LMFDB - Embedded newform 6018.2.a.v.1.4

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:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 21x^{7} + 42x^{6} + 121x^{5} - 127x^{4} - 141x^{3} + 27x^{2} + 26x - 1 $ x^9 - 3x^8 - 21x^7 + 42x^6 + 121x^5 - 127x^4 - 141x^3 + 27x^2 + 26x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.460972$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.539028 q^{5} +1.00000 q^{6} +0.211506 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.539028 q^{5} +1.00000 q^{6} +0.211506 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.539028 q^{10} -0.438866 q^{11} -1.00000 q^{12} -2.12175 q^{13} -0.211506 q^{14} -0.539028 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +1.46680 q^{19} +0.539028 q^{20} -0.211506 q^{21} +0.438866 q^{22} +5.56633 q^{23} +1.00000 q^{24} -4.70945 q^{25} +2.12175 q^{26} -1.00000 q^{27} +0.211506 q^{28} -4.54548 q^{29} +0.539028 q^{30} +4.41902 q^{31} -1.00000 q^{32} +0.438866 q^{33} +1.00000 q^{34} +0.114008 q^{35} +1.00000 q^{36} +6.05133 q^{37} -1.46680 q^{38} +2.12175 q^{39} -0.539028 q^{40} +3.13941 q^{41} +0.211506 q^{42} -12.5429 q^{43} -0.438866 q^{44} +0.539028 q^{45} -5.56633 q^{46} -3.68645 q^{47} -1.00000 q^{48} -6.95527 q^{49} +4.70945 q^{50} +1.00000 q^{51} -2.12175 q^{52} +3.44950 q^{53} +1.00000 q^{54} -0.236561 q^{55} -0.211506 q^{56} -1.46680 q^{57} +4.54548 q^{58} -1.00000 q^{59} -0.539028 q^{60} +7.40497 q^{61} -4.41902 q^{62} +0.211506 q^{63} +1.00000 q^{64} -1.14368 q^{65} -0.438866 q^{66} -5.96072 q^{67} -1.00000 q^{68} -5.56633 q^{69} -0.114008 q^{70} +16.5135 q^{71} -1.00000 q^{72} +15.6717 q^{73} -6.05133 q^{74} +4.70945 q^{75} +1.46680 q^{76} -0.0928228 q^{77} -2.12175 q^{78} -1.40882 q^{79} +0.539028 q^{80} +1.00000 q^{81} -3.13941 q^{82} -5.92017 q^{83} -0.211506 q^{84} -0.539028 q^{85} +12.5429 q^{86} +4.54548 q^{87} +0.438866 q^{88} -16.8839 q^{89} -0.539028 q^{90} -0.448764 q^{91} +5.56633 q^{92} -4.41902 q^{93} +3.68645 q^{94} +0.790646 q^{95} +1.00000 q^{96} -12.8379 q^{97} +6.95527 q^{98} -0.438866 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9} - 6 q^{10} + q^{11} - 9 q^{12} + 4 q^{13} + 11 q^{14} - 6 q^{15} + 9 q^{16} - 9 q^{17} - 9 q^{18} - 13 q^{19} + 6 q^{20} + 11 q^{21} - q^{22} - 6 q^{23} + 9 q^{24} + 9 q^{25} - 4 q^{26} - 9 q^{27} - 11 q^{28} + 10 q^{29} + 6 q^{30} + q^{31} - 9 q^{32} - q^{33} + 9 q^{34} + 6 q^{35} + 9 q^{36} - 2 q^{37} + 13 q^{38} - 4 q^{39} - 6 q^{40} + 20 q^{41} - 11 q^{42} - 17 q^{43} + q^{44} + 6 q^{45} + 6 q^{46} + 4 q^{47} - 9 q^{48} + 2 q^{49} - 9 q^{50} + 9 q^{51} + 4 q^{52} + 16 q^{53} + 9 q^{54} - 17 q^{55} + 11 q^{56} + 13 q^{57} - 10 q^{58} - 9 q^{59} - 6 q^{60} - 9 q^{61} - q^{62} - 11 q^{63} + 9 q^{64} + q^{66} - 8 q^{67} - 9 q^{68} + 6 q^{69} - 6 q^{70} - 8 q^{71} - 9 q^{72} - 20 q^{73} + 2 q^{74} - 9 q^{75} - 13 q^{76} - 32 q^{77} + 4 q^{78} - 29 q^{79} + 6 q^{80} + 9 q^{81} - 20 q^{82} - 16 q^{83} + 11 q^{84} - 6 q^{85} + 17 q^{86} - 10 q^{87} - q^{88} + 11 q^{89} - 6 q^{90} - 13 q^{91} - 6 q^{92} - q^{93} - 4 q^{94} + 5 q^{95} + 9 q^{96} + 17 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9 - 6 * q^10 + q^11 - 9 * q^12 + 4 * q^13 + 11 * q^14 - 6 * q^15 + 9 * q^16 - 9 * q^17 - 9 * q^18 - 13 * q^19 + 6 * q^20 + 11 * q^21 - q^22 - 6 * q^23 + 9 * q^24 + 9 * q^25 - 4 * q^26 - 9 * q^27 - 11 * q^28 + 10 * q^29 + 6 * q^30 + q^31 - 9 * q^32 - q^33 + 9 * q^34 + 6 * q^35 + 9 * q^36 - 2 * q^37 + 13 * q^38 - 4 * q^39 - 6 * q^40 + 20 * q^41 - 11 * q^42 - 17 * q^43 + q^44 + 6 * q^45 + 6 * q^46 + 4 * q^47 - 9 * q^48 + 2 * q^49 - 9 * q^50 + 9 * q^51 + 4 * q^52 + 16 * q^53 + 9 * q^54 - 17 * q^55 + 11 * q^56 + 13 * q^57 - 10 * q^58 - 9 * q^59 - 6 * q^60 - 9 * q^61 - q^62 - 11 * q^63 + 9 * q^64 + q^66 - 8 * q^67 - 9 * q^68 + 6 * q^69 - 6 * q^70 - 8 * q^71 - 9 * q^72 - 20 * q^73 + 2 * q^74 - 9 * q^75 - 13 * q^76 - 32 * q^77 + 4 * q^78 - 29 * q^79 + 6 * q^80 + 9 * q^81 - 20 * q^82 - 16 * q^83 + 11 * q^84 - 6 * q^85 + 17 * q^86 - 10 * q^87 - q^88 + 11 * q^89 - 6 * q^90 - 13 * q^91 - 6 * q^92 - q^93 - 4 * q^94 + 5 * q^95 + 9 * q^96 + 17 * q^97 - 2 * q^98 + 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
$5$	0.539028	0.241060	0.120530	−	0.992710i	$-0.461541\pi$
$5$	0.539028	0.241060	0.120530	+	0.992710i	$0.461541\pi$
$6$	1.00000	0.408248
$7$	0.211506	0.0799418	0.0399709	−	0.999201i	$-0.487273\pi$
$7$	0.211506	0.0799418	0.0399709	+	0.999201i	$0.487273\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.539028	−0.170455
$11$	−0.438866	−0.132323	−0.0661615	−	0.997809i	$-0.521075\pi$
$11$	−0.438866	−0.132323	−0.0661615	+	0.997809i	$0.521075\pi$
$12$	−1.00000	−0.288675
$13$	−2.12175	−0.588468	−0.294234	−	0.955733i	$-0.595064\pi$
$13$	−2.12175	−0.588468	−0.294234	+	0.955733i	$0.595064\pi$
$14$	−0.211506	−0.0565274
$15$	−0.539028	−0.139176
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	1.46680	0.336507	0.168254	−	0.985744i	$-0.446187\pi$
$19$	1.46680	0.336507	0.168254	+	0.985744i	$0.446187\pi$
$20$	0.539028	0.120530
$21$	−0.211506	−0.0461544
$22$	0.438866	0.0935665
$23$	5.56633	1.16066	0.580330	−	0.814381i	$-0.302924\pi$
$23$	5.56633	1.16066	0.580330	+	0.814381i	$0.302924\pi$
$24$	1.00000	0.204124
$25$	−4.70945	−0.941890
$26$	2.12175	0.416110
$27$	−1.00000	−0.192450
$28$	0.211506	0.0399709
$29$	−4.54548	−0.844074	−0.422037	−	0.906578i	$-0.638685\pi$
$29$	−4.54548	−0.844074	−0.422037	+	0.906578i	$0.638685\pi$
$30$	0.539028	0.0984125
$31$	4.41902	0.793679	0.396839	−	0.917888i	$-0.370107\pi$
$31$	4.41902	0.793679	0.396839	+	0.917888i	$0.370107\pi$
$32$	−1.00000	−0.176777
$33$	0.438866	0.0763967
$34$	1.00000	0.171499
$35$	0.114008	0.0192708
$36$	1.00000	0.166667
$37$	6.05133	0.994832	0.497416	−	0.867512i	$-0.334282\pi$
$37$	6.05133	0.994832	0.497416	+	0.867512i	$0.334282\pi$
$38$	−1.46680	−0.237946
$39$	2.12175	0.339752
$40$	−0.539028	−0.0852277
$41$	3.13941	0.490293	0.245146	−	0.969486i	$-0.421164\pi$
$41$	3.13941	0.490293	0.245146	+	0.969486i	$0.421164\pi$
$42$	0.211506	0.0326361
$43$	−12.5429	−1.91277	−0.956385	−	0.292110i	$-0.905643\pi$
$43$	−12.5429	−1.91277	−0.956385	+	0.292110i	$0.905643\pi$
$44$	−0.438866	−0.0661615
$45$	0.539028	0.0803535
$46$	−5.56633	−0.820711
$47$	−3.68645	−0.537724	−0.268862	−	0.963179i	$-0.586648\pi$
$47$	−3.68645	−0.537724	−0.268862	+	0.963179i	$0.586648\pi$
$48$	−1.00000	−0.144338
$49$	−6.95527	−0.993609
$50$	4.70945	0.666017
$51$	1.00000	0.140028
$52$	−2.12175	−0.294234
$53$	3.44950	0.473826	0.236913	−	0.971531i	$-0.423864\pi$
$53$	3.44950	0.473826	0.236913	+	0.971531i	$0.423864\pi$
$54$	1.00000	0.136083
$55$	−0.236561	−0.0318978
$56$	−0.211506	−0.0282637
$57$	−1.46680	−0.194282
$58$	4.54548	0.596851
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−0.539028	−0.0695882
$61$	7.40497	0.948109	0.474055	−	0.880495i	$-0.342790\pi$
$61$	7.40497	0.948109	0.474055	+	0.880495i	$0.342790\pi$
$62$	−4.41902	−0.561216
$63$	0.211506	0.0266473
$64$	1.00000	0.125000
$65$	−1.14368	−0.141856
$66$	−0.438866	−0.0540206
$67$	−5.96072	−0.728217	−0.364109	−	0.931356i	$-0.618626\pi$
$67$	−5.96072	−0.728217	−0.364109	+	0.931356i	$0.618626\pi$
$68$	−1.00000	−0.121268
$69$	−5.56633	−0.670107
$70$	−0.114008	−0.0136265
$71$	16.5135	1.95979	0.979893	−	0.199524i	$-0.0639394\pi$
$71$	16.5135	1.95979	0.979893	+	0.199524i	$0.0639394\pi$
$72$	−1.00000	−0.117851
$73$	15.6717	1.83423	0.917117	−	0.398617i	$-0.130510\pi$
$73$	15.6717	1.83423	0.917117	+	0.398617i	$0.130510\pi$
$74$	−6.05133	−0.703452
$75$	4.70945	0.543800
$76$	1.46680	0.168254
$77$	−0.0928228	−0.0105781
$78$	−2.12175	−0.240241
$79$	−1.40882	−0.158505	−0.0792525	−	0.996855i	$-0.525253\pi$
$79$	−1.40882	−0.158505	−0.0792525	+	0.996855i	$0.525253\pi$
$80$	0.539028	0.0602651
$81$	1.00000	0.111111
$82$	−3.13941	−0.346689
$83$	−5.92017	−0.649824	−0.324912	−	0.945744i	$-0.605335\pi$
$83$	−5.92017	−0.649824	−0.324912	+	0.945744i	$0.605335\pi$
$84$	−0.211506	−0.0230772
$85$	−0.539028	−0.0584658
$86$	12.5429	1.35253
$87$	4.54548	0.487327
$88$	0.438866	0.0467832
$89$	−16.8839	−1.78969	−0.894844	−	0.446378i	$-0.852714\pi$
$89$	−16.8839	−1.78969	−0.894844	+	0.446378i	$0.852714\pi$
$90$	−0.539028	−0.0568185
$91$	−0.448764	−0.0470432
$92$	5.56633	0.580330
$93$	−4.41902	−0.458231
$94$	3.68645	0.380229
$95$	0.790646	0.0811185
$96$	1.00000	0.102062
$97$	−12.8379	−1.30349	−0.651744	−	0.758439i	$-0.725962\pi$
$97$	−12.8379	−1.30349	−0.651744	+	0.758439i	$0.725962\pi$
$98$	6.95527	0.702588
$99$	−0.438866	−0.0441077
$100$	−4.70945	−0.470945
$101$	7.75113	0.771266	0.385633	−	0.922652i	$-0.373983\pi$
$101$	7.75113	0.771266	0.385633	+	0.922652i	$0.373983\pi$
$102$	−1.00000	−0.0990148
$103$	−16.0367	−1.58015	−0.790073	−	0.613013i	$-0.789957\pi$
$103$	−16.0367	−1.58015	−0.790073	+	0.613013i	$0.789957\pi$
$104$	2.12175	0.208055
$105$	−0.114008	−0.0111260
$106$	−3.44950	−0.335045
$107$	−1.24872	−0.120718	−0.0603591	−	0.998177i	$-0.519225\pi$
$107$	−1.24872	−0.120718	−0.0603591	+	0.998177i	$0.519225\pi$
$108$	−1.00000	−0.0962250
$109$	−6.85017	−0.656128	−0.328064	−	0.944656i	$-0.606396\pi$
$109$	−6.85017	−0.656128	−0.328064	+	0.944656i	$0.606396\pi$
$110$	0.236561	0.0225552
$111$	−6.05133	−0.574366
$112$	0.211506	0.0199855
$113$	−9.66703	−0.909397	−0.454699	−	0.890645i	$-0.650253\pi$
$113$	−9.66703	−0.909397	−0.454699	+	0.890645i	$0.650253\pi$
$114$	1.46680	0.137378
$115$	3.00041	0.279789
$116$	−4.54548	−0.422037
$117$	−2.12175	−0.196156
$118$	1.00000	0.0920575
$119$	−0.211506	−0.0193887
$120$	0.539028	0.0492063
$121$	−10.8074	−0.982491
$122$	−7.40497	−0.670414
$123$	−3.13941	−0.283071
$124$	4.41902	0.396839
$125$	−5.23366	−0.468113
$126$	−0.211506	−0.0188425
$127$	6.20893	0.550954	0.275477	−	0.961308i	$-0.411164\pi$
$127$	6.20893	0.550954	0.275477	+	0.961308i	$0.411164\pi$
$128$	−1.00000	−0.0883883
$129$	12.5429	1.10434
$130$	1.14368	0.100308
$131$	12.9595	1.13228	0.566139	−	0.824310i	$-0.308437\pi$
$131$	12.9595	1.13228	0.566139	+	0.824310i	$0.308437\pi$
$132$	0.438866	0.0381983
$133$	0.310237	0.0269010
$134$	5.96072	0.514928
$135$	−0.539028	−0.0463921
$136$	1.00000	0.0857493
$137$	−1.07309	−0.0916802	−0.0458401	−	0.998949i	$-0.514596\pi$
$137$	−1.07309	−0.0916802	−0.0458401	+	0.998949i	$0.514596\pi$
$138$	5.56633	0.473838
$139$	−22.5370	−1.91157	−0.955783	−	0.294071i	$-0.904990\pi$
$139$	−22.5370	−1.91157	−0.955783	+	0.294071i	$0.904990\pi$
$140$	0.114008	0.00963541
$141$	3.68645	0.310455
$142$	−16.5135	−1.38578
$143$	0.931164	0.0778678
$144$	1.00000	0.0833333
$145$	−2.45014	−0.203473
$146$	−15.6717	−1.29700
$147$	6.95527	0.573661
$148$	6.05133	0.497416
$149$	5.69941	0.466914	0.233457	−	0.972367i	$-0.424996\pi$
$149$	5.69941	0.466914	0.233457	+	0.972367i	$0.424996\pi$
$150$	−4.70945	−0.384525
$151$	−8.91010	−0.725094	−0.362547	−	0.931966i	$-0.618093\pi$
$151$	−8.91010	−0.725094	−0.362547	+	0.931966i	$0.618093\pi$
$152$	−1.46680	−0.118973
$153$	−1.00000	−0.0808452
$154$	0.0928228	0.00747988
$155$	2.38197	0.191325
$156$	2.12175	0.169876
$157$	13.2021	1.05364	0.526820	−	0.849977i	$-0.323384\pi$
$157$	13.2021	1.05364	0.526820	+	0.849977i	$0.323384\pi$
$158$	1.40882	0.112080
$159$	−3.44950	−0.273563
$160$	−0.539028	−0.0426139
$161$	1.17731	0.0927853
$162$	−1.00000	−0.0785674
$163$	9.32418	0.730326	0.365163	−	0.930944i	$-0.381013\pi$
$163$	9.32418	0.730326	0.365163	+	0.930944i	$0.381013\pi$
$164$	3.13941	0.245146
$165$	0.236561	0.0184162
$166$	5.92017	0.459495
$167$	−1.79156	−0.138635	−0.0693174	−	0.997595i	$-0.522082\pi$
$167$	−1.79156	−0.138635	−0.0693174	+	0.997595i	$0.522082\pi$
$168$	0.211506	0.0163181
$169$	−8.49817	−0.653705
$170$	0.539028	0.0413415
$171$	1.46680	0.112169
$172$	−12.5429	−0.956385
$173$	17.3103	1.31608	0.658041	−	0.752982i	$-0.271386\pi$
$173$	17.3103	1.31608	0.658041	+	0.752982i	$0.271386\pi$
$174$	−4.54548	−0.344592
$175$	−0.996078	−0.0752964
$176$	−0.438866	−0.0330807
$177$	1.00000	0.0751646
$178$	16.8839	1.26550
$179$	13.2098	0.987344	0.493672	−	0.869648i	$-0.335654\pi$
$179$	13.2098	0.987344	0.493672	+	0.869648i	$0.335654\pi$
$180$	0.539028	0.0401767
$181$	10.1745	0.756263	0.378131	−	0.925752i	$-0.376567\pi$
$181$	10.1745	0.756263	0.378131	+	0.925752i	$0.376567\pi$
$182$	0.448764	0.0332646
$183$	−7.40497	−0.547391
$184$	−5.56633	−0.410355
$185$	3.26183	0.239815
$186$	4.41902	0.324018
$187$	0.438866	0.0320930
$188$	−3.68645	−0.268862
$189$	−0.211506	−0.0153848
$190$	−0.790646	−0.0573595
$191$	−6.41217	−0.463968	−0.231984	−	0.972720i	$-0.574522\pi$
$191$	−6.41217	−0.463968	−0.231984	+	0.972720i	$0.574522\pi$
$192$	−1.00000	−0.0721688
$193$	−7.78514	−0.560387	−0.280193	−	0.959944i	$-0.590399\pi$
$193$	−7.78514	−0.560387	−0.280193	+	0.959944i	$0.590399\pi$
$194$	12.8379	0.921705
$195$	1.14368	0.0819008
$196$	−6.95527	−0.496805
$197$	3.71958	0.265009	0.132504	−	0.991182i	$-0.457698\pi$
$197$	3.71958	0.265009	0.132504	+	0.991182i	$0.457698\pi$
$198$	0.438866	0.0311888
$199$	13.4826	0.955757	0.477879	−	0.878426i	$-0.341406\pi$
$199$	13.4826	0.955757	0.477879	+	0.878426i	$0.341406\pi$
$200$	4.70945	0.333008
$201$	5.96072	0.420437
$202$	−7.75113	−0.545367
$203$	−0.961397	−0.0674769
$204$	1.00000	0.0700140
$205$	1.69223	0.118190
$206$	16.0367	1.11733
$207$	5.56633	0.386887
$208$	−2.12175	−0.147117
$209$	−0.643728	−0.0445276
$210$	0.114008	0.00786728
$211$	17.8998	1.23227	0.616136	−	0.787639i	$-0.288697\pi$
$211$	17.8998	1.23227	0.616136	+	0.787639i	$0.288697\pi$
$212$	3.44950	0.236913
$213$	−16.5135	−1.13148
$214$	1.24872	0.0853607
$215$	−6.76095	−0.461093
$216$	1.00000	0.0680414
$217$	0.934649	0.0634481
$218$	6.85017	0.463952
$219$	−15.6717	−1.05900
$220$	−0.236561	−0.0159489
$221$	2.12175	0.142724
$222$	6.05133	0.406138
$223$	−16.7755	−1.12337	−0.561684	−	0.827352i	$-0.689846\pi$
$223$	−16.7755	−1.12337	−0.561684	+	0.827352i	$0.689846\pi$
$224$	−0.211506	−0.0141319
$225$	−4.70945	−0.313963
$226$	9.66703	0.643041
$227$	−17.1186	−1.13620	−0.568100	−	0.822960i	$-0.692321\pi$
$227$	−17.1186	−1.13620	−0.568100	+	0.822960i	$0.692321\pi$
$228$	−1.46680	−0.0971412
$229$	−13.1200	−0.866993	−0.433496	−	0.901155i	$-0.642720\pi$
$229$	−13.1200	−0.866993	−0.433496	+	0.901155i	$0.642720\pi$
$230$	−3.00041	−0.197841
$231$	0.0928228	0.00610729
$232$	4.54548	0.298425
$233$	−4.42173	−0.289677	−0.144839	−	0.989455i	$-0.546266\pi$
$233$	−4.42173	−0.289677	−0.144839	+	0.989455i	$0.546266\pi$
$234$	2.12175	0.138703
$235$	−1.98710	−0.129624
$236$	−1.00000	−0.0650945
$237$	1.40882	0.0915129
$238$	0.211506	0.0137099
$239$	−2.99710	−0.193866	−0.0969331	−	0.995291i	$-0.530903\pi$
$239$	−2.99710	−0.193866	−0.0969331	+	0.995291i	$0.530903\pi$
$240$	−0.539028	−0.0347941
$241$	−9.85479	−0.634803	−0.317401	−	0.948291i	$-0.602810\pi$
$241$	−9.85479	−0.634803	−0.317401	+	0.948291i	$0.602810\pi$
$242$	10.8074	0.694726
$243$	−1.00000	−0.0641500
$244$	7.40497	0.474055
$245$	−3.74908	−0.239520
$246$	3.13941	0.200161
$247$	−3.11219	−0.198024
$248$	−4.41902	−0.280608
$249$	5.92017	0.375176
$250$	5.23366	0.331006
$251$	4.23635	0.267396	0.133698	−	0.991022i	$-0.457315\pi$
$251$	4.23635	0.267396	0.133698	+	0.991022i	$0.457315\pi$
$252$	0.211506	0.0133236
$253$	−2.44287	−0.153582
$254$	−6.20893	−0.389583
$255$	0.539028	0.0337552
$256$	1.00000	0.0625000
$257$	−21.3977	−1.33475	−0.667377	−	0.744720i	$-0.732583\pi$
$257$	−21.3977	−1.33475	−0.667377	+	0.744720i	$0.732583\pi$
$258$	−12.5429	−0.780885
$259$	1.27989	0.0795287
$260$	−1.14368	−0.0709282
$261$	−4.54548	−0.281358
$262$	−12.9595	−0.800641
$263$	18.4208	1.13588	0.567938	−	0.823071i	$-0.307741\pi$
$263$	18.4208	1.13588	0.567938	+	0.823071i	$0.307741\pi$
$264$	−0.438866	−0.0270103
$265$	1.85938	0.114221
$266$	−0.310237	−0.0190219
$267$	16.8839	1.03328
$268$	−5.96072	−0.364109
$269$	15.2337	0.928817	0.464409	−	0.885621i	$-0.346267\pi$
$269$	15.2337	0.928817	0.464409	+	0.885621i	$0.346267\pi$
$270$	0.539028	0.0328042
$271$	11.5622	0.702353	0.351177	−	0.936309i	$-0.385782\pi$
$271$	11.5622	0.702353	0.351177	+	0.936309i	$0.385782\pi$
$272$	−1.00000	−0.0606339
$273$	0.448764	0.0271604
$274$	1.07309	0.0648277
$275$	2.06682	0.124634
$276$	−5.56633	−0.335054
$277$	−3.45542	−0.207616	−0.103808	−	0.994597i	$-0.533103\pi$
$277$	−3.45542	−0.207616	−0.103808	+	0.994597i	$0.533103\pi$
$278$	22.5370	1.35168
$279$	4.41902	0.264560
$280$	−0.114008	−0.00681326
$281$	−20.8551	−1.24411	−0.622055	−	0.782973i	$-0.713702\pi$
$281$	−20.8551	−1.24411	−0.622055	+	0.782973i	$0.713702\pi$
$282$	−3.68645	−0.219525
$283$	−23.9561	−1.42404	−0.712021	−	0.702158i	$-0.752220\pi$
$283$	−23.9561	−1.42404	−0.712021	+	0.702158i	$0.752220\pi$
$284$	16.5135	0.979893
$285$	−0.790646	−0.0468338
$286$	−0.931164	−0.0550609
$287$	0.664004	0.0391949
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	2.45014	0.143877
$291$	12.8379	0.752569
$292$	15.6717	0.917117
$293$	13.9518	0.815074	0.407537	−	0.913189i	$-0.366388\pi$
$293$	13.9518	0.815074	0.407537	+	0.913189i	$0.366388\pi$
$294$	−6.95527	−0.405639
$295$	−0.539028	−0.0313834
$296$	−6.05133	−0.351726
$297$	0.438866	0.0254656
$298$	−5.69941	−0.330158
$299$	−11.8104	−0.683011
$300$	4.70945	0.271900
$301$	−2.65289	−0.152910
$302$	8.91010	0.512719
$303$	−7.75113	−0.445291
$304$	1.46680	0.0841268
$305$	3.99148	0.228552
$306$	1.00000	0.0571662
$307$	−26.2365	−1.49740	−0.748698	−	0.662911i	$-0.769321\pi$
$307$	−26.2365	−1.49740	−0.748698	+	0.662911i	$0.769321\pi$
$308$	−0.0928228	−0.00528907
$309$	16.0367	0.912297
$310$	−2.38197	−0.135287
$311$	−18.3831	−1.04241	−0.521205	−	0.853432i	$-0.674517\pi$
$311$	−18.3831	−1.04241	−0.521205	+	0.853432i	$0.674517\pi$
$312$	−2.12175	−0.120121
$313$	−33.8390	−1.91269	−0.956345	−	0.292239i	$-0.905600\pi$
$313$	−33.8390	−1.91269	−0.956345	+	0.292239i	$0.905600\pi$
$314$	−13.2021	−0.745036
$315$	0.114008	0.00642361
$316$	−1.40882	−0.0792525
$317$	6.55955	0.368421	0.184211	−	0.982887i	$-0.441027\pi$
$317$	6.55955	0.368421	0.184211	+	0.982887i	$0.441027\pi$
$318$	3.44950	0.193439
$319$	1.99485	0.111690
$320$	0.539028	0.0301326
$321$	1.24872	0.0696967
$322$	−1.17731	−0.0656091
$323$	−1.46680	−0.0816149
$324$	1.00000	0.0555556
$325$	9.99228	0.554272
$326$	−9.32418	−0.516419
$327$	6.85017	0.378816
$328$	−3.13941	−0.173345
$329$	−0.779708	−0.0429867
$330$	−0.236561	−0.0130222
$331$	6.13447	0.337181	0.168590	−	0.985686i	$-0.446078\pi$
$331$	6.13447	0.337181	0.168590	+	0.985686i	$0.446078\pi$
$332$	−5.92017	−0.324912
$333$	6.05133	0.331611
$334$	1.79156	0.0980296
$335$	−3.21299	−0.175544
$336$	−0.211506	−0.0115386
$337$	−0.735362	−0.0400577	−0.0200289	−	0.999799i	$-0.506376\pi$
$337$	−0.735362	−0.0400577	−0.0200289	+	0.999799i	$0.506376\pi$
$338$	8.49817	0.462240
$339$	9.66703	0.525041
$340$	−0.539028	−0.0292329
$341$	−1.93935	−0.105022
$342$	−1.46680	−0.0793155
$343$	−2.95163	−0.159373
$344$	12.5429	0.676266
$345$	−3.00041	−0.161536
$346$	−17.3103	−0.930610
$347$	−22.3832	−1.20159	−0.600796	−	0.799403i	$-0.705149\pi$
$347$	−22.3832	−1.20159	−0.600796	+	0.799403i	$0.705149\pi$
$348$	4.54548	0.243663
$349$	23.9783	1.28353	0.641765	−	0.766901i	$-0.278202\pi$
$349$	23.9783	1.28353	0.641765	+	0.766901i	$0.278202\pi$
$350$	0.996078	0.0532426
$351$	2.12175	0.113251
$352$	0.438866	0.0233916
$353$	33.9101	1.80485	0.902425	−	0.430847i	$-0.141785\pi$
$353$	33.9101	1.80485	0.902425	+	0.430847i	$0.141785\pi$
$354$	−1.00000	−0.0531494
$355$	8.90121	0.472427
$356$	−16.8839	−0.894844
$357$	0.211506	0.0111941
$358$	−13.2098	−0.698157
$359$	−4.45057	−0.234892	−0.117446	−	0.993079i	$-0.537471\pi$
$359$	−4.45057	−0.234892	−0.117446	+	0.993079i	$0.537471\pi$
$360$	−0.539028	−0.0284092
$361$	−16.8485	−0.886763
$362$	−10.1745	−0.534759
$363$	10.8074	0.567241
$364$	−0.448764	−0.0235216
$365$	8.44748	0.442161
$366$	7.40497	0.387064
$367$	−34.7031	−1.81149	−0.905744	−	0.423825i	$-0.860687\pi$
$367$	−34.7031	−1.81149	−0.905744	+	0.423825i	$0.860687\pi$
$368$	5.56633	0.290165
$369$	3.13941	0.163431
$370$	−3.26183	−0.169575
$371$	0.729591	0.0378785
$372$	−4.41902	−0.229115
$373$	−20.2021	−1.04602	−0.523012	−	0.852325i	$-0.675192\pi$
$373$	−20.2021	−1.04602	−0.523012	+	0.852325i	$0.675192\pi$
$374$	−0.438866	−0.0226932
$375$	5.23366	0.270265
$376$	3.68645	0.190114
$377$	9.64438	0.496711
$378$	0.211506	0.0108787
$379$	−23.6280	−1.21369	−0.606844	−	0.794821i	$-0.707565\pi$
$379$	−23.6280	−1.21369	−0.606844	+	0.794821i	$0.707565\pi$
$380$	0.790646	0.0405593
$381$	−6.20893	−0.318093
$382$	6.41217	0.328075
$383$	6.51425	0.332863	0.166431	−	0.986053i	$-0.446776\pi$
$383$	6.51425	0.332863	0.166431	+	0.986053i	$0.446776\pi$
$384$	1.00000	0.0510310
$385$	−0.0500341	−0.00254997
$386$	7.78514	0.396253
$387$	−12.5429	−0.637590
$388$	−12.8379	−0.651744
$389$	36.1981	1.83531	0.917657	−	0.397372i	$-0.130078\pi$
$389$	36.1981	1.83531	0.917657	+	0.397372i	$0.130078\pi$
$390$	−1.14368	−0.0579126
$391$	−5.56633	−0.281501
$392$	6.95527	0.351294
$393$	−12.9595	−0.653721
$394$	−3.71958	−0.187390
$395$	−0.759394	−0.0382093
$396$	−0.438866	−0.0220538
$397$	0.608826	0.0305561	0.0152781	−	0.999883i	$-0.495137\pi$
$397$	0.608826	0.0305561	0.0152781	+	0.999883i	$0.495137\pi$
$398$	−13.4826	−0.675823
$399$	−0.310237	−0.0155313
$400$	−4.70945	−0.235472
$401$	1.93078	0.0964187	0.0482094	−	0.998837i	$-0.484649\pi$
$401$	1.93078	0.0964187	0.0482094	+	0.998837i	$0.484649\pi$
$402$	−5.96072	−0.297294
$403$	−9.37605	−0.467054
$404$	7.75113	0.385633
$405$	0.539028	0.0267845
$406$	0.961397	0.0477134
$407$	−2.65572	−0.131639
$408$	−1.00000	−0.0495074
$409$	4.42657	0.218880	0.109440	−	0.993993i	$-0.465094\pi$
$409$	4.42657	0.218880	0.109440	+	0.993993i	$0.465094\pi$
$410$	−1.69223	−0.0835731
$411$	1.07309	0.0529316
$412$	−16.0367	−0.790073
$413$	−0.211506	−0.0104075
$414$	−5.56633	−0.273570
$415$	−3.19114	−0.156647
$416$	2.12175	0.104027
$417$	22.5370	1.10364
$418$	0.643728	0.0314858
$419$	0.140900	0.00688343	0.00344172	−	0.999994i	$-0.498904\pi$
$419$	0.140900	0.00688343	0.00344172	+	0.999994i	$0.498904\pi$
$420$	−0.114008	−0.00556301
$421$	0.179517	0.00874910	0.00437455	−	0.999990i	$-0.498608\pi$
$421$	0.179517	0.00874910	0.00437455	+	0.999990i	$0.498608\pi$
$422$	−17.8998	−0.871348
$423$	−3.68645	−0.179241
$424$	−3.44950	−0.167523
$425$	4.70945	0.228442
$426$	16.5135	0.800079
$427$	1.56620	0.0757936
$428$	−1.24872	−0.0603591
$429$	−0.931164	−0.0449570
$430$	6.76095	0.326042
$431$	−10.1503	−0.488922	−0.244461	−	0.969659i	$-0.578611\pi$
$431$	−10.1503	−0.488922	−0.244461	+	0.969659i	$0.578611\pi$
$432$	−1.00000	−0.0481125
$433$	11.9389	0.573748	0.286874	−	0.957968i	$-0.407384\pi$
$433$	11.9389	0.573748	0.286874	+	0.957968i	$0.407384\pi$
$434$	−0.934649	−0.0448646
$435$	2.45014	0.117475
$436$	−6.85017	−0.328064
$437$	8.16469	0.390570
$438$	15.6717	0.748823
$439$	−29.0640	−1.38715	−0.693575	−	0.720385i	$-0.743965\pi$
$439$	−29.0640	−1.38715	−0.693575	+	0.720385i	$0.743965\pi$
$440$	0.236561	0.0112776
$441$	−6.95527	−0.331203
$442$	−2.12175	−0.100921
$443$	−24.1041	−1.14522	−0.572611	−	0.819827i	$-0.694070\pi$
$443$	−24.1041	−1.14522	−0.572611	+	0.819827i	$0.694070\pi$
$444$	−6.05133	−0.287183
$445$	−9.10088	−0.431423
$446$	16.7755	0.794341
$447$	−5.69941	−0.269573
$448$	0.211506	0.00999273
$449$	−0.949278	−0.0447992	−0.0223996	−	0.999749i	$-0.507131\pi$
$449$	−0.949278	−0.0447992	−0.0223996	+	0.999749i	$0.507131\pi$
$450$	4.70945	0.222006
$451$	−1.37778	−0.0648770
$452$	−9.66703	−0.454699
$453$	8.91010	0.418633
$454$	17.1186	0.803414
$455$	−0.241896	−0.0113403
$456$	1.46680	0.0686892
$457$	−6.77458	−0.316901	−0.158451	−	0.987367i	$-0.550650\pi$
$457$	−6.77458	−0.316901	−0.158451	+	0.987367i	$0.550650\pi$
$458$	13.1200	0.613056
$459$	1.00000	0.0466760
$460$	3.00041	0.139895
$461$	−20.6995	−0.964073	−0.482037	−	0.876151i	$-0.660103\pi$
$461$	−20.6995	−0.964073	−0.482037	+	0.876151i	$0.660103\pi$
$462$	−0.0928228	−0.00431851
$463$	−27.0311	−1.25624	−0.628120	−	0.778116i	$-0.716175\pi$
$463$	−27.0311	−1.25624	−0.628120	+	0.778116i	$0.716175\pi$
$464$	−4.54548	−0.211019
$465$	−2.38197	−0.110461
$466$	4.42173	0.204833
$467$	−30.7402	−1.42249	−0.711244	−	0.702946i	$-0.751868\pi$
$467$	−30.7402	−1.42249	−0.711244	+	0.702946i	$0.751868\pi$
$468$	−2.12175	−0.0980780
$469$	−1.26073	−0.0582150
$470$	1.98710	0.0916581
$471$	−13.2021	−0.608319
$472$	1.00000	0.0460287
$473$	5.50463	0.253103
$474$	−1.40882	−0.0647094
$475$	−6.90782	−0.316953
$476$	−0.211506	−0.00969437
$477$	3.44950	0.157942
$478$	2.99710	0.137084
$479$	−40.0644	−1.83059	−0.915296	−	0.402783i	$-0.868043\pi$
$479$	−40.0644	−1.83059	−0.915296	+	0.402783i	$0.868043\pi$
$480$	0.539028	0.0246031
$481$	−12.8394	−0.585427
$482$	9.85479	0.448873
$483$	−1.17731	−0.0535696
$484$	−10.8074	−0.491245
$485$	−6.91996	−0.314219
$486$	1.00000	0.0453609
$487$	2.55945	0.115980	0.0579899	−	0.998317i	$-0.481531\pi$
$487$	2.55945	0.115980	0.0579899	+	0.998317i	$0.481531\pi$
$488$	−7.40497	−0.335207
$489$	−9.32418	−0.421654
$490$	3.74908	0.169366
$491$	−16.3895	−0.739647	−0.369824	−	0.929102i	$-0.620582\pi$
$491$	−16.3895	−0.739647	−0.369824	+	0.929102i	$0.620582\pi$
$492$	−3.13941	−0.141535
$493$	4.54548	0.204718
$494$	3.11219	0.140024
$495$	−0.236561	−0.0106326
$496$	4.41902	0.198420
$497$	3.49270	0.156669
$498$	−5.92017	−0.265289
$499$	−41.1581	−1.84249	−0.921244	−	0.388986i	$-0.872826\pi$
$499$	−41.1581	−1.84249	−0.921244	+	0.388986i	$0.872826\pi$
$500$	−5.23366	−0.234056
$501$	1.79156	0.0800408
$502$	−4.23635	−0.189078
$503$	−25.8571	−1.15291	−0.576454	−	0.817129i	$-0.695564\pi$
$503$	−25.8571	−1.15291	−0.576454	+	0.817129i	$0.695564\pi$
$504$	−0.211506	−0.00942124
$505$	4.17807	0.185922
$506$	2.44287	0.108599
$507$	8.49817	0.377417
$508$	6.20893	0.275477
$509$	−28.5132	−1.26383	−0.631914	−	0.775039i	$-0.717730\pi$
$509$	−28.5132	−1.26383	−0.631914	+	0.775039i	$0.717730\pi$
$510$	−0.539028	−0.0238685
$511$	3.31466	0.146632
$512$	−1.00000	−0.0441942
$513$	−1.46680	−0.0647608
$514$	21.3977	0.943814
$515$	−8.64424	−0.380911
$516$	12.5429	0.552169
$517$	1.61786	0.0711533
$518$	−1.27989	−0.0562353
$519$	−17.3103	−0.759840
$520$	1.14368	0.0501538
$521$	13.5418	0.593276	0.296638	−	0.954990i	$-0.404135\pi$
$521$	13.5418	0.593276	0.296638	+	0.954990i	$0.404135\pi$
$522$	4.54548	0.198950
$523$	11.0886	0.484872	0.242436	−	0.970167i	$-0.422054\pi$
$523$	11.0886	0.484872	0.242436	+	0.970167i	$0.422054\pi$
$524$	12.9595	0.566139
$525$	0.996078	0.0434724
$526$	−18.4208	−0.803186
$527$	−4.41902	−0.192495
$528$	0.438866	0.0190992
$529$	7.98403	0.347132
$530$	−1.85938	−0.0807662
$531$	−1.00000	−0.0433963
$532$	0.310237	0.0134505
$533$	−6.66104	−0.288522
$534$	−16.8839	−0.730637
$535$	−0.673094	−0.0291004
$536$	5.96072	0.257464
$537$	−13.2098	−0.570043
$538$	−15.2337	−0.656773
$539$	3.05243	0.131477
$540$	−0.539028	−0.0231961
$541$	−31.9945	−1.37555	−0.687776	−	0.725923i	$-0.741413\pi$
$541$	−31.9945	−1.37555	−0.687776	+	0.725923i	$0.741413\pi$
$542$	−11.5622	−0.496639
$543$	−10.1745	−0.436629
$544$	1.00000	0.0428746
$545$	−3.69243	−0.158166
$546$	−0.448764	−0.0192053
$547$	26.2785	1.12359	0.561793	−	0.827278i	$-0.310112\pi$
$547$	26.2785	1.12359	0.561793	+	0.827278i	$0.310112\pi$
$548$	−1.07309	−0.0458401
$549$	7.40497	0.316036
$550$	−2.06682	−0.0881293
$551$	−6.66731	−0.284037
$552$	5.56633	0.236919
$553$	−0.297975	−0.0126712
$554$	3.45542	0.146807
$555$	−3.26183	−0.138457
$556$	−22.5370	−0.955783
$557$	33.2841	1.41029	0.705147	−	0.709061i	$-0.250881\pi$
$557$	33.2841	1.41029	0.705147	+	0.709061i	$0.250881\pi$
$558$	−4.41902	−0.187072
$559$	26.6128	1.12560
$560$	0.114008	0.00481770
$561$	−0.438866	−0.0185289
$562$	20.8551	0.879719
$563$	−3.32705	−0.140218	−0.0701092	−	0.997539i	$-0.522335\pi$
$563$	−3.32705	−0.140218	−0.0701092	+	0.997539i	$0.522335\pi$
$564$	3.68645	0.155228
$565$	−5.21079	−0.219220
$566$	23.9561	1.00695
$567$	0.211506	0.00888243
$568$	−16.5135	−0.692889
$569$	18.1936	0.762713	0.381357	−	0.924428i	$-0.375457\pi$
$569$	18.1936	0.762713	0.381357	+	0.924428i	$0.375457\pi$
$570$	0.790646	0.0331165
$571$	−16.3061	−0.682389	−0.341194	−	0.939993i	$-0.610831\pi$
$571$	−16.3061	−0.682389	−0.341194	+	0.939993i	$0.610831\pi$
$572$	0.931164	0.0389339
$573$	6.41217	0.267872
$574$	−0.664004	−0.0277150
$575$	−26.2144	−1.09321
$576$	1.00000	0.0416667
$577$	29.3488	1.22181	0.610904	−	0.791705i	$-0.290806\pi$
$577$	29.3488	1.22181	0.610904	+	0.791705i	$0.290806\pi$
$578$	−1.00000	−0.0415945
$579$	7.78514	0.323539
$580$	−2.45014	−0.101736
$581$	−1.25215	−0.0519481
$582$	−12.8379	−0.532147
$583$	−1.51387	−0.0626980
$584$	−15.6717	−0.648500
$585$	−1.14368	−0.0472855
$586$	−13.9518	−0.576344
$587$	−28.6575	−1.18282	−0.591411	−	0.806371i	$-0.701429\pi$
$587$	−28.6575	−1.18282	−0.591411	+	0.806371i	$0.701429\pi$
$588$	6.95527	0.286830
$589$	6.48181	0.267078
$590$	0.539028	0.0221914
$591$	−3.71958	−0.153003
$592$	6.05133	0.248708
$593$	1.68840	0.0693341	0.0346671	−	0.999399i	$-0.488963\pi$
$593$	1.68840	0.0693341	0.0346671	+	0.999399i	$0.488963\pi$
$594$	−0.438866	−0.0180069
$595$	−0.114008	−0.00467386
$596$	5.69941	0.233457
$597$	−13.4826	−0.551807
$598$	11.8104	0.482962
$599$	40.8972	1.67101	0.835506	−	0.549481i	$-0.185174\pi$
$599$	40.8972	1.67101	0.835506	+	0.549481i	$0.185174\pi$
$600$	−4.70945	−0.192262
$601$	41.8343	1.70646	0.853228	−	0.521538i	$-0.174642\pi$
$601$	41.8343	1.70646	0.853228	+	0.521538i	$0.174642\pi$
$602$	2.65289	0.108124
$603$	−5.96072	−0.242739
$604$	−8.91010	−0.362547
$605$	−5.82549	−0.236840
$606$	7.75113	0.314868
$607$	−39.5868	−1.60678	−0.803389	−	0.595454i	$-0.796972\pi$
$607$	−39.5868	−1.60678	−0.803389	+	0.595454i	$0.796972\pi$
$608$	−1.46680	−0.0594866
$609$	0.961397	0.0389578
$610$	−3.99148	−0.161610
$611$	7.82174	0.316434
$612$	−1.00000	−0.0404226
$613$	−27.6076	−1.11506	−0.557530	−	0.830157i	$-0.688251\pi$
$613$	−27.6076	−1.11506	−0.557530	+	0.830157i	$0.688251\pi$
$614$	26.2365	1.05882
$615$	−1.69223	−0.0682372
$616$	0.0928228	0.00373994
$617$	−35.0611	−1.41151	−0.705754	−	0.708457i	$-0.749391\pi$
$617$	−35.0611	−1.41151	−0.705754	+	0.708457i	$0.749391\pi$
$618$	−16.0367	−0.645092
$619$	33.6253	1.35151	0.675757	−	0.737124i	$-0.263817\pi$
$619$	33.6253	1.35151	0.675757	+	0.737124i	$0.263817\pi$
$620$	2.38197	0.0956623
$621$	−5.56633	−0.223369
$622$	18.3831	0.737095
$623$	−3.57105	−0.143071
$624$	2.12175	0.0849380
$625$	20.7262	0.829046
$626$	33.8390	1.35248
$627$	0.643728	0.0257080
$628$	13.2021	0.526820
$629$	−6.05133	−0.241282
$630$	−0.114008	−0.00454218
$631$	−32.4730	−1.29273	−0.646365	−	0.763029i	$-0.723712\pi$
$631$	−32.4730	−1.29273	−0.646365	+	0.763029i	$0.723712\pi$
$632$	1.40882	0.0560400
$633$	−17.8998	−0.711453
$634$	−6.55955	−0.260513
$635$	3.34679	0.132813
$636$	−3.44950	−0.136782
$637$	14.7573	0.584707
$638$	−1.99485	−0.0789771
$639$	16.5135	0.653262
$640$	−0.539028	−0.0213069
$641$	7.90895	0.312385	0.156192	−	0.987727i	$-0.450078\pi$
$641$	7.90895	0.312385	0.156192	+	0.987727i	$0.450078\pi$
$642$	−1.24872	−0.0492830
$643$	7.82653	0.308648	0.154324	−	0.988020i	$-0.450680\pi$
$643$	7.82653	0.308648	0.154324	+	0.988020i	$0.450680\pi$
$644$	1.17731	0.0463927
$645$	6.76095	0.266212
$646$	1.46680	0.0577105
$647$	−30.0438	−1.18115	−0.590573	−	0.806985i	$-0.701098\pi$
$647$	−30.0438	−1.18115	−0.590573	+	0.806985i	$0.701098\pi$
$648$	−1.00000	−0.0392837
$649$	0.438866	0.0172270
$650$	−9.99228	−0.391929
$651$	−0.934649	−0.0366318
$652$	9.32418	0.365163
$653$	−34.1931	−1.33808	−0.669040	−	0.743226i	$-0.733295\pi$
$653$	−34.1931	−1.33808	−0.669040	+	0.743226i	$0.733295\pi$
$654$	−6.85017	−0.267863
$655$	6.98553	0.272947
$656$	3.13941	0.122573
$657$	15.6717	0.611412
$658$	0.779708	0.0303962
$659$	29.3351	1.14273	0.571367	−	0.820695i	$-0.306413\pi$
$659$	29.3351	1.14273	0.571367	+	0.820695i	$0.306413\pi$
$660$	0.236561	0.00920811
$661$	−23.2967	−0.906138	−0.453069	−	0.891475i	$-0.649671\pi$
$661$	−23.2967	−0.906138	−0.453069	+	0.891475i	$0.649671\pi$
$662$	−6.13447	−0.238423
$663$	−2.12175	−0.0824020
$664$	5.92017	0.229747
$665$	0.167227	0.00648477
$666$	−6.05133	−0.234484
$667$	−25.3016	−0.979684
$668$	−1.79156	−0.0693174
$669$	16.7755	0.648576
$670$	3.21299	0.124129
$671$	−3.24979	−0.125457
$672$	0.211506	0.00815903
$673$	9.70042	0.373924	0.186962	−	0.982367i	$-0.440136\pi$
$673$	9.70042	0.373924	0.186962	+	0.982367i	$0.440136\pi$
$674$	0.735362	0.0283251
$675$	4.70945	0.181267
$676$	−8.49817	−0.326853
$677$	37.3161	1.43417	0.717087	−	0.696984i	$-0.245475\pi$
$677$	37.3161	1.43417	0.717087	+	0.696984i	$0.245475\pi$
$678$	−9.66703	−0.371260
$679$	−2.71529	−0.104203
$680$	0.539028	0.0206708
$681$	17.1186	0.655985
$682$	1.93935	0.0742617
$683$	22.6132	0.865272	0.432636	−	0.901569i	$-0.357584\pi$
$683$	22.6132	0.865272	0.432636	+	0.901569i	$0.357584\pi$
$684$	1.46680	0.0560845
$685$	−0.578425	−0.0221005
$686$	2.95163	0.112694
$687$	13.1200	0.500558
$688$	−12.5429	−0.478192
$689$	−7.31899	−0.278831
$690$	3.00041	0.114223
$691$	−41.2023	−1.56741	−0.783705	−	0.621133i	$-0.786673\pi$
$691$	−41.2023	−1.56741	−0.783705	+	0.621133i	$0.786673\pi$
$692$	17.3103	0.658041
$693$	−0.0928228	−0.00352605
$694$	22.3832	0.849653
$695$	−12.1481	−0.460803
$696$	−4.54548	−0.172296
$697$	−3.13941	−0.118913
$698$	−23.9783	−0.907593
$699$	4.42173	0.167245
$700$	−0.996078	−0.0376482
$701$	−7.54376	−0.284924	−0.142462	−	0.989800i	$-0.545502\pi$
$701$	−7.54376	−0.284924	−0.142462	+	0.989800i	$0.545502\pi$
$702$	−2.12175	−0.0800803
$703$	8.87608	0.334768
$704$	−0.438866	−0.0165404
$705$	1.98710	0.0748385
$706$	−33.9101	−1.27622
$707$	1.63941	0.0616564
$708$	1.00000	0.0375823
$709$	−6.73497	−0.252937	−0.126469	−	0.991971i	$-0.540364\pi$
$709$	−6.73497	−0.252937	−0.126469	+	0.991971i	$0.540364\pi$
$710$	−8.90121	−0.334056
$711$	−1.40882	−0.0528350
$712$	16.8839	0.632751
$713$	24.5977	0.921191
$714$	−0.211506	−0.00791542
$715$	0.501923	0.0187709
$716$	13.2098	0.493672
$717$	2.99710	0.111929
$718$	4.45057	0.166094
$719$	23.4588	0.874864	0.437432	−	0.899251i	$-0.355888\pi$
$719$	23.4588	0.874864	0.437432	+	0.899251i	$0.355888\pi$
$720$	0.539028	0.0200884
$721$	−3.39187	−0.126320
$722$	16.8485	0.627036
$723$	9.85479	0.366503
$724$	10.1745	0.378131
$725$	21.4067	0.795025
$726$	−10.8074	−0.401100
$727$	13.5103	0.501071	0.250535	−	0.968107i	$-0.419393\pi$
$727$	13.5103	0.501071	0.250535	+	0.968107i	$0.419393\pi$
$728$	0.448764	0.0166323
$729$	1.00000	0.0370370
$730$	−8.44748	−0.312655
$731$	12.5429	0.463915
$732$	−7.40497	−0.273696
$733$	13.7655	0.508441	0.254221	−	0.967146i	$-0.418181\pi$
$733$	13.7655	0.508441	0.254221	+	0.967146i	$0.418181\pi$
$734$	34.7031	1.28092
$735$	3.74908	0.138287
$736$	−5.56633	−0.205178
$737$	2.61595	0.0963599
$738$	−3.13941	−0.115563
$739$	−28.4909	−1.04805	−0.524027	−	0.851702i	$-0.675571\pi$
$739$	−28.4909	−1.04805	−0.524027	+	0.851702i	$0.675571\pi$
$740$	3.26183	0.119907
$741$	3.11219	0.114329
$742$	−0.729591	−0.0267841
$743$	−10.3317	−0.379032	−0.189516	−	0.981878i	$-0.560692\pi$
$743$	−10.3317	−0.379032	−0.189516	+	0.981878i	$0.560692\pi$
$744$	4.41902	0.162009
$745$	3.07214	0.112554
$746$	20.2021	0.739650
$747$	−5.92017	−0.216608
$748$	0.438866	0.0160465
$749$	−0.264112	−0.00965043
$750$	−5.23366	−0.191106
$751$	0.744006	0.0271491	0.0135746	−	0.999908i	$-0.495679\pi$
$751$	0.744006	0.0271491	0.0135746	+	0.999908i	$0.495679\pi$
$752$	−3.68645	−0.134431
$753$	−4.23635	−0.154381
$754$	−9.64438	−0.351228
$755$	−4.80279	−0.174791
$756$	−0.211506	−0.00769241
$757$	12.1056	0.439985	0.219992	−	0.975502i	$-0.429397\pi$
$757$	12.1056	0.439985	0.219992	+	0.975502i	$0.429397\pi$
$758$	23.6280	0.858207
$759$	2.44287	0.0886706
$760$	−0.790646	−0.0286797
$761$	12.5077	0.453404	0.226702	−	0.973964i	$-0.427206\pi$
$761$	12.5077	0.453404	0.226702	+	0.973964i	$0.427206\pi$
$762$	6.20893	0.224926
$763$	−1.44885	−0.0524521
$764$	−6.41217	−0.231984
$765$	−0.539028	−0.0194886
$766$	−6.51425	−0.235369
$767$	2.12175	0.0766120
$768$	−1.00000	−0.0360844
$769$	−26.8112	−0.966838	−0.483419	−	0.875389i	$-0.660605\pi$
$769$	−26.8112	−0.966838	−0.483419	+	0.875389i	$0.660605\pi$
$770$	0.0500341	0.00180310
$771$	21.3977	0.770621
$772$	−7.78514	−0.280193
$773$	8.97768	0.322905	0.161452	−	0.986881i	$-0.448382\pi$
$773$	8.97768	0.322905	0.161452	+	0.986881i	$0.448382\pi$
$774$	12.5429	0.450844
$775$	−20.8111	−0.747558
$776$	12.8379	0.460853
$777$	−1.27989	−0.0459159
$778$	−36.1981	−1.29776
$779$	4.60488	0.164987
$780$	1.14368	0.0409504
$781$	−7.24719	−0.259325
$782$	5.56633	0.199052
$783$	4.54548	0.162442
$784$	−6.95527	−0.248402
$785$	7.11628	0.253991
$786$	12.9595	0.462250
$787$	−52.0718	−1.85616	−0.928080	−	0.372382i	$-0.878541\pi$
$787$	−52.0718	−1.85616	−0.928080	+	0.372382i	$0.878541\pi$
$788$	3.71958	0.132504
$789$	−18.4208	−0.655798
$790$	0.759394	0.0270180
$791$	−2.04464	−0.0726989
$792$	0.438866	0.0155944
$793$	−15.7115	−0.557932
$794$	−0.608826	−0.0216064
$795$	−1.85938	−0.0659453
$796$	13.4826	0.477879
$797$	−38.8981	−1.37784	−0.688920	−	0.724837i	$-0.741915\pi$
$797$	−38.8981	−1.37784	−0.688920	+	0.724837i	$0.741915\pi$
$798$	0.310237	0.0109823
$799$	3.68645	0.130417
$800$	4.70945	0.166504
$801$	−16.8839	−0.596563
$802$	−1.93078	−0.0681783
$803$	−6.87777	−0.242711
$804$	5.96072	0.210218
$805$	0.634605	0.0223669
$806$	9.37605	0.330257
$807$	−15.2337	−0.536253
$808$	−7.75113	−0.272684
$809$	−40.9085	−1.43827	−0.719133	−	0.694873i	$-0.755461\pi$
$809$	−40.9085	−1.43827	−0.719133	+	0.694873i	$0.755461\pi$
$810$	−0.539028	−0.0189395
$811$	−47.4225	−1.66523	−0.832614	−	0.553854i	$-0.813157\pi$
$811$	−47.4225	−1.66523	−0.832614	+	0.553854i	$0.813157\pi$
$812$	−0.961397	−0.0337384
$813$	−11.5622	−0.405504
$814$	2.65572	0.0930829
$815$	5.02599	0.176053
$816$	1.00000	0.0350070
$817$	−18.3979	−0.643660
$818$	−4.42657	−0.154772
$819$	−0.448764	−0.0156811
$820$	1.69223	0.0590951
$821$	34.2865	1.19661	0.598303	−	0.801270i	$-0.295842\pi$
$821$	34.2865	1.19661	0.598303	+	0.801270i	$0.295842\pi$
$822$	−1.07309	−0.0374283
$823$	−8.78439	−0.306205	−0.153102	−	0.988210i	$-0.548926\pi$
$823$	−8.78439	−0.306205	−0.153102	+	0.988210i	$0.548926\pi$
$824$	16.0367	0.558666
$825$	−2.06682	−0.0719573
$826$	0.211506	0.00735924
$827$	−49.5039	−1.72142	−0.860710	−	0.509096i	$-0.829980\pi$
$827$	−49.5039	−1.72142	−0.860710	+	0.509096i	$0.829980\pi$
$828$	5.56633	0.193443
$829$	−24.8680	−0.863700	−0.431850	−	0.901946i	$-0.642139\pi$
$829$	−24.8680	−0.863700	−0.431850	+	0.901946i	$0.642139\pi$
$830$	3.19114	0.110766
$831$	3.45542	0.119867
$832$	−2.12175	−0.0735585
$833$	6.95527	0.240986
$834$	−22.5370	−0.780394
$835$	−0.965698	−0.0334194
$836$	−0.643728	−0.0222638
$837$	−4.41902	−0.152744
$838$	−0.140900	−0.00486732
$839$	−18.0088	−0.621731	−0.310866	−	0.950454i	$-0.600619\pi$
$839$	−18.0088	−0.621731	−0.310866	+	0.950454i	$0.600619\pi$
$840$	0.114008	0.00393364
$841$	−8.33861	−0.287538
$842$	−0.179517	−0.00618655
$843$	20.8551	0.718287
$844$	17.8998	0.616136
$845$	−4.58075	−0.157583
$846$	3.68645	0.126743
$847$	−2.28583	−0.0785421
$848$	3.44950	0.118456
$849$	23.9561	0.822171
$850$	−4.70945	−0.161533
$851$	33.6837	1.15466
$852$	−16.5135	−0.565742
$853$	−50.3682	−1.72457	−0.862287	−	0.506420i	$-0.830969\pi$
$853$	−50.3682	−1.72457	−0.862287	+	0.506420i	$0.830969\pi$
$854$	−1.56620	−0.0535942
$855$	0.790646	0.0270395
$856$	1.24872	0.0426803
$857$	−41.6692	−1.42339	−0.711696	−	0.702487i	$-0.752073\pi$
$857$	−41.6692	−1.42339	−0.711696	+	0.702487i	$0.752073\pi$
$858$	0.931164	0.0317894
$859$	44.2210	1.50880	0.754401	−	0.656414i	$-0.227928\pi$
$859$	44.2210	1.50880	0.754401	+	0.656414i	$0.227928\pi$
$860$	−6.76095	−0.230547
$861$	−0.664004	−0.0226292
$862$	10.1503	0.345720
$863$	6.25889	0.213055	0.106527	−	0.994310i	$-0.466027\pi$
$863$	6.25889	0.213055	0.106527	+	0.994310i	$0.466027\pi$
$864$	1.00000	0.0340207
$865$	9.33075	0.317255
$866$	−11.9389	−0.405701
$867$	−1.00000	−0.0339618
$868$	0.934649	0.0317241
$869$	0.618284	0.0209738
$870$	−2.45014	−0.0830675
$871$	12.6472	0.428533
$872$	6.85017	0.231976
$873$	−12.8379	−0.434496
$874$	−8.16469	−0.276175
$875$	−1.10695	−0.0374218
$876$	−15.6717	−0.529498
$877$	23.7244	0.801117	0.400558	−	0.916271i	$-0.368816\pi$
$877$	23.7244	0.801117	0.400558	+	0.916271i	$0.368816\pi$
$878$	29.0640	0.980863
$879$	−13.9518	−0.470583
$880$	−0.236561	−0.00797446
$881$	36.7669	1.23871	0.619354	−	0.785112i	$-0.287395\pi$
$881$	36.7669	1.23871	0.619354	+	0.785112i	$0.287395\pi$
$882$	6.95527	0.234196
$883$	48.5757	1.63470	0.817351	−	0.576140i	$-0.195442\pi$
$883$	48.5757	1.63470	0.817351	+	0.576140i	$0.195442\pi$
$884$	2.12175	0.0713622
$885$	0.539028	0.0181192
$886$	24.1041	0.809795
$887$	−33.0801	−1.11072	−0.555360	−	0.831610i	$-0.687420\pi$
$887$	−33.0801	−1.11072	−0.555360	+	0.831610i	$0.687420\pi$
$888$	6.05133	0.203069
$889$	1.31323	0.0440443
$890$	9.10088	0.305062
$891$	−0.438866	−0.0147026
$892$	−16.7755	−0.561684
$893$	−5.40729	−0.180948
$894$	5.69941	0.190617
$895$	7.12042	0.238010
$896$	−0.211506	−0.00706593
$897$	11.8104	0.394337
$898$	0.949278	0.0316778
$899$	−20.0865	−0.669924
$900$	−4.70945	−0.156982
$901$	−3.44950	−0.114920
$902$	1.37778	0.0458750
$903$	2.65289	0.0882828
$904$	9.66703	0.321520
$905$	5.48432	0.182305
$906$	−8.91010	−0.296018
$907$	−32.8325	−1.09018	−0.545092	−	0.838376i	$-0.683505\pi$
$907$	−32.8325	−1.09018	−0.545092	+	0.838376i	$0.683505\pi$
$908$	−17.1186	−0.568100
$909$	7.75113	0.257089
$910$	0.241896	0.00801877
$911$	34.0063	1.12668	0.563340	−	0.826225i	$-0.309516\pi$
$911$	34.0063	1.12668	0.563340	+	0.826225i	$0.309516\pi$
$912$	−1.46680	−0.0485706
$913$	2.59816	0.0859866
$914$	6.77458	0.224083
$915$	−3.99148	−0.131954
$916$	−13.1200	−0.433496
$917$	2.74102	0.0905164
$918$	−1.00000	−0.0330049
$919$	22.6974	0.748719	0.374360	−	0.927284i	$-0.377863\pi$
$919$	22.6974	0.748719	0.374360	+	0.927284i	$0.377863\pi$
$920$	−3.00041	−0.0989204
$921$	26.2365	0.864522
$922$	20.6995	0.681703
$923$	−35.0374	−1.15327
$924$	0.0928228	0.00305365
$925$	−28.4984	−0.937022
$926$	27.0311	0.888296
$927$	−16.0367	−0.526715
$928$	4.54548	0.149213
$929$	−7.52463	−0.246875	−0.123438	−	0.992352i	$-0.539392\pi$
$929$	−7.52463	−0.246875	−0.123438	+	0.992352i	$0.539392\pi$
$930$	2.38197	0.0781079
$931$	−10.2020	−0.334357
$932$	−4.42173	−0.144839
$933$	18.3831	0.601836
$934$	30.7402	1.00585
$935$	0.236561	0.00773636
$936$	2.12175	0.0693516
$937$	41.2745	1.34838	0.674190	−	0.738558i	$-0.264493\pi$
$937$	41.2745	1.34838	0.674190	+	0.738558i	$0.264493\pi$
$938$	1.26073	0.0411643
$939$	33.8390	1.10429
$940$	−1.98710	−0.0648121
$941$	37.5672	1.22466	0.612328	−	0.790603i	$-0.290233\pi$
$941$	37.5672	1.22466	0.612328	+	0.790603i	$0.290233\pi$
$942$	13.2021	0.430147
$943$	17.4750	0.569063
$944$	−1.00000	−0.0325472
$945$	−0.114008	−0.00370867
$946$	−5.50463	−0.178971
$947$	44.8040	1.45593	0.727967	−	0.685612i	$-0.240465\pi$
$947$	44.8040	1.45593	0.727967	+	0.685612i	$0.240465\pi$
$948$	1.40882	0.0457564
$949$	−33.2515	−1.07939
$950$	6.90782	0.224119
$951$	−6.55955	−0.212708
$952$	0.211506	0.00685496
$953$	−17.8320	−0.577636	−0.288818	−	0.957384i	$-0.593262\pi$
$953$	−17.8320	−0.577636	−0.288818	+	0.957384i	$0.593262\pi$
$954$	−3.44950	−0.111682
$955$	−3.45634	−0.111844
$956$	−2.99710	−0.0969331
$957$	−1.99485	−0.0644845
$958$	40.0644	1.29442
$959$	−0.226965	−0.00732909
$960$	−0.539028	−0.0173970
$961$	−11.4723	−0.370074
$962$	12.8394	0.413959
$963$	−1.24872	−0.0402394
$964$	−9.85479	−0.317401
$965$	−4.19641	−0.135087
$966$	1.17731	0.0378794
$967$	−48.0470	−1.54509	−0.772544	−	0.634961i	$-0.781016\pi$
$967$	−48.0470	−1.54509	−0.772544	+	0.634961i	$0.781016\pi$
$968$	10.8074	0.347363
$969$	1.46680	0.0471204
$970$	6.91996	0.222187
$971$	44.8342	1.43880	0.719399	−	0.694597i	$-0.244417\pi$
$971$	44.8342	1.43880	0.719399	+	0.694597i	$0.244417\pi$
$972$	−1.00000	−0.0320750
$973$	−4.76672	−0.152814
$974$	−2.55945	−0.0820102
$975$	−9.99228	−0.320009
$976$	7.40497	0.237027
$977$	13.9821	0.447328	0.223664	−	0.974666i	$-0.428198\pi$
$977$	13.9821	0.447328	0.223664	+	0.974666i	$0.428198\pi$
$978$	9.32418	0.298154
$979$	7.40976	0.236817
$980$	−3.74908	−0.119760
$981$	−6.85017	−0.218709
$982$	16.3895	0.523009
$983$	45.6759	1.45684	0.728418	−	0.685133i	$-0.240256\pi$
$983$	45.6759	1.45684	0.728418	+	0.685133i	$0.240256\pi$
$984$	3.13941	0.100081
$985$	2.00495	0.0638832
$986$	−4.54548	−0.144758
$987$	0.779708	0.0248184
$988$	−3.11219	−0.0990118
$989$	−69.8177	−2.22008
$990$	0.236561	0.00751839
$991$	46.7111	1.48383	0.741914	−	0.670495i	$-0.233918\pi$
$991$	46.7111	1.48383	0.741914	+	0.670495i	$0.233918\pi$
$992$	−4.41902	−0.140304
$993$	−6.13447	−0.194671
$994$	−3.49270	−0.110782
$995$	7.26750	0.230395
$996$	5.92017	0.187588
$997$	39.5453	1.25241	0.626206	−	0.779657i	$-0.284607\pi$
$997$	39.5453	1.25241	0.626206	+	0.779657i	$0.284607\pi$
$998$	41.1581	1.30284
$999$	−6.05133	−0.191455

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.v.1.4	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.v.1.4	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.539028 q^{5} +1.00000 q^{6} +0.211506 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.539028 q^{5} +1.00000 q^{6} +0.211506 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.539028 q^{10} -0.438866 q^{11} -1.00000 q^{12} -2.12175 q^{13} -0.211506 q^{14} -0.539028 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +1.46680 q^{19} +0.539028 q^{20} -0.211506 q^{21} +0.438866 q^{22} +5.56633 q^{23} +1.00000 q^{24} -4.70945 q^{25} +2.12175 q^{26} -1.00000 q^{27} +0.211506 q^{28} -4.54548 q^{29} +0.539028 q^{30} +4.41902 q^{31} -1.00000 q^{32} +0.438866 q^{33} +1.00000 q^{34} +0.114008 q^{35} +1.00000 q^{36} +6.05133 q^{37} -1.46680 q^{38} +2.12175 q^{39} -0.539028 q^{40} +3.13941 q^{41} +0.211506 q^{42} -12.5429 q^{43} -0.438866 q^{44} +0.539028 q^{45} -5.56633 q^{46} -3.68645 q^{47} -1.00000 q^{48} -6.95527 q^{49} +4.70945 q^{50} +1.00000 q^{51} -2.12175 q^{52} +3.44950 q^{53} +1.00000 q^{54} -0.236561 q^{55} -0.211506 q^{56} -1.46680 q^{57} +4.54548 q^{58} -1.00000 q^{59} -0.539028 q^{60} +7.40497 q^{61} -4.41902 q^{62} +0.211506 q^{63} +1.00000 q^{64} -1.14368 q^{65} -0.438866 q^{66} -5.96072 q^{67} -1.00000 q^{68} -5.56633 q^{69} -0.114008 q^{70} +16.5135 q^{71} -1.00000 q^{72} +15.6717 q^{73} -6.05133 q^{74} +4.70945 q^{75} +1.46680 q^{76} -0.0928228 q^{77} -2.12175 q^{78} -1.40882 q^{79} +0.539028 q^{80} +1.00000 q^{81} -3.13941 q^{82} -5.92017 q^{83} -0.211506 q^{84} -0.539028 q^{85} +12.5429 q^{86} +4.54548 q^{87} +0.438866 q^{88} -16.8839 q^{89} -0.539028 q^{90} -0.448764 q^{91} +5.56633 q^{92} -4.41902 q^{93} +3.68645 q^{94} +0.790646 q^{95} +1.00000 q^{96} -12.8379 q^{97} +6.95527 q^{98} -0.438866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9} - 6 q^{10} + q^{11} - 9 q^{12} + 4 q^{13} + 11 q^{14} - 6 q^{15} + 9 q^{16} - 9 q^{17} - 9 q^{18} - 13 q^{19} + 6 q^{20} + 11 q^{21} - q^{22} - 6 q^{23} + 9 q^{24} + 9 q^{25} - 4 q^{26} - 9 q^{27} - 11 q^{28} + 10 q^{29} + 6 q^{30} + q^{31} - 9 q^{32} - q^{33} + 9 q^{34} + 6 q^{35} + 9 q^{36} - 2 q^{37} + 13 q^{38} - 4 q^{39} - 6 q^{40} + 20 q^{41} - 11 q^{42} - 17 q^{43} + q^{44} + 6 q^{45} + 6 q^{46} + 4 q^{47} - 9 q^{48} + 2 q^{49} - 9 q^{50} + 9 q^{51} + 4 q^{52} + 16 q^{53} + 9 q^{54} - 17 q^{55} + 11 q^{56} + 13 q^{57} - 10 q^{58} - 9 q^{59} - 6 q^{60} - 9 q^{61} - q^{62} - 11 q^{63} + 9 q^{64} + q^{66} - 8 q^{67} - 9 q^{68} + 6 q^{69} - 6 q^{70} - 8 q^{71} - 9 q^{72} - 20 q^{73} + 2 q^{74} - 9 q^{75} - 13 q^{76} - 32 q^{77} + 4 q^{78} - 29 q^{79} + 6 q^{80} + 9 q^{81} - 20 q^{82} - 16 q^{83} + 11 q^{84} - 6 q^{85} + 17 q^{86} - 10 q^{87} - q^{88} + 11 q^{89} - 6 q^{90} - 13 q^{91} - 6 q^{92} - q^{93} - 4 q^{94} + 5 q^{95} + 9 q^{96} + 17 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9 - 6 * q^10 + q^11 - 9 * q^12 + 4 * q^13 + 11 * q^14 - 6 * q^15 + 9 * q^16 - 9 * q^17 - 9 * q^18 - 13 * q^19 + 6 * q^20 + 11 * q^21 - q^22 - 6 * q^23 + 9 * q^24 + 9 * q^25 - 4 * q^26 - 9 * q^27 - 11 * q^28 + 10 * q^29 + 6 * q^30 + q^31 - 9 * q^32 - q^33 + 9 * q^34 + 6 * q^35 + 9 * q^36 - 2 * q^37 + 13 * q^38 - 4 * q^39 - 6 * q^40 + 20 * q^41 - 11 * q^42 - 17 * q^43 + q^44 + 6 * q^45 + 6 * q^46 + 4 * q^47 - 9 * q^48 + 2 * q^49 - 9 * q^50 + 9 * q^51 + 4 * q^52 + 16 * q^53 + 9 * q^54 - 17 * q^55 + 11 * q^56 + 13 * q^57 - 10 * q^58 - 9 * q^59 - 6 * q^60 - 9 * q^61 - q^62 - 11 * q^63 + 9 * q^64 + q^66 - 8 * q^67 - 9 * q^68 + 6 * q^69 - 6 * q^70 - 8 * q^71 - 9 * q^72 - 20 * q^73 + 2 * q^74 - 9 * q^75 - 13 * q^76 - 32 * q^77 + 4 * q^78 - 29 * q^79 + 6 * q^80 + 9 * q^81 - 20 * q^82 - 16 * q^83 + 11 * q^84 - 6 * q^85 + 17 * q^86 - 10 * q^87 - q^88 + 11 * q^89 - 6 * q^90 - 13 * q^91 - 6 * q^92 - q^93 - 4 * q^94 + 5 * q^95 + 9 * q^96 + 17 * q^97 - 2 * q^98 + q^99

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