LMFDB - Embedded newform 6041.2.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$112$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52776 q^{2} +3.15958 q^{3} +4.38957 q^{4} +3.22941 q^{5} -7.98667 q^{6} -1.00000 q^{7} -6.04026 q^{8} +6.98297 q^{9} +O(q^{10})$	\(q-2.52776 q^{2} +3.15958 q^{3} +4.38957 q^{4} +3.22941 q^{5} -7.98667 q^{6} -1.00000 q^{7} -6.04026 q^{8} +6.98297 q^{9} -8.16316 q^{10} +5.38286 q^{11} +13.8692 q^{12} +0.253460 q^{13} +2.52776 q^{14} +10.2036 q^{15} +6.48918 q^{16} +5.79170 q^{17} -17.6513 q^{18} -4.98436 q^{19} +14.1757 q^{20} -3.15958 q^{21} -13.6066 q^{22} +2.36308 q^{23} -19.0847 q^{24} +5.42907 q^{25} -0.640685 q^{26} +12.5845 q^{27} -4.38957 q^{28} -2.75487 q^{29} -25.7922 q^{30} -4.63610 q^{31} -4.32257 q^{32} +17.0076 q^{33} -14.6400 q^{34} -3.22941 q^{35} +30.6522 q^{36} -7.17507 q^{37} +12.5993 q^{38} +0.800827 q^{39} -19.5064 q^{40} +2.62147 q^{41} +7.98667 q^{42} -9.96807 q^{43} +23.6284 q^{44} +22.5508 q^{45} -5.97330 q^{46} +8.26585 q^{47} +20.5031 q^{48} +1.00000 q^{49} -13.7234 q^{50} +18.2993 q^{51} +1.11258 q^{52} +2.84491 q^{53} -31.8106 q^{54} +17.3834 q^{55} +6.04026 q^{56} -15.7485 q^{57} +6.96366 q^{58} +0.549950 q^{59} +44.7893 q^{60} +9.01997 q^{61} +11.7189 q^{62} -6.98297 q^{63} -2.05194 q^{64} +0.818525 q^{65} -42.9911 q^{66} +3.37981 q^{67} +25.4230 q^{68} +7.46635 q^{69} +8.16316 q^{70} +8.92620 q^{71} -42.1789 q^{72} -4.87479 q^{73} +18.1369 q^{74} +17.1536 q^{75} -21.8792 q^{76} -5.38286 q^{77} -2.02430 q^{78} +3.91997 q^{79} +20.9562 q^{80} +18.8129 q^{81} -6.62645 q^{82} -12.8724 q^{83} -13.8692 q^{84} +18.7037 q^{85} +25.1969 q^{86} -8.70425 q^{87} -32.5139 q^{88} -10.9835 q^{89} -57.0031 q^{90} -0.253460 q^{91} +10.3729 q^{92} -14.6481 q^{93} -20.8941 q^{94} -16.0965 q^{95} -13.6575 q^{96} +4.26295 q^{97} -2.52776 q^{98} +37.5884 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) $ 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * 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 $

$2$	−2.52776	−1.78740	−0.893698	−	0.448669i	$-0.851898\pi$
$2$	−2.52776	−1.78740	−0.893698	+	0.448669i	$0.851898\pi$
$3$	3.15958	1.82419	0.912093	−	0.409983i	$-0.134465\pi$
$3$	3.15958	1.82419	0.912093	+	0.409983i	$0.134465\pi$
$4$	4.38957	2.19478
$5$	3.22941	1.44423	0.722117	−	0.691771i	$-0.243169\pi$
$5$	3.22941	1.44423	0.722117	+	0.691771i	$0.243169\pi$
$6$	−7.98667	−3.26054
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.04026	−2.13555
$9$	6.98297	2.32766
$10$	−8.16316	−2.58142
$11$	5.38286	1.62299	0.811497	−	0.584357i	$-0.198653\pi$
$11$	5.38286	1.62299	0.811497	+	0.584357i	$0.198653\pi$
$12$	13.8692	4.00370
$13$	0.253460	0.0702971	0.0351485	−	0.999382i	$-0.488810\pi$
$13$	0.253460	0.0702971	0.0351485	+	0.999382i	$0.488810\pi$
$14$	2.52776	0.675572
$15$	10.2036	2.63455
$16$	6.48918	1.62229
$17$	5.79170	1.40469	0.702346	−	0.711835i	$-0.252136\pi$
$17$	5.79170	1.40469	0.702346	+	0.711835i	$0.252136\pi$
$18$	−17.6513	−4.16044
$19$	−4.98436	−1.14349	−0.571745	−	0.820431i	$-0.693733\pi$
$19$	−4.98436	−1.14349	−0.571745	+	0.820431i	$0.693733\pi$
$20$	14.1757	3.16978
$21$	−3.15958	−0.689478
$22$	−13.6066	−2.90093
$23$	2.36308	0.492736	0.246368	−	0.969176i	$-0.420763\pi$
$23$	2.36308	0.492736	0.246368	+	0.969176i	$0.420763\pi$
$24$	−19.0847	−3.89565
$25$	5.42907	1.08581
$26$	−0.640685	−0.125649
$27$	12.5845	2.42189
$28$	−4.38957	−0.829551
$29$	−2.75487	−0.511567	−0.255784	−	0.966734i	$-0.582333\pi$
$29$	−2.75487	−0.511567	−0.255784	+	0.966734i	$0.582333\pi$
$30$	−25.7922	−4.70899
$31$	−4.63610	−0.832668	−0.416334	−	0.909212i	$-0.636685\pi$
$31$	−4.63610	−0.832668	−0.416334	+	0.909212i	$0.636685\pi$
$32$	−4.32257	−0.764130
$33$	17.0076	2.96064
$34$	−14.6400	−2.51074
$35$	−3.22941	−0.545869
$36$	30.6522	5.10870
$37$	−7.17507	−1.17957	−0.589787	−	0.807559i	$-0.700788\pi$
$37$	−7.17507	−1.17957	−0.589787	+	0.807559i	$0.700788\pi$
$38$	12.5993	2.04387
$39$	0.800827	0.128235
$40$	−19.5064	−3.08424
$41$	2.62147	0.409405	0.204702	−	0.978824i	$-0.434377\pi$
$41$	2.62147	0.409405	0.204702	+	0.978824i	$0.434377\pi$
$42$	7.98667	1.23237
$43$	−9.96807	−1.52012	−0.760058	−	0.649855i	$-0.774830\pi$
$43$	−9.96807	−1.52012	−0.760058	+	0.649855i	$0.774830\pi$
$44$	23.6284	3.56212
$45$	22.5508	3.36168
$46$	−5.97330	−0.880715
$47$	8.26585	1.20570	0.602849	−	0.797855i	$-0.294032\pi$
$47$	8.26585	1.20570	0.602849	+	0.797855i	$0.294032\pi$
$48$	20.5031	2.95937
$49$	1.00000	0.142857
$50$	−13.7234	−1.94078
$51$	18.2993	2.56242
$52$	1.11258	0.154287
$53$	2.84491	0.390779	0.195389	−	0.980726i	$-0.437403\pi$
$53$	2.84491	0.390779	0.195389	+	0.980726i	$0.437403\pi$
$54$	−31.8106	−4.32888
$55$	17.3834	2.34398
$56$	6.04026	0.807163
$57$	−15.7485	−2.08594
$58$	6.96366	0.914373
$59$	0.549950	0.0715974	0.0357987	−	0.999359i	$-0.488602\pi$
$59$	0.549950	0.0715974	0.0357987	+	0.999359i	$0.488602\pi$
$60$	44.7893	5.78228
$61$	9.01997	1.15489	0.577444	−	0.816430i	$-0.304050\pi$
$61$	9.01997	1.15489	0.577444	+	0.816430i	$0.304050\pi$
$62$	11.7189	1.48831
$63$	−6.98297	−0.879771
$64$	−2.05194	−0.256492
$65$	0.818525	0.101525
$66$	−42.9911	−5.29184
$67$	3.37981	0.412910	0.206455	−	0.978456i	$-0.433807\pi$
$67$	3.37981	0.412910	0.206455	+	0.978456i	$0.433807\pi$
$68$	25.4230	3.08300
$69$	7.46635	0.898843
$70$	8.16316	0.975685
$71$	8.92620	1.05934	0.529672	−	0.848202i	$-0.322315\pi$
$71$	8.92620	1.05934	0.529672	+	0.848202i	$0.322315\pi$
$72$	−42.1789	−4.97083
$73$	−4.87479	−0.570551	−0.285275	−	0.958446i	$-0.592085\pi$
$73$	−4.87479	−0.570551	−0.285275	+	0.958446i	$0.592085\pi$
$74$	18.1369	2.10837
$75$	17.1536	1.98073
$76$	−21.8792	−2.50971
$77$	−5.38286	−0.613434
$78$	−2.02430	−0.229207
$79$	3.91997	0.441031	0.220516	−	0.975383i	$-0.429226\pi$
$79$	3.91997	0.441031	0.220516	+	0.975383i	$0.429226\pi$
$80$	20.9562	2.34297
$81$	18.8129	2.09033
$82$	−6.62645	−0.731769
$83$	−12.8724	−1.41293	−0.706465	−	0.707748i	$-0.749711\pi$
$83$	−12.8724	−1.41293	−0.706465	+	0.707748i	$0.749711\pi$
$84$	−13.8692	−1.51325
$85$	18.7037	2.02871
$86$	25.1969	2.71705
$87$	−8.70425	−0.933194
$88$	−32.5139	−3.46599
$89$	−10.9835	−1.16425	−0.582123	−	0.813101i	$-0.697778\pi$
$89$	−10.9835	−1.16425	−0.582123	+	0.813101i	$0.697778\pi$
$90$	−57.0031	−6.00866
$91$	−0.253460	−0.0265698
$92$	10.3729	1.08145
$93$	−14.6481	−1.51894
$94$	−20.8941	−2.15506
$95$	−16.0965	−1.65147
$96$	−13.6575	−1.39392
$97$	4.26295	0.432837	0.216418	−	0.976301i	$-0.430562\pi$
$97$	4.26295	0.432837	0.216418	+	0.976301i	$0.430562\pi$
$98$	−2.52776	−0.255342
$99$	37.5884	3.77777
$100$	23.8313	2.38313
$101$	−2.25755	−0.224635	−0.112317	−	0.993672i	$-0.535827\pi$
$101$	−2.25755	−0.224635	−0.112317	+	0.993672i	$0.535827\pi$
$102$	−46.2563	−4.58006
$103$	1.10884	0.109258	0.0546288	−	0.998507i	$-0.482602\pi$
$103$	1.10884	0.109258	0.0546288	+	0.998507i	$0.482602\pi$
$104$	−1.53096	−0.150123
$105$	−10.2036	−0.995767
$106$	−7.19125	−0.698476
$107$	5.79698	0.560415	0.280208	−	0.959939i	$-0.409597\pi$
$107$	5.79698	0.560415	0.280208	+	0.959939i	$0.409597\pi$
$108$	55.2406	5.31553
$109$	−10.9505	−1.04887	−0.524433	−	0.851451i	$-0.675723\pi$
$109$	−10.9505	−1.04887	−0.524433	+	0.851451i	$0.675723\pi$
$110$	−43.9412	−4.18963
$111$	−22.6702	−2.15176
$112$	−6.48918	−0.613170
$113$	14.0277	1.31961	0.659807	−	0.751435i	$-0.270638\pi$
$113$	14.0277	1.31961	0.659807	+	0.751435i	$0.270638\pi$
$114$	39.8084	3.72840
$115$	7.63135	0.711627
$116$	−12.0927	−1.12278
$117$	1.76990	0.163627
$118$	−1.39014	−0.127973
$119$	−5.79170	−0.530924
$120$	−61.6322	−5.62623
$121$	17.9752	1.63411
$122$	−22.8003	−2.06424
$123$	8.28275	0.746831
$124$	−20.3505	−1.82753
$125$	1.38563	0.123934
$126$	17.6513	1.57250
$127$	−13.8049	−1.22499	−0.612495	−	0.790474i	$-0.709834\pi$
$127$	−13.8049	−1.22499	−0.612495	+	0.790474i	$0.709834\pi$
$128$	13.8319	1.22258
$129$	−31.4950	−2.77298
$130$	−2.06903	−0.181466
$131$	−20.2333	−1.76779	−0.883895	−	0.467686i	$-0.845088\pi$
$131$	−20.2333	−1.76779	−0.883895	+	0.467686i	$0.845088\pi$
$132$	74.6560	6.49797
$133$	4.98436	0.432199
$134$	−8.54335	−0.738033
$135$	40.6405	3.49778
$136$	−34.9833	−2.99980
$137$	−15.9387	−1.36173	−0.680867	−	0.732407i	$-0.738397\pi$
$137$	−15.9387	−1.36173	−0.680867	+	0.732407i	$0.738397\pi$
$138$	−18.8731	−1.60659
$139$	21.2580	1.80308	0.901541	−	0.432693i	$-0.142437\pi$
$139$	21.2580	1.80308	0.901541	+	0.432693i	$0.142437\pi$
$140$	−14.1757	−1.19807
$141$	26.1166	2.19942
$142$	−22.5633	−1.89347
$143$	1.36434	0.114092
$144$	45.3137	3.77614
$145$	−8.89661	−0.738823
$146$	12.3223	1.01980
$147$	3.15958	0.260598
$148$	−31.4955	−2.58891
$149$	20.1001	1.64666	0.823331	−	0.567562i	$-0.192113\pi$
$149$	20.1001	1.64666	0.823331	+	0.567562i	$0.192113\pi$
$150$	−43.3601	−3.54034
$151$	1.59793	0.130038	0.0650190	−	0.997884i	$-0.479289\pi$
$151$	1.59793	0.130038	0.0650190	+	0.997884i	$0.479289\pi$
$152$	30.1068	2.44198
$153$	40.4432	3.26964
$154$	13.6066	1.09645
$155$	−14.9719	−1.20257
$156$	3.51529	0.281448
$157$	−9.27502	−0.740227	−0.370114	−	0.928986i	$-0.620681\pi$
$157$	−9.27502	−0.740227	−0.370114	+	0.928986i	$0.620681\pi$
$158$	−9.90875	−0.788298
$159$	8.98873	0.712853
$160$	−13.9593	−1.10358
$161$	−2.36308	−0.186237
$162$	−47.5546	−3.73624
$163$	11.1324	0.871954	0.435977	−	0.899958i	$-0.356403\pi$
$163$	11.1324	0.871954	0.435977	+	0.899958i	$0.356403\pi$
$164$	11.5071	0.898555
$165$	54.9245	4.27586
$166$	32.5383	2.52546
$167$	10.3931	0.804241	0.402121	−	0.915587i	$-0.368273\pi$
$167$	10.3931	0.804241	0.402121	+	0.915587i	$0.368273\pi$
$168$	19.0847	1.47242
$169$	−12.9358	−0.995058
$170$	−47.2786	−3.62610
$171$	−34.8056	−2.66165
$172$	−43.7555	−3.33633
$173$	−12.9428	−0.984024	−0.492012	−	0.870588i	$-0.663738\pi$
$173$	−12.9428	−0.984024	−0.492012	+	0.870588i	$0.663738\pi$
$174$	22.0023	1.66799
$175$	−5.42907	−0.410399
$176$	34.9303	2.63297
$177$	1.73761	0.130607
$178$	27.7636	2.08097
$179$	−17.1070	−1.27864	−0.639320	−	0.768941i	$-0.720784\pi$
$179$	−17.1070	−1.27864	−0.639320	+	0.768941i	$0.720784\pi$
$180$	98.9885	7.37817
$181$	3.74570	0.278416	0.139208	−	0.990263i	$-0.455544\pi$
$181$	3.74570	0.278416	0.139208	+	0.990263i	$0.455544\pi$
$182$	0.640685	0.0474908
$183$	28.4993	2.10673
$184$	−14.2736	−1.05226
$185$	−23.1712	−1.70358
$186$	37.0270	2.71495
$187$	31.1759	2.27981
$188$	36.2835	2.64625
$189$	−12.5845	−0.915389
$190$	40.6881	2.95183
$191$	2.80970	0.203303	0.101651	−	0.994820i	$-0.467587\pi$
$191$	2.80970	0.203303	0.101651	+	0.994820i	$0.467587\pi$
$192$	−6.48327	−0.467890
$193$	−20.5942	−1.48240	−0.741200	−	0.671284i	$-0.765743\pi$
$193$	−20.5942	−1.48240	−0.741200	+	0.671284i	$0.765743\pi$
$194$	−10.7757	−0.773651
$195$	2.58620	0.185201
$196$	4.38957	0.313541
$197$	11.8095	0.841389	0.420694	−	0.907202i	$-0.361787\pi$
$197$	11.8095	0.841389	0.420694	+	0.907202i	$0.361787\pi$
$198$	−95.0143	−6.75237
$199$	15.5555	1.10270	0.551352	−	0.834273i	$-0.314112\pi$
$199$	15.5555	1.10270	0.551352	+	0.834273i	$0.314112\pi$
$200$	−32.7930	−2.31881
$201$	10.6788	0.753225
$202$	5.70655	0.401511
$203$	2.75487	0.193354
$204$	80.3262	5.62396
$205$	8.46579	0.591277
$206$	−2.80289	−0.195287
$207$	16.5013	1.14692
$208$	1.64475	0.114043
$209$	−26.8301	−1.85588
$210$	25.7922	1.77983
$211$	−11.5420	−0.794581	−0.397290	−	0.917693i	$-0.630049\pi$
$211$	−11.5420	−0.794581	−0.397290	+	0.917693i	$0.630049\pi$
$212$	12.4879	0.857675
$213$	28.2031	1.93244
$214$	−14.6534	−1.00168
$215$	−32.1910	−2.19541
$216$	−76.0137	−5.17208
$217$	4.63610	0.314719
$218$	27.6802	1.87474
$219$	−15.4023	−1.04079
$220$	76.3058	5.14454
$221$	1.46796	0.0987458
$222$	57.3049	3.84605
$223$	8.49022	0.568547	0.284274	−	0.958743i	$-0.408248\pi$
$223$	8.49022	0.568547	0.284274	+	0.958743i	$0.408248\pi$
$224$	4.32257	0.288814
$225$	37.9110	2.52740
$226$	−35.4586	−2.35867
$227$	11.5223	0.764761	0.382380	−	0.924005i	$-0.375104\pi$
$227$	11.5223	0.764761	0.382380	+	0.924005i	$0.375104\pi$
$228$	−69.1291	−4.57819
$229$	6.47381	0.427801	0.213901	−	0.976855i	$-0.431383\pi$
$229$	6.47381	0.427801	0.213901	+	0.976855i	$0.431383\pi$
$230$	−19.2902	−1.27196
$231$	−17.0076	−1.11902
$232$	16.6401	1.09248
$233$	−2.26396	−0.148317	−0.0741584	−	0.997246i	$-0.523627\pi$
$233$	−2.26396	−0.148317	−0.0741584	+	0.997246i	$0.523627\pi$
$234$	−4.47389	−0.292467
$235$	26.6938	1.74131
$236$	2.41404	0.157141
$237$	12.3855	0.804523
$238$	14.6400	0.948971
$239$	19.7413	1.27696	0.638481	−	0.769638i	$-0.279563\pi$
$239$	19.7413	1.27696	0.638481	+	0.769638i	$0.279563\pi$
$240$	66.2128	4.27402
$241$	−10.5332	−0.678505	−0.339252	−	0.940695i	$-0.610174\pi$
$241$	−10.5332	−0.678505	−0.339252	+	0.940695i	$0.610174\pi$
$242$	−45.4370	−2.92080
$243$	21.6875	1.39125
$244$	39.5938	2.53473
$245$	3.22941	0.206319
$246$	−20.9368	−1.33488
$247$	−1.26333	−0.0803840
$248$	28.0032	1.77821
$249$	−40.6714	−2.57745
$250$	−3.50254	−0.221520
$251$	30.9746	1.95510	0.977549	−	0.210707i	$-0.0675766\pi$
$251$	30.9746	1.95510	0.977549	+	0.210707i	$0.0675766\pi$
$252$	−30.6522	−1.93091
$253$	12.7201	0.799708
$254$	34.8956	2.18954
$255$	59.0960	3.70074
$256$	−30.8600	−1.92875
$257$	14.2875	0.891227	0.445613	−	0.895226i	$-0.352986\pi$
$257$	14.2875	0.891227	0.445613	+	0.895226i	$0.352986\pi$
$258$	79.6117	4.95641
$259$	7.17507	0.445837
$260$	3.59297	0.222827
$261$	−19.2372	−1.19075
$262$	51.1449	3.15974
$263$	17.2643	1.06456	0.532282	−	0.846567i	$-0.321335\pi$
$263$	17.2643	1.06456	0.532282	+	0.846567i	$0.321335\pi$
$264$	−102.730	−6.32261
$265$	9.18737	0.564376
$266$	−12.5993	−0.772510
$267$	−34.7032	−2.12380
$268$	14.8359	0.906248
$269$	−27.6898	−1.68828	−0.844138	−	0.536126i	$-0.819887\pi$
$269$	−27.6898	−1.68828	−0.844138	+	0.536126i	$0.819887\pi$
$270$	−102.730	−6.25192
$271$	−23.9991	−1.45784	−0.728922	−	0.684597i	$-0.759978\pi$
$271$	−23.9991	−1.45784	−0.728922	+	0.684597i	$0.759978\pi$
$272$	37.5833	2.27882
$273$	−0.800827	−0.0484683
$274$	40.2892	2.43396
$275$	29.2239	1.76227
$276$	32.7741	1.97277
$277$	31.8520	1.91380	0.956899	−	0.290421i	$-0.0937952\pi$
$277$	31.8520	1.91380	0.956899	+	0.290421i	$0.0937952\pi$
$278$	−53.7352	−3.22282
$279$	−32.3737	−1.93817
$280$	19.5064	1.16573
$281$	−14.2533	−0.850282	−0.425141	−	0.905127i	$-0.639775\pi$
$281$	−14.2533	−0.850282	−0.425141	+	0.905127i	$0.639775\pi$
$282$	−66.0166	−3.93123
$283$	−15.7319	−0.935166	−0.467583	−	0.883949i	$-0.654875\pi$
$283$	−15.7319	−0.935166	−0.467583	+	0.883949i	$0.654875\pi$
$284$	39.1822	2.32503
$285$	−50.8583	−3.01259
$286$	−3.44872	−0.203927
$287$	−2.62147	−0.154740
$288$	−30.1844	−1.77863
$289$	16.5437	0.973161
$290$	22.4885	1.32057
$291$	13.4691	0.789575
$292$	−21.3982	−1.25224
$293$	−25.6655	−1.49939	−0.749697	−	0.661781i	$-0.769801\pi$
$293$	−25.6655	−1.49939	−0.749697	+	0.661781i	$0.769801\pi$
$294$	−7.98667	−0.465792
$295$	1.77601	0.103403
$296$	43.3393	2.51904
$297$	67.7407	3.93072
$298$	−50.8081	−2.94324
$299$	0.598946	0.0346379
$300$	75.2969	4.34727
$301$	9.96807	0.574550
$302$	−4.03919	−0.232429
$303$	−7.13292	−0.409776
$304$	−32.3444	−1.85508
$305$	29.1291	1.66793
$306$	−102.231	−5.84414
$307$	−22.0015	−1.25569	−0.627846	−	0.778338i	$-0.716063\pi$
$307$	−22.0015	−1.25569	−0.627846	+	0.778338i	$0.716063\pi$
$308$	−23.6284	−1.34636
$309$	3.50348	0.199306
$310$	37.8453	2.14947
$311$	−5.64303	−0.319987	−0.159994	−	0.987118i	$-0.551147\pi$
$311$	−5.64303	−0.319987	−0.159994	+	0.987118i	$0.551147\pi$
$312$	−4.83720	−0.273853
$313$	−16.5913	−0.937794	−0.468897	−	0.883253i	$-0.655348\pi$
$313$	−16.5913	−0.937794	−0.468897	+	0.883253i	$0.655348\pi$
$314$	23.4450	1.32308
$315$	−22.5508	−1.27060
$316$	17.2070	0.967969
$317$	−10.5355	−0.591731	−0.295865	−	0.955230i	$-0.595608\pi$
$317$	−10.5355	−0.591731	−0.295865	+	0.955230i	$0.595608\pi$
$318$	−22.7214	−1.27415
$319$	−14.8291	−0.830270
$320$	−6.62654	−0.370435
$321$	18.3160	1.02230
$322$	5.97330	0.332879
$323$	−28.8679	−1.60625
$324$	82.5807	4.58782
$325$	1.37605	0.0763295
$326$	−28.1399	−1.55853
$327$	−34.5990	−1.91333
$328$	−15.8343	−0.874306
$329$	−8.26585	−0.455711
$330$	−138.836	−7.64266
$331$	−12.3031	−0.676237	−0.338119	−	0.941103i	$-0.609791\pi$
$331$	−12.3031	−0.676237	−0.338119	+	0.941103i	$0.609791\pi$
$332$	−56.5043	−3.10107
$333$	−50.1033	−2.74564
$334$	−26.2712	−1.43750
$335$	10.9148	0.596339
$336$	−20.5031	−1.11854
$337$	−27.9957	−1.52502	−0.762510	−	0.646976i	$-0.776033\pi$
$337$	−27.9957	−1.52502	−0.762510	+	0.646976i	$0.776033\pi$
$338$	32.6985	1.77856
$339$	44.3216	2.40722
$340$	82.1014	4.45257
$341$	−24.9555	−1.35142
$342$	87.9802	4.75743
$343$	−1.00000	−0.0539949
$344$	60.2097	3.24629
$345$	24.1119	1.29814
$346$	32.7163	1.75884
$347$	−36.1434	−1.94028	−0.970138	−	0.242552i	$-0.922016\pi$
$347$	−36.1434	−1.94028	−0.970138	+	0.242552i	$0.922016\pi$
$348$	−38.2079	−2.04816
$349$	11.8099	0.632170	0.316085	−	0.948731i	$-0.397632\pi$
$349$	11.8099	0.632170	0.316085	+	0.948731i	$0.397632\pi$
$350$	13.7234	0.733545
$351$	3.18967	0.170252
$352$	−23.2678	−1.24018
$353$	−17.0394	−0.906917	−0.453458	−	0.891277i	$-0.649810\pi$
$353$	−17.0394	−0.906917	−0.453458	+	0.891277i	$0.649810\pi$
$354$	−4.39227	−0.233446
$355$	28.8263	1.52994
$356$	−48.2127	−2.55527
$357$	−18.2993	−0.968504
$358$	43.2425	2.28544
$359$	4.04369	0.213418	0.106709	−	0.994290i	$-0.465969\pi$
$359$	4.04369	0.213418	0.106709	+	0.994290i	$0.465969\pi$
$360$	−136.213	−7.17905
$361$	5.84383	0.307570
$362$	−9.46823	−0.497639
$363$	56.7941	2.98092
$364$	−1.11258	−0.0583150
$365$	−15.7427	−0.824009
$366$	−72.0395	−3.76556
$367$	36.7623	1.91898	0.959488	−	0.281751i	$-0.0909151\pi$
$367$	36.7623	1.91898	0.959488	+	0.281751i	$0.0909151\pi$
$368$	15.3344	0.799363
$369$	18.3056	0.952954
$370$	58.5713	3.04498
$371$	−2.84491	−0.147700
$372$	−64.2991	−3.33375
$373$	11.9160	0.616987	0.308493	−	0.951227i	$-0.400175\pi$
$373$	11.9160	0.616987	0.308493	+	0.951227i	$0.400175\pi$
$374$	−78.8052	−4.07492
$375$	4.37801	0.226080
$376$	−49.9278	−2.57483
$377$	−0.698250	−0.0359617
$378$	31.8106	1.63616
$379$	−19.7930	−1.01670	−0.508348	−	0.861152i	$-0.669744\pi$
$379$	−19.7930	−1.01670	−0.508348	+	0.861152i	$0.669744\pi$
$380$	−70.6568	−3.62462
$381$	−43.6179	−2.23461
$382$	−7.10224	−0.363382
$383$	−28.9871	−1.48117	−0.740586	−	0.671961i	$-0.765452\pi$
$383$	−28.9871	−1.48117	−0.740586	+	0.671961i	$0.765452\pi$
$384$	43.7032	2.23022
$385$	−17.3834	−0.885943
$386$	52.0571	2.64964
$387$	−69.6067	−3.53831
$388$	18.7125	0.949984
$389$	10.9761	0.556510	0.278255	−	0.960507i	$-0.410244\pi$
$389$	10.9761	0.556510	0.278255	+	0.960507i	$0.410244\pi$
$390$	−6.53728	−0.331028
$391$	13.6862	0.692143
$392$	−6.04026	−0.305079
$393$	−63.9287	−3.22478
$394$	−29.8515	−1.50389
$395$	12.6592	0.636953
$396$	164.997	8.29139
$397$	−1.86844	−0.0937745	−0.0468873	−	0.998900i	$-0.514930\pi$
$397$	−1.86844	−0.0937745	−0.0468873	+	0.998900i	$0.514930\pi$
$398$	−39.3207	−1.97097
$399$	15.7485	0.788411
$400$	35.2302	1.76151
$401$	2.84641	0.142143	0.0710716	−	0.997471i	$-0.477358\pi$
$401$	2.84641	0.142143	0.0710716	+	0.997471i	$0.477358\pi$
$402$	−26.9934	−1.34631
$403$	−1.17507	−0.0585342
$404$	−9.90968	−0.493025
$405$	60.7546	3.01892
$406$	−6.96366	−0.345601
$407$	−38.6224	−1.91444
$408$	−110.533	−5.47219
$409$	−29.7712	−1.47209	−0.736047	−	0.676931i	$-0.763310\pi$
$409$	−29.7712	−1.47209	−0.736047	+	0.676931i	$0.763310\pi$
$410$	−21.3995	−1.05685
$411$	−50.3596	−2.48406
$412$	4.86734	0.239797
$413$	−0.549950	−0.0270613
$414$	−41.7114	−2.05000
$415$	−41.5702	−2.04060
$416$	−1.09560	−0.0537161
$417$	67.1665	3.28916
$418$	67.8201	3.31719
$419$	34.6708	1.69378	0.846891	−	0.531767i	$-0.178472\pi$
$419$	34.6708	1.69378	0.846891	+	0.531767i	$0.178472\pi$
$420$	−44.7893	−2.18549
$421$	−27.6593	−1.34803	−0.674016	−	0.738717i	$-0.735432\pi$
$421$	−27.6593	−1.34803	−0.674016	+	0.738717i	$0.735432\pi$
$422$	29.1753	1.42023
$423$	57.7202	2.80645
$424$	−17.1840	−0.834528
$425$	31.4435	1.52523
$426$	−71.2906	−3.45404
$427$	−9.01997	−0.436507
$428$	25.4462	1.22999
$429$	4.31074	0.208125
$430$	81.3710	3.92406
$431$	−21.8390	−1.05195	−0.525975	−	0.850500i	$-0.676299\pi$
$431$	−21.8390	−1.05195	−0.525975	+	0.850500i	$0.676299\pi$
$432$	81.6632	3.92902
$433$	17.4315	0.837704	0.418852	−	0.908054i	$-0.362433\pi$
$433$	17.4315	0.837704	0.418852	+	0.908054i	$0.362433\pi$
$434$	−11.7189	−0.562528
$435$	−28.1096	−1.34775
$436$	−48.0679	−2.30204
$437$	−11.7784	−0.563439
$438$	38.9333	1.86031
$439$	21.2008	1.01186	0.505929	−	0.862575i	$-0.331150\pi$
$439$	21.2008	1.01186	0.505929	+	0.862575i	$0.331150\pi$
$440$	−105.000	−5.00570
$441$	6.98297	0.332522
$442$	−3.71065	−0.176498
$443$	14.7042	0.698618	0.349309	−	0.937008i	$-0.386416\pi$
$443$	14.7042	0.698618	0.349309	+	0.937008i	$0.386416\pi$
$444$	−99.5126	−4.72266
$445$	−35.4701	−1.68144
$446$	−21.4612	−1.01622
$447$	63.5079	3.00382
$448$	2.05194	0.0969449
$449$	38.2511	1.80518	0.902591	−	0.430500i	$-0.141663\pi$
$449$	38.2511	1.80518	0.902591	+	0.430500i	$0.141663\pi$
$450$	−95.8299	−4.51746
$451$	14.1110	0.664461
$452$	61.5755	2.89627
$453$	5.04881	0.237214
$454$	−29.1256	−1.36693
$455$	−0.818525	−0.0383730
$456$	95.1250	4.45463
$457$	−6.23318	−0.291576	−0.145788	−	0.989316i	$-0.546572\pi$
$457$	−6.23318	−0.291576	−0.145788	+	0.989316i	$0.546572\pi$
$458$	−16.3642	−0.764650
$459$	72.8857	3.40201
$460$	33.4983	1.56187
$461$	3.87166	0.180321	0.0901606	−	0.995927i	$-0.471262\pi$
$461$	3.87166	0.180321	0.0901606	+	0.995927i	$0.471262\pi$
$462$	42.9911	2.00013
$463$	−20.1859	−0.938118	−0.469059	−	0.883167i	$-0.655407\pi$
$463$	−20.1859	−0.938118	−0.469059	+	0.883167i	$0.655407\pi$
$464$	−17.8769	−0.829913
$465$	−47.3048	−2.19371
$466$	5.72274	0.265101
$467$	2.35207	0.108841	0.0544204	−	0.998518i	$-0.482669\pi$
$467$	2.35207	0.108841	0.0544204	+	0.998518i	$0.482669\pi$
$468$	7.76910	0.359127
$469$	−3.37981	−0.156065
$470$	−67.4755	−3.11241
$471$	−29.3052	−1.35031
$472$	−3.32184	−0.152900
$473$	−53.6568	−2.46714
$474$	−31.3075	−1.43800
$475$	−27.0604	−1.24162
$476$	−25.4230	−1.16526
$477$	19.8659	0.909598
$478$	−49.9014	−2.28244
$479$	34.2447	1.56468	0.782340	−	0.622852i	$-0.214026\pi$
$479$	34.2447	1.56468	0.782340	+	0.622852i	$0.214026\pi$
$480$	−44.1057	−2.01314
$481$	−1.81859	−0.0829206
$482$	26.6255	1.21276
$483$	−7.46635	−0.339731
$484$	78.9034	3.58652
$485$	13.7668	0.625118
$486$	−54.8208	−2.48672
$487$	10.7645	0.487787	0.243893	−	0.969802i	$-0.421575\pi$
$487$	10.7645	0.487787	0.243893	+	0.969802i	$0.421575\pi$
$488$	−54.4829	−2.46633
$489$	35.1736	1.59061
$490$	−8.16316	−0.368774
$491$	−34.2949	−1.54771	−0.773854	−	0.633364i	$-0.781674\pi$
$491$	−34.2949	−1.54771	−0.773854	+	0.633364i	$0.781674\pi$
$492$	36.3577	1.63913
$493$	−15.9554	−0.718595
$494$	3.19341	0.143678
$495$	121.388	5.45599
$496$	−30.0845	−1.35083
$497$	−8.92620	−0.400395
$498$	102.808	4.60692
$499$	12.9588	0.580117	0.290058	−	0.957009i	$-0.406325\pi$
$499$	12.9588	0.580117	0.290058	+	0.957009i	$0.406325\pi$
$500$	6.08232	0.272009
$501$	32.8378	1.46709
$502$	−78.2963	−3.49454
$503$	−16.2918	−0.726418	−0.363209	−	0.931708i	$-0.618319\pi$
$503$	−16.2918	−0.726418	−0.363209	+	0.931708i	$0.618319\pi$
$504$	42.1789	1.87880
$505$	−7.29055	−0.324425
$506$	−32.1534	−1.42939
$507$	−40.8716	−1.81517
$508$	−60.5977	−2.68859
$509$	18.2585	0.809292	0.404646	−	0.914473i	$-0.367395\pi$
$509$	18.2585	0.809292	0.404646	+	0.914473i	$0.367395\pi$
$510$	−149.381	−6.61468
$511$	4.87479	0.215648
$512$	50.3427	2.22485
$513$	−62.7258	−2.76941
$514$	−36.1152	−1.59297
$515$	3.58090	0.157794
$516$	−138.249	−6.08609
$517$	44.4939	1.95684
$518$	−18.1369	−0.796888
$519$	−40.8939	−1.79504
$520$	−4.94410	−0.216813
$521$	5.34906	0.234346	0.117173	−	0.993111i	$-0.462617\pi$
$521$	5.34906	0.234346	0.117173	+	0.993111i	$0.462617\pi$
$522$	48.6270	2.12835
$523$	−20.9719	−0.917035	−0.458518	−	0.888685i	$-0.651619\pi$
$523$	−20.9719	−0.917035	−0.458518	+	0.888685i	$0.651619\pi$
$524$	−88.8154	−3.87992
$525$	−17.1536	−0.748644
$526$	−43.6400	−1.90280
$527$	−26.8509	−1.16964
$528$	110.365	4.80304
$529$	−17.4159	−0.757211
$530$	−23.2235	−1.00876
$531$	3.84028	0.166654
$532$	21.8792	0.948583
$533$	0.664437	0.0287800
$534$	87.7214	3.79608
$535$	18.7208	0.809371
$536$	−20.4149	−0.881791
$537$	−54.0511	−2.33248
$538$	69.9931	3.01762
$539$	5.38286	0.231856
$540$	178.394	7.67687
$541$	6.36999	0.273867	0.136934	−	0.990580i	$-0.456275\pi$
$541$	6.36999	0.273867	0.136934	+	0.990580i	$0.456275\pi$
$542$	60.6641	2.60575
$543$	11.8348	0.507882
$544$	−25.0350	−1.07337
$545$	−35.3636	−1.51481
$546$	2.02430	0.0866320
$547$	9.43672	0.403485	0.201742	−	0.979439i	$-0.435340\pi$
$547$	9.43672	0.403485	0.201742	+	0.979439i	$0.435340\pi$
$548$	−69.9639	−2.98871
$549$	62.9862	2.68818
$550$	−73.8710	−3.14987
$551$	13.7313	0.584972
$552$	−45.0987	−1.91953
$553$	−3.91997	−0.166694
$554$	−80.5141	−3.42072
$555$	−73.2114	−3.10765
$556$	93.3136	3.95738
$557$	3.46552	0.146839	0.0734194	−	0.997301i	$-0.476609\pi$
$557$	3.46552	0.146839	0.0734194	+	0.997301i	$0.476609\pi$
$558$	81.8331	3.46427
$559$	−2.52651	−0.106860
$560$	−20.9562	−0.885561
$561$	98.5028	4.15879
$562$	36.0290	1.51979
$563$	2.37957	0.100287	0.0501435	−	0.998742i	$-0.484032\pi$
$563$	2.37957	0.100287	0.0501435	+	0.998742i	$0.484032\pi$
$564$	114.641	4.82725
$565$	45.3011	1.90583
$566$	39.7665	1.67151
$567$	−18.8129	−0.790069
$568$	−53.9165	−2.26229
$569$	37.3394	1.56535	0.782675	−	0.622431i	$-0.213855\pi$
$569$	37.3394	1.56535	0.782675	+	0.622431i	$0.213855\pi$
$570$	128.558	5.38468
$571$	32.7066	1.36873	0.684365	−	0.729140i	$-0.260079\pi$
$571$	32.7066	1.36873	0.684365	+	0.729140i	$0.260079\pi$
$572$	5.98886	0.250407
$573$	8.87748	0.370862
$574$	6.62645	0.276582
$575$	12.8293	0.535020
$576$	−14.3286	−0.597026
$577$	−34.8005	−1.44876	−0.724382	−	0.689399i	$-0.757875\pi$
$577$	−34.8005	−1.44876	−0.724382	+	0.689399i	$0.757875\pi$
$578$	−41.8186	−1.73942
$579$	−65.0690	−2.70417
$580$	−39.0523	−1.62156
$581$	12.8724	0.534037
$582$	−34.0468	−1.41128
$583$	15.3138	0.634231
$584$	29.4450	1.21844
$585$	5.71573	0.236316
$586$	64.8762	2.68001
$587$	22.0555	0.910330	0.455165	−	0.890407i	$-0.349580\pi$
$587$	22.0555	0.910330	0.455165	+	0.890407i	$0.349580\pi$
$588$	13.8692	0.571957
$589$	23.1080	0.952148
$590$	−4.48933	−0.184823
$591$	37.3129	1.53485
$592$	−46.5603	−1.91362
$593$	−18.4007	−0.755625	−0.377812	−	0.925882i	$-0.623324\pi$
$593$	−18.4007	−0.755625	−0.377812	+	0.925882i	$0.623324\pi$
$594$	−171.232	−7.02575
$595$	−18.7037	−0.766779
$596$	88.2306	3.61407
$597$	49.1490	2.01154
$598$	−1.51399	−0.0619117
$599$	6.92333	0.282880	0.141440	−	0.989947i	$-0.454827\pi$
$599$	6.92333	0.282880	0.141440	+	0.989947i	$0.454827\pi$
$600$	−103.612	−4.22995
$601$	27.6411	1.12750	0.563752	−	0.825944i	$-0.309357\pi$
$601$	27.6411	1.12750	0.563752	+	0.825944i	$0.309357\pi$
$602$	−25.1969	−1.02695
$603$	23.6011	0.961112
$604$	7.01424	0.285405
$605$	58.0492	2.36004
$606$	18.0303	0.732431
$607$	13.4352	0.545318	0.272659	−	0.962111i	$-0.412097\pi$
$607$	13.4352	0.545318	0.272659	+	0.962111i	$0.412097\pi$
$608$	21.5452	0.873775
$609$	8.70425	0.352714
$610$	−73.6315	−2.98125
$611$	2.09506	0.0847571
$612$	177.528	7.17616
$613$	−1.77059	−0.0715135	−0.0357568	−	0.999361i	$-0.511384\pi$
$613$	−1.77059	−0.0715135	−0.0357568	+	0.999361i	$0.511384\pi$
$614$	55.6145	2.24442
$615$	26.7484	1.07860
$616$	32.5139	1.31002
$617$	1.23234	0.0496121	0.0248060	−	0.999692i	$-0.492103\pi$
$617$	1.23234	0.0496121	0.0248060	+	0.999692i	$0.492103\pi$
$618$	−8.85596	−0.356239
$619$	−3.62053	−0.145521	−0.0727607	−	0.997349i	$-0.523181\pi$
$619$	−3.62053	−0.145521	−0.0727607	+	0.997349i	$0.523181\pi$
$620$	−65.7200	−2.63938
$621$	29.7382	1.19335
$622$	14.2642	0.571944
$623$	10.9835	0.440044
$624$	5.19671	0.208035
$625$	−22.6706	−0.906823
$626$	41.9387	1.67621
$627$	−84.7720	−3.38547
$628$	−40.7134	−1.62464
$629$	−41.5558	−1.65694
$630$	57.0031	2.27106
$631$	15.6487	0.622964	0.311482	−	0.950252i	$-0.399175\pi$
$631$	15.6487	0.622964	0.311482	+	0.950252i	$0.399175\pi$
$632$	−23.6776	−0.941846
$633$	−36.4678	−1.44946
$634$	26.6311	1.05766
$635$	−44.5818	−1.76917
$636$	39.4567	1.56456
$637$	0.253460	0.0100424
$638$	37.4844	1.48402
$639$	62.3314	2.46579
$640$	44.6690	1.76570
$641$	−4.50489	−0.177932	−0.0889662	−	0.996035i	$-0.528356\pi$
$641$	−4.50489	−0.177932	−0.0889662	+	0.996035i	$0.528356\pi$
$642$	−46.2986	−1.82726
$643$	−41.2077	−1.62507	−0.812536	−	0.582911i	$-0.801913\pi$
$643$	−41.2077	−1.62507	−0.812536	+	0.582911i	$0.801913\pi$
$644$	−10.3729	−0.408750
$645$	−101.710	−4.00483
$646$	72.9711	2.87101
$647$	−16.5007	−0.648710	−0.324355	−	0.945935i	$-0.605147\pi$
$647$	−16.5007	−0.648710	−0.324355	+	0.945935i	$0.605147\pi$
$648$	−113.635	−4.46400
$649$	2.96030	0.116202
$650$	−3.47832	−0.136431
$651$	14.6481	0.574106
$652$	48.8663	1.91375
$653$	−23.2699	−0.910622	−0.455311	−	0.890333i	$-0.650472\pi$
$653$	−23.2699	−0.910622	−0.455311	+	0.890333i	$0.650472\pi$
$654$	87.4579	3.41988
$655$	−65.3415	−2.55310
$656$	17.0112	0.664175
$657$	−34.0405	−1.32805
$658$	20.8941	0.814536
$659$	−33.2147	−1.29386	−0.646930	−	0.762550i	$-0.723947\pi$
$659$	−33.2147	−1.29386	−0.646930	+	0.762550i	$0.723947\pi$
$660$	241.095	9.38460
$661$	−17.7307	−0.689644	−0.344822	−	0.938668i	$-0.612061\pi$
$661$	−17.7307	−0.689644	−0.344822	+	0.938668i	$0.612061\pi$
$662$	31.0992	1.20870
$663$	4.63815	0.180131
$664$	77.7526	3.01739
$665$	16.0965	0.624196
$666$	126.649	4.90755
$667$	−6.50999	−0.252068
$668$	45.6212	1.76514
$669$	26.8256	1.03714
$670$	−27.5900	−1.06589
$671$	48.5532	1.87438
$672$	13.6575	0.526850
$673$	15.2210	0.586727	0.293363	−	0.956001i	$-0.405225\pi$
$673$	15.2210	0.586727	0.293363	+	0.956001i	$0.405225\pi$
$674$	70.7663	2.72582
$675$	68.3222	2.62972
$676$	−56.7824	−2.18394
$677$	10.3492	0.397752	0.198876	−	0.980025i	$-0.436271\pi$
$677$	10.3492	0.397752	0.198876	+	0.980025i	$0.436271\pi$
$678$	−112.034	−4.30266
$679$	−4.26295	−0.163597
$680$	−112.975	−4.33241
$681$	36.4056	1.39507
$682$	63.0815	2.41551
$683$	−41.2018	−1.57654	−0.788272	−	0.615327i	$-0.789024\pi$
$683$	−41.2018	−1.57654	−0.788272	+	0.615327i	$0.789024\pi$
$684$	−152.782	−5.84175
$685$	−51.4725	−1.96666
$686$	2.52776	0.0965103
$687$	20.4545	0.780389
$688$	−64.6846	−2.46608
$689$	0.721070	0.0274706
$690$	−60.9490	−2.32029
$691$	21.1566	0.804836	0.402418	−	0.915456i	$-0.368170\pi$
$691$	21.1566	0.804836	0.402418	+	0.915456i	$0.368170\pi$
$692$	−56.8134	−2.15972
$693$	−37.5884	−1.42786
$694$	91.3617	3.46804
$695$	68.6508	2.60407
$696$	52.5759	1.99289
$697$	15.1828	0.575088
$698$	−29.8526	−1.12994
$699$	−7.15316	−0.270558
$700$	−23.8313	−0.900737
$701$	−13.9964	−0.528636	−0.264318	−	0.964436i	$-0.585147\pi$
$701$	−13.9964	−0.528636	−0.264318	+	0.964436i	$0.585147\pi$
$702$	−8.06272	−0.304308
$703$	35.7631	1.34883
$704$	−11.0453	−0.416285
$705$	84.3413	3.17648
$706$	43.0715	1.62102
$707$	2.25755	0.0849040
$708$	7.62737	0.286654
$709$	10.1386	0.380762	0.190381	−	0.981710i	$-0.439028\pi$
$709$	10.1386	0.380762	0.190381	+	0.981710i	$0.439028\pi$
$710$	−72.8660	−2.73461
$711$	27.3730	1.02657
$712$	66.3430	2.48631
$713$	−10.9555	−0.410286
$714$	46.2563	1.73110
$715$	4.40600	0.164775
$716$	−75.0926	−2.80634
$717$	62.3744	2.32942
$718$	−10.2215	−0.381462
$719$	45.6388	1.70204	0.851021	−	0.525132i	$-0.175984\pi$
$719$	45.6388	1.70204	0.851021	+	0.525132i	$0.175984\pi$
$720$	146.336	5.45364
$721$	−1.10884	−0.0412955
$722$	−14.7718	−0.549749
$723$	−33.2806	−1.23772
$724$	16.4420	0.611062
$725$	−14.9564	−0.555466
$726$	−143.562	−5.32808
$727$	50.9747	1.89055	0.945273	−	0.326281i	$-0.105796\pi$
$727$	50.9747	1.89055	0.945273	+	0.326281i	$0.105796\pi$
$728$	1.53096	0.0567412
$729$	12.0846	0.447580
$730$	39.7937	1.47283
$731$	−57.7320	−2.13530
$732$	125.100	4.62382
$733$	−51.8775	−1.91614	−0.958070	−	0.286535i	$-0.907497\pi$
$733$	−51.8775	−1.91614	−0.958070	+	0.286535i	$0.907497\pi$
$734$	−92.9262	−3.42997
$735$	10.2036	0.376365
$736$	−10.2146	−0.376514
$737$	18.1931	0.670150
$738$	−46.2723	−1.70331
$739$	45.0241	1.65624	0.828119	−	0.560552i	$-0.189411\pi$
$739$	45.0241	1.65624	0.828119	+	0.560552i	$0.189411\pi$
$740$	−101.712	−3.73899
$741$	−3.99161	−0.146635
$742$	7.19125	0.263999
$743$	30.0316	1.10175	0.550876	−	0.834587i	$-0.314294\pi$
$743$	30.0316	1.10175	0.550876	+	0.834587i	$0.314294\pi$
$744$	88.4786	3.24378
$745$	64.9113	2.37817
$746$	−30.1208	−1.10280
$747$	−89.8875	−3.28881
$748$	136.849	5.00369
$749$	−5.79698	−0.211817
$750$	−11.0666	−0.404094
$751$	−28.7207	−1.04803	−0.524016	−	0.851708i	$-0.675567\pi$
$751$	−28.7207	−1.04803	−0.524016	+	0.851708i	$0.675567\pi$
$752$	53.6386	1.95600
$753$	97.8668	3.56646
$754$	1.76501	0.0642778
$755$	5.16038	0.187805
$756$	−55.2406	−2.00908
$757$	−46.6884	−1.69692	−0.848459	−	0.529261i	$-0.822469\pi$
$757$	−46.6884	−1.69692	−0.848459	+	0.529261i	$0.822469\pi$
$758$	50.0318	1.81724
$759$	40.1903	1.45882
$760$	97.2271	3.52680
$761$	22.8456	0.828153	0.414077	−	0.910242i	$-0.364105\pi$
$761$	22.8456	0.828153	0.414077	+	0.910242i	$0.364105\pi$
$762$	110.255	3.99413
$763$	10.9505	0.396434
$764$	12.3334	0.446206
$765$	130.608	4.72213
$766$	73.2725	2.64744
$767$	0.139390	0.00503309
$768$	−97.5046	−3.51839
$769$	−12.8095	−0.461921	−0.230961	−	0.972963i	$-0.574187\pi$
$769$	−12.8095	−0.461921	−0.230961	+	0.972963i	$0.574187\pi$
$770$	43.9412	1.58353
$771$	45.1424	1.62576
$772$	−90.3995	−3.25355
$773$	48.1185	1.73070	0.865350	−	0.501167i	$-0.167096\pi$
$773$	48.1185	1.73070	0.865350	+	0.501167i	$0.167096\pi$
$774$	175.949	6.32436
$775$	−25.1697	−0.904122
$776$	−25.7493	−0.924346
$777$	22.6702	0.813290
$778$	−27.7449	−0.994704
$779$	−13.0663	−0.468150
$780$	11.3523	0.406477
$781$	48.0485	1.71931
$782$	−34.5955	−1.23713
$783$	−34.6688	−1.23896
$784$	6.48918	0.231756
$785$	−29.9528	−1.06906
$786$	161.596	5.76395
$787$	−20.0600	−0.715061	−0.357531	−	0.933901i	$-0.616381\pi$
$787$	−20.0600	−0.715061	−0.357531	+	0.933901i	$0.616381\pi$
$788$	51.8384	1.84667
$789$	54.5480	1.94196
$790$	−31.9994	−1.13849
$791$	−14.0277	−0.498767
$792$	−227.043	−8.06763
$793$	2.28620	0.0811853
$794$	4.72298	0.167612
$795$	29.0283	1.02953
$796$	68.2821	2.42020
$797$	13.9132	0.492830	0.246415	−	0.969164i	$-0.420747\pi$
$797$	13.9132	0.492830	0.246415	+	0.969164i	$0.420747\pi$
$798$	−39.8084	−1.40920
$799$	47.8733	1.69364
$800$	−23.4675	−0.829702
$801$	−76.6973	−2.70996
$802$	−7.19505	−0.254066
$803$	−26.2403	−0.926000
$804$	46.8753	1.65317
$805$	−7.63135	−0.268970
$806$	2.97028	0.104624
$807$	−87.4882	−3.07973
$808$	13.6362	0.479719
$809$	−34.7545	−1.22190	−0.610952	−	0.791668i	$-0.709213\pi$
$809$	−34.7545	−1.22190	−0.610952	+	0.791668i	$0.709213\pi$
$810$	−153.573	−5.39601
$811$	−7.62006	−0.267576	−0.133788	−	0.991010i	$-0.542714\pi$
$811$	−7.62006	−0.267576	−0.133788	+	0.991010i	$0.542714\pi$
$812$	12.0927	0.424371
$813$	−75.8273	−2.65938
$814$	97.6282	3.42187
$815$	35.9509	1.25931
$816$	118.748	4.15700
$817$	49.6844	1.73824
$818$	75.2545	2.63121
$819$	−1.76990	−0.0618454
$820$	37.1612	1.29772
$821$	−31.8096	−1.11016	−0.555081	−	0.831796i	$-0.687313\pi$
$821$	−31.8096	−1.11016	−0.555081	+	0.831796i	$0.687313\pi$
$822$	127.297	4.43999
$823$	35.3672	1.23282	0.616411	−	0.787424i	$-0.288586\pi$
$823$	35.3672	1.23282	0.616411	+	0.787424i	$0.288586\pi$
$824$	−6.69770	−0.233325
$825$	92.3354	3.21471
$826$	1.39014	0.0483692
$827$	36.9891	1.28624	0.643119	−	0.765766i	$-0.277640\pi$
$827$	36.9891	1.28624	0.643119	+	0.765766i	$0.277640\pi$
$828$	72.4337	2.51724
$829$	−17.5853	−0.610763	−0.305382	−	0.952230i	$-0.598784\pi$
$829$	−17.5853	−0.610763	−0.305382	+	0.952230i	$0.598784\pi$
$830$	105.079	3.64736
$831$	100.639	3.49112
$832$	−0.520083	−0.0180307
$833$	5.79170	0.200670
$834$	−169.781	−5.87903
$835$	33.5635	1.16151
$836$	−117.773	−4.07325
$837$	−58.3431	−2.01663
$838$	−87.6396	−3.02746
$839$	−38.1301	−1.31640	−0.658198	−	0.752845i	$-0.728681\pi$
$839$	−38.1301	−1.31640	−0.658198	+	0.752845i	$0.728681\pi$
$840$	61.6322	2.12651
$841$	−21.4107	−0.738299
$842$	69.9160	2.40947
$843$	−45.0346	−1.55107
$844$	−50.6642	−1.74393
$845$	−41.7748	−1.43710
$846$	−145.903	−5.01624
$847$	−17.9752	−0.617635
$848$	18.4611	0.633958
$849$	−49.7064	−1.70592
$850$	−79.4816	−2.72620
$851$	−16.9553	−0.581219
$852$	123.799	4.24129
$853$	−31.4220	−1.07587	−0.537935	−	0.842986i	$-0.680795\pi$
$853$	−31.4220	−1.07587	−0.537935	+	0.842986i	$0.680795\pi$
$854$	22.8003	0.780211
$855$	−112.401	−3.84405
$856$	−35.0152	−1.19680
$857$	−18.2275	−0.622640	−0.311320	−	0.950305i	$-0.600771\pi$
$857$	−18.2275	−0.622640	−0.311320	+	0.950305i	$0.600771\pi$
$858$	−10.8965	−0.372001
$859$	−0.00139570	−4.76208e−5 0	−2.38104e−5	−	1.00000i	$-0.500008\pi$
$859$	−0.00139570	−4.76208e−5 0	−2.38104e−5		1.00000i	$0.500008\pi$
$860$	−141.304	−4.81844
$861$	−8.28275	−0.282275
$862$	55.2038	1.88025
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	−54.3975	−1.85064
$865$	−41.7976	−1.42116
$866$	−44.0626	−1.49731
$867$	52.2713	1.77523
$868$	20.3505	0.690741
$869$	21.1007	0.715791
$870$	71.0543	2.40896
$871$	0.856646	0.0290264
$872$	66.1438	2.23991
$873$	29.7680	1.00750
$874$	29.7731	1.00709
$875$	−1.38563	−0.0468428
$876$	−67.6094	−2.28431
$877$	20.8115	0.702755	0.351378	−	0.936234i	$-0.385713\pi$
$877$	20.8115	0.702755	0.351378	+	0.936234i	$0.385713\pi$
$878$	−53.5905	−1.80859
$879$	−81.0923	−2.73518
$880$	112.804	3.80263
$881$	−5.35698	−0.180481	−0.0902406	−	0.995920i	$-0.528764\pi$
$881$	−5.35698	−0.180481	−0.0902406	+	0.995920i	$0.528764\pi$
$882$	−17.6513	−0.594349
$883$	−15.3244	−0.515709	−0.257854	−	0.966184i	$-0.583015\pi$
$883$	−15.3244	−0.515709	−0.257854	+	0.966184i	$0.583015\pi$
$884$	6.44372	0.216726
$885$	5.61146	0.188627
$886$	−37.1687	−1.24871
$887$	39.8414	1.33774	0.668872	−	0.743378i	$-0.266778\pi$
$887$	39.8414	1.33774	0.668872	+	0.743378i	$0.266778\pi$
$888$	136.934	4.59520
$889$	13.8049	0.463003
$890$	89.6599	3.00541
$891$	101.267	3.39259
$892$	37.2684	1.24784
$893$	−41.2000	−1.37870
$894$	−160.533	−5.36901
$895$	−55.2456	−1.84666
$896$	−13.8319	−0.462093
$897$	1.89242	0.0631860
$898$	−96.6896	−3.22657
$899$	12.7719	0.425966
$900$	166.413	5.54710
$901$	16.4769	0.548924
$902$	−35.6692	−1.18766
$903$	31.4950	1.04809
$904$	−84.7308	−2.81810
$905$	12.0964	0.402097
$906$	−12.7622	−0.423995
$907$	−16.4452	−0.546053	−0.273026	−	0.962007i	$-0.588025\pi$
$907$	−16.4452	−0.546053	−0.273026	+	0.962007i	$0.588025\pi$
$908$	50.5779	1.67849
$909$	−15.7644	−0.522872
$910$	2.06903	0.0685878
$911$	54.0914	1.79213	0.896064	−	0.443925i	$-0.146414\pi$
$911$	54.0914	1.79213	0.896064	+	0.443925i	$0.146414\pi$
$912$	−102.195	−3.38401
$913$	−69.2903	−2.29318
$914$	15.7560	0.521161
$915$	92.0360	3.04262
$916$	28.4172	0.938931
$917$	20.2333	0.668162
$918$	−184.238	−6.08075
$919$	−9.70947	−0.320286	−0.160143	−	0.987094i	$-0.551196\pi$
$919$	−9.70947	−0.320286	−0.160143	+	0.987094i	$0.551196\pi$
$920$	−46.0953	−1.51972
$921$	−69.5156	−2.29062
$922$	−9.78663	−0.322305
$923$	2.26243	0.0744688
$924$	−74.6560	−2.45600
$925$	−38.9539	−1.28080
$926$	51.0251	1.67679
$927$	7.74302	0.254314
$928$	11.9081	0.390904
$929$	51.7019	1.69628	0.848142	−	0.529768i	$-0.177721\pi$
$929$	51.7019	1.69628	0.848142	+	0.529768i	$0.177721\pi$
$930$	119.575	3.92103
$931$	−4.98436	−0.163356
$932$	−9.93780	−0.325523
$933$	−17.8296	−0.583716
$934$	−5.94547	−0.194542
$935$	100.680	3.29258
$936$	−10.6907	−0.349435
$937$	13.2229	0.431974	0.215987	−	0.976396i	$-0.430703\pi$
$937$	13.2229	0.431974	0.215987	+	0.976396i	$0.430703\pi$
$938$	8.54335	0.278950
$939$	−52.4215	−1.71071
$940$	117.174	3.82180
$941$	14.0125	0.456794	0.228397	−	0.973568i	$-0.426652\pi$
$941$	14.0125	0.456794	0.228397	+	0.973568i	$0.426652\pi$
$942$	74.0765	2.41354
$943$	6.19474	0.201729
$944$	3.56872	0.116152
$945$	−40.6405	−1.32204
$946$	135.631	4.40976
$947$	−11.5143	−0.374163	−0.187081	−	0.982344i	$-0.559903\pi$
$947$	−11.5143	−0.374163	−0.187081	+	0.982344i	$0.559903\pi$
$948$	54.3669	1.76576
$949$	−1.23556	−0.0401080
$950$	68.4022	2.21926
$951$	−33.2877	−1.07943
$952$	34.9833	1.13382
$953$	−9.99083	−0.323635	−0.161817	−	0.986821i	$-0.551736\pi$
$953$	−9.99083	−0.323635	−0.161817	+	0.986821i	$0.551736\pi$
$954$	−50.2163	−1.62581
$955$	9.07366	0.293617
$956$	86.6560	2.80266
$957$	−46.8538	−1.51457
$958$	−86.5623	−2.79670
$959$	15.9387	0.514687
$960$	−20.9371	−0.675742
$961$	−9.50657	−0.306663
$962$	4.59696	0.148212
$963$	40.4801	1.30445
$964$	−46.2363	−1.48917
$965$	−66.5069	−2.14093
$966$	18.8731	0.607233
$967$	−35.6322	−1.14586	−0.572928	−	0.819606i	$-0.694192\pi$
$967$	−35.6322	−1.14586	−0.572928	+	0.819606i	$0.694192\pi$
$968$	−108.575	−3.48973
$969$	−91.2105	−2.93010
$970$	−34.7991	−1.11733
$971$	−49.4888	−1.58817	−0.794085	−	0.607806i	$-0.792050\pi$
$971$	−49.4888	−1.58817	−0.794085	+	0.607806i	$0.792050\pi$
$972$	95.1988	3.05350
$973$	−21.2580	−0.681501
$974$	−27.2101	−0.871868
$975$	4.34774	0.139239
$976$	58.5322	1.87357
$977$	22.2347	0.711350	0.355675	−	0.934610i	$-0.384251\pi$
$977$	22.2347	0.711350	0.355675	+	0.934610i	$0.384251\pi$
$978$	−88.9105	−2.84304
$979$	−59.1225	−1.88956
$980$	14.1757	0.452826
$981$	−76.4669	−2.44140
$982$	86.6893	2.76637
$983$	−25.2868	−0.806525	−0.403262	−	0.915084i	$-0.632124\pi$
$983$	−25.2868	−0.806525	−0.403262	+	0.915084i	$0.632124\pi$
$984$	−50.0300	−1.59490
$985$	38.1375	1.21516
$986$	40.3314	1.28441
$987$	−26.1166	−0.831302
$988$	−5.54549	−0.176426
$989$	−23.5554	−0.749017
$990$	−306.840	−9.75201
$991$	40.8013	1.29610	0.648048	−	0.761599i	$-0.275585\pi$
$991$	40.8013	1.29610	0.648048	+	0.761599i	$0.275585\pi$
$992$	20.0399	0.636267
$993$	−38.8726	−1.23358
$994$	22.5633	0.715664
$995$	50.2352	1.59256
$996$	−178.530	−5.65694
$997$	−12.2168	−0.386910	−0.193455	−	0.981109i	$-0.561969\pi$
$997$	−12.2168	−0.386910	−0.193455	+	0.981109i	$0.561969\pi$
$998$	−32.7568	−1.03690
$999$	−90.2948	−2.85680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.e.1.9	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.e.1.9	✓	112	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52776 q^{2} +3.15958 q^{3} +4.38957 q^{4} +3.22941 q^{5} -7.98667 q^{6} -1.00000 q^{7} -6.04026 q^{8} +6.98297 q^{9} +O(q^{10})\)	\(q-2.52776 q^{2} +3.15958 q^{3} +4.38957 q^{4} +3.22941 q^{5} -7.98667 q^{6} -1.00000 q^{7} -6.04026 q^{8} +6.98297 q^{9} -8.16316 q^{10} +5.38286 q^{11} +13.8692 q^{12} +0.253460 q^{13} +2.52776 q^{14} +10.2036 q^{15} +6.48918 q^{16} +5.79170 q^{17} -17.6513 q^{18} -4.98436 q^{19} +14.1757 q^{20} -3.15958 q^{21} -13.6066 q^{22} +2.36308 q^{23} -19.0847 q^{24} +5.42907 q^{25} -0.640685 q^{26} +12.5845 q^{27} -4.38957 q^{28} -2.75487 q^{29} -25.7922 q^{30} -4.63610 q^{31} -4.32257 q^{32} +17.0076 q^{33} -14.6400 q^{34} -3.22941 q^{35} +30.6522 q^{36} -7.17507 q^{37} +12.5993 q^{38} +0.800827 q^{39} -19.5064 q^{40} +2.62147 q^{41} +7.98667 q^{42} -9.96807 q^{43} +23.6284 q^{44} +22.5508 q^{45} -5.97330 q^{46} +8.26585 q^{47} +20.5031 q^{48} +1.00000 q^{49} -13.7234 q^{50} +18.2993 q^{51} +1.11258 q^{52} +2.84491 q^{53} -31.8106 q^{54} +17.3834 q^{55} +6.04026 q^{56} -15.7485 q^{57} +6.96366 q^{58} +0.549950 q^{59} +44.7893 q^{60} +9.01997 q^{61} +11.7189 q^{62} -6.98297 q^{63} -2.05194 q^{64} +0.818525 q^{65} -42.9911 q^{66} +3.37981 q^{67} +25.4230 q^{68} +7.46635 q^{69} +8.16316 q^{70} +8.92620 q^{71} -42.1789 q^{72} -4.87479 q^{73} +18.1369 q^{74} +17.1536 q^{75} -21.8792 q^{76} -5.38286 q^{77} -2.02430 q^{78} +3.91997 q^{79} +20.9562 q^{80} +18.8129 q^{81} -6.62645 q^{82} -12.8724 q^{83} -13.8692 q^{84} +18.7037 q^{85} +25.1969 q^{86} -8.70425 q^{87} -32.5139 q^{88} -10.9835 q^{89} -57.0031 q^{90} -0.253460 q^{91} +10.3729 q^{92} -14.6481 q^{93} -20.8941 q^{94} -16.0965 q^{95} -13.6575 q^{96} +4.26295 q^{97} -2.52776 q^{98} +37.5884 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * q^99

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