LMFDB - Embedded newform 8041.2.a.d.1.17

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			1.17
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)

$f(q)$	$=$	$q-1.47469 q^{2} -1.86783 q^{3} +0.174714 q^{4} +4.42666 q^{5} +2.75448 q^{6} +0.892669 q^{7} +2.69173 q^{8} +0.488806 q^{9} +O(q^{10})$	\(q-1.47469 q^{2} -1.86783 q^{3} +0.174714 q^{4} +4.42666 q^{5} +2.75448 q^{6} +0.892669 q^{7} +2.69173 q^{8} +0.488806 q^{9} -6.52796 q^{10} +1.00000 q^{11} -0.326337 q^{12} -2.41746 q^{13} -1.31641 q^{14} -8.26828 q^{15} -4.31890 q^{16} -1.00000 q^{17} -0.720838 q^{18} -2.21242 q^{19} +0.773401 q^{20} -1.66736 q^{21} -1.47469 q^{22} -7.86585 q^{23} -5.02771 q^{24} +14.5954 q^{25} +3.56501 q^{26} +4.69049 q^{27} +0.155962 q^{28} +0.955383 q^{29} +12.1932 q^{30} -1.41967 q^{31} +0.985583 q^{32} -1.86783 q^{33} +1.47469 q^{34} +3.95155 q^{35} +0.0854014 q^{36} +4.11613 q^{37} +3.26264 q^{38} +4.51542 q^{39} +11.9154 q^{40} -1.64398 q^{41} +2.45884 q^{42} +1.00000 q^{43} +0.174714 q^{44} +2.16378 q^{45} +11.5997 q^{46} +6.33042 q^{47} +8.06700 q^{48} -6.20314 q^{49} -21.5236 q^{50} +1.86783 q^{51} -0.422365 q^{52} -11.3066 q^{53} -6.91703 q^{54} +4.42666 q^{55} +2.40283 q^{56} +4.13244 q^{57} -1.40890 q^{58} +8.16349 q^{59} -1.44459 q^{60} +10.9031 q^{61} +2.09358 q^{62} +0.436342 q^{63} +7.18438 q^{64} -10.7013 q^{65} +2.75448 q^{66} -2.24511 q^{67} -0.174714 q^{68} +14.6921 q^{69} -5.82731 q^{70} -6.91251 q^{71} +1.31574 q^{72} -0.603813 q^{73} -6.07003 q^{74} -27.2617 q^{75} -0.386542 q^{76} +0.892669 q^{77} -6.65884 q^{78} -7.28661 q^{79} -19.1183 q^{80} -10.2275 q^{81} +2.42437 q^{82} -1.28713 q^{83} -0.291311 q^{84} -4.42666 q^{85} -1.47469 q^{86} -1.78450 q^{87} +2.69173 q^{88} -7.95194 q^{89} -3.19091 q^{90} -2.15799 q^{91} -1.37428 q^{92} +2.65172 q^{93} -9.33542 q^{94} -9.79365 q^{95} -1.84091 q^{96} -0.897558 q^{97} +9.14772 q^{98} +0.488806 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.47469	−1.04276	−0.521382	−	0.853323i	$-0.674583\pi$
$2$	−1.47469	−1.04276	−0.521382	+	0.853323i	$0.674583\pi$
$3$	−1.86783	−1.07839	−0.539197	−	0.842179i	$-0.681272\pi$
$3$	−1.86783	−1.07839	−0.539197	+	0.842179i	$0.681272\pi$
$4$	0.174714	0.0873571
$5$	4.42666	1.97966	0.989832	−	0.142239i	$-0.0454303\pi$
$5$	4.42666	1.97966	0.989832	+	0.142239i	$0.0454303\pi$
$6$	2.75448	1.12451
$7$	0.892669	0.337397	0.168699	−	0.985668i	$-0.446044\pi$
$7$	0.892669	0.337397	0.168699	+	0.985668i	$0.446044\pi$
$8$	2.69173	0.951671
$9$	0.488806	0.162935
$10$	−6.52796	−2.06432
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.326337	−0.0942055
$13$	−2.41746	−0.670483	−0.335241	−	0.942132i	$-0.608818\pi$
$13$	−2.41746	−0.670483	−0.335241	+	0.942132i	$0.608818\pi$
$14$	−1.31641	−0.351826
$15$	−8.26828	−2.13486
$16$	−4.31890	−1.07973
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.720838	−0.169903
$19$	−2.21242	−0.507565	−0.253782	−	0.967261i	$-0.581675\pi$
$19$	−2.21242	−0.507565	−0.253782	+	0.967261i	$0.581675\pi$
$20$	0.773401	0.172938
$21$	−1.66736	−0.363847
$22$	−1.47469	−0.314405
$23$	−7.86585	−1.64014	−0.820071	−	0.572262i	$-0.806066\pi$
$23$	−7.86585	−1.64014	−0.820071	+	0.572262i	$0.806066\pi$
$24$	−5.02771	−1.02628
$25$	14.5954	2.91907
$26$	3.56501	0.699155
$27$	4.69049	0.902686
$28$	0.155962	0.0294740
$29$	0.955383	0.177410	0.0887051	−	0.996058i	$-0.471727\pi$
$29$	0.955383	0.177410	0.0887051	+	0.996058i	$0.471727\pi$
$30$	12.1932	2.22616
$31$	−1.41967	−0.254981	−0.127490	−	0.991840i	$-0.540692\pi$
$31$	−1.41967	−0.254981	−0.127490	+	0.991840i	$0.540692\pi$
$32$	0.985583	0.174228
$33$	−1.86783	−0.325148
$34$	1.47469	0.252907
$35$	3.95155	0.667933
$36$	0.0854014	0.0142336
$37$	4.11613	0.676688	0.338344	−	0.941022i	$-0.390133\pi$
$37$	4.11613	0.676688	0.338344	+	0.941022i	$0.390133\pi$
$38$	3.26264	0.529270
$39$	4.51542	0.723045
$40$	11.9154	1.88399
$41$	−1.64398	−0.256747	−0.128374	−	0.991726i	$-0.540976\pi$
$41$	−1.64398	−0.256747	−0.128374	+	0.991726i	$0.540976\pi$
$42$	2.45884	0.379407
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.174714	0.0263392
$45$	2.16378	0.322557
$46$	11.5997	1.71028
$47$	6.33042	0.923387	0.461694	−	0.887039i	$-0.347242\pi$
$47$	6.33042	0.923387	0.461694	+	0.887039i	$0.347242\pi$
$48$	8.06700	1.16437
$49$	−6.20314	−0.886163
$50$	−21.5236	−3.04390
$51$	1.86783	0.261549
$52$	−0.422365	−0.0585714
$53$	−11.3066	−1.55309	−0.776543	−	0.630065i	$-0.783028\pi$
$53$	−11.3066	−1.55309	−0.776543	+	0.630065i	$0.783028\pi$
$54$	−6.91703	−0.941289
$55$	4.42666	0.596891
$56$	2.40283	0.321091
$57$	4.13244	0.547355
$58$	−1.40890	−0.184997
$59$	8.16349	1.06280	0.531398	−	0.847122i	$-0.321667\pi$
$59$	8.16349	1.06280	0.531398	+	0.847122i	$0.321667\pi$
$60$	−1.44459	−0.186495
$61$	10.9031	1.39600	0.698001	−	0.716097i	$-0.254073\pi$
$61$	10.9031	1.39600	0.698001	+	0.716097i	$0.254073\pi$
$62$	2.09358	0.265885
$63$	0.436342	0.0549739
$64$	7.18438	0.898047
$65$	−10.7013	−1.32733
$66$	2.75448	0.339053
$67$	−2.24511	−0.274283	−0.137142	−	0.990551i	$-0.543792\pi$
$67$	−2.24511	−0.274283	−0.137142	+	0.990551i	$0.543792\pi$
$68$	−0.174714	−0.0211872
$69$	14.6921	1.76872
$70$	−5.82731	−0.696497
$71$	−6.91251	−0.820364	−0.410182	−	0.912004i	$-0.634535\pi$
$71$	−6.91251	−0.820364	−0.410182	+	0.912004i	$0.634535\pi$
$72$	1.31574	0.155061
$73$	−0.603813	−0.0706710	−0.0353355	−	0.999376i	$-0.511250\pi$
$73$	−0.603813	−0.0706710	−0.0353355	+	0.999376i	$0.511250\pi$
$74$	−6.07003	−0.705626
$75$	−27.2617	−3.14791
$76$	−0.386542	−0.0443394
$77$	0.892669	0.101729
$78$	−6.65884	−0.753966
$79$	−7.28661	−0.819807	−0.409904	−	0.912129i	$-0.634438\pi$
$79$	−7.28661	−0.819807	−0.409904	+	0.912129i	$0.634438\pi$
$80$	−19.1183	−2.13750
$81$	−10.2275	−1.13639
$82$	2.42437	0.267727
$83$	−1.28713	−0.141281	−0.0706406	−	0.997502i	$-0.522504\pi$
$83$	−1.28713	−0.141281	−0.0706406	+	0.997502i	$0.522504\pi$
$84$	−0.291311	−0.0317847
$85$	−4.42666	−0.480139
$86$	−1.47469	−0.159020
$87$	−1.78450	−0.191318
$88$	2.69173	0.286940
$89$	−7.95194	−0.842904	−0.421452	−	0.906851i	$-0.638479\pi$
$89$	−7.95194	−0.842904	−0.421452	+	0.906851i	$0.638479\pi$
$90$	−3.19091	−0.336351
$91$	−2.15799	−0.226219
$92$	−1.37428	−0.143278
$93$	2.65172	0.274970
$94$	−9.33542	−0.962875
$95$	−9.79365	−1.00481
$96$	−1.84091	−0.187887
$97$	−0.897558	−0.0911332	−0.0455666	−	0.998961i	$-0.514509\pi$
$97$	−0.897558	−0.0911332	−0.0455666	+	0.998961i	$0.514509\pi$
$98$	9.14772	0.924059
$99$	0.488806	0.0491269
$100$	2.55002	0.255002
$101$	12.0610	1.20011	0.600057	−	0.799957i	$-0.295145\pi$
$101$	12.0610	1.20011	0.600057	+	0.799957i	$0.295145\pi$
$102$	−2.75448	−0.272734
$103$	−2.64526	−0.260645	−0.130322	−	0.991472i	$-0.541601\pi$
$103$	−2.64526	−0.260645	−0.130322	+	0.991472i	$0.541601\pi$
$104$	−6.50716	−0.638079
$105$	−7.38083	−0.720296
$106$	16.6738	1.61950
$107$	0.210929	0.0203913	0.0101956	−	0.999948i	$-0.496755\pi$
$107$	0.210929	0.0203913	0.0101956	+	0.999948i	$0.496755\pi$
$108$	0.819496	0.0788561
$109$	−15.2590	−1.46155	−0.730773	−	0.682621i	$-0.760840\pi$
$109$	−15.2590	−1.46155	−0.730773	+	0.682621i	$0.760840\pi$
$110$	−6.52796	−0.622417
$111$	−7.68826	−0.729737
$112$	−3.85535	−0.364296
$113$	−0.669021	−0.0629362	−0.0314681	−	0.999505i	$-0.510018\pi$
$113$	−0.669021	−0.0629362	−0.0314681	+	0.999505i	$0.510018\pi$
$114$	−6.09407	−0.570762
$115$	−34.8195	−3.24693
$116$	0.166919	0.0154980
$117$	−1.18167	−0.109245
$118$	−12.0386	−1.10825
$119$	−0.892669	−0.0818308
$120$	−22.2560	−2.03169
$121$	1.00000	0.0909091
$122$	−16.0787	−1.45570
$123$	3.07069	0.276875
$124$	−0.248037	−0.0222744
$125$	42.4754	3.79912
$126$	−0.643470	−0.0573249
$127$	−6.48826	−0.575740	−0.287870	−	0.957670i	$-0.592947\pi$
$127$	−6.48826	−0.575740	−0.287870	+	0.957670i	$0.592947\pi$
$128$	−12.5659	−1.11068
$129$	−1.86783	−0.164454
$130$	15.7811	1.38409
$131$	−9.27685	−0.810522	−0.405261	−	0.914201i	$-0.632819\pi$
$131$	−9.27685	−0.810522	−0.405261	+	0.914201i	$0.632819\pi$
$132$	−0.326337	−0.0284040
$133$	−1.97496	−0.171251
$134$	3.31084	0.286013
$135$	20.7632	1.78702
$136$	−2.69173	−0.230814
$137$	15.9380	1.36167	0.680836	−	0.732436i	$-0.261617\pi$
$137$	15.9380	1.36167	0.680836	+	0.732436i	$0.261617\pi$
$138$	−21.6663	−1.84436
$139$	−20.2843	−1.72049	−0.860245	−	0.509881i	$-0.829690\pi$
$139$	−20.2843	−1.72049	−0.860245	+	0.509881i	$0.829690\pi$
$140$	0.690391	0.0583487
$141$	−11.8242	−0.995776
$142$	10.1938	0.855447
$143$	−2.41746	−0.202158
$144$	−2.11111	−0.175926
$145$	4.22916	0.351213
$146$	0.890438	0.0736932
$147$	11.5864	0.955634
$148$	0.719147	0.0591135
$149$	−5.85958	−0.480035	−0.240018	−	0.970769i	$-0.577153\pi$
$149$	−5.85958	−0.480035	−0.240018	+	0.970769i	$0.577153\pi$
$150$	40.2026	3.28253
$151$	7.51363	0.611450	0.305725	−	0.952120i	$-0.401101\pi$
$151$	7.51363	0.611450	0.305725	+	0.952120i	$0.401101\pi$
$152$	−5.95525	−0.483035
$153$	−0.488806	−0.0395176
$154$	−1.31641	−0.106079
$155$	−6.28442	−0.504777
$156$	0.788907	0.0631631
$157$	−22.8865	−1.82654	−0.913270	−	0.407355i	$-0.866451\pi$
$157$	−22.8865	−1.82654	−0.913270	+	0.407355i	$0.866451\pi$
$158$	10.7455	0.854866
$159$	21.1189	1.67484
$160$	4.36285	0.344913
$161$	−7.02160	−0.553379
$162$	15.0824	1.18498
$163$	−11.8280	−0.926437	−0.463218	−	0.886244i	$-0.653305\pi$
$163$	−11.8280	−0.926437	−0.463218	+	0.886244i	$0.653305\pi$
$164$	−0.287227	−0.0224287
$165$	−8.26828	−0.643685
$166$	1.89812	0.147323
$167$	−11.2861	−0.873343	−0.436672	−	0.899621i	$-0.643843\pi$
$167$	−11.2861	−0.873343	−0.436672	+	0.899621i	$0.643843\pi$
$168$	−4.48808	−0.346263
$169$	−7.15589	−0.550453
$170$	6.52796	0.500672
$171$	−1.08145	−0.0827003
$172$	0.174714	0.0133218
$173$	10.3733	0.788668	0.394334	−	0.918967i	$-0.370975\pi$
$173$	10.3733	0.788668	0.394334	+	0.918967i	$0.370975\pi$
$174$	2.63158	0.199500
$175$	13.0288	0.984887
$176$	−4.31890	−0.325550
$177$	−15.2481	−1.14611
$178$	11.7267	0.878950
$179$	−17.2601	−1.29008	−0.645038	−	0.764150i	$-0.723159\pi$
$179$	−17.2601	−1.29008	−0.645038	+	0.764150i	$0.723159\pi$
$180$	0.378043	0.0281777
$181$	9.66944	0.718724	0.359362	−	0.933198i	$-0.382994\pi$
$181$	9.66944	0.718724	0.359362	+	0.933198i	$0.382994\pi$
$182$	3.18237	0.235893
$183$	−20.3652	−1.50544
$184$	−21.1728	−1.56088
$185$	18.2207	1.33962
$186$	−3.91046	−0.286729
$187$	−1.00000	−0.0731272
$188$	1.10602	0.0806645
$189$	4.18706	0.304564
$190$	14.4426	1.04778
$191$	−5.51186	−0.398824	−0.199412	−	0.979916i	$-0.563903\pi$
$191$	−5.51186	−0.398824	−0.199412	+	0.979916i	$0.563903\pi$
$192$	−13.4192	−0.968449
$193$	23.8999	1.72035	0.860176	−	0.509997i	$-0.170354\pi$
$193$	23.8999	1.72035	0.860176	+	0.509997i	$0.170354\pi$
$194$	1.32362	0.0950305
$195$	19.9882	1.43139
$196$	−1.08378	−0.0774127
$197$	15.0060	1.06914	0.534568	−	0.845125i	$-0.320474\pi$
$197$	15.0060	1.06914	0.534568	+	0.845125i	$0.320474\pi$
$198$	−0.720838	−0.0512277
$199$	−13.4908	−0.956340	−0.478170	−	0.878267i	$-0.658700\pi$
$199$	−13.4908	−0.956340	−0.478170	+	0.878267i	$0.658700\pi$
$200$	39.2868	2.77800
$201$	4.19349	0.295786
$202$	−17.7862	−1.25144
$203$	0.852841	0.0598577
$204$	0.326337	0.0228482
$205$	−7.27737	−0.508273
$206$	3.90094	0.271791
$207$	−3.84487	−0.267237
$208$	10.4408	0.723938
$209$	−2.21242	−0.153037
$210$	10.8845	0.751099
$211$	1.62425	0.111818	0.0559091	−	0.998436i	$-0.482194\pi$
$211$	1.62425	0.111818	0.0559091	+	0.998436i	$0.482194\pi$
$212$	−1.97543	−0.135673
$213$	12.9114	0.884677
$214$	−0.311055	−0.0212633
$215$	4.42666	0.301896
$216$	12.6256	0.859060
$217$	−1.26730	−0.0860299
$218$	22.5023	1.52405
$219$	1.12782	0.0762112
$220$	0.773401	0.0521427
$221$	2.41746	0.162616
$222$	11.3378	0.760944
$223$	7.28393	0.487768	0.243884	−	0.969804i	$-0.421578\pi$
$223$	7.28393	0.487768	0.243884	+	0.969804i	$0.421578\pi$
$224$	0.879800	0.0587841
$225$	7.13430	0.475620
$226$	0.986599	0.0656276
$227$	−13.3446	−0.885709	−0.442854	−	0.896593i	$-0.646034\pi$
$227$	−13.3446	−0.885709	−0.442854	+	0.896593i	$0.646034\pi$
$228$	0.721996	0.0478154
$229$	9.24172	0.610710	0.305355	−	0.952239i	$-0.401225\pi$
$229$	9.24172	0.610710	0.305355	+	0.952239i	$0.401225\pi$
$230$	51.3480	3.38578
$231$	−1.66736	−0.109704
$232$	2.57164	0.168836
$233$	−11.9498	−0.782855	−0.391428	−	0.920209i	$-0.628019\pi$
$233$	−11.9498	−0.782855	−0.391428	+	0.920209i	$0.628019\pi$
$234$	1.74260	0.113917
$235$	28.0227	1.82800
$236$	1.42628	0.0928428
$237$	13.6102	0.884076
$238$	1.31641	0.0853303
$239$	19.2440	1.24479	0.622394	−	0.782704i	$-0.286160\pi$
$239$	19.2440	1.24479	0.622394	+	0.782704i	$0.286160\pi$
$240$	35.7099	2.30506
$241$	9.71395	0.625731	0.312865	−	0.949797i	$-0.398711\pi$
$241$	9.71395	0.625731	0.312865	+	0.949797i	$0.398711\pi$
$242$	−1.47469	−0.0947967
$243$	5.03177	0.322788
$244$	1.90493	0.121951
$245$	−27.4592	−1.75431
$246$	−4.52832	−0.288715
$247$	5.34844	0.340313
$248$	−3.82138	−0.242658
$249$	2.40415	0.152357
$250$	−62.6382	−3.96158
$251$	25.5445	1.61236	0.806179	−	0.591672i	$-0.201532\pi$
$251$	25.5445	1.61236	0.806179	+	0.591672i	$0.201532\pi$
$252$	0.0762352	0.00480237
$253$	−7.86585	−0.494522
$254$	9.56818	0.600361
$255$	8.26828	0.517780
$256$	4.16207	0.260130
$257$	−13.1573	−0.820727	−0.410363	−	0.911922i	$-0.634598\pi$
$257$	−13.1573	−0.820727	−0.410363	+	0.911922i	$0.634598\pi$
$258$	2.75448	0.171486
$259$	3.67435	0.228313
$260$	−1.86967	−0.115952
$261$	0.466997	0.0289064
$262$	13.6805	0.845184
$263$	29.7170	1.83243	0.916214	−	0.400688i	$-0.131229\pi$
$263$	29.7170	1.83243	0.916214	+	0.400688i	$0.131229\pi$
$264$	−5.02771	−0.309434
$265$	−50.0507	−3.07459
$266$	2.91246	0.178574
$267$	14.8529	0.908983
$268$	−0.392252	−0.0239606
$269$	−25.3632	−1.54642	−0.773212	−	0.634148i	$-0.781351\pi$
$269$	−25.3632	−1.54642	−0.773212	+	0.634148i	$0.781351\pi$
$270$	−30.6194	−1.86344
$271$	5.05766	0.307231	0.153616	−	0.988131i	$-0.450908\pi$
$271$	5.05766	0.307231	0.153616	+	0.988131i	$0.450908\pi$
$272$	4.31890	0.261872
$273$	4.03077	0.243953
$274$	−23.5036	−1.41990
$275$	14.5954	0.880133
$276$	2.56692	0.154510
$277$	7.30712	0.439042	0.219521	−	0.975608i	$-0.429551\pi$
$277$	7.30712	0.439042	0.219521	+	0.975608i	$0.429551\pi$
$278$	29.9131	1.79407
$279$	−0.693946	−0.0415454
$280$	10.6365	0.635653
$281$	12.9791	0.774270	0.387135	−	0.922023i	$-0.373465\pi$
$281$	12.9791	0.774270	0.387135	+	0.922023i	$0.373465\pi$
$282$	17.4370	1.03836
$283$	−20.8382	−1.23870	−0.619350	−	0.785115i	$-0.712604\pi$
$283$	−20.8382	−1.23870	−0.619350	+	0.785115i	$0.712604\pi$
$284$	−1.20771	−0.0716647
$285$	18.2929	1.08358
$286$	3.56501	0.210803
$287$	−1.46753	−0.0866258
$288$	0.481759	0.0283879
$289$	1.00000	0.0588235
$290$	−6.23671	−0.366232
$291$	1.67649	0.0982776
$292$	−0.105495	−0.00617362
$293$	−1.21528	−0.0709972	−0.0354986	−	0.999370i	$-0.511302\pi$
$293$	−1.21528	−0.0709972	−0.0354986	+	0.999370i	$0.511302\pi$
$294$	−17.0864	−0.996501
$295$	36.1370	2.10398
$296$	11.0795	0.643985
$297$	4.69049	0.272170
$298$	8.64107	0.500564
$299$	19.0154	1.09969
$300$	−4.76301	−0.274993
$301$	0.892669	0.0514526
$302$	−11.0803	−0.637598
$303$	−22.5279	−1.29420
$304$	9.55524	0.548031
$305$	48.2644	2.76361
$306$	0.720838	0.0412076
$307$	−15.5848	−0.889473	−0.444736	−	0.895661i	$-0.646703\pi$
$307$	−15.5848	−0.889473	−0.444736	+	0.895661i	$0.646703\pi$
$308$	0.155962	0.00888676
$309$	4.94090	0.281078
$310$	9.26758	0.526363
$311$	10.8053	0.612713	0.306357	−	0.951917i	$-0.400890\pi$
$311$	10.8053	0.612713	0.306357	+	0.951917i	$0.400890\pi$
$312$	12.1543	0.688101
$313$	3.76483	0.212801	0.106400	−	0.994323i	$-0.466067\pi$
$313$	3.76483	0.212801	0.106400	+	0.994323i	$0.466067\pi$
$314$	33.7505	1.90465
$315$	1.93154	0.108830
$316$	−1.27307	−0.0716160
$317$	0.00986562	0.000554109 0	0.000277054	−	1.00000i	$-0.499912\pi$
$317$	0.00986562	0.000554109 0	0.000277054		1.00000i	$0.499912\pi$
$318$	−31.1439	−1.74646
$319$	0.955383	0.0534912
$320$	31.8028	1.77783
$321$	−0.393980	−0.0219898
$322$	10.3547	0.577044
$323$	2.21242	0.123103
$324$	−1.78689	−0.0992715
$325$	−35.2837	−1.95719
$326$	17.4426	0.966055
$327$	28.5013	1.57612
$328$	−4.42517	−0.244339
$329$	5.65097	0.311548
$330$	12.1932	0.671211
$331$	−20.9648	−1.15233	−0.576166	−	0.817333i	$-0.695452\pi$
$331$	−20.9648	−1.15233	−0.576166	+	0.817333i	$0.695452\pi$
$332$	−0.224881	−0.0123419
$333$	2.01199	0.110256
$334$	16.6435	0.910691
$335$	−9.93833	−0.542989
$336$	7.20116	0.392855
$337$	17.4632	0.951284	0.475642	−	0.879639i	$-0.342216\pi$
$337$	17.4632	0.951284	0.475642	+	0.879639i	$0.342216\pi$
$338$	10.5527	0.573993
$339$	1.24962	0.0678701
$340$	−0.773401	−0.0419436
$341$	−1.41967	−0.0768797
$342$	1.59480	0.0862369
$343$	−11.7860	−0.636386
$344$	2.69173	0.145129
$345$	65.0370	3.50147
$346$	−15.2974	−0.822395
$347$	−30.0576	−1.61358	−0.806788	−	0.590841i	$-0.798796\pi$
$347$	−30.0576	−1.61358	−0.806788	+	0.590841i	$0.798796\pi$
$348$	−0.311777	−0.0167130
$349$	−34.4835	−1.84586	−0.922929	−	0.384969i	$-0.874212\pi$
$349$	−34.4835	−1.84586	−0.922929	+	0.384969i	$0.874212\pi$
$350$	−19.2135	−1.02700
$351$	−11.3391	−0.605235
$352$	0.985583	0.0525318
$353$	−29.7136	−1.58149	−0.790747	−	0.612143i	$-0.790308\pi$
$353$	−29.7136	−1.58149	−0.790747	+	0.612143i	$0.790308\pi$
$354$	22.4862	1.19513
$355$	−30.5994	−1.62405
$356$	−1.38932	−0.0736337
$357$	1.66736	0.0882459
$358$	25.4532	1.34525
$359$	−36.3577	−1.91888	−0.959442	−	0.281904i	$-0.909034\pi$
$359$	−36.3577	−1.91888	−0.959442	+	0.281904i	$0.909034\pi$
$360$	5.82432	0.306969
$361$	−14.1052	−0.742378
$362$	−14.2594	−0.749460
$363$	−1.86783	−0.0980359
$364$	−0.377032	−0.0197618
$365$	−2.67288	−0.139905
$366$	30.0324	1.56982
$367$	−11.5583	−0.603340	−0.301670	−	0.953412i	$-0.597544\pi$
$367$	−11.5583	−0.603340	−0.301670	+	0.953412i	$0.597544\pi$
$368$	33.9718	1.77090
$369$	−0.803590	−0.0418332
$370$	−26.8700	−1.39690
$371$	−10.0931	−0.524007
$372$	0.463293	0.0240206
$373$	11.3353	0.586921	0.293461	−	0.955971i	$-0.405193\pi$
$373$	11.3353	0.586921	0.293461	+	0.955971i	$0.405193\pi$
$374$	1.47469	0.0762545
$375$	−79.3371	−4.09695
$376$	17.0398	0.878761
$377$	−2.30960	−0.118950
$378$	−6.17462	−0.317588
$379$	−35.8301	−1.84047	−0.920236	−	0.391365i	$-0.872003\pi$
$379$	−35.8301	−1.84047	−0.920236	+	0.391365i	$0.872003\pi$
$380$	−1.71109	−0.0877771
$381$	12.1190	0.620875
$382$	8.12830	0.415880
$383$	11.2819	0.576480	0.288240	−	0.957558i	$-0.406930\pi$
$383$	11.2819	0.576480	0.288240	+	0.957558i	$0.406930\pi$
$384$	23.4710	1.19775
$385$	3.95155	0.201389
$386$	−35.2450	−1.79392
$387$	0.488806	0.0248474
$388$	−0.156816	−0.00796114
$389$	37.5000	1.90133	0.950663	−	0.310224i	$-0.100404\pi$
$389$	37.5000	1.90133	0.950663	+	0.310224i	$0.100404\pi$
$390$	−29.4765	−1.49260
$391$	7.86585	0.397793
$392$	−16.6972	−0.843336
$393$	17.3276	0.874063
$394$	−22.1293	−1.11486
$395$	−32.2554	−1.62294
$396$	0.0854014	0.00429158
$397$	20.1723	1.01242	0.506208	−	0.862411i	$-0.331047\pi$
$397$	20.1723	1.01242	0.506208	+	0.862411i	$0.331047\pi$
$398$	19.8948	0.997238
$399$	3.68890	0.184676
$400$	−63.0359	−3.15180
$401$	−21.8743	−1.09235	−0.546174	−	0.837671i	$-0.683916\pi$
$401$	−21.8743	−1.09235	−0.546174	+	0.837671i	$0.683916\pi$
$402$	−6.18410	−0.308435
$403$	3.43201	0.170960
$404$	2.10723	0.104838
$405$	−45.2737	−2.24967
$406$	−1.25768	−0.0624175
$407$	4.11613	0.204029
$408$	5.02771	0.248909
$409$	−8.41474	−0.416082	−0.208041	−	0.978120i	$-0.566709\pi$
$409$	−8.41474	−0.416082	−0.208041	+	0.978120i	$0.566709\pi$
$410$	10.7319	0.530009
$411$	−29.7695	−1.46842
$412$	−0.462164	−0.0227692
$413$	7.28730	0.358584
$414$	5.67000	0.278665
$415$	−5.69771	−0.279689
$416$	−2.38261	−0.116817
$417$	37.8877	1.85537
$418$	3.26264	0.159581
$419$	1.90226	0.0929314	0.0464657	−	0.998920i	$-0.485204\pi$
$419$	1.90226	0.0929314	0.0464657	+	0.998920i	$0.485204\pi$
$420$	−1.28954	−0.0629230
$421$	18.0271	0.878586	0.439293	−	0.898344i	$-0.355229\pi$
$421$	18.0271	0.878586	0.439293	+	0.898344i	$0.355229\pi$
$422$	−2.39527	−0.116600
$423$	3.09435	0.150452
$424$	−30.4344	−1.47803
$425$	−14.5954	−0.707979
$426$	−19.0404	−0.922509
$427$	9.73288	0.471007
$428$	0.0368523	0.00178132
$429$	4.51542	0.218006
$430$	−6.52796	−0.314806
$431$	20.6420	0.994292	0.497146	−	0.867667i	$-0.334381\pi$
$431$	20.6420	0.994292	0.497146	+	0.867667i	$0.334381\pi$
$432$	−20.2578	−0.974654
$433$	−22.5378	−1.08310	−0.541548	−	0.840670i	$-0.682161\pi$
$433$	−22.5378	−1.08310	−0.541548	+	0.840670i	$0.682161\pi$
$434$	1.86887	0.0897089
$435$	−7.89937	−0.378746
$436$	−2.66596	−0.127676
$437$	17.4026	0.832478
$438$	−1.66319	−0.0794704
$439$	−10.7993	−0.515421	−0.257711	−	0.966222i	$-0.582968\pi$
$439$	−10.7993	−0.515421	−0.257711	+	0.966222i	$0.582968\pi$
$440$	11.9154	0.568044
$441$	−3.03213	−0.144387
$442$	−3.56501	−0.169570
$443$	3.22589	0.153267	0.0766334	−	0.997059i	$-0.475583\pi$
$443$	3.22589	0.153267	0.0766334	+	0.997059i	$0.475583\pi$
$444$	−1.34325	−0.0637477
$445$	−35.2006	−1.66867
$446$	−10.7416	−0.508627
$447$	10.9447	0.517668
$448$	6.41327	0.302998
$449$	26.7877	1.26419	0.632095	−	0.774891i	$-0.282195\pi$
$449$	26.7877	1.26419	0.632095	+	0.774891i	$0.282195\pi$
$450$	−10.5209	−0.495960
$451$	−1.64398	−0.0774122
$452$	−0.116887	−0.00549792
$453$	−14.0342	−0.659385
$454$	19.6791	0.923586
$455$	−9.55270	−0.447838
$456$	11.1234	0.520902
$457$	−11.3983	−0.533191	−0.266596	−	0.963808i	$-0.585899\pi$
$457$	−11.3983	−0.533191	−0.266596	+	0.963808i	$0.585899\pi$
$458$	−13.6287	−0.636827
$459$	−4.69049	−0.218934
$460$	−6.08346	−0.283643
$461$	18.7430	0.872950	0.436475	−	0.899716i	$-0.356227\pi$
$461$	18.7430	0.872950	0.436475	+	0.899716i	$0.356227\pi$
$462$	2.45884	0.114396
$463$	0.580791	0.0269917	0.0134958	−	0.999909i	$-0.495704\pi$
$463$	0.580791	0.0269917	0.0134958	+	0.999909i	$0.495704\pi$
$464$	−4.12621	−0.191554
$465$	11.7383	0.544349
$466$	17.6222	0.816334
$467$	6.67099	0.308696	0.154348	−	0.988017i	$-0.450672\pi$
$467$	6.67099	0.308696	0.154348	+	0.988017i	$0.450672\pi$
$468$	−0.206454	−0.00954336
$469$	−2.00414	−0.0925424
$470$	−41.3248	−1.90617
$471$	42.7482	1.96973
$472$	21.9739	1.01143
$473$	1.00000	0.0459800
$474$	−20.0708	−0.921883
$475$	−32.2911	−1.48162
$476$	−0.155962	−0.00714851
$477$	−5.52675	−0.253053
$478$	−28.3789	−1.29802
$479$	36.0062	1.64516	0.822582	−	0.568647i	$-0.192533\pi$
$479$	36.0062	1.64516	0.822582	+	0.568647i	$0.192533\pi$
$480$	−8.14908	−0.371953
$481$	−9.95059	−0.453708
$482$	−14.3251	−0.652490
$483$	13.1152	0.596761
$484$	0.174714	0.00794156
$485$	−3.97319	−0.180413
$486$	−7.42031	−0.336592
$487$	2.98508	0.135267	0.0676335	−	0.997710i	$-0.478455\pi$
$487$	2.98508	0.135267	0.0676335	+	0.997710i	$0.478455\pi$
$488$	29.3483	1.32853
$489$	22.0927	0.999065
$490$	40.4939	1.82933
$491$	−40.4691	−1.82634	−0.913172	−	0.407574i	$-0.866375\pi$
$491$	−40.4691	−1.82634	−0.913172	+	0.407574i	$0.866375\pi$
$492$	0.536493	0.0241870
$493$	−0.955383	−0.0430283
$494$	−7.88730	−0.354867
$495$	2.16378	0.0972547
$496$	6.13144	0.275310
$497$	−6.17059	−0.276789
$498$	−3.54538	−0.158872
$499$	−3.17900	−0.142312	−0.0711558	−	0.997465i	$-0.522669\pi$
$499$	−3.17900	−0.142312	−0.0711558	+	0.997465i	$0.522669\pi$
$500$	7.42106	0.331880
$501$	21.0805	0.941809
$502$	−37.6703	−1.68131
$503$	−35.7702	−1.59492	−0.797458	−	0.603374i	$-0.793823\pi$
$503$	−35.7702	−1.59492	−0.797458	+	0.603374i	$0.793823\pi$
$504$	1.17452	0.0523171
$505$	53.3900	2.37582
$506$	11.5997	0.515669
$507$	13.3660	0.593606
$508$	−1.13359	−0.0502950
$509$	−30.3967	−1.34731	−0.673656	−	0.739045i	$-0.735277\pi$
$509$	−30.3967	−1.34731	−0.673656	+	0.739045i	$0.735277\pi$
$510$	−12.1932	−0.539922
$511$	−0.539005	−0.0238442
$512$	18.9940	0.839425
$513$	−10.3774	−0.458172
$514$	19.4029	0.855824
$515$	−11.7097	−0.515990
$516$	−0.326337	−0.0143662
$517$	6.33042	0.278412
$518$	−5.41852	−0.238076
$519$	−19.3756	−0.850496
$520$	−28.8050	−1.26318
$521$	17.1165	0.749888	0.374944	−	0.927048i	$-0.377662\pi$
$521$	17.1165	0.749888	0.374944	+	0.927048i	$0.377662\pi$
$522$	−0.688677	−0.0301426
$523$	−18.0349	−0.788611	−0.394306	−	0.918979i	$-0.629015\pi$
$523$	−18.0349	−0.788611	−0.394306	+	0.918979i	$0.629015\pi$
$524$	−1.62080	−0.0708049
$525$	−24.3357	−1.06210
$526$	−43.8234	−1.91079
$527$	1.41967	0.0618420
$528$	8.06700	0.351071
$529$	38.8715	1.69007
$530$	73.8093	3.20607
$531$	3.99037	0.173167
$532$	−0.345054	−0.0149600
$533$	3.97427	0.172145
$534$	−21.9035	−0.947855
$535$	0.933711	0.0403678
$536$	−6.04323	−0.261028
$537$	32.2389	1.39121
$538$	37.4029	1.61256
$539$	−6.20314	−0.267188
$540$	3.62764	0.156109
$541$	22.4845	0.966684	0.483342	−	0.875432i	$-0.339423\pi$
$541$	22.4845	0.966684	0.483342	+	0.875432i	$0.339423\pi$
$542$	−7.45849	−0.320370
$543$	−18.0609	−0.775068
$544$	−0.985583	−0.0422565
$545$	−67.5464	−2.89337
$546$	−5.94414	−0.254386
$547$	−4.05864	−0.173535	−0.0867674	−	0.996229i	$-0.527654\pi$
$547$	−4.05864	−0.173535	−0.0867674	+	0.996229i	$0.527654\pi$
$548$	2.78459	0.118952
$549$	5.32951	0.227458
$550$	−21.5236	−0.917771
$551$	−2.11371	−0.0900472
$552$	39.5472	1.68324
$553$	−6.50453	−0.276601
$554$	−10.7757	−0.457817
$555$	−34.0333	−1.44463
$556$	−3.54395	−0.150297
$557$	−7.15934	−0.303351	−0.151675	−	0.988430i	$-0.548467\pi$
$557$	−7.15934	−0.303351	−0.151675	+	0.988430i	$0.548467\pi$
$558$	1.02336	0.0433221
$559$	−2.41746	−0.102248
$560$	−17.0663	−0.721185
$561$	1.86783	0.0788600
$562$	−19.1402	−0.807381
$563$	15.0785	0.635484	0.317742	−	0.948177i	$-0.397075\pi$
$563$	15.0785	0.635484	0.317742	+	0.948177i	$0.397075\pi$
$564$	−2.06585	−0.0869881
$565$	−2.96153	−0.124593
$566$	30.7299	1.29167
$567$	−9.12976	−0.383414
$568$	−18.6066	−0.780717
$569$	8.51601	0.357010	0.178505	−	0.983939i	$-0.442874\pi$
$569$	8.51601	0.357010	0.178505	+	0.983939i	$0.442874\pi$
$570$	−26.9764	−1.12992
$571$	8.35661	0.349713	0.174857	−	0.984594i	$-0.444054\pi$
$571$	8.35661	0.349713	0.174857	+	0.984594i	$0.444054\pi$
$572$	−0.422365	−0.0176600
$573$	10.2952	0.430090
$574$	2.16416	0.0903302
$575$	−114.805	−4.78769
$576$	3.51177	0.146324
$577$	31.0319	1.29188	0.645938	−	0.763390i	$-0.276467\pi$
$577$	31.0319	1.29188	0.645938	+	0.763390i	$0.276467\pi$
$578$	−1.47469	−0.0613391
$579$	−44.6411	−1.85522
$580$	0.738895	0.0306809
$581$	−1.14898	−0.0476679
$582$	−2.47231	−0.102480
$583$	−11.3066	−0.468273
$584$	−1.62530	−0.0672556
$585$	−5.23085	−0.216269
$586$	1.79216	0.0740333
$587$	−25.4133	−1.04892	−0.524459	−	0.851435i	$-0.675733\pi$
$587$	−25.4133	−1.04892	−0.524459	+	0.851435i	$0.675733\pi$
$588$	2.02432	0.0834814
$589$	3.14092	0.129419
$590$	−53.2910	−2.19395
$591$	−28.0288	−1.15295
$592$	−17.7772	−0.730638
$593$	−17.0484	−0.700093	−0.350046	−	0.936732i	$-0.613834\pi$
$593$	−17.0484	−0.700093	−0.350046	+	0.936732i	$0.613834\pi$
$594$	−6.91703	−0.283809
$595$	−3.95155	−0.161998
$596$	−1.02375	−0.0419345
$597$	25.1987	1.03131
$598$	−28.0418	−1.14671
$599$	2.13827	0.0873675	0.0436837	−	0.999045i	$-0.486091\pi$
$599$	2.13827	0.0873675	0.0436837	+	0.999045i	$0.486091\pi$
$600$	−73.3813	−2.99578
$601$	−45.8912	−1.87194	−0.935970	−	0.352079i	$-0.885475\pi$
$601$	−45.8912	−1.87194	−0.935970	+	0.352079i	$0.885475\pi$
$602$	−1.31641	−0.0536529
$603$	−1.09742	−0.0446905
$604$	1.31274	0.0534145
$605$	4.42666	0.179970
$606$	33.2217	1.34954
$607$	11.9171	0.483700	0.241850	−	0.970314i	$-0.422246\pi$
$607$	11.9171	0.483700	0.241850	+	0.970314i	$0.422246\pi$
$608$	−2.18053	−0.0884320
$609$	−1.59297	−0.0645502
$610$	−71.1752	−2.88180
$611$	−15.3035	−0.619115
$612$	−0.0854014	−0.00345215
$613$	35.1659	1.42034	0.710169	−	0.704031i	$-0.248618\pi$
$613$	35.1659	1.42034	0.710169	+	0.704031i	$0.248618\pi$
$614$	22.9828	0.927510
$615$	13.5929	0.548119
$616$	2.40283	0.0968126
$617$	−40.6315	−1.63576	−0.817881	−	0.575387i	$-0.804852\pi$
$617$	−40.6315	−1.63576	−0.817881	+	0.575387i	$0.804852\pi$
$618$	−7.28631	−0.293098
$619$	26.6809	1.07240	0.536199	−	0.844092i	$-0.319860\pi$
$619$	26.6809	1.07240	0.536199	+	0.844092i	$0.319860\pi$
$620$	−1.09798	−0.0440959
$621$	−36.8947	−1.48053
$622$	−15.9345	−0.638915
$623$	−7.09845	−0.284393
$624$	−19.5016	−0.780690
$625$	115.048	4.60191
$626$	−5.55196	−0.221901
$627$	4.13244	0.165034
$628$	−3.99859	−0.159561
$629$	−4.11613	−0.164121
$630$	−2.84843	−0.113484
$631$	−17.4766	−0.695731	−0.347866	−	0.937544i	$-0.613093\pi$
$631$	−17.4766	−0.695731	−0.347866	+	0.937544i	$0.613093\pi$
$632$	−19.6136	−0.780187
$633$	−3.03384	−0.120584
$634$	−0.0145487	−0.000577805 0
$635$	−28.7213	−1.13977
$636$	3.68978	0.146309
$637$	14.9958	0.594157
$638$	−1.40890	−0.0557787
$639$	−3.37888	−0.133666
$640$	−55.6250	−2.19877
$641$	−17.2261	−0.680392	−0.340196	−	0.940355i	$-0.610493\pi$
$641$	−17.2261	−0.680392	−0.340196	+	0.940355i	$0.610493\pi$
$642$	0.580999	0.0229302
$643$	−6.81248	−0.268658	−0.134329	−	0.990937i	$-0.542888\pi$
$643$	−6.81248	−0.268658	−0.134329	+	0.990937i	$0.542888\pi$
$644$	−1.22677	−0.0483416
$645$	−8.26828	−0.325563
$646$	−3.26264	−0.128367
$647$	−21.1063	−0.829775	−0.414887	−	0.909873i	$-0.636179\pi$
$647$	−21.1063	−0.829775	−0.414887	+	0.909873i	$0.636179\pi$
$648$	−27.5297	−1.08147
$649$	8.16349	0.320445
$650$	52.0326	2.04088
$651$	2.36710	0.0927742
$652$	−2.06651	−0.0809309
$653$	−5.73513	−0.224433	−0.112216	−	0.993684i	$-0.535795\pi$
$653$	−5.73513	−0.224433	−0.112216	+	0.993684i	$0.535795\pi$
$654$	−42.0305	−1.64352
$655$	−41.0655	−1.60456
$656$	7.10021	0.277217
$657$	−0.295148	−0.0115148
$658$	−8.33344	−0.324871
$659$	−41.2837	−1.60819	−0.804093	−	0.594504i	$-0.797349\pi$
$659$	−41.2837	−1.60819	−0.804093	+	0.594504i	$0.797349\pi$
$660$	−1.44459	−0.0562304
$661$	−44.4284	−1.72806	−0.864032	−	0.503437i	$-0.832069\pi$
$661$	−44.4284	−1.72806	−0.864032	+	0.503437i	$0.832069\pi$
$662$	30.9167	1.20161
$663$	−4.51542	−0.175364
$664$	−3.46462	−0.134453
$665$	−8.74249	−0.339019
$666$	−2.96707	−0.114972
$667$	−7.51490	−0.290978
$668$	−1.97184	−0.0762928
$669$	−13.6052	−0.526007
$670$	14.6560	0.566209
$671$	10.9031	0.420910
$672$	−1.64332	−0.0633924
$673$	17.9554	0.692128	0.346064	−	0.938211i	$-0.387518\pi$
$673$	17.9554	0.692128	0.346064	+	0.938211i	$0.387518\pi$
$674$	−25.7529	−0.991965
$675$	68.4595	2.63501
$676$	−1.25024	−0.0480860
$677$	38.8065	1.49145	0.745727	−	0.666251i	$-0.232102\pi$
$677$	38.8065	1.49145	0.745727	+	0.666251i	$0.232102\pi$
$678$	−1.84280	−0.0707725
$679$	−0.801222	−0.0307481
$680$	−11.9154	−0.456935
$681$	24.9254	0.955144
$682$	2.09358	0.0801674
$683$	22.1218	0.846468	0.423234	−	0.906020i	$-0.360895\pi$
$683$	22.1218	0.846468	0.423234	+	0.906020i	$0.360895\pi$
$684$	−0.188944	−0.00722446
$685$	70.5520	2.69565
$686$	17.3808	0.663601
$687$	−17.2620	−0.658587
$688$	−4.31890	−0.164657
$689$	27.3333	1.04132
$690$	−95.9095	−3.65121
$691$	−34.5050	−1.31263	−0.656317	−	0.754485i	$-0.727887\pi$
$691$	−34.5050	−1.31263	−0.656317	+	0.754485i	$0.727887\pi$
$692$	1.81237	0.0688958
$693$	0.436342	0.0165753
$694$	44.3257	1.68258
$695$	−89.7917	−3.40599
$696$	−4.80339	−0.182072
$697$	1.64398	0.0622703
$698$	50.8525	1.92480
$699$	22.3202	0.844227
$700$	2.27632	0.0860369
$701$	−13.1535	−0.496801	−0.248400	−	0.968657i	$-0.579905\pi$
$701$	−13.1535	−0.496801	−0.248400	+	0.968657i	$0.579905\pi$
$702$	16.7216	0.631118
$703$	−9.10663	−0.343463
$704$	7.18438	0.270771
$705$	−52.3417	−1.97130
$706$	43.8184	1.64913
$707$	10.7665	0.404915
$708$	−2.66405	−0.100121
$709$	−8.90066	−0.334271	−0.167136	−	0.985934i	$-0.553452\pi$
$709$	−8.90066	−0.334271	−0.167136	+	0.985934i	$0.553452\pi$
$710$	45.1246	1.69350
$711$	−3.56174	−0.133576
$712$	−21.4045	−0.802168
$713$	11.1669	0.418205
$714$	−2.45884	−0.0920197
$715$	−10.7013	−0.400205
$716$	−3.01558	−0.112697
$717$	−35.9445	−1.34237
$718$	53.6164	2.00094
$719$	−39.4058	−1.46959	−0.734795	−	0.678289i	$-0.762722\pi$
$719$	−39.4058	−1.46959	−0.734795	+	0.678289i	$0.762722\pi$
$720$	−9.34516	−0.348274
$721$	−2.36134	−0.0879409
$722$	20.8008	0.774125
$723$	−18.1441	−0.674785
$724$	1.68939	0.0627857
$725$	13.9442	0.517873
$726$	2.75448	0.102228
$727$	52.7875	1.95778	0.978890	−	0.204385i	$-0.0655196\pi$
$727$	52.7875	1.95778	0.978890	+	0.204385i	$0.0655196\pi$
$728$	−5.80874	−0.215286
$729$	21.2839	0.788294
$730$	3.94167	0.145888
$731$	−1.00000	−0.0369863
$732$	−3.55809	−0.131511
$733$	−13.7435	−0.507629	−0.253814	−	0.967253i	$-0.581685\pi$
$733$	−13.7435	−0.507629	−0.253814	+	0.967253i	$0.581685\pi$
$734$	17.0450	0.629142
$735$	51.2893	1.89183
$736$	−7.75245	−0.285759
$737$	−2.24511	−0.0826995
$738$	1.18505	0.0436222
$739$	13.5854	0.499745	0.249873	−	0.968279i	$-0.419611\pi$
$739$	13.5854	0.499745	0.249873	+	0.968279i	$0.419611\pi$
$740$	3.18342	0.117025
$741$	−9.99001	−0.366992
$742$	14.8842	0.546415
$743$	−33.8283	−1.24104	−0.620519	−	0.784191i	$-0.713078\pi$
$743$	−33.8283	−1.24104	−0.620519	+	0.784191i	$0.713078\pi$
$744$	7.13771	0.261681
$745$	−25.9384	−0.950309
$746$	−16.7161	−0.612021
$747$	−0.629159	−0.0230197
$748$	−0.174714	−0.00638819
$749$	0.188290	0.00687995
$750$	116.998	4.27215
$751$	52.3228	1.90928	0.954642	−	0.297756i	$-0.0962380\pi$
$751$	52.3228	1.90928	0.954642	+	0.297756i	$0.0962380\pi$
$752$	−27.3405	−0.997005
$753$	−47.7130	−1.73876
$754$	3.40595	0.124037
$755$	33.2603	1.21047
$756$	0.731539	0.0266058
$757$	−42.1226	−1.53097	−0.765487	−	0.643452i	$-0.777502\pi$
$757$	−42.1226	−1.53097	−0.765487	+	0.643452i	$0.777502\pi$
$758$	52.8384	1.91918
$759$	14.6921	0.533289
$760$	−26.3619	−0.956247
$761$	−6.50753	−0.235898	−0.117949	−	0.993020i	$-0.537632\pi$
$761$	−6.50753	−0.235898	−0.117949	+	0.993020i	$0.537632\pi$
$762$	−17.8718	−0.647426
$763$	−13.6212	−0.493121
$764$	−0.963001	−0.0348402
$765$	−2.16378	−0.0782317
$766$	−16.6374	−0.601133
$767$	−19.7349	−0.712586
$768$	−7.77407	−0.280522
$769$	1.31519	0.0474271	0.0237136	−	0.999719i	$-0.492451\pi$
$769$	1.31519	0.0474271	0.0237136	+	0.999719i	$0.492451\pi$
$770$	−5.82731	−0.210002
$771$	24.5756	0.885067
$772$	4.17565	0.150285
$773$	22.3013	0.802121	0.401061	−	0.916052i	$-0.368642\pi$
$773$	22.3013	0.802121	0.401061	+	0.916052i	$0.368642\pi$
$774$	−0.720838	−0.0259100
$775$	−20.7207	−0.744308
$776$	−2.41599	−0.0867289
$777$	−6.86307	−0.246211
$778$	−55.3010	−1.98264
$779$	3.63719	0.130316
$780$	3.49223	0.125042
$781$	−6.91251	−0.247349
$782$	−11.5997	−0.414804
$783$	4.48122	0.160146
$784$	26.7908	0.956813
$785$	−101.311	−3.61594
$786$	−25.5529	−0.911442
$787$	−14.7688	−0.526452	−0.263226	−	0.964734i	$-0.584786\pi$
$787$	−14.7688	−0.526452	−0.263226	+	0.964734i	$0.584786\pi$
$788$	2.62177	0.0933966
$789$	−55.5064	−1.97608
$790$	47.5667	1.69235
$791$	−0.597214	−0.0212345
$792$	1.31574	0.0467526
$793$	−26.3579	−0.935995
$794$	−29.7479	−1.05571
$795$	93.4864	3.31562
$796$	−2.35704	−0.0835431
$797$	−8.56588	−0.303419	−0.151709	−	0.988425i	$-0.548478\pi$
$797$	−8.56588	−0.303419	−0.151709	+	0.988425i	$0.548478\pi$
$798$	−5.43999	−0.192574
$799$	−6.33042	−0.223954
$800$	14.3849	0.508584
$801$	−3.88696	−0.137339
$802$	32.2578	1.13906
$803$	−0.603813	−0.0213081
$804$	0.732662	0.0258390
$805$	−31.0823	−1.09551
$806$	−5.06115	−0.178271
$807$	47.3743	1.66766
$808$	32.4650	1.14211
$809$	32.5656	1.14495	0.572473	−	0.819923i	$-0.305984\pi$
$809$	32.5656	1.14495	0.572473	+	0.819923i	$0.305984\pi$
$810$	66.7647	2.34587
$811$	25.1411	0.882824	0.441412	−	0.897305i	$-0.354478\pi$
$811$	25.1411	0.882824	0.441412	+	0.897305i	$0.354478\pi$
$812$	0.149003	0.00522900
$813$	−9.44687	−0.331316
$814$	−6.07003	−0.212754
$815$	−52.3584	−1.83403
$816$	−8.06700	−0.282401
$817$	−2.21242	−0.0774029
$818$	12.4091	0.433875
$819$	−1.05484	−0.0368591
$820$	−1.27146	−0.0444013
$821$	42.6352	1.48798	0.743989	−	0.668192i	$-0.232931\pi$
$821$	42.6352	1.48798	0.743989	+	0.668192i	$0.232931\pi$
$822$	43.9008	1.53121
$823$	−0.973448	−0.0339323	−0.0169661	−	0.999856i	$-0.505401\pi$
$823$	−0.973448	−0.0339323	−0.0169661	+	0.999856i	$0.505401\pi$
$824$	−7.12033	−0.248048
$825$	−27.2617	−0.949131
$826$	−10.7465	−0.373919
$827$	27.3874	0.952354	0.476177	−	0.879349i	$-0.342022\pi$
$827$	27.3874	0.952354	0.476177	+	0.879349i	$0.342022\pi$
$828$	−0.671754	−0.0233451
$829$	4.70096	0.163271	0.0816356	−	0.996662i	$-0.473986\pi$
$829$	4.70096	0.163271	0.0816356	+	0.996662i	$0.473986\pi$
$830$	8.40236	0.291650
$831$	−13.6485	−0.473461
$832$	−17.3679	−0.602125
$833$	6.20314	0.214926
$834$	−55.8726	−1.93471
$835$	−49.9597	−1.72893
$836$	−0.386542	−0.0133688
$837$	−6.65897	−0.230168
$838$	−2.80524	−0.0969055
$839$	−26.1827	−0.903928	−0.451964	−	0.892036i	$-0.649276\pi$
$839$	−26.1827	−0.903928	−0.451964	+	0.892036i	$0.649276\pi$
$840$	−19.8672	−0.685485
$841$	−28.0872	−0.968526
$842$	−26.5844	−0.916158
$843$	−24.2429	−0.834969
$844$	0.283780	0.00976812
$845$	−31.6767	−1.08971
$846$	−4.56321	−0.156886
$847$	0.892669	0.0306725
$848$	48.8322	1.67691
$849$	38.9222	1.33581
$850$	21.5236	0.738255
$851$	−32.3769	−1.10987
$852$	2.25581	0.0772828
$853$	−48.6332	−1.66517	−0.832585	−	0.553898i	$-0.813140\pi$
$853$	−48.6332	−1.66517	−0.832585	+	0.553898i	$0.813140\pi$
$854$	−14.3530	−0.491149
$855$	−4.78720	−0.163719
$856$	0.567764	0.0194058
$857$	23.9438	0.817904	0.408952	−	0.912556i	$-0.365894\pi$
$857$	23.9438	0.817904	0.408952	+	0.912556i	$0.365894\pi$
$858$	−6.65884	−0.227329
$859$	0.557151	0.0190097	0.00950487	−	0.999955i	$-0.496974\pi$
$859$	0.557151	0.0190097	0.00950487	+	0.999955i	$0.496974\pi$
$860$	0.773401	0.0263728
$861$	2.74111	0.0934168
$862$	−30.4406	−1.03681
$863$	−52.3732	−1.78280	−0.891402	−	0.453214i	$-0.850277\pi$
$863$	−52.3732	−1.78280	−0.891402	+	0.453214i	$0.850277\pi$
$864$	4.62287	0.157273
$865$	45.9192	1.56130
$866$	33.2362	1.12941
$867$	−1.86783	−0.0634350
$868$	−0.221415	−0.00751532
$869$	−7.28661	−0.247181
$870$	11.6491	0.394943
$871$	5.42745	0.183902
$872$	−41.0731	−1.39091
$873$	−0.438732	−0.0148488
$874$	−25.6634	−0.868079
$875$	37.9165	1.28181
$876$	0.197047	0.00665760
$877$	−5.39128	−0.182050	−0.0910252	−	0.995849i	$-0.529014\pi$
$877$	−5.39128	−0.182050	−0.0910252	+	0.995849i	$0.529014\pi$
$878$	15.9256	0.537463
$879$	2.26994	0.0765630
$880$	−19.1183	−0.644479
$881$	−9.16411	−0.308747	−0.154373	−	0.988013i	$-0.549336\pi$
$881$	−9.16411	−0.308747	−0.154373	+	0.988013i	$0.549336\pi$
$882$	4.47146	0.150562
$883$	36.7226	1.23581	0.617907	−	0.786252i	$-0.287981\pi$
$883$	36.7226	1.23581	0.617907	+	0.786252i	$0.287981\pi$
$884$	0.422365	0.0142057
$885$	−67.4980	−2.26892
$886$	−4.75719	−0.159821
$887$	−2.82476	−0.0948461	−0.0474231	−	0.998875i	$-0.515101\pi$
$887$	−2.82476	−0.0948461	−0.0474231	+	0.998875i	$0.515101\pi$
$888$	−20.6947	−0.694470
$889$	−5.79187	−0.194253
$890$	51.9100	1.74003
$891$	−10.2275	−0.342634
$892$	1.27261	0.0426100
$893$	−14.0056	−0.468679
$894$	−16.1401	−0.539805
$895$	−76.4045	−2.55392
$896$	−11.2172	−0.374740
$897$	−35.5176	−1.18590
$898$	−39.5036	−1.31825
$899$	−1.35633	−0.0452362
$900$	1.24646	0.0415488
$901$	11.3066	0.376678
$902$	2.42437	0.0807227
$903$	−1.66736	−0.0554862
$904$	−1.80083	−0.0598946
$905$	42.8034	1.42283
$906$	20.6961	0.687583
$907$	16.9380	0.562418	0.281209	−	0.959647i	$-0.409265\pi$
$907$	16.9380	0.562418	0.281209	+	0.959647i	$0.409265\pi$
$908$	−2.33148	−0.0773730
$909$	5.89549	0.195541
$910$	14.0873	0.466989
$911$	−29.5031	−0.977482	−0.488741	−	0.872429i	$-0.662544\pi$
$911$	−29.5031	−0.977482	−0.488741	+	0.872429i	$0.662544\pi$
$912$	−17.8476	−0.590993
$913$	−1.28713	−0.0425979
$914$	16.8090	0.555993
$915$	−90.1500	−2.98027
$916$	1.61466	0.0533499
$917$	−8.28116	−0.273468
$918$	6.91703	0.228296
$919$	−10.6431	−0.351083	−0.175541	−	0.984472i	$-0.556168\pi$
$919$	−10.6431	−0.351083	−0.175541	+	0.984472i	$0.556168\pi$
$920$	−93.7247	−3.09001
$921$	29.1099	0.959203
$922$	−27.6402	−0.910281
$923$	16.7107	0.550040
$924$	−0.291311	−0.00958343
$925$	60.0765	1.97530
$926$	−0.856488	−0.0281459
$927$	−1.29302	−0.0424683
$928$	0.941610	0.0309099
$929$	−49.4829	−1.62348	−0.811740	−	0.584019i	$-0.801480\pi$
$929$	−49.4829	−1.62348	−0.811740	+	0.584019i	$0.801480\pi$
$930$	−17.3103	−0.567627
$931$	13.7240	0.449785
$932$	−2.08780	−0.0683880
$933$	−20.1825	−0.660747
$934$	−9.83764	−0.321898
$935$	−4.42666	−0.144767
$936$	−3.18074	−0.103966
$937$	39.7478	1.29850	0.649252	−	0.760573i	$-0.275082\pi$
$937$	39.7478	1.29850	0.649252	+	0.760573i	$0.275082\pi$
$938$	2.95548	0.0964999
$939$	−7.03208	−0.229483
$940$	4.89596	0.159689
$941$	−38.9092	−1.26840	−0.634202	−	0.773168i	$-0.718671\pi$
$941$	−38.9092	−1.26840	−0.634202	+	0.773168i	$0.718671\pi$
$942$	−63.0403	−2.05396
$943$	12.9313	0.421102
$944$	−35.2573	−1.14753
$945$	18.5347	0.602934
$946$	−1.47469	−0.0479463
$947$	−6.72779	−0.218624	−0.109312	−	0.994007i	$-0.534865\pi$
$947$	−6.72779	−0.218624	−0.109312	+	0.994007i	$0.534865\pi$
$948$	2.37789	0.0772303
$949$	1.45969	0.0473837
$950$	47.6194	1.54498
$951$	−0.0184274	−0.000597548 0
$952$	−2.40283	−0.0778761
$953$	51.7922	1.67771	0.838857	−	0.544352i	$-0.183224\pi$
$953$	51.7922	1.67771	0.838857	+	0.544352i	$0.183224\pi$
$954$	8.15025	0.263874
$955$	−24.3992	−0.789539
$956$	3.36219	0.108741
$957$	−1.78450	−0.0576846
$958$	−53.0980	−1.71552
$959$	14.2273	0.459424
$960$	−59.4024	−1.91720
$961$	−28.9845	−0.934985
$962$	14.6740	0.473110
$963$	0.103103	0.00332246
$964$	1.69717	0.0546620
$965$	105.797	3.40572
$966$	−19.3408	−0.622281
$967$	18.7947	0.604398	0.302199	−	0.953245i	$-0.402279\pi$
$967$	18.7947	0.604398	0.302199	+	0.953245i	$0.402279\pi$
$968$	2.69173	0.0865156
$969$	−4.13244	−0.132753
$970$	5.85923	0.188128
$971$	−47.5975	−1.52748	−0.763738	−	0.645527i	$-0.776638\pi$
$971$	−47.5975	−1.52748	−0.763738	+	0.645527i	$0.776638\pi$
$972$	0.879122	0.0281979
$973$	−18.1071	−0.580489
$974$	−4.40207	−0.141052
$975$	65.9041	2.11062
$976$	−47.0895	−1.50730
$977$	7.20452	0.230493	0.115246	−	0.993337i	$-0.463234\pi$
$977$	7.20452	0.230493	0.115246	+	0.993337i	$0.463234\pi$
$978$	−32.5799	−1.04179
$979$	−7.95194	−0.254145
$980$	−4.79752	−0.153251
$981$	−7.45869	−0.238137
$982$	59.6794	1.90445
$983$	−33.6053	−1.07184	−0.535921	−	0.844268i	$-0.680035\pi$
$983$	−33.6053	−1.07184	−0.535921	+	0.844268i	$0.680035\pi$
$984$	8.26548	0.263494
$985$	66.4267	2.11653
$986$	1.40890	0.0448684
$987$	−10.5551	−0.335972
$988$	0.934449	0.0297288
$989$	−7.86585	−0.250119
$990$	−3.19091	−0.101414
$991$	−32.5374	−1.03358	−0.516792	−	0.856111i	$-0.672874\pi$
$991$	−32.5374	−1.03358	−0.516792	+	0.856111i	$0.672874\pi$
$992$	−1.39921	−0.0444249
$993$	39.1589	1.24267
$994$	9.09971	0.288625
$995$	−59.7194	−1.89323
$996$	0.420040	0.0133095
$997$	28.5701	0.904823	0.452412	−	0.891809i	$-0.350564\pi$
$997$	28.5701	0.904823	0.452412	+	0.891809i	$0.350564\pi$
$998$	4.68804	0.148397
$999$	19.3067	0.610837

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.d.1.17	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.d.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-1.47469 q^{2} -1.86783 q^{3} +0.174714 q^{4} +4.42666 q^{5} +2.75448 q^{6} +0.892669 q^{7} +2.69173 q^{8} +0.488806 q^{9} +O(q^{10})\)	\(q-1.47469 q^{2} -1.86783 q^{3} +0.174714 q^{4} +4.42666 q^{5} +2.75448 q^{6} +0.892669 q^{7} +2.69173 q^{8} +0.488806 q^{9} -6.52796 q^{10} +1.00000 q^{11} -0.326337 q^{12} -2.41746 q^{13} -1.31641 q^{14} -8.26828 q^{15} -4.31890 q^{16} -1.00000 q^{17} -0.720838 q^{18} -2.21242 q^{19} +0.773401 q^{20} -1.66736 q^{21} -1.47469 q^{22} -7.86585 q^{23} -5.02771 q^{24} +14.5954 q^{25} +3.56501 q^{26} +4.69049 q^{27} +0.155962 q^{28} +0.955383 q^{29} +12.1932 q^{30} -1.41967 q^{31} +0.985583 q^{32} -1.86783 q^{33} +1.47469 q^{34} +3.95155 q^{35} +0.0854014 q^{36} +4.11613 q^{37} +3.26264 q^{38} +4.51542 q^{39} +11.9154 q^{40} -1.64398 q^{41} +2.45884 q^{42} +1.00000 q^{43} +0.174714 q^{44} +2.16378 q^{45} +11.5997 q^{46} +6.33042 q^{47} +8.06700 q^{48} -6.20314 q^{49} -21.5236 q^{50} +1.86783 q^{51} -0.422365 q^{52} -11.3066 q^{53} -6.91703 q^{54} +4.42666 q^{55} +2.40283 q^{56} +4.13244 q^{57} -1.40890 q^{58} +8.16349 q^{59} -1.44459 q^{60} +10.9031 q^{61} +2.09358 q^{62} +0.436342 q^{63} +7.18438 q^{64} -10.7013 q^{65} +2.75448 q^{66} -2.24511 q^{67} -0.174714 q^{68} +14.6921 q^{69} -5.82731 q^{70} -6.91251 q^{71} +1.31574 q^{72} -0.603813 q^{73} -6.07003 q^{74} -27.2617 q^{75} -0.386542 q^{76} +0.892669 q^{77} -6.65884 q^{78} -7.28661 q^{79} -19.1183 q^{80} -10.2275 q^{81} +2.42437 q^{82} -1.28713 q^{83} -0.291311 q^{84} -4.42666 q^{85} -1.47469 q^{86} -1.78450 q^{87} +2.69173 q^{88} -7.95194 q^{89} -3.19091 q^{90} -2.15799 q^{91} -1.37428 q^{92} +2.65172 q^{93} -9.33542 q^{94} -9.79365 q^{95} -1.84091 q^{96} -0.897558 q^{97} +9.14772 q^{98} +0.488806 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) \) 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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