LMFDB - Embedded newform 5239.2.a.m.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5239,2,Mod(1,5239)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5239, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5239.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.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:	$41.8336256189$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 4 x^{16} - 19 x^{15} + 90 x^{14} + 116 x^{13} - 776 x^{12} - 146 x^{11} + 3232 x^{10} + \cdots - 1 $ x^17 - 4x^16 - 19x^15 + 90x^14 + 116x^13 - 776x^12 - 146x^11 + 3232x^10 - 995x^9 - 6763x^8 + 3668x^7 + 6782x^6 - 4160x^5 - 2876x^4 + 1449x^3 + 392x^2 + 6x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 403)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$-2.43732$ of defining polynomial
Character	$\chi$	$=$	5239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.43732 q^{2} -0.331454 q^{3} +3.94051 q^{4} -0.0487430 q^{5} -0.807858 q^{6} -0.899705 q^{7} +4.72962 q^{8} -2.89014 q^{9} +O(q^{10})$	\(q+2.43732 q^{2} -0.331454 q^{3} +3.94051 q^{4} -0.0487430 q^{5} -0.807858 q^{6} -0.899705 q^{7} +4.72962 q^{8} -2.89014 q^{9} -0.118802 q^{10} -1.68825 q^{11} -1.30610 q^{12} -2.19286 q^{14} +0.0161561 q^{15} +3.64657 q^{16} -0.951107 q^{17} -7.04418 q^{18} -6.57840 q^{19} -0.192072 q^{20} +0.298211 q^{21} -4.11479 q^{22} +6.67103 q^{23} -1.56765 q^{24} -4.99762 q^{25} +1.95231 q^{27} -3.54529 q^{28} +8.28130 q^{29} +0.0393774 q^{30} -1.00000 q^{31} -0.571398 q^{32} +0.559576 q^{33} -2.31815 q^{34} +0.0438543 q^{35} -11.3886 q^{36} -6.36781 q^{37} -16.0336 q^{38} -0.230536 q^{40} -1.23586 q^{41} +0.726834 q^{42} -2.52788 q^{43} -6.65254 q^{44} +0.140874 q^{45} +16.2594 q^{46} +8.70641 q^{47} -1.20867 q^{48} -6.19053 q^{49} -12.1808 q^{50} +0.315248 q^{51} -7.18912 q^{53} +4.75839 q^{54} +0.0822901 q^{55} -4.25527 q^{56} +2.18044 q^{57} +20.1841 q^{58} -6.22518 q^{59} +0.0636630 q^{60} -8.60987 q^{61} -2.43732 q^{62} +2.60027 q^{63} -8.68582 q^{64} +1.36386 q^{66} -13.3972 q^{67} -3.74784 q^{68} -2.21114 q^{69} +0.106887 q^{70} -10.6963 q^{71} -13.6693 q^{72} -1.14523 q^{73} -15.5204 q^{74} +1.65648 q^{75} -25.9222 q^{76} +1.51892 q^{77} -3.73386 q^{79} -0.177745 q^{80} +8.02331 q^{81} -3.01219 q^{82} -4.08465 q^{83} +1.17510 q^{84} +0.0463598 q^{85} -6.16125 q^{86} -2.74487 q^{87} -7.98477 q^{88} -3.24372 q^{89} +0.343354 q^{90} +26.2872 q^{92} +0.331454 q^{93} +21.2203 q^{94} +0.320651 q^{95} +0.189392 q^{96} +9.86329 q^{97} -15.0883 q^{98} +4.87926 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9	$ 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9} + 6 q^{10} - 13 q^{11} + 4 q^{12} - 4 q^{15} + 34 q^{16} - 6 q^{17} + 12 q^{18} - 4 q^{19} - 28 q^{20} - 18 q^{21} - 34 q^{22} - 8 q^{23} - 40 q^{24} + 8 q^{25} - 3 q^{27} - 21 q^{28} - 6 q^{29} + 19 q^{30} - 17 q^{31} - 6 q^{32} - 7 q^{33} - 24 q^{34} - 9 q^{35} - 14 q^{37} + 11 q^{38} - 10 q^{40} - 43 q^{41} + 33 q^{42} + 18 q^{43} - 28 q^{44} - 26 q^{45} - 7 q^{46} - 6 q^{47} - 95 q^{48} - q^{49} - 44 q^{50} + 26 q^{51} - 5 q^{53} - 27 q^{54} + 39 q^{55} + 39 q^{56} - 46 q^{57} - 8 q^{58} + q^{59} - 21 q^{60} - 19 q^{61} + 4 q^{62} - 5 q^{63} + 42 q^{64} + 26 q^{66} - 10 q^{67} + 34 q^{68} + 32 q^{69} + 24 q^{70} - 35 q^{71} + 26 q^{72} - 11 q^{73} - 68 q^{74} - 62 q^{75} - 2 q^{76} + 21 q^{77} + q^{79} - 49 q^{80} + 37 q^{81} + 35 q^{82} - 24 q^{83} + 34 q^{84} + 13 q^{85} - 76 q^{86} - 22 q^{87} - 37 q^{88} - 42 q^{89} + 15 q^{90} + 15 q^{92} + 42 q^{94} + 34 q^{95} - 33 q^{96} + 38 q^{97} - 8 q^{98} - 17 q^{99}+O(q^{100}) $ 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9 + 6 * q^10 - 13 * q^11 + 4 * q^12 - 4 * q^15 + 34 * q^16 - 6 * q^17 + 12 * q^18 - 4 * q^19 - 28 * q^20 - 18 * q^21 - 34 * q^22 - 8 * q^23 - 40 * q^24 + 8 * q^25 - 3 * q^27 - 21 * q^28 - 6 * q^29 + 19 * q^30 - 17 * q^31 - 6 * q^32 - 7 * q^33 - 24 * q^34 - 9 * q^35 - 14 * q^37 + 11 * q^38 - 10 * q^40 - 43 * q^41 + 33 * q^42 + 18 * q^43 - 28 * q^44 - 26 * q^45 - 7 * q^46 - 6 * q^47 - 95 * q^48 - q^49 - 44 * q^50 + 26 * q^51 - 5 * q^53 - 27 * q^54 + 39 * q^55 + 39 * q^56 - 46 * q^57 - 8 * q^58 + q^59 - 21 * q^60 - 19 * q^61 + 4 * q^62 - 5 * q^63 + 42 * q^64 + 26 * q^66 - 10 * q^67 + 34 * q^68 + 32 * q^69 + 24 * q^70 - 35 * q^71 + 26 * q^72 - 11 * q^73 - 68 * q^74 - 62 * q^75 - 2 * q^76 + 21 * q^77 + q^79 - 49 * q^80 + 37 * q^81 + 35 * q^82 - 24 * q^83 + 34 * q^84 + 13 * q^85 - 76 * q^86 - 22 * q^87 - 37 * q^88 - 42 * q^89 + 15 * q^90 + 15 * q^92 + 42 * q^94 + 34 * q^95 - 33 * q^96 + 38 * q^97 - 8 * q^98 - 17 * 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 $

$2$	2.43732	1.72344	0.861721	−	0.507382i	$-0.169387\pi$
$2$	2.43732	1.72344	0.861721	+	0.507382i	$0.169387\pi$
$3$	−0.331454	−0.191365	−0.0956825	−	0.995412i	$-0.530503\pi$
$3$	−0.331454	−0.191365	−0.0956825	+	0.995412i	$0.530503\pi$
$4$	3.94051	1.97025
$5$	−0.0487430	−0.0217985	−0.0108993	−	0.999941i	$-0.503469\pi$
$5$	−0.0487430	−0.0217985	−0.0108993	+	0.999941i	$0.503469\pi$
$6$	−0.807858	−0.329807
$7$	−0.899705	−0.340056	−0.170028	−	0.985439i	$-0.554386\pi$
$7$	−0.899705	−0.340056	−0.170028	+	0.985439i	$0.554386\pi$
$8$	4.72962	1.67217
$9$	−2.89014	−0.963379
$10$	−0.118802	−0.0375685
$11$	−1.68825	−0.509025	−0.254513	−	0.967069i	$-0.581915\pi$
$11$	−1.68825	−0.509025	−0.254513	+	0.967069i	$0.581915\pi$
$12$	−1.30610	−0.377038
$13$	0	0
$13$	0	0
$14$	−2.19286	−0.586068
$15$	0.0161561	0.00417147
$16$	3.64657	0.911644
$17$	−0.951107	−0.230677	−0.115339	−	0.993326i	$-0.536795\pi$
$17$	−0.951107	−0.230677	−0.115339	+	0.993326i	$0.536795\pi$
$18$	−7.04418	−1.66033
$19$	−6.57840	−1.50919	−0.754595	−	0.656191i	$-0.772166\pi$
$19$	−6.57840	−1.50919	−0.754595	+	0.656191i	$0.772166\pi$
$20$	−0.192072	−0.0429486
$21$	0.298211	0.0650749
$22$	−4.11479	−0.877275
$23$	6.67103	1.39101	0.695503	−	0.718523i	$-0.255182\pi$
$23$	6.67103	1.39101	0.695503	+	0.718523i	$0.255182\pi$
$24$	−1.56765	−0.319996
$25$	−4.99762	−0.999525
$26$	0	0
$27$	1.95231	0.375722
$28$	−3.54529	−0.669997
$29$	8.28130	1.53780	0.768899	−	0.639370i	$-0.220805\pi$
$29$	8.28130	1.53780	0.768899	+	0.639370i	$0.220805\pi$
$30$	0.0393774	0.00718930
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−0.571398	−0.101010
$33$	0.559576	0.0974096
$34$	−2.31815	−0.397559
$35$	0.0438543	0.00741273
$36$	−11.3886	−1.89810
$37$	−6.36781	−1.04686	−0.523431	−	0.852068i	$-0.675348\pi$
$37$	−6.36781	−1.04686	−0.523431	+	0.852068i	$0.675348\pi$
$38$	−16.0336	−2.60100
$39$	0	0
$40$	−0.230536	−0.0364509
$41$	−1.23586	−0.193010	−0.0965048	−	0.995333i	$-0.530766\pi$
$41$	−1.23586	−0.193010	−0.0965048	+	0.995333i	$0.530766\pi$
$42$	0.726834	0.112153
$43$	−2.52788	−0.385498	−0.192749	−	0.981248i	$-0.561740\pi$
$43$	−2.52788	−0.385498	−0.192749	+	0.981248i	$0.561740\pi$
$44$	−6.65254	−1.00291
$45$	0.140874	0.0210002
$46$	16.2594	2.39732
$47$	8.70641	1.26996	0.634980	−	0.772528i	$-0.281008\pi$
$47$	8.70641	1.26996	0.634980	+	0.772528i	$0.281008\pi$
$48$	−1.20867	−0.174457
$49$	−6.19053	−0.884362
$50$	−12.1808	−1.72262
$51$	0.315248	0.0441436
$52$	0	0
$53$	−7.18912	−0.987501	−0.493751	−	0.869604i	$-0.664374\pi$
$53$	−7.18912	−0.987501	−0.493751	+	0.869604i	$0.664374\pi$
$54$	4.75839	0.647535
$55$	0.0822901	0.0110960
$56$	−4.25527	−0.568634
$57$	2.18044	0.288806
$58$	20.1841	2.65031
$59$	−6.22518	−0.810449	−0.405224	−	0.914217i	$-0.632807\pi$
$59$	−6.22518	−0.810449	−0.405224	+	0.914217i	$0.632807\pi$
$60$	0.0636630	0.00821886
$61$	−8.60987	−1.10238	−0.551191	−	0.834379i	$-0.685826\pi$
$61$	−8.60987	−1.10238	−0.551191	+	0.834379i	$0.685826\pi$
$62$	−2.43732	−0.309539
$63$	2.60027	0.327603
$64$	−8.68582	−1.08573
$65$	0	0
$66$	1.36386	0.167880
$67$	−13.3972	−1.63673	−0.818366	−	0.574697i	$-0.805120\pi$
$67$	−13.3972	−1.63673	−0.818366	+	0.574697i	$0.805120\pi$
$68$	−3.74784	−0.454493
$69$	−2.21114	−0.266190
$70$	0.106887	0.0127754
$71$	−10.6963	−1.26942	−0.634709	−	0.772751i	$-0.718880\pi$
$71$	−10.6963	−1.26942	−0.634709	+	0.772751i	$0.718880\pi$
$72$	−13.6693	−1.61094
$73$	−1.14523	−0.134039	−0.0670193	−	0.997752i	$-0.521349\pi$
$73$	−1.14523	−0.134039	−0.0670193	+	0.997752i	$0.521349\pi$
$74$	−15.5204	−1.80421
$75$	1.65648	0.191274
$76$	−25.9222	−2.97348
$77$	1.51892	0.173097
$78$	0	0
$79$	−3.73386	−0.420092	−0.210046	−	0.977691i	$-0.567361\pi$
$79$	−3.73386	−0.420092	−0.210046	+	0.977691i	$0.567361\pi$
$80$	−0.177745	−0.0198725
$81$	8.02331	0.891479
$82$	−3.01219	−0.332641
$83$	−4.08465	−0.448349	−0.224174	−	0.974549i	$-0.571968\pi$
$83$	−4.08465	−0.448349	−0.224174	+	0.974549i	$0.571968\pi$
$84$	1.17510	0.128214
$85$	0.0463598	0.00502843
$86$	−6.16125	−0.664384
$87$	−2.74487	−0.294281
$88$	−7.98477	−0.851179
$89$	−3.24372	−0.343833	−0.171917	−	0.985112i	$-0.554996\pi$
$89$	−3.24372	−0.343833	−0.171917	+	0.985112i	$0.554996\pi$
$90$	0.343354	0.0361927
$91$	0	0
$92$	26.2872	2.74063
$93$	0.331454	0.0343702
$94$	21.2203	2.18870
$95$	0.320651	0.0328981
$96$	0.189392	0.0193297
$97$	9.86329	1.00147	0.500733	−	0.865602i	$-0.333064\pi$
$97$	9.86329	1.00147	0.500733	+	0.865602i	$0.333064\pi$
$98$	−15.0883	−1.52415
$99$	4.87926	0.490384
$100$	−19.6932	−1.96932
$101$	−9.07113	−0.902611	−0.451305	−	0.892370i	$-0.649042\pi$
$101$	−9.07113	−0.902611	−0.451305	+	0.892370i	$0.649042\pi$
$102$	0.768359	0.0760789
$103$	−2.47755	−0.244120	−0.122060	−	0.992523i	$-0.538950\pi$
$103$	−2.47755	−0.244120	−0.122060	+	0.992523i	$0.538950\pi$
$104$	0	0
$105$	−0.0145357	−0.00141854
$106$	−17.5221	−1.70190
$107$	2.17531	0.210295	0.105148	−	0.994457i	$-0.466468\pi$
$107$	2.17531	0.210295	0.105148	+	0.994457i	$0.466468\pi$
$108$	7.69309	0.740268
$109$	12.1275	1.16160	0.580800	−	0.814046i	$-0.302740\pi$
$109$	12.1275	1.16160	0.580800	+	0.814046i	$0.302740\pi$
$110$	0.200567	0.0191233
$111$	2.11064	0.200333
$112$	−3.28084	−0.310010
$113$	12.3082	1.15786	0.578928	−	0.815379i	$-0.303471\pi$
$113$	12.3082	1.15786	0.578928	+	0.815379i	$0.303471\pi$
$114$	5.31441	0.497741
$115$	−0.325166	−0.0303219
$116$	32.6325	3.02985
$117$	0	0
$118$	−15.1727	−1.39676
$119$	0.855716	0.0784433
$120$	0.0764121	0.00697544
$121$	−8.14983	−0.740893
$122$	−20.9850	−1.89989
$123$	0.409632	0.0369353
$124$	−3.94051	−0.353868
$125$	0.487314	0.0435867
$126$	6.33768	0.564606
$127$	−9.95403	−0.883277	−0.441639	−	0.897193i	$-0.645603\pi$
$127$	−9.95403	−0.883277	−0.441639	+	0.897193i	$0.645603\pi$
$128$	−20.0273	−1.77018
$129$	0.837876	0.0737709
$130$	0	0
$131$	16.4622	1.43831	0.719154	−	0.694851i	$-0.244530\pi$
$131$	16.4622	1.43831	0.719154	+	0.694851i	$0.244530\pi$
$132$	2.20501	0.191922
$133$	5.91862	0.513210
$134$	−32.6533	−2.82081
$135$	−0.0951614	−0.00819019
$136$	−4.49838	−0.385733
$137$	10.1052	0.863345	0.431672	−	0.902031i	$-0.357924\pi$
$137$	10.1052	0.863345	0.431672	+	0.902031i	$0.357924\pi$
$138$	−5.38925	−0.458763
$139$	11.2208	0.951732	0.475866	−	0.879518i	$-0.342135\pi$
$139$	11.2208	0.951732	0.475866	+	0.879518i	$0.342135\pi$
$140$	0.172808	0.0146050
$141$	−2.88577	−0.243026
$142$	−26.0703	−2.18777
$143$	0	0
$144$	−10.5391	−0.878259
$145$	−0.403655	−0.0335217
$146$	−2.79128	−0.231008
$147$	2.05188	0.169236
$148$	−25.0924	−2.06258
$149$	10.8090	0.885509	0.442754	−	0.896643i	$-0.354001\pi$
$149$	10.8090	0.885509	0.442754	+	0.896643i	$0.354001\pi$
$150$	4.03737	0.329650
$151$	−16.2140	−1.31947	−0.659736	−	0.751497i	$-0.729332\pi$
$151$	−16.2140	−1.31947	−0.659736	+	0.751497i	$0.729332\pi$
$152$	−31.1134	−2.52363
$153$	2.74883	0.222230
$154$	3.70209	0.298323
$155$	0.0487430	0.00391513
$156$	0	0
$157$	−10.3030	−0.822265	−0.411133	−	0.911576i	$-0.634867\pi$
$157$	−10.3030	−0.822265	−0.411133	+	0.911576i	$0.634867\pi$
$158$	−9.10060	−0.724005
$159$	2.38286	0.188973
$160$	0.0278516	0.00220186
$161$	−6.00196	−0.473021
$162$	19.5553	1.53641
$163$	1.71980	0.134705	0.0673527	−	0.997729i	$-0.478545\pi$
$163$	1.71980	0.134705	0.0673527	+	0.997729i	$0.478545\pi$
$164$	−4.86993	−0.380278
$165$	−0.0272754	−0.00212339
$166$	−9.95558	−0.772703
$167$	−0.570067	−0.0441131	−0.0220565	−	0.999757i	$-0.507021\pi$
$167$	−0.570067	−0.0441131	−0.0220565	+	0.999757i	$0.507021\pi$
$168$	1.41042	0.108817
$169$	0	0
$170$	0.112993	0.00866620
$171$	19.0125	1.45392
$172$	−9.96113	−0.759529
$173$	17.8742	1.35895	0.679474	−	0.733699i	$-0.262208\pi$
$173$	17.8742	1.35895	0.679474	+	0.733699i	$0.262208\pi$
$174$	−6.69011	−0.507176
$175$	4.49639	0.339895
$176$	−6.15631	−0.464050
$177$	2.06336	0.155092
$178$	−7.90596	−0.592577
$179$	18.0150	1.34651	0.673253	−	0.739412i	$-0.264897\pi$
$179$	18.0150	1.34651	0.673253	+	0.739412i	$0.264897\pi$
$180$	0.555115	0.0413758
$181$	15.6815	1.16560	0.582799	−	0.812616i	$-0.301957\pi$
$181$	15.6815	1.16560	0.582799	+	0.812616i	$0.301957\pi$
$182$	0	0
$183$	2.85378	0.210957
$184$	31.5515	2.32601
$185$	0.310386	0.0228200
$186$	0.807858	0.0592350
$187$	1.60570	0.117421
$188$	34.3077	2.50214
$189$	−1.75650	−0.127767
$190$	0.781527	0.0566980
$191$	11.3480	0.821111	0.410556	−	0.911836i	$-0.365335\pi$
$191$	11.3480	0.821111	0.410556	+	0.911836i	$0.365335\pi$
$192$	2.87895	0.207770
$193$	−18.5294	−1.33378	−0.666888	−	0.745158i	$-0.732374\pi$
$193$	−18.5294	−1.33378	−0.666888	+	0.745158i	$0.732374\pi$
$194$	24.0400	1.72597
$195$	0	0
$196$	−24.3938	−1.74242
$197$	20.0121	1.42580	0.712902	−	0.701264i	$-0.247380\pi$
$197$	20.0121	1.42580	0.712902	+	0.701264i	$0.247380\pi$
$198$	11.8923	0.845149
$199$	−6.54794	−0.464171	−0.232085	−	0.972695i	$-0.574555\pi$
$199$	−6.54794	−0.464171	−0.232085	+	0.972695i	$0.574555\pi$
$200$	−23.6369	−1.67138
$201$	4.44057	0.313213
$202$	−22.1092	−1.55560
$203$	−7.45073	−0.522938
$204$	1.24224	0.0869740
$205$	0.0602397	0.00420732
$206$	−6.03856	−0.420726
$207$	−19.2802	−1.34007
$208$	0	0
$209$	11.1060	0.768215
$210$	−0.0354280	−0.00244477
$211$	6.74738	0.464509	0.232255	−	0.972655i	$-0.425390\pi$
$211$	6.74738	0.464509	0.232255	+	0.972655i	$0.425390\pi$
$212$	−28.3288	−1.94563
$213$	3.54533	0.242922
$214$	5.30192	0.362432
$215$	0.123216	0.00840329
$216$	9.23369	0.628273
$217$	0.899705	0.0610759
$218$	29.5584	2.00195
$219$	0.379590	0.0256503
$220$	0.324265	0.0218619
$221$	0	0
$222$	5.14429	0.345262
$223$	9.96208	0.667110	0.333555	−	0.942731i	$-0.391752\pi$
$223$	9.96208	0.667110	0.333555	+	0.942731i	$0.391752\pi$
$224$	0.514089	0.0343490
$225$	14.4438	0.962922
$226$	29.9989	1.99550
$227$	−9.73285	−0.645992	−0.322996	−	0.946400i	$-0.604690\pi$
$227$	−9.73285	−0.645992	−0.322996	+	0.946400i	$0.604690\pi$
$228$	8.59203	0.569021
$229$	−18.3306	−1.21132	−0.605661	−	0.795723i	$-0.707091\pi$
$229$	−18.3306	−1.21132	−0.605661	+	0.795723i	$0.707091\pi$
$230$	−0.792532	−0.0522580
$231$	−0.503453	−0.0331248
$232$	39.1674	2.57147
$233$	−5.69286	−0.372952	−0.186476	−	0.982460i	$-0.559707\pi$
$233$	−5.69286	−0.372952	−0.186476	+	0.982460i	$0.559707\pi$
$234$	0	0
$235$	−0.424376	−0.0276833
$236$	−24.5303	−1.59679
$237$	1.23760	0.0803910
$238$	2.08565	0.135193
$239$	17.4134	1.12638	0.563188	−	0.826329i	$-0.309575\pi$
$239$	17.4134	1.12638	0.563188	+	0.826329i	$0.309575\pi$
$240$	0.0589142	0.00380290
$241$	21.1130	1.36001	0.680006	−	0.733207i	$-0.261977\pi$
$241$	21.1130	1.36001	0.680006	+	0.733207i	$0.261977\pi$
$242$	−19.8637	−1.27689
$243$	−8.51629	−0.546320
$244$	−33.9272	−2.17197
$245$	0.301745	0.0192778
$246$	0.998403	0.0636558
$247$	0	0
$248$	−4.72962	−0.300331
$249$	1.35387	0.0857982
$250$	1.18774	0.0751191
$251$	5.11422	0.322807	0.161403	−	0.986889i	$-0.448398\pi$
$251$	5.11422	0.322807	0.161403	+	0.986889i	$0.448398\pi$
$252$	10.2464	0.645462
$253$	−11.2623	−0.708057
$254$	−24.2611	−1.52228
$255$	−0.0153661	−0.000962265 0
$256$	−31.4412	−1.96507
$257$	−20.3411	−1.26884	−0.634421	−	0.772988i	$-0.718761\pi$
$257$	−20.3411	−1.26884	−0.634421	+	0.772988i	$0.718761\pi$
$258$	2.04217	0.127140
$259$	5.72915	0.355992
$260$	0	0
$261$	−23.9341	−1.48148
$262$	40.1235	2.47884
$263$	−12.2048	−0.752581	−0.376291	−	0.926502i	$-0.622801\pi$
$263$	−12.2048	−0.752581	−0.376291	+	0.926502i	$0.622801\pi$
$264$	2.64658	0.162886
$265$	0.350419	0.0215261
$266$	14.4255	0.884487
$267$	1.07514	0.0657976
$268$	−52.7919	−3.22478
$269$	26.4861	1.61488	0.807442	−	0.589947i	$-0.200851\pi$
$269$	26.4861	1.61488	0.807442	+	0.589947i	$0.200851\pi$
$270$	−0.231938	−0.0141153
$271$	−4.29748	−0.261053	−0.130527	−	0.991445i	$-0.541667\pi$
$271$	−4.29748	−0.261053	−0.130527	+	0.991445i	$0.541667\pi$
$272$	−3.46828	−0.210296
$273$	0	0
$274$	24.6295	1.48792
$275$	8.43722	0.508783
$276$	−8.71301	−0.524462
$277$	−7.49195	−0.450148	−0.225074	−	0.974342i	$-0.572262\pi$
$277$	−7.49195	−0.450148	−0.225074	+	0.974342i	$0.572262\pi$
$278$	27.3485	1.64025
$279$	2.89014	0.173028
$280$	0.207414	0.0123954
$281$	15.5014	0.924739	0.462369	−	0.886687i	$-0.346999\pi$
$281$	15.5014	0.924739	0.462369	+	0.886687i	$0.346999\pi$
$282$	−7.03354	−0.418841
$283$	−16.3982	−0.974773	−0.487386	−	0.873186i	$-0.662050\pi$
$283$	−16.3982	−0.974773	−0.487386	+	0.873186i	$0.662050\pi$
$284$	−42.1488	−2.50107
$285$	−0.106281	−0.00629554
$286$	0	0
$287$	1.11191	0.0656342
$288$	1.65142	0.0973107
$289$	−16.0954	−0.946788
$290$	−0.983835	−0.0577728
$291$	−3.26923	−0.191646
$292$	−4.51277	−0.264090
$293$	9.55070	0.557958	0.278979	−	0.960297i	$-0.410004\pi$
$293$	9.55070	0.557958	0.278979	+	0.960297i	$0.410004\pi$
$294$	5.00107	0.291668
$295$	0.303434	0.0176666
$296$	−30.1174	−1.75054
$297$	−3.29598	−0.191252
$298$	26.3450	1.52612
$299$	0	0
$300$	6.52738	0.376858
$301$	2.27435	0.131091
$302$	−39.5185	−2.27403
$303$	3.00666	0.172728
$304$	−23.9886	−1.37584
$305$	0.419671	0.0240303
$306$	6.69977	0.383000
$307$	12.5368	0.715512	0.357756	−	0.933815i	$-0.383542\pi$
$307$	12.5368	0.715512	0.357756	+	0.933815i	$0.383542\pi$
$308$	5.98532	0.341045
$309$	0.821192	0.0467160
$310$	0.118802	0.00674750
$311$	9.97394	0.565570	0.282785	−	0.959183i	$-0.408742\pi$
$311$	9.97394	0.565570	0.282785	+	0.959183i	$0.408742\pi$
$312$	0	0
$313$	−21.9564	−1.24105	−0.620526	−	0.784186i	$-0.713081\pi$
$313$	−21.9564	−1.24105	−0.620526	+	0.784186i	$0.713081\pi$
$314$	−25.1115	−1.41713
$315$	−0.126745	−0.00714127
$316$	−14.7133	−0.827688
$317$	−33.2694	−1.86860	−0.934299	−	0.356491i	$-0.883973\pi$
$317$	−33.2694	−1.86860	−0.934299	+	0.356491i	$0.883973\pi$
$318$	5.80778	0.325684
$319$	−13.9809	−0.782778
$320$	0.423373	0.0236673
$321$	−0.721016	−0.0402432
$322$	−14.6287	−0.815224
$323$	6.25677	0.348136
$324$	31.6159	1.75644
$325$	0	0
$326$	4.19170	0.232157
$327$	−4.01970	−0.222290
$328$	−5.84518	−0.322746
$329$	−7.83320	−0.431858
$330$	−0.0664787	−0.00365953
$331$	−28.8558	−1.58606	−0.793030	−	0.609183i	$-0.791498\pi$
$331$	−28.8558	−1.58606	−0.793030	+	0.609183i	$0.791498\pi$
$332$	−16.0956	−0.883360
$333$	18.4039	1.00852
$334$	−1.38943	−0.0760263
$335$	0.653021	0.0356783
$336$	1.08745	0.0593251
$337$	0.603321	0.0328650	0.0164325	−	0.999865i	$-0.494769\pi$
$337$	0.603321	0.0328650	0.0164325	+	0.999865i	$0.494769\pi$
$338$	0	0
$339$	−4.07960	−0.221573
$340$	0.182681	0.00990727
$341$	1.68825	0.0914236
$342$	46.3394	2.50575
$343$	11.8676	0.640789
$344$	−11.9559	−0.644621
$345$	0.107778	0.00580255
$346$	43.5650	2.34207
$347$	31.9818	1.71687	0.858436	−	0.512920i	$-0.171436\pi$
$347$	31.9818	1.71687	0.858436	+	0.512920i	$0.171436\pi$
$348$	−10.8162	−0.579808
$349$	−1.51104	−0.0808840	−0.0404420	−	0.999182i	$-0.512877\pi$
$349$	−1.51104	−0.0808840	−0.0404420	+	0.999182i	$0.512877\pi$
$350$	10.9591	0.585789
$351$	0	0
$352$	0.964659	0.0514165
$353$	8.75939	0.466215	0.233108	−	0.972451i	$-0.425111\pi$
$353$	8.75939	0.466215	0.233108	+	0.972451i	$0.425111\pi$
$354$	5.02906	0.267291
$355$	0.521370	0.0276714
$356$	−12.7819	−0.677438
$357$	−0.283630	−0.0150113
$358$	43.9083	2.32062
$359$	−15.5001	−0.818063	−0.409032	−	0.912520i	$-0.634133\pi$
$359$	−15.5001	−0.818063	−0.409032	+	0.912520i	$0.634133\pi$
$360$	0.666281	0.0351161
$361$	24.2754	1.27765
$362$	38.2208	2.00884
$363$	2.70129	0.141781
$364$	0	0
$365$	0.0558217	0.00292184
$366$	6.95555	0.363573
$367$	19.7641	1.03168	0.515838	−	0.856686i	$-0.327481\pi$
$367$	19.7641	1.03168	0.515838	+	0.856686i	$0.327481\pi$
$368$	24.3264	1.26810
$369$	3.57182	0.185941
$370$	0.756509	0.0393290
$371$	6.46808	0.335806
$372$	1.30610	0.0677179
$373$	−4.14694	−0.214720	−0.107360	−	0.994220i	$-0.534240\pi$
$373$	−4.14694	−0.214720	−0.107360	+	0.994220i	$0.534240\pi$
$374$	3.91360	0.202368
$375$	−0.161522	−0.00834097
$376$	41.1781	2.12360
$377$	0	0
$378$	−4.28115	−0.220199
$379$	−0.946784	−0.0486330	−0.0243165	−	0.999704i	$-0.507741\pi$
$379$	−0.946784	−0.0486330	−0.0243165	+	0.999704i	$0.507741\pi$
$380$	1.26353	0.0648176
$381$	3.29930	0.169028
$382$	27.6586	1.41514
$383$	−14.8502	−0.758811	−0.379405	−	0.925231i	$-0.623871\pi$
$383$	−14.8502	−0.758811	−0.379405	+	0.925231i	$0.623871\pi$
$384$	6.63813	0.338751
$385$	−0.0740368	−0.00377327
$386$	−45.1620	−2.29869
$387$	7.30593	0.371381
$388$	38.8664	1.97314
$389$	−15.7314	−0.797612	−0.398806	−	0.917035i	$-0.630575\pi$
$389$	−15.7314	−0.797612	−0.398806	+	0.917035i	$0.630575\pi$
$390$	0	0
$391$	−6.34487	−0.320874
$392$	−29.2789	−1.47881
$393$	−5.45646	−0.275242
$394$	48.7758	2.45729
$395$	0.182000	0.00915739
$396$	19.2268	0.966181
$397$	−1.11624	−0.0560225	−0.0280113	−	0.999608i	$-0.508917\pi$
$397$	−1.11624	−0.0560225	−0.0280113	+	0.999608i	$0.508917\pi$
$398$	−15.9594	−0.799972
$399$	−1.96175	−0.0982104
$400$	−18.2242	−0.911210
$401$	−27.2884	−1.36272	−0.681358	−	0.731951i	$-0.738610\pi$
$401$	−27.2884	−1.36272	−0.681358	+	0.731951i	$0.738610\pi$
$402$	10.8231	0.539805
$403$	0	0
$404$	−35.7448	−1.77837
$405$	−0.391080	−0.0194329
$406$	−18.1598	−0.901254
$407$	10.7504	0.532879
$408$	1.49101	0.0738158
$409$	4.26805	0.211042	0.105521	−	0.994417i	$-0.466349\pi$
$409$	4.26805	0.211042	0.105521	+	0.994417i	$0.466349\pi$
$410$	0.146823	0.00725108
$411$	−3.34940	−0.165214
$412$	−9.76278	−0.480978
$413$	5.60082	0.275598
$414$	−46.9919	−2.30953
$415$	0.199098	0.00977334
$416$	0	0
$417$	−3.71916	−0.182128
$418$	27.0687	1.32397
$419$	32.7322	1.59907	0.799536	−	0.600618i	$-0.205079\pi$
$419$	32.7322	1.59907	0.799536	+	0.600618i	$0.205079\pi$
$420$	−0.0572779	−0.00279488
$421$	24.5539	1.19669	0.598343	−	0.801240i	$-0.295826\pi$
$421$	24.5539	1.19669	0.598343	+	0.801240i	$0.295826\pi$
$422$	16.4455	0.800555
$423$	−25.1627	−1.22345
$424$	−34.0018	−1.65127
$425$	4.75328	0.230568
$426$	8.64109	0.418662
$427$	7.74634	0.374872
$428$	8.57183	0.414335
$429$	0	0
$430$	0.300317	0.0144826
$431$	−13.8932	−0.669212	−0.334606	−	0.942358i	$-0.608603\pi$
$431$	−13.8932	−0.669212	−0.334606	+	0.942358i	$0.608603\pi$
$432$	7.11924	0.342525
$433$	−18.6412	−0.895838	−0.447919	−	0.894074i	$-0.647835\pi$
$433$	−18.6412	−0.895838	−0.447919	+	0.894074i	$0.647835\pi$
$434$	2.19286	0.105261
$435$	0.133793	0.00641489
$436$	47.7883	2.28865
$437$	−43.8847	−2.09929
$438$	0.925179	0.0442068
$439$	11.1791	0.533549	0.266775	−	0.963759i	$-0.414042\pi$
$439$	11.1791	0.533549	0.266775	+	0.963759i	$0.414042\pi$
$440$	0.389201	0.0185544
$441$	17.8915	0.851976
$442$	0	0
$443$	20.7379	0.985289	0.492644	−	0.870231i	$-0.336030\pi$
$443$	20.7379	0.985289	0.492644	+	0.870231i	$0.336030\pi$
$444$	8.31697	0.394706
$445$	0.158108	0.00749505
$446$	24.2807	1.14973
$447$	−3.58269	−0.169455
$448$	7.81468	0.369209
$449$	−0.392325	−0.0185150	−0.00925748	−	0.999957i	$-0.502947\pi$
$449$	−0.392325	−0.0185150	−0.00925748	+	0.999957i	$0.502947\pi$
$450$	35.2042	1.65954
$451$	2.08644	0.0982468
$452$	48.5005	2.28127
$453$	5.37418	0.252501
$454$	−23.7220	−1.11333
$455$	0	0
$456$	10.3127	0.482934
$457$	−33.3796	−1.56143	−0.780717	−	0.624885i	$-0.785146\pi$
$457$	−33.3796	−1.56143	−0.780717	+	0.624885i	$0.785146\pi$
$458$	−44.6775	−2.08764
$459$	−1.85686	−0.0866706
$460$	−1.28132	−0.0597418
$461$	−35.7897	−1.66689	−0.833445	−	0.552602i	$-0.813635\pi$
$461$	−35.7897	−1.66689	−0.833445	+	0.552602i	$0.813635\pi$
$462$	−1.22707	−0.0570886
$463$	−28.7675	−1.33694	−0.668470	−	0.743739i	$-0.733051\pi$
$463$	−28.7675	−1.33694	−0.668470	+	0.743739i	$0.733051\pi$
$464$	30.1984	1.40192
$465$	−0.0161561	−0.000749219 0
$466$	−13.8753	−0.642761
$467$	−0.117071	−0.00541742	−0.00270871	−	0.999996i	$-0.500862\pi$
$467$	−0.117071	−0.00541742	−0.00270871	+	0.999996i	$0.500862\pi$
$468$	0	0
$469$	12.0536	0.556581
$470$	−1.03434	−0.0477105
$471$	3.41495	0.157353
$472$	−29.4427	−1.35521
$473$	4.26768	0.196228
$474$	3.01643	0.138549
$475$	32.8764	1.50847
$476$	3.37195	0.154553
$477$	20.7775	0.951338
$478$	42.4418	1.94124
$479$	22.1085	1.01016	0.505082	−	0.863071i	$-0.331462\pi$
$479$	22.1085	1.01016	0.505082	+	0.863071i	$0.331462\pi$
$480$	−0.00923153	−0.000421360 0
$481$	0	0
$482$	51.4592	2.34390
$483$	1.98937	0.0905196
$484$	−32.1144	−1.45975
$485$	−0.480766	−0.0218305
$486$	−20.7569	−0.941551
$487$	1.36699	0.0619443	0.0309721	−	0.999520i	$-0.490140\pi$
$487$	1.36699	0.0619443	0.0309721	+	0.999520i	$0.490140\pi$
$488$	−40.7215	−1.84337
$489$	−0.570036	−0.0257779
$490$	0.735447	0.0332241
$491$	−8.27868	−0.373612	−0.186806	−	0.982397i	$-0.559814\pi$
$491$	−8.27868	−0.373612	−0.186806	+	0.982397i	$0.559814\pi$
$492$	1.61416	0.0727719
$493$	−7.87640	−0.354735
$494$	0	0
$495$	−0.237830	−0.0106897
$496$	−3.64657	−0.163736
$497$	9.62351	0.431674
$498$	3.29982	0.147868
$499$	15.1295	0.677288	0.338644	−	0.940915i	$-0.390032\pi$
$499$	15.1295	0.677288	0.338644	+	0.940915i	$0.390032\pi$
$500$	1.92026	0.0858768
$501$	0.188951	0.00844170
$502$	12.4650	0.556338
$503$	17.3363	0.772988	0.386494	−	0.922292i	$-0.373686\pi$
$503$	17.3363	0.772988	0.386494	+	0.922292i	$0.373686\pi$
$504$	12.2983	0.547810
$505$	0.442154	0.0196756
$506$	−27.4499	−1.22030
$507$	0	0
$508$	−39.2239	−1.74028
$509$	−29.2019	−1.29435	−0.647176	−	0.762341i	$-0.724050\pi$
$509$	−29.2019	−1.29435	−0.647176	+	0.762341i	$0.724050\pi$
$510$	−0.0374521	−0.00165841
$511$	1.03037	0.0455807
$512$	−36.5775	−1.61651
$513$	−12.8431	−0.567036
$514$	−49.5776	−2.18677
$515$	0.120763	0.00532145
$516$	3.30166	0.145347
$517$	−14.6986	−0.646442
$518$	13.9637	0.613532
$519$	−5.92447	−0.260055
$520$	0	0
$521$	−9.79007	−0.428911	−0.214455	−	0.976734i	$-0.568798\pi$
$521$	−9.79007	−0.428911	−0.214455	+	0.976734i	$0.568798\pi$
$522$	−58.3349	−2.55325
$523$	41.1161	1.79788	0.898940	−	0.438071i	$-0.144338\pi$
$523$	41.1161	1.79788	0.898940	+	0.438071i	$0.144338\pi$
$524$	64.8693	2.83383
$525$	−1.49035	−0.0650440
$526$	−29.7470	−1.29703
$527$	0.951107	0.0414309
$528$	2.04053	0.0888029
$529$	21.5027	0.934898
$530$	0.854082	0.0370989
$531$	17.9916	0.780770
$532$	23.3224	1.01115
$533$	0	0
$534$	2.62046	0.113398
$535$	−0.106031	−0.00458413
$536$	−63.3639	−2.73690
$537$	−5.97115	−0.257674
$538$	64.5549	2.78316
$539$	10.4511	0.450162
$540$	−0.374984	−0.0161367
$541$	−19.5243	−0.839415	−0.419708	−	0.907659i	$-0.637867\pi$
$541$	−19.5243	−0.839415	−0.419708	+	0.907659i	$0.637867\pi$
$542$	−10.4743	−0.449910
$543$	−5.19770	−0.223055
$544$	0.543460	0.0233007
$545$	−0.591129	−0.0253212
$546$	0	0
$547$	23.0264	0.984538	0.492269	−	0.870443i	$-0.336168\pi$
$547$	23.0264	0.984538	0.492269	+	0.870443i	$0.336168\pi$
$548$	39.8196	1.70101
$549$	24.8837	1.06201
$550$	20.5642	0.876859
$551$	−54.4777	−2.32083
$552$	−10.4579	−0.445116
$553$	3.35938	0.142855
$554$	−18.2602	−0.775803
$555$	−0.102879	−0.00436696
$556$	44.2154	1.87515
$557$	−0.780750	−0.0330814	−0.0165407	−	0.999863i	$-0.505265\pi$
$557$	−0.780750	−0.0330814	−0.0165407	+	0.999863i	$0.505265\pi$
$558$	7.04418	0.298204
$559$	0	0
$560$	0.159918	0.00675777
$561$	−0.532216	−0.0224702
$562$	37.7819	1.59373
$563$	−27.5425	−1.16078	−0.580389	−	0.814339i	$-0.697099\pi$
$563$	−27.5425	−1.16078	−0.580389	+	0.814339i	$0.697099\pi$
$564$	−11.3714	−0.478823
$565$	−0.599937	−0.0252396
$566$	−39.9676	−1.67996
$567$	−7.21861	−0.303153
$568$	−50.5895	−2.12269
$569$	7.07623	0.296651	0.148326	−	0.988939i	$-0.452612\pi$
$569$	7.07623	0.296651	0.148326	+	0.988939i	$0.452612\pi$
$570$	−0.259040	−0.0108500
$571$	37.4320	1.56648	0.783240	−	0.621719i	$-0.213566\pi$
$571$	37.4320	1.56648	0.783240	+	0.621719i	$0.213566\pi$
$572$	0	0
$573$	−3.76133	−0.157132
$574$	2.71008	0.113117
$575$	−33.3393	−1.39035
$576$	25.1032	1.04597
$577$	44.6828	1.86017	0.930085	−	0.367345i	$-0.119733\pi$
$577$	44.6828	1.86017	0.930085	+	0.367345i	$0.119733\pi$
$578$	−39.2296	−1.63173
$579$	6.14165	0.255238
$580$	−1.59061	−0.0660463
$581$	3.67498	0.152464
$582$	−7.96814	−0.330290
$583$	12.1370	0.502663
$584$	−5.41649	−0.224136
$585$	0	0
$586$	23.2781	0.961608
$587$	−34.4835	−1.42328	−0.711642	−	0.702542i	$-0.752048\pi$
$587$	−34.4835	−1.42328	−0.711642	+	0.702542i	$0.752048\pi$
$588$	8.08543	0.333438
$589$	6.57840	0.271058
$590$	0.739563	0.0304473
$591$	−6.63309	−0.272849
$592$	−23.2207	−0.954365
$593$	22.9831	0.943804	0.471902	−	0.881651i	$-0.343568\pi$
$593$	22.9831	0.943804	0.471902	+	0.881651i	$0.343568\pi$
$594$	−8.03334	−0.329612
$595$	−0.0417101	−0.00170995
$596$	42.5930	1.74468
$597$	2.17034	0.0888261
$598$	0	0
$599$	8.62966	0.352598	0.176299	−	0.984337i	$-0.443587\pi$
$599$	8.62966	0.352598	0.176299	+	0.984337i	$0.443587\pi$
$600$	7.83454	0.319844
$601$	−6.54029	−0.266784	−0.133392	−	0.991063i	$-0.542587\pi$
$601$	−6.54029	−0.266784	−0.133392	+	0.991063i	$0.542587\pi$
$602$	5.54330	0.225928
$603$	38.7198	1.57679
$604$	−63.8912	−2.59969
$605$	0.397247	0.0161504
$606$	7.32818	0.297687
$607$	−35.0785	−1.42379	−0.711896	−	0.702285i	$-0.752163\pi$
$607$	−35.0785	−1.42379	−0.711896	+	0.702285i	$0.752163\pi$
$608$	3.75888	0.152443
$609$	2.46957	0.100072
$610$	1.02287	0.0414148
$611$	0	0
$612$	10.8318	0.437849
$613$	−46.8670	−1.89294	−0.946470	−	0.322791i	$-0.895379\pi$
$613$	−46.8670	−1.89294	−0.946470	+	0.322791i	$0.895379\pi$
$614$	30.5561	1.23314
$615$	−0.0199667	−0.000805135 0
$616$	7.18393	0.289449
$617$	−2.30902	−0.0929577	−0.0464789	−	0.998919i	$-0.514800\pi$
$617$	−2.30902	−0.0929577	−0.0464789	+	0.998919i	$0.514800\pi$
$618$	2.00150	0.0805123
$619$	−33.0883	−1.32993	−0.664966	−	0.746873i	$-0.731554\pi$
$619$	−33.0883	−1.32993	−0.664966	+	0.746873i	$0.731554\pi$
$620$	0.192072	0.00771380
$621$	13.0239	0.522632
$622$	24.3096	0.974728
$623$	2.91839	0.116923
$624$	0	0
$625$	24.9644	0.998575
$626$	−53.5148	−2.13888
$627$	−3.68111	−0.147010
$628$	−40.5988	−1.62007
$629$	6.05647	0.241487
$630$	−0.308917	−0.0123076
$631$	−18.6798	−0.743631	−0.371816	−	0.928307i	$-0.621265\pi$
$631$	−18.6798	−0.743631	−0.371816	+	0.928307i	$0.621265\pi$
$632$	−17.6598	−0.702468
$633$	−2.23645	−0.0888908
$634$	−81.0881	−3.22042
$635$	0.485189	0.0192541
$636$	9.38968	0.372325
$637$	0	0
$638$	−34.0758	−1.34907
$639$	30.9138	1.22293
$640$	0.976190	0.0385873
$641$	−45.4185	−1.79392	−0.896961	−	0.442110i	$-0.854230\pi$
$641$	−45.4185	−1.79392	−0.896961	+	0.442110i	$0.854230\pi$
$642$	−1.75734	−0.0693568
$643$	1.08333	0.0427225	0.0213612	−	0.999772i	$-0.493200\pi$
$643$	1.08333	0.0427225	0.0213612	+	0.999772i	$0.493200\pi$
$644$	−23.6508	−0.931970
$645$	−0.0408406	−0.00160810
$646$	15.2497	0.599992
$647$	−14.1600	−0.556687	−0.278344	−	0.960482i	$-0.589785\pi$
$647$	−14.1600	−0.556687	−0.278344	+	0.960482i	$0.589785\pi$
$648$	37.9473	1.49071
$649$	10.5096	0.412539
$650$	0	0
$651$	−0.298211	−0.0116878
$652$	6.77689	0.265404
$653$	48.4254	1.89503	0.947517	−	0.319707i	$-0.103584\pi$
$653$	48.4254	1.89503	0.947517	+	0.319707i	$0.103584\pi$
$654$	−9.79727	−0.383103
$655$	−0.802416	−0.0313530
$656$	−4.50667	−0.175956
$657$	3.30986	0.129130
$658$	−19.0920	−0.744283
$659$	21.0528	0.820099	0.410049	−	0.912063i	$-0.365511\pi$
$659$	21.0528	0.820099	0.410049	+	0.912063i	$0.365511\pi$
$660$	−0.107479	−0.00418361
$661$	18.5523	0.721600	0.360800	−	0.932643i	$-0.382504\pi$
$661$	18.5523	0.721600	0.360800	+	0.932643i	$0.382504\pi$
$662$	−70.3308	−2.73348
$663$	0	0
$664$	−19.3189	−0.749717
$665$	−0.288491	−0.0111872
$666$	44.8560	1.73813
$667$	55.2448	2.13909
$668$	−2.24635	−0.0869139
$669$	−3.30197	−0.127662
$670$	1.59162	0.0614896
$671$	14.5356	0.561140
$672$	−0.170397	−0.00657320
$673$	−7.84637	−0.302455	−0.151228	−	0.988499i	$-0.548323\pi$
$673$	−7.84637	−0.302455	−0.151228	+	0.988499i	$0.548323\pi$
$674$	1.47048	0.0566409
$675$	−9.75691	−0.375544
$676$	0	0
$677$	−24.5015	−0.941667	−0.470834	−	0.882222i	$-0.656047\pi$
$677$	−24.5015	−0.941667	−0.470834	+	0.882222i	$0.656047\pi$
$678$	−9.94326	−0.381869
$679$	−8.87405	−0.340555
$680$	0.219264	0.00840841
$681$	3.22599	0.123620
$682$	4.11479	0.157563
$683$	22.2342	0.850767	0.425383	−	0.905013i	$-0.360139\pi$
$683$	22.2342	0.850767	0.425383	+	0.905013i	$0.360139\pi$
$684$	74.9188	2.86459
$685$	−0.492557	−0.0188196
$686$	28.9250	1.10436
$687$	6.07576	0.231805
$688$	−9.21811	−0.351437
$689$	0	0
$690$	0.262688	0.0100004
$691$	48.7589	1.85487	0.927437	−	0.373978i	$-0.122007\pi$
$691$	48.7589	1.85487	0.927437	+	0.373978i	$0.122007\pi$
$692$	70.4333	2.67747
$693$	−4.38990	−0.166758
$694$	77.9497	2.95893
$695$	−0.546933	−0.0207463
$696$	−12.9822	−0.492089
$697$	1.17544	0.0445229
$698$	−3.68288	−0.139399
$699$	1.88692	0.0713699
$700$	17.7180	0.669679
$701$	−8.75488	−0.330667	−0.165334	−	0.986238i	$-0.552870\pi$
$701$	−8.75488	−0.330667	−0.165334	+	0.986238i	$0.552870\pi$
$702$	0	0
$703$	41.8900	1.57991
$704$	14.6638	0.552663
$705$	0.140661	0.00529761
$706$	21.3494	0.803495
$707$	8.16134	0.306939
$708$	8.13068	0.305570
$709$	−33.5813	−1.26117	−0.630586	−	0.776119i	$-0.717186\pi$
$709$	−33.5813	−1.26117	−0.630586	+	0.776119i	$0.717186\pi$
$710$	1.27074	0.0476901
$711$	10.7914	0.404708
$712$	−15.3416	−0.574949
$713$	−6.67103	−0.249832
$714$	−0.691297	−0.0258711
$715$	0	0
$716$	70.9883	2.65296
$717$	−5.77173	−0.215549
$718$	−37.7786	−1.40988
$719$	40.4860	1.50987	0.754936	−	0.655799i	$-0.227668\pi$
$719$	40.4860	1.50987	0.754936	+	0.655799i	$0.227668\pi$
$720$	0.513707	0.0191447
$721$	2.22906	0.0830145
$722$	59.1668	2.20196
$723$	−6.99800	−0.260259
$724$	61.7931	2.29652
$725$	−41.3868	−1.53707
$726$	6.58390	0.244352
$727$	−36.8726	−1.36753	−0.683765	−	0.729703i	$-0.739658\pi$
$727$	−36.8726	−1.36753	−0.683765	+	0.729703i	$0.739658\pi$
$728$	0	0
$729$	−21.2472	−0.786933
$730$	0.136055	0.00503562
$731$	2.40429	0.0889257
$732$	11.2453	0.415639
$733$	−49.6304	−1.83314	−0.916571	−	0.399872i	$-0.869055\pi$
$733$	−49.6304	−1.83314	−0.916571	+	0.399872i	$0.869055\pi$
$734$	48.1713	1.77803
$735$	−0.100015	−0.00368909
$736$	−3.81181	−0.140505
$737$	22.6178	0.833138
$738$	8.70565	0.320459
$739$	−46.4693	−1.70940	−0.854700	−	0.519123i	$-0.826259\pi$
$739$	−46.4693	−1.70940	−0.854700	+	0.519123i	$0.826259\pi$
$740$	1.22308	0.0449612
$741$	0	0
$742$	15.7648	0.578743
$743$	−26.6137	−0.976361	−0.488180	−	0.872743i	$-0.662339\pi$
$743$	−26.6137	−0.976361	−0.488180	+	0.872743i	$0.662339\pi$
$744$	1.56765	0.0574729
$745$	−0.526863	−0.0193028
$746$	−10.1074	−0.370058
$747$	11.8052	0.431930
$748$	6.32728	0.231348
$749$	−1.95714	−0.0715123
$750$	−0.393680	−0.0143752
$751$	−4.55395	−0.166176	−0.0830880	−	0.996542i	$-0.526478\pi$
$751$	−4.55395	−0.166176	−0.0830880	+	0.996542i	$0.526478\pi$
$752$	31.7486	1.15775
$753$	−1.69513	−0.0617739
$754$	0	0
$755$	0.790316	0.0287626
$756$	−6.92151	−0.251733
$757$	14.2127	0.516570	0.258285	−	0.966069i	$-0.416843\pi$
$757$	14.2127	0.516570	0.258285	+	0.966069i	$0.416843\pi$
$758$	−2.30761	−0.0838162
$759$	3.73295	0.135497
$760$	1.51656	0.0550114
$761$	47.6038	1.72564	0.862819	−	0.505514i	$-0.168697\pi$
$761$	47.6038	1.72564	0.862819	+	0.505514i	$0.168697\pi$
$762$	8.04144	0.291311
$763$	−10.9111	−0.395010
$764$	44.7168	1.61780
$765$	−0.133986	−0.00484428
$766$	−36.1947	−1.30777
$767$	0	0
$768$	10.4213	0.376047
$769$	−20.4338	−0.736863	−0.368431	−	0.929655i	$-0.620105\pi$
$769$	−20.4338	−0.736863	−0.368431	+	0.929655i	$0.620105\pi$
$770$	−0.180451	−0.00650300
$771$	6.74213	0.242812
$772$	−73.0152	−2.62788
$773$	−29.1370	−1.04799	−0.523993	−	0.851723i	$-0.675558\pi$
$773$	−29.1370	−1.04799	−0.523993	+	0.851723i	$0.675558\pi$
$774$	17.8068	0.640054
$775$	4.99762	0.179520
$776$	46.6497	1.67463
$777$	−1.89895	−0.0681244
$778$	−38.3423	−1.37464
$779$	8.13002	0.291288
$780$	0	0
$781$	18.0580	0.646165
$782$	−15.4644	−0.553007
$783$	16.1677	0.577785
$784$	−22.5742	−0.806223
$785$	0.502197	0.0179242
$786$	−13.2991	−0.474363
$787$	17.7126	0.631387	0.315694	−	0.948861i	$-0.397763\pi$
$787$	17.7126	0.631387	0.315694	+	0.948861i	$0.397763\pi$
$788$	78.8578	2.80919
$789$	4.04533	0.144018
$790$	0.443590	0.0157822
$791$	−11.0737	−0.393737
$792$	23.0771	0.820008
$793$	0	0
$794$	−2.72063	−0.0965516
$795$	−0.116148	−0.00411934
$796$	−25.8022	−0.914534
$797$	53.6177	1.89924	0.949619	−	0.313408i	$-0.101471\pi$
$797$	53.6177	1.89924	0.949619	+	0.313408i	$0.101471\pi$
$798$	−4.78140	−0.169260
$799$	−8.28073	−0.292951
$800$	2.85563	0.100962
$801$	9.37479	0.331242
$802$	−66.5103	−2.34856
$803$	1.93342	0.0682290
$804$	17.4981	0.617109
$805$	0.292553	0.0103112
$806$	0	0
$807$	−8.77891	−0.309032
$808$	−42.9030	−1.50932
$809$	−33.8755	−1.19100	−0.595500	−	0.803356i	$-0.703046\pi$
$809$	−33.8755	−1.19100	−0.595500	+	0.803356i	$0.703046\pi$
$810$	−0.953186	−0.0334915
$811$	−26.0448	−0.914555	−0.457277	−	0.889324i	$-0.651175\pi$
$811$	−26.0448	−0.914555	−0.457277	+	0.889324i	$0.651175\pi$
$812$	−29.3596	−1.03032
$813$	1.42442	0.0499565
$814$	26.2022	0.918386
$815$	−0.0838283	−0.00293638
$816$	1.14958	0.0402432
$817$	16.6294	0.581790
$818$	10.4026	0.363718
$819$	0	0
$820$	0.237375	0.00828949
$821$	−26.9270	−0.939759	−0.469880	−	0.882731i	$-0.655703\pi$
$821$	−26.9270	−0.939759	−0.469880	+	0.882731i	$0.655703\pi$
$822$	−8.16356	−0.284737
$823$	−41.6961	−1.45343	−0.726717	−	0.686937i	$-0.758955\pi$
$823$	−41.6961	−1.45343	−0.726717	+	0.686937i	$0.758955\pi$
$824$	−11.7179	−0.408211
$825$	−2.79655	−0.0973633
$826$	13.6510	0.474978
$827$	−28.2054	−0.980799	−0.490400	−	0.871498i	$-0.663149\pi$
$827$	−28.2054	−0.980799	−0.490400	+	0.871498i	$0.663149\pi$
$828$	−75.9738	−2.64027
$829$	36.9039	1.28172	0.640862	−	0.767656i	$-0.278577\pi$
$829$	36.9039	1.28172	0.640862	+	0.767656i	$0.278577\pi$
$830$	0.485265	0.0168438
$831$	2.48324	0.0861425
$832$	0	0
$833$	5.88786	0.204002
$834$	−9.06477	−0.313887
$835$	0.0277867	0.000961600 0
$836$	43.7631	1.51358
$837$	−1.95231	−0.0674817
$838$	79.7787	2.75591
$839$	−57.3883	−1.98126	−0.990631	−	0.136564i	$-0.956394\pi$
$839$	−57.3883	−1.98126	−0.990631	+	0.136564i	$0.956394\pi$
$840$	−0.0687483	−0.00237204
$841$	39.5799	1.36482
$842$	59.8457	2.06242
$843$	−5.13802	−0.176963
$844$	26.5881	0.915200
$845$	0	0
$846$	−61.3295	−2.10855
$847$	7.33244	0.251946
$848$	−26.2157	−0.900249
$849$	5.43525	0.186537
$850$	11.5852	0.397370
$851$	−42.4799	−1.45619
$852$	13.9704	0.478618
$853$	5.54919	0.190001	0.0950003	−	0.995477i	$-0.469715\pi$
$853$	5.54919	0.190001	0.0950003	+	0.995477i	$0.469715\pi$
$854$	18.8803	0.646070
$855$	−0.926726	−0.0316933
$856$	10.2884	0.351651
$857$	8.76743	0.299490	0.149745	−	0.988725i	$-0.452155\pi$
$857$	8.76743	0.299490	0.149745	+	0.988725i	$0.452155\pi$
$858$	0	0
$859$	−45.2067	−1.54243	−0.771216	−	0.636573i	$-0.780351\pi$
$859$	−45.2067	−1.54243	−0.771216	+	0.636573i	$0.780351\pi$
$860$	0.485535	0.0165566
$861$	−0.368548	−0.0125601
$862$	−33.8621	−1.15335
$863$	−10.2601	−0.349257	−0.174629	−	0.984634i	$-0.555872\pi$
$863$	−10.2601	−0.349257	−0.174629	+	0.984634i	$0.555872\pi$
$864$	−1.11555	−0.0379516
$865$	−0.871241	−0.0296231
$866$	−45.4345	−1.54393
$867$	5.33488	0.181182
$868$	3.54529	0.120335
$869$	6.30368	0.213838
$870$	0.326096	0.0110557
$871$	0	0
$872$	57.3583	1.94240
$873$	−28.5063	−0.964792
$874$	−106.961	−3.61801
$875$	−0.438439	−0.0148219
$876$	1.49577	0.0505375
$877$	−43.9866	−1.48532	−0.742662	−	0.669667i	$-0.766437\pi$
$877$	−43.9866	−1.48532	−0.742662	+	0.669667i	$0.766437\pi$
$878$	27.2470	0.919541
$879$	−3.16562	−0.106774
$880$	0.300077	0.0101156
$881$	13.8855	0.467815	0.233907	−	0.972259i	$-0.424849\pi$
$881$	13.8855	0.467815	0.233907	+	0.972259i	$0.424849\pi$
$882$	43.6072	1.46833
$883$	−27.5994	−0.928792	−0.464396	−	0.885628i	$-0.653729\pi$
$883$	−27.5994	−0.928792	−0.464396	+	0.885628i	$0.653729\pi$
$884$	0	0
$885$	−0.100574	−0.00338077
$886$	50.5449	1.69809
$887$	−22.2153	−0.745918	−0.372959	−	0.927848i	$-0.621657\pi$
$887$	−22.2153	−0.745918	−0.372959	+	0.927848i	$0.621657\pi$
$888$	9.98252	0.334991
$889$	8.95569	0.300364
$890$	0.385360	0.0129173
$891$	−13.5453	−0.453785
$892$	39.2556	1.31438
$893$	−57.2743	−1.91661
$894$	−8.73214	−0.292047
$895$	−0.878106	−0.0293518
$896$	18.0187	0.601961
$897$	0	0
$898$	−0.956220	−0.0319095
$899$	−8.28130	−0.276197
$900$	56.9160	1.89720
$901$	6.83762	0.227794
$902$	5.08532	0.169323
$903$	−0.753842	−0.0250863
$904$	58.2131	1.93614
$905$	−0.764364	−0.0254083
$906$	13.0986	0.435171
$907$	−52.6383	−1.74783	−0.873914	−	0.486081i	$-0.838426\pi$
$907$	−52.6383	−1.74783	−0.873914	+	0.486081i	$0.838426\pi$
$908$	−38.3524	−1.27277
$909$	26.2168	0.869557
$910$	0	0
$911$	−2.71762	−0.0900389	−0.0450195	−	0.998986i	$-0.514335\pi$
$911$	−2.71762	−0.0900389	−0.0450195	+	0.998986i	$0.514335\pi$
$912$	7.95113	0.263288
$913$	6.89589	0.228221
$914$	−81.3567	−2.69104
$915$	−0.139102	−0.00459856
$916$	−72.2319	−2.38661
$917$	−14.8111	−0.489106
$918$	−4.52574	−0.149372
$919$	1.47776	0.0487469	0.0243734	−	0.999703i	$-0.492241\pi$
$919$	1.47776	0.0487469	0.0243734	+	0.999703i	$0.492241\pi$
$920$	−1.53791	−0.0507035
$921$	−4.15537	−0.136924
$922$	−87.2307	−2.87279
$923$	0	0
$924$	−1.98386	−0.0652642
$925$	31.8239	1.04636
$926$	−70.1155	−2.30414
$927$	7.16045	0.235180
$928$	−4.73191	−0.155333
$929$	−8.25256	−0.270758	−0.135379	−	0.990794i	$-0.543225\pi$
$929$	−8.25256	−0.270758	−0.135379	+	0.990794i	$0.543225\pi$
$930$	−0.0393774	−0.00129124
$931$	40.7238	1.33467
$932$	−22.4328	−0.734809
$933$	−3.30590	−0.108230
$934$	−0.285340	−0.00933661
$935$	−0.0782667	−0.00255959
$936$	0	0
$937$	29.9258	0.977635	0.488817	−	0.872386i	$-0.337428\pi$
$937$	29.9258	0.977635	0.488817	+	0.872386i	$0.337428\pi$
$938$	29.3783	0.959236
$939$	7.27755	0.237494
$940$	−1.67226	−0.0545430
$941$	19.7675	0.644402	0.322201	−	0.946671i	$-0.395577\pi$
$941$	19.7675	0.644402	0.322201	+	0.946671i	$0.395577\pi$
$942$	8.32332	0.271188
$943$	−8.24449	−0.268478
$944$	−22.7006	−0.738841
$945$	0.0856172	0.00278513
$946$	10.4017	0.338188
$947$	−7.19095	−0.233675	−0.116837	−	0.993151i	$-0.537276\pi$
$947$	−7.19095	−0.233675	−0.116837	+	0.993151i	$0.537276\pi$
$948$	4.87679	0.158391
$949$	0	0
$950$	80.1301	2.59976
$951$	11.0273	0.357584
$952$	4.04721	0.131171
$953$	11.8739	0.384633	0.192316	−	0.981333i	$-0.438400\pi$
$953$	11.8739	0.384633	0.192316	+	0.981333i	$0.438400\pi$
$954$	50.6414	1.63958
$955$	−0.553135	−0.0178990
$956$	68.6174	2.21925
$957$	4.63401	0.149796
$958$	53.8855	1.74096
$959$	−9.09169	−0.293586
$960$	−0.140329	−0.00452909
$961$	1.00000	0.0322581
$962$	0	0
$963$	−6.28695	−0.202594
$964$	83.1961	2.67957
$965$	0.903179	0.0290743
$966$	4.84873	0.156005
$967$	−11.7075	−0.376486	−0.188243	−	0.982122i	$-0.560279\pi$
$967$	−11.7075	−0.376486	−0.188243	+	0.982122i	$0.560279\pi$
$968$	−38.5456	−1.23890
$969$	−2.07383	−0.0666210
$970$	−1.17178	−0.0376236
$971$	23.1617	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$971$	23.1617	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$972$	−33.5585	−1.07639
$973$	−10.0954	−0.323643
$974$	3.33179	0.106757
$975$	0	0
$976$	−31.3965	−1.00498
$977$	15.2554	0.488062	0.244031	−	0.969767i	$-0.421530\pi$
$977$	15.2554	0.488062	0.244031	+	0.969767i	$0.421530\pi$
$978$	−1.38936	−0.0444267
$979$	5.47619	0.175020
$980$	1.18903	0.0379821
$981$	−35.0500	−1.11906
$982$	−20.1778	−0.643898
$983$	60.4366	1.92763	0.963814	−	0.266577i	$-0.0858928\pi$
$983$	60.4366	1.92763	0.963814	+	0.266577i	$0.0858928\pi$
$984$	1.93741	0.0617623
$985$	−0.975450	−0.0310804
$986$	−19.1973	−0.611366
$987$	2.59635	0.0826426
$988$	0	0
$989$	−16.8636	−0.536231
$990$	−0.579666	−0.0184230
$991$	16.6851	0.530019	0.265010	−	0.964246i	$-0.414625\pi$
$991$	16.6851	0.530019	0.265010	+	0.964246i	$0.414625\pi$
$992$	0.571398	0.0181419
$993$	9.56438	0.303516
$994$	23.4555	0.743965
$995$	0.319166	0.0101182
$996$	5.33495	0.169044
$997$	15.8093	0.500686	0.250343	−	0.968157i	$-0.419457\pi$
$997$	15.8093	0.500686	0.250343	+	0.968157i	$0.419457\pi$
$998$	36.8753	1.16727
$999$	−12.4319	−0.393329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.m.1.16		17
13.3	even	3		403.2.f.b.373.2	yes	34
13.9	even	3		403.2.f.b.94.2	✓	34
13.12	even	2		5239.2.a.n.1.2		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.b.94.2	✓	34	13.9	even	3
403.2.f.b.373.2	yes	34	13.3	even	3
5239.2.a.m.1.16		17	1.1	even	1	trivial
5239.2.a.n.1.2		17	13.12	even	2

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:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q+2.43732 q^{2} -0.331454 q^{3} +3.94051 q^{4} -0.0487430 q^{5} -0.807858 q^{6} -0.899705 q^{7} +4.72962 q^{8} -2.89014 q^{9} +O(q^{10})\)	\(q+2.43732 q^{2} -0.331454 q^{3} +3.94051 q^{4} -0.0487430 q^{5} -0.807858 q^{6} -0.899705 q^{7} +4.72962 q^{8} -2.89014 q^{9} -0.118802 q^{10} -1.68825 q^{11} -1.30610 q^{12} -2.19286 q^{14} +0.0161561 q^{15} +3.64657 q^{16} -0.951107 q^{17} -7.04418 q^{18} -6.57840 q^{19} -0.192072 q^{20} +0.298211 q^{21} -4.11479 q^{22} +6.67103 q^{23} -1.56765 q^{24} -4.99762 q^{25} +1.95231 q^{27} -3.54529 q^{28} +8.28130 q^{29} +0.0393774 q^{30} -1.00000 q^{31} -0.571398 q^{32} +0.559576 q^{33} -2.31815 q^{34} +0.0438543 q^{35} -11.3886 q^{36} -6.36781 q^{37} -16.0336 q^{38} -0.230536 q^{40} -1.23586 q^{41} +0.726834 q^{42} -2.52788 q^{43} -6.65254 q^{44} +0.140874 q^{45} +16.2594 q^{46} +8.70641 q^{47} -1.20867 q^{48} -6.19053 q^{49} -12.1808 q^{50} +0.315248 q^{51} -7.18912 q^{53} +4.75839 q^{54} +0.0822901 q^{55} -4.25527 q^{56} +2.18044 q^{57} +20.1841 q^{58} -6.22518 q^{59} +0.0636630 q^{60} -8.60987 q^{61} -2.43732 q^{62} +2.60027 q^{63} -8.68582 q^{64} +1.36386 q^{66} -13.3972 q^{67} -3.74784 q^{68} -2.21114 q^{69} +0.106887 q^{70} -10.6963 q^{71} -13.6693 q^{72} -1.14523 q^{73} -15.5204 q^{74} +1.65648 q^{75} -25.9222 q^{76} +1.51892 q^{77} -3.73386 q^{79} -0.177745 q^{80} +8.02331 q^{81} -3.01219 q^{82} -4.08465 q^{83} +1.17510 q^{84} +0.0463598 q^{85} -6.16125 q^{86} -2.74487 q^{87} -7.98477 q^{88} -3.24372 q^{89} +0.343354 q^{90} +26.2872 q^{92} +0.331454 q^{93} +21.2203 q^{94} +0.320651 q^{95} +0.189392 q^{96} +9.86329 q^{97} -15.0883 q^{98} +4.87926 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9	\( 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9} + 6 q^{10} - 13 q^{11} + 4 q^{12} - 4 q^{15} + 34 q^{16} - 6 q^{17} + 12 q^{18} - 4 q^{19} - 28 q^{20} - 18 q^{21} - 34 q^{22} - 8 q^{23} - 40 q^{24} + 8 q^{25} - 3 q^{27} - 21 q^{28} - 6 q^{29} + 19 q^{30} - 17 q^{31} - 6 q^{32} - 7 q^{33} - 24 q^{34} - 9 q^{35} - 14 q^{37} + 11 q^{38} - 10 q^{40} - 43 q^{41} + 33 q^{42} + 18 q^{43} - 28 q^{44} - 26 q^{45} - 7 q^{46} - 6 q^{47} - 95 q^{48} - q^{49} - 44 q^{50} + 26 q^{51} - 5 q^{53} - 27 q^{54} + 39 q^{55} + 39 q^{56} - 46 q^{57} - 8 q^{58} + q^{59} - 21 q^{60} - 19 q^{61} + 4 q^{62} - 5 q^{63} + 42 q^{64} + 26 q^{66} - 10 q^{67} + 34 q^{68} + 32 q^{69} + 24 q^{70} - 35 q^{71} + 26 q^{72} - 11 q^{73} - 68 q^{74} - 62 q^{75} - 2 q^{76} + 21 q^{77} + q^{79} - 49 q^{80} + 37 q^{81} + 35 q^{82} - 24 q^{83} + 34 q^{84} + 13 q^{85} - 76 q^{86} - 22 q^{87} - 37 q^{88} - 42 q^{89} + 15 q^{90} + 15 q^{92} + 42 q^{94} + 34 q^{95} - 33 q^{96} + 38 q^{97} - 8 q^{98} - 17 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9 + 6 * q^10 - 13 * q^11 + 4 * q^12 - 4 * q^15 + 34 * q^16 - 6 * q^17 + 12 * q^18 - 4 * q^19 - 28 * q^20 - 18 * q^21 - 34 * q^22 - 8 * q^23 - 40 * q^24 + 8 * q^25 - 3 * q^27 - 21 * q^28 - 6 * q^29 + 19 * q^30 - 17 * q^31 - 6 * q^32 - 7 * q^33 - 24 * q^34 - 9 * q^35 - 14 * q^37 + 11 * q^38 - 10 * q^40 - 43 * q^41 + 33 * q^42 + 18 * q^43 - 28 * q^44 - 26 * q^45 - 7 * q^46 - 6 * q^47 - 95 * q^48 - q^49 - 44 * q^50 + 26 * q^51 - 5 * q^53 - 27 * q^54 + 39 * q^55 + 39 * q^56 - 46 * q^57 - 8 * q^58 + q^59 - 21 * q^60 - 19 * q^61 + 4 * q^62 - 5 * q^63 + 42 * q^64 + 26 * q^66 - 10 * q^67 + 34 * q^68 + 32 * q^69 + 24 * q^70 - 35 * q^71 + 26 * q^72 - 11 * q^73 - 68 * q^74 - 62 * q^75 - 2 * q^76 + 21 * q^77 + q^79 - 49 * q^80 + 37 * q^81 + 35 * q^82 - 24 * q^83 + 34 * q^84 + 13 * q^85 - 76 * q^86 - 22 * q^87 - 37 * q^88 - 42 * q^89 + 15 * q^90 + 15 * q^92 + 42 * q^94 + 34 * q^95 - 33 * q^96 + 38 * q^97 - 8 * q^98 - 17 * q^99

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