LMFDB - Embedded newform 1339.2.a.f.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,2,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, 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("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.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:	$10.6919688306$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.56395 q^{2} -2.92532 q^{3} +0.445953 q^{4} -2.35359 q^{5} -4.57507 q^{6} -3.99061 q^{7} -2.43046 q^{8} +5.55751 q^{9} +O(q^{10})$	\(q+1.56395 q^{2} -2.92532 q^{3} +0.445953 q^{4} -2.35359 q^{5} -4.57507 q^{6} -3.99061 q^{7} -2.43046 q^{8} +5.55751 q^{9} -3.68091 q^{10} -1.50338 q^{11} -1.30456 q^{12} +1.00000 q^{13} -6.24113 q^{14} +6.88501 q^{15} -4.69303 q^{16} -1.31171 q^{17} +8.69169 q^{18} -1.39234 q^{19} -1.04959 q^{20} +11.6738 q^{21} -2.35121 q^{22} -5.47901 q^{23} +7.10987 q^{24} +0.539395 q^{25} +1.56395 q^{26} -7.48153 q^{27} -1.77962 q^{28} +0.656407 q^{29} +10.7678 q^{30} +1.87887 q^{31} -2.47877 q^{32} +4.39786 q^{33} -2.05145 q^{34} +9.39226 q^{35} +2.47839 q^{36} +2.08059 q^{37} -2.17756 q^{38} -2.92532 q^{39} +5.72031 q^{40} +9.60166 q^{41} +18.2573 q^{42} +3.18745 q^{43} -0.670436 q^{44} -13.0801 q^{45} -8.56893 q^{46} +4.73188 q^{47} +13.7286 q^{48} +8.92494 q^{49} +0.843589 q^{50} +3.83717 q^{51} +0.445953 q^{52} -2.97949 q^{53} -11.7008 q^{54} +3.53833 q^{55} +9.69900 q^{56} +4.07305 q^{57} +1.02659 q^{58} +12.8854 q^{59} +3.07040 q^{60} +1.56304 q^{61} +2.93847 q^{62} -22.1778 q^{63} +5.50938 q^{64} -2.35359 q^{65} +6.87805 q^{66} -14.1118 q^{67} -0.584962 q^{68} +16.0279 q^{69} +14.6891 q^{70} -13.6980 q^{71} -13.5073 q^{72} -8.44768 q^{73} +3.25394 q^{74} -1.57790 q^{75} -0.620920 q^{76} +5.99938 q^{77} -4.57507 q^{78} -0.168821 q^{79} +11.0455 q^{80} +5.21335 q^{81} +15.0166 q^{82} -3.07087 q^{83} +5.20597 q^{84} +3.08723 q^{85} +4.98502 q^{86} -1.92020 q^{87} +3.65389 q^{88} -0.856360 q^{89} -20.4567 q^{90} -3.99061 q^{91} -2.44339 q^{92} -5.49631 q^{93} +7.40045 q^{94} +3.27701 q^{95} +7.25121 q^{96} -9.78741 q^{97} +13.9582 q^{98} -8.35502 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9}+O(q^{10}) $ 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9	\( 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9} + 5 q^{10} + 9 q^{11} + 15 q^{12} + 28 q^{13} + 20 q^{14} + 4 q^{15} + 32 q^{16} - 7 q^{17} + 10 q^{18} - 3 q^{19} + 53 q^{20} + 25 q^{21} - 14 q^{22} - 6 q^{23} + 10 q^{24} + 45 q^{25} + 6 q^{26} + 8 q^{27} - 12 q^{28} + 25 q^{29} - 43 q^{30} + q^{31} + 28 q^{32} + 17 q^{33} + 10 q^{34} + 11 q^{35} + 27 q^{36} + 18 q^{37} + 2 q^{38} + 5 q^{39} + 37 q^{40} + 56 q^{41} - 29 q^{42} - 30 q^{43} + 30 q^{44} + 38 q^{45} - 27 q^{46} + 40 q^{47} + 19 q^{48} + 36 q^{49} + 20 q^{50} - 18 q^{51} + 32 q^{52} + 51 q^{53} - 36 q^{54} - 5 q^{55} - 13 q^{56} + 31 q^{57} - 29 q^{58} + 29 q^{59} + 48 q^{60} + 16 q^{61} - 38 q^{62} - 23 q^{63} - 5 q^{64} + 27 q^{65} + 25 q^{66} - 2 q^{67} - 43 q^{68} + 38 q^{69} + 10 q^{70} + 34 q^{71} - 28 q^{72} + 14 q^{73} + 21 q^{74} + 19 q^{75} + 5 q^{76} + 34 q^{77} + 9 q^{78} + 3 q^{79} + 58 q^{80} + 4 q^{81} - 9 q^{82} + 38 q^{83} - 78 q^{84} - 27 q^{85} + 49 q^{86} + 8 q^{87} - 25 q^{88} + 125 q^{89} - 74 q^{90} + 6 q^{91} - 35 q^{92} + 36 q^{93} - q^{94} - 12 q^{95} + 26 q^{96} - 2 q^{97} + 18 q^{98} + 56 q^{99}+O(q^{100}) \) 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9 + 5 * q^10 + 9 * q^11 + 15 * q^12 + 28 * q^13 + 20 * q^14 + 4 * q^15 + 32 * q^16 - 7 * q^17 + 10 * q^18 - 3 * q^19 + 53 * q^20 + 25 * q^21 - 14 * q^22 - 6 * q^23 + 10 * q^24 + 45 * q^25 + 6 * q^26 + 8 * q^27 - 12 * q^28 + 25 * q^29 - 43 * q^30 + q^31 + 28 * q^32 + 17 * q^33 + 10 * q^34 + 11 * q^35 + 27 * q^36 + 18 * q^37 + 2 * q^38 + 5 * q^39 + 37 * q^40 + 56 * q^41 - 29 * q^42 - 30 * q^43 + 30 * q^44 + 38 * q^45 - 27 * q^46 + 40 * q^47 + 19 * q^48 + 36 * q^49 + 20 * q^50 - 18 * q^51 + 32 * q^52 + 51 * q^53 - 36 * q^54 - 5 * q^55 - 13 * q^56 + 31 * q^57 - 29 * q^58 + 29 * q^59 + 48 * q^60 + 16 * q^61 - 38 * q^62 - 23 * q^63 - 5 * q^64 + 27 * q^65 + 25 * q^66 - 2 * q^67 - 43 * q^68 + 38 * q^69 + 10 * q^70 + 34 * q^71 - 28 * q^72 + 14 * q^73 + 21 * q^74 + 19 * q^75 + 5 * q^76 + 34 * q^77 + 9 * q^78 + 3 * q^79 + 58 * q^80 + 4 * q^81 - 9 * q^82 + 38 * q^83 - 78 * q^84 - 27 * q^85 + 49 * q^86 + 8 * q^87 - 25 * q^88 + 125 * q^89 - 74 * q^90 + 6 * q^91 - 35 * q^92 + 36 * q^93 - q^94 - 12 * q^95 + 26 * q^96 - 2 * q^97 + 18 * q^98 + 56 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.56395	1.10588	0.552941	−	0.833220i	$-0.313505\pi$
$2$	1.56395	1.10588	0.552941	+	0.833220i	$0.313505\pi$
$3$	−2.92532	−1.68894	−0.844468	−	0.535607i	$-0.820083\pi$
$3$	−2.92532	−1.68894	−0.844468	+	0.535607i	$0.820083\pi$
$4$	0.445953	0.222977
$5$	−2.35359	−1.05256	−0.526279	−	0.850312i	$-0.676413\pi$
$5$	−2.35359	−1.05256	−0.526279	+	0.850312i	$0.676413\pi$
$6$	−4.57507	−1.86776
$7$	−3.99061	−1.50831	−0.754154	−	0.656698i	$-0.771953\pi$
$7$	−3.99061	−1.50831	−0.754154	+	0.656698i	$0.771953\pi$
$8$	−2.43046	−0.859297
$9$	5.55751	1.85250
$10$	−3.68091	−1.16401
$11$	−1.50338	−0.453285	−0.226643	−	0.973978i	$-0.572775\pi$
$11$	−1.50338	−0.453285	−0.226643	+	0.973978i	$0.572775\pi$
$12$	−1.30456	−0.376593
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−6.24113	−1.66801
$15$	6.88501	1.77770
$16$	−4.69303	−1.17326
$17$	−1.31171	−0.318136	−0.159068	−	0.987268i	$-0.550849\pi$
$17$	−1.31171	−0.318136	−0.159068	+	0.987268i	$0.550849\pi$
$18$	8.69169	2.04865
$19$	−1.39234	−0.319426	−0.159713	−	0.987164i	$-0.551057\pi$
$19$	−1.39234	−0.319426	−0.159713	+	0.987164i	$0.551057\pi$
$20$	−1.04959	−0.234696
$21$	11.6738	2.54743
$22$	−2.35121	−0.501280
$23$	−5.47901	−1.14245	−0.571227	−	0.820792i	$-0.693532\pi$
$23$	−5.47901	−1.14245	−0.571227	+	0.820792i	$0.693532\pi$
$24$	7.10987	1.45130
$25$	0.539395	0.107879
$26$	1.56395	0.306717
$27$	−7.48153	−1.43982
$28$	−1.77962	−0.336317
$29$	0.656407	0.121892	0.0609459	−	0.998141i	$-0.480588\pi$
$29$	0.656407	0.121892	0.0609459	+	0.998141i	$0.480588\pi$
$30$	10.7678	1.96593
$31$	1.87887	0.337456	0.168728	−	0.985663i	$-0.446034\pi$
$31$	1.87887	0.337456	0.168728	+	0.985663i	$0.446034\pi$
$32$	−2.47877	−0.438189
$33$	4.39786	0.765569
$34$	−2.05145	−0.351822
$35$	9.39226	1.58758
$36$	2.47839	0.413065
$37$	2.08059	0.342046	0.171023	−	0.985267i	$-0.445293\pi$
$37$	2.08059	0.342046	0.171023	+	0.985267i	$0.445293\pi$
$38$	−2.17756	−0.353247
$39$	−2.92532	−0.468426
$40$	5.72031	0.904460
$41$	9.60166	1.49953	0.749764	−	0.661706i	$-0.230167\pi$
$41$	9.60166	1.49953	0.749764	+	0.661706i	$0.230167\pi$
$42$	18.2573	2.81716
$43$	3.18745	0.486081	0.243041	−	0.970016i	$-0.421855\pi$
$43$	3.18745	0.486081	0.243041	+	0.970016i	$0.421855\pi$
$44$	−0.670436	−0.101072
$45$	−13.0801	−1.94987
$46$	−8.56893	−1.26342
$47$	4.73188	0.690216	0.345108	−	0.938563i	$-0.387842\pi$
$47$	4.73188	0.690216	0.345108	+	0.938563i	$0.387842\pi$
$48$	13.7286	1.98156
$49$	8.92494	1.27499
$50$	0.843589	0.119301
$51$	3.83717	0.537312
$52$	0.445953	0.0618426
$53$	−2.97949	−0.409264	−0.204632	−	0.978839i	$-0.565600\pi$
$53$	−2.97949	−0.409264	−0.204632	+	0.978839i	$0.565600\pi$
$54$	−11.7008	−1.59227
$55$	3.53833	0.477109
$56$	9.69900	1.29608
$57$	4.07305	0.539489
$58$	1.02659	0.134798
$59$	12.8854	1.67754	0.838768	−	0.544489i	$-0.183276\pi$
$59$	12.8854	1.67754	0.838768	+	0.544489i	$0.183276\pi$
$60$	3.07040	0.396386
$61$	1.56304	0.200127	0.100063	−	0.994981i	$-0.468095\pi$
$61$	1.56304	0.200127	0.100063	+	0.994981i	$0.468095\pi$
$62$	2.93847	0.373186
$63$	−22.1778	−2.79414
$64$	5.50938	0.688672
$65$	−2.35359	−0.291927
$66$	6.87805	0.846630
$67$	−14.1118	−1.72403	−0.862016	−	0.506881i	$-0.830798\pi$
$67$	−14.1118	−1.72403	−0.862016	+	0.506881i	$0.830798\pi$
$68$	−0.584962	−0.0709370
$69$	16.0279	1.92953
$70$	14.6891	1.75568
$71$	−13.6980	−1.62565	−0.812827	−	0.582505i	$-0.802073\pi$
$71$	−13.6980	−1.62565	−0.812827	+	0.582505i	$0.802073\pi$
$72$	−13.5073	−1.59185
$73$	−8.44768	−0.988726	−0.494363	−	0.869256i	$-0.664599\pi$
$73$	−8.44768	−0.988726	−0.494363	+	0.869256i	$0.664599\pi$
$74$	3.25394	0.378263
$75$	−1.57790	−0.182201
$76$	−0.620920	−0.0712245
$77$	5.99938	0.683693
$78$	−4.57507	−0.518025
$79$	−0.168821	−0.0189939	−0.00949694	−	0.999955i	$-0.503023\pi$
$79$	−0.168821	−0.0189939	−0.00949694	+	0.999955i	$0.503023\pi$
$80$	11.0455	1.23492
$81$	5.21335	0.579261
$82$	15.0166	1.65830
$83$	−3.07087	−0.337072	−0.168536	−	0.985696i	$-0.553904\pi$
$83$	−3.07087	−0.337072	−0.168536	+	0.985696i	$0.553904\pi$
$84$	5.20597	0.568018
$85$	3.08723	0.334857
$86$	4.98502	0.537549
$87$	−1.92020	−0.205867
$88$	3.65389	0.389506
$89$	−0.856360	−0.0907740	−0.0453870	−	0.998969i	$-0.514452\pi$
$89$	−0.856360	−0.0907740	−0.0453870	+	0.998969i	$0.514452\pi$
$90$	−20.4567	−2.15632
$91$	−3.99061	−0.418329
$92$	−2.44339	−0.254741
$93$	−5.49631	−0.569941
$94$	7.40045	0.763298
$95$	3.27701	0.336214
$96$	7.25121	0.740073
$97$	−9.78741	−0.993761	−0.496881	−	0.867819i	$-0.665521\pi$
$97$	−9.78741	−0.993761	−0.496881	+	0.867819i	$0.665521\pi$
$98$	13.9582	1.40999
$99$	−8.35502	−0.839712
$100$	0.240545	0.0240545
$101$	0.838402	0.0834241	0.0417121	−	0.999130i	$-0.486719\pi$
$101$	0.838402	0.0834241	0.0417121	+	0.999130i	$0.486719\pi$
$102$	6.00116	0.594204
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−2.43046	−0.238326
$105$	−27.4754	−2.68132
$106$	−4.65978	−0.452598
$107$	−13.8363	−1.33761	−0.668803	−	0.743440i	$-0.733193\pi$
$107$	−13.8363	−1.33761	−0.668803	+	0.743440i	$0.733193\pi$
$108$	−3.33641	−0.321046
$109$	13.1657	1.26105	0.630523	−	0.776170i	$-0.282840\pi$
$109$	13.1657	1.26105	0.630523	+	0.776170i	$0.282840\pi$
$110$	5.53379	0.527627
$111$	−6.08638	−0.577694
$112$	18.7280	1.76963
$113$	6.45274	0.607022	0.303511	−	0.952828i	$-0.401841\pi$
$113$	6.45274	0.607022	0.303511	+	0.952828i	$0.401841\pi$
$114$	6.37007	0.596612
$115$	12.8954	1.20250
$116$	0.292727	0.0271790
$117$	5.55751	0.513792
$118$	20.1522	1.85516
$119$	5.23452	0.479847
$120$	−16.7337	−1.52757
$121$	−8.73986	−0.794533
$122$	2.44452	0.221317
$123$	−28.0879	−2.53260
$124$	0.837890	0.0752447
$125$	10.4984	0.939009
$126$	−34.6851	−3.08999
$127$	−5.55146	−0.492612	−0.246306	−	0.969192i	$-0.579217\pi$
$127$	−5.55146	−0.492612	−0.246306	+	0.969192i	$0.579217\pi$
$128$	13.5740	1.19978
$129$	−9.32431	−0.820960
$130$	−3.68091	−0.322837
$131$	−15.4301	−1.34813	−0.674067	−	0.738671i	$-0.735454\pi$
$131$	−15.4301	−1.34813	−0.674067	+	0.738671i	$0.735454\pi$
$132$	1.96124	0.170704
$133$	5.55629	0.481792
$134$	−22.0702	−1.90658
$135$	17.6085	1.51549
$136$	3.18806	0.273374
$137$	13.2804	1.13462	0.567308	−	0.823505i	$-0.307985\pi$
$137$	13.2804	1.13462	0.567308	+	0.823505i	$0.307985\pi$
$138$	25.0669	2.13383
$139$	−15.1360	−1.28382	−0.641908	−	0.766782i	$-0.721857\pi$
$139$	−15.1360	−1.28382	−0.641908	+	0.766782i	$0.721857\pi$
$140$	4.18851	0.353994
$141$	−13.8423	−1.16573
$142$	−21.4231	−1.79778
$143$	−1.50338	−0.125719
$144$	−26.0816	−2.17346
$145$	−1.54491	−0.128298
$146$	−13.2118	−1.09341
$147$	−26.1083	−2.15338
$148$	0.927844	0.0762683
$149$	−7.47076	−0.612028	−0.306014	−	0.952027i	$-0.598996\pi$
$149$	−7.47076	−0.612028	−0.306014	+	0.952027i	$0.598996\pi$
$150$	−2.46777	−0.201492
$151$	−7.94700	−0.646717	−0.323359	−	0.946276i	$-0.604812\pi$
$151$	−7.94700	−0.646717	−0.323359	+	0.946276i	$0.604812\pi$
$152$	3.38403	0.274481
$153$	−7.28983	−0.589348
$154$	9.38276	0.756085
$155$	−4.42210	−0.355192
$156$	−1.30456	−0.104448
$157$	9.17083	0.731912	0.365956	−	0.930632i	$-0.380742\pi$
$157$	9.17083	0.731912	0.365956	+	0.930632i	$0.380742\pi$
$158$	−0.264029	−0.0210050
$159$	8.71596	0.691221
$160$	5.83402	0.461220
$161$	21.8646	1.72317
$162$	8.15345	0.640595
$163$	24.3602	1.90804	0.954018	−	0.299748i	$-0.0969027\pi$
$163$	24.3602	1.90804	0.954018	+	0.299748i	$0.0969027\pi$
$164$	4.28189	0.334360
$165$	−10.3508	−0.805806
$166$	−4.80270	−0.372762
$167$	−2.33942	−0.181030	−0.0905148	−	0.995895i	$-0.528851\pi$
$167$	−2.33942	−0.181030	−0.0905148	+	0.995895i	$0.528851\pi$
$168$	−28.3727	−2.18900
$169$	1.00000	0.0769231
$170$	4.82829	0.370313
$171$	−7.73796	−0.591736
$172$	1.42145	0.108385
$173$	13.4866	1.02537	0.512683	−	0.858578i	$-0.328652\pi$
$173$	13.4866	1.02537	0.512683	+	0.858578i	$0.328652\pi$
$174$	−3.00311	−0.227665
$175$	−2.15251	−0.162715
$176$	7.05540	0.531820
$177$	−37.6939	−2.83325
$178$	−1.33931	−0.100385
$179$	11.5692	0.864723	0.432361	−	0.901700i	$-0.357680\pi$
$179$	11.5692	0.864723	0.432361	+	0.901700i	$0.357680\pi$
$180$	−5.83312	−0.434775
$181$	24.0356	1.78656	0.893278	−	0.449505i	$-0.148400\pi$
$181$	24.0356	1.78656	0.893278	+	0.449505i	$0.148400\pi$
$182$	−6.24113	−0.462623
$183$	−4.57240	−0.338001
$184$	13.3165	0.981706
$185$	−4.89685	−0.360024
$186$	−8.59597	−0.630287
$187$	1.97199	0.144206
$188$	2.11020	0.153902
$189$	29.8558	2.17169
$190$	5.12509	0.371813
$191$	15.4231	1.11597	0.557987	−	0.829849i	$-0.311574\pi$
$191$	15.4231	1.11597	0.557987	+	0.829849i	$0.311574\pi$
$192$	−16.1167	−1.16312
$193$	−14.3881	−1.03568	−0.517839	−	0.855478i	$-0.673263\pi$
$193$	−14.3881	−1.03568	−0.517839	+	0.855478i	$0.673263\pi$
$194$	−15.3071	−1.09898
$195$	6.88501	0.493046
$196$	3.98011	0.284293
$197$	0.411959	0.0293509	0.0146754	−	0.999892i	$-0.495328\pi$
$197$	0.411959	0.0293509	0.0146754	+	0.999892i	$0.495328\pi$
$198$	−13.0669	−0.928622
$199$	10.6700	0.756375	0.378188	−	0.925729i	$-0.376547\pi$
$199$	10.6700	0.756375	0.378188	+	0.925729i	$0.376547\pi$
$200$	−1.31098	−0.0927000
$201$	41.2816	2.91178
$202$	1.31122	0.0922573
$203$	−2.61946	−0.183850
$204$	1.71120	0.119808
$205$	−22.5984	−1.57834
$206$	−1.56395	−0.108966
$207$	−30.4497	−2.11640
$208$	−4.69303	−0.325403
$209$	2.09322	0.144791
$210$	−42.9702	−2.96523
$211$	8.74858	0.602277	0.301139	−	0.953580i	$-0.402633\pi$
$211$	8.74858	0.602277	0.301139	+	0.953580i	$0.402633\pi$
$212$	−1.32871	−0.0912564
$213$	40.0711	2.74563
$214$	−21.6393	−1.47924
$215$	−7.50195	−0.511629
$216$	18.1835	1.23723
$217$	−7.49784	−0.508987
$218$	20.5906	1.39457
$219$	24.7122	1.66989
$220$	1.57793	0.106384
$221$	−1.31171	−0.0882351
$222$	−9.51882	−0.638862
$223$	20.6033	1.37970	0.689851	−	0.723951i	$-0.257676\pi$
$223$	20.6033	1.37970	0.689851	+	0.723951i	$0.257676\pi$
$224$	9.89181	0.660924
$225$	2.99769	0.199846
$226$	10.0918	0.671296
$227$	8.82744	0.585898	0.292949	−	0.956128i	$-0.405363\pi$
$227$	8.82744	0.585898	0.292949	+	0.956128i	$0.405363\pi$
$228$	1.81639	0.120293
$229$	−2.62907	−0.173734	−0.0868669	−	0.996220i	$-0.527685\pi$
$229$	−2.62907	−0.173734	−0.0868669	+	0.996220i	$0.527685\pi$
$230$	20.1678	1.32982
$231$	−17.5501	−1.15471
$232$	−1.59537	−0.104741
$233$	−9.69165	−0.634921	−0.317461	−	0.948271i	$-0.602830\pi$
$233$	−9.69165	−0.634921	−0.317461	+	0.948271i	$0.602830\pi$
$234$	8.69169	0.568193
$235$	−11.1369	−0.726492
$236$	5.74629	0.374051
$237$	0.493857	0.0320794
$238$	8.18655	0.530655
$239$	4.35134	0.281465	0.140733	−	0.990048i	$-0.455054\pi$
$239$	4.35134	0.281465	0.140733	+	0.990048i	$0.455054\pi$
$240$	−32.3116	−2.08570
$241$	−12.6508	−0.814911	−0.407455	−	0.913225i	$-0.633584\pi$
$241$	−12.6508	−0.814911	−0.407455	+	0.913225i	$0.633584\pi$
$242$	−13.6687	−0.878660
$243$	7.19385	0.461486
$244$	0.697043	0.0446236
$245$	−21.0057	−1.34200
$246$	−43.9283	−2.80076
$247$	−1.39234	−0.0885927
$248$	−4.56652	−0.289974
$249$	8.98328	0.569292
$250$	16.4191	1.03843
$251$	11.9192	0.752332	0.376166	−	0.926552i	$-0.377242\pi$
$251$	11.9192	0.752332	0.376166	+	0.926552i	$0.377242\pi$
$252$	−9.89027	−0.623029
$253$	8.23702	0.517857
$254$	−8.68223	−0.544771
$255$	−9.03114	−0.565552
$256$	10.2103	0.638144
$257$	16.0427	1.00072	0.500358	−	0.865818i	$-0.333202\pi$
$257$	16.0427	1.00072	0.500358	+	0.865818i	$0.333202\pi$
$258$	−14.5828	−0.907885
$259$	−8.30280	−0.515911
$260$	−1.04959	−0.0650930
$261$	3.64799	0.225805
$262$	−24.1320	−1.49088
$263$	−18.3377	−1.13075	−0.565375	−	0.824834i	$-0.691269\pi$
$263$	−18.3377	−1.13075	−0.565375	+	0.824834i	$0.691269\pi$
$264$	−10.6888	−0.657851
$265$	7.01250	0.430774
$266$	8.68979	0.532805
$267$	2.50513	0.153311
$268$	−6.29321	−0.384419
$269$	−18.7672	−1.14426	−0.572128	−	0.820164i	$-0.693882\pi$
$269$	−18.7672	−1.14426	−0.572128	+	0.820164i	$0.693882\pi$
$270$	27.5388	1.67596
$271$	16.9729	1.03103	0.515516	−	0.856880i	$-0.327600\pi$
$271$	16.9729	1.03103	0.515516	+	0.856880i	$0.327600\pi$
$272$	6.15590	0.373256
$273$	11.6738	0.706531
$274$	20.7699	1.25475
$275$	−0.810913	−0.0488999
$276$	7.14769	0.430240
$277$	−30.0476	−1.80538	−0.902692	−	0.430288i	$-0.858412\pi$
$277$	−30.0476	−1.80538	−0.902692	+	0.430288i	$0.858412\pi$
$278$	−23.6720	−1.41975
$279$	10.4418	0.625137
$280$	−22.8275	−1.36420
$281$	20.8161	1.24179	0.620893	−	0.783896i	$-0.286770\pi$
$281$	20.8161	1.24179	0.620893	+	0.783896i	$0.286770\pi$
$282$	−21.6487	−1.28916
$283$	16.6971	0.992542	0.496271	−	0.868168i	$-0.334702\pi$
$283$	16.6971	0.992542	0.496271	+	0.868168i	$0.334702\pi$
$284$	−6.10867	−0.362483
$285$	−9.58630	−0.567844
$286$	−2.35121	−0.139030
$287$	−38.3164	−2.26175
$288$	−13.7758	−0.811746
$289$	−15.2794	−0.898789
$290$	−2.41618	−0.141883
$291$	28.6313	1.67840
$292$	−3.76727	−0.220463
$293$	25.8848	1.51221	0.756104	−	0.654452i	$-0.227100\pi$
$293$	25.8848	1.51221	0.756104	+	0.654452i	$0.227100\pi$
$294$	−40.8322	−2.38138
$295$	−30.3270	−1.76570
$296$	−5.05678	−0.293919
$297$	11.2476	0.652649
$298$	−11.6839	−0.676832
$299$	−5.47901	−0.316860
$300$	−0.703671	−0.0406265
$301$	−12.7198	−0.733160
$302$	−12.4287	−0.715194
$303$	−2.45260	−0.140898
$304$	6.53431	0.374769
$305$	−3.67876	−0.210645
$306$	−11.4010	−0.651750
$307$	8.20421	0.468239	0.234120	−	0.972208i	$-0.424779\pi$
$307$	8.20421	0.468239	0.234120	+	0.972208i	$0.424779\pi$
$308$	2.67545	0.152448
$309$	2.92532	0.166416
$310$	−6.91596	−0.392800
$311$	8.97820	0.509107	0.254553	−	0.967059i	$-0.418072\pi$
$311$	8.97820	0.509107	0.254553	+	0.967059i	$0.418072\pi$
$312$	7.10987	0.402517
$313$	−19.0764	−1.07826	−0.539131	−	0.842222i	$-0.681247\pi$
$313$	−19.0764	−1.07826	−0.539131	+	0.842222i	$0.681247\pi$
$314$	14.3428	0.809409
$315$	52.1975	2.94100
$316$	−0.0752865	−0.00423520
$317$	7.09882	0.398709	0.199355	−	0.979927i	$-0.436115\pi$
$317$	7.09882	0.398709	0.199355	+	0.979927i	$0.436115\pi$
$318$	13.6314	0.764409
$319$	−0.986827	−0.0552517
$320$	−12.9668	−0.724868
$321$	40.4756	2.25913
$322$	34.1952	1.90562
$323$	1.82635	0.101621
$324$	2.32491	0.129162
$325$	0.539395	0.0299202
$326$	38.0982	2.11006
$327$	−38.5139	−2.12983
$328$	−23.3364	−1.28854
$329$	−18.8831	−1.04106
$330$	−16.1881	−0.891127
$331$	−1.25350	−0.0688985	−0.0344492	−	0.999406i	$-0.510968\pi$
$331$	−1.25350	−0.0688985	−0.0344492	+	0.999406i	$0.510968\pi$
$332$	−1.36947	−0.0751592
$333$	11.5629	0.633641
$334$	−3.65874	−0.200197
$335$	33.2134	1.81464
$336$	−54.7855	−2.98880
$337$	5.88035	0.320323	0.160162	−	0.987091i	$-0.448798\pi$
$337$	5.88035	0.320323	0.160162	+	0.987091i	$0.448798\pi$
$338$	1.56395	0.0850679
$339$	−18.8763	−1.02522
$340$	1.37676	0.0746653
$341$	−2.82465	−0.152964
$342$	−12.1018	−0.654391
$343$	−7.68166	−0.414771
$344$	−7.74696	−0.417688
$345$	−37.7231	−2.03094
$346$	21.0924	1.13393
$347$	−15.4442	−0.829089	−0.414544	−	0.910029i	$-0.636059\pi$
$347$	−15.4442	−0.829089	−0.414544	+	0.910029i	$0.636059\pi$
$348$	−0.856320	−0.0459036
$349$	16.7340	0.895750	0.447875	−	0.894096i	$-0.352181\pi$
$349$	16.7340	0.895750	0.447875	+	0.894096i	$0.352181\pi$
$350$	−3.36643	−0.179943
$351$	−7.48153	−0.399334
$352$	3.72653	0.198625
$353$	−12.6788	−0.674824	−0.337412	−	0.941357i	$-0.609551\pi$
$353$	−12.6788	−0.674824	−0.337412	+	0.941357i	$0.609551\pi$
$354$	−58.9516	−3.13324
$355$	32.2395	1.71110
$356$	−0.381897	−0.0202405
$357$	−15.3126	−0.810431
$358$	18.0937	0.956282
$359$	−29.9943	−1.58304	−0.791519	−	0.611144i	$-0.790710\pi$
$359$	−29.9943	−1.58304	−0.791519	+	0.611144i	$0.790710\pi$
$360$	31.7906	1.67551
$361$	−17.0614	−0.897967
$362$	37.5907	1.97572
$363$	25.5669	1.34191
$364$	−1.77962	−0.0932777
$365$	19.8824	1.04069
$366$	−7.15102	−0.373790
$367$	−32.0873	−1.67494	−0.837472	−	0.546481i	$-0.815967\pi$
$367$	−32.0873	−1.67494	−0.837472	+	0.546481i	$0.815967\pi$
$368$	25.7132	1.34039
$369$	53.3613	2.77788
$370$	−7.65845	−0.398144
$371$	11.8900	0.617296
$372$	−2.45110	−0.127083
$373$	9.52231	0.493046	0.246523	−	0.969137i	$-0.420712\pi$
$373$	9.52231	0.493046	0.246523	+	0.969137i	$0.420712\pi$
$374$	3.08411	0.159475
$375$	−30.7113	−1.58593
$376$	−11.5006	−0.593100
$377$	0.656407	0.0338067
$378$	46.6931	2.40164
$379$	−18.2896	−0.939471	−0.469736	−	0.882807i	$-0.655651\pi$
$379$	−18.2896	−0.939471	−0.469736	+	0.882807i	$0.655651\pi$
$380$	1.46139	0.0749679
$381$	16.2398	0.831990
$382$	24.1210	1.23414
$383$	22.0801	1.12824	0.564119	−	0.825693i	$-0.309216\pi$
$383$	22.0801	1.12824	0.564119	+	0.825693i	$0.309216\pi$
$384$	−39.7082	−2.02635
$385$	−14.1201	−0.719627
$386$	−22.5023	−1.14534
$387$	17.7143	0.900466
$388$	−4.36473	−0.221586
$389$	28.8480	1.46265	0.731326	−	0.682028i	$-0.238902\pi$
$389$	28.8480	1.46265	0.731326	+	0.682028i	$0.238902\pi$
$390$	10.7678	0.545251
$391$	7.18688	0.363456
$392$	−21.6917	−1.09560
$393$	45.1380	2.27691
$394$	0.644285	0.0324586
$395$	0.397337	0.0199922
$396$	−3.72595	−0.187236
$397$	−11.7496	−0.589695	−0.294848	−	0.955544i	$-0.595269\pi$
$397$	−11.7496	−0.589695	−0.294848	+	0.955544i	$0.595269\pi$
$398$	16.6874	0.836462
$399$	−16.2539	−0.813715
$400$	−2.53140	−0.126570
$401$	−19.8812	−0.992821	−0.496411	−	0.868088i	$-0.665349\pi$
$401$	−19.8812	−0.992821	−0.496411	+	0.868088i	$0.665349\pi$
$402$	64.5625	3.22008
$403$	1.87887	0.0935933
$404$	0.373888	0.0186016
$405$	−12.2701	−0.609706
$406$	−4.09672	−0.203317
$407$	−3.12790	−0.155044
$408$	−9.32609	−0.461710
$409$	−6.47617	−0.320226	−0.160113	−	0.987099i	$-0.551186\pi$
$409$	−6.47617	−0.320226	−0.160113	+	0.987099i	$0.551186\pi$
$410$	−35.3429	−1.74546
$411$	−38.8493	−1.91629
$412$	−0.445953	−0.0219706
$413$	−51.4205	−2.53024
$414$	−47.6219	−2.34049
$415$	7.22758	0.354788
$416$	−2.47877	−0.121532
$417$	44.2776	2.16828
$418$	3.27370	0.160122
$419$	−22.7342	−1.11064	−0.555320	−	0.831637i	$-0.687404\pi$
$419$	−22.7342	−1.11064	−0.555320	+	0.831637i	$0.687404\pi$
$420$	−12.2527	−0.597872
$421$	26.4968	1.29138	0.645688	−	0.763601i	$-0.276571\pi$
$421$	26.4968	1.29138	0.645688	+	0.763601i	$0.276571\pi$
$422$	13.6824	0.666048
$423$	26.2975	1.27863
$424$	7.24152	0.351679
$425$	−0.707529	−0.0343202
$426$	62.6693	3.03634
$427$	−6.23748	−0.301853
$428$	−6.17035	−0.298255
$429$	4.39786	0.212331
$430$	−11.7327	−0.565802
$431$	−6.51214	−0.313679	−0.156839	−	0.987624i	$-0.550131\pi$
$431$	−6.51214	−0.313679	−0.156839	+	0.987624i	$0.550131\pi$
$432$	35.1110	1.68928
$433$	20.7467	0.997021	0.498511	−	0.866884i	$-0.333880\pi$
$433$	20.7467	0.997021	0.498511	+	0.866884i	$0.333880\pi$
$434$	−11.7263	−0.562880
$435$	4.51937	0.216687
$436$	5.87130	0.281184
$437$	7.62867	0.364929
$438$	38.6487	1.84671
$439$	9.49728	0.453281	0.226640	−	0.973979i	$-0.427226\pi$
$439$	9.49728	0.453281	0.226640	+	0.973979i	$0.427226\pi$
$440$	−8.59977	−0.409978
$441$	49.6004	2.36192
$442$	−2.05145	−0.0975777
$443$	31.5155	1.49735	0.748673	−	0.662939i	$-0.230691\pi$
$443$	31.5155	1.49735	0.748673	+	0.662939i	$0.230691\pi$
$444$	−2.71424	−0.128812
$445$	2.01552	0.0955449
$446$	32.2227	1.52579
$447$	21.8544	1.03368
$448$	−21.9858	−1.03873
$449$	40.7721	1.92415	0.962077	−	0.272778i	$-0.0879423\pi$
$449$	40.7721	1.92415	0.962077	+	0.272778i	$0.0879423\pi$
$450$	4.68825	0.221006
$451$	−14.4349	−0.679714
$452$	2.87762	0.135352
$453$	23.2475	1.09226
$454$	13.8057	0.647935
$455$	9.39226	0.440316
$456$	−9.89938	−0.463581
$457$	14.2379	0.666023	0.333012	−	0.942923i	$-0.391935\pi$
$457$	14.2379	0.666023	0.333012	+	0.942923i	$0.391935\pi$
$458$	−4.11175	−0.192129
$459$	9.81359	0.458059
$460$	5.75073	0.268129
$461$	34.9640	1.62843	0.814217	−	0.580561i	$-0.197167\pi$
$461$	34.9640	1.62843	0.814217	+	0.580561i	$0.197167\pi$
$462$	−27.4476	−1.27698
$463$	31.7571	1.47588	0.737940	−	0.674867i	$-0.235799\pi$
$463$	31.7571	1.47588	0.737940	+	0.674867i	$0.235799\pi$
$464$	−3.08054	−0.143010
$465$	12.9361	0.599896
$466$	−15.1573	−0.702148
$467$	25.6573	1.18728	0.593638	−	0.804732i	$-0.297691\pi$
$467$	25.6573	1.18728	0.593638	+	0.804732i	$0.297691\pi$
$468$	2.47839	0.114564
$469$	56.3147	2.60037
$470$	−17.4176	−0.803415
$471$	−26.8276	−1.23615
$472$	−31.3174	−1.44150
$473$	−4.79193	−0.220333
$474$	0.772370	0.0354761
$475$	−0.751023	−0.0344593
$476$	2.33435	0.106995
$477$	−16.5585	−0.758163
$478$	6.80530	0.311267
$479$	−16.6653	−0.761456	−0.380728	−	0.924687i	$-0.624327\pi$
$479$	−16.6653	−0.761456	−0.380728	+	0.924687i	$0.624327\pi$
$480$	−17.0664	−0.778970
$481$	2.08059	0.0948665
$482$	−19.7853	−0.901196
$483$	−63.9609	−2.91032
$484$	−3.89757	−0.177162
$485$	23.0356	1.04599
$486$	11.2508	0.510349
$487$	−33.5677	−1.52110	−0.760549	−	0.649280i	$-0.775070\pi$
$487$	−33.5677	−1.52110	−0.760549	+	0.649280i	$0.775070\pi$
$488$	−3.79890	−0.171968
$489$	−71.2614	−3.22255
$490$	−32.8519	−1.48410
$491$	9.86798	0.445336	0.222668	−	0.974894i	$-0.428523\pi$
$491$	9.86798	0.445336	0.222668	+	0.974894i	$0.428523\pi$
$492$	−12.5259	−0.564712
$493$	−0.861015	−0.0387782
$494$	−2.17756	−0.0979731
$495$	19.6643	0.883845
$496$	−8.81761	−0.395922
$497$	54.6634	2.45199
$498$	14.0494	0.629571
$499$	18.5696	0.831291	0.415646	−	0.909527i	$-0.363556\pi$
$499$	18.5696	0.831291	0.415646	+	0.909527i	$0.363556\pi$
$500$	4.68182	0.209377
$501$	6.84355	0.305747
$502$	18.6411	0.831991
$503$	−2.24495	−0.100098	−0.0500488	−	0.998747i	$-0.515938\pi$
$503$	−2.24495	−0.100098	−0.0500488	+	0.998747i	$0.515938\pi$
$504$	53.9022	2.40100
$505$	−1.97326	−0.0878087
$506$	12.8823	0.572689
$507$	−2.92532	−0.129918
$508$	−2.47569	−0.109841
$509$	26.5760	1.17796	0.588980	−	0.808148i	$-0.299530\pi$
$509$	26.5760	1.17796	0.588980	+	0.808148i	$0.299530\pi$
$510$	−14.1243	−0.625434
$511$	33.7113	1.49130
$512$	−11.1795	−0.494068
$513$	10.4169	0.459915
$514$	25.0901	1.10668
$515$	2.35359	0.103712
$516$	−4.15821	−0.183055
$517$	−7.11380	−0.312865
$518$	−12.9852	−0.570537
$519$	−39.4526	−1.73178
$520$	5.72031	0.250852
$521$	16.6830	0.730894	0.365447	−	0.930832i	$-0.380916\pi$
$521$	16.6830	0.730894	0.365447	+	0.930832i	$0.380916\pi$
$522$	5.70528	0.249713
$523$	−43.3589	−1.89595	−0.947975	−	0.318344i	$-0.896873\pi$
$523$	−43.3589	−1.89595	−0.947975	+	0.318344i	$0.896873\pi$
$524$	−6.88110	−0.300602
$525$	6.29679	0.274814
$526$	−28.6793	−1.25048
$527$	−2.46454	−0.107357
$528$	−20.6393	−0.898210
$529$	7.01960	0.305200
$530$	10.9672	0.476386
$531$	71.6107	3.10764
$532$	2.47785	0.107428
$533$	9.60166	0.415894
$534$	3.91791	0.169544
$535$	32.5650	1.40791
$536$	34.2982	1.48145
$537$	−33.8436	−1.46046
$538$	−29.3510	−1.26541
$539$	−13.4175	−0.577934
$540$	7.85255	0.337920
$541$	4.86233	0.209048	0.104524	−	0.994522i	$-0.466668\pi$
$541$	4.86233	0.209048	0.104524	+	0.994522i	$0.466668\pi$
$542$	26.5449	1.14020
$543$	−70.3120	−3.01738
$544$	3.25143	0.139404
$545$	−30.9867	−1.32733
$546$	18.2573	0.781340
$547$	−16.5902	−0.709344	−0.354672	−	0.934991i	$-0.615407\pi$
$547$	−16.5902	−0.709344	−0.354672	+	0.934991i	$0.615407\pi$
$548$	5.92242	0.252993
$549$	8.68661	0.370735
$550$	−1.26823	−0.0540776
$551$	−0.913944	−0.0389353
$552$	−38.9551	−1.65804
$553$	0.673700	0.0286486
$554$	−46.9930	−1.99654
$555$	14.3249	0.608056
$556$	−6.74993	−0.286261
$557$	−18.6380	−0.789719	−0.394859	−	0.918742i	$-0.629207\pi$
$557$	−18.6380	−0.789719	−0.394859	+	0.918742i	$0.629207\pi$
$558$	16.3306	0.691328
$559$	3.18745	0.134815
$560$	−44.0782	−1.86264
$561$	−5.76872	−0.243555
$562$	32.5555	1.37327
$563$	−12.1090	−0.510333	−0.255166	−	0.966897i	$-0.582130\pi$
$563$	−12.1090	−0.510333	−0.255166	+	0.966897i	$0.582130\pi$
$564$	−6.17301	−0.259931
$565$	−15.1871	−0.638926
$566$	26.1136	1.09764
$567$	−20.8044	−0.873704
$568$	33.2924	1.39692
$569$	−42.2009	−1.76915	−0.884576	−	0.466396i	$-0.845552\pi$
$569$	−42.2009	−1.76915	−0.884576	+	0.466396i	$0.845552\pi$
$570$	−14.9925	−0.627968
$571$	31.5197	1.31906	0.659529	−	0.751679i	$-0.270756\pi$
$571$	31.5197	1.31906	0.659529	+	0.751679i	$0.270756\pi$
$572$	−0.670436	−0.0280323
$573$	−45.1175	−1.88481
$574$	−59.9252	−2.50123
$575$	−2.95535	−0.123247
$576$	30.6184	1.27577
$577$	−26.4066	−1.09932	−0.549661	−	0.835388i	$-0.685243\pi$
$577$	−26.4066	−1.09932	−0.549661	+	0.835388i	$0.685243\pi$
$578$	−23.8963	−0.993956
$579$	42.0898	1.74919
$580$	−0.688960	−0.0286075
$581$	12.2546	0.508408
$582$	44.7781	1.85611
$583$	4.47929	0.185513
$584$	20.5317	0.849609
$585$	−13.0801	−0.540796
$586$	40.4827	1.67232
$587$	−41.7018	−1.72122	−0.860609	−	0.509266i	$-0.829917\pi$
$587$	−41.7018	−1.72122	−0.860609	+	0.509266i	$0.829917\pi$
$588$	−11.6431	−0.480153
$589$	−2.61604	−0.107792
$590$	−47.4300	−1.95266
$591$	−1.20511	−0.0495717
$592$	−9.76426	−0.401308
$593$	38.4981	1.58093	0.790464	−	0.612509i	$-0.209840\pi$
$593$	38.4981	1.58093	0.790464	+	0.612509i	$0.209840\pi$
$594$	17.5907	0.721753
$595$	−12.3199	−0.505067
$596$	−3.33161	−0.136468
$597$	−31.2131	−1.27747
$598$	−8.56893	−0.350410
$599$	45.2844	1.85027	0.925135	−	0.379637i	$-0.123951\pi$
$599$	45.2844	1.85027	0.925135	+	0.379637i	$0.123951\pi$
$600$	3.83503	0.156564
$601$	−13.6144	−0.555345	−0.277672	−	0.960676i	$-0.589563\pi$
$601$	−13.6144	−0.555345	−0.277672	+	0.960676i	$0.589563\pi$
$602$	−19.8933	−0.810789
$603$	−78.4264	−3.19377
$604$	−3.54399	−0.144203
$605$	20.5701	0.836292
$606$	−3.83575	−0.155817
$607$	15.8983	0.645293	0.322646	−	0.946520i	$-0.395428\pi$
$607$	15.8983	0.645293	0.322646	+	0.946520i	$0.395428\pi$
$608$	3.45130	0.139969
$609$	7.66277	0.310511
$610$	−5.75341	−0.232949
$611$	4.73188	0.191431
$612$	−3.25093	−0.131411
$613$	4.99152	0.201605	0.100803	−	0.994906i	$-0.467859\pi$
$613$	4.99152	0.201605	0.100803	+	0.994906i	$0.467859\pi$
$614$	12.8310	0.517818
$615$	66.1076	2.66571
$616$	−14.5812	−0.587495
$617$	−8.94877	−0.360264	−0.180132	−	0.983642i	$-0.557652\pi$
$617$	−8.94877	−0.360264	−0.180132	+	0.983642i	$0.557652\pi$
$618$	4.57507	0.184036
$619$	−29.9206	−1.20261	−0.601305	−	0.799020i	$-0.705352\pi$
$619$	−29.9206	−1.20261	−0.601305	+	0.799020i	$0.705352\pi$
$620$	−1.97205	−0.0791995
$621$	40.9914	1.64493
$622$	14.0415	0.563013
$623$	3.41740	0.136915
$624$	13.7286	0.549585
$625$	−27.4060	−1.09624
$626$	−29.8346	−1.19243
$627$	−6.12333	−0.244542
$628$	4.08976	0.163199
$629$	−2.72912	−0.108817
$630$	81.6346	3.25240
$631$	−4.39205	−0.174845	−0.0874224	−	0.996171i	$-0.527863\pi$
$631$	−4.39205	−0.174845	−0.0874224	+	0.996171i	$0.527863\pi$
$632$	0.410313	0.0163214
$633$	−25.5924	−1.01721
$634$	11.1022	0.440926
$635$	13.0659	0.518503
$636$	3.88691	0.154126
$637$	8.92494	0.353619
$638$	−1.54335	−0.0611019
$639$	−76.1268	−3.01153
$640$	−31.9476	−1.26284
$641$	−19.4093	−0.766622	−0.383311	−	0.923619i	$-0.625216\pi$
$641$	−19.4093	−0.766622	−0.383311	+	0.923619i	$0.625216\pi$
$642$	63.3020	2.49833
$643$	−35.3426	−1.39378	−0.696888	−	0.717180i	$-0.745432\pi$
$643$	−35.3426	−1.39378	−0.696888	+	0.717180i	$0.745432\pi$
$644$	9.75059	0.384227
$645$	21.9456	0.864108
$646$	2.85633	0.112381
$647$	−19.6905	−0.774114	−0.387057	−	0.922056i	$-0.626508\pi$
$647$	−19.6905	−0.774114	−0.387057	+	0.922056i	$0.626508\pi$
$648$	−12.6708	−0.497757
$649$	−19.3716	−0.760402
$650$	0.843589	0.0330883
$651$	21.9336	0.859645
$652$	10.8635	0.425448
$653$	−37.2143	−1.45631	−0.728154	−	0.685413i	$-0.759622\pi$
$653$	−37.2143	−1.45631	−0.728154	+	0.685413i	$0.759622\pi$
$654$	−60.2341	−2.35534
$655$	36.3161	1.41899
$656$	−45.0609	−1.75933
$657$	−46.9480	−1.83162
$658$	−29.5323	−1.15129
$659$	8.05781	0.313888	0.156944	−	0.987608i	$-0.449836\pi$
$659$	8.05781	0.313888	0.156944	+	0.987608i	$0.449836\pi$
$660$	−4.61596	−0.179676
$661$	−41.4215	−1.61111	−0.805556	−	0.592520i	$-0.798133\pi$
$661$	−41.4215	−1.61111	−0.805556	+	0.592520i	$0.798133\pi$
$662$	−1.96041	−0.0761936
$663$	3.83717	0.149023
$664$	7.46362	0.289645
$665$	−13.0772	−0.507114
$666$	18.0838	0.700733
$667$	−3.59646	−0.139256
$668$	−1.04327	−0.0403654
$669$	−60.2714	−2.33023
$670$	51.9443	2.00678
$671$	−2.34984	−0.0907145
$672$	−28.9367	−1.11626
$673$	11.6932	0.450739	0.225370	−	0.974273i	$-0.427641\pi$
$673$	11.6932	0.450739	0.225370	+	0.974273i	$0.427641\pi$
$674$	9.19660	0.354240
$675$	−4.03550	−0.155326
$676$	0.445953	0.0171521
$677$	−18.3897	−0.706774	−0.353387	−	0.935477i	$-0.614970\pi$
$677$	−18.3897	−0.706774	−0.353387	+	0.935477i	$0.614970\pi$
$678$	−29.5217	−1.13377
$679$	39.0577	1.49890
$680$	−7.50338	−0.287742
$681$	−25.8231	−0.989544
$682$	−4.41763	−0.169160
$683$	18.7550	0.717641	0.358821	−	0.933407i	$-0.383179\pi$
$683$	18.7550	0.717641	0.358821	+	0.933407i	$0.383179\pi$
$684$	−3.45077	−0.131943
$685$	−31.2565	−1.19425
$686$	−12.0138	−0.458688
$687$	7.69087	0.293425
$688$	−14.9588	−0.570299
$689$	−2.97949	−0.113509
$690$	−58.9972	−2.24598
$691$	11.2084	0.426387	0.213194	−	0.977010i	$-0.431613\pi$
$691$	11.2084	0.426387	0.213194	+	0.977010i	$0.431613\pi$
$692$	6.01439	0.228633
$693$	33.3416	1.26654
$694$	−24.1540	−0.916875
$695$	35.6239	1.35129
$696$	4.66697	0.176901
$697$	−12.5946	−0.477054
$698$	26.1712	0.990594
$699$	28.3512	1.07234
$700$	−0.959920	−0.0362816
$701$	−11.7848	−0.445106	−0.222553	−	0.974921i	$-0.571439\pi$
$701$	−11.7848	−0.445106	−0.222553	+	0.974921i	$0.571439\pi$
$702$	−11.7008	−0.441617
$703$	−2.89689	−0.109258
$704$	−8.28267	−0.312165
$705$	32.5791	1.22700
$706$	−19.8290	−0.746276
$707$	−3.34573	−0.125829
$708$	−16.8097	−0.631749
$709$	52.2545	1.96246	0.981230	−	0.192840i	$-0.0617698\pi$
$709$	52.2545	1.96246	0.981230	+	0.192840i	$0.0617698\pi$
$710$	50.4211	1.89227
$711$	−0.938226	−0.0351862
$712$	2.08135	0.0780018
$713$	−10.2944	−0.385527
$714$	−23.9483	−0.896242
$715$	3.53833	0.132326
$716$	5.15933	0.192813
$717$	−12.7291	−0.475376
$718$	−46.9097	−1.75066
$719$	−11.2204	−0.418451	−0.209225	−	0.977867i	$-0.567094\pi$
$719$	−11.2204	−0.418451	−0.209225	+	0.977867i	$0.567094\pi$
$720$	61.3853	2.28770
$721$	3.99061	0.148618
$722$	−26.6832	−0.993047
$723$	37.0077	1.37633
$724$	10.7188	0.398360
$725$	0.354062	0.0131496
$726$	39.9855	1.48400
$727$	12.0230	0.445909	0.222954	−	0.974829i	$-0.428430\pi$
$727$	12.0230	0.445909	0.222954	+	0.974829i	$0.428430\pi$
$728$	9.69900	0.359469
$729$	−36.6844	−1.35868
$730$	31.0951	1.15088
$731$	−4.18101	−0.154640
$732$	−2.03908	−0.0753664
$733$	13.4124	0.495400	0.247700	−	0.968837i	$-0.420325\pi$
$733$	13.4124	0.495400	0.247700	+	0.968837i	$0.420325\pi$
$734$	−50.1831	−1.85229
$735$	61.4483	2.26655
$736$	13.5812	0.500611
$737$	21.2154	0.781478
$738$	83.4546	3.07201
$739$	49.1184	1.80685	0.903425	−	0.428747i	$-0.141045\pi$
$739$	49.1184	1.80685	0.903425	+	0.428747i	$0.141045\pi$
$740$	−2.18377	−0.0802769
$741$	4.07305	0.149627
$742$	18.5954	0.682657
$743$	36.5260	1.34001	0.670004	−	0.742358i	$-0.266292\pi$
$743$	36.5260	1.34001	0.670004	+	0.742358i	$0.266292\pi$
$744$	13.3585	0.489748
$745$	17.5831	0.644196
$746$	14.8925	0.545251
$747$	−17.0664	−0.624426
$748$	0.879417	0.0321547
$749$	55.2152	2.01752
$750$	−48.0311	−1.75385
$751$	−37.6255	−1.37297	−0.686487	−	0.727142i	$-0.740848\pi$
$751$	−37.6255	−1.37297	−0.686487	+	0.727142i	$0.740848\pi$
$752$	−22.2069	−0.809801
$753$	−34.8674	−1.27064
$754$	1.02659	0.0373862
$755$	18.7040	0.680708
$756$	13.3143	0.484237
$757$	5.83747	0.212166	0.106083	−	0.994357i	$-0.466169\pi$
$757$	5.83747	0.212166	0.106083	+	0.994357i	$0.466169\pi$
$758$	−28.6040	−1.03895
$759$	−24.0959	−0.874627
$760$	−7.96463	−0.288908
$761$	44.5221	1.61392	0.806962	−	0.590603i	$-0.201110\pi$
$761$	44.5221	1.61392	0.806962	+	0.590603i	$0.201110\pi$
$762$	25.3983	0.920084
$763$	−52.5392	−1.90205
$764$	6.87798	0.248836
$765$	17.1573	0.620323
$766$	34.5322	1.24770
$767$	12.8854	0.465265
$768$	−29.8684	−1.07778
$769$	−12.0745	−0.435419	−0.217709	−	0.976014i	$-0.569858\pi$
$769$	−12.0745	−0.435419	−0.217709	+	0.976014i	$0.569858\pi$
$770$	−22.0832	−0.795823
$771$	−46.9301	−1.69015
$772$	−6.41642	−0.230932
$773$	−6.17242	−0.222007	−0.111003	−	0.993820i	$-0.535406\pi$
$773$	−6.17242	−0.222007	−0.111003	+	0.993820i	$0.535406\pi$
$774$	27.7043	0.995810
$775$	1.01345	0.0364044
$776$	23.7879	0.853936
$777$	24.2884	0.871340
$778$	45.1170	1.61752
$779$	−13.3688	−0.478987
$780$	3.07040	0.109938
$781$	20.5933	0.736885
$782$	11.2399	0.401940
$783$	−4.91093	−0.175502
$784$	−41.8850	−1.49589
$785$	−21.5844	−0.770380
$786$	70.5937	2.51800
$787$	−25.1080	−0.895003	−0.447502	−	0.894283i	$-0.647686\pi$
$787$	−25.1080	−0.895003	−0.447502	+	0.894283i	$0.647686\pi$
$788$	0.183715	0.00654456
$789$	53.6436	1.90976
$790$	0.621416	0.0221090
$791$	−25.7503	−0.915576
$792$	20.3065	0.721561
$793$	1.56304	0.0555052
$794$	−18.3758	−0.652134
$795$	−20.5138	−0.727550
$796$	4.75832	0.168654
$797$	26.0910	0.924191	0.462096	−	0.886830i	$-0.347098\pi$
$797$	26.0910	0.924191	0.462096	+	0.886830i	$0.347098\pi$
$798$	−25.4204	−0.899874
$799$	−6.20685	−0.219583
$800$	−1.33704	−0.0472714
$801$	−4.75923	−0.168159
$802$	−31.0933	−1.09794
$803$	12.7000	0.448175
$804$	18.4097	0.649259
$805$	−51.4603	−1.81374
$806$	2.93847	0.103503
$807$	54.9001	1.93257
$808$	−2.03770	−0.0716861
$809$	13.2223	0.464872	0.232436	−	0.972612i	$-0.425330\pi$
$809$	13.2223	0.464872	0.232436	+	0.972612i	$0.425330\pi$
$810$	−19.1899	−0.674264
$811$	−31.0170	−1.08915	−0.544576	−	0.838711i	$-0.683310\pi$
$811$	−31.0170	−1.08915	−0.544576	+	0.838711i	$0.683310\pi$
$812$	−1.16816	−0.0409943
$813$	−49.6513	−1.74135
$814$	−4.89190	−0.171461
$815$	−57.3339	−2.00832
$816$	−18.0080	−0.630405
$817$	−4.43802	−0.155267
$818$	−10.1284	−0.354133
$819$	−22.1778	−0.774956
$820$	−10.0778	−0.351933
$821$	44.5175	1.55367	0.776835	−	0.629704i	$-0.216824\pi$
$821$	44.5175	1.55367	0.776835	+	0.629704i	$0.216824\pi$
$822$	−60.7585	−2.11920
$823$	24.4202	0.851235	0.425617	−	0.904903i	$-0.360057\pi$
$823$	24.4202	0.851235	0.425617	+	0.904903i	$0.360057\pi$
$824$	2.43046	0.0846690
$825$	2.37218	0.0825888
$826$	−80.4194	−2.79815
$827$	31.1929	1.08468	0.542342	−	0.840158i	$-0.317538\pi$
$827$	31.1929	1.08468	0.542342	+	0.840158i	$0.317538\pi$
$828$	−13.5791	−0.471907
$829$	−23.4900	−0.815842	−0.407921	−	0.913017i	$-0.633746\pi$
$829$	−23.4900	−0.815842	−0.407921	+	0.913017i	$0.633746\pi$
$830$	11.3036	0.392354
$831$	87.8988	3.04918
$832$	5.50938	0.191003
$833$	−11.7069	−0.405621
$834$	69.2481	2.39786
$835$	5.50603	0.190544
$836$	0.933477	0.0322850
$837$	−14.0568	−0.485875
$838$	−35.5553	−1.22824
$839$	−5.95640	−0.205638	−0.102819	−	0.994700i	$-0.532786\pi$
$839$	−5.95640	−0.205638	−0.102819	+	0.994700i	$0.532786\pi$
$840$	66.7777	2.30405
$841$	−28.5691	−0.985142
$842$	41.4398	1.42811
$843$	−60.8938	−2.09730
$844$	3.90146	0.134294
$845$	−2.35359	−0.0809660
$846$	41.1280	1.41401
$847$	34.8773	1.19840
$848$	13.9828	0.480173
$849$	−48.8445	−1.67634
$850$	−1.10654	−0.0379541
$851$	−11.3996	−0.390772
$852$	17.8698	0.612211
$853$	33.8041	1.15743	0.578716	−	0.815529i	$-0.303554\pi$
$853$	33.8041	1.15743	0.578716	+	0.815529i	$0.303554\pi$
$854$	−9.75513	−0.333814
$855$	18.2120	0.622837
$856$	33.6285	1.14940
$857$	−39.4280	−1.34683	−0.673417	−	0.739263i	$-0.735174\pi$
$857$	−39.4280	−1.34683	−0.673417	+	0.739263i	$0.735174\pi$
$858$	6.87805	0.234813
$859$	20.9877	0.716090	0.358045	−	0.933704i	$-0.383444\pi$
$859$	20.9877	0.716090	0.358045	+	0.933704i	$0.383444\pi$
$860$	−3.34552	−0.114081
$861$	112.088	3.81995
$862$	−10.1847	−0.346892
$863$	−50.2515	−1.71058	−0.855291	−	0.518148i	$-0.826622\pi$
$863$	−50.2515	−1.71058	−0.855291	+	0.518148i	$0.826622\pi$
$864$	18.5450	0.630914
$865$	−31.7419	−1.07926
$866$	32.4468	1.10259
$867$	44.6972	1.51800
$868$	−3.34369	−0.113492
$869$	0.253802	0.00860965
$870$	7.06809	0.239631
$871$	−14.1118	−0.478160
$872$	−31.9987	−1.08361
$873$	−54.3936	−1.84094
$874$	11.9309	0.403568
$875$	−41.8952	−1.41631
$876$	11.0205	0.372347
$877$	−13.2063	−0.445946	−0.222973	−	0.974825i	$-0.571576\pi$
$877$	−13.2063	−0.445946	−0.222973	+	0.974825i	$0.571576\pi$
$878$	14.8533	0.501275
$879$	−75.7215	−2.55402
$880$	−16.6055	−0.559772
$881$	2.74489	0.0924778	0.0462389	−	0.998930i	$-0.485276\pi$
$881$	2.74489	0.0924778	0.0462389	+	0.998930i	$0.485276\pi$
$882$	77.5727	2.61201
$883$	49.9620	1.68135	0.840677	−	0.541537i	$-0.182157\pi$
$883$	49.9620	1.68135	0.840677	+	0.541537i	$0.182157\pi$
$884$	−0.584962	−0.0196744
$885$	88.7161	2.98216
$886$	49.2888	1.65589
$887$	−8.59923	−0.288734	−0.144367	−	0.989524i	$-0.546115\pi$
$887$	−8.59923	−0.288734	−0.144367	+	0.989524i	$0.546115\pi$
$888$	14.7927	0.496410
$889$	22.1537	0.743011
$890$	3.15219	0.105661
$891$	−7.83763	−0.262571
$892$	9.18813	0.307641
$893$	−6.58840	−0.220473
$894$	34.1792	1.14312
$895$	−27.2292	−0.910171
$896$	−54.1683	−1.80964
$897$	16.0279	0.535155
$898$	63.7657	2.12789
$899$	1.23331	0.0411330
$900$	1.33683	0.0445610
$901$	3.90822	0.130202
$902$	−22.5755	−0.751683
$903$	37.2096	1.23826
$904$	−15.6831	−0.521612
$905$	−56.5701	−1.88045
$906$	36.3581	1.20792
$907$	−6.17726	−0.205113	−0.102556	−	0.994727i	$-0.532702\pi$
$907$	−6.17726	−0.205113	−0.102556	+	0.994727i	$0.532702\pi$
$908$	3.93663	0.130642
$909$	4.65942	0.154543
$910$	14.6891	0.486938
$911$	17.1415	0.567925	0.283962	−	0.958835i	$-0.408351\pi$
$911$	17.1415	0.567925	0.283962	+	0.958835i	$0.408351\pi$
$912$	−19.1150	−0.632960
$913$	4.61667	0.152790
$914$	22.2675	0.736544
$915$	10.7616	0.355766
$916$	−1.17244	−0.0387386
$917$	61.5754	2.03340
$918$	15.3480	0.506560
$919$	−58.4613	−1.92846	−0.964230	−	0.265068i	$-0.914606\pi$
$919$	−58.4613	−1.92846	−0.964230	+	0.265068i	$0.914606\pi$
$920$	−31.3416	−1.03330
$921$	−24.0000	−0.790825
$922$	54.6820	1.80086
$923$	−13.6980	−0.450875
$924$	−7.82654	−0.257474
$925$	1.12226	0.0368996
$926$	49.6667	1.63215
$927$	−5.55751	−0.182532
$928$	−1.62708	−0.0534116
$929$	47.4253	1.55597	0.777986	−	0.628281i	$-0.216241\pi$
$929$	47.4253	1.55597	0.777986	+	0.628281i	$0.216241\pi$
$930$	20.2314	0.663414
$931$	−12.4266	−0.407265
$932$	−4.32203	−0.141573
$933$	−26.2641	−0.859848
$934$	40.1268	1.31299
$935$	−4.64127	−0.151786
$936$	−13.5073	−0.441499
$937$	−42.2153	−1.37911	−0.689557	−	0.724232i	$-0.742195\pi$
$937$	−42.2153	−1.37911	−0.689557	+	0.724232i	$0.742195\pi$
$938$	88.0736	2.87570
$939$	55.8046	1.82111
$940$	−4.96655	−0.161991
$941$	19.4063	0.632626	0.316313	−	0.948655i	$-0.397555\pi$
$941$	19.4063	0.632626	0.316313	+	0.948655i	$0.397555\pi$
$942$	−41.9572	−1.36704
$943$	−52.6076	−1.71314
$944$	−60.4716	−1.96818
$945$	−70.2684	−2.28583
$946$	−7.49437	−0.243663
$947$	45.3543	1.47382	0.736908	−	0.675993i	$-0.236285\pi$
$947$	45.3543	1.47382	0.736908	+	0.675993i	$0.236285\pi$
$948$	0.220237	0.00715297
$949$	−8.44768	−0.274223
$950$	−1.17457	−0.0381079
$951$	−20.7663	−0.673394
$952$	−12.7223	−0.412331
$953$	−53.7826	−1.74219	−0.871094	−	0.491116i	$-0.836589\pi$
$953$	−53.7826	−1.74219	−0.871094	+	0.491116i	$0.836589\pi$
$954$	−25.8968	−0.838439
$955$	−36.2996	−1.17463
$956$	1.94050	0.0627602
$957$	2.88679	0.0933165
$958$	−26.0637	−0.842081
$959$	−52.9966	−1.71135
$960$	37.9321	1.22425
$961$	−27.4698	−0.886124
$962$	3.25394	0.104911
$963$	−76.8953	−2.47792
$964$	−5.64168	−0.181706
$965$	33.8637	1.09011
$966$	−100.032	−3.21848
$967$	1.97366	0.0634685	0.0317343	−	0.999496i	$-0.489897\pi$
$967$	1.97366	0.0634685	0.0317343	+	0.999496i	$0.489897\pi$
$968$	21.2419	0.682739
$969$	−5.34266	−0.171631
$970$	36.0266	1.15674
$971$	34.1801	1.09689	0.548446	−	0.836186i	$-0.315220\pi$
$971$	34.1801	1.09689	0.548446	+	0.836186i	$0.315220\pi$
$972$	3.20812	0.102901
$973$	60.4017	1.93639
$974$	−52.4984	−1.68216
$975$	−1.57790	−0.0505333
$976$	−7.33540	−0.234800
$977$	−55.2888	−1.76885	−0.884423	−	0.466687i	$-0.845447\pi$
$977$	−55.2888	−1.76885	−0.884423	+	0.466687i	$0.845447\pi$
$978$	−111.450	−3.56376
$979$	1.28743	0.0411465
$980$	−9.36754	−0.299235
$981$	73.1685	2.33609
$982$	15.4331	0.492489
$983$	44.7547	1.42745	0.713727	−	0.700424i	$-0.247006\pi$
$983$	44.7547	1.42745	0.713727	+	0.700424i	$0.247006\pi$
$984$	68.2666	2.17626
$985$	−0.969583	−0.0308935
$986$	−1.34659	−0.0428841
$987$	55.2391	1.75828
$988$	−0.620920	−0.0197541
$989$	−17.4641	−0.555325
$990$	30.7541	0.977429
$991$	8.33068	0.264633	0.132316	−	0.991208i	$-0.457759\pi$
$991$	8.33068	0.264633	0.132316	+	0.991208i	$0.457759\pi$
$992$	−4.65730	−0.147869
$993$	3.66688	0.116365
$994$	85.4910	2.71161
$995$	−25.1128	−0.796129
$996$	4.00613	0.126939
$997$	57.6862	1.82694	0.913470	−	0.406907i	$-0.133393\pi$
$997$	57.6862	1.82694	0.913470	+	0.406907i	$0.133393\pi$
$998$	29.0421	0.919311
$999$	−15.5660	−0.492485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.f.1.19	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.f.1.19	✓	28	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:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q+1.56395 q^{2} -2.92532 q^{3} +0.445953 q^{4} -2.35359 q^{5} -4.57507 q^{6} -3.99061 q^{7} -2.43046 q^{8} +5.55751 q^{9} +O(q^{10})\)	\(q+1.56395 q^{2} -2.92532 q^{3} +0.445953 q^{4} -2.35359 q^{5} -4.57507 q^{6} -3.99061 q^{7} -2.43046 q^{8} +5.55751 q^{9} -3.68091 q^{10} -1.50338 q^{11} -1.30456 q^{12} +1.00000 q^{13} -6.24113 q^{14} +6.88501 q^{15} -4.69303 q^{16} -1.31171 q^{17} +8.69169 q^{18} -1.39234 q^{19} -1.04959 q^{20} +11.6738 q^{21} -2.35121 q^{22} -5.47901 q^{23} +7.10987 q^{24} +0.539395 q^{25} +1.56395 q^{26} -7.48153 q^{27} -1.77962 q^{28} +0.656407 q^{29} +10.7678 q^{30} +1.87887 q^{31} -2.47877 q^{32} +4.39786 q^{33} -2.05145 q^{34} +9.39226 q^{35} +2.47839 q^{36} +2.08059 q^{37} -2.17756 q^{38} -2.92532 q^{39} +5.72031 q^{40} +9.60166 q^{41} +18.2573 q^{42} +3.18745 q^{43} -0.670436 q^{44} -13.0801 q^{45} -8.56893 q^{46} +4.73188 q^{47} +13.7286 q^{48} +8.92494 q^{49} +0.843589 q^{50} +3.83717 q^{51} +0.445953 q^{52} -2.97949 q^{53} -11.7008 q^{54} +3.53833 q^{55} +9.69900 q^{56} +4.07305 q^{57} +1.02659 q^{58} +12.8854 q^{59} +3.07040 q^{60} +1.56304 q^{61} +2.93847 q^{62} -22.1778 q^{63} +5.50938 q^{64} -2.35359 q^{65} +6.87805 q^{66} -14.1118 q^{67} -0.584962 q^{68} +16.0279 q^{69} +14.6891 q^{70} -13.6980 q^{71} -13.5073 q^{72} -8.44768 q^{73} +3.25394 q^{74} -1.57790 q^{75} -0.620920 q^{76} +5.99938 q^{77} -4.57507 q^{78} -0.168821 q^{79} +11.0455 q^{80} +5.21335 q^{81} +15.0166 q^{82} -3.07087 q^{83} +5.20597 q^{84} +3.08723 q^{85} +4.98502 q^{86} -1.92020 q^{87} +3.65389 q^{88} -0.856360 q^{89} -20.4567 q^{90} -3.99061 q^{91} -2.44339 q^{92} -5.49631 q^{93} +7.40045 q^{94} +3.27701 q^{95} +7.25121 q^{96} -9.78741 q^{97} +13.9582 q^{98} -8.35502 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9}+O(q^{10}) \) 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9	\( 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9} + 5 q^{10} + 9 q^{11} + 15 q^{12} + 28 q^{13} + 20 q^{14} + 4 q^{15} + 32 q^{16} - 7 q^{17} + 10 q^{18} - 3 q^{19} + 53 q^{20} + 25 q^{21} - 14 q^{22} - 6 q^{23} + 10 q^{24} + 45 q^{25} + 6 q^{26} + 8 q^{27} - 12 q^{28} + 25 q^{29} - 43 q^{30} + q^{31} + 28 q^{32} + 17 q^{33} + 10 q^{34} + 11 q^{35} + 27 q^{36} + 18 q^{37} + 2 q^{38} + 5 q^{39} + 37 q^{40} + 56 q^{41} - 29 q^{42} - 30 q^{43} + 30 q^{44} + 38 q^{45} - 27 q^{46} + 40 q^{47} + 19 q^{48} + 36 q^{49} + 20 q^{50} - 18 q^{51} + 32 q^{52} + 51 q^{53} - 36 q^{54} - 5 q^{55} - 13 q^{56} + 31 q^{57} - 29 q^{58} + 29 q^{59} + 48 q^{60} + 16 q^{61} - 38 q^{62} - 23 q^{63} - 5 q^{64} + 27 q^{65} + 25 q^{66} - 2 q^{67} - 43 q^{68} + 38 q^{69} + 10 q^{70} + 34 q^{71} - 28 q^{72} + 14 q^{73} + 21 q^{74} + 19 q^{75} + 5 q^{76} + 34 q^{77} + 9 q^{78} + 3 q^{79} + 58 q^{80} + 4 q^{81} - 9 q^{82} + 38 q^{83} - 78 q^{84} - 27 q^{85} + 49 q^{86} + 8 q^{87} - 25 q^{88} + 125 q^{89} - 74 q^{90} + 6 q^{91} - 35 q^{92} + 36 q^{93} - q^{94} - 12 q^{95} + 26 q^{96} - 2 q^{97} + 18 q^{98} + 56 q^{99}+O(q^{100}) \) 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9 + 5 * q^10 + 9 * q^11 + 15 * q^12 + 28 * q^13 + 20 * q^14 + 4 * q^15 + 32 * q^16 - 7 * q^17 + 10 * q^18 - 3 * q^19 + 53 * q^20 + 25 * q^21 - 14 * q^22 - 6 * q^23 + 10 * q^24 + 45 * q^25 + 6 * q^26 + 8 * q^27 - 12 * q^28 + 25 * q^29 - 43 * q^30 + q^31 + 28 * q^32 + 17 * q^33 + 10 * q^34 + 11 * q^35 + 27 * q^36 + 18 * q^37 + 2 * q^38 + 5 * q^39 + 37 * q^40 + 56 * q^41 - 29 * q^42 - 30 * q^43 + 30 * q^44 + 38 * q^45 - 27 * q^46 + 40 * q^47 + 19 * q^48 + 36 * q^49 + 20 * q^50 - 18 * q^51 + 32 * q^52 + 51 * q^53 - 36 * q^54 - 5 * q^55 - 13 * q^56 + 31 * q^57 - 29 * q^58 + 29 * q^59 + 48 * q^60 + 16 * q^61 - 38 * q^62 - 23 * q^63 - 5 * q^64 + 27 * q^65 + 25 * q^66 - 2 * q^67 - 43 * q^68 + 38 * q^69 + 10 * q^70 + 34 * q^71 - 28 * q^72 + 14 * q^73 + 21 * q^74 + 19 * q^75 + 5 * q^76 + 34 * q^77 + 9 * q^78 + 3 * q^79 + 58 * q^80 + 4 * q^81 - 9 * q^82 + 38 * q^83 - 78 * q^84 - 27 * q^85 + 49 * q^86 + 8 * q^87 - 25 * q^88 + 125 * q^89 - 74 * q^90 + 6 * q^91 - 35 * q^92 + 36 * q^93 - q^94 - 12 * q^95 + 26 * q^96 - 2 * q^97 + 18 * q^98 + 56 * q^99

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