LMFDB - Embedded newform 6047.2.a.a.1.19

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			1.19
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)

$f(q)$	$=$	$q-2.45739 q^{2} +0.0299595 q^{3} +4.03876 q^{4} -2.30057 q^{5} -0.0736221 q^{6} -3.67314 q^{7} -5.01004 q^{8} -2.99910 q^{9} +O(q^{10})$	\(q-2.45739 q^{2} +0.0299595 q^{3} +4.03876 q^{4} -2.30057 q^{5} -0.0736221 q^{6} -3.67314 q^{7} -5.01004 q^{8} -2.99910 q^{9} +5.65341 q^{10} +3.96870 q^{11} +0.120999 q^{12} -4.41626 q^{13} +9.02634 q^{14} -0.0689240 q^{15} +4.23409 q^{16} -4.45195 q^{17} +7.36996 q^{18} +3.64597 q^{19} -9.29148 q^{20} -0.110045 q^{21} -9.75264 q^{22} +0.433976 q^{23} -0.150098 q^{24} +0.292644 q^{25} +10.8525 q^{26} -0.179730 q^{27} -14.8350 q^{28} -2.33443 q^{29} +0.169373 q^{30} +7.37324 q^{31} -0.384728 q^{32} +0.118900 q^{33} +10.9402 q^{34} +8.45034 q^{35} -12.1127 q^{36} +2.28378 q^{37} -8.95958 q^{38} -0.132309 q^{39} +11.5260 q^{40} -0.467077 q^{41} +0.270424 q^{42} -1.26591 q^{43} +16.0286 q^{44} +6.89966 q^{45} -1.06645 q^{46} +2.01157 q^{47} +0.126851 q^{48} +6.49197 q^{49} -0.719140 q^{50} -0.133378 q^{51} -17.8362 q^{52} +3.87564 q^{53} +0.441666 q^{54} -9.13028 q^{55} +18.4026 q^{56} +0.109231 q^{57} +5.73660 q^{58} -5.23852 q^{59} -0.278368 q^{60} -1.65719 q^{61} -18.1189 q^{62} +11.0161 q^{63} -7.52275 q^{64} +10.1599 q^{65} -0.292184 q^{66} +1.83199 q^{67} -17.9804 q^{68} +0.0130017 q^{69} -20.7658 q^{70} -0.430424 q^{71} +15.0256 q^{72} +8.72962 q^{73} -5.61213 q^{74} +0.00876745 q^{75} +14.7252 q^{76} -14.5776 q^{77} +0.325135 q^{78} +2.67184 q^{79} -9.74084 q^{80} +8.99192 q^{81} +1.14779 q^{82} -0.878878 q^{83} -0.444447 q^{84} +10.2420 q^{85} +3.11084 q^{86} -0.0699383 q^{87} -19.8833 q^{88} +11.7431 q^{89} -16.9552 q^{90} +16.2216 q^{91} +1.75273 q^{92} +0.220898 q^{93} -4.94321 q^{94} -8.38783 q^{95} -0.0115262 q^{96} -4.51612 q^{97} -15.9533 q^{98} -11.9025 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.45739	−1.73764	−0.868818	−	0.495131i	$-0.835120\pi$
$2$	−2.45739	−1.73764	−0.868818	+	0.495131i	$0.835120\pi$
$3$	0.0299595	0.0172971	0.00864855	−	0.999963i	$-0.497247\pi$
$3$	0.0299595	0.0172971	0.00864855	+	0.999963i	$0.497247\pi$
$4$	4.03876	2.01938
$5$	−2.30057	−1.02885	−0.514424	−	0.857536i	$-0.671994\pi$
$5$	−2.30057	−1.02885	−0.514424	+	0.857536i	$0.671994\pi$
$6$	−0.0736221	−0.0300561
$7$	−3.67314	−1.38832	−0.694159	−	0.719822i	$-0.744223\pi$
$7$	−3.67314	−1.38832	−0.694159	+	0.719822i	$0.744223\pi$
$8$	−5.01004	−1.77132
$9$	−2.99910	−0.999701
$10$	5.65341	1.78776
$11$	3.96870	1.19661	0.598304	−	0.801269i	$-0.295842\pi$
$11$	3.96870	1.19661	0.598304	+	0.801269i	$0.295842\pi$
$12$	0.120999	0.0349295
$13$	−4.41626	−1.22485	−0.612426	−	0.790528i	$-0.709806\pi$
$13$	−4.41626	−1.22485	−0.612426	+	0.790528i	$0.709806\pi$
$14$	9.02634	2.41239
$15$	−0.0689240	−0.0177961
$16$	4.23409	1.05852
$17$	−4.45195	−1.07976	−0.539878	−	0.841743i	$-0.681530\pi$
$17$	−4.45195	−1.07976	−0.539878	+	0.841743i	$0.681530\pi$
$18$	7.36996	1.73712
$19$	3.64597	0.836444	0.418222	−	0.908345i	$-0.362653\pi$
$19$	3.64597	0.836444	0.418222	+	0.908345i	$0.362653\pi$
$20$	−9.29148	−2.07764
$21$	−0.110045	−0.0240139
$22$	−9.75264	−2.07927
$23$	0.433976	0.0904903	0.0452451	−	0.998976i	$-0.485593\pi$
$23$	0.433976	0.0904903	0.0452451	+	0.998976i	$0.485593\pi$
$24$	−0.150098	−0.0306386
$25$	0.292644	0.0585287
$26$	10.8525	2.12835
$27$	−0.179730	−0.0345890
$28$	−14.8350	−2.80354
$29$	−2.33443	−0.433493	−0.216746	−	0.976228i	$-0.569544\pi$
$29$	−2.33443	−0.433493	−0.216746	+	0.976228i	$0.569544\pi$
$30$	0.169373	0.0309232
$31$	7.37324	1.32427	0.662137	−	0.749383i	$-0.269650\pi$
$31$	7.37324	1.32427	0.662137	+	0.749383i	$0.269650\pi$
$32$	−0.384728	−0.0680110
$33$	0.118900	0.0206978
$34$	10.9402	1.87622
$35$	8.45034	1.42837
$36$	−12.1127	−2.01878
$37$	2.28378	0.375451	0.187725	−	0.982222i	$-0.439888\pi$
$37$	2.28378	0.375451	0.187725	+	0.982222i	$0.439888\pi$
$38$	−8.95958	−1.45344
$39$	−0.132309	−0.0211864
$40$	11.5260	1.82242
$41$	−0.467077	−0.0729452	−0.0364726	−	0.999335i	$-0.511612\pi$
$41$	−0.467077	−0.0729452	−0.0364726	+	0.999335i	$0.511612\pi$
$42$	0.270424	0.0417274
$43$	−1.26591	−0.193050	−0.0965251	−	0.995331i	$-0.530773\pi$
$43$	−1.26591	−0.193050	−0.0965251	+	0.995331i	$0.530773\pi$
$44$	16.0286	2.41641
$45$	6.89966	1.02854
$46$	−1.06645	−0.157239
$47$	2.01157	0.293417	0.146709	−	0.989180i	$-0.453132\pi$
$47$	2.01157	0.293417	0.146709	+	0.989180i	$0.453132\pi$
$48$	0.126851	0.0183094
$49$	6.49197	0.927425
$50$	−0.719140	−0.101702
$51$	−0.133378	−0.0186767
$52$	−17.8362	−2.47344
$53$	3.87564	0.532361	0.266180	−	0.963923i	$-0.414238\pi$
$53$	3.87564	0.532361	0.266180	+	0.963923i	$0.414238\pi$
$54$	0.441666	0.0601032
$55$	−9.13028	−1.23113
$56$	18.4026	2.45915
$57$	0.109231	0.0144681
$58$	5.73660	0.753253
$59$	−5.23852	−0.681997	−0.340998	−	0.940064i	$-0.610765\pi$
$59$	−5.23852	−0.681997	−0.340998	+	0.940064i	$0.610765\pi$
$60$	−0.278368	−0.0359371
$61$	−1.65719	−0.212182	−0.106091	−	0.994356i	$-0.533833\pi$
$61$	−1.65719	−0.212182	−0.106091	+	0.994356i	$0.533833\pi$
$62$	−18.1189	−2.30111
$63$	11.0161	1.38790
$64$	−7.52275	−0.940344
$65$	10.1599	1.26019
$66$	−0.292184	−0.0359653
$67$	1.83199	0.223813	0.111906	−	0.993719i	$-0.464304\pi$
$67$	1.83199	0.223813	0.111906	+	0.993719i	$0.464304\pi$
$68$	−17.9804	−2.18044
$69$	0.0130017	0.00156522
$70$	−20.7658	−2.48198
$71$	−0.430424	−0.0510819	−0.0255410	−	0.999674i	$-0.508131\pi$
$71$	−0.430424	−0.0510819	−0.0255410	+	0.999674i	$0.508131\pi$
$72$	15.0256	1.77079
$73$	8.72962	1.02173	0.510863	−	0.859662i	$-0.329326\pi$
$73$	8.72962	1.02173	0.510863	+	0.859662i	$0.329326\pi$
$74$	−5.61213	−0.652397
$75$	0.00876745	0.00101238
$76$	14.7252	1.68910
$77$	−14.5776	−1.66127
$78$	0.325135	0.0368142
$79$	2.67184	0.300605	0.150303	−	0.988640i	$-0.451975\pi$
$79$	2.67184	0.300605	0.150303	+	0.988640i	$0.451975\pi$
$80$	−9.74084	−1.08906
$81$	8.99192	0.999103
$82$	1.14779	0.126752
$83$	−0.878878	−0.0964693	−0.0482347	−	0.998836i	$-0.515360\pi$
$83$	−0.878878	−0.0964693	−0.0482347	+	0.998836i	$0.515360\pi$
$84$	−0.444447	−0.0484932
$85$	10.2420	1.11091
$86$	3.11084	0.335451
$87$	−0.0699383	−0.00749817
$88$	−19.8833	−2.11957
$89$	11.7431	1.24476	0.622382	−	0.782713i	$-0.286165\pi$
$89$	11.7431	1.24476	0.622382	+	0.782713i	$0.286165\pi$
$90$	−16.9552	−1.78723
$91$	16.2216	1.70048
$92$	1.75273	0.182734
$93$	0.220898	0.0229061
$94$	−4.94321	−0.509853
$95$	−8.38783	−0.860574
$96$	−0.0115262	−0.00117639
$97$	−4.51612	−0.458542	−0.229271	−	0.973363i	$-0.573634\pi$
$97$	−4.51612	−0.458542	−0.229271	+	0.973363i	$0.573634\pi$
$98$	−15.9533	−1.61153
$99$	−11.9025	−1.19625
$100$	1.18192	0.118192
$101$	10.3677	1.03163	0.515814	−	0.856701i	$-0.327490\pi$
$101$	10.3677	1.03163	0.515814	+	0.856701i	$0.327490\pi$
$102$	0.327762	0.0324533
$103$	−4.94178	−0.486928	−0.243464	−	0.969910i	$-0.578284\pi$
$103$	−4.94178	−0.486928	−0.243464	+	0.969910i	$0.578284\pi$
$104$	22.1257	2.16960
$105$	0.253168	0.0247066
$106$	−9.52397	−0.925050
$107$	18.0684	1.74674	0.873371	−	0.487055i	$-0.161929\pi$
$107$	18.0684	1.74674	0.873371	+	0.487055i	$0.161929\pi$
$108$	−0.725887	−0.0698485
$109$	12.5145	1.19867	0.599336	−	0.800498i	$-0.295431\pi$
$109$	12.5145	1.19867	0.599336	+	0.800498i	$0.295431\pi$
$110$	22.4367	2.13925
$111$	0.0684208	0.00649421
$112$	−15.5524	−1.46956
$113$	8.61282	0.810226	0.405113	−	0.914267i	$-0.367232\pi$
$113$	8.61282	0.810226	0.405113	+	0.914267i	$0.367232\pi$
$114$	−0.268424	−0.0251402
$115$	−0.998394	−0.0931007
$116$	−9.42821	−0.875388
$117$	13.2448	1.22448
$118$	12.8731	1.18506
$119$	16.3526	1.49904
$120$	0.345312	0.0315225
$121$	4.75056	0.431869
$122$	4.07237	0.368695
$123$	−0.0139934	−0.00126174
$124$	29.7788	2.67421
$125$	10.8296	0.968631
$126$	−27.0709	−2.41167
$127$	−12.1161	−1.07513	−0.537565	−	0.843222i	$-0.680656\pi$
$127$	−12.1161	−1.07513	−0.537565	+	0.843222i	$0.680656\pi$
$128$	19.2558	1.70199
$129$	−0.0379261	−0.00333921
$130$	−24.9669	−2.18975
$131$	0.235248	0.0205537	0.0102768	−	0.999947i	$-0.496729\pi$
$131$	0.235248	0.0205537	0.0102768	+	0.999947i	$0.496729\pi$
$132$	0.480209	0.0417969
$133$	−13.3922	−1.16125
$134$	−4.50190	−0.388905
$135$	0.413482	0.0355869
$136$	22.3044	1.91259
$137$	−19.7097	−1.68391	−0.841956	−	0.539547i	$-0.818596\pi$
$137$	−19.7097	−1.68391	−0.841956	+	0.539547i	$0.818596\pi$
$138$	−0.0319502	−0.00271978
$139$	−8.64297	−0.733087	−0.366543	−	0.930401i	$-0.619459\pi$
$139$	−8.64297	−0.733087	−0.366543	+	0.930401i	$0.619459\pi$
$140$	34.1289	2.88442
$141$	0.0602655	0.00507527
$142$	1.05772	0.0887619
$143$	−17.5268	−1.46567
$144$	−12.6985	−1.05821
$145$	5.37053	0.445998
$146$	−21.4521	−1.77539
$147$	0.194496	0.0160418
$148$	9.22364	0.758179
$149$	12.8144	1.04980	0.524898	−	0.851165i	$-0.324103\pi$
$149$	12.8144	1.04980	0.524898	+	0.851165i	$0.324103\pi$
$150$	−0.0215450	−0.00175915
$151$	8.00201	0.651194	0.325597	−	0.945509i	$-0.394435\pi$
$151$	8.00201	0.651194	0.325597	+	0.945509i	$0.394435\pi$
$152$	−18.2665	−1.48161
$153$	13.3519	1.07943
$154$	35.8228	2.88668
$155$	−16.9627	−1.36248
$156$	−0.534365	−0.0427834
$157$	−17.7755	−1.41864	−0.709320	−	0.704886i	$-0.750998\pi$
$157$	−17.7755	−1.41864	−0.709320	+	0.704886i	$0.750998\pi$
$158$	−6.56575	−0.522343
$159$	0.116112	0.00920830
$160$	0.885096	0.0699730
$161$	−1.59406	−0.125629
$162$	−22.0967	−1.73608
$163$	−11.5339	−0.903404	−0.451702	−	0.892169i	$-0.649183\pi$
$163$	−11.5339	−0.903404	−0.451702	+	0.892169i	$0.649183\pi$
$164$	−1.88642	−0.147304
$165$	−0.273538	−0.0212949
$166$	2.15974	0.167629
$167$	−1.71315	−0.132568	−0.0662838	−	0.997801i	$-0.521114\pi$
$167$	−1.71315	−0.132568	−0.0662838	+	0.997801i	$0.521114\pi$
$168$	0.551332	0.0425362
$169$	6.50339	0.500261
$170$	−25.1687	−1.93035
$171$	−10.9346	−0.836193
$172$	−5.11273	−0.389842
$173$	0.696083	0.0529222	0.0264611	−	0.999650i	$-0.491576\pi$
$173$	0.696083	0.0529222	0.0264611	+	0.999650i	$0.491576\pi$
$174$	0.171866	0.0130291
$175$	−1.07492	−0.0812565
$176$	16.8038	1.26664
$177$	−0.156943	−0.0117966
$178$	−28.8573	−2.16295
$179$	−25.5763	−1.91167	−0.955833	−	0.293910i	$-0.905043\pi$
$179$	−25.5763	−1.91167	−0.955833	+	0.293910i	$0.905043\pi$
$180$	27.8661	2.07702
$181$	21.4620	1.59526	0.797629	−	0.603149i	$-0.206087\pi$
$181$	21.4620	1.59526	0.797629	+	0.603149i	$0.206087\pi$
$182$	−39.8627	−2.95482
$183$	−0.0496486	−0.00367013
$184$	−2.17424	−0.160287
$185$	−5.25400	−0.386282
$186$	−0.542833	−0.0398025
$187$	−17.6684	−1.29204
$188$	8.12425	0.592522
$189$	0.660173	0.0480206
$190$	20.6122	1.49536
$191$	2.42770	0.175662	0.0878310	−	0.996135i	$-0.472006\pi$
$191$	2.42770	0.175662	0.0878310	+	0.996135i	$0.472006\pi$
$192$	−0.225378	−0.0162652
$193$	−17.0805	−1.22948	−0.614739	−	0.788731i	$-0.710739\pi$
$193$	−17.0805	−1.22948	−0.614739	+	0.788731i	$0.710739\pi$
$194$	11.0979	0.796780
$195$	0.304387	0.0217976
$196$	26.2195	1.87282
$197$	24.3559	1.73529	0.867644	−	0.497186i	$-0.165633\pi$
$197$	24.3559	1.73529	0.867644	+	0.497186i	$0.165633\pi$
$198$	29.2492	2.07865
$199$	−9.38482	−0.665272	−0.332636	−	0.943055i	$-0.607938\pi$
$199$	−9.38482	−0.665272	−0.332636	+	0.943055i	$0.607938\pi$
$200$	−1.46616	−0.103673
$201$	0.0548853	0.00387131
$202$	−25.4776	−1.79259
$203$	8.57469	0.601825
$204$	−0.538682	−0.0377153
$205$	1.07455	0.0750496
$206$	12.1439	0.846104
$207$	−1.30154	−0.0904632
$208$	−18.6989	−1.29653
$209$	14.4698	1.00089
$210$	−0.622131	−0.0429311
$211$	−10.8129	−0.744387	−0.372194	−	0.928155i	$-0.621394\pi$
$211$	−10.8129	−0.744387	−0.372194	+	0.928155i	$0.621394\pi$
$212$	15.6528	1.07504
$213$	−0.0128953	−0.000883570 0
$214$	−44.4012	−3.03520
$215$	2.91233	0.198619
$216$	0.900454	0.0612681
$217$	−27.0830	−1.83851
$218$	−30.7530	−2.08286
$219$	0.261535	0.0176729
$220$	−36.8751	−2.48612
$221$	19.6610	1.32254
$222$	−0.168137	−0.0112846
$223$	8.74930	0.585896	0.292948	−	0.956128i	$-0.405364\pi$
$223$	8.74930	0.585896	0.292948	+	0.956128i	$0.405364\pi$
$224$	1.41316	0.0944208
$225$	−0.877669	−0.0585112
$226$	−21.1651	−1.40788
$227$	10.5390	0.699497	0.349748	−	0.936844i	$-0.386267\pi$
$227$	10.5390	0.699497	0.349748	+	0.936844i	$0.386267\pi$
$228$	0.441160	0.0292165
$229$	−24.7555	−1.63589	−0.817946	−	0.575295i	$-0.804887\pi$
$229$	−24.7555	−1.63589	−0.817946	+	0.575295i	$0.804887\pi$
$230$	2.45344	0.161775
$231$	−0.436737	−0.0287352
$232$	11.6956	0.767853
$233$	1.69457	0.111015	0.0555075	−	0.998458i	$-0.482322\pi$
$233$	1.69457	0.111015	0.0555075	+	0.998458i	$0.482322\pi$
$234$	−32.5477	−2.12771
$235$	−4.62776	−0.301882
$236$	−21.1571	−1.37721
$237$	0.0800468	0.00519960
$238$	−40.1848	−2.60479
$239$	0.483451	0.0312719	0.0156359	−	0.999878i	$-0.495023\pi$
$239$	0.483451	0.0312719	0.0156359	+	0.999878i	$0.495023\pi$
$240$	−0.291830	−0.0188376
$241$	3.46950	0.223490	0.111745	−	0.993737i	$-0.464356\pi$
$241$	3.46950	0.223490	0.111745	+	0.993737i	$0.464356\pi$
$242$	−11.6740	−0.750432
$243$	0.808583	0.0518706
$244$	−6.69301	−0.428476
$245$	−14.9353	−0.954179
$246$	0.0343872	0.00219245
$247$	−16.1016	−1.02452
$248$	−36.9402	−2.34571
$249$	−0.0263307	−0.00166864
$250$	−26.6126	−1.68313
$251$	8.04890	0.508042	0.254021	−	0.967199i	$-0.418247\pi$
$251$	8.04890	0.508042	0.254021	+	0.967199i	$0.418247\pi$
$252$	44.4915	2.80270
$253$	1.72232	0.108281
$254$	29.7740	1.86819
$255$	0.306846	0.0192155
$256$	−32.2735	−2.01709
$257$	17.6413	1.10044	0.550219	−	0.835021i	$-0.314544\pi$
$257$	17.6413	1.10044	0.550219	+	0.835021i	$0.314544\pi$
$258$	0.0931992	0.00580233
$259$	−8.38864	−0.521245
$260$	41.0336	2.54480
$261$	7.00119	0.433363
$262$	−0.578096	−0.0357149
$263$	0.603599	0.0372195	0.0186098	−	0.999827i	$-0.494076\pi$
$263$	0.603599	0.0372195	0.0186098	+	0.999827i	$0.494076\pi$
$264$	−0.595694	−0.0366624
$265$	−8.91621	−0.547718
$266$	32.9098	2.01783
$267$	0.351817	0.0215308
$268$	7.39896	0.451963
$269$	12.4266	0.757666	0.378833	−	0.925465i	$-0.376326\pi$
$269$	12.4266	0.757666	0.378833	+	0.925465i	$0.376326\pi$
$270$	−1.01609	−0.0618371
$271$	−12.9612	−0.787337	−0.393668	−	0.919253i	$-0.628794\pi$
$271$	−12.9612	−0.787337	−0.393668	+	0.919253i	$0.628794\pi$
$272$	−18.8499	−1.14295
$273$	0.485989	0.0294134
$274$	48.4344	2.92603
$275$	1.16141	0.0700359
$276$	0.0525108	0.00316078
$277$	13.0113	0.781773	0.390886	−	0.920439i	$-0.372169\pi$
$277$	13.0113	0.781773	0.390886	+	0.920439i	$0.372169\pi$
$278$	21.2391	1.27384
$279$	−22.1131	−1.32388
$280$	−42.3365	−2.53009
$281$	11.4820	0.684957	0.342478	−	0.939526i	$-0.388734\pi$
$281$	11.4820	0.684957	0.342478	+	0.939526i	$0.388734\pi$
$282$	−0.148096	−0.00881898
$283$	6.49250	0.385939	0.192969	−	0.981205i	$-0.438188\pi$
$283$	6.49250	0.385939	0.192969	+	0.981205i	$0.438188\pi$
$284$	−1.73838	−0.103154
$285$	−0.251295	−0.0148854
$286$	43.0702	2.54680
$287$	1.71564	0.101271
$288$	1.15384	0.0679906
$289$	2.81985	0.165874
$290$	−13.1975	−0.774983
$291$	−0.135300	−0.00793145
$292$	35.2569	2.06325
$293$	0.948461	0.0554097	0.0277048	−	0.999616i	$-0.491180\pi$
$293$	0.948461	0.0554097	0.0277048	+	0.999616i	$0.491180\pi$
$294$	−0.477953	−0.0278748
$295$	12.0516	0.701671
$296$	−11.4418	−0.665042
$297$	−0.713294	−0.0413895
$298$	−31.4900	−1.82416
$299$	−1.91655	−0.110837
$300$	0.0354097	0.00204438
$301$	4.64988	0.268015
$302$	−19.6640	−1.13154
$303$	0.310612	0.0178442
$304$	15.4374	0.885394
$305$	3.81249	0.218303
$306$	−32.8107	−1.87566
$307$	−29.0229	−1.65642	−0.828212	−	0.560415i	$-0.810642\pi$
$307$	−29.0229	−1.65642	−0.828212	+	0.560415i	$0.810642\pi$
$308$	−58.8754	−3.35474
$309$	−0.148053	−0.00842244
$310$	41.6839	2.36749
$311$	8.91374	0.505452	0.252726	−	0.967538i	$-0.418673\pi$
$311$	8.91374	0.505452	0.252726	+	0.967538i	$0.418673\pi$
$312$	0.662873	0.0375278
$313$	−9.03011	−0.510412	−0.255206	−	0.966887i	$-0.582143\pi$
$313$	−9.03011	−0.510412	−0.255206	+	0.966887i	$0.582143\pi$
$314$	43.6814	2.46508
$315$	−25.3434	−1.42794
$316$	10.7909	0.607037
$317$	−15.8822	−0.892031	−0.446015	−	0.895025i	$-0.647157\pi$
$317$	−15.8822	−0.892031	−0.446015	+	0.895025i	$0.647157\pi$
$318$	−0.285333	−0.0160007
$319$	−9.26465	−0.518721
$320$	17.3066	0.967471
$321$	0.541321	0.0302136
$322$	3.91722	0.218298
$323$	−16.2317	−0.903155
$324$	36.3163	2.01757
$325$	−1.29239	−0.0716890
$326$	28.3433	1.56979
$327$	0.374928	0.0207336
$328$	2.34008	0.129209
$329$	−7.38878	−0.407357
$330$	0.672191	0.0370029
$331$	12.5592	0.690314	0.345157	−	0.938545i	$-0.387826\pi$
$331$	12.5592	0.690314	0.345157	+	0.938545i	$0.387826\pi$
$332$	−3.54958	−0.194808
$333$	−6.84929	−0.375339
$334$	4.20988	0.230354
$335$	−4.21462	−0.230269
$336$	−0.465942	−0.0254192
$337$	−13.9122	−0.757844	−0.378922	−	0.925429i	$-0.623705\pi$
$337$	−13.9122	−0.757844	−0.378922	+	0.925429i	$0.623705\pi$
$338$	−15.9814	−0.869271
$339$	0.258036	0.0140146
$340$	41.3652	2.24334
$341$	29.2622	1.58464
$342$	26.8707	1.45300
$343$	1.86606	0.100758
$344$	6.34228	0.341953
$345$	−0.0299114	−0.00161037
$346$	−1.71055	−0.0919596
$347$	−5.08480	−0.272966	−0.136483	−	0.990642i	$-0.543580\pi$
$347$	−5.08480	−0.272966	−0.136483	+	0.990642i	$0.543580\pi$
$348$	−0.282464	−0.0151417
$349$	18.6250	0.996975	0.498488	−	0.866897i	$-0.333889\pi$
$349$	18.6250	0.996975	0.498488	+	0.866897i	$0.333889\pi$
$350$	2.64150	0.141194
$351$	0.793735	0.0423664
$352$	−1.52687	−0.0813824
$353$	−30.6953	−1.63375	−0.816873	−	0.576817i	$-0.804294\pi$
$353$	−30.6953	−1.63375	−0.816873	+	0.576817i	$0.804294\pi$
$354$	0.385671	0.0204982
$355$	0.990223	0.0525556
$356$	47.4276	2.51366
$357$	0.489916	0.0259291
$358$	62.8511	3.32178
$359$	35.1299	1.85408	0.927042	−	0.374957i	$-0.122342\pi$
$359$	35.1299	1.85408	0.927042	+	0.374957i	$0.122342\pi$
$360$	−34.5676	−1.82187
$361$	−5.70688	−0.300362
$362$	−52.7405	−2.77198
$363$	0.142324	0.00747009
$364$	65.5151	3.43392
$365$	−20.0832	−1.05120
$366$	0.122006	0.00637735
$367$	21.6804	1.13171	0.565854	−	0.824505i	$-0.308546\pi$
$367$	21.6804	1.13171	0.565854	+	0.824505i	$0.308546\pi$
$368$	1.83749	0.0957859
$369$	1.40081	0.0729234
$370$	12.9111	0.671218
$371$	−14.2358	−0.739086
$372$	0.892156	0.0462562
$373$	−5.22180	−0.270375	−0.135187	−	0.990820i	$-0.543164\pi$
$373$	−5.22180	−0.270375	−0.135187	+	0.990820i	$0.543164\pi$
$374$	43.4182	2.24510
$375$	0.324450	0.0167545
$376$	−10.0780	−0.519735
$377$	10.3095	0.530964
$378$	−1.62230	−0.0834423
$379$	−24.6864	−1.26805	−0.634026	−	0.773311i	$-0.718599\pi$
$379$	−24.6864	−1.26805	−0.634026	+	0.773311i	$0.718599\pi$
$380$	−33.8765	−1.73783
$381$	−0.362992	−0.0185966
$382$	−5.96580	−0.305237
$383$	−0.438123	−0.0223870	−0.0111935	−	0.999937i	$-0.503563\pi$
$383$	−0.438123	−0.0223870	−0.0111935	+	0.999937i	$0.503563\pi$
$384$	0.576893	0.0294394
$385$	33.5368	1.70920
$386$	41.9733	2.13639
$387$	3.79661	0.192992
$388$	−18.2395	−0.925972
$389$	−19.8622	−1.00705	−0.503526	−	0.863980i	$-0.667964\pi$
$389$	−19.8622	−1.00705	−0.503526	+	0.863980i	$0.667964\pi$
$390$	−0.747996	−0.0378763
$391$	−1.93204	−0.0977074
$392$	−32.5250	−1.64276
$393$	0.00704790	0.000355520 0
$394$	−59.8520	−3.01530
$395$	−6.14676	−0.309277
$396$	−48.0715	−2.41568
$397$	1.44135	0.0723392	0.0361696	−	0.999346i	$-0.488484\pi$
$397$	1.44135	0.0723392	0.0361696	+	0.999346i	$0.488484\pi$
$398$	23.0622	1.15600
$399$	−0.401223	−0.0200862
$400$	1.23908	0.0619540
$401$	24.0466	1.20083	0.600415	−	0.799688i	$-0.295002\pi$
$401$	24.0466	1.20083	0.600415	+	0.799688i	$0.295002\pi$
$402$	−0.134875	−0.00672693
$403$	−32.5622	−1.62204
$404$	41.8728	2.08325
$405$	−20.6866	−1.02792
$406$	−21.0714	−1.04575
$407$	9.06363	0.449267
$408$	0.668229	0.0330823
$409$	20.5156	1.01443	0.507216	−	0.861819i	$-0.330675\pi$
$409$	20.5156	1.01443	0.507216	+	0.861819i	$0.330675\pi$
$410$	−2.64058	−0.130409
$411$	−0.590491	−0.0291268
$412$	−19.9587	−0.983294
$413$	19.2418	0.946828
$414$	3.19839	0.157192
$415$	2.02192	0.0992523
$416$	1.69906	0.0833033
$417$	−0.258939	−0.0126803
$418$	−35.5579	−1.73919
$419$	4.30722	0.210421	0.105211	−	0.994450i	$-0.466448\pi$
$419$	4.30722	0.210421	0.105211	+	0.994450i	$0.466448\pi$
$420$	1.02248	0.0498921
$421$	−11.2581	−0.548688	−0.274344	−	0.961632i	$-0.588461\pi$
$421$	−11.2581	−0.548688	−0.274344	+	0.961632i	$0.588461\pi$
$422$	26.5714	1.29347
$423$	−6.03290	−0.293330
$424$	−19.4171	−0.942979
$425$	−1.30284	−0.0631968
$426$	0.0316887	0.00153532
$427$	6.08710	0.294576
$428$	72.9742	3.52734
$429$	−0.525094	−0.0253518
$430$	−7.15673	−0.345128
$431$	−22.5775	−1.08752	−0.543760	−	0.839241i	$-0.683000\pi$
$431$	−22.5775	−1.08752	−0.543760	+	0.839241i	$0.683000\pi$
$432$	−0.760992	−0.0366133
$433$	0.589360	0.0283229	0.0141614	−	0.999900i	$-0.495492\pi$
$433$	0.589360	0.0283229	0.0141614	+	0.999900i	$0.495492\pi$
$434$	66.5534	3.19467
$435$	0.160898	0.00771448
$436$	50.5431	2.42058
$437$	1.58227	0.0756900
$438$	−0.642693	−0.0307091
$439$	7.28817	0.347845	0.173923	−	0.984759i	$-0.444356\pi$
$439$	7.28817	0.347845	0.173923	+	0.984759i	$0.444356\pi$
$440$	45.7431	2.18072
$441$	−19.4701	−0.927147
$442$	−48.3147	−2.29810
$443$	18.5904	0.883256	0.441628	−	0.897198i	$-0.354401\pi$
$443$	18.5904	0.883256	0.441628	+	0.897198i	$0.354401\pi$
$444$	0.276335	0.0131143
$445$	−27.0158	−1.28067
$446$	−21.5004	−1.01808
$447$	0.383912	0.0181584
$448$	27.6321	1.30550
$449$	−2.96617	−0.139982	−0.0699911	−	0.997548i	$-0.522297\pi$
$449$	−2.96617	−0.139982	−0.0699911	+	0.997548i	$0.522297\pi$
$450$	2.15677	0.101671
$451$	−1.85369	−0.0872868
$452$	34.7852	1.63616
$453$	0.239736	0.0112638
$454$	−25.8984	−1.21547
$455$	−37.3189	−1.74954
$456$	−0.547254	−0.0256275
$457$	−9.86488	−0.461460	−0.230730	−	0.973018i	$-0.574111\pi$
$457$	−9.86488	−0.461460	−0.230730	+	0.973018i	$0.574111\pi$
$458$	60.8340	2.84259
$459$	0.800149	0.0373477
$460$	−4.03228	−0.188006
$461$	23.0718	1.07456	0.537280	−	0.843404i	$-0.319452\pi$
$461$	23.0718	1.07456	0.537280	+	0.843404i	$0.319452\pi$
$462$	1.07323	0.0499313
$463$	12.8543	0.597388	0.298694	−	0.954349i	$-0.403449\pi$
$463$	12.8543	0.597388	0.298694	+	0.954349i	$0.403449\pi$
$464$	−9.88418	−0.458862
$465$	−0.508193	−0.0235669
$466$	−4.16422	−0.192904
$467$	−41.5721	−1.92373	−0.961864	−	0.273529i	$-0.911809\pi$
$467$	−41.5721	−1.92373	−0.961864	+	0.273529i	$0.911809\pi$
$468$	53.4927	2.47270
$469$	−6.72914	−0.310723
$470$	11.3722	0.524561
$471$	−0.532545	−0.0245384
$472$	26.2452	1.20803
$473$	−5.02403	−0.231005
$474$	−0.196706	−0.00903502
$475$	1.06697	0.0489560
$476$	66.0445	3.02714
$477$	−11.6235	−0.532201
$478$	−1.18803	−0.0543391
$479$	7.58257	0.346457	0.173228	−	0.984882i	$-0.444580\pi$
$479$	7.58257	0.346457	0.173228	+	0.984882i	$0.444580\pi$
$480$	0.0265170	0.00121033
$481$	−10.0858	−0.459871
$482$	−8.52591	−0.388344
$483$	−0.0477571	−0.00217302
$484$	19.1864	0.872109
$485$	10.3897	0.471770
$486$	−1.98700	−0.0901323
$487$	−9.30755	−0.421766	−0.210883	−	0.977511i	$-0.567634\pi$
$487$	−9.30755	−0.421766	−0.210883	+	0.977511i	$0.567634\pi$
$488$	8.30260	0.375841
$489$	−0.345549	−0.0156263
$490$	36.7018	1.65802
$491$	−39.7365	−1.79329	−0.896643	−	0.442755i	$-0.854001\pi$
$491$	−39.7365	−1.79329	−0.896643	+	0.442755i	$0.854001\pi$
$492$	−0.0565160	−0.00254794
$493$	10.3928	0.468067
$494$	39.5679	1.78024
$495$	27.3827	1.23076
$496$	31.2190	1.40177
$497$	1.58101	0.0709179
$498$	0.0647048	0.00289949
$499$	−40.8012	−1.82651	−0.913255	−	0.407387i	$-0.866440\pi$
$499$	−40.8012	−1.82651	−0.913255	+	0.407387i	$0.866440\pi$
$500$	43.7383	1.95604
$501$	−0.0513251	−0.00229304
$502$	−19.7793	−0.882793
$503$	10.5526	0.470516	0.235258	−	0.971933i	$-0.424406\pi$
$503$	10.5526	0.470516	0.235258	+	0.971933i	$0.424406\pi$
$504$	−55.1912	−2.45841
$505$	−23.8517	−1.06139
$506$	−4.23241	−0.188154
$507$	0.194838	0.00865306
$508$	−48.9341	−2.17110
$509$	14.2606	0.632091	0.316045	−	0.948744i	$-0.397645\pi$
$509$	14.2606	0.632091	0.316045	+	0.948744i	$0.397645\pi$
$510$	−0.754041	−0.0333895
$511$	−32.0651	−1.41848
$512$	40.7969	1.80299
$513$	−0.655290	−0.0289318
$514$	−43.3517	−1.91216
$515$	11.3689	0.500975
$516$	−0.153175	−0.00674314
$517$	7.98331	0.351106
$518$	20.6142	0.905734
$519$	0.0208543	0.000915401 0
$520$	−50.9017	−2.23219
$521$	21.8233	0.956098	0.478049	−	0.878333i	$-0.341344\pi$
$521$	21.8233	0.956098	0.478049	+	0.878333i	$0.341344\pi$
$522$	−17.2047	−0.753028
$523$	29.5610	1.29261	0.646307	−	0.763078i	$-0.276313\pi$
$523$	29.5610	1.29261	0.646307	+	0.763078i	$0.276313\pi$
$524$	0.950111	0.0415058
$525$	−0.0322041	−0.00140550
$526$	−1.48328	−0.0646740
$527$	−32.8253	−1.42989
$528$	0.503433	0.0219091
$529$	−22.8117	−0.991812
$530$	21.9106	0.951736
$531$	15.7108	0.681793
$532$	−54.0879	−2.34501
$533$	2.06274	0.0893471
$534$	−0.864550	−0.0374128
$535$	−41.5678	−1.79713
$536$	−9.17832	−0.396443
$537$	−0.766254	−0.0330663
$538$	−30.5371	−1.31655
$539$	25.7647	1.10976
$540$	1.66996	0.0718635
$541$	5.60431	0.240948	0.120474	−	0.992716i	$-0.461559\pi$
$541$	5.60431	0.240948	0.120474	+	0.992716i	$0.461559\pi$
$542$	31.8507	1.36811
$543$	0.642990	0.0275933
$544$	1.71279	0.0734353
$545$	−28.7906	−1.23325
$546$	−1.19427	−0.0511098
$547$	22.6670	0.969172	0.484586	−	0.874744i	$-0.338970\pi$
$547$	22.6670	0.969172	0.484586	+	0.874744i	$0.338970\pi$
$548$	−79.6027	−3.40046
$549$	4.97009	0.212118
$550$	−2.85405	−0.121697
$551$	−8.51127	−0.362592
$552$	−0.0651390	−0.00277250
$553$	−9.81404	−0.417335
$554$	−31.9738	−1.35844
$555$	−0.157407	−0.00668156
$556$	−34.9069	−1.48038
$557$	4.19796	0.177873	0.0889366	−	0.996037i	$-0.471653\pi$
$557$	4.19796	0.177873	0.0889366	+	0.996037i	$0.471653\pi$
$558$	54.3405	2.30042
$559$	5.59061	0.236458
$560$	35.7795	1.51196
$561$	−0.529337	−0.0223486
$562$	−28.2157	−1.19021
$563$	16.9207	0.713122	0.356561	−	0.934272i	$-0.383949\pi$
$563$	16.9207	0.713122	0.356561	+	0.934272i	$0.383949\pi$
$564$	0.243398	0.0102489
$565$	−19.8144	−0.833600
$566$	−15.9546	−0.670622
$567$	−33.0286	−1.38707
$568$	2.15644	0.0904823
$569$	6.46919	0.271203	0.135601	−	0.990763i	$-0.456703\pi$
$569$	6.46919	0.271203	0.135601	+	0.990763i	$0.456703\pi$
$570$	0.617530	0.0258655
$571$	−17.0713	−0.714410	−0.357205	−	0.934026i	$-0.616270\pi$
$571$	−17.0713	−0.714410	−0.357205	+	0.934026i	$0.616270\pi$
$572$	−70.7867	−2.95974
$573$	0.0727325	0.00303845
$574$	−4.21600	−0.175972
$575$	0.127000	0.00529628
$576$	22.5615	0.940062
$577$	−41.3855	−1.72290	−0.861450	−	0.507842i	$-0.830443\pi$
$577$	−41.3855	−1.72290	−0.861450	+	0.507842i	$0.830443\pi$
$578$	−6.92948	−0.288228
$579$	−0.511721	−0.0212664
$580$	21.6903	0.900641
$581$	3.22824	0.133930
$582$	0.332486	0.0137820
$583$	15.3813	0.637027
$584$	−43.7357	−1.80980
$585$	−30.4707	−1.25981
$586$	−2.33074	−0.0962819
$587$	−19.5429	−0.806623	−0.403312	−	0.915063i	$-0.632141\pi$
$587$	−19.5429	−0.806623	−0.403312	+	0.915063i	$0.632141\pi$
$588$	0.785524	0.0323944
$589$	26.8826	1.10768
$590$	−29.6155	−1.21925
$591$	0.729691	0.0300155
$592$	9.66972	0.397423
$593$	−31.0589	−1.27544	−0.637719	−	0.770269i	$-0.720122\pi$
$593$	−31.0589	−1.27544	−0.637719	+	0.770269i	$0.720122\pi$
$594$	1.75284	0.0719199
$595$	−37.6205	−1.54229
$596$	51.7543	2.11994
$597$	−0.281164	−0.0115073
$598$	4.70972	0.192595
$599$	−13.4871	−0.551068	−0.275534	−	0.961291i	$-0.588855\pi$
$599$	−13.4871	−0.551068	−0.275534	+	0.961291i	$0.588855\pi$
$600$	−0.0439253	−0.00179324
$601$	16.5412	0.674731	0.337365	−	0.941374i	$-0.390464\pi$
$601$	16.5412	0.674731	0.337365	+	0.941374i	$0.390464\pi$
$602$	−11.4266	−0.465712
$603$	−5.49431	−0.223746
$604$	32.3182	1.31501
$605$	−10.9290	−0.444328
$606$	−0.763294	−0.0310067
$607$	16.0877	0.652978	0.326489	−	0.945201i	$-0.394134\pi$
$607$	16.0877	0.652978	0.326489	+	0.945201i	$0.394134\pi$
$608$	−1.40271	−0.0568873
$609$	0.256893	0.0104098
$610$	−9.36878	−0.379331
$611$	−8.88362	−0.359393
$612$	53.9250	2.17979
$613$	−18.5499	−0.749223	−0.374611	−	0.927182i	$-0.622224\pi$
$613$	−18.5499	−0.749223	−0.374611	+	0.927182i	$0.622224\pi$
$614$	71.3206	2.87826
$615$	0.0321928	0.00129814
$616$	73.0343	2.94264
$617$	−26.6845	−1.07428	−0.537138	−	0.843494i	$-0.680495\pi$
$617$	−26.6845	−1.07428	−0.537138	+	0.843494i	$0.680495\pi$
$618$	0.363824	0.0146351
$619$	2.85848	0.114892	0.0574461	−	0.998349i	$-0.481704\pi$
$619$	2.85848	0.114892	0.0574461	+	0.998349i	$0.481704\pi$
$620$	−68.5083	−2.75136
$621$	−0.0779985	−0.00312997
$622$	−21.9045	−0.878292
$623$	−43.1340	−1.72813
$624$	−0.560208	−0.0224263
$625$	−26.3776	−1.05510
$626$	22.1905	0.886911
$627$	0.433506	0.0173126
$628$	−71.7911	−2.86478
$629$	−10.1673	−0.405395
$630$	62.2787	2.48124
$631$	29.2552	1.16463	0.582315	−	0.812963i	$-0.302147\pi$
$631$	29.2552	1.16463	0.582315	+	0.812963i	$0.302147\pi$
$632$	−13.3860	−0.532467
$633$	−0.323947	−0.0128757
$634$	39.0287	1.55003
$635$	27.8740	1.10615
$636$	0.468950	0.0185951
$637$	−28.6703	−1.13596
$638$	22.7668	0.901348
$639$	1.29089	0.0510667
$640$	−44.2994	−1.75109
$641$	−9.48262	−0.374541	−0.187270	−	0.982308i	$-0.559964\pi$
$641$	−9.48262	−0.374541	−0.187270	+	0.982308i	$0.559964\pi$
$642$	−1.33024	−0.0525003
$643$	−39.0757	−1.54100	−0.770498	−	0.637442i	$-0.779992\pi$
$643$	−39.0757	−1.54100	−0.770498	+	0.637442i	$0.779992\pi$
$644$	−6.43801	−0.253693
$645$	0.0872519	0.00343554
$646$	39.8876	1.56936
$647$	31.2789	1.22970	0.614850	−	0.788644i	$-0.289217\pi$
$647$	31.2789	1.22970	0.614850	+	0.788644i	$0.289217\pi$
$648$	−45.0499	−1.76973
$649$	−20.7901	−0.816082
$650$	3.17591	0.124569
$651$	−0.811391	−0.0318009
$652$	−46.5827	−1.82432
$653$	8.63237	0.337811	0.168905	−	0.985632i	$-0.445977\pi$
$653$	8.63237	0.337811	0.168905	+	0.985632i	$0.445977\pi$
$654$	−0.921344	−0.0360274
$655$	−0.541205	−0.0211466
$656$	−1.97765	−0.0772141
$657$	−26.1810	−1.02142
$658$	18.1571	0.707838
$659$	−43.9965	−1.71386	−0.856930	−	0.515432i	$-0.827631\pi$
$659$	−43.9965	−1.71386	−0.856930	+	0.515432i	$0.827631\pi$
$660$	−1.10476	−0.0430026
$661$	−16.7583	−0.651822	−0.325911	−	0.945400i	$-0.605671\pi$
$661$	−16.7583	−0.651822	−0.325911	+	0.945400i	$0.605671\pi$
$662$	−30.8628	−1.19952
$663$	0.589033	0.0228761
$664$	4.40321	0.170878
$665$	30.8097	1.19475
$666$	16.8314	0.652202
$667$	−1.01309	−0.0392269
$668$	−6.91901	−0.267705
$669$	0.262124	0.0101343
$670$	10.3570	0.400124
$671$	−6.57689	−0.253898
$672$	0.0423375	0.00163321
$673$	1.14402	0.0440988	0.0220494	−	0.999757i	$-0.492981\pi$
$673$	1.14402	0.0440988	0.0220494	+	0.999757i	$0.492981\pi$
$674$	34.1876	1.31686
$675$	−0.0525968	−0.00202445
$676$	26.2657	1.01022
$677$	0.318243	0.0122311	0.00611554	−	0.999981i	$-0.498053\pi$
$677$	0.318243	0.0122311	0.00611554	+	0.999981i	$0.498053\pi$
$678$	−0.634094	−0.0243522
$679$	16.5883	0.636602
$680$	−51.3130	−1.96776
$681$	0.315742	0.0120993
$682$	−71.9085	−2.75352
$683$	−3.70899	−0.141921	−0.0709603	−	0.997479i	$-0.522606\pi$
$683$	−3.70899	−0.141921	−0.0709603	+	0.997479i	$0.522606\pi$
$684$	−44.1625	−1.68859
$685$	45.3436	1.73249
$686$	−4.58563	−0.175080
$687$	−0.741663	−0.0282962
$688$	−5.35999	−0.204348
$689$	−17.1159	−0.652063
$690$	0.0735039	0.00279824
$691$	−6.31761	−0.240333	−0.120167	−	0.992754i	$-0.538343\pi$
$691$	−6.31761	−0.240333	−0.120167	+	0.992754i	$0.538343\pi$
$692$	2.81132	0.106870
$693$	43.7197	1.66077
$694$	12.4953	0.474316
$695$	19.8838	0.754235
$696$	0.350393	0.0132816
$697$	2.07940	0.0787631
$698$	−45.7690	−1.73238
$699$	0.0507685	0.00192024
$700$	−4.34136	−0.164088
$701$	−41.8377	−1.58019	−0.790095	−	0.612985i	$-0.789969\pi$
$701$	−41.8377	−1.58019	−0.790095	+	0.612985i	$0.789969\pi$
$702$	−1.95052	−0.0736175
$703$	8.32660	0.314044
$704$	−29.8555	−1.12522
$705$	−0.138645	−0.00522169
$706$	75.4303	2.83886
$707$	−38.0822	−1.43223
$708$	−0.633857	−0.0238218
$709$	−5.26296	−0.197655	−0.0988273	−	0.995105i	$-0.531509\pi$
$709$	−5.26296	−0.197655	−0.0988273	+	0.995105i	$0.531509\pi$
$710$	−2.43336	−0.0913225
$711$	−8.01311	−0.300515
$712$	−58.8333	−2.20487
$713$	3.19981	0.119834
$714$	−1.20392	−0.0450554
$715$	40.3218	1.50795
$716$	−103.297	−3.86038
$717$	0.0144839	0.000540913 0
$718$	−86.3278	−3.22173
$719$	12.2664	0.457459	0.228730	−	0.973490i	$-0.426543\pi$
$719$	12.2664	0.457459	0.228730	+	0.973490i	$0.426543\pi$
$720$	29.2138	1.08873
$721$	18.1519	0.676010
$722$	14.0240	0.521920
$723$	0.103944	0.00386573
$724$	86.6799	3.22143
$725$	−0.683156	−0.0253718
$726$	−0.349746	−0.0129803
$727$	−37.6878	−1.39776	−0.698882	−	0.715237i	$-0.746319\pi$
$727$	−37.6878	−1.39776	−0.698882	+	0.715237i	$0.746319\pi$
$728$	−81.2707	−3.01209
$729$	−26.9515	−0.998205
$730$	49.3521	1.82660
$731$	5.63579	0.208447
$732$	−0.200519	−0.00741139
$733$	−28.0391	−1.03565	−0.517825	−	0.855487i	$-0.673258\pi$
$733$	−28.0391	−1.03565	−0.517825	+	0.855487i	$0.673258\pi$
$734$	−53.2772	−1.96650
$735$	−0.447453	−0.0165045
$736$	−0.166963	−0.00615433
$737$	7.27059	0.267816
$738$	−3.44234	−0.126714
$739$	9.92055	0.364933	0.182467	−	0.983212i	$-0.441592\pi$
$739$	9.92055	0.364933	0.182467	+	0.983212i	$0.441592\pi$
$740$	−21.2197	−0.780051
$741$	−0.482395	−0.0177212
$742$	34.9829	1.28426
$743$	−13.0878	−0.480145	−0.240072	−	0.970755i	$-0.577171\pi$
$743$	−13.0878	−0.480145	−0.240072	+	0.970755i	$0.577171\pi$
$744$	−1.10671	−0.0405739
$745$	−29.4805	−1.08008
$746$	12.8320	0.469813
$747$	2.63584	0.0964405
$748$	−71.3587	−2.60913
$749$	−66.3680	−2.42503
$750$	−0.797300	−0.0291133
$751$	−3.70319	−0.135131	−0.0675656	−	0.997715i	$-0.521523\pi$
$751$	−3.70319	−0.135131	−0.0675656	+	0.997715i	$0.521523\pi$
$752$	8.51716	0.310589
$753$	0.241141	0.00878766
$754$	−25.3344	−0.922623
$755$	−18.4092	−0.669980
$756$	2.66629	0.0969719
$757$	−12.1679	−0.442250	−0.221125	−	0.975245i	$-0.570973\pi$
$757$	−12.1679	−0.442250	−0.221125	+	0.975245i	$0.570973\pi$
$758$	60.6640	2.20342
$759$	0.0515998	0.00187295
$760$	42.0234	1.52435
$761$	37.9926	1.37723	0.688616	−	0.725126i	$-0.258219\pi$
$761$	37.9926	1.37723	0.688616	+	0.725126i	$0.258219\pi$
$762$	0.892013	0.0323142
$763$	−45.9676	−1.66414
$764$	9.80490	0.354729
$765$	−30.7169	−1.11057
$766$	1.07664	0.0389005
$767$	23.1347	0.835345
$768$	−0.966896	−0.0348898
$769$	5.12991	0.184989	0.0924946	−	0.995713i	$-0.470516\pi$
$769$	5.12991	0.184989	0.0924946	+	0.995713i	$0.470516\pi$
$770$	−82.4131	−2.96996
$771$	0.528525	0.0190344
$772$	−68.9839	−2.48279
$773$	−4.63926	−0.166863	−0.0834313	−	0.996514i	$-0.526588\pi$
$773$	−4.63926	−0.166863	−0.0834313	+	0.996514i	$0.526588\pi$
$774$	−9.32974	−0.335351
$775$	2.15773	0.0775081
$776$	22.6259	0.812223
$777$	−0.251319	−0.00901603
$778$	48.8091	1.74989
$779$	−1.70295	−0.0610146
$780$	1.22935	0.0440176
$781$	−1.70822	−0.0611250
$782$	4.74777	0.169780
$783$	0.419567	0.0149941
$784$	27.4876	0.981699
$785$	40.8939	1.45957
$786$	−0.0173194	−0.000617764 0
$787$	15.6019	0.556149	0.278075	−	0.960559i	$-0.410304\pi$
$787$	15.6019	0.556149	0.278075	+	0.960559i	$0.410304\pi$
$788$	98.3679	3.50421
$789$	0.0180835	0.000643790 0
$790$	15.1050	0.537411
$791$	−31.6361	−1.12485
$792$	59.6321	2.11894
$793$	7.31860	0.259891
$794$	−3.54195	−0.125699
$795$	−0.267125	−0.00947394
$796$	−37.9031	−1.34344
$797$	−23.4170	−0.829473	−0.414736	−	0.909942i	$-0.636126\pi$
$797$	−23.4170	−0.829473	−0.414736	+	0.909942i	$0.636126\pi$
$798$	0.985960	0.0349026
$799$	−8.95540	−0.316819
$800$	−0.112588	−0.00398060
$801$	−35.2187	−1.24439
$802$	−59.0919	−2.08661
$803$	34.6452	1.22260
$804$	0.221669	0.00781765
$805$	3.66724	0.129253
$806$	80.0180	2.81851
$807$	0.372296	0.0131054
$808$	−51.9427	−1.82734
$809$	−29.0478	−1.02126	−0.510632	−	0.859799i	$-0.670589\pi$
$809$	−29.0478	−1.02126	−0.510632	+	0.859799i	$0.670589\pi$
$810$	50.8350	1.78616
$811$	14.0219	0.492377	0.246188	−	0.969222i	$-0.420822\pi$
$811$	14.0219	0.492377	0.246188	+	0.969222i	$0.420822\pi$
$812$	34.6312	1.21532
$813$	−0.388311	−0.0136186
$814$	−22.2729	−0.780663
$815$	26.5346	0.929466
$816$	−0.564734	−0.0197697
$817$	−4.61549	−0.161476
$818$	−50.4149	−1.76271
$819$	−48.6501	−1.69997
$820$	4.33984	0.151554
$821$	2.90389	0.101346	0.0506732	−	0.998715i	$-0.483863\pi$
$821$	2.90389	0.101346	0.0506732	+	0.998715i	$0.483863\pi$
$822$	1.45107	0.0506118
$823$	−35.2812	−1.22982	−0.614912	−	0.788595i	$-0.710809\pi$
$823$	−35.2812	−1.22982	−0.614912	+	0.788595i	$0.710809\pi$
$824$	24.7585	0.862503
$825$	0.0347954	0.00121142
$826$	−47.2846	−1.64524
$827$	23.6924	0.823866	0.411933	−	0.911214i	$-0.364854\pi$
$827$	23.6924	0.823866	0.411933	+	0.911214i	$0.364854\pi$
$828$	−5.25661	−0.182680
$829$	23.5014	0.816236	0.408118	−	0.912929i	$-0.366185\pi$
$829$	23.5014	0.816236	0.408118	+	0.912929i	$0.366185\pi$
$830$	−4.96865	−0.172464
$831$	0.389811	0.0135224
$832$	33.2224	1.15178
$833$	−28.9019	−1.00139
$834$	0.636313	0.0220337
$835$	3.94123	0.136392
$836$	58.4400	2.02119
$837$	−1.32519	−0.0458053
$838$	−10.5845	−0.365636
$839$	−17.8511	−0.616290	−0.308145	−	0.951339i	$-0.599708\pi$
$839$	−17.8511	−0.616290	−0.308145	+	0.951339i	$0.599708\pi$
$840$	−1.26838	−0.0437632
$841$	−23.5504	−0.812084
$842$	27.6656	0.953421
$843$	0.343994	0.0118478
$844$	−43.6706	−1.50320
$845$	−14.9615	−0.514692
$846$	14.8252	0.509701
$847$	−17.4495	−0.599571
$848$	16.4098	0.563516
$849$	0.194512	0.00667563
$850$	3.20157	0.109813
$851$	0.991105	0.0339746
$852$	−0.0520810	−0.00178427
$853$	−15.8929	−0.544163	−0.272081	−	0.962274i	$-0.587712\pi$
$853$	−15.8929	−0.544163	−0.272081	+	0.962274i	$0.587712\pi$
$854$	−14.9584	−0.511865
$855$	25.1560	0.860316
$856$	−90.5236	−3.09403
$857$	30.3569	1.03697	0.518487	−	0.855086i	$-0.326496\pi$
$857$	30.3569	1.03697	0.518487	+	0.855086i	$0.326496\pi$
$858$	1.29036	0.0440522
$859$	−32.0070	−1.09207	−0.546033	−	0.837764i	$-0.683863\pi$
$859$	−32.0070	−1.09207	−0.546033	+	0.837764i	$0.683863\pi$
$860$	11.7622	0.401088
$861$	0.0513997	0.00175170
$862$	55.4817	1.88971
$863$	19.4936	0.663569	0.331785	−	0.943355i	$-0.392349\pi$
$863$	19.4936	0.663569	0.331785	+	0.943355i	$0.392349\pi$
$864$	0.0691471	0.00235243
$865$	−1.60139	−0.0544489
$866$	−1.44829	−0.0492148
$867$	0.0844813	0.00286914
$868$	−109.382	−3.71266
$869$	10.6037	0.359706
$870$	−0.395390	−0.0134050
$871$	−8.09053	−0.274137
$872$	−62.6981	−2.12323
$873$	13.5443	0.458405
$874$	−3.88824	−0.131522
$875$	−39.7787	−1.34477
$876$	1.05628	0.0356883
$877$	−19.1594	−0.646969	−0.323484	−	0.946234i	$-0.604854\pi$
$877$	−19.1594	−0.646969	−0.323484	+	0.946234i	$0.604854\pi$
$878$	−17.9099	−0.604429
$879$	0.0284154	0.000958427 0
$880$	−38.6584	−1.30318
$881$	42.9793	1.44801	0.724005	−	0.689795i	$-0.242299\pi$
$881$	42.9793	1.44801	0.724005	+	0.689795i	$0.242299\pi$
$882$	47.8456	1.61105
$883$	57.0739	1.92069	0.960344	−	0.278817i	$-0.0899421\pi$
$883$	57.0739	1.92069	0.960344	+	0.278817i	$0.0899421\pi$
$884$	79.4061	2.67072
$885$	0.361060	0.0121369
$886$	−45.6838	−1.53478
$887$	38.7172	1.30000	0.649998	−	0.759935i	$-0.274770\pi$
$887$	38.7172	1.30000	0.649998	+	0.759935i	$0.274770\pi$
$888$	−0.342791	−0.0115033
$889$	44.5042	1.49262
$890$	66.3885	2.22535
$891$	35.6862	1.19553
$892$	35.3364	1.18315
$893$	7.33413	0.245427
$894$	−0.943422	−0.0315528
$895$	58.8403	1.96681
$896$	−70.7292	−2.36290
$897$	−0.0574189	−0.00191716
$898$	7.28904	0.243238
$899$	−17.2123	−0.574063
$900$	−3.54470	−0.118157
$901$	−17.2542	−0.574820
$902$	4.55524	0.151673
$903$	0.139308	0.00463588
$904$	−43.1506	−1.43517
$905$	−49.3749	−1.64128
$906$	−0.589124	−0.0195723
$907$	42.2984	1.40449	0.702247	−	0.711933i	$-0.252180\pi$
$907$	42.2984	1.40449	0.702247	+	0.711933i	$0.252180\pi$
$908$	42.5645	1.41255
$909$	−31.0939	−1.03132
$910$	91.7071	3.04006
$911$	5.18769	0.171876	0.0859379	−	0.996300i	$-0.472611\pi$
$911$	5.18769	0.171876	0.0859379	+	0.996300i	$0.472611\pi$
$912$	0.462495	0.0153148
$913$	−3.48800	−0.115436
$914$	24.2419	0.801850
$915$	0.114220	0.00377601
$916$	−99.9818	−3.30349
$917$	−0.864099	−0.0285351
$918$	−1.96628	−0.0648968
$919$	−22.7782	−0.751385	−0.375692	−	0.926744i	$-0.622595\pi$
$919$	−22.7782	−0.751385	−0.375692	+	0.926744i	$0.622595\pi$
$920$	5.00199	0.164911
$921$	−0.869510	−0.0286513
$922$	−56.6963	−1.86719
$923$	1.90087	0.0625678
$924$	−1.76388	−0.0580273
$925$	0.668333	0.0219747
$926$	−31.5879	−1.03804
$927$	14.8209	0.486782
$928$	0.898121	0.0294823
$929$	−32.2505	−1.05811	−0.529053	−	0.848589i	$-0.677453\pi$
$929$	−32.2505	−1.05811	−0.529053	+	0.848589i	$0.677453\pi$
$930$	1.24883	0.0409507
$931$	23.6696	0.775738
$932$	6.84397	0.224182
$933$	0.267051	0.00874285
$934$	102.159	3.34274
$935$	40.6476	1.32932
$936$	−66.3571	−2.16895
$937$	23.0020	0.751441	0.375721	−	0.926733i	$-0.377395\pi$
$937$	23.0020	0.751441	0.375721	+	0.926733i	$0.377395\pi$
$938$	16.5361	0.539924
$939$	−0.270537	−0.00882865
$940$	−18.6905	−0.609615
$941$	−44.0625	−1.43640	−0.718198	−	0.695839i	$-0.755033\pi$
$941$	−44.0625	−1.43640	−0.718198	+	0.695839i	$0.755033\pi$
$942$	1.30867	0.0426388
$943$	−0.202700	−0.00660083
$944$	−22.1803	−0.721909
$945$	−1.51878	−0.0494059
$946$	12.3460	0.401403
$947$	27.2627	0.885918	0.442959	−	0.896542i	$-0.353929\pi$
$947$	27.2627	0.885918	0.442959	+	0.896542i	$0.353929\pi$
$948$	0.323290	0.0105000
$949$	−38.5523	−1.25146
$950$	−2.62196	−0.0850678
$951$	−0.475821	−0.0154296
$952$	−81.9274	−2.65528
$953$	5.41403	0.175378	0.0876888	−	0.996148i	$-0.472052\pi$
$953$	5.41403	0.175378	0.0876888	+	0.996148i	$0.472052\pi$
$954$	28.5634	0.924773
$955$	−5.58510	−0.180730
$956$	1.95255	0.0631498
$957$	−0.277564	−0.00897237
$958$	−18.6333	−0.602016
$959$	72.3964	2.33780
$960$	0.518498	0.0167344
$961$	23.3647	0.753700
$962$	24.7847	0.799090
$963$	−54.1891	−1.74622
$964$	14.0125	0.451312
$965$	39.2949	1.26495
$966$	0.117358	0.00377592
$967$	0.766053	0.0246346	0.0123173	−	0.999924i	$-0.496079\pi$
$967$	0.766053	0.0246346	0.0123173	+	0.999924i	$0.496079\pi$
$968$	−23.8005	−0.764977
$969$	−0.486293	−0.0156220
$970$	−25.5314	−0.819765
$971$	−42.5788	−1.36642	−0.683209	−	0.730223i	$-0.739416\pi$
$971$	−42.5788	−1.36642	−0.683209	+	0.730223i	$0.739416\pi$
$972$	3.26568	0.104747
$973$	31.7468	1.01776
$974$	22.8723	0.732875
$975$	−0.0387194	−0.00124001
$976$	−7.01670	−0.224599
$977$	−15.5492	−0.497461	−0.248731	−	0.968573i	$-0.580013\pi$
$977$	−15.5492	−0.497461	−0.248731	+	0.968573i	$0.580013\pi$
$978$	0.849149	0.0271528
$979$	46.6048	1.48949
$980$	−60.3200	−1.92685
$981$	−37.5323	−1.19831
$982$	97.6482	3.11608
$983$	−30.8689	−0.984566	−0.492283	−	0.870435i	$-0.663838\pi$
$983$	−30.8689	−0.984566	−0.492283	+	0.870435i	$0.663838\pi$
$984$	0.0701074	0.00223494
$985$	−56.0326	−1.78535
$986$	−25.5391	−0.813330
$987$	−0.221364	−0.00704609
$988$	−65.0305	−2.06890
$989$	−0.549376	−0.0174692
$990$	−67.2899	−2.13861
$991$	34.5400	1.09720	0.548600	−	0.836085i	$-0.315161\pi$
$991$	34.5400	1.09720	0.548600	+	0.836085i	$0.315161\pi$
$992$	−2.83669	−0.0900651
$993$	0.376266	0.0119404
$994$	−3.88516	−0.123230
$995$	21.5905	0.684464
$996$	−0.106344	−0.00336962
$997$	−53.6381	−1.69873	−0.849367	−	0.527802i	$-0.823016\pi$
$997$	−53.6381	−1.69873	−0.849367	+	0.527802i	$0.823016\pi$
$998$	100.264	3.17381
$999$	−0.410463	−0.0129865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.a.1.19	✓	217

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.a.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-2.45739 q^{2} +0.0299595 q^{3} +4.03876 q^{4} -2.30057 q^{5} -0.0736221 q^{6} -3.67314 q^{7} -5.01004 q^{8} -2.99910 q^{9} +O(q^{10})\)	\(q-2.45739 q^{2} +0.0299595 q^{3} +4.03876 q^{4} -2.30057 q^{5} -0.0736221 q^{6} -3.67314 q^{7} -5.01004 q^{8} -2.99910 q^{9} +5.65341 q^{10} +3.96870 q^{11} +0.120999 q^{12} -4.41626 q^{13} +9.02634 q^{14} -0.0689240 q^{15} +4.23409 q^{16} -4.45195 q^{17} +7.36996 q^{18} +3.64597 q^{19} -9.29148 q^{20} -0.110045 q^{21} -9.75264 q^{22} +0.433976 q^{23} -0.150098 q^{24} +0.292644 q^{25} +10.8525 q^{26} -0.179730 q^{27} -14.8350 q^{28} -2.33443 q^{29} +0.169373 q^{30} +7.37324 q^{31} -0.384728 q^{32} +0.118900 q^{33} +10.9402 q^{34} +8.45034 q^{35} -12.1127 q^{36} +2.28378 q^{37} -8.95958 q^{38} -0.132309 q^{39} +11.5260 q^{40} -0.467077 q^{41} +0.270424 q^{42} -1.26591 q^{43} +16.0286 q^{44} +6.89966 q^{45} -1.06645 q^{46} +2.01157 q^{47} +0.126851 q^{48} +6.49197 q^{49} -0.719140 q^{50} -0.133378 q^{51} -17.8362 q^{52} +3.87564 q^{53} +0.441666 q^{54} -9.13028 q^{55} +18.4026 q^{56} +0.109231 q^{57} +5.73660 q^{58} -5.23852 q^{59} -0.278368 q^{60} -1.65719 q^{61} -18.1189 q^{62} +11.0161 q^{63} -7.52275 q^{64} +10.1599 q^{65} -0.292184 q^{66} +1.83199 q^{67} -17.9804 q^{68} +0.0130017 q^{69} -20.7658 q^{70} -0.430424 q^{71} +15.0256 q^{72} +8.72962 q^{73} -5.61213 q^{74} +0.00876745 q^{75} +14.7252 q^{76} -14.5776 q^{77} +0.325135 q^{78} +2.67184 q^{79} -9.74084 q^{80} +8.99192 q^{81} +1.14779 q^{82} -0.878878 q^{83} -0.444447 q^{84} +10.2420 q^{85} +3.11084 q^{86} -0.0699383 q^{87} -19.8833 q^{88} +11.7431 q^{89} -16.9552 q^{90} +16.2216 q^{91} +1.75273 q^{92} +0.220898 q^{93} -4.94321 q^{94} -8.38783 q^{95} -0.0115262 q^{96} -4.51612 q^{97} -15.9533 q^{98} -11.9025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) \) 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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