LMFDB - Embedded newform 8033.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$1$
Dimension:	$154$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73685 q^{2} -2.64760 q^{3} +5.49034 q^{4} -2.28975 q^{5} +7.24607 q^{6} -2.70237 q^{7} -9.55253 q^{8} +4.00977 q^{9} +O(q^{10})$	\(q-2.73685 q^{2} -2.64760 q^{3} +5.49034 q^{4} -2.28975 q^{5} +7.24607 q^{6} -2.70237 q^{7} -9.55253 q^{8} +4.00977 q^{9} +6.26669 q^{10} +0.863139 q^{11} -14.5362 q^{12} +0.149221 q^{13} +7.39597 q^{14} +6.06233 q^{15} +15.1631 q^{16} +6.81451 q^{17} -10.9741 q^{18} +8.47434 q^{19} -12.5715 q^{20} +7.15478 q^{21} -2.36228 q^{22} +1.02146 q^{23} +25.2912 q^{24} +0.242939 q^{25} -0.408395 q^{26} -2.67346 q^{27} -14.8369 q^{28} +1.00000 q^{29} -16.5917 q^{30} -3.49490 q^{31} -22.3942 q^{32} -2.28524 q^{33} -18.6503 q^{34} +6.18774 q^{35} +22.0150 q^{36} -8.93618 q^{37} -23.1930 q^{38} -0.395077 q^{39} +21.8729 q^{40} +2.38322 q^{41} -19.5816 q^{42} -6.65510 q^{43} +4.73893 q^{44} -9.18136 q^{45} -2.79557 q^{46} +4.10919 q^{47} -40.1459 q^{48} +0.302797 q^{49} -0.664888 q^{50} -18.0421 q^{51} +0.819274 q^{52} -5.48885 q^{53} +7.31686 q^{54} -1.97637 q^{55} +25.8144 q^{56} -22.4366 q^{57} -2.73685 q^{58} +2.45204 q^{59} +33.2842 q^{60} -14.8637 q^{61} +9.56500 q^{62} -10.8359 q^{63} +30.9631 q^{64} -0.341678 q^{65} +6.25437 q^{66} -9.18420 q^{67} +37.4140 q^{68} -2.70440 q^{69} -16.9349 q^{70} -11.8039 q^{71} -38.3034 q^{72} -2.15918 q^{73} +24.4570 q^{74} -0.643206 q^{75} +46.5270 q^{76} -2.33252 q^{77} +1.08127 q^{78} +9.98282 q^{79} -34.7197 q^{80} -4.95106 q^{81} -6.52252 q^{82} +17.4066 q^{83} +39.2822 q^{84} -15.6035 q^{85} +18.2140 q^{86} -2.64760 q^{87} -8.24516 q^{88} +13.5901 q^{89} +25.1280 q^{90} -0.403250 q^{91} +5.60814 q^{92} +9.25307 q^{93} -11.2462 q^{94} -19.4041 q^{95} +59.2907 q^{96} -10.7547 q^{97} -0.828710 q^{98} +3.46099 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) $ 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9 - 40 * q^10 - 36 * q^11 - 67 * q^12 - 51 * q^13 - 19 * q^14 - 48 * q^15 + 122 * q^16 - 54 * q^17 - 46 * q^18 - 73 * q^19 - 21 * q^20 - 8 * q^21 - 23 * q^22 - 38 * q^23 - 17 * q^24 + 133 * q^25 - 20 * q^26 - 129 * q^27 - 99 * q^28 + 154 * q^29 - 10 * q^30 - 91 * q^31 - 88 * q^32 - 39 * q^33 - 42 * q^34 - 36 * q^35 + 101 * q^36 - 50 * q^37 - 17 * q^38 - 33 * q^39 - 92 * q^40 - 31 * q^41 - 62 * q^42 - 154 * q^43 - 42 * q^44 - 14 * q^45 - 24 * q^46 - 140 * q^47 - 118 * q^48 + 126 * q^49 - 5 * q^50 - 16 * q^51 - 133 * q^52 - 40 * q^53 + 14 * q^54 - 203 * q^55 - 44 * q^56 - 16 * q^57 - 12 * q^58 + 5 * q^59 - 28 * q^60 - 106 * q^61 - 30 * q^62 - 145 * q^63 + 111 * q^64 - 15 * q^65 - 49 * q^66 - 78 * q^67 - 118 * q^68 - 32 * q^69 - 43 * q^70 - 4 * q^71 - 152 * q^72 - 137 * q^73 + 9 * q^74 - 129 * q^75 - 204 * q^76 - 76 * q^77 + 15 * q^78 - 141 * q^79 - 44 * q^80 + 122 * q^81 - 71 * q^82 - 90 * q^83 + 92 * q^84 - 41 * q^85 + 9 * q^86 - 36 * q^87 - 109 * q^88 - 51 * q^89 - 82 * q^90 - 22 * q^91 - 8 * q^92 - 10 * q^93 - 106 * q^94 - 55 * q^95 - 49 * q^96 - 140 * q^97 - 4 * q^98 - 101 * 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 $

$2$	−2.73685	−1.93524	−0.967622	−	0.252404i	$-0.918779\pi$
$2$	−2.73685	−1.93524	−0.967622	+	0.252404i	$0.918779\pi$
$3$	−2.64760	−1.52859	−0.764295	−	0.644866i	$-0.776913\pi$
$3$	−2.64760	−1.52859	−0.764295	+	0.644866i	$0.776913\pi$
$4$	5.49034	2.74517
$5$	−2.28975	−1.02401	−0.512003	−	0.858984i	$-0.671096\pi$
$5$	−2.28975	−1.02401	−0.512003	+	0.858984i	$0.671096\pi$
$6$	7.24607	2.95820
$7$	−2.70237	−1.02140	−0.510700	−	0.859759i	$-0.670614\pi$
$7$	−2.70237	−1.02140	−0.510700	+	0.859759i	$0.670614\pi$
$8$	−9.55253	−3.37733
$9$	4.00977	1.33659
$10$	6.26669	1.98170
$11$	0.863139	0.260246	0.130123	−	0.991498i	$-0.458463\pi$
$11$	0.863139	0.260246	0.130123	+	0.991498i	$0.458463\pi$
$12$	−14.5362	−4.19624
$13$	0.149221	0.0413865	0.0206932	−	0.999786i	$-0.493413\pi$
$13$	0.149221	0.0413865	0.0206932	+	0.999786i	$0.493413\pi$
$14$	7.39597	1.97666
$15$	6.06233	1.56529
$16$	15.1631	3.79078
$17$	6.81451	1.65276	0.826381	−	0.563111i	$-0.190396\pi$
$17$	6.81451	1.65276	0.826381	+	0.563111i	$0.190396\pi$
$18$	−10.9741	−2.58663
$19$	8.47434	1.94415	0.972073	−	0.234679i	$-0.0754038\pi$
$19$	8.47434	1.94415	0.972073	+	0.234679i	$0.0754038\pi$
$20$	−12.5715	−2.81107
$21$	7.15478	1.56130
$22$	−2.36228	−0.503640
$23$	1.02146	0.212988	0.106494	−	0.994313i	$-0.466037\pi$
$23$	1.02146	0.212988	0.106494	+	0.994313i	$0.466037\pi$
$24$	25.2912	5.16255
$25$	0.242939	0.0485879
$26$	−0.408395	−0.0800929
$27$	−2.67346	−0.514508
$28$	−14.8369	−2.80391
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−16.5917	−3.02921
$31$	−3.49490	−0.627702	−0.313851	−	0.949472i	$-0.601619\pi$
$31$	−3.49490	−0.627702	−0.313851	+	0.949472i	$0.601619\pi$
$32$	−22.3942	−3.95876
$33$	−2.28524	−0.397810
$34$	−18.6503	−3.19850
$35$	6.18774	1.04592
$36$	22.0150	3.66917
$37$	−8.93618	−1.46910	−0.734549	−	0.678555i	$-0.762606\pi$
$37$	−8.93618	−1.46910	−0.734549	+	0.678555i	$0.762606\pi$
$38$	−23.1930	−3.76240
$39$	−0.395077	−0.0632630
$40$	21.8729	3.45840
$41$	2.38322	0.372197	0.186098	−	0.982531i	$-0.440416\pi$
$41$	2.38322	0.372197	0.186098	+	0.982531i	$0.440416\pi$
$42$	−19.5816	−3.02150
$43$	−6.65510	−1.01489	−0.507447	−	0.861683i	$-0.669411\pi$
$43$	−6.65510	−1.01489	−0.507447	+	0.861683i	$0.669411\pi$
$44$	4.73893	0.714420
$45$	−9.18136	−1.36868
$46$	−2.79557	−0.412184
$47$	4.10919	0.599387	0.299693	−	0.954036i	$-0.403116\pi$
$47$	4.10919	0.599387	0.299693	+	0.954036i	$0.403116\pi$
$48$	−40.1459	−5.79456
$49$	0.302797	0.0432567
$50$	−0.664888	−0.0940294
$51$	−18.0421	−2.52640
$52$	0.819274	0.113613
$53$	−5.48885	−0.753952	−0.376976	−	0.926223i	$-0.623036\pi$
$53$	−5.48885	−0.753952	−0.376976	+	0.926223i	$0.623036\pi$
$54$	7.31686	0.995699
$55$	−1.97637	−0.266494
$56$	25.8144	3.44960
$57$	−22.4366	−2.97180
$58$	−2.73685	−0.359366
$59$	2.45204	0.319228	0.159614	−	0.987179i	$-0.448975\pi$
$59$	2.45204	0.319228	0.159614	+	0.987179i	$0.448975\pi$
$60$	33.2842	4.29697
$61$	−14.8637	−1.90310	−0.951550	−	0.307494i	$-0.900510\pi$
$61$	−14.8637	−1.90310	−0.951550	+	0.307494i	$0.900510\pi$
$62$	9.56500	1.21476
$63$	−10.8359	−1.36519
$64$	30.9631	3.87039
$65$	−0.341678	−0.0423800
$66$	6.25437	0.769859
$67$	−9.18420	−1.12203	−0.561014	−	0.827806i	$-0.689589\pi$
$67$	−9.18420	−1.12203	−0.561014	+	0.827806i	$0.689589\pi$
$68$	37.4140	4.53711
$69$	−2.70440	−0.325572
$70$	−16.9349	−2.02411
$71$	−11.8039	−1.40086	−0.700432	−	0.713719i	$-0.747009\pi$
$71$	−11.8039	−1.40086	−0.700432	+	0.713719i	$0.747009\pi$
$72$	−38.3034	−4.51410
$73$	−2.15918	−0.252713	−0.126356	−	0.991985i	$-0.540328\pi$
$73$	−2.15918	−0.252713	−0.126356	+	0.991985i	$0.540328\pi$
$74$	24.4570	2.84306
$75$	−0.643206	−0.0742710
$76$	46.5270	5.33701
$77$	−2.33252	−0.265815
$78$	1.08127	0.122429
$79$	9.98282	1.12316	0.561578	−	0.827424i	$-0.310195\pi$
$79$	9.98282	1.12316	0.561578	+	0.827424i	$0.310195\pi$
$80$	−34.7197	−3.88179
$81$	−4.95106	−0.550118
$82$	−6.52252	−0.720292
$83$	17.4066	1.91062	0.955312	−	0.295600i	$-0.0955196\pi$
$83$	17.4066	1.91062	0.955312	+	0.295600i	$0.0955196\pi$
$84$	39.2822	4.28604
$85$	−15.6035	−1.69244
$86$	18.2140	1.96407
$87$	−2.64760	−0.283852
$88$	−8.24516	−0.878937
$89$	13.5901	1.44055	0.720275	−	0.693689i	$-0.244016\pi$
$89$	13.5901	1.44055	0.720275	+	0.693689i	$0.244016\pi$
$90$	25.1280	2.64872
$91$	−0.403250	−0.0422721
$92$	5.60814	0.584689
$93$	9.25307	0.959499
$94$	−11.2462	−1.15996
$95$	−19.4041	−1.99082
$96$	59.2907	6.05133
$97$	−10.7547	−1.09198	−0.545988	−	0.837793i	$-0.683846\pi$
$97$	−10.7547	−1.09198	−0.545988	+	0.837793i	$0.683846\pi$
$98$	−0.828710	−0.0837123
$99$	3.46099	0.347842
$100$	1.33382	0.133382
$101$	−2.81697	−0.280299	−0.140149	−	0.990130i	$-0.544758\pi$
$101$	−2.81697	−0.280299	−0.140149	+	0.990130i	$0.544758\pi$
$102$	49.3784	4.88919
$103$	−3.48043	−0.342937	−0.171468	−	0.985190i	$-0.554851\pi$
$103$	−3.48043	−0.342937	−0.171468	+	0.985190i	$0.554851\pi$
$104$	−1.42544	−0.139776
$105$	−16.3826	−1.59878
$106$	15.0222	1.45908
$107$	13.8099	1.33505	0.667527	−	0.744586i	$-0.267353\pi$
$107$	13.8099	1.33505	0.667527	+	0.744586i	$0.267353\pi$
$108$	−14.6782	−1.41241
$109$	15.2278	1.45856	0.729279	−	0.684217i	$-0.239856\pi$
$109$	15.2278	1.45856	0.729279	+	0.684217i	$0.239856\pi$
$110$	5.40902	0.515730
$111$	23.6594	2.24565
$112$	−40.9764	−3.87191
$113$	17.2682	1.62445	0.812226	−	0.583343i	$-0.198256\pi$
$113$	17.2682	1.62445	0.812226	+	0.583343i	$0.198256\pi$
$114$	61.4056	5.75116
$115$	−2.33887	−0.218101
$116$	5.49034	0.509765
$117$	0.598342	0.0553167
$118$	−6.71086	−0.617784
$119$	−18.4153	−1.68813
$120$	−57.9105	−5.28648
$121$	−10.2550	−0.932272
$122$	40.6797	3.68296
$123$	−6.30981	−0.568937
$124$	−19.1882	−1.72315
$125$	10.8925	0.974252
$126$	29.6561	2.64198
$127$	−11.6708	−1.03562	−0.517808	−	0.855497i	$-0.673252\pi$
$127$	−11.6708	−1.03562	−0.517808	+	0.855497i	$0.673252\pi$
$128$	−39.9531	−3.53139
$129$	17.6200	1.55136
$130$	0.935122	0.0820156
$131$	−0.572369	−0.0500081	−0.0250041	−	0.999687i	$-0.507960\pi$
$131$	−0.572369	−0.0500081	−0.0250041	+	0.999687i	$0.507960\pi$
$132$	−12.5468	−1.09206
$133$	−22.9008	−1.98575
$134$	25.1358	2.17140
$135$	6.12155	0.526859
$136$	−65.0958	−5.58192
$137$	−8.30277	−0.709353	−0.354677	−	0.934989i	$-0.615409\pi$
$137$	−8.30277	−0.709353	−0.354677	+	0.934989i	$0.615409\pi$
$138$	7.40154	0.630061
$139$	16.6615	1.41321	0.706606	−	0.707607i	$-0.250225\pi$
$139$	16.6615	1.41321	0.706606	+	0.707607i	$0.250225\pi$
$140$	33.9728	2.87122
$141$	−10.8795	−0.916217
$142$	32.3055	2.71102
$143$	0.128799	0.0107707
$144$	60.8007	5.06672
$145$	−2.28975	−0.190153
$146$	5.90934	0.489061
$147$	−0.801685	−0.0661218
$148$	−49.0627	−4.03293
$149$	10.5324	0.862846	0.431423	−	0.902150i	$-0.358012\pi$
$149$	10.5324	0.862846	0.431423	+	0.902150i	$0.358012\pi$
$150$	1.76036	0.143732
$151$	11.4785	0.934104	0.467052	−	0.884230i	$-0.345316\pi$
$151$	11.4785	0.934104	0.467052	+	0.884230i	$0.345316\pi$
$152$	−80.9513	−6.56602
$153$	27.3246	2.20907
$154$	6.38375	0.514418
$155$	8.00242	0.642770
$156$	−2.16911	−0.173668
$157$	−3.77001	−0.300879	−0.150440	−	0.988619i	$-0.548069\pi$
$157$	−3.77001	−0.300879	−0.150440	+	0.988619i	$0.548069\pi$
$158$	−27.3215	−2.17358
$159$	14.5323	1.15248
$160$	51.2769	4.05380
$161$	−2.76035	−0.217546
$162$	13.5503	1.06461
$163$	−14.8559	−1.16361	−0.581803	−	0.813330i	$-0.697652\pi$
$163$	−14.8559	−1.16361	−0.581803	+	0.813330i	$0.697652\pi$
$164$	13.0847	1.02174
$165$	5.23263	0.407360
$166$	−47.6392	−3.69752
$167$	−3.95871	−0.306334	−0.153167	−	0.988200i	$-0.548947\pi$
$167$	−3.95871	−0.306334	−0.153167	+	0.988200i	$0.548947\pi$
$168$	−68.3463	−5.27303
$169$	−12.9777	−0.998287
$170$	42.7044	3.27528
$171$	33.9801	2.59853
$172$	−36.5388	−2.78605
$173$	1.11167	0.0845185	0.0422592	−	0.999107i	$-0.486544\pi$
$173$	1.11167	0.0845185	0.0422592	+	0.999107i	$0.486544\pi$
$174$	7.24607	0.549323
$175$	−0.656512	−0.0496276
$176$	13.0879	0.986537
$177$	−6.49201	−0.487969
$178$	−37.1941	−2.78781
$179$	−21.4433	−1.60275	−0.801374	−	0.598163i	$-0.795897\pi$
$179$	−21.4433	−1.60275	−0.801374	+	0.598163i	$0.795897\pi$
$180$	−50.4087	−3.75725
$181$	21.1566	1.57256	0.786280	−	0.617870i	$-0.212004\pi$
$181$	21.1566	1.57256	0.786280	+	0.617870i	$0.212004\pi$
$182$	1.10363	0.0818068
$183$	39.3531	2.90906
$184$	−9.75748	−0.719331
$185$	20.4616	1.50437
$186$	−25.3243	−1.85686
$187$	5.88187	0.430125
$188$	22.5608	1.64542
$189$	7.22468	0.525518
$190$	53.1060	3.85272
$191$	−25.3677	−1.83554	−0.917771	−	0.397111i	$-0.870013\pi$
$191$	−25.3677	−1.83554	−0.917771	+	0.397111i	$0.870013\pi$
$192$	−81.9779	−5.91624
$193$	26.3611	1.89752	0.948759	−	0.316002i	$-0.102341\pi$
$193$	26.3611	1.89752	0.948759	+	0.316002i	$0.102341\pi$
$194$	29.4340	2.11324
$195$	0.904627	0.0647816
$196$	1.66246	0.118747
$197$	11.7915	0.840109	0.420055	−	0.907499i	$-0.362011\pi$
$197$	11.7915	0.840109	0.420055	+	0.907499i	$0.362011\pi$
$198$	−9.47220	−0.673160
$199$	0.893815	0.0633609	0.0316804	−	0.999498i	$-0.489914\pi$
$199$	0.893815	0.0633609	0.0316804	+	0.999498i	$0.489914\pi$
$200$	−2.32068	−0.164097
$201$	24.3161	1.71512
$202$	7.70961	0.542447
$203$	−2.70237	−0.189669
$204$	−99.0571	−6.93539
$205$	−5.45698	−0.381132
$206$	9.52541	0.663667
$207$	4.09580	0.284678
$208$	2.26266	0.156887
$209$	7.31453	0.505957
$210$	44.8368	3.09403
$211$	−1.06122	−0.0730577	−0.0365288	−	0.999333i	$-0.511630\pi$
$211$	−1.06122	−0.0730577	−0.0365288	+	0.999333i	$0.511630\pi$
$212$	−30.1356	−2.06972
$213$	31.2520	2.14135
$214$	−37.7956	−2.58365
$215$	15.2385	1.03926
$216$	25.5383	1.73766
$217$	9.44450	0.641134
$218$	−41.6762	−2.82267
$219$	5.71663	0.386294
$220$	−10.8509	−0.731570
$221$	1.01687	0.0684020
$222$	−64.7522	−4.34588
$223$	−16.2353	−1.08720	−0.543599	−	0.839345i	$-0.682939\pi$
$223$	−16.2353	−1.08720	−0.543599	+	0.839345i	$0.682939\pi$
$224$	60.5173	4.04348
$225$	0.974131	0.0649421
$226$	−47.2603	−3.14371
$227$	3.29596	0.218761	0.109380	−	0.994000i	$-0.465113\pi$
$227$	3.29596	0.218761	0.109380	+	0.994000i	$0.465113\pi$
$228$	−123.185	−8.15810
$229$	−4.29270	−0.283669	−0.141835	−	0.989890i	$-0.545300\pi$
$229$	−4.29270	−0.283669	−0.141835	+	0.989890i	$0.545300\pi$
$230$	6.40115	0.422079
$231$	6.17557	0.406323
$232$	−9.55253	−0.627154
$233$	−20.0545	−1.31381	−0.656907	−	0.753972i	$-0.728136\pi$
$233$	−20.0545	−1.31381	−0.656907	+	0.753972i	$0.728136\pi$
$234$	−1.63757	−0.107051
$235$	−9.40900	−0.613776
$236$	13.4625	0.876335
$237$	−26.4305	−1.71684
$238$	50.4000	3.26694
$239$	−2.62854	−0.170026	−0.0850130	−	0.996380i	$-0.527093\pi$
$239$	−2.62854	−0.170026	−0.0850130	+	0.996380i	$0.527093\pi$
$240$	91.9239	5.93366
$241$	6.29334	0.405390	0.202695	−	0.979242i	$-0.435030\pi$
$241$	6.29334	0.405390	0.202695	+	0.979242i	$0.435030\pi$
$242$	28.0664	1.80417
$243$	21.1288	1.35541
$244$	−81.6067	−5.22433
$245$	−0.693329	−0.0442951
$246$	17.2690	1.10103
$247$	1.26455	0.0804613
$248$	33.3851	2.11995
$249$	−46.0857	−2.92056
$250$	−29.8110	−1.88541
$251$	−23.3370	−1.47302	−0.736511	−	0.676426i	$-0.763528\pi$
$251$	−23.3370	−1.47302	−0.736511	+	0.676426i	$0.763528\pi$
$252$	−59.4926	−3.74768
$253$	0.881659	0.0554294
$254$	31.9412	2.00417
$255$	41.3118	2.58705
$256$	47.4192	2.96370
$257$	−14.0149	−0.874228	−0.437114	−	0.899406i	$-0.643999\pi$
$257$	−14.0149	−0.874228	−0.437114	+	0.899406i	$0.643999\pi$
$258$	−48.2233	−3.00225
$259$	24.1489	1.50054
$260$	−1.87593	−0.116340
$261$	4.00977	0.248198
$262$	1.56649	0.0967779
$263$	−19.5197	−1.20363	−0.601817	−	0.798634i	$-0.705556\pi$
$263$	−19.5197	−1.20363	−0.601817	+	0.798634i	$0.705556\pi$
$264$	21.8299	1.34353
$265$	12.5681	0.772051
$266$	62.6760	3.84291
$267$	−35.9811	−2.20201
$268$	−50.4244	−3.08016
$269$	14.7501	0.899329	0.449665	−	0.893198i	$-0.351544\pi$
$269$	14.7501	0.899329	0.449665	+	0.893198i	$0.351544\pi$
$270$	−16.7538	−1.01960
$271$	8.02393	0.487419	0.243710	−	0.969848i	$-0.421636\pi$
$271$	8.02393	0.487419	0.243710	+	0.969848i	$0.421636\pi$
$272$	103.329	6.26527
$273$	1.06764	0.0646168
$274$	22.7234	1.37277
$275$	0.209690	0.0126448
$276$	−14.8481	−0.893750
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	−45.6001	−2.73491
$279$	−14.0137	−0.838980
$280$	−59.1085	−3.53241
$281$	13.8621	0.826944	0.413472	−	0.910517i	$-0.364316\pi$
$281$	13.8621	0.826944	0.413472	+	0.910517i	$0.364316\pi$
$282$	29.7755	1.77310
$283$	24.2036	1.43875	0.719376	−	0.694620i	$-0.244428\pi$
$283$	24.2036	1.43875	0.719376	+	0.694620i	$0.244428\pi$
$284$	−64.8074	−3.84561
$285$	51.3742	3.04314
$286$	−0.352502	−0.0208439
$287$	−6.44035	−0.380162
$288$	−89.7954	−5.29124
$289$	29.4376	1.73162
$290$	6.26669	0.367993
$291$	28.4741	1.66918
$292$	−11.8546	−0.693739
$293$	6.92896	0.404794	0.202397	−	0.979304i	$-0.435127\pi$
$293$	6.92896	0.404794	0.202397	+	0.979304i	$0.435127\pi$
$294$	2.19409	0.127962
$295$	−5.61455	−0.326892
$296$	85.3631	4.96163
$297$	−2.30757	−0.133899
$298$	−28.8255	−1.66982
$299$	0.152423	0.00881483
$300$	−3.53142	−0.203886
$301$	17.9845	1.03661
$302$	−31.4148	−1.80772
$303$	7.45820	0.428462
$304$	128.498	7.36984
$305$	34.0341	1.94879
$306$	−74.7834	−4.27508
$307$	−19.7142	−1.12515	−0.562574	−	0.826747i	$-0.690189\pi$
$307$	−19.7142	−1.12515	−0.562574	+	0.826747i	$0.690189\pi$
$308$	−12.8063	−0.729708
$309$	9.21478	0.524210
$310$	−21.9014	−1.24392
$311$	−6.76341	−0.383518	−0.191759	−	0.981442i	$-0.561419\pi$
$311$	−6.76341	−0.383518	−0.191759	+	0.981442i	$0.561419\pi$
$312$	3.77398	0.213660
$313$	29.1325	1.64667	0.823334	−	0.567558i	$-0.192112\pi$
$313$	29.1325	1.64667	0.823334	+	0.567558i	$0.192112\pi$
$314$	10.3179	0.582275
$315$	24.8114	1.39796
$316$	54.8091	3.08325
$317$	1.62040	0.0910106	0.0455053	−	0.998964i	$-0.485510\pi$
$317$	1.62040	0.0910106	0.0455053	+	0.998964i	$0.485510\pi$
$318$	−39.7726	−2.23034
$319$	0.863139	0.0483265
$320$	−70.8977	−3.96330
$321$	−36.5631	−2.04075
$322$	7.55466	0.421005
$323$	57.7485	3.21321
$324$	−27.1830	−1.51017
$325$	0.0362517	0.00201088
$326$	40.6584	2.25186
$327$	−40.3171	−2.22954
$328$	−22.7658	−1.25703
$329$	−11.1045	−0.612213
$330$	−14.3209	−0.788341
$331$	−14.6008	−0.802530	−0.401265	−	0.915962i	$-0.631429\pi$
$331$	−14.6008	−0.802530	−0.401265	+	0.915962i	$0.631429\pi$
$332$	95.5682	5.24498
$333$	−35.8320	−1.96358
$334$	10.8344	0.592831
$335$	21.0295	1.14896
$336$	108.489	5.91856
$337$	−1.15751	−0.0630538	−0.0315269	−	0.999503i	$-0.510037\pi$
$337$	−1.15751	−0.0630538	−0.0315269	+	0.999503i	$0.510037\pi$
$338$	35.5181	1.93193
$339$	−45.7191	−2.48312
$340$	−85.6685	−4.64603
$341$	−3.01658	−0.163357
$342$	−92.9985	−5.02878
$343$	18.0983	0.977217
$344$	63.5730	3.42763
$345$	6.19240	0.333388
$346$	−3.04246	−0.163564
$347$	−8.32674	−0.447003	−0.223502	−	0.974704i	$-0.571749\pi$
$347$	−8.32674	−0.447003	−0.223502	+	0.974704i	$0.571749\pi$
$348$	−14.5362	−0.779222
$349$	10.6599	0.570613	0.285307	−	0.958436i	$-0.407905\pi$
$349$	10.6599	0.570613	0.285307	+	0.958436i	$0.407905\pi$
$350$	1.79677	0.0960416
$351$	−0.398937	−0.0212937
$352$	−19.3293	−1.03025
$353$	25.0288	1.33215	0.666075	−	0.745884i	$-0.267973\pi$
$353$	25.0288	1.33215	0.666075	+	0.745884i	$0.267973\pi$
$354$	17.7676	0.944340
$355$	27.0279	1.43449
$356$	74.6143	3.95455
$357$	48.7564	2.58046
$358$	58.6871	3.10171
$359$	−3.65006	−0.192643	−0.0963214	−	0.995350i	$-0.530708\pi$
$359$	−3.65006	−0.192643	−0.0963214	+	0.995350i	$0.530708\pi$
$360$	87.7051	4.62247
$361$	52.8144	2.77970
$362$	−57.9025	−3.04329
$363$	27.1511	1.42506
$364$	−2.21398	−0.116044
$365$	4.94397	0.258779
$366$	−107.703	−5.62974
$367$	−32.4458	−1.69366	−0.846828	−	0.531868i	$-0.821490\pi$
$367$	−32.4458	−1.69366	−0.846828	+	0.531868i	$0.821490\pi$
$368$	15.4885	0.807393
$369$	9.55617	0.497474
$370$	−56.0003	−2.91131
$371$	14.8329	0.770086
$372$	50.8025	2.63399
$373$	12.5611	0.650388	0.325194	−	0.945647i	$-0.394570\pi$
$373$	12.5611	0.650388	0.325194	+	0.945647i	$0.394570\pi$
$374$	−16.0978	−0.832397
$375$	−28.8389	−1.48923
$376$	−39.2531	−2.02433
$377$	0.149221	0.00768527
$378$	−19.7729	−1.01701
$379$	15.2020	0.780872	0.390436	−	0.920630i	$-0.372324\pi$
$379$	15.2020	0.780872	0.390436	+	0.920630i	$0.372324\pi$
$380$	−106.535	−5.46513
$381$	30.8996	1.58303
$382$	69.4275	3.55222
$383$	32.8439	1.67824	0.839122	−	0.543944i	$-0.183069\pi$
$383$	32.8439	1.67824	0.839122	+	0.543944i	$0.183069\pi$
$384$	105.780	5.39804
$385$	5.34088	0.272196
$386$	−72.1465	−3.67216
$387$	−26.6854	−1.35650
$388$	−59.0470	−2.99766
$389$	−3.82367	−0.193868	−0.0969339	−	0.995291i	$-0.530904\pi$
$389$	−3.82367	−0.193868	−0.0969339	+	0.995291i	$0.530904\pi$
$390$	−2.47583	−0.125368
$391$	6.96072	0.352019
$392$	−2.89248	−0.146092
$393$	1.51540	0.0764419
$394$	−32.2715	−1.62582
$395$	−22.8581	−1.15012
$396$	19.0020	0.954886
$397$	−29.4563	−1.47837	−0.739185	−	0.673503i	$-0.764789\pi$
$397$	−29.4563	−1.47837	−0.739185	+	0.673503i	$0.764789\pi$
$398$	−2.44624	−0.122619
$399$	60.6320	3.03540
$400$	3.68372	0.184186
$401$	−13.0508	−0.651724	−0.325862	−	0.945417i	$-0.605654\pi$
$401$	−13.0508	−0.651724	−0.325862	+	0.945417i	$0.605654\pi$
$402$	−66.5494	−3.31918
$403$	−0.521512	−0.0259784
$404$	−15.4661	−0.769468
$405$	11.3367	0.563324
$406$	7.39597	0.367056
$407$	−7.71317	−0.382327
$408$	172.347	8.53247
$409$	12.0458	0.595627	0.297813	−	0.954624i	$-0.403743\pi$
$409$	12.0458	0.595627	0.297813	+	0.954624i	$0.403743\pi$
$410$	14.9349	0.737583
$411$	21.9824	1.08431
$412$	−19.1087	−0.941420
$413$	−6.62631	−0.326060
$414$	−11.2096	−0.550921
$415$	−39.8567	−1.95649
$416$	−3.34168	−0.163839
$417$	−44.1130	−2.16022
$418$	−20.0188	−0.979150
$419$	−6.76325	−0.330407	−0.165203	−	0.986260i	$-0.552828\pi$
$419$	−6.76325	−0.330407	−0.165203	+	0.986260i	$0.552828\pi$
$420$	−89.9462	−4.38893
$421$	−7.90463	−0.385248	−0.192624	−	0.981273i	$-0.561700\pi$
$421$	−7.90463	−0.385248	−0.192624	+	0.981273i	$0.561700\pi$
$422$	2.90441	0.141384
$423$	16.4769	0.801134
$424$	52.4324	2.54634
$425$	1.65551	0.0803042
$426$	−85.5319	−4.14403
$427$	40.1672	1.94383
$428$	75.8210	3.66495
$429$	−0.341007	−0.0164640
$430$	−41.7054	−2.01122
$431$	−18.0753	−0.870657	−0.435329	−	0.900272i	$-0.643368\pi$
$431$	−18.0753	−0.870657	−0.435329	+	0.900272i	$0.643368\pi$
$432$	−40.5381	−1.95039
$433$	−0.829719	−0.0398737	−0.0199369	−	0.999801i	$-0.506347\pi$
$433$	−0.829719	−0.0398737	−0.0199369	+	0.999801i	$0.506347\pi$
$434$	−25.8482	−1.24075
$435$	6.06233	0.290666
$436$	83.6057	4.00399
$437$	8.65616	0.414080
$438$	−15.6456	−0.747574
$439$	−33.3484	−1.59163	−0.795815	−	0.605539i	$-0.792957\pi$
$439$	−33.3484	−1.59163	−0.795815	+	0.605539i	$0.792957\pi$
$440$	18.8793	0.900037
$441$	1.21415	0.0578165
$442$	−2.78302	−0.132375
$443$	−32.6001	−1.54888	−0.774439	−	0.632648i	$-0.781968\pi$
$443$	−32.6001	−1.54888	−0.774439	+	0.632648i	$0.781968\pi$
$444$	129.898	6.16469
$445$	−31.1179	−1.47513
$446$	44.4336	2.10399
$447$	−27.8855	−1.31894
$448$	−83.6738	−3.95322
$449$	0.346805	0.0163667	0.00818337	−	0.999967i	$-0.497395\pi$
$449$	0.346805	0.0163667	0.00818337	+	0.999967i	$0.497395\pi$
$450$	−2.66605	−0.125679
$451$	2.05705	0.0968628
$452$	94.8081	4.45940
$453$	−30.3904	−1.42786
$454$	−9.02055	−0.423355
$455$	0.923341	0.0432869
$456$	214.326	10.0368
$457$	−5.45945	−0.255382	−0.127691	−	0.991814i	$-0.540757\pi$
$457$	−5.45945	−0.255382	−0.127691	+	0.991814i	$0.540757\pi$
$458$	11.7485	0.548969
$459$	−18.2183	−0.850359
$460$	−12.8412	−0.598725
$461$	4.37622	0.203821	0.101911	−	0.994794i	$-0.467504\pi$
$461$	4.37622	0.203821	0.101911	+	0.994794i	$0.467504\pi$
$462$	−16.9016	−0.786334
$463$	−0.289367	−0.0134480	−0.00672401	−	0.999977i	$-0.502140\pi$
$463$	−0.289367	−0.0134480	−0.00672401	+	0.999977i	$0.502140\pi$
$464$	15.1631	0.703931
$465$	−21.1872	−0.982533
$466$	54.8861	2.54255
$467$	−10.5773	−0.489458	−0.244729	−	0.969592i	$-0.578699\pi$
$467$	−10.5773	−0.489458	−0.244729	+	0.969592i	$0.578699\pi$
$468$	3.28510	0.151854
$469$	24.8191	1.14604
$470$	25.7510	1.18781
$471$	9.98146	0.459921
$472$	−23.4232	−1.07814
$473$	−5.74428	−0.264122
$474$	72.3362	3.32251
$475$	2.05875	0.0944619
$476$	−101.106	−4.63420
$477$	−22.0090	−1.00772
$478$	7.19391	0.329042
$479$	−3.61740	−0.165283	−0.0826417	−	0.996579i	$-0.526336\pi$
$479$	−3.61740	−0.165283	−0.0826417	+	0.996579i	$0.526336\pi$
$480$	−135.761	−6.19660
$481$	−1.33347	−0.0608008
$482$	−17.2239	−0.784528
$483$	7.30829	0.332539
$484$	−56.3034	−2.55924
$485$	24.6256	1.11819
$486$	−57.8263	−2.62305
$487$	41.0871	1.86183	0.930917	−	0.365231i	$-0.119010\pi$
$487$	41.0871	1.86183	0.930917	+	0.365231i	$0.119010\pi$
$488$	141.986	6.42739
$489$	39.3325	1.77868
$490$	1.89754	0.0857219
$491$	26.6778	1.20395	0.601976	−	0.798514i	$-0.294380\pi$
$491$	26.6778	1.20395	0.601976	+	0.798514i	$0.294380\pi$
$492$	−34.6430	−1.56183
$493$	6.81451	0.306910
$494$	−3.46088	−0.155712
$495$	−7.92479	−0.356193
$496$	−52.9936	−2.37948
$497$	31.8985	1.43084
$498$	126.130	5.65200
$499$	−5.52526	−0.247345	−0.123672	−	0.992323i	$-0.539467\pi$
$499$	−5.52526	−0.247345	−0.123672	+	0.992323i	$0.539467\pi$
$500$	59.8033	2.67449
$501$	10.4811	0.468259
$502$	63.8700	2.85066
$503$	−36.1119	−1.61015	−0.805076	−	0.593172i	$-0.797875\pi$
$503$	−36.1119	−1.61015	−0.805076	+	0.593172i	$0.797875\pi$
$504$	103.510	4.61070
$505$	6.45014	0.287028
$506$	−2.41297	−0.107269
$507$	34.3598	1.52597
$508$	−64.0767	−2.84294
$509$	−6.60513	−0.292767	−0.146384	−	0.989228i	$-0.546763\pi$
$509$	−6.60513	−0.292767	−0.146384	+	0.989228i	$0.546763\pi$
$510$	−113.064	−5.00656
$511$	5.83490	0.258121
$512$	−49.8731	−2.20410
$513$	−22.6558	−1.00028
$514$	38.3568	1.69185
$515$	7.96930	0.351169
$516$	96.7399	4.25874
$517$	3.54680	0.155988
$518$	−66.0917	−2.90390
$519$	−2.94325	−0.129194
$520$	3.26389	0.143131
$521$	4.83236	0.211710	0.105855	−	0.994382i	$-0.466242\pi$
$521$	4.83236	0.211710	0.105855	+	0.994382i	$0.466242\pi$
$522$	−10.9741	−0.480325
$523$	27.8594	1.21821	0.609103	−	0.793091i	$-0.291529\pi$
$523$	27.8594	1.21821	0.609103	+	0.793091i	$0.291529\pi$
$524$	−3.14250	−0.137281
$525$	1.73818	0.0758603
$526$	53.4224	2.32933
$527$	−23.8160	−1.03744
$528$	−34.6515	−1.50801
$529$	−21.9566	−0.954636
$530$	−34.3969	−1.49411
$531$	9.83211	0.426677
$532$	−125.733	−5.45122
$533$	0.355627	0.0154039
$534$	98.4749	4.26143
$535$	−31.6212	−1.36710
$536$	87.7323	3.78946
$537$	56.7733	2.44995
$538$	−40.3688	−1.74042
$539$	0.261356	0.0112574
$540$	33.6094	1.44632
$541$	−8.99679	−0.386802	−0.193401	−	0.981120i	$-0.561952\pi$
$541$	−8.99679	−0.386802	−0.193401	+	0.981120i	$0.561952\pi$
$542$	−21.9603	−0.943275
$543$	−56.0142	−2.40380
$544$	−152.605	−6.54290
$545$	−34.8678	−1.49357
$546$	−2.92198	−0.125049
$547$	5.85665	0.250412	0.125206	−	0.992131i	$-0.460041\pi$
$547$	5.85665	0.250412	0.125206	+	0.992131i	$0.460041\pi$
$548$	−45.5850	−1.94730
$549$	−59.6000	−2.54366
$550$	−0.573891	−0.0244708
$551$	8.47434	0.361019
$552$	25.8339	1.09956
$553$	−26.9773	−1.14719
$554$	−2.73685	−0.116278
$555$	−54.1740	−2.29956
$556$	91.4774	3.87951
$557$	32.4117	1.37333	0.686664	−	0.726975i	$-0.259074\pi$
$557$	32.4117	1.37333	0.686664	+	0.726975i	$0.259074\pi$
$558$	38.3534	1.62363
$559$	−0.993081	−0.0420028
$560$	93.8256	3.96485
$561$	−15.5728	−0.657485
$562$	−37.9385	−1.60034
$563$	−12.6107	−0.531479	−0.265739	−	0.964045i	$-0.585616\pi$
$563$	−12.6107	−0.531479	−0.265739	+	0.964045i	$0.585616\pi$
$564$	−59.7320	−2.51517
$565$	−39.5397	−1.66345
$566$	−66.2415	−2.78434
$567$	13.3796	0.561890
$568$	112.757	4.73118
$569$	10.4193	0.436800	0.218400	−	0.975859i	$-0.429916\pi$
$569$	10.4193	0.436800	0.218400	+	0.975859i	$0.429916\pi$
$570$	−140.603	−5.88923
$571$	−36.2935	−1.51883	−0.759417	−	0.650604i	$-0.774516\pi$
$571$	−36.2935	−1.51883	−0.759417	+	0.650604i	$0.774516\pi$
$572$	0.707147	0.0295673
$573$	67.1634	2.80579
$574$	17.6263	0.735705
$575$	0.248152	0.0103486
$576$	124.155	5.17313
$577$	−9.33972	−0.388818	−0.194409	−	0.980921i	$-0.562279\pi$
$577$	−9.33972	−0.388818	−0.194409	+	0.980921i	$0.562279\pi$
$578$	−80.5662	−3.35111
$579$	−69.7937	−2.90053
$580$	−12.5715	−0.522002
$581$	−47.0391	−1.95151
$582$	−77.9294	−3.23028
$583$	−4.73764	−0.196213
$584$	20.6256	0.853494
$585$	−1.37005	−0.0566447
$586$	−18.9635	−0.783375
$587$	−25.5960	−1.05646	−0.528231	−	0.849101i	$-0.677144\pi$
$587$	−25.5960	−1.05646	−0.528231	+	0.849101i	$0.677144\pi$
$588$	−4.40152	−0.181516
$589$	−29.6169	−1.22034
$590$	15.3662	0.632615
$591$	−31.2191	−1.28418
$592$	−135.501	−5.56904
$593$	22.3119	0.916239	0.458120	−	0.888890i	$-0.348523\pi$
$593$	22.3119	0.916239	0.458120	+	0.888890i	$0.348523\pi$
$594$	6.31547	0.259127
$595$	42.1664	1.72866
$596$	57.8263	2.36866
$597$	−2.36646	−0.0968528
$598$	−0.417158	−0.0170588
$599$	13.4793	0.550750	0.275375	−	0.961337i	$-0.411198\pi$
$599$	13.4793	0.550750	0.275375	+	0.961337i	$0.411198\pi$
$600$	6.14424	0.250837
$601$	0.788398	0.0321594	0.0160797	−	0.999871i	$-0.494881\pi$
$601$	0.788398	0.0321594	0.0160797	+	0.999871i	$0.494881\pi$
$602$	−49.2209	−2.00610
$603$	−36.8265	−1.49969
$604$	63.0207	2.56427
$605$	23.4813	0.954652
$606$	−20.4119	−0.829179
$607$	−28.1817	−1.14386	−0.571930	−	0.820302i	$-0.693805\pi$
$607$	−28.1817	−1.14386	−0.571930	+	0.820302i	$0.693805\pi$
$608$	−189.776	−7.69642
$609$	7.15478	0.289926
$610$	−93.1461	−3.77138
$611$	0.613177	0.0248065
$612$	150.021	6.06426
$613$	8.35657	0.337518	0.168759	−	0.985657i	$-0.446024\pi$
$613$	8.35657	0.337518	0.168759	+	0.985657i	$0.446024\pi$
$614$	53.9548	2.17744
$615$	14.4479	0.582594
$616$	22.2815	0.897746
$617$	17.8976	0.720530	0.360265	−	0.932850i	$-0.382686\pi$
$617$	17.8976	0.720530	0.360265	+	0.932850i	$0.382686\pi$
$618$	−25.2194	−1.01447
$619$	16.5862	0.666658	0.333329	−	0.942811i	$-0.391828\pi$
$619$	16.5862	0.666658	0.333329	+	0.942811i	$0.391828\pi$
$620$	43.9360	1.76451
$621$	−2.73082	−0.109584
$622$	18.5104	0.742200
$623$	−36.7255	−1.47138
$624$	−5.99061	−0.239816
$625$	−26.1557	−1.04623
$626$	−79.7313	−3.18670
$627$	−19.3659	−0.773401
$628$	−20.6986	−0.825964
$629$	−60.8957	−2.42807
$630$	−67.9051	−2.70540
$631$	−44.4286	−1.76868	−0.884338	−	0.466847i	$-0.845390\pi$
$631$	−44.4286	−1.76868	−0.884338	+	0.466847i	$0.845390\pi$
$632$	−95.3612	−3.79326
$633$	2.80969	0.111675
$634$	−4.43478	−0.176128
$635$	26.7232	1.06048
$636$	79.7871	3.16376
$637$	0.0451837	0.00179024
$638$	−2.36228	−0.0935236
$639$	−47.3309	−1.87238
$640$	91.4824	3.61616
$641$	33.3362	1.31670	0.658350	−	0.752712i	$-0.271255\pi$
$641$	33.3362	1.31670	0.658350	+	0.752712i	$0.271255\pi$
$642$	100.068	3.94935
$643$	−29.1660	−1.15019	−0.575097	−	0.818085i	$-0.695036\pi$
$643$	−29.1660	−1.15019	−0.575097	+	0.818085i	$0.695036\pi$
$644$	−15.1553	−0.597201
$645$	−40.3454	−1.58860
$646$	−158.049	−6.21835
$647$	41.5942	1.63524	0.817619	−	0.575760i	$-0.195294\pi$
$647$	41.5942	1.63524	0.817619	+	0.575760i	$0.195294\pi$
$648$	47.2951	1.85793
$649$	2.11645	0.0830779
$650$	−0.0992153	−0.00389154
$651$	−25.0052	−0.980032
$652$	−81.5640	−3.19429
$653$	−15.5482	−0.608447	−0.304224	−	0.952601i	$-0.598397\pi$
$653$	−15.5482	−0.608447	−0.304224	+	0.952601i	$0.598397\pi$
$654$	110.342	4.31470
$655$	1.31058	0.0512086
$656$	36.1371	1.41092
$657$	−8.65781	−0.337773
$658$	30.3914	1.18478
$659$	−7.99990	−0.311632	−0.155816	−	0.987786i	$-0.549801\pi$
$659$	−7.99990	−0.311632	−0.155816	+	0.987786i	$0.549801\pi$
$660$	28.7289	1.11827
$661$	29.1446	1.13360	0.566798	−	0.823857i	$-0.308182\pi$
$661$	29.1446	1.13360	0.566798	+	0.823857i	$0.308182\pi$
$662$	39.9601	1.55309
$663$	−2.69226	−0.104559
$664$	−166.277	−6.45280
$665$	52.4370	2.03342
$666$	98.0668	3.80001
$667$	1.02146	0.0395509
$668$	−21.7346	−0.840938
$669$	42.9846	1.66188
$670$	−57.5545	−2.22353
$671$	−12.8294	−0.495275
$672$	−160.225	−6.18083
$673$	−17.7871	−0.685642	−0.342821	−	0.939401i	$-0.611382\pi$
$673$	−17.7871	−0.685642	−0.342821	+	0.939401i	$0.611382\pi$
$674$	3.16794	0.122024
$675$	−0.649489	−0.0249989
$676$	−71.2521	−2.74047
$677$	23.5508	0.905129	0.452565	−	0.891732i	$-0.350509\pi$
$677$	23.5508	0.905129	0.452565	+	0.891732i	$0.350509\pi$
$678$	125.126	4.80545
$679$	29.0632	1.11534
$680$	149.053	5.71592
$681$	−8.72638	−0.334395
$682$	8.25592	0.316136
$683$	12.7588	0.488202	0.244101	−	0.969750i	$-0.421507\pi$
$683$	12.7588	0.488202	0.244101	+	0.969750i	$0.421507\pi$
$684$	186.562	7.13339
$685$	19.0112	0.726382
$686$	−49.5323	−1.89115
$687$	11.3653	0.433614
$688$	−100.912	−3.84724
$689$	−0.819052	−0.0312034
$690$	−16.9477	−0.645186
$691$	22.7996	0.867339	0.433670	−	0.901072i	$-0.357218\pi$
$691$	22.7996	0.867339	0.433670	+	0.901072i	$0.357218\pi$
$692$	6.10343	0.232018
$693$	−9.35287	−0.355286
$694$	22.7890	0.865060
$695$	−38.1507	−1.44714
$696$	25.2912	0.958662
$697$	16.2405	0.615153
$698$	−29.1746	−1.10428
$699$	53.0962	2.00828
$700$	−3.60447	−0.136236
$701$	−29.4525	−1.11241	−0.556203	−	0.831046i	$-0.687742\pi$
$701$	−29.4525	−1.11241	−0.556203	+	0.831046i	$0.687742\pi$
$702$	1.09183	0.0412084
$703$	−75.7282	−2.85614
$704$	26.7255	1.00725
$705$	24.9112	0.938212
$706$	−68.5002	−2.57804
$707$	7.61249	0.286297
$708$	−35.6433	−1.33956
$709$	3.95074	0.148373	0.0741865	−	0.997244i	$-0.476364\pi$
$709$	3.95074	0.148373	0.0741865	+	0.997244i	$0.476364\pi$
$710$	−73.9714	−2.77610
$711$	40.0288	1.50120
$712$	−129.820	−4.86521
$713$	−3.56988	−0.133693
$714$	−133.439	−4.99382
$715$	−0.294916	−0.0110292
$716$	−117.731	−4.39982
$717$	6.95931	0.259900
$718$	9.98966	0.372811
$719$	−25.4506	−0.949148	−0.474574	−	0.880215i	$-0.657398\pi$
$719$	−25.4506	−0.949148	−0.474574	+	0.880215i	$0.657398\pi$
$720$	−139.218	−5.18835
$721$	9.40541	0.350276
$722$	−144.545	−5.37940
$723$	−16.6622	−0.619675
$724$	116.157	4.31694
$725$	0.242939	0.00902254
$726$	−74.3084	−2.75784
$727$	37.9232	1.40649	0.703247	−	0.710945i	$-0.251733\pi$
$727$	37.9232	1.40649	0.703247	+	0.710945i	$0.251733\pi$
$728$	3.85206	0.142767
$729$	−41.0874	−1.52175
$730$	−13.5309	−0.500801
$731$	−45.3513	−1.67738
$732$	216.062	7.98587
$733$	−1.19837	−0.0442628	−0.0221314	−	0.999755i	$-0.507045\pi$
$733$	−1.19837	−0.0442628	−0.0221314	+	0.999755i	$0.507045\pi$
$734$	88.7991	3.27764
$735$	1.83565	0.0677091
$736$	−22.8746	−0.843170
$737$	−7.92724	−0.292004
$738$	−26.1538	−0.962734
$739$	24.9859	0.919122	0.459561	−	0.888146i	$-0.348007\pi$
$739$	24.9859	0.919122	0.459561	+	0.888146i	$0.348007\pi$
$740$	112.341	4.12974
$741$	−3.34802	−0.122992
$742$	−40.5954	−1.49030
$743$	42.3810	1.55481	0.777404	−	0.629002i	$-0.216536\pi$
$743$	42.3810	1.55481	0.777404	+	0.629002i	$0.216536\pi$
$744$	−88.3902	−3.24054
$745$	−24.1165	−0.883559
$746$	−34.3778	−1.25866
$747$	69.7965	2.55372
$748$	32.2935	1.18077
$749$	−37.3194	−1.36362
$750$	78.9276	2.88203
$751$	17.7537	0.647843	0.323922	−	0.946084i	$-0.394999\pi$
$751$	17.7537	0.647843	0.323922	+	0.946084i	$0.394999\pi$
$752$	62.3082	2.27215
$753$	61.7871	2.25165
$754$	−0.408395	−0.0148729
$755$	−26.2828	−0.956528
$756$	39.6659	1.44264
$757$	28.6567	1.04154	0.520772	−	0.853696i	$-0.325644\pi$
$757$	28.6567	1.04154	0.520772	+	0.853696i	$0.325644\pi$
$758$	−41.6055	−1.51118
$759$	−2.33428	−0.0847289
$760$	185.358	6.72364
$761$	1.91464	0.0694057	0.0347028	−	0.999398i	$-0.488952\pi$
$761$	1.91464	0.0694057	0.0347028	+	0.999398i	$0.488952\pi$
$762$	−84.5675	−3.06356
$763$	−41.1511	−1.48977
$764$	−139.277	−5.03887
$765$	−62.5665	−2.26210
$766$	−89.8887	−3.24781
$767$	0.365896	0.0132117
$768$	−125.547	−4.53029
$769$	−28.9507	−1.04399	−0.521994	−	0.852949i	$-0.674812\pi$
$769$	−28.9507	−1.04399	−0.521994	+	0.852949i	$0.674812\pi$
$770$	−14.6172	−0.526767
$771$	37.1059	1.33634
$772$	144.732	5.20901
$773$	17.3869	0.625362	0.312681	−	0.949858i	$-0.398773\pi$
$773$	17.3869	0.625362	0.312681	+	0.949858i	$0.398773\pi$
$774$	73.0339	2.62515
$775$	−0.849048	−0.0304987
$776$	102.735	3.68796
$777$	−63.9364	−2.29371
$778$	10.4648	0.375181
$779$	20.1962	0.723605
$780$	4.96671	0.177837
$781$	−10.1884	−0.364570
$782$	−19.0504	−0.681243
$783$	−2.67346	−0.0955417
$784$	4.59135	0.163977
$785$	8.63236	0.308102
$786$	−4.14743	−0.147934
$787$	−5.71031	−0.203551	−0.101775	−	0.994807i	$-0.532452\pi$
$787$	−5.71031	−0.203551	−0.101775	+	0.994807i	$0.532452\pi$
$788$	64.7393	2.30624
$789$	51.6802	1.83986
$790$	62.5592	2.22576
$791$	−46.6650	−1.65921
$792$	−33.0612	−1.17478
$793$	−2.21797	−0.0787626
$794$	80.6175	2.86101
$795$	−33.2752	−1.18015
$796$	4.90735	0.173936
$797$	−13.7903	−0.488477	−0.244238	−	0.969715i	$-0.578538\pi$
$797$	−13.7903	−0.488477	−0.244238	+	0.969715i	$0.578538\pi$
$798$	−165.941	−5.87424
$799$	28.0021	0.990644
$800$	−5.44042	−0.192348
$801$	54.4932	1.92542
$802$	35.7180	1.26124
$803$	−1.86367	−0.0657675
$804$	133.503	4.70830
$805$	6.32050	0.222768
$806$	1.42730	0.0502745
$807$	−39.0523	−1.37471
$808$	26.9092	0.946661
$809$	−18.4326	−0.648057	−0.324029	−	0.946047i	$-0.605037\pi$
$809$	−18.4326	−0.648057	−0.324029	+	0.946047i	$0.605037\pi$
$810$	−31.0267	−1.09017
$811$	−3.69306	−0.129681	−0.0648404	−	0.997896i	$-0.520654\pi$
$811$	−3.69306	−0.129681	−0.0648404	+	0.997896i	$0.520654\pi$
$812$	−14.8369	−0.520674
$813$	−21.2441	−0.745065
$814$	21.1098	0.739897
$815$	34.0163	1.19154
$816$	−273.575	−9.57703
$817$	−56.3976	−1.97310
$818$	−32.9675	−1.15268
$819$	−1.61694	−0.0565005
$820$	−29.9606	−1.04627
$821$	43.2818	1.51054	0.755272	−	0.655411i	$-0.227505\pi$
$821$	43.2818	1.51054	0.755272	+	0.655411i	$0.227505\pi$
$822$	−60.1625	−2.09841
$823$	34.0553	1.18709	0.593547	−	0.804799i	$-0.297727\pi$
$823$	34.0553	1.18709	0.593547	+	0.804799i	$0.297727\pi$
$824$	33.2469	1.15821
$825$	−0.555176	−0.0193287
$826$	18.1352	0.631005
$827$	39.2596	1.36519	0.682596	−	0.730796i	$-0.260851\pi$
$827$	39.2596	1.36519	0.682596	+	0.730796i	$0.260851\pi$
$828$	22.4873	0.781489
$829$	−6.41994	−0.222974	−0.111487	−	0.993766i	$-0.535561\pi$
$829$	−6.41994	−0.222974	−0.111487	+	0.993766i	$0.535561\pi$
$830$	109.082	3.78628
$831$	−2.64760	−0.0918441
$832$	4.62035	0.160182
$833$	2.06341	0.0714931
$834$	120.731	4.18056
$835$	9.06443	0.313688
$836$	40.1592	1.38894
$837$	9.34347	0.322958
$838$	18.5100	0.639417
$839$	−35.1029	−1.21189	−0.605943	−	0.795508i	$-0.707204\pi$
$839$	−35.1029	−1.21189	−0.605943	+	0.795508i	$0.707204\pi$
$840$	156.496	5.39961
$841$	1.00000	0.0344828
$842$	21.6338	0.745549
$843$	−36.7013	−1.26406
$844$	−5.82648	−0.200556
$845$	29.7157	1.02225
$846$	−45.0948	−1.55039
$847$	27.7128	0.952222
$848$	−83.2282	−2.85807
$849$	−64.0813	−2.19926
$850$	−4.53089	−0.155408
$851$	−9.12791	−0.312901
$852$	171.584	5.87837
$853$	4.88782	0.167356	0.0836779	−	0.996493i	$-0.473333\pi$
$853$	4.88782	0.167356	0.0836779	+	0.996493i	$0.473333\pi$
$854$	−109.931	−3.76178
$855$	−77.8059	−2.66091
$856$	−131.919	−4.50891
$857$	−10.0492	−0.343275	−0.171637	−	0.985160i	$-0.554906\pi$
$857$	−10.0492	−0.343275	−0.171637	+	0.985160i	$0.554906\pi$
$858$	0.933283	0.0318618
$859$	55.6766	1.89966	0.949830	−	0.312767i	$-0.101256\pi$
$859$	55.6766	1.89966	0.949830	+	0.312767i	$0.101256\pi$
$860$	83.6645	2.85294
$861$	17.0514	0.581112
$862$	49.4694	1.68493
$863$	29.0622	0.989289	0.494645	−	0.869095i	$-0.335298\pi$
$863$	29.0622	0.989289	0.494645	+	0.869095i	$0.335298\pi$
$864$	59.8699	2.03682
$865$	−2.54544	−0.0865474
$866$	2.27081	0.0771654
$867$	−77.9389	−2.64694
$868$	51.8535	1.76002
$869$	8.61657	0.292297
$870$	−16.5917	−0.562510
$871$	−1.37048	−0.0464368
$872$	−145.464	−4.92603
$873$	−43.1239	−1.45952
$874$	−23.6906	−0.801346
$875$	−29.4355	−0.995100
$876$	31.3863	1.06044
$877$	16.1426	0.545098	0.272549	−	0.962142i	$-0.412133\pi$
$877$	16.1426	0.545098	0.272549	+	0.962142i	$0.412133\pi$
$878$	91.2694	3.08019
$879$	−18.3451	−0.618764
$880$	−29.9680	−1.01022
$881$	−44.4931	−1.49901	−0.749505	−	0.661999i	$-0.769708\pi$
$881$	−44.4931	−1.49901	−0.749505	+	0.661999i	$0.769708\pi$
$882$	−3.32293	−0.111889
$883$	−49.5729	−1.66826	−0.834131	−	0.551567i	$-0.814030\pi$
$883$	−49.5729	−1.66826	−0.834131	+	0.551567i	$0.814030\pi$
$884$	5.58295	0.187775
$885$	14.8651	0.499683
$886$	89.2216	2.99746
$887$	−30.3246	−1.01820	−0.509100	−	0.860707i	$-0.670022\pi$
$887$	−30.3246	−1.01820	−0.509100	+	0.860707i	$0.670022\pi$
$888$	−226.007	−7.58430
$889$	31.5388	1.05778
$890$	85.1650	2.85474
$891$	−4.27345	−0.143166
$892$	−89.1374	−2.98454
$893$	34.8226	1.16530
$894$	76.3184	2.55247
$895$	49.0998	1.64122
$896$	107.968	3.60696
$897$	−0.403554	−0.0134743
$898$	−0.949153	−0.0316736
$899$	−3.49490	−0.116561
$900$	5.34831	0.178277
$901$	−37.4038	−1.24610
$902$	−5.62984	−0.187453
$903$	−47.6158	−1.58455
$904$	−164.955	−5.48631
$905$	−48.4433	−1.61031
$906$	83.1738	2.76326
$907$	25.1941	0.836557	0.418279	−	0.908319i	$-0.362634\pi$
$907$	25.1941	0.836557	0.418279	+	0.908319i	$0.362634\pi$
$908$	18.0959	0.600535
$909$	−11.2954	−0.374644
$910$	−2.52704	−0.0837707
$911$	4.56070	0.151103	0.0755513	−	0.997142i	$-0.475928\pi$
$911$	4.56070	0.151103	0.0755513	+	0.997142i	$0.475928\pi$
$912$	−340.210	−11.2655
$913$	15.0243	0.497233
$914$	14.9417	0.494227
$915$	−90.1085	−2.97890
$916$	−23.5684	−0.778720
$917$	1.54675	0.0510783
$918$	49.8608	1.64565
$919$	1.41997	0.0468403	0.0234202	−	0.999726i	$-0.492544\pi$
$919$	1.41997	0.0468403	0.0234202	+	0.999726i	$0.492544\pi$
$920$	22.3422	0.736599
$921$	52.1952	1.71989
$922$	−11.9771	−0.394443
$923$	−1.76139	−0.0579768
$924$	33.9060	1.11543
$925$	−2.17095	−0.0713804
$926$	0.791953	0.0260252
$927$	−13.9557	−0.458366
$928$	−22.3942	−0.735124
$929$	17.0943	0.560846	0.280423	−	0.959877i	$-0.409525\pi$
$929$	17.0943	0.560846	0.280423	+	0.959877i	$0.409525\pi$
$930$	57.9861	1.90144
$931$	2.56600	0.0840974
$932$	−110.106	−3.60664
$933$	17.9068	0.586241
$934$	28.9484	0.947220
$935$	−13.4680	−0.440451
$936$	−5.71568	−0.186823
$937$	−23.4402	−0.765759	−0.382880	−	0.923798i	$-0.625068\pi$
$937$	−23.4402	−0.765759	−0.382880	+	0.923798i	$0.625068\pi$
$938$	−67.9261	−2.21787
$939$	−77.1312	−2.51708
$940$	−51.6586	−1.68492
$941$	5.75312	0.187547	0.0937733	−	0.995594i	$-0.470107\pi$
$941$	5.75312	0.187547	0.0937733	+	0.995594i	$0.470107\pi$
$942$	−27.3177	−0.890060
$943$	2.43436	0.0792736
$944$	37.1806	1.21013
$945$	−16.5427	−0.538134
$946$	15.7212	0.511141
$947$	−45.5666	−1.48072	−0.740358	−	0.672213i	$-0.765344\pi$
$947$	−45.5666	−1.48072	−0.740358	+	0.672213i	$0.765344\pi$
$948$	−145.112	−4.71303
$949$	−0.322195	−0.0104589
$950$	−5.63449	−0.182807
$951$	−4.29016	−0.139118
$952$	175.913	5.70137
$953$	55.2219	1.78881	0.894407	−	0.447254i	$-0.147598\pi$
$953$	55.2219	1.78881	0.894407	+	0.447254i	$0.147598\pi$
$954$	60.2354	1.95019
$955$	58.0856	1.87960
$956$	−14.4316	−0.466750
$957$	−2.28524	−0.0738715
$958$	9.90028	0.319864
$959$	22.4371	0.724533
$960$	187.709	6.05827
$961$	−18.7857	−0.605991
$962$	3.64949	0.117664
$963$	55.3745	1.78442
$964$	34.5526	1.11286
$965$	−60.3604	−1.94307
$966$	−20.0017	−0.643544
$967$	−25.7433	−0.827850	−0.413925	−	0.910311i	$-0.635842\pi$
$967$	−25.7433	−0.827850	−0.413925	+	0.910311i	$0.635842\pi$
$968$	97.9611	3.14859
$969$	−152.895	−4.91168
$970$	−67.3964	−2.16397
$971$	23.6841	0.760060	0.380030	−	0.924974i	$-0.375914\pi$
$971$	23.6841	0.760060	0.380030	+	0.924974i	$0.375914\pi$
$972$	116.004	3.72084
$973$	−45.0256	−1.44345
$974$	−112.449	−3.60310
$975$	−0.0959798	−0.00307381
$976$	−225.380	−7.21424
$977$	−12.7735	−0.408661	−0.204330	−	0.978902i	$-0.565502\pi$
$977$	−12.7735	−0.408661	−0.204330	+	0.978902i	$0.565502\pi$
$978$	−107.647	−3.44217
$979$	11.7302	0.374897
$980$	−3.80661	−0.121598
$981$	61.0599	1.94949
$982$	−73.0131	−2.32994
$983$	7.02817	0.224164	0.112082	−	0.993699i	$-0.464248\pi$
$983$	7.02817	0.224164	0.112082	+	0.993699i	$0.464248\pi$
$984$	60.2747	1.92149
$985$	−26.9995	−0.860277
$986$	−18.6503	−0.593946
$987$	29.4004	0.935824
$988$	6.94280	0.220880
$989$	−6.79789	−0.216160
$990$	21.6889	0.689320
$991$	−5.85899	−0.186117	−0.0930585	−	0.995661i	$-0.529664\pi$
$991$	−5.85899	−0.186117	−0.0930585	+	0.995661i	$0.529664\pi$
$992$	78.2652	2.48492
$993$	38.6569	1.22674
$994$	−87.3013	−2.76903
$995$	−2.04661	−0.0648819
$996$	−253.026	−8.01744
$997$	13.0686	0.413886	0.206943	−	0.978353i	$-0.433649\pi$
$997$	13.0686	0.413886	0.206943	+	0.978353i	$0.433649\pi$
$998$	15.1218	0.478672
$999$	23.8905	0.755863

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.c.1.4	✓	154

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.c.1.4	✓	154	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73685 q^{2} -2.64760 q^{3} +5.49034 q^{4} -2.28975 q^{5} +7.24607 q^{6} -2.70237 q^{7} -9.55253 q^{8} +4.00977 q^{9} +O(q^{10})\)	\(q-2.73685 q^{2} -2.64760 q^{3} +5.49034 q^{4} -2.28975 q^{5} +7.24607 q^{6} -2.70237 q^{7} -9.55253 q^{8} +4.00977 q^{9} +6.26669 q^{10} +0.863139 q^{11} -14.5362 q^{12} +0.149221 q^{13} +7.39597 q^{14} +6.06233 q^{15} +15.1631 q^{16} +6.81451 q^{17} -10.9741 q^{18} +8.47434 q^{19} -12.5715 q^{20} +7.15478 q^{21} -2.36228 q^{22} +1.02146 q^{23} +25.2912 q^{24} +0.242939 q^{25} -0.408395 q^{26} -2.67346 q^{27} -14.8369 q^{28} +1.00000 q^{29} -16.5917 q^{30} -3.49490 q^{31} -22.3942 q^{32} -2.28524 q^{33} -18.6503 q^{34} +6.18774 q^{35} +22.0150 q^{36} -8.93618 q^{37} -23.1930 q^{38} -0.395077 q^{39} +21.8729 q^{40} +2.38322 q^{41} -19.5816 q^{42} -6.65510 q^{43} +4.73893 q^{44} -9.18136 q^{45} -2.79557 q^{46} +4.10919 q^{47} -40.1459 q^{48} +0.302797 q^{49} -0.664888 q^{50} -18.0421 q^{51} +0.819274 q^{52} -5.48885 q^{53} +7.31686 q^{54} -1.97637 q^{55} +25.8144 q^{56} -22.4366 q^{57} -2.73685 q^{58} +2.45204 q^{59} +33.2842 q^{60} -14.8637 q^{61} +9.56500 q^{62} -10.8359 q^{63} +30.9631 q^{64} -0.341678 q^{65} +6.25437 q^{66} -9.18420 q^{67} +37.4140 q^{68} -2.70440 q^{69} -16.9349 q^{70} -11.8039 q^{71} -38.3034 q^{72} -2.15918 q^{73} +24.4570 q^{74} -0.643206 q^{75} +46.5270 q^{76} -2.33252 q^{77} +1.08127 q^{78} +9.98282 q^{79} -34.7197 q^{80} -4.95106 q^{81} -6.52252 q^{82} +17.4066 q^{83} +39.2822 q^{84} -15.6035 q^{85} +18.2140 q^{86} -2.64760 q^{87} -8.24516 q^{88} +13.5901 q^{89} +25.1280 q^{90} -0.403250 q^{91} +5.60814 q^{92} +9.25307 q^{93} -11.2462 q^{94} -19.4041 q^{95} +59.2907 q^{96} -10.7547 q^{97} -0.828710 q^{98} +3.46099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9 - 40 * q^10 - 36 * q^11 - 67 * q^12 - 51 * q^13 - 19 * q^14 - 48 * q^15 + 122 * q^16 - 54 * q^17 - 46 * q^18 - 73 * q^19 - 21 * q^20 - 8 * q^21 - 23 * q^22 - 38 * q^23 - 17 * q^24 + 133 * q^25 - 20 * q^26 - 129 * q^27 - 99 * q^28 + 154 * q^29 - 10 * q^30 - 91 * q^31 - 88 * q^32 - 39 * q^33 - 42 * q^34 - 36 * q^35 + 101 * q^36 - 50 * q^37 - 17 * q^38 - 33 * q^39 - 92 * q^40 - 31 * q^41 - 62 * q^42 - 154 * q^43 - 42 * q^44 - 14 * q^45 - 24 * q^46 - 140 * q^47 - 118 * q^48 + 126 * q^49 - 5 * q^50 - 16 * q^51 - 133 * q^52 - 40 * q^53 + 14 * q^54 - 203 * q^55 - 44 * q^56 - 16 * q^57 - 12 * q^58 + 5 * q^59 - 28 * q^60 - 106 * q^61 - 30 * q^62 - 145 * q^63 + 111 * q^64 - 15 * q^65 - 49 * q^66 - 78 * q^67 - 118 * q^68 - 32 * q^69 - 43 * q^70 - 4 * q^71 - 152 * q^72 - 137 * q^73 + 9 * q^74 - 129 * q^75 - 204 * q^76 - 76 * q^77 + 15 * q^78 - 141 * q^79 - 44 * q^80 + 122 * q^81 - 71 * q^82 - 90 * q^83 + 92 * q^84 - 41 * q^85 + 9 * q^86 - 36 * q^87 - 109 * q^88 - 51 * q^89 - 82 * q^90 - 22 * q^91 - 8 * q^92 - 10 * q^93 - 106 * q^94 - 55 * q^95 - 49 * q^96 - 140 * q^97 - 4 * q^98 - 101 * q^99

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