LMFDB - Embedded newform 8041.2.a.h.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:	$74$
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)

$f(q)$	$=$	$q-2.77350 q^{2} -1.80573 q^{3} +5.69228 q^{4} +3.84925 q^{5} +5.00818 q^{6} -3.56425 q^{7} -10.2405 q^{8} +0.260654 q^{9} +O(q^{10})$	\(q-2.77350 q^{2} -1.80573 q^{3} +5.69228 q^{4} +3.84925 q^{5} +5.00818 q^{6} -3.56425 q^{7} -10.2405 q^{8} +0.260654 q^{9} -10.6759 q^{10} -1.00000 q^{11} -10.2787 q^{12} +6.26707 q^{13} +9.88545 q^{14} -6.95069 q^{15} +17.0175 q^{16} -1.00000 q^{17} -0.722923 q^{18} -2.48834 q^{19} +21.9110 q^{20} +6.43607 q^{21} +2.77350 q^{22} +8.95971 q^{23} +18.4916 q^{24} +9.81671 q^{25} -17.3817 q^{26} +4.94651 q^{27} -20.2888 q^{28} -8.75194 q^{29} +19.2777 q^{30} +2.52090 q^{31} -26.7170 q^{32} +1.80573 q^{33} +2.77350 q^{34} -13.7197 q^{35} +1.48372 q^{36} -9.00518 q^{37} +6.90141 q^{38} -11.3166 q^{39} -39.4184 q^{40} -1.11344 q^{41} -17.8504 q^{42} -1.00000 q^{43} -5.69228 q^{44} +1.00332 q^{45} -24.8497 q^{46} -1.44791 q^{47} -30.7290 q^{48} +5.70391 q^{49} -27.2266 q^{50} +1.80573 q^{51} +35.6740 q^{52} +3.46185 q^{53} -13.7191 q^{54} -3.84925 q^{55} +36.4999 q^{56} +4.49327 q^{57} +24.2735 q^{58} -8.00936 q^{59} -39.5653 q^{60} +2.64293 q^{61} -6.99170 q^{62} -0.929036 q^{63} +40.0645 q^{64} +24.1235 q^{65} -5.00818 q^{66} -2.08873 q^{67} -5.69228 q^{68} -16.1788 q^{69} +38.0515 q^{70} -11.7997 q^{71} -2.66924 q^{72} +9.57166 q^{73} +24.9758 q^{74} -17.7263 q^{75} -14.1644 q^{76} +3.56425 q^{77} +31.3866 q^{78} -12.4217 q^{79} +65.5047 q^{80} -9.71402 q^{81} +3.08812 q^{82} +2.23519 q^{83} +36.6360 q^{84} -3.84925 q^{85} +2.77350 q^{86} +15.8036 q^{87} +10.2405 q^{88} +2.71844 q^{89} -2.78271 q^{90} -22.3374 q^{91} +51.0012 q^{92} -4.55205 q^{93} +4.01578 q^{94} -9.57824 q^{95} +48.2436 q^{96} -2.14689 q^{97} -15.8198 q^{98} -0.260654 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.77350	−1.96116	−0.980579	−	0.196123i	$-0.937165\pi$
$2$	−2.77350	−1.96116	−0.980579	+	0.196123i	$0.937165\pi$
$3$	−1.80573	−1.04254	−0.521269	−	0.853393i	$-0.674541\pi$
$3$	−1.80573	−1.04254	−0.521269	+	0.853393i	$0.674541\pi$
$4$	5.69228	2.84614
$5$	3.84925	1.72144	0.860718	−	0.509082i	$-0.170015\pi$
$5$	3.84925	1.72144	0.860718	+	0.509082i	$0.170015\pi$
$6$	5.00818	2.04458
$7$	−3.56425	−1.34716	−0.673581	−	0.739114i	$-0.735245\pi$
$7$	−3.56425	−1.34716	−0.673581	+	0.739114i	$0.735245\pi$
$8$	−10.2405	−3.62058
$9$	0.260654	0.0868846
$10$	−10.6759	−3.37601
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−10.2787	−2.96721
$13$	6.26707	1.73817	0.869087	−	0.494660i	$-0.164707\pi$
$13$	6.26707	1.73817	0.869087	+	0.494660i	$0.164707\pi$
$14$	9.88545	2.64200
$15$	−6.95069	−1.79466
$16$	17.0175	4.25438
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.722923	−0.170394
$19$	−2.48834	−0.570865	−0.285432	−	0.958399i	$-0.592137\pi$
$19$	−2.48834	−0.570865	−0.285432	+	0.958399i	$0.592137\pi$
$20$	21.9110	4.89945
$21$	6.43607	1.40447
$22$	2.77350	0.591312
$23$	8.95971	1.86823	0.934115	−	0.356973i	$-0.116191\pi$
$23$	8.95971	1.86823	0.934115	+	0.356973i	$0.116191\pi$
$24$	18.4916	3.77459
$25$	9.81671	1.96334
$26$	−17.3817	−3.40883
$27$	4.94651	0.951957
$28$	−20.2888	−3.83421
$29$	−8.75194	−1.62519	−0.812597	−	0.582826i	$-0.801947\pi$
$29$	−8.75194	−1.62519	−0.812597	+	0.582826i	$0.801947\pi$
$30$	19.2777	3.51962
$31$	2.52090	0.452766	0.226383	−	0.974038i	$-0.427310\pi$
$31$	2.52090	0.452766	0.226383	+	0.974038i	$0.427310\pi$
$32$	−26.7170	−4.72294
$33$	1.80573	0.314337
$34$	2.77350	0.475651
$35$	−13.7197	−2.31905
$36$	1.48372	0.247286
$37$	−9.00518	−1.48044	−0.740221	−	0.672364i	$-0.765279\pi$
$37$	−9.00518	−1.48044	−0.740221	+	0.672364i	$0.765279\pi$
$38$	6.90141	1.11956
$39$	−11.3166	−1.81211
$40$	−39.4184	−6.23259
$41$	−1.11344	−0.173890	−0.0869449	−	0.996213i	$-0.527710\pi$
$41$	−1.11344	−0.173890	−0.0869449	+	0.996213i	$0.527710\pi$
$42$	−17.8504	−2.75438
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−5.69228	−0.858144
$45$	1.00332	0.149566
$46$	−24.8497	−3.66389
$47$	−1.44791	−0.211200	−0.105600	−	0.994409i	$-0.533676\pi$
$47$	−1.44791	−0.211200	−0.105600	+	0.994409i	$0.533676\pi$
$48$	−30.7290	−4.43536
$49$	5.70391	0.814844
$50$	−27.2266	−3.85042
$51$	1.80573	0.252853
$52$	35.6740	4.94709
$53$	3.46185	0.475522	0.237761	−	0.971324i	$-0.423587\pi$
$53$	3.46185	0.475522	0.237761	+	0.971324i	$0.423587\pi$
$54$	−13.7191	−1.86694
$55$	−3.84925	−0.519032
$56$	36.4999	4.87750
$57$	4.49327	0.595148
$58$	24.2735	3.18726
$59$	−8.00936	−1.04273	−0.521365	−	0.853334i	$-0.674577\pi$
$59$	−8.00936	−1.04273	−0.521365	+	0.853334i	$0.674577\pi$
$60$	−39.5653	−5.10786
$61$	2.64293	0.338392	0.169196	−	0.985582i	$-0.445883\pi$
$61$	2.64293	0.338392	0.169196	+	0.985582i	$0.445883\pi$
$62$	−6.99170	−0.887947
$63$	−0.929036	−0.117048
$64$	40.0645	5.00806
$65$	24.1235	2.99215
$66$	−5.00818	−0.616464
$67$	−2.08873	−0.255179	−0.127589	−	0.991827i	$-0.540724\pi$
$67$	−2.08873	−0.255179	−0.127589	+	0.991827i	$0.540724\pi$
$68$	−5.69228	−0.690291
$69$	−16.1788	−1.94770
$70$	38.0515	4.54803
$71$	−11.7997	−1.40036	−0.700182	−	0.713964i	$-0.746898\pi$
$71$	−11.7997	−1.40036	−0.700182	+	0.713964i	$0.746898\pi$
$72$	−2.66924	−0.314572
$73$	9.57166	1.12028	0.560139	−	0.828399i	$-0.310748\pi$
$73$	9.57166	1.12028	0.560139	+	0.828399i	$0.310748\pi$
$74$	24.9758	2.90338
$75$	−17.7263	−2.04686
$76$	−14.1644	−1.62476
$77$	3.56425	0.406184
$78$	31.3866	3.55384
$79$	−12.4217	−1.39755	−0.698774	−	0.715342i	$-0.746271\pi$
$79$	−12.4217	−1.39755	−0.698774	+	0.715342i	$0.746271\pi$
$80$	65.5047	7.32365
$81$	−9.71402	−1.07934
$82$	3.08812	0.341025
$83$	2.23519	0.245344	0.122672	−	0.992447i	$-0.460854\pi$
$83$	2.23519	0.245344	0.122672	+	0.992447i	$0.460854\pi$
$84$	36.6360	3.99731
$85$	−3.84925	−0.417509
$86$	2.77350	0.299074
$87$	15.8036	1.69433
$88$	10.2405	1.09165
$89$	2.71844	0.288154	0.144077	−	0.989566i	$-0.453979\pi$
$89$	2.71844	0.288154	0.144077	+	0.989566i	$0.453979\pi$
$90$	−2.78271	−0.293323
$91$	−22.3374	−2.34160
$92$	51.0012	5.31725
$93$	−4.55205	−0.472026
$94$	4.01578	0.414196
$95$	−9.57824	−0.982707
$96$	48.2436	4.92385
$97$	−2.14689	−0.217984	−0.108992	−	0.994043i	$-0.534762\pi$
$97$	−2.14689	−0.217984	−0.108992	+	0.994043i	$0.534762\pi$
$98$	−15.8198	−1.59804
$99$	−0.260654	−0.0261967
$100$	55.8795	5.58795
$101$	14.5465	1.44743	0.723717	−	0.690097i	$-0.242432\pi$
$101$	14.5465	1.44743	0.723717	+	0.690097i	$0.242432\pi$
$102$	−5.00818	−0.495884
$103$	6.00459	0.591650	0.295825	−	0.955242i	$-0.404405\pi$
$103$	6.00459	0.591650	0.295825	+	0.955242i	$0.404405\pi$
$104$	−64.1782	−6.29319
$105$	24.7740	2.41770
$106$	−9.60143	−0.932574
$107$	0.353248	0.0341497	0.0170749	−	0.999854i	$-0.494565\pi$
$107$	0.353248	0.0341497	0.0170749	+	0.999854i	$0.494565\pi$
$108$	28.1570	2.70941
$109$	−3.77960	−0.362020	−0.181010	−	0.983481i	$-0.557937\pi$
$109$	−3.77960	−0.362020	−0.181010	+	0.983481i	$0.557937\pi$
$110$	10.6759	1.01790
$111$	16.2609	1.54342
$112$	−60.6548	−5.73134
$113$	−14.1759	−1.33356	−0.666779	−	0.745256i	$-0.732327\pi$
$113$	−14.1759	−1.33356	−0.666779	+	0.745256i	$0.732327\pi$
$114$	−12.4621	−1.16718
$115$	34.4882	3.21604
$116$	−49.8185	−4.62553
$117$	1.63354	0.151020
$118$	22.2139	2.04496
$119$	3.56425	0.326735
$120$	71.1789	6.49771
$121$	1.00000	0.0909091
$122$	−7.33015	−0.663641
$123$	2.01057	0.181287
$124$	14.3497	1.28864
$125$	18.5407	1.65833
$126$	2.57668	0.229549
$127$	0.209648	0.0186032	0.00930162	−	0.999957i	$-0.497039\pi$
$127$	0.209648	0.0186032	0.00930162	+	0.999957i	$0.497039\pi$
$128$	−57.6846	−5.09865
$129$	1.80573	0.158985
$130$	−66.9065	−5.86809
$131$	−15.5935	−1.36241	−0.681204	−	0.732094i	$-0.738543\pi$
$131$	−15.5935	−1.36241	−0.681204	+	0.732094i	$0.738543\pi$
$132$	10.2787	0.894648
$133$	8.86908	0.769047
$134$	5.79308	0.500446
$135$	19.0404	1.63873
$136$	10.2405	0.878119
$137$	14.6443	1.25115	0.625573	−	0.780166i	$-0.284865\pi$
$137$	14.6443	1.25115	0.625573	+	0.780166i	$0.284865\pi$
$138$	44.8719	3.81975
$139$	−9.16702	−0.777537	−0.388768	−	0.921336i	$-0.627099\pi$
$139$	−9.16702	−0.777537	−0.388768	+	0.921336i	$0.627099\pi$
$140$	−78.0964	−6.60035
$141$	2.61454	0.220184
$142$	32.7264	2.74634
$143$	−6.26707	−0.524079
$144$	4.43569	0.369640
$145$	−33.6884	−2.79767
$146$	−26.5470	−2.19704
$147$	−10.2997	−0.849506
$148$	−51.2600	−4.21355
$149$	−2.07248	−0.169784	−0.0848921	−	0.996390i	$-0.527055\pi$
$149$	−2.07248	−0.169784	−0.0848921	+	0.996390i	$0.527055\pi$
$150$	49.1638	4.01421
$151$	2.25267	0.183320	0.0916600	−	0.995790i	$-0.470783\pi$
$151$	2.25267	0.183320	0.0916600	+	0.995790i	$0.470783\pi$
$152$	25.4820	2.06686
$153$	−0.260654	−0.0210726
$154$	−9.88545	−0.796592
$155$	9.70356	0.779408
$156$	−64.4175	−5.15753
$157$	−1.57248	−0.125498	−0.0627489	−	0.998029i	$-0.519987\pi$
$157$	−1.57248	−0.125498	−0.0627489	+	0.998029i	$0.519987\pi$
$158$	34.4515	2.74081
$159$	−6.25116	−0.495749
$160$	−102.840	−8.13024
$161$	−31.9347	−2.51681
$162$	26.9418	2.11675
$163$	−12.5782	−0.985202	−0.492601	−	0.870255i	$-0.663954\pi$
$163$	−12.5782	−0.985202	−0.492601	+	0.870255i	$0.663954\pi$
$164$	−6.33801	−0.494915
$165$	6.95069	0.541111
$166$	−6.19929	−0.481158
$167$	−21.8027	−1.68714	−0.843571	−	0.537017i	$-0.819551\pi$
$167$	−21.8027	−1.68714	−0.843571	+	0.537017i	$0.819551\pi$
$168$	−65.9089	−5.08498
$169$	26.2762	2.02125
$170$	10.6759	0.818802
$171$	−0.648596	−0.0495994
$172$	−5.69228	−0.434033
$173$	11.0333	0.838848	0.419424	−	0.907791i	$-0.362232\pi$
$173$	11.0333	0.838848	0.419424	+	0.907791i	$0.362232\pi$
$174$	−43.8313	−3.32284
$175$	−34.9892	−2.64494
$176$	−17.0175	−1.28275
$177$	14.4627	1.08709
$178$	−7.53958	−0.565116
$179$	−1.64054	−0.122620	−0.0613099	−	0.998119i	$-0.519528\pi$
$179$	−1.64054	−0.122620	−0.0613099	+	0.998119i	$0.519528\pi$
$180$	5.71119	0.425687
$181$	10.1750	0.756299	0.378149	−	0.925745i	$-0.376561\pi$
$181$	10.1750	0.756299	0.378149	+	0.925745i	$0.376561\pi$
$182$	61.9528	4.59225
$183$	−4.77241	−0.352787
$184$	−91.7523	−6.76407
$185$	−34.6631	−2.54849
$186$	12.6251	0.925718
$187$	1.00000	0.0731272
$188$	−8.24193	−0.601105
$189$	−17.6306	−1.28244
$190$	26.5652	1.92724
$191$	−9.69627	−0.701597	−0.350799	−	0.936451i	$-0.614090\pi$
$191$	−9.69627	−0.701597	−0.350799	+	0.936451i	$0.614090\pi$
$192$	−72.3455	−5.22109
$193$	−6.07431	−0.437238	−0.218619	−	0.975810i	$-0.570155\pi$
$193$	−6.07431	−0.437238	−0.218619	+	0.975810i	$0.570155\pi$
$194$	5.95439	0.427500
$195$	−43.5605	−3.11943
$196$	32.4683	2.31916
$197$	4.74944	0.338384	0.169192	−	0.985583i	$-0.445884\pi$
$197$	4.74944	0.338384	0.169192	+	0.985583i	$0.445884\pi$
$198$	0.722923	0.0513759
$199$	−4.47377	−0.317137	−0.158568	−	0.987348i	$-0.550688\pi$
$199$	−4.47377	−0.317137	−0.158568	+	0.987348i	$0.550688\pi$
$200$	−100.528	−7.10843
$201$	3.77168	0.266034
$202$	−40.3447	−2.83865
$203$	31.1941	2.18940
$204$	10.2787	0.719654
$205$	−4.28590	−0.299340
$206$	−16.6537	−1.16032
$207$	2.33538	0.162320
$208$	106.650	7.39486
$209$	2.48834	0.172122
$210$	−68.7107	−4.74149
$211$	−1.05832	−0.0728576	−0.0364288	−	0.999336i	$-0.511598\pi$
$211$	−1.05832	−0.0728576	−0.0364288	+	0.999336i	$0.511598\pi$
$212$	19.7058	1.35340
$213$	21.3070	1.45993
$214$	−0.979731	−0.0669731
$215$	−3.84925	−0.262516
$216$	−50.6550	−3.44663
$217$	−8.98512	−0.609950
$218$	10.4827	0.709978
$219$	−17.2838	−1.16793
$220$	−21.9110	−1.47724
$221$	−6.26707	−0.421569
$222$	−45.0996	−3.02688
$223$	22.1574	1.48377	0.741885	−	0.670527i	$-0.233932\pi$
$223$	22.1574	1.48377	0.741885	+	0.670527i	$0.233932\pi$
$224$	95.2262	6.36257
$225$	2.55876	0.170584
$226$	39.3169	2.61532
$227$	4.09911	0.272068	0.136034	−	0.990704i	$-0.456564\pi$
$227$	4.09911	0.272068	0.136034	+	0.990704i	$0.456564\pi$
$228$	25.5770	1.69388
$229$	10.1603	0.671414	0.335707	−	0.941966i	$-0.391025\pi$
$229$	10.1603	0.671414	0.335707	+	0.941966i	$0.391025\pi$
$230$	−95.6528	−6.30716
$231$	−6.43607	−0.423463
$232$	89.6246	5.88414
$233$	27.5053	1.80193	0.900966	−	0.433890i	$-0.142859\pi$
$233$	27.5053	1.80193	0.900966	+	0.433890i	$0.142859\pi$
$234$	−4.53061	−0.296175
$235$	−5.57337	−0.363567
$236$	−45.5916	−2.96776
$237$	22.4302	1.45700
$238$	−9.88545	−0.640778
$239$	28.2137	1.82499	0.912495	−	0.409089i	$-0.134153\pi$
$239$	28.2137	1.82499	0.912495	+	0.409089i	$0.134153\pi$
$240$	−118.284	−7.63518
$241$	1.42852	0.0920191	0.0460096	−	0.998941i	$-0.485350\pi$
$241$	1.42852	0.0920191	0.0460096	+	0.998941i	$0.485350\pi$
$242$	−2.77350	−0.178287
$243$	2.70134	0.173291
$244$	15.0443	0.963113
$245$	21.9558	1.40270
$246$	−5.57630	−0.355532
$247$	−15.5946	−0.992262
$248$	−25.8153	−1.63928
$249$	−4.03615	−0.255780
$250$	−51.4225	−3.25225
$251$	−22.1389	−1.39740	−0.698698	−	0.715416i	$-0.746237\pi$
$251$	−22.1389	−1.39740	−0.698698	+	0.715416i	$0.746237\pi$
$252$	−5.28834	−0.333134
$253$	−8.95971	−0.563292
$254$	−0.581458	−0.0364839
$255$	6.95069	0.435269
$256$	79.8592	4.99120
$257$	13.2531	0.826705	0.413353	−	0.910571i	$-0.364358\pi$
$257$	13.2531	0.826705	0.413353	+	0.910571i	$0.364358\pi$
$258$	−5.00818	−0.311796
$259$	32.0967	1.99439
$260$	137.318	8.51610
$261$	−2.28123	−0.141204
$262$	43.2484	2.67190
$263$	−30.9271	−1.90705	−0.953523	−	0.301322i	$-0.902572\pi$
$263$	−30.9271	−1.90705	−0.953523	+	0.301322i	$0.902572\pi$
$264$	−18.4916	−1.13808
$265$	13.3255	0.818580
$266$	−24.5984	−1.50822
$267$	−4.90876	−0.300411
$268$	−11.8896	−0.726276
$269$	8.05317	0.491010	0.245505	−	0.969395i	$-0.421046\pi$
$269$	8.05317	0.491010	0.245505	+	0.969395i	$0.421046\pi$
$270$	−52.8084	−3.21382
$271$	−11.6883	−0.710012	−0.355006	−	0.934864i	$-0.615521\pi$
$271$	−11.6883	−0.710012	−0.355006	+	0.934864i	$0.615521\pi$
$272$	−17.0175	−1.03184
$273$	40.3353	2.44121
$274$	−40.6159	−2.45369
$275$	−9.81671	−0.591970
$276$	−92.0944	−5.54343
$277$	14.2275	0.854849	0.427425	−	0.904051i	$-0.359421\pi$
$277$	14.2275	0.854849	0.427425	+	0.904051i	$0.359421\pi$
$278$	25.4247	1.52487
$279$	0.657081	0.0393384
$280$	140.497	8.39631
$281$	−31.3413	−1.86967	−0.934834	−	0.355085i	$-0.884452\pi$
$281$	−31.3413	−1.86967	−0.934834	+	0.355085i	$0.884452\pi$
$282$	−7.25141	−0.431815
$283$	−8.45132	−0.502379	−0.251189	−	0.967938i	$-0.580822\pi$
$283$	−8.45132	−0.502379	−0.251189	+	0.967938i	$0.580822\pi$
$284$	−67.1671	−3.98564
$285$	17.2957	1.02451
$286$	17.3817	1.02780
$287$	3.96858	0.234258
$288$	−6.96389	−0.410351
$289$	1.00000	0.0588235
$290$	93.4346	5.48667
$291$	3.87670	0.227256
$292$	54.4846	3.18847
$293$	20.3724	1.19017	0.595084	−	0.803664i	$-0.297119\pi$
$293$	20.3724	1.19017	0.595084	+	0.803664i	$0.297119\pi$
$294$	28.5662	1.66601
$295$	−30.8300	−1.79499
$296$	92.2179	5.36005
$297$	−4.94651	−0.287026
$298$	5.74802	0.332974
$299$	56.1512	3.24731
$300$	−100.903	−5.82565
$301$	3.56425	0.205440
$302$	−6.24778	−0.359520
$303$	−26.2671	−1.50900
$304$	−42.3455	−2.42868
$305$	10.1733	0.582521
$306$	0.722923	0.0413267
$307$	−11.3292	−0.646590	−0.323295	−	0.946298i	$-0.604791\pi$
$307$	−11.3292	−0.646590	−0.323295	+	0.946298i	$0.604791\pi$
$308$	20.2888	1.15606
$309$	−10.8427	−0.616817
$310$	−26.9128	−1.52854
$311$	−24.0936	−1.36622	−0.683110	−	0.730315i	$-0.739373\pi$
$311$	−24.0936	−1.36622	−0.683110	+	0.730315i	$0.739373\pi$
$312$	115.888	6.56089
$313$	−14.7810	−0.835471	−0.417736	−	0.908569i	$-0.637176\pi$
$313$	−14.7810	−0.835471	−0.417736	+	0.908569i	$0.637176\pi$
$314$	4.36128	0.246121
$315$	−3.57609	−0.201490
$316$	−70.7078	−3.97762
$317$	−12.5774	−0.706417	−0.353208	−	0.935545i	$-0.614909\pi$
$317$	−12.5774	−0.706417	−0.353208	+	0.935545i	$0.614909\pi$
$318$	17.3376	0.972243
$319$	8.75194	0.490014
$320$	154.218	8.62105
$321$	−0.637869	−0.0356024
$322$	88.5708	4.93586
$323$	2.48834	0.138455
$324$	−55.2950	−3.07194
$325$	61.5220	3.41263
$326$	34.8857	1.93214
$327$	6.82492	0.377419
$328$	11.4022	0.629581
$329$	5.16073	0.284520
$330$	−19.2777	−1.06120
$331$	32.2900	1.77482	0.887411	−	0.460980i	$-0.152502\pi$
$331$	32.2900	1.77482	0.887411	+	0.460980i	$0.152502\pi$
$332$	12.7233	0.698284
$333$	−2.34723	−0.128628
$334$	60.4697	3.30875
$335$	−8.04004	−0.439274
$336$	109.526	5.97514
$337$	7.50767	0.408969	0.204484	−	0.978870i	$-0.434448\pi$
$337$	7.50767	0.408969	0.204484	+	0.978870i	$0.434448\pi$
$338$	−72.8770	−3.96398
$339$	25.5978	1.39028
$340$	−21.9110	−1.18829
$341$	−2.52090	−0.136514
$342$	1.79888	0.0972722
$343$	4.61960	0.249435
$344$	10.2405	0.552133
$345$	−62.2762	−3.35284
$346$	−30.6009	−1.64511
$347$	15.6082	0.837891	0.418945	−	0.908011i	$-0.362400\pi$
$347$	15.6082	0.837891	0.418945	+	0.908011i	$0.362400\pi$
$348$	89.9587	4.82229
$349$	−26.4043	−1.41339	−0.706696	−	0.707517i	$-0.749815\pi$
$349$	−26.4043	−1.41339	−0.706696	+	0.707517i	$0.749815\pi$
$350$	97.0425	5.18714
$351$	31.0002	1.65467
$352$	26.7170	1.42402
$353$	−17.1391	−0.912224	−0.456112	−	0.889922i	$-0.650758\pi$
$353$	−17.1391	−0.912224	−0.456112	+	0.889922i	$0.650758\pi$
$354$	−40.1123	−2.13195
$355$	−45.4199	−2.41064
$356$	15.4741	0.820127
$357$	−6.43607	−0.340633
$358$	4.55003	0.240477
$359$	−37.0404	−1.95492	−0.977459	−	0.211127i	$-0.932287\pi$
$359$	−37.0404	−1.95492	−0.977459	+	0.211127i	$0.932287\pi$
$360$	−10.2745	−0.541516
$361$	−12.8082	−0.674113
$362$	−28.2202	−1.48322
$363$	−1.80573	−0.0947761
$364$	−127.151	−6.66453
$365$	36.8437	1.92849
$366$	13.2363	0.691871
$367$	5.35400	0.279477	0.139738	−	0.990188i	$-0.455374\pi$
$367$	5.35400	0.279477	0.139738	+	0.990188i	$0.455374\pi$
$368$	152.472	7.94817
$369$	−0.290222	−0.0151083
$370$	96.1381	4.99798
$371$	−12.3389	−0.640605
$372$	−25.9116	−1.34345
$373$	14.2608	0.738397	0.369198	−	0.929351i	$-0.379632\pi$
$373$	14.2608	0.738397	0.369198	+	0.929351i	$0.379632\pi$
$374$	−2.77350	−0.143414
$375$	−33.4794	−1.72887
$376$	14.8274	0.764665
$377$	−54.8490	−2.82487
$378$	48.8985	2.51507
$379$	31.8734	1.63722	0.818612	−	0.574346i	$-0.194744\pi$
$379$	31.8734	1.63722	0.818612	+	0.574346i	$0.194744\pi$
$380$	−54.5221	−2.79692
$381$	−0.378567	−0.0193946
$382$	26.8926	1.37594
$383$	−22.8344	−1.16678	−0.583392	−	0.812191i	$-0.698275\pi$
$383$	−22.8344	−1.16678	−0.583392	+	0.812191i	$0.698275\pi$
$384$	104.163	5.31553
$385$	13.7197	0.699220
$386$	16.8471	0.857493
$387$	−0.260654	−0.0132498
$388$	−12.2207	−0.620412
$389$	−14.2765	−0.723847	−0.361924	−	0.932208i	$-0.617880\pi$
$389$	−14.2765	−0.723847	−0.361924	+	0.932208i	$0.617880\pi$
$390$	120.815	6.11770
$391$	−8.95971	−0.453112
$392$	−58.4111	−2.95021
$393$	28.1576	1.42036
$394$	−13.1726	−0.663624
$395$	−47.8141	−2.40579
$396$	−1.48372	−0.0745595
$397$	−23.5833	−1.18361	−0.591807	−	0.806080i	$-0.701585\pi$
$397$	−23.5833	−1.18361	−0.591807	+	0.806080i	$0.701585\pi$
$398$	12.4080	0.621956
$399$	−16.0152	−0.801761
$400$	167.056	8.35281
$401$	−19.1775	−0.957680	−0.478840	−	0.877902i	$-0.658943\pi$
$401$	−19.1775	−0.957680	−0.478840	+	0.877902i	$0.658943\pi$
$402$	−10.4607	−0.521734
$403$	15.7986	0.786987
$404$	82.8029	4.11960
$405$	−37.3917	−1.85801
$406$	−86.5168	−4.29376
$407$	9.00518	0.446370
$408$	−18.4916	−0.915472
$409$	−3.84956	−0.190349	−0.0951743	−	0.995461i	$-0.530341\pi$
$409$	−3.84956	−0.190349	−0.0951743	+	0.995461i	$0.530341\pi$
$410$	11.8869	0.587053
$411$	−26.4436	−1.30437
$412$	34.1799	1.68392
$413$	28.5474	1.40473
$414$	−6.47718	−0.318336
$415$	8.60380	0.422344
$416$	−167.437	−8.20929
$417$	16.5531	0.810611
$418$	−6.90141	−0.337559
$419$	3.91260	0.191143	0.0955715	−	0.995423i	$-0.469532\pi$
$419$	3.91260	0.191143	0.0955715	+	0.995423i	$0.469532\pi$
$420$	141.021	6.88112
$421$	7.29001	0.355293	0.177647	−	0.984094i	$-0.443152\pi$
$421$	7.29001	0.355293	0.177647	+	0.984094i	$0.443152\pi$
$422$	2.93524	0.142885
$423$	−0.377404	−0.0183500
$424$	−35.4512	−1.72166
$425$	−9.81671	−0.476180
$426$	−59.0949	−2.86316
$427$	−9.42007	−0.455869
$428$	2.01079	0.0971950
$429$	11.3166	0.546372
$430$	10.6759	0.514836
$431$	−32.2554	−1.55369	−0.776843	−	0.629694i	$-0.783180\pi$
$431$	−32.2554	−1.55369	−0.776843	+	0.629694i	$0.783180\pi$
$432$	84.1775	4.04999
$433$	−12.6830	−0.609505	−0.304753	−	0.952432i	$-0.598574\pi$
$433$	−12.6830	−0.609505	−0.304753	+	0.952432i	$0.598574\pi$
$434$	24.9202	1.19621
$435$	60.8320	2.91667
$436$	−21.5145	−1.03036
$437$	−22.2948	−1.06651
$438$	47.9366	2.29050
$439$	−13.4586	−0.642344	−0.321172	−	0.947021i	$-0.604077\pi$
$439$	−13.4586	−0.642344	−0.321172	+	0.947021i	$0.604077\pi$
$440$	39.4184	1.87920
$441$	1.48675	0.0707974
$442$	17.3817	0.826763
$443$	−20.9706	−0.996345	−0.498172	−	0.867078i	$-0.665995\pi$
$443$	−20.9706	−0.996345	−0.498172	+	0.867078i	$0.665995\pi$
$444$	92.5617	4.39278
$445$	10.4639	0.496039
$446$	−61.4535	−2.90991
$447$	3.74234	0.177006
$448$	−142.800	−6.74666
$449$	4.27438	0.201721	0.100860	−	0.994901i	$-0.467840\pi$
$449$	4.27438	0.201721	0.100860	+	0.994901i	$0.467840\pi$
$450$	−7.09672	−0.334542
$451$	1.11344	0.0524297
$452$	−80.6933	−3.79550
$453$	−4.06772	−0.191118
$454$	−11.3689	−0.533568
$455$	−85.9823	−4.03091
$456$	−46.0135	−2.15478
$457$	38.8660	1.81808	0.909038	−	0.416713i	$-0.136818\pi$
$457$	38.8660	1.81808	0.909038	+	0.416713i	$0.136818\pi$
$458$	−28.1797	−1.31675
$459$	−4.94651	−0.230884
$460$	196.316	9.15330
$461$	−3.04334	−0.141743	−0.0708713	−	0.997485i	$-0.522578\pi$
$461$	−3.04334	−0.141743	−0.0708713	+	0.997485i	$0.522578\pi$
$462$	17.8504	0.830477
$463$	35.4272	1.64644	0.823221	−	0.567721i	$-0.192175\pi$
$463$	35.4272	1.64644	0.823221	+	0.567721i	$0.192175\pi$
$464$	−148.936	−6.91420
$465$	−17.5220	−0.812563
$466$	−76.2859	−3.53387
$467$	18.7426	0.867304	0.433652	−	0.901080i	$-0.357225\pi$
$467$	18.7426	0.867304	0.433652	+	0.901080i	$0.357225\pi$
$468$	9.29855	0.429826
$469$	7.44476	0.343767
$470$	15.4577	0.713012
$471$	2.83948	0.130836
$472$	82.0202	3.77528
$473$	1.00000	0.0459800
$474$	−62.2100	−2.85740
$475$	−24.4273	−1.12080
$476$	20.2888	0.929933
$477$	0.902345	0.0413155
$478$	−78.2505	−3.57909
$479$	32.5867	1.48892	0.744462	−	0.667665i	$-0.232706\pi$
$479$	32.5867	1.48892	0.744462	+	0.667665i	$0.232706\pi$
$480$	185.702	8.47608
$481$	−56.4361	−2.57326
$482$	−3.96200	−0.180464
$483$	57.6654	2.62387
$484$	5.69228	0.258740
$485$	−8.26391	−0.375245
$486$	−7.49215	−0.339851
$487$	−17.1128	−0.775456	−0.387728	−	0.921774i	$-0.626740\pi$
$487$	−17.1128	−0.775456	−0.387728	+	0.921774i	$0.626740\pi$
$488$	−27.0650	−1.22518
$489$	22.7128	1.02711
$490$	−60.8942	−2.75092
$491$	37.2720	1.68206	0.841031	−	0.540987i	$-0.181949\pi$
$491$	37.2720	1.68206	0.841031	+	0.540987i	$0.181949\pi$
$492$	11.4447	0.515968
$493$	8.75194	0.394167
$494$	43.2516	1.94598
$495$	−1.00332	−0.0450959
$496$	42.8995	1.92624
$497$	42.0570	1.88652
$498$	11.1942	0.501626
$499$	6.73420	0.301464	0.150732	−	0.988575i	$-0.451837\pi$
$499$	6.73420	0.301464	0.150732	+	0.988575i	$0.451837\pi$
$500$	105.539	4.71984
$501$	39.3697	1.75891
$502$	61.4023	2.74052
$503$	−14.8977	−0.664257	−0.332128	−	0.943234i	$-0.607767\pi$
$503$	−14.8977	−0.664257	−0.332128	+	0.943234i	$0.607767\pi$
$504$	9.51383	0.423780
$505$	55.9932	2.49166
$506$	24.8497	1.10471
$507$	−47.4477	−2.10723
$508$	1.19338	0.0529475
$509$	−27.4345	−1.21601	−0.608006	−	0.793933i	$-0.708030\pi$
$509$	−27.4345	−1.21601	−0.608006	+	0.793933i	$0.708030\pi$
$510$	−19.2777	−0.853632
$511$	−34.1158	−1.50919
$512$	−106.120	−4.68989
$513$	−12.3086	−0.543439
$514$	−36.7574	−1.62130
$515$	23.1132	1.01849
$516$	10.2787	0.452495
$517$	1.44791	0.0636791
$518$	−89.0202	−3.91132
$519$	−19.9232	−0.874530
$520$	−247.038	−10.8333
$521$	6.57546	0.288076	0.144038	−	0.989572i	$-0.453991\pi$
$521$	6.57546	0.288076	0.144038	+	0.989572i	$0.453991\pi$
$522$	6.32697	0.276924
$523$	−28.4545	−1.24423	−0.622115	−	0.782926i	$-0.713726\pi$
$523$	−28.4545	−1.24423	−0.622115	+	0.782926i	$0.713726\pi$
$524$	−88.7625	−3.87761
$525$	63.1810	2.75745
$526$	85.7761	3.74002
$527$	−2.52090	−0.109812
$528$	30.7290	1.33731
$529$	57.2765	2.49028
$530$	−36.9583	−1.60537
$531$	−2.08767	−0.0905972
$532$	50.4854	2.18882
$533$	−6.97800	−0.302251
$534$	13.6144	0.589154
$535$	1.35974	0.0587866
$536$	21.3897	0.923895
$537$	2.96237	0.127836
$538$	−22.3354	−0.962949
$539$	−5.70391	−0.245685
$540$	108.383	4.66407
$541$	3.01753	0.129734	0.0648669	−	0.997894i	$-0.479338\pi$
$541$	3.01753	0.129734	0.0648669	+	0.997894i	$0.479338\pi$
$542$	32.4174	1.39245
$543$	−18.3732	−0.788470
$544$	26.7170	1.14548
$545$	−14.5486	−0.623194
$546$	−111.870	−4.78759
$547$	3.25785	0.139296	0.0696479	−	0.997572i	$-0.477812\pi$
$547$	3.25785	0.139296	0.0696479	+	0.997572i	$0.477812\pi$
$548$	83.3594	3.56094
$549$	0.688889	0.0294011
$550$	27.2266	1.16095
$551$	21.7778	0.927766
$552$	165.680	7.05180
$553$	44.2740	1.88272
$554$	−39.4600	−1.67649
$555$	62.5922	2.65689
$556$	−52.1813	−2.21298
$557$	−32.1798	−1.36350	−0.681750	−	0.731585i	$-0.738781\pi$
$557$	−32.1798	−1.36350	−0.681750	+	0.731585i	$0.738781\pi$
$558$	−1.82241	−0.0771489
$559$	−6.26707	−0.265069
$560$	−233.475	−9.86614
$561$	−1.80573	−0.0762379
$562$	86.9251	3.66672
$563$	40.2622	1.69685	0.848425	−	0.529315i	$-0.177551\pi$
$563$	40.2622	1.69685	0.848425	+	0.529315i	$0.177551\pi$
$564$	14.8827	0.626674
$565$	−54.5666	−2.29563
$566$	23.4397	0.985244
$567$	34.6232	1.45404
$568$	120.835	5.07013
$569$	16.0077	0.671076	0.335538	−	0.942027i	$-0.391082\pi$
$569$	16.0077	0.671076	0.335538	+	0.942027i	$0.391082\pi$
$570$	−47.9696	−2.00922
$571$	29.5477	1.23653	0.618267	−	0.785968i	$-0.287835\pi$
$571$	29.5477	1.23653	0.618267	+	0.785968i	$0.287835\pi$
$572$	−35.6740	−1.49160
$573$	17.5088	0.731441
$574$	−11.0068	−0.459416
$575$	87.9549	3.66797
$576$	10.4430	0.435123
$577$	−42.8194	−1.78259	−0.891297	−	0.453421i	$-0.850204\pi$
$577$	−42.8194	−1.78259	−0.891297	+	0.453421i	$0.850204\pi$
$578$	−2.77350	−0.115362
$579$	10.9685	0.455837
$580$	−191.764	−7.96256
$581$	−7.96679	−0.330518
$582$	−10.7520	−0.445685
$583$	−3.46185	−0.143375
$584$	−98.0189	−4.05605
$585$	6.28789	0.259972
$586$	−56.5027	−2.33411
$587$	36.9498	1.52508	0.762540	−	0.646941i	$-0.223952\pi$
$587$	36.9498	1.52508	0.762540	+	0.646941i	$0.223952\pi$
$588$	−58.6289	−2.41781
$589$	−6.27285	−0.258468
$590$	85.5069	3.52026
$591$	−8.57620	−0.352778
$592$	−153.246	−6.29837
$593$	16.3740	0.672398	0.336199	−	0.941791i	$-0.390859\pi$
$593$	16.3740	0.672398	0.336199	+	0.941791i	$0.390859\pi$
$594$	13.7191	0.562903
$595$	13.7197	0.562453
$596$	−11.7971	−0.483230
$597$	8.07841	0.330627
$598$	−155.735	−6.36848
$599$	21.9677	0.897577	0.448788	−	0.893638i	$-0.351856\pi$
$599$	21.9677	0.897577	0.448788	+	0.893638i	$0.351856\pi$
$600$	181.527	7.41080
$601$	22.6367	0.923370	0.461685	−	0.887044i	$-0.347245\pi$
$601$	22.6367	0.923370	0.461685	+	0.887044i	$0.347245\pi$
$602$	−9.88545	−0.402901
$603$	−0.544435	−0.0221711
$604$	12.8229	0.521755
$605$	3.84925	0.156494
$606$	72.8516	2.95939
$607$	38.1846	1.54986	0.774932	−	0.632044i	$-0.217784\pi$
$607$	38.1846	1.54986	0.774932	+	0.632044i	$0.217784\pi$
$608$	66.4810	2.69616
$609$	−56.3281	−2.28253
$610$	−28.2156	−1.14242
$611$	−9.07417	−0.367102
$612$	−1.48372	−0.0599757
$613$	−16.7001	−0.674509	−0.337255	−	0.941413i	$-0.609498\pi$
$613$	−16.7001	−0.674509	−0.337255	+	0.941413i	$0.609498\pi$
$614$	31.4214	1.26807
$615$	7.73917	0.312073
$616$	−36.4999	−1.47062
$617$	−28.0009	−1.12727	−0.563636	−	0.826023i	$-0.690598\pi$
$617$	−28.0009	−1.12727	−0.563636	+	0.826023i	$0.690598\pi$
$618$	30.0721	1.20968
$619$	3.18412	0.127981	0.0639903	−	0.997951i	$-0.479617\pi$
$619$	3.18412	0.127981	0.0639903	+	0.997951i	$0.479617\pi$
$620$	55.2354	2.21831
$621$	44.3194	1.77847
$622$	66.8234	2.67938
$623$	−9.68921	−0.388190
$624$	−192.581	−7.70942
$625$	22.2842	0.891367
$626$	40.9950	1.63849
$627$	−4.49327	−0.179444
$628$	−8.95103	−0.357185
$629$	9.00518	0.359060
$630$	9.91828	0.395154
$631$	−39.6590	−1.57880	−0.789400	−	0.613880i	$-0.789608\pi$
$631$	−39.6590	−1.57880	−0.789400	+	0.613880i	$0.789608\pi$
$632$	127.205	5.05993
$633$	1.91103	0.0759568
$634$	34.8834	1.38540
$635$	0.806986	0.0320243
$636$	−35.5834	−1.41097
$637$	35.7468	1.41634
$638$	−24.2735	−0.960996
$639$	−3.07563	−0.121670
$640$	−222.042	−8.77700
$641$	−19.2912	−0.761956	−0.380978	−	0.924584i	$-0.624413\pi$
$641$	−19.2912	−0.761956	−0.380978	+	0.924584i	$0.624413\pi$
$642$	1.76913	0.0698219
$643$	3.15995	0.124616	0.0623080	−	0.998057i	$-0.480154\pi$
$643$	3.15995	0.124616	0.0623080	+	0.998057i	$0.480154\pi$
$644$	−181.781	−7.16319
$645$	6.95069	0.273683
$646$	−6.90141	−0.271532
$647$	−30.2032	−1.18741	−0.593706	−	0.804682i	$-0.702336\pi$
$647$	−30.2032	−1.18741	−0.593706	+	0.804682i	$0.702336\pi$
$648$	99.4768	3.90782
$649$	8.00936	0.314395
$650$	−170.631	−6.69270
$651$	16.2247	0.635895
$652$	−71.5988	−2.80403
$653$	1.17062	0.0458099	0.0229049	−	0.999738i	$-0.492708\pi$
$653$	1.17062	0.0458099	0.0229049	+	0.999738i	$0.492708\pi$
$654$	−18.9289	−0.740179
$655$	−60.0231	−2.34530
$656$	−18.9480	−0.739794
$657$	2.49489	0.0973349
$658$	−14.3133	−0.557989
$659$	−19.4306	−0.756908	−0.378454	−	0.925620i	$-0.623544\pi$
$659$	−19.4306	−0.756908	−0.378454	+	0.925620i	$0.623544\pi$
$660$	39.5653	1.54008
$661$	−31.0562	−1.20795	−0.603973	−	0.797005i	$-0.706416\pi$
$661$	−31.0562	−1.20795	−0.603973	+	0.797005i	$0.706416\pi$
$662$	−89.5563	−3.48071
$663$	11.3166	0.439501
$664$	−22.8896	−0.888287
$665$	34.1393	1.32387
$666$	6.51004	0.252259
$667$	−78.4148	−3.03623
$668$	−124.107	−4.80185
$669$	−40.0102	−1.54689
$670$	22.2990	0.861486
$671$	−2.64293	−0.102029
$672$	−171.953	−6.63322
$673$	39.0224	1.50420	0.752101	−	0.659048i	$-0.229041\pi$
$673$	39.0224	1.50420	0.752101	+	0.659048i	$0.229041\pi$
$674$	−20.8225	−0.802053
$675$	48.5585	1.86902
$676$	149.572	5.75275
$677$	−11.1102	−0.427001	−0.213501	−	0.976943i	$-0.568487\pi$
$677$	−11.1102	−0.427001	−0.213501	+	0.976943i	$0.568487\pi$
$678$	−70.9956	−2.72657
$679$	7.65206	0.293659
$680$	39.4184	1.51163
$681$	−7.40188	−0.283641
$682$	6.99170	0.267726
$683$	−7.90634	−0.302528	−0.151264	−	0.988493i	$-0.548334\pi$
$683$	−7.90634	−0.302528	−0.151264	+	0.988493i	$0.548334\pi$
$684$	−3.69199	−0.141167
$685$	56.3695	2.15377
$686$	−12.8124	−0.489182
$687$	−18.3468	−0.699975
$688$	−17.0175	−0.648788
$689$	21.6957	0.826539
$690$	172.723	6.57545
$691$	−46.0406	−1.75147	−0.875734	−	0.482794i	$-0.839622\pi$
$691$	−46.0406	−1.75147	−0.875734	+	0.482794i	$0.839622\pi$
$692$	62.8048	2.38748
$693$	0.929036	0.0352912
$694$	−43.2892	−1.64324
$695$	−35.2861	−1.33848
$696$	−161.838	−6.13444
$697$	1.11344	0.0421745
$698$	73.2324	2.77189
$699$	−49.6671	−1.87858
$700$	−199.169	−7.52787
$701$	−42.2458	−1.59560	−0.797802	−	0.602920i	$-0.794004\pi$
$701$	−42.2458	−1.59560	−0.797802	+	0.602920i	$0.794004\pi$
$702$	−85.9789	−3.24506
$703$	22.4080	0.845132
$704$	−40.0645	−1.50999
$705$	10.0640	0.379032
$706$	47.5353	1.78902
$707$	−51.8475	−1.94993
$708$	82.3260	3.09400
$709$	28.4619	1.06891	0.534455	−	0.845197i	$-0.320517\pi$
$709$	28.4619	1.06891	0.534455	+	0.845197i	$0.320517\pi$
$710$	125.972	4.72764
$711$	−3.23776	−0.121425
$712$	−27.8383	−1.04328
$713$	22.5865	0.845872
$714$	17.8504	0.668036
$715$	−24.1235	−0.902168
$716$	−9.33843	−0.348993
$717$	−50.9462	−1.90262
$718$	102.731	3.83390
$719$	−16.0113	−0.597122	−0.298561	−	0.954391i	$-0.596507\pi$
$719$	−16.0113	−0.597122	−0.298561	+	0.954391i	$0.596507\pi$
$720$	17.0741	0.636312
$721$	−21.4019	−0.797048
$722$	35.5234	1.32204
$723$	−2.57952	−0.0959334
$724$	57.9188	2.15253
$725$	−85.9152	−3.19081
$726$	5.00818	0.185871
$727$	14.5958	0.541330	0.270665	−	0.962674i	$-0.412756\pi$
$727$	14.5958	0.541330	0.270665	+	0.962674i	$0.412756\pi$
$728$	228.747	8.47795
$729$	24.2642	0.898673
$730$	−102.186	−3.78207
$731$	1.00000	0.0369863
$732$	−27.1659	−1.00408
$733$	−2.07809	−0.0767561	−0.0383781	−	0.999263i	$-0.512219\pi$
$733$	−2.07809	−0.0767561	−0.0383781	+	0.999263i	$0.512219\pi$
$734$	−14.8493	−0.548098
$735$	−39.6461	−1.46237
$736$	−239.377	−8.82354
$737$	2.08873	0.0769393
$738$	0.804929	0.0296299
$739$	−51.6708	−1.90074	−0.950371	−	0.311118i	$-0.899297\pi$
$739$	−51.6708	−1.90074	−0.950371	+	0.311118i	$0.899297\pi$
$740$	−197.313	−7.25335
$741$	28.1596	1.03447
$742$	34.2219	1.25633
$743$	−31.2559	−1.14667	−0.573335	−	0.819321i	$-0.694351\pi$
$743$	−31.2559	−1.14667	−0.573335	+	0.819321i	$0.694351\pi$
$744$	46.6155	1.70901
$745$	−7.97749	−0.292273
$746$	−39.5523	−1.44811
$747$	0.582611	0.0213166
$748$	5.69228	0.208131
$749$	−1.25906	−0.0460052
$750$	92.8551	3.39059
$751$	11.3296	0.413424	0.206712	−	0.978402i	$-0.433724\pi$
$751$	11.3296	0.413424	0.206712	+	0.978402i	$0.433724\pi$
$752$	−24.6399	−0.898525
$753$	39.9769	1.45684
$754$	152.124	5.54001
$755$	8.67110	0.315574
$756$	−100.359	−3.65001
$757$	−14.6332	−0.531854	−0.265927	−	0.963993i	$-0.585678\pi$
$757$	−14.6332	−0.531854	−0.265927	+	0.963993i	$0.585678\pi$
$758$	−88.4007	−3.21086
$759$	16.1788	0.587253
$760$	98.0864	3.55797
$761$	20.1169	0.729236	0.364618	−	0.931157i	$-0.381200\pi$
$761$	20.1169	0.729236	0.364618	+	0.931157i	$0.381200\pi$
$762$	1.04995	0.0380358
$763$	13.4714	0.487699
$764$	−55.1939	−1.99685
$765$	−1.00332	−0.0362751
$766$	63.3311	2.28825
$767$	−50.1952	−1.81245
$768$	−144.204	−5.20352
$769$	35.2840	1.27238	0.636188	−	0.771534i	$-0.280510\pi$
$769$	35.2840	1.27238	0.636188	+	0.771534i	$0.280510\pi$
$770$	−38.0515	−1.37128
$771$	−23.9315	−0.861871
$772$	−34.5767	−1.24444
$773$	−7.01957	−0.252476	−0.126238	−	0.992000i	$-0.540290\pi$
$773$	−7.01957	−0.252476	−0.126238	+	0.992000i	$0.540290\pi$
$774$	0.722923	0.0259849
$775$	24.7469	0.888935
$776$	21.9853	0.789227
$777$	−57.9580	−2.07923
$778$	39.5958	1.41958
$779$	2.77061	0.0992676
$780$	−247.959	−8.87835
$781$	11.7997	0.422226
$782$	24.8497	0.888625
$783$	−43.2916	−1.54711
$784$	97.0665	3.46666
$785$	−6.05288	−0.216037
$786$	−78.0949	−2.78555
$787$	−43.2764	−1.54264	−0.771318	−	0.636450i	$-0.780402\pi$
$787$	−43.2764	−1.54264	−0.771318	+	0.636450i	$0.780402\pi$
$788$	27.0352	0.963088
$789$	55.8459	1.98817
$790$	132.612	4.71814
$791$	50.5266	1.79652
$792$	2.66924	0.0948472
$793$	16.5634	0.588184
$794$	65.4083	2.32125
$795$	−24.0623	−0.853401
$796$	−25.4660	−0.902617
$797$	−44.6590	−1.58190	−0.790951	−	0.611880i	$-0.790414\pi$
$797$	−44.6590	−1.58190	−0.790951	+	0.611880i	$0.790414\pi$
$798$	44.4180	1.57238
$799$	1.44791	0.0512235
$800$	−262.273	−9.27275
$801$	0.708572	0.0250361
$802$	53.1888	1.87816
$803$	−9.57166	−0.337776
$804$	21.4695	0.757170
$805$	−122.925	−4.33252
$806$	−43.8175	−1.54341
$807$	−14.5418	−0.511897
$808$	−148.964	−5.24054
$809$	−30.3554	−1.06724	−0.533620	−	0.845724i	$-0.679169\pi$
$809$	−30.3554	−1.06724	−0.533620	+	0.845724i	$0.679169\pi$
$810$	103.706	3.64385
$811$	47.8163	1.67906	0.839528	−	0.543316i	$-0.182832\pi$
$811$	47.8163	1.67906	0.839528	+	0.543316i	$0.182832\pi$
$812$	177.566	6.23134
$813$	21.1058	0.740214
$814$	−24.9758	−0.875402
$815$	−48.4167	−1.69596
$816$	30.7290	1.07573
$817$	2.48834	0.0870561
$818$	10.6767	0.373304
$819$	−5.82234	−0.203449
$820$	−24.3966	−0.851965
$821$	6.64247	0.231824	0.115912	−	0.993259i	$-0.463021\pi$
$821$	6.64247	0.231824	0.115912	+	0.993259i	$0.463021\pi$
$822$	73.3412	2.55807
$823$	30.6677	1.06901	0.534505	−	0.845165i	$-0.320498\pi$
$823$	30.6677	1.06901	0.534505	+	0.845165i	$0.320498\pi$
$824$	−61.4903	−2.14212
$825$	17.7263	0.617151
$826$	−79.1761	−2.75489
$827$	−45.2506	−1.57352	−0.786759	−	0.617260i	$-0.788243\pi$
$827$	−45.2506	−1.57352	−0.786759	+	0.617260i	$0.788243\pi$
$828$	13.2937	0.461987
$829$	4.00262	0.139017	0.0695083	−	0.997581i	$-0.477857\pi$
$829$	4.00262	0.139017	0.0695083	+	0.997581i	$0.477857\pi$
$830$	−23.8626	−0.828283
$831$	−25.6910	−0.891213
$832$	251.087	8.70487
$833$	−5.70391	−0.197629
$834$	−45.9101	−1.58974
$835$	−83.9239	−2.90431
$836$	14.1644	0.489884
$837$	12.4697	0.431014
$838$	−10.8516	−0.374862
$839$	9.96377	0.343987	0.171994	−	0.985098i	$-0.444979\pi$
$839$	9.96377	0.343987	0.171994	+	0.985098i	$0.444979\pi$
$840$	−253.700	−8.75347
$841$	47.5964	1.64125
$842$	−20.2188	−0.696786
$843$	56.5940	1.94920
$844$	−6.02424	−0.207363
$845$	101.144	3.47945
$846$	1.04673	0.0359873
$847$	−3.56425	−0.122469
$848$	58.9122	2.02305
$849$	15.2608	0.523749
$850$	27.2266	0.933865
$851$	−80.6838	−2.76580
$852$	121.286	4.15517
$853$	−30.8556	−1.05648	−0.528238	−	0.849096i	$-0.677147\pi$
$853$	−30.8556	−1.05648	−0.528238	+	0.849096i	$0.677147\pi$
$854$	26.1265	0.894031
$855$	−2.49661	−0.0853821
$856$	−3.61745	−0.123642
$857$	0.727408	0.0248478	0.0124239	−	0.999923i	$-0.496045\pi$
$857$	0.727408	0.0248478	0.0124239	+	0.999923i	$0.496045\pi$
$858$	−31.3866	−1.07152
$859$	42.2178	1.44045	0.720226	−	0.693740i	$-0.244038\pi$
$859$	42.2178	1.44045	0.720226	+	0.693740i	$0.244038\pi$
$860$	−21.9110	−0.747159
$861$	−7.16617	−0.244222
$862$	89.4602	3.04703
$863$	−40.9279	−1.39320	−0.696602	−	0.717458i	$-0.745306\pi$
$863$	−40.9279	−1.39320	−0.696602	+	0.717458i	$0.745306\pi$
$864$	−132.156	−4.49604
$865$	42.4700	1.44402
$866$	35.1762	1.19534
$867$	−1.80573	−0.0613257
$868$	−51.1459	−1.73600
$869$	12.4217	0.421377
$870$	−168.717	−5.72006
$871$	−13.0902	−0.443545
$872$	38.7051	1.31072
$873$	−0.559595	−0.0189394
$874$	61.8346	2.09159
$875$	−66.0837	−2.23404
$876$	−98.3844	−3.32410
$877$	10.2566	0.346341	0.173171	−	0.984892i	$-0.444599\pi$
$877$	10.2566	0.346341	0.173171	+	0.984892i	$0.444599\pi$
$878$	37.3274	1.25974
$879$	−36.7870	−1.24079
$880$	−65.5047	−2.20816
$881$	−36.5810	−1.23245	−0.616223	−	0.787572i	$-0.711338\pi$
$881$	−36.5810	−1.23245	−0.616223	+	0.787572i	$0.711338\pi$
$882$	−4.12348	−0.138845
$883$	9.73356	0.327560	0.163780	−	0.986497i	$-0.447631\pi$
$883$	9.73356	0.327560	0.163780	+	0.986497i	$0.447631\pi$
$884$	−35.6740	−1.19985
$885$	55.6706	1.87135
$886$	58.1620	1.95399
$887$	0.438405	0.0147202	0.00736010	−	0.999973i	$-0.497657\pi$
$887$	0.438405	0.0147202	0.00736010	+	0.999973i	$0.497657\pi$
$888$	−166.520	−5.58806
$889$	−0.747238	−0.0250616
$890$	−29.0217	−0.972810
$891$	9.71402	0.325432
$892$	126.126	4.22302
$893$	3.60290	0.120567
$894$	−10.3794	−0.347138
$895$	−6.31485	−0.211082
$896$	205.603	6.86870
$897$	−101.394	−3.38544
$898$	−11.8550	−0.395606
$899$	−22.0627	−0.735833
$900$	14.5652	0.485507
$901$	−3.46185	−0.115331
$902$	−3.08812	−0.102823
$903$	−6.43607	−0.214179
$904$	145.169	4.82825
$905$	39.1659	1.30192
$906$	11.2818	0.374813
$907$	−1.62733	−0.0540348	−0.0270174	−	0.999635i	$-0.508601\pi$
$907$	−1.62733	−0.0540348	−0.0270174	+	0.999635i	$0.508601\pi$
$908$	23.3333	0.774343
$909$	3.79161	0.125760
$910$	238.472	7.90526
$911$	−49.4466	−1.63824	−0.819120	−	0.573622i	$-0.805538\pi$
$911$	−49.4466	−1.63824	−0.819120	+	0.573622i	$0.805538\pi$
$912$	76.4644	2.53199
$913$	−2.23519	−0.0739740
$914$	−107.795	−3.56554
$915$	−18.3702	−0.607300
$916$	57.8355	1.91094
$917$	55.5791	1.83538
$918$	13.7191	0.452799
$919$	38.8636	1.28199	0.640995	−	0.767545i	$-0.278522\pi$
$919$	38.8636	1.28199	0.640995	+	0.767545i	$0.278522\pi$
$920$	−353.177	−11.6439
$921$	20.4574	0.674095
$922$	8.44070	0.277980
$923$	−73.9494	−2.43408
$924$	−36.6360	−1.20523
$925$	−88.4012	−2.90661
$926$	−98.2572	−3.22893
$927$	1.56512	0.0514053
$928$	233.826	7.67570
$929$	−11.7373	−0.385087	−0.192544	−	0.981288i	$-0.561674\pi$
$929$	−11.7373	−0.385087	−0.192544	+	0.981288i	$0.561674\pi$
$930$	48.5972	1.59356
$931$	−14.1933	−0.465166
$932$	156.568	5.12855
$933$	43.5064	1.42434
$934$	−51.9825	−1.70092
$935$	3.84925	0.125884
$936$	−16.7283	−0.546781
$937$	53.6331	1.75212	0.876059	−	0.482204i	$-0.160164\pi$
$937$	53.6331	1.75212	0.876059	+	0.482204i	$0.160164\pi$
$938$	−20.6480	−0.674182
$939$	26.6905	0.871010
$940$	−31.7252	−1.03476
$941$	1.32820	0.0432982	0.0216491	−	0.999766i	$-0.493108\pi$
$941$	1.32820	0.0432982	0.0216491	+	0.999766i	$0.493108\pi$
$942$	−7.87528	−0.256591
$943$	−9.97608	−0.324866
$944$	−136.300	−4.43617
$945$	−67.8647	−2.20764
$946$	−2.77350	−0.0901742
$947$	−15.8497	−0.515046	−0.257523	−	0.966272i	$-0.582906\pi$
$947$	−15.8497	−0.515046	−0.257523	+	0.966272i	$0.582906\pi$
$948$	127.679	4.14682
$949$	59.9863	1.94724
$950$	67.7491	2.19807
$951$	22.7113	0.736466
$952$	−36.4999	−1.18297
$953$	−15.3562	−0.497435	−0.248717	−	0.968576i	$-0.580009\pi$
$953$	−15.3562	−0.497435	−0.248717	+	0.968576i	$0.580009\pi$
$954$	−2.50265	−0.0810263
$955$	−37.3233	−1.20775
$956$	160.600	5.19418
$957$	−15.8036	−0.510858
$958$	−90.3791	−2.92002
$959$	−52.1960	−1.68550
$960$	−278.476	−8.98777
$961$	−24.6451	−0.795003
$962$	156.525	5.04658
$963$	0.0920754	0.00296709
$964$	8.13155	0.261900
$965$	−23.3815	−0.752677
$966$	−159.935	−5.14582
$967$	51.0271	1.64092	0.820460	−	0.571704i	$-0.193717\pi$
$967$	51.0271	1.64092	0.820460	+	0.571704i	$0.193717\pi$
$968$	−10.2405	−0.329143
$969$	−4.49327	−0.144345
$970$	22.9199	0.735915
$971$	−19.5280	−0.626682	−0.313341	−	0.949641i	$-0.601448\pi$
$971$	−19.5280	−0.626682	−0.313341	+	0.949641i	$0.601448\pi$
$972$	15.3768	0.493211
$973$	32.6736	1.04747
$974$	47.4624	1.52079
$975$	−111.092	−3.55779
$976$	44.9761	1.43965
$977$	−16.5647	−0.529952	−0.264976	−	0.964255i	$-0.585364\pi$
$977$	−16.5647	−0.529952	−0.264976	+	0.964255i	$0.585364\pi$
$978$	−62.9940	−2.01433
$979$	−2.71844	−0.0868817
$980$	124.978	3.99229
$981$	−0.985166	−0.0314539
$982$	−103.374	−3.29879
$983$	−10.5875	−0.337690	−0.168845	−	0.985643i	$-0.554004\pi$
$983$	−10.5875	−0.337690	−0.168845	+	0.985643i	$0.554004\pi$
$984$	−20.5893	−0.656362
$985$	18.2818	0.582506
$986$	−24.2735	−0.773025
$987$	−9.31887	−0.296623
$988$	−88.7690	−2.82412
$989$	−8.95971	−0.284902
$990$	2.78271	0.0884403
$991$	30.7791	0.977731	0.488866	−	0.872359i	$-0.337411\pi$
$991$	30.7791	0.977731	0.488866	+	0.872359i	$0.337411\pi$
$992$	−67.3508	−2.13839
$993$	−58.3070	−1.85032
$994$	−116.645	−3.69976
$995$	−17.2206	−0.545931
$996$	−22.9749	−0.727987
$997$	18.3732	0.581886	0.290943	−	0.956740i	$-0.406031\pi$
$997$	18.3732	0.581886	0.290943	+	0.956740i	$0.406031\pi$
$998$	−18.6773	−0.591219
$999$	−44.5442	−1.40932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.2	✓	74

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

\(f(q)\)	\(=\)	\(q-2.77350 q^{2} -1.80573 q^{3} +5.69228 q^{4} +3.84925 q^{5} +5.00818 q^{6} -3.56425 q^{7} -10.2405 q^{8} +0.260654 q^{9} +O(q^{10})\)	\(q-2.77350 q^{2} -1.80573 q^{3} +5.69228 q^{4} +3.84925 q^{5} +5.00818 q^{6} -3.56425 q^{7} -10.2405 q^{8} +0.260654 q^{9} -10.6759 q^{10} -1.00000 q^{11} -10.2787 q^{12} +6.26707 q^{13} +9.88545 q^{14} -6.95069 q^{15} +17.0175 q^{16} -1.00000 q^{17} -0.722923 q^{18} -2.48834 q^{19} +21.9110 q^{20} +6.43607 q^{21} +2.77350 q^{22} +8.95971 q^{23} +18.4916 q^{24} +9.81671 q^{25} -17.3817 q^{26} +4.94651 q^{27} -20.2888 q^{28} -8.75194 q^{29} +19.2777 q^{30} +2.52090 q^{31} -26.7170 q^{32} +1.80573 q^{33} +2.77350 q^{34} -13.7197 q^{35} +1.48372 q^{36} -9.00518 q^{37} +6.90141 q^{38} -11.3166 q^{39} -39.4184 q^{40} -1.11344 q^{41} -17.8504 q^{42} -1.00000 q^{43} -5.69228 q^{44} +1.00332 q^{45} -24.8497 q^{46} -1.44791 q^{47} -30.7290 q^{48} +5.70391 q^{49} -27.2266 q^{50} +1.80573 q^{51} +35.6740 q^{52} +3.46185 q^{53} -13.7191 q^{54} -3.84925 q^{55} +36.4999 q^{56} +4.49327 q^{57} +24.2735 q^{58} -8.00936 q^{59} -39.5653 q^{60} +2.64293 q^{61} -6.99170 q^{62} -0.929036 q^{63} +40.0645 q^{64} +24.1235 q^{65} -5.00818 q^{66} -2.08873 q^{67} -5.69228 q^{68} -16.1788 q^{69} +38.0515 q^{70} -11.7997 q^{71} -2.66924 q^{72} +9.57166 q^{73} +24.9758 q^{74} -17.7263 q^{75} -14.1644 q^{76} +3.56425 q^{77} +31.3866 q^{78} -12.4217 q^{79} +65.5047 q^{80} -9.71402 q^{81} +3.08812 q^{82} +2.23519 q^{83} +36.6360 q^{84} -3.84925 q^{85} +2.77350 q^{86} +15.8036 q^{87} +10.2405 q^{88} +2.71844 q^{89} -2.78271 q^{90} -22.3374 q^{91} +51.0012 q^{92} -4.55205 q^{93} +4.01578 q^{94} -9.57824 q^{95} +48.2436 q^{96} -2.14689 q^{97} -15.8198 q^{98} -0.260654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 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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