LMFDB - Embedded newform 6018.2.a.bb.1.6

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:	$13$
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} - 4 x^{12} - 41 x^{11} + 179 x^{10} + 540 x^{9} - 2773 x^{8} - 2260 x^{7} + 17621 x^{6} + \cdots + 128 $ x^13 - 4x^12 - 41x^11 + 179x^10 + 540x^9 - 2773x^8 - 2260x^7 + 17621x^6 - 838x^5 - 44478x^4 + 16472x^3 + 29944x^2 - 6856x + 128
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			1.6
Root			$0.0205303$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.0205303 q^{5} +1.00000 q^{6} +5.09020 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.0205303 q^{5} +1.00000 q^{6} +5.09020 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.0205303 q^{10} -4.04326 q^{11} +1.00000 q^{12} -2.31576 q^{13} +5.09020 q^{14} +0.0205303 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +5.61146 q^{19} +0.0205303 q^{20} +5.09020 q^{21} -4.04326 q^{22} +7.47510 q^{23} +1.00000 q^{24} -4.99958 q^{25} -2.31576 q^{26} +1.00000 q^{27} +5.09020 q^{28} +9.16732 q^{29} +0.0205303 q^{30} -5.48620 q^{31} +1.00000 q^{32} -4.04326 q^{33} +1.00000 q^{34} +0.104503 q^{35} +1.00000 q^{36} -8.15071 q^{37} +5.61146 q^{38} -2.31576 q^{39} +0.0205303 q^{40} +3.48348 q^{41} +5.09020 q^{42} +3.27176 q^{43} -4.04326 q^{44} +0.0205303 q^{45} +7.47510 q^{46} -10.0597 q^{47} +1.00000 q^{48} +18.9101 q^{49} -4.99958 q^{50} +1.00000 q^{51} -2.31576 q^{52} +4.57111 q^{53} +1.00000 q^{54} -0.0830095 q^{55} +5.09020 q^{56} +5.61146 q^{57} +9.16732 q^{58} -1.00000 q^{59} +0.0205303 q^{60} -7.67929 q^{61} -5.48620 q^{62} +5.09020 q^{63} +1.00000 q^{64} -0.0475432 q^{65} -4.04326 q^{66} +9.93096 q^{67} +1.00000 q^{68} +7.47510 q^{69} +0.104503 q^{70} +1.56437 q^{71} +1.00000 q^{72} +6.72077 q^{73} -8.15071 q^{74} -4.99958 q^{75} +5.61146 q^{76} -20.5810 q^{77} -2.31576 q^{78} +8.14748 q^{79} +0.0205303 q^{80} +1.00000 q^{81} +3.48348 q^{82} +17.2237 q^{83} +5.09020 q^{84} +0.0205303 q^{85} +3.27176 q^{86} +9.16732 q^{87} -4.04326 q^{88} -15.7818 q^{89} +0.0205303 q^{90} -11.7877 q^{91} +7.47510 q^{92} -5.48620 q^{93} -10.0597 q^{94} +0.115205 q^{95} +1.00000 q^{96} -0.494479 q^{97} +18.9101 q^{98} -4.04326 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9 + 4 * q^10 + 7 * q^11 + 13 * q^12 + 6 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 + 13 * q^17 + 13 * q^18 + 9 * q^19 + 4 * q^20 + 11 * q^21 + 7 * q^22 + 2 * q^23 + 13 * q^24 + 33 * q^25 + 6 * q^26 + 13 * q^27 + 11 * q^28 + 14 * q^29 + 4 * q^30 - 5 * q^31 + 13 * q^32 + 7 * q^33 + 13 * q^34 + 24 * q^35 + 13 * q^36 + 4 * q^37 + 9 * q^38 + 6 * q^39 + 4 * q^40 + 28 * q^41 + 11 * q^42 + q^43 + 7 * q^44 + 4 * q^45 + 2 * q^46 + 12 * q^47 + 13 * q^48 + 32 * q^49 + 33 * q^50 + 13 * q^51 + 6 * q^52 + 22 * q^53 + 13 * q^54 - 7 * q^55 + 11 * q^56 + 9 * q^57 + 14 * q^58 - 13 * q^59 + 4 * q^60 - 9 * q^61 - 5 * q^62 + 11 * q^63 + 13 * q^64 + 34 * q^65 + 7 * q^66 + 26 * q^67 + 13 * q^68 + 2 * q^69 + 24 * q^70 + 8 * q^71 + 13 * q^72 + 4 * q^73 + 4 * q^74 + 33 * q^75 + 9 * q^76 + 38 * q^77 + 6 * q^78 - 17 * q^79 + 4 * q^80 + 13 * q^81 + 28 * q^82 + 14 * q^83 + 11 * q^84 + 4 * q^85 + q^86 + 14 * q^87 + 7 * q^88 + 19 * q^89 + 4 * q^90 - 5 * q^91 + 2 * q^92 - 5 * q^93 + 12 * q^94 + 25 * q^95 + 13 * q^96 - 5 * q^97 + 32 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.0205303	0.00918144	0.00459072	−	0.999989i	$-0.498539\pi$
$5$	0.0205303	0.00918144	0.00459072	+	0.999989i	$0.498539\pi$
$6$	1.00000	0.408248
$7$	5.09020	1.92391	0.961957	−	0.273201i	$-0.0880825\pi$
$7$	5.09020	1.92391	0.961957	+	0.273201i	$0.0880825\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.0205303	0.00649226
$11$	−4.04326	−1.21909	−0.609545	−	0.792752i	$-0.708648\pi$
$11$	−4.04326	−1.21909	−0.609545	+	0.792752i	$0.708648\pi$
$12$	1.00000	0.288675
$13$	−2.31576	−0.642275	−0.321138	−	0.947033i	$-0.604065\pi$
$13$	−2.31576	−0.642275	−0.321138	+	0.947033i	$0.604065\pi$
$14$	5.09020	1.36041
$15$	0.0205303	0.00530090
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	5.61146	1.28736	0.643678	−	0.765296i	$-0.277408\pi$
$19$	5.61146	1.28736	0.643678	+	0.765296i	$0.277408\pi$
$20$	0.0205303	0.00459072
$21$	5.09020	1.11077
$22$	−4.04326	−0.862026
$23$	7.47510	1.55867	0.779333	−	0.626610i	$-0.215558\pi$
$23$	7.47510	1.55867	0.779333	+	0.626610i	$0.215558\pi$
$24$	1.00000	0.204124
$25$	−4.99958	−0.999916
$26$	−2.31576	−0.454157
$27$	1.00000	0.192450
$28$	5.09020	0.961957
$29$	9.16732	1.70233	0.851164	−	0.524899i	$-0.175897\pi$
$29$	9.16732	1.70233	0.851164	+	0.524899i	$0.175897\pi$
$30$	0.0205303	0.00374831
$31$	−5.48620	−0.985350	−0.492675	−	0.870213i	$-0.663981\pi$
$31$	−5.48620	−0.985350	−0.492675	+	0.870213i	$0.663981\pi$
$32$	1.00000	0.176777
$33$	−4.04326	−0.703842
$34$	1.00000	0.171499
$35$	0.104503	0.0176643
$36$	1.00000	0.166667
$37$	−8.15071	−1.33997	−0.669984	−	0.742375i	$-0.733699\pi$
$37$	−8.15071	−1.33997	−0.669984	+	0.742375i	$0.733699\pi$
$38$	5.61146	0.910299
$39$	−2.31576	−0.370818
$40$	0.0205303	0.00324613
$41$	3.48348	0.544028	0.272014	−	0.962293i	$-0.412310\pi$
$41$	3.48348	0.544028	0.272014	+	0.962293i	$0.412310\pi$
$42$	5.09020	0.785435
$43$	3.27176	0.498939	0.249469	−	0.968383i	$-0.419744\pi$
$43$	3.27176	0.498939	0.249469	+	0.968383i	$0.419744\pi$
$44$	−4.04326	−0.609545
$45$	0.0205303	0.00306048
$46$	7.47510	1.10214
$47$	−10.0597	−1.46736	−0.733678	−	0.679498i	$-0.762198\pi$
$47$	−10.0597	−1.46736	−0.733678	+	0.679498i	$0.762198\pi$
$48$	1.00000	0.144338
$49$	18.9101	2.70144
$50$	−4.99958	−0.707047
$51$	1.00000	0.140028
$52$	−2.31576	−0.321138
$53$	4.57111	0.627890	0.313945	−	0.949441i	$-0.398349\pi$
$53$	4.57111	0.627890	0.313945	+	0.949441i	$0.398349\pi$
$54$	1.00000	0.136083
$55$	−0.0830095	−0.0111930
$56$	5.09020	0.680206
$57$	5.61146	0.743256
$58$	9.16732	1.20373
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	0.0205303	0.00265045
$61$	−7.67929	−0.983232	−0.491616	−	0.870812i	$-0.663594\pi$
$61$	−7.67929	−0.983232	−0.491616	+	0.870812i	$0.663594\pi$
$62$	−5.48620	−0.696748
$63$	5.09020	0.641305
$64$	1.00000	0.125000
$65$	−0.0475432	−0.00589701
$66$	−4.04326	−0.497691
$67$	9.93096	1.21326	0.606630	−	0.794985i	$-0.292521\pi$
$67$	9.93096	1.21326	0.606630	+	0.794985i	$0.292521\pi$
$68$	1.00000	0.121268
$69$	7.47510	0.899896
$70$	0.104503	0.0124905
$71$	1.56437	0.185656	0.0928281	−	0.995682i	$-0.470409\pi$
$71$	1.56437	0.185656	0.0928281	+	0.995682i	$0.470409\pi$
$72$	1.00000	0.117851
$73$	6.72077	0.786607	0.393304	−	0.919409i	$-0.371332\pi$
$73$	6.72077	0.786607	0.393304	+	0.919409i	$0.371332\pi$
$74$	−8.15071	−0.947501
$75$	−4.99958	−0.577302
$76$	5.61146	0.643678
$77$	−20.5810	−2.34542
$78$	−2.31576	−0.262208
$79$	8.14748	0.916663	0.458331	−	0.888781i	$-0.348447\pi$
$79$	8.14748	0.916663	0.458331	+	0.888781i	$0.348447\pi$
$80$	0.0205303	0.00229536
$81$	1.00000	0.111111
$82$	3.48348	0.384686
$83$	17.2237	1.89054	0.945272	−	0.326284i	$-0.105797\pi$
$83$	17.2237	1.89054	0.945272	+	0.326284i	$0.105797\pi$
$84$	5.09020	0.555386
$85$	0.0205303	0.00222683
$86$	3.27176	0.352803
$87$	9.16732	0.982840
$88$	−4.04326	−0.431013
$89$	−15.7818	−1.67287	−0.836434	−	0.548068i	$-0.815364\pi$
$89$	−15.7818	−1.67287	−0.836434	+	0.548068i	$0.815364\pi$
$90$	0.0205303	0.00216409
$91$	−11.7877	−1.23568
$92$	7.47510	0.779333
$93$	−5.48620	−0.568892
$94$	−10.0597	−1.03758
$95$	0.115205	0.0118198
$96$	1.00000	0.102062
$97$	−0.494479	−0.0502068	−0.0251034	−	0.999685i	$-0.507991\pi$
$97$	−0.494479	−0.0502068	−0.0251034	+	0.999685i	$0.507991\pi$
$98$	18.9101	1.91021
$99$	−4.04326	−0.406363
$100$	−4.99958	−0.499958
$101$	8.06215	0.802214	0.401107	−	0.916031i	$-0.368626\pi$
$101$	8.06215	0.802214	0.401107	+	0.916031i	$0.368626\pi$
$102$	1.00000	0.0990148
$103$	−19.2400	−1.89578	−0.947888	−	0.318605i	$-0.896786\pi$
$103$	−19.2400	−1.89578	−0.947888	+	0.318605i	$0.896786\pi$
$104$	−2.31576	−0.227079
$105$	0.104503	0.0101985
$106$	4.57111	0.443986
$107$	12.8498	1.24223	0.621117	−	0.783718i	$-0.286679\pi$
$107$	12.8498	1.24223	0.621117	+	0.783718i	$0.286679\pi$
$108$	1.00000	0.0962250
$109$	−9.65890	−0.925155	−0.462578	−	0.886579i	$-0.653075\pi$
$109$	−9.65890	−0.925155	−0.462578	+	0.886579i	$0.653075\pi$
$110$	−0.0830095	−0.00791464
$111$	−8.15071	−0.773631
$112$	5.09020	0.480978
$113$	7.29960	0.686689	0.343344	−	0.939210i	$-0.388440\pi$
$113$	7.29960	0.686689	0.343344	+	0.939210i	$0.388440\pi$
$114$	5.61146	0.525561
$115$	0.153466	0.0143108
$116$	9.16732	0.851164
$117$	−2.31576	−0.214092
$118$	−1.00000	−0.0920575
$119$	5.09020	0.466618
$120$	0.0205303	0.00187415
$121$	5.34797	0.486179
$122$	−7.67929	−0.695250
$123$	3.48348	0.314095
$124$	−5.48620	−0.492675
$125$	−0.205295	−0.0183621
$126$	5.09020	0.453471
$127$	−5.19542	−0.461019	−0.230510	−	0.973070i	$-0.574039\pi$
$127$	−5.19542	−0.461019	−0.230510	+	0.973070i	$0.574039\pi$
$128$	1.00000	0.0883883
$129$	3.27176	0.288063
$130$	−0.0475432	−0.00416981
$131$	14.6140	1.27683	0.638414	−	0.769693i	$-0.279591\pi$
$131$	14.6140	1.27683	0.638414	+	0.769693i	$0.279591\pi$
$132$	−4.04326	−0.351921
$133$	28.5634	2.47676
$134$	9.93096	0.857904
$135$	0.0205303	0.00176697
$136$	1.00000	0.0857493
$137$	−5.79706	−0.495276	−0.247638	−	0.968853i	$-0.579654\pi$
$137$	−5.79706	−0.495276	−0.247638	+	0.968853i	$0.579654\pi$
$138$	7.47510	0.636322
$139$	−20.9113	−1.77367	−0.886836	−	0.462084i	$-0.847102\pi$
$139$	−20.9113	−1.77367	−0.886836	+	0.462084i	$0.847102\pi$
$140$	0.104503	0.00883215
$141$	−10.0597	−0.847178
$142$	1.56437	0.131279
$143$	9.36321	0.782991
$144$	1.00000	0.0833333
$145$	0.188208	0.0156298
$146$	6.72077	0.556215
$147$	18.9101	1.55968
$148$	−8.15071	−0.669984
$149$	21.0478	1.72430	0.862151	−	0.506651i	$-0.169117\pi$
$149$	21.0478	1.72430	0.862151	+	0.506651i	$0.169117\pi$
$150$	−4.99958	−0.408214
$151$	−8.94659	−0.728063	−0.364031	−	0.931387i	$-0.618600\pi$
$151$	−8.94659	−0.728063	−0.364031	+	0.931387i	$0.618600\pi$
$152$	5.61146	0.455149
$153$	1.00000	0.0808452
$154$	−20.5810	−1.65846
$155$	−0.112633	−0.00904693
$156$	−2.31576	−0.185409
$157$	−24.4302	−1.94974	−0.974870	−	0.222775i	$-0.928489\pi$
$157$	−24.4302	−1.94974	−0.974870	+	0.222775i	$0.928489\pi$
$158$	8.14748	0.648179
$159$	4.57111	0.362513
$160$	0.0205303	0.00162306
$161$	38.0497	2.99874
$162$	1.00000	0.0785674
$163$	14.6912	1.15070	0.575351	−	0.817907i	$-0.304866\pi$
$163$	14.6912	1.15070	0.575351	+	0.817907i	$0.304866\pi$
$164$	3.48348	0.272014
$165$	−0.0830095	−0.00646228
$166$	17.2237	1.33682
$167$	2.49428	0.193013	0.0965064	−	0.995332i	$-0.469233\pi$
$167$	2.49428	0.193013	0.0965064	+	0.995332i	$0.469233\pi$
$168$	5.09020	0.392717
$169$	−7.63727	−0.587483
$170$	0.0205303	0.00157460
$171$	5.61146	0.429119
$172$	3.27176	0.249469
$173$	−5.03033	−0.382449	−0.191225	−	0.981546i	$-0.561246\pi$
$173$	−5.03033	−0.382449	−0.191225	+	0.981546i	$0.561246\pi$
$174$	9.16732	0.694973
$175$	−25.4488	−1.92375
$176$	−4.04326	−0.304772
$177$	−1.00000	−0.0751646
$178$	−15.7818	−1.18290
$179$	−7.71830	−0.576893	−0.288446	−	0.957496i	$-0.593139\pi$
$179$	−7.71830	−0.576893	−0.288446	+	0.957496i	$0.593139\pi$
$180$	0.0205303	0.00153024
$181$	−8.13107	−0.604377	−0.302189	−	0.953248i	$-0.597717\pi$
$181$	−8.13107	−0.604377	−0.302189	+	0.953248i	$0.597717\pi$
$182$	−11.7877	−0.873759
$183$	−7.67929	−0.567669
$184$	7.47510	0.551071
$185$	−0.167337	−0.0123028
$186$	−5.48620	−0.402268
$187$	−4.04326	−0.295673
$188$	−10.0597	−0.733678
$189$	5.09020	0.370257
$190$	0.115205	0.00835785
$191$	16.9341	1.22531	0.612654	−	0.790351i	$-0.290102\pi$
$191$	16.9341	1.22531	0.612654	+	0.790351i	$0.290102\pi$
$192$	1.00000	0.0721688
$193$	−12.5799	−0.905523	−0.452761	−	0.891632i	$-0.649561\pi$
$193$	−12.5799	−0.905523	−0.452761	+	0.891632i	$0.649561\pi$
$194$	−0.494479	−0.0355016
$195$	−0.0475432	−0.00340464
$196$	18.9101	1.35072
$197$	−10.5544	−0.751969	−0.375984	−	0.926626i	$-0.622695\pi$
$197$	−10.5544	−0.751969	−0.375984	+	0.926626i	$0.622695\pi$
$198$	−4.04326	−0.287342
$199$	27.5119	1.95026	0.975132	−	0.221626i	$-0.0711364\pi$
$199$	27.5119	1.95026	0.975132	+	0.221626i	$0.0711364\pi$
$200$	−4.99958	−0.353524
$201$	9.93096	0.700476
$202$	8.06215	0.567251
$203$	46.6635	3.27513
$204$	1.00000	0.0700140
$205$	0.0715169	0.00499496
$206$	−19.2400	−1.34052
$207$	7.47510	0.519555
$208$	−2.31576	−0.160569
$209$	−22.6886	−1.56940
$210$	0.104503	0.00721142
$211$	−9.27724	−0.638672	−0.319336	−	0.947642i	$-0.603460\pi$
$211$	−9.27724	−0.638672	−0.319336	+	0.947642i	$0.603460\pi$
$212$	4.57111	0.313945
$213$	1.56437	0.107189
$214$	12.8498	0.878393
$215$	0.0671703	0.00458098
$216$	1.00000	0.0680414
$217$	−27.9258	−1.89573
$218$	−9.65890	−0.654183
$219$	6.72077	0.454148
$220$	−0.0830095	−0.00559650
$221$	−2.31576	−0.155775
$222$	−8.15071	−0.547040
$223$	3.67623	0.246179	0.123089	−	0.992396i	$-0.460720\pi$
$223$	3.67623	0.246179	0.123089	+	0.992396i	$0.460720\pi$
$224$	5.09020	0.340103
$225$	−4.99958	−0.333305
$226$	7.29960	0.485562
$227$	−23.6401	−1.56905	−0.784524	−	0.620098i	$-0.787093\pi$
$227$	−23.6401	−1.56905	−0.784524	+	0.620098i	$0.787093\pi$
$228$	5.61146	0.371628
$229$	26.2433	1.73421	0.867103	−	0.498128i	$-0.165979\pi$
$229$	26.2433	1.73421	0.867103	+	0.498128i	$0.165979\pi$
$230$	0.153466	0.0101193
$231$	−20.5810	−1.35413
$232$	9.16732	0.601864
$233$	−9.81573	−0.643050	−0.321525	−	0.946901i	$-0.604195\pi$
$233$	−9.81573	−0.643050	−0.321525	+	0.946901i	$0.604195\pi$
$234$	−2.31576	−0.151386
$235$	−0.206528	−0.0134724
$236$	−1.00000	−0.0650945
$237$	8.14748	0.529236
$238$	5.09020	0.329948
$239$	−8.19014	−0.529776	−0.264888	−	0.964279i	$-0.585335\pi$
$239$	−8.19014	−0.529776	−0.264888	+	0.964279i	$0.585335\pi$
$240$	0.0205303	0.00132523
$241$	−12.9768	−0.835909	−0.417954	−	0.908468i	$-0.637253\pi$
$241$	−12.9768	−0.835909	−0.417954	+	0.908468i	$0.637253\pi$
$242$	5.34797	0.343781
$243$	1.00000	0.0641500
$244$	−7.67929	−0.491616
$245$	0.388231	0.0248031
$246$	3.48348	0.222098
$247$	−12.9948	−0.826837
$248$	−5.48620	−0.348374
$249$	17.2237	1.09151
$250$	−0.205295	−0.0129840
$251$	−3.16254	−0.199618	−0.0998088	−	0.995007i	$-0.531823\pi$
$251$	−3.16254	−0.199618	−0.0998088	+	0.995007i	$0.531823\pi$
$252$	5.09020	0.320652
$253$	−30.2238	−1.90015
$254$	−5.19542	−0.325990
$255$	0.0205303	0.00128566
$256$	1.00000	0.0625000
$257$	−20.5059	−1.27913	−0.639563	−	0.768739i	$-0.720885\pi$
$257$	−20.5059	−1.27913	−0.639563	+	0.768739i	$0.720885\pi$
$258$	3.27176	0.203691
$259$	−41.4887	−2.57798
$260$	−0.0475432	−0.00294850
$261$	9.16732	0.567443
$262$	14.6140	0.902854
$263$	24.6228	1.51831	0.759154	−	0.650911i	$-0.225613\pi$
$263$	24.6228	1.51831	0.759154	+	0.650911i	$0.225613\pi$
$264$	−4.04326	−0.248846
$265$	0.0938464	0.00576494
$266$	28.5634	1.75134
$267$	−15.7818	−0.965831
$268$	9.93096	0.606630
$269$	−4.15686	−0.253448	−0.126724	−	0.991938i	$-0.540446\pi$
$269$	−4.15686	−0.253448	−0.126724	+	0.991938i	$0.540446\pi$
$270$	0.0205303	0.00124944
$271$	−18.3291	−1.11341	−0.556706	−	0.830709i	$-0.687935\pi$
$271$	−18.3291	−1.11341	−0.556706	+	0.830709i	$0.687935\pi$
$272$	1.00000	0.0606339
$273$	−11.7877	−0.713421
$274$	−5.79706	−0.350213
$275$	20.2146	1.21899
$276$	7.47510	0.449948
$277$	12.8955	0.774816	0.387408	−	0.921908i	$-0.373371\pi$
$277$	12.8955	0.774816	0.387408	+	0.921908i	$0.373371\pi$
$278$	−20.9113	−1.25418
$279$	−5.48620	−0.328450
$280$	0.104503	0.00624527
$281$	−20.0722	−1.19741	−0.598703	−	0.800971i	$-0.704317\pi$
$281$	−20.0722	−1.19741	−0.598703	+	0.800971i	$0.704317\pi$
$282$	−10.0597	−0.599045
$283$	−14.2551	−0.847376	−0.423688	−	0.905808i	$-0.639265\pi$
$283$	−14.2551	−0.847376	−0.423688	+	0.905808i	$0.639265\pi$
$284$	1.56437	0.0928281
$285$	0.115205	0.00682415
$286$	9.36321	0.553658
$287$	17.7316	1.04666
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	0.188208	0.0110520
$291$	−0.494479	−0.0289869
$292$	6.72077	0.393304
$293$	−15.5634	−0.909221	−0.454611	−	0.890690i	$-0.650222\pi$
$293$	−15.5634	−0.909221	−0.454611	+	0.890690i	$0.650222\pi$
$294$	18.9101	1.10286
$295$	−0.0205303	−0.00119532
$296$	−8.15071	−0.473750
$297$	−4.04326	−0.234614
$298$	21.0478	1.21927
$299$	−17.3105	−1.00109
$300$	−4.99958	−0.288651
$301$	16.6539	0.959916
$302$	−8.94659	−0.514818
$303$	8.06215	0.463158
$304$	5.61146	0.321839
$305$	−0.157658	−0.00902748
$306$	1.00000	0.0571662
$307$	22.1021	1.26144	0.630718	−	0.776012i	$-0.282760\pi$
$307$	22.1021	1.26144	0.630718	+	0.776012i	$0.282760\pi$
$308$	−20.5810	−1.17271
$309$	−19.2400	−1.09453
$310$	−0.112633	−0.00639715
$311$	−1.45902	−0.0827333	−0.0413666	−	0.999144i	$-0.513171\pi$
$311$	−1.45902	−0.0827333	−0.0413666	+	0.999144i	$0.513171\pi$
$312$	−2.31576	−0.131104
$313$	4.98929	0.282011	0.141006	−	0.990009i	$-0.454966\pi$
$313$	4.98929	0.282011	0.141006	+	0.990009i	$0.454966\pi$
$314$	−24.4302	−1.37867
$315$	0.104503	0.00588810
$316$	8.14748	0.458331
$317$	−12.0128	−0.674705	−0.337352	−	0.941378i	$-0.609531\pi$
$317$	−12.0128	−0.674705	−0.337352	+	0.941378i	$0.609531\pi$
$318$	4.57111	0.256335
$319$	−37.0659	−2.07529
$320$	0.0205303	0.00114768
$321$	12.8498	0.717205
$322$	38.0497	2.12043
$323$	5.61146	0.312230
$324$	1.00000	0.0555556
$325$	11.5778	0.642221
$326$	14.6912	0.813669
$327$	−9.65890	−0.534139
$328$	3.48348	0.192343
$329$	−51.2058	−2.82306
$330$	−0.0830095	−0.00456952
$331$	−0.592516	−0.0325676	−0.0162838	−	0.999867i	$-0.505184\pi$
$331$	−0.592516	−0.0325676	−0.0162838	+	0.999867i	$0.505184\pi$
$332$	17.2237	0.945272
$333$	−8.15071	−0.446656
$334$	2.49428	0.136481
$335$	0.203886	0.0111395
$336$	5.09020	0.277693
$337$	7.17648	0.390928	0.195464	−	0.980711i	$-0.437379\pi$
$337$	7.17648	0.390928	0.195464	+	0.980711i	$0.437379\pi$
$338$	−7.63727	−0.415413
$339$	7.29960	0.396460
$340$	0.0205303	0.00111341
$341$	22.1821	1.20123
$342$	5.61146	0.303433
$343$	60.6248	3.27343
$344$	3.27176	0.176402
$345$	0.153466	0.00826234
$346$	−5.03033	−0.270432
$347$	22.8155	1.22480	0.612401	−	0.790547i	$-0.290204\pi$
$347$	22.8155	1.22480	0.612401	+	0.790547i	$0.290204\pi$
$348$	9.16732	0.491420
$349$	−27.0145	−1.44605	−0.723026	−	0.690821i	$-0.757249\pi$
$349$	−27.0145	−1.44605	−0.723026	+	0.690821i	$0.757249\pi$
$350$	−25.4488	−1.36030
$351$	−2.31576	−0.123606
$352$	−4.04326	−0.215507
$353$	12.5687	0.668963	0.334482	−	0.942402i	$-0.391439\pi$
$353$	12.5687	0.668963	0.334482	+	0.942402i	$0.391439\pi$
$354$	−1.00000	−0.0531494
$355$	0.0321169	0.00170459
$356$	−15.7818	−0.836434
$357$	5.09020	0.269402
$358$	−7.71830	−0.407925
$359$	−12.9040	−0.681049	−0.340525	−	0.940236i	$-0.610605\pi$
$359$	−12.9040	−0.681049	−0.340525	+	0.940236i	$0.610605\pi$
$360$	0.0205303	0.00108204
$361$	12.4884	0.657287
$362$	−8.13107	−0.427359
$363$	5.34797	0.280696
$364$	−11.7877	−0.617841
$365$	0.137980	0.00722218
$366$	−7.67929	−0.401403
$367$	2.59114	0.135256	0.0676282	−	0.997711i	$-0.478457\pi$
$367$	2.59114	0.135256	0.0676282	+	0.997711i	$0.478457\pi$
$368$	7.47510	0.389666
$369$	3.48348	0.181343
$370$	−0.167337	−0.00869942
$371$	23.2679	1.20801
$372$	−5.48620	−0.284446
$373$	−28.6555	−1.48372	−0.741862	−	0.670553i	$-0.766057\pi$
$373$	−28.6555	−1.48372	−0.741862	+	0.670553i	$0.766057\pi$
$374$	−4.04326	−0.209072
$375$	−0.205295	−0.0106014
$376$	−10.0597	−0.518788
$377$	−21.2293	−1.09336
$378$	5.09020	0.261812
$379$	−6.69876	−0.344092	−0.172046	−	0.985089i	$-0.555038\pi$
$379$	−6.69876	−0.344092	−0.172046	+	0.985089i	$0.555038\pi$
$380$	0.115205	0.00590989
$381$	−5.19542	−0.266169
$382$	16.9341	0.866424
$383$	31.4415	1.60659	0.803293	−	0.595585i	$-0.203080\pi$
$383$	31.4415	1.60659	0.803293	+	0.595585i	$0.203080\pi$
$384$	1.00000	0.0510310
$385$	−0.422535	−0.0215344
$386$	−12.5799	−0.640301
$387$	3.27176	0.166313
$388$	−0.494479	−0.0251034
$389$	7.35188	0.372755	0.186378	−	0.982478i	$-0.440325\pi$
$389$	7.35188	0.372755	0.186378	+	0.982478i	$0.440325\pi$
$390$	−0.0475432	−0.00240744
$391$	7.47510	0.378032
$392$	18.9101	0.955105
$393$	14.6140	0.737177
$394$	−10.5544	−0.531722
$395$	0.167270	0.00841628
$396$	−4.04326	−0.203182
$397$	36.8992	1.85192	0.925958	−	0.377627i	$-0.123260\pi$
$397$	36.8992	1.85192	0.925958	+	0.377627i	$0.123260\pi$
$398$	27.5119	1.37904
$399$	28.5634	1.42996
$400$	−4.99958	−0.249979
$401$	2.08851	0.104295	0.0521477	−	0.998639i	$-0.483393\pi$
$401$	2.08851	0.104295	0.0521477	+	0.998639i	$0.483393\pi$
$402$	9.93096	0.495311
$403$	12.7047	0.632866
$404$	8.06215	0.401107
$405$	0.0205303	0.00102016
$406$	46.6635	2.31587
$407$	32.9555	1.63354
$408$	1.00000	0.0495074
$409$	7.24314	0.358150	0.179075	−	0.983835i	$-0.442689\pi$
$409$	7.24314	0.358150	0.179075	+	0.983835i	$0.442689\pi$
$410$	0.0715169	0.00353197
$411$	−5.79706	−0.285948
$412$	−19.2400	−0.947888
$413$	−5.09020	−0.250472
$414$	7.47510	0.367381
$415$	0.353607	0.0173579
$416$	−2.31576	−0.113539
$417$	−20.9113	−1.02403
$418$	−22.6886	−1.10974
$419$	−13.1220	−0.641052	−0.320526	−	0.947240i	$-0.603860\pi$
$419$	−13.1220	−0.641052	−0.320526	+	0.947240i	$0.603860\pi$
$420$	0.104503	0.00509924
$421$	−15.2105	−0.741315	−0.370658	−	0.928770i	$-0.620868\pi$
$421$	−15.2105	−0.741315	−0.370658	+	0.928770i	$0.620868\pi$
$422$	−9.27724	−0.451609
$423$	−10.0597	−0.489118
$424$	4.57111	0.221993
$425$	−4.99958	−0.242515
$426$	1.56437	0.0757938
$427$	−39.0891	−1.89165
$428$	12.8498	0.621117
$429$	9.36321	0.452060
$430$	0.0671703	0.00323924
$431$	−5.67283	−0.273251	−0.136625	−	0.990623i	$-0.543626\pi$
$431$	−5.67283	−0.273251	−0.136625	+	0.990623i	$0.543626\pi$
$432$	1.00000	0.0481125
$433$	21.4100	1.02890	0.514450	−	0.857520i	$-0.327996\pi$
$433$	21.4100	1.02890	0.514450	+	0.857520i	$0.327996\pi$
$434$	−27.9258	−1.34048
$435$	0.188208	0.00902388
$436$	−9.65890	−0.462578
$437$	41.9462	2.00656
$438$	6.72077	0.321131
$439$	−36.1334	−1.72456	−0.862278	−	0.506436i	$-0.830963\pi$
$439$	−36.1334	−1.72456	−0.862278	+	0.506436i	$0.830963\pi$
$440$	−0.0830095	−0.00395732
$441$	18.9101	0.900481
$442$	−2.31576	−0.110149
$443$	7.53548	0.358021	0.179011	−	0.983847i	$-0.442710\pi$
$443$	7.53548	0.358021	0.179011	+	0.983847i	$0.442710\pi$
$444$	−8.15071	−0.386816
$445$	−0.324005	−0.0153593
$446$	3.67623	0.174075
$447$	21.0478	0.995527
$448$	5.09020	0.240489
$449$	−2.28599	−0.107883	−0.0539414	−	0.998544i	$-0.517178\pi$
$449$	−2.28599	−0.107883	−0.0539414	+	0.998544i	$0.517178\pi$
$450$	−4.99958	−0.235682
$451$	−14.0846	−0.663219
$452$	7.29960	0.343344
$453$	−8.94659	−0.420347
$454$	−23.6401	−1.10948
$455$	−0.242004	−0.0113453
$456$	5.61146	0.262781
$457$	−5.17379	−0.242020	−0.121010	−	0.992651i	$-0.538613\pi$
$457$	−5.17379	−0.242020	−0.121010	+	0.992651i	$0.538613\pi$
$458$	26.2433	1.22627
$459$	1.00000	0.0466760
$460$	0.153466	0.00715539
$461$	0.920367	0.0428658	0.0214329	−	0.999770i	$-0.493177\pi$
$461$	0.920367	0.0428658	0.0214329	+	0.999770i	$0.493177\pi$
$462$	−20.5810	−0.957515
$463$	−13.7386	−0.638486	−0.319243	−	0.947673i	$-0.603429\pi$
$463$	−13.7386	−0.638486	−0.319243	+	0.947673i	$0.603429\pi$
$464$	9.16732	0.425582
$465$	−0.112633	−0.00522325
$466$	−9.81573	−0.454705
$467$	−32.3898	−1.49882	−0.749412	−	0.662104i	$-0.769664\pi$
$467$	−32.3898	−1.49882	−0.749412	+	0.662104i	$0.769664\pi$
$468$	−2.31576	−0.107046
$469$	50.5505	2.33421
$470$	−0.206528	−0.00952644
$471$	−24.4302	−1.12568
$472$	−1.00000	−0.0460287
$473$	−13.2286	−0.608251
$474$	8.14748	0.374226
$475$	−28.0549	−1.28725
$476$	5.09020	0.233309
$477$	4.57111	0.209297
$478$	−8.19014	−0.374608
$479$	36.6024	1.67240	0.836202	−	0.548421i	$-0.184771\pi$
$479$	36.6024	1.67240	0.836202	+	0.548421i	$0.184771\pi$
$480$	0.0205303	0.000937076 0
$481$	18.8751	0.860629
$482$	−12.9768	−0.591077
$483$	38.0497	1.73132
$484$	5.34797	0.243090
$485$	−0.0101518	−0.000460970 0
$486$	1.00000	0.0453609
$487$	−8.35034	−0.378390	−0.189195	−	0.981940i	$-0.560588\pi$
$487$	−8.35034	−0.378390	−0.189195	+	0.981940i	$0.560588\pi$
$488$	−7.67929	−0.347625
$489$	14.6912	0.664358
$490$	0.388231	0.0175385
$491$	−13.3702	−0.603390	−0.301695	−	0.953404i	$-0.597552\pi$
$491$	−13.3702	−0.603390	−0.301695	+	0.953404i	$0.597552\pi$
$492$	3.48348	0.157047
$493$	9.16732	0.412875
$494$	−12.9948	−0.584662
$495$	−0.0830095	−0.00373100
$496$	−5.48620	−0.246338
$497$	7.96294	0.357186
$498$	17.2237	0.771811
$499$	27.6053	1.23578	0.617890	−	0.786264i	$-0.287987\pi$
$499$	27.6053	1.23578	0.617890	+	0.786264i	$0.287987\pi$
$500$	−0.205295	−0.00918105
$501$	2.49428	0.111436
$502$	−3.16254	−0.141151
$503$	16.3262	0.727948	0.363974	−	0.931409i	$-0.381420\pi$
$503$	16.3262	0.727948	0.363974	+	0.931409i	$0.381420\pi$
$504$	5.09020	0.226735
$505$	0.165518	0.00736547
$506$	−30.2238	−1.34361
$507$	−7.63727	−0.339183
$508$	−5.19542	−0.230510
$509$	32.7367	1.45103	0.725514	−	0.688208i	$-0.241602\pi$
$509$	32.7367	1.45103	0.725514	+	0.688208i	$0.241602\pi$
$510$	0.0205303	0.000909098 0
$511$	34.2101	1.51336
$512$	1.00000	0.0441942
$513$	5.61146	0.247752
$514$	−20.5059	−0.904478
$515$	−0.395004	−0.0174059
$516$	3.27176	0.144031
$517$	40.6739	1.78884
$518$	−41.4887	−1.82291
$519$	−5.03033	−0.220807
$520$	−0.0475432	−0.00208491
$521$	−7.98004	−0.349612	−0.174806	−	0.984603i	$-0.555930\pi$
$521$	−7.98004	−0.349612	−0.174806	+	0.984603i	$0.555930\pi$
$522$	9.16732	0.401243
$523$	1.50461	0.0657918	0.0328959	−	0.999459i	$-0.489527\pi$
$523$	1.50461	0.0657918	0.0328959	+	0.999459i	$0.489527\pi$
$524$	14.6140	0.638414
$525$	−25.4488	−1.11068
$526$	24.6228	1.07361
$527$	−5.48620	−0.238983
$528$	−4.04326	−0.175960
$529$	32.8771	1.42944
$530$	0.0938464	0.00407643
$531$	−1.00000	−0.0433963
$532$	28.5634	1.23838
$533$	−8.06688	−0.349416
$534$	−15.7818	−0.682946
$535$	0.263810	0.0114055
$536$	9.93096	0.428952
$537$	−7.71830	−0.333069
$538$	−4.15686	−0.179215
$539$	−76.4585	−3.29330
$540$	0.0205303	0.000883484 0
$541$	28.6296	1.23088	0.615442	−	0.788182i	$-0.288977\pi$
$541$	28.6296	1.23088	0.615442	+	0.788182i	$0.288977\pi$
$542$	−18.3291	−0.787302
$543$	−8.13107	−0.348937
$544$	1.00000	0.0428746
$545$	−0.198300	−0.00849425
$546$	−11.7877	−0.504465
$547$	4.23122	0.180914	0.0904569	−	0.995900i	$-0.471167\pi$
$547$	4.23122	0.180914	0.0904569	+	0.995900i	$0.471167\pi$
$548$	−5.79706	−0.247638
$549$	−7.67929	−0.327744
$550$	20.2146	0.861954
$551$	51.4420	2.19150
$552$	7.47510	0.318161
$553$	41.4723	1.76358
$554$	12.8955	0.547878
$555$	−0.167337	−0.00710305
$556$	−20.9113	−0.886836
$557$	−6.10225	−0.258561	−0.129280	−	0.991608i	$-0.541267\pi$
$557$	−6.10225	−0.258561	−0.129280	+	0.991608i	$0.541267\pi$
$558$	−5.48620	−0.232249
$559$	−7.57660	−0.320456
$560$	0.104503	0.00441607
$561$	−4.04326	−0.170707
$562$	−20.0722	−0.846694
$563$	17.1385	0.722300	0.361150	−	0.932508i	$-0.382384\pi$
$563$	17.1385	0.722300	0.361150	+	0.932508i	$0.382384\pi$
$564$	−10.0597	−0.423589
$565$	0.149863	0.00630479
$566$	−14.2551	−0.599185
$567$	5.09020	0.213768
$568$	1.56437	0.0656394
$569$	4.93785	0.207005	0.103503	−	0.994629i	$-0.466995\pi$
$569$	4.93785	0.207005	0.103503	+	0.994629i	$0.466995\pi$
$570$	0.115205	0.00482541
$571$	−6.18069	−0.258654	−0.129327	−	0.991602i	$-0.541282\pi$
$571$	−6.18069	−0.258654	−0.129327	+	0.991602i	$0.541282\pi$
$572$	9.36321	0.391495
$573$	16.9341	0.707432
$574$	17.7316	0.740102
$575$	−37.3723	−1.55853
$576$	1.00000	0.0416667
$577$	−9.48122	−0.394708	−0.197354	−	0.980332i	$-0.563235\pi$
$577$	−9.48122	−0.394708	−0.197354	+	0.980332i	$0.563235\pi$
$578$	1.00000	0.0415945
$579$	−12.5799	−0.522804
$580$	0.188208	0.00781491
$581$	87.6719	3.63724
$582$	−0.494479	−0.0204968
$583$	−18.4822	−0.765455
$584$	6.72077	0.278108
$585$	−0.0475432	−0.00196567
$586$	−15.5634	−0.642917
$587$	−46.5343	−1.92068	−0.960338	−	0.278837i	$-0.910051\pi$
$587$	−46.5343	−1.92068	−0.960338	+	0.278837i	$0.910051\pi$
$588$	18.9101	0.779840
$589$	−30.7856	−1.26850
$590$	−0.0205303	−0.000845220 0
$591$	−10.5544	−0.434149
$592$	−8.15071	−0.334992
$593$	−42.0287	−1.72591	−0.862956	−	0.505279i	$-0.831390\pi$
$593$	−42.0287	−1.72591	−0.862956	+	0.505279i	$0.831390\pi$
$594$	−4.04326	−0.165897
$595$	0.104503	0.00428422
$596$	21.0478	0.862151
$597$	27.5119	1.12599
$598$	−17.3105	−0.707879
$599$	0.971714	0.0397032	0.0198516	−	0.999803i	$-0.493681\pi$
$599$	0.971714	0.0397032	0.0198516	+	0.999803i	$0.493681\pi$
$600$	−4.99958	−0.204107
$601$	−10.0631	−0.410481	−0.205241	−	0.978712i	$-0.565798\pi$
$601$	−10.0631	−0.410481	−0.205241	+	0.978712i	$0.565798\pi$
$602$	16.6539	0.678763
$603$	9.93096	0.404420
$604$	−8.94659	−0.364031
$605$	0.109796	0.00446382
$606$	8.06215	0.327502
$607$	1.27946	0.0519316	0.0259658	−	0.999663i	$-0.491734\pi$
$607$	1.27946	0.0519316	0.0259658	+	0.999663i	$0.491734\pi$
$608$	5.61146	0.227575
$609$	46.6635	1.89090
$610$	−0.157658	−0.00638339
$611$	23.2958	0.942446
$612$	1.00000	0.0404226
$613$	−31.5434	−1.27403	−0.637013	−	0.770853i	$-0.719830\pi$
$613$	−31.5434	−1.27403	−0.637013	+	0.770853i	$0.719830\pi$
$614$	22.1021	0.891970
$615$	0.0715169	0.00288384
$616$	−20.5810	−0.829232
$617$	18.9603	0.763312	0.381656	−	0.924305i	$-0.375354\pi$
$617$	18.9603	0.763312	0.381656	+	0.924305i	$0.375354\pi$
$618$	−19.2400	−0.773947
$619$	−12.3260	−0.495425	−0.247713	−	0.968834i	$-0.579679\pi$
$619$	−12.3260	−0.495425	−0.247713	+	0.968834i	$0.579679\pi$
$620$	−0.112633	−0.00452347
$621$	7.47510	0.299965
$622$	−1.45902	−0.0585013
$623$	−80.3325	−3.21845
$624$	−2.31576	−0.0927044
$625$	24.9937	0.999747
$626$	4.98929	0.199412
$627$	−22.6886	−0.906095
$628$	−24.4302	−0.974870
$629$	−8.15071	−0.324990
$630$	0.104503	0.00416351
$631$	−5.24580	−0.208832	−0.104416	−	0.994534i	$-0.533297\pi$
$631$	−5.24580	−0.208832	−0.104416	+	0.994534i	$0.533297\pi$
$632$	8.14748	0.324089
$633$	−9.27724	−0.368737
$634$	−12.0128	−0.477088
$635$	−0.106664	−0.00423282
$636$	4.57111	0.181256
$637$	−43.7912	−1.73507
$638$	−37.0659	−1.46745
$639$	1.56437	0.0618854
$640$	0.0205303	0.000811532 0
$641$	−18.4314	−0.727996	−0.363998	−	0.931400i	$-0.618588\pi$
$641$	−18.4314	−0.727996	−0.363998	+	0.931400i	$0.618588\pi$
$642$	12.8498	0.507140
$643$	15.4790	0.610433	0.305216	−	0.952283i	$-0.401271\pi$
$643$	15.4790	0.610433	0.305216	+	0.952283i	$0.401271\pi$
$644$	38.0497	1.49937
$645$	0.0671703	0.00264483
$646$	5.61146	0.220780
$647$	−4.10258	−0.161289	−0.0806446	−	0.996743i	$-0.525698\pi$
$647$	−4.10258	−0.161289	−0.0806446	+	0.996743i	$0.525698\pi$
$648$	1.00000	0.0392837
$649$	4.04326	0.158712
$650$	11.5778	0.454119
$651$	−27.9258	−1.09450
$652$	14.6912	0.575351
$653$	12.6456	0.494859	0.247430	−	0.968906i	$-0.420414\pi$
$653$	12.6456	0.494859	0.247430	+	0.968906i	$0.420414\pi$
$654$	−9.65890	−0.377693
$655$	0.300029	0.0117231
$656$	3.48348	0.136007
$657$	6.72077	0.262202
$658$	−51.2058	−1.99621
$659$	45.1501	1.75880	0.879400	−	0.476084i	$-0.157944\pi$
$659$	45.1501	1.75880	0.879400	+	0.476084i	$0.157944\pi$
$660$	−0.0830095	−0.00323114
$661$	−28.8921	−1.12377	−0.561887	−	0.827214i	$-0.689924\pi$
$661$	−28.8921	−1.12377	−0.561887	+	0.827214i	$0.689924\pi$
$662$	−0.592516	−0.0230288
$663$	−2.31576	−0.0899365
$664$	17.2237	0.668408
$665$	0.586416	0.0227402
$666$	−8.15071	−0.315834
$667$	68.5266	2.65336
$668$	2.49428	0.0965064
$669$	3.67623	0.142131
$670$	0.203886	0.00787679
$671$	31.0494	1.19865
$672$	5.09020	0.196359
$673$	−15.1678	−0.584677	−0.292338	−	0.956315i	$-0.594433\pi$
$673$	−15.1678	−0.584677	−0.292338	+	0.956315i	$0.594433\pi$
$674$	7.17648	0.276428
$675$	−4.99958	−0.192434
$676$	−7.63727	−0.293741
$677$	−19.3495	−0.743661	−0.371831	−	0.928301i	$-0.621270\pi$
$677$	−19.3495	−0.743661	−0.371831	+	0.928301i	$0.621270\pi$
$678$	7.29960	0.280339
$679$	−2.51700	−0.0965935
$680$	0.0205303	0.000787302 0
$681$	−23.6401	−0.905890
$682$	22.1821	0.849398
$683$	−40.9380	−1.56645	−0.783224	−	0.621740i	$-0.786426\pi$
$683$	−40.9380	−1.56645	−0.783224	+	0.621740i	$0.786426\pi$
$684$	5.61146	0.214559
$685$	−0.119015	−0.00454735
$686$	60.6248	2.31467
$687$	26.2433	1.00124
$688$	3.27176	0.124735
$689$	−10.5856	−0.403278
$690$	0.153466	0.00584235
$691$	32.0150	1.21791	0.608953	−	0.793206i	$-0.291590\pi$
$691$	32.0150	1.21791	0.608953	+	0.793206i	$0.291590\pi$
$692$	−5.03033	−0.191225
$693$	−20.5810	−0.781808
$694$	22.8155	0.866066
$695$	−0.429315	−0.0162849
$696$	9.16732	0.347486
$697$	3.48348	0.131946
$698$	−27.0145	−1.02251
$699$	−9.81573	−0.371265
$700$	−25.4488	−0.961876
$701$	10.8132	0.408408	0.204204	−	0.978928i	$-0.434539\pi$
$701$	10.8132	0.408408	0.204204	+	0.978928i	$0.434539\pi$
$702$	−2.31576	−0.0874026
$703$	−45.7374	−1.72502
$704$	−4.04326	−0.152386
$705$	−0.206528	−0.00777831
$706$	12.5687	0.473029
$707$	41.0379	1.54339
$708$	−1.00000	−0.0375823
$709$	4.08597	0.153452	0.0767260	−	0.997052i	$-0.475553\pi$
$709$	4.08597	0.153452	0.0767260	+	0.997052i	$0.475553\pi$
$710$	0.0321169	0.00120533
$711$	8.14748	0.305554
$712$	−15.7818	−0.591448
$713$	−41.0099	−1.53583
$714$	5.09020	0.190496
$715$	0.192230	0.00718898
$716$	−7.71830	−0.288446
$717$	−8.19014	−0.305866
$718$	−12.9040	−0.481575
$719$	−26.3692	−0.983404	−0.491702	−	0.870764i	$-0.663625\pi$
$719$	−26.3692	−0.983404	−0.491702	+	0.870764i	$0.663625\pi$
$720$	0.0205303	0.000765120 0
$721$	−97.9355	−3.64731
$722$	12.4884	0.464772
$723$	−12.9768	−0.482612
$724$	−8.13107	−0.302189
$725$	−45.8327	−1.70219
$726$	5.34797	0.198482
$727$	18.0558	0.669652	0.334826	−	0.942280i	$-0.391323\pi$
$727$	18.0558	0.669652	0.334826	+	0.942280i	$0.391323\pi$
$728$	−11.7877	−0.436880
$729$	1.00000	0.0370370
$730$	0.137980	0.00510685
$731$	3.27176	0.121010
$732$	−7.67929	−0.283835
$733$	29.3496	1.08405	0.542026	−	0.840362i	$-0.317657\pi$
$733$	29.3496	1.08405	0.542026	+	0.840362i	$0.317657\pi$
$734$	2.59114	0.0956407
$735$	0.388231	0.0143201
$736$	7.47510	0.275536
$737$	−40.1535	−1.47907
$738$	3.48348	0.128229
$739$	−13.8646	−0.510017	−0.255009	−	0.966939i	$-0.582078\pi$
$739$	−13.8646	−0.510017	−0.255009	+	0.966939i	$0.582078\pi$
$740$	−0.167337	−0.00615142
$741$	−12.9948	−0.477375
$742$	23.2679	0.854190
$743$	−33.8587	−1.24216	−0.621078	−	0.783749i	$-0.713305\pi$
$743$	−33.8587	−1.24216	−0.621078	+	0.783749i	$0.713305\pi$
$744$	−5.48620	−0.201134
$745$	0.432118	0.0158316
$746$	−28.6555	−1.04915
$747$	17.2237	0.630181
$748$	−4.04326	−0.147836
$749$	65.4079	2.38995
$750$	−0.205295	−0.00749630
$751$	−44.1097	−1.60959	−0.804793	−	0.593555i	$-0.797724\pi$
$751$	−44.1097	−1.60959	−0.804793	+	0.593555i	$0.797724\pi$
$752$	−10.0597	−0.366839
$753$	−3.16254	−0.115249
$754$	−21.2293	−0.773125
$755$	−0.183676	−0.00668466
$756$	5.09020	0.185129
$757$	−20.3561	−0.739856	−0.369928	−	0.929060i	$-0.620618\pi$
$757$	−20.3561	−0.739856	−0.369928	+	0.929060i	$0.620618\pi$
$758$	−6.69876	−0.243310
$759$	−30.2238	−1.09705
$760$	0.115205	0.00417892
$761$	−32.5340	−1.17936	−0.589678	−	0.807638i	$-0.700745\pi$
$761$	−32.5340	−1.17936	−0.589678	+	0.807638i	$0.700745\pi$
$762$	−5.19542	−0.188210
$763$	−49.1657	−1.77992
$764$	16.9341	0.612654
$765$	0.0205303	0.000742275 0
$766$	31.4415	1.13603
$767$	2.31576	0.0836171
$768$	1.00000	0.0360844
$769$	−38.4208	−1.38549	−0.692745	−	0.721183i	$-0.743599\pi$
$769$	−38.4208	−1.38549	−0.692745	+	0.721183i	$0.743599\pi$
$770$	−0.422535	−0.0152271
$771$	−20.5059	−0.738504
$772$	−12.5799	−0.452761
$773$	−10.6005	−0.381273	−0.190637	−	0.981661i	$-0.561055\pi$
$773$	−10.6005	−0.381273	−0.190637	+	0.981661i	$0.561055\pi$
$774$	3.27176	0.117601
$775$	27.4287	0.985267
$776$	−0.494479	−0.0177508
$777$	−41.4887	−1.48840
$778$	7.35188	0.263578
$779$	19.5474	0.700358
$780$	−0.0475432	−0.00170232
$781$	−6.32514	−0.226331
$782$	7.47510	0.267309
$783$	9.16732	0.327613
$784$	18.9101	0.675361
$785$	−0.501559	−0.0179014
$786$	14.6140	0.521263
$787$	−24.5916	−0.876596	−0.438298	−	0.898830i	$-0.644419\pi$
$787$	−24.5916	−0.876596	−0.438298	+	0.898830i	$0.644419\pi$
$788$	−10.5544	−0.375984
$789$	24.6228	0.876596
$790$	0.167270	0.00595121
$791$	37.1564	1.32113
$792$	−4.04326	−0.143671
$793$	17.7834	0.631505
$794$	36.8992	1.30950
$795$	0.0938464	0.00332839
$796$	27.5119	0.975132
$797$	19.2076	0.680367	0.340184	−	0.940359i	$-0.389511\pi$
$797$	19.2076	0.680367	0.340184	+	0.940359i	$0.389511\pi$
$798$	28.5634	1.01113
$799$	−10.0597	−0.355886
$800$	−4.99958	−0.176762
$801$	−15.7818	−0.557623
$802$	2.08851	0.0737480
$803$	−27.1739	−0.958944
$804$	9.93096	0.350238
$805$	0.781173	0.0275327
$806$	12.7047	0.447504
$807$	−4.15686	−0.146329
$808$	8.06215	0.283625
$809$	−25.3233	−0.890322	−0.445161	−	0.895451i	$-0.646853\pi$
$809$	−25.3233	−0.890322	−0.445161	+	0.895451i	$0.646853\pi$
$810$	0.0205303	0.000721362 0
$811$	−26.5046	−0.930704	−0.465352	−	0.885126i	$-0.654072\pi$
$811$	−26.5046	−0.930704	−0.465352	+	0.885126i	$0.654072\pi$
$812$	46.6635	1.63757
$813$	−18.3291	−0.642829
$814$	32.9555	1.15509
$815$	0.301614	0.0105651
$816$	1.00000	0.0350070
$817$	18.3593	0.642312
$818$	7.24314	0.253251
$819$	−11.7877	−0.411894
$820$	0.0715169	0.00249748
$821$	−33.5050	−1.16933	−0.584667	−	0.811273i	$-0.698775\pi$
$821$	−33.5050	−1.16933	−0.584667	+	0.811273i	$0.698775\pi$
$822$	−5.79706	−0.202196
$823$	29.2681	1.02022	0.510111	−	0.860109i	$-0.329604\pi$
$823$	29.2681	1.02022	0.510111	+	0.860109i	$0.329604\pi$
$824$	−19.2400	−0.670258
$825$	20.2146	0.703782
$826$	−5.09020	−0.177111
$827$	−50.3826	−1.75197	−0.875987	−	0.482335i	$-0.839789\pi$
$827$	−50.3826	−1.75197	−0.875987	+	0.482335i	$0.839789\pi$
$828$	7.47510	0.259778
$829$	−40.8142	−1.41753	−0.708767	−	0.705443i	$-0.750748\pi$
$829$	−40.8142	−1.41753	−0.708767	+	0.705443i	$0.750748\pi$
$830$	0.353607	0.0122739
$831$	12.8955	0.447340
$832$	−2.31576	−0.0802844
$833$	18.9101	0.655197
$834$	−20.9113	−0.724099
$835$	0.0512083	0.00177213
$836$	−22.6886	−0.784701
$837$	−5.48620	−0.189631
$838$	−13.1220	−0.453292
$839$	0.249231	0.00860441	0.00430221	−	0.999991i	$-0.498631\pi$
$839$	0.249231	0.00860441	0.00430221	+	0.999991i	$0.498631\pi$
$840$	0.104503	0.00360571
$841$	55.0398	1.89792
$842$	−15.2105	−0.524189
$843$	−20.0722	−0.691322
$844$	−9.27724	−0.319336
$845$	−0.156796	−0.00539393
$846$	−10.0597	−0.345859
$847$	27.2222	0.935367
$848$	4.57111	0.156973
$849$	−14.2551	−0.489233
$850$	−4.99958	−0.171484
$851$	−60.9274	−2.08856
$852$	1.56437	0.0535943
$853$	−34.0004	−1.16415	−0.582076	−	0.813135i	$-0.697759\pi$
$853$	−34.0004	−1.16415	−0.582076	+	0.813135i	$0.697759\pi$
$854$	−39.0891	−1.33760
$855$	0.115205	0.00393993
$856$	12.8498	0.439196
$857$	18.2778	0.624358	0.312179	−	0.950023i	$-0.398941\pi$
$857$	18.2778	0.624358	0.312179	+	0.950023i	$0.398941\pi$
$858$	9.36321	0.319655
$859$	29.1321	0.993974	0.496987	−	0.867758i	$-0.334440\pi$
$859$	29.1321	0.993974	0.496987	+	0.867758i	$0.334440\pi$
$860$	0.0671703	0.00229049
$861$	17.7316	0.604291
$862$	−5.67283	−0.193217
$863$	−18.8615	−0.642053	−0.321026	−	0.947070i	$-0.604028\pi$
$863$	−18.8615	−0.642053	−0.321026	+	0.947070i	$0.604028\pi$
$864$	1.00000	0.0340207
$865$	−0.103274	−0.00351143
$866$	21.4100	0.727543
$867$	1.00000	0.0339618
$868$	−27.9258	−0.947865
$869$	−32.9424	−1.11749
$870$	0.188208	0.00638085
$871$	−22.9977	−0.779246
$872$	−9.65890	−0.327092
$873$	−0.494479	−0.0167356
$874$	41.9462	1.41885
$875$	−1.04499	−0.0353271
$876$	6.72077	0.227074
$877$	−28.6581	−0.967715	−0.483857	−	0.875147i	$-0.660765\pi$
$877$	−28.6581	−0.967715	−0.483857	+	0.875147i	$0.660765\pi$
$878$	−36.1334	−1.21944
$879$	−15.5634	−0.524939
$880$	−0.0830095	−0.00279825
$881$	−6.74561	−0.227265	−0.113633	−	0.993523i	$-0.536249\pi$
$881$	−6.74561	−0.227265	−0.113633	+	0.993523i	$0.536249\pi$
$882$	18.9101	0.636737
$883$	38.2047	1.28569	0.642845	−	0.765996i	$-0.277754\pi$
$883$	38.2047	1.28569	0.642845	+	0.765996i	$0.277754\pi$
$884$	−2.31576	−0.0778873
$885$	−0.0205303	−0.000690119 0
$886$	7.53548	0.253159
$887$	−32.4593	−1.08988	−0.544938	−	0.838476i	$-0.683447\pi$
$887$	−32.4593	−1.08988	−0.544938	+	0.838476i	$0.683447\pi$
$888$	−8.15071	−0.273520
$889$	−26.4457	−0.886961
$890$	−0.324005	−0.0108607
$891$	−4.04326	−0.135454
$892$	3.67623	0.123089
$893$	−56.4495	−1.88901
$894$	21.0478	0.703944
$895$	−0.158459	−0.00529670
$896$	5.09020	0.170052
$897$	−17.3105	−0.577981
$898$	−2.28599	−0.0762846
$899$	−50.2937	−1.67739
$900$	−4.99958	−0.166653
$901$	4.57111	0.152286
$902$	−14.0846	−0.468966
$903$	16.6539	0.554208
$904$	7.29960	0.242781
$905$	−0.166933	−0.00554905
$906$	−8.94659	−0.297230
$907$	−6.64233	−0.220555	−0.110277	−	0.993901i	$-0.535174\pi$
$907$	−6.64233	−0.220555	−0.110277	+	0.993901i	$0.535174\pi$
$908$	−23.6401	−0.784524
$909$	8.06215	0.267405
$910$	−0.242004	−0.00802236
$911$	−0.181258	−0.00600535	−0.00300267	−	0.999995i	$-0.500956\pi$
$911$	−0.181258	−0.00600535	−0.00300267	+	0.999995i	$0.500956\pi$
$912$	5.61146	0.185814
$913$	−69.6398	−2.30474
$914$	−5.17379	−0.171134
$915$	−0.157658	−0.00521202
$916$	26.2433	0.867103
$917$	74.3880	2.45651
$918$	1.00000	0.0330049
$919$	−3.04884	−0.100572	−0.0502861	−	0.998735i	$-0.516013\pi$
$919$	−3.04884	−0.100572	−0.0502861	+	0.998735i	$0.516013\pi$
$920$	0.153466	0.00505963
$921$	22.1021	0.728291
$922$	0.920367	0.0303107
$923$	−3.62269	−0.119242
$924$	−20.5810	−0.677065
$925$	40.7501	1.33986
$926$	−13.7386	−0.451478
$927$	−19.2400	−0.631925
$928$	9.16732	0.300932
$929$	−11.2647	−0.369582	−0.184791	−	0.982778i	$-0.559161\pi$
$929$	−11.2647	−0.369582	−0.184791	+	0.982778i	$0.559161\pi$
$930$	−0.112633	−0.00369339
$931$	106.113	3.47772
$932$	−9.81573	−0.321525
$933$	−1.45902	−0.0477661
$934$	−32.3898	−1.05983
$935$	−0.0830095	−0.00271470
$936$	−2.31576	−0.0756929
$937$	−0.571682	−0.0186760	−0.00933801	−	0.999956i	$-0.502972\pi$
$937$	−0.571682	−0.0186760	−0.00933801	+	0.999956i	$0.502972\pi$
$938$	50.5505	1.65053
$939$	4.98929	0.162819
$940$	−0.206528	−0.00673621
$941$	−36.3965	−1.18649	−0.593246	−	0.805021i	$-0.702154\pi$
$941$	−36.3965	−1.18649	−0.593246	+	0.805021i	$0.702154\pi$
$942$	−24.4302	−0.795978
$943$	26.0393	0.847957
$944$	−1.00000	−0.0325472
$945$	0.104503	0.00339949
$946$	−13.2286	−0.430099
$947$	7.84581	0.254954	0.127477	−	0.991841i	$-0.459312\pi$
$947$	7.84581	0.254954	0.127477	+	0.991841i	$0.459312\pi$
$948$	8.14748	0.264618
$949$	−15.5637	−0.505218
$950$	−28.0549	−0.910222
$951$	−12.0128	−0.389541
$952$	5.09020	0.164974
$953$	−7.54055	−0.244262	−0.122131	−	0.992514i	$-0.538973\pi$
$953$	−7.54055	−0.244262	−0.122131	+	0.992514i	$0.538973\pi$
$954$	4.57111	0.147995
$955$	0.347662	0.0112501
$956$	−8.19014	−0.264888
$957$	−37.0659	−1.19817
$958$	36.6024	1.18257
$959$	−29.5082	−0.952869
$960$	0.0205303	0.000662613 0
$961$	−0.901629	−0.0290848
$962$	18.8751	0.608556
$963$	12.8498	0.414078
$964$	−12.9768	−0.417954
$965$	−0.258270	−0.00831400
$966$	38.0497	1.22423
$967$	−25.0437	−0.805351	−0.402675	−	0.915343i	$-0.631920\pi$
$967$	−25.0437	−0.805351	−0.402675	+	0.915343i	$0.631920\pi$
$968$	5.34797	0.171890
$969$	5.61146	0.180266
$970$	−0.0101518	−0.000325955 0
$971$	60.8848	1.95389	0.976944	−	0.213496i	$-0.0684852\pi$
$971$	60.8848	1.95389	0.976944	+	0.213496i	$0.0684852\pi$
$972$	1.00000	0.0320750
$973$	−106.443	−3.41239
$974$	−8.35034	−0.267562
$975$	11.5778	0.370786
$976$	−7.67929	−0.245808
$977$	33.2489	1.06373	0.531864	−	0.846830i	$-0.321492\pi$
$977$	33.2489	1.06373	0.531864	+	0.846830i	$0.321492\pi$
$978$	14.6912	0.469772
$979$	63.8100	2.03938
$980$	0.388231	0.0124016
$981$	−9.65890	−0.308385
$982$	−13.3702	−0.426661
$983$	−11.8113	−0.376721	−0.188361	−	0.982100i	$-0.560317\pi$
$983$	−11.8113	−0.376721	−0.188361	+	0.982100i	$0.560317\pi$
$984$	3.48348	0.111049
$985$	−0.216685	−0.00690415
$986$	9.16732	0.291947
$987$	−51.2058	−1.62990
$988$	−12.9948	−0.413419
$989$	24.4567	0.777679
$990$	−0.0830095	−0.00263821
$991$	22.1309	0.703011	0.351506	−	0.936186i	$-0.385670\pi$
$991$	22.1309	0.703011	0.351506	+	0.936186i	$0.385670\pi$
$992$	−5.48620	−0.174187
$993$	−0.592516	−0.0188029
$994$	7.96294	0.252569
$995$	0.564827	0.0179062
$996$	17.2237	0.545753
$997$	45.2923	1.43442	0.717211	−	0.696856i	$-0.245419\pi$
$997$	45.2923	1.43442	0.717211	+	0.696856i	$0.245419\pi$
$998$	27.6053	0.873829
$999$	−8.15071	−0.257877

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bb.1.6	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bb.1.6	✓	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.0205303 q^{5} +1.00000 q^{6} +5.09020 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.0205303 q^{5} +1.00000 q^{6} +5.09020 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.0205303 q^{10} -4.04326 q^{11} +1.00000 q^{12} -2.31576 q^{13} +5.09020 q^{14} +0.0205303 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +5.61146 q^{19} +0.0205303 q^{20} +5.09020 q^{21} -4.04326 q^{22} +7.47510 q^{23} +1.00000 q^{24} -4.99958 q^{25} -2.31576 q^{26} +1.00000 q^{27} +5.09020 q^{28} +9.16732 q^{29} +0.0205303 q^{30} -5.48620 q^{31} +1.00000 q^{32} -4.04326 q^{33} +1.00000 q^{34} +0.104503 q^{35} +1.00000 q^{36} -8.15071 q^{37} +5.61146 q^{38} -2.31576 q^{39} +0.0205303 q^{40} +3.48348 q^{41} +5.09020 q^{42} +3.27176 q^{43} -4.04326 q^{44} +0.0205303 q^{45} +7.47510 q^{46} -10.0597 q^{47} +1.00000 q^{48} +18.9101 q^{49} -4.99958 q^{50} +1.00000 q^{51} -2.31576 q^{52} +4.57111 q^{53} +1.00000 q^{54} -0.0830095 q^{55} +5.09020 q^{56} +5.61146 q^{57} +9.16732 q^{58} -1.00000 q^{59} +0.0205303 q^{60} -7.67929 q^{61} -5.48620 q^{62} +5.09020 q^{63} +1.00000 q^{64} -0.0475432 q^{65} -4.04326 q^{66} +9.93096 q^{67} +1.00000 q^{68} +7.47510 q^{69} +0.104503 q^{70} +1.56437 q^{71} +1.00000 q^{72} +6.72077 q^{73} -8.15071 q^{74} -4.99958 q^{75} +5.61146 q^{76} -20.5810 q^{77} -2.31576 q^{78} +8.14748 q^{79} +0.0205303 q^{80} +1.00000 q^{81} +3.48348 q^{82} +17.2237 q^{83} +5.09020 q^{84} +0.0205303 q^{85} +3.27176 q^{86} +9.16732 q^{87} -4.04326 q^{88} -15.7818 q^{89} +0.0205303 q^{90} -11.7877 q^{91} +7.47510 q^{92} -5.48620 q^{93} -10.0597 q^{94} +0.115205 q^{95} +1.00000 q^{96} -0.494479 q^{97} +18.9101 q^{98} -4.04326 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9 + 4 * q^10 + 7 * q^11 + 13 * q^12 + 6 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 + 13 * q^17 + 13 * q^18 + 9 * q^19 + 4 * q^20 + 11 * q^21 + 7 * q^22 + 2 * q^23 + 13 * q^24 + 33 * q^25 + 6 * q^26 + 13 * q^27 + 11 * q^28 + 14 * q^29 + 4 * q^30 - 5 * q^31 + 13 * q^32 + 7 * q^33 + 13 * q^34 + 24 * q^35 + 13 * q^36 + 4 * q^37 + 9 * q^38 + 6 * q^39 + 4 * q^40 + 28 * q^41 + 11 * q^42 + q^43 + 7 * q^44 + 4 * q^45 + 2 * q^46 + 12 * q^47 + 13 * q^48 + 32 * q^49 + 33 * q^50 + 13 * q^51 + 6 * q^52 + 22 * q^53 + 13 * q^54 - 7 * q^55 + 11 * q^56 + 9 * q^57 + 14 * q^58 - 13 * q^59 + 4 * q^60 - 9 * q^61 - 5 * q^62 + 11 * q^63 + 13 * q^64 + 34 * q^65 + 7 * q^66 + 26 * q^67 + 13 * q^68 + 2 * q^69 + 24 * q^70 + 8 * q^71 + 13 * q^72 + 4 * q^73 + 4 * q^74 + 33 * q^75 + 9 * q^76 + 38 * q^77 + 6 * q^78 - 17 * q^79 + 4 * q^80 + 13 * q^81 + 28 * q^82 + 14 * q^83 + 11 * q^84 + 4 * q^85 + q^86 + 14 * q^87 + 7 * q^88 + 19 * q^89 + 4 * q^90 - 5 * q^91 + 2 * q^92 - 5 * q^93 + 12 * q^94 + 25 * q^95 + 13 * q^96 - 5 * q^97 + 32 * q^98 + 7 * q^99

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