LMFDB - Embedded newform 1511.2.a.a.1.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1511,2,Mod(1,1511)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1511, 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("1511.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1511 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1511.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:	$12.0653957454$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.33
Character	$\chi$	$=$	1511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.68314 q^{2} -2.46738 q^{3} +0.832944 q^{4} +1.71768 q^{5} -4.15294 q^{6} +2.31892 q^{7} -1.96431 q^{8} +3.08797 q^{9} +O(q^{10})$	\(q+1.68314 q^{2} -2.46738 q^{3} +0.832944 q^{4} +1.71768 q^{5} -4.15294 q^{6} +2.31892 q^{7} -1.96431 q^{8} +3.08797 q^{9} +2.89109 q^{10} -2.61673 q^{11} -2.05519 q^{12} -5.48247 q^{13} +3.90306 q^{14} -4.23817 q^{15} -4.97209 q^{16} +0.913918 q^{17} +5.19747 q^{18} +2.99129 q^{19} +1.43073 q^{20} -5.72167 q^{21} -4.40430 q^{22} -3.04790 q^{23} +4.84671 q^{24} -2.04958 q^{25} -9.22774 q^{26} -0.217053 q^{27} +1.93153 q^{28} +2.41910 q^{29} -7.13341 q^{30} -3.77310 q^{31} -4.44008 q^{32} +6.45646 q^{33} +1.53825 q^{34} +3.98317 q^{35} +2.57210 q^{36} -2.50049 q^{37} +5.03474 q^{38} +13.5273 q^{39} -3.37406 q^{40} -3.91678 q^{41} -9.63034 q^{42} +5.22664 q^{43} -2.17959 q^{44} +5.30414 q^{45} -5.13002 q^{46} -8.64836 q^{47} +12.2680 q^{48} -1.62260 q^{49} -3.44971 q^{50} -2.25498 q^{51} -4.56659 q^{52} -3.96696 q^{53} -0.365330 q^{54} -4.49470 q^{55} -4.55509 q^{56} -7.38064 q^{57} +4.07166 q^{58} -6.73649 q^{59} -3.53016 q^{60} -10.2349 q^{61} -6.35063 q^{62} +7.16076 q^{63} +2.47093 q^{64} -9.41713 q^{65} +10.8671 q^{66} -0.330726 q^{67} +0.761242 q^{68} +7.52032 q^{69} +6.70421 q^{70} -4.58321 q^{71} -6.06574 q^{72} -4.65070 q^{73} -4.20866 q^{74} +5.05709 q^{75} +2.49157 q^{76} -6.06799 q^{77} +22.7684 q^{78} +1.70219 q^{79} -8.54046 q^{80} -8.72835 q^{81} -6.59247 q^{82} +3.53327 q^{83} -4.76583 q^{84} +1.56982 q^{85} +8.79713 q^{86} -5.96883 q^{87} +5.14007 q^{88} -0.363556 q^{89} +8.92759 q^{90} -12.7134 q^{91} -2.53873 q^{92} +9.30967 q^{93} -14.5564 q^{94} +5.13807 q^{95} +10.9554 q^{96} -2.73925 q^{97} -2.73105 q^{98} -8.08037 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 5 q^{2} - 4 q^{3} + 19 q^{4} - 8 q^{5} - 8 q^{6} - 15 q^{7} - 12 q^{8} - q^{9}+O(q^{10}) $ 39 * q - 5 * q^2 - 4 * q^3 + 19 * q^4 - 8 * q^5 - 8 * q^6 - 15 * q^7 - 12 * q^8 - q^9	\( 39 q - 5 q^{2} - 4 q^{3} + 19 q^{4} - 8 q^{5} - 8 q^{6} - 15 q^{7} - 12 q^{8} - q^{9} - 13 q^{10} - 13 q^{11} - 8 q^{12} - 24 q^{13} - 12 q^{14} - 16 q^{15} - 13 q^{16} - 26 q^{17} - 17 q^{18} - 40 q^{19} - 15 q^{20} - 26 q^{21} - 26 q^{22} - 8 q^{23} - 16 q^{24} - 35 q^{25} - 3 q^{26} - 10 q^{27} - 31 q^{28} - 30 q^{29} - 16 q^{30} - 21 q^{31} - 9 q^{32} - 25 q^{33} - 27 q^{34} - 2 q^{35} - 23 q^{36} - 27 q^{37} + q^{38} - 29 q^{39} - 36 q^{40} - 35 q^{41} - 6 q^{42} - 48 q^{43} - 17 q^{44} - 22 q^{45} - 31 q^{46} - 3 q^{47} + q^{48} - 64 q^{49} + 12 q^{50} - 27 q^{51} - 28 q^{52} - 14 q^{53} + q^{54} - 31 q^{55} - 12 q^{56} - 36 q^{57} - 19 q^{58} - 9 q^{59} - 6 q^{60} - 87 q^{61} + 32 q^{62} - 9 q^{63} - 52 q^{64} - 35 q^{65} + 5 q^{66} - 24 q^{67} - 13 q^{68} - 35 q^{69} - 8 q^{70} - 21 q^{71} - 11 q^{72} - 69 q^{73} - 23 q^{74} - 4 q^{75} - 58 q^{76} - 3 q^{77} + q^{78} - 72 q^{79} + 13 q^{80} - 73 q^{81} + 18 q^{82} - 11 q^{83} - 32 q^{84} - 70 q^{85} + 20 q^{86} - 9 q^{87} - 24 q^{88} - 25 q^{89} + 33 q^{90} - 32 q^{91} + 17 q^{92} - 19 q^{93} - 29 q^{94} - 9 q^{95} + 5 q^{96} - 56 q^{97} + 37 q^{98} - 19 q^{99}+O(q^{100}) \) 39 * q - 5 * q^2 - 4 * q^3 + 19 * q^4 - 8 * q^5 - 8 * q^6 - 15 * q^7 - 12 * q^8 - q^9 - 13 * q^10 - 13 * q^11 - 8 * q^12 - 24 * q^13 - 12 * q^14 - 16 * q^15 - 13 * q^16 - 26 * q^17 - 17 * q^18 - 40 * q^19 - 15 * q^20 - 26 * q^21 - 26 * q^22 - 8 * q^23 - 16 * q^24 - 35 * q^25 - 3 * q^26 - 10 * q^27 - 31 * q^28 - 30 * q^29 - 16 * q^30 - 21 * q^31 - 9 * q^32 - 25 * q^33 - 27 * q^34 - 2 * q^35 - 23 * q^36 - 27 * q^37 + q^38 - 29 * q^39 - 36 * q^40 - 35 * q^41 - 6 * q^42 - 48 * q^43 - 17 * q^44 - 22 * q^45 - 31 * q^46 - 3 * q^47 + q^48 - 64 * q^49 + 12 * q^50 - 27 * q^51 - 28 * q^52 - 14 * q^53 + q^54 - 31 * q^55 - 12 * q^56 - 36 * q^57 - 19 * q^58 - 9 * q^59 - 6 * q^60 - 87 * q^61 + 32 * q^62 - 9 * q^63 - 52 * q^64 - 35 * q^65 + 5 * q^66 - 24 * q^67 - 13 * q^68 - 35 * q^69 - 8 * q^70 - 21 * q^71 - 11 * q^72 - 69 * q^73 - 23 * q^74 - 4 * q^75 - 58 * q^76 - 3 * q^77 + q^78 - 72 * q^79 + 13 * q^80 - 73 * q^81 + 18 * q^82 - 11 * q^83 - 32 * q^84 - 70 * q^85 + 20 * q^86 - 9 * q^87 - 24 * q^88 - 25 * q^89 + 33 * q^90 - 32 * q^91 + 17 * q^92 - 19 * q^93 - 29 * q^94 - 9 * q^95 + 5 * q^96 - 56 * q^97 + 37 * q^98 - 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.68314	1.19016	0.595078	−	0.803668i	$-0.297121\pi$
$2$	1.68314	1.19016	0.595078	+	0.803668i	$0.297121\pi$
$3$	−2.46738	−1.42454	−0.712272	−	0.701904i	$-0.752334\pi$
$3$	−2.46738	−1.42454	−0.712272	+	0.701904i	$0.752334\pi$
$4$	0.832944	0.416472
$5$	1.71768	0.768170	0.384085	−	0.923298i	$-0.374517\pi$
$5$	1.71768	0.768170	0.384085	+	0.923298i	$0.374517\pi$
$6$	−4.15294	−1.69543
$7$	2.31892	0.876471	0.438235	−	0.898860i	$-0.355604\pi$
$7$	2.31892	0.876471	0.438235	+	0.898860i	$0.355604\pi$
$8$	−1.96431	−0.694490
$9$	3.08797	1.02932
$10$	2.89109	0.914242
$11$	−2.61673	−0.788973	−0.394486	−	0.918902i	$-0.629077\pi$
$11$	−2.61673	−0.788973	−0.394486	+	0.918902i	$0.629077\pi$
$12$	−2.05519	−0.593282
$13$	−5.48247	−1.52056	−0.760282	−	0.649593i	$-0.774939\pi$
$13$	−5.48247	−1.52056	−0.760282	+	0.649593i	$0.774939\pi$
$14$	3.90306	1.04314
$15$	−4.23817	−1.09429
$16$	−4.97209	−1.24302
$17$	0.913918	0.221658	0.110829	−	0.993840i	$-0.464649\pi$
$17$	0.913918	0.221658	0.110829	+	0.993840i	$0.464649\pi$
$18$	5.19747	1.22506
$19$	2.99129	0.686248	0.343124	−	0.939290i	$-0.388515\pi$
$19$	2.99129	0.686248	0.343124	+	0.939290i	$0.388515\pi$
$20$	1.43073	0.319921
$21$	−5.72167	−1.24857
$22$	−4.40430	−0.939001
$23$	−3.04790	−0.635530	−0.317765	−	0.948169i	$-0.602932\pi$
$23$	−3.04790	−0.635530	−0.317765	+	0.948169i	$0.602932\pi$
$24$	4.84671	0.989330
$25$	−2.04958	−0.409915
$26$	−9.22774	−1.80971
$27$	−0.217053	−0.0417719
$28$	1.93153	0.365025
$29$	2.41910	0.449215	0.224607	−	0.974449i	$-0.427890\pi$
$29$	2.41910	0.449215	0.224607	+	0.974449i	$0.427890\pi$
$30$	−7.13341	−1.30238
$31$	−3.77310	−0.677669	−0.338834	−	0.940846i	$-0.610033\pi$
$31$	−3.77310	−0.677669	−0.338834	+	0.940846i	$0.610033\pi$
$32$	−4.44008	−0.784902
$33$	6.45646	1.12393
$34$	1.53825	0.263807
$35$	3.98317	0.673278
$36$	2.57210	0.428684
$37$	−2.50049	−0.411077	−0.205539	−	0.978649i	$-0.565895\pi$
$37$	−2.50049	−0.411077	−0.205539	+	0.978649i	$0.565895\pi$
$38$	5.03474	0.816742
$39$	13.5273	2.16611
$40$	−3.37406	−0.533486
$41$	−3.91678	−0.611698	−0.305849	−	0.952080i	$-0.598940\pi$
$41$	−3.91678	−0.611698	−0.305849	+	0.952080i	$0.598940\pi$
$42$	−9.63034	−1.48599
$43$	5.22664	0.797054	0.398527	−	0.917156i	$-0.369521\pi$
$43$	5.22664	0.797054	0.398527	+	0.917156i	$0.369521\pi$
$44$	−2.17959	−0.328585
$45$	5.30414	0.790695
$46$	−5.13002	−0.756380
$47$	−8.64836	−1.26149	−0.630746	−	0.775989i	$-0.717251\pi$
$47$	−8.64836	−1.26149	−0.630746	+	0.775989i	$0.717251\pi$
$48$	12.2680	1.77074
$49$	−1.62260	−0.231799
$50$	−3.44971	−0.487863
$51$	−2.25498	−0.315761
$52$	−4.56659	−0.633272
$53$	−3.96696	−0.544903	−0.272452	−	0.962169i	$-0.587834\pi$
$53$	−3.96696	−0.544903	−0.272452	+	0.962169i	$0.587834\pi$
$54$	−0.365330	−0.0497151
$55$	−4.49470	−0.606065
$56$	−4.55509	−0.608700
$57$	−7.38064	−0.977590
$58$	4.07166	0.534636
$59$	−6.73649	−0.877017	−0.438508	−	0.898727i	$-0.644493\pi$
$59$	−6.73649	−0.877017	−0.438508	+	0.898727i	$0.644493\pi$
$60$	−3.53016	−0.455741
$61$	−10.2349	−1.31044	−0.655222	−	0.755437i	$-0.727425\pi$
$61$	−10.2349	−1.31044	−0.655222	+	0.755437i	$0.727425\pi$
$62$	−6.35063	−0.806531
$63$	7.16076	0.902171
$64$	2.47093	0.308867
$65$	−9.41713	−1.16805
$66$	10.8671	1.33765
$67$	−0.330726	−0.0404046	−0.0202023	−	0.999796i	$-0.506431\pi$
$67$	−0.330726	−0.0404046	−0.0202023	+	0.999796i	$0.506431\pi$
$68$	0.761242	0.0923142
$69$	7.52032	0.905340
$70$	6.70421	0.801306
$71$	−4.58321	−0.543927	−0.271964	−	0.962308i	$-0.587673\pi$
$71$	−4.58321	−0.543927	−0.271964	+	0.962308i	$0.587673\pi$
$72$	−6.06574	−0.714854
$73$	−4.65070	−0.544323	−0.272162	−	0.962252i	$-0.587739\pi$
$73$	−4.65070	−0.544323	−0.272162	+	0.962252i	$0.587739\pi$
$74$	−4.20866	−0.489246
$75$	5.05709	0.583942
$76$	2.49157	0.285803
$77$	−6.06799	−0.691511
$78$	22.7684	2.57801
$79$	1.70219	0.191511	0.0957557	−	0.995405i	$-0.469473\pi$
$79$	1.70219	0.191511	0.0957557	+	0.995405i	$0.469473\pi$
$80$	−8.54046	−0.954853
$81$	−8.72835	−0.969817
$82$	−6.59247	−0.728016
$83$	3.53327	0.387827	0.193914	−	0.981019i	$-0.437882\pi$
$83$	3.53327	0.387827	0.193914	+	0.981019i	$0.437882\pi$
$84$	−4.76583	−0.519994
$85$	1.56982	0.170271
$86$	8.79713	0.948619
$87$	−5.96883	−0.639926
$88$	5.14007	0.547933
$89$	−0.363556	−0.0385369	−0.0192684	−	0.999814i	$-0.506134\pi$
$89$	−0.363556	−0.0385369	−0.0192684	+	0.999814i	$0.506134\pi$
$90$	8.92759	0.941050
$91$	−12.7134	−1.33273
$92$	−2.53873	−0.264681
$93$	9.30967	0.965368
$94$	−14.5564	−1.50137
$95$	5.13807	0.527155
$96$	10.9554	1.11813
$97$	−2.73925	−0.278129	−0.139064	−	0.990283i	$-0.544410\pi$
$97$	−2.73925	−0.278129	−0.139064	+	0.990283i	$0.544410\pi$
$98$	−2.73105	−0.275877
$99$	−8.08037	−0.812108
$100$	−1.70718	−0.170718
$101$	4.08272	0.406246	0.203123	−	0.979153i	$-0.434891\pi$
$101$	4.08272	0.406246	0.203123	+	0.979153i	$0.434891\pi$
$102$	−3.79544	−0.375805
$103$	−5.94949	−0.586221	−0.293110	−	0.956079i	$-0.594690\pi$
$103$	−5.94949	−0.586221	−0.293110	+	0.956079i	$0.594690\pi$
$104$	10.7693	1.05602
$105$	−9.82799	−0.959114
$106$	−6.67692	−0.648520
$107$	4.70770	0.455110	0.227555	−	0.973765i	$-0.426927\pi$
$107$	4.70770	0.455110	0.227555	+	0.973765i	$0.426927\pi$
$108$	−0.180793	−0.0173968
$109$	−2.55555	−0.244777	−0.122389	−	0.992482i	$-0.539055\pi$
$109$	−2.55555	−0.244777	−0.122389	+	0.992482i	$0.539055\pi$
$110$	−7.56518	−0.721312
$111$	6.16965	0.585597
$112$	−11.5299	−1.08947
$113$	3.56319	0.335196	0.167598	−	0.985855i	$-0.446399\pi$
$113$	3.56319	0.335196	0.167598	+	0.985855i	$0.446399\pi$
$114$	−12.4226	−1.16348
$115$	−5.23531	−0.488195
$116$	2.01497	0.187085
$117$	−16.9297	−1.56515
$118$	−11.3384	−1.04379
$119$	2.11931	0.194276
$120$	8.32509	0.759974
$121$	−4.15275	−0.377522
$122$	−17.2267	−1.55963
$123$	9.66419	0.871390
$124$	−3.14278	−0.282230
$125$	−12.1089	−1.08305
$126$	12.0525	1.07372
$127$	9.85064	0.874103	0.437052	−	0.899436i	$-0.356023\pi$
$127$	9.85064	0.874103	0.437052	+	0.899436i	$0.356023\pi$
$128$	13.0391	1.15250
$129$	−12.8961	−1.13544
$130$	−15.8503	−1.39016
$131$	15.8839	1.38779	0.693893	−	0.720078i	$-0.255894\pi$
$131$	15.8839	1.38779	0.693893	+	0.720078i	$0.255894\pi$
$132$	5.37787	0.468083
$133$	6.93656	0.601476
$134$	−0.556656	−0.0480878
$135$	−0.372828	−0.0320879
$136$	−1.79522	−0.153939
$137$	7.09399	0.606081	0.303040	−	0.952978i	$-0.401998\pi$
$137$	7.09399	0.606081	0.303040	+	0.952978i	$0.401998\pi$
$138$	12.6577	1.07750
$139$	13.3882	1.13557	0.567787	−	0.823176i	$-0.307800\pi$
$139$	13.3882	1.13557	0.567787	+	0.823176i	$0.307800\pi$
$140$	3.31775	0.280401
$141$	21.3388	1.79705
$142$	−7.71417	−0.647359
$143$	14.3461	1.19968
$144$	−15.3537	−1.27947
$145$	4.15523	0.345073
$146$	−7.82776	−0.647830
$147$	4.00356	0.330208
$148$	−2.08276	−0.171202
$149$	−17.6376	−1.44493	−0.722465	−	0.691407i	$-0.756991\pi$
$149$	−17.6376	−1.44493	−0.722465	+	0.691407i	$0.756991\pi$
$150$	8.51176	0.694982
$151$	7.28238	0.592632	0.296316	−	0.955090i	$-0.404242\pi$
$151$	7.28238	0.592632	0.296316	+	0.955090i	$0.404242\pi$
$152$	−5.87582	−0.476592
$153$	2.82215	0.228157
$154$	−10.2132	−0.823006
$155$	−6.48097	−0.520564
$156$	11.2675	0.902124
$157$	14.0056	1.11777	0.558885	−	0.829245i	$-0.311229\pi$
$157$	14.0056	1.11777	0.558885	+	0.829245i	$0.311229\pi$
$158$	2.86502	0.227928
$159$	9.78799	0.776238
$160$	−7.62663	−0.602938
$161$	−7.06784	−0.557024
$162$	−14.6910	−1.15423
$163$	−8.60078	−0.673665	−0.336833	−	0.941565i	$-0.609356\pi$
$163$	−8.60078	−0.673665	−0.336833	+	0.941565i	$0.609356\pi$
$164$	−3.26246	−0.254755
$165$	11.0901	0.863365
$166$	5.94698	0.461575
$167$	17.2826	1.33736	0.668682	−	0.743548i	$-0.266859\pi$
$167$	17.2826	1.33736	0.668682	+	0.743548i	$0.266859\pi$
$168$	11.2391	0.867119
$169$	17.0575	1.31211
$170$	2.64222	0.202649
$171$	9.23700	0.706371
$172$	4.35349	0.331951
$173$	9.10542	0.692273	0.346136	−	0.938184i	$-0.387493\pi$
$173$	9.10542	0.692273	0.346136	+	0.938184i	$0.387493\pi$
$174$	−10.0463	−0.761612
$175$	−4.75281	−0.359279
$176$	13.0106	0.980711
$177$	16.6215	1.24935
$178$	−0.611914	−0.0458649
$179$	−2.60442	−0.194663	−0.0973316	−	0.995252i	$-0.531031\pi$
$179$	−2.60442	−0.194663	−0.0973316	+	0.995252i	$0.531031\pi$
$180$	4.41805	0.329302
$181$	10.1018	0.750864	0.375432	−	0.926850i	$-0.377494\pi$
$181$	10.1018	0.750864	0.375432	+	0.926850i	$0.377494\pi$
$182$	−21.3984	−1.58616
$183$	25.2534	1.86678
$184$	5.98702	0.441369
$185$	−4.29503	−0.315777
$186$	15.6694	1.14894
$187$	−2.39147	−0.174882
$188$	−7.20360	−0.525376
$189$	−0.503329	−0.0366118
$190$	8.64807	0.627397
$191$	0.788106	0.0570254	0.0285127	−	0.999593i	$-0.490923\pi$
$191$	0.788106	0.0570254	0.0285127	+	0.999593i	$0.490923\pi$
$192$	−6.09674	−0.439994
$193$	−25.2155	−1.81505	−0.907524	−	0.419999i	$-0.862030\pi$
$193$	−25.2155	−1.81505	−0.907524	+	0.419999i	$0.862030\pi$
$194$	−4.61053	−0.331017
$195$	23.2356	1.66394
$196$	−1.35153	−0.0965379
$197$	12.9090	0.919728	0.459864	−	0.887989i	$-0.347898\pi$
$197$	12.9090	0.919728	0.459864	+	0.887989i	$0.347898\pi$
$198$	−13.6004	−0.966535
$199$	−15.5031	−1.09899	−0.549494	−	0.835498i	$-0.685179\pi$
$199$	−15.5031	−1.09899	−0.549494	+	0.835498i	$0.685179\pi$
$200$	4.02601	0.284682
$201$	0.816027	0.0575581
$202$	6.87177	0.483496
$203$	5.60970	0.393723
$204$	−1.87828	−0.131506
$205$	−6.72777	−0.469888
$206$	−10.0138	−0.697694
$207$	−9.41181	−0.654166
$208$	27.2594	1.89010
$209$	−7.82737	−0.541431
$210$	−16.5418	−1.14150
$211$	−4.96359	−0.341707	−0.170854	−	0.985296i	$-0.554653\pi$
$211$	−4.96359	−0.341707	−0.170854	+	0.985296i	$0.554653\pi$
$212$	−3.30425	−0.226937
$213$	11.3085	0.774848
$214$	7.92369	0.541652
$215$	8.97769	0.612273
$216$	0.426360	0.0290101
$217$	−8.74953	−0.593956
$218$	−4.30133	−0.291323
$219$	11.4751	0.775412
$220$	−3.74383	−0.252409
$221$	−5.01053	−0.337045
$222$	10.3844	0.696953
$223$	22.6371	1.51589	0.757947	−	0.652316i	$-0.226203\pi$
$223$	22.6371	1.51589	0.757947	+	0.652316i	$0.226203\pi$
$224$	−10.2962	−0.687944
$225$	−6.32903	−0.421935
$226$	5.99732	0.398936
$227$	−4.57334	−0.303543	−0.151772	−	0.988416i	$-0.548498\pi$
$227$	−4.57334	−0.303543	−0.151772	+	0.988416i	$0.548498\pi$
$228$	−6.14766	−0.407139
$229$	−4.90949	−0.324428	−0.162214	−	0.986756i	$-0.551864\pi$
$229$	−4.90949	−0.324428	−0.162214	+	0.986756i	$0.551864\pi$
$230$	−8.81173	−0.581029
$231$	14.9720	0.985087
$232$	−4.75186	−0.311975
$233$	−25.9319	−1.69886	−0.849428	−	0.527705i	$-0.823053\pi$
$233$	−25.9319	−1.69886	−0.849428	+	0.527705i	$0.823053\pi$
$234$	−28.4950	−1.86277
$235$	−14.8551	−0.969040
$236$	−5.61112	−0.365253
$237$	−4.19995	−0.272816
$238$	3.56708	0.231219
$239$	17.8869	1.15701	0.578505	−	0.815679i	$-0.303637\pi$
$239$	17.8869	1.15701	0.578505	+	0.815679i	$0.303637\pi$
$240$	21.0726	1.36023
$241$	−0.313052	−0.0201655	−0.0100827	−	0.999949i	$-0.503209\pi$
$241$	−0.313052	−0.0201655	−0.0100827	+	0.999949i	$0.503209\pi$
$242$	−6.98963	−0.449311
$243$	22.1873	1.42332
$244$	−8.52509	−0.545763
$245$	−2.78710	−0.178061
$246$	16.2661	1.03709
$247$	−16.3996	−1.04348
$248$	7.41155	0.470634
$249$	−8.71793	−0.552476
$250$	−20.3809	−1.28900
$251$	2.38799	0.150729	0.0753643	−	0.997156i	$-0.475988\pi$
$251$	2.38799	0.150729	0.0753643	+	0.997156i	$0.475988\pi$
$252$	5.96451	0.375729
$253$	7.97551	0.501416
$254$	16.5800	1.04032
$255$	−3.87334	−0.242558
$256$	17.0046	1.06279
$257$	9.23025	0.575767	0.287883	−	0.957665i	$-0.407048\pi$
$257$	9.23025	0.575767	0.287883	+	0.957665i	$0.407048\pi$
$258$	−21.7059	−1.35135
$259$	−5.79844	−0.360297
$260$	−7.84394	−0.486461
$261$	7.47009	0.462387
$262$	26.7348	1.65168
$263$	−4.90112	−0.302216	−0.151108	−	0.988517i	$-0.548284\pi$
$263$	−4.90112	−0.302216	−0.151108	+	0.988517i	$0.548284\pi$
$264$	−12.6825	−0.780554
$265$	−6.81396	−0.418578
$266$	11.6752	0.715851
$267$	0.897032	0.0548974
$268$	−0.275476	−0.0168274
$269$	4.75814	0.290109	0.145054	−	0.989424i	$-0.453664\pi$
$269$	4.75814	0.290109	0.145054	+	0.989424i	$0.453664\pi$
$270$	−0.627519	−0.0381896
$271$	−3.22184	−0.195713	−0.0978565	−	0.995201i	$-0.531199\pi$
$271$	−3.22184	−0.195713	−0.0978565	+	0.995201i	$0.531199\pi$
$272$	−4.54408	−0.275526
$273$	31.3689	1.89853
$274$	11.9401	0.721331
$275$	5.36318	0.323412
$276$	6.26401	0.377049
$277$	−12.0946	−0.726697	−0.363348	−	0.931653i	$-0.618367\pi$
$277$	−12.0946	−0.726697	−0.363348	+	0.931653i	$0.618367\pi$
$278$	22.5342	1.35151
$279$	−11.6512	−0.697540
$280$	−7.82419	−0.467585
$281$	−6.05206	−0.361036	−0.180518	−	0.983572i	$-0.557777\pi$
$281$	−6.05206	−0.361036	−0.180518	+	0.983572i	$0.557777\pi$
$282$	35.9161	2.13877
$283$	−6.89507	−0.409870	−0.204935	−	0.978776i	$-0.565698\pi$
$283$	−6.89507	−0.409870	−0.204935	+	0.978776i	$0.565698\pi$
$284$	−3.81756	−0.226531
$285$	−12.6776	−0.750955
$286$	24.1465	1.42781
$287$	−9.08271	−0.536135
$288$	−13.7108	−0.807918
$289$	−16.1648	−0.950868
$290$	6.99382	0.410691
$291$	6.75878	0.396207
$292$	−3.87377	−0.226695
$293$	26.1781	1.52934	0.764670	−	0.644422i	$-0.222902\pi$
$293$	26.1781	1.52934	0.764670	+	0.644422i	$0.222902\pi$
$294$	6.73853	0.392999
$295$	−11.5711	−0.673698
$296$	4.91174	0.285489
$297$	0.567968	0.0329569
$298$	−29.6865	−1.71969
$299$	16.7100	0.966365
$300$	4.21227	0.243195
$301$	12.1202	0.698595
$302$	12.2572	0.705324
$303$	−10.0736	−0.578714
$304$	−14.8729	−0.853022
$305$	−17.5803	−1.00664
$306$	4.75006	0.271543
$307$	23.5964	1.34672	0.673359	−	0.739315i	$-0.264851\pi$
$307$	23.5964	1.34672	0.673359	+	0.739315i	$0.264851\pi$
$308$	−5.05429	−0.287995
$309$	14.6797	0.835097
$310$	−10.9084	−0.619553
$311$	−0.560848	−0.0318028	−0.0159014	−	0.999874i	$-0.505062\pi$
$311$	−0.560848	−0.0318028	−0.0159014	+	0.999874i	$0.505062\pi$
$312$	−26.5719	−1.50434
$313$	31.7048	1.79206	0.896030	−	0.443993i	$-0.146439\pi$
$313$	31.7048	1.79206	0.896030	+	0.443993i	$0.146439\pi$
$314$	23.5734	1.33032
$315$	12.2999	0.693021
$316$	1.41783	0.0797591
$317$	−25.2156	−1.41625	−0.708124	−	0.706089i	$-0.750458\pi$
$317$	−25.2156	−1.41625	−0.708124	+	0.706089i	$0.750458\pi$
$318$	16.4745	0.923845
$319$	−6.33011	−0.354418
$320$	4.24427	0.237262
$321$	−11.6157	−0.648324
$322$	−11.8961	−0.662945
$323$	2.73379	0.152112
$324$	−7.27023	−0.403902
$325$	11.2367	0.623302
$326$	−14.4763	−0.801767
$327$	6.30551	0.348695
$328$	7.69378	0.424818
$329$	−20.0549	−1.10566
$330$	18.6662	1.02754
$331$	15.2423	0.837793	0.418897	−	0.908034i	$-0.362417\pi$
$331$	15.2423	0.837793	0.418897	+	0.908034i	$0.362417\pi$
$332$	2.94302	0.161519
$333$	−7.72142	−0.423131
$334$	29.0889	1.59167
$335$	−0.568081	−0.0310376
$336$	28.4487	1.55200
$337$	−5.79905	−0.315894	−0.157947	−	0.987448i	$-0.550488\pi$
$337$	−5.79905	−0.315894	−0.157947	+	0.987448i	$0.550488\pi$
$338$	28.7101	1.56162
$339$	−8.79174	−0.477502
$340$	1.30757	0.0709130
$341$	9.87316	0.534662
$342$	15.5471	0.840692
$343$	−19.9951	−1.07964
$344$	−10.2667	−0.553546
$345$	12.9175	0.695455
$346$	15.3257	0.823913
$347$	22.5548	1.21080	0.605402	−	0.795920i	$-0.293012\pi$
$347$	22.5548	1.21080	0.605402	+	0.795920i	$0.293012\pi$
$348$	−4.97170	−0.266511
$349$	23.3467	1.24972	0.624860	−	0.780737i	$-0.285156\pi$
$349$	23.3467	1.24972	0.624860	+	0.780737i	$0.285156\pi$
$350$	−7.99962	−0.427598
$351$	1.18999	0.0635168
$352$	11.6185	0.619266
$353$	−29.6915	−1.58032	−0.790161	−	0.612900i	$-0.790003\pi$
$353$	−29.6915	−1.58032	−0.790161	+	0.612900i	$0.790003\pi$
$354$	27.9762	1.48692
$355$	−7.87249	−0.417829
$356$	−0.302822	−0.0160495
$357$	−5.22913	−0.276755
$358$	−4.38358	−0.231680
$359$	−14.9602	−0.789571	−0.394785	−	0.918773i	$-0.629181\pi$
$359$	−14.9602	−0.789571	−0.394785	+	0.918773i	$0.629181\pi$
$360$	−10.4190	−0.549129
$361$	−10.0522	−0.529064
$362$	17.0028	0.893646
$363$	10.2464	0.537797
$364$	−10.5896	−0.555044
$365$	−7.98842	−0.418133
$366$	42.5048	2.22176
$367$	5.07996	0.265172	0.132586	−	0.991172i	$-0.457672\pi$
$367$	5.07996	0.265172	0.132586	+	0.991172i	$0.457672\pi$
$368$	15.1544	0.789979
$369$	−12.0949	−0.629635
$370$	−7.22912	−0.375824
$371$	−9.19906	−0.477592
$372$	7.75443	0.402049
$373$	29.9516	1.55084	0.775418	−	0.631448i	$-0.217539\pi$
$373$	29.9516	1.55084	0.775418	+	0.631448i	$0.217539\pi$
$374$	−4.02517	−0.208137
$375$	29.8773	1.54286
$376$	16.9881	0.876093
$377$	−13.2626	−0.683060
$378$	−0.847171	−0.0435738
$379$	−10.0744	−0.517485	−0.258743	−	0.965946i	$-0.583308\pi$
$379$	−10.0744	−0.517485	−0.258743	+	0.965946i	$0.583308\pi$
$380$	4.27972	0.219545
$381$	−24.3053	−1.24520
$382$	1.32649	0.0678691
$383$	19.5648	0.999715	0.499858	−	0.866108i	$-0.333386\pi$
$383$	19.5648	0.999715	0.499858	+	0.866108i	$0.333386\pi$
$384$	−32.1724	−1.64179
$385$	−10.4229	−0.531198
$386$	−42.4410	−2.16019
$387$	16.1397	0.820427
$388$	−2.28164	−0.115833
$389$	−14.2713	−0.723584	−0.361792	−	0.932259i	$-0.617835\pi$
$389$	−14.2713	−0.723584	−0.361792	+	0.932259i	$0.617835\pi$
$390$	39.1087	1.98035
$391$	−2.78553	−0.140870
$392$	3.18729	0.160982
$393$	−39.1917	−1.97696
$394$	21.7276	1.09462
$395$	2.92382	0.147113
$396$	−6.73049	−0.338220
$397$	6.23722	0.313037	0.156518	−	0.987675i	$-0.449973\pi$
$397$	6.23722	0.313037	0.156518	+	0.987675i	$0.449973\pi$
$398$	−26.0939	−1.30797
$399$	−17.1151	−0.856829
$400$	10.1907	0.509534
$401$	−3.77237	−0.188383	−0.0941915	−	0.995554i	$-0.530027\pi$
$401$	−3.77237	−0.188383	−0.0941915	+	0.995554i	$0.530027\pi$
$402$	1.37348	0.0685031
$403$	20.6859	1.03044
$404$	3.40068	0.169190
$405$	−14.9925	−0.744984
$406$	9.44188	0.468592
$407$	6.54309	0.324329
$408$	4.42949	0.219293
$409$	−11.9064	−0.588733	−0.294366	−	0.955693i	$-0.595109\pi$
$409$	−11.9064	−0.588733	−0.294366	+	0.955693i	$0.595109\pi$
$410$	−11.3237	−0.559240
$411$	−17.5036	−0.863388
$412$	−4.95559	−0.244145
$413$	−15.6214	−0.768679
$414$	−15.8413	−0.778560
$415$	6.06903	0.297917
$416$	24.3426	1.19349
$417$	−33.0338	−1.61767
$418$	−13.1745	−0.644387
$419$	−5.32189	−0.259992	−0.129996	−	0.991515i	$-0.541496\pi$
$419$	−5.32189	−0.259992	−0.129996	+	0.991515i	$0.541496\pi$
$420$	−8.18617	−0.399444
$421$	−13.3408	−0.650190	−0.325095	−	0.945681i	$-0.605396\pi$
$421$	−13.3408	−0.650190	−0.325095	+	0.945681i	$0.605396\pi$
$422$	−8.35439	−0.406685
$423$	−26.7059	−1.29848
$424$	7.79234	0.378430
$425$	−1.87314	−0.0908609
$426$	19.0338	0.922190
$427$	−23.7339	−1.14856
$428$	3.92125	0.189541
$429$	−35.3974	−1.70900
$430$	15.1107	0.728701
$431$	−21.7597	−1.04813	−0.524065	−	0.851678i	$-0.675585\pi$
$431$	−21.7597	−1.04813	−0.524065	+	0.851678i	$0.675585\pi$
$432$	1.07921	0.0519234
$433$	−25.2411	−1.21301	−0.606505	−	0.795080i	$-0.707429\pi$
$433$	−25.2411	−1.21301	−0.606505	+	0.795080i	$0.707429\pi$
$434$	−14.7266	−0.706901
$435$	−10.2525	−0.491572
$436$	−2.12863	−0.101943
$437$	−9.11713	−0.436131
$438$	19.3141	0.922862
$439$	22.2910	1.06389	0.531945	−	0.846779i	$-0.321461\pi$
$439$	22.2910	1.06389	0.531945	+	0.846779i	$0.321461\pi$
$440$	8.82899	0.420906
$441$	−5.01052	−0.238596
$442$	−8.43340	−0.401136
$443$	−21.7338	−1.03260	−0.516301	−	0.856407i	$-0.672691\pi$
$443$	−21.7338	−1.03260	−0.516301	+	0.856407i	$0.672691\pi$
$444$	5.13897	0.243885
$445$	−0.624473	−0.0296029
$446$	38.1013	1.80415
$447$	43.5187	2.05837
$448$	5.72991	0.270713
$449$	−6.93815	−0.327431	−0.163716	−	0.986508i	$-0.552348\pi$
$449$	−6.93815	−0.327431	−0.163716	+	0.986508i	$0.552348\pi$
$450$	−10.6526	−0.502169
$451$	10.2491	0.482613
$452$	2.96793	0.139600
$453$	−17.9684	−0.844229
$454$	−7.69755	−0.361264
$455$	−21.8376	−1.02376
$456$	14.4979	0.678926
$457$	−8.84011	−0.413523	−0.206761	−	0.978391i	$-0.566292\pi$
$457$	−8.84011	−0.413523	−0.206761	+	0.978391i	$0.566292\pi$
$458$	−8.26334	−0.386120
$459$	−0.198369	−0.00925906
$460$	−4.36072	−0.203320
$461$	−15.2395	−0.709773	−0.354887	−	0.934909i	$-0.615481\pi$
$461$	−15.2395	−0.709773	−0.354887	+	0.934909i	$0.615481\pi$
$462$	25.2000	1.17241
$463$	−31.9664	−1.48560	−0.742802	−	0.669511i	$-0.766504\pi$
$463$	−31.9664	−1.48560	−0.742802	+	0.669511i	$0.766504\pi$
$464$	−12.0280	−0.558384
$465$	15.9910	0.741566
$466$	−43.6469	−2.02190
$467$	−19.7853	−0.915557	−0.457778	−	0.889066i	$-0.651355\pi$
$467$	−19.7853	−0.915557	−0.457778	+	0.889066i	$0.651355\pi$
$468$	−14.1015	−0.651842
$469$	−0.766928	−0.0354134
$470$	−25.0032	−1.15331
$471$	−34.5572	−1.59231
$472$	13.2326	0.609079
$473$	−13.6767	−0.628854
$474$	−7.06909	−0.324694
$475$	−6.13087	−0.281304
$476$	1.76526	0.0809107
$477$	−12.2498	−0.560881
$478$	30.1061	1.37702
$479$	20.7113	0.946322	0.473161	−	0.880976i	$-0.343113\pi$
$479$	20.7113	0.946322	0.473161	+	0.880976i	$0.343113\pi$
$480$	18.8178	0.858911
$481$	13.7088	0.625069
$482$	−0.526909	−0.0240000
$483$	17.4390	0.793504
$484$	−3.45900	−0.157227
$485$	−4.70516	−0.213650
$486$	37.3443	1.69397
$487$	5.26191	0.238440	0.119220	−	0.992868i	$-0.461961\pi$
$487$	5.26191	0.238440	0.119220	+	0.992868i	$0.461961\pi$
$488$	20.1045	0.910089
$489$	21.2214	0.959665
$490$	−4.69107	−0.211921
$491$	37.0543	1.67224	0.836118	−	0.548550i	$-0.184820\pi$
$491$	37.0543	1.67224	0.836118	+	0.548550i	$0.184820\pi$
$492$	8.04973	0.362910
$493$	2.21085	0.0995719
$494$	−27.6028	−1.24191
$495$	−13.8795	−0.623836
$496$	18.7602	0.842358
$497$	−10.6281	−0.476736
$498$	−14.6735	−0.657533
$499$	−19.8491	−0.888570	−0.444285	−	0.895886i	$-0.646542\pi$
$499$	−19.8491	−0.888570	−0.444285	+	0.895886i	$0.646542\pi$
$500$	−10.0860	−0.451062
$501$	−42.6427	−1.90513
$502$	4.01931	0.179391
$503$	10.6544	0.475055	0.237528	−	0.971381i	$-0.423663\pi$
$503$	10.6544	0.475055	0.237528	+	0.971381i	$0.423663\pi$
$504$	−14.0660	−0.626549
$505$	7.01280	0.312066
$506$	13.4239	0.596763
$507$	−42.0873	−1.86916
$508$	8.20503	0.364039
$509$	12.7327	0.564367	0.282184	−	0.959360i	$-0.408941\pi$
$509$	12.7327	0.564367	0.282184	+	0.959360i	$0.408941\pi$
$510$	−6.51935	−0.288682
$511$	−10.7846	−0.477083
$512$	2.54298	0.112385
$513$	−0.649268	−0.0286659
$514$	15.5358	0.685253
$515$	−10.2193	−0.450317
$516$	−10.7417	−0.472878
$517$	22.6304	0.995283
$518$	−9.75955	−0.428810
$519$	−22.4666	−0.986172
$520$	18.4982	0.811199
$521$	−22.0045	−0.964033	−0.482017	−	0.876162i	$-0.660096\pi$
$521$	−22.0045	−0.964033	−0.482017	+	0.876162i	$0.660096\pi$
$522$	12.5732	0.550313
$523$	21.7917	0.952885	0.476443	−	0.879206i	$-0.341926\pi$
$523$	21.7917	0.952885	0.476443	+	0.879206i	$0.341926\pi$
$524$	13.2304	0.577974
$525$	11.7270	0.511808
$526$	−8.24925	−0.359684
$527$	−3.44830	−0.150210
$528$	−32.1021	−1.39707
$529$	−13.7103	−0.596101
$530$	−11.4688	−0.498173
$531$	−20.8021	−0.902733
$532$	5.77777	0.250498
$533$	21.4736	0.930126
$534$	1.50983	0.0653365
$535$	8.08632	0.349602
$536$	0.649649	0.0280606
$537$	6.42609	0.277306
$538$	8.00859	0.345275
$539$	4.24589	0.182883
$540$	−0.310544	−0.0133637
$541$	−26.2246	−1.12748	−0.563741	−	0.825952i	$-0.690638\pi$
$541$	−26.2246	−1.12748	−0.563741	+	0.825952i	$0.690638\pi$
$542$	−5.42279	−0.232929
$543$	−24.9251	−1.06964
$544$	−4.05787	−0.173980
$545$	−4.38961	−0.188030
$546$	52.7981	2.25955
$547$	−21.8178	−0.932862	−0.466431	−	0.884557i	$-0.654460\pi$
$547$	−21.8178	−0.932862	−0.466431	+	0.884557i	$0.654460\pi$
$548$	5.90890	0.252416
$549$	−31.6050	−1.34887
$550$	9.02696	0.384911
$551$	7.23621	0.308273
$552$	−14.7723	−0.628749
$553$	3.94725	0.167854
$554$	−20.3569	−0.864883
$555$	10.5975	0.449838
$556$	11.1516	0.472935
$557$	33.8620	1.43478	0.717389	−	0.696673i	$-0.245337\pi$
$557$	33.8620	1.43478	0.717389	+	0.696673i	$0.245337\pi$
$558$	−19.6106	−0.830181
$559$	−28.6549	−1.21197
$560$	−19.8047	−0.836900
$561$	5.90067	0.249127
$562$	−10.1864	−0.429689
$563$	−1.04362	−0.0439834	−0.0219917	−	0.999758i	$-0.507001\pi$
$563$	−1.04362	−0.0439834	−0.0219917	+	0.999758i	$0.507001\pi$
$564$	17.7740	0.748421
$565$	6.12041	0.257488
$566$	−11.6053	−0.487809
$567$	−20.2404	−0.850016
$568$	9.00287	0.377752
$569$	29.8389	1.25091	0.625456	−	0.780260i	$-0.284913\pi$
$569$	29.8389	1.25091	0.625456	+	0.780260i	$0.284913\pi$
$570$	−21.3381	−0.893754
$571$	−42.9207	−1.79617	−0.898087	−	0.439817i	$-0.855043\pi$
$571$	−42.9207	−1.79617	−0.898087	+	0.439817i	$0.855043\pi$
$572$	11.9495	0.499634
$573$	−1.94456	−0.0812351
$574$	−15.2874	−0.638085
$575$	6.24690	0.260514
$576$	7.63017	0.317924
$577$	−28.9572	−1.20550	−0.602751	−	0.797929i	$-0.705929\pi$
$577$	−28.9572	−1.20550	−0.602751	+	0.797929i	$0.705929\pi$
$578$	−27.2075	−1.13168
$579$	62.2162	2.58562
$580$	3.46107	0.143713
$581$	8.19339	0.339919
$582$	11.3759	0.471548
$583$	10.3804	0.429914
$584$	9.13543	0.378027
$585$	−29.0798	−1.20230
$586$	44.0612	1.82015
$587$	−29.0756	−1.20008	−0.600038	−	0.799971i	$-0.704848\pi$
$587$	−29.0756	−1.20008	−0.600038	+	0.799971i	$0.704848\pi$
$588$	3.33474	0.137522
$589$	−11.2864	−0.465049
$590$	−19.4758	−0.801805
$591$	−31.8514	−1.31019
$592$	12.4326	0.510979
$593$	−25.2963	−1.03880	−0.519398	−	0.854533i	$-0.673844\pi$
$593$	−25.2963	−1.03880	−0.519398	+	0.854533i	$0.673844\pi$
$594$	0.955967	0.0392238
$595$	3.64029	0.149237
$596$	−14.6912	−0.601773
$597$	38.2521	1.56556
$598$	28.1252	1.15012
$599$	−5.59532	−0.228619	−0.114309	−	0.993445i	$-0.536466\pi$
$599$	−5.59532	−0.228619	−0.114309	+	0.993445i	$0.536466\pi$
$600$	−9.93370	−0.405542
$601$	−20.7343	−0.845769	−0.422885	−	0.906184i	$-0.638982\pi$
$601$	−20.7343	−0.845769	−0.422885	+	0.906184i	$0.638982\pi$
$602$	20.3999	0.831437
$603$	−1.02127	−0.0415894
$604$	6.06581	0.246814
$605$	−7.13309	−0.290001
$606$	−16.9553	−0.688761
$607$	−27.1228	−1.10088	−0.550440	−	0.834874i	$-0.685540\pi$
$607$	−27.1228	−1.10088	−0.550440	+	0.834874i	$0.685540\pi$
$608$	−13.2815	−0.538638
$609$	−13.8413	−0.560876
$610$	−29.5900	−1.19806
$611$	47.4144	1.91818
$612$	2.35069	0.0950211
$613$	19.4224	0.784462	0.392231	−	0.919867i	$-0.371703\pi$
$613$	19.4224	0.784462	0.392231	+	0.919867i	$0.371703\pi$
$614$	39.7160	1.60281
$615$	16.6000	0.669376
$616$	11.9194	0.480247
$617$	25.5638	1.02916	0.514581	−	0.857442i	$-0.327948\pi$
$617$	25.5638	1.02916	0.514581	+	0.857442i	$0.327948\pi$
$618$	24.7079	0.993896
$619$	−18.3681	−0.738277	−0.369138	−	0.929374i	$-0.620347\pi$
$619$	−18.3681	−0.738277	−0.369138	+	0.929374i	$0.620347\pi$
$620$	−5.39829	−0.216800
$621$	0.661555	0.0265473
$622$	−0.943983	−0.0378503
$623$	−0.843059	−0.0337764
$624$	−67.2592	−2.69252
$625$	−10.5514	−0.422054
$626$	53.3634	2.13283
$627$	19.3131	0.771292
$628$	11.6659	0.465520
$629$	−2.28524	−0.0911185
$630$	20.7024	0.824803
$631$	−40.8292	−1.62538	−0.812692	−	0.582693i	$-0.801999\pi$
$631$	−40.8292	−1.62538	−0.812692	+	0.582693i	$0.801999\pi$
$632$	−3.34363	−0.133003
$633$	12.2471	0.486777
$634$	−42.4412	−1.68556
$635$	16.9202	0.671459
$636$	8.15285	0.323281
$637$	8.89583	0.352466
$638$	−10.6544	−0.421813
$639$	−14.1528	−0.559877
$640$	22.3969	0.885317
$641$	−13.2393	−0.522920	−0.261460	−	0.965214i	$-0.584204\pi$
$641$	−13.2393	−0.522920	−0.261460	+	0.965214i	$0.584204\pi$
$642$	−19.5508	−0.771607
$643$	17.9134	0.706436	0.353218	−	0.935541i	$-0.385087\pi$
$643$	17.9134	0.706436	0.353218	+	0.935541i	$0.385087\pi$
$644$	−5.88711	−0.231985
$645$	−22.1514	−0.872209
$646$	4.60134	0.181037
$647$	−9.56103	−0.375883	−0.187941	−	0.982180i	$-0.560182\pi$
$647$	−9.56103	−0.375883	−0.187941	+	0.982180i	$0.560182\pi$
$648$	17.1452	0.673528
$649$	17.6276	0.691942
$650$	18.9130	0.741827
$651$	21.5884	0.846117
$652$	−7.16397	−0.280563
$653$	−37.4028	−1.46368	−0.731842	−	0.681475i	$-0.761339\pi$
$653$	−37.4028	−1.46368	−0.731842	+	0.681475i	$0.761339\pi$
$654$	10.6130	0.415002
$655$	27.2835	1.06605
$656$	19.4746	0.760355
$657$	−14.3612	−0.560285
$658$	−33.7551	−1.31591
$659$	32.5047	1.26620	0.633102	−	0.774068i	$-0.281781\pi$
$659$	32.5047	1.26620	0.633102	+	0.774068i	$0.281781\pi$
$660$	9.23746	0.359567
$661$	46.2983	1.80079	0.900397	−	0.435068i	$-0.143276\pi$
$661$	46.2983	1.80079	0.900397	+	0.435068i	$0.143276\pi$
$662$	25.6549	0.997105
$663$	12.3629	0.480135
$664$	−6.94045	−0.269342
$665$	11.9148	0.462036
$666$	−12.9962	−0.503593
$667$	−7.37315	−0.285490
$668$	14.3954	0.556975
$669$	−55.8544	−2.15946
$670$	−0.956158	−0.0369396
$671$	26.7819	1.03390
$672$	25.4046	0.980005
$673$	39.7098	1.53070	0.765350	−	0.643614i	$-0.222566\pi$
$673$	39.7098	1.53070	0.765350	+	0.643614i	$0.222566\pi$
$674$	−9.76058	−0.375964
$675$	0.444867	0.0171229
$676$	14.2079	0.546459
$677$	4.71971	0.181393	0.0906966	−	0.995879i	$-0.471091\pi$
$677$	4.71971	0.181393	0.0906966	+	0.995879i	$0.471091\pi$
$678$	−14.7977	−0.568302
$679$	−6.35212	−0.243772
$680$	−3.08361	−0.118251
$681$	11.2842	0.432411
$682$	16.6179	0.636331
$683$	11.4575	0.438407	0.219204	−	0.975679i	$-0.429654\pi$
$683$	11.4575	0.438407	0.219204	+	0.975679i	$0.429654\pi$
$684$	7.69390	0.294184
$685$	12.1852	0.465573
$686$	−33.6545	−1.28494
$687$	12.1136	0.462162
$688$	−25.9873	−0.990757
$689$	21.7487	0.828560
$690$	21.7419	0.827700
$691$	20.9067	0.795330	0.397665	−	0.917531i	$-0.369821\pi$
$691$	20.9067	0.795330	0.397665	+	0.917531i	$0.369821\pi$
$692$	7.58431	0.288312
$693$	−18.7378	−0.711788
$694$	37.9627	1.44105
$695$	22.9967	0.872313
$696$	11.7247	0.444422
$697$	−3.57961	−0.135588
$698$	39.2956	1.48736
$699$	63.9839	2.42009
$700$	−3.95882	−0.149629
$701$	2.56425	0.0968502	0.0484251	−	0.998827i	$-0.484580\pi$
$701$	2.56425	0.0968502	0.0484251	+	0.998827i	$0.484580\pi$
$702$	2.00291	0.0755949
$703$	−7.47967	−0.282101
$704$	−6.46576	−0.243687
$705$	36.6532	1.38044
$706$	−49.9749	−1.88083
$707$	9.46751	0.356062
$708$	13.8448	0.520318
$709$	0.936429	0.0351683	0.0175842	−	0.999845i	$-0.494402\pi$
$709$	0.936429	0.0351683	0.0175842	+	0.999845i	$0.494402\pi$
$710$	−13.2505	−0.497281
$711$	5.25631	0.197127
$712$	0.714138	0.0267635
$713$	11.5000	0.430679
$714$	−8.80134	−0.329382
$715$	24.6420	0.921560
$716$	−2.16933	−0.0810718
$717$	−44.1339	−1.64821
$718$	−25.1801	−0.939713
$719$	−22.1731	−0.826916	−0.413458	−	0.910523i	$-0.635679\pi$
$719$	−22.1731	−0.826916	−0.413458	+	0.910523i	$0.635679\pi$
$720$	−26.3727	−0.982852
$721$	−13.7964	−0.513805
$722$	−16.9192	−0.629668
$723$	0.772419	0.0287266
$724$	8.41427	0.312714
$725$	−4.95812	−0.184140
$726$	17.2461	0.640062
$727$	4.56086	0.169153	0.0845764	−	0.996417i	$-0.473046\pi$
$727$	4.56086	0.169153	0.0845764	+	0.996417i	$0.473046\pi$
$728$	24.9732	0.925567
$729$	−28.5595	−1.05776
$730$	−13.4456	−0.497643
$731$	4.77672	0.176673
$732$	21.0346	0.777463
$733$	−11.2913	−0.417053	−0.208526	−	0.978017i	$-0.566867\pi$
$733$	−11.2913	−0.417053	−0.208526	+	0.978017i	$0.566867\pi$
$734$	8.55026	0.315596
$735$	6.87684	0.253656
$736$	13.5329	0.498829
$737$	0.865419	0.0318781
$738$	−20.3573	−0.749364
$739$	21.1365	0.777519	0.388760	−	0.921339i	$-0.372904\pi$
$739$	21.1365	0.777519	0.388760	+	0.921339i	$0.372904\pi$
$740$	−3.57752	−0.131512
$741$	40.4642	1.48649
$742$	−15.4833	−0.568409
$743$	−4.67041	−0.171341	−0.0856703	−	0.996324i	$-0.527303\pi$
$743$	−4.67041	−0.171341	−0.0856703	+	0.996324i	$0.527303\pi$
$744$	−18.2871	−0.670438
$745$	−30.2958	−1.10995
$746$	50.4126	1.84574
$747$	10.9106	0.399199
$748$	−1.99196	−0.0728334
$749$	10.9168	0.398891
$750$	50.2875	1.83624
$751$	0.303011	0.0110570	0.00552851	−	0.999985i	$-0.498240\pi$
$751$	0.303011	0.0110570	0.00552851	+	0.999985i	$0.498240\pi$
$752$	43.0004	1.56806
$753$	−5.89208	−0.214719
$754$	−22.3228	−0.812948
$755$	12.5088	0.455242
$756$	−0.419245	−0.0152478
$757$	−34.8060	−1.26505	−0.632524	−	0.774541i	$-0.717981\pi$
$757$	−34.8060	−1.26505	−0.632524	+	0.774541i	$0.717981\pi$
$758$	−16.9565	−0.615888
$759$	−19.6786	−0.714289
$760$	−10.0928	−0.366104
$761$	−1.30003	−0.0471262	−0.0235631	−	0.999722i	$-0.507501\pi$
$761$	−1.30003	−0.0471262	−0.0235631	+	0.999722i	$0.507501\pi$
$762$	−40.9091	−1.48198
$763$	−5.92612	−0.214540
$764$	0.656448	0.0237495
$765$	4.84755	0.175264
$766$	32.9302	1.18982
$767$	36.9326	1.33356
$768$	−41.9569	−1.51399
$769$	6.73823	0.242987	0.121493	−	0.992592i	$-0.461232\pi$
$769$	6.73823	0.242987	0.121493	+	0.992592i	$0.461232\pi$
$770$	−17.5431	−0.632209
$771$	−22.7745	−0.820205
$772$	−21.0031	−0.755917
$773$	−4.18484	−0.150518	−0.0752590	−	0.997164i	$-0.523978\pi$
$773$	−4.18484	−0.150518	−0.0752590	+	0.997164i	$0.523978\pi$
$774$	27.1653	0.976436
$775$	7.73325	0.277787
$776$	5.38075	0.193158
$777$	14.3069	0.513259
$778$	−24.0205	−0.861178
$779$	−11.7162	−0.419777
$780$	19.3540	0.692984
$781$	11.9930	0.429144
$782$	−4.68842	−0.167658
$783$	−0.525072	−0.0187645
$784$	8.06769	0.288132
$785$	24.0572	0.858638
$786$	−65.9649	−2.35289
$787$	11.3280	0.403800	0.201900	−	0.979406i	$-0.435288\pi$
$787$	11.3280	0.403800	0.201900	+	0.979406i	$0.435288\pi$
$788$	10.7525	0.383041
$789$	12.0929	0.430520
$790$	4.92118	0.175088
$791$	8.26276	0.293790
$792$	15.8724	0.564000
$793$	56.1125	1.99261
$794$	10.4981	0.372563
$795$	16.8126	0.596283
$796$	−12.9132	−0.457698
$797$	−7.26915	−0.257487	−0.128743	−	0.991678i	$-0.541094\pi$
$797$	−7.26915	−0.257487	−0.128743	+	0.991678i	$0.541094\pi$
$798$	−28.8071	−1.01976
$799$	−7.90389	−0.279619
$800$	9.10028	0.321743
$801$	−1.12265	−0.0396669
$802$	−6.34941	−0.224205
$803$	12.1696	0.429456
$804$	0.679705	0.0239713
$805$	−12.1403	−0.427889
$806$	34.8172	1.22638
$807$	−11.7401	−0.413273
$808$	−8.01974	−0.282133
$809$	45.6395	1.60460	0.802300	−	0.596921i	$-0.203609\pi$
$809$	45.6395	1.60460	0.802300	+	0.596921i	$0.203609\pi$
$810$	−25.2344	−0.886648
$811$	2.06823	0.0726255	0.0363128	−	0.999340i	$-0.488439\pi$
$811$	2.06823	0.0726255	0.0363128	+	0.999340i	$0.488439\pi$
$812$	4.67256	0.163975
$813$	7.94951	0.278801
$814$	11.0129	0.386002
$815$	−14.7734	−0.517489
$816$	11.2120	0.392498
$817$	15.6344	0.546977
$818$	−20.0400	−0.700684
$819$	−39.2587	−1.37181
$820$	−5.60386	−0.195695
$821$	9.91664	0.346093	0.173047	−	0.984914i	$-0.444639\pi$
$821$	9.91664	0.346093	0.173047	+	0.984914i	$0.444639\pi$
$822$	−29.4609	−1.02757
$823$	−14.7943	−0.515695	−0.257848	−	0.966186i	$-0.583013\pi$
$823$	−14.7943	−0.515695	−0.257848	+	0.966186i	$0.583013\pi$
$824$	11.6867	0.407124
$825$	−13.2330	−0.460714
$826$	−26.2929	−0.914848
$827$	45.6711	1.58814	0.794070	−	0.607826i	$-0.207958\pi$
$827$	45.6711	1.58814	0.794070	+	0.607826i	$0.207958\pi$
$828$	−7.83951	−0.272442
$829$	−48.6292	−1.68896	−0.844481	−	0.535586i	$-0.820091\pi$
$829$	−48.6292	−1.68896	−0.844481	+	0.535586i	$0.820091\pi$
$830$	10.2150	0.354568
$831$	29.8421	1.03521
$832$	−13.5468	−0.469652
$833$	−1.48292	−0.0513801
$834$	−55.6004	−1.92528
$835$	29.6859	1.02732
$836$	−6.51976	−0.225491
$837$	0.818962	0.0283075
$838$	−8.95747	−0.309431
$839$	−0.670620	−0.0231524	−0.0115762	−	0.999933i	$-0.503685\pi$
$839$	−0.670620	−0.0231524	−0.0115762	+	0.999933i	$0.503685\pi$
$840$	19.3053	0.666094
$841$	−23.1480	−0.798206
$842$	−22.4544	−0.773828
$843$	14.9327	0.514311
$844$	−4.13439	−0.142312
$845$	29.2993	1.00793
$846$	−44.9496	−1.54540
$847$	−9.62990	−0.330887
$848$	19.7241	0.677327
$849$	17.0128	0.583877
$850$	−3.15276	−0.108139
$851$	7.62122	0.261252
$852$	9.41938	0.322702
$853$	−6.20727	−0.212533	−0.106266	−	0.994338i	$-0.533890\pi$
$853$	−6.20727	−0.212533	−0.106266	+	0.994338i	$0.533890\pi$
$854$	−39.9474	−1.36697
$855$	15.8662	0.542613
$856$	−9.24739	−0.316069
$857$	19.1761	0.655043	0.327522	−	0.944844i	$-0.393787\pi$
$857$	19.1761	0.655043	0.327522	+	0.944844i	$0.393787\pi$
$858$	−59.5785	−2.03398
$859$	−9.73321	−0.332093	−0.166046	−	0.986118i	$-0.553100\pi$
$859$	−9.73321	−0.332093	−0.166046	+	0.986118i	$0.553100\pi$
$860$	7.47791	0.254995
$861$	22.4105	0.763748
$862$	−36.6246	−1.24744
$863$	13.7315	0.467426	0.233713	−	0.972306i	$-0.424912\pi$
$863$	13.7315	0.467426	0.233713	+	0.972306i	$0.424912\pi$
$864$	0.963732	0.0327868
$865$	15.6402	0.531783
$866$	−42.4842	−1.44367
$867$	39.8846	1.35455
$868$	−7.28786	−0.247366
$869$	−4.45416	−0.151097
$870$	−17.2564	−0.585047
$871$	1.81320	0.0614378
$872$	5.01989	0.169995
$873$	−8.45873	−0.286285
$874$	−15.3454	−0.519065
$875$	−28.0796	−0.949265
$876$	9.55807	0.322937
$877$	−36.5157	−1.23305	−0.616524	−	0.787336i	$-0.711460\pi$
$877$	−36.5157	−1.23305	−0.616524	+	0.787336i	$0.711460\pi$
$878$	37.5187	1.26620
$879$	−64.5913	−2.17861
$880$	22.3480	0.753353
$881$	−6.04092	−0.203524	−0.101762	−	0.994809i	$-0.532448\pi$
$881$	−6.04092	−0.203524	−0.101762	+	0.994809i	$0.532448\pi$
$882$	−8.43339	−0.283967
$883$	−4.40969	−0.148398	−0.0741990	−	0.997243i	$-0.523640\pi$
$883$	−4.40969	−0.148398	−0.0741990	+	0.997243i	$0.523640\pi$
$884$	−4.17349	−0.140370
$885$	28.5504	0.959711
$886$	−36.5809	−1.22896
$887$	−1.70288	−0.0571771	−0.0285886	−	0.999591i	$-0.509101\pi$
$887$	−1.70288	−0.0571771	−0.0285886	+	0.999591i	$0.509101\pi$
$888$	−12.1191	−0.406691
$889$	22.8429	0.766126
$890$	−1.05107	−0.0352320
$891$	22.8397	0.765159
$892$	18.8555	0.631327
$893$	−25.8697	−0.865697
$894$	73.2479	2.44978
$895$	−4.47355	−0.149534
$896$	30.2366	1.01013
$897$	−41.2299	−1.37663
$898$	−11.6778	−0.389694
$899$	−9.12749	−0.304419
$900$	−5.27173	−0.175724
$901$	−3.62547	−0.120782
$902$	17.2507	0.574385
$903$	−29.9051	−0.995178
$904$	−6.99921	−0.232790
$905$	17.3517	0.576791
$906$	−30.2432	−1.00476
$907$	−45.2805	−1.50352	−0.751758	−	0.659440i	$-0.770794\pi$
$907$	−45.2805	−1.50352	−0.751758	+	0.659440i	$0.770794\pi$
$908$	−3.80934	−0.126417
$909$	12.6073	0.418158
$910$	−36.7556	−1.21844
$911$	30.6508	1.01551	0.507753	−	0.861503i	$-0.330476\pi$
$911$	30.6508	1.01551	0.507753	+	0.861503i	$0.330476\pi$
$912$	36.6972	1.21517
$913$	−9.24561	−0.305985
$914$	−14.8791	−0.492157
$915$	43.3772	1.43401
$916$	−4.08933	−0.135115
$917$	36.8336	1.21635
$918$	−0.333881	−0.0110197
$919$	−34.4855	−1.13757	−0.568785	−	0.822486i	$-0.692586\pi$
$919$	−34.4855	−1.13757	−0.568785	+	0.822486i	$0.692586\pi$
$920$	10.2838	0.339046
$921$	−58.2214	−1.91846
$922$	−25.6501	−0.844741
$923$	25.1273	0.827076
$924$	12.4709	0.410261
$925$	5.12494	0.168507
$926$	−53.8037	−1.76810
$927$	−18.3718	−0.603411
$928$	−10.7410	−0.352590
$929$	42.0463	1.37949	0.689747	−	0.724050i	$-0.257722\pi$
$929$	42.0463	1.37949	0.689747	+	0.724050i	$0.257722\pi$
$930$	26.9151	0.882580
$931$	−4.85365	−0.159072
$932$	−21.5998	−0.707526
$933$	1.38383	0.0453044
$934$	−33.3014	−1.08966
$935$	−4.10778	−0.134339
$936$	33.2552	1.08698
$937$	31.4598	1.02775	0.513874	−	0.857866i	$-0.328210\pi$
$937$	31.4598	1.02775	0.513874	+	0.857866i	$0.328210\pi$
$938$	−1.29084	−0.0421475
$939$	−78.2278	−2.55287
$940$	−12.3735	−0.403578
$941$	−13.4466	−0.438346	−0.219173	−	0.975686i	$-0.570336\pi$
$941$	−13.4466	−0.438346	−0.219173	+	0.975686i	$0.570336\pi$
$942$	−58.1645	−1.89510
$943$	11.9379	0.388753
$944$	33.4945	1.09015
$945$	−0.864558	−0.0281241
$946$	−23.0197	−0.748435
$947$	50.1077	1.62828	0.814141	−	0.580667i	$-0.197208\pi$
$947$	50.1077	1.62828	0.814141	+	0.580667i	$0.197208\pi$
$948$	−3.49832	−0.113620
$949$	25.4973	0.827679
$950$	−10.3191	−0.334795
$951$	62.2164	2.01751
$952$	−4.16298	−0.134923
$953$	59.8911	1.94006	0.970032	−	0.242977i	$-0.0781240\pi$
$953$	59.8911	1.94006	0.970032	+	0.242977i	$0.0781240\pi$
$954$	−20.6181	−0.667537
$955$	1.35371	0.0438052
$956$	14.8988	0.481862
$957$	15.6188	0.504884
$958$	34.8599	1.12627
$959$	16.4504	0.531212
$960$	−10.4722	−0.337990
$961$	−16.7637	−0.540765
$962$	23.0738	0.743930
$963$	14.5372	0.468455
$964$	−0.260755	−0.00839835
$965$	−43.3121	−1.39427
$966$	29.3523	0.944394
$967$	−29.5279	−0.949554	−0.474777	−	0.880106i	$-0.657471\pi$
$967$	−29.5279	−0.949554	−0.474777	+	0.880106i	$0.657471\pi$
$968$	8.15729	0.262185
$969$	−6.74530	−0.216690
$970$	−7.91942	−0.254277
$971$	−37.9070	−1.21649	−0.608246	−	0.793748i	$-0.708127\pi$
$971$	−37.9070	−1.21649	−0.608246	+	0.793748i	$0.708127\pi$
$972$	18.4808	0.592772
$973$	31.0462	0.995297
$974$	8.85650	0.283781
$975$	−27.7253	−0.887921
$976$	50.8888	1.62891
$977$	−38.5125	−1.23212	−0.616062	−	0.787698i	$-0.711273\pi$
$977$	−38.5125	−1.23212	−0.616062	+	0.787698i	$0.711273\pi$
$978$	35.7185	1.14215
$979$	0.951327	0.0304045
$980$	−2.32150	−0.0741575
$981$	−7.89145	−0.251955
$982$	62.3673	1.99022
$983$	26.7112	0.851955	0.425977	−	0.904734i	$-0.359930\pi$
$983$	26.7112	0.851955	0.425977	+	0.904734i	$0.359930\pi$
$984$	−18.9835	−0.605171
$985$	22.1735	0.706507
$986$	3.72117	0.118506
$987$	49.4830	1.57506
$988$	−13.6600	−0.434582
$989$	−15.9302	−0.506552
$990$	−23.3610	−0.742463
$991$	30.3178	0.963075	0.481538	−	0.876425i	$-0.340078\pi$
$991$	30.3178	0.963075	0.481538	+	0.876425i	$0.340078\pi$
$992$	16.7528	0.531903
$993$	−37.6086	−1.19347
$994$	−17.8886	−0.567391
$995$	−26.6294	−0.844209
$996$	−7.26155	−0.230091
$997$	44.6297	1.41344	0.706718	−	0.707495i	$-0.250175\pi$
$997$	44.6297	1.41344	0.706718	+	0.707495i	$0.250175\pi$
$998$	−33.4088	−1.05754
$999$	0.542738	0.0171715

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1511.2.a.a.1.33	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1511.2.a.a.1.33	✓	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1511 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1511.a (trivial)

\(f(q)\)	\(=\)	\(q+1.68314 q^{2} -2.46738 q^{3} +0.832944 q^{4} +1.71768 q^{5} -4.15294 q^{6} +2.31892 q^{7} -1.96431 q^{8} +3.08797 q^{9} +O(q^{10})\)	\(q+1.68314 q^{2} -2.46738 q^{3} +0.832944 q^{4} +1.71768 q^{5} -4.15294 q^{6} +2.31892 q^{7} -1.96431 q^{8} +3.08797 q^{9} +2.89109 q^{10} -2.61673 q^{11} -2.05519 q^{12} -5.48247 q^{13} +3.90306 q^{14} -4.23817 q^{15} -4.97209 q^{16} +0.913918 q^{17} +5.19747 q^{18} +2.99129 q^{19} +1.43073 q^{20} -5.72167 q^{21} -4.40430 q^{22} -3.04790 q^{23} +4.84671 q^{24} -2.04958 q^{25} -9.22774 q^{26} -0.217053 q^{27} +1.93153 q^{28} +2.41910 q^{29} -7.13341 q^{30} -3.77310 q^{31} -4.44008 q^{32} +6.45646 q^{33} +1.53825 q^{34} +3.98317 q^{35} +2.57210 q^{36} -2.50049 q^{37} +5.03474 q^{38} +13.5273 q^{39} -3.37406 q^{40} -3.91678 q^{41} -9.63034 q^{42} +5.22664 q^{43} -2.17959 q^{44} +5.30414 q^{45} -5.13002 q^{46} -8.64836 q^{47} +12.2680 q^{48} -1.62260 q^{49} -3.44971 q^{50} -2.25498 q^{51} -4.56659 q^{52} -3.96696 q^{53} -0.365330 q^{54} -4.49470 q^{55} -4.55509 q^{56} -7.38064 q^{57} +4.07166 q^{58} -6.73649 q^{59} -3.53016 q^{60} -10.2349 q^{61} -6.35063 q^{62} +7.16076 q^{63} +2.47093 q^{64} -9.41713 q^{65} +10.8671 q^{66} -0.330726 q^{67} +0.761242 q^{68} +7.52032 q^{69} +6.70421 q^{70} -4.58321 q^{71} -6.06574 q^{72} -4.65070 q^{73} -4.20866 q^{74} +5.05709 q^{75} +2.49157 q^{76} -6.06799 q^{77} +22.7684 q^{78} +1.70219 q^{79} -8.54046 q^{80} -8.72835 q^{81} -6.59247 q^{82} +3.53327 q^{83} -4.76583 q^{84} +1.56982 q^{85} +8.79713 q^{86} -5.96883 q^{87} +5.14007 q^{88} -0.363556 q^{89} +8.92759 q^{90} -12.7134 q^{91} -2.53873 q^{92} +9.30967 q^{93} -14.5564 q^{94} +5.13807 q^{95} +10.9554 q^{96} -2.73925 q^{97} -2.73105 q^{98} -8.08037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 5 q^{2} - 4 q^{3} + 19 q^{4} - 8 q^{5} - 8 q^{6} - 15 q^{7} - 12 q^{8} - q^{9}+O(q^{10}) \) 39 * q - 5 * q^2 - 4 * q^3 + 19 * q^4 - 8 * q^5 - 8 * q^6 - 15 * q^7 - 12 * q^8 - q^9	\( 39 q - 5 q^{2} - 4 q^{3} + 19 q^{4} - 8 q^{5} - 8 q^{6} - 15 q^{7} - 12 q^{8} - q^{9} - 13 q^{10} - 13 q^{11} - 8 q^{12} - 24 q^{13} - 12 q^{14} - 16 q^{15} - 13 q^{16} - 26 q^{17} - 17 q^{18} - 40 q^{19} - 15 q^{20} - 26 q^{21} - 26 q^{22} - 8 q^{23} - 16 q^{24} - 35 q^{25} - 3 q^{26} - 10 q^{27} - 31 q^{28} - 30 q^{29} - 16 q^{30} - 21 q^{31} - 9 q^{32} - 25 q^{33} - 27 q^{34} - 2 q^{35} - 23 q^{36} - 27 q^{37} + q^{38} - 29 q^{39} - 36 q^{40} - 35 q^{41} - 6 q^{42} - 48 q^{43} - 17 q^{44} - 22 q^{45} - 31 q^{46} - 3 q^{47} + q^{48} - 64 q^{49} + 12 q^{50} - 27 q^{51} - 28 q^{52} - 14 q^{53} + q^{54} - 31 q^{55} - 12 q^{56} - 36 q^{57} - 19 q^{58} - 9 q^{59} - 6 q^{60} - 87 q^{61} + 32 q^{62} - 9 q^{63} - 52 q^{64} - 35 q^{65} + 5 q^{66} - 24 q^{67} - 13 q^{68} - 35 q^{69} - 8 q^{70} - 21 q^{71} - 11 q^{72} - 69 q^{73} - 23 q^{74} - 4 q^{75} - 58 q^{76} - 3 q^{77} + q^{78} - 72 q^{79} + 13 q^{80} - 73 q^{81} + 18 q^{82} - 11 q^{83} - 32 q^{84} - 70 q^{85} + 20 q^{86} - 9 q^{87} - 24 q^{88} - 25 q^{89} + 33 q^{90} - 32 q^{91} + 17 q^{92} - 19 q^{93} - 29 q^{94} - 9 q^{95} + 5 q^{96} - 56 q^{97} + 37 q^{98} - 19 q^{99}+O(q^{100}) \) 39 * q - 5 * q^2 - 4 * q^3 + 19 * q^4 - 8 * q^5 - 8 * q^6 - 15 * q^7 - 12 * q^8 - q^9 - 13 * q^10 - 13 * q^11 - 8 * q^12 - 24 * q^13 - 12 * q^14 - 16 * q^15 - 13 * q^16 - 26 * q^17 - 17 * q^18 - 40 * q^19 - 15 * q^20 - 26 * q^21 - 26 * q^22 - 8 * q^23 - 16 * q^24 - 35 * q^25 - 3 * q^26 - 10 * q^27 - 31 * q^28 - 30 * q^29 - 16 * q^30 - 21 * q^31 - 9 * q^32 - 25 * q^33 - 27 * q^34 - 2 * q^35 - 23 * q^36 - 27 * q^37 + q^38 - 29 * q^39 - 36 * q^40 - 35 * q^41 - 6 * q^42 - 48 * q^43 - 17 * q^44 - 22 * q^45 - 31 * q^46 - 3 * q^47 + q^48 - 64 * q^49 + 12 * q^50 - 27 * q^51 - 28 * q^52 - 14 * q^53 + q^54 - 31 * q^55 - 12 * q^56 - 36 * q^57 - 19 * q^58 - 9 * q^59 - 6 * q^60 - 87 * q^61 + 32 * q^62 - 9 * q^63 - 52 * q^64 - 35 * q^65 + 5 * q^66 - 24 * q^67 - 13 * q^68 - 35 * q^69 - 8 * q^70 - 21 * q^71 - 11 * q^72 - 69 * q^73 - 23 * q^74 - 4 * q^75 - 58 * q^76 - 3 * q^77 + q^78 - 72 * q^79 + 13 * q^80 - 73 * q^81 + 18 * q^82 - 11 * q^83 - 32 * q^84 - 70 * q^85 + 20 * q^86 - 9 * q^87 - 24 * q^88 - 25 * q^89 + 33 * q^90 - 32 * q^91 + 17 * q^92 - 19 * q^93 - 29 * q^94 - 9 * q^95 + 5 * q^96 - 56 * q^97 + 37 * q^98 - 19 * q^99

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