LMFDB - Embedded newform 4006.2.a.h.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$31.9880710497$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.01568 q^{3} +1.00000 q^{4} -0.411222 q^{5} +1.01568 q^{6} -2.82966 q^{7} -1.00000 q^{8} -1.96840 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.01568 q^{3} +1.00000 q^{4} -0.411222 q^{5} +1.01568 q^{6} -2.82966 q^{7} -1.00000 q^{8} -1.96840 q^{9} +0.411222 q^{10} +1.33090 q^{11} -1.01568 q^{12} -4.79621 q^{13} +2.82966 q^{14} +0.417670 q^{15} +1.00000 q^{16} -2.87866 q^{17} +1.96840 q^{18} +4.06603 q^{19} -0.411222 q^{20} +2.87402 q^{21} -1.33090 q^{22} -3.97228 q^{23} +1.01568 q^{24} -4.83090 q^{25} +4.79621 q^{26} +5.04630 q^{27} -2.82966 q^{28} -0.335322 q^{29} -0.417670 q^{30} +0.459269 q^{31} -1.00000 q^{32} -1.35177 q^{33} +2.87866 q^{34} +1.16362 q^{35} -1.96840 q^{36} -8.51309 q^{37} -4.06603 q^{38} +4.87142 q^{39} +0.411222 q^{40} +0.433325 q^{41} -2.87402 q^{42} -6.57270 q^{43} +1.33090 q^{44} +0.809447 q^{45} +3.97228 q^{46} -10.7206 q^{47} -1.01568 q^{48} +1.00695 q^{49} +4.83090 q^{50} +2.92380 q^{51} -4.79621 q^{52} +3.83016 q^{53} -5.04630 q^{54} -0.547296 q^{55} +2.82966 q^{56} -4.12978 q^{57} +0.335322 q^{58} -9.99161 q^{59} +0.417670 q^{60} -1.34790 q^{61} -0.459269 q^{62} +5.56988 q^{63} +1.00000 q^{64} +1.97231 q^{65} +1.35177 q^{66} +10.4440 q^{67} -2.87866 q^{68} +4.03456 q^{69} -1.16362 q^{70} +0.0392862 q^{71} +1.96840 q^{72} +5.14659 q^{73} +8.51309 q^{74} +4.90664 q^{75} +4.06603 q^{76} -3.76599 q^{77} -4.87142 q^{78} +6.86654 q^{79} -0.411222 q^{80} +0.779769 q^{81} -0.433325 q^{82} -5.20059 q^{83} +2.87402 q^{84} +1.18377 q^{85} +6.57270 q^{86} +0.340579 q^{87} -1.33090 q^{88} -6.43785 q^{89} -0.809447 q^{90} +13.5716 q^{91} -3.97228 q^{92} -0.466470 q^{93} +10.7206 q^{94} -1.67204 q^{95} +1.01568 q^{96} +2.23776 q^{97} -1.00695 q^{98} -2.61974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) $ 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.01568	−0.586403	−0.293201	−	0.956051i	$-0.594721\pi$
$3$	−1.01568	−0.586403	−0.293201	+	0.956051i	$0.594721\pi$
$4$	1.00000	0.500000
$5$	−0.411222	−0.183904	−0.0919520	−	0.995763i	$-0.529311\pi$
$5$	−0.411222	−0.183904	−0.0919520	+	0.995763i	$0.529311\pi$
$6$	1.01568	0.414649
$7$	−2.82966	−1.06951	−0.534755	−	0.845007i	$-0.679596\pi$
$7$	−2.82966	−1.06951	−0.534755	+	0.845007i	$0.679596\pi$
$8$	−1.00000	−0.353553
$9$	−1.96840	−0.656132
$10$	0.411222	0.130040
$11$	1.33090	0.401282	0.200641	−	0.979665i	$-0.435698\pi$
$11$	1.33090	0.401282	0.200641	+	0.979665i	$0.435698\pi$
$12$	−1.01568	−0.293201
$13$	−4.79621	−1.33023	−0.665115	−	0.746741i	$-0.731618\pi$
$13$	−4.79621	−1.33023	−0.665115	+	0.746741i	$0.731618\pi$
$14$	2.82966	0.756257
$15$	0.417670	0.107842
$16$	1.00000	0.250000
$17$	−2.87866	−0.698179	−0.349089	−	0.937089i	$-0.613509\pi$
$17$	−2.87866	−0.698179	−0.349089	+	0.937089i	$0.613509\pi$
$18$	1.96840	0.463955
$19$	4.06603	0.932811	0.466405	−	0.884571i	$-0.345549\pi$
$19$	4.06603	0.932811	0.466405	+	0.884571i	$0.345549\pi$
$20$	−0.411222	−0.0919520
$21$	2.87402	0.627163
$22$	−1.33090	−0.283749
$23$	−3.97228	−0.828278	−0.414139	−	0.910214i	$-0.635917\pi$
$23$	−3.97228	−0.828278	−0.414139	+	0.910214i	$0.635917\pi$
$24$	1.01568	0.207325
$25$	−4.83090	−0.966179
$26$	4.79621	0.940615
$27$	5.04630	0.971160
$28$	−2.82966	−0.534755
$29$	−0.335322	−0.0622677	−0.0311339	−	0.999515i	$-0.509912\pi$
$29$	−0.335322	−0.0622677	−0.0311339	+	0.999515i	$0.509912\pi$
$30$	−0.417670	−0.0762557
$31$	0.459269	0.0824872	0.0412436	−	0.999149i	$-0.486868\pi$
$31$	0.459269	0.0824872	0.0412436	+	0.999149i	$0.486868\pi$
$32$	−1.00000	−0.176777
$33$	−1.35177	−0.235313
$34$	2.87866	0.493687
$35$	1.16362	0.196687
$36$	−1.96840	−0.328066
$37$	−8.51309	−1.39954	−0.699771	−	0.714367i	$-0.746715\pi$
$37$	−8.51309	−1.39954	−0.699771	+	0.714367i	$0.746715\pi$
$38$	−4.06603	−0.659597
$39$	4.87142	0.780051
$40$	0.411222	0.0650199
$41$	0.433325	0.0676740	0.0338370	−	0.999427i	$-0.489227\pi$
$41$	0.433325	0.0676740	0.0338370	+	0.999427i	$0.489227\pi$
$42$	−2.87402	−0.443471
$43$	−6.57270	−1.00233	−0.501164	−	0.865352i	$-0.667095\pi$
$43$	−6.57270	−1.00233	−0.501164	+	0.865352i	$0.667095\pi$
$44$	1.33090	0.200641
$45$	0.809447	0.120665
$46$	3.97228	0.585681
$47$	−10.7206	−1.56376	−0.781880	−	0.623429i	$-0.785739\pi$
$47$	−10.7206	−1.56376	−0.781880	+	0.623429i	$0.785739\pi$
$48$	−1.01568	−0.146601
$49$	1.00695	0.143850
$50$	4.83090	0.683192
$51$	2.92380	0.409414
$52$	−4.79621	−0.665115
$53$	3.83016	0.526113	0.263057	−	0.964780i	$-0.415269\pi$
$53$	3.83016	0.526113	0.263057	+	0.964780i	$0.415269\pi$
$54$	−5.04630	−0.686714
$55$	−0.547296	−0.0737974
$56$	2.82966	0.378129
$57$	−4.12978	−0.547003
$58$	0.335322	0.0440299
$59$	−9.99161	−1.30080	−0.650398	−	0.759593i	$-0.725398\pi$
$59$	−9.99161	−1.30080	−0.650398	+	0.759593i	$0.725398\pi$
$60$	0.417670	0.0539209
$61$	−1.34790	−0.172581	−0.0862905	−	0.996270i	$-0.527501\pi$
$61$	−1.34790	−0.172581	−0.0862905	+	0.996270i	$0.527501\pi$
$62$	−0.459269	−0.0583273
$63$	5.56988	0.701739
$64$	1.00000	0.125000
$65$	1.97231	0.244635
$66$	1.35177	0.166391
$67$	10.4440	1.27594	0.637971	−	0.770060i	$-0.279774\pi$
$67$	10.4440	1.27594	0.637971	+	0.770060i	$0.279774\pi$
$68$	−2.87866	−0.349089
$69$	4.03456	0.485704
$70$	−1.16362	−0.139079
$71$	0.0392862	0.00466241	0.00233121	−	0.999997i	$-0.499258\pi$
$71$	0.0392862	0.00466241	0.00233121	+	0.999997i	$0.499258\pi$
$72$	1.96840	0.231978
$73$	5.14659	0.602362	0.301181	−	0.953567i	$-0.402619\pi$
$73$	5.14659	0.602362	0.301181	+	0.953567i	$0.402619\pi$
$74$	8.51309	0.989626
$75$	4.90664	0.566570
$76$	4.06603	0.466405
$77$	−3.76599	−0.429175
$78$	−4.87142	−0.551579
$79$	6.86654	0.772546	0.386273	−	0.922384i	$-0.373762\pi$
$79$	6.86654	0.772546	0.386273	+	0.922384i	$0.373762\pi$
$80$	−0.411222	−0.0459760
$81$	0.779769	0.0866410
$82$	−0.433325	−0.0478528
$83$	−5.20059	−0.570839	−0.285419	−	0.958403i	$-0.592133\pi$
$83$	−5.20059	−0.570839	−0.285419	+	0.958403i	$0.592133\pi$
$84$	2.87402	0.313582
$85$	1.18377	0.128398
$86$	6.57270	0.708753
$87$	0.340579	0.0365139
$88$	−1.33090	−0.141875
$89$	−6.43785	−0.682411	−0.341206	−	0.939989i	$-0.610835\pi$
$89$	−6.43785	−0.682411	−0.341206	+	0.939989i	$0.610835\pi$
$90$	−0.809447	−0.0853233
$91$	13.5716	1.42269
$92$	−3.97228	−0.414139
$93$	−0.466470	−0.0483707
$94$	10.7206	1.10574
$95$	−1.67204	−0.171548
$96$	1.01568	0.103662
$97$	2.23776	0.227210	0.113605	−	0.993526i	$-0.463760\pi$
$97$	2.23776	0.227210	0.113605	+	0.993526i	$0.463760\pi$
$98$	−1.00695	−0.101717
$99$	−2.61974	−0.263294
$100$	−4.83090	−0.483090
$101$	−1.20567	−0.119969	−0.0599844	−	0.998199i	$-0.519105\pi$
$101$	−1.20567	−0.119969	−0.0599844	+	0.998199i	$0.519105\pi$
$102$	−2.92380	−0.289499
$103$	17.3775	1.71226	0.856129	−	0.516762i	$-0.172863\pi$
$103$	17.3775	1.71226	0.856129	+	0.516762i	$0.172863\pi$
$104$	4.79621	0.470307
$105$	−1.18186	−0.115338
$106$	−3.83016	−0.372018
$107$	−16.7278	−1.61714	−0.808568	−	0.588403i	$-0.799757\pi$
$107$	−16.7278	−1.61714	−0.808568	+	0.588403i	$0.799757\pi$
$108$	5.04630	0.485580
$109$	−3.99551	−0.382701	−0.191350	−	0.981522i	$-0.561287\pi$
$109$	−3.99551	−0.382701	−0.191350	+	0.981522i	$0.561287\pi$
$110$	0.547296	0.0521826
$111$	8.64656	0.820696
$112$	−2.82966	−0.267377
$113$	5.95086	0.559810	0.279905	−	0.960028i	$-0.409697\pi$
$113$	5.95086	0.559810	0.279905	+	0.960028i	$0.409697\pi$
$114$	4.12978	0.386789
$115$	1.63349	0.152324
$116$	−0.335322	−0.0311339
$117$	9.44085	0.872807
$118$	9.99161	0.919802
$119$	8.14563	0.746708
$120$	−0.417670	−0.0381278
$121$	−9.22870	−0.838973
$122$	1.34790	0.122033
$123$	−0.440119	−0.0396842
$124$	0.459269	0.0412436
$125$	4.04268	0.361588
$126$	−5.56988	−0.496205
$127$	−11.6537	−1.03410	−0.517051	−	0.855955i	$-0.672970\pi$
$127$	−11.6537	−1.03410	−0.517051	+	0.855955i	$0.672970\pi$
$128$	−1.00000	−0.0883883
$129$	6.67576	0.587768
$130$	−1.97231	−0.172983
$131$	−0.322093	−0.0281414	−0.0140707	−	0.999901i	$-0.504479\pi$
$131$	−0.322093	−0.0281414	−0.0140707	+	0.999901i	$0.504479\pi$
$132$	−1.35177	−0.117656
$133$	−11.5055	−0.997650
$134$	−10.4440	−0.902228
$135$	−2.07515	−0.178600
$136$	2.87866	0.246843
$137$	5.66820	0.484267	0.242134	−	0.970243i	$-0.422153\pi$
$137$	5.66820	0.484267	0.242134	+	0.970243i	$0.422153\pi$
$138$	−4.03456	−0.343445
$139$	4.31768	0.366221	0.183110	−	0.983092i	$-0.441383\pi$
$139$	4.31768	0.366221	0.183110	+	0.983092i	$0.441383\pi$
$140$	1.16362	0.0983435
$141$	10.8887	0.916993
$142$	−0.0392862	−0.00329682
$143$	−6.38329	−0.533797
$144$	−1.96840	−0.164033
$145$	0.137892	0.0114513
$146$	−5.14659	−0.425935
$147$	−1.02274	−0.0843541
$148$	−8.51309	−0.699771
$149$	18.7654	1.53732	0.768662	−	0.639655i	$-0.220923\pi$
$149$	18.7654	1.53732	0.768662	+	0.639655i	$0.220923\pi$
$150$	−4.90664	−0.400626
$151$	18.2000	1.48110	0.740549	−	0.672002i	$-0.234565\pi$
$151$	18.2000	1.48110	0.740549	+	0.672002i	$0.234565\pi$
$152$	−4.06603	−0.329798
$153$	5.66635	0.458097
$154$	3.76599	0.303472
$155$	−0.188862	−0.0151697
$156$	4.87142	0.390025
$157$	−17.2999	−1.38068	−0.690339	−	0.723486i	$-0.742539\pi$
$157$	−17.2999	−1.38068	−0.690339	+	0.723486i	$0.742539\pi$
$158$	−6.86654	−0.546273
$159$	−3.89022	−0.308514
$160$	0.411222	0.0325099
$161$	11.2402	0.885851
$162$	−0.779769	−0.0612644
$163$	−13.8794	−1.08712	−0.543561	−	0.839370i	$-0.682924\pi$
$163$	−13.8794	−1.08712	−0.543561	+	0.839370i	$0.682924\pi$
$164$	0.433325	0.0338370
$165$	0.555877	0.0432750
$166$	5.20059	0.403644
$167$	19.0475	1.47394	0.736971	−	0.675924i	$-0.236255\pi$
$167$	19.0475	1.47394	0.736971	+	0.675924i	$0.236255\pi$
$168$	−2.87402	−0.221736
$169$	10.0037	0.769513
$170$	−1.18377	−0.0907910
$171$	−8.00355	−0.612047
$172$	−6.57270	−0.501164
$173$	4.91838	0.373938	0.186969	−	0.982366i	$-0.440134\pi$
$173$	4.91838	0.373938	0.186969	+	0.982366i	$0.440134\pi$
$174$	−0.340579	−0.0258193
$175$	13.6698	1.03334
$176$	1.33090	0.100320
$177$	10.1483	0.762790
$178$	6.43785	0.482538
$179$	6.27130	0.468739	0.234369	−	0.972148i	$-0.424697\pi$
$179$	6.27130	0.468739	0.234369	+	0.972148i	$0.424697\pi$
$180$	0.809447	0.0603327
$181$	−5.37395	−0.399442	−0.199721	−	0.979853i	$-0.564004\pi$
$181$	−5.37395	−0.399442	−0.199721	+	0.979853i	$0.564004\pi$
$182$	−13.5716	−1.00600
$183$	1.36904	0.101202
$184$	3.97228	0.292840
$185$	3.50077	0.257382
$186$	0.466470	0.0342033
$187$	−3.83122	−0.280166
$188$	−10.7206	−0.781880
$189$	−14.2793	−1.03866
$190$	1.67204	0.121303
$191$	24.1114	1.74464	0.872321	−	0.488933i	$-0.162614\pi$
$191$	24.1114	1.74464	0.872321	+	0.488933i	$0.162614\pi$
$192$	−1.01568	−0.0733003
$193$	−23.3883	−1.68353	−0.841763	−	0.539848i	$-0.818482\pi$
$193$	−23.3883	−1.68353	−0.841763	+	0.539848i	$0.818482\pi$
$194$	−2.23776	−0.160661
$195$	−2.00323	−0.143454
$196$	1.00695	0.0719251
$197$	12.1873	0.868307	0.434154	−	0.900839i	$-0.357048\pi$
$197$	12.1873	0.868307	0.434154	+	0.900839i	$0.357048\pi$
$198$	2.61974	0.186177
$199$	−5.07945	−0.360072	−0.180036	−	0.983660i	$-0.557621\pi$
$199$	−5.07945	−0.360072	−0.180036	+	0.983660i	$0.557621\pi$
$200$	4.83090	0.341596
$201$	−10.6078	−0.748216
$202$	1.20567	0.0848307
$203$	0.948845	0.0665959
$204$	2.92380	0.204707
$205$	−0.178193	−0.0124455
$206$	−17.3775	−1.21075
$207$	7.81902	0.543459
$208$	−4.79621	−0.332558
$209$	5.41148	0.374320
$210$	1.18186	0.0815562
$211$	−13.4053	−0.922857	−0.461428	−	0.887177i	$-0.652663\pi$
$211$	−13.4053	−0.922857	−0.461428	+	0.887177i	$0.652663\pi$
$212$	3.83016	0.263057
$213$	−0.0399022	−0.00273405
$214$	16.7278	1.14349
$215$	2.70284	0.184332
$216$	−5.04630	−0.343357
$217$	−1.29957	−0.0882209
$218$	3.99551	0.270610
$219$	−5.22728	−0.353227
$220$	−0.547296	−0.0368987
$221$	13.8067	0.928738
$222$	−8.64656	−0.580319
$223$	−3.19443	−0.213915	−0.106958	−	0.994264i	$-0.534111\pi$
$223$	−3.19443	−0.213915	−0.106958	+	0.994264i	$0.534111\pi$
$224$	2.82966	0.189064
$225$	9.50912	0.633941
$226$	−5.95086	−0.395846
$227$	−22.0104	−1.46088	−0.730442	−	0.682974i	$-0.760686\pi$
$227$	−22.0104	−1.46088	−0.730442	+	0.682974i	$0.760686\pi$
$228$	−4.12978	−0.273501
$229$	8.59551	0.568007	0.284004	−	0.958823i	$-0.408337\pi$
$229$	8.59551	0.568007	0.284004	+	0.958823i	$0.408337\pi$
$230$	−1.63349	−0.107709
$231$	3.82504	0.251669
$232$	0.335322	0.0220150
$233$	12.1975	0.799087	0.399543	−	0.916714i	$-0.369169\pi$
$233$	12.1975	0.799087	0.399543	+	0.916714i	$0.369169\pi$
$234$	−9.44085	−0.617168
$235$	4.40854	0.287582
$236$	−9.99161	−0.650398
$237$	−6.97420	−0.453023
$238$	−8.14563	−0.528003
$239$	2.53842	0.164197	0.0820984	−	0.996624i	$-0.473838\pi$
$239$	2.53842	0.164197	0.0820984	+	0.996624i	$0.473838\pi$
$240$	0.417670	0.0269605
$241$	20.4388	1.31658	0.658289	−	0.752766i	$-0.271281\pi$
$241$	20.4388	1.31658	0.658289	+	0.752766i	$0.271281\pi$
$242$	9.22870	0.593243
$243$	−15.9309	−1.02197
$244$	−1.34790	−0.0862905
$245$	−0.414080	−0.0264546
$246$	0.440119	0.0280610
$247$	−19.5015	−1.24085
$248$	−0.459269	−0.0291636
$249$	5.28213	0.334741
$250$	−4.04268	−0.255682
$251$	0.915212	0.0577677	0.0288838	−	0.999583i	$-0.490805\pi$
$251$	0.915212	0.0577677	0.0288838	+	0.999583i	$0.490805\pi$
$252$	5.56988	0.350870
$253$	−5.28671	−0.332373
$254$	11.6537	0.731221
$255$	−1.20233	−0.0752928
$256$	1.00000	0.0625000
$257$	7.25618	0.452628	0.226314	−	0.974054i	$-0.427332\pi$
$257$	7.25618	0.452628	0.226314	+	0.974054i	$0.427332\pi$
$258$	−6.67576	−0.415614
$259$	24.0891	1.49682
$260$	1.97231	0.122317
$261$	0.660046	0.0408558
$262$	0.322093	0.0198990
$263$	24.1814	1.49109	0.745545	−	0.666455i	$-0.232189\pi$
$263$	24.1814	1.49109	0.745545	+	0.666455i	$0.232189\pi$
$264$	1.35177	0.0831956
$265$	−1.57505	−0.0967544
$266$	11.5055	0.705445
$267$	6.53879	0.400168
$268$	10.4440	0.637971
$269$	30.2970	1.84724	0.923620	−	0.383309i	$-0.125216\pi$
$269$	30.2970	1.84724	0.923620	+	0.383309i	$0.125216\pi$
$270$	2.07515	0.126289
$271$	−21.0080	−1.27614	−0.638072	−	0.769977i	$-0.720268\pi$
$271$	−21.0080	−1.27614	−0.638072	+	0.769977i	$0.720268\pi$
$272$	−2.87866	−0.174545
$273$	−13.7844	−0.834271
$274$	−5.66820	−0.342429
$275$	−6.42945	−0.387710
$276$	4.03456	0.242852
$277$	9.97993	0.599636	0.299818	−	0.953996i	$-0.403074\pi$
$277$	9.97993	0.599636	0.299818	+	0.953996i	$0.403074\pi$
$278$	−4.31768	−0.258957
$279$	−0.904024	−0.0541225
$280$	−1.16362	−0.0695394
$281$	12.3595	0.737308	0.368654	−	0.929567i	$-0.379819\pi$
$281$	12.3595	0.737308	0.368654	+	0.929567i	$0.379819\pi$
$282$	−10.8887	−0.648412
$283$	−2.38392	−0.141710	−0.0708548	−	0.997487i	$-0.522573\pi$
$283$	−2.38392	−0.141710	−0.0708548	+	0.997487i	$0.522573\pi$
$284$	0.0392862	0.00233121
$285$	1.69826	0.100596
$286$	6.38329	0.377452
$287$	−1.22616	−0.0723780
$288$	1.96840	0.115989
$289$	−8.71329	−0.512547
$290$	−0.137892	−0.00809728
$291$	−2.27284	−0.133236
$292$	5.14659	0.301181
$293$	−23.2093	−1.35590	−0.677952	−	0.735106i	$-0.737132\pi$
$293$	−23.2093	−1.35590	−0.677952	+	0.735106i	$0.737132\pi$
$294$	1.02274	0.0596474
$295$	4.10877	0.239222
$296$	8.51309	0.494813
$297$	6.71612	0.389709
$298$	−18.7654	−1.08705
$299$	19.0519	1.10180
$300$	4.90664	0.283285
$301$	18.5985	1.07200
$302$	−18.2000	−1.04729
$303$	1.22458	0.0703500
$304$	4.06603	0.233203
$305$	0.554287	0.0317384
$306$	−5.66635	−0.323924
$307$	−9.41723	−0.537470	−0.268735	−	0.963214i	$-0.586606\pi$
$307$	−9.41723	−0.537470	−0.268735	+	0.963214i	$0.586606\pi$
$308$	−3.76599	−0.214587
$309$	−17.6500	−1.00407
$310$	0.188862	0.0107266
$311$	−11.1192	−0.630512	−0.315256	−	0.949007i	$-0.602090\pi$
$311$	−11.1192	−0.630512	−0.315256	+	0.949007i	$0.602090\pi$
$312$	−4.87142	−0.275790
$313$	4.38617	0.247921	0.123960	−	0.992287i	$-0.460440\pi$
$313$	4.38617	0.247921	0.123960	+	0.992287i	$0.460440\pi$
$314$	17.2999	0.976287
$315$	−2.29046	−0.129053
$316$	6.86654	0.386273
$317$	−0.535559	−0.0300800	−0.0150400	−	0.999887i	$-0.504788\pi$
$317$	−0.535559	−0.0300800	−0.0150400	+	0.999887i	$0.504788\pi$
$318$	3.89022	0.218153
$319$	−0.446280	−0.0249869
$320$	−0.411222	−0.0229880
$321$	16.9901	0.948293
$322$	−11.2402	−0.626391
$323$	−11.7047	−0.651269
$324$	0.779769	0.0433205
$325$	23.1700	1.28524
$326$	13.8794	0.768712
$327$	4.05816	0.224417
$328$	−0.433325	−0.0239264
$329$	30.3356	1.67246
$330$	−0.555877	−0.0306000
$331$	−17.8683	−0.982133	−0.491067	−	0.871122i	$-0.663393\pi$
$331$	−17.8683	−0.982133	−0.491067	+	0.871122i	$0.663393\pi$
$332$	−5.20059	−0.285419
$333$	16.7571	0.918285
$334$	−19.0475	−1.04223
$335$	−4.29482	−0.234651
$336$	2.87402	0.156791
$337$	−8.80039	−0.479388	−0.239694	−	0.970848i	$-0.577047\pi$
$337$	−8.80039	−0.479388	−0.239694	+	0.970848i	$0.577047\pi$
$338$	−10.0037	−0.544128
$339$	−6.04417	−0.328274
$340$	1.18377	0.0641989
$341$	0.611242	0.0331006
$342$	8.00355	0.432783
$343$	16.9583	0.915660
$344$	6.57270	0.354376
$345$	−1.65910	−0.0893230
$346$	−4.91838	−0.264414
$347$	8.01713	0.430382	0.215191	−	0.976572i	$-0.430963\pi$
$347$	8.01713	0.430382	0.215191	+	0.976572i	$0.430963\pi$
$348$	0.340579	0.0182570
$349$	33.0472	1.76897	0.884487	−	0.466565i	$-0.154509\pi$
$349$	33.0472	1.76897	0.884487	+	0.466565i	$0.154509\pi$
$350$	−13.6698	−0.730680
$351$	−24.2031	−1.29187
$352$	−1.33090	−0.0709373
$353$	24.1364	1.28465	0.642326	−	0.766431i	$-0.277969\pi$
$353$	24.1364	1.28465	0.642326	+	0.766431i	$0.277969\pi$
$354$	−10.1483	−0.539374
$355$	−0.0161553	−0.000857437 0
$356$	−6.43785	−0.341206
$357$	−8.27334	−0.437872
$358$	−6.27130	−0.331448
$359$	−6.70305	−0.353773	−0.176887	−	0.984231i	$-0.556603\pi$
$359$	−6.70305	−0.353773	−0.176887	+	0.984231i	$0.556603\pi$
$360$	−0.809447	−0.0426616
$361$	−2.46741	−0.129864
$362$	5.37395	0.282448
$363$	9.37340	0.491976
$364$	13.5716	0.711347
$365$	−2.11639	−0.110777
$366$	−1.36904	−0.0715606
$367$	30.1840	1.57559	0.787797	−	0.615935i	$-0.211222\pi$
$367$	30.1840	1.57559	0.787797	+	0.615935i	$0.211222\pi$
$368$	−3.97228	−0.207069
$369$	−0.852956	−0.0444031
$370$	−3.50077	−0.181996
$371$	−10.8380	−0.562683
$372$	−0.466470	−0.0241854
$373$	28.7854	1.49045	0.745226	−	0.666812i	$-0.232342\pi$
$373$	28.7854	1.49045	0.745226	+	0.666812i	$0.232342\pi$
$374$	3.83122	0.198108
$375$	−4.10607	−0.212036
$376$	10.7206	0.552872
$377$	1.60828	0.0828304
$378$	14.2793	0.734447
$379$	−23.9274	−1.22907	−0.614535	−	0.788889i	$-0.710656\pi$
$379$	−23.9274	−1.22907	−0.614535	+	0.788889i	$0.710656\pi$
$380$	−1.67204	−0.0857738
$381$	11.8365	0.606400
$382$	−24.1114	−1.23365
$383$	−31.9192	−1.63099	−0.815497	−	0.578762i	$-0.803536\pi$
$383$	−31.9192	−1.63099	−0.815497	+	0.578762i	$0.803536\pi$
$384$	1.01568	0.0518312
$385$	1.54866	0.0789270
$386$	23.3883	1.19043
$387$	12.9377	0.657659
$388$	2.23776	0.113605
$389$	9.63885	0.488709	0.244354	−	0.969686i	$-0.421424\pi$
$389$	9.63885	0.488709	0.244354	+	0.969686i	$0.421424\pi$
$390$	2.00323	0.101438
$391$	11.4349	0.578286
$392$	−1.00695	−0.0508587
$393$	0.327143	0.0165022
$394$	−12.1873	−0.613986
$395$	−2.82367	−0.142074
$396$	−2.61974	−0.131647
$397$	10.0465	0.504221	0.252111	−	0.967698i	$-0.418875\pi$
$397$	10.0465	0.504221	0.252111	+	0.967698i	$0.418875\pi$
$398$	5.07945	0.254610
$399$	11.6859	0.585025
$400$	−4.83090	−0.241545
$401$	−5.43995	−0.271658	−0.135829	−	0.990732i	$-0.543370\pi$
$401$	−5.43995	−0.271658	−0.135829	+	0.990732i	$0.543370\pi$
$402$	10.6078	0.529069
$403$	−2.20275	−0.109727
$404$	−1.20567	−0.0599844
$405$	−0.320658	−0.0159336
$406$	−0.948845	−0.0470904
$407$	−11.3301	−0.561611
$408$	−2.92380	−0.144750
$409$	−19.5808	−0.968208	−0.484104	−	0.875010i	$-0.660854\pi$
$409$	−19.5808	−0.968208	−0.484104	+	0.875010i	$0.660854\pi$
$410$	0.178193	0.00880032
$411$	−5.75707	−0.283976
$412$	17.3775	0.856129
$413$	28.2728	1.39121
$414$	−7.81902	−0.384284
$415$	2.13860	0.104980
$416$	4.79621	0.235154
$417$	−4.38538	−0.214753
$418$	−5.41148	−0.264684
$419$	35.8622	1.75198	0.875992	−	0.482325i	$-0.160208\pi$
$419$	35.8622	1.75198	0.875992	+	0.482325i	$0.160208\pi$
$420$	−1.18186	−0.0576689
$421$	40.0169	1.95031	0.975153	−	0.221533i	$-0.0711062\pi$
$421$	40.0169	1.95031	0.975153	+	0.221533i	$0.0711062\pi$
$422$	13.4053	0.652558
$423$	21.1024	1.02603
$424$	−3.83016	−0.186009
$425$	13.9065	0.674566
$426$	0.0399022	0.00193327
$427$	3.81410	0.184577
$428$	−16.7278	−0.808568
$429$	6.48337	0.313020
$430$	−2.70284	−0.130342
$431$	−23.4019	−1.12723	−0.563614	−	0.826038i	$-0.690589\pi$
$431$	−23.4019	−1.12723	−0.563614	+	0.826038i	$0.690589\pi$
$432$	5.04630	0.242790
$433$	−1.26167	−0.0606322	−0.0303161	−	0.999540i	$-0.509651\pi$
$433$	−1.26167	−0.0606322	−0.0303161	+	0.999540i	$0.509651\pi$
$434$	1.29957	0.0623816
$435$	−0.140054	−0.00671506
$436$	−3.99551	−0.191350
$437$	−16.1514	−0.772626
$438$	5.22728	0.249769
$439$	−11.3819	−0.543226	−0.271613	−	0.962407i	$-0.587557\pi$
$439$	−11.3819	−0.543226	−0.271613	+	0.962407i	$0.587557\pi$
$440$	0.547296	0.0260913
$441$	−1.98208	−0.0943847
$442$	−13.8067	−0.656717
$443$	13.1575	0.625133	0.312567	−	0.949896i	$-0.398811\pi$
$443$	13.1575	0.625133	0.312567	+	0.949896i	$0.398811\pi$
$444$	8.64656	0.410348
$445$	2.64739	0.125498
$446$	3.19443	0.151261
$447$	−19.0597	−0.901491
$448$	−2.82966	−0.133689
$449$	13.2931	0.627340	0.313670	−	0.949532i	$-0.398441\pi$
$449$	13.2931	0.627340	0.313670	+	0.949532i	$0.398441\pi$
$450$	−9.50912	−0.448264
$451$	0.576713	0.0271564
$452$	5.95086	0.279905
$453$	−18.4854	−0.868520
$454$	22.0104	1.03300
$455$	−5.58095	−0.261639
$456$	4.12978	0.193395
$457$	−2.24966	−0.105235	−0.0526174	−	0.998615i	$-0.516756\pi$
$457$	−2.24966	−0.105235	−0.0526174	+	0.998615i	$0.516756\pi$
$458$	−8.59551	−0.401642
$459$	−14.5266	−0.678043
$460$	1.63349	0.0761618
$461$	5.70565	0.265738	0.132869	−	0.991134i	$-0.457581\pi$
$461$	5.70565	0.265738	0.132869	+	0.991134i	$0.457581\pi$
$462$	−3.82504	−0.177957
$463$	3.75735	0.174619	0.0873094	−	0.996181i	$-0.472173\pi$
$463$	3.75735	0.174619	0.0873094	+	0.996181i	$0.472173\pi$
$464$	−0.335322	−0.0155669
$465$	0.191823	0.00889557
$466$	−12.1975	−0.565040
$467$	5.43199	0.251363	0.125681	−	0.992071i	$-0.459888\pi$
$467$	5.43199	0.251363	0.125681	+	0.992071i	$0.459888\pi$
$468$	9.44085	0.436403
$469$	−29.5530	−1.36463
$470$	−4.40854	−0.203351
$471$	17.5711	0.809634
$472$	9.99161	0.459901
$473$	−8.74762	−0.402216
$474$	6.97420	0.320336
$475$	−19.6426	−0.901263
$476$	8.14563	0.373354
$477$	−7.53928	−0.345200
$478$	−2.53842	−0.116105
$479$	−23.1212	−1.05644	−0.528218	−	0.849109i	$-0.677140\pi$
$479$	−23.1212	−1.05644	−0.528218	+	0.849109i	$0.677140\pi$
$480$	−0.417670	−0.0190639
$481$	40.8306	1.86171
$482$	−20.4388	−0.930961
$483$	−11.4164	−0.519465
$484$	−9.22870	−0.419486
$485$	−0.920214	−0.0417848
$486$	15.9309	0.722640
$487$	29.1457	1.32072	0.660358	−	0.750951i	$-0.270405\pi$
$487$	29.1457	1.32072	0.660358	+	0.750951i	$0.270405\pi$
$488$	1.34790	0.0610166
$489$	14.0971	0.637491
$490$	0.414080	0.0187062
$491$	23.8501	1.07634	0.538169	−	0.842837i	$-0.319116\pi$
$491$	23.8501	1.07634	0.538169	+	0.842837i	$0.319116\pi$
$492$	−0.440119	−0.0198421
$493$	0.965279	0.0434740
$494$	19.5015	0.877416
$495$	1.07729	0.0484208
$496$	0.459269	0.0206218
$497$	−0.111166	−0.00498649
$498$	−5.28213	−0.236698
$499$	−11.2820	−0.505053	−0.252527	−	0.967590i	$-0.581262\pi$
$499$	−11.2820	−0.505053	−0.252527	+	0.967590i	$0.581262\pi$
$500$	4.04268	0.180794
$501$	−19.3462	−0.864324
$502$	−0.915212	−0.0408479
$503$	34.6730	1.54599	0.772997	−	0.634410i	$-0.218757\pi$
$503$	34.6730	1.54599	0.772997	+	0.634410i	$0.218757\pi$
$504$	−5.56988	−0.248102
$505$	0.495798	0.0220627
$506$	5.28671	0.235023
$507$	−10.1605	−0.451245
$508$	−11.6537	−0.517051
$509$	5.88797	0.260980	0.130490	−	0.991450i	$-0.458345\pi$
$509$	5.88797	0.260980	0.130490	+	0.991450i	$0.458345\pi$
$510$	1.20233	0.0532401
$511$	−14.5631	−0.644232
$512$	−1.00000	−0.0441942
$513$	20.5184	0.905909
$514$	−7.25618	−0.320056
$515$	−7.14602	−0.314891
$516$	6.67576	0.293884
$517$	−14.2681	−0.627508
$518$	−24.0891	−1.05841
$519$	−4.99550	−0.219278
$520$	−1.97231	−0.0864914
$521$	−4.66809	−0.204513	−0.102256	−	0.994758i	$-0.532606\pi$
$521$	−4.66809	−0.204513	−0.102256	+	0.994758i	$0.532606\pi$
$522$	−0.660046	−0.0288894
$523$	−20.1397	−0.880646	−0.440323	−	0.897839i	$-0.645136\pi$
$523$	−20.1397	−0.880646	−0.440323	+	0.897839i	$0.645136\pi$
$524$	−0.322093	−0.0140707
$525$	−13.8841	−0.605952
$526$	−24.1814	−1.05436
$527$	−1.32208	−0.0575908
$528$	−1.35177	−0.0588282
$529$	−7.22099	−0.313956
$530$	1.57505	0.0684157
$531$	19.6674	0.853494
$532$	−11.5055	−0.498825
$533$	−2.07832	−0.0900221
$534$	−6.53879	−0.282961
$535$	6.87883	0.297398
$536$	−10.4440	−0.451114
$537$	−6.36963	−0.274870
$538$	−30.2970	−1.30620
$539$	1.34015	0.0577245
$540$	−2.07515	−0.0893001
$541$	3.62063	0.155663	0.0778315	−	0.996967i	$-0.475200\pi$
$541$	3.62063	0.155663	0.0778315	+	0.996967i	$0.475200\pi$
$542$	21.0080	0.902370
$543$	5.45821	0.234234
$544$	2.87866	0.123422
$545$	1.64304	0.0703802
$546$	13.7844	0.589919
$547$	−7.02713	−0.300458	−0.150229	−	0.988651i	$-0.548001\pi$
$547$	−7.02713	−0.300458	−0.150229	+	0.988651i	$0.548001\pi$
$548$	5.66820	0.242134
$549$	2.65320	0.113236
$550$	6.42945	0.274153
$551$	−1.36343	−0.0580840
$552$	−4.03456	−0.171722
$553$	−19.4299	−0.826245
$554$	−9.97993	−0.424006
$555$	−3.55566	−0.150929
$556$	4.31768	0.183110
$557$	−21.8809	−0.927124	−0.463562	−	0.886064i	$-0.653429\pi$
$557$	−21.8809	−0.927124	−0.463562	+	0.886064i	$0.653429\pi$
$558$	0.904024	0.0382704
$559$	31.5241	1.33333
$560$	1.16362	0.0491718
$561$	3.89129	0.164290
$562$	−12.3595	−0.521355
$563$	22.4553	0.946377	0.473188	−	0.880961i	$-0.343103\pi$
$563$	22.4553	0.946377	0.473188	+	0.880961i	$0.343103\pi$
$564$	10.8887	0.458496
$565$	−2.44713	−0.102951
$566$	2.38392	0.100204
$567$	−2.20648	−0.0926633
$568$	−0.0392862	−0.00164841
$569$	−18.8536	−0.790383	−0.395191	−	0.918599i	$-0.629322\pi$
$569$	−18.8536	−0.790383	−0.395191	+	0.918599i	$0.629322\pi$
$570$	−1.69826	−0.0711321
$571$	−43.9191	−1.83796	−0.918979	−	0.394305i	$-0.870985\pi$
$571$	−43.9191	−1.83796	−0.918979	+	0.394305i	$0.870985\pi$
$572$	−6.38329	−0.266899
$573$	−24.4895	−1.02306
$574$	1.22616	0.0511790
$575$	19.1897	0.800265
$576$	−1.96840	−0.0820165
$577$	28.3339	1.17956	0.589779	−	0.807565i	$-0.299215\pi$
$577$	28.3339	1.17956	0.589779	+	0.807565i	$0.299215\pi$
$578$	8.71329	0.362425
$579$	23.7550	0.987224
$580$	0.137892	0.00572564
$581$	14.7159	0.610517
$582$	2.27284	0.0942123
$583$	5.09757	0.211120
$584$	−5.14659	−0.212967
$585$	−3.88228	−0.160513
$586$	23.2093	0.958769
$587$	15.4414	0.637336	0.318668	−	0.947866i	$-0.396765\pi$
$587$	15.4414	0.637336	0.318668	+	0.947866i	$0.396765\pi$
$588$	−1.02274	−0.0421771
$589$	1.86740	0.0769450
$590$	−4.10877	−0.169155
$591$	−12.3784	−0.509178
$592$	−8.51309	−0.349886
$593$	23.4916	0.964686	0.482343	−	0.875982i	$-0.339786\pi$
$593$	23.4916	0.964686	0.482343	+	0.875982i	$0.339786\pi$
$594$	−6.71612	−0.275566
$595$	−3.34966	−0.137323
$596$	18.7654	0.768662
$597$	5.15909	0.211147
$598$	−19.0519	−0.779090
$599$	0.310107	0.0126706	0.00633531	−	0.999980i	$-0.497983\pi$
$599$	0.310107	0.0126706	0.00633531	+	0.999980i	$0.497983\pi$
$600$	−4.90664	−0.200313
$601$	−27.7631	−1.13248	−0.566240	−	0.824241i	$-0.691602\pi$
$601$	−27.7631	−1.13248	−0.566240	+	0.824241i	$0.691602\pi$
$602$	−18.5985	−0.758018
$603$	−20.5580	−0.837187
$604$	18.2000	0.740549
$605$	3.79504	0.154291
$606$	−1.22458	−0.0497450
$607$	4.41668	0.179268	0.0896338	−	0.995975i	$-0.471430\pi$
$607$	4.41668	0.179268	0.0896338	+	0.995975i	$0.471430\pi$
$608$	−4.06603	−0.164899
$609$	−0.963723	−0.0390520
$610$	−0.554287	−0.0224424
$611$	51.4183	2.08016
$612$	5.66635	0.229049
$613$	46.5280	1.87925	0.939623	−	0.342210i	$-0.111176\pi$
$613$	46.5280	1.87925	0.939623	+	0.342210i	$0.111176\pi$
$614$	9.41723	0.380049
$615$	0.180987	0.00729809
$616$	3.76599	0.151736
$617$	0.991423	0.0399132	0.0199566	−	0.999801i	$-0.493647\pi$
$617$	0.991423	0.0399132	0.0199566	+	0.999801i	$0.493647\pi$
$618$	17.6500	0.709987
$619$	−16.0842	−0.646479	−0.323240	−	0.946317i	$-0.604772\pi$
$619$	−16.0842	−0.646479	−0.323240	+	0.946317i	$0.604772\pi$
$620$	−0.188862	−0.00758487
$621$	−20.0453	−0.804390
$622$	11.1192	0.445840
$623$	18.2169	0.729845
$624$	4.87142	0.195013
$625$	22.4920	0.899682
$626$	−4.38617	−0.175307
$627$	−5.49633	−0.219502
$628$	−17.2999	−0.690339
$629$	24.5063	0.977131
$630$	2.29046	0.0912540
$631$	−13.3683	−0.532185	−0.266093	−	0.963947i	$-0.585733\pi$
$631$	−13.3683	−0.532185	−0.266093	+	0.963947i	$0.585733\pi$
$632$	−6.86654	−0.273136
$633$	13.6155	0.541166
$634$	0.535559	0.0212698
$635$	4.79227	0.190176
$636$	−3.89022	−0.154257
$637$	−4.82955	−0.191354
$638$	0.446280	0.0176684
$639$	−0.0773308	−0.00305916
$640$	0.411222	0.0162550
$641$	3.95481	0.156205	0.0781027	−	0.996945i	$-0.475114\pi$
$641$	3.95481	0.156205	0.0781027	+	0.996945i	$0.475114\pi$
$642$	−16.9901	−0.670544
$643$	−11.2839	−0.444996	−0.222498	−	0.974933i	$-0.571421\pi$
$643$	−11.2839	−0.444996	−0.222498	+	0.974933i	$0.571421\pi$
$644$	11.2402	0.442925
$645$	−2.74522	−0.108093
$646$	11.7047	0.460516
$647$	−37.5482	−1.47617	−0.738086	−	0.674707i	$-0.764270\pi$
$647$	−37.5482	−1.47617	−0.738086	+	0.674707i	$0.764270\pi$
$648$	−0.779769	−0.0306322
$649$	−13.2978	−0.521986
$650$	−23.1700	−0.908803
$651$	1.31995	0.0517329
$652$	−13.8794	−0.543561
$653$	47.3139	1.85154	0.925768	−	0.378093i	$-0.123420\pi$
$653$	47.3139	1.85154	0.925768	+	0.378093i	$0.123420\pi$
$654$	−4.05816	−0.158687
$655$	0.132452	0.00517532
$656$	0.433325	0.0169185
$657$	−10.1305	−0.395229
$658$	−30.3356	−1.18260
$659$	−43.6632	−1.70088	−0.850439	−	0.526073i	$-0.823664\pi$
$659$	−43.6632	−1.70088	−0.850439	+	0.526073i	$0.823664\pi$
$660$	0.555877	0.0216375
$661$	−13.2687	−0.516092	−0.258046	−	0.966133i	$-0.583079\pi$
$661$	−13.2687	−0.516092	−0.258046	+	0.966133i	$0.583079\pi$
$662$	17.8683	0.694473
$663$	−14.0232	−0.544615
$664$	5.20059	0.201822
$665$	4.73130	0.183472
$666$	−16.7571	−0.649325
$667$	1.33199	0.0515749
$668$	19.0475	0.736971
$669$	3.24452	0.125440
$670$	4.29482	0.165923
$671$	−1.79392	−0.0692537
$672$	−2.87402	−0.110868
$673$	−15.7013	−0.605241	−0.302620	−	0.953111i	$-0.597861\pi$
$673$	−15.7013	−0.605241	−0.302620	+	0.953111i	$0.597861\pi$
$674$	8.80039	0.338978
$675$	−24.3781	−0.938315
$676$	10.0037	0.384757
$677$	−18.9759	−0.729304	−0.364652	−	0.931144i	$-0.618812\pi$
$677$	−18.9759	−0.729304	−0.364652	+	0.931144i	$0.618812\pi$
$678$	6.04417	0.232125
$679$	−6.33208	−0.243003
$680$	−1.18377	−0.0453955
$681$	22.3556	0.856667
$682$	−0.611242	−0.0234057
$683$	−8.40820	−0.321731	−0.160865	−	0.986976i	$-0.551429\pi$
$683$	−8.40820	−0.321731	−0.160865	+	0.986976i	$0.551429\pi$
$684$	−8.00355	−0.306023
$685$	−2.33089	−0.0890587
$686$	−16.9583	−0.647470
$687$	−8.73028	−0.333081
$688$	−6.57270	−0.250582
$689$	−18.3703	−0.699852
$690$	1.65910	0.0631609
$691$	−7.99741	−0.304236	−0.152118	−	0.988362i	$-0.548609\pi$
$691$	−7.99741	−0.304236	−0.152118	+	0.988362i	$0.548609\pi$
$692$	4.91838	0.186969
$693$	7.41296	0.281595
$694$	−8.01713	−0.304326
$695$	−1.77553	−0.0673495
$696$	−0.340579	−0.0129096
$697$	−1.24740	−0.0472486
$698$	−33.0472	−1.25085
$699$	−12.3888	−0.468587
$700$	13.6698	0.516669
$701$	3.64456	0.137653	0.0688266	−	0.997629i	$-0.478074\pi$
$701$	3.64456	0.137653	0.0688266	+	0.997629i	$0.478074\pi$
$702$	24.2031	0.913488
$703$	−34.6144	−1.30551
$704$	1.33090	0.0501602
$705$	−4.47767	−0.168639
$706$	−24.1364	−0.908387
$707$	3.41163	0.128308
$708$	10.1483	0.381395
$709$	4.83956	0.181753	0.0908767	−	0.995862i	$-0.471033\pi$
$709$	4.83956	0.181753	0.0908767	+	0.995862i	$0.471033\pi$
$710$	0.0161553	0.000606299 0
$711$	−13.5161	−0.506892
$712$	6.43785	0.241269
$713$	−1.82435	−0.0683223
$714$	8.27334	0.309622
$715$	2.62495	0.0981675
$716$	6.27130	0.234369
$717$	−2.57822	−0.0962854
$718$	6.70305	0.250156
$719$	−17.2200	−0.642198	−0.321099	−	0.947046i	$-0.604052\pi$
$719$	−17.2200	−0.642198	−0.321099	+	0.947046i	$0.604052\pi$
$720$	0.809447	0.0301663
$721$	−49.1724	−1.83128
$722$	2.46741	0.0918277
$723$	−20.7592	−0.772044
$724$	−5.37395	−0.199721
$725$	1.61991	0.0601618
$726$	−9.37340	−0.347880
$727$	−30.3318	−1.12495	−0.562473	−	0.826816i	$-0.690150\pi$
$727$	−30.3318	−1.12495	−0.562473	+	0.826816i	$0.690150\pi$
$728$	−13.5716	−0.502998
$729$	13.8414	0.512643
$730$	2.11639	0.0783311
$731$	18.9206	0.699804
$732$	1.36904	0.0506010
$733$	53.4043	1.97253	0.986266	−	0.165164i	$-0.0528154\pi$
$733$	53.4043	1.97253	0.986266	+	0.165164i	$0.0528154\pi$
$734$	−30.1840	−1.11411
$735$	0.420573	0.0155131
$736$	3.97228	0.146420
$737$	13.9000	0.512013
$738$	0.852956	0.0313977
$739$	−47.5072	−1.74758	−0.873790	−	0.486304i	$-0.838345\pi$
$739$	−47.5072	−1.74758	−0.873790	+	0.486304i	$0.838345\pi$
$740$	3.50077	0.128691
$741$	19.8073	0.727640
$742$	10.8380	0.397877
$743$	50.6251	1.85726	0.928628	−	0.371012i	$-0.120989\pi$
$743$	50.6251	1.85726	0.928628	+	0.371012i	$0.120989\pi$
$744$	0.466470	0.0171016
$745$	−7.71676	−0.282720
$746$	−28.7854	−1.05391
$747$	10.2368	0.374545
$748$	−3.83122	−0.140083
$749$	47.3339	1.72954
$750$	4.10607	0.149932
$751$	−40.5126	−1.47832	−0.739162	−	0.673527i	$-0.764778\pi$
$751$	−40.5126	−1.47832	−0.739162	+	0.673527i	$0.764778\pi$
$752$	−10.7206	−0.390940
$753$	−0.929562	−0.0338751
$754$	−1.60828	−0.0585699
$755$	−7.48426	−0.272380
$756$	−14.2793	−0.519332
$757$	−15.1226	−0.549639	−0.274819	−	0.961496i	$-0.588618\pi$
$757$	−15.1226	−0.549639	−0.274819	+	0.961496i	$0.588618\pi$
$758$	23.9274	0.869084
$759$	5.36960	0.194904
$760$	1.67204	0.0606513
$761$	−12.8798	−0.466892	−0.233446	−	0.972370i	$-0.575000\pi$
$761$	−12.8798	−0.466892	−0.233446	+	0.972370i	$0.575000\pi$
$762$	−11.8365	−0.428790
$763$	11.3059	0.409302
$764$	24.1114	0.872321
$765$	−2.33013	−0.0842459
$766$	31.9192	1.15329
$767$	47.9219	1.73036
$768$	−1.01568	−0.0366502
$769$	−44.4411	−1.60259	−0.801294	−	0.598271i	$-0.795854\pi$
$769$	−44.4411	−1.60259	−0.801294	+	0.598271i	$0.795854\pi$
$770$	−1.54866	−0.0558098
$771$	−7.36995	−0.265422
$772$	−23.3883	−0.841763
$773$	−38.9158	−1.39970	−0.699852	−	0.714288i	$-0.746751\pi$
$773$	−38.9158	−1.39970	−0.699852	+	0.714288i	$0.746751\pi$
$774$	−12.9377	−0.465035
$775$	−2.21868	−0.0796974
$776$	−2.23776	−0.0803307
$777$	−24.4668	−0.877742
$778$	−9.63885	−0.345569
$779$	1.76191	0.0631271
$780$	−2.00323	−0.0717272
$781$	0.0522860	0.00187094
$782$	−11.4349	−0.408910
$783$	−1.69213	−0.0604719
$784$	1.00695	0.0359625
$785$	7.11408	0.253912
$786$	−0.327143	−0.0116688
$787$	6.12671	0.218394	0.109197	−	0.994020i	$-0.465172\pi$
$787$	6.12671	0.218394	0.109197	+	0.994020i	$0.465172\pi$
$788$	12.1873	0.434154
$789$	−24.5606	−0.874380
$790$	2.82367	0.100462
$791$	−16.8389	−0.598722
$792$	2.61974	0.0930884
$793$	6.46482	0.229573
$794$	−10.0465	−0.356538
$795$	1.59974	0.0567370
$796$	−5.07945	−0.180036
$797$	−42.5003	−1.50544	−0.752718	−	0.658343i	$-0.771258\pi$
$797$	−42.5003	−1.50544	−0.752718	+	0.658343i	$0.771258\pi$
$798$	−11.6859	−0.413675
$799$	30.8610	1.09178
$800$	4.83090	0.170798
$801$	12.6722	0.447752
$802$	5.43995	0.192091
$803$	6.84960	0.241717
$804$	−10.6078	−0.374108
$805$	−4.62221	−0.162912
$806$	2.20275	0.0775887
$807$	−30.7720	−1.08323
$808$	1.20567	0.0424154
$809$	14.1785	0.498488	0.249244	−	0.968441i	$-0.419818\pi$
$809$	14.1785	0.498488	0.249244	+	0.968441i	$0.419818\pi$
$810$	0.320658	0.0112668
$811$	52.6636	1.84927	0.924634	−	0.380856i	$-0.124371\pi$
$811$	52.6636	1.84927	0.924634	+	0.380856i	$0.124371\pi$
$812$	0.948845	0.0332979
$813$	21.3374	0.748334
$814$	11.3301	0.397119
$815$	5.70753	0.199926
$816$	2.92380	0.102353
$817$	−26.7248	−0.934982
$818$	19.5808	0.684627
$819$	−26.7143	−0.933475
$820$	−0.178193	−0.00622276
$821$	−5.19624	−0.181350	−0.0906751	−	0.995881i	$-0.528902\pi$
$821$	−5.19624	−0.181350	−0.0906751	+	0.995881i	$0.528902\pi$
$822$	5.75707	0.200801
$823$	−41.8923	−1.46028	−0.730138	−	0.683300i	$-0.760544\pi$
$823$	−41.8923	−1.46028	−0.730138	+	0.683300i	$0.760544\pi$
$824$	−17.3775	−0.605375
$825$	6.53026	0.227354
$826$	−28.2728	−0.983737
$827$	−42.9607	−1.49389	−0.746946	−	0.664885i	$-0.768481\pi$
$827$	−42.9607	−1.49389	−0.746946	+	0.664885i	$0.768481\pi$
$828$	7.81902	0.271730
$829$	−1.40529	−0.0488078	−0.0244039	−	0.999702i	$-0.507769\pi$
$829$	−1.40529	−0.0488078	−0.0244039	+	0.999702i	$0.507769\pi$
$830$	−2.13860	−0.0742317
$831$	−10.1364	−0.351628
$832$	−4.79621	−0.166279
$833$	−2.89867	−0.100433
$834$	4.38538	0.151853
$835$	−7.83276	−0.271064
$836$	5.41148	0.187160
$837$	2.31761	0.0801083
$838$	−35.8622	−1.23884
$839$	−30.3014	−1.04612	−0.523059	−	0.852296i	$-0.675209\pi$
$839$	−30.3014	−1.04612	−0.523059	+	0.852296i	$0.675209\pi$
$840$	1.18186	0.0407781
$841$	−28.8876	−0.996123
$842$	−40.0169	−1.37907
$843$	−12.5533	−0.432359
$844$	−13.4053	−0.461428
$845$	−4.11373	−0.141517
$846$	−21.1024	−0.725514
$847$	26.1140	0.897289
$848$	3.83016	0.131528
$849$	2.42130	0.0830989
$850$	−13.9065	−0.476990
$851$	33.8164	1.15921
$852$	−0.0399022	−0.00136703
$853$	−18.4707	−0.632424	−0.316212	−	0.948689i	$-0.602411\pi$
$853$	−18.4707	−0.632424	−0.316212	+	0.948689i	$0.602411\pi$
$854$	−3.81410	−0.130516
$855$	3.29124	0.112558
$856$	16.7278	0.571744
$857$	19.1670	0.654734	0.327367	−	0.944897i	$-0.393839\pi$
$857$	19.1670	0.654734	0.327367	+	0.944897i	$0.393839\pi$
$858$	−6.48337	−0.221339
$859$	−51.6472	−1.76218	−0.881090	−	0.472948i	$-0.843190\pi$
$859$	−51.6472	−1.76218	−0.881090	+	0.472948i	$0.843190\pi$
$860$	2.70284	0.0921661
$861$	1.24539	0.0424427
$862$	23.4019	0.797070
$863$	−18.1738	−0.618644	−0.309322	−	0.950957i	$-0.600102\pi$
$863$	−18.1738	−0.618644	−0.309322	+	0.950957i	$0.600102\pi$
$864$	−5.04630	−0.171678
$865$	−2.02255	−0.0687687
$866$	1.26167	0.0428734
$867$	8.84991	0.300559
$868$	−1.29957	−0.0441104
$869$	9.13869	0.310009
$870$	0.140054	0.00474827
$871$	−50.0919	−1.69730
$872$	3.99551	0.135305
$873$	−4.40479	−0.149079
$874$	16.1514	0.546329
$875$	−11.4394	−0.386722
$876$	−5.22728	−0.176613
$877$	−30.8438	−1.04152	−0.520761	−	0.853702i	$-0.674352\pi$
$877$	−30.8438	−1.04152	−0.520761	+	0.853702i	$0.674352\pi$
$878$	11.3819	0.384119
$879$	23.5732	0.795106
$880$	−0.547296	−0.0184493
$881$	−15.5611	−0.524267	−0.262134	−	0.965032i	$-0.584426\pi$
$881$	−15.5611	−0.524267	−0.262134	+	0.965032i	$0.584426\pi$
$882$	1.98208	0.0667400
$883$	−34.1022	−1.14763	−0.573815	−	0.818985i	$-0.694537\pi$
$883$	−34.1022	−1.14763	−0.573815	+	0.818985i	$0.694537\pi$
$884$	13.8067	0.464369
$885$	−4.17319	−0.140280
$886$	−13.1575	−0.442036
$887$	11.8030	0.396306	0.198153	−	0.980171i	$-0.436506\pi$
$887$	11.8030	0.396306	0.198153	+	0.980171i	$0.436506\pi$
$888$	−8.64656	−0.290160
$889$	32.9761	1.10598
$890$	−2.64739	−0.0887406
$891$	1.03780	0.0347675
$892$	−3.19443	−0.106958
$893$	−43.5902	−1.45869
$894$	19.0597	0.637451
$895$	−2.57890	−0.0862030
$896$	2.82966	0.0945322
$897$	−19.3506	−0.646099
$898$	−13.2931	−0.443596
$899$	−0.154003	−0.00513629
$900$	9.50912	0.316971
$901$	−11.0258	−0.367321
$902$	−0.576713	−0.0192024
$903$	−18.8901	−0.628623
$904$	−5.95086	−0.197923
$905$	2.20988	0.0734590
$906$	18.4854	0.614136
$907$	0.341295	0.0113325	0.00566625	−	0.999984i	$-0.498196\pi$
$907$	0.341295	0.0113325	0.00566625	+	0.999984i	$0.498196\pi$
$908$	−22.0104	−0.730442
$909$	2.37324	0.0787153
$910$	5.58095	0.185007
$911$	4.49287	0.148855	0.0744277	−	0.997226i	$-0.476287\pi$
$911$	4.49287	0.148855	0.0744277	+	0.997226i	$0.476287\pi$
$912$	−4.12978	−0.136751
$913$	−6.92147	−0.229067
$914$	2.24966	0.0744123
$915$	−0.562977	−0.0186115
$916$	8.59551	0.284004
$917$	0.911413	0.0300975
$918$	14.5266	0.479449
$919$	46.0757	1.51990	0.759949	−	0.649983i	$-0.225224\pi$
$919$	46.0757	1.51990	0.759949	+	0.649983i	$0.225224\pi$
$920$	−1.63349	−0.0538545
$921$	9.56489	0.315174
$922$	−5.70565	−0.187905
$923$	−0.188425	−0.00620208
$924$	3.82504	0.125835
$925$	41.1258	1.35221
$926$	−3.75735	−0.123474
$927$	−34.2059	−1.12347
$928$	0.335322	0.0110075
$929$	−9.40306	−0.308504	−0.154252	−	0.988032i	$-0.549297\pi$
$929$	−9.40306	−0.308504	−0.154252	+	0.988032i	$0.549297\pi$
$930$	−0.191823	−0.00629012
$931$	4.09429	0.134185
$932$	12.1975	0.399543
$933$	11.2935	0.369734
$934$	−5.43199	−0.177740
$935$	1.57548	0.0515237
$936$	−9.44085	−0.308584
$937$	−11.7562	−0.384058	−0.192029	−	0.981389i	$-0.561507\pi$
$937$	−11.7562	−0.384058	−0.192029	+	0.981389i	$0.561507\pi$
$938$	29.5530	0.964941
$939$	−4.45494	−0.145382
$940$	4.40854	0.143791
$941$	−36.7092	−1.19669	−0.598343	−	0.801240i	$-0.704174\pi$
$941$	−36.7092	−1.19669	−0.598343	+	0.801240i	$0.704174\pi$
$942$	−17.5711	−0.572498
$943$	−1.72129	−0.0560529
$944$	−9.99161	−0.325199
$945$	5.87195	0.191015
$946$	8.74762	0.284410
$947$	−6.06271	−0.197012	−0.0985059	−	0.995136i	$-0.531406\pi$
$947$	−6.06271	−0.197012	−0.0985059	+	0.995136i	$0.531406\pi$
$948$	−6.97420	−0.226512
$949$	−24.6841	−0.801281
$950$	19.6426	0.637289
$951$	0.543956	0.0176390
$952$	−8.14563	−0.264001
$953$	6.37627	0.206548	0.103274	−	0.994653i	$-0.467068\pi$
$953$	6.37627	0.206548	0.103274	+	0.994653i	$0.467068\pi$
$954$	7.53928	0.244093
$955$	−9.91515	−0.320847
$956$	2.53842	0.0820984
$957$	0.453278	0.0146524
$958$	23.1212	0.747013
$959$	−16.0391	−0.517928
$960$	0.417670	0.0134802
$961$	−30.7891	−0.993196
$962$	−40.8306	−1.31643
$963$	32.9269	1.06105
$964$	20.4388	0.658289
$965$	9.61777	0.309607
$966$	11.4164	0.367317
$967$	−51.0186	−1.64065	−0.820324	−	0.571899i	$-0.806207\pi$
$967$	−51.0186	−1.64065	−0.820324	+	0.571899i	$0.806207\pi$
$968$	9.22870	0.296622
$969$	11.8882	0.381906
$970$	0.920214	0.0295463
$971$	−23.6976	−0.760491	−0.380245	−	0.924886i	$-0.624160\pi$
$971$	−23.6976	−0.760491	−0.380245	+	0.924886i	$0.624160\pi$
$972$	−15.9309	−0.510983
$973$	−12.2175	−0.391677
$974$	−29.1457	−0.933887
$975$	−23.5333	−0.753669
$976$	−1.34790	−0.0431453
$977$	4.72270	0.151093	0.0755463	−	0.997142i	$-0.475930\pi$
$977$	4.72270	0.151093	0.0755463	+	0.997142i	$0.475930\pi$
$978$	−14.0971	−0.450775
$979$	−8.56815	−0.273839
$980$	−0.414080	−0.0132273
$981$	7.86475	0.251102
$982$	−23.8501	−0.761086
$983$	9.16978	0.292471	0.146235	−	0.989250i	$-0.453284\pi$
$983$	9.16978	0.292471	0.146235	+	0.989250i	$0.453284\pi$
$984$	0.440119	0.0140305
$985$	−5.01167	−0.159685
$986$	−0.965279	−0.0307407
$987$	−30.8112	−0.980732
$988$	−19.5015	−0.620427
$989$	26.1086	0.830206
$990$	−1.07729	−0.0342387
$991$	−11.1527	−0.354278	−0.177139	−	0.984186i	$-0.556684\pi$
$991$	−11.1527	−0.354278	−0.177139	+	0.984186i	$0.556684\pi$
$992$	−0.459269	−0.0145818
$993$	18.1485	0.575926
$994$	0.111166	0.00352598
$995$	2.08878	0.0662188
$996$	5.28213	0.167371
$997$	58.6864	1.85862	0.929308	−	0.369305i	$-0.120404\pi$
$997$	58.6864	1.85862	0.929308	+	0.369305i	$0.120404\pi$
$998$	11.2820	0.357127
$999$	−42.9596	−1.35918

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.h.1.15	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.h.1.15	✓	42	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.01568 q^{3} +1.00000 q^{4} -0.411222 q^{5} +1.01568 q^{6} -2.82966 q^{7} -1.00000 q^{8} -1.96840 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.01568 q^{3} +1.00000 q^{4} -0.411222 q^{5} +1.01568 q^{6} -2.82966 q^{7} -1.00000 q^{8} -1.96840 q^{9} +0.411222 q^{10} +1.33090 q^{11} -1.01568 q^{12} -4.79621 q^{13} +2.82966 q^{14} +0.417670 q^{15} +1.00000 q^{16} -2.87866 q^{17} +1.96840 q^{18} +4.06603 q^{19} -0.411222 q^{20} +2.87402 q^{21} -1.33090 q^{22} -3.97228 q^{23} +1.01568 q^{24} -4.83090 q^{25} +4.79621 q^{26} +5.04630 q^{27} -2.82966 q^{28} -0.335322 q^{29} -0.417670 q^{30} +0.459269 q^{31} -1.00000 q^{32} -1.35177 q^{33} +2.87866 q^{34} +1.16362 q^{35} -1.96840 q^{36} -8.51309 q^{37} -4.06603 q^{38} +4.87142 q^{39} +0.411222 q^{40} +0.433325 q^{41} -2.87402 q^{42} -6.57270 q^{43} +1.33090 q^{44} +0.809447 q^{45} +3.97228 q^{46} -10.7206 q^{47} -1.01568 q^{48} +1.00695 q^{49} +4.83090 q^{50} +2.92380 q^{51} -4.79621 q^{52} +3.83016 q^{53} -5.04630 q^{54} -0.547296 q^{55} +2.82966 q^{56} -4.12978 q^{57} +0.335322 q^{58} -9.99161 q^{59} +0.417670 q^{60} -1.34790 q^{61} -0.459269 q^{62} +5.56988 q^{63} +1.00000 q^{64} +1.97231 q^{65} +1.35177 q^{66} +10.4440 q^{67} -2.87866 q^{68} +4.03456 q^{69} -1.16362 q^{70} +0.0392862 q^{71} +1.96840 q^{72} +5.14659 q^{73} +8.51309 q^{74} +4.90664 q^{75} +4.06603 q^{76} -3.76599 q^{77} -4.87142 q^{78} +6.86654 q^{79} -0.411222 q^{80} +0.779769 q^{81} -0.433325 q^{82} -5.20059 q^{83} +2.87402 q^{84} +1.18377 q^{85} +6.57270 q^{86} +0.340579 q^{87} -1.33090 q^{88} -6.43785 q^{89} -0.809447 q^{90} +13.5716 q^{91} -3.97228 q^{92} -0.466470 q^{93} +10.7206 q^{94} -1.67204 q^{95} +1.01568 q^{96} +2.23776 q^{97} -1.00695 q^{98} -2.61974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * q^99

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