LMFDB - Embedded newform 4006.2.a.i.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.23424 q^{3} +1.00000 q^{4} +1.35082 q^{5} -2.23424 q^{6} +1.10993 q^{7} +1.00000 q^{8} +1.99184 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.23424 q^{3} +1.00000 q^{4} +1.35082 q^{5} -2.23424 q^{6} +1.10993 q^{7} +1.00000 q^{8} +1.99184 q^{9} +1.35082 q^{10} -4.91285 q^{11} -2.23424 q^{12} -6.70297 q^{13} +1.10993 q^{14} -3.01805 q^{15} +1.00000 q^{16} +2.39653 q^{17} +1.99184 q^{18} -2.31770 q^{19} +1.35082 q^{20} -2.47985 q^{21} -4.91285 q^{22} +1.62189 q^{23} -2.23424 q^{24} -3.17529 q^{25} -6.70297 q^{26} +2.25248 q^{27} +1.10993 q^{28} -1.50800 q^{29} -3.01805 q^{30} +8.01965 q^{31} +1.00000 q^{32} +10.9765 q^{33} +2.39653 q^{34} +1.49931 q^{35} +1.99184 q^{36} -0.245916 q^{37} -2.31770 q^{38} +14.9761 q^{39} +1.35082 q^{40} +9.41249 q^{41} -2.47985 q^{42} +8.36285 q^{43} -4.91285 q^{44} +2.69061 q^{45} +1.62189 q^{46} +4.54393 q^{47} -2.23424 q^{48} -5.76806 q^{49} -3.17529 q^{50} -5.35442 q^{51} -6.70297 q^{52} +13.6076 q^{53} +2.25248 q^{54} -6.63637 q^{55} +1.10993 q^{56} +5.17830 q^{57} -1.50800 q^{58} -5.93790 q^{59} -3.01805 q^{60} -0.490368 q^{61} +8.01965 q^{62} +2.21080 q^{63} +1.00000 q^{64} -9.05448 q^{65} +10.9765 q^{66} +10.2481 q^{67} +2.39653 q^{68} -3.62369 q^{69} +1.49931 q^{70} +1.78952 q^{71} +1.99184 q^{72} +15.0804 q^{73} -0.245916 q^{74} +7.09437 q^{75} -2.31770 q^{76} -5.45292 q^{77} +14.9761 q^{78} +11.7453 q^{79} +1.35082 q^{80} -11.0081 q^{81} +9.41249 q^{82} -3.02480 q^{83} -2.47985 q^{84} +3.23727 q^{85} +8.36285 q^{86} +3.36924 q^{87} -4.91285 q^{88} -11.8492 q^{89} +2.69061 q^{90} -7.43983 q^{91} +1.62189 q^{92} -17.9178 q^{93} +4.54393 q^{94} -3.13079 q^{95} -2.23424 q^{96} -5.97799 q^{97} -5.76806 q^{98} -9.78560 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) $ 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.23424	−1.28994	−0.644970	−	0.764208i	$-0.723130\pi$
$3$	−2.23424	−1.28994	−0.644970	+	0.764208i	$0.723130\pi$
$4$	1.00000	0.500000
$5$	1.35082	0.604104	0.302052	−	0.953292i	$-0.402328\pi$
$5$	1.35082	0.604104	0.302052	+	0.953292i	$0.402328\pi$
$6$	−2.23424	−0.912125
$7$	1.10993	0.419514	0.209757	−	0.977754i	$-0.432733\pi$
$7$	1.10993	0.419514	0.209757	+	0.977754i	$0.432733\pi$
$8$	1.00000	0.353553
$9$	1.99184	0.663945
$10$	1.35082	0.427166
$11$	−4.91285	−1.48128	−0.740641	−	0.671901i	$-0.765478\pi$
$11$	−4.91285	−1.48128	−0.740641	+	0.671901i	$0.765478\pi$
$12$	−2.23424	−0.644970
$13$	−6.70297	−1.85907	−0.929535	−	0.368735i	$-0.879791\pi$
$13$	−6.70297	−1.85907	−0.929535	+	0.368735i	$0.879791\pi$
$14$	1.10993	0.296641
$15$	−3.01805	−0.779257
$16$	1.00000	0.250000
$17$	2.39653	0.581243	0.290621	−	0.956838i	$-0.406138\pi$
$17$	2.39653	0.581243	0.290621	+	0.956838i	$0.406138\pi$
$18$	1.99184	0.469480
$19$	−2.31770	−0.531717	−0.265858	−	0.964012i	$-0.585655\pi$
$19$	−2.31770	−0.531717	−0.265858	+	0.964012i	$0.585655\pi$
$20$	1.35082	0.302052
$21$	−2.47985	−0.541148
$22$	−4.91285	−1.04742
$23$	1.62189	0.338187	0.169094	−	0.985600i	$-0.445916\pi$
$23$	1.62189	0.338187	0.169094	+	0.985600i	$0.445916\pi$
$24$	−2.23424	−0.456063
$25$	−3.17529	−0.635059
$26$	−6.70297	−1.31456
$27$	2.25248	0.433491
$28$	1.10993	0.209757
$29$	−1.50800	−0.280029	−0.140015	−	0.990149i	$-0.544715\pi$
$29$	−1.50800	−0.280029	−0.140015	+	0.990149i	$0.544715\pi$
$30$	−3.01805	−0.551018
$31$	8.01965	1.44037	0.720186	−	0.693781i	$-0.244056\pi$
$31$	8.01965	1.44037	0.720186	+	0.693781i	$0.244056\pi$
$32$	1.00000	0.176777
$33$	10.9765	1.91076
$34$	2.39653	0.411001
$35$	1.49931	0.253430
$36$	1.99184	0.331973
$37$	−0.245916	−0.0404284	−0.0202142	−	0.999796i	$-0.506435\pi$
$37$	−0.245916	−0.0404284	−0.0202142	+	0.999796i	$0.506435\pi$
$38$	−2.31770	−0.375981
$39$	14.9761	2.39809
$40$	1.35082	0.213583
$41$	9.41249	1.46998	0.734992	−	0.678075i	$-0.237186\pi$
$41$	9.41249	1.46998	0.734992	+	0.678075i	$0.237186\pi$
$42$	−2.47985	−0.382649
$43$	8.36285	1.27532	0.637661	−	0.770317i	$-0.279902\pi$
$43$	8.36285	1.27532	0.637661	+	0.770317i	$0.279902\pi$
$44$	−4.91285	−0.740641
$45$	2.69061	0.401092
$46$	1.62189	0.239135
$47$	4.54393	0.662800	0.331400	−	0.943490i	$-0.392479\pi$
$47$	4.54393	0.662800	0.331400	+	0.943490i	$0.392479\pi$
$48$	−2.23424	−0.322485
$49$	−5.76806	−0.824008
$50$	−3.17529	−0.449054
$51$	−5.35442	−0.749768
$52$	−6.70297	−0.929535
$53$	13.6076	1.86914	0.934572	−	0.355773i	$-0.115782\pi$
$53$	13.6076	1.86914	0.934572	+	0.355773i	$0.115782\pi$
$54$	2.25248	0.306524
$55$	−6.63637	−0.894847
$56$	1.10993	0.148321
$57$	5.17830	0.685883
$58$	−1.50800	−0.198010
$59$	−5.93790	−0.773049	−0.386525	−	0.922279i	$-0.626325\pi$
$59$	−5.93790	−0.773049	−0.386525	+	0.922279i	$0.626325\pi$
$60$	−3.01805	−0.389629
$61$	−0.490368	−0.0627851	−0.0313926	−	0.999507i	$-0.509994\pi$
$61$	−0.490368	−0.0627851	−0.0313926	+	0.999507i	$0.509994\pi$
$62$	8.01965	1.01850
$63$	2.21080	0.278534
$64$	1.00000	0.125000
$65$	−9.05448	−1.12307
$66$	10.9765	1.35111
$67$	10.2481	1.25201	0.626004	−	0.779820i	$-0.284689\pi$
$67$	10.2481	1.25201	0.626004	+	0.779820i	$0.284689\pi$
$68$	2.39653	0.290621
$69$	−3.62369	−0.436241
$70$	1.49931	0.179202
$71$	1.78952	0.212377	0.106189	−	0.994346i	$-0.466135\pi$
$71$	1.78952	0.212377	0.106189	+	0.994346i	$0.466135\pi$
$72$	1.99184	0.234740
$73$	15.0804	1.76503	0.882514	−	0.470287i	$-0.155850\pi$
$73$	15.0804	1.76503	0.882514	+	0.470287i	$0.155850\pi$
$74$	−0.245916	−0.0285872
$75$	7.09437	0.819188
$76$	−2.31770	−0.265858
$77$	−5.45292	−0.621418
$78$	14.9761	1.69570
$79$	11.7453	1.32144	0.660722	−	0.750630i	$-0.270250\pi$
$79$	11.7453	1.32144	0.660722	+	0.750630i	$0.270250\pi$
$80$	1.35082	0.151026
$81$	−11.0081	−1.22312
$82$	9.41249	1.03944
$83$	−3.02480	−0.332015	−0.166008	−	0.986124i	$-0.553088\pi$
$83$	−3.02480	−0.332015	−0.166008	+	0.986124i	$0.553088\pi$
$84$	−2.47985	−0.270574
$85$	3.23727	0.351131
$86$	8.36285	0.901789
$87$	3.36924	0.361221
$88$	−4.91285	−0.523712
$89$	−11.8492	−1.25601	−0.628006	−	0.778208i	$-0.716129\pi$
$89$	−11.8492	−1.25601	−0.628006	+	0.778208i	$0.716129\pi$
$90$	2.69061	0.283615
$91$	−7.43983	−0.779906
$92$	1.62189	0.169094
$93$	−17.9178	−1.85799
$94$	4.54393	0.468671
$95$	−3.13079	−0.321212
$96$	−2.23424	−0.228031
$97$	−5.97799	−0.606973	−0.303486	−	0.952836i	$-0.598151\pi$
$97$	−5.97799	−0.606973	−0.303486	+	0.952836i	$0.598151\pi$
$98$	−5.76806	−0.582662
$99$	−9.78560	−0.983490
$100$	−3.17529	−0.317529
$101$	13.0576	1.29927	0.649637	−	0.760244i	$-0.274921\pi$
$101$	13.0576	1.29927	0.649637	+	0.760244i	$0.274921\pi$
$102$	−5.35442	−0.530166
$103$	3.71780	0.366325	0.183163	−	0.983083i	$-0.441367\pi$
$103$	3.71780	0.366325	0.183163	+	0.983083i	$0.441367\pi$
$104$	−6.70297	−0.657280
$105$	−3.34983	−0.326909
$106$	13.6076	1.32168
$107$	−20.6211	−1.99351	−0.996757	−	0.0804737i	$-0.974357\pi$
$107$	−20.6211	−1.99351	−0.996757	+	0.0804737i	$0.974357\pi$
$108$	2.25248	0.216745
$109$	7.33277	0.702352	0.351176	−	0.936310i	$-0.385782\pi$
$109$	7.33277	0.702352	0.351176	+	0.936310i	$0.385782\pi$
$110$	−6.63637	−0.632753
$111$	0.549436	0.0521502
$112$	1.10993	0.104879
$113$	−10.1608	−0.955852	−0.477926	−	0.878400i	$-0.658611\pi$
$113$	−10.1608	−0.955852	−0.477926	+	0.878400i	$0.658611\pi$
$114$	5.17830	0.484992
$115$	2.19088	0.204300
$116$	−1.50800	−0.140015
$117$	−13.3512	−1.23432
$118$	−5.93790	−0.546628
$119$	2.65998	0.243840
$120$	−3.01805	−0.275509
$121$	13.1361	1.19419
$122$	−0.490368	−0.0443958
$123$	−21.0298	−1.89619
$124$	8.01965	0.720186
$125$	−11.0433	−0.987745
$126$	2.21080	0.196954
$127$	15.1831	1.34728	0.673642	−	0.739058i	$-0.264729\pi$
$127$	15.1831	1.34728	0.673642	+	0.739058i	$0.264729\pi$
$128$	1.00000	0.0883883
$129$	−18.6846	−1.64509
$130$	−9.05448	−0.794131
$131$	9.65152	0.843257	0.421629	−	0.906769i	$-0.361459\pi$
$131$	9.65152	0.843257	0.421629	+	0.906769i	$0.361459\pi$
$132$	10.9765	0.955382
$133$	−2.57248	−0.223063
$134$	10.2481	0.885303
$135$	3.04269	0.261873
$136$	2.39653	0.205500
$137$	3.30395	0.282275	0.141138	−	0.989990i	$-0.454924\pi$
$137$	3.30395	0.282275	0.141138	+	0.989990i	$0.454924\pi$
$138$	−3.62369	−0.308469
$139$	−8.81357	−0.747557	−0.373778	−	0.927518i	$-0.621938\pi$
$139$	−8.81357	−0.747557	−0.373778	+	0.927518i	$0.621938\pi$
$140$	1.49931	0.126715
$141$	−10.1522	−0.854972
$142$	1.78952	0.150174
$143$	32.9307	2.75380
$144$	1.99184	0.165986
$145$	−2.03704	−0.169167
$146$	15.0804	1.24806
$147$	12.8872	1.06292
$148$	−0.245916	−0.0202142
$149$	1.32373	0.108444	0.0542222	−	0.998529i	$-0.482732\pi$
$149$	1.32373	0.108444	0.0542222	+	0.998529i	$0.482732\pi$
$150$	7.09437	0.579253
$151$	−14.4287	−1.17419	−0.587097	−	0.809517i	$-0.699729\pi$
$151$	−14.4287	−1.17419	−0.587097	+	0.809517i	$0.699729\pi$
$152$	−2.31770	−0.187990
$153$	4.77349	0.385913
$154$	−5.45292	−0.439409
$155$	10.8331	0.870134
$156$	14.9761	1.19904
$157$	2.82657	0.225585	0.112792	−	0.993619i	$-0.464021\pi$
$157$	2.82657	0.225585	0.112792	+	0.993619i	$0.464021\pi$
$158$	11.7453	0.934403
$159$	−30.4026	−2.41108
$160$	1.35082	0.106791
$161$	1.80018	0.141874
$162$	−11.0081	−0.864878
$163$	20.6870	1.62033	0.810166	−	0.586201i	$-0.199377\pi$
$163$	20.6870	1.62033	0.810166	+	0.586201i	$0.199377\pi$
$164$	9.41249	0.734992
$165$	14.8272	1.15430
$166$	−3.02480	−0.234770
$167$	9.23311	0.714479	0.357240	−	0.934013i	$-0.383718\pi$
$167$	9.23311	0.714479	0.357240	+	0.934013i	$0.383718\pi$
$168$	−2.47985	−0.191325
$169$	31.9298	2.45614
$170$	3.23727	0.248287
$171$	−4.61648	−0.353031
$172$	8.36285	0.637661
$173$	−18.4324	−1.40139	−0.700694	−	0.713462i	$-0.747126\pi$
$173$	−18.4324	−1.40139	−0.700694	+	0.713462i	$0.747126\pi$
$174$	3.36924	0.255422
$175$	−3.52435	−0.266416
$176$	−4.91285	−0.370320
$177$	13.2667	0.997187
$178$	−11.8492	−0.888135
$179$	24.3976	1.82356	0.911780	−	0.410680i	$-0.134709\pi$
$179$	24.3976	1.82356	0.911780	+	0.410680i	$0.134709\pi$
$180$	2.69061	0.200546
$181$	−1.89422	−0.140796	−0.0703981	−	0.997519i	$-0.522427\pi$
$181$	−1.89422	−0.140796	−0.0703981	+	0.997519i	$0.522427\pi$
$182$	−7.43983	−0.551477
$183$	1.09560	0.0809891
$184$	1.62189	0.119567
$185$	−0.332188	−0.0244229
$186$	−17.9178	−1.31380
$187$	−11.7738	−0.860984
$188$	4.54393	0.331400
$189$	2.50010	0.181855
$190$	−3.13079	−0.227131
$191$	19.5165	1.41217	0.706083	−	0.708129i	$-0.250461\pi$
$191$	19.5165	1.41217	0.706083	+	0.708129i	$0.250461\pi$
$192$	−2.23424	−0.161242
$193$	−17.5312	−1.26192	−0.630962	−	0.775814i	$-0.717340\pi$
$193$	−17.5312	−1.26192	−0.630962	+	0.775814i	$0.717340\pi$
$194$	−5.97799	−0.429195
$195$	20.2299	1.44869
$196$	−5.76806	−0.412004
$197$	−4.24991	−0.302793	−0.151397	−	0.988473i	$-0.548377\pi$
$197$	−4.24991	−0.302793	−0.151397	+	0.988473i	$0.548377\pi$
$198$	−9.78560	−0.695432
$199$	6.20878	0.440129	0.220064	−	0.975485i	$-0.429373\pi$
$199$	6.20878	0.440129	0.220064	+	0.975485i	$0.429373\pi$
$200$	−3.17529	−0.224527
$201$	−22.8968	−1.61501
$202$	13.0576	0.918726
$203$	−1.67378	−0.117476
$204$	−5.35442	−0.374884
$205$	12.7146	0.888023
$206$	3.71780	0.259031
$207$	3.23054	0.224538
$208$	−6.70297	−0.464767
$209$	11.3865	0.787622
$210$	−3.34983	−0.231160
$211$	−22.4332	−1.54437	−0.772183	−	0.635401i	$-0.780835\pi$
$211$	−22.4332	−1.54437	−0.772183	+	0.635401i	$0.780835\pi$
$212$	13.6076	0.934572
$213$	−3.99823	−0.273954
$214$	−20.6211	−1.40963
$215$	11.2967	0.770427
$216$	2.25248	0.153262
$217$	8.90125	0.604256
$218$	7.33277	0.496638
$219$	−33.6933	−2.27678
$220$	−6.63637	−0.447424
$221$	−16.0638	−1.08057
$222$	0.549436	0.0368757
$223$	5.45195	0.365090	0.182545	−	0.983198i	$-0.441567\pi$
$223$	5.45195	0.365090	0.182545	+	0.983198i	$0.441567\pi$
$224$	1.10993	0.0741603
$225$	−6.32466	−0.421644
$226$	−10.1608	−0.675889
$227$	15.0043	0.995872	0.497936	−	0.867214i	$-0.334091\pi$
$227$	15.0043	0.995872	0.497936	+	0.867214i	$0.334091\pi$
$228$	5.17830	0.342941
$229$	−6.19536	−0.409401	−0.204700	−	0.978825i	$-0.565622\pi$
$229$	−6.19536	−0.409401	−0.204700	+	0.978825i	$0.565622\pi$
$230$	2.19088	0.144462
$231$	12.1832	0.801592
$232$	−1.50800	−0.0990052
$233$	−2.96114	−0.193991	−0.0969954	−	0.995285i	$-0.530923\pi$
$233$	−2.96114	−0.193991	−0.0969954	+	0.995285i	$0.530923\pi$
$234$	−13.3512	−0.872796
$235$	6.13802	0.400400
$236$	−5.93790	−0.386525
$237$	−26.2417	−1.70458
$238$	2.65998	0.172421
$239$	−9.93141	−0.642410	−0.321205	−	0.947010i	$-0.604088\pi$
$239$	−9.93141	−0.642410	−0.321205	+	0.947010i	$0.604088\pi$
$240$	−3.01805	−0.194814
$241$	15.5578	1.00217	0.501083	−	0.865399i	$-0.332935\pi$
$241$	15.5578	1.00217	0.501083	+	0.865399i	$0.332935\pi$
$242$	13.1361	0.844423
$243$	17.8373	1.14426
$244$	−0.490368	−0.0313926
$245$	−7.79159	−0.497786
$246$	−21.0298	−1.34081
$247$	15.5355	0.988498
$248$	8.01965	0.509248
$249$	6.75814	0.428280
$250$	−11.0433	−0.698441
$251$	−3.97756	−0.251061	−0.125531	−	0.992090i	$-0.540063\pi$
$251$	−3.97756	−0.251061	−0.125531	+	0.992090i	$0.540063\pi$
$252$	2.21080	0.139267
$253$	−7.96811	−0.500951
$254$	15.1831	0.952673
$255$	−7.23284	−0.452938
$256$	1.00000	0.0625000
$257$	17.7830	1.10928	0.554638	−	0.832092i	$-0.312857\pi$
$257$	17.7830	1.10928	0.554638	+	0.832092i	$0.312857\pi$
$258$	−18.6846	−1.16325
$259$	−0.272950	−0.0169603
$260$	−9.05448	−0.561535
$261$	−3.00369	−0.185924
$262$	9.65152	0.596273
$263$	6.46481	0.398637	0.199319	−	0.979935i	$-0.436127\pi$
$263$	6.46481	0.398637	0.199319	+	0.979935i	$0.436127\pi$
$264$	10.9765	0.675557
$265$	18.3813	1.12916
$266$	−2.57248	−0.157729
$267$	26.4740	1.62018
$268$	10.2481	0.626004
$269$	−17.6108	−1.07375	−0.536875	−	0.843662i	$-0.680395\pi$
$269$	−17.6108	−1.07375	−0.536875	+	0.843662i	$0.680395\pi$
$270$	3.04269	0.185172
$271$	22.8532	1.38824	0.694118	−	0.719862i	$-0.255795\pi$
$271$	22.8532	1.38824	0.694118	+	0.719862i	$0.255795\pi$
$272$	2.39653	0.145311
$273$	16.6224	1.00603
$274$	3.30395	0.199599
$275$	15.5998	0.940701
$276$	−3.62369	−0.218121
$277$	−2.95544	−0.177575	−0.0887877	−	0.996051i	$-0.528299\pi$
$277$	−2.95544	−0.177575	−0.0887877	+	0.996051i	$0.528299\pi$
$278$	−8.81357	−0.528603
$279$	15.9738	0.956328
$280$	1.49931	0.0896010
$281$	11.4064	0.680450	0.340225	−	0.940344i	$-0.389497\pi$
$281$	11.4064	0.680450	0.340225	+	0.940344i	$0.389497\pi$
$282$	−10.1522	−0.604557
$283$	−2.23549	−0.132886	−0.0664429	−	0.997790i	$-0.521165\pi$
$283$	−2.23549	−0.132886	−0.0664429	+	0.997790i	$0.521165\pi$
$284$	1.78952	0.106189
$285$	6.99494	0.414344
$286$	32.9307	1.94723
$287$	10.4472	0.616679
$288$	1.99184	0.117370
$289$	−11.2567	−0.662157
$290$	−2.03704	−0.119619
$291$	13.3563	0.782958
$292$	15.0804	0.882514
$293$	−23.6822	−1.38353	−0.691764	−	0.722124i	$-0.743166\pi$
$293$	−23.6822	−1.38353	−0.691764	+	0.722124i	$0.743166\pi$
$294$	12.8872	0.751598
$295$	−8.02102	−0.467002
$296$	−0.245916	−0.0142936
$297$	−11.0661	−0.642121
$298$	1.32373	0.0766817
$299$	−10.8715	−0.628714
$300$	7.09437	0.409594
$301$	9.28218	0.535016
$302$	−14.4287	−0.830280
$303$	−29.1737	−1.67599
$304$	−2.31770	−0.132929
$305$	−0.662397	−0.0379287
$306$	4.77349	0.272882
$307$	22.9585	1.31031	0.655154	−	0.755495i	$-0.272604\pi$
$307$	22.9585	1.31031	0.655154	+	0.755495i	$0.272604\pi$
$308$	−5.45292	−0.310709
$309$	−8.30645	−0.472538
$310$	10.8331	0.615278
$311$	22.2661	1.26259	0.631297	−	0.775541i	$-0.282523\pi$
$311$	22.2661	1.26259	0.631297	+	0.775541i	$0.282523\pi$
$312$	14.9761	0.847852
$313$	−17.7258	−1.00192	−0.500960	−	0.865470i	$-0.667020\pi$
$313$	−17.7258	−1.00192	−0.500960	+	0.865470i	$0.667020\pi$
$314$	2.82657	0.159513
$315$	2.98638	0.168264
$316$	11.7453	0.660722
$317$	−1.36317	−0.0765633	−0.0382817	−	0.999267i	$-0.512188\pi$
$317$	−1.36317	−0.0765633	−0.0382817	+	0.999267i	$0.512188\pi$
$318$	−30.4026	−1.70489
$319$	7.40860	0.414802
$320$	1.35082	0.0755130
$321$	46.0724	2.57151
$322$	1.80018	0.100320
$323$	−5.55443	−0.309057
$324$	−11.0081	−0.611561
$325$	21.2839	1.18062
$326$	20.6870	1.14575
$327$	−16.3832	−0.905991
$328$	9.41249	0.519718
$329$	5.04344	0.278054
$330$	14.8272	0.816213
$331$	2.55483	0.140426	0.0702132	−	0.997532i	$-0.477632\pi$
$331$	2.55483	0.140426	0.0702132	+	0.997532i	$0.477632\pi$
$332$	−3.02480	−0.166008
$333$	−0.489824	−0.0268422
$334$	9.23311	0.505213
$335$	13.8433	0.756342
$336$	−2.47985	−0.135287
$337$	7.81314	0.425609	0.212804	−	0.977095i	$-0.431740\pi$
$337$	7.81314	0.425609	0.212804	+	0.977095i	$0.431740\pi$
$338$	31.9298	1.73675
$339$	22.7018	1.23299
$340$	3.23727	0.175565
$341$	−39.3994	−2.13360
$342$	−4.61648	−0.249631
$343$	−14.1716	−0.765197
$344$	8.36285	0.450895
$345$	−4.89495	−0.263535
$346$	−18.4324	−0.990931
$347$	7.12177	0.382317	0.191158	−	0.981559i	$-0.438776\pi$
$347$	7.12177	0.382317	0.191158	+	0.981559i	$0.438776\pi$
$348$	3.36924	0.180610
$349$	7.79750	0.417391	0.208695	−	0.977981i	$-0.433078\pi$
$349$	7.79750	0.417391	0.208695	+	0.977981i	$0.433078\pi$
$350$	−3.52435	−0.188385
$351$	−15.0983	−0.805889
$352$	−4.91285	−0.261856
$353$	−26.3732	−1.40370	−0.701852	−	0.712323i	$-0.747643\pi$
$353$	−26.3732	−1.40370	−0.701852	+	0.712323i	$0.747643\pi$
$354$	13.2667	0.705118
$355$	2.41732	0.128298
$356$	−11.8492	−0.628006
$357$	−5.94303	−0.314538
$358$	24.3976	1.28945
$359$	18.9756	1.00150	0.500748	−	0.865593i	$-0.333058\pi$
$359$	18.9756	1.00150	0.500748	+	0.865593i	$0.333058\pi$
$360$	2.69061	0.141807
$361$	−13.6283	−0.717277
$362$	−1.89422	−0.0995579
$363$	−29.3493	−1.54044
$364$	−7.43983	−0.389953
$365$	20.3709	1.06626
$366$	1.09560	0.0572679
$367$	−1.30234	−0.0679818	−0.0339909	−	0.999422i	$-0.510822\pi$
$367$	−1.30234	−0.0679818	−0.0339909	+	0.999422i	$0.510822\pi$
$368$	1.62189	0.0845468
$369$	18.7481	0.975989
$370$	−0.332188	−0.0172696
$371$	15.1035	0.784133
$372$	−17.9178	−0.928997
$373$	−12.0849	−0.625735	−0.312867	−	0.949797i	$-0.601290\pi$
$373$	−12.0849	−0.625735	−0.312867	+	0.949797i	$0.601290\pi$
$374$	−11.7738	−0.608808
$375$	24.6735	1.27413
$376$	4.54393	0.234335
$377$	10.1081	0.520593
$378$	2.50010	0.128591
$379$	−2.66270	−0.136774	−0.0683869	−	0.997659i	$-0.521785\pi$
$379$	−2.66270	−0.136774	−0.0683869	+	0.997659i	$0.521785\pi$
$380$	−3.13079	−0.160606
$381$	−33.9227	−1.73791
$382$	19.5165	0.998552
$383$	28.4304	1.45272	0.726362	−	0.687313i	$-0.241210\pi$
$383$	28.4304	1.45272	0.726362	+	0.687313i	$0.241210\pi$
$384$	−2.23424	−0.114016
$385$	−7.36590	−0.375401
$386$	−17.5312	−0.892315
$387$	16.6574	0.846744
$388$	−5.97799	−0.303486
$389$	6.13727	0.311172	0.155586	−	0.987822i	$-0.450273\pi$
$389$	6.13727	0.311172	0.155586	+	0.987822i	$0.450273\pi$
$390$	20.2299	1.02438
$391$	3.88690	0.196569
$392$	−5.76806	−0.291331
$393$	−21.5638	−1.08775
$394$	−4.24991	−0.214107
$395$	15.8657	0.798290
$396$	−9.78560	−0.491745
$397$	3.98700	0.200102	0.100051	−	0.994982i	$-0.468099\pi$
$397$	3.98700	0.200102	0.100051	+	0.994982i	$0.468099\pi$
$398$	6.20878	0.311218
$399$	5.74755	0.287738
$400$	−3.17529	−0.158765
$401$	19.2235	0.959976	0.479988	−	0.877275i	$-0.340641\pi$
$401$	19.2235	0.959976	0.479988	+	0.877275i	$0.340641\pi$
$402$	−22.8968	−1.14199
$403$	−53.7555	−2.67775
$404$	13.0576	0.649637
$405$	−14.8699	−0.738892
$406$	−1.67378	−0.0830682
$407$	1.20815	0.0598858
$408$	−5.35442	−0.265083
$409$	18.4937	0.914453	0.457227	−	0.889350i	$-0.348843\pi$
$409$	18.4937	0.914453	0.457227	+	0.889350i	$0.348843\pi$
$410$	12.7146	0.627927
$411$	−7.38182	−0.364118
$412$	3.71780	0.183163
$413$	−6.59066	−0.324305
$414$	3.23054	0.158772
$415$	−4.08595	−0.200572
$416$	−6.70297	−0.328640
$417$	19.6916	0.964304
$418$	11.3865	0.556933
$419$	16.7436	0.817976	0.408988	−	0.912540i	$-0.365882\pi$
$419$	16.7436	0.817976	0.408988	+	0.912540i	$0.365882\pi$
$420$	−3.34983	−0.163455
$421$	13.2547	0.645994	0.322997	−	0.946400i	$-0.395310\pi$
$421$	13.2547	0.645994	0.322997	+	0.946400i	$0.395310\pi$
$422$	−22.4332	−1.09203
$423$	9.05076	0.440063
$424$	13.6076	0.660842
$425$	−7.60967	−0.369123
$426$	−3.99823	−0.193715
$427$	−0.544274	−0.0263393
$428$	−20.6211	−0.996757
$429$	−73.5752	−3.55224
$430$	11.2967	0.544774
$431$	−21.2202	−1.02214	−0.511071	−	0.859538i	$-0.670751\pi$
$431$	−21.2202	−1.02214	−0.511071	+	0.859538i	$0.670751\pi$
$432$	2.25248	0.108373
$433$	0.299573	0.0143965	0.00719827	−	0.999974i	$-0.497709\pi$
$433$	0.299573	0.0143965	0.00719827	+	0.999974i	$0.497709\pi$
$434$	8.90125	0.427274
$435$	4.55123	0.218215
$436$	7.33277	0.351176
$437$	−3.75905	−0.179820
$438$	−33.6933	−1.60993
$439$	−15.8403	−0.756015	−0.378007	−	0.925803i	$-0.623391\pi$
$439$	−15.8403	−0.756015	−0.378007	+	0.925803i	$0.623391\pi$
$440$	−6.63637	−0.316376
$441$	−11.4890	−0.547096
$442$	−16.0638	−0.764079
$443$	−16.9065	−0.803250	−0.401625	−	0.915804i	$-0.631554\pi$
$443$	−16.9065	−0.803250	−0.401625	+	0.915804i	$0.631554\pi$
$444$	0.549436	0.0260751
$445$	−16.0061	−0.758762
$446$	5.45195	0.258157
$447$	−2.95754	−0.139887
$448$	1.10993	0.0524393
$449$	−6.62215	−0.312518	−0.156259	−	0.987716i	$-0.549944\pi$
$449$	−6.62215	−0.312518	−0.156259	+	0.987716i	$0.549944\pi$
$450$	−6.32466	−0.298147
$451$	−46.2422	−2.17746
$452$	−10.1608	−0.477926
$453$	32.2373	1.51464
$454$	15.0043	0.704188
$455$	−10.0498	−0.471144
$456$	5.17830	0.242496
$457$	−12.3119	−0.575928	−0.287964	−	0.957641i	$-0.592978\pi$
$457$	−12.3119	−0.575928	−0.287964	+	0.957641i	$0.592978\pi$
$458$	−6.19536	−0.289490
$459$	5.39813	0.251963
$460$	2.19088	0.102150
$461$	23.7744	1.10728	0.553641	−	0.832755i	$-0.313238\pi$
$461$	23.7744	1.10728	0.553641	+	0.832755i	$0.313238\pi$
$462$	12.1832	0.566811
$463$	−15.9965	−0.743422	−0.371711	−	0.928349i	$-0.621229\pi$
$463$	−15.9965	−0.743422	−0.371711	+	0.928349i	$0.621229\pi$
$464$	−1.50800	−0.0700073
$465$	−24.2037	−1.12242
$466$	−2.96114	−0.137172
$467$	−38.2057	−1.76795	−0.883973	−	0.467537i	$-0.845141\pi$
$467$	−38.2057	−1.76795	−0.883973	+	0.467537i	$0.845141\pi$
$468$	−13.3512	−0.617160
$469$	11.3747	0.525235
$470$	6.13802	0.283126
$471$	−6.31524	−0.290991
$472$	−5.93790	−0.273314
$473$	−41.0855	−1.88911
$474$	−26.2417	−1.20532
$475$	7.35938	0.337671
$476$	2.65998	0.121920
$477$	27.1041	1.24101
$478$	−9.93141	−0.454252
$479$	37.4294	1.71019	0.855096	−	0.518469i	$-0.173498\pi$
$479$	37.4294	1.71019	0.855096	+	0.518469i	$0.173498\pi$
$480$	−3.01805	−0.137755
$481$	1.64837	0.0751591
$482$	15.5578	0.708639
$483$	−4.02205	−0.183009
$484$	13.1361	0.597097
$485$	−8.07517	−0.366674
$486$	17.8373	0.809116
$487$	7.09199	0.321369	0.160684	−	0.987006i	$-0.448630\pi$
$487$	7.09199	0.321369	0.160684	+	0.987006i	$0.448630\pi$
$488$	−0.490368	−0.0221979
$489$	−46.2198	−2.09013
$490$	−7.79159	−0.351988
$491$	−5.59078	−0.252308	−0.126154	−	0.992011i	$-0.540263\pi$
$491$	−5.59078	−0.252308	−0.126154	+	0.992011i	$0.540263\pi$
$492$	−21.0298	−0.948096
$493$	−3.61397	−0.162765
$494$	15.5355	0.698974
$495$	−13.2186	−0.594130
$496$	8.01965	0.360093
$497$	1.98625	0.0890953
$498$	6.75814	0.302839
$499$	−28.3916	−1.27098	−0.635491	−	0.772108i	$-0.719202\pi$
$499$	−28.3916	−1.27098	−0.635491	+	0.772108i	$0.719202\pi$
$500$	−11.0433	−0.493872
$501$	−20.6290	−0.921635
$502$	−3.97756	−0.177527
$503$	19.2660	0.859029	0.429515	−	0.903060i	$-0.358685\pi$
$503$	19.2660	0.859029	0.429515	+	0.903060i	$0.358685\pi$
$504$	2.21080	0.0984768
$505$	17.6384	0.784897
$506$	−7.96811	−0.354226
$507$	−71.3389	−3.16827
$508$	15.1831	0.673642
$509$	35.3255	1.56577	0.782887	−	0.622164i	$-0.213746\pi$
$509$	35.3255	1.56577	0.782887	+	0.622164i	$0.213746\pi$
$510$	−7.23284	−0.320275
$511$	16.7382	0.740454
$512$	1.00000	0.0441942
$513$	−5.22058	−0.230494
$514$	17.7830	0.784376
$515$	5.02206	0.221298
$516$	−18.6846	−0.822545
$517$	−22.3237	−0.981794
$518$	−0.272950	−0.0119927
$519$	41.1824	1.80771
$520$	−9.05448	−0.397065
$521$	−30.4853	−1.33559	−0.667793	−	0.744347i	$-0.732761\pi$
$521$	−30.4853	−1.33559	−0.667793	+	0.744347i	$0.732761\pi$
$522$	−3.00369	−0.131468
$523$	2.85233	0.124724	0.0623619	−	0.998054i	$-0.480137\pi$
$523$	2.85233	0.124724	0.0623619	+	0.998054i	$0.480137\pi$
$524$	9.65152	0.421629
$525$	7.87426	0.343661
$526$	6.46481	0.281879
$527$	19.2193	0.837206
$528$	10.9765	0.477691
$529$	−20.3695	−0.885629
$530$	18.3813	0.798435
$531$	−11.8273	−0.513262
$532$	−2.57248	−0.111531
$533$	−63.0917	−2.73280
$534$	26.4740	1.14564
$535$	−27.8553	−1.20429
$536$	10.2481	0.442652
$537$	−54.5100	−2.35228
$538$	−17.6108	−0.759256
$539$	28.3376	1.22059
$540$	3.04269	0.130937
$541$	−5.35386	−0.230181	−0.115090	−	0.993355i	$-0.536716\pi$
$541$	−5.35386	−0.230181	−0.115090	+	0.993355i	$0.536716\pi$
$542$	22.8532	0.981630
$543$	4.23214	0.181619
$544$	2.39653	0.102750
$545$	9.90522	0.424293
$546$	16.6224	0.711372
$547$	1.13051	0.0483373	0.0241686	−	0.999708i	$-0.492306\pi$
$547$	1.13051	0.0483373	0.0241686	+	0.999708i	$0.492306\pi$
$548$	3.30395	0.141138
$549$	−0.976732	−0.0416859
$550$	15.5998	0.665176
$551$	3.49510	0.148896
$552$	−3.62369	−0.154235
$553$	13.0364	0.554365
$554$	−2.95544	−0.125565
$555$	0.742187	0.0315041
$556$	−8.81357	−0.373778
$557$	−8.84394	−0.374730	−0.187365	−	0.982290i	$-0.559995\pi$
$557$	−8.84394	−0.374730	−0.187365	+	0.982290i	$0.559995\pi$
$558$	15.9738	0.676226
$559$	−56.0559	−2.37091
$560$	1.49931	0.0633575
$561$	26.3055	1.11062
$562$	11.4064	0.481150
$563$	30.7607	1.29641	0.648205	−	0.761466i	$-0.275520\pi$
$563$	30.7607	1.29641	0.648205	+	0.761466i	$0.275520\pi$
$564$	−10.1522	−0.427486
$565$	−13.7254	−0.577434
$566$	−2.23549	−0.0939645
$567$	−12.2182	−0.513117
$568$	1.78952	0.0750868
$569$	30.3792	1.27356	0.636781	−	0.771045i	$-0.280265\pi$
$569$	30.3792	1.27356	0.636781	+	0.771045i	$0.280265\pi$
$570$	6.99494	0.292986
$571$	−45.9299	−1.92211	−0.961054	−	0.276361i	$-0.910871\pi$
$571$	−45.9299	−1.92211	−0.961054	+	0.276361i	$0.910871\pi$
$572$	32.9307	1.37690
$573$	−43.6046	−1.82161
$574$	10.4472	0.436058
$575$	−5.14998	−0.214769
$576$	1.99184	0.0829931
$577$	9.24322	0.384800	0.192400	−	0.981317i	$-0.438373\pi$
$577$	9.24322	0.384800	0.192400	+	0.981317i	$0.438373\pi$
$578$	−11.2567	−0.468216
$579$	39.1690	1.62781
$580$	−2.03704	−0.0845833
$581$	−3.35732	−0.139285
$582$	13.3563	0.553635
$583$	−66.8521	−2.76873
$584$	15.0804	0.624031
$585$	−18.0350	−0.745657
$586$	−23.6822	−0.978302
$587$	−20.8499	−0.860567	−0.430284	−	0.902694i	$-0.641586\pi$
$587$	−20.8499	−0.860567	−0.430284	+	0.902694i	$0.641586\pi$
$588$	12.8872	0.531460
$589$	−18.5871	−0.765870
$590$	−8.02102	−0.330220
$591$	9.49532	0.390585
$592$	−0.245916	−0.0101071
$593$	5.65911	0.232392	0.116196	−	0.993226i	$-0.462930\pi$
$593$	5.65911	0.232392	0.116196	+	0.993226i	$0.462930\pi$
$594$	−11.0661	−0.454048
$595$	3.59314	0.147304
$596$	1.32373	0.0542222
$597$	−13.8719	−0.567740
$598$	−10.8715	−0.444568
$599$	−37.9122	−1.54905	−0.774525	−	0.632543i	$-0.782011\pi$
$599$	−37.9122	−1.54905	−0.774525	+	0.632543i	$0.782011\pi$
$600$	7.09437	0.289627
$601$	40.2136	1.64035	0.820174	−	0.572114i	$-0.193876\pi$
$601$	40.2136	1.64035	0.820174	+	0.572114i	$0.193876\pi$
$602$	9.28218	0.378313
$603$	20.4126	0.831264
$604$	−14.4287	−0.587097
$605$	17.7445	0.721417
$606$	−29.1737	−1.18510
$607$	33.0617	1.34193	0.670967	−	0.741487i	$-0.265879\pi$
$607$	33.0617	1.34193	0.670967	+	0.741487i	$0.265879\pi$
$608$	−2.31770	−0.0939951
$609$	3.73962	0.151537
$610$	−0.662397	−0.0268197
$611$	−30.4578	−1.23219
$612$	4.77349	0.192957
$613$	−22.7266	−0.917920	−0.458960	−	0.888457i	$-0.651778\pi$
$613$	−22.7266	−0.917920	−0.458960	+	0.888457i	$0.651778\pi$
$614$	22.9585	0.926528
$615$	−28.4074	−1.14550
$616$	−5.45292	−0.219705
$617$	−13.5409	−0.545135	−0.272568	−	0.962137i	$-0.587873\pi$
$617$	−13.5409	−0.545135	−0.272568	+	0.962137i	$0.587873\pi$
$618$	−8.30645	−0.334135
$619$	21.7534	0.874343	0.437172	−	0.899378i	$-0.355980\pi$
$619$	21.7534	0.874343	0.437172	+	0.899378i	$0.355980\pi$
$620$	10.8331	0.435067
$621$	3.65328	0.146601
$622$	22.2661	0.892789
$623$	−13.1518	−0.526915
$624$	14.9761	0.599522
$625$	0.958959	0.0383584
$626$	−17.7258	−0.708465
$627$	−25.4402	−1.01599
$628$	2.82657	0.112792
$629$	−0.589344	−0.0234987
$630$	2.98638	0.118980
$631$	−30.4655	−1.21281	−0.606407	−	0.795154i	$-0.707390\pi$
$631$	−30.4655	−1.21281	−0.606407	+	0.795154i	$0.707390\pi$
$632$	11.7453	0.467201
$633$	50.1212	1.99214
$634$	−1.36317	−0.0541384
$635$	20.5096	0.813899
$636$	−30.4026	−1.20554
$637$	38.6631	1.53189
$638$	7.40860	0.293309
$639$	3.56444	0.141007
$640$	1.35082	0.0533957
$641$	38.3964	1.51657	0.758283	−	0.651925i	$-0.226038\pi$
$641$	38.3964	1.51657	0.758283	+	0.651925i	$0.226038\pi$
$642$	46.0724	1.81833
$643$	−39.4073	−1.55407	−0.777035	−	0.629457i	$-0.783277\pi$
$643$	−39.4073	−1.55407	−0.777035	+	0.629457i	$0.783277\pi$
$644$	1.80018	0.0709372
$645$	−25.2395	−0.993805
$646$	−5.55443	−0.218536
$647$	3.64966	0.143483	0.0717415	−	0.997423i	$-0.477144\pi$
$647$	3.64966	0.143483	0.0717415	+	0.997423i	$0.477144\pi$
$648$	−11.0081	−0.432439
$649$	29.1721	1.14510
$650$	21.2839	0.834823
$651$	−19.8875	−0.779454
$652$	20.6870	0.810166
$653$	41.6635	1.63042	0.815210	−	0.579166i	$-0.196622\pi$
$653$	41.6635	1.63042	0.815210	+	0.579166i	$0.196622\pi$
$654$	−16.3832	−0.640633
$655$	13.0374	0.509415
$656$	9.41249	0.367496
$657$	30.0377	1.17188
$658$	5.04344	0.196614
$659$	18.2631	0.711428	0.355714	−	0.934595i	$-0.384238\pi$
$659$	18.2631	0.711428	0.355714	+	0.934595i	$0.384238\pi$
$660$	14.8272	0.577150
$661$	−41.0291	−1.59585	−0.797924	−	0.602758i	$-0.794068\pi$
$661$	−41.0291	−1.59585	−0.797924	+	0.602758i	$0.794068\pi$
$662$	2.55483	0.0992964
$663$	35.8905	1.39387
$664$	−3.02480	−0.117385
$665$	−3.47496	−0.134753
$666$	−0.489824	−0.0189803
$667$	−2.44581	−0.0947023
$668$	9.23311	0.357240
$669$	−12.1810	−0.470944
$670$	13.8433	0.534815
$671$	2.40911	0.0930025
$672$	−2.47985	−0.0956624
$673$	−13.4316	−0.517752	−0.258876	−	0.965911i	$-0.583352\pi$
$673$	−13.4316	−0.517752	−0.258876	+	0.965911i	$0.583352\pi$
$674$	7.81314	0.300951
$675$	−7.15229	−0.275292
$676$	31.9298	1.22807
$677$	18.4751	0.710056	0.355028	−	0.934856i	$-0.384471\pi$
$677$	18.4751	0.710056	0.355028	+	0.934856i	$0.384471\pi$
$678$	22.7018	0.871857
$679$	−6.63515	−0.254634
$680$	3.23727	0.124144
$681$	−33.5233	−1.28462
$682$	−39.3994	−1.50868
$683$	−36.8242	−1.40904	−0.704519	−	0.709685i	$-0.748837\pi$
$683$	−36.8242	−1.40904	−0.704519	+	0.709685i	$0.748837\pi$
$684$	−4.61648	−0.176515
$685$	4.46303	0.170524
$686$	−14.1716	−0.541076
$687$	13.8419	0.528102
$688$	8.36285	0.318831
$689$	−91.2112	−3.47487
$690$	−4.89495	−0.186347
$691$	24.0215	0.913822	0.456911	−	0.889513i	$-0.348956\pi$
$691$	24.0215	0.913822	0.456911	+	0.889513i	$0.348956\pi$
$692$	−18.4324	−0.700694
$693$	−10.8613	−0.412588
$694$	7.12177	0.270339
$695$	−11.9055	−0.451602
$696$	3.36924	0.127711
$697$	22.5573	0.854418
$698$	7.79750	0.295140
$699$	6.61590	0.250236
$700$	−3.52435	−0.133208
$701$	38.5959	1.45775	0.728873	−	0.684649i	$-0.240044\pi$
$701$	38.5959	1.45775	0.728873	+	0.684649i	$0.240044\pi$
$702$	−15.0983	−0.569850
$703$	0.569960	0.0214964
$704$	−4.91285	−0.185160
$705$	−13.7138	−0.516492
$706$	−26.3732	−0.992569
$707$	14.4930	0.545064
$708$	13.2667	0.498594
$709$	−26.6119	−0.999430	−0.499715	−	0.866190i	$-0.666562\pi$
$709$	−26.6119	−0.999430	−0.499715	+	0.866190i	$0.666562\pi$
$710$	2.41732	0.0907204
$711$	23.3946	0.877367
$712$	−11.8492	−0.444067
$713$	13.0070	0.487116
$714$	−5.94303	−0.222412
$715$	44.4834	1.66358
$716$	24.3976	0.911780
$717$	22.1892	0.828670
$718$	18.9756	0.708164
$719$	25.8512	0.964089	0.482044	−	0.876147i	$-0.339894\pi$
$719$	25.8512	0.964089	0.482044	+	0.876147i	$0.339894\pi$
$720$	2.69061	0.100273
$721$	4.12649	0.153679
$722$	−13.6283	−0.507192
$723$	−34.7599	−1.29273
$724$	−1.89422	−0.0703981
$725$	4.78835	0.177835
$726$	−29.3493	−1.08925
$727$	36.4659	1.35244	0.676222	−	0.736698i	$-0.263616\pi$
$727$	36.4659	1.35244	0.676222	+	0.736698i	$0.263616\pi$
$728$	−7.43983	−0.275738
$729$	−6.82855	−0.252909
$730$	20.3709	0.753959
$731$	20.0418	0.741272
$732$	1.09560	0.0404945
$733$	−18.2038	−0.672372	−0.336186	−	0.941796i	$-0.609137\pi$
$733$	−18.2038	−0.672372	−0.336186	+	0.941796i	$0.609137\pi$
$734$	−1.30234	−0.0480704
$735$	17.4083	0.642114
$736$	1.62189	0.0597836
$737$	−50.3475	−1.85458
$738$	18.7481	0.690129
$739$	−31.9168	−1.17408	−0.587039	−	0.809559i	$-0.699706\pi$
$739$	−31.9168	−1.17408	−0.587039	+	0.809559i	$0.699706\pi$
$740$	−0.332188	−0.0122115
$741$	−34.7100	−1.27510
$742$	15.1035	0.554465
$743$	−18.1951	−0.667515	−0.333758	−	0.942659i	$-0.608317\pi$
$743$	−18.1951	−0.667515	−0.333758	+	0.942659i	$0.608317\pi$
$744$	−17.9178	−0.656900
$745$	1.78812	0.0655116
$746$	−12.0849	−0.442461
$747$	−6.02491	−0.220440
$748$	−11.7738	−0.430492
$749$	−22.8879	−0.836307
$750$	24.6735	0.900947
$751$	4.40233	0.160643	0.0803216	−	0.996769i	$-0.474405\pi$
$751$	4.40233	0.160643	0.0803216	+	0.996769i	$0.474405\pi$
$752$	4.54393	0.165700
$753$	8.88682	0.323854
$754$	10.1081	0.368115
$755$	−19.4906	−0.709335
$756$	2.50010	0.0909277
$757$	47.8913	1.74064	0.870319	−	0.492488i	$-0.163913\pi$
$757$	47.8913	1.74064	0.870319	+	0.492488i	$0.163913\pi$
$758$	−2.66270	−0.0967137
$759$	17.8027	0.646196
$760$	−3.13079	−0.113566
$761$	7.19243	0.260725	0.130363	−	0.991466i	$-0.458386\pi$
$761$	7.19243	0.260725	0.130363	+	0.991466i	$0.458386\pi$
$762$	−33.9227	−1.22889
$763$	8.13886	0.294646
$764$	19.5165	0.706083
$765$	6.44810	0.233132
$766$	28.4304	1.02723
$767$	39.8016	1.43715
$768$	−2.23424	−0.0806212
$769$	−20.0642	−0.723532	−0.361766	−	0.932269i	$-0.617826\pi$
$769$	−20.0642	−0.723532	−0.361766	+	0.932269i	$0.617826\pi$
$770$	−7.36590	−0.265449
$771$	−39.7316	−1.43090
$772$	−17.5312	−0.630962
$773$	−1.13969	−0.0409919	−0.0204959	−	0.999790i	$-0.506525\pi$
$773$	−1.13969	−0.0409919	−0.0204959	+	0.999790i	$0.506525\pi$
$774$	16.6574	0.598739
$775$	−25.4647	−0.914721
$776$	−5.97799	−0.214597
$777$	0.609836	0.0218777
$778$	6.13727	0.220032
$779$	−21.8153	−0.781616
$780$	20.2299	0.724347
$781$	−8.79167	−0.314591
$782$	3.88690	0.138995
$783$	−3.39675	−0.121390
$784$	−5.76806	−0.206002
$785$	3.81818	0.136277
$786$	−21.5638	−0.769157
$787$	7.08948	0.252712	0.126356	−	0.991985i	$-0.459672\pi$
$787$	7.08948	0.252712	0.126356	+	0.991985i	$0.459672\pi$
$788$	−4.24991	−0.151397
$789$	−14.4439	−0.514218
$790$	15.8657	0.564476
$791$	−11.2778	−0.400993
$792$	−9.78560	−0.347716
$793$	3.28692	0.116722
$794$	3.98700	0.141493
$795$	−41.0684	−1.45655
$796$	6.20878	0.220064
$797$	32.9646	1.16767	0.583833	−	0.811874i	$-0.301552\pi$
$797$	32.9646	1.16767	0.583833	+	0.811874i	$0.301552\pi$
$798$	5.74755	0.203461
$799$	10.8896	0.385248
$800$	−3.17529	−0.112264
$801$	−23.6016	−0.833923
$802$	19.2235	0.678806
$803$	−74.0878	−2.61450
$804$	−22.8968	−0.807507
$805$	2.43172	0.0857068
$806$	−53.7555	−1.89346
$807$	39.3468	1.38507
$808$	13.0576	0.459363
$809$	−44.6370	−1.56935	−0.784676	−	0.619906i	$-0.787171\pi$
$809$	−44.6370	−1.56935	−0.784676	+	0.619906i	$0.787171\pi$
$810$	−14.8699	−0.522476
$811$	26.5294	0.931573	0.465786	−	0.884897i	$-0.345771\pi$
$811$	26.5294	0.931573	0.465786	+	0.884897i	$0.345771\pi$
$812$	−1.67378	−0.0587381
$813$	−51.0596	−1.79074
$814$	1.20815	0.0423456
$815$	27.9444	0.978848
$816$	−5.35442	−0.187442
$817$	−19.3826	−0.678111
$818$	18.4937	0.646616
$819$	−14.8189	−0.517815
$820$	12.7146	0.444012
$821$	7.93018	0.276765	0.138383	−	0.990379i	$-0.455810\pi$
$821$	7.93018	0.276765	0.138383	+	0.990379i	$0.455810\pi$
$822$	−7.38182	−0.257471
$823$	−45.9519	−1.60178	−0.800891	−	0.598810i	$-0.795641\pi$
$823$	−45.9519	−1.60178	−0.800891	+	0.598810i	$0.795641\pi$
$824$	3.71780	0.129516
$825$	−34.8536	−1.21345
$826$	−6.59066	−0.229318
$827$	20.0224	0.696246	0.348123	−	0.937449i	$-0.386819\pi$
$827$	20.0224	0.696246	0.348123	+	0.937449i	$0.386819\pi$
$828$	3.23054	0.112269
$829$	21.0702	0.731798	0.365899	−	0.930655i	$-0.380762\pi$
$829$	21.0702	0.731798	0.365899	+	0.930655i	$0.380762\pi$
$830$	−4.08595	−0.141825
$831$	6.60318	0.229062
$832$	−6.70297	−0.232384
$833$	−13.8233	−0.478949
$834$	19.6916	0.681866
$835$	12.4722	0.431620
$836$	11.3865	0.393811
$837$	18.0641	0.624388
$838$	16.7436	0.578397
$839$	30.1440	1.04069	0.520344	−	0.853957i	$-0.325804\pi$
$839$	30.1440	1.04069	0.520344	+	0.853957i	$0.325804\pi$
$840$	−3.34983	−0.115580
$841$	−26.7259	−0.921584
$842$	13.2547	0.456787
$843$	−25.4847	−0.877739
$844$	−22.4332	−0.772183
$845$	43.1313	1.48376
$846$	9.05076	0.311172
$847$	14.5802	0.500981
$848$	13.6076	0.467286
$849$	4.99462	0.171415
$850$	−7.60967	−0.261010
$851$	−0.398849	−0.0136724
$852$	−3.99823	−0.136977
$853$	−26.6077	−0.911032	−0.455516	−	0.890228i	$-0.650545\pi$
$853$	−26.6077	−0.911032	−0.455516	+	0.890228i	$0.650545\pi$
$854$	−0.544274	−0.0186247
$855$	−6.23602	−0.213267
$856$	−20.6211	−0.704813
$857$	−11.2491	−0.384262	−0.192131	−	0.981369i	$-0.561540\pi$
$857$	−11.2491	−0.384262	−0.192131	+	0.981369i	$0.561540\pi$
$858$	−73.5752	−2.51181
$859$	−9.88191	−0.337166	−0.168583	−	0.985687i	$-0.553919\pi$
$859$	−9.88191	−0.337166	−0.168583	+	0.985687i	$0.553919\pi$
$860$	11.2967	0.385214
$861$	−23.3416	−0.795479
$862$	−21.2202	−0.722764
$863$	−18.8118	−0.640361	−0.320181	−	0.947356i	$-0.603744\pi$
$863$	−18.8118	−0.640361	−0.320181	+	0.947356i	$0.603744\pi$
$864$	2.25248	0.0766310
$865$	−24.8988	−0.846583
$866$	0.299573	0.0101799
$867$	25.1501	0.854142
$868$	8.90125	0.302128
$869$	−57.7027	−1.95743
$870$	4.55123	0.154301
$871$	−68.6929	−2.32757
$872$	7.33277	0.248319
$873$	−11.9072	−0.402997
$874$	−3.75905	−0.127152
$875$	−12.2573	−0.414373
$876$	−33.6933	−1.13839
$877$	−27.0216	−0.912456	−0.456228	−	0.889863i	$-0.650800\pi$
$877$	−27.0216	−0.912456	−0.456228	+	0.889863i	$0.650800\pi$
$878$	−15.8403	−0.534583
$879$	52.9117	1.78467
$880$	−6.63637	−0.223712
$881$	23.1650	0.780449	0.390225	−	0.920720i	$-0.372397\pi$
$881$	23.1650	0.780449	0.390225	+	0.920720i	$0.372397\pi$
$882$	−11.4890	−0.386855
$883$	49.0986	1.65230	0.826150	−	0.563451i	$-0.190527\pi$
$883$	49.0986	1.65230	0.826150	+	0.563451i	$0.190527\pi$
$884$	−16.0638	−0.540285
$885$	17.9209	0.602404
$886$	−16.9065	−0.567983
$887$	−8.02885	−0.269582	−0.134791	−	0.990874i	$-0.543036\pi$
$887$	−8.02885	−0.269582	−0.134791	+	0.990874i	$0.543036\pi$
$888$	0.549436	0.0184379
$889$	16.8522	0.565204
$890$	−16.0061	−0.536525
$891$	54.0812	1.81179
$892$	5.45195	0.182545
$893$	−10.5315	−0.352422
$894$	−2.95754	−0.0989148
$895$	32.9566	1.10162
$896$	1.10993	0.0370802
$897$	24.2895	0.811003
$898$	−6.62215	−0.220984
$899$	−12.0937	−0.403346
$900$	−6.32466	−0.210822
$901$	32.6109	1.08643
$902$	−46.2422	−1.53970
$903$	−20.7386	−0.690138
$904$	−10.1608	−0.337945
$905$	−2.55874	−0.0850555
$906$	32.2373	1.07101
$907$	−11.7277	−0.389413	−0.194707	−	0.980862i	$-0.562375\pi$
$907$	−11.7277	−0.389413	−0.194707	+	0.980862i	$0.562375\pi$
$908$	15.0043	0.497936
$909$	26.0085	0.862647
$910$	−10.0498	−0.333149
$911$	0.215283	0.00713265	0.00356633	−	0.999994i	$-0.498865\pi$
$911$	0.215283	0.00713265	0.00356633	+	0.999994i	$0.498865\pi$
$912$	5.17830	0.171471
$913$	14.8604	0.491808
$914$	−12.3119	−0.407242
$915$	1.47995	0.0489258
$916$	−6.19536	−0.204700
$917$	10.7125	0.353758
$918$	5.39813	0.178165
$919$	41.0259	1.35332	0.676661	−	0.736295i	$-0.263426\pi$
$919$	41.0259	1.35332	0.676661	+	0.736295i	$0.263426\pi$
$920$	2.19088	0.0722310
$921$	−51.2948	−1.69022
$922$	23.7744	0.782967
$923$	−11.9951	−0.394824
$924$	12.1832	0.400796
$925$	0.780856	0.0256744
$926$	−15.9965	−0.525679
$927$	7.40524	0.243220
$928$	−1.50800	−0.0495026
$929$	1.77543	0.0582500	0.0291250	−	0.999576i	$-0.490728\pi$
$929$	1.77543	0.0582500	0.0291250	+	0.999576i	$0.490728\pi$
$930$	−24.2037	−0.793671
$931$	13.3686	0.438139
$932$	−2.96114	−0.0969954
$933$	−49.7478	−1.62867
$934$	−38.2057	−1.25013
$935$	−15.9042	−0.520124
$936$	−13.3512	−0.436398
$937$	−30.9103	−1.00979	−0.504897	−	0.863179i	$-0.668470\pi$
$937$	−30.9103	−1.00979	−0.504897	+	0.863179i	$0.668470\pi$
$938$	11.3747	0.371397
$939$	39.6037	1.29242
$940$	6.13802	0.200200
$941$	12.3096	0.401283	0.200641	−	0.979665i	$-0.435697\pi$
$941$	12.3096	0.401283	0.200641	+	0.979665i	$0.435697\pi$
$942$	−6.31524	−0.205762
$943$	15.2660	0.497130
$944$	−5.93790	−0.193262
$945$	3.37717	0.109860
$946$	−41.0855	−1.33580
$947$	−28.2237	−0.917147	−0.458574	−	0.888656i	$-0.651639\pi$
$947$	−28.2237	−0.917147	−0.458574	+	0.888656i	$0.651639\pi$
$948$	−26.2417	−0.852292
$949$	−101.083	−3.28131
$950$	7.35938	0.238770
$951$	3.04565	0.0987621
$952$	2.65998	0.0862103
$953$	−49.0268	−1.58814	−0.794068	−	0.607830i	$-0.792040\pi$
$953$	−49.0268	−1.58814	−0.794068	+	0.607830i	$0.792040\pi$
$954$	27.1041	0.877526
$955$	26.3632	0.853094
$956$	−9.93141	−0.321205
$957$	−16.5526	−0.535069
$958$	37.4294	1.20929
$959$	3.66715	0.118419
$960$	−3.01805	−0.0974072
$961$	33.3148	1.07467
$962$	1.64837	0.0531455
$963$	−41.0738	−1.32358
$964$	15.5578	0.501083
$965$	−23.6815	−0.762333
$966$	−4.02205	−0.129407
$967$	54.1806	1.74233	0.871165	−	0.490990i	$-0.163365\pi$
$967$	54.1806	1.74233	0.871165	+	0.490990i	$0.163365\pi$
$968$	13.1361	0.422211
$969$	12.4099	0.398664
$970$	−8.07517	−0.259278
$971$	47.4529	1.52284	0.761418	−	0.648261i	$-0.224504\pi$
$971$	47.4529	1.52284	0.761418	+	0.648261i	$0.224504\pi$
$972$	17.8373	0.572132
$973$	−9.78244	−0.313611
$974$	7.09199	0.227242
$975$	−47.5534	−1.52293
$976$	−0.490368	−0.0156963
$977$	−42.2656	−1.35220	−0.676098	−	0.736811i	$-0.736331\pi$
$977$	−42.2656	−1.35220	−0.676098	+	0.736811i	$0.736331\pi$
$978$	−46.2198	−1.47795
$979$	58.2134	1.86051
$980$	−7.79159	−0.248893
$981$	14.6057	0.466323
$982$	−5.59078	−0.178409
$983$	50.4425	1.60886	0.804432	−	0.594044i	$-0.202470\pi$
$983$	50.4425	1.60886	0.804432	+	0.594044i	$0.202470\pi$
$984$	−21.0298	−0.670405
$985$	−5.74085	−0.182919
$986$	−3.61397	−0.115092
$987$	−11.2683	−0.358673
$988$	15.5355	0.494249
$989$	13.5636	0.431298
$990$	−13.2186	−0.420113
$991$	25.5140	0.810480	0.405240	−	0.914210i	$-0.367188\pi$
$991$	25.5140	0.810480	0.405240	+	0.914210i	$0.367188\pi$
$992$	8.01965	0.254624
$993$	−5.70811	−0.181142
$994$	1.98625	0.0629999
$995$	8.38693	0.265883
$996$	6.75814	0.214140
$997$	−42.3356	−1.34078	−0.670392	−	0.742007i	$-0.733874\pi$
$997$	−42.3356	−1.34078	−0.670392	+	0.742007i	$0.733874\pi$
$998$	−28.3916	−0.898720
$999$	−0.553922	−0.0175253

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.i.1.7	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.i.1.7	✓	46	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.23424 q^{3} +1.00000 q^{4} +1.35082 q^{5} -2.23424 q^{6} +1.10993 q^{7} +1.00000 q^{8} +1.99184 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.23424 q^{3} +1.00000 q^{4} +1.35082 q^{5} -2.23424 q^{6} +1.10993 q^{7} +1.00000 q^{8} +1.99184 q^{9} +1.35082 q^{10} -4.91285 q^{11} -2.23424 q^{12} -6.70297 q^{13} +1.10993 q^{14} -3.01805 q^{15} +1.00000 q^{16} +2.39653 q^{17} +1.99184 q^{18} -2.31770 q^{19} +1.35082 q^{20} -2.47985 q^{21} -4.91285 q^{22} +1.62189 q^{23} -2.23424 q^{24} -3.17529 q^{25} -6.70297 q^{26} +2.25248 q^{27} +1.10993 q^{28} -1.50800 q^{29} -3.01805 q^{30} +8.01965 q^{31} +1.00000 q^{32} +10.9765 q^{33} +2.39653 q^{34} +1.49931 q^{35} +1.99184 q^{36} -0.245916 q^{37} -2.31770 q^{38} +14.9761 q^{39} +1.35082 q^{40} +9.41249 q^{41} -2.47985 q^{42} +8.36285 q^{43} -4.91285 q^{44} +2.69061 q^{45} +1.62189 q^{46} +4.54393 q^{47} -2.23424 q^{48} -5.76806 q^{49} -3.17529 q^{50} -5.35442 q^{51} -6.70297 q^{52} +13.6076 q^{53} +2.25248 q^{54} -6.63637 q^{55} +1.10993 q^{56} +5.17830 q^{57} -1.50800 q^{58} -5.93790 q^{59} -3.01805 q^{60} -0.490368 q^{61} +8.01965 q^{62} +2.21080 q^{63} +1.00000 q^{64} -9.05448 q^{65} +10.9765 q^{66} +10.2481 q^{67} +2.39653 q^{68} -3.62369 q^{69} +1.49931 q^{70} +1.78952 q^{71} +1.99184 q^{72} +15.0804 q^{73} -0.245916 q^{74} +7.09437 q^{75} -2.31770 q^{76} -5.45292 q^{77} +14.9761 q^{78} +11.7453 q^{79} +1.35082 q^{80} -11.0081 q^{81} +9.41249 q^{82} -3.02480 q^{83} -2.47985 q^{84} +3.23727 q^{85} +8.36285 q^{86} +3.36924 q^{87} -4.91285 q^{88} -11.8492 q^{89} +2.69061 q^{90} -7.43983 q^{91} +1.62189 q^{92} -17.9178 q^{93} +4.54393 q^{94} -3.13079 q^{95} -2.23424 q^{96} -5.97799 q^{97} -5.76806 q^{98} -9.78560 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * q^99

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