LMFDB - Embedded newform 8043.2.a.o.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.980315 q^{2} -1.00000 q^{3} -1.03898 q^{4} -1.72725 q^{5} +0.980315 q^{6} +1.00000 q^{7} +2.97916 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.980315 q^{2} -1.00000 q^{3} -1.03898 q^{4} -1.72725 q^{5} +0.980315 q^{6} +1.00000 q^{7} +2.97916 q^{8} +1.00000 q^{9} +1.69325 q^{10} -2.82887 q^{11} +1.03898 q^{12} +1.37439 q^{13} -0.980315 q^{14} +1.72725 q^{15} -0.842547 q^{16} +4.59038 q^{17} -0.980315 q^{18} +0.385819 q^{19} +1.79459 q^{20} -1.00000 q^{21} +2.77319 q^{22} -0.114373 q^{23} -2.97916 q^{24} -2.01660 q^{25} -1.34733 q^{26} -1.00000 q^{27} -1.03898 q^{28} -1.99375 q^{29} -1.69325 q^{30} -7.06293 q^{31} -5.13236 q^{32} +2.82887 q^{33} -4.50001 q^{34} -1.72725 q^{35} -1.03898 q^{36} -2.21026 q^{37} -0.378224 q^{38} -1.37439 q^{39} -5.14576 q^{40} +7.31662 q^{41} +0.980315 q^{42} +6.34087 q^{43} +2.93915 q^{44} -1.72725 q^{45} +0.112122 q^{46} +2.40164 q^{47} +0.842547 q^{48} +1.00000 q^{49} +1.97690 q^{50} -4.59038 q^{51} -1.42796 q^{52} -1.19152 q^{53} +0.980315 q^{54} +4.88618 q^{55} +2.97916 q^{56} -0.385819 q^{57} +1.95450 q^{58} -9.05765 q^{59} -1.79459 q^{60} -4.22208 q^{61} +6.92390 q^{62} +1.00000 q^{63} +6.71642 q^{64} -2.37391 q^{65} -2.77319 q^{66} +10.7278 q^{67} -4.76933 q^{68} +0.114373 q^{69} +1.69325 q^{70} -6.80268 q^{71} +2.97916 q^{72} -10.7141 q^{73} +2.16675 q^{74} +2.01660 q^{75} -0.400859 q^{76} -2.82887 q^{77} +1.34733 q^{78} +2.94189 q^{79} +1.45529 q^{80} +1.00000 q^{81} -7.17259 q^{82} -8.77938 q^{83} +1.03898 q^{84} -7.92874 q^{85} -6.21604 q^{86} +1.99375 q^{87} -8.42767 q^{88} +16.6980 q^{89} +1.69325 q^{90} +1.37439 q^{91} +0.118832 q^{92} +7.06293 q^{93} -2.35436 q^{94} -0.666406 q^{95} +5.13236 q^{96} -11.3417 q^{97} -0.980315 q^{98} -2.82887 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) $ 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9} - 18 q^{10} - 17 q^{11} - 34 q^{12} - 38 q^{13} - 4 q^{14} - 5 q^{15} + 16 q^{16} + 4 q^{17} - 4 q^{18} - 15 q^{19} + 23 q^{20} - 41 q^{21} - 31 q^{22} - 8 q^{23} + 15 q^{24} + 16 q^{25} + 15 q^{26} - 41 q^{27} + 34 q^{28} - 27 q^{29} + 18 q^{30} - 23 q^{31} - 24 q^{32} + 17 q^{33} - 9 q^{34} + 5 q^{35} + 34 q^{36} - 81 q^{37} + 38 q^{39} - 52 q^{40} + 29 q^{41} + 4 q^{42} - 47 q^{43} - 20 q^{44} + 5 q^{45} - 40 q^{46} + 26 q^{47} - 16 q^{48} + 41 q^{49} - 23 q^{50} - 4 q^{51} - 64 q^{52} - 66 q^{53} + 4 q^{54} - 14 q^{55} - 15 q^{56} + 15 q^{57} - 50 q^{58} + 41 q^{59} - 23 q^{60} - 47 q^{61} + 5 q^{62} + 41 q^{63} - 37 q^{64} - 24 q^{65} + 31 q^{66} - 73 q^{67} + 10 q^{68} + 8 q^{69} - 18 q^{70} + q^{71} - 15 q^{72} - 14 q^{73} + 18 q^{74} - 16 q^{75} - 37 q^{76} - 17 q^{77} - 15 q^{78} - 80 q^{79} + 63 q^{80} + 41 q^{81} - 31 q^{82} + 20 q^{83} - 34 q^{84} - 82 q^{85} - 39 q^{86} + 27 q^{87} - 132 q^{88} + 17 q^{89} - 18 q^{90} - 38 q^{91} - 26 q^{92} + 23 q^{93} - 9 q^{94} - q^{95} + 24 q^{96} - 73 q^{97} - 4 q^{98} - 17 q^{99}+O(q^{100}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9 - 18 * q^10 - 17 * q^11 - 34 * q^12 - 38 * q^13 - 4 * q^14 - 5 * q^15 + 16 * q^16 + 4 * q^17 - 4 * q^18 - 15 * q^19 + 23 * q^20 - 41 * q^21 - 31 * q^22 - 8 * q^23 + 15 * q^24 + 16 * q^25 + 15 * q^26 - 41 * q^27 + 34 * q^28 - 27 * q^29 + 18 * q^30 - 23 * q^31 - 24 * q^32 + 17 * q^33 - 9 * q^34 + 5 * q^35 + 34 * q^36 - 81 * q^37 + 38 * q^39 - 52 * q^40 + 29 * q^41 + 4 * q^42 - 47 * q^43 - 20 * q^44 + 5 * q^45 - 40 * q^46 + 26 * q^47 - 16 * q^48 + 41 * q^49 - 23 * q^50 - 4 * q^51 - 64 * q^52 - 66 * q^53 + 4 * q^54 - 14 * q^55 - 15 * q^56 + 15 * q^57 - 50 * q^58 + 41 * q^59 - 23 * q^60 - 47 * q^61 + 5 * q^62 + 41 * q^63 - 37 * q^64 - 24 * q^65 + 31 * q^66 - 73 * q^67 + 10 * q^68 + 8 * q^69 - 18 * q^70 + q^71 - 15 * q^72 - 14 * q^73 + 18 * q^74 - 16 * q^75 - 37 * q^76 - 17 * q^77 - 15 * q^78 - 80 * q^79 + 63 * q^80 + 41 * q^81 - 31 * q^82 + 20 * q^83 - 34 * q^84 - 82 * q^85 - 39 * q^86 + 27 * q^87 - 132 * q^88 + 17 * q^89 - 18 * q^90 - 38 * q^91 - 26 * q^92 + 23 * q^93 - 9 * q^94 - q^95 + 24 * q^96 - 73 * q^97 - 4 * q^98 - 17 * 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 $

$2$	−0.980315	−0.693187	−0.346594	−	0.938015i	$-0.612662\pi$
$2$	−0.980315	−0.693187	−0.346594	+	0.938015i	$0.612662\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.03898	−0.519492
$5$	−1.72725	−0.772451	−0.386225	−	0.922404i	$-0.626221\pi$
$5$	−1.72725	−0.772451	−0.386225	+	0.922404i	$0.626221\pi$
$6$	0.980315	0.400212
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.97916	1.05329
$9$	1.00000	0.333333
$10$	1.69325	0.535453
$11$	−2.82887	−0.852938	−0.426469	−	0.904502i	$-0.640243\pi$
$11$	−2.82887	−0.852938	−0.426469	+	0.904502i	$0.640243\pi$
$12$	1.03898	0.299929
$13$	1.37439	0.381186	0.190593	−	0.981669i	$-0.438959\pi$
$13$	1.37439	0.381186	0.190593	+	0.981669i	$0.438959\pi$
$14$	−0.980315	−0.262000
$15$	1.72725	0.445975
$16$	−0.842547	−0.210637
$17$	4.59038	1.11333	0.556665	−	0.830737i	$-0.312081\pi$
$17$	4.59038	1.11333	0.556665	+	0.830737i	$0.312081\pi$
$18$	−0.980315	−0.231062
$19$	0.385819	0.0885129	0.0442564	−	0.999020i	$-0.485908\pi$
$19$	0.385819	0.0885129	0.0442564	+	0.999020i	$0.485908\pi$
$20$	1.79459	0.401282
$21$	−1.00000	−0.218218
$22$	2.77319	0.591245
$23$	−0.114373	−0.0238484	−0.0119242	−	0.999929i	$-0.503796\pi$
$23$	−0.114373	−0.0238484	−0.0119242	+	0.999929i	$0.503796\pi$
$24$	−2.97916	−0.608118
$25$	−2.01660	−0.403320
$26$	−1.34733	−0.264233
$27$	−1.00000	−0.192450
$28$	−1.03898	−0.196349
$29$	−1.99375	−0.370229	−0.185115	−	0.982717i	$-0.559266\pi$
$29$	−1.99375	−0.370229	−0.185115	+	0.982717i	$0.559266\pi$
$30$	−1.69325	−0.309144
$31$	−7.06293	−1.26854	−0.634270	−	0.773112i	$-0.718699\pi$
$31$	−7.06293	−1.26854	−0.634270	+	0.773112i	$0.718699\pi$
$32$	−5.13236	−0.907281
$33$	2.82887	0.492444
$34$	−4.50001	−0.771746
$35$	−1.72725	−0.291959
$36$	−1.03898	−0.173164
$37$	−2.21026	−0.363365	−0.181682	−	0.983357i	$-0.558154\pi$
$37$	−2.21026	−0.363365	−0.181682	+	0.983357i	$0.558154\pi$
$38$	−0.378224	−0.0613560
$39$	−1.37439	−0.220078
$40$	−5.14576	−0.813616
$41$	7.31662	1.14266	0.571332	−	0.820719i	$-0.306427\pi$
$41$	7.31662	1.14266	0.571332	+	0.820719i	$0.306427\pi$
$42$	0.980315	0.151266
$43$	6.34087	0.966973	0.483487	−	0.875352i	$-0.339370\pi$
$43$	6.34087	0.966973	0.483487	+	0.875352i	$0.339370\pi$
$44$	2.93915	0.443094
$45$	−1.72725	−0.257484
$46$	0.112122	0.0165314
$47$	2.40164	0.350315	0.175158	−	0.984540i	$-0.443957\pi$
$47$	2.40164	0.350315	0.175158	+	0.984540i	$0.443957\pi$
$48$	0.842547	0.121611
$49$	1.00000	0.142857
$50$	1.97690	0.279576
$51$	−4.59038	−0.642781
$52$	−1.42796	−0.198023
$53$	−1.19152	−0.163668	−0.0818339	−	0.996646i	$-0.526078\pi$
$53$	−1.19152	−0.163668	−0.0818339	+	0.996646i	$0.526078\pi$
$54$	0.980315	0.133404
$55$	4.88618	0.658852
$56$	2.97916	0.398107
$57$	−0.385819	−0.0511029
$58$	1.95450	0.256638
$59$	−9.05765	−1.17921	−0.589603	−	0.807693i	$-0.700716\pi$
$59$	−9.05765	−1.17921	−0.589603	+	0.807693i	$0.700716\pi$
$60$	−1.79459	−0.231680
$61$	−4.22208	−0.540582	−0.270291	−	0.962779i	$-0.587120\pi$
$61$	−4.22208	−0.540582	−0.270291	+	0.962779i	$0.587120\pi$
$62$	6.92390	0.879336
$63$	1.00000	0.125988
$64$	6.71642	0.839552
$65$	−2.37391	−0.294448
$66$	−2.77319	−0.341356
$67$	10.7278	1.31061	0.655306	−	0.755363i	$-0.272539\pi$
$67$	10.7278	1.31061	0.655306	+	0.755363i	$0.272539\pi$
$68$	−4.76933	−0.578366
$69$	0.114373	0.0137689
$70$	1.69325	0.202382
$71$	−6.80268	−0.807329	−0.403665	−	0.914907i	$-0.632264\pi$
$71$	−6.80268	−0.807329	−0.403665	+	0.914907i	$0.632264\pi$
$72$	2.97916	0.351097
$73$	−10.7141	−1.25399	−0.626993	−	0.779025i	$-0.715715\pi$
$73$	−10.7141	−1.25399	−0.626993	+	0.779025i	$0.715715\pi$
$74$	2.16675	0.251880
$75$	2.01660	0.232857
$76$	−0.400859	−0.0459817
$77$	−2.82887	−0.322380
$78$	1.34733	0.152555
$79$	2.94189	0.330989	0.165494	−	0.986211i	$-0.447078\pi$
$79$	2.94189	0.330989	0.165494	+	0.986211i	$0.447078\pi$
$80$	1.45529	0.162706
$81$	1.00000	0.111111
$82$	−7.17259	−0.792080
$83$	−8.77938	−0.963662	−0.481831	−	0.876264i	$-0.660028\pi$
$83$	−8.77938	−0.963662	−0.481831	+	0.876264i	$0.660028\pi$
$84$	1.03898	0.113362
$85$	−7.92874	−0.859992
$86$	−6.21604	−0.670293
$87$	1.99375	0.213752
$88$	−8.42767	−0.898392
$89$	16.6980	1.76999	0.884993	−	0.465604i	$-0.154163\pi$
$89$	16.6980	1.76999	0.884993	+	0.465604i	$0.154163\pi$
$90$	1.69325	0.178484
$91$	1.37439	0.144075
$92$	0.118832	0.0123891
$93$	7.06293	0.732392
$94$	−2.35436	−0.242834
$95$	−0.666406	−0.0683718
$96$	5.13236	0.523819
$97$	−11.3417	−1.15158	−0.575789	−	0.817598i	$-0.695305\pi$
$97$	−11.3417	−1.15158	−0.575789	+	0.817598i	$0.695305\pi$
$98$	−0.980315	−0.0990267
$99$	−2.82887	−0.284313
$100$	2.09521	0.209521
$101$	0.298043	0.0296563	0.0148282	−	0.999890i	$-0.495280\pi$
$101$	0.298043	0.0296563	0.0148282	+	0.999890i	$0.495280\pi$
$102$	4.50001	0.445568
$103$	10.8860	1.07263	0.536315	−	0.844018i	$-0.319816\pi$
$103$	10.8860	1.07263	0.536315	+	0.844018i	$0.319816\pi$
$104$	4.09452	0.401500
$105$	1.72725	0.168563
$106$	1.16806	0.113452
$107$	−4.59078	−0.443807	−0.221904	−	0.975069i	$-0.571227\pi$
$107$	−4.59078	−0.443807	−0.221904	+	0.975069i	$0.571227\pi$
$108$	1.03898	0.0999762
$109$	−11.1057	−1.06374	−0.531868	−	0.846827i	$-0.678510\pi$
$109$	−11.1057	−1.06374	−0.531868	+	0.846827i	$0.678510\pi$
$110$	−4.78999	−0.456708
$111$	2.21026	0.209789
$112$	−0.842547	−0.0796132
$113$	20.7828	1.95508	0.977542	−	0.210739i	$-0.0675869\pi$
$113$	20.7828	1.95508	0.977542	+	0.210739i	$0.0675869\pi$
$114$	0.378224	0.0354239
$115$	0.197551	0.0184217
$116$	2.07147	0.192331
$117$	1.37439	0.127062
$118$	8.87935	0.817410
$119$	4.59038	0.420799
$120$	5.14576	0.469741
$121$	−2.99747	−0.272497
$122$	4.13897	0.374724
$123$	−7.31662	−0.659718
$124$	7.33827	0.658996
$125$	12.1194	1.08400
$126$	−0.980315	−0.0873334
$127$	8.74129	0.775664	0.387832	−	0.921730i	$-0.373224\pi$
$127$	8.74129	0.775664	0.387832	+	0.921730i	$0.373224\pi$
$128$	3.68051	0.325315
$129$	−6.34087	−0.558282
$130$	2.32718	0.204107
$131$	21.3802	1.86800	0.933998	−	0.357277i	$-0.116295\pi$
$131$	21.3802	1.86800	0.933998	+	0.357277i	$0.116295\pi$
$132$	−2.93915	−0.255820
$133$	0.385819	0.0334547
$134$	−10.5166	−0.908500
$135$	1.72725	0.148658
$136$	13.6755	1.17266
$137$	5.22812	0.446669	0.223334	−	0.974742i	$-0.428306\pi$
$137$	5.22812	0.446669	0.223334	+	0.974742i	$0.428306\pi$
$138$	−0.112122	−0.00954442
$139$	−3.46372	−0.293789	−0.146894	−	0.989152i	$-0.546928\pi$
$139$	−3.46372	−0.293789	−0.146894	+	0.989152i	$0.546928\pi$
$140$	1.79459	0.151670
$141$	−2.40164	−0.202255
$142$	6.66877	0.559630
$143$	−3.88797	−0.325128
$144$	−0.842547	−0.0702122
$145$	3.44370	0.285984
$146$	10.5032	0.869247
$147$	−1.00000	−0.0824786
$148$	2.29642	0.188765
$149$	−5.00737	−0.410220	−0.205110	−	0.978739i	$-0.565755\pi$
$149$	−5.00737	−0.410220	−0.205110	+	0.978739i	$0.565755\pi$
$150$	−1.97690	−0.161413
$151$	8.01999	0.652657	0.326329	−	0.945256i	$-0.394188\pi$
$151$	8.01999	0.652657	0.326329	+	0.945256i	$0.394188\pi$
$152$	1.14942	0.0932299
$153$	4.59038	0.371110
$154$	2.77319	0.223470
$155$	12.1995	0.979885
$156$	1.42796	0.114329
$157$	−4.59431	−0.366666	−0.183333	−	0.983051i	$-0.558689\pi$
$157$	−4.59431	−0.366666	−0.183333	+	0.983051i	$0.558689\pi$
$158$	−2.88398	−0.229437
$159$	1.19152	0.0944936
$160$	8.86488	0.700830
$161$	−0.114373	−0.00901386
$162$	−0.980315	−0.0770208
$163$	6.55691	0.513577	0.256788	−	0.966468i	$-0.417336\pi$
$163$	6.55691	0.513577	0.256788	+	0.966468i	$0.417336\pi$
$164$	−7.60185	−0.593605
$165$	−4.88618	−0.380388
$166$	8.60655	0.667998
$167$	20.1506	1.55930	0.779652	−	0.626213i	$-0.215396\pi$
$167$	20.1506	1.55930	0.779652	+	0.626213i	$0.215396\pi$
$168$	−2.97916	−0.229847
$169$	−11.1111	−0.854697
$170$	7.77266	0.596136
$171$	0.385819	0.0295043
$172$	−6.58806	−0.502335
$173$	2.39954	0.182434	0.0912169	−	0.995831i	$-0.470924\pi$
$173$	2.39954	0.182434	0.0912169	+	0.995831i	$0.470924\pi$
$174$	−1.95450	−0.148170
$175$	−2.01660	−0.152441
$176$	2.38346	0.179660
$177$	9.05765	0.680815
$178$	−16.3693	−1.22693
$179$	16.8527	1.25963	0.629815	−	0.776745i	$-0.283131\pi$
$179$	16.8527	1.25963	0.629815	+	0.776745i	$0.283131\pi$
$180$	1.79459	0.133761
$181$	−19.7774	−1.47004	−0.735020	−	0.678045i	$-0.762827\pi$
$181$	−19.7774	−1.47004	−0.735020	+	0.678045i	$0.762827\pi$
$182$	−1.34733	−0.0998708
$183$	4.22208	0.312105
$184$	−0.340736	−0.0251194
$185$	3.81768	0.280681
$186$	−6.92390	−0.507685
$187$	−12.9856	−0.949601
$188$	−2.49526	−0.181986
$189$	−1.00000	−0.0727393
$190$	0.653288	0.0473945
$191$	−15.5328	−1.12392	−0.561958	−	0.827165i	$-0.689952\pi$
$191$	−15.5328	−1.12392	−0.561958	+	0.827165i	$0.689952\pi$
$192$	−6.71642	−0.484716
$193$	23.3500	1.68077	0.840385	−	0.541989i	$-0.182329\pi$
$193$	23.3500	1.68077	0.840385	+	0.541989i	$0.182329\pi$
$194$	11.1185	0.798259
$195$	2.37391	0.169999
$196$	−1.03898	−0.0742131
$197$	−1.50277	−0.107068	−0.0535341	−	0.998566i	$-0.517049\pi$
$197$	−1.50277	−0.107068	−0.0535341	+	0.998566i	$0.517049\pi$
$198$	2.77319	0.197082
$199$	−22.3516	−1.58447	−0.792233	−	0.610219i	$-0.791081\pi$
$199$	−22.3516	−1.58447	−0.792233	+	0.610219i	$0.791081\pi$
$200$	−6.00777	−0.424814
$201$	−10.7278	−0.756683
$202$	−0.292175	−0.0205574
$203$	−1.99375	−0.139934
$204$	4.76933	0.333920
$205$	−12.6377	−0.882652
$206$	−10.6717	−0.743533
$207$	−0.114373	−0.00794948
$208$	−1.15798	−0.0802918
$209$	−1.09143	−0.0754960
$210$	−1.69325	−0.116845
$211$	26.3269	1.81242	0.906209	−	0.422829i	$-0.138963\pi$
$211$	26.3269	1.81242	0.906209	+	0.422829i	$0.138963\pi$
$212$	1.23797	0.0850240
$213$	6.80268	0.466112
$214$	4.50041	0.307641
$215$	−10.9523	−0.746939
$216$	−2.97916	−0.202706
$217$	−7.06293	−0.479463
$218$	10.8871	0.737368
$219$	10.7141	0.723990
$220$	−5.07666	−0.342268
$221$	6.30895	0.424386
$222$	−2.16675	−0.145423
$223$	−10.0711	−0.674410	−0.337205	−	0.941431i	$-0.609482\pi$
$223$	−10.0711	−0.674410	−0.337205	+	0.941431i	$0.609482\pi$
$224$	−5.13236	−0.342920
$225$	−2.01660	−0.134440
$226$	−20.3737	−1.35524
$227$	12.6394	0.838909	0.419454	−	0.907776i	$-0.362221\pi$
$227$	12.6394	0.838909	0.419454	+	0.907776i	$0.362221\pi$
$228$	0.400859	0.0265475
$229$	−3.90907	−0.258319	−0.129159	−	0.991624i	$-0.541228\pi$
$229$	−3.90907	−0.258319	−0.129159	+	0.991624i	$0.541228\pi$
$230$	−0.193662	−0.0127697
$231$	2.82887	0.186126
$232$	−5.93969	−0.389960
$233$	−10.9844	−0.719612	−0.359806	−	0.933027i	$-0.617157\pi$
$233$	−10.9844	−0.719612	−0.359806	+	0.933027i	$0.617157\pi$
$234$	−1.34733	−0.0880778
$235$	−4.14824	−0.270601
$236$	9.41075	0.612588
$237$	−2.94189	−0.191097
$238$	−4.50001	−0.291693
$239$	9.00401	0.582421	0.291211	−	0.956659i	$-0.405942\pi$
$239$	9.00401	0.582421	0.291211	+	0.956659i	$0.405942\pi$
$240$	−1.45529	−0.0939386
$241$	−4.60555	−0.296669	−0.148335	−	0.988937i	$-0.547391\pi$
$241$	−4.60555	−0.296669	−0.148335	+	0.988937i	$0.547391\pi$
$242$	2.93846	0.188892
$243$	−1.00000	−0.0641500
$244$	4.38667	0.280828
$245$	−1.72725	−0.110350
$246$	7.17259	0.457308
$247$	0.530264	0.0337399
$248$	−21.0416	−1.33614
$249$	8.77938	0.556370
$250$	−11.8809	−0.751412
$251$	−29.2693	−1.84746	−0.923730	−	0.383044i	$-0.874876\pi$
$251$	−29.2693	−1.84746	−0.923730	+	0.383044i	$0.874876\pi$
$252$	−1.03898	−0.0654498
$253$	0.323547	0.0203412
$254$	−8.56921	−0.537680
$255$	7.92874	0.496517
$256$	−17.0409	−1.06506
$257$	20.8032	1.29767	0.648834	−	0.760930i	$-0.275257\pi$
$257$	20.8032	1.29767	0.648834	+	0.760930i	$0.275257\pi$
$258$	6.21604	0.386994
$259$	−2.21026	−0.137339
$260$	2.46646	0.152963
$261$	−1.99375	−0.123410
$262$	−20.9593	−1.29487
$263$	17.3635	1.07068	0.535339	−	0.844638i	$-0.320184\pi$
$263$	17.3635	1.07068	0.535339	+	0.844638i	$0.320184\pi$
$264$	8.42767	0.518687
$265$	2.05805	0.126425
$266$	−0.378224	−0.0231904
$267$	−16.6980	−1.02190
$268$	−11.1460	−0.680853
$269$	−7.59008	−0.462775	−0.231388	−	0.972862i	$-0.574327\pi$
$269$	−7.59008	−0.462775	−0.231388	+	0.972862i	$0.574327\pi$
$270$	−1.69325	−0.103048
$271$	−8.08500	−0.491129	−0.245564	−	0.969380i	$-0.578973\pi$
$271$	−8.08500	−0.491129	−0.245564	+	0.969380i	$0.578973\pi$
$272$	−3.86761	−0.234508
$273$	−1.37439	−0.0831817
$274$	−5.12520	−0.309625
$275$	5.70471	0.344007
$276$	−0.118832	−0.00715283
$277$	−14.0269	−0.842797	−0.421399	−	0.906876i	$-0.638461\pi$
$277$	−14.0269	−0.842797	−0.421399	+	0.906876i	$0.638461\pi$
$278$	3.39554	0.203651
$279$	−7.06293	−0.422847
$280$	−5.14576	−0.307518
$281$	−31.6295	−1.88686	−0.943429	−	0.331574i	$-0.892420\pi$
$281$	−31.6295	−1.88686	−0.943429	+	0.331574i	$0.892420\pi$
$282$	2.35436	0.140200
$283$	20.7159	1.23143	0.615715	−	0.787969i	$-0.288867\pi$
$283$	20.7159	1.23143	0.615715	+	0.787969i	$0.288867\pi$
$284$	7.06787	0.419401
$285$	0.666406	0.0394745
$286$	3.81143	0.225375
$287$	7.31662	0.431887
$288$	−5.13236	−0.302427
$289$	4.07156	0.239503
$290$	−3.37591	−0.198240
$291$	11.3417	0.664864
$292$	11.1317	0.651436
$293$	0.791481	0.0462388	0.0231194	−	0.999733i	$-0.492640\pi$
$293$	0.791481	0.0462388	0.0231194	+	0.999733i	$0.492640\pi$
$294$	0.980315	0.0571731
$295$	15.6448	0.910878
$296$	−6.58472	−0.382729
$297$	2.82887	0.164148
$298$	4.90880	0.284359
$299$	−0.157193	−0.00909069
$300$	−2.09521	−0.120967
$301$	6.34087	0.365482
$302$	−7.86211	−0.452414
$303$	−0.298043	−0.0171221
$304$	−0.325070	−0.0186441
$305$	7.29260	0.417573
$306$	−4.50001	−0.257249
$307$	6.85525	0.391250	0.195625	−	0.980679i	$-0.437327\pi$
$307$	6.85525	0.391250	0.195625	+	0.980679i	$0.437327\pi$
$308$	2.93915	0.167474
$309$	−10.8860	−0.619283
$310$	−11.9593	−0.679243
$311$	−28.3963	−1.61021	−0.805104	−	0.593134i	$-0.797890\pi$
$311$	−28.3963	−1.61021	−0.805104	+	0.593134i	$0.797890\pi$
$312$	−4.09452	−0.231806
$313$	−12.5470	−0.709199	−0.354599	−	0.935018i	$-0.615383\pi$
$313$	−12.5470	−0.709199	−0.354599	+	0.935018i	$0.615383\pi$
$314$	4.50387	0.254168
$315$	−1.72725	−0.0973196
$316$	−3.05658	−0.171946
$317$	8.74299	0.491055	0.245528	−	0.969390i	$-0.421039\pi$
$317$	8.74299	0.491055	0.245528	+	0.969390i	$0.421039\pi$
$318$	−1.16806	−0.0655017
$319$	5.64006	0.315783
$320$	−11.6009	−0.648513
$321$	4.59078	0.256232
$322$	0.112122	0.00624829
$323$	1.77105	0.0985440
$324$	−1.03898	−0.0577213
$325$	−2.77159	−0.153740
$326$	−6.42783	−0.356005
$327$	11.1057	0.614148
$328$	21.7974	1.20356
$329$	2.40164	0.132407
$330$	4.78999	0.263680
$331$	−2.14161	−0.117713	−0.0588567	−	0.998266i	$-0.518745\pi$
$331$	−2.14161	−0.117713	−0.0588567	+	0.998266i	$0.518745\pi$
$332$	9.12163	0.500614
$333$	−2.21026	−0.121122
$334$	−19.7540	−1.08089
$335$	−18.5297	−1.01238
$336$	0.842547	0.0459647
$337$	19.1801	1.04481	0.522403	−	0.852699i	$-0.325036\pi$
$337$	19.1801	1.04481	0.522403	+	0.852699i	$0.325036\pi$
$338$	10.8923	0.592465
$339$	−20.7828	−1.12877
$340$	8.23783	0.446759
$341$	19.9801	1.08199
$342$	−0.378224	−0.0204520
$343$	1.00000	0.0539949
$344$	18.8905	1.01851
$345$	−0.197551	−0.0106358
$346$	−2.35231	−0.126461
$347$	−29.6017	−1.58910	−0.794550	−	0.607198i	$-0.792293\pi$
$347$	−29.6017	−1.58910	−0.794550	+	0.607198i	$0.792293\pi$
$348$	−2.07147	−0.111042
$349$	−20.7832	−1.11250	−0.556250	−	0.831015i	$-0.687760\pi$
$349$	−20.7832	−1.11250	−0.556250	+	0.831015i	$0.687760\pi$
$350$	1.97690	0.105670
$351$	−1.37439	−0.0733593
$352$	14.5188	0.773854
$353$	5.57883	0.296931	0.148466	−	0.988918i	$-0.452567\pi$
$353$	5.57883	0.296931	0.148466	+	0.988918i	$0.452567\pi$
$354$	−8.87935	−0.471932
$355$	11.7499	0.623622
$356$	−17.3490	−0.919493
$357$	−4.59038	−0.242948
$358$	−16.5209	−0.873159
$359$	−9.65162	−0.509393	−0.254696	−	0.967021i	$-0.581976\pi$
$359$	−9.65162	−0.509393	−0.254696	+	0.967021i	$0.581976\pi$
$360$	−5.14576	−0.271205
$361$	−18.8511	−0.992165
$362$	19.3880	1.01901
$363$	2.99747	0.157326
$364$	−1.42796	−0.0748457
$365$	18.5059	0.968643
$366$	−4.13897	−0.216347
$367$	21.0166	1.09706	0.548528	−	0.836132i	$-0.315188\pi$
$367$	21.0166	1.09706	0.548528	+	0.836132i	$0.315188\pi$
$368$	0.0963646	0.00502335
$369$	7.31662	0.380888
$370$	−3.74252	−0.194565
$371$	−1.19152	−0.0618606
$372$	−7.33827	−0.380472
$373$	−12.0253	−0.622645	−0.311322	−	0.950304i	$-0.600772\pi$
$373$	−12.0253	−0.622645	−0.311322	+	0.950304i	$0.600772\pi$
$374$	12.7300	0.658251
$375$	−12.1194	−0.625845
$376$	7.15487	0.368984
$377$	−2.74018	−0.141126
$378$	0.980315	0.0504219
$379$	4.23233	0.217400	0.108700	−	0.994075i	$-0.465331\pi$
$379$	4.23233	0.217400	0.108700	+	0.994075i	$0.465331\pi$
$380$	0.692385	0.0355186
$381$	−8.74129	−0.447830
$382$	15.2271	0.779085
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	−3.68051	−0.187820
$385$	4.88618	0.249023
$386$	−22.8904	−1.16509
$387$	6.34087	0.322324
$388$	11.7839	0.598236
$389$	−37.5341	−1.90305	−0.951526	−	0.307567i	$-0.900485\pi$
$389$	−37.5341	−1.90305	−0.951526	+	0.307567i	$0.900485\pi$
$390$	−2.32718	−0.117841
$391$	−0.525015	−0.0265512
$392$	2.97916	0.150470
$393$	−21.3802	−1.07849
$394$	1.47319	0.0742182
$395$	−5.08139	−0.255673
$396$	2.93915	0.147698
$397$	4.52322	0.227014	0.113507	−	0.993537i	$-0.463792\pi$
$397$	4.52322	0.227014	0.113507	+	0.993537i	$0.463792\pi$
$398$	21.9116	1.09833
$399$	−0.385819	−0.0193151
$400$	1.69908	0.0849540
$401$	−2.06386	−0.103064	−0.0515322	−	0.998671i	$-0.516410\pi$
$401$	−2.06386	−0.103064	−0.0515322	+	0.998671i	$0.516410\pi$
$402$	10.5166	0.524523
$403$	−9.70720	−0.483550
$404$	−0.309661	−0.0154062
$405$	−1.72725	−0.0858278
$406$	1.95450	0.0970001
$407$	6.25255	0.309927
$408$	−13.6755	−0.677036
$409$	13.0284	0.644213	0.322106	−	0.946704i	$-0.395609\pi$
$409$	13.0284	0.644213	0.322106	+	0.946704i	$0.395609\pi$
$410$	12.3889	0.611843
$411$	−5.22812	−0.257884
$412$	−11.3104	−0.557222
$413$	−9.05765	−0.445698
$414$	0.112122	0.00551047
$415$	15.1642	0.744381
$416$	−7.05385	−0.345843
$417$	3.46372	0.169619
$418$	1.06995	0.0523328
$419$	4.17167	0.203800	0.101900	−	0.994795i	$-0.467508\pi$
$419$	4.17167	0.203800	0.101900	+	0.994795i	$0.467508\pi$
$420$	−1.79459	−0.0875668
$421$	−19.1360	−0.932632	−0.466316	−	0.884618i	$-0.654419\pi$
$421$	−19.1360	−0.932632	−0.466316	+	0.884618i	$0.654419\pi$
$422$	−25.8086	−1.25635
$423$	2.40164	0.116772
$424$	−3.54973	−0.172390
$425$	−9.25695	−0.449028
$426$	−6.66877	−0.323103
$427$	−4.22208	−0.204321
$428$	4.76974	0.230554
$429$	3.88797	0.187713
$430$	10.7367	0.517768
$431$	32.1163	1.54699	0.773494	−	0.633803i	$-0.218507\pi$
$431$	32.1163	1.54699	0.773494	+	0.633803i	$0.218507\pi$
$432$	0.842547	0.0405370
$433$	8.95809	0.430499	0.215249	−	0.976559i	$-0.430944\pi$
$433$	8.95809	0.430499	0.215249	+	0.976559i	$0.430944\pi$
$434$	6.92390	0.332358
$435$	−3.44370	−0.165113
$436$	11.5387	0.552602
$437$	−0.0441273	−0.00211089
$438$	−10.5032	−0.501860
$439$	18.0925	0.863506	0.431753	−	0.901992i	$-0.357895\pi$
$439$	18.0925	0.863506	0.431753	+	0.901992i	$0.357895\pi$
$440$	14.5567	0.693964
$441$	1.00000	0.0476190
$442$	−6.18476	−0.294179
$443$	−7.25064	−0.344488	−0.172244	−	0.985054i	$-0.555102\pi$
$443$	−7.25064	−0.344488	−0.172244	+	0.985054i	$0.555102\pi$
$444$	−2.29642	−0.108983
$445$	−28.8417	−1.36723
$446$	9.87284	0.467492
$447$	5.00737	0.236840
$448$	6.71642	0.317321
$449$	15.8006	0.745678	0.372839	−	0.927896i	$-0.378384\pi$
$449$	15.8006	0.745678	0.372839	+	0.927896i	$0.378384\pi$
$450$	1.97690	0.0931921
$451$	−20.6978	−0.974622
$452$	−21.5930	−1.01565
$453$	−8.01999	−0.376812
$454$	−12.3906	−0.581521
$455$	−2.37391	−0.111291
$456$	−1.14942	−0.0538263
$457$	−4.34169	−0.203096	−0.101548	−	0.994831i	$-0.532379\pi$
$457$	−4.34169	−0.203096	−0.101548	+	0.994831i	$0.532379\pi$
$458$	3.83212	0.179063
$459$	−4.59038	−0.214260
$460$	−0.205252	−0.00956994
$461$	30.6785	1.42884	0.714420	−	0.699717i	$-0.246691\pi$
$461$	30.6785	1.42884	0.714420	+	0.699717i	$0.246691\pi$
$462$	−2.77319	−0.129020
$463$	−18.0138	−0.837170	−0.418585	−	0.908178i	$-0.637474\pi$
$463$	−18.0138	−0.837170	−0.418585	+	0.908178i	$0.637474\pi$
$464$	1.67982	0.0779839
$465$	−12.1995	−0.565737
$466$	10.7682	0.498825
$467$	16.5951	0.767928	0.383964	−	0.923348i	$-0.374559\pi$
$467$	16.5951	0.767928	0.383964	+	0.923348i	$0.374559\pi$
$468$	−1.42796	−0.0660077
$469$	10.7278	0.495365
$470$	4.06658	0.187577
$471$	4.59431	0.211695
$472$	−26.9842	−1.24205
$473$	−17.9375	−0.824768
$474$	2.88398	0.132466
$475$	−0.778042	−0.0356990
$476$	−4.76933	−0.218602
$477$	−1.19152	−0.0545559
$478$	−8.82676	−0.403727
$479$	−33.6942	−1.53953	−0.769764	−	0.638329i	$-0.779626\pi$
$479$	−33.6942	−1.53953	−0.769764	+	0.638329i	$0.779626\pi$
$480$	−8.86488	−0.404624
$481$	−3.03775	−0.138510
$482$	4.51488	0.205647
$483$	0.114373	0.00520415
$484$	3.11432	0.141560
$485$	19.5900	0.889538
$486$	0.980315	0.0444680
$487$	−24.6802	−1.11837	−0.559184	−	0.829044i	$-0.688885\pi$
$487$	−24.6802	−1.11837	−0.559184	+	0.829044i	$0.688885\pi$
$488$	−12.5783	−0.569391
$489$	−6.55691	−0.296514
$490$	1.69325	0.0764933
$491$	−36.2728	−1.63697	−0.818484	−	0.574530i	$-0.805185\pi$
$491$	−36.2728	−1.63697	−0.818484	+	0.574530i	$0.805185\pi$
$492$	7.60185	0.342718
$493$	−9.15205	−0.412187
$494$	−0.519826	−0.0233881
$495$	4.88618	0.219617
$496$	5.95085	0.267201
$497$	−6.80268	−0.305142
$498$	−8.60655	−0.385669
$499$	−15.4281	−0.690658	−0.345329	−	0.938482i	$-0.612233\pi$
$499$	−15.4281	−0.690658	−0.345329	+	0.938482i	$0.612233\pi$
$500$	−12.5919	−0.563127
$501$	−20.1506	−0.900265
$502$	28.6931	1.28064
$503$	39.2634	1.75067	0.875335	−	0.483518i	$-0.160641\pi$
$503$	39.2634	1.75067	0.875335	+	0.483518i	$0.160641\pi$
$504$	2.97916	0.132702
$505$	−0.514795	−0.0229081
$506$	−0.317178	−0.0141003
$507$	11.1111	0.493460
$508$	−9.08205	−0.402951
$509$	−21.2829	−0.943350	−0.471675	−	0.881773i	$-0.656350\pi$
$509$	−21.2829	−0.943350	−0.471675	+	0.881773i	$0.656350\pi$
$510$	−7.77266	−0.344179
$511$	−10.7141	−0.473963
$512$	9.34441	0.412969
$513$	−0.385819	−0.0170343
$514$	−20.3937	−0.899527
$515$	−18.8029	−0.828553
$516$	6.58806	0.290023
$517$	−6.79394	−0.298797
$518$	2.16675	0.0952016
$519$	−2.39954	−0.105328
$520$	−7.07226	−0.310139
$521$	3.52554	0.154457	0.0772284	−	0.997013i	$-0.475393\pi$
$521$	3.52554	0.154457	0.0772284	+	0.997013i	$0.475393\pi$
$522$	1.95450	0.0855461
$523$	−36.8912	−1.61314	−0.806571	−	0.591138i	$-0.798679\pi$
$523$	−36.8912	−1.61314	−0.806571	+	0.591138i	$0.798679\pi$
$524$	−22.2137	−0.970409
$525$	2.01660	0.0880117
$526$	−17.0217	−0.742180
$527$	−32.4215	−1.41230
$528$	−2.38346	−0.103727
$529$	−22.9869	−0.999431
$530$	−2.01754	−0.0876363
$531$	−9.05765	−0.393069
$532$	−0.400859	−0.0173794
$533$	10.0559	0.435568
$534$	16.3693	0.708370
$535$	7.92943	0.342819
$536$	31.9599	1.38046
$537$	−16.8527	−0.727248
$538$	7.44067	0.320790
$539$	−2.82887	−0.121848
$540$	−1.79459	−0.0772267
$541$	3.97770	0.171015	0.0855073	−	0.996338i	$-0.472749\pi$
$541$	3.97770	0.171015	0.0855073	+	0.996338i	$0.472749\pi$
$542$	7.92585	0.340444
$543$	19.7774	0.848728
$544$	−23.5595	−1.01010
$545$	19.1824	0.821684
$546$	1.34733	0.0576605
$547$	−24.6095	−1.05223	−0.526114	−	0.850414i	$-0.676351\pi$
$547$	−24.6095	−1.05223	−0.526114	+	0.850414i	$0.676351\pi$
$548$	−5.43193	−0.232041
$549$	−4.22208	−0.180194
$550$	−5.59241	−0.238461
$551$	−0.769225	−0.0327701
$552$	0.340736	0.0145027
$553$	2.94189	0.125102
$554$	13.7508	0.584216
$555$	−3.81768	−0.162051
$556$	3.59875	0.152621
$557$	−30.7673	−1.30365	−0.651826	−	0.758369i	$-0.725997\pi$
$557$	−30.7673	−1.30365	−0.651826	+	0.758369i	$0.725997\pi$
$558$	6.92390	0.293112
$559$	8.71480	0.368597
$560$	1.45529	0.0614972
$561$	12.9856	0.548252
$562$	31.0069	1.30795
$563$	35.9798	1.51637	0.758184	−	0.652040i	$-0.226087\pi$
$563$	35.9798	1.51637	0.758184	+	0.652040i	$0.226087\pi$
$564$	2.49526	0.105070
$565$	−35.8972	−1.51021
$566$	−20.3081	−0.853611
$567$	1.00000	0.0419961
$568$	−20.2663	−0.850354
$569$	0.747394	0.0313324	0.0156662	−	0.999877i	$-0.495013\pi$
$569$	0.747394	0.0313324	0.0156662	+	0.999877i	$0.495013\pi$
$570$	−0.653288	−0.0273632
$571$	−45.5052	−1.90433	−0.952167	−	0.305579i	$-0.901150\pi$
$571$	−45.5052	−1.90433	−0.952167	+	0.305579i	$0.901150\pi$
$572$	4.03953	0.168901
$573$	15.5328	0.648894
$574$	−7.17259	−0.299378
$575$	0.230645	0.00961855
$576$	6.71642	0.279851
$577$	−14.2743	−0.594249	−0.297124	−	0.954839i	$-0.596028\pi$
$577$	−14.2743	−0.594249	−0.297124	+	0.954839i	$0.596028\pi$
$578$	−3.99141	−0.166021
$579$	−23.3500	−0.970393
$580$	−3.57795	−0.148566
$581$	−8.77938	−0.364230
$582$	−11.1185	−0.460875
$583$	3.37066	0.139598
$584$	−31.9189	−1.32081
$585$	−2.37391	−0.0981492
$586$	−0.775900	−0.0320521
$587$	1.26461	0.0521961	0.0260980	−	0.999659i	$-0.491692\pi$
$587$	1.26461	0.0521961	0.0260980	+	0.999659i	$0.491692\pi$
$588$	1.03898	0.0428470
$589$	−2.72501	−0.112282
$590$	−15.3369	−0.631409
$591$	1.50277	0.0618158
$592$	1.86225	0.0765379
$593$	3.29228	0.135198	0.0675989	−	0.997713i	$-0.478466\pi$
$593$	3.29228	0.135198	0.0675989	+	0.997713i	$0.478466\pi$
$594$	−2.77319	−0.113785
$595$	−7.92874	−0.325047
$596$	5.20257	0.213106
$597$	22.3516	0.914792
$598$	0.154098	0.00630155
$599$	−11.4040	−0.465954	−0.232977	−	0.972482i	$-0.574847\pi$
$599$	−11.4040	−0.465954	−0.232977	+	0.972482i	$0.574847\pi$
$600$	6.00777	0.245266
$601$	−40.5079	−1.65235	−0.826176	−	0.563412i	$-0.809488\pi$
$601$	−40.5079	−1.65235	−0.826176	+	0.563412i	$0.809488\pi$
$602$	−6.21604	−0.253347
$603$	10.7278	0.436871
$604$	−8.33264	−0.339050
$605$	5.17739	0.210491
$606$	0.292175	0.0118688
$607$	8.19620	0.332673	0.166337	−	0.986069i	$-0.446806\pi$
$607$	8.19620	0.332673	0.166337	+	0.986069i	$0.446806\pi$
$608$	−1.98016	−0.0803061
$609$	1.99375	0.0807907
$610$	−7.14904	−0.289456
$611$	3.30078	0.133535
$612$	−4.76933	−0.192789
$613$	−44.2605	−1.78767	−0.893833	−	0.448401i	$-0.851994\pi$
$613$	−44.2605	−1.78767	−0.893833	+	0.448401i	$0.851994\pi$
$614$	−6.72030	−0.271209
$615$	12.6377	0.509599
$616$	−8.42767	−0.339560
$617$	12.2748	0.494163	0.247081	−	0.968995i	$-0.420528\pi$
$617$	12.2748	0.494163	0.247081	+	0.968995i	$0.420528\pi$
$618$	10.6717	0.429279
$619$	−18.6862	−0.751064	−0.375532	−	0.926809i	$-0.622540\pi$
$619$	−18.6862	−0.751064	−0.375532	+	0.926809i	$0.622540\pi$
$620$	−12.6750	−0.509042
$621$	0.114373	0.00458963
$622$	27.8373	1.11618
$623$	16.6980	0.668992
$624$	1.15798	0.0463565
$625$	−10.8503	−0.434013
$626$	12.3000	0.491607
$627$	1.09143	0.0435876
$628$	4.77341	0.190480
$629$	−10.1459	−0.404545
$630$	1.69325	0.0674607
$631$	36.9734	1.47189	0.735943	−	0.677043i	$-0.236739\pi$
$631$	36.9734	1.47189	0.735943	+	0.677043i	$0.236739\pi$
$632$	8.76437	0.348628
$633$	−26.3269	−1.04640
$634$	−8.57088	−0.340393
$635$	−15.0984	−0.599162
$636$	−1.23797	−0.0490886
$637$	1.37439	0.0544552
$638$	−5.52903	−0.218896
$639$	−6.80268	−0.269110
$640$	−6.35718	−0.251289
$641$	1.63490	0.0645746	0.0322873	−	0.999479i	$-0.489721\pi$
$641$	1.63490	0.0645746	0.0322873	+	0.999479i	$0.489721\pi$
$642$	−4.50041	−0.177617
$643$	−11.9186	−0.470023	−0.235011	−	0.971993i	$-0.575513\pi$
$643$	−11.9186	−0.470023	−0.235011	+	0.971993i	$0.575513\pi$
$644$	0.118832	0.00468262
$645$	10.9523	0.431245
$646$	−1.73619	−0.0683094
$647$	−22.2080	−0.873086	−0.436543	−	0.899683i	$-0.643797\pi$
$647$	−22.2080	−0.873086	−0.436543	+	0.899683i	$0.643797\pi$
$648$	2.97916	0.117032
$649$	25.6230	1.00579
$650$	2.71703	0.106571
$651$	7.06293	0.276818
$652$	−6.81252	−0.266799
$653$	−3.24653	−0.127046	−0.0635232	−	0.997980i	$-0.520234\pi$
$653$	−3.24653	−0.127046	−0.0635232	+	0.997980i	$0.520234\pi$
$654$	−10.8871	−0.425720
$655$	−36.9290	−1.44294
$656$	−6.16460	−0.240687
$657$	−10.7141	−0.417996
$658$	−2.35436	−0.0917826
$659$	26.3002	1.02451	0.512255	−	0.858834i	$-0.328810\pi$
$659$	26.3002	1.02451	0.512255	+	0.858834i	$0.328810\pi$
$660$	5.07666	0.197609
$661$	7.86134	0.305771	0.152885	−	0.988244i	$-0.451143\pi$
$661$	7.86134	0.305771	0.152885	+	0.988244i	$0.451143\pi$
$662$	2.09945	0.0815974
$663$	−6.30895	−0.245019
$664$	−26.1552	−1.01502
$665$	−0.666406	−0.0258421
$666$	2.16675	0.0839599
$667$	0.228031	0.00882939
$668$	−20.9362	−0.810046
$669$	10.0711	0.389371
$670$	18.1649	0.701771
$671$	11.9437	0.461083
$672$	5.13236	0.197985
$673$	−39.3188	−1.51563	−0.757815	−	0.652470i	$-0.773733\pi$
$673$	−39.3188	−1.51563	−0.757815	+	0.652470i	$0.773733\pi$
$674$	−18.8025	−0.724246
$675$	2.01660	0.0776190
$676$	11.5442	0.444008
$677$	−27.3777	−1.05221	−0.526106	−	0.850419i	$-0.676348\pi$
$677$	−27.3777	−1.05221	−0.526106	+	0.850419i	$0.676348\pi$
$678$	20.3737	0.782448
$679$	−11.3417	−0.435256
$680$	−23.6210	−0.905823
$681$	−12.6394	−0.484344
$682$	−19.5868	−0.750018
$683$	10.2663	0.392827	0.196414	−	0.980521i	$-0.437070\pi$
$683$	10.2663	0.392827	0.196414	+	0.980521i	$0.437070\pi$
$684$	−0.400859	−0.0153272
$685$	−9.03028	−0.345029
$686$	−0.980315	−0.0374286
$687$	3.90907	0.149140
$688$	−5.34248	−0.203680
$689$	−1.63761	−0.0623879
$690$	0.193662	0.00737259
$691$	28.3779	1.07955	0.539773	−	0.841810i	$-0.318510\pi$
$691$	28.3779	1.07955	0.539773	+	0.841810i	$0.318510\pi$
$692$	−2.49308	−0.0947729
$693$	−2.82887	−0.107460
$694$	29.0189	1.10154
$695$	5.98272	0.226937
$696$	5.93969	0.225143
$697$	33.5861	1.27216
$698$	20.3741	0.771171
$699$	10.9844	0.415468
$700$	2.09521	0.0791917
$701$	18.8436	0.711712	0.355856	−	0.934541i	$-0.384189\pi$
$701$	18.8436	0.711712	0.355856	+	0.934541i	$0.384189\pi$
$702$	1.34733	0.0508517
$703$	−0.852760	−0.0321624
$704$	−18.9999	−0.716086
$705$	4.14824	0.156232
$706$	−5.46901	−0.205829
$707$	0.298043	0.0112090
$708$	−9.41075	−0.353678
$709$	5.58749	0.209843	0.104921	−	0.994481i	$-0.466541\pi$
$709$	5.58749	0.209843	0.104921	+	0.994481i	$0.466541\pi$
$710$	−11.5186	−0.432287
$711$	2.94189	0.110330
$712$	49.7461	1.86431
$713$	0.807809	0.0302527
$714$	4.50001	0.168409
$715$	6.71550	0.251145
$716$	−17.5097	−0.654367
$717$	−9.00401	−0.336261
$718$	9.46162	0.353105
$719$	−17.5855	−0.655829	−0.327914	−	0.944707i	$-0.606346\pi$
$719$	−17.5855	−0.655829	−0.327914	+	0.944707i	$0.606346\pi$
$720$	1.45529	0.0542355
$721$	10.8860	0.405416
$722$	18.4801	0.687756
$723$	4.60555	0.171282
$724$	20.5484	0.763674
$725$	4.02059	0.149321
$726$	−2.93846	−0.109057
$727$	−26.7624	−0.992561	−0.496280	−	0.868162i	$-0.665301\pi$
$727$	−26.7624	−0.992561	−0.496280	+	0.868162i	$0.665301\pi$
$728$	4.09452	0.151753
$729$	1.00000	0.0370370
$730$	−18.1416	−0.671451
$731$	29.1070	1.07656
$732$	−4.38667	−0.162136
$733$	1.03586	0.0382603	0.0191301	−	0.999817i	$-0.493910\pi$
$733$	1.03586	0.0382603	0.0191301	+	0.999817i	$0.493910\pi$
$734$	−20.6028	−0.760465
$735$	1.72725	0.0637107
$736$	0.587003	0.0216372
$737$	−30.3477	−1.11787
$738$	−7.17259	−0.264027
$739$	−17.3532	−0.638348	−0.319174	−	0.947696i	$-0.603405\pi$
$739$	−17.3532	−0.638348	−0.319174	+	0.947696i	$0.603405\pi$
$740$	−3.96650	−0.145812
$741$	−0.530264	−0.0194797
$742$	1.16806	0.0428810
$743$	43.6644	1.60189	0.800946	−	0.598737i	$-0.204331\pi$
$743$	43.6644	1.60189	0.800946	+	0.598737i	$0.204331\pi$
$744$	21.0416	0.771423
$745$	8.64899	0.316874
$746$	11.7885	0.431609
$747$	−8.77938	−0.321221
$748$	13.4918	0.493310
$749$	−4.59078	−0.167743
$750$	11.8809	0.433828
$751$	2.06531	0.0753644	0.0376822	−	0.999290i	$-0.488003\pi$
$751$	2.06531	0.0753644	0.0376822	+	0.999290i	$0.488003\pi$
$752$	−2.02349	−0.0737892
$753$	29.2693	1.06663
$754$	2.68624	0.0978270
$755$	−13.8525	−0.504146
$756$	1.03898	0.0377875
$757$	−36.7194	−1.33459	−0.667294	−	0.744795i	$-0.732547\pi$
$757$	−36.7194	−1.33459	−0.667294	+	0.744795i	$0.732547\pi$
$758$	−4.14902	−0.150699
$759$	−0.323547	−0.0117440
$760$	−1.98533	−0.0720155
$761$	39.6652	1.43786	0.718932	−	0.695080i	$-0.244631\pi$
$761$	39.6652	1.43786	0.718932	+	0.695080i	$0.244631\pi$
$762$	8.56921	0.310430
$763$	−11.1057	−0.402054
$764$	16.1384	0.583866
$765$	−7.92874	−0.286664
$766$	−0.980315	−0.0354202
$767$	−12.4487	−0.449497
$768$	17.0409	0.614910
$769$	33.0367	1.19133	0.595667	−	0.803232i	$-0.296888\pi$
$769$	33.0367	1.19133	0.595667	+	0.803232i	$0.296888\pi$
$770$	−4.78999	−0.172619
$771$	−20.8032	−0.749209
$772$	−24.2603	−0.873146
$773$	−26.7048	−0.960503	−0.480252	−	0.877131i	$-0.659455\pi$
$773$	−26.7048	−0.960503	−0.480252	+	0.877131i	$0.659455\pi$
$774$	−6.21604	−0.223431
$775$	14.2431	0.511628
$776$	−33.7888	−1.21295
$777$	2.21026	0.0792927
$778$	36.7952	1.31917
$779$	2.82289	0.101141
$780$	−2.46646	−0.0883133
$781$	19.2439	0.688602
$782$	0.514680	0.0184049
$783$	1.99375	0.0712507
$784$	−0.842547	−0.0300910
$785$	7.93553	0.283231
$786$	20.9593	0.747594
$787$	−15.7049	−0.559818	−0.279909	−	0.960027i	$-0.590304\pi$
$787$	−15.7049	−0.559818	−0.279909	+	0.960027i	$0.590304\pi$
$788$	1.56136	0.0556210
$789$	−17.3635	−0.618156
$790$	4.98136	0.177229
$791$	20.7828	0.738953
$792$	−8.42767	−0.299464
$793$	−5.80277	−0.206062
$794$	−4.43418	−0.157363
$795$	−2.05805	−0.0729916
$796$	23.2230	0.823117
$797$	19.2873	0.683191	0.341596	−	0.939847i	$-0.389033\pi$
$797$	19.2873	0.683191	0.341596	+	0.939847i	$0.389033\pi$
$798$	0.378224	0.0133890
$799$	11.0244	0.390016
$800$	10.3499	0.365925
$801$	16.6980	0.589996
$802$	2.02324	0.0714429
$803$	30.3088	1.06957
$804$	11.1460	0.393090
$805$	0.197551	0.00696276
$806$	9.51611	0.335191
$807$	7.59008	0.267183
$808$	0.887916	0.0312368
$809$	−37.9747	−1.33512	−0.667559	−	0.744557i	$-0.732661\pi$
$809$	−37.9747	−1.33512	−0.667559	+	0.744557i	$0.732661\pi$
$810$	1.69325	0.0594948
$811$	−13.1643	−0.462261	−0.231130	−	0.972923i	$-0.574242\pi$
$811$	−13.1643	−0.462261	−0.231130	+	0.972923i	$0.574242\pi$
$812$	2.07147	0.0726943
$813$	8.08500	0.283553
$814$	−6.12946	−0.214838
$815$	−11.3254	−0.396713
$816$	3.86761	0.135393
$817$	2.44643	0.0855896
$818$	−12.7719	−0.446560
$819$	1.37439	0.0480250
$820$	13.1303	0.458530
$821$	2.75680	0.0962131	0.0481066	−	0.998842i	$-0.484681\pi$
$821$	2.75680	0.0962131	0.0481066	+	0.998842i	$0.484681\pi$
$822$	5.12520	0.178762
$823$	−35.3590	−1.23254	−0.616268	−	0.787537i	$-0.711356\pi$
$823$	−35.3590	−1.23254	−0.616268	+	0.787537i	$0.711356\pi$
$824$	32.4311	1.12979
$825$	−5.70471	−0.198612
$826$	8.87935	0.308952
$827$	31.8485	1.10748	0.553741	−	0.832689i	$-0.313200\pi$
$827$	31.8485	1.10748	0.553741	+	0.832689i	$0.313200\pi$
$828$	0.118832	0.00412969
$829$	−25.0425	−0.869762	−0.434881	−	0.900488i	$-0.643210\pi$
$829$	−25.0425	−0.869762	−0.434881	+	0.900488i	$0.643210\pi$
$830$	−14.8657	−0.515995
$831$	14.0269	0.486589
$832$	9.23096	0.320026
$833$	4.59038	0.159047
$834$	−3.39554	−0.117578
$835$	−34.8052	−1.20449
$836$	1.13398	0.0392195
$837$	7.06293	0.244131
$838$	−4.08955	−0.141271
$839$	11.1123	0.383638	0.191819	−	0.981430i	$-0.438561\pi$
$839$	11.1123	0.383638	0.191819	+	0.981430i	$0.438561\pi$
$840$	5.14576	0.177546
$841$	−25.0250	−0.862930
$842$	18.7593	0.646488
$843$	31.6295	1.08938
$844$	−27.3532	−0.941536
$845$	19.1916	0.660211
$846$	−2.35436	−0.0809446
$847$	−2.99747	−0.102994
$848$	1.00391	0.0344744
$849$	−20.7159	−0.710967
$850$	9.07473	0.311261
$851$	0.252794	0.00866567
$852$	−7.06787	−0.242141
$853$	30.0144	1.02767	0.513836	−	0.857888i	$-0.328224\pi$
$853$	30.0144	1.02767	0.513836	+	0.857888i	$0.328224\pi$
$854$	4.13897	0.141633
$855$	−0.666406	−0.0227906
$856$	−13.6767	−0.467459
$857$	36.8976	1.26040	0.630199	−	0.776434i	$-0.282973\pi$
$857$	36.8976	1.26040	0.630199	+	0.776434i	$0.282973\pi$
$858$	−3.81143	−0.130120
$859$	14.3238	0.488721	0.244360	−	0.969684i	$-0.421422\pi$
$859$	14.3238	0.488721	0.244360	+	0.969684i	$0.421422\pi$
$860$	11.3792	0.388029
$861$	−7.31662	−0.249350
$862$	−31.4841	−1.07235
$863$	1.23375	0.0419973	0.0209986	−	0.999780i	$-0.493315\pi$
$863$	1.23375	0.0419973	0.0209986	+	0.999780i	$0.493315\pi$
$864$	5.13236	0.174606
$865$	−4.14461	−0.140921
$866$	−8.78175	−0.298416
$867$	−4.07156	−0.138277
$868$	7.33827	0.249077
$869$	−8.32225	−0.282313
$870$	3.37591	0.114454
$871$	14.7442	0.499588
$872$	−33.0857	−1.12042
$873$	−11.3417	−0.383860
$874$	0.0432586	0.00146324
$875$	12.1194	0.409712
$876$	−11.1317	−0.376107
$877$	−41.9207	−1.41556	−0.707781	−	0.706432i	$-0.750304\pi$
$877$	−41.9207	−1.41556	−0.707781	+	0.706432i	$0.750304\pi$
$878$	−17.7363	−0.598571
$879$	−0.791481	−0.0266960
$880$	−4.11683	−0.138778
$881$	−0.262117	−0.00883093	−0.00441547	−	0.999990i	$-0.501405\pi$
$881$	−0.262117	−0.00883093	−0.00441547	+	0.999990i	$0.501405\pi$
$882$	−0.980315	−0.0330089
$883$	−22.9422	−0.772067	−0.386033	−	0.922485i	$-0.626155\pi$
$883$	−22.9422	−0.772067	−0.386033	+	0.922485i	$0.626155\pi$
$884$	−6.55490	−0.220465
$885$	−15.6448	−0.525896
$886$	7.10790	0.238795
$887$	−31.1835	−1.04704	−0.523519	−	0.852014i	$-0.675381\pi$
$887$	−31.1835	−1.04704	−0.523519	+	0.852014i	$0.675381\pi$
$888$	6.58472	0.220969
$889$	8.74129	0.293173
$890$	28.2739	0.947744
$891$	−2.82887	−0.0947708
$892$	10.4637	0.350351
$893$	0.926597	0.0310074
$894$	−4.90880	−0.164175
$895$	−29.1089	−0.973002
$896$	3.68051	0.122957
$897$	0.157193	0.00524851
$898$	−15.4896	−0.516894
$899$	14.0817	0.469651
$900$	2.09521	0.0698405
$901$	−5.46952	−0.182216
$902$	20.2904	0.675595
$903$	−6.34087	−0.211011
$904$	61.9154	2.05928
$905$	34.1605	1.13553
$906$	7.86211	0.261201
$907$	30.3185	1.00671	0.503354	−	0.864080i	$-0.332099\pi$
$907$	30.3185	1.00671	0.503354	+	0.864080i	$0.332099\pi$
$908$	−13.1322	−0.435806
$909$	0.298043	0.00988545
$910$	2.32718	0.0771453
$911$	−49.0483	−1.62504	−0.812522	−	0.582931i	$-0.801906\pi$
$911$	−49.0483	−1.62504	−0.812522	+	0.582931i	$0.801906\pi$
$912$	0.325070	0.0107642
$913$	24.8358	0.821943
$914$	4.25622	0.140783
$915$	−7.29260	−0.241086
$916$	4.06146	0.134194
$917$	21.3802	0.706036
$918$	4.50001	0.148523
$919$	−44.1764	−1.45725	−0.728623	−	0.684915i	$-0.759839\pi$
$919$	−44.1764	−1.45725	−0.728623	+	0.684915i	$0.759839\pi$
$920$	0.588536	0.0194035
$921$	−6.85525	−0.225888
$922$	−30.0746	−0.990453
$923$	−9.34951	−0.307743
$924$	−2.93915	−0.0966910
$925$	4.45721	0.146552
$926$	17.6591	0.580315
$927$	10.8860	0.357543
$928$	10.2326	0.335902
$929$	−42.1611	−1.38326	−0.691631	−	0.722251i	$-0.743107\pi$
$929$	−42.1611	−1.38326	−0.691631	+	0.722251i	$0.743107\pi$
$930$	11.9593	0.392161
$931$	0.385819	0.0126447
$932$	11.4126	0.373832
$933$	28.3963	0.929654
$934$	−16.2684	−0.532318
$935$	22.4294	0.733520
$936$	4.09452	0.133833
$937$	20.7766	0.678741	0.339370	−	0.940653i	$-0.389786\pi$
$937$	20.7766	0.678741	0.339370	+	0.940653i	$0.389786\pi$
$938$	−10.5166	−0.343381
$939$	12.5470	0.409456
$940$	4.30995	0.140575
$941$	−19.1246	−0.623443	−0.311722	−	0.950173i	$-0.600906\pi$
$941$	−19.1246	−0.623443	−0.311722	+	0.950173i	$0.600906\pi$
$942$	−4.50387	−0.146744
$943$	−0.836824	−0.0272507
$944$	7.63149	0.248384
$945$	1.72725	0.0561875
$946$	17.5844	0.571718
$947$	13.8860	0.451235	0.225617	−	0.974216i	$-0.427560\pi$
$947$	13.8860	0.451235	0.225617	+	0.974216i	$0.427560\pi$
$948$	3.05658	0.0992731
$949$	−14.7253	−0.478003
$950$	0.762726	0.0247461
$951$	−8.74299	−0.283511
$952$	13.6755	0.443224
$953$	−20.8542	−0.675533	−0.337766	−	0.941230i	$-0.609671\pi$
$953$	−20.8542	−0.675533	−0.337766	+	0.941230i	$0.609671\pi$
$954$	1.16806	0.0378175
$955$	26.8291	0.868170
$956$	−9.35502	−0.302563
$957$	−5.64006	−0.182317
$958$	33.0309	1.06718
$959$	5.22812	0.168825
$960$	11.6009	0.374419
$961$	18.8850	0.609194
$962$	2.97795	0.0960131
$963$	−4.59078	−0.147936
$964$	4.78509	0.154117
$965$	−40.3314	−1.29831
$966$	−0.112122	−0.00360745
$967$	−32.6364	−1.04952	−0.524758	−	0.851251i	$-0.675844\pi$
$967$	−32.6364	−1.04952	−0.524758	+	0.851251i	$0.675844\pi$
$968$	−8.92995	−0.287019
$969$	−1.77105	−0.0568944
$970$	−19.2044	−0.616616
$971$	−21.2212	−0.681021	−0.340510	−	0.940241i	$-0.610600\pi$
$971$	−21.2212	−0.681021	−0.340510	+	0.940241i	$0.610600\pi$
$972$	1.03898	0.0333254
$973$	−3.46372	−0.111042
$974$	24.1944	0.775238
$975$	2.77159	0.0887619
$976$	3.55730	0.113866
$977$	−43.6377	−1.39609	−0.698047	−	0.716052i	$-0.745947\pi$
$977$	−43.6377	−1.39609	−0.698047	+	0.716052i	$0.745947\pi$
$978$	6.42783	0.205539
$979$	−47.2366	−1.50969
$980$	1.79459	0.0573260
$981$	−11.1057	−0.354579
$982$	35.5587	1.13472
$983$	32.6727	1.04210	0.521048	−	0.853527i	$-0.325541\pi$
$983$	32.6727	1.04210	0.521048	+	0.853527i	$0.325541\pi$
$984$	−21.7974	−0.694875
$985$	2.59567	0.0827048
$986$	8.97188	0.285723
$987$	−2.40164	−0.0764450
$988$	−0.550936	−0.0175276
$989$	−0.725224	−0.0230608
$990$	−4.78999	−0.152236
$991$	49.8495	1.58352	0.791760	−	0.610832i	$-0.209165\pi$
$991$	49.8495	1.58352	0.791760	+	0.610832i	$0.209165\pi$
$992$	36.2495	1.15092
$993$	2.14161	0.0679618
$994$	6.66877	0.211520
$995$	38.6069	1.22392
$996$	−9.12163	−0.289030
$997$	51.1902	1.62121	0.810605	−	0.585594i	$-0.199139\pi$
$997$	51.1902	1.62121	0.810605	+	0.585594i	$0.199139\pi$
$998$	15.1244	0.478755
$999$	2.21026	0.0699295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.o.1.15	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.o.1.15	✓	41	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-0.980315 q^{2} -1.00000 q^{3} -1.03898 q^{4} -1.72725 q^{5} +0.980315 q^{6} +1.00000 q^{7} +2.97916 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.980315 q^{2} -1.00000 q^{3} -1.03898 q^{4} -1.72725 q^{5} +0.980315 q^{6} +1.00000 q^{7} +2.97916 q^{8} +1.00000 q^{9} +1.69325 q^{10} -2.82887 q^{11} +1.03898 q^{12} +1.37439 q^{13} -0.980315 q^{14} +1.72725 q^{15} -0.842547 q^{16} +4.59038 q^{17} -0.980315 q^{18} +0.385819 q^{19} +1.79459 q^{20} -1.00000 q^{21} +2.77319 q^{22} -0.114373 q^{23} -2.97916 q^{24} -2.01660 q^{25} -1.34733 q^{26} -1.00000 q^{27} -1.03898 q^{28} -1.99375 q^{29} -1.69325 q^{30} -7.06293 q^{31} -5.13236 q^{32} +2.82887 q^{33} -4.50001 q^{34} -1.72725 q^{35} -1.03898 q^{36} -2.21026 q^{37} -0.378224 q^{38} -1.37439 q^{39} -5.14576 q^{40} +7.31662 q^{41} +0.980315 q^{42} +6.34087 q^{43} +2.93915 q^{44} -1.72725 q^{45} +0.112122 q^{46} +2.40164 q^{47} +0.842547 q^{48} +1.00000 q^{49} +1.97690 q^{50} -4.59038 q^{51} -1.42796 q^{52} -1.19152 q^{53} +0.980315 q^{54} +4.88618 q^{55} +2.97916 q^{56} -0.385819 q^{57} +1.95450 q^{58} -9.05765 q^{59} -1.79459 q^{60} -4.22208 q^{61} +6.92390 q^{62} +1.00000 q^{63} +6.71642 q^{64} -2.37391 q^{65} -2.77319 q^{66} +10.7278 q^{67} -4.76933 q^{68} +0.114373 q^{69} +1.69325 q^{70} -6.80268 q^{71} +2.97916 q^{72} -10.7141 q^{73} +2.16675 q^{74} +2.01660 q^{75} -0.400859 q^{76} -2.82887 q^{77} +1.34733 q^{78} +2.94189 q^{79} +1.45529 q^{80} +1.00000 q^{81} -7.17259 q^{82} -8.77938 q^{83} +1.03898 q^{84} -7.92874 q^{85} -6.21604 q^{86} +1.99375 q^{87} -8.42767 q^{88} +16.6980 q^{89} +1.69325 q^{90} +1.37439 q^{91} +0.118832 q^{92} +7.06293 q^{93} -2.35436 q^{94} -0.666406 q^{95} +5.13236 q^{96} -11.3417 q^{97} -0.980315 q^{98} -2.82887 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9} - 18 q^{10} - 17 q^{11} - 34 q^{12} - 38 q^{13} - 4 q^{14} - 5 q^{15} + 16 q^{16} + 4 q^{17} - 4 q^{18} - 15 q^{19} + 23 q^{20} - 41 q^{21} - 31 q^{22} - 8 q^{23} + 15 q^{24} + 16 q^{25} + 15 q^{26} - 41 q^{27} + 34 q^{28} - 27 q^{29} + 18 q^{30} - 23 q^{31} - 24 q^{32} + 17 q^{33} - 9 q^{34} + 5 q^{35} + 34 q^{36} - 81 q^{37} + 38 q^{39} - 52 q^{40} + 29 q^{41} + 4 q^{42} - 47 q^{43} - 20 q^{44} + 5 q^{45} - 40 q^{46} + 26 q^{47} - 16 q^{48} + 41 q^{49} - 23 q^{50} - 4 q^{51} - 64 q^{52} - 66 q^{53} + 4 q^{54} - 14 q^{55} - 15 q^{56} + 15 q^{57} - 50 q^{58} + 41 q^{59} - 23 q^{60} - 47 q^{61} + 5 q^{62} + 41 q^{63} - 37 q^{64} - 24 q^{65} + 31 q^{66} - 73 q^{67} + 10 q^{68} + 8 q^{69} - 18 q^{70} + q^{71} - 15 q^{72} - 14 q^{73} + 18 q^{74} - 16 q^{75} - 37 q^{76} - 17 q^{77} - 15 q^{78} - 80 q^{79} + 63 q^{80} + 41 q^{81} - 31 q^{82} + 20 q^{83} - 34 q^{84} - 82 q^{85} - 39 q^{86} + 27 q^{87} - 132 q^{88} + 17 q^{89} - 18 q^{90} - 38 q^{91} - 26 q^{92} + 23 q^{93} - 9 q^{94} - q^{95} + 24 q^{96} - 73 q^{97} - 4 q^{98} - 17 q^{99}+O(q^{100}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9 - 18 * q^10 - 17 * q^11 - 34 * q^12 - 38 * q^13 - 4 * q^14 - 5 * q^15 + 16 * q^16 + 4 * q^17 - 4 * q^18 - 15 * q^19 + 23 * q^20 - 41 * q^21 - 31 * q^22 - 8 * q^23 + 15 * q^24 + 16 * q^25 + 15 * q^26 - 41 * q^27 + 34 * q^28 - 27 * q^29 + 18 * q^30 - 23 * q^31 - 24 * q^32 + 17 * q^33 - 9 * q^34 + 5 * q^35 + 34 * q^36 - 81 * q^37 + 38 * q^39 - 52 * q^40 + 29 * q^41 + 4 * q^42 - 47 * q^43 - 20 * q^44 + 5 * q^45 - 40 * q^46 + 26 * q^47 - 16 * q^48 + 41 * q^49 - 23 * q^50 - 4 * q^51 - 64 * q^52 - 66 * q^53 + 4 * q^54 - 14 * q^55 - 15 * q^56 + 15 * q^57 - 50 * q^58 + 41 * q^59 - 23 * q^60 - 47 * q^61 + 5 * q^62 + 41 * q^63 - 37 * q^64 - 24 * q^65 + 31 * q^66 - 73 * q^67 + 10 * q^68 + 8 * q^69 - 18 * q^70 + q^71 - 15 * q^72 - 14 * q^73 + 18 * q^74 - 16 * q^75 - 37 * q^76 - 17 * q^77 - 15 * q^78 - 80 * q^79 + 63 * q^80 + 41 * q^81 - 31 * q^82 + 20 * q^83 - 34 * q^84 - 82 * q^85 - 39 * q^86 + 27 * q^87 - 132 * q^88 + 17 * q^89 - 18 * q^90 - 38 * q^91 - 26 * q^92 + 23 * q^93 - 9 * q^94 - q^95 + 24 * q^96 - 73 * q^97 - 4 * q^98 - 17 * q^99

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