LMFDB - Embedded newform 4034.2.a.d.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, 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("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.53830 q^{3} +1.00000 q^{4} +3.94371 q^{5} -1.53830 q^{6} -3.54174 q^{7} +1.00000 q^{8} -0.633629 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.53830 q^{3} +1.00000 q^{4} +3.94371 q^{5} -1.53830 q^{6} -3.54174 q^{7} +1.00000 q^{8} -0.633629 q^{9} +3.94371 q^{10} +4.54195 q^{11} -1.53830 q^{12} +3.47054 q^{13} -3.54174 q^{14} -6.06662 q^{15} +1.00000 q^{16} +3.19553 q^{17} -0.633629 q^{18} +1.14712 q^{19} +3.94371 q^{20} +5.44826 q^{21} +4.54195 q^{22} -3.21056 q^{23} -1.53830 q^{24} +10.5529 q^{25} +3.47054 q^{26} +5.58962 q^{27} -3.54174 q^{28} +4.23477 q^{29} -6.06662 q^{30} -8.64344 q^{31} +1.00000 q^{32} -6.98689 q^{33} +3.19553 q^{34} -13.9676 q^{35} -0.633629 q^{36} -4.09499 q^{37} +1.14712 q^{38} -5.33874 q^{39} +3.94371 q^{40} -5.96700 q^{41} +5.44826 q^{42} +7.60529 q^{43} +4.54195 q^{44} -2.49885 q^{45} -3.21056 q^{46} +4.18276 q^{47} -1.53830 q^{48} +5.54389 q^{49} +10.5529 q^{50} -4.91569 q^{51} +3.47054 q^{52} -0.668336 q^{53} +5.58962 q^{54} +17.9122 q^{55} -3.54174 q^{56} -1.76462 q^{57} +4.23477 q^{58} -0.928020 q^{59} -6.06662 q^{60} +8.93473 q^{61} -8.64344 q^{62} +2.24415 q^{63} +1.00000 q^{64} +13.6868 q^{65} -6.98689 q^{66} -4.43454 q^{67} +3.19553 q^{68} +4.93881 q^{69} -13.9676 q^{70} -11.0025 q^{71} -0.633629 q^{72} -14.9609 q^{73} -4.09499 q^{74} -16.2335 q^{75} +1.14712 q^{76} -16.0864 q^{77} -5.33874 q^{78} +13.8183 q^{79} +3.94371 q^{80} -6.69763 q^{81} -5.96700 q^{82} +9.97381 q^{83} +5.44826 q^{84} +12.6023 q^{85} +7.60529 q^{86} -6.51436 q^{87} +4.54195 q^{88} +8.67852 q^{89} -2.49885 q^{90} -12.2917 q^{91} -3.21056 q^{92} +13.2962 q^{93} +4.18276 q^{94} +4.52392 q^{95} -1.53830 q^{96} +14.3327 q^{97} +5.54389 q^{98} -2.87791 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) $ 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * 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
$3$	−1.53830	−0.888139	−0.444069	−	0.895992i	$-0.646466\pi$
$3$	−1.53830	−0.888139	−0.444069	+	0.895992i	$0.646466\pi$
$4$	1.00000	0.500000
$5$	3.94371	1.76368	0.881841	−	0.471546i	$-0.156304\pi$
$5$	3.94371	1.76368	0.881841	+	0.471546i	$0.156304\pi$
$6$	−1.53830	−0.628009
$7$	−3.54174	−1.33865	−0.669325	−	0.742970i	$-0.733417\pi$
$7$	−3.54174	−1.33865	−0.669325	+	0.742970i	$0.733417\pi$
$8$	1.00000	0.353553
$9$	−0.633629	−0.211210
$10$	3.94371	1.24711
$11$	4.54195	1.36945	0.684725	−	0.728802i	$-0.259922\pi$
$11$	4.54195	1.36945	0.684725	+	0.728802i	$0.259922\pi$
$12$	−1.53830	−0.444069
$13$	3.47054	0.962556	0.481278	−	0.876568i	$-0.340173\pi$
$13$	3.47054	0.962556	0.481278	+	0.876568i	$0.340173\pi$
$14$	−3.54174	−0.946569
$15$	−6.06662	−1.56639
$16$	1.00000	0.250000
$17$	3.19553	0.775030	0.387515	−	0.921863i	$-0.373334\pi$
$17$	3.19553	0.775030	0.387515	+	0.921863i	$0.373334\pi$
$18$	−0.633629	−0.149348
$19$	1.14712	0.263168	0.131584	−	0.991305i	$-0.457994\pi$
$19$	1.14712	0.263168	0.131584	+	0.991305i	$0.457994\pi$
$20$	3.94371	0.881841
$21$	5.44826	1.18891
$22$	4.54195	0.968347
$23$	−3.21056	−0.669448	−0.334724	−	0.942316i	$-0.608643\pi$
$23$	−3.21056	−0.669448	−0.334724	+	0.942316i	$0.608643\pi$
$24$	−1.53830	−0.314004
$25$	10.5529	2.11058
$26$	3.47054	0.680630
$27$	5.58962	1.07572
$28$	−3.54174	−0.669325
$29$	4.23477	0.786378	0.393189	−	0.919458i	$-0.371372\pi$
$29$	4.23477	0.786378	0.393189	+	0.919458i	$0.371372\pi$
$30$	−6.06662	−1.10761
$31$	−8.64344	−1.55241	−0.776204	−	0.630482i	$-0.782857\pi$
$31$	−8.64344	−1.55241	−0.776204	+	0.630482i	$0.782857\pi$
$32$	1.00000	0.176777
$33$	−6.98689	−1.21626
$34$	3.19553	0.548029
$35$	−13.9676	−2.36095
$36$	−0.633629	−0.105605
$37$	−4.09499	−0.673213	−0.336606	−	0.941645i	$-0.609279\pi$
$37$	−4.09499	−0.673213	−0.336606	+	0.941645i	$0.609279\pi$
$38$	1.14712	0.186088
$39$	−5.33874	−0.854883
$40$	3.94371	0.623556
$41$	−5.96700	−0.931889	−0.465944	−	0.884814i	$-0.654285\pi$
$41$	−5.96700	−0.931889	−0.465944	+	0.884814i	$0.654285\pi$
$42$	5.44826	0.840684
$43$	7.60529	1.15980	0.579898	−	0.814689i	$-0.303092\pi$
$43$	7.60529	1.15980	0.579898	+	0.814689i	$0.303092\pi$
$44$	4.54195	0.684725
$45$	−2.49885	−0.372507
$46$	−3.21056	−0.473372
$47$	4.18276	0.610118	0.305059	−	0.952333i	$-0.401324\pi$
$47$	4.18276	0.610118	0.305059	+	0.952333i	$0.401324\pi$
$48$	−1.53830	−0.222035
$49$	5.54389	0.791985
$50$	10.5529	1.49240
$51$	−4.91569	−0.688334
$52$	3.47054	0.481278
$53$	−0.668336	−0.0918031	−0.0459015	−	0.998946i	$-0.514616\pi$
$53$	−0.668336	−0.0918031	−0.0459015	+	0.998946i	$0.514616\pi$
$54$	5.58962	0.760650
$55$	17.9122	2.41527
$56$	−3.54174	−0.473284
$57$	−1.76462	−0.233729
$58$	4.23477	0.556053
$59$	−0.928020	−0.120818	−0.0604090	−	0.998174i	$-0.519240\pi$
$59$	−0.928020	−0.120818	−0.0604090	+	0.998174i	$0.519240\pi$
$60$	−6.06662	−0.783197
$61$	8.93473	1.14397	0.571987	−	0.820262i	$-0.306173\pi$
$61$	8.93473	1.14397	0.571987	+	0.820262i	$0.306173\pi$
$62$	−8.64344	−1.09772
$63$	2.24415	0.282736
$64$	1.00000	0.125000
$65$	13.6868	1.69764
$66$	−6.98689	−0.860027
$67$	−4.43454	−0.541765	−0.270883	−	0.962612i	$-0.587316\pi$
$67$	−4.43454	−0.541765	−0.270883	+	0.962612i	$0.587316\pi$
$68$	3.19553	0.387515
$69$	4.93881	0.594563
$70$	−13.9676	−1.66945
$71$	−11.0025	−1.30575	−0.652877	−	0.757464i	$-0.726438\pi$
$71$	−11.0025	−1.30575	−0.652877	+	0.757464i	$0.726438\pi$
$72$	−0.633629	−0.0746739
$73$	−14.9609	−1.75104	−0.875521	−	0.483180i	$-0.839482\pi$
$73$	−14.9609	−1.75104	−0.875521	+	0.483180i	$0.839482\pi$
$74$	−4.09499	−0.476033
$75$	−16.2335	−1.87448
$76$	1.14712	0.131584
$77$	−16.0864	−1.83321
$78$	−5.33874	−0.604493
$79$	13.8183	1.55467	0.777337	−	0.629084i	$-0.216570\pi$
$79$	13.8183	1.55467	0.777337	+	0.629084i	$0.216570\pi$
$80$	3.94371	0.440921
$81$	−6.69763	−0.744181
$82$	−5.96700	−0.658945
$83$	9.97381	1.09477	0.547384	−	0.836882i	$-0.315624\pi$
$83$	9.97381	1.09477	0.547384	+	0.836882i	$0.315624\pi$
$84$	5.44826	0.594454
$85$	12.6023	1.36691
$86$	7.60529	0.820100
$87$	−6.51436	−0.698412
$88$	4.54195	0.484174
$89$	8.67852	0.919921	0.459961	−	0.887939i	$-0.347863\pi$
$89$	8.67852	0.919921	0.459961	+	0.887939i	$0.347863\pi$
$90$	−2.49885	−0.263402
$91$	−12.2917	−1.28853
$92$	−3.21056	−0.334724
$93$	13.2962	1.37875
$94$	4.18276	0.431419
$95$	4.52392	0.464144
$96$	−1.53830	−0.157002
$97$	14.3327	1.45526	0.727632	−	0.685968i	$-0.240621\pi$
$97$	14.3327	1.45526	0.727632	+	0.685968i	$0.240621\pi$
$98$	5.54389	0.560018
$99$	−2.87791	−0.289241
$100$	10.5529	1.05529
$101$	16.2470	1.61664	0.808320	−	0.588744i	$-0.200377\pi$
$101$	16.2470	1.61664	0.808320	+	0.588744i	$0.200377\pi$
$102$	−4.91569	−0.486726
$103$	−2.47083	−0.243458	−0.121729	−	0.992563i	$-0.538844\pi$
$103$	−2.47083	−0.243458	−0.121729	+	0.992563i	$0.538844\pi$
$104$	3.47054	0.340315
$105$	21.4864	2.09685
$106$	−0.668336	−0.0649146
$107$	−3.62630	−0.350567	−0.175284	−	0.984518i	$-0.556084\pi$
$107$	−3.62630	−0.350567	−0.175284	+	0.984518i	$0.556084\pi$
$108$	5.58962	0.537861
$109$	11.4090	1.09278	0.546391	−	0.837530i	$-0.316001\pi$
$109$	11.4090	1.09278	0.546391	+	0.837530i	$0.316001\pi$
$110$	17.9122	1.70786
$111$	6.29933	0.597906
$112$	−3.54174	−0.334663
$113$	5.67163	0.533542	0.266771	−	0.963760i	$-0.414043\pi$
$113$	5.67163	0.533542	0.266771	+	0.963760i	$0.414043\pi$
$114$	−1.76462	−0.165272
$115$	−12.6615	−1.18069
$116$	4.23477	0.393189
$117$	−2.19904	−0.203301
$118$	−0.928020	−0.0854312
$119$	−11.3177	−1.03749
$120$	−6.06662	−0.553804
$121$	9.62932	0.875393
$122$	8.93473	0.808912
$123$	9.17904	0.827646
$124$	−8.64344	−0.776204
$125$	21.8990	1.95870
$126$	2.24415	0.199924
$127$	0.710995	0.0630906	0.0315453	−	0.999502i	$-0.489957\pi$
$127$	0.710995	0.0630906	0.0315453	+	0.999502i	$0.489957\pi$
$128$	1.00000	0.0883883
$129$	−11.6992	−1.03006
$130$	13.6868	1.20041
$131$	15.7031	1.37199	0.685995	−	0.727606i	$-0.259367\pi$
$131$	15.7031	1.37199	0.685995	+	0.727606i	$0.259367\pi$
$132$	−6.98689	−0.608131
$133$	−4.06280	−0.352290
$134$	−4.43454	−0.383086
$135$	22.0438	1.89723
$136$	3.19553	0.274014
$137$	7.06102	0.603264	0.301632	−	0.953424i	$-0.402469\pi$
$137$	7.06102	0.603264	0.301632	+	0.953424i	$0.402469\pi$
$138$	4.93881	0.420420
$139$	−13.0236	−1.10465	−0.552325	−	0.833629i	$-0.686259\pi$
$139$	−13.0236	−1.10465	−0.552325	+	0.833629i	$0.686259\pi$
$140$	−13.9676	−1.18048
$141$	−6.43434	−0.541869
$142$	−11.0025	−0.923308
$143$	15.7630	1.31817
$144$	−0.633629	−0.0528024
$145$	16.7007	1.38692
$146$	−14.9609	−1.23817
$147$	−8.52818	−0.703392
$148$	−4.09499	−0.336606
$149$	11.5078	0.942757	0.471379	−	0.881931i	$-0.343756\pi$
$149$	11.5078	0.942757	0.471379	+	0.881931i	$0.343756\pi$
$150$	−16.2335	−1.32546
$151$	−4.74768	−0.386361	−0.193180	−	0.981163i	$-0.561880\pi$
$151$	−4.74768	−0.386361	−0.193180	+	0.981163i	$0.561880\pi$
$152$	1.14712	0.0930438
$153$	−2.02478	−0.163694
$154$	−16.0864	−1.29628
$155$	−34.0872	−2.73795
$156$	−5.33874	−0.427441
$157$	−18.4666	−1.47380	−0.736898	−	0.676004i	$-0.763710\pi$
$157$	−18.4666	−1.47380	−0.736898	+	0.676004i	$0.763710\pi$
$158$	13.8183	1.09932
$159$	1.02810	0.0815339
$160$	3.94371	0.311778
$161$	11.3710	0.896157
$162$	−6.69763	−0.526215
$163$	−22.9352	−1.79642	−0.898211	−	0.439564i	$-0.855133\pi$
$163$	−22.9352	−1.79642	−0.898211	+	0.439564i	$0.855133\pi$
$164$	−5.96700	−0.465944
$165$	−27.5543	−2.14510
$166$	9.97381	0.774118
$167$	−9.37258	−0.725272	−0.362636	−	0.931931i	$-0.618123\pi$
$167$	−9.37258	−0.725272	−0.362636	+	0.931931i	$0.618123\pi$
$168$	5.44826	0.420342
$169$	−0.955327	−0.0734867
$170$	12.6023	0.966549
$171$	−0.726849	−0.0555836
$172$	7.60529	0.579898
$173$	6.83501	0.519656	0.259828	−	0.965655i	$-0.416334\pi$
$173$	6.83501	0.519656	0.259828	+	0.965655i	$0.416334\pi$
$174$	−6.51436	−0.493852
$175$	−37.3755	−2.82532
$176$	4.54195	0.342362
$177$	1.42757	0.107303
$178$	8.67852	0.650483
$179$	2.24249	0.167611	0.0838056	−	0.996482i	$-0.473293\pi$
$179$	2.24249	0.167611	0.0838056	+	0.996482i	$0.473293\pi$
$180$	−2.49885	−0.186253
$181$	3.30251	0.245474	0.122737	−	0.992439i	$-0.460833\pi$
$181$	3.30251	0.245474	0.122737	+	0.992439i	$0.460833\pi$
$182$	−12.2917	−0.911125
$183$	−13.7443	−1.01601
$184$	−3.21056	−0.236686
$185$	−16.1495	−1.18733
$186$	13.2962	0.974925
$187$	14.5139	1.06136
$188$	4.18276	0.305059
$189$	−19.7969	−1.44002
$190$	4.52392	0.328200
$191$	−2.01137	−0.145537	−0.0727687	−	0.997349i	$-0.523183\pi$
$191$	−2.01137	−0.145537	−0.0727687	+	0.997349i	$0.523183\pi$
$192$	−1.53830	−0.111017
$193$	13.1695	0.947962	0.473981	−	0.880535i	$-0.342817\pi$
$193$	13.1695	0.947962	0.473981	+	0.880535i	$0.342817\pi$
$194$	14.3327	1.02903
$195$	−21.0545	−1.50774
$196$	5.54389	0.395992
$197$	15.5252	1.10612	0.553062	−	0.833140i	$-0.313459\pi$
$197$	15.5252	1.10612	0.553062	+	0.833140i	$0.313459\pi$
$198$	−2.87791	−0.204524
$199$	−5.96083	−0.422552	−0.211276	−	0.977426i	$-0.567762\pi$
$199$	−5.96083	−0.422552	−0.211276	+	0.977426i	$0.567762\pi$
$200$	10.5529	0.746201
$201$	6.82166	0.481163
$202$	16.2470	1.14314
$203$	−14.9984	−1.05268
$204$	−4.91569	−0.344167
$205$	−23.5321	−1.64356
$206$	−2.47083	−0.172151
$207$	2.03431	0.141394
$208$	3.47054	0.240639
$209$	5.21017	0.360395
$210$	21.4864	1.48270
$211$	2.41890	0.166524	0.0832619	−	0.996528i	$-0.473466\pi$
$211$	2.41890	0.166524	0.0832619	+	0.996528i	$0.473466\pi$
$212$	−0.668336	−0.0459015
$213$	16.9251	1.15969
$214$	−3.62630	−0.247889
$215$	29.9931	2.04551
$216$	5.58962	0.380325
$217$	30.6128	2.07813
$218$	11.4090	0.772713
$219$	23.0144	1.55517
$220$	17.9122	1.20764
$221$	11.0902	0.746009
$222$	6.29933	0.422784
$223$	−12.9507	−0.867240	−0.433620	−	0.901096i	$-0.642764\pi$
$223$	−12.9507	−0.867240	−0.433620	+	0.901096i	$0.642764\pi$
$224$	−3.54174	−0.236642
$225$	−6.68661	−0.445774
$226$	5.67163	0.377271
$227$	7.68669	0.510183	0.255092	−	0.966917i	$-0.417894\pi$
$227$	7.68669	0.510183	0.255092	+	0.966917i	$0.417894\pi$
$228$	−1.76462	−0.116865
$229$	−30.1383	−1.99160	−0.995798	−	0.0915756i	$-0.970810\pi$
$229$	−30.1383	−1.99160	−0.995798	+	0.0915756i	$0.970810\pi$
$230$	−12.6615	−0.834877
$231$	24.7457	1.62815
$232$	4.23477	0.278026
$233$	16.6289	1.08939	0.544697	−	0.838633i	$-0.316645\pi$
$233$	16.6289	1.08939	0.544697	+	0.838633i	$0.316645\pi$
$234$	−2.19904	−0.143756
$235$	16.4956	1.07605
$236$	−0.928020	−0.0604090
$237$	−21.2566	−1.38077
$238$	−11.3177	−0.733619
$239$	2.46990	0.159765	0.0798824	−	0.996804i	$-0.474546\pi$
$239$	2.46990	0.159765	0.0798824	+	0.996804i	$0.474546\pi$
$240$	−6.06662	−0.391599
$241$	29.0581	1.87179	0.935897	−	0.352273i	$-0.114591\pi$
$241$	29.0581	1.87179	0.935897	+	0.352273i	$0.114591\pi$
$242$	9.62932	0.618996
$243$	−6.46588	−0.414786
$244$	8.93473	0.571987
$245$	21.8635	1.39681
$246$	9.17904	0.585234
$247$	3.98113	0.253314
$248$	−8.64344	−0.548859
$249$	−15.3427	−0.972306
$250$	21.8990	1.38501
$251$	12.6754	0.800065	0.400032	−	0.916501i	$-0.368999\pi$
$251$	12.6754	0.800065	0.400032	+	0.916501i	$0.368999\pi$
$252$	2.24415	0.141368
$253$	−14.5822	−0.916776
$254$	0.710995	0.0446118
$255$	−19.3861	−1.21400
$256$	1.00000	0.0625000
$257$	−10.8375	−0.676024	−0.338012	−	0.941142i	$-0.609754\pi$
$257$	−10.8375	−0.676024	−0.338012	+	0.941142i	$0.609754\pi$
$258$	−11.6992	−0.728362
$259$	14.5034	0.901196
$260$	13.6868	0.848821
$261$	−2.68328	−0.166091
$262$	15.7031	0.970143
$263$	−6.89673	−0.425271	−0.212635	−	0.977132i	$-0.568205\pi$
$263$	−6.89673	−0.425271	−0.212635	+	0.977132i	$0.568205\pi$
$264$	−6.98689	−0.430013
$265$	−2.63573	−0.161911
$266$	−4.06280	−0.249106
$267$	−13.3502	−0.817018
$268$	−4.43454	−0.270883
$269$	−18.2225	−1.11104	−0.555521	−	0.831502i	$-0.687481\pi$
$269$	−18.2225	−1.11104	−0.555521	+	0.831502i	$0.687481\pi$
$270$	22.0438	1.34155
$271$	−11.8484	−0.719738	−0.359869	−	0.933003i	$-0.617179\pi$
$271$	−11.8484	−0.719738	−0.359869	+	0.933003i	$0.617179\pi$
$272$	3.19553	0.193757
$273$	18.9084	1.14439
$274$	7.06102	0.426572
$275$	47.9307	2.89033
$276$	4.93881	0.297282
$277$	−15.4431	−0.927886	−0.463943	−	0.885865i	$-0.653566\pi$
$277$	−15.4431	−0.927886	−0.463943	+	0.885865i	$0.653566\pi$
$278$	−13.0236	−0.781106
$279$	5.47673	0.327883
$280$	−13.9676	−0.834723
$281$	17.7149	1.05678	0.528390	−	0.849002i	$-0.322796\pi$
$281$	17.7149	1.05678	0.528390	+	0.849002i	$0.322796\pi$
$282$	−6.43434	−0.383160
$283$	−14.4636	−0.859770	−0.429885	−	0.902884i	$-0.641446\pi$
$283$	−14.4636	−0.859770	−0.429885	+	0.902884i	$0.641446\pi$
$284$	−11.0025	−0.652877
$285$	−6.95915	−0.412224
$286$	15.7630	0.932088
$287$	21.1335	1.24747
$288$	−0.633629	−0.0373369
$289$	−6.78859	−0.399329
$290$	16.7007	0.980701
$291$	−22.0480	−1.29248
$292$	−14.9609	−0.875521
$293$	−31.4451	−1.83704	−0.918520	−	0.395374i	$-0.870615\pi$
$293$	−31.4451	−1.83704	−0.918520	+	0.395374i	$0.870615\pi$
$294$	−8.52818	−0.497374
$295$	−3.65985	−0.213084
$296$	−4.09499	−0.238017
$297$	25.3878	1.47315
$298$	11.5078	0.666630
$299$	−11.1424	−0.644381
$300$	−16.2335	−0.937242
$301$	−26.9359	−1.55256
$302$	−4.74768	−0.273198
$303$	−24.9928	−1.43580
$304$	1.14712	0.0657919
$305$	35.2360	2.01761
$306$	−2.02478	−0.115749
$307$	25.5046	1.45562	0.727812	−	0.685776i	$-0.240537\pi$
$307$	25.5046	1.45562	0.727812	+	0.685776i	$0.240537\pi$
$308$	−16.0864	−0.916607
$309$	3.80088	0.216224
$310$	−34.0872	−1.93603
$311$	12.6107	0.715086	0.357543	−	0.933897i	$-0.383615\pi$
$311$	12.6107	0.715086	0.357543	+	0.933897i	$0.383615\pi$
$312$	−5.33874	−0.302247
$313$	25.7813	1.45724	0.728621	−	0.684917i	$-0.240161\pi$
$313$	25.7813	1.45724	0.728621	+	0.684917i	$0.240161\pi$
$314$	−18.4666	−1.04213
$315$	8.85027	0.498656
$316$	13.8183	0.777337
$317$	34.2888	1.92585	0.962924	−	0.269772i	$-0.0869482\pi$
$317$	34.2888	1.92585	0.962924	+	0.269772i	$0.0869482\pi$
$318$	1.02810	0.0576531
$319$	19.2341	1.07690
$320$	3.94371	0.220460
$321$	5.57834	0.311352
$322$	11.3710	0.633679
$323$	3.66566	0.203963
$324$	−6.69763	−0.372090
$325$	36.6242	2.03155
$326$	−22.9352	−1.27026
$327$	−17.5504	−0.970541
$328$	−5.96700	−0.329472
$329$	−14.8142	−0.816735
$330$	−27.5543	−1.51681
$331$	0.306690	0.0168572	0.00842860	−	0.999964i	$-0.497317\pi$
$331$	0.306690	0.0168572	0.00842860	+	0.999964i	$0.497317\pi$
$332$	9.97381	0.547384
$333$	2.59471	0.142189
$334$	−9.37258	−0.512845
$335$	−17.4886	−0.955502
$336$	5.44826	0.297227
$337$	−9.17661	−0.499882	−0.249941	−	0.968261i	$-0.580411\pi$
$337$	−9.17661	−0.499882	−0.249941	+	0.968261i	$0.580411\pi$
$338$	−0.955327	−0.0519629
$339$	−8.72468	−0.473860
$340$	12.6023	0.683453
$341$	−39.2581	−2.12594
$342$	−0.726849	−0.0393035
$343$	5.15714	0.278460
$344$	7.60529	0.410050
$345$	19.4773	1.04862
$346$	6.83501	0.367453
$347$	9.75999	0.523944	0.261972	−	0.965075i	$-0.415627\pi$
$347$	9.75999	0.523944	0.261972	+	0.965075i	$0.415627\pi$
$348$	−6.51436	−0.349206
$349$	21.7395	1.16369	0.581845	−	0.813300i	$-0.302331\pi$
$349$	21.7395	1.16369	0.581845	+	0.813300i	$0.302331\pi$
$350$	−37.3755	−1.99781
$351$	19.3990	1.03544
$352$	4.54195	0.242087
$353$	−16.7254	−0.890201	−0.445100	−	0.895481i	$-0.646832\pi$
$353$	−16.7254	−0.890201	−0.445100	+	0.895481i	$0.646832\pi$
$354$	1.42757	0.0758747
$355$	−43.3906	−2.30294
$356$	8.67852	0.459961
$357$	17.4101	0.921439
$358$	2.24249	0.118519
$359$	−8.80493	−0.464707	−0.232353	−	0.972631i	$-0.574643\pi$
$359$	−8.80493	−0.464707	−0.232353	+	0.972631i	$0.574643\pi$
$360$	−2.49885	−0.131701
$361$	−17.6841	−0.930743
$362$	3.30251	0.173576
$363$	−14.8128	−0.777470
$364$	−12.2917	−0.644263
$365$	−59.0016	−3.08828
$366$	−13.7443	−0.718426
$367$	8.30729	0.433637	0.216819	−	0.976212i	$-0.430432\pi$
$367$	8.30729	0.433637	0.216819	+	0.976212i	$0.430432\pi$
$368$	−3.21056	−0.167362
$369$	3.78086	0.196824
$370$	−16.1495	−0.839571
$371$	2.36707	0.122892
$372$	13.2962	0.689376
$373$	−21.1733	−1.09631	−0.548155	−	0.836377i	$-0.684670\pi$
$373$	−21.1733	−1.09631	−0.548155	+	0.836377i	$0.684670\pi$
$374$	14.5139	0.750498
$375$	−33.6872	−1.73960
$376$	4.18276	0.215709
$377$	14.6970	0.756932
$378$	−19.7969	−1.01825
$379$	11.4427	0.587772	0.293886	−	0.955840i	$-0.405051\pi$
$379$	11.4427	0.587772	0.293886	+	0.955840i	$0.405051\pi$
$380$	4.52392	0.232072
$381$	−1.09373	−0.0560332
$382$	−2.01137	−0.102910
$383$	24.9349	1.27411	0.637056	−	0.770818i	$-0.280152\pi$
$383$	24.9349	1.27411	0.637056	+	0.770818i	$0.280152\pi$
$384$	−1.53830	−0.0785011
$385$	−63.4401	−3.23321
$386$	13.1695	0.670310
$387$	−4.81893	−0.244960
$388$	14.3327	0.727632
$389$	−7.95651	−0.403411	−0.201706	−	0.979446i	$-0.564648\pi$
$389$	−7.95651	−0.403411	−0.201706	+	0.979446i	$0.564648\pi$
$390$	−21.0545	−1.06613
$391$	−10.2594	−0.518842
$392$	5.54389	0.280009
$393$	−24.1562	−1.21852
$394$	15.5252	0.782148
$395$	54.4952	2.74195
$396$	−2.87791	−0.144621
$397$	−3.17224	−0.159210	−0.0796052	−	0.996826i	$-0.525366\pi$
$397$	−3.17224	−0.159210	−0.0796052	+	0.996826i	$0.525366\pi$
$398$	−5.96083	−0.298790
$399$	6.24981	0.312882
$400$	10.5529	0.527644
$401$	23.2436	1.16073	0.580364	−	0.814357i	$-0.302910\pi$
$401$	23.2436	1.16073	0.580364	+	0.814357i	$0.302910\pi$
$402$	6.82166	0.340233
$403$	−29.9974	−1.49428
$404$	16.2470	0.808320
$405$	−26.4135	−1.31250
$406$	−14.9984	−0.744361
$407$	−18.5993	−0.921931
$408$	−4.91569	−0.243363
$409$	−3.26133	−0.161263	−0.0806313	−	0.996744i	$-0.525694\pi$
$409$	−3.26133	−0.161263	−0.0806313	+	0.996744i	$0.525694\pi$
$410$	−23.5321	−1.16217
$411$	−10.8620	−0.535782
$412$	−2.47083	−0.121729
$413$	3.28680	0.161733
$414$	2.03431	0.0999806
$415$	39.3339	1.93082
$416$	3.47054	0.170157
$417$	20.0343	0.981083
$418$	5.21017	0.254838
$419$	19.1123	0.933698	0.466849	−	0.884337i	$-0.345389\pi$
$419$	19.1123	0.933698	0.466849	+	0.884337i	$0.345389\pi$
$420$	21.4864	1.04843
$421$	−32.5597	−1.58686	−0.793432	−	0.608658i	$-0.791708\pi$
$421$	−32.5597	−1.58686	−0.793432	+	0.608658i	$0.791708\pi$
$422$	2.41890	0.117750
$423$	−2.65032	−0.128863
$424$	−0.668336	−0.0324573
$425$	33.7220	1.63576
$426$	16.9251	0.820025
$427$	−31.6444	−1.53138
$428$	−3.62630	−0.175284
$429$	−24.2483	−1.17072
$430$	29.9931	1.44640
$431$	18.4181	0.887171	0.443585	−	0.896232i	$-0.353706\pi$
$431$	18.4181	0.887171	0.443585	+	0.896232i	$0.353706\pi$
$432$	5.58962	0.268931
$433$	−5.93243	−0.285094	−0.142547	−	0.989788i	$-0.545529\pi$
$433$	−5.93243	−0.285094	−0.142547	+	0.989788i	$0.545529\pi$
$434$	30.6128	1.46946
$435$	−25.6908	−1.23178
$436$	11.4090	0.546391
$437$	−3.68290	−0.176177
$438$	23.0144	1.09967
$439$	11.5859	0.552967	0.276483	−	0.961019i	$-0.410831\pi$
$439$	11.5859	0.552967	0.276483	+	0.961019i	$0.410831\pi$
$440$	17.9122	0.853929
$441$	−3.51277	−0.167275
$442$	11.0902	0.527508
$443$	−9.60530	−0.456361	−0.228181	−	0.973619i	$-0.573278\pi$
$443$	−9.60530	−0.456361	−0.228181	+	0.973619i	$0.573278\pi$
$444$	6.29933	0.298953
$445$	34.2256	1.62245
$446$	−12.9507	−0.613231
$447$	−17.7025	−0.837299
$448$	−3.54174	−0.167331
$449$	−35.5928	−1.67973	−0.839864	−	0.542796i	$-0.817366\pi$
$449$	−35.5928	−1.67973	−0.839864	+	0.542796i	$0.817366\pi$
$450$	−6.68661	−0.315210
$451$	−27.1018	−1.27617
$452$	5.67163	0.266771
$453$	7.30336	0.343142
$454$	7.68669	0.360754
$455$	−48.4751	−2.27255
$456$	−1.76462	−0.0826358
$457$	−39.0420	−1.82631	−0.913154	−	0.407616i	$-0.866360\pi$
$457$	−39.0420	−1.82631	−0.913154	+	0.407616i	$0.866360\pi$
$458$	−30.1383	−1.40827
$459$	17.8618	0.833717
$460$	−12.6615	−0.590347
$461$	15.9153	0.741249	0.370624	−	0.928783i	$-0.379144\pi$
$461$	15.9153	0.741249	0.370624	+	0.928783i	$0.379144\pi$
$462$	24.7457	1.15127
$463$	−5.96915	−0.277410	−0.138705	−	0.990334i	$-0.544294\pi$
$463$	−5.96915	−0.277410	−0.138705	+	0.990334i	$0.544294\pi$
$464$	4.23477	0.196594
$465$	52.4365	2.43168
$466$	16.6289	0.770318
$467$	−39.0600	−1.80748	−0.903741	−	0.428080i	$-0.859190\pi$
$467$	−39.0600	−1.80748	−0.903741	+	0.428080i	$0.859190\pi$
$468$	−2.19904	−0.101651
$469$	15.7060	0.725234
$470$	16.4956	0.760885
$471$	28.4072	1.30893
$472$	−0.928020	−0.0427156
$473$	34.5429	1.58828
$474$	−21.2566	−0.976349
$475$	12.1054	0.555435
$476$	−11.3177	−0.518747
$477$	0.423477	0.0193897
$478$	2.46990	0.112971
$479$	−38.1035	−1.74099	−0.870497	−	0.492174i	$-0.836202\pi$
$479$	−38.1035	−1.74099	−0.870497	+	0.492174i	$0.836202\pi$
$480$	−6.06662	−0.276902
$481$	−14.2118	−0.648005
$482$	29.0581	1.32356
$483$	−17.4920	−0.795912
$484$	9.62932	0.437696
$485$	56.5240	2.56662
$486$	−6.46588	−0.293298
$487$	−17.7659	−0.805049	−0.402524	−	0.915409i	$-0.631867\pi$
$487$	−17.7659	−0.805049	−0.402524	+	0.915409i	$0.631867\pi$
$488$	8.93473	0.404456
$489$	35.2812	1.59547
$490$	21.8635	0.987694
$491$	11.8118	0.533058	0.266529	−	0.963827i	$-0.414123\pi$
$491$	11.8118	0.533058	0.266529	+	0.963827i	$0.414123\pi$
$492$	9.17904	0.413823
$493$	13.5323	0.609466
$494$	3.98113	0.179120
$495$	−11.3497	−0.510129
$496$	−8.64344	−0.388102
$497$	38.9679	1.74795
$498$	−15.3427	−0.687524
$499$	−34.9022	−1.56244	−0.781218	−	0.624259i	$-0.785401\pi$
$499$	−34.9022	−1.56244	−0.781218	+	0.624259i	$0.785401\pi$
$500$	21.8990	0.979352
$501$	14.4179	0.644142
$502$	12.6754	0.565731
$503$	13.7370	0.612501	0.306250	−	0.951951i	$-0.400926\pi$
$503$	13.7370	0.612501	0.306250	+	0.951951i	$0.400926\pi$
$504$	2.24415	0.0999622
$505$	64.0736	2.85124
$506$	−14.5822	−0.648259
$507$	1.46958	0.0652664
$508$	0.710995	0.0315453
$509$	−37.3000	−1.65329	−0.826647	−	0.562720i	$-0.809755\pi$
$509$	−37.3000	−1.65329	−0.826647	+	0.562720i	$0.809755\pi$
$510$	−19.3861	−0.858429
$511$	52.9876	2.34403
$512$	1.00000	0.0441942
$513$	6.41197	0.283095
$514$	−10.8375	−0.478021
$515$	−9.74424	−0.429382
$516$	−11.6992	−0.515030
$517$	18.9979	0.835526
$518$	14.5034	0.637242
$519$	−10.5143	−0.461527
$520$	13.6868	0.600207
$521$	7.62525	0.334068	0.167034	−	0.985951i	$-0.446581\pi$
$521$	7.62525	0.334068	0.167034	+	0.985951i	$0.446581\pi$
$522$	−2.68328	−0.117444
$523$	−24.4204	−1.06783	−0.533915	−	0.845538i	$-0.679280\pi$
$523$	−24.4204	−1.06783	−0.533915	+	0.845538i	$0.679280\pi$
$524$	15.7031	0.685995
$525$	57.4948	2.50928
$526$	−6.89673	−0.300712
$527$	−27.6204	−1.20316
$528$	−6.98689	−0.304065
$529$	−12.6923	−0.551839
$530$	−2.63573	−0.114489
$531$	0.588020	0.0255179
$532$	−4.06280	−0.176145
$533$	−20.7087	−0.896995
$534$	−13.3502	−0.577719
$535$	−14.3011	−0.618289
$536$	−4.43454	−0.191543
$537$	−3.44962	−0.148862
$538$	−18.2225	−0.785626
$539$	25.1801	1.08458
$540$	22.0438	0.948616
$541$	−3.86417	−0.166134	−0.0830668	−	0.996544i	$-0.526471\pi$
$541$	−3.86417	−0.166134	−0.0830668	+	0.996544i	$0.526471\pi$
$542$	−11.8484	−0.508932
$543$	−5.08026	−0.218015
$544$	3.19553	0.137007
$545$	44.9937	1.92732
$546$	18.9084	0.809205
$547$	−0.334902	−0.0143194	−0.00715968	−	0.999974i	$-0.502279\pi$
$547$	−0.334902	−0.0143194	−0.00715968	+	0.999974i	$0.502279\pi$
$548$	7.06102	0.301632
$549$	−5.66130	−0.241619
$550$	47.9307	2.04377
$551$	4.85780	0.206949
$552$	4.93881	0.210210
$553$	−48.9406	−2.08117
$554$	−15.4431	−0.656114
$555$	24.8428	1.05452
$556$	−13.0236	−0.552325
$557$	−14.8858	−0.630731	−0.315365	−	0.948970i	$-0.602127\pi$
$557$	−14.8858	−0.630731	−0.315365	+	0.948970i	$0.602127\pi$
$558$	5.47673	0.231849
$559$	26.3945	1.11637
$560$	−13.9676	−0.590239
$561$	−22.3268	−0.942639
$562$	17.7149	0.747257
$563$	−28.9218	−1.21891	−0.609454	−	0.792821i	$-0.708611\pi$
$563$	−28.9218	−1.21891	−0.609454	+	0.792821i	$0.708611\pi$
$564$	−6.43434	−0.270935
$565$	22.3673	0.940999
$566$	−14.4636	−0.607949
$567$	23.7212	0.996198
$568$	−11.0025	−0.461654
$569$	38.7476	1.62438	0.812191	−	0.583391i	$-0.198275\pi$
$569$	38.7476	1.62438	0.812191	+	0.583391i	$0.198275\pi$
$570$	−6.95915	−0.291487
$571$	14.9236	0.624532	0.312266	−	0.949995i	$-0.398912\pi$
$571$	14.9236	0.624532	0.312266	+	0.949995i	$0.398912\pi$
$572$	15.7630	0.659086
$573$	3.09409	0.129257
$574$	21.1335	0.882097
$575$	−33.8807	−1.41292
$576$	−0.633629	−0.0264012
$577$	−25.6331	−1.06712	−0.533560	−	0.845762i	$-0.679146\pi$
$577$	−25.6331	−1.06712	−0.533560	+	0.845762i	$0.679146\pi$
$578$	−6.78859	−0.282368
$579$	−20.2587	−0.841921
$580$	16.7007	0.693460
$581$	−35.3246	−1.46551
$582$	−22.0480	−0.913918
$583$	−3.03555	−0.125720
$584$	−14.9609	−0.619087
$585$	−8.67237	−0.358559
$586$	−31.4451	−1.29898
$587$	−12.2524	−0.505713	−0.252856	−	0.967504i	$-0.581370\pi$
$587$	−12.2524	−0.505713	−0.252856	+	0.967504i	$0.581370\pi$
$588$	−8.52818	−0.351696
$589$	−9.91507	−0.408543
$590$	−3.65985	−0.150673
$591$	−23.8824	−0.982392
$592$	−4.09499	−0.168303
$593$	−8.85636	−0.363687	−0.181844	−	0.983327i	$-0.558206\pi$
$593$	−8.85636	−0.363687	−0.181844	+	0.983327i	$0.558206\pi$
$594$	25.3878	1.04167
$595$	−44.6339	−1.82981
$596$	11.5078	0.471379
$597$	9.16956	0.375285
$598$	−11.1424	−0.455646
$599$	36.9916	1.51144	0.755718	−	0.654897i	$-0.227288\pi$
$599$	36.9916	1.51144	0.755718	+	0.654897i	$0.227288\pi$
$600$	−16.2335	−0.662730
$601$	10.3581	0.422516	0.211258	−	0.977430i	$-0.432244\pi$
$601$	10.3581	0.422516	0.211258	+	0.977430i	$0.432244\pi$
$602$	−26.9359	−1.09783
$603$	2.80985	0.114426
$604$	−4.74768	−0.193180
$605$	37.9753	1.54391
$606$	−24.9928	−1.01526
$607$	−9.37971	−0.380711	−0.190355	−	0.981715i	$-0.560964\pi$
$607$	−9.37971	−0.380711	−0.190355	+	0.981715i	$0.560964\pi$
$608$	1.14712	0.0465219
$609$	23.0721	0.934930
$610$	35.2360	1.42666
$611$	14.5164	0.587273
$612$	−2.02478	−0.0818469
$613$	−40.5790	−1.63897	−0.819486	−	0.573100i	$-0.805741\pi$
$613$	−40.5790	−1.63897	−0.819486	+	0.573100i	$0.805741\pi$
$614$	25.5046	1.02928
$615$	36.1995	1.45971
$616$	−16.0864	−0.648139
$617$	−32.2426	−1.29804	−0.649020	−	0.760771i	$-0.724821\pi$
$617$	−32.2426	−1.29804	−0.649020	+	0.760771i	$0.724821\pi$
$618$	3.80088	0.152894
$619$	−22.7199	−0.913190	−0.456595	−	0.889675i	$-0.650931\pi$
$619$	−22.7199	−0.913190	−0.456595	+	0.889675i	$0.650931\pi$
$620$	−34.0872	−1.36898
$621$	−17.9458	−0.720141
$622$	12.6107	0.505642
$623$	−30.7370	−1.23145
$624$	−5.33874	−0.213721
$625$	33.5989	1.34396
$626$	25.7813	1.03043
$627$	−8.01481	−0.320081
$628$	−18.4666	−0.736898
$629$	−13.0857	−0.521760
$630$	8.85027	0.352603
$631$	−6.41711	−0.255461	−0.127731	−	0.991809i	$-0.540769\pi$
$631$	−6.41711	−0.255461	−0.127731	+	0.991809i	$0.540769\pi$
$632$	13.8183	0.549660
$633$	−3.72100	−0.147896
$634$	34.2888	1.36178
$635$	2.80396	0.111272
$636$	1.02810	0.0407669
$637$	19.2403	0.762329
$638$	19.2341	0.761487
$639$	6.97149	0.275788
$640$	3.94371	0.155889
$641$	20.6424	0.815326	0.407663	−	0.913133i	$-0.366344\pi$
$641$	20.6424	0.815326	0.407663	+	0.913133i	$0.366344\pi$
$642$	5.57834	0.220159
$643$	−1.92636	−0.0759684	−0.0379842	−	0.999278i	$-0.512094\pi$
$643$	−1.92636	−0.0759684	−0.0379842	+	0.999278i	$0.512094\pi$
$644$	11.3710	0.448079
$645$	−46.1384	−1.81670
$646$	3.66566	0.144223
$647$	−6.10757	−0.240113	−0.120057	−	0.992767i	$-0.538308\pi$
$647$	−6.10757	−0.240113	−0.120057	+	0.992767i	$0.538308\pi$
$648$	−6.69763	−0.263108
$649$	−4.21502	−0.165454
$650$	36.6242	1.43652
$651$	−47.0917	−1.84567
$652$	−22.9352	−0.898211
$653$	−4.57799	−0.179151	−0.0895753	−	0.995980i	$-0.528551\pi$
$653$	−4.57799	−0.179151	−0.0895753	+	0.995980i	$0.528551\pi$
$654$	−17.5504	−0.686276
$655$	61.9287	2.41975
$656$	−5.96700	−0.232972
$657$	9.47967	0.369837
$658$	−14.8142	−0.577519
$659$	17.9011	0.697328	0.348664	−	0.937248i	$-0.386635\pi$
$659$	17.9011	0.697328	0.348664	+	0.937248i	$0.386635\pi$
$660$	−27.5543	−1.07255
$661$	−17.3864	−0.676251	−0.338125	−	0.941101i	$-0.609793\pi$
$661$	−17.3864	−0.676251	−0.338125	+	0.941101i	$0.609793\pi$
$662$	0.306690	0.0119198
$663$	−17.0601	−0.662560
$664$	9.97381	0.387059
$665$	−16.0225	−0.621327
$666$	2.59471	0.100543
$667$	−13.5960	−0.526439
$668$	−9.37258	−0.362636
$669$	19.9220	0.770230
$670$	−17.4886	−0.675642
$671$	40.5811	1.56662
$672$	5.44826	0.210171
$673$	34.7247	1.33854	0.669269	−	0.743021i	$-0.266608\pi$
$673$	34.7247	1.33854	0.669269	+	0.743021i	$0.266608\pi$
$674$	−9.17661	−0.353470
$675$	58.9866	2.27039
$676$	−0.955327	−0.0367433
$677$	−10.7236	−0.412142	−0.206071	−	0.978537i	$-0.566068\pi$
$677$	−10.7236	−0.412142	−0.206071	+	0.978537i	$0.566068\pi$
$678$	−8.72468	−0.335069
$679$	−50.7626	−1.94809
$680$	12.6023	0.483274
$681$	−11.8244	−0.453114
$682$	−39.2581	−1.50327
$683$	9.72173	0.371992	0.185996	−	0.982551i	$-0.440449\pi$
$683$	9.72173	0.371992	0.185996	+	0.982551i	$0.440449\pi$
$684$	−0.726849	−0.0277918
$685$	27.8467	1.06397
$686$	5.15714	0.196901
$687$	46.3618	1.76881
$688$	7.60529	0.289949
$689$	−2.31949	−0.0883656
$690$	19.4773	0.741487
$691$	20.8484	0.793109	0.396554	−	0.918011i	$-0.370206\pi$
$691$	20.8484	0.793109	0.396554	+	0.918011i	$0.370206\pi$
$692$	6.83501	0.259828
$693$	10.1928	0.387193
$694$	9.75999	0.370484
$695$	−51.3615	−1.94825
$696$	−6.51436	−0.246926
$697$	−19.0677	−0.722242
$698$	21.7395	0.822852
$699$	−25.5802	−0.967533
$700$	−37.3755	−1.41266
$701$	14.7538	0.557245	0.278623	−	0.960401i	$-0.410122\pi$
$701$	14.7538	0.557245	0.278623	+	0.960401i	$0.410122\pi$
$702$	19.3990	0.732168
$703$	−4.69745	−0.177168
$704$	4.54195	0.171181
$705$	−25.3752	−0.955686
$706$	−16.7254	−0.629467
$707$	−57.5427	−2.16411
$708$	1.42757	0.0536515
$709$	−26.0324	−0.977666	−0.488833	−	0.872377i	$-0.662577\pi$
$709$	−26.0324	−0.977666	−0.488833	+	0.872377i	$0.662577\pi$
$710$	−43.3906	−1.62842
$711$	−8.75564	−0.328362
$712$	8.67852	0.325241
$713$	27.7503	1.03926
$714$	17.4101	0.651555
$715$	62.1649	2.32484
$716$	2.24249	0.0838056
$717$	−3.79946	−0.141893
$718$	−8.80493	−0.328597
$719$	5.33942	0.199127	0.0995634	−	0.995031i	$-0.468255\pi$
$719$	5.33942	0.199127	0.0995634	+	0.995031i	$0.468255\pi$
$720$	−2.49885	−0.0931267
$721$	8.75102	0.325905
$722$	−17.6841	−0.658135
$723$	−44.7001	−1.66241
$724$	3.30251	0.122737
$725$	44.6891	1.65971
$726$	−14.8128	−0.549754
$727$	−34.4170	−1.27646	−0.638228	−	0.769848i	$-0.720332\pi$
$727$	−34.4170	−1.27646	−0.638228	+	0.769848i	$0.720332\pi$
$728$	−12.2917	−0.455563
$729$	30.0394	1.11257
$730$	−59.0016	−2.18375
$731$	24.3029	0.898877
$732$	−13.7443	−0.508004
$733$	−51.6198	−1.90662	−0.953310	−	0.301995i	$-0.902348\pi$
$733$	−51.6198	−1.90662	−0.953310	+	0.301995i	$0.902348\pi$
$734$	8.30729	0.306628
$735$	−33.6327	−1.24056
$736$	−3.21056	−0.118343
$737$	−20.1415	−0.741920
$738$	3.78086	0.139176
$739$	−9.38370	−0.345185	−0.172592	−	0.984993i	$-0.555214\pi$
$739$	−9.38370	−0.345185	−0.172592	+	0.984993i	$0.555214\pi$
$740$	−16.1495	−0.593667
$741$	−6.12419	−0.224978
$742$	2.36707	0.0868979
$743$	−28.7225	−1.05373	−0.526863	−	0.849950i	$-0.676632\pi$
$743$	−28.7225	−1.05373	−0.526863	+	0.849950i	$0.676632\pi$
$744$	13.2962	0.487463
$745$	45.3836	1.66272
$746$	−21.1733	−0.775208
$747$	−6.31970	−0.231226
$748$	14.5139	0.530682
$749$	12.8434	0.469287
$750$	−33.6872	−1.23008
$751$	−8.95709	−0.326849	−0.163425	−	0.986556i	$-0.552254\pi$
$751$	−8.95709	−0.326849	−0.163425	+	0.986556i	$0.552254\pi$
$752$	4.18276	0.152530
$753$	−19.4986	−0.710569
$754$	14.6970	0.535232
$755$	−18.7235	−0.681417
$756$	−19.7969	−0.720008
$757$	27.2589	0.990740	0.495370	−	0.868682i	$-0.335032\pi$
$757$	27.2589	0.990740	0.495370	+	0.868682i	$0.335032\pi$
$758$	11.4427	0.415618
$759$	22.4318	0.814224
$760$	4.52392	0.164100
$761$	6.03567	0.218793	0.109396	−	0.993998i	$-0.465108\pi$
$761$	6.03567	0.218793	0.109396	+	0.993998i	$0.465108\pi$
$762$	−1.09373	−0.0396215
$763$	−40.4076	−1.46285
$764$	−2.01137	−0.0727687
$765$	−7.98515	−0.288704
$766$	24.9349	0.900933
$767$	−3.22073	−0.116294
$768$	−1.53830	−0.0555087
$769$	−40.8408	−1.47276	−0.736378	−	0.676571i	$-0.763465\pi$
$769$	−40.8408	−1.47276	−0.736378	+	0.676571i	$0.763465\pi$
$770$	−63.4401	−2.28622
$771$	16.6713	0.600403
$772$	13.1695	0.473981
$773$	36.1085	1.29873	0.649365	−	0.760477i	$-0.275035\pi$
$773$	36.1085	1.29873	0.649365	+	0.760477i	$0.275035\pi$
$774$	−4.81893	−0.173213
$775$	−91.2132	−3.27647
$776$	14.3327	0.514513
$777$	−22.3106	−0.800387
$778$	−7.95651	−0.285255
$779$	−6.84487	−0.245243
$780$	−21.0545	−0.753871
$781$	−49.9727	−1.78817
$782$	−10.2594	−0.366877
$783$	23.6708	0.845924
$784$	5.54389	0.197996
$785$	−72.8270	−2.59931
$786$	−24.1562	−0.861622
$787$	−24.2501	−0.864423	−0.432212	−	0.901772i	$-0.642267\pi$
$787$	−24.2501	−0.864423	−0.432212	+	0.901772i	$0.642267\pi$
$788$	15.5252	0.553062
$789$	10.6093	0.377700
$790$	54.4952	1.93885
$791$	−20.0874	−0.714227
$792$	−2.87791	−0.102262
$793$	31.0084	1.10114
$794$	−3.17224	−0.112579
$795$	4.05454	0.143800
$796$	−5.96083	−0.211276
$797$	−55.4003	−1.96238	−0.981189	−	0.193050i	$-0.938162\pi$
$797$	−55.4003	−1.96238	−0.981189	+	0.193050i	$0.938162\pi$
$798$	6.24981	0.221241
$799$	13.3661	0.472860
$800$	10.5529	0.373101
$801$	−5.49896	−0.194296
$802$	23.2436	0.820758
$803$	−67.9517	−2.39796
$804$	6.82166	0.240581
$805$	44.8438	1.58054
$806$	−29.9974	−1.05661
$807$	28.0316	0.986760
$808$	16.2470	0.571568
$809$	−21.6575	−0.761437	−0.380718	−	0.924691i	$-0.624323\pi$
$809$	−21.6575	−0.761437	−0.380718	+	0.924691i	$0.624323\pi$
$810$	−26.4135	−0.928077
$811$	26.1574	0.918512	0.459256	−	0.888304i	$-0.348116\pi$
$811$	26.1574	0.918512	0.459256	+	0.888304i	$0.348116\pi$
$812$	−14.9984	−0.526342
$813$	18.2264	0.639227
$814$	−18.5993	−0.651904
$815$	−90.4498	−3.16832
$816$	−4.91569	−0.172083
$817$	8.72419	0.305221
$818$	−3.26133	−0.114030
$819$	7.78841	0.272149
$820$	−23.5321	−0.821778
$821$	−39.0897	−1.36424	−0.682120	−	0.731240i	$-0.738942\pi$
$821$	−39.0897	−1.36424	−0.682120	+	0.731240i	$0.738942\pi$
$822$	−10.8620	−0.378855
$823$	23.5206	0.819878	0.409939	−	0.912113i	$-0.365550\pi$
$823$	23.5206	0.819878	0.409939	+	0.912113i	$0.365550\pi$
$824$	−2.47083	−0.0860754
$825$	−73.7318	−2.56701
$826$	3.28680	0.114362
$827$	37.2711	1.29604	0.648022	−	0.761622i	$-0.275597\pi$
$827$	37.2711	1.29604	0.648022	+	0.761622i	$0.275597\pi$
$828$	2.03431	0.0706970
$829$	2.33787	0.0811975	0.0405988	−	0.999176i	$-0.487073\pi$
$829$	2.33787	0.0811975	0.0405988	+	0.999176i	$0.487073\pi$
$830$	39.3339	1.36530
$831$	23.7561	0.824091
$832$	3.47054	0.120319
$833$	17.7157	0.613812
$834$	20.0343	0.693730
$835$	−36.9628	−1.27915
$836$	5.21017	0.180197
$837$	−48.3135	−1.66996
$838$	19.1123	0.660224
$839$	16.1157	0.556377	0.278188	−	0.960527i	$-0.410266\pi$
$839$	16.1157	0.556377	0.278188	+	0.960527i	$0.410266\pi$
$840$	21.4864	0.741350
$841$	−11.0667	−0.381610
$842$	−32.5597	−1.12208
$843$	−27.2508	−0.938568
$844$	2.41890	0.0832619
$845$	−3.76754	−0.129607
$846$	−2.65032	−0.0911198
$847$	−34.1045	−1.17184
$848$	−0.668336	−0.0229508
$849$	22.2493	0.763595
$850$	33.7220	1.15666
$851$	13.1472	0.450681
$852$	16.9251	0.579846
$853$	−22.8859	−0.783599	−0.391800	−	0.920051i	$-0.628147\pi$
$853$	−22.8859	−0.783599	−0.391800	+	0.920051i	$0.628147\pi$
$854$	−31.6444	−1.08285
$855$	−2.86649	−0.0980318
$856$	−3.62630	−0.123944
$857$	−20.7919	−0.710238	−0.355119	−	0.934821i	$-0.615560\pi$
$857$	−20.7919	−0.710238	−0.355119	+	0.934821i	$0.615560\pi$
$858$	−24.2483	−0.827823
$859$	−12.5793	−0.429201	−0.214600	−	0.976702i	$-0.568845\pi$
$859$	−12.5793	−0.429201	−0.214600	+	0.976702i	$0.568845\pi$
$860$	29.9931	1.02276
$861$	−32.5097	−1.10793
$862$	18.4181	0.627325
$863$	38.7324	1.31847	0.659233	−	0.751939i	$-0.270881\pi$
$863$	38.7324	1.31847	0.659233	+	0.751939i	$0.270881\pi$
$864$	5.58962	0.190163
$865$	26.9553	0.916509
$866$	−5.93243	−0.201592
$867$	10.4429	0.354659
$868$	30.6128	1.03907
$869$	62.7618	2.12905
$870$	−25.6908	−0.870998
$871$	−15.3903	−0.521479
$872$	11.4090	0.386357
$873$	−9.08160	−0.307366
$874$	−3.68290	−0.124576
$875$	−77.5604	−2.62202
$876$	23.0144	0.777584
$877$	4.33349	0.146331	0.0731657	−	0.997320i	$-0.476690\pi$
$877$	4.33349	0.146331	0.0731657	+	0.997320i	$0.476690\pi$
$878$	11.5859	0.391006
$879$	48.3720	1.63155
$880$	17.9122	0.603819
$881$	−6.87192	−0.231521	−0.115760	−	0.993277i	$-0.536930\pi$
$881$	−6.87192	−0.231521	−0.115760	+	0.993277i	$0.536930\pi$
$882$	−3.51277	−0.118281
$883$	−31.0302	−1.04425	−0.522125	−	0.852869i	$-0.674861\pi$
$883$	−31.0302	−1.04425	−0.522125	+	0.852869i	$0.674861\pi$
$884$	11.0902	0.373005
$885$	5.62995	0.189249
$886$	−9.60530	−0.322696
$887$	−13.7576	−0.461936	−0.230968	−	0.972961i	$-0.574189\pi$
$887$	−13.7576	−0.461936	−0.230968	+	0.972961i	$0.574189\pi$
$888$	6.29933	0.211392
$889$	−2.51816	−0.0844563
$890$	34.2256	1.14724
$891$	−30.4203	−1.01912
$892$	−12.9507	−0.433620
$893$	4.79813	0.160563
$894$	−17.7025	−0.592060
$895$	8.84372	0.295613
$896$	−3.54174	−0.118321
$897$	17.1404	0.572300
$898$	−35.5928	−1.18775
$899$	−36.6030	−1.22078
$900$	−6.68661	−0.222887
$901$	−2.13569	−0.0711501
$902$	−27.1018	−0.902392
$903$	41.4356	1.37889
$904$	5.67163	0.188636
$905$	13.0242	0.432938
$906$	7.30336	0.242638
$907$	−24.3310	−0.807897	−0.403949	−	0.914782i	$-0.632363\pi$
$907$	−24.3310	−0.807897	−0.403949	+	0.914782i	$0.632363\pi$
$908$	7.68669	0.255092
$909$	−10.2946	−0.341450
$910$	−48.4751	−1.60694
$911$	−51.9475	−1.72110	−0.860548	−	0.509370i	$-0.829879\pi$
$911$	−51.9475	−1.72110	−0.860548	+	0.509370i	$0.829879\pi$
$912$	−1.76462	−0.0584324
$913$	45.3006	1.49923
$914$	−39.0420	−1.29139
$915$	−54.2036	−1.79192
$916$	−30.1383	−0.995798
$917$	−55.6164	−1.83661
$918$	17.8618	0.589527
$919$	−47.1052	−1.55386	−0.776929	−	0.629588i	$-0.783224\pi$
$919$	−47.1052	−1.55386	−0.776929	+	0.629588i	$0.783224\pi$
$920$	−12.6615	−0.417439
$921$	−39.2338	−1.29280
$922$	15.9153	0.524142
$923$	−38.1846	−1.25686
$924$	24.7457	0.814074
$925$	−43.2140	−1.42087
$926$	−5.96915	−0.196158
$927$	1.56559	0.0514207
$928$	4.23477	0.139013
$929$	47.8679	1.57050	0.785248	−	0.619182i	$-0.212536\pi$
$929$	47.8679	1.57050	0.785248	+	0.619182i	$0.212536\pi$
$930$	52.4365	1.71946
$931$	6.35952	0.208425
$932$	16.6289	0.544697
$933$	−19.3990	−0.635095
$934$	−39.0600	−1.27808
$935$	57.2388	1.87191
$936$	−2.19904	−0.0718778
$937$	−29.4302	−0.961442	−0.480721	−	0.876874i	$-0.659625\pi$
$937$	−29.4302	−0.961442	−0.480721	+	0.876874i	$0.659625\pi$
$938$	15.7060	0.512818
$939$	−39.6593	−1.29423
$940$	16.4956	0.538027
$941$	16.6307	0.542146	0.271073	−	0.962559i	$-0.412621\pi$
$941$	16.6307	0.542146	0.271073	+	0.962559i	$0.412621\pi$
$942$	28.4072	0.925557
$943$	19.1574	0.623851
$944$	−0.928020	−0.0302045
$945$	−78.0735	−2.53973
$946$	34.5429	1.12309
$947$	−6.20208	−0.201541	−0.100770	−	0.994910i	$-0.532131\pi$
$947$	−6.20208	−0.201541	−0.100770	+	0.994910i	$0.532131\pi$
$948$	−21.2566	−0.690383
$949$	−51.9225	−1.68548
$950$	12.1054	0.392752
$951$	−52.7464	−1.71042
$952$	−11.3177	−0.366810
$953$	−8.44933	−0.273701	−0.136850	−	0.990592i	$-0.543698\pi$
$953$	−8.44933	−0.273701	−0.136850	+	0.990592i	$0.543698\pi$
$954$	0.423477	0.0137106
$955$	−7.93226	−0.256682
$956$	2.46990	0.0798824
$957$	−29.5879	−0.956441
$958$	−38.1035	−1.23107
$959$	−25.0083	−0.807559
$960$	−6.06662	−0.195799
$961$	43.7090	1.40997
$962$	−14.2118	−0.458208
$963$	2.29773	0.0740432
$964$	29.0581	0.935897
$965$	51.9368	1.67190
$966$	−17.4920	−0.562795
$967$	−30.5271	−0.981687	−0.490843	−	0.871248i	$-0.663311\pi$
$967$	−30.5271	−0.981687	−0.490843	+	0.871248i	$0.663311\pi$
$968$	9.62932	0.309498
$969$	−5.63889	−0.181147
$970$	56.5240	1.81488
$971$	41.0564	1.31756	0.658781	−	0.752335i	$-0.271072\pi$
$971$	41.0564	1.31756	0.658781	+	0.752335i	$0.271072\pi$
$972$	−6.46588	−0.207393
$973$	46.1263	1.47874
$974$	−17.7659	−0.569256
$975$	−56.3391	−1.80430
$976$	8.93473	0.285994
$977$	28.4888	0.911438	0.455719	−	0.890124i	$-0.349382\pi$
$977$	28.4888	0.911438	0.455719	+	0.890124i	$0.349382\pi$
$978$	35.2812	1.12817
$979$	39.4174	1.25979
$980$	21.8635	0.698405
$981$	−7.22906	−0.230806
$982$	11.8118	0.376929
$983$	−0.0729452	−0.00232659	−0.00116330	−	0.999999i	$-0.500370\pi$
$983$	−0.0729452	−0.00232659	−0.00116330	+	0.999999i	$0.500370\pi$
$984$	9.17904	0.292617
$985$	61.2269	1.95085
$986$	13.5323	0.430958
$987$	22.7887	0.725374
$988$	3.98113	0.126657
$989$	−24.4173	−0.776424
$990$	−11.3497	−0.360716
$991$	23.8192	0.756641	0.378320	−	0.925675i	$-0.376502\pi$
$991$	23.8192	0.756641	0.378320	+	0.925675i	$0.376502\pi$
$992$	−8.64344	−0.274429
$993$	−0.471782	−0.0149715
$994$	38.9679	1.23599
$995$	−23.5078	−0.745248
$996$	−15.3427	−0.486153
$997$	32.6055	1.03263	0.516313	−	0.856400i	$-0.327304\pi$
$997$	32.6055	1.03263	0.516313	+	0.856400i	$0.327304\pi$
$998$	−34.9022	−1.10481
$999$	−22.8894	−0.724190

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.12	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.12	✓	52	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.53830 q^{3} +1.00000 q^{4} +3.94371 q^{5} -1.53830 q^{6} -3.54174 q^{7} +1.00000 q^{8} -0.633629 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.53830 q^{3} +1.00000 q^{4} +3.94371 q^{5} -1.53830 q^{6} -3.54174 q^{7} +1.00000 q^{8} -0.633629 q^{9} +3.94371 q^{10} +4.54195 q^{11} -1.53830 q^{12} +3.47054 q^{13} -3.54174 q^{14} -6.06662 q^{15} +1.00000 q^{16} +3.19553 q^{17} -0.633629 q^{18} +1.14712 q^{19} +3.94371 q^{20} +5.44826 q^{21} +4.54195 q^{22} -3.21056 q^{23} -1.53830 q^{24} +10.5529 q^{25} +3.47054 q^{26} +5.58962 q^{27} -3.54174 q^{28} +4.23477 q^{29} -6.06662 q^{30} -8.64344 q^{31} +1.00000 q^{32} -6.98689 q^{33} +3.19553 q^{34} -13.9676 q^{35} -0.633629 q^{36} -4.09499 q^{37} +1.14712 q^{38} -5.33874 q^{39} +3.94371 q^{40} -5.96700 q^{41} +5.44826 q^{42} +7.60529 q^{43} +4.54195 q^{44} -2.49885 q^{45} -3.21056 q^{46} +4.18276 q^{47} -1.53830 q^{48} +5.54389 q^{49} +10.5529 q^{50} -4.91569 q^{51} +3.47054 q^{52} -0.668336 q^{53} +5.58962 q^{54} +17.9122 q^{55} -3.54174 q^{56} -1.76462 q^{57} +4.23477 q^{58} -0.928020 q^{59} -6.06662 q^{60} +8.93473 q^{61} -8.64344 q^{62} +2.24415 q^{63} +1.00000 q^{64} +13.6868 q^{65} -6.98689 q^{66} -4.43454 q^{67} +3.19553 q^{68} +4.93881 q^{69} -13.9676 q^{70} -11.0025 q^{71} -0.633629 q^{72} -14.9609 q^{73} -4.09499 q^{74} -16.2335 q^{75} +1.14712 q^{76} -16.0864 q^{77} -5.33874 q^{78} +13.8183 q^{79} +3.94371 q^{80} -6.69763 q^{81} -5.96700 q^{82} +9.97381 q^{83} +5.44826 q^{84} +12.6023 q^{85} +7.60529 q^{86} -6.51436 q^{87} +4.54195 q^{88} +8.67852 q^{89} -2.49885 q^{90} -12.2917 q^{91} -3.21056 q^{92} +13.2962 q^{93} +4.18276 q^{94} +4.52392 q^{95} -1.53830 q^{96} +14.3327 q^{97} +5.54389 q^{98} -2.87791 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

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