LMFDB - Embedded newform 2013.2.a.e.1.1

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:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} + \cdots - 47 $ x^13 - 2x^12 - 19x^11 + 35x^10 + 136x^9 - 220x^8 - 469x^7 + 610x^6 + 841x^5 - 760x^4 - 742x^3 + 366x^2 + 236x - 47
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.59890$ 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)

$f(q)$	$=$	$q-2.59890 q^{2} -1.00000 q^{3} +4.75428 q^{4} -3.50938 q^{5} +2.59890 q^{6} +0.252288 q^{7} -7.15810 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.59890 q^{2} -1.00000 q^{3} +4.75428 q^{4} -3.50938 q^{5} +2.59890 q^{6} +0.252288 q^{7} -7.15810 q^{8} +1.00000 q^{9} +9.12053 q^{10} +1.00000 q^{11} -4.75428 q^{12} +0.314950 q^{13} -0.655671 q^{14} +3.50938 q^{15} +9.09463 q^{16} +3.13246 q^{17} -2.59890 q^{18} +0.841231 q^{19} -16.6846 q^{20} -0.252288 q^{21} -2.59890 q^{22} +1.45222 q^{23} +7.15810 q^{24} +7.31576 q^{25} -0.818524 q^{26} -1.00000 q^{27} +1.19945 q^{28} -6.76829 q^{29} -9.12053 q^{30} -7.07730 q^{31} -9.31982 q^{32} -1.00000 q^{33} -8.14095 q^{34} -0.885374 q^{35} +4.75428 q^{36} +8.89628 q^{37} -2.18627 q^{38} -0.314950 q^{39} +25.1205 q^{40} -8.43604 q^{41} +0.655671 q^{42} +1.80409 q^{43} +4.75428 q^{44} -3.50938 q^{45} -3.77418 q^{46} +2.30017 q^{47} -9.09463 q^{48} -6.93635 q^{49} -19.0129 q^{50} -3.13246 q^{51} +1.49736 q^{52} -4.41103 q^{53} +2.59890 q^{54} -3.50938 q^{55} -1.80590 q^{56} -0.841231 q^{57} +17.5901 q^{58} +4.48036 q^{59} +16.6846 q^{60} -1.00000 q^{61} +18.3932 q^{62} +0.252288 q^{63} +6.03203 q^{64} -1.10528 q^{65} +2.59890 q^{66} -0.0414722 q^{67} +14.8926 q^{68} -1.45222 q^{69} +2.30100 q^{70} -9.80832 q^{71} -7.15810 q^{72} +8.90879 q^{73} -23.1205 q^{74} -7.31576 q^{75} +3.99945 q^{76} +0.252288 q^{77} +0.818524 q^{78} -8.51680 q^{79} -31.9165 q^{80} +1.00000 q^{81} +21.9244 q^{82} +11.2151 q^{83} -1.19945 q^{84} -10.9930 q^{85} -4.68865 q^{86} +6.76829 q^{87} -7.15810 q^{88} +5.58487 q^{89} +9.12053 q^{90} +0.0794581 q^{91} +6.90427 q^{92} +7.07730 q^{93} -5.97790 q^{94} -2.95220 q^{95} +9.31982 q^{96} +7.54000 q^{97} +18.0269 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 13 q^{11} - 16 q^{12} + 13 q^{13} + q^{14} - 3 q^{15} + 18 q^{16} + 17 q^{17} + 2 q^{18} + 14 q^{19} - 7 q^{20} - 11 q^{21} + 2 q^{22} + 7 q^{23} - 9 q^{24} + 18 q^{25} - 10 q^{26} - 13 q^{27} + 19 q^{28} - 6 q^{29} - 6 q^{30} + 27 q^{31} + 5 q^{32} - 13 q^{33} + 6 q^{34} + 14 q^{35} + 16 q^{36} + 10 q^{37} + 2 q^{38} - 13 q^{39} + 8 q^{40} + 3 q^{41} - q^{42} + 29 q^{43} + 16 q^{44} + 3 q^{45} - 24 q^{46} + 8 q^{47} - 18 q^{48} + 8 q^{49} - 27 q^{50} - 17 q^{51} + 37 q^{52} - 24 q^{53} - 2 q^{54} + 3 q^{55} + 24 q^{56} - 14 q^{57} - 5 q^{58} + 13 q^{59} + 7 q^{60} - 13 q^{61} + 39 q^{62} + 11 q^{63} + 47 q^{64} - 11 q^{65} - 2 q^{66} + 44 q^{67} - 8 q^{68} - 7 q^{69} - 12 q^{70} + 3 q^{71} + 9 q^{72} + 48 q^{73} - 22 q^{74} - 18 q^{75} + 47 q^{76} + 11 q^{77} + 10 q^{78} - 17 q^{79} - 26 q^{80} + 13 q^{81} + 56 q^{82} + 50 q^{83} - 19 q^{84} + 8 q^{85} + 18 q^{86} + 6 q^{87} + 9 q^{88} - 15 q^{89} + 6 q^{90} + 47 q^{91} + 14 q^{92} - 27 q^{93} + 45 q^{94} - q^{95} - 5 q^{96} + 27 q^{97} + 47 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 13 * q^11 - 16 * q^12 + 13 * q^13 + q^14 - 3 * q^15 + 18 * q^16 + 17 * q^17 + 2 * q^18 + 14 * q^19 - 7 * q^20 - 11 * q^21 + 2 * q^22 + 7 * q^23 - 9 * q^24 + 18 * q^25 - 10 * q^26 - 13 * q^27 + 19 * q^28 - 6 * q^29 - 6 * q^30 + 27 * q^31 + 5 * q^32 - 13 * q^33 + 6 * q^34 + 14 * q^35 + 16 * q^36 + 10 * q^37 + 2 * q^38 - 13 * q^39 + 8 * q^40 + 3 * q^41 - q^42 + 29 * q^43 + 16 * q^44 + 3 * q^45 - 24 * q^46 + 8 * q^47 - 18 * q^48 + 8 * q^49 - 27 * q^50 - 17 * q^51 + 37 * q^52 - 24 * q^53 - 2 * q^54 + 3 * q^55 + 24 * q^56 - 14 * q^57 - 5 * q^58 + 13 * q^59 + 7 * q^60 - 13 * q^61 + 39 * q^62 + 11 * q^63 + 47 * q^64 - 11 * q^65 - 2 * q^66 + 44 * q^67 - 8 * q^68 - 7 * q^69 - 12 * q^70 + 3 * q^71 + 9 * q^72 + 48 * q^73 - 22 * q^74 - 18 * q^75 + 47 * q^76 + 11 * q^77 + 10 * q^78 - 17 * q^79 - 26 * q^80 + 13 * q^81 + 56 * q^82 + 50 * q^83 - 19 * q^84 + 8 * q^85 + 18 * q^86 + 6 * q^87 + 9 * q^88 - 15 * q^89 + 6 * q^90 + 47 * q^91 + 14 * q^92 - 27 * q^93 + 45 * q^94 - q^95 - 5 * q^96 + 27 * q^97 + 47 * q^98 + 13 * 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 $

$2$	−2.59890	−1.83770	−0.918850	−	0.394607i	$-0.870881\pi$
$2$	−2.59890	−1.83770	−0.918850	+	0.394607i	$0.870881\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.75428	2.37714
$5$	−3.50938	−1.56944	−0.784721	−	0.619849i	$-0.787194\pi$
$5$	−3.50938	−1.56944	−0.784721	+	0.619849i	$0.787194\pi$
$6$	2.59890	1.06100
$7$	0.252288	0.0953558	0.0476779	−	0.998863i	$-0.484818\pi$
$7$	0.252288	0.0953558	0.0476779	+	0.998863i	$0.484818\pi$
$8$	−7.15810	−2.53077
$9$	1.00000	0.333333
$10$	9.12053	2.88416
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.75428	−1.37244
$13$	0.314950	0.0873514	0.0436757	−	0.999046i	$-0.486093\pi$
$13$	0.314950	0.0873514	0.0436757	+	0.999046i	$0.486093\pi$
$14$	−0.655671	−0.175235
$15$	3.50938	0.906118
$16$	9.09463	2.27366
$17$	3.13246	0.759733	0.379866	−	0.925041i	$-0.375970\pi$
$17$	3.13246	0.759733	0.379866	+	0.925041i	$0.375970\pi$
$18$	−2.59890	−0.612567
$19$	0.841231	0.192992	0.0964958	−	0.995333i	$-0.469237\pi$
$19$	0.841231	0.192992	0.0964958	+	0.995333i	$0.469237\pi$
$20$	−16.6846	−3.73079
$21$	−0.252288	−0.0550537
$22$	−2.59890	−0.554087
$23$	1.45222	0.302809	0.151405	−	0.988472i	$-0.451620\pi$
$23$	1.45222	0.302809	0.151405	+	0.988472i	$0.451620\pi$
$24$	7.15810	1.46114
$25$	7.31576	1.46315
$26$	−0.818524	−0.160526
$27$	−1.00000	−0.192450
$28$	1.19945	0.226674
$29$	−6.76829	−1.25684	−0.628420	−	0.777874i	$-0.716298\pi$
$29$	−6.76829	−1.25684	−0.628420	+	0.777874i	$0.716298\pi$
$30$	−9.12053	−1.66517
$31$	−7.07730	−1.27112	−0.635560	−	0.772051i	$-0.719231\pi$
$31$	−7.07730	−1.27112	−0.635560	+	0.772051i	$0.719231\pi$
$32$	−9.31982	−1.64753
$33$	−1.00000	−0.174078
$34$	−8.14095	−1.39616
$35$	−0.885374	−0.149656
$36$	4.75428	0.792380
$37$	8.89628	1.46254	0.731270	−	0.682088i	$-0.238928\pi$
$37$	8.89628	1.46254	0.731270	+	0.682088i	$0.238928\pi$
$38$	−2.18627	−0.354661
$39$	−0.314950	−0.0504324
$40$	25.1205	3.97190
$41$	−8.43604	−1.31749	−0.658744	−	0.752367i	$-0.728912\pi$
$41$	−8.43604	−1.31749	−0.658744	+	0.752367i	$0.728912\pi$
$42$	0.655671	0.101172
$43$	1.80409	0.275121	0.137561	−	0.990493i	$-0.456074\pi$
$43$	1.80409	0.275121	0.137561	+	0.990493i	$0.456074\pi$
$44$	4.75428	0.716735
$45$	−3.50938	−0.523148
$46$	−3.77418	−0.556473
$47$	2.30017	0.335514	0.167757	−	0.985828i	$-0.446348\pi$
$47$	2.30017	0.335514	0.167757	+	0.985828i	$0.446348\pi$
$48$	−9.09463	−1.31270
$49$	−6.93635	−0.990907
$50$	−19.0129	−2.68883
$51$	−3.13246	−0.438632
$52$	1.49736	0.207647
$53$	−4.41103	−0.605901	−0.302951	−	0.953006i	$-0.597972\pi$
$53$	−4.41103	−0.605901	−0.302951	+	0.953006i	$0.597972\pi$
$54$	2.59890	0.353665
$55$	−3.50938	−0.473205
$56$	−1.80590	−0.241324
$57$	−0.841231	−0.111424
$58$	17.5901	2.30969
$59$	4.48036	0.583293	0.291647	−	0.956526i	$-0.405797\pi$
$59$	4.48036	0.583293	0.291647	+	0.956526i	$0.405797\pi$
$60$	16.6846	2.15397
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	18.3932	2.33594
$63$	0.252288	0.0317853
$64$	6.03203	0.754004
$65$	−1.10528	−0.137093
$66$	2.59890	0.319902
$67$	−0.0414722	−0.00506664	−0.00253332	−	0.999997i	$-0.500806\pi$
$67$	−0.0414722	−0.00506664	−0.00253332	+	0.999997i	$0.500806\pi$
$68$	14.8926	1.80599
$69$	−1.45222	−0.174827
$70$	2.30100	0.275022
$71$	−9.80832	−1.16403	−0.582017	−	0.813177i	$-0.697736\pi$
$71$	−9.80832	−1.16403	−0.582017	+	0.813177i	$0.697736\pi$
$72$	−7.15810	−0.843590
$73$	8.90879	1.04269	0.521347	−	0.853345i	$-0.325430\pi$
$73$	8.90879	1.04269	0.521347	+	0.853345i	$0.325430\pi$
$74$	−23.1205	−2.68771
$75$	−7.31576	−0.844751
$76$	3.99945	0.458768
$77$	0.252288	0.0287509
$78$	0.818524	0.0926796
$79$	−8.51680	−0.958215	−0.479108	−	0.877756i	$-0.659040\pi$
$79$	−8.51680	−0.958215	−0.479108	+	0.877756i	$0.659040\pi$
$80$	−31.9165	−3.56837
$81$	1.00000	0.111111
$82$	21.9244	2.42115
$83$	11.2151	1.23102	0.615509	−	0.788130i	$-0.288950\pi$
$83$	11.2151	1.23102	0.615509	+	0.788130i	$0.288950\pi$
$84$	−1.19945	−0.130870
$85$	−10.9930	−1.19236
$86$	−4.68865	−0.505590
$87$	6.76829	0.725637
$88$	−7.15810	−0.763056
$89$	5.58487	0.591995	0.295997	−	0.955189i	$-0.404348\pi$
$89$	5.58487	0.591995	0.295997	+	0.955189i	$0.404348\pi$
$90$	9.12053	0.961388
$91$	0.0794581	0.00832947
$92$	6.90427	0.719820
$93$	7.07730	0.733882
$94$	−5.97790	−0.616573
$95$	−2.95220	−0.302889
$96$	9.31982	0.951200
$97$	7.54000	0.765571	0.382786	−	0.923837i	$-0.374965\pi$
$97$	7.54000	0.765571	0.382786	+	0.923837i	$0.374965\pi$
$98$	18.0269	1.82099
$99$	1.00000	0.100504
$100$	34.7812	3.47812
$101$	−5.85246	−0.582342	−0.291171	−	0.956671i	$-0.594045\pi$
$101$	−5.85246	−0.582342	−0.291171	+	0.956671i	$0.594045\pi$
$102$	8.14095	0.806074
$103$	−17.3802	−1.71253	−0.856263	−	0.516541i	$-0.827219\pi$
$103$	−17.3802	−1.71253	−0.856263	+	0.516541i	$0.827219\pi$
$104$	−2.25444	−0.221066
$105$	0.885374	0.0864037
$106$	11.4638	1.11346
$107$	−7.20395	−0.696432	−0.348216	−	0.937414i	$-0.613212\pi$
$107$	−7.20395	−0.696432	−0.348216	+	0.937414i	$0.613212\pi$
$108$	−4.75428	−0.457481
$109$	3.06602	0.293672	0.146836	−	0.989161i	$-0.453091\pi$
$109$	3.06602	0.293672	0.146836	+	0.989161i	$0.453091\pi$
$110$	9.12053	0.869608
$111$	−8.89628	−0.844398
$112$	2.29446	0.216806
$113$	−12.0330	−1.13197	−0.565986	−	0.824415i	$-0.691504\pi$
$113$	−12.0330	−1.13197	−0.565986	+	0.824415i	$0.691504\pi$
$114$	2.18627	0.204763
$115$	−5.09640	−0.475242
$116$	−32.1784	−2.98769
$117$	0.314950	0.0291171
$118$	−11.6440	−1.07192
$119$	0.790281	0.0724450
$120$	−25.1205	−2.29318
$121$	1.00000	0.0909091
$122$	2.59890	0.235293
$123$	8.43604	0.760652
$124$	−33.6475	−3.02163
$125$	−8.12687	−0.726889
$126$	−0.655671	−0.0584118
$127$	−7.56103	−0.670933	−0.335466	−	0.942052i	$-0.608894\pi$
$127$	−7.56103	−0.670933	−0.335466	+	0.942052i	$0.608894\pi$
$128$	2.96300	0.261895
$129$	−1.80409	−0.158841
$130$	2.87251	0.251936
$131$	10.0905	0.881613	0.440807	−	0.897602i	$-0.354692\pi$
$131$	10.0905	0.881613	0.440807	+	0.897602i	$0.354692\pi$
$132$	−4.75428	−0.413807
$133$	0.212232	0.0184029
$134$	0.107782	0.00931097
$135$	3.50938	0.302039
$136$	−22.4225	−1.92271
$137$	11.2651	0.962444	0.481222	−	0.876599i	$-0.340193\pi$
$137$	11.2651	0.962444	0.481222	+	0.876599i	$0.340193\pi$
$138$	3.77418	0.321280
$139$	10.2656	0.870720	0.435360	−	0.900257i	$-0.356621\pi$
$139$	10.2656	0.870720	0.435360	+	0.900257i	$0.356621\pi$
$140$	−4.20932	−0.355752
$141$	−2.30017	−0.193709
$142$	25.4908	2.13914
$143$	0.314950	0.0263374
$144$	9.09463	0.757885
$145$	23.7525	1.97254
$146$	−23.1530	−1.91616
$147$	6.93635	0.572101
$148$	42.2954	3.47666
$149$	16.9755	1.39069	0.695345	−	0.718676i	$-0.255252\pi$
$149$	16.9755	1.39069	0.695345	+	0.718676i	$0.255252\pi$
$150$	19.0129	1.55240
$151$	−10.4087	−0.847044	−0.423522	−	0.905886i	$-0.639206\pi$
$151$	−10.4087	−0.847044	−0.423522	+	0.905886i	$0.639206\pi$
$152$	−6.02161	−0.488417
$153$	3.13246	0.253244
$154$	−0.655671	−0.0528355
$155$	24.8369	1.99495
$156$	−1.49736	−0.119885
$157$	−15.3822	−1.22764	−0.613818	−	0.789448i	$-0.710367\pi$
$157$	−15.3822	−1.22764	−0.613818	+	0.789448i	$0.710367\pi$
$158$	22.1343	1.76091
$159$	4.41103	0.349817
$160$	32.7068	2.58570
$161$	0.366378	0.0288746
$162$	−2.59890	−0.204189
$163$	0.539069	0.0422232	0.0211116	−	0.999777i	$-0.493279\pi$
$163$	0.539069	0.0422232	0.0211116	+	0.999777i	$0.493279\pi$
$164$	−40.1073	−3.13185
$165$	3.50938	0.273205
$166$	−29.1470	−2.26224
$167$	21.2985	1.64813	0.824063	−	0.566498i	$-0.191702\pi$
$167$	21.2985	1.64813	0.824063	+	0.566498i	$0.191702\pi$
$168$	1.80590	0.139328
$169$	−12.9008	−0.992370
$170$	28.5697	2.19119
$171$	0.841231	0.0643305
$172$	8.57715	0.654002
$173$	20.9450	1.59242	0.796209	−	0.605022i	$-0.206836\pi$
$173$	20.9450	1.59242	0.796209	+	0.605022i	$0.206836\pi$
$174$	−17.5901	−1.33350
$175$	1.84568	0.139520
$176$	9.09463	0.685533
$177$	−4.48036	−0.336764
$178$	−14.5145	−1.08791
$179$	−2.59129	−0.193682	−0.0968409	−	0.995300i	$-0.530874\pi$
$179$	−2.59129	−0.193682	−0.0968409	+	0.995300i	$0.530874\pi$
$180$	−16.6846	−1.24360
$181$	−10.8521	−0.806634	−0.403317	−	0.915060i	$-0.632143\pi$
$181$	−10.8521	−0.806634	−0.403317	+	0.915060i	$0.632143\pi$
$182$	−0.206504	−0.0153071
$183$	1.00000	0.0739221
$184$	−10.3952	−0.766341
$185$	−31.2204	−2.29537
$186$	−18.3932	−1.34865
$187$	3.13246	0.229068
$188$	10.9356	0.797563
$189$	−0.252288	−0.0183512
$190$	7.67247	0.556620
$191$	14.8806	1.07672	0.538362	−	0.842714i	$-0.319043\pi$
$191$	14.8806	1.07672	0.538362	+	0.842714i	$0.319043\pi$
$192$	−6.03203	−0.435324
$193$	−0.222935	−0.0160472	−0.00802362	−	0.999968i	$-0.502554\pi$
$193$	−0.222935	−0.0160472	−0.00802362	+	0.999968i	$0.502554\pi$
$194$	−19.5957	−1.40689
$195$	1.10528	0.0791507
$196$	−32.9774	−2.35553
$197$	2.16031	0.153916	0.0769580	−	0.997034i	$-0.475479\pi$
$197$	2.16031	0.153916	0.0769580	+	0.997034i	$0.475479\pi$
$198$	−2.59890	−0.184696
$199$	24.6468	1.74716	0.873581	−	0.486678i	$-0.161792\pi$
$199$	24.6468	1.74716	0.873581	+	0.486678i	$0.161792\pi$
$200$	−52.3669	−3.70290
$201$	0.0414722	0.00292523
$202$	15.2100	1.07017
$203$	−1.70756	−0.119847
$204$	−14.8926	−1.04269
$205$	29.6053	2.06772
$206$	45.1695	3.14711
$207$	1.45222	0.100936
$208$	2.86435	0.198607
$209$	0.841231	0.0581891
$210$	−2.30100	−0.158784
$211$	12.6063	0.867851	0.433926	−	0.900949i	$-0.357128\pi$
$211$	12.6063	0.867851	0.433926	+	0.900949i	$0.357128\pi$
$212$	−20.9713	−1.44031
$213$	9.80832	0.672055
$214$	18.7223	1.27983
$215$	−6.33124	−0.431787
$216$	7.15810	0.487047
$217$	−1.78552	−0.121209
$218$	−7.96828	−0.539680
$219$	−8.90879	−0.602000
$220$	−16.6846	−1.12487
$221$	0.986568	0.0663637
$222$	23.1205	1.55175
$223$	10.5825	0.708657	0.354329	−	0.935121i	$-0.384709\pi$
$223$	10.5825	0.708657	0.354329	+	0.935121i	$0.384709\pi$
$224$	−2.35128	−0.157101
$225$	7.31576	0.487717
$226$	31.2726	2.08023
$227$	9.60279	0.637359	0.318680	−	0.947862i	$-0.396761\pi$
$227$	9.60279	0.637359	0.318680	+	0.947862i	$0.396761\pi$
$228$	−3.99945	−0.264870
$229$	4.99502	0.330080	0.165040	−	0.986287i	$-0.447225\pi$
$229$	4.99502	0.330080	0.165040	+	0.986287i	$0.447225\pi$
$230$	13.2450	0.873352
$231$	−0.252288	−0.0165993
$232$	48.4481	3.18077
$233$	18.4718	1.21013	0.605064	−	0.796177i	$-0.293147\pi$
$233$	18.4718	1.21013	0.605064	+	0.796177i	$0.293147\pi$
$234$	−0.818524	−0.0535086
$235$	−8.07216	−0.526569
$236$	21.3009	1.38657
$237$	8.51680	0.553226
$238$	−2.05386	−0.133132
$239$	6.77945	0.438526	0.219263	−	0.975666i	$-0.429635\pi$
$239$	6.77945	0.438526	0.219263	+	0.975666i	$0.429635\pi$
$240$	31.9165	2.06020
$241$	15.6701	1.00940	0.504701	−	0.863294i	$-0.331603\pi$
$241$	15.6701	1.00940	0.504701	+	0.863294i	$0.331603\pi$
$242$	−2.59890	−0.167064
$243$	−1.00000	−0.0641500
$244$	−4.75428	−0.304362
$245$	24.3423	1.55517
$246$	−21.9244	−1.39785
$247$	0.264946	0.0168581
$248$	50.6600	3.21691
$249$	−11.2151	−0.710729
$250$	21.1209	1.33580
$251$	15.5439	0.981120	0.490560	−	0.871407i	$-0.336792\pi$
$251$	15.5439	0.981120	0.490560	+	0.871407i	$0.336792\pi$
$252$	1.19945	0.0755581
$253$	1.45222	0.0913004
$254$	19.6504	1.23297
$255$	10.9930	0.688408
$256$	−19.7646	−1.23529
$257$	17.3834	1.08434	0.542172	−	0.840267i	$-0.317602\pi$
$257$	17.3834	1.08434	0.542172	+	0.840267i	$0.317602\pi$
$258$	4.68865	0.291903
$259$	2.24442	0.139462
$260$	−5.25481	−0.325890
$261$	−6.76829	−0.418947
$262$	−26.2243	−1.62014
$263$	−13.4938	−0.832062	−0.416031	−	0.909350i	$-0.636579\pi$
$263$	−13.4938	−0.832062	−0.416031	+	0.909350i	$0.636579\pi$
$264$	7.15810	0.440551
$265$	15.4800	0.950928
$266$	−0.551571	−0.0338190
$267$	−5.58487	−0.341788
$268$	−0.197171	−0.0120441
$269$	17.3064	1.05519	0.527594	−	0.849497i	$-0.323094\pi$
$269$	17.3064	1.05519	0.527594	+	0.849497i	$0.323094\pi$
$270$	−9.12053	−0.555058
$271$	−2.53256	−0.153842	−0.0769210	−	0.997037i	$-0.524509\pi$
$271$	−2.53256	−0.153842	−0.0769210	+	0.997037i	$0.524509\pi$
$272$	28.4885	1.72737
$273$	−0.0794581	−0.00480902
$274$	−29.2769	−1.76868
$275$	7.31576	0.441157
$276$	−6.90427	−0.415588
$277$	23.6178	1.41906	0.709529	−	0.704676i	$-0.248908\pi$
$277$	23.6178	1.41906	0.709529	+	0.704676i	$0.248908\pi$
$278$	−26.6794	−1.60012
$279$	−7.07730	−0.423707
$280$	6.33760	0.378744
$281$	10.4991	0.626323	0.313162	−	0.949700i	$-0.398612\pi$
$281$	10.4991	0.626323	0.313162	+	0.949700i	$0.398612\pi$
$282$	5.97790	0.355979
$283$	7.65586	0.455093	0.227547	−	0.973767i	$-0.426930\pi$
$283$	7.65586	0.455093	0.227547	+	0.973767i	$0.426930\pi$
$284$	−46.6315	−2.76707
$285$	2.95220	0.174873
$286$	−0.818524	−0.0484003
$287$	−2.12831	−0.125630
$288$	−9.31982	−0.549176
$289$	−7.18771	−0.422806
$290$	−61.7304	−3.62493
$291$	−7.54000	−0.442003
$292$	42.3549	2.47863
$293$	13.3177	0.778026	0.389013	−	0.921232i	$-0.372816\pi$
$293$	13.3177	0.778026	0.389013	+	0.921232i	$0.372816\pi$
$294$	−18.0269	−1.05135
$295$	−15.7233	−0.915445
$296$	−63.6805	−3.70135
$297$	−1.00000	−0.0580259
$298$	−44.1177	−2.55567
$299$	0.457378	0.0264508
$300$	−34.7812	−2.00809
$301$	0.455150	0.0262344
$302$	27.0510	1.55661
$303$	5.85246	0.336215
$304$	7.65068	0.438797
$305$	3.50938	0.200947
$306$	−8.14095	−0.465387
$307$	−7.23744	−0.413063	−0.206531	−	0.978440i	$-0.566218\pi$
$307$	−7.23744	−0.413063	−0.206531	+	0.978440i	$0.566218\pi$
$308$	1.19945	0.0683449
$309$	17.3802	0.988727
$310$	−64.5487	−3.66612
$311$	−8.38540	−0.475492	−0.237746	−	0.971327i	$-0.576409\pi$
$311$	−8.38540	−0.475492	−0.237746	+	0.971327i	$0.576409\pi$
$312$	2.25444	0.127633
$313$	8.07210	0.456262	0.228131	−	0.973630i	$-0.426739\pi$
$313$	8.07210	0.456262	0.228131	+	0.973630i	$0.426739\pi$
$314$	39.9769	2.25603
$315$	−0.885374	−0.0498852
$316$	−40.4913	−2.27781
$317$	−26.3618	−1.48063	−0.740314	−	0.672261i	$-0.765323\pi$
$317$	−26.3618	−1.48063	−0.740314	+	0.672261i	$0.765323\pi$
$318$	−11.4638	−0.642859
$319$	−6.76829	−0.378952
$320$	−21.1687	−1.18337
$321$	7.20395	0.402085
$322$	−0.952180	−0.0530629
$323$	2.63512	0.146622
$324$	4.75428	0.264127
$325$	2.30410	0.127808
$326$	−1.40099	−0.0775935
$327$	−3.06602	−0.169551
$328$	60.3860	3.33426
$329$	0.580304	0.0319932
$330$	−9.12053	−0.502069
$331$	20.6870	1.13706	0.568531	−	0.822662i	$-0.307512\pi$
$331$	20.6870	1.13706	0.568531	+	0.822662i	$0.307512\pi$
$332$	53.3198	2.92630
$333$	8.89628	0.487513
$334$	−55.3526	−3.02876
$335$	0.145542	0.00795180
$336$	−2.29446	−0.125173
$337$	2.66866	0.145371	0.0726856	−	0.997355i	$-0.476843\pi$
$337$	2.66866	0.145371	0.0726856	+	0.997355i	$0.476843\pi$
$338$	33.5279	1.82368
$339$	12.0330	0.653545
$340$	−52.2638	−2.83440
$341$	−7.07730	−0.383257
$342$	−2.18627	−0.118220
$343$	−3.51597	−0.189845
$344$	−12.9139	−0.696269
$345$	5.09640	0.274381
$346$	−54.4339	−2.92638
$347$	−10.6683	−0.572707	−0.286354	−	0.958124i	$-0.592443\pi$
$347$	−10.6683	−0.572707	−0.286354	+	0.958124i	$0.592443\pi$
$348$	32.1784	1.72494
$349$	25.9644	1.38984	0.694922	−	0.719085i	$-0.255439\pi$
$349$	25.9644	1.38984	0.694922	+	0.719085i	$0.255439\pi$
$350$	−4.79673	−0.256396
$351$	−0.314950	−0.0168108
$352$	−9.31982	−0.496748
$353$	−29.9585	−1.59453	−0.797266	−	0.603629i	$-0.793721\pi$
$353$	−29.9585	−1.59453	−0.797266	+	0.603629i	$0.793721\pi$
$354$	11.6440	0.618872
$355$	34.4211	1.82688
$356$	26.5520	1.40725
$357$	−0.790281	−0.0418261
$358$	6.73449	0.355929
$359$	22.7413	1.20024	0.600121	−	0.799909i	$-0.295119\pi$
$359$	22.7413	1.20024	0.600121	+	0.799909i	$0.295119\pi$
$360$	25.1205	1.32397
$361$	−18.2923	−0.962754
$362$	28.2036	1.48235
$363$	−1.00000	−0.0524864
$364$	0.377766	0.0198003
$365$	−31.2643	−1.63645
$366$	−2.59890	−0.135847
$367$	−3.01744	−0.157509	−0.0787545	−	0.996894i	$-0.525094\pi$
$367$	−3.01744	−0.157509	−0.0787545	+	0.996894i	$0.525094\pi$
$368$	13.2074	0.688484
$369$	−8.43604	−0.439163
$370$	81.1388	4.21821
$371$	−1.11285	−0.0577762
$372$	33.6475	1.74454
$373$	−2.16528	−0.112114	−0.0560570	−	0.998428i	$-0.517853\pi$
$373$	−2.16528	−0.112114	−0.0560570	+	0.998428i	$0.517853\pi$
$374$	−8.14095	−0.420958
$375$	8.12687	0.419670
$376$	−16.4648	−0.849108
$377$	−2.13167	−0.109787
$378$	0.655671	0.0337241
$379$	4.56064	0.234264	0.117132	−	0.993116i	$-0.462630\pi$
$379$	4.56064	0.234264	0.117132	+	0.993116i	$0.462630\pi$
$380$	−14.0356	−0.720010
$381$	7.56103	0.387363
$382$	−38.6732	−1.97869
$383$	−21.2912	−1.08793	−0.543964	−	0.839109i	$-0.683077\pi$
$383$	−21.2912	−1.08793	−0.543964	+	0.839109i	$0.683077\pi$
$384$	−2.96300	−0.151205
$385$	−0.885374	−0.0451228
$386$	0.579386	0.0294900
$387$	1.80409	0.0917071
$388$	35.8473	1.81987
$389$	−30.9732	−1.57041	−0.785203	−	0.619238i	$-0.787441\pi$
$389$	−30.9732	−1.57041	−0.785203	+	0.619238i	$0.787441\pi$
$390$	−2.87251	−0.145455
$391$	4.54903	0.230054
$392$	49.6511	2.50776
$393$	−10.0905	−0.509000
$394$	−5.61444	−0.282851
$395$	29.8887	1.50386
$396$	4.75428	0.238912
$397$	23.5944	1.18417	0.592085	−	0.805875i	$-0.298305\pi$
$397$	23.5944	1.18417	0.592085	+	0.805875i	$0.298305\pi$
$398$	−64.0545	−3.21076
$399$	−0.212232	−0.0106249
$400$	66.5341	3.32670
$401$	−20.4153	−1.01949	−0.509745	−	0.860326i	$-0.670260\pi$
$401$	−20.4153	−1.01949	−0.509745	+	0.860326i	$0.670260\pi$
$402$	−0.107782	−0.00537569
$403$	−2.22900	−0.111034
$404$	−27.8243	−1.38431
$405$	−3.50938	−0.174383
$406$	4.43777	0.220243
$407$	8.89628	0.440972
$408$	22.4225	1.11008
$409$	−17.8248	−0.881379	−0.440689	−	0.897660i	$-0.645266\pi$
$409$	−17.8248	−0.881379	−0.440689	+	0.897660i	$0.645266\pi$
$410$	−76.9411	−3.79985
$411$	−11.2651	−0.555667
$412$	−82.6305	−4.07091
$413$	1.13034	0.0556204
$414$	−3.77418	−0.185491
$415$	−39.3581	−1.93201
$416$	−2.93528	−0.143914
$417$	−10.2656	−0.502710
$418$	−2.18627	−0.106934
$419$	−5.42075	−0.264821	−0.132410	−	0.991195i	$-0.542272\pi$
$419$	−5.42075	−0.264821	−0.132410	+	0.991195i	$0.542272\pi$
$420$	4.20932	0.205394
$421$	38.0113	1.85256	0.926279	−	0.376840i	$-0.122989\pi$
$421$	38.0113	1.85256	0.926279	+	0.376840i	$0.122989\pi$
$422$	−32.7624	−1.59485
$423$	2.30017	0.111838
$424$	31.5746	1.53340
$425$	22.9163	1.11160
$426$	−25.4908	−1.23504
$427$	−0.252288	−0.0122091
$428$	−34.2496	−1.65552
$429$	−0.314950	−0.0152059
$430$	16.4543	0.793495
$431$	14.5523	0.700961	0.350480	−	0.936570i	$-0.386018\pi$
$431$	14.5523	0.700961	0.350480	+	0.936570i	$0.386018\pi$
$432$	−9.09463	−0.437565
$433$	−1.86310	−0.0895346	−0.0447673	−	0.998997i	$-0.514255\pi$
$433$	−1.86310	−0.0895346	−0.0447673	+	0.998997i	$0.514255\pi$
$434$	4.64038	0.222745
$435$	−23.7525	−1.13885
$436$	14.5767	0.698099
$437$	1.22165	0.0584396
$438$	23.1530	1.10630
$439$	0.643741	0.0307241	0.0153620	−	0.999882i	$-0.495110\pi$
$439$	0.643741	0.0307241	0.0153620	+	0.999882i	$0.495110\pi$
$440$	25.1205	1.19757
$441$	−6.93635	−0.330302
$442$	−2.56399	−0.121957
$443$	−18.0271	−0.856492	−0.428246	−	0.903662i	$-0.640868\pi$
$443$	−18.0271	−0.856492	−0.428246	+	0.903662i	$0.640868\pi$
$444$	−42.2954	−2.00725
$445$	−19.5994	−0.929102
$446$	−27.5029	−1.30230
$447$	−16.9755	−0.802915
$448$	1.52181	0.0718987
$449$	27.3932	1.29277	0.646383	−	0.763013i	$-0.276281\pi$
$449$	27.3932	1.29277	0.646383	+	0.763013i	$0.276281\pi$
$450$	−19.0129	−0.896277
$451$	−8.43604	−0.397237
$452$	−57.2084	−2.69086
$453$	10.4087	0.489041
$454$	−24.9567	−1.17128
$455$	−0.278849	−0.0130726
$456$	6.02161	0.281988
$457$	−25.1056	−1.17439	−0.587196	−	0.809445i	$-0.699768\pi$
$457$	−25.1056	−1.17439	−0.587196	+	0.809445i	$0.699768\pi$
$458$	−12.9816	−0.606589
$459$	−3.13246	−0.146211
$460$	−24.2297	−1.12972
$461$	38.5232	1.79421	0.897103	−	0.441822i	$-0.145668\pi$
$461$	38.5232	1.79421	0.897103	+	0.441822i	$0.145668\pi$
$462$	0.655671	0.0305046
$463$	−3.29366	−0.153070	−0.0765348	−	0.997067i	$-0.524386\pi$
$463$	−3.29366	−0.153070	−0.0765348	+	0.997067i	$0.524386\pi$
$464$	−61.5551	−2.85762
$465$	−24.8369	−1.15179
$466$	−48.0064	−2.22385
$467$	−33.9437	−1.57073	−0.785364	−	0.619035i	$-0.787524\pi$
$467$	−33.9437	−1.57073	−0.785364	+	0.619035i	$0.787524\pi$
$468$	1.49736	0.0692155
$469$	−0.0104629	−0.000483134 0
$470$	20.9787	0.967676
$471$	15.3822	0.708776
$472$	−32.0709	−1.47618
$473$	1.80409	0.0829522
$474$	−22.1343	−1.01666
$475$	6.15424	0.282376
$476$	3.75722	0.172212
$477$	−4.41103	−0.201967
$478$	−17.6191	−0.805879
$479$	10.0038	0.457084	0.228542	−	0.973534i	$-0.426604\pi$
$479$	10.0038	0.457084	0.228542	+	0.973534i	$0.426604\pi$
$480$	−32.7068	−1.49285
$481$	2.80188	0.127755
$482$	−40.7251	−1.85498
$483$	−0.366378	−0.0166708
$484$	4.75428	0.216104
$485$	−26.4607	−1.20152
$486$	2.59890	0.117888
$487$	−10.7252	−0.486005	−0.243002	−	0.970026i	$-0.578132\pi$
$487$	−10.7252	−0.486005	−0.243002	+	0.970026i	$0.578132\pi$
$488$	7.15810	0.324032
$489$	−0.539069	−0.0243776
$490$	−63.2632	−2.85794
$491$	8.35754	0.377170	0.188585	−	0.982057i	$-0.439610\pi$
$491$	8.35754	0.377170	0.188585	+	0.982057i	$0.439610\pi$
$492$	40.1073	1.80818
$493$	−21.2014	−0.954863
$494$	−0.688567	−0.0309801
$495$	−3.50938	−0.157735
$496$	−64.3654	−2.89009
$497$	−2.47452	−0.110997
$498$	29.1470	1.30611
$499$	11.9000	0.532715	0.266358	−	0.963874i	$-0.414180\pi$
$499$	11.9000	0.532715	0.266358	+	0.963874i	$0.414180\pi$
$500$	−38.6374	−1.72792
$501$	−21.2985	−0.951546
$502$	−40.3970	−1.80300
$503$	−21.4919	−0.958278	−0.479139	−	0.877739i	$-0.659051\pi$
$503$	−21.4919	−0.958278	−0.479139	+	0.877739i	$0.659051\pi$
$504$	−1.80590	−0.0804413
$505$	20.5385	0.913952
$506$	−3.77418	−0.167783
$507$	12.9008	0.572945
$508$	−35.9473	−1.59490
$509$	−37.0220	−1.64097	−0.820485	−	0.571668i	$-0.806297\pi$
$509$	−37.0220	−1.64097	−0.820485	+	0.571668i	$0.806297\pi$
$510$	−28.5697	−1.26509
$511$	2.24758	0.0994270
$512$	45.4402	2.00819
$513$	−0.841231	−0.0371412
$514$	−45.1776	−1.99270
$515$	60.9939	2.68771
$516$	−8.57715	−0.377588
$517$	2.30017	0.101161
$518$	−5.83303	−0.256289
$519$	−20.9450	−0.919382
$520$	7.91170	0.346951
$521$	25.1196	1.10051	0.550256	−	0.834996i	$-0.314530\pi$
$521$	25.1196	1.10051	0.550256	+	0.834996i	$0.314530\pi$
$522$	17.5901	0.769898
$523$	29.0802	1.27159	0.635794	−	0.771859i	$-0.280673\pi$
$523$	29.0802	1.27159	0.635794	+	0.771859i	$0.280673\pi$
$524$	47.9732	2.09572
$525$	−1.84568	−0.0805519
$526$	35.0690	1.52908
$527$	−22.1693	−0.965712
$528$	−9.09463	−0.395793
$529$	−20.8911	−0.908307
$530$	−40.2309	−1.74752
$531$	4.48036	0.194431
$532$	1.00901	0.0437462
$533$	−2.65693	−0.115084
$534$	14.5145	0.628104
$535$	25.2814	1.09301
$536$	0.296863	0.0128225
$537$	2.59129	0.111822
$538$	−44.9775	−1.93912
$539$	−6.93635	−0.298770
$540$	16.6846	0.717990
$541$	−0.392586	−0.0168786	−0.00843929	−	0.999964i	$-0.502686\pi$
$541$	−0.392586	−0.0168786	−0.00843929	+	0.999964i	$0.502686\pi$
$542$	6.58186	0.282715
$543$	10.8521	0.465710
$544$	−29.1939	−1.25168
$545$	−10.7598	−0.460901
$546$	0.206504	0.00883754
$547$	15.1084	0.645990	0.322995	−	0.946401i	$-0.395310\pi$
$547$	15.1084	0.645990	0.322995	+	0.946401i	$0.395310\pi$
$548$	53.5575	2.28786
$549$	−1.00000	−0.0426790
$550$	−19.0129	−0.810713
$551$	−5.69370	−0.242560
$552$	10.3952	0.442447
$553$	−2.14869	−0.0913714
$554$	−61.3804	−2.60780
$555$	31.2204	1.32523
$556$	48.8057	2.06982
$557$	−44.8252	−1.89931	−0.949653	−	0.313304i	$-0.898564\pi$
$557$	−44.8252	−1.89931	−0.949653	+	0.313304i	$0.898564\pi$
$558$	18.3932	0.778646
$559$	0.568198	0.0240322
$560$	−8.05215	−0.340265
$561$	−3.13246	−0.132252
$562$	−27.2861	−1.15099
$563$	18.8989	0.796492	0.398246	−	0.917279i	$-0.369619\pi$
$563$	18.8989	0.796492	0.398246	+	0.917279i	$0.369619\pi$
$564$	−10.9356	−0.460473
$565$	42.2285	1.77657
$566$	−19.8968	−0.836325
$567$	0.252288	0.0105951
$568$	70.2089	2.94590
$569$	2.20824	0.0925744	0.0462872	−	0.998928i	$-0.485261\pi$
$569$	2.20824	0.0925744	0.0462872	+	0.998928i	$0.485261\pi$
$570$	−7.67247	−0.321364
$571$	−12.1493	−0.508431	−0.254216	−	0.967148i	$-0.581817\pi$
$571$	−12.1493	−0.508431	−0.254216	+	0.967148i	$0.581817\pi$
$572$	1.49736	0.0626078
$573$	−14.8806	−0.621646
$574$	5.53126	0.230870
$575$	10.6241	0.443056
$576$	6.03203	0.251335
$577$	−11.7039	−0.487238	−0.243619	−	0.969871i	$-0.578335\pi$
$577$	−11.7039	−0.487238	−0.243619	+	0.969871i	$0.578335\pi$
$578$	18.6801	0.776991
$579$	0.222935	0.00926487
$580$	112.926	4.68900
$581$	2.82944	0.117385
$582$	19.5957	0.812268
$583$	−4.41103	−0.182686
$584$	−63.7700	−2.63882
$585$	−1.10528	−0.0456977
$586$	−34.6113	−1.42978
$587$	32.9310	1.35921	0.679604	−	0.733580i	$-0.262152\pi$
$587$	32.9310	1.35921	0.679604	+	0.733580i	$0.262152\pi$
$588$	32.9774	1.35996
$589$	−5.95364	−0.245315
$590$	40.8632	1.68231
$591$	−2.16031	−0.0888634
$592$	80.9084	3.32531
$593$	35.1041	1.44155	0.720776	−	0.693168i	$-0.243786\pi$
$593$	35.1041	1.44155	0.720776	+	0.693168i	$0.243786\pi$
$594$	2.59890	0.106634
$595$	−2.77340	−0.113698
$596$	80.7064	3.30586
$597$	−24.6468	−1.00872
$598$	−1.18868	−0.0486087
$599$	−35.7935	−1.46248	−0.731241	−	0.682119i	$-0.761059\pi$
$599$	−35.7935	−1.46248	−0.731241	+	0.682119i	$0.761059\pi$
$600$	52.3669	2.13787
$601$	−8.14840	−0.332380	−0.166190	−	0.986094i	$-0.553147\pi$
$601$	−8.14840	−0.332380	−0.166190	+	0.986094i	$0.553147\pi$
$602$	−1.18289	−0.0482110
$603$	−0.0414722	−0.00168888
$604$	−49.4857	−2.01354
$605$	−3.50938	−0.142677
$606$	−15.2100	−0.617863
$607$	23.1424	0.939320	0.469660	−	0.882847i	$-0.344377\pi$
$607$	23.1424	0.939320	0.469660	+	0.882847i	$0.344377\pi$
$608$	−7.84012	−0.317959
$609$	1.70756	0.0691937
$610$	−9.12053	−0.369279
$611$	0.724437	0.0293076
$612$	14.8926	0.601997
$613$	−4.11938	−0.166380	−0.0831901	−	0.996534i	$-0.526511\pi$
$613$	−4.11938	−0.166380	−0.0831901	+	0.996534i	$0.526511\pi$
$614$	18.8094	0.759085
$615$	−29.6053	−1.19380
$616$	−1.80590	−0.0727619
$617$	−25.0455	−1.00829	−0.504146	−	0.863618i	$-0.668193\pi$
$617$	−25.0455	−1.00829	−0.504146	+	0.863618i	$0.668193\pi$
$618$	−45.1695	−1.81698
$619$	42.8615	1.72275	0.861374	−	0.507972i	$-0.169605\pi$
$619$	42.8615	1.72275	0.861374	+	0.507972i	$0.169605\pi$
$620$	118.082	4.74228
$621$	−1.45222	−0.0582757
$622$	21.7928	0.873812
$623$	1.40899	0.0564502
$624$	−2.86435	−0.114666
$625$	−8.05850	−0.322340
$626$	−20.9786	−0.838473
$627$	−0.841231	−0.0335955
$628$	−73.1314	−2.91826
$629$	27.8672	1.11114
$630$	2.30100	0.0916740
$631$	−13.0422	−0.519204	−0.259602	−	0.965716i	$-0.583591\pi$
$631$	−13.0422	−0.519204	−0.259602	+	0.965716i	$0.583591\pi$
$632$	60.9641	2.42502
$633$	−12.6063	−0.501054
$634$	68.5118	2.72095
$635$	26.5345	1.05299
$636$	20.9713	0.831565
$637$	−2.18460	−0.0865572
$638$	17.5901	0.696399
$639$	−9.80832	−0.388011
$640$	−10.3983	−0.411028
$641$	41.7027	1.64716	0.823580	−	0.567201i	$-0.191974\pi$
$641$	41.7027	1.64716	0.823580	+	0.567201i	$0.191974\pi$
$642$	−18.7223	−0.738912
$643$	18.6948	0.737249	0.368625	−	0.929578i	$-0.379829\pi$
$643$	18.6948	0.737249	0.368625	+	0.929578i	$0.379829\pi$
$644$	1.74186	0.0686391
$645$	6.33124	0.249292
$646$	−6.84841	−0.269447
$647$	37.1905	1.46211	0.731055	−	0.682319i	$-0.239028\pi$
$647$	37.1905	1.46211	0.731055	+	0.682319i	$0.239028\pi$
$648$	−7.15810	−0.281197
$649$	4.48036	0.175869
$650$	−5.98812	−0.234873
$651$	1.78552	0.0699799
$652$	2.56289	0.100370
$653$	35.5250	1.39020	0.695100	−	0.718914i	$-0.255360\pi$
$653$	35.5250	1.39020	0.695100	+	0.718914i	$0.255360\pi$
$654$	7.96828	0.311585
$655$	−35.4115	−1.38364
$656$	−76.7226	−2.99551
$657$	8.90879	0.347565
$658$	−1.50815	−0.0587939
$659$	−25.4043	−0.989613	−0.494806	−	0.869003i	$-0.664761\pi$
$659$	−25.4043	−0.989613	−0.494806	+	0.869003i	$0.664761\pi$
$660$	16.6846	0.649447
$661$	−22.8515	−0.888819	−0.444409	−	0.895824i	$-0.646586\pi$
$661$	−22.8515	−0.888819	−0.444409	+	0.895824i	$0.646586\pi$
$662$	−53.7635	−2.08958
$663$	−0.986568	−0.0383151
$664$	−80.2789	−3.11543
$665$	−0.744804	−0.0288823
$666$	−23.1205	−0.895903
$667$	−9.82906	−0.380583
$668$	101.259	3.91783
$669$	−10.5825	−0.409143
$670$	−0.378249	−0.0146130
$671$	−1.00000	−0.0386046
$672$	2.35128	0.0907025
$673$	24.2548	0.934954	0.467477	−	0.884005i	$-0.345163\pi$
$673$	24.2548	0.934954	0.467477	+	0.884005i	$0.345163\pi$
$674$	−6.93558	−0.267148
$675$	−7.31576	−0.281584
$676$	−61.3341	−2.35900
$677$	−17.7813	−0.683390	−0.341695	−	0.939811i	$-0.611001\pi$
$677$	−17.7813	−0.683390	−0.341695	+	0.939811i	$0.611001\pi$
$678$	−31.2726	−1.20102
$679$	1.90225	0.0730017
$680$	78.6889	3.01758
$681$	−9.60279	−0.367980
$682$	18.3932	0.704312
$683$	40.4477	1.54769	0.773844	−	0.633376i	$-0.218331\pi$
$683$	40.4477	1.54769	0.773844	+	0.633376i	$0.218331\pi$
$684$	3.99945	0.152923
$685$	−39.5336	−1.51050
$686$	9.13766	0.348877
$687$	−4.99502	−0.190572
$688$	16.4075	0.625531
$689$	−1.38925	−0.0529264
$690$	−13.2450	−0.504230
$691$	49.4541	1.88132	0.940661	−	0.339349i	$-0.110207\pi$
$691$	49.4541	1.88132	0.940661	+	0.339349i	$0.110207\pi$
$692$	99.5783	3.78540
$693$	0.252288	0.00958362
$694$	27.7260	1.05246
$695$	−36.0260	−1.36654
$696$	−48.4481	−1.83642
$697$	−26.4255	−1.00094
$698$	−67.4789	−2.55411
$699$	−18.4718	−0.698668
$700$	8.77486	0.331659
$701$	−8.75971	−0.330850	−0.165425	−	0.986222i	$-0.552900\pi$
$701$	−8.75971	−0.330850	−0.165425	+	0.986222i	$0.552900\pi$
$702$	0.818524	0.0308932
$703$	7.48383	0.282258
$704$	6.03203	0.227341
$705$	8.07216	0.304015
$706$	77.8592	2.93027
$707$	−1.47651	−0.0555297
$708$	−21.3009	−0.800536
$709$	1.59624	0.0599480	0.0299740	−	0.999551i	$-0.490458\pi$
$709$	1.59624	0.0599480	0.0299740	+	0.999551i	$0.490458\pi$
$710$	−89.4571	−3.35726
$711$	−8.51680	−0.319405
$712$	−39.9770	−1.49820
$713$	−10.2778	−0.384907
$714$	2.05386	0.0768638
$715$	−1.10528	−0.0413351
$716$	−12.3197	−0.460409
$717$	−6.77945	−0.253183
$718$	−59.1025	−2.20568
$719$	24.2156	0.903091	0.451545	−	0.892248i	$-0.350873\pi$
$719$	24.2156	0.903091	0.451545	+	0.892248i	$0.350873\pi$
$720$	−31.9165	−1.18946
$721$	−4.38482	−0.163299
$722$	47.5399	1.76925
$723$	−15.6701	−0.582778
$724$	−51.5942	−1.91748
$725$	−49.5152	−1.83895
$726$	2.59890	0.0964542
$727$	6.33810	0.235067	0.117534	−	0.993069i	$-0.462501\pi$
$727$	6.33810	0.235067	0.117534	+	0.993069i	$0.462501\pi$
$728$	−0.568769	−0.0210800
$729$	1.00000	0.0370370
$730$	81.2529	3.00730
$731$	5.65124	0.209019
$732$	4.75428	0.175723
$733$	−23.5758	−0.870790	−0.435395	−	0.900239i	$-0.643391\pi$
$733$	−23.5758	−0.870790	−0.435395	+	0.900239i	$0.643391\pi$
$734$	7.84202	0.289454
$735$	−24.3423	−0.897879
$736$	−13.5345	−0.498887
$737$	−0.0414722	−0.00152765
$738$	21.9244	0.807049
$739$	35.2908	1.29819	0.649096	−	0.760706i	$-0.275147\pi$
$739$	35.2908	1.29819	0.649096	+	0.760706i	$0.275147\pi$
$740$	−148.431	−5.45642
$741$	−0.264946	−0.00973302
$742$	2.89218	0.106175
$743$	37.4102	1.37245	0.686224	−	0.727390i	$-0.259267\pi$
$743$	37.4102	1.37245	0.686224	+	0.727390i	$0.259267\pi$
$744$	−50.6600	−1.85729
$745$	−59.5736	−2.18261
$746$	5.62735	0.206032
$747$	11.2151	0.410339
$748$	14.8926	0.544527
$749$	−1.81747	−0.0664089
$750$	−21.1209	−0.771227
$751$	−4.73838	−0.172906	−0.0864530	−	0.996256i	$-0.527553\pi$
$751$	−4.73838	−0.172906	−0.0864530	+	0.996256i	$0.527553\pi$
$752$	20.9191	0.762843
$753$	−15.5439	−0.566450
$754$	5.54001	0.201755
$755$	36.5279	1.32939
$756$	−1.19945	−0.0436235
$757$	6.11168	0.222133	0.111066	−	0.993813i	$-0.464573\pi$
$757$	6.11168	0.222133	0.111066	+	0.993813i	$0.464573\pi$
$758$	−11.8526	−0.430507
$759$	−1.45222	−0.0527123
$760$	21.1321	0.766543
$761$	−33.3959	−1.21060	−0.605300	−	0.795998i	$-0.706947\pi$
$761$	−33.3959	−1.21060	−0.605300	+	0.795998i	$0.706947\pi$
$762$	−19.6504	−0.711857
$763$	0.773520	0.0280033
$764$	70.7466	2.55952
$765$	−10.9930	−0.397452
$766$	55.3336	1.99928
$767$	1.41109	0.0509515
$768$	19.7646	0.713193
$769$	−5.52203	−0.199130	−0.0995648	−	0.995031i	$-0.531745\pi$
$769$	−5.52203	−0.199130	−0.0995648	+	0.995031i	$0.531745\pi$
$770$	2.30100	0.0829222
$771$	−17.3834	−0.626047
$772$	−1.05990	−0.0381465
$773$	35.4489	1.27501	0.637504	−	0.770447i	$-0.279967\pi$
$773$	35.4489	1.27501	0.637504	+	0.770447i	$0.279967\pi$
$774$	−4.68865	−0.168530
$775$	−51.7758	−1.85984
$776$	−53.9721	−1.93749
$777$	−2.24442	−0.0805183
$778$	80.4964	2.88593
$779$	−7.09665	−0.254264
$780$	5.25481	0.188152
$781$	−9.80832	−0.350969
$782$	−11.8225	−0.422770
$783$	6.76829	0.241879
$784$	−63.0835	−2.25298
$785$	53.9821	1.92670
$786$	26.2243	0.935389
$787$	18.2222	0.649551	0.324776	−	0.945791i	$-0.394711\pi$
$787$	18.2222	0.649551	0.324776	+	0.945791i	$0.394711\pi$
$788$	10.2707	0.365880
$789$	13.4938	0.480391
$790$	−77.6778	−2.76365
$791$	−3.03579	−0.107940
$792$	−7.15810	−0.254352
$793$	−0.314950	−0.0111842
$794$	−61.3196	−2.17615
$795$	−15.4800	−0.549018
$796$	117.178	4.15325
$797$	−40.8082	−1.44550	−0.722751	−	0.691109i	$-0.757123\pi$
$797$	−40.8082	−1.44550	−0.722751	+	0.691109i	$0.757123\pi$
$798$	0.551571	0.0195254
$799$	7.20517	0.254901
$800$	−68.1815	−2.41058
$801$	5.58487	0.197332
$802$	53.0572	1.87352
$803$	8.90879	0.314384
$804$	0.197171	0.00695368
$805$	−1.28576	−0.0453171
$806$	5.79294	0.204047
$807$	−17.3064	−0.609213
$808$	41.8925	1.47377
$809$	−47.5619	−1.67219	−0.836094	−	0.548586i	$-0.815166\pi$
$809$	−47.5619	−1.67219	−0.836094	+	0.548586i	$0.815166\pi$
$810$	9.12053	0.320463
$811$	−10.5129	−0.369157	−0.184578	−	0.982818i	$-0.559092\pi$
$811$	−10.5129	−0.369157	−0.184578	+	0.982818i	$0.559092\pi$
$812$	−8.11821	−0.284893
$813$	2.53256	0.0888207
$814$	−23.1205	−0.810375
$815$	−1.89180	−0.0662668
$816$	−28.4885	−0.997298
$817$	1.51766	0.0530961
$818$	46.3248	1.61971
$819$	0.0794581	0.00277649
$820$	140.752	4.91526
$821$	21.5569	0.752339	0.376170	−	0.926551i	$-0.377241\pi$
$821$	21.5569	0.752339	0.376170	+	0.926551i	$0.377241\pi$
$822$	29.2769	1.02115
$823$	−5.18282	−0.180662	−0.0903309	−	0.995912i	$-0.528792\pi$
$823$	−5.18282	−0.180662	−0.0903309	+	0.995912i	$0.528792\pi$
$824$	124.409	4.33401
$825$	−7.31576	−0.254702
$826$	−2.93764	−0.102214
$827$	8.46918	0.294502	0.147251	−	0.989099i	$-0.452957\pi$
$827$	8.46918	0.294502	0.147251	+	0.989099i	$0.452957\pi$
$828$	6.90427	0.239940
$829$	23.7804	0.825927	0.412964	−	0.910748i	$-0.364494\pi$
$829$	23.7804	0.825927	0.412964	+	0.910748i	$0.364494\pi$
$830$	102.288	3.55046
$831$	−23.6178	−0.819293
$832$	1.89979	0.0658633
$833$	−21.7278	−0.752825
$834$	26.6794	0.923830
$835$	−74.7445	−2.58664
$836$	3.99945	0.138324
$837$	7.07730	0.244627
$838$	14.0880	0.486661
$839$	0.710743	0.0245376	0.0122688	−	0.999925i	$-0.496095\pi$
$839$	0.710743	0.0245376	0.0122688	+	0.999925i	$0.496095\pi$
$840$	−6.33760	−0.218668
$841$	16.8098	0.579647
$842$	−98.7875	−3.40444
$843$	−10.4991	−0.361608
$844$	59.9337	2.06300
$845$	45.2738	1.55747
$846$	−5.97790	−0.205524
$847$	0.252288	0.00866871
$848$	−40.1167	−1.37761
$849$	−7.65586	−0.262748
$850$	−59.5572	−2.04279
$851$	12.9194	0.442871
$852$	46.6315	1.59757
$853$	24.6568	0.844231	0.422116	−	0.906542i	$-0.361288\pi$
$853$	24.6568	0.844231	0.422116	+	0.906542i	$0.361288\pi$
$854$	0.655671	0.0224366
$855$	−2.95220	−0.100963
$856$	51.5666	1.76251
$857$	−3.62125	−0.123699	−0.0618497	−	0.998085i	$-0.519700\pi$
$857$	−3.62125	−0.123699	−0.0618497	+	0.998085i	$0.519700\pi$
$858$	0.818524	0.0279439
$859$	14.1354	0.482295	0.241147	−	0.970488i	$-0.422476\pi$
$859$	14.1354	0.482295	0.241147	+	0.970488i	$0.422476\pi$
$860$	−30.1005	−1.02642
$861$	2.12831	0.0725326
$862$	−37.8200	−1.28816
$863$	−10.6439	−0.362324	−0.181162	−	0.983453i	$-0.557986\pi$
$863$	−10.6439	−0.362324	−0.181162	+	0.983453i	$0.557986\pi$
$864$	9.31982	0.317067
$865$	−73.5039	−2.49921
$866$	4.84200	0.164538
$867$	7.18771	0.244107
$868$	−8.48885	−0.288130
$869$	−8.51680	−0.288913
$870$	61.7304	2.09286
$871$	−0.0130617	−0.000442578 0
$872$	−21.9469	−0.743216
$873$	7.54000	0.255190
$874$	−3.17496	−0.107395
$875$	−2.05031	−0.0693131
$876$	−42.3549	−1.43104
$877$	7.29331	0.246278	0.123139	−	0.992389i	$-0.460704\pi$
$877$	7.29331	0.246278	0.123139	+	0.992389i	$0.460704\pi$
$878$	−1.67302	−0.0564616
$879$	−13.3177	−0.449194
$880$	−31.9165	−1.07591
$881$	−12.8614	−0.433311	−0.216655	−	0.976248i	$-0.569515\pi$
$881$	−12.8614	−0.433311	−0.216655	+	0.976248i	$0.569515\pi$
$882$	18.0269	0.606997
$883$	21.2952	0.716639	0.358319	−	0.933599i	$-0.383350\pi$
$883$	21.2952	0.716639	0.358319	+	0.933599i	$0.383350\pi$
$884$	4.69042	0.157756
$885$	15.7233	0.528532
$886$	46.8505	1.57397
$887$	57.3228	1.92471	0.962356	−	0.271793i	$-0.0876167\pi$
$887$	57.3228	1.92471	0.962356	+	0.271793i	$0.0876167\pi$
$888$	63.6805	2.13698
$889$	−1.90756	−0.0639774
$890$	50.9370	1.70741
$891$	1.00000	0.0335013
$892$	50.3122	1.68458
$893$	1.93497	0.0647513
$894$	44.1177	1.47552
$895$	9.09381	0.303973
$896$	0.747528	0.0249732
$897$	−0.457378	−0.0152714
$898$	−71.1922	−2.37572
$899$	47.9012	1.59759
$900$	34.7812	1.15937
$901$	−13.8174	−0.460323
$902$	21.9244	0.730003
$903$	−0.455150	−0.0151464
$904$	86.1337	2.86476
$905$	38.0843	1.26597
$906$	−27.0510	−0.898711
$907$	19.1793	0.636838	0.318419	−	0.947950i	$-0.396848\pi$
$907$	19.1793	0.636838	0.318419	+	0.947950i	$0.396848\pi$
$908$	45.6543	1.51509
$909$	−5.85246	−0.194114
$910$	0.724700	0.0240236
$911$	−10.8028	−0.357912	−0.178956	−	0.983857i	$-0.557272\pi$
$911$	−10.8028	−0.357912	−0.178956	+	0.983857i	$0.557272\pi$
$912$	−7.65068	−0.253339
$913$	11.2151	0.371166
$914$	65.2470	2.15818
$915$	−3.50938	−0.116017
$916$	23.7477	0.784648
$917$	2.54572	0.0840670
$918$	8.14095	0.268691
$919$	18.6484	0.615155	0.307578	−	0.951523i	$-0.400482\pi$
$919$	18.6484	0.615155	0.307578	+	0.951523i	$0.400482\pi$
$920$	36.4806	1.20273
$921$	7.23744	0.238482
$922$	−100.118	−3.29721
$923$	−3.08913	−0.101680
$924$	−1.19945	−0.0394589
$925$	65.0830	2.13992
$926$	8.55990	0.281296
$927$	−17.3802	−0.570842
$928$	63.0793	2.07068
$929$	−47.6052	−1.56188	−0.780938	−	0.624608i	$-0.785259\pi$
$929$	−47.6052	−1.56188	−0.780938	+	0.624608i	$0.785259\pi$
$930$	64.5487	2.11664
$931$	−5.83507	−0.191237
$932$	87.8201	2.87664
$933$	8.38540	0.274526
$934$	88.2163	2.88652
$935$	−10.9930	−0.359509
$936$	−2.25444	−0.0736888
$937$	9.10229	0.297359	0.148680	−	0.988885i	$-0.452498\pi$
$937$	9.10229	0.297359	0.148680	+	0.988885i	$0.452498\pi$
$938$	0.0271921	0.000887855 0
$939$	−8.07210	−0.263423
$940$	−38.3773	−1.25173
$941$	−34.9570	−1.13956	−0.569782	−	0.821796i	$-0.692972\pi$
$941$	−34.9570	−1.13956	−0.569782	+	0.821796i	$0.692972\pi$
$942$	−39.9769	−1.30252
$943$	−12.2510	−0.398947
$944$	40.7472	1.32621
$945$	0.885374	0.0288012
$946$	−4.68865	−0.152441
$947$	−19.1383	−0.621910	−0.310955	−	0.950425i	$-0.600649\pi$
$947$	−19.1383	−0.621910	−0.310955	+	0.950425i	$0.600649\pi$
$948$	40.4913	1.31510
$949$	2.80582	0.0910809
$950$	−15.9943	−0.518922
$951$	26.3618	0.854841
$952$	−5.65691	−0.183342
$953$	45.7828	1.48305	0.741525	−	0.670925i	$-0.234103\pi$
$953$	45.7828	1.48305	0.741525	+	0.670925i	$0.234103\pi$
$954$	11.4638	0.371155
$955$	−52.2217	−1.68986
$956$	32.2314	1.04244
$957$	6.76829	0.218788
$958$	−25.9988	−0.839982
$959$	2.84205	0.0917747
$960$	21.1687	0.683217
$961$	19.0881	0.615746
$962$	−7.28182	−0.234775
$963$	−7.20395	−0.232144
$964$	74.5002	2.39949
$965$	0.782365	0.0251852
$966$	0.952180	0.0306359
$967$	−9.33277	−0.300122	−0.150061	−	0.988677i	$-0.547947\pi$
$967$	−9.33277	−0.300122	−0.150061	+	0.988677i	$0.547947\pi$
$968$	−7.15810	−0.230070
$969$	−2.63512	−0.0846523
$970$	68.7688	2.20803
$971$	2.32628	0.0746540	0.0373270	−	0.999303i	$-0.488116\pi$
$971$	2.32628	0.0746540	0.0373270	+	0.999303i	$0.488116\pi$
$972$	−4.75428	−0.152494
$973$	2.58989	0.0830282
$974$	27.8737	0.893131
$975$	−2.30410	−0.0737902
$976$	−9.09463	−0.291112
$977$	−38.7073	−1.23836	−0.619178	−	0.785251i	$-0.712534\pi$
$977$	−38.7073	−1.23836	−0.619178	+	0.785251i	$0.712534\pi$
$978$	1.40099	0.0447986
$979$	5.58487	0.178493
$980$	115.730	3.69686
$981$	3.06602	0.0978905
$982$	−21.7204	−0.693126
$983$	−43.4665	−1.38637	−0.693184	−	0.720761i	$-0.743793\pi$
$983$	−43.4665	−1.38637	−0.693184	+	0.720761i	$0.743793\pi$
$984$	−60.3860	−1.92504
$985$	−7.58136	−0.241562
$986$	55.1003	1.75475
$987$	−0.580304	−0.0184713
$988$	1.25963	0.0400740
$989$	2.61994	0.0833093
$990$	9.12053	0.289869
$991$	50.1426	1.59283	0.796417	−	0.604748i	$-0.206726\pi$
$991$	50.1426	1.59283	0.796417	+	0.604748i	$0.206726\pi$
$992$	65.9591	2.09420
$993$	−20.6870	−0.656483
$994$	6.43103	0.203980
$995$	−86.4949	−2.74207
$996$	−53.3198	−1.68950
$997$	−46.5501	−1.47426	−0.737128	−	0.675753i	$-0.763818\pi$
$997$	−46.5501	−1.47426	−0.737128	+	0.675753i	$0.763818\pi$
$998$	−30.9268	−0.978971
$999$	−8.89628	−0.281466

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.e.1.1	✓	13
3.2	odd	2		6039.2.a.i.1.13		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.e.1.1	✓	13	1.1	even	1	trivial
6039.2.a.i.1.13		13	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)

\(f(q)\)	\(=\)	\(q-2.59890 q^{2} -1.00000 q^{3} +4.75428 q^{4} -3.50938 q^{5} +2.59890 q^{6} +0.252288 q^{7} -7.15810 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.59890 q^{2} -1.00000 q^{3} +4.75428 q^{4} -3.50938 q^{5} +2.59890 q^{6} +0.252288 q^{7} -7.15810 q^{8} +1.00000 q^{9} +9.12053 q^{10} +1.00000 q^{11} -4.75428 q^{12} +0.314950 q^{13} -0.655671 q^{14} +3.50938 q^{15} +9.09463 q^{16} +3.13246 q^{17} -2.59890 q^{18} +0.841231 q^{19} -16.6846 q^{20} -0.252288 q^{21} -2.59890 q^{22} +1.45222 q^{23} +7.15810 q^{24} +7.31576 q^{25} -0.818524 q^{26} -1.00000 q^{27} +1.19945 q^{28} -6.76829 q^{29} -9.12053 q^{30} -7.07730 q^{31} -9.31982 q^{32} -1.00000 q^{33} -8.14095 q^{34} -0.885374 q^{35} +4.75428 q^{36} +8.89628 q^{37} -2.18627 q^{38} -0.314950 q^{39} +25.1205 q^{40} -8.43604 q^{41} +0.655671 q^{42} +1.80409 q^{43} +4.75428 q^{44} -3.50938 q^{45} -3.77418 q^{46} +2.30017 q^{47} -9.09463 q^{48} -6.93635 q^{49} -19.0129 q^{50} -3.13246 q^{51} +1.49736 q^{52} -4.41103 q^{53} +2.59890 q^{54} -3.50938 q^{55} -1.80590 q^{56} -0.841231 q^{57} +17.5901 q^{58} +4.48036 q^{59} +16.6846 q^{60} -1.00000 q^{61} +18.3932 q^{62} +0.252288 q^{63} +6.03203 q^{64} -1.10528 q^{65} +2.59890 q^{66} -0.0414722 q^{67} +14.8926 q^{68} -1.45222 q^{69} +2.30100 q^{70} -9.80832 q^{71} -7.15810 q^{72} +8.90879 q^{73} -23.1205 q^{74} -7.31576 q^{75} +3.99945 q^{76} +0.252288 q^{77} +0.818524 q^{78} -8.51680 q^{79} -31.9165 q^{80} +1.00000 q^{81} +21.9244 q^{82} +11.2151 q^{83} -1.19945 q^{84} -10.9930 q^{85} -4.68865 q^{86} +6.76829 q^{87} -7.15810 q^{88} +5.58487 q^{89} +9.12053 q^{90} +0.0794581 q^{91} +6.90427 q^{92} +7.07730 q^{93} -5.97790 q^{94} -2.95220 q^{95} +9.31982 q^{96} +7.54000 q^{97} +18.0269 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 13 q^{11} - 16 q^{12} + 13 q^{13} + q^{14} - 3 q^{15} + 18 q^{16} + 17 q^{17} + 2 q^{18} + 14 q^{19} - 7 q^{20} - 11 q^{21} + 2 q^{22} + 7 q^{23} - 9 q^{24} + 18 q^{25} - 10 q^{26} - 13 q^{27} + 19 q^{28} - 6 q^{29} - 6 q^{30} + 27 q^{31} + 5 q^{32} - 13 q^{33} + 6 q^{34} + 14 q^{35} + 16 q^{36} + 10 q^{37} + 2 q^{38} - 13 q^{39} + 8 q^{40} + 3 q^{41} - q^{42} + 29 q^{43} + 16 q^{44} + 3 q^{45} - 24 q^{46} + 8 q^{47} - 18 q^{48} + 8 q^{49} - 27 q^{50} - 17 q^{51} + 37 q^{52} - 24 q^{53} - 2 q^{54} + 3 q^{55} + 24 q^{56} - 14 q^{57} - 5 q^{58} + 13 q^{59} + 7 q^{60} - 13 q^{61} + 39 q^{62} + 11 q^{63} + 47 q^{64} - 11 q^{65} - 2 q^{66} + 44 q^{67} - 8 q^{68} - 7 q^{69} - 12 q^{70} + 3 q^{71} + 9 q^{72} + 48 q^{73} - 22 q^{74} - 18 q^{75} + 47 q^{76} + 11 q^{77} + 10 q^{78} - 17 q^{79} - 26 q^{80} + 13 q^{81} + 56 q^{82} + 50 q^{83} - 19 q^{84} + 8 q^{85} + 18 q^{86} + 6 q^{87} + 9 q^{88} - 15 q^{89} + 6 q^{90} + 47 q^{91} + 14 q^{92} - 27 q^{93} + 45 q^{94} - q^{95} - 5 q^{96} + 27 q^{97} + 47 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 13 * q^11 - 16 * q^12 + 13 * q^13 + q^14 - 3 * q^15 + 18 * q^16 + 17 * q^17 + 2 * q^18 + 14 * q^19 - 7 * q^20 - 11 * q^21 + 2 * q^22 + 7 * q^23 - 9 * q^24 + 18 * q^25 - 10 * q^26 - 13 * q^27 + 19 * q^28 - 6 * q^29 - 6 * q^30 + 27 * q^31 + 5 * q^32 - 13 * q^33 + 6 * q^34 + 14 * q^35 + 16 * q^36 + 10 * q^37 + 2 * q^38 - 13 * q^39 + 8 * q^40 + 3 * q^41 - q^42 + 29 * q^43 + 16 * q^44 + 3 * q^45 - 24 * q^46 + 8 * q^47 - 18 * q^48 + 8 * q^49 - 27 * q^50 - 17 * q^51 + 37 * q^52 - 24 * q^53 - 2 * q^54 + 3 * q^55 + 24 * q^56 - 14 * q^57 - 5 * q^58 + 13 * q^59 + 7 * q^60 - 13 * q^61 + 39 * q^62 + 11 * q^63 + 47 * q^64 - 11 * q^65 - 2 * q^66 + 44 * q^67 - 8 * q^68 - 7 * q^69 - 12 * q^70 + 3 * q^71 + 9 * q^72 + 48 * q^73 - 22 * q^74 - 18 * q^75 + 47 * q^76 + 11 * q^77 + 10 * q^78 - 17 * q^79 - 26 * q^80 + 13 * q^81 + 56 * q^82 + 50 * q^83 - 19 * q^84 + 8 * q^85 + 18 * q^86 + 6 * q^87 + 9 * q^88 - 15 * q^89 + 6 * q^90 + 47 * q^91 + 14 * q^92 - 27 * q^93 + 45 * q^94 - q^95 - 5 * q^96 + 27 * q^97 + 47 * q^98 + 13 * q^99

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