LMFDB - Embedded newform 4029.2.a.e.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 10 x^{16} + 120 x^{15} - 56 x^{14} - 921 x^{13} + 1181 x^{12} + 3316 x^{11} + \cdots + 138 $ x^18 - 6x^17 - 10x^16 + 120x^15 - 56x^14 - 921x^13 + 1181x^12 + 3316x^11 - 6280x^10 - 5249x^9 + 15005x^8 + 1809x^7 - 16711x^6 + 2434x^5 + 8758x^4 - 1858x^3 - 1942x^2 + 318*x + 138
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-0.823313$ of defining polynomial
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.823313 q^{2} +1.00000 q^{3} -1.32216 q^{4} +0.963284 q^{5} +0.823313 q^{6} +4.26360 q^{7} -2.73517 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.823313 q^{2} +1.00000 q^{3} -1.32216 q^{4} +0.963284 q^{5} +0.823313 q^{6} +4.26360 q^{7} -2.73517 q^{8} +1.00000 q^{9} +0.793084 q^{10} -2.44529 q^{11} -1.32216 q^{12} -3.54478 q^{13} +3.51028 q^{14} +0.963284 q^{15} +0.392407 q^{16} +1.00000 q^{17} +0.823313 q^{18} -7.65748 q^{19} -1.27361 q^{20} +4.26360 q^{21} -2.01324 q^{22} -7.52588 q^{23} -2.73517 q^{24} -4.07208 q^{25} -2.91847 q^{26} +1.00000 q^{27} -5.63714 q^{28} -5.79250 q^{29} +0.793084 q^{30} +3.12277 q^{31} +5.79342 q^{32} -2.44529 q^{33} +0.823313 q^{34} +4.10706 q^{35} -1.32216 q^{36} -5.09076 q^{37} -6.30450 q^{38} -3.54478 q^{39} -2.63475 q^{40} -9.59502 q^{41} +3.51028 q^{42} -11.5415 q^{43} +3.23306 q^{44} +0.963284 q^{45} -6.19615 q^{46} +6.99984 q^{47} +0.392407 q^{48} +11.1783 q^{49} -3.35260 q^{50} +1.00000 q^{51} +4.68676 q^{52} +3.49155 q^{53} +0.823313 q^{54} -2.35551 q^{55} -11.6617 q^{56} -7.65748 q^{57} -4.76904 q^{58} +4.03503 q^{59} -1.27361 q^{60} -4.13357 q^{61} +2.57101 q^{62} +4.26360 q^{63} +3.98499 q^{64} -3.41463 q^{65} -2.01324 q^{66} +6.28597 q^{67} -1.32216 q^{68} -7.52588 q^{69} +3.38139 q^{70} -0.123956 q^{71} -2.73517 q^{72} +16.8684 q^{73} -4.19129 q^{74} -4.07208 q^{75} +10.1244 q^{76} -10.4257 q^{77} -2.91847 q^{78} -1.00000 q^{79} +0.377999 q^{80} +1.00000 q^{81} -7.89971 q^{82} -4.40130 q^{83} -5.63714 q^{84} +0.963284 q^{85} -9.50230 q^{86} -5.79250 q^{87} +6.68830 q^{88} +11.1717 q^{89} +0.793084 q^{90} -15.1135 q^{91} +9.95038 q^{92} +3.12277 q^{93} +5.76306 q^{94} -7.37633 q^{95} +5.79342 q^{96} +3.97117 q^{97} +9.20323 q^{98} -2.44529 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * 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 $

$2$	0.823313	0.582170	0.291085	−	0.956697i	$-0.405984\pi$
$2$	0.823313	0.582170	0.291085	+	0.956697i	$0.405984\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.32216	−0.661078
$5$	0.963284	0.430794	0.215397	−	0.976527i	$-0.430895\pi$
$5$	0.963284	0.430794	0.215397	+	0.976527i	$0.430895\pi$
$6$	0.823313	0.336116
$7$	4.26360	1.61149	0.805745	−	0.592263i	$-0.201765\pi$
$7$	4.26360	1.61149	0.805745	+	0.592263i	$0.201765\pi$
$8$	−2.73517	−0.967030
$9$	1.00000	0.333333
$10$	0.793084	0.250795
$11$	−2.44529	−0.737283	−0.368642	−	0.929572i	$-0.620177\pi$
$11$	−2.44529	−0.737283	−0.368642	+	0.929572i	$0.620177\pi$
$12$	−1.32216	−0.381673
$13$	−3.54478	−0.983146	−0.491573	−	0.870836i	$-0.663578\pi$
$13$	−3.54478	−0.983146	−0.491573	+	0.870836i	$0.663578\pi$
$14$	3.51028	0.938161
$15$	0.963284	0.248719
$16$	0.392407	0.0981017
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.823313	0.194057
$19$	−7.65748	−1.75675	−0.878373	−	0.477976i	$-0.841371\pi$
$19$	−7.65748	−1.75675	−0.878373	+	0.477976i	$0.841371\pi$
$20$	−1.27361	−0.284788
$21$	4.26360	0.930394
$22$	−2.01324	−0.429224
$23$	−7.52588	−1.56925	−0.784627	−	0.619968i	$-0.787145\pi$
$23$	−7.52588	−1.56925	−0.784627	+	0.619968i	$0.787145\pi$
$24$	−2.73517	−0.558315
$25$	−4.07208	−0.814417
$26$	−2.91847	−0.572358
$27$	1.00000	0.192450
$28$	−5.63714	−1.06532
$29$	−5.79250	−1.07564	−0.537820	−	0.843060i	$-0.680752\pi$
$29$	−5.79250	−1.07564	−0.537820	+	0.843060i	$0.680752\pi$
$30$	0.793084	0.144797
$31$	3.12277	0.560866	0.280433	−	0.959874i	$-0.409522\pi$
$31$	3.12277	0.560866	0.280433	+	0.959874i	$0.409522\pi$
$32$	5.79342	1.02414
$33$	−2.44529	−0.425671
$34$	0.823313	0.141197
$35$	4.10706	0.694220
$36$	−1.32216	−0.220359
$37$	−5.09076	−0.836915	−0.418458	−	0.908236i	$-0.637429\pi$
$37$	−5.09076	−0.836915	−0.418458	+	0.908236i	$0.637429\pi$
$38$	−6.30450	−1.02272
$39$	−3.54478	−0.567620
$40$	−2.63475	−0.416591
$41$	−9.59502	−1.49849	−0.749246	−	0.662292i	$-0.769584\pi$
$41$	−9.59502	−1.49849	−0.749246	+	0.662292i	$0.769584\pi$
$42$	3.51028	0.541648
$43$	−11.5415	−1.76007	−0.880034	−	0.474911i	$-0.842480\pi$
$43$	−11.5415	−1.76007	−0.880034	+	0.474911i	$0.842480\pi$
$44$	3.23306	0.487402
$45$	0.963284	0.143598
$46$	−6.19615	−0.913573
$47$	6.99984	1.02103	0.510516	−	0.859868i	$-0.329455\pi$
$47$	6.99984	1.02103	0.510516	+	0.859868i	$0.329455\pi$
$48$	0.392407	0.0566390
$49$	11.1783	1.59690
$50$	−3.35260	−0.474129
$51$	1.00000	0.140028
$52$	4.68676	0.649936
$53$	3.49155	0.479602	0.239801	−	0.970822i	$-0.422918\pi$
$53$	3.49155	0.479602	0.239801	+	0.970822i	$0.422918\pi$
$54$	0.823313	0.112039
$55$	−2.35551	−0.317617
$56$	−11.6617	−1.55836
$57$	−7.65748	−1.01426
$58$	−4.76904	−0.626206
$59$	4.03503	0.525316	0.262658	−	0.964889i	$-0.415401\pi$
$59$	4.03503	0.525316	0.262658	+	0.964889i	$0.415401\pi$
$60$	−1.27361	−0.164423
$61$	−4.13357	−0.529249	−0.264625	−	0.964352i	$-0.585248\pi$
$61$	−4.13357	−0.529249	−0.264625	+	0.964352i	$0.585248\pi$
$62$	2.57101	0.326519
$63$	4.26360	0.537163
$64$	3.98499	0.498123
$65$	−3.41463	−0.423533
$66$	−2.01324	−0.247813
$67$	6.28597	0.767953	0.383977	−	0.923343i	$-0.374554\pi$
$67$	6.28597	0.767953	0.383977	+	0.923343i	$0.374554\pi$
$68$	−1.32216	−0.160335
$69$	−7.52588	−0.906009
$70$	3.38139	0.404154
$71$	−0.123956	−0.0147108	−0.00735542	−	0.999973i	$-0.502341\pi$
$71$	−0.123956	−0.0147108	−0.00735542	+	0.999973i	$0.502341\pi$
$72$	−2.73517	−0.322343
$73$	16.8684	1.97430	0.987149	−	0.159801i	$-0.0510852\pi$
$73$	16.8684	1.97430	0.987149	+	0.159801i	$0.0510852\pi$
$74$	−4.19129	−0.487227
$75$	−4.07208	−0.470204
$76$	10.1244	1.16135
$77$	−10.4257	−1.18812
$78$	−2.91847	−0.330451
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	0.377999	0.0422616
$81$	1.00000	0.111111
$82$	−7.89971	−0.872377
$83$	−4.40130	−0.483105	−0.241552	−	0.970388i	$-0.577657\pi$
$83$	−4.40130	−0.483105	−0.241552	+	0.970388i	$0.577657\pi$
$84$	−5.63714	−0.615063
$85$	0.963284	0.104483
$86$	−9.50230	−1.02466
$87$	−5.79250	−0.621021
$88$	6.68830	0.712975
$89$	11.1717	1.18419	0.592097	−	0.805866i	$-0.298300\pi$
$89$	11.1717	1.18419	0.592097	+	0.805866i	$0.298300\pi$
$90$	0.793084	0.0835984
$91$	−15.1135	−1.58433
$92$	9.95038	1.03740
$93$	3.12277	0.323816
$94$	5.76306	0.594414
$95$	−7.37633	−0.756795
$96$	5.79342	0.591289
$97$	3.97117	0.403211	0.201606	−	0.979467i	$-0.435384\pi$
$97$	3.97117	0.403211	0.201606	+	0.979467i	$0.435384\pi$
$98$	9.20323	0.929667
$99$	−2.44529	−0.245761
$100$	5.38393	0.538393
$101$	−11.7110	−1.16529	−0.582643	−	0.812728i	$-0.697981\pi$
$101$	−11.7110	−1.16529	−0.582643	+	0.812728i	$0.697981\pi$
$102$	0.823313	0.0815201
$103$	10.1978	1.00482	0.502408	−	0.864631i	$-0.332448\pi$
$103$	10.1978	1.00482	0.502408	+	0.864631i	$0.332448\pi$
$104$	9.69560	0.950732
$105$	4.10706	0.400808
$106$	2.87464	0.279210
$107$	−13.3137	−1.28708	−0.643540	−	0.765412i	$-0.722535\pi$
$107$	−13.3137	−1.28708	−0.643540	+	0.765412i	$0.722535\pi$
$108$	−1.32216	−0.127224
$109$	11.9020	1.14001	0.570003	−	0.821642i	$-0.306942\pi$
$109$	11.9020	1.14001	0.570003	+	0.821642i	$0.306942\pi$
$110$	−1.93932	−0.184907
$111$	−5.09076	−0.483193
$112$	1.67307	0.158090
$113$	−5.78517	−0.544223	−0.272111	−	0.962266i	$-0.587722\pi$
$113$	−5.78517	−0.544223	−0.272111	+	0.962266i	$0.587722\pi$
$114$	−6.30450	−0.590471
$115$	−7.24956	−0.676025
$116$	7.65858	0.711082
$117$	−3.54478	−0.327715
$118$	3.32209	0.305824
$119$	4.26360	0.390844
$120$	−2.63475	−0.240519
$121$	−5.02055	−0.456413
$122$	−3.40322	−0.308113
$123$	−9.59502	−0.865154
$124$	−4.12878	−0.370776
$125$	−8.73899	−0.781639
$126$	3.51028	0.312720
$127$	−14.0991	−1.25109	−0.625544	−	0.780189i	$-0.715123\pi$
$127$	−14.0991	−1.25109	−0.625544	+	0.780189i	$0.715123\pi$
$128$	−8.30595	−0.734149
$129$	−11.5415	−1.01618
$130$	−2.81131	−0.246568
$131$	6.27253	0.548033	0.274017	−	0.961725i	$-0.411648\pi$
$131$	6.27253	0.548033	0.274017	+	0.961725i	$0.411648\pi$
$132$	3.23306	0.281401
$133$	−32.6484	−2.83098
$134$	5.17532	0.447080
$135$	0.963284	0.0829063
$136$	−2.73517	−0.234539
$137$	−3.18136	−0.271802	−0.135901	−	0.990722i	$-0.543393\pi$
$137$	−3.18136	−0.271802	−0.135901	+	0.990722i	$0.543393\pi$
$138$	−6.19615	−0.527452
$139$	11.1062	0.942019	0.471010	−	0.882128i	$-0.343890\pi$
$139$	11.1062	0.942019	0.471010	+	0.882128i	$0.343890\pi$
$140$	−5.43017	−0.458933
$141$	6.99984	0.589493
$142$	−0.102054	−0.00856421
$143$	8.66803	0.724857
$144$	0.392407	0.0327006
$145$	−5.57982	−0.463379
$146$	13.8880	1.14938
$147$	11.1783	0.921970
$148$	6.73077	0.553266
$149$	8.08540	0.662382	0.331191	−	0.943564i	$-0.392550\pi$
$149$	8.08540	0.662382	0.331191	+	0.943564i	$0.392550\pi$
$150$	−3.35260	−0.273739
$151$	13.7668	1.12033	0.560164	−	0.828382i	$-0.310738\pi$
$151$	13.7668	1.12033	0.560164	+	0.828382i	$0.310738\pi$
$152$	20.9445	1.69883
$153$	1.00000	0.0808452
$154$	−8.58365	−0.691691
$155$	3.00811	0.241617
$156$	4.68676	0.375241
$157$	5.75832	0.459564	0.229782	−	0.973242i	$-0.426199\pi$
$157$	5.75832	0.459564	0.229782	+	0.973242i	$0.426199\pi$
$158$	−0.823313	−0.0654993
$159$	3.49155	0.276898
$160$	5.58071	0.441194
$161$	−32.0873	−2.52884
$162$	0.823313	0.0646856
$163$	−1.98373	−0.155378	−0.0776888	−	0.996978i	$-0.524754\pi$
$163$	−1.98373	−0.155378	−0.0776888	+	0.996978i	$0.524754\pi$
$164$	12.6861	0.990619
$165$	−2.35551	−0.183376
$166$	−3.62364	−0.281249
$167$	2.22404	0.172101	0.0860505	−	0.996291i	$-0.472575\pi$
$167$	2.22404	0.172101	0.0860505	+	0.996291i	$0.472575\pi$
$168$	−11.6617	−0.899719
$169$	−0.434508	−0.0334237
$170$	0.793084	0.0608268
$171$	−7.65748	−0.585582
$172$	15.2597	1.16354
$173$	10.1515	0.771804	0.385902	−	0.922540i	$-0.373890\pi$
$173$	10.1515	0.771804	0.385902	+	0.922540i	$0.373890\pi$
$174$	−4.76904	−0.361540
$175$	−17.3617	−1.31242
$176$	−0.959549	−0.0723288
$177$	4.03503	0.303291
$178$	9.19778	0.689403
$179$	−18.5142	−1.38382	−0.691909	−	0.721985i	$-0.743230\pi$
$179$	−18.5142	−1.38382	−0.691909	+	0.721985i	$0.743230\pi$
$180$	−1.27361	−0.0949294
$181$	−14.7956	−1.09975	−0.549873	−	0.835249i	$-0.685324\pi$
$181$	−14.7956	−1.09975	−0.549873	+	0.835249i	$0.685324\pi$
$182$	−12.4432	−0.922350
$183$	−4.13357	−0.305562
$184$	20.5846	1.51752
$185$	−4.90384	−0.360538
$186$	2.57101	0.188516
$187$	−2.44529	−0.178817
$188$	−9.25488	−0.674981
$189$	4.26360	0.310131
$190$	−6.07302	−0.440584
$191$	−11.5425	−0.835187	−0.417594	−	0.908634i	$-0.637126\pi$
$191$	−11.5425	−0.835187	−0.417594	+	0.908634i	$0.637126\pi$
$192$	3.98499	0.287592
$193$	3.87077	0.278624	0.139312	−	0.990249i	$-0.455511\pi$
$193$	3.87077	0.278624	0.139312	+	0.990249i	$0.455511\pi$
$194$	3.26951	0.234737
$195$	−3.41463	−0.244527
$196$	−14.7794	−1.05567
$197$	−23.1091	−1.64646	−0.823229	−	0.567710i	$-0.807830\pi$
$197$	−23.1091	−1.64646	−0.823229	+	0.567710i	$0.807830\pi$
$198$	−2.01324	−0.143075
$199$	19.4557	1.37918	0.689590	−	0.724200i	$-0.257791\pi$
$199$	19.4557	1.37918	0.689590	+	0.724200i	$0.257791\pi$
$200$	11.1379	0.787565
$201$	6.28597	0.443378
$202$	−9.64180	−0.678395
$203$	−24.6969	−1.73338
$204$	−1.32216	−0.0925694
$205$	−9.24273	−0.645541
$206$	8.39595	0.584974
$207$	−7.52588	−0.523085
$208$	−1.39100	−0.0964483
$209$	18.7248	1.29522
$210$	3.38139	0.233338
$211$	−17.2847	−1.18993	−0.594963	−	0.803753i	$-0.702833\pi$
$211$	−17.2847	−1.18993	−0.594963	+	0.803753i	$0.702833\pi$
$212$	−4.61638	−0.317054
$213$	−0.123956	−0.00849330
$214$	−10.9613	−0.749300
$215$	−11.1178	−0.758226
$216$	−2.73517	−0.186105
$217$	13.3142	0.903829
$218$	9.79909	0.663678
$219$	16.8684	1.13986
$220$	3.11435	0.209970
$221$	−3.54478	−0.238448
$222$	−4.19129	−0.281301
$223$	2.44817	0.163942	0.0819709	−	0.996635i	$-0.473879\pi$
$223$	2.44817	0.163942	0.0819709	+	0.996635i	$0.473879\pi$
$224$	24.7008	1.65039
$225$	−4.07208	−0.271472
$226$	−4.76300	−0.316830
$227$	13.3047	0.883067	0.441534	−	0.897245i	$-0.354435\pi$
$227$	13.3047	0.883067	0.441534	+	0.897245i	$0.354435\pi$
$228$	10.1244	0.670503
$229$	−9.37547	−0.619548	−0.309774	−	0.950810i	$-0.600253\pi$
$229$	−9.37547	−0.619548	−0.309774	+	0.950810i	$0.600253\pi$
$230$	−5.96866	−0.393561
$231$	−10.4257	−0.685964
$232$	15.8435	1.04018
$233$	9.31938	0.610533	0.305266	−	0.952267i	$-0.401255\pi$
$233$	9.31938	0.610533	0.305266	+	0.952267i	$0.401255\pi$
$234$	−2.91847	−0.190786
$235$	6.74283	0.439854
$236$	−5.33494	−0.347275
$237$	−1.00000	−0.0649570
$238$	3.51028	0.227538
$239$	1.52171	0.0984313	0.0492156	−	0.998788i	$-0.484328\pi$
$239$	1.52171	0.0984313	0.0492156	+	0.998788i	$0.484328\pi$
$240$	0.377999	0.0243997
$241$	16.1214	1.03847	0.519237	−	0.854630i	$-0.326216\pi$
$241$	16.1214	1.03847	0.519237	+	0.854630i	$0.326216\pi$
$242$	−4.13348	−0.265710
$243$	1.00000	0.0641500
$244$	5.46522	0.349875
$245$	10.7679	0.687934
$246$	−7.89971	−0.503667
$247$	27.1441	1.72714
$248$	−8.54131	−0.542374
$249$	−4.40130	−0.278921
$250$	−7.19493	−0.455047
$251$	9.82125	0.619912	0.309956	−	0.950751i	$-0.399686\pi$
$251$	9.82125	0.619912	0.309956	+	0.950751i	$0.399686\pi$
$252$	−5.63714	−0.355107
$253$	18.4030	1.15698
$254$	−11.6079	−0.728347
$255$	0.963284	0.0603232
$256$	−14.8084	−0.925523
$257$	12.1754	0.759481	0.379740	−	0.925093i	$-0.376013\pi$
$257$	12.1754	0.759481	0.379740	+	0.925093i	$0.376013\pi$
$258$	−9.50230	−0.591587
$259$	−21.7049	−1.34868
$260$	4.51468	0.279988
$261$	−5.79250	−0.358547
$262$	5.16425	0.319049
$263$	18.5810	1.14575	0.572877	−	0.819642i	$-0.305827\pi$
$263$	18.5810	1.14575	0.572877	+	0.819642i	$0.305827\pi$
$264$	6.68830	0.411636
$265$	3.36336	0.206609
$266$	−26.8799	−1.64811
$267$	11.1717	0.683695
$268$	−8.31103	−0.507677
$269$	18.9011	1.15242	0.576210	−	0.817302i	$-0.304531\pi$
$269$	18.9011	1.15242	0.576210	+	0.817302i	$0.304531\pi$
$270$	0.793084	0.0482656
$271$	−19.0528	−1.15738	−0.578688	−	0.815549i	$-0.696435\pi$
$271$	−19.0528	−1.15738	−0.578688	+	0.815549i	$0.696435\pi$
$272$	0.392407	0.0237932
$273$	−15.1135	−0.914713
$274$	−2.61925	−0.158235
$275$	9.95743	0.600456
$276$	9.95038	0.598943
$277$	17.8404	1.07193	0.535963	−	0.844242i	$-0.319949\pi$
$277$	17.8404	1.07193	0.535963	+	0.844242i	$0.319949\pi$
$278$	9.14392	0.548416
$279$	3.12277	0.186955
$280$	−11.2335	−0.671331
$281$	−12.7357	−0.759746	−0.379873	−	0.925039i	$-0.624032\pi$
$281$	−12.7357	−0.759746	−0.379873	+	0.925039i	$0.624032\pi$
$282$	5.76306	0.343185
$283$	−28.3119	−1.68297	−0.841483	−	0.540283i	$-0.818317\pi$
$283$	−28.3119	−1.68297	−0.841483	+	0.540283i	$0.818317\pi$
$284$	0.163889	0.00972500
$285$	−7.37633	−0.436936
$286$	7.13650	0.421990
$287$	−40.9093	−2.41480
$288$	5.79342	0.341381
$289$	1.00000	0.0588235
$290$	−4.59394	−0.269765
$291$	3.97117	0.232794
$292$	−22.3027	−1.30517
$293$	−33.3732	−1.94968	−0.974841	−	0.222903i	$-0.928447\pi$
$293$	−33.3732	−1.94968	−0.974841	+	0.222903i	$0.928447\pi$
$294$	9.20323	0.536743
$295$	3.88688	0.226303
$296$	13.9241	0.809322
$297$	−2.44529	−0.141890
$298$	6.65682	0.385619
$299$	26.6776	1.54281
$300$	5.38393	0.310841
$301$	−49.2085	−2.83633
$302$	11.3344	0.652222
$303$	−11.7110	−0.672778
$304$	−3.00485	−0.172340
$305$	−3.98180	−0.227997
$306$	0.823313	0.0470657
$307$	9.66150	0.551411	0.275705	−	0.961242i	$-0.411089\pi$
$307$	9.66150	0.551411	0.275705	+	0.961242i	$0.411089\pi$
$308$	13.7845	0.785443
$309$	10.1978	0.580130
$310$	2.47662	0.140662
$311$	−9.27296	−0.525822	−0.262911	−	0.964820i	$-0.584682\pi$
$311$	−9.27296	−0.525822	−0.262911	+	0.964820i	$0.584682\pi$
$312$	9.69560	0.548905
$313$	28.8128	1.62860	0.814299	−	0.580446i	$-0.197122\pi$
$313$	28.8128	1.62860	0.814299	+	0.580446i	$0.197122\pi$
$314$	4.74090	0.267545
$315$	4.10706	0.231407
$316$	1.32216	0.0743771
$317$	−21.3350	−1.19829	−0.599146	−	0.800640i	$-0.704493\pi$
$317$	−21.3350	−1.19829	−0.599146	+	0.800640i	$0.704493\pi$
$318$	2.87464	0.161202
$319$	14.1644	0.793051
$320$	3.83867	0.214588
$321$	−13.3137	−0.743096
$322$	−26.4179	−1.47221
$323$	−7.65748	−0.426073
$324$	−1.32216	−0.0734531
$325$	14.4347	0.800691
$326$	−1.63323	−0.0904562
$327$	11.9020	0.658183
$328$	26.2441	1.44909
$329$	29.8445	1.64538
$330$	−1.93932	−0.106756
$331$	−1.07123	−0.0588799	−0.0294399	−	0.999567i	$-0.509372\pi$
$331$	−1.07123	−0.0588799	−0.0294399	+	0.999567i	$0.509372\pi$
$332$	5.81920	0.319370
$333$	−5.09076	−0.278972
$334$	1.83108	0.100192
$335$	6.05517	0.330829
$336$	1.67307	0.0912732
$337$	−35.1521	−1.91486	−0.957428	−	0.288673i	$-0.906786\pi$
$337$	−35.1521	−1.91486	−0.957428	+	0.288673i	$0.906786\pi$
$338$	−0.357736	−0.0194583
$339$	−5.78517	−0.314207
$340$	−1.27361	−0.0690713
$341$	−7.63608	−0.413517
$342$	−6.30450	−0.340908
$343$	17.8145	0.961895
$344$	31.5681	1.70204
$345$	−7.24956	−0.390303
$346$	8.35786	0.449321
$347$	2.10563	0.113036	0.0565180	−	0.998402i	$-0.482000\pi$
$347$	2.10563	0.113036	0.0565180	+	0.998402i	$0.482000\pi$
$348$	7.65858	0.410543
$349$	−27.6614	−1.48068	−0.740339	−	0.672233i	$-0.765335\pi$
$349$	−27.6614	−1.48068	−0.740339	+	0.672233i	$0.765335\pi$
$350$	−14.2941	−0.764054
$351$	−3.54478	−0.189207
$352$	−14.1666	−0.755083
$353$	−20.4025	−1.08591	−0.542957	−	0.839761i	$-0.682695\pi$
$353$	−20.4025	−1.08591	−0.542957	+	0.839761i	$0.682695\pi$
$354$	3.32209	0.176567
$355$	−0.119405	−0.00633733
$356$	−14.7707	−0.782845
$357$	4.26360	0.225654
$358$	−15.2430	−0.805618
$359$	−29.4427	−1.55392	−0.776962	−	0.629547i	$-0.783240\pi$
$359$	−29.4427	−1.55392	−0.776962	+	0.629547i	$0.783240\pi$
$360$	−2.63475	−0.138864
$361$	39.6369	2.08615
$362$	−12.1814	−0.640239
$363$	−5.02055	−0.263510
$364$	19.9825	1.04737
$365$	16.2491	0.850516
$366$	−3.40322	−0.177889
$367$	−6.52757	−0.340736	−0.170368	−	0.985380i	$-0.554496\pi$
$367$	−6.52757	−0.340736	−0.170368	+	0.985380i	$0.554496\pi$
$368$	−2.95321	−0.153946
$369$	−9.59502	−0.499497
$370$	−4.03740	−0.209894
$371$	14.8866	0.772873
$372$	−4.12878	−0.214067
$373$	−2.41017	−0.124794	−0.0623970	−	0.998051i	$-0.519874\pi$
$373$	−2.41017	−0.124794	−0.0623970	+	0.998051i	$0.519874\pi$
$374$	−2.01324	−0.104102
$375$	−8.73899	−0.451280
$376$	−19.1458	−0.987368
$377$	20.5332	1.05751
$378$	3.51028	0.180549
$379$	−30.3045	−1.55664	−0.778319	−	0.627869i	$-0.783927\pi$
$379$	−30.3045	−1.55664	−0.778319	+	0.627869i	$0.783927\pi$
$380$	9.75265	0.500300
$381$	−14.0991	−0.722317
$382$	−9.50310	−0.486221
$383$	−1.32674	−0.0677932	−0.0338966	−	0.999425i	$-0.510792\pi$
$383$	−1.32674	−0.0677932	−0.0338966	+	0.999425i	$0.510792\pi$
$384$	−8.30595	−0.423861
$385$	−10.0430	−0.511837
$386$	3.18685	0.162207
$387$	−11.5415	−0.586689
$388$	−5.25050	−0.266554
$389$	27.6745	1.40315	0.701577	−	0.712594i	$-0.252480\pi$
$389$	27.6745	1.40315	0.701577	+	0.712594i	$0.252480\pi$
$390$	−2.81131	−0.142356
$391$	−7.52588	−0.380600
$392$	−30.5746	−1.54425
$393$	6.27253	0.316407
$394$	−19.0261	−0.958519
$395$	−0.963284	−0.0484681
$396$	3.23306	0.162467
$397$	34.9804	1.75562	0.877808	−	0.479012i	$-0.159005\pi$
$397$	34.9804	1.75562	0.877808	+	0.479012i	$0.159005\pi$
$398$	16.0181	0.802917
$399$	−32.6484	−1.63447
$400$	−1.59791	−0.0798957
$401$	−30.7496	−1.53556	−0.767780	−	0.640713i	$-0.778639\pi$
$401$	−30.7496	−1.53556	−0.767780	+	0.640713i	$0.778639\pi$
$402$	5.17532	0.258122
$403$	−11.0695	−0.551413
$404$	15.4837	0.770344
$405$	0.963284	0.0478660
$406$	−20.3333	−1.00912
$407$	12.4484	0.617044
$408$	−2.73517	−0.135411
$409$	−20.0199	−0.989920	−0.494960	−	0.868916i	$-0.664817\pi$
$409$	−20.0199	−0.989920	−0.494960	+	0.868916i	$0.664817\pi$
$410$	−7.60966	−0.375815
$411$	−3.18136	−0.156925
$412$	−13.4830	−0.664261
$413$	17.2038	0.846542
$414$	−6.19615	−0.304524
$415$	−4.23970	−0.208119
$416$	−20.5364	−1.00688
$417$	11.1062	0.543875
$418$	15.4163	0.754038
$419$	−7.55702	−0.369185	−0.184592	−	0.982815i	$-0.559096\pi$
$419$	−7.55702	−0.369185	−0.184592	+	0.982815i	$0.559096\pi$
$420$	−5.43017	−0.264965
$421$	5.49415	0.267768	0.133884	−	0.990997i	$-0.457255\pi$
$421$	5.49415	0.267768	0.133884	+	0.990997i	$0.457255\pi$
$422$	−14.2307	−0.692740
$423$	6.99984	0.340344
$424$	−9.55001	−0.463789
$425$	−4.07208	−0.197525
$426$	−0.102054	−0.00494455
$427$	−17.6239	−0.852879
$428$	17.6027	0.850861
$429$	8.66803	0.418497
$430$	−9.15341	−0.441417
$431$	4.23873	0.204173	0.102086	−	0.994776i	$-0.467448\pi$
$431$	4.23873	0.204173	0.102086	+	0.994776i	$0.467448\pi$
$432$	0.392407	0.0188797
$433$	13.9927	0.672445	0.336222	−	0.941783i	$-0.390851\pi$
$433$	13.9927	0.672445	0.336222	+	0.941783i	$0.390851\pi$
$434$	10.9618	0.526182
$435$	−5.57982	−0.267532
$436$	−15.7363	−0.753633
$437$	57.6292	2.75678
$438$	13.8880	0.663594
$439$	−15.0903	−0.720220	−0.360110	−	0.932910i	$-0.617261\pi$
$439$	−15.0903	−0.720220	−0.360110	+	0.932910i	$0.617261\pi$
$440$	6.44273	0.307145
$441$	11.1783	0.532299
$442$	−2.91847	−0.138817
$443$	20.3775	0.968164	0.484082	−	0.875023i	$-0.339154\pi$
$443$	20.3775	0.968164	0.484082	+	0.875023i	$0.339154\pi$
$444$	6.73077	0.319428
$445$	10.7615	0.510144
$446$	2.01561	0.0954420
$447$	8.08540	0.382426
$448$	16.9904	0.802720
$449$	20.1823	0.952464	0.476232	−	0.879320i	$-0.342002\pi$
$449$	20.1823	0.952464	0.476232	+	0.879320i	$0.342002\pi$
$450$	−3.35260	−0.158043
$451$	23.4626	1.10481
$452$	7.64889	0.359774
$453$	13.7668	0.646822
$454$	10.9540	0.514095
$455$	−14.5586	−0.682519
$456$	20.9445	0.980818
$457$	−22.4252	−1.04901	−0.524503	−	0.851409i	$-0.675749\pi$
$457$	−22.4252	−1.04901	−0.524503	+	0.851409i	$0.675749\pi$
$458$	−7.71894	−0.360683
$459$	1.00000	0.0466760
$460$	9.58504	0.446905
$461$	−32.2458	−1.50184	−0.750919	−	0.660395i	$-0.770389\pi$
$461$	−32.2458	−1.50184	−0.750919	+	0.660395i	$0.770389\pi$
$462$	−8.58365	−0.399348
$463$	4.84776	0.225294	0.112647	−	0.993635i	$-0.464067\pi$
$463$	4.84776	0.225294	0.112647	+	0.993635i	$0.464067\pi$
$464$	−2.27302	−0.105522
$465$	3.00811	0.139498
$466$	7.67276	0.355434
$467$	−25.3175	−1.17156	−0.585778	−	0.810472i	$-0.699211\pi$
$467$	−25.3175	−1.17156	−0.585778	+	0.810472i	$0.699211\pi$
$468$	4.68676	0.216645
$469$	26.8009	1.23755
$470$	5.55146	0.256070
$471$	5.75832	0.265330
$472$	−11.0365	−0.507997
$473$	28.2224	1.29767
$474$	−0.823313	−0.0378160
$475$	31.1819	1.43072
$476$	−5.63714	−0.258378
$477$	3.49155	0.159867
$478$	1.25284	0.0573038
$479$	−21.0980	−0.963992	−0.481996	−	0.876174i	$-0.660088\pi$
$479$	−21.0980	−0.963992	−0.481996	+	0.876174i	$0.660088\pi$
$480$	5.58071	0.254723
$481$	18.0456	0.822810
$482$	13.2730	0.604568
$483$	−32.0873	−1.46002
$484$	6.63794	0.301725
$485$	3.82536	0.173701
$486$	0.823313	0.0373462
$487$	18.5653	0.841274	0.420637	−	0.907229i	$-0.361807\pi$
$487$	18.5653	0.841274	0.420637	+	0.907229i	$0.361807\pi$
$488$	11.3060	0.511800
$489$	−1.98373	−0.0897072
$490$	8.86533	0.400495
$491$	−17.8436	−0.805269	−0.402634	−	0.915361i	$-0.631905\pi$
$491$	−17.8436	−0.805269	−0.402634	+	0.915361i	$0.631905\pi$
$492$	12.6861	0.571934
$493$	−5.79250	−0.260881
$494$	22.3481	1.00549
$495$	−2.35551	−0.105872
$496$	1.22540	0.0550219
$497$	−0.528497	−0.0237064
$498$	−3.62364	−0.162379
$499$	19.1383	0.856747	0.428373	−	0.903602i	$-0.359087\pi$
$499$	19.1383	0.856747	0.428373	+	0.903602i	$0.359087\pi$
$500$	11.5543	0.516724
$501$	2.22404	0.0993626
$502$	8.08596	0.360894
$503$	3.55214	0.158382	0.0791910	−	0.996859i	$-0.474766\pi$
$503$	3.55214	0.158382	0.0791910	+	0.996859i	$0.474766\pi$
$504$	−11.6617	−0.519453
$505$	−11.2810	−0.501998
$506$	15.1514	0.673562
$507$	−0.434508	−0.0192972
$508$	18.6411	0.827067
$509$	23.5037	1.04178	0.520892	−	0.853623i	$-0.325600\pi$
$509$	23.5037	1.04178	0.520892	+	0.853623i	$0.325600\pi$
$510$	0.793084	0.0351184
$511$	71.9202	3.18156
$512$	4.41998	0.195337
$513$	−7.65748	−0.338086
$514$	10.0242	0.442147
$515$	9.82334	0.432868
$516$	15.2597	0.671771
$517$	−17.1166	−0.752789
$518$	−17.8700	−0.785161
$519$	10.1515	0.445601
$520$	9.33962	0.409569
$521$	27.8442	1.21987	0.609937	−	0.792450i	$-0.291195\pi$
$521$	27.8442	1.21987	0.609937	+	0.792450i	$0.291195\pi$
$522$	−4.76904	−0.208735
$523$	33.2652	1.45458	0.727292	−	0.686328i	$-0.240779\pi$
$523$	33.2652	1.45458	0.727292	+	0.686328i	$0.240779\pi$
$524$	−8.29326	−0.362293
$525$	−17.3617	−0.757728
$526$	15.2980	0.667024
$527$	3.12277	0.136030
$528$	−0.959549	−0.0417590
$529$	33.6388	1.46256
$530$	2.76910	0.120282
$531$	4.03503	0.175105
$532$	43.1663	1.87150
$533$	34.0123	1.47324
$534$	9.19778	0.398027
$535$	−12.8248	−0.554466
$536$	−17.1932	−0.742634
$537$	−18.5142	−0.798948
$538$	15.5615	0.670905
$539$	−27.3342	−1.17737
$540$	−1.27361	−0.0548075
$541$	−16.1774	−0.695520	−0.347760	−	0.937584i	$-0.613058\pi$
$541$	−16.1774	−0.695520	−0.347760	+	0.937584i	$0.613058\pi$
$542$	−15.6864	−0.673789
$543$	−14.7956	−0.634938
$544$	5.79342	0.248391
$545$	11.4650	0.491108
$546$	−12.4432	−0.532519
$547$	40.3412	1.72487	0.862433	−	0.506171i	$-0.168940\pi$
$547$	40.3412	1.72487	0.862433	+	0.506171i	$0.168940\pi$
$548$	4.20625	0.179682
$549$	−4.13357	−0.176416
$550$	8.19809	0.349568
$551$	44.3559	1.88963
$552$	20.5846	0.876138
$553$	−4.26360	−0.181307
$554$	14.6882	0.624043
$555$	−4.90384	−0.208157
$556$	−14.6842	−0.622748
$557$	−43.1113	−1.82669	−0.913343	−	0.407192i	$-0.866508\pi$
$557$	−43.1113	−1.82669	−0.913343	+	0.407192i	$0.866508\pi$
$558$	2.57101	0.108840
$559$	40.9122	1.73040
$560$	1.61164	0.0681041
$561$	−2.44529	−0.103240
$562$	−10.4854	−0.442302
$563$	−14.7931	−0.623457	−0.311728	−	0.950171i	$-0.600908\pi$
$563$	−14.7931	−0.623457	−0.311728	+	0.950171i	$0.600908\pi$
$564$	−9.25488	−0.389701
$565$	−5.57276	−0.234448
$566$	−23.3095	−0.979773
$567$	4.26360	0.179054
$568$	0.339040	0.0142258
$569$	12.6512	0.530367	0.265184	−	0.964198i	$-0.414567\pi$
$569$	12.6512	0.530367	0.265184	+	0.964198i	$0.414567\pi$
$570$	−6.07302	−0.254371
$571$	41.7065	1.74536	0.872681	−	0.488291i	$-0.162379\pi$
$571$	41.7065	1.74536	0.872681	+	0.488291i	$0.162379\pi$
$572$	−11.4605	−0.479187
$573$	−11.5425	−0.482196
$574$	−33.6812	−1.40583
$575$	30.6460	1.27803
$576$	3.98499	0.166041
$577$	−4.70835	−0.196011	−0.0980056	−	0.995186i	$-0.531246\pi$
$577$	−4.70835	−0.196011	−0.0980056	+	0.995186i	$0.531246\pi$
$578$	0.823313	0.0342453
$579$	3.87077	0.160864
$580$	7.37739	0.306330
$581$	−18.7654	−0.778519
$582$	3.26951	0.135526
$583$	−8.53787	−0.353602
$584$	−46.1380	−1.90921
$585$	−3.41463	−0.141178
$586$	−27.4766	−1.13505
$587$	39.3720	1.62506	0.812528	−	0.582923i	$-0.198091\pi$
$587$	39.3720	1.62506	0.812528	+	0.582923i	$0.198091\pi$
$588$	−14.7794	−0.609494
$589$	−23.9125	−0.985298
$590$	3.20012	0.131747
$591$	−23.1091	−0.950583
$592$	−1.99765	−0.0821028
$593$	11.9825	0.492062	0.246031	−	0.969262i	$-0.420874\pi$
$593$	11.9825	0.492062	0.246031	+	0.969262i	$0.420874\pi$
$594$	−2.01324	−0.0826043
$595$	4.10706	0.168373
$596$	−10.6902	−0.437886
$597$	19.4557	0.796269
$598$	21.9640	0.898176
$599$	−12.1286	−0.495563	−0.247781	−	0.968816i	$-0.579701\pi$
$599$	−12.1286	−0.495563	−0.247781	+	0.968816i	$0.579701\pi$
$600$	11.1379	0.454701
$601$	20.7027	0.844482	0.422241	−	0.906484i	$-0.361244\pi$
$601$	20.7027	0.844482	0.422241	+	0.906484i	$0.361244\pi$
$602$	−40.5140	−1.65123
$603$	6.28597	0.255984
$604$	−18.2019	−0.740624
$605$	−4.83621	−0.196620
$606$	−9.64180	−0.391671
$607$	2.57697	0.104596	0.0522980	−	0.998632i	$-0.483345\pi$
$607$	2.57697	0.104596	0.0522980	+	0.998632i	$0.483345\pi$
$608$	−44.3630	−1.79916
$609$	−24.6969	−1.00077
$610$	−3.27827	−0.132733
$611$	−24.8129	−1.00382
$612$	−1.32216	−0.0534450
$613$	−46.6796	−1.88537	−0.942685	−	0.333683i	$-0.891709\pi$
$613$	−46.6796	−1.88537	−0.942685	+	0.333683i	$0.891709\pi$
$614$	7.95444	0.321015
$615$	−9.24273	−0.372703
$616$	28.5162	1.14895
$617$	−37.1017	−1.49366	−0.746830	−	0.665015i	$-0.768425\pi$
$617$	−37.1017	−1.49366	−0.746830	+	0.665015i	$0.768425\pi$
$618$	8.39595	0.337735
$619$	14.8794	0.598052	0.299026	−	0.954245i	$-0.403338\pi$
$619$	14.8794	0.598052	0.299026	+	0.954245i	$0.403338\pi$
$620$	−3.97719	−0.159728
$621$	−7.52588	−0.302003
$622$	−7.63455	−0.306118
$623$	47.6315	1.90832
$624$	−1.39100	−0.0556845
$625$	11.9423	0.477691
$626$	23.7220	0.948121
$627$	18.7248	0.747795
$628$	−7.61340	−0.303808
$629$	−5.09076	−0.202982
$630$	3.38139	0.134718
$631$	42.1274	1.67707	0.838533	−	0.544851i	$-0.183414\pi$
$631$	42.1274	1.67707	0.838533	+	0.544851i	$0.183414\pi$
$632$	2.73517	0.108799
$633$	−17.2847	−0.687004
$634$	−17.5654	−0.697609
$635$	−13.5814	−0.538961
$636$	−4.61638	−0.183051
$637$	−39.6246	−1.56998
$638$	11.6617	0.461691
$639$	−0.123956	−0.00490361
$640$	−8.00099	−0.316267
$641$	16.8337	0.664889	0.332445	−	0.943123i	$-0.392127\pi$
$641$	16.8337	0.664889	0.332445	+	0.943123i	$0.392127\pi$
$642$	−10.9613	−0.432609
$643$	−17.3223	−0.683126	−0.341563	−	0.939859i	$-0.610956\pi$
$643$	−17.3223	−0.683126	−0.341563	+	0.939859i	$0.610956\pi$
$644$	42.4244	1.67176
$645$	−11.1178	−0.437762
$646$	−6.30450	−0.248047
$647$	−16.2162	−0.637524	−0.318762	−	0.947835i	$-0.603267\pi$
$647$	−16.2162	−0.637524	−0.318762	+	0.947835i	$0.603267\pi$
$648$	−2.73517	−0.107448
$649$	−9.86683	−0.387307
$650$	11.8842	0.466138
$651$	13.3142	0.521826
$652$	2.62280	0.102717
$653$	−29.5791	−1.15752	−0.578759	−	0.815499i	$-0.696463\pi$
$653$	−29.5791	−1.15752	−0.578759	+	0.815499i	$0.696463\pi$
$654$	9.79909	0.383175
$655$	6.04223	0.236089
$656$	−3.76515	−0.147005
$657$	16.8684	0.658100
$658$	24.5714	0.957892
$659$	−31.3576	−1.22152	−0.610759	−	0.791817i	$-0.709136\pi$
$659$	−31.3576	−1.22152	−0.610759	+	0.791817i	$0.709136\pi$
$660$	3.11435	0.121226
$661$	39.8469	1.54986	0.774932	−	0.632045i	$-0.217784\pi$
$661$	39.8469	1.54986	0.774932	+	0.632045i	$0.217784\pi$
$662$	−0.881954	−0.0342781
$663$	−3.54478	−0.137668
$664$	12.0383	0.467177
$665$	−31.4497	−1.21957
$666$	−4.19129	−0.162409
$667$	43.5936	1.68795
$668$	−2.94052	−0.113772
$669$	2.44817	0.0946518
$670$	4.98530	0.192599
$671$	10.1078	0.390207
$672$	24.7008	0.952855
$673$	−13.1353	−0.506330	−0.253165	−	0.967423i	$-0.581472\pi$
$673$	−13.1353	−0.506330	−0.253165	+	0.967423i	$0.581472\pi$
$674$	−28.9412	−1.11477
$675$	−4.07208	−0.156735
$676$	0.574487	0.0220957
$677$	35.5091	1.36472	0.682362	−	0.731014i	$-0.260953\pi$
$677$	35.5091	1.36472	0.682362	+	0.731014i	$0.260953\pi$
$678$	−4.76300	−0.182922
$679$	16.9315	0.649770
$680$	−2.63475	−0.101038
$681$	13.3047	0.509839
$682$	−6.28688	−0.240737
$683$	4.38317	0.167717	0.0838587	−	0.996478i	$-0.473276\pi$
$683$	4.38317	0.167717	0.0838587	+	0.996478i	$0.473276\pi$
$684$	10.1244	0.387115
$685$	−3.06455	−0.117091
$686$	14.6669	0.559987
$687$	−9.37547	−0.357696
$688$	−4.52898	−0.172666
$689$	−12.3768	−0.471519
$690$	−5.96866	−0.227223
$691$	46.3672	1.76389	0.881947	−	0.471349i	$-0.156233\pi$
$691$	46.3672	1.76389	0.881947	+	0.471349i	$0.156233\pi$
$692$	−13.4219	−0.510222
$693$	−10.4257	−0.396041
$694$	1.73359	0.0658062
$695$	10.6985	0.405816
$696$	15.8435	0.600546
$697$	−9.59502	−0.363437
$698$	−22.7740	−0.862007
$699$	9.31938	0.352491
$700$	22.9549	0.867614
$701$	41.6970	1.57488	0.787438	−	0.616394i	$-0.211407\pi$
$701$	41.6970	1.57488	0.787438	+	0.616394i	$0.211407\pi$
$702$	−2.91847	−0.110150
$703$	38.9823	1.47025
$704$	−9.74446	−0.367258
$705$	6.74283	0.253950
$706$	−16.7976	−0.632186
$707$	−49.9309	−1.87785
$708$	−5.33494	−0.200499
$709$	23.6714	0.888998	0.444499	−	0.895779i	$-0.353382\pi$
$709$	23.6714	0.888998	0.444499	+	0.895779i	$0.353382\pi$
$710$	−0.0983073	−0.00368941
$711$	−1.00000	−0.0375029
$712$	−30.5565	−1.14515
$713$	−23.5016	−0.880140
$714$	3.51028	0.131369
$715$	8.34978	0.312264
$716$	24.4787	0.914811
$717$	1.52171	0.0568293
$718$	−24.2405	−0.904649
$719$	−22.8504	−0.852178	−0.426089	−	0.904681i	$-0.640109\pi$
$719$	−22.8504	−0.852178	−0.426089	+	0.904681i	$0.640109\pi$
$720$	0.377999	0.0140872
$721$	43.4792	1.61925
$722$	32.6336	1.21450
$723$	16.1214	0.599563
$724$	19.5620	0.727017
$725$	23.5875	0.876019
$726$	−4.13348	−0.153408
$727$	−7.08197	−0.262656	−0.131328	−	0.991339i	$-0.541924\pi$
$727$	−7.08197	−0.262656	−0.131328	+	0.991339i	$0.541924\pi$
$728$	41.3382	1.53209
$729$	1.00000	0.0370370
$730$	13.3781	0.495145
$731$	−11.5415	−0.426879
$732$	5.46522	0.202000
$733$	35.9024	1.32609	0.663043	−	0.748581i	$-0.269265\pi$
$733$	35.9024	1.32609	0.663043	+	0.748581i	$0.269265\pi$
$734$	−5.37423	−0.198367
$735$	10.7679	0.397179
$736$	−43.6006	−1.60714
$737$	−15.3710	−0.566199
$738$	−7.89971	−0.290792
$739$	6.64068	0.244282	0.122141	−	0.992513i	$-0.461024\pi$
$739$	6.64068	0.244282	0.122141	+	0.992513i	$0.461024\pi$
$740$	6.48365	0.238344
$741$	27.1441	0.997163
$742$	12.2563	0.449944
$743$	−42.8421	−1.57172	−0.785861	−	0.618403i	$-0.787780\pi$
$743$	−42.8421	−1.57172	−0.785861	+	0.618403i	$0.787780\pi$
$744$	−8.54131	−0.313140
$745$	7.78854	0.285350
$746$	−1.98433	−0.0726513
$747$	−4.40130	−0.161035
$748$	3.23306	0.118212
$749$	−56.7642	−2.07412
$750$	−7.19493	−0.262722
$751$	−0.133789	−0.00488204	−0.00244102	−	0.999997i	$-0.500777\pi$
$751$	−0.133789	−0.00488204	−0.00244102	+	0.999997i	$0.500777\pi$
$752$	2.74678	0.100165
$753$	9.82125	0.357906
$754$	16.9052	0.615652
$755$	13.2614	0.482631
$756$	−5.63714	−0.205021
$757$	−52.4291	−1.90557	−0.952785	−	0.303646i	$-0.901796\pi$
$757$	−52.4291	−1.90557	−0.952785	+	0.303646i	$0.901796\pi$
$758$	−24.9501	−0.906228
$759$	18.4030	0.667985
$760$	20.1755	0.731844
$761$	−22.9656	−0.832501	−0.416251	−	0.909250i	$-0.636656\pi$
$761$	−22.9656	−0.832501	−0.416251	+	0.909250i	$0.636656\pi$
$762$	−11.6079	−0.420511
$763$	50.7455	1.83711
$764$	15.2610	0.552124
$765$	0.963284	0.0348276
$766$	−1.09232	−0.0394672
$767$	−14.3033	−0.516463
$768$	−14.8084	−0.534351
$769$	7.74025	0.279121	0.139560	−	0.990214i	$-0.455431\pi$
$769$	7.74025	0.279121	0.139560	+	0.990214i	$0.455431\pi$
$770$	−8.26850	−0.297976
$771$	12.1754	0.438486
$772$	−5.11776	−0.184192
$773$	−49.6643	−1.78630	−0.893150	−	0.449758i	$-0.851510\pi$
$773$	−49.6643	−1.78630	−0.893150	+	0.449758i	$0.851510\pi$
$774$	−9.50230	−0.341553
$775$	−12.7162	−0.456778
$776$	−10.8618	−0.389917
$777$	−21.7049	−0.778661
$778$	22.7848	0.816874
$779$	73.4737	2.63247
$780$	4.51468	0.161651
$781$	0.303108	0.0108461
$782$	−6.19615	−0.221574
$783$	−5.79250	−0.207007
$784$	4.38644	0.156658
$785$	5.54690	0.197977
$786$	5.16425	0.184203
$787$	−23.9365	−0.853245	−0.426623	−	0.904430i	$-0.640297\pi$
$787$	−23.9365	−0.853245	−0.426623	+	0.904430i	$0.640297\pi$
$788$	30.5539	1.08844
$789$	18.5810	0.661501
$790$	−0.793084	−0.0282167
$791$	−24.6656	−0.877009
$792$	6.68830	0.237658
$793$	14.6526	0.520329
$794$	28.7998	1.02207
$795$	3.36336	0.119286
$796$	−25.7235	−0.911745
$797$	16.6860	0.591048	0.295524	−	0.955335i	$-0.404506\pi$
$797$	16.6860	0.591048	0.295524	+	0.955335i	$0.404506\pi$
$798$	−26.8799	−0.951537
$799$	6.99984	0.247636
$800$	−23.5913	−0.834078
$801$	11.1717	0.394732
$802$	−25.3165	−0.893958
$803$	−41.2482	−1.45562
$804$	−8.31103	−0.293107
$805$	−30.9092	−1.08941
$806$	−9.11369	−0.321016
$807$	18.9011	0.665350
$808$	32.0316	1.12687
$809$	−41.8173	−1.47022	−0.735109	−	0.677949i	$-0.762869\pi$
$809$	−41.8173	−1.47022	−0.735109	+	0.677949i	$0.762869\pi$
$810$	0.793084	0.0278661
$811$	19.7180	0.692394	0.346197	−	0.938162i	$-0.387473\pi$
$811$	19.7180	0.692394	0.346197	+	0.938162i	$0.387473\pi$
$812$	32.6531	1.14590
$813$	−19.0528	−0.668211
$814$	10.2489	0.359224
$815$	−1.91089	−0.0669357
$816$	0.392407	0.0137370
$817$	88.3790	3.09199
$818$	−16.4826	−0.576302
$819$	−15.1135	−0.528110
$820$	12.2203	0.426753
$821$	−30.9054	−1.07861	−0.539304	−	0.842111i	$-0.681312\pi$
$821$	−30.9054	−1.07861	−0.539304	+	0.842111i	$0.681312\pi$
$822$	−2.61925	−0.0913570
$823$	−2.67038	−0.0930836	−0.0465418	−	0.998916i	$-0.514820\pi$
$823$	−2.67038	−0.0930836	−0.0465418	+	0.998916i	$0.514820\pi$
$824$	−27.8927	−0.971687
$825$	9.95743	0.346673
$826$	14.1641	0.492831
$827$	−21.5036	−0.747754	−0.373877	−	0.927478i	$-0.621972\pi$
$827$	−21.5036	−0.747754	−0.373877	+	0.927478i	$0.621972\pi$
$828$	9.95038	0.345800
$829$	3.43290	0.119230	0.0596148	−	0.998221i	$-0.481013\pi$
$829$	3.43290	0.119230	0.0596148	+	0.998221i	$0.481013\pi$
$830$	−3.49060	−0.121160
$831$	17.8404	0.618876
$832$	−14.1259	−0.489728
$833$	11.1783	0.387305
$834$	9.14392	0.316628
$835$	2.14238	0.0741401
$836$	−24.7571	−0.856241
$837$	3.12277	0.107939
$838$	−6.22179	−0.214928
$839$	−33.5303	−1.15759	−0.578797	−	0.815471i	$-0.696478\pi$
$839$	−33.5303	−1.15759	−0.578797	+	0.815471i	$0.696478\pi$
$840$	−11.2335	−0.387593
$841$	4.55304	0.157001
$842$	4.52340	0.155887
$843$	−12.7357	−0.438640
$844$	22.8530	0.786634
$845$	−0.418555	−0.0143987
$846$	5.76306	0.198138
$847$	−21.4056	−0.735505
$848$	1.37011	0.0470498
$849$	−28.3119	−0.971661
$850$	−3.35260	−0.114993
$851$	38.3124	1.31333
$852$	0.163889	0.00561473
$853$	−25.2739	−0.865362	−0.432681	−	0.901547i	$-0.642432\pi$
$853$	−25.2739	−0.865362	−0.432681	+	0.901547i	$0.642432\pi$
$854$	−14.5100	−0.496521
$855$	−7.37633	−0.252265
$856$	36.4152	1.24465
$857$	15.7673	0.538601	0.269300	−	0.963056i	$-0.413208\pi$
$857$	15.7673	0.538601	0.269300	+	0.963056i	$0.413208\pi$
$858$	7.13650	0.243636
$859$	−4.73545	−0.161571	−0.0807857	−	0.996731i	$-0.525743\pi$
$859$	−4.73545	−0.161571	−0.0807857	+	0.996731i	$0.525743\pi$
$860$	14.6994	0.501246
$861$	−40.9093	−1.39419
$862$	3.48980	0.118863
$863$	−38.0155	−1.29406	−0.647031	−	0.762463i	$-0.723990\pi$
$863$	−38.0155	−1.29406	−0.647031	+	0.762463i	$0.723990\pi$
$864$	5.79342	0.197096
$865$	9.77877	0.332488
$866$	11.5204	0.391477
$867$	1.00000	0.0339618
$868$	−17.6035	−0.597501
$869$	2.44529	0.0829509
$870$	−4.59394	−0.155749
$871$	−22.2824	−0.755010
$872$	−32.5541	−1.10242
$873$	3.97117	0.134404
$874$	47.4469	1.60492
$875$	−37.2596	−1.25960
$876$	−22.3027	−0.753537
$877$	−15.9142	−0.537384	−0.268692	−	0.963226i	$-0.586591\pi$
$877$	−15.9142	−0.537384	−0.268692	+	0.963226i	$0.586591\pi$
$878$	−12.4240	−0.419290
$879$	−33.3732	−1.12565
$880$	−0.924319	−0.0311588
$881$	19.8644	0.669250	0.334625	−	0.942351i	$-0.391390\pi$
$881$	19.8644	0.669250	0.334625	+	0.942351i	$0.391390\pi$
$882$	9.20323	0.309889
$883$	22.1110	0.744094	0.372047	−	0.928214i	$-0.378656\pi$
$883$	22.1110	0.744094	0.372047	+	0.928214i	$0.378656\pi$
$884$	4.68676	0.157633
$885$	3.88688	0.130656
$886$	16.7771	0.563636
$887$	−20.0039	−0.671666	−0.335833	−	0.941922i	$-0.609018\pi$
$887$	−20.0039	−0.671666	−0.335833	+	0.941922i	$0.609018\pi$
$888$	13.9241	0.467262
$889$	−60.1127	−2.01612
$890$	8.86008	0.296990
$891$	−2.44529	−0.0819204
$892$	−3.23687	−0.108378
$893$	−53.6011	−1.79369
$894$	6.65682	0.222637
$895$	−17.8345	−0.596140
$896$	−35.4133	−1.18307
$897$	26.6776	0.890739
$898$	16.6164	0.554496
$899$	−18.0886	−0.603289
$900$	5.38393	0.179464
$901$	3.49155	0.116321
$902$	19.3171	0.643189
$903$	−49.2085	−1.63756
$904$	15.8234	0.526280
$905$	−14.2523	−0.473763
$906$	11.3344	0.376560
$907$	−11.4656	−0.380710	−0.190355	−	0.981715i	$-0.560964\pi$
$907$	−11.4656	−0.380710	−0.190355	+	0.981715i	$0.560964\pi$
$908$	−17.5909	−0.583776
$909$	−11.7110	−0.388428
$910$	−11.9863	−0.397342
$911$	−5.34816	−0.177192	−0.0885962	−	0.996068i	$-0.528238\pi$
$911$	−5.34816	−0.177192	−0.0885962	+	0.996068i	$0.528238\pi$
$912$	−3.00485	−0.0995004
$913$	10.7625	0.356185
$914$	−18.4629	−0.610700
$915$	−3.98180	−0.131634
$916$	12.3958	0.409570
$917$	26.7435	0.883150
$918$	0.823313	0.0271734
$919$	41.3599	1.36434	0.682169	−	0.731194i	$-0.261037\pi$
$919$	41.3599	1.36434	0.682169	+	0.731194i	$0.261037\pi$
$920$	19.8288	0.653736
$921$	9.66150	0.318357
$922$	−26.5484	−0.874325
$923$	0.439396	0.0144629
$924$	13.7845	0.453476
$925$	20.7300	0.681598
$926$	3.99122	0.131160
$927$	10.1978	0.334938
$928$	−33.5584	−1.10161
$929$	17.9217	0.587993	0.293997	−	0.955806i	$-0.405015\pi$
$929$	17.9217	0.587993	0.293997	+	0.955806i	$0.405015\pi$
$930$	2.47662	0.0812115
$931$	−85.5975	−2.80534
$932$	−12.3217	−0.403610
$933$	−9.27296	−0.303583
$934$	−20.8443	−0.682045
$935$	−2.35551	−0.0770335
$936$	9.69560	0.316911
$937$	8.27223	0.270242	0.135121	−	0.990829i	$-0.456858\pi$
$937$	8.27223	0.270242	0.135121	+	0.990829i	$0.456858\pi$
$938$	22.0655	0.720464
$939$	28.8128	0.940271
$940$	−8.91507	−0.290778
$941$	−25.2604	−0.823466	−0.411733	−	0.911305i	$-0.635076\pi$
$941$	−25.2604	−0.823466	−0.411733	+	0.911305i	$0.635076\pi$
$942$	4.74090	0.154467
$943$	72.2110	2.35151
$944$	1.58337	0.0515344
$945$	4.10706	0.133603
$946$	23.2359	0.755464
$947$	37.7481	1.22665	0.613324	−	0.789831i	$-0.289832\pi$
$947$	37.7481	1.22665	0.613324	+	0.789831i	$0.289832\pi$
$948$	1.32216	0.0429416
$949$	−59.7949	−1.94102
$950$	25.6725	0.832924
$951$	−21.3350	−0.691834
$952$	−11.6617	−0.377958
$953$	−16.4553	−0.533039	−0.266520	−	0.963830i	$-0.585874\pi$
$953$	−16.4553	−0.533039	−0.266520	+	0.963830i	$0.585874\pi$
$954$	2.87464	0.0930700
$955$	−11.1187	−0.359793
$956$	−2.01194	−0.0650707
$957$	14.1644	0.457868
$958$	−17.3702	−0.561207
$959$	−13.5640	−0.438006
$960$	3.83867	0.123893
$961$	−21.2483	−0.685430
$962$	14.8572	0.479015
$963$	−13.3137	−0.429027
$964$	−21.3151	−0.686512
$965$	3.72865	0.120029
$966$	−26.4179	−0.849983
$967$	39.2706	1.26286	0.631428	−	0.775435i	$-0.282469\pi$
$967$	39.2706	1.26286	0.631428	+	0.775435i	$0.282469\pi$
$968$	13.7321	0.441365
$969$	−7.65748	−0.245994
$970$	3.14947	0.101123
$971$	−19.1352	−0.614078	−0.307039	−	0.951697i	$-0.599338\pi$
$971$	−19.1352	−0.614078	−0.307039	+	0.951697i	$0.599338\pi$
$972$	−1.32216	−0.0424082
$973$	47.3526	1.51805
$974$	15.2851	0.489765
$975$	14.4347	0.462279
$976$	−1.62204	−0.0519202
$977$	14.0777	0.450387	0.225193	−	0.974314i	$-0.427699\pi$
$977$	14.0777	0.450387	0.225193	+	0.974314i	$0.427699\pi$
$978$	−1.63323	−0.0522249
$979$	−27.3180	−0.873087
$980$	−14.2368	−0.454778
$981$	11.9020	0.380002
$982$	−14.6908	−0.468803
$983$	−9.89290	−0.315534	−0.157767	−	0.987476i	$-0.550430\pi$
$983$	−9.89290	−0.315534	−0.157767	+	0.987476i	$0.550430\pi$
$984$	26.2441	0.836630
$985$	−22.2607	−0.709284
$986$	−4.76904	−0.151877
$987$	29.8445	0.949961
$988$	−35.8887	−1.14177
$989$	86.8602	2.76199
$990$	−1.93932	−0.0616357
$991$	46.5078	1.47737	0.738685	−	0.674051i	$-0.235447\pi$
$991$	46.5078	1.47737	0.738685	+	0.674051i	$0.235447\pi$
$992$	18.0915	0.574406
$993$	−1.07123	−0.0339943
$994$	−0.435119	−0.0138011
$995$	18.7414	0.594142
$996$	5.81920	0.184388
$997$	−9.04309	−0.286398	−0.143199	−	0.989694i	$-0.545739\pi$
$997$	−9.04309	−0.286398	−0.143199	+	0.989694i	$0.545739\pi$
$998$	15.7568	0.498772
$999$	−5.09076	−0.161064

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.e.1.13	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.e.1.13	✓	18	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+0.823313 q^{2} +1.00000 q^{3} -1.32216 q^{4} +0.963284 q^{5} +0.823313 q^{6} +4.26360 q^{7} -2.73517 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.823313 q^{2} +1.00000 q^{3} -1.32216 q^{4} +0.963284 q^{5} +0.823313 q^{6} +4.26360 q^{7} -2.73517 q^{8} +1.00000 q^{9} +0.793084 q^{10} -2.44529 q^{11} -1.32216 q^{12} -3.54478 q^{13} +3.51028 q^{14} +0.963284 q^{15} +0.392407 q^{16} +1.00000 q^{17} +0.823313 q^{18} -7.65748 q^{19} -1.27361 q^{20} +4.26360 q^{21} -2.01324 q^{22} -7.52588 q^{23} -2.73517 q^{24} -4.07208 q^{25} -2.91847 q^{26} +1.00000 q^{27} -5.63714 q^{28} -5.79250 q^{29} +0.793084 q^{30} +3.12277 q^{31} +5.79342 q^{32} -2.44529 q^{33} +0.823313 q^{34} +4.10706 q^{35} -1.32216 q^{36} -5.09076 q^{37} -6.30450 q^{38} -3.54478 q^{39} -2.63475 q^{40} -9.59502 q^{41} +3.51028 q^{42} -11.5415 q^{43} +3.23306 q^{44} +0.963284 q^{45} -6.19615 q^{46} +6.99984 q^{47} +0.392407 q^{48} +11.1783 q^{49} -3.35260 q^{50} +1.00000 q^{51} +4.68676 q^{52} +3.49155 q^{53} +0.823313 q^{54} -2.35551 q^{55} -11.6617 q^{56} -7.65748 q^{57} -4.76904 q^{58} +4.03503 q^{59} -1.27361 q^{60} -4.13357 q^{61} +2.57101 q^{62} +4.26360 q^{63} +3.98499 q^{64} -3.41463 q^{65} -2.01324 q^{66} +6.28597 q^{67} -1.32216 q^{68} -7.52588 q^{69} +3.38139 q^{70} -0.123956 q^{71} -2.73517 q^{72} +16.8684 q^{73} -4.19129 q^{74} -4.07208 q^{75} +10.1244 q^{76} -10.4257 q^{77} -2.91847 q^{78} -1.00000 q^{79} +0.377999 q^{80} +1.00000 q^{81} -7.89971 q^{82} -4.40130 q^{83} -5.63714 q^{84} +0.963284 q^{85} -9.50230 q^{86} -5.79250 q^{87} +6.68830 q^{88} +11.1717 q^{89} +0.793084 q^{90} -15.1135 q^{91} +9.95038 q^{92} +3.12277 q^{93} +5.76306 q^{94} -7.37633 q^{95} +5.79342 q^{96} +3.97117 q^{97} +9.20323 q^{98} -2.44529 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * q^99

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