LMFDB - Embedded newform 6018.2.a.q.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:	$6$
Coefficient field:	6.6.5173625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 8x^{3} + 10x^{2} - 7x + 1 $ x^6 - x^5 - 8x^4 + 8x^3 + 10x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.353486$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.646514 q^{5} -1.00000 q^{6} +4.78830 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.646514 q^{5} -1.00000 q^{6} +4.78830 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.646514 q^{10} -2.66547 q^{11} -1.00000 q^{12} -0.293863 q^{13} +4.78830 q^{14} +0.646514 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -7.66334 q^{19} -0.646514 q^{20} -4.78830 q^{21} -2.66547 q^{22} +3.48843 q^{23} -1.00000 q^{24} -4.58202 q^{25} -0.293863 q^{26} -1.00000 q^{27} +4.78830 q^{28} -6.98665 q^{29} +0.646514 q^{30} +0.738677 q^{31} +1.00000 q^{32} +2.66547 q^{33} -1.00000 q^{34} -3.09570 q^{35} +1.00000 q^{36} -7.50197 q^{37} -7.66334 q^{38} +0.293863 q^{39} -0.646514 q^{40} -2.26167 q^{41} -4.78830 q^{42} -6.52240 q^{43} -2.66547 q^{44} -0.646514 q^{45} +3.48843 q^{46} -4.77771 q^{47} -1.00000 q^{48} +15.9278 q^{49} -4.58202 q^{50} +1.00000 q^{51} -0.293863 q^{52} +11.4621 q^{53} -1.00000 q^{54} +1.72326 q^{55} +4.78830 q^{56} +7.66334 q^{57} -6.98665 q^{58} +1.00000 q^{59} +0.646514 q^{60} -14.5071 q^{61} +0.738677 q^{62} +4.78830 q^{63} +1.00000 q^{64} +0.189986 q^{65} +2.66547 q^{66} -14.5462 q^{67} -1.00000 q^{68} -3.48843 q^{69} -3.09570 q^{70} +1.01024 q^{71} +1.00000 q^{72} -6.75222 q^{73} -7.50197 q^{74} +4.58202 q^{75} -7.66334 q^{76} -12.7630 q^{77} +0.293863 q^{78} -15.4436 q^{79} -0.646514 q^{80} +1.00000 q^{81} -2.26167 q^{82} -7.51009 q^{83} -4.78830 q^{84} +0.646514 q^{85} -6.52240 q^{86} +6.98665 q^{87} -2.66547 q^{88} -10.0891 q^{89} -0.646514 q^{90} -1.40710 q^{91} +3.48843 q^{92} -0.738677 q^{93} -4.77771 q^{94} +4.95446 q^{95} -1.00000 q^{96} +16.1496 q^{97} +15.9278 q^{98} -2.66547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 + 6 * q^9	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} + 6 q^{9} - 5 q^{10} - 6 q^{12} + 2 q^{13} - q^{14} + 5 q^{15} + 6 q^{16} - 6 q^{17} + 6 q^{18} - 5 q^{20} + q^{21} - 10 q^{23} - 6 q^{24} - 9 q^{25} + 2 q^{26} - 6 q^{27} - q^{28} - 3 q^{29} + 5 q^{30} - 7 q^{31} + 6 q^{32} - 6 q^{34} + 6 q^{35} + 6 q^{36} - 23 q^{37} - 2 q^{39} - 5 q^{40} - 12 q^{41} + q^{42} - 18 q^{43} - 5 q^{45} - 10 q^{46} - 14 q^{47} - 6 q^{48} + 9 q^{49} - 9 q^{50} + 6 q^{51} + 2 q^{52} + 21 q^{53} - 6 q^{54} + 4 q^{55} - q^{56} - 3 q^{58} + 6 q^{59} + 5 q^{60} - 2 q^{61} - 7 q^{62} - q^{63} + 6 q^{64} - 6 q^{65} + q^{67} - 6 q^{68} + 10 q^{69} + 6 q^{70} + 4 q^{71} + 6 q^{72} - 38 q^{73} - 23 q^{74} + 9 q^{75} - 22 q^{77} - 2 q^{78} - 30 q^{79} - 5 q^{80} + 6 q^{81} - 12 q^{82} + 23 q^{83} + q^{84} + 5 q^{85} - 18 q^{86} + 3 q^{87} - 7 q^{89} - 5 q^{90} - 5 q^{91} - 10 q^{92} + 7 q^{93} - 14 q^{94} - 7 q^{95} - 6 q^{96} - 10 q^{97} + 9 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 + 6 * q^9 - 5 * q^10 - 6 * q^12 + 2 * q^13 - q^14 + 5 * q^15 + 6 * q^16 - 6 * q^17 + 6 * q^18 - 5 * q^20 + q^21 - 10 * q^23 - 6 * q^24 - 9 * q^25 + 2 * q^26 - 6 * q^27 - q^28 - 3 * q^29 + 5 * q^30 - 7 * q^31 + 6 * q^32 - 6 * q^34 + 6 * q^35 + 6 * q^36 - 23 * q^37 - 2 * q^39 - 5 * q^40 - 12 * q^41 + q^42 - 18 * q^43 - 5 * q^45 - 10 * q^46 - 14 * q^47 - 6 * q^48 + 9 * q^49 - 9 * q^50 + 6 * q^51 + 2 * q^52 + 21 * q^53 - 6 * q^54 + 4 * q^55 - q^56 - 3 * q^58 + 6 * q^59 + 5 * q^60 - 2 * q^61 - 7 * q^62 - q^63 + 6 * q^64 - 6 * q^65 + q^67 - 6 * q^68 + 10 * q^69 + 6 * q^70 + 4 * q^71 + 6 * q^72 - 38 * q^73 - 23 * q^74 + 9 * q^75 - 22 * q^77 - 2 * q^78 - 30 * q^79 - 5 * q^80 + 6 * q^81 - 12 * q^82 + 23 * q^83 + q^84 + 5 * q^85 - 18 * q^86 + 3 * q^87 - 7 * q^89 - 5 * q^90 - 5 * q^91 - 10 * q^92 + 7 * q^93 - 14 * q^94 - 7 * q^95 - 6 * q^96 - 10 * q^97 + 9 * q^98

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
$5$	−0.646514	−0.289130	−0.144565	−	0.989495i	$-0.546178\pi$
$5$	−0.646514	−0.289130	−0.144565	+	0.989495i	$0.546178\pi$
$6$	−1.00000	−0.408248
$7$	4.78830	1.80981	0.904903	−	0.425618i	$-0.139943\pi$
$7$	4.78830	1.80981	0.904903	+	0.425618i	$0.139943\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.646514	−0.204446
$11$	−2.66547	−0.803668	−0.401834	−	0.915712i	$-0.631627\pi$
$11$	−2.66547	−0.803668	−0.401834	+	0.915712i	$0.631627\pi$
$12$	−1.00000	−0.288675
$13$	−0.293863	−0.0815029	−0.0407514	−	0.999169i	$-0.512975\pi$
$13$	−0.293863	−0.0815029	−0.0407514	+	0.999169i	$0.512975\pi$
$14$	4.78830	1.27973
$15$	0.646514	0.166929
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−7.66334	−1.75809	−0.879046	−	0.476737i	$-0.841819\pi$
$19$	−7.66334	−1.75809	−0.879046	+	0.476737i	$0.841819\pi$
$20$	−0.646514	−0.144565
$21$	−4.78830	−1.04489
$22$	−2.66547	−0.568279
$23$	3.48843	0.727387	0.363693	−	0.931519i	$-0.381516\pi$
$23$	3.48843	0.727387	0.363693	+	0.931519i	$0.381516\pi$
$24$	−1.00000	−0.204124
$25$	−4.58202	−0.916404
$26$	−0.293863	−0.0576312
$27$	−1.00000	−0.192450
$28$	4.78830	0.904903
$29$	−6.98665	−1.29739	−0.648694	−	0.761049i	$-0.724685\pi$
$29$	−6.98665	−1.29739	−0.648694	+	0.761049i	$0.724685\pi$
$30$	0.646514	0.118037
$31$	0.738677	0.132670	0.0663352	−	0.997797i	$-0.478869\pi$
$31$	0.738677	0.132670	0.0663352	+	0.997797i	$0.478869\pi$
$32$	1.00000	0.176777
$33$	2.66547	0.463998
$34$	−1.00000	−0.171499
$35$	−3.09570	−0.523269
$36$	1.00000	0.166667
$37$	−7.50197	−1.23332	−0.616658	−	0.787231i	$-0.711514\pi$
$37$	−7.50197	−1.23332	−0.616658	+	0.787231i	$0.711514\pi$
$38$	−7.66334	−1.24316
$39$	0.293863	0.0470557
$40$	−0.646514	−0.102223
$41$	−2.26167	−0.353214	−0.176607	−	0.984281i	$-0.556512\pi$
$41$	−2.26167	−0.353214	−0.176607	+	0.984281i	$0.556512\pi$
$42$	−4.78830	−0.738850
$43$	−6.52240	−0.994656	−0.497328	−	0.867563i	$-0.665685\pi$
$43$	−6.52240	−0.994656	−0.497328	+	0.867563i	$0.665685\pi$
$44$	−2.66547	−0.401834
$45$	−0.646514	−0.0963766
$46$	3.48843	0.514340
$47$	−4.77771	−0.696901	−0.348450	−	0.937327i	$-0.613292\pi$
$47$	−4.77771	−0.696901	−0.348450	+	0.937327i	$0.613292\pi$
$48$	−1.00000	−0.144338
$49$	15.9278	2.27540
$50$	−4.58202	−0.647995
$51$	1.00000	0.140028
$52$	−0.293863	−0.0407514
$53$	11.4621	1.57444	0.787222	−	0.616669i	$-0.211518\pi$
$53$	11.4621	1.57444	0.787222	+	0.616669i	$0.211518\pi$
$54$	−1.00000	−0.136083
$55$	1.72326	0.232365
$56$	4.78830	0.639863
$57$	7.66334	1.01503
$58$	−6.98665	−0.917392
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0.646514	0.0834646
$61$	−14.5071	−1.85744	−0.928721	−	0.370780i	$-0.879090\pi$
$61$	−14.5071	−1.85744	−0.928721	+	0.370780i	$0.879090\pi$
$62$	0.738677	0.0938121
$63$	4.78830	0.603269
$64$	1.00000	0.125000
$65$	0.189986	0.0235649
$66$	2.66547	0.328096
$67$	−14.5462	−1.77710	−0.888551	−	0.458778i	$-0.848287\pi$
$67$	−14.5462	−1.77710	−0.888551	+	0.458778i	$0.848287\pi$
$68$	−1.00000	−0.121268
$69$	−3.48843	−0.419957
$70$	−3.09570	−0.370007
$71$	1.01024	0.119893	0.0599465	−	0.998202i	$-0.480907\pi$
$71$	1.01024	0.119893	0.0599465	+	0.998202i	$0.480907\pi$
$72$	1.00000	0.117851
$73$	−6.75222	−0.790287	−0.395144	−	0.918619i	$-0.629305\pi$
$73$	−6.75222	−0.790287	−0.395144	+	0.918619i	$0.629305\pi$
$74$	−7.50197	−0.872086
$75$	4.58202	0.529086
$76$	−7.66334	−0.879046
$77$	−12.7630	−1.45448
$78$	0.293863	0.0332734
$79$	−15.4436	−1.73754	−0.868769	−	0.495218i	$-0.835088\pi$
$79$	−15.4436	−1.73754	−0.868769	+	0.495218i	$0.835088\pi$
$80$	−0.646514	−0.0722825
$81$	1.00000	0.111111
$82$	−2.26167	−0.249760
$83$	−7.51009	−0.824339	−0.412170	−	0.911107i	$-0.635229\pi$
$83$	−7.51009	−0.824339	−0.412170	+	0.911107i	$0.635229\pi$
$84$	−4.78830	−0.522446
$85$	0.646514	0.0701243
$86$	−6.52240	−0.703328
$87$	6.98665	0.749048
$88$	−2.66547	−0.284140
$89$	−10.0891	−1.06944	−0.534719	−	0.845030i	$-0.679582\pi$
$89$	−10.0891	−1.06944	−0.534719	+	0.845030i	$0.679582\pi$
$90$	−0.646514	−0.0681486
$91$	−1.40710	−0.147504
$92$	3.48843	0.363693
$93$	−0.738677	−0.0765972
$94$	−4.77771	−0.492783
$95$	4.95446	0.508317
$96$	−1.00000	−0.102062
$97$	16.1496	1.63975	0.819874	−	0.572544i	$-0.194043\pi$
$97$	16.1496	1.63975	0.819874	+	0.572544i	$0.194043\pi$
$98$	15.9278	1.60895
$99$	−2.66547	−0.267889
$100$	−4.58202	−0.458202
$101$	17.2930	1.72072	0.860359	−	0.509688i	$-0.170239\pi$
$101$	17.2930	1.72072	0.860359	+	0.509688i	$0.170239\pi$
$102$	1.00000	0.0990148
$103$	11.1710	1.10071	0.550355	−	0.834931i	$-0.314493\pi$
$103$	11.1710	1.10071	0.550355	+	0.834931i	$0.314493\pi$
$104$	−0.293863	−0.0288156
$105$	3.09570	0.302109
$106$	11.4621	1.11330
$107$	5.48651	0.530401	0.265201	−	0.964193i	$-0.414562\pi$
$107$	5.48651	0.530401	0.265201	+	0.964193i	$0.414562\pi$
$108$	−1.00000	−0.0962250
$109$	11.5163	1.10306	0.551530	−	0.834155i	$-0.314044\pi$
$109$	11.5163	1.10306	0.551530	+	0.834155i	$0.314044\pi$
$110$	1.72326	0.164307
$111$	7.50197	0.712055
$112$	4.78830	0.452451
$113$	−2.18035	−0.205110	−0.102555	−	0.994727i	$-0.532702\pi$
$113$	−2.18035	−0.205110	−0.102555	+	0.994727i	$0.532702\pi$
$114$	7.66334	0.717738
$115$	−2.25532	−0.210309
$116$	−6.98665	−0.648694
$117$	−0.293863	−0.0271676
$118$	1.00000	0.0920575
$119$	−4.78830	−0.438942
$120$	0.646514	0.0590184
$121$	−3.89529	−0.354117
$122$	−14.5071	−1.31341
$123$	2.26167	0.203928
$124$	0.738677	0.0663352
$125$	6.19491	0.554090
$126$	4.78830	0.426575
$127$	16.2285	1.44005	0.720024	−	0.693949i	$-0.244131\pi$
$127$	16.2285	1.44005	0.720024	+	0.693949i	$0.244131\pi$
$128$	1.00000	0.0883883
$129$	6.52240	0.574265
$130$	0.189986	0.0166629
$131$	21.8156	1.90603	0.953017	−	0.302916i	$-0.0979603\pi$
$131$	21.8156	1.90603	0.953017	+	0.302916i	$0.0979603\pi$
$132$	2.66547	0.231999
$133$	−36.6943	−3.18180
$134$	−14.5462	−1.25660
$135$	0.646514	0.0556431
$136$	−1.00000	−0.0857493
$137$	1.38493	0.118323	0.0591615	−	0.998248i	$-0.481157\pi$
$137$	1.38493	0.118323	0.0591615	+	0.998248i	$0.481157\pi$
$138$	−3.48843	−0.296954
$139$	7.73734	0.656273	0.328136	−	0.944630i	$-0.393579\pi$
$139$	7.73734	0.656273	0.328136	+	0.944630i	$0.393579\pi$
$140$	−3.09570	−0.261634
$141$	4.77771	0.402356
$142$	1.01024	0.0847771
$143$	0.783281	0.0655013
$144$	1.00000	0.0833333
$145$	4.51697	0.375114
$146$	−6.75222	−0.558818
$147$	−15.9278	−1.31370
$148$	−7.50197	−0.616658
$149$	5.37268	0.440147	0.220073	−	0.975483i	$-0.429370\pi$
$149$	5.37268	0.440147	0.220073	+	0.975483i	$0.429370\pi$
$150$	4.58202	0.374120
$151$	−5.36407	−0.436522	−0.218261	−	0.975890i	$-0.570038\pi$
$151$	−5.36407	−0.436522	−0.218261	+	0.975890i	$0.570038\pi$
$152$	−7.66334	−0.621579
$153$	−1.00000	−0.0808452
$154$	−12.7630	−1.02848
$155$	−0.477565	−0.0383589
$156$	0.293863	0.0235279
$157$	−1.68772	−0.134695	−0.0673475	−	0.997730i	$-0.521454\pi$
$157$	−1.68772	−0.134695	−0.0673475	+	0.997730i	$0.521454\pi$
$158$	−15.4436	−1.22862
$159$	−11.4621	−0.909006
$160$	−0.646514	−0.0511114
$161$	16.7036	1.31643
$162$	1.00000	0.0785674
$163$	10.3399	0.809883	0.404941	−	0.914343i	$-0.367292\pi$
$163$	10.3399	0.809883	0.404941	+	0.914343i	$0.367292\pi$
$164$	−2.26167	−0.176607
$165$	−1.72326	−0.134156
$166$	−7.51009	−0.582896
$167$	6.32880	0.489737	0.244869	−	0.969556i	$-0.421255\pi$
$167$	6.32880	0.489737	0.244869	+	0.969556i	$0.421255\pi$
$168$	−4.78830	−0.369425
$169$	−12.9136	−0.993357
$170$	0.646514	0.0495854
$171$	−7.66334	−0.586030
$172$	−6.52240	−0.497328
$173$	17.3597	1.31983	0.659916	−	0.751340i	$-0.270592\pi$
$173$	17.3597	1.31983	0.659916	+	0.751340i	$0.270592\pi$
$174$	6.98665	0.529657
$175$	−21.9401	−1.65851
$176$	−2.66547	−0.200917
$177$	−1.00000	−0.0751646
$178$	−10.0891	−0.756206
$179$	−20.5994	−1.53967	−0.769837	−	0.638241i	$-0.779662\pi$
$179$	−20.5994	−1.53967	−0.769837	+	0.638241i	$0.779662\pi$
$180$	−0.646514	−0.0481883
$181$	−22.6792	−1.68573	−0.842866	−	0.538123i	$-0.819134\pi$
$181$	−22.6792	−1.68573	−0.842866	+	0.538123i	$0.819134\pi$
$182$	−1.40710	−0.104301
$183$	14.5071	1.07239
$184$	3.48843	0.257170
$185$	4.85013	0.356588
$186$	−0.738677	−0.0541624
$187$	2.66547	0.194918
$188$	−4.77771	−0.348450
$189$	−4.78830	−0.348297
$190$	4.95446	0.359434
$191$	−21.0941	−1.52631	−0.763157	−	0.646213i	$-0.776352\pi$
$191$	−21.0941	−1.52631	−0.763157	+	0.646213i	$0.776352\pi$
$192$	−1.00000	−0.0721688
$193$	−5.21751	−0.375565	−0.187782	−	0.982211i	$-0.560130\pi$
$193$	−5.21751	−0.375565	−0.187782	+	0.982211i	$0.560130\pi$
$194$	16.1496	1.15948
$195$	−0.189986	−0.0136052
$196$	15.9278	1.13770
$197$	4.04530	0.288216	0.144108	−	0.989562i	$-0.453969\pi$
$197$	4.04530	0.288216	0.144108	+	0.989562i	$0.453969\pi$
$198$	−2.66547	−0.189426
$199$	−1.91857	−0.136004	−0.0680021	−	0.997685i	$-0.521662\pi$
$199$	−1.91857	−0.136004	−0.0680021	+	0.997685i	$0.521662\pi$
$200$	−4.58202	−0.323998
$201$	14.5462	1.02601
$202$	17.2930	1.21673
$203$	−33.4541	−2.34802
$204$	1.00000	0.0700140
$205$	1.46220	0.102125
$206$	11.1710	0.778319
$207$	3.48843	0.242462
$208$	−0.293863	−0.0203757
$209$	20.4264	1.41292
$210$	3.09570	0.213624
$211$	−13.3278	−0.917527	−0.458763	−	0.888558i	$-0.651707\pi$
$211$	−13.3278	−0.917527	−0.458763	+	0.888558i	$0.651707\pi$
$212$	11.4621	0.787222
$213$	−1.01024	−0.0692202
$214$	5.48651	0.375050
$215$	4.21682	0.287585
$216$	−1.00000	−0.0680414
$217$	3.53700	0.240107
$218$	11.5163	0.779981
$219$	6.75222	0.456273
$220$	1.72326	0.116182
$221$	0.293863	0.0197674
$222$	7.50197	0.503499
$223$	−17.9106	−1.19938	−0.599690	−	0.800232i	$-0.704710\pi$
$223$	−17.9106	−1.19938	−0.599690	+	0.800232i	$0.704710\pi$
$224$	4.78830	0.319931
$225$	−4.58202	−0.305468
$226$	−2.18035	−0.145035
$227$	5.11386	0.339419	0.169710	−	0.985494i	$-0.445717\pi$
$227$	5.11386	0.339419	0.169710	+	0.985494i	$0.445717\pi$
$228$	7.66334	0.507517
$229$	−7.44482	−0.491968	−0.245984	−	0.969274i	$-0.579111\pi$
$229$	−7.44482	−0.491968	−0.245984	+	0.969274i	$0.579111\pi$
$230$	−2.25532	−0.148711
$231$	12.7630	0.839746
$232$	−6.98665	−0.458696
$233$	10.7762	0.705971	0.352985	−	0.935629i	$-0.385167\pi$
$233$	10.7762	0.705971	0.352985	+	0.935629i	$0.385167\pi$
$234$	−0.293863	−0.0192104
$235$	3.08886	0.201495
$236$	1.00000	0.0650945
$237$	15.4436	1.00317
$238$	−4.78830	−0.310379
$239$	22.4605	1.45285	0.726424	−	0.687247i	$-0.241181\pi$
$239$	22.4605	1.45285	0.726424	+	0.687247i	$0.241181\pi$
$240$	0.646514	0.0417323
$241$	−10.9753	−0.706980	−0.353490	−	0.935438i	$-0.615005\pi$
$241$	−10.9753	−0.706980	−0.353490	+	0.935438i	$0.615005\pi$
$242$	−3.89529	−0.250399
$243$	−1.00000	−0.0641500
$244$	−14.5071	−0.928721
$245$	−10.2975	−0.657885
$246$	2.26167	0.144199
$247$	2.25197	0.143290
$248$	0.738677	0.0469060
$249$	7.51009	0.475932
$250$	6.19491	0.391800
$251$	2.24600	0.141766	0.0708831	−	0.997485i	$-0.477418\pi$
$251$	2.24600	0.141766	0.0708831	+	0.997485i	$0.477418\pi$
$252$	4.78830	0.301634
$253$	−9.29828	−0.584578
$254$	16.2285	1.01827
$255$	−0.646514	−0.0404863
$256$	1.00000	0.0625000
$257$	20.9285	1.30549	0.652743	−	0.757579i	$-0.273618\pi$
$257$	20.9285	1.30549	0.652743	+	0.757579i	$0.273618\pi$
$258$	6.52240	0.406067
$259$	−35.9216	−2.23206
$260$	0.189986	0.0117825
$261$	−6.98665	−0.432463
$262$	21.8156	1.34777
$263$	18.7525	1.15633	0.578164	−	0.815921i	$-0.303769\pi$
$263$	18.7525	1.15633	0.578164	+	0.815921i	$0.303769\pi$
$264$	2.66547	0.164048
$265$	−7.41043	−0.455219
$266$	−36.6943	−2.24987
$267$	10.0891	0.617440
$268$	−14.5462	−0.888551
$269$	−16.6739	−1.01662	−0.508312	−	0.861173i	$-0.669730\pi$
$269$	−16.6739	−1.01662	−0.508312	+	0.861173i	$0.669730\pi$
$270$	0.646514	0.0393456
$271$	−19.4123	−1.17922	−0.589608	−	0.807690i	$-0.700718\pi$
$271$	−19.4123	−1.17922	−0.589608	+	0.807690i	$0.700718\pi$
$272$	−1.00000	−0.0606339
$273$	1.40710	0.0851617
$274$	1.38493	0.0836669
$275$	12.2132	0.736485
$276$	−3.48843	−0.209979
$277$	−32.4840	−1.95177	−0.975886	−	0.218280i	$-0.929955\pi$
$277$	−32.4840	−1.95177	−0.975886	+	0.218280i	$0.929955\pi$
$278$	7.73734	0.464055
$279$	0.738677	0.0442234
$280$	−3.09570	−0.185003
$281$	−13.3213	−0.794681	−0.397340	−	0.917671i	$-0.630067\pi$
$281$	−13.3213	−0.794681	−0.397340	+	0.917671i	$0.630067\pi$
$282$	4.77771	0.284509
$283$	−16.6025	−0.986917	−0.493459	−	0.869769i	$-0.664268\pi$
$283$	−16.6025	−0.986917	−0.493459	+	0.869769i	$0.664268\pi$
$284$	1.01024	0.0599465
$285$	−4.95446	−0.293477
$286$	0.783281	0.0463164
$287$	−10.8295	−0.639248
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	4.51697	0.265245
$291$	−16.1496	−0.946709
$292$	−6.75222	−0.395144
$293$	1.41390	0.0826009	0.0413004	−	0.999147i	$-0.486850\pi$
$293$	1.41390	0.0826009	0.0413004	+	0.999147i	$0.486850\pi$
$294$	−15.9278	−0.928927
$295$	−0.646514	−0.0376415
$296$	−7.50197	−0.436043
$297$	2.66547	0.154666
$298$	5.37268	0.311231
$299$	−1.02512	−0.0592841
$300$	4.58202	0.264543
$301$	−31.2312	−1.80013
$302$	−5.36407	−0.308668
$303$	−17.2930	−0.993457
$304$	−7.66334	−0.439523
$305$	9.37903	0.537042
$306$	−1.00000	−0.0571662
$307$	−2.71032	−0.154686	−0.0773432	−	0.997005i	$-0.524644\pi$
$307$	−2.71032	−0.154686	−0.0773432	+	0.997005i	$0.524644\pi$
$308$	−12.7630	−0.727242
$309$	−11.1710	−0.635495
$310$	−0.477565	−0.0271239
$311$	−17.2453	−0.977893	−0.488947	−	0.872314i	$-0.662619\pi$
$311$	−17.2453	−0.977893	−0.488947	+	0.872314i	$0.662619\pi$
$312$	0.293863	0.0166367
$313$	12.6979	0.717726	0.358863	−	0.933390i	$-0.383165\pi$
$313$	12.6979	0.717726	0.358863	+	0.933390i	$0.383165\pi$
$314$	−1.68772	−0.0952438
$315$	−3.09570	−0.174423
$316$	−15.4436	−0.868769
$317$	−12.5462	−0.704664	−0.352332	−	0.935875i	$-0.614611\pi$
$317$	−12.5462	−0.704664	−0.352332	+	0.935875i	$0.614611\pi$
$318$	−11.4621	−0.642764
$319$	18.6227	1.04267
$320$	−0.646514	−0.0361412
$321$	−5.48651	−0.306227
$322$	16.7036	0.930856
$323$	7.66334	0.426400
$324$	1.00000	0.0555556
$325$	1.34649	0.0746896
$326$	10.3399	0.572673
$327$	−11.5163	−0.636852
$328$	−2.26167	−0.124880
$329$	−22.8771	−1.26126
$330$	−1.72326	−0.0948624
$331$	−21.5440	−1.18417	−0.592083	−	0.805877i	$-0.701694\pi$
$331$	−21.5440	−1.18417	−0.592083	+	0.805877i	$0.701694\pi$
$332$	−7.51009	−0.412170
$333$	−7.50197	−0.411105
$334$	6.32880	0.346296
$335$	9.40432	0.513813
$336$	−4.78830	−0.261223
$337$	18.8482	1.02673	0.513363	−	0.858172i	$-0.328400\pi$
$337$	18.8482	1.02673	0.513363	+	0.858172i	$0.328400\pi$
$338$	−12.9136	−0.702410
$339$	2.18035	0.118420
$340$	0.646514	0.0350621
$341$	−1.96892	−0.106623
$342$	−7.66334	−0.414386
$343$	42.7488	2.30822
$344$	−6.52240	−0.351664
$345$	2.25532	0.121422
$346$	17.3597	0.933262
$347$	−29.9625	−1.60847	−0.804234	−	0.594312i	$-0.797424\pi$
$347$	−29.9625	−1.60847	−0.804234	+	0.594312i	$0.797424\pi$
$348$	6.98665	0.374524
$349$	3.97276	0.212657	0.106329	−	0.994331i	$-0.466090\pi$
$349$	3.97276	0.212657	0.106329	+	0.994331i	$0.466090\pi$
$350$	−21.9401	−1.17275
$351$	0.293863	0.0156852
$352$	−2.66547	−0.142070
$353$	−23.3068	−1.24050	−0.620248	−	0.784406i	$-0.712968\pi$
$353$	−23.3068	−1.24050	−0.620248	+	0.784406i	$0.712968\pi$
$354$	−1.00000	−0.0531494
$355$	−0.653132	−0.0346646
$356$	−10.0891	−0.534719
$357$	4.78830	0.253423
$358$	−20.5994	−1.08871
$359$	25.4484	1.34312	0.671559	−	0.740951i	$-0.265625\pi$
$359$	25.4484	1.34312	0.671559	+	0.740951i	$0.265625\pi$
$360$	−0.646514	−0.0340743
$361$	39.7268	2.09089
$362$	−22.6792	−1.19199
$363$	3.89529	0.204450
$364$	−1.40710	−0.0737522
$365$	4.36540	0.228496
$366$	14.5071	0.758297
$367$	9.68515	0.505561	0.252780	−	0.967524i	$-0.418655\pi$
$367$	9.68515	0.505561	0.252780	+	0.967524i	$0.418655\pi$
$368$	3.48843	0.181847
$369$	−2.26167	−0.117738
$370$	4.85013	0.252146
$371$	54.8841	2.84944
$372$	−0.738677	−0.0382986
$373$	−5.53743	−0.286717	−0.143359	−	0.989671i	$-0.545790\pi$
$373$	−5.53743	−0.286717	−0.143359	+	0.989671i	$0.545790\pi$
$374$	2.66547	0.137828
$375$	−6.19491	−0.319904
$376$	−4.77771	−0.246392
$377$	2.05312	0.105741
$378$	−4.78830	−0.246283
$379$	13.5494	0.695987	0.347993	−	0.937497i	$-0.386863\pi$
$379$	13.5494	0.695987	0.347993	+	0.937497i	$0.386863\pi$
$380$	4.95446	0.254158
$381$	−16.2285	−0.831413
$382$	−21.0941	−1.07927
$383$	6.30813	0.322330	0.161165	−	0.986927i	$-0.448475\pi$
$383$	6.30813	0.322330	0.161165	+	0.986927i	$0.448475\pi$
$384$	−1.00000	−0.0510310
$385$	8.25148	0.420535
$386$	−5.21751	−0.265564
$387$	−6.52240	−0.331552
$388$	16.1496	0.819874
$389$	−35.5869	−1.80433	−0.902165	−	0.431392i	$-0.858023\pi$
$389$	−35.5869	−1.80433	−0.902165	+	0.431392i	$0.858023\pi$
$390$	−0.189986	−0.00962034
$391$	−3.48843	−0.176417
$392$	15.9278	0.804474
$393$	−21.8156	−1.10045
$394$	4.04530	0.203799
$395$	9.98449	0.502374
$396$	−2.66547	−0.133945
$397$	14.3517	0.720289	0.360145	−	0.932897i	$-0.382727\pi$
$397$	14.3517	0.720289	0.360145	+	0.932897i	$0.382727\pi$
$398$	−1.91857	−0.0961694
$399$	36.6943	1.83702
$400$	−4.58202	−0.229101
$401$	−26.3446	−1.31558	−0.657792	−	0.753200i	$-0.728509\pi$
$401$	−26.3446	−1.31558	−0.657792	+	0.753200i	$0.728509\pi$
$402$	14.5462	0.725499
$403$	−0.217070	−0.0108130
$404$	17.2930	0.860359
$405$	−0.646514	−0.0321255
$406$	−33.4541	−1.66030
$407$	19.9962	0.991177
$408$	1.00000	0.0495074
$409$	5.70928	0.282306	0.141153	−	0.989988i	$-0.454919\pi$
$409$	5.70928	0.282306	0.141153	+	0.989988i	$0.454919\pi$
$410$	1.46220	0.0722130
$411$	−1.38493	−0.0683138
$412$	11.1710	0.550355
$413$	4.78830	0.235617
$414$	3.48843	0.171447
$415$	4.85538	0.238341
$416$	−0.293863	−0.0144078
$417$	−7.73734	−0.378899
$418$	20.4264	0.999087
$419$	−1.54177	−0.0753205	−0.0376603	−	0.999291i	$-0.511990\pi$
$419$	−1.54177	−0.0753205	−0.0376603	+	0.999291i	$0.511990\pi$
$420$	3.09570	0.151055
$421$	−7.85662	−0.382908	−0.191454	−	0.981502i	$-0.561320\pi$
$421$	−7.85662	−0.382908	−0.191454	+	0.981502i	$0.561320\pi$
$422$	−13.3278	−0.648789
$423$	−4.77771	−0.232300
$424$	11.4621	0.556650
$425$	4.58202	0.222261
$426$	−1.01024	−0.0489461
$427$	−69.4642	−3.36161
$428$	5.48651	0.265201
$429$	−0.783281	−0.0378172
$430$	4.21682	0.203353
$431$	−25.0737	−1.20776	−0.603878	−	0.797077i	$-0.706379\pi$
$431$	−25.0737	−1.20776	−0.603878	+	0.797077i	$0.706379\pi$
$432$	−1.00000	−0.0481125
$433$	28.3158	1.36077	0.680385	−	0.732855i	$-0.261813\pi$
$433$	28.3158	1.36077	0.680385	+	0.732855i	$0.261813\pi$
$434$	3.53700	0.169782
$435$	−4.51697	−0.216572
$436$	11.5163	0.551530
$437$	−26.7330	−1.27881
$438$	6.75222	0.322633
$439$	24.0144	1.14614	0.573072	−	0.819505i	$-0.305751\pi$
$439$	24.0144	1.14614	0.573072	+	0.819505i	$0.305751\pi$
$440$	1.72326	0.0821533
$441$	15.9278	0.758465
$442$	0.293863	0.0139776
$443$	11.3370	0.538639	0.269319	−	0.963051i	$-0.413201\pi$
$443$	11.3370	0.538639	0.269319	+	0.963051i	$0.413201\pi$
$444$	7.50197	0.356028
$445$	6.52271	0.309206
$446$	−17.9106	−0.848090
$447$	−5.37268	−0.254119
$448$	4.78830	0.226226
$449$	−23.8266	−1.12445	−0.562224	−	0.826985i	$-0.690054\pi$
$449$	−23.8266	−1.12445	−0.562224	+	0.826985i	$0.690054\pi$
$450$	−4.58202	−0.215998
$451$	6.02841	0.283867
$452$	−2.18035	−0.102555
$453$	5.36407	0.252026
$454$	5.11386	0.240005
$455$	0.909711	0.0426479
$456$	7.66334	0.358869
$457$	21.8591	1.02252	0.511262	−	0.859425i	$-0.329178\pi$
$457$	21.8591	1.02252	0.511262	+	0.859425i	$0.329178\pi$
$458$	−7.44482	−0.347874
$459$	1.00000	0.0466760
$460$	−2.25532	−0.105155
$461$	7.83715	0.365012	0.182506	−	0.983205i	$-0.441579\pi$
$461$	7.83715	0.365012	0.182506	+	0.983205i	$0.441579\pi$
$462$	12.7630	0.593790
$463$	−6.81140	−0.316553	−0.158276	−	0.987395i	$-0.550594\pi$
$463$	−6.81140	−0.316553	−0.158276	+	0.987395i	$0.550594\pi$
$464$	−6.98665	−0.324347
$465$	0.477565	0.0221465
$466$	10.7762	0.499197
$467$	−0.845285	−0.0391151	−0.0195576	−	0.999809i	$-0.506226\pi$
$467$	−0.845285	−0.0391151	−0.0195576	+	0.999809i	$0.506226\pi$
$468$	−0.293863	−0.0135838
$469$	−69.6515	−3.21621
$470$	3.08886	0.142478
$471$	1.68772	0.0777662
$472$	1.00000	0.0460287
$473$	17.3852	0.799374
$474$	15.4436	0.709347
$475$	35.1136	1.61112
$476$	−4.78830	−0.219471
$477$	11.4621	0.524815
$478$	22.4605	1.02732
$479$	13.8154	0.631240	0.315620	−	0.948886i	$-0.397788\pi$
$479$	13.8154	0.631240	0.315620	+	0.948886i	$0.397788\pi$
$480$	0.646514	0.0295092
$481$	2.20455	0.100519
$482$	−10.9753	−0.499910
$483$	−16.7036	−0.760041
$484$	−3.89529	−0.177059
$485$	−10.4410	−0.474100
$486$	−1.00000	−0.0453609
$487$	16.3161	0.739355	0.369677	−	0.929160i	$-0.379468\pi$
$487$	16.3161	0.739355	0.369677	+	0.929160i	$0.379468\pi$
$488$	−14.5071	−0.656705
$489$	−10.3399	−0.467586
$490$	−10.2975	−0.465195
$491$	7.13979	0.322214	0.161107	−	0.986937i	$-0.448494\pi$
$491$	7.13979	0.322214	0.161107	+	0.986937i	$0.448494\pi$
$492$	2.26167	0.101964
$493$	6.98665	0.314663
$494$	2.25197	0.101321
$495$	1.72326	0.0774548
$496$	0.738677	0.0331676
$497$	4.83731	0.216983
$498$	7.51009	0.336535
$499$	−40.3465	−1.80616	−0.903078	−	0.429477i	$-0.858698\pi$
$499$	−40.3465	−1.80616	−0.903078	+	0.429477i	$0.858698\pi$
$500$	6.19491	0.277045
$501$	−6.32880	−0.282750
$502$	2.24600	0.100244
$503$	−31.6902	−1.41299	−0.706497	−	0.707716i	$-0.749726\pi$
$503$	−31.6902	−1.41299	−0.706497	+	0.707716i	$0.749726\pi$
$504$	4.78830	0.213288
$505$	−11.1802	−0.497511
$506$	−9.29828	−0.413359
$507$	12.9136	0.573515
$508$	16.2285	0.720024
$509$	20.2284	0.896610	0.448305	−	0.893881i	$-0.352028\pi$
$509$	20.2284	0.896610	0.448305	+	0.893881i	$0.352028\pi$
$510$	−0.646514	−0.0286281
$511$	−32.3316	−1.43027
$512$	1.00000	0.0441942
$513$	7.66334	0.338345
$514$	20.9285	0.923118
$515$	−7.22219	−0.318248
$516$	6.52240	0.287132
$517$	12.7348	0.560077
$518$	−35.9216	−1.57831
$519$	−17.3597	−0.762005
$520$	0.189986	0.00833146
$521$	−21.1737	−0.927639	−0.463819	−	0.885930i	$-0.653521\pi$
$521$	−21.1737	−0.927639	−0.463819	+	0.885930i	$0.653521\pi$
$522$	−6.98665	−0.305797
$523$	32.1833	1.40728	0.703638	−	0.710559i	$-0.251558\pi$
$523$	32.1833	1.40728	0.703638	+	0.710559i	$0.251558\pi$
$524$	21.8156	0.953017
$525$	21.9401	0.957543
$526$	18.7525	0.817647
$527$	−0.738677	−0.0321773
$528$	2.66547	0.116000
$529$	−10.8309	−0.470908
$530$	−7.41043	−0.321888
$531$	1.00000	0.0433963
$532$	−36.6943	−1.59090
$533$	0.664621	0.0287879
$534$	10.0891	0.436596
$535$	−3.54711	−0.153355
$536$	−14.5462	−0.628300
$537$	20.5994	0.888931
$538$	−16.6739	−0.718862
$539$	−42.4549	−1.82866
$540$	0.646514	0.0278215
$541$	7.85730	0.337812	0.168906	−	0.985632i	$-0.445977\pi$
$541$	7.85730	0.337812	0.168906	+	0.985632i	$0.445977\pi$
$542$	−19.4123	−0.833831
$543$	22.6792	0.973258
$544$	−1.00000	−0.0428746
$545$	−7.44544	−0.318928
$546$	1.40710	0.0602184
$547$	17.2187	0.736217	0.368108	−	0.929783i	$-0.380006\pi$
$547$	17.2187	0.736217	0.368108	+	0.929783i	$0.380006\pi$
$548$	1.38493	0.0591615
$549$	−14.5071	−0.619147
$550$	12.2132	0.520773
$551$	53.5411	2.28093
$552$	−3.48843	−0.148477
$553$	−73.9484	−3.14461
$554$	−32.4840	−1.38011
$555$	−4.85013	−0.205876
$556$	7.73734	0.328136
$557$	−7.86007	−0.333042	−0.166521	−	0.986038i	$-0.553253\pi$
$557$	−7.86007	−0.333042	−0.166521	+	0.986038i	$0.553253\pi$
$558$	0.738677	0.0312707
$559$	1.91669	0.0810673
$560$	−3.09570	−0.130817
$561$	−2.66547	−0.112536
$562$	−13.3213	−0.561924
$563$	45.5894	1.92137	0.960683	−	0.277649i	$-0.0895551\pi$
$563$	45.5894	1.92137	0.960683	+	0.277649i	$0.0895551\pi$
$564$	4.77771	0.201178
$565$	1.40962	0.0593034
$566$	−16.6025	−0.697856
$567$	4.78830	0.201090
$568$	1.01024	0.0423886
$569$	−2.93116	−0.122880	−0.0614402	−	0.998111i	$-0.519569\pi$
$569$	−2.93116	−0.122880	−0.0614402	+	0.998111i	$0.519569\pi$
$570$	−4.95446	−0.207519
$571$	15.9151	0.666025	0.333013	−	0.942922i	$-0.391935\pi$
$571$	15.9151	0.666025	0.333013	+	0.942922i	$0.391935\pi$
$572$	0.783281	0.0327506
$573$	21.0941	0.881218
$574$	−10.8295	−0.452016
$575$	−15.9840	−0.666580
$576$	1.00000	0.0416667
$577$	10.9251	0.454819	0.227409	−	0.973799i	$-0.426974\pi$
$577$	10.9251	0.454819	0.227409	+	0.973799i	$0.426974\pi$
$578$	1.00000	0.0415945
$579$	5.21751	0.216832
$580$	4.51697	0.187557
$581$	−35.9605	−1.49189
$582$	−16.1496	−0.669424
$583$	−30.5519	−1.26533
$584$	−6.75222	−0.279409
$585$	0.189986	0.00785497
$586$	1.41390	0.0584076
$587$	23.4646	0.968487	0.484243	−	0.874933i	$-0.339095\pi$
$587$	23.4646	0.968487	0.484243	+	0.874933i	$0.339095\pi$
$588$	−15.9278	−0.656850
$589$	−5.66074	−0.233247
$590$	−0.646514	−0.0266166
$591$	−4.04530	−0.166401
$592$	−7.50197	−0.308329
$593$	25.9549	1.06584	0.532920	−	0.846166i	$-0.321095\pi$
$593$	25.9549	1.06584	0.532920	+	0.846166i	$0.321095\pi$
$594$	2.66547	0.109365
$595$	3.09570	0.126911
$596$	5.37268	0.220073
$597$	1.91857	0.0785220
$598$	−1.02512	−0.0419202
$599$	9.20566	0.376133	0.188067	−	0.982156i	$-0.439778\pi$
$599$	9.20566	0.376133	0.188067	+	0.982156i	$0.439778\pi$
$600$	4.58202	0.187060
$601$	−21.6228	−0.882011	−0.441005	−	0.897504i	$-0.645378\pi$
$601$	−21.6228	−0.882011	−0.441005	+	0.897504i	$0.645378\pi$
$602$	−31.2312	−1.27289
$603$	−14.5462	−0.592367
$604$	−5.36407	−0.218261
$605$	2.51836	0.102386
$606$	−17.2930	−0.702480
$607$	−32.7399	−1.32887	−0.664436	−	0.747345i	$-0.731328\pi$
$607$	−32.7399	−1.32887	−0.664436	+	0.747345i	$0.731328\pi$
$608$	−7.66334	−0.310790
$609$	33.4541	1.35563
$610$	9.37903	0.379746
$611$	1.40399	0.0567994
$612$	−1.00000	−0.0404226
$613$	18.9285	0.764514	0.382257	−	0.924056i	$-0.375147\pi$
$613$	18.9285	0.764514	0.382257	+	0.924056i	$0.375147\pi$
$614$	−2.71032	−0.109380
$615$	−1.46220	−0.0589616
$616$	−12.7630	−0.514238
$617$	24.1339	0.971594	0.485797	−	0.874072i	$-0.338529\pi$
$617$	24.1339	0.971594	0.485797	+	0.874072i	$0.338529\pi$
$618$	−11.1710	−0.449363
$619$	19.1883	0.771245	0.385622	−	0.922657i	$-0.373987\pi$
$619$	19.1883	0.771245	0.385622	+	0.922657i	$0.373987\pi$
$620$	−0.477565	−0.0191795
$621$	−3.48843	−0.139986
$622$	−17.2453	−0.691475
$623$	−48.3094	−1.93547
$624$	0.293863	0.0117639
$625$	18.9050	0.756200
$626$	12.6979	0.507509
$627$	−20.4264	−0.815751
$628$	−1.68772	−0.0673475
$629$	7.50197	0.299123
$630$	−3.09570	−0.123336
$631$	−8.94777	−0.356205	−0.178103	−	0.984012i	$-0.556996\pi$
$631$	−8.94777	−0.356205	−0.178103	+	0.984012i	$0.556996\pi$
$632$	−15.4436	−0.614312
$633$	13.3278	0.529734
$634$	−12.5462	−0.498273
$635$	−10.4920	−0.416361
$636$	−11.4621	−0.454503
$637$	−4.68058	−0.185451
$638$	18.6227	0.737279
$639$	1.01024	0.0399643
$640$	−0.646514	−0.0255557
$641$	17.3093	0.683678	0.341839	−	0.939759i	$-0.388950\pi$
$641$	17.3093	0.683678	0.341839	+	0.939759i	$0.388950\pi$
$642$	−5.48651	−0.216535
$643$	24.3384	0.959813	0.479907	−	0.877320i	$-0.340671\pi$
$643$	24.3384	0.959813	0.479907	+	0.877320i	$0.340671\pi$
$644$	16.7036	0.658214
$645$	−4.21682	−0.166037
$646$	7.66334	0.301510
$647$	−29.0520	−1.14215	−0.571075	−	0.820898i	$-0.693474\pi$
$647$	−29.0520	−1.14215	−0.571075	+	0.820898i	$0.693474\pi$
$648$	1.00000	0.0392837
$649$	−2.66547	−0.104629
$650$	1.34649	0.0528135
$651$	−3.53700	−0.138626
$652$	10.3399	0.404941
$653$	−43.6931	−1.70984	−0.854922	−	0.518756i	$-0.826395\pi$
$653$	−43.6931	−1.70984	−0.854922	+	0.518756i	$0.826395\pi$
$654$	−11.5163	−0.450322
$655$	−14.1041	−0.551091
$656$	−2.26167	−0.0883034
$657$	−6.75222	−0.263429
$658$	−22.8771	−0.891842
$659$	3.33657	0.129974	0.0649871	−	0.997886i	$-0.479299\pi$
$659$	3.33657	0.129974	0.0649871	+	0.997886i	$0.479299\pi$
$660$	−1.72326	−0.0670779
$661$	23.8937	0.929359	0.464679	−	0.885479i	$-0.346170\pi$
$661$	23.8937	0.929359	0.464679	+	0.885479i	$0.346170\pi$
$662$	−21.5440	−0.837331
$663$	−0.293863	−0.0114127
$664$	−7.51009	−0.291448
$665$	23.7234	0.919954
$666$	−7.50197	−0.290695
$667$	−24.3724	−0.943703
$668$	6.32880	0.244869
$669$	17.9106	0.692463
$670$	9.40432	0.363321
$671$	38.6681	1.49277
$672$	−4.78830	−0.184713
$673$	37.6620	1.45176	0.725882	−	0.687819i	$-0.241432\pi$
$673$	37.6620	1.45176	0.725882	+	0.687819i	$0.241432\pi$
$674$	18.8482	0.726005
$675$	4.58202	0.176362
$676$	−12.9136	−0.496679
$677$	0.388791	0.0149424	0.00747122	−	0.999972i	$-0.497622\pi$
$677$	0.388791	0.0149424	0.00747122	+	0.999972i	$0.497622\pi$
$678$	2.18035	0.0837357
$679$	77.3293	2.96762
$680$	0.646514	0.0247927
$681$	−5.11386	−0.195964
$682$	−1.96892	−0.0753938
$683$	24.7494	0.947009	0.473505	−	0.880791i	$-0.342989\pi$
$683$	24.7494	0.947009	0.473505	+	0.880791i	$0.342989\pi$
$684$	−7.66334	−0.293015
$685$	−0.895379	−0.0342107
$686$	42.7488	1.63216
$687$	7.44482	0.284038
$688$	−6.52240	−0.248664
$689$	−3.36829	−0.128322
$690$	2.25532	0.0858584
$691$	−25.6900	−0.977293	−0.488647	−	0.872482i	$-0.662509\pi$
$691$	−25.6900	−0.977293	−0.488647	+	0.872482i	$0.662509\pi$
$692$	17.3597	0.659916
$693$	−12.7630	−0.484828
$694$	−29.9625	−1.13736
$695$	−5.00230	−0.189748
$696$	6.98665	0.264828
$697$	2.26167	0.0856669
$698$	3.97276	0.150371
$699$	−10.7762	−0.407592
$700$	−21.9401	−0.829256
$701$	1.67332	0.0632003	0.0316001	−	0.999501i	$-0.489940\pi$
$701$	1.67332	0.0632003	0.0316001	+	0.999501i	$0.489940\pi$
$702$	0.293863	0.0110911
$703$	57.4901	2.16828
$704$	−2.66547	−0.100459
$705$	−3.08886	−0.116333
$706$	−23.3068	−0.877163
$707$	82.8040	3.11417
$708$	−1.00000	−0.0375823
$709$	−12.1577	−0.456593	−0.228296	−	0.973592i	$-0.573315\pi$
$709$	−12.1577	−0.456593	−0.228296	+	0.973592i	$0.573315\pi$
$710$	−0.653132	−0.0245116
$711$	−15.4436	−0.579179
$712$	−10.0891	−0.378103
$713$	2.57682	0.0965027
$714$	4.78830	0.179197
$715$	−0.506402	−0.0189384
$716$	−20.5994	−0.769837
$717$	−22.4605	−0.838802
$718$	25.4484	0.949727
$719$	3.80787	0.142010	0.0710048	−	0.997476i	$-0.477379\pi$
$719$	3.80787	0.142010	0.0710048	+	0.997476i	$0.477379\pi$
$720$	−0.646514	−0.0240942
$721$	53.4899	1.99207
$722$	39.7268	1.47848
$723$	10.9753	0.408175
$724$	−22.6792	−0.842866
$725$	32.0130	1.18893
$726$	3.89529	0.144568
$727$	42.2617	1.56740	0.783700	−	0.621140i	$-0.213330\pi$
$727$	42.2617	1.56740	0.783700	+	0.621140i	$0.213330\pi$
$728$	−1.40710	−0.0521507
$729$	1.00000	0.0370370
$730$	4.36540	0.161571
$731$	6.52240	0.241240
$732$	14.5071	0.536197
$733$	9.86656	0.364430	0.182215	−	0.983259i	$-0.441673\pi$
$733$	9.86656	0.364430	0.182215	+	0.983259i	$0.441673\pi$
$734$	9.68515	0.357485
$735$	10.2975	0.379830
$736$	3.48843	0.128585
$737$	38.7724	1.42820
$738$	−2.26167	−0.0832532
$739$	46.3772	1.70601	0.853006	−	0.521901i	$-0.174777\pi$
$739$	46.3772	1.70601	0.853006	+	0.521901i	$0.174777\pi$
$740$	4.85013	0.178294
$741$	−2.25197	−0.0827282
$742$	54.8841	2.01486
$743$	0.825224	0.0302745	0.0151373	−	0.999885i	$-0.495181\pi$
$743$	0.825224	0.0302745	0.0151373	+	0.999885i	$0.495181\pi$
$744$	−0.738677	−0.0270812
$745$	−3.47351	−0.127260
$746$	−5.53743	−0.202740
$747$	−7.51009	−0.274780
$748$	2.66547	0.0974591
$749$	26.2710	0.959923
$750$	−6.19491	−0.226206
$751$	5.78708	0.211173	0.105587	−	0.994410i	$-0.466328\pi$
$751$	5.78708	0.211173	0.105587	+	0.994410i	$0.466328\pi$
$752$	−4.77771	−0.174225
$753$	−2.24600	−0.0818487
$754$	2.05312	0.0747701
$755$	3.46795	0.126211
$756$	−4.78830	−0.174149
$757$	−49.2017	−1.78827	−0.894133	−	0.447801i	$-0.852207\pi$
$757$	−49.2017	−1.78827	−0.894133	+	0.447801i	$0.852207\pi$
$758$	13.5494	0.492137
$759$	9.29828	0.337506
$760$	4.95446	0.179717
$761$	−15.5792	−0.564747	−0.282374	−	0.959305i	$-0.591122\pi$
$761$	−15.5792	−0.564747	−0.282374	+	0.959305i	$0.591122\pi$
$762$	−16.2285	−0.587897
$763$	55.1434	1.99632
$764$	−21.0941	−0.763157
$765$	0.646514	0.0233748
$766$	6.30813	0.227922
$767$	−0.293863	−0.0106108
$768$	−1.00000	−0.0360844
$769$	−38.0660	−1.37270	−0.686348	−	0.727273i	$-0.740787\pi$
$769$	−38.0660	−1.37270	−0.686348	+	0.727273i	$0.740787\pi$
$770$	8.25148	0.297363
$771$	−20.9285	−0.753723
$772$	−5.21751	−0.187782
$773$	16.4513	0.591713	0.295856	−	0.955232i	$-0.404395\pi$
$773$	16.4513	0.591713	0.295856	+	0.955232i	$0.404395\pi$
$774$	−6.52240	−0.234443
$775$	−3.38463	−0.121580
$776$	16.1496	0.579738
$777$	35.9216	1.28868
$778$	−35.5869	−1.27585
$779$	17.3320	0.620982
$780$	−0.189986	−0.00680260
$781$	−2.69275	−0.0963542
$782$	−3.48843	−0.124746
$783$	6.98665	0.249683
$784$	15.9278	0.568849
$785$	1.09114	0.0389444
$786$	−21.8156	−0.778135
$787$	8.01387	0.285664	0.142832	−	0.989747i	$-0.454379\pi$
$787$	8.01387	0.285664	0.142832	+	0.989747i	$0.454379\pi$
$788$	4.04530	0.144108
$789$	−18.7525	−0.667606
$790$	9.98449	0.355232
$791$	−10.4401	−0.371209
$792$	−2.66547	−0.0947132
$793$	4.26309	0.151387
$794$	14.3517	0.509321
$795$	7.41043	0.262821
$796$	−1.91857	−0.0680021
$797$	−7.09095	−0.251174	−0.125587	−	0.992083i	$-0.540081\pi$
$797$	−7.09095	−0.251174	−0.125587	+	0.992083i	$0.540081\pi$
$798$	36.6943	1.29897
$799$	4.77771	0.169023
$800$	−4.58202	−0.161999
$801$	−10.0891	−0.356479
$802$	−26.3446	−0.930259
$803$	17.9978	0.635129
$804$	14.5462	0.513005
$805$	−10.7991	−0.380619
$806$	−0.217070	−0.00764596
$807$	16.6739	0.586949
$808$	17.2930	0.608366
$809$	10.0145	0.352091	0.176045	−	0.984382i	$-0.443669\pi$
$809$	10.0145	0.352091	0.176045	+	0.984382i	$0.443669\pi$
$810$	−0.646514	−0.0227162
$811$	−11.8695	−0.416795	−0.208397	−	0.978044i	$-0.566825\pi$
$811$	−11.8695	−0.416795	−0.208397	+	0.978044i	$0.566825\pi$
$812$	−33.4541	−1.17401
$813$	19.4123	0.680820
$814$	19.9962	0.700868
$815$	−6.68488	−0.234161
$816$	1.00000	0.0350070
$817$	49.9834	1.74870
$818$	5.70928	0.199620
$819$	−1.40710	−0.0491681
$820$	1.46220	0.0510623
$821$	−54.9860	−1.91902	−0.959512	−	0.281668i	$-0.909112\pi$
$821$	−54.9860	−1.91902	−0.959512	+	0.281668i	$0.909112\pi$
$822$	−1.38493	−0.0483051
$823$	46.7601	1.62995	0.814977	−	0.579493i	$-0.196749\pi$
$823$	46.7601	1.62995	0.814977	+	0.579493i	$0.196749\pi$
$824$	11.1710	0.389159
$825$	−12.2132	−0.425210
$826$	4.78830	0.166606
$827$	−23.2636	−0.808955	−0.404477	−	0.914548i	$-0.632547\pi$
$827$	−23.2636	−0.808955	−0.404477	+	0.914548i	$0.632547\pi$
$828$	3.48843	0.121231
$829$	9.75490	0.338802	0.169401	−	0.985547i	$-0.445817\pi$
$829$	9.75490	0.338802	0.169401	+	0.985547i	$0.445817\pi$
$830$	4.85538	0.168533
$831$	32.4840	1.12686
$832$	−0.293863	−0.0101879
$833$	−15.9278	−0.551865
$834$	−7.73734	−0.267922
$835$	−4.09166	−0.141598
$836$	20.4264	0.706461
$837$	−0.738677	−0.0255324
$838$	−1.54177	−0.0532597
$839$	−38.3409	−1.32368	−0.661838	−	0.749647i	$-0.730223\pi$
$839$	−38.3409	−1.32368	−0.661838	+	0.749647i	$0.730223\pi$
$840$	3.09570	0.106812
$841$	19.8133	0.683217
$842$	−7.85662	−0.270757
$843$	13.3213	0.458809
$844$	−13.3278	−0.458763
$845$	8.34885	0.287209
$846$	−4.77771	−0.164261
$847$	−18.6518	−0.640883
$848$	11.4621	0.393611
$849$	16.6025	0.569797
$850$	4.58202	0.157162
$851$	−26.1700	−0.897098
$852$	−1.01024	−0.0346101
$853$	−20.3003	−0.695069	−0.347535	−	0.937667i	$-0.612981\pi$
$853$	−20.3003	−0.695069	−0.347535	+	0.937667i	$0.612981\pi$
$854$	−69.4642	−2.37702
$855$	4.95446	0.169439
$856$	5.48651	0.187525
$857$	6.34690	0.216806	0.108403	−	0.994107i	$-0.465426\pi$
$857$	6.34690	0.216806	0.108403	+	0.994107i	$0.465426\pi$
$858$	−0.783281	−0.0267408
$859$	2.20598	0.0752670	0.0376335	−	0.999292i	$-0.488018\pi$
$859$	2.20598	0.0752670	0.0376335	+	0.999292i	$0.488018\pi$
$860$	4.21682	0.143792
$861$	10.8295	0.369070
$862$	−25.0737	−0.854013
$863$	−7.62343	−0.259505	−0.129752	−	0.991546i	$-0.541418\pi$
$863$	−7.62343	−0.259505	−0.129752	+	0.991546i	$0.541418\pi$
$864$	−1.00000	−0.0340207
$865$	−11.2233	−0.381603
$866$	28.3158	0.962210
$867$	−1.00000	−0.0339618
$868$	3.53700	0.120054
$869$	41.1643	1.39640
$870$	−4.51697	−0.153140
$871$	4.27459	0.144839
$872$	11.5163	0.389991
$873$	16.1496	0.546583
$874$	−26.7330	−0.904257
$875$	29.6631	1.00279
$876$	6.75222	0.228136
$877$	−8.45958	−0.285660	−0.142830	−	0.989747i	$-0.545620\pi$
$877$	−8.45958	−0.285660	−0.142830	+	0.989747i	$0.545620\pi$
$878$	24.0144	0.810446
$879$	−1.41390	−0.0476896
$880$	1.72326	0.0580911
$881$	−42.8799	−1.44466	−0.722330	−	0.691549i	$-0.756929\pi$
$881$	−42.8799	−1.44466	−0.722330	+	0.691549i	$0.756929\pi$
$882$	15.9278	0.536316
$883$	35.4661	1.19353	0.596765	−	0.802416i	$-0.296452\pi$
$883$	35.4661	1.19353	0.596765	+	0.802416i	$0.296452\pi$
$884$	0.293863	0.00988368
$885$	0.646514	0.0217323
$886$	11.3370	0.380875
$887$	−40.5779	−1.36247	−0.681236	−	0.732064i	$-0.738557\pi$
$887$	−40.5779	−1.36247	−0.681236	+	0.732064i	$0.738557\pi$
$888$	7.50197	0.251750
$889$	77.7070	2.60621
$890$	6.52271	0.218642
$891$	−2.66547	−0.0892965
$892$	−17.9106	−0.599690
$893$	36.6132	1.22522
$894$	−5.37268	−0.179689
$895$	13.3178	0.445166
$896$	4.78830	0.159966
$897$	1.02512	0.0342277
$898$	−23.8266	−0.795105
$899$	−5.16088	−0.172125
$900$	−4.58202	−0.152734
$901$	−11.4621	−0.381859
$902$	6.02841	0.200724
$903$	31.2312	1.03931
$904$	−2.18035	−0.0725173
$905$	14.6624	0.487396
$906$	5.36407	0.178209
$907$	−22.4200	−0.744442	−0.372221	−	0.928144i	$-0.621404\pi$
$907$	−22.4200	−0.744442	−0.372221	+	0.928144i	$0.621404\pi$
$908$	5.11386	0.169710
$909$	17.2930	0.573573
$910$	0.909711	0.0301566
$911$	27.3548	0.906305	0.453153	−	0.891433i	$-0.350299\pi$
$911$	27.3548	0.906305	0.453153	+	0.891433i	$0.350299\pi$
$912$	7.66334	0.253759
$913$	20.0179	0.662495
$914$	21.8591	0.723033
$915$	−9.37903	−0.310061
$916$	−7.44482	−0.245984
$917$	104.459	3.44955
$918$	1.00000	0.0330049
$919$	−53.8736	−1.77712	−0.888562	−	0.458756i	$-0.848295\pi$
$919$	−53.8736	−1.77712	−0.888562	+	0.458756i	$0.848295\pi$
$920$	−2.25532	−0.0743556
$921$	2.71032	0.0893082
$922$	7.83715	0.258103
$923$	−0.296871	−0.00977162
$924$	12.7630	0.419873
$925$	34.3742	1.13022
$926$	−6.81140	−0.223836
$927$	11.1710	0.366903
$928$	−6.98665	−0.229348
$929$	−48.0782	−1.57740	−0.788698	−	0.614781i	$-0.789244\pi$
$929$	−48.0782	−1.57740	−0.788698	+	0.614781i	$0.789244\pi$
$930$	0.477565	0.0156600
$931$	−122.060	−4.00035
$932$	10.7762	0.352985
$933$	17.2453	0.564587
$934$	−0.845285	−0.0276586
$935$	−1.72326	−0.0563567
$936$	−0.293863	−0.00960521
$937$	31.9454	1.04361	0.521805	−	0.853065i	$-0.325259\pi$
$937$	31.9454	1.04361	0.521805	+	0.853065i	$0.325259\pi$
$938$	−69.6515	−2.27420
$939$	−12.6979	−0.414379
$940$	3.08886	0.100747
$941$	−9.57356	−0.312089	−0.156044	−	0.987750i	$-0.549874\pi$
$941$	−9.57356	−0.312089	−0.156044	+	0.987750i	$0.549874\pi$
$942$	1.68772	0.0549890
$943$	−7.88967	−0.256923
$944$	1.00000	0.0325472
$945$	3.09570	0.100703
$946$	17.3852	0.565243
$947$	31.5644	1.02570	0.512852	−	0.858477i	$-0.328589\pi$
$947$	31.5644	1.02570	0.512852	+	0.858477i	$0.328589\pi$
$948$	15.4436	0.501584
$949$	1.98423	0.0644107
$950$	35.1136	1.13924
$951$	12.5462	0.406838
$952$	−4.78830	−0.155190
$953$	−6.61646	−0.214328	−0.107164	−	0.994241i	$-0.534177\pi$
$953$	−6.61646	−0.214328	−0.107164	+	0.994241i	$0.534177\pi$
$954$	11.4621	0.371100
$955$	13.6376	0.441303
$956$	22.4605	0.726424
$957$	−18.6227	−0.601986
$958$	13.8154	0.446354
$959$	6.63147	0.214141
$960$	0.646514	0.0208661
$961$	−30.4544	−0.982399
$962$	2.20455	0.0710775
$963$	5.48651	0.176800
$964$	−10.9753	−0.353490
$965$	3.37319	0.108587
$966$	−16.7036	−0.537430
$967$	−25.0434	−0.805341	−0.402670	−	0.915345i	$-0.631918\pi$
$967$	−25.0434	−0.805341	−0.402670	+	0.915345i	$0.631918\pi$
$968$	−3.89529	−0.125199
$969$	−7.66334	−0.246182
$970$	−10.4410	−0.335239
$971$	35.7709	1.14794	0.573971	−	0.818875i	$-0.305402\pi$
$971$	35.7709	1.14794	0.573971	+	0.818875i	$0.305402\pi$
$972$	−1.00000	−0.0320750
$973$	37.0487	1.18773
$974$	16.3161	0.522803
$975$	−1.34649	−0.0431220
$976$	−14.5071	−0.464360
$977$	62.1207	1.98742	0.993709	−	0.111989i	$-0.0357222\pi$
$977$	62.1207	1.98742	0.993709	+	0.111989i	$0.0357222\pi$
$978$	−10.3399	−0.330633
$979$	26.8920	0.859473
$980$	−10.2975	−0.328942
$981$	11.5163	0.367687
$982$	7.13979	0.227840
$983$	29.0856	0.927686	0.463843	−	0.885917i	$-0.346470\pi$
$983$	29.0856	0.927686	0.463843	+	0.885917i	$0.346470\pi$
$984$	2.26167	0.0720994
$985$	−2.61534	−0.0833317
$986$	6.98665	0.222500
$987$	22.8771	0.728186
$988$	2.25197	0.0716448
$989$	−22.7529	−0.723500
$990$	1.72326	0.0547688
$991$	−42.6797	−1.35577	−0.677883	−	0.735170i	$-0.737102\pi$
$991$	−42.6797	−1.35577	−0.677883	+	0.735170i	$0.737102\pi$
$992$	0.738677	0.0234530
$993$	21.5440	0.683678
$994$	4.83731	0.153430
$995$	1.24039	0.0393228
$996$	7.51009	0.237966
$997$	−8.05592	−0.255133	−0.127567	−	0.991830i	$-0.540717\pi$
$997$	−8.05592	−0.255133	−0.127567	+	0.991830i	$0.540717\pi$
$998$	−40.3465	−1.27715
$999$	7.50197	0.237352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.q.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.q.1.4	✓	6	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.646514 q^{5} -1.00000 q^{6} +4.78830 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.646514 q^{5} -1.00000 q^{6} +4.78830 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.646514 q^{10} -2.66547 q^{11} -1.00000 q^{12} -0.293863 q^{13} +4.78830 q^{14} +0.646514 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -7.66334 q^{19} -0.646514 q^{20} -4.78830 q^{21} -2.66547 q^{22} +3.48843 q^{23} -1.00000 q^{24} -4.58202 q^{25} -0.293863 q^{26} -1.00000 q^{27} +4.78830 q^{28} -6.98665 q^{29} +0.646514 q^{30} +0.738677 q^{31} +1.00000 q^{32} +2.66547 q^{33} -1.00000 q^{34} -3.09570 q^{35} +1.00000 q^{36} -7.50197 q^{37} -7.66334 q^{38} +0.293863 q^{39} -0.646514 q^{40} -2.26167 q^{41} -4.78830 q^{42} -6.52240 q^{43} -2.66547 q^{44} -0.646514 q^{45} +3.48843 q^{46} -4.77771 q^{47} -1.00000 q^{48} +15.9278 q^{49} -4.58202 q^{50} +1.00000 q^{51} -0.293863 q^{52} +11.4621 q^{53} -1.00000 q^{54} +1.72326 q^{55} +4.78830 q^{56} +7.66334 q^{57} -6.98665 q^{58} +1.00000 q^{59} +0.646514 q^{60} -14.5071 q^{61} +0.738677 q^{62} +4.78830 q^{63} +1.00000 q^{64} +0.189986 q^{65} +2.66547 q^{66} -14.5462 q^{67} -1.00000 q^{68} -3.48843 q^{69} -3.09570 q^{70} +1.01024 q^{71} +1.00000 q^{72} -6.75222 q^{73} -7.50197 q^{74} +4.58202 q^{75} -7.66334 q^{76} -12.7630 q^{77} +0.293863 q^{78} -15.4436 q^{79} -0.646514 q^{80} +1.00000 q^{81} -2.26167 q^{82} -7.51009 q^{83} -4.78830 q^{84} +0.646514 q^{85} -6.52240 q^{86} +6.98665 q^{87} -2.66547 q^{88} -10.0891 q^{89} -0.646514 q^{90} -1.40710 q^{91} +3.48843 q^{92} -0.738677 q^{93} -4.77771 q^{94} +4.95446 q^{95} -1.00000 q^{96} +16.1496 q^{97} +15.9278 q^{98} -2.66547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} + 6 q^{9} - 5 q^{10} - 6 q^{12} + 2 q^{13} - q^{14} + 5 q^{15} + 6 q^{16} - 6 q^{17} + 6 q^{18} - 5 q^{20} + q^{21} - 10 q^{23} - 6 q^{24} - 9 q^{25} + 2 q^{26} - 6 q^{27} - q^{28} - 3 q^{29} + 5 q^{30} - 7 q^{31} + 6 q^{32} - 6 q^{34} + 6 q^{35} + 6 q^{36} - 23 q^{37} - 2 q^{39} - 5 q^{40} - 12 q^{41} + q^{42} - 18 q^{43} - 5 q^{45} - 10 q^{46} - 14 q^{47} - 6 q^{48} + 9 q^{49} - 9 q^{50} + 6 q^{51} + 2 q^{52} + 21 q^{53} - 6 q^{54} + 4 q^{55} - q^{56} - 3 q^{58} + 6 q^{59} + 5 q^{60} - 2 q^{61} - 7 q^{62} - q^{63} + 6 q^{64} - 6 q^{65} + q^{67} - 6 q^{68} + 10 q^{69} + 6 q^{70} + 4 q^{71} + 6 q^{72} - 38 q^{73} - 23 q^{74} + 9 q^{75} - 22 q^{77} - 2 q^{78} - 30 q^{79} - 5 q^{80} + 6 q^{81} - 12 q^{82} + 23 q^{83} + q^{84} + 5 q^{85} - 18 q^{86} + 3 q^{87} - 7 q^{89} - 5 q^{90} - 5 q^{91} - 10 q^{92} + 7 q^{93} - 14 q^{94} - 7 q^{95} - 6 q^{96} - 10 q^{97} + 9 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 + 6 * q^9 - 5 * q^10 - 6 * q^12 + 2 * q^13 - q^14 + 5 * q^15 + 6 * q^16 - 6 * q^17 + 6 * q^18 - 5 * q^20 + q^21 - 10 * q^23 - 6 * q^24 - 9 * q^25 + 2 * q^26 - 6 * q^27 - q^28 - 3 * q^29 + 5 * q^30 - 7 * q^31 + 6 * q^32 - 6 * q^34 + 6 * q^35 + 6 * q^36 - 23 * q^37 - 2 * q^39 - 5 * q^40 - 12 * q^41 + q^42 - 18 * q^43 - 5 * q^45 - 10 * q^46 - 14 * q^47 - 6 * q^48 + 9 * q^49 - 9 * q^50 + 6 * q^51 + 2 * q^52 + 21 * q^53 - 6 * q^54 + 4 * q^55 - q^56 - 3 * q^58 + 6 * q^59 + 5 * q^60 - 2 * q^61 - 7 * q^62 - q^63 + 6 * q^64 - 6 * q^65 + q^67 - 6 * q^68 + 10 * q^69 + 6 * q^70 + 4 * q^71 + 6 * q^72 - 38 * q^73 - 23 * q^74 + 9 * q^75 - 22 * q^77 - 2 * q^78 - 30 * q^79 - 5 * q^80 + 6 * q^81 - 12 * q^82 + 23 * q^83 + q^84 + 5 * q^85 - 18 * q^86 + 3 * q^87 - 7 * q^89 - 5 * q^90 - 5 * q^91 - 10 * q^92 + 7 * q^93 - 14 * q^94 - 7 * q^95 - 6 * q^96 - 10 * q^97 + 9 * q^98

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