LMFDB - Embedded newform 4002.2.a.be.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4002,2,Mod(1,4002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4002, 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("4002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4002 = 2 \cdot 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4002.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:	$31.9561308889$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.2389280.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 11x^{3} + 7x^{2} + 26x - 18 $ x^5 - x^4 - 11x^3 + 7x^2 + 26*x - 18
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$3.13869$ of defining polynomial
Character	$\chi$	$=$	4002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.53070 q^{5} +1.00000 q^{6} -0.614480 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.53070 q^{5} +1.00000 q^{6} -0.614480 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.53070 q^{10} +0.607988 q^{11} -1.00000 q^{12} -5.13869 q^{13} +0.614480 q^{14} -3.53070 q^{15} +1.00000 q^{16} -4.89186 q^{17} -1.00000 q^{18} +4.89186 q^{19} +3.53070 q^{20} +0.614480 q^{21} -0.607988 q^{22} -1.00000 q^{23} +1.00000 q^{24} +7.46585 q^{25} +5.13869 q^{26} -1.00000 q^{27} -0.614480 q^{28} -1.00000 q^{29} +3.53070 q^{30} -0.273696 q^{31} -1.00000 q^{32} -0.607988 q^{33} +4.89186 q^{34} -2.16954 q^{35} +1.00000 q^{36} -5.09540 q^{37} -4.89186 q^{38} +5.13869 q^{39} -3.53070 q^{40} +5.34872 q^{41} -0.614480 q^{42} -1.78997 q^{43} +0.607988 q^{44} +3.53070 q^{45} +1.00000 q^{46} -11.4953 q^{47} -1.00000 q^{48} -6.62241 q^{49} -7.46585 q^{50} +4.89186 q^{51} -5.13869 q^{52} +1.81684 q^{53} +1.00000 q^{54} +2.14663 q^{55} +0.614480 q^{56} -4.89186 q^{57} +1.00000 q^{58} -2.87293 q^{59} -3.53070 q^{60} +12.9700 q^{61} +0.273696 q^{62} -0.614480 q^{63} +1.00000 q^{64} -18.1432 q^{65} +0.607988 q^{66} -11.7945 q^{67} -4.89186 q^{68} +1.00000 q^{69} +2.16954 q^{70} -7.92271 q^{71} -1.00000 q^{72} -6.01561 q^{73} +5.09540 q^{74} -7.46585 q^{75} +4.89186 q^{76} -0.373596 q^{77} -5.13869 q^{78} +0.712684 q^{79} +3.53070 q^{80} +1.00000 q^{81} -5.34872 q^{82} -12.8507 q^{83} +0.614480 q^{84} -17.2717 q^{85} +1.78997 q^{86} +1.00000 q^{87} -0.607988 q^{88} +13.0889 q^{89} -3.53070 q^{90} +3.15762 q^{91} -1.00000 q^{92} +0.273696 q^{93} +11.4953 q^{94} +17.2717 q^{95} +1.00000 q^{96} -5.81684 q^{97} +6.62241 q^{98} +0.607988 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} + 5 q^{6} - 4 q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 + 5 * q^6 - 4 * q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} + 5 q^{6} - 4 q^{7} - 5 q^{8} + 5 q^{9} - q^{10} + 5 q^{11} - 5 q^{12} - 11 q^{13} + 4 q^{14} - q^{15} + 5 q^{16} + 4 q^{17} - 5 q^{18} - 4 q^{19} + q^{20} + 4 q^{21} - 5 q^{22} - 5 q^{23} + 5 q^{24} + 12 q^{25} + 11 q^{26} - 5 q^{27} - 4 q^{28} - 5 q^{29} + q^{30} + 5 q^{31} - 5 q^{32} - 5 q^{33} - 4 q^{34} - 6 q^{35} + 5 q^{36} + 9 q^{37} + 4 q^{38} + 11 q^{39} - q^{40} + 5 q^{41} - 4 q^{42} - 16 q^{43} + 5 q^{44} + q^{45} + 5 q^{46} + 8 q^{47} - 5 q^{48} - 5 q^{49} - 12 q^{50} - 4 q^{51} - 11 q^{52} - 4 q^{53} + 5 q^{54} - 33 q^{55} + 4 q^{56} + 4 q^{57} + 5 q^{58} + 23 q^{59} - q^{60} + 7 q^{61} - 5 q^{62} - 4 q^{63} + 5 q^{64} - 5 q^{65} + 5 q^{66} + 5 q^{67} + 4 q^{68} + 5 q^{69} + 6 q^{70} - 21 q^{71} - 5 q^{72} - 8 q^{73} - 9 q^{74} - 12 q^{75} - 4 q^{76} - 11 q^{78} - 8 q^{79} + q^{80} + 5 q^{81} - 5 q^{82} - 18 q^{83} + 4 q^{84} - 10 q^{85} + 16 q^{86} + 5 q^{87} - 5 q^{88} + 32 q^{89} - q^{90} + 10 q^{91} - 5 q^{92} - 5 q^{93} - 8 q^{94} + 10 q^{95} + 5 q^{96} - 16 q^{97} + 5 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 + 5 * q^6 - 4 * q^7 - 5 * q^8 + 5 * q^9 - q^10 + 5 * q^11 - 5 * q^12 - 11 * q^13 + 4 * q^14 - q^15 + 5 * q^16 + 4 * q^17 - 5 * q^18 - 4 * q^19 + q^20 + 4 * q^21 - 5 * q^22 - 5 * q^23 + 5 * q^24 + 12 * q^25 + 11 * q^26 - 5 * q^27 - 4 * q^28 - 5 * q^29 + q^30 + 5 * q^31 - 5 * q^32 - 5 * q^33 - 4 * q^34 - 6 * q^35 + 5 * q^36 + 9 * q^37 + 4 * q^38 + 11 * q^39 - q^40 + 5 * q^41 - 4 * q^42 - 16 * q^43 + 5 * q^44 + q^45 + 5 * q^46 + 8 * q^47 - 5 * q^48 - 5 * q^49 - 12 * q^50 - 4 * q^51 - 11 * q^52 - 4 * q^53 + 5 * q^54 - 33 * q^55 + 4 * q^56 + 4 * q^57 + 5 * q^58 + 23 * q^59 - q^60 + 7 * q^61 - 5 * q^62 - 4 * q^63 + 5 * q^64 - 5 * q^65 + 5 * q^66 + 5 * q^67 + 4 * q^68 + 5 * q^69 + 6 * q^70 - 21 * q^71 - 5 * q^72 - 8 * q^73 - 9 * q^74 - 12 * q^75 - 4 * q^76 - 11 * q^78 - 8 * q^79 + q^80 + 5 * q^81 - 5 * q^82 - 18 * q^83 + 4 * q^84 - 10 * q^85 + 16 * q^86 + 5 * q^87 - 5 * q^88 + 32 * q^89 - q^90 + 10 * q^91 - 5 * q^92 - 5 * q^93 - 8 * q^94 + 10 * q^95 + 5 * q^96 - 16 * q^97 + 5 * q^98 + 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
$5$	3.53070	1.57898	0.789489	−	0.613765i	$-0.210346\pi$
$5$	3.53070	1.57898	0.789489	+	0.613765i	$0.210346\pi$
$6$	1.00000	0.408248
$7$	−0.614480	−0.232251	−0.116126	−	0.993235i	$-0.537048\pi$
$7$	−0.614480	−0.232251	−0.116126	+	0.993235i	$0.537048\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.53070	−1.11651
$11$	0.607988	0.183315	0.0916577	−	0.995791i	$-0.470783\pi$
$11$	0.607988	0.183315	0.0916577	+	0.995791i	$0.470783\pi$
$12$	−1.00000	−0.288675
$13$	−5.13869	−1.42522	−0.712608	−	0.701562i	$-0.752486\pi$
$13$	−5.13869	−1.42522	−0.712608	+	0.701562i	$0.752486\pi$
$14$	0.614480	0.164227
$15$	−3.53070	−0.911623
$16$	1.00000	0.250000
$17$	−4.89186	−1.18645	−0.593225	−	0.805037i	$-0.702146\pi$
$17$	−4.89186	−1.18645	−0.593225	+	0.805037i	$0.702146\pi$
$18$	−1.00000	−0.235702
$19$	4.89186	1.12227	0.561135	−	0.827724i	$-0.310365\pi$
$19$	4.89186	1.12227	0.561135	+	0.827724i	$0.310365\pi$
$20$	3.53070	0.789489
$21$	0.614480	0.134090
$22$	−0.607988	−0.129624
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.00000	0.204124
$25$	7.46585	1.49317
$26$	5.13869	1.00778
$27$	−1.00000	−0.192450
$28$	−0.614480	−0.116126
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	3.53070	0.644615
$31$	−0.273696	−0.0491572	−0.0245786	−	0.999698i	$-0.507824\pi$
$31$	−0.273696	−0.0491572	−0.0245786	+	0.999698i	$0.507824\pi$
$32$	−1.00000	−0.176777
$33$	−0.607988	−0.105837
$34$	4.89186	0.838947
$35$	−2.16954	−0.366720
$36$	1.00000	0.166667
$37$	−5.09540	−0.837678	−0.418839	−	0.908060i	$-0.637563\pi$
$37$	−5.09540	−0.837678	−0.418839	+	0.908060i	$0.637563\pi$
$38$	−4.89186	−0.793564
$39$	5.13869	0.822849
$40$	−3.53070	−0.558253
$41$	5.34872	0.835330	0.417665	−	0.908601i	$-0.362849\pi$
$41$	5.34872	0.835330	0.417665	+	0.908601i	$0.362849\pi$
$42$	−0.614480	−0.0948163
$43$	−1.78997	−0.272968	−0.136484	−	0.990642i	$-0.543580\pi$
$43$	−1.78997	−0.272968	−0.136484	+	0.990642i	$0.543580\pi$
$44$	0.607988	0.0916577
$45$	3.53070	0.526326
$46$	1.00000	0.147442
$47$	−11.4953	−1.67677	−0.838384	−	0.545080i	$-0.816499\pi$
$47$	−11.4953	−1.67677	−0.838384	+	0.545080i	$0.816499\pi$
$48$	−1.00000	−0.144338
$49$	−6.62241	−0.946059
$50$	−7.46585	−1.05583
$51$	4.89186	0.684997
$52$	−5.13869	−0.712608
$53$	1.81684	0.249562	0.124781	−	0.992184i	$-0.460177\pi$
$53$	1.81684	0.249562	0.124781	+	0.992184i	$0.460177\pi$
$54$	1.00000	0.136083
$55$	2.14663	0.289451
$56$	0.614480	0.0821133
$57$	−4.89186	−0.647943
$58$	1.00000	0.131306
$59$	−2.87293	−0.374024	−0.187012	−	0.982358i	$-0.559880\pi$
$59$	−2.87293	−0.374024	−0.187012	+	0.982358i	$0.559880\pi$
$60$	−3.53070	−0.455812
$61$	12.9700	1.66063	0.830316	−	0.557293i	$-0.188160\pi$
$61$	12.9700	1.66063	0.830316	+	0.557293i	$0.188160\pi$
$62$	0.273696	0.0347594
$63$	−0.614480	−0.0774171
$64$	1.00000	0.125000
$65$	−18.1432	−2.25038
$66$	0.607988	0.0748382
$67$	−11.7945	−1.44092	−0.720461	−	0.693495i	$-0.756070\pi$
$67$	−11.7945	−1.44092	−0.720461	+	0.693495i	$0.756070\pi$
$68$	−4.89186	−0.593225
$69$	1.00000	0.120386
$70$	2.16954	0.259310
$71$	−7.92271	−0.940253	−0.470127	−	0.882599i	$-0.655792\pi$
$71$	−7.92271	−0.940253	−0.470127	+	0.882599i	$0.655792\pi$
$72$	−1.00000	−0.117851
$73$	−6.01561	−0.704074	−0.352037	−	0.935986i	$-0.614511\pi$
$73$	−6.01561	−0.704074	−0.352037	+	0.935986i	$0.614511\pi$
$74$	5.09540	0.592328
$75$	−7.46585	−0.862083
$76$	4.89186	0.561135
$77$	−0.373596	−0.0425753
$78$	−5.13869	−0.581842
$79$	0.712684	0.0801832	0.0400916	−	0.999196i	$-0.487235\pi$
$79$	0.712684	0.0801832	0.0400916	+	0.999196i	$0.487235\pi$
$80$	3.53070	0.394744
$81$	1.00000	0.111111
$82$	−5.34872	−0.590667
$83$	−12.8507	−1.41055	−0.705276	−	0.708933i	$-0.749177\pi$
$83$	−12.8507	−1.41055	−0.705276	+	0.708933i	$0.749177\pi$
$84$	0.614480	0.0670452
$85$	−17.2717	−1.87338
$86$	1.78997	0.193018
$87$	1.00000	0.107211
$88$	−0.607988	−0.0648118
$89$	13.0889	1.38742	0.693711	−	0.720254i	$-0.255975\pi$
$89$	13.0889	1.38742	0.693711	+	0.720254i	$0.255975\pi$
$90$	−3.53070	−0.372169
$91$	3.15762	0.331008
$92$	−1.00000	−0.104257
$93$	0.273696	0.0283809
$94$	11.4953	1.18565
$95$	17.2717	1.77204
$96$	1.00000	0.102062
$97$	−5.81684	−0.590610	−0.295305	−	0.955403i	$-0.595421\pi$
$97$	−5.81684	−0.590610	−0.295305	+	0.955403i	$0.595421\pi$
$98$	6.62241	0.668965
$99$	0.607988	0.0611051
$100$	7.46585	0.746585
$101$	−10.9403	−1.08860	−0.544299	−	0.838891i	$-0.683204\pi$
$101$	−10.9403	−1.08860	−0.544299	+	0.838891i	$0.683204\pi$
$102$	−4.89186	−0.484366
$103$	−1.01643	−0.100152	−0.0500758	−	0.998745i	$-0.515946\pi$
$103$	−1.01643	−0.100152	−0.0500758	+	0.998745i	$0.515946\pi$
$104$	5.13869	0.503890
$105$	2.16954	0.211726
$106$	−1.81684	−0.176467
$107$	−12.7064	−1.22838	−0.614189	−	0.789159i	$-0.710517\pi$
$107$	−12.7064	−1.22838	−0.614189	+	0.789159i	$0.710517\pi$
$108$	−1.00000	−0.0962250
$109$	0.0431107	0.00412925	0.00206463	−	0.999998i	$-0.499343\pi$
$109$	0.0431107	0.00412925	0.00206463	+	0.999998i	$0.499343\pi$
$110$	−2.14663	−0.204673
$111$	5.09540	0.483634
$112$	−0.614480	−0.0580629
$113$	12.5541	1.18099	0.590496	−	0.807040i	$-0.298932\pi$
$113$	12.5541	1.18099	0.590496	+	0.807040i	$0.298932\pi$
$114$	4.89186	0.458165
$115$	−3.53070	−0.329240
$116$	−1.00000	−0.0928477
$117$	−5.13869	−0.475072
$118$	2.87293	0.264475
$119$	3.00595	0.275555
$120$	3.53070	0.322307
$121$	−10.6304	−0.966395
$122$	−12.9700	−1.17424
$123$	−5.34872	−0.482278
$124$	−0.273696	−0.0245786
$125$	8.70619	0.778706
$126$	0.614480	0.0547422
$127$	−2.60917	−0.231526	−0.115763	−	0.993277i	$-0.536931\pi$
$127$	−2.60917	−0.231526	−0.115763	+	0.993277i	$0.536931\pi$
$128$	−1.00000	−0.0883883
$129$	1.78997	0.157598
$130$	18.1432	1.59126
$131$	−5.35403	−0.467784	−0.233892	−	0.972263i	$-0.575146\pi$
$131$	−5.35403	−0.467784	−0.233892	+	0.972263i	$0.575146\pi$
$132$	−0.607988	−0.0529186
$133$	−3.00595	−0.260649
$134$	11.7945	1.01889
$135$	−3.53070	−0.303874
$136$	4.89186	0.419473
$137$	12.1503	1.03807	0.519035	−	0.854753i	$-0.326291\pi$
$137$	12.1503	1.03807	0.519035	+	0.854753i	$0.326291\pi$
$138$	−1.00000	−0.0851257
$139$	−7.67652	−0.651114	−0.325557	−	0.945522i	$-0.605552\pi$
$139$	−7.67652	−0.651114	−0.325557	+	0.945522i	$0.605552\pi$
$140$	−2.16954	−0.183360
$141$	11.4953	0.968083
$142$	7.92271	0.664859
$143$	−3.12426	−0.261264
$144$	1.00000	0.0833333
$145$	−3.53070	−0.293209
$146$	6.01561	0.497855
$147$	6.62241	0.546208
$148$	−5.09540	−0.418839
$149$	12.9587	1.06162	0.530809	−	0.847492i	$-0.321888\pi$
$149$	12.9587	1.06162	0.530809	+	0.847492i	$0.321888\pi$
$150$	7.46585	0.609584
$151$	2.37558	0.193322	0.0966612	−	0.995317i	$-0.469184\pi$
$151$	2.37558	0.193322	0.0966612	+	0.995317i	$0.469184\pi$
$152$	−4.89186	−0.396782
$153$	−4.89186	−0.395483
$154$	0.373596	0.0301053
$155$	−0.966339	−0.0776182
$156$	5.13869	0.411424
$157$	20.0757	1.60222	0.801108	−	0.598520i	$-0.204244\pi$
$157$	20.0757	1.60222	0.801108	+	0.598520i	$0.204244\pi$
$158$	−0.712684	−0.0566981
$159$	−1.81684	−0.144084
$160$	−3.53070	−0.279126
$161$	0.614480	0.0484278
$162$	−1.00000	−0.0785674
$163$	17.0816	1.33793	0.668967	−	0.743292i	$-0.266737\pi$
$163$	17.0816	1.33793	0.668967	+	0.743292i	$0.266737\pi$
$164$	5.34872	0.417665
$165$	−2.14663	−0.167115
$166$	12.8507	0.997411
$167$	21.0475	1.62870	0.814351	−	0.580372i	$-0.197093\pi$
$167$	21.0475	1.62870	0.814351	+	0.580372i	$0.197093\pi$
$168$	−0.614480	−0.0474081
$169$	13.4061	1.03124
$170$	17.2717	1.32468
$171$	4.89186	0.374090
$172$	−1.78997	−0.136484
$173$	5.91740	0.449892	0.224946	−	0.974371i	$-0.427779\pi$
$173$	5.91740	0.449892	0.224946	+	0.974371i	$0.427779\pi$
$174$	−1.00000	−0.0758098
$175$	−4.58761	−0.346791
$176$	0.607988	0.0458288
$177$	2.87293	0.215943
$178$	−13.0889	−0.981055
$179$	22.0310	1.64667	0.823336	−	0.567554i	$-0.192110\pi$
$179$	22.0310	1.64667	0.823336	+	0.567554i	$0.192110\pi$
$180$	3.53070	0.263163
$181$	−13.2542	−0.985177	−0.492588	−	0.870262i	$-0.663949\pi$
$181$	−13.2542	−0.985177	−0.492588	+	0.870262i	$0.663949\pi$
$182$	−3.15762	−0.234058
$183$	−12.9700	−0.958766
$184$	1.00000	0.0737210
$185$	−17.9903	−1.32268
$186$	−0.273696	−0.0200684
$187$	−2.97419	−0.217495
$188$	−11.4953	−0.838384
$189$	0.614480	0.0446968
$190$	−17.2717	−1.25302
$191$	−19.0549	−1.37877	−0.689383	−	0.724398i	$-0.742118\pi$
$191$	−19.0549	−1.37877	−0.689383	+	0.724398i	$0.742118\pi$
$192$	−1.00000	−0.0721688
$193$	−8.39147	−0.604031	−0.302016	−	0.953303i	$-0.597659\pi$
$193$	−8.39147	−0.604031	−0.302016	+	0.953303i	$0.597659\pi$
$194$	5.81684	0.417624
$195$	18.1432	1.29926
$196$	−6.62241	−0.473030
$197$	−22.0222	−1.56902	−0.784510	−	0.620116i	$-0.787085\pi$
$197$	−22.0222	−1.56902	−0.784510	+	0.620116i	$0.787085\pi$
$198$	−0.607988	−0.0432078
$199$	−21.8887	−1.55165	−0.775824	−	0.630950i	$-0.782665\pi$
$199$	−21.8887	−1.55165	−0.775824	+	0.630950i	$0.782665\pi$
$200$	−7.46585	−0.527916
$201$	11.7945	0.831917
$202$	10.9403	0.769755
$203$	0.614480	0.0431280
$204$	4.89186	0.342499
$205$	18.8847	1.31897
$206$	1.01643	0.0708179
$207$	−1.00000	−0.0695048
$208$	−5.13869	−0.356304
$209$	2.97419	0.205729
$210$	−2.16954	−0.149713
$211$	−2.97950	−0.205117	−0.102559	−	0.994727i	$-0.532703\pi$
$211$	−2.97950	−0.205117	−0.102559	+	0.994727i	$0.532703\pi$
$212$	1.81684	0.124781
$213$	7.92271	0.542855
$214$	12.7064	0.868594
$215$	−6.31985	−0.431010
$216$	1.00000	0.0680414
$217$	0.168181	0.0114168
$218$	−0.0431107	−0.00291982
$219$	6.01561	0.406497
$220$	2.14663	0.144725
$221$	25.1377	1.69095
$222$	−5.09540	−0.341981
$223$	−9.51458	−0.637143	−0.318572	−	0.947899i	$-0.603203\pi$
$223$	−9.51458	−0.637143	−0.318572	+	0.947899i	$0.603203\pi$
$224$	0.614480	0.0410566
$225$	7.46585	0.497724
$226$	−12.5541	−0.835088
$227$	−1.55081	−0.102931	−0.0514655	−	0.998675i	$-0.516389\pi$
$227$	−1.55081	−0.102931	−0.0514655	+	0.998675i	$0.516389\pi$
$228$	−4.89186	−0.323971
$229$	−16.4316	−1.08583	−0.542914	−	0.839788i	$-0.682679\pi$
$229$	−16.4316	−1.08583	−0.542914	+	0.839788i	$0.682679\pi$
$230$	3.53070	0.232808
$231$	0.373596	0.0245808
$232$	1.00000	0.0656532
$233$	−4.59050	−0.300734	−0.150367	−	0.988630i	$-0.548045\pi$
$233$	−4.59050	−0.300734	−0.150367	+	0.988630i	$0.548045\pi$
$234$	5.13869	0.335927
$235$	−40.5866	−2.64758
$236$	−2.87293	−0.187012
$237$	−0.712684	−0.0462938
$238$	−3.00595	−0.194847
$239$	−23.5054	−1.52044	−0.760219	−	0.649667i	$-0.774908\pi$
$239$	−23.5054	−1.52044	−0.760219	+	0.649667i	$0.774908\pi$
$240$	−3.53070	−0.227906
$241$	−15.9841	−1.02963	−0.514814	−	0.857302i	$-0.672139\pi$
$241$	−15.9841	−1.02963	−0.514814	+	0.857302i	$0.672139\pi$
$242$	10.6304	0.683345
$243$	−1.00000	−0.0641500
$244$	12.9700	0.830316
$245$	−23.3818	−1.49381
$246$	5.34872	0.341022
$247$	−25.1377	−1.59948
$248$	0.273696	0.0173797
$249$	12.8507	0.814382
$250$	−8.70619	−0.550628
$251$	28.3752	1.79103	0.895513	−	0.445036i	$-0.146809\pi$
$251$	28.3752	1.79103	0.895513	+	0.445036i	$0.146809\pi$
$252$	−0.614480	−0.0387086
$253$	−0.607988	−0.0382239
$254$	2.60917	0.163714
$255$	17.2717	1.08160
$256$	1.00000	0.0625000
$257$	29.2724	1.82597	0.912983	−	0.407999i	$-0.133773\pi$
$257$	29.2724	1.82597	0.912983	+	0.407999i	$0.133773\pi$
$258$	−1.78997	−0.111439
$259$	3.13102	0.194552
$260$	−18.1432	−1.12519
$261$	−1.00000	−0.0618984
$262$	5.35403	0.330773
$263$	9.93539	0.612642	0.306321	−	0.951928i	$-0.400902\pi$
$263$	9.93539	0.612642	0.306321	+	0.951928i	$0.400902\pi$
$264$	0.607988	0.0374191
$265$	6.41471	0.394052
$266$	3.00595	0.184306
$267$	−13.0889	−0.801028
$268$	−11.7945	−0.720461
$269$	−17.7327	−1.08118	−0.540590	−	0.841286i	$-0.681799\pi$
$269$	−17.7327	−1.08118	−0.540590	+	0.841286i	$0.681799\pi$
$270$	3.53070	0.214872
$271$	−15.1509	−0.920354	−0.460177	−	0.887827i	$-0.652214\pi$
$271$	−15.1509	−0.920354	−0.460177	+	0.887827i	$0.652214\pi$
$272$	−4.89186	−0.296613
$273$	−3.15762	−0.191108
$274$	−12.1503	−0.734027
$275$	4.53915	0.273721
$276$	1.00000	0.0601929
$277$	−23.4648	−1.40986	−0.704931	−	0.709275i	$-0.749022\pi$
$277$	−23.4648	−1.40986	−0.704931	+	0.709275i	$0.749022\pi$
$278$	7.67652	0.460407
$279$	−0.273696	−0.0163857
$280$	2.16954	0.129655
$281$	13.7591	0.820799	0.410400	−	0.911906i	$-0.365389\pi$
$281$	13.7591	0.820799	0.410400	+	0.911906i	$0.365389\pi$
$282$	−11.4953	−0.684538
$283$	−21.6445	−1.28663	−0.643316	−	0.765600i	$-0.722442\pi$
$283$	−21.6445	−1.28663	−0.643316	+	0.765600i	$0.722442\pi$
$284$	−7.92271	−0.470127
$285$	−17.2717	−1.02309
$286$	3.12426	0.184742
$287$	−3.28668	−0.194006
$288$	−1.00000	−0.0589256
$289$	6.93029	0.407664
$290$	3.53070	0.207330
$291$	5.81684	0.340989
$292$	−6.01561	−0.352037
$293$	2.54450	0.148651	0.0743257	−	0.997234i	$-0.476320\pi$
$293$	2.54450	0.148651	0.0743257	+	0.997234i	$0.476320\pi$
$294$	−6.62241	−0.386227
$295$	−10.1435	−0.590575
$296$	5.09540	0.296164
$297$	−0.607988	−0.0352791
$298$	−12.9587	−0.750677
$299$	5.13869	0.297178
$300$	−7.46585	−0.431041
$301$	1.09990	0.0633972
$302$	−2.37558	−0.136700
$303$	10.9403	0.628503
$304$	4.89186	0.280567
$305$	45.7930	2.62210
$306$	4.89186	0.279649
$307$	−22.7296	−1.29725	−0.648624	−	0.761109i	$-0.724655\pi$
$307$	−22.7296	−1.29725	−0.648624	+	0.761109i	$0.724655\pi$
$308$	−0.373596	−0.0212876
$309$	1.01643	0.0578225
$310$	0.966339	0.0548843
$311$	9.02765	0.511911	0.255955	−	0.966689i	$-0.417610\pi$
$311$	9.02765	0.511911	0.255955	+	0.966689i	$0.417610\pi$
$312$	−5.13869	−0.290921
$313$	−13.2001	−0.746113	−0.373057	−	0.927809i	$-0.621690\pi$
$313$	−13.2001	−0.746113	−0.373057	+	0.927809i	$0.621690\pi$
$314$	−20.0757	−1.13294
$315$	−2.16954	−0.122240
$316$	0.712684	0.0400916
$317$	11.6125	0.652222	0.326111	−	0.945332i	$-0.394262\pi$
$317$	11.6125	0.652222	0.326111	+	0.945332i	$0.394262\pi$
$318$	1.81684	0.101883
$319$	−0.607988	−0.0340408
$320$	3.53070	0.197372
$321$	12.7064	0.709204
$322$	−0.614480	−0.0342436
$323$	−23.9303	−1.33152
$324$	1.00000	0.0555556
$325$	−38.3647	−2.12809
$326$	−17.0816	−0.946062
$327$	−0.0431107	−0.00238402
$328$	−5.34872	−0.295334
$329$	7.06365	0.389432
$330$	2.14663	0.118168
$331$	−8.36260	−0.459650	−0.229825	−	0.973232i	$-0.573815\pi$
$331$	−8.36260	−0.459650	−0.229825	+	0.973232i	$0.573815\pi$
$332$	−12.8507	−0.705276
$333$	−5.09540	−0.279226
$334$	−21.0475	−1.15167
$335$	−41.6427	−2.27518
$336$	0.614480	0.0335226
$337$	25.3392	1.38031	0.690156	−	0.723660i	$-0.257542\pi$
$337$	25.3392	1.38031	0.690156	+	0.723660i	$0.257542\pi$
$338$	−13.4061	−0.729198
$339$	−12.5541	−0.681846
$340$	−17.2717	−0.936689
$341$	−0.166404	−0.00901128
$342$	−4.89186	−0.264521
$343$	8.37070	0.451975
$344$	1.78997	0.0965088
$345$	3.53070	0.190087
$346$	−5.91740	−0.318122
$347$	8.48741	0.455628	0.227814	−	0.973705i	$-0.426842\pi$
$347$	8.48741	0.455628	0.227814	+	0.973705i	$0.426842\pi$
$348$	1.00000	0.0536056
$349$	−29.5570	−1.58215	−0.791075	−	0.611719i	$-0.790478\pi$
$349$	−29.5570	−1.58215	−0.791075	+	0.611719i	$0.790478\pi$
$350$	4.58761	0.245218
$351$	5.13869	0.274283
$352$	−0.607988	−0.0324059
$353$	33.7901	1.79846	0.899232	−	0.437472i	$-0.144126\pi$
$353$	33.7901	1.79846	0.899232	+	0.437472i	$0.144126\pi$
$354$	−2.87293	−0.152694
$355$	−27.9727	−1.48464
$356$	13.0889	0.693711
$357$	−3.00595	−0.159092
$358$	−22.0310	−1.16437
$359$	−22.9516	−1.21134	−0.605669	−	0.795717i	$-0.707094\pi$
$359$	−22.9516	−1.21134	−0.605669	+	0.795717i	$0.707094\pi$
$360$	−3.53070	−0.186084
$361$	4.93029	0.259489
$362$	13.2542	0.696625
$363$	10.6304	0.557949
$364$	3.15762	0.165504
$365$	−21.2393	−1.11172
$366$	12.9700	0.677950
$367$	33.3095	1.73874	0.869372	−	0.494158i	$-0.164524\pi$
$367$	33.3095	1.73874	0.869372	+	0.494158i	$0.164524\pi$
$368$	−1.00000	−0.0521286
$369$	5.34872	0.278443
$370$	17.9903	0.935273
$371$	−1.11641	−0.0579610
$372$	0.273696	0.0141905
$373$	26.3647	1.36511	0.682556	−	0.730833i	$-0.260868\pi$
$373$	26.3647	1.36511	0.682556	+	0.730833i	$0.260868\pi$
$374$	2.97419	0.153792
$375$	−8.70619	−0.449586
$376$	11.4953	0.592827
$377$	5.13869	0.264656
$378$	−0.614480	−0.0316054
$379$	−21.6448	−1.11182	−0.555908	−	0.831244i	$-0.687629\pi$
$379$	−21.6448	−1.11182	−0.555908	+	0.831244i	$0.687629\pi$
$380$	17.2717	0.886019
$381$	2.60917	0.133672
$382$	19.0549	0.974934
$383$	−11.0030	−0.562229	−0.281115	−	0.959674i	$-0.590704\pi$
$383$	−11.0030	−0.562229	−0.281115	+	0.959674i	$0.590704\pi$
$384$	1.00000	0.0510310
$385$	−1.31906	−0.0672254
$386$	8.39147	0.427114
$387$	−1.78997	−0.0909893
$388$	−5.81684	−0.295305
$389$	23.3305	1.18291	0.591453	−	0.806340i	$-0.298555\pi$
$389$	23.3305	1.18291	0.591453	+	0.806340i	$0.298555\pi$
$390$	−18.1432	−0.918716
$391$	4.89186	0.247392
$392$	6.62241	0.334482
$393$	5.35403	0.270075
$394$	22.0222	1.10946
$395$	2.51627	0.126608
$396$	0.607988	0.0305526
$397$	6.09884	0.306092	0.153046	−	0.988219i	$-0.451092\pi$
$397$	6.09884	0.306092	0.153046	+	0.988219i	$0.451092\pi$
$398$	21.8887	1.09718
$399$	3.00595	0.150486
$400$	7.46585	0.373293
$401$	−21.2632	−1.06183	−0.530917	−	0.847424i	$-0.678152\pi$
$401$	−21.2632	−1.06183	−0.530917	+	0.847424i	$0.678152\pi$
$402$	−11.7945	−0.588254
$403$	1.40644	0.0700597
$404$	−10.9403	−0.544299
$405$	3.53070	0.175442
$406$	−0.614480	−0.0304961
$407$	−3.09794	−0.153559
$408$	−4.89186	−0.242183
$409$	−15.1812	−0.750663	−0.375332	−	0.926891i	$-0.622471\pi$
$409$	−15.1812	−0.750663	−0.375332	+	0.926891i	$0.622471\pi$
$410$	−18.8847	−0.932650
$411$	−12.1503	−0.599331
$412$	−1.01643	−0.0500758
$413$	1.76536	0.0868675
$414$	1.00000	0.0491473
$415$	−45.3721	−2.22723
$416$	5.13869	0.251945
$417$	7.67652	0.375921
$418$	−2.97419	−0.145473
$419$	−13.2146	−0.645576	−0.322788	−	0.946471i	$-0.604620\pi$
$419$	−13.2146	−0.645576	−0.322788	+	0.946471i	$0.604620\pi$
$420$	2.16954	0.105863
$421$	−19.6648	−0.958402	−0.479201	−	0.877705i	$-0.659074\pi$
$421$	−19.6648	−0.958402	−0.479201	+	0.877705i	$0.659074\pi$
$422$	2.97950	0.145040
$423$	−11.4953	−0.558923
$424$	−1.81684	−0.0882334
$425$	−36.5219	−1.77157
$426$	−7.92271	−0.383857
$427$	−7.96977	−0.385684
$428$	−12.7064	−0.614189
$429$	3.12426	0.150841
$430$	6.31985	0.304770
$431$	0.429690	0.0206974	0.0103487	−	0.999946i	$-0.496706\pi$
$431$	0.429690	0.0206974	0.0103487	+	0.999946i	$0.496706\pi$
$432$	−1.00000	−0.0481125
$433$	6.61312	0.317806	0.158903	−	0.987294i	$-0.449204\pi$
$433$	6.61312	0.317806	0.158903	+	0.987294i	$0.449204\pi$
$434$	−0.168181	−0.00807292
$435$	3.53070	0.169284
$436$	0.0431107	0.00206463
$437$	−4.89186	−0.234009
$438$	−6.01561	−0.287437
$439$	−1.50559	−0.0718577	−0.0359288	−	0.999354i	$-0.511439\pi$
$439$	−1.50559	−0.0718577	−0.0359288	+	0.999354i	$0.511439\pi$
$440$	−2.14663	−0.102336
$441$	−6.62241	−0.315353
$442$	−25.1377	−1.19568
$443$	−24.0942	−1.14475	−0.572375	−	0.819992i	$-0.693978\pi$
$443$	−24.0942	−1.14475	−0.572375	+	0.819992i	$0.693978\pi$
$444$	5.09540	0.241817
$445$	46.2130	2.19071
$446$	9.51458	0.450528
$447$	−12.9587	−0.612925
$448$	−0.614480	−0.0290314
$449$	30.6301	1.44553	0.722763	−	0.691096i	$-0.242872\pi$
$449$	30.6301	1.44553	0.722763	+	0.691096i	$0.242872\pi$
$450$	−7.46585	−0.351944
$451$	3.25196	0.153129
$452$	12.5541	0.590496
$453$	−2.37558	−0.111615
$454$	1.55081	0.0727833
$455$	11.1486	0.522655
$456$	4.89186	0.229082
$457$	−39.2943	−1.83811	−0.919055	−	0.394129i	$-0.871046\pi$
$457$	−39.2943	−1.83811	−0.919055	+	0.394129i	$0.871046\pi$
$458$	16.4316	0.767796
$459$	4.89186	0.228332
$460$	−3.53070	−0.164620
$461$	15.6924	0.730870	0.365435	−	0.930837i	$-0.380920\pi$
$461$	15.6924	0.730870	0.365435	+	0.930837i	$0.380920\pi$
$462$	−0.373596	−0.0173813
$463$	−5.09452	−0.236762	−0.118381	−	0.992968i	$-0.537770\pi$
$463$	−5.09452	−0.236762	−0.118381	+	0.992968i	$0.537770\pi$
$464$	−1.00000	−0.0464238
$465$	0.966339	0.0448129
$466$	4.59050	0.212651
$467$	−20.3616	−0.942221	−0.471111	−	0.882074i	$-0.656147\pi$
$467$	−20.3616	−0.942221	−0.471111	+	0.882074i	$0.656147\pi$
$468$	−5.13869	−0.237536
$469$	7.24746	0.334656
$470$	40.5866	1.87212
$471$	−20.0757	−0.925040
$472$	2.87293	0.132237
$473$	−1.08828	−0.0500392
$474$	0.712684	0.0327347
$475$	36.5219	1.67574
$476$	3.00595	0.137777
$477$	1.81684	0.0831872
$478$	23.5054	1.07511
$479$	13.9805	0.638786	0.319393	−	0.947622i	$-0.396521\pi$
$479$	13.9805	0.638786	0.319393	+	0.947622i	$0.396521\pi$
$480$	3.53070	0.161154
$481$	26.1837	1.19387
$482$	15.9841	0.728057
$483$	−0.614480	−0.0279598
$484$	−10.6304	−0.483198
$485$	−20.5375	−0.932560
$486$	1.00000	0.0453609
$487$	12.4420	0.563802	0.281901	−	0.959443i	$-0.409035\pi$
$487$	12.4420	0.563802	0.281901	+	0.959443i	$0.409035\pi$
$488$	−12.9700	−0.587122
$489$	−17.0816	−0.772456
$490$	23.3818	1.05628
$491$	−39.8690	−1.79926	−0.899632	−	0.436648i	$-0.856165\pi$
$491$	−39.8690	−1.79926	−0.899632	+	0.436648i	$0.856165\pi$
$492$	−5.34872	−0.241139
$493$	4.89186	0.220318
$494$	25.1377	1.13100
$495$	2.14663	0.0964836
$496$	−0.273696	−0.0122893
$497$	4.86835	0.218375
$498$	−12.8507	−0.575855
$499$	−24.2777	−1.08682	−0.543410	−	0.839467i	$-0.682867\pi$
$499$	−24.2777	−1.08682	−0.543410	+	0.839467i	$0.682867\pi$
$500$	8.70619	0.389353
$501$	−21.0475	−0.940332
$502$	−28.3752	−1.26645
$503$	−26.7528	−1.19285	−0.596424	−	0.802669i	$-0.703412\pi$
$503$	−26.7528	−1.19285	−0.596424	+	0.802669i	$0.703412\pi$
$504$	0.614480	0.0273711
$505$	−38.6269	−1.71887
$506$	0.607988	0.0270284
$507$	−13.4061	−0.595387
$508$	−2.60917	−0.115763
$509$	−15.3597	−0.680805	−0.340403	−	0.940280i	$-0.610563\pi$
$509$	−15.3597	−0.680805	−0.340403	+	0.940280i	$0.610563\pi$
$510$	−17.2717	−0.764804
$511$	3.69647	0.163522
$512$	−1.00000	−0.0441942
$513$	−4.89186	−0.215981
$514$	−29.2724	−1.29115
$515$	−3.58870	−0.158137
$516$	1.78997	0.0787991
$517$	−6.98903	−0.307377
$518$	−3.13102	−0.137569
$519$	−5.91740	−0.259745
$520$	18.1432	0.795631
$521$	40.3188	1.76640	0.883198	−	0.469000i	$-0.155385\pi$
$521$	40.3188	1.76640	0.883198	+	0.469000i	$0.155385\pi$
$522$	1.00000	0.0437688
$523$	27.0512	1.18287	0.591433	−	0.806354i	$-0.298562\pi$
$523$	27.0512	1.18287	0.591433	+	0.806354i	$0.298562\pi$
$524$	−5.35403	−0.233892
$525$	4.58761	0.200220
$526$	−9.93539	−0.433204
$527$	1.33888	0.0583226
$528$	−0.607988	−0.0264593
$529$	1.00000	0.0434783
$530$	−6.41471	−0.278637
$531$	−2.87293	−0.124675
$532$	−3.00595	−0.130324
$533$	−27.4854	−1.19053
$534$	13.0889	0.566412
$535$	−44.8626	−1.93958
$536$	11.7945	0.509443
$537$	−22.0310	−0.950707
$538$	17.7327	0.764509
$539$	−4.02635	−0.173427
$540$	−3.53070	−0.151937
$541$	−29.0227	−1.24778	−0.623891	−	0.781512i	$-0.714449\pi$
$541$	−29.0227	−1.24778	−0.623891	+	0.781512i	$0.714449\pi$
$542$	15.1509	0.650789
$543$	13.2542	0.568792
$544$	4.89186	0.209737
$545$	0.152211	0.00652000
$546$	3.15762	0.135134
$547$	23.7088	1.01372	0.506858	−	0.862029i	$-0.330807\pi$
$547$	23.7088	1.01372	0.506858	+	0.862029i	$0.330807\pi$
$548$	12.1503	0.519035
$549$	12.9700	0.553544
$550$	−4.53915	−0.193550
$551$	−4.89186	−0.208400
$552$	−1.00000	−0.0425628
$553$	−0.437930	−0.0186227
$554$	23.4648	0.996924
$555$	17.9903	0.763647
$556$	−7.67652	−0.325557
$557$	11.4860	0.486675	0.243338	−	0.969942i	$-0.421758\pi$
$557$	11.4860	0.486675	0.243338	+	0.969942i	$0.421758\pi$
$558$	0.273696	0.0115865
$559$	9.19811	0.389038
$560$	−2.16954	−0.0916800
$561$	2.97419	0.125571
$562$	−13.7591	−0.580393
$563$	−31.2272	−1.31607	−0.658035	−	0.752988i	$-0.728612\pi$
$563$	−31.2272	−1.31607	−0.658035	+	0.752988i	$0.728612\pi$
$564$	11.4953	0.484041
$565$	44.3249	1.86476
$566$	21.6445	0.909787
$567$	−0.614480	−0.0258057
$568$	7.92271	0.332430
$569$	26.8003	1.12353	0.561763	−	0.827298i	$-0.310123\pi$
$569$	26.8003	1.12353	0.561763	+	0.827298i	$0.310123\pi$
$570$	17.2717	0.723432
$571$	11.2327	0.470074	0.235037	−	0.971986i	$-0.424479\pi$
$571$	11.2327	0.470074	0.235037	+	0.971986i	$0.424479\pi$
$572$	−3.12426	−0.130632
$573$	19.0549	0.796030
$574$	3.28668	0.137183
$575$	−7.46585	−0.311348
$576$	1.00000	0.0416667
$577$	−35.5509	−1.48000	−0.740002	−	0.672605i	$-0.765175\pi$
$577$	−35.5509	−1.48000	−0.740002	+	0.672605i	$0.765175\pi$
$578$	−6.93029	−0.288262
$579$	8.39147	0.348738
$580$	−3.53070	−0.146604
$581$	7.89651	0.327603
$582$	−5.81684	−0.241116
$583$	1.10462	0.0457485
$584$	6.01561	0.248928
$585$	−18.1432	−0.750128
$586$	−2.54450	−0.105112
$587$	10.1849	0.420376	0.210188	−	0.977661i	$-0.432592\pi$
$587$	10.1849	0.420376	0.210188	+	0.977661i	$0.432592\pi$
$588$	6.62241	0.273104
$589$	−1.33888	−0.0551677
$590$	10.1435	0.417599
$591$	22.0222	0.905874
$592$	−5.09540	−0.209420
$593$	−16.9833	−0.697421	−0.348711	−	0.937230i	$-0.613380\pi$
$593$	−16.9833	−0.697421	−0.348711	+	0.937230i	$0.613380\pi$
$594$	0.607988	0.0249461
$595$	10.6131	0.435095
$596$	12.9587	0.530809
$597$	21.8887	0.895844
$598$	−5.13869	−0.210137
$599$	−6.57201	−0.268525	−0.134262	−	0.990946i	$-0.542867\pi$
$599$	−6.57201	−0.268525	−0.134262	+	0.990946i	$0.542867\pi$
$600$	7.46585	0.304792
$601$	22.6191	0.922652	0.461326	−	0.887231i	$-0.347374\pi$
$601$	22.6191	0.922652	0.461326	+	0.887231i	$0.347374\pi$
$602$	−1.09990	−0.0448286
$603$	−11.7945	−0.480308
$604$	2.37558	0.0966612
$605$	−37.5326	−1.52592
$606$	−10.9403	−0.444418
$607$	−46.2754	−1.87826	−0.939130	−	0.343562i	$-0.888366\pi$
$607$	−46.2754	−1.87826	−0.939130	+	0.343562i	$0.888366\pi$
$608$	−4.89186	−0.198391
$609$	−0.614480	−0.0249000
$610$	−45.7930	−1.85411
$611$	59.0710	2.38976
$612$	−4.89186	−0.197742
$613$	28.0254	1.13193	0.565967	−	0.824428i	$-0.308503\pi$
$613$	28.0254	1.13193	0.565967	+	0.824428i	$0.308503\pi$
$614$	22.7296	0.917293
$615$	−18.8847	−0.761506
$616$	0.373596	0.0150526
$617$	1.50461	0.0605735	0.0302867	−	0.999541i	$-0.490358\pi$
$617$	1.50461	0.0605735	0.0302867	+	0.999541i	$0.490358\pi$
$618$	−1.01643	−0.0408867
$619$	39.3600	1.58201	0.791007	−	0.611808i	$-0.209557\pi$
$619$	39.3600	1.58201	0.791007	+	0.611808i	$0.209557\pi$
$620$	−0.966339	−0.0388091
$621$	1.00000	0.0401286
$622$	−9.02765	−0.361976
$623$	−8.04286	−0.322231
$624$	5.13869	0.205712
$625$	−6.59030	−0.263612
$626$	13.2001	0.527582
$627$	−2.97419	−0.118778
$628$	20.0757	0.801108
$629$	24.9260	0.993863
$630$	2.16954	0.0864367
$631$	−32.7818	−1.30502	−0.652512	−	0.757779i	$-0.726285\pi$
$631$	−32.7818	−1.30502	−0.652512	+	0.757779i	$0.726285\pi$
$632$	−0.712684	−0.0283491
$633$	2.97950	0.118425
$634$	−11.6125	−0.461190
$635$	−9.21220	−0.365575
$636$	−1.81684	−0.0720422
$637$	34.0305	1.34834
$638$	0.607988	0.0240705
$639$	−7.92271	−0.313418
$640$	−3.53070	−0.139563
$641$	1.29342	0.0510871	0.0255435	−	0.999674i	$-0.491868\pi$
$641$	1.29342	0.0510871	0.0255435	+	0.999674i	$0.491868\pi$
$642$	−12.7064	−0.501483
$643$	21.7254	0.856765	0.428382	−	0.903598i	$-0.359084\pi$
$643$	21.7254	0.856765	0.428382	+	0.903598i	$0.359084\pi$
$644$	0.614480	0.0242139
$645$	6.31985	0.248844
$646$	23.9303	0.941525
$647$	39.2877	1.54456	0.772280	−	0.635282i	$-0.219116\pi$
$647$	39.2877	1.54456	0.772280	+	0.635282i	$0.219116\pi$
$648$	−1.00000	−0.0392837
$649$	−1.74671	−0.0685643
$650$	38.3647	1.50479
$651$	−0.168181	−0.00659151
$652$	17.0816	0.668967
$653$	−16.1028	−0.630151	−0.315075	−	0.949067i	$-0.602030\pi$
$653$	−16.1028	−0.630151	−0.315075	+	0.949067i	$0.602030\pi$
$654$	0.0431107	0.00168576
$655$	−18.9035	−0.738620
$656$	5.34872	0.208832
$657$	−6.01561	−0.234691
$658$	−7.06365	−0.275370
$659$	−35.7836	−1.39393	−0.696966	−	0.717104i	$-0.745467\pi$
$659$	−35.7836	−1.39393	−0.696966	+	0.717104i	$0.745467\pi$
$660$	−2.14663	−0.0835573
$661$	48.0343	1.86832	0.934160	−	0.356856i	$-0.116151\pi$
$661$	48.0343	1.86832	0.934160	+	0.356856i	$0.116151\pi$
$662$	8.36260	0.325022
$663$	−25.1377	−0.976269
$664$	12.8507	0.498705
$665$	−10.6131	−0.411558
$666$	5.09540	0.197443
$667$	1.00000	0.0387202
$668$	21.0475	0.814351
$669$	9.51458	0.367855
$670$	41.6427	1.60880
$671$	7.88558	0.304419
$672$	−0.614480	−0.0237041
$673$	19.1801	0.739339	0.369670	−	0.929163i	$-0.379471\pi$
$673$	19.1801	0.739339	0.369670	+	0.929163i	$0.379471\pi$
$674$	−25.3392	−0.976028
$675$	−7.46585	−0.287361
$676$	13.4061	0.515621
$677$	14.7763	0.567899	0.283950	−	0.958839i	$-0.408355\pi$
$677$	14.7763	0.567899	0.283950	+	0.958839i	$0.408355\pi$
$678$	12.5541	0.482138
$679$	3.57433	0.137170
$680$	17.2717	0.662339
$681$	1.55081	0.0594273
$682$	0.166404	0.00637193
$683$	−20.3985	−0.780528	−0.390264	−	0.920703i	$-0.627616\pi$
$683$	−20.3985	−0.780528	−0.390264	+	0.920703i	$0.627616\pi$
$684$	4.89186	0.187045
$685$	42.8991	1.63909
$686$	−8.37070	−0.319595
$687$	16.4316	0.626903
$688$	−1.78997	−0.0682420
$689$	−9.33616	−0.355679
$690$	−3.53070	−0.134412
$691$	−11.2648	−0.428534	−0.214267	−	0.976775i	$-0.568736\pi$
$691$	−11.2648	−0.428534	−0.214267	+	0.976775i	$0.568736\pi$
$692$	5.91740	0.224946
$693$	−0.373596	−0.0141918
$694$	−8.48741	−0.322178
$695$	−27.1035	−1.02809
$696$	−1.00000	−0.0379049
$697$	−26.1652	−0.991077
$698$	29.5570	1.11875
$699$	4.59050	0.173629
$700$	−4.58761	−0.173396
$701$	−36.1628	−1.36585	−0.682925	−	0.730489i	$-0.739292\pi$
$701$	−36.1628	−1.36585	−0.682925	+	0.730489i	$0.739292\pi$
$702$	−5.13869	−0.193947
$703$	−24.9260	−0.940101
$704$	0.607988	0.0229144
$705$	40.5866	1.52858
$706$	−33.7901	−1.27171
$707$	6.72258	0.252829
$708$	2.87293	0.107971
$709$	16.3670	0.614674	0.307337	−	0.951601i	$-0.400562\pi$
$709$	16.3670	0.614674	0.307337	+	0.951601i	$0.400562\pi$
$710$	27.9727	1.04980
$711$	0.712684	0.0267277
$712$	−13.0889	−0.490527
$713$	0.273696	0.0102500
$714$	3.00595	0.112495
$715$	−11.0308	−0.412530
$716$	22.0310	0.823336
$717$	23.5054	0.877825
$718$	22.9516	0.856545
$719$	−6.20987	−0.231589	−0.115795	−	0.993273i	$-0.536941\pi$
$719$	−6.20987	−0.231589	−0.115795	+	0.993273i	$0.536941\pi$
$720$	3.53070	0.131581
$721$	0.624574	0.0232603
$722$	−4.93029	−0.183486
$723$	15.9841	0.594456
$724$	−13.2542	−0.492588
$725$	−7.46585	−0.277275
$726$	−10.6304	−0.394529
$727$	−20.1469	−0.747208	−0.373604	−	0.927588i	$-0.621878\pi$
$727$	−20.1469	−0.747208	−0.373604	+	0.927588i	$0.621878\pi$
$728$	−3.15762	−0.117029
$729$	1.00000	0.0370370
$730$	21.2393	0.786102
$731$	8.75629	0.323863
$732$	−12.9700	−0.479383
$733$	35.2928	1.30357	0.651785	−	0.758404i	$-0.274020\pi$
$733$	35.2928	1.30357	0.651785	+	0.758404i	$0.274020\pi$
$734$	−33.3095	−1.22948
$735$	23.3818	0.862450
$736$	1.00000	0.0368605
$737$	−7.17089	−0.264143
$738$	−5.34872	−0.196889
$739$	36.5798	1.34561	0.672805	−	0.739820i	$-0.265090\pi$
$739$	36.5798	1.34561	0.672805	+	0.739820i	$0.265090\pi$
$740$	−17.9903	−0.661338
$741$	25.1377	0.923458
$742$	1.11641	0.0409847
$743$	−19.9765	−0.732868	−0.366434	−	0.930444i	$-0.619421\pi$
$743$	−19.9765	−0.732868	−0.366434	+	0.930444i	$0.619421\pi$
$744$	−0.273696	−0.0100342
$745$	45.7533	1.67627
$746$	−26.3647	−0.965280
$747$	−12.8507	−0.470184
$748$	−2.97419	−0.108747
$749$	7.80784	0.285292
$750$	8.70619	0.317905
$751$	2.50365	0.0913596	0.0456798	−	0.998956i	$-0.485455\pi$
$751$	2.50365	0.0913596	0.0456798	+	0.998956i	$0.485455\pi$
$752$	−11.4953	−0.419192
$753$	−28.3752	−1.03405
$754$	−5.13869	−0.187140
$755$	8.38748	0.305252
$756$	0.614480	0.0223484
$757$	21.2816	0.773491	0.386746	−	0.922186i	$-0.373599\pi$
$757$	21.2816	0.773491	0.386746	+	0.922186i	$0.373599\pi$
$758$	21.6448	0.786173
$759$	0.607988	0.0220686
$760$	−17.2717	−0.626510
$761$	1.99861	0.0724495	0.0362248	−	0.999344i	$-0.488467\pi$
$761$	1.99861	0.0724495	0.0362248	+	0.999344i	$0.488467\pi$
$762$	−2.60917	−0.0945202
$763$	−0.0264906	−0.000959025 0
$764$	−19.0549	−0.689383
$765$	−17.2717	−0.624459
$766$	11.0030	0.397556
$767$	14.7631	0.533064
$768$	−1.00000	−0.0360844
$769$	38.8605	1.40135	0.700673	−	0.713483i	$-0.252883\pi$
$769$	38.8605	1.40135	0.700673	+	0.713483i	$0.252883\pi$
$770$	1.31906	0.0475355
$771$	−29.2724	−1.05422
$772$	−8.39147	−0.302016
$773$	34.1892	1.22970	0.614849	−	0.788645i	$-0.289217\pi$
$773$	34.1892	1.22970	0.614849	+	0.788645i	$0.289217\pi$
$774$	1.78997	0.0643392
$775$	−2.04337	−0.0734001
$776$	5.81684	0.208812
$777$	−3.13102	−0.112325
$778$	−23.3305	−0.836440
$779$	26.1652	0.937465
$780$	18.1432	0.649630
$781$	−4.81692	−0.172363
$782$	−4.89186	−0.174933
$783$	1.00000	0.0357371
$784$	−6.62241	−0.236515
$785$	70.8813	2.52986
$786$	−5.35403	−0.190972
$787$	12.1130	0.431780	0.215890	−	0.976418i	$-0.430735\pi$
$787$	12.1130	0.431780	0.215890	+	0.976418i	$0.430735\pi$
$788$	−22.0222	−0.784510
$789$	−9.93539	−0.353709
$790$	−2.51627	−0.0895250
$791$	−7.71425	−0.274287
$792$	−0.607988	−0.0216039
$793$	−66.6486	−2.36676
$794$	−6.09884	−0.216440
$795$	−6.41471	−0.227506
$796$	−21.8887	−0.775824
$797$	19.9628	0.707117	0.353559	−	0.935412i	$-0.384971\pi$
$797$	19.9628	0.707117	0.353559	+	0.935412i	$0.384971\pi$
$798$	−3.00595	−0.106409
$799$	56.2336	1.98940
$800$	−7.46585	−0.263958
$801$	13.0889	0.462474
$802$	21.2632	0.750830
$803$	−3.65742	−0.129068
$804$	11.7945	0.415959
$805$	2.16954	0.0764664
$806$	−1.40644	−0.0495397
$807$	17.7327	0.624219
$808$	10.9403	0.384878
$809$	4.77374	0.167836	0.0839178	−	0.996473i	$-0.473257\pi$
$809$	4.77374	0.167836	0.0839178	+	0.996473i	$0.473257\pi$
$810$	−3.53070	−0.124056
$811$	−9.67652	−0.339789	−0.169894	−	0.985462i	$-0.554343\pi$
$811$	−9.67652	−0.339789	−0.169894	+	0.985462i	$0.554343\pi$
$812$	0.614480	0.0215640
$813$	15.1509	0.531367
$814$	3.09794	0.108583
$815$	60.3100	2.11257
$816$	4.89186	0.171249
$817$	−8.75629	−0.306344
$818$	15.1812	0.530799
$819$	3.15762	0.110336
$820$	18.8847	0.659483
$821$	−16.8899	−0.589463	−0.294732	−	0.955580i	$-0.595230\pi$
$821$	−16.8899	−0.589463	−0.294732	+	0.955580i	$0.595230\pi$
$822$	12.1503	0.423791
$823$	−42.2212	−1.47174	−0.735870	−	0.677123i	$-0.763226\pi$
$823$	−42.2212	−1.47174	−0.735870	+	0.677123i	$0.763226\pi$
$824$	1.01643	0.0354089
$825$	−4.53915	−0.158033
$826$	−1.76536	−0.0614246
$827$	41.3989	1.43958	0.719791	−	0.694191i	$-0.244238\pi$
$827$	41.3989	1.43958	0.719791	+	0.694191i	$0.244238\pi$
$828$	−1.00000	−0.0347524
$829$	−30.6301	−1.06383	−0.531914	−	0.846799i	$-0.678527\pi$
$829$	−30.6301	−1.06383	−0.531914	+	0.846799i	$0.678527\pi$
$830$	45.3721	1.57489
$831$	23.4648	0.813985
$832$	−5.13869	−0.178152
$833$	32.3959	1.12245
$834$	−7.67652	−0.265816
$835$	74.3124	2.57169
$836$	2.97419	0.102865
$837$	0.273696	0.00946031
$838$	13.2146	0.456491
$839$	17.4665	0.603011	0.301506	−	0.953464i	$-0.402511\pi$
$839$	17.4665	0.603011	0.301506	+	0.953464i	$0.402511\pi$
$840$	−2.16954	−0.0748564
$841$	1.00000	0.0344828
$842$	19.6648	0.677693
$843$	−13.7591	−0.473889
$844$	−2.97950	−0.102559
$845$	47.3331	1.62831
$846$	11.4953	0.395218
$847$	6.53213	0.224447
$848$	1.81684	0.0623904
$849$	21.6445	0.742838
$850$	36.5219	1.25269
$851$	5.09540	0.174668
$852$	7.92271	0.271428
$853$	−23.8382	−0.816203	−0.408102	−	0.912937i	$-0.633809\pi$
$853$	−23.8382	−0.816203	−0.408102	+	0.912937i	$0.633809\pi$
$854$	7.96977	0.272720
$855$	17.2717	0.590680
$856$	12.7064	0.434297
$857$	25.7558	0.879800	0.439900	−	0.898047i	$-0.355014\pi$
$857$	25.7558	0.879800	0.439900	+	0.898047i	$0.355014\pi$
$858$	−3.12426	−0.106661
$859$	−56.7124	−1.93500	−0.967501	−	0.252865i	$-0.918627\pi$
$859$	−56.7124	−1.93500	−0.967501	+	0.252865i	$0.918627\pi$
$860$	−6.31985	−0.215505
$861$	3.28668	0.112010
$862$	−0.429690	−0.0146353
$863$	−24.3205	−0.827881	−0.413940	−	0.910304i	$-0.635848\pi$
$863$	−24.3205	−0.827881	−0.413940	+	0.910304i	$0.635848\pi$
$864$	1.00000	0.0340207
$865$	20.8926	0.710369
$866$	−6.61312	−0.224723
$867$	−6.93029	−0.235365
$868$	0.168181	0.00570842
$869$	0.433304	0.0146988
$870$	−3.53070	−0.119702
$871$	60.6081	2.05363
$872$	−0.0431107	−0.00145991
$873$	−5.81684	−0.196870
$874$	4.89186	0.165470
$875$	−5.34978	−0.180855
$876$	6.01561	0.203249
$877$	17.3056	0.584367	0.292184	−	0.956362i	$-0.405618\pi$
$877$	17.3056	0.584367	0.292184	+	0.956362i	$0.405618\pi$
$878$	1.50559	0.0508110
$879$	−2.54450	−0.0858240
$880$	2.14663	0.0723627
$881$	−7.28454	−0.245423	−0.122711	−	0.992442i	$-0.539159\pi$
$881$	−7.28454	−0.245423	−0.122711	+	0.992442i	$0.539159\pi$
$882$	6.62241	0.222988
$883$	21.8651	0.735818	0.367909	−	0.929862i	$-0.380074\pi$
$883$	21.8651	0.735818	0.367909	+	0.929862i	$0.380074\pi$
$884$	25.1377	0.845474
$885$	10.1435	0.340969
$886$	24.0942	0.809461
$887$	40.4634	1.35863	0.679315	−	0.733847i	$-0.262277\pi$
$887$	40.4634	1.35863	0.679315	+	0.733847i	$0.262277\pi$
$888$	−5.09540	−0.170990
$889$	1.60328	0.0537723
$890$	−46.2130	−1.54906
$891$	0.607988	0.0203684
$892$	−9.51458	−0.318572
$893$	−56.2336	−1.88179
$894$	12.9587	0.433404
$895$	77.7848	2.60006
$896$	0.614480	0.0205283
$897$	−5.13869	−0.171576
$898$	−30.6301	−1.02214
$899$	0.273696	0.00912827
$900$	7.46585	0.248862
$901$	−8.88771	−0.296092
$902$	−3.25196	−0.108278
$903$	−1.09990	−0.0366024
$904$	−12.5541	−0.417544
$905$	−46.7966	−1.55557
$906$	2.37558	0.0789235
$907$	12.0675	0.400694	0.200347	−	0.979725i	$-0.435793\pi$
$907$	12.0675	0.400694	0.200347	+	0.979725i	$0.435793\pi$
$908$	−1.55081	−0.0514655
$909$	−10.9403	−0.362866
$910$	−11.1486	−0.369573
$911$	6.97395	0.231057	0.115529	−	0.993304i	$-0.463144\pi$
$911$	6.97395	0.231057	0.115529	+	0.993304i	$0.463144\pi$
$912$	−4.89186	−0.161986
$913$	−7.81310	−0.258576
$914$	39.2943	1.29974
$915$	−45.7930	−1.51387
$916$	−16.4316	−0.542914
$917$	3.28994	0.108643
$918$	−4.89186	−0.161455
$919$	50.0176	1.64993	0.824965	−	0.565184i	$-0.191195\pi$
$919$	50.0176	1.64993	0.824965	+	0.565184i	$0.191195\pi$
$920$	3.53070	0.116404
$921$	22.7296	0.748966
$922$	−15.6924	−0.516803
$923$	40.7124	1.34006
$924$	0.373596	0.0122904
$925$	−38.0415	−1.25080
$926$	5.09452	0.167416
$927$	−1.01643	−0.0333839
$928$	1.00000	0.0328266
$929$	35.5627	1.16677	0.583387	−	0.812194i	$-0.301727\pi$
$929$	35.5627	1.16677	0.583387	+	0.812194i	$0.301727\pi$
$930$	−0.966339	−0.0316875
$931$	−32.3959	−1.06173
$932$	−4.59050	−0.150367
$933$	−9.02765	−0.295552
$934$	20.3616	0.666251
$935$	−10.5010	−0.343419
$936$	5.13869	0.167963
$937$	−38.4968	−1.25763	−0.628817	−	0.777553i	$-0.716461\pi$
$937$	−38.4968	−1.25763	−0.628817	+	0.777553i	$0.716461\pi$
$938$	−7.24746	−0.236638
$939$	13.2001	0.430769
$940$	−40.5866	−1.32379
$941$	−39.8828	−1.30014	−0.650071	−	0.759873i	$-0.725261\pi$
$941$	−39.8828	−1.30014	−0.650071	+	0.759873i	$0.725261\pi$
$942$	20.0757	0.654102
$943$	−5.34872	−0.174178
$944$	−2.87293	−0.0935059
$945$	2.16954	0.0705753
$946$	1.08828	0.0353831
$947$	12.8926	0.418954	0.209477	−	0.977814i	$-0.432824\pi$
$947$	12.8926	0.418954	0.209477	+	0.977814i	$0.432824\pi$
$948$	−0.712684	−0.0231469
$949$	30.9123	1.00346
$950$	−36.5219	−1.18493
$951$	−11.6125	−0.376560
$952$	−3.00595	−0.0974233
$953$	−1.94303	−0.0629411	−0.0314705	−	0.999505i	$-0.510019\pi$
$953$	−1.94303	−0.0629411	−0.0314705	+	0.999505i	$0.510019\pi$
$954$	−1.81684	−0.0588222
$955$	−67.2772	−2.17704
$956$	−23.5054	−0.760219
$957$	0.607988	0.0196535
$958$	−13.9805	−0.451690
$959$	−7.46612	−0.241093
$960$	−3.53070	−0.113953
$961$	−30.9251	−0.997584
$962$	−26.1837	−0.844195
$963$	−12.7064	−0.409459
$964$	−15.9841	−0.514814
$965$	−29.6278	−0.953752
$966$	0.614480	0.0197706
$967$	10.2701	0.330265	0.165133	−	0.986271i	$-0.447195\pi$
$967$	10.2701	0.330265	0.165133	+	0.986271i	$0.447195\pi$
$968$	10.6304	0.341672
$969$	23.9303	0.768752
$970$	20.5375	0.659420
$971$	−6.44342	−0.206779	−0.103390	−	0.994641i	$-0.532969\pi$
$971$	−6.44342	−0.206779	−0.103390	+	0.994641i	$0.532969\pi$
$972$	−1.00000	−0.0320750
$973$	4.71706	0.151222
$974$	−12.4420	−0.398669
$975$	38.3647	1.22865
$976$	12.9700	0.415158
$977$	−8.47330	−0.271085	−0.135543	−	0.990772i	$-0.543278\pi$
$977$	−8.47330	−0.271085	−0.135543	+	0.990772i	$0.543278\pi$
$978$	17.0816	0.546209
$979$	7.95790	0.254336
$980$	−23.3818	−0.746903
$981$	0.0431107	0.00137642
$982$	39.8690	1.27227
$983$	26.5393	0.846474	0.423237	−	0.906019i	$-0.360894\pi$
$983$	26.5393	0.846474	0.423237	+	0.906019i	$0.360894\pi$
$984$	5.34872	0.170511
$985$	−77.7540	−2.47745
$986$	−4.89186	−0.155789
$987$	−7.06365	−0.224839
$988$	−25.1377	−0.799738
$989$	1.78997	0.0569178
$990$	−2.14663	−0.0682242
$991$	31.3288	0.995191	0.497596	−	0.867409i	$-0.334216\pi$
$991$	31.3288	0.995191	0.497596	+	0.867409i	$0.334216\pi$
$992$	0.273696	0.00868985
$993$	8.36260	0.265379
$994$	−4.86835	−0.154415
$995$	−77.2824	−2.45002
$996$	12.8507	0.407191
$997$	6.56339	0.207865	0.103932	−	0.994584i	$-0.466857\pi$
$997$	6.56339	0.207865	0.103932	+	0.994584i	$0.466857\pi$
$998$	24.2777	0.768498
$999$	5.09540	0.161211

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.be.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.be.1.5	✓	5	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:	\( N \)	\(=\)	\( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.53070 q^{5} +1.00000 q^{6} -0.614480 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.53070 q^{5} +1.00000 q^{6} -0.614480 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.53070 q^{10} +0.607988 q^{11} -1.00000 q^{12} -5.13869 q^{13} +0.614480 q^{14} -3.53070 q^{15} +1.00000 q^{16} -4.89186 q^{17} -1.00000 q^{18} +4.89186 q^{19} +3.53070 q^{20} +0.614480 q^{21} -0.607988 q^{22} -1.00000 q^{23} +1.00000 q^{24} +7.46585 q^{25} +5.13869 q^{26} -1.00000 q^{27} -0.614480 q^{28} -1.00000 q^{29} +3.53070 q^{30} -0.273696 q^{31} -1.00000 q^{32} -0.607988 q^{33} +4.89186 q^{34} -2.16954 q^{35} +1.00000 q^{36} -5.09540 q^{37} -4.89186 q^{38} +5.13869 q^{39} -3.53070 q^{40} +5.34872 q^{41} -0.614480 q^{42} -1.78997 q^{43} +0.607988 q^{44} +3.53070 q^{45} +1.00000 q^{46} -11.4953 q^{47} -1.00000 q^{48} -6.62241 q^{49} -7.46585 q^{50} +4.89186 q^{51} -5.13869 q^{52} +1.81684 q^{53} +1.00000 q^{54} +2.14663 q^{55} +0.614480 q^{56} -4.89186 q^{57} +1.00000 q^{58} -2.87293 q^{59} -3.53070 q^{60} +12.9700 q^{61} +0.273696 q^{62} -0.614480 q^{63} +1.00000 q^{64} -18.1432 q^{65} +0.607988 q^{66} -11.7945 q^{67} -4.89186 q^{68} +1.00000 q^{69} +2.16954 q^{70} -7.92271 q^{71} -1.00000 q^{72} -6.01561 q^{73} +5.09540 q^{74} -7.46585 q^{75} +4.89186 q^{76} -0.373596 q^{77} -5.13869 q^{78} +0.712684 q^{79} +3.53070 q^{80} +1.00000 q^{81} -5.34872 q^{82} -12.8507 q^{83} +0.614480 q^{84} -17.2717 q^{85} +1.78997 q^{86} +1.00000 q^{87} -0.607988 q^{88} +13.0889 q^{89} -3.53070 q^{90} +3.15762 q^{91} -1.00000 q^{92} +0.273696 q^{93} +11.4953 q^{94} +17.2717 q^{95} +1.00000 q^{96} -5.81684 q^{97} +6.62241 q^{98} +0.607988 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} + 5 q^{6} - 4 q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 + 5 * q^6 - 4 * q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} + 5 q^{6} - 4 q^{7} - 5 q^{8} + 5 q^{9} - q^{10} + 5 q^{11} - 5 q^{12} - 11 q^{13} + 4 q^{14} - q^{15} + 5 q^{16} + 4 q^{17} - 5 q^{18} - 4 q^{19} + q^{20} + 4 q^{21} - 5 q^{22} - 5 q^{23} + 5 q^{24} + 12 q^{25} + 11 q^{26} - 5 q^{27} - 4 q^{28} - 5 q^{29} + q^{30} + 5 q^{31} - 5 q^{32} - 5 q^{33} - 4 q^{34} - 6 q^{35} + 5 q^{36} + 9 q^{37} + 4 q^{38} + 11 q^{39} - q^{40} + 5 q^{41} - 4 q^{42} - 16 q^{43} + 5 q^{44} + q^{45} + 5 q^{46} + 8 q^{47} - 5 q^{48} - 5 q^{49} - 12 q^{50} - 4 q^{51} - 11 q^{52} - 4 q^{53} + 5 q^{54} - 33 q^{55} + 4 q^{56} + 4 q^{57} + 5 q^{58} + 23 q^{59} - q^{60} + 7 q^{61} - 5 q^{62} - 4 q^{63} + 5 q^{64} - 5 q^{65} + 5 q^{66} + 5 q^{67} + 4 q^{68} + 5 q^{69} + 6 q^{70} - 21 q^{71} - 5 q^{72} - 8 q^{73} - 9 q^{74} - 12 q^{75} - 4 q^{76} - 11 q^{78} - 8 q^{79} + q^{80} + 5 q^{81} - 5 q^{82} - 18 q^{83} + 4 q^{84} - 10 q^{85} + 16 q^{86} + 5 q^{87} - 5 q^{88} + 32 q^{89} - q^{90} + 10 q^{91} - 5 q^{92} - 5 q^{93} - 8 q^{94} + 10 q^{95} + 5 q^{96} - 16 q^{97} + 5 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 + 5 * q^6 - 4 * q^7 - 5 * q^8 + 5 * q^9 - q^10 + 5 * q^11 - 5 * q^12 - 11 * q^13 + 4 * q^14 - q^15 + 5 * q^16 + 4 * q^17 - 5 * q^18 - 4 * q^19 + q^20 + 4 * q^21 - 5 * q^22 - 5 * q^23 + 5 * q^24 + 12 * q^25 + 11 * q^26 - 5 * q^27 - 4 * q^28 - 5 * q^29 + q^30 + 5 * q^31 - 5 * q^32 - 5 * q^33 - 4 * q^34 - 6 * q^35 + 5 * q^36 + 9 * q^37 + 4 * q^38 + 11 * q^39 - q^40 + 5 * q^41 - 4 * q^42 - 16 * q^43 + 5 * q^44 + q^45 + 5 * q^46 + 8 * q^47 - 5 * q^48 - 5 * q^49 - 12 * q^50 - 4 * q^51 - 11 * q^52 - 4 * q^53 + 5 * q^54 - 33 * q^55 + 4 * q^56 + 4 * q^57 + 5 * q^58 + 23 * q^59 - q^60 + 7 * q^61 - 5 * q^62 - 4 * q^63 + 5 * q^64 - 5 * q^65 + 5 * q^66 + 5 * q^67 + 4 * q^68 + 5 * q^69 + 6 * q^70 - 21 * q^71 - 5 * q^72 - 8 * q^73 - 9 * q^74 - 12 * q^75 - 4 * q^76 - 11 * q^78 - 8 * q^79 + q^80 + 5 * q^81 - 5 * q^82 - 18 * q^83 + 4 * q^84 - 10 * q^85 + 16 * q^86 + 5 * q^87 - 5 * q^88 + 32 * q^89 - q^90 + 10 * q^91 - 5 * q^92 - 5 * q^93 - 8 * q^94 + 10 * q^95 + 5 * q^96 - 16 * q^97 + 5 * q^98 + 5 * q^99

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