LMFDB - Embedded newform 547.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, 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("547.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.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:	$4.36781699056$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} + \cdots + 328 $ x^18 - 4x^17 - 18x^16 + 84x^15 + 116x^14 - 708x^13 - 282x^12 + 3104x^11 - 137x^10 - 7703x^9 + 2068x^8 + 11068x^7 - 4274x^6 - 9021x^5 + 4048x^4 + 3834x^3 - 1851x^2 - 654*x + 328
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.04467$ of defining polynomial
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.04467 q^{2} -2.71791 q^{3} -0.908666 q^{4} +0.714085 q^{5} +2.83932 q^{6} -2.03236 q^{7} +3.03859 q^{8} +4.38705 q^{9} +O(q^{10})$	\(q-1.04467 q^{2} -2.71791 q^{3} -0.908666 q^{4} +0.714085 q^{5} +2.83932 q^{6} -2.03236 q^{7} +3.03859 q^{8} +4.38705 q^{9} -0.745983 q^{10} +5.43392 q^{11} +2.46968 q^{12} -3.96770 q^{13} +2.12315 q^{14} -1.94082 q^{15} -1.35699 q^{16} -1.30793 q^{17} -4.58302 q^{18} +8.24470 q^{19} -0.648865 q^{20} +5.52379 q^{21} -5.67665 q^{22} -2.44824 q^{23} -8.25864 q^{24} -4.49008 q^{25} +4.14494 q^{26} -3.76989 q^{27} +1.84674 q^{28} +1.49405 q^{29} +2.02752 q^{30} -6.02301 q^{31} -4.65958 q^{32} -14.7689 q^{33} +1.36635 q^{34} -1.45128 q^{35} -3.98637 q^{36} -6.36158 q^{37} -8.61299 q^{38} +10.7839 q^{39} +2.16982 q^{40} -2.87189 q^{41} -5.77053 q^{42} -5.76713 q^{43} -4.93762 q^{44} +3.13273 q^{45} +2.55760 q^{46} +6.42848 q^{47} +3.68819 q^{48} -2.86949 q^{49} +4.69065 q^{50} +3.55483 q^{51} +3.60532 q^{52} -0.932545 q^{53} +3.93829 q^{54} +3.88028 q^{55} -6.17553 q^{56} -22.4084 q^{57} -1.56079 q^{58} +1.57369 q^{59} +1.76356 q^{60} -7.93215 q^{61} +6.29205 q^{62} -8.91609 q^{63} +7.58170 q^{64} -2.83328 q^{65} +15.4286 q^{66} +10.5294 q^{67} +1.18847 q^{68} +6.65410 q^{69} +1.51611 q^{70} -12.8929 q^{71} +13.3305 q^{72} +9.81833 q^{73} +6.64575 q^{74} +12.2037 q^{75} -7.49168 q^{76} -11.0437 q^{77} -11.2656 q^{78} -2.80129 q^{79} -0.969009 q^{80} -2.91492 q^{81} +3.00017 q^{82} -15.3935 q^{83} -5.01928 q^{84} -0.933971 q^{85} +6.02474 q^{86} -4.06069 q^{87} +16.5115 q^{88} -1.89811 q^{89} -3.27267 q^{90} +8.06382 q^{91} +2.22463 q^{92} +16.3700 q^{93} -6.71563 q^{94} +5.88742 q^{95} +12.6643 q^{96} +0.276333 q^{97} +2.99767 q^{98} +23.8389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9} - 5 q^{10} + 2 q^{11} - 32 q^{12} - 25 q^{13} - 7 q^{14} + 9 q^{15} + 8 q^{16} - 30 q^{17} - 10 q^{18} + 4 q^{19} - 41 q^{20} - 16 q^{21} - 24 q^{22} - 26 q^{23} - 12 q^{24} + 31 q^{25} - 18 q^{26} - 37 q^{27} - 16 q^{28} - 18 q^{29} + 8 q^{30} - 5 q^{31} - 28 q^{32} - 10 q^{33} + 5 q^{34} - 9 q^{35} + 31 q^{36} - 18 q^{37} - 45 q^{38} + 7 q^{39} + 7 q^{40} - 17 q^{41} + 4 q^{42} + 8 q^{43} + 12 q^{44} - 44 q^{45} + 30 q^{46} - 52 q^{47} - 7 q^{48} + 29 q^{49} + 13 q^{50} + 19 q^{51} - 14 q^{52} - 60 q^{53} + 11 q^{54} + 11 q^{55} + 7 q^{56} + 4 q^{57} + 14 q^{58} - 8 q^{59} + 86 q^{60} - 26 q^{61} + 4 q^{62} - q^{63} + 44 q^{64} - 6 q^{65} + 18 q^{66} + 12 q^{67} - 61 q^{68} - 38 q^{69} + 35 q^{70} - q^{71} + 28 q^{72} - 2 q^{73} + 16 q^{74} - 17 q^{75} + 66 q^{76} - 73 q^{77} + 115 q^{78} + 18 q^{79} - 32 q^{80} + 18 q^{81} + 44 q^{82} - 43 q^{83} + 41 q^{84} + 51 q^{85} + 4 q^{86} + 3 q^{87} - 17 q^{88} - 28 q^{89} + 58 q^{90} - q^{91} - 68 q^{92} - 60 q^{93} + 78 q^{94} - 18 q^{95} + 29 q^{96} - 34 q^{97} + 34 q^{98} + 15 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9 - 5 * q^10 + 2 * q^11 - 32 * q^12 - 25 * q^13 - 7 * q^14 + 9 * q^15 + 8 * q^16 - 30 * q^17 - 10 * q^18 + 4 * q^19 - 41 * q^20 - 16 * q^21 - 24 * q^22 - 26 * q^23 - 12 * q^24 + 31 * q^25 - 18 * q^26 - 37 * q^27 - 16 * q^28 - 18 * q^29 + 8 * q^30 - 5 * q^31 - 28 * q^32 - 10 * q^33 + 5 * q^34 - 9 * q^35 + 31 * q^36 - 18 * q^37 - 45 * q^38 + 7 * q^39 + 7 * q^40 - 17 * q^41 + 4 * q^42 + 8 * q^43 + 12 * q^44 - 44 * q^45 + 30 * q^46 - 52 * q^47 - 7 * q^48 + 29 * q^49 + 13 * q^50 + 19 * q^51 - 14 * q^52 - 60 * q^53 + 11 * q^54 + 11 * q^55 + 7 * q^56 + 4 * q^57 + 14 * q^58 - 8 * q^59 + 86 * q^60 - 26 * q^61 + 4 * q^62 - q^63 + 44 * q^64 - 6 * q^65 + 18 * q^66 + 12 * q^67 - 61 * q^68 - 38 * q^69 + 35 * q^70 - q^71 + 28 * q^72 - 2 * q^73 + 16 * q^74 - 17 * q^75 + 66 * q^76 - 73 * q^77 + 115 * q^78 + 18 * q^79 - 32 * q^80 + 18 * q^81 + 44 * q^82 - 43 * q^83 + 41 * q^84 + 51 * q^85 + 4 * q^86 + 3 * q^87 - 17 * q^88 - 28 * q^89 + 58 * q^90 - q^91 - 68 * q^92 - 60 * q^93 + 78 * q^94 - 18 * q^95 + 29 * q^96 - 34 * q^97 + 34 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.04467	−0.738693	−0.369346	−	0.929292i	$-0.620418\pi$
$2$	−1.04467	−0.738693	−0.369346	+	0.929292i	$0.620418\pi$
$3$	−2.71791	−1.56919	−0.784594	−	0.620010i	$-0.787129\pi$
$3$	−2.71791	−1.56919	−0.784594	+	0.620010i	$0.787129\pi$
$4$	−0.908666	−0.454333
$5$	0.714085	0.319349	0.159674	−	0.987170i	$-0.448956\pi$
$5$	0.714085	0.319349	0.159674	+	0.987170i	$0.448956\pi$
$6$	2.83932	1.15915
$7$	−2.03236	−0.768162	−0.384081	−	0.923299i	$-0.625482\pi$
$7$	−2.03236	−0.768162	−0.384081	+	0.923299i	$0.625482\pi$
$8$	3.03859	1.07431
$9$	4.38705	1.46235
$10$	−0.745983	−0.235901
$11$	5.43392	1.63839	0.819194	−	0.573516i	$-0.194421\pi$
$11$	5.43392	1.63839	0.819194	+	0.573516i	$0.194421\pi$
$12$	2.46968	0.712934
$13$	−3.96770	−1.10044	−0.550221	−	0.835019i	$-0.685457\pi$
$13$	−3.96770	−1.10044	−0.550221	+	0.835019i	$0.685457\pi$
$14$	2.12315	0.567435
$15$	−1.94082	−0.501118
$16$	−1.35699	−0.339248
$17$	−1.30793	−0.317219	−0.158609	−	0.987341i	$-0.550701\pi$
$17$	−1.30793	−0.317219	−0.158609	+	0.987341i	$0.550701\pi$
$18$	−4.58302	−1.08023
$19$	8.24470	1.89146	0.945732	−	0.324947i	$-0.105346\pi$
$19$	8.24470	1.89146	0.945732	+	0.324947i	$0.105346\pi$
$20$	−0.648865	−0.145091
$21$	5.52379	1.20539
$22$	−5.67665	−1.21027
$23$	−2.44824	−0.510493	−0.255246	−	0.966876i	$-0.582157\pi$
$23$	−2.44824	−0.510493	−0.255246	+	0.966876i	$0.582157\pi$
$24$	−8.25864	−1.68579
$25$	−4.49008	−0.898016
$26$	4.14494	0.812889
$27$	−3.76989	−0.725517
$28$	1.84674	0.349001
$29$	1.49405	0.277438	0.138719	−	0.990332i	$-0.455702\pi$
$29$	1.49405	0.277438	0.138719	+	0.990332i	$0.455702\pi$
$30$	2.02752	0.370172
$31$	−6.02301	−1.08176	−0.540882	−	0.841098i	$-0.681909\pi$
$31$	−6.02301	−1.08176	−0.540882	+	0.841098i	$0.681909\pi$
$32$	−4.65958	−0.823705
$33$	−14.7689	−2.57094
$34$	1.36635	0.234327
$35$	−1.45128	−0.245311
$36$	−3.98637	−0.664395
$37$	−6.36158	−1.04584	−0.522919	−	0.852383i	$-0.675157\pi$
$37$	−6.36158	−1.04584	−0.522919	+	0.852383i	$0.675157\pi$
$38$	−8.61299	−1.39721
$39$	10.7839	1.72680
$40$	2.16982	0.343078
$41$	−2.87189	−0.448514	−0.224257	−	0.974530i	$-0.571995\pi$
$41$	−2.87189	−0.448514	−0.224257	+	0.974530i	$0.571995\pi$
$42$	−5.77053	−0.890413
$43$	−5.76713	−0.879478	−0.439739	−	0.898125i	$-0.644929\pi$
$43$	−5.76713	−0.879478	−0.439739	+	0.898125i	$0.644929\pi$
$44$	−4.93762	−0.744374
$45$	3.13273	0.467000
$46$	2.55760	0.377097
$47$	6.42848	0.937689	0.468845	−	0.883281i	$-0.344670\pi$
$47$	6.42848	0.937689	0.468845	+	0.883281i	$0.344670\pi$
$48$	3.68819	0.532344
$49$	−2.86949	−0.409928
$50$	4.69065	0.663358
$51$	3.55483	0.497776
$52$	3.60532	0.499967
$53$	−0.932545	−0.128095	−0.0640474	−	0.997947i	$-0.520401\pi$
$53$	−0.932545	−0.128095	−0.0640474	+	0.997947i	$0.520401\pi$
$54$	3.93829	0.535934
$55$	3.88028	0.523217
$56$	−6.17553	−0.825240
$57$	−22.4084	−2.96806
$58$	−1.56079	−0.204941
$59$	1.57369	0.204877	0.102438	−	0.994739i	$-0.467336\pi$
$59$	1.57369	0.204877	0.102438	+	0.994739i	$0.467336\pi$
$60$	1.76356	0.227675
$61$	−7.93215	−1.01561	−0.507804	−	0.861473i	$-0.669542\pi$
$61$	−7.93215	−1.01561	−0.507804	+	0.861473i	$0.669542\pi$
$62$	6.29205	0.799091
$63$	−8.91609	−1.12332
$64$	7.58170	0.947713
$65$	−2.83328	−0.351425
$66$	15.4286	1.89913
$67$	10.5294	1.28637	0.643186	−	0.765710i	$-0.277612\pi$
$67$	10.5294	1.28637	0.643186	+	0.765710i	$0.277612\pi$
$68$	1.18847	0.144123
$69$	6.65410	0.801059
$70$	1.51611	0.181210
$71$	−12.8929	−1.53011	−0.765054	−	0.643966i	$-0.777288\pi$
$71$	−12.8929	−1.53011	−0.765054	+	0.643966i	$0.777288\pi$
$72$	13.3305	1.57101
$73$	9.81833	1.14915	0.574574	−	0.818452i	$-0.305168\pi$
$73$	9.81833	1.14915	0.574574	+	0.818452i	$0.305168\pi$
$74$	6.64575	0.772552
$75$	12.2037	1.40916
$76$	−7.49168	−0.859355
$77$	−11.0437	−1.25855
$78$	−11.2656	−1.27558
$79$	−2.80129	−0.315170	−0.157585	−	0.987505i	$-0.550371\pi$
$79$	−2.80129	−0.315170	−0.157585	+	0.987505i	$0.550371\pi$
$80$	−0.969009	−0.108338
$81$	−2.91492	−0.323880
$82$	3.00017	0.331314
$83$	−15.3935	−1.68966	−0.844829	−	0.535037i	$-0.820298\pi$
$83$	−15.3935	−1.68966	−0.844829	+	0.535037i	$0.820298\pi$
$84$	−5.01928	−0.547649
$85$	−0.933971	−0.101303
$86$	6.02474	0.649664
$87$	−4.06069	−0.435352
$88$	16.5115	1.76013
$89$	−1.89811	−0.201199	−0.100600	−	0.994927i	$-0.532076\pi$
$89$	−1.89811	−0.201199	−0.100600	+	0.994927i	$0.532076\pi$
$90$	−3.27267	−0.344969
$91$	8.06382	0.845318
$92$	2.22463	0.231934
$93$	16.3700	1.69749
$94$	−6.71563	−0.692664
$95$	5.88742	0.604037
$96$	12.6643	1.29255
$97$	0.276333	0.0280574	0.0140287	−	0.999902i	$-0.495534\pi$
$97$	0.276333	0.0280574	0.0140287	+	0.999902i	$0.495534\pi$
$98$	2.99767	0.302811
$99$	23.8389	2.39590
$100$	4.07999	0.407999
$101$	−17.0451	−1.69605	−0.848024	−	0.529958i	$-0.822208\pi$
$101$	−17.0451	−1.69605	−0.848024	+	0.529958i	$0.822208\pi$
$102$	−3.71362	−0.367703
$103$	6.40415	0.631020	0.315510	−	0.948922i	$-0.397824\pi$
$103$	6.40415	0.631020	0.315510	+	0.948922i	$0.397824\pi$
$104$	−12.0562	−1.18221
$105$	3.94446	0.384940
$106$	0.974201	0.0946227
$107$	6.34857	0.613739	0.306870	−	0.951752i	$-0.400718\pi$
$107$	6.34857	0.613739	0.306870	+	0.951752i	$0.400718\pi$
$108$	3.42558	0.329626
$109$	9.33636	0.894261	0.447130	−	0.894469i	$-0.352446\pi$
$109$	9.33636	0.894261	0.447130	+	0.894469i	$0.352446\pi$
$110$	−4.05361	−0.386497
$111$	17.2902	1.64112
$112$	2.75790	0.260597
$113$	−1.89369	−0.178144	−0.0890718	−	0.996025i	$-0.528390\pi$
$113$	−1.89369	−0.178144	−0.0890718	+	0.996025i	$0.528390\pi$
$114$	23.4094	2.19249
$115$	−1.74825	−0.163025
$116$	−1.35759	−0.126049
$117$	−17.4065	−1.60923
$118$	−1.64398	−0.151341
$119$	2.65818	0.243675
$120$	−5.89737	−0.538354
$121$	18.5275	1.68432
$122$	8.28647	0.750222
$123$	7.80555	0.703802
$124$	5.47290	0.491481
$125$	−6.77673	−0.606129
$126$	9.31437	0.829790
$127$	10.2086	0.905867	0.452933	−	0.891544i	$-0.350378\pi$
$127$	10.2086	0.905867	0.452933	+	0.891544i	$0.350378\pi$
$128$	1.39879	0.123636
$129$	15.6746	1.38007
$130$	2.95984	0.259595
$131$	−13.9590	−1.21960	−0.609801	−	0.792554i	$-0.708751\pi$
$131$	−13.9590	−1.21960	−0.609801	+	0.792554i	$0.708751\pi$
$132$	13.4200	1.16806
$133$	−16.7562	−1.45295
$134$	−10.9997	−0.950233
$135$	−2.69203	−0.231693
$136$	−3.97426	−0.340790
$137$	−2.19310	−0.187369	−0.0936845	−	0.995602i	$-0.529864\pi$
$137$	−2.19310	−0.187369	−0.0936845	+	0.995602i	$0.529864\pi$
$138$	−6.95133	−0.591737
$139$	−19.6789	−1.66914	−0.834572	−	0.550899i	$-0.814285\pi$
$139$	−19.6789	−1.66914	−0.834572	+	0.550899i	$0.814285\pi$
$140$	1.31873	0.111453
$141$	−17.4720	−1.47141
$142$	13.4688	1.13028
$143$	−21.5602	−1.80295
$144$	−5.95320	−0.496100
$145$	1.06688	0.0885994
$146$	−10.2569	−0.848868
$147$	7.79904	0.643254
$148$	5.78055	0.475159
$149$	−11.0882	−0.908379	−0.454189	−	0.890905i	$-0.650071\pi$
$149$	−11.0882	−0.908379	−0.454189	+	0.890905i	$0.650071\pi$
$150$	−12.7488	−1.04093
$151$	7.03425	0.572439	0.286219	−	0.958164i	$-0.407601\pi$
$151$	7.03425	0.572439	0.286219	+	0.958164i	$0.407601\pi$
$152$	25.0523	2.03201
$153$	−5.73795	−0.463885
$154$	11.5370	0.929679
$155$	−4.30094	−0.345460
$156$	−9.79894	−0.784543
$157$	−24.2151	−1.93257	−0.966287	−	0.257468i	$-0.917112\pi$
$157$	−24.2151	−1.93257	−0.966287	+	0.257468i	$0.917112\pi$
$158$	2.92642	0.232814
$159$	2.53458	0.201005
$160$	−3.32734	−0.263049
$161$	4.97571	0.392141
$162$	3.04512	0.239247
$163$	0.672203	0.0526510	0.0263255	−	0.999653i	$-0.491619\pi$
$163$	0.672203	0.0526510	0.0263255	+	0.999653i	$0.491619\pi$
$164$	2.60959	0.203775
$165$	−10.5463	−0.821026
$166$	16.0811	1.24814
$167$	−13.2184	−1.02287	−0.511436	−	0.859321i	$-0.670886\pi$
$167$	−13.2184	−1.02287	−0.511436	+	0.859321i	$0.670886\pi$
$168$	16.7846	1.29496
$169$	2.74265	0.210973
$170$	0.975691	0.0748321
$171$	36.1700	2.76599
$172$	5.24039	0.399576
$173$	−18.2674	−1.38884	−0.694421	−	0.719569i	$-0.744339\pi$
$173$	−18.2674	−1.38884	−0.694421	+	0.719569i	$0.744339\pi$
$174$	4.24208	0.321591
$175$	9.12548	0.689822
$176$	−7.37379	−0.555820
$177$	−4.27715	−0.321490
$178$	1.98290	0.148624
$179$	21.6343	1.61702	0.808511	−	0.588481i	$-0.200274\pi$
$179$	21.6343	1.61702	0.808511	+	0.588481i	$0.200274\pi$
$180$	−2.84661	−0.212174
$181$	0.765562	0.0569038	0.0284519	−	0.999595i	$-0.490942\pi$
$181$	0.765562	0.0569038	0.0284519	+	0.999595i	$0.490942\pi$
$182$	−8.42402	−0.624430
$183$	21.5589	1.59368
$184$	−7.43920	−0.548425
$185$	−4.54271	−0.333987
$186$	−17.1012	−1.25392
$187$	−7.10717	−0.519728
$188$	−5.84134	−0.426023
$189$	7.66180	0.557314
$190$	−6.15041	−0.446197
$191$	−3.52515	−0.255071	−0.127535	−	0.991834i	$-0.540707\pi$
$191$	−3.52515	−0.255071	−0.127535	+	0.991834i	$0.540707\pi$
$192$	−20.6064	−1.48714
$193$	−8.94657	−0.643988	−0.321994	−	0.946742i	$-0.604353\pi$
$193$	−8.94657	−0.643988	−0.321994	+	0.946742i	$0.604353\pi$
$194$	−0.288677	−0.0207258
$195$	7.70060	0.551452
$196$	2.60741	0.186244
$197$	−20.1670	−1.43684	−0.718418	−	0.695612i	$-0.755133\pi$
$197$	−20.1670	−1.43684	−0.718418	+	0.695612i	$0.755133\pi$
$198$	−24.9038	−1.76983
$199$	3.72704	0.264203	0.132101	−	0.991236i	$-0.457828\pi$
$199$	3.72704	0.264203	0.132101	+	0.991236i	$0.457828\pi$
$200$	−13.6435	−0.964744
$201$	−28.6180	−2.01856
$202$	17.8065	1.25286
$203$	−3.03645	−0.213117
$204$	−3.23016	−0.226156
$205$	−2.05077	−0.143232
$206$	−6.69022	−0.466130
$207$	−10.7406	−0.746520
$208$	5.38414	0.373323
$209$	44.8011	3.09895
$210$	−4.12065	−0.284352
$211$	17.9812	1.23788	0.618940	−	0.785438i	$-0.287562\pi$
$211$	17.9812	1.23788	0.618940	+	0.785438i	$0.287562\pi$
$212$	0.847372	0.0581977
$213$	35.0419	2.40103
$214$	−6.63215	−0.453365
$215$	−4.11822	−0.280860
$216$	−11.4552	−0.779426
$217$	12.2409	0.830970
$218$	−9.75341	−0.660584
$219$	−26.6854	−1.80323
$220$	−3.52588	−0.237715
$221$	5.18946	0.349081
$222$	−18.0626	−1.21228
$223$	−19.2192	−1.28701	−0.643507	−	0.765440i	$-0.722521\pi$
$223$	−19.2192	−1.28701	−0.643507	+	0.765440i	$0.722521\pi$
$224$	9.46996	0.632739
$225$	−19.6982	−1.31322
$226$	1.97828	0.131593
$227$	23.2733	1.54470	0.772350	−	0.635197i	$-0.219081\pi$
$227$	23.2733	1.54470	0.772350	+	0.635197i	$0.219081\pi$
$228$	20.3617	1.34849
$229$	1.04868	0.0692987	0.0346494	−	0.999400i	$-0.488969\pi$
$229$	1.04868	0.0692987	0.0346494	+	0.999400i	$0.488969\pi$
$230$	1.82634	0.120426
$231$	30.0158	1.97490
$232$	4.53981	0.298053
$233$	10.4018	0.681441	0.340721	−	0.940165i	$-0.389329\pi$
$233$	10.4018	0.681441	0.340721	+	0.940165i	$0.389329\pi$
$234$	18.1841	1.18873
$235$	4.59048	0.299450
$236$	−1.42996	−0.0930823
$237$	7.61367	0.494561
$238$	−2.77692	−0.180001
$239$	5.21082	0.337060	0.168530	−	0.985697i	$-0.446098\pi$
$239$	5.21082	0.337060	0.168530	+	0.985697i	$0.446098\pi$
$240$	2.63368	0.170003
$241$	−23.1270	−1.48974	−0.744871	−	0.667209i	$-0.767489\pi$
$241$	−23.1270	−1.48974	−0.744871	+	0.667209i	$0.767489\pi$
$242$	−19.3551	−1.24419
$243$	19.2322	1.23374
$244$	7.20767	0.461424
$245$	−2.04906	−0.130910
$246$	−8.15421	−0.519894
$247$	−32.7125	−2.08145
$248$	−18.3015	−1.16214
$249$	41.8382	2.65139
$250$	7.07944	0.447743
$251$	−18.2828	−1.15400	−0.577001	−	0.816744i	$-0.695777\pi$
$251$	−18.2828	−1.15400	−0.577001	+	0.816744i	$0.695777\pi$
$252$	8.10175	0.510363
$253$	−13.3035	−0.836386
$254$	−10.6646	−0.669157
$255$	2.53845	0.158964
$256$	−16.6247	−1.03904
$257$	30.4924	1.90207	0.951033	−	0.309091i	$-0.100025\pi$
$257$	30.4924	1.90207	0.951033	+	0.309091i	$0.100025\pi$
$258$	−16.3747	−1.01945
$259$	12.9291	0.803372
$260$	2.57450	0.159664
$261$	6.55447	0.405712
$262$	14.5825	0.900911
$263$	−11.2828	−0.695730	−0.347865	−	0.937545i	$-0.613093\pi$
$263$	−11.2828	−0.695730	−0.347865	+	0.937545i	$0.613093\pi$
$264$	−44.8768	−2.76197
$265$	−0.665916	−0.0409069
$266$	17.5047	1.07328
$267$	5.15890	0.315720
$268$	−9.56772	−0.584441
$269$	−1.54283	−0.0940679	−0.0470339	−	0.998893i	$-0.514977\pi$
$269$	−1.54283	−0.0940679	−0.0470339	+	0.998893i	$0.514977\pi$
$270$	2.81228	0.171150
$271$	−23.6023	−1.43374	−0.716870	−	0.697207i	$-0.754426\pi$
$271$	−23.6023	−1.43374	−0.716870	+	0.697207i	$0.754426\pi$
$272$	1.77485	0.107616
$273$	−21.9168	−1.32646
$274$	2.29106	0.138408
$275$	−24.3987	−1.47130
$276$	−6.04635	−0.363948
$277$	14.2694	0.857367	0.428684	−	0.903455i	$-0.358978\pi$
$277$	14.2694	0.857367	0.428684	+	0.903455i	$0.358978\pi$
$278$	20.5580	1.23298
$279$	−26.4233	−1.58192
$280$	−4.40986	−0.263539
$281$	22.6952	1.35388	0.676942	−	0.736037i	$-0.263305\pi$
$281$	22.6952	1.35388	0.676942	+	0.736037i	$0.263305\pi$
$282$	18.2525	1.08692
$283$	−22.9783	−1.36592	−0.682958	−	0.730458i	$-0.739307\pi$
$283$	−22.9783	−1.36592	−0.682958	+	0.730458i	$0.739307\pi$
$284$	11.7154	0.695179
$285$	−16.0015	−0.947847
$286$	22.5232	1.33183
$287$	5.83672	0.344531
$288$	−20.4418	−1.20455
$289$	−15.2893	−0.899372
$290$	−1.11453	−0.0654477
$291$	−0.751051	−0.0440274
$292$	−8.92158	−0.522096
$293$	−25.1176	−1.46739	−0.733694	−	0.679480i	$-0.762205\pi$
$293$	−25.1176	−1.46739	−0.733694	+	0.679480i	$0.762205\pi$
$294$	−8.14742	−0.475167
$295$	1.12375	0.0654271
$296$	−19.3303	−1.12355
$297$	−20.4853	−1.18868
$298$	11.5835	0.671013
$299$	9.71388	0.561768
$300$	−11.0891	−0.640227
$301$	11.7209	0.675582
$302$	−7.34846	−0.422856
$303$	46.3270	2.66142
$304$	−11.1880	−0.641676
$305$	−5.66423	−0.324333
$306$	5.99425	0.342669
$307$	−14.5944	−0.832947	−0.416473	−	0.909148i	$-0.636734\pi$
$307$	−14.5944	−0.832947	−0.416473	+	0.909148i	$0.636734\pi$
$308$	10.0350	0.571800
$309$	−17.4059	−0.990188
$310$	4.49306	0.255189
$311$	8.99147	0.509860	0.254930	−	0.966960i	$-0.417948\pi$
$311$	8.99147	0.509860	0.254930	+	0.966960i	$0.417948\pi$
$312$	32.7678	1.85511
$313$	−4.56361	−0.257951	−0.128975	−	0.991648i	$-0.541169\pi$
$313$	−4.56361	−0.257951	−0.128975	+	0.991648i	$0.541169\pi$
$314$	25.2967	1.42758
$315$	−6.36685	−0.358731
$316$	2.54544	0.143192
$317$	−7.39682	−0.415447	−0.207723	−	0.978188i	$-0.566605\pi$
$317$	−7.39682	−0.415447	−0.207723	+	0.978188i	$0.566605\pi$
$318$	−2.64779	−0.148481
$319$	8.11854	0.454551
$320$	5.41398	0.302651
$321$	−17.2549	−0.963072
$322$	−5.19797	−0.289672
$323$	−10.7835	−0.600008
$324$	2.64869	0.147149
$325$	17.8153	0.988215
$326$	−0.702230	−0.0388929
$327$	−25.3754	−1.40326
$328$	−8.72650	−0.481841
$329$	−13.0650	−0.720297
$330$	11.0174	0.606486
$331$	−23.5847	−1.29633	−0.648166	−	0.761499i	$-0.724464\pi$
$331$	−23.5847	−1.29633	−0.648166	+	0.761499i	$0.724464\pi$
$332$	13.9876	0.767667
$333$	−27.9086	−1.52938
$334$	13.8089	0.755588
$335$	7.51890	0.410801
$336$	−7.49575	−0.408926
$337$	25.0637	1.36531	0.682653	−	0.730743i	$-0.260826\pi$
$337$	25.0637	1.36531	0.682653	+	0.730743i	$0.260826\pi$
$338$	−2.86517	−0.155845
$339$	5.14689	0.279541
$340$	0.848668	0.0460255
$341$	−32.7285	−1.77235
$342$	−37.7856	−2.04321
$343$	20.0584	1.08305
$344$	−17.5240	−0.944828
$345$	4.75159	0.255817
$346$	19.0834	1.02593
$347$	11.1374	0.597888	0.298944	−	0.954271i	$-0.403366\pi$
$347$	11.1374	0.597888	0.298944	+	0.954271i	$0.403366\pi$
$348$	3.68982	0.197795
$349$	34.3068	1.83640	0.918202	−	0.396114i	$-0.129641\pi$
$349$	34.3068	1.83640	0.918202	+	0.396114i	$0.129641\pi$
$350$	−9.53311	−0.509566
$351$	14.9578	0.798389
$352$	−25.3198	−1.34955
$353$	18.3887	0.978731	0.489366	−	0.872079i	$-0.337228\pi$
$353$	18.3887	0.978731	0.489366	+	0.872079i	$0.337228\pi$
$354$	4.46821	0.237482
$355$	−9.20665	−0.488638
$356$	1.72475	0.0914115
$357$	−7.22471	−0.382372
$358$	−22.6007	−1.19448
$359$	16.8572	0.889688	0.444844	−	0.895608i	$-0.353259\pi$
$359$	16.8572	0.889688	0.444844	+	0.895608i	$0.353259\pi$
$360$	9.51910	0.501701
$361$	48.9751	2.57764
$362$	−0.799759	−0.0420344
$363$	−50.3561	−2.64301
$364$	−7.32732	−0.384056
$365$	7.01112	0.366979
$366$	−22.5219	−1.17724
$367$	20.9807	1.09518	0.547592	−	0.836745i	$-0.315544\pi$
$367$	20.9807	1.09518	0.547592	+	0.836745i	$0.315544\pi$
$368$	3.32224	0.173184
$369$	−12.5991	−0.655885
$370$	4.74563	0.246714
$371$	1.89527	0.0983975
$372$	−14.8749	−0.771227
$373$	8.57191	0.443837	0.221918	−	0.975065i	$-0.428768\pi$
$373$	8.57191	0.443837	0.221918	+	0.975065i	$0.428768\pi$
$374$	7.42464	0.383919
$375$	18.4186	0.951130
$376$	19.5335	1.00736
$377$	−5.92794	−0.305304
$378$	−8.00405	−0.411684
$379$	−24.0731	−1.23655	−0.618275	−	0.785962i	$-0.712168\pi$
$379$	−24.0731	−1.23655	−0.618275	+	0.785962i	$0.712168\pi$
$380$	−5.34970	−0.274434
$381$	−27.7461	−1.42148
$382$	3.68261	0.188419
$383$	−28.2472	−1.44336	−0.721682	−	0.692225i	$-0.756631\pi$
$383$	−28.2472	−1.44336	−0.721682	+	0.692225i	$0.756631\pi$
$384$	−3.80178	−0.194009
$385$	−7.88615	−0.401915
$386$	9.34621	0.475709
$387$	−25.3007	−1.28611
$388$	−0.251095	−0.0127474
$389$	20.2718	1.02782	0.513911	−	0.857843i	$-0.328196\pi$
$389$	20.2718	1.02782	0.513911	+	0.857843i	$0.328196\pi$
$390$	−8.04458	−0.407353
$391$	3.20211	0.161938
$392$	−8.71923	−0.440388
$393$	37.9393	1.91379
$394$	21.0678	1.06138
$395$	−2.00036	−0.100649
$396$	−21.6616	−1.08854
$397$	9.39156	0.471349	0.235674	−	0.971832i	$-0.424270\pi$
$397$	9.39156	0.471349	0.235674	+	0.971832i	$0.424270\pi$
$398$	−3.89352	−0.195165
$399$	45.5420	2.27995
$400$	6.09301	0.304650
$401$	8.35327	0.417143	0.208571	−	0.978007i	$-0.433119\pi$
$401$	8.35327	0.417143	0.208571	+	0.978007i	$0.433119\pi$
$402$	29.8964	1.49110
$403$	23.8975	1.19042
$404$	15.4883	0.770571
$405$	−2.08150	−0.103431
$406$	3.17209	0.157428
$407$	−34.5683	−1.71349
$408$	10.8017	0.534763
$409$	−9.04325	−0.447160	−0.223580	−	0.974686i	$-0.571774\pi$
$409$	−9.04325	−0.447160	−0.223580	+	0.974686i	$0.571774\pi$
$410$	2.14238	0.105805
$411$	5.96065	0.294017
$412$	−5.81923	−0.286693
$413$	−3.19831	−0.157378
$414$	11.2203	0.551449
$415$	−10.9923	−0.539590
$416$	18.4878	0.906440
$417$	53.4856	2.61920
$418$	−46.8023	−2.28917
$419$	−21.2265	−1.03698	−0.518491	−	0.855083i	$-0.673506\pi$
$419$	−21.2265	−1.03698	−0.518491	+	0.855083i	$0.673506\pi$
$420$	−3.58420	−0.174891
$421$	16.3175	0.795269	0.397634	−	0.917544i	$-0.369831\pi$
$421$	16.3175	0.795269	0.397634	+	0.917544i	$0.369831\pi$
$422$	−18.7844	−0.914412
$423$	28.2021	1.37123
$424$	−2.83362	−0.137613
$425$	5.87270	0.284868
$426$	−36.6071	−1.77362
$427$	16.1210	0.780151
$428$	−5.76873	−0.278842
$429$	58.5987	2.82917
$430$	4.30218	0.207469
$431$	17.2192	0.829420	0.414710	−	0.909954i	$-0.363883\pi$
$431$	17.2192	0.829420	0.414710	+	0.909954i	$0.363883\pi$
$432$	5.11572	0.246130
$433$	0.155714	0.00748312	0.00374156	−	0.999993i	$-0.498809\pi$
$433$	0.155714	0.00748312	0.00374156	+	0.999993i	$0.498809\pi$
$434$	−12.7877	−0.613831
$435$	−2.89968	−0.139029
$436$	−8.48363	−0.406292
$437$	−20.1850	−0.965579
$438$	27.8774	1.33203
$439$	23.1300	1.10394	0.551968	−	0.833865i	$-0.313877\pi$
$439$	23.1300	1.10394	0.551968	+	0.833865i	$0.313877\pi$
$440$	11.7906	0.562095
$441$	−12.5886	−0.599459
$442$	−5.42127	−0.257864
$443$	12.5268	0.595168	0.297584	−	0.954696i	$-0.403819\pi$
$443$	12.5268	0.595168	0.297584	+	0.954696i	$0.403819\pi$
$444$	−15.7110	−0.745613
$445$	−1.35541	−0.0642527
$446$	20.0777	0.950708
$447$	30.1367	1.42542
$448$	−15.4088	−0.727997
$449$	−38.0487	−1.79563	−0.897814	−	0.440375i	$-0.854846\pi$
$449$	−38.0487	−1.79563	−0.897814	+	0.440375i	$0.854846\pi$
$450$	20.5781	0.970063
$451$	−15.6056	−0.734840
$452$	1.72074	0.0809366
$453$	−19.1185	−0.898264
$454$	−24.3129	−1.14106
$455$	5.75825	0.269951
$456$	−68.0900	−3.18861
$457$	25.4956	1.19263	0.596317	−	0.802749i	$-0.296630\pi$
$457$	25.4956	1.19263	0.596317	+	0.802749i	$0.296630\pi$
$458$	−1.09552	−0.0511905
$459$	4.93075	0.230147
$460$	1.58858	0.0740677
$461$	22.5869	1.05198	0.525988	−	0.850492i	$-0.323696\pi$
$461$	22.5869	1.05198	0.525988	+	0.850492i	$0.323696\pi$
$462$	−31.3566	−1.45884
$463$	42.2153	1.96191	0.980956	−	0.194232i	$-0.0622214\pi$
$463$	42.2153	1.96191	0.980956	+	0.194232i	$0.0622214\pi$
$464$	−2.02741	−0.0941203
$465$	11.6896	0.542092
$466$	−10.8664	−0.503376
$467$	4.29006	0.198520	0.0992601	−	0.995062i	$-0.468352\pi$
$467$	4.29006	0.198520	0.0992601	+	0.995062i	$0.468352\pi$
$468$	15.8167	0.731128
$469$	−21.3996	−0.988141
$470$	−4.79553	−0.221201
$471$	65.8145	3.03257
$472$	4.78180	0.220100
$473$	−31.3381	−1.44093
$474$	−7.95376	−0.365328
$475$	−37.0194	−1.69857
$476$	−2.41540	−0.110710
$477$	−4.09112	−0.187320
$478$	−5.44358	−0.248984
$479$	−7.74802	−0.354016	−0.177008	−	0.984209i	$-0.556642\pi$
$479$	−7.74802	−0.354016	−0.177008	+	0.984209i	$0.556642\pi$
$480$	9.04342	0.412774
$481$	25.2409	1.15088
$482$	24.1601	1.10046
$483$	−13.5236	−0.615343
$484$	−16.8353	−0.765241
$485$	0.197326	0.00896010
$486$	−20.0913	−0.911358
$487$	3.12687	0.141692	0.0708459	−	0.997487i	$-0.477430\pi$
$487$	3.12687	0.141692	0.0708459	+	0.997487i	$0.477430\pi$
$488$	−24.1026	−1.09107
$489$	−1.82699	−0.0826193
$490$	2.14059	0.0967022
$491$	−17.8547	−0.805771	−0.402886	−	0.915250i	$-0.631993\pi$
$491$	−17.8547	−0.805771	−0.402886	+	0.915250i	$0.631993\pi$
$492$	−7.09264	−0.319761
$493$	−1.95411	−0.0880085
$494$	34.1738	1.53755
$495$	17.0230	0.765127
$496$	8.17318	0.366987
$497$	26.2031	1.17537
$498$	−43.7071	−1.95856
$499$	2.04004	0.0913246	0.0456623	−	0.998957i	$-0.485460\pi$
$499$	2.04004	0.0913246	0.0456623	+	0.998957i	$0.485460\pi$
$500$	6.15778	0.275385
$501$	35.9265	1.60508
$502$	19.0995	0.852452
$503$	7.07972	0.315669	0.157835	−	0.987466i	$-0.449549\pi$
$503$	7.07972	0.315669	0.157835	+	0.987466i	$0.449549\pi$
$504$	−27.0924	−1.20679
$505$	−12.1716	−0.541631
$506$	13.8978	0.617832
$507$	−7.45430	−0.331057
$508$	−9.27621	−0.411565
$509$	17.9368	0.795037	0.397518	−	0.917594i	$-0.369871\pi$
$509$	17.9368	0.795037	0.397518	+	0.917594i	$0.369871\pi$
$510$	−2.65184	−0.117426
$511$	−19.9544	−0.882732
$512$	14.5697	0.643897
$513$	−31.0817	−1.37229
$514$	−31.8545	−1.40504
$515$	4.57311	0.201515
$516$	−14.2429	−0.627010
$517$	34.9318	1.53630
$518$	−13.5066	−0.593445
$519$	49.6491	2.17935
$520$	−8.60918	−0.377538
$521$	−3.19375	−0.139921	−0.0699603	−	0.997550i	$-0.522287\pi$
$521$	−3.19375	−0.139921	−0.0699603	+	0.997550i	$0.522287\pi$
$522$	−6.84726	−0.299696
$523$	−15.7713	−0.689630	−0.344815	−	0.938671i	$-0.612058\pi$
$523$	−15.7713	−0.689630	−0.344815	+	0.938671i	$0.612058\pi$
$524$	12.6841	0.554106
$525$	−24.8023	−1.08246
$526$	11.7868	0.513931
$527$	7.87765	0.343156
$528$	20.0413	0.872187
$529$	−17.0061	−0.739397
$530$	0.695662	0.0302176
$531$	6.90386	0.299602
$532$	15.2258	0.660123
$533$	11.3948	0.493563
$534$	−5.38935	−0.233220
$535$	4.53342	0.195997
$536$	31.9946	1.38196
$537$	−58.8001	−2.53741
$538$	1.61175	0.0694873
$539$	−15.5926	−0.671621
$540$	2.44615	0.105266
$541$	28.1775	1.21144	0.605722	−	0.795676i	$-0.292884\pi$
$541$	28.1775	1.21144	0.605722	+	0.795676i	$0.292884\pi$
$542$	24.6566	1.05909
$543$	−2.08073	−0.0892927
$544$	6.09439	0.261295
$545$	6.66696	0.285581
$546$	22.8958	0.979848
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	1.99279	0.0851280
$549$	−34.7988	−1.48517
$550$	25.4886	1.08684
$551$	12.3180	0.524764
$552$	20.2191	0.860582
$553$	5.69324	0.242101
$554$	−14.9068	−0.633331
$555$	12.3467	0.524088
$556$	17.8816	0.758348
$557$	−11.6421	−0.493290	−0.246645	−	0.969106i	$-0.579328\pi$
$557$	−11.6421	−0.493290	−0.246645	+	0.969106i	$0.579328\pi$
$558$	27.6036	1.16855
$559$	22.8822	0.967815
$560$	1.96938	0.0832214
$561$	19.3167	0.815550
$562$	−23.7090	−1.00010
$563$	35.1631	1.48195	0.740974	−	0.671534i	$-0.234364\pi$
$563$	35.1631	1.48195	0.740974	+	0.671534i	$0.234364\pi$
$564$	15.8763	0.668511
$565$	−1.35226	−0.0568899
$566$	24.0047	1.00899
$567$	5.92417	0.248792
$568$	−39.1764	−1.64380
$569$	−5.54994	−0.232665	−0.116333	−	0.993210i	$-0.537114\pi$
$569$	−5.54994	−0.232665	−0.116333	+	0.993210i	$0.537114\pi$
$570$	16.7163	0.700168
$571$	−12.2975	−0.514633	−0.257317	−	0.966327i	$-0.582838\pi$
$571$	−12.2975	−0.514633	−0.257317	+	0.966327i	$0.582838\pi$
$572$	19.5910	0.819141
$573$	9.58105	0.400254
$574$	−6.09745	−0.254502
$575$	10.9928	0.458431
$576$	33.2614	1.38589
$577$	−21.7654	−0.906105	−0.453052	−	0.891484i	$-0.649665\pi$
$577$	−21.7654	−0.906105	−0.453052	+	0.891484i	$0.649665\pi$
$578$	15.9723	0.664360
$579$	24.3160	1.01054
$580$	−0.969436	−0.0402536
$581$	31.2852	1.29793
$582$	0.784599	0.0325227
$583$	−5.06737	−0.209869
$584$	29.8339	1.23454
$585$	−12.4297	−0.513907
$586$	26.2396	1.08395
$587$	−1.32577	−0.0547206	−0.0273603	−	0.999626i	$-0.508710\pi$
$587$	−1.32577	−0.0547206	−0.0273603	+	0.999626i	$0.508710\pi$
$588$	−7.08672	−0.292252
$589$	−49.6579	−2.04612
$590$	−1.17394	−0.0483305
$591$	54.8120	2.25467
$592$	8.63262	0.354799
$593$	−0.00527691	−0.000216697 0	−0.000108348	−	1.00000i	$-0.500034\pi$
$593$	−0.00527691	−0.000216697 0	−0.000108348		1.00000i	$0.500034\pi$
$594$	21.4004	0.878068
$595$	1.89817	0.0778174
$596$	10.0755	0.412707
$597$	−10.1298	−0.414584
$598$	−10.1478	−0.414974
$599$	−26.4628	−1.08124	−0.540620	−	0.841267i	$-0.681810\pi$
$599$	−26.4628	−1.08124	−0.540620	+	0.841267i	$0.681810\pi$
$600$	37.0820	1.51386
$601$	−17.3745	−0.708719	−0.354360	−	0.935109i	$-0.615301\pi$
$601$	−17.3745	−0.708719	−0.354360	+	0.935109i	$0.615301\pi$
$602$	−12.2445	−0.499047
$603$	46.1931	1.88113
$604$	−6.39178	−0.260078
$605$	13.2302	0.537884
$606$	−48.3964	−1.96597
$607$	−28.3811	−1.15195	−0.575977	−	0.817466i	$-0.695378\pi$
$607$	−28.3811	−1.15195	−0.575977	+	0.817466i	$0.695378\pi$
$608$	−38.4168	−1.55801
$609$	8.25281	0.334421
$610$	5.91725	0.239582
$611$	−25.5063	−1.03187
$612$	5.21388	0.210759
$613$	−31.8417	−1.28607	−0.643036	−	0.765836i	$-0.722326\pi$
$613$	−31.8417	−1.28607	−0.643036	+	0.765836i	$0.722326\pi$
$614$	15.2463	0.615292
$615$	5.57383	0.224758
$616$	−33.5573	−1.35206
$617$	−41.2687	−1.66141	−0.830707	−	0.556710i	$-0.812064\pi$
$617$	−41.2687	−1.66141	−0.830707	+	0.556710i	$0.812064\pi$
$618$	18.1834	0.731445
$619$	36.6519	1.47316	0.736582	−	0.676348i	$-0.236439\pi$
$619$	36.6519	1.47316	0.736582	+	0.676348i	$0.236439\pi$
$620$	3.90812	0.156954
$621$	9.22960	0.370371
$622$	−9.39311	−0.376630
$623$	3.85765	0.154554
$624$	−14.6336	−0.585814
$625$	17.6112	0.704450
$626$	4.76747	0.190546
$627$	−121.765	−4.86284
$628$	22.0034	0.878032
$629$	8.32048	0.331759
$630$	6.65125	0.264992
$631$	−33.4006	−1.32966	−0.664829	−	0.746996i	$-0.731495\pi$
$631$	−33.4006	−1.32966	−0.664829	+	0.746996i	$0.731495\pi$
$632$	−8.51199	−0.338589
$633$	−48.8715	−1.94247
$634$	7.72723	0.306887
$635$	7.28981	0.289287
$636$	−2.30308	−0.0913232
$637$	11.3853	0.451102
$638$	−8.48119	−0.335773
$639$	−56.5620	−2.23756
$640$	0.998852	0.0394831
$641$	6.94918	0.274476	0.137238	−	0.990538i	$-0.456177\pi$
$641$	6.94918	0.274476	0.137238	+	0.990538i	$0.456177\pi$
$642$	18.0256	0.711414
$643$	4.52617	0.178495	0.0892474	−	0.996009i	$-0.471554\pi$
$643$	4.52617	0.178495	0.0892474	+	0.996009i	$0.471554\pi$
$644$	−4.52126	−0.178163
$645$	11.1930	0.440723
$646$	11.2652	0.443222
$647$	25.3439	0.996371	0.498185	−	0.867071i	$-0.334000\pi$
$647$	25.3439	0.996371	0.498185	+	0.867071i	$0.334000\pi$
$648$	−8.85725	−0.347946
$649$	8.55130	0.335668
$650$	−18.6111	−0.729987
$651$	−33.2698	−1.30395
$652$	−0.610808	−0.0239211
$653$	−8.49304	−0.332358	−0.166179	−	0.986096i	$-0.553143\pi$
$653$	−8.49304	−0.332358	−0.166179	+	0.986096i	$0.553143\pi$
$654$	26.5089	1.03658
$655$	−9.96791	−0.389478
$656$	3.89713	0.152157
$657$	43.0735	1.68046
$658$	13.6486	0.532078
$659$	18.2273	0.710036	0.355018	−	0.934859i	$-0.384475\pi$
$659$	18.2273	0.710036	0.355018	+	0.934859i	$0.384475\pi$
$660$	9.58304	0.373019
$661$	−16.2494	−0.632027	−0.316013	−	0.948755i	$-0.602344\pi$
$661$	−16.2494	−0.632027	−0.316013	+	0.948755i	$0.602344\pi$
$662$	24.6382	0.957591
$663$	−14.1045	−0.547774
$664$	−46.7746	−1.81521
$665$	−11.9654	−0.463998
$666$	29.1553	1.12974
$667$	−3.65779	−0.141630
$668$	12.0111	0.464725
$669$	52.2362	2.01957
$670$	−7.85476	−0.303456
$671$	−43.1027	−1.66396
$672$	−25.7385	−0.992886
$673$	39.3776	1.51789	0.758947	−	0.651153i	$-0.225714\pi$
$673$	39.3776	1.51789	0.758947	+	0.651153i	$0.225714\pi$
$674$	−26.1832	−1.00854
$675$	16.9271	0.651526
$676$	−2.49216	−0.0958522
$677$	−39.4458	−1.51602	−0.758012	−	0.652241i	$-0.773829\pi$
$677$	−39.4458	−1.51602	−0.758012	+	0.652241i	$0.773829\pi$
$678$	−5.37680	−0.206495
$679$	−0.561610	−0.0215526
$680$	−2.83796	−0.108831
$681$	−63.2547	−2.42393
$682$	34.1905	1.30922
$683$	25.8506	0.989144	0.494572	−	0.869137i	$-0.335325\pi$
$683$	25.8506	0.989144	0.494572	+	0.869137i	$0.335325\pi$
$684$	−32.8664	−1.25668
$685$	−1.56606	−0.0598360
$686$	−20.9544	−0.800043
$687$	−2.85022	−0.108743
$688$	7.82595	0.298362
$689$	3.70006	0.140961
$690$	−4.96384	−0.188970
$691$	−34.6845	−1.31946	−0.659729	−	0.751503i	$-0.729329\pi$
$691$	−34.6845	−1.31946	−0.659729	+	0.751503i	$0.729329\pi$
$692$	16.5989	0.630997
$693$	−48.4493	−1.84044
$694$	−11.6349	−0.441656
$695$	−14.0524	−0.533039
$696$	−12.3388	−0.467701
$697$	3.75622	0.142277
$698$	−35.8393	−1.35654
$699$	−28.2711	−1.06931
$700$	−8.29202	−0.313409
$701$	−38.7984	−1.46540	−0.732698	−	0.680553i	$-0.761739\pi$
$701$	−38.7984	−1.46540	−0.732698	+	0.680553i	$0.761739\pi$
$702$	−15.6260	−0.589764
$703$	−52.4493	−1.97816
$704$	41.1984	1.55272
$705$	−12.4765	−0.469893
$706$	−19.2101	−0.722982
$707$	34.6418	1.30284
$708$	3.88650	0.146064
$709$	−40.9056	−1.53624	−0.768121	−	0.640305i	$-0.778808\pi$
$709$	−40.9056	−1.53624	−0.768121	+	0.640305i	$0.778808\pi$
$710$	9.61790	0.360953
$711$	−12.2894	−0.460889
$712$	−5.76759	−0.216150
$713$	14.7458	0.552233
$714$	7.54744	0.282456
$715$	−15.3958	−0.575770
$716$	−19.6583	−0.734667
$717$	−14.1626	−0.528910
$718$	−17.6102	−0.657206
$719$	4.65393	0.173562	0.0867812	−	0.996227i	$-0.472342\pi$
$719$	4.65393	0.173562	0.0867812	+	0.996227i	$0.472342\pi$
$720$	−4.25109	−0.158429
$721$	−13.0156	−0.484725
$722$	−51.1628	−1.90408
$723$	62.8572	2.33768
$724$	−0.695640	−0.0258533
$725$	−6.70840	−0.249144
$726$	52.6055	1.95237
$727$	8.00848	0.297018	0.148509	−	0.988911i	$-0.452553\pi$
$727$	8.00848	0.297018	0.148509	+	0.988911i	$0.452553\pi$
$728$	24.5027	0.908129
$729$	−43.5266	−1.61210
$730$	−7.32431	−0.271085
$731$	7.54298	0.278987
$732$	−19.5898	−0.724061
$733$	20.7022	0.764652	0.382326	−	0.924028i	$-0.375123\pi$
$733$	20.7022	0.764652	0.382326	+	0.924028i	$0.375123\pi$
$734$	−21.9179	−0.809005
$735$	5.56918	0.205422
$736$	11.4078	0.420495
$737$	57.2160	2.10758
$738$	13.1619	0.484497
$739$	10.3160	0.379479	0.189740	−	0.981834i	$-0.439236\pi$
$739$	10.3160	0.379479	0.189740	+	0.981834i	$0.439236\pi$
$740$	4.12781	0.151741
$741$	88.9098	3.26618
$742$	−1.97993	−0.0726855
$743$	−27.5334	−1.01010	−0.505051	−	0.863090i	$-0.668526\pi$
$743$	−27.5334	−1.01010	−0.505051	+	0.863090i	$0.668526\pi$
$744$	49.7418	1.82362
$745$	−7.91790	−0.290090
$746$	−8.95481	−0.327859
$747$	−67.5322	−2.47087
$748$	6.45804	0.236129
$749$	−12.9026	−0.471451
$750$	−19.2413	−0.702593
$751$	30.6714	1.11922	0.559608	−	0.828758i	$-0.310952\pi$
$751$	30.6714	1.11922	0.559608	+	0.828758i	$0.310952\pi$
$752$	−8.72340	−0.318110
$753$	49.6911	1.81084
$754$	6.19273	0.225526
$755$	5.02305	0.182808
$756$	−6.96202	−0.253206
$757$	29.0720	1.05664	0.528320	−	0.849046i	$-0.322822\pi$
$757$	29.0720	1.05664	0.528320	+	0.849046i	$0.322822\pi$
$758$	25.1484	0.913431
$759$	36.1578	1.31245
$760$	17.8895	0.648920
$761$	−46.1332	−1.67233	−0.836163	−	0.548481i	$-0.815206\pi$
$761$	−46.1332	−1.67233	−0.836163	+	0.548481i	$0.815206\pi$
$762$	28.9855	1.05003
$763$	−18.9749	−0.686937
$764$	3.20318	0.115887
$765$	−4.09738	−0.148141
$766$	29.5090	1.06620
$767$	−6.24393	−0.225455
$768$	45.1844	1.63045
$769$	39.6177	1.42865	0.714326	−	0.699813i	$-0.246733\pi$
$769$	39.6177	1.42865	0.714326	+	0.699813i	$0.246733\pi$
$770$	8.23842	0.296892
$771$	−82.8758	−2.98470
$772$	8.12945	0.292585
$773$	−2.07610	−0.0746722	−0.0373361	−	0.999303i	$-0.511887\pi$
$773$	−2.07610	−0.0746722	−0.0373361	+	0.999303i	$0.511887\pi$
$774$	26.4309	0.950038
$775$	27.0438	0.971442
$776$	0.839665	0.0301422
$777$	−35.1400	−1.26064
$778$	−21.1774	−0.759245
$779$	−23.6779	−0.848348
$780$	−6.99728	−0.250543
$781$	−70.0591	−2.50691
$782$	−3.34515	−0.119622
$783$	−5.63241	−0.201286
$784$	3.89388	0.139067
$785$	−17.2916	−0.617165
$786$	−39.6340	−1.41370
$787$	−7.33613	−0.261505	−0.130752	−	0.991415i	$-0.541739\pi$
$787$	−7.33613	−0.261505	−0.130752	+	0.991415i	$0.541739\pi$
$788$	18.3250	0.652802
$789$	30.6658	1.09173
$790$	2.08972	0.0743487
$791$	3.84867	0.136843
$792$	72.4367	2.57393
$793$	31.4724	1.11762
$794$	−9.81107	−0.348182
$795$	1.80990	0.0641907
$796$	−3.38663	−0.120036
$797$	−19.2052	−0.680283	−0.340141	−	0.940374i	$-0.610475\pi$
$797$	−19.2052	−0.680283	−0.340141	+	0.940374i	$0.610475\pi$
$798$	−47.5763	−1.68418
$799$	−8.40797	−0.297453
$800$	20.9219	0.739701
$801$	−8.32712	−0.294224
$802$	−8.72641	−0.308140
$803$	53.3520	1.88275
$804$	26.0042	0.917098
$805$	3.55308	0.125230
$806$	−24.9650	−0.879354
$807$	4.19327	0.147610
$808$	−51.7931	−1.82207
$809$	15.0621	0.529554	0.264777	−	0.964310i	$-0.414702\pi$
$809$	15.0621	0.529554	0.264777	+	0.964310i	$0.414702\pi$
$810$	2.17448	0.0764034
$811$	−3.10727	−0.109111	−0.0545554	−	0.998511i	$-0.517374\pi$
$811$	−3.10727	−0.109111	−0.0545554	+	0.998511i	$0.517374\pi$
$812$	2.75912	0.0968262
$813$	64.1491	2.24981
$814$	36.1125	1.26574
$815$	0.480010	0.0168140
$816$	−4.82388	−0.168870
$817$	−47.5482	−1.66350
$818$	9.44720	0.330314
$819$	35.3764	1.23615
$820$	1.86347	0.0650752
$821$	−39.3045	−1.37174	−0.685869	−	0.727725i	$-0.740577\pi$
$821$	−39.3045	−1.37174	−0.685869	+	0.727725i	$0.740577\pi$
$822$	−6.22691	−0.217188
$823$	−24.7300	−0.862033	−0.431017	−	0.902344i	$-0.641845\pi$
$823$	−24.7300	−0.862033	−0.431017	+	0.902344i	$0.641845\pi$
$824$	19.4596	0.677908
$825$	66.3137	2.30875
$826$	3.34117	0.116254
$827$	−37.2644	−1.29581	−0.647905	−	0.761721i	$-0.724355\pi$
$827$	−37.2644	−1.29581	−0.647905	+	0.761721i	$0.724355\pi$
$828$	9.75958	0.339169
$829$	52.3014	1.81650	0.908251	−	0.418425i	$-0.137418\pi$
$829$	52.3014	1.81650	0.908251	+	0.418425i	$0.137418\pi$
$830$	11.4833	0.398591
$831$	−38.7831	−1.34537
$832$	−30.0819	−1.04290
$833$	3.75309	0.130037
$834$	−55.8748	−1.93478
$835$	−9.43908	−0.326653
$836$	−40.7092	−1.40796
$837$	22.7061	0.784838
$838$	22.1747	0.766011
$839$	18.0759	0.624050	0.312025	−	0.950074i	$-0.398993\pi$
$839$	18.0759	0.624050	0.312025	+	0.950074i	$0.398993\pi$
$840$	11.9856	0.413543
$841$	−26.7678	−0.923028
$842$	−17.0464	−0.587459
$843$	−61.6836	−2.12450
$844$	−16.3389	−0.562410
$845$	1.95849	0.0673741
$846$	−29.4618	−1.01292
$847$	−37.6546	−1.29383
$848$	1.26546	0.0434560
$849$	62.4529	2.14338
$850$	−6.13503	−0.210430
$851$	15.5747	0.533892
$852$	−31.8414	−1.09087
$853$	2.26471	0.0775422	0.0387711	−	0.999248i	$-0.487656\pi$
$853$	2.26471	0.0775422	0.0387711	+	0.999248i	$0.487656\pi$
$854$	−16.8411	−0.576291
$855$	25.8284	0.883314
$856$	19.2907	0.659343
$857$	−34.0377	−1.16271	−0.581353	−	0.813652i	$-0.697476\pi$
$857$	−34.0377	−1.16271	−0.581353	+	0.813652i	$0.697476\pi$
$858$	−61.2162	−2.08989
$859$	41.4218	1.41329	0.706646	−	0.707567i	$-0.250207\pi$
$859$	41.4218	1.41329	0.706646	+	0.707567i	$0.250207\pi$
$860$	3.74209	0.127604
$861$	−15.8637	−0.540634
$862$	−17.9884	−0.612686
$863$	27.5129	0.936551	0.468275	−	0.883583i	$-0.344876\pi$
$863$	27.5129	0.936551	0.468275	+	0.883583i	$0.344876\pi$
$864$	17.5661	0.597612
$865$	−13.0445	−0.443525
$866$	−0.162669	−0.00552773
$867$	41.5551	1.41128
$868$	−11.1229	−0.377537
$869$	−15.2220	−0.516371
$870$	3.02921	0.102700
$871$	−41.7775	−1.41558
$872$	28.3694	0.960709
$873$	1.21229	0.0410298
$874$	21.0866	0.713266
$875$	13.7728	0.465605
$876$	24.2481	0.819267
$877$	24.8045	0.837589	0.418794	−	0.908081i	$-0.362453\pi$
$877$	24.8045	0.837589	0.418794	+	0.908081i	$0.362453\pi$
$878$	−24.1632	−0.815469
$879$	68.2675	2.30261
$880$	−5.26552	−0.177501
$881$	25.2629	0.851128	0.425564	−	0.904928i	$-0.360076\pi$
$881$	25.2629	0.851128	0.425564	+	0.904928i	$0.360076\pi$
$882$	13.1510	0.442816
$883$	−19.5417	−0.657631	−0.328815	−	0.944394i	$-0.606649\pi$
$883$	−19.5417	−0.657631	−0.328815	+	0.944394i	$0.606649\pi$
$884$	−4.71549	−0.158599
$885$	−3.05425	−0.102667
$886$	−13.0864	−0.439646
$887$	−34.5222	−1.15914	−0.579571	−	0.814922i	$-0.696780\pi$
$887$	−34.5222	−1.15914	−0.579571	+	0.814922i	$0.696780\pi$
$888$	52.5380	1.76306
$889$	−20.7476	−0.695852
$890$	1.41596	0.0474630
$891$	−15.8394	−0.530641
$892$	17.4639	0.584733
$893$	53.0009	1.77361
$894$	−31.4829	−1.05295
$895$	15.4487	0.516394
$896$	−2.84284	−0.0949727
$897$	−26.4015	−0.881520
$898$	39.7483	1.32642
$899$	−8.99867	−0.300122
$900$	17.8991	0.596637
$901$	1.21970	0.0406341
$902$	16.3027	0.542821
$903$	−31.8564	−1.06011
$904$	−5.75416	−0.191381
$905$	0.546677	0.0181721
$906$	19.9725	0.663541
$907$	48.4647	1.60924	0.804622	−	0.593787i	$-0.202368\pi$
$907$	48.4647	1.60924	0.804622	+	0.593787i	$0.202368\pi$
$908$	−21.1476	−0.701809
$909$	−74.7777	−2.48022
$910$	−6.01547	−0.199411
$911$	14.4271	0.477990	0.238995	−	0.971021i	$-0.423182\pi$
$911$	14.4271	0.477990	0.238995	+	0.971021i	$0.423182\pi$
$912$	30.4080	1.00691
$913$	−83.6471	−2.76832
$914$	−26.6345	−0.880990
$915$	15.3949	0.508939
$916$	−0.952900	−0.0314847
$917$	28.3698	0.936852
$918$	−5.15100	−0.170008
$919$	14.9071	0.491741	0.245871	−	0.969303i	$-0.420926\pi$
$919$	14.9071	0.491741	0.245871	+	0.969303i	$0.420926\pi$
$920$	−5.31222	−0.175139
$921$	39.6663	1.30705
$922$	−23.5958	−0.777088
$923$	51.1553	1.68380
$924$	−27.2744	−0.897261
$925$	28.5640	0.939179
$926$	−44.1010	−1.44925
$927$	28.0954	0.922772
$928$	−6.96164	−0.228527
$929$	−19.0507	−0.625033	−0.312517	−	0.949912i	$-0.601172\pi$
$929$	−19.0507	−0.625033	−0.312517	+	0.949912i	$0.601172\pi$
$930$	−12.2118	−0.400439
$931$	−23.6581	−0.775364
$932$	−9.45172	−0.309601
$933$	−24.4380	−0.800066
$934$	−4.48169	−0.146645
$935$	−5.07512	−0.165974
$936$	−52.8914	−1.72881
$937$	1.62214	0.0529931	0.0264965	−	0.999649i	$-0.491565\pi$
$937$	1.62214	0.0529931	0.0264965	+	0.999649i	$0.491565\pi$
$938$	22.3555	0.729933
$939$	12.4035	0.404773
$940$	−4.17121	−0.136050
$941$	−1.42371	−0.0464115	−0.0232058	−	0.999731i	$-0.507387\pi$
$941$	−1.42371	−0.0464115	−0.0232058	+	0.999731i	$0.507387\pi$
$942$	−68.7544	−2.24014
$943$	7.03107	0.228963
$944$	−2.13548	−0.0695041
$945$	5.47118	0.177977
$946$	32.7379	1.06440
$947$	−42.2934	−1.37435	−0.687175	−	0.726492i	$-0.741150\pi$
$947$	−42.2934	−1.37435	−0.687175	+	0.726492i	$0.741150\pi$
$948$	−6.91828	−0.224695
$949$	−38.9562	−1.26457
$950$	38.6730	1.25472
$951$	20.1039	0.651914
$952$	8.07714	0.261782
$953$	−30.0275	−0.972686	−0.486343	−	0.873768i	$-0.661670\pi$
$953$	−30.0275	−0.972686	−0.486343	+	0.873768i	$0.661670\pi$
$954$	4.27387	0.138372
$955$	−2.51726	−0.0814565
$956$	−4.73490	−0.153137
$957$	−22.0655	−0.713276
$958$	8.09412	0.261509
$959$	4.45717	0.143930
$960$	−14.7147	−0.474916
$961$	5.27662	0.170213
$962$	−26.3683	−0.850149
$963$	27.8515	0.897502
$964$	21.0147	0.676839
$965$	−6.38862	−0.205657
$966$	14.1276	0.454549
$967$	−26.6788	−0.857933	−0.428966	−	0.903320i	$-0.641122\pi$
$967$	−26.6788	−0.857933	−0.428966	+	0.903320i	$0.641122\pi$
$968$	56.2975	1.80947
$969$	29.3085	0.941526
$970$	−0.206140	−0.00661876
$971$	11.1042	0.356351	0.178175	−	0.983999i	$-0.442981\pi$
$971$	11.1042	0.356351	0.178175	+	0.983999i	$0.442981\pi$
$972$	−17.4756	−0.560531
$973$	39.9947	1.28217
$974$	−3.26654	−0.104667
$975$	−48.4205	−1.55070
$976$	10.7639	0.344543
$977$	16.4245	0.525467	0.262733	−	0.964868i	$-0.415376\pi$
$977$	16.4245	0.525467	0.262733	+	0.964868i	$0.415376\pi$
$978$	1.90860	0.0610303
$979$	−10.3142	−0.329643
$980$	1.86192	0.0594767
$981$	40.9591	1.30772
$982$	18.6523	0.595217
$983$	8.61161	0.274668	0.137334	−	0.990525i	$-0.456147\pi$
$983$	8.61161	0.274668	0.137334	+	0.990525i	$0.456147\pi$
$984$	23.7179	0.756099
$985$	−14.4009	−0.458852
$986$	2.04139	0.0650112
$987$	35.5096	1.13028
$988$	29.7248	0.945671
$989$	14.1193	0.448967
$990$	−17.7834	−0.565194
$991$	30.1651	0.958227	0.479114	−	0.877753i	$-0.340958\pi$
$991$	30.1651	0.958227	0.479114	+	0.877753i	$0.340958\pi$
$992$	28.0647	0.891055
$993$	64.1012	2.03419
$994$	−27.3736	−0.868238
$995$	2.66142	0.0843728
$996$	−38.0170	−1.20461
$997$	6.84091	0.216654	0.108327	−	0.994115i	$-0.465451\pi$
$997$	6.84091	0.216654	0.108327	+	0.994115i	$0.465451\pi$
$998$	−2.13116	−0.0674608
$999$	23.9825	0.758772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.b.1.7	✓	18
3.2	odd	2		4923.2.a.l.1.12		18
4.3	odd	2		8752.2.a.s.1.15		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.b.1.7	✓	18	1.1	even	1	trivial
4923.2.a.l.1.12		18	3.2	odd	2
8752.2.a.s.1.15		18	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-1.04467 q^{2} -2.71791 q^{3} -0.908666 q^{4} +0.714085 q^{5} +2.83932 q^{6} -2.03236 q^{7} +3.03859 q^{8} +4.38705 q^{9} +O(q^{10})\)	\(q-1.04467 q^{2} -2.71791 q^{3} -0.908666 q^{4} +0.714085 q^{5} +2.83932 q^{6} -2.03236 q^{7} +3.03859 q^{8} +4.38705 q^{9} -0.745983 q^{10} +5.43392 q^{11} +2.46968 q^{12} -3.96770 q^{13} +2.12315 q^{14} -1.94082 q^{15} -1.35699 q^{16} -1.30793 q^{17} -4.58302 q^{18} +8.24470 q^{19} -0.648865 q^{20} +5.52379 q^{21} -5.67665 q^{22} -2.44824 q^{23} -8.25864 q^{24} -4.49008 q^{25} +4.14494 q^{26} -3.76989 q^{27} +1.84674 q^{28} +1.49405 q^{29} +2.02752 q^{30} -6.02301 q^{31} -4.65958 q^{32} -14.7689 q^{33} +1.36635 q^{34} -1.45128 q^{35} -3.98637 q^{36} -6.36158 q^{37} -8.61299 q^{38} +10.7839 q^{39} +2.16982 q^{40} -2.87189 q^{41} -5.77053 q^{42} -5.76713 q^{43} -4.93762 q^{44} +3.13273 q^{45} +2.55760 q^{46} +6.42848 q^{47} +3.68819 q^{48} -2.86949 q^{49} +4.69065 q^{50} +3.55483 q^{51} +3.60532 q^{52} -0.932545 q^{53} +3.93829 q^{54} +3.88028 q^{55} -6.17553 q^{56} -22.4084 q^{57} -1.56079 q^{58} +1.57369 q^{59} +1.76356 q^{60} -7.93215 q^{61} +6.29205 q^{62} -8.91609 q^{63} +7.58170 q^{64} -2.83328 q^{65} +15.4286 q^{66} +10.5294 q^{67} +1.18847 q^{68} +6.65410 q^{69} +1.51611 q^{70} -12.8929 q^{71} +13.3305 q^{72} +9.81833 q^{73} +6.64575 q^{74} +12.2037 q^{75} -7.49168 q^{76} -11.0437 q^{77} -11.2656 q^{78} -2.80129 q^{79} -0.969009 q^{80} -2.91492 q^{81} +3.00017 q^{82} -15.3935 q^{83} -5.01928 q^{84} -0.933971 q^{85} +6.02474 q^{86} -4.06069 q^{87} +16.5115 q^{88} -1.89811 q^{89} -3.27267 q^{90} +8.06382 q^{91} +2.22463 q^{92} +16.3700 q^{93} -6.71563 q^{94} +5.88742 q^{95} +12.6643 q^{96} +0.276333 q^{97} +2.99767 q^{98} +23.8389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9} - 5 q^{10} + 2 q^{11} - 32 q^{12} - 25 q^{13} - 7 q^{14} + 9 q^{15} + 8 q^{16} - 30 q^{17} - 10 q^{18} + 4 q^{19} - 41 q^{20} - 16 q^{21} - 24 q^{22} - 26 q^{23} - 12 q^{24} + 31 q^{25} - 18 q^{26} - 37 q^{27} - 16 q^{28} - 18 q^{29} + 8 q^{30} - 5 q^{31} - 28 q^{32} - 10 q^{33} + 5 q^{34} - 9 q^{35} + 31 q^{36} - 18 q^{37} - 45 q^{38} + 7 q^{39} + 7 q^{40} - 17 q^{41} + 4 q^{42} + 8 q^{43} + 12 q^{44} - 44 q^{45} + 30 q^{46} - 52 q^{47} - 7 q^{48} + 29 q^{49} + 13 q^{50} + 19 q^{51} - 14 q^{52} - 60 q^{53} + 11 q^{54} + 11 q^{55} + 7 q^{56} + 4 q^{57} + 14 q^{58} - 8 q^{59} + 86 q^{60} - 26 q^{61} + 4 q^{62} - q^{63} + 44 q^{64} - 6 q^{65} + 18 q^{66} + 12 q^{67} - 61 q^{68} - 38 q^{69} + 35 q^{70} - q^{71} + 28 q^{72} - 2 q^{73} + 16 q^{74} - 17 q^{75} + 66 q^{76} - 73 q^{77} + 115 q^{78} + 18 q^{79} - 32 q^{80} + 18 q^{81} + 44 q^{82} - 43 q^{83} + 41 q^{84} + 51 q^{85} + 4 q^{86} + 3 q^{87} - 17 q^{88} - 28 q^{89} + 58 q^{90} - q^{91} - 68 q^{92} - 60 q^{93} + 78 q^{94} - 18 q^{95} + 29 q^{96} - 34 q^{97} + 34 q^{98} + 15 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9 - 5 * q^10 + 2 * q^11 - 32 * q^12 - 25 * q^13 - 7 * q^14 + 9 * q^15 + 8 * q^16 - 30 * q^17 - 10 * q^18 + 4 * q^19 - 41 * q^20 - 16 * q^21 - 24 * q^22 - 26 * q^23 - 12 * q^24 + 31 * q^25 - 18 * q^26 - 37 * q^27 - 16 * q^28 - 18 * q^29 + 8 * q^30 - 5 * q^31 - 28 * q^32 - 10 * q^33 + 5 * q^34 - 9 * q^35 + 31 * q^36 - 18 * q^37 - 45 * q^38 + 7 * q^39 + 7 * q^40 - 17 * q^41 + 4 * q^42 + 8 * q^43 + 12 * q^44 - 44 * q^45 + 30 * q^46 - 52 * q^47 - 7 * q^48 + 29 * q^49 + 13 * q^50 + 19 * q^51 - 14 * q^52 - 60 * q^53 + 11 * q^54 + 11 * q^55 + 7 * q^56 + 4 * q^57 + 14 * q^58 - 8 * q^59 + 86 * q^60 - 26 * q^61 + 4 * q^62 - q^63 + 44 * q^64 - 6 * q^65 + 18 * q^66 + 12 * q^67 - 61 * q^68 - 38 * q^69 + 35 * q^70 - q^71 + 28 * q^72 - 2 * q^73 + 16 * q^74 - 17 * q^75 + 66 * q^76 - 73 * q^77 + 115 * q^78 + 18 * q^79 - 32 * q^80 + 18 * q^81 + 44 * q^82 - 43 * q^83 + 41 * q^84 + 51 * q^85 + 4 * q^86 + 3 * q^87 - 17 * q^88 - 28 * q^89 + 58 * q^90 - q^91 - 68 * q^92 - 60 * q^93 + 78 * q^94 - 18 * q^95 + 29 * q^96 - 34 * q^97 + 34 * q^98 + 15 * q^99

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