LMFDB - Embedded newform 349.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(1,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, 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("349.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 5 x^{16} - 14 x^{15} + 102 x^{14} + 26 x^{13} - 792 x^{12} + 474 x^{11} + 2887 x^{10} + \cdots - 4 $ x^17 - 5x^16 - 14x^15 + 102x^14 + 26x^13 - 792x^12 + 474x^11 + 2887x^10 - 3021x^9 - 4835x^8 + 6673x^7 + 2880x^6 - 5373x^5 - 164x^4 + 1075x^3 + 75x^2 - 41x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$0.695551$ of defining polynomial
Character	$\chi$	$=$	349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.695551 q^{2} +1.81098 q^{3} -1.51621 q^{4} +3.87525 q^{5} +1.25963 q^{6} +2.52014 q^{7} -2.44570 q^{8} +0.279648 q^{9} +O(q^{10})$	\(q+0.695551 q^{2} +1.81098 q^{3} -1.51621 q^{4} +3.87525 q^{5} +1.25963 q^{6} +2.52014 q^{7} -2.44570 q^{8} +0.279648 q^{9} +2.69543 q^{10} -1.66189 q^{11} -2.74582 q^{12} -4.41380 q^{13} +1.75289 q^{14} +7.01800 q^{15} +1.33131 q^{16} -0.598349 q^{17} +0.194509 q^{18} -4.17651 q^{19} -5.87569 q^{20} +4.56392 q^{21} -1.15593 q^{22} +3.57420 q^{23} -4.42912 q^{24} +10.0176 q^{25} -3.07002 q^{26} -4.92650 q^{27} -3.82106 q^{28} -0.938241 q^{29} +4.88138 q^{30} +6.86813 q^{31} +5.81740 q^{32} -3.00965 q^{33} -0.416182 q^{34} +9.76618 q^{35} -0.424004 q^{36} +8.17254 q^{37} -2.90497 q^{38} -7.99330 q^{39} -9.47771 q^{40} -10.5139 q^{41} +3.17444 q^{42} -6.61824 q^{43} +2.51978 q^{44} +1.08371 q^{45} +2.48603 q^{46} -12.6911 q^{47} +2.41097 q^{48} -0.648892 q^{49} +6.96774 q^{50} -1.08360 q^{51} +6.69224 q^{52} +0.697016 q^{53} -3.42663 q^{54} -6.44025 q^{55} -6.16351 q^{56} -7.56357 q^{57} -0.652594 q^{58} +6.97922 q^{59} -10.6408 q^{60} +2.61558 q^{61} +4.77713 q^{62} +0.704751 q^{63} +1.38367 q^{64} -17.1046 q^{65} -2.09337 q^{66} +1.81747 q^{67} +0.907223 q^{68} +6.47280 q^{69} +6.79287 q^{70} +7.78788 q^{71} -0.683935 q^{72} -8.36858 q^{73} +5.68441 q^{74} +18.1416 q^{75} +6.33246 q^{76} -4.18820 q^{77} -5.55974 q^{78} -3.75626 q^{79} +5.15916 q^{80} -9.76074 q^{81} -7.31294 q^{82} +9.81408 q^{83} -6.91986 q^{84} -2.31875 q^{85} -4.60332 q^{86} -1.69914 q^{87} +4.06449 q^{88} -9.86347 q^{89} +0.753772 q^{90} -11.1234 q^{91} -5.41923 q^{92} +12.4380 q^{93} -8.82730 q^{94} -16.1850 q^{95} +10.5352 q^{96} +12.2262 q^{97} -0.451337 q^{98} -0.464744 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) $ 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9} - 6 q^{10} + 39 q^{11} + 4 q^{12} - 6 q^{13} + 11 q^{14} + 12 q^{15} + 23 q^{16} + q^{17} + 7 q^{19} + 8 q^{20} - 3 q^{21} - q^{22} + 8 q^{23} - 21 q^{24} + 14 q^{25} + q^{26} + 9 q^{27} - 23 q^{28} + 9 q^{29} - 27 q^{30} - 2 q^{31} + 23 q^{32} - 5 q^{33} - 12 q^{34} + 16 q^{35} + 10 q^{36} - 7 q^{37} - 8 q^{38} - 39 q^{40} + 3 q^{41} - 30 q^{42} + q^{43} + 56 q^{44} - 21 q^{45} - q^{46} + 16 q^{47} - 31 q^{48} + 6 q^{49} - 5 q^{50} + 29 q^{51} - 37 q^{52} + 27 q^{53} - 36 q^{54} - 16 q^{55} + 14 q^{56} - 21 q^{57} - 44 q^{58} + 74 q^{59} - 27 q^{60} - 30 q^{61} - 18 q^{62} - 9 q^{63} - 17 q^{64} - 3 q^{65} - 66 q^{66} + 9 q^{67} - 51 q^{68} - 23 q^{69} - 77 q^{70} + 70 q^{71} - 55 q^{72} - 38 q^{73} + 26 q^{74} + 22 q^{75} - 50 q^{76} - 38 q^{77} - 75 q^{78} + 7 q^{79} - 28 q^{80} + 5 q^{81} - 56 q^{82} + 47 q^{83} - 69 q^{84} - 49 q^{85} + 17 q^{86} - 37 q^{87} - 30 q^{88} + 23 q^{89} - 64 q^{90} + 6 q^{91} + 17 q^{92} - 31 q^{93} - 40 q^{94} - 11 q^{95} - 49 q^{96} - 14 q^{97} + 5 q^{98} + 79 q^{99}+O(q^{100}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9 - 6 * q^10 + 39 * q^11 + 4 * q^12 - 6 * q^13 + 11 * q^14 + 12 * q^15 + 23 * q^16 + q^17 + 7 * q^19 + 8 * q^20 - 3 * q^21 - q^22 + 8 * q^23 - 21 * q^24 + 14 * q^25 + q^26 + 9 * q^27 - 23 * q^28 + 9 * q^29 - 27 * q^30 - 2 * q^31 + 23 * q^32 - 5 * q^33 - 12 * q^34 + 16 * q^35 + 10 * q^36 - 7 * q^37 - 8 * q^38 - 39 * q^40 + 3 * q^41 - 30 * q^42 + q^43 + 56 * q^44 - 21 * q^45 - q^46 + 16 * q^47 - 31 * q^48 + 6 * q^49 - 5 * q^50 + 29 * q^51 - 37 * q^52 + 27 * q^53 - 36 * q^54 - 16 * q^55 + 14 * q^56 - 21 * q^57 - 44 * q^58 + 74 * q^59 - 27 * q^60 - 30 * q^61 - 18 * q^62 - 9 * q^63 - 17 * q^64 - 3 * q^65 - 66 * q^66 + 9 * q^67 - 51 * q^68 - 23 * q^69 - 77 * q^70 + 70 * q^71 - 55 * q^72 - 38 * q^73 + 26 * q^74 + 22 * q^75 - 50 * q^76 - 38 * q^77 - 75 * q^78 + 7 * q^79 - 28 * q^80 + 5 * q^81 - 56 * q^82 + 47 * q^83 - 69 * q^84 - 49 * q^85 + 17 * q^86 - 37 * q^87 - 30 * q^88 + 23 * q^89 - 64 * q^90 + 6 * q^91 + 17 * q^92 - 31 * q^93 - 40 * q^94 - 11 * q^95 - 49 * q^96 - 14 * q^97 + 5 * q^98 + 79 * 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 $

$2$	0.695551	0.491829	0.245914	−	0.969292i	$-0.420912\pi$
$2$	0.695551	0.491829	0.245914	+	0.969292i	$0.420912\pi$
$3$	1.81098	1.04557	0.522785	−	0.852465i	$-0.324893\pi$
$3$	1.81098	1.04557	0.522785	+	0.852465i	$0.324893\pi$
$4$	−1.51621	−0.758105
$5$	3.87525	1.73307	0.866533	−	0.499120i	$-0.166343\pi$
$5$	3.87525	1.73307	0.866533	+	0.499120i	$0.166343\pi$
$6$	1.25963	0.514241
$7$	2.52014	0.952524	0.476262	−	0.879304i	$-0.341991\pi$
$7$	2.52014	0.952524	0.476262	+	0.879304i	$0.341991\pi$
$8$	−2.44570	−0.864686
$9$	0.279648	0.0932159
$10$	2.69543	0.852371
$11$	−1.66189	−0.501079	−0.250540	−	0.968106i	$-0.580608\pi$
$11$	−1.66189	−0.501079	−0.250540	+	0.968106i	$0.580608\pi$
$12$	−2.74582	−0.792651
$13$	−4.41380	−1.22417	−0.612083	−	0.790793i	$-0.709668\pi$
$13$	−4.41380	−1.22417	−0.612083	+	0.790793i	$0.709668\pi$
$14$	1.75289	0.468478
$15$	7.01800	1.81204
$16$	1.33131	0.332827
$17$	−0.598349	−0.145121	−0.0725605	−	0.997364i	$-0.523117\pi$
$17$	−0.598349	−0.145121	−0.0725605	+	0.997364i	$0.523117\pi$
$18$	0.194509	0.0458462
$19$	−4.17651	−0.958156	−0.479078	−	0.877772i	$-0.659029\pi$
$19$	−4.17651	−0.958156	−0.479078	+	0.877772i	$0.659029\pi$
$20$	−5.87569	−1.31385
$21$	4.56392	0.995930
$22$	−1.15593	−0.246445
$23$	3.57420	0.745271	0.372636	−	0.927978i	$-0.378454\pi$
$23$	3.57420	0.745271	0.372636	+	0.927978i	$0.378454\pi$
$24$	−4.42912	−0.904090
$25$	10.0176	2.00352
$26$	−3.07002	−0.602080
$27$	−4.92650	−0.948106
$28$	−3.82106	−0.722113
$29$	−0.938241	−0.174227	−0.0871135	−	0.996198i	$-0.527764\pi$
$29$	−0.938241	−0.174227	−0.0871135	+	0.996198i	$0.527764\pi$
$30$	4.88138	0.891213
$31$	6.86813	1.23355	0.616776	−	0.787139i	$-0.288438\pi$
$31$	6.86813	1.23355	0.616776	+	0.787139i	$0.288438\pi$
$32$	5.81740	1.02838
$33$	−3.00965	−0.523913
$34$	−0.416182	−0.0713746
$35$	9.76618	1.65079
$36$	−0.424004	−0.0706674
$37$	8.17254	1.34356	0.671778	−	0.740752i	$-0.265531\pi$
$37$	8.17254	1.34356	0.671778	+	0.740752i	$0.265531\pi$
$38$	−2.90497	−0.471249
$39$	−7.99330	−1.27995
$40$	−9.47771	−1.49856
$41$	−10.5139	−1.64199	−0.820996	−	0.570934i	$-0.806581\pi$
$41$	−10.5139	−1.64199	−0.820996	+	0.570934i	$0.806581\pi$
$42$	3.17444	0.489827
$43$	−6.61824	−1.00927	−0.504636	−	0.863332i	$-0.668373\pi$
$43$	−6.61824	−1.00927	−0.504636	+	0.863332i	$0.668373\pi$
$44$	2.51978	0.379871
$45$	1.08371	0.161549
$46$	2.48603	0.366546
$47$	−12.6911	−1.85119	−0.925593	−	0.378519i	$-0.876433\pi$
$47$	−12.6911	−1.85119	−0.925593	+	0.378519i	$0.876433\pi$
$48$	2.41097	0.347994
$49$	−0.648892	−0.0926989
$50$	6.96774	0.985387
$51$	−1.08360	−0.151734
$52$	6.69224	0.928047
$53$	0.697016	0.0957425	0.0478712	−	0.998854i	$-0.484756\pi$
$53$	0.697016	0.0957425	0.0478712	+	0.998854i	$0.484756\pi$
$54$	−3.42663	−0.466306
$55$	−6.44025	−0.868404
$56$	−6.16351	−0.823634
$57$	−7.56357	−1.00182
$58$	−0.652594	−0.0856898
$59$	6.97922	0.908617	0.454309	−	0.890844i	$-0.349886\pi$
$59$	6.97922	0.908617	0.454309	+	0.890844i	$0.349886\pi$
$60$	−10.6408	−1.37372
$61$	2.61558	0.334891	0.167446	−	0.985881i	$-0.446448\pi$
$61$	2.61558	0.334891	0.167446	+	0.985881i	$0.446448\pi$
$62$	4.77713	0.606696
$63$	0.704751	0.0887903
$64$	1.38367	0.172959
$65$	−17.1046	−2.12156
$66$	−2.09337	−0.257676
$67$	1.81747	0.222039	0.111020	−	0.993818i	$-0.464588\pi$
$67$	1.81747	0.222039	0.111020	+	0.993818i	$0.464588\pi$
$68$	0.907223	0.110017
$69$	6.47280	0.779233
$70$	6.79287	0.811904
$71$	7.78788	0.924252	0.462126	−	0.886814i	$-0.347087\pi$
$71$	7.78788	0.924252	0.462126	+	0.886814i	$0.347087\pi$
$72$	−0.683935	−0.0806025
$73$	−8.36858	−0.979469	−0.489734	−	0.871872i	$-0.662906\pi$
$73$	−8.36858	−0.979469	−0.489734	+	0.871872i	$0.662906\pi$
$74$	5.68441	0.660800
$75$	18.1416	2.09482
$76$	6.33246	0.726383
$77$	−4.18820	−0.477290
$78$	−5.55974	−0.629517
$79$	−3.75626	−0.422612	−0.211306	−	0.977420i	$-0.567772\pi$
$79$	−3.75626	−0.422612	−0.211306	+	0.977420i	$0.567772\pi$
$80$	5.15916	0.576812
$81$	−9.76074	−1.08453
$82$	−7.31294	−0.807579
$83$	9.81408	1.07724	0.538618	−	0.842550i	$-0.318947\pi$
$83$	9.81408	1.07724	0.538618	+	0.842550i	$0.318947\pi$
$84$	−6.91986	−0.755019
$85$	−2.31875	−0.251504
$86$	−4.60332	−0.496389
$87$	−1.69914	−0.182167
$88$	4.06449	0.433276
$89$	−9.86347	−1.04553	−0.522763	−	0.852478i	$-0.675099\pi$
$89$	−9.86347	−1.04553	−0.522763	+	0.852478i	$0.675099\pi$
$90$	0.753772	0.0794545
$91$	−11.1234	−1.16605
$92$	−5.41923	−0.564994
$93$	12.4380	1.28976
$94$	−8.82730	−0.910467
$95$	−16.1850	−1.66055
$96$	10.5352	1.07524
$97$	12.2262	1.24138	0.620692	−	0.784054i	$-0.286852\pi$
$97$	12.2262	1.24138	0.620692	+	0.784054i	$0.286852\pi$
$98$	−0.451337	−0.0455920
$99$	−0.464744	−0.0467086
$100$	−15.1888	−1.51888
$101$	7.94703	0.790759	0.395379	−	0.918518i	$-0.370613\pi$
$101$	7.94703	0.790759	0.395379	+	0.918518i	$0.370613\pi$
$102$	−0.753697	−0.0746272
$103$	12.1682	1.19897	0.599486	−	0.800385i	$-0.295372\pi$
$103$	12.1682	1.19897	0.599486	+	0.800385i	$0.295372\pi$
$104$	10.7948	1.05852
$105$	17.6864	1.72601
$106$	0.484810	0.0470889
$107$	9.84320	0.951578	0.475789	−	0.879559i	$-0.342163\pi$
$107$	9.84320	0.951578	0.475789	+	0.879559i	$0.342163\pi$
$108$	7.46961	0.718764
$109$	−13.2863	−1.27259	−0.636297	−	0.771444i	$-0.719535\pi$
$109$	−13.2863	−1.27259	−0.636297	+	0.771444i	$0.719535\pi$
$110$	−4.47952	−0.427106
$111$	14.8003	1.40478
$112$	3.35509	0.317026
$113$	−11.8292	−1.11279	−0.556397	−	0.830917i	$-0.687817\pi$
$113$	−11.8292	−1.11279	−0.556397	+	0.830917i	$0.687817\pi$
$114$	−5.26084	−0.492723
$115$	13.8509	1.29160
$116$	1.42257	0.132082
$117$	−1.23431	−0.114112
$118$	4.85440	0.446884
$119$	−1.50792	−0.138231
$120$	−17.1639	−1.56685
$121$	−8.23811	−0.748919
$122$	1.81927	0.164709
$123$	−19.0404	−1.71682
$124$	−10.4135	−0.935161
$125$	19.4444	1.73916
$126$	0.490190	0.0436696
$127$	16.8719	1.49714	0.748569	−	0.663057i	$-0.230741\pi$
$127$	16.8719	1.49714	0.748569	+	0.663057i	$0.230741\pi$
$128$	−10.6724	−0.943314
$129$	−11.9855	−1.05526
$130$	−11.8971	−1.04344
$131$	−10.9648	−0.957995	−0.478998	−	0.877816i	$-0.659000\pi$
$131$	−10.9648	−0.957995	−0.478998	+	0.877816i	$0.659000\pi$
$132$	4.56327	0.397181
$133$	−10.5254	−0.912666
$134$	1.26414	0.109205
$135$	−19.0914	−1.64313
$136$	1.46338	0.125484
$137$	17.5317	1.49783	0.748916	−	0.662664i	$-0.230574\pi$
$137$	17.5317	1.49783	0.748916	+	0.662664i	$0.230574\pi$
$138$	4.50216	0.383249
$139$	−14.2718	−1.21052	−0.605260	−	0.796028i	$-0.706931\pi$
$139$	−14.2718	−1.21052	−0.605260	+	0.796028i	$0.706931\pi$
$140$	−14.8076	−1.25147
$141$	−22.9833	−1.93554
$142$	5.41687	0.454573
$143$	7.33526	0.613405
$144$	0.372298	0.0310248
$145$	−3.63592	−0.301947
$146$	−5.82077	−0.481731
$147$	−1.17513	−0.0969232
$148$	−12.3913	−1.01856
$149$	16.9809	1.39113	0.695566	−	0.718462i	$-0.255154\pi$
$149$	16.9809	1.39113	0.695566	+	0.718462i	$0.255154\pi$
$150$	12.6184	1.03029
$151$	−1.95234	−0.158879	−0.0794396	−	0.996840i	$-0.525313\pi$
$151$	−1.95234	−0.158879	−0.0794396	+	0.996840i	$0.525313\pi$
$152$	10.2145	0.828504
$153$	−0.167327	−0.0135276
$154$	−2.91311	−0.234745
$155$	26.6157	2.13783
$156$	12.1195	0.970337
$157$	−13.8042	−1.10169	−0.550847	−	0.834606i	$-0.685695\pi$
$157$	−13.8042	−1.10169	−0.550847	+	0.834606i	$0.685695\pi$
$158$	−2.61267	−0.207853
$159$	1.26228	0.100105
$160$	22.5439	1.78225
$161$	9.00748	0.709889
$162$	−6.78909	−0.533401
$163$	7.88557	0.617645	0.308823	−	0.951120i	$-0.400065\pi$
$163$	7.88557	0.617645	0.308823	+	0.951120i	$0.400065\pi$
$164$	15.9412	1.24480
$165$	−11.6632	−0.907977
$166$	6.82619	0.529815
$167$	12.2735	0.949756	0.474878	−	0.880052i	$-0.342492\pi$
$167$	12.2735	0.949756	0.474878	+	0.880052i	$0.342492\pi$
$168$	−11.1620	−0.861167
$169$	6.48160	0.498584
$170$	−1.61281	−0.123697
$171$	−1.16795	−0.0893154
$172$	10.0346	0.765134
$173$	9.84722	0.748671	0.374335	−	0.927293i	$-0.377871\pi$
$173$	9.84722	0.748671	0.374335	+	0.927293i	$0.377871\pi$
$174$	−1.18184	−0.0895947
$175$	25.2457	1.90840
$176$	−2.21249	−0.166773
$177$	12.6392	0.950022
$178$	−6.86054	−0.514219
$179$	15.4595	1.15550	0.577749	−	0.816215i	$-0.303931\pi$
$179$	15.4595	1.15550	0.577749	+	0.816215i	$0.303931\pi$
$180$	−1.64312	−0.122471
$181$	−13.1630	−0.978399	−0.489199	−	0.872172i	$-0.662711\pi$
$181$	−13.1630	−0.978399	−0.489199	+	0.872172i	$0.662711\pi$
$182$	−7.73688	−0.573496
$183$	4.73677	0.350152
$184$	−8.74142	−0.644426
$185$	31.6706	2.32847
$186$	8.65128	0.634343
$187$	0.994392	0.0727171
$188$	19.2424	1.40339
$189$	−12.4155	−0.903093
$190$	−11.2575	−0.816705
$191$	12.8575	0.930339	0.465170	−	0.885222i	$-0.345993\pi$
$191$	12.8575	0.930339	0.465170	+	0.885222i	$0.345993\pi$
$192$	2.50581	0.180841
$193$	−19.2795	−1.38777	−0.693883	−	0.720088i	$-0.744101\pi$
$193$	−19.2795	−1.38777	−0.693883	+	0.720088i	$0.744101\pi$
$194$	8.50395	0.610548
$195$	−30.9760	−2.21824
$196$	0.983857	0.0702755
$197$	25.7736	1.83629	0.918146	−	0.396243i	$-0.129686\pi$
$197$	25.7736	1.83629	0.918146	+	0.396243i	$0.129686\pi$
$198$	−0.323253	−0.0229726
$199$	12.0140	0.851648	0.425824	−	0.904806i	$-0.359984\pi$
$199$	12.0140	0.851648	0.425824	+	0.904806i	$0.359984\pi$
$200$	−24.5000	−1.73241
$201$	3.29140	0.232157
$202$	5.52756	0.388918
$203$	−2.36450	−0.165955
$204$	1.64296	0.115030
$205$	−40.7439	−2.84568
$206$	8.46363	0.589689
$207$	0.999516	0.0694711
$208$	−5.87613	−0.407436
$209$	6.94090	0.480112
$210$	12.3018	0.848902
$211$	9.86523	0.679151	0.339575	−	0.940579i	$-0.389717\pi$
$211$	9.86523	0.679151	0.339575	+	0.940579i	$0.389717\pi$
$212$	−1.05682	−0.0725828
$213$	14.1037	0.966370
$214$	6.84644	0.468013
$215$	−25.6474	−1.74913
$216$	12.0488	0.819814
$217$	17.3086	1.17499
$218$	−9.24128	−0.625898
$219$	−15.1553	−1.02410
$220$	9.76477	0.658341
$221$	2.64099	0.177652
$222$	10.2944	0.690912
$223$	−24.1726	−1.61872	−0.809358	−	0.587315i	$-0.800185\pi$
$223$	−24.1726	−1.61872	−0.809358	+	0.587315i	$0.800185\pi$
$224$	14.6607	0.979556
$225$	2.80139	0.186760
$226$	−8.22778	−0.547304
$227$	−5.94649	−0.394683	−0.197341	−	0.980335i	$-0.563231\pi$
$227$	−5.94649	−0.394683	−0.197341	+	0.980335i	$0.563231\pi$
$228$	11.4680	0.759484
$229$	3.74888	0.247733	0.123867	−	0.992299i	$-0.460471\pi$
$229$	3.74888	0.247733	0.123867	+	0.992299i	$0.460471\pi$
$230$	9.63401	0.635248
$231$	−7.58475	−0.499040
$232$	2.29466	0.150652
$233$	6.35672	0.416443	0.208221	−	0.978082i	$-0.433233\pi$
$233$	6.35672	0.416443	0.208221	+	0.978082i	$0.433233\pi$
$234$	−0.858524	−0.0561234
$235$	−49.1812	−3.20823
$236$	−10.5820	−0.688827
$237$	−6.80251	−0.441870
$238$	−1.04884	−0.0679860
$239$	−4.28151	−0.276948	−0.138474	−	0.990366i	$-0.544220\pi$
$239$	−4.28151	−0.276948	−0.138474	+	0.990366i	$0.544220\pi$
$240$	9.34314	0.603097
$241$	12.3230	0.793794	0.396897	−	0.917863i	$-0.370087\pi$
$241$	12.3230	0.793794	0.396897	+	0.917863i	$0.370087\pi$
$242$	−5.73002	−0.368340
$243$	−2.89699	−0.185842
$244$	−3.96577	−0.253883
$245$	−2.51462	−0.160653
$246$	−13.2436	−0.844380
$247$	18.4342	1.17294
$248$	−16.7974	−1.06664
$249$	17.7731	1.12632
$250$	13.5246	0.855369
$251$	2.90707	0.183493	0.0917463	−	0.995782i	$-0.470755\pi$
$251$	2.90707	0.183493	0.0917463	+	0.995782i	$0.470755\pi$
$252$	−1.06855	−0.0673124
$253$	−5.93993	−0.373440
$254$	11.7352	0.736335
$255$	−4.19922	−0.262965
$256$	−10.1905	−0.636908
$257$	19.2336	1.19976	0.599881	−	0.800089i	$-0.295215\pi$
$257$	19.2336	1.19976	0.599881	+	0.800089i	$0.295215\pi$
$258$	−8.33652	−0.519009
$259$	20.5959	1.27977
$260$	25.9341	1.60837
$261$	−0.262377	−0.0162407
$262$	−7.62654	−0.471170
$263$	9.97036	0.614798	0.307399	−	0.951581i	$-0.400541\pi$
$263$	9.97036	0.614798	0.307399	+	0.951581i	$0.400541\pi$
$264$	7.36071	0.453021
$265$	2.70111	0.165928
$266$	−7.32094	−0.448875
$267$	−17.8625	−1.09317
$268$	−2.75566	−0.168329
$269$	−4.12715	−0.251637	−0.125818	−	0.992053i	$-0.540156\pi$
$269$	−4.12715	−0.251637	−0.125818	+	0.992053i	$0.540156\pi$
$270$	−13.2791	−0.808138
$271$	−9.35886	−0.568510	−0.284255	−	0.958749i	$-0.591746\pi$
$271$	−9.35886	−0.568510	−0.284255	+	0.958749i	$0.591746\pi$
$272$	−0.796588	−0.0483002
$273$	−20.1442	−1.21918
$274$	12.1942	0.736677
$275$	−16.6482	−1.00392
$276$	−9.81412	−0.590740
$277$	14.9514	0.898340	0.449170	−	0.893446i	$-0.351720\pi$
$277$	14.9514	0.898340	0.449170	+	0.893446i	$0.351720\pi$
$278$	−9.92677	−0.595368
$279$	1.92066	0.114987
$280$	−23.8852	−1.42741
$281$	−23.2135	−1.38480	−0.692399	−	0.721514i	$-0.743446\pi$
$281$	−23.2135	−1.38480	−0.692399	+	0.721514i	$0.743446\pi$
$282$	−15.9861	−0.951956
$283$	10.9617	0.651605	0.325803	−	0.945438i	$-0.394365\pi$
$283$	10.9617	0.651605	0.325803	+	0.945438i	$0.394365\pi$
$284$	−11.8081	−0.700680
$285$	−29.3107	−1.73622
$286$	5.10204	0.301690
$287$	−26.4965	−1.56404
$288$	1.62682	0.0958614
$289$	−16.6420	−0.978940
$290$	−2.52897	−0.148506
$291$	22.1414	1.29795
$292$	12.6885	0.742540
$293$	−17.4807	−1.02124	−0.510618	−	0.859808i	$-0.670583\pi$
$293$	−17.4807	−1.02124	−0.510618	+	0.859808i	$0.670583\pi$
$294$	−0.817363	−0.0476696
$295$	27.0462	1.57469
$296$	−19.9876	−1.16175
$297$	8.18732	0.475076
$298$	11.8111	0.684198
$299$	−15.7758	−0.912337
$300$	−27.5065	−1.58809
$301$	−16.6789	−0.961355
$302$	−1.35795	−0.0781414
$303$	14.3919	0.826793
$304$	−5.56022	−0.318901
$305$	10.1361	0.580389
$306$	−0.116384	−0.00665325
$307$	21.2221	1.21121	0.605604	−	0.795766i	$-0.292931\pi$
$307$	21.2221	1.21121	0.605604	+	0.795766i	$0.292931\pi$
$308$	6.35019	0.361836
$309$	22.0364	1.25361
$310$	18.5126	1.05144
$311$	34.7230	1.96896	0.984480	−	0.175496i	$-0.0561529\pi$
$311$	34.7230	1.96896	0.984480	+	0.175496i	$0.0561529\pi$
$312$	19.5492	1.10676
$313$	−13.1495	−0.743254	−0.371627	−	0.928382i	$-0.621200\pi$
$313$	−13.1495	−0.743254	−0.371627	+	0.928382i	$0.621200\pi$
$314$	−9.60151	−0.541845
$315$	2.73109	0.153879
$316$	5.69527	0.320384
$317$	−30.0399	−1.68721	−0.843604	−	0.536965i	$-0.819571\pi$
$317$	−30.0399	−1.68721	−0.843604	+	0.536965i	$0.819571\pi$
$318$	0.877981	0.0492347
$319$	1.55926	0.0873016
$320$	5.36209	0.299750
$321$	17.8258	0.994941
$322$	6.26516	0.349144
$323$	2.49901	0.139049
$324$	14.7993	0.822185
$325$	−44.2156	−2.45264
$326$	5.48481	0.303776
$327$	−24.0612	−1.33059
$328$	25.7138	1.41981
$329$	−31.9833	−1.76330
$330$	−8.11232	−0.446569
$331$	4.32235	0.237578	0.118789	−	0.992920i	$-0.462099\pi$
$331$	4.32235	0.237578	0.118789	+	0.992920i	$0.462099\pi$
$332$	−14.8802	−0.816657
$333$	2.28543	0.125241
$334$	8.53687	0.467117
$335$	7.04315	0.384809
$336$	6.07599	0.331473
$337$	−25.8619	−1.40879	−0.704394	−	0.709809i	$-0.748781\pi$
$337$	−25.8619	−1.40879	−0.704394	+	0.709809i	$0.748781\pi$
$338$	4.50828	0.245218
$339$	−21.4224	−1.16350
$340$	3.51572	0.190667
$341$	−11.4141	−0.618107
$342$	−0.812368	−0.0439278
$343$	−19.2763	−1.04082
$344$	16.1862	0.872704
$345$	25.0837	1.35046
$346$	6.84924	0.368218
$347$	18.0237	0.967563	0.483781	−	0.875189i	$-0.339263\pi$
$347$	18.0237	0.967563	0.483781	+	0.875189i	$0.339263\pi$
$348$	2.57625	0.138101
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	17.5597	0.938604
$351$	21.7446	1.16064
$352$	−9.66789	−0.515300
$353$	7.51906	0.400199	0.200100	−	0.979776i	$-0.435873\pi$
$353$	7.51906	0.400199	0.200100	+	0.979776i	$0.435873\pi$
$354$	8.79122	0.467248
$355$	30.1800	1.60179
$356$	14.9551	0.792618
$357$	−2.73082	−0.144530
$358$	10.7529	0.568307
$359$	−22.7899	−1.20281	−0.601403	−	0.798946i	$-0.705391\pi$
$359$	−22.7899	−1.20281	−0.601403	+	0.798946i	$0.705391\pi$
$360$	−2.65042	−0.139689
$361$	−1.55680	−0.0819368
$362$	−9.15554	−0.481204
$363$	−14.9191	−0.783047
$364$	16.8654	0.883986
$365$	−32.4304	−1.69748
$366$	3.29466	0.172215
$367$	−32.5088	−1.69694	−0.848472	−	0.529241i	$-0.822477\pi$
$367$	−32.5088	−1.69694	−0.848472	+	0.529241i	$0.822477\pi$
$368$	4.75836	0.248047
$369$	−2.94018	−0.153060
$370$	22.0285	1.14521
$371$	1.75658	0.0911970
$372$	−18.8587	−0.977776
$373$	8.99286	0.465633	0.232816	−	0.972521i	$-0.425206\pi$
$373$	8.99286	0.465633	0.232816	+	0.972521i	$0.425206\pi$
$374$	0.691650	0.0357644
$375$	35.2134	1.81841
$376$	31.0386	1.60070
$377$	4.14121	0.213283
$378$	−8.63559	−0.444167
$379$	25.6442	1.31725	0.658627	−	0.752470i	$-0.271138\pi$
$379$	25.6442	1.31725	0.658627	+	0.752470i	$0.271138\pi$
$380$	24.5399	1.25887
$381$	30.5546	1.56536
$382$	8.94307	0.457567
$383$	−6.56008	−0.335204	−0.167602	−	0.985855i	$-0.553602\pi$
$383$	−6.56008	−0.335204	−0.167602	+	0.985855i	$0.553602\pi$
$384$	−19.3275	−0.986300
$385$	−16.2303	−0.827175
$386$	−13.4098	−0.682543
$387$	−1.85078	−0.0940802
$388$	−18.5375	−0.941099
$389$	−23.6571	−1.19946	−0.599732	−	0.800201i	$-0.704726\pi$
$389$	−23.6571	−1.19946	−0.599732	+	0.800201i	$0.704726\pi$
$390$	−21.5454	−1.09099
$391$	−2.13862	−0.108155
$392$	1.58700	0.0801554
$393$	−19.8570	−1.00165
$394$	17.9268	0.903141
$395$	−14.5564	−0.732414
$396$	0.704650	0.0354100
$397$	−19.3796	−0.972632	−0.486316	−	0.873783i	$-0.661660\pi$
$397$	−19.3796	−0.972632	−0.486316	+	0.873783i	$0.661660\pi$
$398$	8.35633	0.418865
$399$	−19.0613	−0.954256
$400$	13.3365	0.666825
$401$	5.42650	0.270987	0.135493	−	0.990778i	$-0.456738\pi$
$401$	5.42650	0.270987	0.135493	+	0.990778i	$0.456738\pi$
$402$	2.28933	0.114182
$403$	−30.3145	−1.51007
$404$	−12.0494	−0.599478
$405$	−37.8253	−1.87956
$406$	−1.64463	−0.0816216
$407$	−13.5819	−0.673229
$408$	2.65016	0.131202
$409$	4.08155	0.201820	0.100910	−	0.994896i	$-0.467825\pi$
$409$	4.08155	0.201820	0.100910	+	0.994896i	$0.467825\pi$
$410$	−28.3395	−1.39959
$411$	31.7495	1.56609
$412$	−18.4496	−0.908947
$413$	17.5886	0.865479
$414$	0.695214	0.0341679
$415$	38.0320	1.86692
$416$	−25.6768	−1.25891
$417$	−25.8460	−1.26568
$418$	4.82775	0.236133
$419$	20.7981	1.01605	0.508026	−	0.861342i	$-0.330375\pi$
$419$	20.7981	1.01605	0.508026	+	0.861342i	$0.330375\pi$
$420$	−26.8162	−1.30850
$421$	−10.7963	−0.526178	−0.263089	−	0.964772i	$-0.584741\pi$
$421$	−10.7963	−0.526178	−0.263089	+	0.964772i	$0.584741\pi$
$422$	6.86177	0.334026
$423$	−3.54904	−0.172560
$424$	−1.70469	−0.0827872
$425$	−5.99401	−0.290752
$426$	9.80984	0.475288
$427$	6.59164	0.318992
$428$	−14.9244	−0.721396
$429$	13.2840	0.641357
$430$	−17.8390	−0.860275
$431$	−4.01776	−0.193529	−0.0967644	−	0.995307i	$-0.530849\pi$
$431$	−4.01776	−0.193529	−0.0967644	+	0.995307i	$0.530849\pi$
$432$	−6.55870	−0.315556
$433$	3.63736	0.174801	0.0874003	−	0.996173i	$-0.472144\pi$
$433$	3.63736	0.174801	0.0874003	+	0.996173i	$0.472144\pi$
$434$	12.0390	0.577892
$435$	−6.58458	−0.315707
$436$	20.1448	0.964760
$437$	−14.9277	−0.714086
$438$	−10.5413	−0.503683
$439$	33.4985	1.59880	0.799398	−	0.600802i	$-0.205152\pi$
$439$	33.4985	1.59880	0.799398	+	0.600802i	$0.205152\pi$
$440$	15.7509	0.750897
$441$	−0.181461	−0.00864101
$442$	1.83694	0.0873745
$443$	9.35458	0.444449	0.222225	−	0.974995i	$-0.428668\pi$
$443$	9.35458	0.444449	0.222225	+	0.974995i	$0.428668\pi$
$444$	−22.4404	−1.06497
$445$	−38.2234	−1.81197
$446$	−16.8133	−0.796131
$447$	30.7521	1.45453
$448$	3.48705	0.164748
$449$	−25.2366	−1.19099	−0.595495	−	0.803359i	$-0.703044\pi$
$449$	−25.2366	−1.19099	−0.595495	+	0.803359i	$0.703044\pi$
$450$	1.94851	0.0918537
$451$	17.4729	0.822769
$452$	17.9355	0.843614
$453$	−3.53565	−0.166119
$454$	−4.13609	−0.194116
$455$	−43.1059	−2.02084
$456$	18.4982	0.866259
$457$	11.8440	0.554040	0.277020	−	0.960864i	$-0.410653\pi$
$457$	11.8440	0.554040	0.277020	+	0.960864i	$0.410653\pi$
$458$	2.60754	0.121842
$459$	2.94777	0.137590
$460$	−21.0009	−0.979171
$461$	−13.8400	−0.644591	−0.322296	−	0.946639i	$-0.604455\pi$
$461$	−13.8400	−0.644591	−0.322296	+	0.946639i	$0.604455\pi$
$462$	−5.27558	−0.245442
$463$	20.5235	0.953807	0.476904	−	0.878956i	$-0.341759\pi$
$463$	20.5235	0.953807	0.476904	+	0.878956i	$0.341759\pi$
$464$	−1.24909	−0.0579875
$465$	48.2005	2.23525
$466$	4.42142	0.204818
$467$	−18.2391	−0.844006	−0.422003	−	0.906594i	$-0.638673\pi$
$467$	−18.2391	−0.844006	−0.422003	+	0.906594i	$0.638673\pi$
$468$	1.87147	0.0865087
$469$	4.58028	0.211498
$470$	−34.2080	−1.57790
$471$	−24.9991	−1.15190
$472$	−17.0691	−0.785668
$473$	10.9988	0.505726
$474$	−4.73149	−0.217324
$475$	−41.8385	−1.91968
$476$	2.28633	0.104794
$477$	0.194919	0.00892472
$478$	−2.97801	−0.136211
$479$	20.2574	0.925585	0.462793	−	0.886467i	$-0.346847\pi$
$479$	20.2574	0.925585	0.462793	+	0.886467i	$0.346847\pi$
$480$	40.8265	1.86347
$481$	−36.0719	−1.64474
$482$	8.57126	0.390410
$483$	16.3124	0.742238
$484$	12.4907	0.567759
$485$	47.3797	2.15140
$486$	−2.01501	−0.0914025
$487$	−41.1991	−1.86691	−0.933455	−	0.358695i	$-0.883222\pi$
$487$	−41.1991	−1.86691	−0.933455	+	0.358695i	$0.883222\pi$
$488$	−6.39694	−0.289576
$489$	14.2806	0.645791
$490$	−1.74905	−0.0790139
$491$	37.6871	1.70080	0.850398	−	0.526140i	$-0.176361\pi$
$491$	37.6871	1.70080	0.850398	+	0.526140i	$0.176361\pi$
$492$	28.8693	1.30153
$493$	0.561396	0.0252840
$494$	12.8220	0.576887
$495$	−1.80100	−0.0809490
$496$	9.14360	0.410560
$497$	19.6266	0.880372
$498$	12.3621	0.553959
$499$	−29.9728	−1.34177	−0.670883	−	0.741563i	$-0.734085\pi$
$499$	−29.9728	−1.34177	−0.670883	+	0.741563i	$0.734085\pi$
$500$	−29.4818	−1.31847
$501$	22.2271	0.993036
$502$	2.02201	0.0902469
$503$	−23.9259	−1.06680	−0.533401	−	0.845862i	$-0.679086\pi$
$503$	−23.9259	−1.06680	−0.533401	+	0.845862i	$0.679086\pi$
$504$	−1.72361	−0.0767758
$505$	30.7967	1.37044
$506$	−4.13152	−0.183669
$507$	11.7380	0.521305
$508$	−25.5813	−1.13499
$509$	0.194475	0.00861994	0.00430997	−	0.999991i	$-0.498628\pi$
$509$	0.194475	0.00861994	0.00430997	+	0.999991i	$0.498628\pi$
$510$	−2.92077	−0.129334
$511$	−21.0900	−0.932967
$512$	14.2567	0.630064
$513$	20.5756	0.908434
$514$	13.3780	0.590077
$515$	47.1550	2.07790
$516$	18.1725	0.800001
$517$	21.0912	0.927592
$518$	14.3255	0.629427
$519$	17.8331	0.782787
$520$	41.8327	1.83448
$521$	5.74029	0.251486	0.125743	−	0.992063i	$-0.459868\pi$
$521$	5.74029	0.251486	0.125743	+	0.992063i	$0.459868\pi$
$522$	−0.182496	−0.00798765
$523$	4.41335	0.192982	0.0964912	−	0.995334i	$-0.469238\pi$
$523$	4.41335	0.192982	0.0964912	+	0.995334i	$0.469238\pi$
$524$	16.6249	0.726261
$525$	45.7195	1.99536
$526$	6.93489	0.302375
$527$	−4.10954	−0.179014
$528$	−4.00678	−0.174373
$529$	−10.2251	−0.444570
$530$	1.87876	0.0816081
$531$	1.95172	0.0846975
$532$	15.9587	0.691897
$533$	46.4061	2.01007
$534$	−12.4243	−0.537652
$535$	38.1449	1.64915
$536$	−4.44499	−0.191994
$537$	27.9968	1.20815
$538$	−2.87064	−0.123762
$539$	1.07839	0.0464495
$540$	28.9466	1.24566
$541$	38.1935	1.64207	0.821033	−	0.570880i	$-0.193398\pi$
$541$	38.1935	1.64207	0.821033	+	0.570880i	$0.193398\pi$
$542$	−6.50956	−0.279609
$543$	−23.8379	−1.02298
$544$	−3.48083	−0.149240
$545$	−51.4877	−2.20549
$546$	−14.0113	−0.599630
$547$	18.8814	0.807308	0.403654	−	0.914912i	$-0.367740\pi$
$547$	18.8814	0.807308	0.403654	+	0.914912i	$0.367740\pi$
$548$	−26.5817	−1.13551
$549$	0.731442	0.0312172
$550$	−11.5796	−0.493757
$551$	3.91857	0.166937
$552$	−15.8305	−0.673792
$553$	−9.46630	−0.402548
$554$	10.3994	0.441829
$555$	57.3549	2.43458
$556$	21.6391	0.917700
$557$	−14.5193	−0.615203	−0.307602	−	0.951515i	$-0.599526\pi$
$557$	−14.5193	−0.615203	−0.307602	+	0.951515i	$0.599526\pi$
$558$	1.33591	0.0565537
$559$	29.2116	1.23552
$560$	13.0018	0.549427
$561$	1.80082	0.0760308
$562$	−16.1461	−0.681084
$563$	−43.1345	−1.81790	−0.908951	−	0.416902i	$-0.863116\pi$
$563$	−43.1345	−1.81790	−0.908951	+	0.416902i	$0.863116\pi$
$564$	34.8475	1.46735
$565$	−45.8410	−1.92855
$566$	7.62442	0.320478
$567$	−24.5984	−1.03304
$568$	−19.0468	−0.799188
$569$	18.3731	0.770240	0.385120	−	0.922866i	$-0.374160\pi$
$569$	18.3731	0.770240	0.385120	+	0.922866i	$0.374160\pi$
$570$	−20.3871	−0.853922
$571$	−9.27106	−0.387982	−0.193991	−	0.981003i	$-0.562143\pi$
$571$	−9.27106	−0.387982	−0.193991	+	0.981003i	$0.562143\pi$
$572$	−11.1218	−0.465025
$573$	23.2847	0.972734
$574$	−18.4296	−0.769238
$575$	35.8048	1.49316
$576$	0.386941	0.0161226
$577$	−40.2352	−1.67501	−0.837507	−	0.546426i	$-0.815988\pi$
$577$	−40.2352	−1.67501	−0.837507	+	0.546426i	$0.815988\pi$
$578$	−11.5753	−0.481471
$579$	−34.9147	−1.45101
$580$	5.51282	0.228907
$581$	24.7329	1.02609
$582$	15.4005	0.638371
$583$	−1.15837	−0.0479746
$584$	20.4671	0.846933
$585$	−4.78325	−0.197763
$586$	−12.1587	−0.502273
$587$	−6.62968	−0.273636	−0.136818	−	0.990596i	$-0.543688\pi$
$587$	−6.62968	−0.273636	−0.136818	+	0.990596i	$0.543688\pi$
$588$	1.78174	0.0734779
$589$	−28.6848	−1.18194
$590$	18.8120	0.774479
$591$	46.6754	1.91997
$592$	10.8802	0.447173
$593$	−9.19111	−0.377434	−0.188717	−	0.982032i	$-0.560433\pi$
$593$	−9.19111	−0.377434	−0.188717	+	0.982032i	$0.560433\pi$
$594$	5.69469	0.233656
$595$	−5.84359	−0.239564
$596$	−25.7466	−1.05462
$597$	21.7571	0.890457
$598$	−10.9729	−0.448713
$599$	−1.10390	−0.0451040	−0.0225520	−	0.999746i	$-0.507179\pi$
$599$	−1.10390	−0.0451040	−0.0225520	+	0.999746i	$0.507179\pi$
$600$	−44.3690	−1.81136
$601$	−32.8707	−1.34082	−0.670412	−	0.741989i	$-0.733883\pi$
$601$	−32.8707	−1.34082	−0.670412	+	0.741989i	$0.733883\pi$
$602$	−11.6010	−0.472822
$603$	0.508251	0.0206976
$604$	2.96016	0.120447
$605$	−31.9248	−1.29793
$606$	10.0103	0.406641
$607$	−21.4903	−0.872265	−0.436132	−	0.899883i	$-0.643652\pi$
$607$	−21.4903	−0.872265	−0.436132	+	0.899883i	$0.643652\pi$
$608$	−24.2964	−0.985349
$609$	−4.28206	−0.173518
$610$	7.05014	0.285452
$611$	56.0159	2.26616
$612$	0.253703	0.0102553
$613$	−22.2048	−0.896843	−0.448421	−	0.893822i	$-0.648014\pi$
$613$	−22.2048	−0.896843	−0.448421	+	0.893822i	$0.648014\pi$
$614$	14.7610	0.595707
$615$	−73.7865	−2.97536
$616$	10.2431	0.412706
$617$	8.76704	0.352948	0.176474	−	0.984305i	$-0.443531\pi$
$617$	8.76704	0.352948	0.176474	+	0.984305i	$0.443531\pi$
$618$	15.3275	0.616561
$619$	13.2003	0.530564	0.265282	−	0.964171i	$-0.414535\pi$
$619$	13.2003	0.530564	0.265282	+	0.964171i	$0.414535\pi$
$620$	−40.3550	−1.62070
$621$	−17.6083	−0.706596
$622$	24.1516	0.968391
$623$	−24.8573	−0.995888
$624$	−10.6416	−0.426003
$625$	25.2641	1.01056
$626$	−9.14615	−0.365554
$627$	12.5698	0.501991
$628$	20.9300	0.835200
$629$	−4.89003	−0.194978
$630$	1.89961	0.0756823
$631$	12.0176	0.478412	0.239206	−	0.970969i	$-0.423113\pi$
$631$	12.0176	0.478412	0.239206	+	0.970969i	$0.423113\pi$
$632$	9.18668	0.365427
$633$	17.8657	0.710099
$634$	−20.8943	−0.829817
$635$	65.3828	2.59464
$636$	−1.91388	−0.0758904
$637$	2.86408	0.113479
$638$	1.08454	0.0429374
$639$	2.17786	0.0861550
$640$	−41.3582	−1.63482
$641$	23.2273	0.917424	0.458712	−	0.888585i	$-0.348311\pi$
$641$	23.2273	0.917424	0.458712	+	0.888585i	$0.348311\pi$
$642$	12.3988	0.489341
$643$	30.7444	1.21244	0.606220	−	0.795297i	$-0.292685\pi$
$643$	30.7444	1.21244	0.606220	+	0.795297i	$0.292685\pi$
$644$	−13.6572	−0.538170
$645$	−46.4468	−1.82884
$646$	1.73819	0.0683880
$647$	1.95450	0.0768394	0.0384197	−	0.999262i	$-0.487768\pi$
$647$	1.95450	0.0768394	0.0384197	+	0.999262i	$0.487768\pi$
$648$	23.8719	0.937775
$649$	−11.5987	−0.455289
$650$	−30.7542	−1.20628
$651$	31.3456	1.22853
$652$	−11.9562	−0.468240
$653$	44.2822	1.73290	0.866449	−	0.499266i	$-0.166397\pi$
$653$	44.2822	1.73290	0.866449	+	0.499266i	$0.166397\pi$
$654$	−16.7358	−0.654420
$655$	−42.4912	−1.66027
$656$	−13.9972	−0.546500
$657$	−2.34025	−0.0913020
$658$	−22.2460	−0.867241
$659$	−21.5036	−0.837663	−0.418832	−	0.908064i	$-0.637560\pi$
$659$	−21.5036	−0.837663	−0.418832	+	0.908064i	$0.637560\pi$
$660$	17.6838	0.688341
$661$	−0.582442	−0.0226544	−0.0113272	−	0.999936i	$-0.503606\pi$
$661$	−0.582442	−0.0226544	−0.0113272	+	0.999936i	$0.503606\pi$
$662$	3.00641	0.116847
$663$	4.78278	0.185748
$664$	−24.0023	−0.931470
$665$	−40.7885	−1.58171
$666$	1.58963	0.0615970
$667$	−3.35346	−0.129846
$668$	−18.6093	−0.720014
$669$	−43.7761	−1.69248
$670$	4.89887	0.189260
$671$	−4.34682	−0.167807
$672$	26.5502	1.02419
$673$	47.6045	1.83502	0.917510	−	0.397713i	$-0.130196\pi$
$673$	47.6045	1.83502	0.917510	+	0.397713i	$0.130196\pi$
$674$	−17.9883	−0.692882
$675$	−49.3517	−1.89955
$676$	−9.82746	−0.377979
$677$	−2.39764	−0.0921488	−0.0460744	−	0.998938i	$-0.514671\pi$
$677$	−2.39764	−0.0921488	−0.0460744	+	0.998938i	$0.514671\pi$
$678$	−14.9003	−0.572244
$679$	30.8118	1.18245
$680$	5.67098	0.217472
$681$	−10.7690	−0.412668
$682$	−7.93908	−0.304003
$683$	1.08458	0.0415003	0.0207502	−	0.999785i	$-0.493395\pi$
$683$	1.08458	0.0415003	0.0207502	+	0.999785i	$0.493395\pi$
$684$	1.77086	0.0677104
$685$	67.9397	2.59584
$686$	−13.4076	−0.511906
$687$	6.78915	0.259022
$688$	−8.81093	−0.335913
$689$	−3.07649	−0.117205
$690$	17.4470	0.664196
$691$	10.5410	0.401000	0.200500	−	0.979694i	$-0.435743\pi$
$691$	10.5410	0.401000	0.200500	+	0.979694i	$0.435743\pi$
$692$	−14.9305	−0.567571
$693$	−1.17122	−0.0444910
$694$	12.5364	0.475875
$695$	−55.3069	−2.09791
$696$	4.15558	0.157517
$697$	6.29097	0.238288
$698$	0.695551	0.0263270
$699$	11.5119	0.435420
$700$	−38.2778	−1.44676
$701$	−8.74909	−0.330449	−0.165224	−	0.986256i	$-0.552835\pi$
$701$	−8.74909	−0.330449	−0.165224	+	0.986256i	$0.552835\pi$
$702$	15.1245	0.570836
$703$	−34.1326	−1.28734
$704$	−2.29952	−0.0866664
$705$	−89.0662	−3.35443
$706$	5.22989	0.196830
$707$	20.0276	0.753216
$708$	−19.1637	−0.720216
$709$	−22.8608	−0.858557	−0.429278	−	0.903172i	$-0.641232\pi$
$709$	−22.8608	−0.858557	−0.429278	+	0.903172i	$0.641232\pi$
$710$	20.9917	0.787806
$711$	−1.05043	−0.0393941
$712$	24.1231	0.904052
$713$	24.5480	0.919331
$714$	−1.89942	−0.0710841
$715$	28.4260	1.06307
$716$	−23.4398	−0.875988
$717$	−7.75374	−0.289569
$718$	−15.8515	−0.591574
$719$	−19.7126	−0.735157	−0.367578	−	0.929993i	$-0.619813\pi$
$719$	−19.7126	−0.735157	−0.367578	+	0.929993i	$0.619813\pi$
$720$	1.44275	0.0537680
$721$	30.6657	1.14205
$722$	−1.08283	−0.0402989
$723$	22.3167	0.829966
$724$	19.9579	0.741729
$725$	−9.39891	−0.349067
$726$	−10.3770	−0.385125
$727$	−4.13214	−0.153253	−0.0766263	−	0.997060i	$-0.524415\pi$
$727$	−4.13214	−0.153253	−0.0766263	+	0.997060i	$0.524415\pi$
$728$	27.2045	1.00827
$729$	24.0358	0.890216
$730$	−22.5570	−0.834871
$731$	3.96002	0.146467
$732$	−7.18194	−0.265452
$733$	−11.2429	−0.415266	−0.207633	−	0.978207i	$-0.566576\pi$
$733$	−11.2429	−0.415266	−0.207633	+	0.978207i	$0.566576\pi$
$734$	−22.6115	−0.834605
$735$	−4.55393	−0.167974
$736$	20.7925	0.766422
$737$	−3.02044	−0.111259
$738$	−2.04505	−0.0752792
$739$	−36.2605	−1.33387	−0.666933	−	0.745118i	$-0.732393\pi$
$739$	−36.2605	−1.33387	−0.666933	+	0.745118i	$0.732393\pi$
$740$	−48.0193	−1.76523
$741$	33.3840	1.22639
$742$	1.22179	0.0448533
$743$	11.2477	0.412638	0.206319	−	0.978485i	$-0.433852\pi$
$743$	11.2477	0.412638	0.206319	+	0.978485i	$0.433852\pi$
$744$	−30.4197	−1.11524
$745$	65.8054	2.41092
$746$	6.25499	0.229011
$747$	2.74448	0.100415
$748$	−1.50771	−0.0551272
$749$	24.8062	0.906401
$750$	24.4927	0.894348
$751$	4.51180	0.164638	0.0823190	−	0.996606i	$-0.473767\pi$
$751$	4.51180	0.164638	0.0823190	+	0.996606i	$0.473767\pi$
$752$	−16.8958	−0.616126
$753$	5.26464	0.191854
$754$	2.88042	0.104899
$755$	−7.56582	−0.275348
$756$	18.8245	0.684639
$757$	−48.6751	−1.76913	−0.884564	−	0.466419i	$-0.845544\pi$
$757$	−48.6751	−1.76913	−0.884564	+	0.466419i	$0.845544\pi$
$758$	17.8368	0.647863
$759$	−10.7571	−0.390458
$760$	39.5837	1.43585
$761$	28.8887	1.04722	0.523608	−	0.851960i	$-0.324586\pi$
$761$	28.8887	1.04722	0.523608	+	0.851960i	$0.324586\pi$
$762$	21.2523	0.769889
$763$	−33.4833	−1.21218
$764$	−19.4947	−0.705294
$765$	−0.648434	−0.0234442
$766$	−4.56286	−0.164863
$767$	−30.8049	−1.11230
$768$	−18.4548	−0.665932
$769$	−41.9724	−1.51356	−0.756782	−	0.653667i	$-0.773230\pi$
$769$	−41.9724	−1.51356	−0.756782	+	0.653667i	$0.773230\pi$
$770$	−11.2890	−0.406828
$771$	34.8317	1.25443
$772$	29.2317	1.05207
$773$	−47.5671	−1.71087	−0.855436	−	0.517909i	$-0.826711\pi$
$773$	−47.5671	−1.71087	−0.855436	+	0.517909i	$0.826711\pi$
$774$	−1.28731	−0.0462713
$775$	68.8020	2.47144
$776$	−29.9017	−1.07341
$777$	37.2988	1.33809
$778$	−16.4547	−0.589931
$779$	43.9113	1.57329
$780$	46.9662	1.68166
$781$	−12.9426	−0.463124
$782$	−1.48752	−0.0531935
$783$	4.62225	0.165186
$784$	−0.863876	−0.0308527
$785$	−53.4947	−1.90931
$786$	−13.8115	−0.492641
$787$	−37.1642	−1.32476	−0.662381	−	0.749167i	$-0.730454\pi$
$787$	−37.1642	−1.32476	−0.662381	+	0.749167i	$0.730454\pi$
$788$	−39.0781	−1.39210
$789$	18.0561	0.642815
$790$	−10.1247	−0.360222
$791$	−29.8112	−1.05996
$792$	1.13663	0.0403882
$793$	−11.5447	−0.409963
$794$	−13.4795	−0.478368
$795$	4.89166	0.173489
$796$	−18.2157	−0.645638
$797$	−39.3241	−1.39293	−0.696466	−	0.717589i	$-0.745245\pi$
$797$	−39.3241	−1.39293	−0.696466	+	0.717589i	$0.745245\pi$
$798$	−13.2581	−0.469330
$799$	7.59371	0.268646
$800$	58.2763	2.06038
$801$	−2.75830	−0.0974596
$802$	3.77441	0.133279
$803$	13.9077	0.490792
$804$	−4.99045	−0.176000
$805$	34.9063	1.23028
$806$	−21.0853	−0.742697
$807$	−7.47419	−0.263104
$808$	−19.4361	−0.683758
$809$	14.4369	0.507575	0.253788	−	0.967260i	$-0.418324\pi$
$809$	14.4369	0.507575	0.253788	+	0.967260i	$0.418324\pi$
$810$	−26.3094	−0.924419
$811$	12.5686	0.441343	0.220671	−	0.975348i	$-0.429175\pi$
$811$	12.5686	0.441343	0.220671	+	0.975348i	$0.429175\pi$
$812$	3.58508	0.125812
$813$	−16.9487	−0.594417
$814$	−9.44688	−0.331113
$815$	30.5586	1.07042
$816$	−1.44260	−0.0505013
$817$	27.6411	0.967040
$818$	2.83892	0.0992607
$819$	−3.11063	−0.108694
$820$	61.7764	2.15732
$821$	−3.40890	−0.118971	−0.0594857	−	0.998229i	$-0.518946\pi$
$821$	−3.40890	−0.118971	−0.0594857	+	0.998229i	$0.518946\pi$
$822$	22.0834	0.770247
$823$	−20.0130	−0.697608	−0.348804	−	0.937196i	$-0.613412\pi$
$823$	−20.0130	−0.697608	−0.348804	+	0.937196i	$0.613412\pi$
$824$	−29.7599	−1.03674
$825$	−30.1495	−1.04967
$826$	12.2338	0.425667
$827$	−29.9850	−1.04268	−0.521341	−	0.853349i	$-0.674568\pi$
$827$	−29.9850	−1.04268	−0.521341	+	0.853349i	$0.674568\pi$
$828$	−1.51547	−0.0526664
$829$	31.9347	1.10914	0.554570	−	0.832137i	$-0.312883\pi$
$829$	31.9347	1.10914	0.554570	+	0.832137i	$0.312883\pi$
$830$	26.4532	0.918204
$831$	27.0766	0.939277
$832$	−6.10726	−0.211731
$833$	0.388264	0.0134526
$834$	−17.9772	−0.622499
$835$	47.5631	1.64599
$836$	−10.5239	−0.363975
$837$	−33.8358	−1.16954
$838$	14.4661	0.499724
$839$	25.9265	0.895084	0.447542	−	0.894263i	$-0.352300\pi$
$839$	25.9265	0.895084	0.447542	+	0.894263i	$0.352300\pi$
$840$	−43.2556	−1.49246
$841$	−28.1197	−0.969645
$842$	−7.50935	−0.258789
$843$	−42.0391	−1.44790
$844$	−14.9578	−0.514867
$845$	25.1178	0.864080
$846$	−2.46853	−0.0848699
$847$	−20.7612	−0.713363
$848$	0.927944	0.0318657
$849$	19.8514	0.681299
$850$	−4.16914	−0.143000
$851$	29.2103	1.00131
$852$	−21.3842	−0.732609
$853$	42.5555	1.45707	0.728536	−	0.685008i	$-0.240201\pi$
$853$	42.5555	1.45707	0.728536	+	0.685008i	$0.240201\pi$
$854$	4.58482	0.156889
$855$	−4.52610	−0.154789
$856$	−24.0735	−0.822816
$857$	21.9401	0.749459	0.374730	−	0.927134i	$-0.377736\pi$
$857$	21.9401	0.749459	0.374730	+	0.927134i	$0.377736\pi$
$858$	9.23969	0.315438
$859$	3.31222	0.113011	0.0565057	−	0.998402i	$-0.482004\pi$
$859$	3.31222	0.113011	0.0565057	+	0.998402i	$0.482004\pi$
$860$	38.8868	1.32603
$861$	−47.9845	−1.63531
$862$	−2.79456	−0.0951830
$863$	−36.1723	−1.23132	−0.615660	−	0.788012i	$-0.711111\pi$
$863$	−36.1723	−1.23132	−0.615660	+	0.788012i	$0.711111\pi$
$864$	−28.6594	−0.975013
$865$	38.1605	1.29750
$866$	2.52997	0.0859719
$867$	−30.1383	−1.02355
$868$	−26.2435	−0.890763
$869$	6.24250	0.211762
$870$	−4.57991	−0.155273
$871$	−8.02194	−0.271813
$872$	32.4943	1.10039
$873$	3.41903	0.115717
$874$	−10.3829	−0.351208
$875$	49.0026	1.65659
$876$	22.9787	0.776377
$877$	35.3405	1.19336	0.596682	−	0.802478i	$-0.296485\pi$
$877$	35.3405	1.19336	0.596682	+	0.802478i	$0.296485\pi$
$878$	23.2999	0.786334
$879$	−31.6573	−1.06777
$880$	−8.57397	−0.289029
$881$	19.7381	0.664995	0.332497	−	0.943104i	$-0.392109\pi$
$881$	19.7381	0.664995	0.332497	+	0.943104i	$0.392109\pi$
$882$	−0.126215	−0.00424990
$883$	−36.1653	−1.21706	−0.608530	−	0.793531i	$-0.708241\pi$
$883$	−36.1653	−1.21706	−0.608530	+	0.793531i	$0.708241\pi$
$884$	−4.00430	−0.134679
$885$	48.9802	1.64645
$886$	6.50658	0.218593
$887$	−20.8461	−0.699942	−0.349971	−	0.936760i	$-0.613809\pi$
$887$	−20.8461	−0.699942	−0.349971	+	0.936760i	$0.613809\pi$
$888$	−36.1971	−1.21470
$889$	42.5195	1.42606
$890$	−26.5863	−0.891176
$891$	16.2213	0.543434
$892$	36.6507	1.22716
$893$	53.0044	1.77373
$894$	21.3897	0.715377
$895$	59.9095	2.00255
$896$	−26.8959	−0.898529
$897$	−28.5696	−0.953912
$898$	−17.5533	−0.585762
$899$	−6.44396	−0.214918
$900$	−4.24750	−0.141583
$901$	−0.417059	−0.0138942
$902$	12.1533	0.404661
$903$	−30.2051	−1.00516
$904$	28.9306	0.962217
$905$	−51.0100	−1.69563
$906$	−2.45922	−0.0817022
$907$	−37.3752	−1.24102	−0.620512	−	0.784197i	$-0.713075\pi$
$907$	−37.3752	−1.24102	−0.620512	+	0.784197i	$0.713075\pi$
$908$	9.01613	0.299211
$909$	2.22237	0.0737113
$910$	−29.9824	−0.993906
$911$	38.3698	1.27125	0.635623	−	0.771999i	$-0.280743\pi$
$911$	38.3698	1.27125	0.635623	+	0.771999i	$0.280743\pi$
$912$	−10.0694	−0.333433
$913$	−16.3099	−0.539780
$914$	8.23812	0.272493
$915$	18.3562	0.606837
$916$	−5.68409	−0.187808
$917$	−27.6327	−0.912513
$918$	2.05032	0.0676707
$919$	−25.9267	−0.855243	−0.427621	−	0.903958i	$-0.640648\pi$
$919$	−25.9267	−0.855243	−0.427621	+	0.903958i	$0.640648\pi$
$920$	−33.8752	−1.11683
$921$	38.4328	1.26640
$922$	−9.62639	−0.317028
$923$	−34.3741	−1.13144
$924$	11.5001	0.378324
$925$	81.8691	2.69184
$926$	14.2751	0.469110
$927$	3.40282	0.111763
$928$	−5.45812	−0.179172
$929$	51.4236	1.68715	0.843576	−	0.537010i	$-0.180446\pi$
$929$	51.4236	1.68715	0.843576	+	0.537010i	$0.180446\pi$
$930$	33.5259	1.09936
$931$	2.71010	0.0888200
$932$	−9.63812	−0.315707
$933$	62.8826	2.05869
$934$	−12.6862	−0.415106
$935$	3.85352	0.126024
$936$	3.01875	0.0986709
$937$	−59.3828	−1.93995	−0.969975	−	0.243203i	$-0.921802\pi$
$937$	−59.3828	−1.93995	−0.969975	+	0.243203i	$0.921802\pi$
$938$	3.18581	0.104021
$939$	−23.8135	−0.777124
$940$	74.5690	2.43217
$941$	−10.5894	−0.345204	−0.172602	−	0.984992i	$-0.555217\pi$
$941$	−10.5894	−0.345204	−0.172602	+	0.984992i	$0.555217\pi$
$942$	−17.3881	−0.566536
$943$	−37.5787	−1.22373
$944$	9.29150	0.302413
$945$	−48.1131	−1.56512
$946$	7.65022	0.248730
$947$	36.6564	1.19117	0.595587	−	0.803291i	$-0.296920\pi$
$947$	36.6564	1.19117	0.595587	+	0.803291i	$0.296920\pi$
$948$	10.3140	0.334984
$949$	36.9372	1.19903
$950$	−29.1008	−0.944155
$951$	−54.4016	−1.76409
$952$	3.68793	0.119527
$953$	37.3853	1.21103	0.605514	−	0.795835i	$-0.292968\pi$
$953$	37.3853	1.21103	0.605514	+	0.795835i	$0.292968\pi$
$954$	0.135576	0.00438943
$955$	49.8262	1.61234
$956$	6.49167	0.209956
$957$	2.82378	0.0912799
$958$	14.0901	0.455229
$959$	44.1823	1.42672
$960$	9.71063	0.313409
$961$	16.1712	0.521650
$962$	−25.0898	−0.808929
$963$	2.75263	0.0887022
$964$	−18.6842	−0.601779
$965$	−74.7128	−2.40509
$966$	11.3461	0.365054
$967$	30.0327	0.965787	0.482893	−	0.875679i	$-0.339586\pi$
$967$	30.0327	0.965787	0.482893	+	0.875679i	$0.339586\pi$
$968$	20.1480	0.647580
$969$	4.52565	0.145385
$970$	32.9550	1.05812
$971$	3.48982	0.111994	0.0559969	−	0.998431i	$-0.482166\pi$
$971$	3.48982	0.111994	0.0559969	+	0.998431i	$0.482166\pi$
$972$	4.39245	0.140888
$973$	−35.9670	−1.15305
$974$	−28.6561	−0.918199
$975$	−80.0735	−2.56441
$976$	3.48215	0.111461
$977$	7.85635	0.251347	0.125673	−	0.992072i	$-0.459891\pi$
$977$	7.85635	0.251347	0.125673	+	0.992072i	$0.459891\pi$
$978$	9.93288	0.317618
$979$	16.3920	0.523892
$980$	3.81269	0.121792
$981$	−3.71548	−0.118626
$982$	26.2133	0.836500
$983$	−9.15722	−0.292070	−0.146035	−	0.989279i	$-0.546651\pi$
$983$	−9.15722	−0.292070	−0.146035	+	0.989279i	$0.546651\pi$
$984$	46.5672	1.48451
$985$	99.8791	3.18241
$986$	0.390479	0.0124354
$987$	−57.9212	−1.84365
$988$	−27.9502	−0.889214
$989$	−23.6549	−0.752182
$990$	−1.25269	−0.0398130
$991$	−35.2186	−1.11876	−0.559378	−	0.828913i	$-0.688960\pi$
$991$	−35.2186	−1.11876	−0.559378	+	0.828913i	$0.688960\pi$
$992$	39.9546	1.26856
$993$	7.82768	0.248404
$994$	13.6513	0.432992
$995$	46.5572	1.47596
$996$	−26.9477	−0.853872
$997$	30.2117	0.956814	0.478407	−	0.878138i	$-0.341214\pi$
$997$	30.2117	0.956814	0.478407	+	0.878138i	$0.341214\pi$
$998$	−20.8476	−0.659919
$999$	−40.2620	−1.27383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.b.1.10	✓	17
3.2	odd	2		3141.2.a.e.1.8		17
4.3	odd	2		5584.2.a.m.1.6		17
5.4	even	2		8725.2.a.m.1.8		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.b.1.10	✓	17	1.1	even	1	trivial
3141.2.a.e.1.8		17	3.2	odd	2
5584.2.a.m.1.6		17	4.3	odd	2
8725.2.a.m.1.8		17	5.4	even	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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.a (trivial)

\(f(q)\)	\(=\)	\(q+0.695551 q^{2} +1.81098 q^{3} -1.51621 q^{4} +3.87525 q^{5} +1.25963 q^{6} +2.52014 q^{7} -2.44570 q^{8} +0.279648 q^{9} +O(q^{10})\)	\(q+0.695551 q^{2} +1.81098 q^{3} -1.51621 q^{4} +3.87525 q^{5} +1.25963 q^{6} +2.52014 q^{7} -2.44570 q^{8} +0.279648 q^{9} +2.69543 q^{10} -1.66189 q^{11} -2.74582 q^{12} -4.41380 q^{13} +1.75289 q^{14} +7.01800 q^{15} +1.33131 q^{16} -0.598349 q^{17} +0.194509 q^{18} -4.17651 q^{19} -5.87569 q^{20} +4.56392 q^{21} -1.15593 q^{22} +3.57420 q^{23} -4.42912 q^{24} +10.0176 q^{25} -3.07002 q^{26} -4.92650 q^{27} -3.82106 q^{28} -0.938241 q^{29} +4.88138 q^{30} +6.86813 q^{31} +5.81740 q^{32} -3.00965 q^{33} -0.416182 q^{34} +9.76618 q^{35} -0.424004 q^{36} +8.17254 q^{37} -2.90497 q^{38} -7.99330 q^{39} -9.47771 q^{40} -10.5139 q^{41} +3.17444 q^{42} -6.61824 q^{43} +2.51978 q^{44} +1.08371 q^{45} +2.48603 q^{46} -12.6911 q^{47} +2.41097 q^{48} -0.648892 q^{49} +6.96774 q^{50} -1.08360 q^{51} +6.69224 q^{52} +0.697016 q^{53} -3.42663 q^{54} -6.44025 q^{55} -6.16351 q^{56} -7.56357 q^{57} -0.652594 q^{58} +6.97922 q^{59} -10.6408 q^{60} +2.61558 q^{61} +4.77713 q^{62} +0.704751 q^{63} +1.38367 q^{64} -17.1046 q^{65} -2.09337 q^{66} +1.81747 q^{67} +0.907223 q^{68} +6.47280 q^{69} +6.79287 q^{70} +7.78788 q^{71} -0.683935 q^{72} -8.36858 q^{73} +5.68441 q^{74} +18.1416 q^{75} +6.33246 q^{76} -4.18820 q^{77} -5.55974 q^{78} -3.75626 q^{79} +5.15916 q^{80} -9.76074 q^{81} -7.31294 q^{82} +9.81408 q^{83} -6.91986 q^{84} -2.31875 q^{85} -4.60332 q^{86} -1.69914 q^{87} +4.06449 q^{88} -9.86347 q^{89} +0.753772 q^{90} -11.1234 q^{91} -5.41923 q^{92} +12.4380 q^{93} -8.82730 q^{94} -16.1850 q^{95} +10.5352 q^{96} +12.2262 q^{97} -0.451337 q^{98} -0.464744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9} - 6 q^{10} + 39 q^{11} + 4 q^{12} - 6 q^{13} + 11 q^{14} + 12 q^{15} + 23 q^{16} + q^{17} + 7 q^{19} + 8 q^{20} - 3 q^{21} - q^{22} + 8 q^{23} - 21 q^{24} + 14 q^{25} + q^{26} + 9 q^{27} - 23 q^{28} + 9 q^{29} - 27 q^{30} - 2 q^{31} + 23 q^{32} - 5 q^{33} - 12 q^{34} + 16 q^{35} + 10 q^{36} - 7 q^{37} - 8 q^{38} - 39 q^{40} + 3 q^{41} - 30 q^{42} + q^{43} + 56 q^{44} - 21 q^{45} - q^{46} + 16 q^{47} - 31 q^{48} + 6 q^{49} - 5 q^{50} + 29 q^{51} - 37 q^{52} + 27 q^{53} - 36 q^{54} - 16 q^{55} + 14 q^{56} - 21 q^{57} - 44 q^{58} + 74 q^{59} - 27 q^{60} - 30 q^{61} - 18 q^{62} - 9 q^{63} - 17 q^{64} - 3 q^{65} - 66 q^{66} + 9 q^{67} - 51 q^{68} - 23 q^{69} - 77 q^{70} + 70 q^{71} - 55 q^{72} - 38 q^{73} + 26 q^{74} + 22 q^{75} - 50 q^{76} - 38 q^{77} - 75 q^{78} + 7 q^{79} - 28 q^{80} + 5 q^{81} - 56 q^{82} + 47 q^{83} - 69 q^{84} - 49 q^{85} + 17 q^{86} - 37 q^{87} - 30 q^{88} + 23 q^{89} - 64 q^{90} + 6 q^{91} + 17 q^{92} - 31 q^{93} - 40 q^{94} - 11 q^{95} - 49 q^{96} - 14 q^{97} + 5 q^{98} + 79 q^{99}+O(q^{100}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9 - 6 * q^10 + 39 * q^11 + 4 * q^12 - 6 * q^13 + 11 * q^14 + 12 * q^15 + 23 * q^16 + q^17 + 7 * q^19 + 8 * q^20 - 3 * q^21 - q^22 + 8 * q^23 - 21 * q^24 + 14 * q^25 + q^26 + 9 * q^27 - 23 * q^28 + 9 * q^29 - 27 * q^30 - 2 * q^31 + 23 * q^32 - 5 * q^33 - 12 * q^34 + 16 * q^35 + 10 * q^36 - 7 * q^37 - 8 * q^38 - 39 * q^40 + 3 * q^41 - 30 * q^42 + q^43 + 56 * q^44 - 21 * q^45 - q^46 + 16 * q^47 - 31 * q^48 + 6 * q^49 - 5 * q^50 + 29 * q^51 - 37 * q^52 + 27 * q^53 - 36 * q^54 - 16 * q^55 + 14 * q^56 - 21 * q^57 - 44 * q^58 + 74 * q^59 - 27 * q^60 - 30 * q^61 - 18 * q^62 - 9 * q^63 - 17 * q^64 - 3 * q^65 - 66 * q^66 + 9 * q^67 - 51 * q^68 - 23 * q^69 - 77 * q^70 + 70 * q^71 - 55 * q^72 - 38 * q^73 + 26 * q^74 + 22 * q^75 - 50 * q^76 - 38 * q^77 - 75 * q^78 + 7 * q^79 - 28 * q^80 + 5 * q^81 - 56 * q^82 + 47 * q^83 - 69 * q^84 - 49 * q^85 + 17 * q^86 - 37 * q^87 - 30 * q^88 + 23 * q^89 - 64 * q^90 + 6 * q^91 + 17 * q^92 - 31 * q^93 - 40 * q^94 - 11 * q^95 - 49 * q^96 - 14 * q^97 + 5 * q^98 + 79 * q^99

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