LMFDB - Embedded newform 1441.2.a.d.1.10

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:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-0.850138 q^{2} -0.411295 q^{3} -1.27727 q^{4} -3.81435 q^{5} +0.349658 q^{6} +2.53746 q^{7} +2.78613 q^{8} -2.83084 q^{9} +O(q^{10})$	\(q-0.850138 q^{2} -0.411295 q^{3} -1.27727 q^{4} -3.81435 q^{5} +0.349658 q^{6} +2.53746 q^{7} +2.78613 q^{8} -2.83084 q^{9} +3.24272 q^{10} -1.00000 q^{11} +0.525333 q^{12} +4.31436 q^{13} -2.15719 q^{14} +1.56882 q^{15} +0.185940 q^{16} +3.85874 q^{17} +2.40660 q^{18} -4.33710 q^{19} +4.87194 q^{20} -1.04365 q^{21} +0.850138 q^{22} -3.70579 q^{23} -1.14592 q^{24} +9.54924 q^{25} -3.66780 q^{26} +2.39819 q^{27} -3.24102 q^{28} +9.77700 q^{29} -1.33372 q^{30} +2.69350 q^{31} -5.73033 q^{32} +0.411295 q^{33} -3.28046 q^{34} -9.67876 q^{35} +3.61573 q^{36} +1.89288 q^{37} +3.68713 q^{38} -1.77447 q^{39} -10.6273 q^{40} -5.55444 q^{41} +0.887243 q^{42} -3.90214 q^{43} +1.27727 q^{44} +10.7978 q^{45} +3.15043 q^{46} -0.482047 q^{47} -0.0764764 q^{48} -0.561281 q^{49} -8.11817 q^{50} -1.58708 q^{51} -5.51058 q^{52} -5.87525 q^{53} -2.03880 q^{54} +3.81435 q^{55} +7.06969 q^{56} +1.78383 q^{57} -8.31180 q^{58} +1.11357 q^{59} -2.00380 q^{60} +12.3497 q^{61} -2.28984 q^{62} -7.18314 q^{63} +4.49969 q^{64} -16.4565 q^{65} -0.349658 q^{66} +2.60122 q^{67} -4.92863 q^{68} +1.52417 q^{69} +8.22828 q^{70} -9.93410 q^{71} -7.88707 q^{72} -13.8969 q^{73} -1.60921 q^{74} -3.92756 q^{75} +5.53963 q^{76} -2.53746 q^{77} +1.50855 q^{78} -5.91094 q^{79} -0.709241 q^{80} +7.50614 q^{81} +4.72204 q^{82} -16.0066 q^{83} +1.33301 q^{84} -14.7186 q^{85} +3.31735 q^{86} -4.02123 q^{87} -2.78613 q^{88} -6.30248 q^{89} -9.17961 q^{90} +10.9475 q^{91} +4.73328 q^{92} -1.10782 q^{93} +0.409806 q^{94} +16.5432 q^{95} +2.35686 q^{96} -18.1164 q^{97} +0.477166 q^{98} +2.83084 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) $ 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9 - 2 * q^10 - 23 * q^11 - 12 * q^12 + 6 * q^13 - 13 * q^14 - 27 * q^15 - q^16 - 11 * q^17 - 16 * q^19 - 24 * q^20 - 7 * q^21 + 7 * q^22 - 30 * q^23 - 20 * q^24 + 10 * q^25 - 22 * q^26 - 15 * q^27 + 11 * q^28 - 15 * q^29 + 17 * q^30 - 31 * q^31 - 22 * q^32 + 3 * q^33 - 18 * q^34 - 34 * q^35 - 18 * q^36 - 26 * q^37 - 32 * q^39 + 16 * q^40 - 21 * q^41 - 37 * q^42 - 2 * q^43 - 19 * q^44 - 18 * q^45 - 6 * q^46 - 25 * q^47 + 14 * q^48 + 7 * q^49 - 27 * q^50 - 7 * q^51 + 23 * q^52 - 34 * q^53 + 26 * q^54 + 9 * q^55 - 42 * q^56 + 6 * q^57 - 5 * q^58 - 31 * q^59 - 7 * q^60 + 19 * q^61 + 24 * q^62 - 34 * q^63 - 17 * q^64 - 13 * q^65 + 5 * q^66 - 39 * q^67 - 59 * q^68 - 12 * q^69 + 17 * q^70 - 103 * q^71 + 19 * q^72 + q^73 - 9 * q^74 - 19 * q^75 + 10 * q^76 + 8 * q^77 - 43 * q^78 - 14 * q^79 - q^80 - 29 * q^81 + 20 * q^82 - 14 * q^83 + 57 * q^84 + 20 * q^85 - 54 * q^86 - 23 * q^87 + 15 * q^88 - 71 * q^89 - 52 * q^90 - 18 * q^91 - 24 * q^92 - q^93 + q^94 - 38 * q^95 - 31 * q^96 - 26 * q^97 + 19 * q^98 - 12 * 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 $

$2$	−0.850138	−0.601138	−0.300569	−	0.953760i	$-0.597177\pi$
$2$	−0.850138	−0.601138	−0.300569	+	0.953760i	$0.597177\pi$
$3$	−0.411295	−0.237461	−0.118731	−	0.992926i	$-0.537883\pi$
$3$	−0.411295	−0.237461	−0.118731	+	0.992926i	$0.537883\pi$
$4$	−1.27727	−0.638633
$5$	−3.81435	−1.70583	−0.852914	−	0.522052i	$-0.825167\pi$
$5$	−3.81435	−1.70583	−0.852914	+	0.522052i	$0.825167\pi$
$6$	0.349658	0.142747
$7$	2.53746	0.959071	0.479535	−	0.877523i	$-0.340805\pi$
$7$	2.53746	0.959071	0.479535	+	0.877523i	$0.340805\pi$
$8$	2.78613	0.985045
$9$	−2.83084	−0.943612
$10$	3.24272	1.02544
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.525333	0.151651
$13$	4.31436	1.19659	0.598294	−	0.801277i	$-0.295846\pi$
$13$	4.31436	1.19659	0.598294	+	0.801277i	$0.295846\pi$
$14$	−2.15719	−0.576534
$15$	1.56882	0.405068
$16$	0.185940	0.0464851
$17$	3.85874	0.935881	0.467941	−	0.883760i	$-0.344996\pi$
$17$	3.85874	0.935881	0.467941	+	0.883760i	$0.344996\pi$
$18$	2.40660	0.567241
$19$	−4.33710	−0.994998	−0.497499	−	0.867464i	$-0.665748\pi$
$19$	−4.33710	−0.994998	−0.497499	+	0.867464i	$0.665748\pi$
$20$	4.87194	1.08940
$21$	−1.04365	−0.227742
$22$	0.850138	0.181250
$23$	−3.70579	−0.772711	−0.386355	−	0.922350i	$-0.626266\pi$
$23$	−3.70579	−0.772711	−0.386355	+	0.922350i	$0.626266\pi$
$24$	−1.14592	−0.233910
$25$	9.54924	1.90985
$26$	−3.66780	−0.719314
$27$	2.39819	0.461533
$28$	−3.24102	−0.612494
$29$	9.77700	1.81554	0.907772	−	0.419464i	$-0.137782\pi$
$29$	9.77700	1.81554	0.907772	+	0.419464i	$0.137782\pi$
$30$	−1.33372	−0.243502
$31$	2.69350	0.483766	0.241883	−	0.970305i	$-0.422235\pi$
$31$	2.69350	0.483766	0.241883	+	0.970305i	$0.422235\pi$
$32$	−5.73033	−1.01299
$33$	0.411295	0.0715973
$34$	−3.28046	−0.562594
$35$	−9.67876	−1.63601
$36$	3.61573	0.602622
$37$	1.89288	0.311187	0.155594	−	0.987821i	$-0.450271\pi$
$37$	1.89288	0.311187	0.155594	+	0.987821i	$0.450271\pi$
$38$	3.68713	0.598131
$39$	−1.77447	−0.284143
$40$	−10.6273	−1.68032
$41$	−5.55444	−0.867458	−0.433729	−	0.901043i	$-0.642802\pi$
$41$	−5.55444	−0.867458	−0.433729	+	0.901043i	$0.642802\pi$
$42$	0.887243	0.136905
$43$	−3.90214	−0.595070	−0.297535	−	0.954711i	$-0.596165\pi$
$43$	−3.90214	−0.595070	−0.297535	+	0.954711i	$0.596165\pi$
$44$	1.27727	0.192555
$45$	10.7978	1.60964
$46$	3.15043	0.464506
$47$	−0.482047	−0.0703137	−0.0351569	−	0.999382i	$-0.511193\pi$
$47$	−0.482047	−0.0703137	−0.0351569	+	0.999382i	$0.511193\pi$
$48$	−0.0764764	−0.0110384
$49$	−0.561281	−0.0801830
$50$	−8.11817	−1.14808
$51$	−1.58708	−0.222236
$52$	−5.51058	−0.764180
$53$	−5.87525	−0.807027	−0.403514	−	0.914974i	$-0.632211\pi$
$53$	−5.87525	−0.807027	−0.403514	+	0.914974i	$0.632211\pi$
$54$	−2.03880	−0.277445
$55$	3.81435	0.514326
$56$	7.06969	0.944728
$57$	1.78383	0.236274
$58$	−8.31180	−1.09139
$59$	1.11357	0.144975	0.0724875	−	0.997369i	$-0.476906\pi$
$59$	1.11357	0.144975	0.0724875	+	0.997369i	$0.476906\pi$
$60$	−2.00380	−0.258690
$61$	12.3497	1.58122	0.790610	−	0.612320i	$-0.209764\pi$
$61$	12.3497	1.58122	0.790610	+	0.612320i	$0.209764\pi$
$62$	−2.28984	−0.290810
$63$	−7.18314	−0.904991
$64$	4.49969	0.562461
$65$	−16.4565	−2.04117
$66$	−0.349658	−0.0430399
$67$	2.60122	0.317789	0.158895	−	0.987296i	$-0.449207\pi$
$67$	2.60122	0.317789	0.158895	+	0.987296i	$0.449207\pi$
$68$	−4.92863	−0.597685
$69$	1.52417	0.183489
$70$	8.22828	0.983468
$71$	−9.93410	−1.17896	−0.589480	−	0.807783i	$-0.700667\pi$
$71$	−9.93410	−1.17896	−0.589480	+	0.807783i	$0.700667\pi$
$72$	−7.88707	−0.929500
$73$	−13.8969	−1.62651	−0.813254	−	0.581908i	$-0.802306\pi$
$73$	−13.8969	−1.62651	−0.813254	+	0.581908i	$0.802306\pi$
$74$	−1.60921	−0.187067
$75$	−3.92756	−0.453515
$76$	5.53963	0.635439
$77$	−2.53746	−0.289171
$78$	1.50855	0.170809
$79$	−5.91094	−0.665033	−0.332516	−	0.943097i	$-0.607898\pi$
$79$	−5.91094	−0.665033	−0.332516	+	0.943097i	$0.607898\pi$
$80$	−0.709241	−0.0792956
$81$	7.50614	0.834016
$82$	4.72204	0.521462
$83$	−16.0066	−1.75695	−0.878476	−	0.477787i	$-0.841439\pi$
$83$	−16.0066	−1.75695	−0.878476	+	0.477787i	$0.841439\pi$
$84$	1.33301	0.145444
$85$	−14.7186	−1.59645
$86$	3.31735	0.357719
$87$	−4.02123	−0.431122
$88$	−2.78613	−0.297002
$89$	−6.30248	−0.668061	−0.334031	−	0.942562i	$-0.608409\pi$
$89$	−6.30248	−0.668061	−0.334031	+	0.942562i	$0.608409\pi$
$90$	−9.17961	−0.967616
$91$	10.9475	1.14761
$92$	4.73328	0.493479
$93$	−1.10782	−0.114876
$94$	0.409806	0.0422683
$95$	16.5432	1.69730
$96$	2.35686	0.240546
$97$	−18.1164	−1.83944	−0.919719	−	0.392577i	$-0.871584\pi$
$97$	−18.1164	−1.83944	−0.919719	+	0.392577i	$0.871584\pi$
$98$	0.477166	0.0482010
$99$	2.83084	0.284510
$100$	−12.1969	−1.21969
$101$	−17.4483	−1.73617	−0.868083	−	0.496418i	$-0.834648\pi$
$101$	−17.4483	−1.73617	−0.868083	+	0.496418i	$0.834648\pi$
$102$	1.34924	0.133594
$103$	12.6252	1.24399	0.621997	−	0.783020i	$-0.286322\pi$
$103$	12.6252	1.24399	0.621997	+	0.783020i	$0.286322\pi$
$104$	12.0203	1.17869
$105$	3.98083	0.388489
$106$	4.99477	0.485135
$107$	−15.1870	−1.46818	−0.734091	−	0.679051i	$-0.762391\pi$
$107$	−15.1870	−1.46818	−0.734091	+	0.679051i	$0.762391\pi$
$108$	−3.06313	−0.294750
$109$	12.8476	1.23058	0.615288	−	0.788302i	$-0.289040\pi$
$109$	12.8476	1.23058	0.615288	+	0.788302i	$0.289040\pi$
$110$	−3.24272	−0.309181
$111$	−0.778532	−0.0738950
$112$	0.471817	0.0445825
$113$	−3.02625	−0.284686	−0.142343	−	0.989817i	$-0.545464\pi$
$113$	−3.02625	−0.284686	−0.142343	+	0.989817i	$0.545464\pi$
$114$	−1.51650	−0.142033
$115$	14.1352	1.31811
$116$	−12.4878	−1.15947
$117$	−12.2132	−1.12911
$118$	−0.946692	−0.0871500
$119$	9.79140	0.897576
$120$	4.37094	0.399010
$121$	1.00000	0.0909091
$122$	−10.4990	−0.950531
$123$	2.28451	0.205988
$124$	−3.44031	−0.308949
$125$	−17.3524	−1.55205
$126$	6.10666	0.544025
$127$	3.38532	0.300398	0.150199	−	0.988656i	$-0.452009\pi$
$127$	3.38532	0.300398	0.150199	+	0.988656i	$0.452009\pi$
$128$	7.63530	0.674872
$129$	1.60493	0.141306
$130$	13.9903	1.22703
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−0.525333	−0.0457244
$133$	−11.0052	−0.954274
$134$	−2.21139	−0.191035
$135$	−9.14755	−0.787295
$136$	10.7509	0.921885
$137$	21.2763	1.81776	0.908878	−	0.417063i	$-0.136940\pi$
$137$	21.2763	1.81776	0.908878	+	0.417063i	$0.136940\pi$
$138$	−1.29576	−0.110302
$139$	18.1439	1.53894	0.769471	−	0.638682i	$-0.220520\pi$
$139$	18.1439	1.53894	0.769471	+	0.638682i	$0.220520\pi$
$140$	12.3624	1.04481
$141$	0.198263	0.0166968
$142$	8.44535	0.708718
$143$	−4.31436	−0.360785
$144$	−0.526367	−0.0438639
$145$	−37.2929	−3.09701
$146$	11.8143	0.977756
$147$	0.230852	0.0190404
$148$	−2.41771	−0.198735
$149$	−10.7337	−0.879338	−0.439669	−	0.898160i	$-0.644904\pi$
$149$	−10.7337	−0.879338	−0.439669	+	0.898160i	$0.644904\pi$
$150$	3.33896	0.272625
$151$	−16.6445	−1.35451	−0.677254	−	0.735749i	$-0.736830\pi$
$151$	−16.6445	−1.35451	−0.677254	+	0.735749i	$0.736830\pi$
$152$	−12.0837	−0.980118
$153$	−10.9235	−0.883109
$154$	2.15719	0.173832
$155$	−10.2739	−0.825222
$156$	2.26648	0.181463
$157$	20.9344	1.67074	0.835372	−	0.549685i	$-0.185252\pi$
$157$	20.9344	1.67074	0.835372	+	0.549685i	$0.185252\pi$
$158$	5.02511	0.399777
$159$	2.41646	0.191638
$160$	21.8575	1.72798
$161$	−9.40331	−0.741084
$162$	−6.38125	−0.501359
$163$	−23.7526	−1.86044	−0.930222	−	0.366997i	$-0.880386\pi$
$163$	−23.7526	−1.86044	−0.930222	+	0.366997i	$0.880386\pi$
$164$	7.09450	0.553987
$165$	−1.56882	−0.122133
$166$	13.6078	1.05617
$167$	17.5239	1.35604	0.678021	−	0.735042i	$-0.262838\pi$
$167$	17.5239	1.35604	0.678021	+	0.735042i	$0.262838\pi$
$168$	−2.90773	−0.224336
$169$	5.61368	0.431821
$170$	12.5128	0.959688
$171$	12.2776	0.938892
$172$	4.98407	0.380031
$173$	−3.30081	−0.250956	−0.125478	−	0.992096i	$-0.540046\pi$
$173$	−3.30081	−0.250956	−0.125478	+	0.992096i	$0.540046\pi$
$174$	3.41860	0.259164
$175$	24.2309	1.83168
$176$	−0.185940	−0.0140158
$177$	−0.458008	−0.0344260
$178$	5.35797	0.401597
$179$	9.28408	0.693925	0.346962	−	0.937879i	$-0.387213\pi$
$179$	9.28408	0.693925	0.346962	+	0.937879i	$0.387213\pi$
$180$	−13.7917	−1.02797
$181$	7.73166	0.574690	0.287345	−	0.957827i	$-0.407227\pi$
$181$	7.73166	0.574690	0.287345	+	0.957827i	$0.407227\pi$
$182$	−9.30690	−0.689873
$183$	−5.07938	−0.375479
$184$	−10.3248	−0.761155
$185$	−7.22010	−0.530832
$186$	0.941801	0.0690562
$187$	−3.85874	−0.282179
$188$	0.615702	0.0449047
$189$	6.08533	0.442643
$190$	−14.0640	−1.02031
$191$	−4.67694	−0.338411	−0.169206	−	0.985581i	$-0.554120\pi$
$191$	−4.67694	−0.338411	−0.169206	+	0.985581i	$0.554120\pi$
$192$	−1.85070	−0.133563
$193$	−2.76944	−0.199349	−0.0996744	−	0.995020i	$-0.531780\pi$
$193$	−2.76944	−0.199349	−0.0996744	+	0.995020i	$0.531780\pi$
$194$	15.4014	1.10576
$195$	6.76846	0.484700
$196$	0.716905	0.0512075
$197$	−12.3706	−0.881366	−0.440683	−	0.897663i	$-0.645264\pi$
$197$	−12.3706	−0.881366	−0.440683	+	0.897663i	$0.645264\pi$
$198$	−2.40660	−0.171030
$199$	−2.96823	−0.210412	−0.105206	−	0.994450i	$-0.533550\pi$
$199$	−2.96823	−0.210412	−0.105206	+	0.994450i	$0.533550\pi$
$200$	26.6054	1.88129
$201$	−1.06987	−0.0754627
$202$	14.8334	1.04368
$203$	24.8088	1.74124
$204$	2.02712	0.141927
$205$	21.1866	1.47973
$206$	−10.7331	−0.747812
$207$	10.4905	0.729139
$208$	0.802213	0.0556235
$209$	4.33710	0.300003
$210$	−3.38425	−0.233536
$211$	8.14103	0.560452	0.280226	−	0.959934i	$-0.409591\pi$
$211$	8.14103	0.560452	0.280226	+	0.959934i	$0.409591\pi$
$212$	7.50425	0.515394
$213$	4.08585	0.279958
$214$	12.9110	0.882580
$215$	14.8841	1.01509
$216$	6.68168	0.454630
$217$	6.83465	0.463966
$218$	−10.9222	−0.739747
$219$	5.71573	0.386233
$220$	−4.87194	−0.328466
$221$	16.6480	1.11986
$222$	0.661859	0.0444211
$223$	−23.6143	−1.58133	−0.790664	−	0.612250i	$-0.790265\pi$
$223$	−23.6143	−1.58133	−0.790664	+	0.612250i	$0.790265\pi$
$224$	−14.5405	−0.971528
$225$	−27.0323	−1.80216
$226$	2.57273	0.171136
$227$	−13.9312	−0.924645	−0.462323	−	0.886712i	$-0.652984\pi$
$227$	−13.9312	−0.924645	−0.462323	+	0.886712i	$0.652984\pi$
$228$	−2.27842	−0.150892
$229$	−19.4705	−1.28665	−0.643325	−	0.765593i	$-0.722446\pi$
$229$	−19.4705	−1.28665	−0.643325	+	0.765593i	$0.722446\pi$
$230$	−12.0168	−0.792367
$231$	1.04365	0.0686669
$232$	27.2400	1.78839
$233$	−7.81959	−0.512278	−0.256139	−	0.966640i	$-0.582451\pi$
$233$	−7.81959	−0.512278	−0.256139	+	0.966640i	$0.582451\pi$
$234$	10.3829	0.678754
$235$	1.83869	0.119943
$236$	−1.42233	−0.0925859
$237$	2.43114	0.157920
$238$	−8.32404	−0.539567
$239$	−6.71195	−0.434160	−0.217080	−	0.976154i	$-0.569653\pi$
$239$	−6.71195	−0.434160	−0.217080	+	0.976154i	$0.569653\pi$
$240$	0.291708	0.0188296
$241$	−2.31836	−0.149339	−0.0746694	−	0.997208i	$-0.523790\pi$
$241$	−2.31836	−0.149339	−0.0746694	+	0.997208i	$0.523790\pi$
$242$	−0.850138	−0.0546489
$243$	−10.2818	−0.659579
$244$	−15.7739	−1.00982
$245$	2.14092	0.136778
$246$	−1.94215	−0.123827
$247$	−18.7118	−1.19060
$248$	7.50442	0.476531
$249$	6.58343	0.417208
$250$	14.7519	0.932993
$251$	−3.64429	−0.230026	−0.115013	−	0.993364i	$-0.536691\pi$
$251$	−3.64429	−0.230026	−0.115013	+	0.993364i	$0.536691\pi$
$252$	9.17478	0.577957
$253$	3.70579	0.232981
$254$	−2.87798	−0.180581
$255$	6.05367	0.379096
$256$	−15.4904	−0.968152
$257$	−14.3358	−0.894245	−0.447123	−	0.894473i	$-0.647551\pi$
$257$	−14.3358	−0.894245	−0.447123	+	0.894473i	$0.647551\pi$
$258$	−1.36441	−0.0849445
$259$	4.80311	0.298451
$260$	21.0193	1.30356
$261$	−27.6771	−1.71317
$262$	0.850138	0.0525217
$263$	10.3266	0.636768	0.318384	−	0.947962i	$-0.396860\pi$
$263$	10.3266	0.636768	0.318384	+	0.947962i	$0.396860\pi$
$264$	1.14592	0.0705265
$265$	22.4102	1.37665
$266$	9.35596	0.573650
$267$	2.59218	0.158639
$268$	−3.32245	−0.202951
$269$	−23.7805	−1.44992	−0.724962	−	0.688789i	$-0.758143\pi$
$269$	−23.7805	−1.44992	−0.724962	+	0.688789i	$0.758143\pi$
$270$	7.77667	0.473273
$271$	5.72779	0.347938	0.173969	−	0.984751i	$-0.444341\pi$
$271$	5.72779	0.347938	0.173969	+	0.984751i	$0.444341\pi$
$272$	0.717495	0.0435045
$273$	−4.50266	−0.272514
$274$	−18.0878	−1.09272
$275$	−9.54924	−0.575841
$276$	−1.94678	−0.117182
$277$	25.4022	1.52627	0.763136	−	0.646238i	$-0.223659\pi$
$277$	25.4022	1.52627	0.763136	+	0.646238i	$0.223659\pi$
$278$	−15.4248	−0.925116
$279$	−7.62485	−0.456488
$280$	−26.9663	−1.61154
$281$	−5.14451	−0.306896	−0.153448	−	0.988157i	$-0.549038\pi$
$281$	−5.14451	−0.306896	−0.153448	+	0.988157i	$0.549038\pi$
$282$	−0.168551	−0.0100371
$283$	−4.10742	−0.244161	−0.122080	−	0.992520i	$-0.538957\pi$
$283$	−4.10742	−0.244161	−0.122080	+	0.992520i	$0.538957\pi$
$284$	12.6885	0.752923
$285$	−6.80414	−0.403042
$286$	3.66780	0.216881
$287$	−14.0942	−0.831954
$288$	16.2216	0.955868
$289$	−2.11015	−0.124126
$290$	31.7041	1.86173
$291$	7.45117	0.436796
$292$	17.7500	1.03874
$293$	11.9860	0.700231	0.350115	−	0.936707i	$-0.386142\pi$
$293$	11.9860	0.700231	0.350115	+	0.936707i	$0.386142\pi$
$294$	−0.196256	−0.0114459
$295$	−4.24756	−0.247302
$296$	5.27380	0.306533
$297$	−2.39819	−0.139157
$298$	9.12511	0.528603
$299$	−15.9881	−0.924616
$300$	5.01654	0.289630
$301$	−9.90153	−0.570715
$302$	14.1501	0.814247
$303$	7.17639	0.412273
$304$	−0.806442	−0.0462526
$305$	−47.1061	−2.69729
$306$	9.28644	0.530870
$307$	29.4549	1.68108	0.840540	−	0.541750i	$-0.182238\pi$
$307$	29.4549	1.68108	0.840540	+	0.541750i	$0.182238\pi$
$308$	3.24102	0.184674
$309$	−5.19267	−0.295401
$310$	8.73426	0.496072
$311$	6.86545	0.389304	0.194652	−	0.980872i	$-0.437642\pi$
$311$	6.86545	0.389304	0.194652	+	0.980872i	$0.437642\pi$
$312$	−4.94391	−0.279894
$313$	−2.59220	−0.146520	−0.0732600	−	0.997313i	$-0.523340\pi$
$313$	−2.59220	−0.146520	−0.0732600	+	0.997313i	$0.523340\pi$
$314$	−17.7971	−1.00435
$315$	27.3990	1.54376
$316$	7.54984	0.424712
$317$	−10.7400	−0.603218	−0.301609	−	0.953432i	$-0.597524\pi$
$317$	−10.7400	−0.603218	−0.301609	+	0.953432i	$0.597524\pi$
$318$	−2.05432	−0.115201
$319$	−9.77700	−0.547407
$320$	−17.1634	−0.959462
$321$	6.24633	0.348636
$322$	7.99410	0.445494
$323$	−16.7357	−0.931200
$324$	−9.58734	−0.532630
$325$	41.1988	2.28530
$326$	20.1929	1.11838
$327$	−5.28416	−0.292214
$328$	−15.4754	−0.854485
$329$	−1.22318	−0.0674358
$330$	1.33372	0.0734186
$331$	−9.38621	−0.515913	−0.257956	−	0.966157i	$-0.583049\pi$
$331$	−9.38621	−0.515913	−0.257956	+	0.966157i	$0.583049\pi$
$332$	20.4447	1.12205
$333$	−5.35843	−0.293640
$334$	−14.8978	−0.815169
$335$	−9.92195	−0.542094
$336$	−0.194056	−0.0105866
$337$	−19.9135	−1.08476	−0.542380	−	0.840133i	$-0.682477\pi$
$337$	−19.9135	−1.08476	−0.542380	+	0.840133i	$0.682477\pi$
$338$	−4.77240	−0.259584
$339$	1.24468	0.0676019
$340$	18.7995	1.01955
$341$	−2.69350	−0.145861
$342$	−10.4377	−0.564404
$343$	−19.1865	−1.03597
$344$	−10.8718	−0.586171
$345$	−5.81373	−0.313001
$346$	2.80615	0.150859
$347$	8.26392	0.443631	0.221815	−	0.975089i	$-0.428802\pi$
$347$	8.26392	0.443631	0.221815	+	0.975089i	$0.428802\pi$
$348$	5.13619	0.275328
$349$	4.84322	0.259252	0.129626	−	0.991563i	$-0.458622\pi$
$349$	4.84322	0.259252	0.129626	+	0.991563i	$0.458622\pi$
$350$	−20.5996	−1.10109
$351$	10.3467	0.552264
$352$	5.73033	0.305428
$353$	21.7015	1.15505	0.577527	−	0.816372i	$-0.304018\pi$
$353$	21.7015	1.15505	0.577527	+	0.816372i	$0.304018\pi$
$354$	0.389370	0.0206948
$355$	37.8921	2.01110
$356$	8.04994	0.426646
$357$	−4.02716	−0.213140
$358$	−7.89275	−0.417145
$359$	−27.3154	−1.44165	−0.720827	−	0.693115i	$-0.756238\pi$
$359$	−27.3154	−1.44165	−0.720827	+	0.693115i	$0.756238\pi$
$360$	30.0840	1.58557
$361$	−0.189588	−0.00997832
$362$	−6.57297	−0.345468
$363$	−0.411295	−0.0215874
$364$	−13.9829	−0.732903
$365$	53.0076	2.77454
$366$	4.31817	0.225714
$367$	−28.1088	−1.46727	−0.733633	−	0.679546i	$-0.762177\pi$
$367$	−28.1088	−1.46727	−0.733633	+	0.679546i	$0.762177\pi$
$368$	−0.689056	−0.0359195
$369$	15.7237	0.818544
$370$	6.13808	0.319103
$371$	−14.9082	−0.773996
$372$	1.41498	0.0733635
$373$	−31.5182	−1.63195	−0.815975	−	0.578087i	$-0.803800\pi$
$373$	−31.5182	−1.63195	−0.815975	+	0.578087i	$0.803800\pi$
$374$	3.28046	0.169628
$375$	7.13695	0.368551
$376$	−1.34304	−0.0692622
$377$	42.1815	2.17246
$378$	−5.17337	−0.266089
$379$	20.9980	1.07860	0.539298	−	0.842115i	$-0.318690\pi$
$379$	20.9980	1.07860	0.539298	+	0.842115i	$0.318690\pi$
$380$	−21.1301	−1.08395
$381$	−1.39236	−0.0713330
$382$	3.97604	0.203432
$383$	9.22226	0.471236	0.235618	−	0.971846i	$-0.424289\pi$
$383$	9.22226	0.471236	0.235618	+	0.971846i	$0.424289\pi$
$384$	−3.14036	−0.160256
$385$	9.67876	0.493276
$386$	2.35441	0.119836
$387$	11.0463	0.561515
$388$	23.1394	1.17473
$389$	25.1765	1.27650	0.638248	−	0.769830i	$-0.279659\pi$
$389$	25.1765	1.27650	0.638248	+	0.769830i	$0.279659\pi$
$390$	−5.75412	−0.291371
$391$	−14.2997	−0.723165
$392$	−1.56380	−0.0789838
$393$	0.411295	0.0207471
$394$	10.5167	0.529823
$395$	22.5464	1.13443
$396$	−3.61573	−0.181697
$397$	−4.31964	−0.216796	−0.108398	−	0.994108i	$-0.534572\pi$
$397$	−4.31964	−0.216796	−0.108398	+	0.994108i	$0.534572\pi$
$398$	2.52341	0.126487
$399$	4.52640	0.226603
$400$	1.77559	0.0887795
$401$	27.2177	1.35919	0.679594	−	0.733589i	$-0.262156\pi$
$401$	27.2177	1.35919	0.679594	+	0.733589i	$0.262156\pi$
$402$	0.909535	0.0453635
$403$	11.6207	0.578869
$404$	22.2861	1.10877
$405$	−28.6310	−1.42269
$406$	−21.0909	−1.04672
$407$	−1.89288	−0.0938265
$408$	−4.42181	−0.218912
$409$	−18.5052	−0.915022	−0.457511	−	0.889204i	$-0.651259\pi$
$409$	−18.5052	−0.915022	−0.457511	+	0.889204i	$0.651259\pi$
$410$	−18.0115	−0.889524
$411$	−8.75083	−0.431647
$412$	−16.1257	−0.794456
$413$	2.82565	0.139041
$414$	−8.91836	−0.438313
$415$	61.0547	2.99706
$416$	−24.7227	−1.21213
$417$	−7.46248	−0.365439
$418$	−3.68713	−0.180343
$419$	−6.70939	−0.327775	−0.163887	−	0.986479i	$-0.552403\pi$
$419$	−6.70939	−0.327775	−0.163887	+	0.986479i	$0.552403\pi$
$420$	−5.08458	−0.248102
$421$	18.0653	0.880451	0.440226	−	0.897887i	$-0.354898\pi$
$421$	18.0653	0.880451	0.440226	+	0.897887i	$0.354898\pi$
$422$	−6.92100	−0.336909
$423$	1.36459	0.0663489
$424$	−16.3692	−0.794958
$425$	36.8480	1.78739
$426$	−3.47353	−0.168293
$427$	31.3370	1.51650
$428$	19.3978	0.937629
$429$	1.77447	0.0856724
$430$	−12.6535	−0.610208
$431$	−39.9632	−1.92496	−0.962479	−	0.271357i	$-0.912528\pi$
$431$	−39.9632	−1.92496	−0.962479	+	0.271357i	$0.912528\pi$
$432$	0.445921	0.0214544
$433$	−22.3580	−1.07446	−0.537229	−	0.843437i	$-0.680529\pi$
$433$	−22.3580	−1.07446	−0.537229	+	0.843437i	$0.680529\pi$
$434$	−5.81039	−0.278908
$435$	15.3384	0.735419
$436$	−16.4098	−0.785887
$437$	16.0724	0.768846
$438$	−4.85915	−0.232179
$439$	10.8917	0.519831	0.259916	−	0.965631i	$-0.416305\pi$
$439$	10.8917	0.519831	0.259916	+	0.965631i	$0.416305\pi$
$440$	10.6273	0.506635
$441$	1.58889	0.0756616
$442$	−14.1531	−0.673193
$443$	16.8106	0.798696	0.399348	−	0.916799i	$-0.369237\pi$
$443$	16.8106	0.798696	0.399348	+	0.916799i	$0.369237\pi$
$444$	0.994392	0.0471918
$445$	24.0398	1.13960
$446$	20.0754	0.950597
$447$	4.41471	0.208809
$448$	11.4178	0.539440
$449$	18.7783	0.886202	0.443101	−	0.896472i	$-0.353878\pi$
$449$	18.7783	0.886202	0.443101	+	0.896472i	$0.353878\pi$
$450$	22.9812	1.08334
$451$	5.55444	0.261548
$452$	3.86533	0.181810
$453$	6.84580	0.321644
$454$	11.8434	0.555839
$455$	−41.7576	−1.95763
$456$	4.96997	0.232740
$457$	14.4620	0.676503	0.338251	−	0.941056i	$-0.390165\pi$
$457$	14.4620	0.676503	0.338251	+	0.941056i	$0.390165\pi$
$458$	16.5526	0.773454
$459$	9.25400	0.431940
$460$	−18.0544	−0.841789
$461$	−2.86841	−0.133595	−0.0667977	−	0.997767i	$-0.521278\pi$
$461$	−2.86841	−0.133595	−0.0667977	+	0.997767i	$0.521278\pi$
$462$	−0.887243	−0.0412783
$463$	−40.1295	−1.86497	−0.932487	−	0.361204i	$-0.882366\pi$
$463$	−40.1295	−1.86497	−0.932487	+	0.361204i	$0.882366\pi$
$464$	1.81794	0.0843958
$465$	4.22562	0.195958
$466$	6.64773	0.307950
$467$	10.0853	0.466693	0.233346	−	0.972394i	$-0.425032\pi$
$467$	10.0853	0.466693	0.233346	+	0.972394i	$0.425032\pi$
$468$	15.5996	0.721090
$469$	6.60049	0.304783
$470$	−1.56314	−0.0721024
$471$	−8.61021	−0.396737
$472$	3.10256	0.142807
$473$	3.90214	0.179420
$474$	−2.06680	−0.0949315
$475$	−41.4160	−1.90030
$476$	−12.5062	−0.573222
$477$	16.6319	0.761521
$478$	5.70608	0.260990
$479$	9.31015	0.425391	0.212696	−	0.977118i	$-0.431776\pi$
$479$	9.31015	0.425391	0.212696	+	0.977118i	$0.431776\pi$
$480$	−8.98987	−0.410330
$481$	8.16655	0.372363
$482$	1.97093	0.0897733
$483$	3.86753	0.175979
$484$	−1.27727	−0.0580575
$485$	69.1021	3.13776
$486$	8.74097	0.396498
$487$	−6.68686	−0.303010	−0.151505	−	0.988456i	$-0.548412\pi$
$487$	−6.68686	−0.303010	−0.151505	+	0.988456i	$0.548412\pi$
$488$	34.4079	1.55757
$489$	9.76931	0.441784
$490$	−1.82008	−0.0822227
$491$	−14.9241	−0.673516	−0.336758	−	0.941591i	$-0.609330\pi$
$491$	−14.9241	−0.673516	−0.336758	+	0.941591i	$0.609330\pi$
$492$	−2.91793	−0.131551
$493$	37.7269	1.69913
$494$	15.9076	0.715716
$495$	−10.7978	−0.485325
$496$	0.500830	0.0224879
$497$	−25.2074	−1.13071
$498$	−5.59682	−0.250800
$499$	−16.2017	−0.725286	−0.362643	−	0.931928i	$-0.618126\pi$
$499$	−16.2017	−0.725286	−0.362643	+	0.931928i	$0.618126\pi$
$500$	22.1636	0.991187
$501$	−7.20751	−0.322008
$502$	3.09815	0.138277
$503$	−25.4103	−1.13299	−0.566495	−	0.824065i	$-0.691701\pi$
$503$	−25.4103	−1.13299	−0.566495	+	0.824065i	$0.691701\pi$
$504$	−20.0131	−0.891457
$505$	66.5537	2.96160
$506$	−3.15043	−0.140054
$507$	−2.30888	−0.102541
$508$	−4.32395	−0.191844
$509$	18.9393	0.839471	0.419735	−	0.907646i	$-0.362123\pi$
$509$	18.9393	0.839471	0.419735	+	0.907646i	$0.362123\pi$
$510$	−5.14646	−0.227889
$511$	−35.2629	−1.55994
$512$	−2.10161	−0.0928788
$513$	−10.4012	−0.459224
$514$	12.1874	0.537565
$515$	−48.1567	−2.12204
$516$	−2.04992	−0.0902428
$517$	0.482047	0.0212004
$518$	−4.08330	−0.179410
$519$	1.35761	0.0595924
$520$	−45.8498	−2.01065
$521$	−28.0837	−1.23037	−0.615185	−	0.788383i	$-0.710919\pi$
$521$	−28.0837	−1.23037	−0.615185	+	0.788383i	$0.710919\pi$
$522$	23.5293	1.02985
$523$	30.2466	1.32259	0.661295	−	0.750126i	$-0.270007\pi$
$523$	30.2466	1.32259	0.661295	+	0.750126i	$0.270007\pi$
$524$	1.27727	0.0557976
$525$	−9.96603	−0.434953
$526$	−8.77907	−0.382786
$527$	10.3935	0.452748
$528$	0.0764764	0.00332821
$529$	−9.26712	−0.402918
$530$	−19.0518	−0.827556
$531$	−3.15235	−0.136800
$532$	14.0566	0.609431
$533$	−23.9638	−1.03799
$534$	−2.20371	−0.0953638
$535$	57.9284	2.50446
$536$	7.24732	0.313037
$537$	−3.81850	−0.164780
$538$	20.2167	0.871604
$539$	0.561281	0.0241761
$540$	11.6839	0.502793
$541$	16.4048	0.705296	0.352648	−	0.935756i	$-0.385281\pi$
$541$	16.4048	0.705296	0.352648	+	0.935756i	$0.385281\pi$
$542$	−4.86941	−0.209159
$543$	−3.17999	−0.136467
$544$	−22.1118	−0.948037
$545$	−49.0052	−2.09915
$546$	3.82788	0.163818
$547$	27.4480	1.17359	0.586795	−	0.809736i	$-0.300389\pi$
$547$	27.4480	1.17359	0.586795	+	0.809736i	$0.300389\pi$
$548$	−27.1755	−1.16088
$549$	−34.9600	−1.49206
$550$	8.11817	0.346160
$551$	−42.4038	−1.80646
$552$	4.24654	0.180745
$553$	−14.9988	−0.637814
$554$	−21.5954	−0.917500
$555$	2.96959	0.126052
$556$	−23.1745	−0.982819
$557$	−11.5581	−0.489734	−0.244867	−	0.969557i	$-0.578744\pi$
$557$	−11.5581	−0.489734	−0.244867	+	0.969557i	$0.578744\pi$
$558$	6.48217	0.274412
$559$	−16.8352	−0.712054
$560$	−1.79967	−0.0760501
$561$	1.58708	0.0670066
$562$	4.37354	0.184487
$563$	−33.3998	−1.40763	−0.703816	−	0.710382i	$-0.748522\pi$
$563$	−33.3998	−1.40763	−0.703816	+	0.710382i	$0.748522\pi$
$564$	−0.253235	−0.0106631
$565$	11.5432	0.485625
$566$	3.49187	0.146774
$567$	19.0466	0.799880
$568$	−27.6777	−1.16133
$569$	6.57946	0.275826	0.137913	−	0.990444i	$-0.455961\pi$
$569$	6.57946	0.275826	0.137913	+	0.990444i	$0.455961\pi$
$570$	5.78445	0.242284
$571$	−2.73979	−0.114657	−0.0573283	−	0.998355i	$-0.518258\pi$
$571$	−2.73979	−0.114657	−0.0573283	+	0.998355i	$0.518258\pi$
$572$	5.51058	0.230409
$573$	1.92360	0.0803596
$574$	11.9820	0.500119
$575$	−35.3875	−1.47576
$576$	−12.7379	−0.530745
$577$	−14.5820	−0.607058	−0.303529	−	0.952822i	$-0.598165\pi$
$577$	−14.5820	−0.607058	−0.303529	+	0.952822i	$0.598165\pi$
$578$	1.79392	0.0746171
$579$	1.13906	0.0473376
$580$	47.6329	1.97785
$581$	−40.6161	−1.68504
$582$	−6.33452	−0.262574
$583$	5.87525	0.243328
$584$	−38.7185	−1.60218
$585$	46.5855	1.92607
$586$	−10.1898	−0.420935
$587$	−17.2790	−0.713181	−0.356590	−	0.934261i	$-0.616061\pi$
$587$	−17.2790	−0.713181	−0.356590	+	0.934261i	$0.616061\pi$
$588$	−0.294860	−0.0121598
$589$	−11.6820	−0.481347
$590$	3.61101	0.148663
$591$	5.08795	0.209290
$592$	0.351963	0.0144656
$593$	−24.1999	−0.993772	−0.496886	−	0.867816i	$-0.665523\pi$
$593$	−24.1999	−0.993772	−0.496886	+	0.867816i	$0.665523\pi$
$594$	2.03880	0.0836528
$595$	−37.3478	−1.53111
$596$	13.7098	0.561574
$597$	1.22082	0.0499648
$598$	13.5921	0.555822
$599$	7.83896	0.320291	0.160146	−	0.987093i	$-0.448804\pi$
$599$	7.83896	0.320291	0.160146	+	0.987093i	$0.448804\pi$
$600$	−10.9427	−0.446733
$601$	−45.8480	−1.87018	−0.935090	−	0.354410i	$-0.884682\pi$
$601$	−45.8480	−1.87018	−0.935090	+	0.354410i	$0.884682\pi$
$602$	8.41766	0.343078
$603$	−7.36362	−0.299870
$604$	21.2594	0.865034
$605$	−3.81435	−0.155075
$606$	−6.10092	−0.247833
$607$	−31.7549	−1.28889	−0.644447	−	0.764649i	$-0.722912\pi$
$607$	−31.7549	−1.28889	−0.644447	+	0.764649i	$0.722912\pi$
$608$	24.8530	1.00792
$609$	−10.2037	−0.413476
$610$	40.0467	1.62144
$611$	−2.07972	−0.0841365
$612$	13.9522	0.563982
$613$	11.1194	0.449110	0.224555	−	0.974461i	$-0.427907\pi$
$613$	11.1194	0.449110	0.224555	+	0.974461i	$0.427907\pi$
$614$	−25.0407	−1.01056
$615$	−8.71393	−0.351380
$616$	−7.06969	−0.284846
$617$	−16.4041	−0.660405	−0.330202	−	0.943910i	$-0.607117\pi$
$617$	−16.4041	−0.660405	−0.330202	+	0.943910i	$0.607117\pi$
$618$	4.41448	0.177577
$619$	−36.3186	−1.45977	−0.729884	−	0.683571i	$-0.760426\pi$
$619$	−36.3186	−1.45977	−0.729884	+	0.683571i	$0.760426\pi$
$620$	13.1225	0.527014
$621$	−8.88721	−0.356631
$622$	−5.83658	−0.234025
$623$	−15.9923	−0.640718
$624$	−0.329947	−0.0132084
$625$	18.4418	0.737673
$626$	2.20373	0.0880787
$627$	−1.78383	−0.0712392
$628$	−26.7388	−1.06699
$629$	7.30412	0.291234
$630$	−23.2929	−0.928012
$631$	5.04183	0.200712	0.100356	−	0.994952i	$-0.468002\pi$
$631$	5.04183	0.200712	0.100356	+	0.994952i	$0.468002\pi$
$632$	−16.4686	−0.655087
$633$	−3.34837	−0.133086
$634$	9.13047	0.362617
$635$	−12.9128	−0.512428
$636$	−3.08646	−0.122386
$637$	−2.42157	−0.0959459
$638$	8.31180	0.329067
$639$	28.1218	1.11248
$640$	−29.1237	−1.15122
$641$	38.4806	1.51989	0.759946	−	0.649987i	$-0.225226\pi$
$641$	38.4806	1.51989	0.759946	+	0.649987i	$0.225226\pi$
$642$	−5.31024	−0.209579
$643$	48.9126	1.92892	0.964462	−	0.264223i	$-0.0851154\pi$
$643$	48.9126	1.92892	0.964462	+	0.264223i	$0.0851154\pi$
$644$	12.0105	0.473281
$645$	−6.12176	−0.241044
$646$	14.2277	0.559780
$647$	−27.8027	−1.09304	−0.546519	−	0.837447i	$-0.684047\pi$
$647$	−27.8027	−1.09304	−0.546519	+	0.837447i	$0.684047\pi$
$648$	20.9131	0.821543
$649$	−1.11357	−0.0437116
$650$	−35.0247	−1.37378
$651$	−2.81106	−0.110174
$652$	30.3383	1.18814
$653$	−10.0989	−0.395199	−0.197600	−	0.980283i	$-0.563315\pi$
$653$	−10.0989	−0.395199	−0.197600	+	0.980283i	$0.563315\pi$
$654$	4.49226	0.175661
$655$	3.81435	0.149039
$656$	−1.03280	−0.0403239
$657$	39.3398	1.53479
$658$	1.03987	0.0405383
$659$	−46.8946	−1.82676	−0.913378	−	0.407113i	$-0.866536\pi$
$659$	−46.8946	−1.82676	−0.913378	+	0.407113i	$0.866536\pi$
$660$	2.00380	0.0779979
$661$	17.5073	0.680954	0.340477	−	0.940253i	$-0.389412\pi$
$661$	17.5073	0.680954	0.340477	+	0.940253i	$0.389412\pi$
$662$	7.97957	0.310135
$663$	−6.84723	−0.265924
$664$	−44.5964	−1.73068
$665$	41.9777	1.62783
$666$	4.55540	0.176518
$667$	−36.2315	−1.40289
$668$	−22.3827	−0.866014
$669$	9.71244	0.375504
$670$	8.43502	0.325873
$671$	−12.3497	−0.476756
$672$	5.98044	0.230700
$673$	12.1782	0.469434	0.234717	−	0.972064i	$-0.424584\pi$
$673$	12.1782	0.469434	0.234717	+	0.972064i	$0.424584\pi$
$674$	16.9293	0.652090
$675$	22.9009	0.881458
$676$	−7.17016	−0.275775
$677$	3.97535	0.152785	0.0763926	−	0.997078i	$-0.475660\pi$
$677$	3.97535	0.152785	0.0763926	+	0.997078i	$0.475660\pi$
$678$	−1.05815	−0.0406381
$679$	−45.9696	−1.76415
$680$	−41.0078	−1.57258
$681$	5.72983	0.219568
$682$	2.28984	0.0876826
$683$	10.5718	0.404518	0.202259	−	0.979332i	$-0.435172\pi$
$683$	10.5718	0.404518	0.202259	+	0.979332i	$0.435172\pi$
$684$	−15.6818	−0.599608
$685$	−81.1551	−3.10078
$686$	16.3111	0.622762
$687$	8.00814	0.305530
$688$	−0.725565	−0.0276619
$689$	−25.3479	−0.965678
$690$	4.94247	0.188157
$691$	−13.2628	−0.504541	−0.252270	−	0.967657i	$-0.581177\pi$
$691$	−13.2628	−0.504541	−0.252270	+	0.967657i	$0.581177\pi$
$692$	4.21602	0.160269
$693$	7.18314	0.272865
$694$	−7.02547	−0.266683
$695$	−69.2069	−2.62517
$696$	−11.2037	−0.424674
$697$	−21.4331	−0.811838
$698$	−4.11740	−0.155846
$699$	3.21616	0.121646
$700$	−30.9492	−1.16977
$701$	−3.12061	−0.117864	−0.0589320	−	0.998262i	$-0.518770\pi$
$701$	−3.12061	−0.117864	−0.0589320	+	0.998262i	$0.518770\pi$
$702$	−8.79609	−0.331987
$703$	−8.20960	−0.309631
$704$	−4.49969	−0.169588
$705$	−0.756246	−0.0284819
$706$	−18.4493	−0.694347
$707$	−44.2743	−1.66511
$708$	0.584998	0.0219856
$709$	−43.7100	−1.64156	−0.820781	−	0.571243i	$-0.806461\pi$
$709$	−43.7100	−1.64156	−0.820781	+	0.571243i	$0.806461\pi$
$710$	−32.2135	−1.20895
$711$	16.7329	0.627533
$712$	−17.5595	−0.658070
$713$	−9.98153	−0.373811
$714$	3.42364	0.128126
$715$	16.4565	0.615437
$716$	−11.8582	−0.443163
$717$	2.76059	0.103096
$718$	23.2219	0.866633
$719$	11.7147	0.436884	0.218442	−	0.975850i	$-0.429903\pi$
$719$	11.7147	0.436884	0.218442	+	0.975850i	$0.429903\pi$
$720$	2.00775	0.0748243
$721$	32.0359	1.19308
$722$	0.161176	0.00599835
$723$	0.953531	0.0354622
$724$	−9.87538	−0.367016
$725$	93.3630	3.46741
$726$	0.349658	0.0129770
$727$	32.3549	1.19998	0.599988	−	0.800009i	$-0.295172\pi$
$727$	32.3549	1.19998	0.599988	+	0.800009i	$0.295172\pi$
$728$	30.5012	1.13045
$729$	−18.2896	−0.677391
$730$	−45.0637	−1.66788
$731$	−15.0573	−0.556915
$732$	6.48772	0.239793
$733$	8.26086	0.305122	0.152561	−	0.988294i	$-0.451248\pi$
$733$	8.26086	0.305122	0.152561	+	0.988294i	$0.451248\pi$
$734$	23.8963	0.882029
$735$	−0.880550	−0.0324796
$736$	21.2354	0.782747
$737$	−2.60122	−0.0958171
$738$	−13.3673	−0.492058
$739$	−47.0866	−1.73211	−0.866055	−	0.499949i	$-0.833352\pi$
$739$	−47.0866	−1.73211	−0.866055	+	0.499949i	$0.833352\pi$
$740$	9.22198	0.339007
$741$	7.69607	0.282722
$742$	12.6740	0.465279
$743$	−14.7406	−0.540780	−0.270390	−	0.962751i	$-0.587153\pi$
$743$	−14.7406	−0.540780	−0.270390	+	0.962751i	$0.587153\pi$
$744$	−3.08653	−0.113158
$745$	40.9420	1.50000
$746$	26.7948	0.981028
$747$	45.3120	1.65788
$748$	4.92863	0.180209
$749$	−38.5364	−1.40809
$750$	−6.06739	−0.221550
$751$	7.70316	0.281092	0.140546	−	0.990074i	$-0.455114\pi$
$751$	7.70316	0.281092	0.140546	+	0.990074i	$0.455114\pi$
$752$	−0.0896320	−0.00326854
$753$	1.49888	0.0546222
$754$	−35.8601	−1.30595
$755$	63.4878	2.31056
$756$	−7.77259	−0.282686
$757$	44.1057	1.60305	0.801524	−	0.597963i	$-0.204023\pi$
$757$	44.1057	1.60305	0.801524	+	0.597963i	$0.204023\pi$
$758$	−17.8512	−0.648385
$759$	−1.52417	−0.0553240
$760$	46.0914	1.67191
$761$	16.3087	0.591189	0.295595	−	0.955313i	$-0.404482\pi$
$761$	16.3087	0.591189	0.295595	+	0.955313i	$0.404482\pi$
$762$	1.18370	0.0428810
$763$	32.6003	1.18021
$764$	5.97369	0.216121
$765$	41.6658	1.50643
$766$	−7.84019	−0.283278
$767$	4.80436	0.173475
$768$	6.37114	0.229899
$769$	11.7738	0.424573	0.212286	−	0.977208i	$-0.431909\pi$
$769$	11.7738	0.424573	0.212286	+	0.977208i	$0.431909\pi$
$770$	−8.22828	−0.296527
$771$	5.89626	0.212349
$772$	3.53731	0.127311
$773$	−14.5578	−0.523607	−0.261803	−	0.965121i	$-0.584317\pi$
$773$	−14.5578	−0.523607	−0.261803	+	0.965121i	$0.584317\pi$
$774$	−9.39088	−0.337548
$775$	25.7209	0.923920
$776$	−50.4745	−1.81193
$777$	−1.97550	−0.0708705
$778$	−21.4034	−0.767351
$779$	24.0901	0.863119
$780$	−8.64512	−0.309545
$781$	9.93410	0.355470
$782$	12.1567	0.434722
$783$	23.4472	0.837933
$784$	−0.104365	−0.00372731
$785$	−79.8510	−2.85000
$786$	−0.349658	−0.0124719
$787$	−5.42261	−0.193295	−0.0966476	−	0.995319i	$-0.530812\pi$
$787$	−5.42261	−0.193295	−0.0966476	+	0.995319i	$0.530812\pi$
$788$	15.8005	0.562870
$789$	−4.24730	−0.151208
$790$	−19.1675	−0.681950
$791$	−7.67900	−0.273034
$792$	7.88707	0.280255
$793$	53.2811	1.89207
$794$	3.67229	0.130325
$795$	−9.21722	−0.326901
$796$	3.79122	0.134376
$797$	29.8668	1.05793	0.528967	−	0.848642i	$-0.322579\pi$
$797$	29.8668	1.05793	0.528967	+	0.848642i	$0.322579\pi$
$798$	−3.84806	−0.136220
$799$	−1.86009	−0.0658053
$800$	−54.7203	−1.93465
$801$	17.8413	0.630391
$802$	−23.1388	−0.817060
$803$	13.8969	0.490411
$804$	1.36651	0.0481930
$805$	35.8675	1.26416
$806$	−9.87920	−0.347980
$807$	9.78081	0.344301
$808$	−48.6131	−1.71020
$809$	−39.5353	−1.38999	−0.694993	−	0.719016i	$-0.744593\pi$
$809$	−39.5353	−1.38999	−0.694993	+	0.719016i	$0.744593\pi$
$810$	24.3403	0.855232
$811$	−30.3671	−1.06633	−0.533166	−	0.846011i	$-0.678998\pi$
$811$	−30.3671	−1.06633	−0.533166	+	0.846011i	$0.678998\pi$
$812$	−31.6874	−1.11201
$813$	−2.35581	−0.0826219
$814$	1.60921	0.0564027
$815$	90.6005	3.17360
$816$	−0.295102	−0.0103306
$817$	16.9239	0.592094
$818$	15.7319	0.550054
$819$	−30.9906	−1.08290
$820$	−27.0609	−0.945007
$821$	6.96399	0.243045	0.121522	−	0.992589i	$-0.461222\pi$
$821$	6.96399	0.243045	0.121522	+	0.992589i	$0.461222\pi$
$822$	7.43941	0.259479
$823$	9.25259	0.322525	0.161263	−	0.986912i	$-0.448443\pi$
$823$	9.25259	0.322525	0.161263	+	0.986912i	$0.448443\pi$
$824$	35.1753	1.22539
$825$	3.92756	0.136740
$826$	−2.40220	−0.0835831
$827$	−24.0527	−0.836394	−0.418197	−	0.908356i	$-0.637338\pi$
$827$	−24.0527	−0.836394	−0.418197	+	0.908356i	$0.637338\pi$
$828$	−13.3991	−0.465652
$829$	24.3272	0.844920	0.422460	−	0.906382i	$-0.361167\pi$
$829$	24.3272	0.844920	0.422460	+	0.906382i	$0.361167\pi$
$830$	−51.9049	−1.80164
$831$	−10.4478	−0.362430
$832$	19.4133	0.673034
$833$	−2.16584	−0.0750417
$834$	6.34413	0.219679
$835$	−66.8424	−2.31318
$836$	−5.53963	−0.191592
$837$	6.45953	0.223274
$838$	5.70390	0.197038
$839$	−18.9090	−0.652810	−0.326405	−	0.945230i	$-0.605837\pi$
$839$	−18.9090	−0.652810	−0.326405	+	0.945230i	$0.605837\pi$
$840$	11.0911	0.382679
$841$	66.5898	2.29620
$842$	−15.3580	−0.529273
$843$	2.11591	0.0728759
$844$	−10.3983	−0.357923
$845$	−21.4125	−0.736613
$846$	−1.16009	−0.0398848
$847$	2.53746	0.0871883
$848$	−1.09245	−0.0375147
$849$	1.68936	0.0579788
$850$	−31.3259	−1.07447
$851$	−7.01461	−0.240458
$852$	−5.21871	−0.178790
$853$	37.1844	1.27317	0.636584	−	0.771207i	$-0.280347\pi$
$853$	37.1844	1.27317	0.636584	+	0.771207i	$0.280347\pi$
$854$	−26.6407	−0.911627
$855$	−46.8311	−1.60159
$856$	−42.3129	−1.44622
$857$	−9.79842	−0.334708	−0.167354	−	0.985897i	$-0.553522\pi$
$857$	−9.79842	−0.334708	−0.167354	+	0.985897i	$0.553522\pi$
$858$	−1.50855	−0.0515010
$859$	3.35685	0.114534	0.0572671	−	0.998359i	$-0.481761\pi$
$859$	3.35685	0.114534	0.0572671	+	0.998359i	$0.481761\pi$
$860$	−19.0110	−0.648268
$861$	5.79687	0.197557
$862$	33.9742	1.15717
$863$	28.3422	0.964780	0.482390	−	0.875956i	$-0.339769\pi$
$863$	28.3422	0.964780	0.482390	+	0.875956i	$0.339769\pi$
$864$	−13.7424	−0.467528
$865$	12.5904	0.428088
$866$	19.0074	0.645897
$867$	0.867893	0.0294752
$868$	−8.72966	−0.296304
$869$	5.91094	0.200515
$870$	−13.0397	−0.442088
$871$	11.2226	0.380263
$872$	35.7950	1.21217
$873$	51.2845	1.73572
$874$	−13.6637	−0.462183
$875$	−44.0311	−1.48852
$876$	−7.30050	−0.246661
$877$	−14.4074	−0.486504	−0.243252	−	0.969963i	$-0.578214\pi$
$877$	−14.4074	−0.486504	−0.243252	+	0.969963i	$0.578214\pi$
$878$	−9.25942	−0.312490
$879$	−4.92979	−0.166278
$880$	0.709241	0.0239085
$881$	50.3228	1.69542	0.847710	−	0.530460i	$-0.177981\pi$
$881$	50.3228	1.69542	0.847710	+	0.530460i	$0.177981\pi$
$882$	−1.35078	−0.0454831
$883$	−32.4235	−1.09114	−0.545569	−	0.838066i	$-0.683687\pi$
$883$	−32.4235	−1.09114	−0.545569	+	0.838066i	$0.683687\pi$
$884$	−21.2639	−0.715182
$885$	1.74700	0.0587248
$886$	−14.2913	−0.480127
$887$	17.1574	0.576088	0.288044	−	0.957617i	$-0.406995\pi$
$887$	17.1574	0.576088	0.288044	+	0.957617i	$0.406995\pi$
$888$	−2.16909	−0.0727899
$889$	8.59011	0.288103
$890$	−20.4372	−0.685055
$891$	−7.50614	−0.251465
$892$	30.1617	1.00989
$893$	2.09068	0.0699620
$894$	−3.75311	−0.125523
$895$	−35.4127	−1.18372
$896$	19.3743	0.647250
$897$	6.57583	0.219561
$898$	−15.9641	−0.532730
$899$	26.3343	0.878299
$900$	34.5275	1.15092
$901$	−22.6710	−0.755281
$902$	−4.72204	−0.157227
$903$	4.07245	0.135523
$904$	−8.43152	−0.280428
$905$	−29.4912	−0.980322
$906$	−5.81987	−0.193352
$907$	16.8282	0.558772	0.279386	−	0.960179i	$-0.409869\pi$
$907$	16.8282	0.558772	0.279386	+	0.960179i	$0.409869\pi$
$908$	17.7938	0.590509
$909$	49.3932	1.63827
$910$	35.4997	1.17681
$911$	−54.8865	−1.81847	−0.909235	−	0.416282i	$-0.863333\pi$
$911$	−54.8865	−1.81847	−0.909235	+	0.416282i	$0.863333\pi$
$912$	0.331686	0.0109832
$913$	16.0066	0.529741
$914$	−12.2947	−0.406672
$915$	19.3745	0.640502
$916$	24.8691	0.821697
$917$	−2.53746	−0.0837944
$918$	−7.86718	−0.259656
$919$	41.5120	1.36936	0.684678	−	0.728846i	$-0.259943\pi$
$919$	41.5120	1.36936	0.684678	+	0.728846i	$0.259943\pi$
$920$	39.3824	1.29840
$921$	−12.1147	−0.399191
$922$	2.43855	0.0803093
$923$	−42.8592	−1.41073
$924$	−1.33301	−0.0438529
$925$	18.0756	0.594321
$926$	34.1156	1.12111
$927$	−35.7398	−1.17385
$928$	−56.0255	−1.83913
$929$	44.0967	1.44677	0.723383	−	0.690447i	$-0.242586\pi$
$929$	44.0967	1.44677	0.723383	+	0.690447i	$0.242586\pi$
$930$	−3.59236	−0.117798
$931$	2.43433	0.0797819
$932$	9.98769	0.327158
$933$	−2.82373	−0.0924447
$934$	−8.57390	−0.280547
$935$	14.7186	0.481348
$936$	−34.0276	−1.11223
$937$	−29.6400	−0.968296	−0.484148	−	0.874986i	$-0.660870\pi$
$937$	−29.6400	−0.968296	−0.484148	+	0.874986i	$0.660870\pi$
$938$	−5.61133	−0.183216
$939$	1.06616	0.0347928
$940$	−2.34850	−0.0765996
$941$	−7.41322	−0.241664	−0.120832	−	0.992673i	$-0.538556\pi$
$941$	−7.41322	−0.241664	−0.120832	+	0.992673i	$0.538556\pi$
$942$	7.31986	0.238494
$943$	20.5836	0.670294
$944$	0.207059	0.00673918
$945$	−23.2116	−0.755072
$946$	−3.31735	−0.107856
$947$	−24.2936	−0.789437	−0.394719	−	0.918802i	$-0.629158\pi$
$947$	−24.2936	−0.789437	−0.394719	+	0.918802i	$0.629158\pi$
$948$	−3.10521	−0.100853
$949$	−59.9562	−1.94626
$950$	35.2093	1.14234
$951$	4.41731	0.143241
$952$	27.2801	0.884153
$953$	7.10858	0.230270	0.115135	−	0.993350i	$-0.463270\pi$
$953$	7.10858	0.230270	0.115135	+	0.993350i	$0.463270\pi$
$954$	−14.1394	−0.457779
$955$	17.8395	0.577272
$956$	8.57294	0.277269
$957$	4.02123	0.129988
$958$	−7.91491	−0.255719
$959$	53.9878	1.74336
$960$	7.05921	0.227835
$961$	−23.7451	−0.765970
$962$	−6.94270	−0.223841
$963$	42.9919	1.38539
$964$	2.96117	0.0953727
$965$	10.5636	0.340055
$966$	−3.28794	−0.105788
$967$	16.8226	0.540979	0.270489	−	0.962723i	$-0.412814\pi$
$967$	16.8226	0.540979	0.270489	+	0.962723i	$0.412814\pi$
$968$	2.78613	0.0895495
$969$	6.88332	0.221124
$970$	−58.7463	−1.88623
$971$	9.55554	0.306652	0.153326	−	0.988176i	$-0.451002\pi$
$971$	9.55554	0.306652	0.153326	+	0.988176i	$0.451002\pi$
$972$	13.1326	0.421229
$973$	46.0394	1.47595
$974$	5.68475	0.182151
$975$	−16.9449	−0.542671
$976$	2.29631	0.0735032
$977$	25.4632	0.814640	0.407320	−	0.913285i	$-0.366463\pi$
$977$	25.4632	0.814640	0.407320	+	0.913285i	$0.366463\pi$
$978$	−8.30526	−0.265573
$979$	6.30248	0.201428
$980$	−2.73452	−0.0873512
$981$	−36.3694	−1.16119
$982$	12.6875	0.404876
$983$	23.6851	0.755439	0.377719	−	0.925920i	$-0.376708\pi$
$983$	23.6851	0.755439	0.377719	+	0.925920i	$0.376708\pi$
$984$	6.36495	0.202907
$985$	47.1856	1.50346
$986$	−32.0730	−1.02141
$987$	0.503086	0.0160134
$988$	23.8999	0.760358
$989$	14.4605	0.459817
$990$	9.17961	0.291747
$991$	−54.4685	−1.73025	−0.865125	−	0.501556i	$-0.832761\pi$
$991$	−54.4685	−1.73025	−0.865125	+	0.501556i	$0.832761\pi$
$992$	−15.4346	−0.490050
$993$	3.86050	0.122509
$994$	21.4298	0.679711
$995$	11.3219	0.358927
$996$	−8.40879	−0.266443
$997$	−7.24668	−0.229505	−0.114752	−	0.993394i	$-0.536607\pi$
$997$	−7.24668	−0.229505	−0.114752	+	0.993394i	$0.536607\pi$
$998$	13.7736	0.435997
$999$	4.53949	0.143623

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.d.1.10	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.d.1.10	✓	23	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)

\(f(q)\)	\(=\)	\(q-0.850138 q^{2} -0.411295 q^{3} -1.27727 q^{4} -3.81435 q^{5} +0.349658 q^{6} +2.53746 q^{7} +2.78613 q^{8} -2.83084 q^{9} +O(q^{10})\)	\(q-0.850138 q^{2} -0.411295 q^{3} -1.27727 q^{4} -3.81435 q^{5} +0.349658 q^{6} +2.53746 q^{7} +2.78613 q^{8} -2.83084 q^{9} +3.24272 q^{10} -1.00000 q^{11} +0.525333 q^{12} +4.31436 q^{13} -2.15719 q^{14} +1.56882 q^{15} +0.185940 q^{16} +3.85874 q^{17} +2.40660 q^{18} -4.33710 q^{19} +4.87194 q^{20} -1.04365 q^{21} +0.850138 q^{22} -3.70579 q^{23} -1.14592 q^{24} +9.54924 q^{25} -3.66780 q^{26} +2.39819 q^{27} -3.24102 q^{28} +9.77700 q^{29} -1.33372 q^{30} +2.69350 q^{31} -5.73033 q^{32} +0.411295 q^{33} -3.28046 q^{34} -9.67876 q^{35} +3.61573 q^{36} +1.89288 q^{37} +3.68713 q^{38} -1.77447 q^{39} -10.6273 q^{40} -5.55444 q^{41} +0.887243 q^{42} -3.90214 q^{43} +1.27727 q^{44} +10.7978 q^{45} +3.15043 q^{46} -0.482047 q^{47} -0.0764764 q^{48} -0.561281 q^{49} -8.11817 q^{50} -1.58708 q^{51} -5.51058 q^{52} -5.87525 q^{53} -2.03880 q^{54} +3.81435 q^{55} +7.06969 q^{56} +1.78383 q^{57} -8.31180 q^{58} +1.11357 q^{59} -2.00380 q^{60} +12.3497 q^{61} -2.28984 q^{62} -7.18314 q^{63} +4.49969 q^{64} -16.4565 q^{65} -0.349658 q^{66} +2.60122 q^{67} -4.92863 q^{68} +1.52417 q^{69} +8.22828 q^{70} -9.93410 q^{71} -7.88707 q^{72} -13.8969 q^{73} -1.60921 q^{74} -3.92756 q^{75} +5.53963 q^{76} -2.53746 q^{77} +1.50855 q^{78} -5.91094 q^{79} -0.709241 q^{80} +7.50614 q^{81} +4.72204 q^{82} -16.0066 q^{83} +1.33301 q^{84} -14.7186 q^{85} +3.31735 q^{86} -4.02123 q^{87} -2.78613 q^{88} -6.30248 q^{89} -9.17961 q^{90} +10.9475 q^{91} +4.73328 q^{92} -1.10782 q^{93} +0.409806 q^{94} +16.5432 q^{95} +2.35686 q^{96} -18.1164 q^{97} +0.477166 q^{98} +2.83084 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9 - 2 * q^10 - 23 * q^11 - 12 * q^12 + 6 * q^13 - 13 * q^14 - 27 * q^15 - q^16 - 11 * q^17 - 16 * q^19 - 24 * q^20 - 7 * q^21 + 7 * q^22 - 30 * q^23 - 20 * q^24 + 10 * q^25 - 22 * q^26 - 15 * q^27 + 11 * q^28 - 15 * q^29 + 17 * q^30 - 31 * q^31 - 22 * q^32 + 3 * q^33 - 18 * q^34 - 34 * q^35 - 18 * q^36 - 26 * q^37 - 32 * q^39 + 16 * q^40 - 21 * q^41 - 37 * q^42 - 2 * q^43 - 19 * q^44 - 18 * q^45 - 6 * q^46 - 25 * q^47 + 14 * q^48 + 7 * q^49 - 27 * q^50 - 7 * q^51 + 23 * q^52 - 34 * q^53 + 26 * q^54 + 9 * q^55 - 42 * q^56 + 6 * q^57 - 5 * q^58 - 31 * q^59 - 7 * q^60 + 19 * q^61 + 24 * q^62 - 34 * q^63 - 17 * q^64 - 13 * q^65 + 5 * q^66 - 39 * q^67 - 59 * q^68 - 12 * q^69 + 17 * q^70 - 103 * q^71 + 19 * q^72 + q^73 - 9 * q^74 - 19 * q^75 + 10 * q^76 + 8 * q^77 - 43 * q^78 - 14 * q^79 - q^80 - 29 * q^81 + 20 * q^82 - 14 * q^83 + 57 * q^84 + 20 * q^85 - 54 * q^86 - 23 * q^87 + 15 * q^88 - 71 * q^89 - 52 * q^90 - 18 * q^91 - 24 * q^92 - q^93 + q^94 - 38 * q^95 - 31 * q^96 - 26 * q^97 + 19 * q^98 - 12 * q^99

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