$	14.0597	0.835763	0.417882	−	0.908501i	$-0.362773\pi$
$283$	14.0597	0.835763	0.417882	+	0.908501i	$0.362773\pi$
$284$	9.89099	0.586922
$285$	−3.54278	−0.209856
$286$	19.7239	1.16630
$287$	7.63283	0.450552
$288$	1.00000	0.0589256
$289$	−4.46094	−0.262408
$290$	7.90809	0.464379
$291$	18.5661	1.08836
$292$	2.42558	0.141946
$293$	−10.6937	−0.624735	−0.312368	−	0.949961i	$-0.601122\pi$
$293$	−10.6937	−0.624735	−0.312368	+	0.949961i	$0.601122\pi$
$294$	−6.18302	−0.360601
$295$	−10.2506	−0.596812
$296$	4.62976	0.269099
$297$	3.40249	0.197433
$298$	0.245347	0.0142126
$299$	1.52812	0.0883736
$300$	7.55132	0.435975
$301$	1.51197	0.0871486
$302$	−1.59670	−0.0918796
$303$	19.8244	1.13888
$304$	1.00000	0.0573539
$305$	−15.2198	−0.871481
$306$	−3.54105	−0.202429
$307$	11.1636	0.637141	0.318570	−	0.947899i	$-0.396797\pi$
$307$	11.1636	0.637141	0.318570	+	0.947899i	$0.396797\pi$
$308$	−3.07540	−0.175237
$309$	19.9128	1.13280
$310$	−3.48953	−0.198192
$311$	−1.69071	−0.0958716	−0.0479358	−	0.998850i	$-0.515264\pi$
$311$	−1.69071	−0.0958716	−0.0479358	+	0.998850i	$0.515264\pi$
$312$	5.79690	0.328185
$313$	8.97910	0.507529	0.253764	−	0.967266i	$-0.418331\pi$
$313$	8.97910	0.507529	0.253764	+	0.967266i	$0.418331\pi$
$314$	3.27375	0.184748
$315$	3.20221	0.180424
$316$	−8.43325	−0.474407
$317$	17.8074	1.00016	0.500082	−	0.865978i	$-0.333303\pi$
$317$	17.8074	1.00016	0.500082	+	0.865978i	$0.333303\pi$
$318$	−1.00000	−0.0560772
$319$	−7.59493	−0.425234
$320$	−3.54278	−0.198048
$321$	2.66757	0.148889
$322$	−0.238269	−0.0132782
$323$	−3.54105	−0.197029
$324$	1.00000	0.0555556
$325$	43.7742	2.42816
$326$	−1.76604	−0.0978119
$327$	14.2645	0.788831
$328$	−8.44464	−0.466277
$329$	1.04131	0.0574092
$330$	−12.0543	−0.663567
$331$	−3.82360	−0.210164	−0.105082	−	0.994464i	$-0.533511\pi$
$331$	−3.82360	−0.210164	−0.105082	+	0.994464i	$0.533511\pi$
$332$	2.41831	0.132722
$333$	4.62976	0.253709
$334$	−5.88705	−0.322125
$335$	−48.8574	−2.66936
$336$	−0.903867	−0.0493100
$337$	−7.52055	−0.409670	−0.204835	−	0.978796i	$-0.565666\pi$
$337$	−7.52055	−0.409670	−0.204835	+	0.978796i	$0.565666\pi$
$338$	20.6041	1.12071
$339$	−5.22389	−0.283723
$340$	12.5452	0.680358
$341$	3.35134	0.181485
$342$	1.00000	0.0540738
$343$	11.9157	0.643388
$344$	−1.67278	−0.0901903
$345$	−0.933914	−0.0502803
$346$	21.8396	1.17411
$347$	−28.1458	−1.51095	−0.755473	−	0.655180i	$-0.772593\pi$
$347$	−28.1458	−1.51095	−0.755473	+	0.655180i	$0.772593\pi$
$348$	−2.23217	−0.119657
$349$	−19.3860	−1.03771	−0.518855	−	0.854862i	$-0.673642\pi$
$349$	−19.3860	−1.03771	−0.518855	+	0.854862i	$0.673642\pi$
$350$	−6.82539	−0.364832
$351$	5.79690	0.309416
$352$	3.40249	0.181353
$353$	−30.2909	−1.61222	−0.806112	−	0.591763i	$-0.798432\pi$
$353$	−30.2909	−1.61222	−0.806112	+	0.591763i	$0.798432\pi$
$354$	2.89337	0.153781
$355$	−35.0416	−1.85982
$356$	−4.26049	−0.225806
$357$	3.20064	0.169396
$358$	−0.919039	−0.0485727
$359$	3.75747	0.198312	0.0991558	−	0.995072i	$-0.468386\pi$
$359$	3.75747	0.198312	0.0991558	+	0.995072i	$0.468386\pi$
$360$	−3.54278	−0.186721
$361$	1.00000	0.0526316
$362$	−11.5691	−0.608057
$363$	0.576943	0.0302817
$364$	−5.23963	−0.274631
$365$	−8.59330	−0.449794
$366$	4.29599	0.224555
$367$	26.5266	1.38468	0.692340	−	0.721572i	$-0.256580\pi$
$367$	26.5266	1.38468	0.692340	+	0.721572i	$0.256580\pi$
$368$	0.263610	0.0137416
$369$	−8.44464	−0.439610
$370$	−16.4022	−0.852711
$371$	0.903867	0.0469265
$372$	0.984967	0.0510682
$373$	−1.96567	−0.101779	−0.0508893	−	0.998704i	$-0.516206\pi$
$373$	−1.96567	−0.101779	−0.0508893	+	0.998704i	$0.516206\pi$
$374$	−12.0484	−0.623008
$375$	−9.03876	−0.466760
$376$	−1.15206	−0.0594129
$377$	−12.9397	−0.666426
$378$	−0.903867	−0.0464899
$379$	−12.8098	−0.657995	−0.328998	−	0.944331i	$-0.606711\pi$
$379$	−12.8098	−0.657995	−0.328998	+	0.944331i	$0.606711\pi$
$380$	−3.54278	−0.181741
$381$	−14.0777	−0.721224
$382$	14.6006	0.747030
$383$	23.8156	1.21692	0.608459	−	0.793585i	$-0.291788\pi$
$383$	23.8156	1.21692	0.608459	+	0.793585i	$0.291788\pi$
$384$	1.00000	0.0510310
$385$	10.8955	0.555285
$386$	−11.7966	−0.600429
$387$	−1.67278	−0.0850322
$388$	18.5661	0.942550
$389$	−28.6602	−1.45313	−0.726564	−	0.687099i	$-0.758884\pi$
$389$	−28.6602	−1.45313	−0.726564	+	0.687099i	$0.758884\pi$
$390$	−20.5372	−1.03994
$391$	−0.933458	−0.0472070
$392$	−6.18302	−0.312290
$393$	13.7318	0.692678
$394$	1.28148	0.0645601
$395$	29.8772	1.50328
$396$	3.40249	0.170982
$397$	35.4820	1.78079	0.890395	−	0.455189i	$-0.150428\pi$
$397$	35.4820	1.78079	0.890395	+	0.455189i	$0.150428\pi$
$398$	−17.1405	−0.859176
$399$	−0.903867	−0.0452500
$400$	7.55132	0.377566
$401$	−1.34486	−0.0671590	−0.0335795	−	0.999436i	$-0.510691\pi$
$401$	−1.34486	−0.0671590	−0.0335795	+	0.999436i	$0.510691\pi$
$402$	13.7907	0.687817
$403$	5.70976	0.284423
$404$	19.8244	0.986301
$405$	−3.54278	−0.176042
$406$	2.01758	0.100131
$407$	15.7527	0.780833
$408$	−3.54105	−0.175308
$409$	−9.10803	−0.450363	−0.225181	−	0.974317i	$-0.572297\pi$
$409$	−9.10803	−0.450363	−0.225181	+	0.974317i	$0.572297\pi$
$410$	29.9175	1.47752
$411$	−2.24585	−0.110779
$412$	19.9128	0.981032
$413$	−2.61522	−0.128687
$414$	0.263610	0.0129557
$415$	−8.56754	−0.420564
$416$	5.79690	0.284216
$417$	18.0065	0.881781
$418$	3.40249	0.166421
$419$	6.48468	0.316798	0.158399	−	0.987375i	$-0.449367\pi$
$419$	6.48468	0.316798	0.158399	+	0.987375i	$0.449367\pi$
$420$	3.20221	0.156252
$421$	−15.7112	−0.765719	−0.382859	−	0.923807i	$-0.625061\pi$
$421$	−15.7112	−0.765719	−0.382859	+	0.923807i	$0.625061\pi$
$422$	12.6213	0.614397
$423$	−1.15206	−0.0560151
$424$	−1.00000	−0.0485643
$425$	−26.7396	−1.29706
$426$	9.89099	0.479220
$427$	−3.88300	−0.187912
$428$	2.66757	0.128942
$429$	19.7239	0.952279
$430$	5.92630	0.285791
$431$	8.73803	0.420896	0.210448	−	0.977605i	$-0.432508\pi$
$431$	8.73803	0.420896	0.210448	+	0.977605i	$0.432508\pi$
$432$	1.00000	0.0481125
$433$	−24.6037	−1.18238	−0.591190	−	0.806532i	$-0.701342\pi$
$433$	−24.6037	−1.18238	−0.591190	+	0.806532i	$0.701342\pi$
$434$	−0.890280	−0.0427348
$435$	7.90809	0.379164
$436$	14.2645	0.683148
$437$	0.263610	0.0126102
$438$	2.42558	0.115899
$439$	30.3124	1.44673	0.723367	−	0.690464i	$-0.242593\pi$
$439$	30.3124	1.44673	0.723367	+	0.690464i	$0.242593\pi$
$440$	−12.0543	−0.574666
$441$	−6.18302	−0.294430
$442$	−20.5271	−0.976376
$443$	−29.8419	−1.41783	−0.708917	−	0.705292i	$-0.750816\pi$
$443$	−29.8419	−1.41783	−0.708917	+	0.705292i	$0.750816\pi$
$444$	4.62976	0.219719
$445$	15.0940	0.715524
$446$	−15.9386	−0.754713
$447$	0.245347	0.0116045
$448$	−0.903867	−0.0427037
$449$	−27.5559	−1.30044	−0.650222	−	0.759744i	$-0.725324\pi$
$449$	−27.5559	−1.30044	−0.650222	+	0.759744i	$0.725324\pi$
$450$	7.55132	0.355972
$451$	−28.7328	−1.35297
$452$	−5.22389	−0.245711
$453$	−1.59670	−0.0750193
$454$	−7.50788	−0.352362
$455$	18.5629	0.870241
$456$	1.00000	0.0468293
$457$	−9.00418	−0.421198	−0.210599	−	0.977573i	$-0.567541\pi$
$457$	−9.00418	−0.421198	−0.210599	+	0.977573i	$0.567541\pi$
$458$	−7.61475	−0.355814
$459$	−3.54105	−0.165282
$460$	−0.933914	−0.0435440
$461$	9.40418	0.437996	0.218998	−	0.975725i	$-0.429721\pi$
$461$	9.40418	0.437996	0.218998	+	0.975725i	$0.429721\pi$
$462$	−3.07540	−0.143081
$463$	−21.4706	−0.997823	−0.498911	−	0.866653i	$-0.666267\pi$
$463$	−21.4706	−0.997823	−0.498911	+	0.866653i	$0.666267\pi$
$464$	−2.23217	−0.103626
$465$	−3.48953	−0.161823
$466$	−26.4084	−1.22334
$467$	−13.4948	−0.624464	−0.312232	−	0.950006i	$-0.601077\pi$
$467$	−13.4948	−0.624464	−0.312232	+	0.950006i	$0.601077\pi$
$468$	5.79690	0.267962
$469$	−12.4649	−0.575578
$470$	4.08150	0.188265
$471$	3.27375	0.150846
$472$	2.89337	0.133178
$473$	−5.69162	−0.261701
$474$	−8.43325	−0.387352
$475$	7.55132	0.346478
$476$	3.20064	0.146701
$477$	−1.00000	−0.0457869
$478$	−6.65750	−0.304507
$479$	−8.63033	−0.394330	−0.197165	−	0.980370i	$-0.563173\pi$
$479$	−8.63033	−0.394330	−0.197165	+	0.980370i	$0.563173\pi$
$480$	−3.54278	−0.161705
$481$	26.8382	1.22372
$482$	15.4489	0.703677
$483$	−0.238269	−0.0108416
$484$	0.576943	0.0262247
$485$	−65.7756	−2.98672
$486$	1.00000	0.0453609
$487$	−17.8038	−0.806765	−0.403383	−	0.915031i	$-0.632166\pi$
$487$	−17.8038	−0.806765	−0.403383	+	0.915031i	$0.632166\pi$
$488$	4.29599	0.194470
$489$	−1.76604	−0.0798631
$490$	21.9051	0.989572
$491$	−21.7898	−0.983361	−0.491681	−	0.870776i	$-0.663617\pi$
$491$	−21.7898	−0.983361	−0.491681	+	0.870776i	$0.663617\pi$
$492$	−8.44464	−0.380714
$493$	7.90423	0.355988
$494$	5.79690	0.260815
$495$	−12.0543	−0.541800
$496$	0.984967	0.0442263
$497$	−8.94014	−0.401020
$498$	2.41831	0.108367
$499$	36.5324	1.63541	0.817707	−	0.575634i	$-0.195245\pi$
$499$	36.5324	1.63541	0.817707	+	0.575634i	$0.195245\pi$
$500$	−9.03876	−0.404226
$501$	−5.88705	−0.263014
$502$	21.7248	0.969627
$503$	19.3513	0.862831	0.431415	−	0.902153i	$-0.358014\pi$
$503$	19.3513	0.862831	0.431415	+	0.902153i	$0.358014\pi$
$504$	−0.903867	−0.0402615
$505$	−70.2336	−3.12535
$506$	0.896932	0.0398735
$507$	20.6041	0.915058
$508$	−14.0777	−0.624598
$509$	−35.3827	−1.56831	−0.784156	−	0.620563i	$-0.786904\pi$
$509$	−35.3827	−1.56831	−0.784156	+	0.620563i	$0.786904\pi$
$510$	12.5452	0.555510
$511$	−2.19240	−0.0969862
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	4.48222	0.197702
$515$	−70.5467	−3.10866
$516$	−1.67278	−0.0736400
$517$	−3.91987	−0.172396
$518$	−4.18469	−0.183865
$519$	21.8396	0.958654
$520$	−20.5372	−0.900614
$521$	8.50645	0.372674	0.186337	−	0.982486i	$-0.440338\pi$
$521$	8.50645	0.372674	0.186337	+	0.982486i	$0.440338\pi$
$522$	−2.23217	−0.0976993
$523$	−39.6869	−1.73539	−0.867693	−	0.497100i	$-0.834398\pi$
$523$	−39.6869	−1.73539	−0.867693	+	0.497100i	$0.834398\pi$
$524$	13.7318	0.599876
$525$	−6.82539	−0.297884
$526$	−17.6364	−0.768984
$527$	−3.48782	−0.151932
$528$	3.40249	0.148074
$529$	−22.9305	−0.996979
$530$	3.54278	0.153889
$531$	2.89337	0.125561
$532$	−0.903867	−0.0391876
$533$	−48.9527	−2.12038
$534$	−4.26049	−0.184370
$535$	−9.45063	−0.408586
$536$	13.7907	0.595667
$537$	−0.919039	−0.0396595
$538$	14.7204	0.634641
$539$	−21.0377	−0.906157
$540$	−3.54278	−0.152457
$541$	1.04841	0.0450748	0.0225374	−	0.999746i	$-0.492826\pi$
$541$	1.04841	0.0450748	0.0225374	+	0.999746i	$0.492826\pi$
$542$	26.0130	1.11735
$543$	−11.5691	−0.496476
$544$	−3.54105	−0.151821
$545$	−50.5362	−2.16473
$546$	−5.23963	−0.224235
$547$	21.6246	0.924601	0.462301	−	0.886723i	$-0.347024\pi$
$547$	21.6246	0.924601	0.462301	+	0.886723i	$0.347024\pi$
$548$	−2.24585	−0.0959379
$549$	4.29599	0.183348
$550$	25.6933	1.09557
$551$	−2.23217	−0.0950936
$552$	0.263610	0.0112200
$553$	7.62254	0.324143
$554$	−16.4991	−0.700978
$555$	−16.4022	−0.696236
$556$	18.0065	0.763645
$557$	−21.7223	−0.920402	−0.460201	−	0.887815i	$-0.652223\pi$
$557$	−21.7223	−0.920402	−0.460201	+	0.887815i	$0.652223\pi$
$558$	0.984967	0.0416970
$559$	−9.69694	−0.410137
$560$	3.20221	0.135318
$561$	−12.0484	−0.508684
$562$	1.30812	0.0551795
$563$	18.0943	0.762584	0.381292	−	0.924455i	$-0.375479\pi$
$563$	18.0943	0.762584	0.381292	+	0.924455i	$0.375479\pi$
$564$	−1.15206	−0.0485105
$565$	18.5071	0.778600
$566$	14.0597	0.590974
$567$	−0.903867	−0.0379589
$568$	9.89099	0.415017
$569$	1.38392	0.0580171	0.0290085	−	0.999579i	$-0.490765\pi$
$569$	1.38392	0.0580171	0.0290085	+	0.999579i	$0.490765\pi$
$570$	−3.54278	−0.148391
$571$	11.4268	0.478195	0.239098	−	0.970996i	$-0.423148\pi$
$571$	11.4268	0.478195	0.239098	+	0.970996i	$0.423148\pi$
$572$	19.7239	0.824698
$573$	14.6006	0.609947
$574$	7.63283	0.318588
$575$	1.99060	0.0830140
$576$	1.00000	0.0416667
$577$	−2.22675	−0.0927009	−0.0463505	−	0.998925i	$-0.514759\pi$
$577$	−2.22675	−0.0927009	−0.0463505	+	0.998925i	$0.514759\pi$
$578$	−4.46094	−0.185551
$579$	−11.7966	−0.490248
$580$	7.90809	0.328365
$581$	−2.18583	−0.0906835
$582$	18.5661	0.769589
$583$	−3.40249	−0.140917
$584$	2.42558	0.100371
$585$	−20.5372	−0.849107
$586$	−10.6937	−0.441755
$587$	−43.8441	−1.80964	−0.904820	−	0.425794i	$-0.859995\pi$
$587$	−43.8441	−1.80964	−0.904820	+	0.425794i	$0.859995\pi$
$588$	−6.18302	−0.254984
$589$	0.984967	0.0405849
$590$	−10.2506	−0.422010
$591$	1.28148	0.0527131
$592$	4.62976	0.190282
$593$	−1.54550	−0.0634660	−0.0317330	−	0.999496i	$-0.510103\pi$
$593$	−1.54550	−0.0634660	−0.0317330	+	0.999496i	$0.510103\pi$
$594$	3.40249	0.139606
$595$	−11.3392	−0.464861
$596$	0.245347	0.0100498
$597$	−17.1405	−0.701514
$598$	1.52812	0.0624896
$599$	22.6726	0.926377	0.463188	−	0.886260i	$-0.346705\pi$
$599$	22.6726	0.926377	0.463188	+	0.886260i	$0.346705\pi$
$600$	7.55132	0.308281
$601$	−11.3803	−0.464211	−0.232105	−	0.972691i	$-0.574561\pi$
$601$	−11.3803	−0.464211	−0.232105	+	0.972691i	$0.574561\pi$
$602$	1.51197	0.0616234
$603$	13.7907	0.561600
$604$	−1.59670	−0.0649687
$605$	−2.04399	−0.0830998
$606$	19.8244	0.805312
$607$	−34.4456	−1.39810	−0.699052	−	0.715071i	$-0.746394\pi$
$607$	−34.4456	−1.39810	−0.699052	+	0.715071i	$0.746394\pi$
$608$	1.00000	0.0405554
$609$	2.01758	0.0817566
$610$	−15.2198	−0.616230
$611$	−6.67838	−0.270178
$612$	−3.54105	−0.143139
$613$	−0.000213829 0	−8.63648e−6 0	−4.31824e−6	−	1.00000i	$-0.500001\pi$
$613$	−0.000213829 0	−8.63648e−6 0	−4.31824e−6		1.00000i	$0.500001\pi$
$614$	11.1636	0.450526
$615$	29.9175	1.20639
$616$	−3.07540	−0.123911
$617$	23.5585	0.948431	0.474216	−	0.880409i	$-0.342732\pi$
$617$	23.5585	0.948431	0.474216	+	0.880409i	$0.342732\pi$
$618$	19.9128	0.801009
$619$	−4.39246	−0.176548	−0.0882739	−	0.996096i	$-0.528135\pi$
$619$	−4.39246	−0.176548	−0.0882739	+	0.996096i	$0.528135\pi$
$620$	−3.48953	−0.140143
$621$	0.263610	0.0105783
$622$	−1.69071	−0.0677914
$623$	3.85092	0.154284
$624$	5.79690	0.232062
$625$	−5.73420	−0.229368
$626$	8.97910	0.358877
$627$	3.40249	0.135882
$628$	3.27375	0.130637
$629$	−16.3942	−0.653680
$630$	3.20221	0.127579
$631$	33.5731	1.33653	0.668263	−	0.743925i	$-0.267038\pi$
$631$	33.5731	1.33653	0.668263	+	0.743925i	$0.267038\pi$
$632$	−8.43325	−0.335457
$633$	12.6213	0.501653
$634$	17.8074	0.707223
$635$	49.8743	1.97920
$636$	−1.00000	−0.0396526
$637$	−35.8424	−1.42013
$638$	−7.59493	−0.300686
$639$	9.89099	0.391282
$640$	−3.54278	−0.140041
$641$	1.70135	0.0671993	0.0335996	−	0.999435i	$-0.489303\pi$
$641$	1.70135	0.0671993	0.0335996	+	0.999435i	$0.489303\pi$
$642$	2.66757	0.105281
$643$	14.7463	0.581536	0.290768	−	0.956794i	$-0.406089\pi$
$643$	14.7463	0.581536	0.290768	+	0.956794i	$0.406089\pi$
$644$	−0.238269	−0.00938910
$645$	5.92630	0.233348
$646$	−3.54105	−0.139321
$647$	39.3642	1.54757	0.773784	−	0.633450i	$-0.218362\pi$
$647$	39.3642	1.54757	0.773784	+	0.633450i	$0.218362\pi$
$648$	1.00000	0.0392837
$649$	9.84466	0.386437
$650$	43.7742	1.71697
$651$	−0.890280	−0.0348928
$652$	−1.76604	−0.0691634
$653$	−9.06612	−0.354785	−0.177392	−	0.984140i	$-0.556766\pi$
$653$	−9.06612	−0.354785	−0.177392	+	0.984140i	$0.556766\pi$
$654$	14.2645	0.557788
$655$	−48.6488	−1.90087
$656$	−8.44464	−0.329708
$657$	2.42558	0.0946309
$658$	1.04131	0.0405945
$659$	−42.0497	−1.63802	−0.819012	−	0.573777i	$-0.805478\pi$
$659$	−42.0497	−1.63802	−0.819012	+	0.573777i	$0.805478\pi$
$660$	−12.0543	−0.469213
$661$	−11.7589	−0.457369	−0.228684	−	0.973501i	$-0.573442\pi$
$661$	−11.7589	−0.457369	−0.228684	+	0.973501i	$0.573442\pi$
$662$	−3.82360	−0.148609
$663$	−20.5271	−0.797208
$664$	2.41831	0.0938485
$665$	3.20221	0.124176
$666$	4.62976	0.179399
$667$	−0.588422	−0.0227838
$668$	−5.88705	−0.227777
$669$	−15.9386	−0.616220
$670$	−48.8574	−1.88753
$671$	14.6171	0.564285
$672$	−0.903867	−0.0348674
$673$	20.6395	0.795594	0.397797	−	0.917473i	$-0.369775\pi$
$673$	20.6395	0.795594	0.397797	+	0.917473i	$0.369775\pi$
$674$	−7.52055	−0.289681
$675$	7.55132	0.290650
$676$	20.6041	0.792464
$677$	38.5461	1.48145	0.740724	−	0.671809i	$-0.234483\pi$
$677$	38.5461	1.48145	0.740724	+	0.671809i	$0.234483\pi$
$678$	−5.22389	−0.200622
$679$	−16.7813	−0.644006
$680$	12.5452	0.481086
$681$	−7.50788	−0.287703
$682$	3.35134	0.128330
$683$	−16.5036	−0.631492	−0.315746	−	0.948844i	$-0.602255\pi$
$683$	−16.5036	−0.631492	−0.315746	+	0.948844i	$0.602255\pi$
$684$	1.00000	0.0382360
$685$	7.95655	0.304004
$686$	11.9157	0.454944
$687$	−7.61475	−0.290521
$688$	−1.67278	−0.0637741
$689$	−5.79690	−0.220844
$690$	−0.933914	−0.0355535
$691$	−19.8913	−0.756703	−0.378351	−	0.925662i	$-0.623509\pi$
$691$	−19.8913	−0.756703	−0.378351	+	0.925662i	$0.623509\pi$
$692$	21.8396	0.830218
$693$	−3.07540	−0.116825
$694$	−28.1458	−1.06840
$695$	−63.7931	−2.41981
$696$	−2.23217	−0.0846101
$697$	29.9029	1.13265
$698$	−19.3860	−0.733772
$699$	−26.4084	−0.998856
$700$	−6.82539	−0.257975
$701$	48.0244	1.81386	0.906928	−	0.421286i	$-0.138421\pi$
$701$	48.0244	1.81386	0.906928	+	0.421286i	$0.138421\pi$
$702$	5.79690	0.218790
$703$	4.62976	0.174615
$704$	3.40249	0.128236
$705$	4.08150	0.153718
$706$	−30.2909	−1.14001
$707$	−17.9186	−0.673900
$708$	2.89337	0.108739
$709$	33.2151	1.24742	0.623709	−	0.781656i	$-0.285625\pi$
$709$	33.2151	1.24742	0.623709	+	0.781656i	$0.285625\pi$
$710$	−35.0416	−1.31509
$711$	−8.43325	−0.316272
$712$	−4.26049	−0.159669
$713$	0.259647	0.00972387
$714$	3.20064	0.119781
$715$	−69.8775	−2.61327
$716$	−0.919039	−0.0343461
$717$	−6.65750	−0.248629
$718$	3.75747	0.140227
$719$	4.18231	0.155974	0.0779870	−	0.996954i	$-0.475151\pi$
$719$	4.18231	0.155974	0.0779870	+	0.996954i	$0.475151\pi$
$720$	−3.54278	−0.132032
$721$	−17.9985	−0.670299
$722$	1.00000	0.0372161
$723$	15.4489	0.574550
$724$	−11.5691	−0.429961
$725$	−16.8558	−0.626009
$726$	0.576943	0.0214124
$727$	13.5763	0.503519	0.251759	−	0.967790i	$-0.418991\pi$
$727$	13.5763	0.503519	0.251759	+	0.967790i	$0.418991\pi$
$728$	−5.23963	−0.194194
$729$	1.00000	0.0370370
$730$	−8.59330	−0.318052
$731$	5.92340	0.219085
$732$	4.29599	0.158784
$733$	−2.77472	−0.102487	−0.0512433	−	0.998686i	$-0.516318\pi$
$733$	−2.77472	−0.102487	−0.0512433	+	0.998686i	$0.516318\pi$
$734$	26.5266	0.979116
$735$	21.9051	0.807982
$736$	0.263610	0.00971680
$737$	46.9227	1.72842
$738$	−8.44464	−0.310851
$739$	1.47906	0.0544083	0.0272041	−	0.999630i	$-0.491340\pi$
$739$	1.47906	0.0544083	0.0272041	+	0.999630i	$0.491340\pi$
$740$	−16.4022	−0.602958
$741$	5.79690	0.212954
$742$	0.903867	0.0331820
$743$	−5.81823	−0.213450	−0.106725	−	0.994289i	$-0.534036\pi$
$743$	−5.81823	−0.213450	−0.106725	+	0.994289i	$0.534036\pi$
$744$	0.984967	0.0361106
$745$	−0.869212	−0.0318455
$746$	−1.96567	−0.0719683
$747$	2.41831	0.0884812
$748$	−12.0484	−0.440533
$749$	−2.41113	−0.0881008
$750$	−9.03876	−0.330049
$751$	14.0129	0.511336	0.255668	−	0.966765i	$-0.417705\pi$
$751$	14.0129	0.511336	0.255668	+	0.966765i	$0.417705\pi$
$752$	−1.15206	−0.0420113
$753$	21.7248	0.791698
$754$	−12.9397	−0.471234
$755$	5.65675	0.205870
$756$	−0.903867	−0.0328733
$757$	50.6034	1.83921	0.919605	−	0.392844i	$-0.128509\pi$
$757$	50.6034	1.83921	0.919605	+	0.392844i	$0.128509\pi$
$758$	−12.8098	−0.465273
$759$	0.896932	0.0325566
$760$	−3.54278	−0.128510
$761$	11.5596	0.419034	0.209517	−	0.977805i	$-0.432811\pi$
$761$	11.5596	0.419034	0.209517	+	0.977805i	$0.432811\pi$
$762$	−14.0777	−0.509982
$763$	−12.8933	−0.466767
$764$	14.6006	0.528230
$765$	12.5452	0.453572
$766$	23.8156	0.860491
$767$	16.7726	0.605622
$768$	1.00000	0.0360844
$769$	7.29606	0.263103	0.131551	−	0.991309i	$-0.458004\pi$
$769$	7.29606	0.263103	0.131551	+	0.991309i	$0.458004\pi$
$770$	10.8955	0.392646
$771$	4.48222	0.161423
$772$	−11.7966	−0.424567
$773$	−18.4411	−0.663278	−0.331639	−	0.943406i	$-0.607602\pi$
$773$	−18.4411	−0.663278	−0.331639	+	0.943406i	$0.607602\pi$
$774$	−1.67278	−0.0601268
$775$	7.43780	0.267174
$776$	18.5661	0.666484
$777$	−4.18469	−0.150125
$778$	−28.6602	−1.02752
$779$	−8.44464	−0.302561
$780$	−20.5372	−0.735348
$781$	33.6540	1.20424
$782$	−0.933458	−0.0333804
$783$	−2.23217	−0.0797712
$784$	−6.18302	−0.220822
$785$	−11.5982	−0.413957
$786$	13.7318	0.489797
$787$	34.0483	1.21369	0.606845	−	0.794820i	$-0.292435\pi$
$787$	34.0483	1.21369	0.606845	+	0.794820i	$0.292435\pi$
$788$	1.28148	0.0456509
$789$	−17.6364	−0.627873
$790$	29.8772	1.06298
$791$	4.72171	0.167885
$792$	3.40249	0.120902
$793$	24.9034	0.884346
$794$	35.4820	1.25921
$795$	3.54278	0.125650
$796$	−17.1405	−0.607529
$797$	12.8443	0.454968	0.227484	−	0.973782i	$-0.426950\pi$
$797$	12.8443	0.454968	0.227484	+	0.973782i	$0.426950\pi$
$798$	−0.903867	−0.0319966
$799$	4.07951	0.144323
$800$	7.55132	0.266979
$801$	−4.26049	−0.150537
$802$	−1.34486	−0.0474886
$803$	8.25301	0.291242
$804$	13.7907	0.486360
$805$	0.844135	0.0297518
$806$	5.70976	0.201118
$807$	14.7204	0.518182
$808$	19.8244	0.697420
$809$	−43.3523	−1.52418	−0.762092	−	0.647469i	$-0.775828\pi$
$809$	−43.3523	−1.52418	−0.762092	+	0.647469i	$0.775828\pi$
$810$	−3.54278	−0.124481
$811$	−6.37801	−0.223962	−0.111981	−	0.993710i	$-0.535720\pi$
$811$	−6.37801	−0.223962	−0.111981	+	0.993710i	$0.535720\pi$
$812$	2.01758	0.0708033
$813$	26.0130	0.912315
$814$	15.7527	0.552132
$815$	6.25670	0.219163
$816$	−3.54105	−0.123962
$817$	−1.67278	−0.0585232
$818$	−9.10803	−0.318455
$819$	−5.23963	−0.183087
$820$	29.9175	1.04477
$821$	32.3144	1.12778	0.563891	−	0.825849i	$-0.309304\pi$
$821$	32.3144	1.12778	0.563891	+	0.825849i	$0.309304\pi$
$822$	−2.24585	−0.0783329
$823$	38.1298	1.32912	0.664560	−	0.747235i	$-0.268619\pi$
$823$	38.1298	1.32912	0.664560	+	0.747235i	$0.268619\pi$
$824$	19.9128	0.693694
$825$	25.6933	0.894525
$826$	−2.61522	−0.0909952
$827$	41.9630	1.45920	0.729599	−	0.683875i	$-0.239707\pi$
$827$	41.9630	1.45920	0.729599	+	0.683875i	$0.239707\pi$
$828$	0.263610	0.00916109
$829$	−54.4144	−1.88989	−0.944944	−	0.327231i	$-0.893884\pi$
$829$	−54.4144	−1.88989	−0.944944	+	0.327231i	$0.893884\pi$
$830$	−8.56754	−0.297384
$831$	−16.4991	−0.572346
$832$	5.79690	0.200971
$833$	21.8944	0.758597
$834$	18.0065	0.623513
$835$	20.8565	0.721771
$836$	3.40249	0.117678
$837$	0.984967	0.0340454
$838$	6.48468	0.224010
$839$	−24.9420	−0.861095	−0.430548	−	0.902568i	$-0.641680\pi$
$839$	−24.9420	−0.861095	−0.430548	+	0.902568i	$0.641680\pi$
$840$	3.20221	0.110487
$841$	−24.0174	−0.828187
$842$	−15.7112	−0.541445
$843$	1.30812	0.0450539
$844$	12.6213	0.434444
$845$	−72.9957	−2.51113
$846$	−1.15206	−0.0396086
$847$	−0.521480	−0.0179183
$848$	−1.00000	−0.0343401
$849$	14.0597	0.482528
$850$	−26.7396	−0.917161
$851$	1.22045	0.0418365
$852$	9.89099	0.338860
$853$	14.9785	0.512856	0.256428	−	0.966563i	$-0.417454\pi$
$853$	14.9785	0.512856	0.256428	+	0.966563i	$0.417454\pi$
$854$	−3.88300	−0.132874
$855$	−3.54278	−0.121161
$856$	2.66757	0.0911757
$857$	−30.4639	−1.04063	−0.520314	−	0.853975i	$-0.674185\pi$
$857$	−30.4639	−1.04063	−0.520314	+	0.853975i	$0.674185\pi$
$858$	19.7239	0.673363
$859$	−37.5696	−1.28186	−0.640929	−	0.767600i	$-0.721451\pi$
$859$	−37.5696	−1.28186	−0.640929	+	0.767600i	$0.721451\pi$
$860$	5.92630	0.202085
$861$	7.63283	0.260126
$862$	8.73803	0.297619
$863$	−53.2474	−1.81256	−0.906282	−	0.422674i	$-0.861092\pi$
$863$	−53.2474	−1.81256	−0.906282	+	0.422674i	$0.861092\pi$
$864$	1.00000	0.0340207
$865$	−77.3731	−2.63076
$866$	−24.6037	−0.836069
$867$	−4.46094	−0.151501
$868$	−0.890280	−0.0302181
$869$	−28.6941	−0.973379
$870$	7.90809	0.268109
$871$	79.9432	2.70877
$872$	14.2645	0.483058
$873$	18.5661	0.628367
$874$	0.263610	0.00891675
$875$	8.16984	0.276191
$876$	2.42558	0.0819527
$877$	−18.9128	−0.638638	−0.319319	−	0.947647i	$-0.603454\pi$
$877$	−18.9128	−0.638638	−0.319319	+	0.947647i	$0.603454\pi$
$878$	30.3124	1.02300
$879$	−10.6937	−0.360691
$880$	−12.0543	−0.406350
$881$	−10.6092	−0.357434	−0.178717	−	0.983901i	$-0.557195\pi$
$881$	−10.6092	−0.357434	−0.178717	+	0.983901i	$0.557195\pi$
$882$	−6.18302	−0.208193
$883$	−16.3564	−0.550437	−0.275218	−	0.961382i	$-0.588750\pi$
$883$	−16.3564	−0.550437	−0.275218	+	0.961382i	$0.588750\pi$
$884$	−20.5271	−0.690402
$885$	−10.2506	−0.344569
$886$	−29.8419	−1.00256
$887$	−33.1078	−1.11165	−0.555825	−	0.831299i	$-0.687597\pi$
$887$	−33.1078	−1.11165	−0.555825	+	0.831299i	$0.687597\pi$
$888$	4.62976	0.155364
$889$	12.7244	0.426762
$890$	15.0940	0.505952
$891$	3.40249	0.113988
$892$	−15.9386	−0.533662
$893$	−1.15206	−0.0385522
$894$	0.245347	0.00820564
$895$	3.25596	0.108835
$896$	−0.903867	−0.0301961
$897$	1.52812	0.0510225
$898$	−27.5559	−0.919553
$899$	−2.19861	−0.0733278
$900$	7.55132	0.251711
$901$	3.54105	0.117970
$902$	−28.7328	−0.956698
$903$	1.51197	0.0503153
$904$	−5.22389	−0.173744
$905$	40.9867	1.36244
$906$	−1.59670	−0.0530467
$907$	−39.3452	−1.30643	−0.653217	−	0.757170i	$-0.726581\pi$
$907$	−39.3452	−1.30643	−0.653217	+	0.757170i	$0.726581\pi$
$908$	−7.50788	−0.249158
$909$	19.8244	0.657534
$910$	18.5629	0.615353
$911$	−2.63678	−0.0873605	−0.0436803	−	0.999046i	$-0.513908\pi$
$911$	−2.63678	−0.0873605	−0.0436803	+	0.999046i	$0.513908\pi$
$912$	1.00000	0.0331133
$913$	8.22827	0.272316
$914$	−9.00418	−0.297832
$915$	−15.2198	−0.503150
$916$	−7.61475	−0.251599
$917$	−12.4117	−0.409871
$918$	−3.54105	−0.116872
$919$	−28.1142	−0.927402	−0.463701	−	0.885992i	$-0.653479\pi$
$919$	−28.1142	−0.927402	−0.463701	+	0.885992i	$0.653479\pi$
$920$	−0.933914	−0.0307902
$921$	11.1636	0.367853
$922$	9.40418	0.309710
$923$	57.3371	1.88727
$924$	−3.07540	−0.101173
$925$	34.9608	1.14950
$926$	−21.4706	−0.705567
$927$	19.9128	0.654021
$928$	−2.23217	−0.0732745
$929$	−43.1132	−1.41450	−0.707249	−	0.706965i	$-0.750064\pi$
$929$	−43.1132	−1.41450	−0.707249	+	0.706965i	$0.750064\pi$
$930$	−3.48953	−0.114426
$931$	−6.18302	−0.202640
$932$	−26.4084	−0.865035
$933$	−1.69071	−0.0553515
$934$	−13.4948	−0.441563
$935$	42.6849	1.39594
$936$	5.79690	0.189478
$937$	11.8770	0.388005	0.194002	−	0.981001i	$-0.437853\pi$
$937$	11.8770	0.388005	0.194002	+	0.981001i	$0.437853\pi$
$938$	−12.4649	−0.406995
$939$	8.97910	0.293022
$940$	4.08150	0.133124
$941$	43.1719	1.40737	0.703683	−	0.710515i	$-0.251538\pi$
$941$	43.1719	1.40737	0.703683	+	0.710515i	$0.251538\pi$
$942$	3.27375	0.106664
$943$	−2.22609	−0.0724916
$944$	2.89337	0.0941711
$945$	3.20221	0.104168
$946$	−5.69162	−0.185050
$947$	45.4045	1.47545	0.737725	−	0.675102i	$-0.235900\pi$
$947$	45.4045	1.47545	0.737725	+	0.675102i	$0.235900\pi$
$948$	−8.43325	−0.273899
$949$	14.0608	0.456434
$950$	7.55132	0.244997
$951$	17.8074	0.577445
$952$	3.20064	0.103733
$953$	5.41124	0.175287	0.0876436	−	0.996152i	$-0.472066\pi$
$953$	5.41124	0.175287	0.0876436	+	0.996152i	$0.472066\pi$
$954$	−1.00000	−0.0323762
$955$	−51.7266	−1.67383
$956$	−6.65750	−0.215319
$957$	−7.59493	−0.245509
$958$	−8.63033	−0.278833
$959$	2.02995	0.0655504
$960$	−3.54278	−0.114343
$961$	−30.0298	−0.968705
$962$	26.8382	0.865300
$963$	2.66757	0.0859613
$964$	15.4489	0.497575
$965$	41.7926	1.34535
$966$	−0.238269	−0.00766617
$967$	2.84224	0.0914002	0.0457001	−	0.998955i	$-0.485448\pi$
$967$	2.84224	0.0914002	0.0457001	+	0.998955i	$0.485448\pi$
$968$	0.576943	0.0185437
$969$	−3.54105	−0.113755
$970$	−65.7756	−2.11193
$971$	−23.9669	−0.769134	−0.384567	−	0.923097i	$-0.625649\pi$
$971$	−23.9669	−0.769134	−0.384567	+	0.923097i	$0.625649\pi$
$972$	1.00000	0.0320750
$973$	−16.2755	−0.521768
$974$	−17.8038	−0.570469
$975$	43.7742	1.40190
$976$	4.29599	0.137511
$977$	−40.5042	−1.29585	−0.647923	−	0.761706i	$-0.724362\pi$
$977$	−40.5042	−1.29585	−0.647923	+	0.761706i	$0.724362\pi$
$978$	−1.76604	−0.0564717
$979$	−14.4963	−0.463303
$980$	21.9051	0.699733
$981$	14.2645	0.455432
$982$	−21.7898	−0.695341
$983$	−33.7883	−1.07768	−0.538840	−	0.842408i	$-0.681137\pi$
$983$	−33.7883	−1.07768	−0.538840	+	0.842408i	$0.681137\pi$
$984$	−8.44464	−0.269205
$985$	−4.54001	−0.144657
$986$	7.90423	0.251722
$987$	1.04131	0.0331452
$988$	5.79690	0.184424
$989$	−0.440962	−0.0140218
$990$	−12.0543	−0.383110
$991$	−8.23452	−0.261578	−0.130789	−	0.991410i	$-0.541751\pi$
$991$	−8.23452	−0.261578	−0.130789	+	0.991410i	$0.541751\pi$
$992$	0.984967	0.0312727
$993$	−3.82360	−0.121338
$994$	−8.94014	−0.283564
$995$	60.7251	1.92512
$996$	2.41831	0.0766270
$997$	−15.6162	−0.494568	−0.247284	−	0.968943i	$-0.579538\pi$
$997$	−15.6162	−0.494568	−0.247284	+	0.968943i	$0.579538\pi$
$998$	36.5324	1.15641
$999$	4.62976	0.146479

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bh.1.2	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bh.1.2	✓	13	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.54278 q^{5} +1.00000 q^{6} -0.903867 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.54278 q^{5} +1.00000 q^{6} -0.903867 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.54278 q^{10} +3.40249 q^{11} +1.00000 q^{12} +5.79690 q^{13} -0.903867 q^{14} -3.54278 q^{15} +1.00000 q^{16} -3.54105 q^{17} +1.00000 q^{18} +1.00000 q^{19} -3.54278 q^{20} -0.903867 q^{21} +3.40249 q^{22} +0.263610 q^{23} +1.00000 q^{24} +7.55132 q^{25} +5.79690 q^{26} +1.00000 q^{27} -0.903867 q^{28} -2.23217 q^{29} -3.54278 q^{30} +0.984967 q^{31} +1.00000 q^{32} +3.40249 q^{33} -3.54105 q^{34} +3.20221 q^{35} +1.00000 q^{36} +4.62976 q^{37} +1.00000 q^{38} +5.79690 q^{39} -3.54278 q^{40} -8.44464 q^{41} -0.903867 q^{42} -1.67278 q^{43} +3.40249 q^{44} -3.54278 q^{45} +0.263610 q^{46} -1.15206 q^{47} +1.00000 q^{48} -6.18302 q^{49} +7.55132 q^{50} -3.54105 q^{51} +5.79690 q^{52} -1.00000 q^{53} +1.00000 q^{54} -12.0543 q^{55} -0.903867 q^{56} +1.00000 q^{57} -2.23217 q^{58} +2.89337 q^{59} -3.54278 q^{60} +4.29599 q^{61} +0.984967 q^{62} -0.903867 q^{63} +1.00000 q^{64} -20.5372 q^{65} +3.40249 q^{66} +13.7907 q^{67} -3.54105 q^{68} +0.263610 q^{69} +3.20221 q^{70} +9.89099 q^{71} +1.00000 q^{72} +2.42558 q^{73} +4.62976 q^{74} +7.55132 q^{75} +1.00000 q^{76} -3.07540 q^{77} +5.79690 q^{78} -8.43325 q^{79} -3.54278 q^{80} +1.00000 q^{81} -8.44464 q^{82} +2.41831 q^{83} -0.903867 q^{84} +12.5452 q^{85} -1.67278 q^{86} -2.23217 q^{87} +3.40249 q^{88} -4.26049 q^{89} -3.54278 q^{90} -5.23963 q^{91} +0.263610 q^{92} +0.984967 q^{93} -1.15206 q^{94} -3.54278 q^{95} +1.00000 q^{96} +18.5661 q^{97} -6.18302 q^{98} +3.40249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 4 q^{11} + 13 q^{12} + 18 q^{13} + 12 q^{14} + 3 q^{15} + 13 q^{16} + 3 q^{17} + 13 q^{18} + 13 q^{19} + 3 q^{20} + 12 q^{21} + 4 q^{22} + 8 q^{23} + 13 q^{24} + 24 q^{25} + 18 q^{26} + 13 q^{27} + 12 q^{28} + 11 q^{29} + 3 q^{30} + 2 q^{31} + 13 q^{32} + 4 q^{33} + 3 q^{34} - 6 q^{35} + 13 q^{36} + 26 q^{37} + 13 q^{38} + 18 q^{39} + 3 q^{40} + 3 q^{41} + 12 q^{42} + 24 q^{43} + 4 q^{44} + 3 q^{45} + 8 q^{46} + 4 q^{47} + 13 q^{48} + 41 q^{49} + 24 q^{50} + 3 q^{51} + 18 q^{52} - 13 q^{53} + 13 q^{54} + 23 q^{55} + 12 q^{56} + 13 q^{57} + 11 q^{58} + 8 q^{59} + 3 q^{60} + 29 q^{61} + 2 q^{62} + 12 q^{63} + 13 q^{64} + 13 q^{65} + 4 q^{66} - 5 q^{67} + 3 q^{68} + 8 q^{69} - 6 q^{70} + 29 q^{71} + 13 q^{72} + 15 q^{73} + 26 q^{74} + 24 q^{75} + 13 q^{76} + 3 q^{77} + 18 q^{78} + 15 q^{79} + 3 q^{80} + 13 q^{81} + 3 q^{82} + 4 q^{83} + 12 q^{84} - q^{85} + 24 q^{86} + 11 q^{87} + 4 q^{88} + 3 q^{89} + 3 q^{90} - 29 q^{91} + 8 q^{92} + 2 q^{93} + 4 q^{94} + 3 q^{95} + 13 q^{96} + 50 q^{97} + 41 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 4 * q^11 + 13 * q^12 + 18 * q^13 + 12 * q^14 + 3 * q^15 + 13 * q^16 + 3 * q^17 + 13 * q^18 + 13 * q^19 + 3 * q^20 + 12 * q^21 + 4 * q^22 + 8 * q^23 + 13 * q^24 + 24 * q^25 + 18 * q^26 + 13 * q^27 + 12 * q^28 + 11 * q^29 + 3 * q^30 + 2 * q^31 + 13 * q^32 + 4 * q^33 + 3 * q^34 - 6 * q^35 + 13 * q^36 + 26 * q^37 + 13 * q^38 + 18 * q^39 + 3 * q^40 + 3 * q^41 + 12 * q^42 + 24 * q^43 + 4 * q^44 + 3 * q^45 + 8 * q^46 + 4 * q^47 + 13 * q^48 + 41 * q^49 + 24 * q^50 + 3 * q^51 + 18 * q^52 - 13 * q^53 + 13 * q^54 + 23 * q^55 + 12 * q^56 + 13 * q^57 + 11 * q^58 + 8 * q^59 + 3 * q^60 + 29 * q^61 + 2 * q^62 + 12 * q^63 + 13 * q^64 + 13 * q^65 + 4 * q^66 - 5 * q^67 + 3 * q^68 + 8 * q^69 - 6 * q^70 + 29 * q^71 + 13 * q^72 + 15 * q^73 + 26 * q^74 + 24 * q^75 + 13 * q^76 + 3 * q^77 + 18 * q^78 + 15 * q^79 + 3 * q^80 + 13 * q^81 + 3 * q^82 + 4 * q^83 + 12 * q^84 - q^85 + 24 * q^86 + 11 * q^87 + 4 * q^88 + 3 * q^89 + 3 * q^90 - 29 * q^91 + 8 * q^92 + 2 * q^93 + 4 * q^94 + 3 * q^95 + 13 * q^96 + 50 * q^97 + 41 * q^98 + 4 * q^99

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