LMFDB - Embedded newform 6042.2.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 3 $ x^3 - x^2 - 4*x + 3
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			1.1
Root			$2.19869$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.83424 q^{5} +1.00000 q^{6} -4.03293 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.83424 q^{5} +1.00000 q^{6} -4.03293 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.83424 q^{10} +1.63555 q^{11} -1.00000 q^{12} +2.83424 q^{13} +4.03293 q^{14} +2.83424 q^{15} +1.00000 q^{16} +6.03293 q^{17} -1.00000 q^{18} +1.00000 q^{19} -2.83424 q^{20} +4.03293 q^{21} -1.63555 q^{22} +5.46980 q^{23} +1.00000 q^{24} +3.03293 q^{25} -2.83424 q^{26} -1.00000 q^{27} -4.03293 q^{28} -8.62901 q^{29} -2.83424 q^{30} +1.27110 q^{31} -1.00000 q^{32} -1.63555 q^{33} -6.03293 q^{34} +11.4303 q^{35} +1.00000 q^{36} +3.63555 q^{37} -1.00000 q^{38} -2.83424 q^{39} +2.83424 q^{40} -0.867178 q^{41} -4.03293 q^{42} -5.46980 q^{43} +1.63555 q^{44} -2.83424 q^{45} -5.46980 q^{46} -7.39738 q^{47} -1.00000 q^{48} +9.26456 q^{49} -3.03293 q^{50} -6.03293 q^{51} +2.83424 q^{52} -1.00000 q^{53} +1.00000 q^{54} -4.63555 q^{55} +4.03293 q^{56} -1.00000 q^{57} +8.62901 q^{58} +11.3579 q^{59} +2.83424 q^{60} -12.6290 q^{61} -1.27110 q^{62} -4.03293 q^{63} +1.00000 q^{64} -8.03293 q^{65} +1.63555 q^{66} +0.768374 q^{67} +6.03293 q^{68} -5.46980 q^{69} -11.4303 q^{70} +1.60262 q^{71} -1.00000 q^{72} -0.761831 q^{73} -3.63555 q^{74} -3.03293 q^{75} +1.00000 q^{76} -6.59607 q^{77} +2.83424 q^{78} -12.4094 q^{79} -2.83424 q^{80} +1.00000 q^{81} +0.867178 q^{82} -7.93305 q^{83} +4.03293 q^{84} -17.0988 q^{85} +5.46980 q^{86} +8.62901 q^{87} -1.63555 q^{88} -8.70142 q^{89} +2.83424 q^{90} -11.4303 q^{91} +5.46980 q^{92} -1.27110 q^{93} +7.39738 q^{94} -2.83424 q^{95} +1.00000 q^{96} -9.13828 q^{97} -9.26456 q^{98} +1.63555 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 5 q^{11} - 3 q^{12} + 3 q^{13} + q^{14} + 3 q^{15} + 3 q^{16} + 7 q^{17} - 3 q^{18} + 3 q^{19} - 3 q^{20} + q^{21} - 5 q^{22} + 11 q^{23} + 3 q^{24} - 2 q^{25} - 3 q^{26} - 3 q^{27} - q^{28} + 2 q^{29} - 3 q^{30} + 4 q^{31} - 3 q^{32} - 5 q^{33} - 7 q^{34} + 12 q^{35} + 3 q^{36} + 11 q^{37} - 3 q^{38} - 3 q^{39} + 3 q^{40} + 14 q^{41} - q^{42} - 11 q^{43} + 5 q^{44} - 3 q^{45} - 11 q^{46} - 11 q^{47} - 3 q^{48} + 2 q^{50} - 7 q^{51} + 3 q^{52} - 3 q^{53} + 3 q^{54} - 14 q^{55} + q^{56} - 3 q^{57} - 2 q^{58} + 6 q^{59} + 3 q^{60} - 10 q^{61} - 4 q^{62} - q^{63} + 3 q^{64} - 13 q^{65} + 5 q^{66} + 19 q^{67} + 7 q^{68} - 11 q^{69} - 12 q^{70} + 16 q^{71} - 3 q^{72} + 9 q^{73} - 11 q^{74} + 2 q^{75} + 3 q^{76} - 3 q^{77} + 3 q^{78} - 21 q^{79} - 3 q^{80} + 3 q^{81} - 14 q^{82} + 15 q^{83} + q^{84} - 18 q^{85} + 11 q^{86} - 2 q^{87} - 5 q^{88} - 4 q^{89} + 3 q^{90} - 12 q^{91} + 11 q^{92} - 4 q^{93} + 11 q^{94} - 3 q^{95} + 3 q^{96} - 11 q^{97} + 5 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 5 * q^11 - 3 * q^12 + 3 * q^13 + q^14 + 3 * q^15 + 3 * q^16 + 7 * q^17 - 3 * q^18 + 3 * q^19 - 3 * q^20 + q^21 - 5 * q^22 + 11 * q^23 + 3 * q^24 - 2 * q^25 - 3 * q^26 - 3 * q^27 - q^28 + 2 * q^29 - 3 * q^30 + 4 * q^31 - 3 * q^32 - 5 * q^33 - 7 * q^34 + 12 * q^35 + 3 * q^36 + 11 * q^37 - 3 * q^38 - 3 * q^39 + 3 * q^40 + 14 * q^41 - q^42 - 11 * q^43 + 5 * q^44 - 3 * q^45 - 11 * q^46 - 11 * q^47 - 3 * q^48 + 2 * q^50 - 7 * q^51 + 3 * q^52 - 3 * q^53 + 3 * q^54 - 14 * q^55 + q^56 - 3 * q^57 - 2 * q^58 + 6 * q^59 + 3 * q^60 - 10 * q^61 - 4 * q^62 - q^63 + 3 * q^64 - 13 * q^65 + 5 * q^66 + 19 * q^67 + 7 * q^68 - 11 * q^69 - 12 * q^70 + 16 * q^71 - 3 * q^72 + 9 * q^73 - 11 * q^74 + 2 * q^75 + 3 * q^76 - 3 * q^77 + 3 * q^78 - 21 * q^79 - 3 * q^80 + 3 * q^81 - 14 * q^82 + 15 * q^83 + q^84 - 18 * q^85 + 11 * q^86 - 2 * q^87 - 5 * q^88 - 4 * q^89 + 3 * q^90 - 12 * q^91 + 11 * q^92 - 4 * q^93 + 11 * q^94 - 3 * q^95 + 3 * q^96 - 11 * q^97 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.83424	−1.26751	−0.633756	−	0.773533i	$-0.718488\pi$
$5$	−2.83424	−1.26751	−0.633756	+	0.773533i	$0.718488\pi$
$6$	1.00000	0.408248
$7$	−4.03293	−1.52431	−0.762153	−	0.647397i	$-0.775858\pi$
$7$	−4.03293	−1.52431	−0.762153	+	0.647397i	$0.775858\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.83424	0.896266
$11$	1.63555	0.493137	0.246569	−	0.969125i	$-0.420697\pi$
$11$	1.63555	0.493137	0.246569	+	0.969125i	$0.420697\pi$
$12$	−1.00000	−0.288675
$13$	2.83424	0.786078	0.393039	−	0.919522i	$-0.371424\pi$
$13$	2.83424	0.786078	0.393039	+	0.919522i	$0.371424\pi$
$14$	4.03293	1.07785
$15$	2.83424	0.731798
$16$	1.00000	0.250000
$17$	6.03293	1.46320	0.731601	−	0.681733i	$-0.238774\pi$
$17$	6.03293	1.46320	0.731601	+	0.681733i	$0.238774\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.83424	−0.633756
$21$	4.03293	0.880058
$22$	−1.63555	−0.348701
$23$	5.46980	1.14053	0.570266	−	0.821460i	$-0.306840\pi$
$23$	5.46980	1.14053	0.570266	+	0.821460i	$0.306840\pi$
$24$	1.00000	0.204124
$25$	3.03293	0.606587
$26$	−2.83424	−0.555841
$27$	−1.00000	−0.192450
$28$	−4.03293	−0.762153
$29$	−8.62901	−1.60237	−0.801183	−	0.598419i	$-0.795796\pi$
$29$	−8.62901	−1.60237	−0.801183	+	0.598419i	$0.795796\pi$
$30$	−2.83424	−0.517460
$31$	1.27110	0.228297	0.114148	−	0.993464i	$-0.463586\pi$
$31$	1.27110	0.228297	0.114148	+	0.993464i	$0.463586\pi$
$32$	−1.00000	−0.176777
$33$	−1.63555	−0.284713
$34$	−6.03293	−1.03464
$35$	11.4303	1.93208
$36$	1.00000	0.166667
$37$	3.63555	0.597681	0.298841	−	0.954303i	$-0.403400\pi$
$37$	3.63555	0.597681	0.298841	+	0.954303i	$0.403400\pi$
$38$	−1.00000	−0.162221
$39$	−2.83424	−0.453842
$40$	2.83424	0.448133
$41$	−0.867178	−0.135430	−0.0677152	−	0.997705i	$-0.521571\pi$
$41$	−0.867178	−0.135430	−0.0677152	+	0.997705i	$0.521571\pi$
$42$	−4.03293	−0.622295
$43$	−5.46980	−0.834136	−0.417068	−	0.908875i	$-0.636942\pi$
$43$	−5.46980	−0.834136	−0.417068	+	0.908875i	$0.636942\pi$
$44$	1.63555	0.246569
$45$	−2.83424	−0.422504
$46$	−5.46980	−0.806477
$47$	−7.39738	−1.07902	−0.539510	−	0.841979i	$-0.681390\pi$
$47$	−7.39738	−1.07902	−0.539510	+	0.841979i	$0.681390\pi$
$48$	−1.00000	−0.144338
$49$	9.26456	1.32351
$50$	−3.03293	−0.428922
$51$	−6.03293	−0.844780
$52$	2.83424	0.393039
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	1.00000	0.136083
$55$	−4.63555	−0.625058
$56$	4.03293	0.538924
$57$	−1.00000	−0.132453
$58$	8.62901	1.13304
$59$	11.3579	1.47867	0.739337	−	0.673336i	$-0.235139\pi$
$59$	11.3579	1.47867	0.739337	+	0.673336i	$0.235139\pi$
$60$	2.83424	0.365899
$61$	−12.6290	−1.61698	−0.808489	−	0.588511i	$-0.799714\pi$
$61$	−12.6290	−1.61698	−0.808489	+	0.588511i	$0.799714\pi$
$62$	−1.27110	−0.161430
$63$	−4.03293	−0.508102
$64$	1.00000	0.125000
$65$	−8.03293	−0.996363
$66$	1.63555	0.201323
$67$	0.768374	0.0938719	0.0469359	−	0.998898i	$-0.485054\pi$
$67$	0.768374	0.0938719	0.0469359	+	0.998898i	$0.485054\pi$
$68$	6.03293	0.731601
$69$	−5.46980	−0.658486
$70$	−11.4303	−1.36618
$71$	1.60262	0.190196	0.0950979	−	0.995468i	$-0.469684\pi$
$71$	1.60262	0.190196	0.0950979	+	0.995468i	$0.469684\pi$
$72$	−1.00000	−0.117851
$73$	−0.761831	−0.0891655	−0.0445828	−	0.999006i	$-0.514196\pi$
$73$	−0.761831	−0.0891655	−0.0445828	+	0.999006i	$0.514196\pi$
$74$	−3.63555	−0.422624
$75$	−3.03293	−0.350213
$76$	1.00000	0.114708
$77$	−6.59607	−0.751692
$78$	2.83424	0.320915
$79$	−12.4094	−1.39616	−0.698082	−	0.716017i	$-0.745963\pi$
$79$	−12.4094	−1.39616	−0.698082	+	0.716017i	$0.745963\pi$
$80$	−2.83424	−0.316878
$81$	1.00000	0.111111
$82$	0.867178	0.0957637
$83$	−7.93305	−0.870765	−0.435382	−	0.900246i	$-0.643387\pi$
$83$	−7.93305	−0.870765	−0.435382	+	0.900246i	$0.643387\pi$
$84$	4.03293	0.440029
$85$	−17.0988	−1.85463
$86$	5.46980	0.589823
$87$	8.62901	0.925127
$88$	−1.63555	−0.174350
$89$	−8.70142	−0.922349	−0.461174	−	0.887310i	$-0.652572\pi$
$89$	−8.70142	−0.922349	−0.461174	+	0.887310i	$0.652572\pi$
$90$	2.83424	0.298755
$91$	−11.4303	−1.19822
$92$	5.46980	0.570266
$93$	−1.27110	−0.131807
$94$	7.39738	0.762982
$95$	−2.83424	−0.290787
$96$	1.00000	0.102062
$97$	−9.13828	−0.927852	−0.463926	−	0.885874i	$-0.653560\pi$
$97$	−9.13828	−0.927852	−0.463926	+	0.885874i	$0.653560\pi$
$98$	−9.26456	−0.935862
$99$	1.63555	0.164379
$100$	3.03293	0.303293
$101$	−0.894653	−0.0890213	−0.0445106	−	0.999009i	$-0.514173\pi$
$101$	−0.894653	−0.0890213	−0.0445106	+	0.999009i	$0.514173\pi$
$102$	6.03293	0.597350
$103$	3.36445	0.331509	0.165754	−	0.986167i	$-0.446994\pi$
$103$	3.36445	0.331509	0.165754	+	0.986167i	$0.446994\pi$
$104$	−2.83424	−0.277920
$105$	−11.4303	−1.11548
$106$	1.00000	0.0971286
$107$	7.16576	0.692740	0.346370	−	0.938098i	$-0.387414\pi$
$107$	7.16576	0.692740	0.346370	+	0.938098i	$0.387414\pi$
$108$	−1.00000	−0.0962250
$109$	10.8277	1.03711	0.518553	−	0.855046i	$-0.326471\pi$
$109$	10.8277	1.03711	0.518553	+	0.855046i	$0.326471\pi$
$110$	4.63555	0.441983
$111$	−3.63555	−0.345071
$112$	−4.03293	−0.381076
$113$	−4.33697	−0.407988	−0.203994	−	0.978972i	$-0.565392\pi$
$113$	−4.33697	−0.407988	−0.203994	+	0.978972i	$0.565392\pi$
$114$	1.00000	0.0936586
$115$	−15.5027	−1.44564
$116$	−8.62901	−0.801183
$117$	2.83424	0.262026
$118$	−11.3579	−1.04558
$119$	−24.3304	−2.23037
$120$	−2.83424	−0.258730
$121$	−8.32497	−0.756815
$122$	12.6290	1.14338
$123$	0.867178	0.0781908
$124$	1.27110	0.114148
$125$	5.57514	0.498656
$126$	4.03293	0.359282
$127$	−0.238169	−0.0211341	−0.0105671	−	0.999944i	$-0.503364\pi$
$127$	−0.238169	−0.0211341	−0.0105671	+	0.999944i	$0.503364\pi$
$128$	−1.00000	−0.0883883
$129$	5.46980	0.481589
$130$	8.03293	0.704535
$131$	14.4512	1.26261	0.631306	−	0.775534i	$-0.282519\pi$
$131$	14.4512	1.26261	0.631306	+	0.775534i	$0.282519\pi$
$132$	−1.63555	−0.142357
$133$	−4.03293	−0.349700
$134$	−0.768374	−0.0663774
$135$	2.83424	0.243933
$136$	−6.03293	−0.517320
$137$	16.4907	1.40890	0.704449	−	0.709755i	$-0.251194\pi$
$137$	16.4907	1.40890	0.704449	+	0.709755i	$0.251194\pi$
$138$	5.46980	0.465620
$139$	16.4962	1.39919	0.699594	−	0.714540i	$-0.253364\pi$
$139$	16.4962	1.39919	0.699594	+	0.714540i	$0.253364\pi$
$140$	11.4303	0.966038
$141$	7.39738	0.622972
$142$	−1.60262	−0.134489
$143$	4.63555	0.387644
$144$	1.00000	0.0833333
$145$	24.4567	2.03102
$146$	0.761831	0.0630495
$147$	−9.26456	−0.764128
$148$	3.63555	0.298841
$149$	−4.60262	−0.377061	−0.188531	−	0.982067i	$-0.560372\pi$
$149$	−4.60262	−0.377061	−0.188531	+	0.982067i	$0.560372\pi$
$150$	3.03293	0.247638
$151$	−8.72890	−0.710347	−0.355174	−	0.934800i	$-0.615578\pi$
$151$	−8.72890	−0.710347	−0.355174	+	0.934800i	$0.615578\pi$
$152$	−1.00000	−0.0811107
$153$	6.03293	0.487734
$154$	6.59607	0.531527
$155$	−3.60262	−0.289369
$156$	−2.83424	−0.226921
$157$	−5.83424	−0.465623	−0.232812	−	0.972522i	$-0.574793\pi$
$157$	−5.83424	−0.465623	−0.232812	+	0.972522i	$0.574793\pi$
$158$	12.4094	0.987238
$159$	1.00000	0.0793052
$160$	2.83424	0.224067
$161$	−22.0593	−1.73852
$162$	−1.00000	−0.0785674
$163$	−5.33697	−0.418024	−0.209012	−	0.977913i	$-0.567025\pi$
$163$	−5.33697	−0.418024	−0.209012	+	0.977913i	$0.567025\pi$
$164$	−0.867178	−0.0677152
$165$	4.63555	0.360877
$166$	7.93305	0.615724
$167$	10.6685	0.825552	0.412776	−	0.910833i	$-0.364559\pi$
$167$	10.6685	0.825552	0.412776	+	0.910833i	$0.364559\pi$
$168$	−4.03293	−0.311148
$169$	−4.96707	−0.382082
$170$	17.0988	1.31142
$171$	1.00000	0.0764719
$172$	−5.46980	−0.417068
$173$	12.0449	0.915760	0.457880	−	0.889014i	$-0.348609\pi$
$173$	12.0449	0.915760	0.457880	+	0.889014i	$0.348609\pi$
$174$	−8.62901	−0.654163
$175$	−12.2316	−0.924624
$176$	1.63555	0.123284
$177$	−11.3579	−0.853712
$178$	8.70142	0.652199
$179$	16.8606	1.26022	0.630111	−	0.776505i	$-0.283009\pi$
$179$	16.8606	1.26022	0.630111	+	0.776505i	$0.283009\pi$
$180$	−2.83424	−0.211252
$181$	−5.50927	−0.409501	−0.204751	−	0.978814i	$-0.565638\pi$
$181$	−5.50927	−0.409501	−0.204751	+	0.978814i	$0.565638\pi$
$182$	11.4303	0.847271
$183$	12.6290	0.933563
$184$	−5.46980	−0.403239
$185$	−10.3040	−0.757568
$186$	1.27110	0.0932019
$187$	9.86718	0.721559
$188$	−7.39738	−0.539510
$189$	4.03293	0.293353
$190$	2.83424	0.205618
$191$	23.1317	1.67375	0.836877	−	0.547391i	$-0.184379\pi$
$191$	23.1317	1.67375	0.836877	+	0.547391i	$0.184379\pi$
$192$	−1.00000	−0.0721688
$193$	17.0055	1.22408	0.612040	−	0.790827i	$-0.290349\pi$
$193$	17.0055	1.22408	0.612040	+	0.790827i	$0.290349\pi$
$194$	9.13828	0.656090
$195$	8.03293	0.575250
$196$	9.26456	0.661754
$197$	−2.30404	−0.164156	−0.0820780	−	0.996626i	$-0.526156\pi$
$197$	−2.30404	−0.164156	−0.0820780	+	0.996626i	$0.526156\pi$
$198$	−1.63555	−0.116234
$199$	5.55114	0.393510	0.196755	−	0.980453i	$-0.436960\pi$
$199$	5.55114	0.393510	0.196755	+	0.980453i	$0.436960\pi$
$200$	−3.03293	−0.214461
$201$	−0.768374	−0.0541969
$202$	0.894653	0.0629476
$203$	34.8002	2.44250
$204$	−6.03293	−0.422390
$205$	2.45779	0.171660
$206$	−3.36445	−0.234412
$207$	5.46980	0.380177
$208$	2.83424	0.196519
$209$	1.63555	0.113133
$210$	11.4303	0.788767
$211$	−0.238169	−0.0163963	−0.00819813	−	0.999966i	$-0.502610\pi$
$211$	−0.238169	−0.0163963	−0.00819813	+	0.999966i	$0.502610\pi$
$212$	−1.00000	−0.0686803
$213$	−1.60262	−0.109810
$214$	−7.16576	−0.489841
$215$	15.5027	1.05728
$216$	1.00000	0.0680414
$217$	−5.12628	−0.347994
$218$	−10.8277	−0.733344
$219$	0.761831	0.0514797
$220$	−4.63555	−0.312529
$221$	17.0988	1.15019
$222$	3.63555	0.244002
$223$	−19.3963	−1.29887	−0.649436	−	0.760416i	$-0.724995\pi$
$223$	−19.3963	−1.29887	−0.649436	+	0.760416i	$0.724995\pi$
$224$	4.03293	0.269462
$225$	3.03293	0.202196
$226$	4.33697	0.288491
$227$	10.2436	0.679894	0.339947	−	0.940445i	$-0.389591\pi$
$227$	10.2436	0.679894	0.339947	+	0.940445i	$0.389591\pi$
$228$	−1.00000	−0.0662266
$229$	−29.3843	−1.94177	−0.970884	−	0.239548i	$-0.923001\pi$
$229$	−29.3843	−1.94177	−0.970884	+	0.239548i	$0.923001\pi$
$230$	15.5027	1.02222
$231$	6.59607	0.433990
$232$	8.62901	0.566522
$233$	−6.07787	−0.398175	−0.199087	−	0.979982i	$-0.563798\pi$
$233$	−6.07787	−0.398175	−0.199087	+	0.979982i	$0.563798\pi$
$234$	−2.83424	−0.185280
$235$	20.9660	1.36767
$236$	11.3579	0.739337
$237$	12.4094	0.806076
$238$	24.3304	1.57711
$239$	0.436861	0.0282582	0.0141291	−	0.999900i	$-0.495502\pi$
$239$	0.436861	0.0282582	0.0141291	+	0.999900i	$0.495502\pi$
$240$	2.83424	0.182950
$241$	−19.1581	−1.23408	−0.617042	−	0.786930i	$-0.711669\pi$
$241$	−19.1581	−1.23408	−0.617042	+	0.786930i	$0.711669\pi$
$242$	8.32497	0.535149
$243$	−1.00000	−0.0641500
$244$	−12.6290	−0.808489
$245$	−26.2580	−1.67756
$246$	−0.867178	−0.0552892
$247$	2.83424	0.180339
$248$	−1.27110	−0.0807152
$249$	7.93305	0.502736
$250$	−5.57514	−0.352603
$251$	10.5147	0.663684	0.331842	−	0.943335i	$-0.392330\pi$
$251$	10.5147	0.663684	0.331842	+	0.943335i	$0.392330\pi$
$252$	−4.03293	−0.254051
$253$	8.94613	0.562439
$254$	0.238169	0.0149441
$255$	17.0988	1.07077
$256$	1.00000	0.0625000
$257$	7.37099	0.459790	0.229895	−	0.973215i	$-0.426162\pi$
$257$	7.37099	0.459790	0.229895	+	0.973215i	$0.426162\pi$
$258$	−5.46980	−0.340535
$259$	−14.6619	−0.911049
$260$	−8.03293	−0.498181
$261$	−8.62901	−0.534122
$262$	−14.4512	−0.892801
$263$	1.17122	0.0722203	0.0361101	−	0.999348i	$-0.488503\pi$
$263$	1.17122	0.0722203	0.0361101	+	0.999348i	$0.488503\pi$
$264$	1.63555	0.100661
$265$	2.83424	0.174106
$266$	4.03293	0.247275
$267$	8.70142	0.532518
$268$	0.768374	0.0469359
$269$	−15.9540	−0.972731	−0.486366	−	0.873755i	$-0.661678\pi$
$269$	−15.9540	−0.972731	−0.486366	+	0.873755i	$0.661678\pi$
$270$	−2.83424	−0.172487
$271$	−2.19869	−0.133561	−0.0667805	−	0.997768i	$-0.521273\pi$
$271$	−2.19869	−0.133561	−0.0667805	+	0.997768i	$0.521273\pi$
$272$	6.03293	0.365800
$273$	11.4303	0.691794
$274$	−16.4907	−0.996241
$275$	4.96052	0.299131
$276$	−5.46980	−0.329243
$277$	21.1437	1.27040	0.635202	−	0.772346i	$-0.280917\pi$
$277$	21.1437	1.27040	0.635202	+	0.772346i	$0.280917\pi$
$278$	−16.4962	−0.989375
$279$	1.27110	0.0760990
$280$	−11.4303	−0.683092
$281$	15.1801	0.905572	0.452786	−	0.891619i	$-0.350430\pi$
$281$	15.1801	0.905572	0.452786	+	0.891619i	$0.350430\pi$
$282$	−7.39738	−0.440508
$283$	19.0868	1.13459	0.567296	−	0.823514i	$-0.307989\pi$
$283$	19.0868	1.13459	0.567296	+	0.823514i	$0.307989\pi$
$284$	1.60262	0.0950979
$285$	2.83424	0.167886
$286$	−4.63555	−0.274106
$287$	3.49727	0.206437
$288$	−1.00000	−0.0589256
$289$	19.3963	1.14096
$290$	−24.4567	−1.43615
$291$	9.13828	0.535696
$292$	−0.761831	−0.0445828
$293$	−2.53566	−0.148135	−0.0740675	−	0.997253i	$-0.523598\pi$
$293$	−2.53566	−0.148135	−0.0740675	+	0.997253i	$0.523598\pi$
$294$	9.26456	0.540320
$295$	−32.1911	−1.87424
$296$	−3.63555	−0.211312
$297$	−1.63555	−0.0949043
$298$	4.60262	0.266622
$299$	15.5027	0.896546
$300$	−3.03293	−0.175107
$301$	22.0593	1.27148
$302$	8.72890	0.502292
$303$	0.894653	0.0513965
$304$	1.00000	0.0573539
$305$	35.7937	2.04954
$306$	−6.03293	−0.344880
$307$	−0.768374	−0.0438534	−0.0219267	−	0.999760i	$-0.506980\pi$
$307$	−0.768374	−0.0438534	−0.0219267	+	0.999760i	$0.506980\pi$
$308$	−6.59607	−0.375846
$309$	−3.36445	−0.191397
$310$	3.60262	0.204615
$311$	5.76075	0.326662	0.163331	−	0.986571i	$-0.447776\pi$
$311$	5.76075	0.326662	0.163331	+	0.986571i	$0.447776\pi$
$312$	2.83424	0.160457
$313$	17.9594	1.01513	0.507564	−	0.861614i	$-0.330546\pi$
$313$	17.9594	1.01513	0.507564	+	0.861614i	$0.330546\pi$
$314$	5.83424	0.329245
$315$	11.4303	0.644025
$316$	−12.4094	−0.698082
$317$	16.7553	0.941071	0.470535	−	0.882381i	$-0.344061\pi$
$317$	16.7553	0.941071	0.470535	+	0.882381i	$0.344061\pi$
$318$	−1.00000	−0.0560772
$319$	−14.1132	−0.790187
$320$	−2.83424	−0.158439
$321$	−7.16576	−0.399954
$322$	22.0593	1.22932
$323$	6.03293	0.335681
$324$	1.00000	0.0555556
$325$	8.59607	0.476824
$326$	5.33697	0.295588
$327$	−10.8277	−0.598773
$328$	0.867178	0.0478819
$329$	29.8332	1.64476
$330$	−4.63555	−0.255179
$331$	−18.7937	−1.03299	−0.516497	−	0.856289i	$-0.672764\pi$
$331$	−18.7937	−1.03299	−0.516497	+	0.856289i	$0.672764\pi$
$332$	−7.93305	−0.435382
$333$	3.63555	0.199227
$334$	−10.6685	−0.583754
$335$	−2.17776	−0.118984
$336$	4.03293	0.220015
$337$	−16.8277	−0.916663	−0.458332	−	0.888781i	$-0.651553\pi$
$337$	−16.8277	−0.916663	−0.458332	+	0.888781i	$0.651553\pi$
$338$	4.96707	0.270173
$339$	4.33697	0.235552
$340$	−17.0988	−0.927313
$341$	2.07896	0.112582
$342$	−1.00000	−0.0540738
$343$	−9.13282	−0.493126
$344$	5.46980	0.294912
$345$	15.5027	0.834639
$346$	−12.0449	−0.647540
$347$	4.78822	0.257045	0.128523	−	0.991707i	$-0.458977\pi$
$347$	4.78822	0.257045	0.128523	+	0.991707i	$0.458977\pi$
$348$	8.62901	0.462563
$349$	5.56968	0.298138	0.149069	−	0.988827i	$-0.452372\pi$
$349$	5.56968	0.298138	0.149069	+	0.988827i	$0.452372\pi$
$350$	12.2316	0.653808
$351$	−2.83424	−0.151281
$352$	−1.63555	−0.0871752
$353$	−18.4238	−0.980598	−0.490299	−	0.871554i	$-0.663113\pi$
$353$	−18.4238	−0.980598	−0.490299	+	0.871554i	$0.663113\pi$
$354$	11.3579	0.603666
$355$	−4.54221	−0.241075
$356$	−8.70142	−0.461174
$357$	24.3304	1.28770
$358$	−16.8606	−0.891112
$359$	−33.2065	−1.75257	−0.876287	−	0.481790i	$-0.839987\pi$
$359$	−33.2065	−1.75257	−0.876287	+	0.481790i	$0.839987\pi$
$360$	2.83424	0.149378
$361$	1.00000	0.0526316
$362$	5.50927	0.289561
$363$	8.32497	0.436948
$364$	−11.4303	−0.599111
$365$	2.15921	0.113018
$366$	−12.6290	−0.660129
$367$	−0.861719	−0.0449813	−0.0224907	−	0.999747i	$-0.507160\pi$
$367$	−0.861719	−0.0449813	−0.0224907	+	0.999747i	$0.507160\pi$
$368$	5.46980	0.285133
$369$	−0.867178	−0.0451435
$370$	10.3040	0.535681
$371$	4.03293	0.209380
$372$	−1.27110	−0.0659037
$373$	−14.6894	−0.760589	−0.380295	−	0.924865i	$-0.624177\pi$
$373$	−14.6894	−0.760589	−0.380295	+	0.924865i	$0.624177\pi$
$374$	−9.86718	−0.510220
$375$	−5.57514	−0.287899
$376$	7.39738	0.381491
$377$	−24.4567	−1.25958
$378$	−4.03293	−0.207432
$379$	−23.7738	−1.22118	−0.610590	−	0.791947i	$-0.709068\pi$
$379$	−23.7738	−1.22118	−0.610590	+	0.791947i	$0.709068\pi$
$380$	−2.83424	−0.145394
$381$	0.238169	0.0122018
$382$	−23.1317	−1.18352
$383$	−35.3228	−1.80491	−0.902455	−	0.430783i	$-0.858237\pi$
$383$	−35.3228	−1.80491	−0.902455	+	0.430783i	$0.858237\pi$
$384$	1.00000	0.0510310
$385$	18.6949	0.952779
$386$	−17.0055	−0.865555
$387$	−5.46980	−0.278045
$388$	−9.13828	−0.463926
$389$	−22.8781	−1.15997	−0.579983	−	0.814629i	$-0.696941\pi$
$389$	−22.8781	−1.15997	−0.579983	+	0.814629i	$0.696941\pi$
$390$	−8.03293	−0.406763
$391$	32.9989	1.66883
$392$	−9.26456	−0.467931
$393$	−14.4512	−0.728969
$394$	2.30404	0.116076
$395$	35.1712	1.76966
$396$	1.63555	0.0821896
$397$	−10.6894	−0.536487	−0.268243	−	0.963351i	$-0.586443\pi$
$397$	−10.6894	−0.536487	−0.268243	+	0.963351i	$0.586443\pi$
$398$	−5.55114	−0.278253
$399$	4.03293	0.201899
$400$	3.03293	0.151647
$401$	14.7224	0.735199	0.367600	−	0.929984i	$-0.380180\pi$
$401$	14.7224	0.735199	0.367600	+	0.929984i	$0.380180\pi$
$402$	0.768374	0.0383230
$403$	3.60262	0.179459
$404$	−0.894653	−0.0445106
$405$	−2.83424	−0.140835
$406$	−34.8002	−1.72711
$407$	5.94613	0.294739
$408$	6.03293	0.298675
$409$	−14.3819	−0.711140	−0.355570	−	0.934650i	$-0.615713\pi$
$409$	−14.3819	−0.711140	−0.355570	+	0.934650i	$0.615713\pi$
$410$	−2.45779	−0.121382
$411$	−16.4907	−0.813428
$412$	3.36445	0.165754
$413$	−45.8057	−2.25395
$414$	−5.46980	−0.268826
$415$	22.4842	1.10371
$416$	−2.83424	−0.138960
$417$	−16.4962	−0.807822
$418$	−1.63555	−0.0799975
$419$	16.7498	0.818283	0.409141	−	0.912471i	$-0.365828\pi$
$419$	16.7498	0.818283	0.409141	+	0.912471i	$0.365828\pi$
$420$	−11.4303	−0.557742
$421$	19.9815	0.973836	0.486918	−	0.873448i	$-0.338121\pi$
$421$	19.9815	0.973836	0.486918	+	0.873448i	$0.338121\pi$
$422$	0.238169	0.0115939
$423$	−7.39738	−0.359673
$424$	1.00000	0.0485643
$425$	18.2975	0.887559
$426$	1.60262	0.0776471
$427$	50.9320	2.46477
$428$	7.16576	0.346370
$429$	−4.63555	−0.223807
$430$	−15.5027	−0.747608
$431$	33.5357	1.61536	0.807678	−	0.589624i	$-0.200724\pi$
$431$	33.5357	1.61536	0.807678	+	0.589624i	$0.200724\pi$
$432$	−1.00000	−0.0481125
$433$	10.7684	0.517495	0.258748	−	0.965945i	$-0.416690\pi$
$433$	10.7684	0.517495	0.258748	+	0.965945i	$0.416690\pi$
$434$	5.12628	0.246069
$435$	−24.4567	−1.17261
$436$	10.8277	0.518553
$437$	5.46980	0.261656
$438$	−0.761831	−0.0364017
$439$	12.8222	0.611972	0.305986	−	0.952036i	$-0.401014\pi$
$439$	12.8222	0.611972	0.305986	+	0.952036i	$0.401014\pi$
$440$	4.63555	0.220991
$441$	9.26456	0.441170
$442$	−17.0988	−0.813307
$443$	26.0408	1.23723	0.618617	−	0.785692i	$-0.287693\pi$
$443$	26.0408	1.23723	0.618617	+	0.785692i	$0.287693\pi$
$444$	−3.63555	−0.172536
$445$	24.6619	1.16909
$446$	19.3963	0.918441
$447$	4.60262	0.217696
$448$	−4.03293	−0.190538
$449$	−29.7727	−1.40506	−0.702531	−	0.711653i	$-0.747947\pi$
$449$	−29.7727	−1.40506	−0.702531	+	0.711653i	$0.747947\pi$
$450$	−3.03293	−0.142974
$451$	−1.41831	−0.0667858
$452$	−4.33697	−0.203994
$453$	8.72890	0.410119
$454$	−10.2436	−0.480757
$455$	32.3963	1.51876
$456$	1.00000	0.0468293
$457$	15.3843	0.719647	0.359823	−	0.933020i	$-0.382837\pi$
$457$	15.3843	0.719647	0.359823	+	0.933020i	$0.382837\pi$
$458$	29.3843	1.37304
$459$	−6.03293	−0.281593
$460$	−15.5027	−0.722818
$461$	27.6949	1.28988	0.644940	−	0.764234i	$-0.276883\pi$
$461$	27.6949	1.28988	0.644940	+	0.764234i	$0.276883\pi$
$462$	−6.59607	−0.306877
$463$	−7.40939	−0.344343	−0.172172	−	0.985067i	$-0.555078\pi$
$463$	−7.40939	−0.344343	−0.172172	+	0.985067i	$0.555078\pi$
$464$	−8.62901	−0.400592
$465$	3.60262	0.167067
$466$	6.07787	0.281552
$467$	39.5686	1.83102	0.915508	−	0.402299i	$-0.131789\pi$
$467$	39.5686	1.83102	0.915508	+	0.402299i	$0.131789\pi$
$468$	2.83424	0.131013
$469$	−3.09880	−0.143089
$470$	−20.9660	−0.967089
$471$	5.83424	0.268828
$472$	−11.3579	−0.522790
$473$	−8.94613	−0.411344
$474$	−12.4094	−0.569982
$475$	3.03293	0.139161
$476$	−24.3304	−1.11518
$477$	−1.00000	−0.0457869
$478$	−0.436861	−0.0199815
$479$	15.5697	0.711397	0.355698	−	0.934601i	$-0.384243\pi$
$479$	15.5697	0.711397	0.355698	+	0.934601i	$0.384243\pi$
$480$	−2.83424	−0.129365
$481$	10.3040	0.469824
$482$	19.1581	0.872629
$483$	22.0593	1.00373
$484$	−8.32497	−0.378408
$485$	25.9001	1.17606
$486$	1.00000	0.0453609
$487$	32.2371	1.46080	0.730401	−	0.683019i	$-0.239333\pi$
$487$	32.2371	1.46080	0.730401	+	0.683019i	$0.239333\pi$
$488$	12.6290	0.571688
$489$	5.33697	0.241346
$490$	26.2580	1.18622
$491$	−27.9529	−1.26150	−0.630748	−	0.775988i	$-0.717252\pi$
$491$	−27.9529	−1.26150	−0.630748	+	0.775988i	$0.717252\pi$
$492$	0.867178	0.0390954
$493$	−52.0582	−2.34459
$494$	−2.83424	−0.127519
$495$	−4.63555	−0.208353
$496$	1.27110	0.0570742
$497$	−6.46325	−0.289916
$498$	−7.93305	−0.355488
$499$	−21.2515	−0.951347	−0.475673	−	0.879622i	$-0.657796\pi$
$499$	−21.2515	−0.951347	−0.475673	+	0.879622i	$0.657796\pi$
$500$	5.57514	0.249328
$501$	−10.6685	−0.476633
$502$	−10.5147	−0.469295
$503$	23.2855	1.03825	0.519124	−	0.854699i	$-0.326258\pi$
$503$	23.2855	1.03825	0.519124	+	0.854699i	$0.326258\pi$
$504$	4.03293	0.179641
$505$	2.53566	0.112836
$506$	−8.94613	−0.397704
$507$	4.96707	0.220595
$508$	−0.238169	−0.0105671
$509$	−14.2591	−0.632024	−0.316012	−	0.948755i	$-0.602344\pi$
$509$	−14.2591	−0.632024	−0.316012	+	0.948755i	$0.602344\pi$
$510$	−17.0988	−0.757148
$511$	3.07241	0.135916
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−7.37099	−0.325121
$515$	−9.53566	−0.420192
$516$	5.46980	0.240794
$517$	−12.0988	−0.532105
$518$	14.6619	0.644209
$519$	−12.0449	−0.528714
$520$	8.03293	0.352267
$521$	−11.8288	−0.518228	−0.259114	−	0.965847i	$-0.583431\pi$
$521$	−11.8288	−0.518228	−0.259114	+	0.965847i	$0.583431\pi$
$522$	8.62901	0.377681
$523$	−1.28549	−0.0562106	−0.0281053	−	0.999605i	$-0.508947\pi$
$523$	−1.28549	−0.0562106	−0.0281053	+	0.999605i	$0.508947\pi$
$524$	14.4512	0.631306
$525$	12.2316	0.533832
$526$	−1.17122	−0.0510674
$527$	7.66849	0.334045
$528$	−1.63555	−0.0711783
$529$	6.91866	0.300811
$530$	−2.83424	−0.123112
$531$	11.3579	0.492891
$532$	−4.03293	−0.174850
$533$	−2.45779	−0.106459
$534$	−8.70142	−0.376547
$535$	−20.3095	−0.878056
$536$	−0.768374	−0.0331887
$537$	−16.8606	−0.727590
$538$	15.9540	0.687825
$539$	15.1527	0.652672
$540$	2.83424	0.121966
$541$	−8.31951	−0.357684	−0.178842	−	0.983878i	$-0.557235\pi$
$541$	−8.31951	−0.357684	−0.178842	+	0.983878i	$0.557235\pi$
$542$	2.19869	0.0944419
$543$	5.50927	0.236426
$544$	−6.03293	−0.258660
$545$	−30.6883	−1.31454
$546$	−11.4303	−0.489172
$547$	17.2766	0.738692	0.369346	−	0.929292i	$-0.379582\pi$
$547$	17.2766	0.738692	0.369346	+	0.929292i	$0.379582\pi$
$548$	16.4907	0.704449
$549$	−12.6290	−0.538993
$550$	−4.96052	−0.211517
$551$	−8.62901	−0.367608
$552$	5.46980	0.232810
$553$	50.0462	2.12818
$554$	−21.1437	−0.898311
$555$	10.3040	0.437382
$556$	16.4962	0.699594
$557$	7.97599	0.337954	0.168977	−	0.985620i	$-0.445954\pi$
$557$	7.97599	0.337954	0.168977	+	0.985620i	$0.445954\pi$
$558$	−1.27110	−0.0538101
$559$	−15.5027	−0.655696
$560$	11.4303	0.483019
$561$	−9.86718	−0.416593
$562$	−15.1801	−0.640336
$563$	43.9474	1.85216	0.926082	−	0.377323i	$-0.123155\pi$
$563$	43.9474	1.85216	0.926082	+	0.377323i	$0.123155\pi$
$564$	7.39738	0.311486
$565$	12.2920	0.517130
$566$	−19.0868	−0.802278
$567$	−4.03293	−0.169367
$568$	−1.60262	−0.0672443
$569$	33.8541	1.41924	0.709619	−	0.704586i	$-0.248867\pi$
$569$	33.8541	1.41924	0.709619	+	0.704586i	$0.248867\pi$
$570$	−2.83424	−0.118713
$571$	−39.7597	−1.66389	−0.831945	−	0.554858i	$-0.812773\pi$
$571$	−39.7597	−1.66389	−0.831945	+	0.554858i	$0.812773\pi$
$572$	4.63555	0.193822
$573$	−23.1317	−0.966342
$574$	−3.49727	−0.145973
$575$	16.5895	0.691831
$576$	1.00000	0.0416667
$577$	−19.3699	−0.806380	−0.403190	−	0.915116i	$-0.632099\pi$
$577$	−19.3699	−0.806380	−0.403190	+	0.915116i	$0.632099\pi$
$578$	−19.3963	−0.806780
$579$	−17.0055	−0.706723
$580$	24.4567	1.01551
$581$	31.9935	1.32731
$582$	−9.13828	−0.378794
$583$	−1.63555	−0.0677376
$584$	0.761831	0.0315248
$585$	−8.03293	−0.332121
$586$	2.53566	0.104747
$587$	−37.5610	−1.55031	−0.775154	−	0.631773i	$-0.782328\pi$
$587$	−37.5610	−1.55031	−0.775154	+	0.631773i	$0.782328\pi$
$588$	−9.26456	−0.382064
$589$	1.27110	0.0523749
$590$	32.1911	1.32529
$591$	2.30404	0.0947755
$592$	3.63555	0.149420
$593$	2.10426	0.0864117	0.0432058	−	0.999066i	$-0.486243\pi$
$593$	2.10426	0.0864117	0.0432058	+	0.999066i	$0.486243\pi$
$594$	1.63555	0.0671075
$595$	68.9584	2.82702
$596$	−4.60262	−0.188531
$597$	−5.55114	−0.227193
$598$	−15.5027	−0.633954
$599$	−35.6094	−1.45496	−0.727480	−	0.686129i	$-0.759309\pi$
$599$	−35.6094	−1.45496	−0.727480	+	0.686129i	$0.759309\pi$
$600$	3.03293	0.123819
$601$	−18.8816	−0.770195	−0.385098	−	0.922876i	$-0.625832\pi$
$601$	−18.8816	−0.770195	−0.385098	+	0.922876i	$0.625832\pi$
$602$	−22.0593	−0.899071
$603$	0.768374	0.0312906
$604$	−8.72890	−0.355174
$605$	23.5950	0.959273
$606$	−0.894653	−0.0363428
$607$	43.2031	1.75356	0.876779	−	0.480893i	$-0.159688\pi$
$607$	43.2031	1.75356	0.876779	+	0.480893i	$0.159688\pi$
$608$	−1.00000	−0.0405554
$609$	−34.8002	−1.41018
$610$	−35.7937	−1.44924
$611$	−20.9660	−0.848193
$612$	6.03293	0.243867
$613$	26.0988	1.05412	0.527060	−	0.849828i	$-0.323294\pi$
$613$	26.0988	1.05412	0.527060	+	0.849828i	$0.323294\pi$
$614$	0.768374	0.0310091
$615$	−2.45779	−0.0991077
$616$	6.59607	0.265763
$617$	19.5830	0.788381	0.394191	−	0.919029i	$-0.371025\pi$
$617$	19.5830	0.788381	0.394191	+	0.919029i	$0.371025\pi$
$618$	3.36445	0.135338
$619$	22.7344	0.913771	0.456885	−	0.889526i	$-0.348965\pi$
$619$	22.7344	0.913771	0.456885	+	0.889526i	$0.348965\pi$
$620$	−3.60262	−0.144685
$621$	−5.46980	−0.219495
$622$	−5.76075	−0.230985
$623$	35.0923	1.40594
$624$	−2.83424	−0.113461
$625$	−30.9660	−1.23864
$626$	−17.9594	−0.717803
$627$	−1.63555	−0.0653177
$628$	−5.83424	−0.232812
$629$	21.9330	0.874528
$630$	−11.4303	−0.455395
$631$	−6.15028	−0.244839	−0.122419	−	0.992478i	$-0.539065\pi$
$631$	−6.15028	−0.244839	−0.122419	+	0.992478i	$0.539065\pi$
$632$	12.4094	0.493619
$633$	0.238169	0.00946639
$634$	−16.7553	−0.665437
$635$	0.675030	0.0267878
$636$	1.00000	0.0396526
$637$	26.2580	1.04038
$638$	14.1132	0.558747
$639$	1.60262	0.0633986
$640$	2.83424	0.112033
$641$	−8.76183	−0.346071	−0.173036	−	0.984916i	$-0.555358\pi$
$641$	−8.76183	−0.346071	−0.173036	+	0.984916i	$0.555358\pi$
$642$	7.16576	0.282810
$643$	−2.61046	−0.102947	−0.0514733	−	0.998674i	$-0.516392\pi$
$643$	−2.61046	−0.102947	−0.0514733	+	0.998674i	$0.516392\pi$
$644$	−22.0593	−0.869259
$645$	−15.5027	−0.610419
$646$	−6.03293	−0.237363
$647$	−29.3963	−1.15569	−0.577844	−	0.816147i	$-0.696106\pi$
$647$	−29.3963	−1.15569	−0.577844	+	0.816147i	$0.696106\pi$
$648$	−1.00000	−0.0392837
$649$	18.5764	0.729189
$650$	−8.59607	−0.337166
$651$	5.12628	0.200915
$652$	−5.33697	−0.209012
$653$	−32.7991	−1.28353	−0.641765	−	0.766902i	$-0.721797\pi$
$653$	−32.7991	−1.28353	−0.641765	+	0.766902i	$0.721797\pi$
$654$	10.8277	0.423397
$655$	−40.9584	−1.60038
$656$	−0.867178	−0.0338576
$657$	−0.761831	−0.0297218
$658$	−29.8332	−1.16302
$659$	30.3160	1.18095	0.590473	−	0.807058i	$-0.298941\pi$
$659$	30.3160	1.18095	0.590473	+	0.807058i	$0.298941\pi$
$660$	4.63555	0.180439
$661$	−0.545677	−0.0212244	−0.0106122	−	0.999944i	$-0.503378\pi$
$661$	−0.545677	−0.0212244	−0.0106122	+	0.999944i	$0.503378\pi$
$662$	18.7937	0.730437
$663$	−17.0988	−0.664062
$664$	7.93305	0.307862
$665$	11.4303	0.443249
$666$	−3.63555	−0.140875
$667$	−47.1989	−1.82755
$668$	10.6685	0.412776
$669$	19.3963	0.749904
$670$	2.17776	0.0841342
$671$	−20.6554	−0.797393
$672$	−4.03293	−0.155574
$673$	41.6334	1.60485	0.802424	−	0.596754i	$-0.203543\pi$
$673$	41.6334	1.60485	0.802424	+	0.596754i	$0.203543\pi$
$674$	16.8277	0.648179
$675$	−3.03293	−0.116738
$676$	−4.96707	−0.191041
$677$	49.5915	1.90596	0.952978	−	0.303038i	$-0.0980009\pi$
$677$	49.5915	1.90596	0.952978	+	0.303038i	$0.0980009\pi$
$678$	−4.33697	−0.166560
$679$	36.8541	1.41433
$680$	17.0988	0.655709
$681$	−10.2436	−0.392537
$682$	−2.07896	−0.0796074
$683$	−15.1437	−0.579459	−0.289730	−	0.957109i	$-0.593565\pi$
$683$	−15.1437	−0.579459	−0.289730	+	0.957109i	$0.593565\pi$
$684$	1.00000	0.0382360
$685$	−46.7387	−1.78580
$686$	9.13282	0.348693
$687$	29.3843	1.12108
$688$	−5.46980	−0.208534
$689$	−2.83424	−0.107976
$690$	−15.5027	−0.590179
$691$	12.2591	0.466358	0.233179	−	0.972434i	$-0.425087\pi$
$691$	12.2591	0.466358	0.233179	+	0.972434i	$0.425087\pi$
$692$	12.0449	0.457880
$693$	−6.59607	−0.250564
$694$	−4.78822	−0.181758
$695$	−46.7542	−1.77349
$696$	−8.62901	−0.327082
$697$	−5.23163	−0.198162
$698$	−5.56968	−0.210816
$699$	6.07787	0.229886
$700$	−12.2316	−0.462312
$701$	−34.6530	−1.30883	−0.654413	−	0.756137i	$-0.727084\pi$
$701$	−34.6530	−1.30883	−0.654413	+	0.756137i	$0.727084\pi$
$702$	2.83424	0.106972
$703$	3.63555	0.137117
$704$	1.63555	0.0616422
$705$	−20.9660	−0.789625
$706$	18.4238	0.693388
$707$	3.60808	0.135696
$708$	−11.3579	−0.426856
$709$	11.6410	0.437187	0.218594	−	0.975816i	$-0.429853\pi$
$709$	11.6410	0.437187	0.218594	+	0.975816i	$0.429853\pi$
$710$	4.54221	0.170466
$711$	−12.4094	−0.465388
$712$	8.70142	0.326100
$713$	6.95268	0.260380
$714$	−24.3304	−0.910543
$715$	−13.1383	−0.491344
$716$	16.8606	0.630111
$717$	−0.436861	−0.0163149
$718$	33.2065	1.23926
$719$	−15.0779	−0.562310	−0.281155	−	0.959662i	$-0.590717\pi$
$719$	−15.0779	−0.562310	−0.281155	+	0.959662i	$0.590717\pi$
$720$	−2.83424	−0.105626
$721$	−13.5686	−0.505321
$722$	−1.00000	−0.0372161
$723$	19.1581	0.712498
$724$	−5.50927	−0.204751
$725$	−26.1712	−0.971975
$726$	−8.32497	−0.308969
$727$	22.8870	0.848833	0.424416	−	0.905467i	$-0.360479\pi$
$727$	22.8870	0.848833	0.424416	+	0.905467i	$0.360479\pi$
$728$	11.4303	0.423636
$729$	1.00000	0.0370370
$730$	−2.15921	−0.0799161
$731$	−32.9989	−1.22051
$732$	12.6290	0.466782
$733$	44.0188	1.62587	0.812935	−	0.582354i	$-0.197868\pi$
$733$	44.0188	1.62587	0.812935	+	0.582354i	$0.197868\pi$
$734$	0.861719	0.0318066
$735$	26.2580	0.968542
$736$	−5.46980	−0.201619
$737$	1.25672	0.0462917
$738$	0.867178	0.0319212
$739$	16.8990	0.621641	0.310820	−	0.950469i	$-0.399396\pi$
$739$	16.8990	0.621641	0.310820	+	0.950469i	$0.399396\pi$
$740$	−10.3040	−0.378784
$741$	−2.83424	−0.104119
$742$	−4.03293	−0.148054
$743$	0.521276	0.0191238	0.00956188	−	0.999954i	$-0.496956\pi$
$743$	0.521276	0.0191238	0.00956188	+	0.999954i	$0.496956\pi$
$744$	1.27110	0.0466009
$745$	13.0449	0.477930
$746$	14.6894	0.537818
$747$	−7.93305	−0.290255
$748$	9.86718	0.360780
$749$	−28.8990	−1.05595
$750$	5.57514	0.203575
$751$	38.6070	1.40879	0.704395	−	0.709809i	$-0.251219\pi$
$751$	38.6070	1.40879	0.704395	+	0.709809i	$0.251219\pi$
$752$	−7.39738	−0.269755
$753$	−10.5147	−0.383178
$754$	24.4567	0.890661
$755$	24.7398	0.900374
$756$	4.03293	0.146676
$757$	19.7738	0.718692	0.359346	−	0.933204i	$-0.383000\pi$
$757$	19.7738	0.718692	0.359346	+	0.933204i	$0.383000\pi$
$758$	23.7738	0.863505
$759$	−8.94613	−0.324724
$760$	2.83424	0.102809
$761$	−11.9001	−0.431379	−0.215689	−	0.976462i	$-0.569200\pi$
$761$	−11.9001	−0.431379	−0.215689	+	0.976462i	$0.569200\pi$
$762$	−0.238169	−0.00862797
$763$	−43.6674	−1.58087
$764$	23.1317	0.836877
$765$	−17.0988	−0.618209
$766$	35.3228	1.27626
$767$	32.1911	1.16235
$768$	−1.00000	−0.0360844
$769$	7.38538	0.266324	0.133162	−	0.991094i	$-0.457487\pi$
$769$	7.38538	0.266324	0.133162	+	0.991094i	$0.457487\pi$
$770$	−18.6949	−0.673717
$771$	−7.37099	−0.265460
$772$	17.0055	0.612040
$773$	31.3370	1.12711	0.563556	−	0.826078i	$-0.309433\pi$
$773$	31.3370	1.12711	0.563556	+	0.826078i	$0.309433\pi$
$774$	5.46980	0.196608
$775$	3.85517	0.138482
$776$	9.13828	0.328045
$777$	14.6619	0.525994
$778$	22.8781	0.820219
$779$	−0.867178	−0.0310699
$780$	8.03293	0.287625
$781$	2.62116	0.0937926
$782$	−32.9989	−1.18004
$783$	8.62901	0.308376
$784$	9.26456	0.330877
$785$	16.5357	0.590183
$786$	14.4512	0.515459
$787$	20.8936	0.744775	0.372388	−	0.928077i	$-0.378539\pi$
$787$	20.8936	0.744775	0.372388	+	0.928077i	$0.378539\pi$
$788$	−2.30404	−0.0820780
$789$	−1.17122	−0.0416964
$790$	−35.1712	−1.25134
$791$	17.4907	0.621899
$792$	−1.63555	−0.0581168
$793$	−35.7937	−1.27107
$794$	10.6894	0.379353
$795$	−2.83424	−0.100520
$796$	5.55114	0.196755
$797$	6.57514	0.232903	0.116452	−	0.993196i	$-0.462848\pi$
$797$	6.57514	0.232903	0.116452	+	0.993196i	$0.462848\pi$
$798$	−4.03293	−0.142764
$799$	−44.6279	−1.57882
$800$	−3.03293	−0.107230
$801$	−8.70142	−0.307450
$802$	−14.7224	−0.519864
$803$	−1.24601	−0.0439709
$804$	−0.768374	−0.0270985
$805$	62.5215	2.20359
$806$	−3.60262	−0.126897
$807$	15.9540	0.561607
$808$	0.894653	0.0314738
$809$	43.7806	1.53924	0.769622	−	0.638500i	$-0.220445\pi$
$809$	43.7806	1.53924	0.769622	+	0.638500i	$0.220445\pi$
$810$	2.83424	0.0995852
$811$	10.7049	0.375900	0.187950	−	0.982179i	$-0.439816\pi$
$811$	10.7049	0.375900	0.187950	+	0.982179i	$0.439816\pi$
$812$	34.8002	1.22125
$813$	2.19869	0.0771115
$814$	−5.94613	−0.208412
$815$	15.1263	0.529850
$816$	−6.03293	−0.211195
$817$	−5.46980	−0.191364
$818$	14.3819	0.502852
$819$	−11.4303	−0.399408
$820$	2.45779	0.0858298
$821$	2.75637	0.0961980	0.0480990	−	0.998843i	$-0.484684\pi$
$821$	2.75637	0.0961980	0.0480990	+	0.998843i	$0.484684\pi$
$822$	16.4907	0.575180
$823$	−7.45779	−0.259962	−0.129981	−	0.991516i	$-0.541492\pi$
$823$	−7.45779	−0.259962	−0.129981	+	0.991516i	$0.541492\pi$
$824$	−3.36445	−0.117206
$825$	−4.96052	−0.172703
$826$	45.8057	1.59378
$827$	3.25364	0.113140	0.0565701	−	0.998399i	$-0.481984\pi$
$827$	3.25364	0.113140	0.0565701	+	0.998399i	$0.481984\pi$
$828$	5.46980	0.190089
$829$	22.7025	0.788491	0.394245	−	0.919005i	$-0.371006\pi$
$829$	22.7025	0.788491	0.394245	+	0.919005i	$0.371006\pi$
$830$	−22.4842	−0.780437
$831$	−21.1437	−0.733468
$832$	2.83424	0.0982597
$833$	55.8925	1.93656
$834$	16.4962	0.571216
$835$	−30.2371	−1.04640
$836$	1.63555	0.0565667
$837$	−1.27110	−0.0439358
$838$	−16.7498	−0.578613
$839$	6.46871	0.223325	0.111662	−	0.993746i	$-0.464382\pi$
$839$	6.46871	0.223325	0.111662	+	0.993746i	$0.464382\pi$
$840$	11.4303	0.394383
$841$	45.4598	1.56758
$842$	−19.9815	−0.688606
$843$	−15.1801	−0.522832
$844$	−0.238169	−0.00819813
$845$	14.0779	0.484294
$846$	7.39738	0.254327
$847$	33.5741	1.15362
$848$	−1.00000	−0.0343401
$849$	−19.0868	−0.655057
$850$	−18.2975	−0.627599
$851$	19.8857	0.681674
$852$	−1.60262	−0.0549048
$853$	36.7398	1.25795	0.628974	−	0.777427i	$-0.283475\pi$
$853$	36.7398	1.25795	0.628974	+	0.777427i	$0.283475\pi$
$854$	−50.9320	−1.74286
$855$	−2.83424	−0.0969291
$856$	−7.16576	−0.244921
$857$	1.11081	0.0379444	0.0189722	−	0.999820i	$-0.493961\pi$
$857$	1.11081	0.0379444	0.0189722	+	0.999820i	$0.493961\pi$
$858$	4.63555	0.158255
$859$	49.4041	1.68565	0.842824	−	0.538190i	$-0.180892\pi$
$859$	49.4041	1.68565	0.842824	+	0.538190i	$0.180892\pi$
$860$	15.5027	0.528639
$861$	−3.49727	−0.119187
$862$	−33.5357	−1.14223
$863$	25.7882	0.877841	0.438921	−	0.898526i	$-0.355361\pi$
$863$	25.7882	0.877841	0.438921	+	0.898526i	$0.355361\pi$
$864$	1.00000	0.0340207
$865$	−34.1383	−1.16074
$866$	−10.7684	−0.365924
$867$	−19.3963	−0.658733
$868$	−5.12628	−0.173997
$869$	−20.2962	−0.688501
$870$	24.4567	0.829160
$871$	2.17776	0.0737906
$872$	−10.8277	−0.366672
$873$	−9.13828	−0.309284
$874$	−5.46980	−0.185019
$875$	−22.4842	−0.760104
$876$	0.761831	0.0257399
$877$	−23.7708	−0.802682	−0.401341	−	0.915929i	$-0.631456\pi$
$877$	−23.7708	−0.802682	−0.401341	+	0.915929i	$0.631456\pi$
$878$	−12.8222	−0.432730
$879$	2.53566	0.0855258
$880$	−4.63555	−0.156264
$881$	43.8859	1.47855	0.739277	−	0.673401i	$-0.235167\pi$
$881$	43.8859	1.47855	0.739277	+	0.673401i	$0.235167\pi$
$882$	−9.26456	−0.311954
$883$	−15.9900	−0.538106	−0.269053	−	0.963125i	$-0.586711\pi$
$883$	−15.9900	−0.538106	−0.269053	+	0.963125i	$0.586711\pi$
$884$	17.0988	0.575095
$885$	32.1911	1.08209
$886$	−26.0408	−0.874857
$887$	−2.22508	−0.0747109	−0.0373555	−	0.999302i	$-0.511893\pi$
$887$	−2.22508	−0.0747109	−0.0373555	+	0.999302i	$0.511893\pi$
$888$	3.63555	0.122001
$889$	0.960522	0.0322149
$890$	−24.6619	−0.826670
$891$	1.63555	0.0547931
$892$	−19.3963	−0.649436
$893$	−7.39738	−0.247544
$894$	−4.60262	−0.153935
$895$	−47.7871	−1.59735
$896$	4.03293	0.134731
$897$	−15.5027	−0.517621
$898$	29.7727	0.993529
$899$	−10.9684	−0.365815
$900$	3.03293	0.101098
$901$	−6.03293	−0.200986
$902$	1.41831	0.0472247
$903$	−22.0593	−0.734088
$904$	4.33697	0.144246
$905$	15.6146	0.519048
$906$	−8.72890	−0.289998
$907$	36.8026	1.22201	0.611005	−	0.791627i	$-0.290765\pi$
$907$	36.8026	1.22201	0.611005	+	0.791627i	$0.290765\pi$
$908$	10.2436	0.339947
$909$	−0.894653	−0.0296738
$910$	−32.3963	−1.07393
$911$	−7.21178	−0.238937	−0.119468	−	0.992838i	$-0.538119\pi$
$911$	−7.21178	−0.238937	−0.119468	+	0.992838i	$0.538119\pi$
$912$	−1.00000	−0.0331133
$913$	−12.9749	−0.429407
$914$	−15.3843	−0.508867
$915$	−35.7937	−1.18330
$916$	−29.3843	−0.970884
$917$	−58.2809	−1.92461
$918$	6.03293	0.199117
$919$	−15.9341	−0.525618	−0.262809	−	0.964848i	$-0.584649\pi$
$919$	−15.9341	−0.525618	−0.262809	+	0.964848i	$0.584649\pi$
$920$	15.5027	0.511110
$921$	0.768374	0.0253188
$922$	−27.6949	−0.912082
$923$	4.54221	0.149509
$924$	6.59607	0.216995
$925$	11.0264	0.362545
$926$	7.40939	0.243488
$927$	3.36445	0.110503
$928$	8.62901	0.283261
$929$	20.2162	0.663270	0.331635	−	0.943408i	$-0.392400\pi$
$929$	20.2162	0.663270	0.331635	+	0.943408i	$0.392400\pi$
$930$	−3.60262	−0.118134
$931$	9.26456	0.303634
$932$	−6.07787	−0.199087
$933$	−5.76075	−0.188598
$934$	−39.5686	−1.29472
$935$	−27.9660	−0.914585
$936$	−2.83424	−0.0926401
$937$	39.2604	1.28258	0.641291	−	0.767298i	$-0.278399\pi$
$937$	39.2604	1.28258	0.641291	+	0.767298i	$0.278399\pi$
$938$	3.09880	0.101180
$939$	−17.9594	−0.586084
$940$	20.9660	0.683835
$941$	7.30096	0.238005	0.119002	−	0.992894i	$-0.462030\pi$
$941$	7.30096	0.238005	0.119002	+	0.992894i	$0.462030\pi$
$942$	−5.83424	−0.190090
$943$	−4.74328	−0.154463
$944$	11.3579	0.369668
$945$	−11.4303	−0.371828
$946$	8.94613	0.290864
$947$	37.9420	1.23295	0.616474	−	0.787375i	$-0.288560\pi$
$947$	37.9420	1.23295	0.616474	+	0.787375i	$0.288560\pi$
$948$	12.4094	0.403038
$949$	−2.15921	−0.0700910
$950$	−3.03293	−0.0984014
$951$	−16.7553	−0.543327
$952$	24.3304	0.788554
$953$	36.6279	1.18649	0.593247	−	0.805020i	$-0.297846\pi$
$953$	36.6279	1.18649	0.593247	+	0.805020i	$0.297846\pi$
$954$	1.00000	0.0323762
$955$	−65.5610	−2.12150
$956$	0.436861	0.0141291
$957$	14.1132	0.456215
$958$	−15.5697	−0.503034
$959$	−66.5060	−2.14759
$960$	2.83424	0.0914748
$961$	−29.3843	−0.947880
$962$	−10.3040	−0.332216
$963$	7.16576	0.230913
$964$	−19.1581	−0.617042
$965$	−48.1976	−1.55154
$966$	−22.0593	−0.709747
$967$	40.6663	1.30774	0.653870	−	0.756607i	$-0.273144\pi$
$967$	40.6663	1.30774	0.653870	+	0.756607i	$0.273144\pi$
$968$	8.32497	0.267575
$969$	−6.03293	−0.193806
$970$	−25.9001	−0.831602
$971$	20.5991	0.661058	0.330529	−	0.943796i	$-0.392773\pi$
$971$	20.5991	0.661058	0.330529	+	0.943796i	$0.392773\pi$
$972$	−1.00000	−0.0320750
$973$	−66.5280	−2.13279
$974$	−32.2371	−1.03294
$975$	−8.59607	−0.275295
$976$	−12.6290	−0.404245
$977$	34.9869	1.11933	0.559665	−	0.828719i	$-0.310930\pi$
$977$	34.9869	1.11933	0.559665	+	0.828719i	$0.310930\pi$
$978$	−5.33697	−0.170658
$979$	−14.2316	−0.454845
$980$	−26.2580	−0.838782
$981$	10.8277	0.345702
$982$	27.9529	0.892013
$983$	43.2789	1.38038	0.690192	−	0.723626i	$-0.257526\pi$
$983$	43.2789	1.38038	0.690192	+	0.723626i	$0.257526\pi$
$984$	−0.867178	−0.0276446
$985$	6.53020	0.208070
$986$	52.0582	1.65787
$987$	−29.8332	−0.949600
$988$	2.83424	0.0901693
$989$	−29.9187	−0.951358
$990$	4.63555	0.147328
$991$	−3.91211	−0.124272	−0.0621362	−	0.998068i	$-0.519791\pi$
$991$	−3.91211	−0.124272	−0.0621362	+	0.998068i	$0.519791\pi$
$992$	−1.27110	−0.0403576
$993$	18.7937	0.596399
$994$	6.46325	0.205002
$995$	−15.7333	−0.498778
$996$	7.93305	0.251368
$997$	33.4622	1.05976	0.529879	−	0.848073i	$-0.322237\pi$
$997$	33.4622	1.05976	0.529879	+	0.848073i	$0.322237\pi$
$998$	21.2515	0.672704
$999$	−3.63555	−0.115024

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.q.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.q.1.1	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.83424 q^{5} +1.00000 q^{6} -4.03293 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.83424 q^{5} +1.00000 q^{6} -4.03293 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.83424 q^{10} +1.63555 q^{11} -1.00000 q^{12} +2.83424 q^{13} +4.03293 q^{14} +2.83424 q^{15} +1.00000 q^{16} +6.03293 q^{17} -1.00000 q^{18} +1.00000 q^{19} -2.83424 q^{20} +4.03293 q^{21} -1.63555 q^{22} +5.46980 q^{23} +1.00000 q^{24} +3.03293 q^{25} -2.83424 q^{26} -1.00000 q^{27} -4.03293 q^{28} -8.62901 q^{29} -2.83424 q^{30} +1.27110 q^{31} -1.00000 q^{32} -1.63555 q^{33} -6.03293 q^{34} +11.4303 q^{35} +1.00000 q^{36} +3.63555 q^{37} -1.00000 q^{38} -2.83424 q^{39} +2.83424 q^{40} -0.867178 q^{41} -4.03293 q^{42} -5.46980 q^{43} +1.63555 q^{44} -2.83424 q^{45} -5.46980 q^{46} -7.39738 q^{47} -1.00000 q^{48} +9.26456 q^{49} -3.03293 q^{50} -6.03293 q^{51} +2.83424 q^{52} -1.00000 q^{53} +1.00000 q^{54} -4.63555 q^{55} +4.03293 q^{56} -1.00000 q^{57} +8.62901 q^{58} +11.3579 q^{59} +2.83424 q^{60} -12.6290 q^{61} -1.27110 q^{62} -4.03293 q^{63} +1.00000 q^{64} -8.03293 q^{65} +1.63555 q^{66} +0.768374 q^{67} +6.03293 q^{68} -5.46980 q^{69} -11.4303 q^{70} +1.60262 q^{71} -1.00000 q^{72} -0.761831 q^{73} -3.63555 q^{74} -3.03293 q^{75} +1.00000 q^{76} -6.59607 q^{77} +2.83424 q^{78} -12.4094 q^{79} -2.83424 q^{80} +1.00000 q^{81} +0.867178 q^{82} -7.93305 q^{83} +4.03293 q^{84} -17.0988 q^{85} +5.46980 q^{86} +8.62901 q^{87} -1.63555 q^{88} -8.70142 q^{89} +2.83424 q^{90} -11.4303 q^{91} +5.46980 q^{92} -1.27110 q^{93} +7.39738 q^{94} -2.83424 q^{95} +1.00000 q^{96} -9.13828 q^{97} -9.26456 q^{98} +1.63555 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 5 q^{11} - 3 q^{12} + 3 q^{13} + q^{14} + 3 q^{15} + 3 q^{16} + 7 q^{17} - 3 q^{18} + 3 q^{19} - 3 q^{20} + q^{21} - 5 q^{22} + 11 q^{23} + 3 q^{24} - 2 q^{25} - 3 q^{26} - 3 q^{27} - q^{28} + 2 q^{29} - 3 q^{30} + 4 q^{31} - 3 q^{32} - 5 q^{33} - 7 q^{34} + 12 q^{35} + 3 q^{36} + 11 q^{37} - 3 q^{38} - 3 q^{39} + 3 q^{40} + 14 q^{41} - q^{42} - 11 q^{43} + 5 q^{44} - 3 q^{45} - 11 q^{46} - 11 q^{47} - 3 q^{48} + 2 q^{50} - 7 q^{51} + 3 q^{52} - 3 q^{53} + 3 q^{54} - 14 q^{55} + q^{56} - 3 q^{57} - 2 q^{58} + 6 q^{59} + 3 q^{60} - 10 q^{61} - 4 q^{62} - q^{63} + 3 q^{64} - 13 q^{65} + 5 q^{66} + 19 q^{67} + 7 q^{68} - 11 q^{69} - 12 q^{70} + 16 q^{71} - 3 q^{72} + 9 q^{73} - 11 q^{74} + 2 q^{75} + 3 q^{76} - 3 q^{77} + 3 q^{78} - 21 q^{79} - 3 q^{80} + 3 q^{81} - 14 q^{82} + 15 q^{83} + q^{84} - 18 q^{85} + 11 q^{86} - 2 q^{87} - 5 q^{88} - 4 q^{89} + 3 q^{90} - 12 q^{91} + 11 q^{92} - 4 q^{93} + 11 q^{94} - 3 q^{95} + 3 q^{96} - 11 q^{97} + 5 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 5 * q^11 - 3 * q^12 + 3 * q^13 + q^14 + 3 * q^15 + 3 * q^16 + 7 * q^17 - 3 * q^18 + 3 * q^19 - 3 * q^20 + q^21 - 5 * q^22 + 11 * q^23 + 3 * q^24 - 2 * q^25 - 3 * q^26 - 3 * q^27 - q^28 + 2 * q^29 - 3 * q^30 + 4 * q^31 - 3 * q^32 - 5 * q^33 - 7 * q^34 + 12 * q^35 + 3 * q^36 + 11 * q^37 - 3 * q^38 - 3 * q^39 + 3 * q^40 + 14 * q^41 - q^42 - 11 * q^43 + 5 * q^44 - 3 * q^45 - 11 * q^46 - 11 * q^47 - 3 * q^48 + 2 * q^50 - 7 * q^51 + 3 * q^52 - 3 * q^53 + 3 * q^54 - 14 * q^55 + q^56 - 3 * q^57 - 2 * q^58 + 6 * q^59 + 3 * q^60 - 10 * q^61 - 4 * q^62 - q^63 + 3 * q^64 - 13 * q^65 + 5 * q^66 + 19 * q^67 + 7 * q^68 - 11 * q^69 - 12 * q^70 + 16 * q^71 - 3 * q^72 + 9 * q^73 - 11 * q^74 + 2 * q^75 + 3 * q^76 - 3 * q^77 + 3 * q^78 - 21 * q^79 - 3 * q^80 + 3 * q^81 - 14 * q^82 + 15 * q^83 + q^84 - 18 * q^85 + 11 * q^86 - 2 * q^87 - 5 * q^88 - 4 * q^89 + 3 * q^90 - 12 * q^91 + 11 * q^92 - 4 * q^93 + 11 * q^94 - 3 * q^95 + 3 * q^96 - 11 * q^97 + 5 * q^99

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