LMFDB - Embedded newform 6047.2.a.a.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.79459 q^{2} -1.21209 q^{3} +5.80974 q^{4} -0.914621 q^{5} +3.38731 q^{6} -4.48023 q^{7} -10.6467 q^{8} -1.53083 q^{9} +O(q^{10})$	\(q-2.79459 q^{2} -1.21209 q^{3} +5.80974 q^{4} -0.914621 q^{5} +3.38731 q^{6} -4.48023 q^{7} -10.6467 q^{8} -1.53083 q^{9} +2.55599 q^{10} -0.426492 q^{11} -7.04195 q^{12} +1.28558 q^{13} +12.5204 q^{14} +1.10861 q^{15} +18.1336 q^{16} +0.227643 q^{17} +4.27803 q^{18} -1.98146 q^{19} -5.31371 q^{20} +5.43046 q^{21} +1.19187 q^{22} +4.20384 q^{23} +12.9048 q^{24} -4.16347 q^{25} -3.59268 q^{26} +5.49179 q^{27} -26.0289 q^{28} +6.36822 q^{29} -3.09810 q^{30} -5.34668 q^{31} -29.3826 q^{32} +0.516949 q^{33} -0.636168 q^{34} +4.09771 q^{35} -8.89370 q^{36} -3.57269 q^{37} +5.53737 q^{38} -1.55825 q^{39} +9.73766 q^{40} -3.75719 q^{41} -15.1759 q^{42} -7.55646 q^{43} -2.47781 q^{44} +1.40013 q^{45} -11.7480 q^{46} -8.56097 q^{47} -21.9796 q^{48} +13.0724 q^{49} +11.6352 q^{50} -0.275924 q^{51} +7.46890 q^{52} -5.56404 q^{53} -15.3473 q^{54} +0.390079 q^{55} +47.6994 q^{56} +2.40172 q^{57} -17.7966 q^{58} +0.103212 q^{59} +6.44072 q^{60} +2.40502 q^{61} +14.9418 q^{62} +6.85845 q^{63} +45.8453 q^{64} -1.17582 q^{65} -1.44466 q^{66} +13.5164 q^{67} +1.32254 q^{68} -5.09545 q^{69} -11.4514 q^{70} +10.0796 q^{71} +16.2982 q^{72} +1.33086 q^{73} +9.98422 q^{74} +5.04652 q^{75} -11.5118 q^{76} +1.91078 q^{77} +4.35467 q^{78} +11.1553 q^{79} -16.5854 q^{80} -2.06409 q^{81} +10.4998 q^{82} -8.22887 q^{83} +31.5495 q^{84} -0.208207 q^{85} +21.1172 q^{86} -7.71888 q^{87} +4.54072 q^{88} +9.10999 q^{89} -3.91278 q^{90} -5.75970 q^{91} +24.4232 q^{92} +6.48068 q^{93} +23.9244 q^{94} +1.81228 q^{95} +35.6145 q^{96} -3.49954 q^{97} -36.5321 q^{98} +0.652885 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.79459	−1.97607	−0.988037	−	0.154216i	$-0.950715\pi$
$2$	−2.79459	−1.97607	−0.988037	+	0.154216i	$0.950715\pi$
$3$	−1.21209	−0.699803	−0.349902	−	0.936786i	$-0.613785\pi$
$3$	−1.21209	−0.699803	−0.349902	+	0.936786i	$0.613785\pi$
$4$	5.80974	2.90487
$5$	−0.914621	−0.409031	−0.204516	−	0.978863i	$-0.565562\pi$
$5$	−0.914621	−0.409031	−0.204516	+	0.978863i	$0.565562\pi$
$6$	3.38731	1.38286
$7$	−4.48023	−1.69337	−0.846683	−	0.532098i	$-0.821404\pi$
$7$	−4.48023	−1.69337	−0.846683	+	0.532098i	$0.821404\pi$
$8$	−10.6467	−3.76416
$9$	−1.53083	−0.510276
$10$	2.55599	0.808276
$11$	−0.426492	−0.128592	−0.0642961	−	0.997931i	$-0.520480\pi$
$11$	−0.426492	−0.128592	−0.0642961	+	0.997931i	$0.520480\pi$
$12$	−7.04195	−2.03284
$13$	1.28558	0.356557	0.178278	−	0.983980i	$-0.442947\pi$
$13$	1.28558	0.356557	0.178278	+	0.983980i	$0.442947\pi$
$14$	12.5204	3.34622
$15$	1.10861	0.286241
$16$	18.1336	4.53340
$17$	0.227643	0.0552115	0.0276057	−	0.999619i	$-0.491212\pi$
$17$	0.227643	0.0552115	0.0276057	+	0.999619i	$0.491212\pi$
$18$	4.27803	1.00834
$19$	−1.98146	−0.454578	−0.227289	−	0.973827i	$-0.572986\pi$
$19$	−1.98146	−0.454578	−0.227289	+	0.973827i	$0.572986\pi$
$20$	−5.31371	−1.18818
$21$	5.43046	1.18502
$22$	1.19187	0.254108
$23$	4.20384	0.876560	0.438280	−	0.898838i	$-0.355588\pi$
$23$	4.20384	0.876560	0.438280	+	0.898838i	$0.355588\pi$
$24$	12.9048	2.63417
$25$	−4.16347	−0.832694
$26$	−3.59268	−0.704582
$27$	5.49179	1.05690
$28$	−26.0289	−4.91901
$29$	6.36822	1.18255	0.591274	−	0.806471i	$-0.298625\pi$
$29$	6.36822	1.18255	0.591274	+	0.806471i	$0.298625\pi$
$30$	−3.09810	−0.565634
$31$	−5.34668	−0.960292	−0.480146	−	0.877189i	$-0.659416\pi$
$31$	−5.34668	−0.960292	−0.480146	+	0.877189i	$0.659416\pi$
$32$	−29.3826	−5.19416
$33$	0.516949	0.0899892
$34$	−0.636168	−0.109102
$35$	4.09771	0.692639
$36$	−8.89370	−1.48228
$37$	−3.57269	−0.587347	−0.293674	−	0.955906i	$-0.594878\pi$
$37$	−3.57269	−0.587347	−0.293674	+	0.955906i	$0.594878\pi$
$38$	5.53737	0.898279
$39$	−1.55825	−0.249519
$40$	9.73766	1.53966
$41$	−3.75719	−0.586775	−0.293387	−	0.955994i	$-0.594783\pi$
$41$	−3.75719	−0.586775	−0.293387	+	0.955994i	$0.594783\pi$
$42$	−15.1759	−2.34169
$43$	−7.55646	−1.15235	−0.576174	−	0.817327i	$-0.695455\pi$
$43$	−7.55646	−1.15235	−0.576174	+	0.817327i	$0.695455\pi$
$44$	−2.47781	−0.373543
$45$	1.40013	0.208719
$46$	−11.7480	−1.73215
$47$	−8.56097	−1.24875	−0.624373	−	0.781126i	$-0.714646\pi$
$47$	−8.56097	−1.24875	−0.624373	+	0.781126i	$0.714646\pi$
$48$	−21.9796	−3.17248
$49$	13.0724	1.86749
$50$	11.6352	1.64546
$51$	−0.275924	−0.0386372
$52$	7.46890	1.03575
$53$	−5.56404	−0.764280	−0.382140	−	0.924104i	$-0.624813\pi$
$53$	−5.56404	−0.764280	−0.382140	+	0.924104i	$0.624813\pi$
$54$	−15.3473	−2.08850
$55$	0.390079	0.0525982
$56$	47.6994	6.37411
$57$	2.40172	0.318115
$58$	−17.7966	−2.33680
$59$	0.103212	0.0134370	0.00671850	−	0.999977i	$-0.497861\pi$
$59$	0.103212	0.0134370	0.00671850	+	0.999977i	$0.497861\pi$
$60$	6.44072	0.831493
$61$	2.40502	0.307931	0.153966	−	0.988076i	$-0.450795\pi$
$61$	2.40502	0.307931	0.153966	+	0.988076i	$0.450795\pi$
$62$	14.9418	1.89761
$63$	6.85845	0.864083
$64$	45.8453	5.73066
$65$	−1.17582	−0.145843
$66$	−1.44466	−0.177825
$67$	13.5164	1.65129	0.825645	−	0.564190i	$-0.190812\pi$
$67$	13.5164	1.65129	0.825645	+	0.564190i	$0.190812\pi$
$68$	1.32254	0.160382
$69$	−5.09545	−0.613420
$70$	−11.4514	−1.36871
$71$	10.0796	1.19623	0.598117	−	0.801409i	$-0.295916\pi$
$71$	10.0796	1.19623	0.598117	+	0.801409i	$0.295916\pi$
$72$	16.2982	1.92076
$73$	1.33086	0.155765	0.0778825	−	0.996963i	$-0.475184\pi$
$73$	1.33086	0.155765	0.0778825	+	0.996963i	$0.475184\pi$
$74$	9.98422	1.16064
$75$	5.04652	0.582722
$76$	−11.5118	−1.32049
$77$	1.91078	0.217754
$78$	4.35467	0.493069
$79$	11.1553	1.25507	0.627533	−	0.778590i	$-0.284065\pi$
$79$	11.1553	1.25507	0.627533	+	0.778590i	$0.284065\pi$
$80$	−16.5854	−1.85430
$81$	−2.06409	−0.229343
$82$	10.4998	1.15951
$83$	−8.22887	−0.903235	−0.451618	−	0.892212i	$-0.649153\pi$
$83$	−8.22887	−0.903235	−0.451618	+	0.892212i	$0.649153\pi$
$84$	31.5495	3.44234
$85$	−0.208207	−0.0225832
$86$	21.1172	2.27713
$87$	−7.71888	−0.827551
$88$	4.54072	0.484042
$89$	9.10999	0.965657	0.482828	−	0.875715i	$-0.339609\pi$
$89$	9.10999	0.965657	0.482828	+	0.875715i	$0.339609\pi$
$90$	−3.91278	−0.412443
$91$	−5.75970	−0.603781
$92$	24.4232	2.54629
$93$	6.48068	0.672015
$94$	23.9244	2.46762
$95$	1.81228	0.185936
$96$	35.6145	3.63489
$97$	−3.49954	−0.355325	−0.177662	−	0.984092i	$-0.556853\pi$
$97$	−3.49954	−0.355325	−0.177662	+	0.984092i	$0.556853\pi$
$98$	−36.5321	−3.69030
$99$	0.652885	0.0656174
$100$	−24.1887	−2.41887
$101$	14.2807	1.42098	0.710491	−	0.703706i	$-0.248473\pi$
$101$	14.2807	1.42098	0.710491	+	0.703706i	$0.248473\pi$
$102$	0.771096	0.0763499
$103$	8.44198	0.831813	0.415906	−	0.909407i	$-0.363464\pi$
$103$	8.44198	0.831813	0.415906	+	0.909407i	$0.363464\pi$
$104$	−13.6872	−1.34214
$105$	−4.96681	−0.484711
$106$	15.5492	1.51027
$107$	13.1668	1.27288	0.636442	−	0.771325i	$-0.280405\pi$
$107$	13.1668	1.27288	0.636442	+	0.771325i	$0.280405\pi$
$108$	31.9059	3.07014
$109$	−19.9674	−1.91253	−0.956266	−	0.292499i	$-0.905513\pi$
$109$	−19.9674	−1.91253	−0.956266	+	0.292499i	$0.905513\pi$
$110$	−1.09011	−0.103938
$111$	4.33044	0.411027
$112$	−81.2425	−7.67670
$113$	−8.46305	−0.796137	−0.398069	−	0.917356i	$-0.630319\pi$
$113$	−8.46305	−0.796137	−0.398069	+	0.917356i	$0.630319\pi$
$114$	−6.71181	−0.628619
$115$	−3.84492	−0.358540
$116$	36.9977	3.43515
$117$	−1.96801	−0.181942
$118$	−0.288434	−0.0265525
$119$	−1.01989	−0.0934932
$120$	−11.8030	−1.07746
$121$	−10.8181	−0.983464
$122$	−6.72105	−0.608495
$123$	4.55407	0.410627
$124$	−31.0628	−2.78952
$125$	8.38110	0.749629
$126$	−19.1666	−1.70749
$127$	3.29113	0.292041	0.146020	−	0.989282i	$-0.453354\pi$
$127$	3.29113	0.292041	0.146020	+	0.989282i	$0.453354\pi$
$128$	−69.3535	−6.13004
$129$	9.15914	0.806417
$130$	3.28594	0.288196
$131$	16.5949	1.44990	0.724951	−	0.688801i	$-0.241863\pi$
$131$	16.5949	1.44990	0.724951	+	0.688801i	$0.241863\pi$
$132$	3.00334	0.261407
$133$	8.87738	0.769766
$134$	−37.7728	−3.26307
$135$	−5.02291	−0.432303
$136$	−2.42363	−0.207825
$137$	12.5911	1.07573	0.537867	−	0.843030i	$-0.319230\pi$
$137$	12.5911	1.07573	0.537867	+	0.843030i	$0.319230\pi$
$138$	14.2397	1.21216
$139$	8.71606	0.739286	0.369643	−	0.929174i	$-0.379480\pi$
$139$	8.71606	0.739286	0.369643	+	0.929174i	$0.379480\pi$
$140$	23.8066	2.01203
$141$	10.3767	0.873877
$142$	−28.1685	−2.36385
$143$	−0.548291	−0.0458504
$144$	−27.7594	−2.31328
$145$	−5.82451	−0.483699
$146$	−3.71920	−0.307803
$147$	−15.8450	−1.30687
$148$	−20.7564	−1.70617
$149$	5.23431	0.428811	0.214406	−	0.976745i	$-0.431219\pi$
$149$	5.23431	0.428811	0.214406	+	0.976745i	$0.431219\pi$
$150$	−14.1030	−1.15150
$151$	18.4396	1.50059	0.750295	−	0.661103i	$-0.229911\pi$
$151$	18.4396	1.50059	0.750295	+	0.661103i	$0.229911\pi$
$152$	21.0959	1.71110
$153$	−0.348482	−0.0281731
$154$	−5.33985	−0.430297
$155$	4.89019	0.392789
$156$	−9.05302	−0.724821
$157$	−16.8694	−1.34632	−0.673161	−	0.739496i	$-0.735064\pi$
$157$	−16.8694	−1.34632	−0.673161	+	0.739496i	$0.735064\pi$
$158$	−31.1744	−2.48010
$159$	6.74414	0.534845
$160$	26.8740	2.12457
$161$	−18.8341	−1.48434
$162$	5.76828	0.453199
$163$	−8.95554	−0.701452	−0.350726	−	0.936478i	$-0.614065\pi$
$163$	−8.95554	−0.701452	−0.350726	+	0.936478i	$0.614065\pi$
$164$	−21.8283	−1.70450
$165$	−0.472812	−0.0368084
$166$	22.9963	1.78486
$167$	15.5230	1.20121	0.600604	−	0.799547i	$-0.294927\pi$
$167$	15.5230	1.20121	0.600604	+	0.799547i	$0.294927\pi$
$168$	−57.8162	−4.46062
$169$	−11.3473	−0.872867
$170$	0.581853	0.0446261
$171$	3.03327	0.231960
$172$	−43.9010	−3.34742
$173$	21.4978	1.63444	0.817222	−	0.576323i	$-0.195513\pi$
$173$	21.4978	1.63444	0.817222	+	0.576323i	$0.195513\pi$
$174$	21.5711	1.63530
$175$	18.6533	1.41005
$176$	−7.73383	−0.582959
$177$	−0.125102	−0.00940326
$178$	−25.4587	−1.90821
$179$	22.0751	1.64997	0.824985	−	0.565155i	$-0.191184\pi$
$179$	22.0751	1.64997	0.824985	+	0.565155i	$0.191184\pi$
$180$	8.13437	0.606300
$181$	−2.76545	−0.205554	−0.102777	−	0.994704i	$-0.532773\pi$
$181$	−2.76545	−0.205554	−0.102777	+	0.994704i	$0.532773\pi$
$182$	16.0960	1.19312
$183$	−2.91511	−0.215491
$184$	−44.7568	−3.29952
$185$	3.26766	0.240243
$186$	−18.1109	−1.32795
$187$	−0.0970878	−0.00709976
$188$	−49.7370	−3.62745
$189$	−24.6045	−1.78971
$190$	−5.06459	−0.367424
$191$	−5.13896	−0.371842	−0.185921	−	0.982565i	$-0.559527\pi$
$191$	−5.13896	−0.371842	−0.185921	+	0.982565i	$0.559527\pi$
$192$	−55.5688	−4.01033
$193$	10.7492	0.773743	0.386871	−	0.922134i	$-0.373556\pi$
$193$	10.7492	0.773743	0.386871	+	0.922134i	$0.373556\pi$
$194$	9.77979	0.702148
$195$	1.42521	0.102061
$196$	75.9473	5.42481
$197$	−9.37150	−0.667692	−0.333846	−	0.942628i	$-0.608347\pi$
$197$	−9.37150	−0.667692	−0.333846	+	0.942628i	$0.608347\pi$
$198$	−1.82455	−0.129665
$199$	−10.9046	−0.773008	−0.386504	−	0.922288i	$-0.626317\pi$
$199$	−10.9046	−0.773008	−0.386504	+	0.922288i	$0.626317\pi$
$200$	44.3270	3.13439
$201$	−16.3831	−1.15558
$202$	−39.9087	−2.80797
$203$	−28.5310	−2.00249
$204$	−1.60305	−0.112236
$205$	3.43641	0.240009
$206$	−23.5919	−1.64372
$207$	−6.43534	−0.447287
$208$	23.3122	1.61641
$209$	0.845076	0.0584551
$210$	13.8802	0.957825
$211$	17.8231	1.22699	0.613496	−	0.789697i	$-0.289762\pi$
$211$	17.8231	1.22699	0.613496	+	0.789697i	$0.289762\pi$
$212$	−32.3256	−2.22013
$213$	−12.2175	−0.837128
$214$	−36.7959	−2.51531
$215$	6.91130	0.471346
$216$	−58.4692	−3.97833
$217$	23.9543	1.62613
$218$	55.8008	3.77931
$219$	−1.61312	−0.109005
$220$	2.26625	0.152791
$221$	0.292654	0.0196860
$222$	−12.1018	−0.812221
$223$	−12.7356	−0.852841	−0.426420	−	0.904525i	$-0.640226\pi$
$223$	−12.7356	−0.852841	−0.426420	+	0.904525i	$0.640226\pi$
$224$	131.641	8.79562
$225$	6.37355	0.424903
$226$	23.6508	1.57323
$227$	12.2520	0.813193	0.406596	−	0.913608i	$-0.366716\pi$
$227$	12.2520	0.813193	0.406596	+	0.913608i	$0.366716\pi$
$228$	13.9533	0.924082
$229$	−18.1485	−1.19929	−0.599644	−	0.800267i	$-0.704691\pi$
$229$	−18.1485	−1.19929	−0.599644	+	0.800267i	$0.704691\pi$
$230$	10.7450	0.708502
$231$	−2.31605	−0.152385
$232$	−67.8003	−4.45130
$233$	9.03271	0.591753	0.295876	−	0.955226i	$-0.404388\pi$
$233$	9.03271	0.591753	0.295876	+	0.955226i	$0.404388\pi$
$234$	5.49977	0.359531
$235$	7.83005	0.510776
$236$	0.599632	0.0390327
$237$	−13.5212	−0.878299
$238$	2.85018	0.184750
$239$	8.44914	0.546529	0.273265	−	0.961939i	$-0.411897\pi$
$239$	8.44914	0.546529	0.273265	+	0.961939i	$0.411897\pi$
$240$	20.1030	1.29764
$241$	2.43983	0.157163	0.0785816	−	0.996908i	$-0.474961\pi$
$241$	2.43983	0.157163	0.0785816	+	0.996908i	$0.474961\pi$
$242$	30.2322	1.94340
$243$	−13.9735	−0.896400
$244$	13.9725	0.894500
$245$	−11.9563	−0.763861
$246$	−12.7268	−0.811429
$247$	−2.54733	−0.162083
$248$	56.9243	3.61470
$249$	9.97416	0.632087
$250$	−23.4218	−1.48132
$251$	17.0662	1.07721	0.538605	−	0.842559i	$-0.318952\pi$
$251$	17.0662	1.07721	0.538605	+	0.842559i	$0.318952\pi$
$252$	39.8458	2.51005
$253$	−1.79290	−0.112719
$254$	−9.19736	−0.577094
$255$	0.252366	0.0158038
$256$	102.124	6.38276
$257$	−11.6261	−0.725218	−0.362609	−	0.931941i	$-0.618114\pi$
$257$	−11.6261	−0.725218	−0.362609	+	0.931941i	$0.618114\pi$
$258$	−25.5961	−1.59354
$259$	16.0065	0.994594
$260$	−6.83122	−0.423654
$261$	−9.74864	−0.603426
$262$	−46.3759	−2.86511
$263$	−23.8543	−1.47092	−0.735461	−	0.677567i	$-0.763034\pi$
$263$	−23.8543	−1.47092	−0.735461	+	0.677567i	$0.763034\pi$
$264$	−5.50378	−0.338734
$265$	5.08899	0.312614
$266$	−24.8086	−1.52112
$267$	−11.0422	−0.675770
$268$	78.5267	4.79678
$269$	−6.57940	−0.401153	−0.200577	−	0.979678i	$-0.564282\pi$
$269$	−6.57940	−0.401153	−0.200577	+	0.979678i	$0.564282\pi$
$270$	14.0370	0.854263
$271$	−5.30090	−0.322007	−0.161003	−	0.986954i	$-0.551473\pi$
$271$	−5.30090	−0.322007	−0.161003	+	0.986954i	$0.551473\pi$
$272$	4.12798	0.250295
$273$	6.98130	0.422528
$274$	−35.1871	−2.12573
$275$	1.77569	0.107078
$276$	−29.6032	−1.78190
$277$	−0.197680	−0.0118774	−0.00593872	−	0.999982i	$-0.501890\pi$
$277$	−0.197680	−0.0118774	−0.00593872	+	0.999982i	$0.501890\pi$
$278$	−24.3578	−1.46088
$279$	8.18484	0.490014
$280$	−43.6269	−2.60721
$281$	2.34482	0.139880	0.0699401	−	0.997551i	$-0.477719\pi$
$281$	2.34482	0.139880	0.0699401	+	0.997551i	$0.477719\pi$
$282$	−28.9987	−1.72685
$283$	−11.2977	−0.671581	−0.335791	−	0.941937i	$-0.609003\pi$
$283$	−11.2977	−0.671581	−0.335791	+	0.941937i	$0.609003\pi$
$284$	58.5601	3.47490
$285$	−2.19666	−0.130119
$286$	1.53225	0.0906038
$287$	16.8331	0.993624
$288$	44.9797	2.65046
$289$	−16.9482	−0.996952
$290$	16.2771	0.955825
$291$	4.24178	0.248657
$292$	7.73193	0.452477
$293$	−4.08951	−0.238912	−0.119456	−	0.992840i	$-0.538115\pi$
$293$	−4.08951	−0.238912	−0.119456	+	0.992840i	$0.538115\pi$
$294$	44.2803	2.58248
$295$	−0.0943995	−0.00549615
$296$	38.0373	2.21087
$297$	−2.34220	−0.135908
$298$	−14.6277	−0.847363
$299$	5.40438	0.312543
$300$	29.3189	1.69273
$301$	33.8546	1.95135
$302$	−51.5310	−2.96528
$303$	−17.3096	−0.994408
$304$	−35.9309	−2.06078
$305$	−2.19968	−0.125953
$306$	0.973863	0.0556721
$307$	−19.5149	−1.11377	−0.556887	−	0.830588i	$-0.688005\pi$
$307$	−19.5149	−1.11377	−0.556887	+	0.830588i	$0.688005\pi$
$308$	11.1011	0.632546
$309$	−10.2325	−0.582105
$310$	−13.6661	−0.776181
$311$	9.29974	0.527340	0.263670	−	0.964613i	$-0.415067\pi$
$311$	9.29974	0.527340	0.263670	+	0.964613i	$0.415067\pi$
$312$	16.5901	0.939232
$313$	24.8537	1.40481	0.702406	−	0.711777i	$-0.252109\pi$
$313$	24.8537	1.40481	0.702406	+	0.711777i	$0.252109\pi$
$314$	47.1430	2.66043
$315$	−6.27288	−0.353437
$316$	64.8092	3.64580
$317$	−15.6566	−0.879361	−0.439680	−	0.898154i	$-0.644908\pi$
$317$	−15.6566	−0.879361	−0.439680	+	0.898154i	$0.644908\pi$
$318$	−18.8471	−1.05689
$319$	−2.71599	−0.152066
$320$	−41.9311	−2.34402
$321$	−15.9594	−0.890768
$322$	52.6337	2.93316
$323$	−0.451065	−0.0250979
$324$	−11.9918	−0.666212
$325$	−5.35249	−0.296902
$326$	25.0271	1.38612
$327$	24.2024	1.33840
$328$	40.0015	2.20872
$329$	38.3551	2.11458
$330$	1.32132	0.0727361
$331$	−16.7878	−0.922742	−0.461371	−	0.887207i	$-0.652642\pi$
$331$	−16.7878	−0.922742	−0.461371	+	0.887207i	$0.652642\pi$
$332$	−47.8076	−2.62378
$333$	5.46917	0.299709
$334$	−43.3805	−2.37368
$335$	−12.3624	−0.675429
$336$	98.4736	5.37218
$337$	−11.2959	−0.615327	−0.307663	−	0.951495i	$-0.599547\pi$
$337$	−11.2959	−0.615327	−0.307663	+	0.951495i	$0.599547\pi$
$338$	31.7110	1.72485
$339$	10.2580	0.557139
$340$	−1.20963	−0.0656013
$341$	2.28032	0.123486
$342$	−8.47675	−0.458370
$343$	−27.2058	−1.46897
$344$	80.4510	4.33763
$345$	4.66040	0.250908
$346$	−60.0774	−3.22978
$347$	−21.4097	−1.14933	−0.574666	−	0.818388i	$-0.694868\pi$
$347$	−21.4097	−1.14933	−0.574666	+	0.818388i	$0.694868\pi$
$348$	−44.8447	−2.40393
$349$	30.0560	1.60886	0.804430	−	0.594047i	$-0.202471\pi$
$349$	30.0560	1.60886	0.804430	+	0.594047i	$0.202471\pi$
$350$	−52.1283	−2.78637
$351$	7.06015	0.376843
$352$	12.5315	0.667929
$353$	30.1272	1.60351	0.801754	−	0.597654i	$-0.203900\pi$
$353$	30.1272	1.60351	0.801754	+	0.597654i	$0.203900\pi$
$354$	0.349609	0.0185815
$355$	−9.21906	−0.489297
$356$	52.9267	2.80511
$357$	1.23620	0.0654268
$358$	−61.6909	−3.26046
$359$	10.5728	0.558014	0.279007	−	0.960289i	$-0.409995\pi$
$359$	10.5728	0.558014	0.279007	+	0.960289i	$0.409995\pi$
$360$	−14.9067	−0.785651
$361$	−15.0738	−0.793359
$362$	7.72829	0.406190
$363$	13.1126	0.688231
$364$	−33.4624	−1.75390
$365$	−1.21723	−0.0637127
$366$	8.14654	0.425827
$367$	22.3650	1.16744	0.583722	−	0.811953i	$-0.301596\pi$
$367$	22.3650	1.16744	0.583722	+	0.811953i	$0.301596\pi$
$368$	76.2306	3.97379
$369$	5.75161	0.299417
$370$	−9.13178	−0.474738
$371$	24.9282	1.29421
$372$	37.6511	1.95212
$373$	6.94599	0.359650	0.179825	−	0.983699i	$-0.442447\pi$
$373$	6.94599	0.359650	0.179825	+	0.983699i	$0.442447\pi$
$374$	0.271321	0.0140297
$375$	−10.1587	−0.524592
$376$	91.1458	4.70049
$377$	8.18688	0.421646
$378$	68.7594	3.53660
$379$	−9.23700	−0.474473	−0.237236	−	0.971452i	$-0.576242\pi$
$379$	−9.23700	−0.474473	−0.237236	+	0.971452i	$0.576242\pi$
$380$	10.5289	0.540121
$381$	−3.98916	−0.204371
$382$	14.3613	0.734788
$383$	20.9399	1.06998	0.534990	−	0.844858i	$-0.320315\pi$
$383$	20.9399	1.06998	0.534990	+	0.844858i	$0.320315\pi$
$384$	84.0630	4.28982
$385$	−1.74764	−0.0890680
$386$	−30.0396	−1.52897
$387$	11.5676	0.588016
$388$	−20.3314	−1.03217
$389$	−0.0122573	−0.000621468 0	−0.000310734	−	1.00000i	$-0.500099\pi$
$389$	−0.0122573	−0.000621468 0	−0.000310734		1.00000i	$0.500099\pi$
$390$	−3.98287	−0.201681
$391$	0.956972	0.0483962
$392$	−139.178	−7.02953
$393$	−20.1146	−1.01465
$394$	26.1895	1.31941
$395$	−10.2028	−0.513361
$396$	3.79309	0.190610
$397$	−30.7464	−1.54312	−0.771560	−	0.636157i	$-0.780523\pi$
$397$	−30.7464	−1.54312	−0.771560	+	0.636157i	$0.780523\pi$
$398$	30.4739	1.52752
$399$	−10.7602	−0.538685
$400$	−75.4986	−3.77493
$401$	2.95771	0.147701	0.0738506	−	0.997269i	$-0.476471\pi$
$401$	2.95771	0.147701	0.0738506	+	0.997269i	$0.476471\pi$
$402$	45.7842	2.28351
$403$	−6.87360	−0.342399
$404$	82.9671	4.12777
$405$	1.88786	0.0938085
$406$	79.7326	3.95706
$407$	1.52372	0.0755282
$408$	2.93767	0.145437
$409$	−14.5776	−0.720815	−0.360407	−	0.932795i	$-0.617362\pi$
$409$	−14.5776	−0.720815	−0.360407	+	0.932795i	$0.617362\pi$
$410$	−9.60335	−0.474276
$411$	−15.2616	−0.752801
$412$	49.0457	2.41631
$413$	−0.462411	−0.0227538
$414$	17.9842	0.883873
$415$	7.52630	0.369451
$416$	−37.7738	−1.85201
$417$	−10.5647	−0.517355
$418$	−2.36164	−0.115512
$419$	−15.6697	−0.765516	−0.382758	−	0.923849i	$-0.625026\pi$
$419$	−15.6697	−0.765516	−0.382758	+	0.923849i	$0.625026\pi$
$420$	−28.8559	−1.40802
$421$	3.49158	0.170169	0.0850845	−	0.996374i	$-0.472884\pi$
$421$	3.49158	0.170169	0.0850845	+	0.996374i	$0.472884\pi$
$422$	−49.8083	−2.42463
$423$	13.1054	0.637205
$424$	59.2385	2.87687
$425$	−0.947783	−0.0459742
$426$	34.1429	1.65423
$427$	−10.7750	−0.521440
$428$	76.4958	3.69756
$429$	0.664580	0.0320862
$430$	−19.3142	−0.931416
$431$	11.1372	0.536458	0.268229	−	0.963355i	$-0.413562\pi$
$431$	11.1372	0.536458	0.268229	+	0.963355i	$0.413562\pi$
$432$	99.5859	4.79133
$433$	16.9007	0.812195	0.406097	−	0.913830i	$-0.366889\pi$
$433$	16.9007	0.812195	0.406097	+	0.913830i	$0.366889\pi$
$434$	−66.9426	−3.21335
$435$	7.05985	0.338494
$436$	−116.005	−5.55566
$437$	−8.32972	−0.398465
$438$	4.50802	0.215402
$439$	10.5749	0.504712	0.252356	−	0.967634i	$-0.418795\pi$
$439$	10.5749	0.504712	0.252356	+	0.967634i	$0.418795\pi$
$440$	−4.15303	−0.197988
$441$	−20.0116	−0.952934
$442$	−0.817847	−0.0389010
$443$	−32.2616	−1.53280	−0.766398	−	0.642366i	$-0.777953\pi$
$443$	−32.2616	−1.53280	−0.766398	+	0.642366i	$0.777953\pi$
$444$	25.1587	1.19398
$445$	−8.33219	−0.394984
$446$	35.5909	1.68528
$447$	−6.34447	−0.300083
$448$	−205.397	−9.70410
$449$	−29.3845	−1.38674	−0.693370	−	0.720582i	$-0.743875\pi$
$449$	−29.3845	−1.38674	−0.693370	+	0.720582i	$0.743875\pi$
$450$	−17.8115	−0.839640
$451$	1.60241	0.0754546
$452$	−49.1681	−2.31267
$453$	−22.3505	−1.05012
$454$	−34.2393	−1.60693
$455$	5.26795	0.246965
$456$	−25.5702	−1.19744
$457$	33.0180	1.54452	0.772259	−	0.635308i	$-0.219127\pi$
$457$	33.0180	1.54452	0.772259	+	0.635308i	$0.219127\pi$
$458$	50.7177	2.36988
$459$	1.25017	0.0583528
$460$	−22.3380	−1.04151
$461$	−23.1621	−1.07877	−0.539383	−	0.842060i	$-0.681343\pi$
$461$	−23.1621	−1.07877	−0.539383	+	0.842060i	$0.681343\pi$
$462$	6.47240	0.301123
$463$	−36.2814	−1.68614	−0.843071	−	0.537803i	$-0.819255\pi$
$463$	−36.2814	−1.68614	−0.843071	+	0.537803i	$0.819255\pi$
$464$	115.479	5.36096
$465$	−5.92737	−0.274875
$466$	−25.2427	−1.16935
$467$	11.9344	0.552259	0.276129	−	0.961120i	$-0.410948\pi$
$467$	11.9344	0.552259	0.276129	+	0.961120i	$0.410948\pi$
$468$	−11.4336	−0.528518
$469$	−60.5565	−2.79624
$470$	−21.8818	−1.00933
$471$	20.4473	0.942161
$472$	−1.09886	−0.0505791
$473$	3.22277	0.148183
$474$	37.7863	1.73558
$475$	8.24974	0.378524
$476$	−5.92530	−0.271586
$477$	8.51758	0.389993
$478$	−23.6119	−1.07998
$479$	−5.21423	−0.238244	−0.119122	−	0.992880i	$-0.538008\pi$
$479$	−5.21423	−0.238244	−0.119122	+	0.992880i	$0.538008\pi$
$480$	−32.5738	−1.48678
$481$	−4.59300	−0.209423
$482$	−6.81832	−0.310566
$483$	22.8287	1.03874
$484$	−62.8504	−2.85683
$485$	3.20076	0.145339
$486$	39.0502	1.77135
$487$	8.81548	0.399467	0.199734	−	0.979850i	$-0.435992\pi$
$487$	8.81548	0.399467	0.199734	+	0.979850i	$0.435992\pi$
$488$	−25.6054	−1.15910
$489$	10.8550	0.490878
$490$	33.4130	1.50945
$491$	40.2465	1.81630	0.908150	−	0.418644i	$-0.137495\pi$
$491$	40.2465	1.81630	0.908150	+	0.418644i	$0.137495\pi$
$492$	26.4580	1.19282
$493$	1.44968	0.0652902
$494$	7.11875	0.320288
$495$	−0.597143	−0.0268396
$496$	−96.9545	−4.35339
$497$	−45.1591	−2.02566
$498$	−27.8737	−1.24905
$499$	−39.4831	−1.76751	−0.883753	−	0.467954i	$-0.844991\pi$
$499$	−39.4831	−1.76751	−0.883753	+	0.467954i	$0.844991\pi$
$500$	48.6920	2.17757
$501$	−18.8154	−0.840609
$502$	−47.6931	−2.12865
$503$	9.67938	0.431582	0.215791	−	0.976440i	$-0.430767\pi$
$503$	9.67938	0.431582	0.215791	+	0.976440i	$0.430767\pi$
$504$	−73.0196	−3.25255
$505$	−13.0614	−0.581226
$506$	5.01043	0.222741
$507$	13.7540	0.610835
$508$	19.1206	0.848340
$509$	−9.00561	−0.399167	−0.199583	−	0.979881i	$-0.563959\pi$
$509$	−9.00561	−0.399167	−0.199583	+	0.979881i	$0.563959\pi$
$510$	−0.705261	−0.0312295
$511$	−5.96254	−0.263767
$512$	−146.688	−6.48276
$513$	−10.8818	−0.480441
$514$	32.4903	1.43308
$515$	−7.72121	−0.340237
$516$	53.2122	2.34254
$517$	3.65119	0.160579
$518$	−44.7315	−1.96539
$519$	−26.0573	−1.14379
$520$	12.5186	0.548976
$521$	−31.6804	−1.38794	−0.693972	−	0.720002i	$-0.744141\pi$
$521$	−31.6804	−1.38794	−0.693972	+	0.720002i	$0.744141\pi$
$522$	27.2435	1.19241
$523$	−26.6852	−1.16686	−0.583432	−	0.812162i	$-0.698290\pi$
$523$	−26.6852	−1.16686	−0.583432	+	0.812162i	$0.698290\pi$
$524$	96.4119	4.21177
$525$	−22.6095	−0.986761
$526$	66.6631	2.90665
$527$	−1.21713	−0.0530191
$528$	9.37413	0.407957
$529$	−5.32777	−0.231642
$530$	−14.2216	−0.617749
$531$	−0.157999	−0.00685658
$532$	51.5753	2.23607
$533$	−4.83018	−0.209218
$534$	30.8583	1.33537
$535$	−12.0426	−0.520649
$536$	−143.904	−6.21572
$537$	−26.7571	−1.15465
$538$	18.3867	0.792708
$539$	−5.57528	−0.240144
$540$	−29.1818	−1.25578
$541$	−30.1681	−1.29703	−0.648513	−	0.761203i	$-0.724609\pi$
$541$	−30.1681	−1.29703	−0.648513	+	0.761203i	$0.724609\pi$
$542$	14.8138	0.636309
$543$	3.35198	0.143847
$544$	−6.68874	−0.286777
$545$	18.2626	0.782285
$546$	−19.5099	−0.834946
$547$	25.7822	1.10237	0.551184	−	0.834384i	$-0.314176\pi$
$547$	25.7822	1.10237	0.551184	+	0.834384i	$0.314176\pi$
$548$	73.1512	3.12486
$549$	−3.68167	−0.157130
$550$	−4.96231	−0.211594
$551$	−12.6184	−0.537560
$552$	54.2495	2.30901
$553$	−49.9781	−2.12529
$554$	0.552435	0.0234707
$555$	−3.96071	−0.168123
$556$	50.6380	2.14753
$557$	3.17946	0.134718	0.0673589	−	0.997729i	$-0.478543\pi$
$557$	3.17946	0.134718	0.0673589	+	0.997729i	$0.478543\pi$
$558$	−22.8733	−0.968303
$559$	−9.71446	−0.410878
$560$	74.3062	3.14001
$561$	0.117680	0.00496844
$562$	−6.55281	−0.276414
$563$	−23.5743	−0.993536	−0.496768	−	0.867883i	$-0.665480\pi$
$563$	−23.5743	−0.993536	−0.496768	+	0.867883i	$0.665480\pi$
$564$	60.2860	2.53850
$565$	7.74049	0.325645
$566$	31.5726	1.32709
$567$	9.24758	0.388362
$568$	−107.315	−4.50282
$569$	−29.3245	−1.22934	−0.614672	−	0.788782i	$-0.710712\pi$
$569$	−29.3245	−1.22934	−0.614672	+	0.788782i	$0.710712\pi$
$570$	6.13877	0.257125
$571$	−25.9696	−1.08679	−0.543397	−	0.839476i	$-0.682862\pi$
$571$	−25.9696	−1.08679	−0.543397	+	0.839476i	$0.682862\pi$
$572$	−3.18543	−0.133189
$573$	6.22891	0.260216
$574$	−47.0415	−1.96348
$575$	−17.5025	−0.729906
$576$	−70.1812	−2.92422
$577$	−10.2125	−0.425153	−0.212577	−	0.977144i	$-0.568185\pi$
$577$	−10.2125	−0.425153	−0.212577	+	0.977144i	$0.568185\pi$
$578$	47.3632	1.97005
$579$	−13.0290	−0.541468
$580$	−33.8389	−1.40508
$581$	36.8672	1.52951
$582$	−11.8540	−0.491365
$583$	2.37302	0.0982804
$584$	−14.1692	−0.586325
$585$	1.79998	0.0744200
$586$	11.4285	0.472107
$587$	15.8686	0.654967	0.327484	−	0.944857i	$-0.393799\pi$
$587$	15.8686	0.654967	0.327484	+	0.944857i	$0.393799\pi$
$588$	−92.0553	−3.79630
$589$	10.5942	0.436527
$590$	0.263808	0.0108608
$591$	11.3591	0.467253
$592$	−64.7857	−2.66268
$593$	41.3461	1.69788	0.848940	−	0.528489i	$-0.177241\pi$
$593$	41.3461	1.69788	0.848940	+	0.528489i	$0.177241\pi$
$594$	6.54550	0.268565
$595$	0.932814	0.0382416
$596$	30.4100	1.24564
$597$	13.2174	0.540953
$598$	−15.1030	−0.617609
$599$	−13.5022	−0.551683	−0.275842	−	0.961203i	$-0.588957\pi$
$599$	−13.5022	−0.551683	−0.275842	+	0.961203i	$0.588957\pi$
$600$	−53.7286	−2.19346
$601$	22.8606	0.932503	0.466252	−	0.884652i	$-0.345604\pi$
$601$	22.8606	0.932503	0.466252	+	0.884652i	$0.345604\pi$
$602$	−94.6098	−3.85601
$603$	−20.6912	−0.842613
$604$	107.129	4.35902
$605$	9.89447	0.402267
$606$	48.3731	1.96502
$607$	−38.0555	−1.54463	−0.772313	−	0.635242i	$-0.780900\pi$
$607$	−38.0555	−1.54463	−0.772313	+	0.635242i	$0.780900\pi$
$608$	58.2205	2.36115
$609$	34.5823	1.40135
$610$	6.14721	0.248893
$611$	−11.0058	−0.445249
$612$	−2.02459	−0.0818391
$613$	38.4979	1.55491	0.777457	−	0.628936i	$-0.216509\pi$
$613$	38.4979	1.55491	0.777457	+	0.628936i	$0.216509\pi$
$614$	54.5362	2.20090
$615$	−4.16525	−0.167959
$616$	−20.3434	−0.819660
$617$	27.8232	1.12012	0.560060	−	0.828452i	$-0.310778\pi$
$617$	27.8232	1.12012	0.560060	+	0.828452i	$0.310778\pi$
$618$	28.5956	1.15028
$619$	27.6730	1.11227	0.556136	−	0.831091i	$-0.312283\pi$
$619$	27.6730	1.11227	0.556136	+	0.831091i	$0.312283\pi$
$620$	28.4107	1.14100
$621$	23.0866	0.926433
$622$	−25.9890	−1.04206
$623$	−40.8148	−1.63521
$624$	−28.2566	−1.13117
$625$	13.1518	0.526072
$626$	−69.4558	−2.77601
$627$	−1.02431	−0.0409071
$628$	−98.0067	−3.91089
$629$	−0.813297	−0.0324283
$630$	17.5301	0.698418
$631$	0.0369019	0.00146904	0.000734521	−	1.00000i	$-0.499766\pi$
$631$	0.0369019	0.00146904	0.000734521		1.00000i	$0.499766\pi$
$632$	−118.766	−4.72427
$633$	−21.6033	−0.858653
$634$	43.7537	1.73768
$635$	−3.01014	−0.119454
$636$	39.1817	1.55366
$637$	16.8057	0.665865
$638$	7.59009	0.300495
$639$	−15.4302	−0.610409
$640$	63.4322	2.50738
$641$	−26.9179	−1.06319	−0.531596	−	0.846998i	$-0.678408\pi$
$641$	−26.9179	−1.06319	−0.531596	+	0.846998i	$0.678408\pi$
$642$	44.6001	1.76022
$643$	30.4760	1.20186	0.600928	−	0.799303i	$-0.294798\pi$
$643$	30.4760	1.20186	0.600928	+	0.799303i	$0.294798\pi$
$644$	−109.421	−4.31181
$645$	−8.37714	−0.329850
$646$	1.26054	0.0495953
$647$	−46.9008	−1.84386	−0.921930	−	0.387357i	$-0.873388\pi$
$647$	−46.9008	−1.84386	−0.921930	+	0.387357i	$0.873388\pi$
$648$	21.9757	0.863285
$649$	−0.0440189	−0.00172789
$650$	14.9580	0.586701
$651$	−29.0349	−1.13797
$652$	−52.0293	−2.03763
$653$	−31.6870	−1.24001	−0.620005	−	0.784598i	$-0.712869\pi$
$653$	−31.6870	−1.24001	−0.620005	+	0.784598i	$0.712869\pi$
$654$	−67.6358	−2.64477
$655$	−15.1780	−0.593055
$656$	−68.1314	−2.66008
$657$	−2.03731	−0.0794831
$658$	−107.187	−4.17858
$659$	−10.7854	−0.420141	−0.210071	−	0.977686i	$-0.567369\pi$
$659$	−10.7854	−0.420141	−0.210071	+	0.977686i	$0.567369\pi$
$660$	−2.74691	−0.106924
$661$	−3.41140	−0.132688	−0.0663440	−	0.997797i	$-0.521133\pi$
$661$	−3.41140	−0.132688	−0.0663440	+	0.997797i	$0.521133\pi$
$662$	46.9151	1.82341
$663$	−0.354724	−0.0137763
$664$	87.6100	3.39993
$665$	−8.11944	−0.314858
$666$	−15.2841	−0.592247
$667$	26.7709	1.03657
$668$	90.1848	3.48935
$669$	15.4368	0.596821
$670$	34.5478	1.33470
$671$	−1.02572	−0.0395975
$672$	−159.561	−6.15520
$673$	−5.59360	−0.215617	−0.107809	−	0.994172i	$-0.534383\pi$
$673$	−5.59360	−0.215617	−0.107809	+	0.994172i	$0.534383\pi$
$674$	31.5674	1.21593
$675$	−22.8649	−0.880070
$676$	−65.9247	−2.53557
$677$	21.3254	0.819601	0.409800	−	0.912175i	$-0.365598\pi$
$677$	21.3254	0.819601	0.409800	+	0.912175i	$0.365598\pi$
$678$	−28.6670	−1.10095
$679$	15.6787	0.601695
$680$	2.21671	0.0850069
$681$	−14.8506	−0.569075
$682$	−6.37255	−0.244018
$683$	−34.8788	−1.33460	−0.667299	−	0.744790i	$-0.732550\pi$
$683$	−34.8788	−1.33460	−0.667299	+	0.744790i	$0.732550\pi$
$684$	17.6225	0.673813
$685$	−11.5161	−0.440008
$686$	76.0291	2.90280
$687$	21.9977	0.839265
$688$	−137.026	−5.22405
$689$	−7.15304	−0.272509
$690$	−13.0239	−0.495812
$691$	10.0091	0.380764	0.190382	−	0.981710i	$-0.439027\pi$
$691$	10.0091	0.380764	0.190382	+	0.981710i	$0.439027\pi$
$692$	124.896	4.74785
$693$	−2.92507	−0.111114
$694$	59.8313	2.27116
$695$	−7.97189	−0.302391
$696$	82.1803	3.11504
$697$	−0.855297	−0.0323967
$698$	−83.9942	−3.17923
$699$	−10.9485	−0.414110
$700$	108.371	4.09603
$701$	−38.9663	−1.47174	−0.735868	−	0.677124i	$-0.763226\pi$
$701$	−38.9663	−1.47174	−0.735868	+	0.677124i	$0.763226\pi$
$702$	−19.7302	−0.744670
$703$	7.07914	0.266995
$704$	−19.5526	−0.736918
$705$	−9.49076	−0.357443
$706$	−84.1932	−3.16865
$707$	−63.9807	−2.40624
$708$	−0.726811	−0.0273152
$709$	−36.8485	−1.38387	−0.691937	−	0.721958i	$-0.743243\pi$
$709$	−36.8485	−1.38387	−0.691937	+	0.721958i	$0.743243\pi$
$710$	25.7635	0.966887
$711$	−17.0768	−0.640430
$712$	−96.9910	−3.63489
$713$	−22.4766	−0.841754
$714$	−3.45468	−0.129288
$715$	0.501479	0.0187542
$716$	128.251	4.79295
$717$	−10.2412	−0.382463
$718$	−29.5468	−1.10268
$719$	−2.88709	−0.107670	−0.0538351	−	0.998550i	$-0.517145\pi$
$719$	−2.88709	−0.107670	−0.0538351	+	0.998550i	$0.517145\pi$
$720$	25.3893	0.946204
$721$	−37.8220	−1.40856
$722$	42.1252	1.56774
$723$	−2.95730	−0.109983
$724$	−16.0665	−0.597108
$725$	−26.5139	−0.984700
$726$	−36.6443	−1.36000
$727$	17.1855	0.637376	0.318688	−	0.947860i	$-0.396758\pi$
$727$	17.1855	0.637376	0.318688	+	0.947860i	$0.396758\pi$
$728$	61.3216	2.27273
$729$	23.1295	0.856647
$730$	3.40166	0.125901
$731$	−1.72017	−0.0636229
$732$	−16.9360	−0.625974
$733$	30.4233	1.12371	0.561856	−	0.827235i	$-0.310088\pi$
$733$	30.4233	1.12371	0.561856	+	0.827235i	$0.310088\pi$
$734$	−62.5011	−2.30696
$735$	14.4922	0.534552
$736$	−123.520	−4.55300
$737$	−5.76463	−0.212343
$738$	−16.0734	−0.591670
$739$	39.9471	1.46948	0.734739	−	0.678350i	$-0.237305\pi$
$739$	39.9471	1.46948	0.734739	+	0.678350i	$0.237305\pi$
$740$	18.9843	0.697875
$741$	3.08761	0.113426
$742$	−69.6640	−2.55745
$743$	11.1408	0.408716	0.204358	−	0.978896i	$-0.434489\pi$
$743$	11.1408	0.408716	0.204358	+	0.978896i	$0.434489\pi$
$744$	−68.9976	−2.52958
$745$	−4.78741	−0.175397
$746$	−19.4112	−0.710694
$747$	12.5970	0.460899
$748$	−0.564055	−0.0206239
$749$	−58.9903	−2.15546
$750$	28.3894	1.03663
$751$	21.2368	0.774942	0.387471	−	0.921882i	$-0.373349\pi$
$751$	21.2368	0.774942	0.387471	+	0.921882i	$0.373349\pi$
$752$	−155.241	−5.66106
$753$	−20.6859	−0.753835
$754$	−22.8790	−0.833203
$755$	−16.8652	−0.613788
$756$	−142.945	−5.19888
$757$	29.9585	1.08886	0.544429	−	0.838807i	$-0.316746\pi$
$757$	29.9585	1.08886	0.544429	+	0.838807i	$0.316746\pi$
$758$	25.8136	0.937593
$759$	2.17317	0.0788809
$760$	−19.2948	−0.699895
$761$	−38.3616	−1.39061	−0.695303	−	0.718717i	$-0.744730\pi$
$761$	−38.3616	−1.39061	−0.695303	+	0.718717i	$0.744730\pi$
$762$	11.1481	0.403852
$763$	89.4585	3.23862
$764$	−29.8560	−1.08015
$765$	0.318729	0.0115237
$766$	−58.5185	−2.11436
$767$	0.132687	0.00479105
$768$	−123.784	−4.46667
$769$	−16.4140	−0.591902	−0.295951	−	0.955203i	$-0.595637\pi$
$769$	−16.4140	−0.591902	−0.295951	+	0.955203i	$0.595637\pi$
$770$	4.88394	0.176005
$771$	14.0920	0.507510
$772$	62.4499	2.24762
$773$	−42.1091	−1.51456	−0.757280	−	0.653090i	$-0.773472\pi$
$773$	−42.1091	−1.51456	−0.757280	+	0.653090i	$0.773472\pi$
$774$	−32.3268	−1.16196
$775$	22.2607	0.799629
$776$	37.2584	1.33750
$777$	−19.4014	−0.696020
$778$	0.0342541	0.00122807
$779$	7.44472	0.266735
$780$	8.28008	0.296475
$781$	−4.29889	−0.153826
$782$	−2.67435	−0.0956344
$783$	34.9729	1.24983
$784$	237.050	8.46606
$785$	15.4291	0.550688
$786$	56.2120	2.00501
$787$	−53.9572	−1.92337	−0.961684	−	0.274161i	$-0.911600\pi$
$787$	−53.9572	−1.92337	−0.961684	+	0.274161i	$0.911600\pi$
$788$	−54.4460	−1.93956
$789$	28.9137	1.02936
$790$	28.5128	1.01444
$791$	37.9164	1.34815
$792$	−6.95105	−0.246995
$793$	3.09185	0.109795
$794$	85.9237	3.04932
$795$	−6.16834	−0.218768
$796$	−63.3530	−2.24549
$797$	−49.1935	−1.74252	−0.871262	−	0.490817i	$-0.836698\pi$
$797$	−49.1935	−1.74252	−0.871262	+	0.490817i	$0.836698\pi$
$798$	30.0704	1.06448
$799$	−1.94884	−0.0689451
$800$	122.334	4.32515
$801$	−13.9458	−0.492751
$802$	−8.26560	−0.291868
$803$	−0.567600	−0.0200302
$804$	−95.1818	−3.35680
$805$	17.2261	0.607140
$806$	19.2089	0.676605
$807$	7.97485	0.280728
$808$	−152.042	−5.34881
$809$	8.87847	0.312151	0.156075	−	0.987745i	$-0.450116\pi$
$809$	8.87847	0.312151	0.156075	+	0.987745i	$0.450116\pi$
$810$	−5.27580	−0.185373
$811$	1.38301	0.0485642	0.0242821	−	0.999705i	$-0.492270\pi$
$811$	1.38301	0.0485642	0.0242821	+	0.999705i	$0.492270\pi$
$812$	−165.758	−5.81696
$813$	6.42519	0.225341
$814$	−4.25819	−0.149249
$815$	8.19092	0.286916
$816$	−5.00350	−0.175158
$817$	14.9728	0.523832
$818$	40.7384	1.42438
$819$	8.81711	0.308095
$820$	19.9646	0.697195
$821$	47.8397	1.66962	0.834809	−	0.550540i	$-0.185578\pi$
$821$	47.8397	1.66962	0.834809	+	0.550540i	$0.185578\pi$
$822$	42.6501	1.48759
$823$	−11.3481	−0.395570	−0.197785	−	0.980245i	$-0.563375\pi$
$823$	−11.3481	−0.395570	−0.197785	+	0.980245i	$0.563375\pi$
$824$	−89.8789	−3.13108
$825$	−2.15230	−0.0749334
$826$	1.29225	0.0449631
$827$	0.795162	0.0276505	0.0138252	−	0.999904i	$-0.495599\pi$
$827$	0.795162	0.0276505	0.0138252	+	0.999904i	$0.495599\pi$
$828$	−37.3877	−1.29931
$829$	25.1587	0.873798	0.436899	−	0.899511i	$-0.356077\pi$
$829$	25.1587	0.873798	0.436899	+	0.899511i	$0.356077\pi$
$830$	−21.0329	−0.730063
$831$	0.239607	0.00831187
$832$	58.9379	2.04330
$833$	2.97584	0.103107
$834$	29.5240	1.02233
$835$	−14.1977	−0.491332
$836$	4.90967	0.169805
$837$	−29.3628	−1.01493
$838$	43.7905	1.51272
$839$	54.2019	1.87126	0.935628	−	0.352987i	$-0.114834\pi$
$839$	54.2019	1.87126	0.935628	+	0.352987i	$0.114834\pi$
$840$	52.8800	1.82453
$841$	11.5542	0.398421
$842$	−9.75752	−0.336267
$843$	−2.84214	−0.0978885
$844$	103.548	3.56425
$845$	10.3785	0.357030
$846$	−36.6241	−1.25916
$847$	48.4675	1.66536
$848$	−100.896	−3.46478
$849$	13.6939	0.469975
$850$	2.64867	0.0908485
$851$	−15.0190	−0.514845
$852$	−70.9804	−2.43175
$853$	−3.84709	−0.131722	−0.0658609	−	0.997829i	$-0.520979\pi$
$853$	−3.84709	−0.131722	−0.0658609	+	0.997829i	$0.520979\pi$
$854$	30.1118	1.03040
$855$	−2.77429	−0.0948788
$856$	−140.183	−4.79134
$857$	−11.2926	−0.385748	−0.192874	−	0.981224i	$-0.561781\pi$
$857$	−11.2926	−0.385748	−0.192874	+	0.981224i	$0.561781\pi$
$858$	−1.85723	−0.0634048
$859$	7.22184	0.246406	0.123203	−	0.992381i	$-0.460683\pi$
$859$	7.22184	0.246406	0.123203	+	0.992381i	$0.460683\pi$
$860$	40.1528	1.36920
$861$	−20.4033	−0.695341
$862$	−31.1238	−1.06008
$863$	23.0466	0.784515	0.392257	−	0.919856i	$-0.371694\pi$
$863$	23.0466	0.784515	0.392257	+	0.919856i	$0.371694\pi$
$864$	−161.363	−5.48969
$865$	−19.6623	−0.668538
$866$	−47.2305	−1.60496
$867$	20.5428	0.697670
$868$	139.168	4.72368
$869$	−4.75763	−0.161392
$870$	−19.7294	−0.668889
$871$	17.3764	0.588778
$872$	212.586	7.19908
$873$	5.35719	0.181314
$874$	23.2782	0.787396
$875$	−37.5492	−1.26940
$876$	−9.37183	−0.316645
$877$	29.6086	0.999810	0.499905	−	0.866080i	$-0.333368\pi$
$877$	29.6086	0.999810	0.499905	+	0.866080i	$0.333368\pi$
$878$	−29.5525	−0.997349
$879$	4.95687	0.167191
$880$	7.07352	0.238448
$881$	10.2676	0.345924	0.172962	−	0.984928i	$-0.444666\pi$
$881$	10.2676	0.345924	0.172962	+	0.984928i	$0.444666\pi$
$882$	55.9243	1.88307
$883$	−5.32155	−0.179084	−0.0895422	−	0.995983i	$-0.528540\pi$
$883$	−5.32155	−0.179084	−0.0895422	+	0.995983i	$0.528540\pi$
$884$	1.70024	0.0571853
$885$	0.114421	0.00384622
$886$	90.1580	3.02892
$887$	−20.6600	−0.693694	−0.346847	−	0.937922i	$-0.612748\pi$
$887$	−20.6600	−0.693694	−0.346847	+	0.937922i	$0.612748\pi$
$888$	−46.1047	−1.54717
$889$	−14.7450	−0.494532
$890$	23.2851	0.780517
$891$	0.880317	0.0294917
$892$	−73.9907	−2.47739
$893$	16.9632	0.567652
$894$	17.7302	0.592987
$895$	−20.1904	−0.674889
$896$	310.719	10.3804
$897$	−6.55062	−0.218719
$898$	82.1177	2.74030
$899$	−34.0488	−1.13559
$900$	37.0287	1.23429
$901$	−1.26661	−0.0421970
$902$	−4.47809	−0.149104
$903$	−41.0350	−1.36556
$904$	90.1033	2.99679
$905$	2.52934	0.0840780
$906$	62.4605	2.07511
$907$	−21.9746	−0.729655	−0.364828	−	0.931075i	$-0.618872\pi$
$907$	−21.9746	−0.729655	−0.364828	+	0.931075i	$0.618872\pi$
$908$	71.1808	2.36222
$909$	−21.8613	−0.725093
$910$	−14.7218	−0.488021
$911$	24.0125	0.795569	0.397784	−	0.917479i	$-0.369779\pi$
$911$	24.0125	0.795569	0.397784	+	0.917479i	$0.369779\pi$
$912$	43.5517	1.44214
$913$	3.50955	0.116149
$914$	−92.2719	−3.05208
$915$	2.66622	0.0881426
$916$	−105.438	−3.48377
$917$	−74.3488	−2.45521
$918$	−3.49370	−0.115309
$919$	−18.7279	−0.617778	−0.308889	−	0.951098i	$-0.599957\pi$
$919$	−18.7279	−0.617778	−0.308889	+	0.951098i	$0.599957\pi$
$920$	40.9355	1.34960
$921$	23.6539	0.779423
$922$	64.7286	2.13172
$923$	12.9582	0.426525
$924$	−13.4556	−0.442657
$925$	14.8748	0.489080
$926$	101.392	3.33194
$927$	−12.9232	−0.424454
$928$	−187.115	−6.14235
$929$	−1.43056	−0.0469353	−0.0234677	−	0.999725i	$-0.507471\pi$
$929$	−1.43056	−0.0469353	−0.0234677	+	0.999725i	$0.507471\pi$
$930$	16.5646	0.543174
$931$	−25.9025	−0.848919
$932$	52.4777	1.71896
$933$	−11.2722	−0.369034
$934$	−33.3518	−1.09130
$935$	0.0887985	0.00290402
$936$	20.9527	0.684860
$937$	0.896442	0.0292855	0.0146427	−	0.999893i	$-0.495339\pi$
$937$	0.896442	0.0292855	0.0146427	+	0.999893i	$0.495339\pi$
$938$	169.231	5.52557
$939$	−30.1250	−0.983092
$940$	45.4905	1.48374
$941$	−20.4367	−0.666217	−0.333108	−	0.942889i	$-0.608098\pi$
$941$	−20.4367	−0.666217	−0.333108	+	0.942889i	$0.608098\pi$
$942$	−57.1418	−1.86178
$943$	−15.7946	−0.514343
$944$	1.87160	0.0609153
$945$	22.5038	0.732047
$946$	−9.00632	−0.292821
$947$	9.65097	0.313615	0.156807	−	0.987629i	$-0.449880\pi$
$947$	9.65097	0.313615	0.156807	+	0.987629i	$0.449880\pi$
$948$	−78.5549	−2.55134
$949$	1.71093	0.0555390
$950$	−23.0546	−0.747991
$951$	18.9772	0.615379
$952$	10.8584	0.351924
$953$	27.5063	0.891018	0.445509	−	0.895278i	$-0.353023\pi$
$953$	27.5063	0.891018	0.445509	+	0.895278i	$0.353023\pi$
$954$	−23.8032	−0.770656
$955$	4.70021	0.152095
$956$	49.0873	1.58760
$957$	3.29204	0.106417
$958$	14.5716	0.470789
$959$	−56.4111	−1.82161
$960$	50.8244	1.64035
$961$	−2.41301	−0.0778389
$962$	12.8355	0.413834
$963$	−20.1561	−0.649522
$964$	14.1748	0.456538
$965$	−9.83143	−0.316485
$966$	−63.7970	−2.05263
$967$	−19.8724	−0.639054	−0.319527	−	0.947577i	$-0.603524\pi$
$967$	−19.8724	−0.639054	−0.319527	+	0.947577i	$0.603524\pi$
$968$	115.177	3.70192
$969$	0.546733	0.0175636
$970$	−8.94480	−0.287200
$971$	2.58129	0.0828376	0.0414188	−	0.999142i	$-0.486812\pi$
$971$	2.58129	0.0828376	0.0414188	+	0.999142i	$0.486812\pi$
$972$	−81.1824	−2.60393
$973$	−39.0499	−1.25188
$974$	−24.6357	−0.789377
$975$	6.48772	0.207773
$976$	43.6116	1.39597
$977$	17.6102	0.563399	0.281700	−	0.959503i	$-0.409102\pi$
$977$	17.6102	0.563399	0.281700	+	0.959503i	$0.409102\pi$
$978$	−30.3352	−0.970011
$979$	−3.88534	−0.124176
$980$	−69.4630	−2.21892
$981$	30.5667	0.975918
$982$	−112.473	−3.58914
$983$	45.5776	1.45370	0.726850	−	0.686796i	$-0.240984\pi$
$983$	45.5776	1.45370	0.726850	+	0.686796i	$0.240984\pi$
$984$	−48.4857	−1.54567
$985$	8.57138	0.273107
$986$	−4.05126	−0.129018
$987$	−46.4900	−1.47979
$988$	−14.7993	−0.470829
$989$	−31.7661	−1.01010
$990$	1.66877	0.0530370
$991$	8.83722	0.280723	0.140362	−	0.990100i	$-0.455173\pi$
$991$	8.83722	0.280723	0.140362	+	0.990100i	$0.455173\pi$
$992$	157.100	4.98792
$993$	20.3484	0.645737
$994$	126.201	4.00286
$995$	9.97359	0.316184
$996$	57.9473	1.83613
$997$	−23.2496	−0.736322	−0.368161	−	0.929762i	$-0.620012\pi$
$997$	−23.2496	−0.736322	−0.368161	+	0.929762i	$0.620012\pi$
$998$	110.339	3.49272
$999$	−19.6205	−0.620765

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.79459 q^{2} -1.21209 q^{3} +5.80974 q^{4} -0.914621 q^{5} +3.38731 q^{6} -4.48023 q^{7} -10.6467 q^{8} -1.53083 q^{9} +O(q^{10})\)	\(q-2.79459 q^{2} -1.21209 q^{3} +5.80974 q^{4} -0.914621 q^{5} +3.38731 q^{6} -4.48023 q^{7} -10.6467 q^{8} -1.53083 q^{9} +2.55599 q^{10} -0.426492 q^{11} -7.04195 q^{12} +1.28558 q^{13} +12.5204 q^{14} +1.10861 q^{15} +18.1336 q^{16} +0.227643 q^{17} +4.27803 q^{18} -1.98146 q^{19} -5.31371 q^{20} +5.43046 q^{21} +1.19187 q^{22} +4.20384 q^{23} +12.9048 q^{24} -4.16347 q^{25} -3.59268 q^{26} +5.49179 q^{27} -26.0289 q^{28} +6.36822 q^{29} -3.09810 q^{30} -5.34668 q^{31} -29.3826 q^{32} +0.516949 q^{33} -0.636168 q^{34} +4.09771 q^{35} -8.89370 q^{36} -3.57269 q^{37} +5.53737 q^{38} -1.55825 q^{39} +9.73766 q^{40} -3.75719 q^{41} -15.1759 q^{42} -7.55646 q^{43} -2.47781 q^{44} +1.40013 q^{45} -11.7480 q^{46} -8.56097 q^{47} -21.9796 q^{48} +13.0724 q^{49} +11.6352 q^{50} -0.275924 q^{51} +7.46890 q^{52} -5.56404 q^{53} -15.3473 q^{54} +0.390079 q^{55} +47.6994 q^{56} +2.40172 q^{57} -17.7966 q^{58} +0.103212 q^{59} +6.44072 q^{60} +2.40502 q^{61} +14.9418 q^{62} +6.85845 q^{63} +45.8453 q^{64} -1.17582 q^{65} -1.44466 q^{66} +13.5164 q^{67} +1.32254 q^{68} -5.09545 q^{69} -11.4514 q^{70} +10.0796 q^{71} +16.2982 q^{72} +1.33086 q^{73} +9.98422 q^{74} +5.04652 q^{75} -11.5118 q^{76} +1.91078 q^{77} +4.35467 q^{78} +11.1553 q^{79} -16.5854 q^{80} -2.06409 q^{81} +10.4998 q^{82} -8.22887 q^{83} +31.5495 q^{84} -0.208207 q^{85} +21.1172 q^{86} -7.71888 q^{87} +4.54072 q^{88} +9.10999 q^{89} -3.91278 q^{90} -5.75970 q^{91} +24.4232 q^{92} +6.48068 q^{93} +23.9244 q^{94} +1.81228 q^{95} +35.6145 q^{96} -3.49954 q^{97} -36.5321 q^{98} +0.652885 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) \) 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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