LMFDB - Embedded newform 8033.2.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36338 q^{2} -0.800416 q^{3} +3.58557 q^{4} +2.26233 q^{5} +1.89169 q^{6} +3.86578 q^{7} -3.74731 q^{8} -2.35933 q^{9} +O(q^{10})$	\(q-2.36338 q^{2} -0.800416 q^{3} +3.58557 q^{4} +2.26233 q^{5} +1.89169 q^{6} +3.86578 q^{7} -3.74731 q^{8} -2.35933 q^{9} -5.34676 q^{10} -5.33951 q^{11} -2.86995 q^{12} +3.18448 q^{13} -9.13631 q^{14} -1.81081 q^{15} +1.68517 q^{16} -0.887841 q^{17} +5.57601 q^{18} +2.10701 q^{19} +8.11176 q^{20} -3.09423 q^{21} +12.6193 q^{22} +5.01998 q^{23} +2.99940 q^{24} +0.118160 q^{25} -7.52614 q^{26} +4.28969 q^{27} +13.8610 q^{28} -1.00000 q^{29} +4.27963 q^{30} +8.01222 q^{31} +3.51191 q^{32} +4.27383 q^{33} +2.09831 q^{34} +8.74569 q^{35} -8.45956 q^{36} +3.05489 q^{37} -4.97968 q^{38} -2.54891 q^{39} -8.47766 q^{40} +11.5244 q^{41} +7.31284 q^{42} -6.13567 q^{43} -19.1452 q^{44} -5.33761 q^{45} -11.8641 q^{46} -8.94607 q^{47} -1.34884 q^{48} +7.94425 q^{49} -0.279256 q^{50} +0.710641 q^{51} +11.4182 q^{52} +1.50989 q^{53} -10.1382 q^{54} -12.0798 q^{55} -14.4863 q^{56} -1.68649 q^{57} +2.36338 q^{58} +5.27152 q^{59} -6.49278 q^{60} -1.02502 q^{61} -18.9359 q^{62} -9.12067 q^{63} -11.6703 q^{64} +7.20436 q^{65} -10.1007 q^{66} +2.14684 q^{67} -3.18341 q^{68} -4.01807 q^{69} -20.6694 q^{70} -3.12121 q^{71} +8.84115 q^{72} -9.65507 q^{73} -7.21986 q^{74} -0.0945768 q^{75} +7.55485 q^{76} -20.6414 q^{77} +6.02404 q^{78} -1.31382 q^{79} +3.81243 q^{80} +3.64447 q^{81} -27.2366 q^{82} -0.569206 q^{83} -11.0946 q^{84} -2.00859 q^{85} +14.5009 q^{86} +0.800416 q^{87} +20.0088 q^{88} +4.76350 q^{89} +12.6148 q^{90} +12.3105 q^{91} +17.9995 q^{92} -6.41311 q^{93} +21.1430 q^{94} +4.76677 q^{95} -2.81098 q^{96} +1.39272 q^{97} -18.7753 q^{98} +12.5977 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) $ 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * 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 $

$2$	−2.36338	−1.67116	−0.835581	−	0.549367i	$-0.814869\pi$
$2$	−2.36338	−1.67116	−0.835581	+	0.549367i	$0.814869\pi$
$3$	−0.800416	−0.462120	−0.231060	−	0.972939i	$-0.574219\pi$
$3$	−0.800416	−0.462120	−0.231060	+	0.972939i	$0.574219\pi$
$4$	3.58557	1.79279
$5$	2.26233	1.01175	0.505873	−	0.862608i	$-0.331170\pi$
$5$	2.26233	1.01175	0.505873	+	0.862608i	$0.331170\pi$
$6$	1.89169	0.772278
$7$	3.86578	1.46113	0.730564	−	0.682845i	$-0.239257\pi$
$7$	3.86578	1.46113	0.730564	+	0.682845i	$0.239257\pi$
$8$	−3.74731	−1.32487
$9$	−2.35933	−0.786445
$10$	−5.34676	−1.69079
$11$	−5.33951	−1.60992	−0.804962	−	0.593326i	$-0.797814\pi$
$11$	−5.33951	−1.60992	−0.804962	+	0.593326i	$0.797814\pi$
$12$	−2.86995	−0.828482
$13$	3.18448	0.883216	0.441608	−	0.897208i	$-0.354408\pi$
$13$	3.18448	0.883216	0.441608	+	0.897208i	$0.354408\pi$
$14$	−9.13631	−2.44178
$15$	−1.81081	−0.467549
$16$	1.68517	0.421293
$17$	−0.887841	−0.215333	−0.107666	−	0.994187i	$-0.534338\pi$
$17$	−0.887841	−0.215333	−0.107666	+	0.994187i	$0.534338\pi$
$18$	5.57601	1.31428
$19$	2.10701	0.483382	0.241691	−	0.970353i	$-0.422298\pi$
$19$	2.10701	0.483382	0.241691	+	0.970353i	$0.422298\pi$
$20$	8.11176	1.81384
$21$	−3.09423	−0.675216
$22$	12.6193	2.69044
$23$	5.01998	1.04674	0.523369	−	0.852106i	$-0.324675\pi$
$23$	5.01998	1.04674	0.523369	+	0.852106i	$0.324675\pi$
$24$	2.99940	0.612250
$25$	0.118160	0.0236319
$26$	−7.52614	−1.47600
$27$	4.28969	0.825552
$28$	13.8610	2.61949
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	4.27963	0.781350
$31$	8.01222	1.43904	0.719519	−	0.694473i	$-0.244362\pi$
$31$	8.01222	1.43904	0.719519	+	0.694473i	$0.244362\pi$
$32$	3.51191	0.620823
$33$	4.27383	0.743978
$34$	2.09831	0.359856
$35$	8.74569	1.47829
$36$	−8.45956	−1.40993
$37$	3.05489	0.502220	0.251110	−	0.967959i	$-0.419204\pi$
$37$	3.05489	0.502220	0.251110	+	0.967959i	$0.419204\pi$
$38$	−4.97968	−0.807810
$39$	−2.54891	−0.408152
$40$	−8.47766	−1.34044
$41$	11.5244	1.79981	0.899906	−	0.436085i	$-0.143635\pi$
$41$	11.5244	1.79981	0.899906	+	0.436085i	$0.143635\pi$
$42$	7.31284	1.12840
$43$	−6.13567	−0.935681	−0.467840	−	0.883813i	$-0.654968\pi$
$43$	−6.13567	−0.935681	−0.467840	+	0.883813i	$0.654968\pi$
$44$	−19.1452	−2.88625
$45$	−5.33761	−0.795683
$46$	−11.8641	−1.74927
$47$	−8.94607	−1.30492	−0.652459	−	0.757824i	$-0.726263\pi$
$47$	−8.94607	−1.30492	−0.652459	+	0.757824i	$0.726263\pi$
$48$	−1.34884	−0.194688
$49$	7.94425	1.13489
$50$	−0.279256	−0.0394928
$51$	0.710641	0.0995097
$52$	11.4182	1.58342
$53$	1.50989	0.207399	0.103700	−	0.994609i	$-0.466932\pi$
$53$	1.50989	0.207399	0.103700	+	0.994609i	$0.466932\pi$
$54$	−10.1382	−1.37963
$55$	−12.0798	−1.62884
$56$	−14.4863	−1.93581
$57$	−1.68649	−0.223381
$58$	2.36338	0.310327
$59$	5.27152	0.686294	0.343147	−	0.939282i	$-0.388507\pi$
$59$	5.27152	0.686294	0.343147	+	0.939282i	$0.388507\pi$
$60$	−6.49278	−0.838214
$61$	−1.02502	−0.131240	−0.0656202	−	0.997845i	$-0.520903\pi$
$61$	−1.02502	−0.131240	−0.0656202	+	0.997845i	$0.520903\pi$
$62$	−18.9359	−2.40487
$63$	−9.12067	−1.14910
$64$	−11.6703	−1.45879
$65$	7.20436	0.893591
$66$	−10.1007	−1.24331
$67$	2.14684	0.262279	0.131139	−	0.991364i	$-0.458136\pi$
$67$	2.14684	0.262279	0.131139	+	0.991364i	$0.458136\pi$
$68$	−3.18341	−0.386046
$69$	−4.01807	−0.483719
$70$	−20.6694	−2.47046
$71$	−3.12121	−0.370420	−0.185210	−	0.982699i	$-0.559297\pi$
$71$	−3.12121	−0.370420	−0.185210	+	0.982699i	$0.559297\pi$
$72$	8.84115	1.04194
$73$	−9.65507	−1.13004	−0.565020	−	0.825077i	$-0.691132\pi$
$73$	−9.65507	−1.13004	−0.565020	+	0.825077i	$0.691132\pi$
$74$	−7.21986	−0.839292
$75$	−0.0945768	−0.0109208
$76$	7.55485	0.866600
$77$	−20.6414	−2.35230
$78$	6.02404	0.682088
$79$	−1.31382	−0.147817	−0.0739083	−	0.997265i	$-0.523547\pi$
$79$	−1.31382	−0.147817	−0.0739083	+	0.997265i	$0.523547\pi$
$80$	3.81243	0.426242
$81$	3.64447	0.404941
$82$	−27.2366	−3.00778
$83$	−0.569206	−0.0624784	−0.0312392	−	0.999512i	$-0.509945\pi$
$83$	−0.569206	−0.0624784	−0.0312392	+	0.999512i	$0.509945\pi$
$84$	−11.0946	−1.21052
$85$	−2.00859	−0.217862
$86$	14.5009	1.56368
$87$	0.800416	0.0858136
$88$	20.0088	2.13294
$89$	4.76350	0.504930	0.252465	−	0.967606i	$-0.418759\pi$
$89$	4.76350	0.504930	0.252465	+	0.967606i	$0.418759\pi$
$90$	12.6148	1.32972
$91$	12.3105	1.29049
$92$	17.9995	1.87658
$93$	−6.41311	−0.665008
$94$	21.1430	2.18073
$95$	4.76677	0.489060
$96$	−2.81098	−0.286895
$97$	1.39272	0.141409	0.0707047	−	0.997497i	$-0.477475\pi$
$97$	1.39272	0.141409	0.0707047	+	0.997497i	$0.477475\pi$
$98$	−18.7753	−1.89659
$99$	12.5977	1.26612
$100$	0.423669	0.0423669
$101$	2.91354	0.289908	0.144954	−	0.989438i	$-0.453697\pi$
$101$	2.91354	0.289908	0.144954	+	0.989438i	$0.453697\pi$
$102$	−1.67952	−0.166297
$103$	17.4616	1.72054	0.860269	−	0.509840i	$-0.170295\pi$
$103$	17.4616	1.72054	0.860269	+	0.509840i	$0.170295\pi$
$104$	−11.9332	−1.17015
$105$	−7.00018	−0.683148
$106$	−3.56845	−0.346598
$107$	−10.4825	−1.01338	−0.506689	−	0.862129i	$-0.669131\pi$
$107$	−10.4825	−1.01338	−0.506689	+	0.862129i	$0.669131\pi$
$108$	15.3810	1.48004
$109$	13.1267	1.25731	0.628655	−	0.777685i	$-0.283606\pi$
$109$	13.1267	1.25731	0.628655	+	0.777685i	$0.283606\pi$
$110$	28.5491	2.72205
$111$	−2.44518	−0.232086
$112$	6.51451	0.615563
$113$	−8.49416	−0.799063	−0.399532	−	0.916719i	$-0.630827\pi$
$113$	−8.49416	−0.799063	−0.399532	+	0.916719i	$0.630827\pi$
$114$	3.98581	0.373305
$115$	11.3569	1.05903
$116$	−3.58557	−0.332912
$117$	−7.51326	−0.694601
$118$	−12.4586	−1.14691
$119$	−3.43220	−0.314629
$120$	6.78565	0.619443
$121$	17.5104	1.59186
$122$	2.42252	0.219324
$123$	−9.22432	−0.831729
$124$	28.7284	2.57988
$125$	−11.0444	−0.987837
$126$	21.5556	1.92033
$127$	7.86509	0.697914	0.348957	−	0.937139i	$-0.386536\pi$
$127$	7.86509	0.697914	0.348957	+	0.937139i	$0.386536\pi$
$128$	20.5576	1.81705
$129$	4.91109	0.432397
$130$	−17.0267	−1.49334
$131$	−20.8819	−1.82446	−0.912232	−	0.409674i	$-0.865643\pi$
$131$	−20.8819	−1.82446	−0.912232	+	0.409674i	$0.865643\pi$
$132$	15.3241	1.33379
$133$	8.14525	0.706283
$134$	−5.07381	−0.438311
$135$	9.70473	0.835250
$136$	3.32701	0.285289
$137$	−21.1466	−1.80667	−0.903337	−	0.428931i	$-0.858890\pi$
$137$	−21.1466	−1.80667	−0.903337	+	0.428931i	$0.858890\pi$
$138$	9.49624	0.808373
$139$	15.6694	1.32907	0.664533	−	0.747259i	$-0.268631\pi$
$139$	15.6694	1.32907	0.664533	+	0.747259i	$0.268631\pi$
$140$	31.3583	2.65026
$141$	7.16058	0.603029
$142$	7.37662	0.619032
$143$	−17.0036	−1.42191
$144$	−3.97589	−0.331324
$145$	−2.26233	−0.187877
$146$	22.8186	1.88848
$147$	−6.35870	−0.524457
$148$	10.9535	0.900373
$149$	−3.87777	−0.317679	−0.158839	−	0.987304i	$-0.550775\pi$
$149$	−3.87777	−0.317679	−0.158839	+	0.987304i	$0.550775\pi$
$150$	0.223521	0.0182504
$151$	14.4803	1.17839	0.589196	−	0.807990i	$-0.299445\pi$
$151$	14.4803	1.17839	0.589196	+	0.807990i	$0.299445\pi$
$152$	−7.89563	−0.640420
$153$	2.09471	0.169348
$154$	48.7834	3.93108
$155$	18.1263	1.45594
$156$	−9.13929	−0.731729
$157$	8.66710	0.691710	0.345855	−	0.938288i	$-0.387589\pi$
$157$	8.66710	0.691710	0.345855	+	0.938288i	$0.387589\pi$
$158$	3.10506	0.247026
$159$	−1.20854	−0.0958434
$160$	7.94511	0.628116
$161$	19.4061	1.52942
$162$	−8.61326	−0.676722
$163$	−8.90490	−0.697485	−0.348743	−	0.937218i	$-0.613391\pi$
$163$	−8.90490	−0.697485	−0.348743	+	0.937218i	$0.613391\pi$
$164$	41.3216	3.22667
$165$	9.66883	0.752718
$166$	1.34525	0.104412
$167$	17.6198	1.36346	0.681732	−	0.731602i	$-0.261227\pi$
$167$	17.6198	1.36346	0.681732	+	0.731602i	$0.261227\pi$
$168$	11.5950	0.894576
$169$	−2.85909	−0.219930
$170$	4.74707	0.364084
$171$	−4.97115	−0.380153
$172$	−21.9999	−1.67747
$173$	11.2262	0.853511	0.426756	−	0.904367i	$-0.359656\pi$
$173$	11.2262	0.853511	0.426756	+	0.904367i	$0.359656\pi$
$174$	−1.89169	−0.143408
$175$	0.456779	0.0345292
$176$	−8.99801	−0.678250
$177$	−4.21941	−0.317150
$178$	−11.2580	−0.843820
$179$	−9.22787	−0.689723	−0.344862	−	0.938654i	$-0.612074\pi$
$179$	−9.22787	−0.689723	−0.344862	+	0.938654i	$0.612074\pi$
$180$	−19.1384	−1.42649
$181$	−4.12140	−0.306341	−0.153171	−	0.988200i	$-0.548948\pi$
$181$	−4.12140	−0.306341	−0.153171	+	0.988200i	$0.548948\pi$
$182$	−29.0944	−2.15662
$183$	0.820443	0.0606489
$184$	−18.8114	−1.38680
$185$	6.91117	0.508120
$186$	15.1566	1.11134
$187$	4.74064	0.346670
$188$	−32.0768	−2.33944
$189$	16.5830	1.20624
$190$	−11.2657	−0.817300
$191$	9.29435	0.672515	0.336258	−	0.941770i	$-0.390839\pi$
$191$	9.29435	0.672515	0.336258	+	0.941770i	$0.390839\pi$
$192$	9.34111	0.674136
$193$	1.48317	0.106761	0.0533806	−	0.998574i	$-0.483000\pi$
$193$	1.48317	0.106761	0.0533806	+	0.998574i	$0.483000\pi$
$194$	−3.29153	−0.236318
$195$	−5.76648	−0.412946
$196$	28.4847	2.03462
$197$	2.58554	0.184212	0.0921062	−	0.995749i	$-0.470640\pi$
$197$	2.58554	0.184212	0.0921062	+	0.995749i	$0.470640\pi$
$198$	−29.7732	−2.11589
$199$	2.30192	0.163179	0.0815893	−	0.996666i	$-0.474000\pi$
$199$	2.30192	0.163179	0.0815893	+	0.996666i	$0.474000\pi$
$200$	−0.442780	−0.0313093
$201$	−1.71837	−0.121204
$202$	−6.88580	−0.484483
$203$	−3.86578	−0.271325
$204$	2.54805	0.178400
$205$	26.0721	1.82095
$206$	−41.2683	−2.87530
$207$	−11.8438	−0.823202
$208$	5.36640	0.372093
$209$	−11.2504	−0.778208
$210$	16.5441	1.14165
$211$	−8.80033	−0.605840	−0.302920	−	0.953016i	$-0.597961\pi$
$211$	−8.80033	−0.605840	−0.302920	+	0.953016i	$0.597961\pi$
$212$	5.41382	0.371823
$213$	2.49827	0.171178
$214$	24.7740	1.69352
$215$	−13.8809	−0.946672
$216$	−16.0748	−1.09375
$217$	30.9735	2.10262
$218$	−31.0234	−2.10117
$219$	7.72806	0.522214
$220$	−43.3129	−2.92015
$221$	−2.82731	−0.190186
$222$	5.77889	0.387854
$223$	19.8496	1.32923	0.664615	−	0.747186i	$-0.268596\pi$
$223$	19.8496	1.32923	0.664615	+	0.747186i	$0.268596\pi$
$224$	13.5763	0.907102
$225$	−0.278778	−0.0185852
$226$	20.0749	1.33536
$227$	−11.6991	−0.776497	−0.388249	−	0.921555i	$-0.626920\pi$
$227$	−11.6991	−0.776497	−0.388249	+	0.921555i	$0.626920\pi$
$228$	−6.04702	−0.400473
$229$	13.5189	0.893351	0.446676	−	0.894696i	$-0.352608\pi$
$229$	13.5189	0.893351	0.446676	+	0.894696i	$0.352608\pi$
$230$	−26.8406	−1.76982
$231$	16.5217	1.08705
$232$	3.74731	0.246023
$233$	2.17352	0.142392	0.0711960	−	0.997462i	$-0.477318\pi$
$233$	2.17352	0.142392	0.0711960	+	0.997462i	$0.477318\pi$
$234$	17.7567	1.16079
$235$	−20.2390	−1.32025
$236$	18.9014	1.23038
$237$	1.05160	0.0683090
$238$	8.11159	0.525796
$239$	4.23602	0.274005	0.137003	−	0.990571i	$-0.456253\pi$
$239$	4.23602	0.274005	0.137003	+	0.990571i	$0.456253\pi$
$240$	−3.05153	−0.196975
$241$	−6.35994	−0.409680	−0.204840	−	0.978795i	$-0.565667\pi$
$241$	−6.35994	−0.409680	−0.204840	+	0.978795i	$0.565667\pi$
$242$	−41.3838	−2.66025
$243$	−15.7862	−1.01268
$244$	−3.67528	−0.235286
$245$	17.9726	1.14822
$246$	21.8006	1.38995
$247$	6.70974	0.426931
$248$	−30.0243	−1.90654
$249$	0.455601	0.0288725
$250$	26.1020	1.65084
$251$	1.86179	0.117515	0.0587574	−	0.998272i	$-0.481286\pi$
$251$	1.86179	0.117515	0.0587574	+	0.998272i	$0.481286\pi$
$252$	−32.7028	−2.06008
$253$	−26.8043	−1.68517
$254$	−18.5882	−1.16633
$255$	1.60771	0.100679
$256$	−25.2448	−1.57780
$257$	−3.46192	−0.215949	−0.107974	−	0.994154i	$-0.534436\pi$
$257$	−3.46192	−0.215949	−0.107974	+	0.994154i	$0.534436\pi$
$258$	−11.6068	−0.722606
$259$	11.8095	0.733807
$260$	25.8317	1.60202
$261$	2.35933	0.146039
$262$	49.3520	3.04898
$263$	14.5394	0.896539	0.448270	−	0.893898i	$-0.352040\pi$
$263$	14.5394	0.896539	0.448270	+	0.893898i	$0.352040\pi$
$264$	−16.0154	−0.985677
$265$	3.41588	0.209836
$266$	−19.2503	−1.18031
$267$	−3.81278	−0.233338
$268$	7.69766	0.470210
$269$	12.0819	0.736649	0.368325	−	0.929697i	$-0.379931\pi$
$269$	12.0819	0.736649	0.368325	+	0.929697i	$0.379931\pi$
$270$	−22.9360	−1.39584
$271$	−12.4835	−0.758317	−0.379159	−	0.925332i	$-0.623787\pi$
$271$	−12.4835	−0.758317	−0.379159	+	0.925332i	$0.623787\pi$
$272$	−1.49617	−0.0907184
$273$	−9.85351	−0.596362
$274$	49.9774	3.01925
$275$	−0.630915	−0.0380456
$276$	−14.4071	−0.867204
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	−37.0329	−2.22108
$279$	−18.9035	−1.13172
$280$	−32.7728	−1.95855
$281$	13.0002	0.775528	0.387764	−	0.921759i	$-0.373248\pi$
$281$	13.0002	0.775528	0.387764	+	0.921759i	$0.373248\pi$
$282$	−16.9232	−1.00776
$283$	−5.21429	−0.309957	−0.154979	−	0.987918i	$-0.549531\pi$
$283$	−5.21429	−0.309957	−0.154979	+	0.987918i	$0.549531\pi$
$284$	−11.1913	−0.664083
$285$	−3.81540	−0.226005
$286$	40.1859	2.37624
$287$	44.5508	2.62975
$288$	−8.28576	−0.488243
$289$	−16.2117	−0.953632
$290$	5.34676	0.313973
$291$	−1.11475	−0.0653481
$292$	−34.6189	−2.02592
$293$	14.2380	0.831794	0.415897	−	0.909412i	$-0.363468\pi$
$293$	14.2380	0.831794	0.415897	+	0.909412i	$0.363468\pi$
$294$	15.0280	0.876453
$295$	11.9259	0.694355
$296$	−11.4476	−0.665378
$297$	−22.9049	−1.32908
$298$	9.16464	0.530893
$299$	15.9860	0.924496
$300$	−0.339112	−0.0195786
$301$	−23.7191	−1.36715
$302$	−34.2225	−1.96928
$303$	−2.33204	−0.133972
$304$	3.55068	0.203646
$305$	−2.31894	−0.132782
$306$	−4.95061	−0.283007
$307$	13.3815	0.763722	0.381861	−	0.924220i	$-0.375283\pi$
$307$	13.3815	0.763722	0.381861	+	0.924220i	$0.375283\pi$
$308$	−74.0111	−4.21717
$309$	−13.9765	−0.795096
$310$	−42.8394	−2.43312
$311$	11.3178	0.641775	0.320888	−	0.947117i	$-0.396019\pi$
$311$	11.3178	0.641775	0.320888	+	0.947117i	$0.396019\pi$
$312$	9.55154	0.540749
$313$	10.2964	0.581986	0.290993	−	0.956725i	$-0.406014\pi$
$313$	10.2964	0.581986	0.290993	+	0.956725i	$0.406014\pi$
$314$	−20.4837	−1.15596
$315$	−20.6340	−1.16259
$316$	−4.71080	−0.265003
$317$	−29.8702	−1.67768	−0.838838	−	0.544381i	$-0.816765\pi$
$317$	−29.8702	−1.67768	−0.838838	+	0.544381i	$0.816765\pi$
$318$	2.85624	0.160170
$319$	5.33951	0.298955
$320$	−26.4022	−1.47593
$321$	8.39032	0.468302
$322$	−45.8641	−2.55591
$323$	−1.87069	−0.104088
$324$	13.0675	0.725972
$325$	0.376277	0.0208721
$326$	21.0457	1.16561
$327$	−10.5068	−0.581028
$328$	−43.1855	−2.38452
$329$	−34.5835	−1.90665
$330$	−22.8511	−1.25791
$331$	17.3961	0.956178	0.478089	−	0.878311i	$-0.341330\pi$
$331$	17.3961	0.956178	0.478089	+	0.878311i	$0.341330\pi$
$332$	−2.04093	−0.112010
$333$	−7.20750	−0.394969
$334$	−41.6424	−2.27857
$335$	4.85688	0.265360
$336$	−5.21431	−0.284464
$337$	7.09018	0.386227	0.193113	−	0.981176i	$-0.438142\pi$
$337$	7.09018	0.386227	0.193113	+	0.981176i	$0.438142\pi$
$338$	6.75711	0.367538
$339$	6.79886	0.369263
$340$	−7.20195	−0.390581
$341$	−42.7814	−2.31674
$342$	11.7487	0.635298
$343$	3.65026	0.197095
$344$	22.9922	1.23966
$345$	−9.09022	−0.489401
$346$	−26.5318	−1.42636
$347$	−18.6447	−1.00090	−0.500451	−	0.865765i	$-0.666832\pi$
$347$	−18.6447	−1.00090	−0.500451	+	0.865765i	$0.666832\pi$
$348$	2.86995	0.153845
$349$	6.21278	0.332562	0.166281	−	0.986078i	$-0.446824\pi$
$349$	6.21278	0.332562	0.166281	+	0.986078i	$0.446824\pi$
$350$	−1.07954	−0.0577040
$351$	13.6604	0.729141
$352$	−18.7519	−0.999478
$353$	−6.12422	−0.325959	−0.162980	−	0.986629i	$-0.552111\pi$
$353$	−6.12422	−0.325959	−0.162980	+	0.986629i	$0.552111\pi$
$354$	9.97207	0.530009
$355$	−7.06123	−0.374771
$356$	17.0799	0.905230
$357$	2.74718	0.145396
$358$	21.8090	1.15264
$359$	−3.43257	−0.181164	−0.0905820	−	0.995889i	$-0.528873\pi$
$359$	−3.43257	−0.181164	−0.0905820	+	0.995889i	$0.528873\pi$
$360$	20.0016	1.05418
$361$	−14.5605	−0.766342
$362$	9.74043	0.511946
$363$	−14.0156	−0.735628
$364$	44.1402	2.31357
$365$	−21.8430	−1.14331
$366$	−1.93902	−0.101354
$367$	11.6382	0.607509	0.303755	−	0.952750i	$-0.401760\pi$
$367$	11.6382	0.607509	0.303755	+	0.952750i	$0.401760\pi$
$368$	8.45954	0.440984
$369$	−27.1900	−1.41545
$370$	−16.3337	−0.849151
$371$	5.83690	0.303037
$372$	−22.9946	−1.19222
$373$	−9.07818	−0.470050	−0.235025	−	0.971989i	$-0.575517\pi$
$373$	−9.07818	−0.470050	−0.235025	+	0.971989i	$0.575517\pi$
$374$	−11.2039	−0.579342
$375$	8.84008	0.456500
$376$	33.5237	1.72885
$377$	−3.18448	−0.164009
$378$	−39.1920	−2.01582
$379$	−10.3835	−0.533364	−0.266682	−	0.963785i	$-0.585927\pi$
$379$	−10.3835	−0.533364	−0.266682	+	0.963785i	$0.585927\pi$
$380$	17.0916	0.876780
$381$	−6.29534	−0.322520
$382$	−21.9661	−1.12388
$383$	29.9240	1.52905	0.764523	−	0.644596i	$-0.222974\pi$
$383$	29.9240	1.52905	0.764523	+	0.644596i	$0.222974\pi$
$384$	−16.4546	−0.839696
$385$	−46.6977	−2.37994
$386$	−3.50530	−0.178415
$387$	14.4761	0.735862
$388$	4.99370	0.253517
$389$	−18.1760	−0.921560	−0.460780	−	0.887514i	$-0.652430\pi$
$389$	−18.1760	−0.921560	−0.460780	+	0.887514i	$0.652430\pi$
$390$	13.6284	0.690101
$391$	−4.45694	−0.225397
$392$	−29.7695	−1.50359
$393$	16.7142	0.843122
$394$	−6.11063	−0.307849
$395$	−2.97231	−0.149553
$396$	45.1699	2.26988
$397$	22.8116	1.14488	0.572440	−	0.819947i	$-0.305997\pi$
$397$	22.8116	1.14488	0.572440	+	0.819947i	$0.305997\pi$
$398$	−5.44031	−0.272698
$399$	−6.51959	−0.326387
$400$	0.199119	0.00995597
$401$	−9.23974	−0.461411	−0.230705	−	0.973024i	$-0.574103\pi$
$401$	−9.23974	−0.461411	−0.230705	+	0.973024i	$0.574103\pi$
$402$	4.06116	0.202552
$403$	25.5148	1.27098
$404$	10.4467	0.519742
$405$	8.24500	0.409698
$406$	9.13631	0.453427
$407$	−16.3116	−0.808536
$408$	−2.66299	−0.131838
$409$	33.9228	1.67737	0.838687	−	0.544613i	$-0.183324\pi$
$409$	33.9228	1.67737	0.838687	+	0.544613i	$0.183324\pi$
$410$	−61.6183	−3.04311
$411$	16.9261	0.834901
$412$	62.6097	3.08456
$413$	20.3785	1.00276
$414$	27.9915	1.37571
$415$	−1.28773	−0.0632124
$416$	11.1836	0.548321
$417$	−12.5421	−0.614188
$418$	26.5891	1.30051
$419$	−17.3074	−0.845522	−0.422761	−	0.906241i	$-0.638939\pi$
$419$	−17.3074	−0.845522	−0.422761	+	0.906241i	$0.638939\pi$
$420$	−25.0997	−1.22474
$421$	29.0106	1.41389	0.706944	−	0.707269i	$-0.250073\pi$
$421$	29.0106	1.41389	0.706944	+	0.707269i	$0.250073\pi$
$422$	20.7985	1.01246
$423$	21.1068	1.02625
$424$	−5.65802	−0.274778
$425$	−0.104907	−0.00508873
$426$	−5.90436	−0.286067
$427$	−3.96251	−0.191759
$428$	−37.5856	−1.81677
$429$	13.6099	0.657093
$430$	32.8060	1.58204
$431$	−13.1166	−0.631805	−0.315903	−	0.948792i	$-0.602307\pi$
$431$	−13.1166	−0.631805	−0.315903	+	0.948792i	$0.602307\pi$
$432$	7.22888	0.347800
$433$	−31.5201	−1.51476	−0.757380	−	0.652975i	$-0.773521\pi$
$433$	−31.5201	−1.51476	−0.757380	+	0.652975i	$0.773521\pi$
$434$	−73.2021	−3.51381
$435$	1.81081	0.0868216
$436$	47.0667	2.25409
$437$	10.5772	0.505975
$438$	−18.2644	−0.872705
$439$	−33.1093	−1.58022	−0.790110	−	0.612966i	$-0.789976\pi$
$439$	−33.1093	−1.58022	−0.790110	+	0.612966i	$0.789976\pi$
$440$	45.2666	2.15800
$441$	−18.7431	−0.892531
$442$	6.68201	0.317831
$443$	33.0975	1.57251	0.786255	−	0.617902i	$-0.212017\pi$
$443$	33.0975	1.57251	0.786255	+	0.617902i	$0.212017\pi$
$444$	−8.76736	−0.416080
$445$	10.7766	0.510861
$446$	−46.9122	−2.22136
$447$	3.10382	0.146806
$448$	−45.1149	−2.13148
$449$	11.6070	0.547766	0.273883	−	0.961763i	$-0.411692\pi$
$449$	11.6070	0.547766	0.273883	+	0.961763i	$0.411692\pi$
$450$	0.658859	0.0310589
$451$	−61.5348	−2.89756
$452$	−30.4564	−1.43255
$453$	−11.5903	−0.544558
$454$	27.6494	1.29765
$455$	27.8505	1.30565
$456$	6.31978	0.295951
$457$	−3.18518	−0.148996	−0.0744982	−	0.997221i	$-0.523736\pi$
$457$	−3.18518	−0.148996	−0.0744982	+	0.997221i	$0.523736\pi$
$458$	−31.9502	−1.49294
$459$	−3.80857	−0.177769
$460$	40.7209	1.89862
$461$	37.5656	1.74960	0.874802	−	0.484481i	$-0.160992\pi$
$461$	37.5656	1.74960	0.874802	+	0.484481i	$0.160992\pi$
$462$	−39.0470	−1.81663
$463$	22.8313	1.06106	0.530530	−	0.847666i	$-0.321993\pi$
$463$	22.8313	1.06106	0.530530	+	0.847666i	$0.321993\pi$
$464$	−1.68517	−0.0782322
$465$	−14.5086	−0.672820
$466$	−5.13686	−0.237960
$467$	6.49453	0.300531	0.150265	−	0.988646i	$-0.451987\pi$
$467$	6.49453	0.300531	0.150265	+	0.988646i	$0.451987\pi$
$468$	−26.9393	−1.24527
$469$	8.29923	0.383223
$470$	47.8325	2.20635
$471$	−6.93728	−0.319653
$472$	−19.7540	−0.909252
$473$	32.7615	1.50638
$474$	−2.48534	−0.114155
$475$	0.248964	0.0114232
$476$	−12.3064	−0.564062
$477$	−3.56234	−0.163108
$478$	−10.0113	−0.457908
$479$	0.390432	0.0178393	0.00891965	−	0.999960i	$-0.497161\pi$
$479$	0.390432	0.0178393	0.00891965	+	0.999960i	$0.497161\pi$
$480$	−6.35939	−0.290265
$481$	9.72822	0.443569
$482$	15.0310	0.684642
$483$	−15.5330	−0.706775
$484$	62.7848	2.85385
$485$	3.15080	0.143070
$486$	37.3087	1.69236
$487$	4.12751	0.187036	0.0935178	−	0.995618i	$-0.470189\pi$
$487$	4.12751	0.187036	0.0935178	+	0.995618i	$0.470189\pi$
$488$	3.84107	0.173877
$489$	7.12762	0.322322
$490$	−42.4760	−1.91887
$491$	−12.4477	−0.561759	−0.280879	−	0.959743i	$-0.590626\pi$
$491$	−12.4477	−0.561759	−0.280879	+	0.959743i	$0.590626\pi$
$492$	−33.0744	−1.49111
$493$	0.887841	0.0399863
$494$	−15.8577	−0.713471
$495$	28.5002	1.28099
$496$	13.5020	0.606257
$497$	−12.0659	−0.541230
$498$	−1.07676	−0.0482507
$499$	0.129856	0.00581317	0.00290659	−	0.999996i	$-0.499075\pi$
$499$	0.129856	0.00581317	0.00290659	+	0.999996i	$0.499075\pi$
$500$	−39.6003	−1.77098
$501$	−14.1032	−0.630084
$502$	−4.40011	−0.196386
$503$	−13.0250	−0.580758	−0.290379	−	0.956912i	$-0.593781\pi$
$503$	−13.0250	−0.580758	−0.290379	+	0.956912i	$0.593781\pi$
$504$	34.1779	1.52241
$505$	6.59140	0.293313
$506$	63.3487	2.81619
$507$	2.28846	0.101634
$508$	28.2008	1.25121
$509$	35.7659	1.58530	0.792648	−	0.609679i	$-0.208702\pi$
$509$	35.7659	1.58530	0.792648	+	0.609679i	$0.208702\pi$
$510$	−3.79963	−0.168250
$511$	−37.3244	−1.65113
$512$	18.5479	0.819709
$513$	9.03845	0.399057
$514$	8.18185	0.360886
$515$	39.5039	1.74075
$516$	17.6090	0.775195
$517$	47.7677	2.10082
$518$	−27.9104	−1.22631
$519$	−8.98562	−0.394425
$520$	−26.9969	−1.18389
$521$	38.8689	1.70288	0.851438	−	0.524454i	$-0.175731\pi$
$521$	38.8689	1.70288	0.851438	+	0.524454i	$0.175731\pi$
$522$	−5.57601	−0.244055
$523$	25.1258	1.09867	0.549337	−	0.835601i	$-0.314880\pi$
$523$	25.1258	1.09867	0.549337	+	0.835601i	$0.314880\pi$
$524$	−74.8737	−3.27087
$525$	−0.365613	−0.0159567
$526$	−34.3622	−1.49826
$527$	−7.11358	−0.309872
$528$	7.20214	0.313433
$529$	2.20022	0.0956619
$530$	−8.07302	−0.350670
$531$	−12.4373	−0.539732
$532$	29.2054	1.26621
$533$	36.6993	1.58962
$534$	9.01104	0.389946
$535$	−23.7148	−1.02528
$536$	−8.04489	−0.347486
$537$	7.38613	0.318735
$538$	−28.5543	−1.23106
$539$	−42.4184	−1.82709
$540$	34.7970	1.49742
$541$	−12.5003	−0.537431	−0.268716	−	0.963220i	$-0.586599\pi$
$541$	−12.5003	−0.537431	−0.268716	+	0.963220i	$0.586599\pi$
$542$	29.5032	1.26727
$543$	3.29883	0.141566
$544$	−3.11801	−0.133684
$545$	29.6970	1.27208
$546$	23.2876	0.996618
$547$	43.3605	1.85396	0.926980	−	0.375110i	$-0.122395\pi$
$547$	43.3605	1.85396	0.926980	+	0.375110i	$0.122395\pi$
$548$	−75.8226	−3.23898
$549$	2.41837	0.103213
$550$	1.49109	0.0635804
$551$	−2.10701	−0.0897618
$552$	15.0569	0.640866
$553$	−5.07895	−0.215979
$554$	−2.36338	−0.100410
$555$	−5.53181	−0.234812
$556$	56.1839	2.38273
$557$	40.4196	1.71263	0.856316	−	0.516452i	$-0.172748\pi$
$557$	40.4196	1.71263	0.856316	+	0.516452i	$0.172748\pi$
$558$	44.6762	1.89129
$559$	−19.5389	−0.826408
$560$	14.7380	0.622794
$561$	−3.79448	−0.160203
$562$	−30.7245	−1.29603
$563$	−38.5736	−1.62568	−0.812841	−	0.582485i	$-0.802080\pi$
$563$	−38.5736	−1.62568	−0.812841	+	0.582485i	$0.802080\pi$
$564$	25.6747	1.08110
$565$	−19.2166	−0.808450
$566$	12.3234	0.517989
$567$	14.0887	0.591670
$568$	11.6961	0.490759
$569$	−38.5784	−1.61729	−0.808645	−	0.588296i	$-0.799799\pi$
$569$	−38.5784	−1.61729	−0.808645	+	0.588296i	$0.799799\pi$
$570$	9.01724	0.377691
$571$	8.81645	0.368957	0.184478	−	0.982837i	$-0.440940\pi$
$571$	8.81645	0.368957	0.184478	+	0.982837i	$0.440940\pi$
$572$	−60.9675	−2.54918
$573$	−7.43934	−0.310783
$574$	−105.291	−4.39475
$575$	0.593159	0.0247364
$576$	27.5342	1.14726
$577$	27.8311	1.15862	0.579312	−	0.815106i	$-0.303321\pi$
$577$	27.8311	1.15862	0.579312	+	0.815106i	$0.303321\pi$
$578$	38.3145	1.59367
$579$	−1.18715	−0.0493365
$580$	−8.11176	−0.336823
$581$	−2.20042	−0.0912889
$582$	2.63459	0.109207
$583$	−8.06208	−0.333897
$584$	36.1805	1.49716
$585$	−16.9975	−0.702760
$586$	−33.6499	−1.39006
$587$	−24.7461	−1.02138	−0.510690	−	0.859765i	$-0.670610\pi$
$587$	−24.7461	−1.02138	−0.510690	+	0.859765i	$0.670610\pi$
$588$	−22.7996	−0.940238
$589$	16.8819	0.695605
$590$	−28.1856	−1.16038
$591$	−2.06951	−0.0851283
$592$	5.14801	0.211582
$593$	34.5770	1.41991	0.709954	−	0.704248i	$-0.248716\pi$
$593$	34.5770	1.41991	0.709954	+	0.704248i	$0.248716\pi$
$594$	54.1330	2.22110
$595$	−7.76478	−0.318325
$596$	−13.9040	−0.569530
$597$	−1.84249	−0.0754081
$598$	−37.7811	−1.54498
$599$	−25.7838	−1.05350	−0.526750	−	0.850021i	$-0.676589\pi$
$599$	−25.7838	−1.05350	−0.526750	+	0.850021i	$0.676589\pi$
$600$	0.354408	0.0144687
$601$	−11.7634	−0.479838	−0.239919	−	0.970793i	$-0.577121\pi$
$601$	−11.7634	−0.479838	−0.239919	+	0.970793i	$0.577121\pi$
$602$	56.0574	2.28473
$603$	−5.06513	−0.206268
$604$	51.9202	2.11260
$605$	39.6144	1.61055
$606$	5.51150	0.223889
$607$	−39.3498	−1.59716	−0.798579	−	0.601889i	$-0.794415\pi$
$607$	−39.3498	−1.59716	−0.798579	+	0.601889i	$0.794415\pi$
$608$	7.39964	0.300095
$609$	3.09423	0.125385
$610$	5.48054	0.221901
$611$	−28.4886	−1.15253
$612$	7.51074	0.303604
$613$	−19.8123	−0.800212	−0.400106	−	0.916469i	$-0.631027\pi$
$613$	−19.8123	−0.800212	−0.400106	+	0.916469i	$0.631027\pi$
$614$	−31.6256	−1.27630
$615$	−20.8685	−0.841499
$616$	77.3496	3.11650
$617$	9.22589	0.371420	0.185710	−	0.982605i	$-0.440541\pi$
$617$	9.22589	0.371420	0.185710	+	0.982605i	$0.440541\pi$
$618$	33.0318	1.32873
$619$	−4.95196	−0.199036	−0.0995181	−	0.995036i	$-0.531730\pi$
$619$	−4.95196	−0.199036	−0.0995181	+	0.995036i	$0.531730\pi$
$620$	64.9932	2.61019
$621$	21.5342	0.864137
$622$	−26.7483	−1.07251
$623$	18.4146	0.737766
$624$	−4.29535	−0.171952
$625$	−25.5768	−1.02307
$626$	−24.3343	−0.972594
$627$	9.00502	0.359626
$628$	31.0765	1.24009
$629$	−2.71225	−0.108145
$630$	48.7660	1.94288
$631$	41.1133	1.63670	0.818348	−	0.574724i	$-0.194890\pi$
$631$	41.1133	1.63670	0.818348	+	0.574724i	$0.194890\pi$
$632$	4.92329	0.195838
$633$	7.04392	0.279971
$634$	70.5946	2.80367
$635$	17.7935	0.706112
$636$	−4.33330	−0.171827
$637$	25.2983	1.00236
$638$	−12.6193	−0.499603
$639$	7.36399	0.291315
$640$	46.5082	1.83840
$641$	−24.4421	−0.965404	−0.482702	−	0.875785i	$-0.660344\pi$
$641$	−24.4421	−0.965404	−0.482702	+	0.875785i	$0.660344\pi$
$642$	−19.8295	−0.782609
$643$	−13.2549	−0.522721	−0.261361	−	0.965241i	$-0.584171\pi$
$643$	−13.2549	−0.522721	−0.261361	+	0.965241i	$0.584171\pi$
$644$	69.5821	2.74192
$645$	11.1105	0.437476
$646$	4.42116	0.173948
$647$	36.5315	1.43620	0.718101	−	0.695939i	$-0.245012\pi$
$647$	36.5315	1.43620	0.718101	+	0.695939i	$0.245012\pi$
$648$	−13.6569	−0.536495
$649$	−28.1474	−1.10488
$650$	−0.889286	−0.0348806
$651$	−24.7917	−0.971661
$652$	−31.9291	−1.25044
$653$	−30.3707	−1.18850	−0.594248	−	0.804282i	$-0.702550\pi$
$653$	−30.3707	−1.18850	−0.594248	+	0.804282i	$0.702550\pi$
$654$	24.8316	0.970992
$655$	−47.2420	−1.84590
$656$	19.4206	0.758248
$657$	22.7795	0.888714
$658$	81.7341	3.18633
$659$	45.5947	1.77612	0.888059	−	0.459730i	$-0.152054\pi$
$659$	45.5947	1.77612	0.888059	+	0.459730i	$0.152054\pi$
$660$	34.6683	1.34946
$661$	27.4437	1.06743	0.533717	−	0.845663i	$-0.320795\pi$
$661$	27.4437	1.06743	0.533717	+	0.845663i	$0.320795\pi$
$662$	−41.1137	−1.59793
$663$	2.26302	0.0878886
$664$	2.13299	0.0827760
$665$	18.4273	0.714579
$666$	17.0341	0.660057
$667$	−5.01998	−0.194374
$668$	63.1771	2.44440
$669$	−15.8879	−0.614264
$670$	−11.4787	−0.443459
$671$	5.47311	0.211287
$672$	−10.8666	−0.419190
$673$	−25.0163	−0.964306	−0.482153	−	0.876087i	$-0.660145\pi$
$673$	−25.0163	−0.964306	−0.482153	+	0.876087i	$0.660145\pi$
$674$	−16.7568	−0.645447
$675$	0.506869	0.0195094
$676$	−10.2515	−0.394287
$677$	9.45697	0.363461	0.181731	−	0.983348i	$-0.441830\pi$
$677$	9.45697	0.363461	0.181731	+	0.983348i	$0.441830\pi$
$678$	−16.0683	−0.617099
$679$	5.38395	0.206617
$680$	7.52681	0.288640
$681$	9.36415	0.358835
$682$	101.109	3.87165
$683$	23.6963	0.906713	0.453357	−	0.891329i	$-0.350226\pi$
$683$	23.6963	0.906713	0.453357	+	0.891329i	$0.350226\pi$
$684$	−17.8244	−0.681533
$685$	−47.8407	−1.82790
$686$	−8.62695	−0.329379
$687$	−10.8207	−0.412835
$688$	−10.3397	−0.394196
$689$	4.80822	0.183178
$690$	21.4837	0.817869
$691$	2.90007	0.110324	0.0551619	−	0.998477i	$-0.482432\pi$
$691$	2.90007	0.110324	0.0551619	+	0.998477i	$0.482432\pi$
$692$	40.2523	1.53016
$693$	48.6999	1.84996
$694$	44.0646	1.67267
$695$	35.4495	1.34468
$696$	−2.99940	−0.113692
$697$	−10.2318	−0.387559
$698$	−14.6832	−0.555766
$699$	−1.73972	−0.0658023
$700$	1.63781	0.0619035
$701$	27.9238	1.05467	0.527333	−	0.849658i	$-0.323192\pi$
$701$	27.9238	1.05467	0.527333	+	0.849658i	$0.323192\pi$
$702$	−32.2848	−1.21851
$703$	6.43669	0.242764
$704$	62.3138	2.34854
$705$	16.1996	0.610113
$706$	14.4739	0.544731
$707$	11.2631	0.423592
$708$	−15.1290	−0.568582
$709$	−41.3307	−1.55221	−0.776104	−	0.630605i	$-0.782807\pi$
$709$	−41.3307	−1.55221	−0.776104	+	0.630605i	$0.782807\pi$
$710$	16.6884	0.626304
$711$	3.09975	0.116250
$712$	−17.8503	−0.668968
$713$	40.2212	1.50630
$714$	−6.49264	−0.242981
$715$	−38.4678	−1.43861
$716$	−33.0872	−1.23653
$717$	−3.39058	−0.126623
$718$	8.11246	0.302754
$719$	18.7514	0.699308	0.349654	−	0.936879i	$-0.386299\pi$
$719$	18.7514	0.699308	0.349654	+	0.936879i	$0.386299\pi$
$720$	−8.99479	−0.335216
$721$	67.5025	2.51393
$722$	34.4120	1.28068
$723$	5.09060	0.189321
$724$	−14.7776	−0.549204
$725$	−0.118160	−0.00438834
$726$	33.1242	1.22935
$727$	26.1851	0.971151	0.485576	−	0.874195i	$-0.338610\pi$
$727$	26.1851	0.971151	0.485576	+	0.874195i	$0.338610\pi$
$728$	−46.1312	−1.70974
$729$	1.70210	0.0630407
$730$	51.6233	1.91066
$731$	5.44750	0.201483
$732$	2.94176	0.108730
$733$	−20.0635	−0.741064	−0.370532	−	0.928820i	$-0.620825\pi$
$733$	−20.0635	−0.741064	−0.370532	+	0.928820i	$0.620825\pi$
$734$	−27.5055	−1.01525
$735$	−14.3855	−0.530618
$736$	17.6297	0.649840
$737$	−11.4631	−0.422249
$738$	64.2602	2.36545
$739$	−21.2068	−0.780105	−0.390053	−	0.920793i	$-0.627543\pi$
$739$	−21.2068	−0.780105	−0.390053	+	0.920793i	$0.627543\pi$
$740$	24.7805	0.910949
$741$	−5.37058	−0.197293
$742$	−13.7948	−0.506424
$743$	49.4430	1.81389	0.906943	−	0.421253i	$-0.138410\pi$
$743$	49.4430	1.81389	0.906943	+	0.421253i	$0.138410\pi$
$744$	24.0319	0.881051
$745$	−8.77280	−0.321411
$746$	21.4552	0.785531
$747$	1.34295	0.0491359
$748$	16.9979	0.621504
$749$	−40.5229	−1.48067
$750$	−20.8925	−0.762885
$751$	−10.1170	−0.369175	−0.184587	−	0.982816i	$-0.559095\pi$
$751$	−10.1170	−0.369175	−0.184587	+	0.982816i	$0.559095\pi$
$752$	−15.0757	−0.549754
$753$	−1.49020	−0.0543060
$754$	7.52614	0.274086
$755$	32.7593	1.19223
$756$	59.4596	2.16252
$757$	−1.50017	−0.0545246	−0.0272623	−	0.999628i	$-0.508679\pi$
$757$	−1.50017	−0.0545246	−0.0272623	+	0.999628i	$0.508679\pi$
$758$	24.5401	0.891338
$759$	21.4545	0.778751
$760$	−17.8626	−0.647943
$761$	−49.7733	−1.80428	−0.902141	−	0.431442i	$-0.858005\pi$
$761$	−49.7733	−1.80428	−0.902141	+	0.431442i	$0.858005\pi$
$762$	14.8783	0.538984
$763$	50.7449	1.83709
$764$	33.3255	1.20568
$765$	4.73894	0.171337
$766$	−70.7219	−2.55529
$767$	16.7871	0.606145
$768$	20.2063	0.729133
$769$	8.61362	0.310615	0.155307	−	0.987866i	$-0.450363\pi$
$769$	8.61362	0.310615	0.155307	+	0.987866i	$0.450363\pi$
$770$	110.365	3.97726
$771$	2.77098	0.0997943
$772$	5.31802	0.191400
$773$	4.13886	0.148864	0.0744322	−	0.997226i	$-0.476286\pi$
$773$	4.13886	0.148864	0.0744322	+	0.997226i	$0.476286\pi$
$774$	−34.2125	−1.22974
$775$	0.946721	0.0340072
$776$	−5.21895	−0.187349
$777$	−9.45252	−0.339107
$778$	42.9568	1.54008
$779$	24.2821	0.869997
$780$	−20.6761	−0.740324
$781$	16.6658	0.596348
$782$	10.5335	0.376676
$783$	−4.28969	−0.153301
$784$	13.3874	0.478123
$785$	19.6079	0.699835
$786$	−39.5021	−1.40899
$787$	−47.0850	−1.67840	−0.839200	−	0.543823i	$-0.816976\pi$
$787$	−47.0850	−1.67840	−0.839200	+	0.543823i	$0.816976\pi$
$788$	9.27065	0.330253
$789$	−11.6376	−0.414309
$790$	7.02469	0.249927
$791$	−32.8365	−1.16753
$792$	−47.2075	−1.67744
$793$	−3.26416	−0.115914
$794$	−53.9125	−1.91328
$795$	−2.73412	−0.0969693
$796$	8.25368	0.292544
$797$	−8.48374	−0.300509	−0.150255	−	0.988647i	$-0.548009\pi$
$797$	−8.48374	−0.300509	−0.150255	+	0.988647i	$0.548009\pi$
$798$	15.4083	0.545447
$799$	7.94269	0.280992
$800$	0.414965	0.0146712
$801$	−11.2387	−0.397099
$802$	21.8370	0.771092
$803$	51.5534	1.81928
$804$	−6.16133	−0.217293
$805$	43.9032	1.54738
$806$	−60.3011	−2.12402
$807$	−9.67058	−0.340421
$808$	−10.9179	−0.384091
$809$	−6.45139	−0.226819	−0.113409	−	0.993548i	$-0.536177\pi$
$809$	−6.45139	−0.226819	−0.113409	+	0.993548i	$0.536177\pi$
$810$	−19.4861	−0.684671
$811$	3.34527	0.117468	0.0587342	−	0.998274i	$-0.481294\pi$
$811$	3.34527	0.117468	0.0587342	+	0.998274i	$0.481294\pi$
$812$	−13.8610	−0.486427
$813$	9.99197	0.350434
$814$	38.5505	1.35120
$815$	−20.1459	−0.705679
$816$	1.19755	0.0419228
$817$	−12.9279	−0.452291
$818$	−80.1725	−2.80317
$819$	−29.0446	−1.01490
$820$	93.4833	3.26458
$821$	−41.3265	−1.44231	−0.721153	−	0.692776i	$-0.756387\pi$
$821$	−41.3265	−1.44231	−0.721153	+	0.692776i	$0.756387\pi$
$822$	−40.0027	−1.39526
$823$	20.9173	0.729131	0.364565	−	0.931178i	$-0.381218\pi$
$823$	20.9173	0.729131	0.364565	+	0.931178i	$0.381218\pi$
$824$	−65.4338	−2.27950
$825$	0.504994	0.0175816
$826$	−48.1623	−1.67578
$827$	−5.48198	−0.190627	−0.0953136	−	0.995447i	$-0.530385\pi$
$827$	−5.48198	−0.190627	−0.0953136	+	0.995447i	$0.530385\pi$
$828$	−42.4668	−1.47583
$829$	39.5437	1.37341	0.686705	−	0.726937i	$-0.259057\pi$
$829$	39.5437	1.37341	0.686705	+	0.726937i	$0.259057\pi$
$830$	3.04341	0.105638
$831$	−0.800416	−0.0277661
$832$	−37.1639	−1.28843
$833$	−7.05323	−0.244380
$834$	29.6417	1.02641
$835$	39.8620	1.37948
$836$	−40.3392	−1.39516
$837$	34.3700	1.18800
$838$	40.9040	1.41300
$839$	34.0637	1.17601	0.588005	−	0.808857i	$-0.299914\pi$
$839$	34.0637	1.17601	0.588005	+	0.808857i	$0.299914\pi$
$840$	26.2318	0.905084
$841$	1.00000	0.0344828
$842$	−68.5630	−2.36284
$843$	−10.4056	−0.358387
$844$	−31.5542	−1.08614
$845$	−6.46821	−0.222513
$846$	−49.8834	−1.71503
$847$	67.6914	2.32590
$848$	2.54443	0.0873760
$849$	4.17360	0.143238
$850$	0.247935	0.00850410
$851$	15.3355	0.525693
$852$	8.95771	0.306886
$853$	−47.0445	−1.61077	−0.805386	−	0.592751i	$-0.798042\pi$
$853$	−47.0445	−1.61077	−0.805386	+	0.592751i	$0.798042\pi$
$854$	9.36491	0.320461
$855$	−11.2464	−0.384619
$856$	39.2810	1.34260
$857$	12.1340	0.414490	0.207245	−	0.978289i	$-0.433550\pi$
$857$	12.1340	0.414490	0.207245	+	0.978289i	$0.433550\pi$
$858$	−32.1654	−1.09811
$859$	51.7902	1.76706	0.883529	−	0.468376i	$-0.155161\pi$
$859$	51.7902	1.76706	0.883529	+	0.468376i	$0.155161\pi$
$860$	−49.7711	−1.69718
$861$	−35.6592	−1.21526
$862$	30.9996	1.05585
$863$	36.0689	1.22780	0.613901	−	0.789383i	$-0.289600\pi$
$863$	36.0689	1.22780	0.613901	+	0.789383i	$0.289600\pi$
$864$	15.0650	0.512522
$865$	25.3974	0.863538
$866$	74.4940	2.53141
$867$	12.9761	0.440692
$868$	111.058	3.76954
$869$	7.01517	0.237973
$870$	−4.27963	−0.145093
$871$	6.83658	0.231649
$872$	−49.1897	−1.66578
$873$	−3.28589	−0.111211
$874$	−24.9979	−0.845566
$875$	−42.6951	−1.44336
$876$	27.7095	0.936218
$877$	37.3310	1.26058	0.630289	−	0.776361i	$-0.282937\pi$
$877$	37.3310	1.26058	0.630289	+	0.776361i	$0.282937\pi$
$878$	78.2498	2.64080
$879$	−11.3963	−0.384389
$880$	−20.3565	−0.686218
$881$	58.8904	1.98407	0.992033	−	0.125976i	$-0.0402063\pi$
$881$	58.8904	1.98407	0.992033	+	0.125976i	$0.0402063\pi$
$882$	44.2972	1.49156
$883$	−46.7441	−1.57306	−0.786532	−	0.617549i	$-0.788126\pi$
$883$	−46.7441	−1.57306	−0.786532	+	0.617549i	$0.788126\pi$
$884$	−10.1375	−0.340962
$885$	−9.54571	−0.320876
$886$	−78.2221	−2.62792
$887$	−25.3915	−0.852563	−0.426282	−	0.904590i	$-0.640177\pi$
$887$	−25.3915	−0.852563	−0.426282	+	0.904590i	$0.640177\pi$
$888$	9.16283	0.307485
$889$	30.4047	1.01974
$890$	−25.4693	−0.853732
$891$	−19.4597	−0.651924
$892$	71.1722	2.38302
$893$	−18.8495	−0.630775
$894$	−7.33552	−0.245336
$895$	−20.8765	−0.697825
$896$	79.4711	2.65494
$897$	−12.7955	−0.427228
$898$	−27.4317	−0.915407
$899$	−8.01222	−0.267223
$900$	−0.999578	−0.0333193
$901$	−1.34054	−0.0446599
$902$	145.430	4.84229
$903$	18.9852	0.631787
$904$	31.8302	1.05866
$905$	−9.32398	−0.309940
$906$	27.3922	0.910046
$907$	50.3883	1.67312	0.836558	−	0.547878i	$-0.184564\pi$
$907$	50.3883	1.67312	0.836558	+	0.547878i	$0.184564\pi$
$908$	−41.9480	−1.39209
$909$	−6.87401	−0.227997
$910$	−65.8213	−2.18195
$911$	21.6709	0.717989	0.358994	−	0.933340i	$-0.383120\pi$
$911$	21.6709	0.717989	0.358994	+	0.933340i	$0.383120\pi$
$912$	−2.84202	−0.0941088
$913$	3.03928	0.100586
$914$	7.52779	0.248997
$915$	1.85612	0.0613613
$916$	48.4728	1.60159
$917$	−80.7250	−2.66577
$918$	9.00109	0.297080
$919$	41.2398	1.36038	0.680188	−	0.733038i	$-0.261898\pi$
$919$	41.2398	1.36038	0.680188	+	0.733038i	$0.261898\pi$
$920$	−42.5577	−1.40309
$921$	−10.7108	−0.352931
$922$	−88.7818	−2.92387
$923$	−9.93944	−0.327161
$924$	59.2396	1.94884
$925$	0.360964	0.0118684
$926$	−53.9590	−1.77320
$927$	−41.1977	−1.35311
$928$	−3.51191	−0.115284
$929$	−50.5972	−1.66004	−0.830020	−	0.557734i	$-0.811671\pi$
$929$	−50.5972	−1.66004	−0.830020	+	0.557734i	$0.811671\pi$
$930$	34.2893	1.12439
$931$	16.7386	0.548587
$932$	7.79331	0.255278
$933$	−9.05897	−0.296577
$934$	−15.3490	−0.502236
$935$	10.7249	0.350742
$936$	28.1545	0.920258
$937$	44.8858	1.46635	0.733177	−	0.680038i	$-0.238037\pi$
$937$	44.8858	1.46635	0.733177	+	0.680038i	$0.238037\pi$
$938$	−19.6142	−0.640428
$939$	−8.24139	−0.268947
$940$	−72.5684	−2.36692
$941$	−47.7740	−1.55739	−0.778694	−	0.627404i	$-0.784117\pi$
$941$	−47.7740	−1.55739	−0.778694	+	0.627404i	$0.784117\pi$
$942$	16.3954	0.534192
$943$	57.8524	1.88393
$944$	8.88343	0.289131
$945$	37.5163	1.22041
$946$	−77.4279	−2.51740
$947$	−35.3132	−1.14752	−0.573762	−	0.819022i	$-0.694517\pi$
$947$	−35.3132	−1.14752	−0.573762	+	0.819022i	$0.694517\pi$
$948$	3.77060	0.122463
$949$	−30.7464	−0.998069
$950$	−0.588397	−0.0190901
$951$	23.9086	0.775288
$952$	12.8615	0.416843
$953$	−1.22703	−0.0397473	−0.0198737	−	0.999802i	$-0.506326\pi$
$953$	−1.22703	−0.0397473	−0.0198737	+	0.999802i	$0.506326\pi$
$954$	8.41916	0.272580
$955$	21.0269	0.680415
$956$	15.1886	0.491233
$957$	−4.27383	−0.138153
$958$	−0.922740	−0.0298124
$959$	−81.7480	−2.63978
$960$	21.1327	0.682055
$961$	33.1957	1.07083
$962$	−22.9915	−0.741276
$963$	24.7316	0.796966
$964$	−22.8040	−0.734468
$965$	3.35543	0.108015
$966$	36.7103	1.18114
$967$	24.1253	0.775819	0.387909	−	0.921698i	$-0.373197\pi$
$967$	24.1253	0.775819	0.387909	+	0.921698i	$0.373197\pi$
$968$	−65.6169	−2.10901
$969$	1.49733	0.0481012
$970$	−7.44654	−0.239094
$971$	−40.4389	−1.29775	−0.648874	−	0.760896i	$-0.724760\pi$
$971$	−40.4389	−1.29775	−0.648874	+	0.760896i	$0.724760\pi$
$972$	−56.6024	−1.81552
$973$	60.5746	1.94193
$974$	−9.75489	−0.312567
$975$	−0.301178	−0.00964541
$976$	−1.72734	−0.0552908
$977$	−48.5792	−1.55419	−0.777093	−	0.629386i	$-0.783307\pi$
$977$	−48.5792	−1.55419	−0.777093	+	0.629386i	$0.783307\pi$
$978$	−16.8453	−0.538653
$979$	−25.4348	−0.812898
$980$	64.4419	2.05852
$981$	−30.9703	−0.988805
$982$	29.4188	0.938790
$983$	−4.78118	−0.152496	−0.0762480	−	0.997089i	$-0.524294\pi$
$983$	−4.78118	−0.152496	−0.0762480	+	0.997089i	$0.524294\pi$
$984$	34.5664	1.10194
$985$	5.84937	0.186376
$986$	−2.09831	−0.0668237
$987$	27.6812	0.881102
$988$	24.0583	0.765395
$989$	−30.8010	−0.979413
$990$	−67.3569	−2.14074
$991$	−14.4729	−0.459748	−0.229874	−	0.973220i	$-0.573831\pi$
$991$	−14.4729	−0.459748	−0.229874	+	0.973220i	$0.573831\pi$
$992$	28.1382	0.893388
$993$	−13.9241	−0.441869
$994$	28.5164	0.904484
$995$	5.20771	0.165095
$996$	1.63359	0.0517623
$997$	−13.9658	−0.442302	−0.221151	−	0.975240i	$-0.570981\pi$
$997$	−13.9658	−0.442302	−0.221151	+	0.975240i	$0.570981\pi$
$998$	−0.306900	−0.00971476
$999$	13.1045	0.414609

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.e.1.17	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.e.1.17	✓	169	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36338 q^{2} -0.800416 q^{3} +3.58557 q^{4} +2.26233 q^{5} +1.89169 q^{6} +3.86578 q^{7} -3.74731 q^{8} -2.35933 q^{9} +O(q^{10})\)	\(q-2.36338 q^{2} -0.800416 q^{3} +3.58557 q^{4} +2.26233 q^{5} +1.89169 q^{6} +3.86578 q^{7} -3.74731 q^{8} -2.35933 q^{9} -5.34676 q^{10} -5.33951 q^{11} -2.86995 q^{12} +3.18448 q^{13} -9.13631 q^{14} -1.81081 q^{15} +1.68517 q^{16} -0.887841 q^{17} +5.57601 q^{18} +2.10701 q^{19} +8.11176 q^{20} -3.09423 q^{21} +12.6193 q^{22} +5.01998 q^{23} +2.99940 q^{24} +0.118160 q^{25} -7.52614 q^{26} +4.28969 q^{27} +13.8610 q^{28} -1.00000 q^{29} +4.27963 q^{30} +8.01222 q^{31} +3.51191 q^{32} +4.27383 q^{33} +2.09831 q^{34} +8.74569 q^{35} -8.45956 q^{36} +3.05489 q^{37} -4.97968 q^{38} -2.54891 q^{39} -8.47766 q^{40} +11.5244 q^{41} +7.31284 q^{42} -6.13567 q^{43} -19.1452 q^{44} -5.33761 q^{45} -11.8641 q^{46} -8.94607 q^{47} -1.34884 q^{48} +7.94425 q^{49} -0.279256 q^{50} +0.710641 q^{51} +11.4182 q^{52} +1.50989 q^{53} -10.1382 q^{54} -12.0798 q^{55} -14.4863 q^{56} -1.68649 q^{57} +2.36338 q^{58} +5.27152 q^{59} -6.49278 q^{60} -1.02502 q^{61} -18.9359 q^{62} -9.12067 q^{63} -11.6703 q^{64} +7.20436 q^{65} -10.1007 q^{66} +2.14684 q^{67} -3.18341 q^{68} -4.01807 q^{69} -20.6694 q^{70} -3.12121 q^{71} +8.84115 q^{72} -9.65507 q^{73} -7.21986 q^{74} -0.0945768 q^{75} +7.55485 q^{76} -20.6414 q^{77} +6.02404 q^{78} -1.31382 q^{79} +3.81243 q^{80} +3.64447 q^{81} -27.2366 q^{82} -0.569206 q^{83} -11.0946 q^{84} -2.00859 q^{85} +14.5009 q^{86} +0.800416 q^{87} +20.0088 q^{88} +4.76350 q^{89} +12.6148 q^{90} +12.3105 q^{91} +17.9995 q^{92} -6.41311 q^{93} +21.1430 q^{94} +4.76677 q^{95} -2.81098 q^{96} +1.39272 q^{97} -18.7753 q^{98} +12.5977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * q^99

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