LMFDB - Embedded newform 503.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [503,2,Mod(1,503)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(503, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("503.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.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:	$4.01647522167$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 $ x^10 - 2x^9 - 9x^8 + 14x^7 + 27x^6 - 27x^5 - 34x^4 + 14x^3 + 17x^2 + x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.858231$ of defining polynomial
Character	$\chi$	$=$	503.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58686 q^{2} -1.85823 q^{3} +4.69185 q^{4} +1.44291 q^{5} +4.80698 q^{6} -1.96509 q^{7} -6.96343 q^{8} +0.453023 q^{9} +O(q^{10})$	\(q-2.58686 q^{2} -1.85823 q^{3} +4.69185 q^{4} +1.44291 q^{5} +4.80698 q^{6} -1.96509 q^{7} -6.96343 q^{8} +0.453023 q^{9} -3.73261 q^{10} +2.85614 q^{11} -8.71853 q^{12} -3.84427 q^{13} +5.08341 q^{14} -2.68126 q^{15} +8.62972 q^{16} +1.30329 q^{17} -1.17191 q^{18} +3.53196 q^{19} +6.76991 q^{20} +3.65159 q^{21} -7.38845 q^{22} +4.20650 q^{23} +12.9397 q^{24} -2.91801 q^{25} +9.94458 q^{26} +4.73287 q^{27} -9.21989 q^{28} -1.10402 q^{29} +6.93604 q^{30} -3.53201 q^{31} -8.39703 q^{32} -5.30738 q^{33} -3.37144 q^{34} -2.83545 q^{35} +2.12551 q^{36} -6.61903 q^{37} -9.13668 q^{38} +7.14353 q^{39} -10.0476 q^{40} +0.671095 q^{41} -9.44615 q^{42} -4.32289 q^{43} +13.4006 q^{44} +0.653672 q^{45} -10.8816 q^{46} -0.378524 q^{47} -16.0360 q^{48} -3.13843 q^{49} +7.54849 q^{50} -2.42182 q^{51} -18.0367 q^{52} -7.13700 q^{53} -12.2433 q^{54} +4.12116 q^{55} +13.6838 q^{56} -6.56319 q^{57} +2.85594 q^{58} -13.8806 q^{59} -12.5801 q^{60} -6.51374 q^{61} +9.13682 q^{62} -0.890231 q^{63} +4.46249 q^{64} -5.54693 q^{65} +13.7294 q^{66} -7.55189 q^{67} +6.11485 q^{68} -7.81664 q^{69} +7.33490 q^{70} +0.0744967 q^{71} -3.15459 q^{72} +3.29052 q^{73} +17.1225 q^{74} +5.42234 q^{75} +16.5714 q^{76} -5.61258 q^{77} -18.4793 q^{78} +8.57578 q^{79} +12.4519 q^{80} -10.1538 q^{81} -1.73603 q^{82} +14.8165 q^{83} +17.1327 q^{84} +1.88053 q^{85} +11.1827 q^{86} +2.05152 q^{87} -19.8886 q^{88} -17.5415 q^{89} -1.69096 q^{90} +7.55432 q^{91} +19.7362 q^{92} +6.56329 q^{93} +0.979188 q^{94} +5.09630 q^{95} +15.6036 q^{96} -8.01702 q^{97} +8.11867 q^{98} +1.29390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9} - 4 q^{10} - 3 q^{11} - 7 q^{12} - 18 q^{13} + q^{14} - 2 q^{15} - 4 q^{16} - 11 q^{17} - q^{18} - 3 q^{20} + q^{21} - 18 q^{22} - 2 q^{23} + 10 q^{24} - 27 q^{25} + 11 q^{26} - 2 q^{27} - 22 q^{28} - 9 q^{29} + 12 q^{30} - 22 q^{31} - 10 q^{32} - 10 q^{33} - 10 q^{34} - 6 q^{35} + 2 q^{36} - 35 q^{37} + 2 q^{38} + 8 q^{39} - 19 q^{40} - 4 q^{41} + 4 q^{42} - 20 q^{43} + 9 q^{44} + 2 q^{45} - q^{46} + 7 q^{47} - 27 q^{49} + 16 q^{50} + 9 q^{51} - 7 q^{52} - 24 q^{53} + 17 q^{54} - 11 q^{55} + 12 q^{56} - 23 q^{57} + 2 q^{58} + 17 q^{59} - 4 q^{61} + 8 q^{62} + 10 q^{63} + 3 q^{64} - 16 q^{65} + 46 q^{66} - 6 q^{67} + 28 q^{68} - 2 q^{69} + 26 q^{70} - q^{71} - q^{72} - 31 q^{73} + 11 q^{74} + 30 q^{75} + 20 q^{76} + 3 q^{77} + 11 q^{78} - 10 q^{79} + 24 q^{80} - 6 q^{81} - 9 q^{82} + 22 q^{83} + 22 q^{84} - 6 q^{85} + 38 q^{86} + 25 q^{87} - 3 q^{88} + q^{89} + 2 q^{90} + 10 q^{91} + 27 q^{92} - 6 q^{93} + 33 q^{94} + 39 q^{95} + 46 q^{96} - 57 q^{97} + 40 q^{98} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9 - 4 * q^10 - 3 * q^11 - 7 * q^12 - 18 * q^13 + q^14 - 2 * q^15 - 4 * q^16 - 11 * q^17 - q^18 - 3 * q^20 + q^21 - 18 * q^22 - 2 * q^23 + 10 * q^24 - 27 * q^25 + 11 * q^26 - 2 * q^27 - 22 * q^28 - 9 * q^29 + 12 * q^30 - 22 * q^31 - 10 * q^32 - 10 * q^33 - 10 * q^34 - 6 * q^35 + 2 * q^36 - 35 * q^37 + 2 * q^38 + 8 * q^39 - 19 * q^40 - 4 * q^41 + 4 * q^42 - 20 * q^43 + 9 * q^44 + 2 * q^45 - q^46 + 7 * q^47 - 27 * q^49 + 16 * q^50 + 9 * q^51 - 7 * q^52 - 24 * q^53 + 17 * q^54 - 11 * q^55 + 12 * q^56 - 23 * q^57 + 2 * q^58 + 17 * q^59 - 4 * q^61 + 8 * q^62 + 10 * q^63 + 3 * q^64 - 16 * q^65 + 46 * q^66 - 6 * q^67 + 28 * q^68 - 2 * q^69 + 26 * q^70 - q^71 - q^72 - 31 * q^73 + 11 * q^74 + 30 * q^75 + 20 * q^76 + 3 * q^77 + 11 * q^78 - 10 * q^79 + 24 * q^80 - 6 * q^81 - 9 * q^82 + 22 * q^83 + 22 * q^84 - 6 * q^85 + 38 * q^86 + 25 * q^87 - 3 * q^88 + q^89 + 2 * q^90 + 10 * q^91 + 27 * q^92 - 6 * q^93 + 33 * q^94 + 39 * q^95 + 46 * q^96 - 57 * q^97 + 40 * q^98 + 35 * 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 $

$2$	−2.58686	−1.82919	−0.914593	−	0.404375i	$-0.867489\pi$
$2$	−2.58686	−1.82919	−0.914593	+	0.404375i	$0.867489\pi$
$3$	−1.85823	−1.07285	−0.536425	−	0.843948i	$-0.680226\pi$
$3$	−1.85823	−1.07285	−0.536425	+	0.843948i	$0.680226\pi$
$4$	4.69185	2.34592
$5$	1.44291	0.645289	0.322644	−	0.946520i	$-0.395428\pi$
$5$	1.44291	0.645289	0.322644	+	0.946520i	$0.395428\pi$
$6$	4.80698	1.96244
$7$	−1.96509	−0.742734	−0.371367	−	0.928486i	$-0.621111\pi$
$7$	−1.96509	−0.742734	−0.371367	+	0.928486i	$0.621111\pi$
$8$	−6.96343	−2.46194
$9$	0.453023	0.151008
$10$	−3.73261	−1.18035
$11$	2.85614	0.861160	0.430580	−	0.902552i	$-0.358309\pi$
$11$	2.85614	0.861160	0.430580	+	0.902552i	$0.358309\pi$
$12$	−8.71853	−2.51682
$13$	−3.84427	−1.06621	−0.533104	−	0.846050i	$-0.678974\pi$
$13$	−3.84427	−1.06621	−0.533104	+	0.846050i	$0.678974\pi$
$14$	5.08341	1.35860
$15$	−2.68126	−0.692298
$16$	8.62972	2.15743
$17$	1.30329	0.316095	0.158047	−	0.987432i	$-0.449480\pi$
$17$	1.30329	0.316095	0.158047	+	0.987432i	$0.449480\pi$
$18$	−1.17191	−0.276221
$19$	3.53196	0.810287	0.405143	−	0.914253i	$-0.367222\pi$
$19$	3.53196	0.810287	0.405143	+	0.914253i	$0.367222\pi$
$20$	6.76991	1.51380
$21$	3.65159	0.796842
$22$	−7.38845	−1.57522
$23$	4.20650	0.877115	0.438558	−	0.898703i	$-0.355490\pi$
$23$	4.20650	0.877115	0.438558	+	0.898703i	$0.355490\pi$
$24$	12.9397	2.64130
$25$	−2.91801	−0.583602
$26$	9.94458	1.95029
$27$	4.73287	0.910842
$28$	−9.21989	−1.74240
$29$	−1.10402	−0.205011	−0.102506	−	0.994732i	$-0.532686\pi$
$29$	−1.10402	−0.205011	−0.102506	+	0.994732i	$0.532686\pi$
$30$	6.93604	1.26634
$31$	−3.53201	−0.634368	−0.317184	−	0.948364i	$-0.602737\pi$
$31$	−3.53201	−0.634368	−0.317184	+	0.948364i	$0.602737\pi$
$32$	−8.39703	−1.48440
$33$	−5.30738	−0.923896
$34$	−3.37144	−0.578196
$35$	−2.83545	−0.479278
$36$	2.12551	0.354252
$37$	−6.61903	−1.08816	−0.544081	−	0.839033i	$-0.683121\pi$
$37$	−6.61903	−1.08816	−0.544081	+	0.839033i	$0.683121\pi$
$38$	−9.13668	−1.48217
$39$	7.14353	1.14388
$40$	−10.0476	−1.58866
$41$	0.671095	0.104807	0.0524037	−	0.998626i	$-0.483312\pi$
$41$	0.671095	0.104807	0.0524037	+	0.998626i	$0.483312\pi$
$42$	−9.44615	−1.45757
$43$	−4.32289	−0.659235	−0.329617	−	0.944115i	$-0.606920\pi$
$43$	−4.32289	−0.659235	−0.329617	+	0.944115i	$0.606920\pi$
$44$	13.4006	2.02021
$45$	0.653672	0.0974436
$46$	−10.8816	−1.60441
$47$	−0.378524	−0.0552134	−0.0276067	−	0.999619i	$-0.508789\pi$
$47$	−0.378524	−0.0552134	−0.0276067	+	0.999619i	$0.508789\pi$
$48$	−16.0360	−2.31460
$49$	−3.13843	−0.448347
$50$	7.54849	1.06752
$51$	−2.42182	−0.339122
$52$	−18.0367	−2.50124
$53$	−7.13700	−0.980342	−0.490171	−	0.871626i	$-0.663066\pi$
$53$	−7.13700	−0.980342	−0.490171	+	0.871626i	$0.663066\pi$
$54$	−12.2433	−1.66610
$55$	4.12116	0.555697
$56$	13.6838	1.82857
$57$	−6.56319	−0.869316
$58$	2.85594	0.375004
$59$	−13.8806	−1.80709	−0.903547	−	0.428489i	$-0.859046\pi$
$59$	−13.8806	−1.80709	−0.903547	+	0.428489i	$0.859046\pi$
$60$	−12.5801	−1.62408
$61$	−6.51374	−0.833999	−0.417000	−	0.908907i	$-0.636918\pi$
$61$	−6.51374	−0.833999	−0.417000	+	0.908907i	$0.636918\pi$
$62$	9.13682	1.16038
$63$	−0.890231	−0.112159
$64$	4.46249	0.557812
$65$	−5.54693	−0.688012
$66$	13.7294	1.68998
$67$	−7.55189	−0.922610	−0.461305	−	0.887242i	$-0.652619\pi$
$67$	−7.55189	−0.922610	−0.461305	+	0.887242i	$0.652619\pi$
$68$	6.11485	0.741534
$69$	−7.81664	−0.941013
$70$	7.33490	0.876688
$71$	0.0744967	0.00884113	0.00442057	−	0.999990i	$-0.498593\pi$
$71$	0.0744967	0.00884113	0.00442057	+	0.999990i	$0.498593\pi$
$72$	−3.15459	−0.371772
$73$	3.29052	0.385126	0.192563	−	0.981285i	$-0.438320\pi$
$73$	3.29052	0.385126	0.192563	+	0.981285i	$0.438320\pi$
$74$	17.1225	1.99045
$75$	5.42234	0.626118
$76$	16.5714	1.90087
$77$	−5.61258	−0.639612
$78$	−18.4793	−2.09237
$79$	8.57578	0.964850	0.482425	−	0.875937i	$-0.339756\pi$
$79$	8.57578	0.964850	0.482425	+	0.875937i	$0.339756\pi$
$80$	12.4519	1.39217
$81$	−10.1538	−1.12820
$82$	−1.73603	−0.191712
$83$	14.8165	1.62632	0.813158	−	0.582042i	$-0.197746\pi$
$83$	14.8165	1.62632	0.813158	+	0.582042i	$0.197746\pi$
$84$	17.1327	1.86933
$85$	1.88053	0.203973
$86$	11.1827	1.20586
$87$	2.05152	0.219946
$88$	−19.8886	−2.12013
$89$	−17.5415	−1.85940	−0.929700	−	0.368318i	$-0.879934\pi$
$89$	−17.5415	−1.85940	−0.929700	+	0.368318i	$0.879934\pi$
$90$	−1.69096	−0.178243
$91$	7.55432	0.791908
$92$	19.7362	2.05764
$93$	6.56329	0.680582
$94$	0.979188	0.100996
$95$	5.09630	0.522869
$96$	15.6036	1.59254
$97$	−8.01702	−0.814005	−0.407003	−	0.913427i	$-0.633426\pi$
$97$	−8.01702	−0.814005	−0.407003	+	0.913427i	$0.633426\pi$
$98$	8.11867	0.820110
$99$	1.29390	0.130042
$100$	−13.6909	−1.36909
$101$	9.11148	0.906626	0.453313	−	0.891351i	$-0.350242\pi$
$101$	9.11148	0.906626	0.453313	+	0.891351i	$0.350242\pi$
$102$	6.26491	0.620318
$103$	−15.2943	−1.50699	−0.753494	−	0.657455i	$-0.771633\pi$
$103$	−15.2943	−1.50699	−0.753494	+	0.657455i	$0.771633\pi$
$104$	26.7693	2.62494
$105$	5.26891	0.514193
$106$	18.4624	1.79323
$107$	3.50420	0.338764	0.169382	−	0.985550i	$-0.445823\pi$
$107$	3.50420	0.338764	0.169382	+	0.985550i	$0.445823\pi$
$108$	22.2059	2.13676
$109$	2.49301	0.238787	0.119393	−	0.992847i	$-0.461905\pi$
$109$	2.49301	0.238787	0.119393	+	0.992847i	$0.461905\pi$
$110$	−10.6609	−1.01647
$111$	12.2997	1.16743
$112$	−16.9582	−1.60240
$113$	−14.5343	−1.36727	−0.683634	−	0.729825i	$-0.739601\pi$
$113$	−14.5343	−1.36727	−0.683634	+	0.729825i	$0.739601\pi$
$114$	16.9781	1.59014
$115$	6.06959	0.565993
$116$	−5.17989	−0.480941
$117$	−1.74154	−0.161006
$118$	35.9070	3.30551
$119$	−2.56109	−0.234774
$120$	18.6708	1.70440
$121$	−2.84244	−0.258404
$122$	16.8501	1.52554
$123$	−1.24705	−0.112443
$124$	−16.5716	−1.48818
$125$	−11.4250	−1.02188
$126$	2.30290	0.205159
$127$	5.52702	0.490443	0.245222	−	0.969467i	$-0.421139\pi$
$127$	5.52702	0.490443	0.245222	+	0.969467i	$0.421139\pi$
$128$	5.25021	0.464057
$129$	8.03293	0.707260
$130$	14.3491	1.25850
$131$	−21.2174	−1.85377	−0.926885	−	0.375346i	$-0.877524\pi$
$131$	−21.2174	−1.85377	−0.926885	+	0.375346i	$0.877524\pi$
$132$	−24.9014	−2.16739
$133$	−6.94061	−0.601827
$134$	19.5357	1.68763
$135$	6.82911	0.587756
$136$	−9.07538	−0.778208
$137$	11.6794	0.997835	0.498917	−	0.866650i	$-0.333731\pi$
$137$	11.6794	0.997835	0.498917	+	0.866650i	$0.333731\pi$
$138$	20.2206	1.72129
$139$	−10.8676	−0.921778	−0.460889	−	0.887458i	$-0.652469\pi$
$139$	−10.8676	−0.921778	−0.460889	+	0.887458i	$0.652469\pi$
$140$	−13.3035	−1.12435
$141$	0.703385	0.0592357
$142$	−0.192713	−0.0161721
$143$	−10.9798	−0.918175
$144$	3.90946	0.325789
$145$	−1.59300	−0.132292
$146$	−8.51212	−0.704468
$147$	5.83192	0.481009
$148$	−31.0555	−2.55274
$149$	−7.40209	−0.606403	−0.303202	−	0.952926i	$-0.598056\pi$
$149$	−7.40209	−0.606403	−0.303202	+	0.952926i	$0.598056\pi$
$150$	−14.0268	−1.14529
$151$	6.09188	0.495750	0.247875	−	0.968792i	$-0.420268\pi$
$151$	6.09188	0.495750	0.247875	+	0.968792i	$0.420268\pi$
$152$	−24.5945	−1.99488
$153$	0.590422	0.0477328
$154$	14.5189	1.16997
$155$	−5.09637	−0.409350
$156$	33.5164	2.68346
$157$	2.22790	0.177806	0.0889028	−	0.996040i	$-0.471664\pi$
$157$	2.22790	0.177806	0.0889028	+	0.996040i	$0.471664\pi$
$158$	−22.1843	−1.76489
$159$	13.2622	1.05176
$160$	−12.1162	−0.957866
$161$	−8.26614	−0.651463
$162$	26.2666	2.06370
$163$	−18.7370	−1.46759	−0.733797	−	0.679368i	$-0.762254\pi$
$163$	−18.7370	−1.46759	−0.733797	+	0.679368i	$0.762254\pi$
$164$	3.14867	0.245870
$165$	−7.65807	−0.596180
$166$	−38.3281	−2.97484
$167$	22.7237	1.75841	0.879205	−	0.476443i	$-0.158074\pi$
$167$	22.7237	1.75841	0.879205	+	0.476443i	$0.158074\pi$
$168$	−25.4276	−1.96178
$169$	1.77838	0.136798
$170$	−4.86468	−0.373104
$171$	1.60006	0.122360
$172$	−20.2823	−1.54651
$173$	−2.25141	−0.171172	−0.0855859	−	0.996331i	$-0.527276\pi$
$173$	−2.25141	−0.171172	−0.0855859	+	0.996331i	$0.527276\pi$
$174$	−5.30701	−0.402323
$175$	5.73415	0.433461
$176$	24.6477	1.85789
$177$	25.7933	1.93874
$178$	45.3775	3.40119
$179$	15.8986	1.18832	0.594159	−	0.804348i	$-0.297485\pi$
$179$	15.8986	1.18832	0.594159	+	0.804348i	$0.297485\pi$
$180$	3.06693	0.228595
$181$	16.5942	1.23344	0.616718	−	0.787184i	$-0.288462\pi$
$181$	16.5942	1.23344	0.616718	+	0.787184i	$0.288462\pi$
$182$	−19.5420	−1.44855
$183$	12.1040	0.894756
$184$	−29.2916	−2.15941
$185$	−9.55066	−0.702179
$186$	−16.9783	−1.24491
$187$	3.72239	0.272208
$188$	−1.77598	−0.129526
$189$	−9.30051	−0.676513
$190$	−13.1834	−0.956425
$191$	−2.03640	−0.147348	−0.0736742	−	0.997282i	$-0.523473\pi$
$191$	−2.03640	−0.147348	−0.0736742	+	0.997282i	$0.523473\pi$
$192$	−8.29235	−0.598448
$193$	−15.1384	−1.08968	−0.544841	−	0.838539i	$-0.683410\pi$
$193$	−15.1384	−1.08968	−0.544841	+	0.838539i	$0.683410\pi$
$194$	20.7389	1.48897
$195$	10.3075	0.738134
$196$	−14.7250	−1.05179
$197$	−6.01285	−0.428398	−0.214199	−	0.976790i	$-0.568714\pi$
$197$	−6.01285	−0.428398	−0.214199	+	0.976790i	$0.568714\pi$
$198$	−3.34714	−0.237871
$199$	23.5513	1.66951	0.834753	−	0.550624i	$-0.185610\pi$
$199$	23.5513	1.66951	0.834753	+	0.550624i	$0.185610\pi$
$200$	20.3194	1.43680
$201$	14.0332	0.989823
$202$	−23.5701	−1.65839
$203$	2.16950	0.152269
$204$	−11.3628	−0.795555
$205$	0.968329	0.0676311
$206$	39.5641	2.75656
$207$	1.90564	0.132451
$208$	−33.1749	−2.30027
$209$	10.0878	0.697786
$210$	−13.6299	−0.940555
$211$	2.35555	0.162163	0.0810814	−	0.996707i	$-0.474163\pi$
$211$	2.35555	0.162163	0.0810814	+	0.996707i	$0.474163\pi$
$212$	−33.4857	−2.29981
$213$	−0.138432	−0.00948521
$214$	−9.06488	−0.619662
$215$	−6.23754	−0.425397
$216$	−32.9570	−2.24244
$217$	6.94071	0.471166
$218$	−6.44906	−0.436785
$219$	−6.11455	−0.413183
$220$	19.3358	1.30362
$221$	−5.01020	−0.337023
$222$	−31.8176	−2.13546
$223$	13.6268	0.912519	0.456260	−	0.889847i	$-0.349189\pi$
$223$	13.6268	0.912519	0.456260	+	0.889847i	$0.349189\pi$
$224$	16.5009	1.10251
$225$	−1.32193	−0.0881285
$226$	37.5981	2.50099
$227$	11.9812	0.795218	0.397609	−	0.917555i	$-0.369840\pi$
$227$	11.9812	0.795218	0.397609	+	0.917555i	$0.369840\pi$
$228$	−30.7935	−2.03935
$229$	27.2066	1.79786	0.898932	−	0.438087i	$-0.144344\pi$
$229$	27.2066	1.79786	0.898932	+	0.438087i	$0.144344\pi$
$230$	−15.7012	−1.03531
$231$	10.4295	0.686208
$232$	7.68776	0.504726
$233$	14.4504	0.946679	0.473339	−	0.880880i	$-0.343048\pi$
$233$	14.4504	0.946679	0.473339	+	0.880880i	$0.343048\pi$
$234$	4.50512	0.294509
$235$	−0.546176	−0.0356286
$236$	−65.1254	−4.23930
$237$	−15.9358	−1.03514
$238$	6.62517	0.429446
$239$	−23.9361	−1.54830	−0.774148	−	0.633005i	$-0.781821\pi$
$239$	−23.9361	−1.54830	−0.774148	+	0.633005i	$0.781821\pi$
$240$	−23.1385	−1.49359
$241$	−13.7734	−0.887224	−0.443612	−	0.896219i	$-0.646303\pi$
$241$	−13.7734	−0.887224	−0.443612	+	0.896219i	$0.646303\pi$
$242$	7.35300	0.472668
$243$	4.66957	0.299553
$244$	−30.5615	−1.95650
$245$	−4.52847	−0.289313
$246$	3.22594	0.205679
$247$	−13.5778	−0.863934
$248$	24.5949	1.56178
$249$	−27.5324	−1.74479
$250$	29.5548	1.86921
$251$	−8.26975	−0.521982	−0.260991	−	0.965341i	$-0.584049\pi$
$251$	−8.26975	−0.521982	−0.260991	+	0.965341i	$0.584049\pi$
$252$	−4.17682	−0.263115
$253$	12.0144	0.755336
$254$	−14.2976	−0.897112
$255$	−3.49447	−0.218832
$256$	−22.5065	−1.40666
$257$	−20.1486	−1.25684	−0.628418	−	0.777876i	$-0.716297\pi$
$257$	−20.1486	−1.25684	−0.628418	+	0.777876i	$0.716297\pi$
$258$	−20.7801	−1.29371
$259$	13.0070	0.808214
$260$	−26.0253	−1.61402
$261$	−0.500147	−0.0309583
$262$	54.8863	3.39089
$263$	−27.9229	−1.72180	−0.860900	−	0.508774i	$-0.830099\pi$
$263$	−27.9229	−1.72180	−0.860900	+	0.508774i	$0.830099\pi$
$264$	36.9575	2.27458
$265$	−10.2980	−0.632604
$266$	17.9544	1.10085
$267$	32.5962	1.99486
$268$	−35.4323	−2.16437
$269$	11.6165	0.708269	0.354135	−	0.935194i	$-0.384775\pi$
$269$	11.6165	0.708269	0.354135	+	0.935194i	$0.384775\pi$
$270$	−17.6659	−1.07512
$271$	−3.27787	−0.199117	−0.0995583	−	0.995032i	$-0.531743\pi$
$271$	−3.27787	−0.199117	−0.0995583	+	0.995032i	$0.531743\pi$
$272$	11.2471	0.681953
$273$	−14.0377	−0.849599
$274$	−30.2129	−1.82523
$275$	−8.33426	−0.502575
$276$	−36.6745	−2.20754
$277$	10.1157	0.607795	0.303897	−	0.952705i	$-0.401712\pi$
$277$	10.1157	0.607795	0.303897	+	0.952705i	$0.401712\pi$
$278$	28.1130	1.68610
$279$	−1.60008	−0.0957944
$280$	19.7444	1.17995
$281$	16.7656	1.00015	0.500077	−	0.865981i	$-0.333305\pi$
$281$	16.7656	1.00015	0.500077	+	0.865981i	$0.333305\pi$
$282$	−1.81956	−0.108353
$283$	15.4382	0.917705	0.458852	−	0.888513i	$-0.348261\pi$
$283$	15.4382	0.917705	0.458852	+	0.888513i	$0.348261\pi$
$284$	0.349527	0.0207406
$285$	−9.47010	−0.560960
$286$	28.4031	1.67951
$287$	−1.31876	−0.0778440
$288$	−3.80405	−0.224156
$289$	−15.3014	−0.900084
$290$	4.12087	0.241986
$291$	14.8975	0.873306
$292$	15.4386	0.903477
$293$	−7.52887	−0.439841	−0.219921	−	0.975518i	$-0.570580\pi$
$293$	−7.52887	−0.439841	−0.219921	+	0.975518i	$0.570580\pi$
$294$	−15.0864	−0.879855
$295$	−20.0284	−1.16610
$296$	46.0911	2.67899
$297$	13.5178	0.784380
$298$	19.1482	1.10922
$299$	−16.1709	−0.935187
$300$	25.4408	1.46882
$301$	8.49487	0.489636
$302$	−15.7588	−0.906819
$303$	−16.9312	−0.972674
$304$	30.4798	1.74814
$305$	−9.39874	−0.538170
$306$	−1.52734	−0.0873121
$307$	17.1932	0.981265	0.490632	−	0.871367i	$-0.336766\pi$
$307$	17.1932	0.981265	0.490632	+	0.871367i	$0.336766\pi$
$308$	−26.3333	−1.50048
$309$	28.4203	1.61677
$310$	13.1836	0.748778
$311$	10.1595	0.576094	0.288047	−	0.957616i	$-0.406994\pi$
$311$	10.1595	0.576094	0.288047	+	0.957616i	$0.406994\pi$
$312$	−49.7435	−2.81617
$313$	26.6909	1.50866	0.754329	−	0.656496i	$-0.227962\pi$
$313$	26.6909	1.50866	0.754329	+	0.656496i	$0.227962\pi$
$314$	−5.76326	−0.325240
$315$	−1.28452	−0.0723746
$316$	40.2362	2.26346
$317$	19.3855	1.08880	0.544398	−	0.838827i	$-0.316758\pi$
$317$	19.3855	1.08880	0.544398	+	0.838827i	$0.316758\pi$
$318$	−34.3074	−1.92386
$319$	−3.15324	−0.176548
$320$	6.43898	0.359950
$321$	−6.51161	−0.363443
$322$	21.3833	1.19165
$323$	4.60317	0.256127
$324$	−47.6402	−2.64668
$325$	11.2176	0.622241
$326$	48.4700	2.68450
$327$	−4.63258	−0.256182
$328$	−4.67312	−0.258030
$329$	0.743833	0.0410088
$330$	19.8103	1.09052
$331$	−26.0579	−1.43227	−0.716135	−	0.697962i	$-0.754090\pi$
$331$	−26.0579	−1.43227	−0.716135	+	0.697962i	$0.754090\pi$
$332$	69.5165	3.81521
$333$	−2.99857	−0.164321
$334$	−58.7830	−3.21646
$335$	−10.8967	−0.595350
$336$	31.5122	1.71913
$337$	−11.6240	−0.633199	−0.316600	−	0.948559i	$-0.602541\pi$
$337$	−11.6240	−0.633199	−0.316600	+	0.948559i	$0.602541\pi$
$338$	−4.60042	−0.250230
$339$	27.0080	1.46687
$340$	8.82317	0.478504
$341$	−10.0879	−0.546292
$342$	−4.13913	−0.223818
$343$	19.9229	1.07574
$344$	30.1021	1.62300
$345$	−11.2787	−0.607225
$346$	5.82409	0.313105
$347$	24.5102	1.31578	0.657888	−	0.753115i	$-0.271450\pi$
$347$	24.5102	1.31578	0.657888	+	0.753115i	$0.271450\pi$
$348$	9.62543	0.515977
$349$	10.6510	0.570133	0.285066	−	0.958508i	$-0.407984\pi$
$349$	10.6510	0.570133	0.285066	+	0.958508i	$0.407984\pi$
$350$	−14.8334	−0.792881
$351$	−18.1944	−0.971146
$352$	−23.9831	−1.27830
$353$	1.04651	0.0557003	0.0278501	−	0.999612i	$-0.491134\pi$
$353$	1.04651	0.0557003	0.0278501	+	0.999612i	$0.491134\pi$
$354$	−66.7236	−3.54632
$355$	0.107492	0.00570508
$356$	−82.3022	−4.36201
$357$	4.75909	0.251878
$358$	−41.1275	−2.17365
$359$	−24.0194	−1.26769	−0.633847	−	0.773459i	$-0.718525\pi$
$359$	−24.0194	−1.26769	−0.633847	+	0.773459i	$0.718525\pi$
$360$	−4.55179	−0.239901
$361$	−6.52528	−0.343436
$362$	−42.9268	−2.25618
$363$	5.28191	0.277228
$364$	35.4437	1.85776
$365$	4.74793	0.248518
$366$	−31.3115	−1.63668
$367$	−18.6963	−0.975937	−0.487969	−	0.872861i	$-0.662262\pi$
$367$	−18.6963	−0.975937	−0.487969	+	0.872861i	$0.662262\pi$
$368$	36.3009	1.89231
$369$	0.304022	0.0158267
$370$	24.7062	1.28442
$371$	14.0248	0.728133
$372$	30.7939	1.59659
$373$	−23.3008	−1.20647	−0.603235	−	0.797564i	$-0.706122\pi$
$373$	−23.3008	−1.20647	−0.603235	+	0.797564i	$0.706122\pi$
$374$	−9.62931	−0.497920
$375$	21.2302	1.09633
$376$	2.63582	0.135932
$377$	4.24415	0.218585
$378$	24.0591	1.23747
$379$	−9.79951	−0.503367	−0.251683	−	0.967810i	$-0.580984\pi$
$379$	−9.79951	−0.503367	−0.251683	+	0.967810i	$0.580984\pi$
$380$	23.9110	1.22661
$381$	−10.2705	−0.526172
$382$	5.26787	0.269528
$383$	−1.97295	−0.100813	−0.0504066	−	0.998729i	$-0.516052\pi$
$383$	−1.97295	−0.100813	−0.0504066	+	0.998729i	$0.516052\pi$
$384$	−9.75610	−0.497864
$385$	−8.09844	−0.412735
$386$	39.1608	1.99323
$387$	−1.95837	−0.0995496
$388$	−37.6146	−1.90959
$389$	−6.61202	−0.335243	−0.167621	−	0.985851i	$-0.553609\pi$
$389$	−6.61202	−0.335243	−0.167621	+	0.985851i	$0.553609\pi$
$390$	−26.6640	−1.35018
$391$	5.48230	0.277252
$392$	21.8542	1.10380
$393$	39.4268	1.98882
$394$	15.5544	0.783619
$395$	12.3741	0.622607
$396$	6.07078	0.305068
$397$	−7.61750	−0.382311	−0.191156	−	0.981560i	$-0.561224\pi$
$397$	−7.61750	−0.382311	−0.191156	+	0.981560i	$0.561224\pi$
$398$	−60.9239	−3.05384
$399$	12.8973	0.645670
$400$	−25.1816	−1.25908
$401$	25.8162	1.28920	0.644601	−	0.764519i	$-0.277024\pi$
$401$	25.8162	1.28920	0.644601	+	0.764519i	$0.277024\pi$
$402$	−36.3018	−1.81057
$403$	13.5780	0.676368
$404$	42.7497	2.12687
$405$	−14.6511	−0.728018
$406$	−5.61218	−0.278528
$407$	−18.9049	−0.937081
$408$	16.8642	0.834900
$409$	−13.6924	−0.677044	−0.338522	−	0.940958i	$-0.609927\pi$
$409$	−13.6924	−0.677044	−0.338522	+	0.940958i	$0.609927\pi$
$410$	−2.50493	−0.123710
$411$	−21.7029	−1.07053
$412$	−71.7583	−3.53528
$413$	27.2765	1.34219
$414$	−4.92962	−0.242278
$415$	21.3788	1.04944
$416$	32.2804	1.58268
$417$	20.1945	0.988930
$418$	−26.0957	−1.27638
$419$	24.0027	1.17261	0.586305	−	0.810091i	$-0.300582\pi$
$419$	24.0027	1.17261	0.586305	+	0.810091i	$0.300582\pi$
$420$	24.7209	1.20626
$421$	31.1293	1.51715	0.758573	−	0.651588i	$-0.225897\pi$
$421$	31.1293	1.51715	0.758573	+	0.651588i	$0.225897\pi$
$422$	−6.09348	−0.296626
$423$	−0.171480	−0.00833765
$424$	49.6979	2.41355
$425$	−3.80302	−0.184474
$426$	0.358104	0.0173502
$427$	12.8001	0.619439
$428$	16.4412	0.794714
$429$	20.4030	0.985064
$430$	16.1357	0.778130
$431$	28.0585	1.35153	0.675766	−	0.737116i	$-0.263813\pi$
$431$	28.0585	1.35153	0.675766	+	0.737116i	$0.263813\pi$
$432$	40.8434	1.96508
$433$	−20.6011	−0.990026	−0.495013	−	0.868886i	$-0.664837\pi$
$433$	−20.6011	−0.990026	−0.495013	+	0.868886i	$0.664837\pi$
$434$	−17.9547	−0.861851
$435$	2.96016	0.141929
$436$	11.6968	0.560175
$437$	14.8572	0.710715
$438$	15.8175	0.755789
$439$	−36.4050	−1.73752	−0.868758	−	0.495238i	$-0.835081\pi$
$439$	−36.4050	−1.73752	−0.868758	+	0.495238i	$0.835081\pi$
$440$	−28.6974	−1.36809
$441$	−1.42178	−0.0677038
$442$	12.9607	0.616477
$443$	−28.1192	−1.33598	−0.667992	−	0.744169i	$-0.732846\pi$
$443$	−28.1192	−1.33598	−0.667992	+	0.744169i	$0.732846\pi$
$444$	57.7082	2.73871
$445$	−25.3109	−1.19985
$446$	−35.2507	−1.66917
$447$	13.7548	0.650580
$448$	−8.76920	−0.414306
$449$	−12.9493	−0.611116	−0.305558	−	0.952173i	$-0.598843\pi$
$449$	−12.9493	−0.611116	−0.305558	+	0.952173i	$0.598843\pi$
$450$	3.41964	0.161203
$451$	1.91674	0.0902559
$452$	−68.1925	−3.20750
$453$	−11.3201	−0.531866
$454$	−30.9936	−1.45460
$455$	10.9002	0.511010
$456$	45.7023	2.14021
$457$	0.149626	0.00699919	0.00349960	−	0.999994i	$-0.498886\pi$
$457$	0.149626	0.00699919	0.00349960	+	0.999994i	$0.498886\pi$
$458$	−70.3797	−3.28863
$459$	6.16832	0.287912
$460$	28.4776	1.32777
$461$	38.9917	1.81603	0.908013	−	0.418942i	$-0.137599\pi$
$461$	38.9917	1.81603	0.908013	+	0.418942i	$0.137599\pi$
$462$	−26.9796	−1.25520
$463$	−20.1386	−0.935918	−0.467959	−	0.883750i	$-0.655011\pi$
$463$	−20.1386	−0.935918	−0.467959	+	0.883750i	$0.655011\pi$
$464$	−9.52738	−0.442298
$465$	9.47024	0.439172
$466$	−37.3812	−1.73165
$467$	14.8664	0.687936	0.343968	−	0.938981i	$-0.388229\pi$
$467$	14.8664	0.687936	0.343968	+	0.938981i	$0.388229\pi$
$468$	−8.17104	−0.377707
$469$	14.8401	0.685254
$470$	1.41288	0.0651713
$471$	−4.13995	−0.190759
$472$	96.6562	4.44896
$473$	−12.3468	−0.567707
$474$	41.2236	1.89346
$475$	−10.3063	−0.472885
$476$	−12.0162	−0.550762
$477$	−3.23322	−0.148039
$478$	61.9193	2.83212
$479$	−35.2515	−1.61068	−0.805342	−	0.592810i	$-0.798018\pi$
$479$	−35.2515	−1.61068	−0.805342	+	0.592810i	$0.798018\pi$
$480$	22.5146	1.02765
$481$	25.4453	1.16021
$482$	35.6299	1.62290
$483$	15.3604	0.698922
$484$	−13.3363	−0.606195
$485$	−11.5678	−0.525268
$486$	−12.0795	−0.547938
$487$	27.4362	1.24325	0.621626	−	0.783314i	$-0.286472\pi$
$487$	27.4362	1.24325	0.621626	+	0.783314i	$0.286472\pi$
$488$	45.3580	2.05326
$489$	34.8177	1.57451
$490$	11.7145	0.529208
$491$	−4.83937	−0.218398	−0.109199	−	0.994020i	$-0.534829\pi$
$491$	−4.83937	−0.218398	−0.109199	+	0.994020i	$0.534829\pi$
$492$	−5.85096	−0.263782
$493$	−1.43886	−0.0648030
$494$	35.1238	1.58030
$495$	1.86698	0.0839145
$496$	−30.4803	−1.36860
$497$	−0.146393	−0.00656661
$498$	71.2225	3.19155
$499$	16.7739	0.750904	0.375452	−	0.926842i	$-0.377488\pi$
$499$	16.7739	0.750904	0.375452	+	0.926842i	$0.377488\pi$
$500$	−53.6042	−2.39725
$501$	−42.2258	−1.88651
$502$	21.3927	0.954803
$503$	−1.00000	−0.0445878
$503$	−1.00000	−0.0445878
$504$	6.19906	0.276128
$505$	13.1470	0.585036
$506$	−31.0795	−1.38165
$507$	−3.30464	−0.146764
$508$	25.9319	1.15054
$509$	−27.5401	−1.22069	−0.610347	−	0.792134i	$-0.708970\pi$
$509$	−27.5401	−1.22069	−0.610347	+	0.792134i	$0.708970\pi$
$510$	9.03970	0.400284
$511$	−6.46617	−0.286046
$512$	47.7209	2.10898
$513$	16.7163	0.738043
$514$	52.1216	2.29899
$515$	−22.0682	−0.972443
$516$	37.6893	1.65918
$517$	−1.08112	−0.0475475
$518$	−33.6472	−1.47837
$519$	4.18365	0.183642
$520$	38.6256	1.69385
$521$	25.7250	1.12703	0.563515	−	0.826106i	$-0.309449\pi$
$521$	25.7250	1.12703	0.563515	+	0.826106i	$0.309449\pi$
$522$	1.29381	0.0566285
$523$	−29.5746	−1.29321	−0.646605	−	0.762825i	$-0.723812\pi$
$523$	−29.5746	−1.29321	−0.646605	+	0.762825i	$0.723812\pi$
$524$	−99.5486	−4.34880
$525$	−10.6554	−0.465039
$526$	72.2327	3.14949
$527$	−4.60324	−0.200520
$528$	−45.8012	−1.99324
$529$	−5.30539	−0.230669
$530$	26.6396	1.15715
$531$	−6.28821	−0.272885
$532$	−32.5643	−1.41184
$533$	−2.57987	−0.111746
$534$	−84.3219	−3.64897
$535$	5.05624	0.218601
$536$	52.5870	2.27141
$537$	−29.5433	−1.27489
$538$	−30.0502	−1.29556
$539$	−8.96380	−0.386098
$540$	32.0411	1.37883
$541$	−13.1889	−0.567035	−0.283517	−	0.958967i	$-0.591501\pi$
$541$	−13.1889	−0.567035	−0.283517	+	0.958967i	$0.591501\pi$
$542$	8.47940	0.364222
$543$	−30.8358	−1.32329
$544$	−10.9438	−0.469211
$545$	3.59718	0.154086
$546$	36.3135	1.55407
$547$	−17.9543	−0.767673	−0.383836	−	0.923401i	$-0.625397\pi$
$547$	−17.9543	−0.767673	−0.383836	+	0.923401i	$0.625397\pi$
$548$	54.7977	2.34084
$549$	−2.95088	−0.125940
$550$	21.5596	0.919303
$551$	−3.89935	−0.166118
$552$	54.4306	2.31672
$553$	−16.8522	−0.716627
$554$	−26.1680	−1.11177
$555$	17.7473	0.753332
$556$	−50.9891	−2.16242
$557$	9.47412	0.401431	0.200716	−	0.979650i	$-0.435673\pi$
$557$	9.47412	0.401431	0.200716	+	0.979650i	$0.435673\pi$
$558$	4.13919	0.175226
$559$	16.6183	0.702881
$560$	−24.4691	−1.03401
$561$	−6.91706	−0.292039
$562$	−43.3703	−1.82947
$563$	−33.2995	−1.40341	−0.701704	−	0.712469i	$-0.747577\pi$
$563$	−33.2995	−1.40341	−0.701704	+	0.712469i	$0.747577\pi$
$564$	3.30017	0.138962
$565$	−20.9716	−0.882283
$566$	−39.9364	−1.67865
$567$	19.9532	0.837955
$568$	−0.518752	−0.0217664
$569$	−28.8525	−1.20956	−0.604780	−	0.796393i	$-0.706739\pi$
$569$	−28.8525	−1.20956	−0.604780	+	0.796393i	$0.706739\pi$
$570$	24.4978	1.02610
$571$	22.7379	0.951550	0.475775	−	0.879567i	$-0.342168\pi$
$571$	22.7379	0.951550	0.475775	+	0.879567i	$0.342168\pi$
$572$	−51.5154	−2.15397
$573$	3.78409	0.158083
$574$	3.41145	0.142391
$575$	−12.2746	−0.511886
$576$	2.02161	0.0842339
$577$	−4.60031	−0.191513	−0.0957567	−	0.995405i	$-0.530527\pi$
$577$	−4.60031	−0.191513	−0.0957567	+	0.995405i	$0.530527\pi$
$578$	39.5827	1.64642
$579$	28.1306	1.16907
$580$	−7.47411	−0.310346
$581$	−29.1156	−1.20792
$582$	−38.5377	−1.59744
$583$	−20.3843	−0.844231
$584$	−22.9133	−0.948159
$585$	−2.51289	−0.103895
$586$	19.4761	0.804552
$587$	32.6537	1.34776	0.673881	−	0.738839i	$-0.264626\pi$
$587$	32.6537	1.34776	0.673881	+	0.738839i	$0.264626\pi$
$588$	27.3625	1.12841
$589$	−12.4749	−0.514020
$590$	51.8106	2.13301
$591$	11.1733	0.459607
$592$	−57.1204	−2.34763
$593$	−36.4077	−1.49509	−0.747543	−	0.664214i	$-0.768767\pi$
$593$	−36.4077	−1.49509	−0.747543	+	0.664214i	$0.768767\pi$
$594$	−34.9686	−1.43478
$595$	−3.69542	−0.151497
$596$	−34.7295	−1.42257
$597$	−43.7637	−1.79113
$598$	41.8318	1.71063
$599$	−40.2375	−1.64406	−0.822031	−	0.569443i	$-0.807159\pi$
$599$	−40.2375	−1.64406	−0.822031	+	0.569443i	$0.807159\pi$
$600$	−37.7581	−1.54147
$601$	8.80257	0.359065	0.179532	−	0.983752i	$-0.442542\pi$
$601$	8.80257	0.359065	0.179532	+	0.983752i	$0.442542\pi$
$602$	−21.9750	−0.895635
$603$	−3.42118	−0.139321
$604$	28.5822	1.16299
$605$	−4.10139	−0.166745
$606$	43.7987	1.77920
$607$	13.3824	0.543176	0.271588	−	0.962414i	$-0.412451\pi$
$607$	13.3824	0.543176	0.271588	+	0.962414i	$0.412451\pi$
$608$	−29.6579	−1.20279
$609$	−4.03143	−0.163362
$610$	24.3132	0.984414
$611$	1.45515	0.0588689
$612$	2.77017	0.111977
$613$	−15.6160	−0.630725	−0.315363	−	0.948971i	$-0.602126\pi$
$613$	−15.6160	−0.630725	−0.315363	+	0.948971i	$0.602126\pi$
$614$	−44.4763	−1.79492
$615$	−1.79938	−0.0725580
$616$	39.0828	1.57469
$617$	4.29634	0.172964	0.0864820	−	0.996253i	$-0.472437\pi$
$617$	4.29634	0.172964	0.0864820	+	0.996253i	$0.472437\pi$
$618$	−73.5193	−2.95738
$619$	−10.8380	−0.435614	−0.217807	−	0.975992i	$-0.569890\pi$
$619$	−10.8380	−0.435614	−0.217807	+	0.975992i	$0.569890\pi$
$620$	−23.9114	−0.960305
$621$	19.9088	0.798913
$622$	−26.2813	−1.05378
$623$	34.4707	1.38104
$624$	61.6467	2.46784
$625$	−1.89515	−0.0758062
$626$	−69.0456	−2.75962
$627$	−18.7454	−0.748620
$628$	10.4529	0.417118
$629$	−8.62653	−0.343962
$630$	3.32288	0.132387
$631$	29.5073	1.17467	0.587334	−	0.809345i	$-0.300178\pi$
$631$	29.5073	1.17467	0.587334	+	0.809345i	$0.300178\pi$
$632$	−59.7168	−2.37541
$633$	−4.37716	−0.173976
$634$	−50.1475	−1.99161
$635$	7.97499	0.316478
$636$	62.2241	2.46735
$637$	12.0649	0.478031
$638$	8.15699	0.322938
$639$	0.0337487	0.00133508
$640$	7.57558	0.299451
$641$	7.72732	0.305211	0.152605	−	0.988287i	$-0.451234\pi$
$641$	7.72732	0.305211	0.152605	+	0.988287i	$0.451234\pi$
$642$	16.8446	0.664805
$643$	10.0167	0.395021	0.197511	−	0.980301i	$-0.436714\pi$
$643$	10.0167	0.395021	0.197511	+	0.980301i	$0.436714\pi$
$644$	−38.7834	−1.52828
$645$	11.5908	0.456387
$646$	−11.9078	−0.468505
$647$	−13.6884	−0.538147	−0.269074	−	0.963120i	$-0.586718\pi$
$647$	−13.6884	−0.538147	−0.269074	+	0.963120i	$0.586718\pi$
$648$	70.7055	2.77758
$649$	−39.6449	−1.55620
$650$	−29.0184	−1.13819
$651$	−12.8974	−0.505491
$652$	−87.9111	−3.44286
$653$	38.1399	1.49253	0.746264	−	0.665650i	$-0.231845\pi$
$653$	38.1399	1.49253	0.746264	+	0.665650i	$0.231845\pi$
$654$	11.9838	0.468605
$655$	−30.6147	−1.19622
$656$	5.79136	0.226115
$657$	1.49068	0.0581571
$658$	−1.92419	−0.0750128
$659$	31.5253	1.22805	0.614026	−	0.789286i	$-0.289549\pi$
$659$	31.5253	1.22805	0.614026	+	0.789286i	$0.289549\pi$
$660$	−35.9305	−1.39859
$661$	−30.1122	−1.17123	−0.585614	−	0.810590i	$-0.699146\pi$
$661$	−30.1122	−1.17123	−0.585614	+	0.810590i	$0.699146\pi$
$662$	67.4080	2.61989
$663$	9.31012	0.361575
$664$	−103.173	−4.00390
$665$	−10.0147	−0.388352
$666$	7.75689	0.300573
$667$	−4.64405	−0.179818
$668$	106.616	4.12510
$669$	−25.3218	−0.978996
$670$	28.1882	1.08901
$671$	−18.6042	−0.718207
$672$	−30.6625	−1.18283
$673$	−40.7982	−1.57265	−0.786327	−	0.617810i	$-0.788020\pi$
$673$	−40.7982	−1.57265	−0.786327	+	0.617810i	$0.788020\pi$
$674$	30.0697	1.15824
$675$	−13.8106	−0.531569
$676$	8.34388	0.320918
$677$	3.18994	0.122599	0.0612997	−	0.998119i	$-0.480475\pi$
$677$	3.18994	0.122599	0.0612997	+	0.998119i	$0.480475\pi$
$678$	−69.8659	−2.68319
$679$	15.7542	0.604589
$680$	−13.0950	−0.502169
$681$	−22.2638	−0.853150
$682$	26.0961	0.999270
$683$	25.0239	0.957512	0.478756	−	0.877948i	$-0.341088\pi$
$683$	25.0239	0.957512	0.478756	+	0.877948i	$0.341088\pi$
$684$	7.50723	0.287046
$685$	16.8523	0.643892
$686$	−51.5378	−1.96772
$687$	−50.5562	−1.92884
$688$	−37.3054	−1.42225
$689$	27.4365	1.04525
$690$	29.1764	1.11073
$691$	36.5349	1.38985	0.694927	−	0.719081i	$-0.255437\pi$
$691$	36.5349	1.38985	0.694927	+	0.719081i	$0.255437\pi$
$692$	−10.5633	−0.401556
$693$	−2.54263	−0.0965864
$694$	−63.4045	−2.40680
$695$	−15.6810	−0.594813
$696$	−14.2856	−0.541496
$697$	0.874633	0.0331291
$698$	−27.5525	−1.04288
$699$	−26.8522	−1.01564
$700$	26.9037	1.01687
$701$	40.6252	1.53439	0.767196	−	0.641413i	$-0.221652\pi$
$701$	40.6252	1.53439	0.767196	+	0.641413i	$0.221652\pi$
$702$	47.0664	1.77641
$703$	−23.3781	−0.881723
$704$	12.7455	0.480365
$705$	1.01492	0.0382241
$706$	−2.70718	−0.101886
$707$	−17.9049	−0.673382
$708$	121.018	4.54814
$709$	−29.3401	−1.10189	−0.550945	−	0.834542i	$-0.685733\pi$
$709$	−29.3401	−1.10189	−0.550945	+	0.834542i	$0.685733\pi$
$710$	−0.278067	−0.0104357
$711$	3.88503	0.145700
$712$	122.149	4.57774
$713$	−14.8574	−0.556414
$714$	−12.3111	−0.460731
$715$	−15.8428	−0.592488
$716$	74.5938	2.78770
$717$	44.4788	1.66109
$718$	62.1347	2.31885
$719$	−5.69273	−0.212303	−0.106152	−	0.994350i	$-0.533853\pi$
$719$	−5.69273	−0.212303	−0.106152	+	0.994350i	$0.533853\pi$
$720$	5.64100	0.210228
$721$	30.0546	1.11929
$722$	16.8800	0.628208
$723$	25.5942	0.951858
$724$	77.8574	2.89355
$725$	3.22154	0.119645
$726$	−13.6636	−0.507102
$727$	31.4072	1.16483	0.582414	−	0.812892i	$-0.302108\pi$
$727$	31.4072	1.16483	0.582414	+	0.812892i	$0.302108\pi$
$728$	−52.6040	−1.94963
$729$	21.7844	0.806829
$730$	−12.2822	−0.454585
$731$	−5.63399	−0.208381
$732$	56.7903	2.09903
$733$	47.6365	1.75949	0.879747	−	0.475441i	$-0.157712\pi$
$733$	47.6365	1.75949	0.879747	+	0.475441i	$0.157712\pi$
$734$	48.3646	1.78517
$735$	8.41494	0.310390
$736$	−35.3221	−1.30199
$737$	−21.5693	−0.794515
$738$	−0.786461	−0.0289500
$739$	9.88794	0.363734	0.181867	−	0.983323i	$-0.441786\pi$
$739$	9.88794	0.363734	0.181867	+	0.983323i	$0.441786\pi$
$740$	−44.8102	−1.64726
$741$	25.2307	0.926871
$742$	−36.2803	−1.33189
$743$	17.7935	0.652782	0.326391	−	0.945235i	$-0.394167\pi$
$743$	17.7935	0.652782	0.326391	+	0.945235i	$0.394167\pi$
$744$	−45.7030	−1.67555
$745$	−10.6806	−0.391305
$746$	60.2759	2.20686
$747$	6.71220	0.245586
$748$	17.4649	0.638579
$749$	−6.88606	−0.251611
$750$	−54.9197	−2.00538
$751$	−43.7934	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$751$	−43.7934	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$752$	−3.26656	−0.119119
$753$	15.3671	0.560009
$754$	−10.9790	−0.399832
$755$	8.79003	0.319902
$756$	−43.6366	−1.58705
$757$	0.950190	0.0345353	0.0172676	−	0.999851i	$-0.494503\pi$
$757$	0.950190	0.0345353	0.0172676	+	0.999851i	$0.494503\pi$
$758$	25.3499	0.920752
$759$	−22.3255	−0.810363
$760$	−35.4877	−1.28727
$761$	−5.00434	−0.181407	−0.0907035	−	0.995878i	$-0.528912\pi$
$761$	−5.00434	−0.181407	−0.0907035	+	0.995878i	$0.528912\pi$
$762$	26.5683	0.962467
$763$	−4.89898	−0.177355
$764$	−9.55445	−0.345668
$765$	0.851925	0.0308014
$766$	5.10375	0.184406
$767$	53.3605	1.92674
$768$	41.8224	1.50913
$769$	16.5794	0.597870	0.298935	−	0.954274i	$-0.403369\pi$
$769$	16.5794	0.597870	0.298935	+	0.954274i	$0.403369\pi$
$770$	20.9495	0.754969
$771$	37.4408	1.34840
$772$	−71.0268	−2.55631
$773$	−30.4696	−1.09592	−0.547958	−	0.836506i	$-0.684595\pi$
$773$	−30.4696	−1.09592	−0.547958	+	0.836506i	$0.684595\pi$
$774$	5.06603	0.182095
$775$	10.3064	0.370218
$776$	55.8259	2.00403
$777$	−24.1700	−0.867093
$778$	17.1044	0.613221
$779$	2.37028	0.0849240
$780$	48.3611	1.73160
$781$	0.212773	0.00761363
$782$	−14.1819	−0.507145
$783$	−5.22518	−0.186733
$784$	−27.0837	−0.967277
$785$	3.21465	0.114736
$786$	−101.992	−3.63792
$787$	29.7903	1.06191	0.530954	−	0.847400i	$-0.321834\pi$
$787$	29.7903	1.06191	0.530954	+	0.847400i	$0.321834\pi$
$788$	−28.2114	−1.00499
$789$	51.8872	1.84723
$790$	−32.0100	−1.13886
$791$	28.5611	1.01552
$792$	−9.00998	−0.320156
$793$	25.0406	0.889216
$794$	19.7054	0.699318
$795$	19.1361	0.678689
$796$	110.499	3.91653
$797$	0.503125	0.0178216	0.00891081	−	0.999960i	$-0.497164\pi$
$797$	0.503125	0.0178216	0.00891081	+	0.999960i	$0.497164\pi$
$798$	−33.3634	−1.18105
$799$	−0.493327	−0.0174527
$800$	24.5026	0.866299
$801$	−7.94673	−0.280784
$802$	−66.7830	−2.35819
$803$	9.39820	0.331655
$804$	65.8414	2.32205
$805$	−11.9273	−0.420382
$806$	−35.1244	−1.23720
$807$	−21.5861	−0.759867
$808$	−63.4471	−2.23206
$809$	−21.1371	−0.743142	−0.371571	−	0.928405i	$-0.621181\pi$
$809$	−21.1371	−0.743142	−0.371571	+	0.928405i	$0.621181\pi$
$810$	37.9003	1.33168
$811$	15.7238	0.552139	0.276069	−	0.961138i	$-0.410968\pi$
$811$	15.7238	0.552139	0.276069	+	0.961138i	$0.410968\pi$
$812$	10.1789	0.357211
$813$	6.09105	0.213622
$814$	48.9043	1.71410
$815$	−27.0358	−0.947023
$816$	−20.8996	−0.731633
$817$	−15.2683	−0.534169
$818$	35.4202	1.23844
$819$	3.42228	0.119584
$820$	4.54325	0.158657
$821$	−42.7588	−1.49229	−0.746147	−	0.665781i	$-0.768098\pi$
$821$	−42.7588	−1.49229	−0.746147	+	0.665781i	$0.768098\pi$
$822$	56.1425	1.95819
$823$	−33.2920	−1.16049	−0.580243	−	0.814444i	$-0.697042\pi$
$823$	−33.2920	−1.16049	−0.580243	+	0.814444i	$0.697042\pi$
$824$	106.500	3.71012
$825$	15.4870	0.539188
$826$	−70.5605	−2.45511
$827$	14.2343	0.494975	0.247487	−	0.968891i	$-0.420395\pi$
$827$	14.2343	0.494975	0.247487	+	0.968891i	$0.420395\pi$
$828$	8.94097	0.310720
$829$	−12.3766	−0.429855	−0.214928	−	0.976630i	$-0.568952\pi$
$829$	−12.3766	−0.429855	−0.214928	+	0.976630i	$0.568952\pi$
$830$	−55.3040	−1.91963
$831$	−18.7973	−0.652073
$832$	−17.1550	−0.594743
$833$	−4.09029	−0.141720
$834$	−52.2404	−1.80894
$835$	32.7882	1.13468
$836$	47.3303	1.63695
$837$	−16.7166	−0.577809
$838$	−62.0917	−2.14492
$839$	31.6864	1.09394	0.546969	−	0.837153i	$-0.315782\pi$
$839$	31.6864	1.09394	0.546969	+	0.837153i	$0.315782\pi$
$840$	−36.6897	−1.26591
$841$	−27.7811	−0.957970
$842$	−80.5270	−2.77514
$843$	−31.1544	−1.07301
$844$	11.0519	0.380421
$845$	2.56604	0.0882745
$846$	0.443595	0.0152511
$847$	5.58565	0.191925
$848$	−61.5903	−2.11502
$849$	−28.6877	−0.984560
$850$	9.83789	0.337437
$851$	−27.8429	−0.954443
$852$	−0.649502	−0.0222516
$853$	30.2234	1.03483	0.517416	−	0.855734i	$-0.326894\pi$
$853$	30.2234	1.03483	0.517416	+	0.855734i	$0.326894\pi$
$854$	−33.1120	−1.13307
$855$	2.30874	0.0789573
$856$	−24.4012	−0.834017
$857$	−31.4206	−1.07331	−0.536653	−	0.843803i	$-0.680312\pi$
$857$	−31.4206	−1.07331	−0.536653	+	0.843803i	$0.680312\pi$
$858$	−52.7796	−1.80187
$859$	27.5866	0.941244	0.470622	−	0.882335i	$-0.344030\pi$
$859$	27.5866	0.941244	0.470622	+	0.882335i	$0.344030\pi$
$860$	−29.2656	−0.997948
$861$	2.45056	0.0835149
$862$	−72.5835	−2.47220
$863$	40.3690	1.37418	0.687088	−	0.726574i	$-0.258889\pi$
$863$	40.3690	1.37418	0.687088	+	0.726574i	$0.258889\pi$
$864$	−39.7421	−1.35205
$865$	−3.24859	−0.110455
$866$	53.2922	1.81094
$867$	28.4336	0.965655
$868$	32.5648	1.10532
$869$	24.4937	0.830890
$870$	−7.65753	−0.259615
$871$	29.0315	0.983694
$872$	−17.3599	−0.587879
$873$	−3.63190	−0.122921
$874$	−38.4334	−1.30003
$875$	22.4511	0.758985
$876$	−28.6885	−0.969295
$877$	−0.330616	−0.0111641	−0.00558205	−	0.999984i	$-0.501777\pi$
$877$	−0.330616	−0.0111641	−0.00558205	+	0.999984i	$0.501777\pi$
$878$	94.1746	3.17824
$879$	13.9904	0.471884
$880$	35.5644	1.19888
$881$	−4.51734	−0.152193	−0.0760965	−	0.997100i	$-0.524246\pi$
$881$	−4.51734	−0.152193	−0.0760965	+	0.997100i	$0.524246\pi$
$882$	3.67795	0.123843
$883$	−46.7445	−1.57308	−0.786539	−	0.617540i	$-0.788129\pi$
$883$	−46.7445	−1.57308	−0.786539	+	0.617540i	$0.788129\pi$
$884$	−23.5071	−0.790629
$885$	37.2174	1.25105
$886$	72.7404	2.44376
$887$	−9.29057	−0.311947	−0.155973	−	0.987761i	$-0.549851\pi$
$887$	−9.29057	−0.311947	−0.155973	+	0.987761i	$0.549851\pi$
$888$	−85.6480	−2.87416
$889$	−10.8611	−0.364269
$890$	65.4757	2.19475
$891$	−29.0008	−0.971564
$892$	63.9349	2.14070
$893$	−1.33693	−0.0447387
$894$	−35.5817	−1.19003
$895$	22.9403	0.766808
$896$	−10.3171	−0.344671
$897$	30.0492	1.00332
$898$	33.4981	1.11785
$899$	3.89941	0.130053
$900$	−6.20228	−0.206743
$901$	−9.30159	−0.309881
$902$	−4.95835	−0.165095
$903$	−15.7854	−0.525306
$904$	101.208	3.36614
$905$	23.9439	0.795923
$906$	29.2836	0.972881
$907$	−24.0423	−0.798313	−0.399156	−	0.916883i	$-0.630697\pi$
$907$	−24.0423	−0.798313	−0.399156	+	0.916883i	$0.630697\pi$
$908$	56.2138	1.86552
$909$	4.12771	0.136908
$910$	−28.1973	−0.934732
$911$	6.04735	0.200358	0.100179	−	0.994969i	$-0.468059\pi$
$911$	6.04735	0.200358	0.100179	+	0.994969i	$0.468059\pi$
$912$	−56.6385	−1.87549
$913$	42.3179	1.40052
$914$	−0.387061	−0.0128028
$915$	17.4650	0.577376
$916$	127.649	4.21765
$917$	41.6940	1.37686
$918$	−15.9566	−0.526645
$919$	−34.8990	−1.15121	−0.575606	−	0.817727i	$-0.695234\pi$
$919$	−34.8990	−1.15121	−0.575606	+	0.817727i	$0.695234\pi$
$920$	−42.2652	−1.39344
$921$	−31.9488	−1.05275
$922$	−100.866	−3.32185
$923$	−0.286385	−0.00942648
$924$	48.9334	1.60979
$925$	19.3144	0.635054
$926$	52.0956	1.71197
$927$	−6.92866	−0.227567
$928$	9.27048	0.304319
$929$	39.8343	1.30692	0.653460	−	0.756961i	$-0.273317\pi$
$929$	39.8343	1.30692	0.653460	+	0.756961i	$0.273317\pi$
$930$	−24.4982	−0.803327
$931$	−11.0848	−0.363289
$932$	67.7992	2.22084
$933$	−18.8788	−0.618063
$934$	−38.4573	−1.25836
$935$	5.37108	0.175653
$936$	12.1271	0.396387
$937$	10.6822	0.348971	0.174485	−	0.984660i	$-0.444174\pi$
$937$	10.6822	0.348971	0.174485	+	0.984660i	$0.444174\pi$
$938$	−38.3894	−1.25346
$939$	−49.5978	−1.61856
$940$	−2.56257	−0.0835819
$941$	−1.40329	−0.0457459	−0.0228729	−	0.999738i	$-0.507281\pi$
$941$	−1.40329	−0.0457459	−0.0228729	+	0.999738i	$0.507281\pi$
$942$	10.7095	0.348933
$943$	2.82296	0.0919281
$944$	−119.785	−3.89868
$945$	−13.4198	−0.436546
$946$	31.9395	1.03844
$947$	9.93625	0.322885	0.161442	−	0.986882i	$-0.448385\pi$
$947$	9.93625	0.322885	0.161442	+	0.986882i	$0.448385\pi$
$948$	−74.7682	−2.42836
$949$	−12.6496	−0.410625
$950$	26.6609	0.864995
$951$	−36.0227	−1.16812
$952$	17.8339	0.578001
$953$	11.4560	0.371097	0.185548	−	0.982635i	$-0.440594\pi$
$953$	11.4560	0.371097	0.185548	+	0.982635i	$0.440594\pi$
$954$	8.36390	0.270791
$955$	−2.93834	−0.0950823
$956$	−112.304	−3.63218
$957$	5.85945	0.189409
$958$	91.1908	2.94624
$959$	−22.9510	−0.741126
$960$	−11.9651	−0.386172
$961$	−18.5249	−0.597578
$962$	−65.8234	−2.12223
$963$	1.58748	0.0511560
$964$	−64.6227	−2.08136
$965$	−21.8433	−0.703160
$966$	−39.7352	−1.27846
$967$	−32.0337	−1.03014	−0.515068	−	0.857150i	$-0.672233\pi$
$967$	−32.0337	−1.03014	−0.515068	+	0.857150i	$0.672233\pi$
$968$	19.7931	0.636175
$969$	−8.55376	−0.274786
$970$	29.9244	0.960814
$971$	−21.7771	−0.698859	−0.349429	−	0.936963i	$-0.613625\pi$
$971$	−21.7771	−0.698859	−0.349429	+	0.936963i	$0.613625\pi$
$972$	21.9089	0.702728
$973$	21.3558	0.684636
$974$	−70.9736	−2.27414
$975$	−20.8449	−0.667572
$976$	−56.2118	−1.79930
$977$	48.8640	1.56330	0.781649	−	0.623719i	$-0.214379\pi$
$977$	48.8640	1.56330	0.781649	+	0.623719i	$0.214379\pi$
$978$	−90.0684	−2.88007
$979$	−50.1012	−1.60124
$980$	−21.2469	−0.678706
$981$	1.12939	0.0360586
$982$	12.5188	0.399490
$983$	43.9288	1.40111	0.700555	−	0.713598i	$-0.252936\pi$
$983$	43.9288	1.40111	0.700555	+	0.713598i	$0.252936\pi$
$984$	8.68374	0.276827
$985$	−8.67600	−0.276440
$986$	3.72213	0.118537
$987$	−1.38221	−0.0439963
$988$	−63.7049	−2.02672
$989$	−18.1842	−0.578225
$990$	−4.82962	−0.153495
$991$	18.0715	0.574060	0.287030	−	0.957922i	$-0.407332\pi$
$991$	18.0715	0.574060	0.287030	+	0.957922i	$0.407332\pi$
$992$	29.6584	0.941655
$993$	48.4215	1.53661
$994$	0.378697	0.0120115
$995$	33.9824	1.07731
$996$	−129.178	−4.09315
$997$	−36.5966	−1.15903	−0.579514	−	0.814963i	$-0.696757\pi$
$997$	−36.5966	−1.15903	−0.579514	+	0.814963i	$0.696757\pi$
$998$	−43.3918	−1.37354
$999$	−31.3270	−0.991143

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.e.1.1	✓	10
3.2	odd	2		4527.2.a.k.1.10		10
4.3	odd	2		8048.2.a.p.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.e.1.1	✓	10	1.1	even	1	trivial
4527.2.a.k.1.10		10	3.2	odd	2
8048.2.a.p.1.8		10	4.3	odd	2

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:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58686 q^{2} -1.85823 q^{3} +4.69185 q^{4} +1.44291 q^{5} +4.80698 q^{6} -1.96509 q^{7} -6.96343 q^{8} +0.453023 q^{9} +O(q^{10})\)	\(q-2.58686 q^{2} -1.85823 q^{3} +4.69185 q^{4} +1.44291 q^{5} +4.80698 q^{6} -1.96509 q^{7} -6.96343 q^{8} +0.453023 q^{9} -3.73261 q^{10} +2.85614 q^{11} -8.71853 q^{12} -3.84427 q^{13} +5.08341 q^{14} -2.68126 q^{15} +8.62972 q^{16} +1.30329 q^{17} -1.17191 q^{18} +3.53196 q^{19} +6.76991 q^{20} +3.65159 q^{21} -7.38845 q^{22} +4.20650 q^{23} +12.9397 q^{24} -2.91801 q^{25} +9.94458 q^{26} +4.73287 q^{27} -9.21989 q^{28} -1.10402 q^{29} +6.93604 q^{30} -3.53201 q^{31} -8.39703 q^{32} -5.30738 q^{33} -3.37144 q^{34} -2.83545 q^{35} +2.12551 q^{36} -6.61903 q^{37} -9.13668 q^{38} +7.14353 q^{39} -10.0476 q^{40} +0.671095 q^{41} -9.44615 q^{42} -4.32289 q^{43} +13.4006 q^{44} +0.653672 q^{45} -10.8816 q^{46} -0.378524 q^{47} -16.0360 q^{48} -3.13843 q^{49} +7.54849 q^{50} -2.42182 q^{51} -18.0367 q^{52} -7.13700 q^{53} -12.2433 q^{54} +4.12116 q^{55} +13.6838 q^{56} -6.56319 q^{57} +2.85594 q^{58} -13.8806 q^{59} -12.5801 q^{60} -6.51374 q^{61} +9.13682 q^{62} -0.890231 q^{63} +4.46249 q^{64} -5.54693 q^{65} +13.7294 q^{66} -7.55189 q^{67} +6.11485 q^{68} -7.81664 q^{69} +7.33490 q^{70} +0.0744967 q^{71} -3.15459 q^{72} +3.29052 q^{73} +17.1225 q^{74} +5.42234 q^{75} +16.5714 q^{76} -5.61258 q^{77} -18.4793 q^{78} +8.57578 q^{79} +12.4519 q^{80} -10.1538 q^{81} -1.73603 q^{82} +14.8165 q^{83} +17.1327 q^{84} +1.88053 q^{85} +11.1827 q^{86} +2.05152 q^{87} -19.8886 q^{88} -17.5415 q^{89} -1.69096 q^{90} +7.55432 q^{91} +19.7362 q^{92} +6.56329 q^{93} +0.979188 q^{94} +5.09630 q^{95} +15.6036 q^{96} -8.01702 q^{97} +8.11867 q^{98} +1.29390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9} - 4 q^{10} - 3 q^{11} - 7 q^{12} - 18 q^{13} + q^{14} - 2 q^{15} - 4 q^{16} - 11 q^{17} - q^{18} - 3 q^{20} + q^{21} - 18 q^{22} - 2 q^{23} + 10 q^{24} - 27 q^{25} + 11 q^{26} - 2 q^{27} - 22 q^{28} - 9 q^{29} + 12 q^{30} - 22 q^{31} - 10 q^{32} - 10 q^{33} - 10 q^{34} - 6 q^{35} + 2 q^{36} - 35 q^{37} + 2 q^{38} + 8 q^{39} - 19 q^{40} - 4 q^{41} + 4 q^{42} - 20 q^{43} + 9 q^{44} + 2 q^{45} - q^{46} + 7 q^{47} - 27 q^{49} + 16 q^{50} + 9 q^{51} - 7 q^{52} - 24 q^{53} + 17 q^{54} - 11 q^{55} + 12 q^{56} - 23 q^{57} + 2 q^{58} + 17 q^{59} - 4 q^{61} + 8 q^{62} + 10 q^{63} + 3 q^{64} - 16 q^{65} + 46 q^{66} - 6 q^{67} + 28 q^{68} - 2 q^{69} + 26 q^{70} - q^{71} - q^{72} - 31 q^{73} + 11 q^{74} + 30 q^{75} + 20 q^{76} + 3 q^{77} + 11 q^{78} - 10 q^{79} + 24 q^{80} - 6 q^{81} - 9 q^{82} + 22 q^{83} + 22 q^{84} - 6 q^{85} + 38 q^{86} + 25 q^{87} - 3 q^{88} + q^{89} + 2 q^{90} + 10 q^{91} + 27 q^{92} - 6 q^{93} + 33 q^{94} + 39 q^{95} + 46 q^{96} - 57 q^{97} + 40 q^{98} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9 - 4 * q^10 - 3 * q^11 - 7 * q^12 - 18 * q^13 + q^14 - 2 * q^15 - 4 * q^16 - 11 * q^17 - q^18 - 3 * q^20 + q^21 - 18 * q^22 - 2 * q^23 + 10 * q^24 - 27 * q^25 + 11 * q^26 - 2 * q^27 - 22 * q^28 - 9 * q^29 + 12 * q^30 - 22 * q^31 - 10 * q^32 - 10 * q^33 - 10 * q^34 - 6 * q^35 + 2 * q^36 - 35 * q^37 + 2 * q^38 + 8 * q^39 - 19 * q^40 - 4 * q^41 + 4 * q^42 - 20 * q^43 + 9 * q^44 + 2 * q^45 - q^46 + 7 * q^47 - 27 * q^49 + 16 * q^50 + 9 * q^51 - 7 * q^52 - 24 * q^53 + 17 * q^54 - 11 * q^55 + 12 * q^56 - 23 * q^57 + 2 * q^58 + 17 * q^59 - 4 * q^61 + 8 * q^62 + 10 * q^63 + 3 * q^64 - 16 * q^65 + 46 * q^66 - 6 * q^67 + 28 * q^68 - 2 * q^69 + 26 * q^70 - q^71 - q^72 - 31 * q^73 + 11 * q^74 + 30 * q^75 + 20 * q^76 + 3 * q^77 + 11 * q^78 - 10 * q^79 + 24 * q^80 - 6 * q^81 - 9 * q^82 + 22 * q^83 + 22 * q^84 - 6 * q^85 + 38 * q^86 + 25 * q^87 - 3 * q^88 + q^89 + 2 * q^90 + 10 * q^91 + 27 * q^92 - 6 * q^93 + 33 * q^94 + 39 * q^95 + 46 * q^96 - 57 * q^97 + 40 * q^98 + 35 * q^99

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