LMFDB - Embedded newform 1339.2.a.g.1.10

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			1.10
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)

$f(q)$	$=$	$q-1.25596 q^{2} +2.77119 q^{3} -0.422559 q^{4} -3.18202 q^{5} -3.48051 q^{6} +3.63505 q^{7} +3.04264 q^{8} +4.67947 q^{9} +O(q^{10})$	\(q-1.25596 q^{2} +2.77119 q^{3} -0.422559 q^{4} -3.18202 q^{5} -3.48051 q^{6} +3.63505 q^{7} +3.04264 q^{8} +4.67947 q^{9} +3.99650 q^{10} +2.33209 q^{11} -1.17099 q^{12} -1.00000 q^{13} -4.56548 q^{14} -8.81798 q^{15} -2.97633 q^{16} -1.15111 q^{17} -5.87724 q^{18} +0.749660 q^{19} +1.34459 q^{20} +10.0734 q^{21} -2.92902 q^{22} +3.47342 q^{23} +8.43173 q^{24} +5.12527 q^{25} +1.25596 q^{26} +4.65414 q^{27} -1.53602 q^{28} +8.01226 q^{29} +11.0750 q^{30} -5.92087 q^{31} -2.34713 q^{32} +6.46267 q^{33} +1.44575 q^{34} -11.5668 q^{35} -1.97735 q^{36} -10.3093 q^{37} -0.941545 q^{38} -2.77119 q^{39} -9.68176 q^{40} +5.56935 q^{41} -12.6518 q^{42} +0.0136198 q^{43} -0.985447 q^{44} -14.8902 q^{45} -4.36248 q^{46} +12.7163 q^{47} -8.24796 q^{48} +6.21358 q^{49} -6.43714 q^{50} -3.18993 q^{51} +0.422559 q^{52} +8.86216 q^{53} -5.84542 q^{54} -7.42078 q^{55} +11.0602 q^{56} +2.07745 q^{57} -10.0631 q^{58} +0.498406 q^{59} +3.72611 q^{60} +10.4810 q^{61} +7.43639 q^{62} +17.0101 q^{63} +8.90056 q^{64} +3.18202 q^{65} -8.11687 q^{66} -9.20070 q^{67} +0.486410 q^{68} +9.62548 q^{69} +14.5275 q^{70} +5.49956 q^{71} +14.2380 q^{72} -4.39641 q^{73} +12.9480 q^{74} +14.2031 q^{75} -0.316775 q^{76} +8.47728 q^{77} +3.48051 q^{78} +13.5970 q^{79} +9.47074 q^{80} -1.14094 q^{81} -6.99489 q^{82} +4.87270 q^{83} -4.25660 q^{84} +3.66285 q^{85} -0.0171060 q^{86} +22.2035 q^{87} +7.09573 q^{88} -8.79038 q^{89} +18.7015 q^{90} -3.63505 q^{91} -1.46772 q^{92} -16.4078 q^{93} -15.9711 q^{94} -2.38543 q^{95} -6.50434 q^{96} +0.309080 q^{97} -7.80402 q^{98} +10.9130 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.25596	−0.888099	−0.444050	−	0.896002i	$-0.646459\pi$
$2$	−1.25596	−0.888099	−0.444050	+	0.896002i	$0.646459\pi$
$3$	2.77119	1.59995	0.799973	−	0.600037i	$-0.204847\pi$
$3$	2.77119	1.59995	0.799973	+	0.600037i	$0.204847\pi$
$4$	−0.422559	−0.211279
$5$	−3.18202	−1.42304	−0.711522	−	0.702664i	$-0.751994\pi$
$5$	−3.18202	−1.42304	−0.711522	+	0.702664i	$0.751994\pi$
$6$	−3.48051	−1.42091
$7$	3.63505	1.37392	0.686960	−	0.726696i	$-0.258945\pi$
$7$	3.63505	1.37392	0.686960	+	0.726696i	$0.258945\pi$
$8$	3.04264	1.07574
$9$	4.67947	1.55982
$10$	3.99650	1.26380
$11$	2.33209	0.703153	0.351577	−	0.936159i	$-0.385646\pi$
$11$	2.33209	0.703153	0.351577	+	0.936159i	$0.385646\pi$
$12$	−1.17099	−0.338035
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.56548	−1.22018
$15$	−8.81798	−2.27679
$16$	−2.97633	−0.744082
$17$	−1.15111	−0.279185	−0.139592	−	0.990209i	$-0.544579\pi$
$17$	−1.15111	−0.279185	−0.139592	+	0.990209i	$0.544579\pi$
$18$	−5.87724	−1.38528
$19$	0.749660	0.171984	0.0859919	−	0.996296i	$-0.472594\pi$
$19$	0.749660	0.171984	0.0859919	+	0.996296i	$0.472594\pi$
$20$	1.34459	0.300660
$21$	10.0734	2.19820
$22$	−2.92902	−0.624470
$23$	3.47342	0.724257	0.362129	−	0.932128i	$-0.382050\pi$
$23$	3.47342	0.724257	0.362129	+	0.932128i	$0.382050\pi$
$24$	8.43173	1.72112
$25$	5.12527	1.02505
$26$	1.25596	0.246314
$27$	4.65414	0.895689
$28$	−1.53602	−0.290281
$29$	8.01226	1.48784	0.743920	−	0.668269i	$-0.232964\pi$
$29$	8.01226	1.48784	0.743920	+	0.668269i	$0.232964\pi$
$30$	11.0750	2.02202
$31$	−5.92087	−1.06342	−0.531710	−	0.846926i	$-0.678450\pi$
$31$	−5.92087	−1.06342	−0.531710	+	0.846926i	$0.678450\pi$
$32$	−2.34713	−0.414918
$33$	6.46267	1.12501
$34$	1.44575	0.247944
$35$	−11.5668	−1.95515
$36$	−1.97735	−0.329559
$37$	−10.3093	−1.69483	−0.847416	−	0.530929i	$-0.821843\pi$
$37$	−10.3093	−1.69483	−0.847416	+	0.530929i	$0.821843\pi$
$38$	−0.941545	−0.152739
$39$	−2.77119	−0.443745
$40$	−9.68176	−1.53082
$41$	5.56935	0.869786	0.434893	−	0.900482i	$-0.356786\pi$
$41$	5.56935	0.869786	0.434893	+	0.900482i	$0.356786\pi$
$42$	−12.6518	−1.95222
$43$	0.0136198	0.00207700	0.00103850	−	0.999999i	$-0.499669\pi$
$43$	0.0136198	0.00207700	0.00103850	+	0.999999i	$0.499669\pi$
$44$	−0.985447	−0.148562
$45$	−14.8902	−2.21970
$46$	−4.36248	−0.643213
$47$	12.7163	1.85486	0.927428	−	0.374001i	$-0.122014\pi$
$47$	12.7163	1.85486	0.927428	+	0.374001i	$0.122014\pi$
$48$	−8.24796	−1.19049
$49$	6.21358	0.887654
$50$	−6.43714	−0.910349
$51$	−3.18993	−0.446680
$52$	0.422559	0.0585983
$53$	8.86216	1.21731	0.608656	−	0.793435i	$-0.291709\pi$
$53$	8.86216	1.21731	0.608656	+	0.793435i	$0.291709\pi$
$54$	−5.84542	−0.795461
$55$	−7.42078	−1.00062
$56$	11.0602	1.47798
$57$	2.07745	0.275165
$58$	−10.0631	−1.32135
$59$	0.498406	0.0648870	0.0324435	−	0.999474i	$-0.489671\pi$
$59$	0.498406	0.0648870	0.0324435	+	0.999474i	$0.489671\pi$
$60$	3.72611	0.481039
$61$	10.4810	1.34195	0.670977	−	0.741478i	$-0.265875\pi$
$61$	10.4810	1.34195	0.670977	+	0.741478i	$0.265875\pi$
$62$	7.43639	0.944423
$63$	17.0101	2.14307
$64$	8.90056	1.11257
$65$	3.18202	0.394681
$66$	−8.11687	−0.999118
$67$	−9.20070	−1.12404	−0.562022	−	0.827122i	$-0.689977\pi$
$67$	−9.20070	−1.12404	−0.562022	+	0.827122i	$0.689977\pi$
$68$	0.486410	0.0589859
$69$	9.62548	1.15877
$70$	14.5275	1.73637
$71$	5.49956	0.652678	0.326339	−	0.945253i	$-0.394185\pi$
$71$	5.49956	0.652678	0.326339	+	0.945253i	$0.394185\pi$
$72$	14.2380	1.67796
$73$	−4.39641	−0.514561	−0.257281	−	0.966337i	$-0.582826\pi$
$73$	−4.39641	−0.514561	−0.257281	+	0.966337i	$0.582826\pi$
$74$	12.9480	1.50518
$75$	14.2031	1.64003
$76$	−0.316775	−0.0363366
$77$	8.47728	0.966075
$78$	3.48051	0.394090
$79$	13.5970	1.52978	0.764891	−	0.644160i	$-0.222793\pi$
$79$	13.5970	1.52978	0.764891	+	0.644160i	$0.222793\pi$
$80$	9.47074	1.05886
$81$	−1.14094	−0.126771
$82$	−6.99489	−0.772456
$83$	4.87270	0.534848	0.267424	−	0.963579i	$-0.413828\pi$
$83$	4.87270	0.534848	0.267424	+	0.963579i	$0.413828\pi$
$84$	−4.25660	−0.464433
$85$	3.66285	0.397292
$86$	−0.0171060	−0.00184459
$87$	22.2035	2.38046
$88$	7.09573	0.756407
$89$	−8.79038	−0.931779	−0.465889	−	0.884843i	$-0.654266\pi$
$89$	−8.79038	−0.931779	−0.465889	+	0.884843i	$0.654266\pi$
$90$	18.7015	1.97131
$91$	−3.63505	−0.381057
$92$	−1.46772	−0.153021
$93$	−16.4078	−1.70141
$94$	−15.9711	−1.64730
$95$	−2.38543	−0.244740
$96$	−6.50434	−0.663846
$97$	0.309080	0.0313823	0.0156912	−	0.999877i	$-0.495005\pi$
$97$	0.309080	0.0313823	0.0156912	+	0.999877i	$0.495005\pi$
$98$	−7.80402	−0.788325
$99$	10.9130	1.09680
$100$	−2.16573	−0.216573
$101$	16.7849	1.67016	0.835078	−	0.550132i	$-0.185423\pi$
$101$	16.7849	1.67016	0.835078	+	0.550132i	$0.185423\pi$
$102$	4.00644	0.396696
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−3.04264	−0.298356
$105$	−32.0538	−3.12813
$106$	−11.1305	−1.08109
$107$	5.62127	0.543429	0.271715	−	0.962378i	$-0.412409\pi$
$107$	5.62127	0.543429	0.271715	+	0.962378i	$0.412409\pi$
$108$	−1.96665	−0.189241
$109$	10.0403	0.961685	0.480842	−	0.876807i	$-0.340331\pi$
$109$	10.0403	0.961685	0.480842	+	0.876807i	$0.340331\pi$
$110$	9.32022	0.888648
$111$	−28.5689	−2.71164
$112$	−10.8191	−1.02231
$113$	−7.34116	−0.690598	−0.345299	−	0.938493i	$-0.612223\pi$
$113$	−7.34116	−0.690598	−0.345299	+	0.938493i	$0.612223\pi$
$114$	−2.60920	−0.244374
$115$	−11.0525	−1.03065
$116$	−3.38565	−0.314350
$117$	−4.67947	−0.432618
$118$	−0.625979	−0.0576261
$119$	−4.18433	−0.383577
$120$	−26.8300	−2.44923
$121$	−5.56133	−0.505576
$122$	−13.1637	−1.19179
$123$	15.4337	1.39161
$124$	2.50192	0.224679
$125$	−0.398605	−0.0356523
$126$	−21.3641	−1.90326
$127$	4.64960	0.412585	0.206293	−	0.978490i	$-0.433860\pi$
$127$	4.64960	0.412585	0.206293	+	0.978490i	$0.433860\pi$
$128$	−6.48451	−0.573155
$129$	0.0377431	0.00332309
$130$	−3.99650	−0.350516
$131$	9.29310	0.811942	0.405971	−	0.913886i	$-0.366933\pi$
$131$	9.29310	0.811942	0.405971	+	0.913886i	$0.366933\pi$
$132$	−2.73086	−0.237691
$133$	2.72505	0.236292
$134$	11.5557	0.998264
$135$	−14.8096	−1.27460
$136$	−3.50241	−0.300329
$137$	−12.8451	−1.09743	−0.548715	−	0.836010i	$-0.684883\pi$
$137$	−12.8451	−1.09743	−0.548715	+	0.836010i	$0.684883\pi$
$138$	−12.0892	−1.02910
$139$	−1.53359	−0.130077	−0.0650387	−	0.997883i	$-0.520717\pi$
$139$	−1.53359	−0.130077	−0.0650387	+	0.997883i	$0.520717\pi$
$140$	4.88765	0.413082
$141$	35.2391	2.96767
$142$	−6.90724	−0.579643
$143$	−2.33209	−0.195020
$144$	−13.9276	−1.16064
$145$	−25.4952	−2.11726
$146$	5.52173	0.456981
$147$	17.2190	1.42020
$148$	4.35627	0.358083
$149$	−20.4184	−1.67274	−0.836370	−	0.548165i	$-0.815326\pi$
$149$	−20.4184	−1.67274	−0.836370	+	0.548165i	$0.815326\pi$
$150$	−17.8385	−1.45651
$151$	−11.4873	−0.934819	−0.467410	−	0.884041i	$-0.654813\pi$
$151$	−11.4873	−0.934819	−0.467410	+	0.884041i	$0.654813\pi$
$152$	2.28095	0.185009
$153$	−5.38658	−0.435479
$154$	−10.6471	−0.857971
$155$	18.8403	1.51329
$156$	1.17099	0.0937541
$157$	−4.56965	−0.364697	−0.182349	−	0.983234i	$-0.558370\pi$
$157$	−4.56965	−0.364697	−0.182349	+	0.983234i	$0.558370\pi$
$158$	−17.0773	−1.35860
$159$	24.5587	1.94763
$160$	7.46862	0.590446
$161$	12.6260	0.995071
$162$	1.43298	0.112586
$163$	18.4365	1.44405	0.722027	−	0.691864i	$-0.243210\pi$
$163$	18.4365	1.44405	0.722027	+	0.691864i	$0.243210\pi$
$164$	−2.35338	−0.183768
$165$	−20.5644	−1.60093
$166$	−6.11993	−0.474998
$167$	−11.9693	−0.926210	−0.463105	−	0.886303i	$-0.653265\pi$
$167$	−11.9693	−0.926210	−0.463105	+	0.886303i	$0.653265\pi$
$168$	30.6497	2.36468
$169$	1.00000	0.0769231
$170$	−4.60040	−0.352835
$171$	3.50801	0.268265
$172$	−0.00575517	−0.000438828 0
$173$	−2.93658	−0.223264	−0.111632	−	0.993750i	$-0.535608\pi$
$173$	−2.93658	−0.223264	−0.111632	+	0.993750i	$0.535608\pi$
$174$	−27.8867	−2.11409
$175$	18.6306	1.40834
$176$	−6.94108	−0.523203
$177$	1.38118	0.103816
$178$	11.0404	0.827512
$179$	−1.95394	−0.146044	−0.0730221	−	0.997330i	$-0.523264\pi$
$179$	−1.95394	−0.146044	−0.0730221	+	0.997330i	$0.523264\pi$
$180$	6.29198	0.468977
$181$	−19.3557	−1.43870	−0.719349	−	0.694648i	$-0.755560\pi$
$181$	−19.3557	−1.43870	−0.719349	+	0.694648i	$0.755560\pi$
$182$	4.56548	0.338416
$183$	29.0448	2.14705
$184$	10.5684	0.779110
$185$	32.8043	2.41182
$186$	20.6076	1.51102
$187$	−2.68449	−0.196309
$188$	−5.37336	−0.391893
$189$	16.9180	1.23060
$190$	2.99602	0.217354
$191$	−17.6617	−1.27795	−0.638977	−	0.769225i	$-0.720642\pi$
$191$	−17.6617	−1.27795	−0.638977	+	0.769225i	$0.720642\pi$
$192$	24.6651	1.78005
$193$	−12.7246	−0.915936	−0.457968	−	0.888969i	$-0.651423\pi$
$193$	−12.7246	−0.915936	−0.457968	+	0.888969i	$0.651423\pi$
$194$	−0.388193	−0.0278706
$195$	8.81798	0.631469
$196$	−2.62560	−0.187543
$197$	9.97573	0.710741	0.355371	−	0.934725i	$-0.384355\pi$
$197$	9.97573	0.710741	0.355371	+	0.934725i	$0.384355\pi$
$198$	−13.7063	−0.974064
$199$	15.1772	1.07588	0.537940	−	0.842983i	$-0.319203\pi$
$199$	15.1772	1.07588	0.537940	+	0.842983i	$0.319203\pi$
$200$	15.5944	1.10269
$201$	−25.4969	−1.79841
$202$	−21.0811	−1.48326
$203$	29.1250	2.04417
$204$	1.34793	0.0943742
$205$	−17.7218	−1.23774
$206$	−1.25596	−0.0875070
$207$	16.2538	1.12971
$208$	2.97633	0.206371
$209$	1.74828	0.120931
$210$	40.2583	2.77809
$211$	−2.63745	−0.181570	−0.0907848	−	0.995871i	$-0.528938\pi$
$211$	−2.63745	−0.181570	−0.0907848	+	0.995871i	$0.528938\pi$
$212$	−3.74478	−0.257193
$213$	15.2403	1.04425
$214$	−7.06011	−0.482619
$215$	−0.0433386	−0.00295567
$216$	14.1609	0.963525
$217$	−21.5227	−1.46105
$218$	−12.6102	−0.854072
$219$	−12.1833	−0.823270
$220$	3.13571	0.211410
$221$	1.15111	0.0774319
$222$	35.8814	2.40821
$223$	14.4910	0.970386	0.485193	−	0.874407i	$-0.338749\pi$
$223$	14.4910	0.970386	0.485193	+	0.874407i	$0.338749\pi$
$224$	−8.53193	−0.570064
$225$	23.9836	1.59890
$226$	9.22022	0.613320
$227$	5.36728	0.356239	0.178119	−	0.984009i	$-0.442999\pi$
$227$	5.36728	0.356239	0.178119	+	0.984009i	$0.442999\pi$
$228$	−0.877843	−0.0581366
$229$	−20.3619	−1.34555	−0.672777	−	0.739845i	$-0.734899\pi$
$229$	−20.3619	−1.34555	−0.672777	+	0.739845i	$0.734899\pi$
$230$	13.8815	0.915320
$231$	23.4921	1.54567
$232$	24.3784	1.60052
$233$	−9.56379	−0.626545	−0.313272	−	0.949663i	$-0.601425\pi$
$233$	−9.56379	−0.626545	−0.313272	+	0.949663i	$0.601425\pi$
$234$	5.87724	0.384207
$235$	−40.4634	−2.63954
$236$	−0.210606	−0.0137093
$237$	37.6798	2.44757
$238$	5.25536	0.340655
$239$	−6.61679	−0.428005	−0.214002	−	0.976833i	$-0.568650\pi$
$239$	−6.61679	−0.428005	−0.214002	+	0.976833i	$0.568650\pi$
$240$	26.2452	1.69412
$241$	−1.49340	−0.0961983	−0.0480992	−	0.998843i	$-0.515316\pi$
$241$	−1.49340	−0.0961983	−0.0480992	+	0.998843i	$0.515316\pi$
$242$	6.98483	0.449002
$243$	−17.1242	−1.09852
$244$	−4.42884	−0.283527
$245$	−19.7717	−1.26317
$246$	−19.3841	−1.23589
$247$	−0.749660	−0.0476997
$248$	−18.0151	−1.14396
$249$	13.5032	0.855728
$250$	0.500632	0.0316628
$251$	−28.0957	−1.77339	−0.886694	−	0.462357i	$-0.847004\pi$
$251$	−28.0957	−1.77339	−0.886694	+	0.462357i	$0.847004\pi$
$252$	−7.18777	−0.452787
$253$	8.10034	0.509264
$254$	−5.83972	−0.366417
$255$	10.1504	0.635645
$256$	−9.65682	−0.603552
$257$	−29.1418	−1.81781	−0.908907	−	0.416999i	$-0.863082\pi$
$257$	−29.1418	−1.81781	−0.908907	+	0.416999i	$0.863082\pi$
$258$	−0.0474039	−0.00295124
$259$	−37.4747	−2.32856
$260$	−1.34459	−0.0833880
$261$	37.4932	2.32077
$262$	−11.6718	−0.721085
$263$	16.8256	1.03751	0.518756	−	0.854922i	$-0.326395\pi$
$263$	16.8256	1.03751	0.518756	+	0.854922i	$0.326395\pi$
$264$	19.6636	1.21021
$265$	−28.1996	−1.73229
$266$	−3.42256	−0.209851
$267$	−24.3598	−1.49079
$268$	3.88784	0.237487
$269$	29.4773	1.79726	0.898631	−	0.438706i	$-0.144563\pi$
$269$	29.4773	1.79726	0.898631	+	0.438706i	$0.144563\pi$
$270$	18.6003	1.13198
$271$	8.12474	0.493543	0.246771	−	0.969074i	$-0.420630\pi$
$271$	8.12474	0.493543	0.246771	+	0.969074i	$0.420630\pi$
$272$	3.42607	0.207736
$273$	−10.0734	−0.609670
$274$	16.1329	0.974627
$275$	11.9526	0.720770
$276$	−4.06733	−0.244825
$277$	11.3380	0.681233	0.340617	−	0.940202i	$-0.389364\pi$
$277$	11.3380	0.681233	0.340617	+	0.940202i	$0.389364\pi$
$278$	1.92613	0.115522
$279$	−27.7066	−1.65875
$280$	−35.1937	−2.10322
$281$	−24.4177	−1.45664	−0.728318	−	0.685239i	$-0.759698\pi$
$281$	−24.4177	−1.45664	−0.728318	+	0.685239i	$0.759698\pi$
$282$	−44.2590	−2.63559
$283$	27.6328	1.64260	0.821300	−	0.570497i	$-0.193249\pi$
$283$	27.6328	1.64260	0.821300	+	0.570497i	$0.193249\pi$
$284$	−2.32389	−0.137897
$285$	−6.61048	−0.391571
$286$	2.92902	0.173197
$287$	20.2448	1.19502
$288$	−10.9833	−0.647199
$289$	−15.6750	−0.922056
$290$	32.0210	1.88034
$291$	0.856518	0.0502100
$292$	1.85774	0.108716
$293$	−11.9728	−0.699458	−0.349729	−	0.936851i	$-0.613726\pi$
$293$	−11.9728	−0.699458	−0.349729	+	0.936851i	$0.613726\pi$
$294$	−21.6264	−1.26128
$295$	−1.58594	−0.0923370
$296$	−31.3674	−1.82319
$297$	10.8539	0.629806
$298$	25.6447	1.48556
$299$	−3.47342	−0.200873
$300$	−6.00163	−0.346504
$301$	0.0495087	0.00285363
$302$	14.4276	0.830212
$303$	46.5139	2.67216
$304$	−2.23123	−0.127970
$305$	−33.3508	−1.90966
$306$	6.76534	0.386749
$307$	13.0453	0.744534	0.372267	−	0.928126i	$-0.378580\pi$
$307$	13.0453	0.744534	0.372267	+	0.928126i	$0.378580\pi$
$308$	−3.58215	−0.204112
$309$	2.77119	0.157647
$310$	−23.6628	−1.34395
$311$	4.74425	0.269022	0.134511	−	0.990912i	$-0.457054\pi$
$311$	4.74425	0.269022	0.134511	+	0.990912i	$0.457054\pi$
$312$	−8.43173	−0.477353
$313$	−10.4438	−0.590318	−0.295159	−	0.955448i	$-0.595373\pi$
$313$	−10.4438	−0.590318	−0.295159	+	0.955448i	$0.595373\pi$
$314$	5.73930	0.323888
$315$	−54.1266	−3.04969
$316$	−5.74553	−0.323211
$317$	5.65743	0.317753	0.158876	−	0.987298i	$-0.449213\pi$
$317$	5.65743	0.317753	0.158876	+	0.987298i	$0.449213\pi$
$318$	−30.8448	−1.72969
$319$	18.6854	1.04618
$320$	−28.3218	−1.58324
$321$	15.5776	0.869457
$322$	−15.8578	−0.883722
$323$	−0.862939	−0.0480152
$324$	0.482115	0.0267842
$325$	−5.12527	−0.284299
$326$	−23.1555	−1.28246
$327$	27.8235	1.53864
$328$	16.9455	0.935660
$329$	46.2242	2.54842
$330$	25.8281	1.42179
$331$	−27.0604	−1.48738	−0.743688	−	0.668527i	$-0.766925\pi$
$331$	−27.0604	−1.48738	−0.743688	+	0.668527i	$0.766925\pi$
$332$	−2.05900	−0.113002
$333$	−48.2419	−2.64364
$334$	15.0330	0.822567
$335$	29.2768	1.59956
$336$	−29.9817	−1.63564
$337$	34.2190	1.86403	0.932014	−	0.362422i	$-0.118050\pi$
$337$	34.2190	1.86403	0.932014	+	0.362422i	$0.118050\pi$
$338$	−1.25596	−0.0683153
$339$	−20.3437	−1.10492
$340$	−1.54777	−0.0839396
$341$	−13.8080	−0.747747
$342$	−4.40593	−0.238246
$343$	−2.85868	−0.154354
$344$	0.0414402	0.00223431
$345$	−30.6285	−1.64898
$346$	3.68823	0.198280
$347$	13.1018	0.703344	0.351672	−	0.936123i	$-0.385613\pi$
$347$	13.1018	0.703344	0.351672	+	0.936123i	$0.385613\pi$
$348$	−9.38227	−0.502942
$349$	3.07750	0.164735	0.0823674	−	0.996602i	$-0.473752\pi$
$349$	3.07750	0.164735	0.0823674	+	0.996602i	$0.473752\pi$
$350$	−23.3993	−1.25075
$351$	−4.65414	−0.248419
$352$	−5.47373	−0.291751
$353$	−18.2016	−0.968774	−0.484387	−	0.874854i	$-0.660957\pi$
$353$	−18.2016	−0.968774	−0.484387	+	0.874854i	$0.660957\pi$
$354$	−1.73471	−0.0921986
$355$	−17.4997	−0.928789
$356$	3.71445	0.196866
$357$	−11.5956	−0.613702
$358$	2.45407	0.129702
$359$	2.47794	0.130780	0.0653902	−	0.997860i	$-0.479171\pi$
$359$	2.47794	0.130780	0.0653902	+	0.997860i	$0.479171\pi$
$360$	−45.3055	−2.38781
$361$	−18.4380	−0.970422
$362$	24.3100	1.27771
$363$	−15.4115	−0.808894
$364$	1.53602	0.0805094
$365$	13.9895	0.732243
$366$	−36.4792	−1.90680
$367$	−6.17446	−0.322304	−0.161152	−	0.986930i	$-0.551521\pi$
$367$	−6.17446	−0.322304	−0.161152	+	0.986930i	$0.551521\pi$
$368$	−10.3380	−0.538907
$369$	26.0616	1.35671
$370$	−41.2010	−2.14194
$371$	32.2144	1.67249
$372$	6.93328	0.359474
$373$	−26.8526	−1.39038	−0.695189	−	0.718827i	$-0.744679\pi$
$373$	−26.8526	−1.39038	−0.695189	+	0.718827i	$0.744679\pi$
$374$	3.37162	0.174342
$375$	−1.10461	−0.0570417
$376$	38.6910	1.99534
$377$	−8.01226	−0.412653
$378$	−21.2484	−1.09290
$379$	34.3863	1.76630	0.883152	−	0.469087i	$-0.155417\pi$
$379$	34.3863	1.76630	0.883152	+	0.469087i	$0.155417\pi$
$380$	1.00799	0.0517086
$381$	12.8849	0.660114
$382$	22.1824	1.13495
$383$	−16.4219	−0.839117	−0.419559	−	0.907728i	$-0.637815\pi$
$383$	−16.4219	−0.839117	−0.419559	+	0.907728i	$0.637815\pi$
$384$	−17.9698	−0.917017
$385$	−26.9749	−1.37477
$386$	15.9816	0.813442
$387$	0.0637336	0.00323976
$388$	−0.130604	−0.00663043
$389$	−25.3545	−1.28553	−0.642763	−	0.766065i	$-0.722212\pi$
$389$	−25.3545	−1.28553	−0.642763	+	0.766065i	$0.722212\pi$
$390$	−11.0750	−0.560807
$391$	−3.99827	−0.202201
$392$	18.9057	0.954882
$393$	25.7529	1.29906
$394$	−12.5291	−0.631209
$395$	−43.2659	−2.17695
$396$	−4.61137	−0.231730
$397$	−20.7465	−1.04124	−0.520619	−	0.853789i	$-0.674299\pi$
$397$	−20.7465	−1.04124	−0.520619	+	0.853789i	$0.674299\pi$
$398$	−19.0619	−0.955488
$399$	7.55162	0.378054
$400$	−15.2545	−0.762724
$401$	−25.1563	−1.25624	−0.628122	−	0.778115i	$-0.716176\pi$
$401$	−25.1563	−1.25624	−0.628122	+	0.778115i	$0.716176\pi$
$402$	32.0231	1.59717
$403$	5.92087	0.294940
$404$	−7.09258	−0.352869
$405$	3.63051	0.180401
$406$	−36.5799	−1.81543
$407$	−24.0422	−1.19173
$408$	−9.70583	−0.480510
$409$	12.5674	0.621420	0.310710	−	0.950505i	$-0.399433\pi$
$409$	12.5674	0.621420	0.310710	+	0.950505i	$0.399433\pi$
$410$	22.2579	1.09924
$411$	−35.5961	−1.75583
$412$	−0.422559	−0.0208180
$413$	1.81173	0.0891494
$414$	−20.4141	−1.00330
$415$	−15.5050	−0.761112
$416$	2.34713	0.115078
$417$	−4.24987	−0.208117
$418$	−2.19577	−0.107399
$419$	20.4891	1.00096	0.500479	−	0.865749i	$-0.333157\pi$
$419$	20.4891	1.00096	0.500479	+	0.865749i	$0.333157\pi$
$420$	13.5446	0.660909
$421$	−14.8545	−0.723966	−0.361983	−	0.932185i	$-0.617900\pi$
$421$	−14.8545	−0.723966	−0.361983	+	0.932185i	$0.617900\pi$
$422$	3.31254	0.161252
$423$	59.5054	2.89325
$424$	26.9644	1.30951
$425$	−5.89973	−0.286179
$426$	−19.1413	−0.927397
$427$	38.0989	1.84374
$428$	−2.37532	−0.114815
$429$	−6.46267	−0.312021
$430$	0.0544316	0.00262493
$431$	21.9398	1.05680	0.528401	−	0.848995i	$-0.322792\pi$
$431$	21.9398	1.05680	0.528401	+	0.848995i	$0.322792\pi$
$432$	−13.8522	−0.666466
$433$	12.4487	0.598248	0.299124	−	0.954214i	$-0.403306\pi$
$433$	12.4487	0.598248	0.299124	+	0.954214i	$0.403306\pi$
$434$	27.0316	1.29756
$435$	−70.6520	−3.38750
$436$	−4.24261	−0.203184
$437$	2.60388	0.124561
$438$	15.3017	0.731145
$439$	−30.7360	−1.46695	−0.733474	−	0.679718i	$-0.762102\pi$
$439$	−30.7360	−1.46695	−0.733474	+	0.679718i	$0.762102\pi$
$440$	−22.5788	−1.07640
$441$	29.0763	1.38458
$442$	−1.44575	−0.0687672
$443$	−26.4726	−1.25775	−0.628876	−	0.777506i	$-0.716485\pi$
$443$	−26.4726	−1.25775	−0.628876	+	0.777506i	$0.716485\pi$
$444$	12.0720	0.572913
$445$	27.9712	1.32596
$446$	−18.2001	−0.861799
$447$	−56.5832	−2.67629
$448$	32.3540	1.52858
$449$	10.9783	0.518100	0.259050	−	0.965864i	$-0.416591\pi$
$449$	10.9783	0.518100	0.259050	+	0.965864i	$0.416591\pi$
$450$	−30.1224	−1.41999
$451$	12.9882	0.611593
$452$	3.10207	0.145909
$453$	−31.8333	−1.49566
$454$	−6.74110	−0.316375
$455$	11.5668	0.542260
$456$	6.32093	0.296005
$457$	−12.1462	−0.568177	−0.284088	−	0.958798i	$-0.591691\pi$
$457$	−12.1462	−0.568177	−0.284088	+	0.958798i	$0.591691\pi$
$458$	25.5738	1.19499
$459$	−5.35741	−0.250063
$460$	4.67033	0.217755
$461$	1.91714	0.0892903	0.0446451	−	0.999003i	$-0.485784\pi$
$461$	1.91714	0.0892903	0.0446451	+	0.999003i	$0.485784\pi$
$462$	−29.5052	−1.37271
$463$	−4.35107	−0.202211	−0.101106	−	0.994876i	$-0.532238\pi$
$463$	−4.35107	−0.202211	−0.101106	+	0.994876i	$0.532238\pi$
$464$	−23.8471	−1.10707
$465$	52.2101	2.42119
$466$	12.0118	0.556434
$467$	−23.1301	−1.07033	−0.535166	−	0.844747i	$-0.679751\pi$
$467$	−23.1301	−1.07033	−0.535166	+	0.844747i	$0.679751\pi$
$468$	1.97735	0.0914032
$469$	−33.4450	−1.54435
$470$	50.8205	2.34418
$471$	−12.6633	−0.583496
$472$	1.51647	0.0698013
$473$	0.0317627	0.00146045
$474$	−47.3244	−2.17368
$475$	3.84221	0.176293
$476$	1.76813	0.0810419
$477$	41.4702	1.89879
$478$	8.31044	0.380111
$479$	2.04555	0.0934635	0.0467318	−	0.998907i	$-0.485119\pi$
$479$	2.04555	0.0934635	0.0467318	+	0.998907i	$0.485119\pi$
$480$	20.6969	0.944682
$481$	10.3093	0.470062
$482$	1.87565	0.0854337
$483$	34.9891	1.59206
$484$	2.34999	0.106818
$485$	−0.983499	−0.0446584
$486$	21.5073	0.975592
$487$	−12.5127	−0.567002	−0.283501	−	0.958972i	$-0.591496\pi$
$487$	−12.5127	−0.567002	−0.283501	+	0.958972i	$0.591496\pi$
$488$	31.8899	1.44359
$489$	51.0909	2.31041
$490$	24.8326	1.12182
$491$	9.73731	0.439439	0.219719	−	0.975563i	$-0.429486\pi$
$491$	9.73731	0.439439	0.219719	+	0.975563i	$0.429486\pi$
$492$	−6.52164	−0.294018
$493$	−9.22297	−0.415382
$494$	0.941545	0.0423621
$495$	−34.7253	−1.56079
$496$	17.6224	0.791271
$497$	19.9912	0.896727
$498$	−16.9595	−0.759971
$499$	−0.0739893	−0.00331222	−0.00165611	−	0.999999i	$-0.500527\pi$
$499$	−0.0739893	−0.00331222	−0.00165611	+	0.999999i	$0.500527\pi$
$500$	0.168434	0.00753259
$501$	−33.1691	−1.48189
$502$	35.2872	1.57494
$503$	2.33982	0.104327	0.0521637	−	0.998639i	$-0.483388\pi$
$503$	2.33982	0.104327	0.0521637	+	0.998639i	$0.483388\pi$
$504$	51.7557	2.30538
$505$	−53.4098	−2.37670
$506$	−10.1737	−0.452277
$507$	2.77119	0.123073
$508$	−1.96473	−0.0871707
$509$	26.8441	1.18984	0.594922	−	0.803784i	$-0.297183\pi$
$509$	26.8441	1.18984	0.594922	+	0.803784i	$0.297183\pi$
$510$	−12.7486	−0.564516
$511$	−15.9812	−0.706965
$512$	25.0976	1.10917
$513$	3.48902	0.154044
$514$	36.6010	1.61440
$515$	−3.18202	−0.140217
$516$	−0.0159487	−0.000702100 0
$517$	29.6555	1.30425
$518$	47.0668	2.06800
$519$	−8.13780	−0.357210
$520$	9.68176	0.424573
$521$	−29.9301	−1.31126	−0.655631	−	0.755082i	$-0.727597\pi$
$521$	−29.9301	−1.31126	−0.655631	+	0.755082i	$0.727597\pi$
$522$	−47.0900	−2.06107
$523$	−34.4330	−1.50565	−0.752825	−	0.658220i	$-0.771310\pi$
$523$	−34.4330	−1.50565	−0.752825	+	0.658220i	$0.771310\pi$
$524$	−3.92688	−0.171546
$525$	51.6289	2.25327
$526$	−21.1323	−0.921414
$527$	6.81556	0.296890
$528$	−19.2350	−0.837097
$529$	−10.9354	−0.475451
$530$	35.4176	1.53844
$531$	2.33228	0.101212
$532$	−1.15149	−0.0499236
$533$	−5.56935	−0.241235
$534$	30.5950	1.32397
$535$	−17.8870	−0.773323
$536$	−27.9944	−1.20918
$537$	−5.41473	−0.233663
$538$	−37.0224	−1.59615
$539$	14.4907	0.624157
$540$	6.25791	0.269298
$541$	−40.7784	−1.75320	−0.876601	−	0.481218i	$-0.840195\pi$
$541$	−40.7784	−1.75320	−0.876601	+	0.481218i	$0.840195\pi$
$542$	−10.2044	−0.438315
$543$	−53.6383	−2.30184
$544$	2.70180	0.115839
$545$	−31.9484	−1.36852
$546$	12.6518	0.541447
$547$	−7.55693	−0.323111	−0.161556	−	0.986864i	$-0.551651\pi$
$547$	−7.55693	−0.323111	−0.161556	+	0.986864i	$0.551651\pi$
$548$	5.42780	0.231864
$549$	49.0456	2.09321
$550$	−15.0120	−0.640115
$551$	6.00647	0.255884
$552$	29.2869	1.24653
$553$	49.4257	2.10180
$554$	−14.2401	−0.605003
$555$	90.9069	3.85878
$556$	0.648032	0.0274827
$557$	−30.1928	−1.27931	−0.639656	−	0.768662i	$-0.720923\pi$
$557$	−30.1928	−1.27931	−0.639656	+	0.768662i	$0.720923\pi$
$558$	34.7984	1.47313
$559$	−0.0136198	−0.000576057 0
$560$	34.4266	1.45479
$561$	−7.43923	−0.314084
$562$	30.6677	1.29364
$563$	33.2147	1.39983	0.699916	−	0.714225i	$-0.253221\pi$
$563$	33.2147	1.39983	0.699916	+	0.714225i	$0.253221\pi$
$564$	−14.8906	−0.627007
$565$	23.3597	0.982752
$566$	−34.7058	−1.45879
$567$	−4.14738	−0.174174
$568$	16.7332	0.702109
$569$	12.8077	0.536928	0.268464	−	0.963290i	$-0.413484\pi$
$569$	12.8077	0.536928	0.268464	+	0.963290i	$0.413484\pi$
$570$	8.30252	0.347754
$571$	−37.9316	−1.58739	−0.793695	−	0.608317i	$-0.791845\pi$
$571$	−37.9316	−1.58739	−0.793695	+	0.608317i	$0.791845\pi$
$572$	0.985447	0.0412036
$573$	−48.9438	−2.04466
$574$	−25.4268	−1.06129
$575$	17.8022	0.742403
$576$	41.6499	1.73541
$577$	13.4151	0.558476	0.279238	−	0.960222i	$-0.409918\pi$
$577$	13.4151	0.558476	0.279238	+	0.960222i	$0.409918\pi$
$578$	19.6871	0.818877
$579$	−35.2622	−1.46545
$580$	10.7732	0.447334
$581$	17.7125	0.734838
$582$	−1.07575	−0.0445915
$583$	20.6674	0.855956
$584$	−13.3767	−0.553532
$585$	14.8902	0.615634
$586$	15.0374	0.621188
$587$	12.1072	0.499717	0.249858	−	0.968282i	$-0.419616\pi$
$587$	12.1072	0.499717	0.249858	+	0.968282i	$0.419616\pi$
$588$	−7.27603	−0.300058
$589$	−4.43864	−0.182891
$590$	1.99188	0.0820044
$591$	27.6446	1.13715
$592$	30.6837	1.26109
$593$	7.46342	0.306486	0.153243	−	0.988189i	$-0.451028\pi$
$593$	7.46342	0.306486	0.153243	+	0.988189i	$0.451028\pi$
$594$	−13.6321	−0.559331
$595$	13.3146	0.545847
$596$	8.62797	0.353415
$597$	42.0587	1.72135
$598$	4.36248	0.178395
$599$	25.6243	1.04698	0.523490	−	0.852032i	$-0.324630\pi$
$599$	25.6243	1.04698	0.523490	+	0.852032i	$0.324630\pi$
$600$	43.2149	1.76424
$601$	32.1081	1.30972	0.654859	−	0.755751i	$-0.272728\pi$
$601$	32.1081	1.30972	0.654859	+	0.755751i	$0.272728\pi$
$602$	−0.0621811	−0.00253431
$603$	−43.0545	−1.75331
$604$	4.85404	0.197508
$605$	17.6963	0.719456
$606$	−58.4198	−2.37314
$607$	11.3690	0.461455	0.230727	−	0.973018i	$-0.425889\pi$
$607$	11.3690	0.461455	0.230727	+	0.973018i	$0.425889\pi$
$608$	−1.75955	−0.0713592
$609$	80.7107	3.27056
$610$	41.8873	1.69597
$611$	−12.7163	−0.514445
$612$	2.27614	0.0920077
$613$	5.61461	0.226772	0.113386	−	0.993551i	$-0.463830\pi$
$613$	5.61461	0.226772	0.113386	+	0.993551i	$0.463830\pi$
$614$	−16.3844	−0.661221
$615$	−49.1104	−1.98032
$616$	25.7933	1.03924
$617$	−23.0847	−0.929356	−0.464678	−	0.885480i	$-0.653830\pi$
$617$	−23.0847	−0.929356	−0.464678	+	0.885480i	$0.653830\pi$
$618$	−3.48051	−0.140006
$619$	40.5616	1.63031	0.815155	−	0.579243i	$-0.196652\pi$
$619$	40.5616	1.63031	0.815155	+	0.579243i	$0.196652\pi$
$620$	−7.96115	−0.319728
$621$	16.1658	0.648709
$622$	−5.95860	−0.238918
$623$	−31.9535	−1.28019
$624$	8.24796	0.330183
$625$	−24.3580	−0.974319
$626$	13.1170	0.524261
$627$	4.84480	0.193483
$628$	1.93094	0.0770530
$629$	11.8671	0.473171
$630$	67.9809	2.70843
$631$	−0.900821	−0.0358611	−0.0179306	−	0.999839i	$-0.505708\pi$
$631$	−0.900821	−0.0358611	−0.0179306	+	0.999839i	$0.505708\pi$
$632$	41.3708	1.64564
$633$	−7.30887	−0.290501
$634$	−7.10552	−0.282196
$635$	−14.7951	−0.587127
$636$	−10.3775	−0.411494
$637$	−6.21358	−0.246191
$638$	−23.4681	−0.929111
$639$	25.7351	1.01806
$640$	20.6339	0.815625
$641$	−31.3058	−1.23650	−0.618252	−	0.785980i	$-0.712159\pi$
$641$	−31.3058	−1.23650	−0.618252	+	0.785980i	$0.712159\pi$
$642$	−19.5649	−0.772164
$643$	−26.2596	−1.03558	−0.517789	−	0.855508i	$-0.673245\pi$
$643$	−26.2596	−1.03558	−0.517789	+	0.855508i	$0.673245\pi$
$644$	−5.33524	−0.210238
$645$	−0.120099	−0.00472890
$646$	1.08382	0.0426423
$647$	−25.1146	−0.987356	−0.493678	−	0.869645i	$-0.664348\pi$
$647$	−25.1146	−0.987356	−0.493678	+	0.869645i	$0.664348\pi$
$648$	−3.47148	−0.136373
$649$	1.16233	0.0456255
$650$	6.43714	0.252486
$651$	−59.6433	−2.33760
$652$	−7.79049	−0.305099
$653$	22.6558	0.886591	0.443296	−	0.896375i	$-0.353809\pi$
$653$	22.6558	0.886591	0.443296	+	0.896375i	$0.353809\pi$
$654$	−34.9453	−1.36647
$655$	−29.5708	−1.15543
$656$	−16.5762	−0.647192
$657$	−20.5729	−0.802625
$658$	−58.0559	−2.26325
$659$	37.2851	1.45242	0.726211	−	0.687472i	$-0.241280\pi$
$659$	37.2851	1.45242	0.726211	+	0.687472i	$0.241280\pi$
$660$	8.68965	0.338244
$661$	13.7456	0.534642	0.267321	−	0.963608i	$-0.413862\pi$
$661$	13.7456	0.534642	0.267321	+	0.963608i	$0.413862\pi$
$662$	33.9869	1.32094
$663$	3.18993	0.123887
$664$	14.8259	0.575356
$665$	−8.67117	−0.336254
$666$	60.5900	2.34782
$667$	27.8299	1.07758
$668$	5.05772	0.195689
$669$	40.1571	1.55256
$670$	−36.7706	−1.42057
$671$	24.4427	0.943599
$672$	−23.6436	−0.912071
$673$	−45.7686	−1.76425	−0.882126	−	0.471014i	$-0.843888\pi$
$673$	−45.7686	−1.76425	−0.882126	+	0.471014i	$0.843888\pi$
$674$	−42.9778	−1.65544
$675$	23.8537	0.918129
$676$	−0.422559	−0.0162523
$677$	3.89986	0.149884	0.0749419	−	0.997188i	$-0.476123\pi$
$677$	3.89986	0.149884	0.0749419	+	0.997188i	$0.476123\pi$
$678$	25.5510	0.981279
$679$	1.12352	0.0431168
$680$	11.1447	0.427381
$681$	14.8737	0.569962
$682$	17.3424	0.664074
$683$	−10.6814	−0.408712	−0.204356	−	0.978897i	$-0.565510\pi$
$683$	−10.6814	−0.408712	−0.204356	+	0.978897i	$0.565510\pi$
$684$	−1.48234	−0.0566788
$685$	40.8734	1.56169
$686$	3.59040	0.137082
$687$	−56.4267	−2.15281
$688$	−0.0405370	−0.00154546
$689$	−8.86216	−0.337621
$690$	38.4682	1.46446
$691$	40.0326	1.52291	0.761457	−	0.648216i	$-0.224485\pi$
$691$	40.0326	1.52291	0.761457	+	0.648216i	$0.224485\pi$
$692$	1.24088	0.0471710
$693$	39.6692	1.50691
$694$	−16.4554	−0.624639
$695$	4.87992	0.185106
$696$	67.5572	2.56075
$697$	−6.41092	−0.242831
$698$	−3.86522	−0.146301
$699$	−26.5031	−1.00244
$700$	−7.87252	−0.297553
$701$	−7.29540	−0.275543	−0.137772	−	0.990464i	$-0.543994\pi$
$701$	−7.29540	−0.275543	−0.137772	+	0.990464i	$0.543994\pi$
$702$	5.84542	0.220621
$703$	−7.72844	−0.291484
$704$	20.7570	0.782307
$705$	−112.132	−4.22312
$706$	22.8605	0.860368
$707$	61.0137	2.29466
$708$	−0.583628	−0.0219341
$709$	−29.8952	−1.12274	−0.561369	−	0.827565i	$-0.689725\pi$
$709$	−29.8952	−1.12274	−0.561369	+	0.827565i	$0.689725\pi$
$710$	21.9790	0.824857
$711$	63.6268	2.38619
$712$	−26.7460	−1.00235
$713$	−20.5657	−0.770190
$714$	14.5636	0.545029
$715$	7.42078	0.277521
$716$	0.825654	0.0308561
$717$	−18.3364	−0.684784
$718$	−3.11219	−0.116146
$719$	35.8547	1.33716	0.668578	−	0.743642i	$-0.266903\pi$
$719$	35.8547	1.33716	0.668578	+	0.743642i	$0.266903\pi$
$720$	44.3181	1.65164
$721$	3.63505	0.135376
$722$	23.1574	0.861831
$723$	−4.13849	−0.153912
$724$	8.17893	0.303967
$725$	41.0650	1.52512
$726$	19.3563	0.718378
$727$	−6.16300	−0.228573	−0.114286	−	0.993448i	$-0.536458\pi$
$727$	−6.16300	−0.228573	−0.114286	+	0.993448i	$0.536458\pi$
$728$	−11.0602	−0.409917
$729$	−44.0315	−1.63079
$730$	−17.5703	−0.650305
$731$	−0.0156779	−0.000579867 0
$732$	−12.2731	−0.453628
$733$	38.0254	1.40450	0.702250	−	0.711931i	$-0.252179\pi$
$733$	38.0254	1.40450	0.702250	+	0.711931i	$0.252179\pi$
$734$	7.75489	0.286238
$735$	−54.7912	−2.02100
$736$	−8.15256	−0.300507
$737$	−21.4569	−0.790375
$738$	−32.7324	−1.20490
$739$	18.9288	0.696307	0.348153	−	0.937438i	$-0.386809\pi$
$739$	18.9288	0.696307	0.348153	+	0.937438i	$0.386809\pi$
$740$	−13.8617	−0.509568
$741$	−2.07745	−0.0763169
$742$	−40.4600	−1.48533
$743$	−24.7448	−0.907799	−0.453900	−	0.891053i	$-0.649968\pi$
$743$	−24.7448	−0.907799	−0.453900	+	0.891053i	$0.649968\pi$
$744$	−49.9232	−1.83027
$745$	64.9718	2.38038
$746$	33.7259	1.23479
$747$	22.8017	0.834270
$748$	1.13436	0.0414761
$749$	20.4336	0.746628
$750$	1.38735	0.0506587
$751$	−25.3347	−0.924478	−0.462239	−	0.886755i	$-0.652954\pi$
$751$	−25.3347	−0.924478	−0.462239	+	0.886755i	$0.652954\pi$
$752$	−37.8477	−1.38016
$753$	−77.8585	−2.83732
$754$	10.0631	0.366476
$755$	36.5527	1.33029
$756$	−7.14885	−0.260001
$757$	20.9817	0.762593	0.381297	−	0.924453i	$-0.375478\pi$
$757$	20.9817	0.762593	0.381297	+	0.924453i	$0.375478\pi$
$758$	−43.1879	−1.56865
$759$	22.4475	0.814794
$760$	−7.25802	−0.263276
$761$	28.8583	1.04611	0.523056	−	0.852298i	$-0.324792\pi$
$761$	28.8583	1.04611	0.523056	+	0.852298i	$0.324792\pi$
$762$	−16.1830	−0.586247
$763$	36.4969	1.32128
$764$	7.46310	0.270005
$765$	17.1402	0.619706
$766$	20.6252	0.745220
$767$	−0.498406	−0.0179964
$768$	−26.7609	−0.965649
$769$	−15.2398	−0.549561	−0.274780	−	0.961507i	$-0.588605\pi$
$769$	−15.2398	−0.549561	−0.274780	+	0.961507i	$0.588605\pi$
$770$	33.8794	1.22093
$771$	−80.7573	−2.90840
$772$	5.37689	0.193518
$773$	46.4270	1.66986	0.834931	−	0.550354i	$-0.185507\pi$
$773$	46.4270	1.66986	0.834931	+	0.550354i	$0.185507\pi$
$774$	−0.0800470	−0.00287723
$775$	−30.3461	−1.09006
$776$	0.940420	0.0337591
$777$	−103.849	−3.72557
$778$	31.8443	1.14167
$779$	4.17512	0.149589
$780$	−3.72611	−0.133416
$781$	12.8255	0.458932
$782$	5.02168	0.179575
$783$	37.2902	1.33264
$784$	−18.4936	−0.660487
$785$	14.5407	0.518980
$786$	−32.3447	−1.15370
$787$	51.4313	1.83333	0.916664	−	0.399658i	$-0.130871\pi$
$787$	51.4313	1.83333	0.916664	+	0.399658i	$0.130871\pi$
$788$	−4.21533	−0.150165
$789$	46.6269	1.65996
$790$	54.3404	1.93334
$791$	−26.6855	−0.948826
$792$	33.2043	1.17986
$793$	−10.4810	−0.372191
$794$	26.0569	0.924724
$795$	−78.1463	−2.77156
$796$	−6.41324	−0.227311
$797$	36.4343	1.29057	0.645285	−	0.763942i	$-0.276739\pi$
$797$	36.4343	1.29057	0.645285	+	0.763942i	$0.276739\pi$
$798$	−9.48455	−0.335749
$799$	−14.6378	−0.517847
$800$	−12.0297	−0.425313
$801$	−41.1344	−1.45341
$802$	31.5953	1.11567
$803$	−10.2529	−0.361815
$804$	10.7739	0.379967
$805$	−40.1763	−1.41603
$806$	−7.43639	−0.261936
$807$	81.6870	2.87552
$808$	51.0703	1.79665
$809$	−8.10944	−0.285113	−0.142556	−	0.989787i	$-0.545532\pi$
$809$	−8.10944	−0.285113	−0.142556	+	0.989787i	$0.545532\pi$
$810$	−4.55978	−0.160214
$811$	17.3411	0.608928	0.304464	−	0.952524i	$-0.401523\pi$
$811$	17.3411	0.608928	0.304464	+	0.952524i	$0.401523\pi$
$812$	−12.3070	−0.431891
$813$	22.5152	0.789641
$814$	30.1961	1.05837
$815$	−58.6652	−2.05495
$816$	9.49428	0.332366
$817$	0.0102102	0.000357211 0
$818$	−15.7842	−0.551883
$819$	−17.0101	−0.594382
$820$	7.48850	0.261510
$821$	−27.6488	−0.964949	−0.482474	−	0.875910i	$-0.660262\pi$
$821$	−27.6488	−0.964949	−0.482474	+	0.875910i	$0.660262\pi$
$822$	44.7074	1.55935
$823$	−17.8179	−0.621092	−0.310546	−	0.950558i	$-0.600512\pi$
$823$	−17.8179	−0.621092	−0.310546	+	0.950558i	$0.600512\pi$
$824$	3.04264	0.105995
$825$	33.1229	1.15319
$826$	−2.27547	−0.0791736
$827$	14.9649	0.520380	0.260190	−	0.965557i	$-0.416215\pi$
$827$	14.9649	0.520380	0.260190	+	0.965557i	$0.416215\pi$
$828$	−6.86817	−0.238685
$829$	−1.43603	−0.0498754	−0.0249377	−	0.999689i	$-0.507939\pi$
$829$	−1.43603	−0.0498754	−0.0249377	+	0.999689i	$0.507939\pi$
$830$	19.4737	0.675944
$831$	31.4197	1.08994
$832$	−8.90056	−0.308571
$833$	−7.15249	−0.247819
$834$	5.33767	0.184828
$835$	38.0865	1.31804
$836$	−0.738750	−0.0255502
$837$	−27.5565	−0.952494
$838$	−25.7335	−0.888950
$839$	41.0982	1.41887	0.709433	−	0.704772i	$-0.248951\pi$
$839$	41.0982	1.41887	0.709433	+	0.704772i	$0.248951\pi$
$840$	−97.5282	−3.36504
$841$	35.1964	1.21367
$842$	18.6567	0.642954
$843$	−67.6659	−2.33054
$844$	1.11448	0.0383619
$845$	−3.18202	−0.109465
$846$	−74.7365	−2.56949
$847$	−20.2157	−0.694620
$848$	−26.3767	−0.905779
$849$	76.5757	2.62807
$850$	7.40984	0.254155
$851$	−35.8084	−1.22749
$852$	−6.43992	−0.220628
$853$	−49.0697	−1.68012	−0.840058	−	0.542497i	$-0.817479\pi$
$853$	−49.0697	−1.68012	−0.840058	+	0.542497i	$0.817479\pi$
$854$	−47.8508	−1.63742
$855$	−11.1626	−0.381752
$856$	17.1035	0.584587
$857$	−3.74096	−0.127789	−0.0638944	−	0.997957i	$-0.520352\pi$
$857$	−3.74096	−0.127789	−0.0638944	+	0.997957i	$0.520352\pi$
$858$	8.11687	0.277105
$859$	−52.6778	−1.79734	−0.898672	−	0.438622i	$-0.855467\pi$
$859$	−52.6778	−1.79734	−0.898672	+	0.438622i	$0.855467\pi$
$860$	0.0183131	0.000624471 0
$861$	56.1022	1.91196
$862$	−27.5555	−0.938545
$863$	−21.4662	−0.730718	−0.365359	−	0.930867i	$-0.619054\pi$
$863$	−21.4662	−0.730718	−0.365359	+	0.930867i	$0.619054\pi$
$864$	−10.9239	−0.371637
$865$	9.34425	0.317714
$866$	−15.6351	−0.531304
$867$	−43.4382	−1.47524
$868$	9.09459	0.308690
$869$	31.7095	1.07567
$870$	88.7362	3.00844
$871$	9.20070	0.311754
$872$	30.5490	1.03452
$873$	1.44633	0.0489509
$874$	−3.27038	−0.110622
$875$	−1.44895	−0.0489833
$876$	5.14815	0.173940
$877$	−24.0444	−0.811923	−0.405961	−	0.913890i	$-0.633063\pi$
$877$	−24.0444	−0.811923	−0.405961	+	0.913890i	$0.633063\pi$
$878$	38.6032	1.30280
$879$	−33.1788	−1.11909
$880$	22.0867	0.744541
$881$	31.3919	1.05762	0.528810	−	0.848740i	$-0.322638\pi$
$881$	31.3919	1.05762	0.528810	+	0.848740i	$0.322638\pi$
$882$	−36.5187	−1.22965
$883$	40.8262	1.37391	0.686956	−	0.726699i	$-0.258946\pi$
$883$	40.8262	1.37391	0.686956	+	0.726699i	$0.258946\pi$
$884$	−0.486410	−0.0163598
$885$	−4.39493	−0.147734
$886$	33.2486	1.11701
$887$	29.3643	0.985958	0.492979	−	0.870041i	$-0.335908\pi$
$887$	29.3643	0.985958	0.492979	+	0.870041i	$0.335908\pi$
$888$	−86.9249	−2.91701
$889$	16.9015	0.566859
$890$	−35.1308	−1.17759
$891$	−2.66079	−0.0891397
$892$	−6.12328	−0.205023
$893$	9.53287	0.319005
$894$	71.0663	2.37681
$895$	6.21748	0.207827
$896$	−23.5715	−0.787469
$897$	−9.62548	−0.321386
$898$	−13.7884	−0.460125
$899$	−47.4396	−1.58220
$900$	−10.1345	−0.337815
$901$	−10.2013	−0.339854
$902$	−16.3127	−0.543155
$903$	0.137198	0.00456566
$904$	−22.3365	−0.742902
$905$	61.5903	2.04733
$906$	39.9814	1.32829
$907$	−10.3599	−0.343996	−0.171998	−	0.985097i	$-0.555022\pi$
$907$	−10.3599	−0.343996	−0.171998	+	0.985097i	$0.555022\pi$
$908$	−2.26799	−0.0752658
$909$	78.5443	2.60515
$910$	−14.5275	−0.481581
$911$	−17.5085	−0.580082	−0.290041	−	0.957014i	$-0.593669\pi$
$911$	−17.5085	−0.580082	−0.290041	+	0.957014i	$0.593669\pi$
$912$	−6.18316	−0.204745
$913$	11.3636	0.376080
$914$	15.2552	0.504598
$915$	−92.4212	−3.05535
$916$	8.60411	0.284288
$917$	33.7809	1.11554
$918$	6.72871	0.222080
$919$	−27.8579	−0.918947	−0.459474	−	0.888191i	$-0.651962\pi$
$919$	−27.8579	−0.918947	−0.459474	+	0.888191i	$0.651962\pi$
$920$	−33.6288	−1.10871
$921$	36.1510	1.19121
$922$	−2.40786	−0.0792986
$923$	−5.49956	−0.181020
$924$	−9.92680	−0.326568
$925$	−52.8377	−1.73729
$926$	5.46478	0.179584
$927$	4.67947	0.153694
$928$	−18.8058	−0.617331
$929$	40.3403	1.32352	0.661761	−	0.749715i	$-0.269809\pi$
$929$	40.3403	1.32352	0.661761	+	0.749715i	$0.269809\pi$
$930$	−65.5739	−2.15025
$931$	4.65807	0.152662
$932$	4.04126	0.132376
$933$	13.1472	0.430420
$934$	29.0505	0.950562
$935$	8.54211	0.279357
$936$	−14.2380	−0.465383
$937$	−21.2397	−0.693870	−0.346935	−	0.937889i	$-0.612778\pi$
$937$	−21.2397	−0.693870	−0.346935	+	0.937889i	$0.612778\pi$
$938$	42.0057	1.37153
$939$	−28.9417	−0.944476
$940$	17.0982	0.557681
$941$	13.2471	0.431843	0.215921	−	0.976411i	$-0.430725\pi$
$941$	13.2471	0.431843	0.215921	+	0.976411i	$0.430725\pi$
$942$	15.9047	0.518202
$943$	19.3447	0.629949
$944$	−1.48342	−0.0482812
$945$	−53.8335	−1.75120
$946$	−0.0398928	−0.00129703
$947$	−3.26571	−0.106121	−0.0530607	−	0.998591i	$-0.516898\pi$
$947$	−3.26571	−0.106121	−0.0530607	+	0.998591i	$0.516898\pi$
$948$	−15.9219	−0.517120
$949$	4.39641	0.142714
$950$	−4.82567	−0.156565
$951$	15.6778	0.508387
$952$	−12.7314	−0.412628
$953$	13.6717	0.442869	0.221434	−	0.975175i	$-0.428926\pi$
$953$	13.6717	0.442869	0.221434	+	0.975175i	$0.428926\pi$
$954$	−52.0851	−1.68632
$955$	56.1999	1.81859
$956$	2.79598	0.0904285
$957$	51.7806	1.67383
$958$	−2.56913	−0.0830049
$959$	−46.6925	−1.50778
$960$	−78.4849	−2.53309
$961$	4.05672	0.130862
$962$	−12.9480	−0.417462
$963$	26.3046	0.847654
$964$	0.631049	0.0203247
$965$	40.4899	1.30342
$966$	−43.9450	−1.41391
$967$	−25.2618	−0.812364	−0.406182	−	0.913792i	$-0.633140\pi$
$967$	−25.2618	−0.812364	−0.406182	+	0.913792i	$0.633140\pi$
$968$	−16.9211	−0.543866
$969$	−2.39136	−0.0768217
$970$	1.23524	0.0396611
$971$	−20.7129	−0.664709	−0.332354	−	0.943155i	$-0.607843\pi$
$971$	−20.7129	−0.664709	−0.332354	+	0.943155i	$0.607843\pi$
$972$	7.23597	0.232094
$973$	−5.57468	−0.178716
$974$	15.7154	0.503555
$975$	−14.2031	−0.454862
$976$	−31.1949	−0.998524
$977$	15.9059	0.508874	0.254437	−	0.967089i	$-0.418110\pi$
$977$	15.9059	0.508874	0.254437	+	0.967089i	$0.418110\pi$
$978$	−64.1682	−2.05187
$979$	−20.5000	−0.655183
$980$	8.35472	0.266882
$981$	46.9832	1.50006
$982$	−12.2297	−0.390265
$983$	−34.3279	−1.09489	−0.547445	−	0.836842i	$-0.684399\pi$
$983$	−34.3279	−1.09489	−0.547445	+	0.836842i	$0.684399\pi$
$984$	46.9592	1.49701
$985$	−31.7430	−1.01142
$986$	11.5837	0.368900
$987$	128.096	4.07734
$988$	0.316775	0.0100780
$989$	0.0473073	0.00150428
$990$	43.6137	1.38614
$991$	15.6563	0.497337	0.248669	−	0.968589i	$-0.420007\pi$
$991$	15.6563	0.497337	0.248669	+	0.968589i	$0.420007\pi$
$992$	13.8971	0.441232
$993$	−74.9895	−2.37972
$994$	−25.1082	−0.796382
$995$	−48.2940	−1.53102
$996$	−5.70588	−0.180798
$997$	−30.9150	−0.979089	−0.489544	−	0.871978i	$-0.662837\pi$
$997$	−30.9150	−0.979089	−0.489544	+	0.871978i	$0.662837\pi$
$998$	0.0929278	0.00294158
$999$	−47.9807	−1.51804

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.g.1.10	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.g.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-1.25596 q^{2} +2.77119 q^{3} -0.422559 q^{4} -3.18202 q^{5} -3.48051 q^{6} +3.63505 q^{7} +3.04264 q^{8} +4.67947 q^{9} +O(q^{10})\)	\(q-1.25596 q^{2} +2.77119 q^{3} -0.422559 q^{4} -3.18202 q^{5} -3.48051 q^{6} +3.63505 q^{7} +3.04264 q^{8} +4.67947 q^{9} +3.99650 q^{10} +2.33209 q^{11} -1.17099 q^{12} -1.00000 q^{13} -4.56548 q^{14} -8.81798 q^{15} -2.97633 q^{16} -1.15111 q^{17} -5.87724 q^{18} +0.749660 q^{19} +1.34459 q^{20} +10.0734 q^{21} -2.92902 q^{22} +3.47342 q^{23} +8.43173 q^{24} +5.12527 q^{25} +1.25596 q^{26} +4.65414 q^{27} -1.53602 q^{28} +8.01226 q^{29} +11.0750 q^{30} -5.92087 q^{31} -2.34713 q^{32} +6.46267 q^{33} +1.44575 q^{34} -11.5668 q^{35} -1.97735 q^{36} -10.3093 q^{37} -0.941545 q^{38} -2.77119 q^{39} -9.68176 q^{40} +5.56935 q^{41} -12.6518 q^{42} +0.0136198 q^{43} -0.985447 q^{44} -14.8902 q^{45} -4.36248 q^{46} +12.7163 q^{47} -8.24796 q^{48} +6.21358 q^{49} -6.43714 q^{50} -3.18993 q^{51} +0.422559 q^{52} +8.86216 q^{53} -5.84542 q^{54} -7.42078 q^{55} +11.0602 q^{56} +2.07745 q^{57} -10.0631 q^{58} +0.498406 q^{59} +3.72611 q^{60} +10.4810 q^{61} +7.43639 q^{62} +17.0101 q^{63} +8.90056 q^{64} +3.18202 q^{65} -8.11687 q^{66} -9.20070 q^{67} +0.486410 q^{68} +9.62548 q^{69} +14.5275 q^{70} +5.49956 q^{71} +14.2380 q^{72} -4.39641 q^{73} +12.9480 q^{74} +14.2031 q^{75} -0.316775 q^{76} +8.47728 q^{77} +3.48051 q^{78} +13.5970 q^{79} +9.47074 q^{80} -1.14094 q^{81} -6.99489 q^{82} +4.87270 q^{83} -4.25660 q^{84} +3.66285 q^{85} -0.0171060 q^{86} +22.2035 q^{87} +7.09573 q^{88} -8.79038 q^{89} +18.7015 q^{90} -3.63505 q^{91} -1.46772 q^{92} -16.4078 q^{93} -15.9711 q^{94} -2.38543 q^{95} -6.50434 q^{96} +0.309080 q^{97} -7.80402 q^{98} +10.9130 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) \) 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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