LMFDB - Embedded newform 8041.2.a.c.1.16

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:	$60$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-1.50893 q^{2} -3.04602 q^{3} +0.276872 q^{4} -1.87360 q^{5} +4.59624 q^{6} -2.31151 q^{7} +2.60008 q^{8} +6.27825 q^{9} +O(q^{10})$	\(q-1.50893 q^{2} -3.04602 q^{3} +0.276872 q^{4} -1.87360 q^{5} +4.59624 q^{6} -2.31151 q^{7} +2.60008 q^{8} +6.27825 q^{9} +2.82713 q^{10} +1.00000 q^{11} -0.843360 q^{12} +3.18686 q^{13} +3.48790 q^{14} +5.70702 q^{15} -4.47709 q^{16} +1.00000 q^{17} -9.47345 q^{18} -3.80255 q^{19} -0.518748 q^{20} +7.04090 q^{21} -1.50893 q^{22} +9.20981 q^{23} -7.91990 q^{24} -1.48963 q^{25} -4.80875 q^{26} -9.98563 q^{27} -0.639992 q^{28} +2.20319 q^{29} -8.61150 q^{30} +1.51074 q^{31} +1.55545 q^{32} -3.04602 q^{33} -1.50893 q^{34} +4.33083 q^{35} +1.73827 q^{36} -9.13923 q^{37} +5.73778 q^{38} -9.70725 q^{39} -4.87151 q^{40} +3.36267 q^{41} -10.6242 q^{42} -1.00000 q^{43} +0.276872 q^{44} -11.7629 q^{45} -13.8970 q^{46} -6.24097 q^{47} +13.6373 q^{48} -1.65694 q^{49} +2.24775 q^{50} -3.04602 q^{51} +0.882354 q^{52} -4.56790 q^{53} +15.0676 q^{54} -1.87360 q^{55} -6.01010 q^{56} +11.5826 q^{57} -3.32446 q^{58} -1.39891 q^{59} +1.58012 q^{60} -0.00163327 q^{61} -2.27960 q^{62} -14.5122 q^{63} +6.60710 q^{64} -5.97090 q^{65} +4.59624 q^{66} +12.2495 q^{67} +0.276872 q^{68} -28.0533 q^{69} -6.53493 q^{70} +2.29627 q^{71} +16.3240 q^{72} -5.50244 q^{73} +13.7905 q^{74} +4.53744 q^{75} -1.05282 q^{76} -2.31151 q^{77} +14.6476 q^{78} -17.2429 q^{79} +8.38826 q^{80} +11.5817 q^{81} -5.07404 q^{82} -0.918687 q^{83} +1.94943 q^{84} -1.87360 q^{85} +1.50893 q^{86} -6.71097 q^{87} +2.60008 q^{88} +15.0269 q^{89} +17.7494 q^{90} -7.36645 q^{91} +2.54994 q^{92} -4.60175 q^{93} +9.41720 q^{94} +7.12445 q^{95} -4.73795 q^{96} +1.82615 q^{97} +2.50021 q^{98} +6.27825 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) $ 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.50893	−1.06698	−0.533488	−	0.845808i	$-0.679119\pi$
$2$	−1.50893	−1.06698	−0.533488	+	0.845808i	$0.679119\pi$
$3$	−3.04602	−1.75862	−0.879311	−	0.476248i	$-0.841996\pi$
$3$	−3.04602	−1.75862	−0.879311	+	0.476248i	$0.841996\pi$
$4$	0.276872	0.138436
$5$	−1.87360	−0.837899	−0.418949	−	0.908010i	$-0.637602\pi$
$5$	−1.87360	−0.837899	−0.418949	+	0.908010i	$0.637602\pi$
$6$	4.59624	1.87641
$7$	−2.31151	−0.873667	−0.436833	−	0.899542i	$-0.643900\pi$
$7$	−2.31151	−0.873667	−0.436833	+	0.899542i	$0.643900\pi$
$8$	2.60008	0.919267
$9$	6.27825	2.09275
$10$	2.82713	0.894017
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.843360	−0.243457
$13$	3.18686	0.883876	0.441938	−	0.897045i	$-0.354291\pi$
$13$	3.18686	0.883876	0.441938	+	0.897045i	$0.354291\pi$
$14$	3.48790	0.932181
$15$	5.70702	1.47355
$16$	−4.47709	−1.11927
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−9.47345	−2.23291
$19$	−3.80255	−0.872365	−0.436182	−	0.899858i	$-0.643670\pi$
$19$	−3.80255	−0.872365	−0.436182	+	0.899858i	$0.643670\pi$
$20$	−0.518748	−0.115996
$21$	7.04090	1.53645
$22$	−1.50893	−0.321705
$23$	9.20981	1.92038	0.960189	−	0.279352i	$-0.0901196\pi$
$23$	9.20981	1.92038	0.960189	+	0.279352i	$0.0901196\pi$
$24$	−7.91990	−1.61664
$25$	−1.48963	−0.297926
$26$	−4.80875	−0.943074
$27$	−9.98563	−1.92173
$28$	−0.639992	−0.120947
$29$	2.20319	0.409122	0.204561	−	0.978854i	$-0.434423\pi$
$29$	2.20319	0.409122	0.204561	+	0.978854i	$0.434423\pi$
$30$	−8.61150	−1.57224
$31$	1.51074	0.271337	0.135668	−	0.990754i	$-0.456682\pi$
$31$	1.51074	0.271337	0.135668	+	0.990754i	$0.456682\pi$
$32$	1.55545	0.274968
$33$	−3.04602	−0.530244
$34$	−1.50893	−0.258780
$35$	4.33083	0.732044
$36$	1.73827	0.289712
$37$	−9.13923	−1.50248	−0.751240	−	0.660029i	$-0.770544\pi$
$37$	−9.13923	−1.50248	−0.751240	+	0.660029i	$0.770544\pi$
$38$	5.73778	0.930791
$39$	−9.70725	−1.55440
$40$	−4.87151	−0.770253
$41$	3.36267	0.525161	0.262580	−	0.964910i	$-0.415427\pi$
$41$	3.36267	0.525161	0.262580	+	0.964910i	$0.415427\pi$
$42$	−10.6242	−1.63935
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.276872	0.0417401
$45$	−11.7629	−1.75351
$46$	−13.8970	−2.04900
$47$	−6.24097	−0.910339	−0.455170	−	0.890405i	$-0.650421\pi$
$47$	−6.24097	−0.910339	−0.455170	+	0.890405i	$0.650421\pi$
$48$	13.6373	1.96838
$49$	−1.65694	−0.236706
$50$	2.24775	0.317879
$51$	−3.04602	−0.426528
$52$	0.882354	0.122360
$53$	−4.56790	−0.627449	−0.313724	−	0.949514i	$-0.601577\pi$
$53$	−4.56790	−0.627449	−0.313724	+	0.949514i	$0.601577\pi$
$54$	15.0676	2.05044
$55$	−1.87360	−0.252636
$56$	−6.01010	−0.803133
$57$	11.5826	1.53416
$58$	−3.32446	−0.436523
$59$	−1.39891	−0.182122	−0.0910610	−	0.995845i	$-0.529026\pi$
$59$	−1.39891	−0.182122	−0.0910610	+	0.995845i	$0.529026\pi$
$60$	1.58012	0.203992
$61$	−0.00163327	−0.000209118 0	−0.000104559	−	1.00000i	$-0.500033\pi$
$61$	−0.00163327	−0.000209118 0	−0.000104559		1.00000i	$0.500033\pi$
$62$	−2.27960	−0.289510
$63$	−14.5122	−1.82837
$64$	6.60710	0.825888
$65$	−5.97090	−0.740599
$66$	4.59624	0.565758
$67$	12.2495	1.49651	0.748256	−	0.663410i	$-0.230891\pi$
$67$	12.2495	1.49651	0.748256	+	0.663410i	$0.230891\pi$
$68$	0.276872	0.0335757
$69$	−28.0533	−3.37722
$70$	−6.53493	−0.781073
$71$	2.29627	0.272517	0.136258	−	0.990673i	$-0.456492\pi$
$71$	2.29627	0.272517	0.136258	+	0.990673i	$0.456492\pi$
$72$	16.3240	1.92380
$73$	−5.50244	−0.644012	−0.322006	−	0.946738i	$-0.604357\pi$
$73$	−5.50244	−0.644012	−0.322006	+	0.946738i	$0.604357\pi$
$74$	13.7905	1.60311
$75$	4.53744	0.523939
$76$	−1.05282	−0.120767
$77$	−2.31151	−0.263421
$78$	14.6476	1.65851
$79$	−17.2429	−1.93998	−0.969990	−	0.243144i	$-0.921821\pi$
$79$	−17.2429	−1.93998	−0.969990	+	0.243144i	$0.921821\pi$
$80$	8.38826	0.937836
$81$	11.5817	1.28685
$82$	−5.07404	−0.560333
$83$	−0.918687	−0.100839	−0.0504195	−	0.998728i	$-0.516056\pi$
$83$	−0.918687	−0.100839	−0.0504195	+	0.998728i	$0.516056\pi$
$84$	1.94943	0.212700
$85$	−1.87360	−0.203220
$86$	1.50893	0.162712
$87$	−6.71097	−0.719492
$88$	2.60008	0.277170
$89$	15.0269	1.59285	0.796424	−	0.604739i	$-0.206722\pi$
$89$	15.0269	1.59285	0.796424	+	0.604739i	$0.206722\pi$
$90$	17.7494	1.87095
$91$	−7.36645	−0.772214
$92$	2.54994	0.265850
$93$	−4.60175	−0.477179
$94$	9.41720	0.971310
$95$	7.12445	0.730953
$96$	−4.73795	−0.483565
$97$	1.82615	0.185417	0.0927087	−	0.995693i	$-0.470447\pi$
$97$	1.82615	0.185417	0.0927087	+	0.995693i	$0.470447\pi$
$98$	2.50021	0.252559
$99$	6.27825	0.630988
$100$	−0.412437	−0.0412437
$101$	−9.94124	−0.989190	−0.494595	−	0.869123i	$-0.664684\pi$
$101$	−9.94124	−0.989190	−0.494595	+	0.869123i	$0.664684\pi$
$102$	4.59624	0.455095
$103$	−13.7206	−1.35193	−0.675963	−	0.736935i	$-0.736272\pi$
$103$	−13.7206	−1.35193	−0.675963	+	0.736935i	$0.736272\pi$
$104$	8.28610	0.812519
$105$	−13.1918	−1.28739
$106$	6.89264	0.669472
$107$	12.1970	1.17913	0.589565	−	0.807721i	$-0.299299\pi$
$107$	12.1970	1.17913	0.589565	+	0.807721i	$0.299299\pi$
$108$	−2.76474	−0.266038
$109$	0.503367	0.0482139	0.0241069	−	0.999709i	$-0.492326\pi$
$109$	0.503367	0.0482139	0.0241069	+	0.999709i	$0.492326\pi$
$110$	2.82713	0.269556
$111$	27.8383	2.64229
$112$	10.3488	0.977871
$113$	−8.45357	−0.795245	−0.397622	−	0.917549i	$-0.630165\pi$
$113$	−8.45357	−0.795245	−0.397622	+	0.917549i	$0.630165\pi$
$114$	−17.4774	−1.63691
$115$	−17.2555	−1.60908
$116$	0.610003	0.0566373
$117$	20.0079	1.84973
$118$	2.11085	0.194320
$119$	−2.31151	−0.211895
$120$	14.8387	1.35458
$121$	1.00000	0.0909091
$122$	0.00246449	0.000223124 0
$123$	−10.2428	−0.923559
$124$	0.418282	0.0375629
$125$	12.1590	1.08753
$126$	21.8979	1.95082
$127$	6.87892	0.610406	0.305203	−	0.952287i	$-0.401276\pi$
$127$	6.87892	0.610406	0.305203	+	0.952287i	$0.401276\pi$
$128$	−13.0806	−1.15617
$129$	3.04602	0.268187
$130$	9.00967	0.790201
$131$	−5.04870	−0.441107	−0.220554	−	0.975375i	$-0.570786\pi$
$131$	−5.04870	−0.441107	−0.220554	+	0.975375i	$0.570786\pi$
$132$	−0.843360	−0.0734050
$133$	8.78961	0.762156
$134$	−18.4836	−1.59674
$135$	18.7091	1.61022
$136$	2.60008	0.222955
$137$	3.33949	0.285312	0.142656	−	0.989772i	$-0.454436\pi$
$137$	3.33949	0.285312	0.142656	+	0.989772i	$0.454436\pi$
$138$	42.3305	3.60341
$139$	16.5005	1.39956	0.699778	−	0.714360i	$-0.253282\pi$
$139$	16.5005	1.39956	0.699778	+	0.714360i	$0.253282\pi$
$140$	1.19909	0.101341
$141$	19.0101	1.60094
$142$	−3.46491	−0.290769
$143$	3.18686	0.266499
$144$	−28.1083	−2.34236
$145$	−4.12790	−0.342803
$146$	8.30280	0.687145
$147$	5.04708	0.416276
$148$	−2.53040	−0.207998
$149$	16.9563	1.38911	0.694557	−	0.719438i	$-0.255600\pi$
$149$	16.9563	1.38911	0.694557	+	0.719438i	$0.255600\pi$
$150$	−6.84669	−0.559030
$151$	−22.1556	−1.80300	−0.901498	−	0.432784i	$-0.857531\pi$
$151$	−22.1556	−1.80300	−0.901498	+	0.432784i	$0.857531\pi$
$152$	−9.88693	−0.801936
$153$	6.27825	0.507567
$154$	3.48790	0.281063
$155$	−2.83052	−0.227353
$156$	−2.68767	−0.215186
$157$	15.9812	1.27544	0.637720	−	0.770268i	$-0.279878\pi$
$157$	15.9812	1.27544	0.637720	+	0.770268i	$0.279878\pi$
$158$	26.0184	2.06991
$159$	13.9139	1.10344
$160$	−2.91429	−0.230395
$161$	−21.2885	−1.67777
$162$	−17.4760	−1.37304
$163$	−5.54331	−0.434186	−0.217093	−	0.976151i	$-0.569657\pi$
$163$	−5.54331	−0.434186	−0.217093	+	0.976151i	$0.569657\pi$
$164$	0.931030	0.0727013
$165$	5.70702	0.444291
$166$	1.38624	0.107593
$167$	6.60044	0.510758	0.255379	−	0.966841i	$-0.417800\pi$
$167$	6.60044	0.510758	0.255379	+	0.966841i	$0.417800\pi$
$168$	18.3069	1.41241
$169$	−2.84391	−0.218762
$170$	2.82713	0.216831
$171$	−23.8734	−1.82564
$172$	−0.276872	−0.0211113
$173$	−1.59452	−0.121229	−0.0606144	−	0.998161i	$-0.519306\pi$
$173$	−1.59452	−0.121229	−0.0606144	+	0.998161i	$0.519306\pi$
$174$	10.1264	0.767680
$175$	3.44329	0.260288
$176$	−4.47709	−0.337473
$177$	4.26110	0.320284
$178$	−22.6746	−1.69953
$179$	−16.3387	−1.22121	−0.610606	−	0.791935i	$-0.709074\pi$
$179$	−16.3387	−1.22121	−0.610606	+	0.791935i	$0.709074\pi$
$180$	−3.25683	−0.242750
$181$	14.3771	1.06864	0.534320	−	0.845282i	$-0.320568\pi$
$181$	14.3771	1.06864	0.534320	+	0.845282i	$0.320568\pi$
$182$	11.1155	0.823933
$183$	0.00497497	0.000367760 0
$184$	23.9462	1.76534
$185$	17.1232	1.25893
$186$	6.94372	0.509138
$187$	1.00000	0.0731272
$188$	−1.72795	−0.126024
$189$	23.0818	1.67896
$190$	−10.7503	−0.779909
$191$	−16.5148	−1.19497	−0.597483	−	0.801881i	$-0.703833\pi$
$191$	−16.5148	−1.19497	−0.597483	+	0.801881i	$0.703833\pi$
$192$	−20.1254	−1.45242
$193$	14.0305	1.00994	0.504970	−	0.863137i	$-0.331503\pi$
$193$	14.0305	1.00994	0.504970	+	0.863137i	$0.331503\pi$
$194$	−2.75553	−0.197836
$195$	18.1875	1.30243
$196$	−0.458762	−0.0327687
$197$	15.4739	1.10247	0.551236	−	0.834349i	$-0.314156\pi$
$197$	15.4739	1.10247	0.551236	+	0.834349i	$0.314156\pi$
$198$	−9.47345	−0.673249
$199$	5.15246	0.365248	0.182624	−	0.983183i	$-0.441541\pi$
$199$	5.15246	0.365248	0.182624	+	0.983183i	$0.441541\pi$
$200$	−3.87316	−0.273873
$201$	−37.3122	−2.63180
$202$	15.0006	1.05544
$203$	−5.09269	−0.357437
$204$	−0.843360	−0.0590470
$205$	−6.30029	−0.440031
$206$	20.7034	1.44247
$207$	57.8215	4.01887
$208$	−14.2679	−0.989298
$209$	−3.80255	−0.263028
$210$	19.9055	1.37361
$211$	7.04899	0.485272	0.242636	−	0.970117i	$-0.421988\pi$
$211$	7.04899	0.485272	0.242636	+	0.970117i	$0.421988\pi$
$212$	−1.26472	−0.0868616
$213$	−6.99448	−0.479254
$214$	−18.4044	−1.25810
$215$	1.87360	0.127778
$216$	−25.9634	−1.76659
$217$	−3.49208	−0.237058
$218$	−0.759547	−0.0514430
$219$	16.7606	1.13257
$220$	−0.518748	−0.0349740
$221$	3.18686	0.214372
$222$	−42.0061	−2.81926
$223$	5.66953	0.379660	0.189830	−	0.981817i	$-0.439206\pi$
$223$	5.66953	0.379660	0.189830	+	0.981817i	$0.439206\pi$
$224$	−3.59544	−0.240230
$225$	−9.35227	−0.623484
$226$	12.7559	0.848507
$227$	19.6120	1.30169	0.650847	−	0.759209i	$-0.274414\pi$
$227$	19.6120	1.30169	0.650847	+	0.759209i	$0.274414\pi$
$228$	3.20692	0.212383
$229$	−14.2753	−0.943341	−0.471670	−	0.881775i	$-0.656349\pi$
$229$	−14.2753	−0.943341	−0.471670	+	0.881775i	$0.656349\pi$
$230$	26.0373	1.71685
$231$	7.04090	0.463257
$232$	5.72847	0.376093
$233$	−4.98429	−0.326532	−0.163266	−	0.986582i	$-0.552203\pi$
$233$	−4.98429	−0.326532	−0.163266	+	0.986582i	$0.552203\pi$
$234$	−30.1906	−1.97362
$235$	11.6931	0.762772
$236$	−0.387318	−0.0252123
$237$	52.5223	3.41169
$238$	3.48790	0.226087
$239$	10.9360	0.707388	0.353694	−	0.935361i	$-0.384925\pi$
$239$	10.9360	0.707388	0.353694	+	0.935361i	$0.384925\pi$
$240$	−25.5508	−1.64930
$241$	24.0185	1.54717	0.773585	−	0.633693i	$-0.218462\pi$
$241$	24.0185	1.54717	0.773585	+	0.633693i	$0.218462\pi$
$242$	−1.50893	−0.0969978
$243$	−5.32120	−0.341355
$244$	−0.000452206 0	−2.89495e−5 0
$245$	3.10444	0.198336
$246$	15.4556	0.985415
$247$	−12.1182	−0.771063
$248$	3.92805	0.249431
$249$	2.79834	0.177338
$250$	−18.3470	−1.16037
$251$	3.14996	0.198824	0.0994120	−	0.995046i	$-0.468304\pi$
$251$	3.14996	0.198824	0.0994120	+	0.995046i	$0.468304\pi$
$252$	−4.01803	−0.253112
$253$	9.20981	0.579016
$254$	−10.3798	−0.651288
$255$	5.70702	0.357388
$256$	6.52347	0.407717
$257$	11.9514	0.745507	0.372753	−	0.927930i	$-0.378414\pi$
$257$	11.9514	0.745507	0.372753	+	0.927930i	$0.378414\pi$
$258$	−4.59624	−0.286149
$259$	21.1254	1.31267
$260$	−1.65318	−0.102526
$261$	13.8322	0.856191
$262$	7.61815	0.470651
$263$	−29.8313	−1.83948	−0.919740	−	0.392529i	$-0.871600\pi$
$263$	−29.8313	−1.83948	−0.919740	+	0.392529i	$0.871600\pi$
$264$	−7.91990	−0.487436
$265$	8.55840	0.525738
$266$	−13.2629	−0.813202
$267$	−45.7723	−2.80122
$268$	3.39154	0.207172
$269$	16.2511	0.990847	0.495423	−	0.868652i	$-0.335013\pi$
$269$	16.2511	0.990847	0.495423	+	0.868652i	$0.335013\pi$
$270$	−28.2307	−1.71806
$271$	−9.14881	−0.555751	−0.277875	−	0.960617i	$-0.589630\pi$
$271$	−9.14881	−0.555751	−0.277875	+	0.960617i	$0.589630\pi$
$272$	−4.47709	−0.271463
$273$	22.4384	1.35803
$274$	−5.03907	−0.304421
$275$	−1.48963	−0.0898280
$276$	−7.76718	−0.467529
$277$	−2.34376	−0.140823	−0.0704114	−	0.997518i	$-0.522431\pi$
$277$	−2.34376	−0.140823	−0.0704114	+	0.997518i	$0.522431\pi$
$278$	−24.8982	−1.49329
$279$	9.48481	0.567841
$280$	11.2605	0.672944
$281$	−13.9047	−0.829483	−0.414741	−	0.909939i	$-0.636128\pi$
$281$	−13.9047	−0.829483	−0.414741	+	0.909939i	$0.636128\pi$
$282$	−28.6850	−1.70817
$283$	11.2518	0.668847	0.334424	−	0.942423i	$-0.391458\pi$
$283$	11.2518	0.668847	0.334424	+	0.942423i	$0.391458\pi$
$284$	0.635773	0.0377262
$285$	−21.7012	−1.28547
$286$	−4.80875	−0.284348
$287$	−7.77283	−0.458816
$288$	9.76553	0.575439
$289$	1.00000	0.0588235
$290$	6.22871	0.365762
$291$	−5.56249	−0.326079
$292$	−1.52347	−0.0891546
$293$	17.4032	1.01670	0.508352	−	0.861150i	$-0.330255\pi$
$293$	17.4032	1.01670	0.508352	+	0.861150i	$0.330255\pi$
$294$	−7.61570	−0.444157
$295$	2.62099	0.152600
$296$	−23.7627	−1.38118
$297$	−9.98563	−0.579425
$298$	−25.5859	−1.48215
$299$	29.3504	1.69738
$300$	1.25629	0.0725321
$301$	2.31151	0.133233
$302$	33.4312	1.92375
$303$	30.2812	1.73961
$304$	17.0243	0.976413
$305$	0.00306009	0.000175220 0
$306$	−9.47345	−0.541561
$307$	−3.36515	−0.192059	−0.0960296	−	0.995378i	$-0.530614\pi$
$307$	−3.36515	−0.192059	−0.0960296	+	0.995378i	$0.530614\pi$
$308$	−0.639992	−0.0364669
$309$	41.7931	2.37753
$310$	4.27106	0.242580
$311$	−26.6674	−1.51217	−0.756085	−	0.654473i	$-0.772890\pi$
$311$	−26.6674	−1.51217	−0.756085	+	0.654473i	$0.772890\pi$
$312$	−25.2396	−1.42891
$313$	−3.50650	−0.198199	−0.0990994	−	0.995078i	$-0.531596\pi$
$313$	−3.50650	−0.198199	−0.0990994	+	0.995078i	$0.531596\pi$
$314$	−24.1146	−1.36086
$315$	27.1901	1.53199
$316$	−4.77409	−0.268564
$317$	−6.80358	−0.382127	−0.191063	−	0.981578i	$-0.561194\pi$
$317$	−6.80358	−0.382127	−0.191063	+	0.981578i	$0.561194\pi$
$318$	−20.9951	−1.17735
$319$	2.20319	0.123355
$320$	−12.3791	−0.692010
$321$	−37.1524	−2.07364
$322$	32.1229	1.79014
$323$	−3.80255	−0.211580
$324$	3.20665	0.178147
$325$	−4.74724	−0.263330
$326$	8.36448	0.463266
$327$	−1.53327	−0.0847899
$328$	8.74321	0.482763
$329$	14.4260	0.795333
$330$	−8.61150	−0.474048
$331$	−34.4594	−1.89406	−0.947031	−	0.321143i	$-0.895933\pi$
$331$	−34.4594	−1.89406	−0.947031	+	0.321143i	$0.895933\pi$
$332$	−0.254359	−0.0139598
$333$	−57.3784	−3.14432
$334$	−9.95961	−0.544966
$335$	−22.9506	−1.25393
$336$	−31.5227	−1.71970
$337$	−9.69226	−0.527971	−0.263985	−	0.964527i	$-0.585037\pi$
$337$	−9.69226	−0.527971	−0.263985	+	0.964527i	$0.585037\pi$
$338$	4.29127	0.233414
$339$	25.7498	1.39853
$340$	−0.518748	−0.0281330
$341$	1.51074	0.0818112
$342$	36.0233	1.94791
$343$	20.0106	1.08047
$344$	−2.60008	−0.140187
$345$	52.5606	2.82977
$346$	2.40601	0.129348
$347$	−13.1959	−0.708393	−0.354196	−	0.935171i	$-0.615246\pi$
$347$	−13.1959	−0.708393	−0.354196	+	0.935171i	$0.615246\pi$
$348$	−1.85808	−0.0996037
$349$	−14.4977	−0.776041	−0.388021	−	0.921651i	$-0.626841\pi$
$349$	−14.4977	−0.776041	−0.388021	+	0.921651i	$0.626841\pi$
$350$	−5.19568	−0.277721
$351$	−31.8228	−1.69858
$352$	1.55545	0.0829059
$353$	34.9011	1.85760	0.928799	−	0.370583i	$-0.120842\pi$
$353$	34.9011	1.85760	0.928799	+	0.370583i	$0.120842\pi$
$354$	−6.42970	−0.341735
$355$	−4.30228	−0.228341
$356$	4.16053	0.220508
$357$	7.04090	0.372644
$358$	24.6540	1.30300
$359$	−15.2090	−0.802702	−0.401351	−	0.915924i	$-0.631459\pi$
$359$	−15.2090	−0.802702	−0.401351	+	0.915924i	$0.631459\pi$
$360$	−30.5845	−1.61195
$361$	−4.54062	−0.238980
$362$	−21.6940	−1.14021
$363$	−3.04602	−0.159875
$364$	−2.03957	−0.106902
$365$	10.3094	0.539617
$366$	−0.00750688	−0.000392391 0
$367$	21.6966	1.13255	0.566277	−	0.824215i	$-0.308383\pi$
$367$	21.6966	1.13255	0.566277	+	0.824215i	$0.308383\pi$
$368$	−41.2331	−2.14942
$369$	21.1117	1.09903
$370$	−25.8378	−1.34324
$371$	10.5587	0.548181
$372$	−1.27410	−0.0660589
$373$	20.3324	1.05277	0.526387	−	0.850245i	$-0.323546\pi$
$373$	20.3324	1.05277	0.526387	+	0.850245i	$0.323546\pi$
$374$	−1.50893	−0.0780250
$375$	−37.0365	−1.91255
$376$	−16.2270	−0.836845
$377$	7.02127	0.361614
$378$	−34.8289	−1.79140
$379$	−22.3996	−1.15059	−0.575294	−	0.817947i	$-0.695112\pi$
$379$	−22.3996	−1.15059	−0.575294	+	0.817947i	$0.695112\pi$
$380$	1.97256	0.101190
$381$	−20.9534	−1.07347
$382$	24.9196	1.27500
$383$	−12.5728	−0.642442	−0.321221	−	0.947004i	$-0.604093\pi$
$383$	−12.5728	−0.642442	−0.321221	+	0.947004i	$0.604093\pi$
$384$	39.8437	2.03327
$385$	4.33083	0.220720
$386$	−21.1711	−1.07758
$387$	−6.27825	−0.319141
$388$	0.505610	0.0256685
$389$	13.8306	0.701238	0.350619	−	0.936518i	$-0.385971\pi$
$389$	13.8306	0.701238	0.350619	+	0.936518i	$0.385971\pi$
$390$	−27.4437	−1.38966
$391$	9.20981	0.465760
$392$	−4.30818	−0.217596
$393$	15.3785	0.775741
$394$	−23.3491	−1.17631
$395$	32.3063	1.62551
$396$	1.73827	0.0873516
$397$	34.9455	1.75386	0.876932	−	0.480614i	$-0.159586\pi$
$397$	34.9455	1.75386	0.876932	+	0.480614i	$0.159586\pi$
$398$	−7.77471	−0.389711
$399$	−26.7734	−1.34034
$400$	6.66920	0.333460
$401$	−7.52933	−0.375997	−0.187999	−	0.982169i	$-0.560200\pi$
$401$	−7.52933	−0.375997	−0.187999	+	0.982169i	$0.560200\pi$
$402$	56.3015	2.80806
$403$	4.81452	0.239828
$404$	−2.75246	−0.136940
$405$	−21.6994	−1.07825
$406$	7.68452	0.381376
$407$	−9.13923	−0.453015
$408$	−7.91990	−0.392094
$409$	23.7151	1.17263	0.586317	−	0.810082i	$-0.300577\pi$
$409$	23.7151	1.17263	0.586317	+	0.810082i	$0.300577\pi$
$410$	9.50670	0.469503
$411$	−10.1722	−0.501756
$412$	−3.79884	−0.187156
$413$	3.23358	0.159114
$414$	−87.2486	−4.28804
$415$	1.72125	0.0844929
$416$	4.95701	0.243038
$417$	−50.2610	−2.46129
$418$	5.73778	0.280644
$419$	−24.1542	−1.18001	−0.590005	−	0.807400i	$-0.700874\pi$
$419$	−24.1542	−1.18001	−0.590005	+	0.807400i	$0.700874\pi$
$420$	−3.65245	−0.178221
$421$	14.4652	0.704992	0.352496	−	0.935813i	$-0.385333\pi$
$421$	14.4652	0.704992	0.352496	+	0.935813i	$0.385333\pi$
$422$	−10.6364	−0.517774
$423$	−39.1824	−1.90511
$424$	−11.8769	−0.576793
$425$	−1.48963	−0.0722576
$426$	10.5542	0.511352
$427$	0.00377530	0.000182700 0
$428$	3.37702	0.163234
$429$	−9.70725	−0.468671
$430$	−2.82713	−0.136336
$431$	−32.3968	−1.56050	−0.780248	−	0.625470i	$-0.784907\pi$
$431$	−32.3968	−1.56050	−0.780248	+	0.625470i	$0.784907\pi$
$432$	44.7065	2.15094
$433$	−29.1170	−1.39928	−0.699638	−	0.714497i	$-0.746655\pi$
$433$	−29.1170	−1.39928	−0.699638	+	0.714497i	$0.746655\pi$
$434$	5.26931	0.252935
$435$	12.5737	0.602861
$436$	0.139369	0.00667454
$437$	−35.0207	−1.67527
$438$	−25.2905	−1.20843
$439$	−5.98486	−0.285642	−0.142821	−	0.989749i	$-0.545617\pi$
$439$	−5.98486	−0.285642	−0.142821	+	0.989749i	$0.545617\pi$
$440$	−4.87151	−0.232240
$441$	−10.4027	−0.495367
$442$	−4.80875	−0.228729
$443$	25.9213	1.23156	0.615779	−	0.787919i	$-0.288841\pi$
$443$	25.9213	1.23156	0.615779	+	0.787919i	$0.288841\pi$
$444$	7.70766	0.365789
$445$	−28.1544	−1.33465
$446$	−8.55493	−0.405088
$447$	−51.6493	−2.44293
$448$	−15.2724	−0.721551
$449$	−11.1977	−0.528453	−0.264227	−	0.964461i	$-0.585117\pi$
$449$	−11.1977	−0.528453	−0.264227	+	0.964461i	$0.585117\pi$
$450$	14.1119	0.665242
$451$	3.36267	0.158342
$452$	−2.34056	−0.110091
$453$	67.4864	3.17079
$454$	−29.5932	−1.38888
$455$	13.8018	0.647037
$456$	30.1158	1.41030
$457$	−27.6572	−1.29375	−0.646875	−	0.762596i	$-0.723925\pi$
$457$	−27.6572	−1.29375	−0.646875	+	0.762596i	$0.723925\pi$
$458$	21.5405	1.00652
$459$	−9.98563	−0.466089
$460$	−4.77757	−0.222755
$461$	−6.44602	−0.300221	−0.150111	−	0.988669i	$-0.547963\pi$
$461$	−6.44602	−0.300221	−0.150111	+	0.988669i	$0.547963\pi$
$462$	−10.6242	−0.494284
$463$	−15.4300	−0.717094	−0.358547	−	0.933512i	$-0.616728\pi$
$463$	−15.4300	−0.717094	−0.358547	+	0.933512i	$0.616728\pi$
$464$	−9.86388	−0.457919
$465$	8.62183	0.399828
$466$	7.52095	0.348401
$467$	22.6868	1.04982	0.524911	−	0.851157i	$-0.324099\pi$
$467$	22.6868	1.04982	0.524911	+	0.851157i	$0.324099\pi$
$468$	5.53964	0.256070
$469$	−28.3147	−1.30745
$470$	−17.6440	−0.813859
$471$	−48.6792	−2.24302
$472$	−3.63727	−0.167419
$473$	−1.00000	−0.0459800
$474$	−79.2526	−3.64019
$475$	5.66439	0.259900
$476$	−0.639992	−0.0293340
$477$	−28.6784	−1.31309
$478$	−16.5016	−0.754765
$479$	−1.84016	−0.0840792	−0.0420396	−	0.999116i	$-0.513386\pi$
$479$	−1.84016	−0.0840792	−0.0420396	+	0.999116i	$0.513386\pi$
$480$	8.87701	0.405178
$481$	−29.1255	−1.32801
$482$	−36.2423	−1.65079
$483$	64.8453	2.95056
$484$	0.276872	0.0125851
$485$	−3.42147	−0.155361
$486$	8.02932	0.364217
$487$	30.6348	1.38819	0.694097	−	0.719881i	$-0.255804\pi$
$487$	30.6348	1.38819	0.694097	+	0.719881i	$0.255804\pi$
$488$	−0.00424662	−0.000192236 0
$489$	16.8851	0.763569
$490$	−4.68439	−0.211619
$491$	−31.3251	−1.41368	−0.706840	−	0.707374i	$-0.749880\pi$
$491$	−31.3251	−1.41368	−0.706840	+	0.707374i	$0.749880\pi$
$492$	−2.83594	−0.127854
$493$	2.20319	0.0992267
$494$	18.2855	0.822705
$495$	−11.7629	−0.528704
$496$	−6.76371	−0.303700
$497$	−5.30783	−0.238089
$498$	−4.22250	−0.189215
$499$	35.1124	1.57184	0.785922	−	0.618325i	$-0.212189\pi$
$499$	35.1124	1.57184	0.785922	+	0.618325i	$0.212189\pi$
$500$	3.36648	0.150554
$501$	−20.1051	−0.898230
$502$	−4.75308	−0.212140
$503$	−11.6090	−0.517618	−0.258809	−	0.965928i	$-0.583330\pi$
$503$	−11.6090	−0.517618	−0.258809	+	0.965928i	$0.583330\pi$
$504$	−37.7329	−1.68076
$505$	18.6259	0.828841
$506$	−13.8970	−0.617795
$507$	8.66262	0.384720
$508$	1.90458	0.0845023
$509$	31.8542	1.41191	0.705956	−	0.708256i	$-0.250518\pi$
$509$	31.8542	1.41191	0.705956	+	0.708256i	$0.250518\pi$
$510$	−8.61150	−0.381324
$511$	12.7189	0.562652
$512$	16.3177	0.721146
$513$	37.9708	1.67645
$514$	−18.0338	−0.795437
$515$	25.7068	1.13278
$516$	0.843360	0.0371268
$517$	−6.24097	−0.274478
$518$	−31.8767	−1.40058
$519$	4.85693	0.213196
$520$	−15.5248	−0.680808
$521$	14.7512	0.646261	0.323130	−	0.946354i	$-0.395265\pi$
$521$	14.7512	0.646261	0.323130	+	0.946354i	$0.395265\pi$
$522$	−20.8718	−0.913535
$523$	−5.49742	−0.240385	−0.120193	−	0.992751i	$-0.538351\pi$
$523$	−5.49742	−0.240385	−0.120193	+	0.992751i	$0.538351\pi$
$524$	−1.39785	−0.0610652
$525$	−10.4883	−0.457748
$526$	45.0134	1.96268
$527$	1.51074	0.0658089
$528$	13.6373	0.593488
$529$	61.8206	2.68785
$530$	−12.9140	−0.560950
$531$	−8.78268	−0.381136
$532$	2.43360	0.105510
$533$	10.7164	0.464177
$534$	69.0672	2.98883
$535$	−22.8523	−0.987991
$536$	31.8496	1.37569
$537$	49.7680	2.14765
$538$	−24.5218	−1.05721
$539$	−1.65694	−0.0713696
$540$	5.18002	0.222913
$541$	4.21143	0.181063	0.0905317	−	0.995894i	$-0.471143\pi$
$541$	4.21143	0.181063	0.0905317	+	0.995894i	$0.471143\pi$
$542$	13.8049	0.592972
$543$	−43.7929	−1.87934
$544$	1.55545	0.0666895
$545$	−0.943109	−0.0403983
$546$	−33.8579	−1.44899
$547$	−29.9697	−1.28141	−0.640706	−	0.767786i	$-0.721358\pi$
$547$	−29.9697	−1.28141	−0.640706	+	0.767786i	$0.721358\pi$
$548$	0.924614	0.0394976
$549$	−0.0102541	−0.000437632 0
$550$	2.24775	0.0958443
$551$	−8.37774	−0.356904
$552$	−72.9408	−3.10457
$553$	39.8571	1.69490
$554$	3.53657	0.150254
$555$	−52.1578	−2.21398
$556$	4.56854	0.193749
$557$	−5.91521	−0.250635	−0.125318	−	0.992117i	$-0.539995\pi$
$557$	−5.91521	−0.250635	−0.125318	+	0.992117i	$0.539995\pi$
$558$	−14.3119	−0.605872
$559$	−3.18686	−0.134790
$560$	−19.3895	−0.819357
$561$	−3.04602	−0.128603
$562$	20.9812	0.885037
$563$	−16.3099	−0.687379	−0.343689	−	0.939083i	$-0.611677\pi$
$563$	−16.3099	−0.687379	−0.343689	+	0.939083i	$0.611677\pi$
$564$	5.26338	0.221628
$565$	15.8386	0.666335
$566$	−16.9781	−0.713643
$567$	−26.7711	−1.12428
$568$	5.97048	0.250516
$569$	10.3013	0.431853	0.215926	−	0.976410i	$-0.430723\pi$
$569$	10.3013	0.431853	0.215926	+	0.976410i	$0.430723\pi$
$570$	32.7457	1.37156
$571$	1.19205	0.0498858	0.0249429	−	0.999689i	$-0.492060\pi$
$571$	1.19205	0.0498858	0.0249429	+	0.999689i	$0.492060\pi$
$572$	0.882354	0.0368931
$573$	50.3043	2.10149
$574$	11.7287	0.489545
$575$	−13.7192	−0.572130
$576$	41.4810	1.72838
$577$	44.1023	1.83600	0.918002	−	0.396575i	$-0.129801\pi$
$577$	44.1023	1.83600	0.918002	+	0.396575i	$0.129801\pi$
$578$	−1.50893	−0.0627633
$579$	−42.7373	−1.77610
$580$	−1.14290	−0.0474564
$581$	2.12355	0.0880997
$582$	8.39341	0.347918
$583$	−4.56790	−0.189183
$584$	−14.3068	−0.592019
$585$	−37.4868	−1.54989
$586$	−26.2602	−1.08480
$587$	15.7015	0.648070	0.324035	−	0.946045i	$-0.394960\pi$
$587$	15.7015	0.648070	0.324035	+	0.946045i	$0.394960\pi$
$588$	1.39740	0.0576277
$589$	−5.74466	−0.236705
$590$	−3.95489	−0.162820
$591$	−47.1340	−1.93883
$592$	40.9171	1.68168
$593$	−16.6288	−0.682863	−0.341432	−	0.939907i	$-0.610912\pi$
$593$	−16.6288	−0.682863	−0.341432	+	0.939907i	$0.610912\pi$
$594$	15.0676	0.618232
$595$	4.33083	0.177547
$596$	4.69473	0.192304
$597$	−15.6945	−0.642334
$598$	−44.2877	−1.81106
$599$	−48.1967	−1.96926	−0.984632	−	0.174644i	$-0.944122\pi$
$599$	−48.1967	−1.96926	−0.984632	+	0.174644i	$0.944122\pi$
$600$	11.7977	0.481640
$601$	−0.0564790	−0.00230382	−0.00115191	−	0.999999i	$-0.500367\pi$
$601$	−0.0564790	−0.00230382	−0.00115191	+	0.999999i	$0.500367\pi$
$602$	−3.48790	−0.142156
$603$	76.9053	3.13183
$604$	−6.13427	−0.249600
$605$	−1.87360	−0.0761726
$606$	−45.6923	−1.85612
$607$	12.6149	0.512025	0.256012	−	0.966673i	$-0.417591\pi$
$607$	12.6149	0.512025	0.256012	+	0.966673i	$0.417591\pi$
$608$	−5.91469	−0.239872
$609$	15.5124	0.628596
$610$	−0.00461746	−0.000186955 0
$611$	−19.8891	−0.804628
$612$	1.73827	0.0702656
$613$	−25.9134	−1.04663	−0.523317	−	0.852138i	$-0.675306\pi$
$613$	−25.9134	−1.04663	−0.523317	+	0.852138i	$0.675306\pi$
$614$	5.07778	0.204922
$615$	19.1908	0.773849
$616$	−6.01010	−0.242154
$617$	43.3981	1.74714	0.873572	−	0.486695i	$-0.161798\pi$
$617$	43.3981	1.74714	0.873572	+	0.486695i	$0.161798\pi$
$618$	−63.0629	−2.53676
$619$	37.2571	1.49749	0.748745	−	0.662859i	$-0.230657\pi$
$619$	37.2571	1.49749	0.748745	+	0.662859i	$0.230657\pi$
$620$	−0.783693	−0.0314739
$621$	−91.9657	−3.69046
$622$	40.2393	1.61345
$623$	−34.7348	−1.39162
$624$	43.4602	1.73980
$625$	−15.3329	−0.613314
$626$	5.29106	0.211473
$627$	11.5826	0.462566
$628$	4.42476	0.176567
$629$	−9.13923	−0.364405
$630$	−41.0279	−1.63459
$631$	−17.9520	−0.714658	−0.357329	−	0.933979i	$-0.616313\pi$
$631$	−17.9520	−0.714658	−0.357329	+	0.933979i	$0.616313\pi$
$632$	−44.8330	−1.78336
$633$	−21.4714	−0.853411
$634$	10.2661	0.407720
$635$	−12.8883	−0.511458
$636$	3.85238	0.152757
$637$	−5.28045	−0.209219
$638$	−3.32446	−0.131617
$639$	14.4165	0.570310
$640$	24.5077	0.968753
$641$	42.8282	1.69161	0.845806	−	0.533490i	$-0.179120\pi$
$641$	42.8282	1.69161	0.845806	+	0.533490i	$0.179120\pi$
$642$	56.0604	2.21253
$643$	15.5819	0.614490	0.307245	−	0.951630i	$-0.400593\pi$
$643$	15.5819	0.614490	0.307245	+	0.951630i	$0.400593\pi$
$644$	−5.89420	−0.232264
$645$	−5.70702	−0.224714
$646$	5.73778	0.225750
$647$	−5.07479	−0.199511	−0.0997554	−	0.995012i	$-0.531806\pi$
$647$	−5.07479	−0.199511	−0.0997554	+	0.995012i	$0.531806\pi$
$648$	30.1133	1.18296
$649$	−1.39891	−0.0549118
$650$	7.16326	0.280966
$651$	10.6370	0.416896
$652$	−1.53479	−0.0601070
$653$	−43.1711	−1.68942	−0.844708	−	0.535227i	$-0.820226\pi$
$653$	−43.1711	−1.68942	−0.844708	+	0.535227i	$0.820226\pi$
$654$	2.31360	0.0904688
$655$	9.45924	0.369603
$656$	−15.0550	−0.587797
$657$	−34.5457	−1.34776
$658$	−21.7679	−0.848601
$659$	−24.1056	−0.939020	−0.469510	−	0.882927i	$-0.655569\pi$
$659$	−24.1056	−0.939020	−0.469510	+	0.882927i	$0.655569\pi$
$660$	1.58012	0.0615060
$661$	11.7037	0.455222	0.227611	−	0.973752i	$-0.426909\pi$
$661$	11.7037	0.455222	0.227611	+	0.973752i	$0.426909\pi$
$662$	51.9969	2.02092
$663$	−9.70725	−0.376998
$664$	−2.38866	−0.0926980
$665$	−16.4682	−0.638610
$666$	86.5800	3.35491
$667$	20.2910	0.785669
$668$	1.82748	0.0707074
$669$	−17.2695	−0.667678
$670$	34.6309	1.33791
$671$	−0.00163327	−6.30515e−5 0
$672$	10.9518	0.422474
$673$	11.2392	0.433240	0.216620	−	0.976256i	$-0.430497\pi$
$673$	11.2392	0.433240	0.216620	+	0.976256i	$0.430497\pi$
$674$	14.6249	0.563332
$675$	14.8749	0.572534
$676$	−0.787401	−0.0302846
$677$	6.82624	0.262354	0.131177	−	0.991359i	$-0.458124\pi$
$677$	6.82624	0.262354	0.131177	+	0.991359i	$0.458124\pi$
$678$	−38.8546	−1.49220
$679$	−4.22115	−0.161993
$680$	−4.87151	−0.186814
$681$	−59.7386	−2.28919
$682$	−2.27960	−0.0872905
$683$	−37.7535	−1.44460	−0.722300	−	0.691580i	$-0.756915\pi$
$683$	−37.7535	−1.44460	−0.722300	+	0.691580i	$0.756915\pi$
$684$	−6.60988	−0.252735
$685$	−6.25687	−0.239063
$686$	−30.1946	−1.15283
$687$	43.4830	1.65898
$688$	4.47709	0.170687
$689$	−14.5573	−0.554587
$690$	−79.3103	−3.01929
$691$	17.7025	0.673436	0.336718	−	0.941606i	$-0.390683\pi$
$691$	17.7025	0.673436	0.336718	+	0.941606i	$0.390683\pi$
$692$	−0.441478	−0.0167825
$693$	−14.5122	−0.551273
$694$	19.9117	0.755838
$695$	−30.9154	−1.17269
$696$	−17.4491	−0.661405
$697$	3.36267	0.127370
$698$	21.8760	0.828017
$699$	15.1823	0.574246
$700$	0.953351	0.0360333
$701$	49.5336	1.87086	0.935428	−	0.353516i	$-0.115014\pi$
$701$	49.5336	1.87086	0.935428	+	0.353516i	$0.115014\pi$
$702$	48.0184	1.81234
$703$	34.7524	1.31071
$704$	6.60710	0.249015
$705$	−35.6174	−1.34143
$706$	−52.6634	−1.98201
$707$	22.9792	0.864223
$708$	1.17978	0.0443389
$709$	−48.1827	−1.80954	−0.904769	−	0.425902i	$-0.859957\pi$
$709$	−48.1827	−1.80954	−0.904769	+	0.425902i	$0.859957\pi$
$710$	6.49185	0.243635
$711$	−108.255	−4.05990
$712$	39.0711	1.46425
$713$	13.9136	0.521069
$714$	−10.6242	−0.397602
$715$	−5.97090	−0.223299
$716$	−4.52373	−0.169060
$717$	−33.3111	−1.24403
$718$	22.9494	0.856463
$719$	−0.251897	−0.00939416	−0.00469708	−	0.999989i	$-0.501495\pi$
$719$	−0.251897	−0.00939416	−0.00469708	+	0.999989i	$0.501495\pi$
$720$	52.6636	1.96266
$721$	31.7151	1.18113
$722$	6.85148	0.254986
$723$	−73.1610	−2.72089
$724$	3.98062	0.147939
$725$	−3.28194	−0.121888
$726$	4.59624	0.170582
$727$	−42.5409	−1.57776	−0.788878	−	0.614550i	$-0.789338\pi$
$727$	−42.5409	−1.57776	−0.788878	+	0.614550i	$0.789338\pi$
$728$	−19.1534	−0.709871
$729$	−18.5366	−0.686540
$730$	−15.5561	−0.575758
$731$	−1.00000	−0.0369863
$732$	0.00137743	5.09113e−5 0
$733$	0.188760	0.00697200	0.00348600	−	0.999994i	$-0.498890\pi$
$733$	0.188760	0.00697200	0.00348600	+	0.999994i	$0.498890\pi$
$734$	−32.7387	−1.20841
$735$	−9.45621	−0.348797
$736$	14.3254	0.528042
$737$	12.2495	0.451216
$738$	−31.8561	−1.17264
$739$	14.5568	0.535479	0.267739	−	0.963491i	$-0.413723\pi$
$739$	14.5568	0.535479	0.267739	+	0.963491i	$0.413723\pi$
$740$	4.74096	0.174281
$741$	36.9123	1.35601
$742$	−15.9324	−0.584896
$743$	1.97017	0.0722785	0.0361393	−	0.999347i	$-0.488494\pi$
$743$	1.97017	0.0722785	0.0361393	+	0.999347i	$0.488494\pi$
$744$	−11.9649	−0.438655
$745$	−31.7693	−1.16394
$746$	−30.6802	−1.12328
$747$	−5.76775	−0.211031
$748$	0.276872	0.0101235
$749$	−28.1935	−1.03017
$750$	55.8855	2.04065
$751$	−3.95729	−0.144404	−0.0722018	−	0.997390i	$-0.523003\pi$
$751$	−3.95729	−0.144404	−0.0722018	+	0.997390i	$0.523003\pi$
$752$	27.9414	1.01892
$753$	−9.59486	−0.349656
$754$	−10.5946	−0.385833
$755$	41.5106	1.51073
$756$	6.39072	0.232428
$757$	16.6535	0.605282	0.302641	−	0.953105i	$-0.402132\pi$
$757$	16.6535	0.605282	0.302641	+	0.953105i	$0.402132\pi$
$758$	33.7994	1.22765
$759$	−28.0533	−1.01827
$760$	18.5241	0.671941
$761$	−24.3219	−0.881669	−0.440834	−	0.897588i	$-0.645317\pi$
$761$	−24.3219	−0.881669	−0.440834	+	0.897588i	$0.645317\pi$
$762$	31.6172	1.14537
$763$	−1.16354	−0.0421229
$764$	−4.57248	−0.165427
$765$	−11.7629	−0.425289
$766$	18.9715	0.685469
$767$	−4.45812	−0.160973
$768$	−19.8706	−0.717019
$769$	43.9742	1.58575	0.792876	−	0.609383i	$-0.208583\pi$
$769$	43.9742	1.58575	0.792876	+	0.609383i	$0.208583\pi$
$770$	−6.53493	−0.235502
$771$	−36.4042	−1.31106
$772$	3.88467	0.139812
$773$	29.1112	1.04706	0.523528	−	0.852008i	$-0.324615\pi$
$773$	29.1112	1.04706	0.523528	+	0.852008i	$0.324615\pi$
$774$	9.47345	0.340516
$775$	−2.25044	−0.0808383
$776$	4.74813	0.170448
$777$	−64.3484	−2.30849
$778$	−20.8694	−0.748204
$779$	−12.7867	−0.458132
$780$	5.03561	0.180304
$781$	2.29627	0.0821669
$782$	−13.8970	−0.496954
$783$	−22.0002	−0.786225
$784$	7.41827	0.264938
$785$	−29.9424	−1.06869
$786$	−23.2050	−0.827696
$787$	−4.76922	−0.170004	−0.0850022	−	0.996381i	$-0.527090\pi$
$787$	−4.76922	−0.170004	−0.0850022	+	0.996381i	$0.527090\pi$
$788$	4.28431	0.152622
$789$	90.8669	3.23495
$790$	−48.7480	−1.73438
$791$	19.5405	0.694779
$792$	16.3240	0.580047
$793$	−0.00520499	−0.000184835 0
$794$	−52.7303	−1.87133
$795$	−26.0691	−0.924575
$796$	1.42657	0.0505636
$797$	7.20080	0.255065	0.127533	−	0.991834i	$-0.459294\pi$
$797$	7.20080	0.255065	0.127533	+	0.991834i	$0.459294\pi$
$798$	40.3991	1.43011
$799$	−6.24097	−0.220790
$800$	−2.31705	−0.0819200
$801$	94.3427	3.33343
$802$	11.3612	0.401180
$803$	−5.50244	−0.194177
$804$	−10.3307	−0.364336
$805$	39.8861	1.40580
$806$	−7.26478	−0.255891
$807$	−49.5012	−1.74252
$808$	−25.8480	−0.909330
$809$	−18.0486	−0.634556	−0.317278	−	0.948333i	$-0.602769\pi$
$809$	−18.0486	−0.634556	−0.317278	+	0.948333i	$0.602769\pi$
$810$	32.7429	1.15047
$811$	55.0039	1.93145	0.965724	−	0.259571i	$-0.0835812\pi$
$811$	55.0039	1.93145	0.965724	+	0.259571i	$0.0835812\pi$
$812$	−1.41003	−0.0494822
$813$	27.8675	0.977356
$814$	13.7905	0.483356
$815$	10.3859	0.363804
$816$	13.6373	0.477401
$817$	3.80255	0.133034
$818$	−35.7844	−1.25117
$819$	−46.2484	−1.61605
$820$	−1.74438	−0.0609163
$821$	25.9465	0.905539	0.452769	−	0.891628i	$-0.350436\pi$
$821$	25.9465	0.905539	0.452769	+	0.891628i	$0.350436\pi$
$822$	15.3491	0.535362
$823$	−11.5760	−0.403514	−0.201757	−	0.979436i	$-0.564665\pi$
$823$	−11.5760	−0.403514	−0.201757	+	0.979436i	$0.564665\pi$
$824$	−35.6745	−1.24278
$825$	4.53744	0.157973
$826$	−4.87925	−0.169771
$827$	−8.07406	−0.280763	−0.140381	−	0.990098i	$-0.544833\pi$
$827$	−8.07406	−0.280763	−0.140381	+	0.990098i	$0.544833\pi$
$828$	16.0092	0.556357
$829$	4.99605	0.173520	0.0867600	−	0.996229i	$-0.472349\pi$
$829$	4.99605	0.173520	0.0867600	+	0.996229i	$0.472349\pi$
$830$	−2.59725	−0.0901518
$831$	7.13914	0.247654
$832$	21.0559	0.729983
$833$	−1.65694	−0.0574096
$834$	75.8403	2.62614
$835$	−12.3666	−0.427963
$836$	−1.05282	−0.0364126
$837$	−15.0857	−0.521438
$838$	36.4470	1.25904
$839$	12.6671	0.437318	0.218659	−	0.975801i	$-0.429832\pi$
$839$	12.6671	0.437318	0.218659	+	0.975801i	$0.429832\pi$
$840$	−34.2998	−1.18345
$841$	−24.1459	−0.832619
$842$	−21.8270	−0.752209
$843$	42.3539	1.45875
$844$	1.95167	0.0671793
$845$	5.32835	0.183301
$846$	59.1235	2.03271
$847$	−2.31151	−0.0794243
$848$	20.4509	0.702286
$849$	−34.2731	−1.17625
$850$	2.24775	0.0770971
$851$	−84.1706	−2.88533
$852$	−1.93658	−0.0663461
$853$	−30.3164	−1.03801	−0.519007	−	0.854770i	$-0.673698\pi$
$853$	−30.3164	−1.03801	−0.519007	+	0.854770i	$0.673698\pi$
$854$	−0.00569667	−0.000194936 0
$855$	44.7291	1.52970
$856$	31.7132	1.08394
$857$	−55.1040	−1.88232	−0.941159	−	0.337964i	$-0.890262\pi$
$857$	−55.1040	−1.88232	−0.941159	+	0.337964i	$0.890262\pi$
$858$	14.6476	0.500060
$859$	−32.2170	−1.09923	−0.549616	−	0.835418i	$-0.685226\pi$
$859$	−32.2170	−1.09923	−0.549616	+	0.835418i	$0.685226\pi$
$860$	0.518748	0.0176892
$861$	23.6762	0.806883
$862$	48.8845	1.66501
$863$	24.7503	0.842511	0.421256	−	0.906942i	$-0.361589\pi$
$863$	24.7503	0.842511	0.421256	+	0.906942i	$0.361589\pi$
$864$	−15.5322	−0.528415
$865$	2.98748	0.101577
$866$	43.9356	1.49299
$867$	−3.04602	−0.103448
$868$	−0.966862	−0.0328174
$869$	−17.2429	−0.584926
$870$	−18.9728	−0.643238
$871$	39.0374	1.32273
$872$	1.30880	0.0443214
$873$	11.4650	0.388032
$874$	52.8439	1.78747
$875$	−28.1055	−0.950139
$876$	4.64054	0.156789
$877$	14.7512	0.498114	0.249057	−	0.968489i	$-0.419879\pi$
$877$	14.7512	0.498114	0.249057	+	0.968489i	$0.419879\pi$
$878$	9.03073	0.304773
$879$	−53.0104	−1.78800
$880$	8.38826	0.282768
$881$	−30.3053	−1.02101	−0.510505	−	0.859875i	$-0.670542\pi$
$881$	−30.3053	−1.02101	−0.510505	+	0.859875i	$0.670542\pi$
$882$	15.6970	0.528544
$883$	40.3013	1.35625	0.678124	−	0.734948i	$-0.262793\pi$
$883$	40.3013	1.35625	0.678124	+	0.734948i	$0.262793\pi$
$884$	0.882354	0.0296768
$885$	−7.98358	−0.268365
$886$	−39.1135	−1.31404
$887$	−12.3679	−0.415272	−0.207636	−	0.978206i	$-0.566577\pi$
$887$	−12.3679	−0.415272	−0.207636	+	0.978206i	$0.566577\pi$
$888$	72.3818	2.42897
$889$	−15.9007	−0.533291
$890$	42.4830	1.42403
$891$	11.5817	0.388001
$892$	1.56974	0.0525587
$893$	23.7316	0.794148
$894$	77.9352	2.60654
$895$	30.6122	1.02325
$896$	30.2358	1.01011
$897$	−89.4019	−2.98504
$898$	16.8966	0.563847
$899$	3.32845	0.111010
$900$	−2.58938	−0.0863128
$901$	−4.56790	−0.152179
$902$	−5.07404	−0.168947
$903$	−7.04090	−0.234306
$904$	−21.9800	−0.731043
$905$	−26.9369	−0.895413
$906$	−101.832	−3.38315
$907$	1.80184	0.0598291	0.0299145	−	0.999552i	$-0.490476\pi$
$907$	1.80184	0.0598291	0.0299145	+	0.999552i	$0.490476\pi$
$908$	5.43003	0.180202
$909$	−62.4136	−2.07013
$910$	−20.8259	−0.690372
$911$	38.1355	1.26348	0.631742	−	0.775178i	$-0.282340\pi$
$911$	38.1355	1.26348	0.631742	+	0.775178i	$0.282340\pi$
$912$	−51.8565	−1.71714
$913$	−0.918687	−0.0304041
$914$	41.7328	1.38040
$915$	−0.00932109	−0.000308146 0
$916$	−3.95245	−0.130592
$917$	11.6701	0.385381
$918$	15.0676	0.497306
$919$	−44.8499	−1.47946	−0.739731	−	0.672902i	$-0.765047\pi$
$919$	−44.8499	−1.47946	−0.739731	+	0.672902i	$0.765047\pi$
$920$	−44.8656	−1.47918
$921$	10.2503	0.337760
$922$	9.72660	0.320328
$923$	7.31788	0.240871
$924$	1.94943	0.0641315
$925$	13.6141	0.447628
$926$	23.2828	0.765121
$927$	−86.1411	−2.82924
$928$	3.42696	0.112496
$929$	−51.7460	−1.69773	−0.848865	−	0.528609i	$-0.822714\pi$
$929$	−51.7460	−1.69773	−0.848865	+	0.528609i	$0.822714\pi$
$930$	−13.0097	−0.426606
$931$	6.30060	0.206494
$932$	−1.38001	−0.0452038
$933$	81.2295	2.65934
$934$	−34.2329	−1.12013
$935$	−1.87360	−0.0612732
$936$	52.0222	1.70040
$937$	44.8723	1.46591	0.732957	−	0.680275i	$-0.238140\pi$
$937$	44.8723	1.46591	0.732957	+	0.680275i	$0.238140\pi$
$938$	42.7250	1.39502
$939$	10.6809	0.348557
$940$	3.23749	0.105595
$941$	−32.2683	−1.05192	−0.525959	−	0.850510i	$-0.676293\pi$
$941$	−32.2683	−1.05192	−0.525959	+	0.850510i	$0.676293\pi$
$942$	73.4535	2.39324
$943$	30.9695	1.00851
$944$	6.26302	0.203844
$945$	−43.2461	−1.40680
$946$	1.50893	0.0490596
$947$	−1.97096	−0.0640476	−0.0320238	−	0.999487i	$-0.510195\pi$
$947$	−1.97096	−0.0640476	−0.0320238	+	0.999487i	$0.510195\pi$
$948$	14.5420	0.472302
$949$	−17.5355	−0.569227
$950$	−8.54717	−0.277307
$951$	20.7238	0.672017
$952$	−6.01010	−0.194788
$953$	21.2545	0.688500	0.344250	−	0.938878i	$-0.388133\pi$
$953$	21.2545	0.688500	0.344250	+	0.938878i	$0.388133\pi$
$954$	43.2737	1.40104
$955$	30.9420	1.00126
$956$	3.02786	0.0979281
$957$	−6.71097	−0.216935
$958$	2.77668	0.0897104
$959$	−7.71926	−0.249268
$960$	37.7069	1.21698
$961$	−28.7177	−0.926376
$962$	43.9483	1.41695
$963$	76.5759	2.46762
$964$	6.65007	0.214184
$965$	−26.2876	−0.846228
$966$	−97.8471	−3.14818
$967$	56.1170	1.80460	0.902300	−	0.431109i	$-0.141878\pi$
$967$	56.1170	1.80460	0.902300	+	0.431109i	$0.141878\pi$
$968$	2.60008	0.0835698
$969$	11.5826	0.372088
$970$	5.16276	0.165766
$971$	−19.7946	−0.635238	−0.317619	−	0.948218i	$-0.602883\pi$
$971$	−19.7946	−0.635238	−0.317619	+	0.948218i	$0.602883\pi$
$972$	−1.47329	−0.0472559
$973$	−38.1411	−1.22275
$974$	−46.2258	−1.48117
$975$	14.4602	0.463097
$976$	0.00731227	0.000234060 0
$977$	36.9098	1.18085	0.590424	−	0.807093i	$-0.298960\pi$
$977$	36.9098	1.18085	0.590424	+	0.807093i	$0.298960\pi$
$978$	−25.4784	−0.814709
$979$	15.0269	0.480262
$980$	0.859535	0.0274568
$981$	3.16027	0.100900
$982$	47.2673	1.50836
$983$	−18.0779	−0.576596	−0.288298	−	0.957541i	$-0.593089\pi$
$983$	−18.0779	−0.576596	−0.288298	+	0.957541i	$0.593089\pi$
$984$	−26.6320	−0.848998
$985$	−28.9920	−0.923761
$986$	−3.32446	−0.105872
$987$	−43.9420	−1.39869
$988$	−3.35519	−0.106743
$989$	−9.20981	−0.292855
$990$	17.7494	0.564114
$991$	12.8011	0.406641	0.203320	−	0.979112i	$-0.434827\pi$
$991$	12.8011	0.406641	0.203320	+	0.979112i	$0.434827\pi$
$992$	2.34989	0.0746089
$993$	104.964	3.33094
$994$	8.00915	0.254035
$995$	−9.65364	−0.306041
$996$	0.774783	0.0245500
$997$	4.01169	0.127051	0.0635257	−	0.997980i	$-0.479766\pi$
$997$	4.01169	0.127051	0.0635257	+	0.997980i	$0.479766\pi$
$998$	−52.9821	−1.67712
$999$	91.2610	2.88737

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.16	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.16	✓	60	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)

\(f(q)\)	\(=\)	\(q-1.50893 q^{2} -3.04602 q^{3} +0.276872 q^{4} -1.87360 q^{5} +4.59624 q^{6} -2.31151 q^{7} +2.60008 q^{8} +6.27825 q^{9} +O(q^{10})\)	\(q-1.50893 q^{2} -3.04602 q^{3} +0.276872 q^{4} -1.87360 q^{5} +4.59624 q^{6} -2.31151 q^{7} +2.60008 q^{8} +6.27825 q^{9} +2.82713 q^{10} +1.00000 q^{11} -0.843360 q^{12} +3.18686 q^{13} +3.48790 q^{14} +5.70702 q^{15} -4.47709 q^{16} +1.00000 q^{17} -9.47345 q^{18} -3.80255 q^{19} -0.518748 q^{20} +7.04090 q^{21} -1.50893 q^{22} +9.20981 q^{23} -7.91990 q^{24} -1.48963 q^{25} -4.80875 q^{26} -9.98563 q^{27} -0.639992 q^{28} +2.20319 q^{29} -8.61150 q^{30} +1.51074 q^{31} +1.55545 q^{32} -3.04602 q^{33} -1.50893 q^{34} +4.33083 q^{35} +1.73827 q^{36} -9.13923 q^{37} +5.73778 q^{38} -9.70725 q^{39} -4.87151 q^{40} +3.36267 q^{41} -10.6242 q^{42} -1.00000 q^{43} +0.276872 q^{44} -11.7629 q^{45} -13.8970 q^{46} -6.24097 q^{47} +13.6373 q^{48} -1.65694 q^{49} +2.24775 q^{50} -3.04602 q^{51} +0.882354 q^{52} -4.56790 q^{53} +15.0676 q^{54} -1.87360 q^{55} -6.01010 q^{56} +11.5826 q^{57} -3.32446 q^{58} -1.39891 q^{59} +1.58012 q^{60} -0.00163327 q^{61} -2.27960 q^{62} -14.5122 q^{63} +6.60710 q^{64} -5.97090 q^{65} +4.59624 q^{66} +12.2495 q^{67} +0.276872 q^{68} -28.0533 q^{69} -6.53493 q^{70} +2.29627 q^{71} +16.3240 q^{72} -5.50244 q^{73} +13.7905 q^{74} +4.53744 q^{75} -1.05282 q^{76} -2.31151 q^{77} +14.6476 q^{78} -17.2429 q^{79} +8.38826 q^{80} +11.5817 q^{81} -5.07404 q^{82} -0.918687 q^{83} +1.94943 q^{84} -1.87360 q^{85} +1.50893 q^{86} -6.71097 q^{87} +2.60008 q^{88} +15.0269 q^{89} +17.7494 q^{90} -7.36645 q^{91} +2.54994 q^{92} -4.60175 q^{93} +9.41720 q^{94} +7.12445 q^{95} -4.73795 q^{96} +1.82615 q^{97} +2.50021 q^{98} +6.27825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

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