LMFDB - Embedded newform 4006.2.a.g.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$31.9880710497$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.82093 q^{3} +1.00000 q^{4} -3.80048 q^{5} +1.82093 q^{6} -3.54475 q^{7} -1.00000 q^{8} +0.315788 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.82093 q^{3} +1.00000 q^{4} -3.80048 q^{5} +1.82093 q^{6} -3.54475 q^{7} -1.00000 q^{8} +0.315788 q^{9} +3.80048 q^{10} -4.23704 q^{11} -1.82093 q^{12} +1.93193 q^{13} +3.54475 q^{14} +6.92040 q^{15} +1.00000 q^{16} -7.25106 q^{17} -0.315788 q^{18} +1.65314 q^{19} -3.80048 q^{20} +6.45474 q^{21} +4.23704 q^{22} +2.77810 q^{23} +1.82093 q^{24} +9.44361 q^{25} -1.93193 q^{26} +4.88776 q^{27} -3.54475 q^{28} +6.62357 q^{29} -6.92040 q^{30} -9.37689 q^{31} -1.00000 q^{32} +7.71535 q^{33} +7.25106 q^{34} +13.4717 q^{35} +0.315788 q^{36} -1.32098 q^{37} -1.65314 q^{38} -3.51791 q^{39} +3.80048 q^{40} +7.72437 q^{41} -6.45474 q^{42} +12.2401 q^{43} -4.23704 q^{44} -1.20015 q^{45} -2.77810 q^{46} +2.77894 q^{47} -1.82093 q^{48} +5.56523 q^{49} -9.44361 q^{50} +13.2037 q^{51} +1.93193 q^{52} -8.53389 q^{53} -4.88776 q^{54} +16.1028 q^{55} +3.54475 q^{56} -3.01025 q^{57} -6.62357 q^{58} -10.9129 q^{59} +6.92040 q^{60} -12.6169 q^{61} +9.37689 q^{62} -1.11939 q^{63} +1.00000 q^{64} -7.34226 q^{65} -7.71535 q^{66} +11.2323 q^{67} -7.25106 q^{68} -5.05873 q^{69} -13.4717 q^{70} -2.85150 q^{71} -0.315788 q^{72} +5.54156 q^{73} +1.32098 q^{74} -17.1962 q^{75} +1.65314 q^{76} +15.0192 q^{77} +3.51791 q^{78} +11.7255 q^{79} -3.80048 q^{80} -9.84764 q^{81} -7.72437 q^{82} +9.05386 q^{83} +6.45474 q^{84} +27.5575 q^{85} -12.2401 q^{86} -12.0611 q^{87} +4.23704 q^{88} -1.09101 q^{89} +1.20015 q^{90} -6.84821 q^{91} +2.77810 q^{92} +17.0747 q^{93} -2.77894 q^{94} -6.28271 q^{95} +1.82093 q^{96} -3.33585 q^{97} -5.56523 q^{98} -1.33801 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) $ 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.82093	−1.05131	−0.525657	−	0.850696i	$-0.676181\pi$
$3$	−1.82093	−1.05131	−0.525657	+	0.850696i	$0.676181\pi$
$4$	1.00000	0.500000
$5$	−3.80048	−1.69962	−0.849812	−	0.527086i	$-0.823285\pi$
$5$	−3.80048	−1.69962	−0.849812	+	0.527086i	$0.823285\pi$
$6$	1.82093	0.743392
$7$	−3.54475	−1.33979	−0.669894	−	0.742457i	$-0.733661\pi$
$7$	−3.54475	−1.33979	−0.669894	+	0.742457i	$0.733661\pi$
$8$	−1.00000	−0.353553
$9$	0.315788	0.105263
$10$	3.80048	1.20182
$11$	−4.23704	−1.27752	−0.638758	−	0.769408i	$-0.720551\pi$
$11$	−4.23704	−1.27752	−0.638758	+	0.769408i	$0.720551\pi$
$12$	−1.82093	−0.525657
$13$	1.93193	0.535821	0.267911	−	0.963444i	$-0.413667\pi$
$13$	1.93193	0.535821	0.267911	+	0.963444i	$0.413667\pi$
$14$	3.54475	0.947373
$15$	6.92040	1.78684
$16$	1.00000	0.250000
$17$	−7.25106	−1.75864	−0.879320	−	0.476232i	$-0.842002\pi$
$17$	−7.25106	−1.75864	−0.879320	+	0.476232i	$0.842002\pi$
$18$	−0.315788	−0.0744321
$19$	1.65314	0.379256	0.189628	−	0.981856i	$-0.439272\pi$
$19$	1.65314	0.379256	0.189628	+	0.981856i	$0.439272\pi$
$20$	−3.80048	−0.849812
$21$	6.45474	1.40854
$22$	4.23704	0.903340
$23$	2.77810	0.579274	0.289637	−	0.957137i	$-0.406465\pi$
$23$	2.77810	0.579274	0.289637	+	0.957137i	$0.406465\pi$
$24$	1.82093	0.371696
$25$	9.44361	1.88872
$26$	−1.93193	−0.378883
$27$	4.88776	0.940650
$28$	−3.54475	−0.669894
$29$	6.62357	1.22997	0.614983	−	0.788540i	$-0.289163\pi$
$29$	6.62357	1.22997	0.614983	+	0.788540i	$0.289163\pi$
$30$	−6.92040	−1.26349
$31$	−9.37689	−1.68414	−0.842069	−	0.539369i	$-0.818663\pi$
$31$	−9.37689	−1.68414	−0.842069	+	0.539369i	$0.818663\pi$
$32$	−1.00000	−0.176777
$33$	7.71535	1.34307
$34$	7.25106	1.24355
$35$	13.4717	2.27714
$36$	0.315788	0.0526314
$37$	−1.32098	−0.217168	−0.108584	−	0.994087i	$-0.534632\pi$
$37$	−1.32098	−0.217168	−0.108584	+	0.994087i	$0.534632\pi$
$38$	−1.65314	−0.268174
$39$	−3.51791	−0.563317
$40$	3.80048	0.600908
$41$	7.72437	1.20634	0.603172	−	0.797611i	$-0.293903\pi$
$41$	7.72437	1.20634	0.603172	+	0.797611i	$0.293903\pi$
$42$	−6.45474	−0.995988
$43$	12.2401	1.86659	0.933297	−	0.359106i	$-0.116918\pi$
$43$	12.2401	1.86659	0.933297	+	0.359106i	$0.116918\pi$
$44$	−4.23704	−0.638758
$45$	−1.20015	−0.178907
$46$	−2.77810	−0.409609
$47$	2.77894	0.405350	0.202675	−	0.979246i	$-0.435036\pi$
$47$	2.77894	0.405350	0.202675	+	0.979246i	$0.435036\pi$
$48$	−1.82093	−0.262829
$49$	5.56523	0.795033
$50$	−9.44361	−1.33553
$51$	13.2037	1.84888
$52$	1.93193	0.267911
$53$	−8.53389	−1.17222	−0.586110	−	0.810231i	$-0.699341\pi$
$53$	−8.53389	−1.17222	−0.586110	+	0.810231i	$0.699341\pi$
$54$	−4.88776	−0.665140
$55$	16.1028	2.17130
$56$	3.54475	0.473687
$57$	−3.01025	−0.398717
$58$	−6.62357	−0.869718
$59$	−10.9129	−1.42073	−0.710367	−	0.703831i	$-0.751471\pi$
$59$	−10.9129	−1.42073	−0.710367	+	0.703831i	$0.751471\pi$
$60$	6.92040	0.893420
$61$	−12.6169	−1.61543	−0.807716	−	0.589572i	$-0.799296\pi$
$61$	−12.6169	−1.61543	−0.807716	+	0.589572i	$0.799296\pi$
$62$	9.37689	1.19087
$63$	−1.11939	−0.141030
$64$	1.00000	0.125000
$65$	−7.34226	−0.910695
$66$	−7.71535	−0.949694
$67$	11.2323	1.37224	0.686119	−	0.727489i	$-0.259313\pi$
$67$	11.2323	1.37224	0.686119	+	0.727489i	$0.259313\pi$
$68$	−7.25106	−0.879320
$69$	−5.05873	−0.609000
$70$	−13.4717	−1.61018
$71$	−2.85150	−0.338410	−0.169205	−	0.985581i	$-0.554120\pi$
$71$	−2.85150	−0.338410	−0.169205	+	0.985581i	$0.554120\pi$
$72$	−0.315788	−0.0372160
$73$	5.54156	0.648590	0.324295	−	0.945956i	$-0.394873\pi$
$73$	5.54156	0.648590	0.324295	+	0.945956i	$0.394873\pi$
$74$	1.32098	0.153561
$75$	−17.1962	−1.98564
$76$	1.65314	0.189628
$77$	15.0192	1.71160
$78$	3.51791	0.398325
$79$	11.7255	1.31923	0.659613	−	0.751605i	$-0.270720\pi$
$79$	11.7255	1.31923	0.659613	+	0.751605i	$0.270720\pi$
$80$	−3.80048	−0.424906
$81$	−9.84764	−1.09418
$82$	−7.72437	−0.853014
$83$	9.05386	0.993790	0.496895	−	0.867811i	$-0.334473\pi$
$83$	9.05386	0.993790	0.496895	+	0.867811i	$0.334473\pi$
$84$	6.45474	0.704270
$85$	27.5575	2.98903
$86$	−12.2401	−1.31988
$87$	−12.0611	−1.29308
$88$	4.23704	0.451670
$89$	−1.09101	−0.115646	−0.0578232	−	0.998327i	$-0.518416\pi$
$89$	−1.09101	−0.115646	−0.0578232	+	0.998327i	$0.518416\pi$
$90$	1.20015	0.126507
$91$	−6.84821	−0.717887
$92$	2.77810	0.289637
$93$	17.0747	1.77056
$94$	−2.77894	−0.286626
$95$	−6.28271	−0.644592
$96$	1.82093	0.185848
$97$	−3.33585	−0.338704	−0.169352	−	0.985556i	$-0.554167\pi$
$97$	−3.33585	−0.338704	−0.169352	+	0.985556i	$0.554167\pi$
$98$	−5.56523	−0.562173
$99$	−1.33801	−0.134475
$100$	9.44361	0.944361
$101$	17.3615	1.72753	0.863765	−	0.503894i	$-0.168100\pi$
$101$	17.3615	1.72753	0.863765	+	0.503894i	$0.168100\pi$
$102$	−13.2037	−1.30736
$103$	5.49812	0.541746	0.270873	−	0.962615i	$-0.412688\pi$
$103$	5.49812	0.541746	0.270873	+	0.962615i	$0.412688\pi$
$104$	−1.93193	−0.189441
$105$	−24.5311	−2.39399
$106$	8.53389	0.828885
$107$	−10.1626	−0.982460	−0.491230	−	0.871030i	$-0.663453\pi$
$107$	−10.1626	−0.982460	−0.491230	+	0.871030i	$0.663453\pi$
$108$	4.88776	0.470325
$109$	−6.14727	−0.588802	−0.294401	−	0.955682i	$-0.595120\pi$
$109$	−6.14727	−0.588802	−0.294401	+	0.955682i	$0.595120\pi$
$110$	−16.1028	−1.53534
$111$	2.40541	0.228312
$112$	−3.54475	−0.334947
$113$	−8.41808	−0.791906	−0.395953	−	0.918271i	$-0.629586\pi$
$113$	−8.41808	−0.791906	−0.395953	+	0.918271i	$0.629586\pi$
$114$	3.01025	0.281936
$115$	−10.5581	−0.984548
$116$	6.62357	0.614983
$117$	0.610082	0.0564021
$118$	10.9129	1.00461
$119$	25.7032	2.35620
$120$	−6.92040	−0.631743
$121$	6.95249	0.632045
$122$	12.6169	1.14228
$123$	−14.0655	−1.26825
$124$	−9.37689	−0.842069
$125$	−16.8878	−1.51049
$126$	1.11939	0.0997232
$127$	10.0912	0.895445	0.447722	−	0.894173i	$-0.352235\pi$
$127$	10.0912	0.895445	0.447722	+	0.894173i	$0.352235\pi$
$128$	−1.00000	−0.0883883
$129$	−22.2883	−1.96238
$130$	7.34226	0.643959
$131$	−20.2477	−1.76905	−0.884525	−	0.466493i	$-0.845517\pi$
$131$	−20.2477	−1.76905	−0.884525	+	0.466493i	$0.845517\pi$
$132$	7.71535	0.671535
$133$	−5.85995	−0.508122
$134$	−11.2323	−0.970319
$135$	−18.5758	−1.59875
$136$	7.25106	0.621773
$137$	5.37282	0.459031	0.229515	−	0.973305i	$-0.426286\pi$
$137$	5.37282	0.459031	0.229515	+	0.973305i	$0.426286\pi$
$138$	5.05873	0.430628
$139$	1.01967	0.0864874	0.0432437	−	0.999065i	$-0.486231\pi$
$139$	1.01967	0.0864874	0.0432437	+	0.999065i	$0.486231\pi$
$140$	13.4717	1.13857
$141$	−5.06026	−0.426150
$142$	2.85150	0.239292
$143$	−8.18567	−0.684520
$144$	0.315788	0.0263157
$145$	−25.1727	−2.09048
$146$	−5.54156	−0.458623
$147$	−10.1339	−0.835829
$148$	−1.32098	−0.108584
$149$	−5.09976	−0.417789	−0.208895	−	0.977938i	$-0.566987\pi$
$149$	−5.09976	−0.417789	−0.208895	+	0.977938i	$0.566987\pi$
$150$	17.1962	1.40406
$151$	−10.3479	−0.842104	−0.421052	−	0.907037i	$-0.638339\pi$
$151$	−10.3479	−0.842104	−0.421052	+	0.907037i	$0.638339\pi$
$152$	−1.65314	−0.134087
$153$	−2.28980	−0.185119
$154$	−15.0192	−1.21028
$155$	35.6366	2.86240
$156$	−3.51791	−0.281659
$157$	8.43226	0.672968	0.336484	−	0.941689i	$-0.390762\pi$
$157$	8.43226	0.672968	0.336484	+	0.941689i	$0.390762\pi$
$158$	−11.7255	−0.932834
$159$	15.5396	1.23237
$160$	3.80048	0.300454
$161$	−9.84767	−0.776105
$162$	9.84764	0.773704
$163$	22.8876	1.79270	0.896349	−	0.443349i	$-0.146210\pi$
$163$	22.8876	1.79270	0.896349	+	0.443349i	$0.146210\pi$
$164$	7.72437	0.603172
$165$	−29.3220	−2.28272
$166$	−9.05386	−0.702716
$167$	−3.29537	−0.255004	−0.127502	−	0.991838i	$-0.540696\pi$
$167$	−3.29537	−0.255004	−0.127502	+	0.991838i	$0.540696\pi$
$168$	−6.45474	−0.497994
$169$	−9.26764	−0.712895
$170$	−27.5575	−2.11356
$171$	0.522042	0.0399215
$172$	12.2401	0.933297
$173$	−8.41833	−0.640034	−0.320017	−	0.947412i	$-0.603689\pi$
$173$	−8.41833	−0.640034	−0.320017	+	0.947412i	$0.603689\pi$
$174$	12.0611	0.914347
$175$	−33.4752	−2.53049
$176$	−4.23704	−0.319379
$177$	19.8716	1.49364
$178$	1.09101	0.0817743
$179$	18.2974	1.36761	0.683807	−	0.729663i	$-0.260323\pi$
$179$	18.2974	1.36761	0.683807	+	0.729663i	$0.260323\pi$
$180$	−1.20015	−0.0894536
$181$	−5.28677	−0.392962	−0.196481	−	0.980508i	$-0.562951\pi$
$181$	−5.28677	−0.392962	−0.196481	+	0.980508i	$0.562951\pi$
$182$	6.84821	0.507623
$183$	22.9745	1.69833
$184$	−2.77810	−0.204804
$185$	5.02035	0.369104
$186$	−17.0747	−1.25198
$187$	30.7230	2.24669
$188$	2.77894	0.202675
$189$	−17.3259	−1.26027
$190$	6.28271	0.455795
$191$	−14.4080	−1.04252	−0.521262	−	0.853397i	$-0.674539\pi$
$191$	−14.4080	−1.04252	−0.521262	+	0.853397i	$0.674539\pi$
$192$	−1.82093	−0.131414
$193$	19.9624	1.43692	0.718461	−	0.695567i	$-0.244847\pi$
$193$	19.9624	1.43692	0.718461	+	0.695567i	$0.244847\pi$
$194$	3.33585	0.239500
$195$	13.3697	0.957427
$196$	5.56523	0.397516
$197$	−6.27526	−0.447093	−0.223547	−	0.974693i	$-0.571764\pi$
$197$	−6.27526	−0.447093	−0.223547	+	0.974693i	$0.571764\pi$
$198$	1.33801	0.0950881
$199$	8.50276	0.602745	0.301372	−	0.953506i	$-0.402555\pi$
$199$	8.50276	0.602745	0.301372	+	0.953506i	$0.402555\pi$
$200$	−9.44361	−0.667764
$201$	−20.4532	−1.44266
$202$	−17.3615	−1.22155
$203$	−23.4789	−1.64789
$204$	13.2037	0.924442
$205$	−29.3563	−2.05033
$206$	−5.49812	−0.383072
$207$	0.877292	0.0609760
$208$	1.93193	0.133955
$209$	−7.00441	−0.484505
$210$	24.5311	1.69280
$211$	3.50204	0.241090	0.120545	−	0.992708i	$-0.461536\pi$
$211$	3.50204	0.241090	0.120545	+	0.992708i	$0.461536\pi$
$212$	−8.53389	−0.586110
$213$	5.19238	0.355776
$214$	10.1626	0.694704
$215$	−46.5181	−3.17251
$216$	−4.88776	−0.332570
$217$	33.2387	2.25639
$218$	6.14727	0.416346
$219$	−10.0908	−0.681873
$220$	16.1028	1.08565
$221$	−14.0085	−0.942317
$222$	−2.40541	−0.161441
$223$	8.62891	0.577834	0.288917	−	0.957354i	$-0.406705\pi$
$223$	8.62891	0.577834	0.288917	+	0.957354i	$0.406705\pi$
$224$	3.54475	0.236843
$225$	2.98218	0.198812
$226$	8.41808	0.559962
$227$	−18.6343	−1.23680	−0.618401	−	0.785863i	$-0.712219\pi$
$227$	−18.6343	−1.23680	−0.618401	+	0.785863i	$0.712219\pi$
$228$	−3.01025	−0.199359
$229$	4.45951	0.294693	0.147346	−	0.989085i	$-0.452927\pi$
$229$	4.45951	0.294693	0.147346	+	0.989085i	$0.452927\pi$
$230$	10.5581	0.696181
$231$	−27.3490	−1.79943
$232$	−6.62357	−0.434859
$233$	27.1983	1.78182	0.890910	−	0.454180i	$-0.150068\pi$
$233$	27.1983	1.78182	0.890910	+	0.454180i	$0.150068\pi$
$234$	−0.610082	−0.0398823
$235$	−10.5613	−0.688943
$236$	−10.9129	−0.710367
$237$	−21.3514	−1.38692
$238$	−25.7032	−1.66609
$239$	28.7485	1.85959	0.929794	−	0.368080i	$-0.119985\pi$
$239$	28.7485	1.85959	0.929794	+	0.368080i	$0.119985\pi$
$240$	6.92040	0.446710
$241$	−12.7200	−0.819366	−0.409683	−	0.912228i	$-0.634361\pi$
$241$	−12.7200	−0.819366	−0.409683	+	0.912228i	$0.634361\pi$
$242$	−6.95249	−0.446923
$243$	3.26859	0.209680
$244$	−12.6169	−0.807716
$245$	−21.1505	−1.35126
$246$	14.0655	0.896786
$247$	3.19375	0.203213
$248$	9.37689	0.595433
$249$	−16.4864	−1.04479
$250$	16.8878	1.06808
$251$	5.69500	0.359465	0.179733	−	0.983716i	$-0.442477\pi$
$251$	5.69500	0.359465	0.179733	+	0.983716i	$0.442477\pi$
$252$	−1.11939	−0.0705149
$253$	−11.7709	−0.740032
$254$	−10.0912	−0.633175
$255$	−50.1802	−3.14241
$256$	1.00000	0.0625000
$257$	−17.3344	−1.08129	−0.540645	−	0.841251i	$-0.681820\pi$
$257$	−17.3344	−1.08129	−0.540645	+	0.841251i	$0.681820\pi$
$258$	22.2883	1.38761
$259$	4.68254	0.290959
$260$	−7.34226	−0.455348
$261$	2.09165	0.129470
$262$	20.2477	1.25091
$263$	0.573248	0.0353480	0.0176740	−	0.999844i	$-0.494374\pi$
$263$	0.573248	0.0353480	0.0176740	+	0.999844i	$0.494374\pi$
$264$	−7.71535	−0.474847
$265$	32.4329	1.99233
$266$	5.85995	0.359297
$267$	1.98665	0.121581
$268$	11.2323	0.686119
$269$	−11.7841	−0.718490	−0.359245	−	0.933243i	$-0.616966\pi$
$269$	−11.7841	−0.718490	−0.359245	+	0.933243i	$0.616966\pi$
$270$	18.5758	1.13049
$271$	1.72211	0.104611	0.0523054	−	0.998631i	$-0.483343\pi$
$271$	1.72211	0.104611	0.0523054	+	0.998631i	$0.483343\pi$
$272$	−7.25106	−0.439660
$273$	12.4701	0.754725
$274$	−5.37282	−0.324584
$275$	−40.0129	−2.41287
$276$	−5.05873	−0.304500
$277$	−0.604596	−0.0363266	−0.0181633	−	0.999835i	$-0.505782\pi$
$277$	−0.604596	−0.0363266	−0.0181633	+	0.999835i	$0.505782\pi$
$278$	−1.01967	−0.0611558
$279$	−2.96111	−0.177277
$280$	−13.4717	−0.805089
$281$	3.80725	0.227121	0.113561	−	0.993531i	$-0.463774\pi$
$281$	3.80725	0.227121	0.113561	+	0.993531i	$0.463774\pi$
$282$	5.06026	0.301334
$283$	−0.610355	−0.0362818	−0.0181409	−	0.999835i	$-0.505775\pi$
$283$	−0.610355	−0.0362818	−0.0181409	+	0.999835i	$0.505775\pi$
$284$	−2.85150	−0.169205
$285$	11.4404	0.677669
$286$	8.18567	0.484029
$287$	−27.3809	−1.61625
$288$	−0.315788	−0.0186080
$289$	35.5778	2.09281
$290$	25.1727	1.47819
$291$	6.07435	0.356084
$292$	5.54156	0.324295
$293$	−2.88815	−0.168728	−0.0843638	−	0.996435i	$-0.526886\pi$
$293$	−2.88815	−0.168728	−0.0843638	+	0.996435i	$0.526886\pi$
$294$	10.1339	0.591021
$295$	41.4741	2.41472
$296$	1.32098	0.0767804
$297$	−20.7096	−1.20170
$298$	5.09976	0.295421
$299$	5.36710	0.310388
$300$	−17.1962	−0.992821
$301$	−43.3879	−2.50084
$302$	10.3479	0.595457
$303$	−31.6140	−1.81618
$304$	1.65314	0.0948139
$305$	47.9503	2.74563
$306$	2.28980	0.130899
$307$	−21.8437	−1.24668	−0.623342	−	0.781949i	$-0.714226\pi$
$307$	−21.8437	−1.24668	−0.623342	+	0.781949i	$0.714226\pi$
$308$	15.0192	0.855800
$309$	−10.0117	−0.569546
$310$	−35.6366	−2.02402
$311$	19.5894	1.11081	0.555407	−	0.831579i	$-0.312563\pi$
$311$	19.5894	1.11081	0.555407	+	0.831579i	$0.312563\pi$
$312$	3.51791	0.199163
$313$	25.3964	1.43549	0.717745	−	0.696306i	$-0.245174\pi$
$313$	25.3964	1.43549	0.717745	+	0.696306i	$0.245174\pi$
$314$	−8.43226	−0.475860
$315$	4.25421	0.239698
$316$	11.7255	0.659613
$317$	−5.85823	−0.329031	−0.164516	−	0.986374i	$-0.552606\pi$
$317$	−5.85823	−0.329031	−0.164516	+	0.986374i	$0.552606\pi$
$318$	−15.5396	−0.871419
$319$	−28.0643	−1.57130
$320$	−3.80048	−0.212453
$321$	18.5055	1.03287
$322$	9.84767	0.548789
$323$	−11.9870	−0.666974
$324$	−9.84764	−0.547091
$325$	18.2444	1.01202
$326$	−22.8876	−1.26763
$327$	11.1938	0.619016
$328$	−7.72437	−0.426507
$329$	−9.85064	−0.543083
$330$	29.3220	1.61412
$331$	−32.5253	−1.78775	−0.893875	−	0.448316i	$-0.852024\pi$
$331$	−32.5253	−1.78775	−0.893875	+	0.448316i	$0.852024\pi$
$332$	9.05386	0.496895
$333$	−0.417150	−0.0228597
$334$	3.29537	0.180315
$335$	−42.6879	−2.33229
$336$	6.45474	0.352135
$337$	−34.0500	−1.85482	−0.927412	−	0.374042i	$-0.877972\pi$
$337$	−34.0500	−1.85482	−0.927412	+	0.374042i	$0.877972\pi$
$338$	9.26764	0.504093
$339$	15.3287	0.832542
$340$	27.5575	1.49451
$341$	39.7302	2.15151
$342$	−0.522042	−0.0282288
$343$	5.08590	0.274613
$344$	−12.2401	−0.659940
$345$	19.2256	1.03507
$346$	8.41833	0.452572
$347$	−6.91669	−0.371307	−0.185654	−	0.982615i	$-0.559440\pi$
$347$	−6.91669	−0.371307	−0.185654	+	0.982615i	$0.559440\pi$
$348$	−12.0611	−0.646541
$349$	−6.42314	−0.343823	−0.171911	−	0.985112i	$-0.554994\pi$
$349$	−6.42314	−0.343823	−0.171911	+	0.985112i	$0.554994\pi$
$350$	33.4752	1.78933
$351$	9.44282	0.504021
$352$	4.23704	0.225835
$353$	4.64082	0.247006	0.123503	−	0.992344i	$-0.460587\pi$
$353$	4.64082	0.247006	0.123503	+	0.992344i	$0.460587\pi$
$354$	−19.8716	−1.05616
$355$	10.8370	0.575170
$356$	−1.09101	−0.0578232
$357$	−46.8037	−2.47711
$358$	−18.2974	−0.967049
$359$	−13.8789	−0.732501	−0.366251	−	0.930516i	$-0.619359\pi$
$359$	−13.8789	−0.732501	−0.366251	+	0.930516i	$0.619359\pi$
$360$	1.20015	0.0632533
$361$	−16.2671	−0.856165
$362$	5.28677	0.277866
$363$	−12.6600	−0.664478
$364$	−6.84821	−0.358944
$365$	−21.0606	−1.10236
$366$	−22.9745	−1.20090
$367$	17.2289	0.899343	0.449672	−	0.893194i	$-0.351541\pi$
$367$	17.2289	0.899343	0.449672	+	0.893194i	$0.351541\pi$
$368$	2.77810	0.144819
$369$	2.43927	0.126983
$370$	−5.02035	−0.260996
$371$	30.2505	1.57053
$372$	17.0747	0.885280
$373$	5.54848	0.287289	0.143645	−	0.989629i	$-0.454118\pi$
$373$	5.54848	0.287289	0.143645	+	0.989629i	$0.454118\pi$
$374$	−30.7230	−1.58865
$375$	30.7516	1.58800
$376$	−2.77894	−0.143313
$377$	12.7963	0.659042
$378$	17.3259	0.891147
$379$	26.7795	1.37557	0.687785	−	0.725915i	$-0.258583\pi$
$379$	26.7795	1.37557	0.687785	+	0.725915i	$0.258583\pi$
$380$	−6.28271	−0.322296
$381$	−18.3753	−0.941394
$382$	14.4080	0.737176
$383$	19.7557	1.00947	0.504736	−	0.863274i	$-0.331590\pi$
$383$	19.7557	1.00947	0.504736	+	0.863274i	$0.331590\pi$
$384$	1.82093	0.0929240
$385$	−57.0802	−2.90908
$386$	−19.9624	−1.01606
$387$	3.86527	0.196483
$388$	−3.33585	−0.169352
$389$	5.74262	0.291162	0.145581	−	0.989346i	$-0.453495\pi$
$389$	5.74262	0.291162	0.145581	+	0.989346i	$0.453495\pi$
$390$	−13.3697	−0.677003
$391$	−20.1442	−1.01873
$392$	−5.56523	−0.281086
$393$	36.8697	1.85983
$394$	6.27526	0.316143
$395$	−44.5626	−2.24219
$396$	−1.33801	−0.0672374
$397$	−3.86966	−0.194213	−0.0971063	−	0.995274i	$-0.530959\pi$
$397$	−3.86966	−0.194213	−0.0971063	+	0.995274i	$0.530959\pi$
$398$	−8.50276	−0.426205
$399$	10.6706	0.534197
$400$	9.44361	0.472181
$401$	−13.3000	−0.664170	−0.332085	−	0.943250i	$-0.607752\pi$
$401$	−13.3000	−0.664170	−0.332085	+	0.943250i	$0.607752\pi$
$402$	20.4532	1.02011
$403$	−18.1155	−0.902398
$404$	17.3615	0.863765
$405$	37.4257	1.85970
$406$	23.4789	1.16524
$407$	5.59704	0.277435
$408$	−13.2037	−0.653679
$409$	13.1153	0.648509	0.324255	−	0.945970i	$-0.394887\pi$
$409$	13.1153	0.648509	0.324255	+	0.945970i	$0.394887\pi$
$410$	29.3563	1.44980
$411$	−9.78353	−0.482586
$412$	5.49812	0.270873
$413$	38.6834	1.90348
$414$	−0.877292	−0.0431166
$415$	−34.4090	−1.68907
$416$	−1.93193	−0.0947207
$417$	−1.85675	−0.0909254
$418$	7.00441	0.342597
$419$	35.9124	1.75443	0.877217	−	0.480094i	$-0.159398\pi$
$419$	35.9124	1.75443	0.877217	+	0.480094i	$0.159398\pi$
$420$	−24.5311	−1.19699
$421$	−4.37921	−0.213429	−0.106715	−	0.994290i	$-0.534033\pi$
$421$	−4.37921	−0.213429	−0.106715	+	0.994290i	$0.534033\pi$
$422$	−3.50204	−0.170477
$423$	0.877557	0.0426683
$424$	8.53389	0.414443
$425$	−68.4762	−3.32158
$426$	−5.19238	−0.251571
$427$	44.7238	2.16434
$428$	−10.1626	−0.491230
$429$	14.9055	0.719646
$430$	46.5181	2.24330
$431$	−6.34634	−0.305693	−0.152846	−	0.988250i	$-0.548844\pi$
$431$	−6.34634	−0.305693	−0.152846	+	0.988250i	$0.548844\pi$
$432$	4.88776	0.235163
$433$	−12.1995	−0.586272	−0.293136	−	0.956071i	$-0.594699\pi$
$433$	−12.1995	−0.586272	−0.293136	+	0.956071i	$0.594699\pi$
$434$	−33.2387	−1.59551
$435$	45.8378	2.19775
$436$	−6.14727	−0.294401
$437$	4.59258	0.219693
$438$	10.0908	0.482157
$439$	−32.3638	−1.54464	−0.772320	−	0.635233i	$-0.780904\pi$
$439$	−32.3638	−1.54464	−0.772320	+	0.635233i	$0.780904\pi$
$440$	−16.1028	−0.767669
$441$	1.75743	0.0836874
$442$	14.0085	0.666319
$443$	11.8677	0.563852	0.281926	−	0.959436i	$-0.409027\pi$
$443$	11.8677	0.563852	0.281926	+	0.959436i	$0.409027\pi$
$444$	2.40541	0.114156
$445$	4.14634	0.196555
$446$	−8.62891	−0.408591
$447$	9.28632	0.439228
$448$	−3.54475	−0.167474
$449$	−1.98188	−0.0935308	−0.0467654	−	0.998906i	$-0.514891\pi$
$449$	−1.98188	−0.0935308	−0.0467654	+	0.998906i	$0.514891\pi$
$450$	−2.98218	−0.140581
$451$	−32.7285	−1.54112
$452$	−8.41808	−0.395953
$453$	18.8429	0.885316
$454$	18.6343	0.874551
$455$	26.0264	1.22014
$456$	3.01025	0.140968
$457$	24.4134	1.14201	0.571006	−	0.820946i	$-0.306553\pi$
$457$	24.4134	1.14201	0.571006	+	0.820946i	$0.306553\pi$
$458$	−4.45951	−0.208379
$459$	−35.4414	−1.65427
$460$	−10.5581	−0.492274
$461$	−39.3419	−1.83234	−0.916168	−	0.400793i	$-0.868735\pi$
$461$	−39.3419	−1.83234	−0.916168	+	0.400793i	$0.868735\pi$
$462$	27.3490	1.27239
$463$	10.7789	0.500938	0.250469	−	0.968125i	$-0.419415\pi$
$463$	10.7789	0.500938	0.250469	+	0.968125i	$0.419415\pi$
$464$	6.62357	0.307492
$465$	−64.8918	−3.00929
$466$	−27.1983	−1.25994
$467$	−4.75747	−0.220150	−0.110075	−	0.993923i	$-0.535109\pi$
$467$	−4.75747	−0.220150	−0.110075	+	0.993923i	$0.535109\pi$
$468$	0.610082	0.0282010
$469$	−39.8155	−1.83851
$470$	10.5613	0.487156
$471$	−15.3546	−0.707501
$472$	10.9129	0.502306
$473$	−51.8616	−2.38460
$474$	21.3514	0.980702
$475$	15.6116	0.716309
$476$	25.7032	1.17810
$477$	−2.69491	−0.123391
$478$	−28.7485	−1.31493
$479$	−20.4210	−0.933061	−0.466530	−	0.884505i	$-0.654496\pi$
$479$	−20.4210	−0.933061	−0.466530	+	0.884505i	$0.654496\pi$
$480$	−6.92040	−0.315872
$481$	−2.55204	−0.116363
$482$	12.7200	0.579379
$483$	17.9319	0.815930
$484$	6.95249	0.316022
$485$	12.6778	0.575669
$486$	−3.26859	−0.148266
$487$	35.8756	1.62568	0.812840	−	0.582487i	$-0.197920\pi$
$487$	35.8756	1.62568	0.812840	+	0.582487i	$0.197920\pi$
$488$	12.6169	0.571141
$489$	−41.6768	−1.88469
$490$	21.1505	0.955483
$491$	9.30422	0.419893	0.209947	−	0.977713i	$-0.432671\pi$
$491$	9.30422	0.419893	0.209947	+	0.977713i	$0.432671\pi$
$492$	−14.0655	−0.634124
$493$	−48.0279	−2.16307
$494$	−3.19375	−0.143694
$495$	5.08507	0.228557
$496$	−9.37689	−0.421035
$497$	10.1078	0.453398
$498$	16.4864	0.738775
$499$	−21.5100	−0.962919	−0.481459	−	0.876468i	$-0.659893\pi$
$499$	−21.5100	−0.962919	−0.481459	+	0.876468i	$0.659893\pi$
$500$	−16.8878	−0.755247
$501$	6.00065	0.268089
$502$	−5.69500	−0.254180
$503$	−35.4074	−1.57874	−0.789370	−	0.613918i	$-0.789593\pi$
$503$	−35.4074	−1.57874	−0.789370	+	0.613918i	$0.789593\pi$
$504$	1.11939	0.0498616
$505$	−65.9818	−2.93615
$506$	11.7709	0.523281
$507$	16.8757	0.749477
$508$	10.0912	0.447722
$509$	3.08047	0.136539	0.0682697	−	0.997667i	$-0.478252\pi$
$509$	3.08047	0.136539	0.0682697	+	0.997667i	$0.478252\pi$
$510$	50.1802	2.22202
$511$	−19.6434	−0.868974
$512$	−1.00000	−0.0441942
$513$	8.08014	0.356747
$514$	17.3344	0.764588
$515$	−20.8955	−0.920765
$516$	−22.2883	−0.981189
$517$	−11.7745	−0.517841
$518$	−4.68254	−0.205739
$519$	15.3292	0.672877
$520$	7.34226	0.321979
$521$	18.2326	0.798786	0.399393	−	0.916780i	$-0.369221\pi$
$521$	18.2326	0.798786	0.399393	+	0.916780i	$0.369221\pi$
$522$	−2.09165	−0.0915489
$523$	−2.60504	−0.113911	−0.0569553	−	0.998377i	$-0.518139\pi$
$523$	−2.60504	−0.113911	−0.0569553	+	0.998377i	$0.518139\pi$
$524$	−20.2477	−0.884525
$525$	60.9560	2.66034
$526$	−0.573248	−0.0249948
$527$	67.9924	2.96179
$528$	7.71535	0.335768
$529$	−15.2822	−0.664441
$530$	−32.4329	−1.40879
$531$	−3.44616	−0.149551
$532$	−5.85995	−0.254061
$533$	14.9230	0.646385
$534$	−1.98665	−0.0859706
$535$	38.6229	1.66981
$536$	−11.2323	−0.485160
$537$	−33.3184	−1.43779
$538$	11.7841	0.508050
$539$	−23.5801	−1.01567
$540$	−18.5758	−0.799376
$541$	−30.9651	−1.33129	−0.665647	−	0.746267i	$-0.731844\pi$
$541$	−30.9651	−1.33129	−0.665647	+	0.746267i	$0.731844\pi$
$542$	−1.72211	−0.0739710
$543$	9.62683	0.413127
$544$	7.25106	0.310887
$545$	23.3626	1.00074
$546$	−12.4701	−0.533672
$547$	−15.4319	−0.659821	−0.329910	−	0.944012i	$-0.607019\pi$
$547$	−15.4319	−0.659821	−0.329910	+	0.944012i	$0.607019\pi$
$548$	5.37282	0.229515
$549$	−3.98428	−0.170045
$550$	40.0129	1.70616
$551$	10.9497	0.466472
$552$	5.05873	0.215314
$553$	−41.5641	−1.76748
$554$	0.604596	0.0256868
$555$	−9.14171	−0.388044
$556$	1.01967	0.0432437
$557$	−20.9715	−0.888592	−0.444296	−	0.895880i	$-0.646546\pi$
$557$	−20.9715	−0.888592	−0.444296	+	0.895880i	$0.646546\pi$
$558$	2.96111	0.125354
$559$	23.6470	1.00016
$560$	13.4717	0.569284
$561$	−55.9445	−2.36198
$562$	−3.80725	−0.160599
$563$	1.78839	0.0753716	0.0376858	−	0.999290i	$-0.488001\pi$
$563$	1.78839	0.0753716	0.0376858	+	0.999290i	$0.488001\pi$
$564$	−5.06026	−0.213075
$565$	31.9927	1.34594
$566$	0.610355	0.0256551
$567$	34.9074	1.46597
$568$	2.85150	0.119646
$569$	16.6280	0.697081	0.348540	−	0.937294i	$-0.386677\pi$
$569$	16.6280	0.697081	0.348540	+	0.937294i	$0.386677\pi$
$570$	−11.4404	−0.479185
$571$	17.3291	0.725201	0.362601	−	0.931945i	$-0.381889\pi$
$571$	17.3291	0.725201	0.362601	+	0.931945i	$0.381889\pi$
$572$	−8.18567	−0.342260
$573$	26.2359	1.09602
$574$	27.3809	1.14286
$575$	26.2353	1.09409
$576$	0.315788	0.0131579
$577$	−12.6121	−0.525049	−0.262524	−	0.964925i	$-0.584555\pi$
$577$	−12.6121	−0.525049	−0.262524	+	0.964925i	$0.584555\pi$
$578$	−35.5778	−1.47984
$579$	−36.3501	−1.51066
$580$	−25.1727	−1.04524
$581$	−32.0936	−1.33147
$582$	−6.07435	−0.251790
$583$	36.1584	1.49753
$584$	−5.54156	−0.229311
$585$	−2.31860	−0.0958623
$586$	2.88815	0.119308
$587$	29.9048	1.23430	0.617151	−	0.786845i	$-0.288287\pi$
$587$	29.9048	1.23430	0.617151	+	0.786845i	$0.288287\pi$
$588$	−10.1339	−0.417915
$589$	−15.5013	−0.638719
$590$	−41.4741	−1.70746
$591$	11.4268	0.470036
$592$	−1.32098	−0.0542920
$593$	−28.4837	−1.16968	−0.584842	−	0.811147i	$-0.698844\pi$
$593$	−28.4837	−1.16968	−0.584842	+	0.811147i	$0.698844\pi$
$594$	20.7096	0.849727
$595$	−97.6842	−4.00466
$596$	−5.09976	−0.208895
$597$	−15.4829	−0.633675
$598$	−5.36710	−0.219477
$599$	13.6918	0.559430	0.279715	−	0.960083i	$-0.409760\pi$
$599$	13.6918	0.559430	0.279715	+	0.960083i	$0.409760\pi$
$600$	17.1962	0.702030
$601$	33.9178	1.38353	0.691767	−	0.722121i	$-0.256833\pi$
$601$	33.9178	1.38353	0.691767	+	0.722121i	$0.256833\pi$
$602$	43.3879	1.76836
$603$	3.54702	0.144446
$604$	−10.3479	−0.421052
$605$	−26.4228	−1.07424
$606$	31.6140	1.28423
$607$	23.3715	0.948620	0.474310	−	0.880358i	$-0.342698\pi$
$607$	23.3715	0.948620	0.474310	+	0.880358i	$0.342698\pi$
$608$	−1.65314	−0.0670436
$609$	42.7534	1.73246
$610$	−47.9503	−1.94145
$611$	5.36872	0.217195
$612$	−2.28980	−0.0925597
$613$	−7.62645	−0.308029	−0.154015	−	0.988069i	$-0.549220\pi$
$613$	−7.62645	−0.308029	−0.154015	+	0.988069i	$0.549220\pi$
$614$	21.8437	0.881539
$615$	53.4558	2.15554
$616$	−15.0192	−0.605142
$617$	27.2887	1.09860	0.549301	−	0.835625i	$-0.314894\pi$
$617$	27.2887	1.09860	0.549301	+	0.835625i	$0.314894\pi$
$618$	10.0117	0.402730
$619$	34.6326	1.39200	0.696001	−	0.718041i	$-0.254961\pi$
$619$	34.6326	1.39200	0.696001	+	0.718041i	$0.254961\pi$
$620$	35.6366	1.43120
$621$	13.5787	0.544895
$622$	−19.5894	−0.785464
$623$	3.86734	0.154942
$624$	−3.51791	−0.140829
$625$	16.9637	0.678550
$626$	−25.3964	−1.01504
$627$	12.7545	0.509367
$628$	8.43226	0.336484
$629$	9.57850	0.381920
$630$	−4.25421	−0.169492
$631$	−26.4862	−1.05440	−0.527199	−	0.849742i	$-0.676758\pi$
$631$	−26.4862	−1.05440	−0.527199	+	0.849742i	$0.676758\pi$
$632$	−11.7255	−0.466417
$633$	−6.37697	−0.253462
$634$	5.85823	0.232660
$635$	−38.3512	−1.52192
$636$	15.5396	0.616186
$637$	10.7516	0.425995
$638$	28.0643	1.11108
$639$	−0.900469	−0.0356220
$640$	3.80048	0.150227
$641$	21.7321	0.858365	0.429183	−	0.903218i	$-0.358802\pi$
$641$	21.7321	0.858365	0.429183	+	0.903218i	$0.358802\pi$
$642$	−18.5055	−0.730353
$643$	37.2441	1.46876	0.734382	−	0.678737i	$-0.237472\pi$
$643$	37.2441	1.46876	0.734382	+	0.678737i	$0.237472\pi$
$644$	−9.84767	−0.388052
$645$	84.7062	3.33530
$646$	11.9870	0.471622
$647$	34.3429	1.35016	0.675079	−	0.737745i	$-0.264109\pi$
$647$	34.3429	1.35016	0.675079	+	0.737745i	$0.264109\pi$
$648$	9.84764	0.386852
$649$	46.2383	1.81501
$650$	−18.2444	−0.715605
$651$	−60.5254	−2.37218
$652$	22.8876	0.896349
$653$	28.8878	1.13047	0.565234	−	0.824931i	$-0.308786\pi$
$653$	28.8878	1.13047	0.565234	+	0.824931i	$0.308786\pi$
$654$	−11.1938	−0.437711
$655$	76.9509	3.00672
$656$	7.72437	0.301586
$657$	1.74996	0.0682725
$658$	9.85064	0.384018
$659$	−39.0221	−1.52008	−0.760042	−	0.649874i	$-0.774822\pi$
$659$	−39.0221	−1.52008	−0.760042	+	0.649874i	$0.774822\pi$
$660$	−29.3220	−1.14136
$661$	−2.31263	−0.0899511	−0.0449755	−	0.998988i	$-0.514321\pi$
$661$	−2.31263	−0.0899511	−0.0449755	+	0.998988i	$0.514321\pi$
$662$	32.5253	1.26413
$663$	25.5086	0.990672
$664$	−9.05386	−0.351358
$665$	22.2706	0.863617
$666$	0.417150	0.0161642
$667$	18.4010	0.712488
$668$	−3.29537	−0.127502
$669$	−15.7126	−0.607486
$670$	42.6879	1.64918
$671$	53.4584	2.06374
$672$	−6.45474	−0.248997
$673$	−38.9917	−1.50302	−0.751509	−	0.659723i	$-0.770674\pi$
$673$	−38.9917	−1.50302	−0.751509	+	0.659723i	$0.770674\pi$
$674$	34.0500	1.31156
$675$	46.1581	1.77663
$676$	−9.26764	−0.356448
$677$	5.38730	0.207051	0.103525	−	0.994627i	$-0.466988\pi$
$677$	5.38730	0.207051	0.103525	+	0.994627i	$0.466988\pi$
$678$	−15.3287	−0.588696
$679$	11.8247	0.453792
$680$	−27.5575	−1.05678
$681$	33.9318	1.30027
$682$	−39.7302	−1.52135
$683$	29.7789	1.13946	0.569729	−	0.821833i	$-0.307048\pi$
$683$	29.7789	1.13946	0.569729	+	0.821833i	$0.307048\pi$
$684$	0.522042	0.0199608
$685$	−20.4193	−0.780180
$686$	−5.08590	−0.194181
$687$	−8.12045	−0.309815
$688$	12.2401	0.466648
$689$	−16.4869	−0.628101
$690$	−19.2256	−0.731905
$691$	−2.89807	−0.110248	−0.0551238	−	0.998480i	$-0.517555\pi$
$691$	−2.89807	−0.110248	−0.0551238	+	0.998480i	$0.517555\pi$
$692$	−8.41833	−0.320017
$693$	4.74290	0.180168
$694$	6.91669	0.262554
$695$	−3.87523	−0.146996
$696$	12.0611	0.457174
$697$	−56.0099	−2.12152
$698$	6.42314	0.243119
$699$	−49.5262	−1.87325
$700$	−33.4752	−1.26524
$701$	40.7677	1.53977	0.769887	−	0.638181i	$-0.220313\pi$
$701$	40.7677	1.53977	0.769887	+	0.638181i	$0.220313\pi$
$702$	−9.44282	−0.356396
$703$	−2.18376	−0.0823621
$704$	−4.23704	−0.159689
$705$	19.2314	0.724296
$706$	−4.64082	−0.174660
$707$	−61.5420	−2.31453
$708$	19.8716	0.746820
$709$	−12.9280	−0.485522	−0.242761	−	0.970086i	$-0.578053\pi$
$709$	−12.9280	−0.485522	−0.242761	+	0.970086i	$0.578053\pi$
$710$	−10.8370	−0.406707
$711$	3.70279	0.138866
$712$	1.09101	0.0408872
$713$	−26.0499	−0.975578
$714$	46.8037	1.75158
$715$	31.1094	1.16343
$716$	18.2974	0.683807
$717$	−52.3491	−1.95501
$718$	13.8789	0.517957
$719$	18.6463	0.695391	0.347696	−	0.937607i	$-0.386964\pi$
$719$	18.6463	0.695391	0.347696	+	0.937607i	$0.386964\pi$
$720$	−1.20015	−0.0447268
$721$	−19.4894	−0.725825
$722$	16.2671	0.605400
$723$	23.1622	0.861412
$724$	−5.28677	−0.196481
$725$	62.5504	2.32307
$726$	12.6600	0.469857
$727$	19.3731	0.718509	0.359254	−	0.933240i	$-0.383031\pi$
$727$	19.3731	0.718509	0.359254	+	0.933240i	$0.383031\pi$
$728$	6.84821	0.253811
$729$	23.5911	0.873743
$730$	21.0606	0.779486
$731$	−88.7534	−3.28266
$732$	22.9745	0.849164
$733$	−31.7529	−1.17282	−0.586410	−	0.810014i	$-0.699459\pi$
$733$	−31.7529	−1.17282	−0.586410	+	0.810014i	$0.699459\pi$
$734$	−17.2289	−0.635932
$735$	38.5136	1.42060
$736$	−2.77810	−0.102402
$737$	−47.5915	−1.75306
$738$	−2.43927	−0.0897907
$739$	−8.70497	−0.320218	−0.160109	−	0.987099i	$-0.551185\pi$
$739$	−8.70497	−0.320218	−0.160109	+	0.987099i	$0.551185\pi$
$740$	5.02035	0.184552
$741$	−5.81559	−0.213641
$742$	−30.2505	−1.11053
$743$	16.4876	0.604872	0.302436	−	0.953170i	$-0.402200\pi$
$743$	16.4876	0.604872	0.302436	+	0.953170i	$0.402200\pi$
$744$	−17.0747	−0.625988
$745$	19.3815	0.710084
$746$	−5.54848	−0.203144
$747$	2.85910	0.104609
$748$	30.7230	1.12334
$749$	36.0240	1.31629
$750$	−30.7516	−1.12289
$751$	−12.5440	−0.457735	−0.228868	−	0.973458i	$-0.573502\pi$
$751$	−12.5440	−0.457735	−0.228868	+	0.973458i	$0.573502\pi$
$752$	2.77894	0.101338
$753$	−10.3702	−0.377911
$754$	−12.7963	−0.466013
$755$	39.3271	1.43126
$756$	−17.3259	−0.630136
$757$	16.3930	0.595815	0.297908	−	0.954595i	$-0.403711\pi$
$757$	16.3930	0.595815	0.297908	+	0.954595i	$0.403711\pi$
$758$	−26.7795	−0.972674
$759$	21.4340	0.778006
$760$	6.28271	0.227898
$761$	17.2389	0.624911	0.312455	−	0.949932i	$-0.398849\pi$
$761$	17.2389	0.624911	0.312455	+	0.949932i	$0.398849\pi$
$762$	18.3753	0.665666
$763$	21.7905	0.788870
$764$	−14.4080	−0.521262
$765$	8.70233	0.314633
$766$	−19.7557	−0.713804
$767$	−21.0829	−0.761260
$768$	−1.82093	−0.0657072
$769$	−1.92188	−0.0693049	−0.0346524	−	0.999399i	$-0.511032\pi$
$769$	−1.92188	−0.0693049	−0.0346524	+	0.999399i	$0.511032\pi$
$770$	57.0802	2.05703
$771$	31.5648	1.13678
$772$	19.9624	0.718461
$773$	0.651155	0.0234204	0.0117102	−	0.999931i	$-0.496272\pi$
$773$	0.651155	0.0234204	0.0117102	+	0.999931i	$0.496272\pi$
$774$	−3.86527	−0.138934
$775$	−88.5517	−3.18087
$776$	3.33585	0.119750
$777$	−8.52658	−0.305889
$778$	−5.74262	−0.205883
$779$	12.7694	0.457513
$780$	13.3697	0.478714
$781$	12.0819	0.432324
$782$	20.1442	0.720354
$783$	32.3745	1.15697
$784$	5.56523	0.198758
$785$	−32.0466	−1.14379
$786$	−36.8697	−1.31510
$787$	20.8161	0.742015	0.371007	−	0.928630i	$-0.379012\pi$
$787$	20.8161	0.742015	0.371007	+	0.928630i	$0.379012\pi$
$788$	−6.27526	−0.223547
$789$	−1.04384	−0.0371618
$790$	44.5626	1.58547
$791$	29.8399	1.06099
$792$	1.33801	0.0475440
$793$	−24.3750	−0.865583
$794$	3.86966	0.137329
$795$	−59.0580	−2.09457
$796$	8.50276	0.301372
$797$	−12.8114	−0.453801	−0.226901	−	0.973918i	$-0.572859\pi$
$797$	−12.8114	−0.453801	−0.226901	+	0.973918i	$0.572859\pi$
$798$	−10.6706	−0.377734
$799$	−20.1503	−0.712865
$800$	−9.44361	−0.333882
$801$	−0.344527	−0.0121733
$802$	13.3000	0.469639
$803$	−23.4798	−0.828584
$804$	−20.4532	−0.721328
$805$	37.4258	1.31909
$806$	18.1155	0.638092
$807$	21.4581	0.755360
$808$	−17.3615	−0.610774
$809$	12.4630	0.438174	0.219087	−	0.975705i	$-0.429692\pi$
$809$	12.4630	0.438174	0.219087	+	0.975705i	$0.429692\pi$
$810$	−37.4257	−1.31501
$811$	−32.9912	−1.15848	−0.579238	−	0.815158i	$-0.696650\pi$
$811$	−32.9912	−1.15848	−0.579238	+	0.815158i	$0.696650\pi$
$812$	−23.4789	−0.823947
$813$	−3.13584	−0.109979
$814$	−5.59704	−0.196176
$815$	−86.9839	−3.04691
$816$	13.2037	0.462221
$817$	20.2345	0.707916
$818$	−13.1153	−0.458565
$819$	−2.16259	−0.0755668
$820$	−29.3563	−1.02517
$821$	21.2066	0.740116	0.370058	−	0.929009i	$-0.379338\pi$
$821$	21.2066	0.740116	0.370058	+	0.929009i	$0.379338\pi$
$822$	9.78353	0.341240
$823$	−3.53700	−0.123292	−0.0616461	−	0.998098i	$-0.519635\pi$
$823$	−3.53700	−0.123292	−0.0616461	+	0.998098i	$0.519635\pi$
$824$	−5.49812	−0.191536
$825$	72.8608	2.53669
$826$	−38.6834	−1.34597
$827$	−47.9059	−1.66585	−0.832925	−	0.553386i	$-0.813335\pi$
$827$	−47.9059	−1.66585	−0.832925	+	0.553386i	$0.813335\pi$
$828$	0.877292	0.0304880
$829$	32.5398	1.13015	0.565077	−	0.825038i	$-0.308846\pi$
$829$	32.5398	1.13015	0.565077	+	0.825038i	$0.308846\pi$
$830$	34.4090	1.19435
$831$	1.10093	0.0381907
$832$	1.93193	0.0669777
$833$	−40.3538	−1.39818
$834$	1.85675	0.0642940
$835$	12.5240	0.433410
$836$	−7.00441	−0.242252
$837$	−45.8320	−1.58419
$838$	−35.9124	−1.24057
$839$	−32.9144	−1.13633	−0.568165	−	0.822914i	$-0.692347\pi$
$839$	−32.9144	−1.13633	−0.568165	+	0.822914i	$0.692347\pi$
$840$	24.5311	0.846402
$841$	14.8717	0.512818
$842$	4.37921	0.150917
$843$	−6.93274	−0.238776
$844$	3.50204	0.120545
$845$	35.2214	1.21165
$846$	−0.877557	−0.0301710
$847$	−24.6448	−0.846806
$848$	−8.53389	−0.293055
$849$	1.11141	0.0381436
$850$	68.4762	2.34871
$851$	−3.66982	−0.125800
$852$	5.19238	0.177888
$853$	3.99008	0.136618	0.0683088	−	0.997664i	$-0.478240\pi$
$853$	3.99008	0.136618	0.0683088	+	0.997664i	$0.478240\pi$
$854$	−44.7238	−1.53042
$855$	−1.98401	−0.0678516
$856$	10.1626	0.347352
$857$	24.7741	0.846269	0.423134	−	0.906067i	$-0.360930\pi$
$857$	24.7741	0.846269	0.423134	+	0.906067i	$0.360930\pi$
$858$	−14.9055	−0.508867
$859$	45.9502	1.56780	0.783900	−	0.620887i	$-0.213227\pi$
$859$	45.9502	1.56780	0.783900	+	0.620887i	$0.213227\pi$
$860$	−46.5181	−1.58625
$861$	49.8588	1.69918
$862$	6.34634	0.216157
$863$	17.8391	0.607251	0.303626	−	0.952791i	$-0.401803\pi$
$863$	17.8391	0.607251	0.303626	+	0.952791i	$0.401803\pi$
$864$	−4.88776	−0.166285
$865$	31.9937	1.08782
$866$	12.1995	0.414557
$867$	−64.7848	−2.20021
$868$	33.2387	1.12819
$869$	−49.6816	−1.68533
$870$	−45.8378	−1.55405
$871$	21.7000	0.735275
$872$	6.14727	0.208173
$873$	−1.05342	−0.0356529
$874$	−4.59258	−0.155346
$875$	59.8631	2.02374
$876$	−10.0908	−0.340936
$877$	15.4239	0.520829	0.260414	−	0.965497i	$-0.416141\pi$
$877$	15.4239	0.520829	0.260414	+	0.965497i	$0.416141\pi$
$878$	32.3638	1.09223
$879$	5.25912	0.177386
$880$	16.1028	0.542824
$881$	−10.0524	−0.338673	−0.169336	−	0.985558i	$-0.554162\pi$
$881$	−10.0524	−0.338673	−0.169336	+	0.985558i	$0.554162\pi$
$882$	−1.75743	−0.0591759
$883$	38.3801	1.29159	0.645797	−	0.763510i	$-0.276525\pi$
$883$	38.3801	1.29159	0.645797	+	0.763510i	$0.276525\pi$
$884$	−14.0085	−0.471158
$885$	−75.5215	−2.53863
$886$	−11.8677	−0.398704
$887$	4.83508	0.162346	0.0811730	−	0.996700i	$-0.474133\pi$
$887$	4.83508	0.162346	0.0811730	+	0.996700i	$0.474133\pi$
$888$	−2.40541	−0.0807204
$889$	−35.7706	−1.19971
$890$	−4.14634	−0.138986
$891$	41.7248	1.39783
$892$	8.62891	0.288917
$893$	4.59397	0.153731
$894$	−9.28632	−0.310581
$895$	−69.5389	−2.32443
$896$	3.54475	0.118422
$897$	−9.77312	−0.326315
$898$	1.98188	0.0661363
$899$	−62.1085	−2.07143
$900$	2.98218	0.0994061
$901$	61.8798	2.06151
$902$	32.7285	1.08974
$903$	79.0064	2.62917
$904$	8.41808	0.279981
$905$	20.0922	0.667888
$906$	−18.8429	−0.626013
$907$	−33.0893	−1.09871	−0.549356	−	0.835588i	$-0.685127\pi$
$907$	−33.0893	−1.09871	−0.549356	+	0.835588i	$0.685127\pi$
$908$	−18.6343	−0.618401
$909$	5.48255	0.181845
$910$	−26.0264	−0.862768
$911$	−27.4193	−0.908441	−0.454220	−	0.890889i	$-0.650082\pi$
$911$	−27.4193	−0.908441	−0.454220	+	0.890889i	$0.650082\pi$
$912$	−3.01025	−0.0996793
$913$	−38.3615	−1.26958
$914$	−24.4134	−0.807524
$915$	−87.3142	−2.88652
$916$	4.45951	0.147346
$917$	71.7730	2.37015
$918$	35.4414	1.16974
$919$	47.5869	1.56975	0.784874	−	0.619655i	$-0.212728\pi$
$919$	47.5869	1.56975	0.784874	+	0.619655i	$0.212728\pi$
$920$	10.5581	0.348090
$921$	39.7758	1.31066
$922$	39.3419	1.29566
$923$	−5.50889	−0.181327
$924$	−27.3490	−0.899715
$925$	−12.4748	−0.410170
$926$	−10.7789	−0.354216
$927$	1.73624	0.0570257
$928$	−6.62357	−0.217429
$929$	0.714612	0.0234457	0.0117228	−	0.999931i	$-0.496268\pi$
$929$	0.714612	0.0234457	0.0117228	+	0.999931i	$0.496268\pi$
$930$	64.8918	2.12789
$931$	9.20009	0.301521
$932$	27.1983	0.890910
$933$	−35.6710	−1.16781
$934$	4.75747	0.155669
$935$	−116.762	−3.81853
$936$	−0.610082	−0.0199411
$937$	33.9434	1.10888	0.554442	−	0.832223i	$-0.312932\pi$
$937$	33.9434	1.10888	0.554442	+	0.832223i	$0.312932\pi$
$938$	39.8155	1.30002
$939$	−46.2451	−1.50915
$940$	−10.5613	−0.344471
$941$	−35.6616	−1.16254	−0.581268	−	0.813713i	$-0.697443\pi$
$941$	−35.6616	−1.16254	−0.581268	+	0.813713i	$0.697443\pi$
$942$	15.3546	0.500279
$943$	21.4591	0.698804
$944$	−10.9129	−0.355184
$945$	65.8466	2.14199
$946$	51.8616	1.68617
$947$	2.03154	0.0660163	0.0330082	−	0.999455i	$-0.489491\pi$
$947$	2.03154	0.0660163	0.0330082	+	0.999455i	$0.489491\pi$
$948$	−21.3514	−0.693461
$949$	10.7059	0.347529
$950$	−15.6116	−0.506507
$951$	10.6674	0.345915
$952$	−25.7032	−0.833044
$953$	29.6684	0.961052	0.480526	−	0.876980i	$-0.340446\pi$
$953$	29.6684	0.961052	0.480526	+	0.876980i	$0.340446\pi$
$954$	2.69491	0.0872508
$955$	54.7571	1.77190
$956$	28.7485	0.929794
$957$	51.1032	1.65193
$958$	20.4210	0.659774
$959$	−19.0453	−0.615004
$960$	6.92040	0.223355
$961$	56.9260	1.83632
$962$	2.55204	0.0822812
$963$	−3.20925	−0.103417
$964$	−12.7200	−0.409683
$965$	−75.8664	−2.44223
$966$	−17.9319	−0.576950
$967$	−13.9503	−0.448611	−0.224306	−	0.974519i	$-0.572011\pi$
$967$	−13.9503	−0.448611	−0.224306	+	0.974519i	$0.572011\pi$
$968$	−6.95249	−0.223462
$969$	21.8275	0.701200
$970$	−12.6778	−0.407060
$971$	−19.6661	−0.631115	−0.315558	−	0.948906i	$-0.602192\pi$
$971$	−19.6661	−0.631115	−0.315558	+	0.948906i	$0.602192\pi$
$972$	3.26859	0.104840
$973$	−3.61447	−0.115875
$974$	−35.8756	−1.14953
$975$	−33.2218	−1.06395
$976$	−12.6169	−0.403858
$977$	−2.46901	−0.0789905	−0.0394953	−	0.999220i	$-0.512575\pi$
$977$	−2.46901	−0.0789905	−0.0394953	+	0.999220i	$0.512575\pi$
$978$	41.6768	1.33268
$979$	4.62263	0.147740
$980$	−21.1505	−0.675628
$981$	−1.94124	−0.0619790
$982$	−9.30422	−0.296909
$983$	−15.8743	−0.506311	−0.253155	−	0.967426i	$-0.581468\pi$
$983$	−15.8743	−0.506311	−0.253155	+	0.967426i	$0.581468\pi$
$984$	14.0655	0.448393
$985$	23.8490	0.759891
$986$	48.0279	1.52952
$987$	17.9373	0.570951
$988$	3.19375	0.101607
$989$	34.0042	1.08127
$990$	−5.08507	−0.161614
$991$	56.4317	1.79261	0.896305	−	0.443437i	$-0.146241\pi$
$991$	56.4317	1.79261	0.896305	+	0.443437i	$0.146241\pi$
$992$	9.37689	0.297717
$993$	59.2263	1.87949
$994$	−10.1078	−0.320601
$995$	−32.3145	−1.02444
$996$	−16.4864	−0.522393
$997$	−35.6360	−1.12860	−0.564302	−	0.825568i	$-0.690855\pi$
$997$	−35.6360	−1.12860	−0.564302	+	0.825568i	$0.690855\pi$
$998$	21.5100	0.680886
$999$	−6.45664	−0.204279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.11	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.11	✓	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.82093 q^{3} +1.00000 q^{4} -3.80048 q^{5} +1.82093 q^{6} -3.54475 q^{7} -1.00000 q^{8} +0.315788 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.82093 q^{3} +1.00000 q^{4} -3.80048 q^{5} +1.82093 q^{6} -3.54475 q^{7} -1.00000 q^{8} +0.315788 q^{9} +3.80048 q^{10} -4.23704 q^{11} -1.82093 q^{12} +1.93193 q^{13} +3.54475 q^{14} +6.92040 q^{15} +1.00000 q^{16} -7.25106 q^{17} -0.315788 q^{18} +1.65314 q^{19} -3.80048 q^{20} +6.45474 q^{21} +4.23704 q^{22} +2.77810 q^{23} +1.82093 q^{24} +9.44361 q^{25} -1.93193 q^{26} +4.88776 q^{27} -3.54475 q^{28} +6.62357 q^{29} -6.92040 q^{30} -9.37689 q^{31} -1.00000 q^{32} +7.71535 q^{33} +7.25106 q^{34} +13.4717 q^{35} +0.315788 q^{36} -1.32098 q^{37} -1.65314 q^{38} -3.51791 q^{39} +3.80048 q^{40} +7.72437 q^{41} -6.45474 q^{42} +12.2401 q^{43} -4.23704 q^{44} -1.20015 q^{45} -2.77810 q^{46} +2.77894 q^{47} -1.82093 q^{48} +5.56523 q^{49} -9.44361 q^{50} +13.2037 q^{51} +1.93193 q^{52} -8.53389 q^{53} -4.88776 q^{54} +16.1028 q^{55} +3.54475 q^{56} -3.01025 q^{57} -6.62357 q^{58} -10.9129 q^{59} +6.92040 q^{60} -12.6169 q^{61} +9.37689 q^{62} -1.11939 q^{63} +1.00000 q^{64} -7.34226 q^{65} -7.71535 q^{66} +11.2323 q^{67} -7.25106 q^{68} -5.05873 q^{69} -13.4717 q^{70} -2.85150 q^{71} -0.315788 q^{72} +5.54156 q^{73} +1.32098 q^{74} -17.1962 q^{75} +1.65314 q^{76} +15.0192 q^{77} +3.51791 q^{78} +11.7255 q^{79} -3.80048 q^{80} -9.84764 q^{81} -7.72437 q^{82} +9.05386 q^{83} +6.45474 q^{84} +27.5575 q^{85} -12.2401 q^{86} -12.0611 q^{87} +4.23704 q^{88} -1.09101 q^{89} +1.20015 q^{90} -6.84821 q^{91} +2.77810 q^{92} +17.0747 q^{93} -2.77894 q^{94} -6.28271 q^{95} +1.82093 q^{96} -3.33585 q^{97} -5.56523 q^{98} -1.33801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

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