LMFDB - Embedded newform 6047.2.a.a.1.14

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			1.14
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)

$f(q)$	$=$	$q-2.50842 q^{2} +0.797647 q^{3} +4.29216 q^{4} -3.82675 q^{5} -2.00083 q^{6} -2.73995 q^{7} -5.74970 q^{8} -2.36376 q^{9} +O(q^{10})$	\(q-2.50842 q^{2} +0.797647 q^{3} +4.29216 q^{4} -3.82675 q^{5} -2.00083 q^{6} -2.73995 q^{7} -5.74970 q^{8} -2.36376 q^{9} +9.59909 q^{10} -5.60819 q^{11} +3.42363 q^{12} -3.88072 q^{13} +6.87293 q^{14} -3.05239 q^{15} +5.83833 q^{16} +5.63162 q^{17} +5.92930 q^{18} +2.10379 q^{19} -16.4250 q^{20} -2.18551 q^{21} +14.0677 q^{22} +7.90160 q^{23} -4.58623 q^{24} +9.64401 q^{25} +9.73447 q^{26} -4.27839 q^{27} -11.7603 q^{28} +0.651671 q^{29} +7.65668 q^{30} -5.09052 q^{31} -3.14556 q^{32} -4.47335 q^{33} -14.1265 q^{34} +10.4851 q^{35} -10.1456 q^{36} -6.71710 q^{37} -5.27719 q^{38} -3.09545 q^{39} +22.0027 q^{40} -4.35077 q^{41} +5.48217 q^{42} -1.70416 q^{43} -24.0713 q^{44} +9.04552 q^{45} -19.8205 q^{46} +4.66238 q^{47} +4.65692 q^{48} +0.507306 q^{49} -24.1912 q^{50} +4.49204 q^{51} -16.6567 q^{52} +11.1345 q^{53} +10.7320 q^{54} +21.4611 q^{55} +15.7539 q^{56} +1.67808 q^{57} -1.63466 q^{58} +9.47754 q^{59} -13.1014 q^{60} +2.91065 q^{61} +12.7692 q^{62} +6.47658 q^{63} -3.78626 q^{64} +14.8506 q^{65} +11.2210 q^{66} -1.65908 q^{67} +24.1718 q^{68} +6.30268 q^{69} -26.3010 q^{70} +0.503886 q^{71} +13.5909 q^{72} -9.84757 q^{73} +16.8493 q^{74} +7.69252 q^{75} +9.02981 q^{76} +15.3661 q^{77} +7.76467 q^{78} -3.32775 q^{79} -22.3418 q^{80} +3.67864 q^{81} +10.9135 q^{82} +1.28193 q^{83} -9.38056 q^{84} -21.5508 q^{85} +4.27474 q^{86} +0.519804 q^{87} +32.2454 q^{88} +5.89206 q^{89} -22.6899 q^{90} +10.6330 q^{91} +33.9149 q^{92} -4.06044 q^{93} -11.6952 q^{94} -8.05068 q^{95} -2.50905 q^{96} +6.57155 q^{97} -1.27254 q^{98} +13.2564 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.50842	−1.77372	−0.886860	−	0.462039i	$-0.847118\pi$
$2$	−2.50842	−1.77372	−0.886860	+	0.462039i	$0.847118\pi$
$3$	0.797647	0.460522	0.230261	−	0.973129i	$-0.426042\pi$
$3$	0.797647	0.460522	0.230261	+	0.973129i	$0.426042\pi$
$4$	4.29216	2.14608
$5$	−3.82675	−1.71137	−0.855687	−	0.517493i	$-0.826865\pi$
$5$	−3.82675	−1.71137	−0.855687	+	0.517493i	$0.826865\pi$
$6$	−2.00083	−0.816836
$7$	−2.73995	−1.03560	−0.517801	−	0.855501i	$-0.673249\pi$
$7$	−2.73995	−1.03560	−0.517801	+	0.855501i	$0.673249\pi$
$8$	−5.74970	−2.03283
$9$	−2.36376	−0.787920
$10$	9.59909	3.03550
$11$	−5.60819	−1.69093	−0.845466	−	0.534029i	$-0.820677\pi$
$11$	−5.60819	−1.69093	−0.845466	+	0.534029i	$0.820677\pi$
$12$	3.42363	0.988316
$13$	−3.88072	−1.07632	−0.538159	−	0.842843i	$-0.680880\pi$
$13$	−3.88072	−1.07632	−0.538159	+	0.842843i	$0.680880\pi$
$14$	6.87293	1.83687
$15$	−3.05239	−0.788125
$16$	5.83833	1.45958
$17$	5.63162	1.36587	0.682935	−	0.730480i	$-0.260703\pi$
$17$	5.63162	1.36587	0.682935	+	0.730480i	$0.260703\pi$
$18$	5.92930	1.39755
$19$	2.10379	0.482643	0.241321	−	0.970445i	$-0.422419\pi$
$19$	2.10379	0.482643	0.241321	+	0.970445i	$0.422419\pi$
$20$	−16.4250	−3.67275
$21$	−2.18551	−0.476917
$22$	14.0677	2.99924
$23$	7.90160	1.64760	0.823799	−	0.566883i	$-0.191851\pi$
$23$	7.90160	1.64760	0.823799	+	0.566883i	$0.191851\pi$
$24$	−4.58623	−0.936160
$25$	9.64401	1.92880
$26$	9.73447	1.90909
$27$	−4.27839	−0.823376
$28$	−11.7603	−2.22249
$29$	0.651671	0.121012	0.0605062	−	0.998168i	$-0.480729\pi$
$29$	0.651671	0.121012	0.0605062	+	0.998168i	$0.480729\pi$
$30$	7.65668	1.39791
$31$	−5.09052	−0.914285	−0.457142	−	0.889393i	$-0.651127\pi$
$31$	−5.09052	−0.914285	−0.457142	+	0.889393i	$0.651127\pi$
$32$	−3.14556	−0.556063
$33$	−4.47335	−0.778711
$34$	−14.1265	−2.42267
$35$	10.4851	1.77230
$36$	−10.1456	−1.69094
$37$	−6.71710	−1.10428	−0.552142	−	0.833750i	$-0.686189\pi$
$37$	−6.71710	−1.10428	−0.552142	+	0.833750i	$0.686189\pi$
$38$	−5.27719	−0.856073
$39$	−3.09545	−0.495668
$40$	22.0027	3.47893
$41$	−4.35077	−0.679475	−0.339738	−	0.940520i	$-0.610338\pi$
$41$	−4.35077	−0.679475	−0.339738	+	0.940520i	$0.610338\pi$
$42$	5.48217	0.845917
$43$	−1.70416	−0.259882	−0.129941	−	0.991522i	$-0.541479\pi$
$43$	−1.70416	−0.259882	−0.129941	+	0.991522i	$0.541479\pi$
$44$	−24.0713	−3.62888
$45$	9.04552	1.34843
$46$	−19.8205	−2.92237
$47$	4.66238	0.680078	0.340039	−	0.940411i	$-0.389560\pi$
$47$	4.66238	0.680078	0.340039	+	0.940411i	$0.389560\pi$
$48$	4.65692	0.672169
$49$	0.507306	0.0724723
$50$	−24.1912	−3.42115
$51$	4.49204	0.629012
$52$	−16.6567	−2.30987
$53$	11.1345	1.52944	0.764721	−	0.644362i	$-0.222877\pi$
$53$	11.1345	1.52944	0.764721	+	0.644362i	$0.222877\pi$
$54$	10.7320	1.46044
$55$	21.4611	2.89382
$56$	15.7539	2.10520
$57$	1.67808	0.222267
$58$	−1.63466	−0.214642
$59$	9.47754	1.23387	0.616935	−	0.787014i	$-0.288374\pi$
$59$	9.47754	1.23387	0.616935	+	0.787014i	$0.288374\pi$
$60$	−13.1014	−1.69138
$61$	2.91065	0.372670	0.186335	−	0.982486i	$-0.440339\pi$
$61$	2.91065	0.372670	0.186335	+	0.982486i	$0.440339\pi$
$62$	12.7692	1.62169
$63$	6.47658	0.815972
$64$	−3.78626	−0.473283
$65$	14.8506	1.84198
$66$	11.2210	1.38121
$67$	−1.65908	−0.202689	−0.101344	−	0.994851i	$-0.532314\pi$
$67$	−1.65908	−0.202689	−0.101344	+	0.994851i	$0.532314\pi$
$68$	24.1718	2.93127
$69$	6.30268	0.758754
$70$	−26.3010	−3.14357
$71$	0.503886	0.0598003	0.0299002	−	0.999553i	$-0.490481\pi$
$71$	0.503886	0.0598003	0.0299002	+	0.999553i	$0.490481\pi$
$72$	13.5909	1.60170
$73$	−9.84757	−1.15257	−0.576286	−	0.817248i	$-0.695498\pi$
$73$	−9.84757	−1.15257	−0.576286	+	0.817248i	$0.695498\pi$
$74$	16.8493	1.95869
$75$	7.69252	0.888255
$76$	9.02981	1.03579
$77$	15.3661	1.75113
$78$	7.76467	0.879176
$79$	−3.32775	−0.374401	−0.187201	−	0.982322i	$-0.559941\pi$
$79$	−3.32775	−0.374401	−0.187201	+	0.982322i	$0.559941\pi$
$80$	−22.3418	−2.49789
$81$	3.67864	0.408738
$82$	10.9135	1.20520
$83$	1.28193	0.140711	0.0703553	−	0.997522i	$-0.477587\pi$
$83$	1.28193	0.140711	0.0703553	+	0.997522i	$0.477587\pi$
$84$	−9.38056	−1.02350
$85$	−21.5508	−2.33751
$86$	4.27474	0.460957
$87$	0.519804	0.0557288
$88$	32.2454	3.43737
$89$	5.89206	0.624557	0.312279	−	0.949991i	$-0.398908\pi$
$89$	5.89206	0.624557	0.312279	+	0.949991i	$0.398908\pi$
$90$	−22.6899	−2.39173
$91$	10.6330	1.11464
$92$	33.9149	3.53588
$93$	−4.06044	−0.421048
$94$	−11.6952	−1.20627
$95$	−8.05068	−0.825983
$96$	−2.50905	−0.256079
$97$	6.57155	0.667240	0.333620	−	0.942708i	$-0.391730\pi$
$97$	6.57155	0.667240	0.333620	+	0.942708i	$0.391730\pi$
$98$	−1.27254	−0.128546
$99$	13.2564	1.33232
$100$	41.3937	4.13937
$101$	7.85113	0.781217	0.390608	−	0.920557i	$-0.372265\pi$
$101$	7.85113	0.781217	0.390608	+	0.920557i	$0.372265\pi$
$102$	−11.2679	−1.11569
$103$	−9.47514	−0.933613	−0.466807	−	0.884359i	$-0.654596\pi$
$103$	−9.47514	−0.933613	−0.466807	+	0.884359i	$0.654596\pi$
$104$	22.3130	2.18797
$105$	8.36340	0.816184
$106$	−27.9300	−2.71280
$107$	7.97421	0.770896	0.385448	−	0.922730i	$-0.374047\pi$
$107$	7.97421	0.770896	0.385448	+	0.922730i	$0.374047\pi$
$108$	−18.3635	−1.76703
$109$	14.8357	1.42100	0.710501	−	0.703696i	$-0.248468\pi$
$109$	14.8357	1.42100	0.710501	+	0.703696i	$0.248468\pi$
$110$	−53.8335	−5.13282
$111$	−5.35787	−0.508547
$112$	−15.9967	−1.51155
$113$	−2.59495	−0.244112	−0.122056	−	0.992523i	$-0.538949\pi$
$113$	−2.59495	−0.244112	−0.122056	+	0.992523i	$0.538949\pi$
$114$	−4.20933	−0.394240
$115$	−30.2374	−2.81966
$116$	2.79708	0.259702
$117$	9.17310	0.848053
$118$	−23.7736	−2.18854
$119$	−15.4303	−1.41450
$120$	17.5503	1.60212
$121$	20.4518	1.85925
$122$	−7.30112	−0.661012
$123$	−3.47037	−0.312913
$124$	−21.8493	−1.96213
$125$	−17.7715	−1.58953
$126$	−16.2460	−1.44730
$127$	20.2609	1.79786	0.898932	−	0.438087i	$-0.144344\pi$
$127$	20.2609	1.79786	0.898932	+	0.438087i	$0.144344\pi$
$128$	15.7887	1.39553
$129$	−1.35932	−0.119681
$130$	−37.2514	−3.26716
$131$	2.83667	0.247841	0.123921	−	0.992292i	$-0.460453\pi$
$131$	2.83667	0.247841	0.123921	+	0.992292i	$0.460453\pi$
$132$	−19.2004	−1.67118
$133$	−5.76428	−0.499826
$134$	4.16166	0.359513
$135$	16.3723	1.40910
$136$	−32.3801	−2.77657
$137$	−0.181981	−0.0155477	−0.00777386	−	0.999970i	$-0.502475\pi$
$137$	−0.181981	−0.0155477	−0.00777386	+	0.999970i	$0.502475\pi$
$138$	−15.8098	−1.34582
$139$	−2.61399	−0.221715	−0.110858	−	0.993836i	$-0.535360\pi$
$139$	−2.61399	−0.221715	−0.110858	+	0.993836i	$0.535360\pi$
$140$	45.0037	3.80351
$141$	3.71893	0.313191
$142$	−1.26396	−0.106069
$143$	21.7638	1.81998
$144$	−13.8004	−1.15003
$145$	−2.49378	−0.207097
$146$	24.7018	2.04434
$147$	0.404651	0.0333751
$148$	−28.8309	−2.36988
$149$	6.06087	0.496526	0.248263	−	0.968693i	$-0.420140\pi$
$149$	6.06087	0.496526	0.248263	+	0.968693i	$0.420140\pi$
$150$	−19.2960	−1.57552
$151$	−7.24202	−0.589348	−0.294674	−	0.955598i	$-0.595211\pi$
$151$	−7.24202	−0.589348	−0.294674	+	0.955598i	$0.595211\pi$
$152$	−12.0962	−0.981129
$153$	−13.3118	−1.07620
$154$	−38.5447	−3.10602
$155$	19.4802	1.56468
$156$	−13.2862	−1.06374
$157$	6.79982	0.542685	0.271342	−	0.962483i	$-0.412532\pi$
$157$	6.79982	0.542685	0.271342	+	0.962483i	$0.412532\pi$
$158$	8.34739	0.664083
$159$	8.88140	0.704341
$160$	12.0373	0.951631
$161$	−21.6500	−1.70626
$162$	−9.22757	−0.724986
$163$	8.07057	0.632136	0.316068	−	0.948737i	$-0.397637\pi$
$163$	8.07057	0.632136	0.316068	+	0.948737i	$0.397637\pi$
$164$	−18.6742	−1.45821
$165$	17.1184	1.33267
$166$	−3.21563	−0.249581
$167$	−17.7922	−1.37680	−0.688401	−	0.725331i	$-0.741687\pi$
$167$	−17.7922	−1.37680	−0.688401	+	0.725331i	$0.741687\pi$
$168$	12.5660	0.969489
$169$	2.06001	0.158462
$170$	54.0584	4.14609
$171$	−4.97286	−0.380284
$172$	−7.31452	−0.557727
$173$	18.9038	1.43723	0.718614	−	0.695410i	$-0.244777\pi$
$173$	18.9038	1.43723	0.718614	+	0.695410i	$0.244777\pi$
$174$	−1.30388	−0.0988472
$175$	−26.4241	−1.99747
$176$	−32.7424	−2.46805
$177$	7.55973	0.568224
$178$	−14.7798	−1.10779
$179$	−1.92075	−0.143564	−0.0717818	−	0.997420i	$-0.522869\pi$
$179$	−1.92075	−0.143564	−0.0717818	+	0.997420i	$0.522869\pi$
$180$	38.8248	2.89383
$181$	−8.96377	−0.666272	−0.333136	−	0.942879i	$-0.608107\pi$
$181$	−8.96377	−0.666272	−0.333136	+	0.942879i	$0.608107\pi$
$182$	−26.6719	−1.97706
$183$	2.32167	0.171623
$184$	−45.4318	−3.34928
$185$	25.7047	1.88984
$186$	10.1853	0.746821
$187$	−31.5832	−2.30959
$188$	20.0117	1.45950
$189$	11.7225	0.852690
$190$	20.1945	1.46506
$191$	−14.1041	−1.02054	−0.510270	−	0.860014i	$-0.670455\pi$
$191$	−14.1041	−1.02054	−0.510270	+	0.860014i	$0.670455\pi$
$192$	−3.02010	−0.217957
$193$	−25.5029	−1.83574	−0.917868	−	0.396885i	$-0.870091\pi$
$193$	−25.5029	−1.83574	−0.917868	+	0.396885i	$0.870091\pi$
$194$	−16.4842	−1.18350
$195$	11.8455	0.848273
$196$	2.17744	0.155531
$197$	−15.9911	−1.13932	−0.569660	−	0.821880i	$-0.692925\pi$
$197$	−15.9911	−1.13932	−0.569660	+	0.821880i	$0.692925\pi$
$198$	−33.2526	−2.36316
$199$	18.3626	1.30169	0.650843	−	0.759212i	$-0.274415\pi$
$199$	18.3626	1.30169	0.650843	+	0.759212i	$0.274415\pi$
$200$	−55.4502	−3.92092
$201$	−1.32336	−0.0933425
$202$	−19.6939	−1.38566
$203$	−1.78554	−0.125321
$204$	19.2806	1.34991
$205$	16.6493	1.16284
$206$	23.7676	1.65597
$207$	−18.6775	−1.29817
$208$	−22.6569	−1.57097
$209$	−11.7985	−0.816117
$210$	−20.9789	−1.44768
$211$	−15.3314	−1.05546	−0.527729	−	0.849413i	$-0.676956\pi$
$211$	−15.3314	−1.05546	−0.527729	+	0.849413i	$0.676956\pi$
$212$	47.7911	3.28231
$213$	0.401923	0.0275393
$214$	−20.0026	−1.36735
$215$	6.52138	0.444755
$216$	24.5994	1.67378
$217$	13.9478	0.946836
$218$	−37.2141	−2.52046
$219$	−7.85488	−0.530784
$220$	92.1147	6.21037
$221$	−21.8548	−1.47011
$222$	13.4398	0.902019
$223$	0.206615	0.0138359	0.00691797	−	0.999976i	$-0.497798\pi$
$223$	0.206615	0.0138359	0.00691797	+	0.999976i	$0.497798\pi$
$224$	8.61868	0.575860
$225$	−22.7961	−1.51974
$226$	6.50922	0.432987
$227$	24.5613	1.63019	0.815096	−	0.579326i	$-0.196684\pi$
$227$	24.5613	1.63019	0.815096	+	0.579326i	$0.196684\pi$
$228$	7.20260	0.477004
$229$	3.46125	0.228726	0.114363	−	0.993439i	$-0.463517\pi$
$229$	3.46125	0.228726	0.114363	+	0.993439i	$0.463517\pi$
$230$	75.8481	5.00128
$231$	12.2567	0.806435
$232$	−3.74691	−0.245997
$233$	−11.6876	−0.765677	−0.382839	−	0.923815i	$-0.625053\pi$
$233$	−11.6876	−0.765677	−0.382839	+	0.923815i	$0.625053\pi$
$234$	−23.0100	−1.50421
$235$	−17.8418	−1.16387
$236$	40.6791	2.64799
$237$	−2.65437	−0.172420
$238$	38.7058	2.50892
$239$	0.445399	0.0288104	0.0144052	−	0.999896i	$-0.495415\pi$
$239$	0.445399	0.0288104	0.0144052	+	0.999896i	$0.495415\pi$
$240$	−17.8209	−1.15033
$241$	17.8012	1.14668	0.573339	−	0.819318i	$-0.305648\pi$
$241$	17.8012	1.14668	0.573339	+	0.819318i	$0.305648\pi$
$242$	−51.3016	−3.29779
$243$	15.7694	1.01161
$244$	12.4930	0.799780
$245$	−1.94133	−0.124027
$246$	8.70515	0.555020
$247$	−8.16423	−0.519478
$248$	29.2690	1.85858
$249$	1.02253	0.0648002
$250$	44.5783	2.81938
$251$	−20.6732	−1.30488	−0.652440	−	0.757840i	$-0.726255\pi$
$251$	−20.6732	−1.30488	−0.652440	+	0.757840i	$0.726255\pi$
$252$	27.7985	1.75114
$253$	−44.3137	−2.78598
$254$	−50.8228	−3.18891
$255$	−17.1899	−1.07648
$256$	−32.0320	−2.00200
$257$	−27.3898	−1.70853	−0.854266	−	0.519837i	$-0.825993\pi$
$257$	−27.3898	−1.70853	−0.854266	+	0.519837i	$0.825993\pi$
$258$	3.40973	0.212281
$259$	18.4045	1.14360
$260$	63.7410	3.95305
$261$	−1.54039	−0.0953480
$262$	−7.11555	−0.439600
$263$	−7.33219	−0.452122	−0.226061	−	0.974113i	$-0.572585\pi$
$263$	−7.33219	−0.452122	−0.226061	+	0.974113i	$0.572585\pi$
$264$	25.7204	1.58298
$265$	−42.6090	−2.61745
$266$	14.4592	0.886551
$267$	4.69978	0.287622
$268$	−7.12104	−0.434986
$269$	−11.7942	−0.719104	−0.359552	−	0.933125i	$-0.617070\pi$
$269$	−11.7942	−0.719104	−0.359552	+	0.933125i	$0.617070\pi$
$270$	−41.0686	−2.49936
$271$	32.1286	1.95167	0.975837	−	0.218499i	$-0.0701160\pi$
$271$	32.1286	1.95167	0.975837	+	0.218499i	$0.0701160\pi$
$272$	32.8792	1.99360
$273$	8.48135	0.513315
$274$	0.456485	0.0275773
$275$	−54.0855	−3.26148
$276$	27.0521	1.62835
$277$	13.5855	0.816275	0.408138	−	0.912920i	$-0.366178\pi$
$277$	13.5855	0.816275	0.408138	+	0.912920i	$0.366178\pi$
$278$	6.55697	0.393261
$279$	12.0328	0.720383
$280$	−60.2861	−3.60278
$281$	5.27350	0.314590	0.157295	−	0.987552i	$-0.449723\pi$
$281$	5.27350	0.314590	0.157295	+	0.987552i	$0.449723\pi$
$282$	−9.32864	−0.555512
$283$	−23.4347	−1.39305	−0.696525	−	0.717532i	$-0.745272\pi$
$283$	−23.4347	−1.39305	−0.696525	+	0.717532i	$0.745272\pi$
$284$	2.16276	0.128336
$285$	−6.42160	−0.380383
$286$	−54.5928	−3.22814
$287$	11.9209	0.703666
$288$	7.43536	0.438133
$289$	14.7152	0.865598
$290$	6.25545	0.367333
$291$	5.24178	0.307278
$292$	−42.2674	−2.47351
$293$	−29.9421	−1.74924	−0.874618	−	0.484812i	$-0.838888\pi$
$293$	−29.9421	−1.74924	−0.874618	+	0.484812i	$0.838888\pi$
$294$	−1.01503	−0.0591980
$295$	−36.2682	−2.11161
$296$	38.6213	2.24482
$297$	23.9940	1.39227
$298$	−15.2032	−0.880698
$299$	−30.6639	−1.77334
$300$	33.0175	1.90627
$301$	4.66930	0.269134
$302$	18.1660	1.04534
$303$	6.26243	0.359767
$304$	12.2826	0.704457
$305$	−11.1383	−0.637778
$306$	33.3916	1.90887
$307$	20.4527	1.16730	0.583648	−	0.812007i	$-0.301625\pi$
$307$	20.4527	1.16730	0.583648	+	0.812007i	$0.301625\pi$
$308$	65.9539	3.75807
$309$	−7.55781	−0.429949
$310$	−48.8644	−2.77531
$311$	−4.10842	−0.232967	−0.116484	−	0.993193i	$-0.537162\pi$
$311$	−4.10842	−0.232967	−0.116484	+	0.993193i	$0.537162\pi$
$312$	17.7979	1.00761
$313$	8.95959	0.506426	0.253213	−	0.967411i	$-0.418513\pi$
$313$	8.95959	0.506426	0.253213	+	0.967411i	$0.418513\pi$
$314$	−17.0568	−0.962571
$315$	−24.7842	−1.39643
$316$	−14.2832	−0.803495
$317$	19.4562	1.09277	0.546384	−	0.837535i	$-0.316004\pi$
$317$	19.4562	1.09277	0.546384	+	0.837535i	$0.316004\pi$
$318$	−22.2783	−1.24930
$319$	−3.65470	−0.204624
$320$	14.4891	0.809964
$321$	6.36060	0.355014
$322$	54.3071	3.02642
$323$	11.8478	0.659227
$324$	15.7893	0.877184
$325$	−37.4257	−2.07601
$326$	−20.2444	−1.12123
$327$	11.8336	0.654402
$328$	25.0156	1.38125
$329$	−12.7747	−0.704290
$330$	−42.9401	−2.36378
$331$	−29.6941	−1.63214	−0.816069	−	0.577955i	$-0.803851\pi$
$331$	−29.6941	−1.63214	−0.816069	+	0.577955i	$0.803851\pi$
$332$	5.50227	0.301976
$333$	15.8776	0.870087
$334$	44.6303	2.44206
$335$	6.34888	0.346876
$336$	−12.7597	−0.696099
$337$	−30.8021	−1.67789	−0.838947	−	0.544213i	$-0.816829\pi$
$337$	−30.8021	−1.67789	−0.838947	+	0.544213i	$0.816829\pi$
$338$	−5.16736	−0.281067
$339$	−2.06985	−0.112419
$340$	−92.4995	−5.01649
$341$	28.5486	1.54599
$342$	12.4740	0.674517
$343$	17.7896	0.960550
$344$	9.79839	0.528294
$345$	−24.1188	−1.29851
$346$	−47.4186	−2.54924
$347$	23.9740	1.28699	0.643496	−	0.765450i	$-0.277483\pi$
$347$	23.9740	1.28699	0.643496	+	0.765450i	$0.277483\pi$
$348$	2.23108	0.119598
$349$	21.1679	1.13309	0.566546	−	0.824030i	$-0.308279\pi$
$349$	21.1679	1.13309	0.566546	+	0.824030i	$0.308279\pi$
$350$	66.2826	3.54296
$351$	16.6032	0.886215
$352$	17.6409	0.940264
$353$	−37.4900	−1.99539	−0.997695	−	0.0678605i	$-0.978383\pi$
$353$	−37.4900	−1.99539	−0.997695	+	0.0678605i	$0.978383\pi$
$354$	−18.9630	−1.00787
$355$	−1.92825	−0.102341
$356$	25.2897	1.34035
$357$	−12.3080	−0.651406
$358$	4.81805	0.254642
$359$	1.48284	0.0782615	0.0391308	−	0.999234i	$-0.487541\pi$
$359$	1.48284	0.0782615	0.0391308	+	0.999234i	$0.487541\pi$
$360$	−52.0090	−2.74111
$361$	−14.5741	−0.767056
$362$	22.4849	1.18178
$363$	16.3133	0.856226
$364$	45.6384	2.39210
$365$	37.6842	1.97248
$366$	−5.82371	−0.304410
$367$	−8.13675	−0.424735	−0.212367	−	0.977190i	$-0.568117\pi$
$367$	−8.13675	−0.424735	−0.212367	+	0.977190i	$0.568117\pi$
$368$	46.1321	2.40480
$369$	10.2842	0.535372
$370$	−64.4780	−3.35205
$371$	−30.5079	−1.58389
$372$	−17.4281	−0.903603
$373$	14.2159	0.736071	0.368036	−	0.929812i	$-0.380030\pi$
$373$	14.2159	0.736071	0.368036	+	0.929812i	$0.380030\pi$
$374$	79.2239	4.09657
$375$	−14.1754	−0.732013
$376$	−26.8073	−1.38248
$377$	−2.52896	−0.130248
$378$	−29.4050	−1.51243
$379$	18.3273	0.941411	0.470706	−	0.882290i	$-0.343999\pi$
$379$	18.3273	0.941411	0.470706	+	0.882290i	$0.343999\pi$
$380$	−34.5548	−1.77263
$381$	16.1610	0.827956
$382$	35.3791	1.81015
$383$	6.48635	0.331437	0.165719	−	0.986173i	$-0.447006\pi$
$383$	6.48635	0.331437	0.165719	+	0.986173i	$0.447006\pi$
$384$	12.5938	0.642673
$385$	−58.8024	−2.99685
$386$	63.9719	3.25608
$387$	4.02822	0.204766
$388$	28.2062	1.43195
$389$	0.363153	0.0184126	0.00920630	−	0.999958i	$-0.497070\pi$
$389$	0.363153	0.0184126	0.00920630	+	0.999958i	$0.497070\pi$
$390$	−29.7135	−1.50460
$391$	44.4988	2.25040
$392$	−2.91686	−0.147324
$393$	2.26266	0.114136
$394$	40.1124	2.02084
$395$	12.7345	0.640741
$396$	56.8987	2.85927
$397$	−6.43917	−0.323173	−0.161586	−	0.986859i	$-0.551661\pi$
$397$	−6.43917	−0.323173	−0.161586	+	0.986859i	$0.551661\pi$
$398$	−46.0610	−2.30883
$399$	−4.59786	−0.230181
$400$	56.3049	2.81524
$401$	−12.7008	−0.634246	−0.317123	−	0.948384i	$-0.602717\pi$
$401$	−12.7008	−0.634246	−0.317123	+	0.948384i	$0.602717\pi$
$402$	3.31954	0.165563
$403$	19.7549	0.984062
$404$	33.6983	1.67655
$405$	−14.0772	−0.699503
$406$	4.47889	0.222284
$407$	37.6708	1.86727
$408$	−25.8279	−1.27867
$409$	−34.9491	−1.72812	−0.864062	−	0.503385i	$-0.832088\pi$
$409$	−34.9491	−1.72812	−0.864062	+	0.503385i	$0.832088\pi$
$410$	−41.7634	−2.06255
$411$	−0.145157	−0.00716006
$412$	−40.6688	−2.00361
$413$	−25.9680	−1.27780
$414$	46.8509	2.30260
$415$	−4.90564	−0.240808
$416$	12.2071	0.598501
$417$	−2.08504	−0.102105
$418$	29.5955	1.44756
$419$	−13.0082	−0.635495	−0.317747	−	0.948175i	$-0.602926\pi$
$419$	−13.0082	−0.635495	−0.317747	+	0.948175i	$0.602926\pi$
$420$	35.8970	1.75160
$421$	27.2192	1.32658	0.663290	−	0.748362i	$-0.269159\pi$
$421$	27.2192	1.32658	0.663290	+	0.748362i	$0.269159\pi$
$422$	38.4576	1.87209
$423$	−11.0207	−0.535847
$424$	−64.0201	−3.10909
$425$	54.3114	2.63449
$426$	−1.00819	−0.0488470
$427$	−7.97502	−0.385938
$428$	34.2266	1.65440
$429$	17.3598	0.838141
$430$	−16.3584	−0.788870
$431$	−15.6792	−0.755240	−0.377620	−	0.925961i	$-0.623258\pi$
$431$	−15.6792	−0.755240	−0.377620	+	0.925961i	$0.623258\pi$
$432$	−24.9786	−1.20178
$433$	−1.19642	−0.0574962	−0.0287481	−	0.999587i	$-0.509152\pi$
$433$	−1.19642	−0.0574962	−0.0287481	+	0.999587i	$0.509152\pi$
$434$	−34.9868	−1.67942
$435$	−1.98916	−0.0953728
$436$	63.6772	3.04959
$437$	16.6233	0.795201
$438$	19.7033	0.941461
$439$	12.3969	0.591670	0.295835	−	0.955239i	$-0.404402\pi$
$439$	12.3969	0.591670	0.295835	+	0.955239i	$0.404402\pi$
$440$	−123.395	−5.88263
$441$	−1.19915	−0.0571024
$442$	54.8209	2.60756
$443$	−9.10072	−0.432388	−0.216194	−	0.976350i	$-0.569364\pi$
$443$	−9.10072	−0.432388	−0.216194	+	0.976350i	$0.569364\pi$
$444$	−22.9968	−1.09138
$445$	−22.5474	−1.06885
$446$	−0.518276	−0.0245411
$447$	4.83443	0.228661
$448$	10.3742	0.490133
$449$	28.0838	1.32535	0.662677	−	0.748905i	$-0.269420\pi$
$449$	28.0838	1.32535	0.662677	+	0.748905i	$0.269420\pi$
$450$	57.1822	2.69560
$451$	24.3999	1.14895
$452$	−11.1379	−0.523885
$453$	−5.77658	−0.271407
$454$	−61.6101	−2.89150
$455$	−40.6897	−1.90756
$456$	−9.64847	−0.451831
$457$	−22.9255	−1.07241	−0.536205	−	0.844088i	$-0.680143\pi$
$457$	−22.9255	−1.07241	−0.536205	+	0.844088i	$0.680143\pi$
$458$	−8.68225	−0.405695
$459$	−24.0942	−1.12462
$460$	−129.784	−6.05121
$461$	29.7326	1.38478	0.692392	−	0.721522i	$-0.256557\pi$
$461$	29.7326	1.38478	0.692392	+	0.721522i	$0.256557\pi$
$462$	−30.7451	−1.43039
$463$	22.2063	1.03201	0.516006	−	0.856585i	$-0.327418\pi$
$463$	22.2063	1.03201	0.516006	+	0.856585i	$0.327418\pi$
$464$	3.80467	0.176627
$465$	15.5383	0.720571
$466$	29.3173	1.35810
$467$	−15.3562	−0.710601	−0.355301	−	0.934752i	$-0.615622\pi$
$467$	−15.3562	−0.710601	−0.355301	+	0.934752i	$0.615622\pi$
$468$	39.3724	1.81999
$469$	4.54579	0.209905
$470$	44.7546	2.06438
$471$	5.42385	0.249918
$472$	−54.4930	−2.50824
$473$	9.55724	0.439442
$474$	6.65827	0.305824
$475$	20.2890	0.930923
$476$	−66.2295	−3.03563
$477$	−26.3193	−1.20508
$478$	−1.11725	−0.0511016
$479$	−11.9476	−0.545902	−0.272951	−	0.962028i	$-0.588000\pi$
$479$	−11.9476	−0.545902	−0.272951	+	0.962028i	$0.588000\pi$
$480$	9.60150	0.438247
$481$	26.0672	1.18856
$482$	−44.6530	−2.03389
$483$	−17.2690	−0.785767
$484$	87.7824	3.99011
$485$	−25.1477	−1.14190
$486$	−39.5563	−1.79431
$487$	−27.2350	−1.23414	−0.617068	−	0.786910i	$-0.711680\pi$
$487$	−27.2350	−1.23414	−0.617068	+	0.786910i	$0.711680\pi$
$488$	−16.7353	−0.757574
$489$	6.43746	0.291112
$490$	4.86968	0.219990
$491$	10.5833	0.477620	0.238810	−	0.971066i	$-0.423243\pi$
$491$	10.5833	0.477620	0.238810	+	0.971066i	$0.423243\pi$
$492$	−14.8954	−0.671537
$493$	3.66997	0.165287
$494$	20.4793	0.921407
$495$	−50.7290	−2.28010
$496$	−29.7201	−1.33447
$497$	−1.38062	−0.0619293
$498$	−2.56493	−0.114937
$499$	16.8036	0.752233	0.376117	−	0.926572i	$-0.377259\pi$
$499$	16.8036	0.752233	0.376117	+	0.926572i	$0.377259\pi$
$500$	−76.2781	−3.41126
$501$	−14.1919	−0.634047
$502$	51.8570	2.31449
$503$	−6.51389	−0.290440	−0.145220	−	0.989399i	$-0.546389\pi$
$503$	−6.51389	−0.290440	−0.145220	+	0.989399i	$0.546389\pi$
$504$	−37.2384	−1.65873
$505$	−30.0443	−1.33695
$506$	111.157	4.94154
$507$	1.64316	0.0729752
$508$	86.9631	3.85836
$509$	26.7959	1.18771	0.593854	−	0.804573i	$-0.297606\pi$
$509$	26.7959	1.18771	0.593854	+	0.804573i	$0.297606\pi$
$510$	43.1195	1.90937
$511$	26.9818	1.19361
$512$	48.7724	2.15546
$513$	−9.00083	−0.397396
$514$	68.7052	3.03046
$515$	36.2590	1.59776
$516$	−5.83440	−0.256845
$517$	−26.1475	−1.14997
$518$	−46.1662	−2.02842
$519$	15.0785	0.661874
$520$	−85.3862	−3.74443
$521$	15.0458	0.659169	0.329584	−	0.944126i	$-0.393091\pi$
$521$	15.0458	0.659169	0.329584	+	0.944126i	$0.393091\pi$
$522$	3.86395	0.169121
$523$	−25.8335	−1.12962	−0.564809	−	0.825221i	$-0.691050\pi$
$523$	−25.8335	−1.12962	−0.564809	+	0.825221i	$0.691050\pi$
$524$	12.1754	0.531887
$525$	−21.0771	−0.919879
$526$	18.3922	0.801938
$527$	−28.6679	−1.24879
$528$	−26.1169	−1.13659
$529$	39.4352	1.71458
$530$	106.881	4.64262
$531$	−22.4026	−0.972191
$532$	−24.7412	−1.07267
$533$	16.8841	0.731332
$534$	−11.7890	−0.510161
$535$	−30.5153	−1.31929
$536$	9.53921	0.412031
$537$	−1.53208	−0.0661142
$538$	29.5847	1.27549
$539$	−2.84507	−0.122546
$540$	70.2726	3.02405
$541$	35.1762	1.51234	0.756171	−	0.654375i	$-0.227068\pi$
$541$	35.1762	1.51234	0.756171	+	0.654375i	$0.227068\pi$
$542$	−80.5920	−3.46172
$543$	−7.14992	−0.306833
$544$	−17.7146	−0.759509
$545$	−56.7725	−2.43187
$546$	−21.2748	−0.910477
$547$	28.7830	1.23067	0.615335	−	0.788266i	$-0.289021\pi$
$547$	28.7830	1.23067	0.615335	+	0.788266i	$0.289021\pi$
$548$	−0.781093	−0.0333667
$549$	−6.88007	−0.293634
$550$	135.669	5.78494
$551$	1.37098	0.0584057
$552$	−36.2385	−1.54241
$553$	9.11786	0.387731
$554$	−34.0782	−1.44784
$555$	20.5032	0.870314
$556$	−11.2197	−0.475819
$557$	0.761025	0.0322456	0.0161228	−	0.999870i	$-0.494868\pi$
$557$	0.761025	0.0322456	0.0161228	+	0.999870i	$0.494868\pi$
$558$	−30.1832	−1.27776
$559$	6.61336	0.279715
$560$	61.2154	2.58682
$561$	−25.1922	−1.06362
$562$	−13.2281	−0.557995
$563$	−15.7133	−0.662237	−0.331119	−	0.943589i	$-0.607426\pi$
$563$	−15.7133	−0.662237	−0.331119	+	0.943589i	$0.607426\pi$
$564$	15.9623	0.672132
$565$	9.93022	0.417768
$566$	58.7841	2.47088
$567$	−10.0793	−0.423290
$568$	−2.89720	−0.121564
$569$	−42.9261	−1.79956	−0.899778	−	0.436348i	$-0.856272\pi$
$569$	−42.9261	−1.79956	−0.899778	+	0.436348i	$0.856272\pi$
$570$	16.1081	0.674692
$571$	−2.59736	−0.108696	−0.0543480	−	0.998522i	$-0.517308\pi$
$571$	−2.59736	−0.108696	−0.0543480	+	0.998522i	$0.517308\pi$
$572$	93.4139	3.90583
$573$	−11.2501	−0.469981
$574$	−29.9025	−1.24811
$575$	76.2031	3.17789
$576$	8.94981	0.372909
$577$	28.5632	1.18910	0.594550	−	0.804059i	$-0.297330\pi$
$577$	28.5632	1.18910	0.594550	+	0.804059i	$0.297330\pi$
$578$	−36.9118	−1.53533
$579$	−20.3423	−0.845396
$580$	−10.7037	−0.444448
$581$	−3.51243	−0.145720
$582$	−13.1486	−0.545026
$583$	−62.4444	−2.58618
$584$	56.6206	2.34298
$585$	−35.1031	−1.45134
$586$	75.1073	3.10265
$587$	23.9417	0.988178	0.494089	−	0.869411i	$-0.335502\pi$
$587$	23.9417	0.988178	0.494089	+	0.869411i	$0.335502\pi$
$588$	1.73683	0.0716255
$589$	−10.7094	−0.441273
$590$	90.9757	3.74541
$591$	−12.7553	−0.524682
$592$	−39.2166	−1.61179
$593$	17.1447	0.704048	0.352024	−	0.935991i	$-0.385494\pi$
$593$	17.1447	0.704048	0.352024	+	0.935991i	$0.385494\pi$
$594$	−60.1870	−2.46950
$595$	59.0481	2.42073
$596$	26.0142	1.06558
$597$	14.6468	0.599455
$598$	76.9179	3.14541
$599$	−34.0951	−1.39309	−0.696543	−	0.717515i	$-0.745280\pi$
$599$	−34.0951	−1.39309	−0.696543	+	0.717515i	$0.745280\pi$
$600$	−44.2296	−1.80567
$601$	−42.9126	−1.75044	−0.875221	−	0.483723i	$-0.839284\pi$
$601$	−42.9126	−1.75044	−0.875221	+	0.483723i	$0.839284\pi$
$602$	−11.7126	−0.477368
$603$	3.92166	0.159703
$604$	−31.0839	−1.26479
$605$	−78.2639	−3.18188
$606$	−15.7088	−0.638126
$607$	−38.2094	−1.55087	−0.775435	−	0.631427i	$-0.782469\pi$
$607$	−38.2094	−1.55087	−0.775435	+	0.631427i	$0.782469\pi$
$608$	−6.61761	−0.268380
$609$	−1.42423	−0.0577129
$610$	27.9396	1.13124
$611$	−18.0934	−0.731981
$612$	−57.1364	−2.30960
$613$	−32.0675	−1.29519	−0.647596	−	0.761984i	$-0.724226\pi$
$613$	−32.0675	−1.29519	−0.647596	+	0.761984i	$0.724226\pi$
$614$	−51.3038	−2.07045
$615$	13.2803	0.535511
$616$	−88.3507	−3.55975
$617$	−20.5144	−0.825878	−0.412939	−	0.910759i	$-0.635498\pi$
$617$	−20.5144	−0.825878	−0.412939	+	0.910759i	$0.635498\pi$
$618$	18.9582	0.762609
$619$	−1.64660	−0.0661826	−0.0330913	−	0.999452i	$-0.510535\pi$
$619$	−1.64660	−0.0661826	−0.0330913	+	0.999452i	$0.510535\pi$
$620$	83.6120	3.35794
$621$	−33.8061	−1.35659
$622$	10.3056	0.413218
$623$	−16.1439	−0.646793
$624$	−18.0722	−0.723468
$625$	19.7869	0.791477
$626$	−22.4744	−0.898257
$627$	−9.41100	−0.375839
$628$	29.1859	1.16465
$629$	−37.8282	−1.50831
$630$	62.1692	2.47688
$631$	7.19763	0.286533	0.143267	−	0.989684i	$-0.454239\pi$
$631$	7.19763	0.286533	0.143267	+	0.989684i	$0.454239\pi$
$632$	19.1336	0.761092
$633$	−12.2290	−0.486061
$634$	−48.8042	−1.93826
$635$	−77.5334	−3.07682
$636$	38.1204	1.51157
$637$	−1.96871	−0.0780033
$638$	9.16751	0.362945
$639$	−1.19107	−0.0471179
$640$	−60.4192	−2.38828
$641$	32.4144	1.28029	0.640146	−	0.768253i	$-0.278874\pi$
$641$	32.4144	1.28029	0.640146	+	0.768253i	$0.278874\pi$
$642$	−15.9550	−0.629695
$643$	−0.706102	−0.0278460	−0.0139230	−	0.999903i	$-0.504432\pi$
$643$	−0.706102	−0.0278460	−0.0139230	+	0.999903i	$0.504432\pi$
$644$	−92.9251	−3.66176
$645$	5.20176	0.204819
$646$	−29.7191	−1.16928
$647$	−2.10828	−0.0828852	−0.0414426	−	0.999141i	$-0.513195\pi$
$647$	−2.10828	−0.0828852	−0.0414426	+	0.999141i	$0.513195\pi$
$648$	−21.1511	−0.830893
$649$	−53.1518	−2.08639
$650$	93.8794	3.68225
$651$	11.1254	0.436038
$652$	34.6402	1.35661
$653$	−21.0453	−0.823564	−0.411782	−	0.911282i	$-0.635094\pi$
$653$	−21.0453	−0.823564	−0.411782	+	0.911282i	$0.635094\pi$
$654$	−29.6837	−1.16073
$655$	−10.8552	−0.424149
$656$	−25.4012	−0.991750
$657$	23.2773	0.908134
$658$	32.0442	1.24921
$659$	2.44396	0.0952031	0.0476015	−	0.998866i	$-0.484842\pi$
$659$	2.44396	0.0952031	0.0476015	+	0.998866i	$0.484842\pi$
$660$	73.4750	2.86001
$661$	33.5690	1.30568	0.652841	−	0.757495i	$-0.273577\pi$
$661$	33.5690	1.30568	0.652841	+	0.757495i	$0.273577\pi$
$662$	74.4853	2.89495
$663$	−17.4324	−0.677017
$664$	−7.37073	−0.286040
$665$	22.0584	0.855390
$666$	−39.8277	−1.54329
$667$	5.14925	0.199380
$668$	−76.3670	−2.95473
$669$	0.164805	0.00637175
$670$	−15.9256	−0.615261
$671$	−16.3235	−0.630160
$672$	6.87466	0.265196
$673$	−15.8190	−0.609777	−0.304888	−	0.952388i	$-0.598619\pi$
$673$	−15.8190	−0.609777	−0.304888	+	0.952388i	$0.598619\pi$
$674$	77.2644	2.97611
$675$	−41.2608	−1.58813
$676$	8.84188	0.340072
$677$	−26.5728	−1.02128	−0.510638	−	0.859796i	$-0.670591\pi$
$677$	−26.5728	−1.02128	−0.510638	+	0.859796i	$0.670591\pi$
$678$	5.19206	0.199400
$679$	−18.0057	−0.690996
$680$	123.911	4.75176
$681$	19.5913	0.750739
$682$	−71.6119	−2.74216
$683$	22.9405	0.877792	0.438896	−	0.898538i	$-0.355370\pi$
$683$	22.9405	0.877792	0.438896	+	0.898538i	$0.355370\pi$
$684$	−21.3443	−0.816120
$685$	0.696397	0.0266080
$686$	−44.6238	−1.70375
$687$	2.76085	0.105333
$688$	−9.94943	−0.379318
$689$	−43.2099	−1.64617
$690$	60.5000	2.30320
$691$	27.9413	1.06294	0.531468	−	0.847078i	$-0.321641\pi$
$691$	27.9413	1.06294	0.531468	+	0.847078i	$0.321641\pi$
$692$	81.1380	3.08441
$693$	−36.3219	−1.37975
$694$	−60.1368	−2.28276
$695$	10.0031	0.379438
$696$	−2.98871	−0.113287
$697$	−24.5019	−0.928074
$698$	−53.0979	−2.00979
$699$	−9.32254	−0.352611
$700$	−113.416	−4.28674
$701$	29.5810	1.11726	0.558629	−	0.829417i	$-0.311327\pi$
$701$	29.5810	1.11726	0.558629	+	0.829417i	$0.311327\pi$
$702$	−41.6478	−1.57190
$703$	−14.1314	−0.532975
$704$	21.2341	0.800289
$705$	−14.2314	−0.535986
$706$	94.0405	3.53926
$707$	−21.5117	−0.809030
$708$	32.4476	1.21945
$709$	−2.12544	−0.0798226	−0.0399113	−	0.999203i	$-0.512708\pi$
$709$	−2.12544	−0.0798226	−0.0399113	+	0.999203i	$0.512708\pi$
$710$	4.83685	0.181524
$711$	7.86600	0.294998
$712$	−33.8776	−1.26962
$713$	−40.2233	−1.50637
$714$	30.8735	1.15541
$715$	−83.2847	−3.11467
$716$	−8.24417	−0.308099
$717$	0.355271	0.0132678
$718$	−3.71959	−0.138814
$719$	−21.0245	−0.784082	−0.392041	−	0.919948i	$-0.628231\pi$
$719$	−21.0245	−0.784082	−0.392041	+	0.919948i	$0.628231\pi$
$720$	52.8107	1.96814
$721$	25.9614	0.966852
$722$	36.5578	1.36054
$723$	14.1991	0.528070
$724$	−38.4740	−1.42987
$725$	6.28473	0.233409
$726$	−40.9206	−1.51871
$727$	−13.9034	−0.515647	−0.257823	−	0.966192i	$-0.583005\pi$
$727$	−13.9034	−0.515647	−0.257823	+	0.966192i	$0.583005\pi$
$728$	−61.1364	−2.26587
$729$	1.54250	0.0571296
$730$	−94.5277	−3.49863
$731$	−9.59717	−0.354964
$732$	9.96497	0.368316
$733$	−2.53149	−0.0935029	−0.0467514	−	0.998907i	$-0.514887\pi$
$733$	−2.53149	−0.0935029	−0.0467514	+	0.998907i	$0.514887\pi$
$734$	20.4104	0.753361
$735$	−1.54850	−0.0571172
$736$	−24.8550	−0.916167
$737$	9.30443	0.342733
$738$	−25.7970	−0.949600
$739$	25.3154	0.931243	0.465622	−	0.884984i	$-0.345831\pi$
$739$	25.3154	0.931243	0.465622	+	0.884984i	$0.345831\pi$
$740$	110.329	4.05576
$741$	−6.51217	−0.239231
$742$	76.5267	2.80938
$743$	18.2816	0.670685	0.335343	−	0.942096i	$-0.391148\pi$
$743$	18.2816	0.670685	0.335343	+	0.942096i	$0.391148\pi$
$744$	23.3463	0.855917
$745$	−23.1934	−0.849742
$746$	−35.6594	−1.30558
$747$	−3.03018	−0.110869
$748$	−135.560	−4.95657
$749$	−21.8489	−0.798341
$750$	35.5577	1.29838
$751$	−40.0447	−1.46125	−0.730626	−	0.682778i	$-0.760772\pi$
$751$	−40.0447	−1.46125	−0.730626	+	0.682778i	$0.760772\pi$
$752$	27.2205	0.992629
$753$	−16.4899	−0.600925
$754$	6.34368	0.231023
$755$	27.7134	1.00859
$756$	50.3151	1.82994
$757$	−12.8028	−0.465325	−0.232663	−	0.972557i	$-0.574744\pi$
$757$	−12.8028	−0.465325	−0.232663	+	0.972557i	$0.574744\pi$
$758$	−45.9726	−1.66980
$759$	−35.3466	−1.28300
$760$	46.2890	1.67908
$761$	50.1377	1.81749	0.908745	−	0.417353i	$-0.137042\pi$
$761$	50.1377	1.81749	0.908745	+	0.417353i	$0.137042\pi$
$762$	−40.5387	−1.46856
$763$	−40.6490	−1.47159
$764$	−60.5373	−2.19016
$765$	50.9409	1.84177
$766$	−16.2705	−0.587876
$767$	−36.7797	−1.32804
$768$	−25.5502	−0.921965
$769$	31.0656	1.12025	0.560127	−	0.828406i	$-0.310752\pi$
$769$	31.0656	1.12025	0.560127	+	0.828406i	$0.310752\pi$
$770$	147.501	5.31556
$771$	−21.8474	−0.786816
$772$	−109.462	−3.93964
$773$	−18.7560	−0.674605	−0.337303	−	0.941396i	$-0.609515\pi$
$773$	−18.7560	−0.674605	−0.337303	+	0.941396i	$0.609515\pi$
$774$	−10.1045	−0.363197
$775$	−49.0931	−1.76348
$776$	−37.7845	−1.35638
$777$	14.6803	0.526652
$778$	−0.910940	−0.0326588
$779$	−9.15310	−0.327944
$780$	50.8428	1.82046
$781$	−2.82589	−0.101118
$782$	−111.622	−3.99158
$783$	−2.78810	−0.0996386
$784$	2.96182	0.105779
$785$	−26.0212	−0.928737
$786$	−5.67570	−0.202445
$787$	−42.8730	−1.52826	−0.764129	−	0.645064i	$-0.776831\pi$
$787$	−42.8730	−1.52826	−0.764129	+	0.645064i	$0.776831\pi$
$788$	−68.6365	−2.44507
$789$	−5.84850	−0.208212
$790$	−31.9434	−1.13649
$791$	7.11002	0.252803
$792$	−76.2204	−2.70837
$793$	−11.2954	−0.401112
$794$	16.1521	0.573217
$795$	−33.9869	−1.20539
$796$	78.8150	2.79352
$797$	51.5677	1.82662	0.913311	−	0.407263i	$-0.133517\pi$
$797$	51.5677	1.82662	0.913311	+	0.407263i	$0.133517\pi$
$798$	11.5333	0.408276
$799$	26.2568	0.928897
$800$	−30.3359	−1.07253
$801$	−13.9274	−0.492101
$802$	31.8588	1.12497
$803$	55.2270	1.94892
$804$	−5.68007	−0.200321
$805$	82.8490	2.92004
$806$	−49.5536	−1.74545
$807$	−9.40759	−0.331163
$808$	−45.1416	−1.58808
$809$	−42.5983	−1.49768	−0.748838	−	0.662753i	$-0.769388\pi$
$809$	−42.5983	−1.49768	−0.748838	+	0.662753i	$0.769388\pi$
$810$	35.3116	1.24072
$811$	5.71588	0.200712	0.100356	−	0.994952i	$-0.468002\pi$
$811$	5.71588	0.200712	0.100356	+	0.994952i	$0.468002\pi$
$812$	−7.66385	−0.268948
$813$	25.6273	0.898788
$814$	−94.4940	−3.31201
$815$	−30.8840	−1.08182
$816$	26.2260	0.918094
$817$	−3.58519	−0.125430
$818$	87.6671	3.06521
$819$	−25.1338	−0.878246
$820$	71.4614	2.49554
$821$	−8.05202	−0.281017	−0.140509	−	0.990079i	$-0.544874\pi$
$821$	−8.05202	−0.281017	−0.140509	+	0.990079i	$0.544874\pi$
$822$	0.364114	0.0126999
$823$	4.53633	0.158126	0.0790632	−	0.996870i	$-0.474807\pi$
$823$	4.53633	0.158126	0.0790632	+	0.996870i	$0.474807\pi$
$824$	54.4792	1.89787
$825$	−43.1411	−1.50198
$826$	65.1385	2.26646
$827$	−16.9814	−0.590501	−0.295250	−	0.955420i	$-0.595403\pi$
$827$	−16.9814	−0.590501	−0.295250	+	0.955420i	$0.595403\pi$
$828$	−80.1668	−2.78599
$829$	49.4435	1.71724	0.858622	−	0.512609i	$-0.171321\pi$
$829$	49.4435	1.71724	0.858622	+	0.512609i	$0.171321\pi$
$830$	12.3054	0.427127
$831$	10.8365	0.375912
$832$	14.6934	0.509403
$833$	2.85696	0.0989877
$834$	5.23015	0.181105
$835$	68.0863	2.35622
$836$	−50.6409	−1.75145
$837$	21.7792	0.752800
$838$	32.6301	1.12719
$839$	17.1288	0.591353	0.295677	−	0.955288i	$-0.404455\pi$
$839$	17.1288	0.591353	0.295677	+	0.955288i	$0.404455\pi$
$840$	−48.0870	−1.65916
$841$	−28.5753	−0.985356
$842$	−68.2770	−2.35298
$843$	4.20639	0.144876
$844$	−65.8049	−2.26510
$845$	−7.88313	−0.271188
$846$	27.6446	0.950442
$847$	−56.0368	−1.92545
$848$	65.0069	2.23235
$849$	−18.6926	−0.641530
$850$	−136.236	−4.67285
$851$	−53.0758	−1.81942
$852$	1.72512	0.0591016
$853$	−24.0109	−0.822117	−0.411059	−	0.911609i	$-0.634841\pi$
$853$	−24.0109	−0.822117	−0.411059	+	0.911609i	$0.634841\pi$
$854$	20.0047	0.684546
$855$	19.0299	0.650808
$856$	−45.8493	−1.56710
$857$	57.4068	1.96098	0.980489	−	0.196573i	$-0.0629811\pi$
$857$	57.4068	1.96098	0.980489	+	0.196573i	$0.0629811\pi$
$858$	−43.5457	−1.48663
$859$	17.6436	0.601992	0.300996	−	0.953625i	$-0.402681\pi$
$859$	17.6436	0.601992	0.300996	+	0.953625i	$0.402681\pi$
$860$	27.9908	0.954479
$861$	9.50864	0.324053
$862$	39.3300	1.33958
$863$	36.3579	1.23764	0.618819	−	0.785534i	$-0.287612\pi$
$863$	36.3579	1.23764	0.618819	+	0.785534i	$0.287612\pi$
$864$	13.4579	0.457848
$865$	−72.3400	−2.45963
$866$	3.00112	0.101982
$867$	11.7375	0.398627
$868$	59.8660	2.03199
$869$	18.6627	0.633087
$870$	4.98964	0.169165
$871$	6.43843	0.218158
$872$	−85.3008	−2.88865
$873$	−15.5336	−0.525732
$874$	−41.6982	−1.41046
$875$	48.6929	1.64612
$876$	−33.7144	−1.13910
$877$	9.19392	0.310456	0.155228	−	0.987879i	$-0.450389\pi$
$877$	9.19392	0.310456	0.155228	+	0.987879i	$0.450389\pi$
$878$	−31.0965	−1.04946
$879$	−23.8832	−0.805561
$880$	125.297	4.22377
$881$	27.3249	0.920600	0.460300	−	0.887763i	$-0.347742\pi$
$881$	27.3249	0.920600	0.460300	+	0.887763i	$0.347742\pi$
$882$	3.00797	0.101284
$883$	34.0764	1.14676	0.573380	−	0.819289i	$-0.305632\pi$
$883$	34.0764	1.14676	0.573380	+	0.819289i	$0.305632\pi$
$884$	−93.8042	−3.15498
$885$	−28.9292	−0.972444
$886$	22.8284	0.766936
$887$	−6.80463	−0.228477	−0.114239	−	0.993453i	$-0.536443\pi$
$887$	−6.80463	−0.228477	−0.114239	+	0.993453i	$0.536443\pi$
$888$	30.8061	1.03379
$889$	−55.5138	−1.86187
$890$	56.5584	1.89584
$891$	−20.6305	−0.691148
$892$	0.886823	0.0296930
$893$	9.80867	0.328235
$894$	−12.1268	−0.405580
$895$	7.35023	0.245691
$896$	−43.2601	−1.44522
$897$	−24.4590	−0.816661
$898$	−70.4458	−2.35081
$899$	−3.31735	−0.110640
$900$	−97.8447	−3.26149
$901$	62.7053	2.08902
$902$	−61.2052	−2.03791
$903$	3.72445	0.123942
$904$	14.9202	0.496238
$905$	34.3021	1.14024
$906$	14.4901	0.481400
$907$	−45.5504	−1.51248	−0.756238	−	0.654297i	$-0.772965\pi$
$907$	−45.5504	−1.51248	−0.756238	+	0.654297i	$0.772965\pi$
$908$	105.421	3.49852
$909$	−18.5582	−0.615536
$910$	102.067	3.38348
$911$	35.2174	1.16681	0.583403	−	0.812183i	$-0.301721\pi$
$911$	35.2174	1.16681	0.583403	+	0.812183i	$0.301721\pi$
$912$	9.79719	0.324417
$913$	−7.18933	−0.237932
$914$	57.5067	1.90215
$915$	−8.88444	−0.293711
$916$	14.8562	0.490863
$917$	−7.77232	−0.256665
$918$	60.4384	1.99477
$919$	−56.1119	−1.85096	−0.925481	−	0.378794i	$-0.876339\pi$
$919$	−56.1119	−1.85096	−0.925481	+	0.378794i	$0.876339\pi$
$920$	173.856	5.73187
$921$	16.3140	0.537565
$922$	−74.5817	−2.45622
$923$	−1.95544	−0.0643642
$924$	52.6079	1.73067
$925$	−64.7798	−2.12995
$926$	−55.7026	−1.83050
$927$	22.3970	0.735613
$928$	−2.04987	−0.0672904
$929$	−1.26998	−0.0416667	−0.0208334	−	0.999783i	$-0.506632\pi$
$929$	−1.26998	−0.0416667	−0.0208334	+	0.999783i	$0.506632\pi$
$930$	−38.9765	−1.27809
$931$	1.06727	0.0349782
$932$	−50.1649	−1.64321
$933$	−3.27707	−0.107286
$934$	38.5198	1.26041
$935$	120.861	3.95258
$936$	−52.7425	−1.72394
$937$	26.7226	0.872988	0.436494	−	0.899707i	$-0.356220\pi$
$937$	26.7226	0.872988	0.436494	+	0.899707i	$0.356220\pi$
$938$	−11.4027	−0.372313
$939$	7.14658	0.233220
$940$	−76.5797	−2.49775
$941$	28.1404	0.917351	0.458675	−	0.888604i	$-0.348324\pi$
$941$	28.1404	0.917351	0.458675	+	0.888604i	$0.348324\pi$
$942$	−13.6053	−0.443284
$943$	−34.3780	−1.11950
$944$	55.3330	1.80093
$945$	−44.8592	−1.45927
$946$	−23.9735	−0.779447
$947$	16.9564	0.551008	0.275504	−	0.961300i	$-0.411155\pi$
$947$	16.9564	0.551008	0.275504	+	0.961300i	$0.411155\pi$
$948$	−11.3930	−0.370027
$949$	38.2157	1.24053
$950$	−50.8933	−1.65120
$951$	15.5192	0.503243
$952$	88.7198	2.87543
$953$	52.9495	1.71520	0.857601	−	0.514316i	$-0.171954\pi$
$953$	52.9495	1.71520	0.857601	+	0.514316i	$0.171954\pi$
$954$	66.0198	2.13747
$955$	53.9730	1.74653
$956$	1.91172	0.0618295
$957$	−2.91516	−0.0942336
$958$	29.9697	0.968276
$959$	0.498619	0.0161013
$960$	11.5572	0.373006
$961$	−5.08657	−0.164083
$962$	−65.3874	−2.10818
$963$	−18.8491	−0.607404
$964$	76.4058	2.46087
$965$	97.5931	3.14163
$966$	43.3179	1.39373
$967$	−24.0207	−0.772453	−0.386226	−	0.922404i	$-0.626222\pi$
$967$	−24.0207	−0.772453	−0.386226	+	0.922404i	$0.626222\pi$
$968$	−117.592	−3.77954
$969$	9.45032	0.303588
$970$	63.0809	2.02541
$971$	52.9204	1.69830	0.849148	−	0.528154i	$-0.177116\pi$
$971$	52.9204	1.69830	0.849148	+	0.528154i	$0.177116\pi$
$972$	67.6849	2.17099
$973$	7.16218	0.229609
$974$	68.3168	2.18901
$975$	−29.8525	−0.956046
$976$	16.9933	0.543943
$977$	6.71563	0.214852	0.107426	−	0.994213i	$-0.465739\pi$
$977$	6.71563	0.214852	0.107426	+	0.994213i	$0.465739\pi$
$978$	−16.1478	−0.516351
$979$	−33.0438	−1.05608
$980$	−8.33252	−0.266172
$981$	−35.0680	−1.11964
$982$	−26.5475	−0.847163
$983$	−48.6912	−1.55301	−0.776503	−	0.630113i	$-0.783009\pi$
$983$	−48.6912	−1.55301	−0.776503	+	0.630113i	$0.783009\pi$
$984$	19.9536	0.636098
$985$	61.1940	1.94980
$986$	−9.20581	−0.293173
$987$	−10.1897	−0.324341
$988$	−35.0422	−1.11484
$989$	−13.4656	−0.428180
$990$	127.249	4.04425
$991$	5.87714	0.186693	0.0933467	−	0.995634i	$-0.470244\pi$
$991$	5.87714	0.186693	0.0933467	+	0.995634i	$0.470244\pi$
$992$	16.0126	0.508400
$993$	−23.6854	−0.751634
$994$	3.46318	0.109845
$995$	−70.2689	−2.22767
$996$	4.38886	0.139067
$997$	5.41215	0.171404	0.0857022	−	0.996321i	$-0.472687\pi$
$997$	5.41215	0.171404	0.0857022	+	0.996321i	$0.472687\pi$
$998$	−42.1505	−1.33425
$999$	28.7383	0.909241

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.a.1.14	✓	217

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.a.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-2.50842 q^{2} +0.797647 q^{3} +4.29216 q^{4} -3.82675 q^{5} -2.00083 q^{6} -2.73995 q^{7} -5.74970 q^{8} -2.36376 q^{9} +O(q^{10})\)	\(q-2.50842 q^{2} +0.797647 q^{3} +4.29216 q^{4} -3.82675 q^{5} -2.00083 q^{6} -2.73995 q^{7} -5.74970 q^{8} -2.36376 q^{9} +9.59909 q^{10} -5.60819 q^{11} +3.42363 q^{12} -3.88072 q^{13} +6.87293 q^{14} -3.05239 q^{15} +5.83833 q^{16} +5.63162 q^{17} +5.92930 q^{18} +2.10379 q^{19} -16.4250 q^{20} -2.18551 q^{21} +14.0677 q^{22} +7.90160 q^{23} -4.58623 q^{24} +9.64401 q^{25} +9.73447 q^{26} -4.27839 q^{27} -11.7603 q^{28} +0.651671 q^{29} +7.65668 q^{30} -5.09052 q^{31} -3.14556 q^{32} -4.47335 q^{33} -14.1265 q^{34} +10.4851 q^{35} -10.1456 q^{36} -6.71710 q^{37} -5.27719 q^{38} -3.09545 q^{39} +22.0027 q^{40} -4.35077 q^{41} +5.48217 q^{42} -1.70416 q^{43} -24.0713 q^{44} +9.04552 q^{45} -19.8205 q^{46} +4.66238 q^{47} +4.65692 q^{48} +0.507306 q^{49} -24.1912 q^{50} +4.49204 q^{51} -16.6567 q^{52} +11.1345 q^{53} +10.7320 q^{54} +21.4611 q^{55} +15.7539 q^{56} +1.67808 q^{57} -1.63466 q^{58} +9.47754 q^{59} -13.1014 q^{60} +2.91065 q^{61} +12.7692 q^{62} +6.47658 q^{63} -3.78626 q^{64} +14.8506 q^{65} +11.2210 q^{66} -1.65908 q^{67} +24.1718 q^{68} +6.30268 q^{69} -26.3010 q^{70} +0.503886 q^{71} +13.5909 q^{72} -9.84757 q^{73} +16.8493 q^{74} +7.69252 q^{75} +9.02981 q^{76} +15.3661 q^{77} +7.76467 q^{78} -3.32775 q^{79} -22.3418 q^{80} +3.67864 q^{81} +10.9135 q^{82} +1.28193 q^{83} -9.38056 q^{84} -21.5508 q^{85} +4.27474 q^{86} +0.519804 q^{87} +32.2454 q^{88} +5.89206 q^{89} -22.6899 q^{90} +10.6330 q^{91} +33.9149 q^{92} -4.06044 q^{93} -11.6952 q^{94} -8.05068 q^{95} -2.50905 q^{96} +6.57155 q^{97} -1.27254 q^{98} +13.2564 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) \) 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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