LMFDB - Embedded newform 1441.2.a.e.1.15

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			1.15
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)

$f(q)$	$=$	$q+0.544027 q^{2} +2.32406 q^{3} -1.70404 q^{4} -4.20016 q^{5} +1.26435 q^{6} -0.904548 q^{7} -2.01509 q^{8} +2.40124 q^{9} +O(q^{10})$	\(q+0.544027 q^{2} +2.32406 q^{3} -1.70404 q^{4} -4.20016 q^{5} +1.26435 q^{6} -0.904548 q^{7} -2.01509 q^{8} +2.40124 q^{9} -2.28500 q^{10} +1.00000 q^{11} -3.96027 q^{12} +5.43311 q^{13} -0.492098 q^{14} -9.76142 q^{15} +2.31181 q^{16} +0.465560 q^{17} +1.30634 q^{18} +1.07775 q^{19} +7.15723 q^{20} -2.10222 q^{21} +0.544027 q^{22} +5.68068 q^{23} -4.68319 q^{24} +12.6414 q^{25} +2.95576 q^{26} -1.39155 q^{27} +1.54138 q^{28} +3.69306 q^{29} -5.31047 q^{30} +5.71691 q^{31} +5.28787 q^{32} +2.32406 q^{33} +0.253277 q^{34} +3.79925 q^{35} -4.09180 q^{36} -4.58360 q^{37} +0.586325 q^{38} +12.6269 q^{39} +8.46372 q^{40} +5.85143 q^{41} -1.14366 q^{42} -11.7417 q^{43} -1.70404 q^{44} -10.0856 q^{45} +3.09044 q^{46} +9.11945 q^{47} +5.37277 q^{48} -6.18179 q^{49} +6.87724 q^{50} +1.08199 q^{51} -9.25821 q^{52} -5.81702 q^{53} -0.757040 q^{54} -4.20016 q^{55} +1.82275 q^{56} +2.50476 q^{57} +2.00912 q^{58} +8.84906 q^{59} +16.6338 q^{60} +8.97346 q^{61} +3.11015 q^{62} -2.17204 q^{63} -1.74687 q^{64} -22.8200 q^{65} +1.26435 q^{66} -6.46137 q^{67} -0.793331 q^{68} +13.2022 q^{69} +2.06689 q^{70} +13.6584 q^{71} -4.83872 q^{72} -3.44327 q^{73} -2.49360 q^{74} +29.3793 q^{75} -1.83653 q^{76} -0.904548 q^{77} +6.86935 q^{78} -9.22001 q^{79} -9.70996 q^{80} -10.4378 q^{81} +3.18333 q^{82} +3.96831 q^{83} +3.58226 q^{84} -1.95543 q^{85} -6.38780 q^{86} +8.58288 q^{87} -2.01509 q^{88} +4.73586 q^{89} -5.48684 q^{90} -4.91451 q^{91} -9.68008 q^{92} +13.2864 q^{93} +4.96122 q^{94} -4.52673 q^{95} +12.2893 q^{96} -2.78350 q^{97} -3.36306 q^{98} +2.40124 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.544027	0.384685	0.192342	−	0.981328i	$-0.438392\pi$
$2$	0.544027	0.384685	0.192342	+	0.981328i	$0.438392\pi$
$3$	2.32406	1.34179	0.670897	−	0.741550i	$-0.265909\pi$
$3$	2.32406	1.34179	0.670897	+	0.741550i	$0.265909\pi$
$4$	−1.70404	−0.852018
$5$	−4.20016	−1.87837	−0.939185	−	0.343411i	$-0.888418\pi$
$5$	−4.20016	−1.87837	−0.939185	+	0.343411i	$0.888418\pi$
$6$	1.26435	0.516168
$7$	−0.904548	−0.341887	−0.170943	−	0.985281i	$-0.554682\pi$
$7$	−0.904548	−0.341887	−0.170943	+	0.985281i	$0.554682\pi$
$8$	−2.01509	−0.712443
$9$	2.40124	0.800414
$10$	−2.28500	−0.722581
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.96027	−1.14323
$13$	5.43311	1.50687	0.753437	−	0.657520i	$-0.228394\pi$
$13$	5.43311	1.50687	0.753437	+	0.657520i	$0.228394\pi$
$14$	−0.492098	−0.131519
$15$	−9.76142	−2.52039
$16$	2.31181	0.577952
$17$	0.465560	0.112915	0.0564575	−	0.998405i	$-0.482019\pi$
$17$	0.465560	0.112915	0.0564575	+	0.998405i	$0.482019\pi$
$18$	1.30634	0.307907
$19$	1.07775	0.247253	0.123627	−	0.992329i	$-0.460548\pi$
$19$	1.07775	0.247253	0.123627	+	0.992329i	$0.460548\pi$
$20$	7.15723	1.60040
$21$	−2.10222	−0.458742
$22$	0.544027	0.115987
$23$	5.68068	1.18450	0.592252	−	0.805753i	$-0.298239\pi$
$23$	5.68068	1.18450	0.592252	+	0.805753i	$0.298239\pi$
$24$	−4.68319	−0.955953
$25$	12.6414	2.52828
$26$	2.95576	0.579672
$27$	−1.39155	−0.267804
$28$	1.54138	0.291294
$29$	3.69306	0.685784	0.342892	−	0.939375i	$-0.388594\pi$
$29$	3.69306	0.685784	0.342892	+	0.939375i	$0.388594\pi$
$30$	−5.31047	−0.969555
$31$	5.71691	1.02679	0.513394	−	0.858153i	$-0.328388\pi$
$31$	5.71691	1.02679	0.513394	+	0.858153i	$0.328388\pi$
$32$	5.28787	0.934772
$33$	2.32406	0.404566
$34$	0.253277	0.0434367
$35$	3.79925	0.642190
$36$	−4.09180	−0.681967
$37$	−4.58360	−0.753539	−0.376769	−	0.926307i	$-0.622965\pi$
$37$	−4.58360	−0.753539	−0.376769	+	0.926307i	$0.622965\pi$
$38$	0.586325	0.0951145
$39$	12.6269	2.02192
$40$	8.46372	1.33823
$41$	5.85143	0.913840	0.456920	−	0.889508i	$-0.348953\pi$
$41$	5.85143	0.913840	0.456920	+	0.889508i	$0.348953\pi$
$42$	−1.14366	−0.176471
$43$	−11.7417	−1.79059	−0.895297	−	0.445469i	$-0.853037\pi$
$43$	−11.7417	−1.79059	−0.895297	+	0.445469i	$0.853037\pi$
$44$	−1.70404	−0.256893
$45$	−10.0856	−1.50347
$46$	3.09044	0.455661
$47$	9.11945	1.33021	0.665105	−	0.746750i	$-0.268387\pi$
$47$	9.11945	1.33021	0.665105	+	0.746750i	$0.268387\pi$
$48$	5.37277	0.775492
$49$	−6.18179	−0.883113
$50$	6.87724	0.972589
$51$	1.08199	0.151509
$52$	−9.25821	−1.28388
$53$	−5.81702	−0.799029	−0.399514	−	0.916727i	$-0.630821\pi$
$53$	−5.81702	−0.799029	−0.399514	+	0.916727i	$0.630821\pi$
$54$	−0.757040	−0.103020
$55$	−4.20016	−0.566350
$56$	1.82275	0.243575
$57$	2.50476	0.331763
$58$	2.00912	0.263811
$59$	8.84906	1.15205	0.576024	−	0.817432i	$-0.304603\pi$
$59$	8.84906	1.15205	0.576024	+	0.817432i	$0.304603\pi$
$60$	16.6338	2.14741
$61$	8.97346	1.14893	0.574467	−	0.818528i	$-0.305209\pi$
$61$	8.97346	1.14893	0.574467	+	0.818528i	$0.305209\pi$
$62$	3.11015	0.394990
$63$	−2.17204	−0.273651
$64$	−1.74687	−0.218359
$65$	−22.8200	−2.83047
$66$	1.26435	0.155631
$67$	−6.46137	−0.789382	−0.394691	−	0.918814i	$-0.629148\pi$
$67$	−6.46137	−0.789382	−0.394691	+	0.918814i	$0.629148\pi$
$68$	−0.793331	−0.0962055
$69$	13.2022	1.58936
$70$	2.06689	0.247041
$71$	13.6584	1.62096	0.810480	−	0.585767i	$-0.199206\pi$
$71$	13.6584	1.62096	0.810480	+	0.585767i	$0.199206\pi$
$72$	−4.83872	−0.570249
$73$	−3.44327	−0.403004	−0.201502	−	0.979488i	$-0.564582\pi$
$73$	−3.44327	−0.403004	−0.201502	+	0.979488i	$0.564582\pi$
$74$	−2.49360	−0.289875
$75$	29.3793	3.39243
$76$	−1.83653	−0.210664
$77$	−0.904548	−0.103083
$78$	6.86935	0.777800
$79$	−9.22001	−1.03733	−0.518666	−	0.854977i	$-0.673571\pi$
$79$	−9.22001	−1.03733	−0.518666	+	0.854977i	$0.673571\pi$
$80$	−9.70996	−1.08561
$81$	−10.4378	−1.15975
$82$	3.18333	0.351540
$83$	3.96831	0.435578	0.217789	−	0.975996i	$-0.430116\pi$
$83$	3.96831	0.435578	0.217789	+	0.975996i	$0.430116\pi$
$84$	3.58226	0.390856
$85$	−1.95543	−0.212096
$86$	−6.38780	−0.688815
$87$	8.58288	0.920181
$88$	−2.01509	−0.214810
$89$	4.73586	0.502000	0.251000	−	0.967987i	$-0.419241\pi$
$89$	4.73586	0.502000	0.251000	+	0.967987i	$0.419241\pi$
$90$	−5.48684	−0.578363
$91$	−4.91451	−0.515181
$92$	−9.68008	−1.00922
$93$	13.2864	1.37774
$94$	4.96122	0.511711
$95$	−4.52673	−0.464433
$96$	12.2893	1.25427
$97$	−2.78350	−0.282622	−0.141311	−	0.989965i	$-0.545132\pi$
$97$	−2.78350	−0.282622	−0.141311	+	0.989965i	$0.545132\pi$
$98$	−3.36306	−0.339720
$99$	2.40124	0.241334
$100$	−21.5414	−2.15414
$101$	14.5913	1.45189	0.725945	−	0.687753i	$-0.241403\pi$
$101$	14.5913	1.45189	0.725945	+	0.687753i	$0.241403\pi$
$102$	0.588631	0.0582831
$103$	15.9282	1.56945	0.784724	−	0.619846i	$-0.212805\pi$
$103$	15.9282	1.56945	0.784724	+	0.619846i	$0.212805\pi$
$104$	−10.9482	−1.07356
$105$	8.82967	0.861688
$106$	−3.16461	−0.307374
$107$	4.77258	0.461382	0.230691	−	0.973027i	$-0.425901\pi$
$107$	4.77258	0.461382	0.230691	+	0.973027i	$0.425901\pi$
$108$	2.37125	0.228174
$109$	−5.94891	−0.569803	−0.284901	−	0.958557i	$-0.591961\pi$
$109$	−5.94891	−0.569803	−0.284901	+	0.958557i	$0.591961\pi$
$110$	−2.28500	−0.217866
$111$	−10.6525	−1.01109
$112$	−2.09114	−0.197594
$113$	10.2951	0.968486	0.484243	−	0.874934i	$-0.339095\pi$
$113$	10.2951	0.968486	0.484243	+	0.874934i	$0.339095\pi$
$114$	1.36265	0.127624
$115$	−23.8598	−2.22494
$116$	−6.29310	−0.584300
$117$	13.0462	1.20612
$118$	4.81412	0.443176
$119$	−0.421122	−0.0386042
$120$	19.6702	1.79563
$121$	1.00000	0.0909091
$122$	4.88180	0.441977
$123$	13.5991	1.22619
$124$	−9.74182	−0.874841
$125$	−32.0950	−2.87067
$126$	−1.18165	−0.105269
$127$	−10.1876	−0.904002	−0.452001	−	0.892017i	$-0.649290\pi$
$127$	−10.1876	−0.904002	−0.452001	+	0.892017i	$0.649290\pi$
$128$	−11.5261	−1.01877
$129$	−27.2884	−2.40261
$130$	−12.4147	−1.08884
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−3.96027	−0.344698
$133$	−0.974878	−0.0845326
$134$	−3.51516	−0.303663
$135$	5.84474	0.503035
$136$	−0.938147	−0.0804455
$137$	−1.08486	−0.0926855	−0.0463428	−	0.998926i	$-0.514757\pi$
$137$	−1.08486	−0.0926855	−0.0463428	+	0.998926i	$0.514757\pi$
$138$	7.18236	0.611403
$139$	−4.75413	−0.403240	−0.201620	−	0.979464i	$-0.564621\pi$
$139$	−4.75413	−0.403240	−0.201620	+	0.979464i	$0.564621\pi$
$140$	−6.47406	−0.547158
$141$	21.1941	1.78487
$142$	7.43056	0.623559
$143$	5.43311	0.454340
$144$	5.55120	0.462600
$145$	−15.5114	−1.28816
$146$	−1.87323	−0.155030
$147$	−14.3668	−1.18496
$148$	7.81061	0.642028
$149$	−1.30212	−0.106674	−0.0533368	−	0.998577i	$-0.516986\pi$
$149$	−1.30212	−0.106674	−0.0533368	+	0.998577i	$0.516986\pi$
$150$	15.9831	1.30502
$151$	16.4242	1.33659	0.668293	−	0.743898i	$-0.267025\pi$
$151$	16.4242	1.33659	0.668293	+	0.743898i	$0.267025\pi$
$152$	−2.17177	−0.176154
$153$	1.11792	0.0903787
$154$	−0.492098	−0.0396544
$155$	−24.0120	−1.92869
$156$	−21.5166	−1.72271
$157$	−18.6879	−1.49145	−0.745727	−	0.666252i	$-0.767898\pi$
$157$	−18.6879	−1.49145	−0.745727	+	0.666252i	$0.767898\pi$
$158$	−5.01593	−0.399046
$159$	−13.5191	−1.07213
$160$	−22.2099	−1.75585
$161$	−5.13845	−0.404966
$162$	−5.67842	−0.446139
$163$	5.64911	0.442473	0.221236	−	0.975220i	$-0.428991\pi$
$163$	5.64911	0.442473	0.221236	+	0.975220i	$0.428991\pi$
$164$	−9.97104	−0.778607
$165$	−9.76142	−0.759926
$166$	2.15886	0.167560
$167$	−17.4869	−1.35317	−0.676587	−	0.736362i	$-0.736542\pi$
$167$	−17.4869	−1.35317	−0.676587	+	0.736362i	$0.736542\pi$
$168$	4.23617	0.326828
$169$	16.5187	1.27067
$170$	−1.06381	−0.0815902
$171$	2.58794	0.197905
$172$	20.0083	1.52562
$173$	−1.40384	−0.106732	−0.0533659	−	0.998575i	$-0.516995\pi$
$173$	−1.40384	−0.106732	−0.0533659	+	0.998575i	$0.516995\pi$
$174$	4.66931	0.353980
$175$	−11.4347	−0.864384
$176$	2.31181	0.174259
$177$	20.5657	1.54581
$178$	2.57643	0.193112
$179$	15.6810	1.17205	0.586025	−	0.810293i	$-0.300692\pi$
$179$	15.6810	1.17205	0.586025	+	0.810293i	$0.300692\pi$
$180$	17.1862	1.28099
$181$	8.08923	0.601268	0.300634	−	0.953740i	$-0.402802\pi$
$181$	8.08923	0.601268	0.300634	+	0.953740i	$0.402802\pi$
$182$	−2.67362	−0.198182
$183$	20.8548	1.54163
$184$	−11.4471	−0.843891
$185$	19.2519	1.41543
$186$	7.22817	0.529995
$187$	0.465560	0.0340451
$188$	−15.5399	−1.13336
$189$	1.25872	0.0915587
$190$	−2.46266	−0.178660
$191$	−0.428769	−0.0310246	−0.0155123	−	0.999880i	$-0.504938\pi$
$191$	−0.428769	−0.0310246	−0.0155123	+	0.999880i	$0.504938\pi$
$192$	−4.05983	−0.292993
$193$	7.11620	0.512235	0.256118	−	0.966646i	$-0.417557\pi$
$193$	7.11620	0.512235	0.256118	+	0.966646i	$0.417557\pi$
$194$	−1.51430	−0.108720
$195$	−53.0349	−3.79791
$196$	10.5340	0.752428
$197$	2.81203	0.200349	0.100175	−	0.994970i	$-0.468060\pi$
$197$	2.81203	0.200349	0.100175	+	0.994970i	$0.468060\pi$
$198$	1.30634	0.0928375
$199$	−7.77668	−0.551274	−0.275637	−	0.961262i	$-0.588889\pi$
$199$	−7.77668	−0.551274	−0.275637	+	0.961262i	$0.588889\pi$
$200$	−25.4736	−1.80125
$201$	−15.0166	−1.05919
$202$	7.93806	0.558520
$203$	−3.34055	−0.234460
$204$	−1.84375	−0.129088
$205$	−24.5770	−1.71653
$206$	8.66534	0.603743
$207$	13.6407	0.948093
$208$	12.5603	0.870900
$209$	1.07775	0.0745496
$210$	4.80358	0.331478
$211$	−19.3259	−1.33045	−0.665226	−	0.746642i	$-0.731665\pi$
$211$	−19.3259	−1.33045	−0.665226	+	0.746642i	$0.731665\pi$
$212$	9.91240	0.680787
$213$	31.7430	2.17500
$214$	2.59641	0.177487
$215$	49.3171	3.36340
$216$	2.80410	0.190795
$217$	−5.17122	−0.351045
$218$	−3.23637	−0.219194
$219$	−8.00235	−0.540749
$220$	7.15723	0.482540
$221$	2.52944	0.170149
$222$	−5.79527	−0.388953
$223$	−16.1125	−1.07897	−0.539486	−	0.841994i	$-0.681381\pi$
$223$	−16.1125	−1.07897	−0.539486	+	0.841994i	$0.681381\pi$
$224$	−4.78313	−0.319586
$225$	30.3550	2.02367
$226$	5.60083	0.372562
$227$	−13.6008	−0.902717	−0.451359	−	0.892343i	$-0.649060\pi$
$227$	−13.6008	−0.902717	−0.451359	+	0.892343i	$0.649060\pi$
$228$	−4.26819	−0.282668
$229$	23.2725	1.53789	0.768945	−	0.639315i	$-0.220782\pi$
$229$	23.2725	1.53789	0.768945	+	0.639315i	$0.220782\pi$
$230$	−12.9804	−0.855899
$231$	−2.10222	−0.138316
$232$	−7.44186	−0.488582
$233$	14.2803	0.935536	0.467768	−	0.883851i	$-0.345058\pi$
$233$	14.2803	0.935536	0.467768	+	0.883851i	$0.345058\pi$
$234$	7.09749	0.463977
$235$	−38.3032	−2.49863
$236$	−15.0791	−0.981566
$237$	−21.4278	−1.39189
$238$	−0.229101	−0.0148504
$239$	10.3060	0.666641	0.333321	−	0.942814i	$-0.391831\pi$
$239$	10.3060	0.666641	0.333321	+	0.942814i	$0.391831\pi$
$240$	−22.5665	−1.45666
$241$	25.6186	1.65024	0.825121	−	0.564956i	$-0.191107\pi$
$241$	25.6186	1.65024	0.825121	+	0.564956i	$0.191107\pi$
$242$	0.544027	0.0349713
$243$	−20.0833	−1.28834
$244$	−15.2911	−0.978911
$245$	25.9645	1.65881
$246$	7.39825	0.471695
$247$	5.85554	0.372579
$248$	−11.5201	−0.731528
$249$	9.22257	0.584457
$250$	−17.4606	−1.10430
$251$	−14.7332	−0.929953	−0.464976	−	0.885323i	$-0.653937\pi$
$251$	−14.7332	−0.929953	−0.464976	+	0.885323i	$0.653937\pi$
$252$	3.70123	0.233155
$253$	5.68068	0.357141
$254$	−5.54231	−0.347756
$255$	−4.54453	−0.284589
$256$	−2.77675	−0.173547
$257$	13.8393	0.863273	0.431636	−	0.902048i	$-0.357936\pi$
$257$	13.8393	0.863273	0.431636	+	0.902048i	$0.357936\pi$
$258$	−14.8456	−0.924248
$259$	4.14608	0.257625
$260$	38.8860	2.41161
$261$	8.86792	0.548911
$262$	−0.544027	−0.0336101
$263$	21.9373	1.35271	0.676357	−	0.736574i	$-0.263558\pi$
$263$	21.9373	1.35271	0.676357	+	0.736574i	$0.263558\pi$
$264$	−4.68319	−0.288231
$265$	24.4324	1.50087
$266$	−0.530359	−0.0325184
$267$	11.0064	0.673582
$268$	11.0104	0.672567
$269$	10.9400	0.667025	0.333513	−	0.942746i	$-0.391766\pi$
$269$	10.9400	0.667025	0.333513	+	0.942746i	$0.391766\pi$
$270$	3.17969	0.193510
$271$	29.2966	1.77964	0.889821	−	0.456309i	$-0.150829\pi$
$271$	29.2966	1.77964	0.889821	+	0.456309i	$0.150829\pi$
$272$	1.07629	0.0652594
$273$	−11.4216	−0.691267
$274$	−0.590191	−0.0356547
$275$	12.6414	0.762304
$276$	−22.4971	−1.35416
$277$	0.923422	0.0554830	0.0277415	−	0.999615i	$-0.491168\pi$
$277$	0.923422	0.0554830	0.0277415	+	0.999615i	$0.491168\pi$
$278$	−2.58637	−0.155120
$279$	13.7277	0.821855
$280$	−7.65584	−0.457524
$281$	5.57411	0.332524	0.166262	−	0.986082i	$-0.446830\pi$
$281$	5.57411	0.332524	0.166262	+	0.986082i	$0.446830\pi$
$282$	11.5302	0.686612
$283$	−15.3235	−0.910888	−0.455444	−	0.890265i	$-0.650519\pi$
$283$	−15.3235	−0.910888	−0.455444	+	0.890265i	$0.650519\pi$
$284$	−23.2745	−1.38109
$285$	−10.5204	−0.623174
$286$	2.95576	0.174778
$287$	−5.29290	−0.312430
$288$	12.6975	0.748205
$289$	−16.7833	−0.987250
$290$	−8.43864	−0.495534
$291$	−6.46902	−0.379220
$292$	5.86745	0.343367
$293$	−8.03631	−0.469486	−0.234743	−	0.972057i	$-0.575425\pi$
$293$	−8.03631	−0.469486	−0.234743	+	0.972057i	$0.575425\pi$
$294$	−7.81594	−0.455835
$295$	−37.1675	−2.16397
$296$	9.23638	0.536854
$297$	−1.39155	−0.0807459
$298$	−0.708386	−0.0410357
$299$	30.8638	1.78490
$300$	−50.0633	−2.89041
$301$	10.6209	0.612181
$302$	8.93522	0.514164
$303$	33.9110	1.94814
$304$	2.49155	0.142900
$305$	−37.6900	−2.15812
$306$	0.608179	0.0347673
$307$	−11.2723	−0.643342	−0.321671	−	0.946851i	$-0.604245\pi$
$307$	−11.2723	−0.643342	−0.321671	+	0.946851i	$0.604245\pi$
$308$	1.54138	0.0878284
$309$	37.0179	2.10588
$310$	−13.0631	−0.741937
$311$	5.92094	0.335746	0.167873	−	0.985809i	$-0.446310\pi$
$311$	5.92094	0.335746	0.167873	+	0.985809i	$0.446310\pi$
$312$	−25.4443	−1.44050
$313$	−7.77600	−0.439526	−0.219763	−	0.975553i	$-0.570528\pi$
$313$	−7.77600	−0.439526	−0.219763	+	0.975553i	$0.570528\pi$
$314$	−10.1667	−0.573740
$315$	9.12291	0.514018
$316$	15.7112	0.883826
$317$	−22.7567	−1.27814	−0.639072	−	0.769147i	$-0.720681\pi$
$317$	−22.7567	−1.27814	−0.639072	+	0.769147i	$0.720681\pi$
$318$	−7.35474	−0.412433
$319$	3.69306	0.206772
$320$	7.33714	0.410159
$321$	11.0917	0.619080
$322$	−2.79545	−0.155784
$323$	0.501758	0.0279186
$324$	17.7863	0.988129
$325$	68.6820	3.80979
$326$	3.07327	0.170213
$327$	−13.8256	−0.764558
$328$	−11.7912	−0.651059
$329$	−8.24898	−0.454781
$330$	−5.31047	−0.292332
$331$	−0.878198	−0.0482701	−0.0241351	−	0.999709i	$-0.507683\pi$
$331$	−0.878198	−0.0482701	−0.0241351	+	0.999709i	$0.507683\pi$
$332$	−6.76213	−0.371120
$333$	−11.0063	−0.603143
$334$	−9.51332	−0.520546
$335$	27.1388	1.48275
$336$	−4.85993	−0.265131
$337$	29.0311	1.58142	0.790712	−	0.612188i	$-0.209710\pi$
$337$	29.0311	1.58142	0.790712	+	0.612188i	$0.209710\pi$
$338$	8.98661	0.488807
$339$	23.9265	1.29951
$340$	3.33212	0.180710
$341$	5.71691	0.309588
$342$	1.40791	0.0761310
$343$	11.9236	0.643812
$344$	23.6607	1.27570
$345$	−55.4515	−2.98541
$346$	−0.763724	−0.0410581
$347$	−8.69496	−0.466770	−0.233385	−	0.972384i	$-0.574980\pi$
$347$	−8.69496	−0.466770	−0.233385	+	0.972384i	$0.574980\pi$
$348$	−14.6255	−0.784010
$349$	27.6542	1.48030	0.740148	−	0.672444i	$-0.234755\pi$
$349$	27.6542	1.48030	0.740148	+	0.672444i	$0.234755\pi$
$350$	−6.22080	−0.332516
$351$	−7.56045	−0.403547
$352$	5.28787	0.281844
$353$	−24.1961	−1.28783	−0.643914	−	0.765097i	$-0.722691\pi$
$353$	−24.1961	−1.28783	−0.643914	+	0.765097i	$0.722691\pi$
$354$	11.1883	0.594651
$355$	−57.3677	−3.04476
$356$	−8.07008	−0.427713
$357$	−0.978711	−0.0517989
$358$	8.53086	0.450870
$359$	17.8525	0.942218	0.471109	−	0.882075i	$-0.343854\pi$
$359$	17.8525	0.942218	0.471109	+	0.882075i	$0.343854\pi$
$360$	20.3234	1.07114
$361$	−17.8385	−0.938866
$362$	4.40076	0.231299
$363$	2.32406	0.121981
$364$	8.37450	0.438943
$365$	14.4623	0.756991
$366$	11.3456	0.593043
$367$	−9.36033	−0.488605	−0.244303	−	0.969699i	$-0.578559\pi$
$367$	−9.36033	−0.488605	−0.244303	+	0.969699i	$0.578559\pi$
$368$	13.1326	0.684586
$369$	14.0507	0.731450
$370$	10.4735	0.544493
$371$	5.26177	0.273178
$372$	−22.6405	−1.17386
$373$	38.6043	1.99886	0.999428	−	0.0338310i	$-0.0107708\pi$
$373$	38.6043	1.99886	0.999428	+	0.0338310i	$0.0107708\pi$
$374$	0.253277	0.0130966
$375$	−74.5907	−3.85185
$376$	−18.3766	−0.947698
$377$	20.0648	1.03339
$378$	0.684779	0.0352212
$379$	1.98961	0.102199	0.0510996	−	0.998694i	$-0.483727\pi$
$379$	1.98961	0.102199	0.0510996	+	0.998694i	$0.483727\pi$
$380$	7.71371	0.395705
$381$	−23.6765	−1.21298
$382$	−0.233262	−0.0119347
$383$	−20.2825	−1.03639	−0.518195	−	0.855263i	$-0.673396\pi$
$383$	−20.2825	−1.03639	−0.518195	+	0.855263i	$0.673396\pi$
$384$	−26.7873	−1.36698
$385$	3.79925	0.193628
$386$	3.87140	0.197049
$387$	−28.1947	−1.43322
$388$	4.74318	0.240799
$389$	−24.9265	−1.26383	−0.631913	−	0.775040i	$-0.717730\pi$
$389$	−24.9265	−1.26383	−0.631913	+	0.775040i	$0.717730\pi$
$390$	−28.8524	−1.46100
$391$	2.64470	0.133748
$392$	12.4569	0.629168
$393$	−2.32406	−0.117233
$394$	1.52982	0.0770713
$395$	38.7256	1.94849
$396$	−4.09180	−0.205621
$397$	28.1324	1.41192	0.705962	−	0.708250i	$-0.250515\pi$
$397$	28.1324	1.41192	0.705962	+	0.708250i	$0.250515\pi$
$398$	−4.23072	−0.212067
$399$	−2.26567	−0.113425
$400$	29.2244	1.46122
$401$	−12.6702	−0.632717	−0.316359	−	0.948640i	$-0.602460\pi$
$401$	−12.6702	−0.632717	−0.316359	+	0.948640i	$0.602460\pi$
$402$	−8.16942	−0.407454
$403$	31.0606	1.54724
$404$	−24.8641	−1.23703
$405$	43.8403	2.17844
$406$	−1.81735	−0.0901934
$407$	−4.58360	−0.227201
$408$	−2.18031	−0.107941
$409$	−26.1272	−1.29191	−0.645954	−	0.763377i	$-0.723540\pi$
$409$	−26.1272	−1.29191	−0.645954	+	0.763377i	$0.723540\pi$
$410$	−13.3705	−0.660323
$411$	−2.52127	−0.124365
$412$	−27.1421	−1.33720
$413$	−8.00440	−0.393871
$414$	7.42089	0.364717
$415$	−16.6675	−0.818177
$416$	28.7296	1.40858
$417$	−11.0489	−0.541066
$418$	0.586325	0.0286781
$419$	3.48130	0.170073	0.0850363	−	0.996378i	$-0.472899\pi$
$419$	3.48130	0.170073	0.0850363	+	0.996378i	$0.472899\pi$
$420$	−15.0461	−0.734173
$421$	−30.1556	−1.46970	−0.734848	−	0.678232i	$-0.762746\pi$
$421$	−30.1556	−1.46970	−0.734848	+	0.678232i	$0.762746\pi$
$422$	−10.5138	−0.511805
$423$	21.8980	1.06472
$424$	11.7218	0.569263
$425$	5.88532	0.285480
$426$	17.2690	0.836688
$427$	−8.11692	−0.392805
$428$	−8.13264	−0.393106
$429$	12.6269	0.609631
$430$	26.8298	1.29385
$431$	−24.1364	−1.16261	−0.581304	−	0.813687i	$-0.697457\pi$
$431$	−24.1364	−1.16261	−0.581304	+	0.813687i	$0.697457\pi$
$432$	−3.21699	−0.154778
$433$	−26.1428	−1.25634	−0.628172	−	0.778074i	$-0.716197\pi$
$433$	−26.1428	−1.25634	−0.628172	+	0.778074i	$0.716197\pi$
$434$	−2.81328	−0.135042
$435$	−36.0495	−1.72844
$436$	10.1372	0.485482
$437$	6.12236	0.292872
$438$	−4.35349	−0.208018
$439$	−22.8008	−1.08822	−0.544111	−	0.839013i	$-0.683133\pi$
$439$	−22.8008	−1.08822	−0.544111	+	0.839013i	$0.683133\pi$
$440$	8.46372	0.403492
$441$	−14.8440	−0.706856
$442$	1.37608	0.0654536
$443$	−34.1017	−1.62022	−0.810110	−	0.586277i	$-0.800593\pi$
$443$	−34.1017	−1.62022	−0.810110	+	0.586277i	$0.800593\pi$
$444$	18.1523	0.861471
$445$	−19.8914	−0.942943
$446$	−8.76562	−0.415064
$447$	−3.02619	−0.143134
$448$	1.58013	0.0746540
$449$	22.1950	1.04744	0.523722	−	0.851889i	$-0.324543\pi$
$449$	22.1950	1.04744	0.523722	+	0.851889i	$0.324543\pi$
$450$	16.5139	0.778474
$451$	5.85143	0.275533
$452$	−17.5433	−0.825167
$453$	38.1709	1.79342
$454$	−7.39920	−0.347262
$455$	20.6417	0.967700
$456$	−5.04732	−0.236362
$457$	−15.3531	−0.718189	−0.359095	−	0.933301i	$-0.616914\pi$
$457$	−15.3531	−0.718189	−0.359095	+	0.933301i	$0.616914\pi$
$458$	12.6609	0.591603
$459$	−0.647850	−0.0302391
$460$	40.6579	1.89568
$461$	−12.9418	−0.602760	−0.301380	−	0.953504i	$-0.597447\pi$
$461$	−12.9418	−0.602760	−0.301380	+	0.953504i	$0.597447\pi$
$462$	−1.14366	−0.0532081
$463$	1.22958	0.0571435	0.0285718	−	0.999592i	$-0.490904\pi$
$463$	1.22958	0.0571435	0.0285718	+	0.999592i	$0.490904\pi$
$464$	8.53763	0.396350
$465$	−55.8052	−2.58790
$466$	7.76888	0.359887
$467$	32.9368	1.52413	0.762066	−	0.647500i	$-0.224185\pi$
$467$	32.9368	1.52413	0.762066	+	0.647500i	$0.224185\pi$
$468$	−22.2312	−1.02764
$469$	5.84462	0.269879
$470$	−20.8380	−0.961183
$471$	−43.4317	−2.00123
$472$	−17.8317	−0.820769
$473$	−11.7417	−0.539885
$474$	−11.6573	−0.535438
$475$	13.6243	0.625124
$476$	0.717606	0.0328914
$477$	−13.9681	−0.639554
$478$	5.60675	0.256447
$479$	−43.2504	−1.97616	−0.988080	−	0.153942i	$-0.950803\pi$
$479$	−43.2504	−1.97616	−0.988080	+	0.153942i	$0.950803\pi$
$480$	−51.6171	−2.35599
$481$	−24.9032	−1.13549
$482$	13.9372	0.634823
$483$	−11.9420	−0.543382
$484$	−1.70404	−0.0774561
$485$	11.6912	0.530868
$486$	−10.9259	−0.495607
$487$	−1.60669	−0.0728063	−0.0364031	−	0.999337i	$-0.511590\pi$
$487$	−1.60669	−0.0728063	−0.0364031	+	0.999337i	$0.511590\pi$
$488$	−18.0824	−0.818550
$489$	13.1289	0.593708
$490$	14.1254	0.638121
$491$	−36.4794	−1.64629	−0.823146	−	0.567830i	$-0.807783\pi$
$491$	−36.4794	−1.64629	−0.823146	+	0.567830i	$0.807783\pi$
$492$	−23.1733	−1.04473
$493$	1.71934	0.0774352
$494$	3.18557	0.143326
$495$	−10.0856	−0.453314
$496$	13.2164	0.593433
$497$	−12.3547	−0.554185
$498$	5.01732	0.224832
$499$	−29.8488	−1.33621	−0.668107	−	0.744065i	$-0.732895\pi$
$499$	−29.8488	−1.33621	−0.668107	+	0.744065i	$0.732895\pi$
$500$	54.6911	2.44586
$501$	−40.6405	−1.81568
$502$	−8.01526	−0.357739
$503$	30.5866	1.36379	0.681895	−	0.731450i	$-0.261156\pi$
$503$	30.5866	1.36379	0.681895	+	0.731450i	$0.261156\pi$
$504$	4.37686	0.194961
$505$	−61.2859	−2.72719
$506$	3.09044	0.137387
$507$	38.3904	1.70498
$508$	17.3600	0.770225
$509$	1.25011	0.0554100	0.0277050	−	0.999616i	$-0.491180\pi$
$509$	1.25011	0.0554100	0.0277050	+	0.999616i	$0.491180\pi$
$510$	−2.47234	−0.109477
$511$	3.11460	0.137782
$512$	21.5415	0.952011
$513$	−1.49974	−0.0662153
$514$	7.52896	0.332088
$515$	−66.9009	−2.94800
$516$	46.5004	2.04707
$517$	9.11945	0.401073
$518$	2.25558	0.0991045
$519$	−3.26260	−0.143212
$520$	45.9844	2.01655
$521$	−24.6520	−1.08002	−0.540011	−	0.841658i	$-0.681580\pi$
$521$	−24.6520	−1.08002	−0.540011	+	0.841658i	$0.681580\pi$
$522$	4.82438	0.211158
$523$	−24.0181	−1.05024	−0.525119	−	0.851029i	$-0.675979\pi$
$523$	−24.0181	−1.05024	−0.525119	+	0.851029i	$0.675979\pi$
$524$	1.70404	0.0744411
$525$	−26.5750	−1.15983
$526$	11.9345	0.520369
$527$	2.66157	0.115940
$528$	5.37277	0.233820
$529$	9.27011	0.403048
$530$	13.2919	0.577363
$531$	21.2487	0.922116
$532$	1.66123	0.0720233
$533$	31.7915	1.37704
$534$	5.98778	0.259117
$535$	−20.0456	−0.866647
$536$	13.0203	0.562390
$537$	36.4434	1.57265
$538$	5.95167	0.256595
$539$	−6.18179	−0.266269
$540$	−9.95964	−0.428595
$541$	34.4632	1.48169	0.740845	−	0.671676i	$-0.234425\pi$
$541$	34.4632	1.48169	0.740845	+	0.671676i	$0.234425\pi$
$542$	15.9381	0.684601
$543$	18.7998	0.806778
$544$	2.46182	0.105550
$545$	24.9864	1.07030
$546$	−6.21365	−0.265920
$547$	32.7072	1.39846	0.699229	−	0.714898i	$-0.253527\pi$
$547$	32.7072	1.39846	0.699229	+	0.714898i	$0.253527\pi$
$548$	1.84863	0.0789697
$549$	21.5474	0.919622
$550$	6.87724	0.293247
$551$	3.98020	0.169562
$552$	−26.6037	−1.13233
$553$	8.33994	0.354650
$554$	0.502366	0.0213435
$555$	44.7424	1.89921
$556$	8.10121	0.343568
$557$	20.8397	0.883006	0.441503	−	0.897260i	$-0.354445\pi$
$557$	20.8397	0.883006	0.441503	+	0.897260i	$0.354445\pi$
$558$	7.46822	0.316155
$559$	−63.7941	−2.69820
$560$	8.78313	0.371155
$561$	1.08199	0.0456816
$562$	3.03246	0.127917
$563$	−17.9943	−0.758368	−0.379184	−	0.925321i	$-0.623795\pi$
$563$	−17.9943	−0.758368	−0.379184	+	0.925321i	$0.623795\pi$
$564$	−36.1155	−1.52074
$565$	−43.2413	−1.81918
$566$	−8.33639	−0.350405
$567$	9.44146	0.396504
$568$	−27.5230	−1.15484
$569$	26.8109	1.12397	0.561985	−	0.827148i	$-0.310038\pi$
$569$	26.8109	1.12397	0.561985	+	0.827148i	$0.310038\pi$
$570$	−5.72337	−0.239726
$571$	−32.6183	−1.36504	−0.682518	−	0.730869i	$-0.739115\pi$
$571$	−32.6183	−1.36504	−0.682518	+	0.730869i	$0.739115\pi$
$572$	−9.25821	−0.387105
$573$	−0.996484	−0.0416287
$574$	−2.87948	−0.120187
$575$	71.8116	2.99475
$576$	−4.19466	−0.174777
$577$	9.84304	0.409771	0.204885	−	0.978786i	$-0.434318\pi$
$577$	9.84304	0.409771	0.204885	+	0.978786i	$0.434318\pi$
$578$	−9.13053	−0.379780
$579$	16.5385	0.687315
$580$	26.4321	1.09753
$581$	−3.58952	−0.148918
$582$	−3.51932	−0.145880
$583$	−5.81702	−0.240916
$584$	6.93851	0.287117
$585$	−54.7962	−2.26555
$586$	−4.37197	−0.180604
$587$	−27.5653	−1.13774	−0.568870	−	0.822427i	$-0.692619\pi$
$587$	−27.5653	−1.13774	−0.568870	+	0.822427i	$0.692619\pi$
$588$	24.4816	1.00960
$589$	6.16141	0.253876
$590$	−20.2201	−0.832448
$591$	6.53533	0.268827
$592$	−10.5964	−0.435509
$593$	3.29368	0.135255	0.0676277	−	0.997711i	$-0.478457\pi$
$593$	3.29368	0.135255	0.0676277	+	0.997711i	$0.478457\pi$
$594$	−0.757040	−0.0310617
$595$	1.76878	0.0725129
$596$	2.21885	0.0908877
$597$	−18.0734	−0.739697
$598$	16.7907	0.686623
$599$	12.4630	0.509224	0.254612	−	0.967043i	$-0.418052\pi$
$599$	12.4630	0.509224	0.254612	+	0.967043i	$0.418052\pi$
$600$	−59.2020	−2.41691
$601$	−33.7124	−1.37516	−0.687578	−	0.726110i	$-0.741326\pi$
$601$	−33.7124	−1.37516	−0.687578	+	0.726110i	$0.741326\pi$
$602$	5.77808	0.235497
$603$	−15.5153	−0.631832
$604$	−27.9875	−1.13879
$605$	−4.20016	−0.170761
$606$	18.4485	0.749419
$607$	42.8724	1.74014	0.870069	−	0.492931i	$-0.164074\pi$
$607$	42.8724	1.74014	0.870069	+	0.492931i	$0.164074\pi$
$608$	5.69901	0.231125
$609$	−7.76362	−0.314598
$610$	−20.5044	−0.830197
$611$	49.5470	2.00446
$612$	−1.90498	−0.0770042
$613$	4.23641	0.171107	0.0855534	−	0.996334i	$-0.472734\pi$
$613$	4.23641	0.171107	0.0855534	+	0.996334i	$0.472734\pi$
$614$	−6.13241	−0.247484
$615$	−57.1183	−2.30323
$616$	1.82275	0.0734406
$617$	−25.4559	−1.02482	−0.512408	−	0.858742i	$-0.671246\pi$
$617$	−25.4559	−1.02482	−0.512408	+	0.858742i	$0.671246\pi$
$618$	20.1387	0.810099
$619$	47.2031	1.89725	0.948627	−	0.316396i	$-0.102473\pi$
$619$	47.2031	1.89725	0.948627	+	0.316396i	$0.102473\pi$
$620$	40.9172	1.64328
$621$	−7.90495	−0.317215
$622$	3.22115	0.129156
$623$	−4.28381	−0.171627
$624$	29.1909	1.16857
$625$	71.5975	2.86390
$626$	−4.23035	−0.169079
$627$	2.50476	0.100030
$628$	31.8448	1.27075
$629$	−2.13394	−0.0850858
$630$	4.96311	0.197735
$631$	17.4690	0.695429	0.347715	−	0.937600i	$-0.386958\pi$
$631$	17.4690	0.695429	0.347715	+	0.937600i	$0.386958\pi$
$632$	18.5792	0.739040
$633$	−44.9146	−1.78519
$634$	−12.3803	−0.491683
$635$	42.7895	1.69805
$636$	23.0370	0.913476
$637$	−33.5864	−1.33074
$638$	2.00912	0.0795419
$639$	32.7972	1.29744
$640$	48.4114	1.91363
$641$	1.79113	0.0707453	0.0353726	−	0.999374i	$-0.488738\pi$
$641$	1.79113	0.0707453	0.0353726	+	0.999374i	$0.488738\pi$
$642$	6.03420	0.238151
$643$	31.0302	1.22371	0.611857	−	0.790969i	$-0.290423\pi$
$643$	31.0302	1.22371	0.611857	+	0.790969i	$0.290423\pi$
$644$	8.75609	0.345038
$645$	114.616	4.51299
$646$	0.272970	0.0107399
$647$	−34.3434	−1.35018	−0.675089	−	0.737737i	$-0.735895\pi$
$647$	−34.3434	−1.35018	−0.675089	+	0.737737i	$0.735895\pi$
$648$	21.0331	0.826257
$649$	8.84906	0.347356
$650$	37.3648	1.46557
$651$	−12.0182	−0.471031
$652$	−9.62629	−0.376995
$653$	−24.0102	−0.939591	−0.469795	−	0.882775i	$-0.655672\pi$
$653$	−24.0102	−0.939591	−0.469795	+	0.882775i	$0.655672\pi$
$654$	−7.52150	−0.294114
$655$	4.20016	0.164114
$656$	13.5274	0.528155
$657$	−8.26812	−0.322570
$658$	−4.48767	−0.174947
$659$	−4.09196	−0.159400	−0.0797001	−	0.996819i	$-0.525396\pi$
$659$	−4.09196	−0.159400	−0.0797001	+	0.996819i	$0.525396\pi$
$660$	16.6338	0.647470
$661$	−26.9036	−1.04643	−0.523214	−	0.852202i	$-0.675267\pi$
$661$	−26.9036	−1.04643	−0.523214	+	0.852202i	$0.675267\pi$
$662$	−0.477763	−0.0185688
$663$	5.87857	0.228305
$664$	−7.99651	−0.310325
$665$	4.09465	0.158784
$666$	−5.98773	−0.232020
$667$	20.9791	0.812313
$668$	29.7982	1.15293
$669$	−37.4464	−1.44776
$670$	14.7642	0.570392
$671$	8.97346	0.346416
$672$	−11.1163	−0.428820
$673$	−6.10412	−0.235297	−0.117648	−	0.993055i	$-0.537536\pi$
$673$	−6.10412	−0.235297	−0.117648	+	0.993055i	$0.537536\pi$
$674$	15.7937	0.608350
$675$	−17.5911	−0.677082
$676$	−28.1485	−1.08263
$677$	5.66925	0.217887	0.108944	−	0.994048i	$-0.465253\pi$
$677$	5.66925	0.217887	0.108944	+	0.994048i	$0.465253\pi$
$678$	13.0167	0.499902
$679$	2.51781	0.0966247
$680$	3.94037	0.151106
$681$	−31.6091	−1.21126
$682$	3.11015	0.119094
$683$	35.7397	1.36754	0.683771	−	0.729697i	$-0.260339\pi$
$683$	35.7397	1.36754	0.683771	+	0.729697i	$0.260339\pi$
$684$	−4.40994	−0.168618
$685$	4.55657	0.174098
$686$	6.48673	0.247665
$687$	54.0866	2.06353
$688$	−27.1446	−1.03488
$689$	−31.6045	−1.20404
$690$	−30.1671	−1.14844
$691$	−1.25670	−0.0478073	−0.0239036	−	0.999714i	$-0.507609\pi$
$691$	−1.25670	−0.0478073	−0.0239036	+	0.999714i	$0.507609\pi$
$692$	2.39219	0.0909373
$693$	−2.17204	−0.0825089
$694$	−4.73029	−0.179559
$695$	19.9681	0.757434
$696$	−17.2953	−0.655577
$697$	2.72419	0.103186
$698$	15.0446	0.569447
$699$	33.1883	1.25530
$700$	19.4852	0.736471
$701$	43.0621	1.62643	0.813217	−	0.581961i	$-0.197714\pi$
$701$	43.0621	1.62643	0.813217	+	0.581961i	$0.197714\pi$
$702$	−4.11308	−0.155238
$703$	−4.93998	−0.186315
$704$	−1.74687	−0.0658377
$705$	−89.0188	−3.35264
$706$	−13.1633	−0.495408
$707$	−13.1985	−0.496382
$708$	−35.0447	−1.31706
$709$	−33.1017	−1.24316	−0.621580	−	0.783350i	$-0.713509\pi$
$709$	−33.1017	−1.24316	−0.621580	+	0.783350i	$0.713509\pi$
$710$	−31.2096	−1.17127
$711$	−22.1395	−0.830295
$712$	−9.54320	−0.357647
$713$	32.4759	1.21623
$714$	−0.532445	−0.0199262
$715$	−22.8200	−0.853418
$716$	−26.7209	−0.998607
$717$	23.9518	0.894496
$718$	9.71222	0.362457
$719$	−8.67296	−0.323447	−0.161723	−	0.986836i	$-0.551705\pi$
$719$	−8.67296	−0.323447	−0.161723	+	0.986836i	$0.551705\pi$
$720$	−23.3160	−0.868935
$721$	−14.4078	−0.536574
$722$	−9.70459	−0.361167
$723$	59.5392	2.21429
$724$	−13.7843	−0.512291
$725$	46.6853	1.73385
$726$	1.26435	0.0469244
$727$	18.4314	0.683584	0.341792	−	0.939776i	$-0.388966\pi$
$727$	18.4314	0.683584	0.341792	+	0.939776i	$0.388966\pi$
$728$	9.90320	0.367037
$729$	−15.3615	−0.568943
$730$	7.86787	0.291203
$731$	−5.46648	−0.202185
$732$	−35.5374	−1.31350
$733$	23.4783	0.867192	0.433596	−	0.901107i	$-0.357245\pi$
$733$	23.4783	0.867192	0.433596	+	0.901107i	$0.357245\pi$
$734$	−5.09227	−0.187959
$735$	60.3431	2.22579
$736$	30.0387	1.10724
$737$	−6.46137	−0.238008
$738$	7.64395	0.281378
$739$	35.1131	1.29166	0.645828	−	0.763483i	$-0.276512\pi$
$739$	35.1131	1.29166	0.645828	+	0.763483i	$0.276512\pi$
$740$	−32.8059	−1.20597
$741$	13.6086	0.499925
$742$	2.86254	0.105087
$743$	−28.3315	−1.03938	−0.519691	−	0.854355i	$-0.673953\pi$
$743$	−28.3315	−1.03938	−0.519691	+	0.854355i	$0.673953\pi$
$744$	−26.7734	−0.981560
$745$	5.46910	0.200372
$746$	21.0018	0.768929
$747$	9.52886	0.348643
$748$	−0.793331	−0.0290071
$749$	−4.31702	−0.157741
$750$	−40.5793	−1.48175
$751$	15.1401	0.552469	0.276234	−	0.961090i	$-0.410913\pi$
$751$	15.1401	0.552469	0.276234	+	0.961090i	$0.410913\pi$
$752$	21.0824	0.768796
$753$	−34.2409	−1.24781
$754$	10.9158	0.397529
$755$	−68.9845	−2.51060
$756$	−2.14491	−0.0780096
$757$	−51.5954	−1.87527	−0.937633	−	0.347628i	$-0.886987\pi$
$757$	−51.5954	−1.87527	−0.937633	+	0.347628i	$0.886987\pi$
$758$	1.08240	0.0393145
$759$	13.2022	0.479210
$760$	9.12179	0.330882
$761$	−11.6361	−0.421808	−0.210904	−	0.977507i	$-0.567641\pi$
$761$	−11.6361	−0.421808	−0.210904	+	0.977507i	$0.567641\pi$
$762$	−12.8807	−0.466617
$763$	5.38108	0.194808
$764$	0.730638	0.0264335
$765$	−4.69546	−0.169765
$766$	−11.0342	−0.398683
$767$	48.0779	1.73599
$768$	−6.45334	−0.232865
$769$	17.9332	0.646688	0.323344	−	0.946282i	$-0.395193\pi$
$769$	17.9332	0.646688	0.323344	+	0.946282i	$0.395193\pi$
$770$	2.06689	0.0744856
$771$	32.1634	1.15834
$772$	−12.1263	−0.436433
$773$	1.91012	0.0687021	0.0343510	−	0.999410i	$-0.489064\pi$
$773$	1.91012	0.0687021	0.0343510	+	0.999410i	$0.489064\pi$
$774$	−15.3387	−0.551337
$775$	72.2696	2.59600
$776$	5.60902	0.201352
$777$	9.63574	0.345680
$778$	−13.5607	−0.486174
$779$	6.30639	0.225950
$780$	90.3733	3.23588
$781$	13.6584	0.488738
$782$	1.43879	0.0514509
$783$	−5.13907	−0.183655
$784$	−14.2911	−0.510397
$785$	78.4921	2.80150
$786$	−1.26435	−0.0450978
$787$	−22.5338	−0.803244	−0.401622	−	0.915806i	$-0.631553\pi$
$787$	−22.5338	−0.803244	−0.401622	+	0.915806i	$0.631553\pi$
$788$	−4.79180	−0.170701
$789$	50.9836	1.81507
$790$	21.0677	0.749556
$791$	−9.31245	−0.331113
$792$	−4.83872	−0.171937
$793$	48.7538	1.73130
$794$	15.3048	0.543146
$795$	56.7824	2.01386
$796$	13.2517	0.469695
$797$	12.1977	0.432066	0.216033	−	0.976386i	$-0.430688\pi$
$797$	12.1977	0.432066	0.216033	+	0.976386i	$0.430688\pi$
$798$	−1.23259	−0.0436331
$799$	4.24566	0.150201
$800$	66.8460	2.36336
$801$	11.3719	0.401808
$802$	−6.89290	−0.243397
$803$	−3.44327	−0.121510
$804$	25.5888	0.902447
$805$	21.5823	0.760677
$806$	16.8978	0.595200
$807$	25.4253	0.895011
$808$	−29.4028	−1.03439
$809$	0.193991	0.00682037	0.00341018	−	0.999994i	$-0.498915\pi$
$809$	0.193991	0.00682037	0.00341018	+	0.999994i	$0.498915\pi$
$810$	23.8503	0.838014
$811$	−22.1914	−0.779247	−0.389624	−	0.920974i	$-0.627395\pi$
$811$	−22.1914	−0.779247	−0.389624	+	0.920974i	$0.627395\pi$
$812$	5.69241	0.199764
$813$	68.0870	2.38792
$814$	−2.49360	−0.0874006
$815$	−23.7272	−0.831128
$816$	2.50135	0.0875647
$817$	−12.6546	−0.442730
$818$	−14.2139	−0.496977
$819$	−11.8009	−0.412358
$820$	41.8800	1.46251
$821$	41.4813	1.44771	0.723854	−	0.689953i	$-0.242369\pi$
$821$	41.4813	1.44771	0.723854	+	0.689953i	$0.242369\pi$
$822$	−1.37164	−0.0478413
$823$	−0.956976	−0.0333581	−0.0166790	−	0.999861i	$-0.505309\pi$
$823$	−0.956976	−0.0333581	−0.0166790	+	0.999861i	$0.505309\pi$
$824$	−32.0967	−1.11814
$825$	29.3793	1.02286
$826$	−4.35460	−0.151516
$827$	30.8942	1.07430	0.537148	−	0.843488i	$-0.319502\pi$
$827$	30.8942	1.07430	0.537148	+	0.843488i	$0.319502\pi$
$828$	−23.2442	−0.807792
$829$	16.8949	0.586785	0.293392	−	0.955992i	$-0.405216\pi$
$829$	16.8949	0.586785	0.293392	+	0.955992i	$0.405216\pi$
$830$	−9.06758	−0.314740
$831$	2.14608	0.0744469
$832$	−9.49094	−0.329039
$833$	−2.87800	−0.0997167
$834$	−6.01088	−0.208140
$835$	73.4477	2.54176
$836$	−1.83653	−0.0635176
$837$	−7.95536	−0.274978
$838$	1.89392	0.0654244
$839$	1.07226	0.0370186	0.0185093	−	0.999829i	$-0.494108\pi$
$839$	1.07226	0.0370186	0.0185093	+	0.999829i	$0.494108\pi$
$840$	−17.7926	−0.613904
$841$	−15.3613	−0.529701
$842$	−16.4055	−0.565369
$843$	12.9546	0.446178
$844$	32.9321	1.13357
$845$	−69.3813	−2.38679
$846$	11.9131	0.409581
$847$	−0.904548	−0.0310806
$848$	−13.4478	−0.461800
$849$	−35.6127	−1.22222
$850$	3.20177	0.109820
$851$	−26.0380	−0.892570
$852$	−54.0912	−1.85313
$853$	38.8272	1.32942	0.664709	−	0.747102i	$-0.268555\pi$
$853$	38.8272	1.32942	0.664709	+	0.747102i	$0.268555\pi$
$854$	−4.41582	−0.151106
$855$	−10.8698	−0.371739
$856$	−9.61719	−0.328709
$857$	−50.0610	−1.71005	−0.855025	−	0.518586i	$-0.826458\pi$
$857$	−50.0610	−1.71005	−0.855025	+	0.518586i	$0.826458\pi$
$858$	6.86935	0.234516
$859$	−48.7823	−1.66443	−0.832216	−	0.554451i	$-0.812928\pi$
$859$	−48.7823	−1.66443	−0.832216	+	0.554451i	$0.812928\pi$
$860$	−84.0381	−2.86568
$861$	−12.3010	−0.419217
$862$	−13.1308	−0.447237
$863$	36.5684	1.24480	0.622401	−	0.782699i	$-0.286157\pi$
$863$	36.5684	1.24480	0.622401	+	0.782699i	$0.286157\pi$
$864$	−7.35833	−0.250336
$865$	5.89634	0.200482
$866$	−14.2224	−0.483296
$867$	−39.0052	−1.32469
$868$	8.81194	0.299097
$869$	−9.22001	−0.312768
$870$	−19.6119	−0.664905
$871$	−35.1053	−1.18950
$872$	11.9876	0.405952
$873$	−6.68386	−0.226214
$874$	3.33073	0.112663
$875$	29.0315	0.981444
$876$	13.6363	0.460727
$877$	−9.75032	−0.329245	−0.164622	−	0.986357i	$-0.552641\pi$
$877$	−9.75032	−0.329245	−0.164622	+	0.986357i	$0.552641\pi$
$878$	−12.4042	−0.418623
$879$	−18.6769	−0.629955
$880$	−9.70996	−0.327323
$881$	23.0011	0.774928	0.387464	−	0.921885i	$-0.373351\pi$
$881$	23.0011	0.774928	0.387464	+	0.921885i	$0.373351\pi$
$882$	−8.07552	−0.271917
$883$	−35.6339	−1.19918	−0.599588	−	0.800309i	$-0.704669\pi$
$883$	−35.6339	−1.19918	−0.599588	+	0.800309i	$0.704669\pi$
$884$	−4.31026	−0.144970
$885$	−86.3794	−2.90361
$886$	−18.5522	−0.623274
$887$	16.2140	0.544412	0.272206	−	0.962239i	$-0.412247\pi$
$887$	16.2140	0.544412	0.272206	+	0.962239i	$0.412247\pi$
$888$	21.4659	0.720347
$889$	9.21516	0.309066
$890$	−10.8214	−0.362736
$891$	−10.4378	−0.349678
$892$	27.4563	0.919303
$893$	9.82850	0.328898
$894$	−1.64633	−0.0550615
$895$	−65.8626	−2.20154
$896$	10.4259	0.348305
$897$	71.7292	2.39497
$898$	12.0746	0.402936
$899$	21.1129	0.704154
$900$	−51.7260	−1.72420
$901$	−2.70817	−0.0902223
$902$	3.18333	0.105993
$903$	24.6837	0.821421
$904$	−20.7457	−0.689991
$905$	−33.9761	−1.12940
$906$	20.7660	0.689903
$907$	−2.43321	−0.0807935	−0.0403967	−	0.999184i	$-0.512862\pi$
$907$	−2.43321	−0.0807935	−0.0403967	+	0.999184i	$0.512862\pi$
$908$	23.1763	0.769131
$909$	35.0372	1.16211
$910$	11.2297	0.372260
$911$	−58.0965	−1.92482	−0.962411	−	0.271597i	$-0.912448\pi$
$911$	−58.0965	−1.92482	−0.962411	+	0.271597i	$0.912448\pi$
$912$	5.79051	0.191743
$913$	3.96831	0.131332
$914$	−8.35251	−0.276277
$915$	−87.5937	−2.89576
$916$	−39.6572	−1.31031
$917$	0.904548	0.0298708
$918$	−0.352448	−0.0116325
$919$	7.51942	0.248043	0.124021	−	0.992280i	$-0.460421\pi$
$919$	7.51942	0.248043	0.124021	+	0.992280i	$0.460421\pi$
$920$	48.0797	1.58514
$921$	−26.1974	−0.863233
$922$	−7.04068	−0.231873
$923$	74.2079	2.44258
$924$	3.58226	0.117848
$925$	−57.9430	−1.90515
$926$	0.668925	0.0219822
$927$	38.2473	1.25621
$928$	19.5284	0.641051
$929$	−12.6483	−0.414978	−0.207489	−	0.978237i	$-0.566529\pi$
$929$	−12.6483	−0.414978	−0.207489	+	0.978237i	$0.566529\pi$
$930$	−30.3595	−0.995527
$931$	−6.66244	−0.218353
$932$	−24.3342	−0.797093
$933$	13.7606	0.450502
$934$	17.9185	0.586310
$935$	−1.95543	−0.0639494
$936$	−26.2893	−0.859294
$937$	−48.7597	−1.59291	−0.796454	−	0.604698i	$-0.793294\pi$
$937$	−48.7597	−1.59291	−0.796454	+	0.604698i	$0.793294\pi$
$938$	3.17963	0.103818
$939$	−18.0719	−0.589753
$940$	65.2700	2.12887
$941$	−51.4264	−1.67645	−0.838227	−	0.545321i	$-0.816408\pi$
$941$	−51.4264	−1.67645	−0.838227	+	0.545321i	$0.816408\pi$
$942$	−23.6280	−0.769841
$943$	33.2401	1.08245
$944$	20.4573	0.665828
$945$	−5.28684	−0.171981
$946$	−6.38780	−0.207685
$947$	12.7493	0.414298	0.207149	−	0.978309i	$-0.433582\pi$
$947$	12.7493	0.414298	0.207149	+	0.978309i	$0.433582\pi$
$948$	36.5138	1.18591
$949$	−18.7077	−0.607276
$950$	7.41196	0.240476
$951$	−52.8879	−1.71501
$952$	0.848599	0.0275033
$953$	−39.9252	−1.29331	−0.646653	−	0.762784i	$-0.723832\pi$
$953$	−39.9252	−1.29331	−0.646653	+	0.762784i	$0.723832\pi$
$954$	−7.59900	−0.246027
$955$	1.80090	0.0582758
$956$	−17.5618	−0.567990
$957$	8.58288	0.277445
$958$	−23.5293	−0.760199
$959$	0.981305	0.0316880
$960$	17.0519	0.550349
$961$	1.68306	0.0542923
$962$	−13.5480	−0.436805
$963$	11.4601	0.369297
$964$	−43.6551	−1.40604
$965$	−29.8892	−0.962167
$966$	−6.49679	−0.209031
$967$	−18.1873	−0.584865	−0.292433	−	0.956286i	$-0.594465\pi$
$967$	−18.1873	−0.584865	−0.292433	+	0.956286i	$0.594465\pi$
$968$	−2.01509	−0.0647676
$969$	1.16611	0.0374610
$970$	6.36030	0.204217
$971$	−3.01324	−0.0966996	−0.0483498	−	0.998830i	$-0.515396\pi$
$971$	−3.01324	−0.0966996	−0.0483498	+	0.998830i	$0.515396\pi$
$972$	34.2227	1.09769
$973$	4.30034	0.137863
$974$	−0.874084	−0.0280075
$975$	159.621	5.11196
$976$	20.7449	0.664028
$977$	−14.3133	−0.457923	−0.228961	−	0.973435i	$-0.573533\pi$
$977$	−14.3133	−0.457923	−0.228961	+	0.973435i	$0.573533\pi$
$978$	7.14245	0.228390
$979$	4.73586	0.151359
$980$	−44.2445	−1.41334
$981$	−14.2848	−0.456078
$982$	−19.8458	−0.633303
$983$	4.95866	0.158157	0.0790784	−	0.996868i	$-0.474802\pi$
$983$	4.95866	0.158157	0.0790784	+	0.996868i	$0.474802\pi$
$984$	−27.4034	−0.873587
$985$	−11.8110	−0.376330
$986$	0.935367	0.0297882
$987$	−19.1711	−0.610223
$988$	−9.97805	−0.317444
$989$	−66.7009	−2.12097
$990$	−5.48684	−0.174383
$991$	−11.4778	−0.364605	−0.182303	−	0.983242i	$-0.558355\pi$
$991$	−11.4778	−0.364605	−0.182303	+	0.983242i	$0.558355\pi$
$992$	30.2303	0.959812
$993$	−2.04098	−0.0647686
$994$	−6.72130	−0.213187
$995$	32.6633	1.03550
$996$	−15.7156	−0.497967
$997$	−21.0166	−0.665602	−0.332801	−	0.942997i	$-0.607994\pi$
$997$	−21.0166	−0.665602	−0.332801	+	0.942997i	$0.607994\pi$
$998$	−16.2385	−0.514021
$999$	6.37831	0.201801

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.e.1.15	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.e.1.15	✓	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)

\(f(q)\)	\(=\)	\(q+0.544027 q^{2} +2.32406 q^{3} -1.70404 q^{4} -4.20016 q^{5} +1.26435 q^{6} -0.904548 q^{7} -2.01509 q^{8} +2.40124 q^{9} +O(q^{10})\)	\(q+0.544027 q^{2} +2.32406 q^{3} -1.70404 q^{4} -4.20016 q^{5} +1.26435 q^{6} -0.904548 q^{7} -2.01509 q^{8} +2.40124 q^{9} -2.28500 q^{10} +1.00000 q^{11} -3.96027 q^{12} +5.43311 q^{13} -0.492098 q^{14} -9.76142 q^{15} +2.31181 q^{16} +0.465560 q^{17} +1.30634 q^{18} +1.07775 q^{19} +7.15723 q^{20} -2.10222 q^{21} +0.544027 q^{22} +5.68068 q^{23} -4.68319 q^{24} +12.6414 q^{25} +2.95576 q^{26} -1.39155 q^{27} +1.54138 q^{28} +3.69306 q^{29} -5.31047 q^{30} +5.71691 q^{31} +5.28787 q^{32} +2.32406 q^{33} +0.253277 q^{34} +3.79925 q^{35} -4.09180 q^{36} -4.58360 q^{37} +0.586325 q^{38} +12.6269 q^{39} +8.46372 q^{40} +5.85143 q^{41} -1.14366 q^{42} -11.7417 q^{43} -1.70404 q^{44} -10.0856 q^{45} +3.09044 q^{46} +9.11945 q^{47} +5.37277 q^{48} -6.18179 q^{49} +6.87724 q^{50} +1.08199 q^{51} -9.25821 q^{52} -5.81702 q^{53} -0.757040 q^{54} -4.20016 q^{55} +1.82275 q^{56} +2.50476 q^{57} +2.00912 q^{58} +8.84906 q^{59} +16.6338 q^{60} +8.97346 q^{61} +3.11015 q^{62} -2.17204 q^{63} -1.74687 q^{64} -22.8200 q^{65} +1.26435 q^{66} -6.46137 q^{67} -0.793331 q^{68} +13.2022 q^{69} +2.06689 q^{70} +13.6584 q^{71} -4.83872 q^{72} -3.44327 q^{73} -2.49360 q^{74} +29.3793 q^{75} -1.83653 q^{76} -0.904548 q^{77} +6.86935 q^{78} -9.22001 q^{79} -9.70996 q^{80} -10.4378 q^{81} +3.18333 q^{82} +3.96831 q^{83} +3.58226 q^{84} -1.95543 q^{85} -6.38780 q^{86} +8.58288 q^{87} -2.01509 q^{88} +4.73586 q^{89} -5.48684 q^{90} -4.91451 q^{91} -9.68008 q^{92} +13.2864 q^{93} +4.96122 q^{94} -4.52673 q^{95} +12.2893 q^{96} -2.78350 q^{97} -3.36306 q^{98} +2.40124 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) \) 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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