LMFDB - Embedded newform 2013.2.a.b.1.3

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			1.3
Root			$2.04468$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.04468 q^{2} -1.00000 q^{3} +2.18073 q^{4} -1.44717 q^{5} +2.04468 q^{6} -4.07149 q^{7} -0.369530 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.04468 q^{2} -1.00000 q^{3} +2.18073 q^{4} -1.44717 q^{5} +2.04468 q^{6} -4.07149 q^{7} -0.369530 q^{8} +1.00000 q^{9} +2.95900 q^{10} +1.00000 q^{11} -2.18073 q^{12} -0.740706 q^{13} +8.32491 q^{14} +1.44717 q^{15} -3.60588 q^{16} -5.60076 q^{17} -2.04468 q^{18} +7.10000 q^{19} -3.15588 q^{20} +4.07149 q^{21} -2.04468 q^{22} +6.31883 q^{23} +0.369530 q^{24} -2.90570 q^{25} +1.51451 q^{26} -1.00000 q^{27} -8.87881 q^{28} +1.15314 q^{29} -2.95900 q^{30} -1.07924 q^{31} +8.11195 q^{32} -1.00000 q^{33} +11.4518 q^{34} +5.89214 q^{35} +2.18073 q^{36} +2.50117 q^{37} -14.5173 q^{38} +0.740706 q^{39} +0.534772 q^{40} +9.71861 q^{41} -8.32491 q^{42} -8.07420 q^{43} +2.18073 q^{44} -1.44717 q^{45} -12.9200 q^{46} +1.61740 q^{47} +3.60588 q^{48} +9.57703 q^{49} +5.94123 q^{50} +5.60076 q^{51} -1.61528 q^{52} +6.83711 q^{53} +2.04468 q^{54} -1.44717 q^{55} +1.50454 q^{56} -7.10000 q^{57} -2.35781 q^{58} +3.83596 q^{59} +3.15588 q^{60} +1.00000 q^{61} +2.20669 q^{62} -4.07149 q^{63} -9.37459 q^{64} +1.07193 q^{65} +2.04468 q^{66} +7.40024 q^{67} -12.2137 q^{68} -6.31883 q^{69} -12.0476 q^{70} -8.48228 q^{71} -0.369530 q^{72} -15.3493 q^{73} -5.11411 q^{74} +2.90570 q^{75} +15.4832 q^{76} -4.07149 q^{77} -1.51451 q^{78} -2.39760 q^{79} +5.21833 q^{80} +1.00000 q^{81} -19.8715 q^{82} +12.8107 q^{83} +8.87881 q^{84} +8.10526 q^{85} +16.5092 q^{86} -1.15314 q^{87} -0.369530 q^{88} +17.3600 q^{89} +2.95900 q^{90} +3.01578 q^{91} +13.7796 q^{92} +1.07924 q^{93} -3.30707 q^{94} -10.2749 q^{95} -8.11195 q^{96} -11.1188 q^{97} -19.5820 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 2 * q^2 - 11 * q^3 + 10 * q^4 - q^5 + 2 * q^6 - 11 * q^7 - 3 * q^8 + 11 * q^9	\( 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9} - 8 q^{10} + 11 q^{11} - 10 q^{12} - 13 q^{13} + 5 q^{14} + q^{15} + 4 q^{16} - 13 q^{17} - 2 q^{18} - 12 q^{19} - 7 q^{20} + 11 q^{21} - 2 q^{22} - 3 q^{23} + 3 q^{24} + 12 q^{25} + 12 q^{26} - 11 q^{27} - 13 q^{28} + 2 q^{29} + 8 q^{30} + q^{31} - 23 q^{32} - 11 q^{33} - 14 q^{34} - 4 q^{35} + 10 q^{36} - 14 q^{37} - 8 q^{38} + 13 q^{39} - 34 q^{40} + 3 q^{41} - 5 q^{42} - 21 q^{43} + 10 q^{44} - q^{45} - 12 q^{46} - 16 q^{47} - 4 q^{48} - 18 q^{49} - 13 q^{50} + 13 q^{51} - 33 q^{52} + 2 q^{54} - q^{55} + 16 q^{56} + 12 q^{57} - 17 q^{58} + 3 q^{59} + 7 q^{60} + 11 q^{61} - 21 q^{62} - 11 q^{63} - 7 q^{64} - q^{65} + 2 q^{66} - 24 q^{67} + 2 q^{68} + 3 q^{69} + 4 q^{70} + 7 q^{71} - 3 q^{72} - 42 q^{73} - 16 q^{74} - 12 q^{75} - 13 q^{76} - 11 q^{77} - 12 q^{78} - 11 q^{79} + 42 q^{80} + 11 q^{81} - 38 q^{82} - 34 q^{83} + 13 q^{84} - 14 q^{85} + 42 q^{86} - 2 q^{87} - 3 q^{88} + 29 q^{89} - 8 q^{90} + 9 q^{91} + 42 q^{92} - q^{93} - 33 q^{94} - 31 q^{95} + 23 q^{96} - 45 q^{97} - 33 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q - 2 * q^2 - 11 * q^3 + 10 * q^4 - q^5 + 2 * q^6 - 11 * q^7 - 3 * q^8 + 11 * q^9 - 8 * q^10 + 11 * q^11 - 10 * q^12 - 13 * q^13 + 5 * q^14 + q^15 + 4 * q^16 - 13 * q^17 - 2 * q^18 - 12 * q^19 - 7 * q^20 + 11 * q^21 - 2 * q^22 - 3 * q^23 + 3 * q^24 + 12 * q^25 + 12 * q^26 - 11 * q^27 - 13 * q^28 + 2 * q^29 + 8 * q^30 + q^31 - 23 * q^32 - 11 * q^33 - 14 * q^34 - 4 * q^35 + 10 * q^36 - 14 * q^37 - 8 * q^38 + 13 * q^39 - 34 * q^40 + 3 * q^41 - 5 * q^42 - 21 * q^43 + 10 * q^44 - q^45 - 12 * q^46 - 16 * q^47 - 4 * q^48 - 18 * q^49 - 13 * q^50 + 13 * q^51 - 33 * q^52 + 2 * q^54 - q^55 + 16 * q^56 + 12 * q^57 - 17 * q^58 + 3 * q^59 + 7 * q^60 + 11 * q^61 - 21 * q^62 - 11 * q^63 - 7 * q^64 - q^65 + 2 * q^66 - 24 * q^67 + 2 * q^68 + 3 * q^69 + 4 * q^70 + 7 * q^71 - 3 * q^72 - 42 * q^73 - 16 * q^74 - 12 * q^75 - 13 * q^76 - 11 * q^77 - 12 * q^78 - 11 * q^79 + 42 * q^80 + 11 * q^81 - 38 * q^82 - 34 * q^83 + 13 * q^84 - 14 * q^85 + 42 * q^86 - 2 * q^87 - 3 * q^88 + 29 * q^89 - 8 * q^90 + 9 * q^91 + 42 * q^92 - q^93 - 33 * q^94 - 31 * q^95 + 23 * q^96 - 45 * q^97 - 33 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.04468	−1.44581	−0.722904	−	0.690948i	$-0.757193\pi$
$2$	−2.04468	−1.44581	−0.722904	+	0.690948i	$0.757193\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.18073	1.09036
$5$	−1.44717	−0.647194	−0.323597	−	0.946195i	$-0.604892\pi$
$5$	−1.44717	−0.647194	−0.323597	+	0.946195i	$0.604892\pi$
$6$	2.04468	0.834738
$7$	−4.07149	−1.53888	−0.769439	−	0.638720i	$-0.779464\pi$
$7$	−4.07149	−1.53888	−0.769439	+	0.638720i	$0.779464\pi$
$8$	−0.369530	−0.130649
$9$	1.00000	0.333333
$10$	2.95900	0.935719
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.18073	−0.629522
$13$	−0.740706	−0.205435	−0.102717	−	0.994711i	$-0.532754\pi$
$13$	−0.740706	−0.205435	−0.102717	+	0.994711i	$0.532754\pi$
$14$	8.32491	2.22492
$15$	1.44717	0.373658
$16$	−3.60588	−0.901471
$17$	−5.60076	−1.35839	−0.679193	−	0.733960i	$-0.737670\pi$
$17$	−5.60076	−1.35839	−0.679193	+	0.733960i	$0.737670\pi$
$18$	−2.04468	−0.481936
$19$	7.10000	1.62885	0.814426	−	0.580267i	$-0.197052\pi$
$19$	7.10000	1.62885	0.814426	+	0.580267i	$0.197052\pi$
$20$	−3.15588	−0.705677
$21$	4.07149	0.888472
$22$	−2.04468	−0.435928
$23$	6.31883	1.31757	0.658783	−	0.752333i	$-0.271071\pi$
$23$	6.31883	1.31757	0.658783	+	0.752333i	$0.271071\pi$
$24$	0.369530	0.0754300
$25$	−2.90570	−0.581140
$26$	1.51451	0.297019
$27$	−1.00000	−0.192450
$28$	−8.87881	−1.67794
$29$	1.15314	0.214133	0.107067	−	0.994252i	$-0.465854\pi$
$29$	1.15314	0.214133	0.107067	+	0.994252i	$0.465854\pi$
$30$	−2.95900	−0.540238
$31$	−1.07924	−0.193836	−0.0969182	−	0.995292i	$-0.530899\pi$
$31$	−1.07924	−0.193836	−0.0969182	+	0.995292i	$0.530899\pi$
$32$	8.11195	1.43400
$33$	−1.00000	−0.174078
$34$	11.4518	1.96397
$35$	5.89214	0.995953
$36$	2.18073	0.363455
$37$	2.50117	0.411190	0.205595	−	0.978637i	$-0.434087\pi$
$37$	2.50117	0.411190	0.205595	+	0.978637i	$0.434087\pi$
$38$	−14.5173	−2.35501
$39$	0.740706	0.118608
$40$	0.534772	0.0845549
$41$	9.71861	1.51779	0.758896	−	0.651212i	$-0.225739\pi$
$41$	9.71861	1.51779	0.758896	+	0.651212i	$0.225739\pi$
$42$	−8.32491	−1.28456
$43$	−8.07420	−1.23130	−0.615652	−	0.788018i	$-0.711107\pi$
$43$	−8.07420	−1.23130	−0.615652	+	0.788018i	$0.711107\pi$
$44$	2.18073	0.328757
$45$	−1.44717	−0.215731
$46$	−12.9200	−1.90495
$47$	1.61740	0.235922	0.117961	−	0.993018i	$-0.462364\pi$
$47$	1.61740	0.235922	0.117961	+	0.993018i	$0.462364\pi$
$48$	3.60588	0.520464
$49$	9.57703	1.36815
$50$	5.94123	0.840217
$51$	5.60076	0.784264
$52$	−1.61528	−0.223999
$53$	6.83711	0.939149	0.469574	−	0.882893i	$-0.344407\pi$
$53$	6.83711	0.939149	0.469574	+	0.882893i	$0.344407\pi$
$54$	2.04468	0.278246
$55$	−1.44717	−0.195136
$56$	1.50454	0.201052
$57$	−7.10000	−0.940418
$58$	−2.35781	−0.309596
$59$	3.83596	0.499400	0.249700	−	0.968323i	$-0.419668\pi$
$59$	3.83596	0.499400	0.249700	+	0.968323i	$0.419668\pi$
$60$	3.15588	0.407423
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	2.20669	0.280250
$63$	−4.07149	−0.512960
$64$	−9.37459	−1.17182
$65$	1.07193	0.132956
$66$	2.04468	0.251683
$67$	7.40024	0.904083	0.452042	−	0.891997i	$-0.350696\pi$
$67$	7.40024	0.904083	0.452042	+	0.891997i	$0.350696\pi$
$68$	−12.2137	−1.48113
$69$	−6.31883	−0.760697
$70$	−12.0476	−1.43996
$71$	−8.48228	−1.00666	−0.503331	−	0.864094i	$-0.667892\pi$
$71$	−8.48228	−1.00666	−0.503331	+	0.864094i	$0.667892\pi$
$72$	−0.369530	−0.0435495
$73$	−15.3493	−1.79650	−0.898249	−	0.439487i	$-0.855160\pi$
$73$	−15.3493	−1.79650	−0.898249	+	0.439487i	$0.855160\pi$
$74$	−5.11411	−0.594503
$75$	2.90570	0.335521
$76$	15.4832	1.77604
$77$	−4.07149	−0.463989
$78$	−1.51451	−0.171484
$79$	−2.39760	−0.269751	−0.134875	−	0.990863i	$-0.543063\pi$
$79$	−2.39760	−0.269751	−0.134875	+	0.990863i	$0.543063\pi$
$80$	5.21833	0.583427
$81$	1.00000	0.111111
$82$	−19.8715	−2.19444
$83$	12.8107	1.40616	0.703078	−	0.711113i	$-0.251808\pi$
$83$	12.8107	1.40616	0.703078	+	0.711113i	$0.251808\pi$
$84$	8.87881	0.968757
$85$	8.10526	0.879139
$86$	16.5092	1.78023
$87$	−1.15314	−0.123630
$88$	−0.369530	−0.0393920
$89$	17.3600	1.84016	0.920078	−	0.391736i	$-0.128125\pi$
$89$	17.3600	1.84016	0.920078	+	0.391736i	$0.128125\pi$
$90$	2.95900	0.311906
$91$	3.01578	0.316139
$92$	13.7796	1.43663
$93$	1.07924	0.111912
$94$	−3.30707	−0.341098
$95$	−10.2749	−1.05418
$96$	−8.11195	−0.827922
$97$	−11.1188	−1.12894	−0.564469	−	0.825454i	$-0.690919\pi$
$97$	−11.1188	−1.12894	−0.564469	+	0.825454i	$0.690919\pi$
$98$	−19.5820	−1.97808
$99$	1.00000	0.100504
$100$	−6.33654	−0.633654
$101$	2.11972	0.210920	0.105460	−	0.994424i	$-0.466368\pi$
$101$	2.11972	0.210920	0.105460	+	0.994424i	$0.466368\pi$
$102$	−11.4518	−1.13390
$103$	7.22437	0.711838	0.355919	−	0.934517i	$-0.384168\pi$
$103$	7.22437	0.711838	0.355919	+	0.934517i	$0.384168\pi$
$104$	0.273713	0.0268397
$105$	−5.89214	−0.575014
$106$	−13.9797	−1.35783
$107$	−10.1453	−0.980786	−0.490393	−	0.871501i	$-0.663147\pi$
$107$	−10.1453	−0.980786	−0.490393	+	0.871501i	$0.663147\pi$
$108$	−2.18073	−0.209841
$109$	−9.99279	−0.957135	−0.478568	−	0.878051i	$-0.658844\pi$
$109$	−9.99279	−0.957135	−0.478568	+	0.878051i	$0.658844\pi$
$110$	2.95900	0.282130
$111$	−2.50117	−0.237401
$112$	14.6813	1.38725
$113$	−18.2778	−1.71943	−0.859717	−	0.510771i	$-0.829360\pi$
$113$	−18.2778	−1.71943	−0.859717	+	0.510771i	$0.829360\pi$
$114$	14.5173	1.35967
$115$	−9.14441	−0.852721
$116$	2.51469	0.233483
$117$	−0.740706	−0.0684783
$118$	−7.84332	−0.722036
$119$	22.8035	2.09039
$120$	−0.534772	−0.0488178
$121$	1.00000	0.0909091
$122$	−2.04468	−0.185117
$123$	−9.71861	−0.876297
$124$	−2.35352	−0.211352
$125$	11.4409	1.02330
$126$	8.32491	0.741641
$127$	−0.473275	−0.0419964	−0.0209982	−	0.999780i	$-0.506684\pi$
$127$	−0.473275	−0.0419964	−0.0209982	+	0.999780i	$0.506684\pi$
$128$	2.94417	0.260230
$129$	8.07420	0.710894
$130$	−2.19175	−0.192229
$131$	−15.1344	−1.32230	−0.661151	−	0.750253i	$-0.729932\pi$
$131$	−15.1344	−1.32230	−0.661151	+	0.750253i	$0.729932\pi$
$132$	−2.18073	−0.189808
$133$	−28.9076	−2.50661
$134$	−15.1311	−1.30713
$135$	1.44717	0.124553
$136$	2.06965	0.177471
$137$	18.9353	1.61775	0.808876	−	0.587979i	$-0.200076\pi$
$137$	18.9353	1.61775	0.808876	+	0.587979i	$0.200076\pi$
$138$	12.9200	1.09982
$139$	−8.26538	−0.701061	−0.350530	−	0.936551i	$-0.613999\pi$
$139$	−8.26538	−0.701061	−0.350530	+	0.936551i	$0.613999\pi$
$140$	12.8491	1.08595
$141$	−1.61740	−0.136210
$142$	17.3436	1.45544
$143$	−0.740706	−0.0619409
$144$	−3.60588	−0.300490
$145$	−1.66879	−0.138586
$146$	31.3844	2.59739
$147$	−9.57703	−0.789900
$148$	5.45438	0.448347
$149$	19.3987	1.58920	0.794600	−	0.607133i	$-0.207681\pi$
$149$	19.3987	1.58920	0.794600	+	0.607133i	$0.207681\pi$
$150$	−5.94123	−0.485100
$151$	8.62794	0.702132	0.351066	−	0.936351i	$-0.385819\pi$
$151$	8.62794	0.702132	0.351066	+	0.936351i	$0.385819\pi$
$152$	−2.62366	−0.212807
$153$	−5.60076	−0.452795
$154$	8.32491	0.670840
$155$	1.56184	0.125450
$156$	1.61528	0.129326
$157$	21.2730	1.69777	0.848886	−	0.528575i	$-0.177274\pi$
$157$	21.2730	1.69777	0.848886	+	0.528575i	$0.177274\pi$
$158$	4.90232	0.390008
$159$	−6.83711	−0.542218
$160$	−11.7394	−0.928078
$161$	−25.7270	−2.02757
$162$	−2.04468	−0.160645
$163$	−8.12673	−0.636535	−0.318267	−	0.948001i	$-0.603101\pi$
$163$	−8.12673	−0.636535	−0.318267	+	0.948001i	$0.603101\pi$
$164$	21.1936	1.65494
$165$	1.44717	0.112662
$166$	−26.1938	−2.03303
$167$	−16.2163	−1.25486	−0.627429	−	0.778674i	$-0.715893\pi$
$167$	−16.2163	−1.25486	−0.627429	+	0.778674i	$0.715893\pi$
$168$	−1.50454	−0.116078
$169$	−12.4514	−0.957797
$170$	−16.5727	−1.27107
$171$	7.10000	0.542951
$172$	−17.6076	−1.34257
$173$	−1.46570	−0.111435	−0.0557176	−	0.998447i	$-0.517745\pi$
$173$	−1.46570	−0.111435	−0.0557176	+	0.998447i	$0.517745\pi$
$174$	2.35781	0.178745
$175$	11.8305	0.894304
$176$	−3.60588	−0.271804
$177$	−3.83596	−0.288328
$178$	−35.4957	−2.66051
$179$	−8.60631	−0.643266	−0.321633	−	0.946864i	$-0.604232\pi$
$179$	−8.60631	−0.643266	−0.321633	+	0.946864i	$0.604232\pi$
$180$	−3.15588	−0.235226
$181$	−11.5037	−0.855064	−0.427532	−	0.904000i	$-0.640617\pi$
$181$	−11.5037	−0.855064	−0.427532	+	0.904000i	$0.640617\pi$
$182$	−6.16630	−0.457077
$183$	−1.00000	−0.0739221
$184$	−2.33499	−0.172138
$185$	−3.61962	−0.266120
$186$	−2.20669	−0.161803
$187$	−5.60076	−0.409568
$188$	3.52710	0.257241
$189$	4.07149	0.296157
$190$	21.0089	1.52415
$191$	−22.8628	−1.65429	−0.827147	−	0.561986i	$-0.810038\pi$
$191$	−22.8628	−1.65429	−0.827147	+	0.561986i	$0.810038\pi$
$192$	9.37459	0.676553
$193$	−21.2488	−1.52952	−0.764760	−	0.644315i	$-0.777142\pi$
$193$	−21.2488	−1.52952	−0.764760	+	0.644315i	$0.777142\pi$
$194$	22.7343	1.63223
$195$	−1.07193	−0.0767623
$196$	20.8849	1.49178
$197$	6.54697	0.466452	0.233226	−	0.972423i	$-0.425072\pi$
$197$	6.54697	0.466452	0.233226	+	0.972423i	$0.425072\pi$
$198$	−2.04468	−0.145309
$199$	−2.57524	−0.182554	−0.0912771	−	0.995826i	$-0.529095\pi$
$199$	−2.57524	−0.182554	−0.0912771	+	0.995826i	$0.529095\pi$
$200$	1.07374	0.0759250
$201$	−7.40024	−0.521973
$202$	−4.33416	−0.304950
$203$	−4.69501	−0.329525
$204$	12.2137	0.855133
$205$	−14.0645	−0.982306
$206$	−14.7715	−1.02918
$207$	6.31883	0.439189
$208$	2.67090	0.185193
$209$	7.10000	0.491117
$210$	12.0476	0.831360
$211$	7.24000	0.498422	0.249211	−	0.968449i	$-0.419829\pi$
$211$	7.24000	0.498422	0.249211	+	0.968449i	$0.419829\pi$
$212$	14.9099	1.02401
$213$	8.48228	0.581196
$214$	20.7440	1.41803
$215$	11.6847	0.796893
$216$	0.369530	0.0251433
$217$	4.39410	0.298291
$218$	20.4321	1.38384
$219$	15.3493	1.03721
$220$	−3.15588	−0.212770
$221$	4.14852	0.279060
$222$	5.11411	0.343236
$223$	−20.1564	−1.34977	−0.674885	−	0.737923i	$-0.735807\pi$
$223$	−20.1564	−1.34977	−0.674885	+	0.737923i	$0.735807\pi$
$224$	−33.0277	−2.20676
$225$	−2.90570	−0.193713
$226$	37.3724	2.48597
$227$	−23.3579	−1.55032	−0.775160	−	0.631765i	$-0.782331\pi$
$227$	−23.3579	−1.55032	−0.775160	+	0.631765i	$0.782331\pi$
$228$	−15.4832	−1.02540
$229$	−16.7406	−1.10625	−0.553124	−	0.833099i	$-0.686564\pi$
$229$	−16.7406	−1.10625	−0.553124	+	0.833099i	$0.686564\pi$
$230$	18.6974	1.23287
$231$	4.07149	0.267884
$232$	−0.426121	−0.0279762
$233$	−7.71096	−0.505162	−0.252581	−	0.967576i	$-0.581279\pi$
$233$	−7.71096	−0.505162	−0.252581	+	0.967576i	$0.581279\pi$
$234$	1.51451	0.0990065
$235$	−2.34065	−0.152687
$236$	8.36518	0.544527
$237$	2.39760	0.155741
$238$	−46.6258	−3.02230
$239$	−14.4472	−0.934511	−0.467256	−	0.884122i	$-0.654757\pi$
$239$	−14.4472	−0.934511	−0.467256	+	0.884122i	$0.654757\pi$
$240$	−5.21833	−0.336842
$241$	−16.3602	−1.05385	−0.526927	−	0.849911i	$-0.676656\pi$
$241$	−16.3602	−1.05385	−0.526927	+	0.849911i	$0.676656\pi$
$242$	−2.04468	−0.131437
$243$	−1.00000	−0.0641500
$244$	2.18073	0.139607
$245$	−13.8596	−0.885457
$246$	19.8715	1.26696
$247$	−5.25901	−0.334623
$248$	0.398810	0.0253244
$249$	−12.8107	−0.811845
$250$	−23.3930	−1.47950
$251$	−10.4139	−0.657317	−0.328659	−	0.944449i	$-0.606597\pi$
$251$	−10.4139	−0.657317	−0.328659	+	0.944449i	$0.606597\pi$
$252$	−8.87881	−0.559312
$253$	6.31883	0.397261
$254$	0.967697	0.0607187
$255$	−8.10526	−0.507571
$256$	12.7293	0.795581
$257$	−13.5328	−0.844150	−0.422075	−	0.906561i	$-0.638698\pi$
$257$	−13.5328	−0.844150	−0.422075	+	0.906561i	$0.638698\pi$
$258$	−16.5092	−1.02782
$259$	−10.1835	−0.632772
$260$	2.33758	0.144971
$261$	1.15314	0.0713777
$262$	30.9451	1.91180
$263$	−21.0936	−1.30069	−0.650344	−	0.759640i	$-0.725375\pi$
$263$	−21.0936	−1.30069	−0.650344	+	0.759640i	$0.725375\pi$
$264$	0.369530	0.0227430
$265$	−9.89446	−0.607812
$266$	59.1068	3.62407
$267$	−17.3600	−1.06241
$268$	16.1379	0.985779
$269$	15.6473	0.954031	0.477016	−	0.878895i	$-0.341719\pi$
$269$	15.6473	0.954031	0.477016	+	0.878895i	$0.341719\pi$
$270$	−2.95900	−0.180079
$271$	−25.4707	−1.54723	−0.773617	−	0.633653i	$-0.781555\pi$
$271$	−25.4707	−1.54723	−0.773617	+	0.633653i	$0.781555\pi$
$272$	20.1957	1.22454
$273$	−3.01578	−0.182523
$274$	−38.7167	−2.33896
$275$	−2.90570	−0.175220
$276$	−13.7796	−0.829437
$277$	15.0665	0.905256	0.452628	−	0.891699i	$-0.350487\pi$
$277$	15.0665	0.905256	0.452628	+	0.891699i	$0.350487\pi$
$278$	16.9001	1.01360
$279$	−1.07924	−0.0646121
$280$	−2.17732	−0.130120
$281$	2.59901	0.155044	0.0775220	−	0.996991i	$-0.475299\pi$
$281$	2.59901	0.155044	0.0775220	+	0.996991i	$0.475299\pi$
$282$	3.30707	0.196933
$283$	7.61074	0.452412	0.226206	−	0.974080i	$-0.427368\pi$
$283$	7.61074	0.452412	0.226206	+	0.974080i	$0.427368\pi$
$284$	−18.4975	−1.09763
$285$	10.2749	0.608633
$286$	1.51451	0.0895547
$287$	−39.5692	−2.33570
$288$	8.11195	0.478001
$289$	14.3686	0.845210
$290$	3.41215	0.200369
$291$	11.1188	0.651793
$292$	−33.4726	−1.95884
$293$	−27.0321	−1.57923	−0.789617	−	0.613600i	$-0.789721\pi$
$293$	−27.0321	−1.57923	−0.789617	+	0.613600i	$0.789721\pi$
$294$	19.5820	1.14204
$295$	−5.55129	−0.323208
$296$	−0.924258	−0.0537214
$297$	−1.00000	−0.0580259
$298$	−39.6641	−2.29768
$299$	−4.68039	−0.270674
$300$	6.33654	0.365840
$301$	32.8740	1.89483
$302$	−17.6414	−1.01515
$303$	−2.11972	−0.121775
$304$	−25.6018	−1.46836
$305$	−1.44717	−0.0828647
$306$	11.4518	0.654655
$307$	−15.8588	−0.905108	−0.452554	−	0.891737i	$-0.649487\pi$
$307$	−15.8588	−0.905108	−0.452554	+	0.891737i	$0.649487\pi$
$308$	−8.87881	−0.505917
$309$	−7.22437	−0.410980
$310$	−3.19346	−0.181376
$311$	15.7482	0.893000	0.446500	−	0.894784i	$-0.352670\pi$
$311$	15.7482	0.893000	0.446500	+	0.894784i	$0.352670\pi$
$312$	−0.273713	−0.0154959
$313$	22.6053	1.27772	0.638862	−	0.769321i	$-0.279405\pi$
$313$	22.6053	1.27772	0.638862	+	0.769321i	$0.279405\pi$
$314$	−43.4966	−2.45466
$315$	5.89214	0.331984
$316$	−5.22850	−0.294126
$317$	−18.9866	−1.06639	−0.533197	−	0.845991i	$-0.679009\pi$
$317$	−18.9866	−1.06639	−0.533197	+	0.845991i	$0.679009\pi$
$318$	13.9797	0.783944
$319$	1.15314	0.0645636
$320$	13.5666	0.758397
$321$	10.1453	0.566257
$322$	52.6036	2.93149
$323$	−39.7654	−2.21261
$324$	2.18073	0.121152
$325$	2.15227	0.119386
$326$	16.6166	0.920308
$327$	9.99279	0.552602
$328$	−3.59132	−0.198297
$329$	−6.58522	−0.363055
$330$	−2.95900	−0.162888
$331$	16.9998	0.934394	0.467197	−	0.884153i	$-0.345264\pi$
$331$	16.9998	0.934394	0.467197	+	0.884153i	$0.345264\pi$
$332$	27.9366	1.53322
$333$	2.50117	0.137063
$334$	33.1572	1.81428
$335$	−10.7094	−0.585117
$336$	−14.6813	−0.800932
$337$	28.9661	1.57788	0.788941	−	0.614469i	$-0.210630\pi$
$337$	28.9661	1.57788	0.788941	+	0.614469i	$0.210630\pi$
$338$	25.4591	1.38479
$339$	18.2778	0.992716
$340$	17.6754	0.958581
$341$	−1.07924	−0.0584439
$342$	−14.5173	−0.785003
$343$	−10.4924	−0.566534
$344$	2.98366	0.160868
$345$	9.14441	0.492319
$346$	2.99689	0.161114
$347$	−2.97654	−0.159789	−0.0798946	−	0.996803i	$-0.525458\pi$
$347$	−2.97654	−0.159789	−0.0798946	+	0.996803i	$0.525458\pi$
$348$	−2.51469	−0.134801
$349$	10.0358	0.537204	0.268602	−	0.963251i	$-0.413438\pi$
$349$	10.0358	0.537204	0.268602	+	0.963251i	$0.413438\pi$
$350$	−24.1897	−1.29299
$351$	0.740706	0.0395359
$352$	8.11195	0.432368
$353$	36.7036	1.95354	0.976768	−	0.214298i	$-0.0687464\pi$
$353$	36.7036	1.95354	0.976768	+	0.214298i	$0.0687464\pi$
$354$	7.84332	0.416868
$355$	12.2753	0.651505
$356$	37.8574	2.00644
$357$	−22.8035	−1.20689
$358$	17.5972	0.930040
$359$	6.80160	0.358975	0.179487	−	0.983760i	$-0.442556\pi$
$359$	6.80160	0.358975	0.179487	+	0.983760i	$0.442556\pi$
$360$	0.534772	0.0281850
$361$	31.4100	1.65316
$362$	23.5214	1.23626
$363$	−1.00000	−0.0524864
$364$	6.57658	0.344707
$365$	22.2130	1.16268
$366$	2.04468	0.106877
$367$	15.4103	0.804411	0.402206	−	0.915549i	$-0.368244\pi$
$367$	15.4103	0.804411	0.402206	+	0.915549i	$0.368244\pi$
$368$	−22.7849	−1.18775
$369$	9.71861	0.505931
$370$	7.40098	0.384759
$371$	−27.8372	−1.44524
$372$	2.35352	0.122024
$373$	31.7452	1.64370	0.821852	−	0.569701i	$-0.192941\pi$
$373$	31.7452	1.64370	0.821852	+	0.569701i	$0.192941\pi$
$374$	11.4518	0.592158
$375$	−11.4409	−0.590805
$376$	−0.597677	−0.0308228
$377$	−0.854139	−0.0439904
$378$	−8.32491	−0.428187
$379$	17.5353	0.900728	0.450364	−	0.892845i	$-0.351294\pi$
$379$	17.5353	0.900728	0.450364	+	0.892845i	$0.351294\pi$
$380$	−22.4068	−1.14944
$381$	0.473275	0.0242466
$382$	46.7472	2.39179
$383$	−25.9264	−1.32478	−0.662388	−	0.749161i	$-0.730457\pi$
$383$	−25.9264	−1.32478	−0.662388	+	0.749161i	$0.730457\pi$
$384$	−2.94417	−0.150244
$385$	5.89214	0.300291
$386$	43.4470	2.21139
$387$	−8.07420	−0.410435
$388$	−24.2470	−1.23095
$389$	26.0307	1.31981	0.659906	−	0.751348i	$-0.270596\pi$
$389$	26.0307	1.31981	0.659906	+	0.751348i	$0.270596\pi$
$390$	2.19175	0.110984
$391$	−35.3903	−1.78976
$392$	−3.53900	−0.178746
$393$	15.1344	0.763432
$394$	−13.3865	−0.674401
$395$	3.46973	0.174581
$396$	2.18073	0.109586
$397$	−6.96177	−0.349401	−0.174701	−	0.984622i	$-0.555896\pi$
$397$	−6.96177	−0.349401	−0.174701	+	0.984622i	$0.555896\pi$
$398$	5.26556	0.263939
$399$	28.9076	1.44719
$400$	10.4776	0.523881
$401$	4.17547	0.208513	0.104257	−	0.994550i	$-0.466754\pi$
$401$	4.17547	0.208513	0.104257	+	0.994550i	$0.466754\pi$
$402$	15.1311	0.754673
$403$	0.799396	0.0398207
$404$	4.62253	0.229980
$405$	−1.44717	−0.0719105
$406$	9.59980	0.476430
$407$	2.50117	0.123979
$408$	−2.06965	−0.102463
$409$	−17.8558	−0.882912	−0.441456	−	0.897283i	$-0.645538\pi$
$409$	−17.8558	−0.882912	−0.441456	+	0.897283i	$0.645538\pi$
$410$	28.7574	1.42023
$411$	−18.9353	−0.934009
$412$	15.7544	0.776163
$413$	−15.6181	−0.768515
$414$	−12.9200	−0.634983
$415$	−18.5393	−0.910056
$416$	−6.00856	−0.294594
$417$	8.26538	0.404758
$418$	−14.5173	−0.710062
$419$	13.6815	0.668383	0.334191	−	0.942505i	$-0.391537\pi$
$419$	13.6815	0.668383	0.334191	+	0.942505i	$0.391537\pi$
$420$	−12.8491	−0.626974
$421$	−15.6057	−0.760575	−0.380287	−	0.924868i	$-0.624175\pi$
$421$	−15.6057	−0.760575	−0.380287	+	0.924868i	$0.624175\pi$
$422$	−14.8035	−0.720623
$423$	1.61740	0.0786406
$424$	−2.52651	−0.122698
$425$	16.2741	0.789412
$426$	−17.3436	−0.840298
$427$	−4.07149	−0.197033
$428$	−22.1242	−1.06941
$429$	0.740706	0.0357616
$430$	−23.8916	−1.15216
$431$	16.0638	0.773765	0.386883	−	0.922129i	$-0.373552\pi$
$431$	16.0638	0.773765	0.386883	+	0.922129i	$0.373552\pi$
$432$	3.60588	0.173488
$433$	6.63126	0.318678	0.159339	−	0.987224i	$-0.449064\pi$
$433$	6.63126	0.318678	0.159339	+	0.987224i	$0.449064\pi$
$434$	−8.98453	−0.431271
$435$	1.66879	0.0800125
$436$	−21.7915	−1.04363
$437$	44.8637	2.14612
$438$	−31.3844	−1.49961
$439$	9.17035	0.437677	0.218839	−	0.975761i	$-0.429773\pi$
$439$	9.17035	0.437677	0.218839	+	0.975761i	$0.429773\pi$
$440$	0.534772	0.0254943
$441$	9.57703	0.456049
$442$	−8.48240	−0.403467
$443$	27.6106	1.31182	0.655910	−	0.754839i	$-0.272285\pi$
$443$	27.6106	1.31182	0.655910	+	0.754839i	$0.272285\pi$
$444$	−5.45438	−0.258853
$445$	−25.1229	−1.19094
$446$	41.2134	1.95151
$447$	−19.3987	−0.917525
$448$	38.1685	1.80329
$449$	5.84547	0.275865	0.137932	−	0.990442i	$-0.455954\pi$
$449$	5.84547	0.275865	0.137932	+	0.990442i	$0.455954\pi$
$450$	5.94123	0.280072
$451$	9.71861	0.457631
$452$	−39.8590	−1.87481
$453$	−8.62794	−0.405376
$454$	47.7595	2.24147
$455$	−4.36434	−0.204603
$456$	2.62366	0.122864
$457$	−9.44032	−0.441600	−0.220800	−	0.975319i	$-0.570867\pi$
$457$	−9.44032	−0.441600	−0.220800	+	0.975319i	$0.570867\pi$
$458$	34.2292	1.59942
$459$	5.60076	0.261421
$460$	−19.9415	−0.929776
$461$	9.18658	0.427862	0.213931	−	0.976849i	$-0.431373\pi$
$461$	9.18658	0.427862	0.213931	+	0.976849i	$0.431373\pi$
$462$	−8.32491	−0.387310
$463$	14.6517	0.680921	0.340461	−	0.940259i	$-0.389417\pi$
$463$	14.6517	0.680921	0.340461	+	0.940259i	$0.389417\pi$
$464$	−4.15810	−0.193035
$465$	−1.56184	−0.0724285
$466$	15.7665	0.730367
$467$	−30.3828	−1.40595	−0.702973	−	0.711216i	$-0.748145\pi$
$467$	−30.3828	−1.40595	−0.702973	+	0.711216i	$0.748145\pi$
$468$	−1.61528	−0.0746662
$469$	−30.1300	−1.39127
$470$	4.78589	0.220757
$471$	−21.2730	−0.980210
$472$	−1.41750	−0.0652458
$473$	−8.07420	−0.371252
$474$	−4.90232	−0.225171
$475$	−20.6305	−0.946591
$476$	49.7281	2.27928
$477$	6.83711	0.313050
$478$	29.5399	1.35112
$479$	−31.6302	−1.44522	−0.722611	−	0.691254i	$-0.757058\pi$
$479$	−31.6302	−1.44522	−0.722611	+	0.691254i	$0.757058\pi$
$480$	11.7394	0.535826
$481$	−1.85263	−0.0844728
$482$	33.4514	1.52367
$483$	25.7270	1.17062
$484$	2.18073	0.0991240
$485$	16.0907	0.730642
$486$	2.04468	0.0927487
$487$	23.1748	1.05015	0.525074	−	0.851056i	$-0.324037\pi$
$487$	23.1748	1.05015	0.525074	+	0.851056i	$0.324037\pi$
$488$	−0.369530	−0.0167278
$489$	8.12673	0.367504
$490$	28.3385	1.28020
$491$	5.95367	0.268685	0.134343	−	0.990935i	$-0.457108\pi$
$491$	5.95367	0.268685	0.134343	+	0.990935i	$0.457108\pi$
$492$	−21.1936	−0.955483
$493$	−6.45848	−0.290875
$494$	10.7530	0.483801
$495$	−1.44717	−0.0650455
$496$	3.89160	0.174738
$497$	34.5355	1.54913
$498$	26.1938	1.17377
$499$	−42.7364	−1.91315	−0.956573	−	0.291494i	$-0.905848\pi$
$499$	−42.7364	−1.91315	−0.956573	+	0.291494i	$0.905848\pi$
$500$	24.9495	1.11577
$501$	16.2163	0.724492
$502$	21.2931	0.950355
$503$	−11.6626	−0.520012	−0.260006	−	0.965607i	$-0.583724\pi$
$503$	−11.6626	−0.520012	−0.260006	+	0.965607i	$0.583724\pi$
$504$	1.50454	0.0670174
$505$	−3.06760	−0.136506
$506$	−12.9200	−0.574364
$507$	12.4514	0.552984
$508$	−1.03208	−0.0457913
$509$	−12.1527	−0.538657	−0.269328	−	0.963048i	$-0.586802\pi$
$509$	−12.1527	−0.538657	−0.269328	+	0.963048i	$0.586802\pi$
$510$	16.5727	0.733851
$511$	62.4945	2.76459
$512$	−31.9157	−1.41049
$513$	−7.10000	−0.313473
$514$	27.6702	1.22048
$515$	−10.4549	−0.460698
$516$	17.6076	0.775133
$517$	1.61740	0.0711331
$518$	20.8220	0.914868
$519$	1.46570	0.0643371
$520$	−0.396109	−0.0173705
$521$	−14.0906	−0.617321	−0.308661	−	0.951172i	$-0.599881\pi$
$521$	−14.0906	−0.617321	−0.308661	+	0.951172i	$0.599881\pi$
$522$	−2.35781	−0.103199
$523$	−19.8069	−0.866097	−0.433048	−	0.901371i	$-0.642562\pi$
$523$	−19.8069	−0.866097	−0.433048	+	0.901371i	$0.642562\pi$
$524$	−33.0041	−1.44179
$525$	−11.8305	−0.516326
$526$	43.1297	1.88055
$527$	6.04455	0.263305
$528$	3.60588	0.156926
$529$	16.9276	0.735981
$530$	20.2310	0.878780
$531$	3.83596	0.166467
$532$	−63.0396	−2.73311
$533$	−7.19863	−0.311807
$534$	35.4957	1.53605
$535$	14.6820	0.634759
$536$	−2.73461	−0.118117
$537$	8.60631	0.371390
$538$	−31.9937	−1.37935
$539$	9.57703	0.412512
$540$	3.15588	0.135808
$541$	6.82761	0.293542	0.146771	−	0.989171i	$-0.453112\pi$
$541$	6.82761	0.293542	0.146771	+	0.989171i	$0.453112\pi$
$542$	52.0795	2.23701
$543$	11.5037	0.493671
$544$	−45.4331	−1.94793
$545$	14.4613	0.619452
$546$	6.16630	0.263893
$547$	−13.8897	−0.593881	−0.296940	−	0.954896i	$-0.595966\pi$
$547$	−13.8897	−0.593881	−0.296940	+	0.954896i	$0.595966\pi$
$548$	41.2927	1.76394
$549$	1.00000	0.0426790
$550$	5.94123	0.253335
$551$	8.18731	0.348791
$552$	2.33499	0.0993840
$553$	9.76179	0.415114
$554$	−30.8061	−1.30883
$555$	3.61962	0.153644
$556$	−18.0245	−0.764411
$557$	28.8327	1.22168	0.610841	−	0.791753i	$-0.290832\pi$
$557$	28.8327	1.22168	0.610841	+	0.791753i	$0.290832\pi$
$558$	2.20669	0.0934168
$559$	5.98061	0.252953
$560$	−21.2464	−0.897823
$561$	5.60076	0.236464
$562$	−5.31415	−0.224164
$563$	−23.1212	−0.974443	−0.487221	−	0.873279i	$-0.661990\pi$
$563$	−23.1212	−0.974443	−0.487221	+	0.873279i	$0.661990\pi$
$564$	−3.52710	−0.148518
$565$	26.4511	1.11281
$566$	−15.5616	−0.654101
$567$	−4.07149	−0.170987
$568$	3.13445	0.131519
$569$	−38.5704	−1.61695	−0.808477	−	0.588527i	$-0.799708\pi$
$569$	−38.5704	−1.61695	−0.808477	+	0.588527i	$0.799708\pi$
$570$	−21.0089	−0.879967
$571$	5.71501	0.239166	0.119583	−	0.992824i	$-0.461844\pi$
$571$	5.71501	0.239166	0.119583	+	0.992824i	$0.461844\pi$
$572$	−1.61528	−0.0675381
$573$	22.8628	0.955107
$574$	80.9065	3.37697
$575$	−18.3606	−0.765690
$576$	−9.37459	−0.390608
$577$	28.1422	1.17158	0.585788	−	0.810464i	$-0.300785\pi$
$577$	28.1422	1.17158	0.585788	+	0.810464i	$0.300785\pi$
$578$	−29.3792	−1.22201
$579$	21.2488	0.883069
$580$	−3.63918	−0.151109
$581$	−52.1586	−2.16390
$582$	−22.7343	−0.942368
$583$	6.83711	0.283164
$584$	5.67202	0.234710
$585$	1.07193	0.0443187
$586$	55.2721	2.28327
$587$	15.6826	0.647290	0.323645	−	0.946179i	$-0.395092\pi$
$587$	15.6826	0.647290	0.323645	+	0.946179i	$0.395092\pi$
$588$	−20.8849	−0.861278
$589$	−7.66258	−0.315731
$590$	11.3506	0.467298
$591$	−6.54697	−0.269306
$592$	−9.01894	−0.370676
$593$	3.88783	0.159654	0.0798271	−	0.996809i	$-0.474563\pi$
$593$	3.88783	0.159654	0.0798271	+	0.996809i	$0.474563\pi$
$594$	2.04468	0.0838943
$595$	−33.0005	−1.35289
$596$	42.3032	1.73281
$597$	2.57524	0.105398
$598$	9.56991	0.391343
$599$	43.0055	1.75716	0.878578	−	0.477598i	$-0.158492\pi$
$599$	43.0055	1.75716	0.878578	+	0.477598i	$0.158492\pi$
$600$	−1.07374	−0.0438353
$601$	−41.9728	−1.71211	−0.856053	−	0.516889i	$-0.827090\pi$
$601$	−41.9728	−1.71211	−0.856053	+	0.516889i	$0.827090\pi$
$602$	−67.2170	−2.73956
$603$	7.40024	0.301361
$604$	18.8152	0.765579
$605$	−1.44717	−0.0588358
$606$	4.33416	0.176063
$607$	−2.30498	−0.0935561	−0.0467780	−	0.998905i	$-0.514895\pi$
$607$	−2.30498	−0.0935561	−0.0467780	+	0.998905i	$0.514895\pi$
$608$	57.5948	2.33578
$609$	4.69501	0.190251
$610$	2.95900	0.119807
$611$	−1.19802	−0.0484665
$612$	−12.2137	−0.493711
$613$	−26.7026	−1.07851	−0.539254	−	0.842143i	$-0.681294\pi$
$613$	−26.7026	−1.07851	−0.539254	+	0.842143i	$0.681294\pi$
$614$	32.4262	1.30861
$615$	14.0645	0.567135
$616$	1.50454	0.0606195
$617$	−19.9600	−0.803558	−0.401779	−	0.915737i	$-0.631608\pi$
$617$	−19.9600	−0.803558	−0.401779	+	0.915737i	$0.631608\pi$
$618$	14.7715	0.594199
$619$	−25.1992	−1.01284	−0.506420	−	0.862287i	$-0.669031\pi$
$619$	−25.1992	−1.01284	−0.506420	+	0.862287i	$0.669031\pi$
$620$	3.40594	0.136786
$621$	−6.31883	−0.253566
$622$	−32.2001	−1.29111
$623$	−70.6810	−2.83178
$624$	−2.67090	−0.106921
$625$	−2.02842	−0.0811368
$626$	−46.2206	−1.84735
$627$	−7.10000	−0.283547
$628$	46.3907	1.85119
$629$	−14.0085	−0.558555
$630$	−12.0476	−0.479986
$631$	−35.9723	−1.43204	−0.716018	−	0.698082i	$-0.754037\pi$
$631$	−35.9723	−1.43204	−0.716018	+	0.698082i	$0.754037\pi$
$632$	0.885983	0.0352425
$633$	−7.24000	−0.287764
$634$	38.8216	1.54180
$635$	0.684910	0.0271798
$636$	−14.9099	−0.591215
$637$	−7.09376	−0.281065
$638$	−2.35781	−0.0933466
$639$	−8.48228	−0.335554
$640$	−4.26071	−0.168419
$641$	15.4545	0.610414	0.305207	−	0.952286i	$-0.401274\pi$
$641$	15.4545	0.610414	0.305207	+	0.952286i	$0.401274\pi$
$642$	−20.7440	−0.818700
$643$	−36.0968	−1.42352	−0.711760	−	0.702422i	$-0.752102\pi$
$643$	−36.0968	−1.42352	−0.711760	+	0.702422i	$0.752102\pi$
$644$	−56.1036	−2.21079
$645$	−11.6847	−0.460086
$646$	81.3077	3.19901
$647$	11.6484	0.457947	0.228973	−	0.973433i	$-0.426463\pi$
$647$	11.6484	0.457947	0.228973	+	0.973433i	$0.426463\pi$
$648$	−0.369530	−0.0145165
$649$	3.83596	0.150575
$650$	−4.40070	−0.172610
$651$	−4.39410	−0.172218
$652$	−17.7222	−0.694055
$653$	37.3130	1.46017	0.730086	−	0.683356i	$-0.239480\pi$
$653$	37.3130	1.46017	0.730086	+	0.683356i	$0.239480\pi$
$654$	−20.4321	−0.798958
$655$	21.9021	0.855786
$656$	−35.0442	−1.36824
$657$	−15.3493	−0.598833
$658$	13.4647	0.524908
$659$	18.2219	0.709823	0.354912	−	0.934900i	$-0.384511\pi$
$659$	18.2219	0.709823	0.354912	+	0.934900i	$0.384511\pi$
$660$	3.15588	0.122843
$661$	37.8870	1.47363	0.736816	−	0.676093i	$-0.236328\pi$
$661$	37.8870	1.47363	0.736816	+	0.676093i	$0.236328\pi$
$662$	−34.7592	−1.35096
$663$	−4.14852	−0.161115
$664$	−4.73393	−0.183712
$665$	41.8342	1.62226
$666$	−5.11411	−0.198168
$667$	7.28651	0.282135
$668$	−35.3634	−1.36825
$669$	20.1564	0.779291
$670$	21.8973	0.845968
$671$	1.00000	0.0386046
$672$	33.0277	1.27407
$673$	2.54686	0.0981741	0.0490870	−	0.998795i	$-0.484369\pi$
$673$	2.54686	0.0981741	0.0490870	+	0.998795i	$0.484369\pi$
$674$	−59.2264	−2.28132
$675$	2.90570	0.111840
$676$	−27.1530	−1.04435
$677$	−24.4268	−0.938797	−0.469399	−	0.882986i	$-0.655529\pi$
$677$	−24.4268	−0.938797	−0.469399	+	0.882986i	$0.655529\pi$
$678$	−37.3724	−1.43528
$679$	45.2699	1.73730
$680$	−2.99513	−0.114858
$681$	23.3579	0.895077
$682$	2.20669	0.0844987
$683$	0.981478	0.0375552	0.0187776	−	0.999824i	$-0.494023\pi$
$683$	0.981478	0.0375552	0.0187776	+	0.999824i	$0.494023\pi$
$684$	15.4832	0.592014
$685$	−27.4026	−1.04700
$686$	21.4535	0.819100
$687$	16.7406	0.638693
$688$	29.1146	1.10999
$689$	−5.06428	−0.192934
$690$	−18.6974	−0.711799
$691$	−16.8873	−0.642425	−0.321212	−	0.947007i	$-0.604090\pi$
$691$	−16.8873	−0.642425	−0.321212	+	0.947007i	$0.604090\pi$
$692$	−3.19629	−0.121505
$693$	−4.07149	−0.154663
$694$	6.08608	0.231025
$695$	11.9614	0.453722
$696$	0.426121	0.0161521
$697$	−54.4316	−2.06175
$698$	−20.5200	−0.776695
$699$	7.71096	0.291655
$700$	25.7991	0.975116
$701$	−43.8138	−1.65482	−0.827411	−	0.561596i	$-0.810187\pi$
$701$	−43.8138	−1.65482	−0.827411	+	0.561596i	$0.810187\pi$
$702$	−1.51451	−0.0571614
$703$	17.7583	0.669768
$704$	−9.37459	−0.353318
$705$	2.34065	0.0881540
$706$	−75.0473	−2.82444
$707$	−8.63042	−0.324581
$708$	−8.36518	−0.314383
$709$	25.3548	0.952218	0.476109	−	0.879386i	$-0.342047\pi$
$709$	25.3548	0.952218	0.476109	+	0.879386i	$0.342047\pi$
$710$	−25.0991	−0.941952
$711$	−2.39760	−0.0899169
$712$	−6.41503	−0.240414
$713$	−6.81950	−0.255392
$714$	46.6258	1.74493
$715$	1.07193	0.0400878
$716$	−18.7680	−0.701394
$717$	14.4472	0.539540
$718$	−13.9071	−0.519009
$719$	−15.7035	−0.585641	−0.292820	−	0.956167i	$-0.594594\pi$
$719$	−15.7035	−0.585641	−0.292820	+	0.956167i	$0.594594\pi$
$720$	5.21833	0.194476
$721$	−29.4139	−1.09543
$722$	−64.2236	−2.39015
$723$	16.3602	0.608443
$724$	−25.0864	−0.932331
$725$	−3.35068	−0.124441
$726$	2.04468	0.0758853
$727$	−23.8393	−0.884150	−0.442075	−	0.896978i	$-0.645758\pi$
$727$	−23.8393	−0.884150	−0.442075	+	0.896978i	$0.645758\pi$
$728$	−1.11442	−0.0413031
$729$	1.00000	0.0370370
$730$	−45.4186	−1.68102
$731$	45.2217	1.67259
$732$	−2.18073	−0.0806020
$733$	−4.19737	−0.155033	−0.0775167	−	0.996991i	$-0.524699\pi$
$733$	−4.19737	−0.155033	−0.0775167	+	0.996991i	$0.524699\pi$
$734$	−31.5092	−1.16303
$735$	13.8596	0.511219
$736$	51.2580	1.88939
$737$	7.40024	0.272591
$738$	−19.8715	−0.731479
$739$	−30.9947	−1.14016	−0.570080	−	0.821589i	$-0.693088\pi$
$739$	−30.9947	−1.14016	−0.570080	+	0.821589i	$0.693088\pi$
$740$	−7.89341	−0.290168
$741$	5.25901	0.193195
$742$	56.9183	2.08954
$743$	20.9689	0.769275	0.384637	−	0.923068i	$-0.374327\pi$
$743$	20.9689	0.769275	0.384637	+	0.923068i	$0.374327\pi$
$744$	−0.398810	−0.0146211
$745$	−28.0732	−1.02852
$746$	−64.9089	−2.37648
$747$	12.8107	0.468719
$748$	−12.2137	−0.446579
$749$	41.3066	1.50931
$750$	23.3930	0.854191
$751$	43.9910	1.60526	0.802628	−	0.596480i	$-0.203434\pi$
$751$	43.9910	1.60526	0.802628	+	0.596480i	$0.203434\pi$
$752$	−5.83215	−0.212677
$753$	10.4139	0.379502
$754$	1.74644	0.0636017
$755$	−12.4861	−0.454416
$756$	8.87881	0.322919
$757$	−3.66470	−0.133196	−0.0665979	−	0.997780i	$-0.521214\pi$
$757$	−3.66470	−0.133196	−0.0665979	+	0.997780i	$0.521214\pi$
$758$	−35.8541	−1.30228
$759$	−6.31883	−0.229359
$760$	3.79689	0.137728
$761$	−35.2087	−1.27631	−0.638156	−	0.769907i	$-0.720303\pi$
$761$	−35.2087	−1.27631	−0.638156	+	0.769907i	$0.720303\pi$
$762$	−0.967697	−0.0350560
$763$	40.6855	1.47292
$764$	−49.8575	−1.80378
$765$	8.10526	0.293046
$766$	53.0112	1.91537
$767$	−2.84132	−0.102594
$768$	−12.7293	−0.459329
$769$	16.0943	0.580376	0.290188	−	0.956970i	$-0.406282\pi$
$769$	16.0943	0.580376	0.290188	+	0.956970i	$0.406282\pi$
$770$	−12.0476	−0.434164
$771$	13.5328	0.487370
$772$	−46.3378	−1.66773
$773$	18.8173	0.676810	0.338405	−	0.941000i	$-0.390113\pi$
$773$	18.8173	0.676810	0.338405	+	0.941000i	$0.390113\pi$
$774$	16.5092	0.593410
$775$	3.13593	0.112646
$776$	4.10871	0.147494
$777$	10.1835	0.365331
$778$	−53.2246	−1.90820
$779$	69.0021	2.47226
$780$	−2.33758	−0.0836988
$781$	−8.48228	−0.303520
$782$	72.3618	2.58765
$783$	−1.15314	−0.0412100
$784$	−34.5337	−1.23334
$785$	−30.7857	−1.09879
$786$	−30.9451	−1.10378
$787$	8.87393	0.316321	0.158161	−	0.987413i	$-0.449444\pi$
$787$	8.87393	0.316321	0.158161	+	0.987413i	$0.449444\pi$
$788$	14.2771	0.508602
$789$	21.0936	0.750952
$790$	−7.09450	−0.252411
$791$	74.4180	2.64600
$792$	−0.369530	−0.0131307
$793$	−0.740706	−0.0263032
$794$	14.2346	0.505167
$795$	9.89446	0.350920
$796$	−5.61590	−0.199050
$797$	5.70100	0.201940	0.100970	−	0.994889i	$-0.467805\pi$
$797$	5.70100	0.201940	0.100970	+	0.994889i	$0.467805\pi$
$798$	−59.1068	−2.09236
$799$	−9.05867	−0.320473
$800$	−23.5709	−0.833356
$801$	17.3600	0.613385
$802$	−8.53752	−0.301470
$803$	−15.3493	−0.541664
$804$	−16.1379	−0.569140
$805$	37.2314	1.31223
$806$	−1.63451	−0.0575732
$807$	−15.6473	−0.550810
$808$	−0.783300	−0.0275564
$809$	47.3288	1.66399	0.831995	−	0.554783i	$-0.187199\pi$
$809$	47.3288	1.66399	0.831995	+	0.554783i	$0.187199\pi$
$810$	2.95900	0.103969
$811$	10.8788	0.382007	0.191004	−	0.981589i	$-0.438826\pi$
$811$	10.8788	0.382007	0.191004	+	0.981589i	$0.438826\pi$
$812$	−10.2385	−0.359302
$813$	25.4707	0.893296
$814$	−5.11411	−0.179249
$815$	11.7608	0.411962
$816$	−20.1957	−0.706991
$817$	−57.3269	−2.00561
$818$	36.5094	1.27652
$819$	3.01578	0.105380
$820$	−30.6708	−1.07107
$821$	32.1239	1.12113	0.560567	−	0.828109i	$-0.310583\pi$
$821$	32.1239	1.12113	0.560567	+	0.828109i	$0.310583\pi$
$822$	38.7167	1.35040
$823$	27.7817	0.968408	0.484204	−	0.874955i	$-0.339109\pi$
$823$	27.7817	0.968408	0.484204	+	0.874955i	$0.339109\pi$
$824$	−2.66962	−0.0930006
$825$	2.90570	0.101163
$826$	31.9340	1.11113
$827$	−1.89584	−0.0659247	−0.0329623	−	0.999457i	$-0.510494\pi$
$827$	−1.89584	−0.0659247	−0.0329623	+	0.999457i	$0.510494\pi$
$828$	13.7796	0.478875
$829$	−48.7687	−1.69381	−0.846903	−	0.531748i	$-0.821535\pi$
$829$	−48.7687	−1.69381	−0.846903	+	0.531748i	$0.821535\pi$
$830$	37.9069	1.31577
$831$	−15.0665	−0.522650
$832$	6.94381	0.240733
$833$	−53.6387	−1.85847
$834$	−16.9001	−0.585202
$835$	23.4678	0.812136
$836$	15.4832	0.535497
$837$	1.07924	0.0373038
$838$	−27.9742	−0.966354
$839$	−29.2860	−1.01106	−0.505532	−	0.862808i	$-0.668704\pi$
$839$	−29.2860	−1.01106	−0.505532	+	0.862808i	$0.668704\pi$
$840$	2.17732	0.0751247
$841$	−27.6703	−0.954147
$842$	31.9087	1.09965
$843$	−2.59901	−0.0895147
$844$	15.7885	0.543461
$845$	18.0192	0.619880
$846$	−3.30707	−0.113699
$847$	−4.07149	−0.139898
$848$	−24.6538	−0.846615
$849$	−7.61074	−0.261200
$850$	−33.2754	−1.14134
$851$	15.8045	0.541771
$852$	18.4975	0.633715
$853$	−25.0886	−0.859017	−0.429508	−	0.903063i	$-0.641313\pi$
$853$	−25.0886	−0.859017	−0.429508	+	0.903063i	$0.641313\pi$
$854$	8.32491	0.284872
$855$	−10.2749	−0.351395
$856$	3.74900	0.128138
$857$	−21.0458	−0.718911	−0.359455	−	0.933162i	$-0.617037\pi$
$857$	−21.0458	−0.718911	−0.359455	+	0.933162i	$0.617037\pi$
$858$	−1.51451	−0.0517044
$859$	−56.8269	−1.93891	−0.969454	−	0.245271i	$-0.921123\pi$
$859$	−56.8269	−1.93891	−0.969454	+	0.245271i	$0.921123\pi$
$860$	25.4812	0.868903
$861$	39.5692	1.34852
$862$	−32.8453	−1.11872
$863$	11.1171	0.378430	0.189215	−	0.981936i	$-0.439406\pi$
$863$	11.1171	0.378430	0.189215	+	0.981936i	$0.439406\pi$
$864$	−8.11195	−0.275974
$865$	2.12112	0.0721202
$866$	−13.5588	−0.460748
$867$	−14.3686	−0.487982
$868$	9.58233	0.325245
$869$	−2.39760	−0.0813329
$870$	−3.41215	−0.115683
$871$	−5.48140	−0.185730
$872$	3.69263	0.125048
$873$	−11.1188	−0.376313
$874$	−91.7320	−3.10288
$875$	−46.5815	−1.57474
$876$	33.4726	1.13093
$877$	2.90200	0.0979934	0.0489967	−	0.998799i	$-0.484398\pi$
$877$	2.90200	0.0979934	0.0489967	+	0.998799i	$0.484398\pi$
$878$	−18.7505	−0.632798
$879$	27.0321	0.911771
$880$	5.21833	0.175910
$881$	−8.58937	−0.289383	−0.144692	−	0.989477i	$-0.546219\pi$
$881$	−8.58937	−0.289383	−0.144692	+	0.989477i	$0.546219\pi$
$882$	−19.5820	−0.659360
$883$	−14.4738	−0.487081	−0.243541	−	0.969891i	$-0.578309\pi$
$883$	−14.4738	−0.487081	−0.243541	+	0.969891i	$0.578309\pi$
$884$	9.04679	0.304276
$885$	5.55129	0.186605
$886$	−56.4550	−1.89664
$887$	−13.7110	−0.460372	−0.230186	−	0.973147i	$-0.573933\pi$
$887$	−13.7110	−0.460372	−0.230186	+	0.973147i	$0.573933\pi$
$888$	0.924258	0.0310161
$889$	1.92693	0.0646273
$890$	51.3683	1.72187
$891$	1.00000	0.0335013
$892$	−43.9556	−1.47174
$893$	11.4835	0.384282
$894$	39.6641	1.32657
$895$	12.4548	0.416318
$896$	−11.9872	−0.400463
$897$	4.68039	0.156274
$898$	−11.9521	−0.398848
$899$	−1.24451	−0.0415068
$900$	−6.33654	−0.211218
$901$	−38.2930	−1.27573
$902$	−19.8715	−0.661648
$903$	−32.8740	−1.09398
$904$	6.75420	0.224641
$905$	16.6478	0.553392
$906$	17.6414	0.586096
$907$	−21.8465	−0.725402	−0.362701	−	0.931906i	$-0.618145\pi$
$907$	−21.8465	−0.725402	−0.362701	+	0.931906i	$0.618145\pi$
$908$	−50.9372	−1.69041
$909$	2.11972	0.0703067
$910$	8.92369	0.295817
$911$	12.3484	0.409120	0.204560	−	0.978854i	$-0.434424\pi$
$911$	12.3484	0.409120	0.204560	+	0.978854i	$0.434424\pi$
$912$	25.6018	0.847760
$913$	12.8107	0.423972
$914$	19.3025	0.638469
$915$	1.44717	0.0478420
$916$	−36.5066	−1.20621
$917$	61.6197	2.03486
$918$	−11.4518	−0.377965
$919$	20.8359	0.687314	0.343657	−	0.939095i	$-0.388334\pi$
$919$	20.8359	0.687314	0.343657	+	0.939095i	$0.388334\pi$
$920$	3.37913	0.111407
$921$	15.8588	0.522565
$922$	−18.7837	−0.618607
$923$	6.28287	0.206803
$924$	8.87881	0.292091
$925$	−7.26766	−0.238959
$926$	−29.9580	−0.984482
$927$	7.22437	0.237279
$928$	9.35423	0.307068
$929$	17.0696	0.560035	0.280018	−	0.959995i	$-0.409660\pi$
$929$	17.0696	0.560035	0.280018	+	0.959995i	$0.409660\pi$
$930$	3.19346	0.104718
$931$	67.9969	2.22851
$932$	−16.8155	−0.550810
$933$	−15.7482	−0.515574
$934$	62.1231	2.03273
$935$	8.10526	0.265070
$936$	0.273713	0.00894658
$937$	−18.2974	−0.597750	−0.298875	−	0.954292i	$-0.596611\pi$
$937$	−18.2974	−0.597750	−0.298875	+	0.954292i	$0.596611\pi$
$938$	61.6063	2.01152
$939$	−22.6053	−0.737695
$940$	−5.10432	−0.166485
$941$	21.3137	0.694807	0.347403	−	0.937716i	$-0.387063\pi$
$941$	21.3137	0.694807	0.347403	+	0.937716i	$0.387063\pi$
$942$	43.4966	1.41720
$943$	61.4102	1.99979
$944$	−13.8320	−0.450194
$945$	−5.89214	−0.191671
$946$	16.5092	0.536760
$947$	−41.4178	−1.34590	−0.672948	−	0.739690i	$-0.734972\pi$
$947$	−41.4178	−1.34590	−0.672948	+	0.739690i	$0.734972\pi$
$948$	5.22850	0.169814
$949$	11.3693	0.369063
$950$	42.1828	1.36859
$951$	18.9866	0.615682
$952$	−8.42656	−0.273106
$953$	−49.4594	−1.60215	−0.801074	−	0.598565i	$-0.795738\pi$
$953$	−49.4594	−1.60215	−0.801074	+	0.598565i	$0.795738\pi$
$954$	−13.9797	−0.452610
$955$	33.0863	1.07065
$956$	−31.5054	−1.01896
$957$	−1.15314	−0.0372758
$958$	64.6738	2.08952
$959$	−77.0949	−2.48952
$960$	−13.5666	−0.437861
$961$	−29.8353	−0.962427
$962$	3.78805	0.122132
$963$	−10.1453	−0.326929
$964$	−35.6772	−1.14908
$965$	30.7506	0.989896
$966$	−52.6036	−1.69249
$967$	−42.3155	−1.36078	−0.680388	−	0.732852i	$-0.738189\pi$
$967$	−42.3155	−1.36078	−0.680388	+	0.732852i	$0.738189\pi$
$968$	−0.369530	−0.0118771
$969$	39.7654	1.27745
$970$	−32.9004	−1.05637
$971$	51.6151	1.65641	0.828204	−	0.560426i	$-0.189363\pi$
$971$	51.6151	1.65641	0.828204	+	0.560426i	$0.189363\pi$
$972$	−2.18073	−0.0699469
$973$	33.6524	1.07885
$974$	−47.3850	−1.51831
$975$	−2.15227	−0.0689277
$976$	−3.60588	−0.115422
$977$	16.5726	0.530203	0.265102	−	0.964221i	$-0.414595\pi$
$977$	16.5726	0.530203	0.265102	+	0.964221i	$0.414595\pi$
$978$	−16.6166	−0.531340
$979$	17.3600	0.554828
$980$	−30.2240	−0.965470
$981$	−9.99279	−0.319045
$982$	−12.1734	−0.388468
$983$	−26.2431	−0.837025	−0.418512	−	0.908211i	$-0.637448\pi$
$983$	−26.2431	−0.837025	−0.418512	+	0.908211i	$0.637448\pi$
$984$	3.59132	0.114487
$985$	−9.47457	−0.301885
$986$	13.2055	0.420550
$987$	6.58522	0.209610
$988$	−11.4685	−0.364861
$989$	−51.0195	−1.62233
$990$	2.95900	0.0940433
$991$	−5.33475	−0.169464	−0.0847320	−	0.996404i	$-0.527003\pi$
$991$	−5.33475	−0.169464	−0.0847320	+	0.996404i	$0.527003\pi$
$992$	−8.75470	−0.277962
$993$	−16.9998	−0.539473
$994$	−70.6142	−2.23974
$995$	3.72682	0.118148
$996$	−27.9366	−0.885206
$997$	3.87270	0.122650	0.0613249	−	0.998118i	$-0.480467\pi$
$997$	3.87270	0.122650	0.0613249	+	0.998118i	$0.480467\pi$
$998$	87.3824	2.76604
$999$	−2.50117	−0.0791336

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.04468 q^{2} -1.00000 q^{3} +2.18073 q^{4} -1.44717 q^{5} +2.04468 q^{6} -4.07149 q^{7} -0.369530 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.04468 q^{2} -1.00000 q^{3} +2.18073 q^{4} -1.44717 q^{5} +2.04468 q^{6} -4.07149 q^{7} -0.369530 q^{8} +1.00000 q^{9} +2.95900 q^{10} +1.00000 q^{11} -2.18073 q^{12} -0.740706 q^{13} +8.32491 q^{14} +1.44717 q^{15} -3.60588 q^{16} -5.60076 q^{17} -2.04468 q^{18} +7.10000 q^{19} -3.15588 q^{20} +4.07149 q^{21} -2.04468 q^{22} +6.31883 q^{23} +0.369530 q^{24} -2.90570 q^{25} +1.51451 q^{26} -1.00000 q^{27} -8.87881 q^{28} +1.15314 q^{29} -2.95900 q^{30} -1.07924 q^{31} +8.11195 q^{32} -1.00000 q^{33} +11.4518 q^{34} +5.89214 q^{35} +2.18073 q^{36} +2.50117 q^{37} -14.5173 q^{38} +0.740706 q^{39} +0.534772 q^{40} +9.71861 q^{41} -8.32491 q^{42} -8.07420 q^{43} +2.18073 q^{44} -1.44717 q^{45} -12.9200 q^{46} +1.61740 q^{47} +3.60588 q^{48} +9.57703 q^{49} +5.94123 q^{50} +5.60076 q^{51} -1.61528 q^{52} +6.83711 q^{53} +2.04468 q^{54} -1.44717 q^{55} +1.50454 q^{56} -7.10000 q^{57} -2.35781 q^{58} +3.83596 q^{59} +3.15588 q^{60} +1.00000 q^{61} +2.20669 q^{62} -4.07149 q^{63} -9.37459 q^{64} +1.07193 q^{65} +2.04468 q^{66} +7.40024 q^{67} -12.2137 q^{68} -6.31883 q^{69} -12.0476 q^{70} -8.48228 q^{71} -0.369530 q^{72} -15.3493 q^{73} -5.11411 q^{74} +2.90570 q^{75} +15.4832 q^{76} -4.07149 q^{77} -1.51451 q^{78} -2.39760 q^{79} +5.21833 q^{80} +1.00000 q^{81} -19.8715 q^{82} +12.8107 q^{83} +8.87881 q^{84} +8.10526 q^{85} +16.5092 q^{86} -1.15314 q^{87} -0.369530 q^{88} +17.3600 q^{89} +2.95900 q^{90} +3.01578 q^{91} +13.7796 q^{92} +1.07924 q^{93} -3.30707 q^{94} -10.2749 q^{95} -8.11195 q^{96} -11.1188 q^{97} -19.5820 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) \) 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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