LMFDB - Embedded newform 2013.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$16.0738859269$
Analytic rank:	$1$
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			1.1
Root			$2.70023$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70023 q^{2} -1.00000 q^{3} +5.29122 q^{4} +2.21957 q^{5} +2.70023 q^{6} -2.11895 q^{7} -8.88702 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.70023 q^{2} -1.00000 q^{3} +5.29122 q^{4} +2.21957 q^{5} +2.70023 q^{6} -2.11895 q^{7} -8.88702 q^{8} +1.00000 q^{9} -5.99333 q^{10} +1.00000 q^{11} -5.29122 q^{12} -2.52367 q^{13} +5.72165 q^{14} -2.21957 q^{15} +13.4145 q^{16} +1.86251 q^{17} -2.70023 q^{18} -1.62262 q^{19} +11.7442 q^{20} +2.11895 q^{21} -2.70023 q^{22} +0.232397 q^{23} +8.88702 q^{24} -0.0735266 q^{25} +6.81449 q^{26} -1.00000 q^{27} -11.2118 q^{28} +8.99969 q^{29} +5.99333 q^{30} -0.0529540 q^{31} -18.4482 q^{32} -1.00000 q^{33} -5.02921 q^{34} -4.70316 q^{35} +5.29122 q^{36} -1.12092 q^{37} +4.38144 q^{38} +2.52367 q^{39} -19.7253 q^{40} -8.95321 q^{41} -5.72165 q^{42} -8.83041 q^{43} +5.29122 q^{44} +2.21957 q^{45} -0.627524 q^{46} -8.15644 q^{47} -13.4145 q^{48} -2.51004 q^{49} +0.198539 q^{50} -1.86251 q^{51} -13.3533 q^{52} +11.4915 q^{53} +2.70023 q^{54} +2.21957 q^{55} +18.8312 q^{56} +1.62262 q^{57} -24.3012 q^{58} -1.89372 q^{59} -11.7442 q^{60} +1.00000 q^{61} +0.142988 q^{62} -2.11895 q^{63} +22.9853 q^{64} -5.60146 q^{65} +2.70023 q^{66} -1.07486 q^{67} +9.85497 q^{68} -0.232397 q^{69} +12.6996 q^{70} +5.42037 q^{71} -8.88702 q^{72} -8.03508 q^{73} +3.02673 q^{74} +0.0735266 q^{75} -8.58564 q^{76} -2.11895 q^{77} -6.81449 q^{78} -6.67275 q^{79} +29.7744 q^{80} +1.00000 q^{81} +24.1757 q^{82} +3.06257 q^{83} +11.2118 q^{84} +4.13397 q^{85} +23.8441 q^{86} -8.99969 q^{87} -8.88702 q^{88} +5.40932 q^{89} -5.99333 q^{90} +5.34755 q^{91} +1.22966 q^{92} +0.0529540 q^{93} +22.0242 q^{94} -3.60151 q^{95} +18.4482 q^{96} +12.0599 q^{97} +6.77767 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.70023	−1.90935	−0.954674	−	0.297654i	$-0.903796\pi$
$2$	−2.70023	−1.90935	−0.954674	+	0.297654i	$0.903796\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.29122	2.64561
$5$	2.21957	0.992620	0.496310	−	0.868145i	$-0.334688\pi$
$5$	2.21957	0.992620	0.496310	+	0.868145i	$0.334688\pi$
$6$	2.70023	1.10236
$7$	−2.11895	−0.800889	−0.400444	−	0.916321i	$-0.631144\pi$
$7$	−2.11895	−0.800889	−0.400444	+	0.916321i	$0.631144\pi$
$8$	−8.88702	−3.14204
$9$	1.00000	0.333333
$10$	−5.99333	−1.89526
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−5.29122	−1.52744
$13$	−2.52367	−0.699941	−0.349971	−	0.936761i	$-0.613808\pi$
$13$	−2.52367	−0.699941	−0.349971	+	0.936761i	$0.613808\pi$
$14$	5.72165	1.52918
$15$	−2.21957	−0.573089
$16$	13.4145	3.35363
$17$	1.86251	0.451726	0.225863	−	0.974159i	$-0.427480\pi$
$17$	1.86251	0.451726	0.225863	+	0.974159i	$0.427480\pi$
$18$	−2.70023	−0.636449
$19$	−1.62262	−0.372255	−0.186127	−	0.982526i	$-0.559594\pi$
$19$	−1.62262	−0.372255	−0.186127	+	0.982526i	$0.559594\pi$
$20$	11.7442	2.62608
$21$	2.11895	0.462393
$22$	−2.70023	−0.575690
$23$	0.232397	0.0484581	0.0242291	−	0.999706i	$-0.492287\pi$
$23$	0.232397	0.0484581	0.0242291	+	0.999706i	$0.492287\pi$
$24$	8.88702	1.81406
$25$	−0.0735266	−0.0147053
$26$	6.81449	1.33643
$27$	−1.00000	−0.192450
$28$	−11.2118	−2.11884
$29$	8.99969	1.67120	0.835601	−	0.549337i	$-0.185120\pi$
$29$	8.99969	1.67120	0.835601	+	0.549337i	$0.185120\pi$
$30$	5.99333	1.09423
$31$	−0.0529540	−0.00951081	−0.00475541	−	0.999989i	$-0.501514\pi$
$31$	−0.0529540	−0.00951081	−0.00475541	+	0.999989i	$0.501514\pi$
$32$	−18.4482	−3.26121
$33$	−1.00000	−0.174078
$34$	−5.02921	−0.862502
$35$	−4.70316	−0.794978
$36$	5.29122	0.881869
$37$	−1.12092	−0.184278	−0.0921389	−	0.995746i	$-0.529370\pi$
$37$	−1.12092	−0.184278	−0.0921389	+	0.995746i	$0.529370\pi$
$38$	4.38144	0.710764
$39$	2.52367	0.404111
$40$	−19.7253	−3.11885
$41$	−8.95321	−1.39826	−0.699128	−	0.714996i	$-0.746428\pi$
$41$	−8.95321	−1.39826	−0.699128	+	0.714996i	$0.746428\pi$
$42$	−5.72165	−0.882870
$43$	−8.83041	−1.34662	−0.673312	−	0.739358i	$-0.735129\pi$
$43$	−8.83041	−1.34662	−0.673312	+	0.739358i	$0.735129\pi$
$44$	5.29122	0.797681
$45$	2.21957	0.330873
$46$	−0.627524	−0.0925234
$47$	−8.15644	−1.18974	−0.594869	−	0.803822i	$-0.702796\pi$
$47$	−8.15644	−1.18974	−0.594869	+	0.803822i	$0.702796\pi$
$48$	−13.4145	−1.93622
$49$	−2.51004	−0.358577
$50$	0.198539	0.0280776
$51$	−1.86251	−0.260804
$52$	−13.3533	−1.85177
$53$	11.4915	1.57847	0.789237	−	0.614089i	$-0.210476\pi$
$53$	11.4915	1.57847	0.789237	+	0.614089i	$0.210476\pi$
$54$	2.70023	0.367454
$55$	2.21957	0.299286
$56$	18.8312	2.51642
$57$	1.62262	0.214921
$58$	−24.3012	−3.19090
$59$	−1.89372	−0.246542	−0.123271	−	0.992373i	$-0.539338\pi$
$59$	−1.89372	−0.246542	−0.123271	+	0.992373i	$0.539338\pi$
$60$	−11.7442	−1.51617
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	0.142988	0.0181594
$63$	−2.11895	−0.266963
$64$	22.9853	2.87316
$65$	−5.60146	−0.694776
$66$	2.70023	0.332375
$67$	−1.07486	−0.131315	−0.0656577	−	0.997842i	$-0.520915\pi$
$67$	−1.07486	−0.131315	−0.0656577	+	0.997842i	$0.520915\pi$
$68$	9.85497	1.19509
$69$	−0.232397	−0.0279773
$70$	12.6996	1.51789
$71$	5.42037	0.643279	0.321640	−	0.946862i	$-0.395766\pi$
$71$	5.42037	0.643279	0.321640	+	0.946862i	$0.395766\pi$
$72$	−8.88702	−1.04735
$73$	−8.03508	−0.940435	−0.470217	−	0.882551i	$-0.655824\pi$
$73$	−8.03508	−0.940435	−0.470217	+	0.882551i	$0.655824\pi$
$74$	3.02673	0.351850
$75$	0.0735266	0.00849013
$76$	−8.58564	−0.984840
$77$	−2.11895	−0.241477
$78$	−6.81449	−0.771589
$79$	−6.67275	−0.750743	−0.375371	−	0.926875i	$-0.622485\pi$
$79$	−6.67275	−0.750743	−0.375371	+	0.926875i	$0.622485\pi$
$80$	29.7744	3.32888
$81$	1.00000	0.111111
$82$	24.1757	2.66976
$83$	3.06257	0.336161	0.168081	−	0.985773i	$-0.446243\pi$
$83$	3.06257	0.336161	0.168081	+	0.985773i	$0.446243\pi$
$84$	11.2118	1.22331
$85$	4.13397	0.448392
$86$	23.8441	2.57117
$87$	−8.99969	−0.964869
$88$	−8.88702	−0.947360
$89$	5.40932	0.573387	0.286693	−	0.958022i	$-0.407444\pi$
$89$	5.40932	0.573387	0.286693	+	0.958022i	$0.407444\pi$
$90$	−5.99333	−0.631752
$91$	5.34755	0.560575
$92$	1.22966	0.128201
$93$	0.0529540	0.00549107
$94$	22.0242	2.27162
$95$	−3.60151	−0.369508
$96$	18.4482	1.88286
$97$	12.0599	1.22450	0.612251	−	0.790664i	$-0.290264\pi$
$97$	12.0599	1.22450	0.612251	+	0.790664i	$0.290264\pi$
$98$	6.77767	0.684648
$99$	1.00000	0.100504
$100$	−0.389045	−0.0389045
$101$	−10.2401	−1.01893	−0.509464	−	0.860492i	$-0.670156\pi$
$101$	−10.2401	−1.01893	−0.509464	+	0.860492i	$0.670156\pi$
$102$	5.02921	0.497966
$103$	−10.9576	−1.07968	−0.539842	−	0.841766i	$-0.681516\pi$
$103$	−10.9576	−1.07968	−0.539842	+	0.841766i	$0.681516\pi$
$104$	22.4280	2.19924
$105$	4.70316	0.458981
$106$	−31.0295	−3.01386
$107$	0.334129	0.0323015	0.0161507	−	0.999870i	$-0.494859\pi$
$107$	0.334129	0.0323015	0.0161507	+	0.999870i	$0.494859\pi$
$108$	−5.29122	−0.509147
$109$	8.41756	0.806256	0.403128	−	0.915144i	$-0.367923\pi$
$109$	8.41756	0.806256	0.403128	+	0.915144i	$0.367923\pi$
$110$	−5.99333	−0.571441
$111$	1.12092	0.106393
$112$	−28.4248	−2.68589
$113$	13.6712	1.28608	0.643038	−	0.765834i	$-0.277674\pi$
$113$	13.6712	1.28608	0.643038	+	0.765834i	$0.277674\pi$
$114$	−4.38144	−0.410360
$115$	0.515820	0.0481005
$116$	47.6193	4.42134
$117$	−2.52367	−0.233314
$118$	5.11348	0.470734
$119$	−3.94658	−0.361782
$120$	19.7253	1.80067
$121$	1.00000	0.0909091
$122$	−2.70023	−0.244467
$123$	8.95321	0.807284
$124$	−0.280191	−0.0251619
$125$	−11.2610	−1.00722
$126$	5.72165	0.509725
$127$	−3.78595	−0.335949	−0.167974	−	0.985791i	$-0.553723\pi$
$127$	−3.78595	−0.335949	−0.167974	+	0.985791i	$0.553723\pi$
$128$	−25.1690	−2.22464
$129$	8.83041	0.777474
$130$	15.1252	1.32657
$131$	10.5360	0.920533	0.460267	−	0.887781i	$-0.347754\pi$
$131$	10.5360	0.920533	0.460267	+	0.887781i	$0.347754\pi$
$132$	−5.29122	−0.460541
$133$	3.43826	0.298135
$134$	2.90237	0.250727
$135$	−2.21957	−0.191030
$136$	−16.5522	−1.41934
$137$	−17.4642	−1.49207	−0.746033	−	0.665909i	$-0.768044\pi$
$137$	−17.4642	−1.49207	−0.746033	+	0.665909i	$0.768044\pi$
$138$	0.627524	0.0534184
$139$	−0.0929980	−0.00788799	−0.00394399	−	0.999992i	$-0.501255\pi$
$139$	−0.0929980	−0.00788799	−0.00394399	+	0.999992i	$0.501255\pi$
$140$	−24.8854	−2.10320
$141$	8.15644	0.686896
$142$	−14.6362	−1.22824
$143$	−2.52367	−0.211040
$144$	13.4145	1.11788
$145$	19.9754	1.65887
$146$	21.6965	1.79562
$147$	2.51004	0.207025
$148$	−5.93102	−0.487527
$149$	−9.89650	−0.810753	−0.405376	−	0.914150i	$-0.632860\pi$
$149$	−9.89650	−0.810753	−0.405376	+	0.914150i	$0.632860\pi$
$150$	−0.198539	−0.0162106
$151$	−7.47873	−0.608611	−0.304305	−	0.952575i	$-0.598424\pi$
$151$	−7.47873	−0.608611	−0.304305	+	0.952575i	$0.598424\pi$
$152$	14.4203	1.16964
$153$	1.86251	0.150575
$154$	5.72165	0.461064
$155$	−0.117535	−0.00944062
$156$	13.3533	1.06912
$157$	−15.5758	−1.24309	−0.621543	−	0.783380i	$-0.713494\pi$
$157$	−15.5758	−1.24309	−0.621543	+	0.783380i	$0.713494\pi$
$158$	18.0179	1.43343
$159$	−11.4915	−0.911332
$160$	−40.9470	−3.23715
$161$	−0.492438	−0.0388096
$162$	−2.70023	−0.212150
$163$	7.47058	0.585141	0.292571	−	0.956244i	$-0.405489\pi$
$163$	7.47058	0.585141	0.292571	+	0.956244i	$0.405489\pi$
$164$	−47.3734	−3.69924
$165$	−2.21957	−0.172793
$166$	−8.26964	−0.641848
$167$	−17.0129	−1.31650	−0.658248	−	0.752801i	$-0.728702\pi$
$167$	−17.0129	−1.31650	−0.658248	+	0.752801i	$0.728702\pi$
$168$	−18.8312	−1.45286
$169$	−6.63107	−0.510082
$170$	−11.1627	−0.856137
$171$	−1.62262	−0.124085
$172$	−46.7236	−3.56264
$173$	−7.59030	−0.577079	−0.288540	−	0.957468i	$-0.593170\pi$
$173$	−7.59030	−0.577079	−0.288540	+	0.957468i	$0.593170\pi$
$174$	24.3012	1.84227
$175$	0.155799	0.0117773
$176$	13.4145	1.01116
$177$	1.89372	0.142341
$178$	−14.6064	−1.09479
$179$	5.63139	0.420910	0.210455	−	0.977604i	$-0.432505\pi$
$179$	5.63139	0.420910	0.210455	+	0.977604i	$0.432505\pi$
$180$	11.7442	0.875361
$181$	23.6253	1.75605	0.878027	−	0.478610i	$-0.158859\pi$
$181$	23.6253	1.75605	0.878027	+	0.478610i	$0.158859\pi$
$182$	−14.4396	−1.07033
$183$	−1.00000	−0.0739221
$184$	−2.06532	−0.152257
$185$	−2.48795	−0.182918
$186$	−0.142988	−0.0104844
$187$	1.86251	0.136201
$188$	−43.1575	−3.14758
$189$	2.11895	0.154131
$190$	9.72490	0.705518
$191$	−12.1022	−0.875681	−0.437841	−	0.899053i	$-0.644257\pi$
$191$	−12.1022	−0.875681	−0.437841	+	0.899053i	$0.644257\pi$
$192$	−22.9853	−1.65882
$193$	0.690719	0.0497190	0.0248595	−	0.999691i	$-0.492086\pi$
$193$	0.690719	0.0497190	0.0248595	+	0.999691i	$0.492086\pi$
$194$	−32.5646	−2.33800
$195$	5.60146	0.401129
$196$	−13.2812	−0.948654
$197$	−12.5268	−0.892500	−0.446250	−	0.894908i	$-0.647241\pi$
$197$	−12.5268	−0.892500	−0.446250	+	0.894908i	$0.647241\pi$
$198$	−2.70023	−0.191897
$199$	−10.6668	−0.756146	−0.378073	−	0.925776i	$-0.623413\pi$
$199$	−10.6668	−0.756146	−0.378073	+	0.925776i	$0.623413\pi$
$200$	0.653433	0.0462047
$201$	1.07486	0.0758149
$202$	27.6506	1.94549
$203$	−19.0699	−1.33845
$204$	−9.85497	−0.689986
$205$	−19.8722	−1.38794
$206$	29.5880	2.06149
$207$	0.232397	0.0161527
$208$	−33.8539	−2.34735
$209$	−1.62262	−0.112239
$210$	−12.6996	−0.876354
$211$	−11.3412	−0.780764	−0.390382	−	0.920653i	$-0.627657\pi$
$211$	−11.3412	−0.780764	−0.390382	+	0.920653i	$0.627657\pi$
$212$	60.8038	4.17602
$213$	−5.42037	−0.371398
$214$	−0.902224	−0.0616748
$215$	−19.5997	−1.33669
$216$	8.88702	0.604685
$217$	0.112207	0.00761710
$218$	−22.7293	−1.53942
$219$	8.03508	0.542960
$220$	11.7442	0.791794
$221$	−4.70038	−0.316182
$222$	−3.02673	−0.203141
$223$	−10.0996	−0.676318	−0.338159	−	0.941089i	$-0.609804\pi$
$223$	−10.0996	−0.676318	−0.338159	+	0.941089i	$0.609804\pi$
$224$	39.0909	2.61187
$225$	−0.0735266	−0.00490178
$226$	−36.9153	−2.45557
$227$	−24.4371	−1.62195	−0.810973	−	0.585084i	$-0.801061\pi$
$227$	−24.4371	−1.62195	−0.810973	+	0.585084i	$0.801061\pi$
$228$	8.58564	0.568598
$229$	−13.2077	−0.872787	−0.436393	−	0.899756i	$-0.643744\pi$
$229$	−13.2077	−0.872787	−0.436393	+	0.899756i	$0.643744\pi$
$230$	−1.39283	−0.0918406
$231$	2.11895	0.139417
$232$	−79.9805	−5.25098
$233$	−0.140516	−0.00920550	−0.00460275	−	0.999989i	$-0.501465\pi$
$233$	−0.140516	−0.00920550	−0.00460275	+	0.999989i	$0.501465\pi$
$234$	6.81449	0.445477
$235$	−18.1037	−1.18096
$236$	−10.0201	−0.652253
$237$	6.67275	0.433442
$238$	10.6567	0.690768
$239$	4.97217	0.321623	0.160812	−	0.986985i	$-0.448589\pi$
$239$	4.97217	0.321623	0.160812	+	0.986985i	$0.448589\pi$
$240$	−29.7744	−1.92193
$241$	−12.4794	−0.803871	−0.401936	−	0.915668i	$-0.631662\pi$
$241$	−12.4794	−0.803871	−0.401936	+	0.915668i	$0.631662\pi$
$242$	−2.70023	−0.173577
$243$	−1.00000	−0.0641500
$244$	5.29122	0.338735
$245$	−5.57120	−0.355931
$246$	−24.1757	−1.54139
$247$	4.09497	0.260556
$248$	0.470603	0.0298833
$249$	−3.06257	−0.194083
$250$	30.4073	1.92313
$251$	5.84977	0.369234	0.184617	−	0.982811i	$-0.440896\pi$
$251$	5.84977	0.369234	0.184617	+	0.982811i	$0.440896\pi$
$252$	−11.2118	−0.706279
$253$	0.232397	0.0146107
$254$	10.2229	0.641443
$255$	−4.13397	−0.258880
$256$	21.9913	1.37446
$257$	13.3927	0.835414	0.417707	−	0.908582i	$-0.362834\pi$
$257$	13.3927	0.835414	0.417707	+	0.908582i	$0.362834\pi$
$258$	−23.8441	−1.48447
$259$	2.37517	0.147586
$260$	−29.6385	−1.83810
$261$	8.99969	0.557067
$262$	−28.4495	−1.75762
$263$	21.6822	1.33698	0.668490	−	0.743721i	$-0.266941\pi$
$263$	21.6822	1.33698	0.668490	+	0.743721i	$0.266941\pi$
$264$	8.88702	0.546959
$265$	25.5061	1.56682
$266$	−9.28407	−0.569243
$267$	−5.40932	−0.331045
$268$	−5.68733	−0.347409
$269$	−27.6844	−1.68795	−0.843974	−	0.536383i	$-0.819790\pi$
$269$	−27.6844	−1.68795	−0.843974	+	0.536383i	$0.819790\pi$
$270$	5.99333	0.364742
$271$	−17.6848	−1.07428	−0.537138	−	0.843494i	$-0.680495\pi$
$271$	−17.6848	−1.07428	−0.537138	+	0.843494i	$0.680495\pi$
$272$	24.9848	1.51492
$273$	−5.34755	−0.323648
$274$	47.1572	2.84887
$275$	−0.0735266	−0.00443382
$276$	−1.22966	−0.0740170
$277$	28.1120	1.68908	0.844542	−	0.535489i	$-0.179873\pi$
$277$	28.1120	1.68908	0.844542	+	0.535489i	$0.179873\pi$
$278$	0.251116	0.0150609
$279$	−0.0529540	−0.00317027
$280$	41.7971	2.49785
$281$	28.9616	1.72770	0.863851	−	0.503748i	$-0.168046\pi$
$281$	28.9616	1.72770	0.863851	+	0.503748i	$0.168046\pi$
$282$	−22.0242	−1.31152
$283$	16.5238	0.982236	0.491118	−	0.871093i	$-0.336588\pi$
$283$	16.5238	0.982236	0.491118	+	0.871093i	$0.336588\pi$
$284$	28.6803	1.70187
$285$	3.60151	0.213335
$286$	6.81449	0.402949
$287$	18.9714	1.11985
$288$	−18.4482	−1.08707
$289$	−13.5310	−0.795943
$290$	−53.9381	−3.16736
$291$	−12.0599	−0.706966
$292$	−42.5153	−2.48802
$293$	−25.5646	−1.49350	−0.746750	−	0.665105i	$-0.768387\pi$
$293$	−25.5646	−1.49350	−0.746750	+	0.665105i	$0.768387\pi$
$294$	−6.77767	−0.395282
$295$	−4.20324	−0.244722
$296$	9.96163	0.579008
$297$	−1.00000	−0.0580259
$298$	26.7228	1.54801
$299$	−0.586494	−0.0339178
$300$	0.389045	0.0224615
$301$	18.7112	1.07850
$302$	20.1943	1.16205
$303$	10.2401	0.588279
$304$	−21.7667	−1.24841
$305$	2.21957	0.127092
$306$	−5.02921	−0.287501
$307$	14.8707	0.848717	0.424358	−	0.905494i	$-0.360500\pi$
$307$	14.8707	0.848717	0.424358	+	0.905494i	$0.360500\pi$
$308$	−11.2118	−0.638854
$309$	10.9576	0.623356
$310$	0.317371	0.0180254
$311$	−26.8797	−1.52421	−0.762104	−	0.647454i	$-0.775834\pi$
$311$	−26.8797	−1.52421	−0.762104	+	0.647454i	$0.775834\pi$
$312$	−22.4280	−1.26973
$313$	−32.7560	−1.85148	−0.925738	−	0.378166i	$-0.876555\pi$
$313$	−32.7560	−1.85148	−0.925738	+	0.378166i	$0.876555\pi$
$314$	42.0582	2.37348
$315$	−4.70316	−0.264993
$316$	−35.3069	−1.98617
$317$	−8.10496	−0.455220	−0.227610	−	0.973752i	$-0.573091\pi$
$317$	−8.10496	−0.455220	−0.227610	+	0.973752i	$0.573091\pi$
$318$	31.0295	1.74005
$319$	8.99969	0.503886
$320$	51.0173	2.85195
$321$	−0.334129	−0.0186493
$322$	1.32969	0.0741010
$323$	−3.02216	−0.168157
$324$	5.29122	0.293956
$325$	0.185557	0.0102929
$326$	−20.1723	−1.11724
$327$	−8.41756	−0.465492
$328$	79.5674	4.39337
$329$	17.2831	0.952848
$330$	5.99333	0.329922
$331$	−13.6297	−0.749158	−0.374579	−	0.927195i	$-0.622213\pi$
$331$	−13.6297	−0.749158	−0.374579	+	0.927195i	$0.622213\pi$
$332$	16.2047	0.889351
$333$	−1.12092	−0.0614259
$334$	45.9386	2.51365
$335$	−2.38573	−0.130346
$336$	28.4248	1.55070
$337$	8.22312	0.447942	0.223971	−	0.974596i	$-0.428098\pi$
$337$	8.22312	0.447942	0.223971	+	0.974596i	$0.428098\pi$
$338$	17.9054	0.973924
$339$	−13.6712	−0.742516
$340$	21.8738	1.18627
$341$	−0.0529540	−0.00286762
$342$	4.38144	0.236921
$343$	20.1513	1.08807
$344$	78.4760	4.23114
$345$	−0.515820	−0.0277708
$346$	20.4955	1.10185
$347$	6.21388	0.333579	0.166789	−	0.985993i	$-0.446660\pi$
$347$	6.21388	0.333579	0.166789	+	0.985993i	$0.446660\pi$
$348$	−47.6193	−2.55266
$349$	−9.65556	−0.516850	−0.258425	−	0.966031i	$-0.583204\pi$
$349$	−9.65556	−0.516850	−0.258425	+	0.966031i	$0.583204\pi$
$350$	−0.420694	−0.0224870
$351$	2.52367	0.134704
$352$	−18.4482	−0.983293
$353$	9.59868	0.510886	0.255443	−	0.966824i	$-0.417779\pi$
$353$	9.59868	0.510886	0.255443	+	0.966824i	$0.417779\pi$
$354$	−5.11348	−0.271778
$355$	12.0309	0.638532
$356$	28.6219	1.51696
$357$	3.94658	0.208875
$358$	−15.2060	−0.803663
$359$	−8.24709	−0.435265	−0.217632	−	0.976031i	$-0.569833\pi$
$359$	−8.24709	−0.435265	−0.217632	+	0.976031i	$0.569833\pi$
$360$	−19.7253	−1.03962
$361$	−16.3671	−0.861426
$362$	−63.7936	−3.35292
$363$	−1.00000	−0.0524864
$364$	28.2950	1.48306
$365$	−17.8344	−0.933494
$366$	2.70023	0.141143
$367$	−14.0837	−0.735164	−0.367582	−	0.929991i	$-0.619814\pi$
$367$	−14.0837	−0.735164	−0.367582	+	0.929991i	$0.619814\pi$
$368$	3.11750	0.162511
$369$	−8.95321	−0.466086
$370$	6.71803	0.349254
$371$	−24.3499	−1.26418
$372$	0.280191	0.0145272
$373$	27.9601	1.44772	0.723859	−	0.689948i	$-0.242367\pi$
$373$	27.9601	1.44772	0.723859	+	0.689948i	$0.242367\pi$
$374$	−5.02921	−0.260054
$375$	11.2610	0.581517
$376$	72.4864	3.73820
$377$	−22.7123	−1.16974
$378$	−5.72165	−0.294290
$379$	−14.9564	−0.768258	−0.384129	−	0.923279i	$-0.625498\pi$
$379$	−14.9564	−0.768258	−0.384129	+	0.923279i	$0.625498\pi$
$380$	−19.0564	−0.977572
$381$	3.78595	0.193960
$382$	32.6785	1.67198
$383$	−35.7729	−1.82791	−0.913954	−	0.405818i	$-0.866987\pi$
$383$	−35.7729	−1.82791	−0.913954	+	0.405818i	$0.866987\pi$
$384$	25.1690	1.28440
$385$	−4.70316	−0.239695
$386$	−1.86510	−0.0949309
$387$	−8.83041	−0.448875
$388$	63.8118	3.23955
$389$	15.8009	0.801136	0.400568	−	0.916267i	$-0.368813\pi$
$389$	15.8009	0.801136	0.400568	+	0.916267i	$0.368813\pi$
$390$	−15.1252	−0.765895
$391$	0.432843	0.0218898
$392$	22.3068	1.12666
$393$	−10.5360	−0.531470
$394$	33.8253	1.70409
$395$	−14.8106	−0.745202
$396$	5.29122	0.265894
$397$	13.4452	0.674794	0.337397	−	0.941362i	$-0.390454\pi$
$397$	13.4452	0.674794	0.337397	+	0.941362i	$0.390454\pi$
$398$	28.8026	1.44375
$399$	−3.43826	−0.172128
$400$	−0.986326	−0.0493163
$401$	11.2339	0.560995	0.280498	−	0.959855i	$-0.409501\pi$
$401$	11.2339	0.560995	0.280498	+	0.959855i	$0.409501\pi$
$402$	−2.90237	−0.144757
$403$	0.133639	0.00665701
$404$	−54.1826	−2.69569
$405$	2.21957	0.110291
$406$	51.4931	2.55556
$407$	−1.12092	−0.0555619
$408$	16.5522	0.819457
$409$	22.0149	1.08857	0.544284	−	0.838901i	$-0.316802\pi$
$409$	22.0149	1.08857	0.544284	+	0.838901i	$0.316802\pi$
$410$	53.6595	2.65006
$411$	17.4642	0.861444
$412$	−57.9790	−2.85642
$413$	4.01271	0.197452
$414$	−0.627524	−0.0308411
$415$	6.79758	0.333680
$416$	46.5573	2.28266
$417$	0.0929980	0.00455413
$418$	4.38144	0.214303
$419$	−10.0502	−0.490982	−0.245491	−	0.969399i	$-0.578949\pi$
$419$	−10.0502	−0.490982	−0.245491	+	0.969399i	$0.578949\pi$
$420$	24.8854	1.21428
$421$	−32.7041	−1.59390	−0.796950	−	0.604046i	$-0.793555\pi$
$421$	−32.7041	−1.59390	−0.796950	+	0.604046i	$0.793555\pi$
$422$	30.6239	1.49075
$423$	−8.15644	−0.396580
$424$	−102.125	−4.95962
$425$	−0.136944	−0.00664278
$426$	14.6362	0.709127
$427$	−2.11895	−0.102543
$428$	1.76795	0.0854571
$429$	2.52367	0.121844
$430$	52.9235	2.55220
$431$	−27.2073	−1.31053	−0.655264	−	0.755400i	$-0.727443\pi$
$431$	−27.2073	−1.31053	−0.655264	+	0.755400i	$0.727443\pi$
$432$	−13.4145	−0.645407
$433$	6.25089	0.300399	0.150199	−	0.988656i	$-0.452008\pi$
$433$	6.25089	0.300399	0.150199	+	0.988656i	$0.452008\pi$
$434$	−0.302984	−0.0145437
$435$	−19.9754	−0.957748
$436$	44.5391	2.13304
$437$	−0.377092	−0.0180388
$438$	−21.6965	−1.03670
$439$	−6.23945	−0.297793	−0.148896	−	0.988853i	$-0.547572\pi$
$439$	−6.23945	−0.297793	−0.148896	+	0.988853i	$0.547572\pi$
$440$	−19.7253	−0.940369
$441$	−2.51004	−0.119526
$442$	12.6921	0.603701
$443$	−27.2602	−1.29517	−0.647586	−	0.761993i	$-0.724221\pi$
$443$	−27.2602	−1.29517	−0.647586	+	0.761993i	$0.724221\pi$
$444$	5.93102	0.281474
$445$	12.0063	0.569155
$446$	27.2711	1.29133
$447$	9.89650	0.468088
$448$	−48.7047	−2.30108
$449$	−3.39049	−0.160007	−0.0800036	−	0.996795i	$-0.525493\pi$
$449$	−3.39049	−0.160007	−0.0800036	+	0.996795i	$0.525493\pi$
$450$	0.198539	0.00935919
$451$	−8.95321	−0.421590
$452$	72.3371	3.40245
$453$	7.47873	0.351381
$454$	65.9856	3.09686
$455$	11.8692	0.556438
$456$	−14.4203	−0.675291
$457$	−6.49576	−0.303859	−0.151929	−	0.988391i	$-0.548549\pi$
$457$	−6.49576	−0.303859	−0.151929	+	0.988391i	$0.548549\pi$
$458$	35.6637	1.66645
$459$	−1.86251	−0.0869347
$460$	2.72932	0.127255
$461$	6.12439	0.285241	0.142621	−	0.989777i	$-0.454447\pi$
$461$	6.12439	0.285241	0.142621	+	0.989777i	$0.454447\pi$
$462$	−5.72165	−0.266195
$463$	−38.3973	−1.78447	−0.892237	−	0.451567i	$-0.850865\pi$
$463$	−38.3973	−1.78447	−0.892237	+	0.451567i	$0.850865\pi$
$464$	120.727	5.60460
$465$	0.117535	0.00545055
$466$	0.379424	0.0175765
$467$	12.3597	0.571941	0.285970	−	0.958238i	$-0.407684\pi$
$467$	12.3597	0.571941	0.285970	+	0.958238i	$0.407684\pi$
$468$	−13.3533	−0.617257
$469$	2.27758	0.105169
$470$	48.8842	2.25486
$471$	15.5758	0.717696
$472$	16.8296	0.774643
$473$	−8.83041	−0.406022
$474$	−18.0179	−0.827590
$475$	0.119306	0.00547413
$476$	−20.8822	−0.957135
$477$	11.4915	0.526158
$478$	−13.4260	−0.614090
$479$	19.7415	0.902012	0.451006	−	0.892521i	$-0.351065\pi$
$479$	19.7415	0.902012	0.451006	+	0.892521i	$0.351065\pi$
$480$	40.9470	1.86897
$481$	2.82883	0.128984
$482$	33.6973	1.53487
$483$	0.492438	0.0224067
$484$	5.29122	0.240510
$485$	26.7678	1.21546
$486$	2.70023	0.122485
$487$	31.5416	1.42929	0.714644	−	0.699488i	$-0.246589\pi$
$487$	31.5416	1.42929	0.714644	+	0.699488i	$0.246589\pi$
$488$	−8.88702	−0.402297
$489$	−7.47058	−0.337831
$490$	15.0435	0.679595
$491$	−40.3483	−1.82089	−0.910446	−	0.413628i	$-0.864261\pi$
$491$	−40.3483	−1.82089	−0.910446	+	0.413628i	$0.864261\pi$
$492$	47.3734	2.13576
$493$	16.7621	0.754925
$494$	−11.0573	−0.497493
$495$	2.21957	0.0997621
$496$	−0.710353	−0.0318958
$497$	−11.4855	−0.515195
$498$	8.26964	0.370571
$499$	25.0651	1.12207	0.561034	−	0.827793i	$-0.310404\pi$
$499$	25.0651	1.12207	0.561034	+	0.827793i	$0.310404\pi$
$500$	−59.5845	−2.66470
$501$	17.0129	0.760080
$502$	−15.7957	−0.704996
$503$	12.7643	0.569131	0.284565	−	0.958657i	$-0.408151\pi$
$503$	12.7643	0.569131	0.284565	+	0.958657i	$0.408151\pi$
$504$	18.8312	0.838808
$505$	−22.7286	−1.01141
$506$	−0.627524	−0.0278969
$507$	6.63107	0.294496
$508$	−20.0323	−0.888788
$509$	5.82491	0.258184	0.129092	−	0.991633i	$-0.458794\pi$
$509$	5.82491	0.258184	0.129092	+	0.991633i	$0.458794\pi$
$510$	11.1627	0.494291
$511$	17.0260	0.753184
$512$	−9.04363	−0.399676
$513$	1.62262	0.0716405
$514$	−36.1633	−1.59509
$515$	−24.3211	−1.07172
$516$	46.7236	2.05689
$517$	−8.15644	−0.358720
$518$	−6.41350	−0.281793
$519$	7.59030	0.333177
$520$	49.7803	2.18301
$521$	24.0360	1.05304	0.526518	−	0.850164i	$-0.323497\pi$
$521$	24.0360	1.05304	0.526518	+	0.850164i	$0.323497\pi$
$522$	−24.3012	−1.06363
$523$	−36.6082	−1.60076	−0.800382	−	0.599491i	$-0.795370\pi$
$523$	−36.6082	−1.60076	−0.800382	+	0.599491i	$0.795370\pi$
$524$	55.7482	2.43537
$525$	−0.155799	−0.00679965
$526$	−58.5467	−2.55276
$527$	−0.0986275	−0.00429628
$528$	−13.4145	−0.583793
$529$	−22.9460	−0.997652
$530$	−68.8721	−2.99161
$531$	−1.89372	−0.0821805
$532$	18.1926	0.788748
$533$	22.5950	0.978697
$534$	14.6064	0.632080
$535$	0.741622	0.0320631
$536$	9.55233	0.412598
$537$	−5.63139	−0.243012
$538$	74.7542	3.22288
$539$	−2.51004	−0.108115
$540$	−11.7442	−0.505390
$541$	27.1649	1.16791	0.583956	−	0.811786i	$-0.301504\pi$
$541$	27.1649	1.16791	0.583956	+	0.811786i	$0.301504\pi$
$542$	47.7530	2.05117
$543$	−23.6253	−1.01386
$544$	−34.3601	−1.47318
$545$	18.6833	0.800306
$546$	14.4396	0.617957
$547$	−13.8935	−0.594043	−0.297022	−	0.954871i	$-0.595993\pi$
$547$	−13.8935	−0.594043	−0.297022	+	0.954871i	$0.595993\pi$
$548$	−92.4067	−3.94742
$549$	1.00000	0.0426790
$550$	0.198539	0.00846571
$551$	−14.6031	−0.622113
$552$	2.06532	0.0879058
$553$	14.1392	0.601261
$554$	−75.9086	−3.22505
$555$	2.48795	0.105608
$556$	−0.492073	−0.0208685
$557$	−4.83132	−0.204710	−0.102355	−	0.994748i	$-0.532638\pi$
$557$	−4.83132	−0.204710	−0.102355	+	0.994748i	$0.532638\pi$
$558$	0.142988	0.00605315
$559$	22.2851	0.942558
$560$	−63.0906	−2.66607
$561$	−1.86251	−0.0786354
$562$	−78.2027	−3.29878
$563$	15.6746	0.660606	0.330303	−	0.943875i	$-0.392849\pi$
$563$	15.6746	0.660606	0.330303	+	0.943875i	$0.392849\pi$
$564$	43.1575	1.81726
$565$	30.3441	1.27658
$566$	−44.6179	−1.87543
$567$	−2.11895	−0.0889877
$568$	−48.1709	−2.02121
$569$	−16.9647	−0.711199	−0.355600	−	0.934638i	$-0.615723\pi$
$569$	−16.9647	−0.711199	−0.355600	+	0.934638i	$0.615723\pi$
$570$	−9.72490	−0.407331
$571$	−0.161872	−0.00677414	−0.00338707	−	0.999994i	$-0.501078\pi$
$571$	−0.161872	−0.00677414	−0.00338707	+	0.999994i	$0.501078\pi$
$572$	−13.3533	−0.558330
$573$	12.1022	0.505575
$574$	−51.2271	−2.13818
$575$	−0.0170874	−0.000712593 0
$576$	22.9853	0.957719
$577$	−23.1526	−0.963854	−0.481927	−	0.876211i	$-0.660063\pi$
$577$	−23.1526	−0.963854	−0.481927	+	0.876211i	$0.660063\pi$
$578$	36.5369	1.51973
$579$	−0.690719	−0.0287053
$580$	105.694	4.38871
$581$	−6.48945	−0.269228
$582$	32.5646	1.34984
$583$	11.4915	0.475928
$584$	71.4079	2.95488
$585$	−5.60146	−0.231592
$586$	69.0302	2.85161
$587$	−29.9787	−1.23735	−0.618677	−	0.785645i	$-0.712331\pi$
$587$	−29.9787	−1.23735	−0.618677	+	0.785645i	$0.712331\pi$
$588$	13.2812	0.547706
$589$	0.0859242	0.00354045
$590$	11.3497	0.467260
$591$	12.5268	0.515285
$592$	−15.0366	−0.618000
$593$	−23.2983	−0.956747	−0.478374	−	0.878156i	$-0.658774\pi$
$593$	−23.2983	−0.956747	−0.478374	+	0.878156i	$0.658774\pi$
$594$	2.70023	0.110792
$595$	−8.75970	−0.359113
$596$	−52.3645	−2.14493
$597$	10.6668	0.436561
$598$	1.58367	0.0647609
$599$	8.01939	0.327664	0.163832	−	0.986488i	$-0.447615\pi$
$599$	8.01939	0.327664	0.163832	+	0.986488i	$0.447615\pi$
$600$	−0.653433	−0.0266763
$601$	−16.6438	−0.678914	−0.339457	−	0.940622i	$-0.610243\pi$
$601$	−16.6438	−0.678914	−0.339457	+	0.940622i	$0.610243\pi$
$602$	−50.5245	−2.05922
$603$	−1.07486	−0.0437718
$604$	−39.5716	−1.61015
$605$	2.21957	0.0902382
$606$	−27.6506	−1.12323
$607$	−0.200635	−0.00814351	−0.00407175	−	0.999992i	$-0.501296\pi$
$607$	−0.200635	−0.00814351	−0.00407175	+	0.999992i	$0.501296\pi$
$608$	29.9345	1.21400
$609$	19.0699	0.772752
$610$	−5.99333	−0.242663
$611$	20.5842	0.832747
$612$	9.85497	0.398363
$613$	−23.3942	−0.944884	−0.472442	−	0.881362i	$-0.656627\pi$
$613$	−23.3942	−0.944884	−0.472442	+	0.881362i	$0.656627\pi$
$614$	−40.1543	−1.62050
$615$	19.8722	0.801326
$616$	18.8312	0.758730
$617$	20.5613	0.827765	0.413882	−	0.910330i	$-0.364172\pi$
$617$	20.5613	0.827765	0.413882	+	0.910330i	$0.364172\pi$
$618$	−29.5880	−1.19020
$619$	−31.0796	−1.24920	−0.624598	−	0.780947i	$-0.714737\pi$
$619$	−31.0796	−1.24920	−0.624598	+	0.780947i	$0.714737\pi$
$620$	−0.621902	−0.0249762
$621$	−0.232397	−0.00932577
$622$	72.5813	2.91024
$623$	−11.4621	−0.459219
$624$	33.8539	1.35524
$625$	−24.6270	−0.985078
$626$	88.4485	3.53511
$627$	1.62262	0.0648012
$628$	−82.4150	−3.28872
$629$	−2.08773	−0.0832431
$630$	12.6996	0.505963
$631$	−8.46876	−0.337136	−0.168568	−	0.985690i	$-0.553914\pi$
$631$	−8.46876	−0.337136	−0.168568	+	0.985690i	$0.553914\pi$
$632$	59.3009	2.35886
$633$	11.3412	0.450774
$634$	21.8852	0.869173
$635$	−8.40316	−0.333469
$636$	−60.8038	−2.41103
$637$	6.33452	0.250983
$638$	−24.3012	−0.962094
$639$	5.42037	0.214426
$640$	−55.8642	−2.20823
$641$	30.1870	1.19231	0.596157	−	0.802868i	$-0.296693\pi$
$641$	30.1870	1.19231	0.596157	+	0.802868i	$0.296693\pi$
$642$	0.902224	0.0356080
$643$	−18.9252	−0.746337	−0.373168	−	0.927764i	$-0.621729\pi$
$643$	−18.9252	−0.746337	−0.373168	+	0.927764i	$0.621729\pi$
$644$	−2.60560	−0.102675
$645$	19.5997	0.771736
$646$	8.16050	0.321071
$647$	19.0510	0.748973	0.374486	−	0.927232i	$-0.377819\pi$
$647$	19.0510	0.748973	0.374486	+	0.927232i	$0.377819\pi$
$648$	−8.88702	−0.349115
$649$	−1.89372	−0.0743351
$650$	−0.501046	−0.0196527
$651$	−0.112207	−0.00439774
$652$	39.5285	1.54805
$653$	−34.8338	−1.36315	−0.681576	−	0.731748i	$-0.738705\pi$
$653$	−34.8338	−1.36315	−0.681576	+	0.731748i	$0.738705\pi$
$654$	22.7293	0.888786
$655$	23.3853	0.913740
$656$	−120.103	−4.68924
$657$	−8.03508	−0.313478
$658$	−46.6683	−1.81932
$659$	−18.0958	−0.704912	−0.352456	−	0.935828i	$-0.614653\pi$
$659$	−18.0958	−0.704912	−0.352456	+	0.935828i	$0.614653\pi$
$660$	−11.7442	−0.457142
$661$	−5.52684	−0.214969	−0.107485	−	0.994207i	$-0.534280\pi$
$661$	−5.52684	−0.214969	−0.107485	+	0.994207i	$0.534280\pi$
$662$	36.8033	1.43040
$663$	4.70038	0.182548
$664$	−27.2172	−1.05623
$665$	7.63144	0.295935
$666$	3.02673	0.117283
$667$	2.09150	0.0809833
$668$	−90.0188	−3.48293
$669$	10.0996	0.390472
$670$	6.44200	0.248876
$671$	1.00000	0.0386046
$672$	−39.0909	−1.50796
$673$	31.0228	1.19584	0.597921	−	0.801555i	$-0.295994\pi$
$673$	31.0228	1.19584	0.597921	+	0.801555i	$0.295994\pi$
$674$	−22.2043	−0.855277
$675$	0.0735266	0.00283004
$676$	−35.0864	−1.34948
$677$	−7.79875	−0.299730	−0.149865	−	0.988706i	$-0.547884\pi$
$677$	−7.79875	−0.299730	−0.149865	+	0.988706i	$0.547884\pi$
$678$	36.9153	1.41772
$679$	−25.5544	−0.980690
$680$	−36.7387	−1.40887
$681$	24.4371	0.936430
$682$	0.142988	0.00547528
$683$	4.80839	0.183988	0.0919940	−	0.995760i	$-0.470676\pi$
$683$	4.80839	0.183988	0.0919940	+	0.995760i	$0.470676\pi$
$684$	−8.58564	−0.328280
$685$	−38.7629	−1.48105
$686$	−54.4131	−2.07750
$687$	13.2077	0.503904
$688$	−118.456	−4.51608
$689$	−29.0007	−1.10484
$690$	1.39283	0.0530242
$691$	38.0308	1.44676	0.723381	−	0.690449i	$-0.242587\pi$
$691$	38.0308	1.44676	0.723381	+	0.690449i	$0.242587\pi$
$692$	−40.1619	−1.52673
$693$	−2.11895	−0.0804924
$694$	−16.7789	−0.636918
$695$	−0.206415	−0.00782977
$696$	79.9805	3.03165
$697$	−16.6755	−0.631629
$698$	26.0722	0.986847
$699$	0.140516	0.00531480
$700$	0.824369	0.0311582
$701$	31.4813	1.18903	0.594517	−	0.804083i	$-0.297343\pi$
$701$	31.4813	1.18903	0.594517	+	0.804083i	$0.297343\pi$
$702$	−6.81449	−0.257196
$703$	1.81883	0.0685983
$704$	22.9853	0.866290
$705$	18.1037	0.681827
$706$	−25.9186	−0.975459
$707$	21.6983	0.816049
$708$	10.0201	0.376578
$709$	35.2230	1.32283	0.661414	−	0.750021i	$-0.269957\pi$
$709$	35.2230	1.32283	0.661414	+	0.750021i	$0.269957\pi$
$710$	−32.4860	−1.21918
$711$	−6.67275	−0.250248
$712$	−48.0727	−1.80160
$713$	−0.0123063	−0.000460876 0
$714$	−10.6567	−0.398815
$715$	−5.60146	−0.209483
$716$	29.7969	1.11356
$717$	−4.97217	−0.185689
$718$	22.2690	0.831072
$719$	44.5756	1.66239	0.831195	−	0.555982i	$-0.187658\pi$
$719$	44.5756	1.66239	0.831195	+	0.555982i	$0.187658\pi$
$720$	29.7744	1.10963
$721$	23.2186	0.864707
$722$	44.1949	1.64476
$723$	12.4794	0.464115
$724$	125.007	4.64583
$725$	−0.661717	−0.0245756
$726$	2.70023	0.100215
$727$	30.1879	1.11961	0.559804	−	0.828625i	$-0.310876\pi$
$727$	30.1879	1.11961	0.559804	+	0.828625i	$0.310876\pi$
$728$	−47.5238	−1.76135
$729$	1.00000	0.0370370
$730$	48.1569	1.78237
$731$	−16.4468	−0.608305
$732$	−5.29122	−0.195569
$733$	37.2407	1.37552	0.687758	−	0.725940i	$-0.258595\pi$
$733$	37.2407	1.37552	0.687758	+	0.725940i	$0.258595\pi$
$734$	38.0292	1.40368
$735$	5.57120	0.205497
$736$	−4.28731	−0.158032
$737$	−1.07486	−0.0395931
$738$	24.1757	0.889919
$739$	−12.8770	−0.473687	−0.236844	−	0.971548i	$-0.576113\pi$
$739$	−12.8770	−0.473687	−0.236844	+	0.971548i	$0.576113\pi$
$740$	−13.1643	−0.483929
$741$	−4.09497	−0.150432
$742$	65.7501	2.41376
$743$	4.28620	0.157245	0.0786227	−	0.996904i	$-0.474948\pi$
$743$	4.28620	0.157245	0.0786227	+	0.996904i	$0.474948\pi$
$744$	−0.470603	−0.0172532
$745$	−21.9659	−0.804770
$746$	−75.4985	−2.76420
$747$	3.06257	0.112054
$748$	9.85497	0.360333
$749$	−0.708004	−0.0258699
$750$	−30.4073	−1.11032
$751$	−27.8015	−1.01449	−0.507246	−	0.861801i	$-0.669336\pi$
$751$	−27.8015	−1.01449	−0.507246	+	0.861801i	$0.669336\pi$
$752$	−109.415	−3.98995
$753$	−5.84977	−0.213177
$754$	61.3283	2.23345
$755$	−16.5995	−0.604119
$756$	11.2118	0.407771
$757$	−34.7648	−1.26355	−0.631775	−	0.775152i	$-0.717673\pi$
$757$	−34.7648	−1.26355	−0.631775	+	0.775152i	$0.717673\pi$
$758$	40.3856	1.46687
$759$	−0.232397	−0.00843548
$760$	32.0067	1.16101
$761$	−33.2917	−1.20682	−0.603412	−	0.797430i	$-0.706192\pi$
$761$	−33.2917	−1.20682	−0.603412	+	0.797430i	$0.706192\pi$
$762$	−10.2229	−0.370337
$763$	−17.8364	−0.645721
$764$	−64.0351	−2.31671
$765$	4.13397	0.149464
$766$	96.5948	3.49011
$767$	4.77914	0.172565
$768$	−21.9913	−0.793544
$769$	24.8893	0.897530	0.448765	−	0.893650i	$-0.351864\pi$
$769$	24.8893	0.897530	0.448765	+	0.893650i	$0.351864\pi$
$770$	12.6996	0.457661
$771$	−13.3927	−0.482326
$772$	3.65474	0.131537
$773$	0.379382	0.0136454	0.00682270	−	0.999977i	$-0.497828\pi$
$773$	0.379382	0.0136454	0.00682270	+	0.999977i	$0.497828\pi$
$774$	23.8441	0.857058
$775$	0.00389353	0.000139860 0
$776$	−107.177	−3.84743
$777$	−2.37517	−0.0852089
$778$	−42.6659	−1.52965
$779$	14.5277	0.520508
$780$	29.6385	1.06123
$781$	5.42037	0.193956
$782$	−1.16877	−0.0417952
$783$	−8.99969	−0.321623
$784$	−33.6710	−1.20254
$785$	−34.5716	−1.23391
$786$	28.4495	1.01476
$787$	51.6649	1.84165	0.920827	−	0.389971i	$-0.127515\pi$
$787$	51.6649	1.84165	0.920827	+	0.389971i	$0.127515\pi$
$788$	−66.2822	−2.36120
$789$	−21.6822	−0.771906
$790$	39.9920	1.42285
$791$	−28.9686	−1.03000
$792$	−8.88702	−0.315787
$793$	−2.52367	−0.0896183
$794$	−36.3050	−1.28842
$795$	−25.5061	−0.904607
$796$	−56.4401	−2.00047
$797$	45.8832	1.62527	0.812634	−	0.582775i	$-0.198033\pi$
$797$	45.8832	1.62527	0.812634	+	0.582775i	$0.198033\pi$
$798$	9.28407	0.328652
$799$	−15.1915	−0.537436
$800$	1.35644	0.0479572
$801$	5.40932	0.191129
$802$	−30.3341	−1.07113
$803$	−8.03508	−0.283552
$804$	5.68733	0.200577
$805$	−1.09300	−0.0385232
$806$	−0.360854	−0.0127105
$807$	27.6844	0.974538
$808$	91.0041	3.20151
$809$	38.7974	1.36405	0.682023	−	0.731331i	$-0.261101\pi$
$809$	38.7974	1.36405	0.682023	+	0.731331i	$0.261101\pi$
$810$	−5.99333	−0.210584
$811$	8.13554	0.285678	0.142839	−	0.989746i	$-0.454377\pi$
$811$	8.13554	0.285678	0.142839	+	0.989746i	$0.454377\pi$
$812$	−100.903	−3.54100
$813$	17.6848	0.620233
$814$	3.02673	0.106087
$815$	16.5814	0.580823
$816$	−24.9848	−0.874642
$817$	14.3284	0.501287
$818$	−59.4452	−2.07845
$819$	5.34755	0.186858
$820$	−105.148	−3.67194
$821$	10.5549	0.368370	0.184185	−	0.982892i	$-0.441035\pi$
$821$	10.5549	0.368370	0.184185	+	0.982892i	$0.441035\pi$
$822$	−47.1572	−1.64480
$823$	26.5350	0.924953	0.462477	−	0.886632i	$-0.346961\pi$
$823$	26.5350	0.924953	0.462477	+	0.886632i	$0.346961\pi$
$824$	97.3804	3.39241
$825$	0.0735266	0.00255987
$826$	−10.8352	−0.377005
$827$	42.2012	1.46748	0.733739	−	0.679431i	$-0.237773\pi$
$827$	42.2012	1.46748	0.733739	+	0.679431i	$0.237773\pi$
$828$	1.22966	0.0427337
$829$	32.9471	1.14430	0.572150	−	0.820149i	$-0.306109\pi$
$829$	32.9471	1.14430	0.572150	+	0.820149i	$0.306109\pi$
$830$	−18.3550	−0.637112
$831$	−28.1120	−0.975193
$832$	−58.0073	−2.01104
$833$	−4.67498	−0.161979
$834$	−0.251116	−0.00869542
$835$	−37.7612	−1.30678
$836$	−8.58564	−0.296941
$837$	0.0529540	0.00183036
$838$	27.1377	0.937455
$839$	−27.8310	−0.960831	−0.480416	−	0.877041i	$-0.659514\pi$
$839$	−27.8310	−0.960831	−0.480416	+	0.877041i	$0.659514\pi$
$840$	−41.7971	−1.44214
$841$	51.9945	1.79291
$842$	88.3084	3.04331
$843$	−28.9616	−0.997489
$844$	−60.0090	−2.06559
$845$	−14.7181	−0.506318
$846$	22.0242	0.757208
$847$	−2.11895	−0.0728081
$848$	154.153	5.29362
$849$	−16.5238	−0.567094
$850$	0.369781	0.0126834
$851$	−0.260498	−0.00892976
$852$	−28.6803	−0.982572
$853$	−16.5400	−0.566319	−0.283159	−	0.959073i	$-0.591383\pi$
$853$	−16.5400	−0.566319	−0.283159	+	0.959073i	$0.591383\pi$
$854$	5.72165	0.195791
$855$	−3.60151	−0.123169
$856$	−2.96942	−0.101493
$857$	34.2189	1.16890	0.584448	−	0.811431i	$-0.301311\pi$
$857$	34.2189	1.16890	0.584448	+	0.811431i	$0.301311\pi$
$858$	−6.81449	−0.232643
$859$	−41.1854	−1.40523	−0.702615	−	0.711571i	$-0.747984\pi$
$859$	−41.1854	−1.40523	−0.702615	+	0.711571i	$0.747984\pi$
$860$	−103.706	−3.53635
$861$	−18.9714	−0.646545
$862$	73.4657	2.50225
$863$	45.1683	1.53755	0.768774	−	0.639520i	$-0.220867\pi$
$863$	45.1683	1.53755	0.768774	+	0.639520i	$0.220867\pi$
$864$	18.4482	0.627621
$865$	−16.8472	−0.572821
$866$	−16.8788	−0.573566
$867$	13.5310	0.459538
$868$	0.593711	0.0201519
$869$	−6.67275	−0.226357
$870$	53.9381	1.82867
$871$	2.71260	0.0919130
$872$	−74.8070	−2.53329
$873$	12.0599	0.408167
$874$	1.01823	0.0344423
$875$	23.8616	0.806669
$876$	42.5153	1.43646
$877$	56.3413	1.90251	0.951256	−	0.308404i	$-0.0997948\pi$
$877$	56.3413	1.90251	0.951256	+	0.308404i	$0.0997948\pi$
$878$	16.8479	0.568590
$879$	25.5646	0.862272
$880$	29.7744	1.00370
$881$	48.9192	1.64813	0.824065	−	0.566495i	$-0.191701\pi$
$881$	48.9192	1.64813	0.824065	+	0.566495i	$0.191701\pi$
$882$	6.77767	0.228216
$883$	3.36882	0.113370	0.0566849	−	0.998392i	$-0.481947\pi$
$883$	3.36882	0.113370	0.0566849	+	0.998392i	$0.481947\pi$
$884$	−24.8707	−0.836493
$885$	4.20324	0.141290
$886$	73.6087	2.47293
$887$	16.3667	0.549539	0.274770	−	0.961510i	$-0.411398\pi$
$887$	16.3667	0.549539	0.274770	+	0.961510i	$0.411398\pi$
$888$	−9.96163	−0.334290
$889$	8.02225	0.269058
$890$	−32.4198	−1.08671
$891$	1.00000	0.0335013
$892$	−53.4390	−1.78927
$893$	13.2348	0.442886
$894$	−26.7228	−0.893743
$895$	12.4992	0.417804
$896$	53.3318	1.78169
$897$	0.586494	0.0195825
$898$	9.15510	0.305509
$899$	−0.476570	−0.0158945
$900$	−0.389045	−0.0129682
$901$	21.4030	0.713038
$902$	24.1757	0.804962
$903$	−18.7112	−0.622670
$904$	−121.496	−4.04090
$905$	52.4379	1.74310
$906$	−20.1943	−0.670909
$907$	44.5370	1.47883	0.739413	−	0.673252i	$-0.235103\pi$
$907$	44.5370	1.47883	0.739413	+	0.673252i	$0.235103\pi$
$908$	−129.302	−4.29103
$909$	−10.2401	−0.339643
$910$	−32.0496	−1.06243
$911$	−32.4292	−1.07443	−0.537214	−	0.843446i	$-0.680523\pi$
$911$	−32.4292	−1.07443	−0.537214	+	0.843446i	$0.680523\pi$
$912$	21.7667	0.720768
$913$	3.06257	0.101356
$914$	17.5400	0.580172
$915$	−2.21957	−0.0733766
$916$	−69.8846	−2.30905
$917$	−22.3253	−0.737245
$918$	5.02921	0.165989
$919$	43.4762	1.43415	0.717074	−	0.696997i	$-0.245481\pi$
$919$	43.4762	1.43415	0.717074	+	0.696997i	$0.245481\pi$
$920$	−4.58411	−0.151134
$921$	−14.8707	−0.490007
$922$	−16.5372	−0.544624
$923$	−13.6792	−0.450258
$924$	11.2118	0.368842
$925$	0.0824174	0.00270987
$926$	103.681	3.40718
$927$	−10.9576	−0.359895
$928$	−166.028	−5.45015
$929$	−2.48926	−0.0816699	−0.0408349	−	0.999166i	$-0.513002\pi$
$929$	−2.48926	−0.0816699	−0.0408349	+	0.999166i	$0.513002\pi$
$930$	−0.317371	−0.0104070
$931$	4.07284	0.133482
$932$	−0.743500	−0.0243541
$933$	26.8797	0.880002
$934$	−33.3741	−1.09203
$935$	4.13397	0.135195
$936$	22.4280	0.733081
$937$	−37.0461	−1.21024	−0.605122	−	0.796133i	$-0.706876\pi$
$937$	−37.0461	−1.21024	−0.605122	+	0.796133i	$0.706876\pi$
$938$	−6.14998	−0.200804
$939$	32.7560	1.06895
$940$	−95.7908	−3.12435
$941$	20.6828	0.674239	0.337119	−	0.941462i	$-0.390547\pi$
$941$	20.6828	0.674239	0.337119	+	0.941462i	$0.390547\pi$
$942$	−42.0582	−1.37033
$943$	−2.08070	−0.0677569
$944$	−25.4034	−0.826810
$945$	4.70316	0.152994
$946$	23.8441	0.775238
$947$	5.40266	0.175563	0.0877814	−	0.996140i	$-0.472022\pi$
$947$	5.40266	0.175563	0.0877814	+	0.996140i	$0.472022\pi$
$948$	35.3069	1.14672
$949$	20.2779	0.658249
$950$	−0.322153	−0.0104520
$951$	8.10496	0.262821
$952$	35.0734	1.13673
$953$	−38.9975	−1.26325	−0.631627	−	0.775272i	$-0.717613\pi$
$953$	−38.9975	−1.26325	−0.631627	+	0.775272i	$0.717613\pi$
$954$	−31.0295	−1.00462
$955$	−26.8615	−0.869219
$956$	26.3088	0.850888
$957$	−8.99969	−0.290919
$958$	−53.3065	−1.72225
$959$	37.0058	1.19498
$960$	−51.0173	−1.64658
$961$	−30.9972	−0.999910
$962$	−7.63848	−0.246275
$963$	0.334129	0.0107672
$964$	−66.0314	−2.12673
$965$	1.53310	0.0493521
$966$	−1.32969	−0.0427822
$967$	−41.4580	−1.33320	−0.666600	−	0.745416i	$-0.732251\pi$
$967$	−41.4580	−1.33320	−0.666600	+	0.745416i	$0.732251\pi$
$968$	−8.88702	−0.285640
$969$	3.02216	0.0970856
$970$	−72.2792	−2.32075
$971$	−26.4228	−0.847946	−0.423973	−	0.905675i	$-0.639365\pi$
$971$	−26.4228	−0.847946	−0.423973	+	0.905675i	$0.639365\pi$
$972$	−5.29122	−0.169716
$973$	0.197058	0.00631740
$974$	−85.1696	−2.72901
$975$	−0.185557	−0.00594259
$976$	13.4145	0.429389
$977$	32.0940	1.02678	0.513388	−	0.858156i	$-0.328390\pi$
$977$	32.0940	1.02678	0.513388	+	0.858156i	$0.328390\pi$
$978$	20.1723	0.645038
$979$	5.40932	0.172883
$980$	−29.4784	−0.941653
$981$	8.41756	0.268752
$982$	108.949	3.47672
$983$	−52.2389	−1.66616	−0.833082	−	0.553150i	$-0.813426\pi$
$983$	−52.2389	−1.66616	−0.833082	+	0.553150i	$0.813426\pi$
$984$	−79.5674	−2.53652
$985$	−27.8041	−0.885913
$986$	−45.2613	−1.44141
$987$	−17.2831	−0.550127
$988$	21.6674	0.689330
$989$	−2.05216	−0.0652549
$990$	−5.99333	−0.190480
$991$	−9.78273	−0.310759	−0.155379	−	0.987855i	$-0.549660\pi$
$991$	−9.78273	−0.310759	−0.155379	+	0.987855i	$0.549660\pi$
$992$	0.976906	0.0310168
$993$	13.6297	0.432526
$994$	31.0134	0.983687
$995$	−23.6756	−0.750566
$996$	−16.2047	−0.513467
$997$	13.5943	0.430537	0.215268	−	0.976555i	$-0.430937\pi$
$997$	13.5943	0.430537	0.215268	+	0.976555i	$0.430937\pi$
$998$	−67.6814	−2.14242
$999$	1.12092	0.0354643

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.b.1.1	✓	11
3.2	odd	2		6039.2.a.c.1.11		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.b.1.1	✓	11	1.1	even	1	trivial
6039.2.a.c.1.11		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)

\(f(q)\)	\(=\)	\(q-2.70023 q^{2} -1.00000 q^{3} +5.29122 q^{4} +2.21957 q^{5} +2.70023 q^{6} -2.11895 q^{7} -8.88702 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.70023 q^{2} -1.00000 q^{3} +5.29122 q^{4} +2.21957 q^{5} +2.70023 q^{6} -2.11895 q^{7} -8.88702 q^{8} +1.00000 q^{9} -5.99333 q^{10} +1.00000 q^{11} -5.29122 q^{12} -2.52367 q^{13} +5.72165 q^{14} -2.21957 q^{15} +13.4145 q^{16} +1.86251 q^{17} -2.70023 q^{18} -1.62262 q^{19} +11.7442 q^{20} +2.11895 q^{21} -2.70023 q^{22} +0.232397 q^{23} +8.88702 q^{24} -0.0735266 q^{25} +6.81449 q^{26} -1.00000 q^{27} -11.2118 q^{28} +8.99969 q^{29} +5.99333 q^{30} -0.0529540 q^{31} -18.4482 q^{32} -1.00000 q^{33} -5.02921 q^{34} -4.70316 q^{35} +5.29122 q^{36} -1.12092 q^{37} +4.38144 q^{38} +2.52367 q^{39} -19.7253 q^{40} -8.95321 q^{41} -5.72165 q^{42} -8.83041 q^{43} +5.29122 q^{44} +2.21957 q^{45} -0.627524 q^{46} -8.15644 q^{47} -13.4145 q^{48} -2.51004 q^{49} +0.198539 q^{50} -1.86251 q^{51} -13.3533 q^{52} +11.4915 q^{53} +2.70023 q^{54} +2.21957 q^{55} +18.8312 q^{56} +1.62262 q^{57} -24.3012 q^{58} -1.89372 q^{59} -11.7442 q^{60} +1.00000 q^{61} +0.142988 q^{62} -2.11895 q^{63} +22.9853 q^{64} -5.60146 q^{65} +2.70023 q^{66} -1.07486 q^{67} +9.85497 q^{68} -0.232397 q^{69} +12.6996 q^{70} +5.42037 q^{71} -8.88702 q^{72} -8.03508 q^{73} +3.02673 q^{74} +0.0735266 q^{75} -8.58564 q^{76} -2.11895 q^{77} -6.81449 q^{78} -6.67275 q^{79} +29.7744 q^{80} +1.00000 q^{81} +24.1757 q^{82} +3.06257 q^{83} +11.2118 q^{84} +4.13397 q^{85} +23.8441 q^{86} -8.99969 q^{87} -8.88702 q^{88} +5.40932 q^{89} -5.99333 q^{90} +5.34755 q^{91} +1.22966 q^{92} +0.0529540 q^{93} +22.0242 q^{94} -3.60151 q^{95} +18.4482 q^{96} +12.0599 q^{97} +6.77767 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) \) 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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