LMFDB - Embedded newform 8033.2.a.d.1.17

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:	$0$
Dimension:	$168$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-2.40677 q^{2} -1.38895 q^{3} +3.79253 q^{4} -2.91778 q^{5} +3.34287 q^{6} +3.15140 q^{7} -4.31420 q^{8} -1.07083 q^{9} +O(q^{10})$	\(q-2.40677 q^{2} -1.38895 q^{3} +3.79253 q^{4} -2.91778 q^{5} +3.34287 q^{6} +3.15140 q^{7} -4.31420 q^{8} -1.07083 q^{9} +7.02241 q^{10} -6.35106 q^{11} -5.26762 q^{12} -2.53666 q^{13} -7.58468 q^{14} +4.05264 q^{15} +2.79822 q^{16} -3.64828 q^{17} +2.57723 q^{18} +8.17581 q^{19} -11.0657 q^{20} -4.37712 q^{21} +15.2855 q^{22} -0.0685980 q^{23} +5.99220 q^{24} +3.51341 q^{25} +6.10515 q^{26} +5.65416 q^{27} +11.9518 q^{28} +1.00000 q^{29} -9.75375 q^{30} -9.41931 q^{31} +1.89374 q^{32} +8.82128 q^{33} +8.78056 q^{34} -9.19507 q^{35} -4.06114 q^{36} -6.69365 q^{37} -19.6773 q^{38} +3.52329 q^{39} +12.5879 q^{40} +7.88581 q^{41} +10.5347 q^{42} +7.78507 q^{43} -24.0866 q^{44} +3.12443 q^{45} +0.165100 q^{46} -8.54987 q^{47} -3.88658 q^{48} +2.93131 q^{49} -8.45597 q^{50} +5.06727 q^{51} -9.62036 q^{52} -11.7013 q^{53} -13.6083 q^{54} +18.5310 q^{55} -13.5958 q^{56} -11.3558 q^{57} -2.40677 q^{58} -8.04980 q^{59} +15.3697 q^{60} -4.66292 q^{61} +22.6701 q^{62} -3.37460 q^{63} -10.1542 q^{64} +7.40141 q^{65} -21.2308 q^{66} -7.51587 q^{67} -13.8362 q^{68} +0.0952791 q^{69} +22.1304 q^{70} +8.02562 q^{71} +4.61975 q^{72} +5.19494 q^{73} +16.1101 q^{74} -4.87995 q^{75} +31.0070 q^{76} -20.0147 q^{77} -8.47974 q^{78} -11.8168 q^{79} -8.16457 q^{80} -4.64086 q^{81} -18.9793 q^{82} +7.15239 q^{83} -16.6004 q^{84} +10.6449 q^{85} -18.7368 q^{86} -1.38895 q^{87} +27.3997 q^{88} +1.09540 q^{89} -7.51977 q^{90} -7.99403 q^{91} -0.260160 q^{92} +13.0829 q^{93} +20.5775 q^{94} -23.8552 q^{95} -2.63031 q^{96} -4.76996 q^{97} -7.05497 q^{98} +6.80087 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) $ 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9} + 41 q^{10} + 29 q^{11} + 82 q^{12} + 62 q^{13} + 23 q^{14} + 31 q^{15} + 204 q^{16} + 56 q^{17} + 35 q^{18} + 83 q^{19} + 6 q^{20} + 30 q^{21} + 56 q^{22} + 54 q^{23} + 28 q^{24} + 210 q^{25} + 21 q^{26} + 140 q^{27} + 151 q^{28} + 168 q^{29} + 29 q^{30} + 72 q^{31} + 40 q^{32} + 32 q^{33} + 34 q^{34} + 18 q^{35} + 152 q^{36} + 42 q^{37} + 29 q^{38} + 70 q^{39} + 97 q^{40} + 41 q^{41} - 20 q^{42} + 119 q^{43} + 37 q^{44} + 22 q^{45} + 24 q^{46} + 119 q^{47} + 135 q^{48} + 216 q^{49} + 38 q^{50} + 18 q^{51} + 154 q^{52} - 7 q^{53} + 35 q^{54} + 224 q^{55} + 46 q^{56} + 12 q^{57} + 12 q^{58} + 25 q^{59} + 13 q^{60} + 82 q^{61} + 27 q^{62} + 211 q^{63} + 217 q^{64} + 8 q^{65} - 6 q^{66} + 76 q^{67} + 132 q^{68} + 36 q^{69} + 39 q^{70} + 32 q^{71} + 39 q^{72} + 89 q^{73} - q^{74} + 123 q^{75} + 180 q^{76} + 68 q^{77} - 54 q^{78} + 176 q^{79} - 11 q^{80} + 192 q^{81} + 51 q^{82} + 76 q^{83} + 86 q^{84} + 65 q^{85} - 72 q^{86} + 35 q^{87} + 178 q^{88} + 55 q^{89} + 2 q^{90} + 80 q^{91} + 44 q^{92} + 39 q^{93} + 89 q^{94} + 77 q^{95} - 68 q^{96} + 82 q^{97} + 80 q^{98} + 67 q^{99}+O(q^{100}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9 + 41 * q^10 + 29 * q^11 + 82 * q^12 + 62 * q^13 + 23 * q^14 + 31 * q^15 + 204 * q^16 + 56 * q^17 + 35 * q^18 + 83 * q^19 + 6 * q^20 + 30 * q^21 + 56 * q^22 + 54 * q^23 + 28 * q^24 + 210 * q^25 + 21 * q^26 + 140 * q^27 + 151 * q^28 + 168 * q^29 + 29 * q^30 + 72 * q^31 + 40 * q^32 + 32 * q^33 + 34 * q^34 + 18 * q^35 + 152 * q^36 + 42 * q^37 + 29 * q^38 + 70 * q^39 + 97 * q^40 + 41 * q^41 - 20 * q^42 + 119 * q^43 + 37 * q^44 + 22 * q^45 + 24 * q^46 + 119 * q^47 + 135 * q^48 + 216 * q^49 + 38 * q^50 + 18 * q^51 + 154 * q^52 - 7 * q^53 + 35 * q^54 + 224 * q^55 + 46 * q^56 + 12 * q^57 + 12 * q^58 + 25 * q^59 + 13 * q^60 + 82 * q^61 + 27 * q^62 + 211 * q^63 + 217 * q^64 + 8 * q^65 - 6 * q^66 + 76 * q^67 + 132 * q^68 + 36 * q^69 + 39 * q^70 + 32 * q^71 + 39 * q^72 + 89 * q^73 - q^74 + 123 * q^75 + 180 * q^76 + 68 * q^77 - 54 * q^78 + 176 * q^79 - 11 * q^80 + 192 * q^81 + 51 * q^82 + 76 * q^83 + 86 * q^84 + 65 * q^85 - 72 * q^86 + 35 * q^87 + 178 * q^88 + 55 * q^89 + 2 * q^90 + 80 * q^91 + 44 * q^92 + 39 * q^93 + 89 * q^94 + 77 * q^95 - 68 * q^96 + 82 * q^97 + 80 * q^98 + 67 * 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 $

$2$	−2.40677	−1.70184	−0.850921	−	0.525294i	$-0.823955\pi$
$2$	−2.40677	−1.70184	−0.850921	+	0.525294i	$0.823955\pi$
$3$	−1.38895	−0.801909	−0.400955	−	0.916098i	$-0.631321\pi$
$3$	−1.38895	−0.801909	−0.400955	+	0.916098i	$0.631321\pi$
$4$	3.79253	1.89626
$5$	−2.91778	−1.30487	−0.652434	−	0.757845i	$-0.726252\pi$
$5$	−2.91778	−1.30487	−0.652434	+	0.757845i	$0.726252\pi$
$6$	3.34287	1.36472
$7$	3.15140	1.19112	0.595558	−	0.803312i	$-0.296931\pi$
$7$	3.15140	1.19112	0.595558	+	0.803312i	$0.296931\pi$
$8$	−4.31420	−1.52530
$9$	−1.07083	−0.356942
$10$	7.02241	2.22068
$11$	−6.35106	−1.91492	−0.957458	−	0.288573i	$-0.906819\pi$
$11$	−6.35106	−1.91492	−0.957458	+	0.288573i	$0.906819\pi$
$12$	−5.26762	−1.52063
$13$	−2.53666	−0.703543	−0.351772	−	0.936086i	$-0.614421\pi$
$13$	−2.53666	−0.703543	−0.351772	+	0.936086i	$0.614421\pi$
$14$	−7.58468	−2.02709
$15$	4.05264	1.04639
$16$	2.79822	0.699554
$17$	−3.64828	−0.884837	−0.442419	−	0.896809i	$-0.645879\pi$
$17$	−3.64828	−0.884837	−0.442419	+	0.896809i	$0.645879\pi$
$18$	2.57723	0.607458
$19$	8.17581	1.87566	0.937830	−	0.347095i	$-0.112832\pi$
$19$	8.17581	1.87566	0.937830	+	0.347095i	$0.112832\pi$
$20$	−11.0657	−2.47438
$21$	−4.37712	−0.955167
$22$	15.2855	3.25888
$23$	−0.0685980	−0.0143037	−0.00715184	−	0.999974i	$-0.502277\pi$
$23$	−0.0685980	−0.0143037	−0.00715184	+	0.999974i	$0.502277\pi$
$24$	5.99220	1.22315
$25$	3.51341	0.702683
$26$	6.10515	1.19732
$27$	5.65416	1.08814
$28$	11.9518	2.25867
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−9.75375	−1.78078
$31$	−9.41931	−1.69176	−0.845879	−	0.533375i	$-0.820923\pi$
$31$	−9.41931	−1.69176	−0.845879	+	0.533375i	$0.820923\pi$
$32$	1.89374	0.334769
$33$	8.82128	1.53559
$34$	8.78056	1.50585
$35$	−9.19507	−1.55425
$36$	−4.06114	−0.676856
$37$	−6.69365	−1.10043	−0.550215	−	0.835023i	$-0.685454\pi$
$37$	−6.69365	−1.10043	−0.550215	+	0.835023i	$0.685454\pi$
$38$	−19.6773	−3.19208
$39$	3.52329	0.564178
$40$	12.5879	1.99032
$41$	7.88581	1.23156	0.615778	−	0.787919i	$-0.288842\pi$
$41$	7.88581	1.23156	0.615778	+	0.787919i	$0.288842\pi$
$42$	10.5347	1.62554
$43$	7.78507	1.18721	0.593606	−	0.804756i	$-0.297704\pi$
$43$	7.78507	1.18721	0.593606	+	0.804756i	$0.297704\pi$
$44$	−24.0866	−3.63119
$45$	3.12443	0.465762
$46$	0.165100	0.0243426
$47$	−8.54987	−1.24713	−0.623563	−	0.781773i	$-0.714316\pi$
$47$	−8.54987	−1.24713	−0.623563	+	0.781773i	$0.714316\pi$
$48$	−3.88658	−0.560979
$49$	2.93131	0.418758
$50$	−8.45597	−1.19585
$51$	5.06727	0.709559
$52$	−9.62036	−1.33410
$53$	−11.7013	−1.60730	−0.803651	−	0.595101i	$-0.797112\pi$
$53$	−11.7013	−1.60730	−0.803651	+	0.595101i	$0.797112\pi$
$54$	−13.6083	−1.85185
$55$	18.5310	2.49871
$56$	−13.5958	−1.81681
$57$	−11.3558	−1.50411
$58$	−2.40677	−0.316024
$59$	−8.04980	−1.04799	−0.523997	−	0.851720i	$-0.675560\pi$
$59$	−8.04980	−1.04799	−0.523997	+	0.851720i	$0.675560\pi$
$60$	15.3697	1.98423
$61$	−4.66292	−0.597026	−0.298513	−	0.954406i	$-0.596491\pi$
$61$	−4.66292	−0.597026	−0.298513	+	0.954406i	$0.596491\pi$
$62$	22.6701	2.87910
$63$	−3.37460	−0.425159
$64$	−10.1542	−1.26928
$65$	7.40141	0.918032
$66$	−21.2308	−2.61333
$67$	−7.51587	−0.918210	−0.459105	−	0.888382i	$-0.651830\pi$
$67$	−7.51587	−0.918210	−0.459105	+	0.888382i	$0.651830\pi$
$68$	−13.8362	−1.67789
$69$	0.0952791	0.0114703
$70$	22.1304	2.64509
$71$	8.02562	0.952466	0.476233	−	0.879319i	$-0.342002\pi$
$71$	8.02562	0.952466	0.476233	+	0.879319i	$0.342002\pi$
$72$	4.61975	0.544443
$73$	5.19494	0.608022	0.304011	−	0.952668i	$-0.401674\pi$
$73$	5.19494	0.608022	0.304011	+	0.952668i	$0.401674\pi$
$74$	16.1101	1.87276
$75$	−4.87995	−0.563488
$76$	31.0070	3.55675
$77$	−20.0147	−2.28089
$78$	−8.47974	−0.960141
$79$	−11.8168	−1.32949	−0.664745	−	0.747070i	$-0.731460\pi$
$79$	−11.8168	−1.32949	−0.664745	+	0.747070i	$0.731460\pi$
$80$	−8.16457	−0.912827
$81$	−4.64086	−0.515651
$82$	−18.9793	−2.09591
$83$	7.15239	0.785077	0.392538	−	0.919736i	$-0.371597\pi$
$83$	7.15239	0.785077	0.392538	+	0.919736i	$0.371597\pi$
$84$	−16.6004	−1.81125
$85$	10.6449	1.15460
$86$	−18.7368	−2.02045
$87$	−1.38895	−0.148911
$88$	27.3997	2.92082
$89$	1.09540	0.116112	0.0580562	−	0.998313i	$-0.481510\pi$
$89$	1.09540	0.116112	0.0580562	+	0.998313i	$0.481510\pi$
$90$	−7.51977	−0.792653
$91$	−7.99403	−0.838002
$92$	−0.260160	−0.0271236
$93$	13.0829	1.35664
$94$	20.5775	2.12241
$95$	−23.8552	−2.44749
$96$	−2.63031	−0.268455
$97$	−4.76996	−0.484316	−0.242158	−	0.970237i	$-0.577855\pi$
$97$	−4.76996	−0.484316	−0.242158	+	0.970237i	$0.577855\pi$
$98$	−7.05497	−0.712660
$99$	6.80087	0.683513
$100$	13.3247	1.33247
$101$	−13.5381	−1.34709	−0.673544	−	0.739147i	$-0.735229\pi$
$101$	−13.5381	−1.34709	−0.673544	+	0.739147i	$0.735229\pi$
$102$	−12.1957	−1.20756
$103$	−13.0612	−1.28695	−0.643477	−	0.765465i	$-0.722509\pi$
$103$	−13.0612	−1.28695	−0.643477	+	0.765465i	$0.722509\pi$
$104$	10.9437	1.07311
$105$	12.7715	1.24637
$106$	28.1624	2.73537
$107$	−9.18672	−0.888113	−0.444057	−	0.895999i	$-0.646461\pi$
$107$	−9.18672	−0.888113	−0.444057	+	0.895999i	$0.646461\pi$
$108$	21.4436	2.06341
$109$	−9.14464	−0.875897	−0.437949	−	0.899000i	$-0.644295\pi$
$109$	−9.14464	−0.875897	−0.437949	+	0.899000i	$0.644295\pi$
$110$	−44.5997	−4.25242
$111$	9.29713	0.882444
$112$	8.81830	0.833251
$113$	−18.9783	−1.78533	−0.892665	−	0.450722i	$-0.851167\pi$
$113$	−18.9783	−1.78533	−0.892665	+	0.450722i	$0.851167\pi$
$114$	27.3307	2.55975
$115$	0.200154	0.0186644
$116$	3.79253	0.352127
$117$	2.71632	0.251124
$118$	19.3740	1.78352
$119$	−11.4972	−1.05394
$120$	−17.4839	−1.59605
$121$	29.3359	2.66690
$122$	11.2226	1.01604
$123$	−10.9530	−0.987597
$124$	−35.7230	−3.20802
$125$	4.33752	0.387960
$126$	8.12187	0.723553
$127$	17.7625	1.57617	0.788085	−	0.615566i	$-0.211073\pi$
$127$	17.7625	1.57617	0.788085	+	0.615566i	$0.211073\pi$
$128$	20.6514	1.82534
$129$	−10.8130	−0.952036
$130$	−17.8135	−1.56234
$131$	−3.04350	−0.265911	−0.132956	−	0.991122i	$-0.542447\pi$
$131$	−3.04350	−0.265911	−0.132956	+	0.991122i	$0.542447\pi$
$132$	33.4550	2.91188
$133$	25.7652	2.23413
$134$	18.0890	1.56265
$135$	−16.4976	−1.41989
$136$	15.7394	1.34964
$137$	13.5858	1.16071	0.580355	−	0.814364i	$-0.302914\pi$
$137$	13.5858	1.16071	0.580355	+	0.814364i	$0.302914\pi$
$138$	−0.229315	−0.0195205
$139$	−7.47475	−0.634000	−0.317000	−	0.948425i	$-0.602676\pi$
$139$	−7.47475	−0.634000	−0.317000	+	0.948425i	$0.602676\pi$
$140$	−34.8726	−2.94727
$141$	11.8753	1.00008
$142$	−19.3158	−1.62095
$143$	16.1105	1.34723
$144$	−2.99640	−0.249700
$145$	−2.91778	−0.242308
$146$	−12.5030	−1.03476
$147$	−4.07143	−0.335806
$148$	−25.3859	−2.08671
$149$	9.65615	0.791063	0.395531	−	0.918452i	$-0.370560\pi$
$149$	9.65615	0.791063	0.395531	+	0.918452i	$0.370560\pi$
$150$	11.7449	0.958967
$151$	4.86283	0.395731	0.197866	−	0.980229i	$-0.436599\pi$
$151$	4.86283	0.395731	0.197866	+	0.980229i	$0.436599\pi$
$152$	−35.2721	−2.86094
$153$	3.90667	0.315835
$154$	48.1707	3.88171
$155$	27.4834	2.20752
$156$	13.3622	1.06983
$157$	11.6900	0.932963	0.466481	−	0.884531i	$-0.345521\pi$
$157$	11.6900	0.932963	0.466481	+	0.884531i	$0.345521\pi$
$158$	28.4402	2.26258
$159$	16.2525	1.28891
$160$	−5.52551	−0.436830
$161$	−0.216180	−0.0170373
$162$	11.1695	0.877556
$163$	−9.38384	−0.734999	−0.367499	−	0.930024i	$-0.619786\pi$
$163$	−9.38384	−0.734999	−0.367499	+	0.930024i	$0.619786\pi$
$164$	29.9072	2.33536
$165$	−25.7385	−2.00374
$166$	−17.2141	−1.33608
$167$	−7.50704	−0.580913	−0.290456	−	0.956888i	$-0.593807\pi$
$167$	−7.50704	−0.580913	−0.290456	+	0.956888i	$0.593807\pi$
$168$	18.8838	1.45692
$169$	−6.56535	−0.505027
$170$	−25.6197	−1.96494
$171$	−8.75487	−0.669501
$172$	29.5251	2.25127
$173$	−13.4761	−1.02457	−0.512286	−	0.858815i	$-0.671201\pi$
$173$	−13.4761	−1.02457	−0.512286	+	0.858815i	$0.671201\pi$
$174$	3.34287	0.253423
$175$	11.0722	0.836977
$176$	−17.7716	−1.33959
$177$	11.1807	0.840396
$178$	−2.63638	−0.197605
$179$	−16.7491	−1.25188	−0.625942	−	0.779870i	$-0.715285\pi$
$179$	−16.7491	−1.25188	−0.625942	+	0.779870i	$0.715285\pi$
$180$	11.8495	0.883208
$181$	−17.9855	−1.33685	−0.668425	−	0.743779i	$-0.733031\pi$
$181$	−17.9855	−1.33685	−0.668425	+	0.743779i	$0.733031\pi$
$182$	19.2398	1.42615
$183$	6.47655	0.478760
$184$	0.295946	0.0218174
$185$	19.5306	1.43592
$186$	−31.4876	−2.30878
$187$	23.1704	1.69439
$188$	−32.4256	−2.36488
$189$	17.8185	1.29611
$190$	57.4139	4.16524
$191$	−4.51435	−0.326647	−0.163324	−	0.986573i	$-0.552221\pi$
$191$	−4.51435	−0.326647	−0.163324	+	0.986573i	$0.552221\pi$
$192$	14.1037	1.01785
$193$	−19.3711	−1.39436	−0.697180	−	0.716896i	$-0.745562\pi$
$193$	−19.3711	−1.39436	−0.697180	+	0.716896i	$0.745562\pi$
$194$	11.4802	0.824230
$195$	−10.2802	−0.736178
$196$	11.1171	0.794076
$197$	0.776587	0.0553296	0.0276648	−	0.999617i	$-0.491193\pi$
$197$	0.776587	0.0553296	0.0276648	+	0.999617i	$0.491193\pi$
$198$	−16.3681	−1.16323
$199$	2.52479	0.178978	0.0894888	−	0.995988i	$-0.471477\pi$
$199$	2.52479	0.178978	0.0894888	+	0.995988i	$0.471477\pi$
$200$	−15.1576	−1.07180
$201$	10.4392	0.736321
$202$	32.5830	2.29253
$203$	3.15140	0.221185
$204$	19.2178	1.34551
$205$	−23.0090	−1.60702
$206$	31.4352	2.19019
$207$	0.0734565	0.00510558
$208$	−7.09813	−0.492167
$209$	−51.9250	−3.59173
$210$	−30.7380	−2.12112
$211$	11.2946	0.777550	0.388775	−	0.921333i	$-0.372898\pi$
$211$	11.2946	0.777550	0.388775	+	0.921333i	$0.372898\pi$
$212$	−44.3776	−3.04787
$213$	−11.1472	−0.763791
$214$	22.1103	1.51143
$215$	−22.7151	−1.54916
$216$	−24.3932	−1.65975
$217$	−29.6840	−2.01508
$218$	22.0090	1.49064
$219$	−7.21550	−0.487579
$220$	70.2792	4.73822
$221$	9.25445	0.622522
$222$	−22.3760	−1.50178
$223$	−4.32819	−0.289837	−0.144918	−	0.989444i	$-0.546292\pi$
$223$	−4.32819	−0.289837	−0.144918	+	0.989444i	$0.546292\pi$
$224$	5.96793	0.398749
$225$	−3.76225	−0.250817
$226$	45.6764	3.03835
$227$	−2.80580	−0.186228	−0.0931138	−	0.995655i	$-0.529682\pi$
$227$	−2.80580	−0.186228	−0.0931138	+	0.995655i	$0.529682\pi$
$228$	−43.0671	−2.85219
$229$	10.0218	0.662257	0.331129	−	0.943586i	$-0.392571\pi$
$229$	10.0218	0.662257	0.331129	+	0.943586i	$0.392571\pi$
$230$	−0.481723	−0.0317639
$231$	27.7994	1.82906
$232$	−4.31420	−0.283241
$233$	−1.72282	−0.112865	−0.0564327	−	0.998406i	$-0.517973\pi$
$233$	−1.72282	−0.112865	−0.0564327	+	0.998406i	$0.517973\pi$
$234$	−6.53755	−0.427373
$235$	24.9466	1.62734
$236$	−30.5291	−1.98727
$237$	16.4129	1.06613
$238$	27.6710	1.79365
$239$	−9.07799	−0.587206	−0.293603	−	0.955927i	$-0.594854\pi$
$239$	−9.07799	−0.587206	−0.293603	+	0.955927i	$0.594854\pi$
$240$	11.3402	0.732004
$241$	−16.3169	−1.05106	−0.525531	−	0.850774i	$-0.676133\pi$
$241$	−16.3169	−1.05106	−0.525531	+	0.850774i	$0.676133\pi$
$242$	−70.6048	−4.53865
$243$	−10.5166	−0.674639
$244$	−17.6843	−1.13212
$245$	−8.55289	−0.546424
$246$	26.3613	1.68073
$247$	−20.7393	−1.31961
$248$	40.6368	2.58044
$249$	−9.93429	−0.629560
$250$	−10.4394	−0.660246
$251$	−26.3219	−1.66142	−0.830712	−	0.556702i	$-0.812067\pi$
$251$	−26.3219	−1.66142	−0.830712	+	0.556702i	$0.812067\pi$
$252$	−12.7983	−0.806214
$253$	0.435670	0.0273903
$254$	−42.7503	−2.68239
$255$	−14.7851	−0.925882
$256$	−29.3946	−1.83716
$257$	−3.44296	−0.214766	−0.107383	−	0.994218i	$-0.534247\pi$
$257$	−3.44296	−0.214766	−0.107383	+	0.994218i	$0.534247\pi$
$258$	26.0245	1.62021
$259$	−21.0944	−1.31074
$260$	28.0701	1.74083
$261$	−1.07083	−0.0662824
$262$	7.32499	0.452539
$263$	−24.8424	−1.53185	−0.765926	−	0.642929i	$-0.777719\pi$
$263$	−24.8424	−1.53185	−0.765926	+	0.642929i	$0.777719\pi$
$264$	−38.0568	−2.34223
$265$	34.1419	2.09732
$266$	−62.0109	−3.80213
$267$	−1.52145	−0.0931115
$268$	−28.5042	−1.74117
$269$	24.8806	1.51700	0.758499	−	0.651674i	$-0.225933\pi$
$269$	24.8806	1.51700	0.758499	+	0.651674i	$0.225933\pi$
$270$	39.7058	2.41642
$271$	−4.23320	−0.257148	−0.128574	−	0.991700i	$-0.541040\pi$
$271$	−4.23320	−0.257148	−0.128574	+	0.991700i	$0.541040\pi$
$272$	−10.2087	−0.618992
$273$	11.1033	0.672001
$274$	−32.6978	−1.97534
$275$	−22.3139	−1.34558
$276$	0.361349	0.0217506
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	17.9900	1.07897
$279$	10.0864	0.603859
$280$	39.6694	2.37070
$281$	3.70608	0.221086	0.110543	−	0.993871i	$-0.464741\pi$
$281$	3.70608	0.221086	0.110543	+	0.993871i	$0.464741\pi$
$282$	−28.5811	−1.70198
$283$	−15.2808	−0.908348	−0.454174	−	0.890913i	$-0.650066\pi$
$283$	−15.2808	−0.908348	−0.454174	+	0.890913i	$0.650066\pi$
$284$	30.4374	1.80613
$285$	33.1336	1.96266
$286$	−38.7742	−2.29277
$287$	24.8513	1.46693
$288$	−2.02787	−0.119493
$289$	−3.69006	−0.217063
$290$	7.02241	0.412370
$291$	6.62523	0.388378
$292$	19.7020	1.15297
$293$	−13.2163	−0.772103	−0.386051	−	0.922477i	$-0.626161\pi$
$293$	−13.2163	−0.772103	−0.386051	+	0.922477i	$0.626161\pi$
$294$	9.79898	0.571488
$295$	23.4875	1.36750
$296$	28.8778	1.67849
$297$	−35.9099	−2.08370
$298$	−23.2401	−1.34626
$299$	0.174010	0.0100633
$300$	−18.5073	−1.06852
$301$	24.5338	1.41411
$302$	−11.7037	−0.673472
$303$	18.8037	1.08024
$304$	22.8777	1.31213
$305$	13.6054	0.779040
$306$	−9.40244	−0.537502
$307$	−14.7387	−0.841184	−0.420592	−	0.907250i	$-0.638178\pi$
$307$	−14.7387	−0.841184	−0.420592	+	0.907250i	$0.638178\pi$
$308$	−75.9064	−4.32517
$309$	18.1413	1.03202
$310$	−66.1462	−3.75685
$311$	−31.2500	−1.77203	−0.886014	−	0.463659i	$-0.846536\pi$
$311$	−31.2500	−1.77203	−0.886014	+	0.463659i	$0.846536\pi$
$312$	−15.2002	−0.860541
$313$	−11.1328	−0.629264	−0.314632	−	0.949214i	$-0.601881\pi$
$313$	−11.1328	−0.629264	−0.314632	+	0.949214i	$0.601881\pi$
$314$	−28.1351	−1.58775
$315$	9.84631	0.554777
$316$	−44.8155	−2.52107
$317$	12.5777	0.706431	0.353216	−	0.935542i	$-0.385088\pi$
$317$	12.5777	0.706431	0.353216	+	0.935542i	$0.385088\pi$
$318$	−39.1161	−2.19352
$319$	−6.35106	−0.355591
$320$	29.6278	1.65624
$321$	12.7599	0.712186
$322$	0.520294	0.0289949
$323$	−29.8276	−1.65965
$324$	−17.6006	−0.977810
$325$	−8.91234	−0.494368
$326$	22.5847	1.25085
$327$	12.7014	0.702390
$328$	−34.0210	−1.87849
$329$	−26.9440	−1.48547
$330$	61.9467	3.41005
$331$	−30.2003	−1.65996	−0.829979	−	0.557795i	$-0.811647\pi$
$331$	−30.2003	−1.65996	−0.829979	+	0.557795i	$0.811647\pi$
$332$	27.1256	1.48871
$333$	7.16773	0.392789
$334$	18.0677	0.988621
$335$	21.9296	1.19814
$336$	−12.2481	−0.668191
$337$	31.6874	1.72612	0.863062	−	0.505099i	$-0.168544\pi$
$337$	31.6874	1.72612	0.863062	+	0.505099i	$0.168544\pi$
$338$	15.8013	0.859475
$339$	26.3599	1.43167
$340$	40.3709	2.18942
$341$	59.8226	3.23957
$342$	21.0709	1.13939
$343$	−12.8221	−0.692327
$344$	−33.5863	−1.81085
$345$	−0.278003	−0.0149672
$346$	32.4339	1.74366
$347$	−16.8721	−0.905743	−0.452872	−	0.891576i	$-0.649600\pi$
$347$	−16.8721	−0.905743	−0.452872	+	0.891576i	$0.649600\pi$
$348$	−5.26762	−0.282374
$349$	−11.9899	−0.641803	−0.320902	−	0.947113i	$-0.603986\pi$
$349$	−11.9899	−0.641803	−0.320902	+	0.947113i	$0.603986\pi$
$350$	−26.6481	−1.42440
$351$	−14.3427	−0.765557
$352$	−12.0273	−0.641055
$353$	27.4838	1.46281	0.731407	−	0.681941i	$-0.238864\pi$
$353$	27.4838	1.46281	0.731407	+	0.681941i	$0.238864\pi$
$354$	−26.9095	−1.43022
$355$	−23.4170	−1.24284
$356$	4.15434	0.220180
$357$	15.9690	0.845168
$358$	40.3111	2.13051
$359$	28.4646	1.50231	0.751153	−	0.660128i	$-0.229498\pi$
$359$	28.4646	1.50231	0.751153	+	0.660128i	$0.229498\pi$
$360$	−13.4794	−0.710427
$361$	47.8439	2.51810
$362$	43.2869	2.27511
$363$	−40.7461	−2.13861
$364$	−30.3176	−1.58907
$365$	−15.1577	−0.793389
$366$	−15.5876	−0.814774
$367$	27.8480	1.45365	0.726826	−	0.686821i	$-0.240995\pi$
$367$	27.8480	1.45365	0.726826	+	0.686821i	$0.240995\pi$
$368$	−0.191952	−0.0100062
$369$	−8.44433	−0.439594
$370$	−47.0055	−2.44370
$371$	−36.8755	−1.91448
$372$	49.6174	2.57254
$373$	−11.2443	−0.582208	−0.291104	−	0.956691i	$-0.594023\pi$
$373$	−11.2443	−0.582208	−0.291104	+	0.956691i	$0.594023\pi$
$374$	−55.7658	−2.88358
$375$	−6.02459	−0.311109
$376$	36.8859	1.90224
$377$	−2.53666	−0.130645
$378$	−42.8850	−2.20577
$379$	−13.9783	−0.718017	−0.359009	−	0.933334i	$-0.616885\pi$
$379$	−13.9783	−0.718017	−0.359009	+	0.933334i	$0.616885\pi$
$380$	−90.4715	−4.64109
$381$	−24.6712	−1.26395
$382$	10.8650	0.555902
$383$	7.72557	0.394758	0.197379	−	0.980327i	$-0.436757\pi$
$383$	7.72557	0.394758	0.197379	+	0.980327i	$0.436757\pi$
$384$	−28.6837	−1.46376
$385$	58.3984	2.97626
$386$	46.6216	2.37298
$387$	−8.33645	−0.423765
$388$	−18.0902	−0.918392
$389$	1.90605	0.0966406	0.0483203	−	0.998832i	$-0.484613\pi$
$389$	1.90605	0.0966406	0.0483203	+	0.998832i	$0.484613\pi$
$390$	24.7420	1.25286
$391$	0.250265	0.0126564
$392$	−12.6462	−0.638731
$393$	4.22725	0.213237
$394$	−1.86906	−0.0941621
$395$	34.4787	1.73481
$396$	25.7925	1.29612
$397$	4.22715	0.212155	0.106077	−	0.994358i	$-0.466171\pi$
$397$	4.22715	0.212155	0.106077	+	0.994358i	$0.466171\pi$
$398$	−6.07658	−0.304592
$399$	−35.7865	−1.79157
$400$	9.83130	0.491565
$401$	−15.0348	−0.750801	−0.375400	−	0.926863i	$-0.622495\pi$
$401$	−15.0348	−0.750801	−0.375400	+	0.926863i	$0.622495\pi$
$402$	−25.1246	−1.25310
$403$	23.8936	1.19023
$404$	−51.3435	−2.55443
$405$	13.5410	0.672857
$406$	−7.58468	−0.376421
$407$	42.5118	2.10723
$408$	−21.8612	−1.08229
$409$	7.38019	0.364927	0.182464	−	0.983213i	$-0.441593\pi$
$409$	7.38019	0.364927	0.182464	+	0.983213i	$0.441593\pi$
$410$	55.3774	2.73489
$411$	−18.8699	−0.930784
$412$	−49.5348	−2.44041
$413$	−25.3681	−1.24828
$414$	−0.176793	−0.00868889
$415$	−20.8691	−1.02442
$416$	−4.80378	−0.235525
$417$	10.3820	0.508411
$418$	124.972	6.11256
$419$	−6.75188	−0.329851	−0.164925	−	0.986306i	$-0.552738\pi$
$419$	−6.75188	−0.329851	−0.164925	+	0.986306i	$0.552738\pi$
$420$	48.4362	2.36344
$421$	2.96601	0.144554	0.0722772	−	0.997385i	$-0.476973\pi$
$421$	2.96601	0.144554	0.0722772	+	0.997385i	$0.476973\pi$
$422$	−27.1834	−1.32327
$423$	9.15542	0.445152
$424$	50.4819	2.45162
$425$	−12.8179	−0.621760
$426$	26.8286	1.29985
$427$	−14.6947	−0.711127
$428$	−34.8409	−1.68410
$429$	−22.3766	−1.08035
$430$	54.6699	2.63642
$431$	17.6278	0.849103	0.424552	−	0.905404i	$-0.360432\pi$
$431$	17.6278	0.849103	0.424552	+	0.905404i	$0.360432\pi$
$432$	15.8216	0.761216
$433$	19.7671	0.949944	0.474972	−	0.880001i	$-0.342458\pi$
$433$	19.7671	0.949944	0.474972	+	0.880001i	$0.342458\pi$
$434$	71.4424	3.42935
$435$	4.05264	0.194309
$436$	−34.6813	−1.66093
$437$	−0.560845	−0.0268288
$438$	17.3660	0.829781
$439$	28.3645	1.35376	0.676881	−	0.736093i	$-0.263331\pi$
$439$	28.3645	1.35376	0.676881	+	0.736093i	$0.263331\pi$
$440$	−79.9463	−3.81129
$441$	−3.13892	−0.149472
$442$	−22.2733	−1.05943
$443$	31.0524	1.47534	0.737671	−	0.675160i	$-0.235926\pi$
$443$	31.0524	1.47534	0.737671	+	0.675160i	$0.235926\pi$
$444$	35.2596	1.67335
$445$	−3.19614	−0.151511
$446$	10.4169	0.493256
$447$	−13.4119	−0.634361
$448$	−32.0000	−1.51186
$449$	−29.2869	−1.38213	−0.691067	−	0.722791i	$-0.742859\pi$
$449$	−29.2869	−1.38213	−0.691067	+	0.722791i	$0.742859\pi$
$450$	9.05487	0.426851
$451$	−50.0832	−2.35833
$452$	−71.9758	−3.38546
$453$	−6.75421	−0.317341
$454$	6.75291	0.316930
$455$	23.3248	1.09348
$456$	48.9911	2.29422
$457$	−33.2630	−1.55598	−0.777988	−	0.628279i	$-0.783760\pi$
$457$	−33.2630	−1.55598	−0.777988	+	0.628279i	$0.783760\pi$
$458$	−24.1201	−1.12706
$459$	−20.6280	−0.962831
$460$	0.759089	0.0353927
$461$	−3.99971	−0.186285	−0.0931426	−	0.995653i	$-0.529691\pi$
$461$	−3.99971	−0.186285	−0.0931426	+	0.995653i	$0.529691\pi$
$462$	−66.9066	−3.11278
$463$	35.6865	1.65849	0.829247	−	0.558883i	$-0.188770\pi$
$463$	35.6865	1.65849	0.829247	+	0.558883i	$0.188770\pi$
$464$	2.79822	0.129904
$465$	−38.1730	−1.77023
$466$	4.14641	0.192079
$467$	29.4508	1.36282	0.681411	−	0.731901i	$-0.261367\pi$
$467$	29.4508	1.36282	0.681411	+	0.731901i	$0.261367\pi$
$468$	10.3017	0.476198
$469$	−23.6855	−1.09369
$470$	−60.0407	−2.76947
$471$	−16.2368	−0.748151
$472$	34.7284	1.59851
$473$	−49.4434	−2.27341
$474$	−39.5020	−1.81439
$475$	28.7250	1.31799
$476$	−43.6034	−1.99856
$477$	12.5301	0.573713
$478$	21.8486	0.999332
$479$	−42.6696	−1.94962	−0.974812	−	0.223027i	$-0.928406\pi$
$479$	−42.6696	−1.94962	−0.974812	+	0.223027i	$0.928406\pi$
$480$	7.67464	0.350298
$481$	16.9795	0.774200
$482$	39.2709	1.78874
$483$	0.300262	0.0136624
$484$	111.257	5.05715
$485$	13.9177	0.631969
$486$	25.3110	1.14813
$487$	−20.6006	−0.933502	−0.466751	−	0.884389i	$-0.654576\pi$
$487$	−20.6006	−0.933502	−0.466751	+	0.884389i	$0.654576\pi$
$488$	20.1168	0.910643
$489$	13.0337	0.589402
$490$	20.5848	0.929927
$491$	−14.8148	−0.668583	−0.334291	−	0.942470i	$-0.608497\pi$
$491$	−14.8148	−0.668583	−0.334291	+	0.942470i	$0.608497\pi$
$492$	−41.5395	−1.87274
$493$	−3.64828	−0.164310
$494$	49.9146	2.24576
$495$	−19.8434	−0.891896
$496$	−26.3573	−1.18348
$497$	25.2919	1.13450
$498$	23.9095	1.07141
$499$	−18.3670	−0.822219	−0.411110	−	0.911586i	$-0.634859\pi$
$499$	−18.3670	−0.822219	−0.411110	+	0.911586i	$0.634859\pi$
$500$	16.4502	0.735675
$501$	10.4269	0.465839
$502$	63.3507	2.82748
$503$	−1.19582	−0.0533191	−0.0266595	−	0.999645i	$-0.508487\pi$
$503$	−1.19582	−0.0533191	−0.0266595	+	0.999645i	$0.508487\pi$
$504$	14.5587	0.648495
$505$	39.5010	1.75777
$506$	−1.04856	−0.0466140
$507$	9.11892	0.404986
$508$	67.3649	2.98884
$509$	−27.0262	−1.19792	−0.598958	−	0.800781i	$-0.704418\pi$
$509$	−27.0262	−1.19792	−0.598958	+	0.800781i	$0.704418\pi$
$510$	35.5844	1.57570
$511$	16.3713	0.724225
$512$	29.4432	1.30122
$513$	46.2274	2.04099
$514$	8.28641	0.365498
$515$	38.1095	1.67931
$516$	−41.0088	−1.80531
$517$	54.3007	2.38814
$518$	50.7692	2.23067
$519$	18.7176	0.821613
$520$	−31.9312	−1.40027
$521$	−11.8335	−0.518433	−0.259217	−	0.965819i	$-0.583464\pi$
$521$	−11.8335	−0.518433	−0.259217	+	0.965819i	$0.583464\pi$
$522$	2.57723	0.112802
$523$	−27.8942	−1.21973	−0.609865	−	0.792505i	$-0.708776\pi$
$523$	−27.8942	−1.21973	−0.609865	+	0.792505i	$0.708776\pi$
$524$	−11.5425	−0.504238
$525$	−15.3787	−0.671179
$526$	59.7900	2.60697
$527$	34.3643	1.49693
$528$	24.6839	1.07423
$529$	−22.9953	−0.999795
$530$	−82.1715	−3.56930
$531$	8.61993	0.374073
$532$	97.7154	4.23650
$533$	−20.0036	−0.866454
$534$	3.66179	0.158461
$535$	26.8048	1.15887
$536$	32.4250	1.40055
$537$	23.2636	1.00390
$538$	−59.8818	−2.58169
$539$	−18.6169	−0.801886
$540$	−62.5675	−2.69248
$541$	41.1916	1.77097	0.885483	−	0.464671i	$-0.153827\pi$
$541$	41.1916	1.77097	0.885483	+	0.464671i	$0.153827\pi$
$542$	10.1883	0.437626
$543$	24.9809	1.07203
$544$	−6.90889	−0.296216
$545$	26.6820	1.14293
$546$	−26.7230	−1.14364
$547$	−26.2873	−1.12397	−0.561983	−	0.827149i	$-0.689961\pi$
$547$	−26.2873	−1.12397	−0.561983	+	0.827149i	$0.689961\pi$
$548$	51.5244	2.20101
$549$	4.99317	0.213103
$550$	53.7044	2.28996
$551$	8.17581	0.348301
$552$	−0.411053	−0.0174956
$553$	−37.2393	−1.58358
$554$	2.40677	0.102254
$555$	−27.1269	−1.15147
$556$	−28.3482	−1.20223
$557$	−43.2533	−1.83270	−0.916351	−	0.400377i	$-0.868879\pi$
$557$	−43.2533	−1.83270	−0.916351	+	0.400377i	$0.868879\pi$
$558$	−24.2757	−1.02767
$559$	−19.7481	−0.835255
$560$	−25.7298	−1.08728
$561$	−32.1825	−1.35875
$562$	−8.91966	−0.376253
$563$	−10.1870	−0.429331	−0.214665	−	0.976688i	$-0.568866\pi$
$563$	−10.1870	−0.429331	−0.214665	+	0.976688i	$0.568866\pi$
$564$	45.0375	1.89642
$565$	55.3744	2.32962
$566$	36.7773	1.54586
$567$	−14.6252	−0.614200
$568$	−34.6241	−1.45280
$569$	27.5026	1.15297	0.576485	−	0.817108i	$-0.304424\pi$
$569$	27.5026	1.15297	0.576485	+	0.817108i	$0.304424\pi$
$570$	−79.7448	−3.34014
$571$	1.88995	0.0790918	0.0395459	−	0.999218i	$-0.487409\pi$
$571$	1.88995	0.0790918	0.0395459	+	0.999218i	$0.487409\pi$
$572$	61.0995	2.55470
$573$	6.27020	0.261941
$574$	−59.8114	−2.49648
$575$	−0.241013	−0.0100509
$576$	10.8734	0.453059
$577$	18.0744	0.752446	0.376223	−	0.926529i	$-0.377223\pi$
$577$	18.0744	0.752446	0.376223	+	0.926529i	$0.377223\pi$
$578$	8.88113	0.369406
$579$	26.9054	1.11815
$580$	−11.0657	−0.459480
$581$	22.5400	0.935118
$582$	−15.9454	−0.660957
$583$	74.3158	3.07785
$584$	−22.4120	−0.927416
$585$	−7.92562	−0.327684
$586$	31.8085	1.31400
$587$	37.8012	1.56022	0.780111	−	0.625641i	$-0.215163\pi$
$587$	37.8012	1.56022	0.780111	+	0.625641i	$0.215163\pi$
$588$	−15.4410	−0.636777
$589$	−77.0105	−3.17316
$590$	−56.5290	−2.32726
$591$	−1.07864	−0.0443693
$592$	−18.7303	−0.769810
$593$	33.2414	1.36506	0.682531	−	0.730857i	$-0.260879\pi$
$593$	33.2414	1.36506	0.682531	+	0.730857i	$0.260879\pi$
$594$	86.4268	3.54613
$595$	33.5462	1.37526
$596$	36.6212	1.50006
$597$	−3.50680	−0.143524
$598$	−0.418802	−0.0171261
$599$	41.5122	1.69614	0.848072	−	0.529882i	$-0.177764\pi$
$599$	41.5122	1.69614	0.848072	+	0.529882i	$0.177764\pi$
$600$	21.0531	0.859488
$601$	−9.48778	−0.387015	−0.193507	−	0.981099i	$-0.561986\pi$
$601$	−9.48778	−0.387015	−0.193507	+	0.981099i	$0.561986\pi$
$602$	−59.0472	−2.40659
$603$	8.04819	0.327747
$604$	18.4424	0.750411
$605$	−85.5957	−3.47996
$606$	−45.2560	−1.83840
$607$	1.92761	0.0782392	0.0391196	−	0.999235i	$-0.487545\pi$
$607$	1.92761	0.0782392	0.0391196	+	0.999235i	$0.487545\pi$
$608$	15.4829	0.627913
$609$	−4.37712	−0.177370
$610$	−32.7449	−1.32580
$611$	21.6881	0.877408
$612$	14.8162	0.598908
$613$	−13.9213	−0.562275	−0.281137	−	0.959668i	$-0.590712\pi$
$613$	−13.9213	−0.562275	−0.281137	+	0.959668i	$0.590712\pi$
$614$	35.4727	1.43156
$615$	31.9583	1.28868
$616$	86.3474	3.47904
$617$	−21.3317	−0.858781	−0.429391	−	0.903119i	$-0.641272\pi$
$617$	−21.3317	−0.858781	−0.429391	+	0.903119i	$0.641272\pi$
$618$	−43.6618	−1.75634
$619$	−13.5842	−0.545995	−0.272997	−	0.962015i	$-0.588015\pi$
$619$	−13.5842	−0.545995	−0.272997	+	0.962015i	$0.588015\pi$
$620$	104.232	4.18605
$621$	−0.387864	−0.0155645
$622$	75.2116	3.01571
$623$	3.45205	0.138303
$624$	9.85893	0.394673
$625$	−30.2230	−1.20892
$626$	26.7941	1.07091
$627$	72.1212	2.88024
$628$	44.3346	1.76914
$629$	24.4203	0.973701
$630$	−23.6978	−0.944142
$631$	23.4862	0.934969	0.467484	−	0.884001i	$-0.345160\pi$
$631$	23.4862	0.934969	0.467484	+	0.884001i	$0.345160\pi$
$632$	50.9799	2.02787
$633$	−15.6875	−0.623524
$634$	−30.2715	−1.20223
$635$	−51.8271	−2.05670
$636$	61.6382	2.44411
$637$	−7.43573	−0.294614
$638$	15.2855	0.605159
$639$	−8.59404	−0.339975
$640$	−60.2561	−2.38183
$641$	20.2042	0.798018	0.399009	−	0.916947i	$-0.369354\pi$
$641$	20.2042	0.798018	0.399009	+	0.916947i	$0.369354\pi$
$642$	−30.7100	−1.21203
$643$	−25.2877	−0.997248	−0.498624	−	0.866818i	$-0.666161\pi$
$643$	−25.2877	−0.997248	−0.498624	+	0.866818i	$0.666161\pi$
$644$	−0.819868	−0.0323073
$645$	31.5500	1.24228
$646$	71.7882	2.82447
$647$	23.3643	0.918546	0.459273	−	0.888295i	$-0.348110\pi$
$647$	23.3643	0.918546	0.459273	+	0.888295i	$0.348110\pi$
$648$	20.0216	0.786522
$649$	51.1247	2.00682
$650$	21.4499	0.841336
$651$	41.2295	1.61591
$652$	−35.5885	−1.39375
$653$	−37.0633	−1.45040	−0.725199	−	0.688539i	$-0.758252\pi$
$653$	−37.0633	−1.45040	−0.725199	+	0.688539i	$0.758252\pi$
$654$	−30.5694	−1.19536
$655$	8.88024	0.346980
$656$	22.0662	0.861541
$657$	−5.56288	−0.217029
$658$	64.8480	2.52804
$659$	−17.1121	−0.666592	−0.333296	−	0.942822i	$-0.608161\pi$
$659$	−17.1121	−0.666592	−0.333296	+	0.942822i	$0.608161\pi$
$660$	−97.6141	−3.79962
$661$	20.5389	0.798869	0.399435	−	0.916762i	$-0.369206\pi$
$661$	20.5389	0.798869	0.399435	+	0.916762i	$0.369206\pi$
$662$	72.6850	2.82498
$663$	−12.8539	−0.499206
$664$	−30.8568	−1.19748
$665$	−75.1772	−2.91525
$666$	−17.2511	−0.668465
$667$	−0.0685980	−0.00265613
$668$	−28.4707	−1.10156
$669$	6.01162	0.232423
$670$	−52.7795	−2.03905
$671$	29.6145	1.14325
$672$	−8.28914	−0.319761
$673$	25.6225	0.987676	0.493838	−	0.869554i	$-0.335594\pi$
$673$	25.6225	0.987676	0.493838	+	0.869554i	$0.335594\pi$
$674$	−76.2642	−2.93759
$675$	19.8654	0.764620
$676$	−24.8993	−0.957664
$677$	40.0237	1.53824	0.769118	−	0.639107i	$-0.220696\pi$
$677$	40.0237	1.53824	0.769118	+	0.639107i	$0.220696\pi$
$678$	−63.4421	−2.43648
$679$	−15.0321	−0.576877
$680$	−45.9240	−1.76111
$681$	3.89711	0.149338
$682$	−143.979	−5.51324
$683$	25.2270	0.965285	0.482642	−	0.875818i	$-0.339677\pi$
$683$	25.2270	0.965285	0.482642	+	0.875818i	$0.339677\pi$
$684$	−33.2031	−1.26955
$685$	−39.6402	−1.51457
$686$	30.8597	1.17823
$687$	−13.9197	−0.531070
$688$	21.7843	0.830519
$689$	29.6823	1.13081
$690$	0.669088	0.0254718
$691$	−37.3926	−1.42248	−0.711241	−	0.702948i	$-0.751866\pi$
$691$	−37.3926	−1.42248	−0.711241	+	0.702948i	$0.751866\pi$
$692$	−51.1086	−1.94286
$693$	21.4323	0.814144
$694$	40.6073	1.54143
$695$	21.8097	0.827287
$696$	5.99220	0.227134
$697$	−28.7696	−1.08973
$698$	28.8568	1.09225
$699$	2.39290	0.0905078
$700$	41.9915	1.58713
$701$	35.2071	1.32975	0.664876	−	0.746953i	$-0.268484\pi$
$701$	35.2071	1.32975	0.664876	+	0.746953i	$0.268484\pi$
$702$	34.5195	1.30286
$703$	−54.7260	−2.06403
$704$	64.4901	2.43056
$705$	−34.6495	−1.30498
$706$	−66.1470	−2.48948
$707$	−42.6638	−1.60454
$708$	42.4033	1.59361
$709$	−4.46145	−0.167553	−0.0837767	−	0.996485i	$-0.526698\pi$
$709$	−4.46145	−0.167553	−0.0837767	+	0.996485i	$0.526698\pi$
$710$	56.3592	2.11512
$711$	12.6537	0.474551
$712$	−4.72578	−0.177106
$713$	0.646146	0.0241984
$714$	−38.4336	−1.43834
$715$	−47.0068	−1.75795
$716$	−63.5213	−2.37390
$717$	12.6088	0.470886
$718$	−68.5077	−2.55669
$719$	−41.4469	−1.54571	−0.772854	−	0.634584i	$-0.781171\pi$
$719$	−41.4469	−1.54571	−0.772854	+	0.634584i	$0.781171\pi$
$720$	8.74283	0.325826
$721$	−41.1609	−1.53291
$722$	−115.149	−4.28541
$723$	22.6633	0.842856
$724$	−68.2105	−2.53502
$725$	3.51341	0.130485
$726$	98.0663	3.63958
$727$	21.2745	0.789026	0.394513	−	0.918890i	$-0.370913\pi$
$727$	21.2745	0.789026	0.394513	+	0.918890i	$0.370913\pi$
$728$	34.4878	1.27820
$729$	28.5295	1.05665
$730$	36.4810	1.35022
$731$	−28.4021	−1.05049
$732$	24.5625	0.907856
$733$	5.83623	0.215566	0.107783	−	0.994174i	$-0.465625\pi$
$733$	5.83623	0.215566	0.107783	+	0.994174i	$0.465625\pi$
$734$	−67.0236	−2.47389
$735$	11.8795	0.438183
$736$	−0.129907	−0.00478843
$737$	47.7337	1.75829
$738$	20.3235	0.748119
$739$	−3.38038	−0.124349	−0.0621746	−	0.998065i	$-0.519804\pi$
$739$	−3.38038	−0.124349	−0.0621746	+	0.998065i	$0.519804\pi$
$740$	74.0703	2.72288
$741$	28.8058	1.05821
$742$	88.7509	3.25815
$743$	−6.29046	−0.230774	−0.115387	−	0.993321i	$-0.536811\pi$
$743$	−6.29046	−0.230774	−0.115387	+	0.993321i	$0.536811\pi$
$744$	−56.4424	−2.06928
$745$	−28.1745	−1.03223
$746$	27.0624	0.990825
$747$	−7.65896	−0.280227
$748$	87.8745	3.21301
$749$	−28.9510	−1.05785
$750$	14.4998	0.529457
$751$	28.3646	1.03504	0.517519	−	0.855671i	$-0.326856\pi$
$751$	28.3646	1.03504	0.517519	+	0.855671i	$0.326856\pi$
$752$	−23.9244	−0.872433
$753$	36.5598	1.33231
$754$	6.10515	0.222337
$755$	−14.1886	−0.516377
$756$	67.5772	2.45776
$757$	7.63782	0.277601	0.138801	−	0.990320i	$-0.455675\pi$
$757$	7.63782	0.277601	0.138801	+	0.990320i	$0.455675\pi$
$758$	33.6425	1.22195
$759$	−0.605123	−0.0219646
$760$	102.916	3.73316
$761$	25.9295	0.939945	0.469972	−	0.882681i	$-0.344264\pi$
$761$	25.9295	0.939945	0.469972	+	0.882681i	$0.344264\pi$
$762$	59.3779	2.15103
$763$	−28.8184	−1.04330
$764$	−17.1208	−0.619410
$765$	−11.3988	−0.412124
$766$	−18.5936	−0.671816
$767$	20.4196	0.737310
$768$	40.8276	1.47324
$769$	−38.9454	−1.40441	−0.702203	−	0.711977i	$-0.747800\pi$
$769$	−38.9454	−1.40441	−0.702203	+	0.711977i	$0.747800\pi$
$770$	−140.551	−5.06512
$771$	4.78210	0.172223
$772$	−73.4653	−2.64407
$773$	7.73728	0.278291	0.139145	−	0.990272i	$-0.455564\pi$
$773$	7.73728	0.278291	0.139145	+	0.990272i	$0.455564\pi$
$774$	20.0639	0.721181
$775$	−33.0939	−1.18877
$776$	20.5786	0.738728
$777$	29.2989	1.05109
$778$	−4.58742	−0.164467
$779$	64.4729	2.30998
$780$	−38.9878	−1.39599
$781$	−50.9712	−1.82389
$782$	−0.602329	−0.0215392
$783$	5.65416	0.202063
$784$	8.20243	0.292944
$785$	−34.1088	−1.21739
$786$	−10.1740	−0.362895
$787$	−1.00023	−0.0356545	−0.0178272	−	0.999841i	$-0.505675\pi$
$787$	−1.00023	−0.0356545	−0.0178272	+	0.999841i	$0.505675\pi$
$788$	2.94523	0.104919
$789$	34.5049	1.22841
$790$	−82.9822	−2.95237
$791$	−59.8082	−2.12653
$792$	−29.3403	−1.04256
$793$	11.8283	0.420034
$794$	−10.1738	−0.361053
$795$	−47.4212	−1.68186
$796$	9.57534	0.339389
$797$	33.9143	1.20130	0.600652	−	0.799510i	$-0.294908\pi$
$797$	33.9143	1.20130	0.600652	+	0.799510i	$0.294908\pi$
$798$	86.1299	3.04897
$799$	31.1923	1.10350
$800$	6.65350	0.235237
$801$	−1.17298	−0.0414453
$802$	36.1852	1.27774
$803$	−32.9934	−1.16431
$804$	39.5908	1.39626
$805$	0.630764	0.0222315
$806$	−57.5063	−2.02557
$807$	−34.5579	−1.21649
$808$	58.4059	2.05471
$809$	0.324674	0.0114149	0.00570746	−	0.999984i	$-0.498183\pi$
$809$	0.324674	0.0114149	0.00570746	+	0.999984i	$0.498183\pi$
$810$	−32.5900	−1.14510
$811$	−35.1284	−1.23352	−0.616762	−	0.787150i	$-0.711556\pi$
$811$	−35.1284	−1.23352	−0.616762	+	0.787150i	$0.711556\pi$
$812$	11.9518	0.419425
$813$	5.87969	0.206210
$814$	−102.316	−3.58617
$815$	27.3799	0.959077
$816$	14.1793	0.496375
$817$	63.6492	2.22680
$818$	−17.7624	−0.621048
$819$	8.56021	0.299118
$820$	−87.2624	−3.04734
$821$	10.9434	0.381928	0.190964	−	0.981597i	$-0.438839\pi$
$821$	10.9434	0.381928	0.190964	+	0.981597i	$0.438839\pi$
$822$	45.4155	1.58405
$823$	−35.9529	−1.25324	−0.626619	−	0.779325i	$-0.715562\pi$
$823$	−35.9529	−1.25324	−0.626619	+	0.779325i	$0.715562\pi$
$824$	56.3485	1.96299
$825$	30.9928	1.07903
$826$	61.0551	2.12438
$827$	54.4265	1.89259	0.946297	−	0.323298i	$-0.104792\pi$
$827$	54.4265	1.89259	0.946297	+	0.323298i	$0.104792\pi$
$828$	0.278586	0.00968153
$829$	36.9144	1.28209	0.641045	−	0.767503i	$-0.278501\pi$
$829$	36.9144	1.28209	0.641045	+	0.767503i	$0.278501\pi$
$830$	50.2270	1.74340
$831$	1.38895	0.0481820
$832$	25.7578	0.892993
$833$	−10.6942	−0.370533
$834$	−24.9872	−0.865234
$835$	21.9039	0.758015
$836$	−196.927	−6.81087
$837$	−53.2583	−1.84088
$838$	16.2502	0.561354
$839$	12.5542	0.433420	0.216710	−	0.976236i	$-0.430467\pi$
$839$	12.5542	0.433420	0.216710	+	0.976236i	$0.430467\pi$
$840$	−55.0987	−1.90108
$841$	1.00000	0.0344828
$842$	−7.13849	−0.246009
$843$	−5.14755	−0.177291
$844$	42.8349	1.47444
$845$	19.1562	0.658994
$846$	−22.0350	−0.757578
$847$	92.4492	3.17659
$848$	−32.7429	−1.12439
$849$	21.2242	0.728413
$850$	30.8497	1.05814
$851$	0.459171	0.0157402
$852$	−42.2759	−1.44835
$853$	−38.1505	−1.30625	−0.653124	−	0.757251i	$-0.726542\pi$
$853$	−38.1505	−1.30625	−0.653124	+	0.757251i	$0.726542\pi$
$854$	35.3668	1.21023
$855$	25.5447	0.873611
$856$	39.6333	1.35464
$857$	35.1511	1.20074	0.600369	−	0.799723i	$-0.295020\pi$
$857$	35.1511	1.20074	0.600369	+	0.799723i	$0.295020\pi$
$858$	53.8553	1.83859
$859$	−26.1360	−0.891748	−0.445874	−	0.895096i	$-0.647107\pi$
$859$	−26.1360	−0.891748	−0.445874	+	0.895096i	$0.647107\pi$
$860$	−86.1476	−2.93761
$861$	−34.5172	−1.17634
$862$	−42.4261	−1.44504
$863$	−1.54641	−0.0526404	−0.0263202	−	0.999654i	$-0.508379\pi$
$863$	−1.54641	−0.0526404	−0.0263202	+	0.999654i	$0.508379\pi$
$864$	10.7075	0.364277
$865$	39.3203	1.33693
$866$	−47.5747	−1.61665
$867$	5.12530	0.174064
$868$	−112.577	−3.82113
$869$	75.0490	2.54586
$870$	−9.75375	−0.330683
$871$	19.0652	0.646001
$872$	39.4518	1.33601
$873$	5.10780	0.172873
$874$	1.34982	0.0456584
$875$	13.6693	0.462105
$876$	−27.3650	−0.924578
$877$	17.0241	0.574864	0.287432	−	0.957801i	$-0.407198\pi$
$877$	17.0241	0.574864	0.287432	+	0.957801i	$0.407198\pi$
$878$	−68.2667	−2.30389
$879$	18.3567	0.619156
$880$	51.8537	1.74799
$881$	−21.3990	−0.720952	−0.360476	−	0.932769i	$-0.617386\pi$
$881$	−21.3990	−0.720952	−0.360476	+	0.932769i	$0.617386\pi$
$882$	7.55464	0.254378
$883$	14.0632	0.473264	0.236632	−	0.971599i	$-0.423956\pi$
$883$	14.0632	0.473264	0.236632	+	0.971599i	$0.423956\pi$
$884$	35.0978	1.18047
$885$	−32.6229	−1.09661
$886$	−74.7358	−2.51080
$887$	39.0542	1.31131	0.655656	−	0.755060i	$-0.272392\pi$
$887$	39.0542	1.31131	0.655656	+	0.755060i	$0.272392\pi$
$888$	−40.1097	−1.34599
$889$	55.9768	1.87740
$890$	7.69235	0.257848
$891$	29.4744	0.987428
$892$	−16.4148	−0.549607
$893$	−69.9021	−2.33919
$894$	32.2793	1.07958
$895$	48.8700	1.63354
$896$	65.0807	2.17419
$897$	−0.241691	−0.00806982
$898$	70.4867	2.35217
$899$	−9.41931	−0.314152
$900$	−14.2685	−0.475615
$901$	42.6897	1.42220
$902$	120.539	4.01350
$903$	−34.0762	−1.13399
$904$	81.8762	2.72316
$905$	52.4776	1.74441
$906$	16.2558	0.540063
$907$	−3.35451	−0.111385	−0.0556924	−	0.998448i	$-0.517737\pi$
$907$	−3.35451	−0.111385	−0.0556924	+	0.998448i	$0.517737\pi$
$908$	−10.6411	−0.353137
$909$	14.4969	0.480832
$910$	−56.1373	−1.86093
$911$	34.3132	1.13685	0.568423	−	0.822736i	$-0.307554\pi$
$911$	34.3132	1.13685	0.568423	+	0.822736i	$0.307554\pi$
$912$	−31.7759	−1.05221
$913$	−45.4252	−1.50336
$914$	80.0562	2.64803
$915$	−18.8971	−0.624720
$916$	38.0078	1.25581
$917$	−9.59126	−0.316731
$918$	49.6467	1.63859
$919$	22.4989	0.742170	0.371085	−	0.928599i	$-0.378986\pi$
$919$	22.4989	0.742170	0.371085	+	0.928599i	$0.378986\pi$
$920$	−0.863503	−0.0284688
$921$	20.4713	0.674553
$922$	9.62638	0.317028
$923$	−20.3583	−0.670101
$924$	105.430	3.46839
$925$	−23.5176	−0.773253
$926$	−85.8891	−2.82249
$927$	13.9862	0.459368
$928$	1.89374	0.0621651
$929$	16.6771	0.547159	0.273579	−	0.961849i	$-0.411792\pi$
$929$	16.6771	0.547159	0.273579	+	0.961849i	$0.411792\pi$
$930$	91.8736	3.01265
$931$	23.9658	0.785447
$932$	−6.53383	−0.214023
$933$	43.4047	1.42100
$934$	−70.8813	−2.31931
$935$	−67.6061	−2.21096
$936$	−11.7188	−0.383039
$937$	17.9302	0.585753	0.292876	−	0.956150i	$-0.405388\pi$
$937$	17.9302	0.585753	0.292876	+	0.956150i	$0.405388\pi$
$938$	57.0055	1.86130
$939$	15.4629	0.504612
$940$	94.6107	3.08586
$941$	−55.3768	−1.80523	−0.902617	−	0.430445i	$-0.858357\pi$
$941$	−55.3768	−1.80523	−0.902617	+	0.430445i	$0.858357\pi$
$942$	39.0781	1.27323
$943$	−0.540951	−0.0176158
$944$	−22.5251	−0.733129
$945$	−51.9904	−1.69125
$946$	118.999	3.86898
$947$	−23.4614	−0.762394	−0.381197	−	0.924494i	$-0.624488\pi$
$947$	−23.4614	−0.762394	−0.381197	+	0.924494i	$0.624488\pi$
$948$	62.2463	2.02167
$949$	−13.1778	−0.427770
$950$	−69.1344	−2.24302
$951$	−17.4697	−0.566494
$952$	49.6011	1.60758
$953$	−35.4509	−1.14837	−0.574183	−	0.818727i	$-0.694680\pi$
$953$	−35.4509	−1.14837	−0.574183	+	0.818727i	$0.694680\pi$
$954$	−30.1570	−0.976369
$955$	13.1719	0.426232
$956$	−34.4285	−1.11350
$957$	8.82128	0.285152
$958$	102.696	3.31795
$959$	42.8141	1.38254
$960$	−41.1514	−1.32816
$961$	57.7234	1.86204
$962$	−40.8658	−1.31757
$963$	9.83737	0.317005
$964$	−61.8822	−1.99309
$965$	56.5204	1.81946
$966$	−0.722661	−0.0232512
$967$	−40.0201	−1.28696	−0.643480	−	0.765463i	$-0.722510\pi$
$967$	−40.0201	−1.28696	−0.643480	+	0.765463i	$0.722510\pi$
$968$	−126.561	−4.06783
$969$	41.4290	1.33089
$970$	−33.4966	−1.07551
$971$	−61.3269	−1.96807	−0.984037	−	0.177966i	$-0.943048\pi$
$971$	−61.3269	−1.96807	−0.984037	+	0.177966i	$0.943048\pi$
$972$	−39.8844	−1.27929
$973$	−23.5559	−0.755168
$974$	49.5809	1.58867
$975$	12.3788	0.396438
$976$	−13.0479	−0.417652
$977$	32.7477	1.04769	0.523846	−	0.851813i	$-0.324497\pi$
$977$	32.7477	1.04769	0.523846	+	0.851813i	$0.324497\pi$
$978$	−31.3690	−1.00307
$979$	−6.95696	−0.222345
$980$	−32.4371	−1.03616
$981$	9.79231	0.312644
$982$	35.6558	1.13782
$983$	49.6950	1.58503	0.792513	−	0.609855i	$-0.208772\pi$
$983$	49.6950	1.58503	0.792513	+	0.609855i	$0.208772\pi$
$984$	47.2533	1.50638
$985$	−2.26591	−0.0721978
$986$	8.78056	0.279630
$987$	37.4239	1.19121
$988$	−78.6543	−2.50233
$989$	−0.534040	−0.0169815
$990$	47.7585	1.51786
$991$	−28.1760	−0.895039	−0.447520	−	0.894274i	$-0.647693\pi$
$991$	−28.1760	−0.895039	−0.447520	+	0.894274i	$0.647693\pi$
$992$	−17.8377	−0.566349
$993$	41.9466	1.33113
$994$	−60.8718	−1.93073
$995$	−7.36677	−0.233542
$996$	−37.6761	−1.19381
$997$	31.2060	0.988304	0.494152	−	0.869376i	$-0.335479\pi$
$997$	31.2060	0.988304	0.494152	+	0.869376i	$0.335479\pi$
$998$	44.2051	1.39929
$999$	−37.8470	−1.19743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.d.1.17	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.d.1.17	✓	168	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)

\(f(q)\)	\(=\)	\(q-2.40677 q^{2} -1.38895 q^{3} +3.79253 q^{4} -2.91778 q^{5} +3.34287 q^{6} +3.15140 q^{7} -4.31420 q^{8} -1.07083 q^{9} +O(q^{10})\)	\(q-2.40677 q^{2} -1.38895 q^{3} +3.79253 q^{4} -2.91778 q^{5} +3.34287 q^{6} +3.15140 q^{7} -4.31420 q^{8} -1.07083 q^{9} +7.02241 q^{10} -6.35106 q^{11} -5.26762 q^{12} -2.53666 q^{13} -7.58468 q^{14} +4.05264 q^{15} +2.79822 q^{16} -3.64828 q^{17} +2.57723 q^{18} +8.17581 q^{19} -11.0657 q^{20} -4.37712 q^{21} +15.2855 q^{22} -0.0685980 q^{23} +5.99220 q^{24} +3.51341 q^{25} +6.10515 q^{26} +5.65416 q^{27} +11.9518 q^{28} +1.00000 q^{29} -9.75375 q^{30} -9.41931 q^{31} +1.89374 q^{32} +8.82128 q^{33} +8.78056 q^{34} -9.19507 q^{35} -4.06114 q^{36} -6.69365 q^{37} -19.6773 q^{38} +3.52329 q^{39} +12.5879 q^{40} +7.88581 q^{41} +10.5347 q^{42} +7.78507 q^{43} -24.0866 q^{44} +3.12443 q^{45} +0.165100 q^{46} -8.54987 q^{47} -3.88658 q^{48} +2.93131 q^{49} -8.45597 q^{50} +5.06727 q^{51} -9.62036 q^{52} -11.7013 q^{53} -13.6083 q^{54} +18.5310 q^{55} -13.5958 q^{56} -11.3558 q^{57} -2.40677 q^{58} -8.04980 q^{59} +15.3697 q^{60} -4.66292 q^{61} +22.6701 q^{62} -3.37460 q^{63} -10.1542 q^{64} +7.40141 q^{65} -21.2308 q^{66} -7.51587 q^{67} -13.8362 q^{68} +0.0952791 q^{69} +22.1304 q^{70} +8.02562 q^{71} +4.61975 q^{72} +5.19494 q^{73} +16.1101 q^{74} -4.87995 q^{75} +31.0070 q^{76} -20.0147 q^{77} -8.47974 q^{78} -11.8168 q^{79} -8.16457 q^{80} -4.64086 q^{81} -18.9793 q^{82} +7.15239 q^{83} -16.6004 q^{84} +10.6449 q^{85} -18.7368 q^{86} -1.38895 q^{87} +27.3997 q^{88} +1.09540 q^{89} -7.51977 q^{90} -7.99403 q^{91} -0.260160 q^{92} +13.0829 q^{93} +20.5775 q^{94} -23.8552 q^{95} -2.63031 q^{96} -4.76996 q^{97} -7.05497 q^{98} +6.80087 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9} + 41 q^{10} + 29 q^{11} + 82 q^{12} + 62 q^{13} + 23 q^{14} + 31 q^{15} + 204 q^{16} + 56 q^{17} + 35 q^{18} + 83 q^{19} + 6 q^{20} + 30 q^{21} + 56 q^{22} + 54 q^{23} + 28 q^{24} + 210 q^{25} + 21 q^{26} + 140 q^{27} + 151 q^{28} + 168 q^{29} + 29 q^{30} + 72 q^{31} + 40 q^{32} + 32 q^{33} + 34 q^{34} + 18 q^{35} + 152 q^{36} + 42 q^{37} + 29 q^{38} + 70 q^{39} + 97 q^{40} + 41 q^{41} - 20 q^{42} + 119 q^{43} + 37 q^{44} + 22 q^{45} + 24 q^{46} + 119 q^{47} + 135 q^{48} + 216 q^{49} + 38 q^{50} + 18 q^{51} + 154 q^{52} - 7 q^{53} + 35 q^{54} + 224 q^{55} + 46 q^{56} + 12 q^{57} + 12 q^{58} + 25 q^{59} + 13 q^{60} + 82 q^{61} + 27 q^{62} + 211 q^{63} + 217 q^{64} + 8 q^{65} - 6 q^{66} + 76 q^{67} + 132 q^{68} + 36 q^{69} + 39 q^{70} + 32 q^{71} + 39 q^{72} + 89 q^{73} - q^{74} + 123 q^{75} + 180 q^{76} + 68 q^{77} - 54 q^{78} + 176 q^{79} - 11 q^{80} + 192 q^{81} + 51 q^{82} + 76 q^{83} + 86 q^{84} + 65 q^{85} - 72 q^{86} + 35 q^{87} + 178 q^{88} + 55 q^{89} + 2 q^{90} + 80 q^{91} + 44 q^{92} + 39 q^{93} + 89 q^{94} + 77 q^{95} - 68 q^{96} + 82 q^{97} + 80 q^{98} + 67 q^{99}+O(q^{100}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9 + 41 * q^10 + 29 * q^11 + 82 * q^12 + 62 * q^13 + 23 * q^14 + 31 * q^15 + 204 * q^16 + 56 * q^17 + 35 * q^18 + 83 * q^19 + 6 * q^20 + 30 * q^21 + 56 * q^22 + 54 * q^23 + 28 * q^24 + 210 * q^25 + 21 * q^26 + 140 * q^27 + 151 * q^28 + 168 * q^29 + 29 * q^30 + 72 * q^31 + 40 * q^32 + 32 * q^33 + 34 * q^34 + 18 * q^35 + 152 * q^36 + 42 * q^37 + 29 * q^38 + 70 * q^39 + 97 * q^40 + 41 * q^41 - 20 * q^42 + 119 * q^43 + 37 * q^44 + 22 * q^45 + 24 * q^46 + 119 * q^47 + 135 * q^48 + 216 * q^49 + 38 * q^50 + 18 * q^51 + 154 * q^52 - 7 * q^53 + 35 * q^54 + 224 * q^55 + 46 * q^56 + 12 * q^57 + 12 * q^58 + 25 * q^59 + 13 * q^60 + 82 * q^61 + 27 * q^62 + 211 * q^63 + 217 * q^64 + 8 * q^65 - 6 * q^66 + 76 * q^67 + 132 * q^68 + 36 * q^69 + 39 * q^70 + 32 * q^71 + 39 * q^72 + 89 * q^73 - q^74 + 123 * q^75 + 180 * q^76 + 68 * q^77 - 54 * q^78 + 176 * q^79 - 11 * q^80 + 192 * q^81 + 51 * q^82 + 76 * q^83 + 86 * q^84 + 65 * q^85 - 72 * q^86 + 35 * q^87 + 178 * q^88 + 55 * q^89 + 2 * q^90 + 80 * q^91 + 44 * q^92 + 39 * q^93 + 89 * q^94 + 77 * q^95 - 68 * q^96 + 82 * q^97 + 80 * q^98 + 67 * q^99

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