LMFDB - Embedded newform 211.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [211,2,Mod(1,211)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(211, 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("211.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	211.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:	$1.68484348265$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.86081$ of defining polynomial
Character	$\chi$	$=$	211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.86081 q^{2} -2.86081 q^{3} +1.46260 q^{4} -4.32340 q^{5} -5.32340 q^{6} +0.860806 q^{7} -1.00000 q^{8} +5.18421 q^{9} +O(q^{10})$	\(q+1.86081 q^{2} -2.86081 q^{3} +1.46260 q^{4} -4.32340 q^{5} -5.32340 q^{6} +0.860806 q^{7} -1.00000 q^{8} +5.18421 q^{9} -8.04502 q^{10} -3.00000 q^{11} -4.18421 q^{12} +1.92520 q^{13} +1.60179 q^{14} +12.3684 q^{15} -4.78600 q^{16} -6.46260 q^{17} +9.64681 q^{18} +1.46260 q^{19} -6.32340 q^{20} -2.46260 q^{21} -5.58242 q^{22} +6.39821 q^{23} +2.86081 q^{24} +13.6918 q^{25} +3.58242 q^{26} -6.24860 q^{27} +1.25901 q^{28} -5.60179 q^{29} +23.0152 q^{30} -1.38780 q^{31} -6.90582 q^{32} +8.58242 q^{33} -12.0256 q^{34} -3.72161 q^{35} +7.58242 q^{36} +0.601793 q^{37} +2.72161 q^{38} -5.50761 q^{39} +4.32340 q^{40} -10.7666 q^{41} -4.58242 q^{42} -6.44322 q^{43} -4.38780 q^{44} -22.4134 q^{45} +11.9058 q^{46} +3.18421 q^{47} +13.6918 q^{48} -6.25901 q^{49} +25.4778 q^{50} +18.4882 q^{51} +2.81579 q^{52} +0.462598 q^{53} -11.6274 q^{54} +12.9702 q^{55} -0.860806 q^{56} -4.18421 q^{57} -10.4238 q^{58} -3.47301 q^{59} +18.0900 q^{60} -7.97021 q^{61} -2.58242 q^{62} +4.46260 q^{63} -3.27839 q^{64} -8.32340 q^{65} +15.9702 q^{66} -9.45219 q^{68} -18.3040 q^{69} -6.92520 q^{70} +9.61702 q^{71} -5.18421 q^{72} -0.860806 q^{73} +1.11982 q^{74} -39.1697 q^{75} +2.13919 q^{76} -2.58242 q^{77} -10.2486 q^{78} -12.8206 q^{79} +20.6918 q^{80} +2.32340 q^{81} -20.0346 q^{82} +7.20359 q^{83} -3.60179 q^{84} +27.9404 q^{85} -11.9896 q^{86} +16.0256 q^{87} +3.00000 q^{88} +17.8760 q^{89} -41.7071 q^{90} +1.65722 q^{91} +9.35801 q^{92} +3.97021 q^{93} +5.92520 q^{94} -6.32340 q^{95} +19.7562 q^{96} -6.43281 q^{97} -11.6468 q^{98} -15.5526 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} - 8 q^{6} - 3 q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 - 8 * q^6 - 3 * q^7 - 3 * q^8 + 2 * q^9	\( 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} - 8 q^{6} - 3 q^{7} - 3 q^{8} + 2 q^{9} - 5 q^{10} - 9 q^{11} + q^{12} + q^{13} + 8 q^{14} + 10 q^{15} - 4 q^{16} - 17 q^{17} + 13 q^{18} + 2 q^{19} - 11 q^{20} - 5 q^{21} + 16 q^{23} + 3 q^{24} + 6 q^{25} - 6 q^{26} - 6 q^{27} - 5 q^{28} - 20 q^{29} + 26 q^{30} + 3 q^{31} + 4 q^{32} + 9 q^{33} + 3 q^{34} + 6 q^{36} + 5 q^{37} - 3 q^{38} + 5 q^{39} + 5 q^{40} - 2 q^{41} + 3 q^{42} + 3 q^{43} - 6 q^{44} - 21 q^{45} + 11 q^{46} - 4 q^{47} + 6 q^{48} - 10 q^{49} + 31 q^{50} + 14 q^{51} + 22 q^{52} - q^{53} + q^{54} + 15 q^{55} + 3 q^{56} + q^{57} + 11 q^{58} - 12 q^{59} + 16 q^{60} + 9 q^{62} + 11 q^{63} - 21 q^{64} - 17 q^{65} + 24 q^{66} - 22 q^{68} - 27 q^{69} - 16 q^{70} - 11 q^{71} - 2 q^{72} + 3 q^{73} - 11 q^{74} - 37 q^{75} + 12 q^{76} + 9 q^{77} - 18 q^{78} - 5 q^{79} + 27 q^{80} - q^{81} - 37 q^{82} + 28 q^{83} - 14 q^{84} + 36 q^{85} - 32 q^{86} + 9 q^{87} + 9 q^{88} + 5 q^{89} - 47 q^{90} - 7 q^{91} - 3 q^{92} - 12 q^{93} + 13 q^{94} - 11 q^{95} + 25 q^{96} + 7 q^{97} - 19 q^{98} - 6 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 - 8 * q^6 - 3 * q^7 - 3 * q^8 + 2 * q^9 - 5 * q^10 - 9 * q^11 + q^12 + q^13 + 8 * q^14 + 10 * q^15 - 4 * q^16 - 17 * q^17 + 13 * q^18 + 2 * q^19 - 11 * q^20 - 5 * q^21 + 16 * q^23 + 3 * q^24 + 6 * q^25 - 6 * q^26 - 6 * q^27 - 5 * q^28 - 20 * q^29 + 26 * q^30 + 3 * q^31 + 4 * q^32 + 9 * q^33 + 3 * q^34 + 6 * q^36 + 5 * q^37 - 3 * q^38 + 5 * q^39 + 5 * q^40 - 2 * q^41 + 3 * q^42 + 3 * q^43 - 6 * q^44 - 21 * q^45 + 11 * q^46 - 4 * q^47 + 6 * q^48 - 10 * q^49 + 31 * q^50 + 14 * q^51 + 22 * q^52 - q^53 + q^54 + 15 * q^55 + 3 * q^56 + q^57 + 11 * q^58 - 12 * q^59 + 16 * q^60 + 9 * q^62 + 11 * q^63 - 21 * q^64 - 17 * q^65 + 24 * q^66 - 22 * q^68 - 27 * q^69 - 16 * q^70 - 11 * q^71 - 2 * q^72 + 3 * q^73 - 11 * q^74 - 37 * q^75 + 12 * q^76 + 9 * q^77 - 18 * q^78 - 5 * q^79 + 27 * q^80 - q^81 - 37 * q^82 + 28 * q^83 - 14 * q^84 + 36 * q^85 - 32 * q^86 + 9 * q^87 + 9 * q^88 + 5 * q^89 - 47 * q^90 - 7 * q^91 - 3 * q^92 - 12 * q^93 + 13 * q^94 - 11 * q^95 + 25 * q^96 + 7 * q^97 - 19 * q^98 - 6 * 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 $

$2$	1.86081	1.31579	0.657894	−	0.753110i	$-0.271447\pi$
$2$	1.86081	1.31579	0.657894	+	0.753110i	$0.271447\pi$
$3$	−2.86081	−1.65169	−0.825844	−	0.563899i	$-0.809301\pi$
$3$	−2.86081	−1.65169	−0.825844	+	0.563899i	$0.809301\pi$
$4$	1.46260	0.731299
$5$	−4.32340	−1.93349	−0.966743	−	0.255751i	$-0.917677\pi$
$5$	−4.32340	−1.93349	−0.966743	+	0.255751i	$0.917677\pi$
$6$	−5.32340	−2.17327
$7$	0.860806	0.325354	0.162677	−	0.986679i	$-0.447987\pi$
$7$	0.860806	0.325354	0.162677	+	0.986679i	$0.447987\pi$
$8$	−1.00000	−0.353553
$9$	5.18421	1.72807
$10$	−8.04502	−2.54406
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	−4.18421	−1.20788
$13$	1.92520	0.533954	0.266977	−	0.963703i	$-0.413975\pi$
$13$	1.92520	0.533954	0.266977	+	0.963703i	$0.413975\pi$
$14$	1.60179	0.428097
$15$	12.3684	3.19351
$16$	−4.78600	−1.19650
$17$	−6.46260	−1.56741	−0.783705	−	0.621133i	$-0.786673\pi$
$17$	−6.46260	−1.56741	−0.783705	+	0.621133i	$0.786673\pi$
$18$	9.64681	2.27377
$19$	1.46260	0.335543	0.167772	−	0.985826i	$-0.446343\pi$
$19$	1.46260	0.335543	0.167772	+	0.985826i	$0.446343\pi$
$20$	−6.32340	−1.41396
$21$	−2.46260	−0.537383
$22$	−5.58242	−1.19018
$23$	6.39821	1.33412	0.667059	−	0.745005i	$-0.267553\pi$
$23$	6.39821	1.33412	0.667059	+	0.745005i	$0.267553\pi$
$24$	2.86081	0.583960
$25$	13.6918	2.73836
$26$	3.58242	0.702570
$27$	−6.24860	−1.20254
$28$	1.25901	0.237931
$29$	−5.60179	−1.04023	−0.520113	−	0.854097i	$-0.674110\pi$
$29$	−5.60179	−1.04023	−0.520113	+	0.854097i	$0.674110\pi$
$30$	23.0152	4.20199
$31$	−1.38780	−0.249255	−0.124628	−	0.992204i	$-0.539774\pi$
$31$	−1.38780	−0.249255	−0.124628	+	0.992204i	$0.539774\pi$
$32$	−6.90582	−1.22079
$33$	8.58242	1.49401
$34$	−12.0256	−2.06238
$35$	−3.72161	−0.629067
$36$	7.58242	1.26374
$37$	0.601793	0.0989341	0.0494670	−	0.998776i	$-0.484248\pi$
$37$	0.601793	0.0989341	0.0494670	+	0.998776i	$0.484248\pi$
$38$	2.72161	0.441504
$39$	−5.50761	−0.881924
$40$	4.32340	0.683590
$41$	−10.7666	−1.68146	−0.840732	−	0.541451i	$-0.817875\pi$
$41$	−10.7666	−1.68146	−0.840732	+	0.541451i	$0.817875\pi$
$42$	−4.58242	−0.707082
$43$	−6.44322	−0.982582	−0.491291	−	0.870995i	$-0.663475\pi$
$43$	−6.44322	−0.982582	−0.491291	+	0.870995i	$0.663475\pi$
$44$	−4.38780	−0.661485
$45$	−22.4134	−3.34120
$46$	11.9058	1.75542
$47$	3.18421	0.464465	0.232232	−	0.972660i	$-0.425397\pi$
$47$	3.18421	0.464465	0.232232	+	0.972660i	$0.425397\pi$
$48$	13.6918	1.97624
$49$	−6.25901	−0.894145
$50$	25.4778	3.60311
$51$	18.4882	2.58887
$52$	2.81579	0.390480
$53$	0.462598	0.0635428	0.0317714	−	0.999495i	$-0.489885\pi$
$53$	0.462598	0.0635428	0.0317714	+	0.999495i	$0.489885\pi$
$54$	−11.6274	−1.58229
$55$	12.9702	1.74890
$56$	−0.860806	−0.115030
$57$	−4.18421	−0.554212
$58$	−10.4238	−1.36872
$59$	−3.47301	−0.452147	−0.226074	−	0.974110i	$-0.572589\pi$
$59$	−3.47301	−0.452147	−0.226074	+	0.974110i	$0.572589\pi$
$60$	18.0900	2.33541
$61$	−7.97021	−1.02048	−0.510241	−	0.860032i	$-0.670444\pi$
$61$	−7.97021	−1.02048	−0.510241	+	0.860032i	$0.670444\pi$
$62$	−2.58242	−0.327967
$63$	4.46260	0.562235
$64$	−3.27839	−0.409799
$65$	−8.32340	−1.03239
$66$	15.9702	1.96580
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	−9.45219	−1.14625
$69$	−18.3040	−2.20355
$70$	−6.92520	−0.827719
$71$	9.61702	1.14133	0.570665	−	0.821183i	$-0.306685\pi$
$71$	9.61702	1.14133	0.570665	+	0.821183i	$0.306685\pi$
$72$	−5.18421	−0.610965
$73$	−0.860806	−0.100750	−0.0503749	−	0.998730i	$-0.516042\pi$
$73$	−0.860806	−0.100750	−0.0503749	+	0.998730i	$0.516042\pi$
$74$	1.11982	0.130176
$75$	−39.1697	−4.52292
$76$	2.13919	0.245382
$77$	−2.58242	−0.294294
$78$	−10.2486	−1.16043
$79$	−12.8206	−1.44243	−0.721215	−	0.692711i	$-0.756416\pi$
$79$	−12.8206	−1.44243	−0.721215	+	0.692711i	$0.756416\pi$
$80$	20.6918	2.31342
$81$	2.32340	0.258156
$82$	−20.0346	−2.21245
$83$	7.20359	0.790696	0.395348	−	0.918531i	$-0.370624\pi$
$83$	7.20359	0.790696	0.395348	+	0.918531i	$0.370624\pi$
$84$	−3.60179	−0.392988
$85$	27.9404	3.03056
$86$	−11.9896	−1.29287
$87$	16.0256	1.71813
$88$	3.00000	0.319801
$89$	17.8760	1.89486	0.947428	−	0.319969i	$-0.103673\pi$
$89$	17.8760	1.89486	0.947428	+	0.319969i	$0.103673\pi$
$90$	−41.7071	−4.39631
$91$	1.65722	0.173724
$92$	9.35801	0.975640
$93$	3.97021	0.411692
$94$	5.92520	0.611137
$95$	−6.32340	−0.648768
$96$	19.7562	2.01636
$97$	−6.43281	−0.653153	−0.326577	−	0.945171i	$-0.605895\pi$
$97$	−6.43281	−0.653153	−0.326577	+	0.945171i	$0.605895\pi$
$98$	−11.6468	−1.17651
$99$	−15.5526	−1.56310
$100$	20.0256	2.00256
$101$	4.10941	0.408901	0.204451	−	0.978877i	$-0.434459\pi$
$101$	4.10941	0.408901	0.204451	+	0.978877i	$0.434459\pi$
$102$	34.4030	3.40641
$103$	10.9404	1.07799	0.538996	−	0.842308i	$-0.318804\pi$
$103$	10.9404	1.07799	0.538996	+	0.842308i	$0.318804\pi$
$104$	−1.92520	−0.188781
$105$	10.6468	1.03902
$106$	0.860806	0.0836089
$107$	16.1094	1.55736	0.778678	−	0.627424i	$-0.215891\pi$
$107$	16.1094	1.55736	0.778678	+	0.627424i	$0.215891\pi$
$108$	−9.13919	−0.879419
$109$	−3.26798	−0.313015	−0.156508	−	0.987677i	$-0.550024\pi$
$109$	−3.26798	−0.313015	−0.156508	+	0.987677i	$0.550024\pi$
$110$	24.1350	2.30119
$111$	−1.72161	−0.163408
$112$	−4.11982	−0.389286
$113$	−0.631580	−0.0594140	−0.0297070	−	0.999559i	$-0.509457\pi$
$113$	−0.631580	−0.0594140	−0.0297070	+	0.999559i	$0.509457\pi$
$114$	−7.78600	−0.729226
$115$	−27.6620	−2.57950
$116$	−8.19317	−0.760717
$117$	9.98062	0.922709
$118$	−6.46260	−0.594930
$119$	−5.56304	−0.509963
$120$	−12.3684	−1.12908
$121$	−2.00000	−0.181818
$122$	−14.8310	−1.34274
$123$	30.8012	2.77725
$124$	−2.02979	−0.182280
$125$	−37.5783	−3.36110
$126$	8.30403	0.739782
$127$	−5.04502	−0.447673	−0.223836	−	0.974627i	$-0.571858\pi$
$127$	−5.04502	−0.447673	−0.223836	+	0.974627i	$0.571858\pi$
$128$	7.71120	0.681580
$129$	18.4328	1.62292
$130$	−15.4882	−1.35841
$131$	4.24860	0.371202	0.185601	−	0.982625i	$-0.440577\pi$
$131$	4.24860	0.371202	0.185601	+	0.982625i	$0.440577\pi$
$132$	12.5526	1.09257
$133$	1.25901	0.109170
$134$	0	0
$135$	27.0152	2.32510
$136$	6.46260	0.554163
$137$	−10.6918	−0.913464	−0.456732	−	0.889604i	$-0.650980\pi$
$137$	−10.6918	−0.913464	−0.456732	+	0.889604i	$0.650980\pi$
$138$	−34.0602	−2.89940
$139$	19.0048	1.61197	0.805984	−	0.591938i	$-0.201637\pi$
$139$	19.0048	1.61197	0.805984	+	0.591938i	$0.201637\pi$
$140$	−5.44322	−0.460036
$141$	−9.10941	−0.767150
$142$	17.8954	1.50175
$143$	−5.77559	−0.482979
$144$	−24.8116	−2.06764
$145$	24.2188	2.01126
$146$	−1.60179	−0.132565
$147$	17.9058	1.47685
$148$	0.880181	0.0723504
$149$	−11.3532	−0.930090	−0.465045	−	0.885287i	$-0.653962\pi$
$149$	−11.3532	−0.930090	−0.465045	+	0.885287i	$0.653962\pi$
$150$	−72.8871	−5.95121
$151$	−8.75622	−0.712571	−0.356285	−	0.934377i	$-0.615957\pi$
$151$	−8.75622	−0.712571	−0.356285	+	0.934377i	$0.615957\pi$
$152$	−1.46260	−0.118632
$153$	−33.5035	−2.70859
$154$	−4.80538	−0.387228
$155$	6.00000	0.481932
$156$	−8.05543	−0.644950
$157$	−10.3774	−0.828205	−0.414103	−	0.910230i	$-0.635905\pi$
$157$	−10.3774	−0.828205	−0.414103	+	0.910230i	$0.635905\pi$
$158$	−23.8567	−1.89793
$159$	−1.32340	−0.104953
$160$	29.8567	2.36038
$161$	5.50761	0.434061
$162$	4.32340	0.339679
$163$	4.45364	0.348836	0.174418	−	0.984672i	$-0.444196\pi$
$163$	4.45364	0.348836	0.174418	+	0.984672i	$0.444196\pi$
$164$	−15.7473	−1.22965
$165$	−37.1053	−2.88864
$166$	13.4045	1.04039
$167$	−16.4238	−1.27092	−0.635458	−	0.772136i	$-0.719189\pi$
$167$	−16.4238	−1.27092	−0.635458	+	0.772136i	$0.719189\pi$
$168$	2.46260	0.189994
$169$	−9.29362	−0.714894
$170$	51.9917	3.98758
$171$	7.58242	0.579842
$172$	−9.42385	−0.718562
$173$	5.38924	0.409737	0.204868	−	0.978790i	$-0.434323\pi$
$173$	5.38924	0.409737	0.204868	+	0.978790i	$0.434323\pi$
$174$	29.8206	2.26069
$175$	11.7860	0.890938
$176$	14.3580	1.08228
$177$	9.93561	0.746806
$178$	33.2638	2.49323
$179$	−10.4987	−0.784706	−0.392353	−	0.919815i	$-0.628339\pi$
$179$	−10.4987	−0.784706	−0.392353	+	0.919815i	$0.628339\pi$
$180$	−32.7819	−2.44342
$181$	−10.6766	−0.793585	−0.396793	−	0.917908i	$-0.629877\pi$
$181$	−10.6766	−0.793585	−0.396793	+	0.917908i	$0.629877\pi$
$182$	3.08377	0.228584
$183$	22.8012	1.68552
$184$	−6.39821	−0.471682
$185$	−2.60179	−0.191288
$186$	7.38780	0.541699
$187$	19.3878	1.41778
$188$	4.65722	0.339663
$189$	−5.37883	−0.391252
$190$	−11.7666	−0.853641
$191$	−18.6170	−1.34708	−0.673540	−	0.739151i	$-0.735227\pi$
$191$	−18.6170	−1.34708	−0.673540	+	0.739151i	$0.735227\pi$
$192$	9.37883	0.676859
$193$	14.3788	1.03501	0.517506	−	0.855680i	$-0.326861\pi$
$193$	14.3788	1.03501	0.517506	+	0.855680i	$0.326861\pi$
$194$	−11.9702	−0.859411
$195$	23.8116	1.70519
$196$	−9.15442	−0.653887
$197$	−3.04502	−0.216948	−0.108474	−	0.994099i	$-0.534596\pi$
$197$	−3.04502	−0.216948	−0.108474	+	0.994099i	$0.534596\pi$
$198$	−28.9404	−2.05671
$199$	14.7473	1.04541	0.522703	−	0.852515i	$-0.324924\pi$
$199$	14.7473	1.04541	0.522703	+	0.852515i	$0.324924\pi$
$200$	−13.6918	−0.968158
$201$	0	0
$202$	7.64681	0.538028
$203$	−4.82206	−0.338442
$204$	27.0409	1.89324
$205$	46.5485	3.25109
$206$	20.3580	1.41841
$207$	33.1697	2.30545
$208$	−9.21400	−0.638876
$209$	−4.38780	−0.303510
$210$	19.8116	1.36713
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	0.676596	0.0464688
$213$	−27.5124	−1.88512
$214$	29.9765	2.04915
$215$	27.8567	1.89981
$216$	6.24860	0.425163
$217$	−1.19462	−0.0810962
$218$	−6.08107	−0.411862
$219$	2.46260	0.166407
$220$	18.9702	1.27897
$221$	−12.4418	−0.836924
$222$	−3.20359	−0.215011
$223$	−0.248601	−0.0166476	−0.00832378	−	0.999965i	$-0.502650\pi$
$223$	−0.248601	−0.0166476	−0.00832378	+	0.999965i	$0.502650\pi$
$224$	−5.94457	−0.397188
$225$	70.9813	4.73209
$226$	−1.17525	−0.0781763
$227$	1.99104	0.132150	0.0660749	−	0.997815i	$-0.478952\pi$
$227$	1.99104	0.132150	0.0660749	+	0.997815i	$0.478952\pi$
$228$	−6.11982	−0.405295
$229$	−12.3982	−0.819297	−0.409648	−	0.912244i	$-0.634349\pi$
$229$	−12.3982	−0.819297	−0.409648	+	0.912244i	$0.634349\pi$
$230$	−51.4737	−3.39407
$231$	7.38780	0.486081
$232$	5.60179	0.367776
$233$	13.4086	0.878428	0.439214	−	0.898383i	$-0.355257\pi$
$233$	13.4086	0.878428	0.439214	+	0.898383i	$0.355257\pi$
$234$	18.5720	1.21409
$235$	−13.7666	−0.898036
$236$	−5.07962	−0.330655
$237$	36.6773	2.38244
$238$	−10.3517	−0.671004
$239$	−13.3026	−0.860472	−0.430236	−	0.902716i	$-0.641570\pi$
$239$	−13.3026	−0.860472	−0.430236	+	0.902716i	$0.641570\pi$
$240$	−59.1953	−3.82104
$241$	−9.91623	−0.638761	−0.319380	−	0.947627i	$-0.603475\pi$
$241$	−9.91623	−0.638761	−0.319380	+	0.947627i	$0.603475\pi$
$242$	−3.72161	−0.239234
$243$	12.0990	0.776151
$244$	−11.6572	−0.746277
$245$	27.0602	1.72882
$246$	57.3151	3.65428
$247$	2.81579	0.179164
$248$	1.38780	0.0881251
$249$	−20.6081	−1.30598
$250$	−69.9259	−4.42250
$251$	0.582418	0.0367619	0.0183809	−	0.999831i	$-0.494149\pi$
$251$	0.582418	0.0367619	0.0183809	+	0.999831i	$0.494149\pi$
$252$	6.52699	0.411162
$253$	−19.1946	−1.20676
$254$	−9.38780	−0.589043
$255$	−79.9321	−5.00554
$256$	20.9058	1.30661
$257$	5.51803	0.344205	0.172103	−	0.985079i	$-0.444944\pi$
$257$	5.51803	0.344205	0.172103	+	0.985079i	$0.444944\pi$
$258$	34.2999	2.13542
$259$	0.518027	0.0321886
$260$	−12.1738	−0.754987
$261$	−29.0409	−1.79758
$262$	7.90582	0.488423
$263$	6.11982	0.377364	0.188682	−	0.982038i	$-0.439578\pi$
$263$	6.11982	0.377364	0.188682	+	0.982038i	$0.439578\pi$
$264$	−8.58242	−0.528211
$265$	−2.00000	−0.122859
$266$	2.34278	0.143645
$267$	−51.1399	−3.12971
$268$	0	0
$269$	−21.5824	−1.31590	−0.657952	−	0.753060i	$-0.728577\pi$
$269$	−21.5824	−1.31590	−0.657952	+	0.753060i	$0.728577\pi$
$270$	50.2701	3.05934
$271$	18.0000	1.09342	0.546711	−	0.837321i	$-0.315880\pi$
$271$	18.0000	1.09342	0.546711	+	0.837321i	$0.315880\pi$
$272$	30.9300	1.87541
$273$	−4.74099	−0.286938
$274$	−19.8954	−1.20193
$275$	−41.0755	−2.47694
$276$	−26.7714	−1.61145
$277$	16.3878	0.984647	0.492324	−	0.870412i	$-0.336148\pi$
$277$	16.3878	0.984647	0.492324	+	0.870412i	$0.336148\pi$
$278$	35.3643	2.12101
$279$	−7.19462	−0.430731
$280$	3.72161	0.222409
$281$	12.8206	0.764813	0.382407	−	0.923994i	$-0.375095\pi$
$281$	12.8206	0.764813	0.382407	+	0.923994i	$0.375095\pi$
$282$	−16.9508	−1.00941
$283$	−19.1648	−1.13923	−0.569616	−	0.821911i	$-0.692908\pi$
$283$	−19.1648	−1.13923	−0.569616	+	0.821911i	$0.692908\pi$
$284$	14.0658	0.834654
$285$	18.0900	1.07156
$286$	−10.7473	−0.635498
$287$	−9.26798	−0.547071
$288$	−35.8012	−2.10961
$289$	24.7652	1.45678
$290$	45.0665	2.64640
$291$	18.4030	1.07880
$292$	−1.25901	−0.0736782
$293$	6.22778	0.363831	0.181915	−	0.983314i	$-0.441770\pi$
$293$	6.22778	0.363831	0.181915	+	0.983314i	$0.441770\pi$
$294$	33.3193	1.94322
$295$	15.0152	0.874220
$296$	−0.601793	−0.0349785
$297$	18.7458	1.08774
$298$	−21.1261	−1.22380
$299$	12.3178	0.712357
$300$	−57.2895	−3.30761
$301$	−5.54636	−0.319687
$302$	−16.2936	−0.937592
$303$	−11.7562	−0.675377
$304$	−7.00000	−0.401478
$305$	34.4585	1.97309
$306$	−62.3434	−3.56394
$307$	−20.6572	−1.17897	−0.589485	−	0.807779i	$-0.700669\pi$
$307$	−20.6572	−1.17897	−0.589485	+	0.807779i	$0.700669\pi$
$308$	−3.77704	−0.215217
$309$	−31.2984	−1.78051
$310$	11.1648	0.634120
$311$	−18.5735	−1.05320	−0.526602	−	0.850112i	$-0.676534\pi$
$311$	−18.5735	−1.05320	−0.526602	+	0.850112i	$0.676534\pi$
$312$	5.50761	0.311807
$313$	−3.01938	−0.170665	−0.0853326	−	0.996353i	$-0.527195\pi$
$313$	−3.01938	−0.170665	−0.0853326	+	0.996353i	$0.527195\pi$
$314$	−19.3103	−1.08974
$315$	−19.2936	−1.08707
$316$	−18.7514	−1.05485
$317$	1.90582	0.107042	0.0535208	−	0.998567i	$-0.482956\pi$
$317$	1.90582	0.107042	0.0535208	+	0.998567i	$0.482956\pi$
$318$	−2.46260	−0.138096
$319$	16.8054	0.940921
$320$	14.1738	0.792339
$321$	−46.0859	−2.57226
$322$	10.2486	0.571132
$323$	−9.45219	−0.525934
$324$	3.39821	0.188789
$325$	26.3595	1.46216
$326$	8.28735	0.458994
$327$	9.34905	0.517003
$328$	10.7666	0.594488
$329$	2.74099	0.151115
$330$	−69.0457	−3.80084
$331$	−13.2099	−0.726079	−0.363040	−	0.931774i	$-0.618261\pi$
$331$	−13.2099	−0.726079	−0.363040	+	0.931774i	$0.618261\pi$
$332$	10.5360	0.578236
$333$	3.11982	0.170965
$334$	−30.5616	−1.67226
$335$	0	0
$336$	11.7860	0.642979
$337$	−22.5124	−1.22633	−0.613165	−	0.789955i	$-0.710104\pi$
$337$	−22.5124	−1.22633	−0.613165	+	0.789955i	$0.710104\pi$
$338$	−17.2936	−0.940649
$339$	1.80683	0.0981334
$340$	40.8656	2.21625
$341$	4.16339	0.225460
$342$	14.1094	0.762949
$343$	−11.4134	−0.616268
$344$	6.44322	0.347395
$345$	79.1357	4.26052
$346$	10.0283	0.539127
$347$	−10.7473	−0.576943	−0.288471	−	0.957489i	$-0.593147\pi$
$347$	−10.7473	−0.576943	−0.288471	+	0.957489i	$0.593147\pi$
$348$	23.4391	1.25647
$349$	36.2445	1.94012	0.970061	−	0.242863i	$-0.0780866\pi$
$349$	36.2445	1.94012	0.970061	+	0.242863i	$0.0780866\pi$
$350$	21.9315	1.17229
$351$	−12.0298	−0.642103
$352$	20.7175	1.10424
$353$	33.7819	1.79803	0.899013	−	0.437921i	$-0.144285\pi$
$353$	33.7819	1.79803	0.899013	+	0.437921i	$0.144285\pi$
$354$	18.4882	0.982639
$355$	−41.5783	−2.20675
$356$	26.1455	1.38571
$357$	15.9148	0.842300
$358$	−19.5360	−1.03251
$359$	−27.3836	−1.44525	−0.722627	−	0.691238i	$-0.757065\pi$
$359$	−27.3836	−1.44525	−0.722627	+	0.691238i	$0.757065\pi$
$360$	22.4134	1.18129
$361$	−16.8608	−0.887411
$362$	−19.8671	−1.04419
$363$	5.72161	0.300307
$364$	2.42385	0.127044
$365$	3.72161	0.194798
$366$	42.4287	2.21778
$367$	−34.9765	−1.82576	−0.912879	−	0.408231i	$-0.866146\pi$
$367$	−34.9765	−1.82576	−0.912879	+	0.408231i	$0.866146\pi$
$368$	−30.6218	−1.59627
$369$	−55.8165	−2.90569
$370$	−4.84143	−0.251694
$371$	0.398207	0.0206739
$372$	5.80683	0.301070
$373$	6.69742	0.346779	0.173390	−	0.984853i	$-0.444528\pi$
$373$	6.69742	0.346779	0.173390	+	0.984853i	$0.444528\pi$
$374$	36.0769	1.86549
$375$	107.504	5.55149
$376$	−3.18421	−0.164213
$377$	−10.7846	−0.555433
$378$	−10.0090	−0.514805
$379$	−6.78455	−0.348499	−0.174250	−	0.984702i	$-0.555750\pi$
$379$	−6.78455	−0.348499	−0.174250	+	0.984702i	$0.555750\pi$
$380$	−9.24860	−0.474443
$381$	14.4328	0.739415
$382$	−34.6427	−1.77247
$383$	−26.9523	−1.37720	−0.688599	−	0.725143i	$-0.741774\pi$
$383$	−26.9523	−1.37720	−0.688599	+	0.725143i	$0.741774\pi$
$384$	−22.0602	−1.12576
$385$	11.1648	0.569013
$386$	26.7562	1.36186
$387$	−33.4030	−1.69797
$388$	−9.40862	−0.477650
$389$	−9.36842	−0.474998	−0.237499	−	0.971388i	$-0.576328\pi$
$389$	−9.36842	−0.474998	−0.237499	+	0.971388i	$0.576328\pi$
$390$	44.3088	2.24367
$391$	−41.3490	−2.09111
$392$	6.25901	0.316128
$393$	−12.1544	−0.613110
$394$	−5.66618	−0.285458
$395$	55.4287	2.78892
$396$	−22.7473	−1.14309
$397$	17.9404	0.900404	0.450202	−	0.892927i	$-0.351352\pi$
$397$	17.9404	0.900404	0.450202	+	0.892927i	$0.351352\pi$
$398$	27.4418	1.37553
$399$	−3.60179	−0.180315
$400$	−65.5291	−3.27646
$401$	−21.7521	−1.08625	−0.543123	−	0.839653i	$-0.682758\pi$
$401$	−21.7521	−1.08625	−0.543123	+	0.839653i	$0.682758\pi$
$402$	0	0
$403$	−2.67178	−0.133091
$404$	6.01041	0.299029
$405$	−10.0450	−0.499141
$406$	−8.97291	−0.445318
$407$	−1.80538	−0.0894893
$408$	−18.4882	−0.915304
$409$	29.2084	1.44426	0.722131	−	0.691756i	$-0.243163\pi$
$409$	29.2084	1.44426	0.722131	+	0.691756i	$0.243163\pi$
$410$	86.6177	4.27774
$411$	30.5872	1.50876
$412$	16.0014	0.788335
$413$	−2.98959	−0.147108
$414$	61.7223	3.03348
$415$	−31.1440	−1.52880
$416$	−13.2951	−0.651844
$417$	−54.3691	−2.66247
$418$	−8.16484	−0.399355
$419$	17.3892	0.849520	0.424760	−	0.905306i	$-0.360358\pi$
$419$	17.3892	0.849520	0.424760	+	0.905306i	$0.360358\pi$
$420$	15.5720	0.759836
$421$	−1.90997	−0.0930861	−0.0465431	−	0.998916i	$-0.514820\pi$
$421$	−1.90997	−0.0930861	−0.0465431	+	0.998916i	$0.514820\pi$
$422$	−1.86081	−0.0905826
$423$	16.5076	0.802628
$424$	−0.462598	−0.0224658
$425$	−88.4848	−4.29214
$426$	−51.1953	−2.48042
$427$	−6.86081	−0.332018
$428$	23.5616	1.13889
$429$	16.5228	0.797730
$430$	51.8358	2.49975
$431$	1.73202	0.0834287	0.0417143	−	0.999130i	$-0.486718\pi$
$431$	1.73202	0.0834287	0.0417143	+	0.999130i	$0.486718\pi$
$432$	29.9058	1.43884
$433$	−14.3684	−0.690502	−0.345251	−	0.938510i	$-0.612206\pi$
$433$	−14.3684	−0.690502	−0.345251	+	0.938510i	$0.612206\pi$
$434$	−2.22296	−0.106706
$435$	−69.2853	−3.32198
$436$	−4.77974	−0.228908
$437$	9.35801	0.447654
$438$	4.58242	0.218956
$439$	16.6766	0.795930	0.397965	−	0.917400i	$-0.369716\pi$
$439$	16.6766	0.795930	0.397965	+	0.917400i	$0.369716\pi$
$440$	−12.9702	−0.618331
$441$	−32.4480	−1.54514
$442$	−23.1517	−1.10122
$443$	−5.28320	−0.251013	−0.125506	−	0.992093i	$-0.540056\pi$
$443$	−5.28320	−0.251013	−0.125506	+	0.992093i	$0.540056\pi$
$444$	−2.51803	−0.119500
$445$	−77.2853	−3.66368
$446$	−0.462598	−0.0219047
$447$	32.4793	1.53622
$448$	−2.82206	−0.133330
$449$	22.5962	1.06638	0.533190	−	0.845995i	$-0.320993\pi$
$449$	22.5962	1.06638	0.533190	+	0.845995i	$0.320993\pi$
$450$	132.082	6.22642
$451$	32.2999	1.52094
$452$	−0.923748	−0.0434494
$453$	25.0498	1.17694
$454$	3.70493	0.173881
$455$	−7.16484	−0.335893
$456$	4.18421	0.195944
$457$	16.0465	0.750622	0.375311	−	0.926899i	$-0.377536\pi$
$457$	16.0465	0.750622	0.375311	+	0.926899i	$0.377536\pi$
$458$	−23.0707	−1.07802
$459$	40.3822	1.88488
$460$	−40.4585	−1.88639
$461$	−9.41758	−0.438621	−0.219310	−	0.975655i	$-0.570381\pi$
$461$	−9.41758	−0.438621	−0.219310	+	0.975655i	$0.570381\pi$
$462$	13.7473	0.639580
$463$	−1.71680	−0.0797862	−0.0398931	−	0.999204i	$-0.512702\pi$
$463$	−1.71680	−0.0797862	−0.0398931	+	0.999204i	$0.512702\pi$
$464$	26.8102	1.24463
$465$	−17.1648	−0.796000
$466$	24.9508	1.15583
$467$	2.50617	0.115971	0.0579857	−	0.998317i	$-0.481532\pi$
$467$	2.50617	0.115971	0.0579857	+	0.998317i	$0.481532\pi$
$468$	14.5976	0.674776
$469$	0	0
$470$	−25.6170	−1.18163
$471$	29.6877	1.36794
$472$	3.47301	0.159858
$473$	19.3297	0.888779
$474$	68.2493	3.13479
$475$	20.0256	0.918839
$476$	−8.13650	−0.372936
$477$	2.39821	0.109806
$478$	−24.7535	−1.13220
$479$	−6.89541	−0.315059	−0.157530	−	0.987514i	$-0.550353\pi$
$479$	−6.89541	−0.315059	−0.157530	+	0.987514i	$0.550353\pi$
$480$	−85.4141	−3.89860
$481$	1.15857	0.0528262
$482$	−18.4522	−0.840474
$483$	−15.7562	−0.716933
$484$	−2.92520	−0.132963
$485$	27.8116	1.26286
$486$	22.5139	1.02125
$487$	−18.4030	−0.833921	−0.416960	−	0.908925i	$-0.636905\pi$
$487$	−18.4030	−0.833921	−0.416960	+	0.908925i	$0.636905\pi$
$488$	7.97021	0.360795
$489$	−12.7410	−0.576167
$490$	50.3539	2.27476
$491$	14.0748	0.635187	0.317593	−	0.948227i	$-0.397125\pi$
$491$	14.0748	0.635187	0.317593	+	0.948227i	$0.397125\pi$
$492$	45.0498	2.03100
$493$	36.2021	1.63046
$494$	5.23964	0.235742
$495$	67.2403	3.02223
$496$	6.64199	0.298234
$497$	8.27839	0.371336
$498$	−38.3476	−1.71840
$499$	34.1849	1.53033	0.765163	−	0.643837i	$-0.222659\pi$
$499$	34.1849	1.53033	0.765163	+	0.643837i	$0.222659\pi$
$500$	−54.9619	−2.45797
$501$	46.9854	2.09915
$502$	1.08377	0.0483708
$503$	42.4599	1.89319	0.946597	−	0.322420i	$-0.104496\pi$
$503$	42.4599	1.89319	0.946597	+	0.322420i	$0.104496\pi$
$504$	−4.46260	−0.198780
$505$	−17.7666	−0.790605
$506$	−35.7175	−1.58784
$507$	26.5872	1.18078
$508$	−7.37883	−0.327383
$509$	8.94043	0.396277	0.198139	−	0.980174i	$-0.436510\pi$
$509$	8.94043	0.396277	0.198139	+	0.980174i	$0.436510\pi$
$510$	−148.738	−6.58624
$511$	−0.740987	−0.0327793
$512$	23.4793	1.03765
$513$	−9.13919	−0.403505
$514$	10.2680	0.452901
$515$	−47.2999	−2.08428
$516$	26.9598	1.18684
$517$	−9.55263	−0.420124
$518$	0.963947	0.0423534
$519$	−15.4176	−0.676757
$520$	8.32340	0.365005
$521$	−23.5408	−1.03134	−0.515670	−	0.856787i	$-0.672457\pi$
$521$	−23.5408	−1.03134	−0.515670	+	0.856787i	$0.672457\pi$
$522$	−54.0394	−2.36524
$523$	−24.0498	−1.05163	−0.525813	−	0.850600i	$-0.676239\pi$
$523$	−24.0498	−1.05163	−0.525813	+	0.850600i	$0.676239\pi$
$524$	6.21400	0.271460
$525$	−33.7175	−1.47155
$526$	11.3878	0.496531
$527$	8.96876	0.390685
$528$	−41.0755	−1.78758
$529$	17.9371	0.779872
$530$	−3.72161	−0.161656
$531$	−18.0048	−0.781342
$532$	1.84143	0.0798362
$533$	−20.7279	−0.897824
$534$	−95.1614	−4.11803
$535$	−69.6475	−3.01112
$536$	0	0
$537$	30.0346	1.29609
$538$	−40.1607	−1.73145
$539$	18.7770	0.808784
$540$	39.5124	1.70034
$541$	−1.72306	−0.0740802	−0.0370401	−	0.999314i	$-0.511793\pi$
$541$	−1.72306	−0.0740802	−0.0370401	+	0.999314i	$0.511793\pi$
$542$	33.4945	1.43871
$543$	30.5437	1.31075
$544$	44.6296	1.91348
$545$	14.1288	0.605211
$546$	−8.82206	−0.377549
$547$	−25.0242	−1.06996	−0.534979	−	0.844866i	$-0.679680\pi$
$547$	−25.0242	−1.06996	−0.534979	+	0.844866i	$0.679680\pi$
$548$	−15.6378	−0.668016
$549$	−41.3193	−1.76346
$550$	−76.4335	−3.25913
$551$	−8.19317	−0.349041
$552$	18.3040	0.779071
$553$	−11.0361	−0.469301
$554$	30.4945	1.29559
$555$	7.44322	0.315947
$556$	27.7964	1.17883
$557$	4.47638	0.189670	0.0948351	−	0.995493i	$-0.469768\pi$
$557$	4.47638	0.189670	0.0948351	+	0.995493i	$0.469768\pi$
$558$	−13.3878	−0.566751
$559$	−12.4045	−0.524653
$560$	17.8116	0.752679
$561$	−55.4647	−2.34172
$562$	23.8567	1.00633
$563$	34.3297	1.44682	0.723412	−	0.690417i	$-0.242573\pi$
$563$	34.3297	1.44682	0.723412	+	0.690417i	$0.242573\pi$
$564$	−13.3234	−0.561017
$565$	2.73057	0.114876
$566$	−35.6620	−1.49899
$567$	2.00000	0.0839921
$568$	−9.61702	−0.403521
$569$	19.9910	0.838068	0.419034	−	0.907971i	$-0.362369\pi$
$569$	19.9910	0.838068	0.419034	+	0.907971i	$0.362369\pi$
$570$	33.6620	1.40995
$571$	−15.6226	−0.653786	−0.326893	−	0.945061i	$-0.606002\pi$
$571$	−15.6226	−0.653786	−0.326893	+	0.945061i	$0.606002\pi$
$572$	−8.44737	−0.353202
$573$	53.2597	2.22496
$574$	−17.2459	−0.719830
$575$	87.6031	3.65330
$576$	−16.9959	−0.708161
$577$	43.8283	1.82460	0.912298	−	0.409526i	$-0.134306\pi$
$577$	43.8283	1.82460	0.912298	+	0.409526i	$0.134306\pi$
$578$	46.0832	1.91681
$579$	−41.1350	−1.70951
$580$	35.4224	1.47084
$581$	6.20089	0.257256
$582$	34.2445	1.41948
$583$	−1.38780	−0.0574766
$584$	0.860806	0.0356204
$585$	−43.1503	−1.78404
$586$	11.5887	0.478724
$587$	9.96607	0.411344	0.205672	−	0.978621i	$-0.434062\pi$
$587$	9.96607	0.411344	0.205672	+	0.978621i	$0.434062\pi$
$588$	26.1890	1.08002
$589$	−2.02979	−0.0836359
$590$	27.9404	1.15029
$591$	8.71120	0.358331
$592$	−2.88018	−0.118375
$593$	−16.1392	−0.662757	−0.331379	−	0.943498i	$-0.607514\pi$
$593$	−16.1392	−0.662757	−0.331379	+	0.943498i	$0.607514\pi$
$594$	34.8823	1.43124
$595$	24.0513	0.986006
$596$	−16.6052	−0.680174
$597$	−42.1890	−1.72668
$598$	22.9211	0.937311
$599$	−38.2999	−1.56489	−0.782445	−	0.622719i	$-0.786028\pi$
$599$	−38.2999	−1.56489	−0.782445	+	0.622719i	$0.786028\pi$
$600$	39.1697	1.59909
$601$	−4.48487	−0.182942	−0.0914709	−	0.995808i	$-0.529157\pi$
$601$	−4.48487	−0.182942	−0.0914709	+	0.995808i	$0.529157\pi$
$602$	−10.3207	−0.420641
$603$	0	0
$604$	−12.8068	−0.521102
$605$	8.64681	0.351543
$606$	−21.8760	−0.888653
$607$	1.26383	0.0512973	0.0256486	−	0.999671i	$-0.491835\pi$
$607$	1.26383	0.0512973	0.0256486	+	0.999671i	$0.491835\pi$
$608$	−10.1004	−0.409627
$609$	13.7950	0.559000
$610$	64.1205	2.59616
$611$	6.13023	0.248003
$612$	−49.0021	−1.98079
$613$	−6.81724	−0.275346	−0.137673	−	0.990478i	$-0.543962\pi$
$613$	−6.81724	−0.275346	−0.137673	+	0.990478i	$0.543962\pi$
$614$	−38.4391	−1.55127
$615$	−133.166	−5.36978
$616$	2.58242	0.104049
$617$	−30.9169	−1.24467	−0.622334	−	0.782752i	$-0.713815\pi$
$617$	−30.9169	−1.24467	−0.622334	+	0.782752i	$0.713815\pi$
$618$	−58.2403	−2.34277
$619$	14.6468	0.588705	0.294352	−	0.955697i	$-0.404896\pi$
$619$	14.6468	0.588705	0.294352	+	0.955697i	$0.404896\pi$
$620$	8.77559	0.352436
$621$	−39.9798	−1.60434
$622$	−34.5616	−1.38579
$623$	15.3878	0.616499
$624$	26.3595	1.05522
$625$	94.0069	3.76028
$626$	−5.61847	−0.224559
$627$	12.5526	0.501304
$628$	−15.1779	−0.605666
$629$	−3.88914	−0.155070
$630$	−35.9017	−1.43036
$631$	27.4016	1.09084	0.545420	−	0.838163i	$-0.316370\pi$
$631$	27.4016	1.09084	0.545420	+	0.838163i	$0.316370\pi$
$632$	12.8206	0.509976
$633$	2.86081	0.113707
$634$	3.54636	0.140844
$635$	21.8116	0.865569
$636$	−1.93561	−0.0767519
$637$	−12.0498	−0.477432
$638$	31.2715	1.23805
$639$	49.8567	1.97230
$640$	−33.3386	−1.31783
$641$	−36.3386	−1.43529	−0.717645	−	0.696409i	$-0.754780\pi$
$641$	−36.3386	−1.43529	−0.717645	+	0.696409i	$0.754780\pi$
$642$	−85.7569	−3.38455
$643$	6.85184	0.270210	0.135105	−	0.990831i	$-0.456863\pi$
$643$	6.85184	0.270210	0.135105	+	0.990831i	$0.456863\pi$
$644$	8.05543	0.317428
$645$	−79.6925	−3.13789
$646$	−17.5887	−0.692017
$647$	45.4376	1.78634	0.893169	−	0.449722i	$-0.148477\pi$
$647$	45.4376	1.78634	0.893169	+	0.449722i	$0.148477\pi$
$648$	−2.32340	−0.0912719
$649$	10.4190	0.408983
$650$	49.0498	1.92389
$651$	3.41758	0.133946
$652$	6.51388	0.255103
$653$	44.6010	1.74537	0.872686	−	0.488281i	$-0.162376\pi$
$653$	44.6010	1.74537	0.872686	+	0.488281i	$0.162376\pi$
$654$	17.3968	0.680267
$655$	−18.3684	−0.717714
$656$	51.5291	2.01187
$657$	−4.46260	−0.174103
$658$	5.10044	0.198836
$659$	−13.0658	−0.508973	−0.254486	−	0.967076i	$-0.581906\pi$
$659$	−13.0658	−0.508973	−0.254486	+	0.967076i	$0.581906\pi$
$660$	−54.2701	−2.11246
$661$	−41.2686	−1.60516	−0.802582	−	0.596542i	$-0.796541\pi$
$661$	−41.2686	−1.60516	−0.802582	+	0.596542i	$0.796541\pi$
$662$	−24.5810	−0.955366
$663$	35.5935	1.38234
$664$	−7.20359	−0.279553
$665$	−5.44322	−0.211079
$666$	5.80538	0.224954
$667$	−35.8414	−1.38779
$668$	−24.0215	−0.929420
$669$	0.711200	0.0274966
$670$	0	0
$671$	23.9106	0.923060
$672$	17.0063	0.656031
$673$	0.800561	0.0308594	0.0154297	−	0.999881i	$-0.495088\pi$
$673$	0.800561	0.0308594	0.0154297	+	0.999881i	$0.495088\pi$
$674$	−41.8913	−1.61359
$675$	−85.5548	−3.29300
$676$	−13.5928	−0.522801
$677$	22.0457	0.847285	0.423642	−	0.905830i	$-0.360751\pi$
$677$	22.0457	0.847285	0.423642	+	0.905830i	$0.360751\pi$
$678$	3.36215	0.129123
$679$	−5.53740	−0.212506
$680$	−27.9404	−1.07147
$681$	−5.69597	−0.218270
$682$	7.74725	0.296658
$683$	35.3055	1.35093	0.675463	−	0.737394i	$-0.263944\pi$
$683$	35.3055	1.35093	0.675463	+	0.737394i	$0.263944\pi$
$684$	11.0900	0.424038
$685$	46.2251	1.76617
$686$	−21.2382	−0.810878
$687$	35.4689	1.35322
$688$	30.8373	1.17566
$689$	0.890593	0.0339289
$690$	147.256	5.60595
$691$	4.45219	0.169369	0.0846846	−	0.996408i	$-0.473012\pi$
$691$	4.45219	0.169369	0.0846846	+	0.996408i	$0.473012\pi$
$692$	7.88230	0.299640
$693$	−13.3878	−0.508560
$694$	−19.9986	−0.759135
$695$	−82.1655	−3.11672
$696$	−16.0256	−0.607450
$697$	69.5804	2.63555
$698$	67.4439	2.55279
$699$	−38.3595	−1.45089
$700$	17.2382	0.651542
$701$	−0.411987	−0.0155605	−0.00778027	−	0.999970i	$-0.502477\pi$
$701$	−0.411987	−0.0155605	−0.00778027	+	0.999970i	$0.502477\pi$
$702$	−22.3851	−0.844871
$703$	0.880181	0.0331967
$704$	9.83516	0.370677
$705$	39.3836	1.48327
$706$	62.8615	2.36582
$707$	3.53740	0.133038
$708$	14.5318	0.546139
$709$	8.22923	0.309055	0.154528	−	0.987988i	$-0.450614\pi$
$709$	8.22923	0.309055	0.154528	+	0.987988i	$0.450614\pi$
$710$	−77.3691	−2.90361
$711$	−66.4647	−2.49262
$712$	−17.8760	−0.669933
$713$	−8.87940	−0.332536
$714$	29.6143	1.10829
$715$	24.9702	0.933833
$716$	−15.3553	−0.573855
$717$	38.0561	1.42123
$718$	−50.9557	−1.90165
$719$	−42.8704	−1.59880	−0.799399	−	0.600801i	$-0.794849\pi$
$719$	−42.8704	−1.59880	−0.799399	+	0.600801i	$0.794849\pi$
$720$	107.271	3.99775
$721$	9.41758	0.350729
$722$	−31.3747	−1.16764
$723$	28.3684	1.05503
$724$	−15.6156	−0.580348
$725$	−76.6988	−2.84852
$726$	10.6468	0.395140
$727$	−16.8310	−0.624228	−0.312114	−	0.950045i	$-0.601037\pi$
$727$	−16.8310	−0.624228	−0.312114	+	0.950045i	$0.601037\pi$
$728$	−1.65722	−0.0614207
$729$	−41.5831	−1.54011
$730$	6.92520	0.256313
$731$	41.6400	1.54011
$732$	33.3490	1.23262
$733$	−22.3628	−0.825990	−0.412995	−	0.910733i	$-0.635517\pi$
$733$	−22.3628	−0.825990	−0.412995	+	0.910733i	$0.635517\pi$
$734$	−65.0844	−2.40231
$735$	−77.4141	−2.85546
$736$	−44.1849	−1.62868
$737$	0	0
$738$	−103.864	−3.82327
$739$	31.1094	1.14438	0.572189	−	0.820122i	$-0.306094\pi$
$739$	31.1094	1.14438	0.572189	+	0.820122i	$0.306094\pi$
$740$	−3.80538	−0.139888
$741$	−8.05543	−0.295924
$742$	0.740987	0.0272025
$743$	−0.595527	−0.0218478	−0.0109239	−	0.999940i	$-0.503477\pi$
$743$	−0.595527	−0.0218478	−0.0109239	+	0.999940i	$0.503477\pi$
$744$	−3.97021	−0.145555
$745$	49.0844	1.79831
$746$	12.4626	0.456288
$747$	37.3449	1.36638
$748$	28.3566	1.03682
$749$	13.8671	0.506692
$750$	200.044	7.30459
$751$	10.8006	0.394118	0.197059	−	0.980392i	$-0.436861\pi$
$751$	10.8006	0.394118	0.197059	+	0.980392i	$0.436861\pi$
$752$	−15.2396	−0.555732
$753$	−1.66618	−0.0607191
$754$	−20.0680	−0.730832
$755$	37.8567	1.37774
$756$	−7.86707	−0.286123
$757$	−0.359457	−0.0130647	−0.00653235	−	0.999979i	$-0.502079\pi$
$757$	−0.359457	−0.0130647	−0.00653235	+	0.999979i	$0.502079\pi$
$758$	−12.6247	−0.458551
$759$	54.9121	1.99318
$760$	6.32340	0.229374
$761$	−38.4287	−1.39304	−0.696519	−	0.717538i	$-0.745269\pi$
$761$	−38.4287	−1.39304	−0.696519	+	0.717538i	$0.745269\pi$
$762$	26.8567	0.972914
$763$	−2.81309	−0.101841
$764$	−27.2292	−0.985119
$765$	144.849	5.23703
$766$	−50.1530	−1.81210
$767$	−6.68623	−0.241426
$768$	−59.8075	−2.15812
$769$	39.6081	1.42830	0.714152	−	0.699991i	$-0.246813\pi$
$769$	39.6081	1.42830	0.714152	+	0.699991i	$0.246813\pi$
$770$	20.7756	0.748700
$771$	−15.7860	−0.568519
$772$	21.0305	0.756903
$773$	−28.2140	−1.01479	−0.507393	−	0.861714i	$-0.669391\pi$
$773$	−28.2140	−1.01479	−0.507393	+	0.861714i	$0.669391\pi$
$774$	−62.1565	−2.23417
$775$	−19.0014	−0.682552
$776$	6.43281	0.230924
$777$	−1.48197	−0.0531655
$778$	−17.4328	−0.624997
$779$	−15.7473	−0.564204
$780$	34.8269	1.24700
$781$	−28.8511	−1.03237
$782$	−76.9425	−2.75146
$783$	35.0034	1.25092
$784$	29.9557	1.06984
$785$	44.8656	1.60132
$786$	−22.6170	−0.806722
$787$	−5.54155	−0.197535	−0.0987674	−	0.995111i	$-0.531490\pi$
$787$	−5.54155	−0.197535	−0.0987674	+	0.995111i	$0.531490\pi$
$788$	−4.45364	−0.158654
$789$	−17.5076	−0.623288
$790$	103.142	3.66963
$791$	−0.543668	−0.0193306
$792$	15.5526	0.552639
$793$	−15.3442	−0.544890
$794$	33.3836	1.18474
$795$	5.72161	0.202925
$796$	21.5693	0.764504
$797$	−46.0305	−1.63048	−0.815241	−	0.579122i	$-0.803396\pi$
$797$	−46.0305	−1.63048	−0.815241	+	0.579122i	$0.803396\pi$
$798$	−6.70224	−0.237257
$799$	−20.5783	−0.728007
$800$	−94.5533	−3.34296
$801$	92.6731	3.27444
$802$	−40.4764	−1.42927
$803$	2.58242	0.0911315
$804$	0	0
$805$	−23.8116	−0.839250
$806$	−4.97166	−0.175119
$807$	61.7431	2.17346
$808$	−4.10941	−0.144568
$809$	−12.2348	−0.430153	−0.215077	−	0.976597i	$-0.569000\pi$
$809$	−12.2348	−0.430153	−0.215077	+	0.976597i	$0.569000\pi$
$810$	−18.6918	−0.656764
$811$	28.5928	1.00403	0.502015	−	0.864859i	$-0.332592\pi$
$811$	28.5928	1.00403	0.502015	+	0.864859i	$0.332592\pi$
$812$	−7.05273	−0.247502
$813$	−51.4945	−1.80599
$814$	−3.35946	−0.117749
$815$	−19.2549	−0.674469
$816$	−88.4848	−3.09759
$817$	−9.42385	−0.329699
$818$	54.3512	1.90034
$819$	8.59138	0.300207
$820$	68.0817	2.37752
$821$	−7.05543	−0.246236	−0.123118	−	0.992392i	$-0.539289\pi$
$821$	−7.05543	−0.246236	−0.123118	+	0.992392i	$0.539289\pi$
$822$	56.9169	1.98521
$823$	−12.9204	−0.450376	−0.225188	−	0.974315i	$-0.572300\pi$
$823$	−12.9204	−0.450376	−0.225188	+	0.974315i	$0.572300\pi$
$824$	−10.9404	−0.381128
$825$	117.509	4.09114
$826$	−5.56304	−0.193563
$827$	38.5284	1.33977	0.669883	−	0.742467i	$-0.266344\pi$
$827$	38.5284	1.33977	0.669883	+	0.742467i	$0.266344\pi$
$828$	48.5139	1.68597
$829$	−23.2701	−0.808204	−0.404102	−	0.914714i	$-0.632416\pi$
$829$	−23.2701	−0.808204	−0.404102	+	0.914714i	$0.632416\pi$
$830$	−57.9530	−2.01158
$831$	−46.8823	−1.62633
$832$	−6.31154	−0.218813
$833$	40.4495	1.40149
$834$	−101.170	−3.50324
$835$	71.0069	2.45730
$836$	−6.41758	−0.221957
$837$	8.67178	0.299741
$838$	32.3580	1.11779
$839$	−26.9896	−0.931784	−0.465892	−	0.884842i	$-0.654266\pi$
$839$	−26.9896	−0.931784	−0.465892	+	0.884842i	$0.654266\pi$
$840$	−10.6468	−0.367350
$841$	2.38008	0.0820717
$842$	−3.55408	−0.122482
$843$	−36.6773	−1.26323
$844$	−1.46260	−0.0503447
$845$	40.1801	1.38224
$846$	30.7175	1.05609
$847$	−1.72161	−0.0591553
$848$	−2.21400	−0.0760290
$849$	54.8269	1.88165
$850$	−164.653	−5.64755
$851$	3.85039	0.131990
$852$	−40.2396	−1.37859
$853$	−0.660588	−0.0226181	−0.0113091	−	0.999936i	$-0.503600\pi$
$853$	−0.660588	−0.0226181	−0.0113091	+	0.999936i	$0.503600\pi$
$854$	−12.7666	−0.436865
$855$	−32.7819	−1.12112
$856$	−16.1094	−0.550608
$857$	21.0138	0.717817	0.358909	−	0.933373i	$-0.383149\pi$
$857$	21.0138	0.717817	0.358909	+	0.933373i	$0.383149\pi$
$858$	30.7458	1.04964
$859$	−33.0111	−1.12632	−0.563162	−	0.826347i	$-0.690415\pi$
$859$	−33.0111	−1.12632	−0.563162	+	0.826347i	$0.690415\pi$
$860$	40.7431	1.38933
$861$	26.5139	0.903591
$862$	3.22296	0.109774
$863$	23.2070	0.789974	0.394987	−	0.918687i	$-0.370749\pi$
$863$	23.2070	0.789974	0.394987	+	0.918687i	$0.370749\pi$
$864$	43.1517	1.46805
$865$	−23.2999	−0.792220
$866$	−26.7368	−0.908555
$867$	−70.8484	−2.40614
$868$	−1.74725	−0.0593056
$869$	38.4618	1.30473
$870$	−128.927	−4.37102
$871$	0	0
$872$	3.26798	0.110668
$873$	−33.3490	−1.12869
$874$	17.4134	0.589018
$875$	−32.3476	−1.09355
$876$	3.60179	0.121693
$877$	−12.5110	−0.422466	−0.211233	−	0.977436i	$-0.567748\pi$
$877$	−12.5110	−0.422466	−0.211233	+	0.977436i	$0.567748\pi$
$878$	31.0319	1.04728
$879$	−17.8165	−0.600934
$880$	−62.0755	−2.09256
$881$	44.8767	1.51193	0.755967	−	0.654609i	$-0.227167\pi$
$881$	44.8767	1.51193	0.755967	+	0.654609i	$0.227167\pi$
$882$	−60.3795	−2.03308
$883$	44.8823	1.51041	0.755205	−	0.655489i	$-0.227537\pi$
$883$	44.8823	1.51041	0.755205	+	0.655489i	$0.227537\pi$
$884$	−18.1973	−0.612042
$885$	−42.9557	−1.44394
$886$	−9.83102	−0.330280
$887$	−16.0852	−0.540089	−0.270044	−	0.962848i	$-0.587038\pi$
$887$	−16.0852	−0.540089	−0.270044	+	0.962848i	$0.587038\pi$
$888$	1.72161	0.0577735
$889$	−4.34278	−0.145652
$890$	−143.813	−4.82062
$891$	−6.97021	−0.233511
$892$	−0.363604	−0.0121743
$893$	4.65722	0.155848
$894$	60.4376	2.02134
$895$	45.3899	1.51722
$896$	6.63785	0.221755
$897$	−35.2389	−1.17659
$898$	42.0471	1.40313
$899$	7.77414	0.259282
$900$	103.817	3.46057
$901$	−2.98959	−0.0995976
$902$	60.1038	2.00124
$903$	15.8671	0.528023
$904$	0.631580	0.0210060
$905$	46.1592	1.53439
$906$	46.6129	1.54861
$907$	43.3539	1.43954	0.719771	−	0.694212i	$-0.244247\pi$
$907$	43.3539	1.43954	0.719771	+	0.694212i	$0.244247\pi$
$908$	2.91209	0.0966410
$909$	21.3040	0.706610
$910$	−13.3324	−0.441964
$911$	16.4841	0.546142	0.273071	−	0.961994i	$-0.411961\pi$
$911$	16.4841	0.546142	0.273071	+	0.961994i	$0.411961\pi$
$912$	20.0256	0.663115
$913$	−21.6108	−0.715212
$914$	29.8594	0.987660
$915$	−98.5789	−3.25892
$916$	−18.1336	−0.599151
$917$	3.65722	0.120772
$918$	75.1434	2.48010
$919$	0.874585	0.0288499	0.0144250	−	0.999896i	$-0.495408\pi$
$919$	0.874585	0.0288499	0.0144250	+	0.999896i	$0.495408\pi$
$920$	27.6620	0.911990
$921$	59.0963	1.94729
$922$	−17.5243	−0.577132
$923$	18.5147	0.609417
$924$	10.8054	0.355471
$925$	8.23964	0.270918
$926$	−3.19462	−0.104982
$927$	56.7175	1.86285
$928$	38.6850	1.26990
$929$	−20.4543	−0.671084	−0.335542	−	0.942025i	$-0.608919\pi$
$929$	−20.4543	−0.671084	−0.335542	+	0.942025i	$0.608919\pi$
$930$	−31.9404	−1.04737
$931$	−9.15442	−0.300024
$932$	19.6114	0.642394
$933$	53.1350	1.73956
$934$	4.66349	0.152594
$935$	−83.8213	−2.74125
$936$	−9.98062	−0.326227
$937$	−48.5991	−1.58766	−0.793832	−	0.608138i	$-0.791917\pi$
$937$	−48.5991	−1.58766	−0.793832	+	0.608138i	$0.791917\pi$
$938$	0	0
$939$	8.63785	0.281885
$940$	−20.1350	−0.656733
$941$	46.6939	1.52218	0.761090	−	0.648647i	$-0.224665\pi$
$941$	46.6939	1.52218	0.761090	+	0.648647i	$0.224665\pi$
$942$	55.2430	1.79991
$943$	−68.8871	−2.24327
$944$	16.6218	0.540995
$945$	23.2549	0.756481
$946$	35.9688	1.16945
$947$	−5.14961	−0.167340	−0.0836699	−	0.996494i	$-0.526664\pi$
$947$	−5.14961	−0.167340	−0.0836699	+	0.996494i	$0.526664\pi$
$948$	53.6441	1.74228
$949$	−1.65722	−0.0537957
$950$	37.2638	1.20900
$951$	−5.45219	−0.176799
$952$	5.56304	0.180299
$953$	−3.44949	−0.111740	−0.0558700	−	0.998438i	$-0.517793\pi$
$953$	−3.44949	−0.111740	−0.0558700	+	0.998438i	$0.517793\pi$
$954$	4.46260	0.144482
$955$	80.4889	2.60456
$956$	−19.4563	−0.629263
$957$	−48.0769	−1.55411
$958$	−12.8310	−0.414551
$959$	−9.20359	−0.297199
$960$	−40.5485	−1.30870
$961$	−29.0740	−0.937872
$962$	2.15587	0.0695081
$963$	83.5146	2.69122
$964$	−14.5035	−0.467125
$965$	−62.1655	−2.00118
$966$	−29.3193	−0.943332
$967$	−3.55678	−0.114378	−0.0571891	−	0.998363i	$-0.518214\pi$
$967$	−3.55678	−0.114378	−0.0571891	+	0.998363i	$0.518214\pi$
$968$	2.00000	0.0642824
$969$	27.0409	0.868678
$970$	51.7521	1.66166
$971$	28.9765	0.929899	0.464950	−	0.885337i	$-0.346072\pi$
$971$	28.9765	0.929899	0.464950	+	0.885337i	$0.346072\pi$
$972$	17.6960	0.567599
$973$	16.3595	0.524460
$974$	−34.2445	−1.09726
$975$	−75.4093	−2.41503
$976$	38.1455	1.22101
$977$	−29.7770	−0.952652	−0.476326	−	0.879269i	$-0.658032\pi$
$977$	−29.7770	−0.952652	−0.476326	+	0.879269i	$0.658032\pi$
$978$	−23.7085	−0.758114
$979$	−53.6281	−1.71396
$980$	39.5783	1.26428
$981$	−16.9419	−0.540912
$982$	26.1905	0.835772
$983$	−22.8269	−0.728064	−0.364032	−	0.931386i	$-0.618600\pi$
$983$	−22.8269	−0.728064	−0.364032	+	0.931386i	$0.618600\pi$
$984$	−30.8012	−0.981907
$985$	13.1648	0.419467
$986$	67.3651	2.14534
$987$	−7.84143	−0.249595
$988$	4.11837	0.131023
$989$	−41.2251	−1.31088
$990$	125.121	3.97661
$991$	5.56786	0.176869	0.0884344	−	0.996082i	$-0.471814\pi$
$991$	5.56786	0.176869	0.0884344	+	0.996082i	$0.471814\pi$
$992$	9.58387	0.304288
$993$	37.7908	1.19926
$994$	15.4045	0.488600
$995$	−63.7583	−2.02128
$996$	−30.1413	−0.955064
$997$	−55.2292	−1.74913	−0.874564	−	0.484911i	$-0.838852\pi$
$997$	−55.2292	−1.74913	−0.874564	+	0.484911i	$0.838852\pi$
$998$	63.6114	2.01358
$999$	−3.76036	−0.118973

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	211.2.a.c.1.3	✓	3
3.2	odd	2		1899.2.a.e.1.1		3
4.3	odd	2		3376.2.a.m.1.3		3
5.4	even	2		5275.2.a.h.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
211.2.a.c.1.3	✓	3	1.1	even	1	trivial
1899.2.a.e.1.1		3	3.2	odd	2
3376.2.a.m.1.3		3	4.3	odd	2
5275.2.a.h.1.1		3	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	211.a (trivial)

\(f(q)\)	\(=\)	\(q+1.86081 q^{2} -2.86081 q^{3} +1.46260 q^{4} -4.32340 q^{5} -5.32340 q^{6} +0.860806 q^{7} -1.00000 q^{8} +5.18421 q^{9} +O(q^{10})\)	\(q+1.86081 q^{2} -2.86081 q^{3} +1.46260 q^{4} -4.32340 q^{5} -5.32340 q^{6} +0.860806 q^{7} -1.00000 q^{8} +5.18421 q^{9} -8.04502 q^{10} -3.00000 q^{11} -4.18421 q^{12} +1.92520 q^{13} +1.60179 q^{14} +12.3684 q^{15} -4.78600 q^{16} -6.46260 q^{17} +9.64681 q^{18} +1.46260 q^{19} -6.32340 q^{20} -2.46260 q^{21} -5.58242 q^{22} +6.39821 q^{23} +2.86081 q^{24} +13.6918 q^{25} +3.58242 q^{26} -6.24860 q^{27} +1.25901 q^{28} -5.60179 q^{29} +23.0152 q^{30} -1.38780 q^{31} -6.90582 q^{32} +8.58242 q^{33} -12.0256 q^{34} -3.72161 q^{35} +7.58242 q^{36} +0.601793 q^{37} +2.72161 q^{38} -5.50761 q^{39} +4.32340 q^{40} -10.7666 q^{41} -4.58242 q^{42} -6.44322 q^{43} -4.38780 q^{44} -22.4134 q^{45} +11.9058 q^{46} +3.18421 q^{47} +13.6918 q^{48} -6.25901 q^{49} +25.4778 q^{50} +18.4882 q^{51} +2.81579 q^{52} +0.462598 q^{53} -11.6274 q^{54} +12.9702 q^{55} -0.860806 q^{56} -4.18421 q^{57} -10.4238 q^{58} -3.47301 q^{59} +18.0900 q^{60} -7.97021 q^{61} -2.58242 q^{62} +4.46260 q^{63} -3.27839 q^{64} -8.32340 q^{65} +15.9702 q^{66} -9.45219 q^{68} -18.3040 q^{69} -6.92520 q^{70} +9.61702 q^{71} -5.18421 q^{72} -0.860806 q^{73} +1.11982 q^{74} -39.1697 q^{75} +2.13919 q^{76} -2.58242 q^{77} -10.2486 q^{78} -12.8206 q^{79} +20.6918 q^{80} +2.32340 q^{81} -20.0346 q^{82} +7.20359 q^{83} -3.60179 q^{84} +27.9404 q^{85} -11.9896 q^{86} +16.0256 q^{87} +3.00000 q^{88} +17.8760 q^{89} -41.7071 q^{90} +1.65722 q^{91} +9.35801 q^{92} +3.97021 q^{93} +5.92520 q^{94} -6.32340 q^{95} +19.7562 q^{96} -6.43281 q^{97} -11.6468 q^{98} -15.5526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} - 8 q^{6} - 3 q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 - 8 * q^6 - 3 * q^7 - 3 * q^8 + 2 * q^9	\( 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} - 8 q^{6} - 3 q^{7} - 3 q^{8} + 2 q^{9} - 5 q^{10} - 9 q^{11} + q^{12} + q^{13} + 8 q^{14} + 10 q^{15} - 4 q^{16} - 17 q^{17} + 13 q^{18} + 2 q^{19} - 11 q^{20} - 5 q^{21} + 16 q^{23} + 3 q^{24} + 6 q^{25} - 6 q^{26} - 6 q^{27} - 5 q^{28} - 20 q^{29} + 26 q^{30} + 3 q^{31} + 4 q^{32} + 9 q^{33} + 3 q^{34} + 6 q^{36} + 5 q^{37} - 3 q^{38} + 5 q^{39} + 5 q^{40} - 2 q^{41} + 3 q^{42} + 3 q^{43} - 6 q^{44} - 21 q^{45} + 11 q^{46} - 4 q^{47} + 6 q^{48} - 10 q^{49} + 31 q^{50} + 14 q^{51} + 22 q^{52} - q^{53} + q^{54} + 15 q^{55} + 3 q^{56} + q^{57} + 11 q^{58} - 12 q^{59} + 16 q^{60} + 9 q^{62} + 11 q^{63} - 21 q^{64} - 17 q^{65} + 24 q^{66} - 22 q^{68} - 27 q^{69} - 16 q^{70} - 11 q^{71} - 2 q^{72} + 3 q^{73} - 11 q^{74} - 37 q^{75} + 12 q^{76} + 9 q^{77} - 18 q^{78} - 5 q^{79} + 27 q^{80} - q^{81} - 37 q^{82} + 28 q^{83} - 14 q^{84} + 36 q^{85} - 32 q^{86} + 9 q^{87} + 9 q^{88} + 5 q^{89} - 47 q^{90} - 7 q^{91} - 3 q^{92} - 12 q^{93} + 13 q^{94} - 11 q^{95} + 25 q^{96} + 7 q^{97} - 19 q^{98} - 6 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 - 8 * q^6 - 3 * q^7 - 3 * q^8 + 2 * q^9 - 5 * q^10 - 9 * q^11 + q^12 + q^13 + 8 * q^14 + 10 * q^15 - 4 * q^16 - 17 * q^17 + 13 * q^18 + 2 * q^19 - 11 * q^20 - 5 * q^21 + 16 * q^23 + 3 * q^24 + 6 * q^25 - 6 * q^26 - 6 * q^27 - 5 * q^28 - 20 * q^29 + 26 * q^30 + 3 * q^31 + 4 * q^32 + 9 * q^33 + 3 * q^34 + 6 * q^36 + 5 * q^37 - 3 * q^38 + 5 * q^39 + 5 * q^40 - 2 * q^41 + 3 * q^42 + 3 * q^43 - 6 * q^44 - 21 * q^45 + 11 * q^46 - 4 * q^47 + 6 * q^48 - 10 * q^49 + 31 * q^50 + 14 * q^51 + 22 * q^52 - q^53 + q^54 + 15 * q^55 + 3 * q^56 + q^57 + 11 * q^58 - 12 * q^59 + 16 * q^60 + 9 * q^62 + 11 * q^63 - 21 * q^64 - 17 * q^65 + 24 * q^66 - 22 * q^68 - 27 * q^69 - 16 * q^70 - 11 * q^71 - 2 * q^72 + 3 * q^73 - 11 * q^74 - 37 * q^75 + 12 * q^76 + 9 * q^77 - 18 * q^78 - 5 * q^79 + 27 * q^80 - q^81 - 37 * q^82 + 28 * q^83 - 14 * q^84 + 36 * q^85 - 32 * q^86 + 9 * q^87 + 9 * q^88 + 5 * q^89 - 47 * q^90 - 7 * q^91 - 3 * q^92 - 12 * q^93 + 13 * q^94 - 11 * q^95 + 25 * q^96 + 7 * q^97 - 19 * q^98 - 6 * q^99

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