LMFDB - Embedded newform 8041.2.a.h.1.22

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:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
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)

$f(q)$	$=$	$q-1.45587 q^{2} -3.18713 q^{3} +0.119559 q^{4} -3.80085 q^{5} +4.64006 q^{6} -2.73964 q^{7} +2.73768 q^{8} +7.15783 q^{9} +O(q^{10})$	\(q-1.45587 q^{2} -3.18713 q^{3} +0.119559 q^{4} -3.80085 q^{5} +4.64006 q^{6} -2.73964 q^{7} +2.73768 q^{8} +7.15783 q^{9} +5.53355 q^{10} -1.00000 q^{11} -0.381049 q^{12} +5.32422 q^{13} +3.98857 q^{14} +12.1138 q^{15} -4.22482 q^{16} -1.00000 q^{17} -10.4209 q^{18} -0.742248 q^{19} -0.454425 q^{20} +8.73161 q^{21} +1.45587 q^{22} -5.03741 q^{23} -8.72535 q^{24} +9.44648 q^{25} -7.75137 q^{26} -13.2516 q^{27} -0.327548 q^{28} -9.65491 q^{29} -17.6362 q^{30} -2.93625 q^{31} +0.675437 q^{32} +3.18713 q^{33} +1.45587 q^{34} +10.4130 q^{35} +0.855780 q^{36} +5.61632 q^{37} +1.08062 q^{38} -16.9690 q^{39} -10.4055 q^{40} +7.72123 q^{41} -12.7121 q^{42} -1.00000 q^{43} -0.119559 q^{44} -27.2059 q^{45} +7.33381 q^{46} -9.21906 q^{47} +13.4651 q^{48} +0.505643 q^{49} -13.7529 q^{50} +3.18713 q^{51} +0.636556 q^{52} +0.331985 q^{53} +19.2926 q^{54} +3.80085 q^{55} -7.50026 q^{56} +2.36564 q^{57} +14.0563 q^{58} -1.83373 q^{59} +1.44831 q^{60} +5.93229 q^{61} +4.27480 q^{62} -19.6099 q^{63} +7.46630 q^{64} -20.2366 q^{65} -4.64006 q^{66} +2.97144 q^{67} -0.119559 q^{68} +16.0549 q^{69} -15.1599 q^{70} -13.4608 q^{71} +19.5958 q^{72} -12.0774 q^{73} -8.17663 q^{74} -30.1072 q^{75} -0.0887421 q^{76} +2.73964 q^{77} +24.7047 q^{78} +1.64030 q^{79} +16.0579 q^{80} +20.7610 q^{81} -11.2411 q^{82} -14.7461 q^{83} +1.04394 q^{84} +3.80085 q^{85} +1.45587 q^{86} +30.7715 q^{87} -2.73768 q^{88} -11.3508 q^{89} +39.6082 q^{90} -14.5865 q^{91} -0.602266 q^{92} +9.35822 q^{93} +13.4218 q^{94} +2.82117 q^{95} -2.15271 q^{96} +8.05817 q^{97} -0.736151 q^{98} -7.15783 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) $ 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * 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 $

$2$	−1.45587	−1.02946	−0.514728	−	0.857354i	$-0.672107\pi$
$2$	−1.45587	−1.02946	−0.514728	+	0.857354i	$0.672107\pi$
$3$	−3.18713	−1.84009	−0.920047	−	0.391809i	$-0.871849\pi$
$3$	−3.18713	−1.84009	−0.920047	+	0.391809i	$0.871849\pi$
$4$	0.119559	0.0597793
$5$	−3.80085	−1.69979	−0.849897	−	0.526950i	$-0.823336\pi$
$5$	−3.80085	−1.69979	−0.849897	+	0.526950i	$0.823336\pi$
$6$	4.64006	1.89429
$7$	−2.73964	−1.03549	−0.517744	−	0.855536i	$-0.673228\pi$
$7$	−2.73964	−1.03549	−0.517744	+	0.855536i	$0.673228\pi$
$8$	2.73768	0.967916
$9$	7.15783	2.38594
$10$	5.53355	1.74986
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.381049	−0.109999
$13$	5.32422	1.47667	0.738336	−	0.674433i	$-0.235612\pi$
$13$	5.32422	1.47667	0.738336	+	0.674433i	$0.235612\pi$
$14$	3.98857	1.06599
$15$	12.1138	3.12778
$16$	−4.22482	−1.05621
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−10.4209	−2.45622
$19$	−0.742248	−0.170283	−0.0851417	−	0.996369i	$-0.527134\pi$
$19$	−0.742248	−0.170283	−0.0851417	+	0.996369i	$0.527134\pi$
$20$	−0.454425	−0.101612
$21$	8.73161	1.90539
$22$	1.45587	0.310393
$23$	−5.03741	−1.05037	−0.525186	−	0.850987i	$-0.676004\pi$
$23$	−5.03741	−1.05037	−0.525186	+	0.850987i	$0.676004\pi$
$24$	−8.72535	−1.78105
$25$	9.44648	1.88930
$26$	−7.75137	−1.52017
$27$	−13.2516	−2.55026
$28$	−0.327548	−0.0619007
$29$	−9.65491	−1.79287	−0.896436	−	0.443174i	$-0.853852\pi$
$29$	−9.65491	−1.79287	−0.896436	+	0.443174i	$0.853852\pi$
$30$	−17.6362	−3.21991
$31$	−2.93625	−0.527366	−0.263683	−	0.964609i	$-0.584937\pi$
$31$	−2.93625	−0.527366	−0.263683	+	0.964609i	$0.584937\pi$
$32$	0.675437	0.119401
$33$	3.18713	0.554809
$34$	1.45587	0.249680
$35$	10.4130	1.76011
$36$	0.855780	0.142630
$37$	5.61632	0.923317	0.461658	−	0.887058i	$-0.347255\pi$
$37$	5.61632	0.923317	0.461658	+	0.887058i	$0.347255\pi$
$38$	1.08062	0.175299
$39$	−16.9690	−2.71721
$40$	−10.4055	−1.64526
$41$	7.72123	1.20585	0.602927	−	0.797796i	$-0.294001\pi$
$41$	7.72123	1.20585	0.602927	+	0.797796i	$0.294001\pi$
$42$	−12.7121	−1.96152
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−0.119559	−0.0180241
$45$	−27.2059	−4.05561
$46$	7.33381	1.08131
$47$	−9.21906	−1.34474	−0.672369	−	0.740216i	$-0.734723\pi$
$47$	−9.21906	−1.34474	−0.672369	+	0.740216i	$0.734723\pi$
$48$	13.4651	1.94352
$49$	0.505643	0.0722347
$50$	−13.7529	−1.94495
$51$	3.18713	0.446288
$52$	0.636556	0.0882745
$53$	0.331985	0.0456016	0.0228008	−	0.999740i	$-0.492742\pi$
$53$	0.331985	0.0456016	0.0228008	+	0.999740i	$0.492742\pi$
$54$	19.2926	2.62538
$55$	3.80085	0.512507
$56$	−7.50026	−1.00226
$57$	2.36564	0.313337
$58$	14.0563	1.84568
$59$	−1.83373	−0.238731	−0.119365	−	0.992850i	$-0.538086\pi$
$59$	−1.83373	−0.238731	−0.119365	+	0.992850i	$0.538086\pi$
$60$	1.44831	0.186976
$61$	5.93229	0.759552	0.379776	−	0.925078i	$-0.376001\pi$
$61$	5.93229	0.759552	0.379776	+	0.925078i	$0.376001\pi$
$62$	4.27480	0.542900
$63$	−19.6099	−2.47061
$64$	7.46630	0.933287
$65$	−20.2366	−2.51004
$66$	−4.64006	−0.571151
$67$	2.97144	0.363019	0.181510	−	0.983389i	$-0.441902\pi$
$67$	2.97144	0.363019	0.181510	+	0.983389i	$0.441902\pi$
$68$	−0.119559	−0.0144986
$69$	16.0549	1.93278
$70$	−15.1599	−1.81196
$71$	−13.4608	−1.59750	−0.798750	−	0.601663i	$-0.794505\pi$
$71$	−13.4608	−1.59750	−0.798750	+	0.601663i	$0.794505\pi$
$72$	19.5958	2.30939
$73$	−12.0774	−1.41355	−0.706774	−	0.707439i	$-0.749850\pi$
$73$	−12.0774	−1.41355	−0.706774	+	0.707439i	$0.749850\pi$
$74$	−8.17663	−0.950514
$75$	−30.1072	−3.47648
$76$	−0.0887421	−0.0101794
$77$	2.73964	0.312211
$78$	24.7047	2.79725
$79$	1.64030	0.184548	0.0922739	−	0.995734i	$-0.470586\pi$
$79$	1.64030	0.184548	0.0922739	+	0.995734i	$0.470586\pi$
$80$	16.0579	1.79533
$81$	20.7610	2.30678
$82$	−11.2411	−1.24137
$83$	−14.7461	−1.61859	−0.809295	−	0.587402i	$-0.800151\pi$
$83$	−14.7461	−1.61859	−0.809295	+	0.587402i	$0.800151\pi$
$84$	1.04394	0.113903
$85$	3.80085	0.412260
$86$	1.45587	0.156991
$87$	30.7715	3.29905
$88$	−2.73768	−0.291838
$89$	−11.3508	−1.20318	−0.601591	−	0.798804i	$-0.705466\pi$
$89$	−11.3508	−1.20318	−0.601591	+	0.798804i	$0.705466\pi$
$90$	39.6082	4.17507
$91$	−14.5865	−1.52908
$92$	−0.602266	−0.0627905
$93$	9.35822	0.970402
$94$	13.4218	1.38435
$95$	2.82117	0.289446
$96$	−2.15271	−0.219710
$97$	8.05817	0.818183	0.409091	−	0.912493i	$-0.365846\pi$
$97$	8.05817	0.818183	0.409091	+	0.912493i	$0.365846\pi$
$98$	−0.736151	−0.0743625
$99$	−7.15783	−0.719389
$100$	1.12941	0.112941
$101$	11.7133	1.16551	0.582757	−	0.812646i	$-0.301974\pi$
$101$	11.7133	1.16551	0.582757	+	0.812646i	$0.301974\pi$
$102$	−4.64006	−0.459434
$103$	1.47180	0.145021	0.0725104	−	0.997368i	$-0.476899\pi$
$103$	1.47180	0.145021	0.0725104	+	0.997368i	$0.476899\pi$
$104$	14.5760	1.42929
$105$	−33.1876	−3.23878
$106$	−0.483327	−0.0469449
$107$	2.21500	0.214132	0.107066	−	0.994252i	$-0.465854\pi$
$107$	2.21500	0.214132	0.107066	+	0.994252i	$0.465854\pi$
$108$	−1.58434	−0.152453
$109$	−14.9858	−1.43538	−0.717692	−	0.696361i	$-0.754801\pi$
$109$	−14.9858	−1.43538	−0.717692	+	0.696361i	$0.754801\pi$
$110$	−5.53355	−0.527603
$111$	−17.9000	−1.69899
$112$	11.5745	1.09369
$113$	19.6651	1.84994	0.924971	−	0.380038i	$-0.124089\pi$
$113$	19.6651	1.84994	0.924971	+	0.380038i	$0.124089\pi$
$114$	−3.44407	−0.322567
$115$	19.1464	1.78542
$116$	−1.15433	−0.107177
$117$	38.1098	3.52326
$118$	2.66967	0.245763
$119$	2.73964	0.251143
$120$	33.1638	3.02742
$121$	1.00000	0.0909091
$122$	−8.63665	−0.781926
$123$	−24.6086	−2.21888
$124$	−0.351054	−0.0315256
$125$	−16.9004	−1.51162
$126$	28.5495	2.54339
$127$	−0.839930	−0.0745317	−0.0372659	−	0.999305i	$-0.511865\pi$
$127$	−0.839930	−0.0745317	−0.0372659	+	0.999305i	$0.511865\pi$
$128$	−12.2208	−1.08018
$129$	3.18713	0.280612
$130$	29.4618	2.58397
$131$	7.03483	0.614636	0.307318	−	0.951607i	$-0.400568\pi$
$131$	7.03483	0.614636	0.307318	+	0.951607i	$0.400568\pi$
$132$	0.381049	0.0331661
$133$	2.03349	0.176326
$134$	−4.32603	−0.373712
$135$	50.3672	4.33492
$136$	−2.73768	−0.234754
$137$	19.5258	1.66821	0.834103	−	0.551609i	$-0.185986\pi$
$137$	19.5258	1.66821	0.834103	+	0.551609i	$0.185986\pi$
$138$	−23.3739	−1.98971
$139$	19.4740	1.65177	0.825883	−	0.563842i	$-0.190677\pi$
$139$	19.4740	1.65177	0.825883	+	0.563842i	$0.190677\pi$
$140$	1.24496	0.105218
$141$	29.3824	2.47444
$142$	19.5971	1.64456
$143$	−5.32422	−0.445233
$144$	−30.2406	−2.52005
$145$	36.6969	3.04751
$146$	17.5831	1.45519
$147$	−1.61155	−0.132919
$148$	0.671479	0.0551952
$149$	−23.9948	−1.96573	−0.982864	−	0.184331i	$-0.940988\pi$
$149$	−23.9948	−1.96573	−0.982864	+	0.184331i	$0.940988\pi$
$150$	43.8322	3.57888
$151$	11.7867	0.959189	0.479594	−	0.877490i	$-0.340784\pi$
$151$	11.7867	0.959189	0.479594	+	0.877490i	$0.340784\pi$
$152$	−2.03204	−0.164820
$153$	−7.15783	−0.578676
$154$	−3.98857	−0.321408
$155$	11.1602	0.896413
$156$	−2.02879	−0.162433
$157$	1.37314	0.109588	0.0547941	−	0.998498i	$-0.482550\pi$
$157$	1.37314	0.109588	0.0547941	+	0.998498i	$0.482550\pi$
$158$	−2.38806	−0.189984
$159$	−1.05808	−0.0839113
$160$	−2.56724	−0.202958
$161$	13.8007	1.08765
$162$	−30.2254	−2.37473
$163$	−14.4262	−1.12994	−0.564972	−	0.825110i	$-0.691113\pi$
$163$	−14.4262	−1.12994	−0.564972	+	0.825110i	$0.691113\pi$
$164$	0.923140	0.0720851
$165$	−12.1138	−0.943060
$166$	21.4684	1.66627
$167$	13.1587	1.01825	0.509127	−	0.860691i	$-0.329968\pi$
$167$	13.1587	1.01825	0.509127	+	0.860691i	$0.329968\pi$
$168$	23.9043	1.84426
$169$	15.3473	1.18056
$170$	−5.53355	−0.424404
$171$	−5.31288	−0.406286
$172$	−0.119559	−0.00911626
$173$	18.2485	1.38741	0.693705	−	0.720259i	$-0.255977\pi$
$173$	18.2485	1.38741	0.693705	+	0.720259i	$0.255977\pi$
$174$	−44.7993	−3.39623
$175$	−25.8800	−1.95634
$176$	4.22482	0.318458
$177$	5.84433	0.439287
$178$	16.5253	1.23862
$179$	1.34624	0.100623	0.0503114	−	0.998734i	$-0.483979\pi$
$179$	1.34624	0.100623	0.0503114	+	0.998734i	$0.483979\pi$
$180$	−3.25269	−0.242441
$181$	9.16564	0.681277	0.340638	−	0.940194i	$-0.389357\pi$
$181$	9.16564	0.681277	0.340638	+	0.940194i	$0.389357\pi$
$182$	21.2360	1.57412
$183$	−18.9070	−1.39765
$184$	−13.7908	−1.01667
$185$	−21.3468	−1.56945
$186$	−13.6244	−0.998986
$187$	1.00000	0.0731272
$188$	−1.10222	−0.0803875
$189$	36.3045	2.64077
$190$	−4.10726	−0.297972
$191$	−11.1745	−0.808556	−0.404278	−	0.914636i	$-0.632477\pi$
$191$	−11.1745	−0.808556	−0.404278	+	0.914636i	$0.632477\pi$
$192$	−23.7961	−1.71734
$193$	−15.1226	−1.08855	−0.544273	−	0.838908i	$-0.683195\pi$
$193$	−15.1226	−1.08855	−0.544273	+	0.838908i	$0.683195\pi$
$194$	−11.7316	−0.842283
$195$	64.4967	4.61870
$196$	0.0604540	0.00431814
$197$	21.2496	1.51397	0.756987	−	0.653430i	$-0.226670\pi$
$197$	21.2496	1.51397	0.756987	+	0.653430i	$0.226670\pi$
$198$	10.4209	0.740579
$199$	5.78739	0.410257	0.205129	−	0.978735i	$-0.434239\pi$
$199$	5.78739	0.410257	0.205129	+	0.978735i	$0.434239\pi$
$200$	25.8614	1.82868
$201$	−9.47038	−0.667989
$202$	−17.0530	−1.19985
$203$	26.4510	1.85650
$204$	0.381049	0.0266788
$205$	−29.3473	−2.04970
$206$	−2.14275	−0.149292
$207$	−36.0569	−2.50613
$208$	−22.4939	−1.55967
$209$	0.742248	0.0513424
$210$	48.3168	3.33418
$211$	−12.9324	−0.890303	−0.445151	−	0.895455i	$-0.646850\pi$
$211$	−12.9324	−0.890303	−0.445151	+	0.895455i	$0.646850\pi$
$212$	0.0396917	0.00272603
$213$	42.9013	2.93955
$214$	−3.22475	−0.220439
$215$	3.80085	0.259216
$216$	−36.2785	−2.46844
$217$	8.04427	0.546081
$218$	21.8175	1.47766
$219$	38.4922	2.60106
$220$	0.454425	0.0306373
$221$	−5.32422	−0.358146
$222$	26.0600	1.74903
$223$	18.4926	1.23836	0.619180	−	0.785249i	$-0.287465\pi$
$223$	18.4926	1.23836	0.619180	+	0.785249i	$0.287465\pi$
$224$	−1.85046	−0.123639
$225$	67.6163	4.50775
$226$	−28.6299	−1.90443
$227$	−2.81832	−0.187058	−0.0935291	−	0.995617i	$-0.529815\pi$
$227$	−2.81832	−0.187058	−0.0935291	+	0.995617i	$0.529815\pi$
$228$	0.282833	0.0187311
$229$	19.7065	1.30224	0.651122	−	0.758973i	$-0.274299\pi$
$229$	19.7065	1.30224	0.651122	+	0.758973i	$0.274299\pi$
$230$	−27.8747	−1.83801
$231$	−8.73161	−0.574498
$232$	−26.4320	−1.73535
$233$	3.81017	0.249613	0.124806	−	0.992181i	$-0.460169\pi$
$233$	3.81017	0.249613	0.124806	+	0.992181i	$0.460169\pi$
$234$	−55.4830	−3.62704
$235$	35.0403	2.28578
$236$	−0.219238	−0.0142712
$237$	−5.22784	−0.339585
$238$	−3.98857	−0.258540
$239$	−2.01915	−0.130608	−0.0653041	−	0.997865i	$-0.520802\pi$
$239$	−2.01915	−0.130608	−0.0653041	+	0.997865i	$0.520802\pi$
$240$	−51.1788	−3.30358
$241$	−30.5760	−1.96957	−0.984786	−	0.173774i	$-0.944404\pi$
$241$	−30.5760	−1.96957	−0.984786	+	0.173774i	$0.944404\pi$
$242$	−1.45587	−0.0935869
$243$	−26.4135	−1.69443
$244$	0.709257	0.0454055
$245$	−1.92188	−0.122784
$246$	35.8270	2.28424
$247$	−3.95189	−0.251453
$248$	−8.03850	−0.510446
$249$	46.9977	2.97836
$250$	24.6048	1.55615
$251$	−24.1619	−1.52508	−0.762542	−	0.646939i	$-0.776049\pi$
$251$	−24.1619	−1.52508	−0.762542	+	0.646939i	$0.776049\pi$
$252$	−2.34453	−0.147692
$253$	5.03741	0.316699
$254$	1.22283	0.0767271
$255$	−12.1138	−0.758597
$256$	2.85936	0.178710
$257$	2.47120	0.154149	0.0770745	−	0.997025i	$-0.475442\pi$
$257$	2.47120	0.154149	0.0770745	+	0.997025i	$0.475442\pi$
$258$	−4.64006	−0.288877
$259$	−15.3867	−0.956083
$260$	−2.41946	−0.150048
$261$	−69.1082	−4.27769
$262$	−10.2418	−0.632741
$263$	25.9101	1.59769	0.798844	−	0.601539i	$-0.205445\pi$
$263$	25.9101	1.59769	0.798844	+	0.601539i	$0.205445\pi$
$264$	8.72535	0.537008
$265$	−1.26183	−0.0775133
$266$	−2.96050	−0.181520
$267$	36.1765	2.21397
$268$	0.355261	0.0217010
$269$	−0.405353	−0.0247148	−0.0123574	−	0.999924i	$-0.503934\pi$
$269$	−0.405353	−0.0247148	−0.0123574	+	0.999924i	$0.503934\pi$
$270$	−73.3282	−4.46261
$271$	−1.93206	−0.117364	−0.0586820	−	0.998277i	$-0.518690\pi$
$271$	−1.93206	−0.117364	−0.0586820	+	0.998277i	$0.518690\pi$
$272$	4.22482	0.256168
$273$	46.4890	2.81364
$274$	−28.4271	−1.71734
$275$	−9.44648	−0.569644
$276$	1.91950	0.115540
$277$	−19.8076	−1.19012	−0.595062	−	0.803680i	$-0.702873\pi$
$277$	−19.8076	−1.19012	−0.595062	+	0.803680i	$0.702873\pi$
$278$	−28.3517	−1.70042
$279$	−21.0172	−1.25826
$280$	28.5074	1.70364
$281$	17.3541	1.03526	0.517628	−	0.855606i	$-0.326815\pi$
$281$	17.3541	1.03526	0.517628	+	0.855606i	$0.326815\pi$
$282$	−42.7769	−2.54733
$283$	11.3121	0.672434	0.336217	−	0.941785i	$-0.390852\pi$
$283$	11.3121	0.672434	0.336217	+	0.941785i	$0.390852\pi$
$284$	−1.60935	−0.0954974
$285$	−8.99146	−0.532608
$286$	7.75137	0.458348
$287$	−21.1534	−1.24865
$288$	4.83466	0.284885
$289$	1.00000	0.0588235
$290$	−53.4259	−3.13728
$291$	−25.6825	−1.50553
$292$	−1.44395	−0.0845010
$293$	−33.0419	−1.93033	−0.965163	−	0.261648i	$-0.915734\pi$
$293$	−33.0419	−1.93033	−0.965163	+	0.261648i	$0.915734\pi$
$294$	2.34621	0.136834
$295$	6.96972	0.405793
$296$	15.3757	0.893693
$297$	13.2516	0.768933
$298$	34.9333	2.02363
$299$	−26.8203	−1.55106
$300$	−3.59958	−0.207822
$301$	2.73964	0.157910
$302$	−17.1599	−0.987442
$303$	−37.3318	−2.14466
$304$	3.13587	0.179854
$305$	−22.5478	−1.29108
$306$	10.4209	0.595722
$307$	12.3521	0.704974	0.352487	−	0.935817i	$-0.385336\pi$
$307$	12.3521	0.704974	0.352487	+	0.935817i	$0.385336\pi$
$308$	0.327548	0.0186638
$309$	−4.69082	−0.266852
$310$	−16.2479	−0.922817
$311$	−18.6634	−1.05830	−0.529151	−	0.848527i	$-0.677490\pi$
$311$	−18.6634	−1.05830	−0.529151	+	0.848527i	$0.677490\pi$
$312$	−46.4557	−2.63003
$313$	−10.9301	−0.617808	−0.308904	−	0.951093i	$-0.599962\pi$
$313$	−10.9301	−0.617808	−0.308904	+	0.951093i	$0.599962\pi$
$314$	−1.99911	−0.112816
$315$	74.5343	4.19953
$316$	0.196112	0.0110321
$317$	30.3804	1.70633	0.853167	−	0.521637i	$-0.174679\pi$
$317$	30.3804	1.70633	0.853167	+	0.521637i	$0.174679\pi$
$318$	1.54043	0.0863829
$319$	9.65491	0.540571
$320$	−28.3783	−1.58640
$321$	−7.05950	−0.394023
$322$	−20.0920	−1.11969
$323$	0.742248	0.0412998
$324$	2.48216	0.137898
$325$	50.2951	2.78987
$326$	21.0026	1.16323
$327$	47.7619	2.64124
$328$	21.1383	1.16717
$329$	25.2569	1.39246
$330$	17.6362	0.970839
$331$	−8.52907	−0.468800	−0.234400	−	0.972140i	$-0.575313\pi$
$331$	−8.52907	−0.468800	−0.234400	+	0.972140i	$0.575313\pi$
$332$	−1.76302	−0.0967582
$333$	40.2006	2.20298
$334$	−19.1574	−1.04825
$335$	−11.2940	−0.617057
$336$	−36.8895	−2.01249
$337$	12.2358	0.666525	0.333262	−	0.942834i	$-0.391851\pi$
$337$	12.2358	0.666525	0.333262	+	0.942834i	$0.391851\pi$
$338$	−22.3437	−1.21534
$339$	−62.6755	−3.40406
$340$	0.454425	0.0246446
$341$	2.93625	0.159007
$342$	7.73487	0.418254
$343$	17.7922	0.960689
$344$	−2.73768	−0.147606
$345$	−61.0223	−3.28533
$346$	−26.5675	−1.42828
$347$	23.5883	1.26629	0.633143	−	0.774035i	$-0.281765\pi$
$347$	23.5883	1.26629	0.633143	+	0.774035i	$0.281765\pi$
$348$	3.67900	0.197215
$349$	15.9516	0.853868	0.426934	−	0.904283i	$-0.359594\pi$
$349$	15.9516	0.853868	0.426934	+	0.904283i	$0.359594\pi$
$350$	37.6779	2.01397
$351$	−70.5542	−3.76590
$352$	−0.675437	−0.0360009
$353$	−26.4245	−1.40643	−0.703216	−	0.710976i	$-0.748253\pi$
$353$	−26.4245	−1.40643	−0.703216	+	0.710976i	$0.748253\pi$
$354$	−8.50859	−0.452226
$355$	51.1624	2.71542
$356$	−1.35709	−0.0719254
$357$	−8.73161	−0.462126
$358$	−1.95995	−0.103587
$359$	−3.80192	−0.200658	−0.100329	−	0.994954i	$-0.531990\pi$
$359$	−3.80192	−0.200658	−0.100329	+	0.994954i	$0.531990\pi$
$360$	−74.4809	−3.92549
$361$	−18.4491	−0.971004
$362$	−13.3440	−0.701344
$363$	−3.18713	−0.167281
$364$	−1.74394	−0.0914071
$365$	45.9043	2.40274
$366$	27.5262	1.43882
$367$	1.90783	0.0995880	0.0497940	−	0.998760i	$-0.484144\pi$
$367$	1.90783	0.0995880	0.0497940	+	0.998760i	$0.484144\pi$
$368$	21.2822	1.10941
$369$	55.2673	2.87710
$370$	31.0782	1.61568
$371$	−0.909520	−0.0472199
$372$	1.11886	0.0580100
$373$	2.50545	0.129728	0.0648638	−	0.997894i	$-0.479339\pi$
$373$	2.50545	0.129728	0.0648638	+	0.997894i	$0.479339\pi$
$374$	−1.45587	−0.0752813
$375$	53.8639	2.78152
$376$	−25.2388	−1.30159
$377$	−51.4048	−2.64748
$378$	−52.8547	−2.71855
$379$	−0.991745	−0.0509425	−0.0254713	−	0.999676i	$-0.508109\pi$
$379$	−0.991745	−0.0509425	−0.0254713	+	0.999676i	$0.508109\pi$
$380$	0.337296	0.0173029
$381$	2.67697	0.137145
$382$	16.2686	0.832372
$383$	15.0920	0.771167	0.385583	−	0.922673i	$-0.374000\pi$
$383$	15.0920	0.771167	0.385583	+	0.922673i	$0.374000\pi$
$384$	38.9494	1.98763
$385$	−10.4130	−0.530695
$386$	22.0165	1.12061
$387$	−7.15783	−0.363853
$388$	0.963423	0.0489104
$389$	17.0420	0.864064	0.432032	−	0.901858i	$-0.357797\pi$
$389$	17.0420	0.864064	0.432032	+	0.901858i	$0.357797\pi$
$390$	−93.8988	−4.75475
$391$	5.03741	0.254753
$392$	1.38429	0.0699171
$393$	−22.4210	−1.13099
$394$	−30.9367	−1.55857
$395$	−6.23452	−0.313693
$396$	−0.855780	−0.0430046
$397$	8.53604	0.428411	0.214206	−	0.976789i	$-0.431284\pi$
$397$	8.53604	0.428411	0.214206	+	0.976789i	$0.431284\pi$
$398$	−8.42569	−0.422342
$399$	−6.48102	−0.324457
$400$	−39.9097	−1.99549
$401$	−24.7775	−1.23733	−0.618666	−	0.785654i	$-0.712326\pi$
$401$	−24.7775	−1.23733	−0.618666	+	0.785654i	$0.712326\pi$
$402$	13.7876	0.687665
$403$	−15.6332	−0.778746
$404$	1.40042	0.0696737
$405$	−78.9096	−3.92105
$406$	−38.5092	−1.91118
$407$	−5.61632	−0.278390
$408$	8.72535	0.431969
$409$	26.0376	1.28748	0.643739	−	0.765246i	$-0.277382\pi$
$409$	26.0376	1.28748	0.643739	+	0.765246i	$0.277382\pi$
$410$	42.7258	2.11008
$411$	−62.2315	−3.06965
$412$	0.175966	0.00866924
$413$	5.02375	0.247203
$414$	52.4942	2.57995
$415$	56.0476	2.75127
$416$	3.59617	0.176317
$417$	−62.0664	−3.03940
$418$	−1.08062	−0.0528547
$419$	2.94733	0.143986	0.0719932	−	0.997405i	$-0.477064\pi$
$419$	2.94733	0.143986	0.0719932	+	0.997405i	$0.477064\pi$
$420$	−3.96786	−0.193612
$421$	32.5890	1.58829	0.794145	−	0.607728i	$-0.207919\pi$
$421$	32.5890	1.58829	0.794145	+	0.607728i	$0.207919\pi$
$422$	18.8279	0.916527
$423$	−65.9884	−3.20847
$424$	0.908868	0.0441385
$425$	−9.44648	−0.458222
$426$	−62.4587	−3.02614
$427$	−16.2524	−0.786507
$428$	0.264822	0.0128007
$429$	16.9690	0.819271
$430$	−5.53355	−0.266851
$431$	−22.2600	−1.07222	−0.536112	−	0.844147i	$-0.680108\pi$
$431$	−22.2600	−1.07222	−0.536112	+	0.844147i	$0.680108\pi$
$432$	55.9855	2.69360
$433$	12.4358	0.597627	0.298814	−	0.954312i	$-0.403409\pi$
$433$	12.4358	0.597627	0.298814	+	0.954312i	$0.403409\pi$
$434$	−11.7114	−0.562166
$435$	−116.958	−5.60770
$436$	−1.79169	−0.0858063
$437$	3.73901	0.178861
$438$	−56.0397	−2.67768
$439$	13.6760	0.652720	0.326360	−	0.945246i	$-0.394178\pi$
$439$	13.6760	0.652720	0.326360	+	0.945246i	$0.394178\pi$
$440$	10.4055	0.496063
$441$	3.61931	0.172348
$442$	7.75137	0.368695
$443$	4.35774	0.207043	0.103521	−	0.994627i	$-0.466989\pi$
$443$	4.35774	0.207043	0.103521	+	0.994627i	$0.466989\pi$
$444$	−2.14009	−0.101564
$445$	43.1427	2.04516
$446$	−26.9229	−1.27484
$447$	76.4746	3.61712
$448$	−20.4550	−0.966407
$449$	6.37259	0.300741	0.150370	−	0.988630i	$-0.451953\pi$
$449$	6.37259	0.300741	0.150370	+	0.988630i	$0.451953\pi$
$450$	−98.4406	−4.64053
$451$	−7.72123	−0.363579
$452$	2.35114	0.110588
$453$	−37.5658	−1.76500
$454$	4.10310	0.192568
$455$	55.4410	2.59911
$456$	6.47637	0.303284
$457$	−31.5629	−1.47645	−0.738224	−	0.674555i	$-0.764335\pi$
$457$	−31.5629	−1.47645	−0.738224	+	0.674555i	$0.764335\pi$
$458$	−28.6901	−1.34060
$459$	13.2516	0.618530
$460$	2.28912	0.106731
$461$	−19.2561	−0.896848	−0.448424	−	0.893821i	$-0.648014\pi$
$461$	−19.2561	−0.896848	−0.448424	+	0.893821i	$0.648014\pi$
$462$	12.7121	0.591420
$463$	−30.2834	−1.40739	−0.703694	−	0.710503i	$-0.748468\pi$
$463$	−30.2834	−1.40739	−0.703694	+	0.710503i	$0.748468\pi$
$464$	40.7903	1.89364
$465$	−35.5692	−1.64948
$466$	−5.54712	−0.256965
$467$	−23.9861	−1.10994	−0.554971	−	0.831870i	$-0.687271\pi$
$467$	−23.9861	−1.10994	−0.554971	+	0.831870i	$0.687271\pi$
$468$	4.55636	0.210618
$469$	−8.14068	−0.375902
$470$	−51.0141	−2.35311
$471$	−4.37637	−0.201653
$472$	−5.02015	−0.231071
$473$	1.00000	0.0459800
$474$	7.61106	0.349588
$475$	−7.01163	−0.321716
$476$	0.327548	0.0150131
$477$	2.37629	0.108803
$478$	2.93962	0.134455
$479$	28.9750	1.32390	0.661951	−	0.749547i	$-0.269729\pi$
$479$	28.9750	1.32390	0.661951	+	0.749547i	$0.269729\pi$
$480$	8.18213	0.373461
$481$	29.9025	1.36344
$482$	44.5146	2.02759
$483$	−43.9847	−2.00137
$484$	0.119559	0.00543448
$485$	−30.6279	−1.39074
$486$	38.4546	1.74434
$487$	−21.2636	−0.963547	−0.481774	−	0.876296i	$-0.660007\pi$
$487$	−21.2636	−0.963547	−0.481774	+	0.876296i	$0.660007\pi$
$488$	16.2407	0.735183
$489$	45.9781	2.07920
$490$	2.79800	0.126401
$491$	39.3564	1.77613	0.888066	−	0.459716i	$-0.152049\pi$
$491$	39.3564	1.77613	0.888066	+	0.459716i	$0.152049\pi$
$492$	−2.94217	−0.132643
$493$	9.65491	0.434835
$494$	5.75344	0.258859
$495$	27.2059	1.22281
$496$	12.4051	0.557007
$497$	36.8777	1.65419
$498$	−68.4225	−3.06609
$499$	34.5208	1.54536	0.772681	−	0.634794i	$-0.218915\pi$
$499$	34.5208	1.54536	0.772681	+	0.634794i	$0.218915\pi$
$500$	−2.02059	−0.0903636
$501$	−41.9387	−1.87368
$502$	35.1765	1.57001
$503$	−25.8109	−1.15085	−0.575426	−	0.817854i	$-0.695164\pi$
$503$	−25.8109	−1.15085	−0.575426	+	0.817854i	$0.695164\pi$
$504$	−53.6856	−2.39135
$505$	−44.5204	−1.98113
$506$	−7.33381	−0.326028
$507$	−48.9139	−2.17234
$508$	−0.100421	−0.00445545
$509$	−25.4113	−1.12634	−0.563168	−	0.826342i	$-0.690418\pi$
$509$	−25.4113	−1.12634	−0.563168	+	0.826342i	$0.690418\pi$
$510$	17.6362	0.780943
$511$	33.0877	1.46371
$512$	20.2788	0.896206
$513$	9.83594	0.434267
$514$	−3.59774	−0.158689
$515$	−5.59409	−0.246505
$516$	0.381049	0.0167748
$517$	9.21906	0.405454
$518$	22.4010	0.984245
$519$	−58.1605	−2.55296
$520$	−55.4012	−2.42950
$521$	4.30319	0.188526	0.0942632	−	0.995547i	$-0.469950\pi$
$521$	4.30319	0.188526	0.0942632	+	0.995547i	$0.469950\pi$
$522$	100.613	4.40369
$523$	27.3428	1.19562	0.597809	−	0.801639i	$-0.296038\pi$
$523$	27.3428	1.19562	0.597809	+	0.801639i	$0.296038\pi$
$524$	0.841075	0.0367425
$525$	82.4830	3.59985
$526$	−37.7218	−1.64475
$527$	2.93625	0.127905
$528$	−13.4651	−0.585992
$529$	2.37548	0.103282
$530$	1.83705	0.0797966
$531$	−13.1255	−0.569598
$532$	0.243122	0.0105407
$533$	41.1095	1.78065
$534$	−52.6683	−2.27918
$535$	−8.41888	−0.363980
$536$	8.13485	0.351372
$537$	−4.29065	−0.185155
$538$	0.590141	0.0254428
$539$	−0.505643	−0.0217796
$540$	6.02184	0.259139
$541$	−6.04603	−0.259939	−0.129970	−	0.991518i	$-0.541488\pi$
$541$	−6.04603	−0.259939	−0.129970	+	0.991518i	$0.541488\pi$
$542$	2.81282	0.120821
$543$	−29.2121	−1.25361
$544$	−0.675437	−0.0289591
$545$	56.9590	2.43986
$546$	−67.6820	−2.89652
$547$	41.5775	1.77773	0.888864	−	0.458172i	$-0.151496\pi$
$547$	41.5775	1.77773	0.888864	+	0.458172i	$0.151496\pi$
$548$	2.33448	0.0997242
$549$	42.4623	1.81225
$550$	13.7529	0.586424
$551$	7.16633	0.305296
$552$	43.9532	1.87077
$553$	−4.49383	−0.191097
$554$	28.8373	1.22518
$555$	68.0351	2.88793
$556$	2.32829	0.0987414
$557$	3.32134	0.140730	0.0703649	−	0.997521i	$-0.477584\pi$
$557$	3.32134	0.140730	0.0703649	+	0.997521i	$0.477584\pi$
$558$	30.5983	1.29533
$559$	−5.32422	−0.225190
$560$	−43.9930	−1.85904
$561$	−3.18713	−0.134561
$562$	−25.2653	−1.06575
$563$	40.3610	1.70101	0.850506	−	0.525965i	$-0.176296\pi$
$563$	40.3610	1.70101	0.850506	+	0.525965i	$0.176296\pi$
$564$	3.51292	0.147920
$565$	−74.7443	−3.14452
$566$	−16.4689	−0.692241
$567$	−56.8778	−2.38864
$568$	−36.8513	−1.54625
$569$	−4.52786	−0.189818	−0.0949089	−	0.995486i	$-0.530256\pi$
$569$	−4.52786	−0.189818	−0.0949089	+	0.995486i	$0.530256\pi$
$570$	13.0904	0.548297
$571$	−15.2291	−0.637316	−0.318658	−	0.947870i	$-0.603232\pi$
$571$	−15.2291	−0.637316	−0.318658	+	0.947870i	$0.603232\pi$
$572$	−0.636556	−0.0266157
$573$	35.6145	1.48782
$574$	30.7966	1.28543
$575$	−47.5858	−1.98446
$576$	53.4425	2.22677
$577$	−2.81940	−0.117373	−0.0586865	−	0.998276i	$-0.518691\pi$
$577$	−2.81940	−0.117373	−0.0586865	+	0.998276i	$0.518691\pi$
$578$	−1.45587	−0.0605562
$579$	48.1977	2.00303
$580$	4.38743	0.182178
$581$	40.3989	1.67603
$582$	37.3903	1.54988
$583$	−0.331985	−0.0137494
$584$	−33.0640	−1.36820
$585$	−144.850	−5.98881
$586$	48.1047	1.98719
$587$	34.4859	1.42339	0.711693	−	0.702490i	$-0.247928\pi$
$587$	34.4859	1.42339	0.711693	+	0.702490i	$0.247928\pi$
$588$	−0.192675	−0.00794579
$589$	2.17942	0.0898016
$590$	−10.1470	−0.417746
$591$	−67.7255	−2.78585
$592$	−23.7279	−0.975212
$593$	8.47780	0.348142	0.174071	−	0.984733i	$-0.444308\pi$
$593$	8.47780	0.348142	0.174071	+	0.984733i	$0.444308\pi$
$594$	−19.2926	−0.791583
$595$	−10.4130	−0.426891
$596$	−2.86878	−0.117510
$597$	−18.4452	−0.754911
$598$	39.0468	1.59674
$599$	−17.8969	−0.731246	−0.365623	−	0.930763i	$-0.619144\pi$
$599$	−17.8969	−0.731246	−0.365623	+	0.930763i	$0.619144\pi$
$600$	−82.4239	−3.36494
$601$	36.6483	1.49491	0.747457	−	0.664310i	$-0.231274\pi$
$601$	36.6483	1.49491	0.747457	+	0.664310i	$0.231274\pi$
$602$	−3.98857	−0.162562
$603$	21.2691	0.866143
$604$	1.40920	0.0573396
$605$	−3.80085	−0.154527
$606$	54.3503	2.20783
$607$	−5.15555	−0.209257	−0.104629	−	0.994511i	$-0.533365\pi$
$607$	−5.15555	−0.209257	−0.104629	+	0.994511i	$0.533365\pi$
$608$	−0.501341	−0.0203321
$609$	−84.3029	−3.41613
$610$	32.8266	1.32911
$611$	−49.0843	−1.98574
$612$	−0.855780	−0.0345929
$613$	13.6360	0.550752	0.275376	−	0.961337i	$-0.411198\pi$
$613$	13.6360	0.550752	0.275376	+	0.961337i	$0.411198\pi$
$614$	−17.9831	−0.725739
$615$	93.5337	3.77164
$616$	7.50026	0.302194
$617$	22.2317	0.895016	0.447508	−	0.894280i	$-0.352312\pi$
$617$	22.2317	0.895016	0.447508	+	0.894280i	$0.352312\pi$
$618$	6.82923	0.274712
$619$	19.0038	0.763828	0.381914	−	0.924198i	$-0.375265\pi$
$619$	19.0038	0.763828	0.381914	+	0.924198i	$0.375265\pi$
$620$	1.33430	0.0535869
$621$	66.7535	2.67873
$622$	27.1715	1.08948
$623$	31.0971	1.24588
$624$	71.6910	2.86994
$625$	17.0036	0.680144
$626$	15.9129	0.636006
$627$	−2.36564	−0.0944747
$628$	0.164170	0.00655111
$629$	−5.61632	−0.223937
$630$	−108.512	−4.32323
$631$	−6.79638	−0.270560	−0.135280	−	0.990807i	$-0.543193\pi$
$631$	−6.79638	−0.270560	−0.135280	+	0.990807i	$0.543193\pi$
$632$	4.49060	0.178627
$633$	41.2173	1.63824
$634$	−44.2300	−1.75660
$635$	3.19245	0.126688
$636$	−0.126503	−0.00501616
$637$	2.69215	0.106667
$638$	−14.0563	−0.556494
$639$	−96.3499	−3.81154
$640$	46.4496	1.83608
$641$	−3.94794	−0.155934	−0.0779671	−	0.996956i	$-0.524843\pi$
$641$	−3.94794	−0.155934	−0.0779671	+	0.996956i	$0.524843\pi$
$642$	10.2777	0.405629
$643$	38.6384	1.52375	0.761874	−	0.647725i	$-0.224279\pi$
$643$	38.6384	1.52375	0.761874	+	0.647725i	$0.224279\pi$
$644$	1.64999	0.0650188
$645$	−12.1138	−0.476982
$646$	−1.08062	−0.0425163
$647$	21.7999	0.857044	0.428522	−	0.903531i	$-0.359034\pi$
$647$	21.7999	0.857044	0.428522	+	0.903531i	$0.359034\pi$
$648$	56.8370	2.23277
$649$	1.83373	0.0719800
$650$	−73.2232	−2.87205
$651$	−25.6382	−1.00484
$652$	−1.72477	−0.0675473
$653$	−5.41544	−0.211923	−0.105961	−	0.994370i	$-0.533792\pi$
$653$	−5.41544	−0.211923	−0.105961	+	0.994370i	$0.533792\pi$
$654$	−69.5352	−2.71904
$655$	−26.7384	−1.04475
$656$	−32.6208	−1.27363
$657$	−86.4477	−3.37265
$658$	−36.7708	−1.43348
$659$	−26.4301	−1.02957	−0.514786	−	0.857319i	$-0.672128\pi$
$659$	−26.4301	−1.02957	−0.514786	+	0.857319i	$0.672128\pi$
$660$	−1.44831	−0.0563755
$661$	−3.47463	−0.135147	−0.0675737	−	0.997714i	$-0.521526\pi$
$661$	−3.47463	−0.135147	−0.0675737	+	0.997714i	$0.521526\pi$
$662$	12.4172	0.482609
$663$	16.9690	0.659021
$664$	−40.3700	−1.56666
$665$	−7.72901	−0.299718
$666$	−58.5269	−2.26787
$667$	48.6357	1.88318
$668$	1.57324	0.0608705
$669$	−58.9386	−2.27870
$670$	16.4426	0.635233
$671$	−5.93229	−0.229014
$672$	5.89765	0.227507
$673$	1.23661	0.0476679	0.0238340	−	0.999716i	$-0.492413\pi$
$673$	1.23661	0.0476679	0.0238340	+	0.999716i	$0.492413\pi$
$674$	−17.8137	−0.686158
$675$	−125.181	−4.81820
$676$	1.83490	0.0705731
$677$	−32.4896	−1.24868	−0.624338	−	0.781155i	$-0.714631\pi$
$677$	−32.4896	−1.24868	−0.624338	+	0.781155i	$0.714631\pi$
$678$	91.2474	3.50433
$679$	−22.0765	−0.847218
$680$	10.4055	0.399033
$681$	8.98236	0.344205
$682$	−4.27480	−0.163690
$683$	−19.5548	−0.748242	−0.374121	−	0.927380i	$-0.622056\pi$
$683$	−19.5548	−0.748242	−0.374121	+	0.927380i	$0.622056\pi$
$684$	−0.635201	−0.0242875
$685$	−74.2149	−2.83560
$686$	−25.9032	−0.988987
$687$	−62.8073	−2.39625
$688$	4.22482	0.161070
$689$	1.76756	0.0673387
$690$	88.8406	3.38210
$691$	−24.9446	−0.948937	−0.474468	−	0.880273i	$-0.657360\pi$
$691$	−24.9446	−0.948937	−0.474468	+	0.880273i	$0.657360\pi$
$692$	2.18177	0.0829384
$693$	19.6099	0.744918
$694$	−34.3415	−1.30358
$695$	−74.0179	−2.80766
$696$	84.2425	3.19320
$697$	−7.72123	−0.292463
$698$	−23.2234	−0.879020
$699$	−12.1435	−0.459310
$700$	−3.09418	−0.116949
$701$	48.0133	1.81344	0.906719	−	0.421734i	$-0.138579\pi$
$701$	48.0133	1.81344	0.906719	+	0.421734i	$0.138579\pi$
$702$	102.718	3.87683
$703$	−4.16870	−0.157225
$704$	−7.46630	−0.281397
$705$	−111.678	−4.20604
$706$	38.4706	1.44786
$707$	−32.0902	−1.20688
$708$	0.698740	0.0262603
$709$	−15.2769	−0.573738	−0.286869	−	0.957970i	$-0.592614\pi$
$709$	−15.2769	−0.573738	−0.286869	+	0.957970i	$0.592614\pi$
$710$	−74.4858	−2.79540
$711$	11.7410	0.440320
$712$	−31.0748	−1.16458
$713$	14.7911	0.553930
$714$	12.7121	0.475738
$715$	20.2366	0.756805
$716$	0.160955	0.00601516
$717$	6.43531	0.240331
$718$	5.53511	0.206568
$719$	−46.5008	−1.73419	−0.867093	−	0.498146i	$-0.834015\pi$
$719$	−46.5008	−1.73419	−0.867093	+	0.498146i	$0.834015\pi$
$720$	114.940	4.28356
$721$	−4.03221	−0.150167
$722$	26.8595	0.999605
$723$	97.4497	3.62419
$724$	1.09583	0.0407262
$725$	−91.2049	−3.38726
$726$	4.64006	0.172209
$727$	29.2906	1.08633	0.543164	−	0.839626i	$-0.317226\pi$
$727$	29.2906	1.08633	0.543164	+	0.839626i	$0.317226\pi$
$728$	−39.9330	−1.48002
$729$	21.9003	0.811123
$730$	−66.8307	−2.47352
$731$	1.00000	0.0369863
$732$	−2.26050	−0.0835504
$733$	27.9699	1.03309	0.516546	−	0.856259i	$-0.327217\pi$
$733$	27.9699	1.03309	0.516546	+	0.856259i	$0.327217\pi$
$734$	−2.77756	−0.102521
$735$	6.12528	0.225934
$736$	−3.40245	−0.125416
$737$	−2.97144	−0.109454
$738$	−80.4620	−2.96185
$739$	−6.69600	−0.246316	−0.123158	−	0.992387i	$-0.539302\pi$
$739$	−6.69600	−0.246316	−0.123158	+	0.992387i	$0.539302\pi$
$740$	−2.55219	−0.0938205
$741$	12.5952	0.462696
$742$	1.32414	0.0486108
$743$	5.12499	0.188018	0.0940089	−	0.995571i	$-0.470032\pi$
$743$	5.12499	0.188018	0.0940089	+	0.995571i	$0.470032\pi$
$744$	25.6198	0.939267
$745$	91.2006	3.34133
$746$	−3.64762	−0.133549
$747$	−105.550	−3.86186
$748$	0.119559	0.00437150
$749$	−6.06831	−0.221731
$750$	−78.4189	−2.86345
$751$	−23.3640	−0.852564	−0.426282	−	0.904590i	$-0.640177\pi$
$751$	−23.3640	−0.852564	−0.426282	+	0.904590i	$0.640177\pi$
$752$	38.9489	1.42032
$753$	77.0071	2.80630
$754$	74.8388	2.72547
$755$	−44.7995	−1.63042
$756$	4.34052	0.157863
$757$	3.42780	0.124586	0.0622928	−	0.998058i	$-0.480159\pi$
$757$	3.42780	0.124586	0.0622928	+	0.998058i	$0.480159\pi$
$758$	1.44385	0.0524431
$759$	−16.0549	−0.582756
$760$	7.72347	0.280160
$761$	−8.48748	−0.307671	−0.153835	−	0.988096i	$-0.549163\pi$
$761$	−8.48748	−0.307671	−0.153835	+	0.988096i	$0.549163\pi$
$762$	−3.89732	−0.141185
$763$	41.0559	1.48632
$764$	−1.33600	−0.0483349
$765$	27.2059	0.983630
$766$	−21.9720	−0.793882
$767$	−9.76315	−0.352527
$768$	−9.11316	−0.328843
$769$	28.0710	1.01227	0.506133	−	0.862455i	$-0.331074\pi$
$769$	28.0710	1.01227	0.506133	+	0.862455i	$0.331074\pi$
$770$	15.1599	0.546327
$771$	−7.87603	−0.283648
$772$	−1.80803	−0.0650726
$773$	5.15203	0.185306	0.0926528	−	0.995698i	$-0.470465\pi$
$773$	5.15203	0.185306	0.0926528	+	0.995698i	$0.470465\pi$
$774$	10.4209	0.374570
$775$	−27.7372	−0.996350
$776$	22.0607	0.791932
$777$	49.0395	1.75928
$778$	−24.8110	−0.889516
$779$	−5.73107	−0.205337
$780$	7.71113	0.276103
$781$	13.4608	0.481664
$782$	−7.33381	−0.262257
$783$	127.943	4.57229
$784$	−2.13625	−0.0762948
$785$	−5.21909	−0.186277
$786$	32.6420	1.16430
$787$	38.2042	1.36183	0.680917	−	0.732361i	$-0.261582\pi$
$787$	38.2042	1.36183	0.680917	+	0.732361i	$0.261582\pi$
$788$	2.54058	0.0905043
$789$	−82.5791	−2.93989
$790$	9.07666	0.322933
$791$	−53.8755	−1.91559
$792$	−19.5958	−0.696308
$793$	31.5848	1.12161
$794$	−12.4274	−0.441031
$795$	4.02161	0.142632
$796$	0.691932	0.0245249
$797$	25.3067	0.896410	0.448205	−	0.893931i	$-0.352064\pi$
$797$	25.3067	0.896410	0.448205	+	0.893931i	$0.352064\pi$
$798$	9.43552	0.334014
$799$	9.21906	0.326147
$800$	6.38050	0.225585
$801$	−81.2471	−2.87072
$802$	36.0729	1.27378
$803$	12.0774	0.426201
$804$	−1.13227	−0.0399319
$805$	−52.4544	−1.84878
$806$	22.7599	0.801685
$807$	1.29191	0.0454775
$808$	32.0672	1.12812
$809$	−27.4789	−0.966107	−0.483053	−	0.875591i	$-0.660472\pi$
$809$	−27.4789	−0.966107	−0.483053	+	0.875591i	$0.660472\pi$
$810$	114.882	4.03655
$811$	−10.7313	−0.376826	−0.188413	−	0.982090i	$-0.560334\pi$
$811$	−10.7313	−0.376826	−0.188413	+	0.982090i	$0.560334\pi$
$812$	3.16244	0.110980
$813$	6.15772	0.215961
$814$	8.17663	0.286591
$815$	54.8317	1.92067
$816$	−13.4651	−0.471372
$817$	0.742248	0.0259680
$818$	−37.9074	−1.32540
$819$	−104.407	−3.64829
$820$	−3.50872	−0.122530
$821$	6.94556	0.242402	0.121201	−	0.992628i	$-0.461325\pi$
$821$	6.94556	0.242402	0.121201	+	0.992628i	$0.461325\pi$
$822$	90.6010	3.16007
$823$	−38.1693	−1.33050	−0.665250	−	0.746621i	$-0.731675\pi$
$823$	−38.1693	−1.33050	−0.665250	+	0.746621i	$0.731675\pi$
$824$	4.02931	0.140368
$825$	30.1072	1.04820
$826$	−7.31393	−0.254484
$827$	46.8318	1.62850	0.814251	−	0.580513i	$-0.197148\pi$
$827$	46.8318	1.62850	0.814251	+	0.580513i	$0.197148\pi$
$828$	−4.31091	−0.149815
$829$	31.9528	1.10977	0.554884	−	0.831928i	$-0.312763\pi$
$829$	31.9528	1.10977	0.554884	+	0.831928i	$0.312763\pi$
$830$	−81.5981	−2.83231
$831$	63.1295	2.18994
$832$	39.7522	1.37816
$833$	−0.505643	−0.0175195
$834$	90.3606	3.12893
$835$	−50.0144	−1.73082
$836$	0.0887421	0.00306921
$837$	38.9099	1.34492
$838$	−4.29093	−0.148228
$839$	−7.11342	−0.245582	−0.122791	−	0.992433i	$-0.539185\pi$
$839$	−7.11342	−0.245582	−0.122791	+	0.992433i	$0.539185\pi$
$840$	−90.8569	−3.13486
$841$	64.2172	2.21439
$842$	−47.4453	−1.63507
$843$	−55.3097	−1.90497
$844$	−1.54618	−0.0532217
$845$	−58.3328	−2.00671
$846$	96.0706	3.30298
$847$	−2.73964	−0.0941352
$848$	−1.40258	−0.0481647
$849$	−36.0532	−1.23734
$850$	13.7529	0.471719
$851$	−28.2917	−0.969826
$852$	5.12922	0.175724
$853$	−11.6257	−0.398058	−0.199029	−	0.979994i	$-0.563779\pi$
$853$	−11.6257	−0.398058	−0.199029	+	0.979994i	$0.563779\pi$
$854$	23.6613	0.809674
$855$	20.1935	0.690603
$856$	6.06395	0.207262
$857$	45.1861	1.54353	0.771764	−	0.635909i	$-0.219375\pi$
$857$	45.1861	1.54353	0.771764	+	0.635909i	$0.219375\pi$
$858$	−24.7047	−0.843403
$859$	45.7043	1.55941	0.779706	−	0.626146i	$-0.215369\pi$
$859$	45.7043	1.55941	0.779706	+	0.626146i	$0.215369\pi$
$860$	0.454425	0.0154958
$861$	67.4188	2.29763
$862$	32.4076	1.10381
$863$	−28.6477	−0.975178	−0.487589	−	0.873073i	$-0.662124\pi$
$863$	−28.6477	−0.975178	−0.487589	+	0.873073i	$0.662124\pi$
$864$	−8.95059	−0.304505
$865$	−69.3600	−2.35831
$866$	−18.1049	−0.615231
$867$	−3.18713	−0.108241
$868$	0.961762	0.0326443
$869$	−1.64030	−0.0556432
$870$	170.276	5.77288
$871$	15.8206	0.536060
$872$	−41.0264	−1.38933
$873$	57.6790	1.95214
$874$	−5.44351	−0.184129
$875$	46.3011	1.56526
$876$	4.60207	0.155490
$877$	5.52480	0.186559	0.0932797	−	0.995640i	$-0.470265\pi$
$877$	5.52480	0.186559	0.0932797	+	0.995640i	$0.470265\pi$
$878$	−19.9105	−0.671946
$879$	105.309	3.55198
$880$	−16.0579	−0.541313
$881$	10.9007	0.367255	0.183627	−	0.982996i	$-0.441216\pi$
$881$	10.9007	0.367255	0.183627	+	0.982996i	$0.441216\pi$
$882$	−5.26924	−0.177425
$883$	−40.4168	−1.36013	−0.680067	−	0.733150i	$-0.738049\pi$
$883$	−40.4168	−1.36013	−0.680067	+	0.733150i	$0.738049\pi$
$884$	−0.636556	−0.0214097
$885$	−22.2134	−0.746697
$886$	−6.34431	−0.213141
$887$	32.9393	1.10600	0.552998	−	0.833183i	$-0.313484\pi$
$887$	32.9393	1.10600	0.552998	+	0.833183i	$0.313484\pi$
$888$	−49.0043	−1.64448
$889$	2.30111	0.0771767
$890$	−62.8102	−2.10540
$891$	−20.7610	−0.695520
$892$	2.21096	0.0740283
$893$	6.84282	0.228986
$894$	−111.337	−3.72367
$895$	−5.11686	−0.171038
$896$	33.4807	1.11851
$897$	85.4798	2.85409
$898$	−9.27766	−0.309599
$899$	28.3492	0.945499
$900$	8.08411	0.269470
$901$	−0.331985	−0.0110600
$902$	11.2411	0.374288
$903$	−8.73161	−0.290570
$904$	53.8369	1.79059
$905$	−34.8372	−1.15803
$906$	54.6910	1.81699
$907$	16.7522	0.556248	0.278124	−	0.960545i	$-0.410287\pi$
$907$	16.7522	0.556248	0.278124	+	0.960545i	$0.410287\pi$
$908$	−0.336954	−0.0111822
$909$	83.8416	2.78085
$910$	−80.7149	−2.67567
$911$	11.9954	0.397425	0.198713	−	0.980058i	$-0.436324\pi$
$911$	11.9954	0.397425	0.198713	+	0.980058i	$0.436324\pi$
$912$	−9.99443	−0.330949
$913$	14.7461	0.488023
$914$	45.9514	1.51994
$915$	71.8628	2.37571
$916$	2.35608	0.0778472
$917$	−19.2729	−0.636448
$918$	−19.2926	−0.636749
$919$	54.0648	1.78343	0.891716	−	0.452595i	$-0.149502\pi$
$919$	54.0648	1.78343	0.891716	+	0.452595i	$0.149502\pi$
$920$	52.4168	1.72813
$921$	−39.3679	−1.29722
$922$	28.0344	0.923265
$923$	−71.6681	−2.35898
$924$	−1.04394	−0.0343431
$925$	53.0544	1.74442
$926$	44.0887	1.44884
$927$	10.5349	0.346011
$928$	−6.52128	−0.214071
$929$	39.0854	1.28235	0.641175	−	0.767395i	$-0.278447\pi$
$929$	39.0854	1.28235	0.641175	+	0.767395i	$0.278447\pi$
$930$	51.7842	1.69807
$931$	−0.375313	−0.0123004
$932$	0.455539	0.0149217
$933$	59.4827	1.94738
$934$	34.9206	1.14264
$935$	−3.80085	−0.124301
$936$	104.333	3.41021
$937$	−13.4513	−0.439436	−0.219718	−	0.975563i	$-0.570514\pi$
$937$	−13.4513	−0.439436	−0.219718	+	0.975563i	$0.570514\pi$
$938$	11.8518	0.386974
$939$	34.8358	1.13682
$940$	4.18937	0.136642
$941$	16.6959	0.544270	0.272135	−	0.962259i	$-0.412270\pi$
$941$	16.6959	0.544270	0.272135	+	0.962259i	$0.412270\pi$
$942$	6.37143	0.207592
$943$	−38.8950	−1.26660
$944$	7.74716	0.252149
$945$	−137.988	−4.48876
$946$	−1.45587	−0.0473344
$947$	4.41328	0.143412	0.0717062	−	0.997426i	$-0.477156\pi$
$947$	4.41328	0.143412	0.0717062	+	0.997426i	$0.477156\pi$
$948$	−0.625034	−0.0203002
$949$	−64.3025	−2.08735
$950$	10.2080	0.331192
$951$	−96.8265	−3.13981
$952$	7.50026	0.243085
$953$	−10.3055	−0.333828	−0.166914	−	0.985971i	$-0.553380\pi$
$953$	−10.3055	−0.333828	−0.166914	+	0.985971i	$0.553380\pi$
$954$	−3.45957	−0.112008
$955$	42.4725	1.37438
$956$	−0.241407	−0.00780766
$957$	−30.7715	−0.994701
$958$	−42.1839	−1.36290
$959$	−53.4939	−1.72741
$960$	90.4455	2.91911
$961$	−22.3784	−0.721885
$962$	−43.5341	−1.40360
$963$	15.8546	0.510907
$964$	−3.65562	−0.117740
$965$	57.4787	1.85030
$966$	64.0360	2.06032
$967$	5.86616	0.188643	0.0943216	−	0.995542i	$-0.469932\pi$
$967$	5.86616	0.188643	0.0943216	+	0.995542i	$0.469932\pi$
$968$	2.73768	0.0879923
$969$	−2.36564	−0.0759954
$970$	44.5903	1.43171
$971$	17.5087	0.561880	0.280940	−	0.959725i	$-0.409354\pi$
$971$	17.5087	0.561880	0.280940	+	0.959725i	$0.409354\pi$
$972$	−3.15796	−0.101292
$973$	−53.3519	−1.71038
$974$	30.9571	0.991929
$975$	−160.297	−5.13362
$976$	−25.0629	−0.802244
$977$	−19.9146	−0.637124	−0.318562	−	0.947902i	$-0.603200\pi$
$977$	−19.9146	−0.637124	−0.318562	+	0.947902i	$0.603200\pi$
$978$	−66.9382	−2.14045
$979$	11.3508	0.362773
$980$	−0.229777	−0.00733995
$981$	−107.266	−3.42474
$982$	−57.2979	−1.82845
$983$	−2.48831	−0.0793649	−0.0396824	−	0.999212i	$-0.512635\pi$
$983$	−2.48831	−0.0793649	−0.0396824	+	0.999212i	$0.512635\pi$
$984$	−67.3705	−2.14769
$985$	−80.7668	−2.57344
$986$	−14.0563	−0.447644
$987$	−80.4972	−2.56225
$988$	−0.472482	−0.0150317
$989$	5.03741	0.160180
$990$	−39.6082	−1.25883
$991$	0.963001	0.0305907	0.0152954	−	0.999883i	$-0.495131\pi$
$991$	0.963001	0.0305907	0.0152954	+	0.999883i	$0.495131\pi$
$992$	−1.98325	−0.0629682
$993$	27.1833	0.862636
$994$	−53.6892	−1.70292
$995$	−21.9970	−0.697352
$996$	5.61898	0.178044
$997$	−42.9220	−1.35935	−0.679677	−	0.733512i	$-0.737880\pi$
$997$	−42.9220	−1.35935	−0.679677	+	0.733512i	$0.737880\pi$
$998$	−50.2578	−1.59088
$999$	−74.4249	−2.35470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.22	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.22	✓	74	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)

\(f(q)\)	\(=\)	\(q-1.45587 q^{2} -3.18713 q^{3} +0.119559 q^{4} -3.80085 q^{5} +4.64006 q^{6} -2.73964 q^{7} +2.73768 q^{8} +7.15783 q^{9} +O(q^{10})\)	\(q-1.45587 q^{2} -3.18713 q^{3} +0.119559 q^{4} -3.80085 q^{5} +4.64006 q^{6} -2.73964 q^{7} +2.73768 q^{8} +7.15783 q^{9} +5.53355 q^{10} -1.00000 q^{11} -0.381049 q^{12} +5.32422 q^{13} +3.98857 q^{14} +12.1138 q^{15} -4.22482 q^{16} -1.00000 q^{17} -10.4209 q^{18} -0.742248 q^{19} -0.454425 q^{20} +8.73161 q^{21} +1.45587 q^{22} -5.03741 q^{23} -8.72535 q^{24} +9.44648 q^{25} -7.75137 q^{26} -13.2516 q^{27} -0.327548 q^{28} -9.65491 q^{29} -17.6362 q^{30} -2.93625 q^{31} +0.675437 q^{32} +3.18713 q^{33} +1.45587 q^{34} +10.4130 q^{35} +0.855780 q^{36} +5.61632 q^{37} +1.08062 q^{38} -16.9690 q^{39} -10.4055 q^{40} +7.72123 q^{41} -12.7121 q^{42} -1.00000 q^{43} -0.119559 q^{44} -27.2059 q^{45} +7.33381 q^{46} -9.21906 q^{47} +13.4651 q^{48} +0.505643 q^{49} -13.7529 q^{50} +3.18713 q^{51} +0.636556 q^{52} +0.331985 q^{53} +19.2926 q^{54} +3.80085 q^{55} -7.50026 q^{56} +2.36564 q^{57} +14.0563 q^{58} -1.83373 q^{59} +1.44831 q^{60} +5.93229 q^{61} +4.27480 q^{62} -19.6099 q^{63} +7.46630 q^{64} -20.2366 q^{65} -4.64006 q^{66} +2.97144 q^{67} -0.119559 q^{68} +16.0549 q^{69} -15.1599 q^{70} -13.4608 q^{71} +19.5958 q^{72} -12.0774 q^{73} -8.17663 q^{74} -30.1072 q^{75} -0.0887421 q^{76} +2.73964 q^{77} +24.7047 q^{78} +1.64030 q^{79} +16.0579 q^{80} +20.7610 q^{81} -11.2411 q^{82} -14.7461 q^{83} +1.04394 q^{84} +3.80085 q^{85} +1.45587 q^{86} +30.7715 q^{87} -2.73768 q^{88} -11.3508 q^{89} +39.6082 q^{90} -14.5865 q^{91} -0.602266 q^{92} +9.35822 q^{93} +13.4218 q^{94} +2.82117 q^{95} -2.15271 q^{96} +8.05817 q^{97} -0.736151 q^{98} -7.15783 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

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