LMFDB - Embedded newform 4006.2.a.g.1.34

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:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.34
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.92514 q^{3} +1.00000 q^{4} -0.783945 q^{5} -1.92514 q^{6} +1.63896 q^{7} -1.00000 q^{8} +0.706178 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.92514 q^{3} +1.00000 q^{4} -0.783945 q^{5} -1.92514 q^{6} +1.63896 q^{7} -1.00000 q^{8} +0.706178 q^{9} +0.783945 q^{10} -5.84001 q^{11} +1.92514 q^{12} +4.41383 q^{13} -1.63896 q^{14} -1.50921 q^{15} +1.00000 q^{16} +3.42161 q^{17} -0.706178 q^{18} +3.30252 q^{19} -0.783945 q^{20} +3.15524 q^{21} +5.84001 q^{22} -8.31134 q^{23} -1.92514 q^{24} -4.38543 q^{25} -4.41383 q^{26} -4.41594 q^{27} +1.63896 q^{28} -5.42007 q^{29} +1.50921 q^{30} -3.07431 q^{31} -1.00000 q^{32} -11.2429 q^{33} -3.42161 q^{34} -1.28486 q^{35} +0.706178 q^{36} +2.32368 q^{37} -3.30252 q^{38} +8.49726 q^{39} +0.783945 q^{40} -10.2983 q^{41} -3.15524 q^{42} -7.48576 q^{43} -5.84001 q^{44} -0.553605 q^{45} +8.31134 q^{46} -2.15950 q^{47} +1.92514 q^{48} -4.31381 q^{49} +4.38543 q^{50} +6.58710 q^{51} +4.41383 q^{52} +10.7404 q^{53} +4.41594 q^{54} +4.57825 q^{55} -1.63896 q^{56} +6.35782 q^{57} +5.42007 q^{58} -4.96236 q^{59} -1.50921 q^{60} +3.45183 q^{61} +3.07431 q^{62} +1.15740 q^{63} +1.00000 q^{64} -3.46020 q^{65} +11.2429 q^{66} +13.4012 q^{67} +3.42161 q^{68} -16.0005 q^{69} +1.28486 q^{70} +15.5160 q^{71} -0.706178 q^{72} +1.81977 q^{73} -2.32368 q^{74} -8.44258 q^{75} +3.30252 q^{76} -9.57156 q^{77} -8.49726 q^{78} +0.540633 q^{79} -0.783945 q^{80} -10.6198 q^{81} +10.2983 q^{82} -5.02085 q^{83} +3.15524 q^{84} -2.68236 q^{85} +7.48576 q^{86} -10.4344 q^{87} +5.84001 q^{88} -13.6067 q^{89} +0.553605 q^{90} +7.23410 q^{91} -8.31134 q^{92} -5.91849 q^{93} +2.15950 q^{94} -2.58899 q^{95} -1.92514 q^{96} -11.6261 q^{97} +4.31381 q^{98} -4.12409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) $ 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * 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
$3$	1.92514	1.11148	0.555741	−	0.831355i	$-0.312435\pi$
$3$	1.92514	1.11148	0.555741	+	0.831355i	$0.312435\pi$
$4$	1.00000	0.500000
$5$	−0.783945	−0.350591	−0.175295	−	0.984516i	$-0.556088\pi$
$5$	−0.783945	−0.350591	−0.175295	+	0.984516i	$0.556088\pi$
$6$	−1.92514	−0.785937
$7$	1.63896	0.619469	0.309735	−	0.950823i	$-0.399760\pi$
$7$	1.63896	0.619469	0.309735	+	0.950823i	$0.399760\pi$
$8$	−1.00000	−0.353553
$9$	0.706178	0.235393
$10$	0.783945	0.247905
$11$	−5.84001	−1.76083	−0.880415	−	0.474204i	$-0.842736\pi$
$11$	−5.84001	−1.76083	−0.880415	+	0.474204i	$0.842736\pi$
$12$	1.92514	0.555741
$13$	4.41383	1.22418	0.612088	−	0.790790i	$-0.290330\pi$
$13$	4.41383	1.22418	0.612088	+	0.790790i	$0.290330\pi$
$14$	−1.63896	−0.438031
$15$	−1.50921	−0.389676
$16$	1.00000	0.250000
$17$	3.42161	0.829863	0.414932	−	0.909853i	$-0.363806\pi$
$17$	3.42161	0.829863	0.414932	+	0.909853i	$0.363806\pi$
$18$	−0.706178	−0.166448
$19$	3.30252	0.757650	0.378825	−	0.925468i	$-0.376328\pi$
$19$	3.30252	0.757650	0.378825	+	0.925468i	$0.376328\pi$
$20$	−0.783945	−0.175295
$21$	3.15524	0.688529
$22$	5.84001	1.24510
$23$	−8.31134	−1.73303	−0.866517	−	0.499148i	$-0.833646\pi$
$23$	−8.31134	−1.73303	−0.866517	+	0.499148i	$0.833646\pi$
$24$	−1.92514	−0.392968
$25$	−4.38543	−0.877086
$26$	−4.41383	−0.865623
$27$	−4.41594	−0.849847
$28$	1.63896	0.309735
$29$	−5.42007	−1.00648	−0.503241	−	0.864146i	$-0.667859\pi$
$29$	−5.42007	−1.00648	−0.503241	+	0.864146i	$0.667859\pi$
$30$	1.50921	0.275542
$31$	−3.07431	−0.552162	−0.276081	−	0.961134i	$-0.589036\pi$
$31$	−3.07431	−0.552162	−0.276081	+	0.961134i	$0.589036\pi$
$32$	−1.00000	−0.176777
$33$	−11.2429	−1.95713
$34$	−3.42161	−0.586802
$35$	−1.28486	−0.217180
$36$	0.706178	0.117696
$37$	2.32368	0.382010	0.191005	−	0.981589i	$-0.438825\pi$
$37$	2.32368	0.382010	0.191005	+	0.981589i	$0.438825\pi$
$38$	−3.30252	−0.535739
$39$	8.49726	1.36065
$40$	0.783945	0.123953
$41$	−10.2983	−1.60832	−0.804162	−	0.594411i	$-0.797385\pi$
$41$	−10.2983	−1.60832	−0.804162	+	0.594411i	$0.797385\pi$
$42$	−3.15524	−0.486863
$43$	−7.48576	−1.14157	−0.570784	−	0.821100i	$-0.693360\pi$
$43$	−7.48576	−1.14157	−0.570784	+	0.821100i	$0.693360\pi$
$44$	−5.84001	−0.880415
$45$	−0.553605	−0.0825265
$46$	8.31134	1.22544
$47$	−2.15950	−0.314995	−0.157498	−	0.987519i	$-0.550343\pi$
$47$	−2.15950	−0.314995	−0.157498	+	0.987519i	$0.550343\pi$
$48$	1.92514	0.277871
$49$	−4.31381	−0.616258
$50$	4.38543	0.620193
$51$	6.58710	0.922378
$52$	4.41383	0.612088
$53$	10.7404	1.47531	0.737655	−	0.675178i	$-0.235933\pi$
$53$	10.7404	1.47531	0.737655	+	0.675178i	$0.235933\pi$
$54$	4.41594	0.600933
$55$	4.57825	0.617331
$56$	−1.63896	−0.219015
$57$	6.35782	0.842114
$58$	5.42007	0.711691
$59$	−4.96236	−0.646044	−0.323022	−	0.946391i	$-0.604699\pi$
$59$	−4.96236	−0.646044	−0.323022	+	0.946391i	$0.604699\pi$
$60$	−1.50921	−0.194838
$61$	3.45183	0.441961	0.220981	−	0.975278i	$-0.429074\pi$
$61$	3.45183	0.441961	0.220981	+	0.975278i	$0.429074\pi$
$62$	3.07431	0.390438
$63$	1.15740	0.145819
$64$	1.00000	0.125000
$65$	−3.46020	−0.429185
$66$	11.2429	1.38390
$67$	13.4012	1.63722	0.818608	−	0.574353i	$-0.194746\pi$
$67$	13.4012	1.63722	0.818608	+	0.574353i	$0.194746\pi$
$68$	3.42161	0.414932
$69$	−16.0005	−1.92624
$70$	1.28486	0.153570
$71$	15.5160	1.84141	0.920703	−	0.390263i	$-0.127616\pi$
$71$	15.5160	1.84141	0.920703	+	0.390263i	$0.127616\pi$
$72$	−0.706178	−0.0832239
$73$	1.81977	0.212988	0.106494	−	0.994313i	$-0.466038\pi$
$73$	1.81977	0.212988	0.106494	+	0.994313i	$0.466038\pi$
$74$	−2.32368	−0.270122
$75$	−8.44258	−0.974866
$76$	3.30252	0.378825
$77$	−9.57156	−1.09078
$78$	−8.49726	−0.962125
$79$	0.540633	0.0608260	0.0304130	−	0.999537i	$-0.490318\pi$
$79$	0.540633	0.0608260	0.0304130	+	0.999537i	$0.490318\pi$
$80$	−0.783945	−0.0876477
$81$	−10.6198	−1.17998
$82$	10.2983	1.13726
$83$	−5.02085	−0.551110	−0.275555	−	0.961285i	$-0.588862\pi$
$83$	−5.02085	−0.551110	−0.275555	+	0.961285i	$0.588862\pi$
$84$	3.15524	0.344264
$85$	−2.68236	−0.290942
$86$	7.48576	0.807210
$87$	−10.4344	−1.11869
$88$	5.84001	0.622548
$89$	−13.6067	−1.44231	−0.721155	−	0.692774i	$-0.756388\pi$
$89$	−13.6067	−1.44231	−0.721155	+	0.692774i	$0.756388\pi$
$90$	0.553605	0.0583551
$91$	7.23410	0.758339
$92$	−8.31134	−0.866517
$93$	−5.91849	−0.613719
$94$	2.15950	0.222735
$95$	−2.58899	−0.265625
$96$	−1.92514	−0.196484
$97$	−11.6261	−1.18046	−0.590228	−	0.807237i	$-0.700962\pi$
$97$	−11.6261	−1.18046	−0.590228	+	0.807237i	$0.700962\pi$
$98$	4.31381	0.435760
$99$	−4.12409	−0.414487
$100$	−4.38543	−0.438543
$101$	4.10842	0.408803	0.204402	−	0.978887i	$-0.434475\pi$
$101$	4.10842	0.408803	0.204402	+	0.978887i	$0.434475\pi$
$102$	−6.58710	−0.652220
$103$	−3.14531	−0.309916	−0.154958	−	0.987921i	$-0.549524\pi$
$103$	−3.14531	−0.309916	−0.154958	+	0.987921i	$0.549524\pi$
$104$	−4.41383	−0.432812
$105$	−2.47353	−0.241392
$106$	−10.7404	−1.04320
$107$	−10.4604	−1.01125	−0.505625	−	0.862754i	$-0.668738\pi$
$107$	−10.4604	−1.01125	−0.505625	+	0.862754i	$0.668738\pi$
$108$	−4.41594	−0.424924
$109$	−9.69578	−0.928687	−0.464344	−	0.885655i	$-0.653710\pi$
$109$	−9.69578	−0.928687	−0.464344	+	0.885655i	$0.653710\pi$
$110$	−4.57825	−0.436519
$111$	4.47341	0.424598
$112$	1.63896	0.154867
$113$	−18.5625	−1.74621	−0.873107	−	0.487529i	$-0.837898\pi$
$113$	−18.5625	−1.74621	−0.873107	+	0.487529i	$0.837898\pi$
$114$	−6.35782	−0.595465
$115$	6.51563	0.607586
$116$	−5.42007	−0.503241
$117$	3.11695	0.288162
$118$	4.96236	0.456822
$119$	5.60789	0.514075
$120$	1.50921	0.137771
$121$	23.1058	2.10052
$122$	−3.45183	−0.312514
$123$	−19.8257	−1.78762
$124$	−3.07431	−0.276081
$125$	7.35766	0.658089
$126$	−1.15740	−0.103109
$127$	−6.16040	−0.546647	−0.273323	−	0.961922i	$-0.588123\pi$
$127$	−6.16040	−0.546647	−0.273323	+	0.961922i	$0.588123\pi$
$128$	−1.00000	−0.0883883
$129$	−14.4112	−1.26883
$130$	3.46020	0.303480
$131$	19.8258	1.73219	0.866094	−	0.499880i	$-0.166623\pi$
$131$	19.8258	1.73219	0.866094	+	0.499880i	$0.166623\pi$
$132$	−11.2429	−0.978566
$133$	5.41270	0.469341
$134$	−13.4012	−1.15769
$135$	3.46185	0.297949
$136$	−3.42161	−0.293401
$137$	10.1001	0.862910	0.431455	−	0.902134i	$-0.358000\pi$
$137$	10.1001	0.862910	0.431455	+	0.902134i	$0.358000\pi$
$138$	16.0005	1.36205
$139$	15.7184	1.33322	0.666608	−	0.745409i	$-0.267746\pi$
$139$	15.7184	1.33322	0.666608	+	0.745409i	$0.267746\pi$
$140$	−1.28486	−0.108590
$141$	−4.15734	−0.350111
$142$	−15.5160	−1.30207
$143$	−25.7768	−2.15557
$144$	0.706178	0.0588482
$145$	4.24904	0.352864
$146$	−1.81977	−0.150605
$147$	−8.30470	−0.684960
$148$	2.32368	0.191005
$149$	−12.4246	−1.01786	−0.508931	−	0.860807i	$-0.669959\pi$
$149$	−12.4246	−1.01786	−0.508931	+	0.860807i	$0.669959\pi$
$150$	8.44258	0.689334
$151$	−13.0961	−1.06575	−0.532874	−	0.846195i	$-0.678888\pi$
$151$	−13.0961	−1.06575	−0.532874	+	0.846195i	$0.678888\pi$
$152$	−3.30252	−0.267870
$153$	2.41627	0.195344
$154$	9.57156	0.771298
$155$	2.41009	0.193583
$156$	8.49726	0.680325
$157$	−9.07290	−0.724096	−0.362048	−	0.932159i	$-0.617922\pi$
$157$	−9.07290	−0.724096	−0.362048	+	0.932159i	$0.617922\pi$
$158$	−0.540633	−0.0430105
$159$	20.6768	1.63978
$160$	0.783945	0.0619763
$161$	−13.6220	−1.07356
$162$	10.6198	0.834374
$163$	18.7459	1.46829	0.734146	−	0.678991i	$-0.237583\pi$
$163$	18.7459	1.46829	0.734146	+	0.678991i	$0.237583\pi$
$164$	−10.2983	−0.804162
$165$	8.81379	0.686153
$166$	5.02085	0.389694
$167$	8.00864	0.619728	0.309864	−	0.950781i	$-0.399717\pi$
$167$	8.00864	0.619728	0.309864	+	0.950781i	$0.399717\pi$
$168$	−3.15524	−0.243432
$169$	6.48190	0.498607
$170$	2.68236	0.205727
$171$	2.33217	0.178345
$172$	−7.48576	−0.570784
$173$	−8.59162	−0.653209	−0.326604	−	0.945161i	$-0.605904\pi$
$173$	−8.59162	−0.653209	−0.326604	+	0.945161i	$0.605904\pi$
$174$	10.4344	0.791031
$175$	−7.18755	−0.543328
$176$	−5.84001	−0.440208
$177$	−9.55325	−0.718066
$178$	13.6067	1.01987
$179$	13.7800	1.02997	0.514983	−	0.857201i	$-0.327798\pi$
$179$	13.7800	1.02997	0.514983	+	0.857201i	$0.327798\pi$
$180$	−0.553605	−0.0412633
$181$	−5.50657	−0.409300	−0.204650	−	0.978835i	$-0.565606\pi$
$181$	−5.50657	−0.409300	−0.204650	+	0.978835i	$0.565606\pi$
$182$	−7.23410	−0.536227
$183$	6.64527	0.491232
$184$	8.31134	0.612720
$185$	−1.82164	−0.133929
$186$	5.91849	0.433965
$187$	−19.9823	−1.46125
$188$	−2.15950	−0.157498
$189$	−7.23755	−0.526454
$190$	2.58899	0.187825
$191$	−12.7568	−0.923047	−0.461524	−	0.887128i	$-0.652697\pi$
$191$	−12.7568	−0.923047	−0.461524	+	0.887128i	$0.652697\pi$
$192$	1.92514	0.138935
$193$	−10.2803	−0.739989	−0.369995	−	0.929034i	$-0.620640\pi$
$193$	−10.2803	−0.739989	−0.369995	+	0.929034i	$0.620640\pi$
$194$	11.6261	0.834708
$195$	−6.66138	−0.477032
$196$	−4.31381	−0.308129
$197$	−9.36615	−0.667311	−0.333655	−	0.942695i	$-0.608282\pi$
$197$	−9.36615	−0.667311	−0.333655	+	0.942695i	$0.608282\pi$
$198$	4.12409	0.293086
$199$	26.3614	1.86871	0.934354	−	0.356346i	$-0.115977\pi$
$199$	26.3614	1.86871	0.934354	+	0.356346i	$0.115977\pi$
$200$	4.38543	0.310097
$201$	25.7992	1.81974
$202$	−4.10842	−0.289068
$203$	−8.88329	−0.623485
$204$	6.58710	0.461189
$205$	8.07330	0.563864
$206$	3.14531	0.219144
$207$	−5.86928	−0.407943
$208$	4.41383	0.306044
$209$	−19.2868	−1.33409
$210$	2.47353	0.170690
$211$	−24.5242	−1.68832	−0.844159	−	0.536093i	$-0.819900\pi$
$211$	−24.5242	−1.68832	−0.844159	+	0.536093i	$0.819900\pi$
$212$	10.7404	0.737655
$213$	29.8705	2.04669
$214$	10.4604	0.715061
$215$	5.86842	0.400223
$216$	4.41594	0.300466
$217$	−5.03867	−0.342047
$218$	9.69578	0.656681
$219$	3.50331	0.236732
$220$	4.57825	0.308666
$221$	15.1024	1.01590
$222$	−4.47341	−0.300236
$223$	−23.3365	−1.56273	−0.781365	−	0.624074i	$-0.785476\pi$
$223$	−23.3365	−1.56273	−0.781365	+	0.624074i	$0.785476\pi$
$224$	−1.63896	−0.109508
$225$	−3.09689	−0.206460
$226$	18.5625	1.23476
$227$	−25.9503	−1.72238	−0.861189	−	0.508284i	$-0.830280\pi$
$227$	−25.9503	−1.72238	−0.861189	+	0.508284i	$0.830280\pi$
$228$	6.35782	0.421057
$229$	−0.498591	−0.0329479	−0.0164739	−	0.999864i	$-0.505244\pi$
$229$	−0.498591	−0.0329479	−0.0164739	+	0.999864i	$0.505244\pi$
$230$	−6.51563	−0.429628
$231$	−18.4266	−1.21238
$232$	5.42007	0.355845
$233$	−10.4114	−0.682072	−0.341036	−	0.940050i	$-0.610778\pi$
$233$	−10.4114	−0.682072	−0.341036	+	0.940050i	$0.610778\pi$
$234$	−3.11695	−0.203761
$235$	1.69293	0.110434
$236$	−4.96236	−0.323022
$237$	1.04080	0.0676070
$238$	−5.60789	−0.363506
$239$	17.9629	1.16193	0.580963	−	0.813930i	$-0.302676\pi$
$239$	17.9629	1.16193	0.580963	+	0.813930i	$0.302676\pi$
$240$	−1.50921	−0.0974189
$241$	−25.8146	−1.66286	−0.831432	−	0.555626i	$-0.812479\pi$
$241$	−25.8146	−1.66286	−0.831432	+	0.555626i	$0.812479\pi$
$242$	−23.1058	−1.48529
$243$	−7.19692	−0.461683
$244$	3.45183	0.220981
$245$	3.38179	0.216054
$246$	19.8257	1.26404
$247$	14.5768	0.927497
$248$	3.07431	0.195219
$249$	−9.66586	−0.612549
$250$	−7.35766	−0.465339
$251$	18.3425	1.15777	0.578883	−	0.815411i	$-0.303489\pi$
$251$	18.3425	1.15777	0.578883	+	0.815411i	$0.303489\pi$
$252$	1.15740	0.0729093
$253$	48.5383	3.05158
$254$	6.16040	0.386538
$255$	−5.16392	−0.323377
$256$	1.00000	0.0625000
$257$	14.7124	0.917736	0.458868	−	0.888504i	$-0.348255\pi$
$257$	14.7124	0.917736	0.458868	+	0.888504i	$0.348255\pi$
$258$	14.4112	0.897200
$259$	3.80842	0.236644
$260$	−3.46020	−0.214593
$261$	−3.82754	−0.236919
$262$	−19.8258	−1.22484
$263$	6.67567	0.411640	0.205820	−	0.978590i	$-0.434014\pi$
$263$	6.67567	0.411640	0.205820	+	0.978590i	$0.434014\pi$
$264$	11.2429	0.691951
$265$	−8.41989	−0.517230
$266$	−5.41270	−0.331874
$267$	−26.1949	−1.60310
$268$	13.4012	0.818608
$269$	−16.6194	−1.01330	−0.506650	−	0.862152i	$-0.669116\pi$
$269$	−16.6194	−1.01330	−0.506650	+	0.862152i	$0.669116\pi$
$270$	−3.46185	−0.210682
$271$	0.524597	0.0318670	0.0159335	−	0.999873i	$-0.494928\pi$
$271$	0.524597	0.0318670	0.0159335	+	0.999873i	$0.494928\pi$
$272$	3.42161	0.207466
$273$	13.9267	0.842881
$274$	−10.1001	−0.610170
$275$	25.6110	1.54440
$276$	−16.0005	−0.963118
$277$	−7.91133	−0.475346	−0.237673	−	0.971345i	$-0.576385\pi$
$277$	−7.91133	−0.475346	−0.237673	+	0.971345i	$0.576385\pi$
$278$	−15.7184	−0.942726
$279$	−2.17101	−0.129975
$280$	1.28486	0.0767848
$281$	10.7406	0.640730	0.320365	−	0.947294i	$-0.396194\pi$
$281$	10.7406	0.640730	0.320365	+	0.947294i	$0.396194\pi$
$282$	4.15734	0.247566
$283$	−11.5618	−0.687280	−0.343640	−	0.939102i	$-0.611660\pi$
$283$	−11.5618	−0.687280	−0.343640	+	0.939102i	$0.611660\pi$
$284$	15.5160	0.920703
$285$	−4.98418	−0.295238
$286$	25.7768	1.52422
$287$	−16.8785	−0.996307
$288$	−0.706178	−0.0416119
$289$	−5.29256	−0.311327
$290$	−4.24904	−0.249512
$291$	−22.3820	−1.31206
$292$	1.81977	0.106494
$293$	15.4937	0.905153	0.452576	−	0.891726i	$-0.350505\pi$
$293$	15.4937	0.905153	0.452576	+	0.891726i	$0.350505\pi$
$294$	8.30470	0.484340
$295$	3.89021	0.226497
$296$	−2.32368	−0.135061
$297$	25.7891	1.49644
$298$	12.4246	0.719737
$299$	−36.6848	−2.12154
$300$	−8.44258	−0.487433
$301$	−12.2689	−0.707166
$302$	13.0961	0.753598
$303$	7.90930	0.454378
$304$	3.30252	0.189412
$305$	−2.70604	−0.154948
$306$	−2.41627	−0.138129
$307$	19.0018	1.08449	0.542244	−	0.840221i	$-0.317575\pi$
$307$	19.0018	1.08449	0.542244	+	0.840221i	$0.317575\pi$
$308$	−9.57156	−0.545390
$309$	−6.05517	−0.344466
$310$	−2.41009	−0.136884
$311$	9.92488	0.562788	0.281394	−	0.959592i	$-0.409203\pi$
$311$	9.92488	0.562788	0.281394	+	0.959592i	$0.409203\pi$
$312$	−8.49726	−0.481062
$313$	28.9693	1.63744	0.818720	−	0.574193i	$-0.194684\pi$
$313$	28.9693	1.63744	0.818720	+	0.574193i	$0.194684\pi$
$314$	9.07290	0.512014
$315$	−0.907337	−0.0511226
$316$	0.540633	0.0304130
$317$	−5.74689	−0.322778	−0.161389	−	0.986891i	$-0.551597\pi$
$317$	−5.74689	−0.322778	−0.161389	+	0.986891i	$0.551597\pi$
$318$	−20.6768	−1.15950
$319$	31.6533	1.77224
$320$	−0.783945	−0.0438239
$321$	−20.1379	−1.12399
$322$	13.6220	0.759122
$323$	11.2999	0.628745
$324$	−10.6198	−0.589991
$325$	−19.3565	−1.07371
$326$	−18.7459	−1.03824
$327$	−18.6658	−1.03222
$328$	10.2983	0.568628
$329$	−3.53933	−0.195130
$330$	−8.81379	−0.485183
$331$	−24.7307	−1.35932	−0.679661	−	0.733526i	$-0.737873\pi$
$331$	−24.7307	−1.35932	−0.679661	+	0.733526i	$0.737873\pi$
$332$	−5.02085	−0.275555
$333$	1.64093	0.0899225
$334$	−8.00864	−0.438214
$335$	−10.5058	−0.573993
$336$	3.15524	0.172132
$337$	−28.1211	−1.53186	−0.765928	−	0.642926i	$-0.777720\pi$
$337$	−28.1211	−1.53186	−0.765928	+	0.642926i	$0.777720\pi$
$338$	−6.48190	−0.352569
$339$	−35.7355	−1.94089
$340$	−2.68236	−0.145471
$341$	17.9540	0.972264
$342$	−2.33217	−0.126109
$343$	−18.5429	−1.00122
$344$	7.48576	0.403605
$345$	12.5435	0.675321
$346$	8.59162	0.461888
$347$	−14.3355	−0.769570	−0.384785	−	0.923006i	$-0.625724\pi$
$347$	−14.3355	−0.769570	−0.384785	+	0.923006i	$0.625724\pi$
$348$	−10.4344	−0.559344
$349$	−1.90144	−0.101782	−0.0508910	−	0.998704i	$-0.516206\pi$
$349$	−1.90144	−0.101782	−0.0508910	+	0.998704i	$0.516206\pi$
$350$	7.18755	0.384191
$351$	−19.4912	−1.04036
$352$	5.84001	0.311274
$353$	−9.59083	−0.510468	−0.255234	−	0.966879i	$-0.582153\pi$
$353$	−9.59083	−0.510468	−0.255234	+	0.966879i	$0.582153\pi$
$354$	9.55325	0.507749
$355$	−12.1637	−0.645580
$356$	−13.6067	−0.721155
$357$	10.7960	0.571385
$358$	−13.7800	−0.728295
$359$	−23.3536	−1.23256	−0.616278	−	0.787529i	$-0.711360\pi$
$359$	−23.3536	−1.23256	−0.616278	+	0.787529i	$0.711360\pi$
$360$	0.553605	0.0291775
$361$	−8.09337	−0.425967
$362$	5.50657	0.289419
$363$	44.4819	2.33470
$364$	7.23410	0.379170
$365$	−1.42660	−0.0746715
$366$	−6.64527	−0.347354
$367$	−0.243163	−0.0126930	−0.00634650	−	0.999980i	$-0.502020\pi$
$367$	−0.243163	−0.0126930	−0.00634650	+	0.999980i	$0.502020\pi$
$368$	−8.31134	−0.433258
$369$	−7.27243	−0.378588
$370$	1.82164	0.0947024
$371$	17.6031	0.913909
$372$	−5.91849	−0.306859
$373$	15.8455	0.820450	0.410225	−	0.911984i	$-0.365450\pi$
$373$	15.8455	0.820450	0.410225	+	0.911984i	$0.365450\pi$
$374$	19.9823	1.03326
$375$	14.1646	0.731455
$376$	2.15950	0.111368
$377$	−23.9233	−1.23211
$378$	7.23755	0.372259
$379$	30.2901	1.55590	0.777948	−	0.628329i	$-0.216261\pi$
$379$	30.2901	1.55590	0.777948	+	0.628329i	$0.216261\pi$
$380$	−2.58899	−0.132813
$381$	−11.8596	−0.607588
$382$	12.7568	0.652693
$383$	9.92896	0.507346	0.253673	−	0.967290i	$-0.418361\pi$
$383$	9.92896	0.507346	0.253673	+	0.967290i	$0.418361\pi$
$384$	−1.92514	−0.0982421
$385$	7.50358	0.382418
$386$	10.2803	0.523251
$387$	−5.28628	−0.268717
$388$	−11.6261	−0.590228
$389$	35.3763	1.79365	0.896824	−	0.442388i	$-0.145869\pi$
$389$	35.3763	1.79365	0.896824	+	0.442388i	$0.145869\pi$
$390$	6.66138	0.337312
$391$	−28.4382	−1.43818
$392$	4.31381	0.217880
$393$	38.1675	1.92530
$394$	9.36615	0.471860
$395$	−0.423827	−0.0213250
$396$	−4.12409	−0.207243
$397$	0.343530	0.0172413	0.00862064	−	0.999963i	$-0.497256\pi$
$397$	0.343530	0.0172413	0.00862064	+	0.999963i	$0.497256\pi$
$398$	−26.3614	−1.32138
$399$	10.4202	0.521664
$400$	−4.38543	−0.219272
$401$	17.7443	0.886110	0.443055	−	0.896494i	$-0.353895\pi$
$401$	17.7443	0.886110	0.443055	+	0.896494i	$0.353895\pi$
$402$	−25.7992	−1.28675
$403$	−13.5695	−0.675944
$404$	4.10842	0.204402
$405$	8.32538	0.413691
$406$	8.88329	0.440870
$407$	−13.5703	−0.672656
$408$	−6.58710	−0.326110
$409$	4.78908	0.236805	0.118402	−	0.992966i	$-0.462223\pi$
$409$	4.78908	0.236805	0.118402	+	0.992966i	$0.462223\pi$
$410$	−8.07330	−0.398712
$411$	19.4441	0.959109
$412$	−3.14531	−0.154958
$413$	−8.13311	−0.400204
$414$	5.86928	0.288460
$415$	3.93607	0.193214
$416$	−4.41383	−0.216406
$417$	30.2601	1.48185
$418$	19.2868	0.943346
$419$	31.3745	1.53275	0.766373	−	0.642396i	$-0.222060\pi$
$419$	31.3745	1.53275	0.766373	+	0.642396i	$0.222060\pi$
$420$	−2.47353	−0.120696
$421$	−9.89677	−0.482339	−0.241170	−	0.970483i	$-0.577531\pi$
$421$	−9.89677	−0.482339	−0.241170	+	0.970483i	$0.577531\pi$
$422$	24.5242	1.19382
$423$	−1.52499	−0.0741475
$424$	−10.7404	−0.521601
$425$	−15.0052	−0.727861
$426$	−29.8705	−1.44723
$427$	5.65742	0.273782
$428$	−10.4604	−0.505625
$429$	−49.6241	−2.39587
$430$	−5.86842	−0.283000
$431$	1.81051	0.0872093	0.0436046	−	0.999049i	$-0.486116\pi$
$431$	1.81051	0.0872093	0.0436046	+	0.999049i	$0.486116\pi$
$432$	−4.41594	−0.212462
$433$	6.37308	0.306271	0.153135	−	0.988205i	$-0.451063\pi$
$433$	6.37308	0.306271	0.153135	+	0.988205i	$0.451063\pi$
$434$	5.03867	0.241864
$435$	8.18001	0.392202
$436$	−9.69578	−0.464344
$437$	−27.4483	−1.31303
$438$	−3.50331	−0.167395
$439$	−34.1743	−1.63105	−0.815524	−	0.578723i	$-0.803551\pi$
$439$	−34.1743	−1.63105	−0.815524	+	0.578723i	$0.803551\pi$
$440$	−4.57825	−0.218260
$441$	−3.04632	−0.145063
$442$	−15.1024	−0.718349
$443$	4.48784	0.213224	0.106612	−	0.994301i	$-0.466000\pi$
$443$	4.48784	0.213224	0.106612	+	0.994301i	$0.466000\pi$
$444$	4.47341	0.212299
$445$	10.6669	0.505661
$446$	23.3365	1.10502
$447$	−23.9191	−1.13134
$448$	1.63896	0.0774336
$449$	−29.1757	−1.37689	−0.688444	−	0.725290i	$-0.741706\pi$
$449$	−29.1757	−1.37689	−0.688444	+	0.725290i	$0.741706\pi$
$450$	3.09689	0.145989
$451$	60.1422	2.83199
$452$	−18.5625	−0.873107
$453$	−25.2119	−1.18456
$454$	25.9503	1.21791
$455$	−5.67113	−0.265867
$456$	−6.35782	−0.297732
$457$	23.2930	1.08960	0.544800	−	0.838566i	$-0.316605\pi$
$457$	23.2930	1.08960	0.544800	+	0.838566i	$0.316605\pi$
$458$	0.498591	0.0232976
$459$	−15.1096	−0.705257
$460$	6.51563	0.303793
$461$	38.7752	1.80594	0.902971	−	0.429703i	$-0.141382\pi$
$461$	38.7752	1.80594	0.902971	+	0.429703i	$0.141382\pi$
$462$	18.4266	0.857284
$463$	−2.75525	−0.128047	−0.0640236	−	0.997948i	$-0.520393\pi$
$463$	−2.75525	−0.128047	−0.0640236	+	0.997948i	$0.520393\pi$
$464$	−5.42007	−0.251621
$465$	4.63977	0.215164
$466$	10.4114	0.482298
$467$	14.3952	0.666129	0.333064	−	0.942904i	$-0.391917\pi$
$467$	14.3952	0.666129	0.333064	+	0.942904i	$0.391917\pi$
$468$	3.11695	0.144081
$469$	21.9640	1.01420
$470$	−1.69293	−0.0780889
$471$	−17.4666	−0.804820
$472$	4.96236	0.228411
$473$	43.7169	2.01011
$474$	−1.04080	−0.0478054
$475$	−14.4830	−0.664524
$476$	5.60789	0.257037
$477$	7.58465	0.347277
$478$	−17.9629	−0.821606
$479$	36.7111	1.67737	0.838686	−	0.544615i	$-0.183324\pi$
$479$	36.7111	1.67737	0.838686	+	0.544615i	$0.183324\pi$
$480$	1.50921	0.0688856
$481$	10.2563	0.467648
$482$	25.8146	1.17582
$483$	−26.2242	−1.19324
$484$	23.1058	1.05026
$485$	9.11425	0.413857
$486$	7.19692	0.326459
$487$	−20.2295	−0.916686	−0.458343	−	0.888775i	$-0.651557\pi$
$487$	−20.2295	−0.916686	−0.458343	+	0.888775i	$0.651557\pi$
$488$	−3.45183	−0.156257
$489$	36.0886	1.63198
$490$	−3.38179	−0.152774
$491$	4.70405	0.212291	0.106145	−	0.994351i	$-0.466149\pi$
$491$	4.70405	0.212291	0.106145	+	0.994351i	$0.466149\pi$
$492$	−19.8257	−0.893812
$493$	−18.5454	−0.835243
$494$	−14.5768	−0.655839
$495$	3.23306	0.145315
$496$	−3.07431	−0.138041
$497$	25.4301	1.14069
$498$	9.66586	0.433138
$499$	−23.2919	−1.04269	−0.521344	−	0.853346i	$-0.674569\pi$
$499$	−23.2919	−1.04269	−0.521344	+	0.853346i	$0.674569\pi$
$500$	7.35766	0.329045
$501$	15.4178	0.688816
$502$	−18.3425	−0.818664
$503$	7.27493	0.324373	0.162187	−	0.986760i	$-0.448145\pi$
$503$	7.27493	0.324373	0.162187	+	0.986760i	$0.448145\pi$
$504$	−1.15740	−0.0515546
$505$	−3.22078	−0.143323
$506$	−48.5383	−2.15779
$507$	12.4786	0.554193
$508$	−6.16040	−0.273323
$509$	−28.6666	−1.27063	−0.635313	−	0.772255i	$-0.719129\pi$
$509$	−28.6666	−1.27063	−0.635313	+	0.772255i	$0.719129\pi$
$510$	5.16392	0.228662
$511$	2.98253	0.131939
$512$	−1.00000	−0.0441942
$513$	−14.5837	−0.643887
$514$	−14.7124	−0.648938
$515$	2.46575	0.108654
$516$	−14.4112	−0.634416
$517$	12.6115	0.554653
$518$	−3.80842	−0.167332
$519$	−16.5401	−0.726030
$520$	3.46020	0.151740
$521$	−16.9174	−0.741165	−0.370583	−	0.928800i	$-0.620842\pi$
$521$	−16.9174	−0.741165	−0.370583	+	0.928800i	$0.620842\pi$
$522$	3.82754	0.167527
$523$	−21.5097	−0.940555	−0.470277	−	0.882519i	$-0.655846\pi$
$523$	−21.5097	−0.940555	−0.470277	+	0.882519i	$0.655846\pi$
$524$	19.8258	0.866094
$525$	−13.8371	−0.603899
$526$	−6.67567	−0.291073
$527$	−10.5191	−0.458219
$528$	−11.2429	−0.489283
$529$	46.0783	2.00341
$530$	8.41989	0.365737
$531$	−3.50431	−0.152074
$532$	5.41270	0.234670
$533$	−45.4549	−1.96887
$534$	26.1949	1.13356
$535$	8.20041	0.354535
$536$	−13.4012	−0.578843
$537$	26.5285	1.14479
$538$	16.6194	0.716511
$539$	25.1927	1.08513
$540$	3.46185	0.148974
$541$	44.5494	1.91533	0.957665	−	0.287886i	$-0.0929526\pi$
$541$	44.5494	1.91533	0.957665	+	0.287886i	$0.0929526\pi$
$542$	−0.524597	−0.0225334
$543$	−10.6009	−0.454930
$544$	−3.42161	−0.146700
$545$	7.60096	0.325589
$546$	−13.9267	−0.596007
$547$	−24.6208	−1.05271	−0.526355	−	0.850265i	$-0.676442\pi$
$547$	−24.6208	−1.05271	−0.526355	+	0.850265i	$0.676442\pi$
$548$	10.1001	0.431455
$549$	2.43761	0.104035
$550$	−25.6110	−1.09206
$551$	−17.8999	−0.762561
$552$	16.0005	0.681027
$553$	0.886077	0.0376798
$554$	7.91133	0.336120
$555$	−3.50691	−0.148860
$556$	15.7184	0.666608
$557$	−8.32931	−0.352924	−0.176462	−	0.984307i	$-0.556465\pi$
$557$	−8.32931	−0.352924	−0.176462	+	0.984307i	$0.556465\pi$
$558$	2.17101	0.0919062
$559$	−33.0409	−1.39748
$560$	−1.28486	−0.0542951
$561$	−38.4687	−1.62415
$562$	−10.7406	−0.453065
$563$	−24.7135	−1.04155	−0.520774	−	0.853694i	$-0.674357\pi$
$563$	−24.7135	−1.04155	−0.520774	+	0.853694i	$0.674357\pi$
$564$	−4.15734	−0.175056
$565$	14.5520	0.612207
$566$	11.5618	0.485980
$567$	−17.4055	−0.730963
$568$	−15.5160	−0.651036
$569$	12.2175	0.512183	0.256091	−	0.966653i	$-0.417565\pi$
$569$	12.2175	0.512183	0.256091	+	0.966653i	$0.417565\pi$
$570$	4.98418	0.208764
$571$	12.5967	0.527153	0.263577	−	0.964638i	$-0.415098\pi$
$571$	12.5967	0.527153	0.263577	+	0.964638i	$0.415098\pi$
$572$	−25.7768	−1.07778
$573$	−24.5586	−1.02595
$574$	16.8785	0.704495
$575$	36.4488	1.52002
$576$	0.706178	0.0294241
$577$	−17.3331	−0.721585	−0.360792	−	0.932646i	$-0.617494\pi$
$577$	−17.3331	−0.721585	−0.360792	+	0.932646i	$0.617494\pi$
$578$	5.29256	0.220142
$579$	−19.7910	−0.822485
$580$	4.24904	0.176432
$581$	−8.22898	−0.341396
$582$	22.3820	0.927763
$583$	−62.7242	−2.59777
$584$	−1.81977	−0.0753025
$585$	−2.44352	−0.101027
$586$	−15.4937	−0.640040
$587$	−36.1191	−1.49080	−0.745398	−	0.666619i	$-0.767741\pi$
$587$	−36.1191	−1.49080	−0.745398	+	0.666619i	$0.767741\pi$
$588$	−8.30470	−0.342480
$589$	−10.1530	−0.418346
$590$	−3.89021	−0.160158
$591$	−18.0312	−0.741704
$592$	2.32368	0.0955026
$593$	47.4379	1.94804	0.974020	−	0.226460i	$-0.0727153\pi$
$593$	47.4379	1.94804	0.974020	+	0.226460i	$0.0727153\pi$
$594$	−25.7891	−1.05814
$595$	−4.39628	−0.180230
$596$	−12.4246	−0.508931
$597$	50.7494	2.07704
$598$	36.6848	1.50015
$599$	−4.05483	−0.165676	−0.0828379	−	0.996563i	$-0.526398\pi$
$599$	−4.05483	−0.165676	−0.0828379	+	0.996563i	$0.526398\pi$
$600$	8.44258	0.344667
$601$	23.7263	0.967816	0.483908	−	0.875119i	$-0.339217\pi$
$601$	23.7263	0.967816	0.483908	+	0.875119i	$0.339217\pi$
$602$	12.2689	0.500042
$603$	9.46362	0.385389
$604$	−13.0961	−0.532874
$605$	−18.1136	−0.736425
$606$	−7.90930	−0.321293
$607$	28.0531	1.13864	0.569320	−	0.822116i	$-0.307206\pi$
$607$	28.0531	1.13864	0.569320	+	0.822116i	$0.307206\pi$
$608$	−3.30252	−0.133935
$609$	−17.1016	−0.692992
$610$	2.70604	0.109565
$611$	−9.53165	−0.385609
$612$	2.41627	0.0976719
$613$	−7.21942	−0.291590	−0.145795	−	0.989315i	$-0.546574\pi$
$613$	−7.21942	−0.291590	−0.145795	+	0.989315i	$0.546574\pi$
$614$	−19.0018	−0.766849
$615$	15.5423	0.626724
$616$	9.57156	0.385649
$617$	−43.0786	−1.73428	−0.867140	−	0.498065i	$-0.834044\pi$
$617$	−43.0786	−1.73428	−0.867140	+	0.498065i	$0.834044\pi$
$618$	6.05517	0.243575
$619$	−5.45743	−0.219353	−0.109676	−	0.993967i	$-0.534981\pi$
$619$	−5.45743	−0.219353	−0.109676	+	0.993967i	$0.534981\pi$
$620$	2.41009	0.0967915
$621$	36.7023	1.47281
$622$	−9.92488	−0.397952
$623$	−22.3009	−0.893467
$624$	8.49726	0.340163
$625$	16.1591	0.646366
$626$	−28.9693	−1.15785
$627$	−37.1298	−1.48282
$628$	−9.07290	−0.362048
$629$	7.95073	0.317016
$630$	0.907337	0.0361492
$631$	−7.07309	−0.281575	−0.140788	−	0.990040i	$-0.544963\pi$
$631$	−7.07309	−0.281575	−0.140788	+	0.990040i	$0.544963\pi$
$632$	−0.540633	−0.0215052
$633$	−47.2127	−1.87653
$634$	5.74689	0.228238
$635$	4.82941	0.191649
$636$	20.6768	0.819890
$637$	−19.0404	−0.754408
$638$	−31.6533	−1.25317
$639$	10.9570	0.433454
$640$	0.783945	0.0309881
$641$	−15.8646	−0.626612	−0.313306	−	0.949652i	$-0.601437\pi$
$641$	−15.8646	−0.626612	−0.313306	+	0.949652i	$0.601437\pi$
$642$	20.1379	0.794778
$643$	−23.9023	−0.942616	−0.471308	−	0.881969i	$-0.656218\pi$
$643$	−23.9023	−0.942616	−0.471308	+	0.881969i	$0.656218\pi$
$644$	−13.6220	−0.536780
$645$	11.2976	0.444841
$646$	−11.2999	−0.444590
$647$	27.7863	1.09239	0.546196	−	0.837658i	$-0.316075\pi$
$647$	27.7863	1.09239	0.546196	+	0.837658i	$0.316075\pi$
$648$	10.6198	0.417187
$649$	28.9802	1.13757
$650$	19.3565	0.759226
$651$	−9.70017	−0.380180
$652$	18.7459	0.734146
$653$	−5.78829	−0.226513	−0.113257	−	0.993566i	$-0.536128\pi$
$653$	−5.78829	−0.226513	−0.113257	+	0.993566i	$0.536128\pi$
$654$	18.6658	0.729889
$655$	−15.5423	−0.607290
$656$	−10.2983	−0.402081
$657$	1.28508	0.0501357
$658$	3.53933	0.137978
$659$	−27.9102	−1.08723	−0.543613	−	0.839336i	$-0.682944\pi$
$659$	−27.9102	−1.08723	−0.543613	+	0.839336i	$0.682944\pi$
$660$	8.81379	0.343076
$661$	19.3354	0.752058	0.376029	−	0.926608i	$-0.377289\pi$
$661$	19.3354	0.752058	0.376029	+	0.926608i	$0.377289\pi$
$662$	24.7307	0.961186
$663$	29.0743	1.12915
$664$	5.02085	0.194847
$665$	−4.24326	−0.164547
$666$	−1.64093	−0.0635848
$667$	45.0481	1.74427
$668$	8.00864	0.309864
$669$	−44.9262	−1.73695
$670$	10.5058	0.405874
$671$	−20.1587	−0.778219
$672$	−3.15524	−0.121716
$673$	13.3377	0.514129	0.257065	−	0.966394i	$-0.417245\pi$
$673$	13.3377	0.514129	0.257065	+	0.966394i	$0.417245\pi$
$674$	28.1211	1.08319
$675$	19.3658	0.745389
$676$	6.48190	0.249304
$677$	12.2723	0.471663	0.235831	−	0.971794i	$-0.424219\pi$
$677$	12.2723	0.471663	0.235831	+	0.971794i	$0.424219\pi$
$678$	35.7355	1.37241
$679$	−19.0548	−0.731256
$680$	2.68236	0.102864
$681$	−49.9580	−1.91439
$682$	−17.9540	−0.687495
$683$	33.8072	1.29360	0.646799	−	0.762661i	$-0.276107\pi$
$683$	33.8072	1.29360	0.646799	+	0.762661i	$0.276107\pi$
$684$	2.33217	0.0891726
$685$	−7.91793	−0.302528
$686$	18.5429	0.707971
$687$	−0.959860	−0.0366210
$688$	−7.48576	−0.285392
$689$	47.4064	1.80604
$690$	−12.5435	−0.477524
$691$	20.2900	0.771867	0.385934	−	0.922527i	$-0.373879\pi$
$691$	20.2900	0.771867	0.385934	+	0.922527i	$0.373879\pi$
$692$	−8.59162	−0.326604
$693$	−6.75922	−0.256762
$694$	14.3355	0.544168
$695$	−12.3223	−0.467413
$696$	10.4344	0.395516
$697$	−35.2368	−1.33469
$698$	1.90144	0.0719707
$699$	−20.0434	−0.758111
$700$	−7.18755	−0.271664
$701$	−29.8095	−1.12589	−0.562945	−	0.826494i	$-0.690332\pi$
$701$	−29.8095	−1.12589	−0.562945	+	0.826494i	$0.690332\pi$
$702$	19.4912	0.735648
$703$	7.67399	0.289430
$704$	−5.84001	−0.220104
$705$	3.25913	0.122746
$706$	9.59083	0.360956
$707$	6.73354	0.253241
$708$	−9.55325	−0.359033
$709$	−23.2262	−0.872279	−0.436139	−	0.899879i	$-0.643655\pi$
$709$	−23.2262	−0.872279	−0.436139	+	0.899879i	$0.643655\pi$
$710$	12.1637	0.456494
$711$	0.381783	0.0143180
$712$	13.6067	0.509934
$713$	25.5516	0.956916
$714$	−10.7960	−0.404030
$715$	20.2076	0.755722
$716$	13.7800	0.514983
$717$	34.5812	1.29146
$718$	23.3536	0.871549
$719$	30.9475	1.15415	0.577074	−	0.816692i	$-0.304194\pi$
$719$	30.9475	1.15415	0.577074	+	0.816692i	$0.304194\pi$
$720$	−0.553605	−0.0206316
$721$	−5.15504	−0.191984
$722$	8.09337	0.301204
$723$	−49.6968	−1.84824
$724$	−5.50657	−0.204650
$725$	23.7694	0.882772
$726$	−44.4819	−1.65088
$727$	9.13628	0.338846	0.169423	−	0.985543i	$-0.445810\pi$
$727$	9.13628	0.338846	0.169423	+	0.985543i	$0.445810\pi$
$728$	−7.23410	−0.268113
$729$	18.0044	0.666831
$730$	1.42660	0.0528007
$731$	−25.6134	−0.947345
$732$	6.64527	0.245616
$733$	−47.2936	−1.74683	−0.873414	−	0.486978i	$-0.838099\pi$
$733$	−47.2936	−1.74683	−0.873414	+	0.486978i	$0.838099\pi$
$734$	0.243163	0.00897531
$735$	6.51043	0.240141
$736$	8.31134	0.306360
$737$	−78.2631	−2.88286
$738$	7.27243	0.267702
$739$	38.0556	1.39990	0.699948	−	0.714193i	$-0.253206\pi$
$739$	38.0556	1.39990	0.699948	+	0.714193i	$0.253206\pi$
$740$	−1.82164	−0.0669647
$741$	28.0623	1.03090
$742$	−17.6031	−0.646231
$743$	34.6528	1.27129	0.635645	−	0.771982i	$-0.280734\pi$
$743$	34.6528	1.27129	0.635645	+	0.771982i	$0.280734\pi$
$744$	5.91849	0.216982
$745$	9.74020	0.356853
$746$	−15.8455	−0.580145
$747$	−3.54562	−0.129727
$748$	−19.9823	−0.730624
$749$	−17.1443	−0.626438
$750$	−14.1646	−0.517216
$751$	35.3651	1.29049	0.645245	−	0.763976i	$-0.276755\pi$
$751$	35.3651	1.29049	0.645245	+	0.763976i	$0.276755\pi$
$752$	−2.15950	−0.0787488
$753$	35.3119	1.28684
$754$	23.9233	0.871235
$755$	10.2667	0.373642
$756$	−7.23755	−0.263227
$757$	−39.4710	−1.43460	−0.717299	−	0.696765i	$-0.754622\pi$
$757$	−39.4710	−1.43460	−0.717299	+	0.696765i	$0.754622\pi$
$758$	−30.2901	−1.10018
$759$	93.4432	3.39178
$760$	2.58899	0.0939126
$761$	−6.82247	−0.247314	−0.123657	−	0.992325i	$-0.539462\pi$
$761$	−6.82247	−0.247314	−0.123657	+	0.992325i	$0.539462\pi$
$762$	11.8596	0.429630
$763$	−15.8910	−0.575293
$764$	−12.7568	−0.461524
$765$	−1.89422	−0.0684857
$766$	−9.92896	−0.358748
$767$	−21.9030	−0.790871
$768$	1.92514	0.0694676
$769$	34.6249	1.24861	0.624303	−	0.781183i	$-0.285383\pi$
$769$	34.6249	1.24861	0.624303	+	0.781183i	$0.285383\pi$
$770$	−7.50358	−0.270410
$771$	28.3235	1.02005
$772$	−10.2803	−0.369995
$773$	−15.7731	−0.567320	−0.283660	−	0.958925i	$-0.591549\pi$
$773$	−15.7731	−0.567320	−0.283660	+	0.958925i	$0.591549\pi$
$774$	5.28628	0.190011
$775$	13.4822	0.484294
$776$	11.6261	0.417354
$777$	7.33175	0.263025
$778$	−35.3763	−1.26830
$779$	−34.0103	−1.21855
$780$	−6.66138	−0.238516
$781$	−90.6135	−3.24241
$782$	28.4382	1.01695
$783$	23.9347	0.855356
$784$	−4.31381	−0.154064
$785$	7.11266	0.253862
$786$	−38.1675	−1.36139
$787$	41.3468	1.47386	0.736928	−	0.675971i	$-0.236276\pi$
$787$	41.3468	1.47386	0.736928	+	0.675971i	$0.236276\pi$
$788$	−9.36615	−0.333655
$789$	12.8516	0.457530
$790$	0.423827	0.0150791
$791$	−30.4232	−1.08173
$792$	4.12409	0.146543
$793$	15.2358	0.541039
$794$	−0.343530	−0.0121914
$795$	−16.2095	−0.574892
$796$	26.3614	0.934354
$797$	29.6263	1.04942	0.524709	−	0.851282i	$-0.324174\pi$
$797$	29.6263	1.04942	0.524709	+	0.851282i	$0.324174\pi$
$798$	−10.4202	−0.368872
$799$	−7.38896	−0.261403
$800$	4.38543	0.155048
$801$	−9.60877	−0.339509
$802$	−17.7443	−0.626574
$803$	−10.6275	−0.375035
$804$	25.7992	0.909868
$805$	10.6789	0.376381
$806$	13.5695	0.477965
$807$	−31.9947	−1.12627
$808$	−4.10842	−0.144534
$809$	14.7706	0.519308	0.259654	−	0.965702i	$-0.416392\pi$
$809$	14.7706	0.519308	0.259654	+	0.965702i	$0.416392\pi$
$810$	−8.32538	−0.292524
$811$	20.1030	0.705910	0.352955	−	0.935640i	$-0.385177\pi$
$811$	20.1030	0.705910	0.352955	+	0.935640i	$0.385177\pi$
$812$	−8.88329	−0.311742
$813$	1.00992	0.0354196
$814$	13.5703	0.475639
$815$	−14.6958	−0.514770
$816$	6.58710	0.230595
$817$	−24.7219	−0.864908
$818$	−4.78908	−0.167446
$819$	5.10856	0.178508
$820$	8.07330	0.281932
$821$	−27.6116	−0.963653	−0.481826	−	0.876267i	$-0.660026\pi$
$821$	−27.6116	−0.963653	−0.481826	+	0.876267i	$0.660026\pi$
$822$	−19.4441	−0.678193
$823$	−7.70886	−0.268714	−0.134357	−	0.990933i	$-0.542897\pi$
$823$	−7.70886	−0.268714	−0.134357	+	0.990933i	$0.542897\pi$
$824$	3.14531	0.109572
$825$	49.3048	1.71657
$826$	8.13311	0.282987
$827$	−29.5396	−1.02719	−0.513595	−	0.858032i	$-0.671687\pi$
$827$	−29.5396	−1.02719	−0.513595	+	0.858032i	$0.671687\pi$
$828$	−5.86928	−0.203972
$829$	−13.7397	−0.477198	−0.238599	−	0.971118i	$-0.576688\pi$
$829$	−13.7397	−0.477198	−0.238599	+	0.971118i	$0.576688\pi$
$830$	−3.93607	−0.136623
$831$	−15.2304	−0.528338
$832$	4.41383	0.153022
$833$	−14.7602	−0.511410
$834$	−30.2601	−1.04782
$835$	−6.27834	−0.217271
$836$	−19.2868	−0.667046
$837$	13.5760	0.469254
$838$	−31.3745	−1.08381
$839$	49.2668	1.70088	0.850440	−	0.526072i	$-0.176336\pi$
$839$	49.2668	1.70088	0.850440	+	0.526072i	$0.176336\pi$
$840$	2.47353	0.0853450
$841$	0.377199	0.0130069
$842$	9.89677	0.341065
$843$	20.6772	0.712160
$844$	−24.5242	−0.844159
$845$	−5.08145	−0.174807
$846$	1.52499	0.0524302
$847$	37.8695	1.30121
$848$	10.7404	0.368827
$849$	−22.2582	−0.763899
$850$	15.0052	0.514676
$851$	−19.3129	−0.662037
$852$	29.8705	1.02335
$853$	−47.5779	−1.62904	−0.814518	−	0.580138i	$-0.802999\pi$
$853$	−47.5779	−1.62904	−0.814518	+	0.580138i	$0.802999\pi$
$854$	−5.65742	−0.193593
$855$	−1.82829	−0.0625262
$856$	10.4604	0.357531
$857$	29.5327	1.00882	0.504409	−	0.863465i	$-0.331710\pi$
$857$	29.5327	1.00882	0.504409	+	0.863465i	$0.331710\pi$
$858$	49.6241	1.69414
$859$	−12.6915	−0.433029	−0.216514	−	0.976279i	$-0.569469\pi$
$859$	−12.6915	−0.433029	−0.216514	+	0.976279i	$0.569469\pi$
$860$	5.86842	0.200112
$861$	−32.4936	−1.10738
$862$	−1.81051	−0.0616663
$863$	−13.6327	−0.464061	−0.232031	−	0.972708i	$-0.574537\pi$
$863$	−13.6327	−0.464061	−0.232031	+	0.972708i	$0.574537\pi$
$864$	4.41594	0.150233
$865$	6.73536	0.229009
$866$	−6.37308	−0.216566
$867$	−10.1889	−0.346035
$868$	−5.03867	−0.171024
$869$	−3.15730	−0.107104
$870$	−8.18001	−0.277328
$871$	59.1506	2.00424
$872$	9.69578	0.328341
$873$	−8.21013	−0.277871
$874$	27.4483	0.928454
$875$	12.0589	0.407666
$876$	3.50331	0.118366
$877$	37.5559	1.26817	0.634086	−	0.773263i	$-0.281377\pi$
$877$	37.5559	1.26817	0.634086	+	0.773263i	$0.281377\pi$
$878$	34.1743	1.15333
$879$	29.8276	1.00606
$880$	4.57825	0.154333
$881$	17.5085	0.589877	0.294939	−	0.955516i	$-0.404701\pi$
$881$	17.5085	0.589877	0.294939	+	0.955516i	$0.404701\pi$
$882$	3.04632	0.102575
$883$	22.2493	0.748750	0.374375	−	0.927277i	$-0.377857\pi$
$883$	22.2493	0.748750	0.374375	+	0.927277i	$0.377857\pi$
$884$	15.1024	0.507949
$885$	7.48922	0.251747
$886$	−4.48784	−0.150772
$887$	21.5021	0.721970	0.360985	−	0.932572i	$-0.382441\pi$
$887$	21.5021	0.721970	0.360985	+	0.932572i	$0.382441\pi$
$888$	−4.47341	−0.150118
$889$	−10.0966	−0.338631
$890$	−10.6669	−0.357556
$891$	62.0201	2.07775
$892$	−23.3365	−0.781365
$893$	−7.13178	−0.238656
$894$	23.9191	0.799975
$895$	−10.8028	−0.361096
$896$	−1.63896	−0.0547539
$897$	−70.6236	−2.35805
$898$	29.1757	0.973606
$899$	16.6630	0.555742
$900$	−3.09689	−0.103230
$901$	36.7495	1.22430
$902$	−60.1422	−2.00252
$903$	−23.6193	−0.786002
$904$	18.5625	0.617380
$905$	4.31685	0.143497
$906$	25.2119	0.837611
$907$	37.6687	1.25077	0.625384	−	0.780317i	$-0.284942\pi$
$907$	37.6687	1.25077	0.625384	+	0.780317i	$0.284942\pi$
$908$	−25.9503	−0.861189
$909$	2.90128	0.0962293
$910$	5.67113	0.187996
$911$	28.4058	0.941125	0.470563	−	0.882367i	$-0.344051\pi$
$911$	28.4058	0.941125	0.470563	+	0.882367i	$0.344051\pi$
$912$	6.35782	0.210529
$913$	29.3219	0.970412
$914$	−23.2930	−0.770464
$915$	−5.20953	−0.172222
$916$	−0.498591	−0.0164739
$917$	32.4937	1.07304
$918$	15.1096	0.498692
$919$	−43.5311	−1.43596	−0.717979	−	0.696064i	$-0.754933\pi$
$919$	−43.5311	−1.43596	−0.717979	+	0.696064i	$0.754933\pi$
$920$	−6.51563	−0.214814
$921$	36.5811	1.20539
$922$	−38.7752	−1.27699
$923$	68.4849	2.25421
$924$	−18.4266	−0.606191
$925$	−10.1903	−0.335056
$926$	2.75525	0.0905430
$927$	−2.22115	−0.0729520
$928$	5.42007	0.177923
$929$	−13.1186	−0.430408	−0.215204	−	0.976569i	$-0.569042\pi$
$929$	−13.1186	−0.430408	−0.215204	+	0.976569i	$0.569042\pi$
$930$	−4.63977	−0.152144
$931$	−14.2464	−0.466908
$932$	−10.4114	−0.341036
$933$	19.1068	0.625529
$934$	−14.3952	−0.471024
$935$	15.6650	0.512300
$936$	−3.11695	−0.101881
$937$	2.56386	0.0837576	0.0418788	−	0.999123i	$-0.486666\pi$
$937$	2.56386	0.0837576	0.0418788	+	0.999123i	$0.486666\pi$
$938$	−21.9640	−0.717151
$939$	55.7700	1.81999
$940$	1.69293	0.0552172
$941$	−43.5844	−1.42081	−0.710405	−	0.703793i	$-0.751488\pi$
$941$	−43.5844	−1.42081	−0.710405	+	0.703793i	$0.751488\pi$
$942$	17.4666	0.569094
$943$	85.5926	2.78728
$944$	−4.96236	−0.161511
$945$	5.67384	0.184570
$946$	−43.7169	−1.42136
$947$	−34.5414	−1.12245	−0.561223	−	0.827665i	$-0.689669\pi$
$947$	−34.5414	−1.12245	−0.561223	+	0.827665i	$0.689669\pi$
$948$	1.04080	0.0338035
$949$	8.03214	0.260734
$950$	14.4830	0.469889
$951$	−11.0636	−0.358762
$952$	−5.60789	−0.181753
$953$	43.4340	1.40697	0.703483	−	0.710712i	$-0.251627\pi$
$953$	43.4340	1.40697	0.703483	+	0.710712i	$0.251627\pi$
$954$	−7.58465	−0.245562
$955$	10.0006	0.323612
$956$	17.9629	0.580963
$957$	60.9372	1.96982
$958$	−36.7111	−1.18608
$959$	16.5537	0.534546
$960$	−1.50921	−0.0487094
$961$	−21.5486	−0.695117
$962$	−10.2563	−0.330677
$963$	−7.38694	−0.238041
$964$	−25.8146	−0.831432
$965$	8.05916	0.259433
$966$	26.2242	0.843751
$967$	−30.2550	−0.972934	−0.486467	−	0.873699i	$-0.661715\pi$
$967$	−30.2550	−0.972934	−0.486467	+	0.873699i	$0.661715\pi$
$968$	−23.1058	−0.742647
$969$	21.7540	0.698839
$970$	−9.11425	−0.292641
$971$	−8.32213	−0.267070	−0.133535	−	0.991044i	$-0.542633\pi$
$971$	−8.32213	−0.267070	−0.133535	+	0.991044i	$0.542633\pi$
$972$	−7.19692	−0.230841
$973$	25.7618	0.825886
$974$	20.2295	0.648195
$975$	−37.2641	−1.19341
$976$	3.45183	0.110490
$977$	−2.33162	−0.0745951	−0.0372976	−	0.999304i	$-0.511875\pi$
$977$	−2.33162	−0.0745951	−0.0372976	+	0.999304i	$0.511875\pi$
$978$	−36.0886	−1.15399
$979$	79.4635	2.53966
$980$	3.38179	0.108027
$981$	−6.84695	−0.218606
$982$	−4.70405	−0.150112
$983$	32.5095	1.03689	0.518445	−	0.855111i	$-0.326511\pi$
$983$	32.5095	1.03689	0.518445	+	0.855111i	$0.326511\pi$
$984$	19.8257	0.632020
$985$	7.34255	0.233953
$986$	18.5454	0.590606
$987$	−6.81372	−0.216883
$988$	14.5768	0.463748
$989$	62.2167	1.97837
$990$	−3.23306	−0.102753
$991$	−0.676184	−0.0214797	−0.0107399	−	0.999942i	$-0.503419\pi$
$991$	−0.676184	−0.0214797	−0.0107399	+	0.999942i	$0.503419\pi$
$992$	3.07431	0.0976094
$993$	−47.6102	−1.51086
$994$	−25.4301	−0.806593
$995$	−20.6659	−0.655152
$996$	−9.66586	−0.306275
$997$	14.3761	0.455296	0.227648	−	0.973743i	$-0.426896\pi$
$997$	14.3761	0.455296	0.227648	+	0.973743i	$0.426896\pi$
$998$	23.2919	0.737292
$999$	−10.2612	−0.324651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.34	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.34	✓	40	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.92514 q^{3} +1.00000 q^{4} -0.783945 q^{5} -1.92514 q^{6} +1.63896 q^{7} -1.00000 q^{8} +0.706178 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.92514 q^{3} +1.00000 q^{4} -0.783945 q^{5} -1.92514 q^{6} +1.63896 q^{7} -1.00000 q^{8} +0.706178 q^{9} +0.783945 q^{10} -5.84001 q^{11} +1.92514 q^{12} +4.41383 q^{13} -1.63896 q^{14} -1.50921 q^{15} +1.00000 q^{16} +3.42161 q^{17} -0.706178 q^{18} +3.30252 q^{19} -0.783945 q^{20} +3.15524 q^{21} +5.84001 q^{22} -8.31134 q^{23} -1.92514 q^{24} -4.38543 q^{25} -4.41383 q^{26} -4.41594 q^{27} +1.63896 q^{28} -5.42007 q^{29} +1.50921 q^{30} -3.07431 q^{31} -1.00000 q^{32} -11.2429 q^{33} -3.42161 q^{34} -1.28486 q^{35} +0.706178 q^{36} +2.32368 q^{37} -3.30252 q^{38} +8.49726 q^{39} +0.783945 q^{40} -10.2983 q^{41} -3.15524 q^{42} -7.48576 q^{43} -5.84001 q^{44} -0.553605 q^{45} +8.31134 q^{46} -2.15950 q^{47} +1.92514 q^{48} -4.31381 q^{49} +4.38543 q^{50} +6.58710 q^{51} +4.41383 q^{52} +10.7404 q^{53} +4.41594 q^{54} +4.57825 q^{55} -1.63896 q^{56} +6.35782 q^{57} +5.42007 q^{58} -4.96236 q^{59} -1.50921 q^{60} +3.45183 q^{61} +3.07431 q^{62} +1.15740 q^{63} +1.00000 q^{64} -3.46020 q^{65} +11.2429 q^{66} +13.4012 q^{67} +3.42161 q^{68} -16.0005 q^{69} +1.28486 q^{70} +15.5160 q^{71} -0.706178 q^{72} +1.81977 q^{73} -2.32368 q^{74} -8.44258 q^{75} +3.30252 q^{76} -9.57156 q^{77} -8.49726 q^{78} +0.540633 q^{79} -0.783945 q^{80} -10.6198 q^{81} +10.2983 q^{82} -5.02085 q^{83} +3.15524 q^{84} -2.68236 q^{85} +7.48576 q^{86} -10.4344 q^{87} +5.84001 q^{88} -13.6067 q^{89} +0.553605 q^{90} +7.23410 q^{91} -8.31134 q^{92} -5.91849 q^{93} +2.15950 q^{94} -2.58899 q^{95} -1.92514 q^{96} -11.6261 q^{97} +4.31381 q^{98} -4.12409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

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