LMFDB - Embedded newform 2013.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,2,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, 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("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.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:	$16.0738859269$
Analytic rank:	$0$
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} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} + \cdots - 1 $ x^14 - x^13 - 21x^12 + 20x^11 + 167x^10 - 148x^9 - 627x^8 + 497x^7 + 1123x^6 - 745x^5 - 802x^4 + 386x^3 + 74x^2 - 15x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.67203$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67203 q^{2} -1.00000 q^{3} +0.795679 q^{4} -1.45953 q^{5} +1.67203 q^{6} -0.113904 q^{7} +2.01366 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.67203 q^{2} -1.00000 q^{3} +0.795679 q^{4} -1.45953 q^{5} +1.67203 q^{6} -0.113904 q^{7} +2.01366 q^{8} +1.00000 q^{9} +2.44037 q^{10} -1.00000 q^{11} -0.795679 q^{12} -2.41931 q^{13} +0.190451 q^{14} +1.45953 q^{15} -4.95825 q^{16} +4.33956 q^{17} -1.67203 q^{18} +5.52946 q^{19} -1.16132 q^{20} +0.113904 q^{21} +1.67203 q^{22} -5.61639 q^{23} -2.01366 q^{24} -2.86978 q^{25} +4.04515 q^{26} -1.00000 q^{27} -0.0906313 q^{28} -2.97696 q^{29} -2.44037 q^{30} +3.23872 q^{31} +4.26302 q^{32} +1.00000 q^{33} -7.25587 q^{34} +0.166247 q^{35} +0.795679 q^{36} +5.47586 q^{37} -9.24541 q^{38} +2.41931 q^{39} -2.93899 q^{40} -3.54936 q^{41} -0.190451 q^{42} +3.64080 q^{43} -0.795679 q^{44} -1.45953 q^{45} +9.39076 q^{46} -6.81812 q^{47} +4.95825 q^{48} -6.98703 q^{49} +4.79835 q^{50} -4.33956 q^{51} -1.92499 q^{52} -0.123290 q^{53} +1.67203 q^{54} +1.45953 q^{55} -0.229364 q^{56} -5.52946 q^{57} +4.97756 q^{58} -14.8361 q^{59} +1.16132 q^{60} +1.00000 q^{61} -5.41523 q^{62} -0.113904 q^{63} +2.78861 q^{64} +3.53104 q^{65} -1.67203 q^{66} +9.16048 q^{67} +3.45290 q^{68} +5.61639 q^{69} -0.277969 q^{70} -9.69135 q^{71} +2.01366 q^{72} -1.05277 q^{73} -9.15579 q^{74} +2.86978 q^{75} +4.39968 q^{76} +0.113904 q^{77} -4.04515 q^{78} +10.0943 q^{79} +7.23671 q^{80} +1.00000 q^{81} +5.93464 q^{82} -2.01215 q^{83} +0.0906313 q^{84} -6.33371 q^{85} -6.08752 q^{86} +2.97696 q^{87} -2.01366 q^{88} +16.8141 q^{89} +2.44037 q^{90} +0.275569 q^{91} -4.46885 q^{92} -3.23872 q^{93} +11.4001 q^{94} -8.07040 q^{95} -4.26302 q^{96} -4.43143 q^{97} +11.6825 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * 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 $

$2$	−1.67203	−1.18230	−0.591151	−	0.806561i	$-0.701326\pi$
$2$	−1.67203	−1.18230	−0.591151	+	0.806561i	$0.701326\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.795679	0.397840
$5$	−1.45953	−0.652721	−0.326360	−	0.945245i	$-0.605822\pi$
$5$	−1.45953	−0.652721	−0.326360	+	0.945245i	$0.605822\pi$
$6$	1.67203	0.682603
$7$	−0.113904	−0.0430518	−0.0215259	−	0.999768i	$-0.506852\pi$
$7$	−0.113904	−0.0430518	−0.0215259	+	0.999768i	$0.506852\pi$
$8$	2.01366	0.711936
$9$	1.00000	0.333333
$10$	2.44037	0.771713
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.795679	−0.229693
$13$	−2.41931	−0.670995	−0.335497	−	0.942041i	$-0.608904\pi$
$13$	−2.41931	−0.670995	−0.335497	+	0.942041i	$0.608904\pi$
$14$	0.190451	0.0509002
$15$	1.45953	0.376848
$16$	−4.95825	−1.23956
$17$	4.33956	1.05250	0.526249	−	0.850330i	$-0.323598\pi$
$17$	4.33956	1.05250	0.526249	+	0.850330i	$0.323598\pi$
$18$	−1.67203	−0.394101
$19$	5.52946	1.26855	0.634273	−	0.773110i	$-0.281300\pi$
$19$	5.52946	1.26855	0.634273	+	0.773110i	$0.281300\pi$
$20$	−1.16132	−0.259678
$21$	0.113904	0.0248560
$22$	1.67203	0.356478
$23$	−5.61639	−1.17110	−0.585549	−	0.810637i	$-0.699121\pi$
$23$	−5.61639	−1.17110	−0.585549	+	0.810637i	$0.699121\pi$
$24$	−2.01366	−0.411036
$25$	−2.86978	−0.573956
$26$	4.04515	0.793319
$27$	−1.00000	−0.192450
$28$	−0.0906313	−0.0171277
$29$	−2.97696	−0.552807	−0.276404	−	0.961042i	$-0.589143\pi$
$29$	−2.97696	−0.552807	−0.276404	+	0.961042i	$0.589143\pi$
$30$	−2.44037	−0.445549
$31$	3.23872	0.581691	0.290846	−	0.956770i	$-0.406063\pi$
$31$	3.23872	0.581691	0.290846	+	0.956770i	$0.406063\pi$
$32$	4.26302	0.753603
$33$	1.00000	0.174078
$34$	−7.25587	−1.24437
$35$	0.166247	0.0281008
$36$	0.795679	0.132613
$37$	5.47586	0.900225	0.450113	−	0.892972i	$-0.351384\pi$
$37$	5.47586	0.900225	0.450113	+	0.892972i	$0.351384\pi$
$38$	−9.24541	−1.49980
$39$	2.41931	0.387399
$40$	−2.93899	−0.464695
$41$	−3.54936	−0.554317	−0.277159	−	0.960824i	$-0.589393\pi$
$41$	−3.54936	−0.554317	−0.277159	+	0.960824i	$0.589393\pi$
$42$	−0.190451	−0.0293873
$43$	3.64080	0.555217	0.277609	−	0.960694i	$-0.410458\pi$
$43$	3.64080	0.555217	0.277609	+	0.960694i	$0.410458\pi$
$44$	−0.795679	−0.119953
$45$	−1.45953	−0.217574
$46$	9.39076	1.38459
$47$	−6.81812	−0.994525	−0.497263	−	0.867600i	$-0.665661\pi$
$47$	−6.81812	−0.994525	−0.497263	+	0.867600i	$0.665661\pi$
$48$	4.95825	0.715662
$49$	−6.98703	−0.998147
$50$	4.79835	0.678589
$51$	−4.33956	−0.607660
$52$	−1.92499	−0.266948
$53$	−0.123290	−0.0169352	−0.00846758	−	0.999964i	$-0.502695\pi$
$53$	−0.123290	−0.0169352	−0.00846758	+	0.999964i	$0.502695\pi$
$54$	1.67203	0.227534
$55$	1.45953	0.196803
$56$	−0.229364	−0.0306501
$57$	−5.52946	−0.732395
$58$	4.97756	0.653585
$59$	−14.8361	−1.93149	−0.965746	−	0.259488i	$-0.916446\pi$
$59$	−14.8361	−1.93149	−0.965746	+	0.259488i	$0.916446\pi$
$60$	1.16132	0.149925
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−5.41523	−0.687735
$63$	−0.113904	−0.0143506
$64$	2.78861	0.348576
$65$	3.53104	0.437972
$66$	−1.67203	−0.205812
$67$	9.16048	1.11913	0.559566	−	0.828786i	$-0.310968\pi$
$67$	9.16048	1.11913	0.559566	+	0.828786i	$0.310968\pi$
$68$	3.45290	0.418726
$69$	5.61639	0.676134
$70$	−0.277969	−0.0332236
$71$	−9.69135	−1.15015	−0.575076	−	0.818100i	$-0.695027\pi$
$71$	−9.69135	−1.15015	−0.575076	+	0.818100i	$0.695027\pi$
$72$	2.01366	0.237312
$73$	−1.05277	−0.123217	−0.0616087	−	0.998100i	$-0.519623\pi$
$73$	−1.05277	−0.123217	−0.0616087	+	0.998100i	$0.519623\pi$
$74$	−9.15579	−1.06434
$75$	2.86978	0.331373
$76$	4.39968	0.504678
$77$	0.113904	0.0129806
$78$	−4.04515	−0.458023
$79$	10.0943	1.13570	0.567850	−	0.823132i	$-0.307775\pi$
$79$	10.0943	1.13570	0.567850	+	0.823132i	$0.307775\pi$
$80$	7.23671	0.809089
$81$	1.00000	0.111111
$82$	5.93464	0.655371
$83$	−2.01215	−0.220862	−0.110431	−	0.993884i	$-0.535223\pi$
$83$	−2.01215	−0.220862	−0.110431	+	0.993884i	$0.535223\pi$
$84$	0.0906313	0.00988869
$85$	−6.33371	−0.686988
$86$	−6.08752	−0.656435
$87$	2.97696	0.319163
$88$	−2.01366	−0.214657
$89$	16.8141	1.78229	0.891145	−	0.453719i	$-0.149903\pi$
$89$	16.8141	1.78229	0.891145	+	0.453719i	$0.149903\pi$
$90$	2.44037	0.257238
$91$	0.275569	0.0288875
$92$	−4.46885	−0.465909
$93$	−3.23872	−0.335839
$94$	11.4001	1.17583
$95$	−8.07040	−0.828006
$96$	−4.26302	−0.435093
$97$	−4.43143	−0.449944	−0.224972	−	0.974365i	$-0.572229\pi$
$97$	−4.43143	−0.449944	−0.224972	+	0.974365i	$0.572229\pi$
$98$	11.6825	1.18011
$99$	−1.00000	−0.100504
$100$	−2.28342	−0.228342
$101$	−9.12365	−0.907837	−0.453918	−	0.891043i	$-0.649974\pi$
$101$	−9.12365	−0.907837	−0.453918	+	0.891043i	$0.649974\pi$
$102$	7.25587	0.718439
$103$	−4.46502	−0.439951	−0.219976	−	0.975505i	$-0.570598\pi$
$103$	−4.46502	−0.439951	−0.219976	+	0.975505i	$0.570598\pi$
$104$	−4.87165	−0.477705
$105$	−0.166247	−0.0162240
$106$	0.206144	0.0200225
$107$	3.58525	0.346599	0.173300	−	0.984869i	$-0.444557\pi$
$107$	3.58525	0.346599	0.173300	+	0.984869i	$0.444557\pi$
$108$	−0.795679	−0.0765643
$109$	3.16796	0.303435	0.151718	−	0.988424i	$-0.451520\pi$
$109$	3.16796	0.303435	0.151718	+	0.988424i	$0.451520\pi$
$110$	−2.44037	−0.232680
$111$	−5.47586	−0.519745
$112$	0.564766	0.0533654
$113$	9.84126	0.925788	0.462894	−	0.886414i	$-0.346811\pi$
$113$	9.84126	0.925788	0.462894	+	0.886414i	$0.346811\pi$
$114$	9.24541	0.865912
$115$	8.19728	0.764400
$116$	−2.36870	−0.219929
$117$	−2.41931	−0.223665
$118$	24.8063	2.28361
$119$	−0.494295	−0.0453119
$120$	2.93899	0.268292
$121$	1.00000	0.0909091
$122$	−1.67203	−0.151378
$123$	3.54936	0.320035
$124$	2.57698	0.231420
$125$	11.4862	1.02735
$126$	0.190451	0.0169667
$127$	7.25474	0.643754	0.321877	−	0.946782i	$-0.395686\pi$
$127$	7.25474	0.643754	0.321877	+	0.946782i	$0.395686\pi$
$128$	−13.1887	−1.16573
$129$	−3.64080	−0.320555
$130$	−5.90401	−0.517816
$131$	5.18052	0.452624	0.226312	−	0.974055i	$-0.427333\pi$
$131$	5.18052	0.452624	0.226312	+	0.974055i	$0.427333\pi$
$132$	0.795679	0.0692550
$133$	−0.629829	−0.0546131
$134$	−15.3166	−1.32315
$135$	1.45953	0.125616
$136$	8.73840	0.749311
$137$	15.9087	1.35918	0.679588	−	0.733594i	$-0.262159\pi$
$137$	15.9087	1.35918	0.679588	+	0.733594i	$0.262159\pi$
$138$	−9.39076	−0.799395
$139$	17.4182	1.47740	0.738698	−	0.674037i	$-0.235441\pi$
$139$	17.4182	1.47740	0.738698	+	0.674037i	$0.235441\pi$
$140$	0.132279	0.0111796
$141$	6.81812	0.574189
$142$	16.2042	1.35983
$143$	2.41931	0.202312
$144$	−4.95825	−0.413188
$145$	4.34495	0.360829
$146$	1.76026	0.145680
$147$	6.98703	0.576280
$148$	4.35703	0.358145
$149$	−20.0971	−1.64642	−0.823208	−	0.567740i	$-0.807818\pi$
$149$	−20.0971	−1.64642	−0.823208	+	0.567740i	$0.807818\pi$
$150$	−4.79835	−0.391784
$151$	14.1784	1.15382	0.576910	−	0.816808i	$-0.304258\pi$
$151$	14.1784	1.15382	0.576910	+	0.816808i	$0.304258\pi$
$152$	11.1344	0.903123
$153$	4.33956	0.350833
$154$	−0.190451	−0.0153470
$155$	−4.72700	−0.379682
$156$	1.92499	0.154123
$157$	4.99242	0.398439	0.199219	−	0.979955i	$-0.436159\pi$
$157$	4.99242	0.398439	0.199219	+	0.979955i	$0.436159\pi$
$158$	−16.8780	−1.34274
$159$	0.123290	0.00977752
$160$	−6.22200	−0.491892
$161$	0.639731	0.0504179
$162$	−1.67203	−0.131367
$163$	−5.98250	−0.468586	−0.234293	−	0.972166i	$-0.575277\pi$
$163$	−5.98250	−0.468586	−0.234293	+	0.972166i	$0.575277\pi$
$164$	−2.82416	−0.220529
$165$	−1.45953	−0.113624
$166$	3.36438	0.261126
$167$	24.2227	1.87441	0.937203	−	0.348784i	$-0.113405\pi$
$167$	24.2227	1.87441	0.937203	+	0.348784i	$0.113405\pi$
$168$	0.229364	0.0176958
$169$	−7.14696	−0.549766
$170$	10.5901	0.812227
$171$	5.52946	0.422848
$172$	2.89691	0.220887
$173$	11.4724	0.872227	0.436114	−	0.899892i	$-0.356355\pi$
$173$	11.4724	0.872227	0.436114	+	0.899892i	$0.356355\pi$
$174$	−4.97756	−0.377348
$175$	0.326880	0.0247098
$176$	4.95825	0.373742
$177$	14.8361	1.11515
$178$	−28.1136	−2.10721
$179$	16.7617	1.25283	0.626413	−	0.779492i	$-0.284523\pi$
$179$	16.7617	1.25283	0.626413	+	0.779492i	$0.284523\pi$
$180$	−1.16132	−0.0865594
$181$	23.4517	1.74315	0.871574	−	0.490264i	$-0.163100\pi$
$181$	23.4517	1.74315	0.871574	+	0.490264i	$0.163100\pi$
$182$	−0.460760	−0.0341538
$183$	−1.00000	−0.0739221
$184$	−11.3095	−0.833747
$185$	−7.99217	−0.587596
$186$	5.41523	0.397064
$187$	−4.33956	−0.317340
$188$	−5.42504	−0.395662
$189$	0.113904	0.00828532
$190$	13.4939	0.978953
$191$	−8.77663	−0.635054	−0.317527	−	0.948249i	$-0.602852\pi$
$191$	−8.77663	−0.635054	−0.317527	+	0.948249i	$0.602852\pi$
$192$	−2.78861	−0.201250
$193$	11.8741	0.854716	0.427358	−	0.904083i	$-0.359444\pi$
$193$	11.8741	0.854716	0.427358	+	0.904083i	$0.359444\pi$
$194$	7.40948	0.531970
$195$	−3.53104	−0.252863
$196$	−5.55943	−0.397102
$197$	−6.68035	−0.475956	−0.237978	−	0.971271i	$-0.576485\pi$
$197$	−6.68035	−0.475956	−0.237978	+	0.971271i	$0.576485\pi$
$198$	1.67203	0.118826
$199$	−12.2108	−0.865602	−0.432801	−	0.901490i	$-0.642475\pi$
$199$	−12.2108	−0.865602	−0.432801	+	0.901490i	$0.642475\pi$
$200$	−5.77875	−0.408620
$201$	−9.16048	−0.646131
$202$	15.2550	1.07334
$203$	0.339088	0.0237993
$204$	−3.45290	−0.241751
$205$	5.18039	0.361814
$206$	7.46564	0.520156
$207$	−5.61639	−0.390366
$208$	11.9955	0.831740
$209$	−5.52946	−0.382481
$210$	0.277969	0.0191817
$211$	2.24877	0.154812	0.0774058	−	0.997000i	$-0.475336\pi$
$211$	2.24877	0.154812	0.0774058	+	0.997000i	$0.475336\pi$
$212$	−0.0980991	−0.00673748
$213$	9.69135	0.664040
$214$	−5.99464	−0.409785
$215$	−5.31385	−0.362402
$216$	−2.01366	−0.137012
$217$	−0.368904	−0.0250428
$218$	−5.29692	−0.358753
$219$	1.05277	0.0711396
$220$	1.16132	0.0782959
$221$	−10.4987	−0.706221
$222$	9.15579	0.614496
$223$	25.2425	1.69036	0.845181	−	0.534480i	$-0.179493\pi$
$223$	25.2425	1.69036	0.845181	+	0.534480i	$0.179493\pi$
$224$	−0.485577	−0.0324440
$225$	−2.86978	−0.191319
$226$	−16.4549	−1.09456
$227$	−15.9227	−1.05682	−0.528412	−	0.848988i	$-0.677212\pi$
$227$	−15.9227	−1.05682	−0.528412	+	0.848988i	$0.677212\pi$
$228$	−4.39968	−0.291376
$229$	4.84415	0.320111	0.160055	−	0.987108i	$-0.448833\pi$
$229$	4.84415	0.320111	0.160055	+	0.987108i	$0.448833\pi$
$230$	−13.7061	−0.903752
$231$	−0.113904	−0.00749435
$232$	−5.99457	−0.393563
$233$	−6.87950	−0.450691	−0.225346	−	0.974279i	$-0.572351\pi$
$233$	−6.87950	−0.450691	−0.225346	+	0.974279i	$0.572351\pi$
$234$	4.04515	0.264440
$235$	9.95124	0.649147
$236$	−11.8048	−0.768425
$237$	−10.0943	−0.655697
$238$	0.826475	0.0535724
$239$	26.2207	1.69607	0.848037	−	0.529938i	$-0.177785\pi$
$239$	26.2207	1.69607	0.848037	+	0.529938i	$0.177785\pi$
$240$	−7.23671	−0.467128
$241$	−21.9334	−1.41286	−0.706428	−	0.707785i	$-0.749694\pi$
$241$	−21.9334	−1.41286	−0.706428	+	0.707785i	$0.749694\pi$
$242$	−1.67203	−0.107482
$243$	−1.00000	−0.0641500
$244$	0.795679	0.0509382
$245$	10.1978	0.651511
$246$	−5.93464	−0.378379
$247$	−13.3775	−0.851187
$248$	6.52167	0.414127
$249$	2.01215	0.127515
$250$	−19.2052	−1.21464
$251$	24.9091	1.57225	0.786125	−	0.618068i	$-0.212084\pi$
$251$	24.9091	1.57225	0.786125	+	0.618068i	$0.212084\pi$
$252$	−0.0906313	−0.00570924
$253$	5.61639	0.353099
$254$	−12.1301	−0.761112
$255$	6.33371	0.396633
$256$	16.4746	1.02966
$257$	0.438875	0.0273763	0.0136881	−	0.999906i	$-0.495643\pi$
$257$	0.438875	0.0273763	0.0136881	+	0.999906i	$0.495643\pi$
$258$	6.08752	0.378993
$259$	−0.623724	−0.0387563
$260$	2.80958	0.174243
$261$	−2.97696	−0.184269
$262$	−8.66198	−0.535139
$263$	21.5826	1.33084	0.665421	−	0.746469i	$-0.268252\pi$
$263$	21.5826	1.33084	0.665421	+	0.746469i	$0.268252\pi$
$264$	2.01366	0.123932
$265$	0.179945	0.0110539
$266$	1.05309	0.0645692
$267$	−16.8141	−1.02901
$268$	7.28881	0.445235
$269$	−24.6911	−1.50544	−0.752720	−	0.658341i	$-0.771259\pi$
$269$	−24.6911	−1.50544	−0.752720	+	0.658341i	$0.771259\pi$
$270$	−2.44037	−0.148516
$271$	−18.7879	−1.14128	−0.570641	−	0.821200i	$-0.693305\pi$
$271$	−18.7879	−1.14128	−0.570641	+	0.821200i	$0.693305\pi$
$272$	−21.5167	−1.30464
$273$	−0.275569	−0.0166782
$274$	−26.5999	−1.60696
$275$	2.86978	0.173054
$276$	4.46885	0.268993
$277$	−1.86162	−0.111854	−0.0559270	−	0.998435i	$-0.517811\pi$
$277$	−1.86162	−0.111854	−0.0559270	+	0.998435i	$0.517811\pi$
$278$	−29.1238	−1.74673
$279$	3.23872	0.193897
$280$	0.334764	0.0200060
$281$	12.0550	0.719140	0.359570	−	0.933118i	$-0.382923\pi$
$281$	12.0550	0.719140	0.359570	+	0.933118i	$0.382923\pi$
$282$	−11.4001	−0.678866
$283$	17.4984	1.04017	0.520084	−	0.854115i	$-0.325900\pi$
$283$	17.4984	1.04017	0.520084	+	0.854115i	$0.325900\pi$
$284$	−7.71121	−0.457576
$285$	8.07040	0.478049
$286$	−4.04515	−0.239195
$287$	0.404288	0.0238644
$288$	4.26302	0.251201
$289$	1.83181	0.107754
$290$	−7.26488	−0.426609
$291$	4.43143	0.259775
$292$	−0.837667	−0.0490208
$293$	−4.01414	−0.234509	−0.117254	−	0.993102i	$-0.537409\pi$
$293$	−4.01414	−0.234509	−0.117254	+	0.993102i	$0.537409\pi$
$294$	−11.6825	−0.681338
$295$	21.6537	1.26073
$296$	11.0265	0.640903
$297$	1.00000	0.0580259
$298$	33.6029	1.94656
$299$	13.5878	0.785801
$300$	2.28342	0.131834
$301$	−0.414703	−0.0239031
$302$	−23.7066	−1.36416
$303$	9.12365	0.524140
$304$	−27.4165	−1.57244
$305$	−1.45953	−0.0835723
$306$	−7.25587	−0.414791
$307$	15.3443	0.875746	0.437873	−	0.899037i	$-0.355732\pi$
$307$	15.3443	0.875746	0.437873	+	0.899037i	$0.355732\pi$
$308$	0.0906313	0.00516420
$309$	4.46502	0.254006
$310$	7.90368	0.448899
$311$	28.3138	1.60553	0.802764	−	0.596297i	$-0.203362\pi$
$311$	28.3138	1.60553	0.802764	+	0.596297i	$0.203362\pi$
$312$	4.87165	0.275803
$313$	26.2747	1.48513	0.742567	−	0.669771i	$-0.233608\pi$
$313$	26.2747	1.48513	0.742567	+	0.669771i	$0.233608\pi$
$314$	−8.34748	−0.471075
$315$	0.166247	0.00936693
$316$	8.03185	0.451827
$317$	31.0474	1.74379	0.871897	−	0.489689i	$-0.162890\pi$
$317$	31.0474	1.74379	0.871897	+	0.489689i	$0.162890\pi$
$318$	−0.206144	−0.0115600
$319$	2.97696	0.166678
$320$	−4.07005	−0.227523
$321$	−3.58525	−0.200109
$322$	−1.06965	−0.0596092
$323$	23.9954	1.33514
$324$	0.795679	0.0442044
$325$	6.94287	0.385121
$326$	10.0029	0.554010
$327$	−3.16796	−0.175189
$328$	−7.14720	−0.394638
$329$	0.776614	0.0428161
$330$	2.44037	0.134338
$331$	−20.5558	−1.12985	−0.564924	−	0.825143i	$-0.691094\pi$
$331$	−20.5558	−1.12985	−0.564924	+	0.825143i	$0.691094\pi$
$332$	−1.60103	−0.0878679
$333$	5.47586	0.300075
$334$	−40.5010	−2.21612
$335$	−13.3700	−0.730480
$336$	−0.564766	−0.0308105
$337$	−0.489461	−0.0266626	−0.0133313	−	0.999911i	$-0.504244\pi$
$337$	−0.489461	−0.0266626	−0.0133313	+	0.999911i	$0.504244\pi$
$338$	11.9499	0.649990
$339$	−9.84126	−0.534504
$340$	−5.03961	−0.273311
$341$	−3.23872	−0.175386
$342$	−9.24541	−0.499935
$343$	1.59318	0.0860238
$344$	7.33133	0.395279
$345$	−8.19728	−0.441327
$346$	−19.1821	−1.03124
$347$	−8.54263	−0.458593	−0.229296	−	0.973357i	$-0.573642\pi$
$347$	−8.54263	−0.458593	−0.229296	+	0.973357i	$0.573642\pi$
$348$	2.36870	0.126976
$349$	28.5046	1.52582	0.762909	−	0.646506i	$-0.223770\pi$
$349$	28.5046	1.52582	0.762909	+	0.646506i	$0.223770\pi$
$350$	−0.546553	−0.0292145
$351$	2.41931	0.129133
$352$	−4.26302	−0.227220
$353$	15.4235	0.820912	0.410456	−	0.911880i	$-0.365370\pi$
$353$	15.4235	0.820912	0.410456	+	0.911880i	$0.365370\pi$
$354$	−24.8063	−1.31844
$355$	14.1448	0.750728
$356$	13.3786	0.709066
$357$	0.494295	0.0261609
$358$	−28.0260	−1.48122
$359$	−30.6063	−1.61534	−0.807669	−	0.589637i	$-0.799271\pi$
$359$	−30.6063	−1.61534	−0.807669	+	0.589637i	$0.799271\pi$
$360$	−2.93899	−0.154898
$361$	11.5749	0.609206
$362$	−39.2118	−2.06093
$363$	−1.00000	−0.0524864
$364$	0.219265	0.0114926
$365$	1.53655	0.0804265
$366$	1.67203	0.0873983
$367$	2.65622	0.138654	0.0693268	−	0.997594i	$-0.477915\pi$
$367$	2.65622	0.138654	0.0693268	+	0.997594i	$0.477915\pi$
$368$	27.8475	1.45165
$369$	−3.54936	−0.184772
$370$	13.3631	0.694716
$371$	0.0140432	0.000729089 0
$372$	−2.57698	−0.133610
$373$	−0.426449	−0.0220807	−0.0110404	−	0.999939i	$-0.503514\pi$
$373$	−0.426449	−0.0220807	−0.0110404	+	0.999939i	$0.503514\pi$
$374$	7.25587	0.375192
$375$	−11.4862	−0.593143
$376$	−13.7294	−0.708038
$377$	7.20217	0.370931
$378$	−0.190451	−0.00979576
$379$	28.8875	1.48385	0.741925	−	0.670483i	$-0.233913\pi$
$379$	28.8875	1.48385	0.741925	+	0.670483i	$0.233913\pi$
$380$	−6.42145	−0.329414
$381$	−7.25474	−0.371671
$382$	14.6748	0.750827
$383$	−29.4474	−1.50469	−0.752346	−	0.658768i	$-0.771078\pi$
$383$	−29.4474	−1.50469	−0.752346	+	0.658768i	$0.771078\pi$
$384$	13.1887	0.673032
$385$	−0.166247	−0.00847271
$386$	−19.8538	−1.01053
$387$	3.64080	0.185072
$388$	−3.52600	−0.179006
$389$	−11.6234	−0.589329	−0.294665	−	0.955601i	$-0.595208\pi$
$389$	−11.6234	−0.589329	−0.294665	+	0.955601i	$0.595208\pi$
$390$	5.90401	0.298961
$391$	−24.3727	−1.23258
$392$	−14.0695	−0.710616
$393$	−5.18052	−0.261323
$394$	11.1697	0.562724
$395$	−14.7330	−0.741295
$396$	−0.795679	−0.0399844
$397$	−25.8143	−1.29558	−0.647791	−	0.761818i	$-0.724307\pi$
$397$	−25.8143	−1.29558	−0.647791	+	0.761818i	$0.724307\pi$
$398$	20.4168	1.02340
$399$	0.629829	0.0315309
$400$	14.2291	0.711454
$401$	−6.33074	−0.316142	−0.158071	−	0.987428i	$-0.550528\pi$
$401$	−6.33074	−0.316142	−0.158071	+	0.987428i	$0.550528\pi$
$402$	15.3166	0.763922
$403$	−7.83545	−0.390312
$404$	−7.25950	−0.361174
$405$	−1.45953	−0.0725245
$406$	−0.566965	−0.0281380
$407$	−5.47586	−0.271428
$408$	−8.73840	−0.432615
$409$	−17.4823	−0.864446	−0.432223	−	0.901767i	$-0.642271\pi$
$409$	−17.4823	−0.864446	−0.432223	+	0.901767i	$0.642271\pi$
$410$	−8.66177	−0.427774
$411$	−15.9087	−0.784720
$412$	−3.55272	−0.175030
$413$	1.68989	0.0831542
$414$	9.39076	0.461531
$415$	2.93679	0.144161
$416$	−10.3136	−0.505664
$417$	−17.4182	−0.852974
$418$	9.24541	0.452208
$419$	16.0311	0.783171	0.391585	−	0.920142i	$-0.371927\pi$
$419$	16.0311	0.783171	0.391585	+	0.920142i	$0.371927\pi$
$420$	−0.132279	−0.00645455
$421$	2.65713	0.129500	0.0647502	−	0.997902i	$-0.479375\pi$
$421$	2.65713	0.129500	0.0647502	+	0.997902i	$0.479375\pi$
$422$	−3.76001	−0.183034
$423$	−6.81812	−0.331508
$424$	−0.248263	−0.0120567
$425$	−12.4536	−0.604088
$426$	−16.2042	−0.785097
$427$	−0.113904	−0.00551222
$428$	2.85271	0.137891
$429$	−2.41931	−0.116805
$430$	8.88491	0.428468
$431$	−16.3460	−0.787358	−0.393679	−	0.919248i	$-0.628798\pi$
$431$	−16.3460	−0.787358	−0.393679	+	0.919248i	$0.628798\pi$
$432$	4.95825	0.238554
$433$	−19.2280	−0.924038	−0.462019	−	0.886870i	$-0.652875\pi$
$433$	−19.2280	−0.924038	−0.462019	+	0.886870i	$0.652875\pi$
$434$	0.616818	0.0296082
$435$	−4.34495	−0.208324
$436$	2.52068	0.120719
$437$	−31.0556	−1.48559
$438$	−1.76026	−0.0841085
$439$	−1.73219	−0.0826728	−0.0413364	−	0.999145i	$-0.513162\pi$
$439$	−1.73219	−0.0826728	−0.0413364	+	0.999145i	$0.513162\pi$
$440$	2.93899	0.140111
$441$	−6.98703	−0.332716
$442$	17.5542	0.834967
$443$	12.1970	0.579497	0.289749	−	0.957103i	$-0.406428\pi$
$443$	12.1970	0.579497	0.289749	+	0.957103i	$0.406428\pi$
$444$	−4.35703	−0.206775
$445$	−24.5406	−1.16334
$446$	−42.2062	−1.99852
$447$	20.0971	0.950559
$448$	−0.317635	−0.0150068
$449$	−17.4644	−0.824195	−0.412098	−	0.911140i	$-0.635204\pi$
$449$	−17.4644	−0.824195	−0.412098	+	0.911140i	$0.635204\pi$
$450$	4.79835	0.226196
$451$	3.54936	0.167133
$452$	7.83049	0.368315
$453$	−14.1784	−0.666158
$454$	26.6232	1.24949
$455$	−0.402201	−0.0188555
$456$	−11.1344	−0.521418
$457$	15.5179	0.725897	0.362949	−	0.931809i	$-0.381770\pi$
$457$	15.5179	0.725897	0.362949	+	0.931809i	$0.381770\pi$
$458$	−8.09956	−0.378468
$459$	−4.33956	−0.202553
$460$	6.52241	0.304109
$461$	−12.5703	−0.585458	−0.292729	−	0.956195i	$-0.594563\pi$
$461$	−12.5703	−0.585458	−0.292729	+	0.956195i	$0.594563\pi$
$462$	0.190451	0.00886059
$463$	12.0019	0.557778	0.278889	−	0.960323i	$-0.410034\pi$
$463$	12.0019	0.557778	0.278889	+	0.960323i	$0.410034\pi$
$464$	14.7605	0.685239
$465$	4.72700	0.219209
$466$	11.5027	0.532853
$467$	37.4089	1.73108	0.865539	−	0.500842i	$-0.166976\pi$
$467$	37.4089	1.73108	0.865539	+	0.500842i	$0.166976\pi$
$468$	−1.92499	−0.0889828
$469$	−1.04342	−0.0481806
$470$	−16.6388	−0.767489
$471$	−4.99242	−0.230039
$472$	−29.8748	−1.37510
$473$	−3.64080	−0.167404
$474$	16.8780	0.775232
$475$	−15.8683	−0.728089
$476$	−0.393300	−0.0180269
$477$	−0.123290	−0.00564505
$478$	−43.8417	−2.00527
$479$	−17.7608	−0.811514	−0.405757	−	0.913981i	$-0.632992\pi$
$479$	−17.7608	−0.811514	−0.405757	+	0.913981i	$0.632992\pi$
$480$	6.22200	0.283994
$481$	−13.2478	−0.604046
$482$	36.6733	1.67042
$483$	−0.639731	−0.0291088
$484$	0.795679	0.0361672
$485$	6.46780	0.293688
$486$	1.67203	0.0758448
$487$	−13.1113	−0.594129	−0.297064	−	0.954857i	$-0.596008\pi$
$487$	−13.1113	−0.594129	−0.297064	+	0.954857i	$0.596008\pi$
$488$	2.01366	0.0911540
$489$	5.98250	0.270538
$490$	−17.0509	−0.770283
$491$	−22.4438	−1.01287	−0.506437	−	0.862277i	$-0.669038\pi$
$491$	−22.4438	−1.01287	−0.506437	+	0.862277i	$0.669038\pi$
$492$	2.82416	0.127323
$493$	−12.9187	−0.581829
$494$	22.3675	1.00636
$495$	1.45953	0.0656009
$496$	−16.0584	−0.721043
$497$	1.10389	0.0495161
$498$	−3.36438	−0.150761
$499$	17.9269	0.802517	0.401259	−	0.915965i	$-0.368573\pi$
$499$	17.9269	0.802517	0.401259	+	0.915965i	$0.368573\pi$
$500$	9.13930	0.408722
$501$	−24.2227	−1.08219
$502$	−41.6487	−1.85887
$503$	−43.4638	−1.93796	−0.968978	−	0.247148i	$-0.920507\pi$
$503$	−43.4638	−1.93796	−0.968978	+	0.247148i	$0.920507\pi$
$504$	−0.229364	−0.0102167
$505$	13.3162	0.592564
$506$	−9.39076	−0.417470
$507$	7.14696	0.317408
$508$	5.77245	0.256111
$509$	3.04838	0.135117	0.0675585	−	0.997715i	$-0.478479\pi$
$509$	3.04838	0.135117	0.0675585	+	0.997715i	$0.478479\pi$
$510$	−10.5901	−0.468940
$511$	0.119915	0.00530473
$512$	−1.16870	−0.0516496
$513$	−5.52946	−0.244132
$514$	−0.733812	−0.0323670
$515$	6.51682	0.287165
$516$	−2.89691	−0.127529
$517$	6.81812	0.299861
$518$	1.04288	0.0458217
$519$	−11.4724	−0.503581
$520$	7.11032	0.311808
$521$	−4.92667	−0.215841	−0.107921	−	0.994160i	$-0.534419\pi$
$521$	−4.92667	−0.215841	−0.107921	+	0.994160i	$0.534419\pi$
$522$	4.97756	0.217862
$523$	1.37122	0.0599595	0.0299797	−	0.999551i	$-0.490456\pi$
$523$	1.37122	0.0599595	0.0299797	+	0.999551i	$0.490456\pi$
$524$	4.12203	0.180072
$525$	−0.326880	−0.0142662
$526$	−36.0867	−1.57346
$527$	14.0546	0.612229
$528$	−4.95825	−0.215780
$529$	8.54384	0.371471
$530$	−0.300873	−0.0130691
$531$	−14.8361	−0.643831
$532$	−0.501142	−0.0217273
$533$	8.58699	0.371944
$534$	28.1136	1.21660
$535$	−5.23277	−0.226232
$536$	18.4461	0.796750
$537$	−16.7617	−0.723319
$538$	41.2842	1.77989
$539$	6.98703	0.300953
$540$	1.16132	0.0499751
$541$	−37.0801	−1.59420	−0.797099	−	0.603848i	$-0.793633\pi$
$541$	−37.0801	−1.59420	−0.797099	+	0.603848i	$0.793633\pi$
$542$	31.4139	1.34934
$543$	−23.4517	−1.00641
$544$	18.4997	0.793167
$545$	−4.62372	−0.198059
$546$	0.460760	0.0197187
$547$	11.1746	0.477790	0.238895	−	0.971045i	$-0.423215\pi$
$547$	11.1746	0.477790	0.238895	+	0.971045i	$0.423215\pi$
$548$	12.6583	0.540734
$549$	1.00000	0.0426790
$550$	−4.79835	−0.204602
$551$	−16.4610	−0.701261
$552$	11.3095	0.481364
$553$	−1.14979	−0.0488939
$554$	3.11268	0.132245
$555$	7.99217	0.339249
$556$	13.8593	0.587766
$557$	−15.3427	−0.650092	−0.325046	−	0.945698i	$-0.605380\pi$
$557$	−15.3427	−0.650092	−0.325046	+	0.945698i	$0.605380\pi$
$558$	−5.41523	−0.229245
$559$	−8.80821	−0.372548
$560$	−0.824292	−0.0348327
$561$	4.33956	0.183217
$562$	−20.1563	−0.850241
$563$	43.3954	1.82890	0.914449	−	0.404701i	$-0.132624\pi$
$563$	43.3954	1.82890	0.914449	+	0.404701i	$0.132624\pi$
$564$	5.42504	0.228435
$565$	−14.3636	−0.604281
$566$	−29.2577	−1.22979
$567$	−0.113904	−0.00478353
$568$	−19.5151	−0.818834
$569$	1.47086	0.0616615	0.0308308	−	0.999525i	$-0.490185\pi$
$569$	1.47086	0.0616615	0.0308308	+	0.999525i	$0.490185\pi$
$570$	−13.4939	−0.565199
$571$	−7.09968	−0.297112	−0.148556	−	0.988904i	$-0.547463\pi$
$571$	−7.09968	−0.297112	−0.148556	+	0.988904i	$0.547463\pi$
$572$	1.92499	0.0804879
$573$	8.77663	0.366649
$574$	−0.675981	−0.0282149
$575$	16.1178	0.672159
$576$	2.78861	0.116192
$577$	−20.6477	−0.859575	−0.429788	−	0.902930i	$-0.641412\pi$
$577$	−20.6477	−0.859575	−0.429788	+	0.902930i	$0.641412\pi$
$578$	−3.06284	−0.127397
$579$	−11.8741	−0.493470
$580$	3.45719	0.143552
$581$	0.229193	0.00950852
$582$	−7.40948	−0.307133
$583$	0.123290	0.00510614
$584$	−2.11992	−0.0877229
$585$	3.53104	0.145991
$586$	6.71176	0.277260
$587$	−3.56601	−0.147185	−0.0735925	−	0.997288i	$-0.523446\pi$
$587$	−3.56601	−0.147185	−0.0735925	+	0.997288i	$0.523446\pi$
$588$	5.55943	0.229267
$589$	17.9084	0.737901
$590$	−36.2056	−1.49056
$591$	6.68035	0.274793
$592$	−27.1507	−1.11589
$593$	23.6716	0.972077	0.486038	−	0.873937i	$-0.338442\pi$
$593$	23.6716	0.972077	0.486038	+	0.873937i	$0.338442\pi$
$594$	−1.67203	−0.0686042
$595$	0.721437	0.0295760
$596$	−15.9908	−0.655010
$597$	12.2108	0.499755
$598$	−22.7191	−0.929054
$599$	34.3309	1.40272	0.701360	−	0.712807i	$-0.252576\pi$
$599$	34.3309	1.40272	0.701360	+	0.712807i	$0.252576\pi$
$600$	5.77875	0.235917
$601$	2.29548	0.0936346	0.0468173	−	0.998903i	$-0.485092\pi$
$601$	2.29548	0.0936346	0.0468173	+	0.998903i	$0.485092\pi$
$602$	0.693395	0.0282607
$603$	9.16048	0.373044
$604$	11.2814	0.459035
$605$	−1.45953	−0.0593382
$606$	−15.2550	−0.619692
$607$	−47.1071	−1.91202	−0.956010	−	0.293335i	$-0.905235\pi$
$607$	−47.1071	−1.91202	−0.956010	+	0.293335i	$0.905235\pi$
$608$	23.5722	0.955980
$609$	−0.339088	−0.0137405
$610$	2.44037	0.0988078
$611$	16.4951	0.667321
$612$	3.45290	0.139575
$613$	19.9949	0.807586	0.403793	−	0.914850i	$-0.367692\pi$
$613$	19.9949	0.807586	0.403793	+	0.914850i	$0.367692\pi$
$614$	−25.6561	−1.03540
$615$	−5.18039	−0.208894
$616$	0.229364	0.00924135
$617$	28.3395	1.14090	0.570452	−	0.821331i	$-0.306768\pi$
$617$	28.3395	1.14090	0.570452	+	0.821331i	$0.306768\pi$
$618$	−7.46564	−0.300312
$619$	−18.4108	−0.739994	−0.369997	−	0.929033i	$-0.620641\pi$
$619$	−18.4108	−0.739994	−0.369997	+	0.929033i	$0.620641\pi$
$620$	−3.76118	−0.151053
$621$	5.61639	0.225378
$622$	−47.3415	−1.89822
$623$	−1.91520	−0.0767308
$624$	−11.9955	−0.480206
$625$	−2.41548	−0.0966192
$626$	−43.9321	−1.75588
$627$	5.52946	0.220825
$628$	3.97237	0.158515
$629$	23.7628	0.947486
$630$	−0.277969	−0.0110745
$631$	7.42123	0.295435	0.147717	−	0.989030i	$-0.452807\pi$
$631$	7.42123	0.295435	0.147717	+	0.989030i	$0.452807\pi$
$632$	20.3265	0.808546
$633$	−2.24877	−0.0893806
$634$	−51.9121	−2.06169
$635$	−10.5885	−0.420191
$636$	0.0980991	0.00388988
$637$	16.9038	0.669751
$638$	−4.97756	−0.197063
$639$	−9.69135	−0.383384
$640$	19.2492	0.760893
$641$	6.86699	0.271230	0.135615	−	0.990762i	$-0.456699\pi$
$641$	6.86699	0.271230	0.135615	+	0.990762i	$0.456699\pi$
$642$	5.99464	0.236589
$643$	45.7495	1.80418	0.902092	−	0.431544i	$-0.142031\pi$
$643$	45.7495	1.80418	0.902092	+	0.431544i	$0.142031\pi$
$644$	0.509021	0.0200582
$645$	5.31385	0.209233
$646$	−40.1211	−1.57854
$647$	−17.7282	−0.696968	−0.348484	−	0.937315i	$-0.613303\pi$
$647$	−17.7282	−0.696968	−0.348484	+	0.937315i	$0.613303\pi$
$648$	2.01366	0.0791040
$649$	14.8361	0.582367
$650$	−11.6087	−0.455330
$651$	0.368904	0.0144585
$652$	−4.76015	−0.186422
$653$	25.1767	0.985239	0.492619	−	0.870245i	$-0.336040\pi$
$653$	25.1767	0.985239	0.492619	+	0.870245i	$0.336040\pi$
$654$	5.29692	0.207126
$655$	−7.56112	−0.295437
$656$	17.5986	0.687111
$657$	−1.05277	−0.0410725
$658$	−1.29852	−0.0506216
$659$	47.2222	1.83951	0.919757	−	0.392487i	$-0.128385\pi$
$659$	47.2222	1.83951	0.919757	+	0.392487i	$0.128385\pi$
$660$	−1.16132	−0.0452042
$661$	−10.8885	−0.423512	−0.211756	−	0.977323i	$-0.567918\pi$
$661$	−10.8885	−0.423512	−0.211756	+	0.977323i	$0.567918\pi$
$662$	34.3698	1.33582
$663$	10.4987	0.407737
$664$	−4.05179	−0.157240
$665$	0.919253	0.0356471
$666$	−9.15579	−0.354780
$667$	16.7198	0.647391
$668$	19.2735	0.745713
$669$	−25.2425	−0.975931
$670$	22.3550	0.863649
$671$	−1.00000	−0.0386046
$672$	0.485577	0.0187315
$673$	−3.19833	−0.123287	−0.0616433	−	0.998098i	$-0.519634\pi$
$673$	−3.19833	−0.123287	−0.0616433	+	0.998098i	$0.519634\pi$
$674$	0.818392	0.0315233
$675$	2.86978	0.110458
$676$	−5.68669	−0.218719
$677$	−20.9309	−0.804439	−0.402219	−	0.915543i	$-0.631761\pi$
$677$	−20.9309	−0.804439	−0.402219	+	0.915543i	$0.631761\pi$
$678$	16.4549	0.631945
$679$	0.504759	0.0193709
$680$	−12.7539	−0.489091
$681$	15.9227	0.610158
$682$	5.41523	0.207360
$683$	9.41323	0.360187	0.180094	−	0.983649i	$-0.442360\pi$
$683$	9.41323	0.360187	0.180094	+	0.983649i	$0.442360\pi$
$684$	4.39968	0.168226
$685$	−23.2193	−0.887162
$686$	−2.66385	−0.101706
$687$	−4.84415	−0.184816
$688$	−18.0520	−0.688227
$689$	0.298276	0.0113634
$690$	13.7061	0.521782
$691$	34.9093	1.32801	0.664006	−	0.747727i	$-0.268855\pi$
$691$	34.9093	1.32801	0.664006	+	0.747727i	$0.268855\pi$
$692$	9.12832	0.347007
$693$	0.113904	0.00432687
$694$	14.2835	0.542195
$695$	−25.4224	−0.964326
$696$	5.99457	0.227224
$697$	−15.4027	−0.583418
$698$	−47.6606	−1.80398
$699$	6.87950	0.260207
$700$	0.260092	0.00983055
$701$	−21.4585	−0.810478	−0.405239	−	0.914211i	$-0.632812\pi$
$701$	−21.4585	−0.810478	−0.405239	+	0.914211i	$0.632812\pi$
$702$	−4.04515	−0.152674
$703$	30.2785	1.14198
$704$	−2.78861	−0.105100
$705$	−9.95124	−0.374785
$706$	−25.7886	−0.970566
$707$	1.03922	0.0390840
$708$	11.8048	0.443650
$709$	14.7920	0.555527	0.277764	−	0.960649i	$-0.410407\pi$
$709$	14.7920	0.555527	0.277764	+	0.960649i	$0.410407\pi$
$710$	−23.6505	−0.887588
$711$	10.0943	0.378567
$712$	33.8578	1.26888
$713$	−18.1899	−0.681217
$714$	−0.826475	−0.0309301
$715$	−3.53104	−0.132054
$716$	13.3369	0.498424
$717$	−26.2207	−0.979228
$718$	51.1746	1.90982
$719$	3.91313	0.145935	0.0729676	−	0.997334i	$-0.476753\pi$
$719$	3.91313	0.145935	0.0729676	+	0.997334i	$0.476753\pi$
$720$	7.23671	0.269696
$721$	0.508585	0.0189407
$722$	−19.3536	−0.720266
$723$	21.9334	0.815712
$724$	18.6600	0.693494
$725$	8.54321	0.317287
$726$	1.67203	0.0620548
$727$	−22.4942	−0.834263	−0.417131	−	0.908846i	$-0.636964\pi$
$727$	−22.4942	−0.834263	−0.417131	+	0.908846i	$0.636964\pi$
$728$	0.554903	0.0205661
$729$	1.00000	0.0370370
$730$	−2.56915	−0.0950885
$731$	15.7995	0.584365
$732$	−0.795679	−0.0294092
$733$	19.0644	0.704161	0.352080	−	0.935970i	$-0.385474\pi$
$733$	19.0644	0.704161	0.352080	+	0.935970i	$0.385474\pi$
$734$	−4.44128	−0.163931
$735$	−10.1978	−0.376150
$736$	−23.9428	−0.882544
$737$	−9.16048	−0.337431
$738$	5.93464	0.218457
$739$	28.1238	1.03455	0.517275	−	0.855819i	$-0.326946\pi$
$739$	28.1238	1.03455	0.517275	+	0.855819i	$0.326946\pi$
$740$	−6.35920	−0.233769
$741$	13.3775	0.491433
$742$	−0.0234807	−0.000862003 0
$743$	26.7820	0.982535	0.491268	−	0.871009i	$-0.336534\pi$
$743$	26.7820	0.982535	0.491268	+	0.871009i	$0.336534\pi$
$744$	−6.52167	−0.239096
$745$	29.3322	1.07465
$746$	0.713036	0.0261061
$747$	−2.01215	−0.0736208
$748$	−3.45290	−0.126251
$749$	−0.408375	−0.0149217
$750$	19.2052	0.701274
$751$	−48.7584	−1.77922	−0.889609	−	0.456722i	$-0.849023\pi$
$751$	−48.7584	−1.77922	−0.889609	+	0.456722i	$0.849023\pi$
$752$	33.8060	1.23278
$753$	−24.9091	−0.907739
$754$	−12.0422	−0.438552
$755$	−20.6937	−0.753122
$756$	0.0906313	0.00329623
$757$	19.1838	0.697246	0.348623	−	0.937263i	$-0.386649\pi$
$757$	19.1838	0.697246	0.348623	+	0.937263i	$0.386649\pi$
$758$	−48.3007	−1.75436
$759$	−5.61639	−0.203862
$760$	−16.2510	−0.589487
$761$	−26.2237	−0.950608	−0.475304	−	0.879822i	$-0.657662\pi$
$761$	−26.2237	−0.950608	−0.475304	+	0.879822i	$0.657662\pi$
$762$	12.1301	0.439428
$763$	−0.360844	−0.0130634
$764$	−6.98338	−0.252650
$765$	−6.33371	−0.228996
$766$	49.2369	1.77900
$767$	35.8930	1.29602
$768$	−16.4746	−0.594477
$769$	−34.4961	−1.24396	−0.621981	−	0.783032i	$-0.713672\pi$
$769$	−34.4961	−1.24396	−0.621981	+	0.783032i	$0.713672\pi$
$770$	0.277969	0.0100173
$771$	−0.438875	−0.0158057
$772$	9.44797	0.340040
$773$	36.7533	1.32192	0.660961	−	0.750420i	$-0.270149\pi$
$773$	36.7533	1.32192	0.660961	+	0.750420i	$0.270149\pi$
$774$	−6.08752	−0.218812
$775$	−9.29441	−0.333865
$776$	−8.92339	−0.320331
$777$	0.623724	0.0223760
$778$	19.4346	0.696766
$779$	−19.6261	−0.703177
$780$	−2.80958	−0.100599
$781$	9.69135	0.346784
$782$	40.7518	1.45728
$783$	2.97696	0.106388
$784$	34.6434	1.23727
$785$	−7.28658	−0.260069
$786$	8.66198	0.308963
$787$	−5.85918	−0.208857	−0.104429	−	0.994532i	$-0.533301\pi$
$787$	−5.85918	−0.208857	−0.104429	+	0.994532i	$0.533301\pi$
$788$	−5.31542	−0.189354
$789$	−21.5826	−0.768361
$790$	24.6339	0.876435
$791$	−1.12096	−0.0398568
$792$	−2.01366	−0.0715522
$793$	−2.41931	−0.0859121
$794$	43.1622	1.53177
$795$	−0.179945	−0.00638199
$796$	−9.71589	−0.344371
$797$	19.2286	0.681112	0.340556	−	0.940224i	$-0.389385\pi$
$797$	19.2286	0.681112	0.340556	+	0.940224i	$0.389385\pi$
$798$	−1.05309	−0.0372791
$799$	−29.5877	−1.04674
$800$	−12.2339	−0.432535
$801$	16.8141	0.594097
$802$	10.5852	0.373776
$803$	1.05277	0.0371514
$804$	−7.28881	−0.257056
$805$	−0.933705	−0.0329088
$806$	13.1011	0.461466
$807$	24.6911	0.869166
$808$	−18.3719	−0.646321
$809$	8.57652	0.301535	0.150767	−	0.988569i	$-0.451826\pi$
$809$	8.57652	0.301535	0.150767	+	0.988569i	$0.451826\pi$
$810$	2.44037	0.0857459
$811$	51.6913	1.81513	0.907564	−	0.419914i	$-0.137940\pi$
$811$	51.6913	1.81513	0.907564	+	0.419914i	$0.137940\pi$
$812$	0.269806	0.00946832
$813$	18.7879	0.658919
$814$	9.15579	0.320910
$815$	8.73163	0.305856
$816$	21.5167	0.753234
$817$	20.1317	0.704318
$818$	29.2310	1.02204
$819$	0.275569	0.00962917
$820$	4.12193	0.143944
$821$	−37.9548	−1.32463	−0.662316	−	0.749224i	$-0.730427\pi$
$821$	−37.9548	−1.32463	−0.662316	+	0.749224i	$0.730427\pi$
$822$	26.5999	0.927777
$823$	23.9123	0.833531	0.416766	−	0.909014i	$-0.363164\pi$
$823$	23.9123	0.833531	0.416766	+	0.909014i	$0.363164\pi$
$824$	−8.99102	−0.313217
$825$	−2.86978	−0.0999129
$826$	−2.82555	−0.0983134
$827$	20.6669	0.718658	0.359329	−	0.933211i	$-0.383006\pi$
$827$	20.6669	0.718658	0.359329	+	0.933211i	$0.383006\pi$
$828$	−4.46885	−0.155303
$829$	9.30470	0.323166	0.161583	−	0.986859i	$-0.448340\pi$
$829$	9.30470	0.323166	0.161583	+	0.986859i	$0.448340\pi$
$830$	−4.91040	−0.170443
$831$	1.86162	0.0645789
$832$	−6.74650	−0.233893
$833$	−30.3206	−1.05055
$834$	29.1238	1.00847
$835$	−35.3537	−1.22346
$836$	−4.39968	−0.152166
$837$	−3.23872	−0.111946
$838$	−26.8045	−0.925945
$839$	28.4780	0.983170	0.491585	−	0.870830i	$-0.336418\pi$
$839$	28.4780	0.983170	0.491585	+	0.870830i	$0.336418\pi$
$840$	−0.334764	−0.0115504
$841$	−20.1377	−0.694404
$842$	−4.44279	−0.153109
$843$	−12.0550	−0.415196
$844$	1.78930	0.0615902
$845$	10.4312	0.358844
$846$	11.4001	0.391943
$847$	−0.113904	−0.00391380
$848$	0.611302	0.0209922
$849$	−17.4984	−0.600542
$850$	20.8228	0.714214
$851$	−30.7545	−1.05425
$852$	7.71121	0.264182
$853$	−16.0864	−0.550789	−0.275395	−	0.961331i	$-0.588808\pi$
$853$	−16.0864	−0.550789	−0.275395	+	0.961331i	$0.588808\pi$
$854$	0.190451	0.00651711
$855$	−8.07040	−0.276002
$856$	7.21947	0.246756
$857$	32.5019	1.11024	0.555122	−	0.831769i	$-0.312672\pi$
$857$	32.5019	1.11024	0.555122	+	0.831769i	$0.312672\pi$
$858$	4.04515	0.138099
$859$	53.0060	1.80854	0.904270	−	0.426961i	$-0.140416\pi$
$859$	53.0060	1.80854	0.904270	+	0.426961i	$0.140416\pi$
$860$	−4.22812	−0.144178
$861$	−0.404288	−0.0137781
$862$	27.3309	0.930895
$863$	18.4211	0.627061	0.313530	−	0.949578i	$-0.398488\pi$
$863$	18.4211	0.627061	0.313530	+	0.949578i	$0.398488\pi$
$864$	−4.26302	−0.145031
$865$	−16.7442	−0.569321
$866$	32.1497	1.09249
$867$	−1.83181	−0.0622115
$868$	−0.293529	−0.00996304
$869$	−10.0943	−0.342427
$870$	7.26488	0.246303
$871$	−22.1620	−0.750931
$872$	6.37919	0.216027
$873$	−4.43143	−0.149981
$874$	51.9259	1.75642
$875$	−1.30832	−0.0442294
$876$	0.837667	0.0283022
$877$	14.6497	0.494684	0.247342	−	0.968928i	$-0.420443\pi$
$877$	14.6497	0.494684	0.247342	+	0.968928i	$0.420443\pi$
$878$	2.89627	0.0977443
$879$	4.01414	0.135394
$880$	−7.23671	−0.243949
$881$	−47.0593	−1.58547	−0.792733	−	0.609569i	$-0.791343\pi$
$881$	−47.0593	−1.58547	−0.792733	+	0.609569i	$0.791343\pi$
$882$	11.6825	0.393370
$883$	16.8945	0.568544	0.284272	−	0.958744i	$-0.408248\pi$
$883$	16.8945	0.568544	0.284272	+	0.958744i	$0.408248\pi$
$884$	−8.35362	−0.280963
$885$	−21.6537	−0.727880
$886$	−20.3938	−0.685141
$887$	38.0179	1.27651	0.638257	−	0.769823i	$-0.279656\pi$
$887$	38.0179	1.27651	0.638257	+	0.769823i	$0.279656\pi$
$888$	−11.0265	−0.370025
$889$	−0.826346	−0.0277147
$890$	41.0326	1.37542
$891$	−1.00000	−0.0335013
$892$	20.0849	0.672493
$893$	−37.7005	−1.26160
$894$	−33.6029	−1.12385
$895$	−24.4641	−0.817745
$896$	1.50225	0.0501866
$897$	−13.5878	−0.453682
$898$	29.2010	0.974448
$899$	−9.64153	−0.321563
$900$	−2.28342	−0.0761141
$901$	−0.535024	−0.0178242
$902$	−5.93464	−0.197602
$903$	0.414703	0.0138005
$904$	19.8169	0.659101
$905$	−34.2283	−1.13779
$906$	23.7066	0.787600
$907$	−3.40956	−0.113213	−0.0566063	−	0.998397i	$-0.518028\pi$
$907$	−3.40956	−0.113213	−0.0566063	+	0.998397i	$0.518028\pi$
$908$	−12.6693	−0.420447
$909$	−9.12365	−0.302612
$910$	0.672492	0.0222929
$911$	−35.6182	−1.18009	−0.590043	−	0.807372i	$-0.700889\pi$
$911$	−35.6182	−1.18009	−0.590043	+	0.807372i	$0.700889\pi$
$912$	27.4165	0.907850
$913$	2.01215	0.0665925
$914$	−25.9464	−0.858230
$915$	1.45953	0.0482505
$916$	3.85439	0.127353
$917$	−0.590084	−0.0194863
$918$	7.25587	0.239480
$919$	−23.5214	−0.775899	−0.387950	−	0.921681i	$-0.626817\pi$
$919$	−23.5214	−0.775899	−0.387950	+	0.921681i	$0.626817\pi$
$920$	16.5065	0.544204
$921$	−15.3443	−0.505612
$922$	21.0179	0.692188
$923$	23.4463	0.771746
$924$	−0.0906313	−0.00298155
$925$	−15.7145	−0.516689
$926$	−20.0676	−0.659462
$927$	−4.46502	−0.146650
$928$	−12.6908	−0.416597
$929$	17.9960	0.590430	0.295215	−	0.955431i	$-0.404609\pi$
$929$	17.9960	0.590430	0.295215	+	0.955431i	$0.404609\pi$
$930$	−7.90368	−0.259172
$931$	−38.6345	−1.26619
$932$	−5.47388	−0.179303
$933$	−28.3138	−0.926952
$934$	−62.5487	−2.04666
$935$	6.33371	0.207135
$936$	−4.87165	−0.159235
$937$	−6.46056	−0.211057	−0.105529	−	0.994416i	$-0.533653\pi$
$937$	−6.46056	−0.211057	−0.105529	+	0.994416i	$0.533653\pi$
$938$	1.74463	0.0569640
$939$	−26.2747	−0.857443
$940$	7.91800	0.258257
$941$	19.8660	0.647614	0.323807	−	0.946123i	$-0.395037\pi$
$941$	19.8660	0.647614	0.323807	+	0.946123i	$0.395037\pi$
$942$	8.34748	0.271975
$943$	19.9346	0.649160
$944$	73.5610	2.39421
$945$	−0.166247	−0.00540800
$946$	6.08752	0.197922
$947$	53.8245	1.74906	0.874531	−	0.484970i	$-0.161169\pi$
$947$	53.8245	1.74906	0.874531	+	0.484970i	$0.161169\pi$
$948$	−8.03185	−0.260862
$949$	2.54697	0.0826782
$950$	26.5323	0.860821
$951$	−31.0474	−1.00678
$952$	−0.995341	−0.0322592
$953$	37.5503	1.21637	0.608186	−	0.793794i	$-0.291897\pi$
$953$	37.5503	1.21637	0.608186	+	0.793794i	$0.291897\pi$
$954$	0.206144	0.00667416
$955$	12.8097	0.414513
$956$	20.8632	0.674765
$957$	−2.97696	−0.0962314
$958$	29.6966	0.959455
$959$	−1.81207	−0.0585149
$960$	4.07005	0.131360
$961$	−20.5107	−0.661636
$962$	22.1507	0.714166
$963$	3.58525	0.115533
$964$	−17.4520	−0.562090
$965$	−17.3306	−0.557891
$966$	1.06965	0.0344154
$967$	29.7039	0.955211	0.477606	−	0.878574i	$-0.341505\pi$
$967$	29.7039	0.955211	0.477606	+	0.878574i	$0.341505\pi$
$968$	2.01366	0.0647214
$969$	−23.9954	−0.770845
$970$	−10.8143	−0.347228
$971$	20.9546	0.672464	0.336232	−	0.941779i	$-0.390847\pi$
$971$	20.9546	0.672464	0.336232	+	0.941779i	$0.390847\pi$
$972$	−0.795679	−0.0255214
$973$	−1.98401	−0.0636045
$974$	21.9224	0.702440
$975$	−6.94287	−0.222350
$976$	−4.95825	−0.158710
$977$	−29.9552	−0.958353	−0.479177	−	0.877718i	$-0.659065\pi$
$977$	−29.9552	−0.958353	−0.479177	+	0.877718i	$0.659065\pi$
$978$	−10.0029	−0.319858
$979$	−16.8141	−0.537381
$980$	8.11415	0.259197
$981$	3.16796	0.101145
$982$	37.5266	1.19752
$983$	52.2964	1.66800	0.833998	−	0.551767i	$-0.186046\pi$
$983$	52.2964	1.66800	0.833998	+	0.551767i	$0.186046\pi$
$984$	7.14720	0.227845
$985$	9.75016	0.310666
$986$	21.6004	0.687898
$987$	−0.776614	−0.0247199
$988$	−10.6442	−0.338636
$989$	−20.4482	−0.650214
$990$	−2.44037	−0.0775601
$991$	23.5537	0.748209	0.374105	−	0.927387i	$-0.377950\pi$
$991$	23.5537	0.748209	0.374105	+	0.927387i	$0.377950\pi$
$992$	13.8067	0.438364
$993$	20.5558	0.652318
$994$	−1.84573	−0.0585430
$995$	17.8220	0.564996
$996$	1.60103	0.0507305
$997$	38.4376	1.21733	0.608665	−	0.793427i	$-0.291705\pi$
$997$	38.4376	1.21733	0.608665	+	0.793427i	$0.291705\pi$
$998$	−29.9743	−0.948818
$999$	−5.47586	−0.173248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.h.1.4	✓	14
3.2	odd	2		6039.2.a.j.1.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.h.1.4	✓	14	1.1	even	1	trivial
6039.2.a.j.1.11		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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.67203 q^{2} -1.00000 q^{3} +0.795679 q^{4} -1.45953 q^{5} +1.67203 q^{6} -0.113904 q^{7} +2.01366 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.67203 q^{2} -1.00000 q^{3} +0.795679 q^{4} -1.45953 q^{5} +1.67203 q^{6} -0.113904 q^{7} +2.01366 q^{8} +1.00000 q^{9} +2.44037 q^{10} -1.00000 q^{11} -0.795679 q^{12} -2.41931 q^{13} +0.190451 q^{14} +1.45953 q^{15} -4.95825 q^{16} +4.33956 q^{17} -1.67203 q^{18} +5.52946 q^{19} -1.16132 q^{20} +0.113904 q^{21} +1.67203 q^{22} -5.61639 q^{23} -2.01366 q^{24} -2.86978 q^{25} +4.04515 q^{26} -1.00000 q^{27} -0.0906313 q^{28} -2.97696 q^{29} -2.44037 q^{30} +3.23872 q^{31} +4.26302 q^{32} +1.00000 q^{33} -7.25587 q^{34} +0.166247 q^{35} +0.795679 q^{36} +5.47586 q^{37} -9.24541 q^{38} +2.41931 q^{39} -2.93899 q^{40} -3.54936 q^{41} -0.190451 q^{42} +3.64080 q^{43} -0.795679 q^{44} -1.45953 q^{45} +9.39076 q^{46} -6.81812 q^{47} +4.95825 q^{48} -6.98703 q^{49} +4.79835 q^{50} -4.33956 q^{51} -1.92499 q^{52} -0.123290 q^{53} +1.67203 q^{54} +1.45953 q^{55} -0.229364 q^{56} -5.52946 q^{57} +4.97756 q^{58} -14.8361 q^{59} +1.16132 q^{60} +1.00000 q^{61} -5.41523 q^{62} -0.113904 q^{63} +2.78861 q^{64} +3.53104 q^{65} -1.67203 q^{66} +9.16048 q^{67} +3.45290 q^{68} +5.61639 q^{69} -0.277969 q^{70} -9.69135 q^{71} +2.01366 q^{72} -1.05277 q^{73} -9.15579 q^{74} +2.86978 q^{75} +4.39968 q^{76} +0.113904 q^{77} -4.04515 q^{78} +10.0943 q^{79} +7.23671 q^{80} +1.00000 q^{81} +5.93464 q^{82} -2.01215 q^{83} +0.0906313 q^{84} -6.33371 q^{85} -6.08752 q^{86} +2.97696 q^{87} -2.01366 q^{88} +16.8141 q^{89} +2.44037 q^{90} +0.275569 q^{91} -4.46885 q^{92} -3.23872 q^{93} +11.4001 q^{94} -8.07040 q^{95} -4.26302 q^{96} -4.43143 q^{97} +11.6825 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * q^99

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