LMFDB - Embedded newform 1849.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, 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("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
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} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 $ x^18 - 5x^17 - 15x^16 + 106x^15 + 47x^14 - 897x^13 + 364x^12 + 3855x^11 - 3223x^10 - 8851x^9 + 9909x^8 + 10400x^7 - 14483x^6 - 5118x^5 + 9945x^4 - 27x^3 - 2493x^2 + 513*x - 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.61223$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61223 q^{2} +1.92275 q^{3} +4.82373 q^{4} -2.98756 q^{5} -5.02267 q^{6} +0.679767 q^{7} -7.37622 q^{8} +0.696981 q^{9} +O(q^{10})$	\(q-2.61223 q^{2} +1.92275 q^{3} +4.82373 q^{4} -2.98756 q^{5} -5.02267 q^{6} +0.679767 q^{7} -7.37622 q^{8} +0.696981 q^{9} +7.80417 q^{10} +2.20120 q^{11} +9.27484 q^{12} -2.41994 q^{13} -1.77571 q^{14} -5.74433 q^{15} +9.62090 q^{16} +2.52765 q^{17} -1.82067 q^{18} -1.64306 q^{19} -14.4112 q^{20} +1.30702 q^{21} -5.75002 q^{22} +0.0392999 q^{23} -14.1827 q^{24} +3.92549 q^{25} +6.32144 q^{26} -4.42814 q^{27} +3.27901 q^{28} -7.61165 q^{29} +15.0055 q^{30} +8.96369 q^{31} -10.3795 q^{32} +4.23236 q^{33} -6.60280 q^{34} -2.03084 q^{35} +3.36205 q^{36} +11.1523 q^{37} +4.29204 q^{38} -4.65296 q^{39} +22.0369 q^{40} -2.49740 q^{41} -3.41424 q^{42} +10.6180 q^{44} -2.08227 q^{45} -0.102660 q^{46} -8.79137 q^{47} +18.4986 q^{48} -6.53792 q^{49} -10.2543 q^{50} +4.86005 q^{51} -11.6732 q^{52} -6.12672 q^{53} +11.5673 q^{54} -6.57619 q^{55} -5.01411 q^{56} -3.15920 q^{57} +19.8834 q^{58} +4.77496 q^{59} -27.7091 q^{60} -5.10393 q^{61} -23.4152 q^{62} +0.473784 q^{63} +7.87190 q^{64} +7.22972 q^{65} -11.0559 q^{66} +2.59619 q^{67} +12.1927 q^{68} +0.0755640 q^{69} +5.30502 q^{70} -9.33264 q^{71} -5.14108 q^{72} -3.93616 q^{73} -29.1323 q^{74} +7.54774 q^{75} -7.92567 q^{76} +1.49630 q^{77} +12.1546 q^{78} -6.20088 q^{79} -28.7430 q^{80} -10.6052 q^{81} +6.52377 q^{82} -5.41691 q^{83} +6.30473 q^{84} -7.55150 q^{85} -14.6353 q^{87} -16.2365 q^{88} -9.96656 q^{89} +5.43936 q^{90} -1.64500 q^{91} +0.189572 q^{92} +17.2350 q^{93} +22.9650 q^{94} +4.90873 q^{95} -19.9573 q^{96} +0.945660 q^{97} +17.0785 q^{98} +1.53419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.61223	−1.84712	−0.923562	−	0.383450i	$-0.874736\pi$
$2$	−2.61223	−1.84712	−0.923562	+	0.383450i	$0.874736\pi$
$3$	1.92275	1.11010	0.555051	−	0.831816i	$-0.312699\pi$
$3$	1.92275	1.11010	0.555051	+	0.831816i	$0.312699\pi$
$4$	4.82373	2.41186
$5$	−2.98756	−1.33608	−0.668038	−	0.744128i	$-0.732865\pi$
$5$	−2.98756	−1.33608	−0.668038	+	0.744128i	$0.732865\pi$
$6$	−5.02267	−2.05050
$7$	0.679767	0.256928	0.128464	−	0.991714i	$-0.458995\pi$
$7$	0.679767	0.256928	0.128464	+	0.991714i	$0.458995\pi$
$8$	−7.37622	−2.60789
$9$	0.696981	0.232327
$10$	7.80417	2.46790
$11$	2.20120	0.663685	0.331843	−	0.943335i	$-0.392330\pi$
$11$	2.20120	0.663685	0.331843	+	0.943335i	$0.392330\pi$
$12$	9.27484	2.67742
$13$	−2.41994	−0.671172	−0.335586	−	0.942010i	$-0.608934\pi$
$13$	−2.41994	−0.671172	−0.335586	+	0.942010i	$0.608934\pi$
$14$	−1.77571	−0.474577
$15$	−5.74433	−1.48318
$16$	9.62090	2.40523
$17$	2.52765	0.613046	0.306523	−	0.951863i	$-0.400834\pi$
$17$	2.52765	0.613046	0.306523	+	0.951863i	$0.400834\pi$
$18$	−1.82067	−0.429136
$19$	−1.64306	−0.376944	−0.188472	−	0.982079i	$-0.560353\pi$
$19$	−1.64306	−0.376944	−0.188472	+	0.982079i	$0.560353\pi$
$20$	−14.4112	−3.22243
$21$	1.30702	0.285216
$22$	−5.75002	−1.22591
$23$	0.0392999	0.00819460	0.00409730	−	0.999992i	$-0.498696\pi$
$23$	0.0392999	0.00819460	0.00409730	+	0.999992i	$0.498696\pi$
$24$	−14.1827	−2.89502
$25$	3.92549	0.785097
$26$	6.32144	1.23974
$27$	−4.42814	−0.852196
$28$	3.27901	0.619675
$29$	−7.61165	−1.41345	−0.706724	−	0.707489i	$-0.749828\pi$
$29$	−7.61165	−1.41345	−0.706724	+	0.707489i	$0.749828\pi$
$30$	15.0055	2.73962
$31$	8.96369	1.60993	0.804963	−	0.593325i	$-0.202185\pi$
$31$	8.96369	1.60993	0.804963	+	0.593325i	$0.202185\pi$
$32$	−10.3795	−1.83486
$33$	4.23236	0.736759
$34$	−6.60280	−1.13237
$35$	−2.03084	−0.343275
$36$	3.36205	0.560341
$37$	11.1523	1.83342	0.916712	−	0.399550i	$-0.130833\pi$
$37$	11.1523	1.83342	0.916712	+	0.399550i	$0.130833\pi$
$38$	4.29204	0.696261
$39$	−4.65296	−0.745069
$40$	22.0369	3.48433
$41$	−2.49740	−0.390028	−0.195014	−	0.980800i	$-0.562475\pi$
$41$	−2.49740	−0.390028	−0.195014	+	0.980800i	$0.562475\pi$
$42$	−3.41424	−0.526829
$43$	0	0
$43$	0	0
$44$	10.6180	1.60072
$45$	−2.08227	−0.310406
$46$	−0.102660	−0.0151364
$47$	−8.79137	−1.28235	−0.641176	−	0.767393i	$-0.721553\pi$
$47$	−8.79137	−1.28235	−0.641176	+	0.767393i	$0.721553\pi$
$48$	18.4986	2.67005
$49$	−6.53792	−0.933988
$50$	−10.2543	−1.45017
$51$	4.86005	0.680544
$52$	−11.6732	−1.61878
$53$	−6.12672	−0.841570	−0.420785	−	0.907161i	$-0.638245\pi$
$53$	−6.12672	−0.841570	−0.420785	+	0.907161i	$0.638245\pi$
$54$	11.5673	1.57411
$55$	−6.57619	−0.886734
$56$	−5.01411	−0.670039
$57$	−3.15920	−0.418446
$58$	19.8834	2.61081
$59$	4.77496	0.621646	0.310823	−	0.950468i	$-0.399395\pi$
$59$	4.77496	0.621646	0.310823	+	0.950468i	$0.399395\pi$
$60$	−27.7091	−3.57723
$61$	−5.10393	−0.653491	−0.326745	−	0.945112i	$-0.605952\pi$
$61$	−5.10393	−0.653491	−0.326745	+	0.945112i	$0.605952\pi$
$62$	−23.4152	−2.97373
$63$	0.473784	0.0596912
$64$	7.87190	0.983987
$65$	7.22972	0.896736
$66$	−11.0559	−1.36088
$67$	2.59619	0.317175	0.158587	−	0.987345i	$-0.449306\pi$
$67$	2.59619	0.317175	0.158587	+	0.987345i	$0.449306\pi$
$68$	12.1927	1.47858
$69$	0.0755640	0.00909684
$70$	5.30502	0.634071
$71$	−9.33264	−1.10758	−0.553790	−	0.832656i	$-0.686819\pi$
$71$	−9.33264	−1.10758	−0.553790	+	0.832656i	$0.686819\pi$
$72$	−5.14108	−0.605882
$73$	−3.93616	−0.460692	−0.230346	−	0.973109i	$-0.573986\pi$
$73$	−3.93616	−0.460692	−0.230346	+	0.973109i	$0.573986\pi$
$74$	−29.1323	−3.38656
$75$	7.54774	0.871538
$76$	−7.92567	−0.909137
$77$	1.49630	0.170519
$78$	12.1546	1.37623
$79$	−6.20088	−0.697653	−0.348827	−	0.937187i	$-0.613420\pi$
$79$	−6.20088	−0.697653	−0.348827	+	0.937187i	$0.613420\pi$
$80$	−28.7430	−3.21356
$81$	−10.6052	−1.17835
$82$	6.52377	0.720430
$83$	−5.41691	−0.594583	−0.297291	−	0.954787i	$-0.596083\pi$
$83$	−5.41691	−0.594583	−0.297291	+	0.954787i	$0.596083\pi$
$84$	6.30473	0.687903
$85$	−7.55150	−0.819075
$86$	0	0
$87$	−14.6353	−1.56907
$88$	−16.2365	−1.73082
$89$	−9.96656	−1.05645	−0.528226	−	0.849104i	$-0.677143\pi$
$89$	−9.96656	−1.05645	−0.528226	+	0.849104i	$0.677143\pi$
$90$	5.43936	0.573358
$91$	−1.64500	−0.172443
$92$	0.189572	0.0197643
$93$	17.2350	1.78718
$94$	22.9650	2.36866
$95$	4.90873	0.503625
$96$	−19.9573	−2.03688
$97$	0.945660	0.0960172	0.0480086	−	0.998847i	$-0.484713\pi$
$97$	0.945660	0.0960172	0.0480086	+	0.998847i	$0.484713\pi$
$98$	17.0785	1.72519
$99$	1.53419	0.154192
$100$	18.9355	1.89355
$101$	−14.5560	−1.44838	−0.724190	−	0.689601i	$-0.757786\pi$
$101$	−14.5560	−1.44838	−0.724190	+	0.689601i	$0.757786\pi$
$102$	−12.6956	−1.25705
$103$	0.480902	0.0473846	0.0236923	−	0.999719i	$-0.492458\pi$
$103$	0.480902	0.0473846	0.0236923	+	0.999719i	$0.492458\pi$
$104$	17.8500	1.75034
$105$	−3.90481	−0.381070
$106$	16.0044	1.55448
$107$	1.86788	0.180575	0.0902874	−	0.995916i	$-0.471221\pi$
$107$	1.86788	0.180575	0.0902874	+	0.995916i	$0.471221\pi$
$108$	−21.3601	−2.05538
$109$	4.58176	0.438853	0.219426	−	0.975629i	$-0.429581\pi$
$109$	4.58176	0.438853	0.219426	+	0.975629i	$0.429581\pi$
$110$	17.1785	1.63791
$111$	21.4431	2.03529
$112$	6.53997	0.617969
$113$	13.4377	1.26411	0.632056	−	0.774923i	$-0.282211\pi$
$113$	13.4377	1.26411	0.632056	+	0.774923i	$0.282211\pi$
$114$	8.25254	0.772921
$115$	−0.117411	−0.0109486
$116$	−36.7165	−3.40905
$117$	−1.68665	−0.155931
$118$	−12.4733	−1.14826
$119$	1.71822	0.157509
$120$	42.3715	3.86797
$121$	−6.15474	−0.559522
$122$	13.3326	1.20708
$123$	−4.80188	−0.432971
$124$	43.2384	3.88292
$125$	3.21017	0.287127
$126$	−1.23763	−0.110257
$127$	−0.209986	−0.0186332	−0.00931660	−	0.999957i	$-0.502966\pi$
$127$	−0.209986	−0.0186332	−0.00931660	+	0.999957i	$0.502966\pi$
$128$	0.195885	0.0173140
$129$	0	0
$130$	−18.8857	−1.65638
$131$	−9.50170	−0.830167	−0.415084	−	0.909783i	$-0.636248\pi$
$131$	−9.50170	−0.830167	−0.415084	+	0.909783i	$0.636248\pi$
$132$	20.4157	1.77696
$133$	−1.11690	−0.0968473
$134$	−6.78183	−0.585861
$135$	13.2293	1.13860
$136$	−18.6445	−1.59875
$137$	5.92678	0.506359	0.253179	−	0.967419i	$-0.418524\pi$
$137$	5.92678	0.506359	0.253179	+	0.967419i	$0.418524\pi$
$138$	−0.197390	−0.0168030
$139$	10.9412	0.928017	0.464008	−	0.885831i	$-0.346411\pi$
$139$	10.9412	0.928017	0.464008	+	0.885831i	$0.346411\pi$
$140$	−9.79623	−0.827932
$141$	−16.9036	−1.42354
$142$	24.3790	2.04584
$143$	−5.32677	−0.445447
$144$	6.70558	0.558798
$145$	22.7402	1.88847
$146$	10.2821	0.850955
$147$	−12.5708	−1.03682
$148$	53.7956	4.42197
$149$	−10.4312	−0.854556	−0.427278	−	0.904120i	$-0.640528\pi$
$149$	−10.4312	−0.854556	−0.427278	+	0.904120i	$0.640528\pi$
$150$	−19.7164	−1.60984
$151$	9.36722	0.762294	0.381147	−	0.924514i	$-0.375529\pi$
$151$	9.36722	0.762294	0.381147	+	0.924514i	$0.375529\pi$
$152$	12.1196	0.983027
$153$	1.76172	0.142427
$154$	−3.90867	−0.314970
$155$	−26.7795	−2.15098
$156$	−22.4446	−1.79701
$157$	−7.21594	−0.575895	−0.287947	−	0.957646i	$-0.592973\pi$
$157$	−7.21594	−0.575895	−0.287947	+	0.957646i	$0.592973\pi$
$158$	16.1981	1.28865
$159$	−11.7802	−0.934228
$160$	31.0094	2.45151
$161$	0.0267148	0.00210542
$162$	27.7031	2.17656
$163$	−7.76987	−0.608583	−0.304291	−	0.952579i	$-0.598420\pi$
$163$	−7.76987	−0.608583	−0.304291	+	0.952579i	$0.598420\pi$
$164$	−12.0468	−0.940695
$165$	−12.6444	−0.984365
$166$	14.1502	1.09827
$167$	−11.6571	−0.902057	−0.451028	−	0.892510i	$-0.648943\pi$
$167$	−11.6571	−0.902057	−0.451028	+	0.892510i	$0.648943\pi$
$168$	−9.64090	−0.743811
$169$	−7.14387	−0.549529
$170$	19.7262	1.51293
$171$	−1.14518	−0.0875741
$172$	0	0
$173$	−5.35127	−0.406849	−0.203425	−	0.979091i	$-0.565207\pi$
$173$	−5.35127	−0.406849	−0.203425	+	0.979091i	$0.565207\pi$
$174$	38.2308	2.89827
$175$	2.66842	0.201713
$176$	21.1775	1.59631
$177$	9.18106	0.690091
$178$	26.0349	1.95140
$179$	14.0351	1.04903	0.524515	−	0.851401i	$-0.324247\pi$
$179$	14.0351	1.04903	0.524515	+	0.851401i	$0.324247\pi$
$180$	−10.0443	−0.748658
$181$	−19.5276	−1.45147	−0.725737	−	0.687972i	$-0.758501\pi$
$181$	−19.5276	−1.45147	−0.725737	+	0.687972i	$0.758501\pi$
$182$	4.29711	0.318523
$183$	−9.81359	−0.725442
$184$	−0.289885	−0.0213706
$185$	−33.3180	−2.44959
$186$	−45.0217	−3.30115
$187$	5.56386	0.406870
$188$	−42.4072	−3.09286
$189$	−3.01010	−0.218953
$190$	−12.8227	−0.930258
$191$	8.72471	0.631298	0.315649	−	0.948876i	$-0.397778\pi$
$191$	8.72471	0.631298	0.315649	+	0.948876i	$0.397778\pi$
$192$	15.1357	1.09233
$193$	−19.4619	−1.40090	−0.700448	−	0.713704i	$-0.747016\pi$
$193$	−19.4619	−1.40090	−0.700448	+	0.713704i	$0.747016\pi$
$194$	−2.47028	−0.177356
$195$	13.9010	0.995469
$196$	−31.5371	−2.25265
$197$	−23.3070	−1.66056	−0.830278	−	0.557349i	$-0.811818\pi$
$197$	−23.3070	−1.66056	−0.830278	+	0.557349i	$0.811818\pi$
$198$	−4.00765	−0.284811
$199$	−18.8282	−1.33470	−0.667348	−	0.744746i	$-0.732571\pi$
$199$	−18.8282	−1.33470	−0.667348	+	0.744746i	$0.732571\pi$
$200$	−28.9552	−2.04744
$201$	4.99183	0.352096
$202$	38.0237	2.67534
$203$	−5.17415	−0.363154
$204$	23.4436	1.64138
$205$	7.46112	0.521107
$206$	−1.25622	−0.0875253
$207$	0.0273913	0.00190383
$208$	−23.2820	−1.61432
$209$	−3.61669	−0.250172
$210$	10.2002	0.703884
$211$	15.5706	1.07192	0.535962	−	0.844242i	$-0.319949\pi$
$211$	15.5706	1.07192	0.535962	+	0.844242i	$0.319949\pi$
$212$	−29.5536	−2.02975
$213$	−17.9444	−1.22953
$214$	−4.87933	−0.333544
$215$	0	0
$216$	32.6629	2.22243
$217$	6.09322	0.413635
$218$	−11.9686	−0.810615
$219$	−7.56826	−0.511415
$220$	−31.7218	−2.13868
$221$	−6.11678	−0.411459
$222$	−56.0142	−3.75943
$223$	−18.1244	−1.21370	−0.606850	−	0.794816i	$-0.707567\pi$
$223$	−18.1244	−1.21370	−0.606850	+	0.794816i	$0.707567\pi$
$224$	−7.05567	−0.471427
$225$	2.73599	0.182399
$226$	−35.1023	−2.33497
$227$	24.9359	1.65505	0.827527	−	0.561426i	$-0.189747\pi$
$227$	24.9359	1.65505	0.827527	+	0.561426i	$0.189747\pi$
$228$	−15.2391	−1.00923
$229$	0.477694	0.0315669	0.0157834	−	0.999875i	$-0.494976\pi$
$229$	0.477694	0.0315669	0.0157834	+	0.999875i	$0.494976\pi$
$230$	0.306703	0.0202234
$231$	2.87702	0.189294
$232$	56.1452	3.68611
$233$	−10.5097	−0.688512	−0.344256	−	0.938876i	$-0.611869\pi$
$233$	−10.5097	−0.688512	−0.344256	+	0.938876i	$0.611869\pi$
$234$	4.40592	0.288024
$235$	26.2647	1.71332
$236$	23.0331	1.49933
$237$	−11.9228	−0.774466
$238$	−4.48837	−0.290938
$239$	12.7454	0.824433	0.412216	−	0.911086i	$-0.364755\pi$
$239$	12.7454	0.824433	0.412216	+	0.911086i	$0.364755\pi$
$240$	−55.2656	−3.56738
$241$	−4.49161	−0.289330	−0.144665	−	0.989481i	$-0.546210\pi$
$241$	−4.49161	−0.289330	−0.144665	+	0.989481i	$0.546210\pi$
$242$	16.0776	1.03351
$243$	−7.10669	−0.455894
$244$	−24.6200	−1.57613
$245$	19.5324	1.24788
$246$	12.5436	0.799751
$247$	3.97611	0.252994
$248$	−66.1182	−4.19851
$249$	−10.4154	−0.660048
$250$	−8.38570	−0.530358
$251$	−2.32015	−0.146447	−0.0732233	−	0.997316i	$-0.523329\pi$
$251$	−2.32015	−0.146447	−0.0732233	+	0.997316i	$0.523329\pi$
$252$	2.28541	0.143967
$253$	0.0865068	0.00543863
$254$	0.548530	0.0344178
$255$	−14.5197	−0.909257
$256$	−16.2555	−1.01597
$257$	0.450674	0.0281123	0.0140561	−	0.999901i	$-0.495526\pi$
$257$	0.450674	0.0281123	0.0140561	+	0.999901i	$0.495526\pi$
$258$	0	0
$259$	7.58095	0.471057
$260$	34.8742	2.16281
$261$	−5.30517	−0.328382
$262$	24.8206	1.53342
$263$	7.64762	0.471573	0.235786	−	0.971805i	$-0.424233\pi$
$263$	7.64762	0.471573	0.235786	+	0.971805i	$0.424233\pi$
$264$	−31.2188	−1.92138
$265$	18.3039	1.12440
$266$	2.91759	0.178889
$267$	−19.1632	−1.17277
$268$	12.5233	0.764982
$269$	−22.4249	−1.36727	−0.683637	−	0.729823i	$-0.739603\pi$
$269$	−22.4249	−1.36727	−0.683637	+	0.729823i	$0.739603\pi$
$270$	−34.5580	−2.10313
$271$	−6.44122	−0.391276	−0.195638	−	0.980676i	$-0.562678\pi$
$271$	−6.44122	−0.391276	−0.195638	+	0.980676i	$0.562678\pi$
$272$	24.3183	1.47451
$273$	−3.16293	−0.191429
$274$	−15.4821	−0.935307
$275$	8.64076	0.521057
$276$	0.364500	0.0219403
$277$	−13.9235	−0.836580	−0.418290	−	0.908314i	$-0.637370\pi$
$277$	−13.9235	−0.836580	−0.418290	+	0.908314i	$0.637370\pi$
$278$	−28.5808	−1.71416
$279$	6.24752	0.374029
$280$	14.9799	0.895222
$281$	−6.17983	−0.368658	−0.184329	−	0.982865i	$-0.559011\pi$
$281$	−6.17983	−0.368658	−0.184329	+	0.982865i	$0.559011\pi$
$282$	44.1561	2.62946
$283$	−1.09351	−0.0650026	−0.0325013	−	0.999472i	$-0.510347\pi$
$283$	−1.09351	−0.0650026	−0.0325013	+	0.999472i	$0.510347\pi$
$284$	−45.0181	−2.67133
$285$	9.43828	0.559075
$286$	13.9147	0.822795
$287$	−1.69765	−0.100209
$288$	−7.23433	−0.426287
$289$	−10.6110	−0.624175
$290$	−59.4026	−3.48824
$291$	1.81827	0.106589
$292$	−18.9870	−1.11113
$293$	18.2585	1.06667	0.533336	−	0.845903i	$-0.320938\pi$
$293$	18.2585	1.06667	0.533336	+	0.845903i	$0.320938\pi$
$294$	32.8378	1.91514
$295$	−14.2654	−0.830566
$296$	−82.2616	−4.78136
$297$	−9.74720	−0.565590
$298$	27.2486	1.57847
$299$	−0.0951036	−0.00549998
$300$	36.4082	2.10203
$301$	0	0
$302$	−24.4693	−1.40805
$303$	−27.9877	−1.60785
$304$	−15.8077	−0.906634
$305$	15.2483	0.873113
$306$	−4.60203	−0.263080
$307$	18.1032	1.03320	0.516601	−	0.856226i	$-0.327197\pi$
$307$	18.1032	1.03320	0.516601	+	0.856226i	$0.327197\pi$
$308$	7.21774	0.411269
$309$	0.924655	0.0526018
$310$	69.9542	3.97313
$311$	−17.3085	−0.981477	−0.490739	−	0.871307i	$-0.663273\pi$
$311$	−17.3085	−0.981477	−0.490739	+	0.871307i	$0.663273\pi$
$312$	34.3212	1.94306
$313$	6.50845	0.367879	0.183940	−	0.982938i	$-0.441115\pi$
$313$	6.50845	0.367879	0.183940	+	0.982938i	$0.441115\pi$
$314$	18.8497	1.06375
$315$	−1.41546	−0.0797520
$316$	−29.9114	−1.68265
$317$	13.2319	0.743179	0.371590	−	0.928397i	$-0.378813\pi$
$317$	13.2319	0.743179	0.371590	+	0.928397i	$0.378813\pi$
$318$	30.7725	1.72563
$319$	−16.7547	−0.938085
$320$	−23.5177	−1.31468
$321$	3.59147	0.200457
$322$	−0.0697851	−0.00388897
$323$	−4.15308	−0.231084
$324$	−51.1564	−2.84202
$325$	−9.49945	−0.526935
$326$	20.2967	1.12413
$327$	8.80959	0.487171
$328$	18.4214	1.01715
$329$	−5.97608	−0.329472
$330$	33.0300	1.81824
$331$	−10.6590	−0.585872	−0.292936	−	0.956132i	$-0.594632\pi$
$331$	−10.6590	−0.585872	−0.292936	+	0.956132i	$0.594632\pi$
$332$	−26.1297	−1.43405
$333$	7.77292	0.425953
$334$	30.4511	1.66621
$335$	−7.75625	−0.423769
$336$	12.5748	0.686009
$337$	−31.6467	−1.72391	−0.861953	−	0.506989i	$-0.830758\pi$
$337$	−31.6467	−1.72391	−0.861953	+	0.506989i	$0.830758\pi$
$338$	18.6614	1.01505
$339$	25.8374	1.40329
$340$	−36.4264	−1.97550
$341$	19.7308	1.06848
$342$	2.99147	0.161760
$343$	−9.20263	−0.496895
$344$	0	0
$345$	−0.225752	−0.0121541
$346$	13.9787	0.751501
$347$	33.9630	1.82323	0.911615	−	0.411046i	$-0.134836\pi$
$347$	33.9630	1.82323	0.911615	+	0.411046i	$0.134836\pi$
$348$	−70.5969	−3.78439
$349$	−35.1463	−1.88134	−0.940669	−	0.339326i	$-0.889801\pi$
$349$	−35.1463	−1.88134	−0.940669	+	0.339326i	$0.889801\pi$
$350$	−6.97051	−0.372589
$351$	10.7158	0.571970
$352$	−22.8474	−1.21777
$353$	10.9868	0.584767	0.292383	−	0.956301i	$-0.405552\pi$
$353$	10.9868	0.584767	0.292383	+	0.956301i	$0.405552\pi$
$354$	−23.9830	−1.27468
$355$	27.8818	1.47981
$356$	−48.0760	−2.54802
$357$	3.30370	0.174851
$358$	−36.6628	−1.93769
$359$	−13.9583	−0.736689	−0.368344	−	0.929689i	$-0.620075\pi$
$359$	−13.9583	−0.736689	−0.368344	+	0.929689i	$0.620075\pi$
$360$	15.3593	0.809504
$361$	−16.3004	−0.857913
$362$	51.0105	2.68105
$363$	−11.8340	−0.621126
$364$	−7.93502	−0.415908
$365$	11.7595	0.615520
$366$	25.6353	1.33998
$367$	27.9579	1.45939	0.729695	−	0.683773i	$-0.239662\pi$
$367$	27.9579	1.45939	0.729695	+	0.683773i	$0.239662\pi$
$368$	0.378101	0.0197099
$369$	−1.74064	−0.0906140
$370$	87.0343	4.52470
$371$	−4.16474	−0.216223
$372$	83.1368	4.31044
$373$	1.19607	0.0619304	0.0309652	−	0.999520i	$-0.490142\pi$
$373$	1.19607	0.0619304	0.0309652	+	0.999520i	$0.490142\pi$
$374$	−14.5341	−0.751538
$375$	6.17237	0.318740
$376$	64.8471	3.34423
$377$	18.4198	0.948667
$378$	7.86307	0.404433
$379$	32.9021	1.69007	0.845035	−	0.534711i	$-0.179580\pi$
$379$	32.9021	1.69007	0.845035	+	0.534711i	$0.179580\pi$
$380$	23.6784	1.21468
$381$	−0.403750	−0.0206848
$382$	−22.7909	−1.16608
$383$	−0.112958	−0.00577189	−0.00288594	−	0.999996i	$-0.500919\pi$
$383$	−0.112958	−0.00577189	−0.00288594	+	0.999996i	$0.500919\pi$
$384$	0.376639	0.0192203
$385$	−4.47028	−0.227826
$386$	50.8388	2.58763
$387$	0	0
$388$	4.56161	0.231580
$389$	−17.7092	−0.897891	−0.448946	−	0.893559i	$-0.648200\pi$
$389$	−17.7092	−0.897891	−0.448946	+	0.893559i	$0.648200\pi$
$390$	−36.3125	−1.83875
$391$	0.0993365	0.00502366
$392$	48.2251	2.43574
$393$	−18.2694	−0.921570
$394$	60.8832	3.06725
$395$	18.5255	0.932117
$396$	7.40052	0.371890
$397$	10.3830	0.521107	0.260554	−	0.965459i	$-0.416095\pi$
$397$	10.3830	0.521107	0.260554	+	0.965459i	$0.416095\pi$
$398$	49.1835	2.46535
$399$	−2.14752	−0.107510
$400$	37.7667	1.88834
$401$	36.2539	1.81043	0.905217	−	0.424950i	$-0.139708\pi$
$401$	36.2539	1.81043	0.905217	+	0.424950i	$0.139708\pi$
$402$	−13.0398	−0.650365
$403$	−21.6916	−1.08054
$404$	−70.2144	−3.49329
$405$	31.6835	1.57437
$406$	13.5161	0.670791
$407$	24.5483	1.21682
$408$	−35.8488	−1.77478
$409$	−19.7385	−0.976005	−0.488003	−	0.872842i	$-0.662274\pi$
$409$	−19.7385	−0.976005	−0.488003	+	0.872842i	$0.662274\pi$
$410$	−19.4901	−0.962549
$411$	11.3957	0.562110
$412$	2.31974	0.114285
$413$	3.24586	0.159718
$414$	−0.0715522	−0.00351660
$415$	16.1833	0.794407
$416$	25.1179	1.23151
$417$	21.0371	1.03019
$418$	9.44763	0.462098
$419$	14.7968	0.722869	0.361434	−	0.932398i	$-0.382287\pi$
$419$	14.7968	0.722869	0.361434	+	0.932398i	$0.382287\pi$
$420$	−18.8357	−0.919090
$421$	26.0686	1.27051	0.635253	−	0.772304i	$-0.280896\pi$
$421$	26.0686	1.27051	0.635253	+	0.772304i	$0.280896\pi$
$422$	−40.6739	−1.97998
$423$	−6.12741	−0.297925
$424$	45.1920	2.19472
$425$	9.92226	0.481300
$426$	46.8748	2.27109
$427$	−3.46948	−0.167900
$428$	9.01015	0.435522
$429$	−10.2421	−0.494491
$430$	0	0
$431$	22.7264	1.09469	0.547345	−	0.836907i	$-0.315638\pi$
$431$	22.7264	1.09469	0.547345	+	0.836907i	$0.315638\pi$
$432$	−42.6027	−2.04972
$433$	−11.7835	−0.566281	−0.283140	−	0.959078i	$-0.591376\pi$
$433$	−11.7835	−0.566281	−0.283140	+	0.959078i	$0.591376\pi$
$434$	−15.9169	−0.764035
$435$	43.7239	2.09640
$436$	22.1011	1.05845
$437$	−0.0645721	−0.00308890
$438$	19.7700	0.944647
$439$	−17.0959	−0.815940	−0.407970	−	0.912995i	$-0.633763\pi$
$439$	−17.0959	−0.815940	−0.407970	+	0.912995i	$0.633763\pi$
$440$	48.5074	2.31250
$441$	−4.55680	−0.216991
$442$	15.9784	0.760016
$443$	39.7352	1.88788	0.943938	−	0.330121i	$-0.107090\pi$
$443$	39.7352	1.88788	0.943938	+	0.330121i	$0.107090\pi$
$444$	103.436	4.90884
$445$	29.7756	1.41150
$446$	47.3451	2.24185
$447$	−20.0566	−0.948645
$448$	5.35106	0.252814
$449$	−20.5380	−0.969249	−0.484625	−	0.874722i	$-0.661044\pi$
$449$	−20.5380	−0.969249	−0.484625	+	0.874722i	$0.661044\pi$
$450$	−7.14702	−0.336914
$451$	−5.49726	−0.258856
$452$	64.8198	3.04887
$453$	18.0109	0.846224
$454$	−65.1382	−3.05709
$455$	4.91452	0.230396
$456$	23.3029	1.09126
$457$	22.1056	1.03406	0.517028	−	0.855968i	$-0.327038\pi$
$457$	22.1056	1.03406	0.517028	+	0.855968i	$0.327038\pi$
$458$	−1.24784	−0.0583079
$459$	−11.1928	−0.522435
$460$	−0.566357	−0.0264065
$461$	4.96668	0.231321	0.115661	−	0.993289i	$-0.463102\pi$
$461$	4.96668	0.231321	0.115661	+	0.993289i	$0.463102\pi$
$462$	−7.51542	−0.349649
$463$	−40.2128	−1.86885	−0.934423	−	0.356166i	$-0.884084\pi$
$463$	−40.2128	−1.86885	−0.934423	+	0.356166i	$0.884084\pi$
$464$	−73.2310	−3.39966
$465$	−51.4904	−2.38781
$466$	27.4537	1.27177
$467$	19.3937	0.897433	0.448717	−	0.893674i	$-0.351881\pi$
$467$	19.3937	0.897433	0.448717	+	0.893674i	$0.351881\pi$
$468$	−8.13596	−0.376085
$469$	1.76480	0.0814910
$470$	−68.6093	−3.16471
$471$	−13.8745	−0.639302
$472$	−35.2211	−1.62118
$473$	0	0
$474$	31.1450	1.43054
$475$	−6.44980	−0.295937
$476$	8.28820	0.379889
$477$	−4.27020	−0.195519
$478$	−33.2939	−1.52283
$479$	2.53789	0.115959	0.0579796	−	0.998318i	$-0.481534\pi$
$479$	2.53789	0.115959	0.0579796	+	0.998318i	$0.481534\pi$
$480$	59.6235	2.72143
$481$	−26.9879	−1.23054
$482$	11.7331	0.534428
$483$	0.0513659	0.00233723
$484$	−29.6888	−1.34949
$485$	−2.82521	−0.128286
$486$	18.5643	0.842093
$487$	0.723092	0.0327664	0.0163832	−	0.999866i	$-0.494785\pi$
$487$	0.723092	0.0327664	0.0163832	+	0.999866i	$0.494785\pi$
$488$	37.6477	1.70423
$489$	−14.9395	−0.675589
$490$	−51.0230	−2.30499
$491$	−5.19999	−0.234672	−0.117336	−	0.993092i	$-0.537436\pi$
$491$	−5.19999	−0.234672	−0.117336	+	0.993092i	$0.537436\pi$
$492$	−23.1630	−1.04427
$493$	−19.2396	−0.866509
$494$	−10.3865	−0.467311
$495$	−4.58348	−0.206012
$496$	86.2388	3.87224
$497$	−6.34402	−0.284568
$498$	27.2073	1.21919
$499$	0.155661	0.00696833	0.00348417	−	0.999994i	$-0.498891\pi$
$499$	0.155661	0.00696833	0.00348417	+	0.999994i	$0.498891\pi$
$500$	15.4850	0.692510
$501$	−22.4138	−1.00137
$502$	6.06076	0.270505
$503$	−19.9502	−0.889536	−0.444768	−	0.895646i	$-0.646714\pi$
$503$	−19.9502	−0.889536	−0.444768	+	0.895646i	$0.646714\pi$
$504$	−3.49474	−0.155668
$505$	43.4870	1.93514
$506$	−0.225975	−0.0100458
$507$	−13.7359	−0.610033
$508$	−1.01291	−0.0449408
$509$	18.6550	0.826868	0.413434	−	0.910534i	$-0.364329\pi$
$509$	18.6550	0.826868	0.413434	+	0.910534i	$0.364329\pi$
$510$	37.9287	1.67951
$511$	−2.67567	−0.118365
$512$	42.0713	1.85931
$513$	7.27569	0.321230
$514$	−1.17726	−0.0519268
$515$	−1.43672	−0.0633094
$516$	0	0
$517$	−19.3515	−0.851079
$518$	−19.8032	−0.870101
$519$	−10.2892	−0.451644
$520$	−53.3280	−2.33859
$521$	14.0088	0.613735	0.306867	−	0.951752i	$-0.400719\pi$
$521$	14.0088	0.613735	0.306867	+	0.951752i	$0.400719\pi$
$522$	13.8583	0.606562
$523$	−32.2273	−1.40920	−0.704602	−	0.709603i	$-0.748874\pi$
$523$	−32.2273	−1.40920	−0.704602	+	0.709603i	$0.748874\pi$
$524$	−45.8336	−2.00225
$525$	5.13070	0.223922
$526$	−19.9773	−0.871053
$527$	22.6571	0.986959
$528$	40.7191	1.77207
$529$	−22.9985	−0.999933
$530$	−47.8140	−2.07691
$531$	3.32805	0.144425
$532$	−5.38761	−0.233583
$533$	6.04357	0.261776
$534$	50.0587	2.16625
$535$	−5.58040	−0.241262
$536$	−19.1500	−0.827156
$537$	26.9860	1.16453
$538$	58.5790	2.52552
$539$	−14.3912	−0.619874
$540$	63.8146	2.74614
$541$	−25.4141	−1.09264	−0.546319	−	0.837577i	$-0.683971\pi$
$541$	−25.4141	−1.09264	−0.546319	+	0.837577i	$0.683971\pi$
$542$	16.8259	0.722735
$543$	−37.5467	−1.61129
$544$	−26.2359	−1.12485
$545$	−13.6882	−0.586340
$546$	8.26228	0.353593
$547$	5.43641	0.232444	0.116222	−	0.993223i	$-0.462922\pi$
$547$	5.43641	0.232444	0.116222	+	0.993223i	$0.462922\pi$
$548$	28.5892	1.22127
$549$	−3.55734	−0.151823
$550$	−22.5716	−0.962457
$551$	12.5064	0.532790
$552$	−0.557377	−0.0237235
$553$	−4.21515	−0.179247
$554$	36.3712	1.54527
$555$	−64.0624	−2.71930
$556$	52.7772	2.23825
$557$	41.8585	1.77360	0.886801	−	0.462151i	$-0.152922\pi$
$557$	41.8585	1.77360	0.886801	+	0.462151i	$0.152922\pi$
$558$	−16.3199	−0.690878
$559$	0	0
$560$	−19.5385	−0.825653
$561$	10.6979	0.451667
$562$	16.1431	0.680956
$563$	−27.7815	−1.17085	−0.585426	−	0.810726i	$-0.699073\pi$
$563$	−27.7815	−1.17085	−0.585426	+	0.810726i	$0.699073\pi$
$564$	−81.5385	−3.43339
$565$	−40.1458	−1.68895
$566$	2.85651	0.120068
$567$	−7.20904	−0.302751
$568$	68.8396	2.88845
$569$	−25.7886	−1.08111	−0.540556	−	0.841308i	$-0.681786\pi$
$569$	−25.7886	−1.08111	−0.540556	+	0.841308i	$0.681786\pi$
$570$	−24.6549	−1.03268
$571$	40.0987	1.67808	0.839039	−	0.544071i	$-0.183118\pi$
$571$	40.0987	1.67808	0.839039	+	0.544071i	$0.183118\pi$
$572$	−25.6949	−1.07436
$573$	16.7755	0.700805
$574$	4.43465	0.185099
$575$	0.154271	0.00643355
$576$	5.48656	0.228607
$577$	20.1755	0.839919	0.419959	−	0.907543i	$-0.362044\pi$
$577$	20.1755	0.839919	0.419959	+	0.907543i	$0.362044\pi$
$578$	27.7183	1.15293
$579$	−37.4204	−1.55514
$580$	109.693	4.55474
$581$	−3.68224	−0.152765
$582$	−4.74973	−0.196883
$583$	−13.4861	−0.558537
$584$	29.0340	1.20143
$585$	5.03897	0.208336
$586$	−47.6953	−1.97028
$587$	11.5940	0.478535	0.239267	−	0.970954i	$-0.423093\pi$
$587$	11.5940	0.478535	0.239267	+	0.970954i	$0.423093\pi$
$588$	−60.6381	−2.50067
$589$	−14.7279	−0.606852
$590$	37.2646	1.53416
$591$	−44.8137	−1.84339
$592$	107.295	4.40980
$593$	12.2185	0.501754	0.250877	−	0.968019i	$-0.419281\pi$
$593$	12.2185	0.501754	0.250877	+	0.968019i	$0.419281\pi$
$594$	25.4619	1.04471
$595$	−5.13326	−0.210443
$596$	−50.3172	−2.06107
$597$	−36.2020	−1.48165
$598$	0.248432	0.0101591
$599$	9.55344	0.390343	0.195171	−	0.980769i	$-0.437474\pi$
$599$	9.55344	0.390343	0.195171	+	0.980769i	$0.437474\pi$
$600$	−55.6738	−2.27287
$601$	−9.69294	−0.395383	−0.197692	−	0.980264i	$-0.563344\pi$
$601$	−9.69294	−0.395383	−0.197692	+	0.980264i	$0.563344\pi$
$602$	0	0
$603$	1.80949	0.0736882
$604$	45.1849	1.83855
$605$	18.3876	0.747563
$606$	73.1101	2.96990
$607$	−1.93527	−0.0785503	−0.0392751	−	0.999228i	$-0.512505\pi$
$607$	−1.93527	−0.0785503	−0.0392751	+	0.999228i	$0.512505\pi$
$608$	17.0542	0.691639
$609$	−9.94862	−0.403138
$610$	−39.8319	−1.61275
$611$	21.2746	0.860679
$612$	8.49808	0.343515
$613$	15.5681	0.628789	0.314394	−	0.949292i	$-0.398199\pi$
$613$	15.5681	0.628789	0.314394	+	0.949292i	$0.398199\pi$
$614$	−47.2895	−1.90845
$615$	14.3459	0.578482
$616$	−11.0370	−0.444695
$617$	20.9492	0.843382	0.421691	−	0.906740i	$-0.361437\pi$
$617$	20.9492	0.843382	0.421691	+	0.906740i	$0.361437\pi$
$618$	−2.41541	−0.0971620
$619$	45.5492	1.83078	0.915389	−	0.402571i	$-0.131883\pi$
$619$	45.5492	1.83078	0.915389	+	0.402571i	$0.131883\pi$
$620$	−129.177	−5.18788
$621$	−0.174025	−0.00698340
$622$	45.2138	1.81291
$623$	−6.77494	−0.271432
$624$	−44.7656	−1.79206
$625$	−29.2180	−1.16872
$626$	−17.0015	−0.679518
$627$	−6.95401	−0.277716
$628$	−34.8077	−1.38898
$629$	28.1891	1.12397
$630$	3.69749	0.147312
$631$	−10.7971	−0.429826	−0.214913	−	0.976633i	$-0.568947\pi$
$631$	−10.7971	−0.429826	−0.214913	+	0.976633i	$0.568947\pi$
$632$	45.7390	1.81940
$633$	29.9384	1.18994
$634$	−34.5648	−1.37274
$635$	0.627343	0.0248954
$636$	−56.8243	−2.25323
$637$	15.8214	0.626866
$638$	43.7672	1.73276
$639$	−6.50467	−0.257321
$640$	−0.585218	−0.0231328
$641$	−6.61495	−0.261275	−0.130637	−	0.991430i	$-0.541702\pi$
$641$	−6.61495	−0.261275	−0.130637	+	0.991430i	$0.541702\pi$
$642$	−9.38174	−0.370268
$643$	38.7461	1.52800	0.763999	−	0.645217i	$-0.223233\pi$
$643$	38.7461	1.52800	0.763999	+	0.645217i	$0.223233\pi$
$644$	0.128865	0.00507799
$645$	0	0
$646$	10.8488	0.426840
$647$	22.9484	0.902195	0.451097	−	0.892475i	$-0.351033\pi$
$647$	22.9484	0.902195	0.451097	+	0.892475i	$0.351033\pi$
$648$	78.2260	3.07301
$649$	10.5106	0.412578
$650$	24.8147	0.973314
$651$	11.7158	0.459177
$652$	−37.4797	−1.46782
$653$	28.5505	1.11727	0.558635	−	0.829414i	$-0.311325\pi$
$653$	28.5505	1.11727	0.558635	+	0.829414i	$0.311325\pi$
$654$	−23.0126	−0.899865
$655$	28.3868	1.10917
$656$	−24.0272	−0.938106
$657$	−2.74342	−0.107031
$658$	15.6109	0.608576
$659$	16.8662	0.657016	0.328508	−	0.944501i	$-0.393454\pi$
$659$	16.8662	0.657016	0.328508	+	0.944501i	$0.393454\pi$
$660$	−60.9931	−2.37415
$661$	8.99989	0.350055	0.175028	−	0.984564i	$-0.443999\pi$
$661$	8.99989	0.350055	0.175028	+	0.984564i	$0.443999\pi$
$662$	27.8437	1.08218
$663$	−11.7611	−0.456762
$664$	39.9563	1.55061
$665$	3.33679	0.129395
$666$	−20.3046	−0.786788
$667$	−0.299137	−0.0115826
$668$	−56.2309	−2.17564
$669$	−34.8488	−1.34733
$670$	20.2611	0.782754
$671$	−11.2347	−0.433712
$672$	−13.5663	−0.523332
$673$	−11.9596	−0.461010	−0.230505	−	0.973071i	$-0.574038\pi$
$673$	−11.9596	−0.461010	−0.230505	+	0.973071i	$0.574038\pi$
$674$	82.6683	3.18427
$675$	−17.3826	−0.669056
$676$	−34.4601	−1.32539
$677$	−43.4314	−1.66920	−0.834602	−	0.550854i	$-0.814302\pi$
$677$	−43.4314	−1.66920	−0.834602	+	0.550854i	$0.814302\pi$
$678$	−67.4931	−2.59206
$679$	0.642828	0.0246695
$680$	55.7015	2.13606
$681$	47.9456	1.83728
$682$	−51.5414	−1.97362
$683$	−7.35121	−0.281286	−0.140643	−	0.990060i	$-0.544917\pi$
$683$	−7.35121	−0.281286	−0.140643	+	0.990060i	$0.544917\pi$
$684$	−5.52404	−0.211217
$685$	−17.7066	−0.676533
$686$	24.0394	0.917827
$687$	0.918487	0.0350425
$688$	0	0
$689$	14.8263	0.564838
$690$	0.589715	0.0224501
$691$	−0.0773691	−0.00294326	−0.00147163	−	0.999999i	$-0.500468\pi$
$691$	−0.0773691	−0.00294326	−0.00147163	+	0.999999i	$0.500468\pi$
$692$	−25.8131	−0.981266
$693$	1.04289	0.0396162
$694$	−88.7191	−3.36773
$695$	−32.6873	−1.23990
$696$	107.953	4.09196
$697$	−6.31256	−0.239105
$698$	91.8101	3.47506
$699$	−20.2075	−0.764319
$700$	12.8717	0.486505
$701$	−7.24869	−0.273779	−0.136890	−	0.990586i	$-0.543711\pi$
$701$	−7.24869	−0.273779	−0.136890	+	0.990586i	$0.543711\pi$
$702$	−27.9922	−1.05650
$703$	−18.3239	−0.691097
$704$	17.3276	0.653058
$705$	50.5005	1.90196
$706$	−28.6999	−1.08014
$707$	−9.89471	−0.372129
$708$	44.2870	1.66441
$709$	−18.2639	−0.685914	−0.342957	−	0.939351i	$-0.611429\pi$
$709$	−18.2639	−0.685914	−0.342957	+	0.939351i	$0.611429\pi$
$710$	−72.8335	−2.73339
$711$	−4.32189	−0.162084
$712$	73.5155	2.75511
$713$	0.352272	0.0131927
$714$	−8.63002	−0.322971
$715$	15.9140	0.595150
$716$	67.7013	2.53012
$717$	24.5063	0.915205
$718$	36.4621	1.36075
$719$	24.6148	0.917977	0.458988	−	0.888442i	$-0.348212\pi$
$719$	24.6148	0.917977	0.458988	+	0.888442i	$0.348212\pi$
$720$	−20.0333	−0.746597
$721$	0.326901	0.0121744
$722$	42.5802	1.58467
$723$	−8.63625	−0.321186
$724$	−94.1958	−3.50076
$725$	−29.8794	−1.10969
$726$	30.9132	1.14730
$727$	34.4425	1.27740	0.638701	−	0.769455i	$-0.279472\pi$
$727$	34.4425	1.27740	0.638701	+	0.769455i	$0.279472\pi$
$728$	12.1339	0.449711
$729$	18.1511	0.672262
$730$	−30.7184	−1.13694
$731$	0	0
$732$	−47.3381	−1.74967
$733$	27.4557	1.01410	0.507050	−	0.861917i	$-0.330736\pi$
$733$	27.4557	1.01410	0.507050	+	0.861917i	$0.330736\pi$
$734$	−73.0323	−2.69567
$735$	37.5560	1.38527
$736$	−0.407915	−0.0150359
$737$	5.71471	0.210504
$738$	4.54694	0.167375
$739$	−43.0960	−1.58531	−0.792656	−	0.609670i	$-0.791302\pi$
$739$	−43.0960	−1.58531	−0.792656	+	0.609670i	$0.791302\pi$
$740$	−160.717	−5.90808
$741$	7.64508	0.280849
$742$	10.8792	0.399390
$743$	−25.4527	−0.933769	−0.466885	−	0.884318i	$-0.654624\pi$
$743$	−25.4527	−0.933769	−0.466885	+	0.884318i	$0.654624\pi$
$744$	−127.129	−4.66077
$745$	31.1638	1.14175
$746$	−3.12442	−0.114393
$747$	−3.77548	−0.138138
$748$	26.8385	0.981314
$749$	1.26972	0.0463947
$750$	−16.1236	−0.588752
$751$	34.0206	1.24143	0.620715	−	0.784037i	$-0.286843\pi$
$751$	34.0206	1.24143	0.620715	+	0.784037i	$0.286843\pi$
$752$	−84.5809	−3.08435
$753$	−4.46108	−0.162571
$754$	−48.1166	−1.75230
$755$	−27.9851	−1.01848
$756$	−14.5199	−0.528084
$757$	0.387966	0.0141009	0.00705043	−	0.999975i	$-0.497756\pi$
$757$	0.387966	0.0141009	0.00705043	+	0.999975i	$0.497756\pi$
$758$	−85.9479	−3.12177
$759$	0.166331	0.00603744
$760$	−36.2079	−1.31340
$761$	−8.03441	−0.291247	−0.145624	−	0.989340i	$-0.546519\pi$
$761$	−8.03441	−0.291247	−0.145624	+	0.989340i	$0.546519\pi$
$762$	1.05469	0.0382073
$763$	3.11453	0.112753
$764$	42.0856	1.52260
$765$	−5.26325	−0.190293
$766$	0.295072	0.0106614
$767$	−11.5551	−0.417231
$768$	−31.2553	−1.12783
$769$	20.5513	0.741099	0.370549	−	0.928813i	$-0.379169\pi$
$769$	20.5513	0.741099	0.370549	+	0.928813i	$0.379169\pi$
$770$	11.6774	0.420824
$771$	0.866535	0.0312075
$772$	−93.8787	−3.37877
$773$	−20.6462	−0.742592	−0.371296	−	0.928515i	$-0.621086\pi$
$773$	−20.6462	−0.742592	−0.371296	+	0.928515i	$0.621086\pi$
$774$	0	0
$775$	35.1868	1.26395
$776$	−6.97539	−0.250402
$777$	14.5763	0.522922
$778$	46.2604	1.65852
$779$	4.10337	0.147019
$780$	67.0545	2.40093
$781$	−20.5430	−0.735085
$782$	−0.259490	−0.00927933
$783$	33.7055	1.20453
$784$	−62.9007	−2.24645
$785$	21.5580	0.769439
$786$	47.7239	1.70225
$787$	33.5985	1.19766	0.598828	−	0.800877i	$-0.295633\pi$
$787$	33.5985	1.19766	0.598828	+	0.800877i	$0.295633\pi$
$788$	−112.427	−4.00504
$789$	14.7045	0.523494
$790$	−48.3927	−1.72174
$791$	9.13450	0.324785
$792$	−11.3165	−0.402115
$793$	12.3512	0.438605
$794$	−27.1227	−0.962549
$795$	35.1939	1.24820
$796$	−90.8221	−3.21911
$797$	23.3004	0.825343	0.412671	−	0.910880i	$-0.364596\pi$
$797$	23.3004	0.825343	0.412671	+	0.910880i	$0.364596\pi$
$798$	5.60981	0.198585
$799$	−22.2215	−0.786141
$800$	−40.7447	−1.44054
$801$	−6.94650	−0.245442
$802$	−94.7034	−3.34409
$803$	−8.66425	−0.305755
$804$	24.0792	0.849208
$805$	−0.0798119	−0.00281300
$806$	56.6635	1.99589
$807$	−43.1176	−1.51781
$808$	107.369	3.77721
$809$	19.0177	0.668626	0.334313	−	0.942462i	$-0.391496\pi$
$809$	19.0177	0.668626	0.334313	+	0.942462i	$0.391496\pi$
$810$	−82.7645	−2.90805
$811$	8.58255	0.301374	0.150687	−	0.988582i	$-0.451851\pi$
$811$	8.58255	0.301374	0.150687	+	0.988582i	$0.451851\pi$
$812$	−24.9587	−0.875879
$813$	−12.3849	−0.434356
$814$	−64.1258	−2.24761
$815$	23.2129	0.813112
$816$	46.7581	1.63686
$817$	0	0
$818$	51.5614	1.80280
$819$	−1.14653	−0.0400631
$820$	35.9904	1.25684
$821$	−26.7183	−0.932474	−0.466237	−	0.884660i	$-0.654391\pi$
$821$	−26.7183	−0.932474	−0.466237	+	0.884660i	$0.654391\pi$
$822$	−29.7682	−1.03829
$823$	10.2554	0.357481	0.178740	−	0.983896i	$-0.442798\pi$
$823$	10.2554	0.357481	0.178740	+	0.983896i	$0.442798\pi$
$824$	−3.54724	−0.123574
$825$	16.6140	0.578427
$826$	−8.47892	−0.295019
$827$	−35.5699	−1.23689	−0.618444	−	0.785829i	$-0.712236\pi$
$827$	−35.5699	−1.23689	−0.618444	+	0.785829i	$0.712236\pi$
$828$	0.132128	0.00459177
$829$	−19.4074	−0.674046	−0.337023	−	0.941496i	$-0.609420\pi$
$829$	−19.4074	−0.674046	−0.337023	+	0.941496i	$0.609420\pi$
$830$	−42.2745	−1.46737
$831$	−26.7714	−0.928689
$832$	−19.0496	−0.660425
$833$	−16.5256	−0.572578
$834$	−54.9538	−1.90289
$835$	34.8263	1.20522
$836$	−17.4460	−0.603381
$837$	−39.6925	−1.37197
$838$	−38.6525	−1.33523
$839$	41.1635	1.42112	0.710561	−	0.703635i	$-0.248441\pi$
$839$	41.1635	1.42112	0.710561	+	0.703635i	$0.248441\pi$
$840$	28.8027	0.993788
$841$	28.9373	0.997837
$842$	−68.0971	−2.34678
$843$	−11.8823	−0.409248
$844$	75.1083	2.58533
$845$	21.3427	0.734211
$846$	16.0062	0.550304
$847$	−4.18379	−0.143757
$848$	−58.9446	−2.02416
$849$	−2.10256	−0.0721596
$850$	−25.9192	−0.889021
$851$	0.438283	0.0150242
$852$	−86.5587	−2.96545
$853$	24.1008	0.825195	0.412598	−	0.910913i	$-0.364622\pi$
$853$	24.1008	0.825195	0.412598	+	0.910913i	$0.364622\pi$
$854$	9.06307	0.310132
$855$	3.42129	0.117006
$856$	−13.7779	−0.470919
$857$	25.0028	0.854081	0.427040	−	0.904233i	$-0.359556\pi$
$857$	25.0028	0.854081	0.427040	+	0.904233i	$0.359556\pi$
$858$	26.7546	0.913387
$859$	49.1887	1.67830	0.839148	−	0.543904i	$-0.183054\pi$
$859$	49.1887	1.67830	0.839148	+	0.543904i	$0.183054\pi$
$860$	0	0
$861$	−3.26416	−0.111242
$862$	−59.3664	−2.02203
$863$	−25.4685	−0.866958	−0.433479	−	0.901164i	$-0.642714\pi$
$863$	−25.4685	−0.866958	−0.433479	+	0.901164i	$0.642714\pi$
$864$	45.9620	1.56366
$865$	15.9872	0.543581
$866$	30.7813	1.04599
$867$	−20.4023	−0.692898
$868$	29.3921	0.997631
$869$	−13.6493	−0.463022
$870$	−114.217	−3.87231
$871$	−6.28263	−0.212879
$872$	−33.7960	−1.14448
$873$	0.659106	0.0223074
$874$	0.168677	0.00570558
$875$	2.18217	0.0737708
$876$	−36.5072	−1.23346
$877$	−44.6732	−1.50851	−0.754253	−	0.656584i	$-0.772001\pi$
$877$	−44.6732	−1.50851	−0.754253	+	0.656584i	$0.772001\pi$
$878$	44.6582	1.50714
$879$	35.1066	1.18412
$880$	−63.2689	−2.13279
$881$	−9.48777	−0.319651	−0.159826	−	0.987145i	$-0.551093\pi$
$881$	−9.48777	−0.319651	−0.159826	+	0.987145i	$0.551093\pi$
$882$	11.9034	0.400808
$883$	17.6537	0.594096	0.297048	−	0.954863i	$-0.403998\pi$
$883$	17.6537	0.594096	0.297048	+	0.954863i	$0.403998\pi$
$884$	−29.5057	−0.992383
$885$	−27.4289	−0.922013
$886$	−103.797	−3.48714
$887$	−40.0969	−1.34632	−0.673161	−	0.739496i	$-0.735064\pi$
$887$	−40.0969	−1.34632	−0.673161	+	0.739496i	$0.735064\pi$
$888$	−158.169	−5.30780
$889$	−0.142741	−0.00478739
$890$	−77.7807	−2.60722
$891$	−23.3440	−0.782054
$892$	−87.4272	−2.92728
$893$	14.4447	0.483375
$894$	52.3924	1.75226
$895$	−41.9305	−1.40158
$896$	0.133156	0.00444844
$897$	−0.182861	−0.00610554
$898$	53.6500	1.79032
$899$	−68.2285	−2.27555
$900$	13.1977	0.439922
$901$	−15.4862	−0.515921
$902$	14.3601	0.478139
$903$	0	0
$904$	−99.1194	−3.29666
$905$	58.3398	1.93928
$906$	−47.0484	−1.56308
$907$	30.1196	1.00011	0.500053	−	0.865995i	$-0.333314\pi$
$907$	30.1196	1.00011	0.500053	+	0.865995i	$0.333314\pi$
$908$	120.284	3.99176
$909$	−10.1453	−0.336497
$910$	−12.8378	−0.425570
$911$	−39.7485	−1.31693	−0.658463	−	0.752613i	$-0.728793\pi$
$911$	−39.7485	−1.31693	−0.658463	+	0.752613i	$0.728793\pi$
$912$	−30.3943	−1.00646
$913$	−11.9237	−0.394616
$914$	−57.7449	−1.91003
$915$	29.3186	0.969245
$916$	2.30426	0.0761351
$917$	−6.45894	−0.213293
$918$	29.2381	0.965002
$919$	−0.385315	−0.0127104	−0.00635518	−	0.999980i	$-0.502023\pi$
$919$	−0.385315	−0.0127104	−0.00635518	+	0.999980i	$0.502023\pi$
$920$	0.866047	0.0285527
$921$	34.8079	1.14696
$922$	−12.9741	−0.427279
$923$	22.5845	0.743377
$924$	13.8779	0.456551
$925$	43.7781	1.43941
$926$	105.045	3.45199
$927$	0.335179	0.0110087
$928$	79.0054	2.59348
$929$	38.3136	1.25703	0.628514	−	0.777798i	$-0.283663\pi$
$929$	38.3136	1.25703	0.628514	+	0.777798i	$0.283663\pi$
$930$	134.505	4.41058
$931$	10.7422	0.352061
$932$	−50.6959	−1.66060
$933$	−33.2800	−1.08954
$934$	−50.6607	−1.65767
$935$	−16.6223	−0.543608
$936$	12.4411	0.406651
$937$	43.2179	1.41187	0.705934	−	0.708277i	$-0.250527\pi$
$937$	43.2179	1.41187	0.705934	+	0.708277i	$0.250527\pi$
$938$	−4.61006	−0.150524
$939$	12.5141	0.408384
$940$	126.694	4.13230
$941$	19.9645	0.650823	0.325411	−	0.945573i	$-0.394497\pi$
$941$	19.9645	0.650823	0.325411	+	0.945573i	$0.394497\pi$
$942$	36.2433	1.18087
$943$	−0.0981476	−0.00319612
$944$	45.9394	1.49520
$945$	8.99285	0.292537
$946$	0	0
$947$	−58.8426	−1.91213	−0.956064	−	0.293159i	$-0.905293\pi$
$947$	−58.8426	−1.91213	−0.956064	+	0.293159i	$0.905293\pi$
$948$	−57.5122	−1.86791
$949$	9.52528	0.309204
$950$	16.8484	0.546633
$951$	25.4417	0.825005
$952$	−12.6739	−0.410764
$953$	3.18233	0.103086	0.0515429	−	0.998671i	$-0.483586\pi$
$953$	3.18233	0.103086	0.0515429	+	0.998671i	$0.483586\pi$
$954$	11.1547	0.361148
$955$	−26.0656	−0.843461
$956$	61.4805	1.98842
$957$	−32.2152	−1.04137
$958$	−6.62955	−0.214191
$959$	4.02883	0.130098
$960$	−45.2188	−1.45943
$961$	49.3478	1.59186
$962$	70.4985	2.27296
$963$	1.30188	0.0419524
$964$	−21.6663	−0.697824
$965$	58.1434	1.87170
$966$	−0.134179	−0.00431715
$967$	36.2820	1.16675	0.583375	−	0.812203i	$-0.301732\pi$
$967$	36.2820	1.16675	0.583375	+	0.812203i	$0.301732\pi$
$968$	45.3987	1.45917
$969$	−7.98536	−0.256527
$970$	7.38009	0.236960
$971$	9.80728	0.314731	0.157365	−	0.987540i	$-0.449700\pi$
$971$	9.80728	0.314731	0.157365	+	0.987540i	$0.449700\pi$
$972$	−34.2808	−1.09956
$973$	7.43744	0.238433
$974$	−1.88888	−0.0605236
$975$	−18.2651	−0.584952
$976$	−49.1044	−1.57179
$977$	43.5684	1.39388	0.696938	−	0.717131i	$-0.254545\pi$
$977$	43.5684	1.39388	0.696938	+	0.717131i	$0.254545\pi$
$978$	39.0255	1.24790
$979$	−21.9383	−0.701152
$980$	94.2189	3.00971
$981$	3.19339	0.101957
$982$	13.5836	0.433469
$983$	8.15789	0.260196	0.130098	−	0.991501i	$-0.458471\pi$
$983$	8.15789	0.260196	0.130098	+	0.991501i	$0.458471\pi$
$984$	35.4197	1.12914
$985$	69.6310	2.21863
$986$	50.2582	1.60055
$987$	−11.4905	−0.365748
$988$	19.1797	0.610187
$989$	0	0
$990$	11.9731	0.380530
$991$	−43.6700	−1.38722	−0.693611	−	0.720350i	$-0.743981\pi$
$991$	−43.6700	−1.38722	−0.693611	+	0.720350i	$0.743981\pi$
$992$	−93.0390	−2.95399
$993$	−20.4946	−0.650378
$994$	16.5720	0.525633
$995$	56.2503	1.78325
$996$	−50.2410	−1.59195
$997$	44.9770	1.42444	0.712218	−	0.701959i	$-0.247691\pi$
$997$	44.9770	1.42444	0.712218	+	0.701959i	$0.247691\pi$
$998$	−0.406621	−0.0128714
$999$	−49.3838	−1.56244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.n.1.2		18
43.15	even	21		43.2.g.a.10.3	✓	36
43.23	even	21		43.2.g.a.13.3	yes	36
43.42	odd	2		1849.2.a.o.1.17		18
129.23	odd	42		387.2.y.c.271.1		36
129.101	odd	42		387.2.y.c.10.1		36
172.15	odd	42		688.2.bg.c.225.3		36
172.23	odd	42		688.2.bg.c.529.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.10.3	✓	36	43.15	even	21
43.2.g.a.13.3	yes	36	43.23	even	21
387.2.y.c.10.1		36	129.101	odd	42
387.2.y.c.271.1		36	129.23	odd	42
688.2.bg.c.225.3		36	172.15	odd	42
688.2.bg.c.529.3		36	172.23	odd	42
1849.2.a.n.1.2		18	1.1	even	1	trivial
1849.2.a.o.1.17		18	43.42	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61223 q^{2} +1.92275 q^{3} +4.82373 q^{4} -2.98756 q^{5} -5.02267 q^{6} +0.679767 q^{7} -7.37622 q^{8} +0.696981 q^{9} +O(q^{10})\)	\(q-2.61223 q^{2} +1.92275 q^{3} +4.82373 q^{4} -2.98756 q^{5} -5.02267 q^{6} +0.679767 q^{7} -7.37622 q^{8} +0.696981 q^{9} +7.80417 q^{10} +2.20120 q^{11} +9.27484 q^{12} -2.41994 q^{13} -1.77571 q^{14} -5.74433 q^{15} +9.62090 q^{16} +2.52765 q^{17} -1.82067 q^{18} -1.64306 q^{19} -14.4112 q^{20} +1.30702 q^{21} -5.75002 q^{22} +0.0392999 q^{23} -14.1827 q^{24} +3.92549 q^{25} +6.32144 q^{26} -4.42814 q^{27} +3.27901 q^{28} -7.61165 q^{29} +15.0055 q^{30} +8.96369 q^{31} -10.3795 q^{32} +4.23236 q^{33} -6.60280 q^{34} -2.03084 q^{35} +3.36205 q^{36} +11.1523 q^{37} +4.29204 q^{38} -4.65296 q^{39} +22.0369 q^{40} -2.49740 q^{41} -3.41424 q^{42} +10.6180 q^{44} -2.08227 q^{45} -0.102660 q^{46} -8.79137 q^{47} +18.4986 q^{48} -6.53792 q^{49} -10.2543 q^{50} +4.86005 q^{51} -11.6732 q^{52} -6.12672 q^{53} +11.5673 q^{54} -6.57619 q^{55} -5.01411 q^{56} -3.15920 q^{57} +19.8834 q^{58} +4.77496 q^{59} -27.7091 q^{60} -5.10393 q^{61} -23.4152 q^{62} +0.473784 q^{63} +7.87190 q^{64} +7.22972 q^{65} -11.0559 q^{66} +2.59619 q^{67} +12.1927 q^{68} +0.0755640 q^{69} +5.30502 q^{70} -9.33264 q^{71} -5.14108 q^{72} -3.93616 q^{73} -29.1323 q^{74} +7.54774 q^{75} -7.92567 q^{76} +1.49630 q^{77} +12.1546 q^{78} -6.20088 q^{79} -28.7430 q^{80} -10.6052 q^{81} +6.52377 q^{82} -5.41691 q^{83} +6.30473 q^{84} -7.55150 q^{85} -14.6353 q^{87} -16.2365 q^{88} -9.96656 q^{89} +5.43936 q^{90} -1.64500 q^{91} +0.189572 q^{92} +17.2350 q^{93} +22.9650 q^{94} +4.90873 q^{95} -19.9573 q^{96} +0.945660 q^{97} +17.0785 q^{98} +1.53419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * q^99

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