LMFDB - Embedded newform 2013.2.a.b.1.6

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			1.6
Root			$0.175402$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.175402 q^{2} -1.00000 q^{3} -1.96923 q^{4} -1.94648 q^{5} +0.175402 q^{6} -2.33819 q^{7} +0.696212 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.175402 q^{2} -1.00000 q^{3} -1.96923 q^{4} -1.94648 q^{5} +0.175402 q^{6} -2.33819 q^{7} +0.696212 q^{8} +1.00000 q^{9} +0.341417 q^{10} +1.00000 q^{11} +1.96923 q^{12} +1.20314 q^{13} +0.410124 q^{14} +1.94648 q^{15} +3.81635 q^{16} +2.45720 q^{17} -0.175402 q^{18} +3.98976 q^{19} +3.83307 q^{20} +2.33819 q^{21} -0.175402 q^{22} -3.96432 q^{23} -0.696212 q^{24} -1.21122 q^{25} -0.211034 q^{26} -1.00000 q^{27} +4.60444 q^{28} +7.09840 q^{29} -0.341417 q^{30} -4.33548 q^{31} -2.06182 q^{32} -1.00000 q^{33} -0.430999 q^{34} +4.55124 q^{35} -1.96923 q^{36} +5.37839 q^{37} -0.699813 q^{38} -1.20314 q^{39} -1.35516 q^{40} -0.658729 q^{41} -0.410124 q^{42} +7.52267 q^{43} -1.96923 q^{44} -1.94648 q^{45} +0.695350 q^{46} +6.40624 q^{47} -3.81635 q^{48} -1.53287 q^{49} +0.212450 q^{50} -2.45720 q^{51} -2.36927 q^{52} -10.4028 q^{53} +0.175402 q^{54} -1.94648 q^{55} -1.62788 q^{56} -3.98976 q^{57} -1.24507 q^{58} -1.28932 q^{59} -3.83307 q^{60} +1.00000 q^{61} +0.760452 q^{62} -2.33819 q^{63} -7.27105 q^{64} -2.34189 q^{65} +0.175402 q^{66} -10.6234 q^{67} -4.83881 q^{68} +3.96432 q^{69} -0.798297 q^{70} -3.13393 q^{71} +0.696212 q^{72} -0.981791 q^{73} -0.943381 q^{74} +1.21122 q^{75} -7.85678 q^{76} -2.33819 q^{77} +0.211034 q^{78} -7.85927 q^{79} -7.42845 q^{80} +1.00000 q^{81} +0.115543 q^{82} -0.543607 q^{83} -4.60444 q^{84} -4.78290 q^{85} -1.31949 q^{86} -7.09840 q^{87} +0.696212 q^{88} -3.63137 q^{89} +0.341417 q^{90} -2.81318 q^{91} +7.80667 q^{92} +4.33548 q^{93} -1.12367 q^{94} -7.76599 q^{95} +2.06182 q^{96} -10.7977 q^{97} +0.268868 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 2 * q^2 - 11 * q^3 + 10 * q^4 - q^5 + 2 * q^6 - 11 * q^7 - 3 * q^8 + 11 * q^9	\( 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9} - 8 q^{10} + 11 q^{11} - 10 q^{12} - 13 q^{13} + 5 q^{14} + q^{15} + 4 q^{16} - 13 q^{17} - 2 q^{18} - 12 q^{19} - 7 q^{20} + 11 q^{21} - 2 q^{22} - 3 q^{23} + 3 q^{24} + 12 q^{25} + 12 q^{26} - 11 q^{27} - 13 q^{28} + 2 q^{29} + 8 q^{30} + q^{31} - 23 q^{32} - 11 q^{33} - 14 q^{34} - 4 q^{35} + 10 q^{36} - 14 q^{37} - 8 q^{38} + 13 q^{39} - 34 q^{40} + 3 q^{41} - 5 q^{42} - 21 q^{43} + 10 q^{44} - q^{45} - 12 q^{46} - 16 q^{47} - 4 q^{48} - 18 q^{49} - 13 q^{50} + 13 q^{51} - 33 q^{52} + 2 q^{54} - q^{55} + 16 q^{56} + 12 q^{57} - 17 q^{58} + 3 q^{59} + 7 q^{60} + 11 q^{61} - 21 q^{62} - 11 q^{63} - 7 q^{64} - q^{65} + 2 q^{66} - 24 q^{67} + 2 q^{68} + 3 q^{69} + 4 q^{70} + 7 q^{71} - 3 q^{72} - 42 q^{73} - 16 q^{74} - 12 q^{75} - 13 q^{76} - 11 q^{77} - 12 q^{78} - 11 q^{79} + 42 q^{80} + 11 q^{81} - 38 q^{82} - 34 q^{83} + 13 q^{84} - 14 q^{85} + 42 q^{86} - 2 q^{87} - 3 q^{88} + 29 q^{89} - 8 q^{90} + 9 q^{91} + 42 q^{92} - q^{93} - 33 q^{94} - 31 q^{95} + 23 q^{96} - 45 q^{97} - 33 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q - 2 * q^2 - 11 * q^3 + 10 * q^4 - q^5 + 2 * q^6 - 11 * q^7 - 3 * q^8 + 11 * q^9 - 8 * q^10 + 11 * q^11 - 10 * q^12 - 13 * q^13 + 5 * q^14 + q^15 + 4 * q^16 - 13 * q^17 - 2 * q^18 - 12 * q^19 - 7 * q^20 + 11 * q^21 - 2 * q^22 - 3 * q^23 + 3 * q^24 + 12 * q^25 + 12 * q^26 - 11 * q^27 - 13 * q^28 + 2 * q^29 + 8 * q^30 + q^31 - 23 * q^32 - 11 * q^33 - 14 * q^34 - 4 * q^35 + 10 * q^36 - 14 * q^37 - 8 * q^38 + 13 * q^39 - 34 * q^40 + 3 * q^41 - 5 * q^42 - 21 * q^43 + 10 * q^44 - q^45 - 12 * q^46 - 16 * q^47 - 4 * q^48 - 18 * q^49 - 13 * q^50 + 13 * q^51 - 33 * q^52 + 2 * q^54 - q^55 + 16 * q^56 + 12 * q^57 - 17 * q^58 + 3 * q^59 + 7 * q^60 + 11 * q^61 - 21 * q^62 - 11 * q^63 - 7 * q^64 - q^65 + 2 * q^66 - 24 * q^67 + 2 * q^68 + 3 * q^69 + 4 * q^70 + 7 * q^71 - 3 * q^72 - 42 * q^73 - 16 * q^74 - 12 * q^75 - 13 * q^76 - 11 * q^77 - 12 * q^78 - 11 * q^79 + 42 * q^80 + 11 * q^81 - 38 * q^82 - 34 * q^83 + 13 * q^84 - 14 * q^85 + 42 * q^86 - 2 * q^87 - 3 * q^88 + 29 * q^89 - 8 * q^90 + 9 * q^91 + 42 * q^92 - q^93 - 33 * q^94 - 31 * q^95 + 23 * q^96 - 45 * q^97 - 33 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.175402	−0.124028	−0.0620140	−	0.998075i	$-0.519752\pi$
$2$	−0.175402	−0.124028	−0.0620140	+	0.998075i	$0.519752\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.96923	−0.984617
$5$	−1.94648	−0.870492	−0.435246	−	0.900312i	$-0.643339\pi$
$5$	−1.94648	−0.870492	−0.435246	+	0.900312i	$0.643339\pi$
$6$	0.175402	0.0716076
$7$	−2.33819	−0.883753	−0.441876	−	0.897076i	$-0.645687\pi$
$7$	−2.33819	−0.883753	−0.441876	+	0.897076i	$0.645687\pi$
$8$	0.696212	0.246148
$9$	1.00000	0.333333
$10$	0.341417	0.107965
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.96923	0.568469
$13$	1.20314	0.333692	0.166846	−	0.985983i	$-0.446642\pi$
$13$	1.20314	0.333692	0.166846	+	0.985983i	$0.446642\pi$
$14$	0.410124	0.109610
$15$	1.94648	0.502579
$16$	3.81635	0.954088
$17$	2.45720	0.595960	0.297980	−	0.954572i	$-0.403687\pi$
$17$	2.45720	0.595960	0.297980	+	0.954572i	$0.403687\pi$
$18$	−0.175402	−0.0413427
$19$	3.98976	0.915314	0.457657	−	0.889129i	$-0.348689\pi$
$19$	3.98976	0.915314	0.457657	+	0.889129i	$0.348689\pi$
$20$	3.83307	0.857101
$21$	2.33819	0.510235
$22$	−0.175402	−0.0373959
$23$	−3.96432	−0.826617	−0.413309	−	0.910591i	$-0.635627\pi$
$23$	−3.96432	−0.826617	−0.413309	+	0.910591i	$0.635627\pi$
$24$	−0.696212	−0.142114
$25$	−1.21122	−0.242243
$26$	−0.211034	−0.0413872
$27$	−1.00000	−0.192450
$28$	4.60444	0.870158
$29$	7.09840	1.31814	0.659070	−	0.752082i	$-0.270950\pi$
$29$	7.09840	1.31814	0.659070	+	0.752082i	$0.270950\pi$
$30$	−0.341417	−0.0623339
$31$	−4.33548	−0.778674	−0.389337	−	0.921095i	$-0.627296\pi$
$31$	−4.33548	−0.778674	−0.389337	+	0.921095i	$0.627296\pi$
$32$	−2.06182	−0.364482
$33$	−1.00000	−0.174078
$34$	−0.430999	−0.0739157
$35$	4.55124	0.769300
$36$	−1.96923	−0.328206
$37$	5.37839	0.884201	0.442101	−	0.896965i	$-0.354233\pi$
$37$	5.37839	0.884201	0.442101	+	0.896965i	$0.354233\pi$
$38$	−0.699813	−0.113525
$39$	−1.20314	−0.192657
$40$	−1.35516	−0.214270
$41$	−0.658729	−0.102876	−0.0514381	−	0.998676i	$-0.516380\pi$
$41$	−0.658729	−0.102876	−0.0514381	+	0.998676i	$0.516380\pi$
$42$	−0.410124	−0.0632834
$43$	7.52267	1.14720	0.573598	−	0.819137i	$-0.305547\pi$
$43$	7.52267	1.14720	0.573598	+	0.819137i	$0.305547\pi$
$44$	−1.96923	−0.296873
$45$	−1.94648	−0.290164
$46$	0.695350	0.102524
$47$	6.40624	0.934447	0.467223	−	0.884139i	$-0.345254\pi$
$47$	6.40624	0.934447	0.467223	+	0.884139i	$0.345254\pi$
$48$	−3.81635	−0.550843
$49$	−1.53287	−0.218981
$50$	0.212450	0.0300450
$51$	−2.45720	−0.344077
$52$	−2.36927	−0.328559
$53$	−10.4028	−1.42893	−0.714464	−	0.699672i	$-0.753330\pi$
$53$	−10.4028	−1.42893	−0.714464	+	0.699672i	$0.753330\pi$
$54$	0.175402	0.0238692
$55$	−1.94648	−0.262463
$56$	−1.62788	−0.217534
$57$	−3.98976	−0.528457
$58$	−1.24507	−0.163486
$59$	−1.28932	−0.167855	−0.0839277	−	0.996472i	$-0.526746\pi$
$59$	−1.28932	−0.167855	−0.0839277	+	0.996472i	$0.526746\pi$
$60$	−3.83307	−0.494848
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	0.760452	0.0965775
$63$	−2.33819	−0.294584
$64$	−7.27105	−0.908882
$65$	−2.34189	−0.290476
$66$	0.175402	0.0215905
$67$	−10.6234	−1.29785	−0.648925	−	0.760852i	$-0.724781\pi$
$67$	−10.6234	−1.29785	−0.648925	+	0.760852i	$0.724781\pi$
$68$	−4.83881	−0.586792
$69$	3.96432	0.477248
$70$	−0.798297	−0.0954148
$71$	−3.13393	−0.371929	−0.185965	−	0.982556i	$-0.559541\pi$
$71$	−3.13393	−0.371929	−0.185965	+	0.982556i	$0.559541\pi$
$72$	0.696212	0.0820494
$73$	−0.981791	−0.114910	−0.0574550	−	0.998348i	$-0.518299\pi$
$73$	−0.981791	−0.114910	−0.0574550	+	0.998348i	$0.518299\pi$
$74$	−0.943381	−0.109666
$75$	1.21122	0.139859
$76$	−7.85678	−0.901234
$77$	−2.33819	−0.266461
$78$	0.211034	0.0238949
$79$	−7.85927	−0.884236	−0.442118	−	0.896957i	$-0.645773\pi$
$79$	−7.85927	−0.884236	−0.442118	+	0.896957i	$0.645773\pi$
$80$	−7.42845	−0.830526
$81$	1.00000	0.111111
$82$	0.115543	0.0127595
$83$	−0.543607	−0.0596686	−0.0298343	−	0.999555i	$-0.509498\pi$
$83$	−0.543607	−0.0596686	−0.0298343	+	0.999555i	$0.509498\pi$
$84$	−4.60444	−0.502386
$85$	−4.78290	−0.518778
$86$	−1.31949	−0.142285
$87$	−7.09840	−0.761028
$88$	0.696212	0.0742165
$89$	−3.63137	−0.384924	−0.192462	−	0.981304i	$-0.561647\pi$
$89$	−3.63137	−0.384924	−0.192462	+	0.981304i	$0.561647\pi$
$90$	0.341417	0.0359885
$91$	−2.81318	−0.294901
$92$	7.80667	0.813901
$93$	4.33548	0.449568
$94$	−1.12367	−0.115898
$95$	−7.76599	−0.796774
$96$	2.06182	0.210434
$97$	−10.7977	−1.09634	−0.548171	−	0.836366i	$-0.684676\pi$
$97$	−10.7977	−1.09634	−0.548171	+	0.836366i	$0.684676\pi$
$98$	0.268868	0.0271598
$99$	1.00000	0.100504
$100$	2.38517	0.238517
$101$	4.93823	0.491373	0.245686	−	0.969349i	$-0.420987\pi$
$101$	4.93823	0.491373	0.245686	+	0.969349i	$0.420987\pi$
$102$	0.430999	0.0426753
$103$	1.91262	0.188456	0.0942278	−	0.995551i	$-0.469962\pi$
$103$	1.91262	0.188456	0.0942278	+	0.995551i	$0.469962\pi$
$104$	0.837643	0.0821376
$105$	−4.55124	−0.444155
$106$	1.82467	0.177227
$107$	−10.8624	−1.05011	−0.525053	−	0.851070i	$-0.675954\pi$
$107$	−10.8624	−1.05011	−0.525053	+	0.851070i	$0.675954\pi$
$108$	1.96923	0.189490
$109$	4.88139	0.467552	0.233776	−	0.972290i	$-0.424892\pi$
$109$	4.88139	0.467552	0.233776	+	0.972290i	$0.424892\pi$
$110$	0.341417	0.0325528
$111$	−5.37839	−0.510494
$112$	−8.92335	−0.843178
$113$	14.1166	1.32798	0.663988	−	0.747743i	$-0.268862\pi$
$113$	14.1166	1.32798	0.663988	+	0.747743i	$0.268862\pi$
$114$	0.699813	0.0655435
$115$	7.71646	0.719564
$116$	−13.9784	−1.29786
$117$	1.20314	0.111231
$118$	0.226150	0.0208188
$119$	−5.74541	−0.526681
$120$	1.35516	0.123709
$121$	1.00000	0.0909091
$122$	−0.175402	−0.0158802
$123$	0.658729	0.0593956
$124$	8.53757	0.766696
$125$	12.0900	1.08136
$126$	0.410124	0.0365367
$127$	−7.11962	−0.631764	−0.315882	−	0.948798i	$-0.602300\pi$
$127$	−7.11962	−0.631764	−0.315882	+	0.948798i	$0.602300\pi$
$128$	5.39900	0.477209
$129$	−7.52267	−0.662334
$130$	0.410773	0.0360272
$131$	−6.50165	−0.568052	−0.284026	−	0.958817i	$-0.591670\pi$
$131$	−6.50165	−0.568052	−0.284026	+	0.958817i	$0.591670\pi$
$132$	1.96923	0.171400
$133$	−9.32882	−0.808911
$134$	1.86336	0.160970
$135$	1.94648	0.167526
$136$	1.71074	0.146694
$137$	−10.0075	−0.854996	−0.427498	−	0.904016i	$-0.640605\pi$
$137$	−10.0075	−0.854996	−0.427498	+	0.904016i	$0.640605\pi$
$138$	−0.695350	−0.0591921
$139$	−7.82988	−0.664122	−0.332061	−	0.943258i	$-0.607744\pi$
$139$	−7.82988	−0.664122	−0.332061	+	0.943258i	$0.607744\pi$
$140$	−8.96245	−0.757466
$141$	−6.40624	−0.539503
$142$	0.549698	0.0461297
$143$	1.20314	0.100612
$144$	3.81635	0.318029
$145$	−13.8169	−1.14743
$146$	0.172208	0.0142521
$147$	1.53287	0.126429
$148$	−10.5913	−0.870600
$149$	14.6290	1.19845	0.599227	−	0.800579i	$-0.295475\pi$
$149$	14.6290	1.19845	0.599227	+	0.800579i	$0.295475\pi$
$150$	−0.212450	−0.0173465
$151$	16.9514	1.37949	0.689743	−	0.724054i	$-0.257724\pi$
$151$	16.9514	1.37949	0.689743	+	0.724054i	$0.257724\pi$
$152$	2.77772	0.225303
$153$	2.45720	0.198653
$154$	0.410124	0.0330487
$155$	8.43892	0.677830
$156$	2.36927	0.189693
$157$	−18.6670	−1.48979	−0.744895	−	0.667182i	$-0.767500\pi$
$157$	−18.6670	−1.48979	−0.744895	+	0.667182i	$0.767500\pi$
$158$	1.37853	0.109670
$159$	10.4028	0.824992
$160$	4.01329	0.317279
$161$	9.26933	0.730525
$162$	−0.175402	−0.0137809
$163$	−24.2887	−1.90244	−0.951221	−	0.308512i	$-0.900169\pi$
$163$	−24.2887	−1.90244	−0.951221	+	0.308512i	$0.900169\pi$
$164$	1.29719	0.101294
$165$	1.94648	0.151533
$166$	0.0953499	0.00740059
$167$	−13.5050	−1.04505	−0.522525	−	0.852624i	$-0.675010\pi$
$167$	−13.5050	−1.04505	−0.522525	+	0.852624i	$0.675010\pi$
$168$	1.62788	0.125593
$169$	−11.5524	−0.888650
$170$	0.838931	0.0643430
$171$	3.98976	0.305105
$172$	−14.8139	−1.12955
$173$	8.07876	0.614217	0.307108	−	0.951675i	$-0.400639\pi$
$173$	8.07876	0.614217	0.307108	+	0.951675i	$0.400639\pi$
$174$	1.24507	0.0943889
$175$	2.83205	0.214083
$176$	3.81635	0.287668
$177$	1.28932	0.0969113
$178$	0.636950	0.0477414
$179$	1.32658	0.0991531	0.0495765	−	0.998770i	$-0.484213\pi$
$179$	1.32658	0.0991531	0.0495765	+	0.998770i	$0.484213\pi$
$180$	3.83307	0.285700
$181$	22.1820	1.64878	0.824388	−	0.566026i	$-0.191520\pi$
$181$	22.1820	1.64878	0.824388	+	0.566026i	$0.191520\pi$
$182$	0.493437	0.0365760
$183$	−1.00000	−0.0739221
$184$	−2.76001	−0.203470
$185$	−10.4689	−0.769690
$186$	−0.760452	−0.0557590
$187$	2.45720	0.179689
$188$	−12.6154	−0.920072
$189$	2.33819	0.170078
$190$	1.36217	0.0988223
$191$	9.45935	0.684454	0.342227	−	0.939617i	$-0.388819\pi$
$191$	9.45935	0.684454	0.342227	+	0.939617i	$0.388819\pi$
$192$	7.27105	0.524743
$193$	−11.9439	−0.859741	−0.429870	−	0.902891i	$-0.641441\pi$
$193$	−11.9439	−0.859741	−0.429870	+	0.902891i	$0.641441\pi$
$194$	1.89394	0.135977
$195$	2.34189	0.167706
$196$	3.01858	0.215613
$197$	19.8342	1.41313	0.706564	−	0.707649i	$-0.250244\pi$
$197$	19.8342	1.41313	0.706564	+	0.707649i	$0.250244\pi$
$198$	−0.175402	−0.0124653
$199$	−16.7890	−1.19014	−0.595070	−	0.803674i	$-0.702876\pi$
$199$	−16.7890	−1.19014	−0.595070	+	0.803674i	$0.702876\pi$
$200$	−0.843264	−0.0596278
$201$	10.6234	0.749314
$202$	−0.866177	−0.0609440
$203$	−16.5974	−1.16491
$204$	4.83881	0.338784
$205$	1.28220	0.0895530
$206$	−0.335477	−0.0233738
$207$	−3.96432	−0.275539
$208$	4.59162	0.318371
$209$	3.98976	0.275978
$210$	0.798297	0.0550877
$211$	−3.40830	−0.234637	−0.117319	−	0.993094i	$-0.537430\pi$
$211$	−3.40830	−0.234637	−0.117319	+	0.993094i	$0.537430\pi$
$212$	20.4855	1.40695
$213$	3.13393	0.214733
$214$	1.90528	0.130243
$215$	−14.6427	−0.998625
$216$	−0.696212	−0.0473712
$217$	10.1372	0.688156
$218$	−0.856206	−0.0579896
$219$	0.981791	0.0663433
$220$	3.83307	0.258426
$221$	2.95637	0.198867
$222$	0.943381	0.0633156
$223$	−17.8213	−1.19340	−0.596701	−	0.802463i	$-0.703522\pi$
$223$	−17.8213	−1.19340	−0.596701	+	0.802463i	$0.703522\pi$
$224$	4.82093	0.322112
$225$	−1.21122	−0.0807478
$226$	−2.47608	−0.164706
$227$	9.93182	0.659198	0.329599	−	0.944121i	$-0.393086\pi$
$227$	9.93182	0.659198	0.329599	+	0.944121i	$0.393086\pi$
$228$	7.85678	0.520328
$229$	−21.1044	−1.39462	−0.697308	−	0.716771i	$-0.745619\pi$
$229$	−21.1044	−1.39462	−0.697308	+	0.716771i	$0.745619\pi$
$230$	−1.35348	−0.0892461
$231$	2.33819	0.153842
$232$	4.94199	0.324458
$233$	−3.55398	−0.232829	−0.116415	−	0.993201i	$-0.537140\pi$
$233$	−3.55398	−0.232829	−0.116415	+	0.993201i	$0.537140\pi$
$234$	−0.211034	−0.0137957
$235$	−12.4696	−0.813428
$236$	2.53898	0.165273
$237$	7.85927	0.510514
$238$	1.00776	0.0653232
$239$	17.9692	1.16233	0.581166	−	0.813785i	$-0.302597\pi$
$239$	17.9692	1.16233	0.581166	+	0.813785i	$0.302597\pi$
$240$	7.42845	0.479504
$241$	1.10303	0.0710521	0.0355260	−	0.999369i	$-0.488689\pi$
$241$	1.10303	0.0710521	0.0355260	+	0.999369i	$0.488689\pi$
$242$	−0.175402	−0.0112753
$243$	−1.00000	−0.0641500
$244$	−1.96923	−0.126067
$245$	2.98370	0.190621
$246$	−0.115543	−0.00736672
$247$	4.80025	0.305433
$248$	−3.01841	−0.191669
$249$	0.543607	0.0344497
$250$	−2.12061	−0.134119
$251$	−0.450745	−0.0284508	−0.0142254	−	0.999899i	$-0.504528\pi$
$251$	−0.450745	−0.0284508	−0.0142254	+	0.999899i	$0.504528\pi$
$252$	4.60444	0.290053
$253$	−3.96432	−0.249234
$254$	1.24880	0.0783565
$255$	4.78290	0.299517
$256$	13.5951	0.849695
$257$	15.6879	0.978587	0.489293	−	0.872119i	$-0.337255\pi$
$257$	15.6879	0.978587	0.489293	+	0.872119i	$0.337255\pi$
$258$	1.31949	0.0821480
$259$	−12.5757	−0.781415
$260$	4.61174	0.286008
$261$	7.09840	0.439380
$262$	1.14040	0.0704543
$263$	15.0345	0.927067	0.463534	−	0.886079i	$-0.346581\pi$
$263$	15.0345	0.927067	0.463534	+	0.886079i	$0.346581\pi$
$264$	−0.696212	−0.0428489
$265$	20.2488	1.24387
$266$	1.63630	0.100328
$267$	3.63137	0.222236
$268$	20.9199	1.27789
$269$	−22.9484	−1.39919	−0.699595	−	0.714539i	$-0.746636\pi$
$269$	−22.9484	−1.39919	−0.699595	+	0.714539i	$0.746636\pi$
$270$	−0.341417	−0.0207780
$271$	15.1679	0.921383	0.460692	−	0.887560i	$-0.347601\pi$
$271$	15.1679	0.921383	0.460692	+	0.887560i	$0.347601\pi$
$272$	9.37755	0.568598
$273$	2.81318	0.170261
$274$	1.75533	0.106043
$275$	−1.21122	−0.0730391
$276$	−7.80667	−0.469906
$277$	−12.2208	−0.734275	−0.367137	−	0.930167i	$-0.619662\pi$
$277$	−12.2208	−0.734275	−0.367137	+	0.930167i	$0.619662\pi$
$278$	1.37338	0.0823698
$279$	−4.33548	−0.259558
$280$	3.16863	0.189362
$281$	−28.2239	−1.68370	−0.841849	−	0.539713i	$-0.818533\pi$
$281$	−28.2239	−1.68370	−0.841849	+	0.539713i	$0.818533\pi$
$282$	1.12367	0.0669135
$283$	11.9759	0.711891	0.355945	−	0.934507i	$-0.384159\pi$
$283$	11.9759	0.711891	0.355945	+	0.934507i	$0.384159\pi$
$284$	6.17145	0.366208
$285$	7.76599	0.460018
$286$	−0.211034	−0.0124787
$287$	1.54023	0.0909171
$288$	−2.06182	−0.121494
$289$	−10.9621	−0.644832
$290$	2.42351	0.142314
$291$	10.7977	0.632973
$292$	1.93338	0.113142
$293$	2.56213	0.149681	0.0748407	−	0.997195i	$-0.476155\pi$
$293$	2.56213	0.149681	0.0748407	+	0.997195i	$0.476155\pi$
$294$	−0.268868	−0.0156807
$295$	2.50964	0.146117
$296$	3.74450	0.217645
$297$	−1.00000	−0.0580259
$298$	−2.56596	−0.148642
$299$	−4.76964	−0.275835
$300$	−2.38517	−0.137708
$301$	−17.5894	−1.01384
$302$	−2.97331	−0.171095
$303$	−4.93823	−0.283694
$304$	15.2263	0.873290
$305$	−1.94648	−0.111455
$306$	−0.430999	−0.0246386
$307$	−28.1050	−1.60404	−0.802019	−	0.597298i	$-0.796241\pi$
$307$	−28.1050	−1.60404	−0.802019	+	0.597298i	$0.796241\pi$
$308$	4.60444	0.262362
$309$	−1.91262	−0.108805
$310$	−1.48020	−0.0840699
$311$	−1.70969	−0.0969478	−0.0484739	−	0.998824i	$-0.515436\pi$
$311$	−1.70969	−0.0969478	−0.0484739	+	0.998824i	$0.515436\pi$
$312$	−0.837643	−0.0474222
$313$	−1.22566	−0.0692786	−0.0346393	−	0.999400i	$-0.511028\pi$
$313$	−1.22566	−0.0692786	−0.0346393	+	0.999400i	$0.511028\pi$
$314$	3.27423	0.184776
$315$	4.55124	0.256433
$316$	15.4767	0.870634
$317$	−6.51024	−0.365652	−0.182826	−	0.983145i	$-0.558524\pi$
$317$	−6.51024	−0.365652	−0.182826	+	0.983145i	$0.558524\pi$
$318$	−1.82467	−0.102322
$319$	7.09840	0.397434
$320$	14.1530	0.791174
$321$	10.8624	0.606279
$322$	−1.62586	−0.0906056
$323$	9.80366	0.545490
$324$	−1.96923	−0.109402
$325$	−1.45727	−0.0808346
$326$	4.26030	0.235956
$327$	−4.88139	−0.269941
$328$	−0.458615	−0.0253228
$329$	−14.9790	−0.825820
$330$	−0.341417	−0.0187944
$331$	−3.58938	−0.197290	−0.0986452	−	0.995123i	$-0.531451\pi$
$331$	−3.58938	−0.197290	−0.0986452	+	0.995123i	$0.531451\pi$
$332$	1.07049	0.0587508
$333$	5.37839	0.294734
$334$	2.36881	0.129615
$335$	20.6782	1.12977
$336$	8.92335	0.486809
$337$	−17.3602	−0.945668	−0.472834	−	0.881152i	$-0.656769\pi$
$337$	−17.3602	−0.945668	−0.472834	+	0.881152i	$0.656769\pi$
$338$	2.02632	0.110218
$339$	−14.1166	−0.766708
$340$	9.41865	0.510798
$341$	−4.33548	−0.234779
$342$	−0.699813	−0.0378416
$343$	19.9515	1.07728
$344$	5.23737	0.282380
$345$	−7.71646	−0.415440
$346$	−1.41703	−0.0761801
$347$	−4.43291	−0.237971	−0.118986	−	0.992896i	$-0.537964\pi$
$347$	−4.43291	−0.237971	−0.118986	+	0.992896i	$0.537964\pi$
$348$	13.9784	0.749321
$349$	−19.0402	−1.01920	−0.509600	−	0.860412i	$-0.670206\pi$
$349$	−19.0402	−1.01920	−0.509600	+	0.860412i	$0.670206\pi$
$350$	−0.496749	−0.0265523
$351$	−1.20314	−0.0642190
$352$	−2.06182	−0.109895
$353$	−29.9310	−1.59307	−0.796534	−	0.604594i	$-0.793335\pi$
$353$	−29.9310	−1.59307	−0.796534	+	0.604594i	$0.793335\pi$
$354$	−0.226150	−0.0120197
$355$	6.10014	0.323762
$356$	7.15102	0.379003
$357$	5.74541	0.304079
$358$	−0.232685	−0.0122978
$359$	−21.5910	−1.13953	−0.569763	−	0.821809i	$-0.692965\pi$
$359$	−21.5910	−1.13953	−0.569763	+	0.821809i	$0.692965\pi$
$360$	−1.35516	−0.0714234
$361$	−3.08180	−0.162200
$362$	−3.89077	−0.204494
$363$	−1.00000	−0.0524864
$364$	5.53980	0.290365
$365$	1.91104	0.100028
$366$	0.175402	0.00916842
$367$	−26.7903	−1.39844	−0.699220	−	0.714907i	$-0.746469\pi$
$367$	−26.7903	−1.39844	−0.699220	+	0.714907i	$0.746469\pi$
$368$	−15.1292	−0.788665
$369$	−0.658729	−0.0342921
$370$	1.83627	0.0954632
$371$	24.3236	1.26282
$372$	−8.53757	−0.442652
$373$	7.21077	0.373359	0.186680	−	0.982421i	$-0.440227\pi$
$373$	7.21077	0.373359	0.186680	+	0.982421i	$0.440227\pi$
$374$	−0.430999	−0.0222864
$375$	−12.0900	−0.624325
$376$	4.46010	0.230012
$377$	8.54039	0.439852
$378$	−0.410124	−0.0210945
$379$	0.711599	0.0365524	0.0182762	−	0.999833i	$-0.494182\pi$
$379$	0.711599	0.0365524	0.0182762	+	0.999833i	$0.494182\pi$
$380$	15.2931	0.784517
$381$	7.11962	0.364749
$382$	−1.65919	−0.0848915
$383$	10.0963	0.515895	0.257947	−	0.966159i	$-0.416954\pi$
$383$	10.0963	0.515895	0.257947	+	0.966159i	$0.416954\pi$
$384$	−5.39900	−0.275517
$385$	4.55124	0.231953
$386$	2.09499	0.106632
$387$	7.52267	0.382399
$388$	21.2632	1.07948
$389$	26.0432	1.32044	0.660221	−	0.751071i	$-0.270463\pi$
$389$	26.0432	1.32044	0.660221	+	0.751071i	$0.270463\pi$
$390$	−0.410773	−0.0208003
$391$	−9.74114	−0.492630
$392$	−1.06720	−0.0539018
$393$	6.50165	0.327965
$394$	−3.47896	−0.175267
$395$	15.2979	0.769721
$396$	−1.96923	−0.0989577
$397$	−5.03626	−0.252763	−0.126381	−	0.991982i	$-0.540336\pi$
$397$	−5.03626	−0.252763	−0.126381	+	0.991982i	$0.540336\pi$
$398$	2.94482	0.147611
$399$	9.32882	0.467025
$400$	−4.62243	−0.231121
$401$	17.6086	0.879331	0.439665	−	0.898162i	$-0.355097\pi$
$401$	17.6086	0.879331	0.439665	+	0.898162i	$0.355097\pi$
$402$	−1.86336	−0.0929360
$403$	−5.21620	−0.259837
$404$	−9.72454	−0.483814
$405$	−1.94648	−0.0967214
$406$	2.91122	0.144481
$407$	5.37839	0.266597
$408$	−1.71074	−0.0846940
$409$	31.6083	1.56293	0.781466	−	0.623948i	$-0.214472\pi$
$409$	31.6083	1.56293	0.781466	+	0.623948i	$0.214472\pi$
$410$	−0.224901	−0.0111071
$411$	10.0075	0.493632
$412$	−3.76639	−0.185557
$413$	3.01468	0.148343
$414$	0.695350	0.0341746
$415$	1.05812	0.0519411
$416$	−2.48067	−0.121625
$417$	7.82988	0.383431
$418$	−0.699813	−0.0342290
$419$	−23.9205	−1.16859	−0.584297	−	0.811540i	$-0.698630\pi$
$419$	−23.9205	−1.16859	−0.584297	+	0.811540i	$0.698630\pi$
$420$	8.96245	0.437323
$421$	19.6492	0.957641	0.478821	−	0.877913i	$-0.341064\pi$
$421$	19.6492	0.957641	0.478821	+	0.877913i	$0.341064\pi$
$422$	0.597824	0.0291016
$423$	6.40624	0.311482
$424$	−7.24253	−0.351728
$425$	−2.97621	−0.144367
$426$	−0.549698	−0.0266330
$427$	−2.33819	−0.113153
$428$	21.3906	1.03395
$429$	−1.20314	−0.0580883
$430$	2.56837	0.123858
$431$	9.23507	0.444838	0.222419	−	0.974951i	$-0.428605\pi$
$431$	9.23507	0.444838	0.222419	+	0.974951i	$0.428605\pi$
$432$	−3.81635	−0.183614
$433$	−12.6256	−0.606747	−0.303374	−	0.952872i	$-0.598113\pi$
$433$	−12.6256	−0.606747	−0.303374	+	0.952872i	$0.598113\pi$
$434$	−1.77808	−0.0853506
$435$	13.8169	0.662469
$436$	−9.61260	−0.460360
$437$	−15.8167	−0.756615
$438$	−0.172208	−0.00822843
$439$	6.21469	0.296611	0.148306	−	0.988942i	$-0.452618\pi$
$439$	6.21469	0.296611	0.148306	+	0.988942i	$0.452618\pi$
$440$	−1.35516	−0.0646049
$441$	−1.53287	−0.0729937
$442$	−0.518553	−0.0246651
$443$	6.48214	0.307976	0.153988	−	0.988073i	$-0.450788\pi$
$443$	6.48214	0.307976	0.153988	+	0.988073i	$0.450788\pi$
$444$	10.5913	0.502641
$445$	7.06839	0.335074
$446$	3.12589	0.148015
$447$	−14.6290	−0.691928
$448$	17.0011	0.803227
$449$	−6.98484	−0.329635	−0.164817	−	0.986324i	$-0.552704\pi$
$449$	−6.98484	−0.329635	−0.164817	+	0.986324i	$0.552704\pi$
$450$	0.212450	0.0100150
$451$	−0.658729	−0.0310184
$452$	−27.7989	−1.30755
$453$	−16.9514	−0.796446
$454$	−1.74206	−0.0817590
$455$	5.47579	0.256709
$456$	−2.77772	−0.130079
$457$	8.26252	0.386504	0.193252	−	0.981149i	$-0.438096\pi$
$457$	8.26252	0.386504	0.193252	+	0.981149i	$0.438096\pi$
$458$	3.70175	0.172972
$459$	−2.45720	−0.114692
$460$	−15.1955	−0.708495
$461$	42.8298	1.99478	0.997390	−	0.0721986i	$-0.0230016\pi$
$461$	42.8298	1.99478	0.997390	+	0.0721986i	$0.0230016\pi$
$462$	−0.410124	−0.0190807
$463$	−17.4064	−0.808942	−0.404471	−	0.914551i	$-0.632544\pi$
$463$	−17.4064	−0.808942	−0.404471	+	0.914551i	$0.632544\pi$
$464$	27.0900	1.25762
$465$	−8.43892	−0.391345
$466$	0.623376	0.0288773
$467$	13.3453	0.617549	0.308774	−	0.951135i	$-0.400081\pi$
$467$	13.3453	0.617549	0.308774	+	0.951135i	$0.400081\pi$
$468$	−2.36927	−0.109520
$469$	24.8394	1.14698
$470$	2.18720	0.100888
$471$	18.6670	0.860130
$472$	−0.897641	−0.0413173
$473$	7.52267	0.345893
$474$	−1.37853	−0.0633181
$475$	−4.83247	−0.221729
$476$	11.3141	0.518579
$477$	−10.4028	−0.476310
$478$	−3.15184	−0.144162
$479$	−31.9549	−1.46006	−0.730029	−	0.683416i	$-0.760493\pi$
$479$	−31.9549	−1.46006	−0.730029	+	0.683416i	$0.760493\pi$
$480$	−4.01329	−0.183181
$481$	6.47097	0.295051
$482$	−0.193473	−0.00881245
$483$	−9.26933	−0.421769
$484$	−1.96923	−0.0895106
$485$	21.0175	0.954357
$486$	0.175402	0.00795640
$487$	−0.149865	−0.00679102	−0.00339551	−	0.999994i	$-0.501081\pi$
$487$	−0.149865	−0.00679102	−0.00339551	+	0.999994i	$0.501081\pi$
$488$	0.696212	0.0315160
$489$	24.2887	1.09837
$490$	−0.523347	−0.0236424
$491$	−26.7529	−1.20734	−0.603671	−	0.797233i	$-0.706296\pi$
$491$	−26.7529	−1.20734	−0.603671	+	0.797233i	$0.706296\pi$
$492$	−1.29719	−0.0584819
$493$	17.4422	0.785558
$494$	−0.841975	−0.0378823
$495$	−1.94648	−0.0874878
$496$	−16.5457	−0.742924
$497$	7.32773	0.328694
$498$	−0.0953499	−0.00427273
$499$	−37.0114	−1.65686	−0.828429	−	0.560094i	$-0.810765\pi$
$499$	−37.0114	−1.65686	−0.828429	+	0.560094i	$0.810765\pi$
$500$	−23.8081	−1.06473
$501$	13.5050	0.603360
$502$	0.0790616	0.00352869
$503$	−23.0422	−1.02740	−0.513700	−	0.857970i	$-0.671726\pi$
$503$	−23.0422	−1.02740	−0.513700	+	0.857970i	$0.671726\pi$
$504$	−1.62788	−0.0725114
$505$	−9.61217	−0.427736
$506$	0.695350	0.0309121
$507$	11.5524	0.513062
$508$	14.0202	0.622046
$509$	−10.4622	−0.463727	−0.231864	−	0.972748i	$-0.574482\pi$
$509$	−10.4622	−0.463727	−0.231864	+	0.972748i	$0.574482\pi$
$510$	−0.838931	−0.0371485
$511$	2.29561	0.101552
$512$	−13.1826	−0.582595
$513$	−3.98976	−0.176152
$514$	−2.75170	−0.121372
$515$	−3.72287	−0.164049
$516$	14.8139	0.652145
$517$	6.40624	0.281746
$518$	2.20580	0.0969174
$519$	−8.07876	−0.354618
$520$	−1.63045	−0.0715002
$521$	14.2583	0.624668	0.312334	−	0.949972i	$-0.398889\pi$
$521$	14.2583	0.624668	0.312334	+	0.949972i	$0.398889\pi$
$522$	−1.24507	−0.0544954
$523$	−9.92075	−0.433804	−0.216902	−	0.976193i	$-0.569595\pi$
$523$	−9.92075	−0.433804	−0.216902	+	0.976193i	$0.569595\pi$
$524$	12.8033	0.559313
$525$	−2.83205	−0.123601
$526$	−2.63708	−0.114982
$527$	−10.6532	−0.464059
$528$	−3.81635	−0.166085
$529$	−7.28419	−0.316704
$530$	−3.55168	−0.154275
$531$	−1.28932	−0.0559518
$532$	18.3706	0.796468
$533$	−0.792546	−0.0343290
$534$	−0.636950	−0.0275635
$535$	21.1434	0.914108
$536$	−7.39611	−0.319463
$537$	−1.32658	−0.0572460
$538$	4.02520	0.173539
$539$	−1.53287	−0.0660253
$540$	−3.83307	−0.164949
$541$	−28.2861	−1.21612	−0.608058	−	0.793892i	$-0.708051\pi$
$541$	−28.2861	−1.21612	−0.608058	+	0.793892i	$0.708051\pi$
$542$	−2.66048	−0.114277
$543$	−22.1820	−0.951921
$544$	−5.06631	−0.217216
$545$	−9.50153	−0.407001
$546$	−0.493437	−0.0211172
$547$	8.25464	0.352943	0.176471	−	0.984306i	$-0.443532\pi$
$547$	8.25464	0.352943	0.176471	+	0.984306i	$0.443532\pi$
$548$	19.7070	0.841843
$549$	1.00000	0.0426790
$550$	0.212450	0.00905890
$551$	28.3209	1.20651
$552$	2.76001	0.117474
$553$	18.3765	0.781446
$554$	2.14355	0.0910706
$555$	10.4689	0.444381
$556$	15.4189	0.653906
$557$	17.7862	0.753626	0.376813	−	0.926289i	$-0.377020\pi$
$557$	17.7862	0.753626	0.376813	+	0.926289i	$0.377020\pi$
$558$	0.760452	0.0321925
$559$	9.05085	0.382810
$560$	17.3691	0.733980
$561$	−2.45720	−0.103743
$562$	4.95054	0.208826
$563$	−18.5702	−0.782641	−0.391320	−	0.920255i	$-0.627982\pi$
$563$	−18.5702	−0.782641	−0.391320	+	0.920255i	$0.627982\pi$
$564$	12.6154	0.531204
$565$	−27.4776	−1.15599
$566$	−2.10059	−0.0882944
$567$	−2.33819	−0.0981947
$568$	−2.18188	−0.0915497
$569$	−13.7784	−0.577622	−0.288811	−	0.957386i	$-0.593260\pi$
$569$	−13.7784	−0.577622	−0.288811	+	0.957386i	$0.593260\pi$
$570$	−1.36217	−0.0570551
$571$	−17.1218	−0.716524	−0.358262	−	0.933621i	$-0.616631\pi$
$571$	−17.1218	−0.716524	−0.358262	+	0.933621i	$0.616631\pi$
$572$	−2.36927	−0.0990642
$573$	−9.45935	−0.395170
$574$	−0.270160	−0.0112763
$575$	4.80165	0.200243
$576$	−7.27105	−0.302961
$577$	−4.76318	−0.198294	−0.0991468	−	0.995073i	$-0.531611\pi$
$577$	−4.76318	−0.198294	−0.0991468	+	0.995073i	$0.531611\pi$
$578$	1.92278	0.0799773
$579$	11.9439	0.496371
$580$	27.2087	1.12978
$581$	1.27106	0.0527323
$582$	−1.89394	−0.0785064
$583$	−10.4028	−0.430838
$584$	−0.683535	−0.0282849
$585$	−2.34189	−0.0968254
$586$	−0.449404	−0.0185647
$587$	−25.4505	−1.05045	−0.525227	−	0.850962i	$-0.676020\pi$
$587$	−25.4505	−1.05045	−0.525227	+	0.850962i	$0.676020\pi$
$588$	−3.01858	−0.124484
$589$	−17.2975	−0.712732
$590$	−0.440196	−0.0181226
$591$	−19.8342	−0.815870
$592$	20.5258	0.843606
$593$	12.8704	0.528522	0.264261	−	0.964451i	$-0.414872\pi$
$593$	12.8704	0.528522	0.264261	+	0.964451i	$0.414872\pi$
$594$	0.175402	0.00719684
$595$	11.1833	0.458472
$596$	−28.8079	−1.18002
$597$	16.7890	0.687127
$598$	0.836605	0.0342113
$599$	6.63541	0.271116	0.135558	−	0.990769i	$-0.456717\pi$
$599$	6.63541	0.271116	0.135558	+	0.990769i	$0.456717\pi$
$600$	0.843264	0.0344261
$601$	−26.2081	−1.06905	−0.534525	−	0.845153i	$-0.679509\pi$
$601$	−26.2081	−1.06905	−0.534525	+	0.845153i	$0.679509\pi$
$602$	3.08522	0.125744
$603$	−10.6234	−0.432617
$604$	−33.3813	−1.35827
$605$	−1.94648	−0.0791357
$606$	0.866177	0.0351860
$607$	22.3966	0.909049	0.454525	−	0.890734i	$-0.349809\pi$
$607$	22.3966	0.909049	0.454525	+	0.890734i	$0.349809\pi$
$608$	−8.22617	−0.333615
$609$	16.5974	0.672561
$610$	0.341417	0.0138236
$611$	7.70763	0.311817
$612$	−4.83881	−0.195597
$613$	4.14353	0.167356	0.0836778	−	0.996493i	$-0.473333\pi$
$613$	4.14353	0.167356	0.0836778	+	0.996493i	$0.473333\pi$
$614$	4.92968	0.198946
$615$	−1.28220	−0.0517034
$616$	−1.62788	−0.0655890
$617$	43.5279	1.75237	0.876184	−	0.481978i	$-0.160081\pi$
$617$	43.5279	1.75237	0.876184	+	0.481978i	$0.160081\pi$
$618$	0.335477	0.0134949
$619$	−9.08565	−0.365183	−0.182592	−	0.983189i	$-0.558449\pi$
$619$	−9.08565	−0.365183	−0.182592	+	0.983189i	$0.558449\pi$
$620$	−16.6182	−0.667403
$621$	3.96432	0.159083
$622$	0.299884	0.0120243
$623$	8.49083	0.340178
$624$	−4.59162	−0.183812
$625$	−17.4769	−0.699075
$626$	0.214984	0.00859250
$627$	−3.98976	−0.159336
$628$	36.7597	1.46687
$629$	13.2158	0.526948
$630$	−0.798297	−0.0318049
$631$	27.2227	1.08372	0.541858	−	0.840470i	$-0.317721\pi$
$631$	27.2227	1.08372	0.541858	+	0.840470i	$0.317721\pi$
$632$	−5.47172	−0.217653
$633$	3.40830	0.135468
$634$	1.14191	0.0453511
$635$	13.8582	0.549946
$636$	−20.4855	−0.812302
$637$	−1.84426	−0.0730722
$638$	−1.24507	−0.0492930
$639$	−3.13393	−0.123976
$640$	−10.5090	−0.415406
$641$	27.4517	1.08428	0.542138	−	0.840289i	$-0.317615\pi$
$641$	27.4517	1.08428	0.542138	+	0.840289i	$0.317615\pi$
$642$	−1.90528	−0.0751956
$643$	14.5385	0.573342	0.286671	−	0.958029i	$-0.407451\pi$
$643$	14.5385	0.573342	0.286671	+	0.958029i	$0.407451\pi$
$644$	−18.2535	−0.719288
$645$	14.6427	0.576557
$646$	−1.71958	−0.0676561
$647$	−40.0601	−1.57492	−0.787462	−	0.616363i	$-0.788605\pi$
$647$	−40.0601	−1.57492	−0.787462	+	0.616363i	$0.788605\pi$
$648$	0.696212	0.0273498
$649$	−1.28932	−0.0506103
$650$	0.255608	0.0100258
$651$	−10.1372	−0.397307
$652$	47.8302	1.87318
$653$	11.1425	0.436040	0.218020	−	0.975944i	$-0.430040\pi$
$653$	11.1425	0.436040	0.218020	+	0.975944i	$0.430040\pi$
$654$	0.856206	0.0334803
$655$	12.6553	0.494484
$656$	−2.51394	−0.0981530
$657$	−0.981791	−0.0383033
$658$	2.62735	0.102425
$659$	−5.19796	−0.202484	−0.101242	−	0.994862i	$-0.532282\pi$
$659$	−5.19796	−0.202484	−0.101242	+	0.994862i	$0.532282\pi$
$660$	−3.83307	−0.149202
$661$	−10.7941	−0.419843	−0.209921	−	0.977718i	$-0.567321\pi$
$661$	−10.7941	−0.419843	−0.209921	+	0.977718i	$0.567321\pi$
$662$	0.629586	0.0244695
$663$	−2.95637	−0.114816
$664$	−0.378466	−0.0146873
$665$	18.1584	0.704151
$666$	−0.943381	−0.0365553
$667$	−28.1403	−1.08960
$668$	26.5945	1.02897
$669$	17.8213	0.689011
$670$	−3.62699	−0.140123
$671$	1.00000	0.0386046
$672$	−4.82093	−0.185971
$673$	11.2743	0.434593	0.217297	−	0.976106i	$-0.430276\pi$
$673$	11.2743	0.434593	0.217297	+	0.976106i	$0.430276\pi$
$674$	3.04501	0.117289
$675$	1.21122	0.0466198
$676$	22.7495	0.874980
$677$	8.45712	0.325034	0.162517	−	0.986706i	$-0.448039\pi$
$677$	8.45712	0.325034	0.162517	+	0.986706i	$0.448039\pi$
$678$	2.47608	0.0950932
$679$	25.2471	0.968895
$680$	−3.32991	−0.127696
$681$	−9.93182	−0.380588
$682$	0.760452	0.0291192
$683$	−27.7894	−1.06333	−0.531665	−	0.846955i	$-0.678433\pi$
$683$	−27.7894	−1.06333	−0.531665	+	0.846955i	$0.678433\pi$
$684$	−7.85678	−0.300411
$685$	19.4793	0.744267
$686$	−3.49953	−0.133613
$687$	21.1044	0.805182
$688$	28.7091	1.09453
$689$	−12.5160	−0.476822
$690$	1.35348	0.0515263
$691$	−48.8213	−1.85725	−0.928625	−	0.371019i	$-0.879008\pi$
$691$	−48.8213	−1.85725	−0.928625	+	0.371019i	$0.879008\pi$
$692$	−15.9090	−0.604768
$693$	−2.33819	−0.0888205
$694$	0.777543	0.0295151
$695$	15.2407	0.578113
$696$	−4.94199	−0.187326
$697$	−1.61863	−0.0613101
$698$	3.33969	0.126409
$699$	3.55398	0.134424
$700$	−5.57698	−0.210790
$701$	13.4661	0.508608	0.254304	−	0.967124i	$-0.418154\pi$
$701$	13.4661	0.508608	0.254304	+	0.967124i	$0.418154\pi$
$702$	0.211034	0.00796496
$703$	21.4585	0.809322
$704$	−7.27105	−0.274038
$705$	12.4696	0.469633
$706$	5.24997	0.197585
$707$	−11.5465	−0.434252
$708$	−2.53898	−0.0954206
$709$	−10.0545	−0.377604	−0.188802	−	0.982015i	$-0.560460\pi$
$709$	−10.0545	−0.377604	−0.188802	+	0.982015i	$0.560460\pi$
$710$	−1.06998	−0.0401555
$711$	−7.85927	−0.294745
$712$	−2.52820	−0.0947485
$713$	17.1872	0.643666
$714$	−1.00776	−0.0377144
$715$	−2.34189	−0.0875819
$716$	−2.61234	−0.0976278
$717$	−17.9692	−0.671073
$718$	3.78710	0.141333
$719$	−4.45172	−0.166021	−0.0830106	−	0.996549i	$-0.526454\pi$
$719$	−4.45172	−0.166021	−0.0830106	+	0.996549i	$0.526454\pi$
$720$	−7.42845	−0.276842
$721$	−4.47206	−0.166548
$722$	0.540554	0.0201173
$723$	−1.10303	−0.0410219
$724$	−43.6816	−1.62341
$725$	−8.59770	−0.319311
$726$	0.175402	0.00650978
$727$	−16.5944	−0.615452	−0.307726	−	0.951475i	$-0.599568\pi$
$727$	−16.5944	−0.615452	−0.307726	+	0.951475i	$0.599568\pi$
$728$	−1.95857	−0.0725894
$729$	1.00000	0.0370370
$730$	−0.335200	−0.0124063
$731$	18.4847	0.683683
$732$	1.96923	0.0727850
$733$	−32.8923	−1.21490	−0.607452	−	0.794357i	$-0.707808\pi$
$733$	−32.8923	−1.21490	−0.607452	+	0.794357i	$0.707808\pi$
$734$	4.69907	0.173446
$735$	−2.98370	−0.110055
$736$	8.17371	0.301287
$737$	−10.6234	−0.391317
$738$	0.115543	0.00425318
$739$	−0.954671	−0.0351182	−0.0175591	−	0.999846i	$-0.505590\pi$
$739$	−0.954671	−0.0351182	−0.0175591	+	0.999846i	$0.505590\pi$
$740$	20.6158	0.757850
$741$	−4.80025	−0.176342
$742$	−4.26642	−0.156625
$743$	−40.3931	−1.48188	−0.740939	−	0.671573i	$-0.765619\pi$
$743$	−40.3931	−1.48188	−0.740939	+	0.671573i	$0.765619\pi$
$744$	3.01841	0.110660
$745$	−28.4750	−1.04324
$746$	−1.26478	−0.0463070
$747$	−0.543607	−0.0198895
$748$	−4.83881	−0.176924
$749$	25.3983	0.928033
$750$	2.12061	0.0774339
$751$	12.8754	0.469832	0.234916	−	0.972016i	$-0.424519\pi$
$751$	12.8754	0.469832	0.234916	+	0.972016i	$0.424519\pi$
$752$	24.4485	0.891544
$753$	0.450745	0.0164261
$754$	−1.49800	−0.0545540
$755$	−32.9956	−1.20083
$756$	−4.60444	−0.167462
$757$	10.2071	0.370982	0.185491	−	0.982646i	$-0.440612\pi$
$757$	10.2071	0.370982	0.185491	+	0.982646i	$0.440612\pi$
$758$	−0.124816	−0.00453352
$759$	3.96432	0.143896
$760$	−5.40678	−0.196124
$761$	34.7993	1.26147	0.630737	−	0.775997i	$-0.282753\pi$
$761$	34.7993	1.26147	0.630737	+	0.775997i	$0.282753\pi$
$762$	−1.24880	−0.0452391
$763$	−11.4136	−0.413201
$764$	−18.6277	−0.673925
$765$	−4.78290	−0.172926
$766$	−1.77091	−0.0639854
$767$	−1.55124	−0.0560120
$768$	−13.5951	−0.490571
$769$	−29.0576	−1.04784	−0.523921	−	0.851767i	$-0.675531\pi$
$769$	−29.0576	−1.04784	−0.523921	+	0.851767i	$0.675531\pi$
$770$	−0.798297	−0.0287686
$771$	−15.6879	−0.564987
$772$	23.5203	0.846515
$773$	7.89899	0.284107	0.142053	−	0.989859i	$-0.454630\pi$
$773$	7.89899	0.284107	0.142053	+	0.989859i	$0.454630\pi$
$774$	−1.31949	−0.0474282
$775$	5.25120	0.188629
$776$	−7.51750	−0.269862
$777$	12.5757	0.451150
$778$	−4.56803	−0.163772
$779$	−2.62817	−0.0941641
$780$	−4.61174	−0.165127
$781$	−3.13393	−0.112141
$782$	1.70862	0.0611000
$783$	−7.09840	−0.253676
$784$	−5.84996	−0.208927
$785$	36.3350	1.29685
$786$	−1.14040	−0.0406768
$787$	−50.8342	−1.81204	−0.906022	−	0.423231i	$-0.860896\pi$
$787$	−50.8342	−1.81204	−0.906022	+	0.423231i	$0.860896\pi$
$788$	−39.0582	−1.39139
$789$	−15.0345	−0.535242
$790$	−2.68328	−0.0954670
$791$	−33.0073	−1.17360
$792$	0.696212	0.0247388
$793$	1.20314	0.0427249
$794$	0.883371	0.0313497
$795$	−20.2488	−0.718150
$796$	33.0614	1.17183
$797$	−17.2545	−0.611184	−0.305592	−	0.952163i	$-0.598854\pi$
$797$	−17.2545	−0.611184	−0.305592	+	0.952163i	$0.598854\pi$
$798$	−1.63630	−0.0579242
$799$	15.7414	0.556892
$800$	2.49731	0.0882933
$801$	−3.63137	−0.128308
$802$	−3.08858	−0.109062
$803$	−0.981791	−0.0346467
$804$	−20.9199	−0.737787
$805$	−18.0426	−0.635916
$806$	0.914932	0.0322271
$807$	22.9484	0.807823
$808$	3.43806	0.120950
$809$	−25.5618	−0.898706	−0.449353	−	0.893354i	$-0.648345\pi$
$809$	−25.5618	−0.898706	−0.449353	+	0.893354i	$0.648345\pi$
$810$	0.341417	0.0119962
$811$	35.0500	1.23077	0.615387	−	0.788225i	$-0.289000\pi$
$811$	35.0500	1.23077	0.615387	+	0.788225i	$0.289000\pi$
$812$	32.6842	1.14699
$813$	−15.1679	−0.531961
$814$	−0.943381	−0.0330655
$815$	47.2775	1.65606
$816$	−9.37755	−0.328280
$817$	30.0137	1.05005
$818$	−5.54417	−0.193847
$819$	−2.81318	−0.0983004
$820$	−2.52496	−0.0881754
$821$	36.6762	1.28001	0.640005	−	0.768371i	$-0.278932\pi$
$821$	36.6762	1.28001	0.640005	+	0.768371i	$0.278932\pi$
$822$	−1.75533	−0.0612242
$823$	17.1754	0.598698	0.299349	−	0.954144i	$-0.403231\pi$
$823$	17.1754	0.598698	0.299349	+	0.954144i	$0.403231\pi$
$824$	1.33159	0.0463880
$825$	1.21122	0.0421692
$826$	−0.528781	−0.0183986
$827$	−38.7176	−1.34634	−0.673171	−	0.739487i	$-0.735068\pi$
$827$	−38.7176	−1.34634	−0.673171	+	0.739487i	$0.735068\pi$
$828$	7.80667	0.271300
$829$	31.1164	1.08072	0.540359	−	0.841434i	$-0.318288\pi$
$829$	31.1164	1.08072	0.540359	+	0.841434i	$0.318288\pi$
$830$	−0.185597	−0.00644215
$831$	12.2208	0.423934
$832$	−8.74812	−0.303286
$833$	−3.76657	−0.130504
$834$	−1.37338	−0.0475562
$835$	26.2872	0.909707
$836$	−7.85678	−0.271732
$837$	4.33548	0.149856
$838$	4.19571	0.144938
$839$	13.4509	0.464376	0.232188	−	0.972671i	$-0.425412\pi$
$839$	13.4509	0.464376	0.232188	+	0.972671i	$0.425412\pi$
$840$	−3.16863	−0.109328
$841$	21.3873	0.737492
$842$	−3.44650	−0.118774
$843$	28.2239	0.972083
$844$	6.71175	0.231028
$845$	22.4866	0.773563
$846$	−1.12367	−0.0386325
$847$	−2.33819	−0.0803412
$848$	−39.7006	−1.36332
$849$	−11.9759	−0.411010
$850$	0.522033	0.0179056
$851$	−21.3216	−0.730896
$852$	−6.17145	−0.211430
$853$	29.2191	1.00044	0.500222	−	0.865897i	$-0.333252\pi$
$853$	29.2191	1.00044	0.500222	+	0.865897i	$0.333252\pi$
$854$	0.410124	0.0140341
$855$	−7.76599	−0.265591
$856$	−7.56252	−0.258482
$857$	0.972589	0.0332230	0.0166115	−	0.999862i	$-0.494712\pi$
$857$	0.972589	0.0332230	0.0166115	+	0.999862i	$0.494712\pi$
$858$	0.211034	0.00720458
$859$	29.8383	1.01807	0.509035	−	0.860746i	$-0.330002\pi$
$859$	29.8383	1.01807	0.509035	+	0.860746i	$0.330002\pi$
$860$	28.8349	0.983264
$861$	−1.54023	−0.0524910
$862$	−1.61985	−0.0551724
$863$	2.08758	0.0710619	0.0355309	−	0.999369i	$-0.488688\pi$
$863$	2.08758	0.0710619	0.0355309	+	0.999369i	$0.488688\pi$
$864$	2.06182	0.0701446
$865$	−15.7251	−0.534671
$866$	2.21456	0.0752537
$867$	10.9621	0.372294
$868$	−19.9625	−0.677570
$869$	−7.85927	−0.266607
$870$	−2.42351	−0.0821648
$871$	−12.7814	−0.433082
$872$	3.39848	0.115087
$873$	−10.7977	−0.365447
$874$	2.77428	0.0938414
$875$	−28.2687	−0.955658
$876$	−1.93338	−0.0653228
$877$	−10.5762	−0.357133	−0.178567	−	0.983928i	$-0.557146\pi$
$877$	−10.5762	−0.357133	−0.178567	+	0.983928i	$0.557146\pi$
$878$	−1.09007	−0.0367881
$879$	−2.56213	−0.0864186
$880$	−7.42845	−0.250413
$881$	47.1685	1.58915	0.794573	−	0.607169i	$-0.207695\pi$
$881$	47.1685	1.58915	0.794573	+	0.607169i	$0.207695\pi$
$882$	0.268868	0.00905327
$883$	9.08871	0.305860	0.152930	−	0.988237i	$-0.451129\pi$
$883$	9.08871	0.305860	0.152930	+	0.988237i	$0.451129\pi$
$884$	−5.82178	−0.195808
$885$	−2.50964	−0.0843606
$886$	−1.13698	−0.0381977
$887$	−45.1590	−1.51629	−0.758146	−	0.652085i	$-0.773895\pi$
$887$	−45.1590	−1.51629	−0.758146	+	0.652085i	$0.773895\pi$
$888$	−3.74450	−0.125657
$889$	16.6470	0.558323
$890$	−1.23981	−0.0415585
$891$	1.00000	0.0335013
$892$	35.0943	1.17504
$893$	25.5594	0.855312
$894$	2.56596	0.0858184
$895$	−2.58216	−0.0863120
$896$	−12.6239	−0.421734
$897$	4.76964	0.159254
$898$	1.22516	0.0408840
$899$	−30.7749	−1.02640
$900$	2.38517	0.0795056
$901$	−25.5617	−0.851584
$902$	0.115543	0.00384715
$903$	17.5894	0.585340
$904$	9.82814	0.326879
$905$	−43.1768	−1.43525
$906$	2.97331	0.0987817
$907$	10.1993	0.338663	0.169332	−	0.985559i	$-0.445839\pi$
$907$	10.1993	0.338663	0.169332	+	0.985559i	$0.445839\pi$
$908$	−19.5581	−0.649058
$909$	4.93823	0.163791
$910$	−0.960466	−0.0318391
$911$	43.0928	1.42773	0.713864	−	0.700284i	$-0.246943\pi$
$911$	43.0928	1.42773	0.713864	+	0.700284i	$0.246943\pi$
$912$	−15.2263	−0.504194
$913$	−0.543607	−0.0179908
$914$	−1.44926	−0.0479374
$915$	1.94648	0.0643486
$916$	41.5595	1.37316
$917$	15.2021	0.502017
$918$	0.430999	0.0142251
$919$	−9.27761	−0.306040	−0.153020	−	0.988223i	$-0.548900\pi$
$919$	−9.27761	−0.306040	−0.153020	+	0.988223i	$0.548900\pi$
$920$	5.37230	0.177119
$921$	28.1050	0.926092
$922$	−7.51243	−0.247409
$923$	−3.77057	−0.124110
$924$	−4.60444	−0.151475
$925$	−6.51439	−0.214192
$926$	3.05311	0.100332
$927$	1.91262	0.0628185
$928$	−14.6356	−0.480438
$929$	7.87934	0.258513	0.129256	−	0.991611i	$-0.458741\pi$
$929$	7.87934	0.258513	0.129256	+	0.991611i	$0.458741\pi$
$930$	1.48020	0.0485378
$931$	−6.11578	−0.200437
$932$	6.99862	0.229247
$933$	1.70969	0.0559729
$934$	−2.34080	−0.0765934
$935$	−4.78290	−0.156417
$936$	0.837643	0.0273792
$937$	−4.11414	−0.134403	−0.0672015	−	0.997739i	$-0.521407\pi$
$937$	−4.11414	−0.134403	−0.0672015	+	0.997739i	$0.521407\pi$
$938$	−4.35689	−0.142258
$939$	1.22566	0.0399980
$940$	24.5556	0.800915
$941$	−56.3009	−1.83536	−0.917678	−	0.397325i	$-0.869939\pi$
$941$	−56.3009	−1.83536	−0.917678	+	0.397325i	$0.869939\pi$
$942$	−3.27423	−0.106680
$943$	2.61141	0.0850393
$944$	−4.92050	−0.160149
$945$	−4.55124	−0.148052
$946$	−1.31949	−0.0429004
$947$	−47.2000	−1.53379	−0.766897	−	0.641770i	$-0.778201\pi$
$947$	−47.2000	−1.53379	−0.766897	+	0.641770i	$0.778201\pi$
$948$	−15.4767	−0.502661
$949$	−1.18124	−0.0383445
$950$	0.847625	0.0275006
$951$	6.51024	0.211109
$952$	−4.00002	−0.129642
$953$	−44.1009	−1.42857	−0.714284	−	0.699856i	$-0.753247\pi$
$953$	−44.1009	−1.42857	−0.714284	+	0.699856i	$0.753247\pi$
$954$	1.82467	0.0590758
$955$	−18.4124	−0.595812
$956$	−35.3856	−1.14445
$957$	−7.09840	−0.229459
$958$	5.60496	0.181088
$959$	23.3994	0.755605
$960$	−14.1530	−0.456785
$961$	−12.2036	−0.393666
$962$	−1.13502	−0.0365946
$963$	−10.8624	−0.350035
$964$	−2.17211	−0.0699591
$965$	23.2486	0.748397
$966$	1.62586	0.0523112
$967$	−10.1271	−0.325665	−0.162832	−	0.986654i	$-0.552063\pi$
$967$	−10.1271	−0.325665	−0.162832	+	0.986654i	$0.552063\pi$
$968$	0.696212	0.0223771
$969$	−9.80366	−0.314939
$970$	−3.68652	−0.118367
$971$	−16.7972	−0.539049	−0.269525	−	0.962994i	$-0.586867\pi$
$971$	−16.7972	−0.539049	−0.269525	+	0.962994i	$0.586867\pi$
$972$	1.96923	0.0631632
$973$	18.3078	0.586920
$974$	0.0262866	0.000842277 0
$975$	1.45727	0.0466699
$976$	3.81635	0.122158
$977$	−49.6683	−1.58903	−0.794514	−	0.607246i	$-0.792274\pi$
$977$	−49.6683	−1.58903	−0.794514	+	0.607246i	$0.792274\pi$
$978$	−4.26030	−0.136229
$979$	−3.63137	−0.116059
$980$	−5.87560	−0.187689
$981$	4.88139	0.155851
$982$	4.69252	0.149744
$983$	−14.4129	−0.459699	−0.229849	−	0.973226i	$-0.573823\pi$
$983$	−14.4129	−0.459699	−0.229849	+	0.973226i	$0.573823\pi$
$984$	0.458615	0.0146201
$985$	−38.6068	−1.23012
$986$	−3.05940	−0.0974312
$987$	14.9790	0.476787
$988$	−9.45283	−0.300734
$989$	−29.8222	−0.948292
$990$	0.341417	0.0108509
$991$	48.1124	1.52834	0.764171	−	0.645014i	$-0.223148\pi$
$991$	48.1124	1.52834	0.764171	+	0.645014i	$0.223148\pi$
$992$	8.93897	0.283813
$993$	3.58938	0.113906
$994$	−1.28530	−0.0407672
$995$	32.6794	1.03601
$996$	−1.07049	−0.0339198
$997$	−31.1416	−0.986263	−0.493132	−	0.869955i	$-0.664148\pi$
$997$	−31.1416	−0.986263	−0.493132	+	0.869955i	$0.664148\pi$
$998$	6.49188	0.205497
$999$	−5.37839	−0.170165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.b.1.6	✓	11
3.2	odd	2		6039.2.a.c.1.6		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.b.1.6	✓	11	1.1	even	1	trivial
6039.2.a.c.1.6		11	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-0.175402 q^{2} -1.00000 q^{3} -1.96923 q^{4} -1.94648 q^{5} +0.175402 q^{6} -2.33819 q^{7} +0.696212 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.175402 q^{2} -1.00000 q^{3} -1.96923 q^{4} -1.94648 q^{5} +0.175402 q^{6} -2.33819 q^{7} +0.696212 q^{8} +1.00000 q^{9} +0.341417 q^{10} +1.00000 q^{11} +1.96923 q^{12} +1.20314 q^{13} +0.410124 q^{14} +1.94648 q^{15} +3.81635 q^{16} +2.45720 q^{17} -0.175402 q^{18} +3.98976 q^{19} +3.83307 q^{20} +2.33819 q^{21} -0.175402 q^{22} -3.96432 q^{23} -0.696212 q^{24} -1.21122 q^{25} -0.211034 q^{26} -1.00000 q^{27} +4.60444 q^{28} +7.09840 q^{29} -0.341417 q^{30} -4.33548 q^{31} -2.06182 q^{32} -1.00000 q^{33} -0.430999 q^{34} +4.55124 q^{35} -1.96923 q^{36} +5.37839 q^{37} -0.699813 q^{38} -1.20314 q^{39} -1.35516 q^{40} -0.658729 q^{41} -0.410124 q^{42} +7.52267 q^{43} -1.96923 q^{44} -1.94648 q^{45} +0.695350 q^{46} +6.40624 q^{47} -3.81635 q^{48} -1.53287 q^{49} +0.212450 q^{50} -2.45720 q^{51} -2.36927 q^{52} -10.4028 q^{53} +0.175402 q^{54} -1.94648 q^{55} -1.62788 q^{56} -3.98976 q^{57} -1.24507 q^{58} -1.28932 q^{59} -3.83307 q^{60} +1.00000 q^{61} +0.760452 q^{62} -2.33819 q^{63} -7.27105 q^{64} -2.34189 q^{65} +0.175402 q^{66} -10.6234 q^{67} -4.83881 q^{68} +3.96432 q^{69} -0.798297 q^{70} -3.13393 q^{71} +0.696212 q^{72} -0.981791 q^{73} -0.943381 q^{74} +1.21122 q^{75} -7.85678 q^{76} -2.33819 q^{77} +0.211034 q^{78} -7.85927 q^{79} -7.42845 q^{80} +1.00000 q^{81} +0.115543 q^{82} -0.543607 q^{83} -4.60444 q^{84} -4.78290 q^{85} -1.31949 q^{86} -7.09840 q^{87} +0.696212 q^{88} -3.63137 q^{89} +0.341417 q^{90} -2.81318 q^{91} +7.80667 q^{92} +4.33548 q^{93} -1.12367 q^{94} -7.76599 q^{95} +2.06182 q^{96} -10.7977 q^{97} +0.268868 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) \) 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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