LMFDB - Embedded newform 4006.2.a.g.1.5

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			1.5
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.39522 q^{3} +1.00000 q^{4} +0.491091 q^{5} +2.39522 q^{6} +3.07111 q^{7} -1.00000 q^{8} +2.73707 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.39522 q^{3} +1.00000 q^{4} +0.491091 q^{5} +2.39522 q^{6} +3.07111 q^{7} -1.00000 q^{8} +2.73707 q^{9} -0.491091 q^{10} +4.17695 q^{11} -2.39522 q^{12} +5.66744 q^{13} -3.07111 q^{14} -1.17627 q^{15} +1.00000 q^{16} -5.34713 q^{17} -2.73707 q^{18} +3.22494 q^{19} +0.491091 q^{20} -7.35598 q^{21} -4.17695 q^{22} -8.14473 q^{23} +2.39522 q^{24} -4.75883 q^{25} -5.66744 q^{26} +0.629784 q^{27} +3.07111 q^{28} +3.25118 q^{29} +1.17627 q^{30} -9.37775 q^{31} -1.00000 q^{32} -10.0047 q^{33} +5.34713 q^{34} +1.50819 q^{35} +2.73707 q^{36} -2.98089 q^{37} -3.22494 q^{38} -13.5748 q^{39} -0.491091 q^{40} -7.26806 q^{41} +7.35598 q^{42} -2.20220 q^{43} +4.17695 q^{44} +1.34415 q^{45} +8.14473 q^{46} -5.87041 q^{47} -2.39522 q^{48} +2.43171 q^{49} +4.75883 q^{50} +12.8075 q^{51} +5.66744 q^{52} -0.642744 q^{53} -0.629784 q^{54} +2.05126 q^{55} -3.07111 q^{56} -7.72443 q^{57} -3.25118 q^{58} -9.99028 q^{59} -1.17627 q^{60} -7.53520 q^{61} +9.37775 q^{62} +8.40583 q^{63} +1.00000 q^{64} +2.78323 q^{65} +10.0047 q^{66} +9.38047 q^{67} -5.34713 q^{68} +19.5084 q^{69} -1.50819 q^{70} -12.1271 q^{71} -2.73707 q^{72} +9.49214 q^{73} +2.98089 q^{74} +11.3984 q^{75} +3.22494 q^{76} +12.8279 q^{77} +13.5748 q^{78} -12.4184 q^{79} +0.491091 q^{80} -9.71967 q^{81} +7.26806 q^{82} +4.34233 q^{83} -7.35598 q^{84} -2.62592 q^{85} +2.20220 q^{86} -7.78728 q^{87} -4.17695 q^{88} -10.1770 q^{89} -1.34415 q^{90} +17.4053 q^{91} -8.14473 q^{92} +22.4617 q^{93} +5.87041 q^{94} +1.58374 q^{95} +2.39522 q^{96} +7.98956 q^{97} -2.43171 q^{98} +11.4326 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.39522	−1.38288	−0.691440	−	0.722434i	$-0.743023\pi$
$3$	−2.39522	−1.38288	−0.691440	+	0.722434i	$0.743023\pi$
$4$	1.00000	0.500000
$5$	0.491091	0.219622	0.109811	−	0.993952i	$-0.464975\pi$
$5$	0.491091	0.219622	0.109811	+	0.993952i	$0.464975\pi$
$6$	2.39522	0.977843
$7$	3.07111	1.16077	0.580385	−	0.814342i	$-0.302902\pi$
$7$	3.07111	1.16077	0.580385	+	0.814342i	$0.302902\pi$
$8$	−1.00000	−0.353553
$9$	2.73707	0.912355
$10$	−0.491091	−0.155296
$11$	4.17695	1.25940	0.629699	−	0.776839i	$-0.283178\pi$
$11$	4.17695	1.25940	0.629699	+	0.776839i	$0.283178\pi$
$12$	−2.39522	−0.691440
$13$	5.66744	1.57187	0.785933	−	0.618312i	$-0.212183\pi$
$13$	5.66744	1.57187	0.785933	+	0.618312i	$0.212183\pi$
$14$	−3.07111	−0.820789
$15$	−1.17627	−0.303711
$16$	1.00000	0.250000
$17$	−5.34713	−1.29687	−0.648434	−	0.761271i	$-0.724576\pi$
$17$	−5.34713	−1.29687	−0.648434	+	0.761271i	$0.724576\pi$
$18$	−2.73707	−0.645133
$19$	3.22494	0.739852	0.369926	−	0.929061i	$-0.379383\pi$
$19$	3.22494	0.739852	0.369926	+	0.929061i	$0.379383\pi$
$20$	0.491091	0.109811
$21$	−7.35598	−1.60521
$22$	−4.17695	−0.890529
$23$	−8.14473	−1.69829	−0.849147	−	0.528157i	$-0.822883\pi$
$23$	−8.14473	−1.69829	−0.849147	+	0.528157i	$0.822883\pi$
$24$	2.39522	0.488922
$25$	−4.75883	−0.951766
$26$	−5.66744	−1.11148
$27$	0.629784	0.121202
$28$	3.07111	0.580385
$29$	3.25118	0.603729	0.301864	−	0.953351i	$-0.402391\pi$
$29$	3.25118	0.603729	0.301864	+	0.953351i	$0.402391\pi$
$30$	1.17627	0.214756
$31$	−9.37775	−1.68429	−0.842147	−	0.539248i	$-0.818708\pi$
$31$	−9.37775	−1.68429	−0.842147	+	0.539248i	$0.818708\pi$
$32$	−1.00000	−0.176777
$33$	−10.0047	−1.74160
$34$	5.34713	0.917024
$35$	1.50819	0.254931
$36$	2.73707	0.456178
$37$	−2.98089	−0.490056	−0.245028	−	0.969516i	$-0.578797\pi$
$37$	−2.98089	−0.490056	−0.245028	+	0.969516i	$0.578797\pi$
$38$	−3.22494	−0.523155
$39$	−13.5748	−2.17370
$40$	−0.491091	−0.0776482
$41$	−7.26806	−1.13508	−0.567540	−	0.823346i	$-0.692105\pi$
$41$	−7.26806	−1.13508	−0.567540	+	0.823346i	$0.692105\pi$
$42$	7.35598	1.13505
$43$	−2.20220	−0.335832	−0.167916	−	0.985801i	$-0.553704\pi$
$43$	−2.20220	−0.335832	−0.167916	+	0.985801i	$0.553704\pi$
$44$	4.17695	0.629699
$45$	1.34415	0.200374
$46$	8.14473	1.20088
$47$	−5.87041	−0.856287	−0.428143	−	0.903711i	$-0.640832\pi$
$47$	−5.87041	−0.856287	−0.428143	+	0.903711i	$0.640832\pi$
$48$	−2.39522	−0.345720
$49$	2.43171	0.347388
$50$	4.75883	0.673000
$51$	12.8075	1.79341
$52$	5.66744	0.785933
$53$	−0.642744	−0.0882876	−0.0441438	−	0.999025i	$-0.514056\pi$
$53$	−0.642744	−0.0882876	−0.0441438	+	0.999025i	$0.514056\pi$
$54$	−0.629784	−0.0857027
$55$	2.05126	0.276592
$56$	−3.07111	−0.410394
$57$	−7.72443	−1.02313
$58$	−3.25118	−0.426901
$59$	−9.99028	−1.30062	−0.650312	−	0.759668i	$-0.725362\pi$
$59$	−9.99028	−1.30062	−0.650312	+	0.759668i	$0.725362\pi$
$60$	−1.17627	−0.151856
$61$	−7.53520	−0.964783	−0.482392	−	0.875956i	$-0.660232\pi$
$61$	−7.53520	−0.964783	−0.482392	+	0.875956i	$0.660232\pi$
$62$	9.37775	1.19098
$63$	8.40583	1.05904
$64$	1.00000	0.125000
$65$	2.78323	0.345217
$66$	10.0047	1.23149
$67$	9.38047	1.14601	0.573003	−	0.819553i	$-0.305778\pi$
$67$	9.38047	1.14601	0.573003	+	0.819553i	$0.305778\pi$
$68$	−5.34713	−0.648434
$69$	19.5084	2.34854
$70$	−1.50819	−0.180264
$71$	−12.1271	−1.43922	−0.719610	−	0.694379i	$-0.755679\pi$
$71$	−12.1271	−1.43922	−0.719610	+	0.694379i	$0.755679\pi$
$72$	−2.73707	−0.322566
$73$	9.49214	1.11097	0.555486	−	0.831526i	$-0.312532\pi$
$73$	9.49214	1.11097	0.555486	+	0.831526i	$0.312532\pi$
$74$	2.98089	0.346522
$75$	11.3984	1.31618
$76$	3.22494	0.369926
$77$	12.8279	1.46187
$78$	13.5748	1.53704
$79$	−12.4184	−1.39717	−0.698587	−	0.715525i	$-0.746188\pi$
$79$	−12.4184	−1.39717	−0.698587	+	0.715525i	$0.746188\pi$
$80$	0.491091	0.0549056
$81$	−9.71967	−1.07996
$82$	7.26806	0.802623
$83$	4.34233	0.476633	0.238316	−	0.971188i	$-0.423405\pi$
$83$	4.34233	0.476633	0.238316	+	0.971188i	$0.423405\pi$
$84$	−7.35598	−0.802603
$85$	−2.62592	−0.284821
$86$	2.20220	0.237469
$87$	−7.78728	−0.834884
$88$	−4.17695	−0.445264
$89$	−10.1770	−1.07876	−0.539378	−	0.842064i	$-0.681340\pi$
$89$	−10.1770	−1.07876	−0.539378	+	0.842064i	$0.681340\pi$
$90$	−1.34415	−0.141686
$91$	17.4053	1.82457
$92$	−8.14473	−0.849147
$93$	22.4617	2.32917
$94$	5.87041	0.605486
$95$	1.58374	0.162488
$96$	2.39522	0.244461
$97$	7.98956	0.811217	0.405608	−	0.914047i	$-0.367060\pi$
$97$	7.98956	0.811217	0.405608	+	0.914047i	$0.367060\pi$
$98$	−2.43171	−0.245640
$99$	11.4326	1.14902
$100$	−4.75883	−0.475883
$101$	−1.68806	−0.167968	−0.0839842	−	0.996467i	$-0.526765\pi$
$101$	−1.68806	−0.167968	−0.0839842	+	0.996467i	$0.526765\pi$
$102$	−12.8075	−1.26813
$103$	−1.91205	−0.188400	−0.0941998	−	0.995553i	$-0.530029\pi$
$103$	−1.91205	−0.188400	−0.0941998	+	0.995553i	$0.530029\pi$
$104$	−5.66744	−0.555738
$105$	−3.61245	−0.352539
$106$	0.642744	0.0624288
$107$	8.77566	0.848376	0.424188	−	0.905574i	$-0.360560\pi$
$107$	8.77566	0.848376	0.424188	+	0.905574i	$0.360560\pi$
$108$	0.629784	0.0606009
$109$	−14.1944	−1.35957	−0.679786	−	0.733410i	$-0.737927\pi$
$109$	−14.1944	−1.35957	−0.679786	+	0.733410i	$0.737927\pi$
$110$	−2.05126	−0.195580
$111$	7.13988	0.677688
$112$	3.07111	0.290193
$113$	9.20454	0.865891	0.432945	−	0.901420i	$-0.357474\pi$
$113$	9.20454	0.865891	0.432945	+	0.901420i	$0.357474\pi$
$114$	7.72443	0.723460
$115$	−3.99980	−0.372983
$116$	3.25118	0.301864
$117$	15.5122	1.43410
$118$	9.99028	0.919679
$119$	−16.4216	−1.50537
$120$	1.17627	0.107378
$121$	6.44691	0.586082
$122$	7.53520	0.682205
$123$	17.4086	1.56968
$124$	−9.37775	−0.842147
$125$	−4.79247	−0.428652
$126$	−8.40583	−0.748851
$127$	−4.22504	−0.374911	−0.187456	−	0.982273i	$-0.560024\pi$
$127$	−4.22504	−0.374911	−0.187456	+	0.982273i	$0.560024\pi$
$128$	−1.00000	−0.0883883
$129$	5.27474	0.464415
$130$	−2.78323	−0.244105
$131$	4.88496	0.426801	0.213401	−	0.976965i	$-0.431546\pi$
$131$	4.88496	0.426801	0.213401	+	0.976965i	$0.431546\pi$
$132$	−10.0047	−0.870798
$133$	9.90415	0.858798
$134$	−9.38047	−0.810349
$135$	0.309281	0.0266187
$136$	5.34713	0.458512
$137$	−0.798475	−0.0682183	−0.0341092	−	0.999418i	$-0.510859\pi$
$137$	−0.798475	−0.0682183	−0.0341092	+	0.999418i	$0.510859\pi$
$138$	−19.5084	−1.66067
$139$	9.77048	0.828722	0.414361	−	0.910113i	$-0.364005\pi$
$139$	9.77048	0.828722	0.414361	+	0.910113i	$0.364005\pi$
$140$	1.50819	0.127466
$141$	14.0609	1.18414
$142$	12.1271	1.01768
$143$	23.6726	1.97960
$144$	2.73707	0.228089
$145$	1.59662	0.132592
$146$	−9.49214	−0.785575
$147$	−5.82448	−0.480395
$148$	−2.98089	−0.245028
$149$	−21.1919	−1.73610	−0.868052	−	0.496473i	$-0.834628\pi$
$149$	−21.1919	−1.73610	−0.868052	+	0.496473i	$0.834628\pi$
$150$	−11.3984	−0.930678
$151$	17.9796	1.46316	0.731578	−	0.681758i	$-0.238784\pi$
$151$	17.9796	1.46316	0.731578	+	0.681758i	$0.238784\pi$
$152$	−3.22494	−0.261577
$153$	−14.6354	−1.18320
$154$	−12.8279	−1.03370
$155$	−4.60532	−0.369909
$156$	−13.5748	−1.08685
$157$	−11.9540	−0.954031	−0.477015	−	0.878895i	$-0.658281\pi$
$157$	−11.9540	−0.954031	−0.477015	+	0.878895i	$0.658281\pi$
$158$	12.4184	0.987952
$159$	1.53951	0.122091
$160$	−0.491091	−0.0388241
$161$	−25.0134	−1.97133
$162$	9.71967	0.763649
$163$	−11.0917	−0.868770	−0.434385	−	0.900727i	$-0.643034\pi$
$163$	−11.0917	−0.868770	−0.434385	+	0.900727i	$0.643034\pi$
$164$	−7.26806	−0.567540
$165$	−4.91321	−0.382493
$166$	−4.34233	−0.337030
$167$	−16.7829	−1.29870	−0.649351	−	0.760489i	$-0.724959\pi$
$167$	−16.7829	−1.29870	−0.649351	+	0.760489i	$0.724959\pi$
$168$	7.35598	0.567526
$169$	19.1199	1.47076
$170$	2.62592	0.201399
$171$	8.82688	0.675008
$172$	−2.20220	−0.167916
$173$	−9.99615	−0.759993	−0.379996	−	0.924988i	$-0.624075\pi$
$173$	−9.99615	−0.759993	−0.379996	+	0.924988i	$0.624075\pi$
$174$	7.78728	0.590352
$175$	−14.6149	−1.10478
$176$	4.17695	0.314849
$177$	23.9289	1.79861
$178$	10.1770	0.762795
$179$	−10.9214	−0.816304	−0.408152	−	0.912914i	$-0.633827\pi$
$179$	−10.9214	−0.816304	−0.408152	+	0.912914i	$0.633827\pi$
$180$	1.34415	0.100187
$181$	3.90061	0.289930	0.144965	−	0.989437i	$-0.453693\pi$
$181$	3.90061	0.289930	0.144965	+	0.989437i	$0.453693\pi$
$182$	−17.4053	−1.29017
$183$	18.0484	1.33418
$184$	8.14473	0.600438
$185$	−1.46389	−0.107627
$186$	−22.4617	−1.64698
$187$	−22.3347	−1.63327
$188$	−5.87041	−0.428143
$189$	1.93413	0.140688
$190$	−1.58374	−0.114896
$191$	2.97007	0.214907	0.107453	−	0.994210i	$-0.465730\pi$
$191$	2.97007	0.214907	0.107453	+	0.994210i	$0.465730\pi$
$192$	−2.39522	−0.172860
$193$	7.73876	0.557048	0.278524	−	0.960429i	$-0.410155\pi$
$193$	7.73876	0.557048	0.278524	+	0.960429i	$0.410155\pi$
$194$	−7.98956	−0.573617
$195$	−6.66643	−0.477393
$196$	2.43171	0.173694
$197$	0.354426	0.0252518	0.0126259	−	0.999920i	$-0.495981\pi$
$197$	0.354426	0.0252518	0.0126259	+	0.999920i	$0.495981\pi$
$198$	−11.4326	−0.812479
$199$	14.1460	1.00278	0.501390	−	0.865221i	$-0.332822\pi$
$199$	14.1460	1.00278	0.501390	+	0.865221i	$0.332822\pi$
$200$	4.75883	0.336500
$201$	−22.4683	−1.58479
$202$	1.68806	0.118772
$203$	9.98472	0.700790
$204$	12.8075	0.896706
$205$	−3.56928	−0.249289
$206$	1.91205	0.133219
$207$	−22.2927	−1.54945
$208$	5.66744	0.392966
$209$	13.4704	0.931768
$210$	3.61245	0.249283
$211$	24.6919	1.69986	0.849931	−	0.526894i	$-0.176644\pi$
$211$	24.6919	1.69986	0.849931	+	0.526894i	$0.176644\pi$
$212$	−0.642744	−0.0441438
$213$	29.0470	1.99027
$214$	−8.77566	−0.599892
$215$	−1.08148	−0.0737563
$216$	−0.629784	−0.0428513
$217$	−28.8001	−1.95508
$218$	14.1944	0.961363
$219$	−22.7357	−1.53634
$220$	2.05126	0.138296
$221$	−30.3045	−2.03850
$222$	−7.13988	−0.479198
$223$	−27.1716	−1.81955	−0.909774	−	0.415105i	$-0.863745\pi$
$223$	−27.1716	−1.81955	−0.909774	+	0.415105i	$0.863745\pi$
$224$	−3.07111	−0.205197
$225$	−13.0252	−0.868349
$226$	−9.20454	−0.612277
$227$	11.4716	0.761400	0.380700	−	0.924699i	$-0.375683\pi$
$227$	11.4716	0.761400	0.380700	+	0.924699i	$0.375683\pi$
$228$	−7.72443	−0.511563
$229$	−6.94051	−0.458642	−0.229321	−	0.973351i	$-0.573651\pi$
$229$	−6.94051	−0.458642	−0.229321	+	0.973351i	$0.573651\pi$
$230$	3.99980	0.263739
$231$	−30.7255	−2.02159
$232$	−3.25118	−0.213450
$233$	−16.4108	−1.07511	−0.537553	−	0.843230i	$-0.680651\pi$
$233$	−16.4108	−1.07511	−0.537553	+	0.843230i	$0.680651\pi$
$234$	−15.5122	−1.01406
$235$	−2.88290	−0.188060
$236$	−9.99028	−0.650312
$237$	29.7447	1.93212
$238$	16.4216	1.06445
$239$	22.3045	1.44276	0.721379	−	0.692540i	$-0.243508\pi$
$239$	22.3045	1.44276	0.721379	+	0.692540i	$0.243508\pi$
$240$	−1.17627	−0.0759278
$241$	−22.4473	−1.44596	−0.722979	−	0.690870i	$-0.757228\pi$
$241$	−22.4473	−1.44596	−0.722979	+	0.690870i	$0.757228\pi$
$242$	−6.44691	−0.414423
$243$	21.3914	1.37226
$244$	−7.53520	−0.482392
$245$	1.19419	0.0762941
$246$	−17.4086	−1.10993
$247$	18.2772	1.16295
$248$	9.37775	0.595488
$249$	−10.4008	−0.659125
$250$	4.79247	0.303102
$251$	20.4423	1.29031	0.645153	−	0.764053i	$-0.276793\pi$
$251$	20.4423	1.29031	0.645153	+	0.764053i	$0.276793\pi$
$252$	8.40583	0.529518
$253$	−34.0201	−2.13883
$254$	4.22504	0.265102
$255$	6.28966	0.393874
$256$	1.00000	0.0625000
$257$	−12.3192	−0.768450	−0.384225	−	0.923239i	$-0.625531\pi$
$257$	−12.3192	−0.768450	−0.384225	+	0.923239i	$0.625531\pi$
$258$	−5.27474	−0.328391
$259$	−9.15465	−0.568842
$260$	2.78323	0.172608
$261$	8.89869	0.550815
$262$	−4.88496	−0.301794
$263$	17.1786	1.05928	0.529640	−	0.848223i	$-0.322327\pi$
$263$	17.1786	1.05928	0.529640	+	0.848223i	$0.322327\pi$
$264$	10.0047	0.615747
$265$	−0.315645	−0.0193899
$266$	−9.90415	−0.607262
$267$	24.3760	1.49179
$268$	9.38047	0.573003
$269$	−0.264663	−0.0161368	−0.00806840	−	0.999967i	$-0.502568\pi$
$269$	−0.264663	−0.0161368	−0.00806840	+	0.999967i	$0.502568\pi$
$270$	−0.309281	−0.0188222
$271$	−9.31291	−0.565719	−0.282859	−	0.959161i	$-0.591283\pi$
$271$	−9.31291	−0.565719	−0.282859	+	0.959161i	$0.591283\pi$
$272$	−5.34713	−0.324217
$273$	−41.6896	−2.52317
$274$	0.798475	0.0482376
$275$	−19.8774	−1.19865
$276$	19.5084	1.17427
$277$	−12.0706	−0.725254	−0.362627	−	0.931934i	$-0.618120\pi$
$277$	−12.0706	−0.725254	−0.362627	+	0.931934i	$0.618120\pi$
$278$	−9.77048	−0.585995
$279$	−25.6675	−1.53667
$280$	−1.50819	−0.0901318
$281$	−20.0764	−1.19766	−0.598828	−	0.800878i	$-0.704367\pi$
$281$	−20.0764	−1.19766	−0.598828	+	0.800878i	$0.704367\pi$
$282$	−14.0609	−0.837314
$283$	33.1312	1.96944	0.984722	−	0.174133i	$-0.0557124\pi$
$283$	33.1312	1.96944	0.984722	+	0.174133i	$0.0557124\pi$
$284$	−12.1271	−0.719610
$285$	−3.79340	−0.224701
$286$	−23.6726	−1.39979
$287$	−22.3210	−1.31757
$288$	−2.73707	−0.161283
$289$	11.5917	0.681868
$290$	−1.59662	−0.0937569
$291$	−19.1367	−1.12182
$292$	9.49214	0.555486
$293$	23.7516	1.38758	0.693792	−	0.720176i	$-0.255939\pi$
$293$	23.7516	1.38758	0.693792	+	0.720176i	$0.255939\pi$
$294$	5.82448	0.339691
$295$	−4.90613	−0.285646
$296$	2.98089	0.173261
$297$	2.63057	0.152641
$298$	21.1919	1.22761
$299$	−46.1598	−2.66949
$300$	11.3984	0.658089
$301$	−6.76319	−0.389824
$302$	−17.9796	−1.03461
$303$	4.04328	0.232280
$304$	3.22494	0.184963
$305$	−3.70046	−0.211888
$306$	14.6354	0.836652
$307$	9.38157	0.535435	0.267717	−	0.963498i	$-0.413731\pi$
$307$	9.38157	0.535435	0.267717	+	0.963498i	$0.413731\pi$
$308$	12.8279	0.730936
$309$	4.57977	0.260534
$310$	4.60532	0.261565
$311$	−5.26368	−0.298476	−0.149238	−	0.988801i	$-0.547682\pi$
$311$	−5.26368	−0.298476	−0.149238	+	0.988801i	$0.547682\pi$
$312$	13.5748	0.768519
$313$	24.8871	1.40670	0.703350	−	0.710844i	$-0.251687\pi$
$313$	24.8871	1.40670	0.703350	+	0.710844i	$0.251687\pi$
$314$	11.9540	0.674602
$315$	4.12802	0.232588
$316$	−12.4184	−0.698587
$317$	16.8876	0.948502	0.474251	−	0.880390i	$-0.342719\pi$
$317$	16.8876	0.948502	0.474251	+	0.880390i	$0.342719\pi$
$318$	−1.53951	−0.0863315
$319$	13.5800	0.760334
$320$	0.491091	0.0274528
$321$	−21.0196	−1.17320
$322$	25.0134	1.39394
$323$	−17.2442	−0.959491
$324$	−9.71967	−0.539982
$325$	−26.9704	−1.49605
$326$	11.0917	0.614313
$327$	33.9986	1.88012
$328$	7.26806	0.401311
$329$	−18.0287	−0.993952
$330$	4.91321	0.270464
$331$	22.3758	1.22988	0.614941	−	0.788573i	$-0.289180\pi$
$331$	22.3758	1.22988	0.614941	+	0.788573i	$0.289180\pi$
$332$	4.34233	0.238316
$333$	−8.15890	−0.447105
$334$	16.7829	0.918321
$335$	4.60666	0.251689
$336$	−7.35598	−0.401301
$337$	21.8971	1.19281	0.596406	−	0.802683i	$-0.296595\pi$
$337$	21.8971	1.19281	0.596406	+	0.802683i	$0.296595\pi$
$338$	−19.1199	−1.03999
$339$	−22.0469	−1.19742
$340$	−2.62592	−0.142411
$341$	−39.1704	−2.12120
$342$	−8.82688	−0.477303
$343$	−14.0297	−0.757533
$344$	2.20220	0.118735
$345$	9.58039	0.515791
$346$	9.99615	0.537396
$347$	−12.6063	−0.676744	−0.338372	−	0.941012i	$-0.609876\pi$
$347$	−12.6063	−0.676744	−0.338372	+	0.941012i	$0.609876\pi$
$348$	−7.78728	−0.417442
$349$	−28.4651	−1.52370	−0.761852	−	0.647752i	$-0.775709\pi$
$349$	−28.4651	−1.52370	−0.761852	+	0.647752i	$0.775709\pi$
$350$	14.6149	0.781199
$351$	3.56926	0.190513
$352$	−4.17695	−0.222632
$353$	8.69186	0.462621	0.231311	−	0.972880i	$-0.425699\pi$
$353$	8.69186	0.462621	0.231311	+	0.972880i	$0.425699\pi$
$354$	−23.9289	−1.27181
$355$	−5.95549	−0.316085
$356$	−10.1770	−0.539378
$357$	39.3333	2.08174
$358$	10.9214	0.577214
$359$	12.1148	0.639394	0.319697	−	0.947520i	$-0.396419\pi$
$359$	12.1148	0.639394	0.319697	+	0.947520i	$0.396419\pi$
$360$	−1.34415	−0.0708428
$361$	−8.59976	−0.452619
$362$	−3.90061	−0.205012
$363$	−15.4417	−0.810481
$364$	17.4053	0.912287
$365$	4.66150	0.243994
$366$	−18.0484	−0.943407
$367$	−32.7058	−1.70723	−0.853615	−	0.520904i	$-0.825595\pi$
$367$	−32.7058	−1.70723	−0.853615	+	0.520904i	$0.825595\pi$
$368$	−8.14473	−0.424573
$369$	−19.8932	−1.03560
$370$	1.46389	0.0761039
$371$	−1.97394	−0.102482
$372$	22.4617	1.16459
$373$	−14.0290	−0.726394	−0.363197	−	0.931712i	$-0.618315\pi$
$373$	−14.0290	−0.726394	−0.363197	+	0.931712i	$0.618315\pi$
$374$	22.3347	1.15490
$375$	11.4790	0.592773
$376$	5.87041	0.302743
$377$	18.4259	0.948980
$378$	−1.93413	−0.0994811
$379$	−7.19822	−0.369748	−0.184874	−	0.982762i	$-0.559188\pi$
$379$	−7.19822	−0.369748	−0.184874	+	0.982762i	$0.559188\pi$
$380$	1.58374	0.0812441
$381$	10.1199	0.518457
$382$	−2.97007	−0.151962
$383$	6.09068	0.311219	0.155610	−	0.987819i	$-0.450266\pi$
$383$	6.09068	0.311219	0.155610	+	0.987819i	$0.450266\pi$
$384$	2.39522	0.122230
$385$	6.29965	0.321060
$386$	−7.73876	−0.393893
$387$	−6.02756	−0.306398
$388$	7.98956	0.405608
$389$	−16.9965	−0.861758	−0.430879	−	0.902410i	$-0.641796\pi$
$389$	−16.9965	−0.861758	−0.430879	+	0.902410i	$0.641796\pi$
$390$	6.66643	0.337568
$391$	43.5509	2.20246
$392$	−2.43171	−0.122820
$393$	−11.7005	−0.590214
$394$	−0.354426	−0.0178557
$395$	−6.09854	−0.306851
$396$	11.4326	0.574509
$397$	−32.9086	−1.65164	−0.825818	−	0.563937i	$-0.809286\pi$
$397$	−32.9086	−1.65164	−0.825818	+	0.563937i	$0.809286\pi$
$398$	−14.1460	−0.709072
$399$	−23.7226	−1.18761
$400$	−4.75883	−0.237942
$401$	−24.4612	−1.22153	−0.610767	−	0.791811i	$-0.709139\pi$
$401$	−24.4612	−1.22153	−0.610767	+	0.791811i	$0.709139\pi$
$402$	22.4683	1.12061
$403$	−53.1478	−2.64748
$404$	−1.68806	−0.0839842
$405$	−4.77324	−0.237184
$406$	−9.98472	−0.495533
$407$	−12.4510	−0.617175
$408$	−12.8075	−0.634067
$409$	2.74577	0.135769	0.0678847	−	0.997693i	$-0.478375\pi$
$409$	2.74577	0.135769	0.0678847	+	0.997693i	$0.478375\pi$
$410$	3.56928	0.176274
$411$	1.91252	0.0943377
$412$	−1.91205	−0.0941998
$413$	−30.6812	−1.50972
$414$	22.2927	1.09562
$415$	2.13248	0.104679
$416$	−5.66744	−0.277869
$417$	−23.4024	−1.14602
$418$	−13.4704	−0.658860
$419$	−12.3308	−0.602398	−0.301199	−	0.953561i	$-0.597387\pi$
$419$	−12.3308	−0.602398	−0.301199	+	0.953561i	$0.597387\pi$
$420$	−3.61245	−0.176270
$421$	−2.41067	−0.117489	−0.0587446	−	0.998273i	$-0.518710\pi$
$421$	−2.41067	−0.117489	−0.0587446	+	0.998273i	$0.518710\pi$
$422$	−24.6919	−1.20198
$423$	−16.0677	−0.781238
$424$	0.642744	0.0312144
$425$	25.4461	1.23432
$426$	−29.0470	−1.40733
$427$	−23.1414	−1.11989
$428$	8.77566	0.424188
$429$	−56.7011	−2.73755
$430$	1.08148	0.0521535
$431$	−12.0286	−0.579396	−0.289698	−	0.957118i	$-0.593555\pi$
$431$	−12.0286	−0.579396	−0.289698	+	0.957118i	$0.593555\pi$
$432$	0.629784	0.0303005
$433$	27.1227	1.30343	0.651716	−	0.758463i	$-0.274049\pi$
$433$	27.1227	1.30343	0.651716	+	0.758463i	$0.274049\pi$
$434$	28.8001	1.38245
$435$	−3.82426	−0.183359
$436$	−14.1944	−0.679786
$437$	−26.2663	−1.25649
$438$	22.7357	1.08636
$439$	−28.9910	−1.38366	−0.691832	−	0.722059i	$-0.743196\pi$
$439$	−28.9910	−1.38366	−0.691832	+	0.722059i	$0.743196\pi$
$440$	−2.05126	−0.0977900
$441$	6.65576	0.316941
$442$	30.3045	1.44144
$443$	11.4191	0.542539	0.271269	−	0.962503i	$-0.412557\pi$
$443$	11.4191	0.542539	0.271269	+	0.962503i	$0.412557\pi$
$444$	7.13988	0.338844
$445$	−4.99781	−0.236919
$446$	27.1716	1.28661
$447$	50.7591	2.40082
$448$	3.07111	0.145096
$449$	−16.5317	−0.780181	−0.390091	−	0.920776i	$-0.627556\pi$
$449$	−16.5317	−0.780181	−0.390091	+	0.920776i	$0.627556\pi$
$450$	13.0252	0.614015
$451$	−30.3583	−1.42952
$452$	9.20454	0.432945
$453$	−43.0650	−2.02337
$454$	−11.4716	−0.538391
$455$	8.54760	0.400718
$456$	7.72443	0.361730
$457$	−26.9824	−1.26218	−0.631092	−	0.775708i	$-0.717393\pi$
$457$	−26.9824	−1.26218	−0.631092	+	0.775708i	$0.717393\pi$
$458$	6.94051	0.324309
$459$	−3.36753	−0.157183
$460$	−3.99980	−0.186492
$461$	16.6346	0.774751	0.387375	−	0.921922i	$-0.373382\pi$
$461$	16.6346	0.774751	0.387375	+	0.921922i	$0.373382\pi$
$462$	30.7255	1.42948
$463$	−26.3819	−1.22607	−0.613036	−	0.790055i	$-0.710052\pi$
$463$	−26.3819	−1.22607	−0.613036	+	0.790055i	$0.710052\pi$
$464$	3.25118	0.150932
$465$	11.0308	0.511539
$466$	16.4108	0.760215
$467$	20.9194	0.968034	0.484017	−	0.875058i	$-0.339177\pi$
$467$	20.9194	0.968034	0.484017	+	0.875058i	$0.339177\pi$
$468$	15.5122	0.717050
$469$	28.8084	1.33025
$470$	2.88290	0.132978
$471$	28.6324	1.31931
$472$	9.99028	0.459840
$473$	−9.19847	−0.422946
$474$	−29.7447	−1.36622
$475$	−15.3469	−0.704166
$476$	−16.4216	−0.752683
$477$	−1.75923	−0.0805497
$478$	−22.3045	−1.02018
$479$	17.9881	0.821898	0.410949	−	0.911658i	$-0.365197\pi$
$479$	17.9881	0.821898	0.410949	+	0.911658i	$0.365197\pi$
$480$	1.17627	0.0536891
$481$	−16.8940	−0.770301
$482$	22.4473	1.02245
$483$	59.9124	2.72611
$484$	6.44691	0.293041
$485$	3.92360	0.178161
$486$	−21.3914	−0.970332
$487$	38.3070	1.73585	0.867927	−	0.496692i	$-0.165452\pi$
$487$	38.3070	1.73585	0.867927	+	0.496692i	$0.165452\pi$
$488$	7.53520	0.341102
$489$	26.5671	1.20140
$490$	−1.19419	−0.0539481
$491$	36.3842	1.64200	0.820998	−	0.570931i	$-0.193418\pi$
$491$	36.3842	1.64200	0.820998	+	0.570931i	$0.193418\pi$
$492$	17.4086	0.784840
$493$	−17.3845	−0.782956
$494$	−18.2772	−0.822329
$495$	5.61444	0.252350
$496$	−9.37775	−0.421073
$497$	−37.2436	−1.67060
$498$	10.4008	0.466072
$499$	24.6930	1.10541	0.552705	−	0.833377i	$-0.313596\pi$
$499$	24.6930	1.10541	0.552705	+	0.833377i	$0.313596\pi$
$500$	−4.79247	−0.214326
$501$	40.1988	1.79595
$502$	−20.4423	−0.912385
$503$	−21.1450	−0.942809	−0.471404	−	0.881917i	$-0.656253\pi$
$503$	−21.1450	−0.942809	−0.471404	+	0.881917i	$0.656253\pi$
$504$	−8.40583	−0.374425
$505$	−0.828992	−0.0368896
$506$	34.0201	1.51238
$507$	−45.7963	−2.03389
$508$	−4.22504	−0.187456
$509$	−12.3985	−0.549553	−0.274776	−	0.961508i	$-0.588604\pi$
$509$	−12.3985	−0.549553	−0.274776	+	0.961508i	$0.588604\pi$
$510$	−6.28966	−0.278511
$511$	29.1514	1.28958
$512$	−1.00000	−0.0441942
$513$	2.03101	0.0896715
$514$	12.3192	0.543376
$515$	−0.938989	−0.0413768
$516$	5.27474	0.232208
$517$	−24.5204	−1.07841
$518$	9.15465	0.402232
$519$	23.9429	1.05098
$520$	−2.78323	−0.122053
$521$	−7.01193	−0.307198	−0.153599	−	0.988133i	$-0.549086\pi$
$521$	−7.01193	−0.307198	−0.153599	+	0.988133i	$0.549086\pi$
$522$	−8.89869	−0.389485
$523$	29.6863	1.29809	0.649045	−	0.760750i	$-0.275169\pi$
$523$	29.6863	1.29809	0.649045	+	0.760750i	$0.275169\pi$
$524$	4.88496	0.213401
$525$	35.0058	1.52778
$526$	−17.1786	−0.749024
$527$	50.1440	2.18431
$528$	−10.0047	−0.435399
$529$	43.3367	1.88420
$530$	0.315645	0.0137108
$531$	−27.3440	−1.18663
$532$	9.90415	0.429399
$533$	−41.1913	−1.78419
$534$	−24.3760	−1.05485
$535$	4.30965	0.186322
$536$	−9.38047	−0.405175
$537$	26.1591	1.12885
$538$	0.264663	0.0114104
$539$	10.1571	0.437499
$540$	0.309281	0.0133093
$541$	−0.402620	−0.0173100	−0.00865499	−	0.999963i	$-0.502755\pi$
$541$	−0.402620	−0.0173100	−0.00865499	+	0.999963i	$0.502755\pi$
$542$	9.31291	0.400024
$543$	−9.34281	−0.400938
$544$	5.34713	0.229256
$545$	−6.97071	−0.298593
$546$	41.6896	1.78415
$547$	25.9079	1.10774	0.553871	−	0.832602i	$-0.313150\pi$
$547$	25.9079	1.10774	0.553871	+	0.832602i	$0.313150\pi$
$548$	−0.798475	−0.0341092
$549$	−20.6243	−0.880225
$550$	19.8774	0.847575
$551$	10.4849	0.446670
$552$	−19.5084	−0.830333
$553$	−38.1381	−1.62180
$554$	12.0706	0.512832
$555$	3.50633	0.148835
$556$	9.77048	0.414361
$557$	−21.2299	−0.899538	−0.449769	−	0.893145i	$-0.648494\pi$
$557$	−21.2299	−0.899538	−0.449769	+	0.893145i	$0.648494\pi$
$558$	25.6675	1.08659
$559$	−12.4808	−0.527883
$560$	1.50819	0.0637328
$561$	53.4964	2.25862
$562$	20.0764	0.846870
$563$	−20.0942	−0.846872	−0.423436	−	0.905926i	$-0.639176\pi$
$563$	−20.0942	−0.846872	−0.423436	+	0.905926i	$0.639176\pi$
$564$	14.0609	0.592071
$565$	4.52027	0.190169
$566$	−33.1312	−1.39261
$567$	−29.8502	−1.25359
$568$	12.1271	0.508841
$569$	18.0634	0.757258	0.378629	−	0.925549i	$-0.376396\pi$
$569$	18.0634	0.757258	0.378629	+	0.925549i	$0.376396\pi$
$570$	3.79340	0.158888
$571$	−16.1702	−0.676702	−0.338351	−	0.941020i	$-0.609869\pi$
$571$	−16.1702	−0.676702	−0.338351	+	0.941020i	$0.609869\pi$
$572$	23.6726	0.989802
$573$	−7.11396	−0.297190
$574$	22.3210	0.931661
$575$	38.7594	1.61638
$576$	2.73707	0.114044
$577$	44.0917	1.83556	0.917781	−	0.397088i	$-0.129979\pi$
$577$	44.0917	1.83556	0.917781	+	0.397088i	$0.129979\pi$
$578$	−11.5917	−0.482153
$579$	−18.5360	−0.770330
$580$	1.59662	0.0662962
$581$	13.3358	0.553261
$582$	19.1367	0.793243
$583$	−2.68471	−0.111189
$584$	−9.49214	−0.392788
$585$	7.61788	0.314960
$586$	−23.7516	−0.981170
$587$	2.45312	0.101251	0.0506256	−	0.998718i	$-0.483878\pi$
$587$	2.45312	0.101251	0.0506256	+	0.998718i	$0.483878\pi$
$588$	−5.82448	−0.240198
$589$	−30.2427	−1.24613
$590$	4.90613	0.201982
$591$	−0.848927	−0.0349202
$592$	−2.98089	−0.122514
$593$	−38.4514	−1.57901	−0.789505	−	0.613744i	$-0.789663\pi$
$593$	−38.4514	−1.57901	−0.789505	+	0.613744i	$0.789663\pi$
$594$	−2.63057	−0.107934
$595$	−8.06450	−0.330612
$596$	−21.1919	−0.868052
$597$	−33.8826	−1.38672
$598$	46.1598	1.88761
$599$	28.2670	1.15496	0.577479	−	0.816406i	$-0.304037\pi$
$599$	28.2670	1.15496	0.577479	+	0.816406i	$0.304037\pi$
$600$	−11.3984	−0.465339
$601$	−35.8944	−1.46416	−0.732082	−	0.681217i	$-0.761451\pi$
$601$	−35.8944	−1.46416	−0.732082	+	0.681217i	$0.761451\pi$
$602$	6.76319	0.275647
$603$	25.6750	1.04557
$604$	17.9796	0.731578
$605$	3.16601	0.128717
$606$	−4.04328	−0.164247
$607$	−10.0515	−0.407976	−0.203988	−	0.978973i	$-0.565390\pi$
$607$	−10.0515	−0.407976	−0.203988	+	0.978973i	$0.565390\pi$
$608$	−3.22494	−0.130789
$609$	−23.9156	−0.969108
$610$	3.70046	0.149827
$611$	−33.2702	−1.34597
$612$	−14.6354	−0.591602
$613$	13.7202	0.554154	0.277077	−	0.960848i	$-0.410634\pi$
$613$	13.7202	0.554154	0.277077	+	0.960848i	$0.410634\pi$
$614$	−9.38157	−0.378609
$615$	8.54919	0.344737
$616$	−12.8279	−0.516850
$617$	4.83317	0.194576	0.0972881	−	0.995256i	$-0.468983\pi$
$617$	4.83317	0.194576	0.0972881	+	0.995256i	$0.468983\pi$
$618$	−4.57977	−0.184225
$619$	9.03192	0.363024	0.181512	−	0.983389i	$-0.441901\pi$
$619$	9.03192	0.363024	0.181512	+	0.983389i	$0.441901\pi$
$620$	−4.60532	−0.184954
$621$	−5.12942	−0.205836
$622$	5.26368	0.211054
$623$	−31.2546	−1.25219
$624$	−13.5748	−0.543425
$625$	21.4406	0.857625
$626$	−24.8871	−0.994687
$627$	−32.2646	−1.28852
$628$	−11.9540	−0.477015
$629$	15.9392	0.635538
$630$	−4.12802	−0.164464
$631$	3.48726	0.138826	0.0694129	−	0.997588i	$-0.477887\pi$
$631$	3.48726	0.138826	0.0694129	+	0.997588i	$0.477887\pi$
$632$	12.4184	0.493976
$633$	−59.1425	−2.35070
$634$	−16.8876	−0.670692
$635$	−2.07488	−0.0823390
$636$	1.53951	0.0610456
$637$	13.7816	0.546047
$638$	−13.5800	−0.537638
$639$	−33.1926	−1.31308
$640$	−0.491091	−0.0194121
$641$	10.2789	0.405992	0.202996	−	0.979180i	$-0.434932\pi$
$641$	10.2789	0.405992	0.202996	+	0.979180i	$0.434932\pi$
$642$	21.0196	0.829578
$643$	−6.19060	−0.244133	−0.122067	−	0.992522i	$-0.538952\pi$
$643$	−6.19060	−0.244133	−0.122067	+	0.992522i	$0.538952\pi$
$644$	−25.0134	−0.985665
$645$	2.59038	0.101996
$646$	17.2442	0.678463
$647$	20.5889	0.809433	0.404717	−	0.914442i	$-0.367370\pi$
$647$	20.5889	0.809433	0.404717	+	0.914442i	$0.367370\pi$
$648$	9.71967	0.381825
$649$	−41.7289	−1.63800
$650$	26.9704	1.05787
$651$	68.9825	2.70364
$652$	−11.0917	−0.434385
$653$	27.1456	1.06229	0.531145	−	0.847281i	$-0.321762\pi$
$653$	27.1456	1.06229	0.531145	+	0.847281i	$0.321762\pi$
$654$	−33.9986	−1.32945
$655$	2.39896	0.0937351
$656$	−7.26806	−0.283770
$657$	25.9806	1.01360
$658$	18.0287	0.702831
$659$	30.8015	1.19986	0.599929	−	0.800053i	$-0.295196\pi$
$659$	30.8015	1.19986	0.599929	+	0.800053i	$0.295196\pi$
$660$	−4.91321	−0.191247
$661$	23.5729	0.916881	0.458441	−	0.888725i	$-0.348408\pi$
$661$	23.5729	0.916881	0.458441	+	0.888725i	$0.348408\pi$
$662$	−22.3758	−0.869659
$663$	72.5859	2.81900
$664$	−4.34233	−0.168515
$665$	4.86383	0.188611
$666$	8.15890	0.316151
$667$	−26.4800	−1.02531
$668$	−16.7829	−0.649351
$669$	65.0820	2.51621
$670$	−4.60666	−0.177971
$671$	−31.4741	−1.21505
$672$	7.35598	0.283763
$673$	8.13234	0.313479	0.156739	−	0.987640i	$-0.449902\pi$
$673$	8.13234	0.313479	0.156739	+	0.987640i	$0.449902\pi$
$674$	−21.8971	−0.843445
$675$	−2.99703	−0.115356
$676$	19.1199	0.735381
$677$	51.4609	1.97780	0.988901	−	0.148578i	$-0.0474696\pi$
$677$	51.4609	1.97780	0.988901	+	0.148578i	$0.0474696\pi$
$678$	22.0469	0.846705
$679$	24.5368	0.941637
$680$	2.62592	0.100700
$681$	−27.4771	−1.05292
$682$	39.1704	1.49991
$683$	−2.92145	−0.111786	−0.0558930	−	0.998437i	$-0.517801\pi$
$683$	−2.92145	−0.111786	−0.0558930	+	0.998437i	$0.517801\pi$
$684$	8.82688	0.337504
$685$	−0.392124	−0.0149823
$686$	14.0297	0.535657
$687$	16.6240	0.634246
$688$	−2.20220	−0.0839580
$689$	−3.64271	−0.138776
$690$	−9.58039	−0.364719
$691$	35.1316	1.33647	0.668234	−	0.743951i	$-0.267050\pi$
$691$	35.1316	1.33647	0.668234	+	0.743951i	$0.267050\pi$
$692$	−9.99615	−0.379996
$693$	35.1107	1.33375
$694$	12.6063	0.478530
$695$	4.79819	0.182006
$696$	7.78728	0.295176
$697$	38.8632	1.47205
$698$	28.4651	1.07742
$699$	39.3074	1.48674
$700$	−14.6149	−0.552391
$701$	9.01787	0.340600	0.170300	−	0.985392i	$-0.445526\pi$
$701$	9.01787	0.340600	0.170300	+	0.985392i	$0.445526\pi$
$702$	−3.56926	−0.134713
$703$	−9.61320	−0.362569
$704$	4.17695	0.157425
$705$	6.90518	0.260064
$706$	−8.69186	−0.327123
$707$	−5.18422	−0.194973
$708$	23.9289	0.899303
$709$	51.0066	1.91559	0.957796	−	0.287450i	$-0.0928074\pi$
$709$	51.0066	1.91559	0.957796	+	0.287450i	$0.0928074\pi$
$710$	5.95549	0.223506
$711$	−33.9899	−1.27472
$712$	10.1770	0.381398
$713$	76.3793	2.86043
$714$	−39.3333	−1.47201
$715$	11.6254	0.434765
$716$	−10.9214	−0.408152
$717$	−53.4242	−1.99516
$718$	−12.1148	−0.452120
$719$	−40.9282	−1.52637	−0.763183	−	0.646183i	$-0.776364\pi$
$719$	−40.9282	−1.52637	−0.763183	+	0.646183i	$0.776364\pi$
$720$	1.34415	0.0500934
$721$	−5.87211	−0.218689
$722$	8.59976	0.320050
$723$	53.7661	1.99958
$724$	3.90061	0.144965
$725$	−15.4718	−0.574608
$726$	15.4417	0.573097
$727$	23.3071	0.864413	0.432206	−	0.901775i	$-0.357735\pi$
$727$	23.3071	0.864413	0.432206	+	0.901775i	$0.357735\pi$
$728$	−17.4053	−0.645085
$729$	−22.0780	−0.817702
$730$	−4.66150	−0.172530
$731$	11.7754	0.435530
$732$	18.0484	0.667089
$733$	−32.1927	−1.18906	−0.594532	−	0.804072i	$-0.702663\pi$
$733$	−32.1927	−1.18906	−0.594532	+	0.804072i	$0.702663\pi$
$734$	32.7058	1.20719
$735$	−2.86035	−0.105506
$736$	8.14473	0.300219
$737$	39.1817	1.44328
$738$	19.8932	0.732277
$739$	−37.3545	−1.37411	−0.687053	−	0.726607i	$-0.741096\pi$
$739$	−37.3545	−1.37411	−0.687053	+	0.726607i	$0.741096\pi$
$740$	−1.46389	−0.0538136
$741$	−43.7778	−1.60822
$742$	1.97394	0.0724655
$743$	−10.6076	−0.389156	−0.194578	−	0.980887i	$-0.562334\pi$
$743$	−10.6076	−0.389156	−0.194578	+	0.980887i	$0.562334\pi$
$744$	−22.4617	−0.823488
$745$	−10.4071	−0.381287
$746$	14.0290	0.513638
$747$	11.8852	0.434858
$748$	−22.3347	−0.816636
$749$	26.9510	0.984769
$750$	−11.4790	−0.419154
$751$	−5.39998	−0.197048	−0.0985240	−	0.995135i	$-0.531412\pi$
$751$	−5.39998	−0.197048	−0.0985240	+	0.995135i	$0.531412\pi$
$752$	−5.87041	−0.214072
$753$	−48.9638	−1.78434
$754$	−18.4259	−0.671030
$755$	8.82959	0.321342
$756$	1.93413	0.0703438
$757$	40.6092	1.47597	0.737983	−	0.674819i	$-0.235778\pi$
$757$	40.6092	1.47597	0.737983	+	0.674819i	$0.235778\pi$
$758$	7.19822	0.261451
$759$	81.4856	2.95774
$760$	−1.58374	−0.0574482
$761$	2.77011	0.100417	0.0502083	−	0.998739i	$-0.484011\pi$
$761$	2.77011	0.100417	0.0502083	+	0.998739i	$0.484011\pi$
$762$	−10.1199	−0.366605
$763$	−43.5924	−1.57815
$764$	2.97007	0.107453
$765$	−7.18733	−0.259858
$766$	−6.09068	−0.220065
$767$	−56.6193	−2.04440
$768$	−2.39522	−0.0864300
$769$	−17.8199	−0.642603	−0.321301	−	0.946977i	$-0.604120\pi$
$769$	−17.8199	−0.642603	−0.321301	+	0.946977i	$0.604120\pi$
$770$	−6.29965	−0.227023
$771$	29.5071	1.06267
$772$	7.73876	0.278524
$773$	−23.3260	−0.838977	−0.419489	−	0.907761i	$-0.637791\pi$
$773$	−23.3260	−0.838977	−0.419489	+	0.907761i	$0.637791\pi$
$774$	6.02756	0.216656
$775$	44.6271	1.60305
$776$	−7.98956	−0.286808
$777$	21.9274	0.786640
$778$	16.9965	0.609355
$779$	−23.4391	−0.839792
$780$	−6.66643	−0.238697
$781$	−50.6542	−1.81255
$782$	−43.5509	−1.55738
$783$	2.04754	0.0731730
$784$	2.43171	0.0868469
$785$	−5.87048	−0.209526
$786$	11.7005	0.417345
$787$	20.2693	0.722523	0.361262	−	0.932464i	$-0.382346\pi$
$787$	20.2693	0.722523	0.361262	+	0.932464i	$0.382346\pi$
$788$	0.354426	0.0126259
$789$	−41.1466	−1.46486
$790$	6.09854	0.216976
$791$	28.2682	1.00510
$792$	−11.4326	−0.406239
$793$	−42.7053	−1.51651
$794$	32.9086	1.16788
$795$	0.756039	0.0268139
$796$	14.1460	0.501390
$797$	12.3513	0.437504	0.218752	−	0.975780i	$-0.429801\pi$
$797$	12.3513	0.437504	0.218752	+	0.975780i	$0.429801\pi$
$798$	23.7226	0.839770
$799$	31.3898	1.11049
$800$	4.75883	0.168250
$801$	−27.8550	−0.984208
$802$	24.4612	0.863754
$803$	39.6482	1.39915
$804$	−22.4683	−0.792394
$805$	−12.2838	−0.432948
$806$	53.1478	1.87205
$807$	0.633926	0.0223152
$808$	1.68806	0.0593858
$809$	19.0325	0.669148	0.334574	−	0.942369i	$-0.391408\pi$
$809$	19.0325	0.669148	0.334574	+	0.942369i	$0.391408\pi$
$810$	4.77324	0.167714
$811$	−27.9661	−0.982022	−0.491011	−	0.871153i	$-0.663373\pi$
$811$	−27.9661	−0.982022	−0.491011	+	0.871153i	$0.663373\pi$
$812$	9.98472	0.350395
$813$	22.3064	0.782321
$814$	12.4510	0.436409
$815$	−5.44704	−0.190801
$816$	12.8075	0.448353
$817$	−7.10196	−0.248466
$818$	−2.74577	−0.0960035
$819$	47.6396	1.66466
$820$	−3.56928	−0.124645
$821$	25.4108	0.886844	0.443422	−	0.896313i	$-0.353764\pi$
$821$	25.4108	0.886844	0.443422	+	0.896313i	$0.353764\pi$
$822$	−1.91252	−0.0667068
$823$	35.1045	1.22367	0.611833	−	0.790987i	$-0.290432\pi$
$823$	35.1045	1.22367	0.611833	+	0.790987i	$0.290432\pi$
$824$	1.91205	0.0666093
$825$	47.6107	1.65759
$826$	30.6812	1.06754
$827$	−33.0004	−1.14754	−0.573768	−	0.819018i	$-0.694519\pi$
$827$	−33.0004	−1.14754	−0.573768	+	0.819018i	$0.694519\pi$
$828$	−22.2927	−0.774724
$829$	9.61320	0.333880	0.166940	−	0.985967i	$-0.446611\pi$
$829$	9.61320	0.333880	0.166940	+	0.985967i	$0.446611\pi$
$830$	−2.13248	−0.0740194
$831$	28.9118	1.00294
$832$	5.66744	0.196483
$833$	−13.0027	−0.450516
$834$	23.4024	0.810360
$835$	−8.24194	−0.285224
$836$	13.4704	0.465884
$837$	−5.90595	−0.204140
$838$	12.3308	0.425959
$839$	−46.8043	−1.61587	−0.807933	−	0.589275i	$-0.799414\pi$
$839$	−46.8043	−1.61587	−0.807933	+	0.589275i	$0.799414\pi$
$840$	3.61245	0.124641
$841$	−18.4298	−0.635512
$842$	2.41067	0.0830773
$843$	48.0873	1.65621
$844$	24.6919	0.849931
$845$	9.38960	0.323012
$846$	16.0677	0.552419
$847$	19.7992	0.680307
$848$	−0.642744	−0.0220719
$849$	−79.3564	−2.72350
$850$	−25.4461	−0.872793
$851$	24.2786	0.832258
$852$	29.0470	0.995133
$853$	−23.6958	−0.811328	−0.405664	−	0.914022i	$-0.632960\pi$
$853$	−23.6958	−0.811328	−0.405664	+	0.914022i	$0.632960\pi$
$854$	23.1414	0.791883
$855$	4.33480	0.148247
$856$	−8.77566	−0.299946
$857$	33.1710	1.13310	0.566550	−	0.824027i	$-0.308278\pi$
$857$	33.1710	1.13310	0.566550	+	0.824027i	$0.308278\pi$
$858$	56.7011	1.93574
$859$	−2.65757	−0.0906751	−0.0453375	−	0.998972i	$-0.514436\pi$
$859$	−2.65757	−0.0906751	−0.0453375	+	0.998972i	$0.514436\pi$
$860$	−1.08148	−0.0368781
$861$	53.4637	1.82204
$862$	12.0286	0.409695
$863$	−36.7289	−1.25027	−0.625133	−	0.780518i	$-0.714955\pi$
$863$	−36.7289	−1.25027	−0.625133	+	0.780518i	$0.714955\pi$
$864$	−0.629784	−0.0214257
$865$	−4.90901	−0.166911
$866$	−27.1227	−0.921666
$867$	−27.7648	−0.942941
$868$	−28.8001	−0.977539
$869$	−51.8709	−1.75960
$870$	3.82426	0.129655
$871$	53.1633	1.80137
$872$	14.1944	0.480681
$873$	21.8680	0.740118
$874$	26.2663	0.888470
$875$	−14.7182	−0.497566
$876$	−22.7357	−0.768170
$877$	0.989371	0.0334087	0.0167043	−	0.999860i	$-0.494683\pi$
$877$	0.989371	0.0334087	0.0167043	+	0.999860i	$0.494683\pi$
$878$	28.9910	0.978398
$879$	−56.8903	−1.91886
$880$	2.05126	0.0691480
$881$	−27.2205	−0.917082	−0.458541	−	0.888673i	$-0.651628\pi$
$881$	−27.2205	−0.917082	−0.458541	+	0.888673i	$0.651628\pi$
$882$	−6.65576	−0.224111
$883$	24.4715	0.823530	0.411765	−	0.911290i	$-0.364912\pi$
$883$	24.4715	0.823530	0.411765	+	0.911290i	$0.364912\pi$
$884$	−30.3045	−1.01925
$885$	11.7512	0.395014
$886$	−11.4191	−0.383633
$887$	−24.1615	−0.811263	−0.405631	−	0.914037i	$-0.632948\pi$
$887$	−24.1615	−0.811263	−0.405631	+	0.914037i	$0.632948\pi$
$888$	−7.13988	−0.239599
$889$	−12.9756	−0.435186
$890$	4.99781	0.167527
$891$	−40.5986	−1.36010
$892$	−27.1716	−0.909774
$893$	−18.9317	−0.633526
$894$	−50.7591	−1.69764
$895$	−5.36340	−0.179279
$896$	−3.07111	−0.102599
$897$	110.563	3.69158
$898$	16.5317	0.551672
$899$	−30.4887	−1.01686
$900$	−13.0252	−0.434174
$901$	3.43683	0.114497
$902$	30.3583	1.01082
$903$	16.1993	0.539080
$904$	−9.20454	−0.306139
$905$	1.91555	0.0636752
$906$	43.0650	1.43074
$907$	47.7732	1.58628	0.793142	−	0.609037i	$-0.208444\pi$
$907$	47.7732	1.58628	0.793142	+	0.609037i	$0.208444\pi$
$908$	11.4716	0.380700
$909$	−4.62034	−0.153247
$910$	−8.54760	−0.283350
$911$	−40.6459	−1.34666	−0.673330	−	0.739342i	$-0.735137\pi$
$911$	−40.6459	−1.34666	−0.673330	+	0.739342i	$0.735137\pi$
$912$	−7.72443	−0.255782
$913$	18.1377	0.600270
$914$	26.9824	0.892499
$915$	8.86342	0.293016
$916$	−6.94051	−0.229321
$917$	15.0023	0.495418
$918$	3.36753	0.111145
$919$	16.1240	0.531881	0.265940	−	0.963989i	$-0.414318\pi$
$919$	16.1240	0.531881	0.265940	+	0.963989i	$0.414318\pi$
$920$	3.99980	0.131870
$921$	−22.4709	−0.740441
$922$	−16.6346	−0.547831
$923$	−68.7295	−2.26226
$924$	−30.7255	−1.01080
$925$	14.1856	0.466418
$926$	26.3819	0.866964
$927$	−5.23340	−0.171887
$928$	−3.25118	−0.106725
$929$	−3.68430	−0.120878	−0.0604390	−	0.998172i	$-0.519250\pi$
$929$	−3.68430	−0.120878	−0.0604390	+	0.998172i	$0.519250\pi$
$930$	−11.0308	−0.361713
$931$	7.84214	0.257016
$932$	−16.4108	−0.537553
$933$	12.6076	0.412756
$934$	−20.9194	−0.684504
$935$	−10.9683	−0.358703
$936$	−15.5122	−0.507031
$937$	30.4101	0.993456	0.496728	−	0.867906i	$-0.334535\pi$
$937$	30.4101	0.993456	0.496728	+	0.867906i	$0.334535\pi$
$938$	−28.8084	−0.940629
$939$	−59.6099	−1.94530
$940$	−2.88290	−0.0940299
$941$	52.1075	1.69866	0.849329	−	0.527865i	$-0.177007\pi$
$941$	52.1075	1.69866	0.849329	+	0.527865i	$0.177007\pi$
$942$	−28.6324	−0.932893
$943$	59.1964	1.92770
$944$	−9.99028	−0.325156
$945$	0.949835	0.0308981
$946$	9.19847	0.299068
$947$	2.95686	0.0960852	0.0480426	−	0.998845i	$-0.484702\pi$
$947$	2.95686	0.0960852	0.0480426	+	0.998845i	$0.484702\pi$
$948$	29.7447	0.966062
$949$	53.7962	1.74630
$950$	15.3469	0.497921
$951$	−40.4495	−1.31166
$952$	16.4216	0.532227
$953$	−25.0877	−0.812669	−0.406334	−	0.913724i	$-0.633193\pi$
$953$	−25.0877	−0.812669	−0.406334	+	0.913724i	$0.633193\pi$
$954$	1.75923	0.0569572
$955$	1.45857	0.0471983
$956$	22.3045	0.721379
$957$	−32.5271	−1.05145
$958$	−17.9881	−0.581170
$959$	−2.45220	−0.0791858
$960$	−1.17627	−0.0379639
$961$	56.9422	1.83684
$962$	16.8940	0.544685
$963$	24.0196	0.774020
$964$	−22.4473	−0.722979
$965$	3.80043	0.122340
$966$	−59.9124	−1.92765
$967$	3.29962	0.106109	0.0530543	−	0.998592i	$-0.483104\pi$
$967$	3.29962	0.106109	0.0530543	+	0.998592i	$0.483104\pi$
$968$	−6.44691	−0.207211
$969$	41.3035	1.32686
$970$	−3.92360	−0.125979
$971$	−3.20895	−0.102980	−0.0514900	−	0.998674i	$-0.516397\pi$
$971$	−3.20895	−0.102980	−0.0514900	+	0.998674i	$0.516397\pi$
$972$	21.3914	0.686128
$973$	30.0062	0.961955
$974$	−38.3070	−1.22743
$975$	64.6000	2.06885
$976$	−7.53520	−0.241196
$977$	−52.1630	−1.66884	−0.834421	−	0.551127i	$-0.814198\pi$
$977$	−52.1630	−1.66884	−0.834421	+	0.551127i	$0.814198\pi$
$978$	−26.5671	−0.849521
$979$	−42.5086	−1.35858
$980$	1.19419	0.0381471
$981$	−38.8509	−1.24041
$982$	−36.3842	−1.16107
$983$	23.5438	0.750930	0.375465	−	0.926837i	$-0.377483\pi$
$983$	23.5438	0.750930	0.375465	+	0.926837i	$0.377483\pi$
$984$	−17.4086	−0.554965
$985$	0.174055	0.00554586
$986$	17.3845	0.553634
$987$	43.1826	1.37452
$988$	18.2772	0.581474
$989$	17.9363	0.570342
$990$	−5.61444	−0.178438
$991$	20.4687	0.650211	0.325105	−	0.945678i	$-0.394600\pi$
$991$	20.4687	0.650211	0.325105	+	0.945678i	$0.394600\pi$
$992$	9.37775	0.297744
$993$	−53.5948	−1.70078
$994$	37.2436	1.18129
$995$	6.94694	0.220233
$996$	−10.4008	−0.329563
$997$	28.5292	0.903530	0.451765	−	0.892137i	$-0.350795\pi$
$997$	28.5292	0.903530	0.451765	+	0.892137i	$0.350795\pi$
$998$	−24.6930	−0.781642
$999$	−1.87732	−0.0593957

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.39522 q^{3} +1.00000 q^{4} +0.491091 q^{5} +2.39522 q^{6} +3.07111 q^{7} -1.00000 q^{8} +2.73707 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.39522 q^{3} +1.00000 q^{4} +0.491091 q^{5} +2.39522 q^{6} +3.07111 q^{7} -1.00000 q^{8} +2.73707 q^{9} -0.491091 q^{10} +4.17695 q^{11} -2.39522 q^{12} +5.66744 q^{13} -3.07111 q^{14} -1.17627 q^{15} +1.00000 q^{16} -5.34713 q^{17} -2.73707 q^{18} +3.22494 q^{19} +0.491091 q^{20} -7.35598 q^{21} -4.17695 q^{22} -8.14473 q^{23} +2.39522 q^{24} -4.75883 q^{25} -5.66744 q^{26} +0.629784 q^{27} +3.07111 q^{28} +3.25118 q^{29} +1.17627 q^{30} -9.37775 q^{31} -1.00000 q^{32} -10.0047 q^{33} +5.34713 q^{34} +1.50819 q^{35} +2.73707 q^{36} -2.98089 q^{37} -3.22494 q^{38} -13.5748 q^{39} -0.491091 q^{40} -7.26806 q^{41} +7.35598 q^{42} -2.20220 q^{43} +4.17695 q^{44} +1.34415 q^{45} +8.14473 q^{46} -5.87041 q^{47} -2.39522 q^{48} +2.43171 q^{49} +4.75883 q^{50} +12.8075 q^{51} +5.66744 q^{52} -0.642744 q^{53} -0.629784 q^{54} +2.05126 q^{55} -3.07111 q^{56} -7.72443 q^{57} -3.25118 q^{58} -9.99028 q^{59} -1.17627 q^{60} -7.53520 q^{61} +9.37775 q^{62} +8.40583 q^{63} +1.00000 q^{64} +2.78323 q^{65} +10.0047 q^{66} +9.38047 q^{67} -5.34713 q^{68} +19.5084 q^{69} -1.50819 q^{70} -12.1271 q^{71} -2.73707 q^{72} +9.49214 q^{73} +2.98089 q^{74} +11.3984 q^{75} +3.22494 q^{76} +12.8279 q^{77} +13.5748 q^{78} -12.4184 q^{79} +0.491091 q^{80} -9.71967 q^{81} +7.26806 q^{82} +4.34233 q^{83} -7.35598 q^{84} -2.62592 q^{85} +2.20220 q^{86} -7.78728 q^{87} -4.17695 q^{88} -10.1770 q^{89} -1.34415 q^{90} +17.4053 q^{91} -8.14473 q^{92} +22.4617 q^{93} +5.87041 q^{94} +1.58374 q^{95} +2.39522 q^{96} +7.98956 q^{97} -2.43171 q^{98} +11.4326 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 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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