LMFDB - Embedded newform 2013.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$16.0738859269$
Analytic rank:	$1$
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			1.4
Root			$1.21038$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.21038 q^{2} -1.00000 q^{3} -0.534974 q^{4} -4.03730 q^{5} +1.21038 q^{6} +0.314382 q^{7} +3.06829 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.21038 q^{2} -1.00000 q^{3} -0.534974 q^{4} -4.03730 q^{5} +1.21038 q^{6} +0.314382 q^{7} +3.06829 q^{8} +1.00000 q^{9} +4.88668 q^{10} +1.00000 q^{11} +0.534974 q^{12} -6.19455 q^{13} -0.380522 q^{14} +4.03730 q^{15} -2.64386 q^{16} +0.522063 q^{17} -1.21038 q^{18} -2.00366 q^{19} +2.15985 q^{20} -0.314382 q^{21} -1.21038 q^{22} +3.83355 q^{23} -3.06829 q^{24} +11.2998 q^{25} +7.49777 q^{26} -1.00000 q^{27} -0.168186 q^{28} +3.25991 q^{29} -4.88668 q^{30} +5.63806 q^{31} -2.93650 q^{32} -1.00000 q^{33} -0.631896 q^{34} -1.26926 q^{35} -0.534974 q^{36} -2.37891 q^{37} +2.42519 q^{38} +6.19455 q^{39} -12.3876 q^{40} -0.175749 q^{41} +0.380522 q^{42} +8.28543 q^{43} -0.534974 q^{44} -4.03730 q^{45} -4.64006 q^{46} +9.19808 q^{47} +2.64386 q^{48} -6.90116 q^{49} -13.6771 q^{50} -0.522063 q^{51} +3.31392 q^{52} +11.5453 q^{53} +1.21038 q^{54} -4.03730 q^{55} +0.964614 q^{56} +2.00366 q^{57} -3.94574 q^{58} +4.20429 q^{59} -2.15985 q^{60} +1.00000 q^{61} -6.82421 q^{62} +0.314382 q^{63} +8.84200 q^{64} +25.0093 q^{65} +1.21038 q^{66} -6.14238 q^{67} -0.279290 q^{68} -3.83355 q^{69} +1.53628 q^{70} +6.65073 q^{71} +3.06829 q^{72} -8.65811 q^{73} +2.87939 q^{74} -11.2998 q^{75} +1.07190 q^{76} +0.314382 q^{77} -7.49777 q^{78} -0.325076 q^{79} +10.6741 q^{80} +1.00000 q^{81} +0.212723 q^{82} -13.4972 q^{83} +0.168186 q^{84} -2.10773 q^{85} -10.0285 q^{86} -3.25991 q^{87} +3.06829 q^{88} -6.50417 q^{89} +4.88668 q^{90} -1.94745 q^{91} -2.05085 q^{92} -5.63806 q^{93} -11.1332 q^{94} +8.08937 q^{95} +2.93650 q^{96} -15.4958 q^{97} +8.35305 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.21038	−0.855870	−0.427935	−	0.903810i	$-0.640759\pi$
$2$	−1.21038	−0.855870	−0.427935	+	0.903810i	$0.640759\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.534974	−0.267487
$5$	−4.03730	−1.80554	−0.902769	−	0.430126i	$-0.858469\pi$
$5$	−4.03730	−1.80554	−0.902769	+	0.430126i	$0.858469\pi$
$6$	1.21038	0.494137
$7$	0.314382	0.118825	0.0594126	−	0.998234i	$-0.481077\pi$
$7$	0.314382	0.118825	0.0594126	+	0.998234i	$0.481077\pi$
$8$	3.06829	1.08480
$9$	1.00000	0.333333
$10$	4.88668	1.54531
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.534974	0.154434
$13$	−6.19455	−1.71806	−0.859029	−	0.511927i	$-0.828932\pi$
$13$	−6.19455	−1.71806	−0.859029	+	0.511927i	$0.828932\pi$
$14$	−0.380522	−0.101699
$15$	4.03730	1.04243
$16$	−2.64386	−0.660964
$17$	0.522063	0.126619	0.0633094	−	0.997994i	$-0.479835\pi$
$17$	0.522063	0.126619	0.0633094	+	0.997994i	$0.479835\pi$
$18$	−1.21038	−0.285290
$19$	−2.00366	−0.459670	−0.229835	−	0.973230i	$-0.573819\pi$
$19$	−2.00366	−0.459670	−0.229835	+	0.973230i	$0.573819\pi$
$20$	2.15985	0.482957
$21$	−0.314382	−0.0686038
$22$	−1.21038	−0.258054
$23$	3.83355	0.799350	0.399675	−	0.916657i	$-0.369123\pi$
$23$	3.83355	0.799350	0.399675	+	0.916657i	$0.369123\pi$
$24$	−3.06829	−0.626312
$25$	11.2998	2.25997
$26$	7.49777	1.47043
$27$	−1.00000	−0.192450
$28$	−0.168186	−0.0317842
$29$	3.25991	0.605350	0.302675	−	0.953094i	$-0.402120\pi$
$29$	3.25991	0.605350	0.302675	+	0.953094i	$0.402120\pi$
$30$	−4.88668	−0.892182
$31$	5.63806	1.01263	0.506313	−	0.862350i	$-0.331008\pi$
$31$	5.63806	1.01263	0.506313	+	0.862350i	$0.331008\pi$
$32$	−2.93650	−0.519105
$33$	−1.00000	−0.174078
$34$	−0.631896	−0.108369
$35$	−1.26926	−0.214543
$36$	−0.534974	−0.0891623
$37$	−2.37891	−0.391091	−0.195545	−	0.980695i	$-0.562648\pi$
$37$	−2.37891	−0.391091	−0.195545	+	0.980695i	$0.562648\pi$
$38$	2.42519	0.393418
$39$	6.19455	0.991921
$40$	−12.3876	−1.95865
$41$	−0.175749	−0.0274473	−0.0137237	−	0.999906i	$-0.504369\pi$
$41$	−0.175749	−0.0274473	−0.0137237	+	0.999906i	$0.504369\pi$
$42$	0.380522	0.0587159
$43$	8.28543	1.26352	0.631758	−	0.775166i	$-0.282334\pi$
$43$	8.28543	1.26352	0.631758	+	0.775166i	$0.282334\pi$
$44$	−0.534974	−0.0806503
$45$	−4.03730	−0.601846
$46$	−4.64006	−0.684140
$47$	9.19808	1.34168	0.670839	−	0.741603i	$-0.265934\pi$
$47$	9.19808	1.34168	0.670839	+	0.741603i	$0.265934\pi$
$48$	2.64386	0.381608
$49$	−6.90116	−0.985881
$50$	−13.6771	−1.93424
$51$	−0.522063	−0.0731034
$52$	3.31392	0.459558
$53$	11.5453	1.58587	0.792936	−	0.609305i	$-0.208551\pi$
$53$	11.5453	1.58587	0.792936	+	0.609305i	$0.208551\pi$
$54$	1.21038	0.164712
$55$	−4.03730	−0.544390
$56$	0.964614	0.128902
$57$	2.00366	0.265391
$58$	−3.94574	−0.518101
$59$	4.20429	0.547352	0.273676	−	0.961822i	$-0.411760\pi$
$59$	4.20429	0.547352	0.273676	+	0.961822i	$0.411760\pi$
$60$	−2.15985	−0.278836
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−6.82421	−0.866676
$63$	0.314382	0.0396084
$64$	8.84200	1.10525
$65$	25.0093	3.10202
$66$	1.21038	0.148988
$67$	−6.14238	−0.750411	−0.375205	−	0.926942i	$-0.622428\pi$
$67$	−6.14238	−0.750411	−0.375205	+	0.926942i	$0.622428\pi$
$68$	−0.279290	−0.0338689
$69$	−3.83355	−0.461505
$70$	1.53628	0.183621
$71$	6.65073	0.789296	0.394648	−	0.918832i	$-0.370867\pi$
$71$	6.65073	0.789296	0.394648	+	0.918832i	$0.370867\pi$
$72$	3.06829	0.361601
$73$	−8.65811	−1.01335	−0.506677	−	0.862136i	$-0.669126\pi$
$73$	−8.65811	−1.01335	−0.506677	+	0.862136i	$0.669126\pi$
$74$	2.87939	0.334723
$75$	−11.2998	−1.30479
$76$	1.07190	0.122956
$77$	0.314382	0.0358271
$78$	−7.49777	−0.848956
$79$	−0.325076	−0.0365739	−0.0182869	−	0.999833i	$-0.505821\pi$
$79$	−0.325076	−0.0365739	−0.0182869	+	0.999833i	$0.505821\pi$
$80$	10.6741	1.19340
$81$	1.00000	0.111111
$82$	0.212723	0.0234913
$83$	−13.4972	−1.48151	−0.740753	−	0.671778i	$-0.765531\pi$
$83$	−13.4972	−1.48151	−0.740753	+	0.671778i	$0.765531\pi$
$84$	0.168186	0.0183506
$85$	−2.10773	−0.228615
$86$	−10.0285	−1.08141
$87$	−3.25991	−0.349499
$88$	3.06829	0.327081
$89$	−6.50417	−0.689441	−0.344720	−	0.938705i	$-0.612026\pi$
$89$	−6.50417	−0.689441	−0.344720	+	0.938705i	$0.612026\pi$
$90$	4.88668	0.515102
$91$	−1.94745	−0.204149
$92$	−2.05085	−0.213816
$93$	−5.63806	−0.584640
$94$	−11.1332	−1.14830
$95$	8.08937	0.829952
$96$	2.93650	0.299705
$97$	−15.4958	−1.57336	−0.786679	−	0.617363i	$-0.788201\pi$
$97$	−15.4958	−1.57336	−0.786679	+	0.617363i	$0.788201\pi$
$98$	8.35305	0.843785
$99$	1.00000	0.100504
$100$	−6.04511	−0.604511
$101$	−2.37859	−0.236678	−0.118339	−	0.992973i	$-0.537757\pi$
$101$	−2.37859	−0.236678	−0.118339	+	0.992973i	$0.537757\pi$
$102$	0.631896	0.0625670
$103$	−18.1789	−1.79122	−0.895612	−	0.444835i	$-0.853262\pi$
$103$	−18.1789	−1.79122	−0.895612	+	0.444835i	$0.853262\pi$
$104$	−19.0067	−1.86376
$105$	1.26926	0.123867
$106$	−13.9743	−1.35730
$107$	11.3899	1.10110	0.550549	−	0.834803i	$-0.314418\pi$
$107$	11.3899	1.10110	0.550549	+	0.834803i	$0.314418\pi$
$108$	0.534974	0.0514779
$109$	−12.0843	−1.15746	−0.578732	−	0.815518i	$-0.696452\pi$
$109$	−12.0843	−1.15746	−0.578732	+	0.815518i	$0.696452\pi$
$110$	4.88668	0.465927
$111$	2.37891	0.225796
$112$	−0.831180	−0.0785392
$113$	−14.2387	−1.33947	−0.669734	−	0.742601i	$-0.733592\pi$
$113$	−14.2387	−1.33947	−0.669734	+	0.742601i	$0.733592\pi$
$114$	−2.42519	−0.227140
$115$	−15.4772	−1.44326
$116$	−1.74397	−0.161923
$117$	−6.19455	−0.572686
$118$	−5.08880	−0.468462
$119$	0.164127	0.0150455
$120$	12.3876	1.13083
$121$	1.00000	0.0909091
$122$	−1.21038	−0.109583
$123$	0.175749	0.0158467
$124$	−3.01621	−0.270864
$125$	−25.4343	−2.27491
$126$	−0.380522	−0.0338996
$127$	10.9449	0.971201	0.485600	−	0.874181i	$-0.338601\pi$
$127$	10.9449	0.971201	0.485600	+	0.874181i	$0.338601\pi$
$128$	−4.82921	−0.426846
$129$	−8.28543	−0.729491
$130$	−30.2708	−2.65492
$131$	17.2051	1.50322	0.751609	−	0.659609i	$-0.229278\pi$
$131$	17.2051	1.50322	0.751609	+	0.659609i	$0.229278\pi$
$132$	0.534974	0.0465635
$133$	−0.629913	−0.0546204
$134$	7.43463	0.642254
$135$	4.03730	0.347476
$136$	1.60184	0.137357
$137$	−6.38652	−0.545637	−0.272818	−	0.962066i	$-0.587956\pi$
$137$	−6.38652	−0.545637	−0.272818	+	0.962066i	$0.587956\pi$
$138$	4.64006	0.394988
$139$	6.29184	0.533667	0.266834	−	0.963743i	$-0.414023\pi$
$139$	6.29184	0.533667	0.266834	+	0.963743i	$0.414023\pi$
$140$	0.679018	0.0573875
$141$	−9.19808	−0.774618
$142$	−8.04993	−0.675535
$143$	−6.19455	−0.518014
$144$	−2.64386	−0.220321
$145$	−13.1613	−1.09298
$146$	10.4796	0.867300
$147$	6.90116	0.569198
$148$	1.27266	0.104612
$149$	−11.9563	−0.979498	−0.489749	−	0.871863i	$-0.662912\pi$
$149$	−11.9563	−0.979498	−0.489749	+	0.871863i	$0.662912\pi$
$150$	13.6771	1.11673
$151$	−3.45555	−0.281209	−0.140604	−	0.990066i	$-0.544905\pi$
$151$	−3.45555	−0.281209	−0.140604	+	0.990066i	$0.544905\pi$
$152$	−6.14780	−0.498652
$153$	0.522063	0.0422063
$154$	−0.380522	−0.0306634
$155$	−22.7626	−1.82833
$156$	−3.31392	−0.265326
$157$	9.21530	0.735461	0.367731	−	0.929932i	$-0.380135\pi$
$157$	9.21530	0.735461	0.367731	+	0.929932i	$0.380135\pi$
$158$	0.393466	0.0313025
$159$	−11.5453	−0.915604
$160$	11.8555	0.937263
$161$	1.20520	0.0949829
$162$	−1.21038	−0.0950967
$163$	−4.82707	−0.378085	−0.189043	−	0.981969i	$-0.560538\pi$
$163$	−4.82707	−0.378085	−0.189043	+	0.981969i	$0.560538\pi$
$164$	0.0940209	0.00734180
$165$	4.03730	0.314304
$166$	16.3367	1.26798
$167$	−4.69854	−0.363584	−0.181792	−	0.983337i	$-0.558190\pi$
$167$	−4.69854	−0.363584	−0.181792	+	0.983337i	$0.558190\pi$
$168$	−0.964614	−0.0744216
$169$	25.3724	1.95172
$170$	2.55116	0.195665
$171$	−2.00366	−0.153223
$172$	−4.43249	−0.337974
$173$	5.20402	0.395655	0.197827	−	0.980237i	$-0.436611\pi$
$173$	5.20402	0.395655	0.197827	+	0.980237i	$0.436611\pi$
$174$	3.94574	0.299126
$175$	3.55246	0.268541
$176$	−2.64386	−0.199288
$177$	−4.20429	−0.316014
$178$	7.87254	0.590072
$179$	18.9380	1.41549	0.707746	−	0.706467i	$-0.249712\pi$
$179$	18.9380	1.41549	0.707746	+	0.706467i	$0.249712\pi$
$180$	2.15985	0.160986
$181$	−21.8031	−1.62061	−0.810305	−	0.586009i	$-0.800698\pi$
$181$	−21.8031	−1.62061	−0.810305	+	0.586009i	$0.800698\pi$
$182$	2.35716	0.174725
$183$	−1.00000	−0.0739221
$184$	11.7624	0.867138
$185$	9.60439	0.706129
$186$	6.82421	0.500375
$187$	0.522063	0.0381770
$188$	−4.92073	−0.358881
$189$	−0.314382	−0.0228679
$190$	−9.79124	−0.710331
$191$	25.3896	1.83712	0.918562	−	0.395277i	$-0.129352\pi$
$191$	25.3896	1.83712	0.918562	+	0.395277i	$0.129352\pi$
$192$	−8.84200	−0.638116
$193$	21.5107	1.54838	0.774188	−	0.632955i	$-0.218158\pi$
$193$	21.5107	1.54838	0.774188	+	0.632955i	$0.218158\pi$
$194$	18.7558	1.34659
$195$	−25.0093	−1.79095
$196$	3.69194	0.263710
$197$	−26.8529	−1.91319	−0.956595	−	0.291420i	$-0.905872\pi$
$197$	−26.8529	−1.91319	−0.956595	+	0.291420i	$0.905872\pi$
$198$	−1.21038	−0.0860182
$199$	6.00152	0.425436	0.212718	−	0.977114i	$-0.431768\pi$
$199$	6.00152	0.425436	0.212718	+	0.977114i	$0.431768\pi$
$200$	34.6711	2.45162
$201$	6.14238	0.433250
$202$	2.87900	0.202566
$203$	1.02486	0.0719309
$204$	0.279290	0.0195542
$205$	0.709551	0.0495572
$206$	22.0035	1.53306
$207$	3.83355	0.266450
$208$	16.3775	1.13557
$209$	−2.00366	−0.138596
$210$	−1.53628	−0.106014
$211$	−19.7675	−1.36085	−0.680425	−	0.732817i	$-0.738205\pi$
$211$	−19.7675	−1.36085	−0.680425	+	0.732817i	$0.738205\pi$
$212$	−6.17644	−0.424200
$213$	−6.65073	−0.455700
$214$	−13.7861	−0.942397
$215$	−33.4508	−2.28133
$216$	−3.06829	−0.208771
$217$	1.77250	0.120325
$218$	14.6266	0.990639
$219$	8.65811	0.585061
$220$	2.15985	0.145617
$221$	−3.23394	−0.217538
$222$	−2.87939	−0.193252
$223$	8.75822	0.586494	0.293247	−	0.956037i	$-0.405264\pi$
$223$	8.75822	0.586494	0.293247	+	0.956037i	$0.405264\pi$
$224$	−0.923182	−0.0616827
$225$	11.2998	0.753322
$226$	17.2343	1.14641
$227$	−24.9379	−1.65519	−0.827594	−	0.561328i	$-0.810291\pi$
$227$	−24.9379	−1.65519	−0.827594	+	0.561328i	$0.810291\pi$
$228$	−1.07190	−0.0709885
$229$	−8.30456	−0.548781	−0.274390	−	0.961618i	$-0.588476\pi$
$229$	−8.30456	−0.548781	−0.274390	+	0.961618i	$0.588476\pi$
$230$	18.7333	1.23524
$231$	−0.314382	−0.0206848
$232$	10.0023	0.656686
$233$	−4.12654	−0.270339	−0.135169	−	0.990822i	$-0.543158\pi$
$233$	−4.12654	−0.270339	−0.135169	+	0.990822i	$0.543158\pi$
$234$	7.49777	0.490145
$235$	−37.1355	−2.42245
$236$	−2.24919	−0.146410
$237$	0.325076	0.0211159
$238$	−0.198657	−0.0128770
$239$	−21.0444	−1.36125	−0.680624	−	0.732633i	$-0.738291\pi$
$239$	−21.0444	−1.36125	−0.680624	+	0.732633i	$0.738291\pi$
$240$	−10.6741	−0.689007
$241$	12.9923	0.836905	0.418452	−	0.908239i	$-0.362573\pi$
$241$	12.9923	0.836905	0.418452	+	0.908239i	$0.362573\pi$
$242$	−1.21038	−0.0778064
$243$	−1.00000	−0.0641500
$244$	−0.534974	−0.0342482
$245$	27.8621	1.78004
$246$	−0.212723	−0.0135627
$247$	12.4117	0.789741
$248$	17.2992	1.09850
$249$	13.4972	0.855348
$250$	30.7853	1.94703
$251$	−25.1998	−1.59060	−0.795298	−	0.606219i	$-0.792685\pi$
$251$	−25.1998	−1.59060	−0.795298	+	0.606219i	$0.792685\pi$
$252$	−0.168186	−0.0105947
$253$	3.83355	0.241013
$254$	−13.2475	−0.831222
$255$	2.10773	0.131991
$256$	−11.8388	−0.739926
$257$	10.7864	0.672835	0.336418	−	0.941713i	$-0.390785\pi$
$257$	10.7864	0.672835	0.336418	+	0.941713i	$0.390785\pi$
$258$	10.0285	0.624350
$259$	−0.747887	−0.0464714
$260$	−13.3793	−0.829749
$261$	3.25991	0.201783
$262$	−20.8248	−1.28656
$263$	12.2801	0.757223	0.378612	−	0.925556i	$-0.376402\pi$
$263$	12.2801	0.757223	0.378612	+	0.925556i	$0.376402\pi$
$264$	−3.06829	−0.188840
$265$	−46.6120	−2.86335
$266$	0.762436	0.0467480
$267$	6.50417	0.398049
$268$	3.28601	0.200725
$269$	14.0164	0.854595	0.427297	−	0.904111i	$-0.359466\pi$
$269$	14.0164	0.854595	0.427297	+	0.904111i	$0.359466\pi$
$270$	−4.88668	−0.297394
$271$	27.2918	1.65786	0.828929	−	0.559353i	$-0.188950\pi$
$271$	27.2918	1.65786	0.828929	+	0.559353i	$0.188950\pi$
$272$	−1.38026	−0.0836905
$273$	1.94745	0.117865
$274$	7.73013	0.466994
$275$	11.2998	0.681405
$276$	2.05085	0.123446
$277$	−13.1459	−0.789863	−0.394932	−	0.918710i	$-0.629232\pi$
$277$	−13.1459	−0.789863	−0.394932	+	0.918710i	$0.629232\pi$
$278$	−7.61554	−0.456750
$279$	5.63806	0.337542
$280$	−3.89444	−0.232737
$281$	25.6093	1.52772	0.763862	−	0.645380i	$-0.223301\pi$
$281$	25.6093	1.52772	0.763862	+	0.645380i	$0.223301\pi$
$282$	11.1332	0.662972
$283$	13.2340	0.786682	0.393341	−	0.919393i	$-0.371319\pi$
$283$	13.2340	0.786682	0.393341	+	0.919393i	$0.371319\pi$
$284$	−3.55796	−0.211126
$285$	−8.08937	−0.479173
$286$	7.49777	0.443353
$287$	−0.0552522	−0.00326143
$288$	−2.93650	−0.173035
$289$	−16.7275	−0.983968
$290$	15.9302	0.935451
$291$	15.4958	0.908378
$292$	4.63186	0.271059
$293$	−0.715933	−0.0418253	−0.0209126	−	0.999781i	$-0.506657\pi$
$293$	−0.715933	−0.0418253	−0.0209126	+	0.999781i	$0.506657\pi$
$294$	−8.35305	−0.487160
$295$	−16.9740	−0.988265
$296$	−7.29919	−0.424257
$297$	−1.00000	−0.0580259
$298$	14.4717	0.838323
$299$	−23.7471	−1.37333
$300$	6.04511	0.349014
$301$	2.60479	0.150138
$302$	4.18254	0.240678
$303$	2.37859	0.136646
$304$	5.29738	0.303826
$305$	−4.03730	−0.231175
$306$	−0.631896	−0.0361231
$307$	−9.56205	−0.545735	−0.272868	−	0.962052i	$-0.587972\pi$
$307$	−9.56205	−0.545735	−0.272868	+	0.962052i	$0.587972\pi$
$308$	−0.168186	−0.00958329
$309$	18.1789	1.03416
$310$	27.5514	1.56482
$311$	0.574628	0.0325841	0.0162921	−	0.999867i	$-0.494814\pi$
$311$	0.574628	0.0325841	0.0162921	+	0.999867i	$0.494814\pi$
$312$	19.0067	1.07604
$313$	−0.387139	−0.0218824	−0.0109412	−	0.999940i	$-0.503483\pi$
$313$	−0.387139	−0.0218824	−0.0109412	+	0.999940i	$0.503483\pi$
$314$	−11.1540	−0.629459
$315$	−1.26926	−0.0715144
$316$	0.173907	0.00978303
$317$	−3.58302	−0.201243	−0.100621	−	0.994925i	$-0.532083\pi$
$317$	−3.58302	−0.201243	−0.100621	+	0.994925i	$0.532083\pi$
$318$	13.9743	0.783638
$319$	3.25991	0.182520
$320$	−35.6978	−1.99557
$321$	−11.3899	−0.635720
$322$	−1.45875	−0.0812930
$323$	−1.04603	−0.0582029
$324$	−0.534974	−0.0297208
$325$	−69.9973	−3.88275
$326$	5.84260	0.323592
$327$	12.0843	0.668262
$328$	−0.539248	−0.0297750
$329$	2.89171	0.159425
$330$	−4.88668	−0.269003
$331$	−14.4223	−0.792721	−0.396361	−	0.918095i	$-0.629727\pi$
$331$	−14.4223	−0.792721	−0.396361	+	0.918095i	$0.629727\pi$
$332$	7.22062	0.396283
$333$	−2.37891	−0.130364
$334$	5.68704	0.311181
$335$	24.7986	1.35489
$336$	0.831180	0.0453446
$337$	−4.23516	−0.230704	−0.115352	−	0.993325i	$-0.536800\pi$
$337$	−4.23516	−0.230704	−0.115352	+	0.993325i	$0.536800\pi$
$338$	−30.7103	−1.67042
$339$	14.2387	0.773342
$340$	1.12758	0.0611515
$341$	5.63806	0.305318
$342$	2.42519	0.131139
$343$	−4.37027	−0.235973
$344$	25.4221	1.37067
$345$	15.4772	0.833265
$346$	−6.29886	−0.338629
$347$	−19.0367	−1.02194	−0.510972	−	0.859597i	$-0.670714\pi$
$347$	−19.0367	−1.02194	−0.510972	+	0.859597i	$0.670714\pi$
$348$	1.74397	0.0934864
$349$	25.1088	1.34404	0.672021	−	0.740532i	$-0.265426\pi$
$349$	25.1088	1.34404	0.672021	+	0.740532i	$0.265426\pi$
$350$	−4.29984	−0.229836
$351$	6.19455	0.330640
$352$	−2.93650	−0.156516
$353$	11.2571	0.599156	0.299578	−	0.954072i	$-0.403154\pi$
$353$	11.2571	0.599156	0.299578	+	0.954072i	$0.403154\pi$
$354$	5.08880	0.270467
$355$	−26.8510	−1.42510
$356$	3.47956	0.184416
$357$	−0.164127	−0.00868652
$358$	−22.9222	−1.21148
$359$	−13.1807	−0.695650	−0.347825	−	0.937560i	$-0.613080\pi$
$359$	−13.1807	−0.695650	−0.347825	+	0.937560i	$0.613080\pi$
$360$	−12.3876	−0.652885
$361$	−14.9854	−0.788703
$362$	26.3901	1.38703
$363$	−1.00000	−0.0524864
$364$	1.04184	0.0546070
$365$	34.9554	1.82965
$366$	1.21038	0.0632677
$367$	−4.84140	−0.252719	−0.126360	−	0.991985i	$-0.540329\pi$
$367$	−4.84140	−0.252719	−0.126360	+	0.991985i	$0.540329\pi$
$368$	−10.1354	−0.528342
$369$	−0.175749	−0.00914911
$370$	−11.6250	−0.604355
$371$	3.62964	0.188442
$372$	3.01621	0.156383
$373$	−34.8357	−1.80372	−0.901861	−	0.432026i	$-0.857799\pi$
$373$	−34.8357	−1.80372	−0.901861	+	0.432026i	$0.857799\pi$
$374$	−0.631896	−0.0326745
$375$	25.4343	1.31342
$376$	28.2224	1.45546
$377$	−20.1937	−1.04003
$378$	0.380522	0.0195720
$379$	1.41343	0.0726032	0.0363016	−	0.999341i	$-0.488442\pi$
$379$	1.41343	0.0726032	0.0363016	+	0.999341i	$0.488442\pi$
$380$	−4.32760	−0.222001
$381$	−10.9449	−0.560723
$382$	−30.7311	−1.57234
$383$	28.2395	1.44297	0.721486	−	0.692429i	$-0.243459\pi$
$383$	28.2395	1.44297	0.721486	+	0.692429i	$0.243459\pi$
$384$	4.82921	0.246439
$385$	−1.26926	−0.0646872
$386$	−26.0362	−1.32521
$387$	8.28543	0.421172
$388$	8.28983	0.420852
$389$	−27.4271	−1.39061	−0.695306	−	0.718714i	$-0.744731\pi$
$389$	−27.4271	−1.39061	−0.695306	+	0.718714i	$0.744731\pi$
$390$	30.2708	1.53282
$391$	2.00135	0.101213
$392$	−21.1748	−1.06949
$393$	−17.2051	−0.867883
$394$	32.5023	1.63744
$395$	1.31243	0.0660355
$396$	−0.534974	−0.0268834
$397$	12.4906	0.626886	0.313443	−	0.949607i	$-0.398518\pi$
$397$	12.4906	0.626886	0.313443	+	0.949607i	$0.398518\pi$
$398$	−7.26414	−0.364118
$399$	0.629913	0.0315351
$400$	−29.8751	−1.49376
$401$	23.9146	1.19424	0.597120	−	0.802152i	$-0.296312\pi$
$401$	23.9146	1.19424	0.597120	+	0.802152i	$0.296312\pi$
$402$	−7.43463	−0.370806
$403$	−34.9252	−1.73975
$404$	1.27248	0.0633083
$405$	−4.03730	−0.200615
$406$	−1.24047	−0.0615635
$407$	−2.37891	−0.117918
$408$	−1.60184	−0.0793028
$409$	−8.06317	−0.398698	−0.199349	−	0.979929i	$-0.563883\pi$
$409$	−8.06317	−0.398698	−0.199349	+	0.979929i	$0.563883\pi$
$410$	−0.858828	−0.0424145
$411$	6.38652	0.315024
$412$	9.72526	0.479129
$413$	1.32175	0.0650392
$414$	−4.64006	−0.228047
$415$	54.4921	2.67491
$416$	18.1903	0.891852
$417$	−6.29184	−0.308113
$418$	2.42519	0.118620
$419$	−19.9664	−0.975421	−0.487711	−	0.873005i	$-0.662168\pi$
$419$	−19.9664	−0.975421	−0.487711	+	0.873005i	$0.662168\pi$
$420$	−0.679018	−0.0331327
$421$	−16.3659	−0.797626	−0.398813	−	0.917032i	$-0.630578\pi$
$421$	−16.3659	−0.797626	−0.398813	+	0.917032i	$0.630578\pi$
$422$	23.9262	1.16471
$423$	9.19808	0.447226
$424$	35.4244	1.72036
$425$	5.89922	0.286154
$426$	8.04993	0.390020
$427$	0.314382	0.0152140
$428$	−6.09327	−0.294529
$429$	6.19455	0.299076
$430$	40.4883	1.95252
$431$	−9.91521	−0.477599	−0.238799	−	0.971069i	$-0.576754\pi$
$431$	−9.91521	−0.477599	−0.238799	+	0.971069i	$0.576754\pi$
$432$	2.64386	0.127203
$433$	−32.4108	−1.55756	−0.778781	−	0.627296i	$-0.784162\pi$
$433$	−32.4108	−1.55756	−0.778781	+	0.627296i	$0.784162\pi$
$434$	−2.14541	−0.102983
$435$	13.1613	0.631034
$436$	6.46477	0.309606
$437$	−7.68112	−0.367438
$438$	−10.4796	−0.500736
$439$	12.8028	0.611043	0.305522	−	0.952185i	$-0.401169\pi$
$439$	12.8028	0.611043	0.305522	+	0.952185i	$0.401169\pi$
$440$	−12.3876	−0.590556
$441$	−6.90116	−0.328627
$442$	3.91431	0.186185
$443$	−18.9228	−0.899050	−0.449525	−	0.893268i	$-0.648407\pi$
$443$	−18.9228	−0.899050	−0.449525	+	0.893268i	$0.648407\pi$
$444$	−1.27266	−0.0603975
$445$	26.2593	1.24481
$446$	−10.6008	−0.501963
$447$	11.9563	0.565514
$448$	2.77976	0.131332
$449$	19.9929	0.943524	0.471762	−	0.881726i	$-0.343618\pi$
$449$	19.9929	0.943524	0.471762	+	0.881726i	$0.343618\pi$
$450$	−13.6771	−0.644745
$451$	−0.175749	−0.00827568
$452$	7.61735	0.358290
$453$	3.45555	0.162356
$454$	30.1844	1.41662
$455$	7.86246	0.368598
$456$	6.14780	0.287897
$457$	−20.3647	−0.952618	−0.476309	−	0.879278i	$-0.658026\pi$
$457$	−20.3647	−0.952618	−0.476309	+	0.879278i	$0.658026\pi$
$458$	10.0517	0.469685
$459$	−0.522063	−0.0243678
$460$	8.27989	0.386052
$461$	−8.04744	−0.374807	−0.187403	−	0.982283i	$-0.560007\pi$
$461$	−8.04744	−0.374807	−0.187403	+	0.982283i	$0.560007\pi$
$462$	0.380522	0.0177035
$463$	17.5099	0.813755	0.406877	−	0.913483i	$-0.366618\pi$
$463$	17.5099	0.813755	0.406877	+	0.913483i	$0.366618\pi$
$464$	−8.61874	−0.400115
$465$	22.7626	1.05559
$466$	4.99470	0.231375
$467$	−8.84632	−0.409359	−0.204679	−	0.978829i	$-0.565615\pi$
$467$	−8.84632	−0.409359	−0.204679	+	0.978829i	$0.565615\pi$
$468$	3.31392	0.153186
$469$	−1.93105	−0.0891677
$470$	44.9481	2.07330
$471$	−9.21530	−0.424619
$472$	12.9000	0.593770
$473$	8.28543	0.380964
$474$	−0.393466	−0.0180725
$475$	−22.6410	−1.03884
$476$	−0.0878036	−0.00402447
$477$	11.5453	0.528624
$478$	25.4718	1.16505
$479$	−39.3610	−1.79845	−0.899225	−	0.437487i	$-0.855869\pi$
$479$	−39.3610	−1.79845	−0.899225	+	0.437487i	$0.855869\pi$
$480$	−11.8555	−0.541129
$481$	14.7363	0.671917
$482$	−15.7256	−0.716281
$483$	−1.20520	−0.0548384
$484$	−0.534974	−0.0243170
$485$	62.5612	2.84076
$486$	1.21038	0.0549041
$487$	42.5865	1.92978	0.964888	−	0.262660i	$-0.0845999\pi$
$487$	42.5865	1.92978	0.964888	+	0.262660i	$0.0845999\pi$
$488$	3.06829	0.138895
$489$	4.82707	0.218288
$490$	−33.7238	−1.52349
$491$	21.9274	0.989567	0.494784	−	0.869016i	$-0.335247\pi$
$491$	21.9274	0.989567	0.494784	+	0.869016i	$0.335247\pi$
$492$	−0.0940209	−0.00423879
$493$	1.70188	0.0766487
$494$	−15.0230	−0.675915
$495$	−4.03730	−0.181463
$496$	−14.9062	−0.669309
$497$	2.09087	0.0937883
$498$	−16.3367	−0.732066
$499$	−6.29614	−0.281854	−0.140927	−	0.990020i	$-0.545008\pi$
$499$	−6.29614	−0.281854	−0.140927	+	0.990020i	$0.545008\pi$
$500$	13.6067	0.608510
$501$	4.69854	0.209915
$502$	30.5014	1.36134
$503$	−0.230589	−0.0102815	−0.00514073	−	0.999987i	$-0.501636\pi$
$503$	−0.230589	−0.0102815	−0.00514073	+	0.999987i	$0.501636\pi$
$504$	0.964614	0.0429673
$505$	9.60309	0.427332
$506$	−4.64006	−0.206276
$507$	−25.3724	−1.12683
$508$	−5.85522	−0.259783
$509$	17.3799	0.770349	0.385174	−	0.922844i	$-0.374141\pi$
$509$	17.3799	0.770349	0.385174	+	0.922844i	$0.374141\pi$
$510$	−2.55116	−0.112967
$511$	−2.72195	−0.120412
$512$	23.9879	1.06013
$513$	2.00366	0.0884636
$514$	−13.0556	−0.575859
$515$	73.3939	3.23412
$516$	4.43249	0.195129
$517$	9.19808	0.404531
$518$	0.905229	0.0397735
$519$	−5.20402	−0.228431
$520$	76.7357	3.36508
$521$	7.33661	0.321423	0.160711	−	0.987001i	$-0.448621\pi$
$521$	7.33661	0.321423	0.160711	+	0.987001i	$0.448621\pi$
$522$	−3.94574	−0.172700
$523$	−25.8032	−1.12829	−0.564147	−	0.825674i	$-0.690795\pi$
$523$	−25.8032	−1.12829	−0.564147	+	0.825674i	$0.690795\pi$
$524$	−9.20428	−0.402091
$525$	−3.55246	−0.155042
$526$	−14.8636	−0.648085
$527$	2.94342	0.128217
$528$	2.64386	0.115059
$529$	−8.30391	−0.361039
$530$	56.4184	2.45066
$531$	4.20429	0.182451
$532$	0.336987	0.0146102
$533$	1.08868	0.0471561
$534$	−7.87254	−0.340678
$535$	−45.9843	−1.98808
$536$	−18.8466	−0.814048
$537$	−18.9380	−0.817234
$538$	−16.9652	−0.731422
$539$	−6.90116	−0.297254
$540$	−2.15985	−0.0929452
$541$	−6.72913	−0.289308	−0.144654	−	0.989482i	$-0.546207\pi$
$541$	−6.72913	−0.289308	−0.144654	+	0.989482i	$0.546207\pi$
$542$	−33.0335	−1.41891
$543$	21.8031	0.935659
$544$	−1.53304	−0.0657284
$545$	48.7879	2.08984
$546$	−2.35716	−0.100877
$547$	27.8351	1.19014	0.595071	−	0.803673i	$-0.297124\pi$
$547$	27.8351	1.19014	0.595071	+	0.803673i	$0.297124\pi$
$548$	3.41662	0.145951
$549$	1.00000	0.0426790
$550$	−13.6771	−0.583194
$551$	−6.53174	−0.278262
$552$	−11.7624	−0.500642
$553$	−0.102198	−0.00434590
$554$	15.9116	0.676020
$555$	−9.60439	−0.407684
$556$	−3.36597	−0.142749
$557$	−34.8830	−1.47804	−0.739020	−	0.673684i	$-0.764711\pi$
$557$	−34.8830	−1.47804	−0.739020	+	0.673684i	$0.764711\pi$
$558$	−6.82421	−0.288892
$559$	−51.3245	−2.17079
$560$	3.35573	0.141805
$561$	−0.522063	−0.0220415
$562$	−30.9971	−1.30753
$563$	−19.2648	−0.811915	−0.405957	−	0.913892i	$-0.633062\pi$
$563$	−19.2648	−0.811915	−0.405957	+	0.913892i	$0.633062\pi$
$564$	4.92073	0.207200
$565$	57.4861	2.41846
$566$	−16.0183	−0.673297
$567$	0.314382	0.0132028
$568$	20.4064	0.856231
$569$	−14.2050	−0.595503	−0.297752	−	0.954643i	$-0.596237\pi$
$569$	−14.2050	−0.595503	−0.297752	+	0.954643i	$0.596237\pi$
$570$	9.79124	0.410110
$571$	29.7282	1.24408	0.622042	−	0.782984i	$-0.286303\pi$
$571$	29.7282	1.24408	0.622042	+	0.782984i	$0.286303\pi$
$572$	3.31392	0.138562
$573$	−25.3896	−1.06066
$574$	0.0668763	0.00279136
$575$	43.3184	1.80650
$576$	8.84200	0.368417
$577$	34.5273	1.43739	0.718696	−	0.695325i	$-0.244739\pi$
$577$	34.5273	1.43739	0.718696	+	0.695325i	$0.244739\pi$
$578$	20.2466	0.842148
$579$	−21.5107	−0.893956
$580$	7.04092	0.292358
$581$	−4.24326	−0.176040
$582$	−18.7558	−0.777454
$583$	11.5453	0.478159
$584$	−26.5656	−1.09929
$585$	25.0093	1.03401
$586$	0.866553	0.0357970
$587$	−15.1630	−0.625843	−0.312922	−	0.949779i	$-0.601308\pi$
$587$	−15.1630	−0.625843	−0.312922	+	0.949779i	$0.601308\pi$
$588$	−3.69194	−0.152253
$589$	−11.2967	−0.465474
$590$	20.5451	0.845826
$591$	26.8529	1.10458
$592$	6.28950	0.258497
$593$	−17.1340	−0.703607	−0.351804	−	0.936074i	$-0.614432\pi$
$593$	−17.1340	−0.703607	−0.351804	+	0.936074i	$0.614432\pi$
$594$	1.21038	0.0496626
$595$	−0.662631	−0.0271652
$596$	6.39630	0.262003
$597$	−6.00152	−0.245626
$598$	28.7431	1.17539
$599$	3.54984	0.145042	0.0725212	−	0.997367i	$-0.476895\pi$
$599$	3.54984	0.145042	0.0725212	+	0.997367i	$0.476895\pi$
$600$	−34.6711	−1.41544
$601$	−25.0301	−1.02100	−0.510499	−	0.859878i	$-0.670539\pi$
$601$	−25.0301	−1.02100	−0.510499	+	0.859878i	$0.670539\pi$
$602$	−3.15279	−0.128498
$603$	−6.14238	−0.250137
$604$	1.84863	0.0752196
$605$	−4.03730	−0.164140
$606$	−2.87900	−0.116951
$607$	−10.8677	−0.441104	−0.220552	−	0.975375i	$-0.570786\pi$
$607$	−10.8677	−0.441104	−0.220552	+	0.975375i	$0.570786\pi$
$608$	5.88374	0.238617
$609$	−1.02486	−0.0415293
$610$	4.88668	0.197856
$611$	−56.9779	−2.30508
$612$	−0.279290	−0.0112896
$613$	11.0413	0.445956	0.222978	−	0.974824i	$-0.428422\pi$
$613$	11.0413	0.445956	0.222978	+	0.974824i	$0.428422\pi$
$614$	11.5737	0.467078
$615$	−0.709551	−0.0286119
$616$	0.964614	0.0388654
$617$	−7.04319	−0.283548	−0.141774	−	0.989899i	$-0.545281\pi$
$617$	−7.04319	−0.283548	−0.141774	+	0.989899i	$0.545281\pi$
$618$	−22.0035	−0.885110
$619$	−19.9905	−0.803488	−0.401744	−	0.915752i	$-0.631596\pi$
$619$	−19.9905	−0.803488	−0.401744	+	0.915752i	$0.631596\pi$
$620$	12.1774	0.489055
$621$	−3.83355	−0.153835
$622$	−0.695519	−0.0278878
$623$	−2.04479	−0.0819229
$624$	−16.3775	−0.655624
$625$	46.1869	1.84748
$626$	0.468587	0.0187285
$627$	2.00366	0.0800184
$628$	−4.92994	−0.196726
$629$	−1.24194	−0.0495194
$630$	1.53628	0.0612071
$631$	0.265655	0.0105756	0.00528779	−	0.999986i	$-0.498317\pi$
$631$	0.265655	0.0105756	0.00528779	+	0.999986i	$0.498317\pi$
$632$	−0.997427	−0.0396755
$633$	19.7675	0.785688
$634$	4.33683	0.172238
$635$	−44.1878	−1.75354
$636$	6.17644	0.244912
$637$	42.7496	1.69380
$638$	−3.94574	−0.156213
$639$	6.65073	0.263099
$640$	19.4970	0.770686
$641$	44.1502	1.74383	0.871913	−	0.489661i	$-0.162879\pi$
$641$	44.1502	1.74383	0.871913	+	0.489661i	$0.162879\pi$
$642$	13.7861	0.544093
$643$	−20.6136	−0.812922	−0.406461	−	0.913668i	$-0.633237\pi$
$643$	−20.6136	−0.812922	−0.406461	+	0.913668i	$0.633237\pi$
$644$	−0.644749	−0.0254067
$645$	33.4508	1.31712
$646$	1.26610	0.0498141
$647$	−47.1387	−1.85321	−0.926607	−	0.376032i	$-0.877288\pi$
$647$	−47.1387	−1.85321	−0.926607	+	0.376032i	$0.877288\pi$
$648$	3.06829	0.120534
$649$	4.20429	0.165033
$650$	84.7235	3.32313
$651$	−1.77250	−0.0694699
$652$	2.58236	0.101133
$653$	−18.5139	−0.724506	−0.362253	−	0.932080i	$-0.617992\pi$
$653$	−18.5139	−0.724506	−0.362253	+	0.932080i	$0.617992\pi$
$654$	−14.6266	−0.571945
$655$	−69.4623	−2.71412
$656$	0.464654	0.0181417
$657$	−8.65811	−0.337785
$658$	−3.50008	−0.136447
$659$	−19.3986	−0.755664	−0.377832	−	0.925874i	$-0.623330\pi$
$659$	−19.3986	−0.755664	−0.377832	+	0.925874i	$0.623330\pi$
$660$	−2.15985	−0.0840721
$661$	32.6977	1.27179	0.635897	−	0.771774i	$-0.280630\pi$
$661$	32.6977	1.27179	0.635897	+	0.771774i	$0.280630\pi$
$662$	17.4565	0.678466
$663$	3.23394	0.125596
$664$	−41.4132	−1.60714
$665$	2.54315	0.0986192
$666$	2.87939	0.111574
$667$	12.4970	0.483887
$668$	2.51360	0.0972540
$669$	−8.75822	−0.338613
$670$	−30.0159	−1.15961
$671$	1.00000	0.0386046
$672$	0.923182	0.0356125
$673$	−17.4320	−0.671953	−0.335977	−	0.941870i	$-0.609066\pi$
$673$	−17.4320	−0.671953	−0.335977	+	0.941870i	$0.609066\pi$
$674$	5.12616	0.197452
$675$	−11.2998	−0.434931
$676$	−13.5736	−0.522060
$677$	30.0768	1.15595	0.577973	−	0.816056i	$-0.303844\pi$
$677$	30.0768	1.15595	0.577973	+	0.816056i	$0.303844\pi$
$678$	−17.2343	−0.661880
$679$	−4.87159	−0.186954
$680$	−6.46711	−0.248002
$681$	24.9379	0.955623
$682$	−6.82421	−0.261313
$683$	−21.9575	−0.840181	−0.420091	−	0.907482i	$-0.638002\pi$
$683$	−21.9575	−0.840181	−0.420091	+	0.907482i	$0.638002\pi$
$684$	1.07190	0.0409853
$685$	25.7843	0.985168
$686$	5.28970	0.201962
$687$	8.30456	0.316839
$688$	−21.9055	−0.835139
$689$	−71.5181	−2.72462
$690$	−18.7333	−0.713166
$691$	−1.40055	−0.0532795	−0.0266398	−	0.999645i	$-0.508481\pi$
$691$	−1.40055	−0.0532795	−0.0266398	+	0.999645i	$0.508481\pi$
$692$	−2.78402	−0.105832
$693$	0.314382	0.0119424
$694$	23.0417	0.874651
$695$	−25.4021	−0.963556
$696$	−10.0023	−0.379138
$697$	−0.0917518	−0.00347535
$698$	−30.3912	−1.15033
$699$	4.12654	0.156080
$700$	−1.90047	−0.0718311
$701$	26.6629	1.00704	0.503522	−	0.863982i	$-0.332037\pi$
$701$	26.6629	1.00704	0.503522	+	0.863982i	$0.332037\pi$
$702$	−7.49777	−0.282985
$703$	4.76652	0.179773
$704$	8.84200	0.333245
$705$	37.1355	1.39860
$706$	−13.6254	−0.512800
$707$	−0.747785	−0.0281234
$708$	2.24919	0.0845296
$709$	30.9787	1.16343	0.581715	−	0.813392i	$-0.302382\pi$
$709$	30.9787	1.16343	0.581715	+	0.813392i	$0.302382\pi$
$710$	32.5000	1.21970
$711$	−0.325076	−0.0121913
$712$	−19.9567	−0.747908
$713$	21.6138	0.809442
$714$	0.198657	0.00743453
$715$	25.0093	0.935294
$716$	−10.1313	−0.378625
$717$	21.0444	0.785917
$718$	15.9537	0.595386
$719$	48.6102	1.81286	0.906428	−	0.422360i	$-0.138798\pi$
$719$	48.6102	1.81286	0.906428	+	0.422360i	$0.138798\pi$
$720$	10.6741	0.397798
$721$	−5.71513	−0.212843
$722$	18.1380	0.675027
$723$	−12.9923	−0.483187
$724$	11.6641	0.433492
$725$	36.8364	1.36807
$726$	1.21038	0.0449215
$727$	26.1481	0.969781	0.484890	−	0.874575i	$-0.338859\pi$
$727$	26.1481	0.969781	0.484890	+	0.874575i	$0.338859\pi$
$728$	−5.97535	−0.221461
$729$	1.00000	0.0370370
$730$	−42.3094	−1.56594
$731$	4.32551	0.159985
$732$	0.534974	0.0197732
$733$	2.37404	0.0876870	0.0438435	−	0.999038i	$-0.486040\pi$
$733$	2.37404	0.0876870	0.0438435	+	0.999038i	$0.486040\pi$
$734$	5.85995	0.216295
$735$	−27.8621	−1.02771
$736$	−11.2572	−0.414946
$737$	−6.14238	−0.226257
$738$	0.212723	0.00783045
$739$	−11.6979	−0.430313	−0.215157	−	0.976580i	$-0.569026\pi$
$739$	−11.6979	−0.430313	−0.215157	+	0.976580i	$0.569026\pi$
$740$	−5.13810	−0.188880
$741$	−12.4117	−0.455957
$742$	−4.39326	−0.161281
$743$	−35.3439	−1.29664	−0.648321	−	0.761367i	$-0.724529\pi$
$743$	−35.3439	−1.29664	−0.648321	+	0.761367i	$0.724529\pi$
$744$	−17.2992	−0.634219
$745$	48.2712	1.76852
$746$	42.1645	1.54375
$747$	−13.4972	−0.493835
$748$	−0.279290	−0.0102118
$749$	3.58076	0.130838
$750$	−30.7853	−1.12412
$751$	23.0859	0.842417	0.421208	−	0.906964i	$-0.361606\pi$
$751$	23.0859	0.842417	0.421208	+	0.906964i	$0.361606\pi$
$752$	−24.3184	−0.886801
$753$	25.1998	0.918330
$754$	24.4421	0.890128
$755$	13.9511	0.507733
$756$	0.168186	0.00611687
$757$	−24.9060	−0.905224	−0.452612	−	0.891708i	$-0.649508\pi$
$757$	−24.9060	−0.905224	−0.452612	+	0.891708i	$0.649508\pi$
$758$	−1.71080	−0.0621389
$759$	−3.83355	−0.139149
$760$	24.8205	0.900335
$761$	40.5425	1.46966	0.734832	−	0.678249i	$-0.237261\pi$
$761$	40.5425	1.46966	0.734832	+	0.678249i	$0.237261\pi$
$762$	13.2475	0.479906
$763$	−3.79908	−0.137536
$764$	−13.5827	−0.491406
$765$	−2.10773	−0.0762050
$766$	−34.1806	−1.23500
$767$	−26.0437	−0.940383
$768$	11.8388	0.427196
$769$	−31.2709	−1.12766	−0.563828	−	0.825892i	$-0.690672\pi$
$769$	−31.2709	−1.12766	−0.563828	+	0.825892i	$0.690672\pi$
$770$	1.53628	0.0553639
$771$	−10.7864	−0.388462
$772$	−11.5077	−0.414170
$773$	−26.9430	−0.969071	−0.484535	−	0.874772i	$-0.661011\pi$
$773$	−26.9430	−0.969071	−0.484535	+	0.874772i	$0.661011\pi$
$774$	−10.0285	−0.360468
$775$	63.7091	2.28850
$776$	−47.5455	−1.70678
$777$	0.747887	0.0268303
$778$	33.1973	1.19018
$779$	0.352140	0.0126167
$780$	13.3793	0.479056
$781$	6.65073	0.237982
$782$	−2.42240	−0.0866249
$783$	−3.25991	−0.116500
$784$	18.2457	0.651632
$785$	−37.2050	−1.32790
$786$	20.8248	0.742795
$787$	−23.9623	−0.854164	−0.427082	−	0.904213i	$-0.640458\pi$
$787$	−23.9623	−0.854164	−0.427082	+	0.904213i	$0.640458\pi$
$788$	14.3656	0.511753
$789$	−12.2801	−0.437183
$790$	−1.58854	−0.0565178
$791$	−4.47640	−0.159163
$792$	3.06829	0.109027
$793$	−6.19455	−0.219975
$794$	−15.1184	−0.536533
$795$	46.6120	1.65316
$796$	−3.21065	−0.113799
$797$	29.3811	1.04073	0.520366	−	0.853943i	$-0.325796\pi$
$797$	29.3811	1.04073	0.520366	+	0.853943i	$0.325796\pi$
$798$	−0.762436	−0.0269900
$799$	4.80197	0.169882
$800$	−33.1819	−1.17316
$801$	−6.50417	−0.229814
$802$	−28.9459	−1.02211
$803$	−8.65811	−0.305538
$804$	−3.28601	−0.115889
$805$	−4.86575	−0.171495
$806$	42.2729	1.48900
$807$	−14.0164	−0.493401
$808$	−7.29820	−0.256750
$809$	40.2508	1.41514	0.707571	−	0.706643i	$-0.249791\pi$
$809$	40.2508	1.41514	0.707571	+	0.706643i	$0.249791\pi$
$810$	4.88668	0.171701
$811$	−17.0398	−0.598347	−0.299173	−	0.954199i	$-0.596711\pi$
$811$	−17.0398	−0.598347	−0.299173	+	0.954199i	$0.596711\pi$
$812$	−0.548271	−0.0192406
$813$	−27.2918	−0.957165
$814$	2.87939	0.100923
$815$	19.4884	0.682647
$816$	1.38026	0.0483187
$817$	−16.6012	−0.580801
$818$	9.75952	0.341234
$819$	−1.94745	−0.0680495
$820$	−0.379591	−0.0132559
$821$	−13.0434	−0.455218	−0.227609	−	0.973753i	$-0.573091\pi$
$821$	−13.0434	−0.455218	−0.227609	+	0.973753i	$0.573091\pi$
$822$	−7.73013	−0.269619
$823$	−24.8451	−0.866047	−0.433024	−	0.901383i	$-0.642553\pi$
$823$	−24.8451	−0.866047	−0.433024	+	0.901383i	$0.642553\pi$
$824$	−55.7783	−1.94313
$825$	−11.2998	−0.393409
$826$	−1.59983	−0.0556651
$827$	−14.6597	−0.509767	−0.254884	−	0.966972i	$-0.582037\pi$
$827$	−14.6597	−0.509767	−0.254884	+	0.966972i	$0.582037\pi$
$828$	−2.05085	−0.0712719
$829$	−29.3157	−1.01818	−0.509088	−	0.860715i	$-0.670017\pi$
$829$	−29.3157	−1.01818	−0.509088	+	0.860715i	$0.670017\pi$
$830$	−65.9563	−2.28938
$831$	13.1459	0.456028
$832$	−54.7722	−1.89888
$833$	−3.60284	−0.124831
$834$	7.61554	0.263705
$835$	18.9695	0.656465
$836$	1.07190	0.0370726
$837$	−5.63806	−0.194880
$838$	24.1670	0.834834
$839$	−6.76747	−0.233639	−0.116819	−	0.993153i	$-0.537270\pi$
$839$	−6.76747	−0.233639	−0.116819	+	0.993153i	$0.537270\pi$
$840$	3.89444	0.134371
$841$	−18.3730	−0.633551
$842$	19.8090	0.682664
$843$	−25.6093	−0.882032
$844$	10.5751	0.364010
$845$	−102.436	−3.52391
$846$	−11.1332	−0.382767
$847$	0.314382	0.0108023
$848$	−30.5242	−1.04820
$849$	−13.2340	−0.454191
$850$	−7.14031	−0.244911
$851$	−9.11968	−0.312618
$852$	3.55796	0.121894
$853$	7.49401	0.256590	0.128295	−	0.991736i	$-0.459050\pi$
$853$	7.49401	0.256590	0.128295	+	0.991736i	$0.459050\pi$
$854$	−0.380522	−0.0130212
$855$	8.08937	0.276651
$856$	34.9474	1.19448
$857$	14.8487	0.507221	0.253610	−	0.967306i	$-0.418382\pi$
$857$	14.8487	0.507221	0.253610	+	0.967306i	$0.418382\pi$
$858$	−7.49777	−0.255970
$859$	−15.5092	−0.529169	−0.264584	−	0.964363i	$-0.585235\pi$
$859$	−15.5092	−0.529169	−0.264584	+	0.964363i	$0.585235\pi$
$860$	17.8953	0.610224
$861$	0.0552522	0.00188299
$862$	12.0012	0.408762
$863$	−15.8856	−0.540753	−0.270377	−	0.962755i	$-0.587148\pi$
$863$	−15.8856	−0.540753	−0.270377	+	0.962755i	$0.587148\pi$
$864$	2.93650	0.0999017
$865$	−21.0102	−0.714369
$866$	39.2294	1.33307
$867$	16.7275	0.568094
$868$	−0.948243	−0.0321855
$869$	−0.325076	−0.0110274
$870$	−15.9302	−0.540083
$871$	38.0492	1.28925
$872$	−37.0780	−1.25562
$873$	−15.4958	−0.524452
$874$	9.29709	0.314479
$875$	−7.99609	−0.270317
$876$	−4.63186	−0.156496
$877$	42.6067	1.43873	0.719363	−	0.694635i	$-0.244434\pi$
$877$	42.6067	1.43873	0.719363	+	0.694635i	$0.244434\pi$
$878$	−15.4963	−0.522974
$879$	0.715933	0.0241478
$880$	10.6741	0.359822
$881$	36.5383	1.23101	0.615503	−	0.788134i	$-0.288953\pi$
$881$	36.5383	1.23101	0.615503	+	0.788134i	$0.288953\pi$
$882$	8.35305	0.281262
$883$	−32.7102	−1.10078	−0.550392	−	0.834906i	$-0.685522\pi$
$883$	−32.7102	−1.10078	−0.550392	+	0.834906i	$0.685522\pi$
$884$	1.73007	0.0581887
$885$	16.9740	0.570575
$886$	22.9038	0.769470
$887$	−19.6783	−0.660734	−0.330367	−	0.943853i	$-0.607172\pi$
$887$	−19.6783	−0.660734	−0.330367	+	0.943853i	$0.607172\pi$
$888$	7.29919	0.244945
$889$	3.44087	0.115403
$890$	−31.7838	−1.06540
$891$	1.00000	0.0335013
$892$	−4.68542	−0.156879
$893$	−18.4298	−0.616730
$894$	−14.4717	−0.484006
$895$	−76.4584	−2.55572
$896$	−1.51822	−0.0507200
$897$	23.7471	0.792892
$898$	−24.1991	−0.807534
$899$	18.3796	0.612993
$900$	−6.04511	−0.201504
$901$	6.02738	0.200801
$902$	0.212723	0.00708291
$903$	−2.60479	−0.0866820
$904$	−43.6886	−1.45306
$905$	88.0256	2.92607
$906$	−4.18254	−0.138956
$907$	14.8609	0.493447	0.246723	−	0.969086i	$-0.420646\pi$
$907$	14.8609	0.493447	0.246723	+	0.969086i	$0.420646\pi$
$908$	13.3411	0.442741
$909$	−2.37859	−0.0788928
$910$	−9.51659	−0.315472
$911$	20.4250	0.676711	0.338355	−	0.941018i	$-0.390129\pi$
$911$	20.4250	0.676711	0.338355	+	0.941018i	$0.390129\pi$
$912$	−5.29738	−0.175414
$913$	−13.4972	−0.446691
$914$	24.6490	0.815317
$915$	4.03730	0.133469
$916$	4.44272	0.146792
$917$	5.40898	0.178620
$918$	0.631896	0.0208557
$919$	40.3278	1.33029	0.665146	−	0.746714i	$-0.268369\pi$
$919$	40.3278	1.33029	0.665146	+	0.746714i	$0.268369\pi$
$920$	−47.4885	−1.56565
$921$	9.56205	0.315080
$922$	9.74049	0.320786
$923$	−41.1982	−1.35606
$924$	0.168186	0.00553291
$925$	−26.8813	−0.883852
$926$	−21.1937	−0.696468
$927$	−18.1789	−0.597075
$928$	−9.57272	−0.314240
$929$	1.79459	0.0588787	0.0294393	−	0.999567i	$-0.490628\pi$
$929$	1.79459	0.0588787	0.0294393	+	0.999567i	$0.490628\pi$
$930$	−27.5514	−0.903446
$931$	13.8276	0.453180
$932$	2.20759	0.0723121
$933$	−0.574628	−0.0188125
$934$	10.7074	0.350358
$935$	−2.10773	−0.0689300
$936$	−19.0067	−0.621252
$937$	−38.7615	−1.26628	−0.633141	−	0.774036i	$-0.718235\pi$
$937$	−38.7615	−1.26628	−0.633141	+	0.774036i	$0.718235\pi$
$938$	2.33731	0.0763159
$939$	0.387139	0.0126338
$940$	19.8665	0.647973
$941$	30.3674	0.989949	0.494975	−	0.868907i	$-0.335177\pi$
$941$	30.3674	0.989949	0.494975	+	0.868907i	$0.335177\pi$
$942$	11.1540	0.363418
$943$	−0.673741	−0.0219400
$944$	−11.1155	−0.361780
$945$	1.26926	0.0412889
$946$	−10.0285	−0.326056
$947$	−50.8165	−1.65132	−0.825658	−	0.564171i	$-0.809196\pi$
$947$	−50.8165	−1.65132	−0.825658	+	0.564171i	$0.809196\pi$
$948$	−0.173907	−0.00564824
$949$	53.6330	1.74100
$950$	27.4042	0.889111
$951$	3.58302	0.116188
$952$	0.503589	0.0163214
$953$	−12.8035	−0.414747	−0.207374	−	0.978262i	$-0.566492\pi$
$953$	−12.8035	−0.414747	−0.207374	+	0.978262i	$0.566492\pi$
$954$	−13.9743	−0.452433
$955$	−102.505	−3.31700
$956$	11.2582	0.364116
$957$	−3.25991	−0.105378
$958$	47.6419	1.53924
$959$	−2.00780	−0.0648354
$960$	35.6978	1.15214
$961$	0.787715	0.0254102
$962$	−17.8365	−0.575073
$963$	11.3899	0.367033
$964$	−6.95051	−0.223861
$965$	−86.8454	−2.79565
$966$	1.45875	0.0469345
$967$	−11.7317	−0.377265	−0.188633	−	0.982048i	$-0.560406\pi$
$967$	−11.7317	−0.377265	−0.188633	+	0.982048i	$0.560406\pi$
$968$	3.06829	0.0986185
$969$	1.04603	0.0336035
$970$	−75.7229	−2.43132
$971$	41.6627	1.33702	0.668510	−	0.743703i	$-0.266932\pi$
$971$	41.6627	1.33702	0.668510	+	0.743703i	$0.266932\pi$
$972$	0.534974	0.0171593
$973$	1.97804	0.0634131
$974$	−51.5459	−1.65164
$975$	69.9973	2.24171
$976$	−2.64386	−0.0846278
$977$	−26.7989	−0.857374	−0.428687	−	0.903453i	$-0.641024\pi$
$977$	−26.7989	−0.857374	−0.428687	+	0.903453i	$0.641024\pi$
$978$	−5.84260	−0.186826
$979$	−6.50417	−0.207874
$980$	−14.9055	−0.476138
$981$	−12.0843	−0.385821
$982$	−26.5405	−0.846941
$983$	3.59975	0.114814	0.0574071	−	0.998351i	$-0.481717\pi$
$983$	3.59975	0.114814	0.0574071	+	0.998351i	$0.481717\pi$
$984$	0.539248	0.0171906
$985$	108.413	3.45434
$986$	−2.05992	−0.0656013
$987$	−2.89171	−0.0920441
$988$	−6.63996	−0.211245
$989$	31.7626	1.00999
$990$	4.88668	0.155309
$991$	−29.2204	−0.928215	−0.464108	−	0.885779i	$-0.653625\pi$
$991$	−29.2204	−0.928215	−0.464108	+	0.885779i	$0.653625\pi$
$992$	−16.5562	−0.525658
$993$	14.4223	0.457678
$994$	−2.53075	−0.0802705
$995$	−24.2300	−0.768141
$996$	−7.22062	−0.228794
$997$	3.77909	0.119685	0.0598424	−	0.998208i	$-0.480940\pi$
$997$	3.77909	0.119685	0.0598424	+	0.998208i	$0.480940\pi$
$998$	7.62074	0.241230
$999$	2.37891	0.0752655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.b.1.4	✓	11
3.2	odd	2		6039.2.a.c.1.8		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.b.1.4	✓	11	1.1	even	1	trivial
6039.2.a.c.1.8		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)

\(f(q)\)	\(=\)	\(q-1.21038 q^{2} -1.00000 q^{3} -0.534974 q^{4} -4.03730 q^{5} +1.21038 q^{6} +0.314382 q^{7} +3.06829 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.21038 q^{2} -1.00000 q^{3} -0.534974 q^{4} -4.03730 q^{5} +1.21038 q^{6} +0.314382 q^{7} +3.06829 q^{8} +1.00000 q^{9} +4.88668 q^{10} +1.00000 q^{11} +0.534974 q^{12} -6.19455 q^{13} -0.380522 q^{14} +4.03730 q^{15} -2.64386 q^{16} +0.522063 q^{17} -1.21038 q^{18} -2.00366 q^{19} +2.15985 q^{20} -0.314382 q^{21} -1.21038 q^{22} +3.83355 q^{23} -3.06829 q^{24} +11.2998 q^{25} +7.49777 q^{26} -1.00000 q^{27} -0.168186 q^{28} +3.25991 q^{29} -4.88668 q^{30} +5.63806 q^{31} -2.93650 q^{32} -1.00000 q^{33} -0.631896 q^{34} -1.26926 q^{35} -0.534974 q^{36} -2.37891 q^{37} +2.42519 q^{38} +6.19455 q^{39} -12.3876 q^{40} -0.175749 q^{41} +0.380522 q^{42} +8.28543 q^{43} -0.534974 q^{44} -4.03730 q^{45} -4.64006 q^{46} +9.19808 q^{47} +2.64386 q^{48} -6.90116 q^{49} -13.6771 q^{50} -0.522063 q^{51} +3.31392 q^{52} +11.5453 q^{53} +1.21038 q^{54} -4.03730 q^{55} +0.964614 q^{56} +2.00366 q^{57} -3.94574 q^{58} +4.20429 q^{59} -2.15985 q^{60} +1.00000 q^{61} -6.82421 q^{62} +0.314382 q^{63} +8.84200 q^{64} +25.0093 q^{65} +1.21038 q^{66} -6.14238 q^{67} -0.279290 q^{68} -3.83355 q^{69} +1.53628 q^{70} +6.65073 q^{71} +3.06829 q^{72} -8.65811 q^{73} +2.87939 q^{74} -11.2998 q^{75} +1.07190 q^{76} +0.314382 q^{77} -7.49777 q^{78} -0.325076 q^{79} +10.6741 q^{80} +1.00000 q^{81} +0.212723 q^{82} -13.4972 q^{83} +0.168186 q^{84} -2.10773 q^{85} -10.0285 q^{86} -3.25991 q^{87} +3.06829 q^{88} -6.50417 q^{89} +4.88668 q^{90} -1.94745 q^{91} -2.05085 q^{92} -5.63806 q^{93} -11.1332 q^{94} +8.08937 q^{95} +2.93650 q^{96} -15.4958 q^{97} +8.35305 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) \) 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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