LMFDB - Embedded newform 8041.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21985 q^{2} +0.267340 q^{3} +2.92774 q^{4} -2.37360 q^{5} -0.593455 q^{6} -4.48408 q^{7} -2.05944 q^{8} -2.92853 q^{9} +O(q^{10})$	\(q-2.21985 q^{2} +0.267340 q^{3} +2.92774 q^{4} -2.37360 q^{5} -0.593455 q^{6} -4.48408 q^{7} -2.05944 q^{8} -2.92853 q^{9} +5.26904 q^{10} +1.00000 q^{11} +0.782702 q^{12} -0.322990 q^{13} +9.95398 q^{14} -0.634559 q^{15} -1.28383 q^{16} -1.00000 q^{17} +6.50090 q^{18} -7.60876 q^{19} -6.94927 q^{20} -1.19877 q^{21} -2.21985 q^{22} -5.04339 q^{23} -0.550570 q^{24} +0.633975 q^{25} +0.716990 q^{26} -1.58493 q^{27} -13.1282 q^{28} +5.33301 q^{29} +1.40863 q^{30} -4.46119 q^{31} +6.96879 q^{32} +0.267340 q^{33} +2.21985 q^{34} +10.6434 q^{35} -8.57396 q^{36} +11.0617 q^{37} +16.8903 q^{38} -0.0863482 q^{39} +4.88828 q^{40} +5.16475 q^{41} +2.66110 q^{42} +1.00000 q^{43} +2.92774 q^{44} +6.95116 q^{45} +11.1956 q^{46} +10.7431 q^{47} -0.343220 q^{48} +13.1070 q^{49} -1.40733 q^{50} -0.267340 q^{51} -0.945630 q^{52} +5.90865 q^{53} +3.51832 q^{54} -2.37360 q^{55} +9.23467 q^{56} -2.03413 q^{57} -11.8385 q^{58} -8.98108 q^{59} -1.85782 q^{60} +12.9656 q^{61} +9.90317 q^{62} +13.1318 q^{63} -12.9020 q^{64} +0.766649 q^{65} -0.593455 q^{66} +1.65922 q^{67} -2.92774 q^{68} -1.34830 q^{69} -23.6268 q^{70} -10.5759 q^{71} +6.03112 q^{72} -7.45121 q^{73} -24.5553 q^{74} +0.169487 q^{75} -22.2764 q^{76} -4.48408 q^{77} +0.191680 q^{78} +12.8163 q^{79} +3.04730 q^{80} +8.36187 q^{81} -11.4650 q^{82} -6.68858 q^{83} -3.50970 q^{84} +2.37360 q^{85} -2.21985 q^{86} +1.42573 q^{87} -2.05944 q^{88} +9.81721 q^{89} -15.4305 q^{90} +1.44831 q^{91} -14.7657 q^{92} -1.19266 q^{93} -23.8480 q^{94} +18.0602 q^{95} +1.86304 q^{96} -8.40664 q^{97} -29.0955 q^{98} -2.92853 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) $ 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * 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 $

$2$	−2.21985	−1.56967	−0.784836	−	0.619704i	$-0.787253\pi$
$2$	−2.21985	−1.56967	−0.784836	+	0.619704i	$0.787253\pi$
$3$	0.267340	0.154349	0.0771745	−	0.997018i	$-0.475410\pi$
$3$	0.267340	0.154349	0.0771745	+	0.997018i	$0.475410\pi$
$4$	2.92774	1.46387
$5$	−2.37360	−1.06151	−0.530753	−	0.847527i	$-0.678091\pi$
$5$	−2.37360	−1.06151	−0.530753	+	0.847527i	$0.678091\pi$
$6$	−0.593455	−0.242277
$7$	−4.48408	−1.69482	−0.847411	−	0.530937i	$-0.821840\pi$
$7$	−4.48408	−1.69482	−0.847411	+	0.530937i	$0.821840\pi$
$8$	−2.05944	−0.728121
$9$	−2.92853	−0.976176
$10$	5.26904	1.66622
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.782702	0.225947
$13$	−0.322990	−0.0895813	−0.0447907	−	0.998996i	$-0.514262\pi$
$13$	−0.322990	−0.0895813	−0.0447907	+	0.998996i	$0.514262\pi$
$14$	9.95398	2.66031
$15$	−0.634559	−0.163842
$16$	−1.28383	−0.320958
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	6.50090	1.53228
$19$	−7.60876	−1.74557	−0.872785	−	0.488105i	$-0.837688\pi$
$19$	−7.60876	−1.74557	−0.872785	+	0.488105i	$0.837688\pi$
$20$	−6.94927	−1.55390
$21$	−1.19877	−0.261594
$22$	−2.21985	−0.473274
$23$	−5.04339	−1.05162	−0.525810	−	0.850602i	$-0.676238\pi$
$23$	−5.04339	−1.05162	−0.525810	+	0.850602i	$0.676238\pi$
$24$	−0.550570	−0.112385
$25$	0.633975	0.126795
$26$	0.716990	0.140613
$27$	−1.58493	−0.305021
$28$	−13.1282	−2.48100
$29$	5.33301	0.990315	0.495157	−	0.868803i	$-0.335110\pi$
$29$	5.33301	0.990315	0.495157	+	0.868803i	$0.335110\pi$
$30$	1.40863	0.257179
$31$	−4.46119	−0.801253	−0.400627	−	0.916241i	$-0.631208\pi$
$31$	−4.46119	−0.801253	−0.400627	+	0.916241i	$0.631208\pi$
$32$	6.96879	1.23192
$33$	0.267340	0.0465380
$34$	2.21985	0.380701
$35$	10.6434	1.79906
$36$	−8.57396	−1.42899
$37$	11.0617	1.81853	0.909267	−	0.416214i	$-0.136643\pi$
$37$	11.0617	1.81853	0.909267	+	0.416214i	$0.136643\pi$
$38$	16.8903	2.73997
$39$	−0.0863482	−0.0138268
$40$	4.88828	0.772904
$41$	5.16475	0.806598	0.403299	−	0.915068i	$-0.367863\pi$
$41$	5.16475	0.806598	0.403299	+	0.915068i	$0.367863\pi$
$42$	2.66110	0.410617
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	2.92774	0.441373
$45$	6.95116	1.03622
$46$	11.1956	1.65070
$47$	10.7431	1.56704	0.783518	−	0.621369i	$-0.213423\pi$
$47$	10.7431	1.56704	0.783518	+	0.621369i	$0.213423\pi$
$48$	−0.343220	−0.0495396
$49$	13.1070	1.87242
$50$	−1.40733	−0.199027
$51$	−0.267340	−0.0374351
$52$	−0.945630	−0.131135
$53$	5.90865	0.811616	0.405808	−	0.913958i	$-0.366990\pi$
$53$	5.90865	0.811616	0.405808	+	0.913958i	$0.366990\pi$
$54$	3.51832	0.478782
$55$	−2.37360	−0.320056
$56$	9.23467	1.23404
$57$	−2.03413	−0.269427
$58$	−11.8385	−1.55447
$59$	−8.98108	−1.16924	−0.584619	−	0.811308i	$-0.698756\pi$
$59$	−8.98108	−1.16924	−0.584619	+	0.811308i	$0.698756\pi$
$60$	−1.85782	−0.239844
$61$	12.9656	1.66008	0.830038	−	0.557707i	$-0.188319\pi$
$61$	12.9656	1.66008	0.830038	+	0.557707i	$0.188319\pi$
$62$	9.90317	1.25770
$63$	13.1318	1.65445
$64$	−12.9020	−1.61275
$65$	0.766649	0.0950911
$66$	−0.593455	−0.0730493
$67$	1.65922	0.202706	0.101353	−	0.994851i	$-0.467683\pi$
$67$	1.65922	0.202706	0.101353	+	0.994851i	$0.467683\pi$
$68$	−2.92774	−0.355040
$69$	−1.34830	−0.162317
$70$	−23.6268	−2.82394
$71$	−10.5759	−1.25513	−0.627565	−	0.778564i	$-0.715948\pi$
$71$	−10.5759	−1.25513	−0.627565	+	0.778564i	$0.715948\pi$
$72$	6.03112	0.710774
$73$	−7.45121	−0.872098	−0.436049	−	0.899923i	$-0.643623\pi$
$73$	−7.45121	−0.872098	−0.436049	+	0.899923i	$0.643623\pi$
$74$	−24.5553	−2.85450
$75$	0.169487	0.0195707
$76$	−22.2764	−2.55528
$77$	−4.48408	−0.511008
$78$	0.191680	0.0217035
$79$	12.8163	1.44194	0.720972	−	0.692964i	$-0.243696\pi$
$79$	12.8163	1.44194	0.720972	+	0.692964i	$0.243696\pi$
$80$	3.04730	0.340699
$81$	8.36187	0.929097
$82$	−11.4650	−1.26609
$83$	−6.68858	−0.734167	−0.367084	−	0.930188i	$-0.619644\pi$
$83$	−6.68858	−0.734167	−0.367084	+	0.930188i	$0.619644\pi$
$84$	−3.50970	−0.382939
$85$	2.37360	0.257453
$86$	−2.21985	−0.239373
$87$	1.42573	0.152854
$88$	−2.05944	−0.219537
$89$	9.81721	1.04062	0.520311	−	0.853977i	$-0.325816\pi$
$89$	9.81721	1.04062	0.520311	+	0.853977i	$0.325816\pi$
$90$	−15.4305	−1.62652
$91$	1.44831	0.151824
$92$	−14.7657	−1.53943
$93$	−1.19266	−0.123673
$94$	−23.8480	−2.45973
$95$	18.0602	1.85293
$96$	1.86304	0.190145
$97$	−8.40664	−0.853565	−0.426783	−	0.904354i	$-0.640353\pi$
$97$	−8.40664	−0.853565	−0.426783	+	0.904354i	$0.640353\pi$
$98$	−29.0955	−2.93909
$99$	−2.92853	−0.294328
$100$	1.85611	0.185611
$101$	−8.64495	−0.860205	−0.430103	−	0.902780i	$-0.641523\pi$
$101$	−8.64495	−0.860205	−0.430103	+	0.902780i	$0.641523\pi$
$102$	0.593455	0.0587608
$103$	1.78915	0.176290	0.0881452	−	0.996108i	$-0.471906\pi$
$103$	1.78915	0.176290	0.0881452	+	0.996108i	$0.471906\pi$
$104$	0.665177	0.0652260
$105$	2.84541	0.277684
$106$	−13.1163	−1.27397
$107$	−4.19647	−0.405688	−0.202844	−	0.979211i	$-0.565018\pi$
$107$	−4.19647	−0.405688	−0.202844	+	0.979211i	$0.565018\pi$
$108$	−4.64027	−0.446510
$109$	4.43011	0.424328	0.212164	−	0.977234i	$-0.431949\pi$
$109$	4.43011	0.424328	0.212164	+	0.977234i	$0.431949\pi$
$110$	5.26904	0.502383
$111$	2.95724	0.280689
$112$	5.75681	0.543967
$113$	0.352353	0.0331466	0.0165733	−	0.999863i	$-0.494724\pi$
$113$	0.352353	0.0331466	0.0165733	+	0.999863i	$0.494724\pi$
$114$	4.51546	0.422912
$115$	11.9710	1.11630
$116$	15.6136	1.44969
$117$	0.945886	0.0874472
$118$	19.9367	1.83532
$119$	4.48408	0.411055
$120$	1.30683	0.119297
$121$	1.00000	0.0909091
$122$	−28.7817	−2.60577
$123$	1.38074	0.124498
$124$	−13.0612	−1.17293
$125$	10.3632	0.926912
$126$	−29.1505	−2.59694
$127$	−19.3674	−1.71858	−0.859291	−	0.511486i	$-0.829095\pi$
$127$	−19.3674	−1.71858	−0.859291	+	0.511486i	$0.829095\pi$
$128$	14.7029	1.29957
$129$	0.267340	0.0235380
$130$	−1.70185	−0.149262
$131$	−6.26907	−0.547731	−0.273866	−	0.961768i	$-0.588302\pi$
$131$	−6.26907	−0.547731	−0.273866	+	0.961768i	$0.588302\pi$
$132$	0.782702	0.0681254
$133$	34.1183	2.95843
$134$	−3.68322	−0.318182
$135$	3.76200	0.323781
$136$	2.05944	0.176595
$137$	21.6667	1.85111	0.925556	−	0.378610i	$-0.123598\pi$
$137$	21.6667	1.85111	0.925556	+	0.378610i	$0.123598\pi$
$138$	2.99303	0.254784
$139$	13.0362	1.10572	0.552860	−	0.833274i	$-0.313536\pi$
$139$	13.0362	1.10572	0.552860	+	0.833274i	$0.313536\pi$
$140$	31.1611	2.63359
$141$	2.87205	0.241870
$142$	23.4770	1.97014
$143$	−0.322990	−0.0270098
$144$	3.75974	0.313312
$145$	−12.6584	−1.05123
$146$	16.5406	1.36891
$147$	3.50402	0.289006
$148$	32.3858	2.66209
$149$	0.0222093	0.00181946	0.000909729	−	1.00000i	$-0.499710\pi$
$149$	0.0222093	0.00181946	0.000909729		1.00000i	$0.499710\pi$
$150$	−0.376236	−0.0307196
$151$	6.65055	0.541214	0.270607	−	0.962690i	$-0.412776\pi$
$151$	6.65055	0.541214	0.270607	+	0.962690i	$0.412776\pi$
$152$	15.6698	1.27099
$153$	2.92853	0.236758
$154$	9.95398	0.802115
$155$	10.5891	0.850535
$156$	−0.252805	−0.0202406
$157$	−1.68265	−0.134290	−0.0671452	−	0.997743i	$-0.521389\pi$
$157$	−1.68265	−0.134290	−0.0671452	+	0.997743i	$0.521389\pi$
$158$	−28.4502	−2.26338
$159$	1.57962	0.125272
$160$	−16.5411	−1.30769
$161$	22.6150	1.78231
$162$	−18.5621	−1.45838
$163$	−21.6242	−1.69374	−0.846871	−	0.531799i	$-0.821516\pi$
$163$	−21.6242	−1.69374	−0.846871	+	0.531799i	$0.821516\pi$
$164$	15.1210	1.18075
$165$	−0.634559	−0.0494003
$166$	14.8477	1.15240
$167$	−20.8796	−1.61571	−0.807856	−	0.589380i	$-0.799372\pi$
$167$	−20.8796	−1.61571	−0.807856	+	0.589380i	$0.799372\pi$
$168$	2.46880	0.190472
$169$	−12.8957	−0.991975
$170$	−5.26904	−0.404117
$171$	22.2825	1.70398
$172$	2.92774	0.223238
$173$	17.2193	1.30916	0.654581	−	0.755991i	$-0.272845\pi$
$173$	17.2193	1.30916	0.654581	+	0.755991i	$0.272845\pi$
$174$	−3.16490	−0.239931
$175$	−2.84280	−0.214895
$176$	−1.28383	−0.0967725
$177$	−2.40100	−0.180471
$178$	−21.7927	−1.63343
$179$	10.6817	0.798387	0.399194	−	0.916867i	$-0.369290\pi$
$179$	10.6817	0.798387	0.399194	+	0.916867i	$0.369290\pi$
$180$	20.3512	1.51689
$181$	2.23774	0.166330	0.0831648	−	0.996536i	$-0.473497\pi$
$181$	2.23774	0.166330	0.0831648	+	0.996536i	$0.473497\pi$
$182$	−3.21504	−0.238314
$183$	3.46623	0.256231
$184$	10.3865	0.765706
$185$	−26.2561	−1.93038
$186$	2.64752	0.194125
$187$	−1.00000	−0.0731272
$188$	31.4528	2.29393
$189$	7.10697	0.516956
$190$	−40.0908	−2.90850
$191$	−17.4810	−1.26488	−0.632442	−	0.774608i	$-0.717947\pi$
$191$	−17.4810	−1.26488	−0.632442	+	0.774608i	$0.717947\pi$
$192$	−3.44922	−0.248926
$193$	18.8103	1.35399	0.676996	−	0.735987i	$-0.263281\pi$
$193$	18.8103	1.35399	0.676996	+	0.735987i	$0.263281\pi$
$194$	18.6615	1.33982
$195$	0.204956	0.0146772
$196$	38.3737	2.74098
$197$	3.13286	0.223207	0.111604	−	0.993753i	$-0.464401\pi$
$197$	3.13286	0.223207	0.111604	+	0.993753i	$0.464401\pi$
$198$	6.50090	0.461999
$199$	−3.15945	−0.223967	−0.111984	−	0.993710i	$-0.535720\pi$
$199$	−3.15945	−0.223967	−0.111984	+	0.993710i	$0.535720\pi$
$200$	−1.30563	−0.0923221
$201$	0.443576	0.0312875
$202$	19.1905	1.35024
$203$	−23.9136	−1.67841
$204$	−0.782702	−0.0548001
$205$	−12.2590	−0.856209
$206$	−3.97165	−0.276718
$207$	14.7697	1.02657
$208$	0.414665	0.0287519
$209$	−7.60876	−0.526309
$210$	−6.31639	−0.435872
$211$	17.5693	1.20952	0.604761	−	0.796407i	$-0.293269\pi$
$211$	17.5693	1.20952	0.604761	+	0.796407i	$0.293269\pi$
$212$	17.2990	1.18810
$213$	−2.82737	−0.193728
$214$	9.31553	0.636797
$215$	−2.37360	−0.161878
$216$	3.26407	0.222092
$217$	20.0043	1.35798
$218$	−9.83418	−0.666055
$219$	−1.99201	−0.134607
$220$	−6.94927	−0.468520
$221$	0.322990	0.0217267
$222$	−6.56463	−0.440589
$223$	−17.8552	−1.19567	−0.597836	−	0.801619i	$-0.703973\pi$
$223$	−17.8552	−1.19567	−0.597836	+	0.801619i	$0.703973\pi$
$224$	−31.2486	−2.08788
$225$	−1.85662	−0.123774
$226$	−0.782171	−0.0520293
$227$	−1.81150	−0.120234	−0.0601169	−	0.998191i	$-0.519147\pi$
$227$	−1.81150	−0.120234	−0.0601169	+	0.998191i	$0.519147\pi$
$228$	−5.95539	−0.394405
$229$	−18.1744	−1.20100	−0.600501	−	0.799624i	$-0.705032\pi$
$229$	−18.1744	−1.20100	−0.600501	+	0.799624i	$0.705032\pi$
$230$	−26.5738	−1.75223
$231$	−1.19877	−0.0788736
$232$	−10.9830	−0.721069
$233$	13.2694	0.869307	0.434653	−	0.900598i	$-0.356871\pi$
$233$	13.2694	0.869307	0.434653	+	0.900598i	$0.356871\pi$
$234$	−2.09973	−0.137263
$235$	−25.4997	−1.66342
$236$	−26.2942	−1.71161
$237$	3.42631	0.222563
$238$	−9.95398	−0.645221
$239$	−0.293335	−0.0189743	−0.00948713	−	0.999955i	$-0.503020\pi$
$239$	−0.293335	−0.0189743	−0.00948713	+	0.999955i	$0.503020\pi$
$240$	0.814667	0.0525865
$241$	25.7199	1.65676	0.828382	−	0.560163i	$-0.189262\pi$
$241$	25.7199	1.65676	0.828382	+	0.560163i	$0.189262\pi$
$242$	−2.21985	−0.142697
$243$	6.99027	0.448426
$244$	37.9599	2.43013
$245$	−31.1107	−1.98759
$246$	−3.06505	−0.195420
$247$	2.45755	0.156370
$248$	9.18753	0.583409
$249$	−1.78813	−0.113318
$250$	−23.0047	−1.45495
$251$	−22.4540	−1.41729	−0.708643	−	0.705567i	$-0.750692\pi$
$251$	−22.4540	−1.41729	−0.708643	+	0.705567i	$0.750692\pi$
$252$	38.4463	2.42189
$253$	−5.04339	−0.317075
$254$	42.9928	2.69761
$255$	0.634559	0.0397376
$256$	−6.83433	−0.427146
$257$	14.6694	0.915055	0.457528	−	0.889195i	$-0.348735\pi$
$257$	14.6694	0.915055	0.457528	+	0.889195i	$0.348735\pi$
$258$	−0.593455	−0.0369469
$259$	−49.6016	−3.08209
$260$	2.24455	0.139201
$261$	−15.6179	−0.966722
$262$	13.9164	0.859758
$263$	−6.08354	−0.375127	−0.187564	−	0.982252i	$-0.560059\pi$
$263$	−6.08354	−0.375127	−0.187564	+	0.982252i	$0.560059\pi$
$264$	−0.550570	−0.0338852
$265$	−14.0248	−0.861535
$266$	−75.7375	−4.64376
$267$	2.62453	0.160619
$268$	4.85776	0.296735
$269$	21.6647	1.32092	0.660460	−	0.750861i	$-0.270361\pi$
$269$	21.6647	1.32092	0.660460	+	0.750861i	$0.270361\pi$
$270$	−8.35108	−0.508230
$271$	24.1937	1.46966	0.734832	−	0.678249i	$-0.237261\pi$
$271$	24.1937	1.46966	0.734832	+	0.678249i	$0.237261\pi$
$272$	1.28383	0.0778438
$273$	0.387192	0.0234339
$274$	−48.0969	−2.90564
$275$	0.633975	0.0382302
$276$	−3.94747	−0.237610
$277$	−22.6454	−1.36063	−0.680315	−	0.732919i	$-0.738157\pi$
$277$	−22.6454	−1.36063	−0.680315	+	0.732919i	$0.738157\pi$
$278$	−28.9385	−1.73562
$279$	13.0647	0.782165
$280$	−21.9194	−1.30994
$281$	−22.5220	−1.34355	−0.671775	−	0.740755i	$-0.734468\pi$
$281$	−22.5220	−1.34355	−0.671775	+	0.740755i	$0.734468\pi$
$282$	−6.37553	−0.379657
$283$	27.3079	1.62329	0.811643	−	0.584154i	$-0.198574\pi$
$283$	27.3079	1.62329	0.811643	+	0.584154i	$0.198574\pi$
$284$	−30.9635	−1.83735
$285$	4.82821	0.285998
$286$	0.716990	0.0423965
$287$	−23.1591	−1.36704
$288$	−20.4083	−1.20257
$289$	1.00000	0.0588235
$290$	28.0998	1.65008
$291$	−2.24743	−0.131747
$292$	−21.8152	−1.27664
$293$	12.3092	0.719112	0.359556	−	0.933124i	$-0.382928\pi$
$293$	12.3092	0.719112	0.359556	+	0.933124i	$0.382928\pi$
$294$	−7.77839	−0.453645
$295$	21.3175	1.24115
$296$	−22.7809	−1.32411
$297$	−1.58493	−0.0919672
$298$	−0.0493013	−0.00285595
$299$	1.62897	0.0942056
$300$	0.496214	0.0286489
$301$	−4.48408	−0.258458
$302$	−14.7632	−0.849528
$303$	−2.31114	−0.132772
$304$	9.76837	0.560255
$305$	−30.7752	−1.76218
$306$	−6.50090	−0.371632
$307$	1.58298	0.0903457	0.0451729	−	0.998979i	$-0.485616\pi$
$307$	1.58298	0.0903457	0.0451729	+	0.998979i	$0.485616\pi$
$308$	−13.1282	−0.748049
$309$	0.478312	0.0272102
$310$	−23.5062	−1.33506
$311$	−18.4536	−1.04641	−0.523205	−	0.852207i	$-0.675264\pi$
$311$	−18.4536	−1.04641	−0.523205	+	0.852207i	$0.675264\pi$
$312$	0.177829	0.0100676
$313$	2.02638	0.114538	0.0572690	−	0.998359i	$-0.481761\pi$
$313$	2.02638	0.114538	0.0572690	+	0.998359i	$0.481761\pi$
$314$	3.73524	0.210792
$315$	−31.1695	−1.75620
$316$	37.5227	2.11082
$317$	−23.3554	−1.31177	−0.655886	−	0.754860i	$-0.727705\pi$
$317$	−23.3554	−1.31177	−0.655886	+	0.754860i	$0.727705\pi$
$318$	−3.50652	−0.196636
$319$	5.33301	0.298591
$320$	30.6242	1.71194
$321$	−1.12189	−0.0626175
$322$	−50.2019	−2.79764
$323$	7.60876	0.423363
$324$	24.4814	1.36008
$325$	−0.204768	−0.0113585
$326$	48.0026	2.65862
$327$	1.18435	0.0654945
$328$	−10.6365	−0.587301
$329$	−48.1727	−2.65585
$330$	1.40863	0.0775423
$331$	12.5867	0.691825	0.345913	−	0.938267i	$-0.387569\pi$
$331$	12.5867	0.691825	0.345913	+	0.938267i	$0.387569\pi$
$332$	−19.5824	−1.07472
$333$	−32.3945	−1.77521
$334$	46.3496	2.53614
$335$	−3.93833	−0.215174
$336$	1.53903	0.0839607
$337$	1.54865	0.0843605	0.0421802	−	0.999110i	$-0.486570\pi$
$337$	1.54865	0.0843605	0.0421802	+	0.999110i	$0.486570\pi$
$338$	28.6265	1.55708
$339$	0.0941982	0.00511614
$340$	6.94927	0.376877
$341$	−4.46119	−0.241587
$342$	−49.4638	−2.67469
$343$	−27.3841	−1.47860
$344$	−2.05944	−0.111037
$345$	3.20033	0.172300
$346$	−38.2244	−2.05496
$347$	4.03123	0.216408	0.108204	−	0.994129i	$-0.465490\pi$
$347$	4.03123	0.216408	0.108204	+	0.994129i	$0.465490\pi$
$348$	4.17416	0.223758
$349$	3.89152	0.208308	0.104154	−	0.994561i	$-0.466786\pi$
$349$	3.89152	0.208308	0.104154	+	0.994561i	$0.466786\pi$
$350$	6.31058	0.337315
$351$	0.511918	0.0273242
$352$	6.96879	0.371438
$353$	32.3937	1.72414	0.862070	−	0.506789i	$-0.169168\pi$
$353$	32.3937	1.72414	0.862070	+	0.506789i	$0.169168\pi$
$354$	5.32987	0.283279
$355$	25.1030	1.33233
$356$	28.7422	1.52333
$357$	1.19877	0.0634459
$358$	−23.7118	−1.25321
$359$	−8.36809	−0.441651	−0.220825	−	0.975313i	$-0.570875\pi$
$359$	−8.36809	−0.441651	−0.220825	+	0.975313i	$0.570875\pi$
$360$	−14.3155	−0.754491
$361$	38.8932	2.04701
$362$	−4.96744	−0.261083
$363$	0.267340	0.0140317
$364$	4.24028	0.222251
$365$	17.6862	0.925738
$366$	−7.69451	−0.402198
$367$	−1.62678	−0.0849173	−0.0424586	−	0.999098i	$-0.513519\pi$
$367$	−1.62678	−0.0849173	−0.0424586	+	0.999098i	$0.513519\pi$
$368$	6.47487	0.337526
$369$	−15.1251	−0.787382
$370$	58.2845	3.03007
$371$	−26.4949	−1.37554
$372$	−3.49178	−0.181040
$373$	26.0540	1.34902	0.674511	−	0.738265i	$-0.264354\pi$
$373$	26.0540	1.34902	0.674511	+	0.738265i	$0.264354\pi$
$374$	2.21985	0.114786
$375$	2.77050	0.143068
$376$	−22.1246	−1.14099
$377$	−1.72251	−0.0887137
$378$	−15.7764	−0.811451
$379$	−33.8374	−1.73811	−0.869055	−	0.494715i	$-0.835272\pi$
$379$	−33.8374	−1.73811	−0.869055	+	0.494715i	$0.835272\pi$
$380$	52.8754	2.71245
$381$	−5.17770	−0.265261
$382$	38.8053	1.98545
$383$	13.9401	0.712305	0.356152	−	0.934428i	$-0.384088\pi$
$383$	13.9401	0.712305	0.356152	+	0.934428i	$0.384088\pi$
$384$	3.93069	0.200587
$385$	10.6434	0.542438
$386$	−41.7560	−2.12532
$387$	−2.92853	−0.148866
$388$	−24.6124	−1.24951
$389$	−1.02692	−0.0520670	−0.0260335	−	0.999661i	$-0.508288\pi$
$389$	−1.02692	−0.0520670	−0.0260335	+	0.999661i	$0.508288\pi$
$390$	−0.454972	−0.0230384
$391$	5.04339	0.255055
$392$	−26.9929	−1.36335
$393$	−1.67598	−0.0845418
$394$	−6.95449	−0.350362
$395$	−30.4207	−1.53063
$396$	−8.57396	−0.430858
$397$	4.50707	0.226203	0.113102	−	0.993583i	$-0.463921\pi$
$397$	4.50707	0.226203	0.113102	+	0.993583i	$0.463921\pi$
$398$	7.01350	0.351555
$399$	9.12119	0.456631
$400$	−0.813918	−0.0406959
$401$	−36.8442	−1.83991	−0.919956	−	0.392021i	$-0.871776\pi$
$401$	−36.8442	−1.83991	−0.919956	+	0.392021i	$0.871776\pi$
$402$	−0.984673	−0.0491110
$403$	1.44092	0.0717773
$404$	−25.3101	−1.25923
$405$	−19.8477	−0.986242
$406$	53.0847	2.63455
$407$	11.0617	0.548308
$408$	0.550570	0.0272573
$409$	38.5078	1.90409	0.952045	−	0.305959i	$-0.0989772\pi$
$409$	38.5078	1.90409	0.952045	+	0.305959i	$0.0989772\pi$
$410$	27.2132	1.34397
$411$	5.79238	0.285717
$412$	5.23816	0.258066
$413$	40.2719	1.98165
$414$	−32.7866	−1.61137
$415$	15.8760	0.779323
$416$	−2.25085	−0.110357
$417$	3.48511	0.170667
$418$	16.8903	0.826132
$419$	−37.2608	−1.82031	−0.910156	−	0.414266i	$-0.864038\pi$
$419$	−37.2608	−1.82031	−0.910156	+	0.414266i	$0.864038\pi$
$420$	8.33061	0.406492
$421$	−13.5550	−0.660628	−0.330314	−	0.943871i	$-0.607155\pi$
$421$	−13.5550	−0.660628	−0.330314	+	0.943871i	$0.607155\pi$
$422$	−39.0013	−1.89855
$423$	−31.4614	−1.52970
$424$	−12.1685	−0.590954
$425$	−0.633975	−0.0307523
$426$	6.27634	0.304089
$427$	−58.1388	−2.81353
$428$	−12.2862	−0.593874
$429$	−0.0863482	−0.00416893
$430$	5.26904	0.254096
$431$	−36.4673	−1.75657	−0.878284	−	0.478139i	$-0.841312\pi$
$431$	−36.4673	−1.75657	−0.878284	+	0.478139i	$0.841312\pi$
$432$	2.03479	0.0978989
$433$	39.6428	1.90511	0.952556	−	0.304362i	$-0.0984434\pi$
$433$	39.6428	1.90511	0.952556	+	0.304362i	$0.0984434\pi$
$434$	−44.4066	−2.13159
$435$	−3.38411	−0.162256
$436$	12.9702	0.621160
$437$	38.3740	1.83568
$438$	4.42196	0.211290
$439$	30.8071	1.47034	0.735171	−	0.677882i	$-0.237102\pi$
$439$	30.8071	1.47034	0.735171	+	0.677882i	$0.237102\pi$
$440$	4.88828	0.233039
$441$	−38.3841	−1.82781
$442$	−0.716990	−0.0341037
$443$	6.61069	0.314083	0.157042	−	0.987592i	$-0.449804\pi$
$443$	6.61069	0.314083	0.157042	+	0.987592i	$0.449804\pi$
$444$	8.65802	0.410891
$445$	−23.3021	−1.10463
$446$	39.6358	1.87681
$447$	0.00593744	0.000280831 0
$448$	57.8536	2.73333
$449$	−26.9658	−1.27259	−0.636297	−	0.771444i	$-0.719535\pi$
$449$	−26.9658	−1.27259	−0.636297	+	0.771444i	$0.719535\pi$
$450$	4.12141	0.194285
$451$	5.16475	0.243198
$452$	1.03160	0.0485222
$453$	1.77796	0.0835358
$454$	4.02127	0.188727
$455$	−3.43771	−0.161163
$456$	4.18916	0.196175
$457$	20.7271	0.969572	0.484786	−	0.874633i	$-0.338897\pi$
$457$	20.7271	0.969572	0.484786	+	0.874633i	$0.338897\pi$
$458$	40.3446	1.88518
$459$	1.58493	0.0739784
$460$	35.0479	1.63412
$461$	−11.1191	−0.517869	−0.258935	−	0.965895i	$-0.583371\pi$
$461$	−11.1191	−0.517869	−0.258935	+	0.965895i	$0.583371\pi$
$462$	2.66110	0.123806
$463$	27.5426	1.28001	0.640006	−	0.768370i	$-0.278932\pi$
$463$	27.5426	1.28001	0.640006	+	0.768370i	$0.278932\pi$
$464$	−6.84669	−0.317850
$465$	2.83089	0.131279
$466$	−29.4561	−1.36453
$467$	−7.17243	−0.331901	−0.165950	−	0.986134i	$-0.553069\pi$
$467$	−7.17243	−0.331901	−0.165950	+	0.986134i	$0.553069\pi$
$468$	2.76930	0.128011
$469$	−7.44008	−0.343551
$470$	56.6056	2.61102
$471$	−0.449841	−0.0207276
$472$	18.4960	0.851346
$473$	1.00000	0.0459800
$474$	−7.60589	−0.349350
$475$	−4.82377	−0.221330
$476$	13.1282	0.601730
$477$	−17.3037	−0.792280
$478$	0.651160	0.0297833
$479$	3.02681	0.138299	0.0691493	−	0.997606i	$-0.477972\pi$
$479$	3.02681	0.138299	0.0691493	+	0.997606i	$0.477972\pi$
$480$	−4.42211	−0.201841
$481$	−3.57282	−0.162907
$482$	−57.0943	−2.60058
$483$	6.04589	0.275098
$484$	2.92774	0.133079
$485$	19.9540	0.906065
$486$	−15.5173	−0.703881
$487$	−0.833981	−0.0377913	−0.0188957	−	0.999821i	$-0.506015\pi$
$487$	−0.833981	−0.0377913	−0.0188957	+	0.999821i	$0.506015\pi$
$488$	−26.7018	−1.20874
$489$	−5.78103	−0.261427
$490$	69.0610	3.11986
$491$	−6.43719	−0.290507	−0.145253	−	0.989395i	$-0.546400\pi$
$491$	−6.43719	−0.290507	−0.145253	+	0.989395i	$0.546400\pi$
$492$	4.04246	0.182248
$493$	−5.33301	−0.240187
$494$	−5.45540	−0.245450
$495$	6.95116	0.312431
$496$	5.72742	0.257169
$497$	47.4232	2.12722
$498$	3.96938	0.177872
$499$	35.5823	1.59288	0.796440	−	0.604717i	$-0.206714\pi$
$499$	35.5823	1.59288	0.796440	+	0.604717i	$0.206714\pi$
$500$	30.3407	1.35688
$501$	−5.58196	−0.249383
$502$	49.8446	2.22467
$503$	16.7152	0.745295	0.372648	−	0.927973i	$-0.378450\pi$
$503$	16.7152	0.745295	0.372648	+	0.927973i	$0.378450\pi$
$504$	−27.0440	−1.20464
$505$	20.5197	0.913113
$506$	11.1956	0.497704
$507$	−3.44753	−0.153110
$508$	−56.7028	−2.51578
$509$	−23.0557	−1.02193	−0.510964	−	0.859602i	$-0.670711\pi$
$509$	−23.0557	−1.02193	−0.510964	+	0.859602i	$0.670711\pi$
$510$	−1.40863	−0.0623750
$511$	33.4118	1.47805
$512$	−14.2347	−0.629091
$513$	12.0594	0.532435
$514$	−32.5640	−1.43634
$515$	−4.24673	−0.187133
$516$	0.782702	0.0344565
$517$	10.7431	0.472479
$518$	110.108	4.83787
$519$	4.60342	0.202068
$520$	−1.57886	−0.0692378
$521$	−38.6761	−1.69443	−0.847216	−	0.531249i	$-0.821723\pi$
$521$	−38.6761	−1.69443	−0.847216	+	0.531249i	$0.821723\pi$
$522$	34.6693	1.51744
$523$	−27.1550	−1.18741	−0.593704	−	0.804684i	$-0.702335\pi$
$523$	−27.1550	−1.18741	−0.593704	+	0.804684i	$0.702335\pi$
$524$	−18.3542	−0.801807
$525$	−0.759994	−0.0331688
$526$	13.5046	0.588827
$527$	4.46119	0.194332
$528$	−0.343220	−0.0149367
$529$	2.43582	0.105905
$530$	31.1329	1.35233
$531$	26.3014	1.14138
$532$	99.8893	4.33075
$533$	−1.66816	−0.0722561
$534$	−5.82607	−0.252119
$535$	9.96074	0.430640
$536$	−3.41706	−0.147594
$537$	2.85565	0.123230
$538$	−48.0924	−2.07341
$539$	13.1070	0.564557
$540$	11.0141	0.473973
$541$	24.7121	1.06246	0.531228	−	0.847229i	$-0.321731\pi$
$541$	24.7121	1.06246	0.531228	+	0.847229i	$0.321731\pi$
$542$	−53.7065	−2.30689
$543$	0.598237	0.0256728
$544$	−6.96879	−0.298784
$545$	−10.5153	−0.450426
$546$	−0.859509	−0.0367836
$547$	−37.5490	−1.60548	−0.802740	−	0.596330i	$-0.796625\pi$
$547$	−37.5490	−1.60548	−0.802740	+	0.596330i	$0.796625\pi$
$548$	63.4344	2.70978
$549$	−37.9701	−1.62053
$550$	−1.40733	−0.0600088
$551$	−40.5776	−1.72866
$552$	2.77674	0.118186
$553$	−57.4692	−2.44384
$554$	50.2694	2.13574
$555$	−7.01930	−0.297953
$556$	38.1667	1.61863
$557$	−31.9438	−1.35350	−0.676751	−	0.736212i	$-0.736613\pi$
$557$	−31.9438	−1.35350	−0.676751	+	0.736212i	$0.736613\pi$
$558$	−29.0017	−1.22774
$559$	−0.322990	−0.0136610
$560$	−13.6644	−0.577424
$561$	−0.267340	−0.0112871
$562$	49.9955	2.10893
$563$	12.8692	0.542371	0.271186	−	0.962527i	$-0.412584\pi$
$563$	12.8692	0.542371	0.271186	+	0.962527i	$0.412584\pi$
$564$	8.40861	0.354066
$565$	−0.836345	−0.0351853
$566$	−60.6194	−2.54802
$567$	−37.4953	−1.57465
$568$	21.7804	0.913886
$569$	−38.1673	−1.60006	−0.800028	−	0.599963i	$-0.795182\pi$
$569$	−38.1673	−1.60006	−0.800028	+	0.599963i	$0.795182\pi$
$570$	−10.7179	−0.448923
$571$	−14.1585	−0.592516	−0.296258	−	0.955108i	$-0.595739\pi$
$571$	−14.1585	−0.592516	−0.296258	+	0.955108i	$0.595739\pi$
$572$	−0.945630	−0.0395388
$573$	−4.67338	−0.195233
$574$	51.4098	2.14580
$575$	−3.19739	−0.133340
$576$	37.7839	1.57433
$577$	−9.92833	−0.413322	−0.206661	−	0.978413i	$-0.566260\pi$
$577$	−9.92833	−0.413322	−0.206661	+	0.978413i	$0.566260\pi$
$578$	−2.21985	−0.0923336
$579$	5.02874	0.208987
$580$	−37.0605	−1.53886
$581$	29.9921	1.24428
$582$	4.98897	0.206799
$583$	5.90865	0.244711
$584$	15.3453	0.634993
$585$	−2.24515	−0.0928257
$586$	−27.3246	−1.12877
$587$	24.1462	0.996619	0.498310	−	0.866999i	$-0.333954\pi$
$587$	24.1462	0.996619	0.498310	+	0.866999i	$0.333954\pi$
$588$	10.2588	0.423067
$589$	33.9441	1.39864
$590$	−47.3216	−1.94820
$591$	0.837541	0.0344518
$592$	−14.2014	−0.583673
$593$	4.54722	0.186732	0.0933661	−	0.995632i	$-0.470237\pi$
$593$	4.54722	0.186732	0.0933661	+	0.995632i	$0.470237\pi$
$594$	3.51832	0.144358
$595$	−10.6434	−0.436337
$596$	0.0650230	0.00266345
$597$	−0.844647	−0.0345691
$598$	−3.61606	−0.147872
$599$	−22.7420	−0.929214	−0.464607	−	0.885517i	$-0.653804\pi$
$599$	−22.7420	−0.929214	−0.464607	+	0.885517i	$0.653804\pi$
$600$	−0.349048	−0.0142498
$601$	−47.9851	−1.95735	−0.978677	−	0.205407i	$-0.934148\pi$
$601$	−47.9851	−1.95735	−0.978677	+	0.205407i	$0.934148\pi$
$602$	9.95398	0.405694
$603$	−4.85908	−0.197877
$604$	19.4711	0.792266
$605$	−2.37360	−0.0965005
$606$	5.13039	0.208408
$607$	38.6582	1.56909	0.784545	−	0.620072i	$-0.212897\pi$
$607$	38.6582	1.56909	0.784545	+	0.620072i	$0.212897\pi$
$608$	−53.0238	−2.15040
$609$	−6.39307	−0.259060
$610$	68.3162	2.76604
$611$	−3.46990	−0.140377
$612$	8.57396	0.346582
$613$	4.69959	0.189815	0.0949073	−	0.995486i	$-0.469745\pi$
$613$	4.69959	0.189815	0.0949073	+	0.995486i	$0.469745\pi$
$614$	−3.51399	−0.141813
$615$	−3.27733	−0.132155
$616$	9.23467	0.372076
$617$	8.69067	0.349873	0.174937	−	0.984580i	$-0.444028\pi$
$617$	8.69067	0.349873	0.174937	+	0.984580i	$0.444028\pi$
$618$	−1.06178	−0.0427111
$619$	−0.856669	−0.0344324	−0.0172162	−	0.999852i	$-0.505480\pi$
$619$	−0.856669	−0.0344324	−0.0172162	+	0.999852i	$0.505480\pi$
$620$	31.0020	1.24507
$621$	7.99345	0.320766
$622$	40.9643	1.64252
$623$	−44.0211	−1.76367
$624$	0.110857	0.00443782
$625$	−27.7680	−1.11072
$626$	−4.49827	−0.179787
$627$	−2.03413	−0.0812352
$628$	−4.92637	−0.196583
$629$	−11.0617	−0.441059
$630$	69.1917	2.75666
$631$	−7.38323	−0.293922	−0.146961	−	0.989142i	$-0.546949\pi$
$631$	−7.38323	−0.293922	−0.146961	+	0.989142i	$0.546949\pi$
$632$	−26.3943	−1.04991
$633$	4.69699	0.186689
$634$	51.8456	2.05905
$635$	45.9706	1.82429
$636$	4.62471	0.183382
$637$	−4.23342	−0.167734
$638$	−11.8385	−0.468690
$639$	30.9719	1.22523
$640$	−34.8989	−1.37950
$641$	−27.2695	−1.07708	−0.538541	−	0.842599i	$-0.681024\pi$
$641$	−27.2695	−1.07708	−0.538541	+	0.842599i	$0.681024\pi$
$642$	2.49042	0.0982889
$643$	33.8263	1.33398	0.666989	−	0.745067i	$-0.267583\pi$
$643$	33.8263	1.33398	0.666989	+	0.745067i	$0.267583\pi$
$644$	66.2107	2.60907
$645$	−0.634559	−0.0249857
$646$	−16.8903	−0.664540
$647$	47.4774	1.86653	0.933265	−	0.359190i	$-0.116947\pi$
$647$	47.4774	1.86653	0.933265	+	0.359190i	$0.116947\pi$
$648$	−17.2207	−0.676495
$649$	−8.98108	−0.352538
$650$	0.454554	0.0178291
$651$	5.34796	0.209603
$652$	−63.3101	−2.47941
$653$	12.3512	0.483341	0.241671	−	0.970358i	$-0.422305\pi$
$653$	12.3512	0.483341	0.241671	+	0.970358i	$0.422305\pi$
$654$	−2.62907	−0.102805
$655$	14.8803	0.581420
$656$	−6.63067	−0.258884
$657$	21.8211	0.851322
$658$	106.936	4.16881
$659$	18.0638	0.703664	0.351832	−	0.936063i	$-0.385559\pi$
$659$	18.0638	0.703664	0.351832	+	0.936063i	$0.385559\pi$
$660$	−1.85782	−0.0723156
$661$	−12.4519	−0.484322	−0.242161	−	0.970236i	$-0.577856\pi$
$661$	−12.4519	−0.484322	−0.242161	+	0.970236i	$0.577856\pi$
$662$	−27.9405	−1.08594
$663$	0.0863482	0.00335349
$664$	13.7747	0.534562
$665$	−80.9831	−3.14039
$666$	71.9110	2.78649
$667$	−26.8965	−1.04144
$668$	−61.1300	−2.36519
$669$	−4.77341	−0.184551
$670$	8.74250	0.337752
$671$	12.9656	0.500532
$672$	−8.35401	−0.322263
$673$	24.4039	0.940701	0.470350	−	0.882480i	$-0.344128\pi$
$673$	24.4039	0.940701	0.470350	+	0.882480i	$0.344128\pi$
$674$	−3.43778	−0.132418
$675$	−1.00481	−0.0386751
$676$	−37.7551	−1.45212
$677$	6.82084	0.262146	0.131073	−	0.991373i	$-0.458158\pi$
$677$	6.82084	0.262146	0.131073	+	0.991373i	$0.458158\pi$
$678$	−0.209106	−0.00803066
$679$	37.6961	1.44664
$680$	−4.88828	−0.187457
$681$	−0.484288	−0.0185579
$682$	9.90317	0.379212
$683$	−7.69881	−0.294587	−0.147293	−	0.989093i	$-0.547056\pi$
$683$	−7.69881	−0.294587	−0.147293	+	0.989093i	$0.547056\pi$
$684$	65.2372	2.49441
$685$	−51.4281	−1.96497
$686$	60.7886	2.32092
$687$	−4.85876	−0.185373
$688$	−1.28383	−0.0489457
$689$	−1.90844	−0.0727056
$690$	−7.10425	−0.270454
$691$	−30.0224	−1.14211	−0.571053	−	0.820913i	$-0.693465\pi$
$691$	−30.0224	−1.14211	−0.571053	+	0.820913i	$0.693465\pi$
$692$	50.4137	1.91644
$693$	13.1318	0.498834
$694$	−8.94873	−0.339689
$695$	−30.9428	−1.17373
$696$	−2.93620	−0.111296
$697$	−5.16475	−0.195629
$698$	−8.63859	−0.326975
$699$	3.54744	0.134177
$700$	−8.32296	−0.314578
$701$	−8.90452	−0.336319	−0.168160	−	0.985760i	$-0.553782\pi$
$701$	−8.90452	−0.336319	−0.168160	+	0.985760i	$0.553782\pi$
$702$	−1.13638	−0.0428900
$703$	−84.1659	−3.17438
$704$	−12.9020	−0.486263
$705$	−6.81710	−0.256747
$706$	−71.9091	−2.70633
$707$	38.7646	1.45789
$708$	−7.02951	−0.264185
$709$	−39.7906	−1.49437	−0.747183	−	0.664618i	$-0.768594\pi$
$709$	−39.7906	−1.49437	−0.747183	+	0.664618i	$0.768594\pi$
$710$	−55.7249	−2.09132
$711$	−37.5329	−1.40759
$712$	−20.2179	−0.757698
$713$	22.4995	0.842614
$714$	−2.66110	−0.0995892
$715$	0.766649	0.0286711
$716$	31.2732	1.16873
$717$	−0.0784202	−0.00292866
$718$	18.5759	0.693247
$719$	33.1680	1.23696	0.618479	−	0.785801i	$-0.287749\pi$
$719$	33.1680	1.23696	0.618479	+	0.785801i	$0.287749\pi$
$720$	−8.92412	−0.332582
$721$	−8.02269	−0.298781
$722$	−86.3372	−3.21314
$723$	6.87596	0.255720
$724$	6.55150	0.243485
$725$	3.38100	0.125567
$726$	−0.593455	−0.0220252
$727$	8.72334	0.323531	0.161765	−	0.986829i	$-0.448281\pi$
$727$	8.72334	0.323531	0.161765	+	0.986829i	$0.448281\pi$
$728$	−2.98271	−0.110546
$729$	−23.2168	−0.859883
$730$	−39.2607	−1.45310
$731$	−1.00000	−0.0369863
$732$	10.1482	0.375088
$733$	−3.85336	−0.142327	−0.0711635	−	0.997465i	$-0.522671\pi$
$733$	−3.85336	−0.142327	−0.0711635	+	0.997465i	$0.522671\pi$
$734$	3.61121	0.133292
$735$	−8.31713	−0.306782
$736$	−35.1463	−1.29551
$737$	1.65922	0.0611182
$738$	33.5755	1.23593
$739$	16.5837	0.610043	0.305021	−	0.952345i	$-0.401336\pi$
$739$	16.5837	0.610043	0.305021	+	0.952345i	$0.401336\pi$
$740$	−76.8708	−2.82583
$741$	0.657003	0.0241356
$742$	58.8146	2.15915
$743$	−41.8949	−1.53698	−0.768488	−	0.639865i	$-0.778990\pi$
$743$	−41.8949	−1.53698	−0.768488	+	0.639865i	$0.778990\pi$
$744$	2.45620	0.0900486
$745$	−0.0527160	−0.00193136
$746$	−57.8359	−2.11752
$747$	19.5877	0.716677
$748$	−2.92774	−0.107049
$749$	18.8173	0.687569
$750$	−6.15009	−0.224570
$751$	52.2366	1.90614	0.953071	−	0.302747i	$-0.0979037\pi$
$751$	52.2366	1.90614	0.953071	+	0.302747i	$0.0979037\pi$
$752$	−13.7923	−0.502953
$753$	−6.00287	−0.218757
$754$	3.82371	0.139251
$755$	−15.7857	−0.574502
$756$	20.8073	0.756755
$757$	−0.551418	−0.0200416	−0.0100208	−	0.999950i	$-0.503190\pi$
$757$	−0.551418	−0.0200416	−0.0100208	+	0.999950i	$0.503190\pi$
$758$	75.1140	2.72826
$759$	−1.34830	−0.0489403
$760$	−37.1937	−1.34916
$761$	−6.90506	−0.250308	−0.125154	−	0.992137i	$-0.539943\pi$
$761$	−6.90506	−0.250308	−0.125154	+	0.992137i	$0.539943\pi$
$762$	11.4937	0.416373
$763$	−19.8650	−0.719160
$764$	−51.1799	−1.85162
$765$	−6.95116	−0.251320
$766$	−30.9449	−1.11808
$767$	2.90080	0.104742
$768$	−1.82709	−0.0659295
$769$	−9.00552	−0.324747	−0.162374	−	0.986729i	$-0.551915\pi$
$769$	−9.00552	−0.324747	−0.162374	+	0.986729i	$0.551915\pi$
$770$	−23.6268	−0.851450
$771$	3.92173	0.141238
$772$	55.0715	1.98207
$773$	7.79724	0.280447	0.140224	−	0.990120i	$-0.455218\pi$
$773$	7.79724	0.280447	0.140224	+	0.990120i	$0.455218\pi$
$774$	6.50090	0.233670
$775$	−2.82828	−0.101595
$776$	17.3129	0.621499
$777$	−13.2605	−0.475717
$778$	2.27961	0.0817281
$779$	−39.2973	−1.40797
$780$	0.600058	0.0214855
$781$	−10.5759	−0.378436
$782$	−11.1956	−0.400353
$783$	−8.45247	−0.302067
$784$	−16.8271	−0.600969
$785$	3.99395	0.142550
$786$	3.72041	0.132703
$787$	40.3667	1.43892	0.719458	−	0.694536i	$-0.244390\pi$
$787$	40.3667	1.43892	0.719458	+	0.694536i	$0.244390\pi$
$788$	9.17220	0.326746
$789$	−1.62638	−0.0579005
$790$	67.5295	2.40259
$791$	−1.57998	−0.0561776
$792$	6.03112	0.214306
$793$	−4.18776	−0.148712
$794$	−10.0050	−0.355065
$795$	−3.74939	−0.132977
$796$	−9.25003	−0.327858
$797$	−18.8516	−0.667757	−0.333878	−	0.942616i	$-0.608357\pi$
$797$	−18.8516	−0.667757	−0.333878	+	0.942616i	$0.608357\pi$
$798$	−20.2477	−0.716760
$799$	−10.7431	−0.380062
$800$	4.41804	0.156201
$801$	−28.7500	−1.01583
$802$	81.7887	2.88806
$803$	−7.45121	−0.262948
$804$	1.29867	0.0458007
$805$	−53.6789	−1.89193
$806$	−3.19863	−0.112667
$807$	5.79184	0.203883
$808$	17.8037	0.626333
$809$	24.6042	0.865038	0.432519	−	0.901625i	$-0.357625\pi$
$809$	24.6042	0.865038	0.432519	+	0.901625i	$0.357625\pi$
$810$	44.0590	1.54808
$811$	−17.1154	−0.601003	−0.300501	−	0.953781i	$-0.597154\pi$
$811$	−17.1154	−0.601003	−0.300501	+	0.953781i	$0.597154\pi$
$812$	−70.0128	−2.45697
$813$	6.46796	0.226841
$814$	−24.5553	−0.860664
$815$	51.3273	1.79792
$816$	0.343220	0.0120151
$817$	−7.60876	−0.266197
$818$	−85.4816	−2.98879
$819$	−4.24143	−0.148207
$820$	−35.8912	−1.25338
$821$	12.0210	0.419535	0.209767	−	0.977751i	$-0.432729\pi$
$821$	12.0210	0.419535	0.209767	+	0.977751i	$0.432729\pi$
$822$	−12.8582	−0.448482
$823$	14.8541	0.517780	0.258890	−	0.965907i	$-0.416643\pi$
$823$	14.8541	0.517780	0.258890	+	0.965907i	$0.416643\pi$
$824$	−3.68464	−0.128361
$825$	0.169487	0.00590079
$826$	−89.3975	−3.11054
$827$	30.3817	1.05648	0.528238	−	0.849097i	$-0.322853\pi$
$827$	30.3817	1.05648	0.528238	+	0.849097i	$0.322853\pi$
$828$	43.2419	1.50276
$829$	−30.7472	−1.06789	−0.533947	−	0.845518i	$-0.679292\pi$
$829$	−30.7472	−1.06789	−0.533947	+	0.845518i	$0.679292\pi$
$830$	−35.2424	−1.22328
$831$	−6.05403	−0.210012
$832$	4.16722	0.144472
$833$	−13.1070	−0.454129
$834$	−7.73643	−0.267891
$835$	49.5598	1.71509
$836$	−22.2764	−0.770447
$837$	7.07069	0.244399
$838$	82.7135	2.85729
$839$	−3.70608	−0.127948	−0.0639740	−	0.997952i	$-0.520377\pi$
$839$	−3.70608	−0.127948	−0.0639740	+	0.997952i	$0.520377\pi$
$840$	−5.85994	−0.202187
$841$	−0.559020	−0.0192766
$842$	30.0900	1.03697
$843$	−6.02104	−0.207375
$844$	51.4384	1.77058
$845$	30.6092	1.05299
$846$	69.8395	2.40113
$847$	−4.48408	−0.154075
$848$	−7.58572	−0.260495
$849$	7.30050	0.250552
$850$	1.40733	0.0482710
$851$	−55.7885	−1.91241
$852$	−8.27779	−0.283592
$853$	13.5755	0.464815	0.232407	−	0.972619i	$-0.425340\pi$
$853$	13.5755	0.464815	0.232407	+	0.972619i	$0.425340\pi$
$854$	129.059	4.41632
$855$	−52.8897	−1.80879
$856$	8.64236	0.295390
$857$	−6.88297	−0.235118	−0.117559	−	0.993066i	$-0.537507\pi$
$857$	−6.88297	−0.235118	−0.117559	+	0.993066i	$0.537507\pi$
$858$	0.191680	0.00654385
$859$	22.4660	0.766529	0.383264	−	0.923639i	$-0.374800\pi$
$859$	22.4660	0.766529	0.383264	+	0.923639i	$0.374800\pi$
$860$	−6.94927	−0.236968
$861$	−6.19137	−0.211001
$862$	80.9520	2.75724
$863$	−9.81220	−0.334011	−0.167006	−	0.985956i	$-0.553410\pi$
$863$	−9.81220	−0.334011	−0.167006	+	0.985956i	$0.553410\pi$
$864$	−11.0451	−0.375761
$865$	−40.8718	−1.38968
$866$	−88.0012	−2.99040
$867$	0.267340	0.00907935
$868$	58.5674	1.98791
$869$	12.8163	0.434763
$870$	7.51221	0.254688
$871$	−0.535912	−0.0181587
$872$	−9.12353	−0.308962
$873$	24.6191	0.833230
$874$	−85.1845	−2.88141
$875$	−46.4694	−1.57095
$876$	−5.83208	−0.197048
$877$	−42.3583	−1.43034	−0.715168	−	0.698952i	$-0.753650\pi$
$877$	−42.3583	−1.43034	−0.715168	+	0.698952i	$0.753650\pi$
$878$	−68.3871	−2.30795
$879$	3.29075	0.110994
$880$	3.04730	0.102725
$881$	−28.5518	−0.961935	−0.480967	−	0.876738i	$-0.659714\pi$
$881$	−28.5518	−0.961935	−0.480967	+	0.876738i	$0.659714\pi$
$882$	85.2070	2.86907
$883$	29.5222	0.993501	0.496750	−	0.867894i	$-0.334526\pi$
$883$	29.5222	0.993501	0.496750	+	0.867894i	$0.334526\pi$
$884$	0.945630	0.0318050
$885$	5.69902	0.191571
$886$	−14.6747	−0.493007
$887$	9.28915	0.311899	0.155950	−	0.987765i	$-0.450156\pi$
$887$	9.28915	0.311899	0.155950	+	0.987765i	$0.450156\pi$
$888$	−6.09024	−0.204375
$889$	86.8451	2.91269
$890$	51.7272	1.73390
$891$	8.36187	0.280133
$892$	−52.2753	−1.75031
$893$	−81.7414	−2.73537
$894$	−0.0131802	−0.000440813 0
$895$	−25.3541	−0.847493
$896$	−65.9291	−2.20254
$897$	0.435488	0.0145405
$898$	59.8600	1.99755
$899$	−23.7916	−0.793493
$900$	−5.43568	−0.181189
$901$	−5.90865	−0.196846
$902$	−11.4650	−0.381742
$903$	−1.19877	−0.0398927
$904$	−0.725649	−0.0241347
$905$	−5.31149	−0.176560
$906$	−3.94681	−0.131124
$907$	−15.4131	−0.511782	−0.255891	−	0.966706i	$-0.582369\pi$
$907$	−15.4131	−0.511782	−0.255891	+	0.966706i	$0.582369\pi$
$908$	−5.30360	−0.176006
$909$	25.3170	0.839712
$910$	7.63121	0.252972
$911$	4.24248	0.140560	0.0702799	−	0.997527i	$-0.477611\pi$
$911$	4.24248	0.140560	0.0702799	+	0.997527i	$0.477611\pi$
$912$	2.61148	0.0864747
$913$	−6.68858	−0.221360
$914$	−46.0110	−1.52191
$915$	−8.22744	−0.271991
$916$	−53.2100	−1.75811
$917$	28.1110	0.928307
$918$	−3.51832	−0.116122
$919$	−31.7794	−1.04830	−0.524152	−	0.851625i	$-0.675618\pi$
$919$	−31.7794	−1.04830	−0.524152	+	0.851625i	$0.675618\pi$
$920$	−24.6535	−0.812802
$921$	0.423195	0.0139448
$922$	24.6828	0.812884
$923$	3.41592	0.112436
$924$	−3.50970	−0.115461
$925$	7.01285	0.230581
$926$	−61.1404	−2.00920
$927$	−5.23958	−0.172090
$928$	37.1646	1.21999
$929$	27.1909	0.892106	0.446053	−	0.895007i	$-0.352829\pi$
$929$	27.1909	0.892106	0.446053	+	0.895007i	$0.352829\pi$
$930$	−6.28415	−0.206065
$931$	−99.7277	−3.26844
$932$	38.8493	1.27255
$933$	−4.93340	−0.161512
$934$	15.9217	0.520975
$935$	2.37360	0.0776250
$936$	−1.94799	−0.0636721
$937$	20.0035	0.653484	0.326742	−	0.945113i	$-0.394049\pi$
$937$	20.0035	0.653484	0.326742	+	0.945113i	$0.394049\pi$
$938$	16.5159	0.539262
$939$	0.541734	0.0176788
$940$	−74.6565	−2.43503
$941$	−15.8219	−0.515780	−0.257890	−	0.966174i	$-0.583027\pi$
$941$	−15.8219	−0.515780	−0.257890	+	0.966174i	$0.583027\pi$
$942$	0.998580	0.0325355
$943$	−26.0479	−0.848235
$944$	11.5302	0.375276
$945$	−16.8691	−0.548752
$946$	−2.21985	−0.0721736
$947$	6.77262	0.220081	0.110040	−	0.993927i	$-0.464902\pi$
$947$	6.77262	0.220081	0.110040	+	0.993927i	$0.464902\pi$
$948$	10.0313	0.325802
$949$	2.40667	0.0781237
$950$	10.7080	0.347415
$951$	−6.24385	−0.202471
$952$	−9.23467	−0.299297
$953$	17.6965	0.573245	0.286622	−	0.958044i	$-0.407468\pi$
$953$	17.6965	0.573245	0.286622	+	0.958044i	$0.407468\pi$
$954$	38.4115	1.24362
$955$	41.4930	1.34268
$956$	−0.858807	−0.0277758
$957$	1.42573	0.0460872
$958$	−6.71907	−0.217083
$959$	−97.1552	−3.13731
$960$	8.18708	0.264237
$961$	−11.0978	−0.357993
$962$	7.93113	0.255710
$963$	12.2895	0.396023
$964$	75.3011	2.42528
$965$	−44.6480	−1.43727
$966$	−13.4210	−0.431813
$967$	32.2548	1.03724	0.518622	−	0.855004i	$-0.326445\pi$
$967$	32.2548	1.03724	0.518622	+	0.855004i	$0.326445\pi$
$968$	−2.05944	−0.0661928
$969$	2.03413	0.0653456
$970$	−44.2949	−1.42222
$971$	1.86163	0.0597427	0.0298713	−	0.999554i	$-0.490490\pi$
$971$	1.86163	0.0597427	0.0298713	+	0.999554i	$0.490490\pi$
$972$	20.4657	0.656436
$973$	−58.4556	−1.87400
$974$	1.85131	0.0593199
$975$	−0.0547427	−0.00175317
$976$	−16.6457	−0.532815
$977$	−11.4173	−0.365273	−0.182637	−	0.983180i	$-0.558463\pi$
$977$	−11.4173	−0.365273	−0.182637	+	0.983180i	$0.558463\pi$
$978$	12.8330	0.410355
$979$	9.81721	0.313759
$980$	−91.0838	−2.90957
$981$	−12.9737	−0.414219
$982$	14.2896	0.456000
$983$	10.1149	0.322615	0.161307	−	0.986904i	$-0.448429\pi$
$983$	10.1149	0.322615	0.161307	+	0.986904i	$0.448429\pi$
$984$	−2.84356	−0.0906492
$985$	−7.43617	−0.236936
$986$	11.8385	0.377014
$987$	−12.8785	−0.409927
$988$	7.19507	0.228906
$989$	−5.04339	−0.160371
$990$	−15.4305	−0.490414
$991$	−50.6447	−1.60878	−0.804391	−	0.594100i	$-0.797508\pi$
$991$	−50.6447	−1.60878	−0.804391	+	0.594100i	$0.797508\pi$
$992$	−31.0891	−0.987079
$993$	3.36492	0.106782
$994$	−105.273	−3.33904
$995$	7.49926	0.237743
$996$	−5.23517	−0.165883
$997$	−26.0508	−0.825037	−0.412518	−	0.910949i	$-0.635351\pi$
$997$	−26.0508	−0.825037	−0.412518	+	0.910949i	$0.635351\pi$
$998$	−78.9873	−2.50030
$999$	−17.5321	−0.554690

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.d.1.9	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.d.1.9	✓	62	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21985 q^{2} +0.267340 q^{3} +2.92774 q^{4} -2.37360 q^{5} -0.593455 q^{6} -4.48408 q^{7} -2.05944 q^{8} -2.92853 q^{9} +O(q^{10})\)	\(q-2.21985 q^{2} +0.267340 q^{3} +2.92774 q^{4} -2.37360 q^{5} -0.593455 q^{6} -4.48408 q^{7} -2.05944 q^{8} -2.92853 q^{9} +5.26904 q^{10} +1.00000 q^{11} +0.782702 q^{12} -0.322990 q^{13} +9.95398 q^{14} -0.634559 q^{15} -1.28383 q^{16} -1.00000 q^{17} +6.50090 q^{18} -7.60876 q^{19} -6.94927 q^{20} -1.19877 q^{21} -2.21985 q^{22} -5.04339 q^{23} -0.550570 q^{24} +0.633975 q^{25} +0.716990 q^{26} -1.58493 q^{27} -13.1282 q^{28} +5.33301 q^{29} +1.40863 q^{30} -4.46119 q^{31} +6.96879 q^{32} +0.267340 q^{33} +2.21985 q^{34} +10.6434 q^{35} -8.57396 q^{36} +11.0617 q^{37} +16.8903 q^{38} -0.0863482 q^{39} +4.88828 q^{40} +5.16475 q^{41} +2.66110 q^{42} +1.00000 q^{43} +2.92774 q^{44} +6.95116 q^{45} +11.1956 q^{46} +10.7431 q^{47} -0.343220 q^{48} +13.1070 q^{49} -1.40733 q^{50} -0.267340 q^{51} -0.945630 q^{52} +5.90865 q^{53} +3.51832 q^{54} -2.37360 q^{55} +9.23467 q^{56} -2.03413 q^{57} -11.8385 q^{58} -8.98108 q^{59} -1.85782 q^{60} +12.9656 q^{61} +9.90317 q^{62} +13.1318 q^{63} -12.9020 q^{64} +0.766649 q^{65} -0.593455 q^{66} +1.65922 q^{67} -2.92774 q^{68} -1.34830 q^{69} -23.6268 q^{70} -10.5759 q^{71} +6.03112 q^{72} -7.45121 q^{73} -24.5553 q^{74} +0.169487 q^{75} -22.2764 q^{76} -4.48408 q^{77} +0.191680 q^{78} +12.8163 q^{79} +3.04730 q^{80} +8.36187 q^{81} -11.4650 q^{82} -6.68858 q^{83} -3.50970 q^{84} +2.37360 q^{85} -2.21985 q^{86} +1.42573 q^{87} -2.05944 q^{88} +9.81721 q^{89} -15.4305 q^{90} +1.44831 q^{91} -14.7657 q^{92} -1.19266 q^{93} -23.8480 q^{94} +18.0602 q^{95} +1.86304 q^{96} -8.40664 q^{97} -29.0955 q^{98} -2.92853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

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