LMFDB - Embedded newform 2013.2.a.b.1.7

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:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2x^{10} - 14x^{9} + 27x^{8} + 66x^{7} - 125x^{6} - 115x^{5} + 227x^{4} + 40x^{3} - 129x^{2} + 26x - 1 $ x^11 - 2x^10 - 14x^9 + 27x^8 + 66x^7 - 125x^6 - 115x^5 + 227x^4 + 40x^3 - 129x^2 + 26x - 1
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			1.7
Root			$0.0512060$ 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)

$f(q)$	$=$	$q-0.0512060 q^{2} -1.00000 q^{3} -1.99738 q^{4} +3.74211 q^{5} +0.0512060 q^{6} -4.65643 q^{7} +0.204690 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.0512060 q^{2} -1.00000 q^{3} -1.99738 q^{4} +3.74211 q^{5} +0.0512060 q^{6} -4.65643 q^{7} +0.204690 q^{8} +1.00000 q^{9} -0.191618 q^{10} +1.00000 q^{11} +1.99738 q^{12} -0.845440 q^{13} +0.238437 q^{14} -3.74211 q^{15} +3.98427 q^{16} +1.99161 q^{17} -0.0512060 q^{18} -0.676988 q^{19} -7.47440 q^{20} +4.65643 q^{21} -0.0512060 q^{22} -3.54686 q^{23} -0.204690 q^{24} +9.00337 q^{25} +0.0432916 q^{26} -1.00000 q^{27} +9.30066 q^{28} -0.677171 q^{29} +0.191618 q^{30} +7.69354 q^{31} -0.613399 q^{32} -1.00000 q^{33} -0.101982 q^{34} -17.4249 q^{35} -1.99738 q^{36} -5.80691 q^{37} +0.0346659 q^{38} +0.845440 q^{39} +0.765971 q^{40} -3.31122 q^{41} -0.238437 q^{42} -8.83130 q^{43} -1.99738 q^{44} +3.74211 q^{45} +0.181620 q^{46} -5.37613 q^{47} -3.98427 q^{48} +14.6824 q^{49} -0.461027 q^{50} -1.99161 q^{51} +1.68866 q^{52} -7.32872 q^{53} +0.0512060 q^{54} +3.74211 q^{55} -0.953125 q^{56} +0.676988 q^{57} +0.0346752 q^{58} +0.636788 q^{59} +7.47440 q^{60} +1.00000 q^{61} -0.393955 q^{62} -4.65643 q^{63} -7.93714 q^{64} -3.16373 q^{65} +0.0512060 q^{66} -6.23733 q^{67} -3.97799 q^{68} +3.54686 q^{69} +0.892259 q^{70} -2.06467 q^{71} +0.204690 q^{72} +7.66830 q^{73} +0.297349 q^{74} -9.00337 q^{75} +1.35220 q^{76} -4.65643 q^{77} -0.0432916 q^{78} +2.09202 q^{79} +14.9096 q^{80} +1.00000 q^{81} +0.169554 q^{82} -3.47537 q^{83} -9.30066 q^{84} +7.45280 q^{85} +0.452216 q^{86} +0.677171 q^{87} +0.204690 q^{88} +8.92973 q^{89} -0.191618 q^{90} +3.93673 q^{91} +7.08441 q^{92} -7.69354 q^{93} +0.275290 q^{94} -2.53336 q^{95} +0.613399 q^{96} -16.1658 q^{97} -0.751826 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 2 * q^2 - 11 * q^3 + 10 * q^4 - q^5 + 2 * q^6 - 11 * q^7 - 3 * q^8 + 11 * q^9	\( 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9} - 8 q^{10} + 11 q^{11} - 10 q^{12} - 13 q^{13} + 5 q^{14} + q^{15} + 4 q^{16} - 13 q^{17} - 2 q^{18} - 12 q^{19} - 7 q^{20} + 11 q^{21} - 2 q^{22} - 3 q^{23} + 3 q^{24} + 12 q^{25} + 12 q^{26} - 11 q^{27} - 13 q^{28} + 2 q^{29} + 8 q^{30} + q^{31} - 23 q^{32} - 11 q^{33} - 14 q^{34} - 4 q^{35} + 10 q^{36} - 14 q^{37} - 8 q^{38} + 13 q^{39} - 34 q^{40} + 3 q^{41} - 5 q^{42} - 21 q^{43} + 10 q^{44} - q^{45} - 12 q^{46} - 16 q^{47} - 4 q^{48} - 18 q^{49} - 13 q^{50} + 13 q^{51} - 33 q^{52} + 2 q^{54} - q^{55} + 16 q^{56} + 12 q^{57} - 17 q^{58} + 3 q^{59} + 7 q^{60} + 11 q^{61} - 21 q^{62} - 11 q^{63} - 7 q^{64} - q^{65} + 2 q^{66} - 24 q^{67} + 2 q^{68} + 3 q^{69} + 4 q^{70} + 7 q^{71} - 3 q^{72} - 42 q^{73} - 16 q^{74} - 12 q^{75} - 13 q^{76} - 11 q^{77} - 12 q^{78} - 11 q^{79} + 42 q^{80} + 11 q^{81} - 38 q^{82} - 34 q^{83} + 13 q^{84} - 14 q^{85} + 42 q^{86} - 2 q^{87} - 3 q^{88} + 29 q^{89} - 8 q^{90} + 9 q^{91} + 42 q^{92} - q^{93} - 33 q^{94} - 31 q^{95} + 23 q^{96} - 45 q^{97} - 33 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q - 2 * q^2 - 11 * q^3 + 10 * q^4 - q^5 + 2 * q^6 - 11 * q^7 - 3 * q^8 + 11 * q^9 - 8 * q^10 + 11 * q^11 - 10 * q^12 - 13 * q^13 + 5 * q^14 + q^15 + 4 * q^16 - 13 * q^17 - 2 * q^18 - 12 * q^19 - 7 * q^20 + 11 * q^21 - 2 * q^22 - 3 * q^23 + 3 * q^24 + 12 * q^25 + 12 * q^26 - 11 * q^27 - 13 * q^28 + 2 * q^29 + 8 * q^30 + q^31 - 23 * q^32 - 11 * q^33 - 14 * q^34 - 4 * q^35 + 10 * q^36 - 14 * q^37 - 8 * q^38 + 13 * q^39 - 34 * q^40 + 3 * q^41 - 5 * q^42 - 21 * q^43 + 10 * q^44 - q^45 - 12 * q^46 - 16 * q^47 - 4 * q^48 - 18 * q^49 - 13 * q^50 + 13 * q^51 - 33 * q^52 + 2 * q^54 - q^55 + 16 * q^56 + 12 * q^57 - 17 * q^58 + 3 * q^59 + 7 * q^60 + 11 * q^61 - 21 * q^62 - 11 * q^63 - 7 * q^64 - q^65 + 2 * q^66 - 24 * q^67 + 2 * q^68 + 3 * q^69 + 4 * q^70 + 7 * q^71 - 3 * q^72 - 42 * q^73 - 16 * q^74 - 12 * q^75 - 13 * q^76 - 11 * q^77 - 12 * q^78 - 11 * q^79 + 42 * q^80 + 11 * q^81 - 38 * q^82 - 34 * q^83 + 13 * q^84 - 14 * q^85 + 42 * q^86 - 2 * q^87 - 3 * q^88 + 29 * q^89 - 8 * q^90 + 9 * q^91 + 42 * q^92 - q^93 - 33 * q^94 - 31 * q^95 + 23 * q^96 - 45 * q^97 - 33 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.0512060	−0.0362081	−0.0181041	−	0.999836i	$-0.505763\pi$
$2$	−0.0512060	−0.0362081	−0.0181041	+	0.999836i	$0.505763\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99738	−0.998689
$5$	3.74211	1.67352	0.836761	−	0.547569i	$-0.184447\pi$
$5$	3.74211	1.67352	0.836761	+	0.547569i	$0.184447\pi$
$6$	0.0512060	0.0209048
$7$	−4.65643	−1.75997	−0.879983	−	0.475005i	$-0.842446\pi$
$7$	−4.65643	−1.75997	−0.879983	+	0.475005i	$0.842446\pi$
$8$	0.204690	0.0723688
$9$	1.00000	0.333333
$10$	−0.191618	−0.0605951
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.99738	0.576593
$13$	−0.845440	−0.234483	−0.117241	−	0.993103i	$-0.537405\pi$
$13$	−0.845440	−0.234483	−0.117241	+	0.993103i	$0.537405\pi$
$14$	0.238437	0.0637251
$15$	−3.74211	−0.966208
$16$	3.98427	0.996069
$17$	1.99161	0.483035	0.241518	−	0.970396i	$-0.422355\pi$
$17$	1.99161	0.483035	0.241518	+	0.970396i	$0.422355\pi$
$18$	−0.0512060	−0.0120694
$19$	−0.676988	−0.155312	−0.0776559	−	0.996980i	$-0.524744\pi$
$19$	−0.676988	−0.155312	−0.0776559	+	0.996980i	$0.524744\pi$
$20$	−7.47440	−1.67133
$21$	4.65643	1.01612
$22$	−0.0512060	−0.0109172
$23$	−3.54686	−0.739570	−0.369785	−	0.929117i	$-0.620569\pi$
$23$	−3.54686	−0.739570	−0.369785	+	0.929117i	$0.620569\pi$
$24$	−0.204690	−0.0417821
$25$	9.00337	1.80067
$26$	0.0432916	0.00849019
$27$	−1.00000	−0.192450
$28$	9.30066	1.75766
$29$	−0.677171	−0.125748	−0.0628738	−	0.998021i	$-0.520027\pi$
$29$	−0.677171	−0.125748	−0.0628738	+	0.998021i	$0.520027\pi$
$30$	0.191618	0.0349846
$31$	7.69354	1.38180	0.690900	−	0.722950i	$-0.257214\pi$
$31$	7.69354	1.38180	0.690900	+	0.722950i	$0.257214\pi$
$32$	−0.613399	−0.108435
$33$	−1.00000	−0.174078
$34$	−0.101982	−0.0174898
$35$	−17.4249	−2.94534
$36$	−1.99738	−0.332896
$37$	−5.80691	−0.954650	−0.477325	−	0.878727i	$-0.658394\pi$
$37$	−5.80691	−0.954650	−0.477325	+	0.878727i	$0.658394\pi$
$38$	0.0346659	0.00562355
$39$	0.845440	0.135379
$40$	0.765971	0.121111
$41$	−3.31122	−0.517126	−0.258563	−	0.965994i	$-0.583249\pi$
$41$	−3.31122	−0.517126	−0.258563	+	0.965994i	$0.583249\pi$
$42$	−0.238437	−0.0367917
$43$	−8.83130	−1.34676	−0.673380	−	0.739297i	$-0.735158\pi$
$43$	−8.83130	−1.34676	−0.673380	+	0.739297i	$0.735158\pi$
$44$	−1.99738	−0.301116
$45$	3.74211	0.557840
$46$	0.181620	0.0267785
$47$	−5.37613	−0.784189	−0.392095	−	0.919925i	$-0.628249\pi$
$47$	−5.37613	−0.784189	−0.392095	+	0.919925i	$0.628249\pi$
$48$	−3.98427	−0.575080
$49$	14.6824	2.09748
$50$	−0.461027	−0.0651990
$51$	−1.99161	−0.278881
$52$	1.68866	0.234175
$53$	−7.32872	−1.00668	−0.503339	−	0.864089i	$-0.667895\pi$
$53$	−7.32872	−1.00668	−0.503339	+	0.864089i	$0.667895\pi$
$54$	0.0512060	0.00696826
$55$	3.74211	0.504586
$56$	−0.953125	−0.127367
$57$	0.676988	0.0896693
$58$	0.0346752	0.00455308
$59$	0.636788	0.0829027	0.0414513	−	0.999141i	$-0.486802\pi$
$59$	0.636788	0.0829027	0.0414513	+	0.999141i	$0.486802\pi$
$60$	7.47440	0.964941
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−0.393955	−0.0500324
$63$	−4.65643	−0.586655
$64$	−7.93714	−0.992142
$65$	−3.16373	−0.392412
$66$	0.0512060	0.00630303
$67$	−6.23733	−0.762012	−0.381006	−	0.924573i	$-0.624422\pi$
$67$	−6.23733	−0.762012	−0.381006	+	0.924573i	$0.624422\pi$
$68$	−3.97799	−0.482402
$69$	3.54686	0.426991
$70$	0.892259	0.106645
$71$	−2.06467	−0.245032	−0.122516	−	0.992467i	$-0.539096\pi$
$71$	−2.06467	−0.245032	−0.122516	+	0.992467i	$0.539096\pi$
$72$	0.204690	0.0241229
$73$	7.66830	0.897506	0.448753	−	0.893656i	$-0.351868\pi$
$73$	7.66830	0.897506	0.448753	+	0.893656i	$0.351868\pi$
$74$	0.297349	0.0345661
$75$	−9.00337	−1.03962
$76$	1.35220	0.155108
$77$	−4.65643	−0.530650
$78$	−0.0432916	−0.00490181
$79$	2.09202	0.235371	0.117685	−	0.993051i	$-0.462453\pi$
$79$	2.09202	0.235371	0.117685	+	0.993051i	$0.462453\pi$
$80$	14.9096	1.66694
$81$	1.00000	0.111111
$82$	0.169554	0.0187242
$83$	−3.47537	−0.381471	−0.190736	−	0.981641i	$-0.561087\pi$
$83$	−3.47537	−0.381471	−0.190736	+	0.981641i	$0.561087\pi$
$84$	−9.30066	−1.01478
$85$	7.45280	0.808370
$86$	0.452216	0.0487637
$87$	0.677171	0.0726004
$88$	0.204690	0.0218200
$89$	8.92973	0.946550	0.473275	−	0.880915i	$-0.343072\pi$
$89$	8.92973	0.946550	0.473275	+	0.880915i	$0.343072\pi$
$90$	−0.191618	−0.0201984
$91$	3.93673	0.412682
$92$	7.08441	0.738601
$93$	−7.69354	−0.797783
$94$	0.275290	0.0283940
$95$	−2.53336	−0.259918
$96$	0.613399	0.0626047
$97$	−16.1658	−1.64138	−0.820692	−	0.571371i	$-0.806412\pi$
$97$	−16.1658	−1.64138	−0.820692	+	0.571371i	$0.806412\pi$
$98$	−0.751826	−0.0759459
$99$	1.00000	0.100504
$100$	−17.9831	−1.79831
$101$	−1.26799	−0.126170	−0.0630851	−	0.998008i	$-0.520094\pi$
$101$	−1.26799	−0.126170	−0.0630851	+	0.998008i	$0.520094\pi$
$102$	0.101982	0.0100977
$103$	−1.31535	−0.129605	−0.0648026	−	0.997898i	$-0.520642\pi$
$103$	−1.31535	−0.129605	−0.0648026	+	0.997898i	$0.520642\pi$
$104$	−0.173053	−0.0169692
$105$	17.4249	1.70049
$106$	0.375275	0.0364499
$107$	−20.2934	−1.96183	−0.980916	−	0.194430i	$-0.937714\pi$
$107$	−20.2934	−1.96183	−0.980916	+	0.194430i	$0.937714\pi$
$108$	1.99738	0.192198
$109$	−17.2096	−1.64838	−0.824189	−	0.566315i	$-0.808369\pi$
$109$	−17.2096	−1.64838	−0.824189	+	0.566315i	$0.808369\pi$
$110$	−0.191618	−0.0182701
$111$	5.80691	0.551167
$112$	−18.5525	−1.75305
$113$	−10.5949	−0.996680	−0.498340	−	0.866982i	$-0.666057\pi$
$113$	−10.5949	−0.996680	−0.498340	+	0.866982i	$0.666057\pi$
$114$	−0.0346659	−0.00324676
$115$	−13.2727	−1.23769
$116$	1.35257	0.125583
$117$	−0.845440	−0.0781609
$118$	−0.0326074	−0.00300175
$119$	−9.27378	−0.850126
$120$	−0.765971	−0.0699233
$121$	1.00000	0.0909091
$122$	−0.0512060	−0.00463598
$123$	3.31122	0.298563
$124$	−15.3669	−1.37999
$125$	14.9810	1.33994
$126$	0.238437	0.0212417
$127$	0.743672	0.0659902	0.0329951	−	0.999456i	$-0.489495\pi$
$127$	0.743672	0.0659902	0.0329951	+	0.999456i	$0.489495\pi$
$128$	1.63323	0.144358
$129$	8.83130	0.777552
$130$	0.162002	0.0142085
$131$	−9.42555	−0.823514	−0.411757	−	0.911294i	$-0.635085\pi$
$131$	−9.42555	−0.823514	−0.411757	+	0.911294i	$0.635085\pi$
$132$	1.99738	0.173849
$133$	3.15235	0.273343
$134$	0.319389	0.0275910
$135$	−3.74211	−0.322069
$136$	0.407662	0.0349567
$137$	14.3819	1.22873	0.614364	−	0.789022i	$-0.289412\pi$
$137$	14.3819	1.22873	0.614364	+	0.789022i	$0.289412\pi$
$138$	−0.181620	−0.0154606
$139$	−15.0951	−1.28035	−0.640177	−	0.768227i	$-0.721139\pi$
$139$	−15.0951	−1.28035	−0.640177	+	0.768227i	$0.721139\pi$
$140$	34.8041	2.94148
$141$	5.37613	0.452752
$142$	0.105724	0.00887215
$143$	−0.845440	−0.0706992
$144$	3.98427	0.332023
$145$	−2.53405	−0.210441
$146$	−0.392663	−0.0324970
$147$	−14.6824	−1.21098
$148$	11.5986	0.953398
$149$	−16.2231	−1.32905	−0.664523	−	0.747268i	$-0.731365\pi$
$149$	−16.2231	−1.32905	−0.664523	+	0.747268i	$0.731365\pi$
$150$	0.461027	0.0376427
$151$	−9.18378	−0.747366	−0.373683	−	0.927557i	$-0.621905\pi$
$151$	−9.18378	−0.747366	−0.373683	+	0.927557i	$0.621905\pi$
$152$	−0.138573	−0.0112397
$153$	1.99161	0.161012
$154$	0.238437	0.0192138
$155$	28.7900	2.31247
$156$	−1.68866	−0.135201
$157$	22.2002	1.77177	0.885886	−	0.463904i	$-0.153552\pi$
$157$	22.2002	1.77177	0.885886	+	0.463904i	$0.153552\pi$
$158$	−0.107124	−0.00852234
$159$	7.32872	0.581206
$160$	−2.29540	−0.181468
$161$	16.5157	1.30162
$162$	−0.0512060	−0.00402313
$163$	−6.88448	−0.539234	−0.269617	−	0.962968i	$-0.586897\pi$
$163$	−6.88448	−0.539234	−0.269617	+	0.962968i	$0.586897\pi$
$164$	6.61376	0.516448
$165$	−3.74211	−0.291323
$166$	0.177960	0.0138124
$167$	11.1697	0.864340	0.432170	−	0.901792i	$-0.357748\pi$
$167$	11.1697	0.864340	0.432170	+	0.901792i	$0.357748\pi$
$168$	0.953125	0.0735352
$169$	−12.2852	−0.945018
$170$	−0.381629	−0.0292696
$171$	−0.676988	−0.0517706
$172$	17.6394	1.34499
$173$	−17.3542	−1.31942	−0.659708	−	0.751522i	$-0.729320\pi$
$173$	−17.3542	−1.31942	−0.659708	+	0.751522i	$0.729320\pi$
$174$	−0.0346752	−0.00262872
$175$	−41.9236	−3.16913
$176$	3.98427	0.300326
$177$	−0.636788	−0.0478639
$178$	−0.457256	−0.0342728
$179$	−10.7455	−0.803160	−0.401580	−	0.915824i	$-0.631539\pi$
$179$	−10.7455	−0.803160	−0.401580	+	0.915824i	$0.631539\pi$
$180$	−7.47440	−0.557109
$181$	6.08954	0.452632	0.226316	−	0.974054i	$-0.427332\pi$
$181$	6.08954	0.452632	0.226316	+	0.974054i	$0.427332\pi$
$182$	−0.201585	−0.0149424
$183$	−1.00000	−0.0739221
$184$	−0.726005	−0.0535218
$185$	−21.7301	−1.59763
$186$	0.393955	0.0288862
$187$	1.99161	0.145641
$188$	10.7382	0.783161
$189$	4.65643	0.338706
$190$	0.129723	0.00941113
$191$	26.7454	1.93523	0.967616	−	0.252426i	$-0.0812285\pi$
$191$	26.7454	1.93523	0.967616	+	0.252426i	$0.0812285\pi$
$192$	7.93714	0.572814
$193$	19.0367	1.37029	0.685147	−	0.728405i	$-0.259738\pi$
$193$	19.0367	1.37029	0.685147	+	0.728405i	$0.259738\pi$
$194$	0.827784	0.0594314
$195$	3.16373	0.226559
$196$	−29.3262	−2.09473
$197$	−25.4318	−1.81194	−0.905970	−	0.423341i	$-0.860857\pi$
$197$	−25.4318	−1.81194	−0.905970	+	0.423341i	$0.860857\pi$
$198$	−0.0512060	−0.00363905
$199$	−27.4140	−1.94333	−0.971663	−	0.236371i	$-0.924042\pi$
$199$	−27.4140	−1.94333	−0.971663	+	0.236371i	$0.924042\pi$
$200$	1.84290	0.130313
$201$	6.23733	0.439948
$202$	0.0649290	0.00456839
$203$	3.15320	0.221311
$204$	3.97799	0.278515
$205$	−12.3909	−0.865421
$206$	0.0673538	0.00469276
$207$	−3.54686	−0.246523
$208$	−3.36846	−0.233561
$209$	−0.676988	−0.0468283
$210$	−0.892259	−0.0615717
$211$	15.3356	1.05575	0.527874	−	0.849323i	$-0.322989\pi$
$211$	15.3356	1.05575	0.527874	+	0.849323i	$0.322989\pi$
$212$	14.6382	1.00536
$213$	2.06467	0.141469
$214$	1.03914	0.0710343
$215$	−33.0477	−2.25383
$216$	−0.204690	−0.0139274
$217$	−35.8244	−2.43192
$218$	0.881234	0.0596847
$219$	−7.66830	−0.518176
$220$	−7.47440	−0.503924
$221$	−1.68378	−0.113264
$222$	−0.297349	−0.0199567
$223$	20.8414	1.39564	0.697821	−	0.716272i	$-0.254153\pi$
$223$	20.8414	1.39564	0.697821	+	0.716272i	$0.254153\pi$
$224$	2.85625	0.190841
$225$	9.00337	0.600225
$226$	0.542520	0.0360879
$227$	−12.4259	−0.824735	−0.412368	−	0.911018i	$-0.635298\pi$
$227$	−12.4259	−0.824735	−0.412368	+	0.911018i	$0.635298\pi$
$228$	−1.35220	−0.0895517
$229$	−7.52577	−0.497317	−0.248658	−	0.968591i	$-0.579990\pi$
$229$	−7.52577	−0.497317	−0.248658	+	0.968591i	$0.579990\pi$
$230$	0.679643	0.0448143
$231$	4.65643	0.306371
$232$	−0.138610	−0.00910020
$233$	3.98849	0.261295	0.130647	−	0.991429i	$-0.458294\pi$
$233$	3.98849	0.261295	0.130647	+	0.991429i	$0.458294\pi$
$234$	0.0432916	0.00283006
$235$	−20.1181	−1.31236
$236$	−1.27191	−0.0827940
$237$	−2.09202	−0.135891
$238$	0.474873	0.0307815
$239$	−7.60269	−0.491777	−0.245889	−	0.969298i	$-0.579080\pi$
$239$	−7.60269	−0.491777	−0.245889	+	0.969298i	$0.579080\pi$
$240$	−14.9096	−0.962409
$241$	2.67663	0.172417	0.0862083	−	0.996277i	$-0.472525\pi$
$241$	2.67663	0.172417	0.0862083	+	0.996277i	$0.472525\pi$
$242$	−0.0512060	−0.00329165
$243$	−1.00000	−0.0641500
$244$	−1.99738	−0.127869
$245$	54.9430	3.51018
$246$	−0.169554	−0.0108104
$247$	0.572353	0.0364179
$248$	1.57479	0.0999992
$249$	3.47537	0.220243
$250$	−0.767119	−0.0485169
$251$	0.514360	0.0324661	0.0162331	−	0.999868i	$-0.494833\pi$
$251$	0.514360	0.0324661	0.0162331	+	0.999868i	$0.494833\pi$
$252$	9.30066	0.585886
$253$	−3.54686	−0.222989
$254$	−0.0380805	−0.00238938
$255$	−7.45280	−0.466713
$256$	15.7906	0.986915
$257$	−6.99608	−0.436404	−0.218202	−	0.975904i	$-0.570019\pi$
$257$	−6.99608	−0.436404	−0.218202	+	0.975904i	$0.570019\pi$
$258$	−0.452216	−0.0281537
$259$	27.0395	1.68015
$260$	6.31916	0.391898
$261$	−0.677171	−0.0419158
$262$	0.482645	0.0298179
$263$	−15.1643	−0.935072	−0.467536	−	0.883974i	$-0.654858\pi$
$263$	−15.1643	−0.935072	−0.467536	+	0.883974i	$0.654858\pi$
$264$	−0.204690	−0.0125978
$265$	−27.4249	−1.68470
$266$	−0.161419	−0.00989726
$267$	−8.92973	−0.546491
$268$	12.4583	0.761013
$269$	26.7507	1.63102	0.815509	−	0.578745i	$-0.196457\pi$
$269$	26.7507	1.63102	0.815509	+	0.578745i	$0.196457\pi$
$270$	0.191618	0.0116615
$271$	3.00706	0.182666	0.0913331	−	0.995820i	$-0.470887\pi$
$271$	3.00706	0.182666	0.0913331	+	0.995820i	$0.470887\pi$
$272$	7.93511	0.481136
$273$	−3.93673	−0.238262
$274$	−0.736440	−0.0444900
$275$	9.00337	0.542924
$276$	−7.08441	−0.426431
$277$	0.761643	0.0457627	0.0228813	−	0.999738i	$-0.492716\pi$
$277$	0.761643	0.0457627	0.0228813	+	0.999738i	$0.492716\pi$
$278$	0.772963	0.0463592
$279$	7.69354	0.460600
$280$	−3.56670	−0.213151
$281$	19.2471	1.14819	0.574094	−	0.818789i	$-0.305354\pi$
$281$	19.2471	1.14819	0.574094	+	0.818789i	$0.305354\pi$
$282$	−0.275290	−0.0163933
$283$	−20.5209	−1.21984	−0.609921	−	0.792463i	$-0.708799\pi$
$283$	−20.5209	−1.21984	−0.609921	+	0.792463i	$0.708799\pi$
$284$	4.12394	0.244711
$285$	2.53336	0.150063
$286$	0.0432916	0.00255989
$287$	15.4185	0.910124
$288$	−0.613399	−0.0361449
$289$	−13.0335	−0.766677
$290$	0.129758	0.00761968
$291$	16.1658	0.947653
$292$	−15.3165	−0.896330
$293$	−11.1033	−0.648660	−0.324330	−	0.945944i	$-0.605139\pi$
$293$	−11.1033	−0.648660	−0.324330	+	0.945944i	$0.605139\pi$
$294$	0.751826	0.0438474
$295$	2.38293	0.138739
$296$	−1.18862	−0.0690869
$297$	−1.00000	−0.0580259
$298$	0.830720	0.0481223
$299$	2.99865	0.173417
$300$	17.9831	1.03826
$301$	41.1223	2.37025
$302$	0.470265	0.0270607
$303$	1.26799	0.0728444
$304$	−2.69731	−0.154701
$305$	3.74211	0.214272
$306$	−0.101982	−0.00582994
$307$	23.7237	1.35398	0.676991	−	0.735991i	$-0.263284\pi$
$307$	23.7237	1.35398	0.676991	+	0.735991i	$0.263284\pi$
$308$	9.30066	0.529954
$309$	1.31535	0.0748276
$310$	−1.47422	−0.0837303
$311$	8.52580	0.483454	0.241727	−	0.970344i	$-0.422286\pi$
$311$	8.52580	0.483454	0.241727	+	0.970344i	$0.422286\pi$
$312$	0.173053	0.00979720
$313$	2.02754	0.114603	0.0573016	−	0.998357i	$-0.481750\pi$
$313$	2.02754	0.114603	0.0573016	+	0.998357i	$0.481750\pi$
$314$	−1.13679	−0.0641525
$315$	−17.4249	−0.981780
$316$	−4.17856	−0.235062
$317$	31.9495	1.79446	0.897231	−	0.441561i	$-0.145575\pi$
$317$	31.9495	1.79446	0.897231	+	0.441561i	$0.145575\pi$
$318$	−0.375275	−0.0210444
$319$	−0.677171	−0.0379143
$320$	−29.7016	−1.66037
$321$	20.2934	1.13266
$322$	−0.845703	−0.0471292
$323$	−1.34829	−0.0750211
$324$	−1.99738	−0.110965
$325$	−7.61181	−0.422227
$326$	0.352527	0.0195247
$327$	17.2096	0.951692
$328$	−0.677773	−0.0374238
$329$	25.0336	1.38015
$330$	0.191618	0.0105483
$331$	−18.3691	−1.00966	−0.504828	−	0.863220i	$-0.668444\pi$
$331$	−18.3691	−1.00966	−0.504828	+	0.863220i	$0.668444\pi$
$332$	6.94163	0.380971
$333$	−5.80691	−0.318217
$334$	−0.571958	−0.0312961
$335$	−23.3408	−1.27524
$336$	18.5525	1.01212
$337$	−8.49840	−0.462937	−0.231469	−	0.972842i	$-0.574353\pi$
$337$	−8.49840	−0.462937	−0.231469	+	0.972842i	$0.574353\pi$
$338$	0.629078	0.0342173
$339$	10.5949	0.575433
$340$	−14.8861	−0.807310
$341$	7.69354	0.416628
$342$	0.0346659	0.00187452
$343$	−35.7724	−1.93153
$344$	−1.80768	−0.0974634
$345$	13.2727	0.714579
$346$	0.888640	0.0477736
$347$	−17.1538	−0.920865	−0.460433	−	0.887695i	$-0.652306\pi$
$347$	−17.1538	−0.920865	−0.460433	+	0.887695i	$0.652306\pi$
$348$	−1.35257	−0.0725052
$349$	−8.06840	−0.431892	−0.215946	−	0.976405i	$-0.569283\pi$
$349$	−8.06840	−0.431892	−0.215946	+	0.976405i	$0.569283\pi$
$350$	2.14674	0.114748
$351$	0.845440	0.0451262
$352$	−0.613399	−0.0326943
$353$	17.6885	0.941462	0.470731	−	0.882277i	$-0.343990\pi$
$353$	17.6885	0.941462	0.470731	+	0.882277i	$0.343990\pi$
$354$	0.0326074	0.00173306
$355$	−7.72624	−0.410066
$356$	−17.8361	−0.945309
$357$	9.27378	0.490820
$358$	0.550237	0.0290809
$359$	19.1909	1.01286	0.506428	−	0.862282i	$-0.330966\pi$
$359$	19.1909	1.01286	0.506428	+	0.862282i	$0.330966\pi$
$360$	0.765971	0.0403702
$361$	−18.5417	−0.975878
$362$	−0.311821	−0.0163890
$363$	−1.00000	−0.0524864
$364$	−7.86315	−0.412141
$365$	28.6956	1.50200
$366$	0.0512060	0.00267658
$367$	6.55481	0.342158	0.171079	−	0.985257i	$-0.445275\pi$
$367$	6.55481	0.342158	0.171079	+	0.985257i	$0.445275\pi$
$368$	−14.1316	−0.736663
$369$	−3.31122	−0.172375
$370$	1.11271	0.0578471
$371$	34.1257	1.77172
$372$	15.3669	0.796737
$373$	35.5579	1.84112	0.920559	−	0.390602i	$-0.127733\pi$
$373$	35.5579	1.84112	0.920559	+	0.390602i	$0.127733\pi$
$374$	−0.101982	−0.00527338
$375$	−14.9810	−0.773617
$376$	−1.10044	−0.0567508
$377$	0.572507	0.0294856
$378$	−0.238437	−0.0122639
$379$	28.4271	1.46020	0.730102	−	0.683338i	$-0.239473\pi$
$379$	28.4271	1.46020	0.730102	+	0.683338i	$0.239473\pi$
$380$	5.06008	0.259577
$381$	−0.743672	−0.0380995
$382$	−1.36953	−0.0700712
$383$	21.6032	1.10387	0.551936	−	0.833887i	$-0.313889\pi$
$383$	21.6032	1.10387	0.551936	+	0.833887i	$0.313889\pi$
$384$	−1.63323	−0.0833452
$385$	−17.4249	−0.888054
$386$	−0.974795	−0.0496158
$387$	−8.83130	−0.448920
$388$	32.2891	1.63923
$389$	−20.4103	−1.03485	−0.517423	−	0.855730i	$-0.673109\pi$
$389$	−20.4103	−1.03485	−0.517423	+	0.855730i	$0.673109\pi$
$390$	−0.162002	−0.00820329
$391$	−7.06394	−0.357239
$392$	3.00533	0.151792
$393$	9.42555	0.475456
$394$	1.30226	0.0656070
$395$	7.82857	0.393898
$396$	−1.99738	−0.100372
$397$	17.7419	0.890439	0.445220	−	0.895421i	$-0.353126\pi$
$397$	17.7419	0.890439	0.445220	+	0.895421i	$0.353126\pi$
$398$	1.40376	0.0703642
$399$	−3.15235	−0.157815
$400$	35.8719	1.79359
$401$	9.35139	0.466986	0.233493	−	0.972358i	$-0.424984\pi$
$401$	9.35139	0.466986	0.233493	+	0.972358i	$0.424984\pi$
$402$	−0.319389	−0.0159297
$403$	−6.50442	−0.324008
$404$	2.53267	0.126005
$405$	3.74211	0.185947
$406$	−0.161463	−0.00801327
$407$	−5.80691	−0.287838
$408$	−0.407662	−0.0201823
$409$	7.73559	0.382500	0.191250	−	0.981541i	$-0.438746\pi$
$409$	7.73559	0.382500	0.191250	+	0.981541i	$0.438746\pi$
$410$	0.634491	0.0313353
$411$	−14.3819	−0.709407
$412$	2.62725	0.129435
$413$	−2.96516	−0.145906
$414$	0.181620	0.00892615
$415$	−13.0052	−0.638401
$416$	0.518592	0.0254260
$417$	15.0951	0.739213
$418$	0.0346659	0.00169556
$419$	28.4807	1.39137	0.695686	−	0.718346i	$-0.255101\pi$
$419$	28.4807	1.39137	0.695686	+	0.718346i	$0.255101\pi$
$420$	−34.8041	−1.69826
$421$	15.6217	0.761357	0.380679	−	0.924707i	$-0.375690\pi$
$421$	15.6217	0.761357	0.380679	+	0.924707i	$0.375690\pi$
$422$	−0.785277	−0.0382267
$423$	−5.37613	−0.261396
$424$	−1.50012	−0.0728520
$425$	17.9312	0.869789
$426$	−0.105724	−0.00512234
$427$	−4.65643	−0.225341
$428$	40.5335	1.95926
$429$	0.845440	0.0408182
$430$	1.69224	0.0816070
$431$	−16.7493	−0.806783	−0.403392	−	0.915027i	$-0.632169\pi$
$431$	−16.7493	−0.806783	−0.403392	+	0.915027i	$0.632169\pi$
$432$	−3.98427	−0.191693
$433$	−7.73632	−0.371784	−0.185892	−	0.982570i	$-0.559517\pi$
$433$	−7.73632	−0.371784	−0.185892	+	0.982570i	$0.559517\pi$
$434$	1.83443	0.0880553
$435$	2.53405	0.121498
$436$	34.3740	1.64622
$437$	2.40118	0.114864
$438$	0.392663	0.0187622
$439$	31.8535	1.52028	0.760142	−	0.649757i	$-0.225130\pi$
$439$	31.8535	1.52028	0.760142	+	0.649757i	$0.225130\pi$
$440$	0.765971	0.0365163
$441$	14.6824	0.699160
$442$	0.0862199	0.00410106
$443$	−5.53681	−0.263062	−0.131531	−	0.991312i	$-0.541989\pi$
$443$	−5.53681	−0.263062	−0.131531	+	0.991312i	$0.541989\pi$
$444$	−11.5986	−0.550445
$445$	33.4160	1.58407
$446$	−1.06720	−0.0505336
$447$	16.2231	0.767325
$448$	36.9588	1.74614
$449$	−22.8076	−1.07636	−0.538179	−	0.842830i	$-0.680888\pi$
$449$	−22.8076	−1.07636	−0.538179	+	0.842830i	$0.680888\pi$
$450$	−0.461027	−0.0217330
$451$	−3.31122	−0.155919
$452$	21.1619	0.995373
$453$	9.18378	0.431492
$454$	0.636280	0.0298621
$455$	14.7317	0.690632
$456$	0.138573	0.00648926
$457$	−25.1371	−1.17587	−0.587933	−	0.808910i	$-0.700058\pi$
$457$	−25.1371	−1.17587	−0.587933	+	0.808910i	$0.700058\pi$
$458$	0.385365	0.0180069
$459$	−1.99161	−0.0929602
$460$	26.5106	1.23606
$461$	−1.84514	−0.0859366	−0.0429683	−	0.999076i	$-0.513681\pi$
$461$	−1.84514	−0.0859366	−0.0429683	+	0.999076i	$0.513681\pi$
$462$	−0.238437	−0.0110931
$463$	27.1385	1.26123	0.630617	−	0.776094i	$-0.282802\pi$
$463$	27.1385	1.26123	0.630617	+	0.776094i	$0.282802\pi$
$464$	−2.69804	−0.125253
$465$	−28.7900	−1.33511
$466$	−0.204235	−0.00946099
$467$	−40.1833	−1.85946	−0.929732	−	0.368238i	$-0.879961\pi$
$467$	−40.1833	−1.85946	−0.929732	+	0.368238i	$0.879961\pi$
$468$	1.68866	0.0780585
$469$	29.0437	1.34111
$470$	1.03017	0.0475180
$471$	−22.2002	−1.02293
$472$	0.130344	0.00599957
$473$	−8.83130	−0.406063
$474$	0.107124	0.00492038
$475$	−6.09518	−0.279666
$476$	18.5232	0.849011
$477$	−7.32872	−0.335559
$478$	0.389304	0.0178063
$479$	35.3352	1.61451	0.807253	−	0.590206i	$-0.200954\pi$
$479$	35.3352	1.61451	0.807253	+	0.590206i	$0.200954\pi$
$480$	2.29540	0.104770
$481$	4.90939	0.223849
$482$	−0.137059	−0.00624289
$483$	−16.5157	−0.751490
$484$	−1.99738	−0.0907899
$485$	−60.4940	−2.74689
$486$	0.0512060	0.00232275
$487$	−23.3147	−1.05649	−0.528244	−	0.849092i	$-0.677149\pi$
$487$	−23.3147	−1.05649	−0.528244	+	0.849092i	$0.677149\pi$
$488$	0.204690	0.00926587
$489$	6.88448	0.311327
$490$	−2.81341	−0.127097
$491$	−21.8539	−0.986253	−0.493127	−	0.869957i	$-0.664146\pi$
$491$	−21.8539	−0.986253	−0.493127	+	0.869957i	$0.664146\pi$
$492$	−6.61376	−0.298171
$493$	−1.34866	−0.0607405
$494$	−0.0293079	−0.00131863
$495$	3.74211	0.168195
$496$	30.6532	1.37637
$497$	9.61402	0.431248
$498$	−0.177960	−0.00797457
$499$	3.66654	0.164137	0.0820685	−	0.996627i	$-0.473847\pi$
$499$	3.66654	0.164137	0.0820685	+	0.996627i	$0.473847\pi$
$500$	−29.9228	−1.33819
$501$	−11.1697	−0.499027
$502$	−0.0263384	−0.00117554
$503$	1.25493	0.0559546	0.0279773	−	0.999609i	$-0.491093\pi$
$503$	1.25493	0.0559546	0.0279773	+	0.999609i	$0.491093\pi$
$504$	−0.953125	−0.0424555
$505$	−4.74497	−0.211149
$506$	0.181620	0.00807401
$507$	12.2852	0.545606
$508$	−1.48539	−0.0659037
$509$	6.93766	0.307507	0.153753	−	0.988109i	$-0.450864\pi$
$509$	6.93766	0.307507	0.153753	+	0.988109i	$0.450864\pi$
$510$	0.381629	0.0168988
$511$	−35.7069	−1.57958
$512$	−4.07503	−0.180093
$513$	0.676988	0.0298898
$514$	0.358242	0.0158014
$515$	−4.92218	−0.216897
$516$	−17.6394	−0.776533
$517$	−5.37613	−0.236442
$518$	−1.38458	−0.0608352
$519$	17.3542	0.761765
$520$	−0.647583	−0.0283984
$521$	−18.4786	−0.809561	−0.404781	−	0.914414i	$-0.632652\pi$
$521$	−18.4786	−0.809561	−0.404781	+	0.914414i	$0.632652\pi$
$522$	0.0346752	0.00151769
$523$	12.3942	0.541961	0.270980	−	0.962585i	$-0.412652\pi$
$523$	12.3942	0.541961	0.270980	+	0.962585i	$0.412652\pi$
$524$	18.8264	0.822434
$525$	41.9236	1.82970
$526$	0.776505	0.0338572
$527$	15.3225	0.667458
$528$	−3.98427	−0.173393
$529$	−10.4198	−0.453036
$530$	1.40432	0.0609997
$531$	0.636788	0.0276342
$532$	−6.29644	−0.272985
$533$	2.79944	0.121257
$534$	0.457256	0.0197874
$535$	−75.9399	−3.28317
$536$	−1.27672	−0.0551459
$537$	10.7455	0.463705
$538$	−1.36980	−0.0590561
$539$	14.6824	0.632414
$540$	7.47440	0.321647
$541$	8.95379	0.384953	0.192477	−	0.981302i	$-0.438348\pi$
$541$	8.95379	0.384953	0.192477	+	0.981302i	$0.438348\pi$
$542$	−0.153980	−0.00661400
$543$	−6.08954	−0.261327
$544$	−1.22165	−0.0523777
$545$	−64.4001	−2.75860
$546$	0.201585	0.00862702
$547$	1.30109	0.0556308	0.0278154	−	0.999613i	$-0.491145\pi$
$547$	1.30109	0.0556308	0.0278154	+	0.999613i	$0.491145\pi$
$548$	−28.7261	−1.22712
$549$	1.00000	0.0426790
$550$	−0.461027	−0.0196582
$551$	0.458437	0.0195301
$552$	0.726005	0.0309008
$553$	−9.74136	−0.414245
$554$	−0.0390007	−0.00165698
$555$	21.7301	0.922390
$556$	30.1507	1.27868
$557$	−7.18106	−0.304271	−0.152136	−	0.988360i	$-0.548615\pi$
$557$	−7.18106	−0.304271	−0.152136	+	0.988360i	$0.548615\pi$
$558$	−0.393955	−0.0166775
$559$	7.46633	0.315792
$560$	−69.4255	−2.93376
$561$	−1.99161	−0.0840857
$562$	−0.985570	−0.0415738
$563$	39.3214	1.65720	0.828599	−	0.559842i	$-0.189138\pi$
$563$	39.3214	1.65720	0.828599	+	0.559842i	$0.189138\pi$
$564$	−10.7382	−0.452158
$565$	−39.6471	−1.66797
$566$	1.05079	0.0441682
$567$	−4.65643	−0.195552
$568$	−0.422618	−0.0177327
$569$	31.0189	1.30038	0.650189	−	0.759772i	$-0.274690\pi$
$569$	31.0189	1.30038	0.650189	+	0.759772i	$0.274690\pi$
$570$	−0.129723	−0.00543352
$571$	−4.12927	−0.172805	−0.0864023	−	0.996260i	$-0.527537\pi$
$571$	−4.12927	−0.172805	−0.0864023	+	0.996260i	$0.527537\pi$
$572$	1.68866	0.0706065
$573$	−26.7454	−1.11731
$574$	−0.789519	−0.0329539
$575$	−31.9336	−1.33173
$576$	−7.93714	−0.330714
$577$	−12.2320	−0.509226	−0.254613	−	0.967043i	$-0.581948\pi$
$577$	−12.2320	−0.509226	−0.254613	+	0.967043i	$0.581948\pi$
$578$	0.667394	0.0277599
$579$	−19.0367	−0.791139
$580$	5.06145	0.210165
$581$	16.1828	0.671377
$582$	−0.827784	−0.0343128
$583$	−7.32872	−0.303525
$584$	1.56962	0.0649515
$585$	−3.16373	−0.130804
$586$	0.568554	0.0234868
$587$	10.0217	0.413642	0.206821	−	0.978379i	$-0.433688\pi$
$587$	10.0217	0.413642	0.206821	+	0.978379i	$0.433688\pi$
$588$	29.3262	1.20939
$589$	−5.20843	−0.214610
$590$	−0.122020	−0.00502350
$591$	25.4318	1.04612
$592$	−23.1363	−0.950897
$593$	−7.55520	−0.310255	−0.155127	−	0.987894i	$-0.549579\pi$
$593$	−7.55520	−0.310255	−0.155127	+	0.987894i	$0.549579\pi$
$594$	0.0512060	0.00210101
$595$	−34.7035	−1.42270
$596$	32.4036	1.32730
$597$	27.4140	1.12198
$598$	−0.153549	−0.00627909
$599$	−35.1654	−1.43682	−0.718410	−	0.695620i	$-0.755130\pi$
$599$	−35.1654	−1.43682	−0.718410	+	0.695620i	$0.755130\pi$
$600$	−1.84290	−0.0752360
$601$	16.4203	0.669799	0.334899	−	0.942254i	$-0.391298\pi$
$601$	16.4203	0.669799	0.334899	+	0.942254i	$0.391298\pi$
$602$	−2.10571	−0.0858224
$603$	−6.23733	−0.254004
$604$	18.3435	0.746386
$605$	3.74211	0.152138
$606$	−0.0649290	−0.00263756
$607$	21.2135	0.861029	0.430515	−	0.902584i	$-0.358332\pi$
$607$	21.2135	0.861029	0.430515	+	0.902584i	$0.358332\pi$
$608$	0.415264	0.0168412
$609$	−3.15320	−0.127774
$610$	−0.191618	−0.00775841
$611$	4.54520	0.183879
$612$	−3.97799	−0.160801
$613$	3.39536	0.137137	0.0685686	−	0.997646i	$-0.478157\pi$
$613$	3.39536	0.137137	0.0685686	+	0.997646i	$0.478157\pi$
$614$	−1.21480	−0.0490252
$615$	12.3909	0.499651
$616$	−0.953125	−0.0384025
$617$	12.9192	0.520109	0.260055	−	0.965594i	$-0.416259\pi$
$617$	12.9192	0.520109	0.260055	+	0.965594i	$0.416259\pi$
$618$	−0.0673538	−0.00270937
$619$	−42.8280	−1.72140	−0.860700	−	0.509112i	$-0.829974\pi$
$619$	−42.8280	−1.72140	−0.860700	+	0.509112i	$0.829974\pi$
$620$	−57.5046	−2.30944
$621$	3.54686	0.142330
$622$	−0.436573	−0.0175050
$623$	−41.5807	−1.66590
$624$	3.36846	0.134847
$625$	11.0438	0.441752
$626$	−0.103822	−0.00414957
$627$	0.676988	0.0270363
$628$	−44.3423	−1.76945
$629$	−11.5651	−0.461130
$630$	0.892259	0.0355484
$631$	−35.0931	−1.39703	−0.698516	−	0.715594i	$-0.746156\pi$
$631$	−35.0931	−1.39703	−0.698516	+	0.715594i	$0.746156\pi$
$632$	0.428216	0.0170335
$633$	−15.3356	−0.609537
$634$	−1.63601	−0.0649741
$635$	2.78290	0.110436
$636$	−14.6382	−0.580444
$637$	−12.4131	−0.491823
$638$	0.0346752	0.00137281
$639$	−2.06467	−0.0816773
$640$	6.11171	0.241587
$641$	−13.2012	−0.521418	−0.260709	−	0.965417i	$-0.583956\pi$
$641$	−13.2012	−0.521418	−0.260709	+	0.965417i	$0.583956\pi$
$642$	−1.03914	−0.0410117
$643$	38.7731	1.52906	0.764532	−	0.644586i	$-0.222970\pi$
$643$	38.7731	1.52906	0.764532	+	0.644586i	$0.222970\pi$
$644$	−32.9881	−1.29991
$645$	33.0477	1.30125
$646$	0.0690408	0.00271637
$647$	8.06386	0.317023	0.158512	−	0.987357i	$-0.449330\pi$
$647$	8.06386	0.317023	0.158512	+	0.987357i	$0.449330\pi$
$648$	0.204690	0.00804098
$649$	0.636788	0.0249961
$650$	0.389770	0.0152881
$651$	35.8244	1.40407
$652$	13.7509	0.538527
$653$	20.3231	0.795304	0.397652	−	0.917536i	$-0.369825\pi$
$653$	20.3231	0.795304	0.397652	+	0.917536i	$0.369825\pi$
$654$	−0.881234	−0.0344590
$655$	−35.2714	−1.37817
$656$	−13.1928	−0.515093
$657$	7.66830	0.299169
$658$	−1.28187	−0.0499725
$659$	−12.8616	−0.501015	−0.250508	−	0.968115i	$-0.580597\pi$
$659$	−12.8616	−0.501015	−0.250508	+	0.968115i	$0.580597\pi$
$660$	7.47440	0.290941
$661$	9.50897	0.369856	0.184928	−	0.982752i	$-0.440795\pi$
$661$	9.50897	0.369856	0.184928	+	0.982752i	$0.440795\pi$
$662$	0.940609	0.0365578
$663$	1.68378	0.0653927
$664$	−0.711373	−0.0276066
$665$	11.7964	0.457446
$666$	0.297349	0.0115220
$667$	2.40183	0.0929991
$668$	−22.3102	−0.863207
$669$	−20.8414	−0.805775
$670$	1.19519	0.0461742
$671$	1.00000	0.0386046
$672$	−2.85625	−0.110182
$673$	−14.0528	−0.541695	−0.270848	−	0.962622i	$-0.587304\pi$
$673$	−14.0528	−0.541695	−0.270848	+	0.962622i	$0.587304\pi$
$674$	0.435169	0.0167621
$675$	−9.00337	−0.346540
$676$	24.5383	0.943779
$677$	−21.7382	−0.835467	−0.417733	−	0.908570i	$-0.637175\pi$
$677$	−21.7382	−0.835467	−0.417733	+	0.908570i	$0.637175\pi$
$678$	−0.542520	−0.0208354
$679$	75.2747	2.88878
$680$	1.52551	0.0585008
$681$	12.4259	0.476161
$682$	−0.393955	−0.0150853
$683$	−31.1910	−1.19349	−0.596745	−	0.802431i	$-0.703539\pi$
$683$	−31.1910	−1.19349	−0.596745	+	0.802431i	$0.703539\pi$
$684$	1.35220	0.0517027
$685$	53.8186	2.05630
$686$	1.83176	0.0699371
$687$	7.52577	0.287126
$688$	−35.1863	−1.34147
$689$	6.19600	0.236049
$690$	−0.679643	−0.0258736
$691$	−21.4676	−0.816666	−0.408333	−	0.912833i	$-0.633890\pi$
$691$	−21.4676	−0.816666	−0.408333	+	0.912833i	$0.633890\pi$
$692$	34.6629	1.31769
$693$	−4.65643	−0.176883
$694$	0.878379	0.0333428
$695$	−56.4877	−2.14270
$696$	0.138610	0.00525400
$697$	−6.59465	−0.249790
$698$	0.413151	0.0156380
$699$	−3.98849	−0.150859
$700$	83.7372	3.16497
$701$	21.0539	0.795195	0.397597	−	0.917560i	$-0.369844\pi$
$701$	21.0539	0.795195	0.397597	+	0.917560i	$0.369844\pi$
$702$	−0.0432916	−0.00163394
$703$	3.93121	0.148268
$704$	−7.93714	−0.299142
$705$	20.1181	0.757690
$706$	−0.905756	−0.0340886
$707$	5.90433	0.222055
$708$	1.27191	0.0478011
$709$	−31.1132	−1.16848	−0.584241	−	0.811581i	$-0.698608\pi$
$709$	−31.1132	−1.16848	−0.584241	+	0.811581i	$0.698608\pi$
$710$	0.395630	0.0148477
$711$	2.09202	0.0784570
$712$	1.82783	0.0685007
$713$	−27.2879	−1.02194
$714$	−0.474873	−0.0177717
$715$	−3.16373	−0.118317
$716$	21.4629	0.802107
$717$	7.60269	0.283928
$718$	−0.982689	−0.0366736
$719$	−5.72958	−0.213677	−0.106839	−	0.994276i	$-0.534073\pi$
$719$	−5.72958	−0.213677	−0.106839	+	0.994276i	$0.534073\pi$
$720$	14.9096	0.555647
$721$	6.12484	0.228101
$722$	0.949446	0.0353347
$723$	−2.67663	−0.0995448
$724$	−12.1631	−0.452039
$725$	−6.09682	−0.226430
$726$	0.0512060	0.00190043
$727$	6.70140	0.248541	0.124271	−	0.992248i	$-0.460341\pi$
$727$	6.70140	0.248541	0.124271	+	0.992248i	$0.460341\pi$
$728$	0.805810	0.0298653
$729$	1.00000	0.0370370
$730$	−1.46939	−0.0543845
$731$	−17.5885	−0.650533
$732$	1.99738	0.0738252
$733$	24.5158	0.905513	0.452756	−	0.891634i	$-0.350441\pi$
$733$	24.5158	0.905513	0.452756	+	0.891634i	$0.350441\pi$
$734$	−0.335646	−0.0123889
$735$	−54.9430	−2.02660
$736$	2.17564	0.0801950
$737$	−6.23733	−0.229755
$738$	0.169554	0.00624139
$739$	−21.1631	−0.778497	−0.389249	−	0.921133i	$-0.627265\pi$
$739$	−21.1631	−0.778497	−0.389249	+	0.921133i	$0.627265\pi$
$740$	43.4032	1.59553
$741$	−0.572353	−0.0210259
$742$	−1.74744	−0.0641506
$743$	−48.0278	−1.76197	−0.880985	−	0.473144i	$-0.843119\pi$
$743$	−48.0278	−1.76197	−0.880985	+	0.473144i	$0.843119\pi$
$744$	−1.57479	−0.0577346
$745$	−60.7085	−2.22419
$746$	−1.82078	−0.0666635
$747$	−3.47537	−0.127157
$748$	−3.97799	−0.145450
$749$	94.4947	3.45276
$750$	0.767119	0.0280112
$751$	4.94046	0.180280	0.0901400	−	0.995929i	$-0.471269\pi$
$751$	4.94046	0.180280	0.0901400	+	0.995929i	$0.471269\pi$
$752$	−21.4200	−0.781106
$753$	−0.514360	−0.0187443
$754$	−0.0293158	−0.00106762
$755$	−34.3667	−1.25073
$756$	−9.30066	−0.338262
$757$	35.6690	1.29641	0.648207	−	0.761464i	$-0.275519\pi$
$757$	35.6690	1.29641	0.648207	+	0.761464i	$0.275519\pi$
$758$	−1.45564	−0.0528712
$759$	3.54686	0.128743
$760$	−0.518554	−0.0188099
$761$	25.9419	0.940393	0.470197	−	0.882562i	$-0.344183\pi$
$761$	25.9419	0.940393	0.470197	+	0.882562i	$0.344183\pi$
$762$	0.0380805	0.00137951
$763$	80.1352	2.90109
$764$	−53.4208	−1.93270
$765$	7.45280	0.269457
$766$	−1.10621	−0.0399691
$767$	−0.538366	−0.0194393
$768$	−15.7906	−0.569796
$769$	−53.2246	−1.91933	−0.959664	−	0.281150i	$-0.909284\pi$
$769$	−53.2246	−1.91933	−0.959664	+	0.281150i	$0.909284\pi$
$770$	0.892259	0.0321548
$771$	6.99608	0.251958
$772$	−38.0235	−1.36850
$773$	−20.0661	−0.721729	−0.360865	−	0.932618i	$-0.617518\pi$
$773$	−20.0661	−0.721729	−0.360865	+	0.932618i	$0.617518\pi$
$774$	0.452216	0.0162546
$775$	69.2677	2.48817
$776$	−3.30897	−0.118785
$777$	−27.0395	−0.970036
$778$	1.04513	0.0374698
$779$	2.24166	0.0803157
$780$	−6.31916	−0.226262
$781$	−2.06467	−0.0738799
$782$	0.361716	0.0129349
$783$	0.677171	0.0242001
$784$	58.4986	2.08924
$785$	83.0756	2.96510
$786$	−0.482645	−0.0172154
$787$	−20.9934	−0.748336	−0.374168	−	0.927361i	$-0.622072\pi$
$787$	−20.9934	−0.748336	−0.374168	+	0.927361i	$0.622072\pi$
$788$	50.7969	1.80957
$789$	15.1643	0.539864
$790$	−0.400870	−0.0142623
$791$	49.3342	1.75412
$792$	0.204690	0.00727334
$793$	−0.845440	−0.0300225
$794$	−0.908491	−0.0322411
$795$	27.4249	0.972660
$796$	54.7561	1.94078
$797$	15.0047	0.531494	0.265747	−	0.964043i	$-0.414381\pi$
$797$	15.0047	0.531494	0.265747	+	0.964043i	$0.414381\pi$
$798$	0.161419	0.00571418
$799$	−10.7071	−0.378791
$800$	−5.52265	−0.195255
$801$	8.92973	0.315517
$802$	−0.478847	−0.0169087
$803$	7.66830	0.270608
$804$	−12.4583	−0.439371
$805$	61.8035	2.17829
$806$	0.333066	0.0117317
$807$	−26.7507	−0.941668
$808$	−0.259546	−0.00913079
$809$	−11.9417	−0.419848	−0.209924	−	0.977718i	$-0.567322\pi$
$809$	−11.9417	−0.419848	−0.209924	+	0.977718i	$0.567322\pi$
$810$	−0.191618	−0.00673279
$811$	28.6992	1.00777	0.503883	−	0.863772i	$-0.331904\pi$
$811$	28.6992	1.00777	0.503883	+	0.863772i	$0.331904\pi$
$812$	−6.29814	−0.221021
$813$	−3.00706	−0.105462
$814$	0.297349	0.0104221
$815$	−25.7625	−0.902420
$816$	−7.93511	−0.277784
$817$	5.97868	0.209168
$818$	−0.396109	−0.0138496
$819$	3.93673	0.137561
$820$	24.7494	0.864287
$821$	−16.2117	−0.565791	−0.282896	−	0.959151i	$-0.591295\pi$
$821$	−16.2117	−0.565791	−0.282896	+	0.959151i	$0.591295\pi$
$822$	0.736440	0.0256863
$823$	9.55261	0.332983	0.166491	−	0.986043i	$-0.446756\pi$
$823$	9.55261	0.332983	0.166491	+	0.986043i	$0.446756\pi$
$824$	−0.269239	−0.00937937
$825$	−9.00337	−0.313457
$826$	0.151834	0.00528298
$827$	44.0421	1.53149	0.765747	−	0.643142i	$-0.222369\pi$
$827$	44.0421	1.53149	0.765747	+	0.643142i	$0.222369\pi$
$828$	7.08441	0.246200
$829$	−36.8291	−1.27913	−0.639564	−	0.768738i	$-0.720885\pi$
$829$	−36.8291	−1.27913	−0.639564	+	0.768738i	$0.720885\pi$
$830$	0.665945	0.0231153
$831$	−0.761643	−0.0264211
$832$	6.71037	0.232640
$833$	29.2415	1.01316
$834$	−0.772963	−0.0267655
$835$	41.7983	1.44649
$836$	1.35220	0.0467669
$837$	−7.69354	−0.265928
$838$	−1.45838	−0.0503790
$839$	−0.737017	−0.0254447	−0.0127223	−	0.999919i	$-0.504050\pi$
$839$	−0.737017	−0.0254447	−0.0127223	+	0.999919i	$0.504050\pi$
$840$	3.56670	0.123063
$841$	−28.5414	−0.984188
$842$	−0.799927	−0.0275673
$843$	−19.2471	−0.662907
$844$	−30.6311	−1.05436
$845$	−45.9727	−1.58151
$846$	0.275290	0.00946468
$847$	−4.65643	−0.159997
$848$	−29.1996	−1.00272
$849$	20.5209	0.704276
$850$	−0.918184	−0.0314934
$851$	20.5963	0.706031
$852$	−4.12394	−0.141284
$853$	−5.92173	−0.202756	−0.101378	−	0.994848i	$-0.532325\pi$
$853$	−5.92173	−0.202756	−0.101378	+	0.994848i	$0.532325\pi$
$854$	0.238437	0.00815916
$855$	−2.53336	−0.0866392
$856$	−4.15384	−0.141975
$857$	27.3082	0.932831	0.466415	−	0.884566i	$-0.345545\pi$
$857$	27.3082	0.932831	0.466415	+	0.884566i	$0.345545\pi$
$858$	−0.0432916	−0.00147795
$859$	−9.24564	−0.315457	−0.157729	−	0.987483i	$-0.550417\pi$
$859$	−9.24564	−0.315457	−0.157729	+	0.987483i	$0.550417\pi$
$860$	66.0087	2.25088
$861$	−15.4185	−0.525460
$862$	0.857663	0.0292121
$863$	−14.7556	−0.502288	−0.251144	−	0.967950i	$-0.580807\pi$
$863$	−14.7556	−0.502288	−0.251144	+	0.967950i	$0.580807\pi$
$864$	0.613399	0.0208682
$865$	−64.9413	−2.20807
$866$	0.396146	0.0134616
$867$	13.0335	0.442641
$868$	71.5549	2.42873
$869$	2.09202	0.0709670
$870$	−0.129758	−0.00439923
$871$	5.27329	0.178679
$872$	−3.52263	−0.119291
$873$	−16.1658	−0.547128
$874$	−0.122955	−0.00415901
$875$	−69.7582	−2.35826
$876$	15.3165	0.517496
$877$	−52.2504	−1.76437	−0.882185	−	0.470903i	$-0.843928\pi$
$877$	−52.2504	−1.76437	−0.882185	+	0.470903i	$0.843928\pi$
$878$	−1.63109	−0.0550466
$879$	11.1033	0.374504
$880$	14.9096	0.502602
$881$	26.3428	0.887510	0.443755	−	0.896148i	$-0.353646\pi$
$881$	26.3428	0.887510	0.443755	+	0.896148i	$0.353646\pi$
$882$	−0.751826	−0.0253153
$883$	45.2865	1.52401	0.762006	−	0.647570i	$-0.224215\pi$
$883$	45.2865	1.52401	0.762006	+	0.647570i	$0.224215\pi$
$884$	3.36315	0.113115
$885$	−2.38293	−0.0801012
$886$	0.283518	0.00952498
$887$	−10.1077	−0.339384	−0.169692	−	0.985497i	$-0.554277\pi$
$887$	−10.1077	−0.339384	−0.169692	+	0.985497i	$0.554277\pi$
$888$	1.18862	0.0398873
$889$	−3.46286	−0.116141
$890$	−1.71110	−0.0573563
$891$	1.00000	0.0335013
$892$	−41.6281	−1.39381
$893$	3.63958	0.121794
$894$	−0.830720	−0.0277834
$895$	−40.2110	−1.34411
$896$	−7.60501	−0.254066
$897$	−2.99865	−0.100122
$898$	1.16789	0.0389729
$899$	−5.20984	−0.173758
$900$	−17.9831	−0.599438
$901$	−14.5959	−0.486261
$902$	0.169554	0.00564555
$903$	−41.1223	−1.36847
$904$	−2.16866	−0.0721285
$905$	22.7877	0.757490
$906$	−0.470265	−0.0156235
$907$	−29.5028	−0.979625	−0.489813	−	0.871828i	$-0.662935\pi$
$907$	−29.5028	−0.979625	−0.489813	+	0.871828i	$0.662935\pi$
$908$	24.8192	0.823654
$909$	−1.26799	−0.0420567
$910$	−0.754351	−0.0250065
$911$	54.3951	1.80219	0.901095	−	0.433623i	$-0.142765\pi$
$911$	54.3951	1.80219	0.901095	+	0.433623i	$0.142765\pi$
$912$	2.69731	0.0893168
$913$	−3.47537	−0.115018
$914$	1.28717	0.0425759
$915$	−3.74211	−0.123710
$916$	15.0318	0.496665
$917$	43.8894	1.44936
$918$	0.101982	0.00336592
$919$	−41.6870	−1.37513	−0.687563	−	0.726125i	$-0.741319\pi$
$919$	−41.6870	−1.37513	−0.687563	+	0.726125i	$0.741319\pi$
$920$	−2.71679	−0.0895699
$921$	−23.7237	−0.781722
$922$	0.0944822	0.00311161
$923$	1.74556	0.0574558
$924$	−9.30066	−0.305969
$925$	−52.2817	−1.71901
$926$	−1.38966	−0.0456669
$927$	−1.31535	−0.0432017
$928$	0.415376	0.0136354
$929$	12.8663	0.422130	0.211065	−	0.977472i	$-0.432307\pi$
$929$	12.8663	0.422130	0.211065	+	0.977472i	$0.432307\pi$
$930$	1.47422	0.0483417
$931$	−9.93979	−0.325764
$932$	−7.96652	−0.260952
$933$	−8.52580	−0.279122
$934$	2.05763	0.0673277
$935$	7.45280	0.243733
$936$	−0.173053	−0.00565641
$937$	−43.3290	−1.41550	−0.707748	−	0.706465i	$-0.750289\pi$
$937$	−43.3290	−1.41550	−0.707748	+	0.706465i	$0.750289\pi$
$938$	−1.48721	−0.0485593
$939$	−2.02754	−0.0661662
$940$	40.1834	1.31064
$941$	−53.7199	−1.75122	−0.875609	−	0.483020i	$-0.839540\pi$
$941$	−53.7199	−1.75122	−0.875609	+	0.483020i	$0.839540\pi$
$942$	1.13679	0.0370385
$943$	11.7444	0.382451
$944$	2.53714	0.0825768
$945$	17.4249	0.566831
$946$	0.452216	0.0147028
$947$	6.94150	0.225568	0.112784	−	0.993620i	$-0.464023\pi$
$947$	6.94150	0.225568	0.112784	+	0.993620i	$0.464023\pi$
$948$	4.17856	0.135713
$949$	−6.48309	−0.210450
$950$	0.312110	0.0101262
$951$	−31.9495	−1.03603
$952$	−1.89825	−0.0615226
$953$	−45.7414	−1.48171	−0.740855	−	0.671665i	$-0.765579\pi$
$953$	−45.7414	−1.48171	−0.740855	+	0.671665i	$0.765579\pi$
$954$	0.375275	0.0121500
$955$	100.084	3.23865
$956$	15.1854	0.491132
$957$	0.677171	0.0218898
$958$	−1.80937	−0.0584582
$959$	−66.9684	−2.16252
$960$	29.7016	0.958616
$961$	28.1905	0.909371
$962$	−0.251390	−0.00810515
$963$	−20.2934	−0.653944
$964$	−5.34624	−0.172191
$965$	71.2375	2.29322
$966$	0.845703	0.0272101
$967$	40.3862	1.29873	0.649366	−	0.760476i	$-0.275034\pi$
$967$	40.3862	1.29873	0.649366	+	0.760476i	$0.275034\pi$
$968$	0.204690	0.00657898
$969$	1.34829	0.0433134
$970$	3.09766	0.0994598
$971$	−17.8315	−0.572240	−0.286120	−	0.958194i	$-0.592366\pi$
$971$	−17.8315	−0.572240	−0.286120	+	0.958194i	$0.592366\pi$
$972$	1.99738	0.0640659
$973$	70.2896	2.25338
$974$	1.19385	0.0382535
$975$	7.61181	0.243773
$976$	3.98427	0.127534
$977$	−14.1563	−0.452899	−0.226449	−	0.974023i	$-0.572712\pi$
$977$	−14.1563	−0.452899	−0.226449	+	0.974023i	$0.572712\pi$
$978$	−0.352527	−0.0112726
$979$	8.92973	0.285396
$980$	−109.742	−3.50558
$981$	−17.2096	−0.549459
$982$	1.11905	0.0357104
$983$	35.7906	1.14154	0.570772	−	0.821109i	$-0.306644\pi$
$983$	35.7906	1.14154	0.570772	+	0.821109i	$0.306644\pi$
$984$	0.677773	0.0216066
$985$	−95.1685	−3.03232
$986$	0.0690594	0.00219930
$987$	−25.0336	−0.796828
$988$	−1.14321	−0.0363702
$989$	31.3233	0.996024
$990$	−0.191618	−0.00609004
$991$	−9.02047	−0.286545	−0.143272	−	0.989683i	$-0.545762\pi$
$991$	−9.02047	−0.286545	−0.143272	+	0.989683i	$0.545762\pi$
$992$	−4.71920	−0.149835
$993$	18.3691	0.582926
$994$	−0.492296	−0.0156147
$995$	−102.586	−3.25220
$996$	−6.94163	−0.219954
$997$	49.2128	1.55858	0.779292	−	0.626661i	$-0.215579\pi$
$997$	49.2128	1.55858	0.779292	+	0.626661i	$0.215579\pi$
$998$	−0.187749	−0.00594309
$999$	5.80691	0.183722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.b.1.7	✓	11
3.2	odd	2		6039.2.a.c.1.5		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.b.1.7	✓	11	1.1	even	1	trivial
6039.2.a.c.1.5		11	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)

\(f(q)\)	\(=\)	\(q-0.0512060 q^{2} -1.00000 q^{3} -1.99738 q^{4} +3.74211 q^{5} +0.0512060 q^{6} -4.65643 q^{7} +0.204690 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.0512060 q^{2} -1.00000 q^{3} -1.99738 q^{4} +3.74211 q^{5} +0.0512060 q^{6} -4.65643 q^{7} +0.204690 q^{8} +1.00000 q^{9} -0.191618 q^{10} +1.00000 q^{11} +1.99738 q^{12} -0.845440 q^{13} +0.238437 q^{14} -3.74211 q^{15} +3.98427 q^{16} +1.99161 q^{17} -0.0512060 q^{18} -0.676988 q^{19} -7.47440 q^{20} +4.65643 q^{21} -0.0512060 q^{22} -3.54686 q^{23} -0.204690 q^{24} +9.00337 q^{25} +0.0432916 q^{26} -1.00000 q^{27} +9.30066 q^{28} -0.677171 q^{29} +0.191618 q^{30} +7.69354 q^{31} -0.613399 q^{32} -1.00000 q^{33} -0.101982 q^{34} -17.4249 q^{35} -1.99738 q^{36} -5.80691 q^{37} +0.0346659 q^{38} +0.845440 q^{39} +0.765971 q^{40} -3.31122 q^{41} -0.238437 q^{42} -8.83130 q^{43} -1.99738 q^{44} +3.74211 q^{45} +0.181620 q^{46} -5.37613 q^{47} -3.98427 q^{48} +14.6824 q^{49} -0.461027 q^{50} -1.99161 q^{51} +1.68866 q^{52} -7.32872 q^{53} +0.0512060 q^{54} +3.74211 q^{55} -0.953125 q^{56} +0.676988 q^{57} +0.0346752 q^{58} +0.636788 q^{59} +7.47440 q^{60} +1.00000 q^{61} -0.393955 q^{62} -4.65643 q^{63} -7.93714 q^{64} -3.16373 q^{65} +0.0512060 q^{66} -6.23733 q^{67} -3.97799 q^{68} +3.54686 q^{69} +0.892259 q^{70} -2.06467 q^{71} +0.204690 q^{72} +7.66830 q^{73} +0.297349 q^{74} -9.00337 q^{75} +1.35220 q^{76} -4.65643 q^{77} -0.0432916 q^{78} +2.09202 q^{79} +14.9096 q^{80} +1.00000 q^{81} +0.169554 q^{82} -3.47537 q^{83} -9.30066 q^{84} +7.45280 q^{85} +0.452216 q^{86} +0.677171 q^{87} +0.204690 q^{88} +8.92973 q^{89} -0.191618 q^{90} +3.93673 q^{91} +7.08441 q^{92} -7.69354 q^{93} +0.275290 q^{94} -2.53336 q^{95} +0.613399 q^{96} -16.1658 q^{97} -0.751826 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q - 2 * q^2 - 11 * q^3 + 10 * q^4 - q^5 + 2 * q^6 - 11 * q^7 - 3 * q^8 + 11 * q^9	\( 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9} - 8 q^{10} + 11 q^{11} - 10 q^{12} - 13 q^{13} + 5 q^{14} + q^{15} + 4 q^{16} - 13 q^{17} - 2 q^{18} - 12 q^{19} - 7 q^{20} + 11 q^{21} - 2 q^{22} - 3 q^{23} + 3 q^{24} + 12 q^{25} + 12 q^{26} - 11 q^{27} - 13 q^{28} + 2 q^{29} + 8 q^{30} + q^{31} - 23 q^{32} - 11 q^{33} - 14 q^{34} - 4 q^{35} + 10 q^{36} - 14 q^{37} - 8 q^{38} + 13 q^{39} - 34 q^{40} + 3 q^{41} - 5 q^{42} - 21 q^{43} + 10 q^{44} - q^{45} - 12 q^{46} - 16 q^{47} - 4 q^{48} - 18 q^{49} - 13 q^{50} + 13 q^{51} - 33 q^{52} + 2 q^{54} - q^{55} + 16 q^{56} + 12 q^{57} - 17 q^{58} + 3 q^{59} + 7 q^{60} + 11 q^{61} - 21 q^{62} - 11 q^{63} - 7 q^{64} - q^{65} + 2 q^{66} - 24 q^{67} + 2 q^{68} + 3 q^{69} + 4 q^{70} + 7 q^{71} - 3 q^{72} - 42 q^{73} - 16 q^{74} - 12 q^{75} - 13 q^{76} - 11 q^{77} - 12 q^{78} - 11 q^{79} + 42 q^{80} + 11 q^{81} - 38 q^{82} - 34 q^{83} + 13 q^{84} - 14 q^{85} + 42 q^{86} - 2 q^{87} - 3 q^{88} + 29 q^{89} - 8 q^{90} + 9 q^{91} + 42 q^{92} - q^{93} - 33 q^{94} - 31 q^{95} + 23 q^{96} - 45 q^{97} - 33 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q - 2 * q^2 - 11 * q^3 + 10 * q^4 - q^5 + 2 * q^6 - 11 * q^7 - 3 * q^8 + 11 * q^9 - 8 * q^10 + 11 * q^11 - 10 * q^12 - 13 * q^13 + 5 * q^14 + q^15 + 4 * q^16 - 13 * q^17 - 2 * q^18 - 12 * q^19 - 7 * q^20 + 11 * q^21 - 2 * q^22 - 3 * q^23 + 3 * q^24 + 12 * q^25 + 12 * q^26 - 11 * q^27 - 13 * q^28 + 2 * q^29 + 8 * q^30 + q^31 - 23 * q^32 - 11 * q^33 - 14 * q^34 - 4 * q^35 + 10 * q^36 - 14 * q^37 - 8 * q^38 + 13 * q^39 - 34 * q^40 + 3 * q^41 - 5 * q^42 - 21 * q^43 + 10 * q^44 - q^45 - 12 * q^46 - 16 * q^47 - 4 * q^48 - 18 * q^49 - 13 * q^50 + 13 * q^51 - 33 * q^52 + 2 * q^54 - q^55 + 16 * q^56 + 12 * q^57 - 17 * q^58 + 3 * q^59 + 7 * q^60 + 11 * q^61 - 21 * q^62 - 11 * q^63 - 7 * q^64 - q^65 + 2 * q^66 - 24 * q^67 + 2 * q^68 + 3 * q^69 + 4 * q^70 + 7 * q^71 - 3 * q^72 - 42 * q^73 - 16 * q^74 - 12 * q^75 - 13 * q^76 - 11 * q^77 - 12 * q^78 - 11 * q^79 + 42 * q^80 + 11 * q^81 - 38 * q^82 - 34 * q^83 + 13 * q^84 - 14 * q^85 + 42 * q^86 - 2 * q^87 - 3 * q^88 + 29 * q^89 - 8 * q^90 + 9 * q^91 + 42 * q^92 - q^93 - 33 * q^94 - 31 * q^95 + 23 * q^96 - 45 * q^97 - 33 * q^98 + 11 * q^99

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