LMFDB - Embedded newform 1339.2.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$10.6919688306$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.86443 q^{2} -1.06486 q^{3} +1.47608 q^{4} -1.98836 q^{5} +1.98536 q^{6} +3.02740 q^{7} +0.976806 q^{8} -1.86606 q^{9} +O(q^{10})$	\(q-1.86443 q^{2} -1.06486 q^{3} +1.47608 q^{4} -1.98836 q^{5} +1.98536 q^{6} +3.02740 q^{7} +0.976806 q^{8} -1.86606 q^{9} +3.70715 q^{10} +2.42757 q^{11} -1.57183 q^{12} +1.00000 q^{13} -5.64437 q^{14} +2.11734 q^{15} -4.77335 q^{16} +4.07964 q^{17} +3.47914 q^{18} -3.36633 q^{19} -2.93499 q^{20} -3.22377 q^{21} -4.52601 q^{22} +5.39068 q^{23} -1.04017 q^{24} -1.04642 q^{25} -1.86443 q^{26} +5.18170 q^{27} +4.46869 q^{28} -0.660947 q^{29} -3.94761 q^{30} -6.17209 q^{31} +6.94594 q^{32} -2.58503 q^{33} -7.60618 q^{34} -6.01957 q^{35} -2.75446 q^{36} -2.56588 q^{37} +6.27626 q^{38} -1.06486 q^{39} -1.94224 q^{40} -4.00216 q^{41} +6.01048 q^{42} +2.06098 q^{43} +3.58329 q^{44} +3.71041 q^{45} -10.0505 q^{46} -1.76376 q^{47} +5.08296 q^{48} +2.16517 q^{49} +1.95096 q^{50} -4.34426 q^{51} +1.47608 q^{52} -3.55452 q^{53} -9.66089 q^{54} -4.82688 q^{55} +2.95719 q^{56} +3.58468 q^{57} +1.23229 q^{58} +9.16593 q^{59} +3.12536 q^{60} -3.46105 q^{61} +11.5074 q^{62} -5.64933 q^{63} -3.40349 q^{64} -1.98836 q^{65} +4.81959 q^{66} +8.66948 q^{67} +6.02188 q^{68} -5.74034 q^{69} +11.2230 q^{70} +3.23458 q^{71} -1.82278 q^{72} -10.2331 q^{73} +4.78390 q^{74} +1.11429 q^{75} -4.96897 q^{76} +7.34922 q^{77} +1.98536 q^{78} +5.49363 q^{79} +9.49114 q^{80} +0.0803902 q^{81} +7.46173 q^{82} +11.4883 q^{83} -4.75855 q^{84} -8.11180 q^{85} -3.84253 q^{86} +0.703819 q^{87} +2.37126 q^{88} +17.1365 q^{89} -6.91779 q^{90} +3.02740 q^{91} +7.95708 q^{92} +6.57244 q^{93} +3.28840 q^{94} +6.69347 q^{95} -7.39648 q^{96} -6.92301 q^{97} -4.03679 q^{98} -4.52999 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9}+O(q^{10}) $ 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9	\( 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9} + 5 q^{10} + 9 q^{11} + 15 q^{12} + 28 q^{13} + 20 q^{14} + 4 q^{15} + 32 q^{16} - 7 q^{17} + 10 q^{18} - 3 q^{19} + 53 q^{20} + 25 q^{21} - 14 q^{22} - 6 q^{23} + 10 q^{24} + 45 q^{25} + 6 q^{26} + 8 q^{27} - 12 q^{28} + 25 q^{29} - 43 q^{30} + q^{31} + 28 q^{32} + 17 q^{33} + 10 q^{34} + 11 q^{35} + 27 q^{36} + 18 q^{37} + 2 q^{38} + 5 q^{39} + 37 q^{40} + 56 q^{41} - 29 q^{42} - 30 q^{43} + 30 q^{44} + 38 q^{45} - 27 q^{46} + 40 q^{47} + 19 q^{48} + 36 q^{49} + 20 q^{50} - 18 q^{51} + 32 q^{52} + 51 q^{53} - 36 q^{54} - 5 q^{55} - 13 q^{56} + 31 q^{57} - 29 q^{58} + 29 q^{59} + 48 q^{60} + 16 q^{61} - 38 q^{62} - 23 q^{63} - 5 q^{64} + 27 q^{65} + 25 q^{66} - 2 q^{67} - 43 q^{68} + 38 q^{69} + 10 q^{70} + 34 q^{71} - 28 q^{72} + 14 q^{73} + 21 q^{74} + 19 q^{75} + 5 q^{76} + 34 q^{77} + 9 q^{78} + 3 q^{79} + 58 q^{80} + 4 q^{81} - 9 q^{82} + 38 q^{83} - 78 q^{84} - 27 q^{85} + 49 q^{86} + 8 q^{87} - 25 q^{88} + 125 q^{89} - 74 q^{90} + 6 q^{91} - 35 q^{92} + 36 q^{93} - q^{94} - 12 q^{95} + 26 q^{96} - 2 q^{97} + 18 q^{98} + 56 q^{99}+O(q^{100}) \) 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9 + 5 * q^10 + 9 * q^11 + 15 * q^12 + 28 * q^13 + 20 * q^14 + 4 * q^15 + 32 * q^16 - 7 * q^17 + 10 * q^18 - 3 * q^19 + 53 * q^20 + 25 * q^21 - 14 * q^22 - 6 * q^23 + 10 * q^24 + 45 * q^25 + 6 * q^26 + 8 * q^27 - 12 * q^28 + 25 * q^29 - 43 * q^30 + q^31 + 28 * q^32 + 17 * q^33 + 10 * q^34 + 11 * q^35 + 27 * q^36 + 18 * q^37 + 2 * q^38 + 5 * q^39 + 37 * q^40 + 56 * q^41 - 29 * q^42 - 30 * q^43 + 30 * q^44 + 38 * q^45 - 27 * q^46 + 40 * q^47 + 19 * q^48 + 36 * q^49 + 20 * q^50 - 18 * q^51 + 32 * q^52 + 51 * q^53 - 36 * q^54 - 5 * q^55 - 13 * q^56 + 31 * q^57 - 29 * q^58 + 29 * q^59 + 48 * q^60 + 16 * q^61 - 38 * q^62 - 23 * q^63 - 5 * q^64 + 27 * q^65 + 25 * q^66 - 2 * q^67 - 43 * q^68 + 38 * q^69 + 10 * q^70 + 34 * q^71 - 28 * q^72 + 14 * q^73 + 21 * q^74 + 19 * q^75 + 5 * q^76 + 34 * q^77 + 9 * q^78 + 3 * q^79 + 58 * q^80 + 4 * q^81 - 9 * q^82 + 38 * q^83 - 78 * q^84 - 27 * q^85 + 49 * q^86 + 8 * q^87 - 25 * q^88 + 125 * q^89 - 74 * q^90 + 6 * q^91 - 35 * q^92 + 36 * q^93 - q^94 - 12 * q^95 + 26 * q^96 - 2 * q^97 + 18 * q^98 + 56 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.86443	−1.31835	−0.659174	−	0.751991i	$-0.729094\pi$
$2$	−1.86443	−1.31835	−0.659174	+	0.751991i	$0.729094\pi$
$3$	−1.06486	−0.614800	−0.307400	−	0.951580i	$-0.599459\pi$
$3$	−1.06486	−0.614800	−0.307400	+	0.951580i	$0.599459\pi$
$4$	1.47608	0.738041
$5$	−1.98836	−0.889223	−0.444611	−	0.895724i	$-0.646658\pi$
$5$	−1.98836	−0.889223	−0.444611	+	0.895724i	$0.646658\pi$
$6$	1.98536	0.810520
$7$	3.02740	1.14425	0.572125	−	0.820166i	$-0.306119\pi$
$7$	3.02740	1.14425	0.572125	+	0.820166i	$0.306119\pi$
$8$	0.976806	0.345353
$9$	−1.86606	−0.622022
$10$	3.70715	1.17230
$11$	2.42757	0.731939	0.365969	−	0.930627i	$-0.380738\pi$
$11$	2.42757	0.731939	0.365969	+	0.930627i	$0.380738\pi$
$12$	−1.57183	−0.453747
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−5.64437	−1.50852
$15$	2.11734	0.546694
$16$	−4.77335	−1.19334
$17$	4.07964	0.989458	0.494729	−	0.869047i	$-0.335267\pi$
$17$	4.07964	0.989458	0.494729	+	0.869047i	$0.335267\pi$
$18$	3.47914	0.820041
$19$	−3.36633	−0.772288	−0.386144	−	0.922439i	$-0.626193\pi$
$19$	−3.36633	−0.772288	−0.386144	+	0.922439i	$0.626193\pi$
$20$	−2.93499	−0.656283
$21$	−3.22377	−0.703485
$22$	−4.52601	−0.964950
$23$	5.39068	1.12403	0.562017	−	0.827126i	$-0.310026\pi$
$23$	5.39068	1.12403	0.562017	+	0.827126i	$0.310026\pi$
$24$	−1.04017	−0.212323
$25$	−1.04642	−0.209283
$26$	−1.86443	−0.365644
$27$	5.18170	0.997218
$28$	4.46869	0.844504
$29$	−0.660947	−0.122735	−0.0613674	−	0.998115i	$-0.519546\pi$
$29$	−0.660947	−0.122735	−0.0613674	+	0.998115i	$0.519546\pi$
$30$	−3.94761	−0.720732
$31$	−6.17209	−1.10854	−0.554270	−	0.832337i	$-0.687003\pi$
$31$	−6.17209	−1.10854	−0.554270	+	0.832337i	$0.687003\pi$
$32$	6.94594	1.22788
$33$	−2.58503	−0.449995
$34$	−7.60618	−1.30445
$35$	−6.01957	−1.01749
$36$	−2.75446	−0.459077
$37$	−2.56588	−0.421828	−0.210914	−	0.977505i	$-0.567644\pi$
$37$	−2.56588	−0.421828	−0.210914	+	0.977505i	$0.567644\pi$
$38$	6.27626	1.01814
$39$	−1.06486	−0.170515
$40$	−1.94224	−0.307096
$41$	−4.00216	−0.625033	−0.312516	−	0.949912i	$-0.601172\pi$
$41$	−4.00216	−0.625033	−0.312516	+	0.949912i	$0.601172\pi$
$42$	6.01048	0.927438
$43$	2.06098	0.314296	0.157148	−	0.987575i	$-0.449770\pi$
$43$	2.06098	0.314296	0.157148	+	0.987575i	$0.449770\pi$
$44$	3.58329	0.540201
$45$	3.71041	0.553116
$46$	−10.0505	−1.48187
$47$	−1.76376	−0.257271	−0.128636	−	0.991692i	$-0.541060\pi$
$47$	−1.76376	−0.257271	−0.128636	+	0.991692i	$0.541060\pi$
$48$	5.08296	0.733663
$49$	2.16517	0.309309
$50$	1.95096	0.275908
$51$	−4.34426	−0.608318
$52$	1.47608	0.204696
$53$	−3.55452	−0.488251	−0.244125	−	0.969744i	$-0.578501\pi$
$53$	−3.55452	−0.488251	−0.244125	+	0.969744i	$0.578501\pi$
$54$	−9.66089	−1.31468
$55$	−4.82688	−0.650856
$56$	2.95719	0.395170
$57$	3.58468	0.474802
$58$	1.23229	0.161807
$59$	9.16593	1.19330	0.596651	−	0.802500i	$-0.296497\pi$
$59$	9.16593	1.19330	0.596651	+	0.802500i	$0.296497\pi$
$60$	3.12536	0.403482
$61$	−3.46105	−0.443142	−0.221571	−	0.975144i	$-0.571118\pi$
$61$	−3.46105	−0.443142	−0.221571	+	0.975144i	$0.571118\pi$
$62$	11.5074	1.46144
$63$	−5.64933	−0.711748
$64$	−3.40349	−0.425436
$65$	−1.98836	−0.246626
$66$	4.81959	0.593251
$67$	8.66948	1.05915	0.529573	−	0.848265i	$-0.322352\pi$
$67$	8.66948	1.05915	0.529573	+	0.848265i	$0.322352\pi$
$68$	6.02188	0.730261
$69$	−5.74034	−0.691055
$70$	11.2230	1.34141
$71$	3.23458	0.383874	0.191937	−	0.981407i	$-0.438523\pi$
$71$	3.23458	0.383874	0.191937	+	0.981407i	$0.438523\pi$
$72$	−1.82278	−0.214817
$73$	−10.2331	−1.19770	−0.598849	−	0.800862i	$-0.704375\pi$
$73$	−10.2331	−1.19770	−0.598849	+	0.800862i	$0.704375\pi$
$74$	4.78390	0.556117
$75$	1.11429	0.128667
$76$	−4.96897	−0.569980
$77$	7.34922	0.837521
$78$	1.98536	0.224798
$79$	5.49363	0.618082	0.309041	−	0.951049i	$-0.399992\pi$
$79$	5.49363	0.618082	0.309041	+	0.951049i	$0.399992\pi$
$80$	9.49114	1.06114
$81$	0.0803902	0.00893225
$82$	7.46173	0.824010
$83$	11.4883	1.26101	0.630504	−	0.776186i	$-0.282848\pi$
$83$	11.4883	1.26101	0.630504	+	0.776186i	$0.282848\pi$
$84$	−4.75855	−0.519201
$85$	−8.11180	−0.879848
$86$	−3.84253	−0.414351
$87$	0.703819	0.0754573
$88$	2.37126	0.252777
$89$	17.1365	1.81647	0.908234	−	0.418462i	$-0.137431\pi$
$89$	17.1365	1.81647	0.908234	+	0.418462i	$0.137431\pi$
$90$	−6.91779	−0.729199
$91$	3.02740	0.317358
$92$	7.95708	0.829583
$93$	6.57244	0.681530
$94$	3.28840	0.339173
$95$	6.69347	0.686736
$96$	−7.39648	−0.754900
$97$	−6.92301	−0.702925	−0.351462	−	0.936202i	$-0.614315\pi$
$97$	−6.92301	−0.702925	−0.351462	+	0.936202i	$0.614315\pi$
$98$	−4.03679	−0.407777
$99$	−4.52999	−0.455281
$100$	−1.54460	−0.154460
$101$	16.9183	1.68343	0.841716	−	0.539920i	$-0.181546\pi$
$101$	16.9183	1.68343	0.841716	+	0.539920i	$0.181546\pi$
$102$	8.09955	0.801975
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	0.976806	0.0957837
$105$	6.41003	0.625555
$106$	6.62714	0.643685
$107$	−7.13693	−0.689953	−0.344976	−	0.938611i	$-0.612113\pi$
$107$	−7.13693	−0.689953	−0.344976	+	0.938611i	$0.612113\pi$
$108$	7.64861	0.735988
$109$	7.80900	0.747967	0.373983	−	0.927435i	$-0.377992\pi$
$109$	7.80900	0.747967	0.373983	+	0.927435i	$0.377992\pi$
$110$	8.99936	0.858055
$111$	2.73232	0.259340
$112$	−14.4508	−1.36548
$113$	−14.0187	−1.31877	−0.659384	−	0.751806i	$-0.729183\pi$
$113$	−14.0187	−1.31877	−0.659384	+	0.751806i	$0.729183\pi$
$114$	−6.68337	−0.625955
$115$	−10.7186	−0.999516
$116$	−0.975612	−0.0905833
$117$	−1.86606	−0.172518
$118$	−17.0892	−1.57319
$119$	12.3507	1.13219
$120$	2.06823	0.188802
$121$	−5.10693	−0.464266
$122$	6.45287	0.584215
$123$	4.26176	0.384270
$124$	−9.11051	−0.818148
$125$	12.0225	1.07532
$126$	10.5328	0.938332
$127$	15.9748	1.41753	0.708765	−	0.705444i	$-0.249252\pi$
$127$	15.9748	1.41753	0.708765	+	0.705444i	$0.249252\pi$
$128$	−7.54633	−0.667007
$129$	−2.19466	−0.193229
$130$	3.70715	0.325139
$131$	14.8208	1.29490	0.647450	−	0.762108i	$-0.275835\pi$
$131$	14.8208	1.29490	0.647450	+	0.762108i	$0.275835\pi$
$132$	−3.81571	−0.332115
$133$	−10.1912	−0.883691
$134$	−16.1636	−1.39632
$135$	−10.3031	−0.886749
$136$	3.98502	0.341712
$137$	−0.540460	−0.0461746	−0.0230873	−	0.999733i	$-0.507350\pi$
$137$	−0.540460	−0.0461746	−0.0230873	+	0.999733i	$0.507350\pi$
$138$	10.7024	0.911051
$139$	3.19024	0.270592	0.135296	−	0.990805i	$-0.456801\pi$
$139$	3.19024	0.270592	0.135296	+	0.990805i	$0.456801\pi$
$140$	−8.88538	−0.750952
$141$	1.87817	0.158170
$142$	−6.03063	−0.506079
$143$	2.42757	0.203003
$144$	8.90737	0.742281
$145$	1.31420	0.109139
$146$	19.0789	1.57898
$147$	−2.30561	−0.190163
$148$	−3.78745	−0.311327
$149$	13.7300	1.12480	0.562401	−	0.826864i	$-0.309878\pi$
$149$	13.7300	1.12480	0.562401	+	0.826864i	$0.309878\pi$
$150$	−2.07751	−0.169628
$151$	14.4363	1.17481	0.587404	−	0.809294i	$-0.300150\pi$
$151$	14.4363	1.17481	0.587404	+	0.809294i	$0.300150\pi$
$152$	−3.28825	−0.266712
$153$	−7.61287	−0.615464
$154$	−13.7021	−1.10414
$155$	12.2724	0.985739
$156$	−1.57183	−0.125847
$157$	24.8178	1.98068	0.990338	−	0.138678i	$-0.0442853\pi$
$157$	24.8178	1.98068	0.990338	+	0.138678i	$0.0442853\pi$
$158$	−10.2425	−0.814847
$159$	3.78508	0.300176
$160$	−13.8110	−1.09186
$161$	16.3197	1.28618
$162$	−0.149882	−0.0117758
$163$	−9.24063	−0.723782	−0.361891	−	0.932220i	$-0.617869\pi$
$163$	−9.24063	−0.723782	−0.361891	+	0.932220i	$0.617869\pi$
$164$	−5.90752	−0.461300
$165$	5.13997	0.400146
$166$	−21.4191	−1.66245
$167$	23.0167	1.78109	0.890543	−	0.454899i	$-0.150325\pi$
$167$	23.0167	1.78109	0.890543	+	0.454899i	$0.150325\pi$
$168$	−3.14900	−0.242951
$169$	1.00000	0.0769231
$170$	15.1238	1.15995
$171$	6.28178	0.480380
$172$	3.04217	0.231963
$173$	−21.0269	−1.59864	−0.799322	−	0.600903i	$-0.794808\pi$
$173$	−21.0269	−1.59864	−0.799322	+	0.600903i	$0.794808\pi$
$174$	−1.31222	−0.0994790
$175$	−3.16792	−0.239472
$176$	−11.5876	−0.873449
$177$	−9.76047	−0.733642
$178$	−31.9498	−2.39474
$179$	−4.88406	−0.365052	−0.182526	−	0.983201i	$-0.558427\pi$
$179$	−4.88406	−0.365052	−0.182526	+	0.983201i	$0.558427\pi$
$180$	5.47687	0.408222
$181$	3.60873	0.268235	0.134117	−	0.990965i	$-0.457180\pi$
$181$	3.60873	0.268235	0.134117	+	0.990965i	$0.457180\pi$
$182$	−5.64437	−0.418388
$183$	3.68555	0.272443
$184$	5.26565	0.388189
$185$	5.10190	0.375099
$186$	−12.2538	−0.898494
$187$	9.90359	0.724222
$188$	−2.60346	−0.189877
$189$	15.6871	1.14107
$190$	−12.4795	−0.905357
$191$	−24.3654	−1.76302	−0.881510	−	0.472165i	$-0.843473\pi$
$191$	−24.3654	−1.76302	−0.881510	+	0.472165i	$0.843473\pi$
$192$	3.62425	0.261558
$193$	10.2996	0.741382	0.370691	−	0.928756i	$-0.379121\pi$
$193$	10.2996	0.741382	0.370691	+	0.928756i	$0.379121\pi$
$194$	12.9074	0.926699
$195$	2.11734	0.151626
$196$	3.19596	0.228283
$197$	−8.47452	−0.603785	−0.301892	−	0.953342i	$-0.597618\pi$
$197$	−8.47452	−0.603785	−0.301892	+	0.953342i	$0.597618\pi$
$198$	8.44584	0.600219
$199$	3.37325	0.239123	0.119562	−	0.992827i	$-0.461851\pi$
$199$	3.37325	0.239123	0.119562	+	0.992827i	$0.461851\pi$
$200$	−1.02215	−0.0722766
$201$	−9.23181	−0.651162
$202$	−31.5429	−2.21935
$203$	−2.00095	−0.140439
$204$	−6.41249	−0.448964
$205$	7.95775	0.555793
$206$	1.86443	0.129901
$207$	−10.0594	−0.699173
$208$	−4.77335	−0.330972
$209$	−8.17197	−0.565267
$210$	−11.9510	−0.824698
$211$	8.11475	0.558642	0.279321	−	0.960198i	$-0.409891\pi$
$211$	8.11475	0.558642	0.279321	+	0.960198i	$0.409891\pi$
$212$	−5.24676	−0.360349
$213$	−3.44439	−0.236005
$214$	13.3063	0.909598
$215$	−4.09797	−0.279479
$216$	5.06151	0.344392
$217$	−18.6854	−1.26845
$218$	−14.5593	−0.986080
$219$	10.8969	0.736344
$220$	−7.12487	−0.480359
$221$	4.07964	0.274426
$222$	−5.09420	−0.341900
$223$	−0.839580	−0.0562224	−0.0281112	−	0.999605i	$-0.508949\pi$
$223$	−0.839580	−0.0562224	−0.0281112	+	0.999605i	$0.508949\pi$
$224$	21.0281	1.40500
$225$	1.95268	0.130179
$226$	26.1368	1.73860
$227$	27.8590	1.84906	0.924532	−	0.381104i	$-0.124456\pi$
$227$	27.8590	1.84906	0.924532	+	0.381104i	$0.124456\pi$
$228$	5.29128	0.350424
$229$	13.0560	0.862768	0.431384	−	0.902169i	$-0.358025\pi$
$229$	13.0560	0.862768	0.431384	+	0.902169i	$0.358025\pi$
$230$	19.9841	1.31771
$231$	−7.82592	−0.514908
$232$	−0.645617	−0.0423869
$233$	8.72020	0.571279	0.285640	−	0.958337i	$-0.407794\pi$
$233$	8.72020	0.571279	0.285640	+	0.958337i	$0.407794\pi$
$234$	3.47914	0.227438
$235$	3.50700	0.228771
$236$	13.5297	0.880706
$237$	−5.84997	−0.379996
$238$	−23.0270	−1.49262
$239$	−12.2401	−0.791749	−0.395875	−	0.918305i	$-0.629558\pi$
$239$	−12.2401	−0.791749	−0.395875	+	0.918305i	$0.629558\pi$
$240$	−10.1068	−0.652390
$241$	29.8024	1.91974	0.959871	−	0.280441i	$-0.0904806\pi$
$241$	29.8024	1.91974	0.959871	+	0.280441i	$0.0904806\pi$
$242$	9.52148	0.612064
$243$	−15.6307	−1.00271
$244$	−5.10879	−0.327057
$245$	−4.30513	−0.275045
$246$	−7.94573	−0.506601
$247$	−3.36633	−0.214194
$248$	−6.02894	−0.382838
$249$	−12.2335	−0.775267
$250$	−22.4150	−1.41765
$251$	−12.4926	−0.788524	−0.394262	−	0.918998i	$-0.629000\pi$
$251$	−12.4926	−0.788524	−0.394262	+	0.918998i	$0.629000\pi$
$252$	−8.33887	−0.525300
$253$	13.0862	0.822724
$254$	−29.7837	−1.86880
$255$	8.63797	0.540930
$256$	20.8765	1.30478
$257$	12.6764	0.790732	0.395366	−	0.918524i	$-0.370618\pi$
$257$	12.6764	0.790732	0.395366	+	0.918524i	$0.370618\pi$
$258$	4.09178	0.254743
$259$	−7.76796	−0.482677
$260$	−2.93499	−0.182020
$261$	1.23337	0.0763437
$262$	−27.6323	−1.70713
$263$	5.74329	0.354146	0.177073	−	0.984198i	$-0.443337\pi$
$263$	5.74329	0.354146	0.177073	+	0.984198i	$0.443337\pi$
$264$	−2.52507	−0.155407
$265$	7.06767	0.434164
$266$	19.0008	1.16501
$267$	−18.2481	−1.11676
$268$	12.7969	0.781693
$269$	−21.3920	−1.30429	−0.652146	−	0.758094i	$-0.726131\pi$
$269$	−21.3920	−1.30429	−0.652146	+	0.758094i	$0.726131\pi$
$270$	19.2093	1.16904
$271$	−26.8286	−1.62972	−0.814862	−	0.579655i	$-0.803187\pi$
$271$	−26.8286	−1.62972	−0.814862	+	0.579655i	$0.803187\pi$
$272$	−19.4735	−1.18076
$273$	−3.22377	−0.195112
$274$	1.00765	0.0608741
$275$	−2.54024	−0.153182
$276$	−8.47321	−0.510027
$277$	−17.2257	−1.03499	−0.517497	−	0.855685i	$-0.673136\pi$
$277$	−17.2257	−1.03499	−0.517497	+	0.855685i	$0.673136\pi$
$278$	−5.94796	−0.356735
$279$	11.5175	0.689536
$280$	−5.87996	−0.351395
$281$	−6.59932	−0.393682	−0.196841	−	0.980435i	$-0.563068\pi$
$281$	−6.59932	−0.393682	−0.196841	+	0.980435i	$0.563068\pi$
$282$	−3.50170	−0.208523
$283$	12.9525	0.769944	0.384972	−	0.922928i	$-0.374211\pi$
$283$	12.9525	0.769944	0.384972	+	0.922928i	$0.374211\pi$
$284$	4.77450	0.283315
$285$	−7.12764	−0.422205
$286$	−4.52601	−0.267629
$287$	−12.1162	−0.715194
$288$	−12.9616	−0.763767
$289$	−0.356540	−0.0209729
$290$	−2.45023	−0.143883
$291$	7.37206	0.432158
$292$	−15.1049	−0.883950
$293$	20.8268	1.21672	0.608358	−	0.793662i	$-0.291828\pi$
$293$	20.8268	1.21672	0.608358	+	0.793662i	$0.291828\pi$
$294$	4.29863	0.250701
$295$	−18.2252	−1.06111
$296$	−2.50637	−0.145680
$297$	12.5789	0.729902
$298$	−25.5985	−1.48288
$299$	5.39068	0.311751
$300$	1.64478	0.0949616
$301$	6.23940	0.359633
$302$	−26.9154	−1.54881
$303$	−18.0157	−1.03497
$304$	16.0686	0.921599
$305$	6.88182	0.394052
$306$	14.1936	0.811396
$307$	16.9846	0.969361	0.484680	−	0.874691i	$-0.338936\pi$
$307$	16.9846	0.969361	0.484680	+	0.874691i	$0.338936\pi$
$308$	10.8480	0.618125
$309$	1.06486	0.0605780
$310$	−22.8809	−1.29955
$311$	−25.5354	−1.44798	−0.723989	−	0.689812i	$-0.757693\pi$
$311$	−25.5354	−1.44798	−0.723989	+	0.689812i	$0.757693\pi$
$312$	−1.04017	−0.0588878
$313$	−11.7809	−0.665896	−0.332948	−	0.942945i	$-0.608043\pi$
$313$	−11.7809	−0.665896	−0.332948	+	0.942945i	$0.608043\pi$
$314$	−46.2709	−2.61122
$315$	11.2329	0.632903
$316$	8.10905	0.456170
$317$	16.2256	0.911319	0.455660	−	0.890154i	$-0.349403\pi$
$317$	16.2256	0.911319	0.455660	+	0.890154i	$0.349403\pi$
$318$	−7.05700	−0.395737
$319$	−1.60449	−0.0898343
$320$	6.76736	0.378307
$321$	7.59986	0.424183
$322$	−30.4270	−1.69563
$323$	−13.7334	−0.764146
$324$	0.118663	0.00659237
$325$	−1.04642	−0.0580447
$326$	17.2285	0.954196
$327$	−8.31553	−0.459850
$328$	−3.90934	−0.215857
$329$	−5.33962	−0.294383
$330$	−9.58309	−0.527532
$331$	1.33974	0.0736388	0.0368194	−	0.999322i	$-0.488277\pi$
$331$	1.33974	0.0736388	0.0368194	+	0.999322i	$0.488277\pi$
$332$	16.9577	0.930675
$333$	4.78810	0.262386
$334$	−42.9129	−2.34809
$335$	−17.2381	−0.941816
$336$	15.3882	0.839494
$337$	−7.19469	−0.391919	−0.195960	−	0.980612i	$-0.562782\pi$
$337$	−7.19469	−0.391919	−0.195960	+	0.980612i	$0.562782\pi$
$338$	−1.86443	−0.101411
$339$	14.9280	0.810778
$340$	−11.9737	−0.649364
$341$	−14.9832	−0.811383
$342$	−11.7119	−0.633308
$343$	−14.6370	−0.790323
$344$	2.01317	0.108543
$345$	11.4139	0.614502
$346$	39.2030	2.10757
$347$	19.1922	1.03029	0.515145	−	0.857103i	$-0.327738\pi$
$347$	19.1922	1.03029	0.515145	+	0.857103i	$0.327738\pi$
$348$	1.03889	0.0556906
$349$	20.9114	1.11936	0.559680	−	0.828709i	$-0.310924\pi$
$349$	20.9114	1.11936	0.559680	+	0.828709i	$0.310924\pi$
$350$	5.90635	0.315708
$351$	5.18170	0.276579
$352$	16.8617	0.898732
$353$	0.252725	0.0134512	0.00672560	−	0.999977i	$-0.497859\pi$
$353$	0.252725	0.0134512	0.00672560	+	0.999977i	$0.497859\pi$
$354$	18.1977	0.967195
$355$	−6.43151	−0.341349
$356$	25.2949	1.34063
$357$	−13.1518	−0.696069
$358$	9.10597	0.481265
$359$	−13.4469	−0.709699	−0.354850	−	0.934923i	$-0.615468\pi$
$359$	−13.4469	−0.709699	−0.354850	+	0.934923i	$0.615468\pi$
$360$	3.62435	0.191020
$361$	−7.66785	−0.403571
$362$	−6.72821	−0.353627
$363$	5.43818	0.285431
$364$	4.46869	0.234223
$365$	20.3472	1.06502
$366$	−6.87143	−0.359175
$367$	−6.02128	−0.314308	−0.157154	−	0.987574i	$-0.550232\pi$
$367$	−6.02128	−0.314308	−0.157154	+	0.987574i	$0.550232\pi$
$368$	−25.7316	−1.34135
$369$	7.46829	0.388784
$370$	−9.51212	−0.494511
$371$	−10.7610	−0.558681
$372$	9.70146	0.502997
$373$	−8.33976	−0.431817	−0.215908	−	0.976414i	$-0.569271\pi$
$373$	−8.33976	−0.431817	−0.215908	+	0.976414i	$0.569271\pi$
$374$	−18.4645	−0.954777
$375$	−12.8023	−0.661107
$376$	−1.72285	−0.0888494
$377$	−0.660947	−0.0340405
$378$	−29.2474	−1.50432
$379$	6.21902	0.319450	0.159725	−	0.987162i	$-0.448939\pi$
$379$	6.21902	0.319450	0.159725	+	0.987162i	$0.448939\pi$
$380$	9.88012	0.506839
$381$	−17.0109	−0.871497
$382$	45.4275	2.32427
$383$	−16.0779	−0.821542	−0.410771	−	0.911739i	$-0.634740\pi$
$383$	−16.0779	−0.821542	−0.410771	+	0.911739i	$0.634740\pi$
$384$	8.03581	0.410076
$385$	−14.6129	−0.744743
$386$	−19.2029	−0.977400
$387$	−3.84591	−0.195499
$388$	−10.2189	−0.518787
$389$	22.9750	1.16488	0.582439	−	0.812874i	$-0.302098\pi$
$389$	22.9750	1.16488	0.582439	+	0.812874i	$0.302098\pi$
$390$	−3.94761	−0.199895
$391$	21.9920	1.11218
$392$	2.11495	0.106821
$393$	−15.7821	−0.796104
$394$	15.8001	0.795998
$395$	−10.9233	−0.549612
$396$	−6.68664	−0.336016
$397$	−18.5698	−0.931993	−0.465997	−	0.884786i	$-0.654304\pi$
$397$	−18.5698	−0.931993	−0.465997	+	0.884786i	$0.654304\pi$
$398$	−6.28917	−0.315248
$399$	10.8523	0.543293
$400$	4.99490	0.249745
$401$	22.6502	1.13110	0.565549	−	0.824715i	$-0.308664\pi$
$401$	22.6502	1.13110	0.565549	+	0.824715i	$0.308664\pi$
$402$	17.2120	0.858458
$403$	−6.17209	−0.307454
$404$	24.9728	1.24244
$405$	−0.159845	−0.00794276
$406$	3.73063	0.185148
$407$	−6.22885	−0.308753
$408$	−4.24350	−0.210085
$409$	−2.03170	−0.100461	−0.0502305	−	0.998738i	$-0.515996\pi$
$409$	−2.03170	−0.100461	−0.0502305	+	0.998738i	$0.515996\pi$
$410$	−14.8366	−0.732729
$411$	0.575516	0.0283881
$412$	−1.47608	−0.0727213
$413$	27.7490	1.36544
$414$	18.7549	0.921753
$415$	−22.8430	−1.12132
$416$	6.94594	0.340552
$417$	−3.39717	−0.166360
$418$	15.2360	0.745219
$419$	−22.7747	−1.11262	−0.556310	−	0.830975i	$-0.687783\pi$
$419$	−22.7747	−1.11262	−0.556310	+	0.830975i	$0.687783\pi$
$420$	9.46172	0.461685
$421$	−33.1551	−1.61588	−0.807939	−	0.589266i	$-0.799417\pi$
$421$	−33.1551	−1.61588	−0.807939	+	0.589266i	$0.799417\pi$
$422$	−15.1293	−0.736485
$423$	3.29130	0.160028
$424$	−3.47208	−0.168619
$425$	−4.26900	−0.207077
$426$	6.42180	0.311137
$427$	−10.4780	−0.507065
$428$	−10.5347	−0.509213
$429$	−2.58503	−0.124806
$430$	7.64035	0.368450
$431$	21.3088	1.02641	0.513205	−	0.858266i	$-0.328458\pi$
$431$	21.3088	1.02641	0.513205	+	0.858266i	$0.328458\pi$
$432$	−24.7340	−1.19002
$433$	13.3100	0.639636	0.319818	−	0.947479i	$-0.396378\pi$
$433$	13.3100	0.639636	0.319818	+	0.947479i	$0.396378\pi$
$434$	34.8375	1.67226
$435$	−1.39945	−0.0670984
$436$	11.5267	0.552030
$437$	−18.1468	−0.868078
$438$	−20.3164	−0.970757
$439$	4.08461	0.194948	0.0974739	−	0.995238i	$-0.468924\pi$
$439$	4.08461	0.194948	0.0974739	+	0.995238i	$0.468924\pi$
$440$	−4.71493	−0.224775
$441$	−4.04034	−0.192397
$442$	−7.60618	−0.361789
$443$	7.44228	0.353594	0.176797	−	0.984247i	$-0.443426\pi$
$443$	7.44228	0.353594	0.176797	+	0.984247i	$0.443426\pi$
$444$	4.03312	0.191404
$445$	−34.0736	−1.61525
$446$	1.56533	0.0741207
$447$	−14.6205	−0.691528
$448$	−10.3037	−0.486805
$449$	−12.2909	−0.580044	−0.290022	−	0.957020i	$-0.593663\pi$
$449$	−12.2909	−0.580044	−0.290022	+	0.957020i	$0.593663\pi$
$450$	−3.64062	−0.171621
$451$	−9.71551	−0.457485
$452$	−20.6928	−0.973305
$453$	−15.3727	−0.722272
$454$	−51.9410	−2.43771
$455$	−6.01957	−0.282202
$456$	3.50154	0.163974
$457$	8.01179	0.374776	0.187388	−	0.982286i	$-0.439998\pi$
$457$	8.01179	0.374776	0.187388	+	0.982286i	$0.439998\pi$
$458$	−24.3420	−1.13743
$459$	21.1395	0.986705
$460$	−15.8216	−0.737684
$461$	35.2348	1.64105	0.820524	−	0.571613i	$-0.193682\pi$
$461$	35.2348	1.64105	0.820524	+	0.571613i	$0.193682\pi$
$462$	14.5908	0.678827
$463$	12.8946	0.599264	0.299632	−	0.954055i	$-0.403136\pi$
$463$	12.8946	0.599264	0.299632	+	0.954055i	$0.403136\pi$
$464$	3.15493	0.146464
$465$	−13.0684	−0.606032
$466$	−16.2582	−0.753145
$467$	21.0576	0.974430	0.487215	−	0.873282i	$-0.338013\pi$
$467$	21.0576	0.974430	0.487215	+	0.873282i	$0.338013\pi$
$468$	−2.75446	−0.127325
$469$	26.2460	1.21193
$470$	−6.53854	−0.301600
$471$	−26.4276	−1.21772
$472$	8.95334	0.412111
$473$	5.00315	0.230045
$474$	10.9068	0.500967
$475$	3.52258	0.161627
$476$	18.2307	0.835601
$477$	6.63296	0.303703
$478$	22.8208	1.04380
$479$	20.9822	0.958700	0.479350	−	0.877624i	$-0.340872\pi$
$479$	20.9822	0.958700	0.479350	+	0.877624i	$0.340872\pi$
$480$	14.7069	0.671274
$481$	−2.56588	−0.116994
$482$	−55.5644	−2.53089
$483$	−17.3783	−0.790741
$484$	−7.53824	−0.342647
$485$	13.7654	0.625057
$486$	29.1423	1.32192
$487$	−9.88329	−0.447855	−0.223927	−	0.974606i	$-0.571888\pi$
$487$	−9.88329	−0.447855	−0.223927	+	0.974606i	$0.571888\pi$
$488$	−3.38077	−0.153040
$489$	9.84001	0.444981
$490$	8.02660	0.362605
$491$	−0.210775	−0.00951213	−0.00475606	−	0.999989i	$-0.501514\pi$
$491$	−0.210775	−0.00951213	−0.00475606	+	0.999989i	$0.501514\pi$
$492$	6.29070	0.283607
$493$	−2.69643	−0.121441
$494$	6.27626	0.282382
$495$	9.00727	0.404847
$496$	29.4615	1.32286
$497$	9.79237	0.439248
$498$	22.8085	1.02207
$499$	14.5021	0.649202	0.324601	−	0.945851i	$-0.394770\pi$
$499$	14.5021	0.649202	0.324601	+	0.945851i	$0.394770\pi$
$500$	17.7461	0.793632
$501$	−24.5097	−1.09501
$502$	23.2915	1.03955
$503$	−11.5725	−0.515993	−0.257997	−	0.966146i	$-0.583062\pi$
$503$	−11.5725	−0.515993	−0.257997	+	0.966146i	$0.583062\pi$
$504$	−5.51830	−0.245805
$505$	−33.6397	−1.49695
$506$	−24.3983	−1.08464
$507$	−1.06486	−0.0472923
$508$	23.5801	1.04620
$509$	18.4253	0.816689	0.408345	−	0.912828i	$-0.366106\pi$
$509$	18.4253	0.816689	0.408345	+	0.912828i	$0.366106\pi$
$510$	−16.1048	−0.713134
$511$	−30.9798	−1.37047
$512$	−23.8301	−1.05315
$513$	−17.4433	−0.770140
$514$	−23.6342	−1.04246
$515$	1.98836	0.0876177
$516$	−3.23950	−0.142611
$517$	−4.28165	−0.188307
$518$	14.4828	0.636337
$519$	22.3908	0.982846
$520$	−1.94224	−0.0851731
$521$	14.5768	0.638622	0.319311	−	0.947650i	$-0.396549\pi$
$521$	14.5768	0.638622	0.319311	+	0.947650i	$0.396549\pi$
$522$	−2.29953	−0.100648
$523$	16.1789	0.707455	0.353727	−	0.935349i	$-0.384914\pi$
$523$	16.1789	0.707455	0.353727	+	0.935349i	$0.384914\pi$
$524$	21.8767	0.955689
$525$	3.37341	0.147227
$526$	−10.7079	−0.466888
$527$	−25.1799	−1.09685
$528$	12.3392	0.536996
$529$	6.05939	0.263452
$530$	−13.1772	−0.572379
$531$	−17.1042	−0.742260
$532$	−15.0431	−0.652200
$533$	−4.00216	−0.173353
$534$	34.0222	1.47228
$535$	14.1908	0.613521
$536$	8.46840	0.365779
$537$	5.20086	0.224434
$538$	39.8837	1.71951
$539$	5.25608	0.226395
$540$	−15.2082	−0.654457
$541$	22.7548	0.978305	0.489152	−	0.872198i	$-0.337306\pi$
$541$	22.7548	0.978305	0.489152	+	0.872198i	$0.337306\pi$
$542$	50.0200	2.14854
$543$	−3.84281	−0.164911
$544$	28.3369	1.21494
$545$	−15.5271	−0.665109
$546$	6.01048	0.257225
$547$	3.36493	0.143874	0.0719371	−	0.997409i	$-0.477082\pi$
$547$	3.36493	0.143874	0.0719371	+	0.997409i	$0.477082\pi$
$548$	−0.797763	−0.0340787
$549$	6.45854	0.275644
$550$	4.73609	0.201948
$551$	2.22496	0.0947866
$552$	−5.60720	−0.238658
$553$	16.6314	0.707240
$554$	32.1161	1.36448
$555$	−5.43283	−0.230611
$556$	4.70905	0.199708
$557$	26.6742	1.13022	0.565111	−	0.825015i	$-0.308833\pi$
$557$	26.6742	1.13022	0.565111	+	0.825015i	$0.308833\pi$
$558$	−21.4736	−0.909048
$559$	2.06098	0.0871700
$560$	28.7335	1.21421
$561$	−10.5460	−0.445252
$562$	12.3039	0.519010
$563$	−0.608018	−0.0256249	−0.0128124	−	0.999918i	$-0.504078\pi$
$563$	−0.608018	−0.0256249	−0.0128124	+	0.999918i	$0.504078\pi$
$564$	2.77233	0.116736
$565$	27.8743	1.17268
$566$	−24.1489	−1.01505
$567$	0.243374	0.0102207
$568$	3.15956	0.132572
$569$	16.9496	0.710564	0.355282	−	0.934759i	$-0.384385\pi$
$569$	16.9496	0.710564	0.355282	+	0.934759i	$0.384385\pi$
$570$	13.2890	0.556613
$571$	17.2842	0.723321	0.361660	−	0.932310i	$-0.382210\pi$
$571$	17.2842	0.723321	0.361660	+	0.932310i	$0.382210\pi$
$572$	3.58329	0.149825
$573$	25.9459	1.08390
$574$	22.5897	0.942874
$575$	−5.64089	−0.235241
$576$	6.35112	0.264630
$577$	2.00433	0.0834414	0.0417207	−	0.999129i	$-0.486716\pi$
$577$	2.00433	0.0834414	0.0417207	+	0.999129i	$0.486716\pi$
$578$	0.664742	0.0276496
$579$	−10.9677	−0.455802
$580$	1.93987	0.0805487
$581$	34.7798	1.44291
$582$	−13.7447	−0.569734
$583$	−8.62883	−0.357370
$584$	−9.99578	−0.413629
$585$	3.71041	0.153407
$586$	−38.8301	−1.60406
$587$	5.70815	0.235601	0.117800	−	0.993037i	$-0.462416\pi$
$587$	5.70815	0.235601	0.117800	+	0.993037i	$0.462416\pi$
$588$	−3.40326	−0.140348
$589$	20.7773	0.856112
$590$	33.9795	1.39891
$591$	9.02422	0.371207
$592$	12.2478	0.503383
$593$	43.8766	1.80180	0.900898	−	0.434031i	$-0.142909\pi$
$593$	43.8766	1.80180	0.900898	+	0.434031i	$0.142909\pi$
$594$	−23.4524	−0.962265
$595$	−24.5577	−1.00677
$596$	20.2666	0.830150
$597$	−3.59205	−0.147013
$598$	−10.0505	−0.410996
$599$	12.1458	0.496266	0.248133	−	0.968726i	$-0.420183\pi$
$599$	12.1458	0.496266	0.248133	+	0.968726i	$0.420183\pi$
$600$	1.08845	0.0444356
$601$	−14.5933	−0.595275	−0.297637	−	0.954679i	$-0.596199\pi$
$601$	−14.5933	−0.595275	−0.297637	+	0.954679i	$0.596199\pi$
$602$	−11.6329	−0.474122
$603$	−16.1778	−0.658811
$604$	21.3091	0.867057
$605$	10.1544	0.412836
$606$	33.5889	1.36446
$607$	24.7816	1.00585	0.502926	−	0.864329i	$-0.332257\pi$
$607$	24.7816	1.00585	0.502926	+	0.864329i	$0.332257\pi$
$608$	−23.3823	−0.948277
$609$	2.13074	0.0863421
$610$	−12.8306	−0.519497
$611$	−1.76376	−0.0713542
$612$	−11.2372	−0.454238
$613$	30.2285	1.22092	0.610458	−	0.792049i	$-0.290985\pi$
$613$	30.2285	1.22092	0.610458	+	0.792049i	$0.290985\pi$
$614$	−31.6665	−1.27795
$615$	−8.47392	−0.341701
$616$	7.17876	0.289241
$617$	27.3613	1.10152	0.550761	−	0.834663i	$-0.314337\pi$
$617$	27.3613	1.10152	0.550761	+	0.834663i	$0.314337\pi$
$618$	−1.98536	−0.0798629
$619$	8.55044	0.343671	0.171836	−	0.985126i	$-0.445030\pi$
$619$	8.55044	0.343671	0.171836	+	0.985126i	$0.445030\pi$
$620$	18.1150	0.727516
$621$	27.9329	1.12091
$622$	47.6088	1.90894
$623$	51.8792	2.07850
$624$	5.08296	0.203481
$625$	−18.6729	−0.746917
$626$	21.9646	0.877883
$627$	8.70204	0.347526
$628$	36.6331	1.46182
$629$	−10.4679	−0.417382
$630$	−20.9429	−0.834386
$631$	−26.8295	−1.06806	−0.534032	−	0.845464i	$-0.679324\pi$
$631$	−26.8295	−1.06806	−0.534032	+	0.845464i	$0.679324\pi$
$632$	5.36621	0.213456
$633$	−8.64110	−0.343453
$634$	−30.2514	−1.20144
$635$	−31.7636	−1.26050
$636$	5.58709	0.221543
$637$	2.16517	0.0857870
$638$	2.99146	0.118433
$639$	−6.03593	−0.238778
$640$	15.0048	0.593118
$641$	35.4976	1.40207	0.701035	−	0.713127i	$-0.252722\pi$
$641$	35.4976	1.40207	0.701035	+	0.713127i	$0.252722\pi$
$642$	−14.1694	−0.559220
$643$	−37.0323	−1.46041	−0.730205	−	0.683228i	$-0.760576\pi$
$643$	−37.0323	−1.46041	−0.730205	+	0.683228i	$0.760576\pi$
$644$	24.0893	0.949251
$645$	4.36378	0.171824
$646$	25.6049	1.00741
$647$	−30.8208	−1.21169	−0.605845	−	0.795583i	$-0.707165\pi$
$647$	−30.8208	−1.21169	−0.605845	+	0.795583i	$0.707165\pi$
$648$	0.0785257	0.00308478
$649$	22.2509	0.873424
$650$	1.95096	0.0765231
$651$	19.8974	0.779841
$652$	−13.6399	−0.534180
$653$	29.6362	1.15975	0.579876	−	0.814705i	$-0.303101\pi$
$653$	29.6362	1.15975	0.579876	+	0.814705i	$0.303101\pi$
$654$	15.5037	0.606242
$655$	−29.4691	−1.15145
$656$	19.1037	0.745874
$657$	19.0957	0.744993
$658$	9.95532	0.388099
$659$	−23.9211	−0.931833	−0.465916	−	0.884829i	$-0.654275\pi$
$659$	−23.9211	−0.931833	−0.465916	+	0.884829i	$0.654275\pi$
$660$	7.58702	0.295324
$661$	−17.6038	−0.684707	−0.342353	−	0.939571i	$-0.611224\pi$
$661$	−17.6038	−0.684707	−0.342353	+	0.939571i	$0.611224\pi$
$662$	−2.49785	−0.0970816
$663$	−4.34426	−0.168717
$664$	11.2219	0.435493
$665$	20.2638	0.785798
$666$	−8.92706	−0.345917
$667$	−3.56295	−0.137958
$668$	33.9745	1.31451
$669$	0.894038	0.0345655
$670$	32.1391	1.24164
$671$	−8.40192	−0.324353
$672$	−22.3921	−0.863794
$673$	−0.243565	−0.00938874	−0.00469437	−	0.999989i	$-0.501494\pi$
$673$	−0.243565	−0.00938874	−0.00469437	+	0.999989i	$0.501494\pi$
$674$	13.4140	0.516686
$675$	−5.42221	−0.208701
$676$	1.47608	0.0567724
$677$	−7.66629	−0.294639	−0.147320	−	0.989089i	$-0.547065\pi$
$677$	−7.66629	−0.294639	−0.147320	+	0.989089i	$0.547065\pi$
$678$	−27.8322	−1.06889
$679$	−20.9587	−0.804322
$680$	−7.92366	−0.303858
$681$	−29.6660	−1.13680
$682$	27.9350	1.06969
$683$	−32.2963	−1.23578	−0.617892	−	0.786263i	$-0.712013\pi$
$683$	−32.2963	−1.23578	−0.617892	+	0.786263i	$0.712013\pi$
$684$	9.27242	0.354540
$685$	1.07463	0.0410595
$686$	27.2896	1.04192
$687$	−13.9029	−0.530429
$688$	−9.83775	−0.375061
$689$	−3.55452	−0.135416
$690$	−21.2803	−0.810128
$691$	−39.5383	−1.50411	−0.752054	−	0.659102i	$-0.770937\pi$
$691$	−39.5383	−1.50411	−0.752054	+	0.659102i	$0.770937\pi$
$692$	−31.0374	−1.17986
$693$	−13.7141	−0.520956
$694$	−35.7824	−1.35828
$695$	−6.34334	−0.240617
$696$	0.687495	0.0260594
$697$	−16.3274	−0.618443
$698$	−38.9877	−1.47571
$699$	−9.28582	−0.351222
$700$	−4.67611	−0.176740
$701$	−5.67973	−0.214520	−0.107260	−	0.994231i	$-0.534208\pi$
$701$	−5.67973	−0.214520	−0.107260	+	0.994231i	$0.534208\pi$
$702$	−9.66089	−0.364627
$703$	8.63759	0.325773
$704$	−8.26218	−0.311393
$705$	−3.73448	−0.140649
$706$	−0.471187	−0.0177334
$707$	51.2185	1.92627
$708$	−14.4073	−0.541458
$709$	32.0132	1.20228	0.601140	−	0.799144i	$-0.294713\pi$
$709$	32.0132	1.20228	0.601140	+	0.799144i	$0.294713\pi$
$710$	11.9911	0.450017
$711$	−10.2515	−0.384460
$712$	16.7391	0.627323
$713$	−33.2717	−1.24604
$714$	24.5206	0.917660
$715$	−4.82688	−0.180515
$716$	−7.20928	−0.269423
$717$	13.0341	0.486767
$718$	25.0707	0.935630
$719$	−4.89714	−0.182633	−0.0913163	−	0.995822i	$-0.529107\pi$
$719$	−4.89714	−0.182633	−0.0913163	+	0.995822i	$0.529107\pi$
$720$	−17.7111	−0.660053
$721$	−3.02740	−0.112746
$722$	14.2961	0.532047
$723$	−31.7355	−1.18026
$724$	5.32678	0.197968
$725$	0.691626	0.0256863
$726$	−10.1391	−0.376297
$727$	−39.6134	−1.46918	−0.734590	−	0.678512i	$-0.762625\pi$
$727$	−39.6134	−1.46918	−0.734590	+	0.678512i	$0.762625\pi$
$728$	2.95719	0.109601
$729$	16.4034	0.607533
$730$	−37.9358	−1.40407
$731$	8.40804	0.310982
$732$	5.44017	0.201074
$733$	−13.6295	−0.503418	−0.251709	−	0.967803i	$-0.580993\pi$
$733$	−13.6295	−0.503418	−0.251709	+	0.967803i	$0.580993\pi$
$734$	11.2262	0.414368
$735$	4.58438	0.169097
$736$	37.4433	1.38018
$737$	21.0457	0.775229
$738$	−13.9241	−0.512552
$739$	−6.49144	−0.238791	−0.119396	−	0.992847i	$-0.538096\pi$
$739$	−6.49144	−0.238791	−0.119396	+	0.992847i	$0.538096\pi$
$740$	7.53083	0.276839
$741$	3.58468	0.131686
$742$	20.0630	0.736536
$743$	−5.17475	−0.189843	−0.0949215	−	0.995485i	$-0.530260\pi$
$743$	−5.17475	−0.189843	−0.0949215	+	0.995485i	$0.530260\pi$
$744$	6.42000	0.235369
$745$	−27.3001	−1.00020
$746$	15.5489	0.569284
$747$	−21.4380	−0.784374
$748$	14.6185	0.534506
$749$	−21.6063	−0.789479
$750$	23.8689	0.871570
$751$	38.1387	1.39170	0.695850	−	0.718187i	$-0.255028\pi$
$751$	38.1387	1.39170	0.695850	+	0.718187i	$0.255028\pi$
$752$	8.41905	0.307011
$753$	13.3029	0.484784
$754$	1.23229	0.0448772
$755$	−28.7046	−1.04467
$756$	23.1554	0.842154
$757$	8.22743	0.299031	0.149516	−	0.988759i	$-0.452229\pi$
$757$	8.22743	0.299031	0.149516	+	0.988759i	$0.452229\pi$
$758$	−11.5949	−0.421146
$759$	−13.9350	−0.505810
$760$	6.53823	0.237166
$761$	33.9794	1.23175	0.615876	−	0.787843i	$-0.288802\pi$
$761$	33.9794	1.23175	0.615876	+	0.787843i	$0.288802\pi$
$762$	31.7156	1.14894
$763$	23.6410	0.855861
$764$	−35.9654	−1.30118
$765$	15.1371	0.547285
$766$	29.9760	1.08308
$767$	9.16593	0.330963
$768$	−22.2307	−0.802180
$769$	3.18429	0.114828	0.0574142	−	0.998350i	$-0.481714\pi$
$769$	3.18429	0.114828	0.0574142	+	0.998350i	$0.481714\pi$
$770$	27.2447	0.981830
$771$	−13.4986	−0.486141
$772$	15.2031	0.547171
$773$	−53.8670	−1.93746	−0.968731	−	0.248113i	$-0.920190\pi$
$773$	−53.8670	−1.93746	−0.968731	+	0.248113i	$0.920190\pi$
$774$	7.17042	0.257735
$775$	6.45857	0.231999
$776$	−6.76244	−0.242757
$777$	8.27182	0.296750
$778$	−42.8352	−1.53571
$779$	13.4726	0.482705
$780$	3.12536	0.111906
$781$	7.85215	0.280972
$782$	−41.0025	−1.46625
$783$	−3.42483	−0.122393
$784$	−10.3351	−0.369110
$785$	−49.3468	−1.76126
$786$	29.4246	1.04954
$787$	−12.0175	−0.428378	−0.214189	−	0.976792i	$-0.568711\pi$
$787$	−12.0175	−0.428378	−0.214189	+	0.976792i	$0.568711\pi$
$788$	−12.5091	−0.445618
$789$	−6.11582	−0.217729
$790$	20.3657	0.724580
$791$	−42.4403	−1.50900
$792$	−4.42493	−0.157233
$793$	−3.46105	−0.122905
$794$	34.6221	1.22869
$795$	−7.52611	−0.266924
$796$	4.97919	0.176483
$797$	35.0214	1.24052	0.620260	−	0.784396i	$-0.287027\pi$
$797$	35.0214	1.24052	0.620260	+	0.784396i	$0.287027\pi$
$798$	−20.2332	−0.716249
$799$	−7.19552	−0.254559
$800$	−7.26833	−0.256974
$801$	−31.9779	−1.12988
$802$	−42.2296	−1.49118
$803$	−24.8416	−0.876641
$804$	−13.6269	−0.480584
$805$	−32.4496	−1.14370
$806$	11.5074	0.405331
$807$	22.7795	0.801878
$808$	16.5259	0.581379
$809$	10.3025	0.362216	0.181108	−	0.983463i	$-0.442032\pi$
$809$	10.3025	0.362216	0.181108	+	0.983463i	$0.442032\pi$
$810$	0.298019	0.0104713
$811$	−3.08729	−0.108410	−0.0542048	−	0.998530i	$-0.517262\pi$
$811$	−3.08729	−0.108410	−0.0542048	+	0.998530i	$0.517262\pi$
$812$	−2.95357	−0.103650
$813$	28.5689	1.00195
$814$	11.6132	0.407043
$815$	18.3737	0.643603
$816$	20.7367	0.725928
$817$	−6.93791	−0.242727
$818$	3.78795	0.132442
$819$	−5.64933	−0.197403
$820$	11.7463	0.410198
$821$	−40.5176	−1.41408	−0.707038	−	0.707176i	$-0.749969\pi$
$821$	−40.5176	−1.41408	−0.707038	+	0.707176i	$0.749969\pi$
$822$	−1.07301	−0.0374254
$823$	−36.5986	−1.27575	−0.637874	−	0.770141i	$-0.720186\pi$
$823$	−36.5986	−1.27575	−0.637874	+	0.770141i	$0.720186\pi$
$824$	−0.976806	−0.0340287
$825$	2.70501	0.0941765
$826$	−51.7359	−1.80012
$827$	−52.5678	−1.82796	−0.913981	−	0.405757i	$-0.867008\pi$
$827$	−52.5678	−1.82796	−0.913981	+	0.405757i	$0.867008\pi$
$828$	−14.8484	−0.516018
$829$	2.29622	0.0797510	0.0398755	−	0.999205i	$-0.487304\pi$
$829$	2.29622	0.0797510	0.0398755	+	0.999205i	$0.487304\pi$
$830$	42.5890	1.47829
$831$	18.3431	0.636314
$832$	−3.40349	−0.117995
$833$	8.83309	0.306049
$834$	6.33376	0.219320
$835$	−45.7655	−1.58378
$836$	−12.0625	−0.417190
$837$	−31.9819	−1.10546
$838$	42.4618	1.46682
$839$	53.7235	1.85474	0.927371	−	0.374143i	$-0.122063\pi$
$839$	53.7235	1.85474	0.927371	+	0.374143i	$0.122063\pi$
$840$	6.26135	0.216037
$841$	−28.5631	−0.984936
$842$	61.8151	2.13029
$843$	7.02738	0.242036
$844$	11.9780	0.412301
$845$	−1.98836	−0.0684017
$846$	−6.13638	−0.210973
$847$	−15.4607	−0.531237
$848$	16.9670	0.582648
$849$	−13.7926	−0.473361
$850$	7.95923	0.272999
$851$	−13.8318	−0.474149
$852$	−5.08420	−0.174182
$853$	−12.3422	−0.422589	−0.211295	−	0.977422i	$-0.567768\pi$
$853$	−12.3422	−0.422589	−0.211295	+	0.977422i	$0.567768\pi$
$854$	19.5354	0.668489
$855$	−12.4905	−0.427165
$856$	−6.97139	−0.238277
$857$	−55.2770	−1.88823	−0.944113	−	0.329622i	$-0.893079\pi$
$857$	−55.2770	−1.88823	−0.944113	+	0.329622i	$0.893079\pi$
$858$	4.81959	0.164538
$859$	46.6503	1.59169	0.795844	−	0.605501i	$-0.207027\pi$
$859$	46.6503	1.59169	0.795844	+	0.605501i	$0.207027\pi$
$860$	−6.04893	−0.206267
$861$	12.9021	0.439701
$862$	−39.7287	−1.35317
$863$	10.9587	0.373040	0.186520	−	0.982451i	$-0.440279\pi$
$863$	10.9587	0.373040	0.186520	+	0.982451i	$0.440279\pi$
$864$	35.9917	1.22446
$865$	41.8090	1.42155
$866$	−24.8155	−0.843263
$867$	0.379666	0.0128941
$868$	−27.5812	−0.936166
$869$	13.3361	0.452398
$870$	2.60916	0.0884590
$871$	8.66948	0.293754
$872$	7.62788	0.258313
$873$	12.9188	0.437234
$874$	33.8333	1.14443
$875$	36.3968	1.23044
$876$	16.0847	0.543452
$877$	−6.10274	−0.206075	−0.103038	−	0.994677i	$-0.532856\pi$
$877$	−6.10274	−0.206075	−0.103038	+	0.994677i	$0.532856\pi$
$878$	−7.61545	−0.257009
$879$	−22.1778	−0.748037
$880$	23.0404	0.776691
$881$	−46.3302	−1.56091	−0.780453	−	0.625215i	$-0.785011\pi$
$881$	−46.3302	−1.56091	−0.780453	+	0.625215i	$0.785011\pi$
$882$	7.53291	0.253646
$883$	−7.59877	−0.255719	−0.127859	−	0.991792i	$-0.540811\pi$
$883$	−7.59877	−0.255719	−0.127859	+	0.991792i	$0.540811\pi$
$884$	6.02188	0.202538
$885$	19.4074	0.652371
$886$	−13.8756	−0.466159
$887$	−22.6034	−0.758949	−0.379474	−	0.925202i	$-0.623895\pi$
$887$	−22.6034	−0.758949	−0.379474	+	0.925202i	$0.623895\pi$
$888$	2.66894	0.0895639
$889$	48.3620	1.62201
$890$	63.5277	2.12945
$891$	0.195153	0.00653786
$892$	−1.23929	−0.0414944
$893$	5.93740	0.198688
$894$	27.2589	0.911675
$895$	9.71129	0.324612
$896$	−22.8458	−0.763223
$897$	−5.74034	−0.191664
$898$	22.9155	0.764700
$899$	4.07943	0.136056
$900$	2.88231	0.0960771
$901$	−14.5012	−0.483104
$902$	18.1138	0.603125
$903$	−6.64411	−0.221102
$904$	−13.6936	−0.455441
$905$	−7.17546	−0.238520
$906$	28.6612	0.952205
$907$	−38.7278	−1.28593	−0.642967	−	0.765894i	$-0.722297\pi$
$907$	−38.7278	−1.28593	−0.642967	+	0.765894i	$0.722297\pi$
$908$	41.1221	1.36469
$909$	−31.5706	−1.04713
$910$	11.2230	0.372040
$911$	−20.2879	−0.672168	−0.336084	−	0.941832i	$-0.609103\pi$
$911$	−20.2879	−0.672168	−0.336084	+	0.941832i	$0.609103\pi$
$912$	−17.1109	−0.566599
$913$	27.8887	0.922980
$914$	−14.9374	−0.494085
$915$	−7.32820	−0.242263
$916$	19.2718	0.636758
$917$	44.8685	1.48169
$918$	−39.4129	−1.30082
$919$	−22.7223	−0.749539	−0.374769	−	0.927118i	$-0.622278\pi$
$919$	−22.7223	−0.749539	−0.374769	+	0.927118i	$0.622278\pi$
$920$	−10.4700	−0.345186
$921$	−18.0863	−0.595962
$922$	−65.6926	−2.16347
$923$	3.23458	0.106467
$924$	−11.5517	−0.380023
$925$	2.68498	0.0882816
$926$	−24.0411	−0.790039
$927$	1.86606	0.0612896
$928$	−4.59090	−0.150704
$929$	−33.6052	−1.10255	−0.551276	−	0.834323i	$-0.685859\pi$
$929$	−33.6052	−1.10255	−0.551276	+	0.834323i	$0.685859\pi$
$930$	24.3650	0.798961
$931$	−7.28865	−0.238876
$932$	12.8717	0.421627
$933$	27.1917	0.890216
$934$	−39.2604	−1.28464
$935$	−19.6919	−0.643995
$936$	−1.82278	−0.0595795
$937$	37.4256	1.22264	0.611321	−	0.791383i	$-0.290638\pi$
$937$	37.4256	1.22264	0.611321	+	0.791383i	$0.290638\pi$
$938$	−48.9337	−1.59774
$939$	12.5451	0.409393
$940$	5.17662	0.168843
$941$	43.0126	1.40217	0.701086	−	0.713077i	$-0.252699\pi$
$941$	43.0126	1.40217	0.701086	+	0.713077i	$0.252699\pi$
$942$	49.2722	1.60538
$943$	−21.5744	−0.702558
$944$	−43.7522	−1.42401
$945$	−31.1916	−1.01466
$946$	−9.32800	−0.303280
$947$	−6.10449	−0.198369	−0.0991847	−	0.995069i	$-0.531623\pi$
$947$	−6.10449	−0.198369	−0.0991847	+	0.995069i	$0.531623\pi$
$948$	−8.63503	−0.280453
$949$	−10.2331	−0.332181
$950$	−6.56758	−0.213080
$951$	−17.2780	−0.560279
$952$	12.0643	0.391005
$953$	−1.23497	−0.0400045	−0.0200023	−	0.999800i	$-0.506367\pi$
$953$	−1.23497	−0.0400045	−0.0200023	+	0.999800i	$0.506367\pi$
$954$	−12.3667	−0.400386
$955$	48.4473	1.56772
$956$	−18.0675	−0.584343
$957$	1.70857	0.0552301
$958$	−39.1197	−1.26390
$959$	−1.63619	−0.0528353
$960$	−7.20632	−0.232583
$961$	7.09471	0.228862
$962$	4.78390	0.154239
$963$	13.3180	0.429165
$964$	43.9908	1.41685
$965$	−20.4794	−0.659254
$966$	32.4006	1.04247
$967$	29.5365	0.949829	0.474915	−	0.880032i	$-0.342479\pi$
$967$	29.5365	0.949829	0.474915	+	0.880032i	$0.342479\pi$
$968$	−4.98848	−0.160336
$969$	14.6242	0.469797
$970$	−25.6646	−0.824042
$971$	−1.80387	−0.0578890	−0.0289445	−	0.999581i	$-0.509215\pi$
$971$	−1.80387	−0.0578890	−0.0289445	+	0.999581i	$0.509215\pi$
$972$	−23.0722	−0.740041
$973$	9.65813	0.309625
$974$	18.4267	0.590428
$975$	1.11429	0.0356859
$976$	16.5208	0.528817
$977$	−25.4886	−0.815454	−0.407727	−	0.913104i	$-0.633678\pi$
$977$	−25.4886	−0.815454	−0.407727	+	0.913104i	$0.633678\pi$
$978$	−18.3460	−0.586639
$979$	41.6001	1.32954
$980$	−6.35473	−0.202994
$981$	−14.5721	−0.465251
$982$	0.392974	0.0125403
$983$	−12.9023	−0.411518	−0.205759	−	0.978603i	$-0.565966\pi$
$983$	−12.9023	−0.411518	−0.205759	+	0.978603i	$0.565966\pi$
$984$	4.16291	0.132709
$985$	16.8504	0.536899
$986$	5.02729	0.160101
$987$	5.68597	0.180986
$988$	−4.96897	−0.158084
$989$	11.1101	0.353279
$990$	−16.7934	−0.533729
$991$	36.3309	1.15409	0.577044	−	0.816713i	$-0.304206\pi$
$991$	36.3309	1.15409	0.577044	+	0.816713i	$0.304206\pi$
$992$	−42.8709	−1.36115
$993$	−1.42664	−0.0452731
$994$	−18.2571	−0.579081
$995$	−6.70724	−0.212634
$996$	−18.0577	−0.572179
$997$	6.64375	0.210410	0.105205	−	0.994451i	$-0.466450\pi$
$997$	6.64375	0.210410	0.105205	+	0.994451i	$0.466450\pi$
$998$	−27.0380	−0.855874
$999$	−13.2956	−0.420655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.f.1.5	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.f.1.5	✓	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q-1.86443 q^{2} -1.06486 q^{3} +1.47608 q^{4} -1.98836 q^{5} +1.98536 q^{6} +3.02740 q^{7} +0.976806 q^{8} -1.86606 q^{9} +O(q^{10})\)	\(q-1.86443 q^{2} -1.06486 q^{3} +1.47608 q^{4} -1.98836 q^{5} +1.98536 q^{6} +3.02740 q^{7} +0.976806 q^{8} -1.86606 q^{9} +3.70715 q^{10} +2.42757 q^{11} -1.57183 q^{12} +1.00000 q^{13} -5.64437 q^{14} +2.11734 q^{15} -4.77335 q^{16} +4.07964 q^{17} +3.47914 q^{18} -3.36633 q^{19} -2.93499 q^{20} -3.22377 q^{21} -4.52601 q^{22} +5.39068 q^{23} -1.04017 q^{24} -1.04642 q^{25} -1.86443 q^{26} +5.18170 q^{27} +4.46869 q^{28} -0.660947 q^{29} -3.94761 q^{30} -6.17209 q^{31} +6.94594 q^{32} -2.58503 q^{33} -7.60618 q^{34} -6.01957 q^{35} -2.75446 q^{36} -2.56588 q^{37} +6.27626 q^{38} -1.06486 q^{39} -1.94224 q^{40} -4.00216 q^{41} +6.01048 q^{42} +2.06098 q^{43} +3.58329 q^{44} +3.71041 q^{45} -10.0505 q^{46} -1.76376 q^{47} +5.08296 q^{48} +2.16517 q^{49} +1.95096 q^{50} -4.34426 q^{51} +1.47608 q^{52} -3.55452 q^{53} -9.66089 q^{54} -4.82688 q^{55} +2.95719 q^{56} +3.58468 q^{57} +1.23229 q^{58} +9.16593 q^{59} +3.12536 q^{60} -3.46105 q^{61} +11.5074 q^{62} -5.64933 q^{63} -3.40349 q^{64} -1.98836 q^{65} +4.81959 q^{66} +8.66948 q^{67} +6.02188 q^{68} -5.74034 q^{69} +11.2230 q^{70} +3.23458 q^{71} -1.82278 q^{72} -10.2331 q^{73} +4.78390 q^{74} +1.11429 q^{75} -4.96897 q^{76} +7.34922 q^{77} +1.98536 q^{78} +5.49363 q^{79} +9.49114 q^{80} +0.0803902 q^{81} +7.46173 q^{82} +11.4883 q^{83} -4.75855 q^{84} -8.11180 q^{85} -3.84253 q^{86} +0.703819 q^{87} +2.37126 q^{88} +17.1365 q^{89} -6.91779 q^{90} +3.02740 q^{91} +7.95708 q^{92} +6.57244 q^{93} +3.28840 q^{94} +6.69347 q^{95} -7.39648 q^{96} -6.92301 q^{97} -4.03679 q^{98} -4.52999 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9}+O(q^{10}) \) 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9	\( 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9} + 5 q^{10} + 9 q^{11} + 15 q^{12} + 28 q^{13} + 20 q^{14} + 4 q^{15} + 32 q^{16} - 7 q^{17} + 10 q^{18} - 3 q^{19} + 53 q^{20} + 25 q^{21} - 14 q^{22} - 6 q^{23} + 10 q^{24} + 45 q^{25} + 6 q^{26} + 8 q^{27} - 12 q^{28} + 25 q^{29} - 43 q^{30} + q^{31} + 28 q^{32} + 17 q^{33} + 10 q^{34} + 11 q^{35} + 27 q^{36} + 18 q^{37} + 2 q^{38} + 5 q^{39} + 37 q^{40} + 56 q^{41} - 29 q^{42} - 30 q^{43} + 30 q^{44} + 38 q^{45} - 27 q^{46} + 40 q^{47} + 19 q^{48} + 36 q^{49} + 20 q^{50} - 18 q^{51} + 32 q^{52} + 51 q^{53} - 36 q^{54} - 5 q^{55} - 13 q^{56} + 31 q^{57} - 29 q^{58} + 29 q^{59} + 48 q^{60} + 16 q^{61} - 38 q^{62} - 23 q^{63} - 5 q^{64} + 27 q^{65} + 25 q^{66} - 2 q^{67} - 43 q^{68} + 38 q^{69} + 10 q^{70} + 34 q^{71} - 28 q^{72} + 14 q^{73} + 21 q^{74} + 19 q^{75} + 5 q^{76} + 34 q^{77} + 9 q^{78} + 3 q^{79} + 58 q^{80} + 4 q^{81} - 9 q^{82} + 38 q^{83} - 78 q^{84} - 27 q^{85} + 49 q^{86} + 8 q^{87} - 25 q^{88} + 125 q^{89} - 74 q^{90} + 6 q^{91} - 35 q^{92} + 36 q^{93} - q^{94} - 12 q^{95} + 26 q^{96} - 2 q^{97} + 18 q^{98} + 56 q^{99}+O(q^{100}) \) 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9 + 5 * q^10 + 9 * q^11 + 15 * q^12 + 28 * q^13 + 20 * q^14 + 4 * q^15 + 32 * q^16 - 7 * q^17 + 10 * q^18 - 3 * q^19 + 53 * q^20 + 25 * q^21 - 14 * q^22 - 6 * q^23 + 10 * q^24 + 45 * q^25 + 6 * q^26 + 8 * q^27 - 12 * q^28 + 25 * q^29 - 43 * q^30 + q^31 + 28 * q^32 + 17 * q^33 + 10 * q^34 + 11 * q^35 + 27 * q^36 + 18 * q^37 + 2 * q^38 + 5 * q^39 + 37 * q^40 + 56 * q^41 - 29 * q^42 - 30 * q^43 + 30 * q^44 + 38 * q^45 - 27 * q^46 + 40 * q^47 + 19 * q^48 + 36 * q^49 + 20 * q^50 - 18 * q^51 + 32 * q^52 + 51 * q^53 - 36 * q^54 - 5 * q^55 - 13 * q^56 + 31 * q^57 - 29 * q^58 + 29 * q^59 + 48 * q^60 + 16 * q^61 - 38 * q^62 - 23 * q^63 - 5 * q^64 + 27 * q^65 + 25 * q^66 - 2 * q^67 - 43 * q^68 + 38 * q^69 + 10 * q^70 + 34 * q^71 - 28 * q^72 + 14 * q^73 + 21 * q^74 + 19 * q^75 + 5 * q^76 + 34 * q^77 + 9 * q^78 + 3 * q^79 + 58 * q^80 + 4 * q^81 - 9 * q^82 + 38 * q^83 - 78 * q^84 - 27 * q^85 + 49 * q^86 + 8 * q^87 - 25 * q^88 + 125 * q^89 - 74 * q^90 + 6 * q^91 - 35 * q^92 + 36 * q^93 - q^94 - 12 * q^95 + 26 * q^96 - 2 * q^97 + 18 * q^98 + 56 * q^99

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