LMFDB - Embedded newform 6018.2.a.t.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:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 15x^{6} + 14x^{5} + 84x^{4} + 9x^{3} - 158x^{2} - 142x - 35 $ x^8 - 2x^7 - 15x^6 + 14x^5 + 84x^4 + 9x^3 - 158x^2 - 142*x - 35
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			$-1.50609$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.00979 q^{5} -1.00000 q^{6} +3.51588 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.00979 q^{5} -1.00000 q^{6} +3.51588 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.00979 q^{10} +4.40175 q^{11} +1.00000 q^{12} +2.32954 q^{13} -3.51588 q^{14} -3.00979 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -6.35647 q^{19} -3.00979 q^{20} +3.51588 q^{21} -4.40175 q^{22} -5.45221 q^{23} -1.00000 q^{24} +4.05882 q^{25} -2.32954 q^{26} +1.00000 q^{27} +3.51588 q^{28} -8.94290 q^{29} +3.00979 q^{30} +4.30375 q^{31} -1.00000 q^{32} +4.40175 q^{33} -1.00000 q^{34} -10.5821 q^{35} +1.00000 q^{36} -11.0755 q^{37} +6.35647 q^{38} +2.32954 q^{39} +3.00979 q^{40} -5.69023 q^{41} -3.51588 q^{42} -6.20902 q^{43} +4.40175 q^{44} -3.00979 q^{45} +5.45221 q^{46} -5.86220 q^{47} +1.00000 q^{48} +5.36142 q^{49} -4.05882 q^{50} +1.00000 q^{51} +2.32954 q^{52} +1.15884 q^{53} -1.00000 q^{54} -13.2483 q^{55} -3.51588 q^{56} -6.35647 q^{57} +8.94290 q^{58} -1.00000 q^{59} -3.00979 q^{60} +7.45057 q^{61} -4.30375 q^{62} +3.51588 q^{63} +1.00000 q^{64} -7.01142 q^{65} -4.40175 q^{66} +11.8688 q^{67} +1.00000 q^{68} -5.45221 q^{69} +10.5821 q^{70} -13.4998 q^{71} -1.00000 q^{72} +3.69041 q^{73} +11.0755 q^{74} +4.05882 q^{75} -6.35647 q^{76} +15.4760 q^{77} -2.32954 q^{78} -15.0826 q^{79} -3.00979 q^{80} +1.00000 q^{81} +5.69023 q^{82} -11.5315 q^{83} +3.51588 q^{84} -3.00979 q^{85} +6.20902 q^{86} -8.94290 q^{87} -4.40175 q^{88} +1.73281 q^{89} +3.00979 q^{90} +8.19039 q^{91} -5.45221 q^{92} +4.30375 q^{93} +5.86220 q^{94} +19.1316 q^{95} -1.00000 q^{96} -1.27160 q^{97} -5.36142 q^{98} +4.40175 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9} + 6 q^{10} + q^{11} + 8 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} + 4 q^{19} - 6 q^{20} - 4 q^{21} - q^{22} - 11 q^{23} - 8 q^{24} + 6 q^{25} + 2 q^{26} + 8 q^{27} - 4 q^{28} - 12 q^{29} + 6 q^{30} - 9 q^{31} - 8 q^{32} + q^{33} - 8 q^{34} - 28 q^{35} + 8 q^{36} - 22 q^{37} - 4 q^{38} - 2 q^{39} + 6 q^{40} - 19 q^{41} + 4 q^{42} - 5 q^{43} + q^{44} - 6 q^{45} + 11 q^{46} - 26 q^{47} + 8 q^{48} - 6 q^{50} + 8 q^{51} - 2 q^{52} - 21 q^{53} - 8 q^{54} - 13 q^{55} + 4 q^{56} + 4 q^{57} + 12 q^{58} - 8 q^{59} - 6 q^{60} + 9 q^{61} + 9 q^{62} - 4 q^{63} + 8 q^{64} + 14 q^{65} - q^{66} + 26 q^{67} + 8 q^{68} - 11 q^{69} + 28 q^{70} - 14 q^{71} - 8 q^{72} + 17 q^{73} + 22 q^{74} + 6 q^{75} + 4 q^{76} - 18 q^{77} + 2 q^{78} - 39 q^{79} - 6 q^{80} + 8 q^{81} + 19 q^{82} - 11 q^{83} - 4 q^{84} - 6 q^{85} + 5 q^{86} - 12 q^{87} - q^{88} + 6 q^{90} + 11 q^{91} - 11 q^{92} - 9 q^{93} + 26 q^{94} - 15 q^{95} - 8 q^{96} + 16 q^{97} + q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9 + 6 * q^10 + q^11 + 8 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 + 4 * q^19 - 6 * q^20 - 4 * q^21 - q^22 - 11 * q^23 - 8 * q^24 + 6 * q^25 + 2 * q^26 + 8 * q^27 - 4 * q^28 - 12 * q^29 + 6 * q^30 - 9 * q^31 - 8 * q^32 + q^33 - 8 * q^34 - 28 * q^35 + 8 * q^36 - 22 * q^37 - 4 * q^38 - 2 * q^39 + 6 * q^40 - 19 * q^41 + 4 * q^42 - 5 * q^43 + q^44 - 6 * q^45 + 11 * q^46 - 26 * q^47 + 8 * q^48 - 6 * q^50 + 8 * q^51 - 2 * q^52 - 21 * q^53 - 8 * q^54 - 13 * q^55 + 4 * q^56 + 4 * q^57 + 12 * q^58 - 8 * q^59 - 6 * q^60 + 9 * q^61 + 9 * q^62 - 4 * q^63 + 8 * q^64 + 14 * q^65 - q^66 + 26 * q^67 + 8 * q^68 - 11 * q^69 + 28 * q^70 - 14 * q^71 - 8 * q^72 + 17 * q^73 + 22 * q^74 + 6 * q^75 + 4 * q^76 - 18 * q^77 + 2 * q^78 - 39 * q^79 - 6 * q^80 + 8 * q^81 + 19 * q^82 - 11 * q^83 - 4 * q^84 - 6 * q^85 + 5 * q^86 - 12 * q^87 - q^88 + 6 * q^90 + 11 * q^91 - 11 * q^92 - 9 * q^93 + 26 * q^94 - 15 * q^95 - 8 * q^96 + 16 * q^97 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.00979	−1.34602	−0.673009	−	0.739634i	$-0.734998\pi$
$5$	−3.00979	−1.34602	−0.673009	+	0.739634i	$0.734998\pi$
$6$	−1.00000	−0.408248
$7$	3.51588	1.32888	0.664439	−	0.747342i	$-0.268670\pi$
$7$	3.51588	1.32888	0.664439	+	0.747342i	$0.268670\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.00979	0.951778
$11$	4.40175	1.32718	0.663588	−	0.748098i	$-0.269033\pi$
$11$	4.40175	1.32718	0.663588	+	0.748098i	$0.269033\pi$
$12$	1.00000	0.288675
$13$	2.32954	0.646098	0.323049	−	0.946382i	$-0.395292\pi$
$13$	2.32954	0.646098	0.323049	+	0.946382i	$0.395292\pi$
$14$	−3.51588	−0.939659
$15$	−3.00979	−0.777124
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−6.35647	−1.45827	−0.729137	−	0.684368i	$-0.760078\pi$
$19$	−6.35647	−1.45827	−0.729137	+	0.684368i	$0.760078\pi$
$20$	−3.00979	−0.673009
$21$	3.51588	0.767228
$22$	−4.40175	−0.938455
$23$	−5.45221	−1.13686	−0.568432	−	0.822730i	$-0.692450\pi$
$23$	−5.45221	−1.13686	−0.568432	+	0.822730i	$0.692450\pi$
$24$	−1.00000	−0.204124
$25$	4.05882	0.811764
$26$	−2.32954	−0.456861
$27$	1.00000	0.192450
$28$	3.51588	0.664439
$29$	−8.94290	−1.66066	−0.830328	−	0.557275i	$-0.811847\pi$
$29$	−8.94290	−1.66066	−0.830328	+	0.557275i	$0.811847\pi$
$30$	3.00979	0.549509
$31$	4.30375	0.772977	0.386488	−	0.922294i	$-0.373688\pi$
$31$	4.30375	0.772977	0.386488	+	0.922294i	$0.373688\pi$
$32$	−1.00000	−0.176777
$33$	4.40175	0.766246
$34$	−1.00000	−0.171499
$35$	−10.5821	−1.78869
$36$	1.00000	0.166667
$37$	−11.0755	−1.82080	−0.910398	−	0.413734i	$-0.864224\pi$
$37$	−11.0755	−1.82080	−0.910398	+	0.413734i	$0.864224\pi$
$38$	6.35647	1.03116
$39$	2.32954	0.373025
$40$	3.00979	0.475889
$41$	−5.69023	−0.888664	−0.444332	−	0.895862i	$-0.646559\pi$
$41$	−5.69023	−0.888664	−0.444332	+	0.895862i	$0.646559\pi$
$42$	−3.51588	−0.542512
$43$	−6.20902	−0.946866	−0.473433	−	0.880830i	$-0.656985\pi$
$43$	−6.20902	−0.946866	−0.473433	+	0.880830i	$0.656985\pi$
$44$	4.40175	0.663588
$45$	−3.00979	−0.448673
$46$	5.45221	0.803885
$47$	−5.86220	−0.855089	−0.427545	−	0.903994i	$-0.640621\pi$
$47$	−5.86220	−0.855089	−0.427545	+	0.903994i	$0.640621\pi$
$48$	1.00000	0.144338
$49$	5.36142	0.765918
$50$	−4.05882	−0.574004
$51$	1.00000	0.140028
$52$	2.32954	0.323049
$53$	1.15884	0.159179	0.0795894	−	0.996828i	$-0.474639\pi$
$53$	1.15884	0.159179	0.0795894	+	0.996828i	$0.474639\pi$
$54$	−1.00000	−0.136083
$55$	−13.2483	−1.78640
$56$	−3.51588	−0.469829
$57$	−6.35647	−0.841935
$58$	8.94290	1.17426
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−3.00979	−0.388562
$61$	7.45057	0.953948	0.476974	−	0.878917i	$-0.341734\pi$
$61$	7.45057	0.953948	0.476974	+	0.878917i	$0.341734\pi$
$62$	−4.30375	−0.546577
$63$	3.51588	0.442959
$64$	1.00000	0.125000
$65$	−7.01142	−0.869660
$66$	−4.40175	−0.541817
$67$	11.8688	1.45000	0.725002	−	0.688747i	$-0.241839\pi$
$67$	11.8688	1.45000	0.725002	+	0.688747i	$0.241839\pi$
$68$	1.00000	0.121268
$69$	−5.45221	−0.656369
$70$	10.5821	1.26480
$71$	−13.4998	−1.60213	−0.801064	−	0.598579i	$-0.795732\pi$
$71$	−13.4998	−1.60213	−0.801064	+	0.598579i	$0.795732\pi$
$72$	−1.00000	−0.117851
$73$	3.69041	0.431930	0.215965	−	0.976401i	$-0.430710\pi$
$73$	3.69041	0.431930	0.215965	+	0.976401i	$0.430710\pi$
$74$	11.0755	1.28750
$75$	4.05882	0.468672
$76$	−6.35647	−0.729137
$77$	15.4760	1.76366
$78$	−2.32954	−0.263769
$79$	−15.0826	−1.69692	−0.848461	−	0.529257i	$-0.822471\pi$
$79$	−15.0826	−1.69692	−0.848461	+	0.529257i	$0.822471\pi$
$80$	−3.00979	−0.336504
$81$	1.00000	0.111111
$82$	5.69023	0.628381
$83$	−11.5315	−1.26574	−0.632872	−	0.774256i	$-0.718124\pi$
$83$	−11.5315	−1.26574	−0.632872	+	0.774256i	$0.718124\pi$
$84$	3.51588	0.383614
$85$	−3.00979	−0.326457
$86$	6.20902	0.669536
$87$	−8.94290	−0.958780
$88$	−4.40175	−0.469228
$89$	1.73281	0.183677	0.0918387	−	0.995774i	$-0.470726\pi$
$89$	1.73281	0.183677	0.0918387	+	0.995774i	$0.470726\pi$
$90$	3.00979	0.317259
$91$	8.19039	0.858586
$92$	−5.45221	−0.568432
$93$	4.30375	0.446278
$94$	5.86220	0.604640
$95$	19.1316	1.96286
$96$	−1.00000	−0.102062
$97$	−1.27160	−0.129112	−0.0645558	−	0.997914i	$-0.520563\pi$
$97$	−1.27160	−0.129112	−0.0645558	+	0.997914i	$0.520563\pi$
$98$	−5.36142	−0.541586
$99$	4.40175	0.442392
$100$	4.05882	0.405882
$101$	−10.0480	−0.999817	−0.499908	−	0.866078i	$-0.666633\pi$
$101$	−10.0480	−0.999817	−0.499908	+	0.866078i	$0.666633\pi$
$102$	−1.00000	−0.0990148
$103$	−18.9454	−1.86675	−0.933373	−	0.358908i	$-0.883149\pi$
$103$	−18.9454	−1.86675	−0.933373	+	0.358908i	$0.883149\pi$
$104$	−2.32954	−0.228430
$105$	−10.5821	−1.03270
$106$	−1.15884	−0.112556
$107$	14.4456	1.39651	0.698253	−	0.715851i	$-0.253961\pi$
$107$	14.4456	1.39651	0.698253	+	0.715851i	$0.253961\pi$
$108$	1.00000	0.0962250
$109$	2.13066	0.204080	0.102040	−	0.994780i	$-0.467463\pi$
$109$	2.13066	0.204080	0.102040	+	0.994780i	$0.467463\pi$
$110$	13.2483	1.26318
$111$	−11.0755	−1.05124
$112$	3.51588	0.332220
$113$	−0.183839	−0.0172941	−0.00864705	−	0.999963i	$-0.502752\pi$
$113$	−0.183839	−0.0172941	−0.00864705	+	0.999963i	$0.502752\pi$
$114$	6.35647	0.595338
$115$	16.4100	1.53024
$116$	−8.94290	−0.830328
$117$	2.32954	0.215366
$118$	1.00000	0.0920575
$119$	3.51588	0.322300
$120$	3.00979	0.274755
$121$	8.37536	0.761397
$122$	−7.45057	−0.674543
$123$	−5.69023	−0.513071
$124$	4.30375	0.386488
$125$	2.83276	0.253370
$126$	−3.51588	−0.313220
$127$	13.2374	1.17463	0.587316	−	0.809358i	$-0.300184\pi$
$127$	13.2374	1.17463	0.587316	+	0.809358i	$0.300184\pi$
$128$	−1.00000	−0.0883883
$129$	−6.20902	−0.546674
$130$	7.01142	0.614942
$131$	−12.2116	−1.06693	−0.533467	−	0.845821i	$-0.679111\pi$
$131$	−12.2116	−1.06693	−0.533467	+	0.845821i	$0.679111\pi$
$132$	4.40175	0.383123
$133$	−22.3486	−1.93787
$134$	−11.8688	−1.02531
$135$	−3.00979	−0.259041
$136$	−1.00000	−0.0857493
$137$	5.20484	0.444679	0.222340	−	0.974969i	$-0.428631\pi$
$137$	5.20484	0.444679	0.222340	+	0.974969i	$0.428631\pi$
$138$	5.45221	0.464123
$139$	18.3651	1.55770	0.778852	−	0.627208i	$-0.215802\pi$
$139$	18.3651	1.55770	0.778852	+	0.627208i	$0.215802\pi$
$140$	−10.5821	−0.894347
$141$	−5.86220	−0.493686
$142$	13.4998	1.13287
$143$	10.2540	0.857486
$144$	1.00000	0.0833333
$145$	26.9162	2.23527
$146$	−3.69041	−0.305420
$147$	5.36142	0.442203
$148$	−11.0755	−0.910398
$149$	7.59864	0.622505	0.311253	−	0.950327i	$-0.399251\pi$
$149$	7.59864	0.622505	0.311253	+	0.950327i	$0.399251\pi$
$150$	−4.05882	−0.331401
$151$	17.5170	1.42551	0.712755	−	0.701413i	$-0.247447\pi$
$151$	17.5170	1.42551	0.712755	+	0.701413i	$0.247447\pi$
$152$	6.35647	0.515578
$153$	1.00000	0.0808452
$154$	−15.4760	−1.24709
$155$	−12.9534	−1.04044
$156$	2.32954	0.186513
$157$	−22.2881	−1.77878	−0.889391	−	0.457148i	$-0.848871\pi$
$157$	−22.2881	−1.77878	−0.889391	+	0.457148i	$0.848871\pi$
$158$	15.0826	1.19991
$159$	1.15884	0.0919019
$160$	3.00979	0.237945
$161$	−19.1693	−1.51075
$162$	−1.00000	−0.0785674
$163$	18.4134	1.44225	0.721126	−	0.692804i	$-0.243625\pi$
$163$	18.4134	1.44225	0.721126	+	0.692804i	$0.243625\pi$
$164$	−5.69023	−0.444332
$165$	−13.2483	−1.03138
$166$	11.5315	0.895017
$167$	−7.14515	−0.552908	−0.276454	−	0.961027i	$-0.589159\pi$
$167$	−7.14515	−0.552908	−0.276454	+	0.961027i	$0.589159\pi$
$168$	−3.51588	−0.271256
$169$	−7.57324	−0.582557
$170$	3.00979	0.230840
$171$	−6.35647	−0.486091
$172$	−6.20902	−0.473433
$173$	19.9167	1.51424	0.757121	−	0.653275i	$-0.226605\pi$
$173$	19.9167	1.51424	0.757121	+	0.653275i	$0.226605\pi$
$174$	8.94290	0.677960
$175$	14.2703	1.07874
$176$	4.40175	0.331794
$177$	−1.00000	−0.0751646
$178$	−1.73281	−0.129880
$179$	−9.56237	−0.714725	−0.357362	−	0.933966i	$-0.616324\pi$
$179$	−9.56237	−0.714725	−0.357362	+	0.933966i	$0.616324\pi$
$180$	−3.00979	−0.224336
$181$	24.4387	1.81652	0.908258	−	0.418411i	$-0.137413\pi$
$181$	24.4387	1.81652	0.908258	+	0.418411i	$0.137413\pi$
$182$	−8.19039	−0.607112
$183$	7.45057	0.550762
$184$	5.45221	0.401942
$185$	33.3348	2.45082
$186$	−4.30375	−0.315566
$187$	4.40175	0.321888
$188$	−5.86220	−0.427545
$189$	3.51588	0.255743
$190$	−19.1316	−1.38795
$191$	−8.92228	−0.645594	−0.322797	−	0.946468i	$-0.604623\pi$
$191$	−8.92228	−0.645594	−0.322797	+	0.946468i	$0.604623\pi$
$192$	1.00000	0.0721688
$193$	−19.0133	−1.36861	−0.684304	−	0.729197i	$-0.739894\pi$
$193$	−19.0133	−1.36861	−0.684304	+	0.729197i	$0.739894\pi$
$194$	1.27160	0.0912956
$195$	−7.01142	−0.502098
$196$	5.36142	0.382959
$197$	−21.6014	−1.53904	−0.769519	−	0.638624i	$-0.779504\pi$
$197$	−21.6014	−1.53904	−0.769519	+	0.638624i	$0.779504\pi$
$198$	−4.40175	−0.312818
$199$	−5.14946	−0.365036	−0.182518	−	0.983203i	$-0.558425\pi$
$199$	−5.14946	−0.365036	−0.182518	+	0.983203i	$0.558425\pi$
$200$	−4.05882	−0.287002
$201$	11.8688	0.837160
$202$	10.0480	0.706977
$203$	−31.4422	−2.20681
$204$	1.00000	0.0700140
$205$	17.1264	1.19616
$206$	18.9454	1.31999
$207$	−5.45221	−0.378955
$208$	2.32954	0.161525
$209$	−27.9796	−1.93539
$210$	10.5821	0.730231
$211$	22.6900	1.56205	0.781024	−	0.624501i	$-0.214698\pi$
$211$	22.6900	1.56205	0.781024	+	0.624501i	$0.214698\pi$
$212$	1.15884	0.0795894
$213$	−13.4998	−0.924988
$214$	−14.4456	−0.987479
$215$	18.6878	1.27450
$216$	−1.00000	−0.0680414
$217$	15.1315	1.02719
$218$	−2.13066	−0.144306
$219$	3.69041	0.249375
$220$	−13.2483	−0.893201
$221$	2.32954	0.156702
$222$	11.0755	0.743337
$223$	−1.93175	−0.129359	−0.0646796	−	0.997906i	$-0.520603\pi$
$223$	−1.93175	−0.129359	−0.0646796	+	0.997906i	$0.520603\pi$
$224$	−3.51588	−0.234915
$225$	4.05882	0.270588
$226$	0.183839	0.0122288
$227$	−19.4875	−1.29343	−0.646715	−	0.762732i	$-0.723858\pi$
$227$	−19.4875	−1.29343	−0.646715	+	0.762732i	$0.723858\pi$
$228$	−6.35647	−0.420968
$229$	−14.4660	−0.955943	−0.477971	−	0.878375i	$-0.658628\pi$
$229$	−14.4660	−0.955943	−0.477971	+	0.878375i	$0.658628\pi$
$230$	−16.4100	−1.08204
$231$	15.4760	1.01825
$232$	8.94290	0.587130
$233$	−7.66524	−0.502167	−0.251083	−	0.967965i	$-0.580787\pi$
$233$	−7.66524	−0.502167	−0.251083	+	0.967965i	$0.580787\pi$
$234$	−2.32954	−0.152287
$235$	17.6440	1.15097
$236$	−1.00000	−0.0650945
$237$	−15.0826	−0.979719
$238$	−3.51588	−0.227901
$239$	−14.6269	−0.946134	−0.473067	−	0.881026i	$-0.656853\pi$
$239$	−14.6269	−0.946134	−0.473067	+	0.881026i	$0.656853\pi$
$240$	−3.00979	−0.194281
$241$	−2.16950	−0.139750	−0.0698750	−	0.997556i	$-0.522260\pi$
$241$	−2.16950	−0.139750	−0.0698750	+	0.997556i	$0.522260\pi$
$242$	−8.37536	−0.538389
$243$	1.00000	0.0641500
$244$	7.45057	0.476974
$245$	−16.1367	−1.03094
$246$	5.69023	0.362796
$247$	−14.8077	−0.942189
$248$	−4.30375	−0.273289
$249$	−11.5315	−0.730778
$250$	−2.83276	−0.179159
$251$	12.3291	0.778208	0.389104	−	0.921194i	$-0.372785\pi$
$251$	12.3291	0.778208	0.389104	+	0.921194i	$0.372785\pi$
$252$	3.51588	0.221480
$253$	−23.9992	−1.50882
$254$	−13.2374	−0.830591
$255$	−3.00979	−0.188480
$256$	1.00000	0.0625000
$257$	11.5505	0.720498	0.360249	−	0.932856i	$-0.382692\pi$
$257$	11.5505	0.720498	0.360249	+	0.932856i	$0.382692\pi$
$258$	6.20902	0.386557
$259$	−38.9400	−2.41962
$260$	−7.01142	−0.434830
$261$	−8.94290	−0.553552
$262$	12.2116	0.754436
$263$	27.0096	1.66548	0.832741	−	0.553663i	$-0.186771\pi$
$263$	27.0096	1.66548	0.832741	+	0.553663i	$0.186771\pi$
$264$	−4.40175	−0.270909
$265$	−3.48786	−0.214257
$266$	22.3486	1.37028
$267$	1.73281	0.106046
$268$	11.8688	0.725002
$269$	−31.9937	−1.95069	−0.975345	−	0.220688i	$-0.929170\pi$
$269$	−31.9937	−1.95069	−0.975345	+	0.220688i	$0.929170\pi$
$270$	3.00979	0.183170
$271$	4.42158	0.268592	0.134296	−	0.990941i	$-0.457123\pi$
$271$	4.42158	0.268592	0.134296	+	0.990941i	$0.457123\pi$
$272$	1.00000	0.0606339
$273$	8.19039	0.495705
$274$	−5.20484	−0.314436
$275$	17.8659	1.07735
$276$	−5.45221	−0.328184
$277$	−22.8595	−1.37349	−0.686746	−	0.726897i	$-0.740962\pi$
$277$	−22.8595	−1.37349	−0.686746	+	0.726897i	$0.740962\pi$
$278$	−18.3651	−1.10146
$279$	4.30375	0.257659
$280$	10.5821	0.632399
$281$	−23.1457	−1.38075	−0.690377	−	0.723450i	$-0.742555\pi$
$281$	−23.1457	−1.38075	−0.690377	+	0.723450i	$0.742555\pi$
$282$	5.86220	0.349089
$283$	0.0700139	0.00416190	0.00208095	−	0.999998i	$-0.499338\pi$
$283$	0.0700139	0.00416190	0.00208095	+	0.999998i	$0.499338\pi$
$284$	−13.4998	−0.801064
$285$	19.1316	1.13326
$286$	−10.2540	−0.606334
$287$	−20.0062	−1.18093
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−26.9162	−1.58058
$291$	−1.27160	−0.0745426
$292$	3.69041	0.215965
$293$	17.8238	1.04128	0.520640	−	0.853777i	$-0.325694\pi$
$293$	17.8238	1.04128	0.520640	+	0.853777i	$0.325694\pi$
$294$	−5.36142	−0.312685
$295$	3.00979	0.175237
$296$	11.0755	0.643748
$297$	4.40175	0.255415
$298$	−7.59864	−0.440178
$299$	−12.7011	−0.734526
$300$	4.05882	0.234336
$301$	−21.8302	−1.25827
$302$	−17.5170	−1.00799
$303$	−10.0480	−0.577244
$304$	−6.35647	−0.364569
$305$	−22.4246	−1.28403
$306$	−1.00000	−0.0571662
$307$	−24.0463	−1.37240	−0.686198	−	0.727415i	$-0.740722\pi$
$307$	−24.0463	−1.37240	−0.686198	+	0.727415i	$0.740722\pi$
$308$	15.4760	0.881828
$309$	−18.9454	−1.07777
$310$	12.9534	0.735702
$311$	16.7659	0.950708	0.475354	−	0.879795i	$-0.342320\pi$
$311$	16.7659	0.950708	0.475354	+	0.879795i	$0.342320\pi$
$312$	−2.32954	−0.131884
$313$	3.10572	0.175546	0.0877729	−	0.996141i	$-0.472025\pi$
$313$	3.10572	0.175546	0.0877729	+	0.996141i	$0.472025\pi$
$314$	22.2881	1.25779
$315$	−10.5821	−0.596231
$316$	−15.0826	−0.848461
$317$	32.7170	1.83757	0.918785	−	0.394759i	$-0.129172\pi$
$317$	32.7170	1.83757	0.918785	+	0.394759i	$0.129172\pi$
$318$	−1.15884	−0.0649844
$319$	−39.3644	−2.20398
$320$	−3.00979	−0.168252
$321$	14.4456	0.806273
$322$	19.1693	1.06826
$323$	−6.35647	−0.353683
$324$	1.00000	0.0555556
$325$	9.45518	0.524479
$326$	−18.4134	−1.01983
$327$	2.13066	0.117826
$328$	5.69023	0.314190
$329$	−20.6108	−1.13631
$330$	13.2483	0.729296
$331$	14.4294	0.793113	0.396556	−	0.918010i	$-0.370205\pi$
$331$	14.4294	0.793113	0.396556	+	0.918010i	$0.370205\pi$
$332$	−11.5315	−0.632872
$333$	−11.0755	−0.606932
$334$	7.14515	0.390965
$335$	−35.7225	−1.95173
$336$	3.51588	0.191807
$337$	−25.1142	−1.36806	−0.684028	−	0.729456i	$-0.739773\pi$
$337$	−25.1142	−1.36806	−0.684028	+	0.729456i	$0.739773\pi$
$338$	7.57324	0.411930
$339$	−0.183839	−0.00998476
$340$	−3.00979	−0.163229
$341$	18.9440	1.02588
$342$	6.35647	0.343719
$343$	−5.76104	−0.311067
$344$	6.20902	0.334768
$345$	16.4100	0.883484
$346$	−19.9167	−1.07073
$347$	−10.2284	−0.549087	−0.274543	−	0.961575i	$-0.588527\pi$
$347$	−10.2284	−0.549087	−0.274543	+	0.961575i	$0.588527\pi$
$348$	−8.94290	−0.479390
$349$	−1.53250	−0.0820331	−0.0410165	−	0.999158i	$-0.513060\pi$
$349$	−1.53250	−0.0820331	−0.0410165	+	0.999158i	$0.513060\pi$
$350$	−14.2703	−0.762781
$351$	2.32954	0.124342
$352$	−4.40175	−0.234614
$353$	6.01518	0.320155	0.160078	−	0.987104i	$-0.448826\pi$
$353$	6.01518	0.320155	0.160078	+	0.987104i	$0.448826\pi$
$354$	1.00000	0.0531494
$355$	40.6314	2.15649
$356$	1.73281	0.0918387
$357$	3.51588	0.186080
$358$	9.56237	0.505387
$359$	−16.4179	−0.866503	−0.433252	−	0.901273i	$-0.642634\pi$
$359$	−16.4179	−0.866503	−0.433252	+	0.901273i	$0.642634\pi$
$360$	3.00979	0.158630
$361$	21.4047	1.12656
$362$	−24.4387	−1.28447
$363$	8.37536	0.439593
$364$	8.19039	0.429293
$365$	−11.1073	−0.581385
$366$	−7.45057	−0.389448
$367$	2.19148	0.114395	0.0571973	−	0.998363i	$-0.481784\pi$
$367$	2.19148	0.114395	0.0571973	+	0.998363i	$0.481784\pi$
$368$	−5.45221	−0.284216
$369$	−5.69023	−0.296221
$370$	−33.3348	−1.73299
$371$	4.07434	0.211529
$372$	4.30375	0.223139
$373$	−10.7745	−0.557883	−0.278942	−	0.960308i	$-0.589984\pi$
$373$	−10.7745	−0.557883	−0.278942	+	0.960308i	$0.589984\pi$
$374$	−4.40175	−0.227609
$375$	2.83276	0.146283
$376$	5.86220	0.302320
$377$	−20.8329	−1.07295
$378$	−3.51588	−0.180837
$379$	16.3205	0.838330	0.419165	−	0.907910i	$-0.362323\pi$
$379$	16.3205	0.838330	0.419165	+	0.907910i	$0.362323\pi$
$380$	19.1316	0.981431
$381$	13.2374	0.678174
$382$	8.92228	0.456504
$383$	−10.0370	−0.512865	−0.256433	−	0.966562i	$-0.582547\pi$
$383$	−10.0370	−0.512865	−0.256433	+	0.966562i	$0.582547\pi$
$384$	−1.00000	−0.0510310
$385$	−46.5795	−2.37391
$386$	19.0133	0.967752
$387$	−6.20902	−0.315622
$388$	−1.27160	−0.0645558
$389$	−16.3077	−0.826834	−0.413417	−	0.910542i	$-0.635665\pi$
$389$	−16.3077	−0.826834	−0.413417	+	0.910542i	$0.635665\pi$
$390$	7.01142	0.355037
$391$	−5.45221	−0.275730
$392$	−5.36142	−0.270793
$393$	−12.2116	−0.615994
$394$	21.6014	1.08826
$395$	45.3953	2.28409
$396$	4.40175	0.221196
$397$	38.5816	1.93635	0.968177	−	0.250265i	$-0.0805178\pi$
$397$	38.5816	1.93635	0.968177	+	0.250265i	$0.0805178\pi$
$398$	5.14946	0.258119
$399$	−22.3486	−1.11883
$400$	4.05882	0.202941
$401$	−21.5952	−1.07841	−0.539207	−	0.842173i	$-0.681276\pi$
$401$	−21.5952	−1.07841	−0.539207	+	0.842173i	$0.681276\pi$
$402$	−11.8688	−0.591961
$403$	10.0258	0.499419
$404$	−10.0480	−0.499908
$405$	−3.00979	−0.149558
$406$	31.4422	1.56045
$407$	−48.7514	−2.41652
$408$	−1.00000	−0.0495074
$409$	−32.0643	−1.58548	−0.792738	−	0.609562i	$-0.791345\pi$
$409$	−32.0643	−1.58548	−0.792738	+	0.609562i	$0.791345\pi$
$410$	−17.1264	−0.845811
$411$	5.20484	0.256736
$412$	−18.9454	−0.933373
$413$	−3.51588	−0.173005
$414$	5.45221	0.267962
$415$	34.7073	1.70371
$416$	−2.32954	−0.114215
$417$	18.3651	0.899341
$418$	27.9796	1.36853
$419$	−25.6201	−1.25162	−0.625811	−	0.779975i	$-0.715232\pi$
$419$	−25.6201	−1.25162	−0.625811	+	0.779975i	$0.715232\pi$
$420$	−10.5821	−0.516351
$421$	28.3094	1.37972	0.689858	−	0.723944i	$-0.257673\pi$
$421$	28.3094	1.37972	0.689858	+	0.723944i	$0.257673\pi$
$422$	−22.6900	−1.10453
$423$	−5.86220	−0.285030
$424$	−1.15884	−0.0562782
$425$	4.05882	0.196882
$426$	13.4998	0.654066
$427$	26.1953	1.26768
$428$	14.4456	0.698253
$429$	10.2540	0.495070
$430$	−18.6878	−0.901207
$431$	12.9776	0.625110	0.312555	−	0.949900i	$-0.398815\pi$
$431$	12.9776	0.625110	0.312555	+	0.949900i	$0.398815\pi$
$432$	1.00000	0.0481125
$433$	−29.3351	−1.40975	−0.704877	−	0.709330i	$-0.748998\pi$
$433$	−29.3351	−1.40975	−0.704877	+	0.709330i	$0.748998\pi$
$434$	−15.1315	−0.726334
$435$	26.9162	1.29053
$436$	2.13066	0.102040
$437$	34.6568	1.65786
$438$	−3.69041	−0.176334
$439$	2.11518	0.100952	0.0504760	−	0.998725i	$-0.483926\pi$
$439$	2.11518	0.100952	0.0504760	+	0.998725i	$0.483926\pi$
$440$	13.2483	0.631589
$441$	5.36142	0.255306
$442$	−2.32954	−0.110805
$443$	21.9004	1.04052	0.520260	−	0.854008i	$-0.325835\pi$
$443$	21.9004	1.04052	0.520260	+	0.854008i	$0.325835\pi$
$444$	−11.0755	−0.525618
$445$	−5.21539	−0.247233
$446$	1.93175	0.0914708
$447$	7.59864	0.359403
$448$	3.51588	0.166110
$449$	18.7940	0.886944	0.443472	−	0.896288i	$-0.353746\pi$
$449$	18.7940	0.886944	0.443472	+	0.896288i	$0.353746\pi$
$450$	−4.05882	−0.191335
$451$	−25.0469	−1.17941
$452$	−0.183839	−0.00864705
$453$	17.5170	0.823019
$454$	19.4875	0.914593
$455$	−24.6513	−1.15567
$456$	6.35647	0.297669
$457$	−11.2594	−0.526693	−0.263347	−	0.964701i	$-0.584826\pi$
$457$	−11.2594	−0.526693	−0.263347	+	0.964701i	$0.584826\pi$
$458$	14.4660	0.675954
$459$	1.00000	0.0466760
$460$	16.4100	0.765120
$461$	1.17777	0.0548541	0.0274271	−	0.999624i	$-0.491269\pi$
$461$	1.17777	0.0548541	0.0274271	+	0.999624i	$0.491269\pi$
$462$	−15.4760	−0.720009
$463$	−28.3063	−1.31550	−0.657752	−	0.753235i	$-0.728492\pi$
$463$	−28.3063	−1.31550	−0.657752	+	0.753235i	$0.728492\pi$
$464$	−8.94290	−0.415164
$465$	−12.9534	−0.600699
$466$	7.66524	0.355085
$467$	31.2666	1.44684	0.723422	−	0.690406i	$-0.242568\pi$
$467$	31.2666	1.44684	0.723422	+	0.690406i	$0.242568\pi$
$468$	2.32954	0.107683
$469$	41.7293	1.92688
$470$	−17.6440	−0.813856
$471$	−22.2881	−1.02698
$472$	1.00000	0.0460287
$473$	−27.3305	−1.25666
$474$	15.0826	0.692766
$475$	−25.7998	−1.18377
$476$	3.51588	0.161150
$477$	1.15884	0.0530596
$478$	14.6269	0.669018
$479$	13.9685	0.638236	0.319118	−	0.947715i	$-0.396613\pi$
$479$	13.9685	0.638236	0.319118	+	0.947715i	$0.396613\pi$
$480$	3.00979	0.137377
$481$	−25.8008	−1.17641
$482$	2.16950	0.0988182
$483$	−19.1693	−0.872235
$484$	8.37536	0.380698
$485$	3.82725	0.173786
$486$	−1.00000	−0.0453609
$487$	33.6323	1.52403	0.762013	−	0.647562i	$-0.224211\pi$
$487$	33.6323	1.52403	0.762013	+	0.647562i	$0.224211\pi$
$488$	−7.45057	−0.337271
$489$	18.4134	0.832685
$490$	16.1367	0.728984
$491$	25.7942	1.16407	0.582037	−	0.813162i	$-0.302256\pi$
$491$	25.7942	1.16407	0.582037	+	0.813162i	$0.302256\pi$
$492$	−5.69023	−0.256535
$493$	−8.94290	−0.402768
$494$	14.8077	0.666228
$495$	−13.2483	−0.595468
$496$	4.30375	0.193244
$497$	−47.4636	−2.12903
$498$	11.5315	0.516738
$499$	13.6060	0.609088	0.304544	−	0.952498i	$-0.401496\pi$
$499$	13.6060	0.609088	0.304544	+	0.952498i	$0.401496\pi$
$500$	2.83276	0.126685
$501$	−7.14515	−0.319222
$502$	−12.3291	−0.550276
$503$	−1.91737	−0.0854913	−0.0427456	−	0.999086i	$-0.513611\pi$
$503$	−1.91737	−0.0854913	−0.0427456	+	0.999086i	$0.513611\pi$
$504$	−3.51588	−0.156610
$505$	30.2424	1.34577
$506$	23.9992	1.06690
$507$	−7.57324	−0.336339
$508$	13.2374	0.587316
$509$	16.1366	0.715243	0.357622	−	0.933867i	$-0.383588\pi$
$509$	16.1366	0.715243	0.357622	+	0.933867i	$0.383588\pi$
$510$	3.00979	0.133276
$511$	12.9750	0.573982
$512$	−1.00000	−0.0441942
$513$	−6.35647	−0.280645
$514$	−11.5505	−0.509469
$515$	57.0216	2.51267
$516$	−6.20902	−0.273337
$517$	−25.8039	−1.13485
$518$	38.9400	1.71093
$519$	19.9167	0.874248
$520$	7.01142	0.307471
$521$	−18.0855	−0.792339	−0.396170	−	0.918177i	$-0.629661\pi$
$521$	−18.0855	−0.792339	−0.396170	+	0.918177i	$0.629661\pi$
$522$	8.94290	0.391420
$523$	26.8273	1.17308	0.586538	−	0.809922i	$-0.300490\pi$
$523$	26.8273	1.17308	0.586538	+	0.809922i	$0.300490\pi$
$524$	−12.2116	−0.533467
$525$	14.2703	0.622808
$526$	−27.0096	−1.17767
$527$	4.30375	0.187474
$528$	4.40175	0.191561
$529$	6.72660	0.292461
$530$	3.48786	0.151503
$531$	−1.00000	−0.0433963
$532$	−22.3486	−0.968935
$533$	−13.2556	−0.574165
$534$	−1.73281	−0.0749860
$535$	−43.4781	−1.87972
$536$	−11.8688	−0.512654
$537$	−9.56237	−0.412647
$538$	31.9937	1.37935
$539$	23.5996	1.01651
$540$	−3.00979	−0.129521
$541$	−18.1888	−0.781996	−0.390998	−	0.920392i	$-0.627870\pi$
$541$	−18.1888	−0.781996	−0.390998	+	0.920392i	$0.627870\pi$
$542$	−4.42158	−0.189923
$543$	24.4387	1.04877
$544$	−1.00000	−0.0428746
$545$	−6.41283	−0.274696
$546$	−8.19039	−0.350516
$547$	−46.1293	−1.97234	−0.986172	−	0.165722i	$-0.947004\pi$
$547$	−46.1293	−1.97234	−0.986172	+	0.165722i	$0.947004\pi$
$548$	5.20484	0.222340
$549$	7.45057	0.317983
$550$	−17.8659	−0.761804
$551$	56.8453	2.42169
$552$	5.45221	0.232061
$553$	−53.0286	−2.25500
$554$	22.8595	0.971206
$555$	33.3348	1.41498
$556$	18.3651	0.778852
$557$	15.5403	0.658463	0.329232	−	0.944249i	$-0.393210\pi$
$557$	15.5403	0.658463	0.329232	+	0.944249i	$0.393210\pi$
$558$	−4.30375	−0.182192
$559$	−14.4642	−0.611769
$560$	−10.5821	−0.447173
$561$	4.40175	0.185842
$562$	23.1457	0.976341
$563$	35.8547	1.51109	0.755547	−	0.655094i	$-0.227371\pi$
$563$	35.8547	1.51109	0.755547	+	0.655094i	$0.227371\pi$
$564$	−5.86220	−0.246843
$565$	0.553316	0.0232782
$566$	−0.0700139	−0.00294291
$567$	3.51588	0.147653
$568$	13.4998	0.566437
$569$	34.7042	1.45488	0.727438	−	0.686173i	$-0.240711\pi$
$569$	34.7042	1.45488	0.727438	+	0.686173i	$0.240711\pi$
$570$	−19.1316	−0.801335
$571$	25.9149	1.08450	0.542252	−	0.840216i	$-0.317572\pi$
$571$	25.9149	1.08450	0.542252	+	0.840216i	$0.317572\pi$
$572$	10.2540	0.428743
$573$	−8.92228	−0.372734
$574$	20.0062	0.835041
$575$	−22.1295	−0.922865
$576$	1.00000	0.0416667
$577$	6.34960	0.264337	0.132169	−	0.991227i	$-0.457806\pi$
$577$	6.34960	0.264337	0.132169	+	0.991227i	$0.457806\pi$
$578$	−1.00000	−0.0415945
$579$	−19.0133	−0.790166
$580$	26.9162	1.11764
$581$	−40.5433	−1.68202
$582$	1.27160	0.0527096
$583$	5.10091	0.211258
$584$	−3.69041	−0.152710
$585$	−7.01142	−0.289887
$586$	−17.8238	−0.736296
$587$	29.7309	1.22712	0.613562	−	0.789646i	$-0.289736\pi$
$587$	29.7309	1.22712	0.613562	+	0.789646i	$0.289736\pi$
$588$	5.36142	0.221101
$589$	−27.3567	−1.12721
$590$	−3.00979	−0.123911
$591$	−21.6014	−0.888564
$592$	−11.0755	−0.455199
$593$	−45.4806	−1.86767	−0.933833	−	0.357710i	$-0.883558\pi$
$593$	−45.4806	−1.86767	−0.933833	+	0.357710i	$0.883558\pi$
$594$	−4.40175	−0.180606
$595$	−10.5821	−0.433822
$596$	7.59864	0.311253
$597$	−5.14946	−0.210754
$598$	12.7011	0.519389
$599$	−5.23583	−0.213930	−0.106965	−	0.994263i	$-0.534113\pi$
$599$	−5.23583	−0.213930	−0.106965	+	0.994263i	$0.534113\pi$
$600$	−4.05882	−0.165701
$601$	−19.6190	−0.800275	−0.400138	−	0.916455i	$-0.631038\pi$
$601$	−19.6190	−0.800275	−0.400138	+	0.916455i	$0.631038\pi$
$602$	21.8302	0.889731
$603$	11.8688	0.483335
$604$	17.5170	0.712755
$605$	−25.2081	−1.02485
$606$	10.0480	0.408173
$607$	−18.3773	−0.745913	−0.372957	−	0.927849i	$-0.621656\pi$
$607$	−18.3773	−0.745913	−0.372957	+	0.927849i	$0.621656\pi$
$608$	6.35647	0.257789
$609$	−31.4422	−1.27410
$610$	22.4246	0.907947
$611$	−13.6562	−0.552472
$612$	1.00000	0.0404226
$613$	−11.7158	−0.473196	−0.236598	−	0.971608i	$-0.576032\pi$
$613$	−11.7158	−0.473196	−0.236598	+	0.971608i	$0.576032\pi$
$614$	24.0463	0.970430
$615$	17.1264	0.690602
$616$	−15.4760	−0.623546
$617$	30.0336	1.20911	0.604553	−	0.796565i	$-0.293352\pi$
$617$	30.0336	1.20911	0.604553	+	0.796565i	$0.293352\pi$
$618$	18.9454	0.762096
$619$	−35.1777	−1.41391	−0.706955	−	0.707259i	$-0.749932\pi$
$619$	−35.1777	−1.41391	−0.706955	+	0.707259i	$0.749932\pi$
$620$	−12.9534	−0.520220
$621$	−5.45221	−0.218790
$622$	−16.7659	−0.672252
$623$	6.09235	0.244085
$624$	2.32954	0.0932563
$625$	−28.8201	−1.15280
$626$	−3.10572	−0.124130
$627$	−27.9796	−1.11740
$628$	−22.2881	−0.889391
$629$	−11.0755	−0.441608
$630$	10.5821	0.421599
$631$	41.5319	1.65336	0.826679	−	0.562673i	$-0.190227\pi$
$631$	41.5319	1.65336	0.826679	+	0.562673i	$0.190227\pi$
$632$	15.0826	0.599953
$633$	22.6900	0.901848
$634$	−32.7170	−1.29936
$635$	−39.8419	−1.58108
$636$	1.15884	0.0459509
$637$	12.4897	0.494858
$638$	39.3644	1.55845
$639$	−13.4998	−0.534042
$640$	3.00979	0.118972
$641$	−14.5909	−0.576304	−0.288152	−	0.957585i	$-0.593041\pi$
$641$	−14.5909	−0.576304	−0.288152	+	0.957585i	$0.593041\pi$
$642$	−14.4456	−0.570121
$643$	−19.2149	−0.757762	−0.378881	−	0.925445i	$-0.623691\pi$
$643$	−19.2149	−0.757762	−0.378881	+	0.925445i	$0.623691\pi$
$644$	−19.1693	−0.755377
$645$	18.6878	0.735832
$646$	6.35647	0.250092
$647$	−0.0150626	−0.000592170 0	−0.000296085	−	1.00000i	$-0.500094\pi$
$647$	−0.0150626	−0.000592170 0	−0.000296085		1.00000i	$0.500094\pi$
$648$	−1.00000	−0.0392837
$649$	−4.40175	−0.172784
$650$	−9.45518	−0.370863
$651$	15.1315	0.593050
$652$	18.4134	0.721126
$653$	−31.9185	−1.24907	−0.624533	−	0.780998i	$-0.714711\pi$
$653$	−31.9185	−1.24907	−0.624533	+	0.780998i	$0.714711\pi$
$654$	−2.13066	−0.0833154
$655$	36.7543	1.43611
$656$	−5.69023	−0.222166
$657$	3.69041	0.143977
$658$	20.6108	0.803492
$659$	10.0548	0.391681	0.195840	−	0.980636i	$-0.437257\pi$
$659$	10.0548	0.391681	0.195840	+	0.980636i	$0.437257\pi$
$660$	−13.2483	−0.515690
$661$	−36.1384	−1.40562	−0.702810	−	0.711378i	$-0.748071\pi$
$661$	−36.1384	−1.40562	−0.702810	+	0.711378i	$0.748071\pi$
$662$	−14.4294	−0.560815
$663$	2.32954	0.0904719
$664$	11.5315	0.447508
$665$	67.2645	2.60841
$666$	11.0755	0.429166
$667$	48.7586	1.88794
$668$	−7.14515	−0.276454
$669$	−1.93175	−0.0746856
$670$	35.7225	1.38008
$671$	32.7955	1.26606
$672$	−3.51588	−0.135628
$673$	−6.15061	−0.237089	−0.118544	−	0.992949i	$-0.537823\pi$
$673$	−6.15061	−0.237089	−0.118544	+	0.992949i	$0.537823\pi$
$674$	25.1142	0.967362
$675$	4.05882	0.156224
$676$	−7.57324	−0.291278
$677$	9.45959	0.363562	0.181781	−	0.983339i	$-0.441814\pi$
$677$	9.45959	0.363562	0.181781	+	0.983339i	$0.441814\pi$
$678$	0.183839	0.00706029
$679$	−4.47080	−0.171574
$680$	3.00979	0.115420
$681$	−19.4875	−0.746762
$682$	−18.9440	−0.725404
$683$	11.6281	0.444935	0.222468	−	0.974940i	$-0.428589\pi$
$683$	11.6281	0.444935	0.222468	+	0.974940i	$0.428589\pi$
$684$	−6.35647	−0.243046
$685$	−15.6655	−0.598546
$686$	5.76104	0.219958
$687$	−14.4660	−0.551914
$688$	−6.20902	−0.236717
$689$	2.69956	0.102845
$690$	−16.4100	−0.624718
$691$	−49.5753	−1.88593	−0.942966	−	0.332890i	$-0.891976\pi$
$691$	−49.5753	−1.88593	−0.942966	+	0.332890i	$0.891976\pi$
$692$	19.9167	0.757121
$693$	15.4760	0.587885
$694$	10.2284	0.388263
$695$	−55.2749	−2.09670
$696$	8.94290	0.338980
$697$	−5.69023	−0.215533
$698$	1.53250	0.0580061
$699$	−7.66524	−0.289926
$700$	14.2703	0.539368
$701$	32.7561	1.23718	0.618590	−	0.785714i	$-0.287704\pi$
$701$	32.7561	1.23718	0.618590	+	0.785714i	$0.287704\pi$
$702$	−2.32954	−0.0879229
$703$	70.4009	2.65522
$704$	4.40175	0.165897
$705$	17.6440	0.664510
$706$	−6.01518	−0.226384
$707$	−35.3277	−1.32863
$708$	−1.00000	−0.0375823
$709$	−27.7116	−1.04073	−0.520366	−	0.853943i	$-0.674205\pi$
$709$	−27.7116	−1.04073	−0.520366	+	0.853943i	$0.674205\pi$
$710$	−40.6314	−1.52487
$711$	−15.0826	−0.565641
$712$	−1.73281	−0.0649398
$713$	−23.4650	−0.878770
$714$	−3.51588	−0.131579
$715$	−30.8625	−1.15419
$716$	−9.56237	−0.357362
$717$	−14.6269	−0.546251
$718$	16.4179	0.612710
$719$	15.4596	0.576546	0.288273	−	0.957548i	$-0.406919\pi$
$719$	15.4596	0.576546	0.288273	+	0.957548i	$0.406919\pi$
$720$	−3.00979	−0.112168
$721$	−66.6098	−2.48068
$722$	−21.4047	−0.796601
$723$	−2.16950	−0.0806847
$724$	24.4387	0.908258
$725$	−36.2976	−1.34806
$726$	−8.37536	−0.310839
$727$	3.89832	0.144581	0.0722903	−	0.997384i	$-0.476969\pi$
$727$	3.89832	0.144581	0.0722903	+	0.997384i	$0.476969\pi$
$728$	−8.19039	−0.303556
$729$	1.00000	0.0370370
$730$	11.1073	0.411101
$731$	−6.20902	−0.229649
$732$	7.45057	0.275381
$733$	31.3572	1.15820	0.579102	−	0.815255i	$-0.303403\pi$
$733$	31.3572	1.15820	0.579102	+	0.815255i	$0.303403\pi$
$734$	−2.19148	−0.0808892
$735$	−16.1367	−0.595213
$736$	5.45221	0.200971
$737$	52.2434	1.92441
$738$	5.69023	0.209460
$739$	−1.16237	−0.0427585	−0.0213792	−	0.999771i	$-0.506806\pi$
$739$	−1.16237	−0.0427585	−0.0213792	+	0.999771i	$0.506806\pi$
$740$	33.3348	1.22541
$741$	−14.8077	−0.543973
$742$	−4.07434	−0.149574
$743$	−2.79441	−0.102517	−0.0512585	−	0.998685i	$-0.516323\pi$
$743$	−2.79441	−0.102517	−0.0512585	+	0.998685i	$0.516323\pi$
$744$	−4.30375	−0.157783
$745$	−22.8703	−0.837903
$746$	10.7745	0.394483
$747$	−11.5315	−0.421915
$748$	4.40175	0.160944
$749$	50.7889	1.85579
$750$	−2.83276	−0.103438
$751$	−47.0618	−1.71731	−0.858654	−	0.512556i	$-0.828699\pi$
$751$	−47.0618	−1.71731	−0.858654	+	0.512556i	$0.828699\pi$
$752$	−5.86220	−0.213772
$753$	12.3291	0.449299
$754$	20.8329	0.758688
$755$	−52.7223	−1.91876
$756$	3.51588	0.127871
$757$	−28.3104	−1.02896	−0.514480	−	0.857503i	$-0.672015\pi$
$757$	−28.3104	−1.02896	−0.514480	+	0.857503i	$0.672015\pi$
$758$	−16.3205	−0.592789
$759$	−23.9992	−0.871117
$760$	−19.1316	−0.693977
$761$	−14.1403	−0.512586	−0.256293	−	0.966599i	$-0.582501\pi$
$761$	−14.1403	−0.512586	−0.256293	+	0.966599i	$0.582501\pi$
$762$	−13.2374	−0.479542
$763$	7.49115	0.271198
$764$	−8.92228	−0.322797
$765$	−3.00979	−0.108819
$766$	10.0370	0.362650
$767$	−2.32954	−0.0841148
$768$	1.00000	0.0360844
$769$	54.5883	1.96851	0.984253	−	0.176768i	$-0.0565643\pi$
$769$	54.5883	1.96851	0.984253	+	0.176768i	$0.0565643\pi$
$770$	46.5795	1.67861
$771$	11.5505	0.415980
$772$	−19.0133	−0.684304
$773$	38.3156	1.37812	0.689058	−	0.724706i	$-0.258025\pi$
$773$	38.3156	1.37812	0.689058	+	0.724706i	$0.258025\pi$
$774$	6.20902	0.223179
$775$	17.4681	0.627474
$776$	1.27160	0.0456478
$777$	−38.9400	−1.39697
$778$	16.3077	0.584660
$779$	36.1698	1.29592
$780$	−7.01142	−0.251049
$781$	−59.4225	−2.12630
$782$	5.45221	0.194971
$783$	−8.94290	−0.319593
$784$	5.36142	0.191479
$785$	67.0823	2.39427
$786$	12.2116	0.435574
$787$	16.1550	0.575863	0.287931	−	0.957651i	$-0.407033\pi$
$787$	16.1550	0.575863	0.287931	+	0.957651i	$0.407033\pi$
$788$	−21.6014	−0.769519
$789$	27.0096	0.961566
$790$	−45.3953	−1.61509
$791$	−0.646356	−0.0229818
$792$	−4.40175	−0.156409
$793$	17.3564	0.616344
$794$	−38.5816	−1.36921
$795$	−3.48786	−0.123702
$796$	−5.14946	−0.182518
$797$	4.63865	0.164309	0.0821547	−	0.996620i	$-0.473820\pi$
$797$	4.63865	0.164309	0.0821547	+	0.996620i	$0.473820\pi$
$798$	22.3486	0.791132
$799$	−5.86220	−0.207390
$800$	−4.05882	−0.143501
$801$	1.73281	0.0612258
$802$	21.5952	0.762555
$803$	16.2442	0.573247
$804$	11.8688	0.418580
$805$	57.6956	2.03350
$806$	−10.0258	−0.353143
$807$	−31.9937	−1.12623
$808$	10.0480	0.353489
$809$	4.99938	0.175769	0.0878844	−	0.996131i	$-0.471989\pi$
$809$	4.99938	0.175769	0.0878844	+	0.996131i	$0.471989\pi$
$810$	3.00979	0.105753
$811$	16.6547	0.584827	0.292413	−	0.956292i	$-0.405542\pi$
$811$	16.6547	0.584827	0.292413	+	0.956292i	$0.405542\pi$
$812$	−31.4422	−1.10340
$813$	4.42158	0.155072
$814$	48.7514	1.70874
$815$	−55.4206	−1.94130
$816$	1.00000	0.0350070
$817$	39.4674	1.38079
$818$	32.0643	1.12110
$819$	8.19039	0.286195
$820$	17.1264	0.598079
$821$	−5.80959	−0.202756	−0.101378	−	0.994848i	$-0.532325\pi$
$821$	−5.80959	−0.202756	−0.101378	+	0.994848i	$0.532325\pi$
$822$	−5.20484	−0.181540
$823$	26.9074	0.937932	0.468966	−	0.883216i	$-0.344627\pi$
$823$	26.9074	0.937932	0.468966	+	0.883216i	$0.344627\pi$
$824$	18.9454	0.659994
$825$	17.8659	0.622010
$826$	3.51588	0.122333
$827$	24.8328	0.863520	0.431760	−	0.901989i	$-0.357893\pi$
$827$	24.8328	0.863520	0.431760	+	0.901989i	$0.357893\pi$
$828$	−5.45221	−0.189477
$829$	−20.5879	−0.715048	−0.357524	−	0.933904i	$-0.616379\pi$
$829$	−20.5879	−0.715048	−0.357524	+	0.933904i	$0.616379\pi$
$830$	−34.7073	−1.20471
$831$	−22.8595	−0.792986
$832$	2.32954	0.0807623
$833$	5.36142	0.185762
$834$	−18.3651	−0.635930
$835$	21.5054	0.744224
$836$	−27.9796	−0.967693
$837$	4.30375	0.148759
$838$	25.6201	0.885031
$839$	−57.4333	−1.98282	−0.991408	−	0.130804i	$-0.958244\pi$
$839$	−57.4333	−1.98282	−0.991408	+	0.130804i	$0.958244\pi$
$840$	10.5821	0.365116
$841$	50.9755	1.75778
$842$	−28.3094	−0.975607
$843$	−23.1457	−0.797179
$844$	22.6900	0.781024
$845$	22.7938	0.784132
$846$	5.86220	0.201547
$847$	29.4468	1.01180
$848$	1.15884	0.0397947
$849$	0.0700139	0.00240287
$850$	−4.05882	−0.139216
$851$	60.3858	2.07000
$852$	−13.4998	−0.462494
$853$	−7.50817	−0.257075	−0.128537	−	0.991705i	$-0.541028\pi$
$853$	−7.50817	−0.257075	−0.128537	+	0.991705i	$0.541028\pi$
$854$	−26.1953	−0.896385
$855$	19.1316	0.654288
$856$	−14.4456	−0.493740
$857$	47.2531	1.61414	0.807068	−	0.590459i	$-0.201053\pi$
$857$	47.2531	1.61414	0.807068	+	0.590459i	$0.201053\pi$
$858$	−10.2540	−0.350067
$859$	−2.01327	−0.0686918	−0.0343459	−	0.999410i	$-0.510935\pi$
$859$	−2.01327	−0.0686918	−0.0343459	+	0.999410i	$0.510935\pi$
$860$	18.6878	0.637249
$861$	−20.0062	−0.681808
$862$	−12.9776	−0.442019
$863$	−16.4488	−0.559923	−0.279962	−	0.960011i	$-0.590322\pi$
$863$	−16.4488	−0.559923	−0.279962	+	0.960011i	$0.590322\pi$
$864$	−1.00000	−0.0340207
$865$	−59.9451	−2.03820
$866$	29.3351	0.996846
$867$	1.00000	0.0339618
$868$	15.1315	0.513596
$869$	−66.3897	−2.25212
$870$	−26.9162	−0.912546
$871$	27.6488	0.936845
$872$	−2.13066	−0.0721532
$873$	−1.27160	−0.0430372
$874$	−34.6568	−1.17228
$875$	9.95964	0.336697
$876$	3.69041	0.124687
$877$	−40.8211	−1.37843	−0.689216	−	0.724556i	$-0.742045\pi$
$877$	−40.8211	−1.37843	−0.689216	+	0.724556i	$0.742045\pi$
$878$	−2.11518	−0.0713838
$879$	17.8238	0.601183
$880$	−13.2483	−0.446601
$881$	2.39386	0.0806512	0.0403256	−	0.999187i	$-0.487160\pi$
$881$	2.39386	0.0806512	0.0403256	+	0.999187i	$0.487160\pi$
$882$	−5.36142	−0.180529
$883$	−32.7325	−1.10154	−0.550769	−	0.834658i	$-0.685665\pi$
$883$	−32.7325	−1.10154	−0.550769	+	0.834658i	$0.685665\pi$
$884$	2.32954	0.0783509
$885$	3.00979	0.101173
$886$	−21.9004	−0.735759
$887$	−24.3879	−0.818866	−0.409433	−	0.912340i	$-0.634273\pi$
$887$	−24.3879	−0.818866	−0.409433	+	0.912340i	$0.634273\pi$
$888$	11.0755	0.371668
$889$	46.5413	1.56094
$890$	5.21539	0.174820
$891$	4.40175	0.147464
$892$	−1.93175	−0.0646796
$893$	37.2629	1.24695
$894$	−7.59864	−0.254137
$895$	28.7807	0.962032
$896$	−3.51588	−0.117457
$897$	−12.7011	−0.424079
$898$	−18.7940	−0.627164
$899$	−38.4880	−1.28365
$900$	4.05882	0.135294
$901$	1.15884	0.0386065
$902$	25.0469	0.833972
$903$	−21.8302	−0.726463
$904$	0.183839	0.00611439
$905$	−73.5553	−2.44506
$906$	−17.5170	−0.581962
$907$	49.2297	1.63465	0.817323	−	0.576179i	$-0.195457\pi$
$907$	49.2297	1.63465	0.817323	+	0.576179i	$0.195457\pi$
$908$	−19.4875	−0.646715
$909$	−10.0480	−0.333272
$910$	24.6513	0.817184
$911$	−52.5742	−1.74186	−0.870930	−	0.491407i	$-0.836483\pi$
$911$	−52.5742	−1.74186	−0.870930	+	0.491407i	$0.836483\pi$
$912$	−6.35647	−0.210484
$913$	−50.7587	−1.67987
$914$	11.2594	0.372429
$915$	−22.4246	−0.741335
$916$	−14.4660	−0.477971
$917$	−42.9346	−1.41782
$918$	−1.00000	−0.0330049
$919$	−9.71423	−0.320443	−0.160221	−	0.987081i	$-0.551221\pi$
$919$	−9.71423	−0.320443	−0.160221	+	0.987081i	$0.551221\pi$
$920$	−16.4100	−0.541021
$921$	−24.0463	−0.792353
$922$	−1.17777	−0.0387877
$923$	−31.4482	−1.03513
$924$	15.4760	0.509124
$925$	−44.9533	−1.47806
$926$	28.3063	0.930201
$927$	−18.9454	−0.622249
$928$	8.94290	0.293565
$929$	9.58104	0.314344	0.157172	−	0.987571i	$-0.449762\pi$
$929$	9.58104	0.314344	0.157172	+	0.987571i	$0.449762\pi$
$930$	12.9534	0.424758
$931$	−34.0797	−1.11692
$932$	−7.66524	−0.251083
$933$	16.7659	0.548892
$934$	−31.2666	−1.02307
$935$	−13.2483	−0.433266
$936$	−2.32954	−0.0761434
$937$	−45.8594	−1.49816	−0.749081	−	0.662479i	$-0.769504\pi$
$937$	−45.8594	−1.49816	−0.749081	+	0.662479i	$0.769504\pi$
$938$	−41.7293	−1.36251
$939$	3.10572	0.101351
$940$	17.6440	0.575483
$941$	−24.4483	−0.796993	−0.398497	−	0.917170i	$-0.630468\pi$
$941$	−24.4483	−0.796993	−0.398497	+	0.917170i	$0.630468\pi$
$942$	22.2881	0.726184
$943$	31.0243	1.01029
$944$	−1.00000	−0.0325472
$945$	−10.5821	−0.344234
$946$	27.3305	0.888592
$947$	−16.9246	−0.549975	−0.274987	−	0.961448i	$-0.588674\pi$
$947$	−16.9246	−0.549975	−0.274987	+	0.961448i	$0.588674\pi$
$948$	−15.0826	−0.489859
$949$	8.59696	0.279069
$950$	25.7998	0.837055
$951$	32.7170	1.06092
$952$	−3.51588	−0.113950
$953$	8.38663	0.271670	0.135835	−	0.990732i	$-0.456628\pi$
$953$	8.38663	0.271670	0.135835	+	0.990732i	$0.456628\pi$
$954$	−1.15884	−0.0375188
$955$	26.8542	0.868980
$956$	−14.6269	−0.473067
$957$	−39.3644	−1.27247
$958$	−13.9685	−0.451301
$959$	18.2996	0.590925
$960$	−3.00979	−0.0971405
$961$	−12.4777	−0.402507
$962$	25.8008	0.831850
$963$	14.4456	0.465502
$964$	−2.16950	−0.0698750
$965$	57.2260	1.84217
$966$	19.1693	0.616763
$967$	7.61159	0.244772	0.122386	−	0.992483i	$-0.460945\pi$
$967$	7.61159	0.244772	0.122386	+	0.992483i	$0.460945\pi$
$968$	−8.37536	−0.269194
$969$	−6.35647	−0.204199
$970$	−3.82725	−0.122886
$971$	−16.8679	−0.541315	−0.270658	−	0.962676i	$-0.587241\pi$
$971$	−16.8679	−0.541315	−0.270658	+	0.962676i	$0.587241\pi$
$972$	1.00000	0.0320750
$973$	64.5694	2.07000
$974$	−33.6323	−1.07765
$975$	9.45518	0.302808
$976$	7.45057	0.238487
$977$	−9.05154	−0.289584	−0.144792	−	0.989462i	$-0.546251\pi$
$977$	−9.05154	−0.289584	−0.144792	+	0.989462i	$0.546251\pi$
$978$	−18.4134	−0.588797
$979$	7.62738	0.243772
$980$	−16.1367	−0.515469
$981$	2.13066	0.0680267
$982$	−25.7942	−0.823125
$983$	−19.5079	−0.622205	−0.311102	−	0.950376i	$-0.600698\pi$
$983$	−19.5079	−0.622205	−0.311102	+	0.950376i	$0.600698\pi$
$984$	5.69023	0.181398
$985$	65.0157	2.07157
$986$	8.94290	0.284800
$987$	−20.6108	−0.656049
$988$	−14.8077	−0.471094
$989$	33.8529	1.07646
$990$	13.2483	0.421059
$991$	−8.61475	−0.273656	−0.136828	−	0.990595i	$-0.543691\pi$
$991$	−8.61475	−0.273656	−0.136828	+	0.990595i	$0.543691\pi$
$992$	−4.30375	−0.136644
$993$	14.4294	0.457904
$994$	47.4636	1.50545
$995$	15.4988	0.491345
$996$	−11.5315	−0.365389
$997$	13.4609	0.426310	0.213155	−	0.977018i	$-0.431626\pi$
$997$	13.4609	0.426310	0.213155	+	0.977018i	$0.431626\pi$
$998$	−13.6060	−0.430690
$999$	−11.0755	−0.350412

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.t.1.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.t.1.2	✓	8	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.00979 q^{5} -1.00000 q^{6} +3.51588 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.00979 q^{5} -1.00000 q^{6} +3.51588 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.00979 q^{10} +4.40175 q^{11} +1.00000 q^{12} +2.32954 q^{13} -3.51588 q^{14} -3.00979 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -6.35647 q^{19} -3.00979 q^{20} +3.51588 q^{21} -4.40175 q^{22} -5.45221 q^{23} -1.00000 q^{24} +4.05882 q^{25} -2.32954 q^{26} +1.00000 q^{27} +3.51588 q^{28} -8.94290 q^{29} +3.00979 q^{30} +4.30375 q^{31} -1.00000 q^{32} +4.40175 q^{33} -1.00000 q^{34} -10.5821 q^{35} +1.00000 q^{36} -11.0755 q^{37} +6.35647 q^{38} +2.32954 q^{39} +3.00979 q^{40} -5.69023 q^{41} -3.51588 q^{42} -6.20902 q^{43} +4.40175 q^{44} -3.00979 q^{45} +5.45221 q^{46} -5.86220 q^{47} +1.00000 q^{48} +5.36142 q^{49} -4.05882 q^{50} +1.00000 q^{51} +2.32954 q^{52} +1.15884 q^{53} -1.00000 q^{54} -13.2483 q^{55} -3.51588 q^{56} -6.35647 q^{57} +8.94290 q^{58} -1.00000 q^{59} -3.00979 q^{60} +7.45057 q^{61} -4.30375 q^{62} +3.51588 q^{63} +1.00000 q^{64} -7.01142 q^{65} -4.40175 q^{66} +11.8688 q^{67} +1.00000 q^{68} -5.45221 q^{69} +10.5821 q^{70} -13.4998 q^{71} -1.00000 q^{72} +3.69041 q^{73} +11.0755 q^{74} +4.05882 q^{75} -6.35647 q^{76} +15.4760 q^{77} -2.32954 q^{78} -15.0826 q^{79} -3.00979 q^{80} +1.00000 q^{81} +5.69023 q^{82} -11.5315 q^{83} +3.51588 q^{84} -3.00979 q^{85} +6.20902 q^{86} -8.94290 q^{87} -4.40175 q^{88} +1.73281 q^{89} +3.00979 q^{90} +8.19039 q^{91} -5.45221 q^{92} +4.30375 q^{93} +5.86220 q^{94} +19.1316 q^{95} -1.00000 q^{96} -1.27160 q^{97} -5.36142 q^{98} +4.40175 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9} + 6 q^{10} + q^{11} + 8 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} + 4 q^{19} - 6 q^{20} - 4 q^{21} - q^{22} - 11 q^{23} - 8 q^{24} + 6 q^{25} + 2 q^{26} + 8 q^{27} - 4 q^{28} - 12 q^{29} + 6 q^{30} - 9 q^{31} - 8 q^{32} + q^{33} - 8 q^{34} - 28 q^{35} + 8 q^{36} - 22 q^{37} - 4 q^{38} - 2 q^{39} + 6 q^{40} - 19 q^{41} + 4 q^{42} - 5 q^{43} + q^{44} - 6 q^{45} + 11 q^{46} - 26 q^{47} + 8 q^{48} - 6 q^{50} + 8 q^{51} - 2 q^{52} - 21 q^{53} - 8 q^{54} - 13 q^{55} + 4 q^{56} + 4 q^{57} + 12 q^{58} - 8 q^{59} - 6 q^{60} + 9 q^{61} + 9 q^{62} - 4 q^{63} + 8 q^{64} + 14 q^{65} - q^{66} + 26 q^{67} + 8 q^{68} - 11 q^{69} + 28 q^{70} - 14 q^{71} - 8 q^{72} + 17 q^{73} + 22 q^{74} + 6 q^{75} + 4 q^{76} - 18 q^{77} + 2 q^{78} - 39 q^{79} - 6 q^{80} + 8 q^{81} + 19 q^{82} - 11 q^{83} - 4 q^{84} - 6 q^{85} + 5 q^{86} - 12 q^{87} - q^{88} + 6 q^{90} + 11 q^{91} - 11 q^{92} - 9 q^{93} + 26 q^{94} - 15 q^{95} - 8 q^{96} + 16 q^{97} + q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9 + 6 * q^10 + q^11 + 8 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 + 4 * q^19 - 6 * q^20 - 4 * q^21 - q^22 - 11 * q^23 - 8 * q^24 + 6 * q^25 + 2 * q^26 + 8 * q^27 - 4 * q^28 - 12 * q^29 + 6 * q^30 - 9 * q^31 - 8 * q^32 + q^33 - 8 * q^34 - 28 * q^35 + 8 * q^36 - 22 * q^37 - 4 * q^38 - 2 * q^39 + 6 * q^40 - 19 * q^41 + 4 * q^42 - 5 * q^43 + q^44 - 6 * q^45 + 11 * q^46 - 26 * q^47 + 8 * q^48 - 6 * q^50 + 8 * q^51 - 2 * q^52 - 21 * q^53 - 8 * q^54 - 13 * q^55 + 4 * q^56 + 4 * q^57 + 12 * q^58 - 8 * q^59 - 6 * q^60 + 9 * q^61 + 9 * q^62 - 4 * q^63 + 8 * q^64 + 14 * q^65 - q^66 + 26 * q^67 + 8 * q^68 - 11 * q^69 + 28 * q^70 - 14 * q^71 - 8 * q^72 + 17 * q^73 + 22 * q^74 + 6 * q^75 + 4 * q^76 - 18 * q^77 + 2 * q^78 - 39 * q^79 - 6 * q^80 + 8 * q^81 + 19 * q^82 - 11 * q^83 - 4 * q^84 - 6 * q^85 + 5 * q^86 - 12 * q^87 - q^88 + 6 * q^90 + 11 * q^91 - 11 * q^92 - 9 * q^93 + 26 * q^94 - 15 * q^95 - 8 * q^96 + 16 * q^97 + q^99

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