LMFDB - Embedded newform 8021.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62889 q^{2} +1.78605 q^{3} +4.91107 q^{4} +1.43411 q^{5} -4.69533 q^{6} +3.37960 q^{7} -7.65290 q^{8} +0.189969 q^{9} +O(q^{10})$	\(q-2.62889 q^{2} +1.78605 q^{3} +4.91107 q^{4} +1.43411 q^{5} -4.69533 q^{6} +3.37960 q^{7} -7.65290 q^{8} +0.189969 q^{9} -3.77012 q^{10} -5.52570 q^{11} +8.77141 q^{12} -1.00000 q^{13} -8.88461 q^{14} +2.56139 q^{15} +10.2965 q^{16} +1.78723 q^{17} -0.499407 q^{18} -4.83956 q^{19} +7.04301 q^{20} +6.03613 q^{21} +14.5265 q^{22} +6.78917 q^{23} -13.6684 q^{24} -2.94333 q^{25} +2.62889 q^{26} -5.01885 q^{27} +16.5975 q^{28} +4.28243 q^{29} -6.73361 q^{30} -2.78948 q^{31} -11.7626 q^{32} -9.86916 q^{33} -4.69842 q^{34} +4.84672 q^{35} +0.932951 q^{36} -3.33060 q^{37} +12.7227 q^{38} -1.78605 q^{39} -10.9751 q^{40} -6.35161 q^{41} -15.8683 q^{42} -6.32490 q^{43} -27.1371 q^{44} +0.272436 q^{45} -17.8480 q^{46} -0.118260 q^{47} +18.3900 q^{48} +4.42171 q^{49} +7.73770 q^{50} +3.19207 q^{51} -4.91107 q^{52} +8.05377 q^{53} +13.1940 q^{54} -7.92445 q^{55} -25.8638 q^{56} -8.64370 q^{57} -11.2580 q^{58} -5.51332 q^{59} +12.5792 q^{60} +2.96804 q^{61} +7.33323 q^{62} +0.642019 q^{63} +10.3296 q^{64} -1.43411 q^{65} +25.9450 q^{66} -8.30612 q^{67} +8.77719 q^{68} +12.1258 q^{69} -12.7415 q^{70} +8.03937 q^{71} -1.45381 q^{72} +1.88100 q^{73} +8.75580 q^{74} -5.25693 q^{75} -23.7675 q^{76} -18.6747 q^{77} +4.69533 q^{78} +0.564163 q^{79} +14.7663 q^{80} -9.53382 q^{81} +16.6977 q^{82} +12.6678 q^{83} +29.6439 q^{84} +2.56308 q^{85} +16.6275 q^{86} +7.64863 q^{87} +42.2876 q^{88} +13.7745 q^{89} -0.716205 q^{90} -3.37960 q^{91} +33.3421 q^{92} -4.98214 q^{93} +0.310892 q^{94} -6.94046 q^{95} -21.0085 q^{96} -15.1032 q^{97} -11.6242 q^{98} -1.04971 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) $ 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * 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 $

$2$	−2.62889	−1.85891	−0.929454	−	0.368939i	$-0.879721\pi$
$2$	−2.62889	−1.85891	−0.929454	+	0.368939i	$0.879721\pi$
$3$	1.78605	1.03118	0.515588	−	0.856837i	$-0.327574\pi$
$3$	1.78605	1.03118	0.515588	+	0.856837i	$0.327574\pi$
$4$	4.91107	2.45554
$5$	1.43411	0.641353	0.320676	−	0.947189i	$-0.396090\pi$
$5$	1.43411	0.641353	0.320676	+	0.947189i	$0.396090\pi$
$6$	−4.69533	−1.91686
$7$	3.37960	1.27737	0.638685	−	0.769468i	$-0.279479\pi$
$7$	3.37960	1.27737	0.638685	+	0.769468i	$0.279479\pi$
$8$	−7.65290	−2.70571
$9$	0.189969	0.0633229
$10$	−3.77012	−1.19222
$11$	−5.52570	−1.66606	−0.833030	−	0.553227i	$-0.813396\pi$
$11$	−5.52570	−1.66606	−0.833030	+	0.553227i	$0.813396\pi$
$12$	8.77141	2.53209
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−8.88461	−2.37451
$15$	2.56139	0.661347
$16$	10.2965	2.57412
$17$	1.78723	0.433466	0.216733	−	0.976231i	$-0.430460\pi$
$17$	1.78723	0.433466	0.216733	+	0.976231i	$0.430460\pi$
$18$	−0.499407	−0.117711
$19$	−4.83956	−1.11027	−0.555136	−	0.831760i	$-0.687334\pi$
$19$	−4.83956	−1.11027	−0.555136	+	0.831760i	$0.687334\pi$
$20$	7.04301	1.57487
$21$	6.03613	1.31719
$22$	14.5265	3.09705
$23$	6.78917	1.41564	0.707820	−	0.706393i	$-0.249679\pi$
$23$	6.78917	1.41564	0.707820	+	0.706393i	$0.249679\pi$
$24$	−13.6684	−2.79006
$25$	−2.94333	−0.588666
$26$	2.62889	0.515568
$27$	−5.01885	−0.965878
$28$	16.5975	3.13663
$29$	4.28243	0.795227	0.397614	−	0.917553i	$-0.369838\pi$
$29$	4.28243	0.795227	0.397614	+	0.917553i	$0.369838\pi$
$30$	−6.73361	−1.22938
$31$	−2.78948	−0.501005	−0.250502	−	0.968116i	$-0.580596\pi$
$31$	−2.78948	−0.501005	−0.250502	+	0.968116i	$0.580596\pi$
$32$	−11.7626	−2.07935
$33$	−9.86916	−1.71800
$34$	−4.69842	−0.805773
$35$	4.84672	0.819245
$36$	0.932951	0.155492
$37$	−3.33060	−0.547548	−0.273774	−	0.961794i	$-0.588272\pi$
$37$	−3.33060	−0.547548	−0.273774	+	0.961794i	$0.588272\pi$
$38$	12.7227	2.06389
$39$	−1.78605	−0.285997
$40$	−10.9751	−1.73531
$41$	−6.35161	−0.991955	−0.495978	−	0.868335i	$-0.665190\pi$
$41$	−6.35161	−0.991955	−0.495978	+	0.868335i	$0.665190\pi$
$42$	−15.8683	−2.44854
$43$	−6.32490	−0.964539	−0.482269	−	0.876023i	$-0.660187\pi$
$43$	−6.32490	−0.964539	−0.482269	+	0.876023i	$0.660187\pi$
$44$	−27.1371	−4.09107
$45$	0.272436	0.0406123
$46$	−17.8480	−2.63154
$47$	−0.118260	−0.0172500	−0.00862498	−	0.999963i	$-0.502745\pi$
$47$	−0.118260	−0.0172500	−0.00862498	+	0.999963i	$0.502745\pi$
$48$	18.3900	2.65437
$49$	4.42171	0.631673
$50$	7.73770	1.09428
$51$	3.19207	0.446979
$52$	−4.91107	−0.681043
$53$	8.05377	1.10627	0.553135	−	0.833092i	$-0.313431\pi$
$53$	8.05377	1.10627	0.553135	+	0.833092i	$0.313431\pi$
$54$	13.1940	1.79548
$55$	−7.92445	−1.06853
$56$	−25.8638	−3.45619
$57$	−8.64370	−1.14489
$58$	−11.2580	−1.47825
$59$	−5.51332	−0.717773	−0.358886	−	0.933381i	$-0.616843\pi$
$59$	−5.51332	−0.717773	−0.358886	+	0.933381i	$0.616843\pi$
$60$	12.5792	1.62396
$61$	2.96804	0.380019	0.190010	−	0.981782i	$-0.439148\pi$
$61$	2.96804	0.380019	0.190010	+	0.981782i	$0.439148\pi$
$62$	7.33323	0.931322
$63$	0.642019	0.0808868
$64$	10.3296	1.29119
$65$	−1.43411	−0.177879
$66$	25.9450	3.19360
$67$	−8.30612	−1.01475	−0.507377	−	0.861724i	$-0.669385\pi$
$67$	−8.30612	−1.01475	−0.507377	+	0.861724i	$0.669385\pi$
$68$	8.77719	1.06439
$69$	12.1258	1.45977
$70$	−12.7415	−1.52290
$71$	8.03937	0.954098	0.477049	−	0.878877i	$-0.341706\pi$
$71$	8.03937	0.954098	0.477049	+	0.878877i	$0.341706\pi$
$72$	−1.45381	−0.171333
$73$	1.88100	0.220155	0.110077	−	0.993923i	$-0.464890\pi$
$73$	1.88100	0.220155	0.110077	+	0.993923i	$0.464890\pi$
$74$	8.75580	1.01784
$75$	−5.25693	−0.607018
$76$	−23.7675	−2.72631
$77$	−18.6747	−2.12818
$78$	4.69533	0.531641
$79$	0.564163	0.0634733	0.0317367	−	0.999496i	$-0.489896\pi$
$79$	0.564163	0.0634733	0.0317367	+	0.999496i	$0.489896\pi$
$80$	14.7663	1.65092
$81$	−9.53382	−1.05931
$82$	16.6977	1.84395
$83$	12.6678	1.39047	0.695234	−	0.718783i	$-0.255301\pi$
$83$	12.6678	1.39047	0.695234	+	0.718783i	$0.255301\pi$
$84$	29.6439	3.23441
$85$	2.56308	0.278005
$86$	16.6275	1.79299
$87$	7.64863	0.820019
$88$	42.2876	4.50787
$89$	13.7745	1.46009	0.730047	−	0.683397i	$-0.239498\pi$
$89$	13.7745	1.46009	0.730047	+	0.683397i	$0.239498\pi$
$90$	−0.716205	−0.0754946
$91$	−3.37960	−0.354279
$92$	33.3421	3.47616
$93$	−4.98214	−0.516624
$94$	0.310892	0.0320661
$95$	−6.94046	−0.712076
$96$	−21.0085	−2.14417
$97$	−15.1032	−1.53350	−0.766749	−	0.641947i	$-0.778127\pi$
$97$	−15.1032	−1.53350	−0.766749	+	0.641947i	$0.778127\pi$
$98$	−11.6242	−1.17422
$99$	−1.04971	−0.105500
$100$	−14.4549	−1.44549
$101$	10.0496	0.999968	0.499984	−	0.866035i	$-0.333339\pi$
$101$	10.0496	0.999968	0.499984	+	0.866035i	$0.333339\pi$
$102$	−8.39161	−0.830893
$103$	−5.75554	−0.567110	−0.283555	−	0.958956i	$-0.591514\pi$
$103$	−5.75554	−0.567110	−0.283555	+	0.958956i	$0.591514\pi$
$104$	7.65290	0.750428
$105$	8.65647	0.844785
$106$	−21.1725	−2.05645
$107$	−9.36363	−0.905216	−0.452608	−	0.891710i	$-0.649506\pi$
$107$	−9.36363	−0.905216	−0.452608	+	0.891710i	$0.649506\pi$
$108$	−24.6479	−2.37175
$109$	−2.17730	−0.208548	−0.104274	−	0.994549i	$-0.533252\pi$
$109$	−2.17730	−0.208548	−0.104274	+	0.994549i	$0.533252\pi$
$110$	20.8325	1.98630
$111$	−5.94862	−0.564618
$112$	34.7981	3.28811
$113$	5.54179	0.521327	0.260664	−	0.965430i	$-0.416059\pi$
$113$	5.54179	0.521327	0.260664	+	0.965430i	$0.416059\pi$
$114$	22.7233	2.12824
$115$	9.73641	0.907925
$116$	21.0313	1.95271
$117$	−0.189969	−0.0175626
$118$	14.4939	1.33427
$119$	6.04011	0.553696
$120$	−19.6020	−1.78941
$121$	19.5333	1.77576
$122$	−7.80267	−0.706420
$123$	−11.3443	−1.02288
$124$	−13.6993	−1.23024
$125$	−11.3916	−1.01890
$126$	−1.68780	−0.150361
$127$	−4.53697	−0.402591	−0.201295	−	0.979531i	$-0.564515\pi$
$127$	−4.53697	−0.402591	−0.201295	+	0.979531i	$0.564515\pi$
$128$	−3.63013	−0.320861
$129$	−11.2966	−0.994609
$130$	3.77012	0.330661
$131$	−8.39308	−0.733307	−0.366653	−	0.930358i	$-0.619497\pi$
$131$	−8.39308	−0.733307	−0.366653	+	0.930358i	$0.619497\pi$
$132$	−48.4682	−4.21861
$133$	−16.3558	−1.41823
$134$	21.8359	1.88633
$135$	−7.19758	−0.619469
$136$	−13.6774	−1.17283
$137$	−19.1881	−1.63935	−0.819675	−	0.572829i	$-0.805846\pi$
$137$	−19.1881	−1.63935	−0.819675	+	0.572829i	$0.805846\pi$
$138$	−31.8774	−2.71358
$139$	−7.26716	−0.616392	−0.308196	−	0.951323i	$-0.599725\pi$
$139$	−7.26716	−0.616392	−0.308196	+	0.951323i	$0.599725\pi$
$140$	23.8026	2.01169
$141$	−0.211218	−0.0177877
$142$	−21.1346	−1.77358
$143$	5.52570	0.462082
$144$	1.95601	0.163001
$145$	6.14147	0.510021
$146$	−4.94495	−0.409247
$147$	7.89740	0.651366
$148$	−16.3568	−1.34452
$149$	3.75452	0.307583	0.153791	−	0.988103i	$-0.450852\pi$
$149$	3.75452	0.307583	0.153791	+	0.988103i	$0.450852\pi$
$150$	13.8199	1.12839
$151$	13.9176	1.13259	0.566297	−	0.824201i	$-0.308375\pi$
$151$	13.9176	1.13259	0.566297	+	0.824201i	$0.308375\pi$
$152$	37.0367	3.00407
$153$	0.339517	0.0274483
$154$	49.0937	3.95608
$155$	−4.00041	−0.321321
$156$	−8.77141	−0.702275
$157$	−10.7958	−0.861601	−0.430800	−	0.902447i	$-0.641769\pi$
$157$	−10.7958	−0.861601	−0.430800	+	0.902447i	$0.641769\pi$
$158$	−1.48312	−0.117991
$159$	14.3844	1.14076
$160$	−16.8688	−1.33360
$161$	22.9447	1.80830
$162$	25.0634	1.96916
$163$	−20.9837	−1.64357	−0.821783	−	0.569800i	$-0.807021\pi$
$163$	−20.9837	−1.64357	−0.821783	+	0.569800i	$0.807021\pi$
$164$	−31.1932	−2.43578
$165$	−14.1535	−1.10184
$166$	−33.3022	−2.58475
$167$	−22.8580	−1.76881	−0.884403	−	0.466723i	$-0.845434\pi$
$167$	−22.8580	−1.76881	−0.884403	+	0.466723i	$0.845434\pi$
$168$	−46.1939	−3.56394
$169$	1.00000	0.0769231
$170$	−6.73805	−0.516785
$171$	−0.919366	−0.0703057
$172$	−31.0621	−2.36846
$173$	−22.8242	−1.73529	−0.867646	−	0.497183i	$-0.834368\pi$
$173$	−22.8242	−1.73529	−0.867646	+	0.497183i	$0.834368\pi$
$174$	−20.1074	−1.52434
$175$	−9.94729	−0.751945
$176$	−56.8953	−4.28865
$177$	−9.84705	−0.740150
$178$	−36.2117	−2.71418
$179$	14.0252	1.04829	0.524145	−	0.851629i	$-0.324385\pi$
$179$	14.0252	1.04829	0.524145	+	0.851629i	$0.324385\pi$
$180$	1.33795	0.0997251
$181$	10.1809	0.756738	0.378369	−	0.925655i	$-0.376485\pi$
$181$	10.1809	0.756738	0.378369	+	0.925655i	$0.376485\pi$
$182$	8.88461	0.658571
$183$	5.30107	0.391866
$184$	−51.9568	−3.83031
$185$	−4.77645	−0.351171
$186$	13.0975	0.960356
$187$	−9.87567	−0.722180
$188$	−0.580782	−0.0423579
$189$	−16.9617	−1.23378
$190$	18.2457	1.32368
$191$	−12.5962	−0.911430	−0.455715	−	0.890126i	$-0.650616\pi$
$191$	−12.5962	−0.911430	−0.455715	+	0.890126i	$0.650616\pi$
$192$	18.4491	1.33145
$193$	4.65613	0.335156	0.167578	−	0.985859i	$-0.446405\pi$
$193$	4.65613	0.335156	0.167578	+	0.985859i	$0.446405\pi$
$194$	39.7047	2.85063
$195$	−2.56139	−0.183425
$196$	21.7154	1.55110
$197$	14.9362	1.06416	0.532082	−	0.846693i	$-0.321410\pi$
$197$	14.9362	1.06416	0.532082	+	0.846693i	$0.321410\pi$
$198$	2.75957	0.196114
$199$	−3.82683	−0.271277	−0.135638	−	0.990758i	$-0.543309\pi$
$199$	−3.82683	−0.271277	−0.135638	+	0.990758i	$0.543309\pi$
$200$	22.5250	1.59276
$201$	−14.8351	−1.04639
$202$	−26.4192	−1.85885
$203$	14.4729	1.01580
$204$	15.6765	1.09757
$205$	−9.10891	−0.636194
$206$	15.1307	1.05420
$207$	1.28973	0.0896425
$208$	−10.2965	−0.713933
$209$	26.7420	1.84978
$210$	−22.7569	−1.57038
$211$	−7.52239	−0.517863	−0.258931	−	0.965896i	$-0.583370\pi$
$211$	−7.52239	−0.517863	−0.258931	+	0.965896i	$0.583370\pi$
$212$	39.5526	2.71649
$213$	14.3587	0.983842
$214$	24.6160	1.68271
$215$	−9.07060	−0.618610
$216$	38.4088	2.61338
$217$	−9.42732	−0.639968
$218$	5.72390	0.387671
$219$	3.35956	0.227018
$220$	−38.9176	−2.62382
$221$	−1.78723	−0.120222
$222$	15.6383	1.04957
$223$	−12.5008	−0.837116	−0.418558	−	0.908190i	$-0.637464\pi$
$223$	−12.5008	−0.837116	−0.418558	+	0.908190i	$0.637464\pi$
$224$	−39.7528	−2.65610
$225$	−0.559141	−0.0372761
$226$	−14.5688	−0.969099
$227$	16.3845	1.08748	0.543738	−	0.839255i	$-0.317009\pi$
$227$	16.3845	1.08748	0.543738	+	0.839255i	$0.317009\pi$
$228$	−42.4498	−2.81131
$229$	−19.8529	−1.31191	−0.655957	−	0.754798i	$-0.727735\pi$
$229$	−19.8529	−1.31191	−0.655957	+	0.754798i	$0.727735\pi$
$230$	−25.5960	−1.68775
$231$	−33.3539	−2.19452
$232$	−32.7730	−2.15165
$233$	−21.5923	−1.41456	−0.707280	−	0.706933i	$-0.750078\pi$
$233$	−21.5923	−1.41456	−0.707280	+	0.706933i	$0.750078\pi$
$234$	0.499407	0.0326473
$235$	−0.169597	−0.0110633
$236$	−27.0763	−1.76252
$237$	1.00762	0.0654522
$238$	−15.8788	−1.02927
$239$	−15.8009	−1.02207	−0.511037	−	0.859559i	$-0.670738\pi$
$239$	−15.8009	−1.02207	−0.511037	+	0.859559i	$0.670738\pi$
$240$	26.3733	1.70239
$241$	0.792065	0.0510214	0.0255107	−	0.999675i	$-0.491879\pi$
$241$	0.792065	0.0510214	0.0255107	+	0.999675i	$0.491879\pi$
$242$	−51.3510	−3.30097
$243$	−1.97131	−0.126459
$244$	14.5763	0.933151
$245$	6.34122	0.405126
$246$	29.8229	1.90144
$247$	4.83956	0.307934
$248$	21.3476	1.35557
$249$	22.6253	1.43382
$250$	29.9473	1.89403
$251$	0.0959044	0.00605343	0.00302672	−	0.999995i	$-0.499037\pi$
$251$	0.0959044	0.00605343	0.00302672	+	0.999995i	$0.499037\pi$
$252$	3.15300	0.198620
$253$	−37.5149	−2.35854
$254$	11.9272	0.748379
$255$	4.57778	0.286671
$256$	−11.1159	−0.694743
$257$	−9.92267	−0.618959	−0.309479	−	0.950906i	$-0.600155\pi$
$257$	−9.92267	−0.618959	−0.309479	+	0.950906i	$0.600155\pi$
$258$	29.6975	1.84889
$259$	−11.2561	−0.699421
$260$	−7.04301	−0.436789
$261$	0.813528	0.0503561
$262$	22.0645	1.36315
$263$	−22.5610	−1.39117	−0.695584	−	0.718444i	$-0.744854\pi$
$263$	−22.5610	−1.39117	−0.695584	+	0.718444i	$0.744854\pi$
$264$	75.5277	4.64841
$265$	11.5500	0.709510
$266$	42.9976	2.63635
$267$	24.6019	1.50561
$268$	−40.7920	−2.49177
$269$	−10.0619	−0.613482	−0.306741	−	0.951793i	$-0.599239\pi$
$269$	−10.0619	−0.613482	−0.306741	+	0.951793i	$0.599239\pi$
$270$	18.9217	1.15154
$271$	1.21964	0.0740881	0.0370441	−	0.999314i	$-0.488206\pi$
$271$	1.21964	0.0740881	0.0370441	+	0.999314i	$0.488206\pi$
$272$	18.4022	1.11579
$273$	−6.03613	−0.365323
$274$	50.4434	3.04740
$275$	16.2640	0.980754
$276$	59.5506	3.58453
$277$	−9.03705	−0.542984	−0.271492	−	0.962441i	$-0.587517\pi$
$277$	−9.03705	−0.542984	−0.271492	+	0.962441i	$0.587517\pi$
$278$	19.1046	1.14582
$279$	−0.529914	−0.0317251
$280$	−37.0914	−2.21664
$281$	18.8122	1.12224	0.561120	−	0.827735i	$-0.310371\pi$
$281$	18.8122	1.12224	0.561120	+	0.827735i	$0.310371\pi$
$282$	0.555268	0.0330658
$283$	−1.54842	−0.0920439	−0.0460219	−	0.998940i	$-0.514654\pi$
$283$	−1.54842	−0.0920439	−0.0460219	+	0.998940i	$0.514654\pi$
$284$	39.4819	2.34282
$285$	−12.3960	−0.734276
$286$	−14.5265	−0.858968
$287$	−21.4659	−1.26709
$288$	−2.23452	−0.131670
$289$	−13.8058	−0.812107
$290$	−16.1453	−0.948083
$291$	−26.9751	−1.58131
$292$	9.23774	0.540598
$293$	−10.4586	−0.611000	−0.305500	−	0.952192i	$-0.598824\pi$
$293$	−10.4586	−0.611000	−0.305500	+	0.952192i	$0.598824\pi$
$294$	−20.7614	−1.21083
$295$	−7.90669	−0.460346
$296$	25.4888	1.48150
$297$	27.7327	1.60921
$298$	−9.87024	−0.571768
$299$	−6.78917	−0.392628
$300$	−25.8172	−1.49056
$301$	−21.3757	−1.23207
$302$	−36.5878	−2.10539
$303$	17.9490	1.03114
$304$	−49.8305	−2.85798
$305$	4.25650	0.243726
$306$	−0.892554	−0.0510239
$307$	−15.9554	−0.910620	−0.455310	−	0.890333i	$-0.650472\pi$
$307$	−15.9554	−0.910620	−0.455310	+	0.890333i	$0.650472\pi$
$308$	−91.7126	−5.22581
$309$	−10.2797	−0.584790
$310$	10.5167	0.597306
$311$	−0.289411	−0.0164110	−0.00820548	−	0.999966i	$-0.502612\pi$
$311$	−0.289411	−0.0164110	−0.00820548	+	0.999966i	$0.502612\pi$
$312$	13.6684	0.773823
$313$	24.0594	1.35992	0.679959	−	0.733250i	$-0.261998\pi$
$313$	24.0594	1.35992	0.679959	+	0.733250i	$0.261998\pi$
$314$	28.3811	1.60164
$315$	0.920725	0.0518770
$316$	2.77065	0.155861
$317$	20.5288	1.15301	0.576505	−	0.817094i	$-0.304416\pi$
$317$	20.5288	1.15301	0.576505	+	0.817094i	$0.304416\pi$
$318$	−37.8151	−2.12056
$319$	−23.6634	−1.32490
$320$	14.8137	0.828111
$321$	−16.7239	−0.933437
$322$	−60.3191	−3.36145
$323$	−8.64939	−0.481265
$324$	−46.8213	−2.60118
$325$	2.94333	0.163267
$326$	55.1638	3.05524
$327$	−3.88877	−0.215049
$328$	48.6082	2.68394
$329$	−0.399671	−0.0220346
$330$	37.2079	2.04823
$331$	−16.1655	−0.888535	−0.444267	−	0.895894i	$-0.646536\pi$
$331$	−16.1655	−0.888535	−0.444267	+	0.895894i	$0.646536\pi$
$332$	62.2124	3.41435
$333$	−0.632711	−0.0346723
$334$	60.0913	3.28805
$335$	−11.9119	−0.650816
$336$	62.1510	3.39062
$337$	25.5151	1.38989	0.694947	−	0.719061i	$-0.255428\pi$
$337$	25.5151	1.38989	0.694947	+	0.719061i	$0.255428\pi$
$338$	−2.62889	−0.142993
$339$	9.89790	0.537580
$340$	12.5875	0.682650
$341$	15.4138	0.834704
$342$	2.41691	0.130692
$343$	−8.71358	−0.470489
$344$	48.4038	2.60976
$345$	17.3897	0.936230
$346$	60.0023	3.22575
$347$	4.61602	0.247801	0.123900	−	0.992295i	$-0.460460\pi$
$347$	4.61602	0.247801	0.123900	+	0.992295i	$0.460460\pi$
$348$	37.5630	2.01359
$349$	−32.4627	−1.73769	−0.868843	−	0.495087i	$-0.835136\pi$
$349$	−32.4627	−1.73769	−0.868843	+	0.495087i	$0.835136\pi$
$350$	26.1504	1.39780
$351$	5.01885	0.267886
$352$	64.9964	3.46432
$353$	−21.1399	−1.12516	−0.562582	−	0.826742i	$-0.690192\pi$
$353$	−21.1399	−1.12516	−0.562582	+	0.826742i	$0.690192\pi$
$354$	25.8868	1.37587
$355$	11.5293	0.611913
$356$	67.6476	3.58531
$357$	10.7879	0.570958
$358$	−36.8706	−1.94867
$359$	−10.5309	−0.555797	−0.277899	−	0.960610i	$-0.589638\pi$
$359$	−10.5309	−0.555797	−0.277899	+	0.960610i	$0.589638\pi$
$360$	−2.08492	−0.109885
$361$	4.42138	0.232704
$362$	−26.7644	−1.40671
$363$	34.8875	1.83112
$364$	−16.5975	−0.869944
$365$	2.69756	0.141197
$366$	−13.9359	−0.728443
$367$	5.54112	0.289244	0.144622	−	0.989487i	$-0.453803\pi$
$367$	5.54112	0.289244	0.144622	+	0.989487i	$0.453803\pi$
$368$	69.9047	3.64403
$369$	−1.20661	−0.0628135
$370$	12.5568	0.652795
$371$	27.2185	1.41312
$372$	−24.4677	−1.26859
$373$	36.1082	1.86961	0.934805	−	0.355162i	$-0.115574\pi$
$373$	36.1082	1.86961	0.934805	+	0.355162i	$0.115574\pi$
$374$	25.9621	1.34247
$375$	−20.3460	−1.05066
$376$	0.905030	0.0466734
$377$	−4.28243	−0.220556
$378$	44.5905	2.29349
$379$	−20.0023	−1.02745	−0.513726	−	0.857954i	$-0.671735\pi$
$379$	−20.0023	−1.02745	−0.513726	+	0.857954i	$0.671735\pi$
$380$	−34.0851	−1.74853
$381$	−8.10325	−0.415142
$382$	33.1141	1.69426
$383$	5.51935	0.282026	0.141013	−	0.990008i	$-0.454964\pi$
$383$	5.51935	0.282026	0.141013	+	0.990008i	$0.454964\pi$
$384$	−6.48358	−0.330864
$385$	−26.7815	−1.36491
$386$	−12.2405	−0.623023
$387$	−1.20153	−0.0610774
$388$	−74.1729	−3.76556
$389$	7.88924	0.400000	0.200000	−	0.979796i	$-0.435906\pi$
$389$	7.88924	0.400000	0.200000	+	0.979796i	$0.435906\pi$
$390$	6.73361	0.340970
$391$	12.1338	0.613632
$392$	−33.8389	−1.70912
$393$	−14.9904	−0.756168
$394$	−39.2658	−1.97818
$395$	0.809072	0.0407088
$396$	−5.15520	−0.259059
$397$	−7.85509	−0.394236	−0.197118	−	0.980380i	$-0.563158\pi$
$397$	−7.85509	−0.394236	−0.197118	+	0.980380i	$0.563158\pi$
$398$	10.0603	0.504278
$399$	−29.2123	−1.46244
$400$	−30.3060	−1.51530
$401$	−28.5648	−1.42646	−0.713230	−	0.700930i	$-0.752768\pi$
$401$	−28.5648	−1.42646	−0.713230	+	0.700930i	$0.752768\pi$
$402$	39.0000	1.94514
$403$	2.78948	0.138954
$404$	49.3541	2.45546
$405$	−13.6725	−0.679394
$406$	−38.0477	−1.88828
$407$	18.4039	0.912248
$408$	−24.4286	−1.20940
$409$	9.35879	0.462762	0.231381	−	0.972863i	$-0.425676\pi$
$409$	9.35879	0.462762	0.231381	+	0.972863i	$0.425676\pi$
$410$	23.9463	1.18262
$411$	−34.2709	−1.69046
$412$	−28.2659	−1.39256
$413$	−18.6328	−0.916861
$414$	−3.39056	−0.166637
$415$	18.1670	0.891781
$416$	11.7626	0.576708
$417$	−12.9795	−0.635609
$418$	−70.3017	−3.43857
$419$	−0.165946	−0.00810701	−0.00405350	−	0.999992i	$-0.501290\pi$
$419$	−0.165946	−0.00810701	−0.00405350	+	0.999992i	$0.501290\pi$
$420$	42.5126	2.07440
$421$	−25.7952	−1.25718	−0.628590	−	0.777737i	$-0.716367\pi$
$421$	−25.7952	−1.25718	−0.628590	+	0.777737i	$0.716367\pi$
$422$	19.7756	0.962659
$423$	−0.0224657	−0.00109232
$424$	−61.6346	−2.99324
$425$	−5.26040	−0.255167
$426$	−37.7475	−1.82887
$427$	10.0308	0.485425
$428$	−45.9855	−2.22279
$429$	9.86916	0.476488
$430$	23.8456	1.14994
$431$	−10.7628	−0.518424	−0.259212	−	0.965820i	$-0.583463\pi$
$431$	−10.7628	−0.518424	−0.259212	+	0.965820i	$0.583463\pi$
$432$	−51.6766	−2.48629
$433$	0.215046	0.0103344	0.00516722	−	0.999987i	$-0.498355\pi$
$433$	0.215046	0.0103344	0.00516722	+	0.999987i	$0.498355\pi$
$434$	24.7834	1.18964
$435$	10.9690	0.525922
$436$	−10.6929	−0.512097
$437$	−32.8566	−1.57175
$438$	−8.83193	−0.422006
$439$	4.30701	0.205562	0.102781	−	0.994704i	$-0.467226\pi$
$439$	4.30701	0.205562	0.102781	+	0.994704i	$0.467226\pi$
$440$	60.6450	2.89114
$441$	0.839988	0.0399994
$442$	4.69842	0.223481
$443$	9.76241	0.463826	0.231913	−	0.972737i	$-0.425501\pi$
$443$	9.76241	0.463826	0.231913	+	0.972737i	$0.425501\pi$
$444$	−29.2141	−1.38644
$445$	19.7541	0.936436
$446$	32.8633	1.55612
$447$	6.70576	0.317172
$448$	34.9098	1.64933
$449$	8.56251	0.404090	0.202045	−	0.979376i	$-0.435241\pi$
$449$	8.56251	0.404090	0.202045	+	0.979376i	$0.435241\pi$
$450$	1.46992	0.0692928
$451$	35.0971	1.65266
$452$	27.2161	1.28014
$453$	24.8574	1.16790
$454$	−43.0730	−2.02152
$455$	−4.84672	−0.227218
$456$	66.1493	3.09773
$457$	11.5995	0.542602	0.271301	−	0.962495i	$-0.412546\pi$
$457$	11.5995	0.542602	0.271301	+	0.962495i	$0.412546\pi$
$458$	52.1910	2.43873
$459$	−8.96982	−0.418675
$460$	47.8162	2.22944
$461$	−18.6172	−0.867088	−0.433544	−	0.901132i	$-0.642737\pi$
$461$	−18.6172	−0.867088	−0.433544	+	0.901132i	$0.642737\pi$
$462$	87.6837	4.07941
$463$	21.0809	0.979714	0.489857	−	0.871803i	$-0.337049\pi$
$463$	21.0809	0.979714	0.489857	+	0.871803i	$0.337049\pi$
$464$	44.0940	2.04701
$465$	−7.14493	−0.331338
$466$	56.7639	2.62954
$467$	5.27846	0.244258	0.122129	−	0.992514i	$-0.461028\pi$
$467$	5.27846	0.244258	0.122129	+	0.992514i	$0.461028\pi$
$468$	−0.932951	−0.0431257
$469$	−28.0714	−1.29622
$470$	0.445853	0.0205657
$471$	−19.2819	−0.888462
$472$	42.1928	1.94208
$473$	34.9495	1.60698
$474$	−2.64893	−0.121669
$475$	14.2444	0.653580
$476$	29.6634	1.35962
$477$	1.52996	0.0700523
$478$	41.5388	1.89994
$479$	−10.9821	−0.501787	−0.250894	−	0.968015i	$-0.580724\pi$
$479$	−10.9821	−0.501787	−0.250894	+	0.968015i	$0.580724\pi$
$480$	−30.1285	−1.37517
$481$	3.33060	0.151862
$482$	−2.08225	−0.0948441
$483$	40.9803	1.86467
$484$	95.9297	4.36044
$485$	−21.6596	−0.983513
$486$	5.18235	0.235076
$487$	−7.58829	−0.343858	−0.171929	−	0.985109i	$-0.555000\pi$
$487$	−7.58829	−0.343858	−0.171929	+	0.985109i	$0.555000\pi$
$488$	−22.7141	−1.02822
$489$	−37.4778	−1.69481
$490$	−16.6704	−0.753091
$491$	−13.6890	−0.617777	−0.308889	−	0.951098i	$-0.599957\pi$
$491$	−13.6890	−0.617777	−0.308889	+	0.951098i	$0.599957\pi$
$492$	−55.7126	−2.51172
$493$	7.65367	0.344704
$494$	−12.7227	−0.572421
$495$	−1.50540	−0.0676626
$496$	−28.7218	−1.28965
$497$	27.1699	1.21874
$498$	−59.4794	−2.66533
$499$	−14.0260	−0.627890	−0.313945	−	0.949441i	$-0.601651\pi$
$499$	−14.0260	−0.627890	−0.313945	+	0.949441i	$0.601651\pi$
$500$	−55.9450	−2.50194
$501$	−40.8255	−1.82395
$502$	−0.252122	−0.0112528
$503$	33.1811	1.47947	0.739735	−	0.672898i	$-0.234951\pi$
$503$	33.1811	1.47947	0.739735	+	0.672898i	$0.234951\pi$
$504$	−4.91331	−0.218856
$505$	14.4122	0.641333
$506$	98.6226	4.38431
$507$	1.78605	0.0793212
$508$	−22.2814	−0.988577
$509$	−31.3791	−1.39085	−0.695426	−	0.718598i	$-0.744784\pi$
$509$	−31.3791	−1.39085	−0.695426	+	0.718598i	$0.744784\pi$
$510$	−12.0345	−0.532896
$511$	6.35704	0.281219
$512$	36.4827	1.61232
$513$	24.2891	1.07239
$514$	26.0856	1.15059
$515$	−8.25406	−0.363718
$516$	−55.4783	−2.44230
$517$	0.653468	0.0287395
$518$	29.5911	1.30016
$519$	−40.7651	−1.78939
$520$	10.9751	0.481289
$521$	−1.44836	−0.0634540	−0.0317270	−	0.999497i	$-0.510101\pi$
$521$	−1.44836	−0.0634540	−0.0317270	+	0.999497i	$0.510101\pi$
$522$	−2.13868	−0.0936074
$523$	−17.5436	−0.767126	−0.383563	−	0.923515i	$-0.625303\pi$
$523$	−17.5436	−0.767126	−0.383563	+	0.923515i	$0.625303\pi$
$524$	−41.2190	−1.80066
$525$	−17.7663	−0.775387
$526$	59.3103	2.58605
$527$	−4.98542	−0.217168
$528$	−101.618	−4.42235
$529$	23.0928	1.00404
$530$	−30.3636	−1.31891
$531$	−1.04736	−0.0454515
$532$	−80.3245	−3.48251
$533$	6.35161	0.275119
$534$	−64.6758	−2.79880
$535$	−13.4285	−0.580563
$536$	63.5659	2.74563
$537$	25.0496	1.08097
$538$	26.4515	1.14041
$539$	−24.4331	−1.05241
$540$	−35.3478	−1.52113
$541$	45.5734	1.95935	0.979676	−	0.200588i	$-0.0642852\pi$
$541$	45.5734	1.95935	0.979676	+	0.200588i	$0.0642852\pi$
$542$	−3.20631	−0.137723
$543$	18.1835	0.780330
$544$	−21.0224	−0.901327
$545$	−3.12249	−0.133753
$546$	15.8683	0.679102
$547$	29.8361	1.27570	0.637849	−	0.770162i	$-0.279824\pi$
$547$	29.8361	1.27570	0.637849	+	0.770162i	$0.279824\pi$
$548$	−94.2341	−4.02548
$549$	0.563836	0.0240639
$550$	−42.7562	−1.82313
$551$	−20.7251	−0.882919
$552$	−92.7974	−3.94972
$553$	1.90665	0.0810789
$554$	23.7574	1.00936
$555$	−8.53097	−0.362119
$556$	−35.6895	−1.51357
$557$	22.3264	0.945998	0.472999	−	0.881063i	$-0.343171\pi$
$557$	22.3264	0.945998	0.472999	+	0.881063i	$0.343171\pi$
$558$	1.39309	0.0589740
$559$	6.32490	0.267515
$560$	49.9042	2.10884
$561$	−17.6384	−0.744695
$562$	−49.4551	−2.08614
$563$	1.63586	0.0689435	0.0344717	−	0.999406i	$-0.489025\pi$
$563$	1.63586	0.0689435	0.0344717	+	0.999406i	$0.489025\pi$
$564$	−1.03731	−0.0436784
$565$	7.94753	0.334355
$566$	4.07062	0.171101
$567$	−32.2205	−1.35313
$568$	−61.5245	−2.58151
$569$	−18.0774	−0.757844	−0.378922	−	0.925429i	$-0.623705\pi$
$569$	−18.0774	−0.757844	−0.378922	+	0.925429i	$0.623705\pi$
$570$	32.5877	1.36495
$571$	20.9270	0.875766	0.437883	−	0.899032i	$-0.355728\pi$
$571$	20.9270	0.875766	0.437883	+	0.899032i	$0.355728\pi$
$572$	27.1371	1.13466
$573$	−22.4974	−0.939844
$574$	56.4316	2.35541
$575$	−19.9828	−0.833340
$576$	1.96229	0.0817622
$577$	21.2912	0.886363	0.443181	−	0.896432i	$-0.353850\pi$
$577$	21.2912	0.886363	0.443181	+	0.896432i	$0.353850\pi$
$578$	36.2940	1.50963
$579$	8.31607	0.345604
$580$	30.1612	1.25238
$581$	42.8120	1.77614
$582$	70.9145	2.93950
$583$	−44.5027	−1.84311
$584$	−14.3951	−0.595674
$585$	−0.272436	−0.0112638
$586$	27.4946	1.13579
$587$	14.8967	0.614851	0.307425	−	0.951572i	$-0.400533\pi$
$587$	14.8967	0.614851	0.307425	+	0.951572i	$0.400533\pi$
$588$	38.7847	1.59945
$589$	13.4999	0.556252
$590$	20.7858	0.855740
$591$	26.6768	1.09734
$592$	−34.2935	−1.40946
$593$	−30.8157	−1.26545	−0.632724	−	0.774378i	$-0.718063\pi$
$593$	−30.8157	−1.26545	−0.632724	+	0.774378i	$0.718063\pi$
$594$	−72.9062	−2.99138
$595$	8.66218	0.355115
$596$	18.4387	0.755280
$597$	−6.83490	−0.279734
$598$	17.8480	0.729859
$599$	−7.56932	−0.309274	−0.154637	−	0.987971i	$-0.549421\pi$
$599$	−7.56932	−0.309274	−0.154637	+	0.987971i	$0.549421\pi$
$600$	40.2308	1.64241
$601$	38.9328	1.58810	0.794050	−	0.607852i	$-0.207969\pi$
$601$	38.9328	1.58810	0.794050	+	0.607852i	$0.207969\pi$
$602$	56.1943	2.29031
$603$	−1.57790	−0.0642572
$604$	68.3501	2.78113
$605$	28.0129	1.13889
$606$	−47.1860	−1.91680
$607$	27.8581	1.13072	0.565362	−	0.824843i	$-0.308736\pi$
$607$	27.8581	1.13072	0.565362	+	0.824843i	$0.308736\pi$
$608$	56.9257	2.30864
$609$	25.8493	1.04747
$610$	−11.1899	−0.453065
$611$	0.118260	0.00478428
$612$	1.66739	0.0674004
$613$	18.5724	0.750133	0.375067	−	0.926998i	$-0.377620\pi$
$613$	18.5724	0.750133	0.375067	+	0.926998i	$0.377620\pi$
$614$	41.9449	1.69276
$615$	−16.2689	−0.656027
$616$	142.915	5.75822
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	27.0241	1.08707
$619$	3.34653	0.134508	0.0672541	−	0.997736i	$-0.478576\pi$
$619$	3.34653	0.134508	0.0672541	+	0.997736i	$0.478576\pi$
$620$	−19.6463	−0.789015
$621$	−34.0738	−1.36734
$622$	0.760829	0.0305065
$623$	46.5523	1.86508
$624$	−18.3900	−0.736191
$625$	−1.62014	−0.0648055
$626$	−63.2495	−2.52796
$627$	47.7625	1.90745
$628$	−53.0191	−2.11569
$629$	−5.95254	−0.237343
$630$	−2.42049	−0.0964345
$631$	−36.8973	−1.46886	−0.734430	−	0.678684i	$-0.762550\pi$
$631$	−36.8973	−1.46886	−0.734430	+	0.678684i	$0.762550\pi$
$632$	−4.31748	−0.171740
$633$	−13.4354	−0.534008
$634$	−53.9679	−2.14334
$635$	−6.50651	−0.258203
$636$	70.6429	2.80117
$637$	−4.42171	−0.175195
$638$	62.2086	2.46286
$639$	1.52723	0.0604163
$640$	−5.20600	−0.205785
$641$	14.7137	0.581155	0.290577	−	0.956851i	$-0.406153\pi$
$641$	14.7137	0.581155	0.290577	+	0.956851i	$0.406153\pi$
$642$	43.9653	1.73517
$643$	1.01603	0.0400683	0.0200342	−	0.999799i	$-0.493623\pi$
$643$	1.01603	0.0400683	0.0200342	+	0.999799i	$0.493623\pi$
$644$	112.683	4.44034
$645$	−16.2005	−0.637895
$646$	22.7383	0.894627
$647$	18.0856	0.711016	0.355508	−	0.934673i	$-0.384308\pi$
$647$	18.0856	0.711016	0.355508	+	0.934673i	$0.384308\pi$
$648$	72.9613	2.86619
$649$	30.4649	1.19585
$650$	−7.73770	−0.303498
$651$	−16.8377	−0.659920
$652$	−103.052	−4.03584
$653$	6.11218	0.239188	0.119594	−	0.992823i	$-0.461841\pi$
$653$	6.11218	0.239188	0.119594	+	0.992823i	$0.461841\pi$
$654$	10.2232	0.399757
$655$	−12.0366	−0.470308
$656$	−65.3993	−2.55342
$657$	0.357332	0.0139408
$658$	1.05069	0.0409602
$659$	−30.8059	−1.20003	−0.600014	−	0.799990i	$-0.704838\pi$
$659$	−30.8059	−1.20003	−0.600014	+	0.799990i	$0.704838\pi$
$660$	−69.5087	−2.70562
$661$	21.6999	0.844029	0.422014	−	0.906589i	$-0.361323\pi$
$661$	21.6999	0.844029	0.422014	+	0.906589i	$0.361323\pi$
$662$	42.4973	1.65170
$663$	−3.19207	−0.123970
$664$	−96.9452	−3.76220
$665$	−23.4560	−0.909585
$666$	1.66333	0.0644527
$667$	29.0742	1.12576
$668$	−112.257	−4.34337
$669$	−22.3270	−0.863213
$670$	31.3150	1.20981
$671$	−16.4005	−0.633135
$672$	−71.0005	−2.73890
$673$	21.5542	0.830854	0.415427	−	0.909626i	$-0.363632\pi$
$673$	21.5542	0.830854	0.415427	+	0.909626i	$0.363632\pi$
$674$	−67.0764	−2.58368
$675$	14.7721	0.568580
$676$	4.91107	0.188887
$677$	−10.3896	−0.399305	−0.199652	−	0.979867i	$-0.563981\pi$
$677$	−10.3896	−0.399305	−0.199652	+	0.979867i	$0.563981\pi$
$678$	−26.0205	−0.999312
$679$	−51.0428	−1.95884
$680$	−19.6150	−0.752199
$681$	29.2635	1.12138
$682$	−40.5212	−1.55164
$683$	29.3632	1.12355	0.561777	−	0.827289i	$-0.310118\pi$
$683$	29.3632	1.12355	0.561777	+	0.827289i	$0.310118\pi$
$684$	−4.51507	−0.172638
$685$	−27.5178	−1.05140
$686$	22.9071	0.874596
$687$	−35.4582	−1.35281
$688$	−65.1243	−2.48284
$689$	−8.05377	−0.306824
$690$	−45.7156	−1.74036
$691$	22.6568	0.861904	0.430952	−	0.902375i	$-0.358178\pi$
$691$	22.6568	0.861904	0.430952	+	0.902375i	$0.358178\pi$
$692$	−112.091	−4.26107
$693$	−3.54760	−0.134762
$694$	−12.1350	−0.460639
$695$	−10.4219	−0.395325
$696$	−58.5342	−2.21873
$697$	−11.3518	−0.429979
$698$	85.3408	3.23020
$699$	−38.5649	−1.45866
$700$	−48.8519	−1.84643
$701$	38.4000	1.45035	0.725174	−	0.688566i	$-0.241759\pi$
$701$	38.4000	1.45035	0.725174	+	0.688566i	$0.241759\pi$
$702$	−13.1940	−0.497976
$703$	16.1187	0.607927
$704$	−57.0780	−2.15121
$705$	−0.302909	−0.0114082
$706$	55.5745	2.09157
$707$	33.9635	1.27733
$708$	−48.3596	−1.81746
$709$	14.8879	0.559126	0.279563	−	0.960127i	$-0.409810\pi$
$709$	14.8879	0.559126	0.279563	+	0.960127i	$0.409810\pi$
$710$	−30.3094	−1.13749
$711$	0.107173	0.00401932
$712$	−105.415	−3.95059
$713$	−18.9382	−0.709242
$714$	−28.3603	−1.06136
$715$	7.92445	0.296358
$716$	68.8786	2.57411
$717$	−28.2211	−1.05394
$718$	27.6845	1.03318
$719$	−20.1007	−0.749630	−0.374815	−	0.927100i	$-0.622294\pi$
$719$	−20.1007	−0.749630	−0.374815	+	0.927100i	$0.622294\pi$
$720$	2.80513	0.104541
$721$	−19.4514	−0.724409
$722$	−11.6233	−0.432575
$723$	1.41467	0.0526120
$724$	49.9990	1.85820
$725$	−12.6046	−0.468124
$726$	−91.7154	−3.40388
$727$	−40.4171	−1.49899	−0.749493	−	0.662012i	$-0.769703\pi$
$727$	−40.4171	−1.49899	−0.749493	+	0.662012i	$0.769703\pi$
$728$	25.8638	0.958574
$729$	25.0806	0.928911
$730$	−7.09160	−0.262472
$731$	−11.3040	−0.418095
$732$	26.0339	0.962242
$733$	10.1029	0.373160	0.186580	−	0.982440i	$-0.440260\pi$
$733$	10.1029	0.373160	0.186580	+	0.982440i	$0.440260\pi$
$734$	−14.5670	−0.537678
$735$	11.3257	0.417756
$736$	−79.8581	−2.94361
$737$	45.8971	1.69064
$738$	3.17204	0.116765
$739$	−23.4114	−0.861201	−0.430601	−	0.902543i	$-0.641698\pi$
$739$	−23.4114	−0.861201	−0.430601	+	0.902543i	$0.641698\pi$
$740$	−23.4575	−0.862314
$741$	8.64370	0.317534
$742$	−71.5546	−2.62685
$743$	−3.38664	−0.124244	−0.0621219	−	0.998069i	$-0.519787\pi$
$743$	−3.38664	−0.124244	−0.0621219	+	0.998069i	$0.519787\pi$
$744$	38.1278	1.39783
$745$	5.38440	0.197269
$746$	−94.9245	−3.47543
$747$	2.40648	0.0880486
$748$	−48.5001	−1.77334
$749$	−31.6453	−1.15630
$750$	53.4873	1.95308
$751$	49.0750	1.79077	0.895387	−	0.445289i	$-0.146899\pi$
$751$	49.0750	1.79077	0.895387	+	0.445289i	$0.146899\pi$
$752$	−1.21766	−0.0444035
$753$	0.171290	0.00624215
$754$	11.2580	0.409994
$755$	19.9593	0.726393
$756$	−83.3003	−3.02960
$757$	−54.1583	−1.96842	−0.984208	−	0.177014i	$-0.943356\pi$
$757$	−54.1583	−1.96842	−0.984208	+	0.177014i	$0.943356\pi$
$758$	52.5840	1.90994
$759$	−67.0034	−2.43207
$760$	53.1146	1.92667
$761$	31.5432	1.14344	0.571720	−	0.820449i	$-0.306276\pi$
$761$	31.5432	1.14344	0.571720	+	0.820449i	$0.306276\pi$
$762$	21.3026	0.771710
$763$	−7.35842	−0.266393
$764$	−61.8609	−2.23805
$765$	0.486904	0.0176041
$766$	−14.5098	−0.524260
$767$	5.51332	0.199074
$768$	−19.8535	−0.716402
$769$	12.7288	0.459011	0.229506	−	0.973307i	$-0.426289\pi$
$769$	12.7288	0.459011	0.229506	+	0.973307i	$0.426289\pi$
$770$	70.4057	2.53724
$771$	−17.7224	−0.638255
$772$	22.8666	0.822987
$773$	−29.7432	−1.06979	−0.534894	−	0.844919i	$-0.679648\pi$
$773$	−29.7432	−1.06979	−0.534894	+	0.844919i	$0.679648\pi$
$774$	3.15870	0.113537
$775$	8.21036	0.294925
$776$	115.583	4.14920
$777$	−20.1040	−0.721226
$778$	−20.7400	−0.743563
$779$	30.7390	1.10134
$780$	−12.5792	−0.450406
$781$	−44.4231	−1.58958
$782$	−31.8984	−1.14068
$783$	−21.4929	−0.768093
$784$	45.5282	1.62601
$785$	−15.4824	−0.552590
$786$	39.4083	1.40565
$787$	−13.3000	−0.474094	−0.237047	−	0.971498i	$-0.576180\pi$
$787$	−13.3000	−0.474094	−0.237047	+	0.971498i	$0.576180\pi$
$788$	73.3530	2.61309
$789$	−40.2950	−1.43454
$790$	−2.12696	−0.0756739
$791$	18.7290	0.665928
$792$	8.03332	0.285452
$793$	−2.96804	−0.105398
$794$	20.6502	0.732848
$795$	20.6288	0.731629
$796$	−18.7938	−0.666130
$797$	−45.1434	−1.59906	−0.799530	−	0.600626i	$-0.794918\pi$
$797$	−45.1434	−1.59906	−0.799530	+	0.600626i	$0.794918\pi$
$798$	76.7959	2.71854
$799$	−0.211357	−0.00747727
$800$	34.6212	1.22404
$801$	2.61673	0.0924574
$802$	75.0939	2.65166
$803$	−10.3939	−0.366791
$804$	−72.8564	−2.56945
$805$	32.9052	1.15976
$806$	−7.33323	−0.258302
$807$	−17.9710	−0.632608
$808$	−76.9082	−2.70562
$809$	8.25749	0.290318	0.145159	−	0.989408i	$-0.453631\pi$
$809$	8.25749	0.290318	0.145159	+	0.989408i	$0.453631\pi$
$810$	35.9436	1.26293
$811$	51.6440	1.81347	0.906733	−	0.421706i	$-0.138568\pi$
$811$	51.6440	1.81347	0.906733	+	0.421706i	$0.138568\pi$
$812$	71.0775	2.49433
$813$	2.17834	0.0763978
$814$	−48.3819	−1.69578
$815$	−30.0928	−1.05411
$816$	32.8671	1.15058
$817$	30.6098	1.07090
$818$	−24.6032	−0.860232
$819$	−0.642019	−0.0224340
$820$	−44.7345	−1.56220
$821$	38.3170	1.33727	0.668637	−	0.743589i	$-0.266878\pi$
$821$	38.3170	1.33727	0.668637	+	0.743589i	$0.266878\pi$
$822$	90.0944	3.14240
$823$	18.8263	0.656244	0.328122	−	0.944635i	$-0.393584\pi$
$823$	18.8263	0.656244	0.328122	+	0.944635i	$0.393584\pi$
$824$	44.0465	1.53443
$825$	29.0482	1.01133
$826$	48.9837	1.70436
$827$	−37.7258	−1.31186	−0.655928	−	0.754823i	$-0.727723\pi$
$827$	−37.7258	−1.31186	−0.655928	+	0.754823i	$0.727723\pi$
$828$	6.33396	0.220120
$829$	30.2563	1.05084	0.525422	−	0.850842i	$-0.323907\pi$
$829$	30.2563	1.05084	0.525422	+	0.850842i	$0.323907\pi$
$830$	−47.7590	−1.65774
$831$	−16.1406	−0.559912
$832$	−10.3296	−0.358113
$833$	7.90260	0.273809
$834$	34.1217	1.18154
$835$	−32.7809	−1.13443
$836$	131.332	4.54220
$837$	14.0000	0.483910
$838$	0.436255	0.0150702
$839$	25.5018	0.880419	0.440209	−	0.897895i	$-0.354904\pi$
$839$	25.5018	0.880419	0.440209	+	0.897895i	$0.354904\pi$
$840$	−66.2471	−2.28574
$841$	−10.6608	−0.367613
$842$	67.8127	2.33698
$843$	33.5994	1.15723
$844$	−36.9430	−1.27163
$845$	1.43411	0.0493348
$846$	0.0590598	0.00203052
$847$	66.0149	2.26830
$848$	82.9256	2.84768
$849$	−2.76555	−0.0949134
$850$	13.8290	0.474331
$851$	−22.6120	−0.775131
$852$	70.5166	2.41586
$853$	38.8309	1.32955	0.664773	−	0.747046i	$-0.268528\pi$
$853$	38.8309	1.32955	0.664773	+	0.747046i	$0.268528\pi$
$854$	−26.3699	−0.902360
$855$	−1.31847	−0.0450908
$856$	71.6589	2.44925
$857$	−3.96530	−0.135452	−0.0677260	−	0.997704i	$-0.521574\pi$
$857$	−3.96530	−0.135452	−0.0677260	+	0.997704i	$0.521574\pi$
$858$	−25.9450	−0.885747
$859$	6.42627	0.219262	0.109631	−	0.993972i	$-0.465033\pi$
$859$	6.42627	0.219262	0.109631	+	0.993972i	$0.465033\pi$
$860$	−44.5464	−1.51902
$861$	−38.3392	−1.30660
$862$	28.2941	0.963702
$863$	−20.0796	−0.683518	−0.341759	−	0.939788i	$-0.611023\pi$
$863$	−20.0796	−0.683518	−0.341759	+	0.939788i	$0.611023\pi$
$864$	59.0346	2.00840
$865$	−32.7324	−1.11293
$866$	−0.565332	−0.0192108
$867$	−24.6579	−0.837425
$868$	−46.2983	−1.57147
$869$	−3.11740	−0.105750
$870$	−28.8362	−0.977640
$871$	8.30612	0.281442
$872$	16.6627	0.564270
$873$	−2.86914	−0.0971056
$874$	86.3765	2.92173
$875$	−38.4991	−1.30151
$876$	16.4991	0.557451
$877$	6.11985	0.206653	0.103326	−	0.994648i	$-0.467051\pi$
$877$	6.11985	0.206653	0.103326	+	0.994648i	$0.467051\pi$
$878$	−11.3227	−0.382121
$879$	−18.6796	−0.630048
$880$	−81.5941	−2.75054
$881$	−41.7594	−1.40691	−0.703455	−	0.710740i	$-0.748360\pi$
$881$	−41.7594	−1.40691	−0.703455	+	0.710740i	$0.748360\pi$
$882$	−2.20824	−0.0743552
$883$	−34.8909	−1.17417	−0.587087	−	0.809524i	$-0.699725\pi$
$883$	−34.8909	−1.17417	−0.587087	+	0.809524i	$0.699725\pi$
$884$	−8.77719	−0.295209
$885$	−14.1217	−0.474697
$886$	−25.6643	−0.862210
$887$	20.2438	0.679719	0.339859	−	0.940476i	$-0.389620\pi$
$887$	20.2438	0.679719	0.339859	+	0.940476i	$0.389620\pi$
$888$	45.5242	1.52769
$889$	−15.3332	−0.514257
$890$	−51.9315	−1.74075
$891$	52.6810	1.76488
$892$	−61.3923	−2.05557
$893$	0.572326	0.0191522
$894$	−17.6287	−0.589593
$895$	20.1136	0.672323
$896$	−12.2684	−0.409858
$897$	−12.1258	−0.404868
$898$	−22.5099	−0.751166
$899$	−11.9457	−0.398413
$900$	−2.74598	−0.0915328
$901$	14.3939	0.479530
$902$	−92.2665	−3.07214
$903$	−38.1780	−1.27048
$904$	−42.4107	−1.41056
$905$	14.6005	0.485336
$906$	−65.3475	−2.17103
$907$	24.4327	0.811276	0.405638	−	0.914034i	$-0.367049\pi$
$907$	24.4327	0.811276	0.405638	+	0.914034i	$0.367049\pi$
$908$	80.4654	2.67034
$909$	1.90910	0.0633209
$910$	12.7415	0.422377
$911$	44.9295	1.48858	0.744290	−	0.667856i	$-0.232788\pi$
$911$	44.9295	1.48858	0.744290	+	0.667856i	$0.232788\pi$
$912$	−88.9997	−2.94708
$913$	−69.9983	−2.31661
$914$	−30.4938	−1.00865
$915$	7.60231	0.251325
$916$	−97.4989	−3.22145
$917$	−28.3653	−0.936704
$918$	23.5807	0.778279
$919$	13.0565	0.430693	0.215346	−	0.976538i	$-0.430912\pi$
$919$	13.0565	0.430693	0.215346	+	0.976538i	$0.430912\pi$
$920$	−74.5117	−2.45658
$921$	−28.4970	−0.939009
$922$	48.9426	1.61184
$923$	−8.03937	−0.264619
$924$	−163.803	−5.38873
$925$	9.80307	0.322323
$926$	−55.4195	−1.82120
$927$	−1.09337	−0.0359111
$928$	−50.3724	−1.65356
$929$	−19.9570	−0.654769	−0.327385	−	0.944891i	$-0.606167\pi$
$929$	−19.9570	−0.654769	−0.327385	+	0.944891i	$0.606167\pi$
$930$	18.7833	0.615927
$931$	−21.3992	−0.701329
$932$	−106.041	−3.47350
$933$	−0.516901	−0.0169226
$934$	−13.8765	−0.454053
$935$	−14.1628	−0.463172
$936$	1.45381	0.0475193
$937$	40.0453	1.30822	0.654111	−	0.756399i	$-0.273043\pi$
$937$	40.0453	1.30822	0.654111	+	0.756399i	$0.273043\pi$
$938$	73.7967	2.40955
$939$	42.9712	1.40231
$940$	−0.832905	−0.0271664
$941$	15.8691	0.517319	0.258659	−	0.965969i	$-0.416719\pi$
$941$	15.8691	0.517319	0.258659	+	0.965969i	$0.416719\pi$
$942$	50.6900	1.65157
$943$	−43.1222	−1.40425
$944$	−56.7678	−1.84764
$945$	−24.3250	−0.791291
$946$	−91.8785	−2.98723
$947$	13.4696	0.437702	0.218851	−	0.975758i	$-0.429769\pi$
$947$	13.4696	0.437702	0.218851	+	0.975758i	$0.429769\pi$
$948$	4.94851	0.160720
$949$	−1.88100	−0.0610599
$950$	−37.4471	−1.21494
$951$	36.6654	1.18896
$952$	−46.2243	−1.49814
$953$	27.0682	0.876826	0.438413	−	0.898774i	$-0.355541\pi$
$953$	27.0682	0.876826	0.438413	+	0.898774i	$0.355541\pi$
$954$	−4.02211	−0.130221
$955$	−18.0643	−0.584548
$956$	−77.5992	−2.50974
$957$	−42.2640	−1.36620
$958$	28.8709	0.932776
$959$	−64.8481	−2.09406
$960$	26.4580	0.853928
$961$	−23.2188	−0.748994
$962$	−8.75580	−0.282298
$963$	−1.77880	−0.0573209
$964$	3.88989	0.125285
$965$	6.67740	0.214953
$966$	−107.733	−3.46625
$967$	−24.6017	−0.791139	−0.395569	−	0.918436i	$-0.629453\pi$
$967$	−24.6017	−0.791139	−0.395569	+	0.918436i	$0.629453\pi$
$968$	−149.487	−4.80468
$969$	−15.4482	−0.496269
$970$	56.9408	1.82826
$971$	35.3988	1.13600	0.568000	−	0.823028i	$-0.307717\pi$
$971$	35.3988	1.13600	0.568000	+	0.823028i	$0.307717\pi$
$972$	−9.68123	−0.310525
$973$	−24.5601	−0.787361
$974$	19.9488	0.639200
$975$	5.25693	0.168357
$976$	30.5604	0.978216
$977$	−50.4935	−1.61543	−0.807714	−	0.589574i	$-0.799296\pi$
$977$	−50.4935	−1.61543	−0.807714	+	0.589574i	$0.799296\pi$
$978$	98.5252	3.15049
$979$	−76.1137	−2.43261
$980$	31.1422	0.994801
$981$	−0.413620	−0.0132059
$982$	35.9870	1.14839
$983$	27.7646	0.885553	0.442776	−	0.896632i	$-0.353994\pi$
$983$	27.7646	0.885553	0.442776	+	0.896632i	$0.353994\pi$
$984$	86.8167	2.76761
$985$	21.4202	0.682504
$986$	−20.1207	−0.640773
$987$	−0.713832	−0.0227215
$988$	23.7675	0.756143
$989$	−42.9409	−1.36544
$990$	3.95753	0.125779
$991$	−45.0542	−1.43119	−0.715597	−	0.698514i	$-0.753845\pi$
$991$	−45.0542	−1.43119	−0.715597	+	0.698514i	$0.753845\pi$
$992$	32.8114	1.04176
$993$	−28.8723	−0.916235
$994$	−71.4267	−2.26552
$995$	−5.48809	−0.173984
$996$	111.114	3.52079
$997$	23.7996	0.753742	0.376871	−	0.926266i	$-0.377000\pi$
$997$	23.7996	0.753742	0.376871	+	0.926266i	$0.377000\pi$
$998$	36.8728	1.16719
$999$	16.7158	0.528865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.b.1.4	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.b.1.4	✓	140	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62889 q^{2} +1.78605 q^{3} +4.91107 q^{4} +1.43411 q^{5} -4.69533 q^{6} +3.37960 q^{7} -7.65290 q^{8} +0.189969 q^{9} +O(q^{10})\)	\(q-2.62889 q^{2} +1.78605 q^{3} +4.91107 q^{4} +1.43411 q^{5} -4.69533 q^{6} +3.37960 q^{7} -7.65290 q^{8} +0.189969 q^{9} -3.77012 q^{10} -5.52570 q^{11} +8.77141 q^{12} -1.00000 q^{13} -8.88461 q^{14} +2.56139 q^{15} +10.2965 q^{16} +1.78723 q^{17} -0.499407 q^{18} -4.83956 q^{19} +7.04301 q^{20} +6.03613 q^{21} +14.5265 q^{22} +6.78917 q^{23} -13.6684 q^{24} -2.94333 q^{25} +2.62889 q^{26} -5.01885 q^{27} +16.5975 q^{28} +4.28243 q^{29} -6.73361 q^{30} -2.78948 q^{31} -11.7626 q^{32} -9.86916 q^{33} -4.69842 q^{34} +4.84672 q^{35} +0.932951 q^{36} -3.33060 q^{37} +12.7227 q^{38} -1.78605 q^{39} -10.9751 q^{40} -6.35161 q^{41} -15.8683 q^{42} -6.32490 q^{43} -27.1371 q^{44} +0.272436 q^{45} -17.8480 q^{46} -0.118260 q^{47} +18.3900 q^{48} +4.42171 q^{49} +7.73770 q^{50} +3.19207 q^{51} -4.91107 q^{52} +8.05377 q^{53} +13.1940 q^{54} -7.92445 q^{55} -25.8638 q^{56} -8.64370 q^{57} -11.2580 q^{58} -5.51332 q^{59} +12.5792 q^{60} +2.96804 q^{61} +7.33323 q^{62} +0.642019 q^{63} +10.3296 q^{64} -1.43411 q^{65} +25.9450 q^{66} -8.30612 q^{67} +8.77719 q^{68} +12.1258 q^{69} -12.7415 q^{70} +8.03937 q^{71} -1.45381 q^{72} +1.88100 q^{73} +8.75580 q^{74} -5.25693 q^{75} -23.7675 q^{76} -18.6747 q^{77} +4.69533 q^{78} +0.564163 q^{79} +14.7663 q^{80} -9.53382 q^{81} +16.6977 q^{82} +12.6678 q^{83} +29.6439 q^{84} +2.56308 q^{85} +16.6275 q^{86} +7.64863 q^{87} +42.2876 q^{88} +13.7745 q^{89} -0.716205 q^{90} -3.37960 q^{91} +33.3421 q^{92} -4.98214 q^{93} +0.310892 q^{94} -6.94046 q^{95} -21.0085 q^{96} -15.1032 q^{97} -11.6242 q^{98} -1.04971 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * q^99

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