LMFDB - Embedded newform 8043.2.a.o.1.13

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			1.13
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)

$f(q)$	$=$	$q-1.34769 q^{2} -1.00000 q^{3} -0.183736 q^{4} +1.68166 q^{5} +1.34769 q^{6} +1.00000 q^{7} +2.94300 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.34769 q^{2} -1.00000 q^{3} -0.183736 q^{4} +1.68166 q^{5} +1.34769 q^{6} +1.00000 q^{7} +2.94300 q^{8} +1.00000 q^{9} -2.26635 q^{10} -0.466089 q^{11} +0.183736 q^{12} +5.47610 q^{13} -1.34769 q^{14} -1.68166 q^{15} -3.59877 q^{16} -1.10797 q^{17} -1.34769 q^{18} +3.56584 q^{19} -0.308981 q^{20} -1.00000 q^{21} +0.628142 q^{22} -0.444637 q^{23} -2.94300 q^{24} -2.17202 q^{25} -7.38007 q^{26} -1.00000 q^{27} -0.183736 q^{28} +6.10743 q^{29} +2.26635 q^{30} +2.34182 q^{31} -1.03597 q^{32} +0.466089 q^{33} +1.49319 q^{34} +1.68166 q^{35} -0.183736 q^{36} -11.6615 q^{37} -4.80564 q^{38} -5.47610 q^{39} +4.94912 q^{40} +6.69141 q^{41} +1.34769 q^{42} -9.14612 q^{43} +0.0856371 q^{44} +1.68166 q^{45} +0.599232 q^{46} -6.86130 q^{47} +3.59877 q^{48} +1.00000 q^{49} +2.92721 q^{50} +1.10797 q^{51} -1.00616 q^{52} -10.1415 q^{53} +1.34769 q^{54} -0.783802 q^{55} +2.94300 q^{56} -3.56584 q^{57} -8.23091 q^{58} -6.20723 q^{59} +0.308981 q^{60} -5.83059 q^{61} -3.15605 q^{62} +1.00000 q^{63} +8.59371 q^{64} +9.20893 q^{65} -0.628142 q^{66} -14.4956 q^{67} +0.203573 q^{68} +0.444637 q^{69} -2.26635 q^{70} -2.18202 q^{71} +2.94300 q^{72} +0.501357 q^{73} +15.7160 q^{74} +2.17202 q^{75} -0.655172 q^{76} -0.466089 q^{77} +7.38007 q^{78} +16.4931 q^{79} -6.05191 q^{80} +1.00000 q^{81} -9.01794 q^{82} -14.0104 q^{83} +0.183736 q^{84} -1.86322 q^{85} +12.3261 q^{86} -6.10743 q^{87} -1.37170 q^{88} -3.04396 q^{89} -2.26635 q^{90} +5.47610 q^{91} +0.0816958 q^{92} -2.34182 q^{93} +9.24689 q^{94} +5.99652 q^{95} +1.03597 q^{96} -17.6923 q^{97} -1.34769 q^{98} -0.466089 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.34769	−0.952960	−0.476480	−	0.879185i	$-0.658087\pi$
$2$	−1.34769	−0.952960	−0.476480	+	0.879185i	$0.658087\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.183736	−0.0918679
$5$	1.68166	0.752061	0.376031	−	0.926607i	$-0.377289\pi$
$5$	1.68166	0.752061	0.376031	+	0.926607i	$0.377289\pi$
$6$	1.34769	0.550192
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.94300	1.04051
$9$	1.00000	0.333333
$10$	−2.26635	−0.716684
$11$	−0.466089	−0.140531	−0.0702655	−	0.997528i	$-0.522385\pi$
$11$	−0.466089	−0.140531	−0.0702655	+	0.997528i	$0.522385\pi$
$12$	0.183736	0.0530400
$13$	5.47610	1.51880	0.759398	−	0.650626i	$-0.225494\pi$
$13$	5.47610	1.51880	0.759398	+	0.650626i	$0.225494\pi$
$14$	−1.34769	−0.360185
$15$	−1.68166	−0.434203
$16$	−3.59877	−0.899692
$17$	−1.10797	−0.268721	−0.134361	−	0.990933i	$-0.542898\pi$
$17$	−1.10797	−0.268721	−0.134361	+	0.990933i	$0.542898\pi$
$18$	−1.34769	−0.317653
$19$	3.56584	0.818059	0.409030	−	0.912521i	$-0.365867\pi$
$19$	3.56584	0.818059	0.409030	+	0.912521i	$0.365867\pi$
$20$	−0.308981	−0.0690903
$21$	−1.00000	−0.218218
$22$	0.628142	0.133920
$23$	−0.444637	−0.0927132	−0.0463566	−	0.998925i	$-0.514761\pi$
$23$	−0.444637	−0.0927132	−0.0463566	+	0.998925i	$0.514761\pi$
$24$	−2.94300	−0.600736
$25$	−2.17202	−0.434404
$26$	−7.38007	−1.44735
$27$	−1.00000	−0.192450
$28$	−0.183736	−0.0347228
$29$	6.10743	1.13412	0.567060	−	0.823676i	$-0.308081\pi$
$29$	6.10743	1.13412	0.567060	+	0.823676i	$0.308081\pi$
$30$	2.26635	0.413778
$31$	2.34182	0.420604	0.210302	−	0.977636i	$-0.432555\pi$
$31$	2.34182	0.420604	0.210302	+	0.977636i	$0.432555\pi$
$32$	−1.03597	−0.183136
$33$	0.466089	0.0811356
$34$	1.49319	0.256080
$35$	1.68166	0.284252
$36$	−0.183736	−0.0306226
$37$	−11.6615	−1.91713	−0.958566	−	0.284871i	$-0.908049\pi$
$37$	−11.6615	−1.91713	−0.958566	+	0.284871i	$0.908049\pi$
$38$	−4.80564	−0.779577
$39$	−5.47610	−0.876877
$40$	4.94912	0.782524
$41$	6.69141	1.04502	0.522512	−	0.852632i	$-0.324995\pi$
$41$	6.69141	1.04502	0.522512	+	0.852632i	$0.324995\pi$
$42$	1.34769	0.207953
$43$	−9.14612	−1.39477	−0.697385	−	0.716697i	$-0.745653\pi$
$43$	−9.14612	−1.39477	−0.697385	+	0.716697i	$0.745653\pi$
$44$	0.0856371	0.0129103
$45$	1.68166	0.250687
$46$	0.599232	0.0883520
$47$	−6.86130	−1.00082	−0.500411	−	0.865788i	$-0.666818\pi$
$47$	−6.86130	−1.00082	−0.500411	+	0.865788i	$0.666818\pi$
$48$	3.59877	0.519438
$49$	1.00000	0.142857
$50$	2.92721	0.413970
$51$	1.10797	0.155146
$52$	−1.00616	−0.139529
$53$	−10.1415	−1.39304	−0.696521	−	0.717537i	$-0.745270\pi$
$53$	−10.1415	−1.39304	−0.696521	+	0.717537i	$0.745270\pi$
$54$	1.34769	0.183397
$55$	−0.783802	−0.105688
$56$	2.94300	0.393274
$57$	−3.56584	−0.472307
$58$	−8.23091	−1.08077
$59$	−6.20723	−0.808113	−0.404056	−	0.914734i	$-0.632400\pi$
$59$	−6.20723	−0.808113	−0.404056	+	0.914734i	$0.632400\pi$
$60$	0.308981	0.0398893
$61$	−5.83059	−0.746531	−0.373266	−	0.927725i	$-0.621762\pi$
$61$	−5.83059	−0.746531	−0.373266	+	0.927725i	$0.621762\pi$
$62$	−3.15605	−0.400819
$63$	1.00000	0.125988
$64$	8.59371	1.07421
$65$	9.20893	1.14223
$66$	−0.628142	−0.0773189
$67$	−14.4956	−1.77092	−0.885462	−	0.464711i	$-0.846158\pi$
$67$	−14.4956	−1.77092	−0.885462	+	0.464711i	$0.846158\pi$
$68$	0.203573	0.0246868
$69$	0.444637	0.0535280
$70$	−2.26635	−0.270881
$71$	−2.18202	−0.258958	−0.129479	−	0.991582i	$-0.541330\pi$
$71$	−2.18202	−0.258958	−0.129479	+	0.991582i	$0.541330\pi$
$72$	2.94300	0.346835
$73$	0.501357	0.0586794	0.0293397	−	0.999569i	$-0.490660\pi$
$73$	0.501357	0.0586794	0.0293397	+	0.999569i	$0.490660\pi$
$74$	15.7160	1.82695
$75$	2.17202	0.250803
$76$	−0.655172	−0.0751534
$77$	−0.466089	−0.0531157
$78$	7.38007	0.835629
$79$	16.4931	1.85562	0.927811	−	0.373051i	$-0.121688\pi$
$79$	16.4931	1.85562	0.927811	+	0.373051i	$0.121688\pi$
$80$	−6.05191	−0.676624
$81$	1.00000	0.111111
$82$	−9.01794	−0.995865
$83$	−14.0104	−1.53784	−0.768919	−	0.639346i	$-0.779205\pi$
$83$	−14.0104	−1.53784	−0.768919	+	0.639346i	$0.779205\pi$
$84$	0.183736	0.0200472
$85$	−1.86322	−0.202095
$86$	12.3261	1.32916
$87$	−6.10743	−0.654785
$88$	−1.37170	−0.146223
$89$	−3.04396	−0.322659	−0.161329	−	0.986901i	$-0.551578\pi$
$89$	−3.04396	−0.322659	−0.161329	+	0.986901i	$0.551578\pi$
$90$	−2.26635	−0.238895
$91$	5.47610	0.574051
$92$	0.0816958	0.00851737
$93$	−2.34182	−0.242836
$94$	9.24689	0.953744
$95$	5.99652	0.615230
$96$	1.03597	0.105733
$97$	−17.6923	−1.79638	−0.898191	−	0.439605i	$-0.855118\pi$
$97$	−17.6923	−1.79638	−0.898191	+	0.439605i	$0.855118\pi$
$98$	−1.34769	−0.136137
$99$	−0.466089	−0.0468437
$100$	0.399078	0.0399078
$101$	−17.9458	−1.78567	−0.892837	−	0.450380i	$-0.851288\pi$
$101$	−17.9458	−1.78567	−0.892837	+	0.450380i	$0.851288\pi$
$102$	−1.49319	−0.147848
$103$	−6.29170	−0.619940	−0.309970	−	0.950746i	$-0.600319\pi$
$103$	−6.29170	−0.619940	−0.309970	+	0.950746i	$0.600319\pi$
$104$	16.1161	1.58032
$105$	−1.68166	−0.164113
$106$	13.6676	1.32751
$107$	18.8588	1.82315	0.911576	−	0.411132i	$-0.134866\pi$
$107$	18.8588	1.82315	0.911576	+	0.411132i	$0.134866\pi$
$108$	0.183736	0.0176800
$109$	−15.7377	−1.50740	−0.753702	−	0.657217i	$-0.771734\pi$
$109$	−15.7377	−1.50740	−0.753702	+	0.657217i	$0.771734\pi$
$110$	1.05632	0.100716
$111$	11.6615	1.10686
$112$	−3.59877	−0.340052
$113$	−6.32082	−0.594613	−0.297306	−	0.954782i	$-0.596088\pi$
$113$	−6.32082	−0.594613	−0.297306	+	0.954782i	$0.596088\pi$
$114$	4.80564	0.450089
$115$	−0.747728	−0.0697260
$116$	−1.12215	−0.104189
$117$	5.47610	0.506265
$118$	8.36541	0.770099
$119$	−1.10797	−0.101567
$120$	−4.94912	−0.451791
$121$	−10.7828	−0.980251
$122$	7.85782	0.711414
$123$	−6.69141	−0.603344
$124$	−0.430277	−0.0386400
$125$	−12.0609	−1.07876
$126$	−1.34769	−0.120062
$127$	12.9038	1.14503	0.572515	−	0.819894i	$-0.305968\pi$
$127$	12.9038	1.14503	0.572515	+	0.819894i	$0.305968\pi$
$128$	−9.50970	−0.840546
$129$	9.14612	0.805271
$130$	−12.4108	−1.08850
$131$	−17.8272	−1.55757	−0.778784	−	0.627293i	$-0.784163\pi$
$131$	−17.8272	−1.55757	−0.778784	+	0.627293i	$0.784163\pi$
$132$	−0.0856371	−0.00745376
$133$	3.56584	0.309197
$134$	19.5356	1.68762
$135$	−1.68166	−0.144734
$136$	−3.26074	−0.279606
$137$	18.7874	1.60511	0.802557	−	0.596575i	$-0.203472\pi$
$137$	18.7874	1.60511	0.802557	+	0.596575i	$0.203472\pi$
$138$	−0.599232	−0.0510100
$139$	−4.32258	−0.366637	−0.183318	−	0.983054i	$-0.558684\pi$
$139$	−4.32258	−0.366637	−0.183318	+	0.983054i	$0.558684\pi$
$140$	−0.308981	−0.0261137
$141$	6.86130	0.577825
$142$	2.94068	0.246776
$143$	−2.55235	−0.213438
$144$	−3.59877	−0.299897
$145$	10.2706	0.852928
$146$	−0.675673	−0.0559191
$147$	−1.00000	−0.0824786
$148$	2.14263	0.176123
$149$	−19.0098	−1.55734	−0.778671	−	0.627433i	$-0.784106\pi$
$149$	−19.0098	−1.55734	−0.778671	+	0.627433i	$0.784106\pi$
$150$	−2.92721	−0.239005
$151$	7.65059	0.622596	0.311298	−	0.950312i	$-0.399236\pi$
$151$	7.65059	0.622596	0.311298	+	0.950312i	$0.399236\pi$
$152$	10.4942	0.851195
$153$	−1.10797	−0.0895737
$154$	0.628142	0.0506171
$155$	3.93815	0.316320
$156$	1.00616	0.0805569
$157$	−15.3140	−1.22219	−0.611096	−	0.791556i	$-0.709271\pi$
$157$	−15.3140	−1.22219	−0.611096	+	0.791556i	$0.709271\pi$
$158$	−22.2276	−1.76833
$159$	10.1415	0.804273
$160$	−1.74215	−0.137729
$161$	−0.444637	−0.0350423
$162$	−1.34769	−0.105884
$163$	−2.16884	−0.169876	−0.0849382	−	0.996386i	$-0.527069\pi$
$163$	−2.16884	−0.169876	−0.0849382	+	0.996386i	$0.527069\pi$
$164$	−1.22945	−0.0960041
$165$	0.783802	0.0610189
$166$	18.8816	1.46550
$167$	−9.95609	−0.770425	−0.385213	−	0.922828i	$-0.625872\pi$
$167$	−9.95609	−0.770425	−0.385213	+	0.922828i	$0.625872\pi$
$168$	−2.94300	−0.227057
$169$	16.9876	1.30674
$170$	2.51104	0.192588
$171$	3.56584	0.272686
$172$	1.68047	0.128135
$173$	−12.5980	−0.957806	−0.478903	−	0.877868i	$-0.658965\pi$
$173$	−12.5980	−0.957806	−0.478903	+	0.877868i	$0.658965\pi$
$174$	8.23091	0.623984
$175$	−2.17202	−0.164189
$176$	1.67735	0.126435
$177$	6.20723	0.466564
$178$	4.10230	0.307481
$179$	16.6063	1.24122	0.620608	−	0.784121i	$-0.286886\pi$
$179$	16.6063	1.24122	0.620608	+	0.784121i	$0.286886\pi$
$180$	−0.308981	−0.0230301
$181$	7.15344	0.531711	0.265855	−	0.964013i	$-0.414346\pi$
$181$	7.15344	0.531711	0.265855	+	0.964013i	$0.414346\pi$
$182$	−7.38007	−0.547047
$183$	5.83059	0.431010
$184$	−1.30856	−0.0964687
$185$	−19.6106	−1.44180
$186$	3.15605	0.231413
$187$	0.516410	0.0377636
$188$	1.26067	0.0919435
$189$	−1.00000	−0.0727393
$190$	−8.08145	−0.586290
$191$	16.7278	1.21038	0.605191	−	0.796080i	$-0.293097\pi$
$191$	16.7278	1.21038	0.605191	+	0.796080i	$0.293097\pi$
$192$	−8.59371	−0.620197
$193$	−22.6318	−1.62908	−0.814538	−	0.580110i	$-0.803009\pi$
$193$	−22.6318	−1.62908	−0.814538	+	0.580110i	$0.803009\pi$
$194$	23.8437	1.71188
$195$	−9.20893	−0.659465
$196$	−0.183736	−0.0131240
$197$	16.5580	1.17971	0.589853	−	0.807510i	$-0.299186\pi$
$197$	16.5580	1.17971	0.589853	+	0.807510i	$0.299186\pi$
$198$	0.628142	0.0446401
$199$	12.2919	0.871347	0.435673	−	0.900105i	$-0.356510\pi$
$199$	12.2919	0.871347	0.435673	+	0.900105i	$0.356510\pi$
$200$	−6.39225	−0.452000
$201$	14.4956	1.02244
$202$	24.1853	1.70167
$203$	6.10743	0.428657
$204$	−0.203573	−0.0142530
$205$	11.2527	0.785921
$206$	8.47925	0.590777
$207$	−0.444637	−0.0309044
$208$	−19.7072	−1.36645
$209$	−1.66200	−0.114963
$210$	2.26635	0.156393
$211$	−3.87459	−0.266738	−0.133369	−	0.991066i	$-0.542580\pi$
$211$	−3.87459	−0.266738	−0.133369	+	0.991066i	$0.542580\pi$
$212$	1.86336	0.127976
$213$	2.18202	0.149509
$214$	−25.4158	−1.73739
$215$	−15.3807	−1.04895
$216$	−2.94300	−0.200245
$217$	2.34182	0.158973
$218$	21.2096	1.43649
$219$	−0.501357	−0.0338786
$220$	0.144013	0.00970932
$221$	−6.06733	−0.408133
$222$	−15.7160	−1.05479
$223$	13.4187	0.898586	0.449293	−	0.893385i	$-0.351676\pi$
$223$	13.4187	0.898586	0.449293	+	0.893385i	$0.351676\pi$
$224$	−1.03597	−0.0692187
$225$	−2.17202	−0.144801
$226$	8.51849	0.566642
$227$	19.9016	1.32091	0.660457	−	0.750864i	$-0.270363\pi$
$227$	19.9016	1.32091	0.660457	+	0.750864i	$0.270363\pi$
$228$	0.655172	0.0433898
$229$	−11.7305	−0.775174	−0.387587	−	0.921833i	$-0.626691\pi$
$229$	−11.7305	−0.775174	−0.387587	+	0.921833i	$0.626691\pi$
$230$	1.00770	0.0664461
$231$	0.466089	0.0306664
$232$	17.9741	1.18006
$233$	3.16970	0.207654	0.103827	−	0.994595i	$-0.466891\pi$
$233$	3.16970	0.207654	0.103827	+	0.994595i	$0.466891\pi$
$234$	−7.38007	−0.482450
$235$	−11.5384	−0.752680
$236$	1.14049	0.0742396
$237$	−16.4931	−1.07134
$238$	1.49319	0.0967893
$239$	10.2319	0.661847	0.330923	−	0.943658i	$-0.392640\pi$
$239$	10.2319	0.661847	0.330923	+	0.943658i	$0.392640\pi$
$240$	6.05191	0.390649
$241$	−0.961431	−0.0619312	−0.0309656	−	0.999520i	$-0.509858\pi$
$241$	−0.961431	−0.0619312	−0.0309656	+	0.999520i	$0.509858\pi$
$242$	14.5318	0.934140
$243$	−1.00000	−0.0641500
$244$	1.07129	0.0685822
$245$	1.68166	0.107437
$246$	9.01794	0.574963
$247$	19.5269	1.24247
$248$	6.89198	0.437641
$249$	14.0104	0.887872
$250$	16.2543	1.02801
$251$	1.36831	0.0863672	0.0431836	−	0.999067i	$-0.486250\pi$
$251$	1.36831	0.0863672	0.0431836	+	0.999067i	$0.486250\pi$
$252$	−0.183736	−0.0115743
$253$	0.207240	0.0130291
$254$	−17.3903	−1.09117
$255$	1.86322	0.116679
$256$	−4.37130	−0.273206
$257$	6.07947	0.379227	0.189613	−	0.981859i	$-0.439277\pi$
$257$	6.07947	0.379227	0.189613	+	0.981859i	$0.439277\pi$
$258$	−12.3261	−0.767390
$259$	−11.6615	−0.724608
$260$	−1.69201	−0.104934
$261$	6.10743	0.378040
$262$	24.0255	1.48430
$263$	−26.1414	−1.61195	−0.805973	−	0.591953i	$-0.798357\pi$
$263$	−26.1414	−1.61195	−0.805973	+	0.591953i	$0.798357\pi$
$264$	1.37170	0.0844221
$265$	−17.0545	−1.04765
$266$	−4.80564	−0.294653
$267$	3.04396	0.186287
$268$	2.66337	0.162691
$269$	18.3774	1.12049	0.560245	−	0.828327i	$-0.310707\pi$
$269$	18.3774	1.12049	0.560245	+	0.828327i	$0.310707\pi$
$270$	2.26635	0.137926
$271$	0.920681	0.0559274	0.0279637	−	0.999609i	$-0.491098\pi$
$271$	0.920681	0.0559274	0.0279637	+	0.999609i	$0.491098\pi$
$272$	3.98731	0.241766
$273$	−5.47610	−0.331429
$274$	−25.3195	−1.52961
$275$	1.01235	0.0610472
$276$	−0.0816958	−0.00491751
$277$	8.24610	0.495460	0.247730	−	0.968829i	$-0.420315\pi$
$277$	8.24610	0.495460	0.247730	+	0.968829i	$0.420315\pi$
$278$	5.82550	0.349390
$279$	2.34182	0.140201
$280$	4.94912	0.295766
$281$	21.9045	1.30671	0.653357	−	0.757050i	$-0.273360\pi$
$281$	21.9045	1.30671	0.653357	+	0.757050i	$0.273360\pi$
$282$	−9.24689	−0.550644
$283$	9.08769	0.540207	0.270104	−	0.962831i	$-0.412942\pi$
$283$	9.08769	0.540207	0.270104	+	0.962831i	$0.412942\pi$
$284$	0.400915	0.0237899
$285$	−5.99652	−0.355203
$286$	3.43977	0.203398
$287$	6.69141	0.394982
$288$	−1.03597	−0.0610452
$289$	−15.7724	−0.927789
$290$	−13.8416	−0.812806
$291$	17.6923	1.03714
$292$	−0.0921172	−0.00539075
$293$	−2.91840	−0.170495	−0.0852475	−	0.996360i	$-0.527168\pi$
$293$	−2.91840	−0.170495	−0.0852475	+	0.996360i	$0.527168\pi$
$294$	1.34769	0.0785988
$295$	−10.4384	−0.607750
$296$	−34.3196	−1.99479
$297$	0.466089	0.0270452
$298$	25.6193	1.48408
$299$	−2.43488	−0.140813
$300$	−0.399078	−0.0230408
$301$	−9.14612	−0.527173
$302$	−10.3106	−0.593309
$303$	17.9458	1.03096
$304$	−12.8326	−0.736002
$305$	−9.80508	−0.561437
$306$	1.49319	0.0853601
$307$	28.4129	1.62161	0.810804	−	0.585318i	$-0.199030\pi$
$307$	28.4129	1.62161	0.810804	+	0.585318i	$0.199030\pi$
$308$	0.0856371	0.00487963
$309$	6.29170	0.357922
$310$	−5.30740	−0.301440
$311$	−1.69937	−0.0963623	−0.0481812	−	0.998839i	$-0.515342\pi$
$311$	−1.69937	−0.0963623	−0.0481812	+	0.998839i	$0.515342\pi$
$312$	−16.1161	−0.912396
$313$	−14.1589	−0.800308	−0.400154	−	0.916448i	$-0.631043\pi$
$313$	−14.1589	−0.800308	−0.400154	+	0.916448i	$0.631043\pi$
$314$	20.6385	1.16470
$315$	1.68166	0.0947508
$316$	−3.03038	−0.170472
$317$	−16.2291	−0.911517	−0.455759	−	0.890103i	$-0.650632\pi$
$317$	−16.2291	−0.911517	−0.455759	+	0.890103i	$0.650632\pi$
$318$	−13.6676	−0.766440
$319$	−2.84660	−0.159379
$320$	14.4517	0.807874
$321$	−18.8588	−1.05260
$322$	0.599232	0.0333939
$323$	−3.95082	−0.219830
$324$	−0.183736	−0.0102075
$325$	−11.8942	−0.659771
$326$	2.92292	0.161885
$327$	15.7377	0.870300
$328$	19.6928	1.08735
$329$	−6.86130	−0.378276
$330$	−1.05632	−0.0581486
$331$	5.95059	0.327074	0.163537	−	0.986537i	$-0.447710\pi$
$331$	5.95059	0.327074	0.163537	+	0.986537i	$0.447710\pi$
$332$	2.57421	0.141278
$333$	−11.6615	−0.639044
$334$	13.4177	0.734184
$335$	−24.3767	−1.33184
$336$	3.59877	0.196329
$337$	−13.5567	−0.738478	−0.369239	−	0.929334i	$-0.620382\pi$
$337$	−13.5567	−0.738478	−0.369239	+	0.929334i	$0.620382\pi$
$338$	−22.8941	−1.24527
$339$	6.32082	0.343300
$340$	0.342340	0.0185660
$341$	−1.09150	−0.0591079
$342$	−4.80564	−0.259859
$343$	1.00000	0.0539949
$344$	−26.9170	−1.45127
$345$	0.747728	0.0402563
$346$	16.9781	0.912750
$347$	0.489799	0.0262938	0.0131469	−	0.999914i	$-0.495815\pi$
$347$	0.489799	0.0262938	0.0131469	+	0.999914i	$0.495815\pi$
$348$	1.12215	0.0601537
$349$	6.63202	0.355004	0.177502	−	0.984120i	$-0.443198\pi$
$349$	6.63202	0.355004	0.177502	+	0.984120i	$0.443198\pi$
$350$	2.92721	0.156466
$351$	−5.47610	−0.292292
$352$	0.482854	0.0257362
$353$	9.08260	0.483418	0.241709	−	0.970349i	$-0.422292\pi$
$353$	9.08260	0.483418	0.241709	+	0.970349i	$0.422292\pi$
$354$	−8.36541	−0.444617
$355$	−3.66941	−0.194752
$356$	0.559284	0.0296420
$357$	1.10797	0.0586398
$358$	−22.3802	−1.18283
$359$	8.66385	0.457260	0.228630	−	0.973513i	$-0.426575\pi$
$359$	8.66385	0.457260	0.228630	+	0.973513i	$0.426575\pi$
$360$	4.94912	0.260841
$361$	−6.28481	−0.330779
$362$	−9.64061	−0.506699
$363$	10.7828	0.565948
$364$	−1.00616	−0.0527369
$365$	0.843112	0.0441305
$366$	−7.85782	−0.410735
$367$	−12.3881	−0.646654	−0.323327	−	0.946287i	$-0.604801\pi$
$367$	−12.3881	−0.646654	−0.323327	+	0.946287i	$0.604801\pi$
$368$	1.60015	0.0834134
$369$	6.69141	0.348341
$370$	26.4290	1.37398
$371$	−10.1415	−0.526520
$372$	0.430277	0.0223088
$373$	−10.1684	−0.526499	−0.263250	−	0.964728i	$-0.584794\pi$
$373$	−10.1684	−0.526499	−0.263250	+	0.964728i	$0.584794\pi$
$374$	−0.695960	−0.0359872
$375$	12.0609	0.622822
$376$	−20.1928	−1.04136
$377$	33.4449	1.72250
$378$	1.34769	0.0693176
$379$	−29.3056	−1.50533	−0.752663	−	0.658406i	$-0.771231\pi$
$379$	−29.3056	−1.50533	−0.752663	+	0.658406i	$0.771231\pi$
$380$	−1.10178	−0.0565199
$381$	−12.9038	−0.661083
$382$	−22.5439	−1.15345
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	9.50970	0.485290
$385$	−0.783802	−0.0399463
$386$	30.5007	1.55244
$387$	−9.14612	−0.464923
$388$	3.25071	0.165030
$389$	−7.41644	−0.376028	−0.188014	−	0.982166i	$-0.560205\pi$
$389$	−7.41644	−0.376028	−0.188014	+	0.982166i	$0.560205\pi$
$390$	12.4108	0.628444
$391$	0.492643	0.0249140
$392$	2.94300	0.148644
$393$	17.8272	0.899262
$394$	−22.3150	−1.12421
$395$	27.7358	1.39554
$396$	0.0856371	0.00430343
$397$	35.1791	1.76559	0.882793	−	0.469761i	$-0.155660\pi$
$397$	35.1791	1.76559	0.882793	+	0.469761i	$0.155660\pi$
$398$	−16.5656	−0.830359
$399$	−3.56584	−0.178515
$400$	7.81660	0.390830
$401$	1.45184	0.0725012	0.0362506	−	0.999343i	$-0.488459\pi$
$401$	1.45184	0.0725012	0.0362506	+	0.999343i	$0.488459\pi$
$402$	−19.5356	−0.974348
$403$	12.8241	0.638812
$404$	3.29729	0.164046
$405$	1.68166	0.0835623
$406$	−8.23091	−0.408493
$407$	5.43527	0.269416
$408$	3.26074	0.161431
$409$	−3.68691	−0.182306	−0.0911529	−	0.995837i	$-0.529055\pi$
$409$	−3.68691	−0.182306	−0.0911529	+	0.995837i	$0.529055\pi$
$410$	−15.1651	−0.748951
$411$	−18.7874	−0.926713
$412$	1.15601	0.0569526
$413$	−6.20723	−0.305438
$414$	0.599232	0.0294507
$415$	−23.5607	−1.15655
$416$	−5.67308	−0.278146
$417$	4.32258	0.211678
$418$	2.23985	0.109555
$419$	−2.87764	−0.140582	−0.0702909	−	0.997527i	$-0.522393\pi$
$419$	−2.87764	−0.140582	−0.0702909	+	0.997527i	$0.522393\pi$
$420$	0.308981	0.0150767
$421$	−13.9212	−0.678479	−0.339239	−	0.940700i	$-0.610170\pi$
$421$	−13.9212	−0.678479	−0.339239	+	0.940700i	$0.610170\pi$
$422$	5.22175	0.254191
$423$	−6.86130	−0.333608
$424$	−29.8464	−1.44947
$425$	2.40652	0.116734
$426$	−2.94068	−0.142476
$427$	−5.83059	−0.282162
$428$	−3.46504	−0.167489
$429$	2.55235	0.123228
$430$	20.7283	0.999609
$431$	19.2192	0.925757	0.462879	−	0.886422i	$-0.346817\pi$
$431$	19.2192	0.925757	0.462879	+	0.886422i	$0.346817\pi$
$432$	3.59877	0.173146
$433$	−1.07268	−0.0515497	−0.0257748	−	0.999668i	$-0.508205\pi$
$433$	−1.07268	−0.0515497	−0.0257748	+	0.999668i	$0.508205\pi$
$434$	−3.15605	−0.151495
$435$	−10.2706	−0.492438
$436$	2.89159	0.138482
$437$	−1.58550	−0.0758449
$438$	0.675673	0.0322849
$439$	−24.7405	−1.18080	−0.590400	−	0.807111i	$-0.701030\pi$
$439$	−24.7405	−1.18080	−0.590400	+	0.807111i	$0.701030\pi$
$440$	−2.30673	−0.109969
$441$	1.00000	0.0476190
$442$	8.17687	0.388934
$443$	11.8995	0.565364	0.282682	−	0.959214i	$-0.408776\pi$
$443$	11.8995	0.565364	0.282682	+	0.959214i	$0.408776\pi$
$444$	−2.14263	−0.101685
$445$	−5.11890	−0.242659
$446$	−18.0843	−0.856316
$447$	19.0098	0.899131
$448$	8.59371	0.406014
$449$	22.0600	1.04108	0.520539	−	0.853838i	$-0.325731\pi$
$449$	22.0600	1.04108	0.520539	+	0.853838i	$0.325731\pi$
$450$	2.92721	0.137990
$451$	−3.11879	−0.146858
$452$	1.16136	0.0546258
$453$	−7.65059	−0.359456
$454$	−26.8211	−1.25878
$455$	9.20893	0.431721
$456$	−10.4942	−0.491438
$457$	19.7214	0.922531	0.461265	−	0.887262i	$-0.347396\pi$
$457$	19.7214	0.922531	0.461265	+	0.887262i	$0.347396\pi$
$458$	15.8091	0.738709
$459$	1.10797	0.0517154
$460$	0.137384	0.00640558
$461$	3.17978	0.148097	0.0740485	−	0.997255i	$-0.476408\pi$
$461$	3.17978	0.148097	0.0740485	+	0.997255i	$0.476408\pi$
$462$	−0.628142	−0.0292238
$463$	34.5772	1.60694	0.803469	−	0.595347i	$-0.202985\pi$
$463$	34.5772	1.60694	0.803469	+	0.595347i	$0.202985\pi$
$464$	−21.9792	−1.02036
$465$	−3.93815	−0.182627
$466$	−4.27176	−0.197886
$467$	−29.6830	−1.37357	−0.686783	−	0.726863i	$-0.740978\pi$
$467$	−29.6830	−1.37357	−0.686783	+	0.726863i	$0.740978\pi$
$468$	−1.00616	−0.0465095
$469$	−14.4956	−0.669347
$470$	15.5501	0.717274
$471$	15.3140	0.705633
$472$	−18.2679	−0.840846
$473$	4.26290	0.196008
$474$	22.2276	1.02095
$475$	−7.74507	−0.355368
$476$	0.203573	0.00933075
$477$	−10.1415	−0.464347
$478$	−13.7894	−0.630713
$479$	−2.75828	−0.126029	−0.0630145	−	0.998013i	$-0.520071\pi$
$479$	−2.75828	−0.126029	−0.0630145	+	0.998013i	$0.520071\pi$
$480$	1.74215	0.0795179
$481$	−63.8593	−2.91173
$482$	1.29571	0.0590180
$483$	0.444637	0.0202317
$484$	1.98118	0.0900536
$485$	−29.7525	−1.35099
$486$	1.34769	0.0611324
$487$	10.4843	0.475091	0.237546	−	0.971376i	$-0.423657\pi$
$487$	10.4843	0.475091	0.237546	+	0.971376i	$0.423657\pi$
$488$	−17.1594	−0.776770
$489$	2.16884	0.0980782
$490$	−2.26635	−0.102383
$491$	32.1391	1.45042	0.725208	−	0.688530i	$-0.241743\pi$
$491$	32.1391	1.45042	0.725208	+	0.688530i	$0.241743\pi$
$492$	1.22945	0.0554280
$493$	−6.76682	−0.304762
$494$	−26.3161	−1.18402
$495$	−0.783802	−0.0352293
$496$	−8.42768	−0.378414
$497$	−2.18202	−0.0978768
$498$	−18.8816	−0.846106
$499$	−7.87455	−0.352513	−0.176257	−	0.984344i	$-0.556399\pi$
$499$	−7.87455	−0.352513	−0.176257	+	0.984344i	$0.556399\pi$
$500$	2.21602	0.0991034
$501$	9.95609	0.444805
$502$	−1.84406	−0.0823044
$503$	−17.3422	−0.773250	−0.386625	−	0.922237i	$-0.626359\pi$
$503$	−17.3422	−0.773250	−0.386625	+	0.922237i	$0.626359\pi$
$504$	2.94300	0.131091
$505$	−30.1787	−1.34294
$506$	−0.279295	−0.0124162
$507$	−16.9876	−0.754448
$508$	−2.37090	−0.105191
$509$	23.1085	1.02427	0.512134	−	0.858905i	$-0.328855\pi$
$509$	23.1085	1.02427	0.512134	+	0.858905i	$0.328855\pi$
$510$	−2.51104	−0.111191
$511$	0.501357	0.0221787
$512$	24.9105	1.10090
$513$	−3.56584	−0.157436
$514$	−8.19323	−0.361388
$515$	−10.5805	−0.466233
$516$	−1.68047	−0.0739785
$517$	3.19797	0.140647
$518$	15.7160	0.690522
$519$	12.5980	0.552989
$520$	27.1018	1.18849
$521$	19.9573	0.874344	0.437172	−	0.899378i	$-0.355980\pi$
$521$	19.9573	0.874344	0.437172	+	0.899378i	$0.355980\pi$
$522$	−8.23091	−0.360257
$523$	−18.5607	−0.811605	−0.405802	−	0.913961i	$-0.633008\pi$
$523$	−18.5607	−0.811605	−0.405802	+	0.913961i	$0.633008\pi$
$524$	3.27549	0.143090
$525$	2.17202	0.0947947
$526$	35.2304	1.53612
$527$	−2.59466	−0.113025
$528$	−1.67735	−0.0729971
$529$	−22.8023	−0.991404
$530$	22.9842	0.998371
$531$	−6.20723	−0.269371
$532$	−0.655172	−0.0284053
$533$	36.6428	1.58718
$534$	−4.10230	−0.177524
$535$	31.7141	1.37112
$536$	−42.6606	−1.84266
$537$	−16.6063	−0.716617
$538$	−24.7670	−1.06778
$539$	−0.466089	−0.0200759
$540$	0.308981	0.0132964
$541$	−0.642301	−0.0276147	−0.0138073	−	0.999905i	$-0.504395\pi$
$541$	−0.642301	−0.0276147	−0.0138073	+	0.999905i	$0.504395\pi$
$542$	−1.24079	−0.0532965
$543$	−7.15344	−0.306983
$544$	1.14782	0.0492124
$545$	−26.4655	−1.13366
$546$	7.38007	0.315838
$547$	−34.1271	−1.45917	−0.729585	−	0.683890i	$-0.760287\pi$
$547$	−34.1271	−1.45917	−0.729585	+	0.683890i	$0.760287\pi$
$548$	−3.45191	−0.147458
$549$	−5.83059	−0.248844
$550$	−1.36434	−0.0581755
$551$	21.7781	0.927778
$552$	1.30856	0.0556962
$553$	16.4931	0.701359
$554$	−11.1132	−0.472154
$555$	19.6106	0.832424
$556$	0.794213	0.0336822
$557$	−30.0683	−1.27403	−0.637016	−	0.770850i	$-0.719832\pi$
$557$	−30.0683	−1.27403	−0.637016	+	0.770850i	$0.719832\pi$
$558$	−3.15605	−0.133606
$559$	−50.0850	−2.11837
$560$	−6.05191	−0.255740
$561$	−0.516410	−0.0218028
$562$	−29.5204	−1.24524
$563$	−32.7189	−1.37894	−0.689468	−	0.724316i	$-0.742156\pi$
$563$	−32.7189	−1.37894	−0.689468	+	0.724316i	$0.742156\pi$
$564$	−1.26067	−0.0530836
$565$	−10.6295	−0.447185
$566$	−12.2474	−0.514796
$567$	1.00000	0.0419961
$568$	−6.42167	−0.269447
$569$	27.1905	1.13989	0.569943	−	0.821684i	$-0.306965\pi$
$569$	27.1905	1.13989	0.569943	+	0.821684i	$0.306965\pi$
$570$	8.08145	0.338495
$571$	−15.6837	−0.656344	−0.328172	−	0.944618i	$-0.606432\pi$
$571$	−15.6837	−0.656344	−0.328172	+	0.944618i	$0.606432\pi$
$572$	0.468957	0.0196081
$573$	−16.7278	−0.698815
$574$	−9.01794	−0.376402
$575$	0.965761	0.0402750
$576$	8.59371	0.358071
$577$	−22.9261	−0.954427	−0.477213	−	0.878787i	$-0.658353\pi$
$577$	−22.9261	−0.954427	−0.477213	+	0.878787i	$0.658353\pi$
$578$	21.2563	0.884145
$579$	22.6318	0.940547
$580$	−1.88708	−0.0783567
$581$	−14.0104	−0.581249
$582$	−23.8437	−0.988354
$583$	4.72683	0.195765
$584$	1.47549	0.0610562
$585$	9.20893	0.380743
$586$	3.93310	0.162475
$587$	−19.7837	−0.816560	−0.408280	−	0.912857i	$-0.633871\pi$
$587$	−19.7837	−0.816560	−0.408280	+	0.912857i	$0.633871\pi$
$588$	0.183736	0.00757714
$589$	8.35056	0.344079
$590$	14.0678	0.579161
$591$	−16.5580	−0.681104
$592$	41.9669	1.72483
$593$	41.9336	1.72201	0.861004	−	0.508598i	$-0.169836\pi$
$593$	41.9336	1.72201	0.861004	+	0.508598i	$0.169836\pi$
$594$	−0.628142	−0.0257730
$595$	−1.86322	−0.0763846
$596$	3.49278	0.143070
$597$	−12.2919	−0.503072
$598$	3.28145	0.134189
$599$	−24.4156	−0.997596	−0.498798	−	0.866718i	$-0.666225\pi$
$599$	−24.4156	−0.997596	−0.498798	+	0.866718i	$0.666225\pi$
$600$	6.39225	0.260962
$601$	4.14155	0.168937	0.0844687	−	0.996426i	$-0.473081\pi$
$601$	4.14155	0.168937	0.0844687	+	0.996426i	$0.473081\pi$
$602$	12.3261	0.502375
$603$	−14.4956	−0.590308
$604$	−1.40569	−0.0571966
$605$	−18.1329	−0.737209
$606$	−24.1853	−0.982462
$607$	−8.20970	−0.333221	−0.166611	−	0.986023i	$-0.553282\pi$
$607$	−8.20970	−0.333221	−0.166611	+	0.986023i	$0.553282\pi$
$608$	−3.69410	−0.149816
$609$	−6.10743	−0.247485
$610$	13.2142	0.535027
$611$	−37.5731	−1.52005
$612$	0.203573	0.00822895
$613$	−42.0602	−1.69880	−0.849398	−	0.527753i	$-0.823035\pi$
$613$	−42.0602	−1.69880	−0.849398	+	0.527753i	$0.823035\pi$
$614$	−38.2917	−1.54533
$615$	−11.2527	−0.453752
$616$	−1.37170	−0.0552672
$617$	9.88843	0.398093	0.199047	−	0.979990i	$-0.436215\pi$
$617$	9.88843	0.398093	0.199047	+	0.979990i	$0.436215\pi$
$618$	−8.47925	−0.341086
$619$	15.3366	0.616430	0.308215	−	0.951317i	$-0.400268\pi$
$619$	15.3366	0.616430	0.308215	+	0.951317i	$0.400268\pi$
$620$	−0.723579	−0.0290596
$621$	0.444637	0.0178427
$622$	2.29022	0.0918294
$623$	−3.04396	−0.121953
$624$	19.7072	0.788920
$625$	−9.42223	−0.376889
$626$	19.0818	0.762662
$627$	1.66200	0.0663737
$628$	2.81374	0.112280
$629$	12.9205	0.515174
$630$	−2.26635	−0.0902937
$631$	4.04891	0.161185	0.0805923	−	0.996747i	$-0.474319\pi$
$631$	4.04891	0.161185	0.0805923	+	0.996747i	$0.474319\pi$
$632$	48.5392	1.93079
$633$	3.87459	0.154001
$634$	21.8718	0.868639
$635$	21.6999	0.861132
$636$	−1.86336	−0.0738869
$637$	5.47610	0.216971
$638$	3.83633	0.151882
$639$	−2.18202	−0.0863192
$640$	−15.9921	−0.632142
$641$	19.2881	0.761832	0.380916	−	0.924610i	$-0.375609\pi$
$641$	19.2881	0.761832	0.380916	+	0.924610i	$0.375609\pi$
$642$	25.4158	1.00308
$643$	−10.7939	−0.425669	−0.212834	−	0.977088i	$-0.568269\pi$
$643$	−10.7939	−0.425669	−0.212834	+	0.977088i	$0.568269\pi$
$644$	0.0816958	0.00321926
$645$	15.3807	0.605613
$646$	5.32448	0.209489
$647$	−21.4191	−0.842071	−0.421035	−	0.907044i	$-0.638333\pi$
$647$	−21.4191	−0.842071	−0.421035	+	0.907044i	$0.638333\pi$
$648$	2.94300	0.115612
$649$	2.89312	0.113565
$650$	16.0297	0.628735
$651$	−2.34182	−0.0917833
$652$	0.398493	0.0156062
$653$	16.7612	0.655918	0.327959	−	0.944692i	$-0.393639\pi$
$653$	16.7612	0.655918	0.327959	+	0.944692i	$0.393639\pi$
$654$	−21.2096	−0.829360
$655$	−29.9792	−1.17139
$656$	−24.0809	−0.940199
$657$	0.501357	0.0195598
$658$	9.24689	0.360481
$659$	17.7844	0.692784	0.346392	−	0.938090i	$-0.387407\pi$
$659$	17.7844	0.692784	0.346392	+	0.938090i	$0.387407\pi$
$660$	−0.144013	−0.00560568
$661$	0.560152	0.0217874	0.0108937	−	0.999941i	$-0.496532\pi$
$661$	0.560152	0.0217874	0.0108937	+	0.999941i	$0.496532\pi$
$662$	−8.01954	−0.311688
$663$	6.06733	0.235635
$664$	−41.2325	−1.60013
$665$	5.99652	0.232535
$666$	15.7160	0.608983
$667$	−2.71559	−0.105148
$668$	1.82929	0.0707773
$669$	−13.4187	−0.518799
$670$	32.8523	1.26919
$671$	2.71757	0.104911
$672$	1.03597	0.0399634
$673$	−7.42925	−0.286376	−0.143188	−	0.989695i	$-0.545735\pi$
$673$	−7.42925	−0.286376	−0.143188	+	0.989695i	$0.545735\pi$
$674$	18.2701	0.703740
$675$	2.17202	0.0836011
$676$	−3.12124	−0.120048
$677$	19.1371	0.735500	0.367750	−	0.929925i	$-0.380128\pi$
$677$	19.1371	0.735500	0.367750	+	0.929925i	$0.380128\pi$
$678$	−8.51849	−0.327151
$679$	−17.6923	−0.678969
$680$	−5.48345	−0.210281
$681$	−19.9016	−0.762630
$682$	1.47100	0.0563274
$683$	34.1982	1.30856	0.654279	−	0.756254i	$-0.272972\pi$
$683$	34.1982	1.30856	0.654279	+	0.756254i	$0.272972\pi$
$684$	−0.655172	−0.0250511
$685$	31.5940	1.20714
$686$	−1.34769	−0.0514550
$687$	11.7305	0.447547
$688$	32.9148	1.25486
$689$	−55.5358	−2.11575
$690$	−1.00770	−0.0383627
$691$	−8.40078	−0.319581	−0.159790	−	0.987151i	$-0.551082\pi$
$691$	−8.40078	−0.319581	−0.159790	+	0.987151i	$0.551082\pi$
$692$	2.31470	0.0879916
$693$	−0.466089	−0.0177052
$694$	−0.660097	−0.0250569
$695$	−7.26912	−0.275733
$696$	−17.9741	−0.681308
$697$	−7.41385	−0.280820
$698$	−8.93789	−0.338304
$699$	−3.16970	−0.119889
$700$	0.399078	0.0150837
$701$	2.88746	0.109058	0.0545289	−	0.998512i	$-0.482634\pi$
$701$	2.88746	0.109058	0.0545289	+	0.998512i	$0.482634\pi$
$702$	7.38007	0.278543
$703$	−41.5829	−1.56833
$704$	−4.00543	−0.150960
$705$	11.5384	0.434560
$706$	−12.2405	−0.460678
$707$	−17.9458	−0.674921
$708$	−1.14049	−0.0428623
$709$	−37.3230	−1.40170	−0.700848	−	0.713310i	$-0.747195\pi$
$709$	−37.3230	−1.40170	−0.700848	+	0.713310i	$0.747195\pi$
$710$	4.94522	0.185591
$711$	16.4931	0.618541
$712$	−8.95835	−0.335728
$713$	−1.04126	−0.0389956
$714$	−1.49319	−0.0558813
$715$	−4.29218	−0.160518
$716$	−3.05118	−0.114028
$717$	−10.2319	−0.382117
$718$	−11.6762	−0.435751
$719$	30.7569	1.14704	0.573519	−	0.819192i	$-0.305578\pi$
$719$	30.7569	1.14704	0.573519	+	0.819192i	$0.305578\pi$
$720$	−6.05191	−0.225541
$721$	−6.29170	−0.234315
$722$	8.46996	0.315219
$723$	0.961431	0.0357560
$724$	−1.31434	−0.0488472
$725$	−13.2655	−0.492667
$726$	−14.5318	−0.539326
$727$	−6.51230	−0.241528	−0.120764	−	0.992681i	$-0.538534\pi$
$727$	−6.51230	−0.241528	−0.120764	+	0.992681i	$0.538534\pi$
$728$	16.1161	0.597304
$729$	1.00000	0.0370370
$730$	−1.13625	−0.0420546
$731$	10.1336	0.374804
$732$	−1.07129	−0.0395960
$733$	−25.5144	−0.942395	−0.471197	−	0.882028i	$-0.656178\pi$
$733$	−25.5144	−0.942395	−0.471197	+	0.882028i	$0.656178\pi$
$734$	16.6953	0.616235
$735$	−1.68166	−0.0620290
$736$	0.460631	0.0169791
$737$	6.75625	0.248870
$738$	−9.01794	−0.331955
$739$	10.7523	0.395532	0.197766	−	0.980249i	$-0.436631\pi$
$739$	10.7523	0.395532	0.197766	+	0.980249i	$0.436631\pi$
$740$	3.60317	0.132455
$741$	−19.5269	−0.717338
$742$	13.6676	0.501753
$743$	6.20899	0.227786	0.113893	−	0.993493i	$-0.463668\pi$
$743$	6.20899	0.227786	0.113893	+	0.993493i	$0.463668\pi$
$744$	−6.89198	−0.252672
$745$	−31.9680	−1.17122
$746$	13.7038	0.501732
$747$	−14.0104	−0.512613
$748$	−0.0948830	−0.00346927
$749$	18.8588	0.689087
$750$	−16.2543	−0.593524
$751$	−39.7233	−1.44952	−0.724761	−	0.689000i	$-0.758050\pi$
$751$	−39.7233	−1.44952	−0.724761	+	0.689000i	$0.758050\pi$
$752$	24.6922	0.900433
$753$	−1.36831	−0.0498641
$754$	−45.0733	−1.64147
$755$	12.8657	0.468230
$756$	0.183736	0.00668241
$757$	−31.7852	−1.15525	−0.577626	−	0.816301i	$-0.696021\pi$
$757$	−31.7852	−1.15525	−0.577626	+	0.816301i	$0.696021\pi$
$758$	39.4948	1.43451
$759$	−0.207240	−0.00752234
$760$	17.6477	0.640151
$761$	5.80609	0.210471	0.105235	−	0.994447i	$-0.466440\pi$
$761$	5.80609	0.210471	0.105235	+	0.994447i	$0.466440\pi$
$762$	17.3903	0.629986
$763$	−15.7377	−0.569745
$764$	−3.07350	−0.111195
$765$	−1.86322	−0.0673649
$766$	−1.34769	−0.0486940
$767$	−33.9914	−1.22736
$768$	4.37130	0.157736
$769$	−16.2838	−0.587210	−0.293605	−	0.955927i	$-0.594855\pi$
$769$	−16.2838	−0.587210	−0.293605	+	0.955927i	$0.594855\pi$
$770$	1.05632	0.0380672
$771$	−6.07947	−0.218947
$772$	4.15828	0.149660
$773$	2.65209	0.0953890	0.0476945	−	0.998862i	$-0.484813\pi$
$773$	2.65209	0.0953890	0.0476945	+	0.998862i	$0.484813\pi$
$774$	12.3261	0.443053
$775$	−5.08649	−0.182712
$776$	−52.0684	−1.86915
$777$	11.6615	0.418353
$778$	9.99505	0.358340
$779$	23.8605	0.854891
$780$	1.69201	0.0605837
$781$	1.01701	0.0363916
$782$	−0.663929	−0.0237420
$783$	−6.10743	−0.218262
$784$	−3.59877	−0.128527
$785$	−25.7530	−0.919164
$786$	−24.0255	−0.856960
$787$	3.20170	0.114128	0.0570641	−	0.998371i	$-0.481826\pi$
$787$	3.20170	0.114128	0.0570641	+	0.998371i	$0.481826\pi$
$788$	−3.04229	−0.108377
$789$	26.1414	0.930657
$790$	−37.3793	−1.32989
$791$	−6.32082	−0.224742
$792$	−1.37170	−0.0487411
$793$	−31.9289	−1.13383
$794$	−47.4104	−1.68253
$795$	17.0545	0.604862
$796$	−2.25846	−0.0800488
$797$	51.1462	1.81169	0.905846	−	0.423607i	$-0.139236\pi$
$797$	51.1462	1.81169	0.905846	+	0.423607i	$0.139236\pi$
$798$	4.80564	0.170118
$799$	7.60208	0.268942
$800$	2.25015	0.0795548
$801$	−3.04396	−0.107553
$802$	−1.95662	−0.0690907
$803$	−0.233677	−0.00824627
$804$	−2.66337	−0.0939298
$805$	−0.747728	−0.0263540
$806$	−17.2828	−0.608762
$807$	−18.3774	−0.646915
$808$	−52.8144	−1.85800
$809$	−47.6031	−1.67364	−0.836818	−	0.547482i	$-0.815587\pi$
$809$	−47.6031	−1.67364	−0.836818	+	0.547482i	$0.815587\pi$
$810$	−2.26635	−0.0796315
$811$	−41.5145	−1.45777	−0.728886	−	0.684636i	$-0.759961\pi$
$811$	−41.5145	−1.45777	−0.728886	+	0.684636i	$0.759961\pi$
$812$	−1.12215	−0.0393798
$813$	−0.920681	−0.0322897
$814$	−7.32505	−0.256743
$815$	−3.64725	−0.127757
$816$	−3.98731	−0.139584
$817$	−32.6136	−1.14100
$818$	4.96880	0.173730
$819$	5.47610	0.191350
$820$	−2.06752	−0.0722009
$821$	−38.0618	−1.32837	−0.664183	−	0.747570i	$-0.731221\pi$
$821$	−38.0618	−1.32837	−0.664183	+	0.747570i	$0.731221\pi$
$822$	25.3195	0.883120
$823$	3.96451	0.138194	0.0690970	−	0.997610i	$-0.477988\pi$
$823$	3.96451	0.138194	0.0690970	+	0.997610i	$0.477988\pi$
$824$	−18.5164	−0.645051
$825$	−1.01235	−0.0352456
$826$	8.36541	0.291070
$827$	−28.6702	−0.996960	−0.498480	−	0.866901i	$-0.666108\pi$
$827$	−28.6702	−0.996960	−0.498480	+	0.866901i	$0.666108\pi$
$828$	0.0816958	0.00283912
$829$	32.1198	1.11557	0.557784	−	0.829986i	$-0.311652\pi$
$829$	32.1198	1.11557	0.557784	+	0.829986i	$0.311652\pi$
$830$	31.7525	1.10214
$831$	−8.24610	−0.286054
$832$	47.0600	1.63151
$833$	−1.10797	−0.0383887
$834$	−5.82550	−0.201720
$835$	−16.7427	−0.579407
$836$	0.305368	0.0105614
$837$	−2.34182	−0.0809453
$838$	3.87816	0.133969
$839$	6.42135	0.221690	0.110845	−	0.993838i	$-0.464644\pi$
$839$	6.42135	0.221690	0.110845	+	0.993838i	$0.464644\pi$
$840$	−4.94912	−0.170761
$841$	8.30066	0.286230
$842$	18.7615	0.646563
$843$	−21.9045	−0.754431
$844$	0.711902	0.0245047
$845$	28.5674	0.982750
$846$	9.24689	0.317915
$847$	−10.7828	−0.370500
$848$	36.4969	1.25331
$849$	−9.08769	−0.311889
$850$	−3.24324	−0.111242
$851$	5.18512	0.177744
$852$	−0.400915	−0.0137351
$853$	−5.27776	−0.180707	−0.0903536	−	0.995910i	$-0.528800\pi$
$853$	−5.27776	−0.180707	−0.0903536	+	0.995910i	$0.528800\pi$
$854$	7.85782	0.268889
$855$	5.99652	0.205077
$856$	55.5014	1.89700
$857$	10.3849	0.354741	0.177371	−	0.984144i	$-0.443241\pi$
$857$	10.3849	0.354741	0.177371	+	0.984144i	$0.443241\pi$
$858$	−3.43977	−0.117432
$859$	27.9861	0.954872	0.477436	−	0.878667i	$-0.341566\pi$
$859$	27.9861	0.954872	0.477436	+	0.878667i	$0.341566\pi$
$860$	2.82598	0.0963650
$861$	−6.69141	−0.228043
$862$	−25.9015	−0.882210
$863$	10.6052	0.361007	0.180503	−	0.983574i	$-0.442227\pi$
$863$	10.6052	0.361007	0.180503	+	0.983574i	$0.442227\pi$
$864$	1.03597	0.0352444
$865$	−21.1855	−0.720328
$866$	1.44564	0.0491248
$867$	15.7724	0.535659
$868$	−0.430277	−0.0146045
$869$	−7.68726	−0.260772
$870$	13.8416	0.469274
$871$	−79.3796	−2.68967
$872$	−46.3161	−1.56846
$873$	−17.6923	−0.598794
$874$	2.13676	0.0722771
$875$	−12.0609	−0.407733
$876$	0.0921172	0.00311235
$877$	42.0061	1.41845	0.709223	−	0.704984i	$-0.249046\pi$
$877$	42.0061	1.41845	0.709223	+	0.704984i	$0.249046\pi$
$878$	33.3425	1.12525
$879$	2.91840	0.0984353
$880$	2.82072	0.0950866
$881$	10.6126	0.357549	0.178774	−	0.983890i	$-0.442787\pi$
$881$	10.6126	0.357549	0.178774	+	0.983890i	$0.442787\pi$
$882$	−1.34769	−0.0453790
$883$	58.3356	1.96315	0.981575	−	0.191076i	$-0.0611975\pi$
$883$	58.3356	1.96315	0.981575	+	0.191076i	$0.0611975\pi$
$884$	1.11479	0.0374943
$885$	10.4384	0.350885
$886$	−16.0369	−0.538769
$887$	13.9656	0.468918	0.234459	−	0.972126i	$-0.424668\pi$
$887$	13.9656	0.468918	0.234459	+	0.972126i	$0.424668\pi$
$888$	34.3196	1.15169
$889$	12.9038	0.432781
$890$	6.89868	0.231244
$891$	−0.466089	−0.0156146
$892$	−2.46550	−0.0825512
$893$	−24.4663	−0.818732
$894$	−25.6193	−0.856836
$895$	27.9262	0.933471
$896$	−9.50970	−0.317697
$897$	2.43488	0.0812981
$898$	−29.7301	−0.992105
$899$	14.3025	0.477016
$900$	0.399078	0.0133026
$901$	11.2364	0.374340
$902$	4.20316	0.139950
$903$	9.14612	0.304364
$904$	−18.6021	−0.618698
$905$	12.0297	0.399879
$906$	10.3106	0.342547
$907$	17.7406	0.589068	0.294534	−	0.955641i	$-0.404836\pi$
$907$	17.7406	0.589068	0.294534	+	0.955641i	$0.404836\pi$
$908$	−3.65663	−0.121350
$909$	−17.9458	−0.595225
$910$	−12.4108	−0.411413
$911$	−15.4629	−0.512309	−0.256154	−	0.966636i	$-0.582456\pi$
$911$	−15.4629	−0.512309	−0.256154	+	0.966636i	$0.582456\pi$
$912$	12.8326	0.424931
$913$	6.53008	0.216114
$914$	−26.5784	−0.879134
$915$	9.80508	0.324146
$916$	2.15531	0.0712136
$917$	−17.8272	−0.588705
$918$	−1.49319	−0.0492827
$919$	−34.8840	−1.15072	−0.575358	−	0.817902i	$-0.695137\pi$
$919$	−34.8840	−1.15072	−0.575358	+	0.817902i	$0.695137\pi$
$920$	−2.20056	−0.0725503
$921$	−28.4129	−0.936235
$922$	−4.28535	−0.141130
$923$	−11.9489	−0.393304
$924$	−0.0856371	−0.00281726
$925$	25.3289	0.832810
$926$	−46.5993	−1.53135
$927$	−6.29170	−0.206647
$928$	−6.32712	−0.207698
$929$	−16.2194	−0.532141	−0.266071	−	0.963954i	$-0.585725\pi$
$929$	−16.2194	−0.532141	−0.266071	+	0.963954i	$0.585725\pi$
$930$	5.30740	0.174037
$931$	3.56584	0.116866
$932$	−0.582387	−0.0190767
$933$	1.69937	0.0556348
$934$	40.0035	1.30895
$935$	0.868426	0.0284006
$936$	16.1161	0.526772
$937$	−25.8358	−0.844020	−0.422010	−	0.906591i	$-0.638675\pi$
$937$	−25.8358	−0.844020	−0.422010	+	0.906591i	$0.638675\pi$
$938$	19.5356	0.637860
$939$	14.1589	0.462058
$940$	2.12001	0.0691471
$941$	54.8284	1.78736	0.893678	−	0.448709i	$-0.148116\pi$
$941$	54.8284	1.78736	0.893678	+	0.448709i	$0.148116\pi$
$942$	−20.6385	−0.672440
$943$	−2.97525	−0.0968875
$944$	22.3384	0.727053
$945$	−1.68166	−0.0547044
$946$	−5.74506	−0.186788
$947$	13.2134	0.429379	0.214690	−	0.976682i	$-0.431126\pi$
$947$	13.2134	0.429379	0.214690	+	0.976682i	$0.431126\pi$
$948$	3.03038	0.0984221
$949$	2.74548	0.0891220
$950$	10.4379	0.338652
$951$	16.2291	0.526265
$952$	−3.26074	−0.105681
$953$	−16.6772	−0.540226	−0.270113	−	0.962829i	$-0.587061\pi$
$953$	−16.6772	−0.540226	−0.270113	+	0.962829i	$0.587061\pi$
$954$	13.6676	0.442504
$955$	28.1305	0.910282
$956$	−1.87997	−0.0608025
$957$	2.84660	0.0920176
$958$	3.71730	0.120101
$959$	18.7874	0.606676
$960$	−14.4517	−0.466426
$961$	−25.5159	−0.823092
$962$	86.0624	2.77476
$963$	18.8588	0.607717
$964$	0.176649	0.00568949
$965$	−38.0591	−1.22516
$966$	−0.599232	−0.0192800
$967$	6.21635	0.199904	0.0999522	−	0.994992i	$-0.468131\pi$
$967$	6.21635	0.199904	0.0999522	+	0.994992i	$0.468131\pi$
$968$	−31.7336	−1.01996
$969$	3.95082	0.126919
$970$	40.0970	1.28744
$971$	51.1270	1.64074	0.820371	−	0.571832i	$-0.193767\pi$
$971$	51.1270	1.64074	0.820371	+	0.571832i	$0.193767\pi$
$972$	0.183736	0.00589333
$973$	−4.32258	−0.138576
$974$	−14.1296	−0.452743
$975$	11.8942	0.380919
$976$	20.9830	0.671648
$977$	8.07711	0.258410	0.129205	−	0.991618i	$-0.458758\pi$
$977$	8.07711	0.258410	0.129205	+	0.991618i	$0.458758\pi$
$978$	−2.92292	−0.0934646
$979$	1.41875	0.0453435
$980$	−0.308981	−0.00987004
$981$	−15.7377	−0.502468
$982$	−43.3135	−1.38219
$983$	52.8452	1.68550	0.842750	−	0.538306i	$-0.180935\pi$
$983$	52.8452	1.68550	0.842750	+	0.538306i	$0.180935\pi$
$984$	−19.6928	−0.627783
$985$	27.8449	0.887211
$986$	9.11956	0.290426
$987$	6.86130	0.218397
$988$	−3.58779	−0.114143
$989$	4.06670	0.129314
$990$	1.05632	0.0335721
$991$	42.6827	1.35586	0.677930	−	0.735127i	$-0.262877\pi$
$991$	42.6827	1.35586	0.677930	+	0.735127i	$0.262877\pi$
$992$	−2.42606	−0.0770275
$993$	−5.95059	−0.188836
$994$	2.94068	0.0932727
$995$	20.6707	0.655306
$996$	−2.57421	−0.0815669
$997$	−52.3583	−1.65820	−0.829102	−	0.559097i	$-0.811148\pi$
$997$	−52.3583	−1.65820	−0.829102	+	0.559097i	$0.811148\pi$
$998$	10.6124	0.335931
$999$	11.6615	0.368952

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.o.1.13	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.o.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-1.34769 q^{2} -1.00000 q^{3} -0.183736 q^{4} +1.68166 q^{5} +1.34769 q^{6} +1.00000 q^{7} +2.94300 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.34769 q^{2} -1.00000 q^{3} -0.183736 q^{4} +1.68166 q^{5} +1.34769 q^{6} +1.00000 q^{7} +2.94300 q^{8} +1.00000 q^{9} -2.26635 q^{10} -0.466089 q^{11} +0.183736 q^{12} +5.47610 q^{13} -1.34769 q^{14} -1.68166 q^{15} -3.59877 q^{16} -1.10797 q^{17} -1.34769 q^{18} +3.56584 q^{19} -0.308981 q^{20} -1.00000 q^{21} +0.628142 q^{22} -0.444637 q^{23} -2.94300 q^{24} -2.17202 q^{25} -7.38007 q^{26} -1.00000 q^{27} -0.183736 q^{28} +6.10743 q^{29} +2.26635 q^{30} +2.34182 q^{31} -1.03597 q^{32} +0.466089 q^{33} +1.49319 q^{34} +1.68166 q^{35} -0.183736 q^{36} -11.6615 q^{37} -4.80564 q^{38} -5.47610 q^{39} +4.94912 q^{40} +6.69141 q^{41} +1.34769 q^{42} -9.14612 q^{43} +0.0856371 q^{44} +1.68166 q^{45} +0.599232 q^{46} -6.86130 q^{47} +3.59877 q^{48} +1.00000 q^{49} +2.92721 q^{50} +1.10797 q^{51} -1.00616 q^{52} -10.1415 q^{53} +1.34769 q^{54} -0.783802 q^{55} +2.94300 q^{56} -3.56584 q^{57} -8.23091 q^{58} -6.20723 q^{59} +0.308981 q^{60} -5.83059 q^{61} -3.15605 q^{62} +1.00000 q^{63} +8.59371 q^{64} +9.20893 q^{65} -0.628142 q^{66} -14.4956 q^{67} +0.203573 q^{68} +0.444637 q^{69} -2.26635 q^{70} -2.18202 q^{71} +2.94300 q^{72} +0.501357 q^{73} +15.7160 q^{74} +2.17202 q^{75} -0.655172 q^{76} -0.466089 q^{77} +7.38007 q^{78} +16.4931 q^{79} -6.05191 q^{80} +1.00000 q^{81} -9.01794 q^{82} -14.0104 q^{83} +0.183736 q^{84} -1.86322 q^{85} +12.3261 q^{86} -6.10743 q^{87} -1.37170 q^{88} -3.04396 q^{89} -2.26635 q^{90} +5.47610 q^{91} +0.0816958 q^{92} -2.34182 q^{93} +9.24689 q^{94} +5.99652 q^{95} +1.03597 q^{96} -17.6923 q^{97} -1.34769 q^{98} -0.466089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) \) 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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