LMFDB - Embedded newform 4010.2.a.l.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 24 x^{15} + 70 x^{14} + 228 x^{13} - 638 x^{12} - 1075 x^{11} + 2854 x^{10} + \cdots - 2 $ x^17 - 3x^16 - 24x^15 + 70x^14 + 228x^13 - 638x^12 - 1075x^11 + 2854x^10 + 2544x^9 - 6415x^8 - 2573x^7 + 6456x^6 + 485x^5 - 1839x^4 + 67x^3 + 136x^2 - 8x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.204745$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.204745 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.204745 q^{6} +0.0646599 q^{7} -1.00000 q^{8} -2.95808 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.204745 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.204745 q^{6} +0.0646599 q^{7} -1.00000 q^{8} -2.95808 q^{9} +1.00000 q^{10} +0.632100 q^{11} +0.204745 q^{12} -4.49351 q^{13} -0.0646599 q^{14} -0.204745 q^{15} +1.00000 q^{16} -7.35571 q^{17} +2.95808 q^{18} -2.97201 q^{19} -1.00000 q^{20} +0.0132388 q^{21} -0.632100 q^{22} -1.30206 q^{23} -0.204745 q^{24} +1.00000 q^{25} +4.49351 q^{26} -1.21989 q^{27} +0.0646599 q^{28} -4.04406 q^{29} +0.204745 q^{30} -9.86401 q^{31} -1.00000 q^{32} +0.129420 q^{33} +7.35571 q^{34} -0.0646599 q^{35} -2.95808 q^{36} +10.8747 q^{37} +2.97201 q^{38} -0.920025 q^{39} +1.00000 q^{40} +10.9747 q^{41} -0.0132388 q^{42} +7.78238 q^{43} +0.632100 q^{44} +2.95808 q^{45} +1.30206 q^{46} +8.52481 q^{47} +0.204745 q^{48} -6.99582 q^{49} -1.00000 q^{50} -1.50605 q^{51} -4.49351 q^{52} +5.61709 q^{53} +1.21989 q^{54} -0.632100 q^{55} -0.0646599 q^{56} -0.608506 q^{57} +4.04406 q^{58} -5.26478 q^{59} -0.204745 q^{60} +2.26246 q^{61} +9.86401 q^{62} -0.191269 q^{63} +1.00000 q^{64} +4.49351 q^{65} -0.129420 q^{66} +7.55071 q^{67} -7.35571 q^{68} -0.266591 q^{69} +0.0646599 q^{70} +6.36850 q^{71} +2.95808 q^{72} -5.56094 q^{73} -10.8747 q^{74} +0.204745 q^{75} -2.97201 q^{76} +0.0408715 q^{77} +0.920025 q^{78} +4.15862 q^{79} -1.00000 q^{80} +8.62447 q^{81} -10.9747 q^{82} -11.5665 q^{83} +0.0132388 q^{84} +7.35571 q^{85} -7.78238 q^{86} -0.828002 q^{87} -0.632100 q^{88} -0.448821 q^{89} -2.95808 q^{90} -0.290550 q^{91} -1.30206 q^{92} -2.01961 q^{93} -8.52481 q^{94} +2.97201 q^{95} -0.204745 q^{96} +16.4953 q^{97} +6.99582 q^{98} -1.86980 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * 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
$3$	0.204745	0.118210	0.0591049	−	0.998252i	$-0.481175\pi$
$3$	0.204745	0.118210	0.0591049	+	0.998252i	$0.481175\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.204745	−0.0835870
$7$	0.0646599	0.0244391	0.0122196	−	0.999925i	$-0.496110\pi$
$7$	0.0646599	0.0244391	0.0122196	+	0.999925i	$0.496110\pi$
$8$	−1.00000	−0.353553
$9$	−2.95808	−0.986026
$10$	1.00000	0.316228
$11$	0.632100	0.190585	0.0952927	−	0.995449i	$-0.469621\pi$
$11$	0.632100	0.190585	0.0952927	+	0.995449i	$0.469621\pi$
$12$	0.204745	0.0591049
$13$	−4.49351	−1.24627	−0.623137	−	0.782112i	$-0.714142\pi$
$13$	−4.49351	−1.24627	−0.623137	+	0.782112i	$0.714142\pi$
$14$	−0.0646599	−0.0172811
$15$	−0.204745	−0.0528650
$16$	1.00000	0.250000
$17$	−7.35571	−1.78402	−0.892011	−	0.452014i	$-0.850706\pi$
$17$	−7.35571	−1.78402	−0.892011	+	0.452014i	$0.850706\pi$
$18$	2.95808	0.697226
$19$	−2.97201	−0.681826	−0.340913	−	0.940095i	$-0.610736\pi$
$19$	−2.97201	−0.681826	−0.340913	+	0.940095i	$0.610736\pi$
$20$	−1.00000	−0.223607
$21$	0.0132388	0.00288895
$22$	−0.632100	−0.134764
$23$	−1.30206	−0.271498	−0.135749	−	0.990743i	$-0.543344\pi$
$23$	−1.30206	−0.271498	−0.135749	+	0.990743i	$0.543344\pi$
$24$	−0.204745	−0.0417935
$25$	1.00000	0.200000
$26$	4.49351	0.881249
$27$	−1.21989	−0.234768
$28$	0.0646599	0.0122196
$29$	−4.04406	−0.750963	−0.375481	−	0.926830i	$-0.622523\pi$
$29$	−4.04406	−0.750963	−0.375481	+	0.926830i	$0.622523\pi$
$30$	0.204745	0.0373812
$31$	−9.86401	−1.77163	−0.885814	−	0.464040i	$-0.846399\pi$
$31$	−9.86401	−1.77163	−0.885814	+	0.464040i	$0.846399\pi$
$32$	−1.00000	−0.176777
$33$	0.129420	0.0225291
$34$	7.35571	1.26149
$35$	−0.0646599	−0.0109295
$36$	−2.95808	−0.493013
$37$	10.8747	1.78780	0.893898	−	0.448270i	$-0.147960\pi$
$37$	10.8747	1.78780	0.893898	+	0.448270i	$0.147960\pi$
$38$	2.97201	0.482124
$39$	−0.920025	−0.147322
$40$	1.00000	0.158114
$41$	10.9747	1.71396	0.856982	−	0.515346i	$-0.172337\pi$
$41$	10.9747	1.71396	0.856982	+	0.515346i	$0.172337\pi$
$42$	−0.0132388	−0.00204279
$43$	7.78238	1.18680	0.593401	−	0.804907i	$-0.297785\pi$
$43$	7.78238	1.18680	0.593401	+	0.804907i	$0.297785\pi$
$44$	0.632100	0.0952927
$45$	2.95808	0.440964
$46$	1.30206	0.191978
$47$	8.52481	1.24347	0.621735	−	0.783227i	$-0.286428\pi$
$47$	8.52481	1.24347	0.621735	+	0.783227i	$0.286428\pi$
$48$	0.204745	0.0295525
$49$	−6.99582	−0.999403
$50$	−1.00000	−0.141421
$51$	−1.50605	−0.210889
$52$	−4.49351	−0.623137
$53$	5.61709	0.771566	0.385783	−	0.922590i	$-0.373931\pi$
$53$	5.61709	0.771566	0.385783	+	0.922590i	$0.373931\pi$
$54$	1.21989	0.166006
$55$	−0.632100	−0.0852323
$56$	−0.0646599	−0.00864054
$57$	−0.608506	−0.0805985
$58$	4.04406	0.531011
$59$	−5.26478	−0.685416	−0.342708	−	0.939442i	$-0.611344\pi$
$59$	−5.26478	−0.685416	−0.342708	+	0.939442i	$0.611344\pi$
$60$	−0.204745	−0.0264325
$61$	2.26246	0.289678	0.144839	−	0.989455i	$-0.453734\pi$
$61$	2.26246	0.289678	0.144839	+	0.989455i	$0.453734\pi$
$62$	9.86401	1.25273
$63$	−0.191269	−0.0240976
$64$	1.00000	0.125000
$65$	4.49351	0.557351
$66$	−0.129420	−0.0159304
$67$	7.55071	0.922466	0.461233	−	0.887279i	$-0.347407\pi$
$67$	7.55071	0.922466	0.461233	+	0.887279i	$0.347407\pi$
$68$	−7.35571	−0.892011
$69$	−0.266591	−0.0320937
$70$	0.0646599	0.00772834
$71$	6.36850	0.755802	0.377901	−	0.925846i	$-0.376646\pi$
$71$	6.36850	0.755802	0.377901	+	0.925846i	$0.376646\pi$
$72$	2.95808	0.348613
$73$	−5.56094	−0.650859	−0.325429	−	0.945566i	$-0.605509\pi$
$73$	−5.56094	−0.650859	−0.325429	+	0.945566i	$0.605509\pi$
$74$	−10.8747	−1.26416
$75$	0.204745	0.0236420
$76$	−2.97201	−0.340913
$77$	0.0408715	0.00465774
$78$	0.920025	0.104172
$79$	4.15862	0.467882	0.233941	−	0.972251i	$-0.424838\pi$
$79$	4.15862	0.467882	0.233941	+	0.972251i	$0.424838\pi$
$80$	−1.00000	−0.111803
$81$	8.62447	0.958275
$82$	−10.9747	−1.21196
$83$	−11.5665	−1.26958	−0.634792	−	0.772683i	$-0.718914\pi$
$83$	−11.5665	−1.26958	−0.634792	+	0.772683i	$0.718914\pi$
$84$	0.0132388	0.00144447
$85$	7.35571	0.797839
$86$	−7.78238	−0.839195
$87$	−0.828002	−0.0887712
$88$	−0.632100	−0.0673821
$89$	−0.448821	−0.0475750	−0.0237875	−	0.999717i	$-0.507573\pi$
$89$	−0.448821	−0.0475750	−0.0237875	+	0.999717i	$0.507573\pi$
$90$	−2.95808	−0.311809
$91$	−0.290550	−0.0304579
$92$	−1.30206	−0.135749
$93$	−2.01961	−0.209424
$94$	−8.52481	−0.879267
$95$	2.97201	0.304922
$96$	−0.204745	−0.0208967
$97$	16.4953	1.67484	0.837422	−	0.546557i	$-0.184062\pi$
$97$	16.4953	1.67484	0.837422	+	0.546557i	$0.184062\pi$
$98$	6.99582	0.706684
$99$	−1.86980	−0.187922
$100$	1.00000	0.100000
$101$	−11.0378	−1.09831	−0.549153	−	0.835722i	$-0.685050\pi$
$101$	−11.0378	−1.09831	−0.549153	+	0.835722i	$0.685050\pi$
$102$	1.50605	0.149121
$103$	13.4435	1.32463	0.662315	−	0.749225i	$-0.269574\pi$
$103$	13.4435	1.32463	0.662315	+	0.749225i	$0.269574\pi$
$104$	4.49351	0.440625
$105$	−0.0132388	−0.00129198
$106$	−5.61709	−0.545580
$107$	−13.3196	−1.28766	−0.643829	−	0.765169i	$-0.722655\pi$
$107$	−13.3196	−1.28766	−0.643829	+	0.765169i	$0.722655\pi$
$108$	−1.21989	−0.117384
$109$	11.3872	1.09070	0.545348	−	0.838210i	$-0.316397\pi$
$109$	11.3872	1.09070	0.545348	+	0.838210i	$0.316397\pi$
$110$	0.632100	0.0602684
$111$	2.22655	0.211335
$112$	0.0646599	0.00610979
$113$	11.9672	1.12578	0.562892	−	0.826531i	$-0.309689\pi$
$113$	11.9672	1.12578	0.562892	+	0.826531i	$0.309689\pi$
$114$	0.608506	0.0569918
$115$	1.30206	0.121418
$116$	−4.04406	−0.375481
$117$	13.2922	1.22886
$118$	5.26478	0.484662
$119$	−0.475619	−0.0436000
$120$	0.204745	0.0186906
$121$	−10.6004	−0.963677
$122$	−2.26246	−0.204833
$123$	2.24703	0.202607
$124$	−9.86401	−0.885814
$125$	−1.00000	−0.0894427
$126$	0.191269	0.0170396
$127$	0.758199	0.0672793	0.0336396	−	0.999434i	$-0.489290\pi$
$127$	0.758199	0.0672793	0.0336396	+	0.999434i	$0.489290\pi$
$128$	−1.00000	−0.0883883
$129$	1.59341	0.140292
$130$	−4.49351	−0.394107
$131$	16.1678	1.41259	0.706294	−	0.707918i	$-0.250366\pi$
$131$	16.1678	1.41259	0.706294	+	0.707918i	$0.250366\pi$
$132$	0.129420	0.0112645
$133$	−0.192170	−0.0166632
$134$	−7.55071	−0.652282
$135$	1.21989	0.104991
$136$	7.35571	0.630747
$137$	−0.135492	−0.0115759	−0.00578794	−	0.999983i	$-0.501842\pi$
$137$	−0.135492	−0.0115759	−0.00578794	+	0.999983i	$0.501842\pi$
$138$	0.266591	0.0226937
$139$	−3.41346	−0.289526	−0.144763	−	0.989466i	$-0.546242\pi$
$139$	−3.41346	−0.289526	−0.144763	+	0.989466i	$0.546242\pi$
$140$	−0.0646599	−0.00546476
$141$	1.74541	0.146990
$142$	−6.36850	−0.534432
$143$	−2.84035	−0.237522
$144$	−2.95808	−0.246507
$145$	4.04406	0.335841
$146$	5.56094	0.460227
$147$	−1.43236	−0.118139
$148$	10.8747	0.893898
$149$	−11.3722	−0.931645	−0.465822	−	0.884878i	$-0.654241\pi$
$149$	−11.3722	−0.931645	−0.465822	+	0.884878i	$0.654241\pi$
$150$	−0.204745	−0.0167174
$151$	−17.5117	−1.42508	−0.712542	−	0.701630i	$-0.752456\pi$
$151$	−17.5117	−1.42508	−0.712542	+	0.701630i	$0.752456\pi$
$152$	2.97201	0.241062
$153$	21.7588	1.75909
$154$	−0.0408715	−0.00329352
$155$	9.86401	0.792296
$156$	−0.920025	−0.0736610
$157$	16.3816	1.30739	0.653696	−	0.756757i	$-0.273218\pi$
$157$	16.3816	1.30739	0.653696	+	0.756757i	$0.273218\pi$
$158$	−4.15862	−0.330842
$159$	1.15007	0.0912067
$160$	1.00000	0.0790569
$161$	−0.0841910	−0.00663518
$162$	−8.62447	−0.677602
$163$	−1.80573	−0.141436	−0.0707178	−	0.997496i	$-0.522529\pi$
$163$	−1.80573	−0.141436	−0.0707178	+	0.997496i	$0.522529\pi$
$164$	10.9747	0.856982
$165$	−0.129420	−0.0100753
$166$	11.5665	0.897731
$167$	−20.4668	−1.58377	−0.791885	−	0.610670i	$-0.790900\pi$
$167$	−20.4668	−1.58377	−0.791885	+	0.610670i	$0.790900\pi$
$168$	−0.0132388	−0.00102140
$169$	7.19162	0.553201
$170$	−7.35571	−0.564157
$171$	8.79144	0.672299
$172$	7.78238	0.593401
$173$	−5.23599	−0.398085	−0.199043	−	0.979991i	$-0.563783\pi$
$173$	−5.23599	−0.398085	−0.199043	+	0.979991i	$0.563783\pi$
$174$	0.828002	0.0627707
$175$	0.0646599	0.00488783
$176$	0.632100	0.0476463
$177$	−1.07794	−0.0810229
$178$	0.448821	0.0336406
$179$	−8.69479	−0.649879	−0.324940	−	0.945735i	$-0.605344\pi$
$179$	−8.69479	−0.649879	−0.324940	+	0.945735i	$0.605344\pi$
$180$	2.95808	0.220482
$181$	2.06506	0.153495	0.0767474	−	0.997051i	$-0.475547\pi$
$181$	2.06506	0.153495	0.0767474	+	0.997051i	$0.475547\pi$
$182$	0.290550	0.0215370
$183$	0.463228	0.0342428
$184$	1.30206	0.0959890
$185$	−10.8747	−0.799527
$186$	2.01961	0.148085
$187$	−4.64954	−0.340008
$188$	8.52481	0.621735
$189$	−0.0788779	−0.00573753
$190$	−2.97201	−0.215612
$191$	0.980386	0.0709383	0.0354691	−	0.999371i	$-0.488707\pi$
$191$	0.980386	0.0709383	0.0354691	+	0.999371i	$0.488707\pi$
$192$	0.204745	0.0147762
$193$	17.5700	1.26472	0.632359	−	0.774675i	$-0.282087\pi$
$193$	17.5700	1.26472	0.632359	+	0.774675i	$0.282087\pi$
$194$	−16.4953	−1.18429
$195$	0.920025	0.0658844
$196$	−6.99582	−0.499701
$197$	5.43670	0.387349	0.193674	−	0.981066i	$-0.437959\pi$
$197$	5.43670	0.387349	0.193674	+	0.981066i	$0.437959\pi$
$198$	1.86980	0.132881
$199$	19.9180	1.41195	0.705974	−	0.708238i	$-0.250510\pi$
$199$	19.9180	1.41195	0.705974	+	0.708238i	$0.250510\pi$
$200$	−1.00000	−0.0707107
$201$	1.54597	0.109045
$202$	11.0378	0.776620
$203$	−0.261488	−0.0183529
$204$	−1.50605	−0.105444
$205$	−10.9747	−0.766508
$206$	−13.4435	−0.936655
$207$	3.85159	0.267704
$208$	−4.49351	−0.311569
$209$	−1.87861	−0.129946
$210$	0.0132388	0.000913565 0
$211$	10.1422	0.698215	0.349108	−	0.937083i	$-0.386485\pi$
$211$	10.1422	0.698215	0.349108	+	0.937083i	$0.386485\pi$
$212$	5.61709	0.385783
$213$	1.30392	0.0893432
$214$	13.3196	0.910512
$215$	−7.78238	−0.530754
$216$	1.21989	0.0830030
$217$	−0.637806	−0.0432971
$218$	−11.3872	−0.771239
$219$	−1.13858	−0.0769379
$220$	−0.632100	−0.0426162
$221$	33.0529	2.22338
$222$	−2.22655	−0.149436
$223$	−28.8127	−1.92944	−0.964719	−	0.263282i	$-0.915195\pi$
$223$	−28.8127	−1.92944	−0.964719	+	0.263282i	$0.915195\pi$
$224$	−0.0646599	−0.00432027
$225$	−2.95808	−0.197205
$226$	−11.9672	−0.796049
$227$	−29.9115	−1.98530	−0.992648	−	0.121040i	$-0.961377\pi$
$227$	−29.9115	−1.98530	−0.992648	+	0.121040i	$0.961377\pi$
$228$	−0.608506	−0.0402993
$229$	−17.6646	−1.16731	−0.583655	−	0.812002i	$-0.698378\pi$
$229$	−17.6646	−1.16731	−0.583655	+	0.812002i	$0.698378\pi$
$230$	−1.30206	−0.0858552
$231$	0.00836826	0.000550591 0
$232$	4.04406	0.265505
$233$	−12.4802	−0.817606	−0.408803	−	0.912623i	$-0.634054\pi$
$233$	−12.4802	−0.817606	−0.408803	+	0.912623i	$0.634054\pi$
$234$	−13.2922	−0.868935
$235$	−8.52481	−0.556097
$236$	−5.26478	−0.342708
$237$	0.851459	0.0553082
$238$	0.475619	0.0308298
$239$	23.8114	1.54023	0.770114	−	0.637906i	$-0.220199\pi$
$239$	23.8114	1.54023	0.770114	+	0.637906i	$0.220199\pi$
$240$	−0.204745	−0.0132163
$241$	4.68705	0.301920	0.150960	−	0.988540i	$-0.451764\pi$
$241$	4.68705	0.301920	0.150960	+	0.988540i	$0.451764\pi$
$242$	10.6004	0.681423
$243$	5.42549	0.348045
$244$	2.26246	0.144839
$245$	6.99582	0.446946
$246$	−2.24703	−0.143265
$247$	13.3548	0.849743
$248$	9.86401	0.626365
$249$	−2.36818	−0.150077
$250$	1.00000	0.0632456
$251$	−11.7024	−0.738650	−0.369325	−	0.929300i	$-0.620411\pi$
$251$	−11.7024	−0.738650	−0.369325	+	0.929300i	$0.620411\pi$
$252$	−0.191269	−0.0120488
$253$	−0.823031	−0.0517435
$254$	−0.758199	−0.0475736
$255$	1.50605	0.0943124
$256$	1.00000	0.0625000
$257$	13.1834	0.822355	0.411177	−	0.911555i	$-0.365118\pi$
$257$	13.1834	0.822355	0.411177	+	0.911555i	$0.365118\pi$
$258$	−1.59341	−0.0992011
$259$	0.703160	0.0436922
$260$	4.49351	0.278676
$261$	11.9626	0.740469
$262$	−16.1678	−0.998851
$263$	−4.94599	−0.304983	−0.152491	−	0.988305i	$-0.548730\pi$
$263$	−4.94599	−0.304983	−0.152491	+	0.988305i	$0.548730\pi$
$264$	−0.129420	−0.00796522
$265$	−5.61709	−0.345055
$266$	0.192170	0.0117827
$267$	−0.0918941	−0.00562383
$268$	7.55071	0.461233
$269$	−10.4531	−0.637338	−0.318669	−	0.947866i	$-0.603236\pi$
$269$	−10.4531	−0.637338	−0.318669	+	0.947866i	$0.603236\pi$
$270$	−1.21989	−0.0742401
$271$	23.7764	1.44431	0.722157	−	0.691729i	$-0.243151\pi$
$271$	23.7764	1.44431	0.722157	+	0.691729i	$0.243151\pi$
$272$	−7.35571	−0.446005
$273$	−0.0594887	−0.00360042
$274$	0.135492	0.00818538
$275$	0.632100	0.0381171
$276$	−0.266591	−0.0160469
$277$	32.7280	1.96643	0.983216	−	0.182445i	$-0.0584013\pi$
$277$	32.7280	1.96643	0.983216	+	0.182445i	$0.0584013\pi$
$278$	3.41346	0.204726
$279$	29.1785	1.74687
$280$	0.0646599	0.00386417
$281$	−1.91809	−0.114424	−0.0572118	−	0.998362i	$-0.518221\pi$
$281$	−1.91809	−0.114424	−0.0572118	+	0.998362i	$0.518221\pi$
$282$	−1.74541	−0.103938
$283$	8.70439	0.517422	0.258711	−	0.965955i	$-0.416702\pi$
$283$	8.70439	0.517422	0.258711	+	0.965955i	$0.416702\pi$
$284$	6.36850	0.377901
$285$	0.608506	0.0360448
$286$	2.84035	0.167953
$287$	0.709625	0.0418878
$288$	2.95808	0.174306
$289$	37.1065	2.18273
$290$	−4.04406	−0.237475
$291$	3.37734	0.197983
$292$	−5.56094	−0.325429
$293$	−16.5205	−0.965137	−0.482568	−	0.875858i	$-0.660296\pi$
$293$	−16.5205	−0.965137	−0.482568	+	0.875858i	$0.660296\pi$
$294$	1.43236	0.0835370
$295$	5.26478	0.306527
$296$	−10.8747	−0.632081
$297$	−0.771092	−0.0447433
$298$	11.3722	0.658772
$299$	5.85081	0.338361
$300$	0.204745	0.0118210
$301$	0.503208	0.0290044
$302$	17.5117	1.00769
$303$	−2.25995	−0.129831
$304$	−2.97201	−0.170457
$305$	−2.26246	−0.129548
$306$	−21.7588	−1.24387
$307$	−0.463529	−0.0264550	−0.0132275	−	0.999913i	$-0.504211\pi$
$307$	−0.463529	−0.0264550	−0.0132275	+	0.999913i	$0.504211\pi$
$308$	0.0408715	0.00232887
$309$	2.75250	0.156584
$310$	−9.86401	−0.560238
$311$	1.72367	0.0977404	0.0488702	−	0.998805i	$-0.484438\pi$
$311$	1.72367	0.0977404	0.0488702	+	0.998805i	$0.484438\pi$
$312$	0.920025	0.0520862
$313$	6.41499	0.362597	0.181298	−	0.983428i	$-0.441970\pi$
$313$	6.41499	0.362597	0.181298	+	0.983428i	$0.441970\pi$
$314$	−16.3816	−0.924465
$315$	0.191269	0.0107768
$316$	4.15862	0.233941
$317$	19.6490	1.10360	0.551800	−	0.833977i	$-0.313941\pi$
$317$	19.6490	1.10360	0.551800	+	0.833977i	$0.313941\pi$
$318$	−1.15007	−0.0644929
$319$	−2.55625	−0.143122
$320$	−1.00000	−0.0559017
$321$	−2.72714	−0.152214
$322$	0.0841910	0.00469178
$323$	21.8612	1.21639
$324$	8.62447	0.479137
$325$	−4.49351	−0.249255
$326$	1.80573	0.100010
$327$	2.33148	0.128931
$328$	−10.9747	−0.605978
$329$	0.551213	0.0303894
$330$	0.129420	0.00712431
$331$	−18.8944	−1.03853	−0.519266	−	0.854613i	$-0.673795\pi$
$331$	−18.8944	−1.03853	−0.519266	+	0.854613i	$0.673795\pi$
$332$	−11.5665	−0.634792
$333$	−32.1683	−1.76281
$334$	20.4668	1.11989
$335$	−7.55071	−0.412539
$336$	0.0132388	0.000722237 0
$337$	25.0978	1.36716	0.683582	−	0.729874i	$-0.260421\pi$
$337$	25.0978	1.36716	0.683582	+	0.729874i	$0.260421\pi$
$338$	−7.19162	−0.391172
$339$	2.45024	0.133079
$340$	7.35571	0.398919
$341$	−6.23504	−0.337646
$342$	−8.79144	−0.475387
$343$	−0.904968	−0.0488637
$344$	−7.78238	−0.419598
$345$	0.266591	0.0143528
$346$	5.23599	0.281489
$347$	35.5592	1.90892	0.954460	−	0.298338i	$-0.0964324\pi$
$347$	35.5592	1.90892	0.954460	+	0.298338i	$0.0964324\pi$
$348$	−0.828002	−0.0443856
$349$	−12.0764	−0.646437	−0.323219	−	0.946324i	$-0.604765\pi$
$349$	−12.0764	−0.646437	−0.323219	+	0.946324i	$0.604765\pi$
$350$	−0.0646599	−0.00345622
$351$	5.48158	0.292585
$352$	−0.632100	−0.0336910
$353$	1.32911	0.0707413	0.0353707	−	0.999374i	$-0.488739\pi$
$353$	1.32911	0.0707413	0.0353707	+	0.999374i	$0.488739\pi$
$354$	1.07794	0.0572918
$355$	−6.36850	−0.338005
$356$	−0.448821	−0.0237875
$357$	−0.0973809	−0.00515394
$358$	8.69479	0.459534
$359$	−14.5672	−0.768826	−0.384413	−	0.923161i	$-0.625596\pi$
$359$	−14.5672	−0.768826	−0.384413	+	0.923161i	$0.625596\pi$
$360$	−2.95808	−0.155904
$361$	−10.1672	−0.535113
$362$	−2.06506	−0.108537
$363$	−2.17039	−0.113916
$364$	−0.290550	−0.0152289
$365$	5.56094	0.291073
$366$	−0.463228	−0.0242133
$367$	−17.8324	−0.930844	−0.465422	−	0.885089i	$-0.654097\pi$
$367$	−17.8324	−0.930844	−0.465422	+	0.885089i	$0.654097\pi$
$368$	−1.30206	−0.0678745
$369$	−32.4641	−1.69001
$370$	10.8747	0.565351
$371$	0.363200	0.0188564
$372$	−2.01961	−0.104712
$373$	−14.8329	−0.768021	−0.384010	−	0.923329i	$-0.625457\pi$
$373$	−14.8329	−0.768021	−0.384010	+	0.923329i	$0.625457\pi$
$374$	4.64954	0.240422
$375$	−0.204745	−0.0105730
$376$	−8.52481	−0.439633
$377$	18.1720	0.935906
$378$	0.0788779	0.00405704
$379$	−22.9266	−1.17766	−0.588830	−	0.808257i	$-0.700411\pi$
$379$	−22.9266	−1.17766	−0.588830	+	0.808257i	$0.700411\pi$
$380$	2.97201	0.152461
$381$	0.155238	0.00795307
$382$	−0.980386	−0.0501609
$383$	16.1189	0.823638	0.411819	−	0.911266i	$-0.364894\pi$
$383$	16.1189	0.823638	0.411819	+	0.911266i	$0.364894\pi$
$384$	−0.204745	−0.0104484
$385$	−0.0408715	−0.00208301
$386$	−17.5700	−0.894291
$387$	−23.0209	−1.17022
$388$	16.4953	0.837422
$389$	−17.3654	−0.880461	−0.440231	−	0.897885i	$-0.645103\pi$
$389$	−17.3654	−0.880461	−0.440231	+	0.897885i	$0.645103\pi$
$390$	−0.920025	−0.0465873
$391$	9.57756	0.484358
$392$	6.99582	0.353342
$393$	3.31029	0.166982
$394$	−5.43670	−0.273897
$395$	−4.15862	−0.209243
$396$	−1.86980	−0.0939611
$397$	−7.16328	−0.359515	−0.179757	−	0.983711i	$-0.557531\pi$
$397$	−7.16328	−0.359515	−0.179757	+	0.983711i	$0.557531\pi$
$398$	−19.9180	−0.998398
$399$	−0.0393459	−0.00196976
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−1.54597	−0.0771061
$403$	44.3240	2.20794
$404$	−11.0378	−0.549153
$405$	−8.62447	−0.428553
$406$	0.261488	0.0129775
$407$	6.87392	0.340728
$408$	1.50605	0.0745605
$409$	−21.4034	−1.05833	−0.529164	−	0.848519i	$-0.677495\pi$
$409$	−21.4034	−1.05833	−0.529164	+	0.848519i	$0.677495\pi$
$410$	10.9747	0.542003
$411$	−0.0277414	−0.00136838
$412$	13.4435	0.662315
$413$	−0.340420	−0.0167510
$414$	−3.85159	−0.189295
$415$	11.5665	0.567775
$416$	4.49351	0.220312
$417$	−0.698890	−0.0342248
$418$	1.87861	0.0918857
$419$	7.77728	0.379945	0.189973	−	0.981789i	$-0.439160\pi$
$419$	7.77728	0.379945	0.189973	+	0.981789i	$0.439160\pi$
$420$	−0.0132388	−0.000645988 0
$421$	−28.3533	−1.38186	−0.690928	−	0.722923i	$-0.742798\pi$
$421$	−28.3533	−1.38186	−0.690928	+	0.722923i	$0.742798\pi$
$422$	−10.1422	−0.493713
$423$	−25.2171	−1.22610
$424$	−5.61709	−0.272790
$425$	−7.35571	−0.356804
$426$	−1.30392	−0.0631752
$427$	0.146290	0.00707948
$428$	−13.3196	−0.643829
$429$	−0.581548	−0.0280774
$430$	7.78238	0.375299
$431$	14.5433	0.700526	0.350263	−	0.936651i	$-0.386092\pi$
$431$	14.5433	0.700526	0.350263	+	0.936651i	$0.386092\pi$
$432$	−1.21989	−0.0586920
$433$	17.1600	0.824656	0.412328	−	0.911035i	$-0.364716\pi$
$433$	17.1600	0.824656	0.412328	+	0.911035i	$0.364716\pi$
$434$	0.637806	0.0306157
$435$	0.828002	0.0396997
$436$	11.3872	0.545348
$437$	3.86973	0.185114
$438$	1.13858	0.0544033
$439$	−2.53392	−0.120937	−0.0604687	−	0.998170i	$-0.519260\pi$
$439$	−2.53392	−0.120937	−0.0604687	+	0.998170i	$0.519260\pi$
$440$	0.632100	0.0301342
$441$	20.6942	0.985438
$442$	−33.0529	−1.57217
$443$	31.0000	1.47286	0.736428	−	0.676516i	$-0.236511\pi$
$443$	31.0000	1.47286	0.736428	+	0.676516i	$0.236511\pi$
$444$	2.22655	0.105668
$445$	0.448821	0.0212762
$446$	28.8127	1.36432
$447$	−2.32840	−0.110130
$448$	0.0646599	0.00305489
$449$	−13.8683	−0.654483	−0.327242	−	0.944941i	$-0.606119\pi$
$449$	−13.8683	−0.654483	−0.327242	+	0.944941i	$0.606119\pi$
$450$	2.95808	0.139445
$451$	6.93712	0.326656
$452$	11.9672	0.562892
$453$	−3.58544	−0.168459
$454$	29.9115	1.40382
$455$	0.290550	0.0136212
$456$	0.608506	0.0284959
$457$	40.0388	1.87294	0.936469	−	0.350750i	$-0.114073\pi$
$457$	40.0388	1.87294	0.936469	+	0.350750i	$0.114073\pi$
$458$	17.6646	0.825412
$459$	8.97315	0.418831
$460$	1.30206	0.0607088
$461$	−3.97107	−0.184951	−0.0924756	−	0.995715i	$-0.529478\pi$
$461$	−3.97107	−0.184951	−0.0924756	+	0.995715i	$0.529478\pi$
$462$	−0.00836826	−0.000389327 0
$463$	13.8381	0.643110	0.321555	−	0.946891i	$-0.395794\pi$
$463$	13.8381	0.643110	0.321555	+	0.946891i	$0.395794\pi$
$464$	−4.04406	−0.187741
$465$	2.01961	0.0936572
$466$	12.4802	0.578135
$467$	33.1500	1.53400	0.767000	−	0.641647i	$-0.221749\pi$
$467$	33.1500	1.53400	0.767000	+	0.641647i	$0.221749\pi$
$468$	13.2922	0.614430
$469$	0.488228	0.0225443
$470$	8.52481	0.393220
$471$	3.35405	0.154547
$472$	5.26478	0.242331
$473$	4.91924	0.226187
$474$	−0.851459	−0.0391088
$475$	−2.97201	−0.136365
$476$	−0.475619	−0.0218000
$477$	−16.6158	−0.760785
$478$	−23.8114	−1.08911
$479$	−22.0062	−1.00549	−0.502745	−	0.864435i	$-0.667677\pi$
$479$	−22.0062	−1.00549	−0.502745	+	0.864435i	$0.667677\pi$
$480$	0.204745	0.00934531
$481$	−48.8657	−2.22809
$482$	−4.68705	−0.213489
$483$	−0.0172377	−0.000784343 0
$484$	−10.6004	−0.481839
$485$	−16.4953	−0.749013
$486$	−5.42549	−0.246105
$487$	37.8587	1.71554	0.857770	−	0.514034i	$-0.171849\pi$
$487$	37.8587	1.71554	0.857770	+	0.514034i	$0.171849\pi$
$488$	−2.26246	−0.102417
$489$	−0.369715	−0.0167191
$490$	−6.99582	−0.316039
$491$	28.3715	1.28039	0.640194	−	0.768213i	$-0.278854\pi$
$491$	28.3715	1.28039	0.640194	+	0.768213i	$0.278854\pi$
$492$	2.24703	0.101304
$493$	29.7469	1.33973
$494$	−13.3548	−0.600859
$495$	1.86980	0.0840413
$496$	−9.86401	−0.442907
$497$	0.411786	0.0184711
$498$	2.36818	0.106121
$499$	18.2919	0.818859	0.409429	−	0.912342i	$-0.365728\pi$
$499$	18.2919	0.818859	0.409429	+	0.912342i	$0.365728\pi$
$500$	−1.00000	−0.0447214
$501$	−4.19049	−0.187217
$502$	11.7024	0.522304
$503$	−25.9229	−1.15584	−0.577921	−	0.816092i	$-0.696136\pi$
$503$	−25.9229	−1.15584	−0.577921	+	0.816092i	$0.696136\pi$
$504$	0.191269	0.00851980
$505$	11.0378	0.491178
$506$	0.823031	0.0365882
$507$	1.47245	0.0653938
$508$	0.758199	0.0336396
$509$	10.9390	0.484864	0.242432	−	0.970168i	$-0.422055\pi$
$509$	10.9390	0.484864	0.242432	+	0.970168i	$0.422055\pi$
$510$	−1.50605	−0.0666889
$511$	−0.359570	−0.0159064
$512$	−1.00000	−0.0441942
$513$	3.62552	0.160071
$514$	−13.1834	−0.581493
$515$	−13.4435	−0.592393
$516$	1.59341	0.0701458
$517$	5.38853	0.236987
$518$	−0.703160	−0.0308951
$519$	−1.07205	−0.0470576
$520$	−4.49351	−0.197053
$521$	45.0381	1.97315	0.986577	−	0.163294i	$-0.0522118\pi$
$521$	45.0381	1.97315	0.986577	+	0.163294i	$0.0522118\pi$
$522$	−11.9626	−0.523591
$523$	17.7209	0.774879	0.387439	−	0.921895i	$-0.373360\pi$
$523$	17.7209	0.774879	0.387439	+	0.921895i	$0.373360\pi$
$524$	16.1678	0.706294
$525$	0.0132388	0.000577789 0
$526$	4.94599	0.215655
$527$	72.5568	3.16062
$528$	0.129420	0.00563226
$529$	−21.3046	−0.926289
$530$	5.61709	0.243991
$531$	15.5736	0.675838
$532$	−0.192170	−0.00833162
$533$	−49.3150	−2.13607
$534$	0.0918941	0.00397665
$535$	13.3196	0.575858
$536$	−7.55071	−0.326141
$537$	−1.78022	−0.0768221
$538$	10.4531	0.450666
$539$	−4.42206	−0.190471
$540$	1.21989	0.0524957
$541$	38.5195	1.65608	0.828041	−	0.560667i	$-0.189455\pi$
$541$	38.5195	1.65608	0.828041	+	0.560667i	$0.189455\pi$
$542$	−23.7764	−1.02128
$543$	0.422812	0.0181446
$544$	7.35571	0.315373
$545$	−11.3872	−0.487774
$546$	0.0594887	0.00254588
$547$	35.6474	1.52417	0.762086	−	0.647476i	$-0.224175\pi$
$547$	35.6474	1.52417	0.762086	+	0.647476i	$0.224175\pi$
$548$	−0.135492	−0.00578794
$549$	−6.69253	−0.285630
$550$	−0.632100	−0.0269528
$551$	12.0190	0.512026
$552$	0.266591	0.0113468
$553$	0.268896	0.0114346
$554$	−32.7280	−1.39048
$555$	−2.22655	−0.0945119
$556$	−3.41346	−0.144763
$557$	−28.6104	−1.21226	−0.606131	−	0.795365i	$-0.707279\pi$
$557$	−28.6104	−1.21226	−0.606131	+	0.795365i	$0.707279\pi$
$558$	−29.1785	−1.23523
$559$	−34.9702	−1.47908
$560$	−0.0646599	−0.00273238
$561$	−0.951973	−0.0401923
$562$	1.91809	0.0809097
$563$	13.6879	0.576876	0.288438	−	0.957499i	$-0.406864\pi$
$563$	13.6879	0.576876	0.288438	+	0.957499i	$0.406864\pi$
$564$	1.74541	0.0734952
$565$	−11.9672	−0.503466
$566$	−8.70439	−0.365873
$567$	0.557657	0.0234194
$568$	−6.36850	−0.267216
$569$	−4.07026	−0.170634	−0.0853171	−	0.996354i	$-0.527190\pi$
$569$	−4.07026	−0.170634	−0.0853171	+	0.996354i	$0.527190\pi$
$570$	−0.608506	−0.0254875
$571$	21.8679	0.915142	0.457571	−	0.889173i	$-0.348720\pi$
$571$	21.8679	0.915142	0.457571	+	0.889173i	$0.348720\pi$
$572$	−2.84035	−0.118761
$573$	0.200730	0.00838560
$574$	−0.709625	−0.0296192
$575$	−1.30206	−0.0542996
$576$	−2.95808	−0.123253
$577$	5.70895	0.237667	0.118833	−	0.992914i	$-0.462085\pi$
$577$	5.70895	0.237667	0.118833	+	0.992914i	$0.462085\pi$
$578$	−37.1065	−1.54343
$579$	3.59738	0.149502
$580$	4.04406	0.167920
$581$	−0.747886	−0.0310275
$582$	−3.37734	−0.139995
$583$	3.55056	0.147049
$584$	5.56094	0.230113
$585$	−13.2922	−0.549563
$586$	16.5205	0.682455
$587$	−0.984741	−0.0406446	−0.0203223	−	0.999793i	$-0.506469\pi$
$587$	−0.984741	−0.0406446	−0.0203223	+	0.999793i	$0.506469\pi$
$588$	−1.43236	−0.0590696
$589$	29.3159	1.20794
$590$	−5.26478	−0.216748
$591$	1.11314	0.0457884
$592$	10.8747	0.446949
$593$	−34.3574	−1.41089	−0.705445	−	0.708765i	$-0.749253\pi$
$593$	−34.3574	−1.41089	−0.705445	+	0.708765i	$0.749253\pi$
$594$	0.771092	0.0316383
$595$	0.475619	0.0194985
$596$	−11.3722	−0.465822
$597$	4.07811	0.166906
$598$	−5.85081	−0.239257
$599$	−5.47081	−0.223531	−0.111766	−	0.993735i	$-0.535651\pi$
$599$	−5.47081	−0.223531	−0.111766	+	0.993735i	$0.535651\pi$
$600$	−0.204745	−0.00835870
$601$	−37.4332	−1.52693	−0.763467	−	0.645847i	$-0.776504\pi$
$601$	−37.4332	−1.52693	−0.763467	+	0.645847i	$0.776504\pi$
$602$	−0.503208	−0.0205092
$603$	−22.3356	−0.909576
$604$	−17.5117	−0.712542
$605$	10.6004	0.430970
$606$	2.25995	0.0918041
$607$	−7.47656	−0.303464	−0.151732	−	0.988422i	$-0.548485\pi$
$607$	−7.47656	−0.303464	−0.151732	+	0.988422i	$0.548485\pi$
$608$	2.97201	0.120531
$609$	−0.0535386	−0.00216949
$610$	2.26246	0.0916042
$611$	−38.3063	−1.54971
$612$	21.7588	0.879546
$613$	43.9477	1.77503	0.887515	−	0.460779i	$-0.152430\pi$
$613$	43.9477	1.77503	0.887515	+	0.460779i	$0.152430\pi$
$614$	0.463529	0.0187065
$615$	−2.24703	−0.0906088
$616$	−0.0408715	−0.00164676
$617$	−28.7527	−1.15754	−0.578771	−	0.815490i	$-0.696468\pi$
$617$	−28.7527	−1.15754	−0.578771	+	0.815490i	$0.696468\pi$
$618$	−2.75250	−0.110722
$619$	21.4630	0.862673	0.431336	−	0.902191i	$-0.358042\pi$
$619$	21.4630	0.862673	0.431336	+	0.902191i	$0.358042\pi$
$620$	9.86401	0.396148
$621$	1.58837	0.0637390
$622$	−1.72367	−0.0691129
$623$	−0.0290208	−0.00116269
$624$	−0.920025	−0.0368305
$625$	1.00000	0.0400000
$626$	−6.41499	−0.256394
$627$	−0.384636	−0.0153609
$628$	16.3816	0.653696
$629$	−79.9914	−3.18947
$630$	−0.191269	−0.00762034
$631$	22.8600	0.910041	0.455021	−	0.890481i	$-0.349632\pi$
$631$	22.8600	0.910041	0.455021	+	0.890481i	$0.349632\pi$
$632$	−4.15862	−0.165421
$633$	2.07656	0.0825359
$634$	−19.6490	−0.780362
$635$	−0.758199	−0.0300882
$636$	1.15007	0.0456033
$637$	31.4358	1.24553
$638$	2.55625	0.101203
$639$	−18.8385	−0.745240
$640$	1.00000	0.0395285
$641$	−8.29219	−0.327522	−0.163761	−	0.986500i	$-0.552363\pi$
$641$	−8.29219	−0.327522	−0.163761	+	0.986500i	$0.552363\pi$
$642$	2.72714	0.107631
$643$	35.7942	1.41159	0.705793	−	0.708418i	$-0.250591\pi$
$643$	35.7942	1.41159	0.705793	+	0.708418i	$0.250591\pi$
$644$	−0.0841910	−0.00331759
$645$	−1.59341	−0.0627403
$646$	−21.8612	−0.860119
$647$	5.41955	0.213065	0.106532	−	0.994309i	$-0.466025\pi$
$647$	5.41955	0.213065	0.106532	+	0.994309i	$0.466025\pi$
$648$	−8.62447	−0.338801
$649$	−3.32787	−0.130630
$650$	4.49351	0.176250
$651$	−0.130588	−0.00511814
$652$	−1.80573	−0.0707178
$653$	3.59354	0.140626	0.0703131	−	0.997525i	$-0.477600\pi$
$653$	3.59354	0.140626	0.0703131	+	0.997525i	$0.477600\pi$
$654$	−2.33148	−0.0911680
$655$	−16.1678	−0.631729
$656$	10.9747	0.428491
$657$	16.4497	0.641764
$658$	−0.551213	−0.0214885
$659$	−41.0439	−1.59884	−0.799422	−	0.600769i	$-0.794861\pi$
$659$	−41.0439	−1.59884	−0.799422	+	0.600769i	$0.794861\pi$
$660$	−0.129420	−0.00503765
$661$	−3.20534	−0.124673	−0.0623365	−	0.998055i	$-0.519855\pi$
$661$	−3.20534	−0.124673	−0.0623365	+	0.998055i	$0.519855\pi$
$662$	18.8944	0.734353
$663$	6.76744	0.262825
$664$	11.5665	0.448866
$665$	0.192170	0.00745203
$666$	32.1683	1.24650
$667$	5.26560	0.203885
$668$	−20.4668	−0.791885
$669$	−5.89926	−0.228078
$670$	7.55071	0.291709
$671$	1.43010	0.0552084
$672$	−0.0132388	−0.000510698 0
$673$	−6.57183	−0.253325	−0.126663	−	0.991946i	$-0.540427\pi$
$673$	−6.57183	−0.253325	−0.126663	+	0.991946i	$0.540427\pi$
$674$	−25.0978	−0.966730
$675$	−1.21989	−0.0469536
$676$	7.19162	0.276601
$677$	−18.6613	−0.717212	−0.358606	−	0.933489i	$-0.616748\pi$
$677$	−18.6613	−0.717212	−0.358606	+	0.933489i	$0.616748\pi$
$678$	−2.45024	−0.0941009
$679$	1.06658	0.0409317
$680$	−7.35571	−0.282079
$681$	−6.12424	−0.234681
$682$	6.23504	0.238752
$683$	12.9753	0.496486	0.248243	−	0.968698i	$-0.420147\pi$
$683$	12.9753	0.496486	0.248243	+	0.968698i	$0.420147\pi$
$684$	8.79144	0.336149
$685$	0.135492	0.00517689
$686$	0.904968	0.0345519
$687$	−3.61674	−0.137987
$688$	7.78238	0.296700
$689$	−25.2404	−0.961583
$690$	−0.266591	−0.0101489
$691$	18.6637	0.710001	0.355001	−	0.934866i	$-0.384481\pi$
$691$	18.6637	0.710001	0.355001	+	0.934866i	$0.384481\pi$
$692$	−5.23599	−0.199043
$693$	−0.120901	−0.00459266
$694$	−35.5592	−1.34981
$695$	3.41346	0.129480
$696$	0.828002	0.0313853
$697$	−80.7269	−3.05775
$698$	12.0764	0.457100
$699$	−2.55527	−0.0966490
$700$	0.0646599	0.00244391
$701$	24.1619	0.912583	0.456292	−	0.889830i	$-0.349177\pi$
$701$	24.1619	0.912583	0.456292	+	0.889830i	$0.349177\pi$
$702$	−5.48158	−0.206889
$703$	−32.3198	−1.21897
$704$	0.632100	0.0238232
$705$	−1.74541	−0.0657361
$706$	−1.32911	−0.0500217
$707$	−0.713706	−0.0268417
$708$	−1.07794	−0.0405114
$709$	7.79910	0.292902	0.146451	−	0.989218i	$-0.453215\pi$
$709$	7.79910	0.292902	0.146451	+	0.989218i	$0.453215\pi$
$710$	6.36850	0.239005
$711$	−12.3015	−0.461344
$712$	0.448821	0.0168203
$713$	12.8435	0.480994
$714$	0.0973809	0.00364439
$715$	2.84035	0.106223
$716$	−8.69479	−0.324940
$717$	4.87527	0.182070
$718$	14.5672	0.543642
$719$	46.4679	1.73296	0.866480	−	0.499212i	$-0.166377\pi$
$719$	46.4679	1.73296	0.866480	+	0.499212i	$0.166377\pi$
$720$	2.95808	0.110241
$721$	0.869257	0.0323728
$722$	10.1672	0.378382
$723$	0.959652	0.0356899
$724$	2.06506	0.0767474
$725$	−4.04406	−0.150193
$726$	2.17039	0.0805509
$727$	−0.437122	−0.0162119	−0.00810597	−	0.999967i	$-0.502580\pi$
$727$	−0.437122	−0.0162119	−0.00810597	+	0.999967i	$0.502580\pi$
$728$	0.290550	0.0107685
$729$	−24.7626	−0.917132
$730$	−5.56094	−0.205820
$731$	−57.2449	−2.11728
$732$	0.463228	0.0171214
$733$	35.9617	1.32828	0.664138	−	0.747610i	$-0.268799\pi$
$733$	35.9617	1.32828	0.664138	+	0.747610i	$0.268799\pi$
$734$	17.8324	0.658206
$735$	1.43236	0.0528335
$736$	1.30206	0.0479945
$737$	4.77280	0.175808
$738$	32.4641	1.19502
$739$	−7.81724	−0.287562	−0.143781	−	0.989610i	$-0.545926\pi$
$739$	−7.81724	−0.287562	−0.143781	+	0.989610i	$0.545926\pi$
$740$	−10.8747	−0.399763
$741$	2.73432	0.100448
$742$	−0.363200	−0.0133335
$743$	−45.4861	−1.66872	−0.834361	−	0.551218i	$-0.814163\pi$
$743$	−45.4861	−1.66872	−0.834361	+	0.551218i	$0.814163\pi$
$744$	2.01961	0.0740425
$745$	11.3722	0.416644
$746$	14.8329	0.543073
$747$	34.2145	1.25184
$748$	−4.64954	−0.170004
$749$	−0.861247	−0.0314693
$750$	0.204745	0.00747625
$751$	−10.0799	−0.367820	−0.183910	−	0.982943i	$-0.558876\pi$
$751$	−10.0799	−0.367820	−0.183910	+	0.982943i	$0.558876\pi$
$752$	8.52481	0.310868
$753$	−2.39602	−0.0873157
$754$	−18.1720	−0.661786
$755$	17.5117	0.637317
$756$	−0.0788779	−0.00286876
$757$	−33.0699	−1.20195	−0.600973	−	0.799269i	$-0.705220\pi$
$757$	−33.0699	−1.20195	−0.600973	+	0.799269i	$0.705220\pi$
$758$	22.9266	0.832732
$759$	−0.168512	−0.00611659
$760$	−2.97201	−0.107806
$761$	19.2030	0.696108	0.348054	−	0.937475i	$-0.386843\pi$
$761$	19.2030	0.696108	0.348054	+	0.937475i	$0.386843\pi$
$762$	−0.155238	−0.00562367
$763$	0.736296	0.0266557
$764$	0.980386	0.0354691
$765$	−21.7588	−0.786690
$766$	−16.1189	−0.582400
$767$	23.6573	0.854217
$768$	0.204745	0.00738811
$769$	−22.6905	−0.818240	−0.409120	−	0.912481i	$-0.634164\pi$
$769$	−22.6905	−0.818240	−0.409120	+	0.912481i	$0.634164\pi$
$770$	0.0408715	0.00147291
$771$	2.69923	0.0972104
$772$	17.5700	0.632359
$773$	6.48483	0.233243	0.116621	−	0.993176i	$-0.462794\pi$
$773$	6.48483	0.233243	0.116621	+	0.993176i	$0.462794\pi$
$774$	23.0209	0.827469
$775$	−9.86401	−0.354326
$776$	−16.4953	−0.592147
$777$	0.143969	0.00516485
$778$	17.3654	0.622580
$779$	−32.6170	−1.16863
$780$	0.920025	0.0329422
$781$	4.02553	0.144045
$782$	−9.57756	−0.342493
$783$	4.93330	0.176302
$784$	−6.99582	−0.249851
$785$	−16.3816	−0.584683
$786$	−3.31029	−0.118074
$787$	−48.7286	−1.73699	−0.868494	−	0.495700i	$-0.834912\pi$
$787$	−48.7286	−1.73699	−0.868494	+	0.495700i	$0.834912\pi$
$788$	5.43670	0.193674
$789$	−1.01267	−0.0360520
$790$	4.15862	0.147957
$791$	0.773801	0.0275132
$792$	1.86980	0.0664405
$793$	−10.1664	−0.361018
$794$	7.16328	0.254215
$795$	−1.15007	−0.0407889
$796$	19.9180	0.705974
$797$	−3.88666	−0.137672	−0.0688362	−	0.997628i	$-0.521929\pi$
$797$	−3.88666	−0.137672	−0.0688362	+	0.997628i	$0.521929\pi$
$798$	0.0393459	0.00139283
$799$	−62.7060	−2.21838
$800$	−1.00000	−0.0353553
$801$	1.32765	0.0469102
$802$	−1.00000	−0.0353112
$803$	−3.51507	−0.124044
$804$	1.54597	0.0545223
$805$	0.0841910	0.00296734
$806$	−44.3240	−1.56125
$807$	−2.14023	−0.0753396
$808$	11.0378	0.388310
$809$	−30.7359	−1.08062	−0.540308	−	0.841467i	$-0.681692\pi$
$809$	−30.7359	−1.08062	−0.540308	+	0.841467i	$0.681692\pi$
$810$	8.62447	0.303033
$811$	28.6474	1.00594	0.502972	−	0.864303i	$-0.332240\pi$
$811$	28.6474	1.00594	0.502972	+	0.864303i	$0.332240\pi$
$812$	−0.261488	−0.00917644
$813$	4.86811	0.170732
$814$	−6.87392	−0.240931
$815$	1.80573	0.0632519
$816$	−1.50605	−0.0527222
$817$	−23.1293	−0.809192
$818$	21.4034	0.748351
$819$	0.859469	0.0300323
$820$	−10.9747	−0.383254
$821$	−4.83648	−0.168794	−0.0843972	−	0.996432i	$-0.526896\pi$
$821$	−4.83648	−0.168794	−0.0843972	+	0.996432i	$0.526896\pi$
$822$	0.0277414	0.000967592 0
$823$	−22.8718	−0.797261	−0.398631	−	0.917112i	$-0.630514\pi$
$823$	−22.8718	−0.797261	−0.398631	+	0.917112i	$0.630514\pi$
$824$	−13.4435	−0.468328
$825$	0.129420	0.00450581
$826$	0.340420	0.0118447
$827$	−43.9988	−1.52999	−0.764994	−	0.644037i	$-0.777258\pi$
$827$	−43.9988	−1.52999	−0.764994	+	0.644037i	$0.777258\pi$
$828$	3.85159	0.133852
$829$	35.5394	1.23433	0.617167	−	0.786832i	$-0.288280\pi$
$829$	35.5394	1.23433	0.617167	+	0.786832i	$0.288280\pi$
$830$	−11.5665	−0.401478
$831$	6.70090	0.232452
$832$	−4.49351	−0.155784
$833$	51.4592	1.78296
$834$	0.698890	0.0242006
$835$	20.4668	0.708283
$836$	−1.87861	−0.0649730
$837$	12.0330	0.415921
$838$	−7.77728	−0.268662
$839$	19.1630	0.661580	0.330790	−	0.943704i	$-0.392685\pi$
$839$	19.1630	0.661580	0.330790	+	0.943704i	$0.392685\pi$
$840$	0.0132388	0.000456783 0
$841$	−12.6456	−0.436055
$842$	28.3533	0.977120
$843$	−0.392720	−0.0135260
$844$	10.1422	0.349108
$845$	−7.19162	−0.247399
$846$	25.2171	0.866980
$847$	−0.685424	−0.0235514
$848$	5.61709	0.192892
$849$	1.78218	0.0611644
$850$	7.35571	0.252299
$851$	−14.1595	−0.485383
$852$	1.30392	0.0446716
$853$	50.4034	1.72578	0.862890	−	0.505392i	$-0.168652\pi$
$853$	50.4034	1.72578	0.862890	+	0.505392i	$0.168652\pi$
$854$	−0.146290	−0.00500595
$855$	−8.79144	−0.300661
$856$	13.3196	0.455256
$857$	−38.2925	−1.30805	−0.654024	−	0.756474i	$-0.726921\pi$
$857$	−38.2925	−1.30805	−0.654024	+	0.756474i	$0.726921\pi$
$858$	0.581548	0.0198537
$859$	−16.0229	−0.546693	−0.273347	−	0.961916i	$-0.588131\pi$
$859$	−16.0229	−0.546693	−0.273347	+	0.961916i	$0.588131\pi$
$860$	−7.78238	−0.265377
$861$	0.145292	0.00495155
$862$	−14.5433	−0.495347
$863$	22.9009	0.779555	0.389777	−	0.920909i	$-0.372552\pi$
$863$	22.9009	0.779555	0.389777	+	0.920909i	$0.372552\pi$
$864$	1.21989	0.0415015
$865$	5.23599	0.178029
$866$	−17.1600	−0.583120
$867$	7.59738	0.258020
$868$	−0.637806	−0.0216485
$869$	2.62866	0.0891713
$870$	−0.828002	−0.0280719
$871$	−33.9292	−1.14965
$872$	−11.3872	−0.385619
$873$	−48.7944	−1.65144
$874$	−3.86973	−0.130896
$875$	−0.0646599	−0.00218590
$876$	−1.13858	−0.0384689
$877$	40.3250	1.36168	0.680839	−	0.732433i	$-0.261615\pi$
$877$	40.3250	1.36168	0.680839	+	0.732433i	$0.261615\pi$
$878$	2.53392	0.0855156
$879$	−3.38249	−0.114089
$880$	−0.632100	−0.0213081
$881$	−23.5357	−0.792938	−0.396469	−	0.918048i	$-0.629765\pi$
$881$	−23.5357	−0.792938	−0.396469	+	0.918048i	$0.629765\pi$
$882$	−20.6942	−0.696810
$883$	−24.9713	−0.840352	−0.420176	−	0.907443i	$-0.638032\pi$
$883$	−24.9713	−0.840352	−0.420176	+	0.907443i	$0.638032\pi$
$884$	33.0529	1.11169
$885$	1.07794	0.0362345
$886$	−31.0000	−1.04147
$887$	8.29479	0.278512	0.139256	−	0.990256i	$-0.455529\pi$
$887$	8.29479	0.278512	0.139256	+	0.990256i	$0.455529\pi$
$888$	−2.22655	−0.0747182
$889$	0.0490251	0.00164425
$890$	−0.448821	−0.0150445
$891$	5.45153	0.182633
$892$	−28.8127	−0.964719
$893$	−25.3358	−0.847831
$894$	2.32840	0.0778734
$895$	8.69479	0.290635
$896$	−0.0646599	−0.00216014
$897$	1.19793	0.0399976
$898$	13.8683	0.462789
$899$	39.8906	1.33043
$900$	−2.95808	−0.0986026
$901$	−41.3177	−1.37649
$902$	−6.93712	−0.230981
$903$	0.103029	0.00342861
$904$	−11.9672	−0.398025
$905$	−2.06506	−0.0686449
$906$	3.58544	0.119118
$907$	3.76492	0.125012	0.0625061	−	0.998045i	$-0.480091\pi$
$907$	3.76492	0.125012	0.0625061	+	0.998045i	$0.480091\pi$
$908$	−29.9115	−0.992648
$909$	32.6508	1.08296
$910$	−0.290550	−0.00963163
$911$	15.7669	0.522380	0.261190	−	0.965287i	$-0.415885\pi$
$911$	15.7669	0.522380	0.261190	+	0.965287i	$0.415885\pi$
$912$	−0.608506	−0.0201496
$913$	−7.31116	−0.241964
$914$	−40.0388	−1.32437
$915$	−0.463228	−0.0153138
$916$	−17.6646	−0.583655
$917$	1.04541	0.0345225
$918$	−8.97315	−0.296158
$919$	27.0392	0.891941	0.445970	−	0.895048i	$-0.352859\pi$
$919$	27.0392	0.891941	0.445970	+	0.895048i	$0.352859\pi$
$920$	−1.30206	−0.0429276
$921$	−0.0949055	−0.00312724
$922$	3.97107	0.130780
$923$	−28.6169	−0.941937
$924$	0.00836826	0.000275295 0
$925$	10.8747	0.357559
$926$	−13.8381	−0.454748
$927$	−39.7670	−1.30612
$928$	4.04406	0.132753
$929$	−9.66620	−0.317138	−0.158569	−	0.987348i	$-0.550688\pi$
$929$	−9.66620	−0.317138	−0.158569	+	0.987348i	$0.550688\pi$
$930$	−2.01961	−0.0662256
$931$	20.7917	0.681419
$932$	−12.4802	−0.408803
$933$	0.352914	0.0115539
$934$	−33.1500	−1.08470
$935$	4.64954	0.152056
$936$	−13.2922	−0.434468
$937$	−0.258524	−0.00844560	−0.00422280	−	0.999991i	$-0.501344\pi$
$937$	−0.258524	−0.00844560	−0.00422280	+	0.999991i	$0.501344\pi$
$938$	−0.488228	−0.0159412
$939$	1.31344	0.0428625
$940$	−8.52481	−0.278049
$941$	−43.4816	−1.41746	−0.708730	−	0.705479i	$-0.750732\pi$
$941$	−43.4816	−1.41746	−0.708730	+	0.705479i	$0.750732\pi$
$942$	−3.35405	−0.109281
$943$	−14.2897	−0.465338
$944$	−5.26478	−0.171354
$945$	0.0788779	0.00256590
$946$	−4.91924	−0.159938
$947$	0.167721	0.00545021	0.00272511	−	0.999996i	$-0.499133\pi$
$947$	0.167721	0.00545021	0.00272511	+	0.999996i	$0.499133\pi$
$948$	0.851459	0.0276541
$949$	24.9881	0.811149
$950$	2.97201	0.0964248
$951$	4.02305	0.130456
$952$	0.475619	0.0154149
$953$	−27.1184	−0.878452	−0.439226	−	0.898377i	$-0.644747\pi$
$953$	−27.1184	−0.878452	−0.439226	+	0.898377i	$0.644747\pi$
$954$	16.6158	0.537956
$955$	−0.980386	−0.0317246
$956$	23.8114	0.770114
$957$	−0.523380	−0.0169185
$958$	22.0062	0.710989
$959$	−0.00876091	−0.000282905 0
$960$	−0.204745	−0.00660813
$961$	66.2987	2.13867
$962$	48.8657	1.57549
$963$	39.4006	1.26967
$964$	4.68705	0.150960
$965$	−17.5700	−0.565599
$966$	0.0172377	0.000554614 0
$967$	−10.2716	−0.330312	−0.165156	−	0.986267i	$-0.552813\pi$
$967$	−10.2716	−0.330312	−0.165156	+	0.986267i	$0.552813\pi$
$968$	10.6004	0.340711
$969$	4.47599	0.143790
$970$	16.4953	0.529632
$971$	−26.7210	−0.857517	−0.428759	−	0.903419i	$-0.641049\pi$
$971$	−26.7210	−0.857517	−0.428759	+	0.903419i	$0.641049\pi$
$972$	5.42549	0.174023
$973$	−0.220714	−0.00707576
$974$	−37.8587	−1.21307
$975$	−0.920025	−0.0294644
$976$	2.26246	0.0724195
$977$	−2.56134	−0.0819444	−0.0409722	−	0.999160i	$-0.513046\pi$
$977$	−2.56134	−0.0819444	−0.0409722	+	0.999160i	$0.513046\pi$
$978$	0.369715	0.0118222
$979$	−0.283700	−0.00906709
$980$	6.99582	0.223473
$981$	−33.6843	−1.07546
$982$	−28.3715	−0.905371
$983$	12.8342	0.409346	0.204673	−	0.978830i	$-0.434387\pi$
$983$	12.8342	0.409346	0.204673	+	0.978830i	$0.434387\pi$
$984$	−2.24703	−0.0716325
$985$	−5.43670	−0.173228
$986$	−29.7469	−0.947335
$987$	0.112858	0.00359232
$988$	13.3548	0.424871
$989$	−10.1331	−0.322214
$990$	−1.86980	−0.0594262
$991$	7.81290	0.248185	0.124092	−	0.992271i	$-0.460398\pi$
$991$	7.81290	0.248185	0.124092	+	0.992271i	$0.460398\pi$
$992$	9.86401	0.313183
$993$	−3.86855	−0.122765
$994$	−0.411786	−0.0130611
$995$	−19.9180	−0.631442
$996$	−2.36818	−0.0750386
$997$	−50.4347	−1.59728	−0.798642	−	0.601807i	$-0.794448\pi$
$997$	−50.4347	−1.59728	−0.798642	+	0.601807i	$0.794448\pi$
$998$	−18.2919	−0.579021
$999$	−13.2660	−0.419717

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.l.1.9	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.l.1.9	✓	17	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.204745 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.204745 q^{6} +0.0646599 q^{7} -1.00000 q^{8} -2.95808 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.204745 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.204745 q^{6} +0.0646599 q^{7} -1.00000 q^{8} -2.95808 q^{9} +1.00000 q^{10} +0.632100 q^{11} +0.204745 q^{12} -4.49351 q^{13} -0.0646599 q^{14} -0.204745 q^{15} +1.00000 q^{16} -7.35571 q^{17} +2.95808 q^{18} -2.97201 q^{19} -1.00000 q^{20} +0.0132388 q^{21} -0.632100 q^{22} -1.30206 q^{23} -0.204745 q^{24} +1.00000 q^{25} +4.49351 q^{26} -1.21989 q^{27} +0.0646599 q^{28} -4.04406 q^{29} +0.204745 q^{30} -9.86401 q^{31} -1.00000 q^{32} +0.129420 q^{33} +7.35571 q^{34} -0.0646599 q^{35} -2.95808 q^{36} +10.8747 q^{37} +2.97201 q^{38} -0.920025 q^{39} +1.00000 q^{40} +10.9747 q^{41} -0.0132388 q^{42} +7.78238 q^{43} +0.632100 q^{44} +2.95808 q^{45} +1.30206 q^{46} +8.52481 q^{47} +0.204745 q^{48} -6.99582 q^{49} -1.00000 q^{50} -1.50605 q^{51} -4.49351 q^{52} +5.61709 q^{53} +1.21989 q^{54} -0.632100 q^{55} -0.0646599 q^{56} -0.608506 q^{57} +4.04406 q^{58} -5.26478 q^{59} -0.204745 q^{60} +2.26246 q^{61} +9.86401 q^{62} -0.191269 q^{63} +1.00000 q^{64} +4.49351 q^{65} -0.129420 q^{66} +7.55071 q^{67} -7.35571 q^{68} -0.266591 q^{69} +0.0646599 q^{70} +6.36850 q^{71} +2.95808 q^{72} -5.56094 q^{73} -10.8747 q^{74} +0.204745 q^{75} -2.97201 q^{76} +0.0408715 q^{77} +0.920025 q^{78} +4.15862 q^{79} -1.00000 q^{80} +8.62447 q^{81} -10.9747 q^{82} -11.5665 q^{83} +0.0132388 q^{84} +7.35571 q^{85} -7.78238 q^{86} -0.828002 q^{87} -0.632100 q^{88} -0.448821 q^{89} -2.95808 q^{90} -0.290550 q^{91} -1.30206 q^{92} -2.01961 q^{93} -8.52481 q^{94} +2.97201 q^{95} -0.204745 q^{96} +16.4953 q^{97} +6.99582 q^{98} -1.86980 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * q^99

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