LMFDB - Embedded newform 1339.2.a.g.1.15

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:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-0.319351 q^{2} +0.543955 q^{3} -1.89802 q^{4} +1.90715 q^{5} -0.173713 q^{6} +0.747001 q^{7} +1.24483 q^{8} -2.70411 q^{9} +O(q^{10})$	\(q-0.319351 q^{2} +0.543955 q^{3} -1.89802 q^{4} +1.90715 q^{5} -0.173713 q^{6} +0.747001 q^{7} +1.24483 q^{8} -2.70411 q^{9} -0.609049 q^{10} -5.00203 q^{11} -1.03243 q^{12} -1.00000 q^{13} -0.238555 q^{14} +1.03740 q^{15} +3.39849 q^{16} +1.16752 q^{17} +0.863561 q^{18} +7.09837 q^{19} -3.61979 q^{20} +0.406335 q^{21} +1.59740 q^{22} +7.48766 q^{23} +0.677134 q^{24} -1.36279 q^{25} +0.319351 q^{26} -3.10278 q^{27} -1.41782 q^{28} +9.53127 q^{29} -0.331295 q^{30} +1.40315 q^{31} -3.57498 q^{32} -2.72088 q^{33} -0.372847 q^{34} +1.42464 q^{35} +5.13245 q^{36} +1.98404 q^{37} -2.26687 q^{38} -0.543955 q^{39} +2.37408 q^{40} +6.59432 q^{41} -0.129763 q^{42} +3.40828 q^{43} +9.49392 q^{44} -5.15714 q^{45} -2.39119 q^{46} +3.48074 q^{47} +1.84863 q^{48} -6.44199 q^{49} +0.435208 q^{50} +0.635076 q^{51} +1.89802 q^{52} -7.21469 q^{53} +0.990876 q^{54} -9.53960 q^{55} +0.929892 q^{56} +3.86119 q^{57} -3.04382 q^{58} -2.48429 q^{59} -1.96901 q^{60} +5.09583 q^{61} -0.448097 q^{62} -2.01997 q^{63} -5.65531 q^{64} -1.90715 q^{65} +0.868914 q^{66} +4.65273 q^{67} -2.21596 q^{68} +4.07295 q^{69} -0.454960 q^{70} -9.57689 q^{71} -3.36617 q^{72} +6.07024 q^{73} -0.633604 q^{74} -0.741297 q^{75} -13.4728 q^{76} -3.73652 q^{77} +0.173713 q^{78} +6.73966 q^{79} +6.48142 q^{80} +6.42456 q^{81} -2.10590 q^{82} +8.33177 q^{83} -0.771230 q^{84} +2.22663 q^{85} -1.08844 q^{86} +5.18458 q^{87} -6.22669 q^{88} +7.74840 q^{89} +1.64694 q^{90} -0.747001 q^{91} -14.2117 q^{92} +0.763250 q^{93} -1.11158 q^{94} +13.5376 q^{95} -1.94463 q^{96} +18.2061 q^{97} +2.05725 q^{98} +13.5260 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) $ 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9} + 5 q^{10} + q^{11} + 15 q^{12} - 30 q^{13} + 24 q^{14} + 6 q^{15} + 38 q^{16} + 17 q^{17} + 8 q^{18} + 9 q^{19} + 31 q^{20} + 27 q^{21} + 2 q^{22} + 14 q^{23} + 26 q^{24} + 47 q^{25} + 14 q^{27} - 6 q^{28} + 53 q^{29} + 25 q^{30} + 19 q^{31} - 4 q^{32} + q^{33} - 22 q^{34} + 9 q^{35} + 61 q^{36} + 46 q^{38} - 5 q^{39} - 35 q^{40} + 28 q^{41} - 7 q^{42} + 6 q^{43} - 12 q^{44} + 68 q^{45} + 7 q^{46} + 12 q^{47} + 13 q^{48} + 54 q^{49} - 18 q^{50} + 10 q^{51} - 34 q^{52} + 37 q^{53} + 22 q^{54} + 11 q^{55} + 67 q^{56} - 57 q^{57} - 5 q^{58} + 61 q^{59} - 102 q^{60} + 16 q^{61} - 2 q^{62} - 7 q^{63} + 29 q^{64} - 17 q^{65} - 83 q^{66} - 2 q^{67} + 57 q^{68} + 98 q^{69} - 10 q^{70} + 50 q^{71} - 8 q^{72} - 10 q^{73} - 13 q^{74} + 5 q^{75} - 19 q^{76} + 54 q^{77} - 3 q^{78} + 3 q^{79} + 76 q^{80} + 118 q^{81} + 7 q^{82} + 6 q^{83} + 44 q^{84} + 33 q^{85} - 29 q^{86} - 10 q^{87} - 13 q^{88} + 77 q^{89} + 38 q^{90} - 2 q^{91} - 3 q^{92} + 34 q^{93} - 25 q^{94} + 24 q^{95} - 28 q^{96} + 12 q^{97} - 14 q^{98} - 58 q^{99}+O(q^{100}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9 + 5 * q^10 + q^11 + 15 * q^12 - 30 * q^13 + 24 * q^14 + 6 * q^15 + 38 * q^16 + 17 * q^17 + 8 * q^18 + 9 * q^19 + 31 * q^20 + 27 * q^21 + 2 * q^22 + 14 * q^23 + 26 * q^24 + 47 * q^25 + 14 * q^27 - 6 * q^28 + 53 * q^29 + 25 * q^30 + 19 * q^31 - 4 * q^32 + q^33 - 22 * q^34 + 9 * q^35 + 61 * q^36 + 46 * q^38 - 5 * q^39 - 35 * q^40 + 28 * q^41 - 7 * q^42 + 6 * q^43 - 12 * q^44 + 68 * q^45 + 7 * q^46 + 12 * q^47 + 13 * q^48 + 54 * q^49 - 18 * q^50 + 10 * q^51 - 34 * q^52 + 37 * q^53 + 22 * q^54 + 11 * q^55 + 67 * q^56 - 57 * q^57 - 5 * q^58 + 61 * q^59 - 102 * q^60 + 16 * q^61 - 2 * q^62 - 7 * q^63 + 29 * q^64 - 17 * q^65 - 83 * q^66 - 2 * q^67 + 57 * q^68 + 98 * q^69 - 10 * q^70 + 50 * q^71 - 8 * q^72 - 10 * q^73 - 13 * q^74 + 5 * q^75 - 19 * q^76 + 54 * q^77 - 3 * q^78 + 3 * q^79 + 76 * q^80 + 118 * q^81 + 7 * q^82 + 6 * q^83 + 44 * q^84 + 33 * q^85 - 29 * q^86 - 10 * q^87 - 13 * q^88 + 77 * q^89 + 38 * q^90 - 2 * q^91 - 3 * q^92 + 34 * q^93 - 25 * q^94 + 24 * q^95 - 28 * q^96 + 12 * q^97 - 14 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.319351	−0.225815	−0.112908	−	0.993605i	$-0.536016\pi$
$2$	−0.319351	−0.225815	−0.112908	+	0.993605i	$0.536016\pi$
$3$	0.543955	0.314053	0.157026	−	0.987594i	$-0.449809\pi$
$3$	0.543955	0.314053	0.157026	+	0.987594i	$0.449809\pi$
$4$	−1.89802	−0.949008
$5$	1.90715	0.852902	0.426451	−	0.904511i	$-0.359764\pi$
$5$	1.90715	0.852902	0.426451	+	0.904511i	$0.359764\pi$
$6$	−0.173713	−0.0709178
$7$	0.747001	0.282340	0.141170	−	0.989985i	$-0.454914\pi$
$7$	0.747001	0.282340	0.141170	+	0.989985i	$0.454914\pi$
$8$	1.24483	0.440115
$9$	−2.70411	−0.901371
$10$	−0.609049	−0.192598
$11$	−5.00203	−1.50817	−0.754084	−	0.656778i	$-0.771919\pi$
$11$	−5.00203	−1.50817	−0.754084	+	0.656778i	$0.771919\pi$
$12$	−1.03243	−0.298038
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.238555	−0.0637566
$15$	1.03740	0.267856
$16$	3.39849	0.849623
$17$	1.16752	0.283164	0.141582	−	0.989927i	$-0.454781\pi$
$17$	1.16752	0.283164	0.141582	+	0.989927i	$0.454781\pi$
$18$	0.863561	0.203543
$19$	7.09837	1.62848	0.814239	−	0.580530i	$-0.197155\pi$
$19$	7.09837	1.62848	0.814239	+	0.580530i	$0.197155\pi$
$20$	−3.61979	−0.809410
$21$	0.406335	0.0886696
$22$	1.59740	0.340567
$23$	7.48766	1.56128	0.780642	−	0.624978i	$-0.214892\pi$
$23$	7.48766	1.56128	0.780642	+	0.624978i	$0.214892\pi$
$24$	0.677134	0.138219
$25$	−1.36279	−0.272558
$26$	0.319351	0.0626298
$27$	−3.10278	−0.597131
$28$	−1.41782	−0.267943
$29$	9.53127	1.76991	0.884956	−	0.465675i	$-0.154188\pi$
$29$	9.53127	1.76991	0.884956	+	0.465675i	$0.154188\pi$
$30$	−0.331295	−0.0604860
$31$	1.40315	0.252013	0.126007	−	0.992029i	$-0.459784\pi$
$31$	1.40315	0.252013	0.126007	+	0.992029i	$0.459784\pi$
$32$	−3.57498	−0.631973
$33$	−2.72088	−0.473644
$34$	−0.372847	−0.0639428
$35$	1.42464	0.240808
$36$	5.13245	0.855408
$37$	1.98404	0.326174	0.163087	−	0.986612i	$-0.447855\pi$
$37$	1.98404	0.326174	0.163087	+	0.986612i	$0.447855\pi$
$38$	−2.26687	−0.367735
$39$	−0.543955	−0.0871025
$40$	2.37408	0.375375
$41$	6.59432	1.02986	0.514930	−	0.857232i	$-0.327818\pi$
$41$	6.59432	1.02986	0.514930	+	0.857232i	$0.327818\pi$
$42$	−0.129763	−0.0200229
$43$	3.40828	0.519757	0.259879	−	0.965641i	$-0.416317\pi$
$43$	3.40828	0.519757	0.259879	+	0.965641i	$0.416317\pi$
$44$	9.49392	1.43126
$45$	−5.15714	−0.768781
$46$	−2.39119	−0.352562
$47$	3.48074	0.507719	0.253859	−	0.967241i	$-0.418300\pi$
$47$	3.48074	0.507719	0.253859	+	0.967241i	$0.418300\pi$
$48$	1.84863	0.266826
$49$	−6.44199	−0.920284
$50$	0.435208	0.0615477
$51$	0.635076	0.0889285
$52$	1.89802	0.263207
$53$	−7.21469	−0.991014	−0.495507	−	0.868604i	$-0.665018\pi$
$53$	−7.21469	−0.991014	−0.495507	+	0.868604i	$0.665018\pi$
$54$	0.990876	0.134841
$55$	−9.53960	−1.28632
$56$	0.929892	0.124262
$57$	3.86119	0.511428
$58$	−3.04382	−0.399673
$59$	−2.48429	−0.323427	−0.161713	−	0.986838i	$-0.551702\pi$
$59$	−2.48429	−0.323427	−0.161713	+	0.986838i	$0.551702\pi$
$60$	−1.96901	−0.254197
$61$	5.09583	0.652454	0.326227	−	0.945291i	$-0.394223\pi$
$61$	5.09583	0.652454	0.326227	+	0.945291i	$0.394223\pi$
$62$	−0.448097	−0.0569084
$63$	−2.01997	−0.254493
$64$	−5.65531	−0.706914
$65$	−1.90715	−0.236552
$66$	0.868914	0.106956
$67$	4.65273	0.568421	0.284211	−	0.958762i	$-0.408268\pi$
$67$	4.65273	0.568421	0.284211	+	0.958762i	$0.408268\pi$
$68$	−2.21596	−0.268725
$69$	4.07295	0.490325
$70$	−0.454960	−0.0543781
$71$	−9.57689	−1.13657	−0.568284	−	0.822832i	$-0.692392\pi$
$71$	−9.57689	−1.13657	−0.568284	+	0.822832i	$0.692392\pi$
$72$	−3.36617	−0.396707
$73$	6.07024	0.710468	0.355234	−	0.934777i	$-0.384401\pi$
$73$	6.07024	0.710468	0.355234	+	0.934777i	$0.384401\pi$
$74$	−0.633604	−0.0736550
$75$	−0.741297	−0.0855976
$76$	−13.4728	−1.54544
$77$	−3.73652	−0.425816
$78$	0.173713	0.0196691
$79$	6.73966	0.758271	0.379136	−	0.925341i	$-0.376221\pi$
$79$	6.73966	0.758271	0.379136	+	0.925341i	$0.376221\pi$
$80$	6.48142	0.724645
$81$	6.42456	0.713841
$82$	−2.10590	−0.232558
$83$	8.33177	0.914530	0.457265	−	0.889330i	$-0.348829\pi$
$83$	8.33177	0.914530	0.457265	+	0.889330i	$0.348829\pi$
$84$	−0.771230	−0.0841481
$85$	2.22663	0.241511
$86$	−1.08844	−0.117369
$87$	5.18458	0.555845
$88$	−6.22669	−0.663768
$89$	7.74840	0.821329	0.410664	−	0.911787i	$-0.365297\pi$
$89$	7.74840	0.821329	0.410664	+	0.911787i	$0.365297\pi$
$90$	1.64694	0.173602
$91$	−0.747001	−0.0783070
$92$	−14.2117	−1.48167
$93$	0.763250	0.0791454
$94$	−1.11158	−0.114651
$95$	13.5376	1.38893
$96$	−1.94463	−0.198473
$97$	18.2061	1.84855	0.924277	−	0.381723i	$-0.124669\pi$
$97$	18.2061	1.84855	0.924277	+	0.381723i	$0.124669\pi$
$98$	2.05725	0.207814
$99$	13.5260	1.35942
$100$	2.58660	0.258660
$101$	13.4018	1.33353	0.666764	−	0.745269i	$-0.267679\pi$
$101$	13.4018	1.33353	0.666764	+	0.745269i	$0.267679\pi$
$102$	−0.202812	−0.0200814
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.24483	−0.122066
$105$	0.774940	0.0756264
$106$	2.30402	0.223786
$107$	9.31009	0.900040	0.450020	−	0.893018i	$-0.351417\pi$
$107$	9.31009	0.900040	0.450020	+	0.893018i	$0.351417\pi$
$108$	5.88913	0.566681
$109$	−13.4113	−1.28457	−0.642287	−	0.766464i	$-0.722014\pi$
$109$	−13.4113	−1.28457	−0.642287	+	0.766464i	$0.722014\pi$
$110$	3.04648	0.290470
$111$	1.07923	0.102436
$112$	2.53868	0.239882
$113$	−10.0757	−0.947838	−0.473919	−	0.880569i	$-0.657161\pi$
$113$	−10.0757	−0.947838	−0.473919	+	0.880569i	$0.657161\pi$
$114$	−1.23308	−0.115488
$115$	14.2801	1.33162
$116$	−18.0905	−1.67966
$117$	2.70411	0.249995
$118$	0.793359	0.0730346
$119$	0.872136	0.0799486
$120$	1.29139	0.117888
$121$	14.0203	1.27457
$122$	−1.62736	−0.147334
$123$	3.58701	0.323430
$124$	−2.66320	−0.239162
$125$	−12.1348	−1.08537
$126$	0.645081	0.0574683
$127$	9.82884	0.872168	0.436084	−	0.899906i	$-0.356365\pi$
$127$	9.82884	0.872168	0.436084	+	0.899906i	$0.356365\pi$
$128$	8.95599	0.791605
$129$	1.85395	0.163231
$130$	0.609049	0.0534171
$131$	−17.4913	−1.52822	−0.764110	−	0.645086i	$-0.776822\pi$
$131$	−17.4913	−1.52822	−0.764110	+	0.645086i	$0.776822\pi$
$132$	5.16427	0.449492
$133$	5.30249	0.459784
$134$	−1.48585	−0.128358
$135$	−5.91746	−0.509294
$136$	1.45336	0.124625
$137$	−6.99654	−0.597754	−0.298877	−	0.954292i	$-0.596612\pi$
$137$	−6.99654	−0.597754	−0.298877	+	0.954292i	$0.596612\pi$
$138$	−1.30070	−0.110723
$139$	−8.43677	−0.715597	−0.357799	−	0.933799i	$-0.616473\pi$
$139$	−8.43677	−0.715597	−0.357799	+	0.933799i	$0.616473\pi$
$140$	−2.70399	−0.228529
$141$	1.89337	0.159450
$142$	3.05839	0.256654
$143$	5.00203	0.418290
$144$	−9.18990	−0.765825
$145$	18.1775	1.50956
$146$	−1.93854	−0.160434
$147$	−3.50415	−0.289018
$148$	−3.76574	−0.309542
$149$	21.0359	1.72333	0.861665	−	0.507478i	$-0.169422\pi$
$149$	21.0359	1.72333	0.861665	+	0.507478i	$0.169422\pi$
$150$	0.236734	0.0193292
$151$	−23.9464	−1.94873	−0.974364	−	0.224976i	$-0.927770\pi$
$151$	−23.9464	−1.94873	−0.974364	+	0.224976i	$0.927770\pi$
$152$	8.83629	0.716718
$153$	−3.15710	−0.255236
$154$	1.19326	0.0961556
$155$	2.67601	0.214942
$156$	1.03243	0.0826610
$157$	−8.52758	−0.680575	−0.340287	−	0.940321i	$-0.610524\pi$
$157$	−8.52758	−0.680575	−0.340287	+	0.940321i	$0.610524\pi$
$158$	−2.15232	−0.171229
$159$	−3.92447	−0.311231
$160$	−6.81801	−0.539011
$161$	5.59329	0.440813
$162$	−2.05169	−0.161196
$163$	5.33810	0.418112	0.209056	−	0.977904i	$-0.432961\pi$
$163$	5.33810	0.418112	0.209056	+	0.977904i	$0.432961\pi$
$164$	−12.5161	−0.977344
$165$	−5.18911	−0.403972
$166$	−2.66076	−0.206515
$167$	22.6380	1.75178	0.875891	−	0.482510i	$-0.160275\pi$
$167$	22.6380	1.75178	0.875891	+	0.482510i	$0.160275\pi$
$168$	0.505820	0.0390248
$169$	1.00000	0.0769231
$170$	−0.711075	−0.0545369
$171$	−19.1948	−1.46786
$172$	−6.46896	−0.493254
$173$	−13.3343	−1.01379	−0.506893	−	0.862009i	$-0.669206\pi$
$173$	−13.3343	−1.01379	−0.506893	+	0.862009i	$0.669206\pi$
$174$	−1.65570	−0.125518
$175$	−1.01801	−0.0769540
$176$	−16.9993	−1.28137
$177$	−1.35134	−0.101573
$178$	−2.47446	−0.185468
$179$	−16.3187	−1.21971	−0.609857	−	0.792512i	$-0.708773\pi$
$179$	−16.3187	−1.21971	−0.609857	+	0.792512i	$0.708773\pi$
$180$	9.78833	0.729579
$181$	13.2572	0.985399	0.492699	−	0.870200i	$-0.336010\pi$
$181$	13.2572	0.985399	0.492699	+	0.870200i	$0.336010\pi$
$182$	0.238555	0.0176829
$183$	2.77190	0.204905
$184$	9.32089	0.687145
$185$	3.78385	0.278194
$186$	−0.243745	−0.0178722
$187$	−5.83995	−0.427059
$188$	−6.60650	−0.481829
$189$	−2.31778	−0.168594
$190$	−4.32325	−0.313642
$191$	−25.6746	−1.85775	−0.928873	−	0.370399i	$-0.879221\pi$
$191$	−25.6746	−1.85775	−0.928873	+	0.370399i	$0.879221\pi$
$192$	−3.07623	−0.222008
$193$	−4.46496	−0.321395	−0.160698	−	0.987004i	$-0.551374\pi$
$193$	−4.46496	−0.321395	−0.160698	+	0.987004i	$0.551374\pi$
$194$	−5.81415	−0.417431
$195$	−1.03740	−0.0742899
$196$	12.2270	0.873357
$197$	3.17369	0.226116	0.113058	−	0.993588i	$-0.463935\pi$
$197$	3.17369	0.226116	0.113058	+	0.993588i	$0.463935\pi$
$198$	−4.31955	−0.306977
$199$	−12.3553	−0.875842	−0.437921	−	0.899013i	$-0.644285\pi$
$199$	−12.3553	−0.875842	−0.437921	+	0.899013i	$0.644285\pi$
$200$	−1.69645	−0.119957
$201$	2.53088	0.178514
$202$	−4.27988	−0.301131
$203$	7.11986	0.499717
$204$	−1.20538	−0.0843938
$205$	12.5763	0.878369
$206$	−0.319351	−0.0222502
$207$	−20.2475	−1.40730
$208$	−3.39849	−0.235643
$209$	−35.5062	−2.45602
$210$	−0.247478	−0.0170776
$211$	7.84411	0.540011	0.270006	−	0.962859i	$-0.412974\pi$
$211$	7.84411	0.540011	0.270006	+	0.962859i	$0.412974\pi$
$212$	13.6936	0.940480
$213$	−5.20940	−0.356942
$214$	−2.97318	−0.203243
$215$	6.50009	0.443302
$216$	−3.86245	−0.262806
$217$	1.04815	0.0711533
$218$	4.28293	0.290076
$219$	3.30194	0.223124
$220$	18.1063	1.22073
$221$	−1.16752	−0.0785357
$222$	−0.344652	−0.0231316
$223$	−26.3244	−1.76282	−0.881408	−	0.472357i	$-0.843403\pi$
$223$	−26.3244	−1.76282	−0.881408	+	0.472357i	$0.843403\pi$
$224$	−2.67051	−0.178431
$225$	3.68514	0.245676
$226$	3.21767	0.214036
$227$	−7.14336	−0.474121	−0.237061	−	0.971495i	$-0.576184\pi$
$227$	−7.14336	−0.474121	−0.237061	+	0.971495i	$0.576184\pi$
$228$	−7.32860	−0.485349
$229$	12.1054	0.799950	0.399975	−	0.916526i	$-0.369019\pi$
$229$	12.1054	0.799950	0.399975	+	0.916526i	$0.369019\pi$
$230$	−4.56035	−0.300700
$231$	−2.03250	−0.133729
$232$	11.8648	0.778965
$233$	26.2238	1.71798	0.858989	−	0.511994i	$-0.171093\pi$
$233$	26.2238	1.71798	0.858989	+	0.511994i	$0.171093\pi$
$234$	−0.863561	−0.0564527
$235$	6.63829	0.433034
$236$	4.71521	0.306934
$237$	3.66607	0.238137
$238$	−0.278517	−0.0180536
$239$	4.18357	0.270613	0.135306	−	0.990804i	$-0.456798\pi$
$239$	4.18357	0.270613	0.135306	+	0.990804i	$0.456798\pi$
$240$	3.52560	0.227577
$241$	11.2688	0.725885	0.362942	−	0.931812i	$-0.381772\pi$
$241$	11.2688	0.725885	0.362942	+	0.931812i	$0.381772\pi$
$242$	−4.47738	−0.287817
$243$	12.8030	0.821314
$244$	−9.67197	−0.619184
$245$	−12.2858	−0.784912
$246$	−1.14552	−0.0730354
$247$	−7.09837	−0.451658
$248$	1.74669	0.110915
$249$	4.53211	0.287211
$250$	3.87525	0.245092
$251$	−2.87311	−0.181349	−0.0906746	−	0.995881i	$-0.528902\pi$
$251$	−2.87311	−0.181349	−0.0906746	+	0.995881i	$0.528902\pi$
$252$	3.83394	0.241516
$253$	−37.4534	−2.35468
$254$	−3.13885	−0.196949
$255$	1.21118	0.0758473
$256$	8.45052	0.528157
$257$	29.8817	1.86397	0.931985	−	0.362498i	$-0.118076\pi$
$257$	29.8817	1.86397	0.931985	+	0.362498i	$0.118076\pi$
$258$	−0.592060	−0.0368601
$259$	1.48208	0.0920919
$260$	3.61979	0.224490
$261$	−25.7736	−1.59535
$262$	5.58585	0.345095
$263$	3.93873	0.242872	0.121436	−	0.992599i	$-0.461250\pi$
$263$	3.93873	0.242872	0.121436	+	0.992599i	$0.461250\pi$
$264$	−3.38704	−0.208458
$265$	−13.7595	−0.845238
$266$	−1.69335	−0.103826
$267$	4.21478	0.257940
$268$	−8.83095	−0.539436
$269$	−20.4879	−1.24917	−0.624585	−	0.780957i	$-0.714732\pi$
$269$	−20.4879	−1.24917	−0.624585	+	0.780957i	$0.714732\pi$
$270$	1.88975	0.115006
$271$	−20.0615	−1.21865	−0.609324	−	0.792922i	$-0.708559\pi$
$271$	−20.0615	−1.21865	−0.609324	+	0.792922i	$0.708559\pi$
$272$	3.96779	0.240583
$273$	−0.406335	−0.0245925
$274$	2.23435	0.134982
$275$	6.81671	0.411063
$276$	−7.73052	−0.465322
$277$	7.50641	0.451016	0.225508	−	0.974241i	$-0.427596\pi$
$277$	7.50641	0.451016	0.225508	+	0.974241i	$0.427596\pi$
$278$	2.69429	0.161593
$279$	−3.79427	−0.227157
$280$	1.77344	0.105983
$281$	7.34530	0.438184	0.219092	−	0.975704i	$-0.429691\pi$
$281$	7.34530	0.438184	0.219092	+	0.975704i	$0.429691\pi$
$282$	−0.604649	−0.0360063
$283$	6.32625	0.376056	0.188028	−	0.982164i	$-0.439790\pi$
$283$	6.32625	0.376056	0.188028	+	0.982164i	$0.439790\pi$
$284$	18.1771	1.07861
$285$	7.36386	0.436198
$286$	−1.59740	−0.0944563
$287$	4.92596	0.290770
$288$	9.66715	0.569642
$289$	−15.6369	−0.919818
$290$	−5.80501	−0.340882
$291$	9.90332	0.580543
$292$	−11.5214	−0.674239
$293$	−7.74321	−0.452363	−0.226181	−	0.974085i	$-0.572624\pi$
$293$	−7.74321	−0.452363	−0.226181	+	0.974085i	$0.572624\pi$
$294$	1.11905	0.0652646
$295$	−4.73790	−0.275851
$296$	2.46980	0.143554
$297$	15.5202	0.900573
$298$	−6.71784	−0.389154
$299$	−7.48766	−0.433022
$300$	1.40699	0.0812328
$301$	2.54599	0.146748
$302$	7.64730	0.440052
$303$	7.28998	0.418798
$304$	24.1237	1.38359
$305$	9.71850	0.556480
$306$	1.00822	0.0576362
$307$	−15.7980	−0.901637	−0.450818	−	0.892616i	$-0.648868\pi$
$307$	−15.7980	−0.901637	−0.450818	+	0.892616i	$0.648868\pi$
$308$	7.09197	0.404102
$309$	0.543955	0.0309445
$310$	−0.854587	−0.0485373
$311$	21.6289	1.22646	0.613231	−	0.789904i	$-0.289870\pi$
$311$	21.6289	1.22646	0.613231	+	0.789904i	$0.289870\pi$
$312$	−0.677134	−0.0383352
$313$	−32.0728	−1.81286	−0.906430	−	0.422356i	$-0.861203\pi$
$313$	−32.0728	−1.81286	−0.906430	+	0.422356i	$0.861203\pi$
$314$	2.72329	0.153684
$315$	−3.85239	−0.217058
$316$	−12.7920	−0.719605
$317$	4.05047	0.227497	0.113749	−	0.993510i	$-0.463714\pi$
$317$	4.05047	0.227497	0.113749	+	0.993510i	$0.463714\pi$
$318$	1.25328	0.0702806
$319$	−47.6756	−2.66932
$320$	−10.7855	−0.602928
$321$	5.06427	0.282660
$322$	−1.78622	−0.0995422
$323$	8.28746	0.461127
$324$	−12.1939	−0.677440
$325$	1.36279	0.0755940
$326$	−1.70473	−0.0944161
$327$	−7.29517	−0.403424
$328$	8.20883	0.453257
$329$	2.60012	0.143349
$330$	1.65715	0.0912230
$331$	−9.32061	−0.512307	−0.256153	−	0.966636i	$-0.582455\pi$
$331$	−9.32061	−0.512307	−0.256153	+	0.966636i	$0.582455\pi$
$332$	−15.8138	−0.867896
$333$	−5.36506	−0.294004
$334$	−7.22946	−0.395579
$335$	8.87344	0.484808
$336$	1.38093	0.0753357
$337$	25.1927	1.37234	0.686168	−	0.727443i	$-0.259291\pi$
$337$	25.1927	1.37234	0.686168	+	0.727443i	$0.259291\pi$
$338$	−0.319351	−0.0173704
$339$	−5.48070	−0.297671
$340$	−4.22617	−0.229196
$341$	−7.01859	−0.380078
$342$	6.12987	0.331465
$343$	−10.0412	−0.542173
$344$	4.24274	0.228753
$345$	7.76771	0.418199
$346$	4.25831	0.228928
$347$	22.3175	1.19807	0.599033	−	0.800724i	$-0.295552\pi$
$347$	22.3175	1.19807	0.599033	+	0.800724i	$0.295552\pi$
$348$	−9.84041	−0.527501
$349$	−23.1670	−1.24010	−0.620051	−	0.784562i	$-0.712888\pi$
$349$	−23.1670	−1.24010	−0.620051	+	0.784562i	$0.712888\pi$
$350$	0.325101	0.0173774
$351$	3.10278	0.165614
$352$	17.8821	0.953121
$353$	−17.1197	−0.911190	−0.455595	−	0.890187i	$-0.650573\pi$
$353$	−17.1197	−0.911190	−0.455595	+	0.890187i	$0.650573\pi$
$354$	0.431552	0.0229367
$355$	−18.2645	−0.969381
$356$	−14.7066	−0.779447
$357$	0.474403	0.0251081
$358$	5.21138	0.275430
$359$	−11.1708	−0.589573	−0.294787	−	0.955563i	$-0.595249\pi$
$359$	−11.1708	−0.589573	−0.294787	+	0.955563i	$0.595249\pi$
$360$	−6.41979	−0.338352
$361$	31.3868	1.65194
$362$	−4.23369	−0.222518
$363$	7.62639	0.400282
$364$	1.41782	0.0743139
$365$	11.5768	0.605959
$366$	−0.885210	−0.0462706
$367$	0.0235347	0.00122850	0.000614251	−	1.00000i	$-0.499804\pi$
$367$	0.0235347	0.00122850	0.000614251		1.00000i	$0.499804\pi$
$368$	25.4467	1.32650
$369$	−17.8318	−0.928285
$370$	−1.20838	−0.0628205
$371$	−5.38938	−0.279803
$372$	−1.44866	−0.0751095
$373$	26.3820	1.36601	0.683004	−	0.730415i	$-0.260673\pi$
$373$	26.3820	1.36601	0.683004	+	0.730415i	$0.260673\pi$
$374$	1.86499	0.0964364
$375$	−6.60077	−0.340862
$376$	4.33295	0.223455
$377$	−9.53127	−0.490885
$378$	0.740185	0.0380710
$379$	0.875008	0.0449462	0.0224731	−	0.999747i	$-0.492846\pi$
$379$	0.875008	0.0449462	0.0224731	+	0.999747i	$0.492846\pi$
$380$	−25.6946	−1.31811
$381$	5.34645	0.273907
$382$	8.19919	0.419507
$383$	−9.77475	−0.499466	−0.249733	−	0.968315i	$-0.580343\pi$
$383$	−9.77475	−0.499466	−0.249733	+	0.968315i	$0.580343\pi$
$384$	4.87165	0.248606
$385$	−7.12609	−0.363179
$386$	1.42589	0.0725759
$387$	−9.21637	−0.468494
$388$	−34.5555	−1.75429
$389$	10.2454	0.519462	0.259731	−	0.965681i	$-0.416366\pi$
$389$	10.2454	0.519462	0.259731	+	0.965681i	$0.416366\pi$
$390$	0.331295	0.0167758
$391$	8.74196	0.442100
$392$	−8.01921	−0.405031
$393$	−9.51447	−0.479941
$394$	−1.01352	−0.0510605
$395$	12.8535	0.646731
$396$	−25.6726	−1.29010
$397$	−18.6564	−0.936338	−0.468169	−	0.883639i	$-0.655086\pi$
$397$	−18.6564	−0.936338	−0.468169	+	0.883639i	$0.655086\pi$
$398$	3.94567	0.197778
$399$	2.88432	0.144396
$400$	−4.63143	−0.231572
$401$	7.01465	0.350295	0.175148	−	0.984542i	$-0.443960\pi$
$401$	7.01465	0.350295	0.175148	+	0.984542i	$0.443960\pi$
$402$	−0.808237	−0.0403112
$403$	−1.40315	−0.0698958
$404$	−25.4368	−1.26553
$405$	12.2526	0.608836
$406$	−2.27373	−0.112844
$407$	−9.92421	−0.491925
$408$	0.790565	0.0391388
$409$	−4.69187	−0.231998	−0.115999	−	0.993249i	$-0.537007\pi$
$409$	−4.69187	−0.231998	−0.115999	+	0.993249i	$0.537007\pi$
$410$	−4.01626	−0.198349
$411$	−3.80580	−0.187726
$412$	−1.89802	−0.0935085
$413$	−1.85576	−0.0913162
$414$	6.46604	0.317789
$415$	15.8899	0.780005
$416$	3.57498	0.175278
$417$	−4.58922	−0.224735
$418$	11.3389	0.554606
$419$	33.7214	1.64740	0.823700	−	0.567026i	$-0.191906\pi$
$419$	33.7214	1.64740	0.823700	+	0.567026i	$0.191906\pi$
$420$	−1.47085	−0.0717701
$421$	15.4220	0.751622	0.375811	−	0.926696i	$-0.377364\pi$
$421$	15.4220	0.751622	0.375811	+	0.926696i	$0.377364\pi$
$422$	−2.50502	−0.121943
$423$	−9.41232	−0.457643
$424$	−8.98109	−0.436160
$425$	−1.59108	−0.0771787
$426$	1.66363	0.0806029
$427$	3.80659	0.184214
$428$	−17.6707	−0.854145
$429$	2.72088	0.131365
$430$	−2.07581	−0.100104
$431$	25.3800	1.22251	0.611255	−	0.791433i	$-0.290665\pi$
$431$	25.3800	1.22251	0.611255	+	0.791433i	$0.290665\pi$
$432$	−10.5448	−0.507336
$433$	−40.2721	−1.93535	−0.967677	−	0.252194i	$-0.918848\pi$
$433$	−40.2721	−1.93535	−0.967677	+	0.252194i	$0.918848\pi$
$434$	−0.334729	−0.0160675
$435$	9.88776	0.474082
$436$	25.4549	1.21907
$437$	53.1501	2.54252
$438$	−1.05448	−0.0503848
$439$	−22.4526	−1.07160	−0.535801	−	0.844344i	$-0.679990\pi$
$439$	−22.4526	−1.07160	−0.535801	+	0.844344i	$0.679990\pi$
$440$	−11.8752	−0.566129
$441$	17.4199	0.829517
$442$	0.372847	0.0177345
$443$	−7.08341	−0.336543	−0.168272	−	0.985741i	$-0.553819\pi$
$443$	−7.08341	−0.336543	−0.168272	+	0.985741i	$0.553819\pi$
$444$	−2.04839	−0.0972123
$445$	14.7773	0.700513
$446$	8.40673	0.398070
$447$	11.4426	0.541216
$448$	−4.22452	−0.199590
$449$	31.4141	1.48252	0.741260	−	0.671218i	$-0.234228\pi$
$449$	31.4141	1.48252	0.741260	+	0.671218i	$0.234228\pi$
$450$	−1.17685	−0.0554773
$451$	−32.9849	−1.55320
$452$	19.1237	0.899505
$453$	−13.0258	−0.612003
$454$	2.28124	0.107064
$455$	−1.42464	−0.0667882
$456$	4.80655	0.225087
$457$	7.34767	0.343710	0.171855	−	0.985122i	$-0.445024\pi$
$457$	7.34767	0.343710	0.171855	+	0.985122i	$0.445024\pi$
$458$	−3.86588	−0.180641
$459$	−3.62255	−0.169086
$460$	−27.1038	−1.26372
$461$	2.18909	0.101956	0.0509780	−	0.998700i	$-0.483766\pi$
$461$	2.18909	0.101956	0.0509780	+	0.998700i	$0.483766\pi$
$462$	0.649080	0.0301979
$463$	−37.9967	−1.76586	−0.882928	−	0.469508i	$-0.844431\pi$
$463$	−37.9967	−1.76586	−0.882928	+	0.469508i	$0.844431\pi$
$464$	32.3919	1.50376
$465$	1.45563	0.0675032
$466$	−8.37459	−0.387946
$467$	30.7096	1.42107	0.710534	−	0.703662i	$-0.248453\pi$
$467$	30.7096	1.42107	0.710534	+	0.703662i	$0.248453\pi$
$468$	−5.13245	−0.237247
$469$	3.47559	0.160488
$470$	−2.11994	−0.0977857
$471$	−4.63862	−0.213736
$472$	−3.09252	−0.142345
$473$	−17.0483	−0.783881
$474$	−1.17076	−0.0537749
$475$	−9.67359	−0.443855
$476$	−1.65533	−0.0758718
$477$	19.5093	0.893271
$478$	−1.33603	−0.0611084
$479$	−14.4262	−0.659152	−0.329576	−	0.944129i	$-0.606906\pi$
$479$	−14.4262	−0.659152	−0.329576	+	0.944129i	$0.606906\pi$
$480$	−3.70869	−0.169278
$481$	−1.98404	−0.0904644
$482$	−3.59869	−0.163916
$483$	3.04250	0.138438
$484$	−26.6107	−1.20958
$485$	34.7218	1.57664
$486$	−4.08865	−0.185465
$487$	−21.3335	−0.966712	−0.483356	−	0.875424i	$-0.660582\pi$
$487$	−21.3335	−0.966712	−0.483356	+	0.875424i	$0.660582\pi$
$488$	6.34347	0.287155
$489$	2.90369	0.131309
$490$	3.92349	0.177245
$491$	−15.3137	−0.691097	−0.345548	−	0.938401i	$-0.612307\pi$
$491$	−15.3137	−0.691097	−0.345548	+	0.938401i	$0.612307\pi$
$492$	−6.80820	−0.306938
$493$	11.1279	0.501176
$494$	2.26687	0.101991
$495$	25.7961	1.15945
$496$	4.76859	0.214116
$497$	−7.15395	−0.320898
$498$	−1.44733	−0.0648565
$499$	−34.6830	−1.55263	−0.776313	−	0.630347i	$-0.782912\pi$
$499$	−34.6830	−1.55263	−0.776313	+	0.630347i	$0.782912\pi$
$500$	23.0320	1.03002
$501$	12.3141	0.550151
$502$	0.917530	0.0409514
$503$	13.7437	0.612803	0.306402	−	0.951902i	$-0.400875\pi$
$503$	13.7437	0.612803	0.306402	+	0.951902i	$0.400875\pi$
$504$	−2.51453	−0.112006
$505$	25.5592	1.13737
$506$	11.9608	0.531722
$507$	0.543955	0.0241579
$508$	−18.6553	−0.827694
$509$	−0.685433	−0.0303813	−0.0151907	−	0.999885i	$-0.504836\pi$
$509$	−0.685433	−0.0303813	−0.0151907	+	0.999885i	$0.504836\pi$
$510$	−0.386793	−0.0171275
$511$	4.53447	0.200593
$512$	−20.6107	−0.910871
$513$	−22.0247	−0.972414
$514$	−9.54275	−0.420912
$515$	1.90715	0.0840389
$516$	−3.51883	−0.154908
$517$	−17.4108	−0.765725
$518$	−0.473303	−0.0207957
$519$	−7.25324	−0.318382
$520$	−2.37408	−0.104110
$521$	−28.9696	−1.26918	−0.634591	−	0.772848i	$-0.718832\pi$
$521$	−28.9696	−1.26918	−0.634591	+	0.772848i	$0.718832\pi$
$522$	8.23083	0.360253
$523$	−10.2420	−0.447852	−0.223926	−	0.974606i	$-0.571887\pi$
$523$	−10.2420	−0.447852	−0.223926	+	0.974606i	$0.571887\pi$
$524$	33.1987	1.45029
$525$	−0.553749	−0.0241676
$526$	−1.25784	−0.0548443
$527$	1.63820	0.0713611
$528$	−9.24688	−0.402419
$529$	33.0650	1.43761
$530$	4.39410	0.190867
$531$	6.71779	0.291527
$532$	−10.0642	−0.436338
$533$	−6.59432	−0.285632
$534$	−1.34599	−0.0582468
$535$	17.7557	0.767646
$536$	5.79188	0.250171
$537$	−8.87662	−0.383054
$538$	6.54283	0.282081
$539$	32.2230	1.38794
$540$	11.2314	0.483324
$541$	−36.3049	−1.56087	−0.780435	−	0.625237i	$-0.785002\pi$
$541$	−36.3049	−1.56087	−0.780435	+	0.625237i	$0.785002\pi$
$542$	6.40665	0.275189
$543$	7.21131	0.309467
$544$	−4.17385	−0.178952
$545$	−25.5774	−1.09562
$546$	0.129763	0.00555336
$547$	18.0281	0.770827	0.385414	−	0.922744i	$-0.374059\pi$
$547$	18.0281	0.770827	0.385414	+	0.922744i	$0.374059\pi$
$548$	13.2795	0.567273
$549$	−13.7797	−0.588103
$550$	−2.17692	−0.0928243
$551$	67.6564	2.88226
$552$	5.07015	0.215800
$553$	5.03453	0.214090
$554$	−2.39718	−0.101846
$555$	2.05825	0.0873677
$556$	16.0131	0.679107
$557$	−21.5020	−0.911068	−0.455534	−	0.890218i	$-0.650552\pi$
$557$	−21.5020	−0.911068	−0.455534	+	0.890218i	$0.650552\pi$
$558$	1.21170	0.0512955
$559$	−3.40828	−0.144155
$560$	4.84163	0.204596
$561$	−3.17667	−0.134119
$562$	−2.34573	−0.0989485
$563$	−38.8300	−1.63649	−0.818245	−	0.574869i	$-0.805053\pi$
$563$	−38.8300	−1.63649	−0.818245	+	0.574869i	$0.805053\pi$
$564$	−3.59364	−0.151320
$565$	−19.2157	−0.808413
$566$	−2.02029	−0.0849192
$567$	4.79916	0.201546
$568$	−11.9216	−0.500221
$569$	7.36197	0.308630	0.154315	−	0.988022i	$-0.450683\pi$
$569$	7.36197	0.308630	0.154315	+	0.988022i	$0.450683\pi$
$570$	−2.35166	−0.0985000
$571$	2.48519	0.104002	0.0520011	−	0.998647i	$-0.483440\pi$
$571$	2.48519	0.104002	0.0520011	+	0.998647i	$0.483440\pi$
$572$	−9.49392	−0.396961
$573$	−13.9658	−0.583430
$574$	−1.57311	−0.0656603
$575$	−10.2041	−0.425541
$576$	15.2926	0.637192
$577$	−10.6722	−0.444290	−0.222145	−	0.975014i	$-0.571306\pi$
$577$	−10.6722	−0.444290	−0.222145	+	0.975014i	$0.571306\pi$
$578$	4.99366	0.207709
$579$	−2.42874	−0.100935
$580$	−34.5012	−1.43259
$581$	6.22384	0.258208
$582$	−3.16263	−0.131095
$583$	36.0881	1.49461
$584$	7.55644	0.312688
$585$	5.15714	0.213222
$586$	2.47280	0.102150
$587$	−16.0543	−0.662631	−0.331315	−	0.943520i	$-0.607492\pi$
$587$	−16.0543	−0.662631	−0.331315	+	0.943520i	$0.607492\pi$
$588$	6.65094	0.274280
$589$	9.96007	0.410398
$590$	1.51305	0.0622914
$591$	1.72635	0.0710124
$592$	6.74274	0.277125
$593$	−14.8533	−0.609951	−0.304975	−	0.952360i	$-0.598648\pi$
$593$	−14.8533	−0.609951	−0.304975	+	0.952360i	$0.598648\pi$
$594$	−4.95639	−0.203363
$595$	1.66329	0.0681883
$596$	−39.9265	−1.63545
$597$	−6.72072	−0.275061
$598$	2.39119	0.0977830
$599$	48.3271	1.97459	0.987295	−	0.158896i	$-0.0507933\pi$
$599$	48.3271	1.97459	0.987295	+	0.158896i	$0.0507933\pi$
$600$	−0.922792	−0.0376728
$601$	33.1880	1.35377	0.676883	−	0.736091i	$-0.263330\pi$
$601$	33.1880	1.35377	0.676883	+	0.736091i	$0.263330\pi$
$602$	−0.813063	−0.0331380
$603$	−12.5815	−0.512359
$604$	45.4506	1.84936
$605$	26.7387	1.08708
$606$	−2.32806	−0.0945710
$607$	−8.44558	−0.342795	−0.171398	−	0.985202i	$-0.554828\pi$
$607$	−8.44558	−0.342795	−0.171398	+	0.985202i	$0.554828\pi$
$608$	−25.3765	−1.02915
$609$	3.87289	0.156937
$610$	−3.10361	−0.125662
$611$	−3.48074	−0.140816
$612$	5.99222	0.242221
$613$	48.1195	1.94353	0.971765	−	0.235952i	$-0.0758207\pi$
$613$	48.1195	1.94353	0.971765	+	0.235952i	$0.0758207\pi$
$614$	5.04509	0.203603
$615$	6.84096	0.275854
$616$	−4.65135	−0.187408
$617$	21.5134	0.866096	0.433048	−	0.901371i	$-0.357438\pi$
$617$	21.5134	0.866096	0.433048	+	0.901371i	$0.357438\pi$
$618$	−0.173713	−0.00698774
$619$	40.3711	1.62265	0.811327	−	0.584593i	$-0.198746\pi$
$619$	40.3711	1.62265	0.811327	+	0.584593i	$0.198746\pi$
$620$	−5.07911	−0.203982
$621$	−23.2326	−0.932290
$622$	−6.90720	−0.276954
$623$	5.78806	0.231894
$624$	−1.84863	−0.0740043
$625$	−16.3288	−0.653154
$626$	10.2425	0.409371
$627$	−19.3138	−0.771318
$628$	16.1855	0.645871
$629$	2.31640	0.0923608
$630$	1.23026	0.0490149
$631$	−22.2476	−0.885662	−0.442831	−	0.896605i	$-0.646026\pi$
$631$	−22.2476	−0.885662	−0.442831	+	0.896605i	$0.646026\pi$
$632$	8.38976	0.333727
$633$	4.26685	0.169592
$634$	−1.29352	−0.0513723
$635$	18.7450	0.743874
$636$	7.44870	0.295360
$637$	6.44199	0.255241
$638$	15.2253	0.602774
$639$	25.8970	1.02447
$640$	17.0804	0.675161
$641$	12.9709	0.512319	0.256159	−	0.966635i	$-0.417543\pi$
$641$	12.9709	0.512319	0.256159	+	0.966635i	$0.417543\pi$
$642$	−1.61728	−0.0638289
$643$	−21.8703	−0.862480	−0.431240	−	0.902237i	$-0.641924\pi$
$643$	−21.8703	−0.862480	−0.431240	+	0.902237i	$0.641924\pi$
$644$	−10.6161	−0.418334
$645$	3.53576	0.139220
$646$	−2.64661	−0.104129
$647$	5.94199	0.233604	0.116802	−	0.993155i	$-0.462736\pi$
$647$	5.94199	0.233604	0.116802	+	0.993155i	$0.462736\pi$
$648$	7.99752	0.314172
$649$	12.4265	0.487781
$650$	−0.435208	−0.0170703
$651$	0.570149	0.0223459
$652$	−10.1318	−0.396792
$653$	42.6004	1.66708	0.833542	−	0.552456i	$-0.186309\pi$
$653$	42.6004	1.66708	0.833542	+	0.552456i	$0.186309\pi$
$654$	2.32972	0.0910992
$655$	−33.3584	−1.30342
$656$	22.4107	0.874992
$657$	−16.4146	−0.640395
$658$	−0.830350	−0.0323704
$659$	−7.48154	−0.291440	−0.145720	−	0.989326i	$-0.546550\pi$
$659$	−7.48154	−0.291440	−0.145720	+	0.989326i	$0.546550\pi$
$660$	9.84901	0.383372
$661$	−41.1078	−1.59891	−0.799454	−	0.600728i	$-0.794878\pi$
$661$	−41.1078	−1.59891	−0.799454	+	0.600728i	$0.794878\pi$
$662$	2.97654	0.115687
$663$	−0.635076	−0.0246643
$664$	10.3717	0.402499
$665$	10.1126	0.392151
$666$	1.71334	0.0663905
$667$	71.3668	2.76333
$668$	−42.9673	−1.66245
$669$	−14.3193	−0.553617
$670$	−2.83374	−0.109477
$671$	−25.4895	−0.984010
$672$	−1.45264	−0.0560368
$673$	−19.5257	−0.752661	−0.376330	−	0.926486i	$-0.622814\pi$
$673$	−19.5257	−0.752661	−0.376330	+	0.926486i	$0.622814\pi$
$674$	−8.04532	−0.309894
$675$	4.22844	0.162753
$676$	−1.89802	−0.0730006
$677$	−46.3473	−1.78127	−0.890637	−	0.454716i	$-0.849741\pi$
$677$	−46.3473	−1.78127	−0.890637	+	0.454716i	$0.849741\pi$
$678$	1.75027	0.0672186
$679$	13.6000	0.521920
$680$	2.77178	0.106293
$681$	−3.88567	−0.148899
$682$	2.24139	0.0858273
$683$	−43.5551	−1.66659	−0.833294	−	0.552830i	$-0.813548\pi$
$683$	−43.5551	−1.66659	−0.833294	+	0.552830i	$0.813548\pi$
$684$	36.4320	1.39301
$685$	−13.3434	−0.509826
$686$	3.20666	0.122431
$687$	6.58482	0.251226
$688$	11.5830	0.441598
$689$	7.21469	0.274858
$690$	−2.48062	−0.0944358
$691$	−3.62194	−0.137785	−0.0688925	−	0.997624i	$-0.521947\pi$
$691$	−3.62194	−0.137785	−0.0688925	+	0.997624i	$0.521947\pi$
$692$	25.3086	0.962090
$693$	10.1040	0.383818
$694$	−7.12711	−0.270542
$695$	−16.0902	−0.610335
$696$	6.45394	0.244636
$697$	7.69897	0.291619
$698$	7.39840	0.280034
$699$	14.2646	0.539536
$700$	1.93219	0.0730299
$701$	36.5004	1.37860	0.689301	−	0.724475i	$-0.257918\pi$
$701$	36.5004	1.37860	0.689301	+	0.724475i	$0.257918\pi$
$702$	−0.990876	−0.0373982
$703$	14.0834	0.531167
$704$	28.2880	1.06614
$705$	3.61093	0.135996
$706$	5.46719	0.205761
$707$	10.0112	0.376508
$708$	2.56486	0.0963935
$709$	−32.2809	−1.21233	−0.606167	−	0.795337i	$-0.707294\pi$
$709$	−32.2809	−1.21233	−0.606167	+	0.795337i	$0.707294\pi$
$710$	5.83280	0.218901
$711$	−18.2248	−0.683484
$712$	9.64547	0.361479
$713$	10.5063	0.393464
$714$	−0.151501	−0.00566978
$715$	9.53960	0.356761
$716$	30.9731	1.15752
$717$	2.27567	0.0849866
$718$	3.56741	0.133135
$719$	17.1827	0.640805	0.320402	−	0.947282i	$-0.396182\pi$
$719$	17.1827	0.640805	0.320402	+	0.947282i	$0.396182\pi$
$720$	−17.5265	−0.653174
$721$	0.747001	0.0278198
$722$	−10.0234	−0.373033
$723$	6.12970	0.227966
$724$	−25.1623	−0.935151
$725$	−12.9891	−0.482404
$726$	−2.43549	−0.0903897
$727$	14.4272	0.535077	0.267538	−	0.963547i	$-0.413790\pi$
$727$	14.4272	0.535077	0.267538	+	0.963547i	$0.413790\pi$
$728$	−0.929892	−0.0344641
$729$	−12.3094	−0.455905
$730$	−3.69707	−0.136835
$731$	3.97922	0.147177
$732$	−5.26111	−0.194456
$733$	15.9346	0.588557	0.294279	−	0.955720i	$-0.404921\pi$
$733$	15.9346	0.588557	0.294279	+	0.955720i	$0.404921\pi$
$734$	−0.00751583	−0.000277414 0
$735$	−6.68293	−0.246504
$736$	−26.7682	−0.986689
$737$	−23.2731	−0.857275
$738$	5.69459	0.209621
$739$	−5.42576	−0.199590	−0.0997949	−	0.995008i	$-0.531819\pi$
$739$	−5.42576	−0.199590	−0.0997949	+	0.995008i	$0.531819\pi$
$740$	−7.18181	−0.264009
$741$	−3.86119	−0.141844
$742$	1.72110	0.0631837
$743$	18.5966	0.682244	0.341122	−	0.940019i	$-0.389193\pi$
$743$	18.5966	0.682244	0.341122	+	0.940019i	$0.389193\pi$
$744$	0.950120	0.0348331
$745$	40.1186	1.46983
$746$	−8.42511	−0.308465
$747$	−22.5300	−0.824331
$748$	11.0843	0.405282
$749$	6.95464	0.254117
$750$	2.10796	0.0769719
$751$	−7.63447	−0.278586	−0.139293	−	0.990251i	$-0.544483\pi$
$751$	−7.63447	−0.278586	−0.139293	+	0.990251i	$0.544483\pi$
$752$	11.8293	0.431369
$753$	−1.56284	−0.0569532
$754$	3.04382	0.110849
$755$	−45.6693	−1.66207
$756$	4.39918	0.159997
$757$	42.8378	1.55696	0.778482	−	0.627666i	$-0.215990\pi$
$757$	42.8378	1.55696	0.778482	+	0.627666i	$0.215990\pi$
$758$	−0.279435	−0.0101495
$759$	−20.3730	−0.739493
$760$	16.8521	0.611290
$761$	49.6007	1.79802	0.899012	−	0.437923i	$-0.144286\pi$
$761$	49.6007	1.79802	0.899012	+	0.437923i	$0.144286\pi$
$762$	−1.70739	−0.0618523
$763$	−10.0183	−0.362686
$764$	48.7307	1.76301
$765$	−6.02105	−0.217691
$766$	3.12157	0.112787
$767$	2.48429	0.0897024
$768$	4.59670	0.165869
$769$	6.96341	0.251107	0.125554	−	0.992087i	$-0.459929\pi$
$769$	6.96341	0.251107	0.125554	+	0.992087i	$0.459929\pi$
$770$	2.27572	0.0820113
$771$	16.2543	0.585384
$772$	8.47457	0.305006
$773$	−13.3052	−0.478556	−0.239278	−	0.970951i	$-0.576911\pi$
$773$	−13.3052	−0.478556	−0.239278	+	0.970951i	$0.576911\pi$
$774$	2.94325	0.105793
$775$	−1.91220	−0.0686882
$776$	22.6636	0.813577
$777$	0.806184	0.0289217
$778$	−3.27188	−0.117302
$779$	46.8089	1.67710
$780$	1.96901	0.0705017
$781$	47.9039	1.71413
$782$	−2.79175	−0.0998329
$783$	−29.5734	−1.05687
$784$	−21.8930	−0.781894
$785$	−16.2633	−0.580464
$786$	3.03845	0.108378
$787$	9.08945	0.324004	0.162002	−	0.986790i	$-0.448205\pi$
$787$	9.08945	0.324004	0.162002	+	0.986790i	$0.448205\pi$
$788$	−6.02372	−0.214586
$789$	2.14249	0.0762747
$790$	−4.10478	−0.146042
$791$	−7.52652	−0.267612
$792$	16.8377	0.598301
$793$	−5.09583	−0.180958
$794$	5.95794	0.211439
$795$	−7.48454	−0.265449
$796$	23.4505	0.831181
$797$	45.0513	1.59580	0.797899	−	0.602791i	$-0.205945\pi$
$797$	45.0513	1.59580	0.797899	+	0.602791i	$0.205945\pi$
$798$	−0.921108	−0.0326069
$799$	4.06382	0.143768
$800$	4.87195	0.172249
$801$	−20.9525	−0.740322
$802$	−2.24014	−0.0791019
$803$	−30.3635	−1.07150
$804$	−4.80364	−0.169411
$805$	10.6672	0.375970
$806$	0.448097	0.0157835
$807$	−11.1445	−0.392305
$808$	16.6830	0.586907
$809$	−11.8663	−0.417195	−0.208598	−	0.978002i	$-0.566890\pi$
$809$	−11.8663	−0.417195	−0.208598	+	0.978002i	$0.566890\pi$
$810$	−3.91287	−0.137484
$811$	−38.2969	−1.34479	−0.672393	−	0.740194i	$-0.734733\pi$
$811$	−38.2969	−1.34479	−0.672393	+	0.740194i	$0.734733\pi$
$812$	−13.5136	−0.474235
$813$	−10.9125	−0.382719
$814$	3.16931	0.111084
$815$	10.1805	0.356609
$816$	2.15830	0.0755557
$817$	24.1932	0.846413
$818$	1.49835	0.0523886
$819$	2.01997	0.0705836
$820$	−23.8701	−0.833579
$821$	−29.3229	−1.02338	−0.511688	−	0.859171i	$-0.670980\pi$
$821$	−29.3229	−1.02338	−0.511688	+	0.859171i	$0.670980\pi$
$822$	1.21539	0.0423914
$823$	−0.179741	−0.00626537	−0.00313268	−	0.999995i	$-0.500997\pi$
$823$	−0.179741	−0.00626537	−0.00313268	+	0.999995i	$0.500997\pi$
$824$	1.24483	0.0433659
$825$	3.70799	0.129095
$826$	0.592640	0.0206206
$827$	30.5393	1.06195	0.530977	−	0.847386i	$-0.321825\pi$
$827$	30.5393	1.06195	0.530977	+	0.847386i	$0.321825\pi$
$828$	38.4300	1.33553
$829$	18.0756	0.627793	0.313896	−	0.949457i	$-0.398366\pi$
$829$	18.0756	0.627793	0.313896	+	0.949457i	$0.398366\pi$
$830$	−5.07445	−0.176137
$831$	4.08315	0.141643
$832$	5.65531	0.196063
$833$	−7.52113	−0.260592
$834$	1.46557	0.0507486
$835$	43.1740	1.49410
$836$	67.3913	2.33078
$837$	−4.35367	−0.150485
$838$	−10.7690	−0.372008
$839$	19.7779	0.682810	0.341405	−	0.939916i	$-0.389097\pi$
$839$	19.7779	0.682810	0.341405	+	0.939916i	$0.389097\pi$
$840$	0.964672	0.0332844
$841$	61.8450	2.13259
$842$	−4.92502	−0.169728
$843$	3.99551	0.137613
$844$	−14.8882	−0.512475
$845$	1.90715	0.0656078
$846$	3.00583	0.103343
$847$	10.4731	0.359862
$848$	−24.5191	−0.841988
$849$	3.44119	0.118101
$850$	0.508113	0.0174281
$851$	14.8558	0.509250
$852$	9.88752	0.338741
$853$	44.8503	1.53564	0.767822	−	0.640663i	$-0.221340\pi$
$853$	44.8503	1.53564	0.767822	+	0.640663i	$0.221340\pi$
$854$	−1.21564	−0.0415983
$855$	−36.6073	−1.25194
$856$	11.5895	0.396122
$857$	−7.66715	−0.261905	−0.130952	−	0.991389i	$-0.541804\pi$
$857$	−7.66715	−0.261905	−0.130952	+	0.991389i	$0.541804\pi$
$858$	−0.868914	−0.0296642
$859$	38.5056	1.31379	0.656897	−	0.753980i	$-0.271868\pi$
$859$	38.5056	1.31379	0.656897	+	0.753980i	$0.271868\pi$
$860$	−12.3373	−0.420697
$861$	2.67950	0.0913172
$862$	−8.10512	−0.276061
$863$	−17.2767	−0.588107	−0.294053	−	0.955789i	$-0.595004\pi$
$863$	−17.2767	−0.588107	−0.294053	+	0.955789i	$0.595004\pi$
$864$	11.0924	0.377370
$865$	−25.4304	−0.864660
$866$	12.8609	0.437032
$867$	−8.50577	−0.288871
$868$	−1.98941	−0.0675250
$869$	−33.7120	−1.14360
$870$	−3.15766	−0.107055
$871$	−4.65273	−0.157652
$872$	−16.6949	−0.565361
$873$	−49.2315	−1.66623
$874$	−16.9735	−0.574139
$875$	−9.06469	−0.306442
$876$	−6.26713	−0.211747
$877$	−4.40930	−0.148891	−0.0744457	−	0.997225i	$-0.523719\pi$
$877$	−4.40930	−0.148891	−0.0744457	+	0.997225i	$0.523719\pi$
$878$	7.17024	0.241984
$879$	−4.21196	−0.142066
$880$	−32.4202	−1.09289
$881$	−4.40500	−0.148408	−0.0742042	−	0.997243i	$-0.523642\pi$
$881$	−4.40500	−0.148408	−0.0742042	+	0.997243i	$0.523642\pi$
$882$	−5.56305	−0.187318
$883$	−36.2644	−1.22040	−0.610198	−	0.792249i	$-0.708910\pi$
$883$	−36.2644	−1.22040	−0.610198	+	0.792249i	$0.708910\pi$
$884$	2.21596	0.0745309
$885$	−2.57720	−0.0866318
$886$	2.26209	0.0759965
$887$	11.6953	0.392690	0.196345	−	0.980535i	$-0.437093\pi$
$887$	11.6953	0.392690	0.196345	+	0.980535i	$0.437093\pi$
$888$	1.34346	0.0450836
$889$	7.34215	0.246248
$890$	−4.71915	−0.158186
$891$	−32.1358	−1.07659
$892$	49.9642	1.67292
$893$	24.7076	0.826808
$894$	−3.65420	−0.122215
$895$	−31.1221	−1.04030
$896$	6.69013	0.223502
$897$	−4.07295	−0.135992
$898$	−10.0321	−0.334776
$899$	13.3738	0.446041
$900$	−6.99445	−0.233148
$901$	−8.42327	−0.280620
$902$	10.5338	0.350736
$903$	1.38490	0.0460867
$904$	−12.5425	−0.417158
$905$	25.2834	0.840449
$906$	4.15979	0.138200
$907$	−33.5281	−1.11328	−0.556640	−	0.830754i	$-0.687910\pi$
$907$	−33.5281	−1.11328	−0.556640	+	0.830754i	$0.687910\pi$
$908$	13.5582	0.449945
$909$	−36.2400	−1.20200
$910$	0.454960	0.0150818
$911$	14.5031	0.480508	0.240254	−	0.970710i	$-0.422769\pi$
$911$	14.5031	0.480508	0.240254	+	0.970710i	$0.422769\pi$
$912$	13.1222	0.434521
$913$	−41.6757	−1.37926
$914$	−2.34648	−0.0776148
$915$	5.28643	0.174764
$916$	−22.9763	−0.759159
$917$	−13.0660	−0.431477
$918$	1.15686	0.0381822
$919$	−29.3644	−0.968643	−0.484321	−	0.874890i	$-0.660933\pi$
$919$	−29.3644	−0.968643	−0.484321	+	0.874890i	$0.660933\pi$
$920$	17.7763	0.586067
$921$	−8.59338	−0.283161
$922$	−0.699087	−0.0230232
$923$	9.57689	0.315227
$924$	3.85771	0.126909
$925$	−2.70383	−0.0889014
$926$	12.1343	0.398757
$927$	−2.70411	−0.0888147
$928$	−34.0741	−1.11854
$929$	10.1422	0.332754	0.166377	−	0.986062i	$-0.446793\pi$
$929$	10.1422	0.332754	0.166377	+	0.986062i	$0.446793\pi$
$930$	−0.464857	−0.0152433
$931$	−45.7276	−1.49866
$932$	−49.7732	−1.63037
$933$	11.7651	0.385174
$934$	−9.80712	−0.320899
$935$	−11.1376	−0.364240
$936$	3.36617	0.110027
$937$	8.23442	0.269007	0.134503	−	0.990913i	$-0.457056\pi$
$937$	8.23442	0.269007	0.134503	+	0.990913i	$0.457056\pi$
$938$	−1.10993	−0.0362406
$939$	−17.4461	−0.569334
$940$	−12.5996	−0.410953
$941$	8.86676	0.289048	0.144524	−	0.989501i	$-0.453835\pi$
$941$	8.86676	0.289048	0.144524	+	0.989501i	$0.453835\pi$
$942$	1.48135	0.0482649
$943$	49.3760	1.60790
$944$	−8.44283	−0.274791
$945$	−4.42035	−0.143794
$946$	5.44439	0.177012
$947$	26.0802	0.847492	0.423746	−	0.905781i	$-0.360715\pi$
$947$	26.0802	0.847492	0.423746	+	0.905781i	$0.360715\pi$
$948$	−6.95826	−0.225994
$949$	−6.07024	−0.197048
$950$	3.08927	0.100229
$951$	2.20327	0.0714461
$952$	1.08566	0.0351866
$953$	21.2634	0.688790	0.344395	−	0.938825i	$-0.388084\pi$
$953$	21.2634	0.688790	0.344395	+	0.938825i	$0.388084\pi$
$954$	−6.23032	−0.201714
$955$	−48.9652	−1.58448
$956$	−7.94048	−0.256814
$957$	−25.9334	−0.838308
$958$	4.60703	0.148846
$959$	−5.22642	−0.168770
$960$	−5.86683	−0.189351
$961$	−29.0312	−0.936489
$962$	0.633604	0.0204282
$963$	−25.1755	−0.811270
$964$	−21.3883	−0.688870
$965$	−8.51534	−0.274119
$966$	−0.971624	−0.0312615
$967$	−54.8315	−1.76326	−0.881630	−	0.471940i	$-0.843554\pi$
$967$	−54.8315	−1.76326	−0.881630	+	0.471940i	$0.843554\pi$
$968$	17.4529	0.560957
$969$	4.50801	0.144818
$970$	−11.0884	−0.356028
$971$	−15.4388	−0.495455	−0.247728	−	0.968830i	$-0.579684\pi$
$971$	−15.4388	−0.495455	−0.247728	+	0.968830i	$0.579684\pi$
$972$	−24.3003	−0.779433
$973$	−6.30227	−0.202042
$974$	6.81286	0.218298
$975$	0.741297	0.0237405
$976$	17.3181	0.554340
$977$	−4.41071	−0.141111	−0.0705556	−	0.997508i	$-0.522477\pi$
$977$	−4.41071	−0.141111	−0.0705556	+	0.997508i	$0.522477\pi$
$978$	−0.927295	−0.0296516
$979$	−38.7577	−1.23870
$980$	23.3187	0.744888
$981$	36.2658	1.15788
$982$	4.89044	0.156060
$983$	−10.7221	−0.341982	−0.170991	−	0.985273i	$-0.554697\pi$
$983$	−10.7221	−0.341982	−0.170991	+	0.985273i	$0.554697\pi$
$984$	4.46524	0.142347
$985$	6.05270	0.192855
$986$	−3.55371	−0.113173
$987$	1.41435	0.0450192
$988$	13.4728	0.428627
$989$	25.5200	0.811489
$990$	−8.23802	−0.261821
$991$	43.0013	1.36598	0.682990	−	0.730428i	$-0.260679\pi$
$991$	43.0013	1.36598	0.682990	+	0.730428i	$0.260679\pi$
$992$	−5.01623	−0.159265
$993$	−5.06999	−0.160891
$994$	2.28462	0.0724637
$995$	−23.5633	−0.747008
$996$	−8.60201	−0.272565
$997$	52.0277	1.64773	0.823867	−	0.566784i	$-0.191812\pi$
$997$	52.0277	1.64773	0.823867	+	0.566784i	$0.191812\pi$
$998$	11.0761	0.350607
$999$	−6.15604	−0.194768

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.g.1.15	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.g.1.15	✓	30	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)

\(f(q)\)	\(=\)	\(q-0.319351 q^{2} +0.543955 q^{3} -1.89802 q^{4} +1.90715 q^{5} -0.173713 q^{6} +0.747001 q^{7} +1.24483 q^{8} -2.70411 q^{9} +O(q^{10})\)	\(q-0.319351 q^{2} +0.543955 q^{3} -1.89802 q^{4} +1.90715 q^{5} -0.173713 q^{6} +0.747001 q^{7} +1.24483 q^{8} -2.70411 q^{9} -0.609049 q^{10} -5.00203 q^{11} -1.03243 q^{12} -1.00000 q^{13} -0.238555 q^{14} +1.03740 q^{15} +3.39849 q^{16} +1.16752 q^{17} +0.863561 q^{18} +7.09837 q^{19} -3.61979 q^{20} +0.406335 q^{21} +1.59740 q^{22} +7.48766 q^{23} +0.677134 q^{24} -1.36279 q^{25} +0.319351 q^{26} -3.10278 q^{27} -1.41782 q^{28} +9.53127 q^{29} -0.331295 q^{30} +1.40315 q^{31} -3.57498 q^{32} -2.72088 q^{33} -0.372847 q^{34} +1.42464 q^{35} +5.13245 q^{36} +1.98404 q^{37} -2.26687 q^{38} -0.543955 q^{39} +2.37408 q^{40} +6.59432 q^{41} -0.129763 q^{42} +3.40828 q^{43} +9.49392 q^{44} -5.15714 q^{45} -2.39119 q^{46} +3.48074 q^{47} +1.84863 q^{48} -6.44199 q^{49} +0.435208 q^{50} +0.635076 q^{51} +1.89802 q^{52} -7.21469 q^{53} +0.990876 q^{54} -9.53960 q^{55} +0.929892 q^{56} +3.86119 q^{57} -3.04382 q^{58} -2.48429 q^{59} -1.96901 q^{60} +5.09583 q^{61} -0.448097 q^{62} -2.01997 q^{63} -5.65531 q^{64} -1.90715 q^{65} +0.868914 q^{66} +4.65273 q^{67} -2.21596 q^{68} +4.07295 q^{69} -0.454960 q^{70} -9.57689 q^{71} -3.36617 q^{72} +6.07024 q^{73} -0.633604 q^{74} -0.741297 q^{75} -13.4728 q^{76} -3.73652 q^{77} +0.173713 q^{78} +6.73966 q^{79} +6.48142 q^{80} +6.42456 q^{81} -2.10590 q^{82} +8.33177 q^{83} -0.771230 q^{84} +2.22663 q^{85} -1.08844 q^{86} +5.18458 q^{87} -6.22669 q^{88} +7.74840 q^{89} +1.64694 q^{90} -0.747001 q^{91} -14.2117 q^{92} +0.763250 q^{93} -1.11158 q^{94} +13.5376 q^{95} -1.94463 q^{96} +18.2061 q^{97} +2.05725 q^{98} +13.5260 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9} + 5 q^{10} + q^{11} + 15 q^{12} - 30 q^{13} + 24 q^{14} + 6 q^{15} + 38 q^{16} + 17 q^{17} + 8 q^{18} + 9 q^{19} + 31 q^{20} + 27 q^{21} + 2 q^{22} + 14 q^{23} + 26 q^{24} + 47 q^{25} + 14 q^{27} - 6 q^{28} + 53 q^{29} + 25 q^{30} + 19 q^{31} - 4 q^{32} + q^{33} - 22 q^{34} + 9 q^{35} + 61 q^{36} + 46 q^{38} - 5 q^{39} - 35 q^{40} + 28 q^{41} - 7 q^{42} + 6 q^{43} - 12 q^{44} + 68 q^{45} + 7 q^{46} + 12 q^{47} + 13 q^{48} + 54 q^{49} - 18 q^{50} + 10 q^{51} - 34 q^{52} + 37 q^{53} + 22 q^{54} + 11 q^{55} + 67 q^{56} - 57 q^{57} - 5 q^{58} + 61 q^{59} - 102 q^{60} + 16 q^{61} - 2 q^{62} - 7 q^{63} + 29 q^{64} - 17 q^{65} - 83 q^{66} - 2 q^{67} + 57 q^{68} + 98 q^{69} - 10 q^{70} + 50 q^{71} - 8 q^{72} - 10 q^{73} - 13 q^{74} + 5 q^{75} - 19 q^{76} + 54 q^{77} - 3 q^{78} + 3 q^{79} + 76 q^{80} + 118 q^{81} + 7 q^{82} + 6 q^{83} + 44 q^{84} + 33 q^{85} - 29 q^{86} - 10 q^{87} - 13 q^{88} + 77 q^{89} + 38 q^{90} - 2 q^{91} - 3 q^{92} + 34 q^{93} - 25 q^{94} + 24 q^{95} - 28 q^{96} + 12 q^{97} - 14 q^{98} - 58 q^{99}+O(q^{100}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9 + 5 * q^10 + q^11 + 15 * q^12 - 30 * q^13 + 24 * q^14 + 6 * q^15 + 38 * q^16 + 17 * q^17 + 8 * q^18 + 9 * q^19 + 31 * q^20 + 27 * q^21 + 2 * q^22 + 14 * q^23 + 26 * q^24 + 47 * q^25 + 14 * q^27 - 6 * q^28 + 53 * q^29 + 25 * q^30 + 19 * q^31 - 4 * q^32 + q^33 - 22 * q^34 + 9 * q^35 + 61 * q^36 + 46 * q^38 - 5 * q^39 - 35 * q^40 + 28 * q^41 - 7 * q^42 + 6 * q^43 - 12 * q^44 + 68 * q^45 + 7 * q^46 + 12 * q^47 + 13 * q^48 + 54 * q^49 - 18 * q^50 + 10 * q^51 - 34 * q^52 + 37 * q^53 + 22 * q^54 + 11 * q^55 + 67 * q^56 - 57 * q^57 - 5 * q^58 + 61 * q^59 - 102 * q^60 + 16 * q^61 - 2 * q^62 - 7 * q^63 + 29 * q^64 - 17 * q^65 - 83 * q^66 - 2 * q^67 + 57 * q^68 + 98 * q^69 - 10 * q^70 + 50 * q^71 - 8 * q^72 - 10 * q^73 - 13 * q^74 + 5 * q^75 - 19 * q^76 + 54 * q^77 - 3 * q^78 + 3 * q^79 + 76 * q^80 + 118 * q^81 + 7 * q^82 + 6 * q^83 + 44 * q^84 + 33 * q^85 - 29 * q^86 - 10 * q^87 - 13 * q^88 + 77 * q^89 + 38 * q^90 - 2 * q^91 - 3 * q^92 + 34 * q^93 - 25 * q^94 + 24 * q^95 - 28 * q^96 + 12 * q^97 - 14 * q^98 - 58 * q^99

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