LMFDB - Embedded newform 2001.2.a.k.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 17x^{8} + 23x^{7} + 69x^{6} - 88x^{5} - 106x^{4} + 101x^{3} + 60x^{2} - 23x - 11 $ x^10 - x^9 - 17x^8 + 23x^7 + 69x^6 - 88x^5 - 106x^4 + 101x^3 + 60x^2 - 23x - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.92359$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.39479 q^{2} -1.00000 q^{3} -0.0545700 q^{4} -2.50233 q^{5} -1.39479 q^{6} +4.61826 q^{7} -2.86569 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.39479 q^{2} -1.00000 q^{3} -0.0545700 q^{4} -2.50233 q^{5} -1.39479 q^{6} +4.61826 q^{7} -2.86569 q^{8} +1.00000 q^{9} -3.49022 q^{10} +6.41359 q^{11} +0.0545700 q^{12} -4.63148 q^{13} +6.44149 q^{14} +2.50233 q^{15} -3.88788 q^{16} -0.986447 q^{17} +1.39479 q^{18} -2.31967 q^{19} +0.136552 q^{20} -4.61826 q^{21} +8.94559 q^{22} -1.00000 q^{23} +2.86569 q^{24} +1.26167 q^{25} -6.45993 q^{26} -1.00000 q^{27} -0.252019 q^{28} +1.00000 q^{29} +3.49022 q^{30} +7.37989 q^{31} +0.308608 q^{32} -6.41359 q^{33} -1.37588 q^{34} -11.5564 q^{35} -0.0545700 q^{36} +4.51800 q^{37} -3.23544 q^{38} +4.63148 q^{39} +7.17090 q^{40} +9.39988 q^{41} -6.44149 q^{42} +0.107858 q^{43} -0.349990 q^{44} -2.50233 q^{45} -1.39479 q^{46} +0.665991 q^{47} +3.88788 q^{48} +14.3284 q^{49} +1.75976 q^{50} +0.986447 q^{51} +0.252740 q^{52} +9.08358 q^{53} -1.39479 q^{54} -16.0489 q^{55} -13.2345 q^{56} +2.31967 q^{57} +1.39479 q^{58} +5.42942 q^{59} -0.136552 q^{60} +7.43286 q^{61} +10.2934 q^{62} +4.61826 q^{63} +8.20621 q^{64} +11.5895 q^{65} -8.94559 q^{66} -10.1253 q^{67} +0.0538304 q^{68} +1.00000 q^{69} -16.1188 q^{70} +10.8149 q^{71} -2.86569 q^{72} -1.36129 q^{73} +6.30164 q^{74} -1.26167 q^{75} +0.126584 q^{76} +29.6196 q^{77} +6.45993 q^{78} +4.07429 q^{79} +9.72878 q^{80} +1.00000 q^{81} +13.1108 q^{82} -11.3089 q^{83} +0.252019 q^{84} +2.46842 q^{85} +0.150439 q^{86} -1.00000 q^{87} -18.3793 q^{88} +3.27283 q^{89} -3.49022 q^{90} -21.3894 q^{91} +0.0545700 q^{92} -7.37989 q^{93} +0.928916 q^{94} +5.80459 q^{95} -0.308608 q^{96} +10.8603 q^{97} +19.9850 q^{98} +6.41359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9} - 4 q^{10} + 9 q^{11} - 17 q^{12} - 16 q^{13} + 16 q^{14} - 6 q^{15} + 27 q^{16} + 3 q^{18} + q^{19} + 21 q^{20} - 3 q^{21} + 17 q^{22} - 10 q^{23} + 6 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{27} - 14 q^{28} + 10 q^{29} + 4 q^{30} + 17 q^{31} + 21 q^{32} - 9 q^{33} - 3 q^{34} + 29 q^{35} + 17 q^{36} + q^{37} + 32 q^{38} + 16 q^{39} + 13 q^{40} - 16 q^{42} - 5 q^{43} + 33 q^{44} + 6 q^{45} - 3 q^{46} + 15 q^{47} - 27 q^{48} + 31 q^{49} - 22 q^{50} - 21 q^{52} + 35 q^{53} - 3 q^{54} - 20 q^{55} + 18 q^{56} - q^{57} + 3 q^{58} + 49 q^{59} - 21 q^{60} + 8 q^{61} + 15 q^{62} + 3 q^{63} + 12 q^{64} - 3 q^{65} - 17 q^{66} + 35 q^{67} - 18 q^{68} + 10 q^{69} - 16 q^{70} + 30 q^{71} - 6 q^{72} - 15 q^{73} + 23 q^{74} + 4 q^{75} + 10 q^{76} + 23 q^{77} - 28 q^{78} + 24 q^{79} + 23 q^{80} + 10 q^{81} - 5 q^{82} + q^{83} + 14 q^{84} - 10 q^{86} - 10 q^{87} + 18 q^{88} + 15 q^{89} - 4 q^{90} + 26 q^{91} - 17 q^{92} - 17 q^{93} + 3 q^{94} + 7 q^{95} - 21 q^{96} - 35 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9 - 4 * q^10 + 9 * q^11 - 17 * q^12 - 16 * q^13 + 16 * q^14 - 6 * q^15 + 27 * q^16 + 3 * q^18 + q^19 + 21 * q^20 - 3 * q^21 + 17 * q^22 - 10 * q^23 + 6 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^27 - 14 * q^28 + 10 * q^29 + 4 * q^30 + 17 * q^31 + 21 * q^32 - 9 * q^33 - 3 * q^34 + 29 * q^35 + 17 * q^36 + q^37 + 32 * q^38 + 16 * q^39 + 13 * q^40 - 16 * q^42 - 5 * q^43 + 33 * q^44 + 6 * q^45 - 3 * q^46 + 15 * q^47 - 27 * q^48 + 31 * q^49 - 22 * q^50 - 21 * q^52 + 35 * q^53 - 3 * q^54 - 20 * q^55 + 18 * q^56 - q^57 + 3 * q^58 + 49 * q^59 - 21 * q^60 + 8 * q^61 + 15 * q^62 + 3 * q^63 + 12 * q^64 - 3 * q^65 - 17 * q^66 + 35 * q^67 - 18 * q^68 + 10 * q^69 - 16 * q^70 + 30 * q^71 - 6 * q^72 - 15 * q^73 + 23 * q^74 + 4 * q^75 + 10 * q^76 + 23 * q^77 - 28 * q^78 + 24 * q^79 + 23 * q^80 + 10 * q^81 - 5 * q^82 + q^83 + 14 * q^84 - 10 * q^86 - 10 * q^87 + 18 * q^88 + 15 * q^89 - 4 * q^90 + 26 * q^91 - 17 * q^92 - 17 * q^93 + 3 * q^94 + 7 * q^95 - 21 * q^96 - 35 * q^97 + 3 * q^98 + 9 * 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 $

$2$	1.39479	0.986263	0.493132	−	0.869955i	$-0.335852\pi$
$2$	1.39479	0.986263	0.493132	+	0.869955i	$0.335852\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.0545700	−0.0272850
$5$	−2.50233	−1.11908	−0.559539	−	0.828804i	$-0.689022\pi$
$5$	−2.50233	−1.11908	−0.559539	+	0.828804i	$0.689022\pi$
$6$	−1.39479	−0.569419
$7$	4.61826	1.74554	0.872770	−	0.488132i	$-0.162322\pi$
$7$	4.61826	1.74554	0.872770	+	0.488132i	$0.162322\pi$
$8$	−2.86569	−1.01317
$9$	1.00000	0.333333
$10$	−3.49022	−1.10370
$11$	6.41359	1.93377	0.966885	−	0.255213i	$-0.0821457\pi$
$11$	6.41359	1.93377	0.966885	+	0.255213i	$0.0821457\pi$
$12$	0.0545700	0.0157530
$13$	−4.63148	−1.28454	−0.642271	−	0.766478i	$-0.722008\pi$
$13$	−4.63148	−1.28454	−0.642271	+	0.766478i	$0.722008\pi$
$14$	6.44149	1.72156
$15$	2.50233	0.646100
$16$	−3.88788	−0.971971
$17$	−0.986447	−0.239249	−0.119624	−	0.992819i	$-0.538169\pi$
$17$	−0.986447	−0.239249	−0.119624	+	0.992819i	$0.538169\pi$
$18$	1.39479	0.328754
$19$	−2.31967	−0.532169	−0.266084	−	0.963950i	$-0.585730\pi$
$19$	−2.31967	−0.532169	−0.266084	+	0.963950i	$0.585730\pi$
$20$	0.136552	0.0305340
$21$	−4.61826	−1.00779
$22$	8.94559	1.90721
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.86569	0.584956
$25$	1.26167	0.252334
$26$	−6.45993	−1.26690
$27$	−1.00000	−0.192450
$28$	−0.252019	−0.0476270
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	3.49022	0.637224
$31$	7.37989	1.32547	0.662734	−	0.748855i	$-0.269396\pi$
$31$	7.37989	1.32547	0.662734	+	0.748855i	$0.269396\pi$
$32$	0.308608	0.0545546
$33$	−6.41359	−1.11646
$34$	−1.37588	−0.235962
$35$	−11.5564	−1.95339
$36$	−0.0545700	−0.00909500
$37$	4.51800	0.742754	0.371377	−	0.928482i	$-0.378886\pi$
$37$	4.51800	0.742754	0.371377	+	0.928482i	$0.378886\pi$
$38$	−3.23544	−0.524858
$39$	4.63148	0.741631
$40$	7.17090	1.13382
$41$	9.39988	1.46801	0.734007	−	0.679142i	$-0.237648\pi$
$41$	9.39988	1.46801	0.734007	+	0.679142i	$0.237648\pi$
$42$	−6.44149	−0.993944
$43$	0.107858	0.0164483	0.00822413	−	0.999966i	$-0.497382\pi$
$43$	0.107858	0.0164483	0.00822413	+	0.999966i	$0.497382\pi$
$44$	−0.349990	−0.0527629
$45$	−2.50233	−0.373026
$46$	−1.39479	−0.205650
$47$	0.665991	0.0971448	0.0485724	−	0.998820i	$-0.484533\pi$
$47$	0.665991	0.0971448	0.0485724	+	0.998820i	$0.484533\pi$
$48$	3.88788	0.561167
$49$	14.3284	2.04691
$50$	1.75976	0.248868
$51$	0.986447	0.138130
$52$	0.252740	0.0350487
$53$	9.08358	1.24773	0.623863	−	0.781534i	$-0.285562\pi$
$53$	9.08358	1.24773	0.623863	+	0.781534i	$0.285562\pi$
$54$	−1.39479	−0.189806
$55$	−16.0489	−2.16404
$56$	−13.2345	−1.76853
$57$	2.31967	0.307248
$58$	1.39479	0.183144
$59$	5.42942	0.706851	0.353425	−	0.935463i	$-0.385017\pi$
$59$	5.42942	0.706851	0.353425	+	0.935463i	$0.385017\pi$
$60$	−0.136552	−0.0176288
$61$	7.43286	0.951680	0.475840	−	0.879532i	$-0.342144\pi$
$61$	7.43286	0.951680	0.475840	+	0.879532i	$0.342144\pi$
$62$	10.2934	1.30726
$63$	4.61826	0.581846
$64$	8.20621	1.02578
$65$	11.5895	1.43750
$66$	−8.94559	−1.10113
$67$	−10.1253	−1.23700	−0.618499	−	0.785786i	$-0.712259\pi$
$67$	−10.1253	−1.23700	−0.618499	+	0.785786i	$0.712259\pi$
$68$	0.0538304	0.00652790
$69$	1.00000	0.120386
$70$	−16.1188	−1.92656
$71$	10.8149	1.28350	0.641748	−	0.766915i	$-0.278209\pi$
$71$	10.8149	1.28350	0.641748	+	0.766915i	$0.278209\pi$
$72$	−2.86569	−0.337724
$73$	−1.36129	−0.159327	−0.0796636	−	0.996822i	$-0.525385\pi$
$73$	−1.36129	−0.159327	−0.0796636	+	0.996822i	$0.525385\pi$
$74$	6.30164	0.732551
$75$	−1.26167	−0.145685
$76$	0.126584	0.0145202
$77$	29.6196	3.37547
$78$	6.45993	0.731443
$79$	4.07429	0.458394	0.229197	−	0.973380i	$-0.426390\pi$
$79$	4.07429	0.458394	0.229197	+	0.973380i	$0.426390\pi$
$80$	9.72878	1.08771
$81$	1.00000	0.111111
$82$	13.1108	1.44785
$83$	−11.3089	−1.24131	−0.620656	−	0.784083i	$-0.713134\pi$
$83$	−11.3089	−1.24131	−0.620656	+	0.784083i	$0.713134\pi$
$84$	0.252019	0.0274975
$85$	2.46842	0.267738
$86$	0.150439	0.0162223
$87$	−1.00000	−0.107211
$88$	−18.3793	−1.95924
$89$	3.27283	0.346919	0.173459	−	0.984841i	$-0.444505\pi$
$89$	3.27283	0.346919	0.173459	+	0.984841i	$0.444505\pi$
$90$	−3.49022	−0.367902
$91$	−21.3894	−2.24222
$92$	0.0545700	0.00568932
$93$	−7.37989	−0.765259
$94$	0.928916	0.0958104
$95$	5.80459	0.595538
$96$	−0.308608	−0.0314971
$97$	10.8603	1.10270	0.551349	−	0.834275i	$-0.314113\pi$
$97$	10.8603	1.10270	0.551349	+	0.834275i	$0.314113\pi$
$98$	19.9850	2.01879
$99$	6.41359	0.644590
$100$	−0.0688494	−0.00688494
$101$	1.91292	0.190343	0.0951713	−	0.995461i	$-0.469660\pi$
$101$	1.91292	0.190343	0.0951713	+	0.995461i	$0.469660\pi$
$102$	1.37588	0.136233
$103$	1.65984	0.163549	0.0817745	−	0.996651i	$-0.473941\pi$
$103$	1.65984	0.163549	0.0817745	+	0.996651i	$0.473941\pi$
$104$	13.2724	1.30146
$105$	11.5564	1.12779
$106$	12.6697	1.23059
$107$	13.6379	1.31843	0.659213	−	0.751957i	$-0.270890\pi$
$107$	13.6379	1.31843	0.659213	+	0.751957i	$0.270890\pi$
$108$	0.0545700	0.00525100
$109$	−19.7417	−1.89091	−0.945456	−	0.325751i	$-0.894383\pi$
$109$	−19.7417	−1.89091	−0.945456	+	0.325751i	$0.894383\pi$
$110$	−22.3848	−2.13431
$111$	−4.51800	−0.428829
$112$	−17.9553	−1.69661
$113$	−10.1807	−0.957718	−0.478859	−	0.877892i	$-0.658949\pi$
$113$	−10.1807	−0.957718	−0.478859	+	0.877892i	$0.658949\pi$
$114$	3.23544	0.303027
$115$	2.50233	0.233344
$116$	−0.0545700	−0.00506670
$117$	−4.63148	−0.428181
$118$	7.57289	0.697141
$119$	−4.55567	−0.417618
$120$	−7.17090	−0.654611
$121$	30.1341	2.73946
$122$	10.3672	0.938607
$123$	−9.39988	−0.847559
$124$	−0.402721	−0.0361654
$125$	9.35454	0.836696
$126$	6.44149	0.573854
$127$	3.12919	0.277671	0.138835	−	0.990315i	$-0.455664\pi$
$127$	3.12919	0.277671	0.138835	+	0.990315i	$0.455664\pi$
$128$	10.8287	0.957130
$129$	−0.107858	−0.00949640
$130$	16.1649	1.41776
$131$	15.1334	1.32221	0.661106	−	0.750292i	$-0.270087\pi$
$131$	15.1334	1.32221	0.661106	+	0.750292i	$0.270087\pi$
$132$	0.349990	0.0304627
$133$	−10.7128	−0.928921
$134$	−14.1226	−1.22001
$135$	2.50233	0.215367
$136$	2.82685	0.242400
$137$	10.5892	0.904701	0.452350	−	0.891840i	$-0.350586\pi$
$137$	10.5892	0.904701	0.452350	+	0.891840i	$0.350586\pi$
$138$	1.39479	0.118732
$139$	−16.6471	−1.41199	−0.705995	−	0.708217i	$-0.749500\pi$
$139$	−16.6471	−1.41199	−0.705995	+	0.708217i	$0.749500\pi$
$140$	0.630635	0.0532984
$141$	−0.665991	−0.0560866
$142$	15.0845	1.26587
$143$	−29.7044	−2.48401
$144$	−3.88788	−0.323990
$145$	−2.50233	−0.207807
$146$	−1.89871	−0.157138
$147$	−14.3284	−1.18178
$148$	−0.246547	−0.0202661
$149$	23.2503	1.90474	0.952370	−	0.304944i	$-0.0986379\pi$
$149$	23.2503	1.90474	0.952370	+	0.304944i	$0.0986379\pi$
$150$	−1.75976	−0.143684
$151$	−18.0705	−1.47055	−0.735276	−	0.677768i	$-0.762948\pi$
$151$	−18.0705	−1.47055	−0.735276	+	0.677768i	$0.762948\pi$
$152$	6.64745	0.539179
$153$	−0.986447	−0.0797495
$154$	41.3131	3.32910
$155$	−18.4670	−1.48330
$156$	−0.252740	−0.0202354
$157$	−19.8113	−1.58112	−0.790558	−	0.612387i	$-0.790209\pi$
$157$	−19.8113	−1.58112	−0.790558	+	0.612387i	$0.790209\pi$
$158$	5.68277	0.452097
$159$	−9.08358	−0.720375
$160$	−0.772239	−0.0610509
$161$	−4.61826	−0.363970
$162$	1.39479	0.109585
$163$	−1.51109	−0.118358	−0.0591789	−	0.998247i	$-0.518848\pi$
$163$	−1.51109	−0.118358	−0.0591789	+	0.998247i	$0.518848\pi$
$164$	−0.512951	−0.0400548
$165$	16.0489	1.24941
$166$	−15.7735	−1.22426
$167$	−20.9485	−1.62104	−0.810522	−	0.585708i	$-0.800816\pi$
$167$	−20.9485	−1.62104	−0.810522	+	0.585708i	$0.800816\pi$
$168$	13.2345	1.02106
$169$	8.45063	0.650048
$170$	3.44292	0.264060
$171$	−2.31967	−0.177390
$172$	−0.00588583	−0.000448791 0
$173$	−14.7018	−1.11776	−0.558879	−	0.829249i	$-0.688768\pi$
$173$	−14.7018	−1.11776	−0.558879	+	0.829249i	$0.688768\pi$
$174$	−1.39479	−0.105739
$175$	5.82673	0.440460
$176$	−24.9353	−1.87957
$177$	−5.42942	−0.408100
$178$	4.56490	0.342153
$179$	22.2648	1.66415	0.832073	−	0.554666i	$-0.187154\pi$
$179$	22.2648	1.66415	0.832073	+	0.554666i	$0.187154\pi$
$180$	0.136552	0.0101780
$181$	−2.17485	−0.161655	−0.0808277	−	0.996728i	$-0.525756\pi$
$181$	−2.17485	−0.161655	−0.0808277	+	0.996728i	$0.525756\pi$
$182$	−29.8337	−2.21142
$183$	−7.43286	−0.549453
$184$	2.86569	0.211261
$185$	−11.3055	−0.831200
$186$	−10.2934	−0.754747
$187$	−6.32667	−0.462652
$188$	−0.0363431	−0.00265060
$189$	−4.61826	−0.335929
$190$	8.09616	0.587357
$191$	−2.72397	−0.197099	−0.0985497	−	0.995132i	$-0.531420\pi$
$191$	−2.72397	−0.197099	−0.0985497	+	0.995132i	$0.531420\pi$
$192$	−8.20621	−0.592232
$193$	18.5378	1.33438	0.667188	−	0.744889i	$-0.267498\pi$
$193$	18.5378	1.33438	0.667188	+	0.744889i	$0.267498\pi$
$194$	15.1478	1.08755
$195$	−11.5895	−0.829942
$196$	−0.781898	−0.0558499
$197$	−6.76449	−0.481950	−0.240975	−	0.970531i	$-0.577467\pi$
$197$	−6.76449	−0.481950	−0.240975	+	0.970531i	$0.577467\pi$
$198$	8.94559	0.635735
$199$	−0.0599479	−0.00424960	−0.00212480	−	0.999998i	$-0.500676\pi$
$199$	−0.0599479	−0.00424960	−0.00212480	+	0.999998i	$0.500676\pi$
$200$	−3.61556	−0.255658
$201$	10.1253	0.714181
$202$	2.66812	0.187728
$203$	4.61826	0.324139
$204$	−0.0538304	−0.00376888
$205$	−23.5216	−1.64282
$206$	2.31512	0.161302
$207$	−1.00000	−0.0695048
$208$	18.0067	1.24854
$209$	−14.8774	−1.02909
$210$	16.1188	1.11230
$211$	11.6932	0.804995	0.402497	−	0.915421i	$-0.368142\pi$
$211$	11.6932	0.804995	0.402497	+	0.915421i	$0.368142\pi$
$212$	−0.495691	−0.0340442
$213$	−10.8149	−0.741027
$214$	19.0220	1.30031
$215$	−0.269898	−0.0184069
$216$	2.86569	0.194985
$217$	34.0823	2.31366
$218$	−27.5354	−1.86494
$219$	1.36129	0.0919876
$220$	0.875790	0.0590458
$221$	4.56871	0.307325
$222$	−6.30164	−0.422939
$223$	12.3168	0.824792	0.412396	−	0.911005i	$-0.364692\pi$
$223$	12.3168	0.824792	0.412396	+	0.911005i	$0.364692\pi$
$224$	1.42523	0.0952273
$225$	1.26167	0.0841115
$226$	−14.1999	−0.944562
$227$	−19.3765	−1.28606	−0.643032	−	0.765839i	$-0.722324\pi$
$227$	−19.3765	−1.28606	−0.643032	+	0.765839i	$0.722324\pi$
$228$	−0.126584	−0.00838325
$229$	5.79473	0.382927	0.191463	−	0.981500i	$-0.438677\pi$
$229$	5.79473	0.382927	0.191463	+	0.981500i	$0.438677\pi$
$230$	3.49022	0.230138
$231$	−29.6196	−1.94883
$232$	−2.86569	−0.188142
$233$	0.575867	0.0377263	0.0188632	−	0.999822i	$-0.493995\pi$
$233$	0.575867	0.0377263	0.0188632	+	0.999822i	$0.493995\pi$
$234$	−6.45993	−0.422299
$235$	−1.66653	−0.108713
$236$	−0.296284	−0.0192864
$237$	−4.07429	−0.264654
$238$	−6.35419	−0.411881
$239$	4.15391	0.268694	0.134347	−	0.990934i	$-0.457106\pi$
$239$	4.15391	0.268694	0.134347	+	0.990934i	$0.457106\pi$
$240$	−9.72878	−0.627990
$241$	−22.6507	−1.45906	−0.729530	−	0.683948i	$-0.760261\pi$
$241$	−22.6507	−1.45906	−0.729530	+	0.683948i	$0.760261\pi$
$242$	42.0307	2.70183
$243$	−1.00000	−0.0641500
$244$	−0.405611	−0.0259666
$245$	−35.8543	−2.29065
$246$	−13.1108	−0.835916
$247$	10.7435	0.683593
$248$	−21.1485	−1.34293
$249$	11.3089	0.716671
$250$	13.0476	0.825202
$251$	−30.7066	−1.93818	−0.969092	−	0.246700i	$-0.920654\pi$
$251$	−30.7066	−1.93818	−0.969092	+	0.246700i	$0.920654\pi$
$252$	−0.252019	−0.0158757
$253$	−6.41359	−0.403219
$254$	4.36455	0.273856
$255$	−2.46842	−0.154578
$256$	−1.30870	−0.0817935
$257$	−3.85463	−0.240445	−0.120223	−	0.992747i	$-0.538361\pi$
$257$	−3.85463	−0.240445	−0.120223	+	0.992747i	$0.538361\pi$
$258$	−0.150439	−0.00936595
$259$	20.8653	1.29651
$260$	−0.632440	−0.0392222
$261$	1.00000	0.0618984
$262$	21.1079	1.30405
$263$	7.92826	0.488877	0.244439	−	0.969665i	$-0.421396\pi$
$263$	7.92826	0.488877	0.244439	+	0.969665i	$0.421396\pi$
$264$	18.3793	1.13117
$265$	−22.7301	−1.39630
$266$	−14.9421	−0.916161
$267$	−3.27283	−0.200294
$268$	0.552536	0.0337515
$269$	−1.86686	−0.113824	−0.0569122	−	0.998379i	$-0.518126\pi$
$269$	−1.86686	−0.113824	−0.0569122	+	0.998379i	$0.518126\pi$
$270$	3.49022	0.212408
$271$	−1.01209	−0.0614802	−0.0307401	−	0.999527i	$-0.509786\pi$
$271$	−1.01209	−0.0614802	−0.0307401	+	0.999527i	$0.509786\pi$
$272$	3.83519	0.232543
$273$	21.3894	1.29455
$274$	14.7697	0.892273
$275$	8.09184	0.487956
$276$	−0.0545700	−0.00328473
$277$	−12.2498	−0.736018	−0.368009	−	0.929822i	$-0.619960\pi$
$277$	−12.2498	−0.736018	−0.368009	+	0.929822i	$0.619960\pi$
$278$	−23.2192	−1.39259
$279$	7.37989	0.441823
$280$	33.1171	1.97913
$281$	7.33020	0.437283	0.218641	−	0.975805i	$-0.429837\pi$
$281$	7.33020	0.437283	0.218641	+	0.975805i	$0.429837\pi$
$282$	−0.928916	−0.0553161
$283$	−13.3292	−0.792341	−0.396171	−	0.918177i	$-0.629661\pi$
$283$	−13.3292	−0.792341	−0.396171	+	0.918177i	$0.629661\pi$
$284$	−0.590171	−0.0350202
$285$	−5.80459	−0.343834
$286$	−41.4313	−2.44989
$287$	43.4111	2.56248
$288$	0.308608	0.0181849
$289$	−16.0269	−0.942760
$290$	−3.49022	−0.204953
$291$	−10.8603	−0.636643
$292$	0.0742857	0.00434724
$293$	−21.2836	−1.24340	−0.621700	−	0.783255i	$-0.713558\pi$
$293$	−21.2836	−1.24340	−0.621700	+	0.783255i	$0.713558\pi$
$294$	−19.9850	−1.16555
$295$	−13.5862	−0.791021
$296$	−12.9472	−0.752539
$297$	−6.41359	−0.372154
$298$	32.4292	1.87858
$299$	4.63148	0.267846
$300$	0.0688494	0.00397502
$301$	0.498118	0.0287111
$302$	−25.2044	−1.45035
$303$	−1.91292	−0.109894
$304$	9.01860	0.517252
$305$	−18.5995	−1.06500
$306$	−1.37588	−0.0786540
$307$	1.14925	0.0655914	0.0327957	−	0.999462i	$-0.489559\pi$
$307$	1.14925	0.0655914	0.0327957	+	0.999462i	$0.489559\pi$
$308$	−1.61634	−0.0920997
$309$	−1.65984	−0.0944250
$310$	−25.7575	−1.46293
$311$	23.1570	1.31311	0.656557	−	0.754276i	$-0.272012\pi$
$311$	23.1570	1.31311	0.656557	+	0.754276i	$0.272012\pi$
$312$	−13.2724	−0.751400
$313$	−17.8633	−1.00970	−0.504848	−	0.863208i	$-0.668451\pi$
$313$	−17.8633	−1.00970	−0.504848	+	0.863208i	$0.668451\pi$
$314$	−27.6326	−1.55940
$315$	−11.5564	−0.651131
$316$	−0.222334	−0.0125073
$317$	−3.33290	−0.187194	−0.0935972	−	0.995610i	$-0.529837\pi$
$317$	−3.33290	−0.187194	−0.0935972	+	0.995610i	$0.529837\pi$
$318$	−12.6697	−0.710479
$319$	6.41359	0.359092
$320$	−20.5347	−1.14792
$321$	−13.6379	−0.761193
$322$	−6.44149	−0.358970
$323$	2.28823	0.127321
$324$	−0.0545700	−0.00303167
$325$	−5.84341	−0.324134
$326$	−2.10765	−0.116732
$327$	19.7417	1.09172
$328$	−26.9371	−1.48735
$329$	3.07572	0.169570
$330$	22.3848	1.23224
$331$	−29.0066	−1.59435	−0.797173	−	0.603751i	$-0.793672\pi$
$331$	−29.0066	−1.59435	−0.797173	+	0.603751i	$0.793672\pi$
$332$	0.617126	0.0338692
$333$	4.51800	0.247585
$334$	−29.2187	−1.59878
$335$	25.3368	1.38430
$336$	17.9553	0.979540
$337$	24.8722	1.35488	0.677438	−	0.735580i	$-0.263090\pi$
$337$	24.8722	1.35488	0.677438	+	0.735580i	$0.263090\pi$
$338$	11.7868	0.641119
$339$	10.1807	0.552938
$340$	−0.134702	−0.00730522
$341$	47.3316	2.56315
$342$	−3.23544	−0.174953
$343$	33.8443	1.82742
$344$	−0.309088	−0.0166649
$345$	−2.50233	−0.134721
$346$	−20.5059	−1.10240
$347$	24.8230	1.33257	0.666284	−	0.745698i	$-0.267884\pi$
$347$	24.8230	1.33257	0.666284	+	0.745698i	$0.267884\pi$
$348$	0.0545700	0.00292526
$349$	22.2572	1.19140	0.595701	−	0.803207i	$-0.296874\pi$
$349$	22.2572	1.19140	0.595701	+	0.803207i	$0.296874\pi$
$350$	8.12705	0.434409
$351$	4.63148	0.247210
$352$	1.97928	0.105496
$353$	1.24400	0.0662113	0.0331056	−	0.999452i	$-0.489460\pi$
$353$	1.24400	0.0662113	0.0331056	+	0.999452i	$0.489460\pi$
$354$	−7.57289	−0.402494
$355$	−27.0626	−1.43633
$356$	−0.178598	−0.00946568
$357$	4.55567	0.241112
$358$	31.0546	1.64129
$359$	30.0137	1.58406	0.792031	−	0.610481i	$-0.209024\pi$
$359$	30.0137	1.58406	0.792031	+	0.610481i	$0.209024\pi$
$360$	7.17090	0.377940
$361$	−13.6191	−0.716797
$362$	−3.03345	−0.159435
$363$	−30.1341	−1.58163
$364$	1.16722	0.0611789
$365$	3.40641	0.178299
$366$	−10.3672	−0.541905
$367$	3.80484	0.198611	0.0993055	−	0.995057i	$-0.468338\pi$
$367$	3.80484	0.198611	0.0993055	+	0.995057i	$0.468338\pi$
$368$	3.88788	0.202670
$369$	9.39988	0.489338
$370$	−15.7688	−0.819782
$371$	41.9504	2.17795
$372$	0.402721	0.0208801
$373$	12.2575	0.634670	0.317335	−	0.948313i	$-0.397212\pi$
$373$	12.2575	0.634670	0.317335	+	0.948313i	$0.397212\pi$
$374$	−8.82435	−0.456296
$375$	−9.35454	−0.483067
$376$	−1.90852	−0.0984245
$377$	−4.63148	−0.238533
$378$	−6.44149	−0.331315
$379$	−12.7959	−0.657280	−0.328640	−	0.944455i	$-0.606590\pi$
$379$	−12.7959	−0.657280	−0.328640	+	0.944455i	$0.606590\pi$
$380$	−0.316756	−0.0162493
$381$	−3.12919	−0.160313
$382$	−3.79935	−0.194392
$383$	−21.9083	−1.11946	−0.559730	−	0.828675i	$-0.689095\pi$
$383$	−21.9083	−1.11946	−0.559730	+	0.828675i	$0.689095\pi$
$384$	−10.8287	−0.552599
$385$	−74.1182	−3.77741
$386$	25.8562	1.31605
$387$	0.107858	0.00548275
$388$	−0.592647	−0.0300871
$389$	16.7327	0.848381	0.424191	−	0.905573i	$-0.360559\pi$
$389$	16.7327	0.848381	0.424191	+	0.905573i	$0.360559\pi$
$390$	−16.1649	−0.818541
$391$	0.986447	0.0498868
$392$	−41.0606	−2.07387
$393$	−15.1334	−0.763380
$394$	−9.43502	−0.475329
$395$	−10.1952	−0.512978
$396$	−0.349990	−0.0175876
$397$	−18.9814	−0.952650	−0.476325	−	0.879269i	$-0.658031\pi$
$397$	−18.9814	−0.952650	−0.476325	+	0.879269i	$0.658031\pi$
$398$	−0.0836146	−0.00419122
$399$	10.7128	0.536313
$400$	−4.90523	−0.245262
$401$	8.22424	0.410699	0.205349	−	0.978689i	$-0.434167\pi$
$401$	8.22424	0.410699	0.205349	+	0.978689i	$0.434167\pi$
$402$	14.1226	0.704370
$403$	−34.1798	−1.70262
$404$	−0.104388	−0.00519350
$405$	−2.50233	−0.124342
$406$	6.44149	0.319686
$407$	28.9766	1.43632
$408$	−2.82685	−0.139950
$409$	−25.9458	−1.28294	−0.641468	−	0.767150i	$-0.721674\pi$
$409$	−25.9458	−1.28294	−0.641468	+	0.767150i	$0.721674\pi$
$410$	−32.8077	−1.62025
$411$	−10.5892	−0.522329
$412$	−0.0905775	−0.00446243
$413$	25.0745	1.23384
$414$	−1.39479	−0.0685500
$415$	28.2986	1.38912
$416$	−1.42931	−0.0700777
$417$	16.6471	0.815212
$418$	−20.7508	−1.01495
$419$	14.0526	0.686516	0.343258	−	0.939241i	$-0.388469\pi$
$419$	14.0526	0.686516	0.343258	+	0.939241i	$0.388469\pi$
$420$	−0.630635	−0.0307718
$421$	18.6291	0.907926	0.453963	−	0.891021i	$-0.350010\pi$
$421$	18.6291	0.907926	0.453963	+	0.891021i	$0.350010\pi$
$422$	16.3096	0.793937
$423$	0.665991	0.0323816
$424$	−26.0307	−1.26416
$425$	−1.24457	−0.0603706
$426$	−15.0845	−0.730848
$427$	34.3269	1.66119
$428$	−0.744220	−0.0359732
$429$	29.7044	1.43414
$430$	−0.376450	−0.0181540
$431$	−24.2173	−1.16651	−0.583253	−	0.812291i	$-0.698220\pi$
$431$	−24.2173	−1.16651	−0.583253	+	0.812291i	$0.698220\pi$
$432$	3.88788	0.187056
$433$	24.2063	1.16328	0.581639	−	0.813447i	$-0.302412\pi$
$433$	24.2063	1.16328	0.581639	+	0.813447i	$0.302412\pi$
$434$	47.5375	2.28187
$435$	2.50233	0.119978
$436$	1.07730	0.0515935
$437$	2.31967	0.110965
$438$	1.89871	0.0907239
$439$	12.9554	0.618329	0.309165	−	0.951009i	$-0.399951\pi$
$439$	12.9554	0.618329	0.309165	+	0.951009i	$0.399951\pi$
$440$	45.9912	2.19255
$441$	14.3284	0.682303
$442$	6.37238	0.303103
$443$	−13.2017	−0.627234	−0.313617	−	0.949550i	$-0.601541\pi$
$443$	−13.2017	−0.627234	−0.313617	+	0.949550i	$0.601541\pi$
$444$	0.246547	0.0117006
$445$	−8.18970	−0.388229
$446$	17.1793	0.813462
$447$	−23.2503	−1.09970
$448$	37.8984	1.79053
$449$	25.9082	1.22269	0.611343	−	0.791366i	$-0.290630\pi$
$449$	25.9082	1.22269	0.611343	+	0.791366i	$0.290630\pi$
$450$	1.75976	0.0829560
$451$	60.2870	2.83880
$452$	0.555560	0.0261313
$453$	18.0705	0.849024
$454$	−27.0261	−1.26840
$455$	53.5234	2.50922
$456$	−6.64745	−0.311295
$457$	−21.7732	−1.01851	−0.509254	−	0.860616i	$-0.670078\pi$
$457$	−21.7732	−1.01851	−0.509254	+	0.860616i	$0.670078\pi$
$458$	8.08242	0.377667
$459$	0.986447	0.0460434
$460$	−0.136552	−0.00636679
$461$	11.2064	0.521934	0.260967	−	0.965348i	$-0.415959\pi$
$461$	11.2064	0.521934	0.260967	+	0.965348i	$0.415959\pi$
$462$	−41.3131	−1.92206
$463$	−12.2954	−0.571415	−0.285707	−	0.958317i	$-0.592229\pi$
$463$	−12.2954	−0.571415	−0.285707	+	0.958317i	$0.592229\pi$
$464$	−3.88788	−0.180490
$465$	18.4670	0.856384
$466$	0.803212	0.0372081
$467$	31.0609	1.43733	0.718663	−	0.695358i	$-0.244754\pi$
$467$	31.0609	1.43733	0.718663	+	0.695358i	$0.244754\pi$
$468$	0.252740	0.0116829
$469$	−46.7611	−2.15923
$470$	−2.32446	−0.107219
$471$	19.8113	0.912858
$472$	−15.5590	−0.716162
$473$	0.691759	0.0318071
$474$	−5.68277	−0.261018
$475$	−2.92666	−0.134284
$476$	0.248603	0.0113947
$477$	9.08358	0.415908
$478$	5.79382	0.265003
$479$	−31.7397	−1.45022	−0.725111	−	0.688632i	$-0.758212\pi$
$479$	−31.7397	−1.45022	−0.725111	+	0.688632i	$0.758212\pi$
$480$	0.772239	0.0352477
$481$	−20.9250	−0.954099
$482$	−31.5929	−1.43902
$483$	4.61826	0.210138
$484$	−1.64442	−0.0747463
$485$	−27.1761	−1.23400
$486$	−1.39479	−0.0632688
$487$	14.5756	0.660482	0.330241	−	0.943897i	$-0.392870\pi$
$487$	14.5756	0.660482	0.330241	+	0.943897i	$0.392870\pi$
$488$	−21.3002	−0.964217
$489$	1.51109	0.0683339
$490$	−50.0091	−2.25918
$491$	−9.94122	−0.448641	−0.224321	−	0.974515i	$-0.572016\pi$
$491$	−9.94122	−0.448641	−0.224321	+	0.974515i	$0.572016\pi$
$492$	0.512951	0.0231256
$493$	−0.986447	−0.0444273
$494$	14.9849	0.674203
$495$	−16.0489	−0.721346
$496$	−28.6922	−1.28832
$497$	49.9462	2.24039
$498$	15.7735	0.706827
$499$	−4.63611	−0.207541	−0.103770	−	0.994601i	$-0.533091\pi$
$499$	−4.63611	−0.207541	−0.103770	+	0.994601i	$0.533091\pi$
$500$	−0.510477	−0.0228292
$501$	20.9485	0.935910
$502$	−42.8292	−1.91156
$503$	7.14673	0.318657	0.159329	−	0.987226i	$-0.449067\pi$
$503$	7.14673	0.318657	0.159329	+	0.987226i	$0.449067\pi$
$504$	−13.2345	−0.589511
$505$	−4.78676	−0.213008
$506$	−8.94559	−0.397680
$507$	−8.45063	−0.375306
$508$	−0.170760	−0.00757625
$509$	38.5325	1.70792	0.853962	−	0.520336i	$-0.174193\pi$
$509$	38.5325	1.70792	0.853962	+	0.520336i	$0.174193\pi$
$510$	−3.44292	−0.152455
$511$	−6.28680	−0.278112
$512$	−23.4827	−1.03780
$513$	2.31967	0.102416
$514$	−5.37639	−0.237143
$515$	−4.15347	−0.183024
$516$	0.00588583	0.000259109 0
$517$	4.27139	0.187856
$518$	29.1027	1.27870
$519$	14.7018	0.645338
$520$	−33.2119	−1.45644
$521$	7.23574	0.317004	0.158502	−	0.987359i	$-0.449334\pi$
$521$	7.23574	0.317004	0.158502	+	0.987359i	$0.449334\pi$
$522$	1.39479	0.0610482
$523$	2.87399	0.125671	0.0628355	−	0.998024i	$-0.479986\pi$
$523$	2.87399	0.125671	0.0628355	+	0.998024i	$0.479986\pi$
$524$	−0.825830	−0.0360766
$525$	−5.82673	−0.254299
$526$	11.0582	0.482162
$527$	−7.27988	−0.317116
$528$	24.9353	1.08517
$529$	1.00000	0.0434783
$530$	−31.7037	−1.37712
$531$	5.42942	0.235617
$532$	0.584600	0.0253456
$533$	−43.5354	−1.88573
$534$	−4.56490	−0.197542
$535$	−34.1266	−1.47542
$536$	29.0158	1.25329
$537$	−22.2648	−0.960795
$538$	−2.60387	−0.112261
$539$	91.8962	3.95825
$540$	−0.136552	−0.00587628
$541$	−0.761604	−0.0327439	−0.0163720	−	0.999866i	$-0.505212\pi$
$541$	−0.761604	−0.0327439	−0.0163720	+	0.999866i	$0.505212\pi$
$542$	−1.41165	−0.0606356
$543$	2.17485	0.0933318
$544$	−0.304425	−0.0130521
$545$	49.4003	2.11608
$546$	29.8337	1.27676
$547$	−21.4518	−0.917211	−0.458606	−	0.888640i	$-0.651651\pi$
$547$	−21.4518	−0.917211	−0.458606	+	0.888640i	$0.651651\pi$
$548$	−0.577855	−0.0246848
$549$	7.43286	0.317227
$550$	11.2864	0.481254
$551$	−2.31967	−0.0988212
$552$	−2.86569	−0.121972
$553$	18.8162	0.800144
$554$	−17.0858	−0.725908
$555$	11.3055	0.479893
$556$	0.908433	0.0385261
$557$	9.40382	0.398452	0.199226	−	0.979954i	$-0.436157\pi$
$557$	9.40382	0.398452	0.199226	+	0.979954i	$0.436157\pi$
$558$	10.2934	0.435753
$559$	−0.499544	−0.0211285
$560$	44.9301	1.89864
$561$	6.32667	0.267112
$562$	10.2241	0.431276
$563$	−22.7588	−0.959170	−0.479585	−	0.877496i	$-0.659213\pi$
$563$	−22.7588	−0.959170	−0.479585	+	0.877496i	$0.659213\pi$
$564$	0.0363431	0.00153032
$565$	25.4754	1.07176
$566$	−18.5915	−0.781457
$567$	4.61826	0.193949
$568$	−30.9922	−1.30040
$569$	−29.8392	−1.25092	−0.625461	−	0.780255i	$-0.715089\pi$
$569$	−29.8392	−1.25092	−0.625461	+	0.780255i	$0.715089\pi$
$570$	−8.09616	−0.339111
$571$	−21.3918	−0.895220	−0.447610	−	0.894229i	$-0.647725\pi$
$571$	−21.3918	−0.895220	−0.447610	+	0.894229i	$0.647725\pi$
$572$	1.62097	0.0677762
$573$	2.72397	0.113795
$574$	60.5493	2.52728
$575$	−1.26167	−0.0526153
$576$	8.20621	0.341925
$577$	−12.4877	−0.519871	−0.259935	−	0.965626i	$-0.583701\pi$
$577$	−12.4877	−0.519871	−0.259935	+	0.965626i	$0.583701\pi$
$578$	−22.3541	−0.929810
$579$	−18.5378	−0.770403
$580$	0.136552	0.00567003
$581$	−52.2274	−2.16676
$582$	−15.1478	−0.627897
$583$	58.2583	2.41281
$584$	3.90104	0.161426
$585$	11.5895	0.479167
$586$	−29.6861	−1.22632
$587$	−22.4462	−0.926454	−0.463227	−	0.886240i	$-0.653309\pi$
$587$	−22.4462	−0.926454	−0.463227	+	0.886240i	$0.653309\pi$
$588$	0.781898	0.0322449
$589$	−17.1189	−0.705372
$590$	−18.9499	−0.780154
$591$	6.76449	0.278254
$592$	−17.5654	−0.721935
$593$	−18.2624	−0.749947	−0.374973	−	0.927036i	$-0.622348\pi$
$593$	−18.2624	−0.749947	−0.374973	+	0.927036i	$0.622348\pi$
$594$	−8.94559	−0.367042
$595$	11.3998	0.467347
$596$	−1.26877	−0.0519708
$597$	0.0599479	0.00245351
$598$	6.45993	0.264166
$599$	23.6299	0.965490	0.482745	−	0.875761i	$-0.339640\pi$
$599$	23.6299	0.965490	0.482745	+	0.875761i	$0.339640\pi$
$600$	3.61556	0.147604
$601$	−46.9123	−1.91359	−0.956797	−	0.290756i	$-0.906093\pi$
$601$	−46.9123	−1.91359	−0.956797	+	0.290756i	$0.906093\pi$
$602$	0.694769	0.0283167
$603$	−10.1253	−0.412333
$604$	0.986105	0.0401240
$605$	−75.4056	−3.06567
$606$	−2.66812	−0.108385
$607$	35.9639	1.45973	0.729864	−	0.683592i	$-0.239583\pi$
$607$	35.9639	1.45973	0.729864	+	0.683592i	$0.239583\pi$
$608$	−0.715867	−0.0290323
$609$	−4.61826	−0.187141
$610$	−25.9423	−1.05037
$611$	−3.08453	−0.124787
$612$	0.0538304	0.00217597
$613$	20.7712	0.838941	0.419470	−	0.907769i	$-0.362216\pi$
$613$	20.7712	0.838941	0.419470	+	0.907769i	$0.362216\pi$
$614$	1.60296	0.0646904
$615$	23.5216	0.948484
$616$	−84.8806	−3.41994
$617$	37.6453	1.51554	0.757772	−	0.652519i	$-0.226288\pi$
$617$	37.6453	1.51554	0.757772	+	0.652519i	$0.226288\pi$
$618$	−2.31512	−0.0931279
$619$	21.4753	0.863165	0.431583	−	0.902073i	$-0.357955\pi$
$619$	21.4753	0.863165	0.431583	+	0.902073i	$0.357955\pi$
$620$	1.00774	0.0404719
$621$	1.00000	0.0401286
$622$	32.2991	1.29508
$623$	15.1148	0.605561
$624$	−18.0067	−0.720843
$625$	−29.7165	−1.18866
$626$	−24.9156	−0.995826
$627$	14.8774	0.594146
$628$	1.08110	0.0431408
$629$	−4.45677	−0.177703
$630$	−16.1188	−0.642187
$631$	20.0076	0.796491	0.398245	−	0.917279i	$-0.369619\pi$
$631$	20.0076	0.796491	0.398245	+	0.917279i	$0.369619\pi$
$632$	−11.6756	−0.464432
$633$	−11.6932	−0.464764
$634$	−4.64869	−0.184623
$635$	−7.83028	−0.310735
$636$	0.495691	0.0196554
$637$	−66.3615	−2.62934
$638$	8.94559	0.354159
$639$	10.8149	0.427832
$640$	−27.0970	−1.07110
$641$	13.3358	0.526732	0.263366	−	0.964696i	$-0.415167\pi$
$641$	13.3358	0.526732	0.263366	+	0.964696i	$0.415167\pi$
$642$	−19.0220	−0.750737
$643$	46.7029	1.84178	0.920892	−	0.389819i	$-0.127462\pi$
$643$	46.7029	1.84178	0.920892	+	0.389819i	$0.127462\pi$
$644$	0.252019	0.00993093
$645$	0.269898	0.0106272
$646$	3.19159	0.125572
$647$	1.75480	0.0689882	0.0344941	−	0.999405i	$-0.489018\pi$
$647$	1.75480	0.0689882	0.0344941	+	0.999405i	$0.489018\pi$
$648$	−2.86569	−0.112575
$649$	34.8221	1.36689
$650$	−8.15031	−0.319682
$651$	−34.0823	−1.33579
$652$	0.0824602	0.00322939
$653$	−27.3833	−1.07159	−0.535796	−	0.844348i	$-0.679988\pi$
$653$	−27.3833	−1.07159	−0.535796	+	0.844348i	$0.679988\pi$
$654$	27.5354	1.07672
$655$	−37.8688	−1.47966
$656$	−36.5456	−1.42687
$657$	−1.36129	−0.0531090
$658$	4.28998	0.167241
$659$	−43.6629	−1.70087	−0.850433	−	0.526084i	$-0.823660\pi$
$659$	−43.6629	−1.70087	−0.850433	+	0.526084i	$0.823660\pi$
$660$	−0.875790	−0.0340901
$661$	31.1204	1.21044	0.605221	−	0.796058i	$-0.293085\pi$
$661$	31.1204	1.21044	0.605221	+	0.796058i	$0.293085\pi$
$662$	−40.4580	−1.57244
$663$	−4.56871	−0.177434
$664$	32.4077	1.25766
$665$	26.8071	1.03953
$666$	6.30164	0.244184
$667$	−1.00000	−0.0387202
$668$	1.14316	0.0442302
$669$	−12.3168	−0.476194
$670$	35.3394	1.36528
$671$	47.6713	1.84033
$672$	−1.42523	−0.0549795
$673$	17.5655	0.677099	0.338549	−	0.940949i	$-0.390064\pi$
$673$	17.5655	0.677099	0.338549	+	0.940949i	$0.390064\pi$
$674$	34.6914	1.33626
$675$	−1.26167	−0.0485618
$676$	−0.461151	−0.0177366
$677$	−45.3371	−1.74245	−0.871223	−	0.490887i	$-0.836673\pi$
$677$	−45.3371	−1.74245	−0.871223	+	0.490887i	$0.836673\pi$
$678$	14.1999	0.545343
$679$	50.1558	1.92480
$680$	−7.07372	−0.271265
$681$	19.3765	0.742509
$682$	66.0175	2.52794
$683$	−16.6077	−0.635475	−0.317738	−	0.948179i	$-0.602923\pi$
$683$	−16.6077	−0.635475	−0.317738	+	0.948179i	$0.602923\pi$
$684$	0.126584	0.00484007
$685$	−26.4978	−1.01243
$686$	47.2055	1.80232
$687$	−5.79473	−0.221083
$688$	−0.419341	−0.0159872
$689$	−42.0704	−1.60276
$690$	−3.49022	−0.132870
$691$	17.5575	0.667917	0.333959	−	0.942588i	$-0.391615\pi$
$691$	17.5575	0.667917	0.333959	+	0.942588i	$0.391615\pi$
$692$	0.802278	0.0304980
$693$	29.6196	1.12516
$694$	34.6228	1.31426
$695$	41.6566	1.58013
$696$	2.86569	0.108624
$697$	−9.27248	−0.351220
$698$	31.0441	1.17504
$699$	−0.575867	−0.0217813
$700$	−0.317965	−0.0120179
$701$	12.5055	0.472325	0.236162	−	0.971714i	$-0.424110\pi$
$701$	12.5055	0.472325	0.236162	+	0.971714i	$0.424110\pi$
$702$	6.45993	0.243814
$703$	−10.4803	−0.395271
$704$	52.6312	1.98361
$705$	1.66653	0.0627652
$706$	1.73511	0.0653018
$707$	8.83437	0.332251
$708$	0.296284	0.0111350
$709$	−36.5122	−1.37125	−0.685623	−	0.727957i	$-0.740470\pi$
$709$	−36.5122	−1.37125	−0.685623	+	0.727957i	$0.740470\pi$
$710$	−37.7465	−1.41660
$711$	4.07429	0.152798
$712$	−9.37890	−0.351489
$713$	−7.37989	−0.276379
$714$	6.35419	0.237800
$715$	74.3304	2.77980
$716$	−1.21499	−0.0454062
$717$	−4.15391	−0.155131
$718$	41.8627	1.56230
$719$	−27.1961	−1.01424	−0.507122	−	0.861874i	$-0.669291\pi$
$719$	−27.1961	−1.01424	−0.507122	+	0.861874i	$0.669291\pi$
$720$	9.72878	0.362570
$721$	7.66558	0.285481
$722$	−18.9958	−0.706950
$723$	22.6507	0.842389
$724$	0.118682	0.00441077
$725$	1.26167	0.0468573
$726$	−42.0307	−1.55990
$727$	0.266634	0.00988892	0.00494446	−	0.999988i	$-0.498426\pi$
$727$	0.266634	0.00988892	0.00494446	+	0.999988i	$0.498426\pi$
$728$	61.2953	2.27176
$729$	1.00000	0.0370370
$730$	4.75121	0.175850
$731$	−0.106397	−0.00393522
$732$	0.405611	0.0149918
$733$	−32.7767	−1.21063	−0.605317	−	0.795985i	$-0.706954\pi$
$733$	−32.7767	−1.21063	−0.605317	+	0.795985i	$0.706954\pi$
$734$	5.30694	0.195883
$735$	35.8543	1.32251
$736$	−0.308608	−0.0113754
$737$	−64.9393	−2.39207
$738$	13.1108	0.482616
$739$	−39.4205	−1.45011	−0.725053	−	0.688693i	$-0.758185\pi$
$739$	−39.4205	−1.45011	−0.725053	+	0.688693i	$0.758185\pi$
$740$	0.616943	0.0226793
$741$	−10.7435	−0.394673
$742$	58.5118	2.14804
$743$	35.0382	1.28543	0.642714	−	0.766107i	$-0.277809\pi$
$743$	35.0382	1.28543	0.642714	+	0.766107i	$0.277809\pi$
$744$	21.1485	0.775340
$745$	−58.1800	−2.13155
$746$	17.0966	0.625952
$747$	−11.3089	−0.413770
$748$	0.345246	0.0126235
$749$	62.9834	2.30136
$750$	−13.0476	−0.476431
$751$	−20.1565	−0.735523	−0.367761	−	0.929920i	$-0.619876\pi$
$751$	−20.1565	−0.735523	−0.367761	+	0.929920i	$0.619876\pi$
$752$	−2.58930	−0.0944219
$753$	30.7066	1.11901
$754$	−6.45993	−0.235257
$755$	45.2183	1.64566
$756$	0.252019	0.00916583
$757$	−35.0219	−1.27289	−0.636446	−	0.771321i	$-0.719596\pi$
$757$	−35.0219	−1.27289	−0.636446	+	0.771321i	$0.719596\pi$
$758$	−17.8475	−0.648251
$759$	6.41359	0.232798
$760$	−16.6341	−0.603383
$761$	7.20416	0.261151	0.130575	−	0.991438i	$-0.458318\pi$
$761$	7.20416	0.261151	0.130575	+	0.991438i	$0.458318\pi$
$762$	−4.36455	−0.158111
$763$	−91.1723	−3.30066
$764$	0.148647	0.00537786
$765$	2.46842	0.0892459
$766$	−30.5574	−1.10408
$767$	−25.1463	−0.907979
$768$	1.30870	0.0472235
$769$	26.2557	0.946806	0.473403	−	0.880846i	$-0.343025\pi$
$769$	26.2557	0.946806	0.473403	+	0.880846i	$0.343025\pi$
$770$	−103.379	−3.72552
$771$	3.85463	0.138821
$772$	−1.01161	−0.0364085
$773$	29.5688	1.06352	0.531758	−	0.846896i	$-0.321532\pi$
$773$	29.5688	1.06352	0.531758	+	0.846896i	$0.321532\pi$
$774$	0.150439	0.00540743
$775$	9.31100	0.334461
$776$	−31.1222	−1.11722
$777$	−20.8653	−0.748539
$778$	23.3385	0.836727
$779$	−21.8046	−0.781231
$780$	0.632440	0.0226450
$781$	69.3625	2.48199
$782$	1.37588	0.0492015
$783$	−1.00000	−0.0357371
$784$	−55.7070	−1.98953
$785$	49.5745	1.76939
$786$	−21.1079	−0.752893
$787$	−6.24715	−0.222687	−0.111343	−	0.993782i	$-0.535515\pi$
$787$	−6.24715	−0.222687	−0.111343	+	0.993782i	$0.535515\pi$
$788$	0.369138	0.0131500
$789$	−7.92826	−0.282254
$790$	−14.2202	−0.505931
$791$	−47.0170	−1.67173
$792$	−18.3793	−0.653081
$793$	−34.4251	−1.22247
$794$	−26.4750	−0.939563
$795$	22.7301	0.806155
$796$	0.00327136	0.000115950 0
$797$	40.4338	1.43224	0.716119	−	0.697978i	$-0.245917\pi$
$797$	40.4338	1.43224	0.716119	+	0.697978i	$0.245917\pi$
$798$	14.9421	0.528946
$799$	−0.656965	−0.0232418
$800$	0.389361	0.0137660
$801$	3.27283	0.115640
$802$	11.4711	0.405057
$803$	−8.73076	−0.308102
$804$	−0.552536	−0.0194864
$805$	11.5564	0.407311
$806$	−47.6736	−1.67923
$807$	1.86686	0.0657166
$808$	−5.48183	−0.192850
$809$	−54.6396	−1.92103	−0.960513	−	0.278237i	$-0.910250\pi$
$809$	−54.6396	−1.92103	−0.960513	+	0.278237i	$0.910250\pi$
$810$	−3.49022	−0.122634
$811$	−5.20954	−0.182932	−0.0914659	−	0.995808i	$-0.529155\pi$
$811$	−5.20954	−0.182932	−0.0914659	+	0.995808i	$0.529155\pi$
$812$	−0.252019	−0.00884412
$813$	1.01209	0.0354956
$814$	40.4162	1.41659
$815$	3.78125	0.132452
$816$	−3.83519	−0.134259
$817$	−0.250196	−0.00875324
$818$	−36.1888	−1.26531
$819$	−21.3894	−0.747406
$820$	1.28358	0.0448244
$821$	−48.3765	−1.68835	−0.844176	−	0.536066i	$-0.819910\pi$
$821$	−48.3765	−1.68835	−0.844176	+	0.536066i	$0.819910\pi$
$822$	−14.7697	−0.515154
$823$	−14.9775	−0.522083	−0.261042	−	0.965328i	$-0.584066\pi$
$823$	−14.9775	−0.522083	−0.261042	+	0.965328i	$0.584066\pi$
$824$	−4.75658	−0.165703
$825$	−8.09184	−0.281722
$826$	34.9736	1.21689
$827$	−34.3322	−1.19385	−0.596924	−	0.802298i	$-0.703610\pi$
$827$	−34.3322	−1.19385	−0.596924	+	0.802298i	$0.703610\pi$
$828$	0.0545700	0.00189644
$829$	−3.10314	−0.107777	−0.0538883	−	0.998547i	$-0.517161\pi$
$829$	−3.10314	−0.107777	−0.0538883	+	0.998547i	$0.517161\pi$
$830$	39.4705	1.37004
$831$	12.2498	0.424940
$832$	−38.0069	−1.31765
$833$	−14.1342	−0.489720
$834$	23.2192	0.804014
$835$	52.4201	1.81407
$836$	0.811860	0.0280788
$837$	−7.37989	−0.255086
$838$	19.6004	0.677085
$839$	−34.6315	−1.19561	−0.597807	−	0.801640i	$-0.703961\pi$
$839$	−34.6315	−1.19561	−0.597807	+	0.801640i	$0.703961\pi$
$840$	−33.1171	−1.14265
$841$	1.00000	0.0344828
$842$	25.9836	0.895454
$843$	−7.33020	−0.252465
$844$	−0.638099	−0.0219643
$845$	−21.1463	−0.727455
$846$	0.928916	0.0319368
$847$	139.167	4.78184
$848$	−35.3159	−1.21275
$849$	13.3292	0.457458
$850$	−1.73591	−0.0595413
$851$	−4.51800	−0.154875
$852$	0.590171	0.0202189
$853$	3.13665	0.107397	0.0536985	−	0.998557i	$-0.482899\pi$
$853$	3.13665	0.107397	0.0536985	+	0.998557i	$0.482899\pi$
$854$	47.8787	1.63837
$855$	5.80459	0.198513
$856$	−39.0819	−1.33579
$857$	22.7250	0.776272	0.388136	−	0.921602i	$-0.373119\pi$
$857$	22.7250	0.776272	0.388136	+	0.921602i	$0.373119\pi$
$858$	41.4313	1.41444
$859$	−38.9334	−1.32839	−0.664196	−	0.747559i	$-0.731226\pi$
$859$	−38.9334	−1.32839	−0.664196	+	0.747559i	$0.731226\pi$
$860$	0.0147283	0.000502231 0
$861$	−43.4111	−1.47945
$862$	−33.7780	−1.15048
$863$	8.80848	0.299844	0.149922	−	0.988698i	$-0.452098\pi$
$863$	8.80848	0.299844	0.149922	+	0.988698i	$0.452098\pi$
$864$	−0.308608	−0.0104990
$865$	36.7888	1.25086
$866$	33.7626	1.14730
$867$	16.0269	0.544303
$868$	−1.85987	−0.0631281
$869$	26.1308	0.886428
$870$	3.49022	0.118330
$871$	46.8950	1.58898
$872$	56.5735	1.91582
$873$	10.8603	0.367566
$874$	3.23544	0.109441
$875$	43.2017	1.46049
$876$	−0.0742857	−0.00250988
$877$	37.9186	1.28042	0.640211	−	0.768199i	$-0.278847\pi$
$877$	37.9186	1.28042	0.640211	+	0.768199i	$0.278847\pi$
$878$	18.0701	0.609835
$879$	21.2836	0.717877
$880$	62.3964	2.10338
$881$	39.8855	1.34378	0.671889	−	0.740652i	$-0.265483\pi$
$881$	39.8855	1.34378	0.671889	+	0.740652i	$0.265483\pi$
$882$	19.9850	0.672930
$883$	38.3760	1.29145	0.645727	−	0.763568i	$-0.276554\pi$
$883$	38.3760	1.29145	0.645727	+	0.763568i	$0.276554\pi$
$884$	−0.249315	−0.00838536
$885$	13.5862	0.456696
$886$	−18.4136	−0.618618
$887$	−37.1535	−1.24749	−0.623746	−	0.781627i	$-0.714390\pi$
$887$	−37.1535	−1.24749	−0.623746	+	0.781627i	$0.714390\pi$
$888$	12.9472	0.434479
$889$	14.4514	0.484685
$890$	−11.4229	−0.382896
$891$	6.41359	0.214863
$892$	−0.672126	−0.0225045
$893$	−1.54488	−0.0516974
$894$	−32.4292	−1.08460
$895$	−55.7139	−1.86231
$896$	50.0098	1.67071
$897$	−4.63148	−0.154641
$898$	36.1365	1.20589
$899$	7.37989	0.246133
$900$	−0.0688494	−0.00229498
$901$	−8.96047	−0.298517
$902$	84.0874	2.79981
$903$	−0.498118	−0.0165763
$904$	29.1746	0.970334
$905$	5.44220	0.180905
$906$	25.2044	0.837361
$907$	45.7862	1.52031	0.760154	−	0.649743i	$-0.225124\pi$
$907$	45.7862	1.52031	0.760154	+	0.649743i	$0.225124\pi$
$908$	1.05738	0.0350903
$909$	1.91292	0.0634476
$910$	74.6538	2.47475
$911$	−4.87510	−0.161519	−0.0807597	−	0.996734i	$-0.525735\pi$
$911$	−4.87510	−0.161519	−0.0807597	+	0.996734i	$0.525735\pi$
$912$	−9.01860	−0.298636
$913$	−72.5305	−2.40041
$914$	−30.3690	−1.00452
$915$	18.5995	0.614880
$916$	−0.316219	−0.0104482
$917$	69.8901	2.30797
$918$	1.37588	0.0454109
$919$	−51.1956	−1.68879	−0.844393	−	0.535724i	$-0.820039\pi$
$919$	−51.1956	−1.68879	−0.844393	+	0.535724i	$0.820039\pi$
$920$	−7.17090	−0.236418
$921$	−1.14925	−0.0378692
$922$	15.6305	0.514764
$923$	−50.0892	−1.64871
$924$	1.61634	0.0531738
$925$	5.70023	0.187422
$926$	−17.1494	−0.563565
$927$	1.65984	0.0545163
$928$	0.308608	0.0101305
$929$	−21.7566	−0.713811	−0.356905	−	0.934141i	$-0.616168\pi$
$929$	−21.7566	−0.713811	−0.356905	+	0.934141i	$0.616168\pi$
$930$	25.7575	0.844620
$931$	−33.2370	−1.08930
$932$	−0.0314251	−0.00102936
$933$	−23.1570	−0.758127
$934$	43.3233	1.41758
$935$	15.8314	0.517743
$936$	13.2724	0.433821
$937$	−50.8293	−1.66052	−0.830260	−	0.557376i	$-0.811808\pi$
$937$	−50.8293	−1.66052	−0.830260	+	0.557376i	$0.811808\pi$
$938$	−65.2218	−2.12957
$939$	17.8633	0.582948
$940$	0.0909427	0.00296622
$941$	−6.67920	−0.217736	−0.108868	−	0.994056i	$-0.534723\pi$
$941$	−6.67920	−0.217736	−0.108868	+	0.994056i	$0.534723\pi$
$942$	27.6326	0.900318
$943$	−9.39988	−0.306102
$944$	−21.1090	−0.687038
$945$	11.5564	0.375931
$946$	0.964857	0.0313702
$947$	−11.3759	−0.369669	−0.184834	−	0.982770i	$-0.559175\pi$
$947$	−11.3759	−0.369669	−0.184834	+	0.982770i	$0.559175\pi$
$948$	0.222334	0.00722108
$949$	6.30480	0.204662
$950$	−4.08207	−0.132440
$951$	3.33290	0.108077
$952$	13.0551	0.423119
$953$	52.7421	1.70848	0.854242	−	0.519876i	$-0.174022\pi$
$953$	52.7421	1.70848	0.854242	+	0.519876i	$0.174022\pi$
$954$	12.6697	0.410195
$955$	6.81627	0.220569
$956$	−0.226679	−0.00733132
$957$	−6.41359	−0.207322
$958$	−44.2700	−1.43030
$959$	48.9039	1.57919
$960$	20.5347	0.662753
$961$	23.4628	0.756866
$962$	−29.1860	−0.940993
$963$	13.6379	0.439475
$964$	1.23605	0.0398105
$965$	−46.3876	−1.49327
$966$	6.44149	0.207252
$967$	26.2173	0.843091	0.421545	−	0.906807i	$-0.361488\pi$
$967$	26.2173	0.843091	0.421545	+	0.906807i	$0.361488\pi$
$968$	−86.3549	−2.77555
$969$	−2.28823	−0.0735086
$970$	−37.9049	−1.21705
$971$	−33.1078	−1.06248	−0.531239	−	0.847222i	$-0.678273\pi$
$971$	−33.1078	−1.06248	−0.531239	+	0.847222i	$0.678273\pi$
$972$	0.0545700	0.00175033
$973$	−76.8807	−2.46468
$974$	20.3298	0.651409
$975$	5.84341	0.187139
$976$	−28.8981	−0.925005
$977$	24.2127	0.774632	0.387316	−	0.921947i	$-0.373402\pi$
$977$	24.2127	0.774632	0.387316	+	0.921947i	$0.373402\pi$
$978$	2.10765	0.0673952
$979$	20.9906	0.670861
$980$	1.95657	0.0625003
$981$	−19.7417	−0.630304
$982$	−13.8659	−0.442478
$983$	26.3114	0.839203	0.419601	−	0.907708i	$-0.362170\pi$
$983$	26.3114	0.839203	0.419601	+	0.907708i	$0.362170\pi$
$984$	26.9371	0.858724
$985$	16.9270	0.539339
$986$	−1.37588	−0.0438171
$987$	−3.07572	−0.0979013
$988$	−0.586273	−0.0186518
$989$	−0.107858	−0.00342970
$990$	−22.3848	−0.711437
$991$	44.4800	1.41295	0.706477	−	0.707736i	$-0.250284\pi$
$991$	44.4800	1.41295	0.706477	+	0.707736i	$0.250284\pi$
$992$	2.27749	0.0723104
$993$	29.0066	0.920496
$994$	69.6643	2.20962
$995$	0.150010	0.00475563
$996$	−0.617126	−0.0195544
$997$	−4.43615	−0.140494	−0.0702471	−	0.997530i	$-0.522379\pi$
$997$	−4.43615	−0.140494	−0.0702471	+	0.997530i	$0.522379\pi$
$998$	−6.46639	−0.204690
$999$	−4.51800	−0.142943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.k.1.7	✓	10
3.2	odd	2		6003.2.a.k.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.k.1.7	✓	10	1.1	even	1	trivial
6003.2.a.k.1.4		10	3.2	odd	2

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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q+1.39479 q^{2} -1.00000 q^{3} -0.0545700 q^{4} -2.50233 q^{5} -1.39479 q^{6} +4.61826 q^{7} -2.86569 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.39479 q^{2} -1.00000 q^{3} -0.0545700 q^{4} -2.50233 q^{5} -1.39479 q^{6} +4.61826 q^{7} -2.86569 q^{8} +1.00000 q^{9} -3.49022 q^{10} +6.41359 q^{11} +0.0545700 q^{12} -4.63148 q^{13} +6.44149 q^{14} +2.50233 q^{15} -3.88788 q^{16} -0.986447 q^{17} +1.39479 q^{18} -2.31967 q^{19} +0.136552 q^{20} -4.61826 q^{21} +8.94559 q^{22} -1.00000 q^{23} +2.86569 q^{24} +1.26167 q^{25} -6.45993 q^{26} -1.00000 q^{27} -0.252019 q^{28} +1.00000 q^{29} +3.49022 q^{30} +7.37989 q^{31} +0.308608 q^{32} -6.41359 q^{33} -1.37588 q^{34} -11.5564 q^{35} -0.0545700 q^{36} +4.51800 q^{37} -3.23544 q^{38} +4.63148 q^{39} +7.17090 q^{40} +9.39988 q^{41} -6.44149 q^{42} +0.107858 q^{43} -0.349990 q^{44} -2.50233 q^{45} -1.39479 q^{46} +0.665991 q^{47} +3.88788 q^{48} +14.3284 q^{49} +1.75976 q^{50} +0.986447 q^{51} +0.252740 q^{52} +9.08358 q^{53} -1.39479 q^{54} -16.0489 q^{55} -13.2345 q^{56} +2.31967 q^{57} +1.39479 q^{58} +5.42942 q^{59} -0.136552 q^{60} +7.43286 q^{61} +10.2934 q^{62} +4.61826 q^{63} +8.20621 q^{64} +11.5895 q^{65} -8.94559 q^{66} -10.1253 q^{67} +0.0538304 q^{68} +1.00000 q^{69} -16.1188 q^{70} +10.8149 q^{71} -2.86569 q^{72} -1.36129 q^{73} +6.30164 q^{74} -1.26167 q^{75} +0.126584 q^{76} +29.6196 q^{77} +6.45993 q^{78} +4.07429 q^{79} +9.72878 q^{80} +1.00000 q^{81} +13.1108 q^{82} -11.3089 q^{83} +0.252019 q^{84} +2.46842 q^{85} +0.150439 q^{86} -1.00000 q^{87} -18.3793 q^{88} +3.27283 q^{89} -3.49022 q^{90} -21.3894 q^{91} +0.0545700 q^{92} -7.37989 q^{93} +0.928916 q^{94} +5.80459 q^{95} -0.308608 q^{96} +10.8603 q^{97} +19.9850 q^{98} +6.41359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9} - 4 q^{10} + 9 q^{11} - 17 q^{12} - 16 q^{13} + 16 q^{14} - 6 q^{15} + 27 q^{16} + 3 q^{18} + q^{19} + 21 q^{20} - 3 q^{21} + 17 q^{22} - 10 q^{23} + 6 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{27} - 14 q^{28} + 10 q^{29} + 4 q^{30} + 17 q^{31} + 21 q^{32} - 9 q^{33} - 3 q^{34} + 29 q^{35} + 17 q^{36} + q^{37} + 32 q^{38} + 16 q^{39} + 13 q^{40} - 16 q^{42} - 5 q^{43} + 33 q^{44} + 6 q^{45} - 3 q^{46} + 15 q^{47} - 27 q^{48} + 31 q^{49} - 22 q^{50} - 21 q^{52} + 35 q^{53} - 3 q^{54} - 20 q^{55} + 18 q^{56} - q^{57} + 3 q^{58} + 49 q^{59} - 21 q^{60} + 8 q^{61} + 15 q^{62} + 3 q^{63} + 12 q^{64} - 3 q^{65} - 17 q^{66} + 35 q^{67} - 18 q^{68} + 10 q^{69} - 16 q^{70} + 30 q^{71} - 6 q^{72} - 15 q^{73} + 23 q^{74} + 4 q^{75} + 10 q^{76} + 23 q^{77} - 28 q^{78} + 24 q^{79} + 23 q^{80} + 10 q^{81} - 5 q^{82} + q^{83} + 14 q^{84} - 10 q^{86} - 10 q^{87} + 18 q^{88} + 15 q^{89} - 4 q^{90} + 26 q^{91} - 17 q^{92} - 17 q^{93} + 3 q^{94} + 7 q^{95} - 21 q^{96} - 35 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9 - 4 * q^10 + 9 * q^11 - 17 * q^12 - 16 * q^13 + 16 * q^14 - 6 * q^15 + 27 * q^16 + 3 * q^18 + q^19 + 21 * q^20 - 3 * q^21 + 17 * q^22 - 10 * q^23 + 6 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^27 - 14 * q^28 + 10 * q^29 + 4 * q^30 + 17 * q^31 + 21 * q^32 - 9 * q^33 - 3 * q^34 + 29 * q^35 + 17 * q^36 + q^37 + 32 * q^38 + 16 * q^39 + 13 * q^40 - 16 * q^42 - 5 * q^43 + 33 * q^44 + 6 * q^45 - 3 * q^46 + 15 * q^47 - 27 * q^48 + 31 * q^49 - 22 * q^50 - 21 * q^52 + 35 * q^53 - 3 * q^54 - 20 * q^55 + 18 * q^56 - q^57 + 3 * q^58 + 49 * q^59 - 21 * q^60 + 8 * q^61 + 15 * q^62 + 3 * q^63 + 12 * q^64 - 3 * q^65 - 17 * q^66 + 35 * q^67 - 18 * q^68 + 10 * q^69 - 16 * q^70 + 30 * q^71 - 6 * q^72 - 15 * q^73 + 23 * q^74 + 4 * q^75 + 10 * q^76 + 23 * q^77 - 28 * q^78 + 24 * q^79 + 23 * q^80 + 10 * q^81 - 5 * q^82 + q^83 + 14 * q^84 - 10 * q^86 - 10 * q^87 + 18 * q^88 + 15 * q^89 - 4 * q^90 + 26 * q^91 - 17 * q^92 - 17 * q^93 + 3 * q^94 + 7 * q^95 - 21 * q^96 - 35 * q^97 + 3 * q^98 + 9 * q^99

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