LMFDB - Embedded newform 6018.2.a.r.1.5

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:	6.6.18461324.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 4x^{4} + 12x^{3} + 3x^{2} - 6x - 2 $ x^6 - 3x^5 - 4x^4 + 12x^3 + 3x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.558656$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.558656 q^{5} +1.00000 q^{6} -3.85965 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.558656 q^{5} +1.00000 q^{6} -3.85965 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.558656 q^{10} -2.45077 q^{11} +1.00000 q^{12} +1.76729 q^{13} -3.85965 q^{14} +0.558656 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -3.31293 q^{19} +0.558656 q^{20} -3.85965 q^{21} -2.45077 q^{22} +8.06226 q^{23} +1.00000 q^{24} -4.68790 q^{25} +1.76729 q^{26} +1.00000 q^{27} -3.85965 q^{28} -2.43851 q^{29} +0.558656 q^{30} -4.81715 q^{31} +1.00000 q^{32} -2.45077 q^{33} -1.00000 q^{34} -2.15621 q^{35} +1.00000 q^{36} -4.21250 q^{37} -3.31293 q^{38} +1.76729 q^{39} +0.558656 q^{40} -3.15338 q^{41} -3.85965 q^{42} -9.71878 q^{43} -2.45077 q^{44} +0.558656 q^{45} +8.06226 q^{46} +9.55422 q^{47} +1.00000 q^{48} +7.89687 q^{49} -4.68790 q^{50} -1.00000 q^{51} +1.76729 q^{52} -4.43584 q^{53} +1.00000 q^{54} -1.36914 q^{55} -3.85965 q^{56} -3.31293 q^{57} -2.43851 q^{58} -1.00000 q^{59} +0.558656 q^{60} -7.75843 q^{61} -4.81715 q^{62} -3.85965 q^{63} +1.00000 q^{64} +0.987309 q^{65} -2.45077 q^{66} +5.49434 q^{67} -1.00000 q^{68} +8.06226 q^{69} -2.15621 q^{70} -16.2029 q^{71} +1.00000 q^{72} -6.49341 q^{73} -4.21250 q^{74} -4.68790 q^{75} -3.31293 q^{76} +9.45912 q^{77} +1.76729 q^{78} -7.02504 q^{79} +0.558656 q^{80} +1.00000 q^{81} -3.15338 q^{82} +17.9718 q^{83} -3.85965 q^{84} -0.558656 q^{85} -9.71878 q^{86} -2.43851 q^{87} -2.45077 q^{88} -8.74066 q^{89} +0.558656 q^{90} -6.82113 q^{91} +8.06226 q^{92} -4.81715 q^{93} +9.55422 q^{94} -1.85079 q^{95} +1.00000 q^{96} +10.8365 q^{97} +7.89687 q^{98} -2.45077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} + 6 q^{6} - 7 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 + 6 * q^6 - 7 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} + 6 q^{6} - 7 q^{7} + 6 q^{8} + 6 q^{9} - 3 q^{10} - 8 q^{11} + 6 q^{12} - 6 q^{13} - 7 q^{14} - 3 q^{15} + 6 q^{16} - 6 q^{17} + 6 q^{18} - 14 q^{19} - 3 q^{20} - 7 q^{21} - 8 q^{22} - 8 q^{23} + 6 q^{24} - 13 q^{25} - 6 q^{26} + 6 q^{27} - 7 q^{28} - 21 q^{29} - 3 q^{30} - 5 q^{31} + 6 q^{32} - 8 q^{33} - 6 q^{34} - 12 q^{35} + 6 q^{36} - 13 q^{37} - 14 q^{38} - 6 q^{39} - 3 q^{40} - 18 q^{41} - 7 q^{42} - 4 q^{43} - 8 q^{44} - 3 q^{45} - 8 q^{46} - 4 q^{47} + 6 q^{48} + 5 q^{49} - 13 q^{50} - 6 q^{51} - 6 q^{52} - 25 q^{53} + 6 q^{54} - 8 q^{55} - 7 q^{56} - 14 q^{57} - 21 q^{58} - 6 q^{59} - 3 q^{60} - 5 q^{62} - 7 q^{63} + 6 q^{64} + 6 q^{65} - 8 q^{66} - 13 q^{67} - 6 q^{68} - 8 q^{69} - 12 q^{70} - 12 q^{71} + 6 q^{72} - 4 q^{73} - 13 q^{74} - 13 q^{75} - 14 q^{76} + 4 q^{77} - 6 q^{78} - 12 q^{79} - 3 q^{80} + 6 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 3 q^{85} - 4 q^{86} - 21 q^{87} - 8 q^{88} - 11 q^{89} - 3 q^{90} - 31 q^{91} - 8 q^{92} - 5 q^{93} - 4 q^{94} + 35 q^{95} + 6 q^{96} + 16 q^{97} + 5 q^{98} - 8 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 + 6 * q^6 - 7 * q^7 + 6 * q^8 + 6 * q^9 - 3 * q^10 - 8 * q^11 + 6 * q^12 - 6 * q^13 - 7 * q^14 - 3 * q^15 + 6 * q^16 - 6 * q^17 + 6 * q^18 - 14 * q^19 - 3 * q^20 - 7 * q^21 - 8 * q^22 - 8 * q^23 + 6 * q^24 - 13 * q^25 - 6 * q^26 + 6 * q^27 - 7 * q^28 - 21 * q^29 - 3 * q^30 - 5 * q^31 + 6 * q^32 - 8 * q^33 - 6 * q^34 - 12 * q^35 + 6 * q^36 - 13 * q^37 - 14 * q^38 - 6 * q^39 - 3 * q^40 - 18 * q^41 - 7 * q^42 - 4 * q^43 - 8 * q^44 - 3 * q^45 - 8 * q^46 - 4 * q^47 + 6 * q^48 + 5 * q^49 - 13 * q^50 - 6 * q^51 - 6 * q^52 - 25 * q^53 + 6 * q^54 - 8 * q^55 - 7 * q^56 - 14 * q^57 - 21 * q^58 - 6 * q^59 - 3 * q^60 - 5 * q^62 - 7 * q^63 + 6 * q^64 + 6 * q^65 - 8 * q^66 - 13 * q^67 - 6 * q^68 - 8 * q^69 - 12 * q^70 - 12 * q^71 + 6 * q^72 - 4 * q^73 - 13 * q^74 - 13 * q^75 - 14 * q^76 + 4 * q^77 - 6 * q^78 - 12 * q^79 - 3 * q^80 + 6 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 3 * q^85 - 4 * q^86 - 21 * q^87 - 8 * q^88 - 11 * q^89 - 3 * q^90 - 31 * q^91 - 8 * q^92 - 5 * q^93 - 4 * q^94 + 35 * q^95 + 6 * q^96 + 16 * q^97 + 5 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.558656	0.249838	0.124919	−	0.992167i	$-0.460133\pi$
$5$	0.558656	0.249838	0.124919	+	0.992167i	$0.460133\pi$
$6$	1.00000	0.408248
$7$	−3.85965	−1.45881	−0.729405	−	0.684082i	$-0.760203\pi$
$7$	−3.85965	−1.45881	−0.729405	+	0.684082i	$0.760203\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.558656	0.176662
$11$	−2.45077	−0.738936	−0.369468	−	0.929243i	$-0.620460\pi$
$11$	−2.45077	−0.738936	−0.369468	+	0.929243i	$0.620460\pi$
$12$	1.00000	0.288675
$13$	1.76729	0.490159	0.245080	−	0.969503i	$-0.421186\pi$
$13$	1.76729	0.490159	0.245080	+	0.969503i	$0.421186\pi$
$14$	−3.85965	−1.03153
$15$	0.558656	0.144244
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−3.31293	−0.760038	−0.380019	−	0.924979i	$-0.624082\pi$
$19$	−3.31293	−0.760038	−0.380019	+	0.924979i	$0.624082\pi$
$20$	0.558656	0.124919
$21$	−3.85965	−0.842244
$22$	−2.45077	−0.522507
$23$	8.06226	1.68110	0.840549	−	0.541736i	$-0.182233\pi$
$23$	8.06226	1.68110	0.840549	+	0.541736i	$0.182233\pi$
$24$	1.00000	0.204124
$25$	−4.68790	−0.937581
$26$	1.76729	0.346595
$27$	1.00000	0.192450
$28$	−3.85965	−0.729405
$29$	−2.43851	−0.452819	−0.226410	−	0.974032i	$-0.572699\pi$
$29$	−2.43851	−0.452819	−0.226410	+	0.974032i	$0.572699\pi$
$30$	0.558656	0.101996
$31$	−4.81715	−0.865186	−0.432593	−	0.901589i	$-0.642401\pi$
$31$	−4.81715	−0.865186	−0.432593	+	0.901589i	$0.642401\pi$
$32$	1.00000	0.176777
$33$	−2.45077	−0.426625
$34$	−1.00000	−0.171499
$35$	−2.15621	−0.364467
$36$	1.00000	0.166667
$37$	−4.21250	−0.692531	−0.346266	−	0.938137i	$-0.612550\pi$
$37$	−4.21250	−0.692531	−0.346266	+	0.938137i	$0.612550\pi$
$38$	−3.31293	−0.537428
$39$	1.76729	0.282994
$40$	0.558656	0.0883312
$41$	−3.15338	−0.492475	−0.246237	−	0.969210i	$-0.579194\pi$
$41$	−3.15338	−0.492475	−0.246237	+	0.969210i	$0.579194\pi$
$42$	−3.85965	−0.595556
$43$	−9.71878	−1.48210	−0.741050	−	0.671450i	$-0.765672\pi$
$43$	−9.71878	−1.48210	−0.741050	+	0.671450i	$0.765672\pi$
$44$	−2.45077	−0.369468
$45$	0.558656	0.0832795
$46$	8.06226	1.18872
$47$	9.55422	1.39363	0.696813	−	0.717253i	$-0.254601\pi$
$47$	9.55422	1.39363	0.696813	+	0.717253i	$0.254601\pi$
$48$	1.00000	0.144338
$49$	7.89687	1.12812
$50$	−4.68790	−0.662970
$51$	−1.00000	−0.140028
$52$	1.76729	0.245080
$53$	−4.43584	−0.609309	−0.304655	−	0.952463i	$-0.598541\pi$
$53$	−4.43584	−0.609309	−0.304655	+	0.952463i	$0.598541\pi$
$54$	1.00000	0.136083
$55$	−1.36914	−0.184615
$56$	−3.85965	−0.515767
$57$	−3.31293	−0.438808
$58$	−2.43851	−0.320192
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	0.558656	0.0721222
$61$	−7.75843	−0.993366	−0.496683	−	0.867932i	$-0.665449\pi$
$61$	−7.75843	−0.993366	−0.496683	+	0.867932i	$0.665449\pi$
$62$	−4.81715	−0.611779
$63$	−3.85965	−0.486270
$64$	1.00000	0.125000
$65$	0.987309	0.122461
$66$	−2.45077	−0.301669
$67$	5.49434	0.671240	0.335620	−	0.941997i	$-0.391054\pi$
$67$	5.49434	0.671240	0.335620	+	0.941997i	$0.391054\pi$
$68$	−1.00000	−0.121268
$69$	8.06226	0.970582
$70$	−2.15621	−0.257717
$71$	−16.2029	−1.92293	−0.961466	−	0.274924i	$-0.911347\pi$
$71$	−16.2029	−1.92293	−0.961466	+	0.274924i	$0.911347\pi$
$72$	1.00000	0.117851
$73$	−6.49341	−0.759996	−0.379998	−	0.924987i	$-0.624075\pi$
$73$	−6.49341	−0.759996	−0.379998	+	0.924987i	$0.624075\pi$
$74$	−4.21250	−0.489693
$75$	−4.68790	−0.541312
$76$	−3.31293	−0.380019
$77$	9.45912	1.07797
$78$	1.76729	0.200107
$79$	−7.02504	−0.790378	−0.395189	−	0.918600i	$-0.629321\pi$
$79$	−7.02504	−0.790378	−0.395189	+	0.918600i	$0.629321\pi$
$80$	0.558656	0.0624596
$81$	1.00000	0.111111
$82$	−3.15338	−0.348232
$83$	17.9718	1.97266	0.986332	−	0.164769i	$-0.0526879\pi$
$83$	17.9718	1.97266	0.986332	+	0.164769i	$0.0526879\pi$
$84$	−3.85965	−0.421122
$85$	−0.558656	−0.0605947
$86$	−9.71878	−1.04800
$87$	−2.43851	−0.261435
$88$	−2.45077	−0.261253
$89$	−8.74066	−0.926508	−0.463254	−	0.886226i	$-0.653318\pi$
$89$	−8.74066	−0.926508	−0.463254	+	0.886226i	$0.653318\pi$
$90$	0.558656	0.0588875
$91$	−6.82113	−0.715049
$92$	8.06226	0.840549
$93$	−4.81715	−0.499515
$94$	9.55422	0.985442
$95$	−1.85079	−0.189887
$96$	1.00000	0.102062
$97$	10.8365	1.10028	0.550139	−	0.835073i	$-0.314575\pi$
$97$	10.8365	1.10028	0.550139	+	0.835073i	$0.314575\pi$
$98$	7.89687	0.797705
$99$	−2.45077	−0.246312
$100$	−4.68790	−0.468790
$101$	−19.1548	−1.90597	−0.952985	−	0.303019i	$-0.902005\pi$
$101$	−19.1548	−1.90597	−0.952985	+	0.303019i	$0.902005\pi$
$102$	−1.00000	−0.0990148
$103$	−6.21339	−0.612224	−0.306112	−	0.951996i	$-0.599028\pi$
$103$	−6.21339	−0.612224	−0.306112	+	0.951996i	$0.599028\pi$
$104$	1.76729	0.173297
$105$	−2.15621	−0.210425
$106$	−4.43584	−0.430847
$107$	2.86348	0.276823	0.138411	−	0.990375i	$-0.455800\pi$
$107$	2.86348	0.276823	0.138411	+	0.990375i	$0.455800\pi$
$108$	1.00000	0.0962250
$109$	−3.74715	−0.358912	−0.179456	−	0.983766i	$-0.557434\pi$
$109$	−3.74715	−0.358912	−0.179456	+	0.983766i	$0.557434\pi$
$110$	−1.36914	−0.130542
$111$	−4.21250	−0.399833
$112$	−3.85965	−0.364702
$113$	17.6711	1.66235	0.831177	−	0.556007i	$-0.187667\pi$
$113$	17.6711	1.66235	0.831177	+	0.556007i	$0.187667\pi$
$114$	−3.31293	−0.310284
$115$	4.50403	0.420003
$116$	−2.43851	−0.226410
$117$	1.76729	0.163386
$118$	−1.00000	−0.0920575
$119$	3.85965	0.353813
$120$	0.558656	0.0509981
$121$	−4.99371	−0.453973
$122$	−7.75843	−0.702416
$123$	−3.15338	−0.284330
$124$	−4.81715	−0.432593
$125$	−5.41220	−0.484082
$126$	−3.85965	−0.343845
$127$	15.2924	1.35698	0.678492	−	0.734608i	$-0.262634\pi$
$127$	15.2924	1.35698	0.678492	+	0.734608i	$0.262634\pi$
$128$	1.00000	0.0883883
$129$	−9.71878	−0.855691
$130$	0.987309	0.0865927
$131$	−17.1734	−1.50045	−0.750223	−	0.661185i	$-0.770054\pi$
$131$	−17.1734	−1.50045	−0.750223	+	0.661185i	$0.770054\pi$
$132$	−2.45077	−0.213313
$133$	12.7867	1.10875
$134$	5.49434	0.474638
$135$	0.558656	0.0480814
$136$	−1.00000	−0.0857493
$137$	7.00617	0.598577	0.299289	−	0.954163i	$-0.403251\pi$
$137$	7.00617	0.598577	0.299289	+	0.954163i	$0.403251\pi$
$138$	8.06226	0.686305
$139$	−6.10729	−0.518013	−0.259007	−	0.965876i	$-0.583395\pi$
$139$	−6.10729	−0.518013	−0.259007	+	0.965876i	$0.583395\pi$
$140$	−2.15621	−0.182233
$141$	9.55422	0.804610
$142$	−16.2029	−1.35972
$143$	−4.33124	−0.362196
$144$	1.00000	0.0833333
$145$	−1.36229	−0.113132
$146$	−6.49341	−0.537398
$147$	7.89687	0.651323
$148$	−4.21250	−0.346266
$149$	−12.8679	−1.05418	−0.527088	−	0.849811i	$-0.676716\pi$
$149$	−12.8679	−1.05418	−0.527088	+	0.849811i	$0.676716\pi$
$150$	−4.68790	−0.382766
$151$	9.12491	0.742574	0.371287	−	0.928518i	$-0.378917\pi$
$151$	9.12491	0.742574	0.371287	+	0.928518i	$0.378917\pi$
$152$	−3.31293	−0.268714
$153$	−1.00000	−0.0808452
$154$	9.45912	0.762238
$155$	−2.69113	−0.216157
$156$	1.76729	0.141497
$157$	−0.861891	−0.0687864	−0.0343932	−	0.999408i	$-0.510950\pi$
$157$	−0.861891	−0.0687864	−0.0343932	+	0.999408i	$0.510950\pi$
$158$	−7.02504	−0.558882
$159$	−4.43584	−0.351785
$160$	0.558656	0.0441656
$161$	−31.1175	−2.45240
$162$	1.00000	0.0785674
$163$	−7.21426	−0.565064	−0.282532	−	0.959258i	$-0.591174\pi$
$163$	−7.21426	−0.565064	−0.282532	+	0.959258i	$0.591174\pi$
$164$	−3.15338	−0.246237
$165$	−1.36914	−0.106587
$166$	17.9718	1.39488
$167$	4.06981	0.314931	0.157466	−	0.987524i	$-0.449668\pi$
$167$	4.06981	0.314931	0.157466	+	0.987524i	$0.449668\pi$
$168$	−3.85965	−0.297778
$169$	−9.87667	−0.759744
$170$	−0.558656	−0.0428469
$171$	−3.31293	−0.253346
$172$	−9.71878	−0.741050
$173$	−6.31928	−0.480446	−0.240223	−	0.970718i	$-0.577221\pi$
$173$	−6.31928	−0.480446	−0.240223	+	0.970718i	$0.577221\pi$
$174$	−2.43851	−0.184863
$175$	18.0937	1.36775
$176$	−2.45077	−0.184734
$177$	−1.00000	−0.0751646
$178$	−8.74066	−0.655140
$179$	−11.4913	−0.858899	−0.429449	−	0.903091i	$-0.641292\pi$
$179$	−11.4913	−0.858899	−0.429449	+	0.903091i	$0.641292\pi$
$180$	0.558656	0.0416397
$181$	8.04835	0.598229	0.299115	−	0.954217i	$-0.403309\pi$
$181$	8.04835	0.598229	0.299115	+	0.954217i	$0.403309\pi$
$182$	−6.82113	−0.505616
$183$	−7.75843	−0.573520
$184$	8.06226	0.594358
$185$	−2.35334	−0.173021
$186$	−4.81715	−0.353211
$187$	2.45077	0.179218
$188$	9.55422	0.696813
$189$	−3.85965	−0.280748
$190$	−1.85079	−0.134270
$191$	2.37999	0.172210	0.0861050	−	0.996286i	$-0.472558\pi$
$191$	2.37999	0.172210	0.0861050	+	0.996286i	$0.472558\pi$
$192$	1.00000	0.0721688
$193$	0.117913	0.00848759	0.00424379	−	0.999991i	$-0.498649\pi$
$193$	0.117913	0.00848759	0.00424379	+	0.999991i	$0.498649\pi$
$194$	10.8365	0.778014
$195$	0.987309	0.0707027
$196$	7.89687	0.564062
$197$	0.587479	0.0418561	0.0209281	−	0.999781i	$-0.493338\pi$
$197$	0.587479	0.0418561	0.0209281	+	0.999781i	$0.493338\pi$
$198$	−2.45077	−0.174169
$199$	−9.26361	−0.656680	−0.328340	−	0.944560i	$-0.606489\pi$
$199$	−9.26361	−0.656680	−0.328340	+	0.944560i	$0.606489\pi$
$200$	−4.68790	−0.331485
$201$	5.49434	0.387541
$202$	−19.1548	−1.34772
$203$	9.41177	0.660577
$204$	−1.00000	−0.0700140
$205$	−1.76165	−0.123039
$206$	−6.21339	−0.432908
$207$	8.06226	0.560366
$208$	1.76729	0.122540
$209$	8.11924	0.561619
$210$	−2.15621	−0.148793
$211$	−9.43101	−0.649258	−0.324629	−	0.945841i	$-0.605239\pi$
$211$	−9.43101	−0.649258	−0.324629	+	0.945841i	$0.605239\pi$
$212$	−4.43584	−0.304655
$213$	−16.2029	−1.11021
$214$	2.86348	0.195743
$215$	−5.42945	−0.370285
$216$	1.00000	0.0680414
$217$	18.5925	1.26214
$218$	−3.74715	−0.253789
$219$	−6.49341	−0.438784
$220$	−1.36914	−0.0923073
$221$	−1.76729	−0.118881
$222$	−4.21250	−0.282725
$223$	−16.9013	−1.13179	−0.565896	−	0.824477i	$-0.691470\pi$
$223$	−16.9013	−1.13179	−0.565896	+	0.824477i	$0.691470\pi$
$224$	−3.85965	−0.257884
$225$	−4.68790	−0.312527
$226$	17.6711	1.17546
$227$	0.523407	0.0347397	0.0173699	−	0.999849i	$-0.494471\pi$
$227$	0.523407	0.0347397	0.0173699	+	0.999849i	$0.494471\pi$
$228$	−3.31293	−0.219404
$229$	−17.6176	−1.16421	−0.582103	−	0.813115i	$-0.697770\pi$
$229$	−17.6176	−1.16421	−0.582103	+	0.813115i	$0.697770\pi$
$230$	4.50403	0.296987
$231$	9.45912	0.622365
$232$	−2.43851	−0.160096
$233$	−15.1728	−0.994004	−0.497002	−	0.867750i	$-0.665566\pi$
$233$	−15.1728	−0.994004	−0.497002	+	0.867750i	$0.665566\pi$
$234$	1.76729	0.115532
$235$	5.33752	0.348181
$236$	−1.00000	−0.0650945
$237$	−7.02504	−0.456325
$238$	3.85965	0.250184
$239$	19.4969	1.26115	0.630575	−	0.776128i	$-0.282819\pi$
$239$	19.4969	1.26115	0.630575	+	0.776128i	$0.282819\pi$
$240$	0.558656	0.0360611
$241$	10.8384	0.698161	0.349080	−	0.937093i	$-0.386494\pi$
$241$	10.8384	0.698161	0.349080	+	0.937093i	$0.386494\pi$
$242$	−4.99371	−0.321008
$243$	1.00000	0.0641500
$244$	−7.75843	−0.496683
$245$	4.41163	0.281849
$246$	−3.15338	−0.201052
$247$	−5.85492	−0.372540
$248$	−4.81715	−0.305889
$249$	17.9718	1.13892
$250$	−5.41220	−0.342298
$251$	29.4811	1.86083	0.930415	−	0.366509i	$-0.119447\pi$
$251$	29.4811	1.86083	0.930415	+	0.366509i	$0.119447\pi$
$252$	−3.85965	−0.243135
$253$	−19.7588	−1.24222
$254$	15.2924	0.959532
$255$	−0.558656	−0.0349844
$256$	1.00000	0.0625000
$257$	−5.31092	−0.331286	−0.165643	−	0.986186i	$-0.552970\pi$
$257$	−5.31092	−0.331286	−0.165643	+	0.986186i	$0.552970\pi$
$258$	−9.71878	−0.605065
$259$	16.2588	1.01027
$260$	0.987309	0.0612303
$261$	−2.43851	−0.150940
$262$	−17.1734	−1.06098
$263$	27.6267	1.70354	0.851769	−	0.523918i	$-0.175530\pi$
$263$	27.6267	1.70354	0.851769	+	0.523918i	$0.175530\pi$
$264$	−2.45077	−0.150835
$265$	−2.47811	−0.152229
$266$	12.7867	0.784005
$267$	−8.74066	−0.534920
$268$	5.49434	0.335620
$269$	−3.36285	−0.205036	−0.102518	−	0.994731i	$-0.532690\pi$
$269$	−3.36285	−0.205036	−0.102518	+	0.994731i	$0.532690\pi$
$270$	0.558656	0.0339987
$271$	7.24018	0.439810	0.219905	−	0.975521i	$-0.429425\pi$
$271$	7.24018	0.439810	0.219905	+	0.975521i	$0.429425\pi$
$272$	−1.00000	−0.0606339
$273$	−6.82113	−0.412834
$274$	7.00617	0.423258
$275$	11.4890	0.692812
$276$	8.06226	0.485291
$277$	8.06912	0.484826	0.242413	−	0.970173i	$-0.422061\pi$
$277$	8.06912	0.484826	0.242413	+	0.970173i	$0.422061\pi$
$278$	−6.10729	−0.366291
$279$	−4.81715	−0.288395
$280$	−2.15621	−0.128858
$281$	5.68261	0.338996	0.169498	−	0.985531i	$-0.445785\pi$
$281$	5.68261	0.338996	0.169498	+	0.985531i	$0.445785\pi$
$282$	9.55422	0.568945
$283$	2.75324	0.163663	0.0818315	−	0.996646i	$-0.473923\pi$
$283$	2.75324	0.163663	0.0818315	+	0.996646i	$0.473923\pi$
$284$	−16.2029	−0.961466
$285$	−1.85079	−0.109631
$286$	−4.33124	−0.256112
$287$	12.1709	0.718427
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−1.36229	−0.0799962
$291$	10.8365	0.635245
$292$	−6.49341	−0.379998
$293$	9.97772	0.582905	0.291452	−	0.956585i	$-0.405861\pi$
$293$	9.97772	0.582905	0.291452	+	0.956585i	$0.405861\pi$
$294$	7.89687	0.460555
$295$	−0.558656	−0.0325262
$296$	−4.21250	−0.244847
$297$	−2.45077	−0.142208
$298$	−12.8679	−0.745415
$299$	14.2484	0.824006
$300$	−4.68790	−0.270656
$301$	37.5110	2.16210
$302$	9.12491	0.525079
$303$	−19.1548	−1.10041
$304$	−3.31293	−0.190009
$305$	−4.33429	−0.248181
$306$	−1.00000	−0.0571662
$307$	−22.9491	−1.30977	−0.654886	−	0.755728i	$-0.727283\pi$
$307$	−22.9491	−1.30977	−0.654886	+	0.755728i	$0.727283\pi$
$308$	9.45912	0.538984
$309$	−6.21339	−0.353468
$310$	−2.69113	−0.152846
$311$	7.20951	0.408814	0.204407	−	0.978886i	$-0.434473\pi$
$311$	7.20951	0.408814	0.204407	+	0.978886i	$0.434473\pi$
$312$	1.76729	0.100053
$313$	4.43024	0.250412	0.125206	−	0.992131i	$-0.460041\pi$
$313$	4.43024	0.250412	0.125206	+	0.992131i	$0.460041\pi$
$314$	−0.861891	−0.0486393
$315$	−2.15621	−0.121489
$316$	−7.02504	−0.395189
$317$	−21.8569	−1.22760	−0.613802	−	0.789460i	$-0.710361\pi$
$317$	−21.8569	−1.22760	−0.613802	+	0.789460i	$0.710361\pi$
$318$	−4.43584	−0.248749
$319$	5.97623	0.334604
$320$	0.558656	0.0312298
$321$	2.86348	0.159824
$322$	−31.1175	−1.73411
$323$	3.31293	0.184336
$324$	1.00000	0.0555556
$325$	−8.28491	−0.459564
$326$	−7.21426	−0.399561
$327$	−3.74715	−0.207218
$328$	−3.15338	−0.174116
$329$	−36.8759	−2.03303
$330$	−1.36914	−0.0753686
$331$	30.9450	1.70089	0.850445	−	0.526064i	$-0.176333\pi$
$331$	30.9450	1.70089	0.850445	+	0.526064i	$0.176333\pi$
$332$	17.9718	0.986332
$333$	−4.21250	−0.230844
$334$	4.06981	0.222690
$335$	3.06944	0.167702
$336$	−3.85965	−0.210561
$337$	−16.8951	−0.920337	−0.460169	−	0.887832i	$-0.652211\pi$
$337$	−16.8951	−0.920337	−0.460169	+	0.887832i	$0.652211\pi$
$338$	−9.87667	−0.537220
$339$	17.6711	0.959761
$340$	−0.558656	−0.0302974
$341$	11.8058	0.639317
$342$	−3.31293	−0.179143
$343$	−3.46162	−0.186910
$344$	−9.71878	−0.524001
$345$	4.50403	0.242489
$346$	−6.31928	−0.339727
$347$	22.0314	1.18271	0.591354	−	0.806412i	$-0.298594\pi$
$347$	22.0314	1.18271	0.591354	+	0.806412i	$0.298594\pi$
$348$	−2.43851	−0.130718
$349$	5.30243	0.283832	0.141916	−	0.989879i	$-0.454674\pi$
$349$	5.30243	0.283832	0.141916	+	0.989879i	$0.454674\pi$
$350$	18.0937	0.967146
$351$	1.76729	0.0943312
$352$	−2.45077	−0.130627
$353$	2.45407	0.130617	0.0653085	−	0.997865i	$-0.479197\pi$
$353$	2.45407	0.130617	0.0653085	+	0.997865i	$0.479197\pi$
$354$	−1.00000	−0.0531494
$355$	−9.05185	−0.480422
$356$	−8.74066	−0.463254
$357$	3.85965	0.204274
$358$	−11.4913	−0.607333
$359$	−19.6042	−1.03467	−0.517336	−	0.855783i	$-0.673076\pi$
$359$	−19.6042	−1.03467	−0.517336	+	0.855783i	$0.673076\pi$
$360$	0.558656	0.0294437
$361$	−8.02451	−0.422343
$362$	8.04835	0.423012
$363$	−4.99371	−0.262102
$364$	−6.82113	−0.357524
$365$	−3.62758	−0.189876
$366$	−7.75843	−0.405540
$367$	7.43872	0.388298	0.194149	−	0.980972i	$-0.437805\pi$
$367$	7.43872	0.388298	0.194149	+	0.980972i	$0.437805\pi$
$368$	8.06226	0.420275
$369$	−3.15338	−0.164158
$370$	−2.35334	−0.122344
$371$	17.1208	0.888866
$372$	−4.81715	−0.249758
$373$	−16.3247	−0.845261	−0.422631	−	0.906302i	$-0.638893\pi$
$373$	−16.3247	−0.845261	−0.422631	+	0.906302i	$0.638893\pi$
$374$	2.45077	0.126727
$375$	−5.41220	−0.279485
$376$	9.55422	0.492721
$377$	−4.30956	−0.221954
$378$	−3.85965	−0.198519
$379$	−7.17562	−0.368587	−0.184293	−	0.982871i	$-0.559000\pi$
$379$	−7.17562	−0.368587	−0.184293	+	0.982871i	$0.559000\pi$
$380$	−1.85079	−0.0949433
$381$	15.2924	0.783455
$382$	2.37999	0.121771
$383$	12.4114	0.634195	0.317098	−	0.948393i	$-0.397292\pi$
$383$	12.4114	0.634195	0.317098	+	0.948393i	$0.397292\pi$
$384$	1.00000	0.0510310
$385$	5.28439	0.269318
$386$	0.117913	0.00600163
$387$	−9.71878	−0.494033
$388$	10.8365	0.550139
$389$	−10.3108	−0.522777	−0.261388	−	0.965234i	$-0.584180\pi$
$389$	−10.3108	−0.522777	−0.261388	+	0.965234i	$0.584180\pi$
$390$	0.987309	0.0499943
$391$	−8.06226	−0.407726
$392$	7.89687	0.398852
$393$	−17.1734	−0.866282
$394$	0.587479	0.0295967
$395$	−3.92458	−0.197467
$396$	−2.45077	−0.123156
$397$	10.5894	0.531465	0.265732	−	0.964047i	$-0.414386\pi$
$397$	10.5894	0.531465	0.265732	+	0.964047i	$0.414386\pi$
$398$	−9.26361	−0.464343
$399$	12.7867	0.640137
$400$	−4.68790	−0.234395
$401$	19.7511	0.986324	0.493162	−	0.869938i	$-0.335841\pi$
$401$	19.7511	0.986324	0.493162	+	0.869938i	$0.335841\pi$
$402$	5.49434	0.274033
$403$	−8.51332	−0.424079
$404$	−19.1548	−0.952985
$405$	0.558656	0.0277598
$406$	9.41177	0.467098
$407$	10.3239	0.511736
$408$	−1.00000	−0.0495074
$409$	−13.7158	−0.678201	−0.339101	−	0.940750i	$-0.610123\pi$
$409$	−13.7158	−0.678201	−0.339101	+	0.940750i	$0.610123\pi$
$410$	−1.76165	−0.0870018
$411$	7.00617	0.345589
$412$	−6.21339	−0.306112
$413$	3.85965	0.189921
$414$	8.06226	0.396239
$415$	10.0401	0.492847
$416$	1.76729	0.0866487
$417$	−6.10729	−0.299075
$418$	8.11924	0.397125
$419$	−6.19894	−0.302838	−0.151419	−	0.988470i	$-0.548384\pi$
$419$	−6.19894	−0.302838	−0.151419	+	0.988470i	$0.548384\pi$
$420$	−2.15621	−0.105212
$421$	−1.20813	−0.0588807	−0.0294404	−	0.999567i	$-0.509373\pi$
$421$	−1.20813	−0.0588807	−0.0294404	+	0.999567i	$0.509373\pi$
$422$	−9.43101	−0.459095
$423$	9.55422	0.464542
$424$	−4.43584	−0.215423
$425$	4.68790	0.227397
$426$	−16.2029	−0.785034
$427$	29.9448	1.44913
$428$	2.86348	0.138411
$429$	−4.33124	−0.209114
$430$	−5.42945	−0.261831
$431$	21.9065	1.05520	0.527600	−	0.849493i	$-0.323092\pi$
$431$	21.9065	1.05520	0.527600	+	0.849493i	$0.323092\pi$
$432$	1.00000	0.0481125
$433$	5.33469	0.256369	0.128184	−	0.991750i	$-0.459085\pi$
$433$	5.33469	0.256369	0.128184	+	0.991750i	$0.459085\pi$
$434$	18.5925	0.892469
$435$	−1.36229	−0.0653166
$436$	−3.74715	−0.179456
$437$	−26.7097	−1.27770
$438$	−6.49341	−0.310267
$439$	24.1712	1.15363	0.576813	−	0.816876i	$-0.304296\pi$
$439$	24.1712	1.15363	0.576813	+	0.816876i	$0.304296\pi$
$440$	−1.36914	−0.0652711
$441$	7.89687	0.376042
$442$	−1.76729	−0.0840616
$443$	−4.69171	−0.222910	−0.111455	−	0.993769i	$-0.535551\pi$
$443$	−4.69171	−0.222910	−0.111455	+	0.993769i	$0.535551\pi$
$444$	−4.21250	−0.199917
$445$	−4.88302	−0.231477
$446$	−16.9013	−0.800297
$447$	−12.8679	−0.608629
$448$	−3.85965	−0.182351
$449$	−7.87513	−0.371650	−0.185825	−	0.982583i	$-0.559496\pi$
$449$	−7.87513	−0.371650	−0.185825	+	0.982583i	$0.559496\pi$
$450$	−4.68790	−0.220990
$451$	7.72821	0.363907
$452$	17.6711	0.831177
$453$	9.12491	0.428725
$454$	0.523407	0.0245647
$455$	−3.81066	−0.178647
$456$	−3.31293	−0.155142
$457$	27.7558	1.29836	0.649181	−	0.760634i	$-0.275112\pi$
$457$	27.7558	1.29836	0.649181	+	0.760634i	$0.275112\pi$
$458$	−17.6176	−0.823218
$459$	−1.00000	−0.0466760
$460$	4.50403	0.210001
$461$	−0.955553	−0.0445046	−0.0222523	−	0.999752i	$-0.507084\pi$
$461$	−0.955553	−0.0445046	−0.0222523	+	0.999752i	$0.507084\pi$
$462$	9.45912	0.440078
$463$	23.1128	1.07414	0.537071	−	0.843537i	$-0.319531\pi$
$463$	23.1128	1.07414	0.537071	+	0.843537i	$0.319531\pi$
$464$	−2.43851	−0.113205
$465$	−2.69113	−0.124798
$466$	−15.1728	−0.702867
$467$	10.0455	0.464848	0.232424	−	0.972615i	$-0.425334\pi$
$467$	10.0455	0.464848	0.232424	+	0.972615i	$0.425334\pi$
$468$	1.76729	0.0816932
$469$	−21.2062	−0.979212
$470$	5.33752	0.246201
$471$	−0.861891	−0.0397139
$472$	−1.00000	−0.0460287
$473$	23.8185	1.09518
$474$	−7.02504	−0.322671
$475$	15.5307	0.712597
$476$	3.85965	0.176907
$477$	−4.43584	−0.203103
$478$	19.4969	0.891768
$479$	23.1469	1.05761	0.528804	−	0.848744i	$-0.322641\pi$
$479$	23.1469	1.05761	0.528804	+	0.848744i	$0.322641\pi$
$480$	0.558656	0.0254990
$481$	−7.44473	−0.339451
$482$	10.8384	0.493674
$483$	−31.1175	−1.41589
$484$	−4.99371	−0.226987
$485$	6.05386	0.274892
$486$	1.00000	0.0453609
$487$	26.9696	1.22211	0.611053	−	0.791589i	$-0.290746\pi$
$487$	26.9696	1.22211	0.611053	+	0.791589i	$0.290746\pi$
$488$	−7.75843	−0.351208
$489$	−7.21426	−0.326240
$490$	4.41163	0.199297
$491$	24.1131	1.08821	0.544105	−	0.839017i	$-0.316869\pi$
$491$	24.1131	1.08821	0.544105	+	0.839017i	$0.316869\pi$
$492$	−3.15338	−0.142165
$493$	2.43851	0.109825
$494$	−5.85492	−0.263425
$495$	−1.36914	−0.0615382
$496$	−4.81715	−0.216296
$497$	62.5375	2.80519
$498$	17.9718	0.805337
$499$	9.28910	0.415837	0.207919	−	0.978146i	$-0.433331\pi$
$499$	9.28910	0.415837	0.207919	+	0.978146i	$0.433331\pi$
$500$	−5.41220	−0.242041
$501$	4.06981	0.181826
$502$	29.4811	1.31580
$503$	−41.8477	−1.86590	−0.932948	−	0.360011i	$-0.882773\pi$
$503$	−41.8477	−1.86590	−0.932948	+	0.360011i	$0.882773\pi$
$504$	−3.85965	−0.171922
$505$	−10.7009	−0.476184
$506$	−19.7588	−0.878385
$507$	−9.87667	−0.438638
$508$	15.2924	0.678492
$509$	−23.6395	−1.04780	−0.523901	−	0.851779i	$-0.675524\pi$
$509$	−23.6395	−1.04780	−0.523901	+	0.851779i	$0.675524\pi$
$510$	−0.558656	−0.0247377
$511$	25.0623	1.10869
$512$	1.00000	0.0441942
$513$	−3.31293	−0.146269
$514$	−5.31092	−0.234255
$515$	−3.47115	−0.152957
$516$	−9.71878	−0.427845
$517$	−23.4152	−1.02980
$518$	16.2588	0.714369
$519$	−6.31928	−0.277386
$520$	0.987309	0.0432964
$521$	15.3042	0.670487	0.335244	−	0.942131i	$-0.391181\pi$
$521$	15.3042	0.670487	0.335244	+	0.942131i	$0.391181\pi$
$522$	−2.43851	−0.106731
$523$	27.7906	1.21520	0.607598	−	0.794245i	$-0.292133\pi$
$523$	27.7906	1.21520	0.607598	+	0.794245i	$0.292133\pi$
$524$	−17.1734	−0.750223
$525$	18.0937	0.789672
$526$	27.6267	1.20458
$527$	4.81715	0.209838
$528$	−2.45077	−0.106656
$529$	42.0001	1.82609
$530$	−2.47811	−0.107642
$531$	−1.00000	−0.0433963
$532$	12.7867	0.554375
$533$	−5.57294	−0.241391
$534$	−8.74066	−0.378245
$535$	1.59970	0.0691610
$536$	5.49434	0.237319
$537$	−11.4913	−0.495885
$538$	−3.36285	−0.144983
$539$	−19.3535	−0.833612
$540$	0.558656	0.0240407
$541$	−17.4478	−0.750138	−0.375069	−	0.926997i	$-0.622381\pi$
$541$	−17.4478	−0.750138	−0.375069	+	0.926997i	$0.622381\pi$
$542$	7.24018	0.310993
$543$	8.04835	0.345388
$544$	−1.00000	−0.0428746
$545$	−2.09337	−0.0896699
$546$	−6.82113	−0.291918
$547$	−20.8101	−0.889775	−0.444887	−	0.895587i	$-0.646756\pi$
$547$	−20.8101	−0.889775	−0.444887	+	0.895587i	$0.646756\pi$
$548$	7.00617	0.299289
$549$	−7.75843	−0.331122
$550$	11.4890	0.489892
$551$	8.07859	0.344160
$552$	8.06226	0.343153
$553$	27.1142	1.15301
$554$	8.06912	0.342824
$555$	−2.35334	−0.0998937
$556$	−6.10729	−0.259007
$557$	19.2091	0.813915	0.406958	−	0.913447i	$-0.366590\pi$
$557$	19.2091	0.813915	0.406958	+	0.913447i	$0.366590\pi$
$558$	−4.81715	−0.203926
$559$	−17.1759	−0.726465
$560$	−2.15621	−0.0911167
$561$	2.45077	0.103472
$562$	5.68261	0.239707
$563$	−31.2335	−1.31634	−0.658168	−	0.752871i	$-0.728669\pi$
$563$	−31.2335	−1.31634	−0.658168	+	0.752871i	$0.728669\pi$
$564$	9.55422	0.402305
$565$	9.87205	0.415320
$566$	2.75324	0.115727
$567$	−3.85965	−0.162090
$568$	−16.2029	−0.679859
$569$	−21.1633	−0.887211	−0.443605	−	0.896222i	$-0.646301\pi$
$569$	−21.1633	−0.887211	−0.443605	+	0.896222i	$0.646301\pi$
$570$	−1.85079	−0.0775209
$571$	−10.9497	−0.458232	−0.229116	−	0.973399i	$-0.573584\pi$
$571$	−10.9497	−0.458232	−0.229116	+	0.973399i	$0.573584\pi$
$572$	−4.33124	−0.181098
$573$	2.37999	0.0994255
$574$	12.1709	0.508004
$575$	−37.7951	−1.57617
$576$	1.00000	0.0416667
$577$	20.5510	0.855550	0.427775	−	0.903885i	$-0.359298\pi$
$577$	20.5510	0.855550	0.427775	+	0.903885i	$0.359298\pi$
$578$	1.00000	0.0415945
$579$	0.117913	0.00490031
$580$	−1.36229	−0.0565658
$581$	−69.3649	−2.87774
$582$	10.8365	0.449186
$583$	10.8712	0.450241
$584$	−6.49341	−0.268699
$585$	0.987309	0.0408202
$586$	9.97772	0.412176
$587$	−3.09803	−0.127869	−0.0639346	−	0.997954i	$-0.520365\pi$
$587$	−3.09803	−0.127869	−0.0639346	+	0.997954i	$0.520365\pi$
$588$	7.89687	0.325662
$589$	15.9589	0.657574
$590$	−0.558656	−0.0229995
$591$	0.587479	0.0241656
$592$	−4.21250	−0.173133
$593$	−13.1739	−0.540987	−0.270493	−	0.962722i	$-0.587187\pi$
$593$	−13.1739	−0.540987	−0.270493	+	0.962722i	$0.587187\pi$
$594$	−2.45077	−0.100556
$595$	2.15621	0.0883962
$596$	−12.8679	−0.527088
$597$	−9.26361	−0.379134
$598$	14.2484	0.582660
$599$	−4.25051	−0.173671	−0.0868356	−	0.996223i	$-0.527675\pi$
$599$	−4.25051	−0.173671	−0.0868356	+	0.996223i	$0.527675\pi$
$600$	−4.68790	−0.191383
$601$	−27.9702	−1.14093	−0.570465	−	0.821322i	$-0.693237\pi$
$601$	−27.9702	−1.14093	−0.570465	+	0.821322i	$0.693237\pi$
$602$	37.5110	1.52884
$603$	5.49434	0.223747
$604$	9.12491	0.371287
$605$	−2.78976	−0.113420
$606$	−19.1548	−0.778109
$607$	14.6430	0.594340	0.297170	−	0.954825i	$-0.403957\pi$
$607$	14.6430	0.594340	0.297170	+	0.954825i	$0.403957\pi$
$608$	−3.31293	−0.134357
$609$	9.41177	0.381384
$610$	−4.33429	−0.175490
$611$	16.8851	0.683099
$612$	−1.00000	−0.0404226
$613$	27.5813	1.11400	0.556999	−	0.830513i	$-0.311953\pi$
$613$	27.5813	1.11400	0.556999	+	0.830513i	$0.311953\pi$
$614$	−22.9491	−0.926148
$615$	−1.76165	−0.0710366
$616$	9.45912	0.381119
$617$	−27.7767	−1.11825	−0.559125	−	0.829084i	$-0.688863\pi$
$617$	−27.7767	−1.11825	−0.559125	+	0.829084i	$0.688863\pi$
$618$	−6.21339	−0.249939
$619$	13.0089	0.522871	0.261435	−	0.965221i	$-0.415804\pi$
$619$	13.0089	0.522871	0.261435	+	0.965221i	$0.415804\pi$
$620$	−2.69113	−0.108078
$621$	8.06226	0.323527
$622$	7.20951	0.289075
$623$	33.7359	1.35160
$624$	1.76729	0.0707484
$625$	20.4160	0.816638
$626$	4.43024	0.177068
$627$	8.11924	0.324251
$628$	−0.861891	−0.0343932
$629$	4.21250	0.167963
$630$	−2.15621	−0.0859056
$631$	26.0052	1.03525	0.517625	−	0.855608i	$-0.326816\pi$
$631$	26.0052	1.03525	0.517625	+	0.855608i	$0.326816\pi$
$632$	−7.02504	−0.279441
$633$	−9.43101	−0.374849
$634$	−21.8569	−0.868047
$635$	8.54320	0.339027
$636$	−4.43584	−0.175892
$637$	13.9561	0.552961
$638$	5.97623	0.236601
$639$	−16.2029	−0.640977
$640$	0.558656	0.0220828
$641$	15.9743	0.630946	0.315473	−	0.948934i	$-0.397837\pi$
$641$	15.9743	0.630946	0.315473	+	0.948934i	$0.397837\pi$
$642$	2.86348	0.113012
$643$	−17.4795	−0.689323	−0.344662	−	0.938727i	$-0.612006\pi$
$643$	−17.4795	−0.689323	−0.344662	+	0.938727i	$0.612006\pi$
$644$	−31.1175	−1.22620
$645$	−5.42945	−0.213784
$646$	3.31293	0.130345
$647$	15.6082	0.613622	0.306811	−	0.951771i	$-0.400738\pi$
$647$	15.6082	0.613622	0.306811	+	0.951771i	$0.400738\pi$
$648$	1.00000	0.0392837
$649$	2.45077	0.0962013
$650$	−8.28491	−0.324961
$651$	18.5925	0.728698
$652$	−7.21426	−0.282532
$653$	−40.5595	−1.58722	−0.793608	−	0.608429i	$-0.791800\pi$
$653$	−40.5595	−1.58722	−0.793608	+	0.608429i	$0.791800\pi$
$654$	−3.74715	−0.146525
$655$	−9.59401	−0.374869
$656$	−3.15338	−0.123119
$657$	−6.49341	−0.253332
$658$	−36.8759	−1.43757
$659$	−38.7781	−1.51058	−0.755290	−	0.655391i	$-0.772504\pi$
$659$	−38.7781	−1.51058	−0.755290	+	0.655391i	$0.772504\pi$
$660$	−1.36914	−0.0532937
$661$	−4.89203	−0.190278	−0.0951389	−	0.995464i	$-0.530330\pi$
$661$	−4.89203	−0.190278	−0.0951389	+	0.995464i	$0.530330\pi$
$662$	30.9450	1.20271
$663$	−1.76729	−0.0686360
$664$	17.9718	0.697442
$665$	7.14338	0.277008
$666$	−4.21250	−0.163231
$667$	−19.6599	−0.761233
$668$	4.06981	0.157466
$669$	−16.9013	−0.653440
$670$	3.06944	0.118583
$671$	19.0142	0.734034
$672$	−3.85965	−0.148889
$673$	24.6973	0.952013	0.476006	−	0.879442i	$-0.342084\pi$
$673$	24.6973	0.952013	0.476006	+	0.879442i	$0.342084\pi$
$674$	−16.8951	−0.650777
$675$	−4.68790	−0.180437
$676$	−9.87667	−0.379872
$677$	−16.4617	−0.632674	−0.316337	−	0.948647i	$-0.602453\pi$
$677$	−16.4617	−0.632674	−0.316337	+	0.948647i	$0.602453\pi$
$678$	17.6711	0.678654
$679$	−41.8250	−1.60510
$680$	−0.558656	−0.0214235
$681$	0.523407	0.0200570
$682$	11.8058	0.452066
$683$	−7.76378	−0.297073	−0.148536	−	0.988907i	$-0.547456\pi$
$683$	−7.76378	−0.297073	−0.148536	+	0.988907i	$0.547456\pi$
$684$	−3.31293	−0.126673
$685$	3.91404	0.149548
$686$	−3.46162	−0.132165
$687$	−17.6176	−0.672155
$688$	−9.71878	−0.370525
$689$	−7.83943	−0.298659
$690$	4.50403	0.171465
$691$	37.1765	1.41426	0.707130	−	0.707083i	$-0.249989\pi$
$691$	37.1765	1.41426	0.707130	+	0.707083i	$0.249989\pi$
$692$	−6.31928	−0.240223
$693$	9.45912	0.359322
$694$	22.0314	0.836301
$695$	−3.41187	−0.129420
$696$	−2.43851	−0.0924313
$697$	3.15338	0.119443
$698$	5.30243	0.200700
$699$	−15.1728	−0.573888
$700$	18.0937	0.683876
$701$	27.4911	1.03833	0.519163	−	0.854676i	$-0.326244\pi$
$701$	27.4911	1.03833	0.519163	+	0.854676i	$0.326244\pi$
$702$	1.76729	0.0667022
$703$	13.9557	0.526350
$704$	−2.45077	−0.0923670
$705$	5.33752	0.201023
$706$	2.45407	0.0923601
$707$	73.9306	2.78045
$708$	−1.00000	−0.0375823
$709$	−1.27291	−0.0478050	−0.0239025	−	0.999714i	$-0.507609\pi$
$709$	−1.27291	−0.0478050	−0.0239025	+	0.999714i	$0.507609\pi$
$710$	−9.05185	−0.339710
$711$	−7.02504	−0.263459
$712$	−8.74066	−0.327570
$713$	−38.8371	−1.45446
$714$	3.85965	0.144444
$715$	−2.41967	−0.0904906
$716$	−11.4913	−0.429449
$717$	19.4969	0.728126
$718$	−19.6042	−0.731623
$719$	−20.0566	−0.747986	−0.373993	−	0.927432i	$-0.622012\pi$
$719$	−20.0566	−0.747986	−0.373993	+	0.927432i	$0.622012\pi$
$720$	0.558656	0.0208199
$721$	23.9815	0.893118
$722$	−8.02451	−0.298641
$723$	10.8384	0.403083
$724$	8.04835	0.299115
$725$	11.4315	0.424555
$726$	−4.99371	−0.185334
$727$	24.7945	0.919576	0.459788	−	0.888029i	$-0.347925\pi$
$727$	24.7945	0.919576	0.459788	+	0.888029i	$0.347925\pi$
$728$	−6.82113	−0.252808
$729$	1.00000	0.0370370
$730$	−3.62758	−0.134263
$731$	9.71878	0.359462
$732$	−7.75843	−0.286760
$733$	−51.3489	−1.89662	−0.948308	−	0.317351i	$-0.897207\pi$
$733$	−51.3489	−1.89662	−0.948308	+	0.317351i	$0.897207\pi$
$734$	7.43872	0.274568
$735$	4.41163	0.162726
$736$	8.06226	0.297179
$737$	−13.4654	−0.496004
$738$	−3.15338	−0.116077
$739$	−8.76176	−0.322307	−0.161153	−	0.986929i	$-0.551521\pi$
$739$	−8.76176	−0.322307	−0.161153	+	0.986929i	$0.551521\pi$
$740$	−2.35334	−0.0865105
$741$	−5.85492	−0.215086
$742$	17.1208	0.628523
$743$	−47.2444	−1.73323	−0.866614	−	0.498978i	$-0.833709\pi$
$743$	−47.2444	−1.73323	−0.866614	+	0.498978i	$0.833709\pi$
$744$	−4.81715	−0.176605
$745$	−7.18871	−0.263374
$746$	−16.3247	−0.597690
$747$	17.9718	0.657555
$748$	2.45077	0.0896092
$749$	−11.0520	−0.403832
$750$	−5.41220	−0.197626
$751$	−0.232153	−0.00847137	−0.00423569	−	0.999991i	$-0.501348\pi$
$751$	−0.232153	−0.00847137	−0.00423569	+	0.999991i	$0.501348\pi$
$752$	9.55422	0.348407
$753$	29.4811	1.07435
$754$	−4.30956	−0.156945
$755$	5.09768	0.185524
$756$	−3.85965	−0.140374
$757$	3.49030	0.126857	0.0634286	−	0.997986i	$-0.479796\pi$
$757$	3.49030	0.126857	0.0634286	+	0.997986i	$0.479796\pi$
$758$	−7.17562	−0.260630
$759$	−19.7588	−0.717198
$760$	−1.85079	−0.0671351
$761$	2.06229	0.0747579	0.0373790	−	0.999301i	$-0.488099\pi$
$761$	2.06229	0.0747579	0.0373790	+	0.999301i	$0.488099\pi$
$762$	15.2924	0.553986
$763$	14.4627	0.523584
$764$	2.37999	0.0861050
$765$	−0.558656	−0.0201982
$766$	12.4114	0.448444
$767$	−1.76729	−0.0638133
$768$	1.00000	0.0360844
$769$	26.5317	0.956759	0.478379	−	0.878153i	$-0.341224\pi$
$769$	26.5317	0.956759	0.478379	+	0.878153i	$0.341224\pi$
$770$	5.28439	0.190436
$771$	−5.31092	−0.191268
$772$	0.117913	0.00424379
$773$	48.8300	1.75629	0.878146	−	0.478393i	$-0.158781\pi$
$773$	48.8300	1.75629	0.878146	+	0.478393i	$0.158781\pi$
$774$	−9.71878	−0.349334
$775$	22.5823	0.811182
$776$	10.8365	0.389007
$777$	16.2588	0.583280
$778$	−10.3108	−0.369659
$779$	10.4469	0.374299
$780$	0.987309	0.0353513
$781$	39.7097	1.42092
$782$	−8.06226	−0.288306
$783$	−2.43851	−0.0871451
$784$	7.89687	0.282031
$785$	−0.481501	−0.0171855
$786$	−17.1734	−0.612554
$787$	−17.7317	−0.632066	−0.316033	−	0.948748i	$-0.602351\pi$
$787$	−17.7317	−0.632066	−0.316033	+	0.948748i	$0.602351\pi$
$788$	0.587479	0.0209281
$789$	27.6267	0.983538
$790$	−3.92458	−0.139630
$791$	−68.2041	−2.42506
$792$	−2.45077	−0.0870845
$793$	−13.7114	−0.486907
$794$	10.5894	0.375802
$795$	−2.47811	−0.0878894
$796$	−9.26361	−0.328340
$797$	20.8248	0.737652	0.368826	−	0.929499i	$-0.379760\pi$
$797$	20.8248	0.737652	0.368826	+	0.929499i	$0.379760\pi$
$798$	12.7867	0.452645
$799$	−9.55422	−0.338004
$800$	−4.68790	−0.165742
$801$	−8.74066	−0.308836
$802$	19.7511	0.697436
$803$	15.9139	0.561588
$804$	5.49434	0.193770
$805$	−17.3840	−0.612704
$806$	−8.51332	−0.299869
$807$	−3.36285	−0.118378
$808$	−19.1548	−0.673862
$809$	−39.6777	−1.39499	−0.697497	−	0.716587i	$-0.745703\pi$
$809$	−39.6777	−1.39499	−0.697497	+	0.716587i	$0.745703\pi$
$810$	0.558656	0.0196292
$811$	−10.6007	−0.372242	−0.186121	−	0.982527i	$-0.559592\pi$
$811$	−10.6007	−0.372242	−0.186121	+	0.982527i	$0.559592\pi$
$812$	9.41177	0.330288
$813$	7.24018	0.253924
$814$	10.3239	0.361852
$815$	−4.03029	−0.141175
$816$	−1.00000	−0.0350070
$817$	32.1976	1.12645
$818$	−13.7158	−0.479561
$819$	−6.82113	−0.238350
$820$	−1.76165	−0.0615195
$821$	−50.0207	−1.74573	−0.872867	−	0.487959i	$-0.837742\pi$
$821$	−50.0207	−1.74573	−0.872867	+	0.487959i	$0.837742\pi$
$822$	7.00617	0.244368
$823$	4.68618	0.163350	0.0816750	−	0.996659i	$-0.473973\pi$
$823$	4.68618	0.163350	0.0816750	+	0.996659i	$0.473973\pi$
$824$	−6.21339	−0.216454
$825$	11.4890	0.399995
$826$	3.85965	0.134294
$827$	−27.9114	−0.970575	−0.485287	−	0.874355i	$-0.661285\pi$
$827$	−27.9114	−0.970575	−0.485287	+	0.874355i	$0.661285\pi$
$828$	8.06226	0.280183
$829$	42.3225	1.46992	0.734961	−	0.678110i	$-0.237201\pi$
$829$	42.3225	1.46992	0.734961	+	0.678110i	$0.237201\pi$
$830$	10.0401	0.348496
$831$	8.06912	0.279915
$832$	1.76729	0.0612699
$833$	−7.89687	−0.273610
$834$	−6.10729	−0.211478
$835$	2.27362	0.0786820
$836$	8.11924	0.280810
$837$	−4.81715	−0.166505
$838$	−6.19894	−0.214139
$839$	17.8842	0.617432	0.308716	−	0.951154i	$-0.400101\pi$
$839$	17.8842	0.617432	0.308716	+	0.951154i	$0.400101\pi$
$840$	−2.15621	−0.0743965
$841$	−23.0537	−0.794955
$842$	−1.20813	−0.0416350
$843$	5.68261	0.195720
$844$	−9.43101	−0.324629
$845$	−5.51766	−0.189813
$846$	9.55422	0.328481
$847$	19.2739	0.662261
$848$	−4.43584	−0.152327
$849$	2.75324	0.0944909
$850$	4.68790	0.160794
$851$	−33.9623	−1.16421
$852$	−16.2029	−0.555103
$853$	11.5524	0.395548	0.197774	−	0.980248i	$-0.436629\pi$
$853$	11.5524	0.395548	0.197774	+	0.980248i	$0.436629\pi$
$854$	29.9448	1.02469
$855$	−1.85079	−0.0632955
$856$	2.86348	0.0978716
$857$	10.4705	0.357665	0.178833	−	0.983880i	$-0.442768\pi$
$857$	10.4705	0.357665	0.178833	+	0.983880i	$0.442768\pi$
$858$	−4.33124	−0.147866
$859$	29.4442	1.00462	0.502312	−	0.864686i	$-0.332483\pi$
$859$	29.4442	1.00462	0.502312	+	0.864686i	$0.332483\pi$
$860$	−5.42945	−0.185143
$861$	12.1709	0.414784
$862$	21.9065	0.746138
$863$	−30.0955	−1.02446	−0.512231	−	0.858848i	$-0.671181\pi$
$863$	−30.0955	−1.02446	−0.512231	+	0.858848i	$0.671181\pi$
$864$	1.00000	0.0340207
$865$	−3.53030	−0.120034
$866$	5.33469	0.181280
$867$	1.00000	0.0339618
$868$	18.5925	0.631071
$869$	17.2168	0.584039
$870$	−1.36229	−0.0461858
$871$	9.71011	0.329015
$872$	−3.74715	−0.126894
$873$	10.8365	0.366759
$874$	−26.7097	−0.903469
$875$	20.8892	0.706184
$876$	−6.49341	−0.219392
$877$	28.9029	0.975980	0.487990	−	0.872849i	$-0.337730\pi$
$877$	28.9029	0.975980	0.487990	+	0.872849i	$0.337730\pi$
$878$	24.1712	0.815737
$879$	9.97772	0.336540
$880$	−1.36914	−0.0461537
$881$	−24.8397	−0.836869	−0.418435	−	0.908247i	$-0.637421\pi$
$881$	−24.8397	−0.836869	−0.418435	+	0.908247i	$0.637421\pi$
$882$	7.89687	0.265902
$883$	−4.73285	−0.159273	−0.0796365	−	0.996824i	$-0.525376\pi$
$883$	−4.73285	−0.159273	−0.0796365	+	0.996824i	$0.525376\pi$
$884$	−1.76729	−0.0594405
$885$	−0.558656	−0.0187790
$886$	−4.69171	−0.157621
$887$	−59.3764	−1.99366	−0.996832	−	0.0795361i	$-0.974656\pi$
$887$	−59.3764	−1.99366	−0.996832	+	0.0795361i	$0.974656\pi$
$888$	−4.21250	−0.141362
$889$	−59.0234	−1.97958
$890$	−4.88302	−0.163679
$891$	−2.45077	−0.0821040
$892$	−16.9013	−0.565896
$893$	−31.6524	−1.05921
$894$	−12.8679	−0.430366
$895$	−6.41967	−0.214586
$896$	−3.85965	−0.128942
$897$	14.2484	0.475740
$898$	−7.87513	−0.262797
$899$	11.7467	0.391773
$900$	−4.68790	−0.156263
$901$	4.43584	0.147779
$902$	7.72821	0.257321
$903$	37.5110	1.24829
$904$	17.6711	0.587731
$905$	4.49626	0.149461
$906$	9.12491	0.303155
$907$	−36.5889	−1.21492	−0.607458	−	0.794352i	$-0.707811\pi$
$907$	−36.5889	−1.21492	−0.607458	+	0.794352i	$0.707811\pi$
$908$	0.523407	0.0173699
$909$	−19.1548	−0.635323
$910$	−3.81066	−0.126322
$911$	13.3931	0.443734	0.221867	−	0.975077i	$-0.428785\pi$
$911$	13.3931	0.443734	0.221867	+	0.975077i	$0.428785\pi$
$912$	−3.31293	−0.109702
$913$	−44.0449	−1.45767
$914$	27.7558	0.918081
$915$	−4.33429	−0.143287
$916$	−17.6176	−0.582103
$917$	66.2832	2.18886
$918$	−1.00000	−0.0330049
$919$	11.6835	0.385404	0.192702	−	0.981257i	$-0.438275\pi$
$919$	11.6835	0.385404	0.192702	+	0.981257i	$0.438275\pi$
$920$	4.50403	0.148493
$921$	−22.9491	−0.756197
$922$	−0.955553	−0.0314695
$923$	−28.6353	−0.942543
$924$	9.45912	0.311182
$925$	19.7478	0.649304
$926$	23.1128	0.759533
$927$	−6.21339	−0.204075
$928$	−2.43851	−0.0800479
$929$	−41.1630	−1.35051	−0.675256	−	0.737583i	$-0.735967\pi$
$929$	−41.1630	−1.35051	−0.675256	+	0.737583i	$0.735967\pi$
$930$	−2.69113	−0.0882456
$931$	−26.1618	−0.857417
$932$	−15.1728	−0.497002
$933$	7.20951	0.236029
$934$	10.0455	0.328697
$935$	1.36914	0.0447756
$936$	1.76729	0.0577658
$937$	−0.992854	−0.0324351	−0.0162176	−	0.999868i	$-0.505162\pi$
$937$	−0.992854	−0.0324351	−0.0162176	+	0.999868i	$0.505162\pi$
$938$	−21.2062	−0.692407
$939$	4.43024	0.144575
$940$	5.33752	0.174091
$941$	38.9229	1.26885	0.634425	−	0.772984i	$-0.281237\pi$
$941$	38.9229	1.26885	0.634425	+	0.772984i	$0.281237\pi$
$942$	−0.861891	−0.0280819
$943$	−25.4233	−0.827898
$944$	−1.00000	−0.0325472
$945$	−2.15621	−0.0701416
$946$	23.8185	0.774407
$947$	−34.6796	−1.12694	−0.563468	−	0.826138i	$-0.690533\pi$
$947$	−34.6796	−1.12694	−0.563468	+	0.826138i	$0.690533\pi$
$948$	−7.02504	−0.228163
$949$	−11.4758	−0.372519
$950$	15.5307	0.503882
$951$	−21.8569	−0.708757
$952$	3.85965	0.125092
$953$	−2.52509	−0.0817958	−0.0408979	−	0.999163i	$-0.513022\pi$
$953$	−2.52509	−0.0817958	−0.0408979	+	0.999163i	$0.513022\pi$
$954$	−4.43584	−0.143616
$955$	1.32959	0.0430247
$956$	19.4969	0.630575
$957$	5.97623	0.193184
$958$	23.1469	0.747841
$959$	−27.0413	−0.873210
$960$	0.558656	0.0180305
$961$	−7.79505	−0.251453
$962$	−7.44473	−0.240028
$963$	2.86348	0.0922743
$964$	10.8384	0.349080
$965$	0.0658730	0.00212053
$966$	−31.1175	−1.00119
$967$	−8.88157	−0.285612	−0.142806	−	0.989751i	$-0.545613\pi$
$967$	−8.88157	−0.285612	−0.142806	+	0.989751i	$0.545613\pi$
$968$	−4.99371	−0.160504
$969$	3.31293	0.106427
$970$	6.05386	0.194378
$971$	−1.00349	−0.0322036	−0.0161018	−	0.999870i	$-0.505126\pi$
$971$	−1.00349	−0.0322036	−0.0161018	+	0.999870i	$0.505126\pi$
$972$	1.00000	0.0320750
$973$	23.5720	0.755683
$974$	26.9696	0.864160
$975$	−8.28491	−0.265329
$976$	−7.75843	−0.248341
$977$	17.7263	0.567114	0.283557	−	0.958955i	$-0.408486\pi$
$977$	17.7263	0.567114	0.283557	+	0.958955i	$0.408486\pi$
$978$	−7.21426	−0.230687
$979$	21.4214	0.684630
$980$	4.41163	0.140924
$981$	−3.74715	−0.119637
$982$	24.1131	0.769481
$983$	−1.81195	−0.0577921	−0.0288960	−	0.999582i	$-0.509199\pi$
$983$	−1.81195	−0.0577921	−0.0288960	+	0.999582i	$0.509199\pi$
$984$	−3.15338	−0.100526
$985$	0.328198	0.0104573
$986$	2.43851	0.0776578
$987$	−36.8759	−1.17377
$988$	−5.85492	−0.186270
$989$	−78.3553	−2.49155
$990$	−1.36914	−0.0435141
$991$	−5.52707	−0.175573	−0.0877866	−	0.996139i	$-0.527979\pi$
$991$	−5.52707	−0.175573	−0.0877866	+	0.996139i	$0.527979\pi$
$992$	−4.81715	−0.152945
$993$	30.9450	0.982009
$994$	62.5375	1.98357
$995$	−5.17517	−0.164064
$996$	17.9718	0.569459
$997$	27.3722	0.866887	0.433444	−	0.901181i	$-0.357298\pi$
$997$	27.3722	0.866887	0.433444	+	0.901181i	$0.357298\pi$
$998$	9.28910	0.294041
$999$	−4.21250	−0.133278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.r.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.r.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.558656 q^{5} +1.00000 q^{6} -3.85965 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.558656 q^{5} +1.00000 q^{6} -3.85965 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.558656 q^{10} -2.45077 q^{11} +1.00000 q^{12} +1.76729 q^{13} -3.85965 q^{14} +0.558656 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -3.31293 q^{19} +0.558656 q^{20} -3.85965 q^{21} -2.45077 q^{22} +8.06226 q^{23} +1.00000 q^{24} -4.68790 q^{25} +1.76729 q^{26} +1.00000 q^{27} -3.85965 q^{28} -2.43851 q^{29} +0.558656 q^{30} -4.81715 q^{31} +1.00000 q^{32} -2.45077 q^{33} -1.00000 q^{34} -2.15621 q^{35} +1.00000 q^{36} -4.21250 q^{37} -3.31293 q^{38} +1.76729 q^{39} +0.558656 q^{40} -3.15338 q^{41} -3.85965 q^{42} -9.71878 q^{43} -2.45077 q^{44} +0.558656 q^{45} +8.06226 q^{46} +9.55422 q^{47} +1.00000 q^{48} +7.89687 q^{49} -4.68790 q^{50} -1.00000 q^{51} +1.76729 q^{52} -4.43584 q^{53} +1.00000 q^{54} -1.36914 q^{55} -3.85965 q^{56} -3.31293 q^{57} -2.43851 q^{58} -1.00000 q^{59} +0.558656 q^{60} -7.75843 q^{61} -4.81715 q^{62} -3.85965 q^{63} +1.00000 q^{64} +0.987309 q^{65} -2.45077 q^{66} +5.49434 q^{67} -1.00000 q^{68} +8.06226 q^{69} -2.15621 q^{70} -16.2029 q^{71} +1.00000 q^{72} -6.49341 q^{73} -4.21250 q^{74} -4.68790 q^{75} -3.31293 q^{76} +9.45912 q^{77} +1.76729 q^{78} -7.02504 q^{79} +0.558656 q^{80} +1.00000 q^{81} -3.15338 q^{82} +17.9718 q^{83} -3.85965 q^{84} -0.558656 q^{85} -9.71878 q^{86} -2.43851 q^{87} -2.45077 q^{88} -8.74066 q^{89} +0.558656 q^{90} -6.82113 q^{91} +8.06226 q^{92} -4.81715 q^{93} +9.55422 q^{94} -1.85079 q^{95} +1.00000 q^{96} +10.8365 q^{97} +7.89687 q^{98} -2.45077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} + 6 q^{6} - 7 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 + 6 * q^6 - 7 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} + 6 q^{6} - 7 q^{7} + 6 q^{8} + 6 q^{9} - 3 q^{10} - 8 q^{11} + 6 q^{12} - 6 q^{13} - 7 q^{14} - 3 q^{15} + 6 q^{16} - 6 q^{17} + 6 q^{18} - 14 q^{19} - 3 q^{20} - 7 q^{21} - 8 q^{22} - 8 q^{23} + 6 q^{24} - 13 q^{25} - 6 q^{26} + 6 q^{27} - 7 q^{28} - 21 q^{29} - 3 q^{30} - 5 q^{31} + 6 q^{32} - 8 q^{33} - 6 q^{34} - 12 q^{35} + 6 q^{36} - 13 q^{37} - 14 q^{38} - 6 q^{39} - 3 q^{40} - 18 q^{41} - 7 q^{42} - 4 q^{43} - 8 q^{44} - 3 q^{45} - 8 q^{46} - 4 q^{47} + 6 q^{48} + 5 q^{49} - 13 q^{50} - 6 q^{51} - 6 q^{52} - 25 q^{53} + 6 q^{54} - 8 q^{55} - 7 q^{56} - 14 q^{57} - 21 q^{58} - 6 q^{59} - 3 q^{60} - 5 q^{62} - 7 q^{63} + 6 q^{64} + 6 q^{65} - 8 q^{66} - 13 q^{67} - 6 q^{68} - 8 q^{69} - 12 q^{70} - 12 q^{71} + 6 q^{72} - 4 q^{73} - 13 q^{74} - 13 q^{75} - 14 q^{76} + 4 q^{77} - 6 q^{78} - 12 q^{79} - 3 q^{80} + 6 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 3 q^{85} - 4 q^{86} - 21 q^{87} - 8 q^{88} - 11 q^{89} - 3 q^{90} - 31 q^{91} - 8 q^{92} - 5 q^{93} - 4 q^{94} + 35 q^{95} + 6 q^{96} + 16 q^{97} + 5 q^{98} - 8 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 + 6 * q^6 - 7 * q^7 + 6 * q^8 + 6 * q^9 - 3 * q^10 - 8 * q^11 + 6 * q^12 - 6 * q^13 - 7 * q^14 - 3 * q^15 + 6 * q^16 - 6 * q^17 + 6 * q^18 - 14 * q^19 - 3 * q^20 - 7 * q^21 - 8 * q^22 - 8 * q^23 + 6 * q^24 - 13 * q^25 - 6 * q^26 + 6 * q^27 - 7 * q^28 - 21 * q^29 - 3 * q^30 - 5 * q^31 + 6 * q^32 - 8 * q^33 - 6 * q^34 - 12 * q^35 + 6 * q^36 - 13 * q^37 - 14 * q^38 - 6 * q^39 - 3 * q^40 - 18 * q^41 - 7 * q^42 - 4 * q^43 - 8 * q^44 - 3 * q^45 - 8 * q^46 - 4 * q^47 + 6 * q^48 + 5 * q^49 - 13 * q^50 - 6 * q^51 - 6 * q^52 - 25 * q^53 + 6 * q^54 - 8 * q^55 - 7 * q^56 - 14 * q^57 - 21 * q^58 - 6 * q^59 - 3 * q^60 - 5 * q^62 - 7 * q^63 + 6 * q^64 + 6 * q^65 - 8 * q^66 - 13 * q^67 - 6 * q^68 - 8 * q^69 - 12 * q^70 - 12 * q^71 + 6 * q^72 - 4 * q^73 - 13 * q^74 - 13 * q^75 - 14 * q^76 + 4 * q^77 - 6 * q^78 - 12 * q^79 - 3 * q^80 + 6 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 3 * q^85 - 4 * q^86 - 21 * q^87 - 8 * q^88 - 11 * q^89 - 3 * q^90 - 31 * q^91 - 8 * q^92 - 5 * q^93 - 4 * q^94 + 35 * q^95 + 6 * q^96 + 16 * q^97 + 5 * q^98 - 8 * q^99

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