LMFDB - Embedded newform 2013.2.a.b.1.10

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			1.10
Root			$-2.09663$ 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)

$f(q)$	$=$	$q+2.09663 q^{2} -1.00000 q^{3} +2.39586 q^{4} -1.65820 q^{5} -2.09663 q^{6} -1.74412 q^{7} +0.829977 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.09663 q^{2} -1.00000 q^{3} +2.39586 q^{4} -1.65820 q^{5} -2.09663 q^{6} -1.74412 q^{7} +0.829977 q^{8} +1.00000 q^{9} -3.47663 q^{10} +1.00000 q^{11} -2.39586 q^{12} +3.68882 q^{13} -3.65678 q^{14} +1.65820 q^{15} -3.05157 q^{16} +4.43676 q^{17} +2.09663 q^{18} -3.87025 q^{19} -3.97282 q^{20} +1.74412 q^{21} +2.09663 q^{22} -5.64634 q^{23} -0.829977 q^{24} -2.25037 q^{25} +7.73410 q^{26} -1.00000 q^{27} -4.17867 q^{28} -7.30348 q^{29} +3.47663 q^{30} -7.12139 q^{31} -8.05797 q^{32} -1.00000 q^{33} +9.30224 q^{34} +2.89210 q^{35} +2.39586 q^{36} +1.15548 q^{37} -8.11450 q^{38} -3.68882 q^{39} -1.37627 q^{40} -4.94085 q^{41} +3.65678 q^{42} +1.04932 q^{43} +2.39586 q^{44} -1.65820 q^{45} -11.8383 q^{46} -6.36194 q^{47} +3.05157 q^{48} -3.95804 q^{49} -4.71821 q^{50} -4.43676 q^{51} +8.83791 q^{52} +11.6737 q^{53} -2.09663 q^{54} -1.65820 q^{55} -1.44758 q^{56} +3.87025 q^{57} -15.3127 q^{58} -3.07863 q^{59} +3.97282 q^{60} +1.00000 q^{61} -14.9309 q^{62} -1.74412 q^{63} -10.7915 q^{64} -6.11680 q^{65} -2.09663 q^{66} -7.85878 q^{67} +10.6299 q^{68} +5.64634 q^{69} +6.06367 q^{70} -10.5509 q^{71} +0.829977 q^{72} -6.98002 q^{73} +2.42261 q^{74} +2.25037 q^{75} -9.27260 q^{76} -1.74412 q^{77} -7.73410 q^{78} +12.6604 q^{79} +5.06011 q^{80} +1.00000 q^{81} -10.3591 q^{82} +0.804210 q^{83} +4.17867 q^{84} -7.35703 q^{85} +2.20004 q^{86} +7.30348 q^{87} +0.829977 q^{88} +1.75911 q^{89} -3.47663 q^{90} -6.43375 q^{91} -13.5279 q^{92} +7.12139 q^{93} -13.3386 q^{94} +6.41765 q^{95} +8.05797 q^{96} +1.26338 q^{97} -8.29856 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.09663	1.48254	0.741271	−	0.671206i	$-0.234223\pi$
$2$	2.09663	1.48254	0.741271	+	0.671206i	$0.234223\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.39586	1.19793
$5$	−1.65820	−0.741569	−0.370785	−	0.928719i	$-0.620911\pi$
$5$	−1.65820	−0.741569	−0.370785	+	0.928719i	$0.620911\pi$
$6$	−2.09663	−0.855946
$7$	−1.74412	−0.659216	−0.329608	−	0.944118i	$-0.606917\pi$
$7$	−1.74412	−0.659216	−0.329608	+	0.944118i	$0.606917\pi$
$8$	0.829977	0.293441
$9$	1.00000	0.333333
$10$	−3.47663	−1.09941
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.39586	−0.691626
$13$	3.68882	1.02309	0.511547	−	0.859255i	$-0.329072\pi$
$13$	3.68882	1.02309	0.511547	+	0.859255i	$0.329072\pi$
$14$	−3.65678	−0.977315
$15$	1.65820	0.428145
$16$	−3.05157	−0.762892
$17$	4.43676	1.07607	0.538036	−	0.842922i	$-0.319167\pi$
$17$	4.43676	1.07607	0.538036	+	0.842922i	$0.319167\pi$
$18$	2.09663	0.494181
$19$	−3.87025	−0.887897	−0.443949	−	0.896052i	$-0.646423\pi$
$19$	−3.87025	−0.887897	−0.443949	+	0.896052i	$0.646423\pi$
$20$	−3.97282	−0.888349
$21$	1.74412	0.380598
$22$	2.09663	0.447003
$23$	−5.64634	−1.17734	−0.588672	−	0.808372i	$-0.700349\pi$
$23$	−5.64634	−1.17734	−0.588672	+	0.808372i	$0.700349\pi$
$24$	−0.829977	−0.169418
$25$	−2.25037	−0.450075
$26$	7.73410	1.51678
$27$	−1.00000	−0.192450
$28$	−4.17867	−0.789695
$29$	−7.30348	−1.35622	−0.678111	−	0.734960i	$-0.737201\pi$
$29$	−7.30348	−1.35622	−0.678111	+	0.734960i	$0.737201\pi$
$30$	3.47663	0.634743
$31$	−7.12139	−1.27904	−0.639519	−	0.768775i	$-0.720867\pi$
$31$	−7.12139	−1.27904	−0.639519	+	0.768775i	$0.720867\pi$
$32$	−8.05797	−1.42446
$33$	−1.00000	−0.174078
$34$	9.30224	1.59532
$35$	2.89210	0.488854
$36$	2.39586	0.399310
$37$	1.15548	0.189959	0.0949795	−	0.995479i	$-0.469721\pi$
$37$	1.15548	0.189959	0.0949795	+	0.995479i	$0.469721\pi$
$38$	−8.11450	−1.31634
$39$	−3.68882	−0.590684
$40$	−1.37627	−0.217607
$41$	−4.94085	−0.771631	−0.385816	−	0.922576i	$-0.626080\pi$
$41$	−4.94085	−0.771631	−0.385816	+	0.922576i	$0.626080\pi$
$42$	3.65678	0.564253
$43$	1.04932	0.160020	0.0800099	−	0.996794i	$-0.474505\pi$
$43$	1.04932	0.160020	0.0800099	+	0.996794i	$0.474505\pi$
$44$	2.39586	0.361190
$45$	−1.65820	−0.247190
$46$	−11.8383	−1.74546
$47$	−6.36194	−0.927984	−0.463992	−	0.885839i	$-0.653583\pi$
$47$	−6.36194	−0.927984	−0.463992	+	0.885839i	$0.653583\pi$
$48$	3.05157	0.440456
$49$	−3.95804	−0.565435
$50$	−4.71821	−0.667255
$51$	−4.43676	−0.621270
$52$	8.83791	1.22560
$53$	11.6737	1.60351	0.801755	−	0.597653i	$-0.203900\pi$
$53$	11.6737	1.60351	0.801755	+	0.597653i	$0.203900\pi$
$54$	−2.09663	−0.285315
$55$	−1.65820	−0.223592
$56$	−1.44758	−0.193441
$57$	3.87025	0.512628
$58$	−15.3127	−2.01066
$59$	−3.07863	−0.400804	−0.200402	−	0.979714i	$-0.564225\pi$
$59$	−3.07863	−0.400804	−0.200402	+	0.979714i	$0.564225\pi$
$60$	3.97282	0.512889
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−14.9309	−1.89623
$63$	−1.74412	−0.219739
$64$	−10.7915	−1.34893
$65$	−6.11680	−0.758696
$66$	−2.09663	−0.258077
$67$	−7.85878	−0.960103	−0.480051	−	0.877240i	$-0.659382\pi$
$67$	−7.85878	−0.960103	−0.480051	+	0.877240i	$0.659382\pi$
$68$	10.6299	1.28906
$69$	5.64634	0.679740
$70$	6.06367	0.724747
$71$	−10.5509	−1.25216	−0.626078	−	0.779760i	$-0.715341\pi$
$71$	−10.5509	−1.25216	−0.626078	+	0.779760i	$0.715341\pi$
$72$	0.829977	0.0978138
$73$	−6.98002	−0.816950	−0.408475	−	0.912770i	$-0.633939\pi$
$73$	−6.98002	−0.816950	−0.408475	+	0.912770i	$0.633939\pi$
$74$	2.42261	0.281622
$75$	2.25037	0.259851
$76$	−9.27260	−1.06364
$77$	−1.74412	−0.198761
$78$	−7.73410	−0.875714
$79$	12.6604	1.42441	0.712203	−	0.701974i	$-0.247698\pi$
$79$	12.6604	1.42441	0.712203	+	0.701974i	$0.247698\pi$
$80$	5.06011	0.565737
$81$	1.00000	0.111111
$82$	−10.3591	−1.14398
$83$	0.804210	0.0882735	0.0441367	−	0.999025i	$-0.485946\pi$
$83$	0.804210	0.0882735	0.0441367	+	0.999025i	$0.485946\pi$
$84$	4.17867	0.455931
$85$	−7.35703	−0.797982
$86$	2.20004	0.237236
$87$	7.30348	0.783015
$88$	0.829977	0.0884759
$89$	1.75911	0.186465	0.0932325	−	0.995644i	$-0.470280\pi$
$89$	1.75911	0.186465	0.0932325	+	0.995644i	$0.470280\pi$
$90$	−3.47663	−0.366469
$91$	−6.43375	−0.674440
$92$	−13.5279	−1.41038
$93$	7.12139	0.738453
$94$	−13.3386	−1.37578
$95$	6.41765	0.658437
$96$	8.05797	0.822413
$97$	1.26338	0.128276	0.0641382	−	0.997941i	$-0.479570\pi$
$97$	1.26338	0.128276	0.0641382	+	0.997941i	$0.479570\pi$
$98$	−8.29856	−0.838281
$99$	1.00000	0.100504
$100$	−5.39159	−0.539159
$101$	9.43775	0.939091	0.469545	−	0.882908i	$-0.344418\pi$
$101$	9.43775	0.939091	0.469545	+	0.882908i	$0.344418\pi$
$102$	−9.30224	−0.921059
$103$	−11.6201	−1.14496	−0.572480	−	0.819919i	$-0.694018\pi$
$103$	−11.6201	−1.14496	−0.572480	+	0.819919i	$0.694018\pi$
$104$	3.06164	0.300218
$105$	−2.89210	−0.282240
$106$	24.4755	2.37727
$107$	6.86086	0.663264	0.331632	−	0.943409i	$-0.392401\pi$
$107$	6.86086	0.663264	0.331632	+	0.943409i	$0.392401\pi$
$108$	−2.39586	−0.230542
$109$	2.33405	0.223562	0.111781	−	0.993733i	$-0.464345\pi$
$109$	2.33405	0.223562	0.111781	+	0.993733i	$0.464345\pi$
$110$	−3.47663	−0.331484
$111$	−1.15548	−0.109673
$112$	5.32230	0.502910
$113$	11.8781	1.11739	0.558697	−	0.829372i	$-0.311302\pi$
$113$	11.8781	1.11739	0.558697	+	0.829372i	$0.311302\pi$
$114$	8.11450	0.759992
$115$	9.36276	0.873082
$116$	−17.4981	−1.62466
$117$	3.68882	0.341032
$118$	−6.45476	−0.594209
$119$	−7.73824	−0.709363
$120$	1.37627	0.125636
$121$	1.00000	0.0909091
$122$	2.09663	0.189820
$123$	4.94085	0.445501
$124$	−17.0619	−1.53220
$125$	12.0226	1.07533
$126$	−3.65678	−0.325772
$127$	12.5382	1.11258	0.556292	−	0.830987i	$-0.312223\pi$
$127$	12.5382	1.11258	0.556292	+	0.830987i	$0.312223\pi$
$128$	−6.50976	−0.575387
$129$	−1.04932	−0.0923875
$130$	−12.8247	−1.12480
$131$	−2.14839	−0.187706	−0.0938528	−	0.995586i	$-0.529918\pi$
$131$	−2.14839	−0.187706	−0.0938528	+	0.995586i	$0.529918\pi$
$132$	−2.39586	−0.208533
$133$	6.75019	0.585316
$134$	−16.4770	−1.42339
$135$	1.65820	0.142715
$136$	3.68241	0.315764
$137$	3.81567	0.325995	0.162997	−	0.986627i	$-0.447884\pi$
$137$	3.81567	0.325995	0.162997	+	0.986627i	$0.447884\pi$
$138$	11.8383	1.00774
$139$	6.73461	0.571222	0.285611	−	0.958346i	$-0.407803\pi$
$139$	6.73461	0.571222	0.285611	+	0.958346i	$0.407803\pi$
$140$	6.92907	0.585614
$141$	6.36194	0.535772
$142$	−22.1213	−1.85637
$143$	3.68882	0.308475
$144$	−3.05157	−0.254297
$145$	12.1106	1.00573
$146$	−14.6345	−1.21116
$147$	3.95804	0.326454
$148$	2.76836	0.227558
$149$	12.7630	1.04559	0.522794	−	0.852459i	$-0.324890\pi$
$149$	12.7630	1.04559	0.522794	+	0.852459i	$0.324890\pi$
$150$	4.71821	0.385240
$151$	−3.00220	−0.244315	−0.122158	−	0.992511i	$-0.538981\pi$
$151$	−3.00220	−0.244315	−0.122158	+	0.992511i	$0.538981\pi$
$152$	−3.21222	−0.260546
$153$	4.43676	0.358691
$154$	−3.65678	−0.294672
$155$	11.8087	0.948496
$156$	−8.83791	−0.707599
$157$	−1.77685	−0.141808	−0.0709042	−	0.997483i	$-0.522588\pi$
$157$	−1.77685	−0.141808	−0.0709042	+	0.997483i	$0.522588\pi$
$158$	26.5442	2.11174
$159$	−11.6737	−0.925787
$160$	13.3617	1.05634
$161$	9.84790	0.776123
$162$	2.09663	0.164727
$163$	3.18992	0.249854	0.124927	−	0.992166i	$-0.460130\pi$
$163$	3.18992	0.249854	0.124927	+	0.992166i	$0.460130\pi$
$164$	−11.8376	−0.924361
$165$	1.65820	0.129091
$166$	1.68613	0.130869
$167$	9.91181	0.766999	0.383499	−	0.923541i	$-0.374719\pi$
$167$	9.91181	0.766999	0.383499	+	0.923541i	$0.374719\pi$
$168$	1.44758	0.111683
$169$	0.607399	0.0467230
$170$	−15.4250	−1.18304
$171$	−3.87025	−0.295966
$172$	2.51403	0.191693
$173$	−6.21584	−0.472582	−0.236291	−	0.971682i	$-0.575932\pi$
$173$	−6.21584	−0.472582	−0.236291	+	0.971682i	$0.575932\pi$
$174$	15.3127	1.16085
$175$	3.92492	0.296696
$176$	−3.05157	−0.230021
$177$	3.07863	0.231404
$178$	3.68820	0.276442
$179$	−16.5704	−1.23853	−0.619266	−	0.785181i	$-0.712570\pi$
$179$	−16.5704	−1.23853	−0.619266	+	0.785181i	$0.712570\pi$
$180$	−3.97282	−0.296116
$181$	−13.5208	−1.00499	−0.502497	−	0.864579i	$-0.667585\pi$
$181$	−13.5208	−1.00499	−0.502497	+	0.864579i	$0.667585\pi$
$182$	−13.4892	−0.999886
$183$	−1.00000	−0.0739221
$184$	−4.68633	−0.345481
$185$	−1.91601	−0.140868
$186$	14.9309	1.09479
$187$	4.43676	0.324448
$188$	−15.2423	−1.11166
$189$	1.74412	0.126866
$190$	13.4555	0.976161
$191$	25.6927	1.85906	0.929530	−	0.368747i	$-0.120213\pi$
$191$	25.6927	1.85906	0.929530	+	0.368747i	$0.120213\pi$
$192$	10.7915	0.778806
$193$	−10.7514	−0.773905	−0.386953	−	0.922100i	$-0.626472\pi$
$193$	−10.7514	−0.773905	−0.386953	+	0.922100i	$0.626472\pi$
$194$	2.64884	0.190175
$195$	6.11680	0.438033
$196$	−9.48293	−0.677352
$197$	−11.2083	−0.798562	−0.399281	−	0.916829i	$-0.630740\pi$
$197$	−11.2083	−0.798562	−0.399281	+	0.916829i	$0.630740\pi$
$198$	2.09663	0.149001
$199$	−19.5782	−1.38786	−0.693931	−	0.720041i	$-0.744123\pi$
$199$	−19.5782	−1.38786	−0.693931	+	0.720041i	$0.744123\pi$
$200$	−1.86776	−0.132071
$201$	7.85878	0.554316
$202$	19.7875	1.39224
$203$	12.7381	0.894043
$204$	−10.6299	−0.744239
$205$	8.19292	0.572218
$206$	−24.3630	−1.69745
$207$	−5.64634	−0.392448
$208$	−11.2567	−0.780511
$209$	−3.87025	−0.267711
$210$	−6.06367	−0.418433
$211$	2.41146	0.166012	0.0830058	−	0.996549i	$-0.473548\pi$
$211$	2.41146	0.166012	0.0830058	+	0.996549i	$0.473548\pi$
$212$	27.9686	1.92089
$213$	10.5509	0.722933
$214$	14.3847	0.983317
$215$	−1.73998	−0.118666
$216$	−0.829977	−0.0564728
$217$	12.4206	0.843162
$218$	4.89364	0.331439
$219$	6.98002	0.471666
$220$	−3.97282	−0.267847
$221$	16.3664	1.10092
$222$	−2.42261	−0.162595
$223$	2.57702	0.172570	0.0862852	−	0.996270i	$-0.472500\pi$
$223$	2.57702	0.172570	0.0862852	+	0.996270i	$0.472500\pi$
$224$	14.0541	0.939027
$225$	−2.25037	−0.150025
$226$	24.9039	1.65658
$227$	−24.1392	−1.60217	−0.801086	−	0.598549i	$-0.795744\pi$
$227$	−24.1392	−1.60217	−0.801086	+	0.598549i	$0.795744\pi$
$228$	9.27260	0.614093
$229$	−6.66615	−0.440512	−0.220256	−	0.975442i	$-0.570689\pi$
$229$	−6.66615	−0.440512	−0.220256	+	0.975442i	$0.570689\pi$
$230$	19.6303	1.29438
$231$	1.74412	0.114755
$232$	−6.06172	−0.397971
$233$	11.6543	0.763498	0.381749	−	0.924266i	$-0.375322\pi$
$233$	11.6543	0.763498	0.381749	+	0.924266i	$0.375322\pi$
$234$	7.73410	0.505594
$235$	10.5494	0.688165
$236$	−7.37598	−0.480136
$237$	−12.6604	−0.822381
$238$	−16.2242	−1.05166
$239$	7.72939	0.499972	0.249986	−	0.968249i	$-0.419574\pi$
$239$	7.72939	0.499972	0.249986	+	0.968249i	$0.419574\pi$
$240$	−5.06011	−0.326629
$241$	−15.7651	−1.01552	−0.507761	−	0.861498i	$-0.669527\pi$
$241$	−15.7651	−1.01552	−0.507761	+	0.861498i	$0.669527\pi$
$242$	2.09663	0.134777
$243$	−1.00000	−0.0641500
$244$	2.39586	0.153379
$245$	6.56322	0.419309
$246$	10.3591	0.660475
$247$	−14.2767	−0.908403
$248$	−5.91059	−0.375323
$249$	−0.804210	−0.0509647
$250$	25.2069	1.59422
$251$	−29.4143	−1.85661	−0.928307	−	0.371816i	$-0.878735\pi$
$251$	−29.4143	−1.85661	−0.928307	+	0.371816i	$0.878735\pi$
$252$	−4.17867	−0.263232
$253$	−5.64634	−0.354982
$254$	26.2880	1.64945
$255$	7.35703	0.460715
$256$	7.93434	0.495897
$257$	3.00364	0.187362	0.0936809	−	0.995602i	$-0.470137\pi$
$257$	3.00364	0.187362	0.0936809	+	0.995602i	$0.470137\pi$
$258$	−2.20004	−0.136968
$259$	−2.01529	−0.125224
$260$	−14.6550	−0.908865
$261$	−7.30348	−0.452074
$262$	−4.50438	−0.278282
$263$	−3.40771	−0.210128	−0.105064	−	0.994465i	$-0.533505\pi$
$263$	−3.40771	−0.210128	−0.105064	+	0.994465i	$0.533505\pi$
$264$	−0.829977	−0.0510816
$265$	−19.3574	−1.18911
$266$	14.1527	0.867755
$267$	−1.75911	−0.107656
$268$	−18.8286	−1.15014
$269$	20.2718	1.23599	0.617996	−	0.786181i	$-0.287945\pi$
$269$	20.2718	1.23599	0.617996	+	0.786181i	$0.287945\pi$
$270$	3.47663	0.211581
$271$	12.8096	0.778128	0.389064	−	0.921211i	$-0.372798\pi$
$271$	12.8096	0.778128	0.389064	+	0.921211i	$0.372798\pi$
$272$	−13.5391	−0.820927
$273$	6.43375	0.389388
$274$	8.00005	0.483301
$275$	−2.25037	−0.135703
$276$	13.5279	0.814281
$277$	−17.8053	−1.06982	−0.534910	−	0.844909i	$-0.679654\pi$
$277$	−17.8053	−1.06982	−0.534910	+	0.844909i	$0.679654\pi$
$278$	14.1200	0.846861
$279$	−7.12139	−0.426346
$280$	2.40038	0.143450
$281$	−14.9901	−0.894232	−0.447116	−	0.894476i	$-0.647549\pi$
$281$	−14.9901	−0.894232	−0.447116	+	0.894476i	$0.647549\pi$
$282$	13.3386	0.794305
$283$	−21.2549	−1.26347	−0.631737	−	0.775183i	$-0.717658\pi$
$283$	−21.2549	−1.26347	−0.631737	+	0.775183i	$0.717658\pi$
$284$	−25.2784	−1.50000
$285$	−6.41765	−0.380149
$286$	7.73410	0.457327
$287$	8.61744	0.508671
$288$	−8.05797	−0.474820
$289$	2.68481	0.157930
$290$	25.3915	1.49104
$291$	−1.26338	−0.0740605
$292$	−16.7232	−0.978650
$293$	−13.3121	−0.777704	−0.388852	−	0.921300i	$-0.627128\pi$
$293$	−13.3121	−0.777704	−0.388852	+	0.921300i	$0.627128\pi$
$294$	8.29856	0.483982
$295$	5.10499	0.297224
$296$	0.959018	0.0557418
$297$	−1.00000	−0.0580259
$298$	26.7594	1.55013
$299$	−20.8283	−1.20453
$300$	5.39159	0.311283
$301$	−1.83014	−0.105488
$302$	−6.29450	−0.362208
$303$	−9.43775	−0.542184
$304$	11.8103	0.677370
$305$	−1.65820	−0.0949482
$306$	9.30224	0.531774
$307$	15.6165	0.891278	0.445639	−	0.895213i	$-0.352976\pi$
$307$	15.6165	0.891278	0.445639	+	0.895213i	$0.352976\pi$
$308$	−4.17867	−0.238102
$309$	11.6201	0.661043
$310$	24.7584	1.40619
$311$	−17.6810	−1.00260	−0.501298	−	0.865274i	$-0.667144\pi$
$311$	−17.6810	−1.00260	−0.501298	+	0.865274i	$0.667144\pi$
$312$	−3.06164	−0.173331
$313$	−19.5864	−1.10709	−0.553545	−	0.832819i	$-0.686725\pi$
$313$	−19.5864	−1.10709	−0.553545	+	0.832819i	$0.686725\pi$
$314$	−3.72541	−0.210237
$315$	2.89210	0.162951
$316$	30.3326	1.70634
$317$	15.8519	0.890331	0.445165	−	0.895448i	$-0.353145\pi$
$317$	15.8519	0.890331	0.445165	+	0.895448i	$0.353145\pi$
$318$	−24.4755	−1.37252
$319$	−7.30348	−0.408916
$320$	17.8944	1.00033
$321$	−6.86086	−0.382936
$322$	20.6474	1.15064
$323$	−17.1714	−0.955441
$324$	2.39586	0.133103
$325$	−8.30123	−0.460469
$326$	6.68809	0.370419
$327$	−2.33405	−0.129073
$328$	−4.10079	−0.226428
$329$	11.0960	0.611742
$330$	3.47663	0.191382
$331$	14.0150	0.770334	0.385167	−	0.922847i	$-0.374144\pi$
$331$	14.0150	0.770334	0.385167	+	0.922847i	$0.374144\pi$
$332$	1.92678	0.105746
$333$	1.15548	0.0633197
$334$	20.7814	1.13711
$335$	13.0314	0.711983
$336$	−5.32230	−0.290355
$337$	15.1943	0.827684	0.413842	−	0.910349i	$-0.364187\pi$
$337$	15.1943	0.827684	0.413842	+	0.910349i	$0.364187\pi$
$338$	1.27349	0.0692688
$339$	−11.8781	−0.645127
$340$	−17.6264	−0.955927
$341$	−7.12139	−0.385645
$342$	−8.11450	−0.438782
$343$	19.1121	1.03196
$344$	0.870912	0.0469564
$345$	−9.36276	−0.504074
$346$	−13.0323	−0.700622
$347$	−30.8325	−1.65517	−0.827587	−	0.561337i	$-0.810287\pi$
$347$	−30.8325	−1.65517	−0.827587	+	0.561337i	$0.810287\pi$
$348$	17.4981	0.937998
$349$	−1.84294	−0.0986503	−0.0493252	−	0.998783i	$-0.515707\pi$
$349$	−1.84294	−0.0986503	−0.0493252	+	0.998783i	$0.515707\pi$
$350$	8.22912	0.439865
$351$	−3.68882	−0.196895
$352$	−8.05797	−0.429491
$353$	20.1378	1.07183	0.535915	−	0.844272i	$-0.319967\pi$
$353$	20.1378	1.07183	0.535915	+	0.844272i	$0.319967\pi$
$354$	6.45476	0.343067
$355$	17.4954	0.928561
$356$	4.21458	0.223372
$357$	7.73824	0.409551
$358$	−34.7421	−1.83618
$359$	36.3150	1.91663	0.958315	−	0.285713i	$-0.0922304\pi$
$359$	36.3150	1.91663	0.958315	+	0.285713i	$0.0922304\pi$
$360$	−1.37627	−0.0725357
$361$	−4.02113	−0.211639
$362$	−28.3482	−1.48995
$363$	−1.00000	−0.0524864
$364$	−15.4144	−0.807933
$365$	11.5743	0.605825
$366$	−2.09663	−0.109593
$367$	14.0061	0.731111	0.365555	−	0.930790i	$-0.380879\pi$
$367$	14.0061	0.731111	0.365555	+	0.930790i	$0.380879\pi$
$368$	17.2302	0.898186
$369$	−4.94085	−0.257210
$370$	−4.01716	−0.208842
$371$	−20.3604	−1.05706
$372$	17.0619	0.884616
$373$	25.6543	1.32833	0.664164	−	0.747586i	$-0.268787\pi$
$373$	25.6543	1.32833	0.664164	+	0.747586i	$0.268787\pi$
$374$	9.30224	0.481008
$375$	−12.0226	−0.620843
$376$	−5.28027	−0.272309
$377$	−26.9412	−1.38754
$378$	3.65678	0.188084
$379$	−3.58785	−0.184295	−0.0921477	−	0.995745i	$-0.529373\pi$
$379$	−3.58785	−0.184295	−0.0921477	+	0.995745i	$0.529373\pi$
$380$	15.3758	0.788763
$381$	−12.5382	−0.642351
$382$	53.8681	2.75613
$383$	−15.5959	−0.796915	−0.398457	−	0.917187i	$-0.630454\pi$
$383$	−15.5959	−0.796915	−0.398457	+	0.917187i	$0.630454\pi$
$384$	6.50976	0.332200
$385$	2.89210	0.147395
$386$	−22.5418	−1.14735
$387$	1.04932	0.0533399
$388$	3.02688	0.153666
$389$	4.09269	0.207508	0.103754	−	0.994603i	$-0.466915\pi$
$389$	4.09269	0.207508	0.103754	+	0.994603i	$0.466915\pi$
$390$	12.8247	0.649403
$391$	−25.0514	−1.26691
$392$	−3.28509	−0.165922
$393$	2.14839	0.108372
$394$	−23.4998	−1.18390
$395$	−20.9935	−1.05630
$396$	2.39586	0.120397
$397$	−0.160452	−0.00805283	−0.00402642	−	0.999992i	$-0.501282\pi$
$397$	−0.160452	−0.00805283	−0.00402642	+	0.999992i	$0.501282\pi$
$398$	−41.0483	−2.05757
$399$	−6.75019	−0.337932
$400$	6.86717	0.343359
$401$	−26.2199	−1.30936	−0.654680	−	0.755906i	$-0.727197\pi$
$401$	−26.2199	−1.30936	−0.654680	+	0.755906i	$0.727197\pi$
$402$	16.4770	0.821796
$403$	−26.2695	−1.30858
$404$	22.6115	1.12497
$405$	−1.65820	−0.0823966
$406$	26.7072	1.32546
$407$	1.15548	0.0572748
$408$	−3.68241	−0.182306
$409$	−10.8982	−0.538879	−0.269440	−	0.963017i	$-0.586838\pi$
$409$	−10.8982	−0.538879	−0.269440	+	0.963017i	$0.586838\pi$
$410$	17.1775	0.848337
$411$	−3.81567	−0.188213
$412$	−27.8401	−1.37158
$413$	5.36951	0.264216
$414$	−11.8383	−0.581820
$415$	−1.33354	−0.0654609
$416$	−29.7244	−1.45736
$417$	−6.73461	−0.329795
$418$	−8.11450	−0.396893
$419$	25.6444	1.25281	0.626405	−	0.779497i	$-0.284525\pi$
$419$	25.6444	1.25281	0.626405	+	0.779497i	$0.284525\pi$
$420$	−6.92907	−0.338104
$421$	−26.6007	−1.29644	−0.648219	−	0.761454i	$-0.724486\pi$
$421$	−26.6007	−1.29644	−0.648219	+	0.761454i	$0.724486\pi$
$422$	5.05594	0.246119
$423$	−6.36194	−0.309328
$424$	9.68893	0.470536
$425$	−9.98436	−0.484313
$426$	22.1213	1.07178
$427$	−1.74412	−0.0844039
$428$	16.4377	0.794545
$429$	−3.68882	−0.178098
$430$	−3.64810	−0.175927
$431$	15.7657	0.759405	0.379703	−	0.925109i	$-0.376026\pi$
$431$	15.7657	0.759405	0.379703	+	0.925109i	$0.376026\pi$
$432$	3.05157	0.146819
$433$	18.2816	0.878556	0.439278	−	0.898351i	$-0.355234\pi$
$433$	18.2816	0.878556	0.439278	+	0.898351i	$0.355234\pi$
$434$	26.0413	1.25002
$435$	−12.1106	−0.580660
$436$	5.59206	0.267811
$437$	21.8528	1.04536
$438$	14.6345	0.699265
$439$	16.1871	0.772570	0.386285	−	0.922379i	$-0.373758\pi$
$439$	16.1871	0.772570	0.386285	+	0.922379i	$0.373758\pi$
$440$	−1.37627	−0.0656110
$441$	−3.95804	−0.188478
$442$	34.3143	1.63217
$443$	−6.39604	−0.303885	−0.151942	−	0.988389i	$-0.548553\pi$
$443$	−6.39604	−0.303885	−0.151942	+	0.988389i	$0.548553\pi$
$444$	−2.76836	−0.131381
$445$	−2.91695	−0.138277
$446$	5.40307	0.255843
$447$	−12.7630	−0.603671
$448$	18.8216	0.889237
$449$	28.4966	1.34484	0.672418	−	0.740171i	$-0.265256\pi$
$449$	28.4966	1.34484	0.672418	+	0.740171i	$0.265256\pi$
$450$	−4.71821	−0.222418
$451$	−4.94085	−0.232656
$452$	28.4582	1.33856
$453$	3.00220	0.141056
$454$	−50.6109	−2.37529
$455$	10.6684	0.500144
$456$	3.21222	0.150426
$457$	2.43680	0.113989	0.0569943	−	0.998375i	$-0.481848\pi$
$457$	2.43680	0.113989	0.0569943	+	0.998375i	$0.481848\pi$
$458$	−13.9765	−0.653077
$459$	−4.43676	−0.207090
$460$	22.4319	1.04589
$461$	−26.0898	−1.21512	−0.607561	−	0.794273i	$-0.707852\pi$
$461$	−26.0898	−1.21512	−0.607561	+	0.794273i	$0.707852\pi$
$462$	3.65678	0.170129
$463$	3.25000	0.151041	0.0755203	−	0.997144i	$-0.475938\pi$
$463$	3.25000	0.151041	0.0755203	+	0.997144i	$0.475938\pi$
$464$	22.2871	1.03465
$465$	−11.8087	−0.547614
$466$	24.4348	1.13192
$467$	36.3052	1.68000	0.840002	−	0.542583i	$-0.182554\pi$
$467$	36.3052	1.68000	0.840002	+	0.542583i	$0.182554\pi$
$468$	8.83791	0.408532
$469$	13.7067	0.632915
$470$	22.1181	1.02023
$471$	1.77685	0.0818731
$472$	−2.55520	−0.117612
$473$	1.04932	0.0482478
$474$	−26.5442	−1.21921
$475$	8.70952	0.399620
$476$	−18.5398	−0.849768
$477$	11.6737	0.534503
$478$	16.2057	0.741230
$479$	27.3433	1.24935	0.624673	−	0.780887i	$-0.285232\pi$
$479$	27.3433	1.24935	0.624673	+	0.780887i	$0.285232\pi$
$480$	−13.3617	−0.609876
$481$	4.26234	0.194346
$482$	−33.0537	−1.50555
$483$	−9.84790	−0.448095
$484$	2.39586	0.108903
$485$	−2.09493	−0.0951259
$486$	−2.09663	−0.0951051
$487$	0.174146	0.00789129	0.00394565	−	0.999992i	$-0.498744\pi$
$487$	0.174146	0.00789129	0.00394565	+	0.999992i	$0.498744\pi$
$488$	0.829977	0.0375713
$489$	−3.18992	−0.144253
$490$	13.7607	0.621643
$491$	21.3379	0.962965	0.481482	−	0.876456i	$-0.340098\pi$
$491$	21.3379	0.962965	0.481482	+	0.876456i	$0.340098\pi$
$492$	11.8376	0.533680
$493$	−32.4038	−1.45939
$494$	−29.9329	−1.34675
$495$	−1.65820	−0.0745305
$496$	21.7314	0.975769
$497$	18.4020	0.825441
$498$	−1.68613	−0.0755573
$499$	−29.3364	−1.31328	−0.656639	−	0.754205i	$-0.728022\pi$
$499$	−29.3364	−1.31328	−0.656639	+	0.754205i	$0.728022\pi$
$500$	28.8044	1.28817
$501$	−9.91181	−0.442827
$502$	−61.6709	−2.75251
$503$	35.3263	1.57512	0.787561	−	0.616237i	$-0.211344\pi$
$503$	35.3263	1.57512	0.787561	+	0.616237i	$0.211344\pi$
$504$	−1.44758	−0.0644804
$505$	−15.6497	−0.696401
$506$	−11.8383	−0.526276
$507$	−0.607399	−0.0269755
$508$	30.0398	1.33280
$509$	38.3326	1.69906	0.849530	−	0.527540i	$-0.176885\pi$
$509$	38.3326	1.69906	0.849530	+	0.527540i	$0.176885\pi$
$510$	15.4250	0.683029
$511$	12.1740	0.538546
$512$	29.6549	1.31057
$513$	3.87025	0.170876
$514$	6.29752	0.277772
$515$	19.2684	0.849067
$516$	−2.51403	−0.110674
$517$	−6.36194	−0.279798
$518$	−4.22532	−0.185650
$519$	6.21584	0.272845
$520$	−5.07681	−0.222633
$521$	−6.24755	−0.273710	−0.136855	−	0.990591i	$-0.543699\pi$
$521$	−6.24755	−0.273710	−0.136855	+	0.990591i	$0.543699\pi$
$522$	−15.3127	−0.670219
$523$	−9.08599	−0.397303	−0.198651	−	0.980070i	$-0.563656\pi$
$523$	−9.08599	−0.397303	−0.198651	+	0.980070i	$0.563656\pi$
$524$	−5.14725	−0.224858
$525$	−3.92492	−0.171298
$526$	−7.14470	−0.311524
$527$	−31.5959	−1.37634
$528$	3.05157	0.132802
$529$	8.88117	0.386138
$530$	−40.5853	−1.76291
$531$	−3.07863	−0.133601
$532$	16.1725	0.701168
$533$	−18.2259	−0.789452
$534$	−3.68820	−0.159604
$535$	−11.3767	−0.491857
$536$	−6.52261	−0.281734
$537$	16.5704	0.715067
$538$	42.5025	1.83241
$539$	−3.95804	−0.170485
$540$	3.97282	0.170963
$541$	−27.9951	−1.20360	−0.601802	−	0.798645i	$-0.705550\pi$
$541$	−27.9951	−1.20360	−0.601802	+	0.798645i	$0.705550\pi$
$542$	26.8570	1.15361
$543$	13.5208	0.580234
$544$	−35.7512	−1.53282
$545$	−3.87032	−0.165786
$546$	13.4892	0.577284
$547$	−8.00715	−0.342361	−0.171181	−	0.985240i	$-0.554758\pi$
$547$	−8.00715	−0.342361	−0.171181	+	0.985240i	$0.554758\pi$
$548$	9.14182	0.390519
$549$	1.00000	0.0426790
$550$	−4.71821	−0.201185
$551$	28.2663	1.20419
$552$	4.68633	0.199464
$553$	−22.0813	−0.938991
$554$	−37.3312	−1.58605
$555$	1.91601	0.0813300
$556$	16.1352	0.684285
$557$	36.7292	1.55627	0.778134	−	0.628099i	$-0.216167\pi$
$557$	36.7292	1.55627	0.778134	+	0.628099i	$0.216167\pi$
$558$	−14.9309	−0.632076
$559$	3.87075	0.163715
$560$	−8.82544	−0.372943
$561$	−4.43676	−0.187320
$562$	−31.4286	−1.32574
$563$	9.93603	0.418754	0.209377	−	0.977835i	$-0.432856\pi$
$563$	9.93603	0.418754	0.209377	+	0.977835i	$0.432856\pi$
$564$	15.2423	0.641818
$565$	−19.6962	−0.828625
$566$	−44.5637	−1.87315
$567$	−1.74412	−0.0732462
$568$	−8.75697	−0.367434
$569$	41.8804	1.75572	0.877859	−	0.478919i	$-0.158971\pi$
$569$	41.8804	1.75572	0.877859	+	0.478919i	$0.158971\pi$
$570$	−13.4555	−0.563587
$571$	13.5154	0.565604	0.282802	−	0.959178i	$-0.408736\pi$
$571$	13.5154	0.565604	0.282802	+	0.959178i	$0.408736\pi$
$572$	8.83791	0.369531
$573$	−25.6927	−1.07333
$574$	18.0676	0.754127
$575$	12.7064	0.529893
$576$	−10.7915	−0.449644
$577$	5.90743	0.245929	0.122965	−	0.992411i	$-0.460760\pi$
$577$	5.90743	0.245929	0.122965	+	0.992411i	$0.460760\pi$
$578$	5.62906	0.234138
$579$	10.7514	0.446814
$580$	29.0154	1.20480
$581$	−1.40264	−0.0581913
$582$	−2.64884	−0.109798
$583$	11.6737	0.483476
$584$	−5.79326	−0.239727
$585$	−6.11680	−0.252899
$586$	−27.9107	−1.15298
$587$	−15.4093	−0.636009	−0.318005	−	0.948089i	$-0.603013\pi$
$587$	−15.4093	−0.636009	−0.318005	+	0.948089i	$0.603013\pi$
$588$	9.48293	0.391069
$589$	27.5616	1.13565
$590$	10.7033	0.440647
$591$	11.2083	0.461050
$592$	−3.52601	−0.144918
$593$	−39.9055	−1.63872	−0.819361	−	0.573278i	$-0.805671\pi$
$593$	−39.9055	−1.63872	−0.819361	+	0.573278i	$0.805671\pi$
$594$	−2.09663	−0.0860258
$595$	12.8315	0.526042
$596$	30.5785	1.25254
$597$	19.5782	0.801283
$598$	−43.6693	−1.78577
$599$	18.2366	0.745126	0.372563	−	0.928007i	$-0.378479\pi$
$599$	18.2366	0.745126	0.372563	+	0.928007i	$0.378479\pi$
$600$	1.86776	0.0762510
$601$	−6.80018	−0.277385	−0.138693	−	0.990335i	$-0.544290\pi$
$601$	−6.80018	−0.277385	−0.138693	+	0.990335i	$0.544290\pi$
$602$	−3.83713	−0.156390
$603$	−7.85878	−0.320034
$604$	−7.19285	−0.292673
$605$	−1.65820	−0.0674154
$606$	−19.7875	−0.803811
$607$	−45.5884	−1.85037	−0.925187	−	0.379511i	$-0.876092\pi$
$607$	−45.5884	−1.85037	−0.925187	+	0.379511i	$0.876092\pi$
$608$	31.1864	1.26477
$609$	−12.7381	−0.516176
$610$	−3.47663	−0.140765
$611$	−23.4681	−0.949416
$612$	10.6299	0.429687
$613$	−10.2045	−0.412156	−0.206078	−	0.978536i	$-0.566070\pi$
$613$	−10.2045	−0.412156	−0.206078	+	0.978536i	$0.566070\pi$
$614$	32.7420	1.32136
$615$	−8.19292	−0.330370
$616$	−1.44758	−0.0583247
$617$	−16.0441	−0.645912	−0.322956	−	0.946414i	$-0.604677\pi$
$617$	−16.0441	−0.645912	−0.322956	+	0.946414i	$0.604677\pi$
$618$	24.3630	0.980024
$619$	−17.6894	−0.710999	−0.355499	−	0.934677i	$-0.615689\pi$
$619$	−17.6894	−0.710999	−0.355499	+	0.934677i	$0.615689\pi$
$620$	28.2920	1.13623
$621$	5.64634	0.226580
$622$	−37.0705	−1.48639
$623$	−3.06810	−0.122921
$624$	11.2567	0.450628
$625$	−8.68394	−0.347358
$626$	−41.0655	−1.64131
$627$	3.87025	0.154563
$628$	−4.25710	−0.169877
$629$	5.12656	0.204409
$630$	6.06367	0.241582
$631$	−28.8828	−1.14980	−0.574902	−	0.818222i	$-0.694960\pi$
$631$	−28.8828	−1.14980	−0.574902	+	0.818222i	$0.694960\pi$
$632$	10.5078	0.417980
$633$	−2.41146	−0.0958468
$634$	33.2356	1.31995
$635$	−20.7908	−0.825059
$636$	−27.9686	−1.10903
$637$	−14.6005	−0.578493
$638$	−15.3127	−0.606236
$639$	−10.5509	−0.417385
$640$	10.7945	0.426689
$641$	7.42591	0.293306	0.146653	−	0.989188i	$-0.453150\pi$
$641$	7.42591	0.293306	0.146653	+	0.989188i	$0.453150\pi$
$642$	−14.3847	−0.567719
$643$	−6.17990	−0.243711	−0.121856	−	0.992548i	$-0.538885\pi$
$643$	−6.17990	−0.243711	−0.121856	+	0.992548i	$0.538885\pi$
$644$	23.5942	0.929742
$645$	1.73998	0.0685117
$646$	−36.0020	−1.41648
$647$	−47.1171	−1.85236	−0.926182	−	0.377078i	$-0.876929\pi$
$647$	−47.1171	−1.85236	−0.926182	+	0.377078i	$0.876929\pi$
$648$	0.829977	0.0326046
$649$	−3.07863	−0.120847
$650$	−17.4046	−0.682665
$651$	−12.4206	−0.486800
$652$	7.64262	0.299308
$653$	−8.46242	−0.331160	−0.165580	−	0.986196i	$-0.552950\pi$
$653$	−8.46242	−0.331160	−0.165580	+	0.986196i	$0.552950\pi$
$654$	−4.89364	−0.191357
$655$	3.56246	0.139197
$656$	15.0773	0.588671
$657$	−6.98002	−0.272317
$658$	23.2642	0.906933
$659$	17.3232	0.674816	0.337408	−	0.941359i	$-0.390450\pi$
$659$	17.3232	0.674816	0.337408	+	0.941359i	$0.390450\pi$
$660$	3.97282	0.154642
$661$	−25.0926	−0.975989	−0.487994	−	0.872847i	$-0.662271\pi$
$661$	−25.0926	−0.975989	−0.487994	+	0.872847i	$0.662271\pi$
$662$	29.3843	1.14205
$663$	−16.3664	−0.635618
$664$	0.667476	0.0259031
$665$	−11.1932	−0.434052
$666$	2.42261	0.0938741
$667$	41.2379	1.59674
$668$	23.7473	0.918811
$669$	−2.57702	−0.0996335
$670$	27.3221	1.05554
$671$	1.00000	0.0386046
$672$	−14.0541	−0.542147
$673$	16.4545	0.634275	0.317138	−	0.948380i	$-0.397278\pi$
$673$	16.4545	0.634275	0.317138	+	0.948380i	$0.397278\pi$
$674$	31.8568	1.22708
$675$	2.25037	0.0866170
$676$	1.45524	0.0559710
$677$	−44.7825	−1.72113	−0.860566	−	0.509339i	$-0.829890\pi$
$677$	−44.7825	−1.72113	−0.860566	+	0.509339i	$0.829890\pi$
$678$	−24.9039	−0.956428
$679$	−2.20348	−0.0845619
$680$	−6.10617	−0.234161
$681$	24.1392	0.925014
$682$	−14.9309	−0.571735
$683$	−32.7165	−1.25186	−0.625932	−	0.779878i	$-0.715281\pi$
$683$	−32.7165	−1.25186	−0.625932	+	0.779878i	$0.715281\pi$
$684$	−9.27260	−0.354547
$685$	−6.32714	−0.241748
$686$	40.0711	1.52992
$687$	6.66615	0.254330
$688$	−3.20207	−0.122078
$689$	43.0623	1.64054
$690$	−19.6303	−0.747311
$691$	−49.4693	−1.88190	−0.940950	−	0.338546i	$-0.890065\pi$
$691$	−49.4693	−1.88190	−0.940950	+	0.338546i	$0.890065\pi$
$692$	−14.8923	−0.566120
$693$	−1.74412	−0.0662537
$694$	−64.6443	−2.45387
$695$	−11.1673	−0.423601
$696$	6.06172	0.229769
$697$	−21.9214	−0.830330
$698$	−3.86396	−0.146253
$699$	−11.6543	−0.440806
$700$	9.40358	0.355422
$701$	41.6251	1.57216	0.786079	−	0.618126i	$-0.212108\pi$
$701$	41.6251	1.57216	0.786079	+	0.618126i	$0.212108\pi$
$702$	−7.73410	−0.291905
$703$	−4.47198	−0.168664
$704$	−10.7915	−0.406718
$705$	−10.5494	−0.397312
$706$	42.2216	1.58903
$707$	−16.4606	−0.619063
$708$	7.37598	0.277206
$709$	−0.208599	−0.00783411	−0.00391705	−	0.999992i	$-0.501247\pi$
$709$	−0.208599	−0.00783411	−0.00391705	+	0.999992i	$0.501247\pi$
$710$	36.6815	1.37663
$711$	12.6604	0.474802
$712$	1.46002	0.0547165
$713$	40.2098	1.50587
$714$	16.2242	0.607177
$715$	−6.11680	−0.228755
$716$	−39.7005	−1.48368
$717$	−7.72939	−0.288659
$718$	76.1391	2.84149
$719$	−30.4553	−1.13579	−0.567896	−	0.823101i	$-0.692242\pi$
$719$	−30.4553	−1.13579	−0.567896	+	0.823101i	$0.692242\pi$
$720$	5.06011	0.188579
$721$	20.2668	0.754775
$722$	−8.43083	−0.313763
$723$	15.7651	0.586312
$724$	−32.3940	−1.20391
$725$	16.4356	0.610401
$726$	−2.09663	−0.0778133
$727$	19.1955	0.711922	0.355961	−	0.934501i	$-0.384154\pi$
$727$	19.1955	0.711922	0.355961	+	0.934501i	$0.384154\pi$
$728$	−5.33987	−0.197909
$729$	1.00000	0.0370370
$730$	24.2670	0.898161
$731$	4.65558	0.172193
$732$	−2.39586	−0.0885536
$733$	−46.2693	−1.70900	−0.854498	−	0.519455i	$-0.826135\pi$
$733$	−46.2693	−1.70900	−0.854498	+	0.519455i	$0.826135\pi$
$734$	29.3656	1.08390
$735$	−6.56322	−0.242088
$736$	45.4980	1.67708
$737$	−7.85878	−0.289482
$738$	−10.3591	−0.381325
$739$	−41.1880	−1.51513	−0.757563	−	0.652762i	$-0.773610\pi$
$739$	−41.1880	−1.51513	−0.757563	+	0.652762i	$0.773610\pi$
$740$	−4.59049	−0.168750
$741$	14.2767	0.524467
$742$	−42.6882	−1.56713
$743$	4.75789	0.174550	0.0872750	−	0.996184i	$-0.472184\pi$
$743$	4.75789	0.174550	0.0872750	+	0.996184i	$0.472184\pi$
$744$	5.91059	0.216693
$745$	−21.1637	−0.775377
$746$	53.7876	1.96930
$747$	0.804210	0.0294245
$748$	10.6299	0.388666
$749$	−11.9662	−0.437234
$750$	−25.2069	−0.920425
$751$	−20.0966	−0.733337	−0.366669	−	0.930352i	$-0.619502\pi$
$751$	−20.0966	−0.733337	−0.366669	+	0.930352i	$0.619502\pi$
$752$	19.4139	0.707952
$753$	29.4143	1.07192
$754$	−56.4858	−2.05709
$755$	4.97824	0.181177
$756$	4.17867	0.151977
$757$	−18.8608	−0.685507	−0.342754	−	0.939425i	$-0.611360\pi$
$757$	−18.8608	−0.685507	−0.342754	+	0.939425i	$0.611360\pi$
$758$	−7.52239	−0.273226
$759$	5.64634	0.204949
$760$	5.32651	0.193213
$761$	−12.3376	−0.447238	−0.223619	−	0.974677i	$-0.571787\pi$
$761$	−12.3376	−0.447238	−0.223619	+	0.974677i	$0.571787\pi$
$762$	−26.2880	−0.952312
$763$	−4.07087	−0.147375
$764$	61.5562	2.22703
$765$	−7.35703	−0.265994
$766$	−32.6989	−1.18146
$767$	−11.3565	−0.410061
$768$	−7.93434	−0.286306
$769$	39.4354	1.42208	0.711038	−	0.703154i	$-0.248225\pi$
$769$	39.4354	1.42208	0.711038	+	0.703154i	$0.248225\pi$
$770$	6.06367	0.218519
$771$	−3.00364	−0.108173
$772$	−25.7590	−0.927085
$773$	17.8673	0.642641	0.321321	−	0.946970i	$-0.395873\pi$
$773$	17.8673	0.642641	0.321321	+	0.946970i	$0.395873\pi$
$774$	2.20004	0.0790787
$775$	16.0258	0.575663
$776$	1.04857	0.0376416
$777$	2.01529	0.0722981
$778$	8.58086	0.307639
$779$	19.1223	0.685129
$780$	14.6550	0.524734
$781$	−10.5509	−0.377539
$782$	−52.5236	−1.87824
$783$	7.30348	0.261005
$784$	12.0782	0.431366
$785$	2.94638	0.105161
$786$	4.50438	0.160666
$787$	−52.4024	−1.86794	−0.933972	−	0.357347i	$-0.883682\pi$
$787$	−52.4024	−1.86794	−0.933972	+	0.357347i	$0.883682\pi$
$788$	−26.8537	−0.956622
$789$	3.40771	0.121318
$790$	−44.0155	−1.56600
$791$	−20.7168	−0.736603
$792$	0.829977	0.0294920
$793$	3.68882	0.130994
$794$	−0.336408	−0.0119387
$795$	19.3574	0.686535
$796$	−46.9067	−1.66256
$797$	−7.58143	−0.268548	−0.134274	−	0.990944i	$-0.542870\pi$
$797$	−7.58143	−0.268548	−0.134274	+	0.990944i	$0.542870\pi$
$798$	−14.1527	−0.500999
$799$	−28.2264	−0.998578
$800$	18.1334	0.641114
$801$	1.75911	0.0621550
$802$	−54.9735	−1.94118
$803$	−6.98002	−0.246320
$804$	18.8286	0.664032
$805$	−16.3298	−0.575549
$806$	−55.0775	−1.94002
$807$	−20.2718	−0.713601
$808$	7.83311	0.275568
$809$	41.8779	1.47235	0.736175	−	0.676791i	$-0.236630\pi$
$809$	41.8779	1.47235	0.736175	+	0.676791i	$0.236630\pi$
$810$	−3.47663	−0.122156
$811$	−23.3432	−0.819689	−0.409845	−	0.912155i	$-0.634417\pi$
$811$	−23.3432	−0.819689	−0.409845	+	0.912155i	$0.634417\pi$
$812$	30.5188	1.07100
$813$	−12.8096	−0.449253
$814$	2.42261	0.0849123
$815$	−5.28953	−0.185284
$816$	13.5391	0.473962
$817$	−4.06113	−0.142081
$818$	−22.8494	−0.798911
$819$	−6.43375	−0.224813
$820$	19.6291	0.685478
$821$	46.6664	1.62867	0.814334	−	0.580396i	$-0.197102\pi$
$821$	46.6664	1.62867	0.814334	+	0.580396i	$0.197102\pi$
$822$	−8.00005	−0.279034
$823$	16.5230	0.575957	0.287979	−	0.957637i	$-0.407017\pi$
$823$	16.5230	0.575957	0.287979	+	0.957637i	$0.407017\pi$
$824$	−9.64439	−0.335978
$825$	2.25037	0.0783480
$826$	11.2579	0.391712
$827$	−30.0794	−1.04596	−0.522982	−	0.852344i	$-0.675181\pi$
$827$	−30.0794	−1.04596	−0.522982	+	0.852344i	$0.675181\pi$
$828$	−13.5279	−0.470125
$829$	−13.7760	−0.478462	−0.239231	−	0.970963i	$-0.576895\pi$
$829$	−13.7760	−0.478462	−0.239231	+	0.970963i	$0.576895\pi$
$830$	−2.79594	−0.0970485
$831$	17.8053	0.617660
$832$	−39.8077	−1.38008
$833$	−17.5609	−0.608448
$834$	−14.1200	−0.488936
$835$	−16.4358	−0.568783
$836$	−9.27260	−0.320699
$837$	7.12139	0.246151
$838$	53.7668	1.85734
$839$	7.85670	0.271243	0.135622	−	0.990761i	$-0.456697\pi$
$839$	7.85670	0.271243	0.135622	+	0.990761i	$0.456697\pi$
$840$	−2.40038	−0.0828209
$841$	24.3408	0.839337
$842$	−55.7718	−1.92202
$843$	14.9901	0.516285
$844$	5.77752	0.198870
$845$	−1.00719	−0.0346484
$846$	−13.3386	−0.458592
$847$	−1.74412	−0.0599287
$848$	−35.6232	−1.22330
$849$	21.2549	0.729467
$850$	−20.9335	−0.718014
$851$	−6.52421	−0.223647
$852$	25.2784	0.866024
$853$	−20.3819	−0.697864	−0.348932	−	0.937148i	$-0.613456\pi$
$853$	−20.3819	−0.697864	−0.348932	+	0.937148i	$0.613456\pi$
$854$	−3.65678	−0.125132
$855$	6.41765	0.219479
$856$	5.69436	0.194629
$857$	−47.1501	−1.61062	−0.805308	−	0.592856i	$-0.798000\pi$
$857$	−47.1501	−1.61062	−0.805308	+	0.592856i	$0.798000\pi$
$858$	−7.73410	−0.264038
$859$	−9.84823	−0.336017	−0.168009	−	0.985786i	$-0.553734\pi$
$859$	−9.84823	−0.336017	−0.168009	+	0.985786i	$0.553734\pi$
$860$	−4.16876	−0.142153
$861$	−8.61744	−0.293682
$862$	33.0548	1.12585
$863$	−7.01219	−0.238698	−0.119349	−	0.992852i	$-0.538081\pi$
$863$	−7.01219	−0.238698	−0.119349	+	0.992852i	$0.538081\pi$
$864$	8.05797	0.274138
$865$	10.3071	0.350452
$866$	38.3297	1.30250
$867$	−2.68481	−0.0911810
$868$	29.7579	1.01005
$869$	12.6604	0.429475
$870$	−25.3915	−0.860853
$871$	−28.9896	−0.982276
$872$	1.93721	0.0656022
$873$	1.26338	0.0427588
$874$	45.8172	1.54979
$875$	−20.9688	−0.708875
$876$	16.7232	0.565024
$877$	7.33785	0.247782	0.123891	−	0.992296i	$-0.460463\pi$
$877$	7.33785	0.247782	0.123891	+	0.992296i	$0.460463\pi$
$878$	33.9385	1.14537
$879$	13.3121	0.449007
$880$	5.06011	0.170576
$881$	45.6277	1.53724	0.768618	−	0.639708i	$-0.220945\pi$
$881$	45.6277	1.53724	0.768618	+	0.639708i	$0.220945\pi$
$882$	−8.29856	−0.279427
$883$	−49.8132	−1.67635	−0.838174	−	0.545404i	$-0.816376\pi$
$883$	−49.8132	−1.67635	−0.838174	+	0.545404i	$0.816376\pi$
$884$	39.2116	1.31883
$885$	−5.10499	−0.171602
$886$	−13.4101	−0.450522
$887$	17.3997	0.584223	0.292112	−	0.956384i	$-0.405642\pi$
$887$	17.3997	0.584223	0.292112	+	0.956384i	$0.405642\pi$
$888$	−0.959018	−0.0321825
$889$	−21.8681	−0.733433
$890$	−6.11577	−0.205001
$891$	1.00000	0.0335013
$892$	6.17420	0.206727
$893$	24.6223	0.823955
$894$	−26.7594	−0.894968
$895$	27.4771	0.918458
$896$	11.3538	0.379304
$897$	20.8283	0.695438
$898$	59.7468	1.99378
$899$	52.0109	1.73466
$900$	−5.39159	−0.179720
$901$	51.7935	1.72549
$902$	−10.3591	−0.344922
$903$	1.83014	0.0609033
$904$	9.85852	0.327889
$905$	22.4202	0.745273
$906$	6.29450	0.209121
$907$	27.0754	0.899025	0.449512	−	0.893274i	$-0.351598\pi$
$907$	27.0754	0.899025	0.449512	+	0.893274i	$0.351598\pi$
$908$	−57.8341	−1.91929
$909$	9.43775	0.313030
$910$	22.3678	0.741485
$911$	0.512145	0.0169681	0.00848405	−	0.999964i	$-0.497299\pi$
$911$	0.512145	0.0169681	0.00848405	+	0.999964i	$0.497299\pi$
$912$	−11.8103	−0.391080
$913$	0.804210	0.0266155
$914$	5.10907	0.168993
$915$	1.65820	0.0548184
$916$	−15.9712	−0.527703
$917$	3.74705	0.123739
$918$	−9.30224	−0.307020
$919$	−10.8058	−0.356449	−0.178224	−	0.983990i	$-0.557035\pi$
$919$	−10.8058	−0.356449	−0.178224	+	0.983990i	$0.557035\pi$
$920$	7.77088	0.256198
$921$	−15.6165	−0.514580
$922$	−54.7006	−1.80147
$923$	−38.9202	−1.28107
$924$	4.17867	0.137468
$925$	−2.60025	−0.0854958
$926$	6.81406	0.223924
$927$	−11.6201	−0.381653
$928$	58.8512	1.93188
$929$	14.1525	0.464327	0.232164	−	0.972677i	$-0.425420\pi$
$929$	14.1525	0.464327	0.232164	+	0.972677i	$0.425420\pi$
$930$	−24.7584	−0.811861
$931$	15.3186	0.502048
$932$	27.9221	0.914618
$933$	17.6810	0.578850
$934$	76.1186	2.49068
$935$	−7.35703	−0.240601
$936$	3.06164	0.100073
$937$	19.2284	0.628166	0.314083	−	0.949396i	$-0.398303\pi$
$937$	19.2284	0.628166	0.314083	+	0.949396i	$0.398303\pi$
$938$	28.7378	0.938323
$939$	19.5864	0.639179
$940$	25.2748	0.824374
$941$	28.5255	0.929904	0.464952	−	0.885336i	$-0.346071\pi$
$941$	28.5255	0.929904	0.464952	+	0.885336i	$0.346071\pi$
$942$	3.72541	0.121380
$943$	27.8977	0.908475
$944$	9.39466	0.305770
$945$	−2.89210	−0.0940800
$946$	2.20004	0.0715294
$947$	10.5876	0.344049	0.172025	−	0.985093i	$-0.444969\pi$
$947$	10.5876	0.344049	0.172025	+	0.985093i	$0.444969\pi$
$948$	−30.3326	−0.985156
$949$	−25.7481	−0.835817
$950$	18.2607	0.592454
$951$	−15.8519	−0.514033
$952$	−6.42256	−0.208156
$953$	4.46197	0.144537	0.0722687	−	0.997385i	$-0.476976\pi$
$953$	4.46197	0.144537	0.0722687	+	0.997385i	$0.476976\pi$
$954$	24.4755	0.792423
$955$	−42.6036	−1.37862
$956$	18.5185	0.598932
$957$	7.30348	0.236088
$958$	57.3287	1.85221
$959$	−6.65499	−0.214901
$960$	−17.8944	−0.577539
$961$	19.7142	0.635940
$962$	8.93656	0.288126
$963$	6.86086	0.221088
$964$	−37.7711	−1.21653
$965$	17.8280	0.573904
$966$	−20.6474	−0.664320
$967$	−12.6172	−0.405741	−0.202870	−	0.979206i	$-0.565027\pi$
$967$	−12.6172	−0.405741	−0.202870	+	0.979206i	$0.565027\pi$
$968$	0.829977	0.0266765
$969$	17.1714	0.551624
$970$	−4.39230	−0.141028
$971$	33.1003	1.06224	0.531120	−	0.847296i	$-0.321771\pi$
$971$	33.1003	1.06224	0.531120	+	0.847296i	$0.321771\pi$
$972$	−2.39586	−0.0768473
$973$	−11.7460	−0.376559
$974$	0.365119	0.0116992
$975$	8.30123	0.265852
$976$	−3.05157	−0.0976783
$977$	−32.7974	−1.04928	−0.524641	−	0.851324i	$-0.675800\pi$
$977$	−32.7974	−1.04928	−0.524641	+	0.851324i	$0.675800\pi$
$978$	−6.68809	−0.213862
$979$	1.75911	0.0562213
$980$	15.7246	0.502303
$981$	2.33405	0.0745205
$982$	44.7377	1.42764
$983$	−3.95579	−0.126170	−0.0630850	−	0.998008i	$-0.520094\pi$
$983$	−3.95579	−0.126170	−0.0630850	+	0.998008i	$0.520094\pi$
$984$	4.10079	0.130729
$985$	18.5857	0.592189
$986$	−67.9387	−2.16361
$987$	−11.0960	−0.353189
$988$	−34.2049	−1.08820
$989$	−5.92482	−0.188398
$990$	−3.47663	−0.110495
$991$	10.4032	0.330468	0.165234	−	0.986254i	$-0.447162\pi$
$991$	10.4032	0.330468	0.165234	+	0.986254i	$0.447162\pi$
$992$	57.3839	1.82194
$993$	−14.0150	−0.444753
$994$	38.5821	1.22375
$995$	32.4646	1.02920
$996$	−1.92678	−0.0610522
$997$	18.3023	0.579641	0.289820	−	0.957081i	$-0.406404\pi$
$997$	18.3023	0.579641	0.289820	+	0.957081i	$0.406404\pi$
$998$	−61.5076	−1.94699
$999$	−1.15548	−0.0365576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.b.1.10	✓	11
3.2	odd	2		6039.2.a.c.1.2		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.b.1.10	✓	11	1.1	even	1	trivial
6039.2.a.c.1.2		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)

\(f(q)\)	\(=\)	\(q+2.09663 q^{2} -1.00000 q^{3} +2.39586 q^{4} -1.65820 q^{5} -2.09663 q^{6} -1.74412 q^{7} +0.829977 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.09663 q^{2} -1.00000 q^{3} +2.39586 q^{4} -1.65820 q^{5} -2.09663 q^{6} -1.74412 q^{7} +0.829977 q^{8} +1.00000 q^{9} -3.47663 q^{10} +1.00000 q^{11} -2.39586 q^{12} +3.68882 q^{13} -3.65678 q^{14} +1.65820 q^{15} -3.05157 q^{16} +4.43676 q^{17} +2.09663 q^{18} -3.87025 q^{19} -3.97282 q^{20} +1.74412 q^{21} +2.09663 q^{22} -5.64634 q^{23} -0.829977 q^{24} -2.25037 q^{25} +7.73410 q^{26} -1.00000 q^{27} -4.17867 q^{28} -7.30348 q^{29} +3.47663 q^{30} -7.12139 q^{31} -8.05797 q^{32} -1.00000 q^{33} +9.30224 q^{34} +2.89210 q^{35} +2.39586 q^{36} +1.15548 q^{37} -8.11450 q^{38} -3.68882 q^{39} -1.37627 q^{40} -4.94085 q^{41} +3.65678 q^{42} +1.04932 q^{43} +2.39586 q^{44} -1.65820 q^{45} -11.8383 q^{46} -6.36194 q^{47} +3.05157 q^{48} -3.95804 q^{49} -4.71821 q^{50} -4.43676 q^{51} +8.83791 q^{52} +11.6737 q^{53} -2.09663 q^{54} -1.65820 q^{55} -1.44758 q^{56} +3.87025 q^{57} -15.3127 q^{58} -3.07863 q^{59} +3.97282 q^{60} +1.00000 q^{61} -14.9309 q^{62} -1.74412 q^{63} -10.7915 q^{64} -6.11680 q^{65} -2.09663 q^{66} -7.85878 q^{67} +10.6299 q^{68} +5.64634 q^{69} +6.06367 q^{70} -10.5509 q^{71} +0.829977 q^{72} -6.98002 q^{73} +2.42261 q^{74} +2.25037 q^{75} -9.27260 q^{76} -1.74412 q^{77} -7.73410 q^{78} +12.6604 q^{79} +5.06011 q^{80} +1.00000 q^{81} -10.3591 q^{82} +0.804210 q^{83} +4.17867 q^{84} -7.35703 q^{85} +2.20004 q^{86} +7.30348 q^{87} +0.829977 q^{88} +1.75911 q^{89} -3.47663 q^{90} -6.43375 q^{91} -13.5279 q^{92} +7.12139 q^{93} -13.3386 q^{94} +6.41765 q^{95} +8.05797 q^{96} +1.26338 q^{97} -8.29856 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) \) 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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