LMFDB - Embedded newform 4002.2.a.bf.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4002,2,Mod(1,4002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4002 = 2 \cdot 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4002.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:	$31.9561308889$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.61157024.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 8x^{4} + 8x^{3} + 17x^{2} - 4x - 4 $ x^6 - 2x^5 - 8x^4 + 8x^3 + 17x^2 - 4*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.44200$ of defining polynomial
Character	$\chi$	$=$	4002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} -1.00000 q^{6} -1.96335 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} -1.00000 q^{6} -1.96335 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.56155 q^{10} -1.94852 q^{11} +1.00000 q^{12} +0.935479 q^{13} +1.96335 q^{14} +2.56155 q^{15} +1.00000 q^{16} +2.08949 q^{17} -1.00000 q^{18} +2.20246 q^{19} +2.56155 q^{20} -1.96335 q^{21} +1.94852 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.56155 q^{25} -0.935479 q^{26} +1.00000 q^{27} -1.96335 q^{28} +1.00000 q^{29} -2.56155 q^{30} +7.28027 q^{31} -1.00000 q^{32} -1.94852 q^{33} -2.08949 q^{34} -5.02924 q^{35} +1.00000 q^{36} -4.14807 q^{37} -2.20246 q^{38} +0.935479 q^{39} -2.56155 q^{40} +5.59024 q^{41} +1.96335 q^{42} +4.97639 q^{43} -1.94852 q^{44} +2.56155 q^{45} -1.00000 q^{46} -2.25531 q^{47} +1.00000 q^{48} -3.14524 q^{49} -1.56155 q^{50} +2.08949 q^{51} +0.935479 q^{52} +3.28182 q^{53} -1.00000 q^{54} -4.99123 q^{55} +1.96335 q^{56} +2.20246 q^{57} -1.00000 q^{58} -1.11938 q^{59} +2.56155 q^{60} -8.24006 q^{61} -7.28027 q^{62} -1.96335 q^{63} +1.00000 q^{64} +2.39628 q^{65} +1.94852 q^{66} +11.4617 q^{67} +2.08949 q^{68} +1.00000 q^{69} +5.02924 q^{70} +4.07756 q^{71} -1.00000 q^{72} -6.10569 q^{73} +4.14807 q^{74} +1.56155 q^{75} +2.20246 q^{76} +3.82563 q^{77} -0.935479 q^{78} +13.0226 q^{79} +2.56155 q^{80} +1.00000 q^{81} -5.59024 q^{82} +3.03980 q^{83} -1.96335 q^{84} +5.35234 q^{85} -4.97639 q^{86} +1.00000 q^{87} +1.94852 q^{88} -10.8368 q^{89} -2.56155 q^{90} -1.83668 q^{91} +1.00000 q^{92} +7.28027 q^{93} +2.25531 q^{94} +5.64173 q^{95} -1.00000 q^{96} +4.74716 q^{97} +3.14524 q^{98} -1.94852 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + 7 q^{11} + 6 q^{12} + 3 q^{13} - 2 q^{14} + 3 q^{15} + 6 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + 3 q^{20} + 2 q^{21} - 7 q^{22} + 6 q^{23} - 6 q^{24} - 3 q^{25} - 3 q^{26} + 6 q^{27} + 2 q^{28} + 6 q^{29} - 3 q^{30} + q^{31} - 6 q^{32} + 7 q^{33} - 8 q^{34} + 18 q^{35} + 6 q^{36} + 7 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} + 13 q^{41} - 2 q^{42} + 7 q^{44} + 3 q^{45} - 6 q^{46} + 22 q^{47} + 6 q^{48} + 8 q^{49} + 3 q^{50} + 8 q^{51} + 3 q^{52} + 10 q^{53} - 6 q^{54} - 5 q^{55} - 2 q^{56} - 4 q^{57} - 6 q^{58} + 17 q^{59} + 3 q^{60} + q^{61} - q^{62} + 2 q^{63} + 6 q^{64} - 7 q^{65} - 7 q^{66} + 3 q^{67} + 8 q^{68} + 6 q^{69} - 18 q^{70} + 11 q^{71} - 6 q^{72} - 7 q^{74} - 3 q^{75} - 4 q^{76} - 3 q^{78} + 2 q^{79} + 3 q^{80} + 6 q^{81} - 13 q^{82} + 16 q^{83} + 2 q^{84} + 4 q^{85} + 6 q^{87} - 7 q^{88} + 16 q^{89} - 3 q^{90} - 28 q^{91} + 6 q^{92} + q^{93} - 22 q^{94} + 32 q^{95} - 6 q^{96} + 2 q^{97} - 8 q^{98} + 7 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + 7 * q^11 + 6 * q^12 + 3 * q^13 - 2 * q^14 + 3 * q^15 + 6 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 + 3 * q^20 + 2 * q^21 - 7 * q^22 + 6 * q^23 - 6 * q^24 - 3 * q^25 - 3 * q^26 + 6 * q^27 + 2 * q^28 + 6 * q^29 - 3 * q^30 + q^31 - 6 * q^32 + 7 * q^33 - 8 * q^34 + 18 * q^35 + 6 * q^36 + 7 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 + 13 * q^41 - 2 * q^42 + 7 * q^44 + 3 * q^45 - 6 * q^46 + 22 * q^47 + 6 * q^48 + 8 * q^49 + 3 * q^50 + 8 * q^51 + 3 * q^52 + 10 * q^53 - 6 * q^54 - 5 * q^55 - 2 * q^56 - 4 * q^57 - 6 * q^58 + 17 * q^59 + 3 * q^60 + q^61 - q^62 + 2 * q^63 + 6 * q^64 - 7 * q^65 - 7 * q^66 + 3 * q^67 + 8 * q^68 + 6 * q^69 - 18 * q^70 + 11 * q^71 - 6 * q^72 - 7 * q^74 - 3 * q^75 - 4 * q^76 - 3 * q^78 + 2 * q^79 + 3 * q^80 + 6 * q^81 - 13 * q^82 + 16 * q^83 + 2 * q^84 + 4 * q^85 + 6 * q^87 - 7 * q^88 + 16 * q^89 - 3 * q^90 - 28 * q^91 + 6 * q^92 + q^93 - 22 * q^94 + 32 * q^95 - 6 * q^96 + 2 * q^97 - 8 * q^98 + 7 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.56155	1.14556	0.572781	−	0.819709i	$-0.305865\pi$
$5$	2.56155	1.14556	0.572781	+	0.819709i	$0.305865\pi$
$6$	−1.00000	−0.408248
$7$	−1.96335	−0.742078	−0.371039	−	0.928617i	$-0.620998\pi$
$7$	−1.96335	−0.742078	−0.371039	+	0.928617i	$0.620998\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.56155	−0.810034
$11$	−1.94852	−0.587500	−0.293750	−	0.955882i	$-0.594903\pi$
$11$	−1.94852	−0.587500	−0.293750	+	0.955882i	$0.594903\pi$
$12$	1.00000	0.288675
$13$	0.935479	0.259455	0.129728	−	0.991550i	$-0.458590\pi$
$13$	0.935479	0.259455	0.129728	+	0.991550i	$0.458590\pi$
$14$	1.96335	0.524729
$15$	2.56155	0.661390
$16$	1.00000	0.250000
$17$	2.08949	0.506775	0.253388	−	0.967365i	$-0.418455\pi$
$17$	2.08949	0.506775	0.253388	+	0.967365i	$0.418455\pi$
$18$	−1.00000	−0.235702
$19$	2.20246	0.505280	0.252640	−	0.967560i	$-0.418701\pi$
$19$	2.20246	0.505280	0.252640	+	0.967560i	$0.418701\pi$
$20$	2.56155	0.572781
$21$	−1.96335	−0.428439
$22$	1.94852	0.415425
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	1.56155	0.312311
$26$	−0.935479	−0.183462
$27$	1.00000	0.192450
$28$	−1.96335	−0.371039
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−2.56155	−0.467673
$31$	7.28027	1.30758	0.653788	−	0.756678i	$-0.273179\pi$
$31$	7.28027	1.30758	0.653788	+	0.756678i	$0.273179\pi$
$32$	−1.00000	−0.176777
$33$	−1.94852	−0.339193
$34$	−2.08949	−0.358344
$35$	−5.02924	−0.850096
$36$	1.00000	0.166667
$37$	−4.14807	−0.681939	−0.340970	−	0.940074i	$-0.610755\pi$
$37$	−4.14807	−0.681939	−0.340970	+	0.940074i	$0.610755\pi$
$38$	−2.20246	−0.357287
$39$	0.935479	0.149796
$40$	−2.56155	−0.405017
$41$	5.59024	0.873050	0.436525	−	0.899692i	$-0.356209\pi$
$41$	5.59024	0.873050	0.436525	+	0.899692i	$0.356209\pi$
$42$	1.96335	0.302952
$43$	4.97639	0.758893	0.379446	−	0.925214i	$-0.376114\pi$
$43$	4.97639	0.758893	0.379446	+	0.925214i	$0.376114\pi$
$44$	−1.94852	−0.293750
$45$	2.56155	0.381854
$46$	−1.00000	−0.147442
$47$	−2.25531	−0.328970	−0.164485	−	0.986380i	$-0.552596\pi$
$47$	−2.25531	−0.328970	−0.164485	+	0.986380i	$0.552596\pi$
$48$	1.00000	0.144338
$49$	−3.14524	−0.449320
$50$	−1.56155	−0.220837
$51$	2.08949	0.292587
$52$	0.935479	0.129728
$53$	3.28182	0.450793	0.225396	−	0.974267i	$-0.427632\pi$
$53$	3.28182	0.450793	0.225396	+	0.974267i	$0.427632\pi$
$54$	−1.00000	−0.136083
$55$	−4.99123	−0.673017
$56$	1.96335	0.262364
$57$	2.20246	0.291723
$58$	−1.00000	−0.131306
$59$	−1.11938	−0.145731	−0.0728655	−	0.997342i	$-0.523214\pi$
$59$	−1.11938	−0.145731	−0.0728655	+	0.997342i	$0.523214\pi$
$60$	2.56155	0.330695
$61$	−8.24006	−1.05503	−0.527516	−	0.849545i	$-0.676876\pi$
$61$	−8.24006	−1.05503	−0.527516	+	0.849545i	$0.676876\pi$
$62$	−7.28027	−0.924596
$63$	−1.96335	−0.247359
$64$	1.00000	0.125000
$65$	2.39628	0.297222
$66$	1.94852	0.239846
$67$	11.4617	1.40028	0.700138	−	0.714008i	$-0.253122\pi$
$67$	11.4617	1.40028	0.700138	+	0.714008i	$0.253122\pi$
$68$	2.08949	0.253388
$69$	1.00000	0.120386
$70$	5.02924	0.601109
$71$	4.07756	0.483917	0.241959	−	0.970287i	$-0.422210\pi$
$71$	4.07756	0.483917	0.241959	+	0.970287i	$0.422210\pi$
$72$	−1.00000	−0.117851
$73$	−6.10569	−0.714616	−0.357308	−	0.933987i	$-0.616305\pi$
$73$	−6.10569	−0.714616	−0.357308	+	0.933987i	$0.616305\pi$
$74$	4.14807	0.482204
$75$	1.56155	0.180313
$76$	2.20246	0.252640
$77$	3.82563	0.435971
$78$	−0.935479	−0.105922
$79$	13.0226	1.46516	0.732580	−	0.680680i	$-0.238316\pi$
$79$	13.0226	1.46516	0.732580	+	0.680680i	$0.238316\pi$
$80$	2.56155	0.286390
$81$	1.00000	0.111111
$82$	−5.59024	−0.617339
$83$	3.03980	0.333662	0.166831	−	0.985986i	$-0.446647\pi$
$83$	3.03980	0.333662	0.166831	+	0.985986i	$0.446647\pi$
$84$	−1.96335	−0.214220
$85$	5.35234	0.580542
$86$	−4.97639	−0.536618
$87$	1.00000	0.107211
$88$	1.94852	0.207713
$89$	−10.8368	−1.14870	−0.574348	−	0.818611i	$-0.694744\pi$
$89$	−10.8368	−1.14870	−0.574348	+	0.818611i	$0.694744\pi$
$90$	−2.56155	−0.270011
$91$	−1.83668	−0.192536
$92$	1.00000	0.104257
$93$	7.28027	0.754929
$94$	2.25531	0.232617
$95$	5.64173	0.578829
$96$	−1.00000	−0.102062
$97$	4.74716	0.482001	0.241001	−	0.970525i	$-0.422524\pi$
$97$	4.74716	0.482001	0.241001	+	0.970525i	$0.422524\pi$
$98$	3.14524	0.317717
$99$	−1.94852	−0.195833
$100$	1.56155	0.156155
$101$	10.1300	1.00797	0.503986	−	0.863712i	$-0.331866\pi$
$101$	10.1300	1.00797	0.503986	+	0.863712i	$0.331866\pi$
$102$	−2.08949	−0.206890
$103$	3.06961	0.302457	0.151229	−	0.988499i	$-0.451677\pi$
$103$	3.06961	0.302457	0.151229	+	0.988499i	$0.451677\pi$
$104$	−0.935479	−0.0917312
$105$	−5.02924	−0.490803
$106$	−3.28182	−0.318759
$107$	7.38987	0.714406	0.357203	−	0.934027i	$-0.383730\pi$
$107$	7.38987	0.714406	0.357203	+	0.934027i	$0.383730\pi$
$108$	1.00000	0.0962250
$109$	7.78988	0.746135	0.373067	−	0.927804i	$-0.378306\pi$
$109$	7.78988	0.746135	0.373067	+	0.927804i	$0.378306\pi$
$110$	4.99123	0.475895
$111$	−4.14807	−0.393718
$112$	−1.96335	−0.185520
$113$	13.2683	1.24818	0.624090	−	0.781352i	$-0.285470\pi$
$113$	13.2683	1.24818	0.624090	+	0.781352i	$0.285470\pi$
$114$	−2.20246	−0.206280
$115$	2.56155	0.238866
$116$	1.00000	0.0928477
$117$	0.935479	0.0864850
$118$	1.11938	0.103047
$119$	−4.10241	−0.376067
$120$	−2.56155	−0.233837
$121$	−7.20328	−0.654844
$122$	8.24006	0.746020
$123$	5.59024	0.504055
$124$	7.28027	0.653788
$125$	−8.80776	−0.787790
$126$	1.96335	0.174910
$127$	15.3014	1.35778	0.678890	−	0.734240i	$-0.262461\pi$
$127$	15.3014	1.35778	0.678890	+	0.734240i	$0.262461\pi$
$128$	−1.00000	−0.0883883
$129$	4.97639	0.438147
$130$	−2.39628	−0.210168
$131$	−6.76538	−0.591094	−0.295547	−	0.955328i	$-0.595502\pi$
$131$	−6.76538	−0.591094	−0.295547	+	0.955328i	$0.595502\pi$
$132$	−1.94852	−0.169597
$133$	−4.32422	−0.374957
$134$	−11.4617	−0.990144
$135$	2.56155	0.220463
$136$	−2.08949	−0.179172
$137$	16.4916	1.40898	0.704488	−	0.709716i	$-0.251177\pi$
$137$	16.4916	1.40898	0.704488	+	0.709716i	$0.251177\pi$
$138$	−1.00000	−0.0851257
$139$	0.405777	0.0344175	0.0172088	−	0.999852i	$-0.494522\pi$
$139$	0.405777	0.0344175	0.0172088	+	0.999852i	$0.494522\pi$
$140$	−5.02924	−0.425048
$141$	−2.25531	−0.189931
$142$	−4.07756	−0.342181
$143$	−1.82280	−0.152430
$144$	1.00000	0.0833333
$145$	2.56155	0.212725
$146$	6.10569	0.505310
$147$	−3.14524	−0.259415
$148$	−4.14807	−0.340970
$149$	8.10778	0.664215	0.332108	−	0.943242i	$-0.392240\pi$
$149$	8.10778	0.664215	0.332108	+	0.943242i	$0.392240\pi$
$150$	−1.56155	−0.127500
$151$	16.3766	1.33271	0.666356	−	0.745633i	$-0.267853\pi$
$151$	16.3766	1.33271	0.666356	+	0.745633i	$0.267853\pi$
$152$	−2.20246	−0.178643
$153$	2.08949	0.168925
$154$	−3.82563	−0.308278
$155$	18.6488	1.49791
$156$	0.935479	0.0748982
$157$	−21.7649	−1.73703	−0.868516	−	0.495662i	$-0.834926\pi$
$157$	−21.7649	−1.73703	−0.868516	+	0.495662i	$0.834926\pi$
$158$	−13.0226	−1.03603
$159$	3.28182	0.260265
$160$	−2.56155	−0.202509
$161$	−1.96335	−0.154734
$162$	−1.00000	−0.0785674
$163$	5.52133	0.432464	0.216232	−	0.976342i	$-0.430623\pi$
$163$	5.52133	0.432464	0.216232	+	0.976342i	$0.430623\pi$
$164$	5.59024	0.436525
$165$	−4.99123	−0.388567
$166$	−3.03980	−0.235935
$167$	11.6501	0.901515	0.450757	−	0.892647i	$-0.351154\pi$
$167$	11.6501	0.901515	0.450757	+	0.892647i	$0.351154\pi$
$168$	1.96335	0.151476
$169$	−12.1249	−0.932683
$170$	−5.35234	−0.410505
$171$	2.20246	0.168427
$172$	4.97639	0.379446
$173$	0.521944	0.0396826	0.0198413	−	0.999803i	$-0.493684\pi$
$173$	0.521944	0.0396826	0.0198413	+	0.999803i	$0.493684\pi$
$174$	−1.00000	−0.0758098
$175$	−3.06588	−0.231759
$176$	−1.94852	−0.146875
$177$	−1.11938	−0.0841378
$178$	10.8368	0.812251
$179$	20.7278	1.54927	0.774634	−	0.632409i	$-0.217934\pi$
$179$	20.7278	1.54927	0.774634	+	0.632409i	$0.217934\pi$
$180$	2.56155	0.190927
$181$	−11.6567	−0.866433	−0.433216	−	0.901290i	$-0.642621\pi$
$181$	−11.6567	−0.866433	−0.433216	+	0.901290i	$0.642621\pi$
$182$	1.83668	0.136144
$183$	−8.24006	−0.609122
$184$	−1.00000	−0.0737210
$185$	−10.6255	−0.781203
$186$	−7.28027	−0.533816
$187$	−4.07140	−0.297731
$188$	−2.25531	−0.164485
$189$	−1.96335	−0.142813
$190$	−5.64173	−0.409294
$191$	−1.16402	−0.0842255	−0.0421128	−	0.999113i	$-0.513409\pi$
$191$	−1.16402	−0.0842255	−0.0421128	+	0.999113i	$0.513409\pi$
$192$	1.00000	0.0721688
$193$	7.21731	0.519513	0.259757	−	0.965674i	$-0.416358\pi$
$193$	7.21731	0.519513	0.259757	+	0.965674i	$0.416358\pi$
$194$	−4.74716	−0.340826
$195$	2.39628	0.171601
$196$	−3.14524	−0.224660
$197$	−20.0951	−1.43172	−0.715860	−	0.698244i	$-0.753965\pi$
$197$	−20.0951	−1.43172	−0.715860	+	0.698244i	$0.753965\pi$
$198$	1.94852	0.138475
$199$	−24.2441	−1.71862	−0.859308	−	0.511459i	$-0.829105\pi$
$199$	−24.2441	−1.71862	−0.859308	+	0.511459i	$0.829105\pi$
$200$	−1.56155	−0.110418
$201$	11.4617	0.808449
$202$	−10.1300	−0.712744
$203$	−1.96335	−0.137800
$204$	2.08949	0.146293
$205$	14.3197	1.00013
$206$	−3.06961	−0.213870
$207$	1.00000	0.0695048
$208$	0.935479	0.0648638
$209$	−4.29154	−0.296852
$210$	5.02924	0.347050
$211$	−10.2109	−0.702949	−0.351475	−	0.936197i	$-0.614320\pi$
$211$	−10.2109	−0.702949	−0.351475	+	0.936197i	$0.614320\pi$
$212$	3.28182	0.225396
$213$	4.07756	0.279390
$214$	−7.38987	−0.505161
$215$	12.7473	0.869358
$216$	−1.00000	−0.0680414
$217$	−14.2938	−0.970324
$218$	−7.78988	−0.527597
$219$	−6.10569	−0.412584
$220$	−4.99123	−0.336509
$221$	1.95467	0.131485
$222$	4.14807	0.278400
$223$	−4.26874	−0.285856	−0.142928	−	0.989733i	$-0.545652\pi$
$223$	−4.26874	−0.285856	−0.142928	+	0.989733i	$0.545652\pi$
$224$	1.96335	0.131182
$225$	1.56155	0.104104
$226$	−13.2683	−0.882597
$227$	10.1317	0.672462	0.336231	−	0.941779i	$-0.390848\pi$
$227$	10.1317	0.672462	0.336231	+	0.941779i	$0.390848\pi$
$228$	2.20246	0.145862
$229$	−22.5182	−1.48804	−0.744021	−	0.668156i	$-0.767084\pi$
$229$	−22.5182	−1.48804	−0.744021	+	0.668156i	$0.767084\pi$
$230$	−2.56155	−0.168904
$231$	3.82563	0.251708
$232$	−1.00000	−0.0656532
$233$	−6.71927	−0.440194	−0.220097	−	0.975478i	$-0.570637\pi$
$233$	−6.71927	−0.440194	−0.220097	+	0.975478i	$0.570637\pi$
$234$	−0.935479	−0.0611542
$235$	−5.77709	−0.376856
$236$	−1.11938	−0.0728655
$237$	13.0226	0.845911
$238$	4.10241	0.265920
$239$	8.10356	0.524176	0.262088	−	0.965044i	$-0.415589\pi$
$239$	8.10356	0.524176	0.262088	+	0.965044i	$0.415589\pi$
$240$	2.56155	0.165348
$241$	−21.6758	−1.39626	−0.698129	−	0.715972i	$-0.745984\pi$
$241$	−21.6758	−1.39626	−0.698129	+	0.715972i	$0.745984\pi$
$242$	7.20328	0.463044
$243$	1.00000	0.0641500
$244$	−8.24006	−0.527516
$245$	−8.05670	−0.514724
$246$	−5.59024	−0.356421
$247$	2.06036	0.131097
$248$	−7.28027	−0.462298
$249$	3.03980	0.192640
$250$	8.80776	0.557052
$251$	0.360562	0.0227585	0.0113792	−	0.999935i	$-0.496378\pi$
$251$	0.360562	0.0227585	0.0113792	+	0.999935i	$0.496378\pi$
$252$	−1.96335	−0.123680
$253$	−1.94852	−0.122502
$254$	−15.3014	−0.960095
$255$	5.35234	0.335176
$256$	1.00000	0.0625000
$257$	25.0130	1.56027	0.780135	−	0.625612i	$-0.215150\pi$
$257$	25.0130	1.56027	0.780135	+	0.625612i	$0.215150\pi$
$258$	−4.97639	−0.309817
$259$	8.14414	0.506052
$260$	2.39628	0.148611
$261$	1.00000	0.0618984
$262$	6.76538	0.417966
$263$	1.81901	0.112165	0.0560824	−	0.998426i	$-0.482139\pi$
$263$	1.81901	0.112165	0.0560824	+	0.998426i	$0.482139\pi$
$264$	1.94852	0.119923
$265$	8.40656	0.516411
$266$	4.32422	0.265135
$267$	−10.8368	−0.663200
$268$	11.4617	0.700138
$269$	19.5554	1.19231	0.596156	−	0.802869i	$-0.296694\pi$
$269$	19.5554	1.19231	0.596156	+	0.802869i	$0.296694\pi$
$270$	−2.56155	−0.155891
$271$	1.71874	0.104406	0.0522031	−	0.998636i	$-0.483376\pi$
$271$	1.71874	0.104406	0.0522031	+	0.998636i	$0.483376\pi$
$272$	2.08949	0.126694
$273$	−1.83668	−0.111161
$274$	−16.4916	−0.996296
$275$	−3.04271	−0.183482
$276$	1.00000	0.0601929
$277$	9.80904	0.589368	0.294684	−	0.955595i	$-0.404786\pi$
$277$	9.80904	0.589368	0.294684	+	0.955595i	$0.404786\pi$
$278$	−0.405777	−0.0243369
$279$	7.28027	0.435859
$280$	5.02924	0.300554
$281$	19.9331	1.18911	0.594555	−	0.804055i	$-0.297328\pi$
$281$	19.9331	1.18911	0.594555	+	0.804055i	$0.297328\pi$
$282$	2.25531	0.134302
$283$	1.76647	0.105006	0.0525029	−	0.998621i	$-0.483280\pi$
$283$	1.76647	0.105006	0.0525029	+	0.998621i	$0.483280\pi$
$284$	4.07756	0.241959
$285$	5.64173	0.334187
$286$	1.82280	0.107784
$287$	−10.9756	−0.647871
$288$	−1.00000	−0.0589256
$289$	−12.6340	−0.743179
$290$	−2.56155	−0.150420
$291$	4.74716	0.278284
$292$	−6.10569	−0.357308
$293$	−6.05975	−0.354014	−0.177007	−	0.984210i	$-0.556642\pi$
$293$	−6.05975	−0.354014	−0.177007	+	0.984210i	$0.556642\pi$
$294$	3.14524	0.183434
$295$	−2.86735	−0.166944
$296$	4.14807	0.241102
$297$	−1.94852	−0.113064
$298$	−8.10778	−0.469671
$299$	0.935479	0.0541001
$300$	1.56155	0.0901563
$301$	−9.77042	−0.563158
$302$	−16.3766	−0.942370
$303$	10.1300	0.581953
$304$	2.20246	0.126320
$305$	−21.1073	−1.20860
$306$	−2.08949	−0.119448
$307$	−5.90674	−0.337116	−0.168558	−	0.985692i	$-0.553911\pi$
$307$	−5.90674	−0.337116	−0.168558	+	0.985692i	$0.553911\pi$
$308$	3.82563	0.217985
$309$	3.06961	0.174624
$310$	−18.6488	−1.05918
$311$	11.2372	0.637205	0.318603	−	0.947888i	$-0.396786\pi$
$311$	11.2372	0.637205	0.318603	+	0.947888i	$0.396786\pi$
$312$	−0.935479	−0.0529611
$313$	−10.5718	−0.597555	−0.298778	−	0.954323i	$-0.596579\pi$
$313$	−10.5718	−0.597555	−0.298778	+	0.954323i	$0.596579\pi$
$314$	21.7649	1.22827
$315$	−5.02924	−0.283365
$316$	13.0226	0.732580
$317$	−2.09654	−0.117753	−0.0588766	−	0.998265i	$-0.518752\pi$
$317$	−2.09654	−0.117753	−0.0588766	+	0.998265i	$0.518752\pi$
$318$	−3.28182	−0.184035
$319$	−1.94852	−0.109096
$320$	2.56155	0.143195
$321$	7.38987	0.412462
$322$	1.96335	0.109413
$323$	4.60202	0.256063
$324$	1.00000	0.0555556
$325$	1.46080	0.0810306
$326$	−5.52133	−0.305798
$327$	7.78988	0.430781
$328$	−5.59024	−0.308670
$329$	4.42797	0.244122
$330$	4.99123	0.274758
$331$	−17.7693	−0.976690	−0.488345	−	0.872651i	$-0.662399\pi$
$331$	−17.7693	−0.976690	−0.488345	+	0.872651i	$0.662399\pi$
$332$	3.03980	0.166831
$333$	−4.14807	−0.227313
$334$	−11.6501	−0.637467
$335$	29.3599	1.60410
$336$	−1.96335	−0.107110
$337$	10.1576	0.553319	0.276659	−	0.960968i	$-0.410773\pi$
$337$	10.1576	0.553319	0.276659	+	0.960968i	$0.410773\pi$
$338$	12.1249	0.659506
$339$	13.2683	0.720638
$340$	5.35234	0.290271
$341$	−14.1857	−0.768201
$342$	−2.20246	−0.119096
$343$	19.9187	1.07551
$344$	−4.97639	−0.268309
$345$	2.56155	0.137909
$346$	−0.521944	−0.0280599
$347$	−12.6032	−0.676574	−0.338287	−	0.941043i	$-0.609847\pi$
$347$	−12.6032	−0.676574	−0.338287	+	0.941043i	$0.609847\pi$
$348$	1.00000	0.0536056
$349$	9.32835	0.499335	0.249668	−	0.968332i	$-0.419679\pi$
$349$	9.32835	0.499335	0.249668	+	0.968332i	$0.419679\pi$
$350$	3.06588	0.163878
$351$	0.935479	0.0499322
$352$	1.94852	0.103856
$353$	−22.3402	−1.18905	−0.594524	−	0.804078i	$-0.702659\pi$
$353$	−22.3402	−1.18905	−0.594524	+	0.804078i	$0.702659\pi$
$354$	1.11938	0.0594944
$355$	10.4449	0.554357
$356$	−10.8368	−0.574348
$357$	−4.10241	−0.217122
$358$	−20.7278	−1.09550
$359$	4.78176	0.252372	0.126186	−	0.992007i	$-0.459726\pi$
$359$	4.78176	0.252372	0.126186	+	0.992007i	$0.459726\pi$
$360$	−2.56155	−0.135006
$361$	−14.1492	−0.744692
$362$	11.6567	0.612661
$363$	−7.20328	−0.378074
$364$	−1.83668	−0.0962680
$365$	−15.6400	−0.818637
$366$	8.24006	0.430715
$367$	0.504572	0.0263384	0.0131692	−	0.999913i	$-0.495808\pi$
$367$	0.504572	0.0263384	0.0131692	+	0.999913i	$0.495808\pi$
$368$	1.00000	0.0521286
$369$	5.59024	0.291017
$370$	10.6255	0.552394
$371$	−6.44338	−0.334524
$372$	7.28027	0.377465
$373$	−10.1704	−0.526601	−0.263301	−	0.964714i	$-0.584811\pi$
$373$	−10.1704	−0.526601	−0.263301	+	0.964714i	$0.584811\pi$
$374$	4.07140	0.210527
$375$	−8.80776	−0.454831
$376$	2.25531	0.116309
$377$	0.935479	0.0481796
$378$	1.96335	0.100984
$379$	−9.05632	−0.465192	−0.232596	−	0.972573i	$-0.574722\pi$
$379$	−9.05632	−0.465192	−0.232596	+	0.972573i	$0.574722\pi$
$380$	5.64173	0.289415
$381$	15.3014	0.783914
$382$	1.16402	0.0595564
$383$	18.6407	0.952496	0.476248	−	0.879311i	$-0.341996\pi$
$383$	18.6407	0.952496	0.476248	+	0.879311i	$0.341996\pi$
$384$	−1.00000	−0.0510310
$385$	9.79955	0.499431
$386$	−7.21731	−0.367351
$387$	4.97639	0.252964
$388$	4.74716	0.241001
$389$	30.3872	1.54069	0.770346	−	0.637626i	$-0.220083\pi$
$389$	30.3872	1.54069	0.770346	+	0.637626i	$0.220083\pi$
$390$	−2.39628	−0.121340
$391$	2.08949	0.105670
$392$	3.14524	0.158859
$393$	−6.76538	−0.341268
$394$	20.0951	1.01238
$395$	33.3582	1.67843
$396$	−1.94852	−0.0979167
$397$	24.3262	1.22089	0.610447	−	0.792057i	$-0.290990\pi$
$397$	24.3262	1.22089	0.610447	+	0.792057i	$0.290990\pi$
$398$	24.2441	1.21524
$399$	−4.32422	−0.216482
$400$	1.56155	0.0780776
$401$	−14.1779	−0.708013	−0.354007	−	0.935243i	$-0.615181\pi$
$401$	−14.1779	−0.708013	−0.354007	+	0.935243i	$0.615181\pi$
$402$	−11.4617	−0.571660
$403$	6.81054	0.339257
$404$	10.1300	0.503986
$405$	2.56155	0.127285
$406$	1.96335	0.0974396
$407$	8.08259	0.400639
$408$	−2.08949	−0.103445
$409$	28.9561	1.43179	0.715894	−	0.698208i	$-0.246019\pi$
$409$	28.9561	1.43179	0.715894	+	0.698208i	$0.246019\pi$
$410$	−14.3197	−0.707200
$411$	16.4916	0.813473
$412$	3.06961	0.151229
$413$	2.19774	0.108144
$414$	−1.00000	−0.0491473
$415$	7.78662	0.382230
$416$	−0.935479	−0.0458656
$417$	0.405777	0.0198710
$418$	4.29154	0.209906
$419$	−5.36488	−0.262092	−0.131046	−	0.991376i	$-0.541834\pi$
$419$	−5.36488	−0.262092	−0.131046	+	0.991376i	$0.541834\pi$
$420$	−5.02924	−0.245402
$421$	−18.6085	−0.906923	−0.453462	−	0.891276i	$-0.649811\pi$
$421$	−18.6085	−0.906923	−0.453462	+	0.891276i	$0.649811\pi$
$422$	10.2109	0.497060
$423$	−2.25531	−0.109657
$424$	−3.28182	−0.159379
$425$	3.26285	0.158271
$426$	−4.07756	−0.197558
$427$	16.1782	0.782916
$428$	7.38987	0.357203
$429$	−1.82280	−0.0880054
$430$	−12.7473	−0.614729
$431$	21.0108	1.01205	0.506027	−	0.862517i	$-0.331113\pi$
$431$	21.0108	1.01205	0.506027	+	0.862517i	$0.331113\pi$
$432$	1.00000	0.0481125
$433$	−40.8723	−1.96420	−0.982099	−	0.188368i	$-0.939680\pi$
$433$	−40.8723	−1.96420	−0.982099	+	0.188368i	$0.939680\pi$
$434$	14.2938	0.686122
$435$	2.56155	0.122817
$436$	7.78988	0.373067
$437$	2.20246	0.105358
$438$	6.10569	0.291741
$439$	17.9368	0.856077	0.428039	−	0.903760i	$-0.359205\pi$
$439$	17.9368	0.856077	0.428039	+	0.903760i	$0.359205\pi$
$440$	4.99123	0.237948
$441$	−3.14524	−0.149773
$442$	−1.95467	−0.0929743
$443$	7.86091	0.373483	0.186742	−	0.982409i	$-0.440207\pi$
$443$	7.86091	0.373483	0.186742	+	0.982409i	$0.440207\pi$
$444$	−4.14807	−0.196859
$445$	−27.7590	−1.31590
$446$	4.26874	0.202131
$447$	8.10778	0.383485
$448$	−1.96335	−0.0927598
$449$	32.4437	1.53111	0.765556	−	0.643369i	$-0.222464\pi$
$449$	32.4437	1.53111	0.765556	+	0.643369i	$0.222464\pi$
$450$	−1.56155	−0.0736123
$451$	−10.8927	−0.512917
$452$	13.2683	0.624090
$453$	16.3766	0.769442
$454$	−10.1317	−0.475503
$455$	−4.70474	−0.220562
$456$	−2.20246	−0.103140
$457$	−9.23644	−0.432062	−0.216031	−	0.976386i	$-0.569311\pi$
$457$	−9.23644	−0.432062	−0.216031	+	0.976386i	$0.569311\pi$
$458$	22.5182	1.05220
$459$	2.08949	0.0975290
$460$	2.56155	0.119433
$461$	−25.5469	−1.18984	−0.594918	−	0.803787i	$-0.702815\pi$
$461$	−25.5469	−1.18984	−0.594918	+	0.803787i	$0.702815\pi$
$462$	−3.82563	−0.177984
$463$	11.9448	0.555124	0.277562	−	0.960708i	$-0.410474\pi$
$463$	11.9448	0.555124	0.277562	+	0.960708i	$0.410474\pi$
$464$	1.00000	0.0464238
$465$	18.6488	0.864818
$466$	6.71927	0.311264
$467$	38.6820	1.78999	0.894994	−	0.446077i	$-0.147179\pi$
$467$	38.6820	1.78999	0.894994	+	0.446077i	$0.147179\pi$
$468$	0.935479	0.0432425
$469$	−22.5035	−1.03911
$470$	5.77709	0.266477
$471$	−21.7649	−1.00288
$472$	1.11938	0.0515237
$473$	−9.69659	−0.445850
$474$	−13.0226	−0.598149
$475$	3.43926	0.157804
$476$	−4.10241	−0.188033
$477$	3.28182	0.150264
$478$	−8.10356	−0.370648
$479$	−7.71889	−0.352685	−0.176342	−	0.984329i	$-0.556427\pi$
$479$	−7.71889	−0.352685	−0.176342	+	0.984329i	$0.556427\pi$
$480$	−2.56155	−0.116918
$481$	−3.88043	−0.176933
$482$	21.6758	0.987304
$483$	−1.96335	−0.0893357
$484$	−7.20328	−0.327422
$485$	12.1601	0.552162
$486$	−1.00000	−0.0453609
$487$	−2.02468	−0.0917472	−0.0458736	−	0.998947i	$-0.514607\pi$
$487$	−2.02468	−0.0917472	−0.0458736	+	0.998947i	$0.514607\pi$
$488$	8.24006	0.373010
$489$	5.52133	0.249683
$490$	8.05670	0.363965
$491$	−5.05255	−0.228018	−0.114009	−	0.993480i	$-0.536369\pi$
$491$	−5.05255	−0.228018	−0.114009	+	0.993480i	$0.536369\pi$
$492$	5.59024	0.252028
$493$	2.08949	0.0941058
$494$	−2.06036	−0.0926999
$495$	−4.99123	−0.224339
$496$	7.28027	0.326894
$497$	−8.00569	−0.359104
$498$	−3.03980	−0.136217
$499$	−18.5223	−0.829173	−0.414587	−	0.910010i	$-0.636074\pi$
$499$	−18.5223	−0.829173	−0.414587	+	0.910010i	$0.636074\pi$
$500$	−8.80776	−0.393895
$501$	11.6501	0.520490
$502$	−0.360562	−0.0160927
$503$	−21.9400	−0.978255	−0.489128	−	0.872212i	$-0.662685\pi$
$503$	−21.9400	−0.978255	−0.489128	+	0.872212i	$0.662685\pi$
$504$	1.96335	0.0874548
$505$	25.9485	1.15469
$506$	1.94852	0.0866222
$507$	−12.1249	−0.538485
$508$	15.3014	0.678890
$509$	9.15539	0.405806	0.202903	−	0.979199i	$-0.434962\pi$
$509$	9.15539	0.405806	0.202903	+	0.979199i	$0.434962\pi$
$510$	−5.35234	−0.237005
$511$	11.9876	0.530301
$512$	−1.00000	−0.0441942
$513$	2.20246	0.0972412
$514$	−25.0130	−1.10328
$515$	7.86296	0.346483
$516$	4.97639	0.219073
$517$	4.39450	0.193270
$518$	−8.14414	−0.357833
$519$	0.521944	0.0229108
$520$	−2.39628	−0.105084
$521$	−16.5182	−0.723673	−0.361837	−	0.932242i	$-0.617850\pi$
$521$	−16.5182	−0.723673	−0.361837	+	0.932242i	$0.617850\pi$
$522$	−1.00000	−0.0437688
$523$	−38.4556	−1.68155	−0.840773	−	0.541388i	$-0.817899\pi$
$523$	−38.4556	−1.68155	−0.840773	+	0.541388i	$0.817899\pi$
$524$	−6.76538	−0.295547
$525$	−3.06588	−0.133806
$526$	−1.81901	−0.0793124
$527$	15.2121	0.662647
$528$	−1.94852	−0.0847983
$529$	1.00000	0.0434783
$530$	−8.40656	−0.365158
$531$	−1.11938	−0.0485770
$532$	−4.32422	−0.187479
$533$	5.22956	0.226517
$534$	10.8368	0.468953
$535$	18.9295	0.818396
$536$	−11.4617	−0.495072
$537$	20.7278	0.894471
$538$	−19.5554	−0.843092
$539$	6.12855	0.263976
$540$	2.56155	0.110232
$541$	38.2759	1.64561	0.822805	−	0.568323i	$-0.192408\pi$
$541$	38.2759	1.64561	0.822805	+	0.568323i	$0.192408\pi$
$542$	−1.71874	−0.0738264
$543$	−11.6567	−0.500235
$544$	−2.08949	−0.0895861
$545$	19.9542	0.854743
$546$	1.83668	0.0786025
$547$	3.90501	0.166966	0.0834831	−	0.996509i	$-0.473396\pi$
$547$	3.90501	0.166966	0.0834831	+	0.996509i	$0.473396\pi$
$548$	16.4916	0.704488
$549$	−8.24006	−0.351677
$550$	3.04271	0.129742
$551$	2.20246	0.0938281
$552$	−1.00000	−0.0425628
$553$	−25.5680	−1.08726
$554$	−9.80904	−0.416746
$555$	−10.6255	−0.451028
$556$	0.405777	0.0172088
$557$	−18.4489	−0.781706	−0.390853	−	0.920453i	$-0.627820\pi$
$557$	−18.4489	−0.781706	−0.390853	+	0.920453i	$0.627820\pi$
$558$	−7.28027	−0.308199
$559$	4.65531	0.196899
$560$	−5.02924	−0.212524
$561$	−4.07140	−0.171895
$562$	−19.9331	−0.840828
$563$	12.9023	0.543765	0.271883	−	0.962330i	$-0.412354\pi$
$563$	12.9023	0.543765	0.271883	+	0.962330i	$0.412354\pi$
$564$	−2.25531	−0.0949656
$565$	33.9876	1.42987
$566$	−1.76647	−0.0742503
$567$	−1.96335	−0.0824531
$568$	−4.07756	−0.171091
$569$	−6.14589	−0.257649	−0.128825	−	0.991667i	$-0.541120\pi$
$569$	−6.14589	−0.257649	−0.128825	+	0.991667i	$0.541120\pi$
$570$	−5.64173	−0.236306
$571$	−22.7053	−0.950185	−0.475093	−	0.879936i	$-0.657585\pi$
$571$	−22.7053	−0.950185	−0.475093	+	0.879936i	$0.657585\pi$
$572$	−1.82280	−0.0762150
$573$	−1.16402	−0.0486276
$574$	10.9756	0.458114
$575$	1.56155	0.0651213
$576$	1.00000	0.0416667
$577$	−13.9189	−0.579453	−0.289727	−	0.957109i	$-0.593564\pi$
$577$	−13.9189	−0.579453	−0.289727	+	0.957109i	$0.593564\pi$
$578$	12.6340	0.525507
$579$	7.21731	0.299941
$580$	2.56155	0.106363
$581$	−5.96821	−0.247603
$582$	−4.74716	−0.196776
$583$	−6.39469	−0.264841
$584$	6.10569	0.252655
$585$	2.39628	0.0990739
$586$	6.05975	0.250326
$587$	−17.9308	−0.740085	−0.370042	−	0.929015i	$-0.620657\pi$
$587$	−17.9308	−0.740085	−0.370042	+	0.929015i	$0.620657\pi$
$588$	−3.14524	−0.129708
$589$	16.0345	0.660692
$590$	2.86735	0.118047
$591$	−20.0951	−0.826604
$592$	−4.14807	−0.170485
$593$	16.7395	0.687410	0.343705	−	0.939078i	$-0.388318\pi$
$593$	16.7395	0.687410	0.343705	+	0.939078i	$0.388318\pi$
$594$	1.94852	0.0799486
$595$	−10.5085	−0.430808
$596$	8.10778	0.332108
$597$	−24.2441	−0.992243
$598$	−0.935479	−0.0382546
$599$	−47.6221	−1.94579	−0.972893	−	0.231255i	$-0.925717\pi$
$599$	−47.6221	−1.94579	−0.972893	+	0.231255i	$0.925717\pi$
$600$	−1.56155	−0.0637501
$601$	44.2700	1.80581	0.902906	−	0.429837i	$-0.141429\pi$
$601$	44.2700	1.80581	0.902906	+	0.429837i	$0.141429\pi$
$602$	9.77042	0.398213
$603$	11.4617	0.466758
$604$	16.3766	0.666356
$605$	−18.4516	−0.750164
$606$	−10.1300	−0.411503
$607$	−6.36612	−0.258393	−0.129196	−	0.991619i	$-0.541240\pi$
$607$	−6.36612	−0.258393	−0.129196	+	0.991619i	$0.541240\pi$
$608$	−2.20246	−0.0893217
$609$	−1.96335	−0.0795591
$610$	21.1073	0.854611
$611$	−2.10979	−0.0853530
$612$	2.08949	0.0844626
$613$	−14.3480	−0.579509	−0.289754	−	0.957101i	$-0.593574\pi$
$613$	−14.3480	−0.579509	−0.289754	+	0.957101i	$0.593574\pi$
$614$	5.90674	0.238377
$615$	14.3197	0.577426
$616$	−3.82563	−0.154139
$617$	19.2302	0.774179	0.387090	−	0.922042i	$-0.373480\pi$
$617$	19.2302	0.774179	0.387090	+	0.922042i	$0.373480\pi$
$618$	−3.06961	−0.123478
$619$	34.9921	1.40645	0.703226	−	0.710966i	$-0.251742\pi$
$619$	34.9921	1.40645	0.703226	+	0.710966i	$0.251742\pi$
$620$	18.6488	0.748954
$621$	1.00000	0.0401286
$622$	−11.2372	−0.450572
$623$	21.2764	0.852423
$624$	0.935479	0.0374491
$625$	−30.3693	−1.21477
$626$	10.5718	0.422536
$627$	−4.29154	−0.171388
$628$	−21.7649	−0.868516
$629$	−8.66735	−0.345590
$630$	5.02924	0.200370
$631$	−39.6260	−1.57749	−0.788743	−	0.614723i	$-0.789268\pi$
$631$	−39.6260	−1.57749	−0.788743	+	0.614723i	$0.789268\pi$
$632$	−13.0226	−0.518013
$633$	−10.2109	−0.405848
$634$	2.09654	0.0832640
$635$	39.1953	1.55542
$636$	3.28182	0.130133
$637$	−2.94231	−0.116578
$638$	1.94852	0.0771425
$639$	4.07756	0.161306
$640$	−2.56155	−0.101254
$641$	30.5846	1.20802	0.604010	−	0.796977i	$-0.293569\pi$
$641$	30.5846	1.20802	0.604010	+	0.796977i	$0.293569\pi$
$642$	−7.38987	−0.291655
$643$	−27.8355	−1.09772	−0.548862	−	0.835913i	$-0.684939\pi$
$643$	−27.8355	−1.09772	−0.548862	+	0.835913i	$0.684939\pi$
$644$	−1.96335	−0.0773670
$645$	12.7473	0.501924
$646$	−4.60202	−0.181064
$647$	−44.7558	−1.75953	−0.879767	−	0.475405i	$-0.842301\pi$
$647$	−44.7558	−1.75953	−0.879767	+	0.475405i	$0.842301\pi$
$648$	−1.00000	−0.0392837
$649$	2.18113	0.0856170
$650$	−1.46080	−0.0572973
$651$	−14.2938	−0.560217
$652$	5.52133	0.216232
$653$	−30.7452	−1.20315	−0.601576	−	0.798815i	$-0.705460\pi$
$653$	−30.7452	−1.20315	−0.601576	+	0.798815i	$0.705460\pi$
$654$	−7.78988	−0.304608
$655$	−17.3299	−0.677134
$656$	5.59024	0.218262
$657$	−6.10569	−0.238205
$658$	−4.42797	−0.172620
$659$	35.8380	1.39605	0.698025	−	0.716073i	$-0.254062\pi$
$659$	35.8380	1.39605	0.698025	+	0.716073i	$0.254062\pi$
$660$	−4.99123	−0.194283
$661$	−39.2409	−1.52629	−0.763146	−	0.646226i	$-0.776347\pi$
$661$	−39.2409	−1.52629	−0.763146	+	0.646226i	$0.776347\pi$
$662$	17.7693	0.690624
$663$	1.95467	0.0759132
$664$	−3.03980	−0.117967
$665$	−11.0767	−0.429536
$666$	4.14807	0.160735
$667$	1.00000	0.0387202
$668$	11.6501	0.450757
$669$	−4.26874	−0.165039
$670$	−29.3599	−1.13427
$671$	16.0559	0.619831
$672$	1.96335	0.0757380
$673$	4.13060	0.159223	0.0796115	−	0.996826i	$-0.474632\pi$
$673$	4.13060	0.159223	0.0796115	+	0.996826i	$0.474632\pi$
$674$	−10.1576	−0.391255
$675$	1.56155	0.0601042
$676$	−12.1249	−0.466342
$677$	47.3867	1.82122	0.910609	−	0.413269i	$-0.135613\pi$
$677$	47.3867	1.82122	0.910609	+	0.413269i	$0.135613\pi$
$678$	−13.2683	−0.509568
$679$	−9.32036	−0.357683
$680$	−5.35234	−0.205253
$681$	10.1317	0.388246
$682$	14.1857	0.543200
$683$	−18.5528	−0.709903	−0.354951	−	0.934885i	$-0.615503\pi$
$683$	−18.5528	−0.709903	−0.354951	+	0.934885i	$0.615503\pi$
$684$	2.20246	0.0842133
$685$	42.2442	1.61407
$686$	−19.9187	−0.760500
$687$	−22.5182	−0.859121
$688$	4.97639	0.189723
$689$	3.07008	0.116961
$690$	−2.56155	−0.0975166
$691$	−14.2501	−0.542101	−0.271050	−	0.962565i	$-0.587371\pi$
$691$	−14.2501	−0.542101	−0.271050	+	0.962565i	$0.587371\pi$
$692$	0.521944	0.0198413
$693$	3.82563	0.145324
$694$	12.6032	0.478410
$695$	1.03942	0.0394274
$696$	−1.00000	−0.0379049
$697$	11.6808	0.442440
$698$	−9.32835	−0.353083
$699$	−6.71927	−0.254146
$700$	−3.06588	−0.115879
$701$	−24.6299	−0.930258	−0.465129	−	0.885243i	$-0.653992\pi$
$701$	−24.6299	−0.930258	−0.465129	+	0.885243i	$0.653992\pi$
$702$	−0.935479	−0.0353074
$703$	−9.13598	−0.344570
$704$	−1.94852	−0.0734375
$705$	−5.77709	−0.217578
$706$	22.3402	0.840784
$707$	−19.8888	−0.747994
$708$	−1.11938	−0.0420689
$709$	−8.35645	−0.313833	−0.156917	−	0.987612i	$-0.550155\pi$
$709$	−8.35645	−0.313833	−0.156917	+	0.987612i	$0.550155\pi$
$710$	−10.4449	−0.391990
$711$	13.0226	0.488387
$712$	10.8368	0.406126
$713$	7.28027	0.272648
$714$	4.10241	0.153529
$715$	−4.66919	−0.174618
$716$	20.7278	0.774634
$717$	8.10356	0.302633
$718$	−4.78176	−0.178454
$719$	−26.0469	−0.971384	−0.485692	−	0.874130i	$-0.661432\pi$
$719$	−26.0469	−0.971384	−0.485692	+	0.874130i	$0.661432\pi$
$720$	2.56155	0.0954634
$721$	−6.02672	−0.224447
$722$	14.1492	0.526577
$723$	−21.6758	−0.806130
$724$	−11.6567	−0.433216
$725$	1.56155	0.0579946
$726$	7.20328	0.267339
$727$	35.1716	1.30444	0.652221	−	0.758029i	$-0.273838\pi$
$727$	35.1716	1.30444	0.652221	+	0.758029i	$0.273838\pi$
$728$	1.83668	0.0680718
$729$	1.00000	0.0370370
$730$	15.6400	0.578864
$731$	10.3981	0.384588
$732$	−8.24006	−0.304561
$733$	11.2599	0.415894	0.207947	−	0.978140i	$-0.433322\pi$
$733$	11.2599	0.415894	0.207947	+	0.978140i	$0.433322\pi$
$734$	−0.504572	−0.0186241
$735$	−8.05670	−0.297176
$736$	−1.00000	−0.0368605
$737$	−22.3334	−0.822662
$738$	−5.59024	−0.205780
$739$	5.07821	0.186805	0.0934025	−	0.995628i	$-0.470226\pi$
$739$	5.07821	0.186805	0.0934025	+	0.995628i	$0.470226\pi$
$740$	−10.6255	−0.390601
$741$	2.06036	0.0756892
$742$	6.44338	0.236544
$743$	−16.7652	−0.615054	−0.307527	−	0.951539i	$-0.599502\pi$
$743$	−16.7652	−0.615054	−0.307527	+	0.951539i	$0.599502\pi$
$744$	−7.28027	−0.266908
$745$	20.7685	0.760899
$746$	10.1704	0.372363
$747$	3.03980	0.111221
$748$	−4.07140	−0.148865
$749$	−14.5089	−0.530145
$750$	8.80776	0.321614
$751$	−34.8620	−1.27213	−0.636067	−	0.771634i	$-0.719440\pi$
$751$	−34.8620	−1.27213	−0.636067	+	0.771634i	$0.719440\pi$
$752$	−2.25531	−0.0822426
$753$	0.360562	0.0131396
$754$	−0.935479	−0.0340681
$755$	41.9496	1.52670
$756$	−1.96335	−0.0714065
$757$	14.3867	0.522894	0.261447	−	0.965218i	$-0.415800\pi$
$757$	14.3867	0.522894	0.261447	+	0.965218i	$0.415800\pi$
$758$	9.05632	0.328940
$759$	−1.94852	−0.0707267
$760$	−5.64173	−0.204647
$761$	−10.9546	−0.397105	−0.198552	−	0.980090i	$-0.563624\pi$
$761$	−10.9546	−0.397105	−0.198552	+	0.980090i	$0.563624\pi$
$762$	−15.3014	−0.554311
$763$	−15.2943	−0.553690
$764$	−1.16402	−0.0421128
$765$	5.35234	0.193514
$766$	−18.6407	−0.673516
$767$	−1.04716	−0.0378107
$768$	1.00000	0.0360844
$769$	2.02142	0.0728944	0.0364472	−	0.999336i	$-0.488396\pi$
$769$	2.02142	0.0728944	0.0364472	+	0.999336i	$0.488396\pi$
$770$	−9.79955	−0.353151
$771$	25.0130	0.900822
$772$	7.21731	0.259757
$773$	41.0480	1.47639	0.738197	−	0.674585i	$-0.235677\pi$
$773$	41.0480	1.47639	0.738197	+	0.674585i	$0.235677\pi$
$774$	−4.97639	−0.178873
$775$	11.3685	0.408370
$776$	−4.74716	−0.170413
$777$	8.14414	0.292169
$778$	−30.3872	−1.08943
$779$	12.3123	0.441134
$780$	2.39628	0.0858005
$781$	−7.94520	−0.284301
$782$	−2.08949	−0.0747200
$783$	1.00000	0.0357371
$784$	−3.14524	−0.112330
$785$	−55.7520	−1.98988
$786$	6.76538	0.241313
$787$	22.0159	0.784782	0.392391	−	0.919798i	$-0.371648\pi$
$787$	22.0159	0.784782	0.392391	+	0.919798i	$0.371648\pi$
$788$	−20.0951	−0.715860
$789$	1.81901	0.0647583
$790$	−33.3582	−1.18683
$791$	−26.0505	−0.926248
$792$	1.94852	0.0692375
$793$	−7.70840	−0.273733
$794$	−24.3262	−0.863303
$795$	8.40656	0.298150
$796$	−24.2441	−0.859308
$797$	−9.36600	−0.331761	−0.165880	−	0.986146i	$-0.553047\pi$
$797$	−9.36600	−0.331761	−0.165880	+	0.986146i	$0.553047\pi$
$798$	4.32422	0.153076
$799$	−4.71244	−0.166714
$800$	−1.56155	−0.0552092
$801$	−10.8368	−0.382899
$802$	14.1779	0.500641
$803$	11.8970	0.419837
$804$	11.4617	0.404225
$805$	−5.02924	−0.177257
$806$	−6.81054	−0.239891
$807$	19.5554	0.688382
$808$	−10.1300	−0.356372
$809$	−33.5737	−1.18039	−0.590195	−	0.807261i	$-0.700949\pi$
$809$	−33.5737	−1.18039	−0.590195	+	0.807261i	$0.700949\pi$
$810$	−2.56155	−0.0900038
$811$	−38.8824	−1.36535	−0.682674	−	0.730723i	$-0.739183\pi$
$811$	−38.8824	−1.36535	−0.682674	+	0.730723i	$0.739183\pi$
$812$	−1.96335	−0.0689002
$813$	1.71874	0.0602790
$814$	−8.08259	−0.283295
$815$	14.1432	0.495414
$816$	2.08949	0.0731467
$817$	10.9603	0.383453
$818$	−28.9561	−1.01243
$819$	−1.83668	−0.0641787
$820$	14.3197	0.500066
$821$	−14.1391	−0.493458	−0.246729	−	0.969085i	$-0.579356\pi$
$821$	−14.1391	−0.493458	−0.246729	+	0.969085i	$0.579356\pi$
$822$	−16.4916	−0.575212
$823$	−33.2984	−1.16071	−0.580354	−	0.814364i	$-0.697086\pi$
$823$	−33.2984	−1.16071	−0.580354	+	0.814364i	$0.697086\pi$
$824$	−3.06961	−0.106935
$825$	−3.04271	−0.105934
$826$	−2.19774	−0.0764692
$827$	−19.1134	−0.664636	−0.332318	−	0.943167i	$-0.607831\pi$
$827$	−19.1134	−0.664636	−0.332318	+	0.943167i	$0.607831\pi$
$828$	1.00000	0.0347524
$829$	−22.6211	−0.785665	−0.392832	−	0.919610i	$-0.628505\pi$
$829$	−22.6211	−0.785665	−0.392832	+	0.919610i	$0.628505\pi$
$830$	−7.78662	−0.270278
$831$	9.80904	0.340272
$832$	0.935479	0.0324319
$833$	−6.57194	−0.227704
$834$	−0.405777	−0.0140509
$835$	29.8424	1.03274
$836$	−4.29154	−0.148426
$837$	7.28027	0.251643
$838$	5.36488	0.185327
$839$	−29.2218	−1.00885	−0.504425	−	0.863456i	$-0.668295\pi$
$839$	−29.2218	−1.00885	−0.504425	+	0.863456i	$0.668295\pi$
$840$	5.02924	0.173525
$841$	1.00000	0.0344828
$842$	18.6085	0.641292
$843$	19.9331	0.686533
$844$	−10.2109	−0.351475
$845$	−31.0585	−1.06845
$846$	2.25531	0.0775390
$847$	14.1426	0.485945
$848$	3.28182	0.112698
$849$	1.76647	0.0606252
$850$	−3.26285	−0.111915
$851$	−4.14807	−0.142194
$852$	4.07756	0.139695
$853$	−0.717118	−0.0245536	−0.0122768	−	0.999925i	$-0.503908\pi$
$853$	−0.717118	−0.0245536	−0.0122768	+	0.999925i	$0.503908\pi$
$854$	−16.1782	−0.553605
$855$	5.64173	0.192943
$856$	−7.38987	−0.252581
$857$	−20.3929	−0.696608	−0.348304	−	0.937382i	$-0.613242\pi$
$857$	−20.3929	−0.696608	−0.348304	+	0.937382i	$0.613242\pi$
$858$	1.82280	0.0622292
$859$	9.83161	0.335450	0.167725	−	0.985834i	$-0.446358\pi$
$859$	9.83161	0.335450	0.167725	+	0.985834i	$0.446358\pi$
$860$	12.7473	0.434679
$861$	−10.9756	−0.374049
$862$	−21.0108	−0.715631
$863$	−11.5292	−0.392460	−0.196230	−	0.980558i	$-0.562870\pi$
$863$	−11.5292	−0.392460	−0.196230	+	0.980558i	$0.562870\pi$
$864$	−1.00000	−0.0340207
$865$	1.33699	0.0454589
$866$	40.8723	1.38890
$867$	−12.6340	−0.429074
$868$	−14.2938	−0.485162
$869$	−25.3748	−0.860782
$870$	−2.56155	−0.0868448
$871$	10.7222	0.363309
$872$	−7.78988	−0.263798
$873$	4.74716	0.160667
$874$	−2.20246	−0.0744995
$875$	17.2928	0.584602
$876$	−6.10569	−0.206292
$877$	47.0392	1.58840	0.794201	−	0.607656i	$-0.207890\pi$
$877$	47.0392	1.58840	0.794201	+	0.607656i	$0.207890\pi$
$878$	−17.9368	−0.605338
$879$	−6.05975	−0.204390
$880$	−4.99123	−0.168254
$881$	−23.8871	−0.804778	−0.402389	−	0.915469i	$-0.631820\pi$
$881$	−23.8871	−0.804778	−0.402389	+	0.915469i	$0.631820\pi$
$882$	3.14524	0.105906
$883$	−2.05088	−0.0690177	−0.0345089	−	0.999404i	$-0.510987\pi$
$883$	−2.05088	−0.0690177	−0.0345089	+	0.999404i	$0.510987\pi$
$884$	1.95467	0.0657427
$885$	−2.86735	−0.0963850
$886$	−7.86091	−0.264092
$887$	−1.22524	−0.0411397	−0.0205698	−	0.999788i	$-0.506548\pi$
$887$	−1.22524	−0.0411397	−0.0205698	+	0.999788i	$0.506548\pi$
$888$	4.14807	0.139200
$889$	−30.0421	−1.00758
$890$	27.7590	0.930483
$891$	−1.94852	−0.0652778
$892$	−4.26874	−0.142928
$893$	−4.96723	−0.166222
$894$	−8.10778	−0.271165
$895$	53.0954	1.77478
$896$	1.96335	0.0655911
$897$	0.935479	0.0312347
$898$	−32.4437	−1.08266
$899$	7.28027	0.242811
$900$	1.56155	0.0520518
$901$	6.85733	0.228451
$902$	10.8927	0.362687
$903$	−9.77042	−0.325139
$904$	−13.2683	−0.441299
$905$	−29.8592	−0.992552
$906$	−16.3766	−0.544078
$907$	43.7019	1.45110	0.725549	−	0.688171i	$-0.241586\pi$
$907$	43.7019	1.45110	0.725549	+	0.688171i	$0.241586\pi$
$908$	10.1317	0.336231
$909$	10.1300	0.335991
$910$	4.70474	0.155961
$911$	−26.0065	−0.861634	−0.430817	−	0.902439i	$-0.641775\pi$
$911$	−26.0065	−0.861634	−0.430817	+	0.902439i	$0.641775\pi$
$912$	2.20246	0.0729309
$913$	−5.92311	−0.196026
$914$	9.23644	0.305514
$915$	−21.1073	−0.697787
$916$	−22.5182	−0.744021
$917$	13.2828	0.438638
$918$	−2.08949	−0.0689634
$919$	−44.1297	−1.45571	−0.727853	−	0.685734i	$-0.759482\pi$
$919$	−44.1297	−1.45571	−0.727853	+	0.685734i	$0.759482\pi$
$920$	−2.56155	−0.0844519
$921$	−5.90674	−0.194634
$922$	25.5469	0.841341
$923$	3.81447	0.125555
$924$	3.82563	0.125854
$925$	−6.47744	−0.212977
$926$	−11.9448	−0.392532
$927$	3.06961	0.100819
$928$	−1.00000	−0.0328266
$929$	24.7176	0.810957	0.405478	−	0.914105i	$-0.367105\pi$
$929$	24.7176	0.810957	0.405478	+	0.914105i	$0.367105\pi$
$930$	−18.6488	−0.611518
$931$	−6.92728	−0.227032
$932$	−6.71927	−0.220097
$933$	11.2372	0.367891
$934$	−38.6820	−1.26571
$935$	−10.4291	−0.341069
$936$	−0.935479	−0.0305771
$937$	−28.3431	−0.925929	−0.462965	−	0.886377i	$-0.653214\pi$
$937$	−28.3431	−0.925929	−0.462965	+	0.886377i	$0.653214\pi$
$938$	22.5035	0.734764
$939$	−10.5718	−0.344999
$940$	−5.77709	−0.188428
$941$	−7.58661	−0.247316	−0.123658	−	0.992325i	$-0.539463\pi$
$941$	−7.58661	−0.247316	−0.123658	+	0.992325i	$0.539463\pi$
$942$	21.7649	0.709140
$943$	5.59024	0.182043
$944$	−1.11938	−0.0364327
$945$	−5.02924	−0.163601
$946$	9.69659	0.315263
$947$	−58.4041	−1.89788	−0.948939	−	0.315459i	$-0.897841\pi$
$947$	−58.4041	−1.89788	−0.948939	+	0.315459i	$0.897841\pi$
$948$	13.0226	0.422956
$949$	−5.71174	−0.185411
$950$	−3.43926	−0.111584
$951$	−2.09654	−0.0679848
$952$	4.10241	0.132960
$953$	14.1596	0.458674	0.229337	−	0.973347i	$-0.426344\pi$
$953$	14.1596	0.458674	0.229337	+	0.973347i	$0.426344\pi$
$954$	−3.28182	−0.106253
$955$	−2.98170	−0.0964855
$956$	8.10356	0.262088
$957$	−1.94852	−0.0629866
$958$	7.71889	0.249386
$959$	−32.3789	−1.04557
$960$	2.56155	0.0826738
$961$	22.0024	0.709755
$962$	3.88043	0.125110
$963$	7.38987	0.238135
$964$	−21.6758	−0.698129
$965$	18.4875	0.595134
$966$	1.96335	0.0631699
$967$	2.99758	0.0963958	0.0481979	−	0.998838i	$-0.484652\pi$
$967$	2.99758	0.0963958	0.0481979	+	0.998838i	$0.484652\pi$
$968$	7.20328	0.231522
$969$	4.60202	0.147838
$970$	−12.1601	−0.390438
$971$	11.5402	0.370342	0.185171	−	0.982706i	$-0.440716\pi$
$971$	11.5402	0.370342	0.185171	+	0.982706i	$0.440716\pi$
$972$	1.00000	0.0320750
$973$	−0.796684	−0.0255405
$974$	2.02468	0.0648751
$975$	1.46080	0.0467830
$976$	−8.24006	−0.263758
$977$	−36.2200	−1.15878	−0.579390	−	0.815051i	$-0.696709\pi$
$977$	−36.2200	−1.15878	−0.579390	+	0.815051i	$0.696709\pi$
$978$	−5.52133	−0.176553
$979$	21.1157	0.674859
$980$	−8.05670	−0.257362
$981$	7.78988	0.248712
$982$	5.05255	0.161233
$983$	−20.5304	−0.654817	−0.327409	−	0.944883i	$-0.606175\pi$
$983$	−20.5304	−0.654817	−0.327409	+	0.944883i	$0.606175\pi$
$984$	−5.59024	−0.178210
$985$	−51.4748	−1.64012
$986$	−2.08949	−0.0665429
$987$	4.42797	0.140944
$988$	2.06036	0.0655487
$989$	4.97639	0.158240
$990$	4.99123	0.158632
$991$	19.1727	0.609041	0.304521	−	0.952506i	$-0.401504\pi$
$991$	19.1727	0.609041	0.304521	+	0.952506i	$0.401504\pi$
$992$	−7.28027	−0.231149
$993$	−17.7693	−0.563892
$994$	8.00569	0.253925
$995$	−62.1024	−1.96878
$996$	3.03980	0.0963199
$997$	38.4443	1.21754	0.608771	−	0.793346i	$-0.291663\pi$
$997$	38.4443	1.21754	0.608771	+	0.793346i	$0.291663\pi$
$998$	18.5223	0.586314
$999$	−4.14807	−0.131239

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bf.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bf.1.4	✓	6	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:	\( N \)	\(=\)	\( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} -1.00000 q^{6} -1.96335 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} -1.00000 q^{6} -1.96335 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.56155 q^{10} -1.94852 q^{11} +1.00000 q^{12} +0.935479 q^{13} +1.96335 q^{14} +2.56155 q^{15} +1.00000 q^{16} +2.08949 q^{17} -1.00000 q^{18} +2.20246 q^{19} +2.56155 q^{20} -1.96335 q^{21} +1.94852 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.56155 q^{25} -0.935479 q^{26} +1.00000 q^{27} -1.96335 q^{28} +1.00000 q^{29} -2.56155 q^{30} +7.28027 q^{31} -1.00000 q^{32} -1.94852 q^{33} -2.08949 q^{34} -5.02924 q^{35} +1.00000 q^{36} -4.14807 q^{37} -2.20246 q^{38} +0.935479 q^{39} -2.56155 q^{40} +5.59024 q^{41} +1.96335 q^{42} +4.97639 q^{43} -1.94852 q^{44} +2.56155 q^{45} -1.00000 q^{46} -2.25531 q^{47} +1.00000 q^{48} -3.14524 q^{49} -1.56155 q^{50} +2.08949 q^{51} +0.935479 q^{52} +3.28182 q^{53} -1.00000 q^{54} -4.99123 q^{55} +1.96335 q^{56} +2.20246 q^{57} -1.00000 q^{58} -1.11938 q^{59} +2.56155 q^{60} -8.24006 q^{61} -7.28027 q^{62} -1.96335 q^{63} +1.00000 q^{64} +2.39628 q^{65} +1.94852 q^{66} +11.4617 q^{67} +2.08949 q^{68} +1.00000 q^{69} +5.02924 q^{70} +4.07756 q^{71} -1.00000 q^{72} -6.10569 q^{73} +4.14807 q^{74} +1.56155 q^{75} +2.20246 q^{76} +3.82563 q^{77} -0.935479 q^{78} +13.0226 q^{79} +2.56155 q^{80} +1.00000 q^{81} -5.59024 q^{82} +3.03980 q^{83} -1.96335 q^{84} +5.35234 q^{85} -4.97639 q^{86} +1.00000 q^{87} +1.94852 q^{88} -10.8368 q^{89} -2.56155 q^{90} -1.83668 q^{91} +1.00000 q^{92} +7.28027 q^{93} +2.25531 q^{94} +5.64173 q^{95} -1.00000 q^{96} +4.74716 q^{97} +3.14524 q^{98} -1.94852 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + 7 q^{11} + 6 q^{12} + 3 q^{13} - 2 q^{14} + 3 q^{15} + 6 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + 3 q^{20} + 2 q^{21} - 7 q^{22} + 6 q^{23} - 6 q^{24} - 3 q^{25} - 3 q^{26} + 6 q^{27} + 2 q^{28} + 6 q^{29} - 3 q^{30} + q^{31} - 6 q^{32} + 7 q^{33} - 8 q^{34} + 18 q^{35} + 6 q^{36} + 7 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} + 13 q^{41} - 2 q^{42} + 7 q^{44} + 3 q^{45} - 6 q^{46} + 22 q^{47} + 6 q^{48} + 8 q^{49} + 3 q^{50} + 8 q^{51} + 3 q^{52} + 10 q^{53} - 6 q^{54} - 5 q^{55} - 2 q^{56} - 4 q^{57} - 6 q^{58} + 17 q^{59} + 3 q^{60} + q^{61} - q^{62} + 2 q^{63} + 6 q^{64} - 7 q^{65} - 7 q^{66} + 3 q^{67} + 8 q^{68} + 6 q^{69} - 18 q^{70} + 11 q^{71} - 6 q^{72} - 7 q^{74} - 3 q^{75} - 4 q^{76} - 3 q^{78} + 2 q^{79} + 3 q^{80} + 6 q^{81} - 13 q^{82} + 16 q^{83} + 2 q^{84} + 4 q^{85} + 6 q^{87} - 7 q^{88} + 16 q^{89} - 3 q^{90} - 28 q^{91} + 6 q^{92} + q^{93} - 22 q^{94} + 32 q^{95} - 6 q^{96} + 2 q^{97} - 8 q^{98} + 7 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + 7 * q^11 + 6 * q^12 + 3 * q^13 - 2 * q^14 + 3 * q^15 + 6 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 + 3 * q^20 + 2 * q^21 - 7 * q^22 + 6 * q^23 - 6 * q^24 - 3 * q^25 - 3 * q^26 + 6 * q^27 + 2 * q^28 + 6 * q^29 - 3 * q^30 + q^31 - 6 * q^32 + 7 * q^33 - 8 * q^34 + 18 * q^35 + 6 * q^36 + 7 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 + 13 * q^41 - 2 * q^42 + 7 * q^44 + 3 * q^45 - 6 * q^46 + 22 * q^47 + 6 * q^48 + 8 * q^49 + 3 * q^50 + 8 * q^51 + 3 * q^52 + 10 * q^53 - 6 * q^54 - 5 * q^55 - 2 * q^56 - 4 * q^57 - 6 * q^58 + 17 * q^59 + 3 * q^60 + q^61 - q^62 + 2 * q^63 + 6 * q^64 - 7 * q^65 - 7 * q^66 + 3 * q^67 + 8 * q^68 + 6 * q^69 - 18 * q^70 + 11 * q^71 - 6 * q^72 - 7 * q^74 - 3 * q^75 - 4 * q^76 - 3 * q^78 + 2 * q^79 + 3 * q^80 + 6 * q^81 - 13 * q^82 + 16 * q^83 + 2 * q^84 + 4 * q^85 + 6 * q^87 - 7 * q^88 + 16 * q^89 - 3 * q^90 - 28 * q^91 + 6 * q^92 + q^93 - 22 * q^94 + 32 * q^95 - 6 * q^96 + 2 * q^97 - 8 * q^98 + 7 * q^99

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