LMFDB - Embedded newform 1441.2.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.89426 q^{2} +2.98322 q^{3} +1.58823 q^{4} +3.71742 q^{5} -5.65101 q^{6} +2.24937 q^{7} +0.780003 q^{8} +5.89963 q^{9} +O(q^{10})$	\(q-1.89426 q^{2} +2.98322 q^{3} +1.58823 q^{4} +3.71742 q^{5} -5.65101 q^{6} +2.24937 q^{7} +0.780003 q^{8} +5.89963 q^{9} -7.04177 q^{10} -1.00000 q^{11} +4.73804 q^{12} +1.33551 q^{13} -4.26089 q^{14} +11.0899 q^{15} -4.65399 q^{16} -0.829059 q^{17} -11.1754 q^{18} -2.17906 q^{19} +5.90412 q^{20} +6.71037 q^{21} +1.89426 q^{22} +2.63499 q^{23} +2.32692 q^{24} +8.81923 q^{25} -2.52981 q^{26} +8.65023 q^{27} +3.57251 q^{28} -6.18508 q^{29} -21.0072 q^{30} -1.56242 q^{31} +7.25586 q^{32} -2.98322 q^{33} +1.57045 q^{34} +8.36185 q^{35} +9.36995 q^{36} +2.72155 q^{37} +4.12772 q^{38} +3.98414 q^{39} +2.89960 q^{40} -7.63344 q^{41} -12.7112 q^{42} -3.49886 q^{43} -1.58823 q^{44} +21.9314 q^{45} -4.99136 q^{46} -6.02799 q^{47} -13.8839 q^{48} -1.94035 q^{49} -16.7059 q^{50} -2.47327 q^{51} +2.12110 q^{52} +7.36654 q^{53} -16.3858 q^{54} -3.71742 q^{55} +1.75451 q^{56} -6.50063 q^{57} +11.7162 q^{58} +6.02919 q^{59} +17.6133 q^{60} -3.28716 q^{61} +2.95964 q^{62} +13.2704 q^{63} -4.43653 q^{64} +4.96467 q^{65} +5.65101 q^{66} +1.56157 q^{67} -1.31674 q^{68} +7.86077 q^{69} -15.8395 q^{70} -12.2092 q^{71} +4.60173 q^{72} -13.6394 q^{73} -5.15532 q^{74} +26.3097 q^{75} -3.46085 q^{76} -2.24937 q^{77} -7.54700 q^{78} -11.4372 q^{79} -17.3008 q^{80} +8.10671 q^{81} +14.4597 q^{82} +9.75016 q^{83} +10.6576 q^{84} -3.08196 q^{85} +6.62777 q^{86} -18.4515 q^{87} -0.780003 q^{88} -8.59385 q^{89} -41.5438 q^{90} +3.00406 q^{91} +4.18497 q^{92} -4.66106 q^{93} +11.4186 q^{94} -8.10050 q^{95} +21.6459 q^{96} +9.51798 q^{97} +3.67553 q^{98} -5.89963 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * 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 $

$2$	−1.89426	−1.33945	−0.669723	−	0.742611i	$-0.733587\pi$
$2$	−1.89426	−1.33945	−0.669723	+	0.742611i	$0.733587\pi$
$3$	2.98322	1.72237	0.861183	−	0.508296i	$-0.169724\pi$
$3$	2.98322	1.72237	0.861183	+	0.508296i	$0.169724\pi$
$4$	1.58823	0.794114
$5$	3.71742	1.66248	0.831241	−	0.555912i	$-0.187631\pi$
$5$	3.71742	1.66248	0.831241	+	0.555912i	$0.187631\pi$
$6$	−5.65101	−2.30701
$7$	2.24937	0.850181	0.425090	−	0.905151i	$-0.360242\pi$
$7$	2.24937	0.850181	0.425090	+	0.905151i	$0.360242\pi$
$8$	0.780003	0.275773
$9$	5.89963	1.96654
$10$	−7.04177	−2.22680
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	4.73804	1.36775
$13$	1.33551	0.370405	0.185202	−	0.982700i	$-0.440706\pi$
$13$	1.33551	0.370405	0.185202	+	0.982700i	$0.440706\pi$
$14$	−4.26089	−1.13877
$15$	11.0899	2.86340
$16$	−4.65399	−1.16350
$17$	−0.829059	−0.201076	−0.100538	−	0.994933i	$-0.532056\pi$
$17$	−0.829059	−0.201076	−0.100538	+	0.994933i	$0.532056\pi$
$18$	−11.1754	−2.63408
$19$	−2.17906	−0.499911	−0.249956	−	0.968257i	$-0.580416\pi$
$19$	−2.17906	−0.499911	−0.249956	+	0.968257i	$0.580416\pi$
$20$	5.90412	1.32020
$21$	6.71037	1.46432
$22$	1.89426	0.403858
$23$	2.63499	0.549433	0.274717	−	0.961525i	$-0.411416\pi$
$23$	2.63499	0.549433	0.274717	+	0.961525i	$0.411416\pi$
$24$	2.32692	0.474981
$25$	8.81923	1.76385
$26$	−2.52981	−0.496137
$27$	8.65023	1.66474
$28$	3.57251	0.675141
$29$	−6.18508	−1.14854	−0.574270	−	0.818666i	$-0.694714\pi$
$29$	−6.18508	−1.14854	−0.574270	+	0.818666i	$0.694714\pi$
$30$	−21.0072	−3.83537
$31$	−1.56242	−0.280620	−0.140310	−	0.990108i	$-0.544810\pi$
$31$	−1.56242	−0.280620	−0.140310	+	0.990108i	$0.544810\pi$
$32$	7.25586	1.28267
$33$	−2.98322	−0.519313
$34$	1.57045	0.269331
$35$	8.36185	1.41341
$36$	9.36995	1.56166
$37$	2.72155	0.447419	0.223710	−	0.974656i	$-0.428183\pi$
$37$	2.72155	0.447419	0.223710	+	0.974656i	$0.428183\pi$
$38$	4.12772	0.669604
$39$	3.98414	0.637972
$40$	2.89960	0.458467
$41$	−7.63344	−1.19214	−0.596072	−	0.802931i	$-0.703273\pi$
$41$	−7.63344	−1.19214	−0.596072	+	0.802931i	$0.703273\pi$
$42$	−12.7112	−1.96138
$43$	−3.49886	−0.533572	−0.266786	−	0.963756i	$-0.585962\pi$
$43$	−3.49886	−0.533572	−0.266786	+	0.963756i	$0.585962\pi$
$44$	−1.58823	−0.239434
$45$	21.9314	3.26934
$46$	−4.99136	−0.735936
$47$	−6.02799	−0.879272	−0.439636	−	0.898176i	$-0.644893\pi$
$47$	−6.02799	−0.879272	−0.439636	+	0.898176i	$0.644893\pi$
$48$	−13.8839	−2.00397
$49$	−1.94035	−0.277193
$50$	−16.7059	−2.36258
$51$	−2.47327	−0.346327
$52$	2.12110	0.294144
$53$	7.36654	1.01187	0.505936	−	0.862571i	$-0.331147\pi$
$53$	7.36654	1.01187	0.505936	+	0.862571i	$0.331147\pi$
$54$	−16.3858	−2.22983
$55$	−3.71742	−0.501257
$56$	1.75451	0.234457
$57$	−6.50063	−0.861030
$58$	11.7162	1.53841
$59$	6.02919	0.784933	0.392467	−	0.919766i	$-0.371622\pi$
$59$	6.02919	0.784933	0.392467	+	0.919766i	$0.371622\pi$
$60$	17.6133	2.27387
$61$	−3.28716	−0.420878	−0.210439	−	0.977607i	$-0.567489\pi$
$61$	−3.28716	−0.420878	−0.210439	+	0.977607i	$0.567489\pi$
$62$	2.95964	0.375875
$63$	13.2704	1.67192
$64$	−4.43653	−0.554567
$65$	4.96467	0.615791
$66$	5.65101	0.695591
$67$	1.56157	0.190776	0.0953880	−	0.995440i	$-0.469591\pi$
$67$	1.56157	0.190776	0.0953880	+	0.995440i	$0.469591\pi$
$68$	−1.31674	−0.159678
$69$	7.86077	0.946325
$70$	−15.8395	−1.89319
$71$	−12.2092	−1.44896	−0.724481	−	0.689294i	$-0.757921\pi$
$71$	−12.2092	−1.44896	−0.724481	+	0.689294i	$0.757921\pi$
$72$	4.60173	0.542319
$73$	−13.6394	−1.59637	−0.798186	−	0.602411i	$-0.794207\pi$
$73$	−13.6394	−1.59637	−0.798186	+	0.602411i	$0.794207\pi$
$74$	−5.15532	−0.599294
$75$	26.3097	3.03799
$76$	−3.46085	−0.396987
$77$	−2.24937	−0.256339
$78$	−7.54700	−0.854529
$79$	−11.4372	−1.28679	−0.643393	−	0.765536i	$-0.722474\pi$
$79$	−11.4372	−1.28679	−0.643393	+	0.765536i	$0.722474\pi$
$80$	−17.3008	−1.93429
$81$	8.10671	0.900746
$82$	14.4597	1.59681
$83$	9.75016	1.07022	0.535109	−	0.844783i	$-0.320270\pi$
$83$	9.75016	1.07022	0.535109	+	0.844783i	$0.320270\pi$
$84$	10.6576	1.16284
$85$	−3.08196	−0.334286
$86$	6.62777	0.714690
$87$	−18.4515	−1.97821
$88$	−0.780003	−0.0831486
$89$	−8.59385	−0.910947	−0.455473	−	0.890249i	$-0.650530\pi$
$89$	−8.59385	−0.910947	−0.455473	+	0.890249i	$0.650530\pi$
$90$	−41.5438	−4.37910
$91$	3.00406	0.314911
$92$	4.18497	0.436313
$93$	−4.66106	−0.483330
$94$	11.4186	1.17774
$95$	−8.10050	−0.831093
$96$	21.6459	2.20922
$97$	9.51798	0.966405	0.483202	−	0.875509i	$-0.339474\pi$
$97$	9.51798	0.966405	0.483202	+	0.875509i	$0.339474\pi$
$98$	3.67553	0.371284
$99$	−5.89963	−0.592935
$100$	14.0070	1.40070
$101$	−14.7637	−1.46905	−0.734523	−	0.678584i	$-0.762594\pi$
$101$	−14.7637	−1.46905	−0.734523	+	0.678584i	$0.762594\pi$
$102$	4.68502	0.463886
$103$	−19.0952	−1.88151	−0.940753	−	0.339091i	$-0.889880\pi$
$103$	−19.0952	−1.88151	−0.940753	+	0.339091i	$0.889880\pi$
$104$	1.04170	0.102148
$105$	24.9453	2.43441
$106$	−13.9542	−1.35535
$107$	17.0864	1.65180	0.825901	−	0.563816i	$-0.190667\pi$
$107$	17.0864	1.65180	0.825901	+	0.563816i	$0.190667\pi$
$108$	13.7385	1.32199
$109$	0.285904	0.0273846	0.0136923	−	0.999906i	$-0.495641\pi$
$109$	0.285904	0.0273846	0.0136923	+	0.999906i	$0.495641\pi$
$110$	7.04177	0.671407
$111$	8.11898	0.770620
$112$	−10.4685	−0.989183
$113$	−3.16843	−0.298061	−0.149031	−	0.988833i	$-0.547615\pi$
$113$	−3.16843	−0.298061	−0.149031	+	0.988833i	$0.547615\pi$
$114$	12.3139	1.15330
$115$	9.79537	0.913423
$116$	−9.82331	−0.912072
$117$	7.87903	0.728417
$118$	−11.4209	−1.05138
$119$	−1.86486	−0.170951
$120$	8.65016	0.789648
$121$	1.00000	0.0909091
$122$	6.22675	0.563743
$123$	−22.7723	−2.05331
$124$	−2.48149	−0.222844
$125$	14.1977	1.26988
$126$	−25.1377	−2.23944
$127$	8.65513	0.768018	0.384009	−	0.923329i	$-0.374543\pi$
$127$	8.65513	0.768018	0.384009	+	0.923329i	$0.374543\pi$
$128$	−6.10777	−0.539856
$129$	−10.4379	−0.919006
$130$	−9.40438	−0.824819
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−4.73804	−0.412394
$133$	−4.90151	−0.425015
$134$	−2.95802	−0.255534
$135$	32.1566	2.76760
$136$	−0.646669	−0.0554514
$137$	−1.74885	−0.149414	−0.0747072	−	0.997206i	$-0.523802\pi$
$137$	−1.74885	−0.149414	−0.0747072	+	0.997206i	$0.523802\pi$
$138$	−14.8904	−1.26755
$139$	0.360920	0.0306128	0.0153064	−	0.999883i	$-0.495128\pi$
$139$	0.360920	0.0306128	0.0153064	+	0.999883i	$0.495128\pi$
$140$	13.2805	1.12241
$141$	−17.9828	−1.51443
$142$	23.1274	1.94081
$143$	−1.33551	−0.111681
$144$	−27.4568	−2.28807
$145$	−22.9925	−1.90943
$146$	25.8366	2.13825
$147$	−5.78849	−0.477427
$148$	4.32244	0.355302
$149$	−1.73452	−0.142097	−0.0710486	−	0.997473i	$-0.522635\pi$
$149$	−1.73452	−0.142097	−0.0710486	+	0.997473i	$0.522635\pi$
$150$	−49.8375	−4.06922
$151$	−3.38461	−0.275436	−0.137718	−	0.990471i	$-0.543977\pi$
$151$	−3.38461	−0.275436	−0.137718	+	0.990471i	$0.543977\pi$
$152$	−1.69968	−0.137862
$153$	−4.89114	−0.395425
$154$	4.26089	0.343352
$155$	−5.80819	−0.466525
$156$	6.32772	0.506623
$157$	16.4901	1.31605	0.658027	−	0.752994i	$-0.271391\pi$
$157$	16.4901	1.31605	0.658027	+	0.752994i	$0.271391\pi$
$158$	21.6650	1.72358
$159$	21.9760	1.74281
$160$	26.9731	2.13241
$161$	5.92706	0.467118
$162$	−15.3562	−1.20650
$163$	8.28664	0.649060	0.324530	−	0.945875i	$-0.394794\pi$
$163$	8.28664	0.649060	0.324530	+	0.945875i	$0.394794\pi$
$164$	−12.1237	−0.946698
$165$	−11.0899	−0.863348
$166$	−18.4693	−1.43350
$167$	25.0518	1.93856	0.969282	−	0.245953i	$-0.0791008\pi$
$167$	25.0518	1.93856	0.969282	+	0.245953i	$0.0791008\pi$
$168$	5.23411	0.403820
$169$	−11.2164	−0.862800
$170$	5.83804	0.447758
$171$	−12.8557	−0.983097
$172$	−5.55700	−0.423717
$173$	14.6837	1.11638	0.558189	−	0.829714i	$-0.311496\pi$
$173$	14.6837	1.11638	0.558189	+	0.829714i	$0.311496\pi$
$174$	34.9519	2.64970
$175$	19.8377	1.49959
$176$	4.65399	0.350807
$177$	17.9864	1.35194
$178$	16.2790	1.22016
$179$	20.4508	1.52857	0.764284	−	0.644880i	$-0.223093\pi$
$179$	20.4508	1.52857	0.764284	+	0.644880i	$0.223093\pi$
$180$	34.8321	2.59623
$181$	5.75490	0.427758	0.213879	−	0.976860i	$-0.431390\pi$
$181$	5.75490	0.427758	0.213879	+	0.976860i	$0.431390\pi$
$182$	−5.69048	−0.421806
$183$	−9.80634	−0.724906
$184$	2.05530	0.151519
$185$	10.1171	0.743827
$186$	8.82928	0.647394
$187$	0.829059	0.0606268
$188$	−9.57382	−0.698243
$189$	19.4576	1.41533
$190$	15.3445	1.11320
$191$	20.5485	1.48684	0.743419	−	0.668826i	$-0.233203\pi$
$191$	20.5485	1.48684	0.743419	+	0.668826i	$0.233203\pi$
$192$	−13.2352	−0.955167
$193$	−0.315911	−0.0227398	−0.0113699	−	0.999935i	$-0.503619\pi$
$193$	−0.315911	−0.0227398	−0.0113699	+	0.999935i	$0.503619\pi$
$194$	−18.0296	−1.29445
$195$	14.8107	1.06062
$196$	−3.08172	−0.220123
$197$	14.5661	1.03779	0.518896	−	0.854838i	$-0.326343\pi$
$197$	14.5661	1.03779	0.518896	+	0.854838i	$0.326343\pi$
$198$	11.1754	0.794204
$199$	−27.2927	−1.93472	−0.967362	−	0.253397i	$-0.918452\pi$
$199$	−27.2927	−1.93472	−0.967362	+	0.253397i	$0.918452\pi$
$200$	6.87903	0.486421
$201$	4.65851	0.328586
$202$	27.9664	1.96771
$203$	−13.9125	−0.976467
$204$	−3.92812	−0.275023
$205$	−28.3767	−1.98192
$206$	36.1713	2.52018
$207$	15.5455	1.08048
$208$	−6.21546	−0.430965
$209$	2.17906	0.150729
$210$	−47.2529	−3.26076
$211$	7.32067	0.503976	0.251988	−	0.967730i	$-0.418916\pi$
$211$	7.32067	0.503976	0.251988	+	0.967730i	$0.418916\pi$
$212$	11.6997	0.803542
$213$	−36.4227	−2.49564
$214$	−32.3661	−2.21250
$215$	−13.0068	−0.887054
$216$	6.74721	0.459090
$217$	−3.51447	−0.238578
$218$	−0.541576	−0.0366802
$219$	−40.6894	−2.74954
$220$	−5.90412	−0.398055
$221$	−1.10722	−0.0744796
$222$	−15.3795	−1.03220
$223$	−7.61217	−0.509749	−0.254874	−	0.966974i	$-0.582034\pi$
$223$	−7.61217	−0.509749	−0.254874	+	0.966974i	$0.582034\pi$
$224$	16.3211	1.09050
$225$	52.0302	3.46868
$226$	6.00184	0.399237
$227$	12.7858	0.848621	0.424310	−	0.905517i	$-0.360517\pi$
$227$	12.7858	0.848621	0.424310	+	0.905517i	$0.360517\pi$
$228$	−10.3245	−0.683756
$229$	18.7912	1.24175	0.620877	−	0.783908i	$-0.286777\pi$
$229$	18.7912	1.24175	0.620877	+	0.783908i	$0.286777\pi$
$230$	−18.5550	−1.22348
$231$	−6.71037	−0.441510
$232$	−4.82438	−0.316736
$233$	15.1216	0.990648	0.495324	−	0.868708i	$-0.335049\pi$
$233$	15.1216	0.990648	0.495324	+	0.868708i	$0.335049\pi$
$234$	−14.9249	−0.975674
$235$	−22.4086	−1.46177
$236$	9.57573	0.623327
$237$	−34.1197	−2.21631
$238$	3.53253	0.228980
$239$	24.5511	1.58808	0.794039	−	0.607867i	$-0.207975\pi$
$239$	24.5511	1.58808	0.794039	+	0.607867i	$0.207975\pi$
$240$	−51.6123	−3.33156
$241$	−5.30008	−0.341408	−0.170704	−	0.985322i	$-0.554604\pi$
$241$	−5.30008	−0.341408	−0.170704	+	0.985322i	$0.554604\pi$
$242$	−1.89426	−0.121768
$243$	−1.76657	−0.113326
$244$	−5.22077	−0.334225
$245$	−7.21310	−0.460828
$246$	43.1367	2.75029
$247$	−2.91017	−0.185170
$248$	−1.21870	−0.0773873
$249$	29.0869	1.84331
$250$	−26.8942	−1.70094
$251$	10.6993	0.675336	0.337668	−	0.941265i	$-0.390362\pi$
$251$	10.6993	0.675336	0.337668	+	0.941265i	$0.390362\pi$
$252$	21.0765	1.32769
$253$	−2.63499	−0.165660
$254$	−16.3951	−1.02872
$255$	−9.19419	−0.575762
$256$	20.4428	1.27767
$257$	−15.6671	−0.977290	−0.488645	−	0.872483i	$-0.662509\pi$
$257$	−15.6671	−0.977290	−0.488645	+	0.872483i	$0.662509\pi$
$258$	19.7721	1.23096
$259$	6.12175	0.380387
$260$	7.88503	0.489009
$261$	−36.4896	−2.25865
$262$	−1.89426	−0.117028
$263$	26.5306	1.63594	0.817972	−	0.575257i	$-0.195098\pi$
$263$	26.5306	1.63594	0.817972	+	0.575257i	$0.195098\pi$
$264$	−2.32692	−0.143212
$265$	27.3845	1.68222
$266$	9.28475	0.569284
$267$	−25.6374	−1.56898
$268$	2.48013	0.151498
$269$	−14.1824	−0.864718	−0.432359	−	0.901702i	$-0.642319\pi$
$269$	−14.1824	−0.864718	−0.432359	+	0.901702i	$0.642319\pi$
$270$	−60.9130	−3.70705
$271$	−24.3889	−1.48152	−0.740760	−	0.671769i	$-0.765535\pi$
$271$	−24.3889	−1.48152	−0.740760	+	0.671769i	$0.765535\pi$
$272$	3.85843	0.233952
$273$	8.96178	0.542392
$274$	3.31278	0.200133
$275$	−8.81923	−0.531820
$276$	12.4847	0.751490
$277$	−18.8168	−1.13059	−0.565297	−	0.824887i	$-0.691238\pi$
$277$	−18.8168	−1.13059	−0.565297	+	0.824887i	$0.691238\pi$
$278$	−0.683676	−0.0410042
$279$	−9.21772	−0.551851
$280$	6.52227	0.389780
$281$	3.49295	0.208372	0.104186	−	0.994558i	$-0.466776\pi$
$281$	3.49295	0.208372	0.104186	+	0.994558i	$0.466776\pi$
$282$	34.0642	2.02849
$283$	22.3076	1.32605	0.663024	−	0.748598i	$-0.269273\pi$
$283$	22.3076	1.32605	0.663024	+	0.748598i	$0.269273\pi$
$284$	−19.3910	−1.15064
$285$	−24.1656	−1.43145
$286$	2.52981	0.149591
$287$	−17.1704	−1.01354
$288$	42.8069	2.52242
$289$	−16.3127	−0.959568
$290$	43.5539	2.55757
$291$	28.3943	1.66450
$292$	−21.6625	−1.26770
$293$	−7.53546	−0.440226	−0.220113	−	0.975474i	$-0.570643\pi$
$293$	−7.53546	−0.440226	−0.220113	+	0.975474i	$0.570643\pi$
$294$	10.9649	0.639487
$295$	22.4130	1.30494
$296$	2.12281	0.123386
$297$	−8.65023	−0.501938
$298$	3.28563	0.190332
$299$	3.51907	0.203513
$300$	41.7859	2.41251
$301$	−7.87023	−0.453633
$302$	6.41135	0.368931
$303$	−44.0435	−2.53023
$304$	10.1413	0.581645
$305$	−12.2198	−0.699702
$306$	9.26510	0.529650
$307$	12.9136	0.737015	0.368508	−	0.929625i	$-0.379869\pi$
$307$	12.9136	0.737015	0.368508	+	0.929625i	$0.379869\pi$
$308$	−3.57251	−0.203563
$309$	−56.9653	−3.24064
$310$	11.0022	0.624885
$311$	27.8608	1.57984	0.789919	−	0.613211i	$-0.210122\pi$
$311$	27.8608	1.57984	0.789919	+	0.613211i	$0.210122\pi$
$312$	3.10764	0.175935
$313$	13.7217	0.775595	0.387798	−	0.921745i	$-0.373236\pi$
$313$	13.7217	0.775595	0.387798	+	0.921745i	$0.373236\pi$
$314$	−31.2366	−1.76278
$315$	49.3318	2.77953
$316$	−18.1649	−1.02185
$317$	8.71062	0.489237	0.244619	−	0.969619i	$-0.421337\pi$
$317$	8.71062	0.489237	0.244619	+	0.969619i	$0.421337\pi$
$318$	−41.6284	−2.33440
$319$	6.18508	0.346298
$320$	−16.4925	−0.921957
$321$	50.9725	2.84501
$322$	−11.2274	−0.625679
$323$	1.80657	0.100520
$324$	12.8753	0.715295
$325$	11.7782	0.653337
$326$	−15.6971	−0.869380
$327$	0.852915	0.0471663
$328$	−5.95411	−0.328761
$329$	−13.5592	−0.747540
$330$	21.0072	1.15641
$331$	−34.7569	−1.91041	−0.955205	−	0.295946i	$-0.904365\pi$
$331$	−34.7569	−1.91041	−0.955205	+	0.295946i	$0.904365\pi$
$332$	15.4855	0.849876
$333$	16.0561	0.879869
$334$	−47.4546	−2.59660
$335$	5.80501	0.317162
$336$	−31.2300	−1.70373
$337$	13.1904	0.718530	0.359265	−	0.933236i	$-0.383027\pi$
$337$	13.1904	0.718530	0.359265	+	0.933236i	$0.383027\pi$
$338$	21.2468	1.15567
$339$	−9.45215	−0.513370
$340$	−4.89486	−0.265461
$341$	1.56242	0.0846100
$342$	24.3520	1.31680
$343$	−20.1101	−1.08584
$344$	−2.72913	−0.147145
$345$	29.2218	1.57325
$346$	−27.8147	−1.49533
$347$	13.1676	0.706876	0.353438	−	0.935458i	$-0.385012\pi$
$347$	13.1676	0.706876	0.353438	+	0.935458i	$0.385012\pi$
$348$	−29.3051	−1.57092
$349$	−18.8738	−1.01029	−0.505147	−	0.863033i	$-0.668562\pi$
$349$	−18.8738	−1.01029	−0.505147	+	0.863033i	$0.668562\pi$
$350$	−37.5778	−2.00862
$351$	11.5525	0.616627
$352$	−7.25586	−0.386739
$353$	−31.6839	−1.68636	−0.843182	−	0.537628i	$-0.819320\pi$
$353$	−31.6839	−1.68636	−0.843182	+	0.537628i	$0.819320\pi$
$354$	−34.0710	−1.81085
$355$	−45.3867	−2.40887
$356$	−13.6490	−0.723396
$357$	−5.56329	−0.294440
$358$	−38.7392	−2.04743
$359$	−3.35798	−0.177228	−0.0886138	−	0.996066i	$-0.528244\pi$
$359$	−3.35798	−0.177228	−0.0886138	+	0.996066i	$0.528244\pi$
$360$	17.1066	0.901595
$361$	−14.2517	−0.750089
$362$	−10.9013	−0.572958
$363$	2.98322	0.156579
$364$	4.77113	0.250075
$365$	−50.7035	−2.65394
$366$	18.5758	0.970972
$367$	−25.2265	−1.31681	−0.658406	−	0.752663i	$-0.728769\pi$
$367$	−25.2265	−1.31681	−0.658406	+	0.752663i	$0.728769\pi$
$368$	−12.2632	−0.639264
$369$	−45.0345	−2.34440
$370$	−19.1645	−0.996315
$371$	16.5700	0.860274
$372$	−7.40283	−0.383819
$373$	1.92774	0.0998146	0.0499073	−	0.998754i	$-0.484107\pi$
$373$	1.92774	0.0998146	0.0499073	+	0.998754i	$0.484107\pi$
$374$	−1.57045	−0.0812063
$375$	42.3549	2.18720
$376$	−4.70185	−0.242479
$377$	−8.26025	−0.425425
$378$	−36.8577	−1.89576
$379$	−5.13350	−0.263690	−0.131845	−	0.991270i	$-0.542090\pi$
$379$	−5.13350	−0.263690	−0.131845	+	0.991270i	$0.542090\pi$
$380$	−12.8654	−0.659983
$381$	25.8202	1.32281
$382$	−38.9242	−1.99154
$383$	−23.4365	−1.19755	−0.598776	−	0.800917i	$-0.704346\pi$
$383$	−23.4365	−1.19755	−0.598776	+	0.800917i	$0.704346\pi$
$384$	−18.2209	−0.929829
$385$	−8.36185	−0.426159
$386$	0.598418	0.0304587
$387$	−20.6420	−1.04929
$388$	15.1167	0.767436
$389$	−0.0532007	−0.00269738	−0.00134869	−	0.999999i	$-0.500429\pi$
$389$	−0.0532007	−0.00269738	−0.00134869	+	0.999999i	$0.500429\pi$
$390$	−28.0554	−1.42064
$391$	−2.18456	−0.110478
$392$	−1.51348	−0.0764422
$393$	2.98322	0.150484
$394$	−27.5920	−1.39006
$395$	−42.5169	−2.13926
$396$	−9.36995	−0.470858
$397$	32.1600	1.61406	0.807031	−	0.590509i	$-0.201073\pi$
$397$	32.1600	1.61406	0.807031	+	0.590509i	$0.201073\pi$
$398$	51.6994	2.59146
$399$	−14.6223	−0.732031
$400$	−41.0446	−2.05223
$401$	18.1100	0.904372	0.452186	−	0.891924i	$-0.350644\pi$
$401$	18.1100	0.904372	0.452186	+	0.891924i	$0.350644\pi$
$402$	−8.82444	−0.440123
$403$	−2.08664	−0.103943
$404$	−23.4482	−1.16659
$405$	30.1361	1.49747
$406$	26.3539	1.30792
$407$	−2.72155	−0.134902
$408$	−1.92916	−0.0955075
$409$	−6.61957	−0.327316	−0.163658	−	0.986517i	$-0.552329\pi$
$409$	−6.61957	−0.327316	−0.163658	+	0.986517i	$0.552329\pi$
$410$	53.7530	2.65467
$411$	−5.21722	−0.257346
$412$	−30.3276	−1.49413
$413$	13.5619	0.667335
$414$	−29.4472	−1.44725
$415$	36.2454	1.77922
$416$	9.69031	0.475106
$417$	1.07670	0.0527264
$418$	−4.12772	−0.201893
$419$	3.86809	0.188969	0.0944844	−	0.995526i	$-0.469880\pi$
$419$	3.86809	0.188969	0.0944844	+	0.995526i	$0.469880\pi$
$420$	39.6188	1.93320
$421$	15.0886	0.735375	0.367688	−	0.929949i	$-0.380150\pi$
$421$	15.0886	0.735375	0.367688	+	0.929949i	$0.380150\pi$
$422$	−13.8673	−0.675048
$423$	−35.5629	−1.72913
$424$	5.74592	0.279047
$425$	−7.31166	−0.354668
$426$	68.9942	3.34278
$427$	−7.39404	−0.357823
$428$	27.1371	1.31172
$429$	−3.98414	−0.192356
$430$	24.6382	1.18816
$431$	−0.916972	−0.0441690	−0.0220845	−	0.999756i	$-0.507030\pi$
$431$	−0.916972	−0.0441690	−0.0220845	+	0.999756i	$0.507030\pi$
$432$	−40.2581	−1.93692
$433$	3.63547	0.174709	0.0873547	−	0.996177i	$-0.472159\pi$
$433$	3.63547	0.174709	0.0873547	+	0.996177i	$0.472159\pi$
$434$	6.65732	0.319562
$435$	−68.5919	−3.28873
$436$	0.454080	0.0217465
$437$	−5.74181	−0.274668
$438$	77.0764	3.68285
$439$	−32.6390	−1.55777	−0.778887	−	0.627164i	$-0.784215\pi$
$439$	−32.6390	−1.55777	−0.778887	+	0.627164i	$0.784215\pi$
$440$	−2.89960	−0.138233
$441$	−11.4473	−0.545111
$442$	2.09736	0.0997614
$443$	17.7210	0.841950	0.420975	−	0.907072i	$-0.361688\pi$
$443$	17.7210	0.841950	0.420975	+	0.907072i	$0.361688\pi$
$444$	12.8948	0.611960
$445$	−31.9470	−1.51443
$446$	14.4195	0.682781
$447$	−5.17446	−0.244743
$448$	−9.97939	−0.471482
$449$	14.0682	0.663918	0.331959	−	0.943294i	$-0.392290\pi$
$449$	14.0682	0.663918	0.331959	+	0.943294i	$0.392290\pi$
$450$	−98.5588	−4.64610
$451$	7.63344	0.359445
$452$	−5.03220	−0.236695
$453$	−10.0971	−0.474401
$454$	−24.2196	−1.13668
$455$	11.1674	0.523534
$456$	−5.07051	−0.237449
$457$	31.6151	1.47889	0.739447	−	0.673215i	$-0.235087\pi$
$457$	31.6151	1.47889	0.739447	+	0.673215i	$0.235087\pi$
$458$	−35.5954	−1.66326
$459$	−7.17155	−0.334740
$460$	15.5573	0.725362
$461$	−35.3772	−1.64768	−0.823841	−	0.566820i	$-0.808173\pi$
$461$	−35.3772	−1.64768	−0.823841	+	0.566820i	$0.808173\pi$
$462$	12.7112	0.591378
$463$	3.63498	0.168932	0.0844659	−	0.996426i	$-0.473082\pi$
$463$	3.63498	0.168932	0.0844659	+	0.996426i	$0.473082\pi$
$464$	28.7853	1.33632
$465$	−17.3271	−0.803527
$466$	−28.6442	−1.32692
$467$	−25.4679	−1.17852	−0.589258	−	0.807945i	$-0.700580\pi$
$467$	−25.4679	−1.17852	−0.589258	+	0.807945i	$0.700580\pi$
$468$	12.5137	0.578446
$469$	3.51254	0.162194
$470$	42.4477	1.95797
$471$	49.1937	2.26673
$472$	4.70278	0.216463
$473$	3.49886	0.160878
$474$	64.6317	2.96863
$475$	−19.2177	−0.881767
$476$	−2.96182	−0.135755
$477$	43.4598	1.98989
$478$	−46.5062	−2.12714
$479$	−9.86978	−0.450962	−0.225481	−	0.974248i	$-0.572395\pi$
$479$	−9.86978	−0.450962	−0.225481	+	0.974248i	$0.572395\pi$
$480$	80.4669	3.67279
$481$	3.63466	0.165726
$482$	10.0397	0.457298
$483$	17.6817	0.804547
$484$	1.58823	0.0721922
$485$	35.3824	1.60663
$486$	3.34635	0.151793
$487$	27.5340	1.24769	0.623843	−	0.781550i	$-0.285570\pi$
$487$	27.5340	1.24769	0.623843	+	0.781550i	$0.285570\pi$
$488$	−2.56400	−0.116067
$489$	24.7209	1.11792
$490$	13.6635	0.617254
$491$	−31.0152	−1.39970	−0.699849	−	0.714291i	$-0.746749\pi$
$491$	−31.0152	−1.39970	−0.699849	+	0.714291i	$0.746749\pi$
$492$	−36.1676	−1.63056
$493$	5.12779	0.230944
$494$	5.51262	0.248024
$495$	−21.9314	−0.985743
$496$	7.27151	0.326500
$497$	−27.4629	−1.23188
$498$	−55.0982	−2.46901
$499$	14.5209	0.650044	0.325022	−	0.945707i	$-0.394628\pi$
$499$	14.5209	0.650044	0.325022	+	0.945707i	$0.394628\pi$
$500$	22.5492	1.00843
$501$	74.7350	3.33891
$502$	−20.2673	−0.904576
$503$	28.3891	1.26581	0.632903	−	0.774231i	$-0.281863\pi$
$503$	28.3891	1.26581	0.632903	+	0.774231i	$0.281863\pi$
$504$	10.3510	0.461069
$505$	−54.8830	−2.44226
$506$	4.99136	0.221893
$507$	−33.4610	−1.48606
$508$	13.7463	0.609894
$509$	−22.0385	−0.976842	−0.488421	−	0.872608i	$-0.662427\pi$
$509$	−22.0385	−0.976842	−0.488421	+	0.872608i	$0.662427\pi$
$510$	17.4162	0.771202
$511$	−30.6800	−1.35721
$512$	−26.5085	−1.17152
$513$	−18.8494	−0.832221
$514$	29.6777	1.30903
$515$	−70.9850	−3.12797
$516$	−16.5778	−0.729795
$517$	6.02799	0.265111
$518$	−11.5962	−0.509508
$519$	43.8047	1.92281
$520$	3.87246	0.169818
$521$	−4.07959	−0.178730	−0.0893650	−	0.995999i	$-0.528484\pi$
$521$	−4.07959	−0.178730	−0.0893650	+	0.995999i	$0.528484\pi$
$522$	69.1209	3.02534
$523$	−18.0556	−0.789516	−0.394758	−	0.918785i	$-0.629172\pi$
$523$	−18.0556	−0.789516	−0.394758	+	0.918785i	$0.629172\pi$
$524$	1.58823	0.0693821
$525$	59.1803	2.58284
$526$	−50.2558	−2.19126
$527$	1.29534	0.0564260
$528$	13.8839	0.604219
$529$	−16.0568	−0.698123
$530$	−51.8735	−2.25324
$531$	35.5699	1.54360
$532$	−7.78472	−0.337510
$533$	−10.1946	−0.441576
$534$	48.5639	2.10157
$535$	63.5172	2.74609
$536$	1.21803	0.0526108
$537$	61.0094	2.63275
$538$	26.8652	1.15824
$539$	1.94035	0.0835767
$540$	51.0720	2.19779
$541$	24.7952	1.06603	0.533014	−	0.846107i	$-0.321059\pi$
$541$	24.7952	1.06603	0.533014	+	0.846107i	$0.321059\pi$
$542$	46.1990	1.98442
$543$	17.1681	0.736755
$544$	−6.01554	−0.257914
$545$	1.06282	0.0455264
$546$	−16.9760	−0.726504
$547$	17.4393	0.745651	0.372826	−	0.927901i	$-0.378389\pi$
$547$	17.4393	0.745651	0.372826	+	0.927901i	$0.378389\pi$
$548$	−2.77758	−0.118652
$549$	−19.3930	−0.827675
$550$	16.7059	0.712343
$551$	13.4777	0.574168
$552$	6.13142	0.260971
$553$	−25.7265	−1.09400
$554$	35.6440	1.51437
$555$	30.1817	1.28114
$556$	0.573223	0.0243101
$557$	26.9444	1.14167	0.570835	−	0.821065i	$-0.306620\pi$
$557$	26.9444	1.14167	0.570835	+	0.821065i	$0.306620\pi$
$558$	17.4608	0.739174
$559$	−4.67278	−0.197638
$560$	−38.9159	−1.64450
$561$	2.47327	0.104421
$562$	−6.61655	−0.279103
$563$	−0.871956	−0.0367486	−0.0183743	−	0.999831i	$-0.505849\pi$
$563$	−0.871956	−0.0367486	−0.0183743	+	0.999831i	$0.505849\pi$
$564$	−28.5609	−1.20263
$565$	−11.7784	−0.495521
$566$	−42.2564	−1.77617
$567$	18.2350	0.765797
$568$	−9.52320	−0.399584
$569$	21.2127	0.889283	0.444642	−	0.895709i	$-0.353331\pi$
$569$	21.2127	0.889283	0.444642	+	0.895709i	$0.353331\pi$
$570$	45.7760	1.91734
$571$	31.8805	1.33416	0.667078	−	0.744988i	$-0.267545\pi$
$571$	31.8805	1.33416	0.667078	+	0.744988i	$0.267545\pi$
$572$	−2.12110	−0.0886877
$573$	61.3008	2.56088
$574$	32.5253	1.35758
$575$	23.2386	0.969116
$576$	−26.1739	−1.09058
$577$	−10.0421	−0.418059	−0.209030	−	0.977909i	$-0.567030\pi$
$577$	−10.0421	−0.418059	−0.209030	+	0.977909i	$0.567030\pi$
$578$	30.9005	1.28529
$579$	−0.942433	−0.0391662
$580$	−36.5174	−1.51630
$581$	21.9317	0.909879
$582$	−53.7862	−2.22951
$583$	−7.36654	−0.305091
$584$	−10.6388	−0.440236
$585$	29.2897	1.21098
$586$	14.2741	0.589659
$587$	−36.7181	−1.51552	−0.757760	−	0.652533i	$-0.773706\pi$
$587$	−36.7181	−1.51552	−0.757760	+	0.652533i	$0.773706\pi$
$588$	−9.19345	−0.379132
$589$	3.40462	0.140285
$590$	−42.4562	−1.74789
$591$	43.4539	1.78746
$592$	−12.6660	−0.520571
$593$	26.8908	1.10427	0.552136	−	0.833754i	$-0.313813\pi$
$593$	26.8908	1.10427	0.552136	+	0.833754i	$0.313813\pi$
$594$	16.3858	0.672318
$595$	−6.93246	−0.284203
$596$	−2.75481	−0.112841
$597$	−81.4201	−3.33230
$598$	−6.66603	−0.272594
$599$	20.4027	0.833633	0.416816	−	0.908991i	$-0.363146\pi$
$599$	20.4027	0.833633	0.416816	+	0.908991i	$0.363146\pi$
$600$	20.5217	0.837794
$601$	−20.0103	−0.816236	−0.408118	−	0.912929i	$-0.633815\pi$
$601$	−20.0103	−0.816236	−0.408118	+	0.912929i	$0.633815\pi$
$602$	14.9083	0.607616
$603$	9.21268	0.375169
$604$	−5.37554	−0.218728
$605$	3.71742	0.151135
$606$	83.4299	3.38911
$607$	41.5929	1.68821	0.844103	−	0.536182i	$-0.180134\pi$
$607$	41.5929	1.68821	0.844103	+	0.536182i	$0.180134\pi$
$608$	−15.8110	−0.641220
$609$	−41.5041	−1.68183
$610$	23.1475	0.937213
$611$	−8.05046	−0.325687
$612$	−7.76824	−0.314013
$613$	−5.23025	−0.211248	−0.105624	−	0.994406i	$-0.533684\pi$
$613$	−5.23025	−0.211248	−0.105624	+	0.994406i	$0.533684\pi$
$614$	−24.4617	−0.987192
$615$	−84.6542	−3.41359
$616$	−1.75451	−0.0706914
$617$	6.65755	0.268023	0.134011	−	0.990980i	$-0.457214\pi$
$617$	6.65755	0.268023	0.134011	+	0.990980i	$0.457214\pi$
$618$	107.907	4.34066
$619$	−11.6271	−0.467335	−0.233667	−	0.972317i	$-0.575073\pi$
$619$	−11.6271	−0.467335	−0.233667	+	0.972317i	$0.575073\pi$
$620$	−9.22474	−0.370474
$621$	22.7933	0.914663
$622$	−52.7756	−2.11611
$623$	−19.3307	−0.774469
$624$	−18.5421	−0.742279
$625$	8.68269	0.347307
$626$	−25.9925	−1.03887
$627$	6.50063	0.259610
$628$	26.1901	1.04510
$629$	−2.25632	−0.0899654
$630$	−93.4473	−3.72303
$631$	44.1171	1.75627	0.878136	−	0.478411i	$-0.158787\pi$
$631$	44.1171	1.75627	0.878136	+	0.478411i	$0.158787\pi$
$632$	−8.92105	−0.354860
$633$	21.8392	0.868031
$634$	−16.5002	−0.655307
$635$	32.1748	1.27682
$636$	34.9030	1.38399
$637$	−2.59136	−0.102673
$638$	−11.7162	−0.463847
$639$	−72.0296	−2.84945
$640$	−22.7052	−0.897501
$641$	10.4881	0.414254	0.207127	−	0.978314i	$-0.433589\pi$
$641$	10.4881	0.414254	0.207127	+	0.978314i	$0.433589\pi$
$642$	−96.5552	−3.81073
$643$	−27.8229	−1.09723	−0.548613	−	0.836076i	$-0.684844\pi$
$643$	−27.8229	−1.09723	−0.548613	+	0.836076i	$0.684844\pi$
$644$	9.41353	0.370945
$645$	−38.8021	−1.52783
$646$	−3.42212	−0.134641
$647$	−32.3228	−1.27074	−0.635370	−	0.772208i	$-0.719152\pi$
$647$	−32.3228	−1.27074	−0.635370	+	0.772208i	$0.719152\pi$
$648$	6.32326	0.248401
$649$	−6.02919	−0.236666
$650$	−22.3110	−0.875109
$651$	−10.4844	−0.410918
$652$	13.1611	0.515427
$653$	−20.6180	−0.806847	−0.403423	−	0.915013i	$-0.632180\pi$
$653$	−20.6180	−0.806847	−0.403423	+	0.915013i	$0.632180\pi$
$654$	−1.61564	−0.0631767
$655$	3.71742	0.145252
$656$	35.5260	1.38706
$657$	−80.4674	−3.13933
$658$	25.6846	1.00129
$659$	42.8413	1.66886	0.834430	−	0.551114i	$-0.185797\pi$
$659$	42.8413	1.66886	0.834430	+	0.551114i	$0.185797\pi$
$660$	−17.6133	−0.685597
$661$	43.5669	1.69456	0.847278	−	0.531149i	$-0.178240\pi$
$661$	43.5669	1.69456	0.847278	+	0.531149i	$0.178240\pi$
$662$	65.8386	2.55889
$663$	−3.30308	−0.128281
$664$	7.60515	0.295137
$665$	−18.2210	−0.706580
$666$	−30.4145	−1.17854
$667$	−16.2976	−0.631046
$668$	39.7879	1.53944
$669$	−22.7088	−0.877974
$670$	−10.9962	−0.424821
$671$	3.28716	0.126900
$672$	48.6895	1.87824
$673$	−41.3787	−1.59503	−0.797515	−	0.603299i	$-0.793853\pi$
$673$	−41.3787	−1.59503	−0.797515	+	0.603299i	$0.793853\pi$
$674$	−24.9862	−0.962431
$675$	76.2884	2.93634
$676$	−17.8142	−0.685162
$677$	29.0720	1.11733	0.558664	−	0.829394i	$-0.311314\pi$
$677$	29.0720	1.11733	0.558664	+	0.829394i	$0.311314\pi$
$678$	17.9048	0.687631
$679$	21.4094	0.821619
$680$	−2.40394	−0.0921869
$681$	38.1428	1.46163
$682$	−2.95964	−0.113331
$683$	16.8620	0.645206	0.322603	−	0.946534i	$-0.395442\pi$
$683$	16.8620	0.645206	0.322603	+	0.946534i	$0.395442\pi$
$684$	−20.4177	−0.780691
$685$	−6.50122	−0.248399
$686$	38.0938	1.45443
$687$	56.0582	2.13875
$688$	16.2837	0.620809
$689$	9.83811	0.374802
$690$	−55.3537	−2.10728
$691$	−1.88099	−0.0715563	−0.0357781	−	0.999360i	$-0.511391\pi$
$691$	−1.88099	−0.0715563	−0.0357781	+	0.999360i	$0.511391\pi$
$692$	23.3210	0.886532
$693$	−13.2704	−0.504102
$694$	−24.9430	−0.946822
$695$	1.34169	0.0508932
$696$	−14.3922	−0.545535
$697$	6.32858	0.239712
$698$	35.7520	1.35323
$699$	45.1111	1.70626
$700$	31.5068	1.19084
$701$	−22.5822	−0.852918	−0.426459	−	0.904507i	$-0.640239\pi$
$701$	−22.5822	−0.852918	−0.426459	+	0.904507i	$0.640239\pi$
$702$	−21.8835	−0.825938
$703$	−5.93042	−0.223670
$704$	4.43653	0.167208
$705$	−66.8498	−2.51771
$706$	60.0176	2.25879
$707$	−33.2090	−1.24895
$708$	28.5665	1.07360
$709$	36.3893	1.36663	0.683314	−	0.730125i	$-0.260538\pi$
$709$	36.3893	1.36663	0.683314	+	0.730125i	$0.260538\pi$
$710$	85.9742	3.22656
$711$	−67.4752	−2.53052
$712$	−6.70323	−0.251214
$713$	−4.11697	−0.154182
$714$	10.5383	0.394387
$715$	−4.96467	−0.185668
$716$	32.4806	1.21386
$717$	73.2414	2.73525
$718$	6.36090	0.237387
$719$	34.9452	1.30323	0.651617	−	0.758548i	$-0.274091\pi$
$719$	34.9452	1.30323	0.651617	+	0.758548i	$0.274091\pi$
$720$	−102.068	−3.80387
$721$	−42.9521	−1.59962
$722$	26.9964	1.00470
$723$	−15.8113	−0.588030
$724$	9.14009	0.339689
$725$	−54.5476	−2.02585
$726$	−5.65101	−0.209729
$727$	−41.0364	−1.52196	−0.760979	−	0.648777i	$-0.775281\pi$
$727$	−41.0364	−1.52196	−0.760979	+	0.648777i	$0.775281\pi$
$728$	2.34318	0.0868439
$729$	−29.5902	−1.09593
$730$	96.0456	3.55481
$731$	2.90077	0.107289
$732$	−15.5747	−0.575658
$733$	−1.42324	−0.0525685	−0.0262843	−	0.999655i	$-0.508368\pi$
$733$	−1.42324	−0.0525685	−0.0262843	+	0.999655i	$0.508368\pi$
$734$	47.7856	1.76380
$735$	−21.5183	−0.793714
$736$	19.1191	0.704741
$737$	−1.56157	−0.0575212
$738$	85.3071	3.14020
$739$	−25.9288	−0.953807	−0.476903	−	0.878956i	$-0.658241\pi$
$739$	−25.9288	−0.953807	−0.476903	+	0.878956i	$0.658241\pi$
$740$	16.0683	0.590683
$741$	−8.68168	−0.318930
$742$	−31.3880	−1.15229
$743$	−15.0848	−0.553408	−0.276704	−	0.960955i	$-0.589242\pi$
$743$	−15.0848	−0.553408	−0.276704	+	0.960955i	$0.589242\pi$
$744$	−3.63564	−0.133289
$745$	−6.44794	−0.236234
$746$	−3.65165	−0.133696
$747$	57.5223	2.10463
$748$	1.31674	0.0481446
$749$	38.4335	1.40433
$750$	−80.2313	−2.92963
$751$	39.0542	1.42511	0.712554	−	0.701617i	$-0.247538\pi$
$751$	39.0542	1.42511	0.712554	+	0.701617i	$0.247538\pi$
$752$	28.0542	1.02303
$753$	31.9185	1.16318
$754$	15.6471	0.569833
$755$	−12.5820	−0.457907
$756$	30.9030	1.12393
$757$	−24.3610	−0.885416	−0.442708	−	0.896666i	$-0.645982\pi$
$757$	−24.3610	−0.885416	−0.442708	+	0.896666i	$0.645982\pi$
$758$	9.72419	0.353199
$759$	−7.86077	−0.285328
$760$	−6.31841	−0.229193
$761$	0.637462	0.0231080	0.0115540	−	0.999933i	$-0.496322\pi$
$761$	0.637462	0.0231080	0.0115540	+	0.999933i	$0.496322\pi$
$762$	−48.9102	−1.77183
$763$	0.643102	0.0232819
$764$	32.6357	1.18072
$765$	−18.1824	−0.657387
$766$	44.3949	1.60405
$767$	8.05206	0.290743
$768$	60.9854	2.20062
$769$	−28.3898	−1.02376	−0.511882	−	0.859056i	$-0.671052\pi$
$769$	−28.3898	−1.02376	−0.511882	+	0.859056i	$0.671052\pi$
$770$	15.8395	0.570817
$771$	−46.7386	−1.68325
$772$	−0.501738	−0.0180580
$773$	−50.8170	−1.82776	−0.913881	−	0.405983i	$-0.866929\pi$
$773$	−50.8170	−1.82776	−0.913881	+	0.405983i	$0.866929\pi$
$774$	39.1013	1.40547
$775$	−13.7794	−0.494970
$776$	7.42406	0.266508
$777$	18.2626	0.655166
$778$	0.100776	0.00361300
$779$	16.6338	0.595966
$780$	23.5228	0.842251
$781$	12.2092	0.436879
$782$	4.13813	0.147979
$783$	−53.5024	−1.91202
$784$	9.03036	0.322513
$785$	61.3007	2.18792
$786$	−5.65101	−0.201565
$787$	10.4228	0.371534	0.185767	−	0.982594i	$-0.440523\pi$
$787$	10.4228	0.371534	0.185767	+	0.982594i	$0.440523\pi$
$788$	23.1343	0.824125
$789$	79.1466	2.81769
$790$	80.5381	2.86542
$791$	−7.12697	−0.253406
$792$	−4.60173	−0.163515
$793$	−4.39005	−0.155895
$794$	−60.9194	−2.16195
$795$	81.6942	2.89739
$796$	−43.3470	−1.53639
$797$	−10.4171	−0.368994	−0.184497	−	0.982833i	$-0.559066\pi$
$797$	−10.4171	−0.368994	−0.184497	+	0.982833i	$0.559066\pi$
$798$	27.6985	0.980516
$799$	4.99756	0.176801
$800$	63.9912	2.26243
$801$	−50.7005	−1.79141
$802$	−34.3051	−1.21136
$803$	13.6394	0.481324
$804$	7.39878	0.260935
$805$	22.0334	0.776575
$806$	3.95264	0.139226
$807$	−42.3094	−1.48936
$808$	−11.5157	−0.405123
$809$	−15.9965	−0.562406	−0.281203	−	0.959648i	$-0.590733\pi$
$809$	−15.9965	−0.562406	−0.281203	+	0.959648i	$0.590733\pi$
$810$	−57.0856	−2.00578
$811$	−37.4233	−1.31411	−0.657054	−	0.753843i	$-0.728198\pi$
$811$	−37.4233	−1.31411	−0.657054	+	0.753843i	$0.728198\pi$
$812$	−22.0962	−0.775426
$813$	−72.7576	−2.55172
$814$	5.15532	0.180694
$815$	30.8049	1.07905
$816$	11.5106	0.402950
$817$	7.62425	0.266739
$818$	12.5392	0.438423
$819$	17.7228	0.619286
$820$	−45.0687	−1.57387
$821$	27.5319	0.960871	0.480435	−	0.877030i	$-0.340479\pi$
$821$	27.5319	0.960871	0.480435	+	0.877030i	$0.340479\pi$
$822$	9.88277	0.344701
$823$	−13.7558	−0.479497	−0.239749	−	0.970835i	$-0.577065\pi$
$823$	−13.7558	−0.479497	−0.239749	+	0.970835i	$0.577065\pi$
$824$	−14.8943	−0.518868
$825$	−26.3097	−0.915988
$826$	−25.6897	−0.893859
$827$	−47.7554	−1.66062	−0.830309	−	0.557304i	$-0.811836\pi$
$827$	−47.7554	−1.66062	−0.830309	+	0.557304i	$0.811836\pi$
$828$	24.6897	0.858028
$829$	−54.5893	−1.89596	−0.947982	−	0.318324i	$-0.896880\pi$
$829$	−54.5893	−1.89596	−0.947982	+	0.318324i	$0.896880\pi$
$830$	−68.6584	−2.38317
$831$	−56.1348	−1.94730
$832$	−5.92505	−0.205414
$833$	1.60866	0.0557369
$834$	−2.03956	−0.0706242
$835$	93.1280	3.22283
$836$	3.46085	0.119696
$837$	−13.5153	−0.467159
$838$	−7.32718	−0.253113
$839$	−18.2026	−0.628422	−0.314211	−	0.949353i	$-0.601740\pi$
$839$	−18.2026	−0.628422	−0.314211	+	0.949353i	$0.601740\pi$
$840$	19.4574	0.671344
$841$	9.25517	0.319144
$842$	−28.5818	−0.984995
$843$	10.4202	0.358892
$844$	11.6269	0.400214
$845$	−41.6961	−1.43439
$846$	67.3654	2.31607
$847$	2.24937	0.0772892
$848$	−34.2838	−1.17731
$849$	66.5486	2.28394
$850$	13.8502	0.475058
$851$	7.17125	0.245827
$852$	−57.8476	−1.98183
$853$	52.4045	1.79430	0.897149	−	0.441729i	$-0.145635\pi$
$853$	52.4045	1.79430	0.897149	+	0.441729i	$0.145635\pi$
$854$	14.0062	0.479284
$855$	−47.7899	−1.63438
$856$	13.3274	0.455522
$857$	−16.4410	−0.561614	−0.280807	−	0.959764i	$-0.590602\pi$
$857$	−16.4410	−0.561614	−0.280807	+	0.959764i	$0.590602\pi$
$858$	7.54700	0.257650
$859$	−32.1696	−1.09761	−0.548806	−	0.835949i	$-0.684918\pi$
$859$	−32.1696	−1.09761	−0.548806	+	0.835949i	$0.684918\pi$
$860$	−20.6577	−0.704422
$861$	−51.2232	−1.74568
$862$	1.73699	0.0591620
$863$	34.4079	1.17126	0.585630	−	0.810579i	$-0.300847\pi$
$863$	34.4079	1.17126	0.585630	+	0.810579i	$0.300847\pi$
$864$	62.7649	2.13531
$865$	54.5854	1.85596
$866$	−6.88652	−0.234014
$867$	−48.6643	−1.65273
$868$	−5.58178	−0.189458
$869$	11.4372	0.387980
$870$	129.931	4.40508
$871$	2.08550	0.0706644
$872$	0.223006	0.00755193
$873$	56.1525	1.90048
$874$	10.8765	0.367903
$875$	31.9358	1.07963
$876$	−64.6241	−2.18345
$877$	24.0089	0.810724	0.405362	−	0.914156i	$-0.367146\pi$
$877$	24.0089	0.810724	0.405362	+	0.914156i	$0.367146\pi$
$878$	61.8268	2.08655
$879$	−22.4800	−0.758231
$880$	17.3008	0.583211
$881$	−50.2899	−1.69431	−0.847155	−	0.531345i	$-0.821687\pi$
$881$	−50.2899	−1.69431	−0.847155	+	0.531345i	$0.821687\pi$
$882$	21.6842	0.730146
$883$	−10.2886	−0.346239	−0.173119	−	0.984901i	$-0.555385\pi$
$883$	−10.2886	−0.346239	−0.173119	+	0.984901i	$0.555385\pi$
$884$	−1.75852	−0.0591453
$885$	66.8631	2.24758
$886$	−33.5682	−1.12775
$887$	−20.6991	−0.695008	−0.347504	−	0.937678i	$-0.612971\pi$
$887$	−20.6991	−0.695008	−0.347504	+	0.937678i	$0.612971\pi$
$888$	6.33283	0.212516
$889$	19.4686	0.652955
$890$	60.5160	2.02850
$891$	−8.10671	−0.271585
$892$	−12.0899	−0.404799
$893$	13.1354	0.439558
$894$	9.80178	0.327821
$895$	76.0244	2.54122
$896$	−13.7386	−0.458975
$897$	10.4982	0.350523
$898$	−26.6488	−0.889281
$899$	9.66372	0.322303
$900$	82.6358	2.75453
$901$	−6.10729	−0.203463
$902$	−14.4597	−0.481457
$903$	−23.4787	−0.781321
$904$	−2.47139	−0.0821971
$905$	21.3934	0.711140
$906$	19.1265	0.635435
$907$	54.5853	1.81248	0.906238	−	0.422769i	$-0.138942\pi$
$907$	54.5853	1.81248	0.906238	+	0.422769i	$0.138942\pi$
$908$	20.3067	0.673902
$909$	−87.1004	−2.88894
$910$	−21.1539	−0.701245
$911$	−19.8956	−0.659170	−0.329585	−	0.944126i	$-0.606909\pi$
$911$	−19.8956	−0.659170	−0.329585	+	0.944126i	$0.606909\pi$
$912$	30.2539	1.00181
$913$	−9.75016	−0.322683
$914$	−59.8873	−1.98090
$915$	−36.4543	−1.20514
$916$	29.8446	0.986095
$917$	2.24937	0.0742806
$918$	13.5848	0.448365
$919$	−17.3729	−0.573078	−0.286539	−	0.958069i	$-0.592505\pi$
$919$	−17.3729	−0.573078	−0.286539	+	0.958069i	$0.592505\pi$
$920$	7.64042	0.251897
$921$	38.5240	1.26941
$922$	67.0138	2.20698
$923$	−16.3055	−0.536703
$924$	−10.6576	−0.350609
$925$	24.0019	0.789179
$926$	−6.88560	−0.226275
$927$	−112.655	−3.70006
$928$	−44.8781	−1.47320
$929$	25.8827	0.849185	0.424592	−	0.905385i	$-0.360417\pi$
$929$	25.8827	0.849185	0.424592	+	0.905385i	$0.360417\pi$
$930$	32.8221	1.07628
$931$	4.22814	0.138572
$932$	24.0165	0.786687
$933$	83.1149	2.72106
$934$	48.2430	1.57856
$935$	3.08196	0.100791
$936$	6.14567	0.200877
$937$	−32.2881	−1.05481	−0.527403	−	0.849616i	$-0.676834\pi$
$937$	−32.2881	−1.05481	−0.527403	+	0.849616i	$0.676834\pi$
$938$	−6.65368	−0.217250
$939$	40.9348	1.33586
$940$	−35.5899	−1.16082
$941$	24.4910	0.798385	0.399192	−	0.916867i	$-0.369291\pi$
$941$	24.4910	0.798385	0.399192	+	0.916867i	$0.369291\pi$
$942$	−93.1858	−3.03616
$943$	−20.1141	−0.655004
$944$	−28.0598	−0.913267
$945$	72.3319	2.35296
$946$	−6.62777	−0.215487
$947$	35.7517	1.16177	0.580886	−	0.813985i	$-0.302706\pi$
$947$	35.7517	1.16177	0.580886	+	0.813985i	$0.302706\pi$
$948$	−54.1899	−1.76001
$949$	−18.2156	−0.591304
$950$	36.4033	1.18108
$951$	25.9857	0.842645
$952$	−1.45460	−0.0471437
$953$	−22.2714	−0.721442	−0.360721	−	0.932674i	$-0.617469\pi$
$953$	−22.2714	−0.721442	−0.360721	+	0.932674i	$0.617469\pi$
$954$	−82.3243	−2.66535
$955$	76.3875	2.47184
$956$	38.9927	1.26112
$957$	18.4515	0.596451
$958$	18.6960	0.604039
$959$	−3.93381	−0.127029
$960$	−49.2007	−1.58795
$961$	−28.5588	−0.921253
$962$	−6.88500	−0.221981
$963$	100.803	3.24834
$964$	−8.41774	−0.271117
$965$	−1.17437	−0.0378044
$966$	−33.4939	−1.07765
$967$	−42.2032	−1.35716	−0.678581	−	0.734525i	$-0.737405\pi$
$967$	−42.2032	−1.35716	−0.678581	+	0.734525i	$0.737405\pi$
$968$	0.780003	0.0250703
$969$	5.38941	0.173133
$970$	−67.0235	−2.15199
$971$	−7.51421	−0.241142	−0.120571	−	0.992705i	$-0.538473\pi$
$971$	−7.51421	−0.241142	−0.120571	+	0.992705i	$0.538473\pi$
$972$	−2.80572	−0.0899934
$973$	0.811841	0.0260264
$974$	−52.1567	−1.67121
$975$	35.1370	1.12529
$976$	15.2984	0.489690
$977$	−34.4365	−1.10172	−0.550860	−	0.834597i	$-0.685700\pi$
$977$	−34.4365	−1.10172	−0.550860	+	0.834597i	$0.685700\pi$
$978$	−46.8279	−1.49739
$979$	8.59385	0.274661
$980$	−11.4560	−0.365950
$981$	1.68672	0.0538530
$982$	58.7510	1.87482
$983$	29.0330	0.926010	0.463005	−	0.886356i	$-0.346771\pi$
$983$	29.0330	0.926010	0.463005	+	0.886356i	$0.346771\pi$
$984$	−17.7624	−0.566246
$985$	54.1483	1.72531
$986$	−9.71338	−0.309337
$987$	−40.4500	−1.28754
$988$	−4.62201	−0.147046
$989$	−9.21948	−0.293162
$990$	41.5438	1.32035
$991$	55.2551	1.75524	0.877618	−	0.479361i	$-0.159131\pi$
$991$	55.2551	1.75524	0.877618	+	0.479361i	$0.159131\pi$
$992$	−11.3367	−0.359942
$993$	−103.687	−3.29042
$994$	52.0220	1.65004
$995$	−101.458	−3.21644
$996$	46.1966	1.46380
$997$	−49.8873	−1.57995	−0.789974	−	0.613141i	$-0.789906\pi$
$997$	−49.8873	−1.57995	−0.789974	+	0.613141i	$0.789906\pi$
$998$	−27.5063	−0.870698
$999$	23.5420	0.744836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.f.1.6	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.6	✓	31	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-1.89426 q^{2} +2.98322 q^{3} +1.58823 q^{4} +3.71742 q^{5} -5.65101 q^{6} +2.24937 q^{7} +0.780003 q^{8} +5.89963 q^{9} +O(q^{10})\)	\(q-1.89426 q^{2} +2.98322 q^{3} +1.58823 q^{4} +3.71742 q^{5} -5.65101 q^{6} +2.24937 q^{7} +0.780003 q^{8} +5.89963 q^{9} -7.04177 q^{10} -1.00000 q^{11} +4.73804 q^{12} +1.33551 q^{13} -4.26089 q^{14} +11.0899 q^{15} -4.65399 q^{16} -0.829059 q^{17} -11.1754 q^{18} -2.17906 q^{19} +5.90412 q^{20} +6.71037 q^{21} +1.89426 q^{22} +2.63499 q^{23} +2.32692 q^{24} +8.81923 q^{25} -2.52981 q^{26} +8.65023 q^{27} +3.57251 q^{28} -6.18508 q^{29} -21.0072 q^{30} -1.56242 q^{31} +7.25586 q^{32} -2.98322 q^{33} +1.57045 q^{34} +8.36185 q^{35} +9.36995 q^{36} +2.72155 q^{37} +4.12772 q^{38} +3.98414 q^{39} +2.89960 q^{40} -7.63344 q^{41} -12.7112 q^{42} -3.49886 q^{43} -1.58823 q^{44} +21.9314 q^{45} -4.99136 q^{46} -6.02799 q^{47} -13.8839 q^{48} -1.94035 q^{49} -16.7059 q^{50} -2.47327 q^{51} +2.12110 q^{52} +7.36654 q^{53} -16.3858 q^{54} -3.71742 q^{55} +1.75451 q^{56} -6.50063 q^{57} +11.7162 q^{58} +6.02919 q^{59} +17.6133 q^{60} -3.28716 q^{61} +2.95964 q^{62} +13.2704 q^{63} -4.43653 q^{64} +4.96467 q^{65} +5.65101 q^{66} +1.56157 q^{67} -1.31674 q^{68} +7.86077 q^{69} -15.8395 q^{70} -12.2092 q^{71} +4.60173 q^{72} -13.6394 q^{73} -5.15532 q^{74} +26.3097 q^{75} -3.46085 q^{76} -2.24937 q^{77} -7.54700 q^{78} -11.4372 q^{79} -17.3008 q^{80} +8.10671 q^{81} +14.4597 q^{82} +9.75016 q^{83} +10.6576 q^{84} -3.08196 q^{85} +6.62777 q^{86} -18.4515 q^{87} -0.780003 q^{88} -8.59385 q^{89} -41.5438 q^{90} +3.00406 q^{91} +4.18497 q^{92} -4.66106 q^{93} +11.4186 q^{94} -8.10050 q^{95} +21.6459 q^{96} +9.51798 q^{97} +3.67553 q^{98} -5.89963 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

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