LMFDB - Embedded newform 4006.2.a.g.1.6

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			1.6
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.30611 q^{3} +1.00000 q^{4} +3.88128 q^{5} +2.30611 q^{6} +0.245423 q^{7} -1.00000 q^{8} +2.31816 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.30611 q^{3} +1.00000 q^{4} +3.88128 q^{5} +2.30611 q^{6} +0.245423 q^{7} -1.00000 q^{8} +2.31816 q^{9} -3.88128 q^{10} -2.29954 q^{11} -2.30611 q^{12} -5.34839 q^{13} -0.245423 q^{14} -8.95067 q^{15} +1.00000 q^{16} -2.60721 q^{17} -2.31816 q^{18} +8.55592 q^{19} +3.88128 q^{20} -0.565974 q^{21} +2.29954 q^{22} +2.94694 q^{23} +2.30611 q^{24} +10.0643 q^{25} +5.34839 q^{26} +1.57240 q^{27} +0.245423 q^{28} -7.74114 q^{29} +8.95067 q^{30} -5.79274 q^{31} -1.00000 q^{32} +5.30300 q^{33} +2.60721 q^{34} +0.952555 q^{35} +2.31816 q^{36} +9.58016 q^{37} -8.55592 q^{38} +12.3340 q^{39} -3.88128 q^{40} -6.77464 q^{41} +0.565974 q^{42} +3.09940 q^{43} -2.29954 q^{44} +8.99742 q^{45} -2.94694 q^{46} -7.31928 q^{47} -2.30611 q^{48} -6.93977 q^{49} -10.0643 q^{50} +6.01252 q^{51} -5.34839 q^{52} +5.03416 q^{53} -1.57240 q^{54} -8.92516 q^{55} -0.245423 q^{56} -19.7309 q^{57} +7.74114 q^{58} -8.17961 q^{59} -8.95067 q^{60} -8.95515 q^{61} +5.79274 q^{62} +0.568930 q^{63} +1.00000 q^{64} -20.7586 q^{65} -5.30300 q^{66} -3.26763 q^{67} -2.60721 q^{68} -6.79598 q^{69} -0.952555 q^{70} +12.8152 q^{71} -2.31816 q^{72} +7.56389 q^{73} -9.58016 q^{74} -23.2094 q^{75} +8.55592 q^{76} -0.564361 q^{77} -12.3340 q^{78} +13.8552 q^{79} +3.88128 q^{80} -10.5806 q^{81} +6.77464 q^{82} -7.26049 q^{83} -0.565974 q^{84} -10.1193 q^{85} -3.09940 q^{86} +17.8519 q^{87} +2.29954 q^{88} -12.3995 q^{89} -8.99742 q^{90} -1.31262 q^{91} +2.94694 q^{92} +13.3587 q^{93} +7.31928 q^{94} +33.2079 q^{95} +2.30611 q^{96} -7.83860 q^{97} +6.93977 q^{98} -5.33070 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.30611	−1.33144	−0.665718	−	0.746204i	$-0.731874\pi$
$3$	−2.30611	−1.33144	−0.665718	+	0.746204i	$0.731874\pi$
$4$	1.00000	0.500000
$5$	3.88128	1.73576	0.867880	−	0.496774i	$-0.165482\pi$
$5$	3.88128	1.73576	0.867880	+	0.496774i	$0.165482\pi$
$6$	2.30611	0.941467
$7$	0.245423	0.0927612	0.0463806	−	0.998924i	$-0.485231\pi$
$7$	0.245423	0.0927612	0.0463806	+	0.998924i	$0.485231\pi$
$8$	−1.00000	−0.353553
$9$	2.31816	0.772720
$10$	−3.88128	−1.22737
$11$	−2.29954	−0.693338	−0.346669	−	0.937988i	$-0.612687\pi$
$11$	−2.29954	−0.693338	−0.346669	+	0.937988i	$0.612687\pi$
$12$	−2.30611	−0.665718
$13$	−5.34839	−1.48338	−0.741689	−	0.670744i	$-0.765975\pi$
$13$	−5.34839	−1.48338	−0.741689	+	0.670744i	$0.765975\pi$
$14$	−0.245423	−0.0655921
$15$	−8.95067	−2.31105
$16$	1.00000	0.250000
$17$	−2.60721	−0.632341	−0.316170	−	0.948702i	$-0.602397\pi$
$17$	−2.60721	−0.632341	−0.316170	+	0.948702i	$0.602397\pi$
$18$	−2.31816	−0.546395
$19$	8.55592	1.96286	0.981431	−	0.191816i	$-0.0614377\pi$
$19$	8.55592	1.96286	0.981431	+	0.191816i	$0.0614377\pi$
$20$	3.88128	0.867880
$21$	−0.565974	−0.123506
$22$	2.29954	0.490264
$23$	2.94694	0.614480	0.307240	−	0.951632i	$-0.400595\pi$
$23$	2.94694	0.614480	0.307240	+	0.951632i	$0.400595\pi$
$24$	2.30611	0.470733
$25$	10.0643	2.01286
$26$	5.34839	1.04891
$27$	1.57240	0.302609
$28$	0.245423	0.0463806
$29$	−7.74114	−1.43749	−0.718747	−	0.695272i	$-0.755284\pi$
$29$	−7.74114	−1.43749	−0.718747	+	0.695272i	$0.755284\pi$
$30$	8.95067	1.63416
$31$	−5.79274	−1.04041	−0.520204	−	0.854042i	$-0.674144\pi$
$31$	−5.79274	−1.04041	−0.520204	+	0.854042i	$0.674144\pi$
$32$	−1.00000	−0.176777
$33$	5.30300	0.923135
$34$	2.60721	0.447132
$35$	0.952555	0.161011
$36$	2.31816	0.386360
$37$	9.58016	1.57497	0.787484	−	0.616335i	$-0.211383\pi$
$37$	9.58016	1.57497	0.787484	+	0.616335i	$0.211383\pi$
$38$	−8.55592	−1.38795
$39$	12.3340	1.97502
$40$	−3.88128	−0.613684
$41$	−6.77464	−1.05802	−0.529010	−	0.848615i	$-0.677437\pi$
$41$	−6.77464	−1.05802	−0.529010	+	0.848615i	$0.677437\pi$
$42$	0.565974	0.0873316
$43$	3.09940	0.472654	0.236327	−	0.971674i	$-0.424056\pi$
$43$	3.09940	0.472654	0.236327	+	0.971674i	$0.424056\pi$
$44$	−2.29954	−0.346669
$45$	8.99742	1.34126
$46$	−2.94694	−0.434503
$47$	−7.31928	−1.06763	−0.533814	−	0.845602i	$-0.679242\pi$
$47$	−7.31928	−1.06763	−0.533814	+	0.845602i	$0.679242\pi$
$48$	−2.30611	−0.332859
$49$	−6.93977	−0.991395
$50$	−10.0643	−1.42331
$51$	6.01252	0.841921
$52$	−5.34839	−0.741689
$53$	5.03416	0.691495	0.345748	−	0.938328i	$-0.387625\pi$
$53$	5.03416	0.691495	0.345748	+	0.938328i	$0.387625\pi$
$54$	−1.57240	−0.213977
$55$	−8.92516	−1.20347
$56$	−0.245423	−0.0327960
$57$	−19.7309	−2.61342
$58$	7.74114	1.01646
$59$	−8.17961	−1.06489	−0.532447	−	0.846463i	$-0.678727\pi$
$59$	−8.17961	−1.06489	−0.532447	+	0.846463i	$0.678727\pi$
$60$	−8.95067	−1.15553
$61$	−8.95515	−1.14659	−0.573295	−	0.819349i	$-0.694335\pi$
$61$	−8.95515	−1.14659	−0.573295	+	0.819349i	$0.694335\pi$
$62$	5.79274	0.735679
$63$	0.568930	0.0716784
$64$	1.00000	0.125000
$65$	−20.7586	−2.57479
$66$	−5.30300	−0.652755
$67$	−3.26763	−0.399204	−0.199602	−	0.979877i	$-0.563965\pi$
$67$	−3.26763	−0.399204	−0.199602	+	0.979877i	$0.563965\pi$
$68$	−2.60721	−0.316170
$69$	−6.79598	−0.818140
$70$	−0.952555	−0.113852
$71$	12.8152	1.52088	0.760440	−	0.649408i	$-0.224983\pi$
$71$	12.8152	1.52088	0.760440	+	0.649408i	$0.224983\pi$
$72$	−2.31816	−0.273198
$73$	7.56389	0.885287	0.442643	−	0.896698i	$-0.354041\pi$
$73$	7.56389	0.885287	0.442643	+	0.896698i	$0.354041\pi$
$74$	−9.58016	−1.11367
$75$	−23.2094	−2.68000
$76$	8.55592	0.981431
$77$	−0.564361	−0.0643149
$78$	−12.3340	−1.39655
$79$	13.8552	1.55883	0.779417	−	0.626506i	$-0.215515\pi$
$79$	13.8552	1.55883	0.779417	+	0.626506i	$0.215515\pi$
$80$	3.88128	0.433940
$81$	−10.5806	−1.17562
$82$	6.77464	0.748134
$83$	−7.26049	−0.796942	−0.398471	−	0.917181i	$-0.630459\pi$
$83$	−7.26049	−0.796942	−0.398471	+	0.917181i	$0.630459\pi$
$84$	−0.565974	−0.0617528
$85$	−10.1193	−1.09759
$86$	−3.09940	−0.334217
$87$	17.8519	1.91393
$88$	2.29954	0.245132
$89$	−12.3995	−1.31434	−0.657172	−	0.753741i	$-0.728247\pi$
$89$	−12.3995	−1.31434	−0.657172	+	0.753741i	$0.728247\pi$
$90$	−8.99742	−0.948411
$91$	−1.31262	−0.137600
$92$	2.94694	0.307240
$93$	13.3587	1.38523
$94$	7.31928	0.754926
$95$	33.2079	3.40706
$96$	2.30611	0.235367
$97$	−7.83860	−0.795889	−0.397944	−	0.917409i	$-0.630276\pi$
$97$	−7.83860	−0.795889	−0.397944	+	0.917409i	$0.630276\pi$
$98$	6.93977	0.701022
$99$	−5.33070	−0.535756
$100$	10.0643	1.00643
$101$	−2.14814	−0.213748	−0.106874	−	0.994273i	$-0.534084\pi$
$101$	−2.14814	−0.213748	−0.106874	+	0.994273i	$0.534084\pi$
$102$	−6.01252	−0.595328
$103$	−9.24718	−0.911152	−0.455576	−	0.890197i	$-0.650567\pi$
$103$	−9.24718	−0.911152	−0.455576	+	0.890197i	$0.650567\pi$
$104$	5.34839	0.524453
$105$	−2.19670	−0.214376
$106$	−5.03416	−0.488961
$107$	16.7483	1.61912	0.809558	−	0.587040i	$-0.199707\pi$
$107$	16.7483	1.61912	0.809558	+	0.587040i	$0.199707\pi$
$108$	1.57240	0.151305
$109$	−13.1018	−1.25492	−0.627461	−	0.778648i	$-0.715906\pi$
$109$	−13.1018	−1.25492	−0.627461	+	0.778648i	$0.715906\pi$
$110$	8.92516	0.850981
$111$	−22.0929	−2.09697
$112$	0.245423	0.0231903
$113$	0.805981	0.0758204	0.0379102	−	0.999281i	$-0.487930\pi$
$113$	0.805981	0.0758204	0.0379102	+	0.999281i	$0.487930\pi$
$114$	19.7309	1.84797
$115$	11.4379	1.06659
$116$	−7.74114	−0.718747
$117$	−12.3984	−1.14623
$118$	8.17961	0.752994
$119$	−0.639869	−0.0586567
$120$	8.95067	0.817080
$121$	−5.71211	−0.519282
$122$	8.95515	0.810761
$123$	15.6231	1.40869
$124$	−5.79274	−0.520204
$125$	19.6560	1.75809
$126$	−0.568930	−0.0506843
$127$	−12.8644	−1.14154	−0.570768	−	0.821112i	$-0.693354\pi$
$127$	−12.8644	−1.14154	−0.570768	+	0.821112i	$0.693354\pi$
$128$	−1.00000	−0.0883883
$129$	−7.14756	−0.629308
$130$	20.7586	1.82065
$131$	1.17305	0.102489	0.0512447	−	0.998686i	$-0.483681\pi$
$131$	1.17305	0.102489	0.0512447	+	0.998686i	$0.483681\pi$
$132$	5.30300	0.461567
$133$	2.09982	0.182077
$134$	3.26763	0.282280
$135$	6.10293	0.525257
$136$	2.60721	0.223566
$137$	3.53163	0.301728	0.150864	−	0.988555i	$-0.451794\pi$
$137$	3.53163	0.301728	0.150864	+	0.988555i	$0.451794\pi$
$138$	6.79598	0.578512
$139$	−1.28089	−0.108644	−0.0543218	−	0.998523i	$-0.517300\pi$
$139$	−1.28089	−0.108644	−0.0543218	+	0.998523i	$0.517300\pi$
$140$	0.952555	0.0805056
$141$	16.8791	1.42148
$142$	−12.8152	−1.07542
$143$	12.2989	1.02848
$144$	2.31816	0.193180
$145$	−30.0455	−2.49514
$146$	−7.56389	−0.625992
$147$	16.0039	1.31998
$148$	9.58016	0.787484
$149$	11.0768	0.907446	0.453723	−	0.891143i	$-0.350096\pi$
$149$	11.0768	0.907446	0.453723	+	0.891143i	$0.350096\pi$
$150$	23.2094	1.89504
$151$	−3.83532	−0.312114	−0.156057	−	0.987748i	$-0.549878\pi$
$151$	−3.83532	−0.312114	−0.156057	+	0.987748i	$0.549878\pi$
$152$	−8.55592	−0.693976
$153$	−6.04392	−0.488622
$154$	0.564361	0.0454775
$155$	−22.4832	−1.80590
$156$	12.3340	0.987510
$157$	3.37953	0.269716	0.134858	−	0.990865i	$-0.456942\pi$
$157$	3.37953	0.269716	0.134858	+	0.990865i	$0.456942\pi$
$158$	−13.8552	−1.10226
$159$	−11.6094	−0.920681
$160$	−3.88128	−0.306842
$161$	0.723247	0.0569999
$162$	10.5806	0.831292
$163$	21.8575	1.71201	0.856004	−	0.516969i	$-0.172940\pi$
$163$	21.8575	1.71201	0.856004	+	0.516969i	$0.172940\pi$
$164$	−6.77464	−0.529010
$165$	20.5824	1.60234
$166$	7.26049	0.563523
$167$	−0.223008	−0.0172569	−0.00862843	−	0.999963i	$-0.502747\pi$
$167$	−0.223008	−0.0172569	−0.00862843	+	0.999963i	$0.502747\pi$
$168$	0.565974	0.0436658
$169$	15.6053	1.20041
$170$	10.1193	0.776114
$171$	19.8340	1.51674
$172$	3.09940	0.236327
$173$	3.38213	0.257139	0.128569	−	0.991701i	$-0.458961\pi$
$173$	3.38213	0.257139	0.128569	+	0.991701i	$0.458961\pi$
$174$	−17.8519	−1.35335
$175$	2.47002	0.186716
$176$	−2.29954	−0.173334
$177$	18.8631	1.41784
$178$	12.3995	0.929381
$179$	−17.8962	−1.33762	−0.668811	−	0.743433i	$-0.733196\pi$
$179$	−17.8962	−1.33762	−0.668811	+	0.743433i	$0.733196\pi$
$180$	8.99742	0.670628
$181$	−20.8892	−1.55268	−0.776340	−	0.630314i	$-0.782926\pi$
$181$	−20.8892	−1.55268	−0.776340	+	0.630314i	$0.782926\pi$
$182$	1.31262	0.0972978
$183$	20.6516	1.52661
$184$	−2.94694	−0.217251
$185$	37.1832	2.73377
$186$	−13.3587	−0.979509
$187$	5.99538	0.438426
$188$	−7.31928	−0.533814
$189$	0.385904	0.0280704
$190$	−33.2079	−2.40915
$191$	−19.5612	−1.41540	−0.707699	−	0.706514i	$-0.750267\pi$
$191$	−19.5612	−1.41540	−0.707699	+	0.706514i	$0.750267\pi$
$192$	−2.30611	−0.166429
$193$	−5.83600	−0.420085	−0.210042	−	0.977692i	$-0.567360\pi$
$193$	−5.83600	−0.420085	−0.210042	+	0.977692i	$0.567360\pi$
$194$	7.83860	0.562778
$195$	47.8717	3.42816
$196$	−6.93977	−0.495698
$197$	5.29845	0.377499	0.188749	−	0.982025i	$-0.439557\pi$
$197$	5.29845	0.377499	0.188749	+	0.982025i	$0.439557\pi$
$198$	5.33070	0.378837
$199$	8.35379	0.592185	0.296092	−	0.955159i	$-0.404316\pi$
$199$	8.35379	0.592185	0.296092	+	0.955159i	$0.404316\pi$
$200$	−10.0643	−0.711654
$201$	7.53552	0.531515
$202$	2.14814	0.151143
$203$	−1.89985	−0.133344
$204$	6.01252	0.420960
$205$	−26.2943	−1.83647
$206$	9.24718	0.644282
$207$	6.83148	0.474820
$208$	−5.34839	−0.370844
$209$	−19.6747	−1.36093
$210$	2.19670	0.151587
$211$	9.73855	0.670430	0.335215	−	0.942142i	$-0.391191\pi$
$211$	9.73855	0.670430	0.335215	+	0.942142i	$0.391191\pi$
$212$	5.03416	0.345748
$213$	−29.5532	−2.02495
$214$	−16.7483	−1.14489
$215$	12.0296	0.820414
$216$	−1.57240	−0.106988
$217$	−1.42167	−0.0965094
$218$	13.1018	0.887364
$219$	−17.4432	−1.17870
$220$	−8.92516	−0.601734
$221$	13.9444	0.938000
$222$	22.0929	1.48278
$223$	−18.3042	−1.22574	−0.612871	−	0.790183i	$-0.709985\pi$
$223$	−18.3042	−1.22574	−0.612871	+	0.790183i	$0.709985\pi$
$224$	−0.245423	−0.0163980
$225$	23.3307	1.55538
$226$	−0.805981	−0.0536131
$227$	−5.33077	−0.353816	−0.176908	−	0.984227i	$-0.556609\pi$
$227$	−5.33077	−0.353816	−0.176908	+	0.984227i	$0.556609\pi$
$228$	−19.7309	−1.30671
$229$	−17.6356	−1.16540	−0.582698	−	0.812689i	$-0.698003\pi$
$229$	−17.6356	−1.16540	−0.582698	+	0.812689i	$0.698003\pi$
$230$	−11.4379	−0.754192
$231$	1.30148	0.0856311
$232$	7.74114	0.508231
$233$	20.1558	1.32045	0.660226	−	0.751067i	$-0.270461\pi$
$233$	20.1558	1.32045	0.660226	+	0.751067i	$0.270461\pi$
$234$	12.3984	0.810510
$235$	−28.4082	−1.85314
$236$	−8.17961	−0.532447
$237$	−31.9517	−2.07549
$238$	0.639869	0.0414766
$239$	−20.4747	−1.32440	−0.662198	−	0.749329i	$-0.730376\pi$
$239$	−20.4747	−1.32440	−0.662198	+	0.749329i	$0.730376\pi$
$240$	−8.95067	−0.577763
$241$	12.6703	0.816167	0.408084	−	0.912945i	$-0.366197\pi$
$241$	12.6703	0.816167	0.408084	+	0.912945i	$0.366197\pi$
$242$	5.71211	0.367188
$243$	19.6829	1.26266
$244$	−8.95515	−0.573295
$245$	−26.9352	−1.72082
$246$	−15.6231	−0.996092
$247$	−45.7604	−2.91166
$248$	5.79274	0.367839
$249$	16.7435	1.06108
$250$	−19.6560	−1.24315
$251$	−13.6399	−0.860941	−0.430471	−	0.902605i	$-0.641652\pi$
$251$	−13.6399	−0.860941	−0.430471	+	0.902605i	$0.641652\pi$
$252$	0.568930	0.0358392
$253$	−6.77661	−0.426042
$254$	12.8644	0.807187
$255$	23.3362	1.46137
$256$	1.00000	0.0625000
$257$	−24.0699	−1.50144	−0.750720	−	0.660621i	$-0.770293\pi$
$257$	−24.0699	−1.50144	−0.750720	+	0.660621i	$0.770293\pi$
$258$	7.14756	0.444988
$259$	2.35119	0.146096
$260$	−20.7586	−1.28739
$261$	−17.9452	−1.11078
$262$	−1.17305	−0.0724710
$263$	27.3360	1.68561	0.842804	−	0.538221i	$-0.180903\pi$
$263$	27.3360	1.68561	0.842804	+	0.538221i	$0.180903\pi$
$264$	−5.30300	−0.326377
$265$	19.5390	1.20027
$266$	−2.09982	−0.128748
$267$	28.5946	1.74996
$268$	−3.26763	−0.199602
$269$	−32.5010	−1.98162	−0.990809	−	0.135265i	$-0.956812\pi$
$269$	−32.5010	−1.98162	−0.990809	+	0.135265i	$0.956812\pi$
$270$	−6.10293	−0.371413
$271$	−3.73702	−0.227008	−0.113504	−	0.993538i	$-0.536207\pi$
$271$	−3.73702	−0.227008	−0.113504	+	0.993538i	$0.536207\pi$
$272$	−2.60721	−0.158085
$273$	3.02705	0.183205
$274$	−3.53163	−0.213354
$275$	−23.1433	−1.39559
$276$	−6.79598	−0.409070
$277$	10.3068	0.619275	0.309638	−	0.950855i	$-0.399792\pi$
$277$	10.3068	0.619275	0.309638	+	0.950855i	$0.399792\pi$
$278$	1.28089	0.0768226
$279$	−13.4285	−0.803943
$280$	−0.952555	−0.0569261
$281$	−14.2098	−0.847687	−0.423843	−	0.905736i	$-0.639319\pi$
$281$	−14.2098	−0.847687	−0.423843	+	0.905736i	$0.639319\pi$
$282$	−16.8791	−1.00514
$283$	21.5215	1.27932	0.639660	−	0.768658i	$-0.279075\pi$
$283$	21.5215	1.27932	0.639660	+	0.768658i	$0.279075\pi$
$284$	12.8152	0.760440
$285$	−76.5811	−4.53628
$286$	−12.2989	−0.727246
$287$	−1.66265	−0.0981433
$288$	−2.31816	−0.136599
$289$	−10.2025	−0.600145
$290$	30.0455	1.76433
$291$	18.0767	1.05967
$292$	7.56389	0.442643
$293$	−4.58164	−0.267662	−0.133831	−	0.991004i	$-0.542728\pi$
$293$	−4.58164	−0.267662	−0.133831	+	0.991004i	$0.542728\pi$
$294$	−16.0039	−0.933366
$295$	−31.7473	−1.84840
$296$	−9.58016	−0.556835
$297$	−3.61581	−0.209810
$298$	−11.0768	−0.641661
$299$	−15.7614	−0.911505
$300$	−23.2094	−1.34000
$301$	0.760664	0.0438440
$302$	3.83532	0.220698
$303$	4.95385	0.284591
$304$	8.55592	0.490715
$305$	−34.7574	−1.99020
$306$	6.04392	0.345508
$307$	−29.3783	−1.67671	−0.838355	−	0.545125i	$-0.816482\pi$
$307$	−29.3783	−1.67671	−0.838355	+	0.545125i	$0.816482\pi$
$308$	−0.564361	−0.0321574
$309$	21.3251	1.21314
$310$	22.4832	1.27696
$311$	7.10079	0.402649	0.201324	−	0.979525i	$-0.435475\pi$
$311$	7.10079	0.402649	0.201324	+	0.979525i	$0.435475\pi$
$312$	−12.3340	−0.698275
$313$	1.74949	0.0988872	0.0494436	−	0.998777i	$-0.484255\pi$
$313$	1.74949	0.0988872	0.0494436	+	0.998777i	$0.484255\pi$
$314$	−3.37953	−0.190718
$315$	2.20817	0.124417
$316$	13.8552	0.779417
$317$	−24.5895	−1.38108	−0.690542	−	0.723292i	$-0.742628\pi$
$317$	−24.5895	−1.38108	−0.690542	+	0.723292i	$0.742628\pi$
$318$	11.6094	0.651020
$319$	17.8011	0.996669
$320$	3.88128	0.216970
$321$	−38.6234	−2.15575
$322$	−0.723247	−0.0403050
$323$	−22.3070	−1.24120
$324$	−10.5806	−0.587812
$325$	−53.8279	−2.98583
$326$	−21.8575	−1.21057
$327$	30.2142	1.67085
$328$	6.77464	0.374067
$329$	−1.79632	−0.0990344
$330$	−20.5824	−1.13303
$331$	−1.60774	−0.0883692	−0.0441846	−	0.999023i	$-0.514069\pi$
$331$	−1.60774	−0.0883692	−0.0441846	+	0.999023i	$0.514069\pi$
$332$	−7.26049	−0.398471
$333$	22.2083	1.21701
$334$	0.223008	0.0122024
$335$	−12.6826	−0.692923
$336$	−0.565974	−0.0308764
$337$	20.8938	1.13816	0.569080	−	0.822282i	$-0.307299\pi$
$337$	20.8938	1.13816	0.569080	+	0.822282i	$0.307299\pi$
$338$	−15.6053	−0.848816
$339$	−1.85868	−0.100950
$340$	−10.1193	−0.548796
$341$	13.3207	0.721354
$342$	−19.8340	−1.07250
$343$	−3.42114	−0.184724
$344$	−3.09940	−0.167108
$345$	−26.3771	−1.42009
$346$	−3.38213	−0.181825
$347$	−3.34010	−0.179306	−0.0896529	−	0.995973i	$-0.528576\pi$
$347$	−3.34010	−0.179306	−0.0896529	+	0.995973i	$0.528576\pi$
$348$	17.8519	0.956965
$349$	1.62440	0.0869522	0.0434761	−	0.999054i	$-0.486157\pi$
$349$	1.62440	0.0869522	0.0434761	+	0.999054i	$0.486157\pi$
$350$	−2.47002	−0.132028
$351$	−8.40983	−0.448883
$352$	2.29954	0.122566
$353$	−33.8642	−1.80241	−0.901206	−	0.433391i	$-0.857317\pi$
$353$	−33.8642	−1.80241	−0.901206	+	0.433391i	$0.857317\pi$
$354$	−18.8631	−1.00256
$355$	49.7392	2.63988
$356$	−12.3995	−0.657172
$357$	1.47561	0.0780976
$358$	17.8962	0.945842
$359$	−12.7402	−0.672400	−0.336200	−	0.941791i	$-0.609142\pi$
$359$	−12.7402	−0.672400	−0.336200	+	0.941791i	$0.609142\pi$
$360$	−8.99742	−0.474206
$361$	54.2037	2.85283
$362$	20.8892	1.09791
$363$	13.1728	0.691391
$364$	−1.31262	−0.0687999
$365$	29.3576	1.53664
$366$	−20.6516	−1.07948
$367$	27.2995	1.42502	0.712511	−	0.701661i	$-0.247558\pi$
$367$	27.2995	1.42502	0.712511	+	0.701661i	$0.247558\pi$
$368$	2.94694	0.153620
$369$	−15.7047	−0.817553
$370$	−37.1832	−1.93306
$371$	1.23550	0.0641440
$372$	13.3587	0.692617
$373$	−12.3032	−0.637036	−0.318518	−	0.947917i	$-0.603185\pi$
$373$	−12.3032	−0.637036	−0.318518	+	0.947917i	$0.603185\pi$
$374$	−5.99538	−0.310014
$375$	−45.3290	−2.34078
$376$	7.31928	0.377463
$377$	41.4026	2.13234
$378$	−0.385904	−0.0198488
$379$	28.5227	1.46511	0.732555	−	0.680708i	$-0.238328\pi$
$379$	28.5227	1.46511	0.732555	+	0.680708i	$0.238328\pi$
$380$	33.2079	1.70353
$381$	29.6669	1.51988
$382$	19.5612	1.00084
$383$	16.0293	0.819057	0.409528	−	0.912297i	$-0.365693\pi$
$383$	16.0293	0.819057	0.409528	+	0.912297i	$0.365693\pi$
$384$	2.30611	0.117683
$385$	−2.19044	−0.111635
$386$	5.83600	0.297045
$387$	7.18490	0.365229
$388$	−7.83860	−0.397944
$389$	−24.6747	−1.25106	−0.625529	−	0.780201i	$-0.715117\pi$
$389$	−24.6747	−1.25106	−0.625529	+	0.780201i	$0.715117\pi$
$390$	−47.8717	−2.42408
$391$	−7.68329	−0.388560
$392$	6.93977	0.350511
$393$	−2.70518	−0.136458
$394$	−5.29845	−0.266932
$395$	53.7759	2.70576
$396$	−5.33070	−0.267878
$397$	−16.4833	−0.827275	−0.413638	−	0.910442i	$-0.635742\pi$
$397$	−16.4833	−0.827275	−0.413638	+	0.910442i	$0.635742\pi$
$398$	−8.35379	−0.418738
$399$	−4.84242	−0.242424
$400$	10.0643	0.503216
$401$	6.14759	0.306996	0.153498	−	0.988149i	$-0.450946\pi$
$401$	6.14759	0.306996	0.153498	+	0.988149i	$0.450946\pi$
$402$	−7.53552	−0.375838
$403$	30.9819	1.54332
$404$	−2.14814	−0.106874
$405$	−41.0663	−2.04060
$406$	1.89985	0.0942882
$407$	−22.0300	−1.09199
$408$	−6.01252	−0.297664
$409$	5.18329	0.256297	0.128149	−	0.991755i	$-0.459097\pi$
$409$	5.18329	0.256297	0.128149	+	0.991755i	$0.459097\pi$
$410$	26.2943	1.29858
$411$	−8.14435	−0.401731
$412$	−9.24718	−0.455576
$413$	−2.00746	−0.0987809
$414$	−6.83148	−0.335749
$415$	−28.1800	−1.38330
$416$	5.34839	0.262226
$417$	2.95387	0.144652
$418$	19.6747	0.962320
$419$	−24.2792	−1.18611	−0.593057	−	0.805160i	$-0.702079\pi$
$419$	−24.2792	−1.18611	−0.593057	+	0.805160i	$0.702079\pi$
$420$	−2.19670	−0.107188
$421$	−39.2970	−1.91522	−0.957609	−	0.288071i	$-0.906986\pi$
$421$	−39.2970	−1.91522	−0.957609	+	0.288071i	$0.906986\pi$
$422$	−9.73855	−0.474065
$423$	−16.9673	−0.824976
$424$	−5.03416	−0.244481
$425$	−26.2398	−1.27281
$426$	29.5532	1.43186
$427$	−2.19780	−0.106359
$428$	16.7483	0.809558
$429$	−28.3625	−1.36936
$430$	−12.0296	−0.580120
$431$	6.91347	0.333010	0.166505	−	0.986041i	$-0.446752\pi$
$431$	6.91347	0.333010	0.166505	+	0.986041i	$0.446752\pi$
$432$	1.57240	0.0756523
$433$	13.6592	0.656420	0.328210	−	0.944605i	$-0.393555\pi$
$433$	13.6592	0.656420	0.328210	+	0.944605i	$0.393555\pi$
$434$	1.42167	0.0682425
$435$	69.2883	3.32212
$436$	−13.1018	−0.627461
$437$	25.2138	1.20614
$438$	17.4432	0.833468
$439$	25.1355	1.19965	0.599825	−	0.800131i	$-0.295237\pi$
$439$	25.1355	1.19965	0.599825	+	0.800131i	$0.295237\pi$
$440$	8.92516	0.425490
$441$	−16.0875	−0.766071
$442$	−13.9444	−0.663266
$443$	10.0652	0.478212	0.239106	−	0.970993i	$-0.423146\pi$
$443$	10.0652	0.478212	0.239106	+	0.970993i	$0.423146\pi$
$444$	−22.0929	−1.04848
$445$	−48.1259	−2.28139
$446$	18.3042	0.866730
$447$	−25.5443	−1.20820
$448$	0.245423	0.0115952
$449$	6.76853	0.319426	0.159713	−	0.987163i	$-0.448943\pi$
$449$	6.76853	0.319426	0.159713	+	0.987163i	$0.448943\pi$
$450$	−23.3307	−1.09982
$451$	15.5786	0.733566
$452$	0.805981	0.0379102
$453$	8.84469	0.415560
$454$	5.33077	0.250185
$455$	−5.09464	−0.238840
$456$	19.7309	0.923985
$457$	−32.9685	−1.54220	−0.771100	−	0.636714i	$-0.780293\pi$
$457$	−32.9685	−1.54220	−0.771100	+	0.636714i	$0.780293\pi$
$458$	17.6356	0.824059
$459$	−4.09958	−0.191352
$460$	11.4379	0.533295
$461$	13.2362	0.616472	0.308236	−	0.951310i	$-0.400261\pi$
$461$	13.2362	0.616472	0.308236	+	0.951310i	$0.400261\pi$
$462$	−1.30148	−0.0605503
$463$	−33.6467	−1.56369	−0.781846	−	0.623471i	$-0.785722\pi$
$463$	−33.6467	−1.56369	−0.781846	+	0.623471i	$0.785722\pi$
$464$	−7.74114	−0.359373
$465$	51.8489	2.40443
$466$	−20.1558	−0.933700
$467$	−26.2198	−1.21331	−0.606654	−	0.794966i	$-0.707489\pi$
$467$	−26.2198	−1.21331	−0.606654	+	0.794966i	$0.707489\pi$
$468$	−12.3984	−0.573117
$469$	−0.801952	−0.0370307
$470$	28.4082	1.31037
$471$	−7.79359	−0.359110
$472$	8.17961	0.376497
$473$	−7.12720	−0.327709
$474$	31.9517	1.46759
$475$	86.1094	3.95097
$476$	−0.639869	−0.0293284
$477$	11.6700	0.534332
$478$	20.4747	0.936489
$479$	17.1251	0.782467	0.391234	−	0.920291i	$-0.372048\pi$
$479$	17.1251	0.782467	0.391234	+	0.920291i	$0.372048\pi$
$480$	8.95067	0.408540
$481$	−51.2384	−2.33627
$482$	−12.6703	−0.577117
$483$	−1.66789	−0.0758917
$484$	−5.71211	−0.259641
$485$	−30.4238	−1.38147
$486$	−19.6829	−0.892834
$487$	−41.8693	−1.89728	−0.948640	−	0.316358i	$-0.897540\pi$
$487$	−41.8693	−1.89728	−0.948640	+	0.316358i	$0.897540\pi$
$488$	8.95515	0.405381
$489$	−50.4058	−2.27943
$490$	26.9352	1.21681
$491$	9.28697	0.419115	0.209558	−	0.977796i	$-0.432798\pi$
$491$	9.28697	0.419115	0.209558	+	0.977796i	$0.432798\pi$
$492$	15.6231	0.704343
$493$	20.1828	0.908986
$494$	45.7604	2.05886
$495$	−20.6899	−0.929944
$496$	−5.79274	−0.260102
$497$	3.14514	0.141079
$498$	−16.7435	−0.750295
$499$	15.5818	0.697539	0.348769	−	0.937209i	$-0.386600\pi$
$499$	15.5818	0.697539	0.348769	+	0.937209i	$0.386600\pi$
$500$	19.6560	0.879043
$501$	0.514281	0.0229764
$502$	13.6399	0.608778
$503$	−17.0783	−0.761485	−0.380742	−	0.924681i	$-0.624332\pi$
$503$	−17.0783	−0.761485	−0.380742	+	0.924681i	$0.624332\pi$
$504$	−0.568930	−0.0253421
$505$	−8.33752	−0.371015
$506$	6.77661	0.301257
$507$	−35.9876	−1.59826
$508$	−12.8644	−0.570768
$509$	−30.8133	−1.36577	−0.682887	−	0.730524i	$-0.739276\pi$
$509$	−30.8133	−1.36577	−0.682887	+	0.730524i	$0.739276\pi$
$510$	−23.3362	−1.03335
$511$	1.85635	0.0821203
$512$	−1.00000	−0.0441942
$513$	13.4533	0.593980
$514$	24.0699	1.06168
$515$	−35.8909	−1.58154
$516$	−7.14756	−0.314654
$517$	16.8310	0.740227
$518$	−2.35119	−0.103305
$519$	−7.79959	−0.342364
$520$	20.7586	0.910324
$521$	25.6533	1.12389	0.561945	−	0.827175i	$-0.310053\pi$
$521$	25.6533	1.12389	0.561945	+	0.827175i	$0.310053\pi$
$522$	17.9452	0.785440
$523$	−10.6299	−0.464812	−0.232406	−	0.972619i	$-0.574660\pi$
$523$	−10.6299	−0.464812	−0.232406	+	0.972619i	$0.574660\pi$
$524$	1.17305	0.0512447
$525$	−5.69614	−0.248600
$526$	−27.3360	−1.19190
$527$	15.1029	0.657892
$528$	5.30300	0.230784
$529$	−14.3155	−0.622415
$530$	−19.5390	−0.848719
$531$	−18.9616	−0.822864
$532$	2.09982	0.0910387
$533$	36.2334	1.56944
$534$	−28.5946	−1.23741
$535$	65.0046	2.81040
$536$	3.26763	0.141140
$537$	41.2706	1.78096
$538$	32.5010	1.40122
$539$	15.9583	0.687372
$540$	6.10293	0.262628
$541$	29.3934	1.26372	0.631860	−	0.775082i	$-0.282292\pi$
$541$	29.3934	1.26372	0.631860	+	0.775082i	$0.282292\pi$
$542$	3.73702	0.160519
$543$	48.1728	2.06729
$544$	2.60721	0.111783
$545$	−50.8516	−2.17824
$546$	−3.02705	−0.129546
$547$	−42.8685	−1.83292	−0.916462	−	0.400121i	$-0.868968\pi$
$547$	−42.8685	−1.83292	−0.916462	+	0.400121i	$0.868968\pi$
$548$	3.53163	0.150864
$549$	−20.7595	−0.885992
$550$	23.1433	0.986834
$551$	−66.2325	−2.82160
$552$	6.79598	0.289256
$553$	3.40039	0.144599
$554$	−10.3068	−0.437894
$555$	−85.7488	−3.63983
$556$	−1.28089	−0.0543218
$557$	8.46717	0.358765	0.179383	−	0.983779i	$-0.442590\pi$
$557$	8.46717	0.358765	0.179383	+	0.983779i	$0.442590\pi$
$558$	13.4285	0.568473
$559$	−16.5768	−0.701124
$560$	0.952555	0.0402528
$561$	−13.8260	−0.583736
$562$	14.2098	0.599405
$563$	−34.7945	−1.46641	−0.733206	−	0.680006i	$-0.761977\pi$
$563$	−34.7945	−1.46641	−0.733206	+	0.680006i	$0.761977\pi$
$564$	16.8791	0.710738
$565$	3.12824	0.131606
$566$	−21.5215	−0.904616
$567$	−2.59673	−0.109052
$568$	−12.8152	−0.537712
$569$	−32.1547	−1.34799	−0.673997	−	0.738734i	$-0.735424\pi$
$569$	−32.1547	−1.34799	−0.673997	+	0.738734i	$0.735424\pi$
$570$	76.5811	3.20763
$571$	10.2750	0.429997	0.214998	−	0.976614i	$-0.431025\pi$
$571$	10.2750	0.429997	0.214998	+	0.976614i	$0.431025\pi$
$572$	12.2989	0.514241
$573$	45.1103	1.88451
$574$	1.66265	0.0693978
$575$	29.6589	1.23686
$576$	2.31816	0.0965899
$577$	8.88109	0.369725	0.184862	−	0.982764i	$-0.440816\pi$
$577$	8.88109	0.369725	0.184862	+	0.982764i	$0.440816\pi$
$578$	10.2025	0.424367
$579$	13.4585	0.559316
$580$	−30.0455	−1.24757
$581$	−1.78189	−0.0739253
$582$	−18.0767	−0.749303
$583$	−11.5763	−0.479440
$584$	−7.56389	−0.312996
$585$	−48.1217	−1.98959
$586$	4.58164	0.189266
$587$	−4.48726	−0.185209	−0.0926044	−	0.995703i	$-0.529519\pi$
$587$	−4.48726	−0.185209	−0.0926044	+	0.995703i	$0.529519\pi$
$588$	16.0039	0.659989
$589$	−49.5622	−2.04218
$590$	31.7473	1.30702
$591$	−12.2188	−0.502615
$592$	9.58016	0.393742
$593$	−21.6360	−0.888486	−0.444243	−	0.895906i	$-0.646527\pi$
$593$	−21.6360	−0.888486	−0.444243	+	0.895906i	$0.646527\pi$
$594$	3.61581	0.148358
$595$	−2.48351	−0.101814
$596$	11.0768	0.453723
$597$	−19.2648	−0.788456
$598$	15.7614	0.644531
$599$	24.4527	0.999110	0.499555	−	0.866282i	$-0.333497\pi$
$599$	24.4527	0.999110	0.499555	+	0.866282i	$0.333497\pi$
$600$	23.2094	0.947522
$601$	0.0653259	0.00266470	0.00133235	−	0.999999i	$-0.499576\pi$
$601$	0.0653259	0.00266470	0.00133235	+	0.999999i	$0.499576\pi$
$602$	−0.760664	−0.0310024
$603$	−7.57488	−0.308473
$604$	−3.83532	−0.156057
$605$	−22.1703	−0.901350
$606$	−4.95385	−0.201236
$607$	34.2157	1.38877	0.694386	−	0.719602i	$-0.255676\pi$
$607$	34.2157	1.38877	0.694386	+	0.719602i	$0.255676\pi$
$608$	−8.55592	−0.346988
$609$	4.38128	0.177538
$610$	34.7574	1.40729
$611$	39.1464	1.58369
$612$	−6.04392	−0.244311
$613$	−20.4991	−0.827952	−0.413976	−	0.910288i	$-0.635860\pi$
$613$	−20.4991	−0.827952	−0.413976	+	0.910288i	$0.635860\pi$
$614$	29.3783	1.18561
$615$	60.6375	2.44514
$616$	0.564361	0.0227387
$617$	−4.26274	−0.171612	−0.0858058	−	0.996312i	$-0.527346\pi$
$617$	−4.26274	−0.171612	−0.0858058	+	0.996312i	$0.527346\pi$
$618$	−21.3251	−0.857819
$619$	−8.01079	−0.321981	−0.160990	−	0.986956i	$-0.551469\pi$
$619$	−8.01079	−0.321981	−0.160990	+	0.986956i	$0.551469\pi$
$620$	−22.4832	−0.902948
$621$	4.63378	0.185947
$622$	−7.10079	−0.284716
$623$	−3.04312	−0.121920
$624$	12.3340	0.493755
$625$	25.9688	1.03875
$626$	−1.74949	−0.0699238
$627$	45.3721	1.81199
$628$	3.37953	0.134858
$629$	−24.9775	−0.995916
$630$	−2.20817	−0.0879758
$631$	15.8989	0.632923	0.316462	−	0.948605i	$-0.397505\pi$
$631$	15.8989	0.632923	0.316462	+	0.948605i	$0.397505\pi$
$632$	−13.8552	−0.551131
$633$	−22.4582	−0.892634
$634$	24.5895	0.976575
$635$	−49.9305	−1.98143
$636$	−11.6094	−0.460341
$637$	37.1166	1.47061
$638$	−17.8011	−0.704751
$639$	29.7076	1.17521
$640$	−3.88128	−0.153421
$641$	3.74559	0.147942	0.0739710	−	0.997260i	$-0.476433\pi$
$641$	3.74559	0.147942	0.0739710	+	0.997260i	$0.476433\pi$
$642$	38.6234	1.52434
$643$	18.7864	0.740862	0.370431	−	0.928860i	$-0.379210\pi$
$643$	18.7864	0.740862	0.370431	+	0.928860i	$0.379210\pi$
$644$	0.723247	0.0284999
$645$	−27.7417	−1.09233
$646$	22.3070	0.877659
$647$	−11.8241	−0.464853	−0.232426	−	0.972614i	$-0.574666\pi$
$647$	−11.8241	−0.464853	−0.232426	+	0.972614i	$0.574666\pi$
$648$	10.5806	0.415646
$649$	18.8093	0.738332
$650$	53.8279	2.11130
$651$	3.27854	0.128496
$652$	21.8575	0.856004
$653$	−18.5143	−0.724522	−0.362261	−	0.932077i	$-0.617995\pi$
$653$	−18.5143	−0.724522	−0.362261	+	0.932077i	$0.617995\pi$
$654$	−30.2142	−1.18147
$655$	4.55292	0.177897
$656$	−6.77464	−0.264505
$657$	17.5343	0.684078
$658$	1.79632	0.0700279
$659$	46.8917	1.82664	0.913321	−	0.407239i	$-0.133509\pi$
$659$	46.8917	1.82664	0.913321	+	0.407239i	$0.133509\pi$
$660$	20.5824	0.801170
$661$	8.68656	0.337868	0.168934	−	0.985627i	$-0.445968\pi$
$661$	8.68656	0.337868	0.168934	+	0.985627i	$0.445968\pi$
$662$	1.60774	0.0624864
$663$	−32.1573	−1.24889
$664$	7.26049	0.281762
$665$	8.14998	0.316043
$666$	−22.2083	−0.860555
$667$	−22.8127	−0.883310
$668$	−0.223008	−0.00862843
$669$	42.2116	1.63200
$670$	12.6826	0.489970
$671$	20.5927	0.794974
$672$	0.565974	0.0218329
$673$	−12.5334	−0.483128	−0.241564	−	0.970385i	$-0.577660\pi$
$673$	−12.5334	−0.483128	−0.241564	+	0.970385i	$0.577660\pi$
$674$	−20.8938	−0.804801
$675$	15.8252	0.609111
$676$	15.6053	0.600204
$677$	9.80719	0.376921	0.188460	−	0.982081i	$-0.439650\pi$
$677$	9.80719	0.376921	0.188460	+	0.982081i	$0.439650\pi$
$678$	1.85868	0.0713823
$679$	−1.92377	−0.0738276
$680$	10.1193	0.388057
$681$	12.2934	0.471083
$682$	−13.3207	−0.510074
$683$	12.9680	0.496205	0.248103	−	0.968734i	$-0.420193\pi$
$683$	12.9680	0.496205	0.248103	+	0.968734i	$0.420193\pi$
$684$	19.8340	0.758371
$685$	13.7072	0.523727
$686$	3.42114	0.130620
$687$	40.6698	1.55165
$688$	3.09940	0.118163
$689$	−26.9247	−1.02575
$690$	26.3771	1.00416
$691$	−38.8397	−1.47753	−0.738765	−	0.673963i	$-0.764591\pi$
$691$	−38.8397	−1.47753	−0.738765	+	0.673963i	$0.764591\pi$
$692$	3.38213	0.128569
$693$	−1.30828	−0.0496974
$694$	3.34010	0.126788
$695$	−4.97148	−0.188579
$696$	−17.8519	−0.676676
$697$	17.6629	0.669030
$698$	−1.62440	−0.0614845
$699$	−46.4816	−1.75809
$700$	2.47002	0.0933578
$701$	−28.6510	−1.08213	−0.541067	−	0.840980i	$-0.681979\pi$
$701$	−28.6510	−1.08213	−0.541067	+	0.840980i	$0.681979\pi$
$702$	8.40983	0.317409
$703$	81.9670	3.09144
$704$	−2.29954	−0.0866672
$705$	65.5125	2.46734
$706$	33.8642	1.27450
$707$	−0.527203	−0.0198275
$708$	18.8631	0.708919
$709$	34.3459	1.28989	0.644943	−	0.764230i	$-0.276881\pi$
$709$	34.3459	1.28989	0.644943	+	0.764230i	$0.276881\pi$
$710$	−49.7392	−1.86668
$711$	32.1186	1.20454
$712$	12.3995	0.464691
$713$	−17.0709	−0.639309
$714$	−1.47561	−0.0552233
$715$	47.7353	1.78520
$716$	−17.8962	−0.668811
$717$	47.2169	1.76335
$718$	12.7402	0.475458
$719$	−22.7182	−0.847247	−0.423624	−	0.905838i	$-0.639242\pi$
$719$	−22.7182	−0.847247	−0.423624	+	0.905838i	$0.639242\pi$
$720$	8.99742	0.335314
$721$	−2.26947	−0.0845196
$722$	−54.2037	−2.01725
$723$	−29.2192	−1.08667
$724$	−20.8892	−0.776340
$725$	−77.9092	−2.89348
$726$	−13.1728	−0.488887
$727$	46.4425	1.72246	0.861229	−	0.508217i	$-0.169695\pi$
$727$	46.4425	1.72246	0.861229	+	0.508217i	$0.169695\pi$
$728$	1.31262	0.0486489
$729$	−13.6491	−0.505523
$730$	−29.3576	−1.08657
$731$	−8.08078	−0.298878
$732$	20.6516	0.763305
$733$	19.4013	0.716604	0.358302	−	0.933606i	$-0.383356\pi$
$733$	19.4013	0.716604	0.358302	+	0.933606i	$0.383356\pi$
$734$	−27.2995	−1.00764
$735$	62.1155	2.29117
$736$	−2.94694	−0.108626
$737$	7.51405	0.276783
$738$	15.7047	0.578098
$739$	−22.5901	−0.830989	−0.415495	−	0.909596i	$-0.636391\pi$
$739$	−22.5901	−0.830989	−0.415495	+	0.909596i	$0.636391\pi$
$740$	37.1832	1.36688
$741$	105.529	3.87669
$742$	−1.23550	−0.0453566
$743$	−17.9253	−0.657614	−0.328807	−	0.944397i	$-0.606647\pi$
$743$	−17.9253	−0.657614	−0.328807	+	0.944397i	$0.606647\pi$
$744$	−13.3587	−0.489754
$745$	42.9921	1.57511
$746$	12.3032	0.450453
$747$	−16.8310	−0.615813
$748$	5.99538	0.219213
$749$	4.11041	0.150191
$750$	45.3290	1.65518
$751$	−7.23733	−0.264094	−0.132047	−	0.991243i	$-0.542155\pi$
$751$	−7.23733	−0.264094	−0.132047	+	0.991243i	$0.542155\pi$
$752$	−7.31928	−0.266907
$753$	31.4551	1.14629
$754$	−41.4026	−1.50780
$755$	−14.8860	−0.541755
$756$	0.385904	0.0140352
$757$	14.5203	0.527749	0.263874	−	0.964557i	$-0.415000\pi$
$757$	14.5203	0.527749	0.263874	+	0.964557i	$0.415000\pi$
$758$	−28.5227	−1.03599
$759$	15.6276	0.567247
$760$	−33.2079	−1.20458
$761$	41.1224	1.49069	0.745343	−	0.666681i	$-0.232286\pi$
$761$	41.1224	1.49069	0.745343	+	0.666681i	$0.232286\pi$
$762$	−29.6669	−1.07472
$763$	−3.21548	−0.116408
$764$	−19.5612	−0.707699
$765$	−23.4581	−0.848131
$766$	−16.0293	−0.579160
$767$	43.7477	1.57964
$768$	−2.30611	−0.0832147
$769$	−18.2255	−0.657227	−0.328614	−	0.944464i	$-0.606581\pi$
$769$	−18.2255	−0.657227	−0.328614	+	0.944464i	$0.606581\pi$
$770$	2.19044	0.0789380
$771$	55.5079	1.99907
$772$	−5.83600	−0.210042
$773$	9.89491	0.355895	0.177948	−	0.984040i	$-0.443054\pi$
$773$	9.89491	0.355895	0.177948	+	0.984040i	$0.443054\pi$
$774$	−7.18490	−0.258256
$775$	−58.3000	−2.09420
$776$	7.83860	0.281389
$777$	−5.42212	−0.194517
$778$	24.6747	0.884632
$779$	−57.9632	−2.07675
$780$	47.8717	1.71408
$781$	−29.4690	−1.05448
$782$	7.68329	0.274754
$783$	−12.1722	−0.434999
$784$	−6.93977	−0.247849
$785$	13.1169	0.468163
$786$	2.70518	0.0964905
$787$	−26.8624	−0.957540	−0.478770	−	0.877940i	$-0.658917\pi$
$787$	−26.8624	−0.957540	−0.478770	+	0.877940i	$0.658917\pi$
$788$	5.29845	0.188749
$789$	−63.0398	−2.24428
$790$	−53.7759	−1.91326
$791$	0.197807	0.00703319
$792$	5.33070	0.189418
$793$	47.8957	1.70082
$794$	16.4833	0.584972
$795$	−45.0591	−1.59808
$796$	8.35379	0.296092
$797$	−34.4149	−1.21904	−0.609518	−	0.792772i	$-0.708637\pi$
$797$	−34.4149	−1.21904	−0.609518	+	0.792772i	$0.708637\pi$
$798$	4.84242	0.171420
$799$	19.0829	0.675104
$800$	−10.0643	−0.355827
$801$	−28.7440	−1.01562
$802$	−6.14759	−0.217079
$803$	−17.3935	−0.613803
$804$	7.53552	0.265757
$805$	2.80712	0.0989381
$806$	−30.9819	−1.09129
$807$	74.9509	2.63840
$808$	2.14814	0.0755713
$809$	14.2937	0.502541	0.251270	−	0.967917i	$-0.419152\pi$
$809$	14.2937	0.502541	0.251270	+	0.967917i	$0.419152\pi$
$810$	41.0663	1.44292
$811$	36.8290	1.29324	0.646620	−	0.762812i	$-0.276182\pi$
$811$	36.8290	1.29324	0.646620	+	0.762812i	$0.276182\pi$
$812$	−1.89985	−0.0666718
$813$	8.61800	0.302246
$814$	22.0300	0.772150
$815$	84.8349	2.97164
$816$	6.01252	0.210480
$817$	26.5182	0.927754
$818$	−5.18329	−0.181230
$819$	−3.04286	−0.106326
$820$	−26.2943	−0.918235
$821$	24.3840	0.851008	0.425504	−	0.904957i	$-0.360097\pi$
$821$	24.3840	0.851008	0.425504	+	0.904957i	$0.360097\pi$
$822$	8.14435	0.284067
$823$	−56.9478	−1.98507	−0.992537	−	0.121943i	$-0.961087\pi$
$823$	−56.9478	−1.98507	−0.992537	+	0.121943i	$0.961087\pi$
$824$	9.24718	0.322141
$825$	53.3711	1.85814
$826$	2.00746	0.0698486
$827$	−23.0295	−0.800814	−0.400407	−	0.916337i	$-0.631131\pi$
$827$	−23.0295	−0.800814	−0.400407	+	0.916337i	$0.631131\pi$
$828$	6.83148	0.237410
$829$	11.1243	0.386364	0.193182	−	0.981163i	$-0.438119\pi$
$829$	11.1243	0.386364	0.193182	+	0.981163i	$0.438119\pi$
$830$	28.1800	0.978141
$831$	−23.7686	−0.824525
$832$	−5.34839	−0.185422
$833$	18.0934	0.626900
$834$	−2.95387	−0.102284
$835$	−0.865555	−0.0299538
$836$	−19.6747	−0.680463
$837$	−9.10852	−0.314837
$838$	24.2792	0.838710
$839$	−27.2044	−0.939199	−0.469599	−	0.882880i	$-0.655602\pi$
$839$	−27.2044	−0.939199	−0.469599	+	0.882880i	$0.655602\pi$
$840$	2.19670	0.0757934
$841$	30.9252	1.06639
$842$	39.2970	1.35426
$843$	32.7695	1.12864
$844$	9.73855	0.335215
$845$	60.5685	2.08362
$846$	16.9673	0.583346
$847$	−1.40188	−0.0481693
$848$	5.03416	0.172874
$849$	−49.6310	−1.70333
$850$	26.2398	0.900016
$851$	28.2322	0.967786
$852$	−29.5532	−1.01248
$853$	−2.33799	−0.0800514	−0.0400257	−	0.999199i	$-0.512744\pi$
$853$	−2.33799	−0.0800514	−0.0400257	+	0.999199i	$0.512744\pi$
$854$	2.19780	0.0752072
$855$	76.9811	2.63270
$856$	−16.7483	−0.572444
$857$	24.7769	0.846363	0.423181	−	0.906045i	$-0.360913\pi$
$857$	24.7769	0.846363	0.423181	+	0.906045i	$0.360913\pi$
$858$	28.3625	0.968281
$859$	−1.10000	−0.0375315	−0.0187657	−	0.999824i	$-0.505974\pi$
$859$	−1.10000	−0.0375315	−0.0187657	+	0.999824i	$0.505974\pi$
$860$	12.0296	0.410207
$861$	3.83427	0.130671
$862$	−6.91347	−0.235474
$863$	−20.1234	−0.685007	−0.342504	−	0.939517i	$-0.611275\pi$
$863$	−20.1234	−0.685007	−0.342504	+	0.939517i	$0.611275\pi$
$864$	−1.57240	−0.0534942
$865$	13.1270	0.446332
$866$	−13.6592	−0.464159
$867$	23.5281	0.799054
$868$	−1.42167	−0.0482547
$869$	−31.8607	−1.08080
$870$	−69.2883	−2.34909
$871$	17.4766	0.592170
$872$	13.1018	0.443682
$873$	−18.1711	−0.614999
$874$	−25.2138	−0.852869
$875$	4.82404	0.163082
$876$	−17.4432	−0.589351
$877$	34.3113	1.15861	0.579305	−	0.815111i	$-0.303324\pi$
$877$	34.3113	1.15861	0.579305	+	0.815111i	$0.303324\pi$
$878$	−25.1355	−0.848281
$879$	10.5658	0.356375
$880$	−8.92516	−0.300867
$881$	−30.3058	−1.02103	−0.510515	−	0.859869i	$-0.670545\pi$
$881$	−30.3058	−1.02103	−0.510515	+	0.859869i	$0.670545\pi$
$882$	16.0875	0.541694
$883$	−28.2442	−0.950492	−0.475246	−	0.879853i	$-0.657641\pi$
$883$	−28.2442	−0.950492	−0.475246	+	0.879853i	$0.657641\pi$
$884$	13.9444	0.469000
$885$	73.2129	2.46103
$886$	−10.0652	−0.338147
$887$	24.7531	0.831129	0.415564	−	0.909564i	$-0.363584\pi$
$887$	24.7531	0.831129	0.415564	+	0.909564i	$0.363584\pi$
$888$	22.0929	0.741390
$889$	−3.15723	−0.105890
$890$	48.1259	1.61318
$891$	24.3306	0.815105
$892$	−18.3042	−0.612871
$893$	−62.6232	−2.09560
$894$	25.5443	0.854330
$895$	−69.4600	−2.32179
$896$	−0.245423	−0.00819901
$897$	36.3476	1.21361
$898$	−6.76853	−0.225869
$899$	44.8424	1.49558
$900$	23.3307	0.777689
$901$	−13.1251	−0.437261
$902$	−15.5786	−0.518710
$903$	−1.75418	−0.0583754
$904$	−0.805981	−0.0268065
$905$	−81.0767	−2.69508
$906$	−8.84469	−0.293845
$907$	−37.3213	−1.23923	−0.619617	−	0.784904i	$-0.712712\pi$
$907$	−37.3213	−1.23923	−0.619617	+	0.784904i	$0.712712\pi$
$908$	−5.33077	−0.176908
$909$	−4.97973	−0.165167
$910$	5.09464	0.168886
$911$	−44.6928	−1.48074	−0.740369	−	0.672201i	$-0.765349\pi$
$911$	−44.6928	−1.48074	−0.740369	+	0.672201i	$0.765349\pi$
$912$	−19.7309	−0.653356
$913$	16.6958	0.552550
$914$	32.9685	1.09050
$915$	80.1546	2.64983
$916$	−17.6356	−0.582698
$917$	0.287893	0.00950705
$918$	4.09958	0.135306
$919$	58.7669	1.93854	0.969271	−	0.245996i	$-0.0791151\pi$
$919$	58.7669	1.93854	0.969271	+	0.245996i	$0.0791151\pi$
$920$	−11.4379	−0.377096
$921$	67.7497	2.23243
$922$	−13.2362	−0.435912
$923$	−68.5405	−2.25604
$924$	1.30148	0.0428156
$925$	96.4177	3.17019
$926$	33.6467	1.10570
$927$	−21.4364	−0.704065
$928$	7.74114	0.254115
$929$	−33.9373	−1.11345	−0.556723	−	0.830698i	$-0.687941\pi$
$929$	−33.9373	−1.11345	−0.556723	+	0.830698i	$0.687941\pi$
$930$	−51.8489	−1.70019
$931$	−59.3761	−1.94597
$932$	20.1558	0.660226
$933$	−16.3752	−0.536101
$934$	26.2198	0.857939
$935$	23.2697	0.761002
$936$	12.3984	0.405255
$937$	16.3375	0.533722	0.266861	−	0.963735i	$-0.414013\pi$
$937$	16.3375	0.533722	0.266861	+	0.963735i	$0.414013\pi$
$938$	0.801952	0.0261846
$939$	−4.03453	−0.131662
$940$	−28.4082	−0.926572
$941$	−28.7689	−0.937839	−0.468919	−	0.883241i	$-0.655356\pi$
$941$	−28.7689	−0.937839	−0.468919	+	0.883241i	$0.655356\pi$
$942$	7.79359	0.253929
$943$	−19.9645	−0.650132
$944$	−8.17961	−0.266224
$945$	1.49780	0.0487235
$946$	7.12720	0.231725
$947$	20.8200	0.676560	0.338280	−	0.941046i	$-0.390155\pi$
$947$	20.8200	0.676560	0.338280	+	0.941046i	$0.390155\pi$
$948$	−31.9517	−1.03774
$949$	−40.4547	−1.31321
$950$	−86.1094	−2.79376
$951$	56.7062	1.83883
$952$	0.639869	0.0207383
$953$	44.5829	1.44418	0.722091	−	0.691798i	$-0.243181\pi$
$953$	44.5829	1.44418	0.722091	+	0.691798i	$0.243181\pi$
$954$	−11.6700	−0.377830
$955$	−75.9224	−2.45679
$956$	−20.4747	−0.662198
$957$	−41.0513	−1.32700
$958$	−17.1251	−0.553288
$959$	0.866745	0.0279886
$960$	−8.95067	−0.288881
$961$	2.55585	0.0824468
$962$	51.2384	1.65199
$963$	38.8251	1.25112
$964$	12.6703	0.408084
$965$	−22.6511	−0.729166
$966$	1.66789	0.0536635
$967$	20.2883	0.652429	0.326214	−	0.945296i	$-0.394227\pi$
$967$	20.2883	0.652429	0.326214	+	0.945296i	$0.394227\pi$
$968$	5.71211	0.183594
$969$	51.4426	1.65257
$970$	30.4238	0.976848
$971$	−16.8673	−0.541297	−0.270648	−	0.962678i	$-0.587238\pi$
$971$	−16.8673	−0.541297	−0.270648	+	0.962678i	$0.587238\pi$
$972$	19.6829	0.631329
$973$	−0.314360	−0.0100779
$974$	41.8693	1.34158
$975$	124.133	3.97544
$976$	−8.95515	−0.286647
$977$	−17.5910	−0.562784	−0.281392	−	0.959593i	$-0.590796\pi$
$977$	−17.5910	−0.562784	−0.281392	+	0.959593i	$0.590796\pi$
$978$	50.4058	1.61180
$979$	28.5132	0.911285
$980$	−26.9352	−0.860412
$981$	−30.3720	−0.969703
$982$	−9.28697	−0.296359
$983$	−44.0687	−1.40557	−0.702786	−	0.711401i	$-0.748061\pi$
$983$	−44.0687	−1.40557	−0.702786	+	0.711401i	$0.748061\pi$
$984$	−15.6231	−0.498046
$985$	20.5647	0.655247
$986$	−20.1828	−0.642750
$987$	4.14252	0.131858
$988$	−45.7604	−1.45583
$989$	9.13374	0.290436
$990$	20.6899	0.657569
$991$	−24.4886	−0.777907	−0.388954	−	0.921257i	$-0.627163\pi$
$991$	−24.4886	−0.777907	−0.388954	+	0.921257i	$0.627163\pi$
$992$	5.79274	0.183920
$993$	3.70762	0.117658
$994$	−3.14514	−0.0997577
$995$	32.4234	1.02789
$996$	16.7435	0.530538
$997$	16.0599	0.508622	0.254311	−	0.967122i	$-0.418151\pi$
$997$	16.0599	0.508622	0.254311	+	0.967122i	$0.418151\pi$
$998$	−15.5818	−0.493234
$999$	15.0639	0.476600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.6	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.30611 q^{3} +1.00000 q^{4} +3.88128 q^{5} +2.30611 q^{6} +0.245423 q^{7} -1.00000 q^{8} +2.31816 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.30611 q^{3} +1.00000 q^{4} +3.88128 q^{5} +2.30611 q^{6} +0.245423 q^{7} -1.00000 q^{8} +2.31816 q^{9} -3.88128 q^{10} -2.29954 q^{11} -2.30611 q^{12} -5.34839 q^{13} -0.245423 q^{14} -8.95067 q^{15} +1.00000 q^{16} -2.60721 q^{17} -2.31816 q^{18} +8.55592 q^{19} +3.88128 q^{20} -0.565974 q^{21} +2.29954 q^{22} +2.94694 q^{23} +2.30611 q^{24} +10.0643 q^{25} +5.34839 q^{26} +1.57240 q^{27} +0.245423 q^{28} -7.74114 q^{29} +8.95067 q^{30} -5.79274 q^{31} -1.00000 q^{32} +5.30300 q^{33} +2.60721 q^{34} +0.952555 q^{35} +2.31816 q^{36} +9.58016 q^{37} -8.55592 q^{38} +12.3340 q^{39} -3.88128 q^{40} -6.77464 q^{41} +0.565974 q^{42} +3.09940 q^{43} -2.29954 q^{44} +8.99742 q^{45} -2.94694 q^{46} -7.31928 q^{47} -2.30611 q^{48} -6.93977 q^{49} -10.0643 q^{50} +6.01252 q^{51} -5.34839 q^{52} +5.03416 q^{53} -1.57240 q^{54} -8.92516 q^{55} -0.245423 q^{56} -19.7309 q^{57} +7.74114 q^{58} -8.17961 q^{59} -8.95067 q^{60} -8.95515 q^{61} +5.79274 q^{62} +0.568930 q^{63} +1.00000 q^{64} -20.7586 q^{65} -5.30300 q^{66} -3.26763 q^{67} -2.60721 q^{68} -6.79598 q^{69} -0.952555 q^{70} +12.8152 q^{71} -2.31816 q^{72} +7.56389 q^{73} -9.58016 q^{74} -23.2094 q^{75} +8.55592 q^{76} -0.564361 q^{77} -12.3340 q^{78} +13.8552 q^{79} +3.88128 q^{80} -10.5806 q^{81} +6.77464 q^{82} -7.26049 q^{83} -0.565974 q^{84} -10.1193 q^{85} -3.09940 q^{86} +17.8519 q^{87} +2.29954 q^{88} -12.3995 q^{89} -8.99742 q^{90} -1.31262 q^{91} +2.94694 q^{92} +13.3587 q^{93} +7.31928 q^{94} +33.2079 q^{95} +2.30611 q^{96} -7.83860 q^{97} +6.93977 q^{98} -5.33070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 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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