LMFDB - Embedded newform 1339.2.a.e.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$10.6919688306$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.499344 q^{2} +0.601343 q^{3} -1.75066 q^{4} -1.13095 q^{5} +0.300277 q^{6} +3.15035 q^{7} -1.87287 q^{8} -2.63839 q^{9} +O(q^{10})$	\(q+0.499344 q^{2} +0.601343 q^{3} -1.75066 q^{4} -1.13095 q^{5} +0.300277 q^{6} +3.15035 q^{7} -1.87287 q^{8} -2.63839 q^{9} -0.564734 q^{10} +1.51191 q^{11} -1.05274 q^{12} -1.00000 q^{13} +1.57311 q^{14} -0.680090 q^{15} +2.56611 q^{16} -6.86672 q^{17} -1.31746 q^{18} +3.58431 q^{19} +1.97991 q^{20} +1.89444 q^{21} +0.754961 q^{22} -1.89864 q^{23} -1.12623 q^{24} -3.72094 q^{25} -0.499344 q^{26} -3.39060 q^{27} -5.51518 q^{28} +5.95095 q^{29} -0.339599 q^{30} -9.99560 q^{31} +5.02710 q^{32} +0.909174 q^{33} -3.42885 q^{34} -3.56290 q^{35} +4.61891 q^{36} -0.596864 q^{37} +1.78980 q^{38} -0.601343 q^{39} +2.11812 q^{40} -8.60616 q^{41} +0.945976 q^{42} -0.0480674 q^{43} -2.64683 q^{44} +2.98389 q^{45} -0.948073 q^{46} -13.3724 q^{47} +1.54311 q^{48} +2.92470 q^{49} -1.85803 q^{50} -4.12925 q^{51} +1.75066 q^{52} +6.04188 q^{53} -1.69308 q^{54} -1.70990 q^{55} -5.90018 q^{56} +2.15540 q^{57} +2.97157 q^{58} -9.03458 q^{59} +1.19060 q^{60} -1.90065 q^{61} -4.99124 q^{62} -8.31184 q^{63} -2.62197 q^{64} +1.13095 q^{65} +0.453990 q^{66} +14.1029 q^{67} +12.0213 q^{68} -1.14173 q^{69} -1.77911 q^{70} -6.95775 q^{71} +4.94134 q^{72} -1.46554 q^{73} -0.298040 q^{74} -2.23756 q^{75} -6.27489 q^{76} +4.76303 q^{77} -0.300277 q^{78} +5.21541 q^{79} -2.90215 q^{80} +5.87625 q^{81} -4.29743 q^{82} -5.84418 q^{83} -3.31651 q^{84} +7.76594 q^{85} -0.0240022 q^{86} +3.57856 q^{87} -2.83160 q^{88} -9.53353 q^{89} +1.48999 q^{90} -3.15035 q^{91} +3.32386 q^{92} -6.01078 q^{93} -6.67742 q^{94} -4.05369 q^{95} +3.02301 q^{96} -15.0823 q^{97} +1.46043 q^{98} -3.98899 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - q^{2} - 6 q^{3} + 15 q^{4} - 18 q^{5} - 8 q^{6} - 2 q^{7} + 6 q^{8} + 11 q^{9}+O(q^{10}) $ 21 * q - q^2 - 6 * q^3 + 15 * q^4 - 18 * q^5 - 8 * q^6 - 2 * q^7 + 6 * q^8 + 11 * q^9	\( 21 q - q^{2} - 6 q^{3} + 15 q^{4} - 18 q^{5} - 8 q^{6} - 2 q^{7} + 6 q^{8} + 11 q^{9} - 10 q^{10} - 5 q^{11} - 22 q^{12} - 21 q^{13} - 24 q^{14} - q^{15} - 5 q^{16} - 18 q^{17} + 10 q^{18} - 6 q^{19} - 30 q^{20} - 17 q^{21} - 8 q^{22} - 14 q^{23} - 13 q^{24} + 11 q^{25} + q^{26} - 33 q^{27} - 2 q^{28} - 36 q^{29} + 2 q^{30} + q^{31} - 9 q^{32} - 11 q^{33} - 25 q^{34} - 37 q^{35} + 3 q^{36} + 5 q^{37} - 13 q^{38} + 6 q^{39} - 2 q^{40} - 32 q^{41} + 7 q^{42} + 2 q^{43} + 4 q^{44} - 32 q^{45} - 5 q^{46} - 12 q^{47} - 18 q^{48} + 5 q^{49} - 2 q^{50} - 27 q^{51} - 15 q^{52} - 49 q^{53} - 31 q^{54} - 9 q^{55} - 53 q^{56} + 14 q^{57} - 2 q^{58} - 34 q^{59} + 25 q^{60} - 27 q^{61} - 12 q^{62} + 41 q^{63} - 70 q^{64} + 18 q^{65} - 15 q^{66} - 12 q^{67} - 20 q^{68} - 70 q^{69} + 70 q^{70} - 26 q^{71} - 14 q^{72} + 23 q^{73} + 20 q^{74} - 9 q^{75} - 36 q^{76} - 62 q^{77} + 8 q^{78} - 7 q^{79} - 41 q^{80} - 3 q^{81} - 33 q^{82} - q^{83} - 48 q^{84} + 10 q^{85} - 23 q^{86} - 7 q^{87} + 9 q^{88} - 16 q^{89} - 30 q^{90} + 2 q^{91} - 27 q^{92} + 2 q^{93} - 37 q^{94} - 35 q^{95} + 55 q^{96} - 30 q^{97} - 43 q^{98} - 42 q^{99}+O(q^{100}) \) 21 * q - q^2 - 6 * q^3 + 15 * q^4 - 18 * q^5 - 8 * q^6 - 2 * q^7 + 6 * q^8 + 11 * q^9 - 10 * q^10 - 5 * q^11 - 22 * q^12 - 21 * q^13 - 24 * q^14 - q^15 - 5 * q^16 - 18 * q^17 + 10 * q^18 - 6 * q^19 - 30 * q^20 - 17 * q^21 - 8 * q^22 - 14 * q^23 - 13 * q^24 + 11 * q^25 + q^26 - 33 * q^27 - 2 * q^28 - 36 * q^29 + 2 * q^30 + q^31 - 9 * q^32 - 11 * q^33 - 25 * q^34 - 37 * q^35 + 3 * q^36 + 5 * q^37 - 13 * q^38 + 6 * q^39 - 2 * q^40 - 32 * q^41 + 7 * q^42 + 2 * q^43 + 4 * q^44 - 32 * q^45 - 5 * q^46 - 12 * q^47 - 18 * q^48 + 5 * q^49 - 2 * q^50 - 27 * q^51 - 15 * q^52 - 49 * q^53 - 31 * q^54 - 9 * q^55 - 53 * q^56 + 14 * q^57 - 2 * q^58 - 34 * q^59 + 25 * q^60 - 27 * q^61 - 12 * q^62 + 41 * q^63 - 70 * q^64 + 18 * q^65 - 15 * q^66 - 12 * q^67 - 20 * q^68 - 70 * q^69 + 70 * q^70 - 26 * q^71 - 14 * q^72 + 23 * q^73 + 20 * q^74 - 9 * q^75 - 36 * q^76 - 62 * q^77 + 8 * q^78 - 7 * q^79 - 41 * q^80 - 3 * q^81 - 33 * q^82 - q^83 - 48 * q^84 + 10 * q^85 - 23 * q^86 - 7 * q^87 + 9 * q^88 - 16 * q^89 - 30 * q^90 + 2 * q^91 - 27 * q^92 + 2 * q^93 - 37 * q^94 - 35 * q^95 + 55 * q^96 - 30 * q^97 - 43 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.499344	0.353089	0.176545	−	0.984293i	$-0.443508\pi$
$2$	0.499344	0.353089	0.176545	+	0.984293i	$0.443508\pi$
$3$	0.601343	0.347185	0.173593	−	0.984818i	$-0.444462\pi$
$3$	0.601343	0.347185	0.173593	+	0.984818i	$0.444462\pi$
$4$	−1.75066	−0.875328
$5$	−1.13095	−0.505778	−0.252889	−	0.967495i	$-0.581381\pi$
$5$	−1.13095	−0.505778	−0.252889	+	0.967495i	$0.581381\pi$
$6$	0.300277	0.122587
$7$	3.15035	1.19072	0.595360	−	0.803459i	$-0.297009\pi$
$7$	3.15035	1.19072	0.595360	+	0.803459i	$0.297009\pi$
$8$	−1.87287	−0.662158
$9$	−2.63839	−0.879462
$10$	−0.564734	−0.178585
$11$	1.51191	0.455857	0.227928	−	0.973678i	$-0.426805\pi$
$11$	1.51191	0.455857	0.227928	+	0.973678i	$0.426805\pi$
$12$	−1.05274	−0.303901
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.57311	0.420430
$15$	−0.680090	−0.175599
$16$	2.56611	0.641527
$17$	−6.86672	−1.66542	−0.832712	−	0.553706i	$-0.813213\pi$
$17$	−6.86672	−1.66542	−0.832712	+	0.553706i	$0.813213\pi$
$18$	−1.31746	−0.310529
$19$	3.58431	0.822297	0.411148	−	0.911568i	$-0.365128\pi$
$19$	3.58431	0.822297	0.411148	+	0.911568i	$0.365128\pi$
$20$	1.97991	0.442721
$21$	1.89444	0.413400
$22$	0.754961	0.160958
$23$	−1.89864	−0.395894	−0.197947	−	0.980213i	$-0.563427\pi$
$23$	−1.89864	−0.395894	−0.197947	+	0.980213i	$0.563427\pi$
$24$	−1.12623	−0.229892
$25$	−3.72094	−0.744189
$26$	−0.499344	−0.0979293
$27$	−3.39060	−0.652522
$28$	−5.51518	−1.04227
$29$	5.95095	1.10506	0.552532	−	0.833492i	$-0.313662\pi$
$29$	5.95095	1.10506	0.552532	+	0.833492i	$0.313662\pi$
$30$	−0.339599	−0.0620020
$31$	−9.99560	−1.79526	−0.897631	−	0.440747i	$-0.854714\pi$
$31$	−9.99560	−1.79526	−0.897631	+	0.440747i	$0.854714\pi$
$32$	5.02710	0.888674
$33$	0.909174	0.158267
$34$	−3.42885	−0.588043
$35$	−3.56290	−0.602240
$36$	4.61891	0.769818
$37$	−0.596864	−0.0981239	−0.0490619	−	0.998796i	$-0.515623\pi$
$37$	−0.596864	−0.0981239	−0.0490619	+	0.998796i	$0.515623\pi$
$38$	1.78980	0.290344
$39$	−0.601343	−0.0962919
$40$	2.11812	0.334905
$41$	−8.60616	−1.34406	−0.672029	−	0.740525i	$-0.734577\pi$
$41$	−8.60616	−1.34406	−0.672029	+	0.740525i	$0.734577\pi$
$42$	0.945976	0.145967
$43$	−0.0480674	−0.00733021	−0.00366511	−	0.999993i	$-0.501167\pi$
$43$	−0.0480674	−0.00733021	−0.00366511	+	0.999993i	$0.501167\pi$
$44$	−2.64683	−0.399024
$45$	2.98389	0.444812
$46$	−0.948073	−0.139786
$47$	−13.3724	−1.95057	−0.975283	−	0.220960i	$-0.929081\pi$
$47$	−13.3724	−1.95057	−0.975283	+	0.220960i	$0.929081\pi$
$48$	1.54311	0.222729
$49$	2.92470	0.417814
$50$	−1.85803	−0.262765
$51$	−4.12925	−0.578211
$52$	1.75066	0.242772
$53$	6.04188	0.829916	0.414958	−	0.909841i	$-0.363796\pi$
$53$	6.04188	0.829916	0.414958	+	0.909841i	$0.363796\pi$
$54$	−1.69308	−0.230398
$55$	−1.70990	−0.230562
$56$	−5.90018	−0.788445
$57$	2.15540	0.285489
$58$	2.97157	0.390186
$59$	−9.03458	−1.17620	−0.588101	−	0.808787i	$-0.700124\pi$
$59$	−9.03458	−1.17620	−0.588101	+	0.808787i	$0.700124\pi$
$60$	1.19060	0.153706
$61$	−1.90065	−0.243354	−0.121677	−	0.992570i	$-0.538827\pi$
$61$	−1.90065	−0.243354	−0.121677	+	0.992570i	$0.538827\pi$
$62$	−4.99124	−0.633888
$63$	−8.31184	−1.04719
$64$	−2.62197	−0.327746
$65$	1.13095	0.140277
$66$	0.453990	0.0558823
$67$	14.1029	1.72294	0.861472	−	0.507806i	$-0.169543\pi$
$67$	14.1029	1.72294	0.861472	+	0.507806i	$0.169543\pi$
$68$	12.0213	1.45779
$69$	−1.14173	−0.137448
$70$	−1.77911	−0.212644
$71$	−6.95775	−0.825732	−0.412866	−	0.910792i	$-0.635472\pi$
$71$	−6.95775	−0.825732	−0.412866	+	0.910792i	$0.635472\pi$
$72$	4.94134	0.582343
$73$	−1.46554	−0.171528	−0.0857641	−	0.996315i	$-0.527333\pi$
$73$	−1.46554	−0.171528	−0.0857641	+	0.996315i	$0.527333\pi$
$74$	−0.298040	−0.0346465
$75$	−2.23756	−0.258371
$76$	−6.27489	−0.719779
$77$	4.76303	0.542798
$78$	−0.300277	−0.0339996
$79$	5.21541	0.586779	0.293390	−	0.955993i	$-0.405217\pi$
$79$	5.21541	0.586779	0.293390	+	0.955993i	$0.405217\pi$
$80$	−2.90215	−0.324470
$81$	5.87625	0.652916
$82$	−4.29743	−0.474572
$83$	−5.84418	−0.641482	−0.320741	−	0.947167i	$-0.603932\pi$
$83$	−5.84418	−0.641482	−0.320741	+	0.947167i	$0.603932\pi$
$84$	−3.31651	−0.361861
$85$	7.76594	0.842334
$86$	−0.0240022	−0.00258822
$87$	3.57856	0.383662
$88$	−2.83160	−0.301849
$89$	−9.53353	−1.01055	−0.505276	−	0.862958i	$-0.668609\pi$
$89$	−9.53353	−1.01055	−0.505276	+	0.862958i	$0.668609\pi$
$90$	1.48999	0.157058
$91$	−3.15035	−0.330246
$92$	3.32386	0.346537
$93$	−6.01078	−0.623289
$94$	−6.67742	−0.688724
$95$	−4.05369	−0.415899
$96$	3.02301	0.308535
$97$	−15.0823	−1.53138	−0.765690	−	0.643210i	$-0.777602\pi$
$97$	−15.0823	−1.53138	−0.765690	+	0.643210i	$0.777602\pi$
$98$	1.46043	0.147526
$99$	−3.98899	−0.400909
$100$	6.51409	0.651409
$101$	6.77373	0.674011	0.337006	−	0.941503i	$-0.390586\pi$
$101$	6.77373	0.674011	0.337006	+	0.941503i	$0.390586\pi$
$102$	−2.06191	−0.204160
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.87287	0.183650
$105$	−2.14252	−0.209089
$106$	3.01697	0.293034
$107$	−18.2853	−1.76770	−0.883852	−	0.467766i	$-0.845059\pi$
$107$	−18.2853	−1.76770	−0.883852	+	0.467766i	$0.845059\pi$
$108$	5.93578	0.571171
$109$	11.8812	1.13801	0.569007	−	0.822333i	$-0.307328\pi$
$109$	11.8812	1.13801	0.569007	+	0.822333i	$0.307328\pi$
$110$	−0.853825	−0.0814091
$111$	−0.358920	−0.0340672
$112$	8.08414	0.763879
$113$	17.0756	1.60634	0.803170	−	0.595749i	$-0.203145\pi$
$113$	17.0756	1.60634	0.803170	+	0.595749i	$0.203145\pi$
$114$	1.07628	0.100803
$115$	2.14727	0.200234
$116$	−10.4181	−0.967294
$117$	2.63839	0.243919
$118$	−4.51136	−0.415304
$119$	−21.6326	−1.98305
$120$	1.27372	0.116274
$121$	−8.71414	−0.792194
$122$	−0.949079	−0.0859255
$123$	−5.17525	−0.466637
$124$	17.4989	1.57144
$125$	9.86298	0.882172
$126$	−4.15046	−0.369753
$127$	−1.93825	−0.171992	−0.0859959	−	0.996295i	$-0.527407\pi$
$127$	−1.93825	−0.171992	−0.0859959	+	0.996295i	$0.527407\pi$
$128$	−11.3635	−1.00440
$129$	−0.0289050	−0.00254494
$130$	0.564734	0.0495305
$131$	−4.37272	−0.382046	−0.191023	−	0.981586i	$-0.561180\pi$
$131$	−4.37272	−0.382046	−0.191023	+	0.981586i	$0.561180\pi$
$132$	−1.59165	−0.138535
$133$	11.2918	0.979125
$134$	7.04219	0.608353
$135$	3.83461	0.330031
$136$	12.8604	1.10277
$137$	10.0118	0.855367	0.427683	−	0.903929i	$-0.359330\pi$
$137$	10.0118	0.855367	0.427683	+	0.903929i	$0.359330\pi$
$138$	−0.570117	−0.0485316
$139$	11.8195	1.00252	0.501260	−	0.865297i	$-0.332870\pi$
$139$	11.8195	1.00252	0.501260	+	0.865297i	$0.332870\pi$
$140$	6.23741	0.527157
$141$	−8.04140	−0.677208
$142$	−3.47430	−0.291557
$143$	−1.51191	−0.126432
$144$	−6.77039	−0.564199
$145$	−6.73025	−0.558917
$146$	−0.731807	−0.0605648
$147$	1.75875	0.145059
$148$	1.04490	0.0858906
$149$	7.19085	0.589097	0.294549	−	0.955636i	$-0.404831\pi$
$149$	7.19085	0.589097	0.294549	+	0.955636i	$0.404831\pi$
$150$	−1.11731	−0.0912282
$151$	−12.7015	−1.03363	−0.516816	−	0.856096i	$-0.672883\pi$
$151$	−12.7015	−1.03363	−0.516816	+	0.856096i	$0.672883\pi$
$152$	−6.71293	−0.544490
$153$	18.1171	1.46468
$154$	2.37839	0.191656
$155$	11.3046	0.908004
$156$	1.05274	0.0842870
$157$	9.93965	0.793270	0.396635	−	0.917976i	$-0.370178\pi$
$157$	9.93965	0.793270	0.396635	+	0.917976i	$0.370178\pi$
$158$	2.60428	0.207185
$159$	3.63324	0.288135
$160$	−5.68542	−0.449472
$161$	−5.98138	−0.471398
$162$	2.93427	0.230538
$163$	18.1800	1.42396	0.711982	−	0.702197i	$-0.247798\pi$
$163$	18.1800	1.42396	0.711982	+	0.702197i	$0.247798\pi$
$164$	15.0664	1.17649
$165$	−1.02823	−0.0800478
$166$	−2.91825	−0.226500
$167$	13.8756	1.07372	0.536862	−	0.843670i	$-0.319609\pi$
$167$	13.8756	1.07372	0.536862	+	0.843670i	$0.319609\pi$
$168$	−3.54803	−0.273736
$169$	1.00000	0.0769231
$170$	3.87787	0.297419
$171$	−9.45679	−0.723179
$172$	0.0841495	0.00641634
$173$	−3.46553	−0.263479	−0.131740	−	0.991284i	$-0.542056\pi$
$173$	−3.46553	−0.263479	−0.131740	+	0.991284i	$0.542056\pi$
$174$	1.78693	0.135467
$175$	−11.7223	−0.886121
$176$	3.87972	0.292445
$177$	−5.43288	−0.408360
$178$	−4.76051	−0.356815
$179$	4.12664	0.308439	0.154220	−	0.988037i	$-0.450714\pi$
$179$	4.12664	0.308439	0.154220	+	0.988037i	$0.450714\pi$
$180$	−5.22377	−0.389357
$181$	−12.0736	−0.897423	−0.448711	−	0.893677i	$-0.648117\pi$
$181$	−12.0736	−0.897423	−0.448711	+	0.893677i	$0.648117\pi$
$182$	−1.57311	−0.116606
$183$	−1.14294	−0.0844888
$184$	3.55590	0.262144
$185$	0.675026	0.0496289
$186$	−3.00144	−0.220077
$187$	−10.3818	−0.759195
$188$	23.4105	1.70738
$189$	−10.6816	−0.776971
$190$	−2.02418	−0.146850
$191$	−7.97268	−0.576883	−0.288441	−	0.957498i	$-0.593137\pi$
$191$	−7.97268	−0.576883	−0.288441	+	0.957498i	$0.593137\pi$
$192$	−1.57670	−0.113789
$193$	21.1480	1.52227	0.761133	−	0.648596i	$-0.224644\pi$
$193$	21.1480	1.52227	0.761133	+	0.648596i	$0.224644\pi$
$194$	−7.53127	−0.540713
$195$	0.680090	0.0487023
$196$	−5.12014	−0.365724
$197$	12.4460	0.886743	0.443372	−	0.896338i	$-0.353782\pi$
$197$	12.4460	0.886743	0.443372	+	0.896338i	$0.353782\pi$
$198$	−1.99188	−0.141557
$199$	12.6675	0.897972	0.448986	−	0.893539i	$-0.351785\pi$
$199$	12.6675	0.897972	0.448986	+	0.893539i	$0.351785\pi$
$200$	6.96883	0.492771
$201$	8.48067	0.598181
$202$	3.38242	0.237986
$203$	18.7476	1.31582
$204$	7.22890	0.506124
$205$	9.73317	0.679794
$206$	−0.499344	−0.0347909
$207$	5.00934	0.348174
$208$	−2.56611	−0.177928
$209$	5.41914	0.374850
$210$	−1.06985	−0.0738270
$211$	−20.4333	−1.40668	−0.703342	−	0.710851i	$-0.748310\pi$
$211$	−20.4333	−1.40668	−0.703342	+	0.710851i	$0.748310\pi$
$212$	−10.5772	−0.726448
$213$	−4.18399	−0.286682
$214$	−9.13064	−0.624157
$215$	0.0543620	0.00370746
$216$	6.35014	0.432072
$217$	−31.4896	−2.13766
$218$	5.93280	0.401820
$219$	−0.881290	−0.0595521
$220$	2.99344	0.201818
$221$	6.86672	0.461906
$222$	−0.179224	−0.0120287
$223$	7.14355	0.478367	0.239184	−	0.970974i	$-0.423120\pi$
$223$	7.14355	0.478367	0.239184	+	0.970974i	$0.423120\pi$
$224$	15.8371	1.05816
$225$	9.81729	0.654486
$226$	8.52661	0.567182
$227$	−8.56174	−0.568262	−0.284131	−	0.958785i	$-0.591705\pi$
$227$	−8.56174	−0.568262	−0.284131	+	0.958785i	$0.591705\pi$
$228$	−3.77336	−0.249897
$229$	1.54924	0.102377	0.0511885	−	0.998689i	$-0.483699\pi$
$229$	1.54924	0.102377	0.0511885	+	0.998689i	$0.483699\pi$
$230$	1.07223	0.0707005
$231$	2.86421	0.188451
$232$	−11.1453	−0.731727
$233$	−3.56907	−0.233817	−0.116909	−	0.993143i	$-0.537299\pi$
$233$	−3.56907	−0.233817	−0.116909	+	0.993143i	$0.537299\pi$
$234$	1.31746	0.0861252
$235$	15.1236	0.986553
$236$	15.8164	1.02956
$237$	3.13625	0.203721
$238$	−10.8021	−0.700195
$239$	27.5595	1.78267	0.891337	−	0.453342i	$-0.149768\pi$
$239$	27.5595	1.78267	0.891337	+	0.453342i	$0.149768\pi$
$240$	−1.74519	−0.112651
$241$	8.42808	0.542900	0.271450	−	0.962452i	$-0.412497\pi$
$241$	8.42808	0.542900	0.271450	+	0.962452i	$0.412497\pi$
$242$	−4.35135	−0.279715
$243$	13.7054	0.879205
$244$	3.32739	0.213014
$245$	−3.30770	−0.211321
$246$	−2.58423	−0.164764
$247$	−3.58431	−0.228064
$248$	18.7204	1.18875
$249$	−3.51435	−0.222713
$250$	4.92502	0.311485
$251$	22.3866	1.41303	0.706514	−	0.707699i	$-0.250267\pi$
$251$	22.3866	1.41303	0.706514	+	0.707699i	$0.250267\pi$
$252$	14.5512	0.916638
$253$	−2.87056	−0.180471
$254$	−0.967852	−0.0607284
$255$	4.66999	0.292446
$256$	−0.430338	−0.0268961
$257$	−23.3419	−1.45603	−0.728015	−	0.685562i	$-0.759557\pi$
$257$	−23.3419	−1.45603	−0.728015	+	0.685562i	$0.759557\pi$
$258$	−0.0144335	−0.000898591 0
$259$	−1.88033	−0.116838
$260$	−1.97991	−0.122789
$261$	−15.7009	−0.971862
$262$	−2.18349	−0.134896
$263$	−22.7160	−1.40073	−0.700364	−	0.713786i	$-0.746979\pi$
$263$	−22.7160	−1.40073	−0.700364	+	0.713786i	$0.746979\pi$
$264$	−1.70276	−0.104798
$265$	−6.83308	−0.419753
$266$	5.63850	0.345718
$267$	−5.73292	−0.350849
$268$	−24.6893	−1.50814
$269$	−6.92259	−0.422078	−0.211039	−	0.977478i	$-0.567685\pi$
$269$	−6.92259	−0.422078	−0.211039	+	0.977478i	$0.567685\pi$
$270$	1.91479	0.116530
$271$	9.00389	0.546948	0.273474	−	0.961879i	$-0.411827\pi$
$271$	9.00389	0.546948	0.273474	+	0.961879i	$0.411827\pi$
$272$	−17.6207	−1.06841
$273$	−1.89444	−0.114657
$274$	4.99933	0.302021
$275$	−5.62572	−0.339244
$276$	1.99878	0.120312
$277$	−18.8330	−1.13156	−0.565782	−	0.824555i	$-0.691426\pi$
$277$	−18.8330	−1.13156	−0.565782	+	0.824555i	$0.691426\pi$
$278$	5.90201	0.353979
$279$	26.3723	1.57887
$280$	6.67283	0.398778
$281$	−14.3343	−0.855112	−0.427556	−	0.903989i	$-0.640625\pi$
$281$	−14.3343	−0.855112	−0.427556	+	0.903989i	$0.640625\pi$
$282$	−4.01542	−0.239115
$283$	−4.80278	−0.285495	−0.142748	−	0.989759i	$-0.545594\pi$
$283$	−4.80278	−0.285495	−0.142748	+	0.989759i	$0.545594\pi$
$284$	12.1806	0.722787
$285$	−2.43765	−0.144394
$286$	−0.754961	−0.0446418
$287$	−27.1124	−1.60040
$288$	−13.2634	−0.781556
$289$	30.1518	1.77364
$290$	−3.36071	−0.197347
$291$	−9.06965	−0.531672
$292$	2.56565	0.150143
$293$	−15.1570	−0.885480	−0.442740	−	0.896650i	$-0.645994\pi$
$293$	−15.1570	−0.885480	−0.442740	+	0.896650i	$0.645994\pi$
$294$	0.878218	0.0512187
$295$	10.2177	0.594897
$296$	1.11785	0.0649735
$297$	−5.12627	−0.297457
$298$	3.59070	0.208004
$299$	1.89864	0.109801
$300$	3.91720	0.226160
$301$	−0.151429	−0.00872823
$302$	−6.34241	−0.364965
$303$	4.07333	0.234007
$304$	9.19772	0.527526
$305$	2.14955	0.123083
$306$	9.04664	0.517162
$307$	13.1510	0.750567	0.375283	−	0.926910i	$-0.377545\pi$
$307$	13.1510	0.750567	0.375283	+	0.926910i	$0.377545\pi$
$308$	−8.33843	−0.475126
$309$	−0.601343	−0.0342092
$310$	5.64486	0.320606
$311$	4.75187	0.269454	0.134727	−	0.990883i	$-0.456984\pi$
$311$	4.75187	0.269454	0.134727	+	0.990883i	$0.456984\pi$
$312$	1.12623	0.0637604
$313$	−32.1161	−1.81531	−0.907654	−	0.419719i	$-0.862129\pi$
$313$	−32.1161	−1.81531	−0.907654	+	0.419719i	$0.862129\pi$
$314$	4.96330	0.280095
$315$	9.40030	0.529647
$316$	−9.13039	−0.513624
$317$	−13.6422	−0.766221	−0.383111	−	0.923702i	$-0.625147\pi$
$317$	−13.6422	−0.766221	−0.383111	+	0.923702i	$0.625147\pi$
$318$	1.81423	0.101737
$319$	8.99728	0.503751
$320$	2.96532	0.165767
$321$	−10.9957	−0.613721
$322$	−2.98676	−0.166446
$323$	−24.6124	−1.36947
$324$	−10.2873	−0.571516
$325$	3.72094	0.206401
$326$	9.07805	0.502787
$327$	7.14467	0.395101
$328$	16.1182	0.889978
$329$	−42.1277	−2.32258
$330$	−0.513442	−0.0282640
$331$	−17.5278	−0.963414	−0.481707	−	0.876332i	$-0.659983\pi$
$331$	−17.5278	−0.963414	−0.481707	+	0.876332i	$0.659983\pi$
$332$	10.2311	0.561507
$333$	1.57476	0.0862962
$334$	6.92868	0.379121
$335$	−15.9497	−0.871426
$336$	4.86134	0.265208
$337$	13.1406	0.715817	0.357908	−	0.933757i	$-0.383490\pi$
$337$	13.1406	0.715817	0.357908	+	0.933757i	$0.383490\pi$
$338$	0.499344	0.0271607
$339$	10.2683	0.557698
$340$	−13.5955	−0.737319
$341$	−15.1124	−0.818383
$342$	−4.72219	−0.255347
$343$	−12.8386	−0.693220
$344$	0.0900238	0.00485376
$345$	1.29125	0.0695184
$346$	−1.73049	−0.0930317
$347$	18.1496	0.974320	0.487160	−	0.873313i	$-0.338033\pi$
$347$	18.1496	0.974320	0.487160	+	0.873313i	$0.338033\pi$
$348$	−6.26483	−0.335830
$349$	13.6119	0.728629	0.364315	−	0.931276i	$-0.381303\pi$
$349$	13.6119	0.728629	0.364315	+	0.931276i	$0.381303\pi$
$350$	−5.85344	−0.312880
$351$	3.39060	0.180977
$352$	7.60051	0.405108
$353$	−12.8837	−0.685733	−0.342866	−	0.939384i	$-0.611398\pi$
$353$	−12.8837	−0.685733	−0.342866	+	0.939384i	$0.611398\pi$
$354$	−2.71287	−0.144188
$355$	7.86889	0.417637
$356$	16.6899	0.884565
$357$	−13.0086	−0.688487
$358$	2.06061	0.108907
$359$	−11.3583	−0.599470	−0.299735	−	0.954022i	$-0.596898\pi$
$359$	−11.3583	−0.599470	−0.299735	+	0.954022i	$0.596898\pi$
$360$	−5.58843	−0.294536
$361$	−6.15273	−0.323828
$362$	−6.02887	−0.316870
$363$	−5.24018	−0.275038
$364$	5.51518	0.289074
$365$	1.65745	0.0867552
$366$	−0.570721	−0.0298321
$367$	−12.5298	−0.654052	−0.327026	−	0.945015i	$-0.606046\pi$
$367$	−12.5298	−0.654052	−0.327026	+	0.945015i	$0.606046\pi$
$368$	−4.87211	−0.253977
$369$	22.7064	1.18205
$370$	0.337070	0.0175234
$371$	19.0340	0.988197
$372$	10.5228	0.545582
$373$	29.7247	1.53909	0.769544	−	0.638593i	$-0.220483\pi$
$373$	29.7247	1.53909	0.769544	+	0.638593i	$0.220483\pi$
$374$	−5.18410	−0.268064
$375$	5.93103	0.306277
$376$	25.0447	1.29158
$377$	−5.95095	−0.306490
$378$	−5.33378	−0.274340
$379$	−15.8791	−0.815656	−0.407828	−	0.913059i	$-0.633714\pi$
$379$	−15.8791	−0.815656	−0.407828	+	0.913059i	$0.633714\pi$
$380$	7.09661	0.364048
$381$	−1.16555	−0.0597130
$382$	−3.98111	−0.203691
$383$	−0.615977	−0.0314750	−0.0157375	−	0.999876i	$-0.505010\pi$
$383$	−0.615977	−0.0314750	−0.0157375	+	0.999876i	$0.505010\pi$
$384$	−6.83333	−0.348712
$385$	−5.38677	−0.274535
$386$	10.5601	0.537495
$387$	0.126820	0.00644665
$388$	26.4040	1.34046
$389$	12.7187	0.644865	0.322432	−	0.946593i	$-0.395500\pi$
$389$	12.7187	0.644865	0.322432	+	0.946593i	$0.395500\pi$
$390$	0.339599	0.0171962
$391$	13.0374	0.659331
$392$	−5.47757	−0.276659
$393$	−2.62950	−0.132641
$394$	6.21485	0.313099
$395$	−5.89838	−0.296780
$396$	6.98336	0.350927
$397$	25.4455	1.27707	0.638536	−	0.769592i	$-0.279540\pi$
$397$	25.4455	1.27707	0.638536	+	0.769592i	$0.279540\pi$
$398$	6.32541	0.317064
$399$	6.79025	0.339938
$400$	−9.54835	−0.477417
$401$	34.0780	1.70177	0.850886	−	0.525350i	$-0.176066\pi$
$401$	34.0780	1.70177	0.850886	+	0.525350i	$0.176066\pi$
$402$	4.23477	0.211211
$403$	9.99560	0.497916
$404$	−11.8585	−0.589981
$405$	−6.64576	−0.330231
$406$	9.36148	0.464603
$407$	−0.902403	−0.0447304
$408$	7.73353	0.382867
$409$	−1.14197	−0.0564666	−0.0282333	−	0.999601i	$-0.508988\pi$
$409$	−1.14197	−0.0564666	−0.0282333	+	0.999601i	$0.508988\pi$
$410$	4.86020	0.240028
$411$	6.02053	0.296971
$412$	1.75066	0.0862486
$413$	−28.4621	−1.40053
$414$	2.50138	0.122936
$415$	6.60949	0.324447
$416$	−5.02710	−0.246474
$417$	7.10759	0.348060
$418$	2.70601	0.132355
$419$	21.9455	1.07211	0.536055	−	0.844183i	$-0.319914\pi$
$419$	21.9455	1.07211	0.536055	+	0.844183i	$0.319914\pi$
$420$	3.75082	0.183021
$421$	6.40666	0.312241	0.156121	−	0.987738i	$-0.450101\pi$
$421$	6.40666	0.312241	0.156121	+	0.987738i	$0.450101\pi$
$422$	−10.2032	−0.496685
$423$	35.2816	1.71545
$424$	−11.3156	−0.549535
$425$	25.5507	1.23939
$426$	−2.08925	−0.101224
$427$	−5.98772	−0.289766
$428$	32.0112	1.54732
$429$	−0.909174	−0.0438953
$430$	0.0271453	0.00130906
$431$	−15.6748	−0.755029	−0.377514	−	0.926004i	$-0.623221\pi$
$431$	−15.6748	−0.755029	−0.377514	+	0.926004i	$0.623221\pi$
$432$	−8.70065	−0.418610
$433$	22.8671	1.09892	0.549461	−	0.835520i	$-0.314833\pi$
$433$	22.8671	1.09892	0.549461	+	0.835520i	$0.314833\pi$
$434$	−15.7241	−0.754783
$435$	−4.04719	−0.194048
$436$	−20.7999	−0.996135
$437$	−6.80531	−0.325542
$438$	−0.440067	−0.0210272
$439$	13.0494	0.622815	0.311407	−	0.950276i	$-0.399200\pi$
$439$	13.0494	0.622815	0.311407	+	0.950276i	$0.399200\pi$
$440$	3.20241	0.152669
$441$	−7.71649	−0.367452
$442$	3.42885	0.163094
$443$	14.4049	0.684399	0.342200	−	0.939627i	$-0.388828\pi$
$443$	14.4049	0.684399	0.342200	+	0.939627i	$0.388828\pi$
$444$	0.628345	0.0298199
$445$	10.7820	0.511115
$446$	3.56708	0.168906
$447$	4.32416	0.204526
$448$	−8.26011	−0.390254
$449$	−39.4344	−1.86103	−0.930513	−	0.366258i	$-0.880639\pi$
$449$	−39.4344	−1.86103	−0.930513	+	0.366258i	$0.880639\pi$
$450$	4.90220	0.231092
$451$	−13.0117	−0.612698
$452$	−29.8936	−1.40608
$453$	−7.63795	−0.358862
$454$	−4.27525	−0.200647
$455$	3.56290	0.167031
$456$	−4.03677	−0.189039
$457$	−23.1058	−1.08084	−0.540421	−	0.841395i	$-0.681735\pi$
$457$	−23.1058	−1.08084	−0.540421	+	0.841395i	$0.681735\pi$
$458$	0.773605	0.0361482
$459$	23.2823	1.08673
$460$	−3.75913	−0.175271
$461$	−33.2962	−1.55076	−0.775379	−	0.631496i	$-0.782441\pi$
$461$	−33.2962	−1.55076	−0.775379	+	0.631496i	$0.782441\pi$
$462$	1.43023	0.0665402
$463$	9.38189	0.436013	0.218007	−	0.975947i	$-0.430045\pi$
$463$	9.38189	0.436013	0.218007	+	0.975947i	$0.430045\pi$
$464$	15.2708	0.708929
$465$	6.79791	0.315246
$466$	−1.78219	−0.0825584
$467$	−41.1965	−1.90635	−0.953173	−	0.302425i	$-0.902204\pi$
$467$	−41.1965	−1.90635	−0.953173	+	0.302425i	$0.902204\pi$
$468$	−4.61891	−0.213509
$469$	44.4290	2.05154
$470$	7.55185	0.348341
$471$	5.97713	0.275412
$472$	16.9206	0.778832
$473$	−0.0726734	−0.00334153
$474$	1.56606	0.0719317
$475$	−13.3370	−0.611944
$476$	37.8712	1.73582
$477$	−15.9408	−0.729880
$478$	13.7616	0.629443
$479$	12.7872	0.584264	0.292132	−	0.956378i	$-0.405635\pi$
$479$	12.7872	0.584264	0.292132	+	0.956378i	$0.405635\pi$
$480$	−3.41888	−0.156050
$481$	0.596864	0.0272147
$482$	4.20851	0.191692
$483$	−3.59686	−0.163663
$484$	15.2555	0.693430
$485$	17.0574	0.774538
$486$	6.84372	0.310438
$487$	16.7039	0.756925	0.378462	−	0.925617i	$-0.376453\pi$
$487$	16.7039	0.756925	0.378462	+	0.925617i	$0.376453\pi$
$488$	3.55967	0.161139
$489$	10.9324	0.494380
$490$	−1.65168	−0.0746152
$491$	−8.66329	−0.390969	−0.195484	−	0.980707i	$-0.562628\pi$
$491$	−8.66329	−0.390969	−0.195484	+	0.980707i	$0.562628\pi$
$492$	9.06009	0.408460
$493$	−40.8635	−1.84040
$494$	−1.78980	−0.0805270
$495$	4.51137	0.202771
$496$	−25.6498	−1.15171
$497$	−21.9193	−0.983216
$498$	−1.75487	−0.0786375
$499$	3.89107	0.174188	0.0870940	−	0.996200i	$-0.472242\pi$
$499$	3.89107	0.174188	0.0870940	+	0.996200i	$0.472242\pi$
$500$	−17.2667	−0.772190
$501$	8.34398	0.372781
$502$	11.1786	0.498925
$503$	−10.3205	−0.460168	−0.230084	−	0.973171i	$-0.573900\pi$
$503$	−10.3205	−0.460168	−0.230084	+	0.973171i	$0.573900\pi$
$504$	15.5670	0.693408
$505$	−7.66077	−0.340900
$506$	−1.43340	−0.0637223
$507$	0.601343	0.0267066
$508$	3.39321	0.150549
$509$	−20.3376	−0.901447	−0.450724	−	0.892664i	$-0.648834\pi$
$509$	−20.3376	−0.901447	−0.450724	+	0.892664i	$0.648834\pi$
$510$	2.33193	0.103260
$511$	−4.61696	−0.204242
$512$	22.5120	0.994901
$513$	−12.1530	−0.536566
$514$	−11.6556	−0.514108
$515$	1.13095	0.0498358
$516$	0.0506027	0.00222766
$517$	−20.2178	−0.889179
$518$	−0.938931	−0.0412543
$519$	−2.08397	−0.0914762
$520$	−2.11812	−0.0928859
$521$	28.3650	1.24269	0.621347	−	0.783536i	$-0.286586\pi$
$521$	28.3650	1.24269	0.621347	+	0.783536i	$0.286586\pi$
$522$	−7.84015	−0.343154
$523$	−41.9473	−1.83423	−0.917114	−	0.398624i	$-0.869488\pi$
$523$	−41.9473	−1.83423	−0.917114	+	0.398624i	$0.869488\pi$
$524$	7.65512	0.334415
$525$	−7.04910	−0.307648
$526$	−11.3431	−0.494582
$527$	68.6370	2.98987
$528$	2.33304	0.101532
$529$	−19.3952	−0.843268
$530$	−3.41205	−0.148210
$531$	23.8367	1.03443
$532$	−19.7681	−0.857056
$533$	8.60616	0.372774
$534$	−2.86270	−0.123881
$535$	20.6798	0.894066
$536$	−26.4128	−1.14086
$537$	2.48152	0.107086
$538$	−3.45675	−0.149031
$539$	4.42187	0.190463
$540$	−6.71309	−0.288885
$541$	16.0946	0.691961	0.345980	−	0.938242i	$-0.387546\pi$
$541$	16.0946	0.691961	0.345980	+	0.938242i	$0.387546\pi$
$542$	4.49604	0.193121
$543$	−7.26036	−0.311572
$544$	−34.5197	−1.48002
$545$	−13.4371	−0.575582
$546$	−0.945976	−0.0404840
$547$	9.68699	0.414186	0.207093	−	0.978321i	$-0.433600\pi$
$547$	9.68699	0.414186	0.207093	+	0.978321i	$0.433600\pi$
$548$	−17.5272	−0.748727
$549$	5.01466	0.214020
$550$	−2.80917	−0.119783
$551$	21.3301	0.908691
$552$	2.13831	0.0910126
$553$	16.4304	0.698690
$554$	−9.40413	−0.399543
$555$	0.405922	0.0172304
$556$	−20.6919	−0.877534
$557$	−40.1181	−1.69986	−0.849929	−	0.526898i	$-0.823355\pi$
$557$	−40.1181	−1.69986	−0.849929	+	0.526898i	$0.823355\pi$
$558$	13.1688	0.557480
$559$	0.0480674	0.00203304
$560$	−9.14278	−0.386353
$561$	−6.24304	−0.263581
$562$	−7.15773	−0.301931
$563$	−14.0977	−0.594148	−0.297074	−	0.954854i	$-0.596011\pi$
$563$	−14.0977	−0.594148	−0.297074	+	0.954854i	$0.596011\pi$
$564$	14.0777	0.592779
$565$	−19.3117	−0.812451
$566$	−2.39824	−0.100805
$567$	18.5122	0.777441
$568$	13.0309	0.546765
$569$	−7.36336	−0.308688	−0.154344	−	0.988017i	$-0.549326\pi$
$569$	−7.36336	−0.308688	−0.154344	+	0.988017i	$0.549326\pi$
$570$	−1.21723	−0.0509840
$571$	−7.38346	−0.308988	−0.154494	−	0.987994i	$-0.549375\pi$
$571$	−7.38346	−0.308988	−0.154494	+	0.987994i	$0.549375\pi$
$572$	2.64683	0.110669
$573$	−4.79431	−0.200285
$574$	−13.5384	−0.565082
$575$	7.06473	0.294620
$576$	6.91776	0.288240
$577$	16.9201	0.704391	0.352195	−	0.935926i	$-0.385435\pi$
$577$	16.9201	0.704391	0.352195	+	0.935926i	$0.385435\pi$
$578$	15.0561	0.626252
$579$	12.7172	0.528508
$580$	11.7824	0.489236
$581$	−18.4112	−0.763825
$582$	−4.52887	−0.187728
$583$	9.13475	0.378323
$584$	2.74476	0.113579
$585$	−2.98389	−0.123369
$586$	−7.56854	−0.312654
$587$	4.73010	0.195232	0.0976160	−	0.995224i	$-0.468878\pi$
$587$	4.73010	0.195232	0.0976160	+	0.995224i	$0.468878\pi$
$588$	−3.07896	−0.126974
$589$	−35.8273	−1.47624
$590$	5.10214	0.210052
$591$	7.48433	0.307864
$592$	−1.53162	−0.0629491
$593$	22.5940	0.927822	0.463911	−	0.885882i	$-0.346446\pi$
$593$	22.5940	0.927822	0.463911	+	0.885882i	$0.346446\pi$
$594$	−2.55977	−0.105029
$595$	24.4654	1.00298
$596$	−12.5887	−0.515653
$597$	7.61748	0.311763
$598$	0.948073	0.0387696
$599$	13.8369	0.565360	0.282680	−	0.959214i	$-0.408777\pi$
$599$	13.8369	0.565360	0.282680	+	0.959214i	$0.408777\pi$
$600$	4.19065	0.171083
$601$	−22.6838	−0.925293	−0.462646	−	0.886543i	$-0.653100\pi$
$601$	−22.6838	−0.925293	−0.462646	+	0.886543i	$0.653100\pi$
$602$	−0.0756152	−0.00308184
$603$	−37.2089	−1.51526
$604$	22.2359	0.904768
$605$	9.85528	0.400674
$606$	2.03399	0.0826253
$607$	−37.7571	−1.53251	−0.766256	−	0.642535i	$-0.777883\pi$
$607$	−37.7571	−1.53251	−0.766256	+	0.642535i	$0.777883\pi$
$608$	18.0187	0.730754
$609$	11.2737	0.456834
$610$	1.07336	0.0434592
$611$	13.3724	0.540990
$612$	−31.7167	−1.28207
$613$	−16.9494	−0.684578	−0.342289	−	0.939595i	$-0.611202\pi$
$613$	−16.9494	−0.684578	−0.342289	+	0.939595i	$0.611202\pi$
$614$	6.56686	0.265017
$615$	5.85297	0.236015
$616$	−8.92052	−0.359418
$617$	6.46648	0.260331	0.130165	−	0.991492i	$-0.458449\pi$
$617$	6.46648	0.260331	0.130165	+	0.991492i	$0.458449\pi$
$618$	−0.300277	−0.0120789
$619$	−47.1787	−1.89627	−0.948135	−	0.317868i	$-0.897033\pi$
$619$	−47.1787	−1.89627	−0.948135	+	0.317868i	$0.897033\pi$
$620$	−19.7904	−0.794801
$621$	6.43753	0.258329
$622$	2.37281	0.0951412
$623$	−30.0340	−1.20328
$624$	−1.54311	−0.0617739
$625$	7.45015	0.298006
$626$	−16.0370	−0.640966
$627$	3.25876	0.130142
$628$	−17.4009	−0.694372
$629$	4.09850	0.163418
$630$	4.69398	0.187013
$631$	−36.5453	−1.45484	−0.727422	−	0.686190i	$-0.759282\pi$
$631$	−36.5453	−1.45484	−0.727422	+	0.686190i	$0.759282\pi$
$632$	−9.76776	−0.388541
$633$	−12.2874	−0.488380
$634$	−6.81214	−0.270545
$635$	2.19207	0.0869896
$636$	−6.36055	−0.252212
$637$	−2.92470	−0.115881
$638$	4.49274	0.177869
$639$	18.3572	0.726201
$640$	12.8515	0.508002
$641$	−0.582307	−0.0229998	−0.0114999	−	0.999934i	$-0.503661\pi$
$641$	−0.582307	−0.0229998	−0.0114999	+	0.999934i	$0.503661\pi$
$642$	−5.49064	−0.216698
$643$	42.9396	1.69337	0.846687	−	0.532091i	$-0.178594\pi$
$643$	42.9396	1.69337	0.846687	+	0.532091i	$0.178594\pi$
$644$	10.4713	0.412628
$645$	0.0326902	0.00128717
$646$	−12.2901	−0.483546
$647$	−35.0200	−1.37678	−0.688390	−	0.725341i	$-0.741682\pi$
$647$	−35.0200	−1.37678	−0.688390	+	0.725341i	$0.741682\pi$
$648$	−11.0054	−0.432334
$649$	−13.6594	−0.536180
$650$	1.85803	0.0728779
$651$	−18.9361	−0.742162
$652$	−31.8269	−1.24644
$653$	−22.6677	−0.887054	−0.443527	−	0.896261i	$-0.646273\pi$
$653$	−22.6677	−0.887054	−0.443527	+	0.896261i	$0.646273\pi$
$654$	3.56765	0.139506
$655$	4.94534	0.193230
$656$	−22.0844	−0.862249
$657$	3.86666	0.150853
$658$	−21.0362	−0.820077
$659$	35.2236	1.37212	0.686058	−	0.727547i	$-0.259340\pi$
$659$	35.2236	1.37212	0.686058	+	0.727547i	$0.259340\pi$
$660$	1.80008	0.0700681
$661$	−2.59259	−0.100840	−0.0504200	−	0.998728i	$-0.516056\pi$
$661$	−2.59259	−0.100840	−0.0504200	+	0.998728i	$0.516056\pi$
$662$	−8.75239	−0.340171
$663$	4.12925	0.160367
$664$	10.9454	0.424762
$665$	−12.7705	−0.495220
$666$	0.786346	0.0304703
$667$	−11.2987	−0.437488
$668$	−24.2914	−0.939861
$669$	4.29572	0.166082
$670$	−7.96439	−0.307691
$671$	−2.87361	−0.110934
$672$	9.52354	0.367378
$673$	12.0992	0.466389	0.233194	−	0.972430i	$-0.425082\pi$
$673$	12.0992	0.466389	0.233194	+	0.972430i	$0.425082\pi$
$674$	6.56170	0.252747
$675$	12.6162	0.485599
$676$	−1.75066	−0.0673329
$677$	3.07141	0.118044	0.0590219	−	0.998257i	$-0.481202\pi$
$677$	3.07141	0.118044	0.0590219	+	0.998257i	$0.481202\pi$
$678$	5.12741	0.196917
$679$	−47.5146	−1.82344
$680$	−14.5446	−0.557758
$681$	−5.14854	−0.197292
$682$	−7.54628	−0.288962
$683$	−32.5945	−1.24719	−0.623597	−	0.781746i	$-0.714329\pi$
$683$	−32.5945	−1.24719	−0.623597	+	0.781746i	$0.714329\pi$
$684$	16.5556	0.633019
$685$	−11.3229	−0.432626
$686$	−6.41088	−0.244769
$687$	0.931627	0.0355438
$688$	−0.123346	−0.00470253
$689$	−6.04188	−0.230177
$690$	0.644775	0.0245462
$691$	−22.0123	−0.837386	−0.418693	−	0.908128i	$-0.637512\pi$
$691$	−22.0123	−0.837386	−0.418693	+	0.908128i	$0.637512\pi$
$692$	6.06695	0.230631
$693$	−12.5667	−0.477370
$694$	9.06287	0.344022
$695$	−13.3673	−0.507052
$696$	−6.70216	−0.254045
$697$	59.0961	2.23843
$698$	6.79702	0.257271
$699$	−2.14623	−0.0811780
$700$	20.5217	0.775646
$701$	−29.6666	−1.12049	−0.560246	−	0.828326i	$-0.689294\pi$
$701$	−29.6666	−1.12049	−0.560246	+	0.828326i	$0.689294\pi$
$702$	1.69308	0.0639010
$703$	−2.13935	−0.0806869
$704$	−3.96417	−0.149405
$705$	9.09444	0.342517
$706$	−6.43342	−0.242125
$707$	21.3396	0.802559
$708$	9.51110	0.357449
$709$	5.53873	0.208012	0.104006	−	0.994577i	$-0.466834\pi$
$709$	5.53873	0.208012	0.104006	+	0.994577i	$0.466834\pi$
$710$	3.92928	0.147463
$711$	−13.7603	−0.516050
$712$	17.8550	0.669145
$713$	18.9780	0.710733
$714$	−6.49575	−0.243097
$715$	1.70990	0.0639465
$716$	−7.22433	−0.269986
$717$	16.5727	0.618918
$718$	−5.67171	−0.211666
$719$	−17.3686	−0.647741	−0.323870	−	0.946101i	$-0.604984\pi$
$719$	−17.3686	−0.647741	−0.323870	+	0.946101i	$0.604984\pi$
$720$	7.65699	0.285359
$721$	−3.15035	−0.117325
$722$	−3.07233	−0.114340
$723$	5.06816	0.188487
$724$	21.1367	0.785539
$725$	−22.1432	−0.822377
$726$	−2.61665	−0.0971130
$727$	5.36631	0.199025	0.0995127	−	0.995036i	$-0.468272\pi$
$727$	5.36631	0.199025	0.0995127	+	0.995036i	$0.468272\pi$
$728$	5.90018	0.218675
$729$	−9.38708	−0.347670
$730$	0.827639	0.0306323
$731$	0.330065	0.0122079
$732$	2.00090	0.0739554
$733$	34.8771	1.28822	0.644108	−	0.764935i	$-0.277229\pi$
$733$	34.8771	1.28822	0.644108	+	0.764935i	$0.277229\pi$
$734$	−6.25669	−0.230939
$735$	−1.98906	−0.0733676
$736$	−9.54465	−0.351820
$737$	21.3223	0.785416
$738$	11.3383	0.417368
$739$	−16.1165	−0.592855	−0.296428	−	0.955055i	$-0.595795\pi$
$739$	−16.1165	−0.592855	−0.296428	+	0.955055i	$0.595795\pi$
$740$	−1.18174	−0.0434415
$741$	−2.15540	−0.0791805
$742$	9.50451	0.348922
$743$	−39.3096	−1.44213	−0.721065	−	0.692867i	$-0.756347\pi$
$743$	−39.3096	−1.44213	−0.721065	+	0.692867i	$0.756347\pi$
$744$	11.2574	0.412716
$745$	−8.13252	−0.297952
$746$	14.8429	0.543436
$747$	15.4192	0.564159
$748$	18.1750	0.664545
$749$	−57.6050	−2.10484
$750$	2.96162	0.108143
$751$	27.6506	1.00898	0.504492	−	0.863417i	$-0.331680\pi$
$751$	27.6506	1.00898	0.504492	+	0.863417i	$0.331680\pi$
$752$	−34.3150	−1.25134
$753$	13.4620	0.490583
$754$	−2.97157	−0.108218
$755$	14.3648	0.522788
$756$	18.6998	0.680104
$757$	−12.8995	−0.468840	−0.234420	−	0.972135i	$-0.575319\pi$
$757$	−12.8995	−0.468840	−0.234420	+	0.972135i	$0.575319\pi$
$758$	−7.92914	−0.287999
$759$	−1.72619	−0.0626568
$760$	7.59201	0.275391
$761$	36.5113	1.32354	0.661768	−	0.749709i	$-0.269807\pi$
$761$	36.5113	1.32354	0.661768	+	0.749709i	$0.269807\pi$
$762$	−0.582011	−0.0210840
$763$	37.4299	1.35505
$764$	13.9574	0.504962
$765$	−20.4896	−0.740801
$766$	−0.307584	−0.0111135
$767$	9.03458	0.326220
$768$	−0.258781	−0.00933794
$769$	12.0166	0.433328	0.216664	−	0.976246i	$-0.430482\pi$
$769$	12.0166	0.433328	0.216664	+	0.976246i	$0.430482\pi$
$770$	−2.68985	−0.0969354
$771$	−14.0365	−0.505512
$772$	−37.0228	−1.33248
$773$	−20.0702	−0.721877	−0.360938	−	0.932590i	$-0.617544\pi$
$773$	−20.0702	−0.721877	−0.360938	+	0.932590i	$0.617544\pi$
$774$	0.0633270	0.00227624
$775$	37.1931	1.33601
$776$	28.2472	1.01402
$777$	−1.13072	−0.0405645
$778$	6.35101	0.227695
$779$	−30.8471	−1.10521
$780$	−1.19060	−0.0426305
$781$	−10.5195	−0.376416
$782$	6.51015	0.232803
$783$	−20.1773	−0.721078
$784$	7.50509	0.268039
$785$	−11.2413	−0.401218
$786$	−1.31302	−0.0468340
$787$	−14.7563	−0.526004	−0.263002	−	0.964795i	$-0.584713\pi$
$787$	−14.7563	−0.526004	−0.263002	+	0.964795i	$0.584713\pi$
$788$	−21.7887	−0.776191
$789$	−13.6601	−0.486312
$790$	−2.94532	−0.104790
$791$	53.7942	1.91270
$792$	7.47085	0.265465
$793$	1.90065	0.0674942
$794$	12.7060	0.450920
$795$	−4.10902	−0.145732
$796$	−22.1764	−0.786020
$797$	46.8453	1.65935	0.829673	−	0.558249i	$-0.188527\pi$
$797$	46.8453	1.65935	0.829673	+	0.558249i	$0.188527\pi$
$798$	3.39067	0.120028
$799$	91.8245	3.24852
$800$	−18.7056	−0.661342
$801$	25.1531	0.888743
$802$	17.0166	0.600877
$803$	−2.21576	−0.0781923
$804$	−14.8467	−0.523604
$805$	6.76466	0.238423
$806$	4.99124	0.175809
$807$	−4.16285	−0.146539
$808$	−12.6863	−0.446302
$809$	−43.7784	−1.53917	−0.769583	−	0.638547i	$-0.779536\pi$
$809$	−43.7784	−1.53917	−0.769583	+	0.638547i	$0.779536\pi$
$810$	−3.31852	−0.116601
$811$	54.4357	1.91150	0.955748	−	0.294186i	$-0.0950485\pi$
$811$	54.4357	1.91150	0.955748	+	0.294186i	$0.0950485\pi$
$812$	−32.8206	−1.15178
$813$	5.41443	0.189892
$814$	−0.450609	−0.0157938
$815$	−20.5607	−0.720210
$816$	−10.5961	−0.370938
$817$	−0.172288	−0.00602761
$818$	−0.570233	−0.0199377
$819$	8.31184	0.290439
$820$	−17.0394	−0.595043
$821$	−24.7632	−0.864240	−0.432120	−	0.901816i	$-0.642234\pi$
$821$	−24.7632	−0.864240	−0.432120	+	0.901816i	$0.642234\pi$
$822$	3.00631	0.104857
$823$	54.7901	1.90986	0.954931	−	0.296827i	$-0.0959283\pi$
$823$	54.7901	1.90986	0.954931	+	0.296827i	$0.0959283\pi$
$824$	1.87287	0.0652444
$825$	−3.38298	−0.117780
$826$	−14.2124	−0.494511
$827$	−32.4517	−1.12845	−0.564227	−	0.825619i	$-0.690826\pi$
$827$	−32.4517	−1.12845	−0.564227	+	0.825619i	$0.690826\pi$
$828$	−8.76964	−0.304766
$829$	−13.6235	−0.473163	−0.236582	−	0.971612i	$-0.576027\pi$
$829$	−13.6235	−0.473163	−0.236582	+	0.971612i	$0.576027\pi$
$830$	3.30041	0.114559
$831$	−11.3251	−0.392863
$832$	2.62197	0.0909004
$833$	−20.0831	−0.695838
$834$	3.54913	0.122896
$835$	−15.6926	−0.543066
$836$	−9.48705	−0.328116
$837$	33.8911	1.17145
$838$	10.9584	0.378550
$839$	−33.4547	−1.15498	−0.577492	−	0.816397i	$-0.695968\pi$
$839$	−33.4547	−1.15498	−0.577492	+	0.816397i	$0.695968\pi$
$840$	4.01266	0.138450
$841$	6.41384	0.221167
$842$	3.19912	0.110249
$843$	−8.61981	−0.296882
$844$	35.7716	1.23131
$845$	−1.13095	−0.0389060
$846$	17.6176	0.605707
$847$	−27.4526	−0.943282
$848$	15.5041	0.532413
$849$	−2.88811	−0.0991198
$850$	12.7586	0.437615
$851$	1.13323	0.0388466
$852$	7.32472	0.250941
$853$	37.1584	1.27228	0.636139	−	0.771574i	$-0.280530\pi$
$853$	37.1584	1.27228	0.636139	+	0.771574i	$0.280530\pi$
$854$	−2.98993	−0.102313
$855$	10.6952	0.365768
$856$	34.2459	1.17050
$857$	−16.6229	−0.567829	−0.283914	−	0.958850i	$-0.591633\pi$
$857$	−16.6229	−0.567829	−0.283914	+	0.958850i	$0.591633\pi$
$858$	−0.453990	−0.0154990
$859$	9.59807	0.327482	0.163741	−	0.986503i	$-0.447644\pi$
$859$	9.59807	0.327482	0.163741	+	0.986503i	$0.447644\pi$
$860$	−0.0951692	−0.00324524
$861$	−16.3039	−0.555634
$862$	−7.82711	−0.266592
$863$	−18.1582	−0.618112	−0.309056	−	0.951044i	$-0.600013\pi$
$863$	−18.1582	−0.618112	−0.309056	+	0.951044i	$0.600013\pi$
$864$	−17.0449	−0.579879
$865$	3.91935	0.133262
$866$	11.4185	0.388017
$867$	18.1316	0.615781
$868$	55.1275	1.87115
$869$	7.88521	0.267487
$870$	−2.02094	−0.0685161
$871$	−14.1029	−0.477858
$872$	−22.2519	−0.753544
$873$	39.7930	1.34679
$874$	−3.39819	−0.114945
$875$	31.0718	1.05042
$876$	1.54284	0.0521276
$877$	−26.9115	−0.908736	−0.454368	−	0.890814i	$-0.650135\pi$
$877$	−26.9115	−0.908736	−0.454368	+	0.890814i	$0.650135\pi$
$878$	6.51614	0.219909
$879$	−9.11454	−0.307426
$880$	−4.38778	−0.147912
$881$	8.64024	0.291097	0.145549	−	0.989351i	$-0.453505\pi$
$881$	8.64024	0.291097	0.145549	+	0.989351i	$0.453505\pi$
$882$	−3.85318	−0.129743
$883$	−27.5417	−0.926850	−0.463425	−	0.886136i	$-0.653380\pi$
$883$	−27.5417	−0.926850	−0.463425	+	0.886136i	$0.653380\pi$
$884$	−12.0213	−0.404319
$885$	6.14433	0.206539
$886$	7.19301	0.241654
$887$	−9.67189	−0.324750	−0.162375	−	0.986729i	$-0.551915\pi$
$887$	−9.67189	−0.324750	−0.162375	+	0.986729i	$0.551915\pi$
$888$	0.672209	0.0225578
$889$	−6.10616	−0.204794
$890$	5.38391	0.180469
$891$	8.88434	0.297637
$892$	−12.5059	−0.418728
$893$	−47.9308	−1.60394
$894$	2.15924	0.0722159
$895$	−4.66704	−0.156002
$896$	−35.7989	−1.19596
$897$	1.14173	0.0381213
$898$	−19.6913	−0.657108
$899$	−59.4833	−1.98388
$900$	−17.1867	−0.572890
$901$	−41.4879	−1.38216
$902$	−6.49732	−0.216337
$903$	−0.0910608	−0.00303031
$904$	−31.9804	−1.06365
$905$	13.6547	0.453896
$906$	−3.81396	−0.126710
$907$	56.5404	1.87739	0.938697	−	0.344743i	$-0.112034\pi$
$907$	56.5404	1.87739	0.938697	+	0.344743i	$0.112034\pi$
$908$	14.9887	0.497416
$909$	−17.8717	−0.592767
$910$	1.77911	0.0589769
$911$	−28.8773	−0.956746	−0.478373	−	0.878157i	$-0.658773\pi$
$911$	−28.8773	−0.956746	−0.478373	+	0.878157i	$0.658773\pi$
$912$	5.53098	0.183149
$913$	−8.83585	−0.292424
$914$	−11.5377	−0.381633
$915$	1.29262	0.0427326
$916$	−2.71219	−0.0896134
$917$	−13.7756	−0.454910
$918$	11.6259	0.383711
$919$	−48.6547	−1.60497	−0.802486	−	0.596671i	$-0.796490\pi$
$919$	−48.6547	−1.60497	−0.802486	+	0.596671i	$0.796490\pi$
$920$	−4.02155	−0.132587
$921$	7.90825	0.260586
$922$	−16.6262	−0.547556
$923$	6.95775	0.229017
$924$	−5.01425	−0.164957
$925$	2.22090	0.0730227
$926$	4.68479	0.153952
$927$	2.63839	0.0866560
$928$	29.9160	0.982042
$929$	−12.8849	−0.422741	−0.211371	−	0.977406i	$-0.567793\pi$
$929$	−12.8849	−0.422741	−0.211371	+	0.977406i	$0.567793\pi$
$930$	3.39449	0.111310
$931$	10.4830	0.343567
$932$	6.24821	0.204667
$933$	2.85750	0.0935503
$934$	−20.5712	−0.673110
$935$	11.7414	0.383984
$936$	−4.94134	−0.161513
$937$	29.4010	0.960487	0.480244	−	0.877135i	$-0.340548\pi$
$937$	29.4010	0.960487	0.480244	+	0.877135i	$0.340548\pi$
$938$	22.1854	0.724378
$939$	−19.3128	−0.630248
$940$	−26.4762	−0.863557
$941$	−47.2203	−1.53934	−0.769669	−	0.638443i	$-0.779579\pi$
$941$	−47.2203	−1.53934	−0.769669	+	0.638443i	$0.779579\pi$
$942$	2.98464	0.0972449
$943$	16.3400	0.532104
$944$	−23.1837	−0.754566
$945$	12.0804	0.392974
$946$	−0.0362890	−0.00117986
$947$	−3.36567	−0.109370	−0.0546848	−	0.998504i	$-0.517415\pi$
$947$	−3.36567	−0.109370	−0.0546848	+	0.998504i	$0.517415\pi$
$948$	−5.49049	−0.178323
$949$	1.46554	0.0475734
$950$	−6.65975	−0.216071
$951$	−8.20363	−0.266021
$952$	40.5149	1.31309
$953$	23.9717	0.776518	0.388259	−	0.921550i	$-0.373077\pi$
$953$	23.9717	0.776518	0.388259	+	0.921550i	$0.373077\pi$
$954$	−7.95994	−0.257713
$955$	9.01673	0.291774
$956$	−48.2471	−1.56042
$957$	5.41045	0.174895
$958$	6.38523	0.206297
$959$	31.5407	1.01850
$960$	1.78317	0.0575517
$961$	68.9120	2.22297
$962$	0.298040	0.00960920
$963$	48.2437	1.55463
$964$	−14.7547	−0.475216
$965$	−23.9174	−0.769928
$966$	−1.79607	−0.0577875
$967$	31.7347	1.02052	0.510259	−	0.860021i	$-0.329550\pi$
$967$	31.7347	1.02052	0.510259	+	0.860021i	$0.329550\pi$
$968$	16.3204	0.524558
$969$	−14.8005	−0.475461
$970$	8.51751	0.273481
$971$	58.6921	1.88352	0.941760	−	0.336286i	$-0.109171\pi$
$971$	58.6921	1.88352	0.941760	+	0.336286i	$0.109171\pi$
$972$	−23.9935	−0.769592
$973$	37.2357	1.19372
$974$	8.34097	0.267262
$975$	2.23756	0.0716593
$976$	−4.87728	−0.156118
$977$	−33.6594	−1.07686	−0.538430	−	0.842670i	$-0.680982\pi$
$977$	−33.6594	−1.07686	−0.538430	+	0.842670i	$0.680982\pi$
$978$	5.45902	0.174560
$979$	−14.4138	−0.460667
$980$	5.79064	0.184975
$981$	−31.3472	−1.00084
$982$	−4.32596	−0.138047
$983$	−7.51037	−0.239544	−0.119772	−	0.992801i	$-0.538216\pi$
$983$	−7.51037	−0.239544	−0.119772	+	0.992801i	$0.538216\pi$
$984$	9.69255	0.308987
$985$	−14.0759	−0.448495
$986$	−20.4049	−0.649826
$987$	−25.3332	−0.806365
$988$	6.27489	0.199631
$989$	0.0912627	0.00290198
$990$	2.25272	0.0715962
$991$	31.5801	1.00318	0.501588	−	0.865107i	$-0.332749\pi$
$991$	31.5801	1.00318	0.501588	+	0.865107i	$0.332749\pi$
$992$	−50.2489	−1.59540
$993$	−10.5402	−0.334483
$994$	−10.9453	−0.347163
$995$	−14.3263	−0.454174
$996$	6.15242	0.194947
$997$	−29.3811	−0.930510	−0.465255	−	0.885177i	$-0.654037\pi$
$997$	−29.3811	−0.930510	−0.465255	+	0.885177i	$0.654037\pi$
$998$	1.94298	0.0615039
$999$	2.02373	0.0640280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.e.1.14	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.e.1.14	✓	21	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.499344 q^{2} +0.601343 q^{3} -1.75066 q^{4} -1.13095 q^{5} +0.300277 q^{6} +3.15035 q^{7} -1.87287 q^{8} -2.63839 q^{9} +O(q^{10})\)	\(q+0.499344 q^{2} +0.601343 q^{3} -1.75066 q^{4} -1.13095 q^{5} +0.300277 q^{6} +3.15035 q^{7} -1.87287 q^{8} -2.63839 q^{9} -0.564734 q^{10} +1.51191 q^{11} -1.05274 q^{12} -1.00000 q^{13} +1.57311 q^{14} -0.680090 q^{15} +2.56611 q^{16} -6.86672 q^{17} -1.31746 q^{18} +3.58431 q^{19} +1.97991 q^{20} +1.89444 q^{21} +0.754961 q^{22} -1.89864 q^{23} -1.12623 q^{24} -3.72094 q^{25} -0.499344 q^{26} -3.39060 q^{27} -5.51518 q^{28} +5.95095 q^{29} -0.339599 q^{30} -9.99560 q^{31} +5.02710 q^{32} +0.909174 q^{33} -3.42885 q^{34} -3.56290 q^{35} +4.61891 q^{36} -0.596864 q^{37} +1.78980 q^{38} -0.601343 q^{39} +2.11812 q^{40} -8.60616 q^{41} +0.945976 q^{42} -0.0480674 q^{43} -2.64683 q^{44} +2.98389 q^{45} -0.948073 q^{46} -13.3724 q^{47} +1.54311 q^{48} +2.92470 q^{49} -1.85803 q^{50} -4.12925 q^{51} +1.75066 q^{52} +6.04188 q^{53} -1.69308 q^{54} -1.70990 q^{55} -5.90018 q^{56} +2.15540 q^{57} +2.97157 q^{58} -9.03458 q^{59} +1.19060 q^{60} -1.90065 q^{61} -4.99124 q^{62} -8.31184 q^{63} -2.62197 q^{64} +1.13095 q^{65} +0.453990 q^{66} +14.1029 q^{67} +12.0213 q^{68} -1.14173 q^{69} -1.77911 q^{70} -6.95775 q^{71} +4.94134 q^{72} -1.46554 q^{73} -0.298040 q^{74} -2.23756 q^{75} -6.27489 q^{76} +4.76303 q^{77} -0.300277 q^{78} +5.21541 q^{79} -2.90215 q^{80} +5.87625 q^{81} -4.29743 q^{82} -5.84418 q^{83} -3.31651 q^{84} +7.76594 q^{85} -0.0240022 q^{86} +3.57856 q^{87} -2.83160 q^{88} -9.53353 q^{89} +1.48999 q^{90} -3.15035 q^{91} +3.32386 q^{92} -6.01078 q^{93} -6.67742 q^{94} -4.05369 q^{95} +3.02301 q^{96} -15.0823 q^{97} +1.46043 q^{98} -3.98899 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - q^{2} - 6 q^{3} + 15 q^{4} - 18 q^{5} - 8 q^{6} - 2 q^{7} + 6 q^{8} + 11 q^{9}+O(q^{10}) \) 21 * q - q^2 - 6 * q^3 + 15 * q^4 - 18 * q^5 - 8 * q^6 - 2 * q^7 + 6 * q^8 + 11 * q^9	\( 21 q - q^{2} - 6 q^{3} + 15 q^{4} - 18 q^{5} - 8 q^{6} - 2 q^{7} + 6 q^{8} + 11 q^{9} - 10 q^{10} - 5 q^{11} - 22 q^{12} - 21 q^{13} - 24 q^{14} - q^{15} - 5 q^{16} - 18 q^{17} + 10 q^{18} - 6 q^{19} - 30 q^{20} - 17 q^{21} - 8 q^{22} - 14 q^{23} - 13 q^{24} + 11 q^{25} + q^{26} - 33 q^{27} - 2 q^{28} - 36 q^{29} + 2 q^{30} + q^{31} - 9 q^{32} - 11 q^{33} - 25 q^{34} - 37 q^{35} + 3 q^{36} + 5 q^{37} - 13 q^{38} + 6 q^{39} - 2 q^{40} - 32 q^{41} + 7 q^{42} + 2 q^{43} + 4 q^{44} - 32 q^{45} - 5 q^{46} - 12 q^{47} - 18 q^{48} + 5 q^{49} - 2 q^{50} - 27 q^{51} - 15 q^{52} - 49 q^{53} - 31 q^{54} - 9 q^{55} - 53 q^{56} + 14 q^{57} - 2 q^{58} - 34 q^{59} + 25 q^{60} - 27 q^{61} - 12 q^{62} + 41 q^{63} - 70 q^{64} + 18 q^{65} - 15 q^{66} - 12 q^{67} - 20 q^{68} - 70 q^{69} + 70 q^{70} - 26 q^{71} - 14 q^{72} + 23 q^{73} + 20 q^{74} - 9 q^{75} - 36 q^{76} - 62 q^{77} + 8 q^{78} - 7 q^{79} - 41 q^{80} - 3 q^{81} - 33 q^{82} - q^{83} - 48 q^{84} + 10 q^{85} - 23 q^{86} - 7 q^{87} + 9 q^{88} - 16 q^{89} - 30 q^{90} + 2 q^{91} - 27 q^{92} + 2 q^{93} - 37 q^{94} - 35 q^{95} + 55 q^{96} - 30 q^{97} - 43 q^{98} - 42 q^{99}+O(q^{100}) \) 21 * q - q^2 - 6 * q^3 + 15 * q^4 - 18 * q^5 - 8 * q^6 - 2 * q^7 + 6 * q^8 + 11 * q^9 - 10 * q^10 - 5 * q^11 - 22 * q^12 - 21 * q^13 - 24 * q^14 - q^15 - 5 * q^16 - 18 * q^17 + 10 * q^18 - 6 * q^19 - 30 * q^20 - 17 * q^21 - 8 * q^22 - 14 * q^23 - 13 * q^24 + 11 * q^25 + q^26 - 33 * q^27 - 2 * q^28 - 36 * q^29 + 2 * q^30 + q^31 - 9 * q^32 - 11 * q^33 - 25 * q^34 - 37 * q^35 + 3 * q^36 + 5 * q^37 - 13 * q^38 + 6 * q^39 - 2 * q^40 - 32 * q^41 + 7 * q^42 + 2 * q^43 + 4 * q^44 - 32 * q^45 - 5 * q^46 - 12 * q^47 - 18 * q^48 + 5 * q^49 - 2 * q^50 - 27 * q^51 - 15 * q^52 - 49 * q^53 - 31 * q^54 - 9 * q^55 - 53 * q^56 + 14 * q^57 - 2 * q^58 - 34 * q^59 + 25 * q^60 - 27 * q^61 - 12 * q^62 + 41 * q^63 - 70 * q^64 + 18 * q^65 - 15 * q^66 - 12 * q^67 - 20 * q^68 - 70 * q^69 + 70 * q^70 - 26 * q^71 - 14 * q^72 + 23 * q^73 + 20 * q^74 - 9 * q^75 - 36 * q^76 - 62 * q^77 + 8 * q^78 - 7 * q^79 - 41 * q^80 - 3 * q^81 - 33 * q^82 - q^83 - 48 * q^84 + 10 * q^85 - 23 * q^86 - 7 * q^87 + 9 * q^88 - 16 * q^89 - 30 * q^90 + 2 * q^91 - 27 * q^92 + 2 * q^93 - 37 * q^94 - 35 * q^95 + 55 * q^96 - 30 * q^97 - 43 * q^98 - 42 * q^99

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