LMFDB - Embedded newform 2001.2.a.m.1.10

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:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 18 x^{12} + 34 x^{11} + 124 x^{10} - 216 x^{9} - 420 x^{8} + 647 x^{7} + 750 x^{6} + \cdots - 64 $ x^14 - 2x^13 - 18x^12 + 34x^11 + 124x^10 - 216x^9 - 420x^8 + 647x^7 + 750x^6 - 939x^5 - 717x^4 + 604x^3 + 352x^2 - 128*x - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.894954$ 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)

$f(q)$	$=$	$q+0.894954 q^{2} -1.00000 q^{3} -1.19906 q^{4} +0.474904 q^{5} -0.894954 q^{6} -1.99579 q^{7} -2.86301 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.894954 q^{2} -1.00000 q^{3} -1.19906 q^{4} +0.474904 q^{5} -0.894954 q^{6} -1.99579 q^{7} -2.86301 q^{8} +1.00000 q^{9} +0.425017 q^{10} +4.21327 q^{11} +1.19906 q^{12} +5.77436 q^{13} -1.78614 q^{14} -0.474904 q^{15} -0.164145 q^{16} -7.31225 q^{17} +0.894954 q^{18} -1.82925 q^{19} -0.569438 q^{20} +1.99579 q^{21} +3.77069 q^{22} -1.00000 q^{23} +2.86301 q^{24} -4.77447 q^{25} +5.16779 q^{26} -1.00000 q^{27} +2.39307 q^{28} -1.00000 q^{29} -0.425017 q^{30} -0.108189 q^{31} +5.57912 q^{32} -4.21327 q^{33} -6.54412 q^{34} -0.947812 q^{35} -1.19906 q^{36} +10.9983 q^{37} -1.63710 q^{38} -5.77436 q^{39} -1.35966 q^{40} -0.314460 q^{41} +1.78614 q^{42} -9.14999 q^{43} -5.05196 q^{44} +0.474904 q^{45} -0.894954 q^{46} +7.26676 q^{47} +0.164145 q^{48} -3.01680 q^{49} -4.27293 q^{50} +7.31225 q^{51} -6.92380 q^{52} -8.53731 q^{53} -0.894954 q^{54} +2.00090 q^{55} +5.71398 q^{56} +1.82925 q^{57} -0.894954 q^{58} -13.6287 q^{59} +0.569438 q^{60} +0.283563 q^{61} -0.0968242 q^{62} -1.99579 q^{63} +5.32134 q^{64} +2.74227 q^{65} -3.77069 q^{66} -13.9767 q^{67} +8.76781 q^{68} +1.00000 q^{69} -0.848248 q^{70} -0.728665 q^{71} -2.86301 q^{72} -1.79211 q^{73} +9.84300 q^{74} +4.77447 q^{75} +2.19338 q^{76} -8.40883 q^{77} -5.16779 q^{78} -13.8676 q^{79} -0.0779533 q^{80} +1.00000 q^{81} -0.281427 q^{82} -8.65060 q^{83} -2.39307 q^{84} -3.47262 q^{85} -8.18882 q^{86} +1.00000 q^{87} -12.0626 q^{88} -1.57598 q^{89} +0.425017 q^{90} -11.5244 q^{91} +1.19906 q^{92} +0.108189 q^{93} +6.50342 q^{94} -0.868720 q^{95} -5.57912 q^{96} -3.65623 q^{97} -2.69990 q^{98} +4.21327 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9} - 5 q^{10} - 12 q^{11} - 12 q^{12} + 13 q^{13} - 9 q^{14} + 3 q^{15} - 14 q^{17} - 2 q^{18} - 9 q^{19} - 2 q^{20} + 3 q^{21} - 9 q^{22} - 14 q^{23} + 6 q^{24} + 13 q^{25} - 16 q^{26} - 14 q^{27} + 3 q^{28} - 14 q^{29} + 5 q^{30} - 28 q^{31} - 4 q^{32} + 12 q^{33} + 14 q^{34} - 9 q^{35} + 12 q^{36} - 12 q^{37} + 2 q^{38} - 13 q^{39} - 20 q^{40} - 25 q^{41} + 9 q^{42} + 5 q^{43} - 37 q^{44} - 3 q^{45} + 2 q^{46} - 17 q^{47} + 17 q^{49} - 44 q^{50} + 14 q^{51} + 25 q^{52} - 17 q^{53} + 2 q^{54} + q^{55} - 54 q^{56} + 9 q^{57} + 2 q^{58} - 18 q^{59} + 2 q^{60} - 13 q^{61} - 8 q^{62} - 3 q^{63} + 20 q^{64} - 16 q^{65} + 9 q^{66} + 2 q^{67} - 19 q^{68} + 14 q^{69} + 14 q^{70} - 55 q^{71} - 6 q^{72} + 19 q^{73} + 4 q^{74} - 13 q^{75} - 32 q^{76} - 19 q^{77} + 16 q^{78} - 68 q^{79} - 2 q^{80} + 14 q^{81} - 12 q^{82} - 21 q^{83} - 3 q^{84} + 16 q^{85} - 22 q^{86} + 14 q^{87} - 25 q^{88} - 17 q^{89} - 5 q^{90} - 30 q^{91} - 12 q^{92} + 28 q^{93} + 16 q^{94} - 55 q^{95} + 4 q^{96} + 25 q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9 - 5 * q^10 - 12 * q^11 - 12 * q^12 + 13 * q^13 - 9 * q^14 + 3 * q^15 - 14 * q^17 - 2 * q^18 - 9 * q^19 - 2 * q^20 + 3 * q^21 - 9 * q^22 - 14 * q^23 + 6 * q^24 + 13 * q^25 - 16 * q^26 - 14 * q^27 + 3 * q^28 - 14 * q^29 + 5 * q^30 - 28 * q^31 - 4 * q^32 + 12 * q^33 + 14 * q^34 - 9 * q^35 + 12 * q^36 - 12 * q^37 + 2 * q^38 - 13 * q^39 - 20 * q^40 - 25 * q^41 + 9 * q^42 + 5 * q^43 - 37 * q^44 - 3 * q^45 + 2 * q^46 - 17 * q^47 + 17 * q^49 - 44 * q^50 + 14 * q^51 + 25 * q^52 - 17 * q^53 + 2 * q^54 + q^55 - 54 * q^56 + 9 * q^57 + 2 * q^58 - 18 * q^59 + 2 * q^60 - 13 * q^61 - 8 * q^62 - 3 * q^63 + 20 * q^64 - 16 * q^65 + 9 * q^66 + 2 * q^67 - 19 * q^68 + 14 * q^69 + 14 * q^70 - 55 * q^71 - 6 * q^72 + 19 * q^73 + 4 * q^74 - 13 * q^75 - 32 * q^76 - 19 * q^77 + 16 * q^78 - 68 * q^79 - 2 * q^80 + 14 * q^81 - 12 * q^82 - 21 * q^83 - 3 * q^84 + 16 * q^85 - 22 * q^86 + 14 * q^87 - 25 * q^88 - 17 * q^89 - 5 * q^90 - 30 * q^91 - 12 * q^92 + 28 * q^93 + 16 * q^94 - 55 * q^95 + 4 * q^96 + 25 * q^97 - 31 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.894954	0.632828	0.316414	−	0.948621i	$-0.397521\pi$
$2$	0.894954	0.632828	0.316414	+	0.948621i	$0.397521\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.19906	−0.599529
$5$	0.474904	0.212384	0.106192	−	0.994346i	$-0.466134\pi$
$5$	0.474904	0.212384	0.106192	+	0.994346i	$0.466134\pi$
$6$	−0.894954	−0.365363
$7$	−1.99579	−0.754339	−0.377170	−	0.926144i	$-0.623103\pi$
$7$	−1.99579	−0.754339	−0.377170	+	0.926144i	$0.623103\pi$
$8$	−2.86301	−1.01223
$9$	1.00000	0.333333
$10$	0.425017	0.134402
$11$	4.21327	1.27035	0.635175	−	0.772368i	$-0.280928\pi$
$11$	4.21327	1.27035	0.635175	+	0.772368i	$0.280928\pi$
$12$	1.19906	0.346138
$13$	5.77436	1.60152	0.800760	−	0.598985i	$-0.204429\pi$
$13$	5.77436	1.60152	0.800760	+	0.598985i	$0.204429\pi$
$14$	−1.78614	−0.477367
$15$	−0.474904	−0.122620
$16$	−0.164145	−0.0410363
$17$	−7.31225	−1.77348	−0.886740	−	0.462268i	$-0.847036\pi$
$17$	−7.31225	−1.77348	−0.886740	+	0.462268i	$0.847036\pi$
$18$	0.894954	0.210943
$19$	−1.82925	−0.419659	−0.209830	−	0.977738i	$-0.567291\pi$
$19$	−1.82925	−0.419659	−0.209830	+	0.977738i	$0.567291\pi$
$20$	−0.569438	−0.127330
$21$	1.99579	0.435518
$22$	3.77069	0.803913
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.86301	0.584409
$25$	−4.77447	−0.954893
$26$	5.16779	1.01349
$27$	−1.00000	−0.192450
$28$	2.39307	0.452248
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.425017	−0.0775972
$31$	−0.108189	−0.0194313	−0.00971567	−	0.999953i	$-0.503093\pi$
$31$	−0.108189	−0.0194313	−0.00971567	+	0.999953i	$0.503093\pi$
$32$	5.57912	0.986258
$33$	−4.21327	−0.733437
$34$	−6.54412	−1.12231
$35$	−0.947812	−0.160209
$36$	−1.19906	−0.199843
$37$	10.9983	1.80811	0.904057	−	0.427411i	$-0.140574\pi$
$37$	10.9983	1.80811	0.904057	+	0.427411i	$0.140574\pi$
$38$	−1.63710	−0.265572
$39$	−5.77436	−0.924638
$40$	−1.35966	−0.214980
$41$	−0.314460	−0.0491104	−0.0245552	−	0.999698i	$-0.507817\pi$
$41$	−0.314460	−0.0491104	−0.0245552	+	0.999698i	$0.507817\pi$
$42$	1.78614	0.275608
$43$	−9.14999	−1.39536	−0.697681	−	0.716409i	$-0.745784\pi$
$43$	−9.14999	−1.39536	−0.697681	+	0.716409i	$0.745784\pi$
$44$	−5.05196	−0.761611
$45$	0.474904	0.0707946
$46$	−0.894954	−0.131954
$47$	7.26676	1.05997	0.529983	−	0.848008i	$-0.322198\pi$
$47$	7.26676	1.05997	0.529983	+	0.848008i	$0.322198\pi$
$48$	0.164145	0.0236923
$49$	−3.01680	−0.430972
$50$	−4.27293	−0.604283
$51$	7.31225	1.02392
$52$	−6.92380	−0.960158
$53$	−8.53731	−1.17269	−0.586345	−	0.810062i	$-0.699434\pi$
$53$	−8.53731	−1.17269	−0.586345	+	0.810062i	$0.699434\pi$
$54$	−0.894954	−0.121788
$55$	2.00090	0.269802
$56$	5.71398	0.763562
$57$	1.82925	0.242290
$58$	−0.894954	−0.117513
$59$	−13.6287	−1.77431	−0.887155	−	0.461472i	$-0.847321\pi$
$59$	−13.6287	−1.77431	−0.887155	+	0.461472i	$0.847321\pi$
$60$	0.569438	0.0735141
$61$	0.283563	0.0363066	0.0181533	−	0.999835i	$-0.494221\pi$
$61$	0.283563	0.0363066	0.0181533	+	0.999835i	$0.494221\pi$
$62$	−0.0968242	−0.0122967
$63$	−1.99579	−0.251446
$64$	5.32134	0.665168
$65$	2.74227	0.340137
$66$	−3.77069	−0.464139
$67$	−13.9767	−1.70752	−0.853761	−	0.520665i	$-0.825684\pi$
$67$	−13.9767	−1.70752	−0.853761	+	0.520665i	$0.825684\pi$
$68$	8.76781	1.06325
$69$	1.00000	0.120386
$70$	−0.848248	−0.101385
$71$	−0.728665	−0.0864766	−0.0432383	−	0.999065i	$-0.513767\pi$
$71$	−0.728665	−0.0864766	−0.0432383	+	0.999065i	$0.513767\pi$
$72$	−2.86301	−0.337409
$73$	−1.79211	−0.209751	−0.104876	−	0.994485i	$-0.533444\pi$
$73$	−1.79211	−0.209751	−0.104876	+	0.994485i	$0.533444\pi$
$74$	9.84300	1.14423
$75$	4.77447	0.551308
$76$	2.19338	0.251598
$77$	−8.40883	−0.958275
$78$	−5.16779	−0.585137
$79$	−13.8676	−1.56022	−0.780111	−	0.625641i	$-0.784837\pi$
$79$	−13.8676	−1.56022	−0.780111	+	0.625641i	$0.784837\pi$
$80$	−0.0779533	−0.00871545
$81$	1.00000	0.111111
$82$	−0.281427	−0.0310784
$83$	−8.65060	−0.949527	−0.474763	−	0.880114i	$-0.657466\pi$
$83$	−8.65060	−0.949527	−0.474763	+	0.880114i	$0.657466\pi$
$84$	−2.39307	−0.261106
$85$	−3.47262	−0.376658
$86$	−8.18882	−0.883023
$87$	1.00000	0.107211
$88$	−12.0626	−1.28588
$89$	−1.57598	−0.167054	−0.0835270	−	0.996506i	$-0.526618\pi$
$89$	−1.57598	−0.167054	−0.0835270	+	0.996506i	$0.526618\pi$
$90$	0.425017	0.0448008
$91$	−11.5244	−1.20809
$92$	1.19906	0.125010
$93$	0.108189	0.0112187
$94$	6.50342	0.670776
$95$	−0.868720	−0.0891288
$96$	−5.57912	−0.569416
$97$	−3.65623	−0.371234	−0.185617	−	0.982622i	$-0.559428\pi$
$97$	−3.65623	−0.371234	−0.185617	+	0.982622i	$0.559428\pi$
$98$	−2.69990	−0.272731
$99$	4.21327	0.423450
$100$	5.72486	0.572486
$101$	−3.45224	−0.343511	−0.171755	−	0.985140i	$-0.554944\pi$
$101$	−3.45224	−0.343511	−0.171755	+	0.985140i	$0.554944\pi$
$102$	6.54412	0.647965
$103$	−6.03689	−0.594833	−0.297416	−	0.954748i	$-0.596125\pi$
$103$	−6.03689	−0.594833	−0.297416	+	0.954748i	$0.596125\pi$
$104$	−16.5321	−1.62110
$105$	0.947812	0.0924969
$106$	−7.64050	−0.742111
$107$	16.2660	1.57249	0.786246	−	0.617914i	$-0.212022\pi$
$107$	16.2660	1.57249	0.786246	+	0.617914i	$0.212022\pi$
$108$	1.19906	0.115379
$109$	−17.6889	−1.69428	−0.847142	−	0.531366i	$-0.821679\pi$
$109$	−17.6889	−1.69428	−0.847142	+	0.531366i	$0.821679\pi$
$110$	1.79072	0.170738
$111$	−10.9983	−1.04392
$112$	0.327600	0.0309553
$113$	−5.80082	−0.545695	−0.272848	−	0.962057i	$-0.587965\pi$
$113$	−5.80082	−0.545695	−0.272848	+	0.962057i	$0.587965\pi$
$114$	1.63710	0.153328
$115$	−0.474904	−0.0442851
$116$	1.19906	0.111330
$117$	5.77436	0.533840
$118$	−12.1971	−1.12283
$119$	14.5937	1.33781
$120$	1.35966	0.124119
$121$	6.75168	0.613789
$122$	0.253776	0.0229758
$123$	0.314460	0.0283539
$124$	0.129725	0.0116496
$125$	−4.64194	−0.415187
$126$	−1.78614	−0.159122
$127$	4.00908	0.355748	0.177874	−	0.984053i	$-0.443078\pi$
$127$	4.00908	0.355748	0.177874	+	0.984053i	$0.443078\pi$
$128$	−6.39588	−0.565321
$129$	9.14999	0.805612
$130$	2.45421	0.215248
$131$	−16.7123	−1.46016	−0.730079	−	0.683363i	$-0.760517\pi$
$131$	−16.7123	−1.46016	−0.730079	+	0.683363i	$0.760517\pi$
$132$	5.05196	0.439717
$133$	3.65081	0.316565
$134$	−12.5085	−1.08057
$135$	−0.474904	−0.0408733
$136$	20.9350	1.79516
$137$	−7.13547	−0.609624	−0.304812	−	0.952413i	$-0.598594\pi$
$137$	−7.13547	−0.609624	−0.304812	+	0.952413i	$0.598594\pi$
$138$	0.894954	0.0761835
$139$	−1.14377	−0.0970136	−0.0485068	−	0.998823i	$-0.515446\pi$
$139$	−1.14377	−0.0970136	−0.0485068	+	0.998823i	$0.515446\pi$
$140$	1.13648	0.0960501
$141$	−7.26676	−0.611972
$142$	−0.652121	−0.0547248
$143$	24.3290	2.03449
$144$	−0.164145	−0.0136788
$145$	−0.474904	−0.0394387
$146$	−1.60386	−0.132736
$147$	3.01680	0.248822
$148$	−13.1876	−1.08402
$149$	5.96369	0.488565	0.244282	−	0.969704i	$-0.421448\pi$
$149$	5.96369	0.488565	0.244282	+	0.969704i	$0.421448\pi$
$150$	4.27293	0.348883
$151$	11.2886	0.918651	0.459326	−	0.888268i	$-0.348091\pi$
$151$	11.2886	0.918651	0.459326	+	0.888268i	$0.348091\pi$
$152$	5.23717	0.424790
$153$	−7.31225	−0.591160
$154$	−7.52551	−0.606423
$155$	−0.0513795	−0.00412690
$156$	6.92380	0.554347
$157$	10.8902	0.869130	0.434565	−	0.900641i	$-0.356902\pi$
$157$	10.8902	0.869130	0.434565	+	0.900641i	$0.356902\pi$
$158$	−12.4108	−0.987352
$159$	8.53731	0.677053
$160$	2.64955	0.209465
$161$	1.99579	0.157291
$162$	0.894954	0.0703142
$163$	15.1857	1.18943	0.594717	−	0.803935i	$-0.297264\pi$
$163$	15.1857	1.18943	0.594717	+	0.803935i	$0.297264\pi$
$164$	0.377055	0.0294431
$165$	−2.00090	−0.155770
$166$	−7.74189	−0.600887
$167$	7.84448	0.607024	0.303512	−	0.952828i	$-0.401841\pi$
$167$	7.84448	0.607024	0.303512	+	0.952828i	$0.401841\pi$
$168$	−5.71398	−0.440843
$169$	20.3433	1.56487
$170$	−3.10783	−0.238360
$171$	−1.82925	−0.139886
$172$	10.9714	0.836559
$173$	22.7107	1.72666	0.863331	−	0.504638i	$-0.168374\pi$
$173$	22.7107	1.72666	0.863331	+	0.504638i	$0.168374\pi$
$174$	0.894954	0.0678463
$175$	9.52885	0.720314
$176$	−0.691589	−0.0521305
$177$	13.6287	1.02440
$178$	−1.41043	−0.105716
$179$	−17.9552	−1.34204	−0.671019	−	0.741440i	$-0.734143\pi$
$179$	−17.9552	−1.34204	−0.671019	+	0.741440i	$0.734143\pi$
$180$	−0.569438	−0.0424434
$181$	20.7321	1.54101	0.770503	−	0.637437i	$-0.220005\pi$
$181$	20.7321	1.54101	0.770503	+	0.637437i	$0.220005\pi$
$182$	−10.3138	−0.764513
$183$	−0.283563	−0.0209616
$184$	2.86301	0.211064
$185$	5.22316	0.384014
$186$	0.0968242	0.00709950
$187$	−30.8085	−2.25294
$188$	−8.71327	−0.635480
$189$	1.99579	0.145173
$190$	−0.777464	−0.0564032
$191$	−1.02970	−0.0745063	−0.0372531	−	0.999306i	$-0.511861\pi$
$191$	−1.02970	−0.0745063	−0.0372531	+	0.999306i	$0.511861\pi$
$192$	−5.32134	−0.384035
$193$	21.8114	1.57002	0.785008	−	0.619485i	$-0.212659\pi$
$193$	21.8114	1.57002	0.785008	+	0.619485i	$0.212659\pi$
$194$	−3.27216	−0.234927
$195$	−2.74227	−0.196378
$196$	3.61732	0.258380
$197$	0.418534	0.0298193	0.0149096	−	0.999889i	$-0.495254\pi$
$197$	0.418534	0.0298193	0.0149096	+	0.999889i	$0.495254\pi$
$198$	3.77069	0.267971
$199$	18.2933	1.29678	0.648388	−	0.761310i	$-0.275443\pi$
$199$	18.2933	1.29678	0.648388	+	0.761310i	$0.275443\pi$
$200$	13.6693	0.966568
$201$	13.9767	0.985838
$202$	−3.08959	−0.217383
$203$	1.99579	0.140077
$204$	−8.76781	−0.613869
$205$	−0.149338	−0.0104302
$206$	−5.40274	−0.376427
$207$	−1.00000	−0.0695048
$208$	−0.947835	−0.0657205
$209$	−7.70714	−0.533114
$210$	0.848248	0.0585346
$211$	−18.8816	−1.29986	−0.649930	−	0.759994i	$-0.725202\pi$
$211$	−18.8816	−1.29986	−0.649930	+	0.759994i	$0.725202\pi$
$212$	10.2367	0.703061
$213$	0.728665	0.0499273
$214$	14.5573	0.995117
$215$	−4.34537	−0.296352
$216$	2.86301	0.194803
$217$	0.215923	0.0146578
$218$	−15.8307	−1.07219
$219$	1.79211	0.121100
$220$	−2.39920	−0.161754
$221$	−42.2236	−2.84027
$222$	−9.84300	−0.660619
$223$	9.85174	0.659722	0.329861	−	0.944030i	$-0.392998\pi$
$223$	9.85174	0.659722	0.329861	+	0.944030i	$0.392998\pi$
$224$	−11.1348	−0.743973
$225$	−4.77447	−0.318298
$226$	−5.19147	−0.345331
$227$	−10.7086	−0.710756	−0.355378	−	0.934723i	$-0.615648\pi$
$227$	−10.7086	−0.710756	−0.355378	+	0.934723i	$0.615648\pi$
$228$	−2.19338	−0.145260
$229$	−19.9167	−1.31613	−0.658067	−	0.752959i	$-0.728626\pi$
$229$	−19.9167	−1.31613	−0.658067	+	0.752959i	$0.728626\pi$
$230$	−0.425017	−0.0280248
$231$	8.40883	0.553260
$232$	2.86301	0.187966
$233$	−18.7066	−1.22551	−0.612755	−	0.790273i	$-0.709939\pi$
$233$	−18.7066	−1.22551	−0.612755	+	0.790273i	$0.709939\pi$
$234$	5.16779	0.337829
$235$	3.45102	0.225120
$236$	16.3416	1.06375
$237$	13.8676	0.900794
$238$	13.0607	0.846601
$239$	10.1460	0.656287	0.328144	−	0.944628i	$-0.393577\pi$
$239$	10.1460	0.656287	0.328144	+	0.944628i	$0.393577\pi$
$240$	0.0779533	0.00503187
$241$	21.3326	1.37415	0.687077	−	0.726585i	$-0.258894\pi$
$241$	21.3326	1.37415	0.687077	+	0.726585i	$0.258894\pi$
$242$	6.04244	0.388423
$243$	−1.00000	−0.0641500
$244$	−0.340009	−0.0217668
$245$	−1.43269	−0.0915315
$246$	0.281427	0.0179431
$247$	−10.5628	−0.672093
$248$	0.309746	0.0196689
$249$	8.65060	0.548209
$250$	−4.15432	−0.262742
$251$	2.32556	0.146788	0.0733941	−	0.997303i	$-0.476617\pi$
$251$	2.32556	0.146788	0.0733941	+	0.997303i	$0.476617\pi$
$252$	2.39307	0.150749
$253$	−4.21327	−0.264886
$254$	3.58794	0.225128
$255$	3.47262	0.217464
$256$	−16.3667	−1.02292
$257$	−0.749025	−0.0467229	−0.0233614	−	0.999727i	$-0.507437\pi$
$257$	−0.749025	−0.0467229	−0.0233614	+	0.999727i	$0.507437\pi$
$258$	8.18882	0.509814
$259$	−21.9504	−1.36393
$260$	−3.28814	−0.203922
$261$	−1.00000	−0.0618984
$262$	−14.9567	−0.924029
$263$	−21.6925	−1.33761	−0.668807	−	0.743436i	$-0.733195\pi$
$263$	−21.6925	−1.33761	−0.668807	+	0.743436i	$0.733195\pi$
$264$	12.0626	0.742404
$265$	−4.05440	−0.249060
$266$	3.26731	0.200331
$267$	1.57598	0.0964487
$268$	16.7588	1.02371
$269$	−5.65243	−0.344635	−0.172317	−	0.985041i	$-0.555125\pi$
$269$	−5.65243	−0.344635	−0.172317	+	0.985041i	$0.555125\pi$
$270$	−0.425017	−0.0258657
$271$	−20.8246	−1.26500	−0.632502	−	0.774559i	$-0.717972\pi$
$271$	−20.8246	−1.26500	−0.632502	+	0.774559i	$0.717972\pi$
$272$	1.20027	0.0727772
$273$	11.5244	0.697491
$274$	−6.38591	−0.385787
$275$	−20.1161	−1.21305
$276$	−1.19906	−0.0721748
$277$	−3.70261	−0.222468	−0.111234	−	0.993794i	$-0.535480\pi$
$277$	−3.70261	−0.222468	−0.111234	+	0.993794i	$0.535480\pi$
$278$	−1.02362	−0.0613929
$279$	−0.108189	−0.00647711
$280$	2.71359	0.162168
$281$	−14.8399	−0.885272	−0.442636	−	0.896701i	$-0.645957\pi$
$281$	−14.8399	−0.885272	−0.442636	+	0.896701i	$0.645957\pi$
$282$	−6.50342	−0.387273
$283$	−18.7147	−1.11248	−0.556238	−	0.831023i	$-0.687756\pi$
$283$	−18.7147	−1.11248	−0.556238	+	0.831023i	$0.687756\pi$
$284$	0.873711	0.0518452
$285$	0.868720	0.0514585
$286$	21.7733	1.28748
$287$	0.627597	0.0370459
$288$	5.57912	0.328753
$289$	36.4690	2.14523
$290$	−0.425017	−0.0249579
$291$	3.65623	0.214332
$292$	2.14885	0.125752
$293$	32.2409	1.88353	0.941767	−	0.336265i	$-0.109164\pi$
$293$	32.2409	1.88353	0.941767	+	0.336265i	$0.109164\pi$
$294$	2.69990	0.157461
$295$	−6.47234	−0.376834
$296$	−31.4883	−1.83022
$297$	−4.21327	−0.244479
$298$	5.33723	0.309177
$299$	−5.77436	−0.333940
$300$	−5.72486	−0.330525
$301$	18.2615	1.05258
$302$	10.1028	0.581348
$303$	3.45224	0.198326
$304$	0.300263	0.0172213
$305$	0.134665	0.00771092
$306$	−6.54412	−0.374103
$307$	−13.1519	−0.750618	−0.375309	−	0.926900i	$-0.622463\pi$
$307$	−13.1519	−0.750618	−0.375309	+	0.926900i	$0.622463\pi$
$308$	10.0827	0.574514
$309$	6.03689	0.343427
$310$	−0.0459823	−0.00261162
$311$	−26.9063	−1.52572	−0.762859	−	0.646564i	$-0.776205\pi$
$311$	−26.9063	−1.52572	−0.762859	+	0.646564i	$0.776205\pi$
$312$	16.5321	0.935943
$313$	−5.97393	−0.337667	−0.168833	−	0.985645i	$-0.554000\pi$
$313$	−5.97393	−0.337667	−0.168833	+	0.985645i	$0.554000\pi$
$314$	9.74619	0.550009
$315$	−0.947812	−0.0534031
$316$	16.6280	0.935398
$317$	26.3200	1.47828	0.739140	−	0.673552i	$-0.235232\pi$
$317$	26.3200	1.47828	0.739140	+	0.673552i	$0.235232\pi$
$318$	7.64050	0.428458
$319$	−4.21327	−0.235898
$320$	2.52713	0.141271
$321$	−16.2660	−0.907878
$322$	1.78614	0.0995379
$323$	13.3759	0.744258
$324$	−1.19906	−0.0666143
$325$	−27.5695	−1.52928
$326$	13.5905	0.752707
$327$	17.6889	0.978196
$328$	0.900301	0.0497108
$329$	−14.5030	−0.799574
$330$	−1.79072	−0.0985756
$331$	7.51683	0.413162	0.206581	−	0.978429i	$-0.433766\pi$
$331$	7.51683	0.413162	0.206581	+	0.978429i	$0.433766\pi$
$332$	10.3726	0.569269
$333$	10.9983	0.602705
$334$	7.02044	0.384142
$335$	−6.63758	−0.362650
$336$	−0.327600	−0.0178721
$337$	31.6701	1.72518	0.862590	−	0.505904i	$-0.168841\pi$
$337$	31.6701	1.72518	0.862590	+	0.505904i	$0.168841\pi$
$338$	18.2063	0.990292
$339$	5.80082	0.315057
$340$	4.16387	0.225818
$341$	−0.455830	−0.0246846
$342$	−1.63710	−0.0885240
$343$	19.9915	1.07944
$344$	26.1965	1.41242
$345$	0.474904	0.0255680
$346$	20.3250	1.09268
$347$	12.4921	0.670612	0.335306	−	0.942109i	$-0.391160\pi$
$347$	12.4921	0.670612	0.335306	+	0.942109i	$0.391160\pi$
$348$	−1.19906	−0.0642762
$349$	35.3247	1.89089	0.945444	−	0.325784i	$-0.105628\pi$
$349$	35.3247	1.89089	0.945444	+	0.325784i	$0.105628\pi$
$350$	8.52788	0.455834
$351$	−5.77436	−0.308213
$352$	23.5063	1.25289
$353$	−13.0353	−0.693798	−0.346899	−	0.937903i	$-0.612765\pi$
$353$	−13.0353	−0.693798	−0.346899	+	0.937903i	$0.612765\pi$
$354$	12.1971	0.648268
$355$	−0.346046	−0.0183662
$356$	1.88970	0.100154
$357$	−14.5937	−0.772383
$358$	−16.0691	−0.849279
$359$	−17.7976	−0.939322	−0.469661	−	0.882847i	$-0.655624\pi$
$359$	−17.7976	−0.939322	−0.469661	+	0.882847i	$0.655624\pi$
$360$	−1.35966	−0.0716601
$361$	−15.6538	−0.823886
$362$	18.5543	0.975191
$363$	−6.75168	−0.354371
$364$	13.8185	0.724285
$365$	−0.851083	−0.0445477
$366$	−0.253776	−0.0132651
$367$	28.2055	1.47231	0.736157	−	0.676811i	$-0.236639\pi$
$367$	28.2055	1.47231	0.736157	+	0.676811i	$0.236639\pi$
$368$	0.164145	0.00855667
$369$	−0.314460	−0.0163701
$370$	4.67448	0.243015
$371$	17.0387	0.884606
$372$	−0.129725	−0.00672593
$373$	3.04203	0.157510	0.0787552	−	0.996894i	$-0.474905\pi$
$373$	3.04203	0.157510	0.0787552	+	0.996894i	$0.474905\pi$
$374$	−27.5722	−1.42572
$375$	4.64194	0.239709
$376$	−20.8048	−1.07293
$377$	−5.77436	−0.297395
$378$	1.78614	0.0918693
$379$	−16.5577	−0.850511	−0.425255	−	0.905073i	$-0.639816\pi$
$379$	−16.5577	−0.850511	−0.425255	+	0.905073i	$0.639816\pi$
$380$	1.04165	0.0534353
$381$	−4.00908	−0.205391
$382$	−0.921531	−0.0471497
$383$	10.9654	0.560305	0.280153	−	0.959955i	$-0.409615\pi$
$383$	10.9654	0.560305	0.280153	+	0.959955i	$0.409615\pi$
$384$	6.39588	0.326388
$385$	−3.99339	−0.203522
$386$	19.5202	0.993550
$387$	−9.14999	−0.465120
$388$	4.38404	0.222566
$389$	−8.65746	−0.438951	−0.219475	−	0.975618i	$-0.570435\pi$
$389$	−8.65746	−0.438951	−0.219475	+	0.975618i	$0.570435\pi$
$390$	−2.45421	−0.124274
$391$	7.31225	0.369796
$392$	8.63714	0.436241
$393$	16.7123	0.843023
$394$	0.374568	0.0188705
$395$	−6.58576	−0.331366
$396$	−5.05196	−0.253870
$397$	−14.9378	−0.749705	−0.374853	−	0.927084i	$-0.622307\pi$
$397$	−14.9378	−0.749705	−0.374853	+	0.927084i	$0.622307\pi$
$398$	16.3716	0.820636
$399$	−3.65081	−0.182769
$400$	0.783706	0.0391853
$401$	−4.02676	−0.201087	−0.100543	−	0.994933i	$-0.532058\pi$
$401$	−4.02676	−0.201087	−0.100543	+	0.994933i	$0.532058\pi$
$402$	12.5085	0.623866
$403$	−0.624723	−0.0311197
$404$	4.13943	0.205945
$405$	0.474904	0.0235982
$406$	1.78614	0.0886448
$407$	46.3390	2.29694
$408$	−20.9350	−1.03644
$409$	−0.983912	−0.0486513	−0.0243257	−	0.999704i	$-0.507744\pi$
$409$	−0.983912	−0.0486513	−0.0243257	+	0.999704i	$0.507744\pi$
$410$	−0.133651	−0.00660055
$411$	7.13547	0.351967
$412$	7.23858	0.356619
$413$	27.2001	1.33843
$414$	−0.894954	−0.0439846
$415$	−4.10821	−0.201664
$416$	32.2158	1.57951
$417$	1.14377	0.0560108
$418$	−6.89754	−0.337370
$419$	−5.17889	−0.253005	−0.126503	−	0.991966i	$-0.540375\pi$
$419$	−5.17889	−0.253005	−0.126503	+	0.991966i	$0.540375\pi$
$420$	−1.13648	−0.0554546
$421$	−8.73075	−0.425511	−0.212755	−	0.977106i	$-0.568244\pi$
$421$	−8.73075	−0.425511	−0.212755	+	0.977106i	$0.568244\pi$
$422$	−16.8981	−0.822588
$423$	7.26676	0.353322
$424$	24.4424	1.18703
$425$	34.9121	1.69348
$426$	0.652121	0.0315954
$427$	−0.565934	−0.0273875
$428$	−19.5038	−0.942754
$429$	−24.3290	−1.17461
$430$	−3.88891	−0.187540
$431$	−10.7660	−0.518580	−0.259290	−	0.965800i	$-0.583488\pi$
$431$	−10.7660	−0.518580	−0.259290	+	0.965800i	$0.583488\pi$
$432$	0.164145	0.00789745
$433$	6.61490	0.317892	0.158946	−	0.987287i	$-0.449190\pi$
$433$	6.61490	0.317892	0.158946	+	0.987287i	$0.449190\pi$
$434$	0.193241	0.00927588
$435$	0.474904	0.0227699
$436$	21.2100	1.01577
$437$	1.82925	0.0875050
$438$	1.60386	0.0766353
$439$	−4.46205	−0.212962	−0.106481	−	0.994315i	$-0.533958\pi$
$439$	−4.46205	−0.212962	−0.106481	+	0.994315i	$0.533958\pi$
$440$	−5.72860	−0.273100
$441$	−3.01680	−0.143657
$442$	−37.7882	−1.79740
$443$	−38.8894	−1.84769	−0.923845	−	0.382768i	$-0.874971\pi$
$443$	−38.8894	−1.84769	−0.923845	+	0.382768i	$0.874971\pi$
$444$	13.1876	0.625857
$445$	−0.748442	−0.0354796
$446$	8.81686	0.417490
$447$	−5.96369	−0.282073
$448$	−10.6203	−0.501762
$449$	−33.2095	−1.56725	−0.783627	−	0.621231i	$-0.786633\pi$
$449$	−33.2095	−1.56725	−0.783627	+	0.621231i	$0.786633\pi$
$450$	−4.27293	−0.201428
$451$	−1.32491	−0.0623873
$452$	6.95552	0.327160
$453$	−11.2886	−0.530384
$454$	−9.58372	−0.449786
$455$	−5.47301	−0.256579
$456$	−5.23717	−0.245253
$457$	3.96363	0.185411	0.0927055	−	0.995694i	$-0.470449\pi$
$457$	3.96363	0.185411	0.0927055	+	0.995694i	$0.470449\pi$
$458$	−17.8246	−0.832887
$459$	7.31225	0.341307
$460$	0.569438	0.0265502
$461$	−13.1510	−0.612505	−0.306253	−	0.951950i	$-0.599075\pi$
$461$	−13.1510	−0.612505	−0.306253	+	0.951950i	$0.599075\pi$
$462$	7.52551	0.350119
$463$	40.8826	1.89997	0.949987	−	0.312289i	$-0.101096\pi$
$463$	40.8826	1.89997	0.949987	+	0.312289i	$0.101096\pi$
$464$	0.164145	0.00762026
$465$	0.0513795	0.00238267
$466$	−16.7415	−0.775537
$467$	−8.60638	−0.398256	−0.199128	−	0.979974i	$-0.563811\pi$
$467$	−8.60638	−0.398256	−0.199128	+	0.979974i	$0.563811\pi$
$468$	−6.92380	−0.320053
$469$	27.8946	1.28805
$470$	3.08850	0.142462
$471$	−10.8902	−0.501792
$472$	39.0192	1.79600
$473$	−38.5514	−1.77260
$474$	12.4108	0.570048
$475$	8.73370	0.400730
$476$	−17.4987	−0.802053
$477$	−8.53731	−0.390896
$478$	9.08016	0.415317
$479$	−31.9634	−1.46045	−0.730223	−	0.683208i	$-0.760584\pi$
$479$	−31.9634	−1.46045	−0.730223	+	0.683208i	$0.760584\pi$
$480$	−2.64955	−0.120935
$481$	63.5084	2.89573
$482$	19.0917	0.869603
$483$	−1.99579	−0.0908118
$484$	−8.09565	−0.367984
$485$	−1.73636	−0.0788441
$486$	−0.894954	−0.0405959
$487$	−40.3554	−1.82868	−0.914339	−	0.404949i	$-0.867289\pi$
$487$	−40.3554	−1.82868	−0.914339	+	0.404949i	$0.867289\pi$
$488$	−0.811844	−0.0367505
$489$	−15.1857	−0.686720
$490$	−1.28219	−0.0579237
$491$	−33.3566	−1.50536	−0.752682	−	0.658384i	$-0.771240\pi$
$491$	−33.3566	−1.50536	−0.752682	+	0.658384i	$0.771240\pi$
$492$	−0.377055	−0.0169990
$493$	7.31225	0.329327
$494$	−9.45319	−0.425319
$495$	2.00090	0.0899339
$496$	0.0177587	0.000797391 0
$497$	1.45426	0.0652327
$498$	7.74189	0.346922
$499$	1.93558	0.0866486	0.0433243	−	0.999061i	$-0.486205\pi$
$499$	1.93558	0.0866486	0.0433243	+	0.999061i	$0.486205\pi$
$500$	5.56595	0.248917
$501$	−7.84448	−0.350465
$502$	2.08127	0.0928917
$503$	40.5468	1.80789	0.903946	−	0.427647i	$-0.140657\pi$
$503$	40.5468	1.80789	0.903946	+	0.427647i	$0.140657\pi$
$504$	5.71398	0.254521
$505$	−1.63948	−0.0729561
$506$	−3.77069	−0.167627
$507$	−20.3433	−0.903477
$508$	−4.80712	−0.213281
$509$	−17.0589	−0.756122	−0.378061	−	0.925781i	$-0.623409\pi$
$509$	−17.0589	−0.756122	−0.378061	+	0.925781i	$0.623409\pi$
$510$	3.10783	0.137617
$511$	3.57669	0.158223
$512$	−1.85569	−0.0820105
$513$	1.82925	0.0807635
$514$	−0.670343	−0.0295675
$515$	−2.86695	−0.126333
$516$	−10.9714	−0.482988
$517$	30.6169	1.34653
$518$	−19.6446	−0.863134
$519$	−22.7107	−0.996889
$520$	−7.85115	−0.344296
$521$	10.8295	0.474448	0.237224	−	0.971455i	$-0.423762\pi$
$521$	10.8295	0.474448	0.237224	+	0.971455i	$0.423762\pi$
$522$	−0.894954	−0.0391711
$523$	−13.6686	−0.597686	−0.298843	−	0.954302i	$-0.596601\pi$
$523$	−13.6686	−0.597686	−0.298843	+	0.954302i	$0.596601\pi$
$524$	20.0390	0.875407
$525$	−9.52885	−0.415873
$526$	−19.4138	−0.846480
$527$	0.791105	0.0344611
$528$	0.691589	0.0300976
$529$	1.00000	0.0434783
$530$	−3.62850	−0.157612
$531$	−13.6287	−0.591436
$532$	−4.37753	−0.189790
$533$	−1.81581	−0.0786513
$534$	1.41043	0.0610354
$535$	7.72478	0.333972
$536$	40.0153	1.72840
$537$	17.9552	0.774826
$538$	−5.05866	−0.218094
$539$	−12.7106	−0.547485
$540$	0.569438	0.0245047
$541$	26.4643	1.13779	0.568895	−	0.822410i	$-0.307371\pi$
$541$	26.4643	1.13779	0.568895	+	0.822410i	$0.307371\pi$
$542$	−18.6371	−0.800530
$543$	−20.7321	−0.889700
$544$	−40.7959	−1.74911
$545$	−8.40051	−0.359839
$546$	10.3138	0.441392
$547$	8.91076	0.380996	0.190498	−	0.981688i	$-0.438990\pi$
$547$	8.91076	0.380996	0.190498	+	0.981688i	$0.438990\pi$
$548$	8.55584	0.365487
$549$	0.283563	0.0121022
$550$	−18.0030	−0.767651
$551$	1.82925	0.0779288
$552$	−2.86301	−0.121858
$553$	27.6768	1.17694
$554$	−3.31367	−0.140784
$555$	−5.22316	−0.221711
$556$	1.37145	0.0581625
$557$	−19.1693	−0.812230	−0.406115	−	0.913822i	$-0.633117\pi$
$557$	−19.1693	−0.812230	−0.406115	+	0.913822i	$0.633117\pi$
$558$	−0.0968242	−0.00409890
$559$	−52.8354	−2.23470
$560$	0.155579	0.00657441
$561$	30.8085	1.30074
$562$	−13.2810	−0.560225
$563$	−1.82432	−0.0768861	−0.0384430	−	0.999261i	$-0.512240\pi$
$563$	−1.82432	−0.0768861	−0.0384430	+	0.999261i	$0.512240\pi$
$564$	8.71327	0.366895
$565$	−2.75483	−0.115897
$566$	−16.7488	−0.704006
$567$	−1.99579	−0.0838155
$568$	2.08617	0.0875339
$569$	11.6679	0.489143	0.244571	−	0.969631i	$-0.421353\pi$
$569$	11.6679	0.489143	0.244571	+	0.969631i	$0.421353\pi$
$570$	0.777464	0.0325644
$571$	31.7168	1.32731	0.663653	−	0.748041i	$-0.269005\pi$
$571$	31.7168	1.32731	0.663653	+	0.748041i	$0.269005\pi$
$572$	−29.1719	−1.21974
$573$	1.02970	0.0430162
$574$	0.561670	0.0234437
$575$	4.77447	0.199109
$576$	5.32134	0.221723
$577$	13.0629	0.543817	0.271909	−	0.962323i	$-0.412345\pi$
$577$	13.0629	0.543817	0.271909	+	0.962323i	$0.412345\pi$
$578$	32.6380	1.35756
$579$	−21.8114	−0.906449
$580$	0.569438	0.0236446
$581$	17.2648	0.716265
$582$	3.27216	0.135635
$583$	−35.9700	−1.48973
$584$	5.13084	0.212316
$585$	2.74227	0.113379
$586$	28.8541	1.19195
$587$	−42.1961	−1.74162	−0.870809	−	0.491621i	$-0.836405\pi$
$587$	−42.1961	−1.74162	−0.870809	+	0.491621i	$0.836405\pi$
$588$	−3.61732	−0.149176
$589$	0.197905	0.00815454
$590$	−5.79245	−0.238471
$591$	−0.418534	−0.0172162
$592$	−1.80533	−0.0741984
$593$	10.2974	0.422863	0.211431	−	0.977393i	$-0.432188\pi$
$593$	10.2974	0.422863	0.211431	+	0.977393i	$0.432188\pi$
$594$	−3.77069	−0.154713
$595$	6.93063	0.284128
$596$	−7.15081	−0.292909
$597$	−18.2933	−0.748694
$598$	−5.16779	−0.211327
$599$	12.2322	0.499795	0.249898	−	0.968272i	$-0.419603\pi$
$599$	12.2322	0.499795	0.249898	+	0.968272i	$0.419603\pi$
$600$	−13.6693	−0.558048
$601$	14.0743	0.574103	0.287051	−	0.957915i	$-0.407325\pi$
$601$	14.0743	0.574103	0.287051	+	0.957915i	$0.407325\pi$
$602$	16.3432	0.666099
$603$	−13.9767	−0.569174
$604$	−13.5357	−0.550758
$605$	3.20640	0.130359
$606$	3.08959	0.125506
$607$	−1.95760	−0.0794564	−0.0397282	−	0.999211i	$-0.512649\pi$
$607$	−1.95760	−0.0794564	−0.0397282	+	0.999211i	$0.512649\pi$
$608$	−10.2056	−0.413892
$609$	−1.99579	−0.0808737
$610$	0.120519	0.00487969
$611$	41.9609	1.69756
$612$	8.76781	0.354418
$613$	−21.6541	−0.874599	−0.437300	−	0.899316i	$-0.644065\pi$
$613$	−21.6541	−0.874599	−0.437300	+	0.899316i	$0.644065\pi$
$614$	−11.7703	−0.475012
$615$	0.149338	0.00602190
$616$	24.0746	0.969991
$617$	19.0826	0.768237	0.384118	−	0.923284i	$-0.374505\pi$
$617$	19.0826	0.768237	0.384118	+	0.923284i	$0.374505\pi$
$618$	5.40274	0.217330
$619$	10.6165	0.426713	0.213356	−	0.976974i	$-0.431560\pi$
$619$	10.6165	0.426713	0.213356	+	0.976974i	$0.431560\pi$
$620$	0.0616070	0.00247419
$621$	1.00000	0.0401286
$622$	−24.0799	−0.965517
$623$	3.14534	0.126015
$624$	0.947835	0.0379438
$625$	21.6679	0.866714
$626$	−5.34639	−0.213685
$627$	7.70714	0.307794
$628$	−13.0579	−0.521068
$629$	−80.4225	−3.20666
$630$	−0.848248	−0.0337950
$631$	19.7674	0.786927	0.393463	−	0.919340i	$-0.371277\pi$
$631$	19.7674	0.786927	0.393463	+	0.919340i	$0.371277\pi$
$632$	39.7029	1.57930
$633$	18.8816	0.750475
$634$	23.5552	0.935497
$635$	1.90393	0.0755552
$636$	−10.2367	−0.405913
$637$	−17.4201	−0.690211
$638$	−3.77069	−0.149283
$639$	−0.728665	−0.0288255
$640$	−3.03743	−0.120065
$641$	30.5690	1.20740	0.603701	−	0.797210i	$-0.293692\pi$
$641$	30.5690	1.20740	0.603701	+	0.797210i	$0.293692\pi$
$642$	−14.5573	−0.574531
$643$	8.22719	0.324449	0.162224	−	0.986754i	$-0.448133\pi$
$643$	8.22719	0.324449	0.162224	+	0.986754i	$0.448133\pi$
$644$	−2.39307	−0.0943003
$645$	4.34537	0.171099
$646$	11.9709	0.470987
$647$	26.6031	1.04587	0.522937	−	0.852371i	$-0.324836\pi$
$647$	26.6031	1.04587	0.522937	+	0.852371i	$0.324836\pi$
$648$	−2.86301	−0.112470
$649$	−57.4216	−2.25399
$650$	−24.6734	−0.967772
$651$	−0.215923	−0.00846270
$652$	−18.2085	−0.713100
$653$	21.9374	0.858477	0.429239	−	0.903191i	$-0.358782\pi$
$653$	21.9374	0.858477	0.429239	+	0.903191i	$0.358782\pi$
$654$	15.8307	0.619030
$655$	−7.93673	−0.310114
$656$	0.0516171	0.00201531
$657$	−1.79211	−0.0699170
$658$	−12.9795	−0.505993
$659$	−30.1637	−1.17501	−0.587505	−	0.809220i	$-0.699890\pi$
$659$	−30.1637	−1.17501	−0.587505	+	0.809220i	$0.699890\pi$
$660$	2.39920	0.0933886
$661$	7.34972	0.285871	0.142936	−	0.989732i	$-0.454346\pi$
$661$	7.34972	0.285871	0.142936	+	0.989732i	$0.454346\pi$
$662$	6.72722	0.261461
$663$	42.2236	1.63983
$664$	24.7667	0.961136
$665$	1.73379	0.0672334
$666$	9.84300	0.381408
$667$	1.00000	0.0387202
$668$	−9.40598	−0.363928
$669$	−9.85174	−0.380890
$670$	−5.94033	−0.229495
$671$	1.19473	0.0461220
$672$	11.1348	0.429533
$673$	7.38112	0.284521	0.142261	−	0.989829i	$-0.454563\pi$
$673$	7.38112	0.284521	0.142261	+	0.989829i	$0.454563\pi$
$674$	28.3433	1.09174
$675$	4.77447	0.183769
$676$	−24.3928	−0.938184
$677$	−30.9453	−1.18933	−0.594663	−	0.803975i	$-0.702714\pi$
$677$	−30.9453	−1.18933	−0.594663	+	0.803975i	$0.702714\pi$
$678$	5.19147	0.199377
$679$	7.29709	0.280037
$680$	9.94214	0.381264
$681$	10.7086	0.410355
$682$	−0.407947	−0.0156211
$683$	−19.0851	−0.730273	−0.365136	−	0.930954i	$-0.618978\pi$
$683$	−19.0851	−0.730273	−0.365136	+	0.930954i	$0.618978\pi$
$684$	2.19338	0.0838659
$685$	−3.38866	−0.129474
$686$	17.8915	0.683099
$687$	19.9167	0.759871
$688$	1.50193	0.0572605
$689$	−49.2975	−1.87809
$690$	0.425017	0.0161801
$691$	−2.88191	−0.109633	−0.0548165	−	0.998496i	$-0.517457\pi$
$691$	−2.88191	−0.109633	−0.0548165	+	0.998496i	$0.517457\pi$
$692$	−27.2314	−1.03518
$693$	−8.40883	−0.319425
$694$	11.1799	0.424382
$695$	−0.543183	−0.0206041
$696$	−2.86301	−0.108522
$697$	2.29941	0.0870963
$698$	31.6140	1.19661
$699$	18.7066	0.707549
$700$	−11.4256	−0.431849
$701$	24.0678	0.909027	0.454513	−	0.890740i	$-0.349813\pi$
$701$	24.0678	0.909027	0.454513	+	0.890740i	$0.349813\pi$
$702$	−5.16779	−0.195046
$703$	−20.1187	−0.758792
$704$	22.4203	0.844996
$705$	−3.45102	−0.129973
$706$	−11.6660	−0.439055
$707$	6.88996	0.259124
$708$	−16.3416	−0.614156
$709$	−21.1696	−0.795041	−0.397521	−	0.917593i	$-0.630129\pi$
$709$	−21.1696	−0.795041	−0.397521	+	0.917593i	$0.630129\pi$
$710$	−0.309695	−0.0116227
$711$	−13.8676	−0.520074
$712$	4.51206	0.169097
$713$	0.108189	0.00405171
$714$	−13.0607	−0.488785
$715$	11.5539	0.432093
$716$	21.5294	0.804590
$717$	−10.1460	−0.378908
$718$	−15.9280	−0.594429
$719$	−3.11667	−0.116232	−0.0581162	−	0.998310i	$-0.518509\pi$
$719$	−3.11667	−0.116232	−0.0581162	+	0.998310i	$0.518509\pi$
$720$	−0.0779533	−0.00290515
$721$	12.0484	0.448706
$722$	−14.0095	−0.521378
$723$	−21.3326	−0.793368
$724$	−24.8590	−0.923877
$725$	4.77447	0.177319
$726$	−6.04244	−0.224256
$727$	−35.2277	−1.30652	−0.653262	−	0.757132i	$-0.726600\pi$
$727$	−35.2277	−1.30652	−0.653262	+	0.757132i	$0.726600\pi$
$728$	32.9946	1.22286
$729$	1.00000	0.0370370
$730$	−0.761680	−0.0281910
$731$	66.9070	2.47465
$732$	0.340009	0.0125671
$733$	−7.52531	−0.277954	−0.138977	−	0.990296i	$-0.544381\pi$
$733$	−7.52531	−0.277954	−0.138977	+	0.990296i	$0.544381\pi$
$734$	25.2426	0.931721
$735$	1.43269	0.0528457
$736$	−5.57912	−0.205649
$737$	−58.8875	−2.16915
$738$	−0.281427	−0.0103595
$739$	8.32114	0.306098	0.153049	−	0.988219i	$-0.451091\pi$
$739$	8.32114	0.306098	0.153049	+	0.988219i	$0.451091\pi$
$740$	−6.26287	−0.230228
$741$	10.5628	0.388033
$742$	15.2489	0.559803
$743$	−50.1220	−1.83880	−0.919398	−	0.393328i	$-0.871324\pi$
$743$	−50.1220	−1.83880	−0.919398	+	0.393328i	$0.871324\pi$
$744$	−0.309746	−0.0113559
$745$	2.83218	0.103763
$746$	2.72248	0.0996769
$747$	−8.65060	−0.316509
$748$	36.9412	1.35070
$749$	−32.4635	−1.18619
$750$	4.15432	0.151694
$751$	6.96312	0.254088	0.127044	−	0.991897i	$-0.459451\pi$
$751$	6.96312	0.254088	0.127044	+	0.991897i	$0.459451\pi$
$752$	−1.19281	−0.0434971
$753$	−2.32556	−0.0847482
$754$	−5.16779	−0.188200
$755$	5.36100	0.195107
$756$	−2.39307	−0.0870352
$757$	−30.7302	−1.11691	−0.558455	−	0.829535i	$-0.688606\pi$
$757$	−30.7302	−1.11691	−0.558455	+	0.829535i	$0.688606\pi$
$758$	−14.8184	−0.538227
$759$	4.21327	0.152932
$760$	2.48715	0.0902185
$761$	36.9406	1.33910	0.669548	−	0.742769i	$-0.266488\pi$
$761$	36.9406	1.33910	0.669548	+	0.742769i	$0.266488\pi$
$762$	−3.58794	−0.129977
$763$	35.3033	1.27807
$764$	1.23467	0.0446687
$765$	−3.47262	−0.125553
$766$	9.81352	0.354577
$767$	−78.6973	−2.84159
$768$	16.3667	0.590582
$769$	−1.80160	−0.0649673	−0.0324837	−	0.999472i	$-0.510342\pi$
$769$	−1.80160	−0.0649673	−0.0324837	+	0.999472i	$0.510342\pi$
$770$	−3.57390	−0.128794
$771$	0.749025	0.0269755
$772$	−26.1531	−0.941270
$773$	18.7139	0.673094	0.336547	−	0.941667i	$-0.390741\pi$
$773$	18.7139	0.673094	0.336547	+	0.941667i	$0.390741\pi$
$774$	−8.18882	−0.294341
$775$	0.516545	0.0185548
$776$	10.4678	0.375773
$777$	21.9504	0.787467
$778$	−7.74803	−0.277780
$779$	0.575226	0.0206096
$780$	3.28814	0.117734
$781$	−3.07006	−0.109856
$782$	6.54412	0.234017
$783$	1.00000	0.0357371
$784$	0.495194	0.0176855
$785$	5.17179	0.184589
$786$	14.9567	0.533488
$787$	11.5837	0.412916	0.206458	−	0.978455i	$-0.433806\pi$
$787$	11.5837	0.412916	0.206458	+	0.978455i	$0.433806\pi$
$788$	−0.501846	−0.0178775
$789$	21.6925	0.772272
$790$	−5.89395	−0.209697
$791$	11.5772	0.411639
$792$	−12.0626	−0.428627
$793$	1.63740	0.0581457
$794$	−13.3686	−0.474434
$795$	4.05440	0.143795
$796$	−21.9347	−0.777455
$797$	−4.87547	−0.172698	−0.0863491	−	0.996265i	$-0.527520\pi$
$797$	−4.87547	−0.172698	−0.0863491	+	0.996265i	$0.527520\pi$
$798$	−3.26731	−0.115661
$799$	−53.1364	−1.87983
$800$	−26.6373	−0.941771
$801$	−1.57598	−0.0556847
$802$	−3.60377	−0.127253
$803$	−7.55067	−0.266457
$804$	−16.7588	−0.591039
$805$	0.947812	0.0334060
$806$	−0.559098	−0.0196934
$807$	5.65243	0.198975
$808$	9.88379	0.347711
$809$	18.2484	0.641580	0.320790	−	0.947150i	$-0.396052\pi$
$809$	18.2484	0.641580	0.320790	+	0.947150i	$0.396052\pi$
$810$	0.425017	0.0149336
$811$	29.9782	1.05268	0.526338	−	0.850275i	$-0.323565\pi$
$811$	29.9782	1.05268	0.526338	+	0.850275i	$0.323565\pi$
$812$	−2.39307	−0.0839804
$813$	20.8246	0.730351
$814$	41.4713	1.45357
$815$	7.21175	0.252616
$816$	−1.20027	−0.0420179
$817$	16.7376	0.585576
$818$	−0.880556	−0.0307879
$819$	−11.5244	−0.402697
$820$	0.179065	0.00625323
$821$	4.24158	0.148032	0.0740161	−	0.997257i	$-0.476418\pi$
$821$	4.24158	0.148032	0.0740161	+	0.997257i	$0.476418\pi$
$822$	6.38591	0.222734
$823$	27.7238	0.966392	0.483196	−	0.875512i	$-0.339476\pi$
$823$	27.7238	0.966392	0.483196	+	0.875512i	$0.339476\pi$
$824$	17.2837	0.602106
$825$	20.1161	0.700354
$826$	24.3429	0.846997
$827$	19.7909	0.688197	0.344098	−	0.938934i	$-0.388185\pi$
$827$	19.7909	0.688197	0.344098	+	0.938934i	$0.388185\pi$
$828$	1.19906	0.0416701
$829$	48.9443	1.69991	0.849953	−	0.526859i	$-0.176630\pi$
$829$	48.9443	1.69991	0.849953	+	0.526859i	$0.176630\pi$
$830$	−3.67666	−0.127619
$831$	3.70261	0.128442
$832$	30.7274	1.06528
$833$	22.0596	0.764321
$834$	1.02362	0.0354452
$835$	3.72538	0.128922
$836$	9.24131	0.319617
$837$	0.108189	0.00373956
$838$	−4.63487	−0.160109
$839$	−30.7814	−1.06269	−0.531347	−	0.847154i	$-0.678314\pi$
$839$	−30.7814	−1.06269	−0.531347	+	0.847154i	$0.678314\pi$
$840$	−2.71359	−0.0936278
$841$	1.00000	0.0344828
$842$	−7.81362	−0.269275
$843$	14.8399	0.511112
$844$	22.6401	0.779304
$845$	9.66112	0.332353
$846$	6.50342	0.223592
$847$	−13.4750	−0.463005
$848$	1.40136	0.0481229
$849$	18.7147	0.642288
$850$	31.2447	1.07168
$851$	−10.9983	−0.377018
$852$	−0.873711	−0.0299328
$853$	−40.1642	−1.37520	−0.687598	−	0.726092i	$-0.741335\pi$
$853$	−40.1642	−1.37520	−0.687598	+	0.726092i	$0.741335\pi$
$854$	−0.506485	−0.0173316
$855$	−0.868720	−0.0297096
$856$	−46.5696	−1.59172
$857$	25.4718	0.870102	0.435051	−	0.900406i	$-0.356730\pi$
$857$	25.4718	0.870102	0.435051	+	0.900406i	$0.356730\pi$
$858$	−21.7733	−0.743329
$859$	−2.41538	−0.0824117	−0.0412059	−	0.999151i	$-0.513120\pi$
$859$	−2.41538	−0.0824117	−0.0412059	+	0.999151i	$0.513120\pi$
$860$	5.21035	0.177672
$861$	−0.627597	−0.0213884
$862$	−9.63507	−0.328172
$863$	20.6291	0.702224	0.351112	−	0.936333i	$-0.385804\pi$
$863$	20.6291	0.702224	0.351112	+	0.936333i	$0.385804\pi$
$864$	−5.57912	−0.189805
$865$	10.7854	0.366715
$866$	5.92003	0.201171
$867$	−36.4690	−1.23855
$868$	−0.258904	−0.00878779
$869$	−58.4278	−1.98203
$870$	0.425017	0.0144094
$871$	−80.7064	−2.73463
$872$	50.6433	1.71500
$873$	−3.65623	−0.123745
$874$	1.63710	0.0553756
$875$	9.26435	0.313192
$876$	−2.14885	−0.0726028
$877$	−1.94556	−0.0656969	−0.0328485	−	0.999460i	$-0.510458\pi$
$877$	−1.94556	−0.0656969	−0.0328485	+	0.999460i	$0.510458\pi$
$878$	−3.99333	−0.134768
$879$	−32.2409	−1.08746
$880$	−0.328439	−0.0110717
$881$	−27.7483	−0.934863	−0.467431	−	0.884029i	$-0.654820\pi$
$881$	−27.7483	−0.934863	−0.467431	+	0.884029i	$0.654820\pi$
$882$	−2.69990	−0.0909104
$883$	23.2234	0.781531	0.390765	−	0.920490i	$-0.372210\pi$
$883$	23.2234	0.781531	0.390765	+	0.920490i	$0.372210\pi$
$884$	50.6285	1.70282
$885$	6.47234	0.217565
$886$	−34.8042	−1.16927
$887$	42.6578	1.43231	0.716154	−	0.697943i	$-0.245901\pi$
$887$	42.6578	1.43231	0.716154	+	0.697943i	$0.245901\pi$
$888$	31.4883	1.05668
$889$	−8.00130	−0.268355
$890$	−0.669821	−0.0224525
$891$	4.21327	0.141150
$892$	−11.8128	−0.395522
$893$	−13.2927	−0.444825
$894$	−5.33723	−0.178504
$895$	−8.52702	−0.285027
$896$	12.7649	0.426444
$897$	5.77436	0.192800
$898$	−29.7210	−0.991803
$899$	0.108189	0.00360831
$900$	5.72486	0.190829
$901$	62.4269	2.07974
$902$	−1.18573	−0.0394805
$903$	−18.2615	−0.607705
$904$	16.6078	0.552367
$905$	9.84577	0.327284
$906$	−10.1028	−0.335642
$907$	7.09985	0.235747	0.117873	−	0.993029i	$-0.462392\pi$
$907$	7.09985	0.235747	0.117873	+	0.993029i	$0.462392\pi$
$908$	12.8403	0.426119
$909$	−3.45224	−0.114504
$910$	−4.89809	−0.162370
$911$	7.31959	0.242509	0.121254	−	0.992621i	$-0.461308\pi$
$911$	7.31959	0.242509	0.121254	+	0.992621i	$0.461308\pi$
$912$	−0.300263	−0.00994271
$913$	−36.4473	−1.20623
$914$	3.54727	0.117333
$915$	−0.134665	−0.00445190
$916$	23.8813	0.789061
$917$	33.3543	1.10145
$918$	6.54412	0.215988
$919$	30.3798	1.00214	0.501068	−	0.865408i	$-0.332940\pi$
$919$	30.3798	1.00214	0.501068	+	0.865408i	$0.332940\pi$
$920$	1.35966	0.0448265
$921$	13.1519	0.433369
$922$	−11.7696	−0.387610
$923$	−4.20758	−0.138494
$924$	−10.0827	−0.331696
$925$	−52.5112	−1.72656
$926$	36.5880	1.20236
$927$	−6.03689	−0.198278
$928$	−5.57912	−0.183143
$929$	−53.5343	−1.75640	−0.878202	−	0.478289i	$-0.841257\pi$
$929$	−53.5343	−1.75640	−0.878202	+	0.478289i	$0.841257\pi$
$930$	0.0459823	0.00150782
$931$	5.51850	0.180861
$932$	22.4303	0.734729
$933$	26.9063	0.880874
$934$	−7.70231	−0.252027
$935$	−14.6311	−0.478488
$936$	−16.5321	−0.540367
$937$	−42.5867	−1.39125	−0.695624	−	0.718406i	$-0.744872\pi$
$937$	−42.5867	−1.39125	−0.695624	+	0.718406i	$0.744872\pi$
$938$	24.9643	0.815115
$939$	5.97393	0.194952
$940$	−4.13797	−0.134966
$941$	8.63427	0.281469	0.140735	−	0.990047i	$-0.455054\pi$
$941$	8.63427	0.281469	0.140735	+	0.990047i	$0.455054\pi$
$942$	−9.74619	−0.317548
$943$	0.314460	0.0102402
$944$	2.23709	0.0728112
$945$	0.947812	0.0308323
$946$	−34.5018	−1.12175
$947$	6.11497	0.198710	0.0993549	−	0.995052i	$-0.468322\pi$
$947$	6.11497	0.198710	0.0993549	+	0.995052i	$0.468322\pi$
$948$	−16.6280	−0.540052
$949$	−10.3483	−0.335921
$950$	7.81626	0.253593
$951$	−26.3200	−0.853486
$952$	−41.7820	−1.35416
$953$	−39.6506	−1.28441	−0.642204	−	0.766533i	$-0.721980\pi$
$953$	−39.6506	−1.28441	−0.642204	+	0.766533i	$0.721980\pi$
$954$	−7.64050	−0.247370
$955$	−0.489008	−0.0158239
$956$	−12.1656	−0.393463
$957$	4.21327	0.136196
$958$	−28.6058	−0.924212
$959$	14.2409	0.459863
$960$	−2.52713	−0.0815627
$961$	−30.9883	−0.999622
$962$	56.8371	1.83250
$963$	16.2660	0.524164
$964$	−25.5790	−0.823845
$965$	10.3583	0.333446
$966$	−1.78614	−0.0574682
$967$	38.2387	1.22967	0.614837	−	0.788655i	$-0.289222\pi$
$967$	38.2387	1.22967	0.614837	+	0.788655i	$0.289222\pi$
$968$	−19.3301	−0.621294
$969$	−13.3759	−0.429697
$970$	−1.55396	−0.0498948
$971$	1.26038	0.0404475	0.0202237	−	0.999795i	$-0.493562\pi$
$971$	1.26038	0.0404475	0.0202237	+	0.999795i	$0.493562\pi$
$972$	1.19906	0.0384598
$973$	2.28274	0.0731812
$974$	−36.1162	−1.15724
$975$	27.5695	0.882931
$976$	−0.0465456	−0.00148989
$977$	22.8546	0.731185	0.365592	−	0.930775i	$-0.380866\pi$
$977$	22.8546	0.731185	0.365592	+	0.930775i	$0.380866\pi$
$978$	−13.5905	−0.434576
$979$	−6.64006	−0.212217
$980$	1.71788	0.0548757
$981$	−17.6889	−0.564762
$982$	−29.8526	−0.952636
$983$	−49.7031	−1.58528	−0.792642	−	0.609688i	$-0.791295\pi$
$983$	−49.7031	−1.58528	−0.792642	+	0.609688i	$0.791295\pi$
$984$	−0.900301	−0.0287005
$985$	0.198763	0.00633313
$986$	6.54412	0.208407
$987$	14.5030	0.461634
$988$	12.6654	0.402939
$989$	9.14999	0.290953
$990$	1.79072	0.0569127
$991$	−12.5663	−0.399181	−0.199590	−	0.979879i	$-0.563961\pi$
$991$	−12.5663	−0.399181	−0.199590	+	0.979879i	$0.563961\pi$
$992$	−0.603599	−0.0191643
$993$	−7.51683	−0.238539
$994$	1.30150	0.0412811
$995$	8.68756	0.275414
$996$	−10.3726	−0.328667
$997$	24.4153	0.773242	0.386621	−	0.922239i	$-0.373642\pi$
$997$	24.4153	0.773242	0.386621	+	0.922239i	$0.373642\pi$
$998$	1.73226	0.0548336
$999$	−10.9983	−0.347972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.m.1.10	✓	14
3.2	odd	2		6003.2.a.p.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.m.1.10	✓	14	1.1	even	1	trivial
6003.2.a.p.1.5		14	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)

\(f(q)\)	\(=\)	\(q+0.894954 q^{2} -1.00000 q^{3} -1.19906 q^{4} +0.474904 q^{5} -0.894954 q^{6} -1.99579 q^{7} -2.86301 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.894954 q^{2} -1.00000 q^{3} -1.19906 q^{4} +0.474904 q^{5} -0.894954 q^{6} -1.99579 q^{7} -2.86301 q^{8} +1.00000 q^{9} +0.425017 q^{10} +4.21327 q^{11} +1.19906 q^{12} +5.77436 q^{13} -1.78614 q^{14} -0.474904 q^{15} -0.164145 q^{16} -7.31225 q^{17} +0.894954 q^{18} -1.82925 q^{19} -0.569438 q^{20} +1.99579 q^{21} +3.77069 q^{22} -1.00000 q^{23} +2.86301 q^{24} -4.77447 q^{25} +5.16779 q^{26} -1.00000 q^{27} +2.39307 q^{28} -1.00000 q^{29} -0.425017 q^{30} -0.108189 q^{31} +5.57912 q^{32} -4.21327 q^{33} -6.54412 q^{34} -0.947812 q^{35} -1.19906 q^{36} +10.9983 q^{37} -1.63710 q^{38} -5.77436 q^{39} -1.35966 q^{40} -0.314460 q^{41} +1.78614 q^{42} -9.14999 q^{43} -5.05196 q^{44} +0.474904 q^{45} -0.894954 q^{46} +7.26676 q^{47} +0.164145 q^{48} -3.01680 q^{49} -4.27293 q^{50} +7.31225 q^{51} -6.92380 q^{52} -8.53731 q^{53} -0.894954 q^{54} +2.00090 q^{55} +5.71398 q^{56} +1.82925 q^{57} -0.894954 q^{58} -13.6287 q^{59} +0.569438 q^{60} +0.283563 q^{61} -0.0968242 q^{62} -1.99579 q^{63} +5.32134 q^{64} +2.74227 q^{65} -3.77069 q^{66} -13.9767 q^{67} +8.76781 q^{68} +1.00000 q^{69} -0.848248 q^{70} -0.728665 q^{71} -2.86301 q^{72} -1.79211 q^{73} +9.84300 q^{74} +4.77447 q^{75} +2.19338 q^{76} -8.40883 q^{77} -5.16779 q^{78} -13.8676 q^{79} -0.0779533 q^{80} +1.00000 q^{81} -0.281427 q^{82} -8.65060 q^{83} -2.39307 q^{84} -3.47262 q^{85} -8.18882 q^{86} +1.00000 q^{87} -12.0626 q^{88} -1.57598 q^{89} +0.425017 q^{90} -11.5244 q^{91} +1.19906 q^{92} +0.108189 q^{93} +6.50342 q^{94} -0.868720 q^{95} -5.57912 q^{96} -3.65623 q^{97} -2.69990 q^{98} +4.21327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9} - 5 q^{10} - 12 q^{11} - 12 q^{12} + 13 q^{13} - 9 q^{14} + 3 q^{15} - 14 q^{17} - 2 q^{18} - 9 q^{19} - 2 q^{20} + 3 q^{21} - 9 q^{22} - 14 q^{23} + 6 q^{24} + 13 q^{25} - 16 q^{26} - 14 q^{27} + 3 q^{28} - 14 q^{29} + 5 q^{30} - 28 q^{31} - 4 q^{32} + 12 q^{33} + 14 q^{34} - 9 q^{35} + 12 q^{36} - 12 q^{37} + 2 q^{38} - 13 q^{39} - 20 q^{40} - 25 q^{41} + 9 q^{42} + 5 q^{43} - 37 q^{44} - 3 q^{45} + 2 q^{46} - 17 q^{47} + 17 q^{49} - 44 q^{50} + 14 q^{51} + 25 q^{52} - 17 q^{53} + 2 q^{54} + q^{55} - 54 q^{56} + 9 q^{57} + 2 q^{58} - 18 q^{59} + 2 q^{60} - 13 q^{61} - 8 q^{62} - 3 q^{63} + 20 q^{64} - 16 q^{65} + 9 q^{66} + 2 q^{67} - 19 q^{68} + 14 q^{69} + 14 q^{70} - 55 q^{71} - 6 q^{72} + 19 q^{73} + 4 q^{74} - 13 q^{75} - 32 q^{76} - 19 q^{77} + 16 q^{78} - 68 q^{79} - 2 q^{80} + 14 q^{81} - 12 q^{82} - 21 q^{83} - 3 q^{84} + 16 q^{85} - 22 q^{86} + 14 q^{87} - 25 q^{88} - 17 q^{89} - 5 q^{90} - 30 q^{91} - 12 q^{92} + 28 q^{93} + 16 q^{94} - 55 q^{95} + 4 q^{96} + 25 q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9 - 5 * q^10 - 12 * q^11 - 12 * q^12 + 13 * q^13 - 9 * q^14 + 3 * q^15 - 14 * q^17 - 2 * q^18 - 9 * q^19 - 2 * q^20 + 3 * q^21 - 9 * q^22 - 14 * q^23 + 6 * q^24 + 13 * q^25 - 16 * q^26 - 14 * q^27 + 3 * q^28 - 14 * q^29 + 5 * q^30 - 28 * q^31 - 4 * q^32 + 12 * q^33 + 14 * q^34 - 9 * q^35 + 12 * q^36 - 12 * q^37 + 2 * q^38 - 13 * q^39 - 20 * q^40 - 25 * q^41 + 9 * q^42 + 5 * q^43 - 37 * q^44 - 3 * q^45 + 2 * q^46 - 17 * q^47 + 17 * q^49 - 44 * q^50 + 14 * q^51 + 25 * q^52 - 17 * q^53 + 2 * q^54 + q^55 - 54 * q^56 + 9 * q^57 + 2 * q^58 - 18 * q^59 + 2 * q^60 - 13 * q^61 - 8 * q^62 - 3 * q^63 + 20 * q^64 - 16 * q^65 + 9 * q^66 + 2 * q^67 - 19 * q^68 + 14 * q^69 + 14 * q^70 - 55 * q^71 - 6 * q^72 + 19 * q^73 + 4 * q^74 - 13 * q^75 - 32 * q^76 - 19 * q^77 + 16 * q^78 - 68 * q^79 - 2 * q^80 + 14 * q^81 - 12 * q^82 - 21 * q^83 - 3 * q^84 + 16 * q^85 - 22 * q^86 + 14 * q^87 - 25 * q^88 - 17 * q^89 - 5 * q^90 - 30 * q^91 - 12 * q^92 + 28 * q^93 + 16 * q^94 - 55 * q^95 + 4 * q^96 + 25 * q^97 - 31 * q^98 - 12 * q^99

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