LMFDB - Embedded newform 6047.2.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6047,2,Mod(1,6047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6047, 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("6047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6047 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6047.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:	$48.2855381023$
Analytic rank:	$1$
Dimension:	$217$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57504 q^{2} +1.64822 q^{3} +4.63081 q^{4} -3.44910 q^{5} -4.24422 q^{6} -0.596125 q^{7} -6.77442 q^{8} -0.283374 q^{9} +O(q^{10})$	\(q-2.57504 q^{2} +1.64822 q^{3} +4.63081 q^{4} -3.44910 q^{5} -4.24422 q^{6} -0.596125 q^{7} -6.77442 q^{8} -0.283374 q^{9} +8.88154 q^{10} +5.70669 q^{11} +7.63258 q^{12} +1.47414 q^{13} +1.53504 q^{14} -5.68486 q^{15} +8.18275 q^{16} +1.39828 q^{17} +0.729699 q^{18} -4.14607 q^{19} -15.9721 q^{20} -0.982545 q^{21} -14.6949 q^{22} -2.33910 q^{23} -11.1657 q^{24} +6.89626 q^{25} -3.79597 q^{26} -5.41172 q^{27} -2.76054 q^{28} +8.25188 q^{29} +14.6387 q^{30} -0.594481 q^{31} -7.52204 q^{32} +9.40588 q^{33} -3.60062 q^{34} +2.05609 q^{35} -1.31225 q^{36} -2.68931 q^{37} +10.6763 q^{38} +2.42971 q^{39} +23.3656 q^{40} -0.691211 q^{41} +2.53009 q^{42} -8.85577 q^{43} +26.4266 q^{44} +0.977385 q^{45} +6.02326 q^{46} +4.31958 q^{47} +13.4870 q^{48} -6.64463 q^{49} -17.7581 q^{50} +2.30467 q^{51} +6.82647 q^{52} -2.55497 q^{53} +13.9354 q^{54} -19.6829 q^{55} +4.03840 q^{56} -6.83363 q^{57} -21.2489 q^{58} -2.50149 q^{59} -26.3255 q^{60} -1.09221 q^{61} +1.53081 q^{62} +0.168927 q^{63} +3.00401 q^{64} -5.08446 q^{65} -24.2205 q^{66} +5.66288 q^{67} +6.47516 q^{68} -3.85534 q^{69} -5.29451 q^{70} +1.96944 q^{71} +1.91970 q^{72} -7.01042 q^{73} +6.92508 q^{74} +11.3665 q^{75} -19.1997 q^{76} -3.40190 q^{77} -6.25659 q^{78} +5.98518 q^{79} -28.2231 q^{80} -8.06958 q^{81} +1.77989 q^{82} +0.0878307 q^{83} -4.54997 q^{84} -4.82280 q^{85} +22.8039 q^{86} +13.6009 q^{87} -38.6595 q^{88} +0.350973 q^{89} -2.51680 q^{90} -0.878774 q^{91} -10.8319 q^{92} -0.979835 q^{93} -11.1231 q^{94} +14.3002 q^{95} -12.3980 q^{96} +6.42779 q^{97} +17.1102 q^{98} -1.61713 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) $ 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9} - 46 q^{10} - 32 q^{11} - 72 q^{12} - 80 q^{13} - 22 q^{14} - 43 q^{15} + 122 q^{16} - 61 q^{17} - 88 q^{18} - 43 q^{19} - 41 q^{20} - 61 q^{21} - 93 q^{22} - 60 q^{23} - 41 q^{24} + 26 q^{25} - 9 q^{26} - 93 q^{27} - 126 q^{28} - 47 q^{29} - 36 q^{30} - 100 q^{31} - 114 q^{32} - 133 q^{33} - 75 q^{34} - 37 q^{35} + 75 q^{36} - 264 q^{37} - 35 q^{38} - 47 q^{39} - 118 q^{40} - 72 q^{41} - 64 q^{42} - 107 q^{43} - 59 q^{44} - 69 q^{45} - 111 q^{46} - 54 q^{47} - 135 q^{48} + 33 q^{49} - 42 q^{50} - 26 q^{51} - 173 q^{52} - 103 q^{53} - 28 q^{54} - 78 q^{55} - 44 q^{56} - 205 q^{57} - 189 q^{58} - 38 q^{59} - 105 q^{60} - 108 q^{61} - 14 q^{62} - 116 q^{63} + 39 q^{64} - 146 q^{65} + 5 q^{66} - 206 q^{67} - 62 q^{68} - 55 q^{69} - 125 q^{70} - 78 q^{71} - 225 q^{72} - 326 q^{73} + 3 q^{74} - 95 q^{75} - 84 q^{76} - 79 q^{77} - 86 q^{78} - 117 q^{79} - 39 q^{80} + q^{81} - 96 q^{82} - 23 q^{83} - 57 q^{84} - 224 q^{85} - 7 q^{86} - 45 q^{87} - 250 q^{88} - 104 q^{89} - 36 q^{90} - 96 q^{91} - 137 q^{92} - 155 q^{93} - 48 q^{94} - 38 q^{95} - 33 q^{96} - 447 q^{97} - 46 q^{98} - 94 q^{99}+O(q^{100}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9 - 46 * q^10 - 32 * q^11 - 72 * q^12 - 80 * q^13 - 22 * q^14 - 43 * q^15 + 122 * q^16 - 61 * q^17 - 88 * q^18 - 43 * q^19 - 41 * q^20 - 61 * q^21 - 93 * q^22 - 60 * q^23 - 41 * q^24 + 26 * q^25 - 9 * q^26 - 93 * q^27 - 126 * q^28 - 47 * q^29 - 36 * q^30 - 100 * q^31 - 114 * q^32 - 133 * q^33 - 75 * q^34 - 37 * q^35 + 75 * q^36 - 264 * q^37 - 35 * q^38 - 47 * q^39 - 118 * q^40 - 72 * q^41 - 64 * q^42 - 107 * q^43 - 59 * q^44 - 69 * q^45 - 111 * q^46 - 54 * q^47 - 135 * q^48 + 33 * q^49 - 42 * q^50 - 26 * q^51 - 173 * q^52 - 103 * q^53 - 28 * q^54 - 78 * q^55 - 44 * q^56 - 205 * q^57 - 189 * q^58 - 38 * q^59 - 105 * q^60 - 108 * q^61 - 14 * q^62 - 116 * q^63 + 39 * q^64 - 146 * q^65 + 5 * q^66 - 206 * q^67 - 62 * q^68 - 55 * q^69 - 125 * q^70 - 78 * q^71 - 225 * q^72 - 326 * q^73 + 3 * q^74 - 95 * q^75 - 84 * q^76 - 79 * q^77 - 86 * q^78 - 117 * q^79 - 39 * q^80 + q^81 - 96 * q^82 - 23 * q^83 - 57 * q^84 - 224 * q^85 - 7 * q^86 - 45 * q^87 - 250 * q^88 - 104 * q^89 - 36 * q^90 - 96 * q^91 - 137 * q^92 - 155 * q^93 - 48 * q^94 - 38 * q^95 - 33 * q^96 - 447 * q^97 - 46 * q^98 - 94 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.57504	−1.82082	−0.910412	−	0.413702i	$-0.864236\pi$
$2$	−2.57504	−1.82082	−0.910412	+	0.413702i	$0.864236\pi$
$3$	1.64822	0.951600	0.475800	−	0.879554i	$-0.342159\pi$
$3$	1.64822	0.951600	0.475800	+	0.879554i	$0.342159\pi$
$4$	4.63081	2.31540
$5$	−3.44910	−1.54248	−0.771241	−	0.636543i	$-0.780364\pi$
$5$	−3.44910	−1.54248	−0.771241	+	0.636543i	$0.780364\pi$
$6$	−4.24422	−1.73270
$7$	−0.596125	−0.225314	−0.112657	−	0.993634i	$-0.535936\pi$
$7$	−0.596125	−0.225314	−0.112657	+	0.993634i	$0.535936\pi$
$8$	−6.77442	−2.39512
$9$	−0.283374	−0.0944581
$10$	8.88154	2.80859
$11$	5.70669	1.72063	0.860316	−	0.509761i	$-0.170266\pi$
$11$	5.70669	1.72063	0.860316	+	0.509761i	$0.170266\pi$
$12$	7.63258	2.20334
$13$	1.47414	0.408854	0.204427	−	0.978882i	$-0.434467\pi$
$13$	1.47414	0.408854	0.204427	+	0.978882i	$0.434467\pi$
$14$	1.53504	0.410258
$15$	−5.68486	−1.46783
$16$	8.18275	2.04569
$17$	1.39828	0.339133	0.169566	−	0.985519i	$-0.445763\pi$
$17$	1.39828	0.339133	0.169566	+	0.985519i	$0.445763\pi$
$18$	0.729699	0.171992
$19$	−4.14607	−0.951174	−0.475587	−	0.879669i	$-0.657764\pi$
$19$	−4.14607	−0.951174	−0.475587	+	0.879669i	$0.657764\pi$
$20$	−15.9721	−3.57147
$21$	−0.982545	−0.214409
$22$	−14.6949	−3.13297
$23$	−2.33910	−0.487735	−0.243868	−	0.969809i	$-0.578416\pi$
$23$	−2.33910	−0.487735	−0.243868	+	0.969809i	$0.578416\pi$
$24$	−11.1657	−2.27919
$25$	6.89626	1.37925
$26$	−3.79597	−0.744451
$27$	−5.41172	−1.04149
$28$	−2.76054	−0.521693
$29$	8.25188	1.53234	0.766168	−	0.642641i	$-0.222161\pi$
$29$	8.25188	1.53234	0.766168	+	0.642641i	$0.222161\pi$
$30$	14.6387	2.67265
$31$	−0.594481	−0.106772	−0.0533860	−	0.998574i	$-0.517001\pi$
$31$	−0.594481	−0.106772	−0.0533860	+	0.998574i	$0.517001\pi$
$32$	−7.52204	−1.32972
$33$	9.40588	1.63735
$34$	−3.60062	−0.617501
$35$	2.05609	0.347543
$36$	−1.31225	−0.218709
$37$	−2.68931	−0.442120	−0.221060	−	0.975260i	$-0.570952\pi$
$37$	−2.68931	−0.442120	−0.221060	+	0.975260i	$0.570952\pi$
$38$	10.6763	1.73192
$39$	2.42971	0.389065
$40$	23.3656	3.69443
$41$	−0.691211	−0.107949	−0.0539745	−	0.998542i	$-0.517189\pi$
$41$	−0.691211	−0.107949	−0.0539745	+	0.998542i	$0.517189\pi$
$42$	2.53009	0.390401
$43$	−8.85577	−1.35049	−0.675246	−	0.737592i	$-0.735963\pi$
$43$	−8.85577	−1.35049	−0.675246	+	0.737592i	$0.735963\pi$
$44$	26.4266	3.98396
$45$	0.977385	0.145700
$46$	6.02326	0.888081
$47$	4.31958	0.630076	0.315038	−	0.949079i	$-0.397983\pi$
$47$	4.31958	0.630076	0.315038	+	0.949079i	$0.397983\pi$
$48$	13.4870	1.94668
$49$	−6.64463	−0.949234
$50$	−17.7581	−2.51138
$51$	2.30467	0.322718
$52$	6.82647	0.946661
$53$	−2.55497	−0.350952	−0.175476	−	0.984484i	$-0.556146\pi$
$53$	−2.55497	−0.350952	−0.175476	+	0.984484i	$0.556146\pi$
$54$	13.9354	1.89636
$55$	−19.6829	−2.65404
$56$	4.03840	0.539654
$57$	−6.83363	−0.905137
$58$	−21.2489	−2.79011
$59$	−2.50149	−0.325666	−0.162833	−	0.986654i	$-0.552063\pi$
$59$	−2.50149	−0.325666	−0.162833	+	0.986654i	$0.552063\pi$
$60$	−26.3255	−3.39861
$61$	−1.09221	−0.139843	−0.0699213	−	0.997553i	$-0.522275\pi$
$61$	−1.09221	−0.139843	−0.0699213	+	0.997553i	$0.522275\pi$
$62$	1.53081	0.194413
$63$	0.168927	0.0212828
$64$	3.00401	0.375501
$65$	−5.08446	−0.630650
$66$	−24.2205	−2.98133
$67$	5.66288	0.691831	0.345915	−	0.938266i	$-0.387568\pi$
$67$	5.66288	0.691831	0.345915	+	0.938266i	$0.387568\pi$
$68$	6.47516	0.785229
$69$	−3.85534	−0.464129
$70$	−5.29451	−0.632815
$71$	1.96944	0.233729	0.116865	−	0.993148i	$-0.462716\pi$
$71$	1.96944	0.233729	0.116865	+	0.993148i	$0.462716\pi$
$72$	1.91970	0.226238
$73$	−7.01042	−0.820508	−0.410254	−	0.911971i	$-0.634560\pi$
$73$	−7.01042	−0.820508	−0.410254	+	0.911971i	$0.634560\pi$
$74$	6.92508	0.805024
$75$	11.3665	1.31250
$76$	−19.1997	−2.20235
$77$	−3.40190	−0.387683
$78$	−6.25659	−0.708419
$79$	5.98518	0.673386	0.336693	−	0.941615i	$-0.390692\pi$
$79$	5.98518	0.673386	0.336693	+	0.941615i	$0.390692\pi$
$80$	−28.2231	−3.15544
$81$	−8.06958	−0.896620
$82$	1.77989	0.196556
$83$	0.0878307	0.00964067	0.00482034	−	0.999988i	$-0.498466\pi$
$83$	0.0878307	0.00964067	0.00482034	+	0.999988i	$0.498466\pi$
$84$	−4.54997	−0.496443
$85$	−4.82280	−0.523106
$86$	22.8039	2.45901
$87$	13.6009	1.45817
$88$	−38.6595	−4.12112
$89$	0.350973	0.0372031	0.0186015	−	0.999827i	$-0.494079\pi$
$89$	0.350973	0.0372031	0.0186015	+	0.999827i	$0.494079\pi$
$90$	−2.51680	−0.265294
$91$	−0.878774	−0.0921205
$92$	−10.8319	−1.12930
$93$	−0.979835	−0.101604
$94$	−11.1231	−1.14726
$95$	14.3002	1.46717
$96$	−12.3980	−1.26536
$97$	6.42779	0.652644	0.326322	−	0.945259i	$-0.394191\pi$
$97$	6.42779	0.652644	0.326322	+	0.945259i	$0.394191\pi$
$98$	17.1102	1.72839
$99$	−1.61713	−0.162528
$100$	31.9352	3.19352
$101$	3.75050	0.373189	0.186594	−	0.982437i	$-0.440255\pi$
$101$	3.75050	0.373189	0.186594	+	0.982437i	$0.440255\pi$
$102$	−5.93461	−0.587614
$103$	2.65885	0.261985	0.130992	−	0.991383i	$-0.458184\pi$
$103$	2.65885	0.261985	0.130992	+	0.991383i	$0.458184\pi$
$104$	−9.98646	−0.979253
$105$	3.38889	0.330722
$106$	6.57914	0.639022
$107$	−2.83515	−0.274084	−0.137042	−	0.990565i	$-0.543760\pi$
$107$	−2.83515	−0.274084	−0.137042	+	0.990565i	$0.543760\pi$
$108$	−25.0606	−2.41146
$109$	−8.78429	−0.841382	−0.420691	−	0.907204i	$-0.638212\pi$
$109$	−8.78429	−0.841382	−0.420691	+	0.907204i	$0.638212\pi$
$110$	50.6842	4.83255
$111$	−4.43258	−0.420722
$112$	−4.87794	−0.460922
$113$	18.5214	1.74235	0.871174	−	0.490975i	$-0.163359\pi$
$113$	18.5214	1.74235	0.871174	+	0.490975i	$0.163359\pi$
$114$	17.5968	1.64810
$115$	8.06777	0.752323
$116$	38.2128	3.54797
$117$	−0.417735	−0.0386196
$118$	6.44141	0.592980
$119$	−0.833550	−0.0764114
$120$	38.5116	3.51562
$121$	21.5663	1.96057
$122$	2.81247	0.254629
$123$	−1.13927	−0.102724
$124$	−2.75293	−0.247220
$125$	−6.54039	−0.584990
$126$	−0.434992	−0.0387522
$127$	−6.86859	−0.609489	−0.304744	−	0.952434i	$-0.598571\pi$
$127$	−6.86859	−0.609489	−0.304744	+	0.952434i	$0.598571\pi$
$128$	7.30865	0.646000
$129$	−14.5963	−1.28513
$130$	13.0927	1.14830
$131$	6.50421	0.568276	0.284138	−	0.958783i	$-0.408293\pi$
$131$	6.50421	0.568276	0.284138	+	0.958783i	$0.408293\pi$
$132$	43.5568	3.79113
$133$	2.47158	0.214313
$134$	−14.5821	−1.25970
$135$	18.6655	1.60647
$136$	−9.47253	−0.812263
$137$	−9.06672	−0.774623	−0.387311	−	0.921949i	$-0.626596\pi$
$137$	−9.06672	−0.774623	−0.387311	+	0.921949i	$0.626596\pi$
$138$	9.92765	0.845097
$139$	9.80496	0.831646	0.415823	−	0.909446i	$-0.363494\pi$
$139$	9.80496	0.831646	0.415823	+	0.909446i	$0.363494\pi$
$140$	9.52137	0.804702
$141$	7.11962	0.599580
$142$	−5.07137	−0.425580
$143$	8.41248	0.703487
$144$	−2.31878	−0.193232
$145$	−28.4615	−2.36360
$146$	18.0521	1.49400
$147$	−10.9518	−0.903290
$148$	−12.4537	−1.02369
$149$	14.2751	1.16946	0.584731	−	0.811227i	$-0.301200\pi$
$149$	14.2751	1.16946	0.584731	+	0.811227i	$0.301200\pi$
$150$	−29.2693	−2.38983
$151$	−6.20078	−0.504612	−0.252306	−	0.967647i	$-0.581189\pi$
$151$	−6.20078	−0.504612	−0.252306	+	0.967647i	$0.581189\pi$
$152$	28.0872	2.27817
$153$	−0.396237	−0.0320338
$154$	8.76002	0.705902
$155$	2.05042	0.164694
$156$	11.2515	0.900843
$157$	7.85452	0.626859	0.313429	−	0.949612i	$-0.398522\pi$
$157$	7.85452	0.626859	0.313429	+	0.949612i	$0.398522\pi$
$158$	−15.4121	−1.22612
$159$	−4.21115	−0.333966
$160$	25.9442	2.05107
$161$	1.39439	0.109894
$162$	20.7794	1.63259
$163$	3.00643	0.235482	0.117741	−	0.993044i	$-0.462435\pi$
$163$	3.00643	0.235482	0.117741	+	0.993044i	$0.462435\pi$
$164$	−3.20086	−0.249945
$165$	−32.4418	−2.52559
$166$	−0.226167	−0.0175540
$167$	−13.5775	−1.05066	−0.525331	−	0.850898i	$-0.676058\pi$
$167$	−13.5775	−1.05066	−0.525331	+	0.850898i	$0.676058\pi$
$168$	6.65617	0.513535
$169$	−10.8269	−0.832839
$170$	12.4189	0.952485
$171$	1.17489	0.0898461
$172$	−41.0094	−3.12693
$173$	−2.80389	−0.213176	−0.106588	−	0.994303i	$-0.533993\pi$
$173$	−2.80389	−0.213176	−0.106588	+	0.994303i	$0.533993\pi$
$174$	−35.0228	−2.65507
$175$	−4.11103	−0.310765
$176$	46.6964	3.51988
$177$	−4.12300	−0.309903
$178$	−0.903768	−0.0677403
$179$	2.89567	0.216432	0.108216	−	0.994127i	$-0.465486\pi$
$179$	2.89567	0.216432	0.108216	+	0.994127i	$0.465486\pi$
$180$	4.52608	0.337354
$181$	−13.3467	−0.992056	−0.496028	−	0.868307i	$-0.665209\pi$
$181$	−13.3467	−0.992056	−0.496028	+	0.868307i	$0.665209\pi$
$182$	2.26287	0.167735
$183$	−1.80019	−0.133074
$184$	15.8460	1.16818
$185$	9.27570	0.681963
$186$	2.52311	0.185003
$187$	7.97955	0.583522
$188$	20.0031	1.45888
$189$	3.22606	0.234661
$190$	−36.8235	−2.67146
$191$	14.9228	1.07978	0.539889	−	0.841736i	$-0.318466\pi$
$191$	14.9228	1.07978	0.539889	+	0.841736i	$0.318466\pi$
$192$	4.95126	0.357326
$193$	−13.9743	−1.00589	−0.502945	−	0.864318i	$-0.667750\pi$
$193$	−13.9743	−1.00589	−0.502945	+	0.864318i	$0.667750\pi$
$194$	−16.5518	−1.18835
$195$	−8.38031	−0.600126
$196$	−30.7700	−2.19786
$197$	−27.8026	−1.98085	−0.990425	−	0.138049i	$-0.955917\pi$
$197$	−27.8026	−1.98085	−0.990425	+	0.138049i	$0.955917\pi$
$198$	4.16417	0.295934
$199$	21.1328	1.49807	0.749033	−	0.662533i	$-0.230519\pi$
$199$	21.1328	1.49807	0.749033	+	0.662533i	$0.230519\pi$
$200$	−46.7182	−3.30347
$201$	9.33366	0.658346
$202$	−9.65768	−0.679512
$203$	−4.91915	−0.345257
$204$	10.6725	0.747223
$205$	2.38405	0.166509
$206$	−6.84664	−0.477028
$207$	0.662840	0.0460706
$208$	12.0625	0.836387
$209$	−23.6604	−1.63662
$210$	−8.72651	−0.602187
$211$	−9.20582	−0.633755	−0.316877	−	0.948467i	$-0.602634\pi$
$211$	−9.20582	−0.633755	−0.316877	+	0.948467i	$0.602634\pi$
$212$	−11.8316	−0.812595
$213$	3.24606	0.222417
$214$	7.30060	0.499059
$215$	30.5444	2.08311
$216$	36.6612	2.49448
$217$	0.354385	0.0240572
$218$	22.6198	1.53201
$219$	−11.5547	−0.780795
$220$	−91.1478	−6.14518
$221$	2.06126	0.138656
$222$	11.4140	0.766061
$223$	−24.1241	−1.61547	−0.807734	−	0.589547i	$-0.799306\pi$
$223$	−24.1241	−1.61547	−0.807734	+	0.589547i	$0.799306\pi$
$224$	4.48408	0.299605
$225$	−1.95422	−0.130282
$226$	−47.6933	−3.17251
$227$	−19.5944	−1.30053	−0.650264	−	0.759709i	$-0.725342\pi$
$227$	−19.5944	−1.30053	−0.650264	+	0.759709i	$0.725342\pi$
$228$	−31.6452	−2.09576
$229$	4.14439	0.273869	0.136935	−	0.990580i	$-0.456275\pi$
$229$	4.14439	0.273869	0.136935	+	0.990580i	$0.456275\pi$
$230$	−20.7748	−1.36985
$231$	−5.60708	−0.368919
$232$	−55.9017	−3.67012
$233$	0.742793	0.0486620	0.0243310	−	0.999704i	$-0.492254\pi$
$233$	0.742793	0.0486620	0.0243310	+	0.999704i	$0.492254\pi$
$234$	1.07568	0.0703195
$235$	−14.8987	−0.971881
$236$	−11.5839	−0.754047
$237$	9.86489	0.640794
$238$	2.14642	0.139132
$239$	−2.70125	−0.174730	−0.0873648	−	0.996176i	$-0.527845\pi$
$239$	−2.70125	−0.174730	−0.0873648	+	0.996176i	$0.527845\pi$
$240$	−46.5178	−3.00271
$241$	−15.7286	−1.01317	−0.506585	−	0.862190i	$-0.669092\pi$
$241$	−15.7286	−1.01317	−0.506585	+	0.862190i	$0.669092\pi$
$242$	−55.5340	−3.56986
$243$	2.93473	0.188263
$244$	−5.05779	−0.323792
$245$	22.9180	1.46418
$246$	2.93365	0.187043
$247$	−6.11190	−0.388891
$248$	4.02726	0.255731
$249$	0.144764	0.00917406
$250$	16.8417	1.06516
$251$	3.69851	0.233448	0.116724	−	0.993164i	$-0.462761\pi$
$251$	3.69851	0.233448	0.116724	+	0.993164i	$0.462761\pi$
$252$	0.782266	0.0492781
$253$	−13.3485	−0.839213
$254$	17.6869	1.10977
$255$	−7.94903	−0.497788
$256$	−24.8280	−1.55175
$257$	1.53829	0.0959560	0.0479780	−	0.998848i	$-0.484722\pi$
$257$	1.53829	0.0959560	0.0479780	+	0.998848i	$0.484722\pi$
$258$	37.5859	2.33999
$259$	1.60317	0.0996160
$260$	−23.5452	−1.46021
$261$	−2.33837	−0.144742
$262$	−16.7486	−1.03473
$263$	−16.4249	−1.01280	−0.506400	−	0.862299i	$-0.669024\pi$
$263$	−16.4249	−1.01280	−0.506400	+	0.862299i	$0.669024\pi$
$264$	−63.7193	−3.92165
$265$	8.81233	0.541337
$266$	−6.36440	−0.390226
$267$	0.578481	0.0354024
$268$	26.2237	1.60187
$269$	−6.75750	−0.412012	−0.206006	−	0.978551i	$-0.566047\pi$
$269$	−6.75750	−0.412012	−0.206006	+	0.978551i	$0.566047\pi$
$270$	−48.0644	−2.92511
$271$	−5.23698	−0.318124	−0.159062	−	0.987269i	$-0.550847\pi$
$271$	−5.23698	−0.318124	−0.159062	+	0.987269i	$0.550847\pi$
$272$	11.4418	0.693760
$273$	−1.44841	−0.0876619
$274$	23.3471	1.41045
$275$	39.3548	2.37319
$276$	−17.8533	−1.07465
$277$	5.71309	0.343266	0.171633	−	0.985161i	$-0.445096\pi$
$277$	5.71309	0.343266	0.171633	+	0.985161i	$0.445096\pi$
$278$	−25.2481	−1.51428
$279$	0.168461	0.0100855
$280$	−13.9288	−0.832407
$281$	−13.4789	−0.804081	−0.402041	−	0.915622i	$-0.631699\pi$
$281$	−13.4789	−0.804081	−0.402041	+	0.915622i	$0.631699\pi$
$282$	−18.3333	−1.09173
$283$	−7.19329	−0.427597	−0.213798	−	0.976878i	$-0.568584\pi$
$283$	−7.19329	−0.427597	−0.213798	+	0.976878i	$0.568584\pi$
$284$	9.12008	0.541177
$285$	23.5699	1.39616
$286$	−21.6624	−1.28093
$287$	0.412048	0.0243224
$288$	2.13155	0.125603
$289$	−15.0448	−0.884989
$290$	73.2894	4.30370
$291$	10.5944	0.621055
$292$	−32.4639	−1.89981
$293$	13.5705	0.792796	0.396398	−	0.918079i	$-0.370260\pi$
$293$	13.5705	0.792796	0.396398	+	0.918079i	$0.370260\pi$
$294$	28.2013	1.64473
$295$	8.62786	0.502334
$296$	18.2185	1.05893
$297$	−30.8830	−1.79201
$298$	−36.7589	−2.12939
$299$	−3.44816	−0.199412
$300$	52.6363	3.03896
$301$	5.27915	0.304285
$302$	15.9672	0.918811
$303$	6.18165	0.355126
$304$	−33.9263	−1.94581
$305$	3.76712	0.215705
$306$	1.02032	0.0583280
$307$	15.0543	0.859195	0.429598	−	0.903020i	$-0.358655\pi$
$307$	15.0543	0.859195	0.429598	+	0.903020i	$0.358655\pi$
$308$	−15.7535	−0.897642
$309$	4.38237	0.249304
$310$	−5.27991	−0.299879
$311$	33.5228	1.90090	0.950450	−	0.310876i	$-0.100622\pi$
$311$	33.5228	1.90090	0.950450	+	0.310876i	$0.100622\pi$
$312$	−16.4599	−0.931857
$313$	−33.3744	−1.88643	−0.943215	−	0.332182i	$-0.892215\pi$
$313$	−33.3744	−1.88643	−0.943215	+	0.332182i	$0.892215\pi$
$314$	−20.2257	−1.14140
$315$	−0.582644	−0.0328283
$316$	27.7162	1.55916
$317$	−26.3395	−1.47937	−0.739686	−	0.672952i	$-0.765026\pi$
$317$	−26.3395	−1.47937	−0.739686	+	0.672952i	$0.765026\pi$
$318$	10.8439	0.608093
$319$	47.0909	2.63659
$320$	−10.3611	−0.579203
$321$	−4.67294	−0.260818
$322$	−3.59061	−0.200097
$323$	−5.79737	−0.322574
$324$	−37.3686	−2.07604
$325$	10.1661	0.563913
$326$	−7.74166	−0.428771
$327$	−14.4784	−0.800659
$328$	4.68255	0.258551
$329$	−2.57501	−0.141965
$330$	83.5387	4.59865
$331$	24.4725	1.34513	0.672564	−	0.740039i	$-0.265193\pi$
$331$	24.4725	1.34513	0.672564	+	0.740039i	$0.265193\pi$
$332$	0.406727	0.0223220
$333$	0.762083	0.0417619
$334$	34.9626	1.91307
$335$	−19.5318	−1.06714
$336$	−8.03992	−0.438614
$337$	12.5012	0.680981	0.340491	−	0.940248i	$-0.389407\pi$
$337$	12.5012	0.680981	0.340491	+	0.940248i	$0.389407\pi$
$338$	27.8797	1.51645
$339$	30.5273	1.65802
$340$	−22.3335	−1.21120
$341$	−3.39252	−0.183715
$342$	−3.02538	−0.163594
$343$	8.13391	0.439190
$344$	59.9927	3.23459
$345$	13.2975	0.715911
$346$	7.22011	0.388156
$347$	−24.4039	−1.31007	−0.655034	−	0.755599i	$-0.727346\pi$
$347$	−24.4039	−1.31007	−0.655034	+	0.755599i	$0.727346\pi$
$348$	62.9831	3.37625
$349$	−6.42710	−0.344035	−0.172017	−	0.985094i	$-0.555029\pi$
$349$	−6.42710	−0.344035	−0.172017	+	0.985094i	$0.555029\pi$
$350$	10.5861	0.565849
$351$	−7.97765	−0.425816
$352$	−42.9259	−2.28796
$353$	15.7126	0.836295	0.418147	−	0.908379i	$-0.362680\pi$
$353$	15.7126	0.836295	0.418147	+	0.908379i	$0.362680\pi$
$354$	10.6169	0.564280
$355$	−6.79278	−0.360523
$356$	1.62529	0.0861401
$357$	−1.37387	−0.0727130
$358$	−7.45644	−0.394085
$359$	−26.1538	−1.38034	−0.690172	−	0.723645i	$-0.742465\pi$
$359$	−26.1538	−1.38034	−0.690172	+	0.723645i	$0.742465\pi$
$360$	−6.62122	−0.348969
$361$	−1.81009	−0.0952677
$362$	34.3683	1.80636
$363$	35.5460	1.86568
$364$	−4.06943	−0.213296
$365$	24.1796	1.26562
$366$	4.63556	0.242305
$367$	−18.7934	−0.981008	−0.490504	−	0.871439i	$-0.663187\pi$
$367$	−18.7934	−0.981008	−0.490504	+	0.871439i	$0.663187\pi$
$368$	−19.1402	−0.997754
$369$	0.195871	0.0101967
$370$	−23.8853	−1.24174
$371$	1.52308	0.0790745
$372$	−4.53742	−0.235254
$373$	−13.0160	−0.673942	−0.336971	−	0.941515i	$-0.609402\pi$
$373$	−13.0160	−0.673942	−0.336971	+	0.941515i	$0.609402\pi$
$374$	−20.5476	−1.06249
$375$	−10.7800	−0.556676
$376$	−29.2627	−1.50911
$377$	12.1645	0.626501
$378$	−8.30722	−0.427277
$379$	−29.0960	−1.49456	−0.747280	−	0.664510i	$-0.768640\pi$
$379$	−29.0960	−1.49456	−0.747280	+	0.664510i	$0.768640\pi$
$380$	66.2214	3.39709
$381$	−11.3209	−0.579989
$382$	−38.4268	−1.96609
$383$	3.16350	0.161647	0.0808237	−	0.996728i	$-0.474245\pi$
$383$	3.16350	0.161647	0.0808237	+	0.996728i	$0.474245\pi$
$384$	12.0463	0.614733
$385$	11.7335	0.597994
$386$	35.9843	1.83155
$387$	2.50950	0.127565
$388$	29.7659	1.51113
$389$	13.1657	0.667528	0.333764	−	0.942657i	$-0.391681\pi$
$389$	13.1657	0.667528	0.333764	+	0.942657i	$0.391681\pi$
$390$	21.5796	1.09272
$391$	−3.27071	−0.165407
$392$	45.0135	2.27353
$393$	10.7204	0.540771
$394$	71.5926	3.60678
$395$	−20.6435	−1.03869
$396$	−7.48862	−0.376317
$397$	0.472606	0.0237194	0.0118597	−	0.999930i	$-0.496225\pi$
$397$	0.472606	0.0237194	0.0118597	+	0.999930i	$0.496225\pi$
$398$	−54.4177	−2.72771
$399$	4.07370	0.203940
$400$	56.4304	2.82152
$401$	−32.0576	−1.60088	−0.800439	−	0.599414i	$-0.795400\pi$
$401$	−32.0576	−1.60088	−0.800439	+	0.599414i	$0.795400\pi$
$402$	−24.0345	−1.19873
$403$	−0.876350	−0.0436541
$404$	17.3678	0.864083
$405$	27.8327	1.38302
$406$	12.6670	0.628652
$407$	−15.3471	−0.760727
$408$	−15.6128	−0.772949
$409$	−10.1232	−0.500562	−0.250281	−	0.968173i	$-0.580523\pi$
$409$	−10.1232	−0.500562	−0.250281	+	0.968173i	$0.580523\pi$
$410$	−6.13902	−0.303185
$411$	−14.9439	−0.737131
$412$	12.3126	0.606600
$413$	1.49120	0.0733771
$414$	−1.70684	−0.0838865
$415$	−0.302937	−0.0148706
$416$	−11.0886	−0.543661
$417$	16.1607	0.791394
$418$	60.9262	2.98000
$419$	−30.1222	−1.47157	−0.735783	−	0.677218i	$-0.763185\pi$
$419$	−30.1222	−1.47157	−0.735783	+	0.677218i	$0.763185\pi$
$420$	15.6933	0.765754
$421$	−31.2589	−1.52346	−0.761732	−	0.647892i	$-0.775651\pi$
$421$	−31.2589	−1.52346	−0.761732	+	0.647892i	$0.775651\pi$
$422$	23.7053	1.15396
$423$	−1.22406	−0.0595158
$424$	17.3084	0.840572
$425$	9.64290	0.467749
$426$	−8.35873	−0.404982
$427$	0.651091	0.0315085
$428$	−13.1290	−0.634615
$429$	13.8656	0.669438
$430$	−78.6529	−3.79298
$431$	−0.774182	−0.0372910	−0.0186455	−	0.999826i	$-0.505935\pi$
$431$	−0.774182	−0.0372910	−0.0186455	+	0.999826i	$0.505935\pi$
$432$	−44.2828	−2.13056
$433$	−3.97971	−0.191253	−0.0956264	−	0.995417i	$-0.530485\pi$
$433$	−3.97971	−0.191253	−0.0956264	+	0.995417i	$0.530485\pi$
$434$	−0.912554	−0.0438040
$435$	−46.9108	−2.24920
$436$	−40.6783	−1.94814
$437$	9.69806	0.463921
$438$	29.7538	1.42169
$439$	18.5761	0.886589	0.443295	−	0.896376i	$-0.353810\pi$
$439$	18.5761	0.886589	0.443295	+	0.896376i	$0.353810\pi$
$440$	133.340	6.35675
$441$	1.88292	0.0896628
$442$	−5.30783	−0.252468
$443$	−34.6861	−1.64799	−0.823994	−	0.566598i	$-0.808259\pi$
$443$	−34.6861	−1.64799	−0.823994	+	0.566598i	$0.808259\pi$
$444$	−20.5264	−0.974140
$445$	−1.21054	−0.0573851
$446$	62.1204	2.94149
$447$	23.5285	1.11286
$448$	−1.79076	−0.0846056
$449$	13.1766	0.621843	0.310922	−	0.950436i	$-0.399362\pi$
$449$	13.1766	0.621843	0.310922	+	0.950436i	$0.399362\pi$
$450$	5.03220	0.237220
$451$	−3.94453	−0.185741
$452$	85.7690	4.03424
$453$	−10.2202	−0.480189
$454$	50.4563	2.36803
$455$	3.03098	0.142094
$456$	46.2939	2.16791
$457$	−0.690301	−0.0322909	−0.0161455	−	0.999870i	$-0.505139\pi$
$457$	−0.690301	−0.0322909	−0.0161455	+	0.999870i	$0.505139\pi$
$458$	−10.6720	−0.498668
$459$	−7.56710	−0.353202
$460$	37.3603	1.74193
$461$	17.5289	0.816401	0.408200	−	0.912892i	$-0.366156\pi$
$461$	17.5289	0.816401	0.408200	+	0.912892i	$0.366156\pi$
$462$	14.4384	0.671736
$463$	−2.16708	−0.100713	−0.0503563	−	0.998731i	$-0.516036\pi$
$463$	−2.16708	−0.100713	−0.0503563	+	0.998731i	$0.516036\pi$
$464$	67.5231	3.13468
$465$	3.37954	0.156723
$466$	−1.91272	−0.0886049
$467$	21.8356	1.01043	0.505216	−	0.862993i	$-0.331413\pi$
$467$	21.8356	1.01043	0.505216	+	0.862993i	$0.331413\pi$
$468$	−1.93445	−0.0894199
$469$	−3.37578	−0.155879
$470$	38.3646	1.76963
$471$	12.9460	0.596519
$472$	16.9461	0.780008
$473$	−50.5372	−2.32370
$474$	−25.4024	−1.16677
$475$	−28.5924	−1.31191
$476$	−3.86001	−0.176923
$477$	0.724013	0.0331503
$478$	6.95582	0.318152
$479$	−42.3867	−1.93670	−0.968349	−	0.249598i	$-0.919701\pi$
$479$	−42.3867	−1.93670	−0.968349	+	0.249598i	$0.919701\pi$
$480$	42.7618	1.95180
$481$	−3.96443	−0.180763
$482$	40.5018	1.84480
$483$	2.29827	0.104575
$484$	99.8694	4.53952
$485$	−22.1701	−1.00669
$486$	−7.55704	−0.342794
$487$	19.6255	0.889318	0.444659	−	0.895700i	$-0.353325\pi$
$487$	19.6255	0.889318	0.444659	+	0.895700i	$0.353325\pi$
$488$	7.39905	0.334939
$489$	4.95525	0.224084
$490$	−59.0146	−2.66601
$491$	−25.0439	−1.13022	−0.565108	−	0.825017i	$-0.691166\pi$
$491$	−25.0439	−1.13022	−0.565108	+	0.825017i	$0.691166\pi$
$492$	−5.27572	−0.237848
$493$	11.5384	0.519665
$494$	15.7384	0.708103
$495$	5.57764	0.250696
$496$	−4.86449	−0.218422
$497$	−1.17403	−0.0526625
$498$	−0.372773	−0.0167044
$499$	21.6423	0.968841	0.484420	−	0.874835i	$-0.339031\pi$
$499$	21.6423	0.968841	0.484420	+	0.874835i	$0.339031\pi$
$500$	−30.2873	−1.35449
$501$	−22.3788	−0.999809
$502$	−9.52380	−0.425068
$503$	−9.17074	−0.408903	−0.204452	−	0.978877i	$-0.565541\pi$
$503$	−9.17074	−0.408903	−0.204452	+	0.978877i	$0.565541\pi$
$504$	−1.14438	−0.0509747
$505$	−12.9358	−0.575637
$506$	34.3729	1.52806
$507$	−17.8451	−0.792529
$508$	−31.8071	−1.41121
$509$	2.89978	0.128531	0.0642653	−	0.997933i	$-0.479530\pi$
$509$	2.89978	0.128531	0.0642653	+	0.997933i	$0.479530\pi$
$510$	20.4690	0.906384
$511$	4.17909	0.184872
$512$	49.3158	2.17947
$513$	22.4374	0.990635
$514$	−3.96115	−0.174719
$515$	−9.17064	−0.404107
$516$	−67.5924	−2.97559
$517$	24.6505	1.08413
$518$	−4.12821	−0.181383
$519$	−4.62142	−0.202858
$520$	34.4443	1.51048
$521$	18.6154	0.815556	0.407778	−	0.913081i	$-0.366304\pi$
$521$	18.6154	0.815556	0.407778	+	0.913081i	$0.366304\pi$
$522$	6.02139	0.263549
$523$	−31.2659	−1.36716	−0.683581	−	0.729875i	$-0.739578\pi$
$523$	−31.2659	−1.36716	−0.683581	+	0.729875i	$0.739578\pi$
$524$	30.1197	1.31579
$525$	−6.77589	−0.295724
$526$	42.2946	1.84413
$527$	−0.831251	−0.0362098
$528$	76.9659	3.34951
$529$	−17.5286	−0.762114
$530$	−22.6921	−0.985681
$531$	0.708857	0.0307618
$532$	11.4454	0.496221
$533$	−1.01894	−0.0441354
$534$	−1.48961	−0.0644617
$535$	9.77870	0.422770
$536$	−38.3627	−1.65702
$537$	4.77269	0.205957
$538$	17.4008	0.750201
$539$	−37.9189	−1.63328
$540$	86.4365	3.71963
$541$	8.67249	0.372859	0.186430	−	0.982468i	$-0.440308\pi$
$541$	8.67249	0.372859	0.186430	+	0.982468i	$0.440308\pi$
$542$	13.4854	0.579247
$543$	−21.9984	−0.944040
$544$	−10.5179	−0.450952
$545$	30.2978	1.29782
$546$	3.72971	0.159617
$547$	−1.15709	−0.0494736	−0.0247368	−	0.999694i	$-0.507875\pi$
$547$	−1.15709	−0.0494736	−0.0247368	+	0.999694i	$0.507875\pi$
$548$	−41.9862	−1.79356
$549$	0.309503	0.0132093
$550$	−101.340	−4.32116
$551$	−34.2129	−1.45752
$552$	26.1177	1.11164
$553$	−3.56792	−0.151723
$554$	−14.7114	−0.625028
$555$	15.2884	0.648956
$556$	45.4049	1.92560
$557$	13.3171	0.564262	0.282131	−	0.959376i	$-0.408959\pi$
$557$	13.3171	0.564262	0.282131	+	0.959376i	$0.408959\pi$
$558$	−0.433792	−0.0183639
$559$	−13.0547	−0.552154
$560$	16.8245	0.710965
$561$	13.1520	0.555280
$562$	34.7085	1.46409
$563$	22.0813	0.930614	0.465307	−	0.885149i	$-0.345944\pi$
$563$	22.0813	0.930614	0.465307	+	0.885149i	$0.345944\pi$
$564$	32.9696	1.38827
$565$	−63.8821	−2.68754
$566$	18.5230	0.778578
$567$	4.81048	0.202021
$568$	−13.3418	−0.559809
$569$	10.9914	0.460784	0.230392	−	0.973098i	$-0.425999\pi$
$569$	10.9914	0.460784	0.230392	+	0.973098i	$0.425999\pi$
$570$	−60.6932	−2.54216
$571$	20.5009	0.857935	0.428968	−	0.903320i	$-0.358877\pi$
$571$	20.5009	0.857935	0.428968	+	0.903320i	$0.358877\pi$
$572$	38.9566	1.62886
$573$	24.5961	1.02752
$574$	−1.06104	−0.0442869
$575$	−16.1310	−0.672710
$576$	−0.851259	−0.0354691
$577$	−27.1346	−1.12963	−0.564814	−	0.825218i	$-0.691052\pi$
$577$	−27.1346	−1.12963	−0.564814	+	0.825218i	$0.691052\pi$
$578$	38.7409	1.61141
$579$	−23.0327	−0.957205
$580$	−131.800	−5.47269
$581$	−0.0523581	−0.00217218
$582$	−27.2810	−1.13083
$583$	−14.5804	−0.603859
$584$	47.4915	1.96521
$585$	1.44081	0.0595700
$586$	−34.9445	−1.44354
$587$	−19.6763	−0.812126	−0.406063	−	0.913845i	$-0.633099\pi$
$587$	−19.6763	−0.812126	−0.406063	+	0.913845i	$0.633099\pi$
$588$	−50.7157	−2.09148
$589$	2.46476	0.101559
$590$	−22.2171	−0.914662
$591$	−45.8247	−1.88498
$592$	−22.0060	−0.904441
$593$	−1.81388	−0.0744870	−0.0372435	−	0.999306i	$-0.511858\pi$
$593$	−1.81388	−0.0744870	−0.0372435	+	0.999306i	$0.511858\pi$
$594$	79.5248	3.26294
$595$	2.87499	0.117863
$596$	66.1052	2.70778
$597$	34.8315	1.42556
$598$	8.87914	0.363095
$599$	−27.1871	−1.11083	−0.555417	−	0.831572i	$-0.687441\pi$
$599$	−27.1871	−1.11083	−0.555417	+	0.831572i	$0.687441\pi$
$600$	−77.0017	−3.14358
$601$	16.0879	0.656241	0.328120	−	0.944636i	$-0.393585\pi$
$601$	16.0879	0.656241	0.328120	+	0.944636i	$0.393585\pi$
$602$	−13.5940	−0.554050
$603$	−1.60471	−0.0653490
$604$	−28.7146	−1.16838
$605$	−74.3843	−3.02415
$606$	−15.9180	−0.646623
$607$	28.4670	1.15544	0.577720	−	0.816235i	$-0.303943\pi$
$607$	28.4670	1.15544	0.577720	+	0.816235i	$0.303943\pi$
$608$	31.1869	1.26480
$609$	−8.10784	−0.328546
$610$	−9.70047	−0.392760
$611$	6.36768	0.257609
$612$	−1.83490	−0.0741712
$613$	15.5549	0.628257	0.314129	−	0.949380i	$-0.398288\pi$
$613$	15.5549	0.628257	0.314129	+	0.949380i	$0.398288\pi$
$614$	−38.7654	−1.56444
$615$	3.92944	0.158450
$616$	23.0459	0.928546
$617$	−38.5796	−1.55315	−0.776577	−	0.630022i	$-0.783046\pi$
$617$	−38.5796	−1.55315	−0.776577	+	0.630022i	$0.783046\pi$
$618$	−11.2848	−0.453940
$619$	−37.3709	−1.50206	−0.751031	−	0.660267i	$-0.770443\pi$
$619$	−37.3709	−1.50206	−0.751031	+	0.660267i	$0.770443\pi$
$620$	9.49510	0.381333
$621$	12.6585	0.507970
$622$	−86.3223	−3.46121
$623$	−0.209224	−0.00838238
$624$	19.8817	0.795906
$625$	−11.9229	−0.476915
$626$	85.9402	3.43486
$627$	−38.9974	−1.55741
$628$	36.3728	1.45143
$629$	−3.76041	−0.149937
$630$	1.50033	0.0597745
$631$	−37.8318	−1.50606	−0.753029	−	0.657987i	$-0.771408\pi$
$631$	−37.8318	−1.50606	−0.753029	+	0.657987i	$0.771408\pi$
$632$	−40.5461	−1.61284
$633$	−15.1732	−0.603081
$634$	67.8251	2.69368
$635$	23.6904	0.940126
$636$	−19.5010	−0.773266
$637$	−9.79514	−0.388098
$638$	−121.261	−4.80076
$639$	−0.558088	−0.0220776
$640$	−25.2082	−0.996443
$641$	11.3189	0.447071	0.223535	−	0.974696i	$-0.428240\pi$
$641$	11.3189	0.447071	0.223535	+	0.974696i	$0.428240\pi$
$642$	12.0330	0.474904
$643$	−22.9295	−0.904253	−0.452126	−	0.891954i	$-0.649334\pi$
$643$	−22.9295	−0.904253	−0.452126	+	0.891954i	$0.649334\pi$
$644$	6.45717	0.254448
$645$	50.3439	1.98229
$646$	14.9284	0.587351
$647$	−2.82046	−0.110884	−0.0554420	−	0.998462i	$-0.517657\pi$
$647$	−2.82046	−0.110884	−0.0554420	+	0.998462i	$0.517657\pi$
$648$	54.6667	2.14751
$649$	−14.2752	−0.560351
$650$	−26.1780	−1.02679
$651$	0.584104	0.0228928
$652$	13.9222	0.545235
$653$	6.93574	0.271416	0.135708	−	0.990749i	$-0.456669\pi$
$653$	6.93574	0.271416	0.135708	+	0.990749i	$0.456669\pi$
$654$	37.2825	1.45786
$655$	−22.4337	−0.876555
$656$	−5.65601	−0.220830
$657$	1.98657	0.0775036
$658$	6.63075	0.258493
$659$	16.4945	0.642533	0.321266	−	0.946989i	$-0.395892\pi$
$659$	16.4945	0.642533	0.321266	+	0.946989i	$0.395892\pi$
$660$	−150.232	−5.84775
$661$	−15.8915	−0.618107	−0.309054	−	0.951045i	$-0.600012\pi$
$661$	−15.8915	−0.618107	−0.309054	+	0.951045i	$0.600012\pi$
$662$	−63.0174	−2.44924
$663$	3.39742	0.131945
$664$	−0.595002	−0.0230906
$665$	−8.52471	−0.330574
$666$	−1.96239	−0.0760411
$667$	−19.3019	−0.747374
$668$	−62.8749	−2.43270
$669$	−39.7618	−1.53728
$670$	50.2951	1.94307
$671$	−6.23288	−0.240618
$672$	7.39074	0.285104
$673$	47.3419	1.82490	0.912448	−	0.409192i	$-0.134189\pi$
$673$	47.3419	1.82490	0.912448	+	0.409192i	$0.134189\pi$
$674$	−32.1909	−1.23995
$675$	−37.3206	−1.43647
$676$	−50.1373	−1.92836
$677$	4.09800	0.157499	0.0787495	−	0.996894i	$-0.474907\pi$
$677$	4.09800	0.157499	0.0787495	+	0.996894i	$0.474907\pi$
$678$	−78.6090	−3.01896
$679$	−3.83177	−0.147050
$680$	32.6717	1.25290
$681$	−32.2959	−1.23758
$682$	8.73585	0.334513
$683$	−31.3469	−1.19945	−0.599727	−	0.800205i	$-0.704724\pi$
$683$	−31.3469	−1.19945	−0.599727	+	0.800205i	$0.704724\pi$
$684$	5.44069	0.208030
$685$	31.2720	1.19484
$686$	−20.9451	−0.799688
$687$	6.83087	0.260614
$688$	−72.4646	−2.76269
$689$	−3.76639	−0.143488
$690$	−34.2414	−1.30355
$691$	4.15799	0.158177	0.0790887	−	0.996868i	$-0.474799\pi$
$691$	4.15799	0.158177	0.0790887	+	0.996868i	$0.474799\pi$
$692$	−12.9843	−0.493588
$693$	0.964012	0.0366198
$694$	62.8408	2.38540
$695$	−33.8182	−1.28280
$696$	−92.1382	−3.49249
$697$	−0.966506	−0.0366090
$698$	16.5500	0.626427
$699$	1.22429	0.0463067
$700$	−19.0374	−0.719546
$701$	17.4032	0.657309	0.328654	−	0.944450i	$-0.393405\pi$
$701$	17.4032	0.657309	0.328654	+	0.944450i	$0.393405\pi$
$702$	20.5427	0.775335
$703$	11.1501	0.420534
$704$	17.1429	0.646099
$705$	−24.5562	−0.924842
$706$	−40.4604	−1.52275
$707$	−2.23577	−0.0840847
$708$	−19.0928	−0.717551
$709$	10.2146	0.383616	0.191808	−	0.981432i	$-0.438565\pi$
$709$	10.2146	0.383616	0.191808	+	0.981432i	$0.438565\pi$
$710$	17.4916	0.656450
$711$	−1.69605	−0.0636068
$712$	−2.37764	−0.0891058
$713$	1.39055	0.0520765
$714$	3.53777	0.132398
$715$	−29.0155	−1.08512
$716$	13.4093	0.501128
$717$	−4.45226	−0.166273
$718$	67.3470	2.51337
$719$	−5.12340	−0.191071	−0.0955353	−	0.995426i	$-0.530456\pi$
$719$	−5.12340	−0.191071	−0.0955353	+	0.995426i	$0.530456\pi$
$720$	7.99770	0.298057
$721$	−1.58501	−0.0590288
$722$	4.66104	0.173466
$723$	−25.9242	−0.964132
$724$	−61.8062	−2.29701
$725$	56.9071	2.11348
$726$	−91.5322	−3.39708
$727$	24.7878	0.919328	0.459664	−	0.888093i	$-0.347970\pi$
$727$	24.7878	0.919328	0.459664	+	0.888093i	$0.347970\pi$
$728$	5.95318	0.220640
$729$	29.0458	1.07577
$730$	−62.2634	−2.30447
$731$	−12.3828	−0.457996
$732$	−8.33634	−0.308120
$733$	9.02701	0.333420	0.166710	−	0.986006i	$-0.446686\pi$
$733$	9.02701	0.333420	0.166710	+	0.986006i	$0.446686\pi$
$734$	48.3937	1.78624
$735$	37.7739	1.39331
$736$	17.5948	0.648552
$737$	32.3163	1.19039
$738$	−0.504376	−0.0185663
$739$	−50.6705	−1.86394	−0.931971	−	0.362532i	$-0.881912\pi$
$739$	−50.6705	−1.86394	−0.931971	+	0.362532i	$0.881912\pi$
$740$	42.9540	1.57902
$741$	−10.0738	−0.370069
$742$	−3.92199	−0.143981
$743$	43.5453	1.59752	0.798760	−	0.601649i	$-0.205490\pi$
$743$	43.5453	1.59752	0.798760	+	0.601649i	$0.205490\pi$
$744$	6.63781	0.243354
$745$	−49.2362	−1.80387
$746$	33.5166	1.22713
$747$	−0.0248890	−0.000910640 0
$748$	36.9517	1.35109
$749$	1.69010	0.0617550
$750$	27.7589	1.01361
$751$	23.3637	0.852553	0.426277	−	0.904593i	$-0.359825\pi$
$751$	23.3637	0.852553	0.426277	+	0.904593i	$0.359825\pi$
$752$	35.3461	1.28894
$753$	6.09596	0.222149
$754$	−31.3239	−1.14075
$755$	21.3871	0.778356
$756$	14.9393	0.543336
$757$	−3.05270	−0.110952	−0.0554761	−	0.998460i	$-0.517668\pi$
$757$	−3.05270	−0.110952	−0.0554761	+	0.998460i	$0.517668\pi$
$758$	74.9231	2.72133
$759$	−22.0013	−0.798595
$760$	−96.8755	−3.51404
$761$	−10.5278	−0.381632	−0.190816	−	0.981626i	$-0.561113\pi$
$761$	−10.5278	−0.381632	−0.190816	+	0.981626i	$0.561113\pi$
$762$	29.1518	1.05606
$763$	5.23653	0.189575
$764$	69.1048	2.50012
$765$	1.36666	0.0494116
$766$	−8.14612	−0.294331
$767$	−3.68755	−0.133150
$768$	−40.9221	−1.47665
$769$	30.8341	1.11191	0.555953	−	0.831214i	$-0.312354\pi$
$769$	30.8341	1.11191	0.555953	+	0.831214i	$0.312354\pi$
$770$	−30.2141	−1.08884
$771$	2.53544	0.0913117
$772$	−64.7122	−2.32904
$773$	7.18857	0.258555	0.129278	−	0.991608i	$-0.458734\pi$
$773$	7.18857	0.258555	0.129278	+	0.991608i	$0.458734\pi$
$774$	−6.46205	−0.232274
$775$	−4.09970	−0.147265
$776$	−43.5446	−1.56316
$777$	2.64237	0.0947945
$778$	−33.9022	−1.21545
$779$	2.86581	0.102678
$780$	−38.8076	−1.38953
$781$	11.2390	0.402162
$782$	8.42220	0.301177
$783$	−44.6569	−1.59591
$784$	−54.3714	−1.94184
$785$	−27.0910	−0.966919
$786$	−27.6053	−0.984649
$787$	5.95920	0.212423	0.106211	−	0.994344i	$-0.466128\pi$
$787$	5.95920	0.212423	0.106211	+	0.994344i	$0.466128\pi$
$788$	−128.748	−4.58647
$789$	−27.0718	−0.963780
$790$	53.1577	1.89126
$791$	−11.0411	−0.392576
$792$	10.9551	0.389273
$793$	−1.61007	−0.0571752
$794$	−1.21698	−0.0431889
$795$	14.5247	0.515136
$796$	97.8620	3.46863
$797$	−36.3653	−1.28813	−0.644063	−	0.764972i	$-0.722753\pi$
$797$	−36.3653	−1.28813	−0.644063	+	0.764972i	$0.722753\pi$
$798$	−10.4899	−0.371339
$799$	6.03998	0.213679
$800$	−51.8739	−1.83402
$801$	−0.0994568	−0.00351413
$802$	82.5493	2.91492
$803$	−40.0063	−1.41179
$804$	43.2224	1.52434
$805$	−4.80940	−0.169509
$806$	2.25663	0.0794865
$807$	−11.1378	−0.392070
$808$	−25.4075	−0.893832
$809$	48.8529	1.71758	0.858788	−	0.512332i	$-0.171218\pi$
$809$	48.8529	1.71758	0.858788	+	0.512332i	$0.171218\pi$
$810$	−71.6703	−2.51824
$811$	30.2522	1.06230	0.531149	−	0.847278i	$-0.321760\pi$
$811$	30.2522	1.06230	0.531149	+	0.847278i	$0.321760\pi$
$812$	−22.7796	−0.799409
$813$	−8.63168	−0.302726
$814$	39.5193	1.38515
$815$	−10.3695	−0.363227
$816$	18.8586	0.660181
$817$	36.7167	1.28455
$818$	26.0677	0.911436
$819$	0.249022	0.00870153
$820$	11.0401	0.385536
$821$	3.20176	0.111742	0.0558711	−	0.998438i	$-0.482206\pi$
$821$	3.20176	0.111742	0.0558711	+	0.998438i	$0.482206\pi$
$822$	38.4812	1.34219
$823$	−22.1016	−0.770413	−0.385207	−	0.922830i	$-0.625870\pi$
$823$	−22.1016	−0.770413	−0.385207	+	0.922830i	$0.625870\pi$
$824$	−18.0122	−0.627484
$825$	64.8654	2.25832
$826$	−3.83989	−0.133607
$827$	−54.8297	−1.90661	−0.953307	−	0.302002i	$-0.902345\pi$
$827$	−54.8297	−1.90661	−0.953307	+	0.302002i	$0.902345\pi$
$828$	3.06948	0.106672
$829$	2.50117	0.0868693	0.0434346	−	0.999056i	$-0.486170\pi$
$829$	2.50117	0.0868693	0.0434346	+	0.999056i	$0.486170\pi$
$830$	0.780072	0.0270767
$831$	9.41642	0.326652
$832$	4.42834	0.153525
$833$	−9.29106	−0.321916
$834$	−41.6144	−1.44099
$835$	46.8302	1.62063
$836$	−109.566	−3.78944
$837$	3.21716	0.111201
$838$	77.5657	2.67946
$839$	−26.7154	−0.922319	−0.461160	−	0.887317i	$-0.652566\pi$
$839$	−26.7154	−0.922319	−0.461160	+	0.887317i	$0.652566\pi$
$840$	−22.9578	−0.792118
$841$	39.0935	1.34805
$842$	80.4927	2.77396
$843$	−22.2161	−0.765163
$844$	−42.6304	−1.46740
$845$	37.3430	1.28464
$846$	3.15200	0.108368
$847$	−12.8562	−0.441745
$848$	−20.9067	−0.717938
$849$	−11.8561	−0.406901
$850$	−24.8308	−0.851690
$851$	6.29057	0.215638
$852$	15.0319	0.514984
$853$	−6.62208	−0.226736	−0.113368	−	0.993553i	$-0.536164\pi$
$853$	−6.62208	−0.226736	−0.113368	+	0.993553i	$0.536164\pi$
$854$	−1.67658	−0.0573714
$855$	−4.05231	−0.138586
$856$	19.2065	0.656464
$857$	21.4937	0.734212	0.367106	−	0.930179i	$-0.380349\pi$
$857$	21.4937	0.734212	0.367106	+	0.930179i	$0.380349\pi$
$858$	−35.7044	−1.21893
$859$	−16.1583	−0.551315	−0.275657	−	0.961256i	$-0.588896\pi$
$859$	−16.1583	−0.551315	−0.275657	+	0.961256i	$0.588896\pi$
$860$	141.445	4.82324
$861$	0.679146	0.0231452
$862$	1.99355	0.0679004
$863$	17.6699	0.601491	0.300746	−	0.953704i	$-0.402764\pi$
$863$	17.6699	0.601491	0.300746	+	0.953704i	$0.402764\pi$
$864$	40.7072	1.38489
$865$	9.67088	0.328820
$866$	10.2479	0.348238
$867$	−24.7971	−0.842155
$868$	1.64109	0.0557022
$869$	34.1556	1.15865
$870$	120.797	4.09540
$871$	8.34789	0.282858
$872$	59.5084	2.01521
$873$	−1.82147	−0.0616475
$874$	−24.9729	−0.844719
$875$	3.89889	0.131807
$876$	−53.5076	−1.80785
$877$	−48.9439	−1.65272	−0.826359	−	0.563144i	$-0.809592\pi$
$877$	−48.9439	−1.65272	−0.826359	+	0.563144i	$0.809592\pi$
$878$	−47.8341	−1.61432
$879$	22.3671	0.754424
$880$	−161.060	−5.42935
$881$	16.2505	0.547493	0.273747	−	0.961802i	$-0.411737\pi$
$881$	16.2505	0.547493	0.273747	+	0.961802i	$0.411737\pi$
$882$	−4.84858	−0.163260
$883$	−45.7323	−1.53901	−0.769507	−	0.638638i	$-0.779498\pi$
$883$	−45.7323	−1.53901	−0.769507	+	0.638638i	$0.779498\pi$
$884$	9.54532	0.321044
$885$	14.2206	0.478020
$886$	89.3180	3.00070
$887$	−43.9844	−1.47685	−0.738425	−	0.674335i	$-0.764430\pi$
$887$	−43.9844	−1.47685	−0.738425	+	0.674335i	$0.764430\pi$
$888$	30.0281	1.00768
$889$	4.09454	0.137326
$890$	3.11718	0.104488
$891$	−46.0506	−1.54275
$892$	−111.714	−3.74046
$893$	−17.9093	−0.599312
$894$	−60.5867	−2.02632
$895$	−9.98743	−0.333843
$896$	−4.35687	−0.145553
$897$	−5.68333	−0.189761
$898$	−33.9303	−1.13227
$899$	−4.90558	−0.163610
$900$	−9.04963	−0.301654
$901$	−3.57256	−0.119019
$902$	10.1573	0.338201
$903$	8.70119	0.289558
$904$	−125.472	−4.17313
$905$	46.0342	1.53023
$906$	26.3175	0.874340
$907$	−28.2690	−0.938656	−0.469328	−	0.883024i	$-0.655504\pi$
$907$	−28.2690	−0.938656	−0.469328	+	0.883024i	$0.655504\pi$
$908$	−90.7379	−3.01124
$909$	−1.06280	−0.0352507
$910$	−7.80487	−0.258729
$911$	1.83829	0.0609053	0.0304527	−	0.999536i	$-0.490305\pi$
$911$	1.83829	0.0609053	0.0304527	+	0.999536i	$0.490305\pi$
$912$	−55.9179	−1.85163
$913$	0.501223	0.0165881
$914$	1.77755	0.0587961
$915$	6.20904	0.205264
$916$	19.1919	0.634118
$917$	−3.87733	−0.128041
$918$	19.4855	0.643119
$919$	25.9691	0.856643	0.428322	−	0.903626i	$-0.359105\pi$
$919$	25.9691	0.856643	0.428322	+	0.903626i	$0.359105\pi$
$920$	−54.6544	−1.80190
$921$	24.8128	0.817610
$922$	−45.1374	−1.48652
$923$	2.90323	0.0955611
$924$	−25.9653	−0.854195
$925$	−18.5462	−0.609796
$926$	5.58030	0.183380
$927$	−0.753451	−0.0247466
$928$	−62.0709	−2.03758
$929$	−29.8617	−0.979730	−0.489865	−	0.871798i	$-0.662954\pi$
$929$	−29.8617	−0.979730	−0.489865	+	0.871798i	$0.662954\pi$
$930$	−8.70244	−0.285364
$931$	27.5491	0.902886
$932$	3.43973	0.112672
$933$	55.2528	1.80890
$934$	−56.2275	−1.83982
$935$	−27.5222	−0.900073
$936$	2.82991	0.0924984
$937$	−7.52610	−0.245867	−0.122934	−	0.992415i	$-0.539230\pi$
$937$	−7.52610	−0.245867	−0.122934	+	0.992415i	$0.539230\pi$
$938$	8.69276	0.283829
$939$	−55.0083	−1.79513
$940$	−68.9928	−2.25030
$941$	6.95149	0.226612	0.113306	−	0.993560i	$-0.463856\pi$
$941$	6.95149	0.226612	0.113306	+	0.993560i	$0.463856\pi$
$942$	−33.3363	−1.08616
$943$	1.61681	0.0526506
$944$	−20.4690	−0.666210
$945$	−11.1270	−0.361961
$946$	130.135	4.23105
$947$	−2.72279	−0.0884787	−0.0442394	−	0.999021i	$-0.514086\pi$
$947$	−2.72279	−0.0884787	−0.0442394	+	0.999021i	$0.514086\pi$
$948$	45.6824	1.48370
$949$	−10.3344	−0.335468
$950$	73.6264	2.38876
$951$	−43.4132	−1.40777
$952$	5.64681	0.183014
$953$	−42.3943	−1.37329	−0.686643	−	0.726995i	$-0.740916\pi$
$953$	−42.3943	−1.37329	−0.686643	+	0.726995i	$0.740916\pi$
$954$	−1.86436	−0.0603608
$955$	−51.4703	−1.66554
$956$	−12.5090	−0.404569
$957$	77.6161	2.50897
$958$	109.147	3.52639
$959$	5.40490	0.174533
$960$	−17.0774	−0.551170
$961$	−30.6466	−0.988600
$962$	10.2086	0.329137
$963$	0.803408	0.0258895
$964$	−72.8362	−2.34590
$965$	48.1986	1.55157
$966$	−5.91812	−0.190412
$967$	−47.1392	−1.51589	−0.757947	−	0.652316i	$-0.773797\pi$
$967$	−47.1392	−1.51589	−0.757947	+	0.652316i	$0.773797\pi$
$968$	−146.099	−4.69581
$969$	−9.55533	−0.306961
$970$	57.0887	1.83301
$971$	28.4220	0.912107	0.456053	−	0.889952i	$-0.349263\pi$
$971$	28.4220	0.912107	0.456053	+	0.889952i	$0.349263\pi$
$972$	13.5902	0.435905
$973$	−5.84498	−0.187382
$974$	−50.5365	−1.61929
$975$	16.7559	0.536619
$976$	−8.93724	−0.286074
$977$	−29.4580	−0.942446	−0.471223	−	0.882014i	$-0.656187\pi$
$977$	−29.4580	−0.942446	−0.471223	+	0.882014i	$0.656187\pi$
$978$	−12.7600	−0.408018
$979$	2.00290	0.0640128
$980$	106.129	3.39016
$981$	2.48924	0.0794754
$982$	64.4890	2.05793
$983$	38.8897	1.24039	0.620194	−	0.784448i	$-0.287054\pi$
$983$	38.8897	1.24039	0.620194	+	0.784448i	$0.287054\pi$
$984$	7.71787	0.246037
$985$	95.8937	3.05543
$986$	−29.7119	−0.946219
$987$	−4.24418	−0.135094
$988$	−28.3030	−0.900440
$989$	20.7145	0.658683
$990$	−14.3626	−0.456474
$991$	17.3180	0.550125	0.275062	−	0.961426i	$-0.411301\pi$
$991$	17.3180	0.550125	0.275062	+	0.961426i	$0.411301\pi$
$992$	4.47171	0.141977
$993$	40.3360	1.28002
$994$	3.02317	0.0958892
$995$	−72.8891	−2.31074
$996$	0.670375	0.0212417
$997$	45.2943	1.43449	0.717243	−	0.696823i	$-0.245404\pi$
$997$	45.2943	1.43449	0.717243	+	0.696823i	$0.245404\pi$
$998$	−55.7296	−1.76409
$999$	14.5538	0.460462

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.a.1.12	✓	217

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.a.1.12	✓	217	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:	\( N \)	\(=\)	\( 6047 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57504 q^{2} +1.64822 q^{3} +4.63081 q^{4} -3.44910 q^{5} -4.24422 q^{6} -0.596125 q^{7} -6.77442 q^{8} -0.283374 q^{9} +O(q^{10})\)	\(q-2.57504 q^{2} +1.64822 q^{3} +4.63081 q^{4} -3.44910 q^{5} -4.24422 q^{6} -0.596125 q^{7} -6.77442 q^{8} -0.283374 q^{9} +8.88154 q^{10} +5.70669 q^{11} +7.63258 q^{12} +1.47414 q^{13} +1.53504 q^{14} -5.68486 q^{15} +8.18275 q^{16} +1.39828 q^{17} +0.729699 q^{18} -4.14607 q^{19} -15.9721 q^{20} -0.982545 q^{21} -14.6949 q^{22} -2.33910 q^{23} -11.1657 q^{24} +6.89626 q^{25} -3.79597 q^{26} -5.41172 q^{27} -2.76054 q^{28} +8.25188 q^{29} +14.6387 q^{30} -0.594481 q^{31} -7.52204 q^{32} +9.40588 q^{33} -3.60062 q^{34} +2.05609 q^{35} -1.31225 q^{36} -2.68931 q^{37} +10.6763 q^{38} +2.42971 q^{39} +23.3656 q^{40} -0.691211 q^{41} +2.53009 q^{42} -8.85577 q^{43} +26.4266 q^{44} +0.977385 q^{45} +6.02326 q^{46} +4.31958 q^{47} +13.4870 q^{48} -6.64463 q^{49} -17.7581 q^{50} +2.30467 q^{51} +6.82647 q^{52} -2.55497 q^{53} +13.9354 q^{54} -19.6829 q^{55} +4.03840 q^{56} -6.83363 q^{57} -21.2489 q^{58} -2.50149 q^{59} -26.3255 q^{60} -1.09221 q^{61} +1.53081 q^{62} +0.168927 q^{63} +3.00401 q^{64} -5.08446 q^{65} -24.2205 q^{66} +5.66288 q^{67} +6.47516 q^{68} -3.85534 q^{69} -5.29451 q^{70} +1.96944 q^{71} +1.91970 q^{72} -7.01042 q^{73} +6.92508 q^{74} +11.3665 q^{75} -19.1997 q^{76} -3.40190 q^{77} -6.25659 q^{78} +5.98518 q^{79} -28.2231 q^{80} -8.06958 q^{81} +1.77989 q^{82} +0.0878307 q^{83} -4.54997 q^{84} -4.82280 q^{85} +22.8039 q^{86} +13.6009 q^{87} -38.6595 q^{88} +0.350973 q^{89} -2.51680 q^{90} -0.878774 q^{91} -10.8319 q^{92} -0.979835 q^{93} -11.1231 q^{94} +14.3002 q^{95} -12.3980 q^{96} +6.42779 q^{97} +17.1102 q^{98} -1.61713 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9} - 46 q^{10} - 32 q^{11} - 72 q^{12} - 80 q^{13} - 22 q^{14} - 43 q^{15} + 122 q^{16} - 61 q^{17} - 88 q^{18} - 43 q^{19} - 41 q^{20} - 61 q^{21} - 93 q^{22} - 60 q^{23} - 41 q^{24} + 26 q^{25} - 9 q^{26} - 93 q^{27} - 126 q^{28} - 47 q^{29} - 36 q^{30} - 100 q^{31} - 114 q^{32} - 133 q^{33} - 75 q^{34} - 37 q^{35} + 75 q^{36} - 264 q^{37} - 35 q^{38} - 47 q^{39} - 118 q^{40} - 72 q^{41} - 64 q^{42} - 107 q^{43} - 59 q^{44} - 69 q^{45} - 111 q^{46} - 54 q^{47} - 135 q^{48} + 33 q^{49} - 42 q^{50} - 26 q^{51} - 173 q^{52} - 103 q^{53} - 28 q^{54} - 78 q^{55} - 44 q^{56} - 205 q^{57} - 189 q^{58} - 38 q^{59} - 105 q^{60} - 108 q^{61} - 14 q^{62} - 116 q^{63} + 39 q^{64} - 146 q^{65} + 5 q^{66} - 206 q^{67} - 62 q^{68} - 55 q^{69} - 125 q^{70} - 78 q^{71} - 225 q^{72} - 326 q^{73} + 3 q^{74} - 95 q^{75} - 84 q^{76} - 79 q^{77} - 86 q^{78} - 117 q^{79} - 39 q^{80} + q^{81} - 96 q^{82} - 23 q^{83} - 57 q^{84} - 224 q^{85} - 7 q^{86} - 45 q^{87} - 250 q^{88} - 104 q^{89} - 36 q^{90} - 96 q^{91} - 137 q^{92} - 155 q^{93} - 48 q^{94} - 38 q^{95} - 33 q^{96} - 447 q^{97} - 46 q^{98} - 94 q^{99}+O(q^{100}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9 - 46 * q^10 - 32 * q^11 - 72 * q^12 - 80 * q^13 - 22 * q^14 - 43 * q^15 + 122 * q^16 - 61 * q^17 - 88 * q^18 - 43 * q^19 - 41 * q^20 - 61 * q^21 - 93 * q^22 - 60 * q^23 - 41 * q^24 + 26 * q^25 - 9 * q^26 - 93 * q^27 - 126 * q^28 - 47 * q^29 - 36 * q^30 - 100 * q^31 - 114 * q^32 - 133 * q^33 - 75 * q^34 - 37 * q^35 + 75 * q^36 - 264 * q^37 - 35 * q^38 - 47 * q^39 - 118 * q^40 - 72 * q^41 - 64 * q^42 - 107 * q^43 - 59 * q^44 - 69 * q^45 - 111 * q^46 - 54 * q^47 - 135 * q^48 + 33 * q^49 - 42 * q^50 - 26 * q^51 - 173 * q^52 - 103 * q^53 - 28 * q^54 - 78 * q^55 - 44 * q^56 - 205 * q^57 - 189 * q^58 - 38 * q^59 - 105 * q^60 - 108 * q^61 - 14 * q^62 - 116 * q^63 + 39 * q^64 - 146 * q^65 + 5 * q^66 - 206 * q^67 - 62 * q^68 - 55 * q^69 - 125 * q^70 - 78 * q^71 - 225 * q^72 - 326 * q^73 + 3 * q^74 - 95 * q^75 - 84 * q^76 - 79 * q^77 - 86 * q^78 - 117 * q^79 - 39 * q^80 + q^81 - 96 * q^82 - 23 * q^83 - 57 * q^84 - 224 * q^85 - 7 * q^86 - 45 * q^87 - 250 * q^88 - 104 * q^89 - 36 * q^90 - 96 * q^91 - 137 * q^92 - 155 * q^93 - 48 * q^94 - 38 * q^95 - 33 * q^96 - 447 * q^97 - 46 * q^98 - 94 * q^99

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