LMFDB - Embedded newform 1339.2.a.d.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:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 9 x^{18} + 13 x^{17} + 106 x^{16} - 351 x^{15} - 279 x^{14} + 2337 x^{13} - 1079 x^{12} + \cdots - 63 $ x^19 - 9x^18 + 13x^17 + 106x^16 - 351x^15 - 279x^14 + 2337x^13 - 1079x^12 - 6826x^11 + 7199x^10 + 9364x^9 - 14841x^8 - 5183x^7 + 14037x^6 - 108x^5 - 6099x^4 + 855x^3 + 1062x^2 - 135x - 63
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Root			$-2.23754$ of defining polynomial
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)

$f(q)$	$=$	$q+2.23754 q^{2} -0.546477 q^{3} +3.00660 q^{4} -3.24055 q^{5} -1.22277 q^{6} +2.54937 q^{7} +2.25232 q^{8} -2.70136 q^{9} +O(q^{10})$	\(q+2.23754 q^{2} -0.546477 q^{3} +3.00660 q^{4} -3.24055 q^{5} -1.22277 q^{6} +2.54937 q^{7} +2.25232 q^{8} -2.70136 q^{9} -7.25087 q^{10} -4.12786 q^{11} -1.64304 q^{12} +1.00000 q^{13} +5.70432 q^{14} +1.77088 q^{15} -0.973541 q^{16} -4.63320 q^{17} -6.04442 q^{18} -3.00525 q^{19} -9.74304 q^{20} -1.39317 q^{21} -9.23626 q^{22} -1.11654 q^{23} -1.23084 q^{24} +5.50115 q^{25} +2.23754 q^{26} +3.11566 q^{27} +7.66494 q^{28} -0.834727 q^{29} +3.96243 q^{30} +1.05163 q^{31} -6.68298 q^{32} +2.25578 q^{33} -10.3670 q^{34} -8.26135 q^{35} -8.12193 q^{36} +2.53014 q^{37} -6.72439 q^{38} -0.546477 q^{39} -7.29875 q^{40} +3.72211 q^{41} -3.11728 q^{42} +4.50475 q^{43} -12.4108 q^{44} +8.75389 q^{45} -2.49831 q^{46} -3.16943 q^{47} +0.532018 q^{48} -0.500727 q^{49} +12.3091 q^{50} +2.53194 q^{51} +3.00660 q^{52} +1.11262 q^{53} +6.97143 q^{54} +13.3765 q^{55} +5.74199 q^{56} +1.64230 q^{57} -1.86774 q^{58} -5.80916 q^{59} +5.32435 q^{60} -13.0617 q^{61} +2.35306 q^{62} -6.88677 q^{63} -13.0064 q^{64} -3.24055 q^{65} +5.04741 q^{66} -1.53624 q^{67} -13.9302 q^{68} +0.610164 q^{69} -18.4851 q^{70} +6.31031 q^{71} -6.08434 q^{72} -1.67375 q^{73} +5.66130 q^{74} -3.00625 q^{75} -9.03561 q^{76} -10.5234 q^{77} -1.22277 q^{78} +5.92761 q^{79} +3.15481 q^{80} +6.40145 q^{81} +8.32839 q^{82} -12.2489 q^{83} -4.18871 q^{84} +15.0141 q^{85} +10.0796 q^{86} +0.456159 q^{87} -9.29726 q^{88} -0.710762 q^{89} +19.5872 q^{90} +2.54937 q^{91} -3.35700 q^{92} -0.574690 q^{93} -7.09174 q^{94} +9.73867 q^{95} +3.65210 q^{96} -0.857607 q^{97} -1.12040 q^{98} +11.1508 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9}+O(q^{10}) $ 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9} - q^{11} + 18 q^{12} + 19 q^{13} - 8 q^{14} - 11 q^{15} + 21 q^{16} - 16 q^{17} - 10 q^{19} - 20 q^{20} - 33 q^{21} + 2 q^{22} - 14 q^{23} - 9 q^{24} + 23 q^{25} - 9 q^{26} + q^{27} + 10 q^{28} - 22 q^{29} + 28 q^{30} - 3 q^{31} - 47 q^{32} - 25 q^{33} - 35 q^{34} - 3 q^{35} - 33 q^{36} - 19 q^{37} - 15 q^{38} - 2 q^{39} + 8 q^{40} - 52 q^{41} - 3 q^{42} - 2 q^{43} - 54 q^{44} - 40 q^{45} + 33 q^{46} - 24 q^{47} - 8 q^{48} + 7 q^{49} - 10 q^{50} - 7 q^{51} + 17 q^{52} - 11 q^{53} - 23 q^{54} - 29 q^{55} - 17 q^{56} - 34 q^{57} + 18 q^{58} - 52 q^{59} - 71 q^{60} - 25 q^{61} - 22 q^{62} - 19 q^{63} + 48 q^{64} - 18 q^{65} + 9 q^{66} - 2 q^{67} + 18 q^{68} - 26 q^{69} - 12 q^{70} - 44 q^{71} - 6 q^{72} - 39 q^{73} - 4 q^{74} + 17 q^{75} - 10 q^{76} - 18 q^{77} - 8 q^{78} + q^{79} - 9 q^{80} - 13 q^{81} + 47 q^{82} - 27 q^{83} - 24 q^{84} - 26 q^{85} - q^{86} + 31 q^{87} + 19 q^{88} - 86 q^{89} + 48 q^{90} - 8 q^{91} - 19 q^{92} + 32 q^{93} + 45 q^{94} + 17 q^{95} - 25 q^{96} - 20 q^{97} + 39 q^{98} + 50 q^{99}+O(q^{100}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9 - q^11 + 18 * q^12 + 19 * q^13 - 8 * q^14 - 11 * q^15 + 21 * q^16 - 16 * q^17 - 10 * q^19 - 20 * q^20 - 33 * q^21 + 2 * q^22 - 14 * q^23 - 9 * q^24 + 23 * q^25 - 9 * q^26 + q^27 + 10 * q^28 - 22 * q^29 + 28 * q^30 - 3 * q^31 - 47 * q^32 - 25 * q^33 - 35 * q^34 - 3 * q^35 - 33 * q^36 - 19 * q^37 - 15 * q^38 - 2 * q^39 + 8 * q^40 - 52 * q^41 - 3 * q^42 - 2 * q^43 - 54 * q^44 - 40 * q^45 + 33 * q^46 - 24 * q^47 - 8 * q^48 + 7 * q^49 - 10 * q^50 - 7 * q^51 + 17 * q^52 - 11 * q^53 - 23 * q^54 - 29 * q^55 - 17 * q^56 - 34 * q^57 + 18 * q^58 - 52 * q^59 - 71 * q^60 - 25 * q^61 - 22 * q^62 - 19 * q^63 + 48 * q^64 - 18 * q^65 + 9 * q^66 - 2 * q^67 + 18 * q^68 - 26 * q^69 - 12 * q^70 - 44 * q^71 - 6 * q^72 - 39 * q^73 - 4 * q^74 + 17 * q^75 - 10 * q^76 - 18 * q^77 - 8 * q^78 + q^79 - 9 * q^80 - 13 * q^81 + 47 * q^82 - 27 * q^83 - 24 * q^84 - 26 * q^85 - q^86 + 31 * q^87 + 19 * q^88 - 86 * q^89 + 48 * q^90 - 8 * q^91 - 19 * q^92 + 32 * q^93 + 45 * q^94 + 17 * q^95 - 25 * q^96 - 20 * q^97 + 39 * q^98 + 50 * 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 $

$2$	2.23754	1.58218	0.791091	−	0.611698i	$-0.209513\pi$
$2$	2.23754	1.58218	0.791091	+	0.611698i	$0.209513\pi$
$3$	−0.546477	−0.315509	−0.157754	−	0.987478i	$-0.550425\pi$
$3$	−0.546477	−0.315509	−0.157754	+	0.987478i	$0.550425\pi$
$4$	3.00660	1.50330
$5$	−3.24055	−1.44922	−0.724608	−	0.689161i	$-0.757979\pi$
$5$	−3.24055	−1.44922	−0.724608	+	0.689161i	$0.757979\pi$
$6$	−1.22277	−0.499192
$7$	2.54937	0.963570	0.481785	−	0.876289i	$-0.339989\pi$
$7$	2.54937	0.963570	0.481785	+	0.876289i	$0.339989\pi$
$8$	2.25232	0.796316
$9$	−2.70136	−0.900454
$10$	−7.25087	−2.29293
$11$	−4.12786	−1.24460	−0.622298	−	0.782780i	$-0.713801\pi$
$11$	−4.12786	−1.24460	−0.622298	+	0.782780i	$0.713801\pi$
$12$	−1.64304	−0.474305
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	5.70432	1.52454
$15$	1.77088	0.457240
$16$	−0.973541	−0.243385
$17$	−4.63320	−1.12372	−0.561859	−	0.827233i	$-0.689913\pi$
$17$	−4.63320	−1.12372	−0.561859	+	0.827233i	$0.689913\pi$
$18$	−6.04442	−1.42468
$19$	−3.00525	−0.689452	−0.344726	−	0.938703i	$-0.612028\pi$
$19$	−3.00525	−0.689452	−0.344726	+	0.938703i	$0.612028\pi$
$20$	−9.74304	−2.17861
$21$	−1.39317	−0.304015
$22$	−9.23626	−1.96918
$23$	−1.11654	−0.232815	−0.116408	−	0.993202i	$-0.537138\pi$
$23$	−1.11654	−0.232815	−0.116408	+	0.993202i	$0.537138\pi$
$24$	−1.23084	−0.251244
$25$	5.50115	1.10023
$26$	2.23754	0.438819
$27$	3.11566	0.599610
$28$	7.66494	1.44854
$29$	−0.834727	−0.155005	−0.0775025	−	0.996992i	$-0.524695\pi$
$29$	−0.834727	−0.155005	−0.0775025	+	0.996992i	$0.524695\pi$
$30$	3.96243	0.723438
$31$	1.05163	0.188878	0.0944390	−	0.995531i	$-0.469894\pi$
$31$	1.05163	0.188878	0.0944390	+	0.995531i	$0.469894\pi$
$32$	−6.68298	−1.18140
$33$	2.25578	0.392681
$34$	−10.3670	−1.77793
$35$	−8.26135	−1.39642
$36$	−8.12193	−1.35365
$37$	2.53014	0.415952	0.207976	−	0.978134i	$-0.433312\pi$
$37$	2.53014	0.415952	0.207976	+	0.978134i	$0.433312\pi$
$38$	−6.72439	−1.09084
$39$	−0.546477	−0.0875063
$40$	−7.29875	−1.15403
$41$	3.72211	0.581296	0.290648	−	0.956830i	$-0.406129\pi$
$41$	3.72211	0.581296	0.290648	+	0.956830i	$0.406129\pi$
$42$	−3.11728	−0.481007
$43$	4.50475	0.686968	0.343484	−	0.939159i	$-0.388393\pi$
$43$	4.50475	0.686968	0.343484	+	0.939159i	$0.388393\pi$
$44$	−12.4108	−1.87100
$45$	8.75389	1.30495
$46$	−2.49831	−0.368356
$47$	−3.16943	−0.462309	−0.231154	−	0.972917i	$-0.574250\pi$
$47$	−3.16943	−0.462309	−0.231154	+	0.972917i	$0.574250\pi$
$48$	0.532018	0.0767901
$49$	−0.500727	−0.0715324
$50$	12.3091	1.74076
$51$	2.53194	0.354542
$52$	3.00660	0.416941
$53$	1.11262	0.152830	0.0764150	−	0.997076i	$-0.475653\pi$
$53$	1.11262	0.152830	0.0764150	+	0.997076i	$0.475653\pi$
$54$	6.97143	0.948692
$55$	13.3765	1.80369
$56$	5.74199	0.767306
$57$	1.64230	0.217528
$58$	−1.86774	−0.245246
$59$	−5.80916	−0.756289	−0.378144	−	0.925747i	$-0.623438\pi$
$59$	−5.80916	−0.756289	−0.378144	+	0.925747i	$0.623438\pi$
$60$	5.32435	0.687370
$61$	−13.0617	−1.67238	−0.836192	−	0.548437i	$-0.815223\pi$
$61$	−13.0617	−1.67238	−0.836192	+	0.548437i	$0.815223\pi$
$62$	2.35306	0.298839
$63$	−6.88677	−0.867651
$64$	−13.0064	−1.62580
$65$	−3.24055	−0.401940
$66$	5.04741	0.621293
$67$	−1.53624	−0.187681	−0.0938406	−	0.995587i	$-0.529914\pi$
$67$	−1.53624	−0.187681	−0.0938406	+	0.995587i	$0.529914\pi$
$68$	−13.9302	−1.68929
$69$	0.610164	0.0734551
$70$	−18.4851	−2.20939
$71$	6.31031	0.748896	0.374448	−	0.927248i	$-0.377832\pi$
$71$	6.31031	0.748896	0.374448	+	0.927248i	$0.377832\pi$
$72$	−6.08434	−0.717046
$73$	−1.67375	−0.195898	−0.0979490	−	0.995191i	$-0.531228\pi$
$73$	−1.67375	−0.195898	−0.0979490	+	0.995191i	$0.531228\pi$
$74$	5.66130	0.658113
$75$	−3.00625	−0.347132
$76$	−9.03561	−1.03646
$77$	−10.5234	−1.19926
$78$	−1.22277	−0.138451
$79$	5.92761	0.666908	0.333454	−	0.942766i	$-0.391786\pi$
$79$	5.92761	0.666908	0.333454	+	0.942766i	$0.391786\pi$
$80$	3.15481	0.352718
$81$	6.40145	0.711272
$82$	8.32839	0.919717
$83$	−12.2489	−1.34450	−0.672248	−	0.740326i	$-0.734671\pi$
$83$	−12.2489	−1.34450	−0.672248	+	0.740326i	$0.734671\pi$
$84$	−4.18871	−0.457026
$85$	15.0141	1.62851
$86$	10.0796	1.08691
$87$	0.456159	0.0489054
$88$	−9.29726	−0.991091
$89$	−0.710762	−0.0753406	−0.0376703	−	0.999290i	$-0.511994\pi$
$89$	−0.710762	−0.0753406	−0.0376703	+	0.999290i	$0.511994\pi$
$90$	19.5872	2.06467
$91$	2.54937	0.267246
$92$	−3.35700	−0.349991
$93$	−0.574690	−0.0595926
$94$	−7.09174	−0.731457
$95$	9.73867	0.999166
$96$	3.65210	0.372740
$97$	−0.857607	−0.0870768	−0.0435384	−	0.999052i	$-0.513863\pi$
$97$	−0.857607	−0.0870768	−0.0435384	+	0.999052i	$0.513863\pi$
$98$	−1.12040	−0.113177
$99$	11.1508	1.12070
$100$	16.5398	1.65398
$101$	18.2651	1.81744	0.908721	−	0.417404i	$-0.137060\pi$
$101$	18.2651	1.81744	0.908721	+	0.417404i	$0.137060\pi$
$102$	5.66533	0.560951
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	2.25232	0.220858
$105$	4.51463	0.440583
$106$	2.48954	0.241805
$107$	−2.51396	−0.243034	−0.121517	−	0.992589i	$-0.538776\pi$
$107$	−2.51396	−0.243034	−0.121517	+	0.992589i	$0.538776\pi$
$108$	9.36756	0.901394
$109$	2.71136	0.259701	0.129851	−	0.991534i	$-0.458550\pi$
$109$	2.71136	0.259701	0.129851	+	0.991534i	$0.458550\pi$
$110$	29.9306	2.85377
$111$	−1.38266	−0.131237
$112$	−2.48191	−0.234519
$113$	−6.09511	−0.573380	−0.286690	−	0.958023i	$-0.592555\pi$
$113$	−6.09511	−0.573380	−0.286690	+	0.958023i	$0.592555\pi$
$114$	3.67472	0.344169
$115$	3.61821	0.337399
$116$	−2.50969	−0.233019
$117$	−2.70136	−0.249741
$118$	−12.9983	−1.19659
$119$	−11.8117	−1.08278
$120$	3.98860	0.364108
$121$	6.03921	0.549019
$122$	−29.2262	−2.64602
$123$	−2.03405	−0.183404
$124$	3.16183	0.283941
$125$	−1.62399	−0.145254
$126$	−15.4094	−1.37278
$127$	5.52379	0.490157	0.245079	−	0.969503i	$-0.421186\pi$
$127$	5.52379	0.490157	0.245079	+	0.969503i	$0.421186\pi$
$128$	−15.7364	−1.39091
$129$	−2.46174	−0.216744
$130$	−7.25087	−0.635943
$131$	−15.3095	−1.33759	−0.668797	−	0.743445i	$-0.733191\pi$
$131$	−15.3095	−1.33759	−0.668797	+	0.743445i	$0.733191\pi$
$132$	6.78223	0.590318
$133$	−7.66149	−0.664336
$134$	−3.43740	−0.296946
$135$	−10.0965	−0.868964
$136$	−10.4355	−0.894833
$137$	20.0155	1.71004	0.855021	−	0.518594i	$-0.173544\pi$
$137$	20.0155	1.71004	0.855021	+	0.518594i	$0.173544\pi$
$138$	1.36527	0.116219
$139$	−8.39612	−0.712150	−0.356075	−	0.934457i	$-0.615885\pi$
$139$	−8.39612	−0.712150	−0.356075	+	0.934457i	$0.615885\pi$
$140$	−24.8386	−2.09924
$141$	1.73202	0.145862
$142$	14.1196	1.18489
$143$	−4.12786	−0.345189
$144$	2.62989	0.219157
$145$	2.70497	0.224636
$146$	−3.74510	−0.309946
$147$	0.273636	0.0225691
$148$	7.60713	0.625302
$149$	3.50284	0.286964	0.143482	−	0.989653i	$-0.454170\pi$
$149$	3.50284	0.286964	0.143482	+	0.989653i	$0.454170\pi$
$150$	−6.72662	−0.549226
$151$	6.96299	0.566640	0.283320	−	0.959025i	$-0.408564\pi$
$151$	6.96299	0.566640	0.283320	+	0.959025i	$0.408564\pi$
$152$	−6.76879	−0.549022
$153$	12.5160	1.01186
$154$	−23.5466	−1.89744
$155$	−3.40785	−0.273725
$156$	−1.64304	−0.131548
$157$	17.2912	1.37999	0.689994	−	0.723815i	$-0.257613\pi$
$157$	17.2912	1.37999	0.689994	+	0.723815i	$0.257613\pi$
$158$	13.2633	1.05517
$159$	−0.608021	−0.0482192
$160$	21.6565	1.71210
$161$	−2.84647	−0.224334
$162$	14.3235	1.12536
$163$	−10.8441	−0.849377	−0.424688	−	0.905340i	$-0.639616\pi$
$163$	−10.8441	−0.849377	−0.424688	+	0.905340i	$0.639616\pi$
$164$	11.1909	0.873864
$165$	−7.30996	−0.569080
$166$	−27.4075	−2.12724
$167$	−17.5697	−1.35959	−0.679793	−	0.733404i	$-0.737930\pi$
$167$	−17.5697	−1.35959	−0.679793	+	0.733404i	$0.737930\pi$
$168$	−3.13787	−0.242092
$169$	1.00000	0.0769231
$170$	33.5948	2.57660
$171$	8.11828	0.620820
$172$	13.5440	1.03272
$173$	−4.73213	−0.359777	−0.179889	−	0.983687i	$-0.557574\pi$
$173$	−4.73213	−0.359777	−0.179889	+	0.983687i	$0.557574\pi$
$174$	1.02068	0.0773773
$175$	14.0244	1.06015
$176$	4.01864	0.302916
$177$	3.17457	0.238616
$178$	−1.59036	−0.119203
$179$	−15.5848	−1.16486	−0.582430	−	0.812881i	$-0.697898\pi$
$179$	−15.5848	−1.16486	−0.582430	+	0.812881i	$0.697898\pi$
$180$	26.3195	1.96174
$181$	15.5619	1.15671	0.578354	−	0.815786i	$-0.303695\pi$
$181$	15.5619	1.15671	0.578354	+	0.815786i	$0.303695\pi$
$182$	5.70432	0.422832
$183$	7.13794	0.527652
$184$	−2.51481	−0.185394
$185$	−8.19904	−0.602805
$186$	−1.28589	−0.0942864
$187$	19.1252	1.39857
$188$	−9.52922	−0.694990
$189$	7.94297	0.577766
$190$	21.7907	1.58086
$191$	9.47642	0.685690	0.342845	−	0.939392i	$-0.388609\pi$
$191$	9.47642	0.685690	0.342845	+	0.939392i	$0.388609\pi$
$192$	7.10769	0.512953
$193$	14.6808	1.05675	0.528375	−	0.849011i	$-0.322801\pi$
$193$	14.6808	1.05675	0.528375	+	0.849011i	$0.322801\pi$
$194$	−1.91893	−0.137771
$195$	1.77088	0.126816
$196$	−1.50549	−0.107535
$197$	−8.64907	−0.616221	−0.308110	−	0.951351i	$-0.599697\pi$
$197$	−8.64907	−0.616221	−0.308110	+	0.951351i	$0.599697\pi$
$198$	24.9505	1.77316
$199$	21.9112	1.55324	0.776621	−	0.629968i	$-0.216932\pi$
$199$	21.9112	1.55324	0.776621	+	0.629968i	$0.216932\pi$
$200$	12.3903	0.876130
$201$	0.839518	0.0592150
$202$	40.8689	2.87553
$203$	−2.12803	−0.149358
$204$	7.61254	0.532984
$205$	−12.0617	−0.842424
$206$	2.23754	0.155897
$207$	3.01618	0.209639
$208$	−0.973541	−0.0675029
$209$	12.4053	0.858090
$210$	10.1017	0.697083
$211$	−12.7771	−0.879609	−0.439805	−	0.898093i	$-0.644952\pi$
$211$	−12.7771	−0.879609	−0.439805	+	0.898093i	$0.644952\pi$
$212$	3.34521	0.229750
$213$	−3.44844	−0.236283
$214$	−5.62510	−0.384524
$215$	−14.5979	−0.995565
$216$	7.01747	0.477478
$217$	2.68099	0.181997
$218$	6.06679	0.410895
$219$	0.914667	0.0618075
$220$	40.2179	2.71149
$221$	−4.63320	−0.311663
$222$	−3.09377	−0.207640
$223$	−26.2550	−1.75817	−0.879083	−	0.476670i	$-0.841844\pi$
$223$	−26.2550	−1.75817	−0.879083	+	0.476670i	$0.841844\pi$
$224$	−17.0374	−1.13836
$225$	−14.8606	−0.990706
$226$	−13.6381	−0.907191
$227$	14.6082	0.969579	0.484789	−	0.874631i	$-0.338896\pi$
$227$	14.6082	0.969579	0.484789	+	0.874631i	$0.338896\pi$
$228$	4.93775	0.327011
$229$	−6.47316	−0.427759	−0.213879	−	0.976860i	$-0.568610\pi$
$229$	−6.47316	−0.427759	−0.213879	+	0.976860i	$0.568610\pi$
$230$	8.09590	0.533828
$231$	5.75081	0.378375
$232$	−1.88007	−0.123433
$233$	−24.4131	−1.59936	−0.799679	−	0.600428i	$-0.794997\pi$
$233$	−24.4131	−1.59936	−0.799679	+	0.600428i	$0.794997\pi$
$234$	−6.04442	−0.395136
$235$	10.2707	0.669986
$236$	−17.4659	−1.13693
$237$	−3.23930	−0.210415
$238$	−26.4293	−1.71316
$239$	23.3812	1.51240	0.756202	−	0.654339i	$-0.227053\pi$
$239$	23.3812	1.51240	0.756202	+	0.654339i	$0.227053\pi$
$240$	−1.72403	−0.111286
$241$	−7.00465	−0.451209	−0.225605	−	0.974219i	$-0.572436\pi$
$241$	−7.00465	−0.451209	−0.225605	+	0.974219i	$0.572436\pi$
$242$	13.5130	0.868649
$243$	−12.8452	−0.824022
$244$	−39.2715	−2.51410
$245$	1.62263	0.103666
$246$	−4.55127	−0.290179
$247$	−3.00525	−0.191220
$248$	2.36860	0.150406
$249$	6.69376	0.424200
$250$	−3.63375	−0.229819
$251$	−27.6055	−1.74244	−0.871222	−	0.490888i	$-0.836672\pi$
$251$	−27.6055	−1.74244	−0.871222	+	0.490888i	$0.836672\pi$
$252$	−20.7058	−1.30434
$253$	4.60892	0.289761
$254$	12.3597	0.775518
$255$	−8.20487	−0.513809
$256$	−9.19811	−0.574882
$257$	−17.7871	−1.10953	−0.554764	−	0.832008i	$-0.687192\pi$
$257$	−17.7871	−1.10953	−0.554764	+	0.832008i	$0.687192\pi$
$258$	−5.50825	−0.342929
$259$	6.45025	0.400799
$260$	−9.74304	−0.604238
$261$	2.25490	0.139575
$262$	−34.2556	−2.11632
$263$	5.94333	0.366482	0.183241	−	0.983068i	$-0.441341\pi$
$263$	5.94333	0.366482	0.183241	+	0.983068i	$0.441341\pi$
$264$	5.08074	0.312698
$265$	−3.60550	−0.221484
$266$	−17.1429	−1.05110
$267$	0.388415	0.0237706
$268$	−4.61886	−0.282142
$269$	−1.34332	−0.0819035	−0.0409517	−	0.999161i	$-0.513039\pi$
$269$	−1.34332	−0.0819035	−0.0409517	+	0.999161i	$0.513039\pi$
$270$	−22.5913	−1.37486
$271$	2.25024	0.136692	0.0683462	−	0.997662i	$-0.478228\pi$
$271$	2.25024	0.136692	0.0683462	+	0.997662i	$0.478228\pi$
$272$	4.51061	0.273496
$273$	−1.39317	−0.0843185
$274$	44.7856	2.70560
$275$	−22.7080	−1.36934
$276$	1.83452	0.110425
$277$	3.18935	0.191629	0.0958147	−	0.995399i	$-0.469454\pi$
$277$	3.18935	0.191629	0.0958147	+	0.995399i	$0.469454\pi$
$278$	−18.7867	−1.12675
$279$	−2.84083	−0.170076
$280$	−18.6072	−1.11199
$281$	−23.0705	−1.37627	−0.688135	−	0.725583i	$-0.741570\pi$
$281$	−23.0705	−1.37627	−0.688135	+	0.725583i	$0.741570\pi$
$282$	3.87547	0.230781
$283$	3.28336	0.195176	0.0975878	−	0.995227i	$-0.468887\pi$
$283$	3.28336	0.195176	0.0975878	+	0.995227i	$0.468887\pi$
$284$	18.9726	1.12582
$285$	−5.32196	−0.315245
$286$	−9.23626	−0.546152
$287$	9.48903	0.560120
$288$	18.0532	1.06379
$289$	4.46659	0.262740
$290$	6.05250	0.355415
$291$	0.468663	0.0274735
$292$	−5.03231	−0.294494
$293$	−29.0625	−1.69785	−0.848925	−	0.528513i	$-0.822750\pi$
$293$	−29.0625	−1.69785	−0.848925	+	0.528513i	$0.822750\pi$
$294$	0.612272	0.0357084
$295$	18.8249	1.09603
$296$	5.69869	0.331229
$297$	−12.8610	−0.746272
$298$	7.83776	0.454029
$299$	−1.11654	−0.0645713
$300$	−9.03860	−0.521844
$301$	11.4843	0.661942
$302$	15.5800	0.896528
$303$	−9.98144	−0.573419
$304$	2.92574	0.167803
$305$	42.3272	2.42365
$306$	28.0050	1.60094
$307$	−33.4331	−1.90813	−0.954064	−	0.299603i	$-0.903146\pi$
$307$	−33.4331	−1.90813	−0.954064	+	0.299603i	$0.903146\pi$
$308$	−31.6398	−1.80284
$309$	−0.546477	−0.0310880
$310$	−7.62521	−0.433083
$311$	−3.76485	−0.213485	−0.106742	−	0.994287i	$-0.534042\pi$
$311$	−3.76485	−0.213485	−0.106742	+	0.994287i	$0.534042\pi$
$312$	−1.23084	−0.0696827
$313$	−3.85757	−0.218043	−0.109021	−	0.994039i	$-0.534772\pi$
$313$	−3.85757	−0.218043	−0.109021	+	0.994039i	$0.534772\pi$
$314$	38.6898	2.18339
$315$	22.3169	1.25741
$316$	17.8220	1.00256
$317$	−19.4789	−1.09404	−0.547021	−	0.837119i	$-0.684238\pi$
$317$	−19.4789	−1.09404	−0.547021	+	0.837119i	$0.684238\pi$
$318$	−1.36047	−0.0762916
$319$	3.44564	0.192919
$320$	42.1478	2.35613
$321$	1.37382	0.0766793
$322$	−6.36911	−0.354937
$323$	13.9240	0.774750
$324$	19.2466	1.06926
$325$	5.50115	0.305149
$326$	−24.2642	−1.34387
$327$	−1.48170	−0.0819379
$328$	8.38339	0.462895
$329$	−8.08004	−0.445467
$330$	−16.3564	−0.900388
$331$	8.52061	0.468335	0.234167	−	0.972196i	$-0.424764\pi$
$331$	8.52061	0.468335	0.234167	+	0.972196i	$0.424764\pi$
$332$	−36.8277	−2.02118
$333$	−6.83483	−0.374546
$334$	−39.3130	−2.15111
$335$	4.97825	0.271991
$336$	1.35631	0.0739927
$337$	13.2107	0.719633	0.359817	−	0.933023i	$-0.382839\pi$
$337$	13.2107	0.719633	0.359817	+	0.933023i	$0.382839\pi$
$338$	2.23754	0.121706
$339$	3.33084	0.180906
$340$	45.1415	2.44814
$341$	−4.34097	−0.235077
$342$	18.1650	0.982251
$343$	−19.1221	−1.03250
$344$	10.1461	0.547043
$345$	−1.97727	−0.106452
$346$	−10.5884	−0.569233
$347$	23.8472	1.28018	0.640092	−	0.768298i	$-0.278896\pi$
$347$	23.8472	1.28018	0.640092	+	0.768298i	$0.278896\pi$
$348$	1.37149	0.0735196
$349$	−26.5969	−1.42370	−0.711850	−	0.702332i	$-0.752142\pi$
$349$	−26.5969	−1.42370	−0.711850	+	0.702332i	$0.752142\pi$
$350$	31.3803	1.67735
$351$	3.11566	0.166302
$352$	27.5864	1.47036
$353$	−22.9176	−1.21978	−0.609889	−	0.792487i	$-0.708786\pi$
$353$	−22.9176	−1.21978	−0.609889	+	0.792487i	$0.708786\pi$
$354$	7.10325	0.377533
$355$	−20.4489	−1.08531
$356$	−2.13698	−0.113260
$357$	6.45484	0.341627
$358$	−34.8716	−1.84302
$359$	−7.71565	−0.407216	−0.203608	−	0.979052i	$-0.565267\pi$
$359$	−7.71565	−0.407216	−0.203608	+	0.979052i	$0.565267\pi$
$360$	19.7166	1.03915
$361$	−9.96845	−0.524655
$362$	34.8204	1.83012
$363$	−3.30029	−0.173220
$364$	7.66494	0.401752
$365$	5.42388	0.283899
$366$	15.9715	0.834841
$367$	5.41771	0.282802	0.141401	−	0.989952i	$-0.454839\pi$
$367$	5.41771	0.282802	0.141401	+	0.989952i	$0.454839\pi$
$368$	1.08700	0.0566637
$369$	−10.0548	−0.523431
$370$	−18.3457	−0.953748
$371$	2.83648	0.147263
$372$	−1.72787	−0.0895857
$373$	11.5700	0.599073	0.299537	−	0.954085i	$-0.403168\pi$
$373$	11.5700	0.599073	0.299537	+	0.954085i	$0.403168\pi$
$374$	42.7935	2.21280
$375$	0.887474	0.0458290
$376$	−7.13857	−0.368144
$377$	−0.834727	−0.0429906
$378$	17.7727	0.914131
$379$	22.7057	1.16632	0.583158	−	0.812359i	$-0.301817\pi$
$379$	22.7057	1.16632	0.583158	+	0.812359i	$0.301817\pi$
$380$	29.2803	1.50205
$381$	−3.01862	−0.154649
$382$	21.2039	1.08489
$383$	−19.5890	−1.00095	−0.500476	−	0.865751i	$-0.666841\pi$
$383$	−19.5890	−1.00095	−0.500476	+	0.865751i	$0.666841\pi$
$384$	8.59958	0.438845
$385$	34.1017	1.73798
$386$	32.8490	1.67197
$387$	−12.1690	−0.618583
$388$	−2.57849	−0.130903
$389$	−29.5104	−1.49624	−0.748118	−	0.663566i	$-0.769042\pi$
$389$	−29.5104	−1.49624	−0.748118	+	0.663566i	$0.769042\pi$
$390$	3.96243	0.200646
$391$	5.17317	0.261618
$392$	−1.12780	−0.0569624
$393$	8.36627	0.422023
$394$	−19.3527	−0.974974
$395$	−19.2087	−0.966494
$396$	33.5262	1.68475
$397$	−35.0462	−1.75892	−0.879459	−	0.475976i	$-0.842095\pi$
$397$	−35.0462	−1.75892	−0.879459	+	0.475976i	$0.842095\pi$
$398$	49.0272	2.45751
$399$	4.18683	0.209604
$400$	−5.35559	−0.267780
$401$	7.02317	0.350721	0.175360	−	0.984504i	$-0.443891\pi$
$401$	7.02317	0.350721	0.175360	+	0.984504i	$0.443891\pi$
$402$	1.87846	0.0936890
$403$	1.05163	0.0523853
$404$	54.9158	2.73216
$405$	−20.7442	−1.03079
$406$	−4.76155	−0.236312
$407$	−10.4441	−0.517693
$408$	5.70274	0.282328
$409$	−9.07731	−0.448844	−0.224422	−	0.974492i	$-0.572049\pi$
$409$	−9.07731	−0.448844	−0.224422	+	0.974492i	$0.572049\pi$
$410$	−26.9885	−1.33287
$411$	−10.9380	−0.539533
$412$	3.00660	0.148125
$413$	−14.8097	−0.728737
$414$	6.74884	0.331688
$415$	39.6933	1.94847
$416$	−6.68298	−0.327660
$417$	4.58829	0.224689
$418$	27.7573	1.35765
$419$	20.6093	1.00683	0.503415	−	0.864045i	$-0.332077\pi$
$419$	20.6093	1.00683	0.503415	+	0.864045i	$0.332077\pi$
$420$	13.5737	0.662330
$421$	19.3101	0.941115	0.470557	−	0.882369i	$-0.344053\pi$
$421$	19.3101	0.941115	0.470557	+	0.882369i	$0.344053\pi$
$422$	−28.5892	−1.39170
$423$	8.56178	0.416288
$424$	2.50598	0.121701
$425$	−25.4879	−1.23635
$426$	−7.71603	−0.373843
$427$	−33.2992	−1.61146
$428$	−7.55849	−0.365353
$429$	2.25578	0.108910
$430$	−32.6633	−1.57517
$431$	19.8006	0.953762	0.476881	−	0.878968i	$-0.341767\pi$
$431$	19.8006	0.953762	0.476881	+	0.878968i	$0.341767\pi$
$432$	−3.03323	−0.145936
$433$	−28.0265	−1.34687	−0.673433	−	0.739248i	$-0.735181\pi$
$433$	−28.0265	−1.34687	−0.673433	+	0.739248i	$0.735181\pi$
$434$	5.99882	0.287953
$435$	−1.47821	−0.0708745
$436$	8.15198	0.390409
$437$	3.35549	0.160515
$438$	2.04661	0.0977907
$439$	23.9923	1.14509	0.572545	−	0.819873i	$-0.305956\pi$
$439$	23.9923	1.14509	0.572545	+	0.819873i	$0.305956\pi$
$440$	30.1282	1.43631
$441$	1.35265	0.0644117
$442$	−10.3670	−0.493108
$443$	−20.7088	−0.983904	−0.491952	−	0.870622i	$-0.663716\pi$
$443$	−20.7088	−0.983904	−0.491952	+	0.870622i	$0.663716\pi$
$444$	−4.15712	−0.197288
$445$	2.30326	0.109185
$446$	−58.7467	−2.78174
$447$	−1.91422	−0.0905396
$448$	−33.1581	−1.56657
$449$	−25.8075	−1.21793	−0.608965	−	0.793197i	$-0.708415\pi$
$449$	−25.8075	−1.21793	−0.608965	+	0.793197i	$0.708415\pi$
$450$	−33.2512	−1.56748
$451$	−15.3643	−0.723479
$452$	−18.3256	−0.861963
$453$	−3.80511	−0.178780
$454$	32.6864	1.53405
$455$	−8.26135	−0.387298
$456$	3.69899	0.173221
$457$	18.5068	0.865712	0.432856	−	0.901463i	$-0.357506\pi$
$457$	18.5068	0.865712	0.432856	+	0.901463i	$0.357506\pi$
$458$	−14.4840	−0.676792
$459$	−14.4355	−0.673792
$460$	10.8785	0.507213
$461$	0.169085	0.00787509	0.00393755	−	0.999992i	$-0.498747\pi$
$461$	0.169085	0.00787509	0.00393755	+	0.999992i	$0.498747\pi$
$462$	12.8677	0.598659
$463$	12.9622	0.602405	0.301202	−	0.953560i	$-0.402612\pi$
$463$	12.9622	0.602405	0.301202	+	0.953560i	$0.402612\pi$
$464$	0.812641	0.0377259
$465$	1.86231	0.0863626
$466$	−54.6255	−2.53048
$467$	33.4259	1.54677	0.773383	−	0.633939i	$-0.218563\pi$
$467$	33.4259	1.54677	0.773383	+	0.633939i	$0.218563\pi$
$468$	−8.12193	−0.375436
$469$	−3.91643	−0.180844
$470$	22.9811	1.06004
$471$	−9.44924	−0.435398
$472$	−13.0841	−0.602245
$473$	−18.5950	−0.854997
$474$	−7.24808	−0.332915
$475$	−16.5323	−0.758556
$476$	−35.5132	−1.62775
$477$	−3.00559	−0.137617
$478$	52.3164	2.39290
$479$	−7.55296	−0.345104	−0.172552	−	0.985000i	$-0.555201\pi$
$479$	−7.55296	−0.345104	−0.172552	+	0.985000i	$0.555201\pi$
$480$	−11.8348	−0.540182
$481$	2.53014	0.115364
$482$	−15.6732	−0.713895
$483$	1.55553	0.0707792
$484$	18.1575	0.825342
$485$	2.77912	0.126193
$486$	−28.7418	−1.30375
$487$	−16.8578	−0.763900	−0.381950	−	0.924183i	$-0.624747\pi$
$487$	−16.8578	−0.763900	−0.381950	+	0.924183i	$0.624747\pi$
$488$	−29.4192	−1.33175
$489$	5.92606	0.267986
$490$	3.63071	0.164019
$491$	13.1228	0.592223	0.296111	−	0.955153i	$-0.404310\pi$
$491$	13.1228	0.592223	0.296111	+	0.955153i	$0.404310\pi$
$492$	−6.11558	−0.275711
$493$	3.86746	0.174182
$494$	−6.72439	−0.302545
$495$	−36.1348	−1.62414
$496$	−1.02380	−0.0459701
$497$	16.0873	0.721614
$498$	14.9776	0.671162
$499$	3.95129	0.176884	0.0884421	−	0.996081i	$-0.471811\pi$
$499$	3.95129	0.176884	0.0884421	+	0.996081i	$0.471811\pi$
$500$	−4.88270	−0.218361
$501$	9.60145	0.428961
$502$	−61.7686	−2.75687
$503$	40.5058	1.80606	0.903031	−	0.429574i	$-0.141336\pi$
$503$	40.5058	1.80606	0.903031	+	0.429574i	$0.141336\pi$
$504$	−15.5112	−0.690924
$505$	−59.1888	−2.63387
$506$	10.3127	0.458454
$507$	−0.546477	−0.0242699
$508$	16.6079	0.736854
$509$	24.0542	1.06619	0.533093	−	0.846057i	$-0.321030\pi$
$509$	24.0542	1.06619	0.533093	+	0.846057i	$0.321030\pi$
$510$	−18.3588	−0.812939
$511$	−4.26701	−0.188761
$512$	10.8916	0.481346
$513$	−9.36336	−0.413402
$514$	−39.7994	−1.75548
$515$	−3.24055	−0.142796
$516$	−7.40148	−0.325832
$517$	13.0830	0.575388
$518$	14.4327	0.634138
$519$	2.58600	0.113513
$520$	−7.29875	−0.320071
$521$	13.3771	0.586060	0.293030	−	0.956103i	$-0.405336\pi$
$521$	13.3771	0.586060	0.293030	+	0.956103i	$0.405336\pi$
$522$	5.04544	0.220833
$523$	−34.5456	−1.51057	−0.755287	−	0.655394i	$-0.772503\pi$
$523$	−34.5456	−1.51057	−0.755287	+	0.655394i	$0.772503\pi$
$524$	−46.0295	−2.01081
$525$	−7.66403	−0.334486
$526$	13.2985	0.579841
$527$	−4.87241	−0.212245
$528$	−2.19609	−0.0955727
$529$	−21.7533	−0.945797
$530$	−8.06746	−0.350428
$531$	15.6927	0.681004
$532$	−23.0351	−0.998697
$533$	3.72211	0.161223
$534$	0.869096	0.0376095
$535$	8.14661	0.352209
$536$	−3.46010	−0.149453
$537$	8.51671	0.367523
$538$	−3.00573	−0.129586
$539$	2.06693	0.0890290
$540$	−30.3560	−1.30632
$541$	−12.6842	−0.545337	−0.272668	−	0.962108i	$-0.587906\pi$
$541$	−12.6842	−0.545337	−0.272668	+	0.962108i	$0.587906\pi$
$542$	5.03501	0.216272
$543$	−8.50422	−0.364951
$544$	30.9636	1.32755
$545$	−8.78629	−0.376363
$546$	−3.11728	−0.133407
$547$	−1.32087	−0.0564761	−0.0282381	−	0.999601i	$-0.508990\pi$
$547$	−1.32087	−0.0564761	−0.0282381	+	0.999601i	$0.508990\pi$
$548$	60.1788	2.57071
$549$	35.2845	1.50591
$550$	−50.8101	−2.16655
$551$	2.50857	0.106869
$552$	1.37429	0.0584935
$553$	15.1116	0.642612
$554$	7.13631	0.303193
$555$	4.48058	0.190190
$556$	−25.2438	−1.07058
$557$	14.2010	0.601715	0.300858	−	0.953669i	$-0.402727\pi$
$557$	14.2010	0.601715	0.300858	+	0.953669i	$0.402727\pi$
$558$	−6.35648	−0.269091
$559$	4.50475	0.190531
$560$	8.04276	0.339869
$561$	−10.4515	−0.441262
$562$	−51.6212	−2.17751
$563$	−17.8305	−0.751467	−0.375734	−	0.926728i	$-0.622609\pi$
$563$	−17.8305	−0.751467	−0.375734	+	0.926728i	$0.622609\pi$
$564$	5.20750	0.219275
$565$	19.7515	0.830951
$566$	7.34666	0.308803
$567$	16.3196	0.685361
$568$	14.2128	0.596357
$569$	19.8814	0.833473	0.416736	−	0.909027i	$-0.363174\pi$
$569$	19.8814	0.833473	0.416736	+	0.909027i	$0.363174\pi$
$570$	−11.9081	−0.498776
$571$	−24.0619	−1.00696	−0.503480	−	0.864007i	$-0.667947\pi$
$571$	−24.0619	−1.00696	−0.503480	+	0.864007i	$0.667947\pi$
$572$	−12.4108	−0.518923
$573$	−5.17865	−0.216341
$574$	21.2321	0.886212
$575$	−6.14226	−0.256150
$576$	35.1350	1.46396
$577$	−35.1234	−1.46221	−0.731104	−	0.682266i	$-0.760995\pi$
$577$	−35.1234	−1.46221	−0.731104	+	0.682266i	$0.760995\pi$
$578$	9.99418	0.415703
$579$	−8.02274	−0.333414
$580$	8.13278	0.337695
$581$	−31.2270	−1.29552
$582$	1.04865	0.0434681
$583$	−4.59274	−0.190212
$584$	−3.76983	−0.155997
$585$	8.75389	0.361929
$586$	−65.0286	−2.68631
$587$	27.1528	1.12072	0.560359	−	0.828250i	$-0.310663\pi$
$587$	27.1528	1.12072	0.560359	+	0.828250i	$0.310663\pi$
$588$	0.822714	0.0339282
$589$	−3.16041	−0.130222
$590$	42.1215	1.73411
$591$	4.72652	0.194423
$592$	−2.46319	−0.101237
$593$	2.56454	0.105313	0.0526566	−	0.998613i	$-0.483231\pi$
$593$	2.56454	0.105313	0.0526566	+	0.998613i	$0.483231\pi$
$594$	−28.7771	−1.18074
$595$	38.2765	1.56918
$596$	10.5317	0.431394
$597$	−11.9740	−0.490061
$598$	−2.49831	−0.102164
$599$	44.9391	1.83616	0.918080	−	0.396395i	$-0.129739\pi$
$599$	44.9391	1.83616	0.918080	+	0.396395i	$0.129739\pi$
$600$	−6.77104	−0.276426
$601$	38.1965	1.55807	0.779035	−	0.626981i	$-0.215710\pi$
$601$	38.1965	1.55807	0.779035	+	0.626981i	$0.215710\pi$
$602$	25.6965	1.04731
$603$	4.14993	0.168998
$604$	20.9350	0.851831
$605$	−19.5703	−0.795648
$606$	−22.3339	−0.907253
$607$	34.9985	1.42055	0.710273	−	0.703926i	$-0.248571\pi$
$607$	34.9985	1.42055	0.710273	+	0.703926i	$0.248571\pi$
$608$	20.0841	0.814516
$609$	1.16292	0.0471238
$610$	94.7089	3.83465
$611$	−3.16943	−0.128221
$612$	37.6306	1.52113
$613$	−29.4383	−1.18900	−0.594501	−	0.804095i	$-0.702651\pi$
$613$	−29.4383	−1.18900	−0.594501	+	0.804095i	$0.702651\pi$
$614$	−74.8080	−3.01901
$615$	6.59143	0.265792
$616$	−23.7021	−0.954986
$617$	18.8551	0.759079	0.379540	−	0.925175i	$-0.376082\pi$
$617$	18.8551	0.759079	0.379540	+	0.925175i	$0.376082\pi$
$618$	−1.22277	−0.0491869
$619$	−43.7928	−1.76018	−0.880091	−	0.474804i	$-0.842519\pi$
$619$	−43.7928	−1.76018	−0.880091	+	0.474804i	$0.842519\pi$
$620$	−10.2461	−0.411491
$621$	−3.47877	−0.139598
$622$	−8.42401	−0.337772
$623$	−1.81199	−0.0725960
$624$	0.532018	0.0212978
$625$	−22.2431	−0.889725
$626$	−8.63148	−0.344983
$627$	−6.77919	−0.270735
$628$	51.9878	2.07454
$629$	−11.7227	−0.467413
$630$	49.9350	1.98946
$631$	0.906445	0.0360850	0.0180425	−	0.999837i	$-0.494257\pi$
$631$	0.906445	0.0360850	0.0180425	+	0.999837i	$0.494257\pi$
$632$	13.3509	0.531069
$633$	6.98237	0.277524
$634$	−43.5848	−1.73097
$635$	−17.9001	−0.710344
$636$	−1.82808	−0.0724880
$637$	−0.500727	−0.0198395
$638$	7.70976	0.305232
$639$	−17.0464	−0.674347
$640$	50.9945	2.01574
$641$	14.7697	0.583369	0.291684	−	0.956515i	$-0.405784\pi$
$641$	14.7697	0.583369	0.291684	+	0.956515i	$0.405784\pi$
$642$	3.07399	0.121321
$643$	−1.45813	−0.0575030	−0.0287515	−	0.999587i	$-0.509153\pi$
$643$	−1.45813	−0.0575030	−0.0287515	+	0.999587i	$0.509153\pi$
$644$	−8.55822	−0.337241
$645$	7.97739	0.314109
$646$	31.1555	1.22580
$647$	−6.89101	−0.270914	−0.135457	−	0.990783i	$-0.543250\pi$
$647$	−6.89101	−0.270914	−0.135457	+	0.990783i	$0.543250\pi$
$648$	14.4181	0.566397
$649$	23.9794	0.941274
$650$	12.3091	0.482801
$651$	−1.46510	−0.0574217
$652$	−32.6040	−1.27687
$653$	−6.97456	−0.272935	−0.136468	−	0.990645i	$-0.543575\pi$
$653$	−6.97456	−0.272935	−0.136468	+	0.990645i	$0.543575\pi$
$654$	−3.31536	−0.129641
$655$	49.6111	1.93846
$656$	−3.62363	−0.141479
$657$	4.52141	0.176397
$658$	−18.0794	−0.704810
$659$	22.1564	0.863091	0.431545	−	0.902091i	$-0.357968\pi$
$659$	22.1564	0.863091	0.431545	+	0.902091i	$0.357968\pi$
$660$	−21.9781	−0.855498
$661$	4.97068	0.193337	0.0966686	−	0.995317i	$-0.469181\pi$
$661$	4.97068	0.193337	0.0966686	+	0.995317i	$0.469181\pi$
$662$	19.0652	0.740991
$663$	2.53194	0.0983324
$664$	−27.5885	−1.07064
$665$	24.8274	0.962767
$666$	−15.2932	−0.592600
$667$	0.932008	0.0360875
$668$	−52.8252	−2.04387
$669$	14.3478	0.554716
$670$	11.1391	0.430339
$671$	53.9170	2.08144
$672$	9.31053	0.359162
$673$	47.6132	1.83536	0.917678	−	0.397325i	$-0.130061\pi$
$673$	47.6132	1.83536	0.917678	+	0.397325i	$0.130061\pi$
$674$	29.5596	1.13859
$675$	17.1397	0.659708
$676$	3.00660	0.115639
$677$	−21.9718	−0.844446	−0.422223	−	0.906492i	$-0.638750\pi$
$677$	−21.9718	−0.844446	−0.422223	+	0.906492i	$0.638750\pi$
$678$	7.45289	0.286227
$679$	−2.18636	−0.0839047
$680$	33.8166	1.29681
$681$	−7.98303	−0.305910
$682$	−9.71311	−0.371934
$683$	−18.5725	−0.710656	−0.355328	−	0.934742i	$-0.615631\pi$
$683$	−18.5725	−0.710656	−0.355328	+	0.934742i	$0.615631\pi$
$684$	24.4085	0.933281
$685$	−64.8613	−2.47822
$686$	−42.7866	−1.63360
$687$	3.53743	0.134962
$688$	−4.38556	−0.167198
$689$	1.11262	0.0423874
$690$	−4.42422	−0.168427
$691$	32.7494	1.24585	0.622924	−	0.782283i	$-0.285945\pi$
$691$	32.7494	1.24585	0.622924	+	0.782283i	$0.285945\pi$
$692$	−14.2276	−0.540854
$693$	28.4276	1.07987
$694$	53.3592	2.02549
$695$	27.2080	1.03206
$696$	1.02742	0.0389441
$697$	−17.2453	−0.653213
$698$	−59.5117	−2.25255
$699$	13.3412	0.504611
$700$	42.1659	1.59372
$701$	−14.1104	−0.532942	−0.266471	−	0.963843i	$-0.585858\pi$
$701$	−14.1104	−0.532942	−0.266471	+	0.963843i	$0.585858\pi$
$702$	6.97143	0.263120
$703$	−7.60371	−0.286779
$704$	53.6885	2.02346
$705$	−5.61269	−0.211386
$706$	−51.2790	−1.92991
$707$	46.5644	1.75123
$708$	9.54469	0.358711
$709$	6.40412	0.240512	0.120256	−	0.992743i	$-0.461629\pi$
$709$	6.40412	0.240512	0.120256	+	0.992743i	$0.461629\pi$
$710$	−45.7552	−1.71716
$711$	−16.0126	−0.600520
$712$	−1.60086	−0.0599949
$713$	−1.17419	−0.0439736
$714$	14.4430	0.540516
$715$	13.3765	0.500253
$716$	−46.8572	−1.75114
$717$	−12.7773	−0.477176
$718$	−17.2641	−0.644290
$719$	33.9658	1.26671	0.633356	−	0.773861i	$-0.281677\pi$
$719$	33.9658	1.26671	0.633356	+	0.773861i	$0.281677\pi$
$720$	−8.52228	−0.317606
$721$	2.54937	0.0949434
$722$	−22.3048	−0.830101
$723$	3.82788	0.142360
$724$	46.7885	1.73888
$725$	−4.59196	−0.170541
$726$	−7.38454	−0.274066
$727$	1.93586	0.0717972	0.0358986	−	0.999355i	$-0.488571\pi$
$727$	1.93586	0.0717972	0.0358986	+	0.999355i	$0.488571\pi$
$728$	5.74199	0.212812
$729$	−12.1847	−0.451286
$730$	12.1362	0.449179
$731$	−20.8714	−0.771957
$732$	21.4610	0.793220
$733$	−17.9628	−0.663470	−0.331735	−	0.943373i	$-0.607634\pi$
$733$	−17.9628	−0.663470	−0.331735	+	0.943373i	$0.607634\pi$
$734$	12.1224	0.447445
$735$	−0.886730	−0.0327075
$736$	7.46183	0.275047
$737$	6.34137	0.233587
$738$	−22.4980	−0.828163
$739$	−27.6125	−1.01574	−0.507871	−	0.861433i	$-0.669567\pi$
$739$	−27.6125	−1.01574	−0.507871	+	0.861433i	$0.669567\pi$
$740$	−24.6513	−0.906198
$741$	1.64230	0.0603315
$742$	6.34674	0.232996
$743$	37.3671	1.37087	0.685433	−	0.728136i	$-0.259613\pi$
$743$	37.3671	1.37087	0.685433	+	0.728136i	$0.259613\pi$
$744$	−1.29439	−0.0474545
$745$	−11.3511	−0.415873
$746$	25.8884	0.947843
$747$	33.0888	1.21066
$748$	57.5019	2.10248
$749$	−6.40901	−0.234180
$750$	1.98576	0.0725098
$751$	−29.4774	−1.07565	−0.537823	−	0.843058i	$-0.680753\pi$
$751$	−29.4774	−1.07565	−0.537823	+	0.843058i	$0.680753\pi$
$752$	3.08557	0.112519
$753$	15.0858	0.549756
$754$	−1.86774	−0.0680191
$755$	−22.5639	−0.821185
$756$	23.8814	0.868557
$757$	−18.5594	−0.674554	−0.337277	−	0.941405i	$-0.609506\pi$
$757$	−18.5594	−0.674554	−0.337277	+	0.941405i	$0.609506\pi$
$758$	50.8051	1.84532
$759$	−2.51867	−0.0914220
$760$	21.9346	0.795652
$761$	−44.3349	−1.60714	−0.803570	−	0.595211i	$-0.797069\pi$
$761$	−44.3349	−1.60714	−0.803570	+	0.595211i	$0.797069\pi$
$762$	−6.75431	−0.244683
$763$	6.91225	0.250240
$764$	28.4919	1.03080
$765$	−40.5586	−1.46640
$766$	−43.8313	−1.58369
$767$	−5.80916	−0.209757
$768$	5.02656	0.181380
$769$	30.8801	1.11356	0.556782	−	0.830658i	$-0.312036\pi$
$769$	30.8801	1.11356	0.556782	+	0.830658i	$0.312036\pi$
$770$	76.3040	2.74980
$771$	9.72024	0.350066
$772$	44.1395	1.58862
$773$	0.329052	0.0118352	0.00591758	−	0.999982i	$-0.498116\pi$
$773$	0.329052	0.0118352	0.00591758	+	0.999982i	$0.498116\pi$
$774$	−27.2286	−0.978711
$775$	5.78516	0.207809
$776$	−1.93161	−0.0693406
$777$	−3.52492	−0.126456
$778$	−66.0308	−2.36732
$779$	−11.1859	−0.400776
$780$	5.32435	0.190642
$781$	−26.0481	−0.932073
$782$	11.5752	0.413928
$783$	−2.60073	−0.0929425
$784$	0.487478	0.0174099
$785$	−56.0329	−1.99990
$786$	18.7199	0.667717
$787$	22.4856	0.801526	0.400763	−	0.916182i	$-0.368745\pi$
$787$	22.4856	0.801526	0.400763	+	0.916182i	$0.368745\pi$
$788$	−26.0043	−0.926366
$789$	−3.24789	−0.115628
$790$	−42.9803	−1.52917
$791$	−15.5387	−0.552491
$792$	25.1153	0.892432
$793$	−13.0617	−0.463836
$794$	−78.4174	−2.78293
$795$	1.97032	0.0698801
$796$	65.8783	2.33499
$797$	−10.2650	−0.363606	−0.181803	−	0.983335i	$-0.558193\pi$
$797$	−10.2650	−0.363606	−0.181803	+	0.983335i	$0.558193\pi$
$798$	9.36822	0.331631
$799$	14.6846	0.519504
$800$	−36.7641	−1.29981
$801$	1.92003	0.0678408
$802$	15.7147	0.554904
$803$	6.90901	0.243814
$804$	2.52410	0.0890181
$805$	9.22413	0.325108
$806$	2.35306	0.0828831
$807$	0.734092	0.0258413
$808$	41.1388	1.44726
$809$	2.55036	0.0896660	0.0448330	−	0.998994i	$-0.485724\pi$
$809$	2.55036	0.0896660	0.0448330	+	0.998994i	$0.485724\pi$
$810$	−46.4161	−1.63089
$811$	32.3368	1.13550	0.567749	−	0.823201i	$-0.307814\pi$
$811$	32.3368	1.13550	0.567749	+	0.823201i	$0.307814\pi$
$812$	−6.39813	−0.224530
$813$	−1.22970	−0.0431276
$814$	−23.3690	−0.819084
$815$	35.1409	1.23093
$816$	−2.46495	−0.0862904
$817$	−13.5379	−0.473632
$818$	−20.3109	−0.710153
$819$	−6.88677	−0.240643
$820$	−36.2647	−1.26642
$821$	−13.7121	−0.478557	−0.239278	−	0.970951i	$-0.576911\pi$
$821$	−13.7121	−0.478557	−0.239278	+	0.970951i	$0.576911\pi$
$822$	−24.4743	−0.853640
$823$	−49.0126	−1.70847	−0.854236	−	0.519886i	$-0.825974\pi$
$823$	−49.0126	−1.70847	−0.854236	+	0.519886i	$0.825974\pi$
$824$	2.25232	0.0784633
$825$	12.4094	0.432039
$826$	−33.1373	−1.15300
$827$	6.55589	0.227971	0.113985	−	0.993482i	$-0.463638\pi$
$827$	6.55589	0.227971	0.113985	+	0.993482i	$0.463638\pi$
$828$	9.06847	0.315151
$829$	0.841326	0.0292205	0.0146102	−	0.999893i	$-0.495349\pi$
$829$	0.841326	0.0292205	0.0146102	+	0.999893i	$0.495349\pi$
$830$	88.8154	3.08283
$831$	−1.74291	−0.0604607
$832$	−13.0064	−0.450915
$833$	2.31997	0.0803822
$834$	10.2665	0.355499
$835$	56.9355	1.97034
$836$	37.2977	1.28997
$837$	3.27652	0.113253
$838$	46.1142	1.59299
$839$	−33.9610	−1.17247	−0.586233	−	0.810143i	$-0.699390\pi$
$839$	−33.9610	−1.17247	−0.586233	+	0.810143i	$0.699390\pi$
$840$	10.1684	0.350843
$841$	−28.3032	−0.975973
$842$	43.2071	1.48902
$843$	12.6075	0.434225
$844$	−38.4156	−1.32232
$845$	−3.24055	−0.111478
$846$	19.1574	0.658643
$847$	15.3962	0.529019
$848$	−1.08318	−0.0371966
$849$	−1.79428	−0.0615795
$850$	−57.0304	−1.95613
$851$	−2.82501	−0.0968400
$852$	−10.3681	−0.355205
$853$	0.298970	0.0102365	0.00511827	−	0.999987i	$-0.498371\pi$
$853$	0.298970	0.0102365	0.00511827	+	0.999987i	$0.498371\pi$
$854$	−74.5083	−2.54962
$855$	−26.3077	−0.899703
$856$	−5.66225	−0.193532
$857$	34.3546	1.17353	0.586766	−	0.809757i	$-0.300401\pi$
$857$	34.3546	1.17353	0.586766	+	0.809757i	$0.300401\pi$
$858$	5.04741	0.172316
$859$	−7.73942	−0.264065	−0.132033	−	0.991245i	$-0.542150\pi$
$859$	−7.73942	−0.264065	−0.132033	+	0.991245i	$0.542150\pi$
$860$	−43.8900	−1.49663
$861$	−5.18554	−0.176723
$862$	44.3047	1.50903
$863$	33.1969	1.13003	0.565017	−	0.825079i	$-0.308870\pi$
$863$	33.1969	1.13003	0.565017	+	0.825079i	$0.308870\pi$
$864$	−20.8219	−0.708376
$865$	15.3347	0.521395
$866$	−62.7105	−2.13099
$867$	−2.44089	−0.0828968
$868$	8.06066	0.273597
$869$	−24.4683	−0.830031
$870$	−3.30755	−0.112136
$871$	−1.53624	−0.0520534
$872$	6.10685	0.206804
$873$	2.31671	0.0784087
$874$	7.50806	0.253964
$875$	−4.14015	−0.139963
$876$	2.75004	0.0929153
$877$	48.4656	1.63657	0.818283	−	0.574815i	$-0.194926\pi$
$877$	48.4656	1.63657	0.818283	+	0.574815i	$0.194926\pi$
$878$	53.6839	1.81174
$879$	15.8820	0.535686
$880$	−13.0226	−0.438991
$881$	9.59949	0.323415	0.161708	−	0.986839i	$-0.448300\pi$
$881$	9.59949	0.323415	0.161708	+	0.986839i	$0.448300\pi$
$882$	3.02660	0.101911
$883$	16.6760	0.561193	0.280597	−	0.959826i	$-0.409468\pi$
$883$	16.6760	0.561193	0.280597	+	0.959826i	$0.409468\pi$
$884$	−13.9302	−0.468524
$885$	−10.2874	−0.345806
$886$	−46.3368	−1.55672
$887$	49.5797	1.66472	0.832361	−	0.554234i	$-0.186989\pi$
$887$	49.5797	1.66472	0.832361	+	0.554234i	$0.186989\pi$
$888$	−3.11420	−0.104506
$889$	14.0822	0.472301
$890$	5.15364	0.172751
$891$	−26.4243	−0.885247
$892$	−78.9384	−2.64305
$893$	9.52494	0.318740
$894$	−4.28316	−0.143250
$895$	50.5031	1.68813
$896$	−40.1179	−1.34024
$897$	0.610164	0.0203728
$898$	−57.7454	−1.92699
$899$	−0.877822	−0.0292770
$900$	−44.6799	−1.48933
$901$	−5.15500	−0.171738
$902$	−34.3784	−1.14468
$903$	−6.27588	−0.208848
$904$	−13.7281	−0.456591
$905$	−50.4291	−1.67632
$906$	−8.51411	−0.282862
$907$	−20.7451	−0.688831	−0.344416	−	0.938817i	$-0.611923\pi$
$907$	−20.7451	−0.688831	−0.344416	+	0.938817i	$0.611923\pi$
$908$	43.9210	1.45757
$909$	−49.3406	−1.63652
$910$	−18.4851	−0.612776
$911$	−25.9187	−0.858724	−0.429362	−	0.903132i	$-0.641262\pi$
$911$	−25.9187	−0.858724	−0.429362	+	0.903132i	$0.641262\pi$
$912$	−1.59885	−0.0529431
$913$	50.5619	1.67335
$914$	41.4098	1.36971
$915$	−23.1308	−0.764681
$916$	−19.4622	−0.643050
$917$	−39.0295	−1.28887
$918$	−32.3001	−1.06606
$919$	8.55960	0.282355	0.141178	−	0.989984i	$-0.454911\pi$
$919$	8.55960	0.282355	0.141178	+	0.989984i	$0.454911\pi$
$920$	8.14936	0.268676
$921$	18.2704	0.602031
$922$	0.378336	0.0124598
$923$	6.31031	0.207706
$924$	17.2904	0.568813
$925$	13.9187	0.457643
$926$	29.0035	0.953114
$927$	−2.70136	−0.0887244
$928$	5.57847	0.183122
$929$	−37.2426	−1.22189	−0.610945	−	0.791673i	$-0.709210\pi$
$929$	−37.2426	−1.22189	−0.610945	+	0.791673i	$0.709210\pi$
$930$	4.16700	0.136641
$931$	1.50481	0.0493182
$932$	−73.4006	−2.40432
$933$	2.05740	0.0673563
$934$	74.7919	2.44727
$935$	−61.9762	−2.02684
$936$	−6.08434	−0.198873
$937$	−1.01737	−0.0332360	−0.0166180	−	0.999862i	$-0.505290\pi$
$937$	−1.01737	−0.0332360	−0.0166180	+	0.999862i	$0.505290\pi$
$938$	−8.76319	−0.286128
$939$	2.10807	0.0687943
$940$	30.8799	1.00719
$941$	12.7412	0.415351	0.207676	−	0.978198i	$-0.433410\pi$
$941$	12.7412	0.415351	0.207676	+	0.978198i	$0.433410\pi$
$942$	−21.1431	−0.688879
$943$	−4.15589	−0.135334
$944$	5.65546	0.184070
$945$	−25.7396	−0.837308
$946$	−41.6070	−1.35276
$947$	38.3267	1.24545	0.622725	−	0.782440i	$-0.286025\pi$
$947$	38.3267	1.24545	0.622725	+	0.782440i	$0.286025\pi$
$948$	−9.73929	−0.316317
$949$	−1.67375	−0.0543323
$950$	−36.9918	−1.20017
$951$	10.6447	0.345180
$952$	−26.6038	−0.862235
$953$	−1.43820	−0.0465878	−0.0232939	−	0.999729i	$-0.507415\pi$
$953$	−1.43820	−0.0465878	−0.0232939	+	0.999729i	$0.507415\pi$
$954$	−6.72514	−0.217734
$955$	−30.7088	−0.993713
$956$	70.2980	2.27360
$957$	−1.88296	−0.0608675
$958$	−16.9001	−0.546017
$959$	51.0269	1.64775
$960$	−23.0328	−0.743381
$961$	−29.8941	−0.964325
$962$	5.66130	0.182528
$963$	6.79112	0.218841
$964$	−21.0602	−0.678304
$965$	−47.5740	−1.53146
$966$	3.48057	0.111986
$967$	−30.2683	−0.973363	−0.486682	−	0.873579i	$-0.661793\pi$
$967$	−30.2683	−0.973363	−0.486682	+	0.873579i	$0.661793\pi$
$968$	13.6022	0.437193
$969$	−7.60912	−0.244440
$970$	6.21840	0.199661
$971$	−53.2089	−1.70755	−0.853777	−	0.520639i	$-0.825694\pi$
$971$	−53.2089	−1.70755	−0.853777	+	0.520639i	$0.825694\pi$
$972$	−38.6205	−1.23875
$973$	−21.4048	−0.686206
$974$	−37.7201	−1.20863
$975$	−3.00625	−0.0962770
$976$	12.7161	0.407034
$977$	11.1027	0.355206	0.177603	−	0.984102i	$-0.443166\pi$
$977$	11.1027	0.355206	0.177603	+	0.984102i	$0.443166\pi$
$978$	13.2598	0.424002
$979$	2.93393	0.0937687
$980$	4.87861	0.155841
$981$	−7.32436	−0.233849
$982$	29.3628	0.937005
$983$	31.1337	0.993012	0.496506	−	0.868033i	$-0.334616\pi$
$983$	31.1337	0.993012	0.496506	+	0.868033i	$0.334616\pi$
$984$	−4.58133	−0.146047
$985$	28.0277	0.893038
$986$	8.65362	0.275587
$987$	4.41555	0.140549
$988$	−9.03561	−0.287461
$989$	−5.02974	−0.159936
$990$	−80.8533	−2.56969
$991$	9.95594	0.316261	0.158130	−	0.987418i	$-0.449453\pi$
$991$	9.95594	0.316261	0.158130	+	0.987418i	$0.449453\pi$
$992$	−7.02801	−0.223140
$993$	−4.65631	−0.147764
$994$	35.9960	1.14172
$995$	−71.0042	−2.25099
$996$	20.1255	0.637701
$997$	28.6648	0.907823	0.453912	−	0.891047i	$-0.350028\pi$
$997$	28.6648	0.907823	0.453912	+	0.891047i	$0.350028\pi$
$998$	8.84119	0.279863
$999$	7.88306	0.249409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.d.1.19	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.d.1.19	✓	19	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)

\(f(q)\)	\(=\)	\(q+2.23754 q^{2} -0.546477 q^{3} +3.00660 q^{4} -3.24055 q^{5} -1.22277 q^{6} +2.54937 q^{7} +2.25232 q^{8} -2.70136 q^{9} +O(q^{10})\)	\(q+2.23754 q^{2} -0.546477 q^{3} +3.00660 q^{4} -3.24055 q^{5} -1.22277 q^{6} +2.54937 q^{7} +2.25232 q^{8} -2.70136 q^{9} -7.25087 q^{10} -4.12786 q^{11} -1.64304 q^{12} +1.00000 q^{13} +5.70432 q^{14} +1.77088 q^{15} -0.973541 q^{16} -4.63320 q^{17} -6.04442 q^{18} -3.00525 q^{19} -9.74304 q^{20} -1.39317 q^{21} -9.23626 q^{22} -1.11654 q^{23} -1.23084 q^{24} +5.50115 q^{25} +2.23754 q^{26} +3.11566 q^{27} +7.66494 q^{28} -0.834727 q^{29} +3.96243 q^{30} +1.05163 q^{31} -6.68298 q^{32} +2.25578 q^{33} -10.3670 q^{34} -8.26135 q^{35} -8.12193 q^{36} +2.53014 q^{37} -6.72439 q^{38} -0.546477 q^{39} -7.29875 q^{40} +3.72211 q^{41} -3.11728 q^{42} +4.50475 q^{43} -12.4108 q^{44} +8.75389 q^{45} -2.49831 q^{46} -3.16943 q^{47} +0.532018 q^{48} -0.500727 q^{49} +12.3091 q^{50} +2.53194 q^{51} +3.00660 q^{52} +1.11262 q^{53} +6.97143 q^{54} +13.3765 q^{55} +5.74199 q^{56} +1.64230 q^{57} -1.86774 q^{58} -5.80916 q^{59} +5.32435 q^{60} -13.0617 q^{61} +2.35306 q^{62} -6.88677 q^{63} -13.0064 q^{64} -3.24055 q^{65} +5.04741 q^{66} -1.53624 q^{67} -13.9302 q^{68} +0.610164 q^{69} -18.4851 q^{70} +6.31031 q^{71} -6.08434 q^{72} -1.67375 q^{73} +5.66130 q^{74} -3.00625 q^{75} -9.03561 q^{76} -10.5234 q^{77} -1.22277 q^{78} +5.92761 q^{79} +3.15481 q^{80} +6.40145 q^{81} +8.32839 q^{82} -12.2489 q^{83} -4.18871 q^{84} +15.0141 q^{85} +10.0796 q^{86} +0.456159 q^{87} -9.29726 q^{88} -0.710762 q^{89} +19.5872 q^{90} +2.54937 q^{91} -3.35700 q^{92} -0.574690 q^{93} -7.09174 q^{94} +9.73867 q^{95} +3.65210 q^{96} -0.857607 q^{97} -1.12040 q^{98} +11.1508 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9}+O(q^{10}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9} - q^{11} + 18 q^{12} + 19 q^{13} - 8 q^{14} - 11 q^{15} + 21 q^{16} - 16 q^{17} - 10 q^{19} - 20 q^{20} - 33 q^{21} + 2 q^{22} - 14 q^{23} - 9 q^{24} + 23 q^{25} - 9 q^{26} + q^{27} + 10 q^{28} - 22 q^{29} + 28 q^{30} - 3 q^{31} - 47 q^{32} - 25 q^{33} - 35 q^{34} - 3 q^{35} - 33 q^{36} - 19 q^{37} - 15 q^{38} - 2 q^{39} + 8 q^{40} - 52 q^{41} - 3 q^{42} - 2 q^{43} - 54 q^{44} - 40 q^{45} + 33 q^{46} - 24 q^{47} - 8 q^{48} + 7 q^{49} - 10 q^{50} - 7 q^{51} + 17 q^{52} - 11 q^{53} - 23 q^{54} - 29 q^{55} - 17 q^{56} - 34 q^{57} + 18 q^{58} - 52 q^{59} - 71 q^{60} - 25 q^{61} - 22 q^{62} - 19 q^{63} + 48 q^{64} - 18 q^{65} + 9 q^{66} - 2 q^{67} + 18 q^{68} - 26 q^{69} - 12 q^{70} - 44 q^{71} - 6 q^{72} - 39 q^{73} - 4 q^{74} + 17 q^{75} - 10 q^{76} - 18 q^{77} - 8 q^{78} + q^{79} - 9 q^{80} - 13 q^{81} + 47 q^{82} - 27 q^{83} - 24 q^{84} - 26 q^{85} - q^{86} + 31 q^{87} + 19 q^{88} - 86 q^{89} + 48 q^{90} - 8 q^{91} - 19 q^{92} + 32 q^{93} + 45 q^{94} + 17 q^{95} - 25 q^{96} - 20 q^{97} + 39 q^{98} + 50 q^{99}+O(q^{100}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9 - q^11 + 18 * q^12 + 19 * q^13 - 8 * q^14 - 11 * q^15 + 21 * q^16 - 16 * q^17 - 10 * q^19 - 20 * q^20 - 33 * q^21 + 2 * q^22 - 14 * q^23 - 9 * q^24 + 23 * q^25 - 9 * q^26 + q^27 + 10 * q^28 - 22 * q^29 + 28 * q^30 - 3 * q^31 - 47 * q^32 - 25 * q^33 - 35 * q^34 - 3 * q^35 - 33 * q^36 - 19 * q^37 - 15 * q^38 - 2 * q^39 + 8 * q^40 - 52 * q^41 - 3 * q^42 - 2 * q^43 - 54 * q^44 - 40 * q^45 + 33 * q^46 - 24 * q^47 - 8 * q^48 + 7 * q^49 - 10 * q^50 - 7 * q^51 + 17 * q^52 - 11 * q^53 - 23 * q^54 - 29 * q^55 - 17 * q^56 - 34 * q^57 + 18 * q^58 - 52 * q^59 - 71 * q^60 - 25 * q^61 - 22 * q^62 - 19 * q^63 + 48 * q^64 - 18 * q^65 + 9 * q^66 - 2 * q^67 + 18 * q^68 - 26 * q^69 - 12 * q^70 - 44 * q^71 - 6 * q^72 - 39 * q^73 - 4 * q^74 + 17 * q^75 - 10 * q^76 - 18 * q^77 - 8 * q^78 + q^79 - 9 * q^80 - 13 * q^81 + 47 * q^82 - 27 * q^83 - 24 * q^84 - 26 * q^85 - q^86 + 31 * q^87 + 19 * q^88 - 86 * q^89 + 48 * q^90 - 8 * q^91 - 19 * q^92 + 32 * q^93 + 45 * q^94 + 17 * q^95 - 25 * q^96 - 20 * q^97 + 39 * q^98 + 50 * q^99

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