LMFDB - Embedded newform 6018.2.a.m.1.2

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:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 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			1.2
Root			$2.17009$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.63090 q^{5} -1.00000 q^{6} +3.87936 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.63090 q^{5} -1.00000 q^{6} +3.87936 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.63090 q^{10} +3.26180 q^{11} +1.00000 q^{12} +2.63090 q^{13} -3.87936 q^{14} +2.63090 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +3.97107 q^{19} +2.63090 q^{20} +3.87936 q^{21} -3.26180 q^{22} +2.46081 q^{23} -1.00000 q^{24} +1.92162 q^{25} -2.63090 q^{26} +1.00000 q^{27} +3.87936 q^{28} +1.70928 q^{29} -2.63090 q^{30} -2.00000 q^{31} -1.00000 q^{32} +3.26180 q^{33} +1.00000 q^{34} +10.2062 q^{35} +1.00000 q^{36} -10.2062 q^{37} -3.97107 q^{38} +2.63090 q^{39} -2.63090 q^{40} +6.70928 q^{41} -3.87936 q^{42} +0.921622 q^{43} +3.26180 q^{44} +2.63090 q^{45} -2.46081 q^{46} -5.70928 q^{47} +1.00000 q^{48} +8.04945 q^{49} -1.92162 q^{50} -1.00000 q^{51} +2.63090 q^{52} +8.03612 q^{53} -1.00000 q^{54} +8.58145 q^{55} -3.87936 q^{56} +3.97107 q^{57} -1.70928 q^{58} -1.00000 q^{59} +2.63090 q^{60} -4.73820 q^{61} +2.00000 q^{62} +3.87936 q^{63} +1.00000 q^{64} +6.92162 q^{65} -3.26180 q^{66} -9.70928 q^{67} -1.00000 q^{68} +2.46081 q^{69} -10.2062 q^{70} +12.2062 q^{71} -1.00000 q^{72} +3.29072 q^{73} +10.2062 q^{74} +1.92162 q^{75} +3.97107 q^{76} +12.6537 q^{77} -2.63090 q^{78} -13.8082 q^{79} +2.63090 q^{80} +1.00000 q^{81} -6.70928 q^{82} -12.8082 q^{83} +3.87936 q^{84} -2.63090 q^{85} -0.921622 q^{86} +1.70928 q^{87} -3.26180 q^{88} -10.2618 q^{89} -2.63090 q^{90} +10.2062 q^{91} +2.46081 q^{92} -2.00000 q^{93} +5.70928 q^{94} +10.4475 q^{95} -1.00000 q^{96} -9.00000 q^{97} -8.04945 q^{98} +3.26180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} - 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 - 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} - 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9} - 4 q^{10} + 2 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 4 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} - 3 q^{19} + 4 q^{20} - q^{21} - 2 q^{22} + 9 q^{23} - 3 q^{24} + 9 q^{25} - 4 q^{26} + 3 q^{27} - q^{28} - 2 q^{29} - 4 q^{30} - 6 q^{31} - 3 q^{32} + 2 q^{33} + 3 q^{34} + 6 q^{35} + 3 q^{36} - 6 q^{37} + 3 q^{38} + 4 q^{39} - 4 q^{40} + 13 q^{41} + q^{42} + 6 q^{43} + 2 q^{44} + 4 q^{45} - 9 q^{46} - 10 q^{47} + 3 q^{48} + 6 q^{49} - 9 q^{50} - 3 q^{51} + 4 q^{52} + 5 q^{53} - 3 q^{54} + 40 q^{55} + q^{56} - 3 q^{57} + 2 q^{58} - 3 q^{59} + 4 q^{60} - 22 q^{61} + 6 q^{62} - q^{63} + 3 q^{64} + 24 q^{65} - 2 q^{66} - 22 q^{67} - 3 q^{68} + 9 q^{69} - 6 q^{70} + 12 q^{71} - 3 q^{72} + 17 q^{73} + 6 q^{74} + 9 q^{75} - 3 q^{76} + 14 q^{77} - 4 q^{78} + 2 q^{79} + 4 q^{80} + 3 q^{81} - 13 q^{82} + 5 q^{83} - q^{84} - 4 q^{85} - 6 q^{86} - 2 q^{87} - 2 q^{88} - 23 q^{89} - 4 q^{90} + 6 q^{91} + 9 q^{92} - 6 q^{93} + 10 q^{94} + 32 q^{95} - 3 q^{96} - 27 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 - 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9 - 4 * q^10 + 2 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 4 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 - 3 * q^19 + 4 * q^20 - q^21 - 2 * q^22 + 9 * q^23 - 3 * q^24 + 9 * q^25 - 4 * q^26 + 3 * q^27 - q^28 - 2 * q^29 - 4 * q^30 - 6 * q^31 - 3 * q^32 + 2 * q^33 + 3 * q^34 + 6 * q^35 + 3 * q^36 - 6 * q^37 + 3 * q^38 + 4 * q^39 - 4 * q^40 + 13 * q^41 + q^42 + 6 * q^43 + 2 * q^44 + 4 * q^45 - 9 * q^46 - 10 * q^47 + 3 * q^48 + 6 * q^49 - 9 * q^50 - 3 * q^51 + 4 * q^52 + 5 * q^53 - 3 * q^54 + 40 * q^55 + q^56 - 3 * q^57 + 2 * q^58 - 3 * q^59 + 4 * q^60 - 22 * q^61 + 6 * q^62 - q^63 + 3 * q^64 + 24 * q^65 - 2 * q^66 - 22 * q^67 - 3 * q^68 + 9 * q^69 - 6 * q^70 + 12 * q^71 - 3 * q^72 + 17 * q^73 + 6 * q^74 + 9 * q^75 - 3 * q^76 + 14 * q^77 - 4 * q^78 + 2 * q^79 + 4 * q^80 + 3 * q^81 - 13 * q^82 + 5 * q^83 - q^84 - 4 * q^85 - 6 * q^86 - 2 * q^87 - 2 * q^88 - 23 * q^89 - 4 * q^90 + 6 * q^91 + 9 * q^92 - 6 * q^93 + 10 * q^94 + 32 * q^95 - 3 * q^96 - 27 * q^97 - 6 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.63090	1.17657	0.588287	−	0.808653i	$-0.299803\pi$
$5$	2.63090	1.17657	0.588287	+	0.808653i	$0.299803\pi$
$6$	−1.00000	−0.408248
$7$	3.87936	1.46626	0.733130	−	0.680088i	$-0.238058\pi$
$7$	3.87936	1.46626	0.733130	+	0.680088i	$0.238058\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.63090	−0.831963
$11$	3.26180	0.983468	0.491734	−	0.870745i	$-0.336363\pi$
$11$	3.26180	0.983468	0.491734	+	0.870745i	$0.336363\pi$
$12$	1.00000	0.288675
$13$	2.63090	0.729680	0.364840	−	0.931070i	$-0.381124\pi$
$13$	2.63090	0.729680	0.364840	+	0.931070i	$0.381124\pi$
$14$	−3.87936	−1.03680
$15$	2.63090	0.679295
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	3.97107	0.911026	0.455513	−	0.890229i	$-0.349456\pi$
$19$	3.97107	0.911026	0.455513	+	0.890229i	$0.349456\pi$
$20$	2.63090	0.588287
$21$	3.87936	0.846546
$22$	−3.26180	−0.695417
$23$	2.46081	0.513115	0.256557	−	0.966529i	$-0.417412\pi$
$23$	2.46081	0.513115	0.256557	+	0.966529i	$0.417412\pi$
$24$	−1.00000	−0.204124
$25$	1.92162	0.384324
$26$	−2.63090	−0.515961
$27$	1.00000	0.192450
$28$	3.87936	0.733130
$29$	1.70928	0.317404	0.158702	−	0.987326i	$-0.449269\pi$
$29$	1.70928	0.317404	0.158702	+	0.987326i	$0.449269\pi$
$30$	−2.63090	−0.480334
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−1.00000	−0.176777
$33$	3.26180	0.567806
$34$	1.00000	0.171499
$35$	10.2062	1.72516
$36$	1.00000	0.166667
$37$	−10.2062	−1.67789	−0.838945	−	0.544217i	$-0.816827\pi$
$37$	−10.2062	−1.67789	−0.838945	+	0.544217i	$0.816827\pi$
$38$	−3.97107	−0.644193
$39$	2.63090	0.421281
$40$	−2.63090	−0.415981
$41$	6.70928	1.04781	0.523906	−	0.851776i	$-0.324474\pi$
$41$	6.70928	1.04781	0.523906	+	0.851776i	$0.324474\pi$
$42$	−3.87936	−0.598599
$43$	0.921622	0.140546	0.0702730	−	0.997528i	$-0.477613\pi$
$43$	0.921622	0.140546	0.0702730	+	0.997528i	$0.477613\pi$
$44$	3.26180	0.491734
$45$	2.63090	0.392191
$46$	−2.46081	−0.362827
$47$	−5.70928	−0.832783	−0.416392	−	0.909185i	$-0.636705\pi$
$47$	−5.70928	−0.832783	−0.416392	+	0.909185i	$0.636705\pi$
$48$	1.00000	0.144338
$49$	8.04945	1.14992
$50$	−1.92162	−0.271758
$51$	−1.00000	−0.140028
$52$	2.63090	0.364840
$53$	8.03612	1.10385	0.551923	−	0.833895i	$-0.313894\pi$
$53$	8.03612	1.10385	0.551923	+	0.833895i	$0.313894\pi$
$54$	−1.00000	−0.136083
$55$	8.58145	1.15712
$56$	−3.87936	−0.518402
$57$	3.97107	0.525981
$58$	−1.70928	−0.224439
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	2.63090	0.339647
$61$	−4.73820	−0.606665	−0.303332	−	0.952885i	$-0.598099\pi$
$61$	−4.73820	−0.606665	−0.303332	+	0.952885i	$0.598099\pi$
$62$	2.00000	0.254000
$63$	3.87936	0.488754
$64$	1.00000	0.125000
$65$	6.92162	0.858522
$66$	−3.26180	−0.401499
$67$	−9.70928	−1.18618	−0.593088	−	0.805137i	$-0.702092\pi$
$67$	−9.70928	−1.18618	−0.593088	+	0.805137i	$0.702092\pi$
$68$	−1.00000	−0.121268
$69$	2.46081	0.296247
$70$	−10.2062	−1.21987
$71$	12.2062	1.44861	0.724305	−	0.689480i	$-0.242161\pi$
$71$	12.2062	1.44861	0.724305	+	0.689480i	$0.242161\pi$
$72$	−1.00000	−0.117851
$73$	3.29072	0.385150	0.192575	−	0.981282i	$-0.438316\pi$
$73$	3.29072	0.385150	0.192575	+	0.981282i	$0.438316\pi$
$74$	10.2062	1.18645
$75$	1.92162	0.221890
$76$	3.97107	0.455513
$77$	12.6537	1.44202
$78$	−2.63090	−0.297890
$79$	−13.8082	−1.55354	−0.776770	−	0.629784i	$-0.783143\pi$
$79$	−13.8082	−1.55354	−0.776770	+	0.629784i	$0.783143\pi$
$80$	2.63090	0.294143
$81$	1.00000	0.111111
$82$	−6.70928	−0.740916
$83$	−12.8082	−1.40588	−0.702940	−	0.711249i	$-0.748130\pi$
$83$	−12.8082	−1.40588	−0.702940	+	0.711249i	$0.748130\pi$
$84$	3.87936	0.423273
$85$	−2.63090	−0.285361
$86$	−0.921622	−0.0993811
$87$	1.70928	0.183254
$88$	−3.26180	−0.347709
$89$	−10.2618	−1.08775	−0.543874	−	0.839167i	$-0.683043\pi$
$89$	−10.2618	−1.08775	−0.543874	+	0.839167i	$0.683043\pi$
$90$	−2.63090	−0.277321
$91$	10.2062	1.06990
$92$	2.46081	0.256557
$93$	−2.00000	−0.207390
$94$	5.70928	0.588867
$95$	10.4475	1.07189
$96$	−1.00000	−0.102062
$97$	−9.00000	−0.913812	−0.456906	−	0.889515i	$-0.651042\pi$
$97$	−9.00000	−0.913812	−0.456906	+	0.889515i	$0.651042\pi$
$98$	−8.04945	−0.813117
$99$	3.26180	0.327823
$100$	1.92162	0.192162
$101$	−7.12783	−0.709245	−0.354623	−	0.935010i	$-0.615391\pi$
$101$	−7.12783	−0.709245	−0.354623	+	0.935010i	$0.615391\pi$
$102$	1.00000	0.0990148
$103$	6.40295	0.630902	0.315451	−	0.948942i	$-0.397844\pi$
$103$	6.40295	0.630902	0.315451	+	0.948942i	$0.397844\pi$
$104$	−2.63090	−0.257981
$105$	10.2062	0.996024
$106$	−8.03612	−0.780537
$107$	−3.63090	−0.351012	−0.175506	−	0.984478i	$-0.556156\pi$
$107$	−3.63090	−0.351012	−0.175506	+	0.984478i	$0.556156\pi$
$108$	1.00000	0.0962250
$109$	−0.764867	−0.0732609	−0.0366305	−	0.999329i	$-0.511662\pi$
$109$	−0.764867	−0.0732609	−0.0366305	+	0.999329i	$0.511662\pi$
$110$	−8.58145	−0.818209
$111$	−10.2062	−0.968730
$112$	3.87936	0.366565
$113$	19.5669	1.84070	0.920349	−	0.391097i	$-0.127904\pi$
$113$	19.5669	1.84070	0.920349	+	0.391097i	$0.127904\pi$
$114$	−3.97107	−0.371925
$115$	6.47414	0.603717
$116$	1.70928	0.158702
$117$	2.63090	0.243227
$118$	1.00000	0.0920575
$119$	−3.87936	−0.355621
$120$	−2.63090	−0.240167
$121$	−0.360692	−0.0327902
$122$	4.73820	0.428977
$123$	6.70928	0.604955
$124$	−2.00000	−0.179605
$125$	−8.09890	−0.724387
$126$	−3.87936	−0.345601
$127$	11.2846	1.00134	0.500672	−	0.865637i	$-0.333086\pi$
$127$	11.2846	1.00134	0.500672	+	0.865637i	$0.333086\pi$
$128$	−1.00000	−0.0883883
$129$	0.921622	0.0811443
$130$	−6.92162	−0.607066
$131$	−13.2267	−1.15562	−0.577812	−	0.816170i	$-0.696093\pi$
$131$	−13.2267	−1.15562	−0.577812	+	0.816170i	$0.696093\pi$
$132$	3.26180	0.283903
$133$	15.4052	1.33580
$134$	9.70928	0.838754
$135$	2.63090	0.226432
$136$	1.00000	0.0857493
$137$	21.4680	1.83413	0.917067	−	0.398732i	$-0.130550\pi$
$137$	21.4680	1.83413	0.917067	+	0.398732i	$0.130550\pi$
$138$	−2.46081	−0.209478
$139$	−12.3896	−1.05087	−0.525437	−	0.850833i	$-0.676098\pi$
$139$	−12.3896	−1.05087	−0.525437	+	0.850833i	$0.676098\pi$
$140$	10.2062	0.862582
$141$	−5.70928	−0.480808
$142$	−12.2062	−1.02432
$143$	8.58145	0.717617
$144$	1.00000	0.0833333
$145$	4.49693	0.373450
$146$	−3.29072	−0.272342
$147$	8.04945	0.663907
$148$	−10.2062	−0.838945
$149$	−7.23513	−0.592725	−0.296363	−	0.955075i	$-0.595774\pi$
$149$	−7.23513	−0.592725	−0.296363	+	0.955075i	$0.595774\pi$
$150$	−1.92162	−0.156900
$151$	−4.82377	−0.392553	−0.196276	−	0.980549i	$-0.562885\pi$
$151$	−4.82377	−0.392553	−0.196276	+	0.980549i	$0.562885\pi$
$152$	−3.97107	−0.322096
$153$	−1.00000	−0.0808452
$154$	−12.6537	−1.01966
$155$	−5.26180	−0.422638
$156$	2.63090	0.210640
$157$	3.14116	0.250692	0.125346	−	0.992113i	$-0.459996\pi$
$157$	3.14116	0.250692	0.125346	+	0.992113i	$0.459996\pi$
$158$	13.8082	1.09852
$159$	8.03612	0.637306
$160$	−2.63090	−0.207991
$161$	9.54638	0.752360
$162$	−1.00000	−0.0785674
$163$	3.52586	0.276167	0.138083	−	0.990421i	$-0.455906\pi$
$163$	3.52586	0.276167	0.138083	+	0.990421i	$0.455906\pi$
$164$	6.70928	0.523906
$165$	8.58145	0.668065
$166$	12.8082	0.994107
$167$	−16.4124	−1.27003	−0.635015	−	0.772500i	$-0.719006\pi$
$167$	−16.4124	−1.27003	−0.635015	+	0.772500i	$0.719006\pi$
$168$	−3.87936	−0.299299
$169$	−6.07838	−0.467568
$170$	2.63090	0.201781
$171$	3.97107	0.303675
$172$	0.921622	0.0702730
$173$	18.9132	1.43794	0.718972	−	0.695039i	$-0.244613\pi$
$173$	18.9132	1.43794	0.718972	+	0.695039i	$0.244613\pi$
$174$	−1.70928	−0.129580
$175$	7.45467	0.563520
$176$	3.26180	0.245867
$177$	−1.00000	−0.0751646
$178$	10.2618	0.769154
$179$	−14.7854	−1.10511	−0.552556	−	0.833476i	$-0.686347\pi$
$179$	−14.7854	−1.10511	−0.552556	+	0.833476i	$0.686347\pi$
$180$	2.63090	0.196096
$181$	3.89269	0.289342	0.144671	−	0.989480i	$-0.453788\pi$
$181$	3.89269	0.289342	0.144671	+	0.989480i	$0.453788\pi$
$182$	−10.2062	−0.756534
$183$	−4.73820	−0.350258
$184$	−2.46081	−0.181413
$185$	−26.8515	−1.97416
$186$	2.00000	0.146647
$187$	−3.26180	−0.238526
$188$	−5.70928	−0.416392
$189$	3.87936	0.282182
$190$	−10.4475	−0.757940
$191$	−7.31124	−0.529023	−0.264512	−	0.964383i	$-0.585211\pi$
$191$	−7.31124	−0.529023	−0.264512	+	0.964383i	$0.585211\pi$
$192$	1.00000	0.0721688
$193$	−20.2062	−1.45447	−0.727237	−	0.686386i	$-0.759196\pi$
$193$	−20.2062	−1.45447	−0.727237	+	0.686386i	$0.759196\pi$
$194$	9.00000	0.646162
$195$	6.92162	0.495668
$196$	8.04945	0.574961
$197$	−19.7587	−1.40775	−0.703875	−	0.710323i	$-0.748549\pi$
$197$	−19.7587	−1.40775	−0.703875	+	0.710323i	$0.748549\pi$
$198$	−3.26180	−0.231806
$199$	9.40522	0.666718	0.333359	−	0.942800i	$-0.391818\pi$
$199$	9.40522	0.666718	0.333359	+	0.942800i	$0.391818\pi$
$200$	−1.92162	−0.135879
$201$	−9.70928	−0.684839
$202$	7.12783	0.501512
$203$	6.63090	0.465398
$204$	−1.00000	−0.0700140
$205$	17.6514	1.23283
$206$	−6.40295	−0.446115
$207$	2.46081	0.171038
$208$	2.63090	0.182420
$209$	12.9528	0.895965
$210$	−10.2062	−0.704295
$211$	−17.5441	−1.20779	−0.603893	−	0.797065i	$-0.706385\pi$
$211$	−17.5441	−1.20779	−0.603893	+	0.797065i	$0.706385\pi$
$212$	8.03612	0.551923
$213$	12.2062	0.836355
$214$	3.63090	0.248203
$215$	2.42469	0.165363
$216$	−1.00000	−0.0680414
$217$	−7.75872	−0.526696
$218$	0.764867	0.0518033
$219$	3.29072	0.222367
$220$	8.58145	0.578561
$221$	−2.63090	−0.176973
$222$	10.2062	0.684996
$223$	−18.3896	−1.23146	−0.615730	−	0.787957i	$-0.711139\pi$
$223$	−18.3896	−1.23146	−0.615730	+	0.787957i	$0.711139\pi$
$224$	−3.87936	−0.259201
$225$	1.92162	0.128108
$226$	−19.5669	−1.30157
$227$	19.0433	1.26395	0.631974	−	0.774989i	$-0.282245\pi$
$227$	19.0433	1.26395	0.631974	+	0.774989i	$0.282245\pi$
$228$	3.97107	0.262991
$229$	−8.61757	−0.569465	−0.284732	−	0.958607i	$-0.591905\pi$
$229$	−8.61757	−0.569465	−0.284732	+	0.958607i	$0.591905\pi$
$230$	−6.47414	−0.426892
$231$	12.6537	0.832551
$232$	−1.70928	−0.112219
$233$	1.31965	0.0864534	0.0432267	−	0.999065i	$-0.486236\pi$
$233$	1.31965	0.0864534	0.0432267	+	0.999065i	$0.486236\pi$
$234$	−2.63090	−0.171987
$235$	−15.0205	−0.979831
$236$	−1.00000	−0.0650945
$237$	−13.8082	−0.896937
$238$	3.87936	0.251462
$239$	10.9711	0.709660	0.354830	−	0.934931i	$-0.384539\pi$
$239$	10.9711	0.709660	0.354830	+	0.934931i	$0.384539\pi$
$240$	2.63090	0.169824
$241$	−8.02279	−0.516793	−0.258397	−	0.966039i	$-0.583194\pi$
$241$	−8.02279	−0.516793	−0.258397	+	0.966039i	$0.583194\pi$
$242$	0.360692	0.0231862
$243$	1.00000	0.0641500
$244$	−4.73820	−0.303332
$245$	21.1773	1.35297
$246$	−6.70928	−0.427768
$247$	10.4475	0.664757
$248$	2.00000	0.127000
$249$	−12.8082	−0.811685
$250$	8.09890	0.512219
$251$	−19.3835	−1.22347	−0.611737	−	0.791061i	$-0.709529\pi$
$251$	−19.3835	−1.22347	−0.611737	+	0.791061i	$0.709529\pi$
$252$	3.87936	0.244377
$253$	8.02666	0.504632
$254$	−11.2846	−0.708058
$255$	−2.63090	−0.164753
$256$	1.00000	0.0625000
$257$	−29.7237	−1.85411	−0.927055	−	0.374925i	$-0.877669\pi$
$257$	−29.7237	−1.85411	−0.927055	+	0.374925i	$0.877669\pi$
$258$	−0.921622	−0.0573777
$259$	−39.5936	−2.46022
$260$	6.92162	0.429261
$261$	1.70928	0.105801
$262$	13.2267	0.817150
$263$	15.6732	0.966448	0.483224	−	0.875497i	$-0.339466\pi$
$263$	15.6732	0.966448	0.483224	+	0.875497i	$0.339466\pi$
$264$	−3.26180	−0.200750
$265$	21.1422	1.29876
$266$	−15.4052	−0.944555
$267$	−10.2618	−0.628012
$268$	−9.70928	−0.593088
$269$	18.1122	1.10432	0.552161	−	0.833738i	$-0.313803\pi$
$269$	18.1122	1.10432	0.552161	+	0.833738i	$0.313803\pi$
$270$	−2.63090	−0.160111
$271$	−13.1773	−0.800462	−0.400231	−	0.916414i	$-0.631070\pi$
$271$	−13.1773	−0.800462	−0.400231	+	0.916414i	$0.631070\pi$
$272$	−1.00000	−0.0606339
$273$	10.2062	0.617708
$274$	−21.4680	−1.29693
$275$	6.26794	0.377971
$276$	2.46081	0.148123
$277$	10.0095	0.601410	0.300705	−	0.953717i	$-0.402778\pi$
$277$	10.0095	0.601410	0.300705	+	0.953717i	$0.402778\pi$
$278$	12.3896	0.743080
$279$	−2.00000	−0.119737
$280$	−10.2062	−0.609937
$281$	18.4885	1.10293	0.551466	−	0.834197i	$-0.314069\pi$
$281$	18.4885	1.10293	0.551466	+	0.834197i	$0.314069\pi$
$282$	5.70928	0.339982
$283$	22.1773	1.31830	0.659151	−	0.752011i	$-0.270916\pi$
$283$	22.1773	1.31830	0.659151	+	0.752011i	$0.270916\pi$
$284$	12.2062	0.724305
$285$	10.4475	0.618855
$286$	−8.58145	−0.507432
$287$	26.0277	1.53637
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−4.49693	−0.264069
$291$	−9.00000	−0.527589
$292$	3.29072	0.192575
$293$	−16.7877	−0.980745	−0.490373	−	0.871513i	$-0.663139\pi$
$293$	−16.7877	−0.980745	−0.490373	+	0.871513i	$0.663139\pi$
$294$	−8.04945	−0.469453
$295$	−2.63090	−0.153177
$296$	10.2062	0.593224
$297$	3.26180	0.189269
$298$	7.23513	0.419120
$299$	6.47414	0.374409
$300$	1.92162	0.110945
$301$	3.57531	0.206077
$302$	4.82377	0.277577
$303$	−7.12783	−0.409483
$304$	3.97107	0.227757
$305$	−12.4657	−0.713786
$306$	1.00000	0.0571662
$307$	−27.4969	−1.56933	−0.784666	−	0.619918i	$-0.787166\pi$
$307$	−27.4969	−1.56933	−0.784666	+	0.619918i	$0.787166\pi$
$308$	12.6537	0.721011
$309$	6.40295	0.364251
$310$	5.26180	0.298850
$311$	−11.3112	−0.641402	−0.320701	−	0.947181i	$-0.603918\pi$
$311$	−11.3112	−0.641402	−0.320701	+	0.947181i	$0.603918\pi$
$312$	−2.63090	−0.148945
$313$	5.50307	0.311052	0.155526	−	0.987832i	$-0.450293\pi$
$313$	5.50307	0.311052	0.155526	+	0.987832i	$0.450293\pi$
$314$	−3.14116	−0.177266
$315$	10.2062	0.575054
$316$	−13.8082	−0.776770
$317$	−17.6598	−0.991875	−0.495937	−	0.868358i	$-0.665175\pi$
$317$	−17.6598	−0.991875	−0.495937	+	0.868358i	$0.665175\pi$
$318$	−8.03612	−0.450643
$319$	5.57531	0.312157
$320$	2.63090	0.147072
$321$	−3.63090	−0.202657
$322$	−9.54638	−0.531999
$323$	−3.97107	−0.220956
$324$	1.00000	0.0555556
$325$	5.05559	0.280434
$326$	−3.52586	−0.195279
$327$	−0.764867	−0.0422972
$328$	−6.70928	−0.370458
$329$	−22.1483	−1.22108
$330$	−8.58145	−0.472393
$331$	30.5174	1.67739	0.838695	−	0.544601i	$-0.183319\pi$
$331$	30.5174	1.67739	0.838695	+	0.544601i	$0.183319\pi$
$332$	−12.8082	−0.702940
$333$	−10.2062	−0.559297
$334$	16.4124	0.898047
$335$	−25.5441	−1.39562
$336$	3.87936	0.211637
$337$	5.78765	0.315274	0.157637	−	0.987497i	$-0.449612\pi$
$337$	5.78765	0.315274	0.157637	+	0.987497i	$0.449612\pi$
$338$	6.07838	0.330620
$339$	19.5669	1.06273
$340$	−2.63090	−0.142680
$341$	−6.52359	−0.353272
$342$	−3.97107	−0.214731
$343$	4.07119	0.219824
$344$	−0.921622	−0.0496905
$345$	6.47414	0.348556
$346$	−18.9132	−1.01678
$347$	17.7503	0.952887	0.476443	−	0.879205i	$-0.341926\pi$
$347$	17.7503	0.952887	0.476443	+	0.879205i	$0.341926\pi$
$348$	1.70928	0.0916268
$349$	−31.6609	−1.69477	−0.847384	−	0.530981i	$-0.821824\pi$
$349$	−31.6609	−1.69477	−0.847384	+	0.530981i	$0.821824\pi$
$350$	−7.45467	−0.398469
$351$	2.63090	0.140427
$352$	−3.26180	−0.173854
$353$	−17.4163	−0.926975	−0.463488	−	0.886103i	$-0.653402\pi$
$353$	−17.4163	−0.926975	−0.463488	+	0.886103i	$0.653402\pi$
$354$	1.00000	0.0531494
$355$	32.1133	1.70440
$356$	−10.2618	−0.543874
$357$	−3.87936	−0.205318
$358$	14.7854	0.781432
$359$	27.0566	1.42799	0.713997	−	0.700148i	$-0.246883\pi$
$359$	27.0566	1.42799	0.713997	+	0.700148i	$0.246883\pi$
$360$	−2.63090	−0.138660
$361$	−3.23060	−0.170031
$362$	−3.89269	−0.204595
$363$	−0.360692	−0.0189314
$364$	10.2062	0.534950
$365$	8.65756	0.453157
$366$	4.73820	0.247670
$367$	7.23513	0.377671	0.188835	−	0.982009i	$-0.439529\pi$
$367$	7.23513	0.377671	0.188835	+	0.982009i	$0.439529\pi$
$368$	2.46081	0.128279
$369$	6.70928	0.349271
$370$	26.8515	1.39594
$371$	31.1750	1.61853
$372$	−2.00000	−0.103695
$373$	−9.39576	−0.486494	−0.243247	−	0.969964i	$-0.578213\pi$
$373$	−9.39576	−0.486494	−0.243247	+	0.969964i	$0.578213\pi$
$374$	3.26180	0.168663
$375$	−8.09890	−0.418225
$376$	5.70928	0.294433
$377$	4.49693	0.231604
$378$	−3.87936	−0.199533
$379$	−6.39803	−0.328645	−0.164322	−	0.986407i	$-0.552544\pi$
$379$	−6.39803	−0.328645	−0.164322	+	0.986407i	$0.552544\pi$
$380$	10.4475	0.535944
$381$	11.2846	0.578127
$382$	7.31124	0.374076
$383$	−28.5330	−1.45797	−0.728985	−	0.684529i	$-0.760008\pi$
$383$	−28.5330	−1.45797	−0.728985	+	0.684529i	$0.760008\pi$
$384$	−1.00000	−0.0510310
$385$	33.2905	1.69664
$386$	20.2062	1.02847
$387$	0.921622	0.0468487
$388$	−9.00000	−0.456906
$389$	36.7175	1.86165	0.930826	−	0.365463i	$-0.119089\pi$
$389$	36.7175	1.86165	0.930826	+	0.365463i	$0.119089\pi$
$390$	−6.92162	−0.350490
$391$	−2.46081	−0.124449
$392$	−8.04945	−0.406559
$393$	−13.2267	−0.667200
$394$	19.7587	0.995430
$395$	−36.3279	−1.82785
$396$	3.26180	0.163911
$397$	−16.6719	−0.836740	−0.418370	−	0.908277i	$-0.637399\pi$
$397$	−16.6719	−0.836740	−0.418370	+	0.908277i	$0.637399\pi$
$398$	−9.40522	−0.471441
$399$	15.4052	0.771226
$400$	1.92162	0.0960811
$401$	9.80817	0.489797	0.244898	−	0.969549i	$-0.421245\pi$
$401$	9.80817	0.489797	0.244898	+	0.969549i	$0.421245\pi$
$402$	9.70928	0.484255
$403$	−5.26180	−0.262109
$404$	−7.12783	−0.354623
$405$	2.63090	0.130730
$406$	−6.63090	−0.329086
$407$	−33.2905	−1.65015
$408$	1.00000	0.0495074
$409$	−9.00614	−0.445325	−0.222663	−	0.974896i	$-0.571475\pi$
$409$	−9.00614	−0.445325	−0.222663	+	0.974896i	$0.571475\pi$
$410$	−17.6514	−0.871741
$411$	21.4680	1.05894
$412$	6.40295	0.315451
$413$	−3.87936	−0.190891
$414$	−2.46081	−0.120942
$415$	−33.6970	−1.65412
$416$	−2.63090	−0.128990
$417$	−12.3896	−0.606722
$418$	−12.9528	−0.633543
$419$	30.8554	1.50738	0.753691	−	0.657229i	$-0.228271\pi$
$419$	30.8554	1.50738	0.753691	+	0.657229i	$0.228271\pi$
$420$	10.2062	0.498012
$421$	21.0566	1.02624	0.513119	−	0.858318i	$-0.328490\pi$
$421$	21.0566	1.02624	0.513119	+	0.858318i	$0.328490\pi$
$422$	17.5441	0.854034
$423$	−5.70928	−0.277594
$424$	−8.03612	−0.390268
$425$	−1.92162	−0.0932124
$426$	−12.2062	−0.591393
$427$	−18.3812	−0.889529
$428$	−3.63090	−0.175506
$429$	8.58145	0.414316
$430$	−2.42469	−0.116929
$431$	−33.7286	−1.62465	−0.812324	−	0.583206i	$-0.801798\pi$
$431$	−33.7286	−1.62465	−0.812324	+	0.583206i	$0.801798\pi$
$432$	1.00000	0.0481125
$433$	5.99386	0.288046	0.144023	−	0.989574i	$-0.453996\pi$
$433$	5.99386	0.288046	0.144023	+	0.989574i	$0.453996\pi$
$434$	7.75872	0.372431
$435$	4.49693	0.215611
$436$	−0.764867	−0.0366305
$437$	9.77205	0.467461
$438$	−3.29072	−0.157237
$439$	3.65142	0.174273	0.0871363	−	0.996196i	$-0.472228\pi$
$439$	3.65142	0.174273	0.0871363	+	0.996196i	$0.472228\pi$
$440$	−8.58145	−0.409105
$441$	8.04945	0.383307
$442$	2.63090	0.125139
$443$	39.9048	1.89593	0.947967	−	0.318368i	$-0.103135\pi$
$443$	39.9048	1.89593	0.947967	+	0.318368i	$0.103135\pi$
$444$	−10.2062	−0.484365
$445$	−26.9977	−1.27982
$446$	18.3896	0.870774
$447$	−7.23513	−0.342210
$448$	3.87936	0.183283
$449$	2.04718	0.0966124	0.0483062	−	0.998833i	$-0.484618\pi$
$449$	2.04718	0.0966124	0.0483062	+	0.998833i	$0.484618\pi$
$450$	−1.92162	−0.0905861
$451$	21.8843	1.03049
$452$	19.5669	0.920349
$453$	−4.82377	−0.226641
$454$	−19.0433	−0.893747
$455$	26.8515	1.25882
$456$	−3.97107	−0.185962
$457$	−7.78151	−0.364004	−0.182002	−	0.983298i	$-0.558258\pi$
$457$	−7.78151	−0.364004	−0.182002	+	0.983298i	$0.558258\pi$
$458$	8.61757	0.402672
$459$	−1.00000	−0.0466760
$460$	6.47414	0.301858
$461$	28.1929	1.31307	0.656536	−	0.754294i	$-0.272021\pi$
$461$	28.1929	1.31307	0.656536	+	0.754294i	$0.272021\pi$
$462$	−12.6537	−0.588703
$463$	14.0228	0.651694	0.325847	−	0.945422i	$-0.394351\pi$
$463$	14.0228	0.651694	0.325847	+	0.945422i	$0.394351\pi$
$464$	1.70928	0.0793511
$465$	−5.26180	−0.244010
$466$	−1.31965	−0.0611318
$467$	−12.7792	−0.591353	−0.295676	−	0.955288i	$-0.595545\pi$
$467$	−12.7792	−0.591353	−0.295676	+	0.955288i	$0.595545\pi$
$468$	2.63090	0.121613
$469$	−37.6658	−1.73924
$470$	15.0205	0.692845
$471$	3.14116	0.144737
$472$	1.00000	0.0460287
$473$	3.00614	0.138223
$474$	13.8082	0.634230
$475$	7.63090	0.350130
$476$	−3.87936	−0.177810
$477$	8.03612	0.367949
$478$	−10.9711	−0.501805
$479$	29.3340	1.34031	0.670153	−	0.742223i	$-0.266228\pi$
$479$	29.3340	1.34031	0.670153	+	0.742223i	$0.266228\pi$
$480$	−2.63090	−0.120083
$481$	−26.8515	−1.22432
$482$	8.02279	0.365428
$483$	9.54638	0.434375
$484$	−0.360692	−0.0163951
$485$	−23.6781	−1.07517
$486$	−1.00000	−0.0453609
$487$	−30.6814	−1.39031	−0.695153	−	0.718862i	$-0.744664\pi$
$487$	−30.6814	−1.39031	−0.695153	+	0.718862i	$0.744664\pi$
$488$	4.73820	0.214488
$489$	3.52586	0.159445
$490$	−21.1773	−0.956692
$491$	5.02893	0.226952	0.113476	−	0.993541i	$-0.463801\pi$
$491$	5.02893	0.226952	0.113476	+	0.993541i	$0.463801\pi$
$492$	6.70928	0.302477
$493$	−1.70928	−0.0769819
$494$	−10.4475	−0.470054
$495$	8.58145	0.385707
$496$	−2.00000	−0.0898027
$497$	47.3523	2.12404
$498$	12.8082	0.573948
$499$	10.4885	0.469531	0.234765	−	0.972052i	$-0.424568\pi$
$499$	10.4885	0.469531	0.234765	+	0.972052i	$0.424568\pi$
$500$	−8.09890	−0.362194
$501$	−16.4124	−0.733252
$502$	19.3835	0.865127
$503$	20.8238	0.928486	0.464243	−	0.885708i	$-0.346326\pi$
$503$	20.8238	0.928486	0.464243	+	0.885708i	$0.346326\pi$
$504$	−3.87936	−0.172801
$505$	−18.7526	−0.834479
$506$	−8.02666	−0.356829
$507$	−6.07838	−0.269950
$508$	11.2846	0.500672
$509$	−0.921622	−0.0408502	−0.0204251	−	0.999791i	$-0.506502\pi$
$509$	−0.921622	−0.0408502	−0.0204251	+	0.999791i	$0.506502\pi$
$510$	2.63090	0.116498
$511$	12.7659	0.564731
$512$	−1.00000	−0.0441942
$513$	3.97107	0.175327
$514$	29.7237	1.31105
$515$	16.8455	0.742302
$516$	0.921622	0.0405722
$517$	−18.6225	−0.819016
$518$	39.5936	1.73964
$519$	18.9132	0.830198
$520$	−6.92162	−0.303533
$521$	11.1978	0.490584	0.245292	−	0.969449i	$-0.421116\pi$
$521$	11.1978	0.490584	0.245292	+	0.969449i	$0.421116\pi$
$522$	−1.70928	−0.0748130
$523$	−16.8104	−0.735069	−0.367535	−	0.930010i	$-0.619798\pi$
$523$	−16.8104	−0.735069	−0.367535	+	0.930010i	$0.619798\pi$
$524$	−13.2267	−0.577812
$525$	7.45467	0.325348
$526$	−15.6732	−0.683382
$527$	2.00000	0.0871214
$528$	3.26180	0.141951
$529$	−16.9444	−0.736713
$530$	−21.1422	−0.918359
$531$	−1.00000	−0.0433963
$532$	15.4052	0.667901
$533$	17.6514	0.764568
$534$	10.2618	0.444071
$535$	−9.55252	−0.412991
$536$	9.70928	0.419377
$537$	−14.7854	−0.638036
$538$	−18.1122	−0.780874
$539$	26.2557	1.13091
$540$	2.63090	0.113216
$541$	−4.99386	−0.214703	−0.107351	−	0.994221i	$-0.534237\pi$
$541$	−4.99386	−0.214703	−0.107351	+	0.994221i	$0.534237\pi$
$542$	13.1773	0.566012
$543$	3.89269	0.167051
$544$	1.00000	0.0428746
$545$	−2.01229	−0.0861969
$546$	−10.2062	−0.436785
$547$	23.9109	1.02236	0.511179	−	0.859474i	$-0.329209\pi$
$547$	23.9109	1.02236	0.511179	+	0.859474i	$0.329209\pi$
$548$	21.4680	0.917067
$549$	−4.73820	−0.202222
$550$	−6.26794	−0.267266
$551$	6.78765	0.289164
$552$	−2.46081	−0.104739
$553$	−53.5669	−2.27790
$554$	−10.0095	−0.425261
$555$	−26.8515	−1.13978
$556$	−12.3896	−0.525437
$557$	−12.9711	−0.549602	−0.274801	−	0.961501i	$-0.588612\pi$
$557$	−12.9711	−0.549602	−0.274801	+	0.961501i	$0.588612\pi$
$558$	2.00000	0.0846668
$559$	2.42469	0.102554
$560$	10.2062	0.431291
$561$	−3.26180	−0.137713
$562$	−18.4885	−0.779891
$563$	15.4969	0.653118	0.326559	−	0.945177i	$-0.394111\pi$
$563$	15.4969	0.653118	0.326559	+	0.945177i	$0.394111\pi$
$564$	−5.70928	−0.240404
$565$	51.4785	2.16572
$566$	−22.1773	−0.932180
$567$	3.87936	0.162918
$568$	−12.2062	−0.512161
$569$	29.9216	1.25438	0.627190	−	0.778866i	$-0.284205\pi$
$569$	29.9216	1.25438	0.627190	+	0.778866i	$0.284205\pi$
$570$	−10.4475	−0.437597
$571$	23.3461	0.977005	0.488503	−	0.872562i	$-0.337543\pi$
$571$	23.3461	0.977005	0.488503	+	0.872562i	$0.337543\pi$
$572$	8.58145	0.358808
$573$	−7.31124	−0.305432
$574$	−26.0277	−1.08638
$575$	4.72875	0.197202
$576$	1.00000	0.0416667
$577$	33.3028	1.38642	0.693208	−	0.720738i	$-0.256197\pi$
$577$	33.3028	1.38642	0.693208	+	0.720738i	$0.256197\pi$
$578$	−1.00000	−0.0415945
$579$	−20.2062	−0.839741
$580$	4.49693	0.186725
$581$	−49.6875	−2.06139
$582$	9.00000	0.373062
$583$	26.2122	1.08560
$584$	−3.29072	−0.136171
$585$	6.92162	0.286174
$586$	16.7877	0.693492
$587$	34.2534	1.41379	0.706894	−	0.707319i	$-0.250096\pi$
$587$	34.2534	1.41379	0.706894	+	0.707319i	$0.250096\pi$
$588$	8.04945	0.331954
$589$	−7.94214	−0.327250
$590$	2.63090	0.108312
$591$	−19.7587	−0.812765
$592$	−10.2062	−0.419472
$593$	19.9688	0.820020	0.410010	−	0.912081i	$-0.365525\pi$
$593$	19.9688	0.820020	0.410010	+	0.912081i	$0.365525\pi$
$594$	−3.26180	−0.133833
$595$	−10.2062	−0.418414
$596$	−7.23513	−0.296363
$597$	9.40522	0.384930
$598$	−6.47414	−0.264747
$599$	17.2401	0.704409	0.352205	−	0.935923i	$-0.385432\pi$
$599$	17.2401	0.704409	0.352205	+	0.935923i	$0.385432\pi$
$600$	−1.92162	−0.0784499
$601$	7.49693	0.305806	0.152903	−	0.988241i	$-0.451138\pi$
$601$	7.49693	0.305806	0.152903	+	0.988241i	$0.451138\pi$
$602$	−3.57531	−0.145719
$603$	−9.70928	−0.395392
$604$	−4.82377	−0.196276
$605$	−0.948943	−0.0385800
$606$	7.12783	0.289548
$607$	18.5558	0.753158	0.376579	−	0.926385i	$-0.377100\pi$
$607$	18.5558	0.753158	0.376579	+	0.926385i	$0.377100\pi$
$608$	−3.97107	−0.161048
$609$	6.63090	0.268698
$610$	12.4657	0.504723
$611$	−15.0205	−0.607665
$612$	−1.00000	−0.0404226
$613$	13.1762	0.532183	0.266091	−	0.963948i	$-0.414268\pi$
$613$	13.1762	0.532183	0.266091	+	0.963948i	$0.414268\pi$
$614$	27.4969	1.10969
$615$	17.6514	0.711774
$616$	−12.6537	−0.509831
$617$	25.0494	1.00845	0.504226	−	0.863571i	$-0.331778\pi$
$617$	25.0494	1.00845	0.504226	+	0.863571i	$0.331778\pi$
$618$	−6.40295	−0.257565
$619$	32.0228	1.28710	0.643552	−	0.765402i	$-0.277460\pi$
$619$	32.0228	1.28710	0.643552	+	0.765402i	$0.277460\pi$
$620$	−5.26180	−0.211319
$621$	2.46081	0.0987489
$622$	11.3112	0.453540
$623$	−39.8092	−1.59492
$624$	2.63090	0.105320
$625$	−30.9155	−1.23662
$626$	−5.50307	−0.219947
$627$	12.9528	0.517286
$628$	3.14116	0.125346
$629$	10.2062	0.406948
$630$	−10.2062	−0.406625
$631$	22.3545	0.889921	0.444960	−	0.895550i	$-0.353218\pi$
$631$	22.3545	0.889921	0.444960	+	0.895550i	$0.353218\pi$
$632$	13.8082	0.549260
$633$	−17.5441	−0.697316
$634$	17.6598	0.701361
$635$	29.6886	1.17816
$636$	8.03612	0.318653
$637$	21.1773	0.839074
$638$	−5.57531	−0.220728
$639$	12.2062	0.482870
$640$	−2.63090	−0.103995
$641$	−18.2534	−0.720965	−0.360483	−	0.932766i	$-0.617388\pi$
$641$	−18.2534	−0.720965	−0.360483	+	0.932766i	$0.617388\pi$
$642$	3.63090	0.143300
$643$	−9.01211	−0.355403	−0.177701	−	0.984084i	$-0.556866\pi$
$643$	−9.01211	−0.355403	−0.177701	+	0.984084i	$0.556866\pi$
$644$	9.54638	0.376180
$645$	2.42469	0.0954722
$646$	3.97107	0.156240
$647$	24.3041	0.955491	0.477746	−	0.878498i	$-0.341454\pi$
$647$	24.3041	0.955491	0.477746	+	0.878498i	$0.341454\pi$
$648$	−1.00000	−0.0392837
$649$	−3.26180	−0.128037
$650$	−5.05559	−0.198297
$651$	−7.75872	−0.304088
$652$	3.52586	0.138083
$653$	−25.9299	−1.01471	−0.507357	−	0.861736i	$-0.669377\pi$
$653$	−25.9299	−1.01471	−0.507357	+	0.861736i	$0.669377\pi$
$654$	0.764867	0.0299087
$655$	−34.7982	−1.35968
$656$	6.70928	0.261953
$657$	3.29072	0.128383
$658$	22.1483	0.863432
$659$	−20.0433	−0.780776	−0.390388	−	0.920650i	$-0.627659\pi$
$659$	−20.0433	−0.780776	−0.390388	+	0.920650i	$0.627659\pi$
$660$	8.58145	0.334032
$661$	19.9011	0.774063	0.387032	−	0.922066i	$-0.373500\pi$
$661$	19.9011	0.774063	0.387032	+	0.922066i	$0.373500\pi$
$662$	−30.5174	−1.18609
$663$	−2.63090	−0.102176
$664$	12.8082	0.497053
$665$	40.5296	1.57167
$666$	10.2062	0.395482
$667$	4.20620	0.162865
$668$	−16.4124	−0.635015
$669$	−18.3896	−0.710984
$670$	25.5441	0.986855
$671$	−15.4551	−0.596636
$672$	−3.87936	−0.149650
$673$	−33.8638	−1.30535	−0.652676	−	0.757637i	$-0.726354\pi$
$673$	−33.8638	−1.30535	−0.652676	+	0.757637i	$0.726354\pi$
$674$	−5.78765	−0.222932
$675$	1.92162	0.0739633
$676$	−6.07838	−0.233784
$677$	4.00388	0.153881	0.0769407	−	0.997036i	$-0.475485\pi$
$677$	4.00388	0.153881	0.0769407	+	0.997036i	$0.475485\pi$
$678$	−19.5669	−0.751462
$679$	−34.9143	−1.33989
$680$	2.63090	0.100890
$681$	19.0433	0.729741
$682$	6.52359	0.249801
$683$	−35.2411	−1.34846	−0.674232	−	0.738520i	$-0.735525\pi$
$683$	−35.2411	−1.34846	−0.674232	+	0.738520i	$0.735525\pi$
$684$	3.97107	0.151838
$685$	56.4801	2.15799
$686$	−4.07119	−0.155439
$687$	−8.61757	−0.328781
$688$	0.921622	0.0351365
$689$	21.1422	0.805454
$690$	−6.47414	−0.246466
$691$	−25.6498	−0.975765	−0.487882	−	0.872909i	$-0.662230\pi$
$691$	−25.6498	−0.975765	−0.487882	+	0.872909i	$0.662230\pi$
$692$	18.9132	0.718972
$693$	12.6537	0.480674
$694$	−17.7503	−0.673793
$695$	−32.5958	−1.23643
$696$	−1.70928	−0.0647899
$697$	−6.70928	−0.254132
$698$	31.6609	1.19838
$699$	1.31965	0.0499139
$700$	7.45467	0.281760
$701$	43.9299	1.65921	0.829604	−	0.558352i	$-0.188566\pi$
$701$	43.9299	1.65921	0.829604	+	0.558352i	$0.188566\pi$
$702$	−2.63090	−0.0992968
$703$	−40.5296	−1.52860
$704$	3.26180	0.122934
$705$	−15.0205	−0.565705
$706$	17.4163	0.655470
$707$	−27.6514	−1.03994
$708$	−1.00000	−0.0375823
$709$	2.36296	0.0887428	0.0443714	−	0.999015i	$-0.485872\pi$
$709$	2.36296	0.0887428	0.0443714	+	0.999015i	$0.485872\pi$
$710$	−32.1133	−1.20519
$711$	−13.8082	−0.517847
$712$	10.2618	0.384577
$713$	−4.92162	−0.184316
$714$	3.87936	0.145181
$715$	22.5769	0.844329
$716$	−14.7854	−0.552556
$717$	10.9711	0.409722
$718$	−27.0566	−1.00974
$719$	−2.02279	−0.0754372	−0.0377186	−	0.999288i	$-0.512009\pi$
$719$	−2.02279	−0.0754372	−0.0377186	+	0.999288i	$0.512009\pi$
$720$	2.63090	0.0980478
$721$	24.8394	0.925066
$722$	3.23060	0.120230
$723$	−8.02279	−0.298371
$724$	3.89269	0.144671
$725$	3.28458	0.121986
$726$	0.360692	0.0133865
$727$	−19.8517	−0.736257	−0.368129	−	0.929775i	$-0.620001\pi$
$727$	−19.8517	−0.736257	−0.368129	+	0.929775i	$0.620001\pi$
$728$	−10.2062	−0.378267
$729$	1.00000	0.0370370
$730$	−8.65756	−0.320431
$731$	−0.921622	−0.0340874
$732$	−4.73820	−0.175129
$733$	16.1340	0.595922	0.297961	−	0.954578i	$-0.403694\pi$
$733$	16.1340	0.595922	0.297961	+	0.954578i	$0.403694\pi$
$734$	−7.23513	−0.267054
$735$	21.1773	0.781136
$736$	−2.46081	−0.0907067
$737$	−31.6697	−1.16657
$738$	−6.70928	−0.246972
$739$	−0.0845208	−0.00310915	−0.00155457	−	0.999999i	$-0.500495\pi$
$739$	−0.0845208	−0.00310915	−0.00155457	+	0.999999i	$0.500495\pi$
$740$	−26.8515	−0.987080
$741$	10.4475	0.383798
$742$	−31.1750	−1.14447
$743$	39.1050	1.43462	0.717312	−	0.696752i	$-0.245372\pi$
$743$	39.1050	1.43462	0.717312	+	0.696752i	$0.245372\pi$
$744$	2.00000	0.0733236
$745$	−19.0349	−0.697385
$746$	9.39576	0.344003
$747$	−12.8082	−0.468627
$748$	−3.26180	−0.119263
$749$	−14.0856	−0.514675
$750$	8.09890	0.295730
$751$	8.20620	0.299449	0.149724	−	0.988728i	$-0.452161\pi$
$751$	8.20620	0.299449	0.149724	+	0.988728i	$0.452161\pi$
$752$	−5.70928	−0.208196
$753$	−19.3835	−0.706373
$754$	−4.49693	−0.163768
$755$	−12.6908	−0.461867
$756$	3.87936	0.141091
$757$	−0.255652	−0.00929184	−0.00464592	−	0.999989i	$-0.501479\pi$
$757$	−0.255652	−0.00929184	−0.00464592	+	0.999989i	$0.501479\pi$
$758$	6.39803	0.232387
$759$	8.02666	0.291349
$760$	−10.4475	−0.378970
$761$	23.6209	0.856256	0.428128	−	0.903718i	$-0.359173\pi$
$761$	23.6209	0.856256	0.428128	+	0.903718i	$0.359173\pi$
$762$	−11.2846	−0.408797
$763$	−2.96719	−0.107420
$764$	−7.31124	−0.264512
$765$	−2.63090	−0.0951203
$766$	28.5330	1.03094
$767$	−2.63090	−0.0949962
$768$	1.00000	0.0360844
$769$	−19.0700	−0.687681	−0.343840	−	0.939028i	$-0.611728\pi$
$769$	−19.0700	−0.687681	−0.343840	+	0.939028i	$0.611728\pi$
$770$	−33.2905	−1.19971
$771$	−29.7237	−1.07047
$772$	−20.2062	−0.727237
$773$	20.9399	0.753155	0.376577	−	0.926385i	$-0.377101\pi$
$773$	20.9399	0.753155	0.376577	+	0.926385i	$0.377101\pi$
$774$	−0.921622	−0.0331270
$775$	−3.84324	−0.138053
$776$	9.00000	0.323081
$777$	−39.5936	−1.42041
$778$	−36.7175	−1.31639
$779$	26.6430	0.954585
$780$	6.92162	0.247834
$781$	39.8141	1.42466
$782$	2.46081	0.0879984
$783$	1.70928	0.0610845
$784$	8.04945	0.287480
$785$	8.26406	0.294957
$786$	13.2267	0.471782
$787$	50.3545	1.79495	0.897473	−	0.441070i	$-0.145401\pi$
$787$	50.3545	1.79495	0.897473	+	0.441070i	$0.145401\pi$
$788$	−19.7587	−0.703875
$789$	15.6732	0.557979
$790$	36.3279	1.29249
$791$	75.9071	2.69894
$792$	−3.26180	−0.115903
$793$	−12.4657	−0.442671
$794$	16.6719	0.591665
$795$	21.1422	0.749837
$796$	9.40522	0.333359
$797$	10.0761	0.356914	0.178457	−	0.983948i	$-0.442889\pi$
$797$	10.0761	0.356914	0.178457	+	0.983948i	$0.442889\pi$
$798$	−15.4052	−0.545339
$799$	5.70928	0.201980
$800$	−1.92162	−0.0679396
$801$	−10.2618	−0.362583
$802$	−9.80817	−0.346339
$803$	10.7337	0.378783
$804$	−9.70928	−0.342420
$805$	25.1155	0.885206
$806$	5.26180	0.185339
$807$	18.1122	0.637581
$808$	7.12783	0.250756
$809$	−20.9444	−0.736366	−0.368183	−	0.929753i	$-0.620020\pi$
$809$	−20.9444	−0.736366	−0.368183	+	0.929753i	$0.620020\pi$
$810$	−2.63090	−0.0924403
$811$	49.4268	1.73561	0.867805	−	0.496906i	$-0.165531\pi$
$811$	49.4268	1.73561	0.867805	+	0.496906i	$0.165531\pi$
$812$	6.63090	0.232699
$813$	−13.1773	−0.462147
$814$	33.2905	1.16683
$815$	9.27617	0.324930
$816$	−1.00000	−0.0350070
$817$	3.65983	0.128041
$818$	9.00614	0.314892
$819$	10.2062	0.356634
$820$	17.6514	0.616414
$821$	−22.4440	−0.783301	−0.391650	−	0.920114i	$-0.628096\pi$
$821$	−22.4440	−0.783301	−0.391650	+	0.920114i	$0.628096\pi$
$822$	−21.4680	−0.748782
$823$	−30.4801	−1.06247	−0.531235	−	0.847225i	$-0.678272\pi$
$823$	−30.4801	−1.06247	−0.531235	+	0.847225i	$0.678272\pi$
$824$	−6.40295	−0.223057
$825$	6.26794	0.218222
$826$	3.87936	0.134980
$827$	25.5814	0.889554	0.444777	−	0.895641i	$-0.353283\pi$
$827$	25.5814	0.889554	0.444777	+	0.895641i	$0.353283\pi$
$828$	2.46081	0.0855191
$829$	16.9711	0.589430	0.294715	−	0.955585i	$-0.404775\pi$
$829$	16.9711	0.589430	0.294715	+	0.955585i	$0.404775\pi$
$830$	33.6970	1.16964
$831$	10.0095	0.347224
$832$	2.63090	0.0912100
$833$	−8.04945	−0.278897
$834$	12.3896	0.429017
$835$	−43.1794	−1.49428
$836$	12.9528	0.447983
$837$	−2.00000	−0.0691301
$838$	−30.8554	−1.06588
$839$	−55.2222	−1.90648	−0.953241	−	0.302212i	$-0.902275\pi$
$839$	−55.2222	−1.90648	−0.953241	+	0.302212i	$0.902275\pi$
$840$	−10.2062	−0.352147
$841$	−26.0784	−0.899254
$842$	−21.0566	−0.725660
$843$	18.4885	0.636778
$844$	−17.5441	−0.603893
$845$	−15.9916	−0.550127
$846$	5.70928	0.196289
$847$	−1.39925	−0.0480789
$848$	8.03612	0.275961
$849$	22.1773	0.761122
$850$	1.92162	0.0659111
$851$	−25.1155	−0.860950
$852$	12.2062	0.418178
$853$	28.0684	0.961042	0.480521	−	0.876983i	$-0.340448\pi$
$853$	28.0684	0.961042	0.480521	+	0.876983i	$0.340448\pi$
$854$	18.3812	0.628992
$855$	10.4475	0.357296
$856$	3.63090	0.124102
$857$	−7.46800	−0.255102	−0.127551	−	0.991832i	$-0.540712\pi$
$857$	−7.46800	−0.255102	−0.127551	+	0.991832i	$0.540712\pi$
$858$	−8.58145	−0.292966
$859$	56.4450	1.92588	0.962940	−	0.269716i	$-0.0869299\pi$
$859$	56.4450	1.92588	0.962940	+	0.269716i	$0.0869299\pi$
$860$	2.42469	0.0826814
$861$	26.0277	0.887022
$862$	33.7286	1.14880
$863$	−15.4680	−0.526537	−0.263268	−	0.964723i	$-0.584800\pi$
$863$	−15.4680	−0.526537	−0.263268	+	0.964723i	$0.584800\pi$
$864$	−1.00000	−0.0340207
$865$	49.7587	1.69185
$866$	−5.99386	−0.203680
$867$	1.00000	0.0339618
$868$	−7.75872	−0.263348
$869$	−45.0394	−1.52786
$870$	−4.49693	−0.152460
$871$	−25.5441	−0.865529
$872$	0.764867	0.0259017
$873$	−9.00000	−0.304604
$874$	−9.77205	−0.330545
$875$	−31.4186	−1.06214
$876$	3.29072	0.111183
$877$	−12.0979	−0.408515	−0.204258	−	0.978917i	$-0.565478\pi$
$877$	−12.0979	−0.408515	−0.204258	+	0.978917i	$0.565478\pi$
$878$	−3.65142	−0.123229
$879$	−16.7877	−0.566233
$880$	8.58145	0.289281
$881$	21.6886	0.730707	0.365353	−	0.930869i	$-0.380948\pi$
$881$	21.6886	0.730707	0.365353	+	0.930869i	$0.380948\pi$
$882$	−8.04945	−0.271039
$883$	−21.9672	−0.739255	−0.369627	−	0.929180i	$-0.620515\pi$
$883$	−21.9672	−0.739255	−0.369627	+	0.929180i	$0.620515\pi$
$884$	−2.63090	−0.0884867
$885$	−2.63090	−0.0884367
$886$	−39.9048	−1.34063
$887$	18.2013	0.611139	0.305570	−	0.952170i	$-0.401153\pi$
$887$	18.2013	0.611139	0.305570	+	0.952170i	$0.401153\pi$
$888$	10.2062	0.342498
$889$	43.7770	1.46823
$890$	26.9977	0.904966
$891$	3.26180	0.109274
$892$	−18.3896	−0.615730
$893$	−22.6719	−0.758687
$894$	7.23513	0.241979
$895$	−38.8988	−1.30024
$896$	−3.87936	−0.129600
$897$	6.47414	0.216165
$898$	−2.04718	−0.0683153
$899$	−3.41855	−0.114015
$900$	1.92162	0.0640541
$901$	−8.03612	−0.267722
$902$	−21.8843	−0.728667
$903$	3.57531	0.118979
$904$	−19.5669	−0.650785
$905$	10.2413	0.340432
$906$	4.82377	0.160259
$907$	45.2762	1.50337	0.751685	−	0.659522i	$-0.229241\pi$
$907$	45.2762	1.50337	0.751685	+	0.659522i	$0.229241\pi$
$908$	19.0433	0.631974
$909$	−7.12783	−0.236415
$910$	−26.8515	−0.890118
$911$	23.5813	0.781282	0.390641	−	0.920543i	$-0.372253\pi$
$911$	23.5813	0.781282	0.390641	+	0.920543i	$0.372253\pi$
$912$	3.97107	0.131495
$913$	−41.7776	−1.38264
$914$	7.78151	0.257389
$915$	−12.4657	−0.412104
$916$	−8.61757	−0.284732
$917$	−51.3112	−1.69445
$918$	1.00000	0.0330049
$919$	29.2723	0.965604	0.482802	−	0.875730i	$-0.339619\pi$
$919$	29.2723	0.965604	0.482802	+	0.875730i	$0.339619\pi$
$920$	−6.47414	−0.213446
$921$	−27.4969	−0.906055
$922$	−28.1929	−0.928483
$923$	32.1133	1.05702
$924$	12.6537	0.416276
$925$	−19.6125	−0.644854
$926$	−14.0228	−0.460817
$927$	6.40295	0.210301
$928$	−1.70928	−0.0561097
$929$	14.0144	0.459797	0.229898	−	0.973215i	$-0.426161\pi$
$929$	14.0144	0.459797	0.229898	+	0.973215i	$0.426161\pi$
$930$	5.26180	0.172541
$931$	31.9649	1.04761
$932$	1.31965	0.0432267
$933$	−11.3112	−0.370313
$934$	12.7792	0.418150
$935$	−8.58145	−0.280643
$936$	−2.63090	−0.0859936
$937$	22.4846	0.734541	0.367271	−	0.930114i	$-0.380292\pi$
$937$	22.4846	0.734541	0.367271	+	0.930114i	$0.380292\pi$
$938$	37.6658	1.22983
$939$	5.50307	0.179586
$940$	−15.0205	−0.489915
$941$	−44.1122	−1.43802	−0.719009	−	0.695001i	$-0.755404\pi$
$941$	−44.1122	−1.43802	−0.719009	+	0.695001i	$0.755404\pi$
$942$	−3.14116	−0.102344
$943$	16.5103	0.537648
$944$	−1.00000	−0.0325472
$945$	10.2062	0.332008
$946$	−3.00614	−0.0977381
$947$	24.0121	0.780289	0.390144	−	0.920754i	$-0.372425\pi$
$947$	24.0121	0.780289	0.390144	+	0.920754i	$0.372425\pi$
$948$	−13.8082	−0.448469
$949$	8.65756	0.281036
$950$	−7.63090	−0.247579
$951$	−17.6598	−0.572659
$952$	3.87936	0.125731
$953$	29.0205	0.940067	0.470033	−	0.882649i	$-0.344242\pi$
$953$	29.0205	0.940067	0.470033	+	0.882649i	$0.344242\pi$
$954$	−8.03612	−0.260179
$955$	−19.2351	−0.622434
$956$	10.9711	0.354830
$957$	5.57531	0.180224
$958$	−29.3340	−0.947739
$959$	83.2821	2.68932
$960$	2.63090	0.0849119
$961$	−27.0000	−0.870968
$962$	26.8515	0.865726
$963$	−3.63090	−0.117004
$964$	−8.02279	−0.258397
$965$	−53.1605	−1.71130
$966$	−9.54638	−0.307150
$967$	37.3740	1.20187	0.600934	−	0.799299i	$-0.294796\pi$
$967$	37.3740	1.20187	0.600934	+	0.799299i	$0.294796\pi$
$968$	0.360692	0.0115931
$969$	−3.97107	−0.127569
$970$	23.6781	0.760257
$971$	8.17113	0.262224	0.131112	−	0.991368i	$-0.458145\pi$
$971$	8.17113	0.262224	0.131112	+	0.991368i	$0.458145\pi$
$972$	1.00000	0.0320750
$973$	−48.0638	−1.54086
$974$	30.6814	0.983095
$975$	5.05559	0.161909
$976$	−4.73820	−0.151666
$977$	43.5364	1.39285	0.696426	−	0.717629i	$-0.254773\pi$
$977$	43.5364	1.39285	0.696426	+	0.717629i	$0.254773\pi$
$978$	−3.52586	−0.112745
$979$	−33.4719	−1.06977
$980$	21.1773	0.676483
$981$	−0.764867	−0.0244203
$982$	−5.02893	−0.160480
$983$	2.60916	0.0832192	0.0416096	−	0.999134i	$-0.486751\pi$
$983$	2.60916	0.0832192	0.0416096	+	0.999134i	$0.486751\pi$
$984$	−6.70928	−0.213884
$985$	−51.9832	−1.65632
$986$	1.70928	0.0544344
$987$	−22.1483	−0.704990
$988$	10.4475	0.332379
$989$	2.26794	0.0721162
$990$	−8.58145	−0.272736
$991$	4.53200	0.143964	0.0719819	−	0.997406i	$-0.477068\pi$
$991$	4.53200	0.143964	0.0719819	+	0.997406i	$0.477068\pi$
$992$	2.00000	0.0635001
$993$	30.5174	0.968442
$994$	−47.3523	−1.50192
$995$	24.7442	0.784443
$996$	−12.8082	−0.405842
$997$	−49.1327	−1.55605	−0.778025	−	0.628234i	$-0.783778\pi$
$997$	−49.1327	−1.55605	−0.778025	+	0.628234i	$0.783778\pi$
$998$	−10.4885	−0.332008
$999$	−10.2062	−0.322910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.m.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.m.1.2	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.63090 q^{5} -1.00000 q^{6} +3.87936 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.63090 q^{5} -1.00000 q^{6} +3.87936 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.63090 q^{10} +3.26180 q^{11} +1.00000 q^{12} +2.63090 q^{13} -3.87936 q^{14} +2.63090 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +3.97107 q^{19} +2.63090 q^{20} +3.87936 q^{21} -3.26180 q^{22} +2.46081 q^{23} -1.00000 q^{24} +1.92162 q^{25} -2.63090 q^{26} +1.00000 q^{27} +3.87936 q^{28} +1.70928 q^{29} -2.63090 q^{30} -2.00000 q^{31} -1.00000 q^{32} +3.26180 q^{33} +1.00000 q^{34} +10.2062 q^{35} +1.00000 q^{36} -10.2062 q^{37} -3.97107 q^{38} +2.63090 q^{39} -2.63090 q^{40} +6.70928 q^{41} -3.87936 q^{42} +0.921622 q^{43} +3.26180 q^{44} +2.63090 q^{45} -2.46081 q^{46} -5.70928 q^{47} +1.00000 q^{48} +8.04945 q^{49} -1.92162 q^{50} -1.00000 q^{51} +2.63090 q^{52} +8.03612 q^{53} -1.00000 q^{54} +8.58145 q^{55} -3.87936 q^{56} +3.97107 q^{57} -1.70928 q^{58} -1.00000 q^{59} +2.63090 q^{60} -4.73820 q^{61} +2.00000 q^{62} +3.87936 q^{63} +1.00000 q^{64} +6.92162 q^{65} -3.26180 q^{66} -9.70928 q^{67} -1.00000 q^{68} +2.46081 q^{69} -10.2062 q^{70} +12.2062 q^{71} -1.00000 q^{72} +3.29072 q^{73} +10.2062 q^{74} +1.92162 q^{75} +3.97107 q^{76} +12.6537 q^{77} -2.63090 q^{78} -13.8082 q^{79} +2.63090 q^{80} +1.00000 q^{81} -6.70928 q^{82} -12.8082 q^{83} +3.87936 q^{84} -2.63090 q^{85} -0.921622 q^{86} +1.70928 q^{87} -3.26180 q^{88} -10.2618 q^{89} -2.63090 q^{90} +10.2062 q^{91} +2.46081 q^{92} -2.00000 q^{93} +5.70928 q^{94} +10.4475 q^{95} -1.00000 q^{96} -9.00000 q^{97} -8.04945 q^{98} +3.26180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} - 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 - 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} - 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9} - 4 q^{10} + 2 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 4 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} - 3 q^{19} + 4 q^{20} - q^{21} - 2 q^{22} + 9 q^{23} - 3 q^{24} + 9 q^{25} - 4 q^{26} + 3 q^{27} - q^{28} - 2 q^{29} - 4 q^{30} - 6 q^{31} - 3 q^{32} + 2 q^{33} + 3 q^{34} + 6 q^{35} + 3 q^{36} - 6 q^{37} + 3 q^{38} + 4 q^{39} - 4 q^{40} + 13 q^{41} + q^{42} + 6 q^{43} + 2 q^{44} + 4 q^{45} - 9 q^{46} - 10 q^{47} + 3 q^{48} + 6 q^{49} - 9 q^{50} - 3 q^{51} + 4 q^{52} + 5 q^{53} - 3 q^{54} + 40 q^{55} + q^{56} - 3 q^{57} + 2 q^{58} - 3 q^{59} + 4 q^{60} - 22 q^{61} + 6 q^{62} - q^{63} + 3 q^{64} + 24 q^{65} - 2 q^{66} - 22 q^{67} - 3 q^{68} + 9 q^{69} - 6 q^{70} + 12 q^{71} - 3 q^{72} + 17 q^{73} + 6 q^{74} + 9 q^{75} - 3 q^{76} + 14 q^{77} - 4 q^{78} + 2 q^{79} + 4 q^{80} + 3 q^{81} - 13 q^{82} + 5 q^{83} - q^{84} - 4 q^{85} - 6 q^{86} - 2 q^{87} - 2 q^{88} - 23 q^{89} - 4 q^{90} + 6 q^{91} + 9 q^{92} - 6 q^{93} + 10 q^{94} + 32 q^{95} - 3 q^{96} - 27 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 - 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9 - 4 * q^10 + 2 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 4 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 - 3 * q^19 + 4 * q^20 - q^21 - 2 * q^22 + 9 * q^23 - 3 * q^24 + 9 * q^25 - 4 * q^26 + 3 * q^27 - q^28 - 2 * q^29 - 4 * q^30 - 6 * q^31 - 3 * q^32 + 2 * q^33 + 3 * q^34 + 6 * q^35 + 3 * q^36 - 6 * q^37 + 3 * q^38 + 4 * q^39 - 4 * q^40 + 13 * q^41 + q^42 + 6 * q^43 + 2 * q^44 + 4 * q^45 - 9 * q^46 - 10 * q^47 + 3 * q^48 + 6 * q^49 - 9 * q^50 - 3 * q^51 + 4 * q^52 + 5 * q^53 - 3 * q^54 + 40 * q^55 + q^56 - 3 * q^57 + 2 * q^58 - 3 * q^59 + 4 * q^60 - 22 * q^61 + 6 * q^62 - q^63 + 3 * q^64 + 24 * q^65 - 2 * q^66 - 22 * q^67 - 3 * q^68 + 9 * q^69 - 6 * q^70 + 12 * q^71 - 3 * q^72 + 17 * q^73 + 6 * q^74 + 9 * q^75 - 3 * q^76 + 14 * q^77 - 4 * q^78 + 2 * q^79 + 4 * q^80 + 3 * q^81 - 13 * q^82 + 5 * q^83 - q^84 - 4 * q^85 - 6 * q^86 - 2 * q^87 - 2 * q^88 - 23 * q^89 - 4 * q^90 + 6 * q^91 + 9 * q^92 - 6 * q^93 + 10 * q^94 + 32 * q^95 - 3 * q^96 - 27 * q^97 - 6 * q^98 + 2 * q^99

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