LMFDB - Embedded newform 6047.2.a.a.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.63907 q^{2} -2.61338 q^{3} +4.96471 q^{4} +2.16033 q^{5} +6.89691 q^{6} -4.93155 q^{7} -7.82409 q^{8} +3.82978 q^{9} +O(q^{10})$	\(q-2.63907 q^{2} -2.61338 q^{3} +4.96471 q^{4} +2.16033 q^{5} +6.89691 q^{6} -4.93155 q^{7} -7.82409 q^{8} +3.82978 q^{9} -5.70128 q^{10} +3.19144 q^{11} -12.9747 q^{12} -1.07068 q^{13} +13.0147 q^{14} -5.64578 q^{15} +10.7189 q^{16} +1.60771 q^{17} -10.1071 q^{18} +6.87862 q^{19} +10.7254 q^{20} +12.8880 q^{21} -8.42244 q^{22} -3.73417 q^{23} +20.4473 q^{24} -0.332958 q^{25} +2.82561 q^{26} -2.16852 q^{27} -24.4837 q^{28} -6.89546 q^{29} +14.8996 q^{30} -0.842199 q^{31} -12.6398 q^{32} -8.34045 q^{33} -4.24287 q^{34} -10.6538 q^{35} +19.0137 q^{36} -7.20247 q^{37} -18.1532 q^{38} +2.79811 q^{39} -16.9026 q^{40} -5.79439 q^{41} -34.0124 q^{42} +10.9683 q^{43} +15.8446 q^{44} +8.27359 q^{45} +9.85476 q^{46} +4.10295 q^{47} -28.0127 q^{48} +17.3201 q^{49} +0.878701 q^{50} -4.20157 q^{51} -5.31563 q^{52} +10.2681 q^{53} +5.72289 q^{54} +6.89457 q^{55} +38.5848 q^{56} -17.9765 q^{57} +18.1976 q^{58} -6.74275 q^{59} -28.0297 q^{60} +4.80345 q^{61} +2.22263 q^{62} -18.8867 q^{63} +11.9196 q^{64} -2.31303 q^{65} +22.0111 q^{66} -7.02579 q^{67} +7.98182 q^{68} +9.75883 q^{69} +28.1161 q^{70} -0.767086 q^{71} -29.9645 q^{72} -7.31240 q^{73} +19.0079 q^{74} +0.870147 q^{75} +34.1504 q^{76} -15.7387 q^{77} -7.38441 q^{78} -0.462629 q^{79} +23.1564 q^{80} -5.82214 q^{81} +15.2918 q^{82} +6.92183 q^{83} +63.9853 q^{84} +3.47320 q^{85} -28.9460 q^{86} +18.0205 q^{87} -24.9701 q^{88} -9.42966 q^{89} -21.8346 q^{90} +5.28012 q^{91} -18.5391 q^{92} +2.20099 q^{93} -10.8280 q^{94} +14.8601 q^{95} +33.0328 q^{96} -18.3317 q^{97} -45.7091 q^{98} +12.2225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.63907	−1.86611	−0.933053	−	0.359738i	$-0.882866\pi$
$2$	−2.63907	−1.86611	−0.933053	+	0.359738i	$0.882866\pi$
$3$	−2.61338	−1.50884	−0.754419	−	0.656393i	$-0.772081\pi$
$3$	−2.61338	−1.50884	−0.754419	+	0.656393i	$0.772081\pi$
$4$	4.96471	2.48235
$5$	2.16033	0.966131	0.483065	−	0.875584i	$-0.339523\pi$
$5$	2.16033	0.966131	0.483065	+	0.875584i	$0.339523\pi$
$6$	6.89691	2.81565
$7$	−4.93155	−1.86395	−0.931975	−	0.362524i	$-0.881915\pi$
$7$	−4.93155	−1.86395	−0.931975	+	0.362524i	$0.881915\pi$
$8$	−7.82409	−2.76623
$9$	3.82978	1.27659
$10$	−5.70128	−1.80290
$11$	3.19144	0.962254	0.481127	−	0.876651i	$-0.340228\pi$
$11$	3.19144	0.962254	0.481127	+	0.876651i	$0.340228\pi$
$12$	−12.9747	−3.74547
$13$	−1.07068	−0.296954	−0.148477	−	0.988916i	$-0.547437\pi$
$13$	−1.07068	−0.296954	−0.148477	+	0.988916i	$0.547437\pi$
$14$	13.0147	3.47833
$15$	−5.64578	−1.45773
$16$	10.7189	2.67973
$17$	1.60771	0.389928	0.194964	−	0.980810i	$-0.437541\pi$
$17$	1.60771	0.389928	0.194964	+	0.980810i	$0.437541\pi$
$18$	−10.1071	−2.38226
$19$	6.87862	1.57806	0.789032	−	0.614352i	$-0.210583\pi$
$19$	6.87862	1.57806	0.789032	+	0.614352i	$0.210583\pi$
$20$	10.7254	2.39828
$21$	12.8880	2.81240
$22$	−8.42244	−1.79567
$23$	−3.73417	−0.778629	−0.389314	−	0.921105i	$-0.627288\pi$
$23$	−3.73417	−0.778629	−0.389314	+	0.921105i	$0.627288\pi$
$24$	20.4473	4.17380
$25$	−0.332958	−0.0665916
$26$	2.82561	0.554148
$27$	−2.16852	−0.417333
$28$	−24.4837	−4.62698
$29$	−6.89546	−1.28045	−0.640227	−	0.768186i	$-0.721160\pi$
$29$	−6.89546	−1.28045	−0.640227	+	0.768186i	$0.721160\pi$
$30$	14.8996	2.72029
$31$	−0.842199	−0.151263	−0.0756317	−	0.997136i	$-0.524097\pi$
$31$	−0.842199	−0.151263	−0.0756317	+	0.997136i	$0.524097\pi$
$32$	−12.6398	−2.23443
$33$	−8.34045	−1.45189
$34$	−4.24287	−0.727646
$35$	−10.6538	−1.80082
$36$	19.0137	3.16895
$37$	−7.20247	−1.18408	−0.592040	−	0.805909i	$-0.701677\pi$
$37$	−7.20247	−1.18408	−0.592040	+	0.805909i	$0.701677\pi$
$38$	−18.1532	−2.94484
$39$	2.79811	0.448055
$40$	−16.9026	−2.67254
$41$	−5.79439	−0.904932	−0.452466	−	0.891782i	$-0.649456\pi$
$41$	−5.79439	−0.904932	−0.452466	+	0.891782i	$0.649456\pi$
$42$	−34.0124	−5.24823
$43$	10.9683	1.67264	0.836322	−	0.548239i	$-0.184702\pi$
$43$	10.9683	1.67264	0.836322	+	0.548239i	$0.184702\pi$
$44$	15.8446	2.38866
$45$	8.27359	1.23335
$46$	9.85476	1.45300
$47$	4.10295	0.598477	0.299238	−	0.954178i	$-0.403267\pi$
$47$	4.10295	0.598477	0.299238	+	0.954178i	$0.403267\pi$
$48$	−28.0127	−4.04328
$49$	17.3201	2.47431
$50$	0.878701	0.124267
$51$	−4.20157	−0.588337
$52$	−5.31563	−0.737145
$53$	10.2681	1.41043	0.705214	−	0.708994i	$-0.250851\pi$
$53$	10.2681	1.41043	0.705214	+	0.708994i	$0.250851\pi$
$54$	5.72289	0.778787
$55$	6.89457	0.929663
$56$	38.5848	5.15612
$57$	−17.9765	−2.38104
$58$	18.1976	2.38946
$59$	−6.74275	−0.877832	−0.438916	−	0.898528i	$-0.644637\pi$
$59$	−6.74275	−0.877832	−0.438916	+	0.898528i	$0.644637\pi$
$60$	−28.0297	−3.61861
$61$	4.80345	0.615018	0.307509	−	0.951545i	$-0.400505\pi$
$61$	4.80345	0.615018	0.307509	+	0.951545i	$0.400505\pi$
$62$	2.22263	0.282274
$63$	−18.8867	−2.37950
$64$	11.9196	1.48996
$65$	−2.31303	−0.286896
$66$	22.0111	2.70937
$67$	−7.02579	−0.858337	−0.429168	−	0.903225i	$-0.641193\pi$
$67$	−7.02579	−0.858337	−0.429168	+	0.903225i	$0.641193\pi$
$68$	7.98182	0.967938
$69$	9.75883	1.17482
$70$	28.1161	3.36052
$71$	−0.767086	−0.0910363	−0.0455182	−	0.998964i	$-0.514494\pi$
$71$	−0.767086	−0.0910363	−0.0455182	+	0.998964i	$0.514494\pi$
$72$	−29.9645	−3.53135
$73$	−7.31240	−0.855852	−0.427926	−	0.903814i	$-0.640756\pi$
$73$	−7.31240	−0.855852	−0.427926	+	0.903814i	$0.640756\pi$
$74$	19.0079	2.20962
$75$	0.870147	0.100476
$76$	34.1504	3.91731
$77$	−15.7387	−1.79359
$78$	−7.38441	−0.836119
$79$	−0.462629	−0.0520498	−0.0260249	−	0.999661i	$-0.508285\pi$
$79$	−0.462629	−0.0520498	−0.0260249	+	0.999661i	$0.508285\pi$
$80$	23.1564	2.58897
$81$	−5.82214	−0.646905
$82$	15.2918	1.68870
$83$	6.92183	0.759770	0.379885	−	0.925034i	$-0.375964\pi$
$83$	6.92183	0.759770	0.379885	+	0.925034i	$0.375964\pi$
$84$	63.9853	6.98137
$85$	3.47320	0.376721
$86$	−28.9460	−3.12133
$87$	18.0205	1.93200
$88$	−24.9701	−2.66182
$89$	−9.42966	−0.999542	−0.499771	−	0.866158i	$-0.666582\pi$
$89$	−9.42966	−0.999542	−0.499771	+	0.866158i	$0.666582\pi$
$90$	−21.8346	−2.30157
$91$	5.28012	0.553507
$92$	−18.5391	−1.93283
$93$	2.20099	0.228232
$94$	−10.8280	−1.11682
$95$	14.8601	1.52462
$96$	33.0328	3.37139
$97$	−18.3317	−1.86131	−0.930653	−	0.365903i	$-0.880760\pi$
$97$	−18.3317	−1.86131	−0.930653	+	0.365903i	$0.880760\pi$
$98$	−45.7091	−4.61732
$99$	12.2225	1.22841
$100$	−1.65304	−0.165304
$101$	−2.26779	−0.225654	−0.112827	−	0.993615i	$-0.535991\pi$
$101$	−2.26779	−0.225654	−0.112827	+	0.993615i	$0.535991\pi$
$102$	11.0883	1.09790
$103$	12.6151	1.24300	0.621502	−	0.783412i	$-0.286523\pi$
$103$	12.6151	1.24300	0.621502	+	0.783412i	$0.286523\pi$
$104$	8.37711	0.821444
$105$	27.8424	2.71714
$106$	−27.0982	−2.63201
$107$	−13.0541	−1.26199	−0.630995	−	0.775787i	$-0.717353\pi$
$107$	−13.0541	−1.26199	−0.630995	+	0.775787i	$0.717353\pi$
$108$	−10.7661	−1.03597
$109$	4.39101	0.420583	0.210291	−	0.977639i	$-0.432559\pi$
$109$	4.39101	0.420583	0.210291	+	0.977639i	$0.432559\pi$
$110$	−18.1953	−1.73485
$111$	18.8228	1.78658
$112$	−52.8608	−4.99488
$113$	15.3052	1.43979	0.719895	−	0.694083i	$-0.244190\pi$
$113$	15.3052	1.43979	0.719895	+	0.694083i	$0.244190\pi$
$114$	47.4413	4.44328
$115$	−8.06706	−0.752257
$116$	−34.2339	−3.17854
$117$	−4.10048	−0.379089
$118$	17.7946	1.63813
$119$	−7.92851	−0.726805
$120$	44.1731	4.03243
$121$	−0.814733	−0.0740667
$122$	−12.6766	−1.14769
$123$	15.1430	1.36540
$124$	−4.18127	−0.375489
$125$	−11.5210	−1.03047
$126$	49.8434	4.44041
$127$	15.6534	1.38902	0.694508	−	0.719485i	$-0.255622\pi$
$127$	15.6534	1.38902	0.694508	+	0.719485i	$0.255622\pi$
$128$	−6.17713	−0.545986
$129$	−28.6643	−2.52375
$130$	6.10426	0.535379
$131$	21.7055	1.89641	0.948207	−	0.317653i	$-0.102895\pi$
$131$	21.7055	1.89641	0.948207	+	0.317653i	$0.102895\pi$
$132$	−41.4079	−3.60410
$133$	−33.9222	−2.94143
$134$	18.5416	1.60175
$135$	−4.68473	−0.403198
$136$	−12.5789	−1.07863
$137$	−10.3435	−0.883709	−0.441854	−	0.897087i	$-0.645679\pi$
$137$	−10.3435	−0.883709	−0.441854	+	0.897087i	$0.645679\pi$
$138$	−25.7543	−2.19235
$139$	−10.2121	−0.866182	−0.433091	−	0.901350i	$-0.642577\pi$
$139$	−10.2121	−0.866182	−0.433091	+	0.901350i	$0.642577\pi$
$140$	−52.8929	−4.47027
$141$	−10.7226	−0.903005
$142$	2.02440	0.169884
$143$	−3.41702	−0.285745
$144$	41.0511	3.42092
$145$	−14.8965	−1.23709
$146$	19.2980	1.59711
$147$	−45.2642	−3.73333
$148$	−35.7582	−2.93930
$149$	−20.0446	−1.64211	−0.821057	−	0.570846i	$-0.806615\pi$
$149$	−20.0446	−1.64211	−0.821057	+	0.570846i	$0.806615\pi$
$150$	−2.29638	−0.187499
$151$	19.6680	1.60056	0.800279	−	0.599627i	$-0.204684\pi$
$151$	19.6680	1.60056	0.800279	+	0.599627i	$0.204684\pi$
$152$	−53.8189	−4.36529
$153$	6.15718	0.497778
$154$	41.5356	3.34704
$155$	−1.81943	−0.146140
$156$	13.8918	1.11223
$157$	9.20843	0.734913	0.367456	−	0.930041i	$-0.380229\pi$
$157$	9.20843	0.734913	0.367456	+	0.930041i	$0.380229\pi$
$158$	1.22091	0.0971305
$159$	−26.8344	−2.12811
$160$	−27.3063	−2.15875
$161$	18.4152	1.45132
$162$	15.3651	1.20719
$163$	12.9973	1.01803	0.509015	−	0.860758i	$-0.330010\pi$
$163$	12.9973	1.01803	0.509015	+	0.860758i	$0.330010\pi$
$164$	−28.7675	−2.24636
$165$	−18.0182	−1.40271
$166$	−18.2672	−1.41781
$167$	−8.50955	−0.658488	−0.329244	−	0.944245i	$-0.606794\pi$
$167$	−8.50955	−0.658488	−0.329244	+	0.944245i	$0.606794\pi$
$168$	−100.837	−7.77974
$169$	−11.8536	−0.911818
$170$	−9.16602	−0.703002
$171$	26.3436	2.01454
$172$	54.4542	4.15209
$173$	2.58531	0.196558	0.0982789	−	0.995159i	$-0.468666\pi$
$173$	2.58531	0.196558	0.0982789	+	0.995159i	$0.468666\pi$
$174$	−47.5574	−3.60531
$175$	1.64200	0.124123
$176$	34.2088	2.57858
$177$	17.6214	1.32451
$178$	24.8856	1.86525
$179$	7.99001	0.597201	0.298601	−	0.954378i	$-0.403480\pi$
$179$	7.99001	0.597201	0.298601	+	0.954378i	$0.403480\pi$
$180$	41.0760	3.06162
$181$	−17.6435	−1.31143	−0.655715	−	0.755009i	$-0.727633\pi$
$181$	−17.6435	−1.31143	−0.655715	+	0.755009i	$0.727633\pi$
$182$	−13.9346	−1.03290
$183$	−12.5533	−0.927963
$184$	29.2165	2.15387
$185$	−15.5597	−1.14398
$186$	−5.80857	−0.425905
$187$	5.13091	0.375209
$188$	20.3700	1.48563
$189$	10.6942	0.777887
$190$	−39.2169	−2.84510
$191$	26.1081	1.88911	0.944556	−	0.328349i	$-0.106492\pi$
$191$	26.1081	1.88911	0.944556	+	0.328349i	$0.106492\pi$
$192$	−31.1506	−2.24810
$193$	−16.4654	−1.18520	−0.592601	−	0.805496i	$-0.701899\pi$
$193$	−16.4654	−1.18520	−0.592601	+	0.805496i	$0.701899\pi$
$194$	48.3788	3.47340
$195$	6.04484	0.432880
$196$	85.9895	6.14211
$197$	10.4944	0.747697	0.373849	−	0.927490i	$-0.378038\pi$
$197$	10.4944	0.747697	0.373849	+	0.927490i	$0.378038\pi$
$198$	−32.2560	−2.29234
$199$	0.713974	0.0506123	0.0253061	−	0.999680i	$-0.491944\pi$
$199$	0.713974	0.0506123	0.0253061	+	0.999680i	$0.491944\pi$
$200$	2.60509	0.184208
$201$	18.3611	1.29509
$202$	5.98487	0.421094
$203$	34.0053	2.38670
$204$	−20.8596	−1.46046
$205$	−12.5178	−0.874283
$206$	−33.2922	−2.31958
$207$	−14.3010	−0.993991
$208$	−11.4766	−0.795756
$209$	21.9527	1.51850
$210$	−73.4782	−5.07048
$211$	−19.9346	−1.37235	−0.686177	−	0.727435i	$-0.740712\pi$
$211$	−19.9346	−1.37235	−0.686177	+	0.727435i	$0.740712\pi$
$212$	50.9780	3.50118
$213$	2.00469	0.137359
$214$	34.4508	2.35501
$215$	23.6951	1.61599
$216$	16.9667	1.15444
$217$	4.15334	0.281947
$218$	−11.5882	−0.784853
$219$	19.1101	1.29134
$220$	34.2295	2.30775
$221$	−1.72135	−0.115791
$222$	−49.6748	−3.33396
$223$	−11.6845	−0.782449	−0.391225	−	0.920295i	$-0.627948\pi$
$223$	−11.6845	−0.782449	−0.391225	+	0.920295i	$0.627948\pi$
$224$	62.3340	4.16486
$225$	−1.27515	−0.0850103
$226$	−40.3915	−2.68680
$227$	−0.752714	−0.0499594	−0.0249797	−	0.999688i	$-0.507952\pi$
$227$	−0.752714	−0.0499594	−0.0249797	+	0.999688i	$0.507952\pi$
$228$	−89.2480	−5.91059
$229$	20.9529	1.38461	0.692304	−	0.721606i	$-0.256596\pi$
$229$	20.9529	1.38461	0.692304	+	0.721606i	$0.256596\pi$
$230$	21.2896	1.40379
$231$	41.1313	2.70624
$232$	53.9507	3.54203
$233$	2.07648	0.136034	0.0680172	−	0.997684i	$-0.478333\pi$
$233$	2.07648	0.136034	0.0680172	+	0.997684i	$0.478333\pi$
$234$	10.8215	0.707421
$235$	8.86374	0.578207
$236$	−33.4758	−2.17909
$237$	1.20903	0.0785347
$238$	20.9239	1.35630
$239$	27.5639	1.78296	0.891480	−	0.453060i	$-0.149668\pi$
$239$	27.5639	1.78296	0.891480	+	0.453060i	$0.149668\pi$
$240$	−60.5167	−3.90634
$241$	23.0386	1.48405	0.742024	−	0.670373i	$-0.233866\pi$
$241$	23.0386	1.48405	0.742024	+	0.670373i	$0.233866\pi$
$242$	2.15014	0.138216
$243$	21.7211	1.39341
$244$	23.8477	1.52669
$245$	37.4173	2.39050
$246$	−39.9634	−2.54797
$247$	−7.36482	−0.468612
$248$	6.58944	0.418430
$249$	−18.0894	−1.14637
$250$	30.4047	1.92296
$251$	−1.70872	−0.107853	−0.0539266	−	0.998545i	$-0.517174\pi$
$251$	−1.70872	−0.107853	−0.0539266	+	0.998545i	$0.517174\pi$
$252$	−93.7671	−5.90677
$253$	−11.9174	−0.749239
$254$	−41.3105	−2.59205
$255$	−9.07679	−0.568411
$256$	−7.53740	−0.471087
$257$	24.8962	1.55298	0.776490	−	0.630129i	$-0.216998\pi$
$257$	24.8962	1.55298	0.776490	+	0.630129i	$0.216998\pi$
$258$	75.6471	4.70958
$259$	35.5193	2.20706
$260$	−11.4835	−0.712178
$261$	−26.4081	−1.63462
$262$	−57.2823	−3.53891
$263$	7.88216	0.486035	0.243017	−	0.970022i	$-0.421863\pi$
$263$	7.88216	0.486035	0.243017	+	0.970022i	$0.421863\pi$
$264$	65.2564	4.01625
$265$	22.1825	1.36266
$266$	89.5233	5.48902
$267$	24.6433	1.50815
$268$	−34.8810	−2.13070
$269$	−1.18365	−0.0721682	−0.0360841	−	0.999349i	$-0.511488\pi$
$269$	−1.18365	−0.0721682	−0.0360841	+	0.999349i	$0.511488\pi$
$270$	12.3634	0.752410
$271$	−12.6181	−0.766497	−0.383249	−	0.923645i	$-0.625195\pi$
$271$	−12.6181	−0.766497	−0.383249	+	0.923645i	$0.625195\pi$
$272$	17.2329	1.04490
$273$	−13.7990	−0.835152
$274$	27.2974	1.64909
$275$	−1.06261	−0.0640780
$276$	48.4497	2.91633
$277$	4.87985	0.293202	0.146601	−	0.989196i	$-0.453167\pi$
$277$	4.87985	0.293202	0.146601	+	0.989196i	$0.453167\pi$
$278$	26.9506	1.61639
$279$	−3.22543	−0.193102
$280$	83.3561	4.98148
$281$	−7.37182	−0.439766	−0.219883	−	0.975526i	$-0.570568\pi$
$281$	−7.37182	−0.439766	−0.219883	+	0.975526i	$0.570568\pi$
$282$	28.2977	1.68510
$283$	−25.2378	−1.50023	−0.750116	−	0.661306i	$-0.770002\pi$
$283$	−25.2378	−1.50023	−0.750116	+	0.661306i	$0.770002\pi$
$284$	−3.80836	−0.225984
$285$	−38.8352	−2.30040
$286$	9.01776	0.533231
$287$	28.5753	1.68675
$288$	−48.4078	−2.85246
$289$	−14.4153	−0.847957
$290$	39.3129	2.30853
$291$	47.9079	2.80841
$292$	−36.3040	−2.12453
$293$	1.59810	0.0933620	0.0466810	−	0.998910i	$-0.485136\pi$
$293$	1.59810	0.0933620	0.0466810	+	0.998910i	$0.485136\pi$
$294$	119.456	6.96679
$295$	−14.5666	−0.848100
$296$	56.3528	3.27544
$297$	−6.92071	−0.401580
$298$	52.8990	3.06436
$299$	3.99811	0.231217
$300$	4.32003	0.249417
$301$	−54.0904	−3.11772
$302$	−51.9053	−2.98681
$303$	5.92661	0.340475
$304$	73.7314	4.22879
$305$	10.3770	0.594188
$306$	−16.2492	−0.928908
$307$	6.57035	0.374990	0.187495	−	0.982266i	$-0.439963\pi$
$307$	6.57035	0.374990	0.187495	+	0.982266i	$0.439963\pi$
$308$	−78.1381	−4.45233
$309$	−32.9681	−1.87549
$310$	4.80161	0.272713
$311$	21.5953	1.22456	0.612279	−	0.790642i	$-0.290253\pi$
$311$	21.5953	1.22456	0.612279	+	0.790642i	$0.290253\pi$
$312$	−21.8926	−1.23943
$313$	2.53635	0.143363	0.0716816	−	0.997428i	$-0.477163\pi$
$313$	2.53635	0.143363	0.0716816	+	0.997428i	$0.477163\pi$
$314$	−24.3017	−1.37143
$315$	−40.8016	−2.29891
$316$	−2.29682	−0.129206
$317$	16.1835	0.908955	0.454477	−	0.890758i	$-0.349826\pi$
$317$	16.1835	0.908955	0.454477	+	0.890758i	$0.349826\pi$
$318$	70.8180	3.97128
$319$	−22.0064	−1.23212
$320$	25.7504	1.43949
$321$	34.1154	1.90414
$322$	−48.5992	−2.70833
$323$	11.0588	0.615331
$324$	−28.9052	−1.60585
$325$	0.356492	0.0197746
$326$	−34.3009	−1.89975
$327$	−11.4754	−0.634591
$328$	45.3358	2.50325
$329$	−20.2339	−1.11553
$330$	47.5512	2.61761
$331$	−10.3701	−0.569990	−0.284995	−	0.958529i	$-0.591992\pi$
$331$	−10.3701	−0.569990	−0.284995	+	0.958529i	$0.591992\pi$
$332$	34.3649	1.88602
$333$	−27.5839	−1.51159
$334$	22.4573	1.22881
$335$	−15.1780	−0.829265
$336$	138.146	7.53647
$337$	18.2753	0.995518	0.497759	−	0.867316i	$-0.334156\pi$
$337$	18.2753	0.995518	0.497759	+	0.867316i	$0.334156\pi$
$338$	31.2826	1.70155
$339$	−39.9983	−2.17241
$340$	17.2434	0.935155
$341$	−2.68783	−0.145554
$342$	−69.5226	−3.75935
$343$	−50.8943	−2.74803
$344$	−85.8166	−4.62692
$345$	21.0823	1.13503
$346$	−6.82283	−0.366798
$347$	10.1150	0.543004	0.271502	−	0.962438i	$-0.412480\pi$
$347$	10.1150	0.543004	0.271502	+	0.962438i	$0.412480\pi$
$348$	89.4664	4.79590
$349$	17.3544	0.928959	0.464480	−	0.885584i	$-0.346241\pi$
$349$	17.3544	0.928959	0.464480	+	0.885584i	$0.346241\pi$
$350$	−4.33335	−0.231627
$351$	2.32180	0.123929
$352$	−40.3393	−2.15009
$353$	−12.4099	−0.660510	−0.330255	−	0.943892i	$-0.607135\pi$
$353$	−12.4099	−0.660510	−0.330255	+	0.943892i	$0.607135\pi$
$354$	−46.5042	−2.47167
$355$	−1.65716	−0.0879530
$356$	−46.8155	−2.48122
$357$	20.7202	1.09663
$358$	−21.0862	−1.11444
$359$	−5.21033	−0.274991	−0.137495	−	0.990502i	$-0.543905\pi$
$359$	−5.21033	−0.274991	−0.137495	+	0.990502i	$0.543905\pi$
$360$	−64.7333	−3.41175
$361$	28.3154	1.49029
$362$	46.5624	2.44727
$363$	2.12921	0.111755
$364$	26.2143	1.37400
$365$	−15.7972	−0.826865
$366$	33.1290	1.73168
$367$	6.55179	0.342000	0.171000	−	0.985271i	$-0.445300\pi$
$367$	6.55179	0.342000	0.171000	+	0.985271i	$0.445300\pi$
$368$	−40.0263	−2.08651
$369$	−22.1912	−1.15523
$370$	41.0633	2.13478
$371$	−50.6375	−2.62897
$372$	10.9273	0.566553
$373$	0.791518	0.0409832	0.0204916	−	0.999790i	$-0.493477\pi$
$373$	0.791518	0.0409832	0.0204916	+	0.999790i	$0.493477\pi$
$374$	−13.5409	−0.700181
$375$	30.1087	1.55481
$376$	−32.1018	−1.65553
$377$	7.38285	0.380236
$378$	−28.2227	−1.45162
$379$	−23.8054	−1.22280	−0.611401	−	0.791321i	$-0.709394\pi$
$379$	−23.8054	−1.22280	−0.611401	+	0.791321i	$0.709394\pi$
$380$	73.7762	3.78464
$381$	−40.9084	−2.09580
$382$	−68.9011	−3.52529
$383$	−24.6059	−1.25730	−0.628652	−	0.777687i	$-0.716393\pi$
$383$	−24.6059	−1.25730	−0.628652	+	0.777687i	$0.716393\pi$
$384$	16.1432	0.823804
$385$	−34.0009	−1.73285
$386$	43.4533	2.21172
$387$	42.0060	2.13528
$388$	−91.0118	−4.62042
$389$	−21.9215	−1.11146	−0.555731	−	0.831362i	$-0.687562\pi$
$389$	−21.9215	−1.11146	−0.555731	+	0.831362i	$0.687562\pi$
$390$	−15.9528	−0.807800
$391$	−6.00348	−0.303609
$392$	−135.514	−6.84451
$393$	−56.7247	−2.86138
$394$	−27.6956	−1.39528
$395$	−0.999433	−0.0502869
$396$	60.6811	3.04934
$397$	−29.0404	−1.45749	−0.728747	−	0.684783i	$-0.759897\pi$
$397$	−29.0404	−1.45749	−0.728747	+	0.684783i	$0.759897\pi$
$398$	−1.88423	−0.0944479
$399$	88.6518	4.43814
$400$	−3.56895	−0.178447
$401$	8.51289	0.425114	0.212557	−	0.977149i	$-0.431821\pi$
$401$	8.51289	0.425114	0.212557	+	0.977149i	$0.431821\pi$
$402$	−48.4562	−2.41678
$403$	0.901728	0.0449183
$404$	−11.2589	−0.560153
$405$	−12.5778	−0.624995
$406$	−89.7424	−4.45384
$407$	−22.9862	−1.13939
$408$	32.8734	1.62748
$409$	−6.36265	−0.314613	−0.157306	−	0.987550i	$-0.550281\pi$
$409$	−6.36265	−0.314613	−0.157306	+	0.987550i	$0.550281\pi$
$410$	33.0355	1.63150
$411$	27.0317	1.33337
$412$	62.6304	3.08558
$413$	33.2522	1.63623
$414$	37.7415	1.85489
$415$	14.9535	0.734037
$416$	13.5333	0.663523
$417$	26.6882	1.30693
$418$	−57.9347	−2.83368
$419$	−2.20293	−0.107620	−0.0538100	−	0.998551i	$-0.517137\pi$
$419$	−2.20293	−0.107620	−0.0538100	+	0.998551i	$0.517137\pi$
$420$	138.230	6.74491
$421$	23.8482	1.16229	0.581144	−	0.813800i	$-0.302605\pi$
$421$	23.8482	1.16229	0.581144	+	0.813800i	$0.302605\pi$
$422$	52.6088	2.56096
$423$	15.7134	0.764011
$424$	−80.3383	−3.90157
$425$	−0.535301	−0.0259659
$426$	−5.29052	−0.256327
$427$	−23.6884	−1.14636
$428$	−64.8099	−3.13270
$429$	8.92997	0.431143
$430$	−62.5331	−3.01561
$431$	−3.43706	−0.165557	−0.0827786	−	0.996568i	$-0.526379\pi$
$431$	−3.43706	−0.165557	−0.0827786	+	0.996568i	$0.526379\pi$
$432$	−23.2442	−1.11834
$433$	4.48870	0.215713	0.107856	−	0.994166i	$-0.465601\pi$
$433$	4.48870	0.215713	0.107856	+	0.994166i	$0.465601\pi$
$434$	−10.9610	−0.526144
$435$	38.9302	1.86656
$436$	21.8001	1.04404
$437$	−25.6860	−1.22873
$438$	−50.4330	−2.40978
$439$	3.69410	0.176310	0.0881549	−	0.996107i	$-0.471903\pi$
$439$	3.69410	0.176310	0.0881549	+	0.996107i	$0.471903\pi$
$440$	−53.9437	−2.57166
$441$	66.3323	3.15868
$442$	4.54277	0.216077
$443$	29.2116	1.38788	0.693942	−	0.720031i	$-0.255872\pi$
$443$	29.2116	1.38788	0.693942	+	0.720031i	$0.255872\pi$
$444$	93.4499	4.43493
$445$	−20.3712	−0.965688
$446$	30.8362	1.46013
$447$	52.3841	2.47768
$448$	−58.7823	−2.77720
$449$	−7.75912	−0.366176	−0.183088	−	0.983097i	$-0.558609\pi$
$449$	−7.75912	−0.366176	−0.183088	+	0.983097i	$0.558609\pi$
$450$	3.36523	0.158638
$451$	−18.4924	−0.870775
$452$	75.9858	3.57407
$453$	−51.4000	−2.41498
$454$	1.98647	0.0932296
$455$	11.4068	0.534760
$456$	140.650	6.58652
$457$	19.3592	0.905587	0.452793	−	0.891616i	$-0.350428\pi$
$457$	19.3592	0.905587	0.452793	+	0.891616i	$0.350428\pi$
$458$	−55.2963	−2.58383
$459$	−3.48636	−0.162729
$460$	−40.0506	−1.86737
$461$	19.5018	0.908288	0.454144	−	0.890928i	$-0.349945\pi$
$461$	19.5018	0.908288	0.454144	+	0.890928i	$0.349945\pi$
$462$	−108.549	−5.05014
$463$	−37.3746	−1.73694	−0.868472	−	0.495739i	$-0.834897\pi$
$463$	−37.3746	−1.73694	−0.868472	+	0.495739i	$0.834897\pi$
$464$	−73.9119	−3.43127
$465$	4.75487	0.220502
$466$	−5.47997	−0.253855
$467$	−3.07291	−0.142198	−0.0710988	−	0.997469i	$-0.522651\pi$
$467$	−3.07291	−0.142198	−0.0710988	+	0.997469i	$0.522651\pi$
$468$	−20.3577	−0.941033
$469$	34.6480	1.59990
$470$	−23.3921	−1.07900
$471$	−24.0652	−1.10886
$472$	52.7559	2.42829
$473$	35.0045	1.60951
$474$	−3.19071	−0.146554
$475$	−2.29029	−0.105086
$476$	−39.3627	−1.80419
$477$	39.3244	1.80054
$478$	−72.7431	−3.32719
$479$	25.1273	1.14810	0.574048	−	0.818822i	$-0.305372\pi$
$479$	25.1273	1.14810	0.574048	+	0.818822i	$0.305372\pi$
$480$	71.3618	3.25721
$481$	7.71156	0.351617
$482$	−60.8006	−2.76939
$483$	−48.1261	−2.18981
$484$	−4.04491	−0.183860
$485$	−39.6027	−1.79827
$486$	−57.3235	−2.60025
$487$	−21.2383	−0.962400	−0.481200	−	0.876611i	$-0.659799\pi$
$487$	−21.2383	−0.962400	−0.481200	+	0.876611i	$0.659799\pi$
$488$	−37.5826	−1.70128
$489$	−33.9670	−1.53604
$490$	−98.7470	−4.46093
$491$	−15.3456	−0.692537	−0.346268	−	0.938135i	$-0.612551\pi$
$491$	−15.3456	−0.692537	−0.346268	+	0.938135i	$0.612551\pi$
$492$	75.1805	3.38940
$493$	−11.0859	−0.499284
$494$	19.4363	0.874481
$495$	26.4047	1.18680
$496$	−9.02747	−0.405345
$497$	3.78292	0.169687
$498$	47.7393	2.13925
$499$	−12.9205	−0.578400	−0.289200	−	0.957269i	$-0.593389\pi$
$499$	−12.9205	−0.578400	−0.289200	+	0.957269i	$0.593389\pi$
$500$	−57.1983	−2.55798
$501$	22.2387	0.993552
$502$	4.50943	0.201266
$503$	1.57060	0.0700294	0.0350147	−	0.999387i	$-0.488852\pi$
$503$	1.57060	0.0700294	0.0350147	+	0.999387i	$0.488852\pi$
$504$	147.771	6.58226
$505$	−4.89919	−0.218011
$506$	31.4508	1.39816
$507$	30.9781	1.37579
$508$	77.7146	3.44803
$509$	21.0386	0.932520	0.466260	−	0.884648i	$-0.345601\pi$
$509$	21.0386	0.932520	0.466260	+	0.884648i	$0.345601\pi$
$510$	23.9543	1.06072
$511$	36.0614	1.59526
$512$	32.2460	1.42509
$513$	−14.9165	−0.658577
$514$	−65.7028	−2.89803
$515$	27.2529	1.20090
$516$	−142.310	−6.26484
$517$	13.0943	0.575887
$518$	−93.7381	−4.11862
$519$	−6.75642	−0.296574
$520$	18.0974	0.793622
$521$	−39.7729	−1.74248	−0.871242	−	0.490854i	$-0.836685\pi$
$521$	−39.7729	−1.74248	−0.871242	+	0.490854i	$0.836685\pi$
$522$	69.6928	3.05037
$523$	−27.1594	−1.18760	−0.593798	−	0.804614i	$-0.702372\pi$
$523$	−27.1594	−1.18760	−0.593798	+	0.804614i	$0.702372\pi$
$524$	107.761	4.70757
$525$	−4.29117	−0.187282
$526$	−20.8016	−0.906992
$527$	−1.35401	−0.0589818
$528$	−89.4006	−3.89066
$529$	−9.05596	−0.393737
$530$	−58.5412	−2.54287
$531$	−25.8232	−1.12063
$532$	−168.414	−7.30167
$533$	6.20396	0.268723
$534$	−65.0355	−2.81436
$535$	−28.2012	−1.21925
$536$	54.9704	2.37436
$537$	−20.8810	−0.901080
$538$	3.12373	0.134673
$539$	55.2761	2.38091
$540$	−23.2583	−1.00088
$541$	4.42692	0.190328	0.0951640	−	0.995462i	$-0.469662\pi$
$541$	4.42692	0.190328	0.0951640	+	0.995462i	$0.469662\pi$
$542$	33.3002	1.43037
$543$	46.1092	1.97873
$544$	−20.3212	−0.871266
$545$	9.48606	0.406338
$546$	36.4165	1.55848
$547$	−24.9234	−1.06565	−0.532824	−	0.846226i	$-0.678869\pi$
$547$	−24.9234	−1.06565	−0.532824	+	0.846226i	$0.678869\pi$
$548$	−51.3527	−2.19368
$549$	18.3961	0.785128
$550$	2.80432	0.119576
$551$	−47.4312	−2.02064
$552$	−76.3539	−3.24984
$553$	2.28148	0.0970182
$554$	−12.8783	−0.547146
$555$	40.6636	1.72607
$556$	−50.7003	−2.15017
$557$	15.2656	0.646825	0.323412	−	0.946258i	$-0.395170\pi$
$557$	15.2656	0.646825	0.323412	+	0.946258i	$0.395170\pi$
$558$	8.51216	0.360348
$559$	−11.7435	−0.496698
$560$	−114.197	−4.82571
$561$	−13.4090	−0.566130
$562$	19.4548	0.820650
$563$	−8.22548	−0.346663	−0.173331	−	0.984864i	$-0.555453\pi$
$563$	−8.22548	−0.346663	−0.173331	+	0.984864i	$0.555453\pi$
$564$	−53.2345	−2.24158
$565$	33.0643	1.39103
$566$	66.6044	2.79959
$567$	28.7122	1.20580
$568$	6.00174	0.251828
$569$	12.5574	0.526433	0.263217	−	0.964737i	$-0.415217\pi$
$569$	12.5574	0.526433	0.263217	+	0.964737i	$0.415217\pi$
$570$	102.489	4.29279
$571$	15.1996	0.636082	0.318041	−	0.948077i	$-0.396975\pi$
$571$	15.1996	0.636082	0.318041	+	0.948077i	$0.396975\pi$
$572$	−16.9645	−0.709321
$573$	−68.2304	−2.85037
$574$	−75.4124	−3.14765
$575$	1.24332	0.0518501
$576$	45.6496	1.90207
$577$	0.0610618	0.00254204	0.00127102	−	0.999999i	$-0.499595\pi$
$577$	0.0610618	0.00254204	0.00127102	+	0.999999i	$0.499595\pi$
$578$	38.0429	1.58238
$579$	43.0303	1.78828
$580$	−73.9567	−3.07089
$581$	−34.1353	−1.41617
$582$	−126.432	−5.24079
$583$	32.7699	1.35719
$584$	57.2129	2.36749
$585$	−8.85839	−0.366250
$586$	−4.21750	−0.174223
$587$	−4.68625	−0.193422	−0.0967112	−	0.995312i	$-0.530832\pi$
$587$	−4.68625	−0.193422	−0.0967112	+	0.995312i	$0.530832\pi$
$588$	−224.724	−9.26744
$589$	−5.79317	−0.238703
$590$	38.4423	1.58265
$591$	−27.4260	−1.12815
$592$	−77.2027	−3.17301
$593$	32.4354	1.33196	0.665982	−	0.745968i	$-0.268013\pi$
$593$	32.4354	1.33196	0.665982	+	0.745968i	$0.268013\pi$
$594$	18.2642	0.749391
$595$	−17.1282	−0.702189
$596$	−99.5154	−4.07631
$597$	−1.86589	−0.0763657
$598$	−10.5513	−0.431475
$599$	−14.5396	−0.594074	−0.297037	−	0.954866i	$-0.595998\pi$
$599$	−14.5396	−0.594074	−0.297037	+	0.954866i	$0.595998\pi$
$600$	−6.80811	−0.277940
$601$	14.7154	0.600254	0.300127	−	0.953899i	$-0.402971\pi$
$601$	14.7154	0.600254	0.300127	+	0.953899i	$0.402971\pi$
$602$	142.749	5.81800
$603$	−26.9072	−1.09575
$604$	97.6459	3.97315
$605$	−1.76010	−0.0715581
$606$	−15.6408	−0.635363
$607$	−38.2022	−1.55058	−0.775290	−	0.631606i	$-0.782396\pi$
$607$	−38.2022	−1.55058	−0.775290	+	0.631606i	$0.782396\pi$
$608$	−86.9447	−3.52607
$609$	−88.8688	−3.60115
$610$	−27.3858	−1.10882
$611$	−4.39296	−0.177720
$612$	30.5686	1.23566
$613$	12.1945	0.492529	0.246265	−	0.969203i	$-0.420797\pi$
$613$	12.1945	0.492529	0.246265	+	0.969203i	$0.420797\pi$
$614$	−17.3396	−0.699771
$615$	32.7139	1.31915
$616$	123.141	4.96149
$617$	2.26798	0.0913053	0.0456527	−	0.998957i	$-0.485463\pi$
$617$	2.26798	0.0913053	0.0456527	+	0.998957i	$0.485463\pi$
$618$	87.0054	3.49987
$619$	−19.8887	−0.799393	−0.399696	−	0.916648i	$-0.630884\pi$
$619$	−19.8887	−0.799393	−0.399696	+	0.916648i	$0.630884\pi$
$620$	−9.03295	−0.362772
$621$	8.09764	0.324947
$622$	−56.9917	−2.28516
$623$	46.5028	1.86309
$624$	29.9927	1.20067
$625$	−23.2243	−0.928974
$626$	−6.69362	−0.267531
$627$	−57.3708	−2.29117
$628$	45.7172	1.82431
$629$	−11.5795	−0.461705
$630$	107.678	4.29001
$631$	−15.5054	−0.617259	−0.308630	−	0.951182i	$-0.599870\pi$
$631$	−15.5054	−0.617259	−0.308630	+	0.951182i	$0.599870\pi$
$632$	3.61965	0.143982
$633$	52.0967	2.07066
$634$	−42.7094	−1.69621
$635$	33.8166	1.34197
$636$	−133.225	−5.28272
$637$	−18.5444	−0.734755
$638$	58.0765	2.29927
$639$	−2.93777	−0.116216
$640$	−13.3447	−0.527494
$641$	20.4038	0.805903	0.402951	−	0.915221i	$-0.367984\pi$
$641$	20.4038	0.805903	0.402951	+	0.915221i	$0.367984\pi$
$642$	−90.0331	−3.55332
$643$	8.54820	0.337108	0.168554	−	0.985692i	$-0.446090\pi$
$643$	8.54820	0.337108	0.168554	+	0.985692i	$0.446090\pi$
$644$	91.4263	3.60270
$645$	−61.9244	−2.43827
$646$	−29.1851	−1.14827
$647$	−1.67458	−0.0658343	−0.0329172	−	0.999458i	$-0.510480\pi$
$647$	−1.67458	−0.0658343	−0.0329172	+	0.999458i	$0.510480\pi$
$648$	45.5530	1.78949
$649$	−21.5191	−0.844697
$650$	−0.940810	−0.0369016
$651$	−10.8543	−0.425413
$652$	64.5279	2.52711
$653$	2.98021	0.116625	0.0583124	−	0.998298i	$-0.481428\pi$
$653$	2.98021	0.116625	0.0583124	+	0.998298i	$0.481428\pi$
$654$	30.2844	1.18422
$655$	46.8910	1.83218
$656$	−62.1096	−2.42497
$657$	−28.0049	−1.09257
$658$	53.3987	2.08170
$659$	−25.7630	−1.00359	−0.501793	−	0.864988i	$-0.667326\pi$
$659$	−25.7630	−1.00359	−0.501793	+	0.864988i	$0.667326\pi$
$660$	−89.4549	−3.48203
$661$	−36.6810	−1.42673	−0.713363	−	0.700795i	$-0.752829\pi$
$661$	−36.6810	−1.42673	−0.713363	+	0.700795i	$0.752829\pi$
$662$	27.3673	1.06366
$663$	4.49855	0.174709
$664$	−54.1570	−2.10170
$665$	−73.2834	−2.84181
$666$	72.7958	2.82078
$667$	25.7488	0.996999
$668$	−42.2474	−1.63460
$669$	30.5360	1.18059
$670$	40.0560	1.54750
$671$	15.3299	0.591804
$672$	−162.903	−6.28411
$673$	20.1544	0.776897	0.388448	−	0.921470i	$-0.373011\pi$
$673$	20.1544	0.776897	0.388448	+	0.921470i	$0.373011\pi$
$674$	−48.2298	−1.85774
$675$	0.722027	0.0277908
$676$	−58.8499	−2.26346
$677$	19.2465	0.739702	0.369851	−	0.929091i	$-0.379409\pi$
$677$	19.2465	0.739702	0.369851	+	0.929091i	$0.379409\pi$
$678$	105.558	4.05395
$679$	90.4038	3.46938
$680$	−27.1746	−1.04210
$681$	1.96713	0.0753807
$682$	7.09337	0.271619
$683$	−38.8796	−1.48769	−0.743844	−	0.668353i	$-0.767000\pi$
$683$	−38.8796	−1.48769	−0.743844	+	0.668353i	$0.767000\pi$
$684$	130.788	5.00081
$685$	−22.3455	−0.853778
$686$	134.314	5.12812
$687$	−54.7580	−2.08915
$688$	117.568	4.48223
$689$	−10.9939	−0.418832
$690$	−55.6378	−2.11809
$691$	16.8904	0.642541	0.321271	−	0.946987i	$-0.395890\pi$
$691$	16.8904	0.642541	0.321271	+	0.946987i	$0.395890\pi$
$692$	12.8353	0.487926
$693$	−60.2758	−2.28969
$694$	−26.6943	−1.01330
$695$	−22.0616	−0.836845
$696$	−140.994	−5.34436
$697$	−9.31572	−0.352858
$698$	−45.7995	−1.73354
$699$	−5.42663	−0.205254
$700$	8.15204	0.308118
$701$	−19.9076	−0.751900	−0.375950	−	0.926640i	$-0.622684\pi$
$701$	−19.9076	−0.751900	−0.375950	+	0.926640i	$0.622684\pi$
$702$	−6.12740	−0.231264
$703$	−49.5431	−1.86855
$704$	38.0408	1.43372
$705$	−23.1644	−0.872420
$706$	32.7505	1.23258
$707$	11.1837	0.420607
$708$	87.4851	3.28789
$709$	−24.0591	−0.903560	−0.451780	−	0.892129i	$-0.649211\pi$
$709$	−24.0591	−0.903560	−0.451780	+	0.892129i	$0.649211\pi$
$710$	4.37337	0.164130
$711$	−1.77176	−0.0664464
$712$	73.7784	2.76496
$713$	3.14492	0.117778
$714$	−54.6822	−2.04643
$715$	−7.38189	−0.276067
$716$	39.6681	1.48247
$717$	−72.0350	−2.69020
$718$	13.7505	0.513162
$719$	−27.4751	−1.02465	−0.512324	−	0.858793i	$-0.671215\pi$
$719$	−27.4751	−1.02465	−0.512324	+	0.858793i	$0.671215\pi$
$720$	88.6840	3.30506
$721$	−62.2120	−2.31690
$722$	−74.7265	−2.78103
$723$	−60.2088	−2.23919
$724$	−87.5947	−3.25543
$725$	2.29590	0.0852675
$726$	−5.61914	−0.208546
$727$	19.1027	0.708478	0.354239	−	0.935155i	$-0.384740\pi$
$727$	19.1027	0.708478	0.354239	+	0.935155i	$0.384740\pi$
$728$	−41.3121	−1.53113
$729$	−39.2991	−1.45552
$730$	41.6901	1.54302
$731$	17.6338	0.652210
$732$	−62.3232	−2.30353
$733$	−20.8917	−0.771652	−0.385826	−	0.922572i	$-0.626084\pi$
$733$	−20.8917	−0.771652	−0.385826	+	0.922572i	$0.626084\pi$
$734$	−17.2906	−0.638209
$735$	−97.7858	−3.60688
$736$	47.1994	1.73979
$737$	−22.4224	−0.825938
$738$	58.5643	2.15578
$739$	−48.3360	−1.77807	−0.889035	−	0.457839i	$-0.848623\pi$
$739$	−48.3360	−1.77807	−0.889035	+	0.457839i	$0.848623\pi$
$740$	−77.2496	−2.83975
$741$	19.2471	0.707060
$742$	133.636	4.90593
$743$	40.0843	1.47055	0.735274	−	0.677770i	$-0.237053\pi$
$743$	40.0843	1.47055	0.735274	+	0.677770i	$0.237053\pi$
$744$	−17.2207	−0.631343
$745$	−43.3029	−1.58650
$746$	−2.08887	−0.0764791
$747$	26.5091	0.969916
$748$	25.4735	0.931403
$749$	64.3770	2.35228
$750$	−79.4591	−2.90144
$751$	−20.4773	−0.747226	−0.373613	−	0.927585i	$-0.621881\pi$
$751$	−20.4773	−0.747226	−0.373613	+	0.927585i	$0.621881\pi$
$752$	43.9792	1.60376
$753$	4.46553	0.162733
$754$	−19.4839	−0.709561
$755$	42.4894	1.54635
$756$	53.0935	1.93099
$757$	−54.5851	−1.98393	−0.991965	−	0.126509i	$-0.959623\pi$
$757$	−54.5851	−1.98393	−0.991965	+	0.126509i	$0.959623\pi$
$758$	62.8242	2.28188
$759$	31.1447	1.13048
$760$	−116.267	−4.21744
$761$	−19.0522	−0.690641	−0.345320	−	0.938485i	$-0.612230\pi$
$761$	−19.0522	−0.690641	−0.345320	+	0.938485i	$0.612230\pi$
$762$	107.960	3.91099
$763$	−21.6545	−0.783945
$764$	129.619	4.68945
$765$	13.3016	0.480919
$766$	64.9368	2.34626
$767$	7.21935	0.260676
$768$	19.6981	0.710795
$769$	−25.2230	−0.909564	−0.454782	−	0.890603i	$-0.650283\pi$
$769$	−25.2230	−0.909564	−0.454782	+	0.890603i	$0.650283\pi$
$770$	89.7308	3.23367
$771$	−65.0632	−2.34320
$772$	−81.7457	−2.94209
$773$	−37.7604	−1.35815	−0.679073	−	0.734071i	$-0.737618\pi$
$773$	−37.7604	−1.35815	−0.679073	+	0.734071i	$0.737618\pi$
$774$	−110.857	−3.98467
$775$	0.280417	0.0100729
$776$	143.429	5.14881
$777$	−92.8256	−3.33010
$778$	57.8523	2.07411
$779$	−39.8574	−1.42804
$780$	30.0109	1.07456
$781$	−2.44811	−0.0876001
$782$	15.8436	0.566566
$783$	14.9530	0.534375
$784$	185.653	6.63047
$785$	19.8933	0.710022
$786$	149.701	5.33964
$787$	−42.8825	−1.52860	−0.764298	−	0.644863i	$-0.776914\pi$
$787$	−42.8825	−1.52860	−0.764298	+	0.644863i	$0.776914\pi$
$788$	52.1018	1.85605
$789$	−20.5991	−0.733347
$790$	2.63758	0.0938408
$791$	−75.4782	−2.68370
$792$	−95.6298	−3.39806
$793$	−5.14297	−0.182632
$794$	76.6396	2.71984
$795$	−57.9713	−2.05603
$796$	3.54467	0.125638
$797$	−22.1168	−0.783417	−0.391708	−	0.920089i	$-0.628116\pi$
$797$	−22.1168	−0.783417	−0.391708	+	0.920089i	$0.628116\pi$
$798$	−233.959	−8.28205
$799$	6.59636	0.233363
$800$	4.20854	0.148794
$801$	−36.1135	−1.27601
$802$	−22.4662	−0.793307
$803$	−23.3371	−0.823547
$804$	91.1574	3.21487
$805$	39.7831	1.40217
$806$	−2.37973	−0.0838223
$807$	3.09332	0.108890
$808$	17.7434	0.624211
$809$	−41.6883	−1.46568	−0.732841	−	0.680400i	$-0.761806\pi$
$809$	−41.6883	−1.46568	−0.732841	+	0.680400i	$0.761806\pi$
$810$	33.1937	1.16631
$811$	3.63013	0.127471	0.0637356	−	0.997967i	$-0.479699\pi$
$811$	3.63013	0.127471	0.0637356	+	0.997967i	$0.479699\pi$
$812$	168.826	5.92464
$813$	32.9760	1.15652
$814$	60.6624	2.12621
$815$	28.0786	0.983549
$816$	−45.0363	−1.57659
$817$	75.4465	2.63954
$818$	16.7915	0.587101
$819$	20.2217	0.706603
$820$	−62.1473	−2.17028
$821$	−34.9767	−1.22069	−0.610347	−	0.792134i	$-0.708970\pi$
$821$	−34.9767	−1.22069	−0.610347	+	0.792134i	$0.708970\pi$
$822$	−71.3385	−2.48822
$823$	16.0144	0.558227	0.279114	−	0.960258i	$-0.409959\pi$
$823$	16.0144	0.558227	0.279114	+	0.960258i	$0.409959\pi$
$824$	−98.7018	−3.43844
$825$	2.77702	0.0966834
$826$	−87.7550	−3.05339
$827$	−44.4318	−1.54504	−0.772522	−	0.634988i	$-0.781005\pi$
$827$	−44.4318	−1.54504	−0.772522	+	0.634988i	$0.781005\pi$
$828$	−71.0005	−2.46744
$829$	−19.1757	−0.665999	−0.332999	−	0.942927i	$-0.608061\pi$
$829$	−19.1757	−0.665999	−0.332999	+	0.942927i	$0.608061\pi$
$830$	−39.4633	−1.36979
$831$	−12.7529	−0.442394
$832$	−12.7622	−0.442448
$833$	27.8458	0.964800
$834$	−70.4322	−2.43887
$835$	−18.3835	−0.636186
$836$	108.989	3.76945
$837$	1.82633	0.0631272
$838$	5.81369	0.200830
$839$	−4.38904	−0.151526	−0.0757632	−	0.997126i	$-0.524139\pi$
$839$	−4.38904	−0.151526	−0.0757632	+	0.997126i	$0.524139\pi$
$840$	−217.842	−7.51625
$841$	18.5473	0.639563
$842$	−62.9371	−2.16895
$843$	19.2654	0.663535
$844$	−98.9694	−3.40667
$845$	−25.6078	−0.880936
$846$	−41.4688	−1.42573
$847$	4.01789	0.138057
$848$	110.063	3.77957
$849$	65.9561	2.26361
$850$	1.41270	0.0484551
$851$	26.8953	0.921958
$852$	9.95270	0.340974
$853$	−9.57344	−0.327788	−0.163894	−	0.986478i	$-0.552406\pi$
$853$	−9.57344	−0.327788	−0.163894	+	0.986478i	$0.552406\pi$
$854$	62.5155	2.13924
$855$	56.9109	1.94631
$856$	102.137	3.49095
$857$	−15.2770	−0.521852	−0.260926	−	0.965359i	$-0.584028\pi$
$857$	−15.2770	−0.521852	−0.260926	+	0.965359i	$0.584028\pi$
$858$	−23.5669	−0.804559
$859$	−24.2200	−0.826375	−0.413187	−	0.910646i	$-0.635585\pi$
$859$	−24.2200	−0.826375	−0.413187	+	0.910646i	$0.635585\pi$
$860$	117.639	4.01146
$861$	−74.6783	−2.54503
$862$	9.07065	0.308948
$863$	40.7869	1.38840	0.694202	−	0.719780i	$-0.255757\pi$
$863$	40.7869	1.38840	0.694202	+	0.719780i	$0.255757\pi$
$864$	27.4098	0.932500
$865$	5.58514	0.189900
$866$	−11.8460	−0.402543
$867$	37.6726	1.27943
$868$	20.6201	0.699893
$869$	−1.47645	−0.0500852
$870$	−102.740	−3.48321
$871$	7.52239	0.254886
$872$	−34.3557	−1.16343
$873$	−70.2065	−2.37613
$874$	67.7871	2.29293
$875$	56.8162	1.92074
$876$	94.8762	3.20557
$877$	−27.8717	−0.941162	−0.470581	−	0.882357i	$-0.655956\pi$
$877$	−27.8717	−0.941162	−0.470581	+	0.882357i	$0.655956\pi$
$878$	−9.74900	−0.329013
$879$	−4.17645	−0.140868
$880$	73.9023	2.49125
$881$	52.2726	1.76111	0.880554	−	0.473946i	$-0.157171\pi$
$881$	52.2726	1.76111	0.880554	+	0.473946i	$0.157171\pi$
$882$	−175.056	−5.89443
$883$	−32.4986	−1.09367	−0.546833	−	0.837242i	$-0.684167\pi$
$883$	−32.4986	−1.09367	−0.546833	+	0.837242i	$0.684167\pi$
$884$	−8.54600	−0.287433
$885$	38.0681	1.27965
$886$	−77.0915	−2.58994
$887$	44.9956	1.51080	0.755402	−	0.655262i	$-0.227442\pi$
$887$	44.9956	1.51080	0.755402	+	0.655262i	$0.227442\pi$
$888$	−147.271	−4.94210
$889$	−77.1955	−2.58905
$890$	53.7611	1.80208
$891$	−18.5810	−0.622487
$892$	−58.0100	−1.94232
$893$	28.2226	0.944435
$894$	−138.246	−4.62362
$895$	17.2611	0.576974
$896$	30.4628	1.01769
$897$	−10.4486	−0.348869
$898$	20.4769	0.683323
$899$	5.80735	0.193686
$900$	−6.33077	−0.211026
$901$	16.5081	0.549965
$902$	48.8029	1.62496
$903$	141.359	4.70414
$904$	−119.749	−3.98279
$905$	−38.1158	−1.26701
$906$	135.648	4.50662
$907$	3.35018	0.111241	0.0556205	−	0.998452i	$-0.482286\pi$
$907$	3.35018	0.111241	0.0556205	+	0.998452i	$0.482286\pi$
$908$	−3.73701	−0.124017
$909$	−8.68514	−0.288068
$910$	−30.1034	−0.997920
$911$	15.6754	0.519349	0.259675	−	0.965696i	$-0.416385\pi$
$911$	15.6754	0.519349	0.259675	+	0.965696i	$0.416385\pi$
$912$	−192.688	−6.38055
$913$	22.0906	0.731092
$914$	−51.0904	−1.68992
$915$	−27.1192	−0.896534
$916$	104.025	3.43709
$917$	−107.041	−3.53482
$918$	9.20077	0.303671
$919$	57.9810	1.91262	0.956308	−	0.292361i	$-0.0944410\pi$
$919$	57.9810	1.91262	0.956308	+	0.292361i	$0.0944410\pi$
$920$	63.1174	2.08092
$921$	−17.1708	−0.565799
$922$	−51.4666	−1.69496
$923$	0.821305	0.0270336
$924$	204.205	6.71785
$925$	2.39812	0.0788497
$926$	98.6342	3.24132
$927$	48.3131	1.58681
$928$	87.1575	2.86109
$929$	−38.5791	−1.26574	−0.632870	−	0.774258i	$-0.718123\pi$
$929$	−38.5791	−1.26574	−0.632870	+	0.774258i	$0.718123\pi$
$930$	−12.5485	−0.411480
$931$	119.139	3.90461
$932$	10.3091	0.337686
$933$	−56.4369	−1.84766
$934$	8.10965	0.265356
$935$	11.0845	0.362501
$936$	32.0825	1.04865
$937$	−7.42711	−0.242633	−0.121317	−	0.992614i	$-0.538712\pi$
$937$	−7.42711	−0.242633	−0.121317	+	0.992614i	$0.538712\pi$
$938$	−91.4386	−2.98558
$939$	−6.62847	−0.216312
$940$	44.0059	1.43531
$941$	53.1892	1.73392	0.866959	−	0.498380i	$-0.166071\pi$
$941$	53.1892	1.73392	0.866959	+	0.498380i	$0.166071\pi$
$942$	63.5098	2.06926
$943$	21.6373	0.704606
$944$	−72.2750	−2.35235
$945$	23.1030	0.751540
$946$	−92.3794	−3.00351
$947$	−17.1430	−0.557073	−0.278537	−	0.960426i	$-0.589849\pi$
$947$	−17.1430	−0.557073	−0.278537	+	0.960426i	$0.589849\pi$
$948$	6.00247	0.194951
$949$	7.82926	0.254149
$950$	6.04425	0.196101
$951$	−42.2937	−1.37147
$952$	62.0333	2.01051
$953$	−8.63477	−0.279708	−0.139854	−	0.990172i	$-0.544663\pi$
$953$	−8.63477	−0.279708	−0.139854	+	0.990172i	$0.544663\pi$
$954$	−103.780	−3.36000
$955$	56.4021	1.82513
$956$	136.847	4.42594
$957$	57.5112	1.85907
$958$	−66.3128	−2.14247
$959$	51.0097	1.64719
$960$	−67.2957	−2.17196
$961$	−30.2907	−0.977119
$962$	−20.3514	−0.656155
$963$	−49.9943	−1.61105
$964$	114.380	3.68393
$965$	−35.5707	−1.14506
$966$	127.008	4.08643
$967$	−24.8735	−0.799879	−0.399940	−	0.916541i	$-0.630969\pi$
$967$	−24.8735	−0.799879	−0.399940	+	0.916541i	$0.630969\pi$
$968$	6.37454	0.204886
$969$	−28.9010	−0.928434
$970$	104.514	3.35575
$971$	−47.1838	−1.51420	−0.757100	−	0.653300i	$-0.773384\pi$
$971$	−47.1838	−1.51420	−0.757100	+	0.653300i	$0.773384\pi$
$972$	107.839	3.45893
$973$	50.3616	1.61452
$974$	56.0495	1.79594
$975$	−0.931651	−0.0298367
$976$	51.4878	1.64808
$977$	39.4494	1.26210	0.631049	−	0.775743i	$-0.282625\pi$
$977$	39.4494	1.26210	0.631049	+	0.775743i	$0.282625\pi$
$978$	89.6414	2.86642
$979$	−30.0941	−0.961813
$980$	185.766	5.93408
$981$	16.8166	0.536913
$982$	40.4981	1.29235
$983$	14.2938	0.455901	0.227951	−	0.973673i	$-0.426798\pi$
$983$	14.2938	0.455901	0.227951	+	0.973673i	$0.426798\pi$
$984$	−118.480	−3.77700
$985$	22.6715	0.722373
$986$	29.2565	0.931718
$987$	52.8789	1.68315
$988$	−36.5642	−1.16326
$989$	−40.9574	−1.30237
$990$	−69.6838	−2.21470
$991$	−8.18171	−0.259900	−0.129950	−	0.991521i	$-0.541482\pi$
$991$	−8.18171	−0.259900	−0.129950	+	0.991521i	$0.541482\pi$
$992$	10.6453	0.337988
$993$	27.1009	0.860022
$994$	−9.98340	−0.316654
$995$	1.54242	0.0488981
$996$	−89.8086	−2.84570
$997$	−27.6249	−0.874888	−0.437444	−	0.899246i	$-0.644116\pi$
$997$	−27.6249	−0.874888	−0.437444	+	0.899246i	$0.644116\pi$
$998$	34.0981	1.07936
$999$	15.6187	0.494155

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.a.1.9	✓	217

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.a.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.63907 q^{2} -2.61338 q^{3} +4.96471 q^{4} +2.16033 q^{5} +6.89691 q^{6} -4.93155 q^{7} -7.82409 q^{8} +3.82978 q^{9} +O(q^{10})\)	\(q-2.63907 q^{2} -2.61338 q^{3} +4.96471 q^{4} +2.16033 q^{5} +6.89691 q^{6} -4.93155 q^{7} -7.82409 q^{8} +3.82978 q^{9} -5.70128 q^{10} +3.19144 q^{11} -12.9747 q^{12} -1.07068 q^{13} +13.0147 q^{14} -5.64578 q^{15} +10.7189 q^{16} +1.60771 q^{17} -10.1071 q^{18} +6.87862 q^{19} +10.7254 q^{20} +12.8880 q^{21} -8.42244 q^{22} -3.73417 q^{23} +20.4473 q^{24} -0.332958 q^{25} +2.82561 q^{26} -2.16852 q^{27} -24.4837 q^{28} -6.89546 q^{29} +14.8996 q^{30} -0.842199 q^{31} -12.6398 q^{32} -8.34045 q^{33} -4.24287 q^{34} -10.6538 q^{35} +19.0137 q^{36} -7.20247 q^{37} -18.1532 q^{38} +2.79811 q^{39} -16.9026 q^{40} -5.79439 q^{41} -34.0124 q^{42} +10.9683 q^{43} +15.8446 q^{44} +8.27359 q^{45} +9.85476 q^{46} +4.10295 q^{47} -28.0127 q^{48} +17.3201 q^{49} +0.878701 q^{50} -4.20157 q^{51} -5.31563 q^{52} +10.2681 q^{53} +5.72289 q^{54} +6.89457 q^{55} +38.5848 q^{56} -17.9765 q^{57} +18.1976 q^{58} -6.74275 q^{59} -28.0297 q^{60} +4.80345 q^{61} +2.22263 q^{62} -18.8867 q^{63} +11.9196 q^{64} -2.31303 q^{65} +22.0111 q^{66} -7.02579 q^{67} +7.98182 q^{68} +9.75883 q^{69} +28.1161 q^{70} -0.767086 q^{71} -29.9645 q^{72} -7.31240 q^{73} +19.0079 q^{74} +0.870147 q^{75} +34.1504 q^{76} -15.7387 q^{77} -7.38441 q^{78} -0.462629 q^{79} +23.1564 q^{80} -5.82214 q^{81} +15.2918 q^{82} +6.92183 q^{83} +63.9853 q^{84} +3.47320 q^{85} -28.9460 q^{86} +18.0205 q^{87} -24.9701 q^{88} -9.42966 q^{89} -21.8346 q^{90} +5.28012 q^{91} -18.5391 q^{92} +2.20099 q^{93} -10.8280 q^{94} +14.8601 q^{95} +33.0328 q^{96} -18.3317 q^{97} -45.7091 q^{98} +12.2225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) \) 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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