LMFDB - Embedded newform 1441.2.a.c.1.9

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			1.9
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)

$f(q)$	$=$	$q-1.24808 q^{2} -0.917360 q^{3} -0.442292 q^{4} +1.92098 q^{5} +1.14494 q^{6} +0.0608487 q^{7} +3.04818 q^{8} -2.15845 q^{9} +O(q^{10})$	\(q-1.24808 q^{2} -0.917360 q^{3} -0.442292 q^{4} +1.92098 q^{5} +1.14494 q^{6} +0.0608487 q^{7} +3.04818 q^{8} -2.15845 q^{9} -2.39755 q^{10} +1.00000 q^{11} +0.405741 q^{12} -3.30567 q^{13} -0.0759442 q^{14} -1.76223 q^{15} -2.91979 q^{16} +7.33860 q^{17} +2.69392 q^{18} -5.40706 q^{19} -0.849636 q^{20} -0.0558201 q^{21} -1.24808 q^{22} -6.61152 q^{23} -2.79628 q^{24} -1.30982 q^{25} +4.12574 q^{26} +4.73215 q^{27} -0.0269129 q^{28} +4.93371 q^{29} +2.19941 q^{30} +0.858408 q^{31} -2.45222 q^{32} -0.917360 q^{33} -9.15917 q^{34} +0.116889 q^{35} +0.954666 q^{36} +1.34055 q^{37} +6.74845 q^{38} +3.03248 q^{39} +5.85551 q^{40} +10.3234 q^{41} +0.0696681 q^{42} -6.15460 q^{43} -0.442292 q^{44} -4.14635 q^{45} +8.25171 q^{46} -5.55083 q^{47} +2.67850 q^{48} -6.99630 q^{49} +1.63476 q^{50} -6.73213 q^{51} +1.46207 q^{52} +0.128966 q^{53} -5.90612 q^{54} +1.92098 q^{55} +0.185478 q^{56} +4.96022 q^{57} -6.15768 q^{58} +10.3722 q^{59} +0.779422 q^{60} -9.45062 q^{61} -1.07136 q^{62} -0.131339 q^{63} +8.90016 q^{64} -6.35013 q^{65} +1.14494 q^{66} +2.52656 q^{67} -3.24580 q^{68} +6.06514 q^{69} -0.145888 q^{70} -2.49971 q^{71} -6.57935 q^{72} -0.195580 q^{73} -1.67312 q^{74} +1.20157 q^{75} +2.39150 q^{76} +0.0608487 q^{77} -3.78479 q^{78} -2.66305 q^{79} -5.60888 q^{80} +2.13427 q^{81} -12.8845 q^{82} -11.5460 q^{83} +0.0246888 q^{84} +14.0973 q^{85} +7.68144 q^{86} -4.52599 q^{87} +3.04818 q^{88} -6.11694 q^{89} +5.17499 q^{90} -0.201145 q^{91} +2.92422 q^{92} -0.787469 q^{93} +6.92788 q^{94} -10.3869 q^{95} +2.24957 q^{96} +3.86692 q^{97} +8.73195 q^{98} -2.15845 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) $ 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * 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 $

$2$	−1.24808	−0.882527	−0.441264	−	0.897378i	$-0.645470\pi$
$2$	−1.24808	−0.882527	−0.441264	+	0.897378i	$0.645470\pi$
$3$	−0.917360	−0.529638	−0.264819	−	0.964298i	$-0.585312\pi$
$3$	−0.917360	−0.529638	−0.264819	+	0.964298i	$0.585312\pi$
$4$	−0.442292	−0.221146
$5$	1.92098	0.859091	0.429545	−	0.903045i	$-0.358674\pi$
$5$	1.92098	0.859091	0.429545	+	0.903045i	$0.358674\pi$
$6$	1.14494	0.467420
$7$	0.0608487	0.0229986	0.0114993	−	0.999934i	$-0.496340\pi$
$7$	0.0608487	0.0229986	0.0114993	+	0.999934i	$0.496340\pi$
$8$	3.04818	1.07769
$9$	−2.15845	−0.719484
$10$	−2.39755	−0.758171
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.405741	0.117127
$13$	−3.30567	−0.916827	−0.458413	−	0.888739i	$-0.651582\pi$
$13$	−3.30567	−0.916827	−0.458413	+	0.888739i	$0.651582\pi$
$14$	−0.0759442	−0.0202969
$15$	−1.76223	−0.455007
$16$	−2.91979	−0.729948
$17$	7.33860	1.77987	0.889936	−	0.456086i	$-0.150749\pi$
$17$	7.33860	1.77987	0.889936	+	0.456086i	$0.150749\pi$
$18$	2.69392	0.634964
$19$	−5.40706	−1.24046	−0.620232	−	0.784418i	$-0.712962\pi$
$19$	−5.40706	−1.24046	−0.620232	+	0.784418i	$0.712962\pi$
$20$	−0.849636	−0.189984
$21$	−0.0558201	−0.0121810
$22$	−1.24808	−0.266092
$23$	−6.61152	−1.37860	−0.689298	−	0.724478i	$-0.742081\pi$
$23$	−6.61152	−1.37860	−0.689298	+	0.724478i	$0.742081\pi$
$24$	−2.79628	−0.570788
$25$	−1.30982	−0.261963
$26$	4.12574	0.809124
$27$	4.73215	0.910704
$28$	−0.0269129	−0.00508606
$29$	4.93371	0.916168	0.458084	−	0.888909i	$-0.348536\pi$
$29$	4.93371	0.916168	0.458084	+	0.888909i	$0.348536\pi$
$30$	2.19941	0.401556
$31$	0.858408	0.154175	0.0770874	−	0.997024i	$-0.475438\pi$
$31$	0.858408	0.154175	0.0770874	+	0.997024i	$0.475438\pi$
$32$	−2.45222	−0.433495
$33$	−0.917360	−0.159692
$34$	−9.15917	−1.57078
$35$	0.116889	0.0197579
$36$	0.954666	0.159111
$37$	1.34055	0.220385	0.110193	−	0.993910i	$-0.464853\pi$
$37$	1.34055	0.220385	0.110193	+	0.993910i	$0.464853\pi$
$38$	6.74845	1.09474
$39$	3.03248	0.485586
$40$	5.85551	0.925837
$41$	10.3234	1.61225	0.806126	−	0.591744i	$-0.201560\pi$
$41$	10.3234	1.61225	0.806126	+	0.591744i	$0.201560\pi$
$42$	0.0696681	0.0107500
$43$	−6.15460	−0.938567	−0.469284	−	0.883047i	$-0.655488\pi$
$43$	−6.15460	−0.938567	−0.469284	+	0.883047i	$0.655488\pi$
$44$	−0.442292	−0.0666780
$45$	−4.14635	−0.618102
$46$	8.25171	1.21665
$47$	−5.55083	−0.809671	−0.404836	−	0.914389i	$-0.632671\pi$
$47$	−5.55083	−0.809671	−0.404836	+	0.914389i	$0.632671\pi$
$48$	2.67850	0.386608
$49$	−6.99630	−0.999471
$50$	1.63476	0.231190
$51$	−6.73213	−0.942687
$52$	1.46207	0.202753
$53$	0.128966	0.0177148	0.00885742	−	0.999961i	$-0.497181\pi$
$53$	0.128966	0.0177148	0.00885742	+	0.999961i	$0.497181\pi$
$54$	−5.90612	−0.803721
$55$	1.92098	0.259026
$56$	0.185478	0.0247855
$57$	4.96022	0.656997
$58$	−6.15768	−0.808543
$59$	10.3722	1.35034	0.675170	−	0.737662i	$-0.264070\pi$
$59$	10.3722	1.35034	0.675170	+	0.737662i	$0.264070\pi$
$60$	0.779422	0.100623
$61$	−9.45062	−1.21003	−0.605014	−	0.796215i	$-0.706832\pi$
$61$	−9.45062	−1.21003	−0.605014	+	0.796215i	$0.706832\pi$
$62$	−1.07136	−0.136063
$63$	−0.131339	−0.0165472
$64$	8.90016	1.11252
$65$	−6.35013	−0.787637
$66$	1.14494	0.140932
$67$	2.52656	0.308669	0.154334	−	0.988019i	$-0.450677\pi$
$67$	2.52656	0.308669	0.154334	+	0.988019i	$0.450677\pi$
$68$	−3.24580	−0.393611
$69$	6.06514	0.730157
$70$	−0.145888	−0.0174369
$71$	−2.49971	−0.296661	−0.148330	−	0.988938i	$-0.547390\pi$
$71$	−2.49971	−0.296661	−0.148330	+	0.988938i	$0.547390\pi$
$72$	−6.57935	−0.775384
$73$	−0.195580	−0.0228909	−0.0114455	−	0.999934i	$-0.503643\pi$
$73$	−0.195580	−0.0228909	−0.0114455	+	0.999934i	$0.503643\pi$
$74$	−1.67312	−0.194496
$75$	1.20157	0.138746
$76$	2.39150	0.274324
$77$	0.0608487	0.00693435
$78$	−3.78479	−0.428543
$79$	−2.66305	−0.299616	−0.149808	−	0.988715i	$-0.547866\pi$
$79$	−2.66305	−0.299616	−0.149808	+	0.988715i	$0.547866\pi$
$80$	−5.60888	−0.627092
$81$	2.13427	0.237141
$82$	−12.8845	−1.42286
$83$	−11.5460	−1.26733	−0.633667	−	0.773606i	$-0.718451\pi$
$83$	−11.5460	−1.26733	−0.633667	+	0.773606i	$0.718451\pi$
$84$	0.0246888	0.00269377
$85$	14.0973	1.52907
$86$	7.68144	0.828311
$87$	−4.52599	−0.485237
$88$	3.04818	0.324937
$89$	−6.11694	−0.648395	−0.324197	−	0.945989i	$-0.605094\pi$
$89$	−6.11694	−0.648395	−0.324197	+	0.945989i	$0.605094\pi$
$90$	5.17499	0.545492
$91$	−0.201145	−0.0210858
$92$	2.92422	0.304871
$93$	−0.787469	−0.0816567
$94$	6.92788	0.714557
$95$	−10.3869	−1.06567
$96$	2.24957	0.229595
$97$	3.86692	0.392626	0.196313	−	0.980541i	$-0.437103\pi$
$97$	3.86692	0.392626	0.196313	+	0.980541i	$0.437103\pi$
$98$	8.73195	0.882060
$99$	−2.15845	−0.216933
$100$	0.579322	0.0579322
$101$	−12.9545	−1.28902	−0.644509	−	0.764597i	$-0.722938\pi$
$101$	−12.9545	−1.28902	−0.644509	+	0.764597i	$0.722938\pi$
$102$	8.40225	0.831947
$103$	−14.9663	−1.47467	−0.737337	−	0.675525i	$-0.763917\pi$
$103$	−14.9663	−1.47467	−0.737337	+	0.675525i	$0.763917\pi$
$104$	−10.0763	−0.988059
$105$	−0.107230	−0.0104645
$106$	−0.160960	−0.0156338
$107$	−2.49520	−0.241220	−0.120610	−	0.992700i	$-0.538485\pi$
$107$	−2.49520	−0.241220	−0.120610	+	0.992700i	$0.538485\pi$
$108$	−2.09299	−0.201398
$109$	−15.6910	−1.50292	−0.751461	−	0.659778i	$-0.770650\pi$
$109$	−15.6910	−1.50292	−0.751461	+	0.659778i	$0.770650\pi$
$110$	−2.39755	−0.228597
$111$	−1.22977	−0.116724
$112$	−0.177666	−0.0167878
$113$	−9.09492	−0.855578	−0.427789	−	0.903879i	$-0.640707\pi$
$113$	−9.09492	−0.855578	−0.427789	+	0.903879i	$0.640707\pi$
$114$	−6.19075	−0.579817
$115$	−12.7006	−1.18434
$116$	−2.18214	−0.202607
$117$	7.13512	0.659642
$118$	−12.9453	−1.19171
$119$	0.446544	0.0409346
$120$	−5.37161	−0.490358
$121$	1.00000	0.0909091
$122$	11.7951	1.06788
$123$	−9.47031	−0.853909
$124$	−0.379667	−0.0340951
$125$	−12.1211	−1.08414
$126$	0.163922	0.0146033
$127$	5.46548	0.484983	0.242491	−	0.970154i	$-0.422035\pi$
$127$	5.46548	0.484983	0.242491	+	0.970154i	$0.422035\pi$
$128$	−6.20368	−0.548333
$129$	5.64598	0.497101
$130$	7.92549	0.695111
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	0.405741	0.0353152
$133$	−0.329012	−0.0285290
$134$	−3.15336	−0.272408
$135$	9.09040	0.782377
$136$	22.3694	1.91816
$137$	−11.9178	−1.01821	−0.509104	−	0.860705i	$-0.670023\pi$
$137$	−11.9178	−1.01821	−0.509104	+	0.860705i	$0.670023\pi$
$138$	−7.56979	−0.644383
$139$	−21.6207	−1.83385	−0.916923	−	0.399065i	$-0.869335\pi$
$139$	−21.6207	−1.83385	−0.916923	+	0.399065i	$0.869335\pi$
$140$	−0.0516993	−0.00436939
$141$	5.09210	0.428832
$142$	3.11984	0.261811
$143$	−3.30567	−0.276434
$144$	6.30223	0.525186
$145$	9.47759	0.787071
$146$	0.244100	0.0202018
$147$	6.41812	0.529358
$148$	−0.592915	−0.0487373
$149$	6.65668	0.545336	0.272668	−	0.962108i	$-0.412094\pi$
$149$	6.65668	0.545336	0.272668	+	0.962108i	$0.412094\pi$
$150$	−1.49966	−0.122447
$151$	−22.9089	−1.86430	−0.932149	−	0.362074i	$-0.882069\pi$
$151$	−22.9089	−1.86430	−0.932149	+	0.362074i	$0.882069\pi$
$152$	−16.4817	−1.33684
$153$	−15.8400	−1.28059
$154$	−0.0759442	−0.00611975
$155$	1.64899	0.132450
$156$	−1.34124	−0.107385
$157$	−9.54560	−0.761822	−0.380911	−	0.924612i	$-0.624390\pi$
$157$	−9.54560	−0.761822	−0.380911	+	0.924612i	$0.624390\pi$
$158$	3.32370	0.264419
$159$	−0.118308	−0.00938245
$160$	−4.71068	−0.372412
$161$	−0.402302	−0.0317059
$162$	−2.66374	−0.209283
$163$	11.1822	0.875861	0.437930	−	0.899009i	$-0.355712\pi$
$163$	11.1822	0.875861	0.437930	+	0.899009i	$0.355712\pi$
$164$	−4.56598	−0.356543
$165$	−1.76223	−0.137190
$166$	14.4103	1.11846
$167$	−8.92174	−0.690385	−0.345192	−	0.938532i	$-0.612186\pi$
$167$	−8.92174	−0.690385	−0.345192	+	0.938532i	$0.612186\pi$
$168$	−0.170150	−0.0131273
$169$	−2.07258	−0.159429
$170$	−17.5946	−1.34945
$171$	11.6709	0.892494
$172$	2.72213	0.207560
$173$	10.1100	0.768647	0.384323	−	0.923199i	$-0.374435\pi$
$173$	10.1100	0.768647	0.384323	+	0.923199i	$0.374435\pi$
$174$	5.64881	0.428235
$175$	−0.0797007	−0.00602481
$176$	−2.91979	−0.220088
$177$	−9.51500	−0.715191
$178$	7.63445	0.572226
$179$	24.2563	1.81300	0.906499	−	0.422207i	$-0.138745\pi$
$179$	24.2563	1.81300	0.906499	+	0.422207i	$0.138745\pi$
$180$	1.83390	0.136691
$181$	−2.03937	−0.151585	−0.0757926	−	0.997124i	$-0.524149\pi$
$181$	−2.03937	−0.151585	−0.0757926	+	0.997124i	$0.524149\pi$
$182$	0.251046	0.0186088
$183$	8.66961	0.640876
$184$	−20.1531	−1.48571
$185$	2.57518	0.189331
$186$	0.982826	0.0720643
$187$	7.33860	0.536651
$188$	2.45509	0.179056
$189$	0.287945	0.0209450
$190$	12.9637	0.940483
$191$	−7.28960	−0.527457	−0.263729	−	0.964597i	$-0.584952\pi$
$191$	−7.28960	−0.527457	−0.263729	+	0.964597i	$0.584952\pi$
$192$	−8.16464	−0.589232
$193$	25.1709	1.81184	0.905922	−	0.423445i	$-0.139179\pi$
$193$	25.1709	1.81184	0.905922	+	0.423445i	$0.139179\pi$
$194$	−4.82623	−0.346503
$195$	5.82536	0.417162
$196$	3.09441	0.221029
$197$	−3.07863	−0.219343	−0.109672	−	0.993968i	$-0.534980\pi$
$197$	−3.07863	−0.219343	−0.109672	+	0.993968i	$0.534980\pi$
$198$	2.69392	0.191449
$199$	−2.76272	−0.195844	−0.0979220	−	0.995194i	$-0.531220\pi$
$199$	−2.76272	−0.195844	−0.0979220	+	0.995194i	$0.531220\pi$
$200$	−3.99256	−0.282317
$201$	−2.31777	−0.163483
$202$	16.1682	1.13759
$203$	0.300210	0.0210706
$204$	2.97757	0.208471
$205$	19.8312	1.38507
$206$	18.6792	1.30144
$207$	14.2706	0.991878
$208$	9.65186	0.669236
$209$	−5.40706	−0.374014
$210$	0.133831	0.00923524
$211$	2.10279	0.144762	0.0723811	−	0.997377i	$-0.476940\pi$
$211$	2.10279	0.144762	0.0723811	+	0.997377i	$0.476940\pi$
$212$	−0.0570406	−0.00391757
$213$	2.29313	0.157123
$214$	3.11421	0.212883
$215$	−11.8229	−0.806314
$216$	14.4245	0.981460
$217$	0.0522330	0.00354581
$218$	19.5836	1.32637
$219$	0.179417	0.0121239
$220$	−0.849636	−0.0572825
$221$	−24.2589	−1.63183
$222$	1.53485	0.103012
$223$	−1.92721	−0.129055	−0.0645277	−	0.997916i	$-0.520554\pi$
$223$	−1.92721	−0.129055	−0.0645277	+	0.997916i	$0.520554\pi$
$224$	−0.149214	−0.00996980
$225$	2.82718	0.188478
$226$	11.3512	0.755070
$227$	−3.71462	−0.246548	−0.123274	−	0.992373i	$-0.539339\pi$
$227$	−3.71462	−0.246548	−0.123274	+	0.992373i	$0.539339\pi$
$228$	−2.19386	−0.145292
$229$	5.24207	0.346406	0.173203	−	0.984886i	$-0.444588\pi$
$229$	5.24207	0.346406	0.173203	+	0.984886i	$0.444588\pi$
$230$	15.8514	1.04521
$231$	−0.0558201	−0.00367270
$232$	15.0389	0.987349
$233$	−23.8888	−1.56501	−0.782504	−	0.622645i	$-0.786058\pi$
$233$	−23.8888	−1.56501	−0.782504	+	0.622645i	$0.786058\pi$
$234$	−8.90521	−0.582152
$235$	−10.6631	−0.695581
$236$	−4.58752	−0.298622
$237$	2.44297	0.158688
$238$	−0.557323	−0.0361259
$239$	17.7269	1.14666	0.573330	−	0.819325i	$-0.305651\pi$
$239$	17.7269	1.14666	0.573330	+	0.819325i	$0.305651\pi$
$240$	5.14536	0.332131
$241$	−1.51764	−0.0977600	−0.0488800	−	0.998805i	$-0.515565\pi$
$241$	−1.51764	−0.0977600	−0.0488800	+	0.998805i	$0.515565\pi$
$242$	−1.24808	−0.0802297
$243$	−16.1544	−1.03630
$244$	4.17993	0.267593
$245$	−13.4398	−0.858636
$246$	11.8197	0.753598
$247$	17.8739	1.13729
$248$	2.61658	0.166153
$249$	10.5918	0.671228
$250$	15.1281	0.956784
$251$	−14.5447	−0.918053	−0.459027	−	0.888422i	$-0.651802\pi$
$251$	−14.5447	−0.918053	−0.459027	+	0.888422i	$0.651802\pi$
$252$	0.0580902	0.00365934
$253$	−6.61152	−0.415663
$254$	−6.82136	−0.428010
$255$	−12.9323	−0.809853
$256$	−10.0576	−0.628601
$257$	13.2983	0.829528	0.414764	−	0.909929i	$-0.363864\pi$
$257$	13.2983	0.829528	0.414764	+	0.909929i	$0.363864\pi$
$258$	−7.04664	−0.438705
$259$	0.0815707	0.00506856
$260$	2.80861	0.174183
$261$	−10.6492	−0.659168
$262$	−1.24808	−0.0771067
$263$	−8.71146	−0.537172	−0.268586	−	0.963256i	$-0.586556\pi$
$263$	−8.71146	−0.537172	−0.268586	+	0.963256i	$0.586556\pi$
$264$	−2.79628	−0.172099
$265$	0.247742	0.0152186
$266$	0.410634	0.0251776
$267$	5.61144	0.343414
$268$	−1.11748	−0.0682608
$269$	0.766551	0.0467375	0.0233687	−	0.999727i	$-0.492561\pi$
$269$	0.766551	0.0467375	0.0233687	+	0.999727i	$0.492561\pi$
$270$	−11.3456	−0.690469
$271$	−16.2581	−0.987611	−0.493805	−	0.869572i	$-0.664395\pi$
$271$	−16.2581	−0.987611	−0.493805	+	0.869572i	$0.664395\pi$
$272$	−21.4272	−1.29921
$273$	0.184523	0.0111678
$274$	14.8744	0.898596
$275$	−1.30982	−0.0789850
$276$	−2.68256	−0.161471
$277$	8.93347	0.536760	0.268380	−	0.963313i	$-0.413512\pi$
$277$	8.93347	0.536760	0.268380	+	0.963313i	$0.413512\pi$
$278$	26.9844	1.61842
$279$	−1.85283	−0.110926
$280$	0.356300	0.0212930
$281$	−26.9832	−1.60968	−0.804841	−	0.593491i	$-0.797749\pi$
$281$	−26.9832	−1.60968	−0.804841	+	0.593491i	$0.797749\pi$
$282$	−6.35536	−0.378456
$283$	13.9297	0.828035	0.414018	−	0.910269i	$-0.364125\pi$
$283$	13.9297	0.828035	0.414018	+	0.910269i	$0.364125\pi$
$284$	1.10560	0.0656054
$285$	9.52850	0.564420
$286$	4.12574	0.243960
$287$	0.628168	0.0370796
$288$	5.29300	0.311893
$289$	36.8550	2.16794
$290$	−11.8288	−0.694612
$291$	−3.54735	−0.207949
$292$	0.0865035	0.00506223
$293$	−0.0551216	−0.00322024	−0.00161012	−	0.999999i	$-0.500513\pi$
$293$	−0.0551216	−0.00322024	−0.00161012	+	0.999999i	$0.500513\pi$
$294$	−8.01034	−0.467172
$295$	19.9248	1.16006
$296$	4.08624	0.237508
$297$	4.73215	0.274587
$298$	−8.30808	−0.481274
$299$	21.8555	1.26393
$300$	−0.531446	−0.0306831
$301$	−0.374499	−0.0215858
$302$	28.5922	1.64529
$303$	11.8839	0.682713
$304$	15.7875	0.905475
$305$	−18.1545	−1.03952
$306$	19.7696	1.13015
$307$	−17.5107	−0.999390	−0.499695	−	0.866202i	$-0.666555\pi$
$307$	−17.5107	−0.999390	−0.499695	+	0.866202i	$0.666555\pi$
$308$	−0.0269129	−0.00153350
$309$	13.7295	0.781043
$310$	−2.05807	−0.116891
$311$	−1.14992	−0.0652060	−0.0326030	−	0.999468i	$-0.510380\pi$
$311$	−1.14992	−0.0652060	−0.0326030	+	0.999468i	$0.510380\pi$
$312$	9.24356	0.523313
$313$	32.1833	1.81911	0.909554	−	0.415586i	$-0.136424\pi$
$313$	32.1833	1.81911	0.909554	+	0.415586i	$0.136424\pi$
$314$	11.9137	0.672328
$315$	−0.252300	−0.0142155
$316$	1.17784	0.0662590
$317$	27.0410	1.51878	0.759388	−	0.650638i	$-0.225498\pi$
$317$	27.0410	1.51878	0.759388	+	0.650638i	$0.225498\pi$
$318$	0.147658	0.00828026
$319$	4.93371	0.276235
$320$	17.0971	0.955755
$321$	2.28899	0.127759
$322$	0.502106	0.0279813
$323$	−39.6802	−2.20787
$324$	−0.943970	−0.0524428
$325$	4.32982	0.240175
$326$	−13.9563	−0.772971
$327$	14.3942	0.796004
$328$	31.4677	1.73751
$329$	−0.337761	−0.0186213
$330$	2.19941	0.121074
$331$	0.554442	0.0304749	0.0152374	−	0.999884i	$-0.495150\pi$
$331$	0.554442	0.0304749	0.0152374	+	0.999884i	$0.495150\pi$
$332$	5.10669	0.280266
$333$	−2.89351	−0.158563
$334$	11.1351	0.609283
$335$	4.85349	0.265174
$336$	0.162983	0.00889147
$337$	18.0728	0.984490	0.492245	−	0.870457i	$-0.336176\pi$
$337$	18.0728	0.984490	0.492245	+	0.870457i	$0.336176\pi$
$338$	2.58674	0.140700
$339$	8.34331	0.453146
$340$	−6.23514	−0.338148
$341$	0.858408	0.0464854
$342$	−14.5662	−0.787650
$343$	−0.851657	−0.0459851
$344$	−18.7603	−1.01149
$345$	11.6510	0.627271
$346$	−12.6181	−0.678351
$347$	26.8488	1.44132	0.720660	−	0.693288i	$-0.243839\pi$
$347$	26.8488	1.44132	0.720660	+	0.693288i	$0.243839\pi$
$348$	2.00181	0.107308
$349$	−15.8836	−0.850230	−0.425115	−	0.905139i	$-0.639766\pi$
$349$	−15.8836	−0.850230	−0.425115	+	0.905139i	$0.639766\pi$
$350$	0.0994730	0.00531705
$351$	−15.6429	−0.834957
$352$	−2.45222	−0.130704
$353$	20.4087	1.08625	0.543123	−	0.839653i	$-0.317242\pi$
$353$	20.4087	1.08625	0.543123	+	0.839653i	$0.317242\pi$
$354$	11.8755	0.631176
$355$	−4.80190	−0.254859
$356$	2.70548	0.143390
$357$	−0.409641	−0.0216805
$358$	−30.2738	−1.60002
$359$	−33.9764	−1.79320	−0.896602	−	0.442837i	$-0.853972\pi$
$359$	−33.9764	−1.79320	−0.896602	+	0.442837i	$0.853972\pi$
$360$	−12.6388	−0.666125
$361$	10.2363	0.538751
$362$	2.54530	0.133778
$363$	−0.917360	−0.0481489
$364$	0.0889650	0.00466304
$365$	−0.375706	−0.0196654
$366$	−10.8204	−0.565591
$367$	6.98658	0.364696	0.182348	−	0.983234i	$-0.441630\pi$
$367$	6.98658	0.364696	0.182348	+	0.983234i	$0.441630\pi$
$368$	19.3043	1.00630
$369$	−22.2827	−1.15999
$370$	−3.21403	−0.167089
$371$	0.00784741	0.000407417 0
$372$	0.348291	0.0180581
$373$	−0.241758	−0.0125177	−0.00625887	−	0.999980i	$-0.501992\pi$
$373$	−0.241758	−0.0125177	−0.00625887	+	0.999980i	$0.501992\pi$
$374$	−9.15917	−0.473609
$375$	11.1194	0.574202
$376$	−16.9199	−0.872578
$377$	−16.3092	−0.839967
$378$	−0.359379	−0.0184845
$379$	−0.555896	−0.0285545	−0.0142772	−	0.999898i	$-0.504545\pi$
$379$	−0.555896	−0.0285545	−0.0142772	+	0.999898i	$0.504545\pi$
$380$	4.59403	0.235669
$381$	−5.01381	−0.256865
$382$	9.09802	0.465495
$383$	4.06033	0.207473	0.103737	−	0.994605i	$-0.466920\pi$
$383$	4.06033	0.207473	0.103737	+	0.994605i	$0.466920\pi$
$384$	5.69101	0.290418
$385$	0.116889	0.00595724
$386$	−31.4154	−1.59900
$387$	13.2844	0.675284
$388$	−1.71031	−0.0868276
$389$	−3.14703	−0.159561	−0.0797803	−	0.996812i	$-0.525422\pi$
$389$	−3.14703	−0.159561	−0.0797803	+	0.996812i	$0.525422\pi$
$390$	−7.27052	−0.368157
$391$	−48.5193	−2.45372
$392$	−21.3260	−1.07712
$393$	−0.917360	−0.0462747
$394$	3.84238	0.193576
$395$	−5.11567	−0.257398
$396$	0.954666	0.0479738
$397$	33.4063	1.67661	0.838306	−	0.545199i	$-0.183546\pi$
$397$	33.4063	1.67661	0.838306	+	0.545199i	$0.183546\pi$
$398$	3.44810	0.172838
$399$	0.301823	0.0151100
$400$	3.82440	0.191220
$401$	14.1312	0.705679	0.352840	−	0.935684i	$-0.385216\pi$
$401$	14.1312	0.705679	0.352840	+	0.935684i	$0.385216\pi$
$402$	2.89276	0.144278
$403$	−2.83761	−0.141351
$404$	5.72966	0.285061
$405$	4.09990	0.203725
$406$	−0.374687	−0.0185954
$407$	1.34055	0.0664486
$408$	−20.5207	−1.01593
$409$	16.5148	0.816605	0.408302	−	0.912847i	$-0.366121\pi$
$409$	16.5148	0.816605	0.408302	+	0.912847i	$0.366121\pi$
$410$	−24.7509	−1.22236
$411$	10.9329	0.539281
$412$	6.61948	0.326118
$413$	0.631132	0.0310560
$414$	−17.8109	−0.875359
$415$	−22.1796	−1.08875
$416$	8.10622	0.397440
$417$	19.8340	0.971274
$418$	6.74845	0.330077
$419$	−8.67141	−0.423626	−0.211813	−	0.977310i	$-0.567937\pi$
$419$	−8.67141	−0.423626	−0.211813	+	0.977310i	$0.567937\pi$
$420$	0.0474268	0.00231419
$421$	15.7718	0.768669	0.384334	−	0.923194i	$-0.374431\pi$
$421$	15.7718	0.768669	0.384334	+	0.923194i	$0.374431\pi$
$422$	−2.62446	−0.127757
$423$	11.9812	0.582545
$424$	0.393111	0.0190912
$425$	−9.61222	−0.466261
$426$	−2.86202	−0.138665
$427$	−0.575058	−0.0278290
$428$	1.10361	0.0533448
$429$	3.03248	0.146410
$430$	14.7559	0.711594
$431$	25.8188	1.24365	0.621824	−	0.783157i	$-0.286392\pi$
$431$	25.8188	1.24365	0.621824	+	0.783157i	$0.286392\pi$
$432$	−13.8169	−0.664767
$433$	13.5863	0.652918	0.326459	−	0.945211i	$-0.394144\pi$
$433$	13.5863	0.652918	0.326459	+	0.945211i	$0.394144\pi$
$434$	−0.0651911	−0.00312927
$435$	−8.69436	−0.416863
$436$	6.93999	0.332365
$437$	35.7489	1.71010
$438$	−0.223927	−0.0106997
$439$	−37.3733	−1.78373	−0.891866	−	0.452300i	$-0.850604\pi$
$439$	−37.3733	−1.78373	−0.891866	+	0.452300i	$0.850604\pi$
$440$	5.85551	0.279150
$441$	15.1012	0.719103
$442$	30.2771	1.44014
$443$	−24.6318	−1.17029	−0.585146	−	0.810928i	$-0.698963\pi$
$443$	−24.6318	−1.17029	−0.585146	+	0.810928i	$0.698963\pi$
$444$	0.543916	0.0258131
$445$	−11.7506	−0.557030
$446$	2.40531	0.113895
$447$	−6.10657	−0.288831
$448$	0.541563	0.0255864
$449$	−10.9534	−0.516925	−0.258462	−	0.966021i	$-0.583216\pi$
$449$	−10.9534	−0.516925	−0.258462	+	0.966021i	$0.583216\pi$
$450$	−3.52855	−0.166337
$451$	10.3234	0.486112
$452$	4.02261	0.189208
$453$	21.0157	0.987403
$454$	4.63614	0.217585
$455$	−0.386397	−0.0181146
$456$	15.1196	0.708042
$457$	−16.7316	−0.782672	−0.391336	−	0.920248i	$-0.627987\pi$
$457$	−16.7316	−0.782672	−0.391336	+	0.920248i	$0.627987\pi$
$458$	−6.54253	−0.305712
$459$	34.7274	1.62093
$460$	5.61739	0.261912
$461$	−24.4701	−1.13969	−0.569844	−	0.821753i	$-0.692996\pi$
$461$	−24.4701	−1.13969	−0.569844	+	0.821753i	$0.692996\pi$
$462$	0.0696681	0.00324125
$463$	21.0482	0.978193	0.489096	−	0.872230i	$-0.337327\pi$
$463$	21.0482	0.978193	0.489096	+	0.872230i	$0.337327\pi$
$464$	−14.4054	−0.668755
$465$	−1.51272	−0.0701505
$466$	29.8152	1.38116
$467$	−17.4910	−0.809389	−0.404694	−	0.914452i	$-0.632622\pi$
$467$	−17.4910	−0.809389	−0.404694	+	0.914452i	$0.632622\pi$
$468$	−3.15581	−0.145877
$469$	0.153738	0.00709896
$470$	13.3084	0.613869
$471$	8.75675	0.403490
$472$	31.6162	1.45525
$473$	−6.15460	−0.282989
$474$	−3.04903	−0.140047
$475$	7.08226	0.324956
$476$	−0.197503	−0.00905253
$477$	−0.278367	−0.0127455
$478$	−22.1247	−1.01196
$479$	13.3867	0.611653	0.305826	−	0.952087i	$-0.401067\pi$
$479$	13.3867	0.611653	0.305826	+	0.952087i	$0.401067\pi$
$480$	4.32138	0.197243
$481$	−4.43141	−0.202055
$482$	1.89414	0.0862759
$483$	0.369056	0.0167926
$484$	−0.442292	−0.0201042
$485$	7.42829	0.337301
$486$	20.1620	0.914565
$487$	−37.1997	−1.68568	−0.842840	−	0.538165i	$-0.819118\pi$
$487$	−37.1997	−1.68568	−0.842840	+	0.538165i	$0.819118\pi$
$488$	−28.8072	−1.30404
$489$	−10.2581	−0.463889
$490$	16.7739	0.757770
$491$	3.20458	0.144621	0.0723104	−	0.997382i	$-0.476963\pi$
$491$	3.20458	0.144621	0.0723104	+	0.997382i	$0.476963\pi$
$492$	4.18864	0.188839
$493$	36.2065	1.63066
$494$	−22.3081	−1.00369
$495$	−4.14635	−0.186365
$496$	−2.50638	−0.112540
$497$	−0.152104	−0.00682280
$498$	−13.2194	−0.592377
$499$	−14.8317	−0.663956	−0.331978	−	0.943287i	$-0.607716\pi$
$499$	−14.8317	−0.663956	−0.331978	+	0.943287i	$0.607716\pi$
$500$	5.36105	0.239753
$501$	8.18444	0.365654
$502$	18.1530	0.810207
$503$	−0.272830	−0.0121649	−0.00608245	−	0.999982i	$-0.501936\pi$
$503$	−0.272830	−0.0121649	−0.00608245	+	0.999982i	$0.501936\pi$
$504$	−0.400345	−0.0178328
$505$	−24.8853	−1.10738
$506$	8.25171	0.366833
$507$	1.90130	0.0844396
$508$	−2.41734	−0.107252
$509$	12.0899	0.535875	0.267937	−	0.963436i	$-0.413658\pi$
$509$	12.0899	0.535875	0.267937	+	0.963436i	$0.413658\pi$
$510$	16.1406	0.714718
$511$	−0.0119008	−0.000526460 0
$512$	24.9601	1.10309
$513$	−25.5870	−1.12970
$514$	−16.5974	−0.732081
$515$	−28.7500	−1.26688
$516$	−2.49717	−0.109932
$517$	−5.55083	−0.244125
$518$	−0.101807	−0.00447314
$519$	−9.27447	−0.407104
$520$	−19.3563	−0.848832
$521$	6.66063	0.291807	0.145904	−	0.989299i	$-0.453391\pi$
$521$	6.66063	0.291807	0.145904	+	0.989299i	$0.453391\pi$
$522$	13.2911	0.581734
$523$	−27.6097	−1.20729	−0.603644	−	0.797254i	$-0.706285\pi$
$523$	−27.6097	−1.20729	−0.603644	+	0.797254i	$0.706285\pi$
$524$	−0.442292	−0.0193216
$525$	0.0731142	0.00319096
$526$	10.8726	0.474069
$527$	6.29951	0.274411
$528$	2.67850	0.116567
$529$	20.7122	0.900529
$530$	−0.309202	−0.0134309
$531$	−22.3878	−0.971548
$532$	0.145520	0.00630907
$533$	−34.1259	−1.47816
$534$	−7.00353	−0.303072
$535$	−4.79324	−0.207230
$536$	7.70142	0.332650
$537$	−22.2517	−0.960232
$538$	−0.956719	−0.0412471
$539$	−6.99630	−0.301352
$540$	−4.02061	−0.173020
$541$	−22.2921	−0.958413	−0.479206	−	0.877702i	$-0.659075\pi$
$541$	−22.2921	−0.958413	−0.479206	+	0.877702i	$0.659075\pi$
$542$	20.2915	0.871593
$543$	1.87084	0.0802853
$544$	−17.9958	−0.771566
$545$	−30.1421	−1.29115
$546$	−0.230299	−0.00985590
$547$	−0.230688	−0.00986352	−0.00493176	−	0.999988i	$-0.501570\pi$
$547$	−0.230688	−0.00986352	−0.00493176	+	0.999988i	$0.501570\pi$
$548$	5.27116	0.225173
$549$	20.3987	0.870595
$550$	1.63476	0.0697064
$551$	−26.6769	−1.13647
$552$	18.4876	0.786886
$553$	−0.162043	−0.00689077
$554$	−11.1497	−0.473705
$555$	−2.36236	−0.100277
$556$	9.56267	0.405548
$557$	27.3879	1.16046	0.580232	−	0.814451i	$-0.302962\pi$
$557$	27.3879	1.16046	0.580232	+	0.814451i	$0.302962\pi$
$558$	2.31249	0.0978954
$559$	20.3450	0.860504
$560$	−0.341293	−0.0144223
$561$	−6.73213	−0.284231
$562$	33.6772	1.42059
$563$	7.58807	0.319799	0.159900	−	0.987133i	$-0.448883\pi$
$563$	7.58807	0.319799	0.159900	+	0.987133i	$0.448883\pi$
$564$	−2.25220	−0.0948346
$565$	−17.4712	−0.735019
$566$	−17.3854	−0.730763
$567$	0.129867	0.00545392
$568$	−7.61956	−0.319710
$569$	32.5628	1.36510	0.682552	−	0.730837i	$-0.260870\pi$
$569$	32.5628	1.36510	0.682552	+	0.730837i	$0.260870\pi$
$570$	−11.8923	−0.498116
$571$	−39.7728	−1.66444	−0.832220	−	0.554446i	$-0.812930\pi$
$571$	−39.7728	−1.66444	−0.832220	+	0.554446i	$0.812930\pi$
$572$	1.46207	0.0611322
$573$	6.68719	0.279361
$574$	−0.784005	−0.0327238
$575$	8.65988	0.361142
$576$	−19.2106	−0.800440
$577$	33.9844	1.41479	0.707394	−	0.706820i	$-0.249871\pi$
$577$	33.9844	1.41479	0.707394	+	0.706820i	$0.249871\pi$
$578$	−45.9980	−1.91327
$579$	−23.0908	−0.959621
$580$	−4.19186	−0.174058
$581$	−0.702557	−0.0291470
$582$	4.42739	0.183521
$583$	0.128966	0.00534122
$584$	−0.596163	−0.0246694
$585$	13.7065	0.566692
$586$	0.0687962	0.00284195
$587$	27.0418	1.11614	0.558068	−	0.829795i	$-0.311543\pi$
$587$	27.0418	1.11614	0.558068	+	0.829795i	$0.311543\pi$
$588$	−2.83868	−0.117065
$589$	−4.64146	−0.191248
$590$	−24.8677	−1.02379
$591$	2.82421	0.116172
$592$	−3.91413	−0.160870
$593$	27.2641	1.11960	0.559801	−	0.828627i	$-0.310877\pi$
$593$	27.2641	1.11960	0.559801	+	0.828627i	$0.310877\pi$
$594$	−5.90612	−0.242331
$595$	0.857804	0.0351665
$596$	−2.94420	−0.120599
$597$	2.53441	0.103726
$598$	−27.2774	−1.11546
$599$	−7.76895	−0.317431	−0.158715	−	0.987324i	$-0.550735\pi$
$599$	−7.76895	−0.317431	−0.158715	+	0.987324i	$0.550735\pi$
$600$	3.66261	0.149526
$601$	−32.6290	−1.33096	−0.665482	−	0.746414i	$-0.731774\pi$
$601$	−32.6290	−1.33096	−0.665482	+	0.746414i	$0.731774\pi$
$602$	0.467406	0.0190500
$603$	−5.45346	−0.222082
$604$	10.1324	0.412282
$605$	1.92098	0.0780991
$606$	−14.8321	−0.602512
$607$	−24.6430	−1.00023	−0.500114	−	0.865959i	$-0.666709\pi$
$607$	−24.6430	−1.00023	−0.500114	+	0.865959i	$0.666709\pi$
$608$	13.2593	0.537735
$609$	−0.275401	−0.0111598
$610$	22.6583	0.917407
$611$	18.3492	0.742328
$612$	7.00591	0.283197
$613$	21.7957	0.880319	0.440160	−	0.897920i	$-0.354922\pi$
$613$	21.7957	0.880319	0.440160	+	0.897920i	$0.354922\pi$
$614$	21.8548	0.881988
$615$	−18.1923	−0.733585
$616$	0.185478	0.00747311
$617$	3.27056	0.131668	0.0658339	−	0.997831i	$-0.479029\pi$
$617$	3.27056	0.131668	0.0658339	+	0.997831i	$0.479029\pi$
$618$	−17.1355	−0.689291
$619$	39.3514	1.58167	0.790833	−	0.612033i	$-0.209648\pi$
$619$	39.3514	1.58167	0.790833	+	0.612033i	$0.209648\pi$
$620$	−0.729335	−0.0292908
$621$	−31.2867	−1.25549
$622$	1.43520	0.0575461
$623$	−0.372208	−0.0149122
$624$	−8.85423	−0.354453
$625$	−16.7353	−0.669412
$626$	−40.1674	−1.60541
$627$	4.96022	0.198092
$628$	4.22194	0.168474
$629$	9.83776	0.392257
$630$	0.314891	0.0125456
$631$	27.3932	1.09050	0.545252	−	0.838272i	$-0.316434\pi$
$631$	27.3932	1.09050	0.545252	+	0.838272i	$0.316434\pi$
$632$	−8.11745	−0.322895
$633$	−1.92902	−0.0766715
$634$	−33.7494	−1.34036
$635$	10.4991	0.416644
$636$	0.0523268	0.00207489
$637$	23.1274	0.916342
$638$	−6.15768	−0.243785
$639$	5.39550	0.213443
$640$	−11.9172	−0.471068
$641$	−47.4476	−1.87407	−0.937033	−	0.349240i	$-0.886440\pi$
$641$	−47.4476	−1.87407	−0.937033	+	0.349240i	$0.886440\pi$
$642$	−2.85685	−0.112751
$643$	−19.1915	−0.756838	−0.378419	−	0.925634i	$-0.623532\pi$
$643$	−19.1915	−0.756838	−0.378419	+	0.925634i	$0.623532\pi$
$644$	0.177935	0.00701162
$645$	10.8458	0.427054
$646$	49.5241	1.94850
$647$	−9.72338	−0.382266	−0.191133	−	0.981564i	$-0.561216\pi$
$647$	−9.72338	−0.382266	−0.191133	+	0.981564i	$0.561216\pi$
$648$	6.50563	0.255565
$649$	10.3722	0.407143
$650$	−5.40397	−0.211961
$651$	−0.0479165	−0.00187799
$652$	−4.94582	−0.193693
$653$	19.1813	0.750622	0.375311	−	0.926899i	$-0.377536\pi$
$653$	19.1813	0.750622	0.375311	+	0.926899i	$0.377536\pi$
$654$	−17.9652	−0.702495
$655$	1.92098	0.0750591
$656$	−30.1423	−1.17686
$657$	0.422150	0.0164696
$658$	0.421553	0.0164338
$659$	−24.9657	−0.972526	−0.486263	−	0.873813i	$-0.661640\pi$
$659$	−24.9657	−0.972526	−0.486263	+	0.873813i	$0.661640\pi$
$660$	0.779422	0.0303390
$661$	−34.1784	−1.32939	−0.664693	−	0.747117i	$-0.731438\pi$
$661$	−34.1784	−1.32939	−0.664693	+	0.747117i	$0.731438\pi$
$662$	−0.691989	−0.0268949
$663$	22.2542	0.864280
$664$	−35.1942	−1.36580
$665$	−0.632028	−0.0245090
$666$	3.61134	0.139937
$667$	−32.6193	−1.26303
$668$	3.94601	0.152676
$669$	1.76794	0.0683526
$670$	−6.05755	−0.234024
$671$	−9.45062	−0.364837
$672$	0.136883	0.00528038
$673$	30.3202	1.16876	0.584380	−	0.811480i	$-0.301338\pi$
$673$	30.3202	1.16876	0.584380	+	0.811480i	$0.301338\pi$
$674$	−22.5564	−0.868839
$675$	−6.19826	−0.238571
$676$	0.916684	0.0352571
$677$	−45.9428	−1.76573	−0.882863	−	0.469631i	$-0.844387\pi$
$677$	−45.9428	−1.76573	−0.882863	+	0.469631i	$0.844387\pi$
$678$	−10.4131	−0.399914
$679$	0.235297	0.00902986
$680$	42.9712	1.64787
$681$	3.40764	0.130581
$682$	−1.07136	−0.0410246
$683$	−0.949089	−0.0363159	−0.0181579	−	0.999835i	$-0.505780\pi$
$683$	−0.949089	−0.0363159	−0.0181579	+	0.999835i	$0.505780\pi$
$684$	−5.16193	−0.197371
$685$	−22.8939	−0.874733
$686$	1.06294	0.0405831
$687$	−4.80886	−0.183470
$688$	17.9702	0.685106
$689$	−0.426318	−0.0162414
$690$	−14.5414	−0.553583
$691$	10.2098	0.388401	0.194200	−	0.980962i	$-0.437789\pi$
$691$	10.2098	0.388401	0.194200	+	0.980962i	$0.437789\pi$
$692$	−4.47156	−0.169983
$693$	−0.131339	−0.00498915
$694$	−33.5095	−1.27200
$695$	−41.5331	−1.57544
$696$	−13.7960	−0.522937
$697$	75.7596	2.86960
$698$	19.8240	0.750351
$699$	21.9146	0.828888
$700$	0.0352510	0.00133236
$701$	31.1816	1.17771	0.588856	−	0.808238i	$-0.299578\pi$
$701$	31.1816	1.17771	0.588856	+	0.808238i	$0.299578\pi$
$702$	19.5236	0.736872
$703$	−7.24843	−0.273380
$704$	8.90016	0.335437
$705$	9.78185	0.368406
$706$	−25.4717	−0.958641
$707$	−0.788263	−0.0296457
$708$	4.20841	0.158162
$709$	5.33044	0.200189	0.100095	−	0.994978i	$-0.468085\pi$
$709$	5.33044	0.200189	0.100095	+	0.994978i	$0.468085\pi$
$710$	5.99317	0.224920
$711$	5.74806	0.215569
$712$	−18.6455	−0.698771
$713$	−5.67538	−0.212545
$714$	0.511266	0.0191336
$715$	−6.35013	−0.237482
$716$	−10.7284	−0.400937
$717$	−16.2620	−0.607314
$718$	42.4053	1.58255
$719$	10.0752	0.375741	0.187870	−	0.982194i	$-0.439841\pi$
$719$	10.0752	0.375741	0.187870	+	0.982194i	$0.439841\pi$
$720$	12.1065	0.451182
$721$	−0.910680	−0.0339155
$722$	−12.7757	−0.475462
$723$	1.39222	0.0517774
$724$	0.901998	0.0335225
$725$	−6.46227	−0.240003
$726$	1.14494	0.0424927
$727$	3.28865	0.121969	0.0609846	−	0.998139i	$-0.480576\pi$
$727$	3.28865	0.121969	0.0609846	+	0.998139i	$0.480576\pi$
$728$	−0.613128	−0.0227240
$729$	8.41655	0.311724
$730$	0.468912	0.0173552
$731$	−45.1661	−1.67053
$732$	−3.83450	−0.141727
$733$	−2.25775	−0.0833920	−0.0416960	−	0.999130i	$-0.513276\pi$
$733$	−2.25775	−0.0833920	−0.0416960	+	0.999130i	$0.513276\pi$
$734$	−8.71982	−0.321854
$735$	12.3291	0.454766
$736$	16.2129	0.597615
$737$	2.52656	0.0930671
$738$	27.8106	1.02372
$739$	−4.67399	−0.171935	−0.0859677	−	0.996298i	$-0.527398\pi$
$739$	−4.67399	−0.171935	−0.0859677	+	0.996298i	$0.527398\pi$
$740$	−1.13898	−0.0418697
$741$	−16.3968	−0.602352
$742$	−0.00979421	−0.000359557 0
$743$	−43.3607	−1.59075	−0.795375	−	0.606118i	$-0.792726\pi$
$743$	−43.3607	−1.59075	−0.795375	+	0.606118i	$0.792726\pi$
$744$	−2.40035	−0.0880010
$745$	12.7874	0.468493
$746$	0.301734	0.0110472
$747$	24.9214	0.911826
$748$	−3.24580	−0.118678
$749$	−0.151830	−0.00554773
$750$	−13.8779	−0.506749
$751$	14.5019	0.529182	0.264591	−	0.964361i	$-0.414763\pi$
$751$	14.5019	0.529182	0.264591	+	0.964361i	$0.414763\pi$
$752$	16.2073	0.591018
$753$	13.3427	0.486236
$754$	20.3552	0.741294
$755$	−44.0076	−1.60160
$756$	−0.127356	−0.00463189
$757$	44.9801	1.63483	0.817415	−	0.576050i	$-0.195407\pi$
$757$	44.9801	1.63483	0.817415	+	0.576050i	$0.195407\pi$
$758$	0.693804	0.0252001
$759$	6.06514	0.220151
$760$	−31.6611	−1.14847
$761$	50.1086	1.81644	0.908218	−	0.418497i	$-0.137443\pi$
$761$	50.1086	1.81644	0.908218	+	0.418497i	$0.137443\pi$
$762$	6.25764	0.226690
$763$	−0.954774	−0.0345652
$764$	3.22413	0.116645
$765$	−30.4284	−1.10014
$766$	−5.06763	−0.183101
$767$	−34.2869	−1.23803
$768$	9.22644	0.332931
$769$	−23.5737	−0.850091	−0.425046	−	0.905172i	$-0.639742\pi$
$769$	−23.5737	−0.850091	−0.425046	+	0.905172i	$0.639742\pi$
$770$	−0.145888	−0.00525742
$771$	−12.1994	−0.439349
$772$	−11.1329	−0.400682
$773$	44.5000	1.60055	0.800276	−	0.599632i	$-0.204686\pi$
$773$	44.5000	1.60055	0.800276	+	0.599632i	$0.204686\pi$
$774$	−16.5800	−0.595956
$775$	−1.12436	−0.0403881
$776$	11.7871	0.423131
$777$	−0.0748297	−0.00268450
$778$	3.92775	0.140817
$779$	−55.8195	−1.99994
$780$	−2.57651	−0.0922538
$781$	−2.49971	−0.0894466
$782$	60.5560	2.16548
$783$	23.3471	0.834357
$784$	20.4277	0.729562
$785$	−18.3370	−0.654474
$786$	1.14494	0.0408386
$787$	44.7458	1.59502	0.797508	−	0.603308i	$-0.206151\pi$
$787$	44.7458	1.59502	0.797508	+	0.603308i	$0.206151\pi$
$788$	1.36165	0.0485069
$789$	7.99155	0.284507
$790$	6.38478	0.227160
$791$	−0.553414	−0.0196771
$792$	−6.57935	−0.233787
$793$	31.2406	1.10939
$794$	−41.6938	−1.47966
$795$	−0.227268	−0.00806037
$796$	1.22193	0.0433101
$797$	−18.3716	−0.650754	−0.325377	−	0.945584i	$-0.605491\pi$
$797$	−18.3716	−0.650754	−0.325377	+	0.945584i	$0.605491\pi$
$798$	−0.376699	−0.0133350
$799$	−40.7353	−1.44111
$800$	3.21196	0.113560
$801$	13.2031	0.466510
$802$	−17.6369	−0.622781
$803$	−0.195580	−0.00690187
$804$	1.02513	0.0361535
$805$	−0.772816	−0.0272382
$806$	3.54157	0.124747
$807$	−0.703203	−0.0247539
$808$	−39.4876	−1.38917
$809$	9.74202	0.342511	0.171256	−	0.985227i	$-0.445218\pi$
$809$	9.74202	0.342511	0.171256	+	0.985227i	$0.445218\pi$
$810$	−5.11700	−0.179793
$811$	−13.3699	−0.469482	−0.234741	−	0.972058i	$-0.575424\pi$
$811$	−13.3699	−0.469482	−0.234741	+	0.972058i	$0.575424\pi$
$812$	−0.132781	−0.00465968
$813$	14.9145	0.523076
$814$	−1.67312	−0.0586427
$815$	21.4809	0.752444
$816$	19.6564	0.688113
$817$	33.2783	1.16426
$818$	−20.6118	−0.720676
$819$	0.434163	0.0151709
$820$	−8.77118	−0.306303
$821$	31.0451	1.08348	0.541741	−	0.840545i	$-0.317765\pi$
$821$	31.0451	1.08348	0.541741	+	0.840545i	$0.317765\pi$
$822$	−13.6452	−0.475930
$823$	−34.7339	−1.21075	−0.605373	−	0.795942i	$-0.706976\pi$
$823$	−34.7339	−1.21075	−0.605373	+	0.795942i	$0.706976\pi$
$824$	−45.6200	−1.58925
$825$	1.20157	0.0418334
$826$	−0.787705	−0.0274078
$827$	−16.6327	−0.578377	−0.289188	−	0.957272i	$-0.593385\pi$
$827$	−16.6327	−0.578377	−0.289188	+	0.957272i	$0.593385\pi$
$828$	−6.31179	−0.219350
$829$	−17.9926	−0.624910	−0.312455	−	0.949933i	$-0.601151\pi$
$829$	−17.9926	−0.624910	−0.312455	+	0.949933i	$0.601151\pi$
$830$	27.6820	0.960856
$831$	−8.19521	−0.284289
$832$	−29.4209	−1.01999
$833$	−51.3430	−1.77893
$834$	−24.7544	−0.857175
$835$	−17.1385	−0.593103
$836$	2.39150	0.0827117
$837$	4.06212	0.140407
$838$	10.8226	0.373862
$839$	23.4382	0.809176	0.404588	−	0.914499i	$-0.367415\pi$
$839$	23.4382	0.809176	0.404588	+	0.914499i	$0.367415\pi$
$840$	−0.326855	−0.0112776
$841$	−4.65846	−0.160636
$842$	−19.6845	−0.678371
$843$	24.7533	0.852548
$844$	−0.930048	−0.0320136
$845$	−3.98139	−0.136964
$846$	−14.9535	−0.514112
$847$	0.0608487	0.00209079
$848$	−0.376554	−0.0129309
$849$	−12.7786	−0.438559
$850$	11.9968	0.411488
$851$	−8.86307	−0.303822
$852$	−1.01423	−0.0347471
$853$	4.07659	0.139580	0.0697898	−	0.997562i	$-0.477767\pi$
$853$	4.07659	0.139580	0.0697898	+	0.997562i	$0.477767\pi$
$854$	0.717719	0.0245598
$855$	22.4196	0.766733
$856$	−7.60581	−0.259961
$857$	−48.5123	−1.65715	−0.828574	−	0.559880i	$-0.810847\pi$
$857$	−48.5123	−1.65715	−0.828574	+	0.559880i	$0.810847\pi$
$858$	−3.78479	−0.129211
$859$	−22.6967	−0.774401	−0.387201	−	0.921995i	$-0.626558\pi$
$859$	−22.6967	−0.774401	−0.387201	+	0.921995i	$0.626558\pi$
$860$	5.22917	0.178313
$861$	−0.576256	−0.0196388
$862$	−32.2240	−1.09755
$863$	10.4169	0.354597	0.177298	−	0.984157i	$-0.443264\pi$
$863$	10.4169	0.354597	0.177298	+	0.984157i	$0.443264\pi$
$864$	−11.6043	−0.394786
$865$	19.4211	0.660337
$866$	−16.9569	−0.576218
$867$	−33.8093	−1.14822
$868$	−0.0231023	−0.000784142 0
$869$	−2.66305	−0.0903377
$870$	10.8513	0.367893
$871$	−8.35197	−0.282996
$872$	−47.8289	−1.61969
$873$	−8.34655	−0.282488
$874$	−44.6175	−1.50921
$875$	−0.737551	−0.0249338
$876$	−0.0793548	−0.00268115
$877$	16.0795	0.542968	0.271484	−	0.962443i	$-0.412486\pi$
$877$	16.0795	0.542968	0.271484	+	0.962443i	$0.412486\pi$
$878$	46.6450	1.57419
$879$	0.0505663	0.00170556
$880$	−5.60888	−0.189075
$881$	15.1934	0.511878	0.255939	−	0.966693i	$-0.417615\pi$
$881$	15.1934	0.511878	0.255939	+	0.966693i	$0.417615\pi$
$882$	−18.8475	−0.634628
$883$	14.4458	0.486140	0.243070	−	0.970009i	$-0.421846\pi$
$883$	14.4458	0.486140	0.243070	+	0.970009i	$0.421846\pi$
$884$	10.7295	0.360873
$885$	−18.2782	−0.614414
$886$	30.7425	1.03281
$887$	−28.5251	−0.957781	−0.478890	−	0.877875i	$-0.658961\pi$
$887$	−28.5251	−0.957781	−0.478890	+	0.877875i	$0.658961\pi$
$888$	−3.74855	−0.125793
$889$	0.332567	0.0111539
$890$	14.6657	0.491594
$891$	2.13427	0.0715007
$892$	0.852388	0.0285401
$893$	30.0136	1.00437
$894$	7.62149	0.254901
$895$	46.5959	1.55753
$896$	−0.377486	−0.0126109
$897$	−20.0493	−0.669427
$898$	13.6708	0.456200
$899$	4.23514	0.141250
$900$	−1.25044	−0.0416813
$901$	0.946429	0.0315301
$902$	−12.8845	−0.429007
$903$	0.343550	0.0114326
$904$	−27.7229	−0.922051
$905$	−3.91760	−0.130225
$906$	−26.2293	−0.871410
$907$	2.07179	0.0687926	0.0343963	−	0.999408i	$-0.489049\pi$
$907$	2.07179	0.0687926	0.0343963	+	0.999408i	$0.489049\pi$
$908$	1.64294	0.0545230
$909$	27.9616	0.927428
$910$	0.482255	0.0159866
$911$	−8.35287	−0.276743	−0.138371	−	0.990380i	$-0.544187\pi$
$911$	−8.35287	−0.276743	−0.138371	+	0.990380i	$0.544187\pi$
$912$	−14.4828	−0.479574
$913$	−11.5460	−0.382116
$914$	20.8824	0.690729
$915$	16.6542	0.550571
$916$	−2.31853	−0.0766063
$917$	0.0608487	0.00200940
$918$	−43.3426	−1.43052
$919$	32.4147	1.06926	0.534631	−	0.845086i	$-0.320451\pi$
$919$	32.4147	1.06926	0.534631	+	0.845086i	$0.320451\pi$
$920$	−38.7138	−1.27636
$921$	16.0636	0.529314
$922$	30.5407	1.00580
$923$	8.26320	0.271987
$924$	0.0246888	0.000812202 0
$925$	−1.75588	−0.0577328
$926$	−26.2699	−0.863281
$927$	32.3040	1.06100
$928$	−12.0986	−0.397154
$929$	−7.47363	−0.245202	−0.122601	−	0.992456i	$-0.539123\pi$
$929$	−7.47363	−0.245202	−0.122601	+	0.992456i	$0.539123\pi$
$930$	1.88799	0.0619097
$931$	37.8294	1.23981
$932$	10.5658	0.346095
$933$	1.05489	0.0345356
$934$	21.8302	0.714307
$935$	14.0973	0.461032
$936$	21.7491	0.710892
$937$	−23.2842	−0.760663	−0.380332	−	0.924850i	$-0.624190\pi$
$937$	−23.2842	−0.760663	−0.380332	+	0.924850i	$0.624190\pi$
$938$	−0.191878	−0.00626503
$939$	−29.5237	−0.963468
$940$	4.71618	0.153825
$941$	−14.0726	−0.458755	−0.229378	−	0.973338i	$-0.573669\pi$
$941$	−14.0726	−0.458755	−0.229378	+	0.973338i	$0.573669\pi$
$942$	−10.9291	−0.356090
$943$	−68.2537	−2.22264
$944$	−30.2846	−0.985679
$945$	0.553139	0.0179936
$946$	7.68144	0.249745
$947$	12.9417	0.420550	0.210275	−	0.977642i	$-0.432564\pi$
$947$	12.9417	0.420550	0.210275	+	0.977642i	$0.432564\pi$
$948$	−1.08051	−0.0350932
$949$	0.646522	0.0209870
$950$	−8.83924	−0.286783
$951$	−24.8064	−0.804401
$952$	1.36115	0.0441150
$953$	−19.6500	−0.636525	−0.318263	−	0.948003i	$-0.603099\pi$
$953$	−19.6500	−0.636525	−0.318263	+	0.948003i	$0.603099\pi$
$954$	0.347424	0.0112483
$955$	−14.0032	−0.453133
$956$	−7.84048	−0.253579
$957$	−4.52599	−0.146304
$958$	−16.7077	−0.539800
$959$	−0.725184	−0.0234174
$960$	−15.6842	−0.506204
$961$	−30.2631	−0.976230
$962$	5.53076	0.178319
$963$	5.38576	0.173554
$964$	0.671242	0.0216192
$965$	48.3530	1.55654
$966$	−0.460612	−0.0148199
$967$	28.1886	0.906485	0.453243	−	0.891387i	$-0.350267\pi$
$967$	28.1886	0.906485	0.453243	+	0.891387i	$0.350267\pi$
$968$	3.04818	0.0979722
$969$	36.4010	1.16937
$970$	−9.27111	−0.297677
$971$	45.3454	1.45520	0.727602	−	0.686000i	$-0.240635\pi$
$971$	45.3454	1.45520	0.727602	+	0.686000i	$0.240635\pi$
$972$	7.14494	0.229174
$973$	−1.31559	−0.0421760
$974$	46.4283	1.48766
$975$	−3.97200	−0.127206
$976$	27.5938	0.883258
$977$	−30.2766	−0.968634	−0.484317	−	0.874892i	$-0.660932\pi$
$977$	−30.2766	−0.968634	−0.484317	+	0.874892i	$0.660932\pi$
$978$	12.8030	0.409394
$979$	−6.11694	−0.195498
$980$	5.94431	0.189884
$981$	33.8682	1.08133
$982$	−3.99958	−0.127632
$983$	22.3700	0.713493	0.356747	−	0.934201i	$-0.383886\pi$
$983$	22.3700	0.713493	0.356747	+	0.934201i	$0.383886\pi$
$984$	−28.8672	−0.920253
$985$	−5.91400	−0.188436
$986$	−45.1887	−1.43910
$987$	0.309848	0.00986257
$988$	−7.90549	−0.251507
$989$	40.6912	1.29391
$990$	5.17499	0.164472
$991$	−25.5946	−0.813039	−0.406520	−	0.913642i	$-0.633258\pi$
$991$	−25.5946	−0.813039	−0.406520	+	0.913642i	$0.633258\pi$
$992$	−2.10501	−0.0668340
$993$	−0.508623	−0.0161406
$994$	0.189838	0.00602130
$995$	−5.30714	−0.168248
$996$	−4.68467	−0.148439
$997$	−33.5656	−1.06303	−0.531517	−	0.847048i	$-0.678378\pi$
$997$	−33.5656	−1.06303	−0.531517	+	0.847048i	$0.678378\pi$
$998$	18.5111	0.585959
$999$	6.34369	0.200705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.c.1.9	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.c.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-1.24808 q^{2} -0.917360 q^{3} -0.442292 q^{4} +1.92098 q^{5} +1.14494 q^{6} +0.0608487 q^{7} +3.04818 q^{8} -2.15845 q^{9} +O(q^{10})\)	\(q-1.24808 q^{2} -0.917360 q^{3} -0.442292 q^{4} +1.92098 q^{5} +1.14494 q^{6} +0.0608487 q^{7} +3.04818 q^{8} -2.15845 q^{9} -2.39755 q^{10} +1.00000 q^{11} +0.405741 q^{12} -3.30567 q^{13} -0.0759442 q^{14} -1.76223 q^{15} -2.91979 q^{16} +7.33860 q^{17} +2.69392 q^{18} -5.40706 q^{19} -0.849636 q^{20} -0.0558201 q^{21} -1.24808 q^{22} -6.61152 q^{23} -2.79628 q^{24} -1.30982 q^{25} +4.12574 q^{26} +4.73215 q^{27} -0.0269129 q^{28} +4.93371 q^{29} +2.19941 q^{30} +0.858408 q^{31} -2.45222 q^{32} -0.917360 q^{33} -9.15917 q^{34} +0.116889 q^{35} +0.954666 q^{36} +1.34055 q^{37} +6.74845 q^{38} +3.03248 q^{39} +5.85551 q^{40} +10.3234 q^{41} +0.0696681 q^{42} -6.15460 q^{43} -0.442292 q^{44} -4.14635 q^{45} +8.25171 q^{46} -5.55083 q^{47} +2.67850 q^{48} -6.99630 q^{49} +1.63476 q^{50} -6.73213 q^{51} +1.46207 q^{52} +0.128966 q^{53} -5.90612 q^{54} +1.92098 q^{55} +0.185478 q^{56} +4.96022 q^{57} -6.15768 q^{58} +10.3722 q^{59} +0.779422 q^{60} -9.45062 q^{61} -1.07136 q^{62} -0.131339 q^{63} +8.90016 q^{64} -6.35013 q^{65} +1.14494 q^{66} +2.52656 q^{67} -3.24580 q^{68} +6.06514 q^{69} -0.145888 q^{70} -2.49971 q^{71} -6.57935 q^{72} -0.195580 q^{73} -1.67312 q^{74} +1.20157 q^{75} +2.39150 q^{76} +0.0608487 q^{77} -3.78479 q^{78} -2.66305 q^{79} -5.60888 q^{80} +2.13427 q^{81} -12.8845 q^{82} -11.5460 q^{83} +0.0246888 q^{84} +14.0973 q^{85} +7.68144 q^{86} -4.52599 q^{87} +3.04818 q^{88} -6.11694 q^{89} +5.17499 q^{90} -0.201145 q^{91} +2.92422 q^{92} -0.787469 q^{93} +6.92788 q^{94} -10.3869 q^{95} +2.24957 q^{96} +3.86692 q^{97} +8.73195 q^{98} -2.15845 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * q^98 + 12 * q^99

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