LMFDB - Embedded newform 8041.2.a.g.1.2

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:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-2.75821 q^{2} +0.843025 q^{3} +5.60771 q^{4} +3.43649 q^{5} -2.32524 q^{6} -0.344850 q^{7} -9.95082 q^{8} -2.28931 q^{9} +O(q^{10})$	\(q-2.75821 q^{2} +0.843025 q^{3} +5.60771 q^{4} +3.43649 q^{5} -2.32524 q^{6} -0.344850 q^{7} -9.95082 q^{8} -2.28931 q^{9} -9.47854 q^{10} -1.00000 q^{11} +4.72744 q^{12} -4.61873 q^{13} +0.951168 q^{14} +2.89704 q^{15} +16.2310 q^{16} +1.00000 q^{17} +6.31439 q^{18} +7.54894 q^{19} +19.2708 q^{20} -0.290717 q^{21} +2.75821 q^{22} +1.39026 q^{23} -8.38879 q^{24} +6.80944 q^{25} +12.7394 q^{26} -4.45902 q^{27} -1.93382 q^{28} -4.70625 q^{29} -7.99065 q^{30} +2.92736 q^{31} -24.8669 q^{32} -0.843025 q^{33} -2.75821 q^{34} -1.18507 q^{35} -12.8378 q^{36} +5.72242 q^{37} -20.8216 q^{38} -3.89370 q^{39} -34.1959 q^{40} -10.2164 q^{41} +0.801858 q^{42} +1.00000 q^{43} -5.60771 q^{44} -7.86718 q^{45} -3.83462 q^{46} +10.5798 q^{47} +13.6832 q^{48} -6.88108 q^{49} -18.7818 q^{50} +0.843025 q^{51} -25.9005 q^{52} -14.0191 q^{53} +12.2989 q^{54} -3.43649 q^{55} +3.43154 q^{56} +6.36395 q^{57} +12.9808 q^{58} +3.89484 q^{59} +16.2458 q^{60} -11.6936 q^{61} -8.07428 q^{62} +0.789469 q^{63} +36.1260 q^{64} -15.8722 q^{65} +2.32524 q^{66} -6.76294 q^{67} +5.60771 q^{68} +1.17202 q^{69} +3.26868 q^{70} -14.7033 q^{71} +22.7805 q^{72} -2.55243 q^{73} -15.7836 q^{74} +5.74052 q^{75} +42.3323 q^{76} +0.344850 q^{77} +10.7396 q^{78} -12.7313 q^{79} +55.7777 q^{80} +3.10887 q^{81} +28.1790 q^{82} +17.1811 q^{83} -1.63026 q^{84} +3.43649 q^{85} -2.75821 q^{86} -3.96748 q^{87} +9.95082 q^{88} +2.44192 q^{89} +21.6993 q^{90} +1.59277 q^{91} +7.79616 q^{92} +2.46784 q^{93} -29.1814 q^{94} +25.9418 q^{95} -20.9634 q^{96} +6.64432 q^{97} +18.9794 q^{98} +2.28931 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) $ 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * 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 $

$2$	−2.75821	−1.95035	−0.975174	−	0.221440i	$-0.928924\pi$
$2$	−2.75821	−1.95035	−0.975174	+	0.221440i	$0.928924\pi$
$3$	0.843025	0.486721	0.243360	−	0.969936i	$-0.421750\pi$
$3$	0.843025	0.486721	0.243360	+	0.969936i	$0.421750\pi$
$4$	5.60771	2.80386
$5$	3.43649	1.53684	0.768422	−	0.639944i	$-0.221042\pi$
$5$	3.43649	1.53684	0.768422	+	0.639944i	$0.221042\pi$
$6$	−2.32524	−0.949274
$7$	−0.344850	−0.130341	−0.0651705	−	0.997874i	$-0.520759\pi$
$7$	−0.344850	−0.130341	−0.0651705	+	0.997874i	$0.520759\pi$
$8$	−9.95082	−3.51815
$9$	−2.28931	−0.763103
$10$	−9.47854	−2.99738
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	4.72744	1.36469
$13$	−4.61873	−1.28101	−0.640503	−	0.767956i	$-0.721274\pi$
$13$	−4.61873	−1.28101	−0.640503	+	0.767956i	$0.721274\pi$
$14$	0.951168	0.254210
$15$	2.89704	0.748013
$16$	16.2310	4.05776
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	6.31439	1.48832
$19$	7.54894	1.73185	0.865923	−	0.500177i	$-0.166732\pi$
$19$	7.54894	1.73185	0.865923	+	0.500177i	$0.166732\pi$
$20$	19.2708	4.30909
$21$	−0.290717	−0.0634397
$22$	2.75821	0.588052
$23$	1.39026	0.289889	0.144944	−	0.989440i	$-0.453700\pi$
$23$	1.39026	0.289889	0.144944	+	0.989440i	$0.453700\pi$
$24$	−8.38879	−1.71235
$25$	6.80944	1.36189
$26$	12.7394	2.49841
$27$	−4.45902	−0.858138
$28$	−1.93382	−0.365458
$29$	−4.70625	−0.873929	−0.436964	−	0.899479i	$-0.643946\pi$
$29$	−4.70625	−0.873929	−0.436964	+	0.899479i	$0.643946\pi$
$30$	−7.99065	−1.45889
$31$	2.92736	0.525770	0.262885	−	0.964827i	$-0.415326\pi$
$31$	2.92736	0.525770	0.262885	+	0.964827i	$0.415326\pi$
$32$	−24.8669	−4.39589
$33$	−0.843025	−0.146752
$34$	−2.75821	−0.473029
$35$	−1.18507	−0.200314
$36$	−12.8378	−2.13963
$37$	5.72242	0.940760	0.470380	−	0.882464i	$-0.344117\pi$
$37$	5.72242	0.940760	0.470380	+	0.882464i	$0.344117\pi$
$38$	−20.8216	−3.37770
$39$	−3.89370	−0.623492
$40$	−34.1959	−5.40684
$41$	−10.2164	−1.59554	−0.797768	−	0.602965i	$-0.793986\pi$
$41$	−10.2164	−1.59554	−0.797768	+	0.602965i	$0.793986\pi$
$42$	0.801858	0.123729
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−5.60771	−0.845395
$45$	−7.86718	−1.17277
$46$	−3.83462	−0.565384
$47$	10.5798	1.54323	0.771614	−	0.636091i	$-0.219450\pi$
$47$	10.5798	1.54323	0.771614	+	0.636091i	$0.219450\pi$
$48$	13.6832	1.97499
$49$	−6.88108	−0.983011
$50$	−18.7818	−2.65615
$51$	0.843025	0.118047
$52$	−25.9005	−3.59176
$53$	−14.0191	−1.92567	−0.962836	−	0.270087i	$-0.912948\pi$
$53$	−14.0191	−1.92567	−0.962836	+	0.270087i	$0.912948\pi$
$54$	12.2989	1.67367
$55$	−3.43649	−0.463376
$56$	3.43154	0.458559
$57$	6.36395	0.842925
$58$	12.9808	1.70446
$59$	3.89484	0.507065	0.253533	−	0.967327i	$-0.418407\pi$
$59$	3.89484	0.507065	0.253533	+	0.967327i	$0.418407\pi$
$60$	16.2458	2.09732
$61$	−11.6936	−1.49721	−0.748603	−	0.663018i	$-0.769275\pi$
$61$	−11.6936	−1.49721	−0.748603	+	0.663018i	$0.769275\pi$
$62$	−8.07428	−1.02543
$63$	0.789469	0.0994637
$64$	36.1260	4.51575
$65$	−15.8722	−1.96870
$66$	2.32524	0.286217
$67$	−6.76294	−0.826225	−0.413113	−	0.910680i	$-0.635558\pi$
$67$	−6.76294	−0.826225	−0.413113	+	0.910680i	$0.635558\pi$
$68$	5.60771	0.680035
$69$	1.17202	0.141095
$70$	3.26868	0.390682
$71$	−14.7033	−1.74496	−0.872481	−	0.488647i	$-0.837490\pi$
$71$	−14.7033	−1.74496	−0.872481	+	0.488647i	$0.837490\pi$
$72$	22.7805	2.68471
$73$	−2.55243	−0.298739	−0.149370	−	0.988781i	$-0.547724\pi$
$73$	−2.55243	−0.298739	−0.149370	+	0.988781i	$0.547724\pi$
$74$	−15.7836	−1.83481
$75$	5.74052	0.662859
$76$	42.3323	4.85585
$77$	0.344850	0.0392993
$78$	10.7396	1.21603
$79$	−12.7313	−1.43238	−0.716191	−	0.697904i	$-0.754116\pi$
$79$	−12.7313	−1.43238	−0.716191	+	0.697904i	$0.754116\pi$
$80$	55.7777	6.23613
$81$	3.10887	0.345430
$82$	28.1790	3.11185
$83$	17.1811	1.88587	0.942934	−	0.332980i	$-0.108054\pi$
$83$	17.1811	1.88587	0.942934	+	0.332980i	$0.108054\pi$
$84$	−1.63026	−0.177876
$85$	3.43649	0.372739
$86$	−2.75821	−0.297425
$87$	−3.96748	−0.425359
$88$	9.95082	1.06076
$89$	2.44192	0.258843	0.129421	−	0.991590i	$-0.458688\pi$
$89$	2.44192	0.258843	0.129421	+	0.991590i	$0.458688\pi$
$90$	21.6993	2.28731
$91$	1.59277	0.166968
$92$	7.79616	0.812806
$93$	2.46784	0.255903
$94$	−29.1814	−3.00983
$95$	25.9418	2.66158
$96$	−20.9634	−2.13957
$97$	6.64432	0.674629	0.337314	−	0.941392i	$-0.390481\pi$
$97$	6.64432	0.674629	0.337314	+	0.941392i	$0.390481\pi$
$98$	18.9794	1.91721
$99$	2.28931	0.230084
$100$	38.1854	3.81854
$101$	−4.18900	−0.416822	−0.208411	−	0.978041i	$-0.566829\pi$
$101$	−4.18900	−0.416822	−0.208411	+	0.978041i	$0.566829\pi$
$102$	−2.32524	−0.230233
$103$	0.197597	0.0194698	0.00973491	−	0.999953i	$-0.496901\pi$
$103$	0.197597	0.0194698	0.00973491	+	0.999953i	$0.496901\pi$
$104$	45.9602	4.50677
$105$	−0.999046	−0.0974969
$106$	38.6676	3.75573
$107$	−15.6538	−1.51331	−0.756654	−	0.653815i	$-0.773167\pi$
$107$	−15.6538	−1.51331	−0.756654	+	0.653815i	$0.773167\pi$
$108$	−25.0049	−2.40610
$109$	−10.6755	−1.02253	−0.511266	−	0.859423i	$-0.670823\pi$
$109$	−10.6755	−1.02253	−0.511266	+	0.859423i	$0.670823\pi$
$110$	9.47854	0.903744
$111$	4.82414	0.457887
$112$	−5.59727	−0.528892
$113$	−12.5996	−1.18527	−0.592633	−	0.805473i	$-0.701912\pi$
$113$	−12.5996	−1.18527	−0.592633	+	0.805473i	$0.701912\pi$
$114$	−17.5531	−1.64400
$115$	4.77760	0.445513
$116$	−26.3913	−2.45037
$117$	10.5737	0.977539
$118$	−10.7428	−0.988954
$119$	−0.344850	−0.0316124
$120$	−28.8280	−2.63162
$121$	1.00000	0.0909091
$122$	32.2533	2.92007
$123$	−8.61269	−0.776580
$124$	16.4158	1.47418
$125$	6.21811	0.556164
$126$	−2.17752	−0.193989
$127$	6.62272	0.587672	0.293836	−	0.955856i	$-0.405068\pi$
$127$	6.62272	0.587672	0.293836	+	0.955856i	$0.405068\pi$
$128$	−49.9093	−4.41140
$129$	0.843025	0.0742242
$130$	43.7788	3.83966
$131$	15.7179	1.37328	0.686638	−	0.726999i	$-0.259086\pi$
$131$	15.7179	1.37328	0.686638	+	0.726999i	$0.259086\pi$
$132$	−4.72744	−0.411471
$133$	−2.60325	−0.225731
$134$	18.6536	1.61143
$135$	−15.3234	−1.31882
$136$	−9.95082	−0.853276
$137$	12.3664	1.05653	0.528267	−	0.849078i	$-0.322842\pi$
$137$	12.3664	1.05653	0.528267	+	0.849078i	$0.322842\pi$
$138$	−3.23268	−0.275184
$139$	9.72315	0.824706	0.412353	−	0.911024i	$-0.364707\pi$
$139$	9.72315	0.824706	0.412353	+	0.911024i	$0.364707\pi$
$140$	−6.64555	−0.561651
$141$	8.91906	0.751121
$142$	40.5548	3.40328
$143$	4.61873	0.386238
$144$	−37.1578	−3.09649
$145$	−16.1730	−1.34309
$146$	7.04013	0.582645
$147$	−5.80092	−0.478452
$148$	32.0897	2.63775
$149$	−10.9685	−0.898572	−0.449286	−	0.893388i	$-0.648322\pi$
$149$	−10.9685	−0.898572	−0.449286	+	0.893388i	$0.648322\pi$
$150$	−15.8336	−1.29280
$151$	−13.2818	−1.08086	−0.540429	−	0.841390i	$-0.681738\pi$
$151$	−13.2818	−1.08086	−0.540429	+	0.841390i	$0.681738\pi$
$152$	−75.1182	−6.09289
$153$	−2.28931	−0.185080
$154$	−0.951168	−0.0766473
$155$	10.0598	0.808026
$156$	−21.8348	−1.74818
$157$	−5.78336	−0.461562	−0.230781	−	0.973006i	$-0.574128\pi$
$157$	−5.78336	−0.461562	−0.230781	+	0.973006i	$0.574128\pi$
$158$	35.1156	2.79364
$159$	−11.8185	−0.937264
$160$	−85.4547	−6.75579
$161$	−0.479430	−0.0377844
$162$	−8.57490	−0.673708
$163$	5.96634	0.467320	0.233660	−	0.972318i	$-0.424930\pi$
$163$	5.96634	0.467320	0.233660	+	0.972318i	$0.424930\pi$
$164$	−57.2907	−4.47365
$165$	−2.89704	−0.225534
$166$	−47.3890	−3.67810
$167$	20.7034	1.60208	0.801040	−	0.598611i	$-0.204280\pi$
$167$	20.7034	1.60208	0.801040	+	0.598611i	$0.204280\pi$
$168$	2.89288	0.223190
$169$	8.33267	0.640975
$170$	−9.47854	−0.726971
$171$	−17.2819	−1.32158
$172$	5.60771	0.427584
$173$	−15.2087	−1.15630	−0.578149	−	0.815931i	$-0.696225\pi$
$173$	−15.2087	−1.15630	−0.578149	+	0.815931i	$0.696225\pi$
$174$	10.9431	0.829598
$175$	−2.34824	−0.177510
$176$	−16.2310	−1.22346
$177$	3.28345	0.246799
$178$	−6.73531	−0.504833
$179$	−13.7044	−1.02431	−0.512157	−	0.858892i	$-0.671153\pi$
$179$	−13.7044	−1.02431	−0.512157	+	0.858892i	$0.671153\pi$
$180$	−44.1169	−3.28828
$181$	−3.65444	−0.271633	−0.135816	−	0.990734i	$-0.543366\pi$
$181$	−3.65444	−0.271633	−0.135816	+	0.990734i	$0.543366\pi$
$182$	−4.39319	−0.325645
$183$	−9.85796	−0.728721
$184$	−13.8342	−1.01987
$185$	19.6650	1.44580
$186$	−6.80681	−0.499100
$187$	−1.00000	−0.0731272
$188$	59.3287	4.32699
$189$	1.53769	0.111851
$190$	−71.5530	−5.19100
$191$	−26.2661	−1.90055	−0.950275	−	0.311413i	$-0.899198\pi$
$191$	−26.2661	−1.90055	−0.950275	+	0.311413i	$0.899198\pi$
$192$	30.4551	2.19791
$193$	17.4791	1.25817	0.629085	−	0.777336i	$-0.283430\pi$
$193$	17.4791	1.25817	0.629085	+	0.777336i	$0.283430\pi$
$194$	−18.3264	−1.31576
$195$	−13.3807	−0.958209
$196$	−38.5871	−2.75622
$197$	−4.26943	−0.304184	−0.152092	−	0.988366i	$-0.548601\pi$
$197$	−4.26943	−0.304184	−0.152092	+	0.988366i	$0.548601\pi$
$198$	−6.31439	−0.448744
$199$	13.3638	0.947337	0.473668	−	0.880703i	$-0.342930\pi$
$199$	13.3638	0.947337	0.473668	+	0.880703i	$0.342930\pi$
$200$	−67.7595	−4.79132
$201$	−5.70133	−0.402141
$202$	11.5541	0.812947
$203$	1.62295	0.113909
$204$	4.72744	0.330987
$205$	−35.1086	−2.45209
$206$	−0.545014	−0.0379729
$207$	−3.18273	−0.221215
$208$	−74.9667	−5.19801
$209$	−7.54894	−0.522171
$210$	2.75558	0.190153
$211$	17.3128	1.19187	0.595933	−	0.803034i	$-0.296782\pi$
$211$	17.3128	1.19187	0.595933	+	0.803034i	$0.296782\pi$
$212$	−78.6151	−5.39931
$213$	−12.3953	−0.849309
$214$	43.1764	2.95148
$215$	3.43649	0.234366
$216$	44.3709	3.01906
$217$	−1.00950	−0.0685294
$218$	29.4454	1.99429
$219$	−2.15176	−0.145402
$220$	−19.2708	−1.29924
$221$	−4.61873	−0.310689
$222$	−13.3060	−0.893039
$223$	−13.9343	−0.933109	−0.466554	−	0.884493i	$-0.654505\pi$
$223$	−13.9343	−0.933109	−0.466554	+	0.884493i	$0.654505\pi$
$224$	8.57535	0.572965
$225$	−15.5889	−1.03926
$226$	34.7522	2.31168
$227$	8.46055	0.561546	0.280773	−	0.959774i	$-0.409409\pi$
$227$	8.46055	0.561546	0.280773	+	0.959774i	$0.409409\pi$
$228$	35.6872	2.36344
$229$	19.4964	1.28836	0.644178	−	0.764876i	$-0.277200\pi$
$229$	19.4964	1.28836	0.644178	+	0.764876i	$0.277200\pi$
$230$	−13.1776	−0.868906
$231$	0.290717	0.0191278
$232$	46.8311	3.07461
$233$	−4.09287	−0.268133	−0.134067	−	0.990972i	$-0.542804\pi$
$233$	−4.09287	−0.268133	−0.134067	+	0.990972i	$0.542804\pi$
$234$	−29.1645	−1.90654
$235$	36.3575	2.37170
$236$	21.8412	1.42174
$237$	−10.7328	−0.697170
$238$	0.951168	0.0616551
$239$	−5.58585	−0.361319	−0.180659	−	0.983546i	$-0.557823\pi$
$239$	−5.58585	−0.361319	−0.180659	+	0.983546i	$0.557823\pi$
$240$	47.0220	3.03525
$241$	−28.7151	−1.84971	−0.924853	−	0.380326i	$-0.875812\pi$
$241$	−28.7151	−1.84971	−0.924853	+	0.380326i	$0.875812\pi$
$242$	−2.75821	−0.177304
$243$	15.9979	1.02627
$244$	−65.5741	−4.19795
$245$	−23.6467	−1.51073
$246$	23.7556	1.51460
$247$	−34.8665	−2.21850
$248$	−29.1297	−1.84974
$249$	14.4841	0.917890
$250$	−17.1508	−1.08471
$251$	−17.5154	−1.10556	−0.552782	−	0.833326i	$-0.686434\pi$
$251$	−17.5154	−1.10556	−0.552782	+	0.833326i	$0.686434\pi$
$252$	4.42711	0.278882
$253$	−1.39026	−0.0874047
$254$	−18.2669	−1.14616
$255$	2.89704	0.181420
$256$	65.4082	4.08801
$257$	11.5112	0.718051	0.359026	−	0.933328i	$-0.383109\pi$
$257$	11.5112	0.718051	0.359026	+	0.933328i	$0.383109\pi$
$258$	−2.32524	−0.144763
$259$	−1.97338	−0.122620
$260$	−89.0068	−5.51997
$261$	10.7741	0.666898
$262$	−43.3531	−2.67837
$263$	17.4672	1.07707	0.538537	−	0.842602i	$-0.318977\pi$
$263$	17.4672	1.07707	0.538537	+	0.842602i	$0.318977\pi$
$264$	8.38879	0.516294
$265$	−48.1765	−2.95946
$266$	7.18032	0.440253
$267$	2.05860	0.125984
$268$	−37.9246	−2.31662
$269$	−5.97011	−0.364004	−0.182002	−	0.983298i	$-0.558258\pi$
$269$	−5.97011	−0.364004	−0.182002	+	0.983298i	$0.558258\pi$
$270$	42.2650	2.57217
$271$	6.15163	0.373685	0.186842	−	0.982390i	$-0.440175\pi$
$271$	6.15163	0.373685	0.186842	+	0.982390i	$0.440175\pi$
$272$	16.2310	0.984150
$273$	1.34274	0.0812666
$274$	−34.1091	−2.06061
$275$	−6.80944	−0.410625
$276$	6.57236	0.395609
$277$	−0.170065	−0.0102182	−0.00510911	−	0.999987i	$-0.501626\pi$
$277$	−0.170065	−0.0102182	−0.00510911	+	0.999987i	$0.501626\pi$
$278$	−26.8185	−1.60846
$279$	−6.70164	−0.401217
$280$	11.7925	0.704734
$281$	2.98153	0.177863	0.0889317	−	0.996038i	$-0.471655\pi$
$281$	2.98153	0.177863	0.0889317	+	0.996038i	$0.471655\pi$
$282$	−24.6006	−1.46495
$283$	−11.8819	−0.706304	−0.353152	−	0.935566i	$-0.614890\pi$
$283$	−11.8819	−0.706304	−0.353152	+	0.935566i	$0.614890\pi$
$284$	−82.4520	−4.89263
$285$	21.8696	1.29544
$286$	−12.7394	−0.753298
$287$	3.52313	0.207964
$288$	56.9280	3.35451
$289$	1.00000	0.0588235
$290$	44.6084	2.61950
$291$	5.60133	0.328356
$292$	−14.3133	−0.837621
$293$	3.53127	0.206299	0.103149	−	0.994666i	$-0.467108\pi$
$293$	3.53127	0.206299	0.103149	+	0.994666i	$0.467108\pi$
$294$	16.0001	0.933147
$295$	13.3846	0.779280
$296$	−56.9428	−3.30973
$297$	4.45902	0.258738
$298$	30.2533	1.75253
$299$	−6.42122	−0.371349
$300$	32.1912	1.85856
$301$	−0.344850	−0.0198768
$302$	36.6340	2.10805
$303$	−3.53143	−0.202876
$304$	122.527	7.02741
$305$	−40.1847	−2.30097
$306$	6.31439	0.360970
$307$	21.1103	1.20483	0.602416	−	0.798183i	$-0.294205\pi$
$307$	21.1103	1.20483	0.602416	+	0.798183i	$0.294205\pi$
$308$	1.93382	0.110190
$309$	0.166579	0.00947636
$310$	−27.7471	−1.57593
$311$	−7.04272	−0.399356	−0.199678	−	0.979862i	$-0.563990\pi$
$311$	−7.04272	−0.399356	−0.199678	+	0.979862i	$0.563990\pi$
$312$	38.7456	2.19354
$313$	32.5421	1.83939	0.919694	−	0.392636i	$-0.128437\pi$
$313$	32.5421	1.83939	0.919694	+	0.392636i	$0.128437\pi$
$314$	15.9517	0.900207
$315$	2.71300	0.152860
$316$	−71.3935	−4.01620
$317$	14.2873	0.802452	0.401226	−	0.915979i	$-0.368584\pi$
$317$	14.2873	0.802452	0.401226	+	0.915979i	$0.368584\pi$
$318$	32.5977	1.82799
$319$	4.70625	0.263499
$320$	124.147	6.94000
$321$	−13.1965	−0.736558
$322$	1.32237	0.0736927
$323$	7.54894	0.420034
$324$	17.4336	0.968535
$325$	−31.4510	−1.74459
$326$	−16.4564	−0.911437
$327$	−8.99975	−0.497687
$328$	101.662	5.61333
$329$	−3.64846	−0.201146
$330$	7.99065	0.439871
$331$	−2.21655	−0.121833	−0.0609164	−	0.998143i	$-0.519402\pi$
$331$	−2.21655	−0.121833	−0.0609164	+	0.998143i	$0.519402\pi$
$332$	96.3465	5.28770
$333$	−13.1004	−0.717897
$334$	−57.1044	−3.12461
$335$	−23.2408	−1.26978
$336$	−4.71864	−0.257423
$337$	−16.2343	−0.884338	−0.442169	−	0.896932i	$-0.645791\pi$
$337$	−16.2343	−0.884338	−0.442169	+	0.896932i	$0.645791\pi$
$338$	−22.9832	−1.25012
$339$	−10.6217	−0.576893
$340$	19.2708	1.04511
$341$	−2.92736	−0.158526
$342$	47.6670	2.57754
$343$	4.78689	0.258468
$344$	−9.95082	−0.536513
$345$	4.02763	0.216840
$346$	41.9488	2.25518
$347$	−2.41004	−0.129378	−0.0646888	−	0.997905i	$-0.520605\pi$
$347$	−2.41004	−0.129378	−0.0646888	+	0.997905i	$0.520605\pi$
$348$	−22.2485	−1.19265
$349$	−15.2425	−0.815910	−0.407955	−	0.913002i	$-0.633758\pi$
$349$	−15.2425	−0.815910	−0.407955	+	0.913002i	$0.633758\pi$
$350$	6.47692	0.346206
$351$	20.5950	1.09928
$352$	24.8669	1.32541
$353$	−15.2917	−0.813894	−0.406947	−	0.913452i	$-0.633407\pi$
$353$	−15.2917	−0.813894	−0.406947	+	0.913452i	$0.633407\pi$
$354$	−9.05644	−0.481344
$355$	−50.5277	−2.68173
$356$	13.6936	0.725758
$357$	−0.290717	−0.0153864
$358$	37.7995	1.99777
$359$	16.2209	0.856107	0.428054	−	0.903753i	$-0.359199\pi$
$359$	16.2209	0.856107	0.428054	+	0.903753i	$0.359199\pi$
$360$	78.2849	4.12598
$361$	37.9865	1.99929
$362$	10.0797	0.529778
$363$	0.843025	0.0442473
$364$	8.93180	0.468153
$365$	−8.77138	−0.459115
$366$	27.1903	1.42126
$367$	14.2452	0.743595	0.371798	−	0.928314i	$-0.378742\pi$
$367$	14.2452	0.743595	0.371798	+	0.928314i	$0.378742\pi$
$368$	22.5653	1.17630
$369$	23.3885	1.21756
$370$	−54.2402	−2.81981
$371$	4.83449	0.250994
$372$	13.8389	0.717515
$373$	−10.2116	−0.528739	−0.264369	−	0.964421i	$-0.585164\pi$
$373$	−10.2116	−0.528739	−0.264369	+	0.964421i	$0.585164\pi$
$374$	2.75821	0.142624
$375$	5.24202	0.270697
$376$	−105.278	−5.42930
$377$	21.7369	1.11951
$378$	−4.24128	−0.218148
$379$	−2.92142	−0.150063	−0.0750317	−	0.997181i	$-0.523906\pi$
$379$	−2.92142	−0.150063	−0.0750317	+	0.997181i	$0.523906\pi$
$380$	145.474	7.46268
$381$	5.58312	0.286032
$382$	72.4474	3.70673
$383$	−38.0155	−1.94250	−0.971250	−	0.238063i	$-0.923487\pi$
$383$	−38.0155	−1.94250	−0.971250	+	0.238063i	$0.923487\pi$
$384$	−42.0748	−2.14712
$385$	1.18507	0.0603969
$386$	−48.2109	−2.45387
$387$	−2.28931	−0.116372
$388$	37.2595	1.89156
$389$	4.57761	0.232094	0.116047	−	0.993244i	$-0.462978\pi$
$389$	4.57761	0.232094	0.116047	+	0.993244i	$0.462978\pi$
$390$	36.9066	1.86884
$391$	1.39026	0.0703083
$392$	68.4724	3.45838
$393$	13.2505	0.668402
$394$	11.7760	0.593265
$395$	−43.7509	−2.20135
$396$	12.8378	0.645123
$397$	10.1736	0.510596	0.255298	−	0.966862i	$-0.417826\pi$
$397$	10.1736	0.510596	0.255298	+	0.966862i	$0.417826\pi$
$398$	−36.8602	−1.84764
$399$	−2.19461	−0.109868
$400$	110.524	5.52621
$401$	−3.30558	−0.165073	−0.0825364	−	0.996588i	$-0.526302\pi$
$401$	−3.30558	−0.165073	−0.0825364	+	0.996588i	$0.526302\pi$
$402$	15.7255	0.784314
$403$	−13.5207	−0.673514
$404$	−23.4907	−1.16871
$405$	10.6836	0.530871
$406$	−4.47644	−0.222162
$407$	−5.72242	−0.283650
$408$	−8.38879	−0.415307
$409$	−21.4341	−1.05985	−0.529925	−	0.848044i	$-0.677780\pi$
$409$	−21.4341	−1.05985	−0.529925	+	0.848044i	$0.677780\pi$
$410$	96.8367	4.78243
$411$	10.4252	0.514237
$412$	1.10807	0.0545906
$413$	−1.34314	−0.0660915
$414$	8.77863	0.431446
$415$	59.0425	2.89828
$416$	114.853	5.63115
$417$	8.19685	0.401402
$418$	20.8216	1.01842
$419$	−29.9182	−1.46160	−0.730800	−	0.682592i	$-0.760853\pi$
$419$	−29.9182	−1.46160	−0.730800	+	0.682592i	$0.760853\pi$
$420$	−5.60236	−0.273367
$421$	28.4782	1.38794	0.693971	−	0.720003i	$-0.255860\pi$
$421$	28.4782	1.38794	0.693971	+	0.720003i	$0.255860\pi$
$422$	−47.7524	−2.32455
$423$	−24.2205	−1.17764
$424$	139.502	6.77480
$425$	6.80944	0.330306
$426$	34.1887	1.65645
$427$	4.03252	0.195148
$428$	−87.7819	−4.24310
$429$	3.89370	0.187990
$430$	−9.47854	−0.457096
$431$	−13.3820	−0.644587	−0.322293	−	0.946640i	$-0.604454\pi$
$431$	−13.3820	−0.644587	−0.322293	+	0.946640i	$0.604454\pi$
$432$	−72.3744	−3.48212
$433$	−15.8188	−0.760204	−0.380102	−	0.924945i	$-0.624111\pi$
$433$	−15.8188	−0.760204	−0.380102	+	0.924945i	$0.624111\pi$
$434$	2.78442	0.133656
$435$	−13.6342	−0.653710
$436$	−59.8654	−2.86703
$437$	10.4950	0.502043
$438$	5.93500	0.283585
$439$	−6.58325	−0.314202	−0.157101	−	0.987583i	$-0.550215\pi$
$439$	−6.58325	−0.314202	−0.157101	+	0.987583i	$0.550215\pi$
$440$	34.1959	1.63022
$441$	15.7529	0.750139
$442$	12.7394	0.605952
$443$	−22.6236	−1.07488	−0.537440	−	0.843302i	$-0.680609\pi$
$443$	−22.6236	−1.07488	−0.537440	+	0.843302i	$0.680609\pi$
$444$	27.0524	1.28385
$445$	8.39161	0.397801
$446$	38.4337	1.81989
$447$	−9.24669	−0.437353
$448$	−12.4581	−0.588588
$449$	0.977299	0.0461216	0.0230608	−	0.999734i	$-0.492659\pi$
$449$	0.977299	0.0461216	0.0230608	+	0.999734i	$0.492659\pi$
$450$	42.9975	2.02692
$451$	10.2164	0.481072
$452$	−70.6547	−3.32332
$453$	−11.1969	−0.526076
$454$	−23.3360	−1.09521
$455$	5.47353	0.256603
$456$	−63.3265	−2.96554
$457$	14.4355	0.675265	0.337633	−	0.941278i	$-0.390374\pi$
$457$	14.4355	0.675265	0.337633	+	0.941278i	$0.390374\pi$
$458$	−53.7750	−2.51274
$459$	−4.45902	−0.208129
$460$	26.7914	1.24916
$461$	−19.2912	−0.898480	−0.449240	−	0.893411i	$-0.648305\pi$
$461$	−19.2912	−0.898480	−0.449240	+	0.893411i	$0.648305\pi$
$462$	−0.801858	−0.0373058
$463$	−31.4459	−1.46142	−0.730708	−	0.682690i	$-0.760810\pi$
$463$	−31.4459	−1.46142	−0.730708	+	0.682690i	$0.760810\pi$
$464$	−76.3872	−3.54619
$465$	8.48070	0.393283
$466$	11.2890	0.522953
$467$	−19.5569	−0.904985	−0.452492	−	0.891768i	$-0.649465\pi$
$467$	−19.5569	−0.904985	−0.452492	+	0.891768i	$0.649465\pi$
$468$	59.2943	2.74088
$469$	2.33220	0.107691
$470$	−100.281	−4.62564
$471$	−4.87551	−0.224652
$472$	−38.7569	−1.78393
$473$	−1.00000	−0.0459800
$474$	29.6033	1.35972
$475$	51.4041	2.35858
$476$	−1.93382	−0.0886365
$477$	32.0941	1.46949
$478$	15.4069	0.704697
$479$	−35.2365	−1.61000	−0.804998	−	0.593277i	$-0.797834\pi$
$479$	−35.2365	−1.61000	−0.804998	+	0.593277i	$0.797834\pi$
$480$	−72.0404	−3.28818
$481$	−26.4303	−1.20512
$482$	79.2023	3.60757
$483$	−0.404172	−0.0183904
$484$	5.60771	0.254896
$485$	22.8331	1.03680
$486$	−44.1256	−2.00158
$487$	29.8165	1.35111	0.675557	−	0.737308i	$-0.263903\pi$
$487$	29.8165	1.35111	0.675557	+	0.737308i	$0.263903\pi$
$488$	116.361	5.26739
$489$	5.02977	0.227454
$490$	65.2226	2.94646
$491$	14.2250	0.641965	0.320983	−	0.947085i	$-0.395987\pi$
$491$	14.2250	0.641965	0.320983	+	0.947085i	$0.395987\pi$
$492$	−48.2975	−2.17742
$493$	−4.70625	−0.211959
$494$	96.1692	4.32686
$495$	7.86718	0.353603
$496$	47.5141	2.13345
$497$	5.07044	0.227440
$498$	−39.9501	−1.79021
$499$	−18.9730	−0.849347	−0.424673	−	0.905347i	$-0.639611\pi$
$499$	−18.9730	−0.849347	−0.424673	+	0.905347i	$0.639611\pi$
$500$	34.8694	1.55941
$501$	17.4535	0.779765
$502$	48.3112	2.15623
$503$	−16.9084	−0.753908	−0.376954	−	0.926232i	$-0.623028\pi$
$503$	−16.9084	−0.753908	−0.376954	+	0.926232i	$0.623028\pi$
$504$	−7.85586	−0.349928
$505$	−14.3955	−0.640589
$506$	3.83462	0.170470
$507$	7.02465	0.311976
$508$	37.1383	1.64775
$509$	−42.8237	−1.89813	−0.949063	−	0.315087i	$-0.897966\pi$
$509$	−42.8237	−1.89813	−0.949063	+	0.315087i	$0.897966\pi$
$510$	−7.99065	−0.353832
$511$	0.880205	0.0389380
$512$	−80.5909	−3.56165
$513$	−33.6609	−1.48616
$514$	−31.7504	−1.40045
$515$	0.679040	0.0299221
$516$	4.72744	0.208114
$517$	−10.5798	−0.465301
$518$	5.44298	0.239151
$519$	−12.8213	−0.562794
$520$	157.942	6.92619
$521$	−11.7046	−0.512790	−0.256395	−	0.966572i	$-0.582535\pi$
$521$	−11.7046	−0.512790	−0.256395	+	0.966572i	$0.582535\pi$
$522$	−29.7171	−1.30068
$523$	−24.2057	−1.05844	−0.529222	−	0.848484i	$-0.677516\pi$
$523$	−24.2057	−1.05844	−0.529222	+	0.848484i	$0.677516\pi$
$524$	88.1413	3.85047
$525$	−1.97962	−0.0863977
$526$	−48.1782	−2.10067
$527$	2.92736	0.127518
$528$	−13.6832	−0.595483
$529$	−21.0672	−0.915965
$530$	132.881	5.77197
$531$	−8.91650	−0.386943
$532$	−14.5983	−0.632917
$533$	47.1869	2.04389
$534$	−5.67804	−0.245713
$535$	−53.7940	−2.32572
$536$	67.2969	2.90678
$537$	−11.5531	−0.498554
$538$	16.4668	0.709935
$539$	6.88108	0.296389
$540$	−85.9290	−3.69779
$541$	−12.1754	−0.523463	−0.261731	−	0.965141i	$-0.584293\pi$
$541$	−12.1754	−0.523463	−0.261731	+	0.965141i	$0.584293\pi$
$542$	−16.9675	−0.728816
$543$	−3.08079	−0.132209
$544$	−24.8669	−1.06616
$545$	−36.6864	−1.57147
$546$	−3.70357	−0.158498
$547$	25.8507	1.10530	0.552648	−	0.833414i	$-0.313617\pi$
$547$	25.8507	1.10530	0.552648	+	0.833414i	$0.313617\pi$
$548$	69.3473	2.96237
$549$	26.7702	1.14252
$550$	18.7818	0.800861
$551$	−35.5272	−1.51351
$552$	−11.6626	−0.496392
$553$	4.39039	0.186698
$554$	0.469075	0.0199291
$555$	16.5781	0.703701
$556$	54.5246	2.31236
$557$	15.9037	0.673861	0.336931	−	0.941529i	$-0.390611\pi$
$557$	15.9037	0.673861	0.336931	+	0.941529i	$0.390611\pi$
$558$	18.4845	0.782512
$559$	−4.61873	−0.195351
$560$	−19.2349	−0.812825
$561$	−0.843025	−0.0355925
$562$	−8.22369	−0.346895
$563$	5.10811	0.215281	0.107641	−	0.994190i	$-0.465670\pi$
$563$	5.10811	0.215281	0.107641	+	0.994190i	$0.465670\pi$
$564$	50.0156	2.10603
$565$	−43.2982	−1.82157
$566$	32.7727	1.37754
$567$	−1.07209	−0.0450237
$568$	146.310	6.13904
$569$	−18.8457	−0.790054	−0.395027	−	0.918670i	$-0.629265\pi$
$569$	−18.8457	−0.790054	−0.395027	+	0.918670i	$0.629265\pi$
$570$	−60.3209	−2.52657
$571$	−4.38995	−0.183714	−0.0918569	−	0.995772i	$-0.529280\pi$
$571$	−4.38995	−0.183714	−0.0918569	+	0.995772i	$0.529280\pi$
$572$	25.9005	1.08295
$573$	−22.1430	−0.925036
$574$	−9.71753	−0.405602
$575$	9.46687	0.394796
$576$	−82.7036	−3.44598
$577$	−15.3782	−0.640204	−0.320102	−	0.947383i	$-0.603717\pi$
$577$	−15.3782	−0.640204	−0.320102	+	0.947383i	$0.603717\pi$
$578$	−2.75821	−0.114726
$579$	14.7353	0.612377
$580$	−90.6933	−3.76584
$581$	−5.92490	−0.245806
$582$	−15.4496	−0.640408
$583$	14.0191	0.580612
$584$	25.3988	1.05101
$585$	36.3364	1.50232
$586$	−9.73998	−0.402355
$587$	−2.12660	−0.0877742	−0.0438871	−	0.999036i	$-0.513974\pi$
$587$	−2.12660	−0.0877742	−0.0438871	+	0.999036i	$0.513974\pi$
$588$	−32.5299	−1.34151
$589$	22.0985	0.910553
$590$	−36.9174	−1.51987
$591$	−3.59923	−0.148053
$592$	92.8807	3.81737
$593$	47.1226	1.93510	0.967548	−	0.252689i	$-0.0813150\pi$
$593$	47.1226	1.93510	0.967548	+	0.252689i	$0.0813150\pi$
$594$	−12.2989	−0.504630
$595$	−1.18507	−0.0485832
$596$	−61.5080	−2.51947
$597$	11.2660	0.461088
$598$	17.7111	0.724259
$599$	−18.0705	−0.738341	−0.369170	−	0.929362i	$-0.620358\pi$
$599$	−18.0705	−0.738341	−0.369170	+	0.929362i	$0.620358\pi$
$600$	−57.1229	−2.33203
$601$	16.9968	0.693315	0.346657	−	0.937992i	$-0.387317\pi$
$601$	16.9968	0.693315	0.346657	+	0.937992i	$0.387317\pi$
$602$	0.951168	0.0387667
$603$	15.4825	0.630495
$604$	−74.4806	−3.03057
$605$	3.43649	0.139713
$606$	9.74043	0.395678
$607$	−40.0404	−1.62519	−0.812594	−	0.582830i	$-0.801945\pi$
$607$	−40.0404	−1.62519	−0.812594	+	0.582830i	$0.801945\pi$
$608$	−187.719	−7.61300
$609$	1.36819	0.0554418
$610$	110.838	4.48769
$611$	−48.8654	−1.97688
$612$	−12.8378	−0.518937
$613$	−22.7463	−0.918716	−0.459358	−	0.888251i	$-0.651921\pi$
$613$	−22.7463	−0.918716	−0.459358	+	0.888251i	$0.651921\pi$
$614$	−58.2267	−2.34984
$615$	−29.5974	−1.19348
$616$	−3.43154	−0.138261
$617$	−18.1913	−0.732355	−0.366178	−	0.930545i	$-0.619334\pi$
$617$	−18.1913	−0.732355	−0.366178	+	0.930545i	$0.619334\pi$
$618$	−0.459460	−0.0184822
$619$	−17.7054	−0.711641	−0.355821	−	0.934554i	$-0.615799\pi$
$619$	−17.7054	−0.711641	−0.355821	+	0.934554i	$0.615799\pi$
$620$	56.4127	2.26559
$621$	−6.19918	−0.248765
$622$	19.4253	0.778883
$623$	−0.842095	−0.0337378
$624$	−63.1988	−2.52998
$625$	−12.6787	−0.507150
$626$	−89.7579	−3.58745
$627$	−6.36395	−0.254151
$628$	−32.4314	−1.29415
$629$	5.72242	0.228168
$630$	−7.48301	−0.298130
$631$	10.7013	0.426012	0.213006	−	0.977051i	$-0.431675\pi$
$631$	10.7013	0.426012	0.213006	+	0.977051i	$0.431675\pi$
$632$	126.687	5.03933
$633$	14.5952	0.580105
$634$	−39.4072	−1.56506
$635$	22.7589	0.903159
$636$	−66.2745	−2.62795
$637$	31.7818	1.25924
$638$	−12.9808	−0.513915
$639$	33.6604	1.33159
$640$	−171.513	−6.77963
$641$	0.451181	0.0178206	0.00891029	−	0.999960i	$-0.497164\pi$
$641$	0.451181	0.0178206	0.00891029	+	0.999960i	$0.497164\pi$
$642$	36.3988	1.43655
$643$	18.5369	0.731023	0.365511	−	0.930807i	$-0.380894\pi$
$643$	18.5369	0.731023	0.365511	+	0.930807i	$0.380894\pi$
$644$	−2.68851	−0.105942
$645$	2.89704	0.114071
$646$	−20.8216	−0.819213
$647$	−13.9157	−0.547081	−0.273541	−	0.961860i	$-0.588195\pi$
$647$	−13.9157	−0.547081	−0.273541	+	0.961860i	$0.588195\pi$
$648$	−30.9358	−1.21527
$649$	−3.89484	−0.152886
$650$	86.7483	3.40255
$651$	−0.851035	−0.0333547
$652$	33.4575	1.31030
$653$	−32.2093	−1.26045	−0.630224	−	0.776413i	$-0.717037\pi$
$653$	−32.2093	−1.26045	−0.630224	+	0.776413i	$0.717037\pi$
$654$	24.8232	0.970663
$655$	54.0142	2.11051
$656$	−165.823	−6.47429
$657$	5.84330	0.227969
$658$	10.0632	0.392305
$659$	−9.15591	−0.356664	−0.178332	−	0.983970i	$-0.557070\pi$
$659$	−9.15591	−0.356664	−0.178332	+	0.983970i	$0.557070\pi$
$660$	−16.2458	−0.632366
$661$	33.8763	1.31764	0.658818	−	0.752302i	$-0.271057\pi$
$661$	33.8763	1.31764	0.658818	+	0.752302i	$0.271057\pi$
$662$	6.11371	0.237616
$663$	−3.89370	−0.151219
$664$	−170.966	−6.63476
$665$	−8.94605	−0.346913
$666$	36.1336	1.40015
$667$	−6.54290	−0.253342
$668$	116.099	4.49200
$669$	−11.7469	−0.454163
$670$	64.1029	2.47651
$671$	11.6936	0.451425
$672$	7.22923	0.278874
$673$	−1.83556	−0.0707557	−0.0353779	−	0.999374i	$-0.511263\pi$
$673$	−1.83556	−0.0707557	−0.0353779	+	0.999374i	$0.511263\pi$
$674$	44.7776	1.72477
$675$	−30.3634	−1.16869
$676$	46.7272	1.79720
$677$	−22.6730	−0.871393	−0.435697	−	0.900094i	$-0.643498\pi$
$677$	−22.6730	−0.871393	−0.435697	+	0.900094i	$0.643498\pi$
$678$	29.2970	1.12514
$679$	−2.29130	−0.0879319
$680$	−34.1959	−1.31135
$681$	7.13245	0.273316
$682$	8.07428	0.309180
$683$	20.3405	0.778306	0.389153	−	0.921173i	$-0.372768\pi$
$683$	20.3405	0.778306	0.389153	+	0.921173i	$0.372768\pi$
$684$	−96.9118	−3.70551
$685$	42.4970	1.62373
$686$	−13.2032	−0.504102
$687$	16.4359	0.627069
$688$	16.2310	0.618802
$689$	64.7505	2.46680
$690$	−11.1091	−0.422914
$691$	13.6126	0.517847	0.258924	−	0.965898i	$-0.416632\pi$
$691$	13.6126	0.517847	0.258924	+	0.965898i	$0.416632\pi$
$692$	−85.2862	−3.24209
$693$	−0.789469	−0.0299894
$694$	6.64738	0.252331
$695$	33.4135	1.26744
$696$	39.4797	1.49648
$697$	−10.2164	−0.386974
$698$	42.0419	1.59131
$699$	−3.45039	−0.130506
$700$	−13.1682	−0.497712
$701$	5.85699	0.221216	0.110608	−	0.993864i	$-0.464720\pi$
$701$	5.85699	0.221216	0.110608	+	0.993864i	$0.464720\pi$
$702$	−56.8053	−2.14398
$703$	43.1982	1.62925
$704$	−36.1260	−1.36155
$705$	30.6502	1.15435
$706$	42.1776	1.58738
$707$	1.44458	0.0543290
$708$	18.4126	0.691989
$709$	38.8223	1.45800	0.729001	−	0.684512i	$-0.239985\pi$
$709$	38.8223	1.45800	0.729001	+	0.684512i	$0.239985\pi$
$710$	139.366	5.23031
$711$	29.1459	1.09306
$712$	−24.2991	−0.910647
$713$	4.06979	0.152415
$714$	0.801858	0.0300088
$715$	15.8722	0.593587
$716$	−76.8502	−2.87203
$717$	−4.70901	−0.175861
$718$	−44.7407	−1.66971
$719$	15.6286	0.582849	0.291424	−	0.956594i	$-0.405871\pi$
$719$	15.6286	0.582849	0.291424	+	0.956594i	$0.405871\pi$
$720$	−127.692	−4.75881
$721$	−0.0681414	−0.00253772
$722$	−104.775	−3.89931
$723$	−24.2076	−0.900289
$724$	−20.4931	−0.761619
$725$	−32.0469	−1.19019
$726$	−2.32524	−0.0862977
$727$	37.9239	1.40652	0.703259	−	0.710934i	$-0.251727\pi$
$727$	37.9239	1.40652	0.703259	+	0.710934i	$0.251727\pi$
$728$	−15.8494	−0.587417
$729$	4.16003	0.154075
$730$	24.1933	0.895434
$731$	1.00000	0.0369863
$732$	−55.2806	−2.04323
$733$	29.4419	1.08746	0.543730	−	0.839260i	$-0.317011\pi$
$733$	29.4419	1.08746	0.543730	+	0.839260i	$0.317011\pi$
$734$	−39.2913	−1.45027
$735$	−19.9348	−0.735305
$736$	−34.5714	−1.27432
$737$	6.76294	0.249116
$738$	−64.5105	−2.37466
$739$	33.7747	1.24242	0.621211	−	0.783643i	$-0.286641\pi$
$739$	33.7747	1.24242	0.621211	+	0.783643i	$0.286641\pi$
$740$	110.276	4.05382
$741$	−29.3933	−1.07979
$742$	−13.3345	−0.489526
$743$	−39.0789	−1.43367	−0.716833	−	0.697245i	$-0.754409\pi$
$743$	−39.0789	−1.43367	−0.716833	+	0.697245i	$0.754409\pi$
$744$	−24.5570	−0.900305
$745$	−37.6930	−1.38096
$746$	28.1658	1.03122
$747$	−39.3328	−1.43911
$748$	−5.60771	−0.205038
$749$	5.39821	0.197246
$750$	−14.4586	−0.527953
$751$	41.3124	1.50751	0.753756	−	0.657154i	$-0.228240\pi$
$751$	41.3124	1.50751	0.753756	+	0.657154i	$0.228240\pi$
$752$	171.722	6.26204
$753$	−14.7659	−0.538101
$754$	−59.9549	−2.18343
$755$	−45.6427	−1.66111
$756$	8.62294	0.313613
$757$	−46.9320	−1.70577	−0.852886	−	0.522097i	$-0.825150\pi$
$757$	−46.9320	−1.70577	−0.852886	+	0.522097i	$0.825150\pi$
$758$	8.05790	0.292676
$759$	−1.17202	−0.0425417
$760$	−258.143	−9.36382
$761$	−40.4801	−1.46740	−0.733701	−	0.679472i	$-0.762209\pi$
$761$	−40.4801	−1.46740	−0.733701	+	0.679472i	$0.762209\pi$
$762$	−15.3994	−0.557862
$763$	3.68146	0.133278
$764$	−147.293	−5.32887
$765$	−7.86718	−0.284439
$766$	104.855	3.78855
$767$	−17.9892	−0.649553
$768$	55.1407	1.98972
$769$	11.1299	0.401356	0.200678	−	0.979657i	$-0.435686\pi$
$769$	11.1299	0.401356	0.200678	+	0.979657i	$0.435686\pi$
$770$	−3.26868	−0.117795
$771$	9.70426	0.349490
$772$	98.0175	3.52773
$773$	−41.1186	−1.47893	−0.739466	−	0.673194i	$-0.764922\pi$
$773$	−41.1186	−1.47893	−0.739466	+	0.673194i	$0.764922\pi$
$774$	6.31439	0.226966
$775$	19.9337	0.716040
$776$	−66.1165	−2.37344
$777$	−1.66360	−0.0596815
$778$	−12.6260	−0.452664
$779$	−77.1231	−2.76322
$780$	−75.0349	−2.68668
$781$	14.7033	0.526126
$782$	−3.83462	−0.137126
$783$	20.9853	0.749952
$784$	−111.687	−3.98882
$785$	−19.8744	−0.709349
$786$	−36.5478	−1.30362
$787$	20.1562	0.718491	0.359245	−	0.933243i	$-0.383034\pi$
$787$	20.1562	0.718491	0.359245	+	0.933243i	$0.383034\pi$
$788$	−23.9417	−0.852889
$789$	14.7253	0.524234
$790$	120.674	4.29339
$791$	4.34496	0.154489
$792$	−22.7805	−0.809470
$793$	54.0094	1.91793
$794$	−28.0608	−0.995841
$795$	−40.6139	−1.44043
$796$	74.9405	2.65620
$797$	−25.3990	−0.899679	−0.449839	−	0.893110i	$-0.648519\pi$
$797$	−25.3990	−0.899679	−0.449839	+	0.893110i	$0.648519\pi$
$798$	6.05318	0.214280
$799$	10.5798	0.374288
$800$	−169.330	−5.98670
$801$	−5.59030	−0.197524
$802$	9.11748	0.321949
$803$	2.55243	0.0900732
$804$	−31.9714	−1.12754
$805$	−1.64756	−0.0580687
$806$	37.2929	1.31359
$807$	−5.03295	−0.177168
$808$	41.6841	1.46644
$809$	8.09152	0.284483	0.142241	−	0.989832i	$-0.454569\pi$
$809$	8.09152	0.284483	0.142241	+	0.989832i	$0.454569\pi$
$810$	−29.4675	−1.03538
$811$	35.0889	1.23214	0.616069	−	0.787692i	$-0.288724\pi$
$811$	35.0889	1.23214	0.616069	+	0.787692i	$0.288724\pi$
$812$	9.10104	0.319384
$813$	5.18598	0.181880
$814$	15.7836	0.553215
$815$	20.5033	0.718198
$816$	13.6832	0.479006
$817$	7.54894	0.264104
$818$	59.1198	2.06708
$819$	−3.64634	−0.127414
$820$	−196.879	−6.87531
$821$	−26.4519	−0.923179	−0.461589	−	0.887094i	$-0.652721\pi$
$821$	−26.4519	−0.923179	−0.461589	+	0.887094i	$0.652721\pi$
$822$	−28.7548	−1.00294
$823$	−23.0387	−0.803080	−0.401540	−	0.915841i	$-0.631525\pi$
$823$	−23.0387	−0.803080	−0.401540	+	0.915841i	$0.631525\pi$
$824$	−1.96625	−0.0684977
$825$	−5.74052	−0.199859
$826$	3.70465	0.128901
$827$	45.0672	1.56714	0.783570	−	0.621303i	$-0.213396\pi$
$827$	45.0672	1.56714	0.783570	+	0.621303i	$0.213396\pi$
$828$	−17.8478	−0.620255
$829$	18.9487	0.658116	0.329058	−	0.944310i	$-0.393269\pi$
$829$	18.9487	0.658116	0.329058	+	0.944310i	$0.393269\pi$
$830$	−162.852	−5.65266
$831$	−0.143369	−0.00497342
$832$	−166.856	−5.78470
$833$	−6.88108	−0.238415
$834$	−22.6086	−0.782873
$835$	71.1471	2.46215
$836$	−42.3323	−1.46409
$837$	−13.0532	−0.451183
$838$	82.5206	2.85063
$839$	−10.6298	−0.366981	−0.183490	−	0.983022i	$-0.558740\pi$
$839$	−10.6298	−0.366981	−0.183490	+	0.983022i	$0.558740\pi$
$840$	9.94133	0.343008
$841$	−6.85122	−0.236249
$842$	−78.5488	−2.70697
$843$	2.51351	0.0865697
$844$	97.0855	3.34182
$845$	28.6351	0.985078
$846$	66.8052	2.29681
$847$	−0.344850	−0.0118492
$848$	−227.544	−7.81391
$849$	−10.0167	−0.343773
$850$	−18.7818	−0.644212
$851$	7.95563	0.272715
$852$	−69.5091	−2.38134
$853$	−25.4605	−0.871752	−0.435876	−	0.900007i	$-0.643561\pi$
$853$	−25.4605	−0.871752	−0.435876	+	0.900007i	$0.643561\pi$
$854$	−11.1225	−0.380606
$855$	−59.3889	−2.03106
$856$	155.768	5.32404
$857$	25.4830	0.870484	0.435242	−	0.900314i	$-0.356663\pi$
$857$	25.4830	0.870484	0.435242	+	0.900314i	$0.356663\pi$
$858$	−10.7396	−0.366645
$859$	−1.97954	−0.0675410	−0.0337705	−	0.999430i	$-0.510752\pi$
$859$	−1.97954	−0.0675410	−0.0337705	+	0.999430i	$0.510752\pi$
$860$	19.2708	0.657130
$861$	2.97009	0.101220
$862$	36.9103	1.25717
$863$	−19.0304	−0.647801	−0.323901	−	0.946091i	$-0.604994\pi$
$863$	−19.0304	−0.647801	−0.323901	+	0.946091i	$0.604994\pi$
$864$	110.882	3.77228
$865$	−52.2646	−1.77705
$866$	43.6316	1.48266
$867$	0.843025	0.0286306
$868$	−5.66100	−0.192147
$869$	12.7313	0.431880
$870$	37.6060	1.27496
$871$	31.2362	1.05840
$872$	106.230	3.59742
$873$	−15.2109	−0.514811
$874$	−28.9473	−0.979158
$875$	−2.14432	−0.0724911
$876$	−12.0664	−0.407688
$877$	2.76349	0.0933165	0.0466582	−	0.998911i	$-0.485143\pi$
$877$	2.76349	0.0933165	0.0466582	+	0.998911i	$0.485143\pi$
$878$	18.1580	0.612802
$879$	2.97695	0.100410
$880$	−55.7777	−1.88027
$881$	−3.25101	−0.109529	−0.0547647	−	0.998499i	$-0.517441\pi$
$881$	−3.25101	−0.109529	−0.0547647	+	0.998499i	$0.517441\pi$
$882$	−43.4498	−1.46303
$883$	−32.5658	−1.09592	−0.547962	−	0.836503i	$-0.684596\pi$
$883$	−32.5658	−1.09592	−0.547962	+	0.836503i	$0.684596\pi$
$884$	−25.9005	−0.871129
$885$	11.2835	0.379292
$886$	62.4006	2.09639
$887$	−51.8203	−1.73995	−0.869977	−	0.493092i	$-0.835867\pi$
$887$	−51.8203	−1.73995	−0.869977	+	0.493092i	$0.835867\pi$
$888$	−48.0042	−1.61091
$889$	−2.28385	−0.0765978
$890$	−23.1458	−0.775849
$891$	−3.10887	−0.104151
$892$	−78.1395	−2.61630
$893$	79.8666	2.67263
$894$	25.5043	0.852991
$895$	−47.0949	−1.57421
$896$	17.2112	0.574987
$897$	−5.41325	−0.180743
$898$	−2.69560	−0.0899532
$899$	−13.7769	−0.459485
$900$	−87.4181	−2.91394
$901$	−14.0191	−0.467044
$902$	−28.1790	−0.938258
$903$	−0.290717	−0.00967446
$904$	125.376	4.16994
$905$	−12.5584	−0.417457
$906$	30.8834	1.02603
$907$	−33.5227	−1.11310	−0.556551	−	0.830813i	$-0.687876\pi$
$907$	−33.5227	−1.11310	−0.556551	+	0.830813i	$0.687876\pi$
$908$	47.4443	1.57450
$909$	9.58993	0.318078
$910$	−15.0971	−0.500465
$911$	38.9582	1.29074	0.645371	−	0.763869i	$-0.276703\pi$
$911$	38.9582	1.29074	0.645371	+	0.763869i	$0.276703\pi$
$912$	103.293	3.42038
$913$	−17.1811	−0.568611
$914$	−39.8162	−1.31700
$915$	−33.8767	−1.11993
$916$	109.330	3.61236
$917$	−5.42031	−0.178994
$918$	12.2989	0.405924
$919$	−52.4566	−1.73038	−0.865192	−	0.501441i	$-0.832803\pi$
$919$	−52.4566	−1.73038	−0.865192	+	0.501441i	$0.832803\pi$
$920$	−47.5410	−1.56738
$921$	17.7965	0.586416
$922$	53.2091	1.75235
$923$	67.9107	2.23531
$924$	1.63026	0.0536316
$925$	38.9664	1.28121
$926$	86.7344	2.85027
$927$	−0.452361	−0.0148575
$928$	117.030	3.84169
$929$	−3.42696	−0.112435	−0.0562174	−	0.998419i	$-0.517904\pi$
$929$	−3.42696	−0.112435	−0.0562174	+	0.998419i	$0.517904\pi$
$930$	−23.3915	−0.767038
$931$	−51.9449	−1.70242
$932$	−22.9517	−0.751807
$933$	−5.93719	−0.194375
$934$	53.9420	1.76504
$935$	−3.43649	−0.112385
$936$	−105.217	−3.43913
$937$	−42.3959	−1.38501	−0.692506	−	0.721412i	$-0.743494\pi$
$937$	−42.3959	−1.38501	−0.692506	+	0.721412i	$0.743494\pi$
$938$	−6.43270	−0.210035
$939$	27.4338	0.895268
$940$	203.882	6.64991
$941$	−48.3639	−1.57662	−0.788310	−	0.615279i	$-0.789043\pi$
$941$	−48.3639	−1.57662	−0.788310	+	0.615279i	$0.789043\pi$
$942$	13.4477	0.438149
$943$	−14.2034	−0.462528
$944$	63.2173	2.05755
$945$	5.28426	0.171897
$946$	2.75821	0.0896771
$947$	−22.7676	−0.739848	−0.369924	−	0.929062i	$-0.620616\pi$
$947$	−22.7676	−0.739848	−0.369924	+	0.929062i	$0.620616\pi$
$948$	−60.1864	−1.95476
$949$	11.7890	0.382686
$950$	−141.783	−4.60005
$951$	12.0445	0.390570
$952$	3.43154	0.111217
$953$	57.5917	1.86558	0.932789	−	0.360423i	$-0.117368\pi$
$953$	57.5917	1.86558	0.932789	+	0.360423i	$0.117368\pi$
$954$	−88.5221	−2.86601
$955$	−90.2631	−2.92085
$956$	−31.3239	−1.01309
$957$	3.96748	0.128251
$958$	97.1896	3.14005
$959$	−4.26456	−0.137710
$960$	104.659	3.37784
$961$	−22.4305	−0.723566
$962$	72.9003	2.35040
$963$	35.8364	1.15481
$964$	−161.026	−5.18631
$965$	60.0665	1.93361
$966$	1.11479	0.0358678
$967$	−43.0726	−1.38512	−0.692561	−	0.721359i	$-0.743518\pi$
$967$	−43.0726	−1.38512	−0.692561	+	0.721359i	$0.743518\pi$
$968$	−9.95082	−0.319832
$969$	6.36395	0.204439
$970$	−62.9785	−2.02212
$971$	11.3293	0.363575	0.181787	−	0.983338i	$-0.441812\pi$
$971$	11.3293	0.363575	0.181787	+	0.983338i	$0.441812\pi$
$972$	89.7117	2.87750
$973$	−3.35303	−0.107493
$974$	−82.2400	−2.63514
$975$	−26.5139	−0.849125
$976$	−189.798	−6.07530
$977$	−21.7646	−0.696310	−0.348155	−	0.937437i	$-0.613192\pi$
$977$	−21.7646	−0.696310	−0.348155	+	0.937437i	$0.613192\pi$
$978$	−13.8732	−0.443615
$979$	−2.44192	−0.0780440
$980$	−132.604	−4.23588
$981$	24.4396	0.780297
$982$	−39.2355	−1.25206
$983$	18.1781	0.579792	0.289896	−	0.957058i	$-0.406379\pi$
$983$	18.1781	0.579792	0.289896	+	0.957058i	$0.406379\pi$
$984$	85.7034	2.73212
$985$	−14.6718	−0.467484
$986$	12.9808	0.413393
$987$	−3.07574	−0.0979019
$988$	−195.522	−6.22037
$989$	1.39026	0.0442076
$990$	−21.6993	−0.689650
$991$	44.0954	1.40074	0.700368	−	0.713782i	$-0.253019\pi$
$991$	44.0954	1.40074	0.700368	+	0.713782i	$0.253019\pi$
$992$	−72.7944	−2.31122
$993$	−1.86861	−0.0592985
$994$	−13.9853	−0.443588
$995$	45.9246	1.45591
$996$	81.2225	2.57363
$997$	−48.7887	−1.54515	−0.772577	−	0.634921i	$-0.781032\pi$
$997$	−48.7887	−1.54515	−0.772577	+	0.634921i	$0.781032\pi$
$998$	52.3314	1.65652
$999$	−25.5164	−0.807302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.g.1.2	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.g.1.2	✓	69	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)

\(f(q)\)	\(=\)	\(q-2.75821 q^{2} +0.843025 q^{3} +5.60771 q^{4} +3.43649 q^{5} -2.32524 q^{6} -0.344850 q^{7} -9.95082 q^{8} -2.28931 q^{9} +O(q^{10})\)	\(q-2.75821 q^{2} +0.843025 q^{3} +5.60771 q^{4} +3.43649 q^{5} -2.32524 q^{6} -0.344850 q^{7} -9.95082 q^{8} -2.28931 q^{9} -9.47854 q^{10} -1.00000 q^{11} +4.72744 q^{12} -4.61873 q^{13} +0.951168 q^{14} +2.89704 q^{15} +16.2310 q^{16} +1.00000 q^{17} +6.31439 q^{18} +7.54894 q^{19} +19.2708 q^{20} -0.290717 q^{21} +2.75821 q^{22} +1.39026 q^{23} -8.38879 q^{24} +6.80944 q^{25} +12.7394 q^{26} -4.45902 q^{27} -1.93382 q^{28} -4.70625 q^{29} -7.99065 q^{30} +2.92736 q^{31} -24.8669 q^{32} -0.843025 q^{33} -2.75821 q^{34} -1.18507 q^{35} -12.8378 q^{36} +5.72242 q^{37} -20.8216 q^{38} -3.89370 q^{39} -34.1959 q^{40} -10.2164 q^{41} +0.801858 q^{42} +1.00000 q^{43} -5.60771 q^{44} -7.86718 q^{45} -3.83462 q^{46} +10.5798 q^{47} +13.6832 q^{48} -6.88108 q^{49} -18.7818 q^{50} +0.843025 q^{51} -25.9005 q^{52} -14.0191 q^{53} +12.2989 q^{54} -3.43649 q^{55} +3.43154 q^{56} +6.36395 q^{57} +12.9808 q^{58} +3.89484 q^{59} +16.2458 q^{60} -11.6936 q^{61} -8.07428 q^{62} +0.789469 q^{63} +36.1260 q^{64} -15.8722 q^{65} +2.32524 q^{66} -6.76294 q^{67} +5.60771 q^{68} +1.17202 q^{69} +3.26868 q^{70} -14.7033 q^{71} +22.7805 q^{72} -2.55243 q^{73} -15.7836 q^{74} +5.74052 q^{75} +42.3323 q^{76} +0.344850 q^{77} +10.7396 q^{78} -12.7313 q^{79} +55.7777 q^{80} +3.10887 q^{81} +28.1790 q^{82} +17.1811 q^{83} -1.63026 q^{84} +3.43649 q^{85} -2.75821 q^{86} -3.96748 q^{87} +9.95082 q^{88} +2.44192 q^{89} +21.6993 q^{90} +1.59277 q^{91} +7.79616 q^{92} +2.46784 q^{93} -29.1814 q^{94} +25.9418 q^{95} -20.9634 q^{96} +6.64432 q^{97} +18.9794 q^{98} +2.28931 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * q^99

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