LMFDB - Embedded newform 2013.2.a.b.1.9

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			1.9
Root			$-1.65258$ 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)

$f(q)$	$=$	$q+1.65258 q^{2} -1.00000 q^{3} +0.731020 q^{4} +2.07534 q^{5} -1.65258 q^{6} -0.262572 q^{7} -2.09709 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.65258 q^{2} -1.00000 q^{3} +0.731020 q^{4} +2.07534 q^{5} -1.65258 q^{6} -0.262572 q^{7} -2.09709 q^{8} +1.00000 q^{9} +3.42966 q^{10} +1.00000 q^{11} -0.731020 q^{12} -6.76197 q^{13} -0.433921 q^{14} -2.07534 q^{15} -4.92765 q^{16} -4.89042 q^{17} +1.65258 q^{18} +0.504392 q^{19} +1.51711 q^{20} +0.262572 q^{21} +1.65258 q^{22} -5.31849 q^{23} +2.09709 q^{24} -0.692971 q^{25} -11.1747 q^{26} -1.00000 q^{27} -0.191945 q^{28} +2.40141 q^{29} -3.42966 q^{30} -0.494478 q^{31} -3.94915 q^{32} -1.00000 q^{33} -8.08181 q^{34} -0.544926 q^{35} +0.731020 q^{36} +5.39134 q^{37} +0.833548 q^{38} +6.76197 q^{39} -4.35217 q^{40} -1.34081 q^{41} +0.433921 q^{42} +0.0199495 q^{43} +0.731020 q^{44} +2.07534 q^{45} -8.78922 q^{46} +3.84468 q^{47} +4.92765 q^{48} -6.93106 q^{49} -1.14519 q^{50} +4.89042 q^{51} -4.94313 q^{52} -1.86186 q^{53} -1.65258 q^{54} +2.07534 q^{55} +0.550638 q^{56} -0.504392 q^{57} +3.96852 q^{58} -6.37570 q^{59} -1.51711 q^{60} +1.00000 q^{61} -0.817164 q^{62} -0.262572 q^{63} +3.32901 q^{64} -14.0334 q^{65} -1.65258 q^{66} -0.908461 q^{67} -3.57499 q^{68} +5.31849 q^{69} -0.900534 q^{70} -10.6643 q^{71} -2.09709 q^{72} +12.7169 q^{73} +8.90962 q^{74} +0.692971 q^{75} +0.368720 q^{76} -0.262572 q^{77} +11.1747 q^{78} -0.205672 q^{79} -10.2265 q^{80} +1.00000 q^{81} -2.21580 q^{82} -8.60396 q^{83} +0.191945 q^{84} -10.1493 q^{85} +0.0329681 q^{86} -2.40141 q^{87} -2.09709 q^{88} +4.11842 q^{89} +3.42966 q^{90} +1.77550 q^{91} -3.88792 q^{92} +0.494478 q^{93} +6.35365 q^{94} +1.04678 q^{95} +3.94915 q^{96} -14.6865 q^{97} -11.4541 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.65258	1.16855	0.584275	−	0.811556i	$-0.301379\pi$
$2$	1.65258	1.16855	0.584275	+	0.811556i	$0.301379\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.731020	0.365510
$5$	2.07534	0.928120	0.464060	−	0.885804i	$-0.346392\pi$
$5$	2.07534	0.928120	0.464060	+	0.885804i	$0.346392\pi$
$6$	−1.65258	−0.674663
$7$	−0.262572	−0.0992430	−0.0496215	−	0.998768i	$-0.515801\pi$
$7$	−0.262572	−0.0992430	−0.0496215	+	0.998768i	$0.515801\pi$
$8$	−2.09709	−0.741434
$9$	1.00000	0.333333
$10$	3.42966	1.08455
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.731020	−0.211027
$13$	−6.76197	−1.87543	−0.937716	−	0.347402i	$-0.887064\pi$
$13$	−6.76197	−1.87543	−0.937716	+	0.347402i	$0.887064\pi$
$14$	−0.433921	−0.115970
$15$	−2.07534	−0.535850
$16$	−4.92765	−1.23191
$17$	−4.89042	−1.18610	−0.593050	−	0.805165i	$-0.702077\pi$
$17$	−4.89042	−1.18610	−0.593050	+	0.805165i	$0.702077\pi$
$18$	1.65258	0.389517
$19$	0.504392	0.115715	0.0578577	−	0.998325i	$-0.481573\pi$
$19$	0.504392	0.115715	0.0578577	+	0.998325i	$0.481573\pi$
$20$	1.51711	0.339237
$21$	0.262572	0.0572980
$22$	1.65258	0.352331
$23$	−5.31849	−1.10898	−0.554490	−	0.832190i	$-0.687087\pi$
$23$	−5.31849	−1.10898	−0.554490	+	0.832190i	$0.687087\pi$
$24$	2.09709	0.428067
$25$	−0.692971	−0.138594
$26$	−11.1747	−2.19154
$27$	−1.00000	−0.192450
$28$	−0.191945	−0.0362743
$29$	2.40141	0.445931	0.222965	−	0.974826i	$-0.428426\pi$
$29$	2.40141	0.445931	0.222965	+	0.974826i	$0.428426\pi$
$30$	−3.42966	−0.626168
$31$	−0.494478	−0.0888108	−0.0444054	−	0.999014i	$-0.514139\pi$
$31$	−0.494478	−0.0888108	−0.0444054	+	0.999014i	$0.514139\pi$
$32$	−3.94915	−0.698118
$33$	−1.00000	−0.174078
$34$	−8.08181	−1.38602
$35$	−0.544926	−0.0921093
$36$	0.731020	0.121837
$37$	5.39134	0.886330	0.443165	−	0.896440i	$-0.353855\pi$
$37$	5.39134	0.886330	0.443165	+	0.896440i	$0.353855\pi$
$38$	0.833548	0.135219
$39$	6.76197	1.08278
$40$	−4.35217	−0.688139
$41$	−1.34081	−0.209400	−0.104700	−	0.994504i	$-0.533388\pi$
$41$	−1.34081	−0.209400	−0.104700	+	0.994504i	$0.533388\pi$
$42$	0.433921	0.0669555
$43$	0.0199495	0.00304227	0.00152113	−	0.999999i	$-0.499516\pi$
$43$	0.0199495	0.00304227	0.00152113	+	0.999999i	$0.499516\pi$
$44$	0.731020	0.110205
$45$	2.07534	0.309373
$46$	−8.78922	−1.29590
$47$	3.84468	0.560805	0.280402	−	0.959883i	$-0.409532\pi$
$47$	3.84468	0.560805	0.280402	+	0.959883i	$0.409532\pi$
$48$	4.92765	0.711245
$49$	−6.93106	−0.990151
$50$	−1.14519	−0.161954
$51$	4.89042	0.684796
$52$	−4.94313	−0.685489
$53$	−1.86186	−0.255747	−0.127873	−	0.991791i	$-0.540815\pi$
$53$	−1.86186	−0.255747	−0.127873	+	0.991791i	$0.540815\pi$
$54$	−1.65258	−0.224888
$55$	2.07534	0.279839
$56$	0.550638	0.0735821
$57$	−0.504392	−0.0668084
$58$	3.96852	0.521093
$59$	−6.37570	−0.830045	−0.415023	−	0.909811i	$-0.636226\pi$
$59$	−6.37570	−0.830045	−0.415023	+	0.909811i	$0.636226\pi$
$60$	−1.51711	−0.195858
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−0.817164	−0.103780
$63$	−0.262572	−0.0330810
$64$	3.32901	0.416127
$65$	−14.0334	−1.74063
$66$	−1.65258	−0.203418
$67$	−0.908461	−0.110986	−0.0554931	−	0.998459i	$-0.517673\pi$
$67$	−0.908461	−0.110986	−0.0554931	+	0.998459i	$0.517673\pi$
$68$	−3.57499	−0.433531
$69$	5.31849	0.640270
$70$	−0.900534	−0.107634
$71$	−10.6643	−1.26562	−0.632808	−	0.774309i	$-0.718098\pi$
$71$	−10.6643	−1.26562	−0.632808	+	0.774309i	$0.718098\pi$
$72$	−2.09709	−0.247145
$73$	12.7169	1.48841	0.744203	−	0.667954i	$-0.232830\pi$
$73$	12.7169	1.48841	0.744203	+	0.667954i	$0.232830\pi$
$74$	8.90962	1.03572
$75$	0.692971	0.0800174
$76$	0.368720	0.0422951
$77$	−0.262572	−0.0299229
$78$	11.1747	1.26528
$79$	−0.205672	−0.0231399	−0.0115699	−	0.999933i	$-0.503683\pi$
$79$	−0.205672	−0.0231399	−0.0115699	+	0.999933i	$0.503683\pi$
$80$	−10.2265	−1.14336
$81$	1.00000	0.111111
$82$	−2.21580	−0.244694
$83$	−8.60396	−0.944407	−0.472203	−	0.881490i	$-0.656541\pi$
$83$	−8.60396	−0.944407	−0.472203	+	0.881490i	$0.656541\pi$
$84$	0.191945	0.0209430
$85$	−10.1493	−1.10084
$86$	0.0329681	0.00355504
$87$	−2.40141	−0.257458
$88$	−2.09709	−0.223551
$89$	4.11842	0.436552	0.218276	−	0.975887i	$-0.429957\pi$
$89$	4.11842	0.436552	0.218276	+	0.975887i	$0.429957\pi$
$90$	3.42966	0.361518
$91$	1.77550	0.186123
$92$	−3.88792	−0.405343
$93$	0.494478	0.0512749
$94$	6.35365	0.655329
$95$	1.04678	0.107398
$96$	3.94915	0.403058
$97$	−14.6865	−1.49118	−0.745592	−	0.666403i	$-0.767833\pi$
$97$	−14.6865	−1.49118	−0.745592	+	0.666403i	$0.767833\pi$
$98$	−11.4541	−1.15704
$99$	1.00000	0.100504
$100$	−0.506575	−0.0506575
$101$	−5.08860	−0.506335	−0.253167	−	0.967423i	$-0.581472\pi$
$101$	−5.08860	−0.506335	−0.253167	+	0.967423i	$0.581472\pi$
$102$	8.08181	0.800218
$103$	−8.44470	−0.832081	−0.416040	−	0.909346i	$-0.636583\pi$
$103$	−8.44470	−0.832081	−0.416040	+	0.909346i	$0.636583\pi$
$104$	14.1805	1.39051
$105$	0.544926	0.0531793
$106$	−3.07688	−0.298853
$107$	16.1231	1.55868	0.779338	−	0.626604i	$-0.215556\pi$
$107$	16.1231	1.55868	0.779338	+	0.626604i	$0.215556\pi$
$108$	−0.731020	−0.0703424
$109$	10.3724	0.993500	0.496750	−	0.867894i	$-0.334527\pi$
$109$	10.3724	0.993500	0.496750	+	0.867894i	$0.334527\pi$
$110$	3.42966	0.327005
$111$	−5.39134	−0.511723
$112$	1.29386	0.122259
$113$	5.95031	0.559758	0.279879	−	0.960035i	$-0.409706\pi$
$113$	5.95031	0.559758	0.279879	+	0.960035i	$0.409706\pi$
$114$	−0.833548	−0.0780689
$115$	−11.0377	−1.02927
$116$	1.75548	0.162992
$117$	−6.76197	−0.625144
$118$	−10.5363	−0.969949
$119$	1.28409	0.117712
$120$	4.35217	0.397297
$121$	1.00000	0.0909091
$122$	1.65258	0.149618
$123$	1.34081	0.120897
$124$	−0.361473	−0.0324612
$125$	−11.8148	−1.05675
$126$	−0.433921	−0.0386568
$127$	−13.8310	−1.22730	−0.613652	−	0.789577i	$-0.710300\pi$
$127$	−13.8310	−1.22730	−0.613652	+	0.789577i	$0.710300\pi$
$128$	13.3998	1.18438
$129$	−0.0199495	−0.00175645
$130$	−23.1913	−2.03401
$131$	−13.6820	−1.19540	−0.597702	−	0.801718i	$-0.703919\pi$
$131$	−13.6820	−1.19540	−0.597702	+	0.801718i	$0.703919\pi$
$132$	−0.731020	−0.0636271
$133$	−0.132439	−0.0114839
$134$	−1.50130	−0.129693
$135$	−2.07534	−0.178617
$136$	10.2557	0.879415
$137$	0.0960789	0.00820857	0.00410429	−	0.999992i	$-0.498694\pi$
$137$	0.0960789	0.00820857	0.00410429	+	0.999992i	$0.498694\pi$
$138$	8.78922	0.748188
$139$	−7.83184	−0.664288	−0.332144	−	0.943229i	$-0.607772\pi$
$139$	−7.83184	−0.664288	−0.332144	+	0.943229i	$0.607772\pi$
$140$	−0.398352	−0.0336669
$141$	−3.84468	−0.323781
$142$	−17.6236	−1.47894
$143$	−6.76197	−0.565464
$144$	−4.92765	−0.410637
$145$	4.98374	0.413877
$146$	21.0158	1.73928
$147$	6.93106	0.571664
$148$	3.94117	0.323962
$149$	−19.2791	−1.57940	−0.789701	−	0.613492i	$-0.789764\pi$
$149$	−19.2791	−1.57940	−0.789701	+	0.613492i	$0.789764\pi$
$150$	1.14519	0.0935043
$151$	−3.95348	−0.321730	−0.160865	−	0.986976i	$-0.551428\pi$
$151$	−3.95348	−0.321730	−0.160865	+	0.986976i	$0.551428\pi$
$152$	−1.05776	−0.0857954
$153$	−4.89042	−0.395367
$154$	−0.433921	−0.0349664
$155$	−1.02621	−0.0824270
$156$	4.94313	0.395767
$157$	12.9922	1.03689	0.518444	−	0.855112i	$-0.326512\pi$
$157$	12.9922	1.03689	0.518444	+	0.855112i	$0.326512\pi$
$158$	−0.339889	−0.0270401
$159$	1.86186	0.147655
$160$	−8.19582	−0.647937
$161$	1.39649	0.110059
$162$	1.65258	0.129839
$163$	10.7635	0.843060	0.421530	−	0.906815i	$-0.361493\pi$
$163$	10.7635	0.843060	0.421530	+	0.906815i	$0.361493\pi$
$164$	−0.980159	−0.0765376
$165$	−2.07534	−0.161565
$166$	−14.2187	−1.10359
$167$	−0.488625	−0.0378109	−0.0189055	−	0.999821i	$-0.506018\pi$
$167$	−0.488625	−0.0378109	−0.0189055	+	0.999821i	$0.506018\pi$
$168$	−0.550638	−0.0424826
$169$	32.7242	2.51725
$170$	−16.7725	−1.28639
$171$	0.504392	0.0385718
$172$	0.0145835	0.00111198
$173$	12.5382	0.953259	0.476629	−	0.879104i	$-0.341858\pi$
$173$	12.5382	0.953259	0.476629	+	0.879104i	$0.341858\pi$
$174$	−3.96852	−0.300853
$175$	0.181955	0.0137545
$176$	−4.92765	−0.371436
$177$	6.37570	0.479227
$178$	6.80602	0.510133
$179$	13.9371	1.04171	0.520853	−	0.853647i	$-0.325614\pi$
$179$	13.9371	1.04171	0.520853	+	0.853647i	$0.325614\pi$
$180$	1.51711	0.113079
$181$	10.2705	0.763399	0.381700	−	0.924286i	$-0.375339\pi$
$181$	10.2705	0.763399	0.381700	+	0.924286i	$0.375339\pi$
$182$	2.93416	0.217495
$183$	−1.00000	−0.0739221
$184$	11.1533	0.822236
$185$	11.1889	0.822621
$186$	0.817164	0.0599174
$187$	−4.89042	−0.357623
$188$	2.81054	0.204980
$189$	0.262572	0.0190993
$190$	1.72989	0.125500
$191$	3.41846	0.247351	0.123676	−	0.992323i	$-0.460532\pi$
$191$	3.41846	0.247351	0.123676	+	0.992323i	$0.460532\pi$
$192$	−3.32901	−0.240251
$193$	−14.3567	−1.03342	−0.516708	−	0.856162i	$-0.672843\pi$
$193$	−14.3567	−1.03342	−0.516708	+	0.856162i	$0.672843\pi$
$194$	−24.2705	−1.74252
$195$	14.0334	1.00495
$196$	−5.06674	−0.361910
$197$	−9.66349	−0.688495	−0.344248	−	0.938879i	$-0.611866\pi$
$197$	−9.66349	−0.688495	−0.344248	+	0.938879i	$0.611866\pi$
$198$	1.65258	0.117444
$199$	23.6197	1.67436	0.837178	−	0.546930i	$-0.184204\pi$
$199$	23.6197	1.67436	0.837178	+	0.546930i	$0.184204\pi$
$200$	1.45322	0.102758
$201$	0.908461	0.0640779
$202$	−8.40932	−0.591677
$203$	−0.630544	−0.0442555
$204$	3.57499	0.250299
$205$	−2.78264	−0.194348
$206$	−13.9555	−0.972328
$207$	−5.31849	−0.369660
$208$	33.3206	2.31037
$209$	0.504392	0.0348895
$210$	0.900534	0.0621427
$211$	8.37901	0.576835	0.288417	−	0.957505i	$-0.406871\pi$
$211$	8.37901	0.576835	0.288417	+	0.957505i	$0.406871\pi$
$212$	−1.36106	−0.0934779
$213$	10.6643	0.730704
$214$	26.6447	1.82139
$215$	0.0414019	0.00282359
$216$	2.09709	0.142689
$217$	0.129836	0.00881385
$218$	17.1413	1.16096
$219$	−12.7169	−0.859331
$220$	1.51711	0.102284
$221$	33.0689	2.22445
$222$	−8.90962	−0.597974
$223$	−21.0910	−1.41236	−0.706179	−	0.708033i	$-0.749583\pi$
$223$	−21.0910	−1.41236	−0.706179	+	0.708033i	$0.749583\pi$
$224$	1.03694	0.0692833
$225$	−0.692971	−0.0461981
$226$	9.83336	0.654105
$227$	4.84415	0.321518	0.160759	−	0.986994i	$-0.448606\pi$
$227$	4.84415	0.321518	0.160759	+	0.986994i	$0.448606\pi$
$228$	−0.368720	−0.0244191
$229$	23.1631	1.53066	0.765331	−	0.643637i	$-0.222575\pi$
$229$	23.1631	1.53066	0.765331	+	0.643637i	$0.222575\pi$
$230$	−18.2406	−1.20275
$231$	0.262572	0.0172760
$232$	−5.03598	−0.330628
$233$	13.8332	0.906244	0.453122	−	0.891449i	$-0.350310\pi$
$233$	13.8332	0.906244	0.453122	+	0.891449i	$0.350310\pi$
$234$	−11.1747	−0.730512
$235$	7.97902	0.520494
$236$	−4.66076	−0.303390
$237$	0.205672	0.0133598
$238$	2.12206	0.137553
$239$	23.8922	1.54546	0.772728	−	0.634737i	$-0.218892\pi$
$239$	23.8922	1.54546	0.772728	+	0.634737i	$0.218892\pi$
$240$	10.2265	0.660120
$241$	−17.5635	−1.13136	−0.565682	−	0.824623i	$-0.691387\pi$
$241$	−17.5635	−1.13136	−0.565682	+	0.824623i	$0.691387\pi$
$242$	1.65258	0.106232
$243$	−1.00000	−0.0641500
$244$	0.731020	0.0467987
$245$	−14.3843	−0.918978
$246$	2.21580	0.141274
$247$	−3.41068	−0.217017
$248$	1.03696	0.0658473
$249$	8.60396	0.545254
$250$	−19.5250	−1.23487
$251$	−3.16092	−0.199516	−0.0997578	−	0.995012i	$-0.531807\pi$
$251$	−3.16092	−0.199516	−0.0997578	+	0.995012i	$0.531807\pi$
$252$	−0.191945	−0.0120914
$253$	−5.31849	−0.334370
$254$	−22.8569	−1.43417
$255$	10.1493	0.635572
$256$	15.4861	0.967884
$257$	−3.27273	−0.204147	−0.102074	−	0.994777i	$-0.532548\pi$
$257$	−3.27273	−0.204147	−0.102074	+	0.994777i	$0.532548\pi$
$258$	−0.0329681	−0.00205250
$259$	−1.41562	−0.0879621
$260$	−10.2587	−0.636216
$261$	2.40141	0.148644
$262$	−22.6106	−1.39689
$263$	−30.9365	−1.90763	−0.953813	−	0.300400i	$-0.902880\pi$
$263$	−30.9365	−1.90763	−0.953813	+	0.300400i	$0.902880\pi$
$264$	2.09709	0.129067
$265$	−3.86400	−0.237363
$266$	−0.218867	−0.0134196
$267$	−4.11842	−0.252043
$268$	−0.664103	−0.0405665
$269$	26.6425	1.62442	0.812210	−	0.583365i	$-0.198264\pi$
$269$	26.6425	1.62442	0.812210	+	0.583365i	$0.198264\pi$
$270$	−3.42966	−0.208723
$271$	−22.4391	−1.36308	−0.681539	−	0.731782i	$-0.738689\pi$
$271$	−22.4391	−1.36308	−0.681539	+	0.731782i	$0.738689\pi$
$272$	24.0983	1.46117
$273$	−1.77550	−0.107458
$274$	0.158778	0.00959213
$275$	−0.692971	−0.0417877
$276$	3.88792	0.234025
$277$	−5.20571	−0.312781	−0.156390	−	0.987695i	$-0.549986\pi$
$277$	−5.20571	−0.312781	−0.156390	+	0.987695i	$0.549986\pi$
$278$	−12.9427	−0.776254
$279$	−0.494478	−0.0296036
$280$	1.14276	0.0682930
$281$	4.65546	0.277721	0.138861	−	0.990312i	$-0.455656\pi$
$281$	4.65546	0.277721	0.138861	+	0.990312i	$0.455656\pi$
$282$	−6.35365	−0.378354
$283$	0.572899	0.0340553	0.0170276	−	0.999855i	$-0.494580\pi$
$283$	0.572899	0.0340553	0.0170276	+	0.999855i	$0.494580\pi$
$284$	−7.79579	−0.462595
$285$	−1.04678	−0.0620061
$286$	−11.1747	−0.660773
$287$	0.352060	0.0207814
$288$	−3.94915	−0.232706
$289$	6.91620	0.406835
$290$	8.23603	0.483636
$291$	14.6865	0.860936
$292$	9.29633	0.544027
$293$	−12.8739	−0.752101	−0.376050	−	0.926599i	$-0.622718\pi$
$293$	−12.8739	−0.752101	−0.376050	+	0.926599i	$0.622718\pi$
$294$	11.4541	0.668018
$295$	−13.2317	−0.770381
$296$	−11.3061	−0.657155
$297$	−1.00000	−0.0580259
$298$	−31.8602	−1.84561
$299$	35.9634	2.07982
$300$	0.506575	0.0292471
$301$	−0.00523818	−0.000301924 0
$302$	−6.53344	−0.375957
$303$	5.08860	0.292332
$304$	−2.48547	−0.142551
$305$	2.07534	0.118834
$306$	−8.08181	−0.462006
$307$	−23.9320	−1.36587	−0.682935	−	0.730479i	$-0.739297\pi$
$307$	−23.9320	−1.36587	−0.682935	+	0.730479i	$0.739297\pi$
$308$	−0.191945	−0.0109371
$309$	8.44470	0.480402
$310$	−1.69589	−0.0963201
$311$	16.5518	0.938567	0.469283	−	0.883048i	$-0.344512\pi$
$311$	16.5518	0.938567	0.469283	+	0.883048i	$0.344512\pi$
$312$	−14.1805	−0.802811
$313$	1.51244	0.0854883	0.0427441	−	0.999086i	$-0.486390\pi$
$313$	1.51244	0.0854883	0.0427441	+	0.999086i	$0.486390\pi$
$314$	21.4706	1.21166
$315$	−0.544926	−0.0307031
$316$	−0.150350	−0.00845786
$317$	−6.84400	−0.384397	−0.192199	−	0.981356i	$-0.561562\pi$
$317$	−6.84400	−0.384397	−0.192199	+	0.981356i	$0.561562\pi$
$318$	3.07688	0.172543
$319$	2.40141	0.134453
$320$	6.90883	0.386215
$321$	−16.1231	−0.899902
$322$	2.30780	0.128609
$323$	−2.46669	−0.137250
$324$	0.731020	0.0406122
$325$	4.68585	0.259924
$326$	17.7875	0.985158
$327$	−10.3724	−0.573598
$328$	2.81180	0.155256
$329$	−1.00951	−0.0556559
$330$	−3.42966	−0.188797
$331$	9.43889	0.518808	0.259404	−	0.965769i	$-0.416474\pi$
$331$	9.43889	0.518808	0.259404	+	0.965769i	$0.416474\pi$
$332$	−6.28966	−0.345190
$333$	5.39134	0.295443
$334$	−0.807491	−0.0441840
$335$	−1.88536	−0.103008
$336$	−1.29386	−0.0705861
$337$	24.6203	1.34115	0.670576	−	0.741841i	$-0.266047\pi$
$337$	24.6203	1.34115	0.670576	+	0.741841i	$0.266047\pi$
$338$	54.0794	2.94153
$339$	−5.95031	−0.323176
$340$	−7.41932	−0.402369
$341$	−0.494478	−0.0267775
$342$	0.833548	0.0450731
$343$	3.65791	0.197508
$344$	−0.0418359	−0.00225564
$345$	11.0377	0.594247
$346$	20.7203	1.11393
$347$	−27.5082	−1.47672	−0.738358	−	0.674409i	$-0.764398\pi$
$347$	−27.5082	−1.47672	−0.738358	+	0.674409i	$0.764398\pi$
$348$	−1.75548	−0.0941035
$349$	−13.6280	−0.729491	−0.364746	−	0.931107i	$-0.618844\pi$
$349$	−13.6280	−0.729491	−0.364746	+	0.931107i	$0.618844\pi$
$350$	0.300695	0.0160728
$351$	6.76197	0.360927
$352$	−3.94915	−0.210490
$353$	6.06814	0.322974	0.161487	−	0.986875i	$-0.448371\pi$
$353$	6.06814	0.322974	0.161487	+	0.986875i	$0.448371\pi$
$354$	10.5363	0.560001
$355$	−22.1320	−1.17464
$356$	3.01065	0.159564
$357$	−1.28409	−0.0679611
$358$	23.0321	1.21729
$359$	−13.2824	−0.701018	−0.350509	−	0.936559i	$-0.613991\pi$
$359$	−13.2824	−0.701018	−0.350509	+	0.936559i	$0.613991\pi$
$360$	−4.35217	−0.229380
$361$	−18.7456	−0.986610
$362$	16.9728	0.892071
$363$	−1.00000	−0.0524864
$364$	1.29793	0.0680299
$365$	26.3920	1.38142
$366$	−1.65258	−0.0863817
$367$	17.7964	0.928963	0.464482	−	0.885583i	$-0.346241\pi$
$367$	17.7964	0.928963	0.464482	+	0.885583i	$0.346241\pi$
$368$	26.2076	1.36617
$369$	−1.34081	−0.0697998
$370$	18.4905	0.961274
$371$	0.488874	0.0253811
$372$	0.361473	0.0187415
$373$	−27.8008	−1.43947	−0.719735	−	0.694249i	$-0.755737\pi$
$373$	−27.8008	−1.43947	−0.719735	+	0.694249i	$0.755737\pi$
$374$	−8.08181	−0.417900
$375$	11.8148	0.610116
$376$	−8.06265	−0.415800
$377$	−16.2383	−0.836313
$378$	0.433921	0.0223185
$379$	−18.7058	−0.960852	−0.480426	−	0.877035i	$-0.659518\pi$
$379$	−18.7058	−0.960852	−0.480426	+	0.877035i	$0.659518\pi$
$380$	0.765220	0.0392549
$381$	13.8310	0.708584
$382$	5.64928	0.289042
$383$	−8.89735	−0.454633	−0.227317	−	0.973821i	$-0.572995\pi$
$383$	−8.89735	−0.454633	−0.227317	+	0.973821i	$0.572995\pi$
$384$	−13.3998	−0.683804
$385$	−0.544926	−0.0277720
$386$	−23.7255	−1.20760
$387$	0.0199495	0.00101409
$388$	−10.7361	−0.545042
$389$	35.0307	1.77613	0.888064	−	0.459721i	$-0.152050\pi$
$389$	35.0307	1.77613	0.888064	+	0.459721i	$0.152050\pi$
$390$	23.1913	1.17434
$391$	26.0096	1.31536
$392$	14.5351	0.734131
$393$	13.6820	0.690167
$394$	−15.9697	−0.804541
$395$	−0.426839	−0.0214766
$396$	0.731020	0.0367351
$397$	28.7529	1.44307	0.721533	−	0.692380i	$-0.243438\pi$
$397$	28.7529	1.44307	0.721533	+	0.692380i	$0.243438\pi$
$398$	39.0334	1.95657
$399$	0.132439	0.00663026
$400$	3.41472	0.170736
$401$	22.3488	1.11605	0.558023	−	0.829825i	$-0.311560\pi$
$401$	22.3488	1.11605	0.558023	+	0.829825i	$0.311560\pi$
$402$	1.50130	0.0748783
$403$	3.34364	0.166559
$404$	−3.71987	−0.185070
$405$	2.07534	0.103124
$406$	−1.04202	−0.0517148
$407$	5.39134	0.267239
$408$	−10.2557	−0.507731
$409$	7.93787	0.392502	0.196251	−	0.980554i	$-0.437123\pi$
$409$	7.93787	0.392502	0.196251	+	0.980554i	$0.437123\pi$
$410$	−4.59853	−0.227105
$411$	−0.0960789	−0.00473922
$412$	−6.17324	−0.304134
$413$	1.67408	0.0823761
$414$	−8.78922	−0.431967
$415$	−17.8561	−0.876523
$416$	26.7040	1.30927
$417$	7.83184	0.383527
$418$	0.833548	0.0407702
$419$	0.545137	0.0266317	0.0133158	−	0.999911i	$-0.495761\pi$
$419$	0.545137	0.0266317	0.0133158	+	0.999911i	$0.495761\pi$
$420$	0.398352	0.0194376
$421$	−8.43534	−0.411113	−0.205557	−	0.978645i	$-0.565900\pi$
$421$	−8.43534	−0.411113	−0.205557	+	0.978645i	$0.565900\pi$
$422$	13.8470	0.674060
$423$	3.84468	0.186935
$424$	3.90450	0.189619
$425$	3.38892	0.164387
$426$	17.6236	0.853864
$427$	−0.262572	−0.0127068
$428$	11.7863	0.569711
$429$	6.76197	0.326471
$430$	0.0684200	0.00329950
$431$	41.1939	1.98424	0.992120	−	0.125294i	$-0.0399873\pi$
$431$	41.1939	1.98424	0.992120	+	0.125294i	$0.0399873\pi$
$432$	4.92765	0.237082
$433$	−1.36482	−0.0655891	−0.0327945	−	0.999462i	$-0.510441\pi$
$433$	−1.36482	−0.0655891	−0.0327945	+	0.999462i	$0.510441\pi$
$434$	0.214564	0.0102994
$435$	−4.98374	−0.238952
$436$	7.58246	0.363134
$437$	−2.68260	−0.128326
$438$	−21.0158	−1.00417
$439$	−28.5432	−1.36229	−0.681147	−	0.732146i	$-0.738519\pi$
$439$	−28.5432	−1.36229	−0.681147	+	0.732146i	$0.738519\pi$
$440$	−4.35217	−0.207482
$441$	−6.93106	−0.330050
$442$	54.6489	2.59938
$443$	−7.86768	−0.373805	−0.186902	−	0.982378i	$-0.559845\pi$
$443$	−7.86768	−0.373805	−0.186902	+	0.982378i	$0.559845\pi$
$444$	−3.94117	−0.187040
$445$	8.54712	0.405172
$446$	−34.8546	−1.65041
$447$	19.2791	0.911868
$448$	−0.874106	−0.0412976
$449$	37.5671	1.77290	0.886451	−	0.462823i	$-0.153164\pi$
$449$	37.5671	1.77290	0.886451	+	0.462823i	$0.153164\pi$
$450$	−1.14519	−0.0539848
$451$	−1.34081	−0.0631363
$452$	4.34979	0.204597
$453$	3.95348	0.185751
$454$	8.00535	0.375710
$455$	3.68477	0.172745
$456$	1.05776	0.0495340
$457$	−18.7266	−0.875994	−0.437997	−	0.898976i	$-0.644312\pi$
$457$	−18.7266	−0.875994	−0.437997	+	0.898976i	$0.644312\pi$
$458$	38.2789	1.78865
$459$	4.89042	0.228265
$460$	−8.06874	−0.376207
$461$	4.51046	0.210073	0.105037	−	0.994468i	$-0.466504\pi$
$461$	4.51046	0.210073	0.105037	+	0.994468i	$0.466504\pi$
$462$	0.433921	0.0201879
$463$	−14.1881	−0.659377	−0.329689	−	0.944090i	$-0.606944\pi$
$463$	−14.1881	−0.659377	−0.329689	+	0.944090i	$0.606944\pi$
$464$	−11.8333	−0.549348
$465$	1.02621	0.0475893
$466$	22.8605	1.05899
$467$	−5.94441	−0.275074	−0.137537	−	0.990497i	$-0.543919\pi$
$467$	−5.94441	−0.275074	−0.137537	+	0.990497i	$0.543919\pi$
$468$	−4.94313	−0.228496
$469$	0.238537	0.0110146
$470$	13.1860	0.608223
$471$	−12.9922	−0.598647
$472$	13.3704	0.615423
$473$	0.0199495	0.000917278 0
$474$	0.339889	0.0156116
$475$	−0.349529	−0.0160375
$476$	0.938693	0.0430249
$477$	−1.86186	−0.0852489
$478$	39.4837	1.80594
$479$	−20.2705	−0.926181	−0.463090	−	0.886311i	$-0.653259\pi$
$479$	−20.2705	−0.926181	−0.463090	+	0.886311i	$0.653259\pi$
$480$	8.19582	0.374086
$481$	−36.4561	−1.66225
$482$	−29.0251	−1.32206
$483$	−1.39649	−0.0635423
$484$	0.731020	0.0332282
$485$	−30.4794	−1.38400
$486$	−1.65258	−0.0749625
$487$	−29.2706	−1.32638	−0.663190	−	0.748451i	$-0.730798\pi$
$487$	−29.2706	−1.32638	−0.663190	+	0.748451i	$0.730798\pi$
$488$	−2.09709	−0.0949309
$489$	−10.7635	−0.486741
$490$	−23.7712	−1.07387
$491$	23.6940	1.06929	0.534647	−	0.845076i	$-0.320445\pi$
$491$	23.6940	1.06929	0.534647	+	0.845076i	$0.320445\pi$
$492$	0.980159	0.0441890
$493$	−11.7439	−0.528919
$494$	−5.63643	−0.253595
$495$	2.07534	0.0932795
$496$	2.43661	0.109407
$497$	2.80014	0.125603
$498$	14.2187	0.637156
$499$	−39.5300	−1.76960	−0.884802	−	0.465967i	$-0.845707\pi$
$499$	−39.5300	−1.76960	−0.884802	+	0.465967i	$0.845707\pi$
$500$	−8.63688	−0.386253
$501$	0.488625	0.0218301
$502$	−5.22368	−0.233144
$503$	22.2417	0.991709	0.495854	−	0.868406i	$-0.334855\pi$
$503$	22.2417	0.991709	0.495854	+	0.868406i	$0.334855\pi$
$504$	0.550638	0.0245274
$505$	−10.5606	−0.469939
$506$	−8.78922	−0.390728
$507$	−32.7242	−1.45333
$508$	−10.1107	−0.448592
$509$	0.0210701	0.000933914 0	0.000466957	−	1.00000i	$-0.499851\pi$
$509$	0.0210701	0.000933914 0	0.000466957		1.00000i	$0.499851\pi$
$510$	16.7725	0.742698
$511$	−3.33912	−0.147714
$512$	−1.20743	−0.0533615
$513$	−0.504392	−0.0222695
$514$	−5.40844	−0.238556
$515$	−17.5256	−0.772270
$516$	−0.0145835	−0.000642001 0
$517$	3.84468	0.169089
$518$	−2.33942	−0.102788
$519$	−12.5382	−0.550364
$520$	29.4293	1.29056
$521$	26.7701	1.17282	0.586410	−	0.810014i	$-0.300541\pi$
$521$	26.7701	1.17282	0.586410	+	0.810014i	$0.300541\pi$
$522$	3.96852	0.173698
$523$	−36.1675	−1.58149	−0.790747	−	0.612143i	$-0.790308\pi$
$523$	−36.1675	−1.58149	−0.790747	+	0.612143i	$0.790308\pi$
$524$	−10.0018	−0.436932
$525$	−0.181955	−0.00794116
$526$	−51.1250	−2.22916
$527$	2.41820	0.105339
$528$	4.92765	0.214448
$529$	5.28628	0.229838
$530$	−6.38556	−0.277371
$531$	−6.37570	−0.276682
$532$	−0.0968157	−0.00419749
$533$	9.06652	0.392715
$534$	−6.80602	−0.294525
$535$	33.4608	1.44664
$536$	1.90513	0.0822889
$537$	−13.9371	−0.601429
$538$	44.0288	1.89822
$539$	−6.93106	−0.298542
$540$	−1.51711	−0.0652861
$541$	40.4469	1.73895	0.869475	−	0.493977i	$-0.164457\pi$
$541$	40.4469	1.73895	0.869475	+	0.493977i	$0.164457\pi$
$542$	−37.0824	−1.59283
$543$	−10.2705	−0.440749
$544$	19.3130	0.828038
$545$	21.5263	0.922087
$546$	−2.93416	−0.125571
$547$	−1.77069	−0.0757092	−0.0378546	−	0.999283i	$-0.512052\pi$
$547$	−1.77069	−0.0757092	−0.0378546	+	0.999283i	$0.512052\pi$
$548$	0.0702355	0.00300031
$549$	1.00000	0.0426790
$550$	−1.14519	−0.0488311
$551$	1.21125	0.0516011
$552$	−11.1533	−0.474718
$553$	0.0540037	0.00229647
$554$	−8.60285	−0.365500
$555$	−11.1889	−0.474940
$556$	−5.72523	−0.242804
$557$	−30.2723	−1.28268	−0.641339	−	0.767257i	$-0.721621\pi$
$557$	−30.2723	−1.28268	−0.641339	+	0.767257i	$0.721621\pi$
$558$	−0.817164	−0.0345933
$559$	−0.134898	−0.00570557
$560$	2.68521	0.113471
$561$	4.89042	0.206474
$562$	7.69351	0.324531
$563$	−38.2543	−1.61223	−0.806114	−	0.591760i	$-0.798433\pi$
$563$	−38.2543	−1.61223	−0.806114	+	0.591760i	$0.798433\pi$
$564$	−2.81054	−0.118345
$565$	12.3489	0.519522
$566$	0.946761	0.0397953
$567$	−0.262572	−0.0110270
$568$	22.3639	0.938370
$569$	1.67424	0.0701878	0.0350939	−	0.999384i	$-0.488827\pi$
$569$	1.67424	0.0701878	0.0350939	+	0.999384i	$0.488827\pi$
$570$	−1.72989	−0.0724573
$571$	−36.5177	−1.52822	−0.764109	−	0.645087i	$-0.776821\pi$
$571$	−36.5177	−1.52822	−0.764109	+	0.645087i	$0.776821\pi$
$572$	−4.94313	−0.206683
$573$	−3.41846	−0.142808
$574$	0.581807	0.0242841
$575$	3.68556	0.153698
$576$	3.32901	0.138709
$577$	−40.0890	−1.66893	−0.834464	−	0.551062i	$-0.814223\pi$
$577$	−40.0890	−1.66893	−0.834464	+	0.551062i	$0.814223\pi$
$578$	11.4296	0.475407
$579$	14.3567	0.596643
$580$	3.64321	0.151276
$581$	2.25916	0.0937257
$582$	24.2705	1.00605
$583$	−1.86186	−0.0771105
$584$	−26.6686	−1.10355
$585$	−14.0334	−0.580208
$586$	−21.2751	−0.878867
$587$	−27.1337	−1.11993	−0.559964	−	0.828517i	$-0.689185\pi$
$587$	−27.1337	−1.11993	−0.559964	+	0.828517i	$0.689185\pi$
$588$	5.06674	0.208949
$589$	−0.249411	−0.0102768
$590$	−21.8665	−0.900229
$591$	9.66349	0.397503
$592$	−26.5666	−1.09188
$593$	−7.06327	−0.290054	−0.145027	−	0.989428i	$-0.546327\pi$
$593$	−7.06327	−0.290054	−0.145027	+	0.989428i	$0.546327\pi$
$594$	−1.65258	−0.0678062
$595$	2.66492	0.109251
$596$	−14.0934	−0.577287
$597$	−23.6197	−0.966690
$598$	59.4324	2.43037
$599$	2.58423	0.105589	0.0527943	−	0.998605i	$-0.483187\pi$
$599$	2.58423	0.105589	0.0527943	+	0.998605i	$0.483187\pi$
$600$	−1.45322	−0.0593276
$601$	−10.2227	−0.416994	−0.208497	−	0.978023i	$-0.566857\pi$
$601$	−10.2227	−0.416994	−0.208497	+	0.978023i	$0.566857\pi$
$602$	−0.00865651	−0.000352813 0
$603$	−0.908461	−0.0369954
$604$	−2.89007	−0.117595
$605$	2.07534	0.0843745
$606$	8.40932	0.341605
$607$	−14.2713	−0.579254	−0.289627	−	0.957140i	$-0.593531\pi$
$607$	−14.2713	−0.579254	−0.289627	+	0.957140i	$0.593531\pi$
$608$	−1.99192	−0.0807830
$609$	0.630544	0.0255509
$610$	3.42966	0.138863
$611$	−25.9976	−1.05175
$612$	−3.57499	−0.144510
$613$	40.7892	1.64746	0.823731	−	0.566981i	$-0.191889\pi$
$613$	40.7892	1.64746	0.823731	+	0.566981i	$0.191889\pi$
$614$	−39.5495	−1.59609
$615$	2.78264	0.112207
$616$	0.550638	0.0221858
$617$	36.8089	1.48187	0.740936	−	0.671576i	$-0.234382\pi$
$617$	36.8089	1.48187	0.740936	+	0.671576i	$0.234382\pi$
$618$	13.9555	0.561374
$619$	10.9755	0.441141	0.220570	−	0.975371i	$-0.429208\pi$
$619$	10.9755	0.441141	0.220570	+	0.975371i	$0.429208\pi$
$620$	−0.750178	−0.0301279
$621$	5.31849	0.213423
$622$	27.3532	1.09676
$623$	−1.08138	−0.0433247
$624$	−33.3206	−1.33389
$625$	−21.0549	−0.842197
$626$	2.49943	0.0998974
$627$	−0.504392	−0.0201435
$628$	9.49752	0.378992
$629$	−26.3659	−1.05128
$630$	−0.900534	−0.0358781
$631$	−47.0160	−1.87168	−0.935839	−	0.352428i	$-0.885356\pi$
$631$	−47.0160	−1.87168	−0.935839	+	0.352428i	$0.885356\pi$
$632$	0.431313	0.0171567
$633$	−8.37901	−0.333036
$634$	−11.3103	−0.449187
$635$	−28.7040	−1.13909
$636$	1.36106	0.0539695
$637$	46.8676	1.85696
$638$	3.96852	0.157115
$639$	−10.6643	−0.421872
$640$	27.8090	1.09925
$641$	16.3549	0.645981	0.322990	−	0.946402i	$-0.395312\pi$
$641$	16.3549	0.645981	0.322990	+	0.946402i	$0.395312\pi$
$642$	−26.6447	−1.05158
$643$	−33.4231	−1.31808	−0.659038	−	0.752109i	$-0.729036\pi$
$643$	−33.4231	−1.31808	−0.659038	+	0.752109i	$0.729036\pi$
$644$	1.02086	0.0402275
$645$	−0.0414019	−0.00163020
$646$	−4.07640	−0.160384
$647$	14.6868	0.577398	0.288699	−	0.957420i	$-0.406777\pi$
$647$	14.6868	0.577398	0.288699	+	0.957420i	$0.406777\pi$
$648$	−2.09709	−0.0823815
$649$	−6.37570	−0.250268
$650$	7.74374	0.303734
$651$	−0.129836	−0.00508868
$652$	7.86830	0.308147
$653$	39.3222	1.53880	0.769399	−	0.638768i	$-0.220556\pi$
$653$	39.3222	1.53880	0.769399	+	0.638768i	$0.220556\pi$
$654$	−17.1413	−0.670278
$655$	−28.3948	−1.10948
$656$	6.60705	0.257962
$657$	12.7169	0.496135
$658$	−1.66829	−0.0650367
$659$	12.0825	0.470667	0.235333	−	0.971915i	$-0.424382\pi$
$659$	12.0825	0.470667	0.235333	+	0.971915i	$0.424382\pi$
$660$	−1.51711	−0.0590535
$661$	15.0735	0.586289	0.293145	−	0.956068i	$-0.405298\pi$
$661$	15.0735	0.586289	0.293145	+	0.956068i	$0.405298\pi$
$662$	15.5985	0.606254
$663$	−33.0689	−1.28429
$664$	18.0433	0.700215
$665$	−0.274856	−0.0106585
$666$	8.90962	0.345241
$667$	−12.7719	−0.494529
$668$	−0.357194	−0.0138203
$669$	21.0910	0.815426
$670$	−3.11572	−0.120371
$671$	1.00000	0.0386046
$672$	−1.03694	−0.0400007
$673$	14.4508	0.557036	0.278518	−	0.960431i	$-0.410157\pi$
$673$	14.4508	0.557036	0.278518	+	0.960431i	$0.410157\pi$
$674$	40.6869	1.56720
$675$	0.692971	0.0266725
$676$	23.9220	0.920078
$677$	−26.3022	−1.01088	−0.505439	−	0.862863i	$-0.668669\pi$
$677$	−26.3022	−1.01088	−0.505439	+	0.862863i	$0.668669\pi$
$678$	−9.83336	−0.377648
$679$	3.85626	0.147990
$680$	21.2840	0.816202
$681$	−4.84415	−0.185628
$682$	−0.817164	−0.0312908
$683$	−0.516662	−0.0197695	−0.00988476	−	0.999951i	$-0.503146\pi$
$683$	−0.516662	−0.0197695	−0.00988476	+	0.999951i	$0.503146\pi$
$684$	0.368720	0.0140984
$685$	0.199396	0.00761853
$686$	6.04498	0.230799
$687$	−23.1631	−0.883728
$688$	−0.0983041	−0.00374781
$689$	12.5899	0.479636
$690$	18.2406	0.694408
$691$	−10.9165	−0.415282	−0.207641	−	0.978205i	$-0.566579\pi$
$691$	−10.9165	−0.415282	−0.207641	+	0.978205i	$0.566579\pi$
$692$	9.16564	0.348425
$693$	−0.262572	−0.00997429
$694$	−45.4594	−1.72562
$695$	−16.2537	−0.616538
$696$	5.03598	0.190888
$697$	6.55713	0.248369
$698$	−22.5214	−0.852447
$699$	−13.8332	−0.523220
$700$	0.133013	0.00502740
$701$	−38.4542	−1.45240	−0.726198	−	0.687486i	$-0.758714\pi$
$701$	−38.4542	−1.45240	−0.726198	+	0.687486i	$0.758714\pi$
$702$	11.1747	0.421761
$703$	2.71935	0.102562
$704$	3.32901	0.125467
$705$	−7.97902	−0.300507
$706$	10.0281	0.377412
$707$	1.33612	0.0502501
$708$	4.66076	0.175162
$709$	10.9555	0.411444	0.205722	−	0.978610i	$-0.434046\pi$
$709$	10.9555	0.411444	0.205722	+	0.978610i	$0.434046\pi$
$710$	−36.5748	−1.37263
$711$	−0.205672	−0.00771330
$712$	−8.63671	−0.323674
$713$	2.62987	0.0984895
$714$	−2.12206	−0.0794160
$715$	−14.0334	−0.524818
$716$	10.1883	0.380754
$717$	−23.8922	−0.892270
$718$	−21.9502	−0.819175
$719$	3.39899	0.126761	0.0633804	−	0.997989i	$-0.479812\pi$
$719$	3.39899	0.126761	0.0633804	+	0.997989i	$0.479812\pi$
$720$	−10.2265	−0.381121
$721$	2.21734	0.0825782
$722$	−30.9786	−1.15290
$723$	17.5635	0.653193
$724$	7.50793	0.279030
$725$	−1.66411	−0.0618034
$726$	−1.65258	−0.0613330
$727$	−37.0284	−1.37331	−0.686655	−	0.726984i	$-0.740922\pi$
$727$	−37.0284	−1.37331	−0.686655	+	0.726984i	$0.740922\pi$
$728$	−3.72340	−0.137998
$729$	1.00000	0.0370370
$730$	43.6148	1.61426
$731$	−0.0975613	−0.00360844
$732$	−0.731020	−0.0270193
$733$	−22.0316	−0.813755	−0.406878	−	0.913483i	$-0.633382\pi$
$733$	−22.0316	−0.813755	−0.406878	+	0.913483i	$0.633382\pi$
$734$	29.4099	1.08554
$735$	14.3843	0.530572
$736$	21.0035	0.774199
$737$	−0.908461	−0.0334636
$738$	−2.21580	−0.0815646
$739$	−22.4004	−0.824011	−0.412006	−	0.911181i	$-0.635172\pi$
$739$	−22.4004	−0.824011	−0.412006	+	0.911181i	$0.635172\pi$
$740$	8.17927	0.300676
$741$	3.41068	0.125295
$742$	0.807903	0.0296590
$743$	−16.4093	−0.601998	−0.300999	−	0.953624i	$-0.597320\pi$
$743$	−16.4093	−0.601998	−0.300999	+	0.953624i	$0.597320\pi$
$744$	−1.03696	−0.0380170
$745$	−40.0106	−1.46587
$746$	−45.9430	−1.68209
$747$	−8.60396	−0.314802
$748$	−3.57499	−0.130715
$749$	−4.23347	−0.154688
$750$	19.5250	0.712951
$751$	15.1005	0.551025	0.275512	−	0.961298i	$-0.411153\pi$
$751$	15.1005	0.551025	0.275512	+	0.961298i	$0.411153\pi$
$752$	−18.9453	−0.690862
$753$	3.16092	0.115190
$754$	−26.8350	−0.977274
$755$	−8.20481	−0.298604
$756$	0.191945	0.00698099
$757$	−8.54064	−0.310415	−0.155207	−	0.987882i	$-0.549605\pi$
$757$	−8.54064	−0.310415	−0.155207	+	0.987882i	$0.549605\pi$
$758$	−30.9128	−1.12280
$759$	5.31849	0.193049
$760$	−2.19520	−0.0796283
$761$	−10.8881	−0.394693	−0.197347	−	0.980334i	$-0.563232\pi$
$761$	−10.8881	−0.394693	−0.197347	+	0.980334i	$0.563232\pi$
$762$	22.8569	0.828017
$763$	−2.72352	−0.0985979
$764$	2.49896	0.0904092
$765$	−10.1493	−0.366948
$766$	−14.7036	−0.531262
$767$	43.1123	1.55669
$768$	−15.4861	−0.558808
$769$	−2.08827	−0.0753048	−0.0376524	−	0.999291i	$-0.511988\pi$
$769$	−2.08827	−0.0753048	−0.0376524	+	0.999291i	$0.511988\pi$
$770$	−0.900534	−0.0324530
$771$	3.27273	0.117864
$772$	−10.4950	−0.377724
$773$	6.16375	0.221695	0.110847	−	0.993837i	$-0.464644\pi$
$773$	6.16375	0.221695	0.110847	+	0.993837i	$0.464644\pi$
$774$	0.0329681	0.00118501
$775$	0.342659	0.0123087
$776$	30.7988	1.10561
$777$	1.41562	0.0507849
$778$	57.8910	2.07549
$779$	−0.676294	−0.0242308
$780$	10.2587	0.367319
$781$	−10.6643	−0.381598
$782$	42.9830	1.53707
$783$	−2.40141	−0.0858194
$784$	34.1538	1.21978
$785$	26.9631	0.962355
$786$	22.6106	0.806494
$787$	5.19703	0.185254	0.0926271	−	0.995701i	$-0.470474\pi$
$787$	5.19703	0.185254	0.0926271	+	0.995701i	$0.470474\pi$
$788$	−7.06420	−0.251652
$789$	30.9365	1.10137
$790$	−0.705385	−0.0250965
$791$	−1.56239	−0.0555520
$792$	−2.09709	−0.0745169
$793$	−6.76197	−0.240125
$794$	47.5164	1.68630
$795$	3.86400	0.137042
$796$	17.2665	0.611994
$797$	13.5524	0.480051	0.240025	−	0.970767i	$-0.422844\pi$
$797$	13.5524	0.480051	0.240025	+	0.970767i	$0.422844\pi$
$798$	0.218867	0.00774779
$799$	−18.8021	−0.665171
$800$	2.73665	0.0967551
$801$	4.11842	0.145517
$802$	36.9332	1.30416
$803$	12.7169	0.448771
$804$	0.664103	0.0234211
$805$	2.89818	0.102147
$806$	5.52563	0.194632
$807$	−26.6425	−0.937859
$808$	10.6713	0.375414
$809$	−12.4845	−0.438932	−0.219466	−	0.975620i	$-0.570432\pi$
$809$	−12.4845	−0.438932	−0.219466	+	0.975620i	$0.570432\pi$
$810$	3.42966	0.120506
$811$	−3.03301	−0.106504	−0.0532518	−	0.998581i	$-0.516959\pi$
$811$	−3.03301	−0.106504	−0.0532518	+	0.998581i	$0.516959\pi$
$812$	−0.460940	−0.0161758
$813$	22.4391	0.786973
$814$	8.90962	0.312282
$815$	22.3378	0.782460
$816$	−24.0983	−0.843608
$817$	0.0100624	0.000352037 0
$818$	13.1180	0.458659
$819$	1.77550	0.0620412
$820$	−2.03416	−0.0710360
$821$	−48.9453	−1.70820	−0.854101	−	0.520107i	$-0.825892\pi$
$821$	−48.9453	−1.70820	−0.854101	+	0.520107i	$0.825892\pi$
$822$	−0.158778	−0.00553802
$823$	−4.36324	−0.152093	−0.0760465	−	0.997104i	$-0.524230\pi$
$823$	−4.36324	−0.152093	−0.0760465	+	0.997104i	$0.524230\pi$
$824$	17.7093	0.616933
$825$	0.692971	0.0241262
$826$	2.76655	0.0962607
$827$	28.5488	0.992740	0.496370	−	0.868111i	$-0.334666\pi$
$827$	28.5488	0.992740	0.496370	+	0.868111i	$0.334666\pi$
$828$	−3.88792	−0.135114
$829$	−0.313789	−0.0108983	−0.00544917	−	0.999985i	$-0.501735\pi$
$829$	−0.313789	−0.0108983	−0.00544917	+	0.999985i	$0.501735\pi$
$830$	−29.5087	−1.02426
$831$	5.20571	0.180584
$832$	−22.5107	−0.780417
$833$	33.8958	1.17442
$834$	12.9427	0.448170
$835$	−1.01406	−0.0350931
$836$	0.368720	0.0127525
$837$	0.494478	0.0170916
$838$	0.900882	0.0311205
$839$	48.0660	1.65942	0.829712	−	0.558192i	$-0.188505\pi$
$839$	48.0660	1.65942	0.829712	+	0.558192i	$0.188505\pi$
$840$	−1.14276	−0.0394290
$841$	−23.2332	−0.801146
$842$	−13.9401	−0.480407
$843$	−4.65546	−0.160342
$844$	6.12522	0.210839
$845$	67.9138	2.33631
$846$	6.35365	0.218443
$847$	−0.262572	−0.00902209
$848$	9.17461	0.315057
$849$	−0.572899	−0.0196618
$850$	5.60046	0.192094
$851$	−28.6738	−0.982924
$852$	7.79579	0.267079
$853$	8.44660	0.289206	0.144603	−	0.989490i	$-0.453809\pi$
$853$	8.44660	0.289206	0.144603	+	0.989490i	$0.453809\pi$
$854$	−0.433921	−0.0148485
$855$	1.04678	0.0357993
$856$	−33.8115	−1.15565
$857$	−32.5392	−1.11152	−0.555760	−	0.831343i	$-0.687572\pi$
$857$	−32.5392	−1.11152	−0.555760	+	0.831343i	$0.687572\pi$
$858$	11.1747	0.381498
$859$	16.2887	0.555764	0.277882	−	0.960615i	$-0.410368\pi$
$859$	16.2887	0.555764	0.277882	+	0.960615i	$0.410368\pi$
$860$	0.0302656	0.00103205
$861$	−0.352060	−0.0119982
$862$	68.0762	2.31868
$863$	−29.1444	−0.992087	−0.496043	−	0.868298i	$-0.665214\pi$
$863$	−29.1444	−0.992087	−0.496043	+	0.868298i	$0.665214\pi$
$864$	3.94915	0.134353
$865$	26.0209	0.884738
$866$	−2.25547	−0.0766441
$867$	−6.91620	−0.234886
$868$	0.0949127	0.00322155
$869$	−0.205672	−0.00697694
$870$	−8.23603	−0.279228
$871$	6.14299	0.208147
$872$	−21.7520	−0.736615
$873$	−14.6865	−0.497061
$874$	−4.43321	−0.149956
$875$	3.10225	0.104875
$876$	−9.29633	−0.314094
$877$	−42.2498	−1.42667	−0.713337	−	0.700821i	$-0.752817\pi$
$877$	−42.2498	−1.42667	−0.713337	+	0.700821i	$0.752817\pi$
$878$	−47.1700	−1.59191
$879$	12.8739	0.434225
$880$	−10.2265	−0.344737
$881$	−8.67465	−0.292257	−0.146128	−	0.989266i	$-0.546681\pi$
$881$	−8.67465	−0.292257	−0.146128	+	0.989266i	$0.546681\pi$
$882$	−11.4541	−0.385680
$883$	14.9384	0.502717	0.251358	−	0.967894i	$-0.419123\pi$
$883$	14.9384	0.502717	0.251358	+	0.967894i	$0.419123\pi$
$884$	24.1740	0.813059
$885$	13.2317	0.444780
$886$	−13.0020	−0.436810
$887$	−14.7994	−0.496914	−0.248457	−	0.968643i	$-0.579923\pi$
$887$	−14.7994	−0.496914	−0.248457	+	0.968643i	$0.579923\pi$
$888$	11.3061	0.379409
$889$	3.63164	0.121801
$890$	14.1248	0.473464
$891$	1.00000	0.0335013
$892$	−15.4179	−0.516231
$893$	1.93923	0.0648938
$894$	31.8602	1.06556
$895$	28.9241	0.966827
$896$	−3.51840	−0.117542
$897$	−35.9634	−1.20078
$898$	62.0826	2.07172
$899$	−1.18744	−0.0396035
$900$	−0.506575	−0.0168858
$901$	9.10529	0.303341
$902$	−2.21580	−0.0737780
$903$	0.00523818	0.000174316 0
$904$	−12.4783	−0.415023
$905$	21.3147	0.708526
$906$	6.53344	0.217059
$907$	−31.5865	−1.04881	−0.524407	−	0.851468i	$-0.675713\pi$
$907$	−31.5865	−1.04881	−0.524407	+	0.851468i	$0.675713\pi$
$908$	3.54117	0.117518
$909$	−5.08860	−0.168778
$910$	6.08938	0.201861
$911$	−22.5932	−0.748545	−0.374272	−	0.927319i	$-0.622108\pi$
$911$	−22.5932	−0.748545	−0.374272	+	0.927319i	$0.622108\pi$
$912$	2.48547	0.0823020
$913$	−8.60396	−0.284749
$914$	−30.9472	−1.02364
$915$	−2.07534	−0.0686086
$916$	16.9327	0.559472
$917$	3.59252	0.118635
$918$	8.08181	0.266739
$919$	14.6678	0.483846	0.241923	−	0.970295i	$-0.422222\pi$
$919$	14.6678	0.483846	0.241923	+	0.970295i	$0.422222\pi$
$920$	23.1470	0.763133
$921$	23.9320	0.788586
$922$	7.45390	0.245481
$923$	72.1114	2.37358
$924$	0.191945	0.00631454
$925$	−3.73604	−0.122840
$926$	−23.4470	−0.770516
$927$	−8.44470	−0.277360
$928$	−9.48354	−0.311312
$929$	1.12549	0.0369262	0.0184631	−	0.999830i	$-0.494123\pi$
$929$	1.12549	0.0369262	0.0184631	+	0.999830i	$0.494123\pi$
$930$	1.69589	0.0556105
$931$	−3.49597	−0.114576
$932$	10.1123	0.331241
$933$	−16.5518	−0.541882
$934$	−9.82361	−0.321438
$935$	−10.1493	−0.331917
$936$	14.1805	0.463503
$937$	7.37880	0.241055	0.120528	−	0.992710i	$-0.461541\pi$
$937$	7.37880	0.241055	0.120528	+	0.992710i	$0.461541\pi$
$938$	0.394201	0.0128711
$939$	−1.51244	−0.0493567
$940$	5.83282	0.190246
$941$	36.4915	1.18959	0.594795	−	0.803878i	$-0.297233\pi$
$941$	36.4915	1.18959	0.594795	+	0.803878i	$0.297233\pi$
$942$	−21.4706	−0.699549
$943$	7.13108	0.232220
$944$	31.4172	1.02254
$945$	0.544926	0.0177264
$946$	0.0329681	0.00107189
$947$	−9.34403	−0.303640	−0.151820	−	0.988408i	$-0.548513\pi$
$947$	−9.34403	−0.303640	−0.151820	+	0.988408i	$0.548513\pi$
$948$	0.150350	0.00488315
$949$	−85.9916	−2.79140
$950$	−0.577625	−0.0187406
$951$	6.84400	0.221932
$952$	−2.69285	−0.0872758
$953$	5.26496	0.170549	0.0852744	−	0.996358i	$-0.472823\pi$
$953$	5.26496	0.170549	0.0852744	+	0.996358i	$0.472823\pi$
$954$	−3.07688	−0.0996176
$955$	7.09446	0.229571
$956$	17.4656	0.564879
$957$	−2.40141	−0.0776266
$958$	−33.4985	−1.08229
$959$	−0.0252276	−0.000814643 0
$960$	−6.90883	−0.222981
$961$	−30.7555	−0.992113
$962$	−60.2465	−1.94243
$963$	16.1231	0.519559
$964$	−12.8393	−0.413525
$965$	−29.7949	−0.959133
$966$	−2.30780	−0.0742524
$967$	52.8835	1.70062	0.850310	−	0.526283i	$-0.176415\pi$
$967$	52.8835	1.70062	0.850310	+	0.526283i	$0.176415\pi$
$968$	−2.09709	−0.0674031
$969$	2.46669	0.0792415
$970$	−50.3696	−1.61727
$971$	−25.7722	−0.827068	−0.413534	−	0.910489i	$-0.635706\pi$
$971$	−25.7722	−0.827068	−0.413534	+	0.910489i	$0.635706\pi$
$972$	−0.731020	−0.0234475
$973$	2.05642	0.0659259
$974$	−48.3721	−1.54994
$975$	−4.68585	−0.150067
$976$	−4.92765	−0.157730
$977$	47.4031	1.51656	0.758280	−	0.651929i	$-0.226040\pi$
$977$	47.4031	1.51656	0.758280	+	0.651929i	$0.226040\pi$
$978$	−17.7875	−0.568781
$979$	4.11842	0.131625
$980$	−10.5152	−0.335896
$981$	10.3724	0.331167
$982$	39.1562	1.24952
$983$	−7.61215	−0.242790	−0.121395	−	0.992604i	$-0.538737\pi$
$983$	−7.61215	−0.242790	−0.121395	+	0.992604i	$0.538737\pi$
$984$	−2.81180	−0.0896370
$985$	−20.0550	−0.639006
$986$	−19.4077	−0.618068
$987$	1.00951	0.0321330
$988$	−2.49328	−0.0793217
$989$	−0.106101	−0.00337382
$990$	3.42966	0.109002
$991$	16.2369	0.515782	0.257891	−	0.966174i	$-0.416973\pi$
$991$	16.2369	0.515782	0.257891	+	0.966174i	$0.416973\pi$
$992$	1.95277	0.0620004
$993$	−9.43889	−0.299534
$994$	4.62746	0.146774
$995$	49.0189	1.55400
$996$	6.28966	0.199296
$997$	−42.6132	−1.34957	−0.674787	−	0.738013i	$-0.735764\pi$
$997$	−42.6132	−1.34957	−0.674787	+	0.738013i	$0.735764\pi$
$998$	−65.3264	−2.06787
$999$	−5.39134	−0.170574

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.b.1.9	✓	11
3.2	odd	2		6039.2.a.c.1.3		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.b.1.9	✓	11	1.1	even	1	trivial
6039.2.a.c.1.3		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)

\(f(q)\)	\(=\)	\(q+1.65258 q^{2} -1.00000 q^{3} +0.731020 q^{4} +2.07534 q^{5} -1.65258 q^{6} -0.262572 q^{7} -2.09709 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.65258 q^{2} -1.00000 q^{3} +0.731020 q^{4} +2.07534 q^{5} -1.65258 q^{6} -0.262572 q^{7} -2.09709 q^{8} +1.00000 q^{9} +3.42966 q^{10} +1.00000 q^{11} -0.731020 q^{12} -6.76197 q^{13} -0.433921 q^{14} -2.07534 q^{15} -4.92765 q^{16} -4.89042 q^{17} +1.65258 q^{18} +0.504392 q^{19} +1.51711 q^{20} +0.262572 q^{21} +1.65258 q^{22} -5.31849 q^{23} +2.09709 q^{24} -0.692971 q^{25} -11.1747 q^{26} -1.00000 q^{27} -0.191945 q^{28} +2.40141 q^{29} -3.42966 q^{30} -0.494478 q^{31} -3.94915 q^{32} -1.00000 q^{33} -8.08181 q^{34} -0.544926 q^{35} +0.731020 q^{36} +5.39134 q^{37} +0.833548 q^{38} +6.76197 q^{39} -4.35217 q^{40} -1.34081 q^{41} +0.433921 q^{42} +0.0199495 q^{43} +0.731020 q^{44} +2.07534 q^{45} -8.78922 q^{46} +3.84468 q^{47} +4.92765 q^{48} -6.93106 q^{49} -1.14519 q^{50} +4.89042 q^{51} -4.94313 q^{52} -1.86186 q^{53} -1.65258 q^{54} +2.07534 q^{55} +0.550638 q^{56} -0.504392 q^{57} +3.96852 q^{58} -6.37570 q^{59} -1.51711 q^{60} +1.00000 q^{61} -0.817164 q^{62} -0.262572 q^{63} +3.32901 q^{64} -14.0334 q^{65} -1.65258 q^{66} -0.908461 q^{67} -3.57499 q^{68} +5.31849 q^{69} -0.900534 q^{70} -10.6643 q^{71} -2.09709 q^{72} +12.7169 q^{73} +8.90962 q^{74} +0.692971 q^{75} +0.368720 q^{76} -0.262572 q^{77} +11.1747 q^{78} -0.205672 q^{79} -10.2265 q^{80} +1.00000 q^{81} -2.21580 q^{82} -8.60396 q^{83} +0.191945 q^{84} -10.1493 q^{85} +0.0329681 q^{86} -2.40141 q^{87} -2.09709 q^{88} +4.11842 q^{89} +3.42966 q^{90} +1.77550 q^{91} -3.88792 q^{92} +0.494478 q^{93} +6.35365 q^{94} +1.04678 q^{95} +3.94915 q^{96} -14.6865 q^{97} -11.4541 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) \) 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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