LMFDB - Embedded newform 1441.2.a.e.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.635564 q^{2} -1.42688 q^{3} -1.59606 q^{4} +2.67263 q^{5} -0.906871 q^{6} -2.11184 q^{7} -2.28553 q^{8} -0.964025 q^{9} +O(q^{10})$	\(q+0.635564 q^{2} -1.42688 q^{3} -1.59606 q^{4} +2.67263 q^{5} -0.906871 q^{6} -2.11184 q^{7} -2.28553 q^{8} -0.964025 q^{9} +1.69862 q^{10} +1.00000 q^{11} +2.27738 q^{12} -5.57292 q^{13} -1.34221 q^{14} -3.81351 q^{15} +1.73952 q^{16} +1.99152 q^{17} -0.612699 q^{18} +5.50206 q^{19} -4.26567 q^{20} +3.01334 q^{21} +0.635564 q^{22} +4.34160 q^{23} +3.26116 q^{24} +2.14293 q^{25} -3.54195 q^{26} +5.65617 q^{27} +3.37063 q^{28} +3.87525 q^{29} -2.42373 q^{30} -6.82261 q^{31} +5.67663 q^{32} -1.42688 q^{33} +1.26574 q^{34} -5.64417 q^{35} +1.53864 q^{36} +10.3711 q^{37} +3.49691 q^{38} +7.95186 q^{39} -6.10835 q^{40} -1.68820 q^{41} +1.91517 q^{42} +2.29977 q^{43} -1.59606 q^{44} -2.57648 q^{45} +2.75936 q^{46} -1.80395 q^{47} -2.48208 q^{48} -2.54012 q^{49} +1.36197 q^{50} -2.84166 q^{51} +8.89470 q^{52} -1.43887 q^{53} +3.59486 q^{54} +2.67263 q^{55} +4.82667 q^{56} -7.85075 q^{57} +2.46297 q^{58} +1.49417 q^{59} +6.08658 q^{60} -3.35507 q^{61} -4.33620 q^{62} +2.03587 q^{63} +0.128819 q^{64} -14.8943 q^{65} -0.906871 q^{66} +15.5903 q^{67} -3.17859 q^{68} -6.19493 q^{69} -3.58723 q^{70} +5.41719 q^{71} +2.20330 q^{72} +12.6822 q^{73} +6.59151 q^{74} -3.05770 q^{75} -8.78160 q^{76} -2.11184 q^{77} +5.05392 q^{78} +12.9340 q^{79} +4.64909 q^{80} -5.17858 q^{81} -1.07296 q^{82} +2.76909 q^{83} -4.80946 q^{84} +5.32260 q^{85} +1.46165 q^{86} -5.52950 q^{87} -2.28553 q^{88} +0.365677 q^{89} -1.63752 q^{90} +11.7691 q^{91} -6.92945 q^{92} +9.73501 q^{93} -1.14652 q^{94} +14.7049 q^{95} -8.09984 q^{96} -2.42204 q^{97} -1.61441 q^{98} -0.964025 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9 + 14 * q^10 + 28 * q^11 - 6 * q^12 + 3 * q^13 - q^14 + 19 * q^15 + 29 * q^16 + 9 * q^17 - 2 * q^18 + 20 * q^19 + 6 * q^20 + 6 * q^21 + 7 * q^22 + 24 * q^23 + 20 * q^24 + 23 * q^25 + 10 * q^26 - 20 * q^27 - 3 * q^28 + 43 * q^29 + 11 * q^30 + 3 * q^31 + 44 * q^32 - 2 * q^33 - 28 * q^34 + 32 * q^35 + 24 * q^36 - 4 * q^37 + 24 * q^38 + 37 * q^39 + 22 * q^40 + 32 * q^41 - 27 * q^42 + 25 * q^43 + 27 * q^44 - 36 * q^45 + 10 * q^46 + 19 * q^47 + 42 * q^48 + 17 * q^49 + q^50 + 39 * q^51 - 19 * q^52 + 5 * q^53 + 6 * q^54 + 3 * q^55 + 8 * q^56 + 2 * q^57 + 21 * q^58 + 44 * q^59 + 65 * q^60 + 28 * q^61 + 60 * q^62 - 8 * q^63 + 5 * q^64 + 33 * q^65 - q^66 + 7 * q^67 + 13 * q^68 - 22 * q^69 + 9 * q^70 + 117 * q^71 - 17 * q^72 + 7 * q^73 + 41 * q^74 - 40 * q^75 + 34 * q^76 + 7 * q^77 - 97 * q^78 + 48 * q^79 + 41 * q^80 + 40 * q^81 + 2 * q^82 + 22 * q^83 + 27 * q^84 + 30 * q^85 + 24 * q^86 + 37 * q^87 + 21 * q^88 - 6 * q^89 + 4 * q^90 - 33 * q^91 + 18 * q^92 + 5 * q^93 - 43 * q^94 + 64 * q^95 + 55 * q^96 - 50 * q^97 + 97 * q^98 + 28 * 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 $

$2$	0.635564	0.449412	0.224706	−	0.974427i	$-0.427858\pi$
$2$	0.635564	0.449412	0.224706	+	0.974427i	$0.427858\pi$
$3$	−1.42688	−0.823807	−0.411904	−	0.911227i	$-0.635136\pi$
$3$	−1.42688	−0.823807	−0.411904	+	0.911227i	$0.635136\pi$
$4$	−1.59606	−0.798029
$5$	2.67263	1.19523	0.597617	−	0.801781i	$-0.296114\pi$
$5$	2.67263	1.19523	0.597617	+	0.801781i	$0.296114\pi$
$6$	−0.906871	−0.370229
$7$	−2.11184	−0.798202	−0.399101	−	0.916907i	$-0.630678\pi$
$7$	−2.11184	−0.798202	−0.399101	+	0.916907i	$0.630678\pi$
$8$	−2.28553	−0.808055
$9$	−0.964025	−0.321342
$10$	1.69862	0.537152
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.27738	0.657422
$13$	−5.57292	−1.54565	−0.772825	−	0.634620i	$-0.781157\pi$
$13$	−5.57292	−1.54565	−0.772825	+	0.634620i	$0.781157\pi$
$14$	−1.34221	−0.358721
$15$	−3.81351	−0.984643
$16$	1.73952	0.434880
$17$	1.99152	0.483015	0.241508	−	0.970399i	$-0.422358\pi$
$17$	1.99152	0.483015	0.241508	+	0.970399i	$0.422358\pi$
$18$	−0.612699	−0.144415
$19$	5.50206	1.26226	0.631129	−	0.775678i	$-0.282592\pi$
$19$	5.50206	1.26226	0.631129	+	0.775678i	$0.282592\pi$
$20$	−4.26567	−0.953832
$21$	3.01334	0.657564
$22$	0.635564	0.135503
$23$	4.34160	0.905286	0.452643	−	0.891692i	$-0.350481\pi$
$23$	4.34160	0.905286	0.452643	+	0.891692i	$0.350481\pi$
$24$	3.26116	0.665682
$25$	2.14293	0.428586
$26$	−3.54195	−0.694633
$27$	5.65617	1.08853
$28$	3.37063	0.636988
$29$	3.87525	0.719615	0.359808	−	0.933027i	$-0.382842\pi$
$29$	3.87525	0.719615	0.359808	+	0.933027i	$0.382842\pi$
$30$	−2.42373	−0.442510
$31$	−6.82261	−1.22538	−0.612688	−	0.790325i	$-0.709912\pi$
$31$	−6.82261	−1.22538	−0.612688	+	0.790325i	$0.709912\pi$
$32$	5.67663	1.00350
$33$	−1.42688	−0.248387
$34$	1.26574	0.217073
$35$	−5.64417	−0.954038
$36$	1.53864	0.256440
$37$	10.3711	1.70500	0.852500	−	0.522727i	$-0.175085\pi$
$37$	10.3711	1.70500	0.852500	+	0.522727i	$0.175085\pi$
$38$	3.49691	0.567273
$39$	7.95186	1.27332
$40$	−6.10835	−0.965816
$41$	−1.68820	−0.263653	−0.131826	−	0.991273i	$-0.542084\pi$
$41$	−1.68820	−0.263653	−0.131826	+	0.991273i	$0.542084\pi$
$42$	1.91517	0.295517
$43$	2.29977	0.350711	0.175355	−	0.984505i	$-0.443893\pi$
$43$	2.29977	0.350711	0.175355	+	0.984505i	$0.443893\pi$
$44$	−1.59606	−0.240615
$45$	−2.57648	−0.384079
$46$	2.75936	0.406846
$47$	−1.80395	−0.263133	−0.131567	−	0.991307i	$-0.542001\pi$
$47$	−1.80395	−0.263133	−0.131567	+	0.991307i	$0.542001\pi$
$48$	−2.48208	−0.358257
$49$	−2.54012	−0.362874
$50$	1.36197	0.192612
$51$	−2.84166	−0.397912
$52$	8.89470	1.23347
$53$	−1.43887	−0.197644	−0.0988221	−	0.995105i	$-0.531507\pi$
$53$	−1.43887	−0.197644	−0.0988221	+	0.995105i	$0.531507\pi$
$54$	3.59486	0.489198
$55$	2.67263	0.360377
$56$	4.82667	0.644991
$57$	−7.85075	−1.03986
$58$	2.46297	0.323403
$59$	1.49417	0.194524	0.0972619	−	0.995259i	$-0.468992\pi$
$59$	1.49417	0.194524	0.0972619	+	0.995259i	$0.468992\pi$
$60$	6.08658	0.785774
$61$	−3.35507	−0.429573	−0.214787	−	0.976661i	$-0.568906\pi$
$61$	−3.35507	−0.429573	−0.214787	+	0.976661i	$0.568906\pi$
$62$	−4.33620	−0.550698
$63$	2.03587	0.256495
$64$	0.128819	0.0161024
$65$	−14.8943	−1.84741
$66$	−0.906871	−0.111628
$67$	15.5903	1.90466	0.952328	−	0.305075i	$-0.0986814\pi$
$67$	15.5903	1.90466	0.952328	+	0.305075i	$0.0986814\pi$
$68$	−3.17859	−0.385460
$69$	−6.19493	−0.745781
$70$	−3.58723	−0.428756
$71$	5.41719	0.642902	0.321451	−	0.946926i	$-0.395829\pi$
$71$	5.41719	0.642902	0.321451	+	0.946926i	$0.395829\pi$
$72$	2.20330	0.259662
$73$	12.6822	1.48434	0.742169	−	0.670213i	$-0.233797\pi$
$73$	12.6822	1.48434	0.742169	+	0.670213i	$0.233797\pi$
$74$	6.59151	0.766247
$75$	−3.05770	−0.353072
$76$	−8.78160	−1.00732
$77$	−2.11184	−0.240667
$78$	5.05392	0.572243
$79$	12.9340	1.45519	0.727594	−	0.686008i	$-0.240639\pi$
$79$	12.9340	1.45519	0.727594	+	0.686008i	$0.240639\pi$
$80$	4.64909	0.519784
$81$	−5.17858	−0.575398
$82$	−1.07296	−0.118489
$83$	2.76909	0.303947	0.151974	−	0.988385i	$-0.451437\pi$
$83$	2.76909	0.303947	0.151974	+	0.988385i	$0.451437\pi$
$84$	−4.80946	−0.524756
$85$	5.32260	0.577317
$86$	1.46165	0.157614
$87$	−5.52950	−0.592824
$88$	−2.28553	−0.243638
$89$	0.365677	0.0387617	0.0193808	−	0.999812i	$-0.493831\pi$
$89$	0.365677	0.0387617	0.0193808	+	0.999812i	$0.493831\pi$
$90$	−1.63752	−0.172609
$91$	11.7691	1.23374
$92$	−6.92945	−0.722445
$93$	9.73501	1.00947
$94$	−1.14652	−0.118255
$95$	14.7049	1.50869
$96$	−8.09984	−0.826687
$97$	−2.42204	−0.245921	−0.122961	−	0.992412i	$-0.539239\pi$
$97$	−2.42204	−0.245921	−0.122961	+	0.992412i	$0.539239\pi$
$98$	−1.61441	−0.163080
$99$	−0.964025	−0.0968881
$100$	−3.42024	−0.342024
$101$	11.1753	1.11198	0.555992	−	0.831187i	$-0.312338\pi$
$101$	11.1753	1.11198	0.555992	+	0.831187i	$0.312338\pi$
$102$	−1.80605	−0.178826
$103$	−7.53982	−0.742920	−0.371460	−	0.928449i	$-0.621143\pi$
$103$	−7.53982	−0.742920	−0.371460	+	0.928449i	$0.621143\pi$
$104$	12.7370	1.24897
$105$	8.05353	0.785944
$106$	−0.914495	−0.0888236
$107$	16.1231	1.55868	0.779341	−	0.626600i	$-0.215554\pi$
$107$	16.1231	1.55868	0.779341	+	0.626600i	$0.215554\pi$
$108$	−9.02758	−0.868679
$109$	12.8708	1.23280	0.616400	−	0.787433i	$-0.288590\pi$
$109$	12.8708	1.23280	0.616400	+	0.787433i	$0.288590\pi$
$110$	1.69862	0.161958
$111$	−14.7983	−1.40459
$112$	−3.67359	−0.347122
$113$	−12.9516	−1.21838	−0.609191	−	0.793024i	$-0.708506\pi$
$113$	−12.9516	−1.21838	−0.609191	+	0.793024i	$0.708506\pi$
$114$	−4.98965	−0.467324
$115$	11.6035	1.08203
$116$	−6.18512	−0.574274
$117$	5.37243	0.496681
$118$	0.949638	0.0874212
$119$	−4.20578	−0.385544
$120$	8.71586	0.795646
$121$	1.00000	0.0909091
$122$	−2.13236	−0.193055
$123$	2.40885	0.217199
$124$	10.8893	0.977886
$125$	−7.63588	−0.682974
$126$	1.29392	0.115272
$127$	−14.5643	−1.29237	−0.646185	−	0.763181i	$-0.723637\pi$
$127$	−14.5643	−1.29237	−0.646185	+	0.763181i	$0.723637\pi$
$128$	−11.2714	−0.996259
$129$	−3.28148	−0.288918
$130$	−9.46630	−0.830249
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	2.27738	0.198220
$133$	−11.6195	−1.00754
$134$	9.90863	0.855975
$135$	15.1168	1.30105
$136$	−4.55168	−0.390303
$137$	−11.5821	−0.989524	−0.494762	−	0.869029i	$-0.664745\pi$
$137$	−11.5821	−0.989524	−0.494762	+	0.869029i	$0.664745\pi$
$138$	−3.93727	−0.335163
$139$	17.1513	1.45475	0.727377	−	0.686238i	$-0.240739\pi$
$139$	17.1513	1.45475	0.727377	+	0.686238i	$0.240739\pi$
$140$	9.00842	0.761351
$141$	2.57401	0.216771
$142$	3.44297	0.288928
$143$	−5.57292	−0.466031
$144$	−1.67694	−0.139745
$145$	10.3571	0.860109
$146$	8.06034	0.667079
$147$	3.62443	0.298938
$148$	−16.5529	−1.36064
$149$	1.68900	0.138368	0.0691840	−	0.997604i	$-0.477960\pi$
$149$	1.68900	0.138368	0.0691840	+	0.997604i	$0.477960\pi$
$150$	−1.94336	−0.158675
$151$	4.70956	0.383258	0.191629	−	0.981467i	$-0.438623\pi$
$151$	4.70956	0.383258	0.191629	+	0.981467i	$0.438623\pi$
$152$	−12.5751	−1.01997
$153$	−1.91988	−0.155213
$154$	−1.34221	−0.108158
$155$	−18.2343	−1.46461
$156$	−12.6916	−1.01614
$157$	−12.0416	−0.961022	−0.480511	−	0.876989i	$-0.659549\pi$
$157$	−12.0416	−0.961022	−0.480511	+	0.876989i	$0.659549\pi$
$158$	8.22038	0.653978
$159$	2.05309	0.162821
$160$	15.1715	1.19941
$161$	−9.16878	−0.722601
$162$	−3.29132	−0.258591
$163$	−5.75891	−0.451073	−0.225536	−	0.974235i	$-0.572413\pi$
$163$	−5.75891	−0.451073	−0.225536	+	0.974235i	$0.572413\pi$
$164$	2.69447	0.210403
$165$	−3.81351	−0.296881
$166$	1.75993	0.136597
$167$	−10.6295	−0.822538	−0.411269	−	0.911514i	$-0.634914\pi$
$167$	−10.6295	−0.822538	−0.411269	+	0.911514i	$0.634914\pi$
$168$	−6.88706	−0.531348
$169$	18.0574	1.38903
$170$	3.38285	0.259453
$171$	−5.30412	−0.405616
$172$	−3.67056	−0.279878
$173$	15.6446	1.18944	0.594718	−	0.803935i	$-0.297264\pi$
$173$	15.6446	1.18944	0.594718	+	0.803935i	$0.297264\pi$
$174$	−3.51435	−0.266422
$175$	−4.52553	−0.342098
$176$	1.73952	0.131121
$177$	−2.13199	−0.160250
$178$	0.232411	0.0174199
$179$	−6.96406	−0.520518	−0.260259	−	0.965539i	$-0.583808\pi$
$179$	−6.96406	−0.520518	−0.260259	+	0.965539i	$0.583808\pi$
$180$	4.11221	0.306506
$181$	9.19270	0.683288	0.341644	−	0.939829i	$-0.389016\pi$
$181$	9.19270	0.683288	0.341644	+	0.939829i	$0.389016\pi$
$182$	7.48003	0.554457
$183$	4.78727	0.353885
$184$	−9.92284	−0.731521
$185$	27.7181	2.03788
$186$	6.18722	0.453669
$187$	1.99152	0.145635
$188$	2.87921	0.209988
$189$	−11.9449	−0.868867
$190$	9.34593	0.678025
$191$	−4.07006	−0.294499	−0.147250	−	0.989099i	$-0.547042\pi$
$191$	−4.07006	−0.294499	−0.147250	+	0.989099i	$0.547042\pi$
$192$	−0.183809	−0.0132653
$193$	−5.79163	−0.416890	−0.208445	−	0.978034i	$-0.566840\pi$
$193$	−5.79163	−0.416890	−0.208445	+	0.978034i	$0.566840\pi$
$194$	−1.53936	−0.110520
$195$	21.2524	1.52191
$196$	4.05418	0.289584
$197$	−20.2491	−1.44269	−0.721343	−	0.692578i	$-0.756475\pi$
$197$	−20.2491	−1.44269	−0.721343	+	0.692578i	$0.756475\pi$
$198$	−0.612699	−0.0435426
$199$	24.0077	1.70186	0.850932	−	0.525276i	$-0.176038\pi$
$199$	24.0077	1.70186	0.850932	+	0.525276i	$0.176038\pi$
$200$	−4.89772	−0.346321
$201$	−22.2454	−1.56907
$202$	7.10262	0.499739
$203$	−8.18391	−0.574398
$204$	4.53545	0.317545
$205$	−4.51193	−0.315127
$206$	−4.79204	−0.333877
$207$	−4.18541	−0.290906
$208$	−9.69420	−0.672172
$209$	5.50206	0.380585
$210$	5.11853	0.353212
$211$	−0.465135	−0.0320212	−0.0160106	−	0.999872i	$-0.505097\pi$
$211$	−0.465135	−0.0320212	−0.0160106	+	0.999872i	$0.505097\pi$
$212$	2.29652	0.157726
$213$	−7.72966	−0.529628
$214$	10.2473	0.700490
$215$	6.14641	0.419182
$216$	−12.9273	−0.879593
$217$	14.4083	0.978097
$218$	8.18023	0.554035
$219$	−18.0959	−1.22281
$220$	−4.26567	−0.287591
$221$	−11.0986	−0.746572
$222$	−9.40526	−0.631240
$223$	27.2043	1.82174	0.910868	−	0.412697i	$-0.135413\pi$
$223$	27.2043	1.82174	0.910868	+	0.412697i	$0.135413\pi$
$224$	−11.9881	−0.800992
$225$	−2.06584	−0.137723
$226$	−8.23155	−0.547555
$227$	−29.5329	−1.96017	−0.980084	−	0.198581i	$-0.936367\pi$
$227$	−29.5329	−1.96017	−0.980084	+	0.198581i	$0.936367\pi$
$228$	12.5303	0.829837
$229$	−24.2066	−1.59962	−0.799809	−	0.600254i	$-0.795066\pi$
$229$	−24.2066	−1.59962	−0.799809	+	0.600254i	$0.795066\pi$
$230$	7.37475	0.486277
$231$	3.01334	0.198263
$232$	−8.85697	−0.581489
$233$	−4.39798	−0.288122	−0.144061	−	0.989569i	$-0.546016\pi$
$233$	−4.39798	−0.288122	−0.144061	+	0.989569i	$0.546016\pi$
$234$	3.41452	0.223214
$235$	−4.82128	−0.314506
$236$	−2.38478	−0.155236
$237$	−18.4552	−1.19879
$238$	−2.67305	−0.173268
$239$	4.92791	0.318760	0.159380	−	0.987217i	$-0.449051\pi$
$239$	4.92791	0.318760	0.159380	+	0.987217i	$0.449051\pi$
$240$	−6.63367	−0.428202
$241$	9.89883	0.637640	0.318820	−	0.947815i	$-0.396714\pi$
$241$	9.89883	0.637640	0.318820	+	0.947815i	$0.396714\pi$
$242$	0.635564	0.0408556
$243$	−9.57932	−0.614514
$244$	5.35489	0.342812
$245$	−6.78879	−0.433720
$246$	1.53098	0.0976118
$247$	−30.6625	−1.95101
$248$	15.5932	0.990171
$249$	−3.95115	−0.250394
$250$	−4.85309	−0.306936
$251$	11.1753	0.705377	0.352688	−	0.935741i	$-0.385268\pi$
$251$	11.1753	0.705377	0.352688	+	0.935741i	$0.385268\pi$
$252$	−3.24937	−0.204691
$253$	4.34160	0.272954
$254$	−9.25652	−0.580806
$255$	−7.59469	−0.475598
$256$	−7.42132	−0.463833
$257$	−25.0885	−1.56498	−0.782490	−	0.622663i	$-0.786051\pi$
$257$	−25.0885	−1.56498	−0.782490	+	0.622663i	$0.786051\pi$
$258$	−2.08559	−0.129843
$259$	−21.9022	−1.36093
$260$	23.7722	1.47429
$261$	−3.73583	−0.231242
$262$	−0.635564	−0.0392653
$263$	29.1202	1.79563	0.897815	−	0.440374i	$-0.145154\pi$
$263$	29.1202	1.79563	0.897815	+	0.440374i	$0.145154\pi$
$264$	3.26116	0.200711
$265$	−3.84557	−0.236231
$266$	−7.38492	−0.452799
$267$	−0.521776	−0.0319321
$268$	−24.8830	−1.51997
$269$	16.9907	1.03594	0.517971	−	0.855398i	$-0.326687\pi$
$269$	16.9907	1.03594	0.517971	+	0.855398i	$0.326687\pi$
$270$	9.60771	0.584707
$271$	23.2644	1.41321	0.706606	−	0.707607i	$-0.250225\pi$
$271$	23.2644	1.41321	0.706606	+	0.707607i	$0.250225\pi$
$272$	3.46429	0.210054
$273$	−16.7931	−1.01636
$274$	−7.36115	−0.444703
$275$	2.14293	0.129224
$276$	9.88746	0.595155
$277$	2.15250	0.129331	0.0646657	−	0.997907i	$-0.479402\pi$
$277$	2.15250	0.129331	0.0646657	+	0.997907i	$0.479402\pi$
$278$	10.9007	0.653783
$279$	6.57716	0.393764
$280$	12.8999	0.770916
$281$	−32.1587	−1.91842	−0.959212	−	0.282687i	$-0.908774\pi$
$281$	−32.1587	−1.91842	−0.959212	+	0.282687i	$0.908774\pi$
$282$	1.63595	0.0974193
$283$	1.63170	0.0969945	0.0484972	−	0.998823i	$-0.484557\pi$
$283$	1.63170	0.0969945	0.0484972	+	0.998823i	$0.484557\pi$
$284$	−8.64616	−0.513055
$285$	−20.9821	−1.24287
$286$	−3.54195	−0.209440
$287$	3.56522	0.210448
$288$	−5.47241	−0.322465
$289$	−13.0338	−0.766696
$290$	6.58259	0.386543
$291$	3.45595	0.202592
$292$	−20.2415	−1.18455
$293$	0.176174	0.0102922	0.00514611	−	0.999987i	$-0.498362\pi$
$293$	0.176174	0.0102922	0.00514611	+	0.999987i	$0.498362\pi$
$294$	2.30356	0.134346
$295$	3.99335	0.232502
$296$	−23.7034	−1.37773
$297$	5.65617	0.328204
$298$	1.07346	0.0621842
$299$	−24.1954	−1.39926
$300$	4.88026	0.281762
$301$	−4.85674	−0.279938
$302$	2.99323	0.172241
$303$	−15.9458	−0.916061
$304$	9.57093	0.548931
$305$	−8.96686	−0.513441
$306$	−1.22020	−0.0697545
$307$	−6.66231	−0.380238	−0.190119	−	0.981761i	$-0.560887\pi$
$307$	−6.66231	−0.380238	−0.190119	+	0.981761i	$0.560887\pi$
$308$	3.37063	0.192059
$309$	10.7584	0.612023
$310$	−11.5890	−0.658214
$311$	8.61808	0.488687	0.244343	−	0.969689i	$-0.421428\pi$
$311$	8.61808	0.488687	0.244343	+	0.969689i	$0.421428\pi$
$312$	−18.1742	−1.02891
$313$	−29.9124	−1.69075	−0.845375	−	0.534174i	$-0.820623\pi$
$313$	−29.9124	−1.69075	−0.845375	+	0.534174i	$0.820623\pi$
$314$	−7.65319	−0.431894
$315$	5.44112	0.306572
$316$	−20.6434	−1.16128
$317$	21.3339	1.19823	0.599117	−	0.800662i	$-0.295518\pi$
$317$	21.3339	1.19823	0.599117	+	0.800662i	$0.295518\pi$
$318$	1.30487	0.0731735
$319$	3.87525	0.216972
$320$	0.344286	0.0192462
$321$	−23.0057	−1.28405
$322$	−5.82735	−0.324745
$323$	10.9575	0.609690
$324$	8.26532	0.459185
$325$	−11.9424	−0.662444
$326$	−3.66016	−0.202717
$327$	−18.3651	−1.01559
$328$	3.85843	0.213046
$329$	3.80966	0.210033
$330$	−2.42373	−0.133422
$331$	−9.19377	−0.505335	−0.252668	−	0.967553i	$-0.581308\pi$
$331$	−9.19377	−0.505335	−0.252668	+	0.967553i	$0.581308\pi$
$332$	−4.41963	−0.242559
$333$	−9.99801	−0.547887
$334$	−6.75575	−0.369658
$335$	41.6670	2.27651
$336$	5.24176	0.285962
$337$	−19.9447	−1.08646	−0.543229	−	0.839585i	$-0.682798\pi$
$337$	−19.9447	−1.08646	−0.543229	+	0.839585i	$0.682798\pi$
$338$	11.4766	0.624247
$339$	18.4803	1.00371
$340$	−8.49518	−0.460716
$341$	−6.82261	−0.369465
$342$	−3.37111	−0.182288
$343$	20.1472	1.08785
$344$	−5.25617	−0.283394
$345$	−16.5567	−0.891384
$346$	9.94313	0.534546
$347$	32.9366	1.76813	0.884065	−	0.467364i	$-0.154796\pi$
$347$	32.9366	1.76813	0.884065	+	0.467364i	$0.154796\pi$
$348$	8.82540	0.473091
$349$	−5.83568	−0.312377	−0.156188	−	0.987727i	$-0.549921\pi$
$349$	−5.83568	−0.312377	−0.156188	+	0.987727i	$0.549921\pi$
$350$	−2.87627	−0.153743
$351$	−31.5214	−1.68249
$352$	5.67663	0.302565
$353$	−34.1036	−1.81515	−0.907575	−	0.419891i	$-0.862068\pi$
$353$	−34.1036	−1.81515	−0.907575	+	0.419891i	$0.862068\pi$
$354$	−1.35502	−0.0720183
$355$	14.4781	0.768419
$356$	−0.583642	−0.0309329
$357$	6.00113	0.317614
$358$	−4.42610	−0.233927
$359$	21.1084	1.11406	0.557031	−	0.830492i	$-0.311941\pi$
$359$	21.1084	1.11406	0.557031	+	0.830492i	$0.311941\pi$
$360$	5.88860	0.310357
$361$	11.2726	0.593295
$362$	5.84255	0.307078
$363$	−1.42688	−0.0748916
$364$	−18.7842	−0.984561
$365$	33.8948	1.77413
$366$	3.04262	0.159040
$367$	−3.58520	−0.187146	−0.0935731	−	0.995612i	$-0.529829\pi$
$367$	−3.58520	−0.187146	−0.0935731	+	0.995612i	$0.529829\pi$
$368$	7.55230	0.393691
$369$	1.62747	0.0847226
$370$	17.6166	0.915845
$371$	3.03867	0.157760
$372$	−15.5376	−0.805590
$373$	20.2202	1.04696	0.523482	−	0.852037i	$-0.324633\pi$
$373$	20.2202	1.04696	0.523482	+	0.852037i	$0.324633\pi$
$374$	1.26574	0.0654499
$375$	10.8955	0.562639
$376$	4.12297	0.212626
$377$	−21.5964	−1.11227
$378$	−7.59178	−0.390479
$379$	37.4368	1.92300	0.961500	−	0.274805i	$-0.0886133\pi$
$379$	37.4368	1.92300	0.961500	+	0.274805i	$0.0886133\pi$
$380$	−23.4699	−1.20398
$381$	20.7814	1.06466
$382$	−2.58678	−0.132351
$383$	−4.75517	−0.242978	−0.121489	−	0.992593i	$-0.538767\pi$
$383$	−4.75517	−0.242978	−0.121489	+	0.992593i	$0.538767\pi$
$384$	16.0829	0.820725
$385$	−5.64417	−0.287653
$386$	−3.68095	−0.187355
$387$	−2.21703	−0.112698
$388$	3.86572	0.196252
$389$	3.93336	0.199429	0.0997147	−	0.995016i	$-0.468207\pi$
$389$	3.93336	0.199429	0.0997147	+	0.995016i	$0.468207\pi$
$390$	13.5072	0.683965
$391$	8.64640	0.437267
$392$	5.80550	0.293222
$393$	1.42688	0.0719764
$394$	−12.8696	−0.648360
$395$	34.5677	1.73929
$396$	1.53864	0.0773195
$397$	26.7803	1.34407	0.672033	−	0.740521i	$-0.265421\pi$
$397$	26.7803	1.34407	0.672033	+	0.740521i	$0.265421\pi$
$398$	15.2585	0.764837
$399$	16.5796	0.830016
$400$	3.72767	0.186383
$401$	34.5771	1.72670	0.863348	−	0.504609i	$-0.168363\pi$
$401$	34.5771	1.72670	0.863348	+	0.504609i	$0.168363\pi$
$402$	−14.1384	−0.705158
$403$	38.0218	1.89400
$404$	−17.8364	−0.887396
$405$	−13.8404	−0.687736
$406$	−5.20140	−0.258141
$407$	10.3711	0.514077
$408$	6.49468	0.321534
$409$	18.9294	0.935997	0.467999	−	0.883729i	$-0.344975\pi$
$409$	18.9294	0.935997	0.467999	+	0.883729i	$0.344975\pi$
$410$	−2.86762	−0.141622
$411$	16.5262	0.815177
$412$	12.0340	0.592872
$413$	−3.15544	−0.155269
$414$	−2.66010	−0.130737
$415$	7.40074	0.363288
$416$	−31.6354	−1.55105
$417$	−24.4728	−1.19844
$418$	3.49691	0.171039
$419$	25.0606	1.22429	0.612145	−	0.790746i	$-0.290307\pi$
$419$	25.0606	1.22429	0.612145	+	0.790746i	$0.290307\pi$
$420$	−12.8539	−0.627206
$421$	0.276791	0.0134900	0.00674498	−	0.999977i	$-0.497853\pi$
$421$	0.276791	0.0134900	0.00674498	+	0.999977i	$0.497853\pi$
$422$	−0.295623	−0.0143907
$423$	1.73905	0.0845556
$424$	3.28858	0.159707
$425$	4.26770	0.207014
$426$	−4.91269	−0.238021
$427$	7.08539	0.342886
$428$	−25.7335	−1.24387
$429$	7.95186	0.383920
$430$	3.90644	0.188385
$431$	−3.17833	−0.153095	−0.0765474	−	0.997066i	$-0.524390\pi$
$431$	−3.17833	−0.153095	−0.0765474	+	0.997066i	$0.524390\pi$
$432$	9.83902	0.473380
$433$	−17.7138	−0.851272	−0.425636	−	0.904895i	$-0.639950\pi$
$433$	−17.7138	−0.851272	−0.425636	+	0.904895i	$0.639950\pi$
$434$	9.15738	0.439568
$435$	−14.7783	−0.708564
$436$	−20.5426	−0.983811
$437$	23.8877	1.14270
$438$	−11.5011	−0.549544
$439$	0.563032	0.0268721	0.0134360	−	0.999910i	$-0.495723\pi$
$439$	0.563032	0.0268721	0.0134360	+	0.999910i	$0.495723\pi$
$440$	−6.10835	−0.291204
$441$	2.44874	0.116606
$442$	−7.05387	−0.335518
$443$	32.0981	1.52502	0.762512	−	0.646974i	$-0.223966\pi$
$443$	32.0981	1.52502	0.762512	+	0.646974i	$0.223966\pi$
$444$	23.6189	1.12091
$445$	0.977318	0.0463293
$446$	17.2901	0.818709
$447$	−2.40999	−0.113989
$448$	−0.272046	−0.0128530
$449$	25.5201	1.20437	0.602184	−	0.798357i	$-0.294297\pi$
$449$	25.5201	1.20437	0.602184	+	0.798357i	$0.294297\pi$
$450$	−1.31297	−0.0618941
$451$	−1.68820	−0.0794943
$452$	20.6715	0.972304
$453$	−6.71996	−0.315731
$454$	−18.7701	−0.880923
$455$	31.4545	1.47461
$456$	17.9431	0.840262
$457$	3.55758	0.166417	0.0832084	−	0.996532i	$-0.473483\pi$
$457$	3.55758	0.166417	0.0832084	+	0.996532i	$0.473483\pi$
$458$	−15.3849	−0.718887
$459$	11.2644	0.525777
$460$	−18.5198	−0.863491
$461$	22.9276	1.06785	0.533923	−	0.845533i	$-0.320717\pi$
$461$	22.9276	1.06785	0.533923	+	0.845533i	$0.320717\pi$
$462$	1.91517	0.0891017
$463$	−24.4052	−1.13420	−0.567102	−	0.823647i	$-0.691936\pi$
$463$	−24.4052	−1.13420	−0.567102	+	0.823647i	$0.691936\pi$
$464$	6.74107	0.312946
$465$	26.0180	1.20656
$466$	−2.79520	−0.129485
$467$	−18.9601	−0.877367	−0.438683	−	0.898642i	$-0.644555\pi$
$467$	−18.9601	−0.877367	−0.438683	+	0.898642i	$0.644555\pi$
$468$	−8.57471	−0.396366
$469$	−32.9242	−1.52030
$470$	−3.06423	−0.141343
$471$	17.1818	0.791697
$472$	−3.41495	−0.157186
$473$	2.29977	0.105743
$474$	−11.7295	−0.538752
$475$	11.7905	0.540986
$476$	6.71268	0.307675
$477$	1.38711	0.0635113
$478$	3.13200	0.143254
$479$	−4.48396	−0.204878	−0.102439	−	0.994739i	$-0.532665\pi$
$479$	−4.48396	−0.204878	−0.102439	+	0.994739i	$0.532665\pi$
$480$	−21.6479	−0.988085
$481$	−57.7974	−2.63533
$482$	6.29134	0.286563
$483$	13.0827	0.595284
$484$	−1.59606	−0.0725481
$485$	−6.47321	−0.293933
$486$	−6.08827	−0.276170
$487$	−11.3910	−0.516174	−0.258087	−	0.966122i	$-0.583092\pi$
$487$	−11.3910	−0.516174	−0.258087	+	0.966122i	$0.583092\pi$
$488$	7.66810	0.347119
$489$	8.21725	0.371597
$490$	−4.31471	−0.194919
$491$	−33.3430	−1.50475	−0.752374	−	0.658736i	$-0.771092\pi$
$491$	−33.3430	−1.50475	−0.752374	+	0.658736i	$0.771092\pi$
$492$	−3.84467	−0.173331
$493$	7.71764	0.347585
$494$	−19.4880	−0.876806
$495$	−2.57648	−0.115804
$496$	−11.8681	−0.532891
$497$	−11.4403	−0.513166
$498$	−2.51121	−0.112530
$499$	6.65723	0.298019	0.149009	−	0.988836i	$-0.452392\pi$
$499$	6.65723	0.298019	0.149009	+	0.988836i	$0.452392\pi$
$500$	12.1873	0.545033
$501$	15.1670	0.677613
$502$	7.10260	0.317005
$503$	−11.0170	−0.491224	−0.245612	−	0.969368i	$-0.578989\pi$
$503$	−11.0170	−0.491224	−0.245612	+	0.969368i	$0.578989\pi$
$504$	−4.65303	−0.207262
$505$	29.8674	1.32908
$506$	2.75936	0.122669
$507$	−25.7657	−1.14429
$508$	23.2454	1.03135
$509$	−19.1620	−0.849340	−0.424670	−	0.905348i	$-0.639610\pi$
$509$	−19.1620	−0.849340	−0.424670	+	0.905348i	$0.639610\pi$
$510$	−4.82691	−0.213739
$511$	−26.7828	−1.18480
$512$	17.8260	0.787807
$513$	31.1206	1.37401
$514$	−15.9454	−0.703320
$515$	−20.1511	−0.887964
$516$	5.23743	0.230565
$517$	−1.80395	−0.0793376
$518$	−13.9202	−0.611620
$519$	−22.3229	−0.979866
$520$	34.0414	1.49281
$521$	−12.8768	−0.564143	−0.282072	−	0.959393i	$-0.591022\pi$
$521$	−12.8768	−0.564143	−0.282072	+	0.959393i	$0.591022\pi$
$522$	−2.37436	−0.103923
$523$	−16.3665	−0.715658	−0.357829	−	0.933787i	$-0.616483\pi$
$523$	−16.3665	−0.715658	−0.357829	+	0.933787i	$0.616483\pi$
$524$	1.59606	0.0697241
$525$	6.45738	0.281823
$526$	18.5078	0.806976
$527$	−13.5874	−0.591875
$528$	−2.48208	−0.108019
$529$	−4.15051	−0.180457
$530$	−2.44410	−0.106165
$531$	−1.44041	−0.0625086
$532$	18.5454	0.804044
$533$	9.40821	0.407515
$534$	−0.331622	−0.0143507
$535$	43.0911	1.86299
$536$	−35.6320	−1.53907
$537$	9.93685	0.428807
$538$	10.7987	0.465565
$539$	−2.54012	−0.109411
$540$	−24.1273	−1.03828
$541$	−20.0475	−0.861909	−0.430955	−	0.902374i	$-0.641823\pi$
$541$	−20.0475	−0.861909	−0.430955	+	0.902374i	$0.641823\pi$
$542$	14.7860	0.635114
$543$	−13.1169	−0.562898
$544$	11.3051	0.484704
$545$	34.3989	1.47349
$546$	−10.6731	−0.456766
$547$	−22.5020	−0.962117	−0.481059	−	0.876688i	$-0.659748\pi$
$547$	−22.5020	−0.962117	−0.481059	+	0.876688i	$0.659748\pi$
$548$	18.4857	0.789669
$549$	3.23437	0.138040
$550$	1.36197	0.0580746
$551$	21.3218	0.908340
$552$	14.1587	0.602632
$553$	−27.3146	−1.16153
$554$	1.36805	0.0581230
$555$	−39.5503	−1.67882
$556$	−27.3745	−1.16094
$557$	41.8190	1.77193	0.885965	−	0.463753i	$-0.153497\pi$
$557$	41.8190	1.77193	0.885965	+	0.463753i	$0.153497\pi$
$558$	4.18021	0.176962
$559$	−12.8164	−0.542076
$560$	−9.81814	−0.414892
$561$	−2.84166	−0.119975
$562$	−20.4389	−0.862162
$563$	−32.4161	−1.36617	−0.683087	−	0.730337i	$-0.739363\pi$
$563$	−32.4161	−1.36617	−0.683087	+	0.730337i	$0.739363\pi$
$564$	−4.10827	−0.172990
$565$	−34.6147	−1.45625
$566$	1.03705	0.0435904
$567$	10.9364	0.459284
$568$	−12.3811	−0.519501
$569$	−5.03951	−0.211267	−0.105634	−	0.994405i	$-0.533687\pi$
$569$	−5.03951	−0.211267	−0.105634	+	0.994405i	$0.533687\pi$
$570$	−13.3355	−0.558562
$571$	11.5574	0.483663	0.241832	−	0.970318i	$-0.422252\pi$
$571$	11.5574	0.483663	0.241832	+	0.970318i	$0.422252\pi$
$572$	8.89470	0.371906
$573$	5.80747	0.242611
$574$	2.26592	0.0945778
$575$	9.30375	0.387993
$576$	−0.124185	−0.00517438
$577$	16.4289	0.683943	0.341972	−	0.939710i	$-0.388905\pi$
$577$	16.4289	0.683943	0.341972	+	0.939710i	$0.388905\pi$
$578$	−8.28384	−0.344562
$579$	8.26393	0.343437
$580$	−16.5305	−0.686392
$581$	−5.84789	−0.242611
$582$	2.19648	0.0910470
$583$	−1.43887	−0.0595920
$584$	−28.9855	−1.19943
$585$	14.3585	0.593651
$586$	0.111970	0.00462544
$587$	23.9600	0.988936	0.494468	−	0.869196i	$-0.335363\pi$
$587$	23.9600	0.988936	0.494468	+	0.869196i	$0.335363\pi$
$588$	−5.78481	−0.238561
$589$	−37.5384	−1.54674
$590$	2.53803	0.104489
$591$	28.8929	1.18850
$592$	18.0408	0.741470
$593$	−0.0630906	−0.00259082	−0.00129541	−	0.999999i	$-0.500412\pi$
$593$	−0.0630906	−0.00259082	−0.00129541	+	0.999999i	$0.500412\pi$
$594$	3.59486	0.147499
$595$	−11.2405	−0.460815
$596$	−2.69574	−0.110422
$597$	−34.2561	−1.40201
$598$	−15.3777	−0.628841
$599$	−14.0417	−0.573728	−0.286864	−	0.957971i	$-0.592613\pi$
$599$	−14.0417	−0.573728	−0.286864	+	0.957971i	$0.592613\pi$
$600$	6.98844	0.285302
$601$	21.4582	0.875297	0.437648	−	0.899146i	$-0.355811\pi$
$601$	21.4582	0.875297	0.437648	+	0.899146i	$0.355811\pi$
$602$	−3.08677	−0.125807
$603$	−15.0294	−0.612045
$604$	−7.51673	−0.305851
$605$	2.67263	0.108658
$606$	−10.1346	−0.411688
$607$	2.74878	0.111570	0.0557849	−	0.998443i	$-0.482234\pi$
$607$	2.74878	0.111570	0.0557849	+	0.998443i	$0.482234\pi$
$608$	31.2331	1.26667
$609$	11.6774	0.473193
$610$	−5.69901	−0.230746
$611$	10.0533	0.406711
$612$	3.06424	0.123864
$613$	−10.2911	−0.415654	−0.207827	−	0.978166i	$-0.566639\pi$
$613$	−10.2911	−0.415654	−0.207827	+	0.978166i	$0.566639\pi$
$614$	−4.23433	−0.170884
$615$	6.43797	0.259604
$616$	4.82667	0.194472
$617$	0.119962	0.00482950	0.00241475	−	0.999997i	$-0.499231\pi$
$617$	0.119962	0.00482950	0.00241475	+	0.999997i	$0.499231\pi$
$618$	6.83764	0.275050
$619$	26.5286	1.06627	0.533136	−	0.846029i	$-0.321013\pi$
$619$	26.5286	1.06627	0.533136	+	0.846029i	$0.321013\pi$
$620$	29.1030	1.16880
$621$	24.5568	0.985432
$622$	5.47734	0.219621
$623$	−0.772252	−0.0309396
$624$	13.8324	0.553740
$625$	−31.1225	−1.24490
$626$	−19.0113	−0.759842
$627$	−7.85075	−0.313529
$628$	19.2191	0.766924
$629$	20.6543	0.823541
$630$	3.45818	0.137777
$631$	−15.9549	−0.635154	−0.317577	−	0.948233i	$-0.602869\pi$
$631$	−15.9549	−0.635154	−0.317577	+	0.948233i	$0.602869\pi$
$632$	−29.5610	−1.17587
$633$	0.663690	0.0263793
$634$	13.5591	0.538500
$635$	−38.9248	−1.54469
$636$	−3.27685	−0.129936
$637$	14.1559	0.560876
$638$	2.46297	0.0975098
$639$	−5.22231	−0.206591
$640$	−30.1242	−1.19076
$641$	29.8856	1.18041	0.590206	−	0.807253i	$-0.299047\pi$
$641$	29.8856	1.18041	0.590206	+	0.807253i	$0.299047\pi$
$642$	−14.6216	−0.577069
$643$	32.8303	1.29470	0.647351	−	0.762192i	$-0.275877\pi$
$643$	32.8303	1.29470	0.647351	+	0.762192i	$0.275877\pi$
$644$	14.6339	0.576657
$645$	−8.77017	−0.345325
$646$	6.96417	0.274002
$647$	−7.21838	−0.283784	−0.141892	−	0.989882i	$-0.545319\pi$
$647$	−7.21838	−0.283784	−0.141892	+	0.989882i	$0.545319\pi$
$648$	11.8358	0.464953
$649$	1.49417	0.0586511
$650$	−7.59014	−0.297710
$651$	−20.5588	−0.805764
$652$	9.19156	0.359969
$653$	9.30484	0.364127	0.182063	−	0.983287i	$-0.441722\pi$
$653$	9.30484	0.364127	0.182063	+	0.983287i	$0.441722\pi$
$654$	−11.6722	−0.456418
$655$	−2.67263	−0.104428
$656$	−2.93666	−0.114657
$657$	−12.2259	−0.476980
$658$	2.42128	0.0943914
$659$	25.3440	0.987262	0.493631	−	0.869671i	$-0.335669\pi$
$659$	25.3440	0.987262	0.493631	+	0.869671i	$0.335669\pi$
$660$	6.08658	0.236920
$661$	−17.7160	−0.689074	−0.344537	−	0.938773i	$-0.611964\pi$
$661$	−17.7160	−0.689074	−0.344537	+	0.938773i	$0.611964\pi$
$662$	−5.84323	−0.227103
$663$	15.8363	0.615032
$664$	−6.32883	−0.245606
$665$	−31.0545	−1.20424
$666$	−6.35437	−0.246227
$667$	16.8248	0.651458
$668$	16.9654	0.656409
$669$	−38.8172	−1.50076
$670$	26.4821	1.02309
$671$	−3.35507	−0.129521
$672$	17.1056	0.659863
$673$	−15.1968	−0.585792	−0.292896	−	0.956144i	$-0.594619\pi$
$673$	−15.1968	−0.585792	−0.292896	+	0.956144i	$0.594619\pi$
$674$	−12.6761	−0.488266
$675$	12.1208	0.466529
$676$	−28.8207	−1.10849
$677$	8.21289	0.315647	0.157823	−	0.987467i	$-0.449552\pi$
$677$	8.21289	0.315647	0.157823	+	0.987467i	$0.449552\pi$
$678$	11.7454	0.451080
$679$	5.11497	0.196295
$680$	−12.1649	−0.466504
$681$	42.1398	1.61480
$682$	−4.33620	−0.166042
$683$	11.1293	0.425853	0.212926	−	0.977068i	$-0.431701\pi$
$683$	11.1293	0.425853	0.212926	+	0.977068i	$0.431701\pi$
$684$	8.46568	0.323693
$685$	−30.9546	−1.18271
$686$	12.8049	0.488892
$687$	34.5399	1.31778
$688$	4.00049	0.152517
$689$	8.01871	0.305489
$690$	−10.5229	−0.400598
$691$	7.84371	0.298389	0.149194	−	0.988808i	$-0.452332\pi$
$691$	7.84371	0.298389	0.149194	+	0.988808i	$0.452332\pi$
$692$	−24.9697	−0.949204
$693$	2.03587	0.0773363
$694$	20.9333	0.794618
$695$	45.8390	1.73877
$696$	12.6378	0.479035
$697$	−3.36209	−0.127348
$698$	−3.70895	−0.140386
$699$	6.27538	0.237357
$700$	7.22302	0.273004
$701$	38.0656	1.43772	0.718858	−	0.695157i	$-0.244665\pi$
$701$	38.0656	1.43772	0.718858	+	0.695157i	$0.244665\pi$
$702$	−20.0339	−0.756129
$703$	57.0624	2.15215
$704$	0.128819	0.00485506
$705$	6.87937	0.259092
$706$	−21.6750	−0.815749
$707$	−23.6005	−0.887588
$708$	3.40278	0.127884
$709$	−13.3013	−0.499539	−0.249770	−	0.968305i	$-0.580355\pi$
$709$	−13.3013	−0.499539	−0.249770	+	0.968305i	$0.580355\pi$
$710$	9.20178	0.345337
$711$	−12.4687	−0.467612
$712$	−0.835764	−0.0313216
$713$	−29.6210	−1.10932
$714$	3.81410	0.142739
$715$	−14.8943	−0.557016
$716$	11.1150	0.415389
$717$	−7.03151	−0.262597
$718$	13.4158	0.500672
$719$	−4.37990	−0.163343	−0.0816714	−	0.996659i	$-0.526026\pi$
$719$	−4.37990	−0.163343	−0.0816714	+	0.996659i	$0.526026\pi$
$720$	−4.48183	−0.167028
$721$	15.9229	0.593000
$722$	7.16447	0.266634
$723$	−14.1244	−0.525292
$724$	−14.6721	−0.545284
$725$	8.30438	0.308417
$726$	−0.906871	−0.0336571
$727$	7.43509	0.275752	0.137876	−	0.990449i	$-0.455972\pi$
$727$	7.43509	0.275752	0.137876	+	0.990449i	$0.455972\pi$
$728$	−26.8986	−0.996930
$729$	29.2043	1.08164
$730$	21.5423	0.797316
$731$	4.58004	0.169399
$732$	−7.64077	−0.282411
$733$	28.6640	1.05873	0.529364	−	0.848395i	$-0.322431\pi$
$733$	28.6640	1.05873	0.529364	+	0.848395i	$0.322431\pi$
$734$	−2.27863	−0.0841056
$735$	9.68676	0.357301
$736$	24.6456	0.908450
$737$	15.5903	0.574276
$738$	1.03436	0.0380753
$739$	−41.9068	−1.54157	−0.770783	−	0.637098i	$-0.780135\pi$
$739$	−41.9068	−1.54157	−0.770783	+	0.637098i	$0.780135\pi$
$740$	−44.2397	−1.62628
$741$	43.7516	1.60725
$742$	1.93127	0.0708992
$743$	−6.95728	−0.255238	−0.127619	−	0.991823i	$-0.540733\pi$
$743$	−6.95728	−0.255238	−0.127619	+	0.991823i	$0.540733\pi$
$744$	−22.2496	−0.815710
$745$	4.51405	0.165382
$746$	12.8512	0.470518
$747$	−2.66947	−0.0976709
$748$	−3.17859	−0.116221
$749$	−34.0495	−1.24414
$750$	6.92476	0.252856
$751$	−21.4473	−0.782624	−0.391312	−	0.920258i	$-0.627979\pi$
$751$	−21.4473	−0.782624	−0.391312	+	0.920258i	$0.627979\pi$
$752$	−3.13800	−0.114431
$753$	−15.9457	−0.581095
$754$	−13.7259	−0.499868
$755$	12.5869	0.458084
$756$	19.0648	0.693381
$757$	−31.4068	−1.14150	−0.570750	−	0.821124i	$-0.693348\pi$
$757$	−31.4068	−1.14150	−0.570750	+	0.821124i	$0.693348\pi$
$758$	23.7935	0.864218
$759$	−6.19493	−0.224862
$760$	−33.6085	−1.21911
$761$	−26.9777	−0.977942	−0.488971	−	0.872300i	$-0.662628\pi$
$761$	−26.9777	−0.977942	−0.488971	+	0.872300i	$0.662628\pi$
$762$	13.2079	0.478472
$763$	−27.1811	−0.984023
$764$	6.49605	0.235019
$765$	−5.13111	−0.185516
$766$	−3.02221	−0.109197
$767$	−8.32686	−0.300666
$768$	10.5893	0.382109
$769$	8.49858	0.306467	0.153233	−	0.988190i	$-0.451031\pi$
$769$	8.49858	0.306467	0.153233	+	0.988190i	$0.451031\pi$
$770$	−3.58723	−0.129275
$771$	35.7982	1.28924
$772$	9.24377	0.332691
$773$	−33.9087	−1.21961	−0.609806	−	0.792551i	$-0.708753\pi$
$773$	−33.9087	−1.21961	−0.609806	+	0.792551i	$0.708753\pi$
$774$	−1.40906	−0.0506478
$775$	−14.6204	−0.525179
$776$	5.53564	0.198718
$777$	31.2517	1.12115
$778$	2.49990	0.0896259
$779$	−9.28858	−0.332798
$780$	−33.9200	−1.21453
$781$	5.41719	0.193842
$782$	5.49534	0.196513
$783$	21.9191	0.783323
$784$	−4.41859	−0.157807
$785$	−32.1826	−1.14865
$786$	0.906871	0.0323470
$787$	−21.9900	−0.783860	−0.391930	−	0.919995i	$-0.628192\pi$
$787$	−21.9900	−0.783860	−0.391930	+	0.919995i	$0.628192\pi$
$788$	32.3187	1.15131
$789$	−41.5509	−1.47925
$790$	21.9700	0.781657
$791$	27.3517	0.972514
$792$	2.20330	0.0782909
$793$	18.6975	0.663969
$794$	17.0206	0.604039
$795$	5.48715	0.194609
$796$	−38.3178	−1.35814
$797$	38.6961	1.37069	0.685344	−	0.728220i	$-0.259652\pi$
$797$	38.6961	1.37069	0.685344	+	0.728220i	$0.259652\pi$
$798$	10.5374	0.373019
$799$	−3.59261	−0.127097
$800$	12.1646	0.430084
$801$	−0.352521	−0.0124557
$802$	21.9759	0.775997
$803$	12.6822	0.447545
$804$	35.5050	1.25216
$805$	−24.5047	−0.863678
$806$	24.1653	0.851186
$807$	−24.2437	−0.853417
$808$	−25.5414	−0.898545
$809$	55.4128	1.94821	0.974105	−	0.226097i	$-0.0725965\pi$
$809$	55.4128	1.94821	0.974105	+	0.226097i	$0.0725965\pi$
$810$	−8.79647	−0.309076
$811$	−26.8038	−0.941210	−0.470605	−	0.882344i	$-0.655964\pi$
$811$	−26.8038	−0.941210	−0.470605	+	0.882344i	$0.655964\pi$
$812$	13.0620	0.458386
$813$	−33.1954	−1.16421
$814$	6.59151	0.231032
$815$	−15.3914	−0.539138
$816$	−4.94312	−0.173044
$817$	12.6534	0.442688
$818$	12.0308	0.420648
$819$	−11.3457	−0.396452
$820$	7.20131	0.251481
$821$	32.2230	1.12459	0.562295	−	0.826937i	$-0.309919\pi$
$821$	32.2230	1.12459	0.562295	+	0.826937i	$0.309919\pi$
$822$	10.5035	0.366350
$823$	−4.88814	−0.170390	−0.0851950	−	0.996364i	$-0.527151\pi$
$823$	−4.88814	−0.170390	−0.0851950	+	0.996364i	$0.527151\pi$
$824$	17.2324	0.600321
$825$	−3.05770	−0.106455
$826$	−2.00549	−0.0697798
$827$	19.6178	0.682178	0.341089	−	0.940031i	$-0.389204\pi$
$827$	19.6178	0.682178	0.341089	+	0.940031i	$0.389204\pi$
$828$	6.68016	0.232152
$829$	25.3895	0.881812	0.440906	−	0.897553i	$-0.354657\pi$
$829$	25.3895	0.881812	0.440906	+	0.897553i	$0.354657\pi$
$830$	4.70365	0.163266
$831$	−3.07135	−0.106544
$832$	−0.717900	−0.0248887
$833$	−5.05870	−0.175274
$834$	−15.5540	−0.538591
$835$	−28.4088	−0.983126
$836$	−8.78160	−0.303718
$837$	−38.5898	−1.33386
$838$	15.9276	0.550210
$839$	42.6669	1.47302	0.736512	−	0.676424i	$-0.236471\pi$
$839$	42.6669	1.47302	0.736512	+	0.676424i	$0.236471\pi$
$840$	−18.4065	−0.635086
$841$	−13.9825	−0.482154
$842$	0.175918	0.00606254
$843$	45.8864	1.58041
$844$	0.742382	0.0255538
$845$	48.2607	1.66022
$846$	1.10528	0.0380002
$847$	−2.11184	−0.0725638
$848$	−2.50295	−0.0859515
$849$	−2.32823	−0.0799048
$850$	2.71239	0.0930343
$851$	45.0272	1.54351
$852$	12.3370	0.422658
$853$	−11.2183	−0.384108	−0.192054	−	0.981384i	$-0.561515\pi$
$853$	−11.2183	−0.384108	−0.192054	+	0.981384i	$0.561515\pi$
$854$	4.50322	0.154097
$855$	−14.1759	−0.484806
$856$	−36.8498	−1.25950
$857$	−5.11034	−0.174566	−0.0872829	−	0.996184i	$-0.527818\pi$
$857$	−5.11034	−0.174566	−0.0872829	+	0.996184i	$0.527818\pi$
$858$	5.05392	0.172538
$859$	40.6977	1.38859	0.694293	−	0.719692i	$-0.255717\pi$
$859$	40.6977	1.38859	0.694293	+	0.719692i	$0.255717\pi$
$860$	−9.81003	−0.334519
$861$	−5.08712	−0.173369
$862$	−2.02003	−0.0688025
$863$	−58.3109	−1.98493	−0.992464	−	0.122538i	$-0.960897\pi$
$863$	−58.3109	−1.98493	−0.992464	+	0.122538i	$0.960897\pi$
$864$	32.1080	1.09234
$865$	41.8121	1.42165
$866$	−11.2583	−0.382571
$867$	18.5977	0.631610
$868$	−22.9964	−0.780550
$869$	12.9340	0.438756
$870$	−9.39254	−0.318437
$871$	−86.8834	−2.94393
$872$	−29.4166	−0.996171
$873$	2.33491	0.0790247
$874$	15.1822	0.513545
$875$	16.1258	0.545151
$876$	28.8821	0.975837
$877$	49.3376	1.66601	0.833006	−	0.553264i	$-0.186618\pi$
$877$	49.3376	1.66601	0.833006	+	0.553264i	$0.186618\pi$
$878$	0.357843	0.0120766
$879$	−0.251379	−0.00847881
$880$	4.64909	0.156721
$881$	−16.3157	−0.549691	−0.274846	−	0.961488i	$-0.588627\pi$
$881$	−16.3157	−0.549691	−0.274846	+	0.961488i	$0.588627\pi$
$882$	1.55633	0.0524043
$883$	−34.6725	−1.16682	−0.583412	−	0.812177i	$-0.698283\pi$
$883$	−34.6725	−1.16682	−0.583412	+	0.812177i	$0.698283\pi$
$884$	17.7140	0.595787
$885$	−5.69801	−0.191537
$886$	20.4004	0.685364
$887$	38.2227	1.28339	0.641697	−	0.766958i	$-0.278231\pi$
$887$	38.2227	1.28339	0.641697	+	0.766958i	$0.278231\pi$
$888$	33.8219	1.13499
$889$	30.7575	1.03157
$890$	0.621148	0.0208209
$891$	−5.17858	−0.173489
$892$	−43.4197	−1.45380
$893$	−9.92543	−0.332142
$894$	−1.53170	−0.0512278
$895$	−18.6123	−0.622141
$896$	23.8034	0.795215
$897$	34.5238	1.15272
$898$	16.2197	0.541257
$899$	−26.4393	−0.881799
$900$	3.29720	0.109907
$901$	−2.86555	−0.0954652
$902$	−1.07296	−0.0357257
$903$	6.92997	0.230615
$904$	29.6011	0.984519
$905$	24.5687	0.816690
$906$	−4.27096	−0.141893
$907$	37.4123	1.24226	0.621128	−	0.783709i	$-0.286675\pi$
$907$	37.4123	1.24226	0.621128	+	0.783709i	$0.286675\pi$
$908$	47.1363	1.56427
$909$	−10.7733	−0.357327
$910$	19.9913	0.662706
$911$	6.46676	0.214253	0.107127	−	0.994245i	$-0.465835\pi$
$911$	6.46676	0.214253	0.107127	+	0.994245i	$0.465835\pi$
$912$	−13.6565	−0.452213
$913$	2.76909	0.0916435
$914$	2.26107	0.0747896
$915$	12.7946	0.422976
$916$	38.6352	1.27654
$917$	2.11184	0.0697392
$918$	7.15924	0.236290
$919$	4.31066	0.142195	0.0710977	−	0.997469i	$-0.477350\pi$
$919$	4.31066	0.142195	0.0710977	+	0.997469i	$0.477350\pi$
$920$	−26.5200	−0.874340
$921$	9.50630	0.313243
$922$	14.5720	0.479902
$923$	−30.1896	−0.993702
$924$	−4.80946	−0.158220
$925$	22.2246	0.730740
$926$	−15.5110	−0.509725
$927$	7.26857	0.238731
$928$	21.9983	0.722130
$929$	32.9996	1.08268	0.541340	−	0.840804i	$-0.317917\pi$
$929$	32.9996	1.08268	0.541340	+	0.840804i	$0.317917\pi$
$930$	16.5361	0.542241
$931$	−13.9759	−0.458041
$932$	7.01944	0.229929
$933$	−12.2969	−0.402584
$934$	−12.0503	−0.394299
$935$	5.32260	0.174068
$936$	−12.2788	−0.401346
$937$	−34.1555	−1.11581	−0.557907	−	0.829904i	$-0.688395\pi$
$937$	−34.1555	−1.11581	−0.557907	+	0.829904i	$0.688395\pi$
$938$	−20.9255	−0.683241
$939$	42.6813	1.39285
$940$	7.69505	0.250985
$941$	33.9088	1.10540	0.552698	−	0.833381i	$-0.313598\pi$
$941$	33.9088	1.10540	0.552698	+	0.833381i	$0.313598\pi$
$942$	10.9202	0.355798
$943$	−7.32950	−0.238681
$944$	2.59913	0.0845945
$945$	−31.9244	−1.03850
$946$	1.46165	0.0475223
$947$	−29.1889	−0.948513	−0.474256	−	0.880387i	$-0.657283\pi$
$947$	−29.1889	−0.948513	−0.474256	+	0.880387i	$0.657283\pi$
$948$	29.4556	0.956673
$949$	−70.6768	−2.29427
$950$	7.49363	0.243125
$951$	−30.4409	−0.987114
$952$	9.61243	0.311541
$953$	35.0681	1.13597	0.567984	−	0.823040i	$-0.307724\pi$
$953$	35.0681	1.13597	0.567984	+	0.823040i	$0.307724\pi$
$954$	0.881596	0.0285427
$955$	−10.8777	−0.351996
$956$	−7.86523	−0.254380
$957$	−5.52950	−0.178743
$958$	−2.84985	−0.0920744
$959$	24.4595	0.789840
$960$	−0.491254	−0.0158551
$961$	15.5479	0.501547
$962$	−36.7339	−1.18435
$963$	−15.5431	−0.500869
$964$	−15.7991	−0.508855
$965$	−15.4789	−0.498282
$966$	8.31490	0.267528
$967$	50.0315	1.60890	0.804452	−	0.594017i	$-0.202459\pi$
$967$	50.0315	1.60890	0.804452	+	0.594017i	$0.202459\pi$
$968$	−2.28553	−0.0734596
$969$	−15.6350	−0.502267
$970$	−4.11414	−0.132097
$971$	−33.6414	−1.07960	−0.539801	−	0.841792i	$-0.681501\pi$
$971$	−33.6414	−1.07960	−0.539801	+	0.841792i	$0.681501\pi$
$972$	15.2892	0.490400
$973$	−36.2209	−1.16119
$974$	−7.23969	−0.231975
$975$	17.0403	0.545726
$976$	−5.83622	−0.186813
$977$	−15.9116	−0.509056	−0.254528	−	0.967065i	$-0.581920\pi$
$977$	−15.9116	−0.509056	−0.254528	+	0.967065i	$0.581920\pi$
$978$	5.22259	0.167000
$979$	0.365677	0.0116871
$980$	10.8353	0.346121
$981$	−12.4078	−0.396150
$982$	−21.1916	−0.676252
$983$	−41.2741	−1.31644	−0.658219	−	0.752826i	$-0.728690\pi$
$983$	−41.2741	−1.31644	−0.658219	+	0.752826i	$0.728690\pi$
$984$	−5.50550	−0.175509
$985$	−54.1182	−1.72435
$986$	4.90506	0.156209
$987$	−5.43591	−0.173027
$988$	48.9391	1.55696
$989$	9.98466	0.317494
$990$	−1.63752	−0.0520437
$991$	−52.0277	−1.65272	−0.826358	−	0.563145i	$-0.809591\pi$
$991$	−52.0277	−1.65272	−0.826358	+	0.563145i	$0.809591\pi$
$992$	−38.7294	−1.22966
$993$	13.1184	0.416299
$994$	−7.27102	−0.230623
$995$	64.1637	2.03413
$996$	6.30627	0.199822
$997$	−52.3540	−1.65807	−0.829034	−	0.559199i	$-0.811109\pi$
$997$	−52.3540	−1.65807	−0.829034	+	0.559199i	$0.811109\pi$
$998$	4.23110	0.133933
$999$	58.6608	1.85595

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.e.1.16	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.e.1.16	✓	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q+0.635564 q^{2} -1.42688 q^{3} -1.59606 q^{4} +2.67263 q^{5} -0.906871 q^{6} -2.11184 q^{7} -2.28553 q^{8} -0.964025 q^{9} +O(q^{10})\)	\(q+0.635564 q^{2} -1.42688 q^{3} -1.59606 q^{4} +2.67263 q^{5} -0.906871 q^{6} -2.11184 q^{7} -2.28553 q^{8} -0.964025 q^{9} +1.69862 q^{10} +1.00000 q^{11} +2.27738 q^{12} -5.57292 q^{13} -1.34221 q^{14} -3.81351 q^{15} +1.73952 q^{16} +1.99152 q^{17} -0.612699 q^{18} +5.50206 q^{19} -4.26567 q^{20} +3.01334 q^{21} +0.635564 q^{22} +4.34160 q^{23} +3.26116 q^{24} +2.14293 q^{25} -3.54195 q^{26} +5.65617 q^{27} +3.37063 q^{28} +3.87525 q^{29} -2.42373 q^{30} -6.82261 q^{31} +5.67663 q^{32} -1.42688 q^{33} +1.26574 q^{34} -5.64417 q^{35} +1.53864 q^{36} +10.3711 q^{37} +3.49691 q^{38} +7.95186 q^{39} -6.10835 q^{40} -1.68820 q^{41} +1.91517 q^{42} +2.29977 q^{43} -1.59606 q^{44} -2.57648 q^{45} +2.75936 q^{46} -1.80395 q^{47} -2.48208 q^{48} -2.54012 q^{49} +1.36197 q^{50} -2.84166 q^{51} +8.89470 q^{52} -1.43887 q^{53} +3.59486 q^{54} +2.67263 q^{55} +4.82667 q^{56} -7.85075 q^{57} +2.46297 q^{58} +1.49417 q^{59} +6.08658 q^{60} -3.35507 q^{61} -4.33620 q^{62} +2.03587 q^{63} +0.128819 q^{64} -14.8943 q^{65} -0.906871 q^{66} +15.5903 q^{67} -3.17859 q^{68} -6.19493 q^{69} -3.58723 q^{70} +5.41719 q^{71} +2.20330 q^{72} +12.6822 q^{73} +6.59151 q^{74} -3.05770 q^{75} -8.78160 q^{76} -2.11184 q^{77} +5.05392 q^{78} +12.9340 q^{79} +4.64909 q^{80} -5.17858 q^{81} -1.07296 q^{82} +2.76909 q^{83} -4.80946 q^{84} +5.32260 q^{85} +1.46165 q^{86} -5.52950 q^{87} -2.28553 q^{88} +0.365677 q^{89} -1.63752 q^{90} +11.7691 q^{91} -6.92945 q^{92} +9.73501 q^{93} -1.14652 q^{94} +14.7049 q^{95} -8.09984 q^{96} -2.42204 q^{97} -1.61441 q^{98} -0.964025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9 + 14 * q^10 + 28 * q^11 - 6 * q^12 + 3 * q^13 - q^14 + 19 * q^15 + 29 * q^16 + 9 * q^17 - 2 * q^18 + 20 * q^19 + 6 * q^20 + 6 * q^21 + 7 * q^22 + 24 * q^23 + 20 * q^24 + 23 * q^25 + 10 * q^26 - 20 * q^27 - 3 * q^28 + 43 * q^29 + 11 * q^30 + 3 * q^31 + 44 * q^32 - 2 * q^33 - 28 * q^34 + 32 * q^35 + 24 * q^36 - 4 * q^37 + 24 * q^38 + 37 * q^39 + 22 * q^40 + 32 * q^41 - 27 * q^42 + 25 * q^43 + 27 * q^44 - 36 * q^45 + 10 * q^46 + 19 * q^47 + 42 * q^48 + 17 * q^49 + q^50 + 39 * q^51 - 19 * q^52 + 5 * q^53 + 6 * q^54 + 3 * q^55 + 8 * q^56 + 2 * q^57 + 21 * q^58 + 44 * q^59 + 65 * q^60 + 28 * q^61 + 60 * q^62 - 8 * q^63 + 5 * q^64 + 33 * q^65 - q^66 + 7 * q^67 + 13 * q^68 - 22 * q^69 + 9 * q^70 + 117 * q^71 - 17 * q^72 + 7 * q^73 + 41 * q^74 - 40 * q^75 + 34 * q^76 + 7 * q^77 - 97 * q^78 + 48 * q^79 + 41 * q^80 + 40 * q^81 + 2 * q^82 + 22 * q^83 + 27 * q^84 + 30 * q^85 + 24 * q^86 + 37 * q^87 + 21 * q^88 - 6 * q^89 + 4 * q^90 - 33 * q^91 + 18 * q^92 + 5 * q^93 - 43 * q^94 + 64 * q^95 + 55 * q^96 - 50 * q^97 + 97 * q^98 + 28 * q^99

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