LMFDB - Embedded newform 4029.2.a.g.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.05356 q^{2} -1.00000 q^{3} +2.21711 q^{4} +2.39106 q^{5} -2.05356 q^{6} -1.51026 q^{7} +0.445844 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.05356 q^{2} -1.00000 q^{3} +2.21711 q^{4} +2.39106 q^{5} -2.05356 q^{6} -1.51026 q^{7} +0.445844 q^{8} +1.00000 q^{9} +4.91018 q^{10} -2.78834 q^{11} -2.21711 q^{12} -0.181133 q^{13} -3.10141 q^{14} -2.39106 q^{15} -3.51865 q^{16} -1.00000 q^{17} +2.05356 q^{18} -3.91990 q^{19} +5.30123 q^{20} +1.51026 q^{21} -5.72602 q^{22} -4.57577 q^{23} -0.445844 q^{24} +0.717149 q^{25} -0.371967 q^{26} -1.00000 q^{27} -3.34841 q^{28} +9.05512 q^{29} -4.91018 q^{30} -2.12427 q^{31} -8.11744 q^{32} +2.78834 q^{33} -2.05356 q^{34} -3.61111 q^{35} +2.21711 q^{36} -6.08335 q^{37} -8.04974 q^{38} +0.181133 q^{39} +1.06604 q^{40} -5.06774 q^{41} +3.10141 q^{42} +8.63148 q^{43} -6.18205 q^{44} +2.39106 q^{45} -9.39663 q^{46} -9.44321 q^{47} +3.51865 q^{48} -4.71912 q^{49} +1.47271 q^{50} +1.00000 q^{51} -0.401591 q^{52} -7.84040 q^{53} -2.05356 q^{54} -6.66708 q^{55} -0.673339 q^{56} +3.91990 q^{57} +18.5952 q^{58} +0.195899 q^{59} -5.30123 q^{60} +1.69383 q^{61} -4.36232 q^{62} -1.51026 q^{63} -9.63236 q^{64} -0.433099 q^{65} +5.72602 q^{66} +8.22662 q^{67} -2.21711 q^{68} +4.57577 q^{69} -7.41564 q^{70} -1.96527 q^{71} +0.445844 q^{72} -5.81994 q^{73} -12.4925 q^{74} -0.717149 q^{75} -8.69083 q^{76} +4.21111 q^{77} +0.371967 q^{78} -1.00000 q^{79} -8.41329 q^{80} +1.00000 q^{81} -10.4069 q^{82} +15.7350 q^{83} +3.34841 q^{84} -2.39106 q^{85} +17.7253 q^{86} -9.05512 q^{87} -1.24316 q^{88} -14.2542 q^{89} +4.91018 q^{90} +0.273557 q^{91} -10.1450 q^{92} +2.12427 q^{93} -19.3922 q^{94} -9.37269 q^{95} +8.11744 q^{96} +4.86229 q^{97} -9.69099 q^{98} -2.78834 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * 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 $

$2$	2.05356	1.45209	0.726043	−	0.687649i	$-0.241357\pi$
$2$	2.05356	1.45209	0.726043	+	0.687649i	$0.241357\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.21711	1.10855
$5$	2.39106	1.06931	0.534656	−	0.845070i	$-0.320441\pi$
$5$	2.39106	1.06931	0.534656	+	0.845070i	$0.320441\pi$
$6$	−2.05356	−0.838362
$7$	−1.51026	−0.570824	−0.285412	−	0.958405i	$-0.592130\pi$
$7$	−1.51026	−0.570824	−0.285412	+	0.958405i	$0.592130\pi$
$8$	0.445844	0.157630
$9$	1.00000	0.333333
$10$	4.91018	1.55273
$11$	−2.78834	−0.840716	−0.420358	−	0.907358i	$-0.638096\pi$
$11$	−2.78834	−0.840716	−0.420358	+	0.907358i	$0.638096\pi$
$12$	−2.21711	−0.640024
$13$	−0.181133	−0.0502372	−0.0251186	−	0.999684i	$-0.507996\pi$
$13$	−0.181133	−0.0502372	−0.0251186	+	0.999684i	$0.507996\pi$
$14$	−3.10141	−0.828886
$15$	−2.39106	−0.617368
$16$	−3.51865	−0.879662
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.05356	0.484029
$19$	−3.91990	−0.899286	−0.449643	−	0.893208i	$-0.648449\pi$
$19$	−3.91990	−0.899286	−0.449643	+	0.893208i	$0.648449\pi$
$20$	5.30123	1.18539
$21$	1.51026	0.329565
$22$	−5.72602	−1.22079
$23$	−4.57577	−0.954115	−0.477057	−	0.878872i	$-0.658297\pi$
$23$	−4.57577	−0.954115	−0.477057	+	0.878872i	$0.658297\pi$
$24$	−0.445844	−0.0910075
$25$	0.717149	0.143430
$26$	−0.371967	−0.0729488
$27$	−1.00000	−0.192450
$28$	−3.34841	−0.632789
$29$	9.05512	1.68149	0.840747	−	0.541428i	$-0.182116\pi$
$29$	9.05512	1.68149	0.840747	+	0.541428i	$0.182116\pi$
$30$	−4.91018	−0.896471
$31$	−2.12427	−0.381530	−0.190765	−	0.981636i	$-0.561097\pi$
$31$	−2.12427	−0.381530	−0.190765	+	0.981636i	$0.561097\pi$
$32$	−8.11744	−1.43497
$33$	2.78834	0.485388
$34$	−2.05356	−0.352183
$35$	−3.61111	−0.610389
$36$	2.21711	0.369518
$37$	−6.08335	−1.00010	−0.500048	−	0.865998i	$-0.666684\pi$
$37$	−6.08335	−1.00010	−0.500048	+	0.865998i	$0.666684\pi$
$38$	−8.04974	−1.30584
$39$	0.181133	0.0290045
$40$	1.06604	0.168555
$41$	−5.06774	−0.791449	−0.395724	−	0.918369i	$-0.629506\pi$
$41$	−5.06774	−0.791449	−0.395724	+	0.918369i	$0.629506\pi$
$42$	3.10141	0.478557
$43$	8.63148	1.31629	0.658144	−	0.752892i	$-0.271342\pi$
$43$	8.63148	1.31629	0.658144	+	0.752892i	$0.271342\pi$
$44$	−6.18205	−0.931979
$45$	2.39106	0.356438
$46$	−9.39663	−1.38546
$47$	−9.44321	−1.37743	−0.688717	−	0.725030i	$-0.741826\pi$
$47$	−9.44321	−1.37743	−0.688717	+	0.725030i	$0.741826\pi$
$48$	3.51865	0.507873
$49$	−4.71912	−0.674160
$50$	1.47271	0.208272
$51$	1.00000	0.140028
$52$	−0.401591	−0.0556907
$53$	−7.84040	−1.07696	−0.538481	−	0.842638i	$-0.681002\pi$
$53$	−7.84040	−1.07696	−0.538481	+	0.842638i	$0.681002\pi$
$54$	−2.05356	−0.279454
$55$	−6.66708	−0.898988
$56$	−0.673339	−0.0899787
$57$	3.91990	0.519203
$58$	18.5952	2.44167
$59$	0.195899	0.0255038	0.0127519	−	0.999919i	$-0.495941\pi$
$59$	0.195899	0.0255038	0.0127519	+	0.999919i	$0.495941\pi$
$60$	−5.30123	−0.684386
$61$	1.69383	0.216873	0.108437	−	0.994103i	$-0.465416\pi$
$61$	1.69383	0.216873	0.108437	+	0.994103i	$0.465416\pi$
$62$	−4.36232	−0.554015
$63$	−1.51026	−0.190275
$64$	−9.63236	−1.20404
$65$	−0.433099	−0.0537193
$66$	5.72602	0.704825
$67$	8.22662	1.00504	0.502521	−	0.864565i	$-0.332406\pi$
$67$	8.22662	1.00504	0.502521	+	0.864565i	$0.332406\pi$
$68$	−2.21711	−0.268864
$69$	4.57577	0.550859
$70$	−7.41564	−0.886338
$71$	−1.96527	−0.233234	−0.116617	−	0.993177i	$-0.537205\pi$
$71$	−1.96527	−0.233234	−0.116617	+	0.993177i	$0.537205\pi$
$72$	0.445844	0.0525432
$73$	−5.81994	−0.681172	−0.340586	−	0.940213i	$-0.610625\pi$
$73$	−5.81994	−0.681172	−0.340586	+	0.940213i	$0.610625\pi$
$74$	−12.4925	−1.45223
$75$	−0.717149	−0.0828093
$76$	−8.69083	−0.996907
$77$	4.21111	0.479901
$78$	0.371967	0.0421170
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−8.41329	−0.940634
$81$	1.00000	0.111111
$82$	−10.4069	−1.14925
$83$	15.7350	1.72714	0.863572	−	0.504225i	$-0.168222\pi$
$83$	15.7350	1.72714	0.863572	+	0.504225i	$0.168222\pi$
$84$	3.34841	0.365341
$85$	−2.39106	−0.259346
$86$	17.7253	1.91136
$87$	−9.05512	−0.970811
$88$	−1.24316	−0.132522
$89$	−14.2542	−1.51095	−0.755474	−	0.655179i	$-0.772593\pi$
$89$	−14.2542	−1.51095	−0.755474	+	0.655179i	$0.772593\pi$
$90$	4.91018	0.517578
$91$	0.273557	0.0286766
$92$	−10.1450	−1.05769
$93$	2.12427	0.220277
$94$	−19.3922	−2.00015
$95$	−9.37269	−0.961618
$96$	8.11744	0.828483
$97$	4.86229	0.493691	0.246845	−	0.969055i	$-0.420606\pi$
$97$	4.86229	0.493691	0.246845	+	0.969055i	$0.420606\pi$
$98$	−9.69099	−0.978938
$99$	−2.78834	−0.280239
$100$	1.59000	0.159000
$101$	13.3103	1.32442	0.662210	−	0.749318i	$-0.269619\pi$
$101$	13.3103	1.32442	0.662210	+	0.749318i	$0.269619\pi$
$102$	2.05356	0.203333
$103$	−7.97839	−0.786134	−0.393067	−	0.919510i	$-0.628586\pi$
$103$	−7.97839	−0.786134	−0.393067	+	0.919510i	$0.628586\pi$
$104$	−0.0807570	−0.00791887
$105$	3.61111	0.352408
$106$	−16.1007	−1.56384
$107$	−1.96835	−0.190287	−0.0951436	−	0.995464i	$-0.530331\pi$
$107$	−1.96835	−0.190287	−0.0951436	+	0.995464i	$0.530331\pi$
$108$	−2.21711	−0.213341
$109$	7.40813	0.709570	0.354785	−	0.934948i	$-0.384554\pi$
$109$	7.40813	0.709570	0.354785	+	0.934948i	$0.384554\pi$
$110$	−13.6912	−1.30541
$111$	6.08335	0.577406
$112$	5.31407	0.502132
$113$	3.27302	0.307900	0.153950	−	0.988079i	$-0.450801\pi$
$113$	3.27302	0.307900	0.153950	+	0.988079i	$0.450801\pi$
$114$	8.04974	0.753927
$115$	−10.9409	−1.02025
$116$	20.0762	1.86403
$117$	−0.181133	−0.0167457
$118$	0.402290	0.0370338
$119$	1.51026	0.138445
$120$	−1.06604	−0.0973155
$121$	−3.22516	−0.293196
$122$	3.47839	0.314918
$123$	5.06774	0.456943
$124$	−4.70974	−0.422947
$125$	−10.2405	−0.915941
$126$	−3.10141	−0.276295
$127$	−13.4948	−1.19747	−0.598734	−	0.800948i	$-0.704329\pi$
$127$	−13.4948	−1.19747	−0.598734	+	0.800948i	$0.704329\pi$
$128$	−3.54573	−0.313402
$129$	−8.63148	−0.759960
$130$	−0.889395	−0.0780051
$131$	0.933728	0.0815802	0.0407901	−	0.999168i	$-0.487012\pi$
$131$	0.933728	0.0815802	0.0407901	+	0.999168i	$0.487012\pi$
$132$	6.18205	0.538078
$133$	5.92005	0.513334
$134$	16.8939	1.45941
$135$	−2.39106	−0.205789
$136$	−0.445844	−0.0382308
$137$	−3.29779	−0.281749	−0.140874	−	0.990027i	$-0.544991\pi$
$137$	−3.29779	−0.281749	−0.140874	+	0.990027i	$0.544991\pi$
$138$	9.39663	0.799894
$139$	−9.91913	−0.841329	−0.420665	−	0.907216i	$-0.638203\pi$
$139$	−9.91913	−0.841329	−0.420665	+	0.907216i	$0.638203\pi$
$140$	−8.00623	−0.676650
$141$	9.44321	0.795262
$142$	−4.03580	−0.338677
$143$	0.505060	0.0422352
$144$	−3.51865	−0.293221
$145$	21.6513	1.79804
$146$	−11.9516	−0.989120
$147$	4.71912	0.389226
$148$	−13.4874	−1.10866
$149$	18.1198	1.48443	0.742217	−	0.670160i	$-0.233775\pi$
$149$	18.1198	1.48443	0.742217	+	0.670160i	$0.233775\pi$
$150$	−1.47271	−0.120246
$151$	−4.55154	−0.370399	−0.185200	−	0.982701i	$-0.559293\pi$
$151$	−4.55154	−0.370399	−0.185200	+	0.982701i	$0.559293\pi$
$152$	−1.74766	−0.141754
$153$	−1.00000	−0.0808452
$154$	8.64777	0.696857
$155$	−5.07925	−0.407975
$156$	0.401591	0.0321530
$157$	10.5757	0.844031	0.422016	−	0.906589i	$-0.361323\pi$
$157$	10.5757	0.844031	0.422016	+	0.906589i	$0.361323\pi$
$158$	−2.05356	−0.163372
$159$	7.84040	0.621784
$160$	−19.4093	−1.53444
$161$	6.91060	0.544632
$162$	2.05356	0.161343
$163$	−9.59964	−0.751902	−0.375951	−	0.926640i	$-0.622684\pi$
$163$	−9.59964	−0.751902	−0.375951	+	0.926640i	$0.622684\pi$
$164$	−11.2357	−0.877363
$165$	6.66708	0.519031
$166$	32.3128	2.50796
$167$	13.6843	1.05893	0.529463	−	0.848333i	$-0.322394\pi$
$167$	13.6843	1.05893	0.529463	+	0.848333i	$0.322394\pi$
$168$	0.673339	0.0519492
$169$	−12.9672	−0.997476
$170$	−4.91018	−0.376593
$171$	−3.91990	−0.299762
$172$	19.1369	1.45918
$173$	5.20890	0.396025	0.198013	−	0.980199i	$-0.436551\pi$
$173$	5.20890	0.396025	0.198013	+	0.980199i	$0.436551\pi$
$174$	−18.5952	−1.40970
$175$	−1.08308	−0.0818732
$176$	9.81119	0.739546
$177$	−0.195899	−0.0147246
$178$	−29.2719	−2.19403
$179$	−14.3798	−1.07479	−0.537397	−	0.843329i	$-0.680592\pi$
$179$	−14.3798	−1.07479	−0.537397	+	0.843329i	$0.680592\pi$
$180$	5.30123	0.395130
$181$	25.8488	1.92133	0.960665	−	0.277711i	$-0.0895759\pi$
$181$	25.8488	1.92133	0.960665	+	0.277711i	$0.0895759\pi$
$182$	0.561767	0.0416409
$183$	−1.69383	−0.125212
$184$	−2.04008	−0.150397
$185$	−14.5456	−1.06942
$186$	4.36232	0.319860
$187$	2.78834	0.203904
$188$	−20.9366	−1.52696
$189$	1.51026	0.109855
$190$	−19.2474	−1.39635
$191$	−22.3731	−1.61886	−0.809431	−	0.587215i	$-0.800224\pi$
$191$	−22.3731	−1.61886	−0.809431	+	0.587215i	$0.800224\pi$
$192$	9.63236	0.695155
$193$	20.2197	1.45544	0.727722	−	0.685872i	$-0.240579\pi$
$193$	20.2197	1.45544	0.727722	+	0.685872i	$0.240579\pi$
$194$	9.98500	0.716881
$195$	0.433099	0.0310149
$196$	−10.4628	−0.747343
$197$	−6.16167	−0.439001	−0.219500	−	0.975612i	$-0.570443\pi$
$197$	−6.16167	−0.439001	−0.219500	+	0.975612i	$0.570443\pi$
$198$	−5.72602	−0.406931
$199$	−16.9449	−1.20119	−0.600595	−	0.799554i	$-0.705069\pi$
$199$	−16.9449	−1.20119	−0.600595	+	0.799554i	$0.705069\pi$
$200$	0.319736	0.0226088
$201$	−8.22662	−0.580261
$202$	27.3334	1.92317
$203$	−13.6756	−0.959837
$204$	2.21711	0.155229
$205$	−12.1173	−0.846306
$206$	−16.3841	−1.14153
$207$	−4.57577	−0.318038
$208$	0.637343	0.0441918
$209$	10.9300	0.756044
$210$	7.41564	0.511727
$211$	3.94974	0.271911	0.135956	−	0.990715i	$-0.456590\pi$
$211$	3.94974	0.271911	0.135956	+	0.990715i	$0.456590\pi$
$212$	−17.3830	−1.19387
$213$	1.96527	0.134658
$214$	−4.04212	−0.276313
$215$	20.6384	1.40752
$216$	−0.445844	−0.0303358
$217$	3.20820	0.217787
$218$	15.2130	1.03036
$219$	5.81994	0.393275
$220$	−14.7816	−0.996577
$221$	0.181133	0.0121843
$222$	12.4925	0.838443
$223$	3.13691	0.210063	0.105032	−	0.994469i	$-0.466506\pi$
$223$	3.13691	0.210063	0.105032	+	0.994469i	$0.466506\pi$
$224$	12.2594	0.819118
$225$	0.717149	0.0478099
$226$	6.72134	0.447097
$227$	6.62160	0.439491	0.219745	−	0.975557i	$-0.429477\pi$
$227$	6.62160	0.439491	0.219745	+	0.975557i	$0.429477\pi$
$228$	8.69083	0.575564
$229$	23.4819	1.55173	0.775865	−	0.630899i	$-0.217314\pi$
$229$	23.4819	1.55173	0.775865	+	0.630899i	$0.217314\pi$
$230$	−22.4679	−1.48149
$231$	−4.21111	−0.277071
$232$	4.03717	0.265053
$233$	−6.14916	−0.402845	−0.201422	−	0.979504i	$-0.564556\pi$
$233$	−6.14916	−0.402845	−0.201422	+	0.979504i	$0.564556\pi$
$234$	−0.371967	−0.0243163
$235$	−22.5793	−1.47291
$236$	0.434329	0.0282724
$237$	1.00000	0.0649570
$238$	3.10141	0.201034
$239$	−11.6258	−0.752012	−0.376006	−	0.926617i	$-0.622703\pi$
$239$	−11.6258	−0.752012	−0.376006	+	0.926617i	$0.622703\pi$
$240$	8.41329	0.543075
$241$	3.83463	0.247010	0.123505	−	0.992344i	$-0.460586\pi$
$241$	3.83463	0.247010	0.123505	+	0.992344i	$0.460586\pi$
$242$	−6.62306	−0.425747
$243$	−1.00000	−0.0641500
$244$	3.75541	0.240416
$245$	−11.2837	−0.720888
$246$	10.4069	0.663521
$247$	0.710022	0.0451776
$248$	−0.947092	−0.0601404
$249$	−15.7350	−0.997167
$250$	−21.0296	−1.33003
$251$	−20.5169	−1.29502	−0.647508	−	0.762059i	$-0.724189\pi$
$251$	−20.5169	−1.29502	−0.647508	+	0.762059i	$0.724189\pi$
$252$	−3.34841	−0.210930
$253$	12.7588	0.802140
$254$	−27.7123	−1.73883
$255$	2.39106	0.149734
$256$	11.9833	0.748958
$257$	−4.65396	−0.290306	−0.145153	−	0.989409i	$-0.546367\pi$
$257$	−4.65396	−0.290306	−0.145153	+	0.989409i	$0.546367\pi$
$258$	−17.7253	−1.10353
$259$	9.18742	0.570879
$260$	−0.960227	−0.0595508
$261$	9.05512	0.560498
$262$	1.91747	0.118462
$263$	−24.8315	−1.53118	−0.765588	−	0.643331i	$-0.777552\pi$
$263$	−24.8315	−1.53118	−0.765588	+	0.643331i	$0.777552\pi$
$264$	1.24316	0.0765114
$265$	−18.7468	−1.15161
$266$	12.1572	0.745405
$267$	14.2542	0.872346
$268$	18.2393	1.11414
$269$	−7.59239	−0.462916	−0.231458	−	0.972845i	$-0.574350\pi$
$269$	−7.59239	−0.462916	−0.231458	+	0.972845i	$0.574350\pi$
$270$	−4.91018	−0.298824
$271$	−8.90576	−0.540986	−0.270493	−	0.962722i	$-0.587187\pi$
$271$	−8.90576	−0.540986	−0.270493	+	0.962722i	$0.587187\pi$
$272$	3.51865	0.213349
$273$	−0.273557	−0.0165565
$274$	−6.77220	−0.409124
$275$	−1.99966	−0.120584
$276$	10.1450	0.610656
$277$	19.9415	1.19817	0.599083	−	0.800687i	$-0.295532\pi$
$277$	19.9415	1.19817	0.599083	+	0.800687i	$0.295532\pi$
$278$	−20.3695	−1.22168
$279$	−2.12427	−0.127177
$280$	−1.60999	−0.0962154
$281$	25.8463	1.54186	0.770931	−	0.636918i	$-0.219791\pi$
$281$	25.8463	1.54186	0.770931	+	0.636918i	$0.219791\pi$
$282$	19.3922	1.15479
$283$	15.3465	0.912257	0.456128	−	0.889914i	$-0.349236\pi$
$283$	15.3465	0.912257	0.456128	+	0.889914i	$0.349236\pi$
$284$	−4.35721	−0.258553
$285$	9.37269	0.555190
$286$	1.03717	0.0613292
$287$	7.65360	0.451778
$288$	−8.11744	−0.478325
$289$	1.00000	0.0588235
$290$	44.4622	2.61091
$291$	−4.86229	−0.285032
$292$	−12.9034	−0.755116
$293$	−21.9587	−1.28284	−0.641420	−	0.767190i	$-0.721654\pi$
$293$	−21.9587	−1.28284	−0.641420	+	0.767190i	$0.721654\pi$
$294$	9.69099	0.565190
$295$	0.468405	0.0272716
$296$	−2.71222	−0.157645
$297$	2.78834	0.161796
$298$	37.2101	2.15552
$299$	0.828823	0.0479321
$300$	−1.59000	−0.0917985
$301$	−13.0358	−0.751369
$302$	−9.34686	−0.537852
$303$	−13.3103	−0.764655
$304$	13.7927	0.791068
$305$	4.05005	0.231905
$306$	−2.05356	−0.117394
$307$	−34.5091	−1.96954	−0.984770	−	0.173861i	$-0.944376\pi$
$307$	−34.5091	−1.96954	−0.984770	+	0.173861i	$0.944376\pi$
$308$	9.33649	0.531996
$309$	7.97839	0.453875
$310$	−10.4305	−0.592415
$311$	−35.0077	−1.98510	−0.992551	−	0.121831i	$-0.961123\pi$
$311$	−35.0077	−1.98510	−0.992551	+	0.121831i	$0.961123\pi$
$312$	0.0807570	0.00457196
$313$	6.91298	0.390745	0.195373	−	0.980729i	$-0.437408\pi$
$313$	6.91298	0.390745	0.195373	+	0.980729i	$0.437408\pi$
$314$	21.7178	1.22561
$315$	−3.61111	−0.203463
$316$	−2.21711	−0.124722
$317$	−8.86345	−0.497821	−0.248911	−	0.968526i	$-0.580073\pi$
$317$	−8.86345	−0.497821	−0.248911	+	0.968526i	$0.580073\pi$
$318$	16.1007	0.902884
$319$	−25.2488	−1.41366
$320$	−23.0315	−1.28750
$321$	1.96835	0.109862
$322$	14.1913	0.790852
$323$	3.91990	0.218109
$324$	2.21711	0.123173
$325$	−0.129899	−0.00720552
$326$	−19.7134	−1.09183
$327$	−7.40813	−0.409671
$328$	−2.25942	−0.124756
$329$	14.2617	0.786273
$330$	13.6912	0.753678
$331$	−30.8255	−1.69432	−0.847162	−	0.531335i	$-0.821690\pi$
$331$	−30.8255	−1.69432	−0.847162	+	0.531335i	$0.821690\pi$
$332$	34.8863	1.91463
$333$	−6.08335	−0.333365
$334$	28.1016	1.53765
$335$	19.6703	1.07470
$336$	−5.31407	−0.289906
$337$	7.02045	0.382428	0.191214	−	0.981548i	$-0.438758\pi$
$337$	7.02045	0.382428	0.191214	+	0.981548i	$0.438758\pi$
$338$	−26.6289	−1.44842
$339$	−3.27302	−0.177766
$340$	−5.30123	−0.287500
$341$	5.92319	0.320759
$342$	−8.04974	−0.435280
$343$	17.6989	0.955651
$344$	3.84829	0.207486
$345$	10.9409	0.589040
$346$	10.6968	0.575063
$347$	18.7308	1.00552	0.502760	−	0.864426i	$-0.332318\pi$
$347$	18.7308	1.00552	0.502760	+	0.864426i	$0.332318\pi$
$348$	−20.0762	−1.07620
$349$	−3.99166	−0.213669	−0.106834	−	0.994277i	$-0.534071\pi$
$349$	−3.99166	−0.213669	−0.106834	+	0.994277i	$0.534071\pi$
$350$	−2.22417	−0.118887
$351$	0.181133	0.00966816
$352$	22.6342	1.20641
$353$	−0.263197	−0.0140086	−0.00700428	−	0.999975i	$-0.502230\pi$
$353$	−0.263197	−0.0140086	−0.00700428	+	0.999975i	$0.502230\pi$
$354$	−0.402290	−0.0213815
$355$	−4.69907	−0.249401
$356$	−31.6032	−1.67497
$357$	−1.51026	−0.0799313
$358$	−29.5297	−1.56069
$359$	−1.26154	−0.0665818	−0.0332909	−	0.999446i	$-0.510599\pi$
$359$	−1.26154	−0.0665818	−0.0332909	+	0.999446i	$0.510599\pi$
$360$	1.06604	0.0561851
$361$	−3.63442	−0.191285
$362$	53.0821	2.78994
$363$	3.22516	0.169277
$364$	0.606506	0.0317896
$365$	−13.9158	−0.728386
$366$	−3.47839	−0.181818
$367$	13.7185	0.716099	0.358049	−	0.933703i	$-0.383442\pi$
$367$	13.7185	0.716099	0.358049	+	0.933703i	$0.383442\pi$
$368$	16.1005	0.839299
$369$	−5.06774	−0.263816
$370$	−29.8703	−1.55288
$371$	11.8410	0.614756
$372$	4.70974	0.244188
$373$	33.7680	1.74844	0.874219	−	0.485531i	$-0.161374\pi$
$373$	33.7680	1.74844	0.874219	+	0.485531i	$0.161374\pi$
$374$	5.72602	0.296086
$375$	10.2405	0.528819
$376$	−4.21020	−0.217124
$377$	−1.64018	−0.0844736
$378$	3.10141	0.159519
$379$	−0.264941	−0.0136091	−0.00680456	−	0.999977i	$-0.502166\pi$
$379$	−0.264941	−0.0136091	−0.00680456	+	0.999977i	$0.502166\pi$
$380$	−20.7803	−1.06600
$381$	13.4948	0.691359
$382$	−45.9445	−2.35073
$383$	20.1696	1.03062	0.515309	−	0.857005i	$-0.327677\pi$
$383$	20.1696	1.03062	0.515309	+	0.857005i	$0.327677\pi$
$384$	3.54573	0.180943
$385$	10.0690	0.513164
$386$	41.5223	2.11343
$387$	8.63148	0.438763
$388$	10.7802	0.547283
$389$	11.8740	0.602038	0.301019	−	0.953618i	$-0.402673\pi$
$389$	11.8740	0.602038	0.301019	+	0.953618i	$0.402673\pi$
$390$	0.889395	0.0450362
$391$	4.57577	0.231407
$392$	−2.10399	−0.106268
$393$	−0.933728	−0.0471004
$394$	−12.6534	−0.637467
$395$	−2.39106	−0.120307
$396$	−6.18205	−0.310660
$397$	28.5851	1.43464	0.717322	−	0.696741i	$-0.245368\pi$
$397$	28.5851	1.43464	0.717322	+	0.696741i	$0.245368\pi$
$398$	−34.7973	−1.74423
$399$	−5.92005	−0.296373
$400$	−2.52340	−0.126170
$401$	−4.51620	−0.225528	−0.112764	−	0.993622i	$-0.535970\pi$
$401$	−4.51620	−0.225528	−0.112764	+	0.993622i	$0.535970\pi$
$402$	−16.8939	−0.842589
$403$	0.384775	0.0191670
$404$	29.5103	1.46819
$405$	2.39106	0.118813
$406$	−28.0836	−1.39377
$407$	16.9624	0.840797
$408$	0.445844	0.0220726
$409$	−2.02441	−0.100101	−0.0500503	−	0.998747i	$-0.515938\pi$
$409$	−2.02441	−0.100101	−0.0500503	+	0.998747i	$0.515938\pi$
$410$	−24.8835	−1.22891
$411$	3.29779	0.162668
$412$	−17.6889	−0.871472
$413$	−0.295858	−0.0145582
$414$	−9.39663	−0.461819
$415$	37.6234	1.84686
$416$	1.47034	0.0720892
$417$	9.91913	0.485742
$418$	22.4454	1.09784
$419$	−19.2627	−0.941046	−0.470523	−	0.882388i	$-0.655935\pi$
$419$	−19.2627	−0.941046	−0.470523	+	0.882388i	$0.655935\pi$
$420$	8.00623	0.390664
$421$	15.9140	0.775603	0.387802	−	0.921743i	$-0.373235\pi$
$421$	15.9140	0.775603	0.387802	+	0.921743i	$0.373235\pi$
$422$	8.11103	0.394839
$423$	−9.44321	−0.459145
$424$	−3.49559	−0.169761
$425$	−0.717149	−0.0347868
$426$	4.03580	0.195535
$427$	−2.55813	−0.123796
$428$	−4.36404	−0.210944
$429$	−0.505060	−0.0243845
$430$	42.3821	2.04385
$431$	32.5552	1.56813	0.784064	−	0.620680i	$-0.213143\pi$
$431$	32.5552	1.56813	0.784064	+	0.620680i	$0.213143\pi$
$432$	3.51865	0.169291
$433$	−14.5318	−0.698352	−0.349176	−	0.937057i	$-0.613539\pi$
$433$	−14.5318	−0.698352	−0.349176	+	0.937057i	$0.613539\pi$
$434$	6.58822	0.316245
$435$	−21.6513	−1.03810
$436$	16.4246	0.786597
$437$	17.9366	0.858022
$438$	11.9516	0.571069
$439$	14.6123	0.697406	0.348703	−	0.937233i	$-0.386622\pi$
$439$	14.6123	0.697406	0.348703	+	0.937233i	$0.386622\pi$
$440$	−2.97247	−0.141707
$441$	−4.71912	−0.224720
$442$	0.371967	0.0176927
$443$	31.4998	1.49660	0.748300	−	0.663360i	$-0.230870\pi$
$443$	31.4998	1.49660	0.748300	+	0.663360i	$0.230870\pi$
$444$	13.4874	0.640085
$445$	−34.0827	−1.61568
$446$	6.44184	0.305030
$447$	−18.1198	−0.857038
$448$	14.5473	0.687298
$449$	−4.40103	−0.207698	−0.103849	−	0.994593i	$-0.533116\pi$
$449$	−4.40103	−0.207698	−0.103849	+	0.994593i	$0.533116\pi$
$450$	1.47271	0.0694242
$451$	14.1306	0.665384
$452$	7.25664	0.341324
$453$	4.55154	0.213850
$454$	13.5978	0.638178
$455$	0.654091	0.0306643
$456$	1.74766	0.0818417
$457$	−25.0212	−1.17044	−0.585221	−	0.810874i	$-0.698992\pi$
$457$	−25.0212	−1.17044	−0.585221	+	0.810874i	$0.698992\pi$
$458$	48.2216	2.25325
$459$	1.00000	0.0466760
$460$	−24.2572	−1.13100
$461$	5.41777	0.252331	0.126165	−	0.992009i	$-0.459733\pi$
$461$	5.41777	0.252331	0.126165	+	0.992009i	$0.459733\pi$
$462$	−8.64777	−0.402331
$463$	−2.42557	−0.112726	−0.0563629	−	0.998410i	$-0.517950\pi$
$463$	−2.42557	−0.112726	−0.0563629	+	0.998410i	$0.517950\pi$
$464$	−31.8618	−1.47915
$465$	5.07925	0.235545
$466$	−12.6277	−0.584965
$467$	27.4945	1.27229	0.636146	−	0.771568i	$-0.280527\pi$
$467$	27.4945	1.27229	0.636146	+	0.771568i	$0.280527\pi$
$468$	−0.401591	−0.0185636
$469$	−12.4243	−0.573702
$470$	−46.3678	−2.13879
$471$	−10.5757	−0.487302
$472$	0.0873402	0.00402016
$473$	−24.0675	−1.10663
$474$	2.05356	0.0943231
$475$	−2.81115	−0.128984
$476$	3.34841	0.153474
$477$	−7.84040	−0.358987
$478$	−23.8743	−1.09199
$479$	−26.0949	−1.19231	−0.596153	−	0.802871i	$-0.703305\pi$
$479$	−26.0949	−1.19231	−0.596153	+	0.802871i	$0.703305\pi$
$480$	19.4093	0.885908
$481$	1.10189	0.0502420
$482$	7.87464	0.358680
$483$	−6.91060	−0.314443
$484$	−7.15053	−0.325024
$485$	11.6260	0.527910
$486$	−2.05356	−0.0931514
$487$	−2.96799	−0.134493	−0.0672463	−	0.997736i	$-0.521421\pi$
$487$	−2.96799	−0.134493	−0.0672463	+	0.997736i	$0.521421\pi$
$488$	0.755185	0.0341856
$489$	9.59964	0.434111
$490$	−23.1717	−1.04679
$491$	27.3113	1.23254	0.616271	−	0.787534i	$-0.288643\pi$
$491$	27.3113	1.23254	0.616271	+	0.787534i	$0.288643\pi$
$492$	11.2357	0.506546
$493$	−9.05512	−0.407822
$494$	1.45807	0.0656018
$495$	−6.66708	−0.299663
$496$	7.47456	0.335618
$497$	2.96806	0.133136
$498$	−32.3128	−1.44797
$499$	14.9326	0.668474	0.334237	−	0.942489i	$-0.391521\pi$
$499$	14.9326	0.668474	0.334237	+	0.942489i	$0.391521\pi$
$500$	−22.7044	−1.01537
$501$	−13.6843	−0.611371
$502$	−42.1327	−1.88047
$503$	32.1293	1.43258	0.716288	−	0.697805i	$-0.245840\pi$
$503$	32.1293	1.43258	0.716288	+	0.697805i	$0.245840\pi$
$504$	−0.673339	−0.0299929
$505$	31.8256	1.41622
$506$	26.2010	1.16478
$507$	12.9672	0.575893
$508$	−29.9194	−1.32746
$509$	−24.8104	−1.09970	−0.549851	−	0.835263i	$-0.685315\pi$
$509$	−24.8104	−1.09970	−0.549851	+	0.835263i	$0.685315\pi$
$510$	4.91018	0.217426
$511$	8.78961	0.388829
$512$	31.7000	1.40095
$513$	3.91990	0.173068
$514$	−9.55719	−0.421549
$515$	−19.0768	−0.840623
$516$	−19.1369	−0.842456
$517$	26.3309	1.15803
$518$	18.8669	0.828965
$519$	−5.20890	−0.228645
$520$	−0.193094	−0.00846775
$521$	35.4420	1.55274	0.776370	−	0.630277i	$-0.217059\pi$
$521$	35.4420	1.55274	0.776370	+	0.630277i	$0.217059\pi$
$522$	18.5952	0.813891
$523$	−6.74241	−0.294825	−0.147412	−	0.989075i	$-0.547094\pi$
$523$	−6.74241	−0.294825	−0.147412	+	0.989075i	$0.547094\pi$
$524$	2.07018	0.0904361
$525$	1.08308	0.0472695
$526$	−50.9930	−2.22340
$527$	2.12427	0.0925347
$528$	−9.81119	−0.426977
$529$	−2.06229	−0.0896647
$530$	−38.4977	−1.67224
$531$	0.195899	0.00850128
$532$	13.1254	0.569058
$533$	0.917935	0.0397602
$534$	29.2719	1.26672
$535$	−4.70643	−0.203477
$536$	3.66779	0.158424
$537$	14.3798	0.620533
$538$	−15.5914	−0.672194
$539$	13.1585	0.566777
$540$	−5.30123	−0.228129
$541$	7.75500	0.333414	0.166707	−	0.986007i	$-0.446687\pi$
$541$	7.75500	0.333414	0.166707	+	0.986007i	$0.446687\pi$
$542$	−18.2885	−0.785559
$543$	−25.8488	−1.10928
$544$	8.11744	0.348032
$545$	17.7133	0.758753
$546$	−0.561767	−0.0240414
$547$	−29.3103	−1.25322	−0.626608	−	0.779334i	$-0.715557\pi$
$547$	−29.3103	−1.25322	−0.626608	+	0.779334i	$0.715557\pi$
$548$	−7.31155	−0.312334
$549$	1.69383	0.0722910
$550$	−4.10641	−0.175098
$551$	−35.4951	−1.51214
$552$	2.04008	0.0868316
$553$	1.51026	0.0642227
$554$	40.9510	1.73984
$555$	14.5456	0.617427
$556$	−21.9918	−0.932659
$557$	−16.1253	−0.683249	−0.341625	−	0.939836i	$-0.610977\pi$
$557$	−16.1253	−0.683249	−0.341625	+	0.939836i	$0.610977\pi$
$558$	−4.36232	−0.184672
$559$	−1.56345	−0.0661267
$560$	12.7062	0.536936
$561$	−2.78834	−0.117724
$562$	53.0770	2.23892
$563$	−19.2552	−0.811509	−0.405755	−	0.913982i	$-0.632991\pi$
$563$	−19.2552	−0.811509	−0.405755	+	0.913982i	$0.632991\pi$
$564$	20.9366	0.881591
$565$	7.82598	0.329241
$566$	31.5150	1.32468
$567$	−1.51026	−0.0634249
$568$	−0.876203	−0.0367647
$569$	12.2540	0.513713	0.256857	−	0.966450i	$-0.417313\pi$
$569$	12.2540	0.513713	0.256857	+	0.966450i	$0.417313\pi$
$570$	19.2474	0.806184
$571$	−9.52639	−0.398667	−0.199333	−	0.979932i	$-0.563878\pi$
$571$	−9.52639	−0.398667	−0.199333	+	0.979932i	$0.563878\pi$
$572$	1.11977	0.0468200
$573$	22.3731	0.934650
$574$	15.7171	0.656020
$575$	−3.28151	−0.136849
$576$	−9.63236	−0.401348
$577$	−29.4511	−1.22607	−0.613033	−	0.790058i	$-0.710051\pi$
$577$	−29.4511	−1.22607	−0.613033	+	0.790058i	$0.710051\pi$
$578$	2.05356	0.0854168
$579$	−20.2197	−0.840301
$580$	48.0033	1.99323
$581$	−23.7640	−0.985896
$582$	−9.98500	−0.413891
$583$	21.8617	0.905419
$584$	−2.59478	−0.107373
$585$	−0.433099	−0.0179064
$586$	−45.0935	−1.86279
$587$	0.980598	0.0404736	0.0202368	−	0.999795i	$-0.493558\pi$
$587$	0.980598	0.0404736	0.0202368	+	0.999795i	$0.493558\pi$
$588$	10.4628	0.431478
$589$	8.32692	0.343105
$590$	0.961897	0.0396007
$591$	6.16167	0.253457
$592$	21.4052	0.879747
$593$	20.5920	0.845613	0.422806	−	0.906220i	$-0.361045\pi$
$593$	20.5920	0.845613	0.422806	+	0.906220i	$0.361045\pi$
$594$	5.72602	0.234942
$595$	3.61111	0.148041
$596$	40.1736	1.64557
$597$	16.9449	0.693507
$598$	1.70204	0.0696015
$599$	23.4077	0.956411	0.478206	−	0.878248i	$-0.341287\pi$
$599$	23.4077	0.956411	0.478206	+	0.878248i	$0.341287\pi$
$600$	−0.319736	−0.0130532
$601$	−17.7849	−0.725460	−0.362730	−	0.931894i	$-0.618155\pi$
$601$	−17.7849	−0.725460	−0.362730	+	0.931894i	$0.618155\pi$
$602$	−26.7697	−1.09105
$603$	8.22662	0.335014
$604$	−10.0913	−0.410608
$605$	−7.71154	−0.313519
$606$	−27.3334	−1.11034
$607$	−29.3852	−1.19271	−0.596354	−	0.802721i	$-0.703385\pi$
$607$	−29.3852	−1.19271	−0.596354	+	0.802721i	$0.703385\pi$
$608$	31.8195	1.29045
$609$	13.6756	0.554162
$610$	8.31702	0.336746
$611$	1.71048	0.0691985
$612$	−2.21711	−0.0896213
$613$	−20.4845	−0.827362	−0.413681	−	0.910422i	$-0.635757\pi$
$613$	−20.4845	−0.827362	−0.413681	+	0.910422i	$0.635757\pi$
$614$	−70.8666	−2.85994
$615$	12.1173	0.488615
$616$	1.87750	0.0756466
$617$	30.6391	1.23348	0.616741	−	0.787166i	$-0.288452\pi$
$617$	30.6391	1.23348	0.616741	+	0.787166i	$0.288452\pi$
$618$	16.3841	0.659065
$619$	−0.0994482	−0.00399716	−0.00199858	−	0.999998i	$-0.500636\pi$
$619$	−0.0994482	−0.00399716	−0.00199858	+	0.999998i	$0.500636\pi$
$620$	−11.2612	−0.452262
$621$	4.57577	0.183620
$622$	−71.8903	−2.88254
$623$	21.5276	0.862485
$624$	−0.637343	−0.0255141
$625$	−28.0714	−1.12286
$626$	14.1962	0.567395
$627$	−10.9300	−0.436502
$628$	23.4474	0.935654
$629$	6.08335	0.242559
$630$	−7.41564	−0.295446
$631$	1.87700	0.0747221	0.0373611	−	0.999302i	$-0.488105\pi$
$631$	1.87700	0.0747221	0.0373611	+	0.999302i	$0.488105\pi$
$632$	−0.445844	−0.0177347
$633$	−3.94974	−0.156988
$634$	−18.2016	−0.722879
$635$	−32.2668	−1.28047
$636$	17.3830	0.689281
$637$	0.854788	0.0338679
$638$	−51.8498	−2.05275
$639$	−1.96527	−0.0777448
$640$	−8.47805	−0.335124
$641$	19.4552	0.768435	0.384217	−	0.923243i	$-0.374471\pi$
$641$	19.4552	0.768435	0.384217	+	0.923243i	$0.374471\pi$
$642$	4.04212	0.159530
$643$	0.633131	0.0249683	0.0124841	−	0.999922i	$-0.496026\pi$
$643$	0.633131	0.0249683	0.0124841	+	0.999922i	$0.496026\pi$
$644$	15.3215	0.603754
$645$	−20.6384	−0.812635
$646$	8.04974	0.316713
$647$	39.5268	1.55396	0.776979	−	0.629527i	$-0.216751\pi$
$647$	39.5268	1.55396	0.776979	+	0.629527i	$0.216751\pi$
$648$	0.445844	0.0175144
$649$	−0.546232	−0.0214415
$650$	−0.266756	−0.0104630
$651$	−3.20820	−0.125739
$652$	−21.2834	−0.833524
$653$	−28.0555	−1.09790	−0.548948	−	0.835857i	$-0.684971\pi$
$653$	−28.0555	−1.09790	−0.548948	+	0.835857i	$0.684971\pi$
$654$	−15.2130	−0.594877
$655$	2.23260	0.0872348
$656$	17.8316	0.696207
$657$	−5.81994	−0.227057
$658$	29.2872	1.14174
$659$	13.5247	0.526849	0.263425	−	0.964680i	$-0.415148\pi$
$659$	13.5247	0.526849	0.263425	+	0.964680i	$0.415148\pi$
$660$	14.7816	0.575374
$661$	−17.2925	−0.672601	−0.336300	−	0.941755i	$-0.609176\pi$
$661$	−17.2925	−0.672601	−0.336300	+	0.941755i	$0.609176\pi$
$662$	−63.3020	−2.46030
$663$	−0.181133	−0.00703462
$664$	7.01537	0.272249
$665$	14.1552	0.548914
$666$	−12.4925	−0.484075
$667$	−41.4342	−1.60434
$668$	30.3396	1.17388
$669$	−3.13691	−0.121280
$670$	40.3942	1.56056
$671$	−4.72298	−0.182329
$672$	−12.2594	−0.472918
$673$	−18.5134	−0.713639	−0.356819	−	0.934173i	$-0.616139\pi$
$673$	−18.5134	−0.713639	−0.356819	+	0.934173i	$0.616139\pi$
$674$	14.4169	0.555319
$675$	−0.717149	−0.0276031
$676$	−28.7497	−1.10576
$677$	29.9027	1.14925	0.574627	−	0.818415i	$-0.305147\pi$
$677$	29.9027	1.14925	0.574627	+	0.818415i	$0.305147\pi$
$678$	−6.72134	−0.258132
$679$	−7.34331	−0.281810
$680$	−1.06604	−0.0408807
$681$	−6.62160	−0.253740
$682$	12.1636	0.465769
$683$	−21.6392	−0.828001	−0.414001	−	0.910277i	$-0.635869\pi$
$683$	−21.6392	−0.828001	−0.414001	+	0.910277i	$0.635869\pi$
$684$	−8.69083	−0.332302
$685$	−7.88519	−0.301278
$686$	36.3457	1.38769
$687$	−23.4819	−0.895892
$688$	−30.3712	−1.15789
$689$	1.42015	0.0541036
$690$	22.4679	0.855337
$691$	24.8399	0.944955	0.472477	−	0.881343i	$-0.343360\pi$
$691$	24.8399	0.944955	0.472477	+	0.881343i	$0.343360\pi$
$692$	11.5487	0.439015
$693$	4.21111	0.159967
$694$	38.4647	1.46010
$695$	−23.7172	−0.899644
$696$	−4.03717	−0.153028
$697$	5.06774	0.191954
$698$	−8.19712	−0.310265
$699$	6.14916	0.232583
$700$	−2.40131	−0.0907608
$701$	−28.5337	−1.07770	−0.538852	−	0.842400i	$-0.681142\pi$
$701$	−28.5337	−1.07770	−0.538852	+	0.842400i	$0.681142\pi$
$702$	0.371967	0.0140390
$703$	23.8461	0.899372
$704$	26.8583	1.01226
$705$	22.5793	0.850384
$706$	−0.540491	−0.0203416
$707$	−20.1019	−0.756011
$708$	−0.434329	−0.0163231
$709$	−43.7593	−1.64341	−0.821707	−	0.569910i	$-0.806978\pi$
$709$	−43.7593	−1.64341	−0.821707	+	0.569910i	$0.806978\pi$
$710$	−9.64982	−0.362151
$711$	−1.00000	−0.0375029
$712$	−6.35517	−0.238170
$713$	9.72018	0.364024
$714$	−3.10141	−0.116067
$715$	1.20763	0.0451627
$716$	−31.8815	−1.19147
$717$	11.6258	0.434174
$718$	−2.59066	−0.0966825
$719$	−32.4958	−1.21189	−0.605944	−	0.795507i	$-0.707205\pi$
$719$	−32.4958	−1.21189	−0.605944	+	0.795507i	$0.707205\pi$
$720$	−8.41329	−0.313545
$721$	12.0494	0.448744
$722$	−7.46350	−0.277763
$723$	−3.83463	−0.142611
$724$	57.3097	2.12990
$725$	6.49387	0.241176
$726$	6.62306	0.245805
$727$	−1.55959	−0.0578421	−0.0289211	−	0.999582i	$-0.509207\pi$
$727$	−1.55959	−0.0578421	−0.0289211	+	0.999582i	$0.509207\pi$
$728$	0.121964	0.00452028
$729$	1.00000	0.0370370
$730$	−28.5769	−1.05768
$731$	−8.63148	−0.319247
$732$	−3.75541	−0.138804
$733$	−5.88312	−0.217298	−0.108649	−	0.994080i	$-0.534652\pi$
$733$	−5.88312	−0.217298	−0.108649	+	0.994080i	$0.534652\pi$
$734$	28.1717	1.03984
$735$	11.2837	0.416205
$736$	37.1436	1.36913
$737$	−22.9386	−0.844955
$738$	−10.4069	−0.383084
$739$	38.4779	1.41543	0.707716	−	0.706497i	$-0.249725\pi$
$739$	38.4779	1.41543	0.707716	+	0.706497i	$0.249725\pi$
$740$	−32.2492	−1.18550
$741$	−0.710022	−0.0260833
$742$	24.3163	0.892678
$743$	13.4447	0.493238	0.246619	−	0.969113i	$-0.420680\pi$
$743$	13.4447	0.493238	0.246619	+	0.969113i	$0.420680\pi$
$744$	0.947092	0.0347221
$745$	43.3255	1.58732
$746$	69.3445	2.53888
$747$	15.7350	0.575715
$748$	6.18205	0.226038
$749$	2.97271	0.108621
$750$	21.0296	0.767891
$751$	−31.5999	−1.15310	−0.576549	−	0.817062i	$-0.695601\pi$
$751$	−31.5999	−1.15310	−0.576549	+	0.817062i	$0.695601\pi$
$752$	33.2274	1.21168
$753$	20.5169	0.747678
$754$	−3.36821	−0.122663
$755$	−10.8830	−0.396073
$756$	3.34841	0.121780
$757$	−39.7475	−1.44465	−0.722324	−	0.691555i	$-0.756926\pi$
$757$	−39.7475	−1.44465	−0.722324	+	0.691555i	$0.756926\pi$
$758$	−0.544073	−0.0197616
$759$	−12.7588	−0.463116
$760$	−4.17875	−0.151579
$761$	−51.3210	−1.86039	−0.930193	−	0.367072i	$-0.880360\pi$
$761$	−51.3210	−1.86039	−0.930193	+	0.367072i	$0.880360\pi$
$762$	27.7123	1.00391
$763$	−11.1882	−0.405040
$764$	−49.6036	−1.79460
$765$	−2.39106	−0.0864488
$766$	41.4195	1.49655
$767$	−0.0354837	−0.00128124
$768$	−11.9833	−0.432411
$769$	−7.55713	−0.272517	−0.136259	−	0.990673i	$-0.543508\pi$
$769$	−7.55713	−0.272517	−0.136259	+	0.990673i	$0.543508\pi$
$770$	20.6773	0.745159
$771$	4.65396	0.167608
$772$	44.8292	1.61344
$773$	−3.07412	−0.110568	−0.0552842	−	0.998471i	$-0.517606\pi$
$773$	−3.07412	−0.110568	−0.0552842	+	0.998471i	$0.517606\pi$
$774$	17.7253	0.637122
$775$	−1.52342	−0.0547228
$776$	2.16782	0.0778202
$777$	−9.18742	−0.329597
$778$	24.3841	0.874211
$779$	19.8650	0.711738
$780$	0.960227	0.0343816
$781$	5.47984	0.196084
$782$	9.39663	0.336023
$783$	−9.05512	−0.323604
$784$	16.6049	0.593033
$785$	25.2870	0.902533
$786$	−1.91747	−0.0683938
$787$	49.2033	1.75391	0.876954	−	0.480574i	$-0.159572\pi$
$787$	49.2033	1.75391	0.876954	+	0.480574i	$0.159572\pi$
$788$	−13.6611	−0.486656
$789$	24.8315	0.884025
$790$	−4.91018	−0.174696
$791$	−4.94311	−0.175757
$792$	−1.24316	−0.0441739
$793$	−0.306809	−0.0108951
$794$	58.7012	2.08323
$795$	18.7468	0.664882
$796$	−37.5686	−1.33158
$797$	−37.0740	−1.31323	−0.656614	−	0.754227i	$-0.728012\pi$
$797$	−37.0740	−1.31323	−0.656614	+	0.754227i	$0.728012\pi$
$798$	−12.1572	−0.430360
$799$	9.44321	0.334077
$800$	−5.82142	−0.205818
$801$	−14.2542	−0.503649
$802$	−9.27429	−0.327487
$803$	16.2280	0.572672
$804$	−18.2393	−0.643251
$805$	16.5236	0.582382
$806$	0.790159	0.0278322
$807$	7.59239	0.267265
$808$	5.93430	0.208768
$809$	26.4993	0.931667	0.465833	−	0.884872i	$-0.345755\pi$
$809$	26.4993	0.931667	0.465833	+	0.884872i	$0.345755\pi$
$810$	4.91018	0.172526
$811$	−5.27339	−0.185174	−0.0925868	−	0.995705i	$-0.529514\pi$
$811$	−5.27339	−0.185174	−0.0925868	+	0.995705i	$0.529514\pi$
$812$	−30.3202	−1.06403
$813$	8.90576	0.312339
$814$	34.8334	1.22091
$815$	−22.9533	−0.804018
$816$	−3.51865	−0.123177
$817$	−33.8345	−1.18372
$818$	−4.15725	−0.145355
$819$	0.273557	0.00955887
$820$	−26.8653	−0.938176
$821$	22.0636	0.770026	0.385013	−	0.922911i	$-0.374197\pi$
$821$	22.0636	0.770026	0.385013	+	0.922911i	$0.374197\pi$
$822$	6.77220	0.236208
$823$	−13.1908	−0.459803	−0.229901	−	0.973214i	$-0.573840\pi$
$823$	−13.1908	−0.459803	−0.229901	+	0.973214i	$0.573840\pi$
$824$	−3.55711	−0.123918
$825$	1.99966	0.0696191
$826$	−0.607561	−0.0211398
$827$	14.4847	0.503682	0.251841	−	0.967769i	$-0.418964\pi$
$827$	14.4847	0.503682	0.251841	+	0.967769i	$0.418964\pi$
$828$	−10.1450	−0.352563
$829$	26.6849	0.926806	0.463403	−	0.886148i	$-0.346628\pi$
$829$	26.6849	0.926806	0.463403	+	0.886148i	$0.346628\pi$
$830$	77.2618	2.68180
$831$	−19.9415	−0.691762
$832$	1.74474	0.0604879
$833$	4.71912	0.163508
$834$	20.3695	0.705339
$835$	32.7200	1.13232
$836$	24.2330	0.838115
$837$	2.12427	0.0734255
$838$	−39.5572	−1.36648
$839$	4.75419	0.164133	0.0820665	−	0.996627i	$-0.473848\pi$
$839$	4.75419	0.164133	0.0820665	+	0.996627i	$0.473848\pi$
$840$	1.60999	0.0555500
$841$	52.9952	1.82742
$842$	32.6804	1.12624
$843$	−25.8463	−0.890195
$844$	8.75700	0.301428
$845$	−31.0053	−1.06661
$846$	−19.3922	−0.666718
$847$	4.87083	0.167364
$848$	27.5876	0.947363
$849$	−15.3465	−0.526692
$850$	−1.47271	−0.0505135
$851$	27.8360	0.954206
$852$	4.35721	0.149276
$853$	−47.2325	−1.61721	−0.808606	−	0.588351i	$-0.799777\pi$
$853$	−47.2325	−1.61721	−0.808606	+	0.588351i	$0.799777\pi$
$854$	−5.25326	−0.179763
$855$	−9.37269	−0.320539
$856$	−0.877575	−0.0299949
$857$	54.3626	1.85699	0.928495	−	0.371344i	$-0.121103\pi$
$857$	54.3626	1.85699	0.928495	+	0.371344i	$0.121103\pi$
$858$	−1.03717	−0.0354084
$859$	25.2161	0.860363	0.430182	−	0.902742i	$-0.358449\pi$
$859$	25.2161	0.860363	0.430182	+	0.902742i	$0.358449\pi$
$860$	45.7575	1.56032
$861$	−7.65360	−0.260834
$862$	66.8540	2.27706
$863$	24.0505	0.818689	0.409344	−	0.912380i	$-0.365757\pi$
$863$	24.0505	0.818689	0.409344	+	0.912380i	$0.365757\pi$
$864$	8.11744	0.276161
$865$	12.4548	0.423475
$866$	−29.8419	−1.01407
$867$	−1.00000	−0.0339618
$868$	7.11292	0.241428
$869$	2.78834	0.0945879
$870$	−44.4622	−1.50741
$871$	−1.49011	−0.0504905
$872$	3.30287	0.111849
$873$	4.86229	0.164564
$874$	36.8338	1.24592
$875$	15.4659	0.522841
$876$	12.9034	0.435966
$877$	−1.41473	−0.0477721	−0.0238860	−	0.999715i	$-0.507604\pi$
$877$	−1.41473	−0.0477721	−0.0238860	+	0.999715i	$0.507604\pi$
$878$	30.0072	1.01269
$879$	21.9587	0.740648
$880$	23.4591	0.790806
$881$	9.53923	0.321385	0.160692	−	0.987005i	$-0.448627\pi$
$881$	9.53923	0.321385	0.160692	+	0.987005i	$0.448627\pi$
$882$	−9.69099	−0.326313
$883$	−41.5733	−1.39905	−0.699527	−	0.714607i	$-0.746606\pi$
$883$	−41.5733	−1.39905	−0.699527	+	0.714607i	$0.746606\pi$
$884$	0.401591	0.0135070
$885$	−0.468405	−0.0157453
$886$	64.6867	2.17319
$887$	−34.8411	−1.16985	−0.584925	−	0.811088i	$-0.698876\pi$
$887$	−34.8411	−1.16985	−0.584925	+	0.811088i	$0.698876\pi$
$888$	2.71222	0.0910162
$889$	20.3806	0.683544
$890$	−69.9909	−2.34610
$891$	−2.78834	−0.0934129
$892$	6.95487	0.232866
$893$	37.0164	1.23871
$894$	−37.2101	−1.24449
$895$	−34.3828	−1.14929
$896$	5.35498	0.178897
$897$	−0.828823	−0.0276736
$898$	−9.03778	−0.301595
$899$	−19.2355	−0.641541
$900$	1.59000	0.0529999
$901$	7.84040	0.261202
$902$	29.0180	0.966194
$903$	13.0358	0.433803
$904$	1.45926	0.0485341
$905$	61.8060	2.05450
$906$	9.34686	0.310529
$907$	−5.37399	−0.178440	−0.0892202	−	0.996012i	$-0.528437\pi$
$907$	−5.37399	−0.178440	−0.0892202	+	0.996012i	$0.528437\pi$
$908$	14.6808	0.487199
$909$	13.3103	0.441474
$910$	1.34322	0.0445272
$911$	29.0777	0.963389	0.481694	−	0.876339i	$-0.340022\pi$
$911$	29.0777	0.963389	0.481694	+	0.876339i	$0.340022\pi$
$912$	−13.7927	−0.456723
$913$	−43.8746	−1.45204
$914$	−51.3825	−1.69958
$915$	−4.05005	−0.133891
$916$	52.0620	1.72018
$917$	−1.41017	−0.0465680
$918$	2.05356	0.0677776
$919$	−6.67776	−0.220279	−0.110139	−	0.993916i	$-0.535130\pi$
$919$	−6.67776	−0.220279	−0.110139	+	0.993916i	$0.535130\pi$
$920$	−4.87795	−0.160821
$921$	34.5091	1.13711
$922$	11.1257	0.366406
$923$	0.355975	0.0117171
$924$	−9.33649	−0.307148
$925$	−4.36267	−0.143444
$926$	−4.98106	−0.163688
$927$	−7.97839	−0.262045
$928$	−73.5044	−2.41290
$929$	50.5761	1.65935	0.829674	−	0.558249i	$-0.188526\pi$
$929$	50.5761	1.65935	0.829674	+	0.558249i	$0.188526\pi$
$930$	10.4305	0.342031
$931$	18.4985	0.606262
$932$	−13.6334	−0.446575
$933$	35.0077	1.14610
$934$	56.4616	1.84748
$935$	6.66708	0.218037
$936$	−0.0807570	−0.00263962
$937$	5.00859	0.163624	0.0818118	−	0.996648i	$-0.473929\pi$
$937$	5.00859	0.163624	0.0818118	+	0.996648i	$0.473929\pi$
$938$	−25.5141	−0.833064
$939$	−6.91298	−0.225597
$940$	−50.0606	−1.63280
$941$	−34.5272	−1.12555	−0.562777	−	0.826609i	$-0.690267\pi$
$941$	−34.5272	−1.12555	−0.562777	+	0.826609i	$0.690267\pi$
$942$	−21.7178	−0.707604
$943$	23.1889	0.755133
$944$	−0.689299	−0.0224348
$945$	3.61111	0.117469
$946$	−49.4241	−1.60691
$947$	44.3337	1.44065	0.720325	−	0.693636i	$-0.243993\pi$
$947$	44.3337	1.44065	0.720325	+	0.693636i	$0.243993\pi$
$948$	2.21711	0.0720083
$949$	1.05418	0.0342202
$950$	−5.77286	−0.187296
$951$	8.86345	0.287417
$952$	0.673339	0.0218230
$953$	4.17372	0.135200	0.0676001	−	0.997713i	$-0.478466\pi$
$953$	4.17372	0.135200	0.0676001	+	0.997713i	$0.478466\pi$
$954$	−16.1007	−0.521280
$955$	−53.4954	−1.73107
$956$	−25.7757	−0.833646
$957$	25.2488	0.816176
$958$	−53.5874	−1.73133
$959$	4.98051	0.160829
$960$	23.0315	0.743339
$961$	−26.4875	−0.854435
$962$	2.26281	0.0729558
$963$	−1.96835	−0.0634291
$964$	8.50179	0.273824
$965$	48.3464	1.55632
$966$	−14.1913	−0.456599
$967$	52.6149	1.69198	0.845991	−	0.533198i	$-0.179010\pi$
$967$	52.6149	1.69198	0.845991	+	0.533198i	$0.179010\pi$
$968$	−1.43792	−0.0462164
$969$	−3.91990	−0.125925
$970$	23.8747	0.766570
$971$	−12.2494	−0.393102	−0.196551	−	0.980494i	$-0.562974\pi$
$971$	−12.2494	−0.393102	−0.196551	+	0.980494i	$0.562974\pi$
$972$	−2.21711	−0.0711138
$973$	14.9804	0.480251
$974$	−6.09495	−0.195295
$975$	0.129899	0.00416011
$976$	−5.96000	−0.190775
$977$	25.9900	0.831494	0.415747	−	0.909480i	$-0.363520\pi$
$977$	25.9900	0.831494	0.415747	+	0.909480i	$0.363520\pi$
$978$	19.7134	0.630366
$979$	39.7457	1.27028
$980$	−25.0171	−0.799143
$981$	7.40813	0.236523
$982$	56.0854	1.78976
$983$	−55.4702	−1.76923	−0.884613	−	0.466327i	$-0.845577\pi$
$983$	−55.4702	−1.76923	−0.884613	+	0.466327i	$0.845577\pi$
$984$	2.25942	0.0720277
$985$	−14.7329	−0.469429
$986$	−18.5952	−0.592193
$987$	−14.2617	−0.453955
$988$	1.57420	0.0500818
$989$	−39.4957	−1.25589
$990$	−13.6912	−0.435136
$991$	28.5751	0.907718	0.453859	−	0.891074i	$-0.350047\pi$
$991$	28.5751	0.907718	0.453859	+	0.891074i	$0.350047\pi$
$992$	17.2436	0.547486
$993$	30.8255	0.978218
$994$	6.09510	0.193325
$995$	−40.5161	−1.28445
$996$	−34.8863	−1.10541
$997$	−54.8759	−1.73794	−0.868969	−	0.494866i	$-0.835217\pi$
$997$	−54.8759	−1.73794	−0.868969	+	0.494866i	$0.835217\pi$
$998$	30.6649	0.970681
$999$	6.08335	0.192469

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.g.1.18	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.g.1.18	✓	22	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+2.05356 q^{2} -1.00000 q^{3} +2.21711 q^{4} +2.39106 q^{5} -2.05356 q^{6} -1.51026 q^{7} +0.445844 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.05356 q^{2} -1.00000 q^{3} +2.21711 q^{4} +2.39106 q^{5} -2.05356 q^{6} -1.51026 q^{7} +0.445844 q^{8} +1.00000 q^{9} +4.91018 q^{10} -2.78834 q^{11} -2.21711 q^{12} -0.181133 q^{13} -3.10141 q^{14} -2.39106 q^{15} -3.51865 q^{16} -1.00000 q^{17} +2.05356 q^{18} -3.91990 q^{19} +5.30123 q^{20} +1.51026 q^{21} -5.72602 q^{22} -4.57577 q^{23} -0.445844 q^{24} +0.717149 q^{25} -0.371967 q^{26} -1.00000 q^{27} -3.34841 q^{28} +9.05512 q^{29} -4.91018 q^{30} -2.12427 q^{31} -8.11744 q^{32} +2.78834 q^{33} -2.05356 q^{34} -3.61111 q^{35} +2.21711 q^{36} -6.08335 q^{37} -8.04974 q^{38} +0.181133 q^{39} +1.06604 q^{40} -5.06774 q^{41} +3.10141 q^{42} +8.63148 q^{43} -6.18205 q^{44} +2.39106 q^{45} -9.39663 q^{46} -9.44321 q^{47} +3.51865 q^{48} -4.71912 q^{49} +1.47271 q^{50} +1.00000 q^{51} -0.401591 q^{52} -7.84040 q^{53} -2.05356 q^{54} -6.66708 q^{55} -0.673339 q^{56} +3.91990 q^{57} +18.5952 q^{58} +0.195899 q^{59} -5.30123 q^{60} +1.69383 q^{61} -4.36232 q^{62} -1.51026 q^{63} -9.63236 q^{64} -0.433099 q^{65} +5.72602 q^{66} +8.22662 q^{67} -2.21711 q^{68} +4.57577 q^{69} -7.41564 q^{70} -1.96527 q^{71} +0.445844 q^{72} -5.81994 q^{73} -12.4925 q^{74} -0.717149 q^{75} -8.69083 q^{76} +4.21111 q^{77} +0.371967 q^{78} -1.00000 q^{79} -8.41329 q^{80} +1.00000 q^{81} -10.4069 q^{82} +15.7350 q^{83} +3.34841 q^{84} -2.39106 q^{85} +17.7253 q^{86} -9.05512 q^{87} -1.24316 q^{88} -14.2542 q^{89} +4.91018 q^{90} +0.273557 q^{91} -10.1450 q^{92} +2.12427 q^{93} -19.3922 q^{94} -9.37269 q^{95} +8.11744 q^{96} +4.86229 q^{97} -9.69099 q^{98} -2.78834 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * q^99

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