LMFDB - Embedded newform 2013.2.a.a.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} - 4x^{10} - 6x^{9} + 37x^{8} - 2x^{7} - 109x^{6} + 55x^{5} + 115x^{4} - 76x^{3} - 29x^{2} + 14x + 3 $ x^11 - 4x^10 - 6x^9 + 37x^8 - 2x^7 - 109x^6 + 55x^5 + 115x^4 - 76x^3 - 29x^2 + 14x + 3
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			$-1.35090$ 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)

$f(q)$	$=$	$q+1.35090 q^{2} +1.00000 q^{3} -0.175068 q^{4} -0.638467 q^{5} +1.35090 q^{6} -0.931245 q^{7} -2.93830 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.35090 q^{2} +1.00000 q^{3} -0.175068 q^{4} -0.638467 q^{5} +1.35090 q^{6} -0.931245 q^{7} -2.93830 q^{8} +1.00000 q^{9} -0.862505 q^{10} -1.00000 q^{11} -0.175068 q^{12} -3.34774 q^{13} -1.25802 q^{14} -0.638467 q^{15} -3.61922 q^{16} +6.34917 q^{17} +1.35090 q^{18} -6.01493 q^{19} +0.111775 q^{20} -0.931245 q^{21} -1.35090 q^{22} +8.35167 q^{23} -2.93830 q^{24} -4.59236 q^{25} -4.52246 q^{26} +1.00000 q^{27} +0.163031 q^{28} -7.15859 q^{29} -0.862505 q^{30} -1.16267 q^{31} +0.987402 q^{32} -1.00000 q^{33} +8.57709 q^{34} +0.594569 q^{35} -0.175068 q^{36} -7.31872 q^{37} -8.12557 q^{38} -3.34774 q^{39} +1.87601 q^{40} -4.22398 q^{41} -1.25802 q^{42} -10.6385 q^{43} +0.175068 q^{44} -0.638467 q^{45} +11.2823 q^{46} -13.3623 q^{47} -3.61922 q^{48} -6.13278 q^{49} -6.20382 q^{50} +6.34917 q^{51} +0.586082 q^{52} +1.73638 q^{53} +1.35090 q^{54} +0.638467 q^{55} +2.73628 q^{56} -6.01493 q^{57} -9.67054 q^{58} -3.21625 q^{59} +0.111775 q^{60} +1.00000 q^{61} -1.57065 q^{62} -0.931245 q^{63} +8.57231 q^{64} +2.13742 q^{65} -1.35090 q^{66} -0.674112 q^{67} -1.11154 q^{68} +8.35167 q^{69} +0.803204 q^{70} -10.5817 q^{71} -2.93830 q^{72} +10.5531 q^{73} -9.88686 q^{74} -4.59236 q^{75} +1.05302 q^{76} +0.931245 q^{77} -4.52246 q^{78} +16.8703 q^{79} +2.31075 q^{80} +1.00000 q^{81} -5.70618 q^{82} +12.3348 q^{83} +0.163031 q^{84} -4.05373 q^{85} -14.3716 q^{86} -7.15859 q^{87} +2.93830 q^{88} -3.25248 q^{89} -0.862505 q^{90} +3.11757 q^{91} -1.46211 q^{92} -1.16267 q^{93} -18.0511 q^{94} +3.84033 q^{95} +0.987402 q^{96} -11.7707 q^{97} -8.28478 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 4 q^{2} + 11 q^{3} + 6 q^{4} - 13 q^{5} - 4 q^{6} - 5 q^{7} - 9 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 4 * q^2 + 11 * q^3 + 6 * q^4 - 13 * q^5 - 4 * q^6 - 5 * q^7 - 9 * q^8 + 11 * q^9	\( 11 q - 4 q^{2} + 11 q^{3} + 6 q^{4} - 13 q^{5} - 4 q^{6} - 5 q^{7} - 9 q^{8} + 11 q^{9} + 6 q^{10} - 11 q^{11} + 6 q^{12} - 3 q^{13} - 9 q^{14} - 13 q^{15} + 4 q^{16} - 7 q^{17} - 4 q^{18} - 8 q^{19} - 25 q^{20} - 5 q^{21} + 4 q^{22} - 15 q^{23} - 9 q^{24} + 4 q^{25} - 2 q^{26} + 11 q^{27} + 13 q^{28} - 8 q^{29} + 6 q^{30} - 17 q^{31} - 27 q^{32} - 11 q^{33} - 18 q^{34} - 2 q^{35} + 6 q^{36} - 10 q^{37} - 30 q^{38} - 3 q^{39} + 10 q^{40} - 25 q^{41} - 9 q^{42} - 7 q^{43} - 6 q^{44} - 13 q^{45} + 32 q^{46} - 30 q^{47} + 4 q^{48} - 2 q^{49} + 11 q^{50} - 7 q^{51} - 7 q^{52} - 18 q^{53} - 4 q^{54} + 13 q^{55} - 20 q^{56} - 8 q^{57} - 13 q^{58} - 43 q^{59} - 25 q^{60} + 11 q^{61} + 7 q^{62} - 5 q^{63} + 25 q^{64} - 27 q^{65} + 4 q^{66} - 30 q^{67} + 10 q^{68} - 15 q^{69} - 4 q^{70} - 7 q^{71} - 9 q^{72} + 6 q^{73} - 44 q^{74} + 4 q^{75} - 19 q^{76} + 5 q^{77} - 2 q^{78} + 17 q^{79} - 22 q^{80} + 11 q^{81} + 8 q^{82} - 34 q^{83} + 13 q^{84} + 10 q^{85} + 2 q^{86} - 8 q^{87} + 9 q^{88} - 41 q^{89} + 6 q^{90} - 39 q^{91} - 32 q^{92} - 17 q^{93} + 55 q^{94} - 9 q^{95} - 27 q^{96} - 41 q^{97} - 29 q^{98} - 11 q^{99}+O(q^{100}) \) 11 * q - 4 * q^2 + 11 * q^3 + 6 * q^4 - 13 * q^5 - 4 * q^6 - 5 * q^7 - 9 * q^8 + 11 * q^9 + 6 * q^10 - 11 * q^11 + 6 * q^12 - 3 * q^13 - 9 * q^14 - 13 * q^15 + 4 * q^16 - 7 * q^17 - 4 * q^18 - 8 * q^19 - 25 * q^20 - 5 * q^21 + 4 * q^22 - 15 * q^23 - 9 * q^24 + 4 * q^25 - 2 * q^26 + 11 * q^27 + 13 * q^28 - 8 * q^29 + 6 * q^30 - 17 * q^31 - 27 * q^32 - 11 * q^33 - 18 * q^34 - 2 * q^35 + 6 * q^36 - 10 * q^37 - 30 * q^38 - 3 * q^39 + 10 * q^40 - 25 * q^41 - 9 * q^42 - 7 * q^43 - 6 * q^44 - 13 * q^45 + 32 * q^46 - 30 * q^47 + 4 * q^48 - 2 * q^49 + 11 * q^50 - 7 * q^51 - 7 * q^52 - 18 * q^53 - 4 * q^54 + 13 * q^55 - 20 * q^56 - 8 * q^57 - 13 * q^58 - 43 * q^59 - 25 * q^60 + 11 * q^61 + 7 * q^62 - 5 * q^63 + 25 * q^64 - 27 * q^65 + 4 * q^66 - 30 * q^67 + 10 * q^68 - 15 * q^69 - 4 * q^70 - 7 * q^71 - 9 * q^72 + 6 * q^73 - 44 * q^74 + 4 * q^75 - 19 * q^76 + 5 * q^77 - 2 * q^78 + 17 * q^79 - 22 * q^80 + 11 * q^81 + 8 * q^82 - 34 * q^83 + 13 * q^84 + 10 * q^85 + 2 * q^86 - 8 * q^87 + 9 * q^88 - 41 * q^89 + 6 * q^90 - 39 * q^91 - 32 * q^92 - 17 * q^93 + 55 * q^94 - 9 * q^95 - 27 * q^96 - 41 * q^97 - 29 * 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 $

$2$	1.35090	0.955231	0.477615	−	0.878569i	$-0.341501\pi$
$2$	1.35090	0.955231	0.477615	+	0.878569i	$0.341501\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.175068	−0.0875340
$5$	−0.638467	−0.285531	−0.142766	−	0.989757i	$-0.545599\pi$
$5$	−0.638467	−0.285531	−0.142766	+	0.989757i	$0.545599\pi$
$6$	1.35090	0.551503
$7$	−0.931245	−0.351978	−0.175989	−	0.984392i	$-0.556312\pi$
$7$	−0.931245	−0.351978	−0.175989	+	0.984392i	$0.556312\pi$
$8$	−2.93830	−1.03885
$9$	1.00000	0.333333
$10$	−0.862505	−0.272748
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.175068	−0.0505378
$13$	−3.34774	−0.928496	−0.464248	−	0.885705i	$-0.653675\pi$
$13$	−3.34774	−0.928496	−0.464248	+	0.885705i	$0.653675\pi$
$14$	−1.25802	−0.336220
$15$	−0.638467	−0.164851
$16$	−3.61922	−0.904804
$17$	6.34917	1.53990	0.769950	−	0.638105i	$-0.220281\pi$
$17$	6.34917	1.53990	0.769950	+	0.638105i	$0.220281\pi$
$18$	1.35090	0.318410
$19$	−6.01493	−1.37992	−0.689959	−	0.723848i	$-0.742372\pi$
$19$	−6.01493	−1.37992	−0.689959	+	0.723848i	$0.742372\pi$
$20$	0.111775	0.0249937
$21$	−0.931245	−0.203214
$22$	−1.35090	−0.288013
$23$	8.35167	1.74144	0.870722	−	0.491775i	$-0.163652\pi$
$23$	8.35167	1.74144	0.870722	+	0.491775i	$0.163652\pi$
$24$	−2.93830	−0.599778
$25$	−4.59236	−0.918472
$26$	−4.52246	−0.886928
$27$	1.00000	0.192450
$28$	0.163031	0.0308100
$29$	−7.15859	−1.32932	−0.664658	−	0.747147i	$-0.731423\pi$
$29$	−7.15859	−1.32932	−0.664658	+	0.747147i	$0.731423\pi$
$30$	−0.862505	−0.157471
$31$	−1.16267	−0.208821	−0.104411	−	0.994534i	$-0.533296\pi$
$31$	−1.16267	−0.208821	−0.104411	+	0.994534i	$0.533296\pi$
$32$	0.987402	0.174550
$33$	−1.00000	−0.174078
$34$	8.57709	1.47096
$35$	0.594569	0.100501
$36$	−0.175068	−0.0291780
$37$	−7.31872	−1.20319	−0.601595	−	0.798801i	$-0.705468\pi$
$37$	−7.31872	−1.20319	−0.601595	+	0.798801i	$0.705468\pi$
$38$	−8.12557	−1.31814
$39$	−3.34774	−0.536067
$40$	1.87601	0.296623
$41$	−4.22398	−0.659675	−0.329838	−	0.944038i	$-0.606994\pi$
$41$	−4.22398	−0.659675	−0.329838	+	0.944038i	$0.606994\pi$
$42$	−1.25802	−0.194117
$43$	−10.6385	−1.62236	−0.811180	−	0.584796i	$-0.801174\pi$
$43$	−10.6385	−1.62236	−0.811180	+	0.584796i	$0.801174\pi$
$44$	0.175068	0.0263925
$45$	−0.638467	−0.0951770
$46$	11.2823	1.66348
$47$	−13.3623	−1.94909	−0.974546	−	0.224189i	$-0.928027\pi$
$47$	−13.3623	−1.94909	−0.974546	+	0.224189i	$0.928027\pi$
$48$	−3.61922	−0.522389
$49$	−6.13278	−0.876112
$50$	−6.20382	−0.877353
$51$	6.34917	0.889061
$52$	0.586082	0.0812750
$53$	1.73638	0.238510	0.119255	−	0.992864i	$-0.461949\pi$
$53$	1.73638	0.238510	0.119255	+	0.992864i	$0.461949\pi$
$54$	1.35090	0.183834
$55$	0.638467	0.0860908
$56$	2.73628	0.365651
$57$	−6.01493	−0.796697
$58$	−9.67054	−1.26980
$59$	−3.21625	−0.418720	−0.209360	−	0.977839i	$-0.567138\pi$
$59$	−3.21625	−0.418720	−0.209360	+	0.977839i	$0.567138\pi$
$60$	0.111775	0.0144301
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−1.57065	−0.199473
$63$	−0.931245	−0.117326
$64$	8.57231	1.07154
$65$	2.13742	0.265114
$66$	−1.35090	−0.166284
$67$	−0.674112	−0.0823559	−0.0411779	−	0.999152i	$-0.513111\pi$
$67$	−0.674112	−0.0823559	−0.0411779	+	0.999152i	$0.513111\pi$
$68$	−1.11154	−0.134794
$69$	8.35167	1.00542
$70$	0.803204	0.0960012
$71$	−10.5817	−1.25582	−0.627908	−	0.778288i	$-0.716089\pi$
$71$	−10.5817	−1.25582	−0.627908	+	0.778288i	$0.716089\pi$
$72$	−2.93830	−0.346282
$73$	10.5531	1.23514	0.617572	−	0.786514i	$-0.288116\pi$
$73$	10.5531	1.23514	0.617572	+	0.786514i	$0.288116\pi$
$74$	−9.88686	−1.14932
$75$	−4.59236	−0.530280
$76$	1.05302	0.120790
$77$	0.931245	0.106125
$78$	−4.52246	−0.512068
$79$	16.8703	1.89806	0.949029	−	0.315190i	$-0.102068\pi$
$79$	16.8703	1.89806	0.949029	+	0.315190i	$0.102068\pi$
$80$	2.31075	0.258350
$81$	1.00000	0.111111
$82$	−5.70618	−0.630142
$83$	12.3348	1.35392	0.676958	−	0.736022i	$-0.263298\pi$
$83$	12.3348	1.35392	0.676958	+	0.736022i	$0.263298\pi$
$84$	0.163031	0.0177882
$85$	−4.05373	−0.439689
$86$	−14.3716	−1.54973
$87$	−7.15859	−0.767482
$88$	2.93830	0.313224
$89$	−3.25248	−0.344762	−0.172381	−	0.985030i	$-0.555146\pi$
$89$	−3.25248	−0.344762	−0.172381	+	0.985030i	$0.555146\pi$
$90$	−0.862505	−0.0909160
$91$	3.11757	0.326810
$92$	−1.46211	−0.152436
$93$	−1.16267	−0.120563
$94$	−18.0511	−1.86183
$95$	3.84033	0.394010
$96$	0.987402	0.100776
$97$	−11.7707	−1.19513	−0.597564	−	0.801821i	$-0.703865\pi$
$97$	−11.7707	−1.19513	−0.597564	+	0.801821i	$0.703865\pi$
$98$	−8.28478	−0.836889
$99$	−1.00000	−0.100504
$100$	0.803976	0.0803976
$101$	0.390337	0.0388399	0.0194200	−	0.999811i	$-0.493818\pi$
$101$	0.390337	0.0388399	0.0194200	+	0.999811i	$0.493818\pi$
$102$	8.57709	0.849259
$103$	17.4149	1.71595	0.857973	−	0.513696i	$-0.171724\pi$
$103$	17.4149	1.71595	0.857973	+	0.513696i	$0.171724\pi$
$104$	9.83666	0.964564
$105$	0.594569	0.0580240
$106$	2.34567	0.227832
$107$	2.87608	0.278041	0.139021	−	0.990289i	$-0.455605\pi$
$107$	2.87608	0.278041	0.139021	+	0.990289i	$0.455605\pi$
$108$	−0.175068	−0.0168459
$109$	16.2537	1.55682	0.778410	−	0.627757i	$-0.216027\pi$
$109$	16.2537	1.55682	0.778410	+	0.627757i	$0.216027\pi$
$110$	0.862505	0.0822366
$111$	−7.31872	−0.694662
$112$	3.37038	0.318471
$113$	5.55484	0.522556	0.261278	−	0.965264i	$-0.415856\pi$
$113$	5.55484	0.522556	0.261278	+	0.965264i	$0.415856\pi$
$114$	−8.12557	−0.761029
$115$	−5.33227	−0.497236
$116$	1.25324	0.116360
$117$	−3.34774	−0.309499
$118$	−4.34483	−0.399974
$119$	−5.91263	−0.542010
$120$	1.87601	0.171255
$121$	1.00000	0.0909091
$122$	1.35090	0.122305
$123$	−4.22398	−0.380864
$124$	0.203546	0.0182790
$125$	6.12440	0.547783
$126$	−1.25802	−0.112073
$127$	9.15795	0.812637	0.406318	−	0.913732i	$-0.366812\pi$
$127$	9.15795	0.812637	0.406318	+	0.913732i	$0.366812\pi$
$128$	9.60554	0.849017
$129$	−10.6385	−0.936670
$130$	2.88744	0.253245
$131$	0.678216	0.0592560	0.0296280	−	0.999561i	$-0.490568\pi$
$131$	0.678216	0.0592560	0.0296280	+	0.999561i	$0.490568\pi$
$132$	0.175068	0.0152377
$133$	5.60137	0.485701
$134$	−0.910658	−0.0786689
$135$	−0.638467	−0.0549505
$136$	−18.6558	−1.59972
$137$	10.0245	0.856447	0.428224	−	0.903673i	$-0.359140\pi$
$137$	10.0245	0.856447	0.428224	+	0.903673i	$0.359140\pi$
$138$	11.2823	0.960411
$139$	−7.17382	−0.608475	−0.304238	−	0.952596i	$-0.598402\pi$
$139$	−7.17382	−0.608475	−0.304238	+	0.952596i	$0.598402\pi$
$140$	−0.104090	−0.00879722
$141$	−13.3623	−1.12531
$142$	−14.2948	−1.19959
$143$	3.34774	0.279952
$144$	−3.61922	−0.301601
$145$	4.57052	0.379561
$146$	14.2562	1.17985
$147$	−6.13278	−0.505823
$148$	1.28127	0.105320
$149$	−18.5586	−1.52038	−0.760188	−	0.649703i	$-0.774893\pi$
$149$	−18.5586	−1.52038	−0.760188	+	0.649703i	$0.774893\pi$
$150$	−6.20382	−0.506540
$151$	7.18661	0.584838	0.292419	−	0.956290i	$-0.405540\pi$
$151$	7.18661	0.584838	0.292419	+	0.956290i	$0.405540\pi$
$152$	17.6737	1.43352
$153$	6.34917	0.513300
$154$	1.25802	0.101374
$155$	0.742325	0.0596249
$156$	0.586082	0.0469241
$157$	1.04007	0.0830065	0.0415032	−	0.999138i	$-0.486785\pi$
$157$	1.04007	0.0830065	0.0415032	+	0.999138i	$0.486785\pi$
$158$	22.7901	1.81308
$159$	1.73638	0.137704
$160$	−0.630423	−0.0498393
$161$	−7.77746	−0.612949
$162$	1.35090	0.106137
$163$	−24.9129	−1.95133	−0.975663	−	0.219275i	$-0.929631\pi$
$163$	−24.9129	−1.95133	−0.975663	+	0.219275i	$0.929631\pi$
$164$	0.739484	0.0577440
$165$	0.638467	0.0497046
$166$	16.6630	1.29330
$167$	−1.59888	−0.123725	−0.0618625	−	0.998085i	$-0.519704\pi$
$167$	−1.59888	−0.123725	−0.0618625	+	0.998085i	$0.519704\pi$
$168$	2.73628	0.211108
$169$	−1.79265	−0.137896
$170$	−5.47619	−0.420005
$171$	−6.01493	−0.459973
$172$	1.86247	0.142012
$173$	14.3956	1.09448	0.547240	−	0.836976i	$-0.315678\pi$
$173$	14.3956	1.09448	0.547240	+	0.836976i	$0.315678\pi$
$174$	−9.67054	−0.733122
$175$	4.27661	0.323282
$176$	3.61922	0.272809
$177$	−3.21625	−0.241748
$178$	−4.39377	−0.329327
$179$	8.23448	0.615474	0.307737	−	0.951471i	$-0.400428\pi$
$179$	8.23448	0.615474	0.307737	+	0.951471i	$0.400428\pi$
$180$	0.111775	0.00833123
$181$	−5.61940	−0.417687	−0.208843	−	0.977949i	$-0.566970\pi$
$181$	−5.61940	−0.417687	−0.208843	+	0.977949i	$0.566970\pi$
$182$	4.21152	0.312179
$183$	1.00000	0.0739221
$184$	−24.5397	−1.80909
$185$	4.67276	0.343548
$186$	−1.57065	−0.115166
$187$	−6.34917	−0.464297
$188$	2.33931	0.170612
$189$	−0.931245	−0.0677381
$190$	5.18790	0.376370
$191$	−18.7995	−1.36029	−0.680143	−	0.733079i	$-0.738082\pi$
$191$	−18.7995	−1.36029	−0.680143	+	0.733079i	$0.738082\pi$
$192$	8.57231	0.618653
$193$	14.2233	1.02381	0.511907	−	0.859041i	$-0.328939\pi$
$193$	14.2233	1.02381	0.511907	+	0.859041i	$0.328939\pi$
$194$	−15.9010	−1.14162
$195$	2.13742	0.153064
$196$	1.07365	0.0766896
$197$	−6.22785	−0.443716	−0.221858	−	0.975079i	$-0.571212\pi$
$197$	−6.22785	−0.443716	−0.221858	+	0.975079i	$0.571212\pi$
$198$	−1.35090	−0.0960043
$199$	−9.47420	−0.671608	−0.335804	−	0.941932i	$-0.609008\pi$
$199$	−9.47420	−0.671608	−0.335804	+	0.941932i	$0.609008\pi$
$200$	13.4937	0.954151
$201$	−0.674112	−0.0475482
$202$	0.527306	0.0371011
$203$	6.66640	0.467890
$204$	−1.11154	−0.0778231
$205$	2.69687	0.188358
$206$	23.5258	1.63912
$207$	8.35167	0.580481
$208$	12.1162	0.840106
$209$	6.01493	0.416061
$210$	0.803204	0.0554263
$211$	−16.8916	−1.16287	−0.581434	−	0.813594i	$-0.697508\pi$
$211$	−16.8916	−1.16287	−0.581434	+	0.813594i	$0.697508\pi$
$212$	−0.303984	−0.0208777
$213$	−10.5817	−0.725045
$214$	3.88530	0.265594
$215$	6.79235	0.463234
$216$	−2.93830	−0.199926
$217$	1.08273	0.0735004
$218$	21.9571	1.48712
$219$	10.5531	0.713111
$220$	−0.111775	−0.00753588
$221$	−21.2554	−1.42979
$222$	−9.88686	−0.663563
$223$	9.14265	0.612237	0.306119	−	0.951993i	$-0.400970\pi$
$223$	9.14265	0.612237	0.306119	+	0.951993i	$0.400970\pi$
$224$	−0.919513	−0.0614376
$225$	−4.59236	−0.306157
$226$	7.50404	0.499161
$227$	−8.70809	−0.577976	−0.288988	−	0.957333i	$-0.593319\pi$
$227$	−8.70809	−0.577976	−0.288988	+	0.957333i	$0.593319\pi$
$228$	1.05302	0.0697381
$229$	21.0052	1.38806	0.694032	−	0.719944i	$-0.255833\pi$
$229$	21.0052	1.38806	0.694032	+	0.719944i	$0.255833\pi$
$230$	−7.20336	−0.474976
$231$	0.931245	0.0612714
$232$	21.0341	1.38096
$233$	5.90539	0.386875	0.193437	−	0.981113i	$-0.438036\pi$
$233$	5.90539	0.386875	0.193437	+	0.981113i	$0.438036\pi$
$234$	−4.52246	−0.295643
$235$	8.53138	0.556526
$236$	0.563062	0.0366522
$237$	16.8703	1.09584
$238$	−7.98738	−0.517745
$239$	−4.71545	−0.305017	−0.152509	−	0.988302i	$-0.548735\pi$
$239$	−4.71545	−0.305017	−0.152509	+	0.988302i	$0.548735\pi$
$240$	2.31075	0.149158
$241$	20.8568	1.34350	0.671752	−	0.740777i	$-0.265542\pi$
$241$	20.8568	1.34350	0.671752	+	0.740777i	$0.265542\pi$
$242$	1.35090	0.0868392
$243$	1.00000	0.0641500
$244$	−0.175068	−0.0112076
$245$	3.91558	0.250157
$246$	−5.70618	−0.363813
$247$	20.1364	1.28125
$248$	3.41627	0.216933
$249$	12.3348	0.781684
$250$	8.27346	0.523259
$251$	2.71069	0.171097	0.0855487	−	0.996334i	$-0.472736\pi$
$251$	2.71069	0.171097	0.0855487	+	0.996334i	$0.472736\pi$
$252$	0.163031	0.0102700
$253$	−8.35167	−0.525065
$254$	12.3715	0.776256
$255$	−4.05373	−0.253855
$256$	−4.16850	−0.260531
$257$	−18.9869	−1.18437	−0.592184	−	0.805803i	$-0.701734\pi$
$257$	−18.9869	−1.18437	−0.592184	+	0.805803i	$0.701734\pi$
$258$	−14.3716	−0.894736
$259$	6.81552	0.423496
$260$	−0.374194	−0.0232065
$261$	−7.15859	−0.443106
$262$	0.916203	0.0566032
$263$	−10.8868	−0.671311	−0.335656	−	0.941985i	$-0.608958\pi$
$263$	−10.8868	−0.671311	−0.335656	+	0.941985i	$0.608958\pi$
$264$	2.93830	0.180840
$265$	−1.10862	−0.0681020
$266$	7.56690	0.463956
$267$	−3.25248	−0.199048
$268$	0.118015	0.00720894
$269$	−19.4158	−1.18380	−0.591900	−	0.806011i	$-0.701622\pi$
$269$	−19.4158	−1.18380	−0.591900	+	0.806011i	$0.701622\pi$
$270$	−0.862505	−0.0524904
$271$	−25.4900	−1.54841	−0.774203	−	0.632938i	$-0.781849\pi$
$271$	−25.4900	−1.54841	−0.774203	+	0.632938i	$0.781849\pi$
$272$	−22.9790	−1.39331
$273$	3.11757	0.188684
$274$	13.5420	0.818105
$275$	4.59236	0.276930
$276$	−1.46211	−0.0880088
$277$	19.6348	1.17974	0.589871	−	0.807497i	$-0.299178\pi$
$277$	19.6348	1.17974	0.589871	+	0.807497i	$0.299178\pi$
$278$	−9.69111	−0.581234
$279$	−1.16267	−0.0696071
$280$	−1.74702	−0.104405
$281$	−17.5405	−1.04638	−0.523190	−	0.852216i	$-0.675258\pi$
$281$	−17.5405	−1.04638	−0.523190	+	0.852216i	$0.675258\pi$
$282$	−18.0511	−1.07493
$283$	21.5895	1.28336	0.641680	−	0.766972i	$-0.278238\pi$
$283$	21.5895	1.28336	0.641680	+	0.766972i	$0.278238\pi$
$284$	1.85252	0.109927
$285$	3.84033	0.227482
$286$	4.52246	0.267419
$287$	3.93356	0.232191
$288$	0.987402	0.0581832
$289$	23.3119	1.37129
$290$	6.17432	0.362569
$291$	−11.7707	−0.690008
$292$	−1.84751	−0.108117
$293$	13.8500	0.809124	0.404562	−	0.914511i	$-0.367424\pi$
$293$	13.8500	0.809124	0.404562	+	0.914511i	$0.367424\pi$
$294$	−8.28478	−0.483178
$295$	2.05347	0.119557
$296$	21.5046	1.24993
$297$	−1.00000	−0.0580259
$298$	−25.0708	−1.45231
$299$	−27.9592	−1.61692
$300$	0.803976	0.0464176
$301$	9.90708	0.571034
$302$	9.70840	0.558656
$303$	0.390337	0.0224242
$304$	21.7693	1.24856
$305$	−0.638467	−0.0365585
$306$	8.57709	0.490320
$307$	−31.2006	−1.78071	−0.890355	−	0.455267i	$-0.849544\pi$
$307$	−31.2006	−1.78071	−0.890355	+	0.455267i	$0.849544\pi$
$308$	−0.163031	−0.00928957
$309$	17.4149	0.990701
$310$	1.00281	0.0569556
$311$	6.02310	0.341538	0.170769	−	0.985311i	$-0.445375\pi$
$311$	6.02310	0.341538	0.170769	+	0.985311i	$0.445375\pi$
$312$	9.83666	0.556891
$313$	−6.31441	−0.356912	−0.178456	−	0.983948i	$-0.557110\pi$
$313$	−6.31441	−0.356912	−0.178456	+	0.983948i	$0.557110\pi$
$314$	1.40503	0.0792904
$315$	0.594569	0.0335002
$316$	−2.95345	−0.166145
$317$	17.8921	1.00492	0.502459	−	0.864601i	$-0.332429\pi$
$317$	17.8921	1.00492	0.502459	+	0.864601i	$0.332429\pi$
$318$	2.34567	0.131539
$319$	7.15859	0.400804
$320$	−5.47314	−0.305958
$321$	2.87608	0.160527
$322$	−10.5066	−0.585508
$323$	−38.1898	−2.12494
$324$	−0.175068	−0.00972600
$325$	15.3740	0.852797
$326$	−33.6548	−1.86397
$327$	16.2537	0.898830
$328$	12.4113	0.685301
$329$	12.4436	0.686037
$330$	0.862505	0.0474793
$331$	−34.5203	−1.89741	−0.948704	−	0.316165i	$-0.897605\pi$
$331$	−34.5203	−1.89741	−0.948704	+	0.316165i	$0.897605\pi$
$332$	−2.15942	−0.118514
$333$	−7.31872	−0.401063
$334$	−2.15993	−0.118186
$335$	0.430398	0.0235152
$336$	3.37038	0.183869
$337$	−6.09124	−0.331811	−0.165905	−	0.986142i	$-0.553055\pi$
$337$	−6.09124	−0.331811	−0.165905	+	0.986142i	$0.553055\pi$
$338$	−2.42169	−0.131722
$339$	5.55484	0.301698
$340$	0.709679	0.0384878
$341$	1.16267	0.0629620
$342$	−8.12557	−0.439380
$343$	12.2298	0.660349
$344$	31.2592	1.68538
$345$	−5.33227	−0.287080
$346$	19.4471	1.04548
$347$	9.96988	0.535211	0.267606	−	0.963529i	$-0.413768\pi$
$347$	9.96988	0.535211	0.267606	+	0.963529i	$0.413768\pi$
$348$	1.25324	0.0671808
$349$	−21.7636	−1.16498	−0.582490	−	0.812838i	$-0.697922\pi$
$349$	−21.7636	−1.16498	−0.582490	+	0.812838i	$0.697922\pi$
$350$	5.77728	0.308809
$351$	−3.34774	−0.178689
$352$	−0.987402	−0.0526287
$353$	−25.1843	−1.34042	−0.670211	−	0.742170i	$-0.733797\pi$
$353$	−25.1843	−1.34042	−0.670211	+	0.742170i	$0.733797\pi$
$354$	−4.34483	−0.230925
$355$	6.75606	0.358574
$356$	0.569405	0.0301784
$357$	−5.91263	−0.312930
$358$	11.1240	0.587920
$359$	7.47369	0.394446	0.197223	−	0.980359i	$-0.436808\pi$
$359$	7.47369	0.394446	0.197223	+	0.980359i	$0.436808\pi$
$360$	1.87601	0.0988743
$361$	17.1793	0.904176
$362$	−7.59125	−0.398987
$363$	1.00000	0.0524864
$364$	−0.545786	−0.0286070
$365$	−6.73779	−0.352672
$366$	1.35090	0.0706127
$367$	18.0040	0.939803	0.469902	−	0.882719i	$-0.344289\pi$
$367$	18.0040	0.939803	0.469902	+	0.882719i	$0.344289\pi$
$368$	−30.2265	−1.57567
$369$	−4.22398	−0.219892
$370$	6.31243	0.328168
$371$	−1.61699	−0.0839501
$372$	0.203546	0.0105534
$373$	30.3691	1.57245	0.786225	−	0.617940i	$-0.212032\pi$
$373$	30.3691	1.57245	0.786225	+	0.617940i	$0.212032\pi$
$374$	−8.57709	−0.443511
$375$	6.12440	0.316263
$376$	39.2624	2.02481
$377$	23.9651	1.23426
$378$	−1.25802	−0.0647055
$379$	−13.2555	−0.680888	−0.340444	−	0.940265i	$-0.610577\pi$
$379$	−13.2555	−0.680888	−0.340444	+	0.940265i	$0.610577\pi$
$380$	−0.672319	−0.0344893
$381$	9.15795	0.469176
$382$	−25.3963	−1.29939
$383$	22.3518	1.14212	0.571062	−	0.820907i	$-0.306532\pi$
$383$	22.3518	1.14212	0.571062	+	0.820907i	$0.306532\pi$
$384$	9.60554	0.490180
$385$	−0.594569	−0.0303020
$386$	19.2142	0.977979
$387$	−10.6385	−0.540787
$388$	2.06067	0.104614
$389$	−25.9280	−1.31460	−0.657300	−	0.753629i	$-0.728302\pi$
$389$	−25.9280	−1.31460	−0.657300	+	0.753629i	$0.728302\pi$
$390$	2.88744	0.146211
$391$	53.0262	2.68165
$392$	18.0200	0.910145
$393$	0.678216	0.0342115
$394$	−8.41321	−0.423851
$395$	−10.7711	−0.541954
$396$	0.175068	0.00879750
$397$	−19.3012	−0.968698	−0.484349	−	0.874875i	$-0.660943\pi$
$397$	−19.3012	−0.968698	−0.484349	+	0.874875i	$0.660943\pi$
$398$	−12.7987	−0.641541
$399$	5.60137	0.280419
$400$	16.6207	0.831037
$401$	8.34024	0.416492	0.208246	−	0.978077i	$-0.433225\pi$
$401$	8.34024	0.416492	0.208246	+	0.978077i	$0.433225\pi$
$402$	−0.910658	−0.0454195
$403$	3.89231	0.193890
$404$	−0.0683355	−0.00339982
$405$	−0.638467	−0.0317257
$406$	9.00565	0.446943
$407$	7.31872	0.362775
$408$	−18.6558	−0.923598
$409$	7.41367	0.366582	0.183291	−	0.983059i	$-0.441325\pi$
$409$	7.41367	0.366582	0.183291	+	0.983059i	$0.441325\pi$
$410$	3.64321	0.179925
$411$	10.0245	0.494470
$412$	−3.04880	−0.150204
$413$	2.99511	0.147380
$414$	11.2823	0.554494
$415$	−7.87534	−0.386585
$416$	−3.30556	−0.162069
$417$	−7.17382	−0.351303
$418$	8.12557	0.397435
$419$	−15.1099	−0.738167	−0.369084	−	0.929396i	$-0.620328\pi$
$419$	−15.1099	−0.738167	−0.369084	+	0.929396i	$0.620328\pi$
$420$	−0.104090	−0.00507908
$421$	−22.5049	−1.09682	−0.548410	−	0.836210i	$-0.684767\pi$
$421$	−22.5049	−1.09682	−0.548410	+	0.836210i	$0.684767\pi$
$422$	−22.8189	−1.11081
$423$	−13.3623	−0.649697
$424$	−5.10200	−0.247775
$425$	−29.1577	−1.41435
$426$	−14.2948	−0.692586
$427$	−0.931245	−0.0450661
$428$	−0.503510	−0.0243381
$429$	3.34774	0.161630
$430$	9.17578	0.442496
$431$	10.5530	0.508319	0.254159	−	0.967162i	$-0.418201\pi$
$431$	10.5530	0.508319	0.254159	+	0.967162i	$0.418201\pi$
$432$	−3.61922	−0.174130
$433$	−25.1751	−1.20984	−0.604919	−	0.796287i	$-0.706794\pi$
$433$	−25.1751	−1.20984	−0.604919	+	0.796287i	$0.706794\pi$
$434$	1.46266	0.0702099
$435$	4.57052	0.219140
$436$	−2.84550	−0.136275
$437$	−50.2347	−2.40305
$438$	14.2562	0.681185
$439$	−1.41468	−0.0675190	−0.0337595	−	0.999430i	$-0.510748\pi$
$439$	−1.41468	−0.0675190	−0.0337595	+	0.999430i	$0.510748\pi$
$440$	−1.87601	−0.0894351
$441$	−6.13278	−0.292037
$442$	−28.7139	−1.36578
$443$	0.122085	0.00580044	0.00290022	−	0.999996i	$-0.499077\pi$
$443$	0.122085	0.00580044	0.00290022	+	0.999996i	$0.499077\pi$
$444$	1.28127	0.0608066
$445$	2.07660	0.0984402
$446$	12.3508	0.584828
$447$	−18.5586	−0.877790
$448$	−7.98292	−0.377158
$449$	38.2500	1.80513	0.902566	−	0.430552i	$-0.141681\pi$
$449$	38.2500	1.80513	0.902566	+	0.430552i	$0.141681\pi$
$450$	−6.20382	−0.292451
$451$	4.22398	0.198900
$452$	−0.972475	−0.0457414
$453$	7.18661	0.337657
$454$	−11.7638	−0.552101
$455$	−1.99046	−0.0933143
$456$	17.6737	0.827645
$457$	−1.71690	−0.0803132	−0.0401566	−	0.999193i	$-0.512786\pi$
$457$	−1.71690	−0.0803132	−0.0401566	+	0.999193i	$0.512786\pi$
$458$	28.3760	1.32592
$459$	6.34917	0.296354
$460$	0.933510	0.0435251
$461$	−26.6182	−1.23973	−0.619867	−	0.784707i	$-0.712814\pi$
$461$	−26.6182	−1.23973	−0.619867	+	0.784707i	$0.712814\pi$
$462$	1.25802	0.0585284
$463$	8.81859	0.409834	0.204917	−	0.978779i	$-0.434307\pi$
$463$	8.81859	0.409834	0.204917	+	0.978779i	$0.434307\pi$
$464$	25.9085	1.20277
$465$	0.742325	0.0344245
$466$	7.97759	0.369555
$467$	−31.2508	−1.44612	−0.723058	−	0.690788i	$-0.757264\pi$
$467$	−31.2508	−1.44612	−0.723058	+	0.690788i	$0.757264\pi$
$468$	0.586082	0.0270917
$469$	0.627764	0.0289874
$470$	11.5250	0.531611
$471$	1.04007	0.0479238
$472$	9.45030	0.434985
$473$	10.6385	0.489160
$474$	22.7901	1.04678
$475$	27.6227	1.26742
$476$	1.03511	0.0474443
$477$	1.73638	0.0795033
$478$	−6.37010	−0.291362
$479$	−7.03633	−0.321498	−0.160749	−	0.986995i	$-0.551391\pi$
$479$	−7.03633	−0.321498	−0.160749	+	0.986995i	$0.551391\pi$
$480$	−0.630423	−0.0287747
$481$	24.5012	1.11716
$482$	28.1754	1.28336
$483$	−7.77746	−0.353887
$484$	−0.175068	−0.00795764
$485$	7.51517	0.341246
$486$	1.35090	0.0612781
$487$	−5.64513	−0.255805	−0.127903	−	0.991787i	$-0.540824\pi$
$487$	−5.64513	−0.255805	−0.127903	+	0.991787i	$0.540824\pi$
$488$	−2.93830	−0.133011
$489$	−24.9129	−1.12660
$490$	5.28956	0.238958
$491$	−1.47085	−0.0663787	−0.0331893	−	0.999449i	$-0.510566\pi$
$491$	−1.47085	−0.0663787	−0.0331893	+	0.999449i	$0.510566\pi$
$492$	0.739484	0.0333385
$493$	−45.4511	−2.04701
$494$	27.2023	1.22389
$495$	0.638467	0.0286969
$496$	4.20794	0.188942
$497$	9.85415	0.442019
$498$	16.6630	0.746689
$499$	−12.5628	−0.562390	−0.281195	−	0.959651i	$-0.590731\pi$
$499$	−12.5628	−0.562390	−0.281195	+	0.959651i	$0.590731\pi$
$500$	−1.07219	−0.0479497
$501$	−1.59888	−0.0714327
$502$	3.66188	0.163438
$503$	27.1983	1.21271	0.606356	−	0.795193i	$-0.292631\pi$
$503$	27.1983	1.21271	0.606356	+	0.795193i	$0.292631\pi$
$504$	2.73628	0.121884
$505$	−0.249217	−0.0110900
$506$	−11.2823	−0.501559
$507$	−1.79265	−0.0796143
$508$	−1.60326	−0.0711334
$509$	−21.9352	−0.972263	−0.486131	−	0.873886i	$-0.661592\pi$
$509$	−21.9352	−0.972263	−0.486131	+	0.873886i	$0.661592\pi$
$510$	−5.47619	−0.242490
$511$	−9.82750	−0.434743
$512$	−24.8423	−1.09788
$513$	−6.01493	−0.265566
$514$	−25.6494	−1.13134
$515$	−11.1189	−0.489956
$516$	1.86247	0.0819905
$517$	13.3623	0.587673
$518$	9.20709	0.404536
$519$	14.3956	0.631899
$520$	−6.28038	−0.275413
$521$	24.3182	1.06540	0.532700	−	0.846304i	$-0.321177\pi$
$521$	24.3182	1.06540	0.532700	+	0.846304i	$0.321177\pi$
$522$	−9.67054	−0.423268
$523$	−20.0218	−0.875491	−0.437746	−	0.899099i	$-0.644223\pi$
$523$	−20.0218	−0.875491	−0.437746	+	0.899099i	$0.644223\pi$
$524$	−0.118734	−0.00518692
$525$	4.27661	0.186647
$526$	−14.7070	−0.641257
$527$	−7.38197	−0.321564
$528$	3.61922	0.157506
$529$	46.7505	2.03263
$530$	−1.49763	−0.0650531
$531$	−3.21625	−0.139573
$532$	−0.980621	−0.0425153
$533$	14.1408	0.612505
$534$	−4.39377	−0.190137
$535$	−1.83628	−0.0793894
$536$	1.98074	0.0855551
$537$	8.23448	0.355344
$538$	−26.2288	−1.13080
$539$	6.13278	0.264158
$540$	0.111775	0.00481004
$541$	3.25567	0.139972	0.0699860	−	0.997548i	$-0.477705\pi$
$541$	3.25567	0.139972	0.0699860	+	0.997548i	$0.477705\pi$
$542$	−34.4344	−1.47908
$543$	−5.61940	−0.241152
$544$	6.26918	0.268789
$545$	−10.3774	−0.444520
$546$	4.21152	0.180236
$547$	15.8946	0.679603	0.339802	−	0.940497i	$-0.389640\pi$
$547$	15.8946	0.679603	0.339802	+	0.940497i	$0.389640\pi$
$548$	−1.75496	−0.0749683
$549$	1.00000	0.0426790
$550$	6.20382	0.264532
$551$	43.0584	1.83435
$552$	−24.5397	−1.04448
$553$	−15.7104	−0.668074
$554$	26.5247	1.12693
$555$	4.67276	0.198348
$556$	1.25591	0.0532623
$557$	−30.5873	−1.29603	−0.648013	−	0.761630i	$-0.724400\pi$
$557$	−30.5873	−1.29603	−0.648013	+	0.761630i	$0.724400\pi$
$558$	−1.57065	−0.0664908
$559$	35.6150	1.50635
$560$	−2.15187	−0.0909332
$561$	−6.34917	−0.268062
$562$	−23.6955	−0.999535
$563$	−22.5414	−0.950007	−0.475004	−	0.879984i	$-0.657553\pi$
$563$	−22.5414	−0.950007	−0.475004	+	0.879984i	$0.657553\pi$
$564$	2.33931	0.0985028
$565$	−3.54658	−0.149206
$566$	29.1652	1.22591
$567$	−0.931245	−0.0391086
$568$	31.0922	1.30460
$569$	−34.1037	−1.42970	−0.714850	−	0.699278i	$-0.753505\pi$
$569$	−34.1037	−1.42970	−0.714850	+	0.699278i	$0.753505\pi$
$570$	5.18790	0.217297
$571$	37.5651	1.57205	0.786025	−	0.618195i	$-0.212136\pi$
$571$	37.5651	1.57205	0.786025	+	0.618195i	$0.212136\pi$
$572$	−0.586082	−0.0245053
$573$	−18.7995	−0.785362
$574$	5.31385	0.221796
$575$	−38.3539	−1.59947
$576$	8.57231	0.357180
$577$	15.4458	0.643018	0.321509	−	0.946906i	$-0.395810\pi$
$577$	15.4458	0.643018	0.321509	+	0.946906i	$0.395810\pi$
$578$	31.4921	1.30990
$579$	14.2233	0.591100
$580$	−0.800153	−0.0332245
$581$	−11.4867	−0.476548
$582$	−15.9010	−0.659117
$583$	−1.73638	−0.0719134
$584$	−31.0081	−1.28312
$585$	2.13742	0.0883714
$586$	18.7099	0.772900
$587$	1.35741	0.0560265	0.0280132	−	0.999608i	$-0.491082\pi$
$587$	1.35741	0.0560265	0.0280132	+	0.999608i	$0.491082\pi$
$588$	1.07365	0.0442768
$589$	6.99336	0.288156
$590$	2.77403	0.114205
$591$	−6.22785	−0.256180
$592$	26.4880	1.08865
$593$	−15.8945	−0.652707	−0.326354	−	0.945248i	$-0.605820\pi$
$593$	−15.8945	−0.652707	−0.326354	+	0.945248i	$0.605820\pi$
$594$	−1.35090	−0.0554281
$595$	3.77502	0.154761
$596$	3.24901	0.133085
$597$	−9.47420	−0.387753
$598$	−37.7701	−1.54454
$599$	−25.3015	−1.03379	−0.516895	−	0.856049i	$-0.672912\pi$
$599$	−25.3015	−1.03379	−0.516895	+	0.856049i	$0.672912\pi$
$600$	13.4937	0.550879
$601$	−31.0943	−1.26836	−0.634181	−	0.773184i	$-0.718663\pi$
$601$	−31.0943	−1.26836	−0.634181	+	0.773184i	$0.718663\pi$
$602$	13.3835	0.545470
$603$	−0.674112	−0.0274520
$604$	−1.25815	−0.0511933
$605$	−0.638467	−0.0259574
$606$	0.527306	0.0214203
$607$	−12.3481	−0.501194	−0.250597	−	0.968091i	$-0.580627\pi$
$607$	−12.3481	−0.501194	−0.250597	+	0.968091i	$0.580627\pi$
$608$	−5.93915	−0.240864
$609$	6.66640	0.270136
$610$	−0.862505	−0.0349218
$611$	44.7335	1.80972
$612$	−1.11154	−0.0449312
$613$	−43.6974	−1.76492	−0.882460	−	0.470387i	$-0.844114\pi$
$613$	−43.6974	−1.76492	−0.882460	+	0.470387i	$0.844114\pi$
$614$	−42.1489	−1.70099
$615$	2.69687	0.108748
$616$	−2.73628	−0.110248
$617$	−20.4272	−0.822368	−0.411184	−	0.911552i	$-0.634885\pi$
$617$	−20.4272	−0.822368	−0.411184	+	0.911552i	$0.634885\pi$
$618$	23.5258	0.946348
$619$	12.3927	0.498104	0.249052	−	0.968490i	$-0.419881\pi$
$619$	12.3927	0.498104	0.249052	+	0.968490i	$0.419881\pi$
$620$	−0.129957	−0.00521921
$621$	8.35167	0.335141
$622$	8.13660	0.326248
$623$	3.02885	0.121349
$624$	12.1162	0.485036
$625$	19.0516	0.762063
$626$	−8.53014	−0.340933
$627$	6.01493	0.240213
$628$	−0.182083	−0.00726589
$629$	−46.4678	−1.85279
$630$	0.803204	0.0320004
$631$	−15.9347	−0.634350	−0.317175	−	0.948367i	$-0.602734\pi$
$631$	−15.9347	−0.634350	−0.317175	+	0.948367i	$0.602734\pi$
$632$	−49.5700	−1.97179
$633$	−16.8916	−0.671382
$634$	24.1704	0.959929
$635$	−5.84705	−0.232033
$636$	−0.303984	−0.0120538
$637$	20.5310	0.813466
$638$	9.67054	0.382860
$639$	−10.5817	−0.418605
$640$	−6.13282	−0.242421
$641$	31.2450	1.23410	0.617051	−	0.786923i	$-0.288327\pi$
$641$	31.2450	1.23410	0.617051	+	0.786923i	$0.288327\pi$
$642$	3.88530	0.153341
$643$	45.0675	1.77729	0.888644	−	0.458597i	$-0.151648\pi$
$643$	45.0675	1.77729	0.888644	+	0.458597i	$0.151648\pi$
$644$	1.36158	0.0536539
$645$	6.79235	0.267448
$646$	−51.5906	−2.02980
$647$	−3.25020	−0.127779	−0.0638893	−	0.997957i	$-0.520350\pi$
$647$	−3.25020	−0.127779	−0.0638893	+	0.997957i	$0.520350\pi$
$648$	−2.93830	−0.115427
$649$	3.21625	0.126249
$650$	20.7688	0.814618
$651$	1.08273	0.0424355
$652$	4.36145	0.170807
$653$	34.0518	1.33255	0.666275	−	0.745706i	$-0.267888\pi$
$653$	34.0518	1.33255	0.666275	+	0.745706i	$0.267888\pi$
$654$	21.9571	0.858590
$655$	−0.433018	−0.0169194
$656$	15.2875	0.596877
$657$	10.5531	0.411715
$658$	16.8100	0.655323
$659$	−21.8331	−0.850496	−0.425248	−	0.905077i	$-0.639813\pi$
$659$	−21.8331	−0.850496	−0.425248	+	0.905077i	$0.639813\pi$
$660$	−0.111775	−0.00435084
$661$	10.1734	0.395698	0.197849	−	0.980233i	$-0.436604\pi$
$661$	10.1734	0.395698	0.197849	+	0.980233i	$0.436604\pi$
$662$	−46.6335	−1.81246
$663$	−21.2554	−0.825489
$664$	−36.2432	−1.40651
$665$	−3.57629	−0.138683
$666$	−9.88686	−0.383108
$667$	−59.7862	−2.31493
$668$	0.279913	0.0108301
$669$	9.14265	0.353475
$670$	0.581425	0.0224624
$671$	−1.00000	−0.0386046
$672$	−0.919513	−0.0354710
$673$	−12.6816	−0.488841	−0.244420	−	0.969669i	$-0.578598\pi$
$673$	−12.6816	−0.488841	−0.244420	+	0.969669i	$0.578598\pi$
$674$	−8.22866	−0.316956
$675$	−4.59236	−0.176760
$676$	0.313835	0.0120706
$677$	−3.72778	−0.143270	−0.0716351	−	0.997431i	$-0.522822\pi$
$677$	−3.72778	−0.143270	−0.0716351	+	0.997431i	$0.522822\pi$
$678$	7.50404	0.288191
$679$	10.9614	0.420659
$680$	11.9111	0.456769
$681$	−8.70809	−0.333695
$682$	1.57065	0.0601432
$683$	−17.1703	−0.657005	−0.328502	−	0.944503i	$-0.606544\pi$
$683$	−17.1703	−0.657005	−0.328502	+	0.944503i	$0.606544\pi$
$684$	1.05302	0.0402633
$685$	−6.40028	−0.244542
$686$	16.5213	0.630786
$687$	21.0052	0.801399
$688$	38.5031	1.46792
$689$	−5.81294	−0.221455
$690$	−7.20336	−0.274227
$691$	11.7402	0.446619	0.223310	−	0.974748i	$-0.428314\pi$
$691$	11.7402	0.446619	0.223310	+	0.974748i	$0.428314\pi$
$692$	−2.52022	−0.0958043
$693$	0.931245	0.0353751
$694$	13.4683	0.511250
$695$	4.58024	0.173739
$696$	21.0341	0.797295
$697$	−26.8188	−1.01583
$698$	−29.4005	−1.11283
$699$	5.90539	0.223362
$700$	−0.748698	−0.0282981
$701$	44.5723	1.68347	0.841737	−	0.539888i	$-0.181533\pi$
$701$	44.5723	1.68347	0.841737	+	0.539888i	$0.181533\pi$
$702$	−4.52246	−0.170689
$703$	44.0216	1.66030
$704$	−8.57231	−0.323081
$705$	8.53138	0.321310
$706$	−34.0214	−1.28041
$707$	−0.363499	−0.0136708
$708$	0.563062	0.0211612
$709$	41.6466	1.56407	0.782035	−	0.623235i	$-0.214182\pi$
$709$	41.6466	1.56407	0.782035	+	0.623235i	$0.214182\pi$
$710$	9.12676	0.342521
$711$	16.8703	0.632686
$712$	9.55676	0.358155
$713$	−9.71022	−0.363651
$714$	−7.98738	−0.298920
$715$	−2.13742	−0.0799350
$716$	−1.44159	−0.0538749
$717$	−4.71545	−0.176102
$718$	10.0962	0.376787
$719$	10.5161	0.392185	0.196092	−	0.980585i	$-0.437175\pi$
$719$	10.5161	0.392185	0.196092	+	0.980585i	$0.437175\pi$
$720$	2.31075	0.0861165
$721$	−16.2176	−0.603974
$722$	23.2076	0.863697
$723$	20.8568	0.775672
$724$	0.983778	0.0365618
$725$	32.8748	1.22094
$726$	1.35090	0.0501366
$727$	3.14361	0.116590	0.0582951	−	0.998299i	$-0.481434\pi$
$727$	3.14361	0.116590	0.0582951	+	0.998299i	$0.481434\pi$
$728$	−9.16034	−0.339505
$729$	1.00000	0.0370370
$730$	−9.10208	−0.336883
$731$	−67.5458	−2.49827
$732$	−0.175068	−0.00647070
$733$	16.4803	0.608716	0.304358	−	0.952558i	$-0.401558\pi$
$733$	16.4803	0.608716	0.304358	+	0.952558i	$0.401558\pi$
$734$	24.3217	0.897729
$735$	3.91558	0.144428
$736$	8.24646	0.303968
$737$	0.674112	0.0248312
$738$	−5.70618	−0.210047
$739$	7.89988	0.290602	0.145301	−	0.989388i	$-0.453585\pi$
$739$	7.89988	0.290602	0.145301	+	0.989388i	$0.453585\pi$
$740$	−0.818051	−0.0300722
$741$	20.1364	0.739729
$742$	−2.18440	−0.0801918
$743$	14.4312	0.529428	0.264714	−	0.964327i	$-0.414722\pi$
$743$	14.4312	0.529428	0.264714	+	0.964327i	$0.414722\pi$
$744$	3.41627	0.125246
$745$	11.8490	0.434115
$746$	41.0256	1.50205
$747$	12.3348	0.451305
$748$	1.11154	0.0406418
$749$	−2.67834	−0.0978643
$750$	8.27346	0.302104
$751$	−14.9468	−0.545418	−0.272709	−	0.962097i	$-0.587920\pi$
$751$	−14.9468	−0.545418	−0.272709	+	0.962097i	$0.587920\pi$
$752$	48.3610	1.76355
$753$	2.71069	0.0987832
$754$	32.3744	1.17901
$755$	−4.58841	−0.166989
$756$	0.163031	0.00592939
$757$	−11.8626	−0.431155	−0.215578	−	0.976487i	$-0.569163\pi$
$757$	−11.8626	−0.431155	−0.215578	+	0.976487i	$0.569163\pi$
$758$	−17.9068	−0.650405
$759$	−8.35167	−0.303147
$760$	−11.2840	−0.409315
$761$	9.32969	0.338201	0.169101	−	0.985599i	$-0.445914\pi$
$761$	9.32969	0.338201	0.169101	+	0.985599i	$0.445914\pi$
$762$	12.3715	0.448171
$763$	−15.1362	−0.547966
$764$	3.29120	0.119071
$765$	−4.05373	−0.146563
$766$	30.1951	1.09099
$767$	10.7672	0.388779
$768$	−4.16850	−0.150418
$769$	−14.1173	−0.509084	−0.254542	−	0.967062i	$-0.581925\pi$
$769$	−14.1173	−0.509084	−0.254542	+	0.967062i	$0.581925\pi$
$770$	−0.803204	−0.0289454
$771$	−18.9869	−0.683795
$772$	−2.49004	−0.0896186
$773$	42.6887	1.53541	0.767703	−	0.640806i	$-0.221400\pi$
$773$	42.6887	1.53541	0.767703	+	0.640806i	$0.221400\pi$
$774$	−14.3716	−0.516576
$775$	5.33939	0.191797
$776$	34.5857	1.24155
$777$	6.81552	0.244506
$778$	−35.0261	−1.25575
$779$	25.4069	0.910298
$780$	−0.374194	−0.0133983
$781$	10.5817	0.378643
$782$	71.6331	2.56159
$783$	−7.15859	−0.255827
$784$	22.1959	0.792709
$785$	−0.664049	−0.0237009
$786$	0.916203	0.0326799
$787$	36.7329	1.30939	0.654694	−	0.755894i	$-0.272797\pi$
$787$	36.7329	1.30939	0.654694	+	0.755894i	$0.272797\pi$
$788$	1.09030	0.0388403
$789$	−10.8868	−0.387582
$790$	−14.5507	−0.517691
$791$	−5.17292	−0.183928
$792$	2.93830	0.104408
$793$	−3.34774	−0.118882
$794$	−26.0739	−0.925330
$795$	−1.10862	−0.0393187
$796$	1.65863	0.0587886
$797$	17.0329	0.603336	0.301668	−	0.953413i	$-0.402457\pi$
$797$	17.0329	0.603336	0.301668	+	0.953413i	$0.402457\pi$
$798$	7.56690	0.267865
$799$	−84.8395	−3.00140
$800$	−4.53450	−0.160319
$801$	−3.25248	−0.114921
$802$	11.2668	0.397846
$803$	−10.5531	−0.372410
$804$	0.118015	0.00416209
$805$	4.96565	0.175016
$806$	5.25812	0.185209
$807$	−19.4158	−0.683468
$808$	−1.14693	−0.0403487
$809$	−28.7341	−1.01024	−0.505119	−	0.863050i	$-0.668551\pi$
$809$	−28.7341	−1.01024	−0.505119	+	0.863050i	$0.668551\pi$
$810$	−0.862505	−0.0303053
$811$	−50.5582	−1.77534	−0.887669	−	0.460483i	$-0.847676\pi$
$811$	−50.5582	−1.77534	−0.887669	+	0.460483i	$0.847676\pi$
$812$	−1.16707	−0.0409563
$813$	−25.4900	−0.893972
$814$	9.88686	0.346534
$815$	15.9060	0.557164
$816$	−22.9790	−0.804426
$817$	63.9900	2.23873
$818$	10.0151	0.350171
$819$	3.11757	0.108937
$820$	−0.472136	−0.0164877
$821$	−1.03772	−0.0362165	−0.0181083	−	0.999836i	$-0.505764\pi$
$821$	−1.03772	−0.0362165	−0.0181083	+	0.999836i	$0.505764\pi$
$822$	13.5420	0.472333
$823$	−15.8787	−0.553498	−0.276749	−	0.960942i	$-0.589257\pi$
$823$	−15.8787	−0.553498	−0.276749	+	0.960942i	$0.589257\pi$
$824$	−51.1703	−1.78260
$825$	4.59236	0.159885
$826$	4.04610	0.140782
$827$	−1.79670	−0.0624774	−0.0312387	−	0.999512i	$-0.509945\pi$
$827$	−1.79670	−0.0624774	−0.0312387	+	0.999512i	$0.509945\pi$
$828$	−1.46211	−0.0508119
$829$	6.36445	0.221047	0.110523	−	0.993874i	$-0.464747\pi$
$829$	6.36445	0.221047	0.110523	+	0.993874i	$0.464747\pi$
$830$	−10.6388	−0.369278
$831$	19.6348	0.681125
$832$	−28.6979	−0.994919
$833$	−38.9381	−1.34912
$834$	−9.69111	−0.335576
$835$	1.02083	0.0353273
$836$	−1.05302	−0.0364195
$837$	−1.16267	−0.0401877
$838$	−20.4120	−0.705120
$839$	46.9487	1.62085	0.810425	−	0.585843i	$-0.199236\pi$
$839$	46.9487	1.62085	0.810425	+	0.585843i	$0.199236\pi$
$840$	−1.74702	−0.0602780
$841$	22.2454	0.767084
$842$	−30.4018	−1.04772
$843$	−17.5405	−0.604128
$844$	2.95718	0.101791
$845$	1.14455	0.0393736
$846$	−18.0511	−0.620611
$847$	−0.931245	−0.0319980
$848$	−6.28433	−0.215805
$849$	21.5895	0.740948
$850$	−39.3891	−1.35104
$851$	−61.1236	−2.09529
$852$	1.85252	0.0634662
$853$	20.8057	0.712373	0.356187	−	0.934415i	$-0.384077\pi$
$853$	20.8057	0.712373	0.356187	+	0.934415i	$0.384077\pi$
$854$	−1.25802	−0.0430485
$855$	3.84033	0.131337
$856$	−8.45079	−0.288842
$857$	0.254872	0.00870627	0.00435314	−	0.999991i	$-0.498614\pi$
$857$	0.254872	0.00870627	0.00435314	+	0.999991i	$0.498614\pi$
$858$	4.52246	0.154394
$859$	4.15632	0.141812	0.0709059	−	0.997483i	$-0.477411\pi$
$859$	4.15632	0.141812	0.0709059	+	0.997483i	$0.477411\pi$
$860$	−1.18912	−0.0405488
$861$	3.93356	0.134055
$862$	14.2560	0.485562
$863$	−44.2369	−1.50584	−0.752920	−	0.658112i	$-0.771355\pi$
$863$	−44.2369	−1.50584	−0.752920	+	0.658112i	$0.771355\pi$
$864$	0.987402	0.0335921
$865$	−9.19114	−0.312508
$866$	−34.0090	−1.15567
$867$	23.3119	0.791715
$868$	−0.189551	−0.00643379
$869$	−16.8703	−0.572286
$870$	6.17432	0.209329
$871$	2.25675	0.0764671
$872$	−47.7582	−1.61730
$873$	−11.7707	−0.398376
$874$	−67.8621	−2.29547
$875$	−5.70332	−0.192807
$876$	−1.84751	−0.0624214
$877$	6.35541	0.214607	0.107304	−	0.994226i	$-0.465778\pi$
$877$	6.35541	0.214607	0.107304	+	0.994226i	$0.465778\pi$
$878$	−1.91109	−0.0644963
$879$	13.8500	0.467148
$880$	−2.31075	−0.0778953
$881$	11.2586	0.379312	0.189656	−	0.981851i	$-0.439263\pi$
$881$	11.2586	0.379312	0.189656	+	0.981851i	$0.439263\pi$
$882$	−8.28478	−0.278963
$883$	10.4824	0.352760	0.176380	−	0.984322i	$-0.443561\pi$
$883$	10.4824	0.352760	0.176380	+	0.984322i	$0.443561\pi$
$884$	3.72113	0.125155
$885$	2.05347	0.0690265
$886$	0.164925	0.00554076
$887$	−24.4932	−0.822403	−0.411201	−	0.911545i	$-0.634891\pi$
$887$	−24.4932	−0.822403	−0.411201	+	0.911545i	$0.634891\pi$
$888$	21.5046	0.721647
$889$	−8.52830	−0.286030
$890$	2.80528	0.0940332
$891$	−1.00000	−0.0335013
$892$	−1.60059	−0.0535916
$893$	80.3733	2.68959
$894$	−25.0708	−0.838492
$895$	−5.25744	−0.175737
$896$	−8.94511	−0.298835
$897$	−27.9592	−0.933531
$898$	51.6720	1.72432
$899$	8.32306	0.277590
$900$	0.803976	0.0267992
$901$	11.0246	0.367281
$902$	5.70618	0.189995
$903$	9.90708	0.329687
$904$	−16.3218	−0.542855
$905$	3.58780	0.119263
$906$	9.70840	0.322540
$907$	−35.6244	−1.18289	−0.591444	−	0.806346i	$-0.701442\pi$
$907$	−35.6244	−1.18289	−0.591444	+	0.806346i	$0.701442\pi$
$908$	1.52451	0.0505926
$909$	0.390337	0.0129466
$910$	−2.68892	−0.0891367
$911$	−3.45463	−0.114457	−0.0572285	−	0.998361i	$-0.518226\pi$
$911$	−3.45463	−0.114457	−0.0572285	+	0.998361i	$0.518226\pi$
$912$	21.7693	0.720854
$913$	−12.3348	−0.408221
$914$	−2.31936	−0.0767177
$915$	−0.638467	−0.0211071
$916$	−3.67734	−0.121503
$917$	−0.631586	−0.0208568
$918$	8.57709	0.283086
$919$	−4.33735	−0.143076	−0.0715379	−	0.997438i	$-0.522791\pi$
$919$	−4.33735	−0.143076	−0.0715379	+	0.997438i	$0.522791\pi$
$920$	15.6678	0.516552
$921$	−31.2006	−1.02809
$922$	−35.9586	−1.18423
$923$	35.4247	1.16602
$924$	−0.163031	−0.00536334
$925$	33.6102	1.10510
$926$	11.9130	0.391487
$927$	17.4149	0.571982
$928$	−7.06840	−0.232032
$929$	15.4605	0.507242	0.253621	−	0.967304i	$-0.418378\pi$
$929$	15.4605	0.507242	0.253621	+	0.967304i	$0.418378\pi$
$930$	1.00281	0.0328833
$931$	36.8882	1.20896
$932$	−1.03384	−0.0338647
$933$	6.02310	0.197187
$934$	−42.2167	−1.38137
$935$	4.05373	0.132571
$936$	9.83666	0.321521
$937$	14.7947	0.483321	0.241660	−	0.970361i	$-0.422308\pi$
$937$	14.7947	0.483321	0.241660	+	0.970361i	$0.422308\pi$
$938$	0.848046	0.0276897
$939$	−6.31441	−0.206063
$940$	−1.49357	−0.0487150
$941$	36.4343	1.18773	0.593863	−	0.804566i	$-0.297602\pi$
$941$	36.4343	1.18773	0.593863	+	0.804566i	$0.297602\pi$
$942$	1.40503	0.0457783
$943$	−35.2773	−1.14879
$944$	11.6403	0.378859
$945$	0.594569	0.0193413
$946$	14.3716	0.467261
$947$	−47.4324	−1.54134	−0.770672	−	0.637231i	$-0.780080\pi$
$947$	−47.4324	−1.54134	−0.770672	+	0.637231i	$0.780080\pi$
$948$	−2.95345	−0.0959236
$949$	−35.3289	−1.14683
$950$	37.3155	1.21068
$951$	17.8921	0.580190
$952$	17.3731	0.563065
$953$	−47.1114	−1.52609	−0.763044	−	0.646347i	$-0.776296\pi$
$953$	−47.1114	−1.52609	−0.763044	+	0.646347i	$0.776296\pi$
$954$	2.34567	0.0759440
$955$	12.0029	0.388404
$956$	0.825525	0.0266994
$957$	7.15859	0.231404
$958$	−9.50538	−0.307105
$959$	−9.33523	−0.301450
$960$	−5.47314	−0.176645
$961$	−29.6482	−0.956394
$962$	33.0986	1.06714
$963$	2.87608	0.0926804
$964$	−3.65136	−0.117602
$965$	−9.08110	−0.292331
$966$	−10.5066	−0.338043
$967$	19.4597	0.625783	0.312891	−	0.949789i	$-0.398702\pi$
$967$	19.4597	0.625783	0.312891	+	0.949789i	$0.398702\pi$
$968$	−2.93830	−0.0944406
$969$	−38.1898	−1.22683
$970$	10.1522	0.325969
$971$	−48.7615	−1.56483	−0.782415	−	0.622757i	$-0.786013\pi$
$971$	−48.7615	−1.56483	−0.782415	+	0.622757i	$0.786013\pi$
$972$	−0.175068	−0.00561531
$973$	6.68058	0.214170
$974$	−7.62600	−0.244353
$975$	15.3740	0.492363
$976$	−3.61922	−0.115848
$977$	43.8091	1.40158	0.700788	−	0.713369i	$-0.252832\pi$
$977$	43.8091	1.40158	0.700788	+	0.713369i	$0.252832\pi$
$978$	−33.6548	−1.07616
$979$	3.25248	0.103950
$980$	−0.685493	−0.0218973
$981$	16.2537	0.518940
$982$	−1.98698	−0.0634069
$983$	−3.34784	−0.106779	−0.0533897	−	0.998574i	$-0.517003\pi$
$983$	−3.34784	−0.106779	−0.0533897	+	0.998574i	$0.517003\pi$
$984$	12.4113	0.395659
$985$	3.97628	0.126695
$986$	−61.3999	−1.95537
$987$	12.4436	0.396083
$988$	−3.52524	−0.112153
$989$	−88.8495	−2.82525
$990$	0.862505	0.0274122
$991$	−12.4423	−0.395241	−0.197621	−	0.980279i	$-0.563321\pi$
$991$	−12.4423	−0.395241	−0.197621	+	0.980279i	$0.563321\pi$
$992$	−1.14802	−0.0364497
$993$	−34.5203	−1.09547
$994$	13.3120	0.422230
$995$	6.04896	0.191765
$996$	−2.15942	−0.0684239
$997$	58.9240	1.86614	0.933071	−	0.359693i	$-0.117119\pi$
$997$	58.9240	1.86614	0.933071	+	0.359693i	$0.117119\pi$
$998$	−16.9712	−0.537213
$999$	−7.31872	−0.231554

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.35090 q^{2} +1.00000 q^{3} -0.175068 q^{4} -0.638467 q^{5} +1.35090 q^{6} -0.931245 q^{7} -2.93830 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.35090 q^{2} +1.00000 q^{3} -0.175068 q^{4} -0.638467 q^{5} +1.35090 q^{6} -0.931245 q^{7} -2.93830 q^{8} +1.00000 q^{9} -0.862505 q^{10} -1.00000 q^{11} -0.175068 q^{12} -3.34774 q^{13} -1.25802 q^{14} -0.638467 q^{15} -3.61922 q^{16} +6.34917 q^{17} +1.35090 q^{18} -6.01493 q^{19} +0.111775 q^{20} -0.931245 q^{21} -1.35090 q^{22} +8.35167 q^{23} -2.93830 q^{24} -4.59236 q^{25} -4.52246 q^{26} +1.00000 q^{27} +0.163031 q^{28} -7.15859 q^{29} -0.862505 q^{30} -1.16267 q^{31} +0.987402 q^{32} -1.00000 q^{33} +8.57709 q^{34} +0.594569 q^{35} -0.175068 q^{36} -7.31872 q^{37} -8.12557 q^{38} -3.34774 q^{39} +1.87601 q^{40} -4.22398 q^{41} -1.25802 q^{42} -10.6385 q^{43} +0.175068 q^{44} -0.638467 q^{45} +11.2823 q^{46} -13.3623 q^{47} -3.61922 q^{48} -6.13278 q^{49} -6.20382 q^{50} +6.34917 q^{51} +0.586082 q^{52} +1.73638 q^{53} +1.35090 q^{54} +0.638467 q^{55} +2.73628 q^{56} -6.01493 q^{57} -9.67054 q^{58} -3.21625 q^{59} +0.111775 q^{60} +1.00000 q^{61} -1.57065 q^{62} -0.931245 q^{63} +8.57231 q^{64} +2.13742 q^{65} -1.35090 q^{66} -0.674112 q^{67} -1.11154 q^{68} +8.35167 q^{69} +0.803204 q^{70} -10.5817 q^{71} -2.93830 q^{72} +10.5531 q^{73} -9.88686 q^{74} -4.59236 q^{75} +1.05302 q^{76} +0.931245 q^{77} -4.52246 q^{78} +16.8703 q^{79} +2.31075 q^{80} +1.00000 q^{81} -5.70618 q^{82} +12.3348 q^{83} +0.163031 q^{84} -4.05373 q^{85} -14.3716 q^{86} -7.15859 q^{87} +2.93830 q^{88} -3.25248 q^{89} -0.862505 q^{90} +3.11757 q^{91} -1.46211 q^{92} -1.16267 q^{93} -18.0511 q^{94} +3.84033 q^{95} +0.987402 q^{96} -11.7707 q^{97} -8.28478 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 4 q^{2} + 11 q^{3} + 6 q^{4} - 13 q^{5} - 4 q^{6} - 5 q^{7} - 9 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q - 4 * q^2 + 11 * q^3 + 6 * q^4 - 13 * q^5 - 4 * q^6 - 5 * q^7 - 9 * q^8 + 11 * q^9	\( 11 q - 4 q^{2} + 11 q^{3} + 6 q^{4} - 13 q^{5} - 4 q^{6} - 5 q^{7} - 9 q^{8} + 11 q^{9} + 6 q^{10} - 11 q^{11} + 6 q^{12} - 3 q^{13} - 9 q^{14} - 13 q^{15} + 4 q^{16} - 7 q^{17} - 4 q^{18} - 8 q^{19} - 25 q^{20} - 5 q^{21} + 4 q^{22} - 15 q^{23} - 9 q^{24} + 4 q^{25} - 2 q^{26} + 11 q^{27} + 13 q^{28} - 8 q^{29} + 6 q^{30} - 17 q^{31} - 27 q^{32} - 11 q^{33} - 18 q^{34} - 2 q^{35} + 6 q^{36} - 10 q^{37} - 30 q^{38} - 3 q^{39} + 10 q^{40} - 25 q^{41} - 9 q^{42} - 7 q^{43} - 6 q^{44} - 13 q^{45} + 32 q^{46} - 30 q^{47} + 4 q^{48} - 2 q^{49} + 11 q^{50} - 7 q^{51} - 7 q^{52} - 18 q^{53} - 4 q^{54} + 13 q^{55} - 20 q^{56} - 8 q^{57} - 13 q^{58} - 43 q^{59} - 25 q^{60} + 11 q^{61} + 7 q^{62} - 5 q^{63} + 25 q^{64} - 27 q^{65} + 4 q^{66} - 30 q^{67} + 10 q^{68} - 15 q^{69} - 4 q^{70} - 7 q^{71} - 9 q^{72} + 6 q^{73} - 44 q^{74} + 4 q^{75} - 19 q^{76} + 5 q^{77} - 2 q^{78} + 17 q^{79} - 22 q^{80} + 11 q^{81} + 8 q^{82} - 34 q^{83} + 13 q^{84} + 10 q^{85} + 2 q^{86} - 8 q^{87} + 9 q^{88} - 41 q^{89} + 6 q^{90} - 39 q^{91} - 32 q^{92} - 17 q^{93} + 55 q^{94} - 9 q^{95} - 27 q^{96} - 41 q^{97} - 29 q^{98} - 11 q^{99}+O(q^{100}) \) 11 * q - 4 * q^2 + 11 * q^3 + 6 * q^4 - 13 * q^5 - 4 * q^6 - 5 * q^7 - 9 * q^8 + 11 * q^9 + 6 * q^10 - 11 * q^11 + 6 * q^12 - 3 * q^13 - 9 * q^14 - 13 * q^15 + 4 * q^16 - 7 * q^17 - 4 * q^18 - 8 * q^19 - 25 * q^20 - 5 * q^21 + 4 * q^22 - 15 * q^23 - 9 * q^24 + 4 * q^25 - 2 * q^26 + 11 * q^27 + 13 * q^28 - 8 * q^29 + 6 * q^30 - 17 * q^31 - 27 * q^32 - 11 * q^33 - 18 * q^34 - 2 * q^35 + 6 * q^36 - 10 * q^37 - 30 * q^38 - 3 * q^39 + 10 * q^40 - 25 * q^41 - 9 * q^42 - 7 * q^43 - 6 * q^44 - 13 * q^45 + 32 * q^46 - 30 * q^47 + 4 * q^48 - 2 * q^49 + 11 * q^50 - 7 * q^51 - 7 * q^52 - 18 * q^53 - 4 * q^54 + 13 * q^55 - 20 * q^56 - 8 * q^57 - 13 * q^58 - 43 * q^59 - 25 * q^60 + 11 * q^61 + 7 * q^62 - 5 * q^63 + 25 * q^64 - 27 * q^65 + 4 * q^66 - 30 * q^67 + 10 * q^68 - 15 * q^69 - 4 * q^70 - 7 * q^71 - 9 * q^72 + 6 * q^73 - 44 * q^74 + 4 * q^75 - 19 * q^76 + 5 * q^77 - 2 * q^78 + 17 * q^79 - 22 * q^80 + 11 * q^81 + 8 * q^82 - 34 * q^83 + 13 * q^84 + 10 * q^85 + 2 * q^86 - 8 * q^87 + 9 * q^88 - 41 * q^89 + 6 * q^90 - 39 * q^91 - 32 * q^92 - 17 * q^93 + 55 * q^94 - 9 * q^95 - 27 * q^96 - 41 * q^97 - 29 * q^98 - 11 * q^99

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