LMFDB - Embedded newform 2013.2.a.b.1.5

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			1.5
Root			$0.942842$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.942842 q^{2} -1.00000 q^{3} -1.11105 q^{4} +3.49194 q^{5} +0.942842 q^{6} +1.81837 q^{7} +2.93323 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.942842 q^{2} -1.00000 q^{3} -1.11105 q^{4} +3.49194 q^{5} +0.942842 q^{6} +1.81837 q^{7} +2.93323 q^{8} +1.00000 q^{9} -3.29234 q^{10} +1.00000 q^{11} +1.11105 q^{12} +0.0495663 q^{13} -1.71444 q^{14} -3.49194 q^{15} -0.543473 q^{16} -7.74735 q^{17} -0.942842 q^{18} -8.43210 q^{19} -3.87971 q^{20} -1.81837 q^{21} -0.942842 q^{22} -2.63679 q^{23} -2.93323 q^{24} +7.19362 q^{25} -0.0467332 q^{26} -1.00000 q^{27} -2.02030 q^{28} -8.93168 q^{29} +3.29234 q^{30} -6.37998 q^{31} -5.35405 q^{32} -1.00000 q^{33} +7.30453 q^{34} +6.34964 q^{35} -1.11105 q^{36} +8.12883 q^{37} +7.95014 q^{38} -0.0495663 q^{39} +10.2426 q^{40} +1.61240 q^{41} +1.71444 q^{42} +1.65032 q^{43} -1.11105 q^{44} +3.49194 q^{45} +2.48607 q^{46} -3.69954 q^{47} +0.543473 q^{48} -3.69353 q^{49} -6.78245 q^{50} +7.74735 q^{51} -0.0550706 q^{52} +1.04707 q^{53} +0.942842 q^{54} +3.49194 q^{55} +5.33370 q^{56} +8.43210 q^{57} +8.42117 q^{58} -8.66125 q^{59} +3.87971 q^{60} +1.00000 q^{61} +6.01531 q^{62} +1.81837 q^{63} +6.13497 q^{64} +0.173082 q^{65} +0.942842 q^{66} -3.49836 q^{67} +8.60768 q^{68} +2.63679 q^{69} -5.98670 q^{70} +13.4818 q^{71} +2.93323 q^{72} -14.2256 q^{73} -7.66420 q^{74} -7.19362 q^{75} +9.36848 q^{76} +1.81837 q^{77} +0.0467332 q^{78} -12.8071 q^{79} -1.89777 q^{80} +1.00000 q^{81} -1.52024 q^{82} -3.54926 q^{83} +2.02030 q^{84} -27.0532 q^{85} -1.55599 q^{86} +8.93168 q^{87} +2.93323 q^{88} +3.49530 q^{89} -3.29234 q^{90} +0.0901300 q^{91} +2.92960 q^{92} +6.37998 q^{93} +3.48808 q^{94} -29.4444 q^{95} +5.35405 q^{96} +2.90558 q^{97} +3.48241 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 2 * q^2 - 11 * q^3 + 10 * q^4 - q^5 + 2 * q^6 - 11 * q^7 - 3 * q^8 + 11 * q^9	\( 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9} - 8 q^{10} + 11 q^{11} - 10 q^{12} - 13 q^{13} + 5 q^{14} + q^{15} + 4 q^{16} - 13 q^{17} - 2 q^{18} - 12 q^{19} - 7 q^{20} + 11 q^{21} - 2 q^{22} - 3 q^{23} + 3 q^{24} + 12 q^{25} + 12 q^{26} - 11 q^{27} - 13 q^{28} + 2 q^{29} + 8 q^{30} + q^{31} - 23 q^{32} - 11 q^{33} - 14 q^{34} - 4 q^{35} + 10 q^{36} - 14 q^{37} - 8 q^{38} + 13 q^{39} - 34 q^{40} + 3 q^{41} - 5 q^{42} - 21 q^{43} + 10 q^{44} - q^{45} - 12 q^{46} - 16 q^{47} - 4 q^{48} - 18 q^{49} - 13 q^{50} + 13 q^{51} - 33 q^{52} + 2 q^{54} - q^{55} + 16 q^{56} + 12 q^{57} - 17 q^{58} + 3 q^{59} + 7 q^{60} + 11 q^{61} - 21 q^{62} - 11 q^{63} - 7 q^{64} - q^{65} + 2 q^{66} - 24 q^{67} + 2 q^{68} + 3 q^{69} + 4 q^{70} + 7 q^{71} - 3 q^{72} - 42 q^{73} - 16 q^{74} - 12 q^{75} - 13 q^{76} - 11 q^{77} - 12 q^{78} - 11 q^{79} + 42 q^{80} + 11 q^{81} - 38 q^{82} - 34 q^{83} + 13 q^{84} - 14 q^{85} + 42 q^{86} - 2 q^{87} - 3 q^{88} + 29 q^{89} - 8 q^{90} + 9 q^{91} + 42 q^{92} - q^{93} - 33 q^{94} - 31 q^{95} + 23 q^{96} - 45 q^{97} - 33 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q - 2 * q^2 - 11 * q^3 + 10 * q^4 - q^5 + 2 * q^6 - 11 * q^7 - 3 * q^8 + 11 * q^9 - 8 * q^10 + 11 * q^11 - 10 * q^12 - 13 * q^13 + 5 * q^14 + q^15 + 4 * q^16 - 13 * q^17 - 2 * q^18 - 12 * q^19 - 7 * q^20 + 11 * q^21 - 2 * q^22 - 3 * q^23 + 3 * q^24 + 12 * q^25 + 12 * q^26 - 11 * q^27 - 13 * q^28 + 2 * q^29 + 8 * q^30 + q^31 - 23 * q^32 - 11 * q^33 - 14 * q^34 - 4 * q^35 + 10 * q^36 - 14 * q^37 - 8 * q^38 + 13 * q^39 - 34 * q^40 + 3 * q^41 - 5 * q^42 - 21 * q^43 + 10 * q^44 - q^45 - 12 * q^46 - 16 * q^47 - 4 * q^48 - 18 * q^49 - 13 * q^50 + 13 * q^51 - 33 * q^52 + 2 * q^54 - q^55 + 16 * q^56 + 12 * q^57 - 17 * q^58 + 3 * q^59 + 7 * q^60 + 11 * q^61 - 21 * q^62 - 11 * q^63 - 7 * q^64 - q^65 + 2 * q^66 - 24 * q^67 + 2 * q^68 + 3 * q^69 + 4 * q^70 + 7 * q^71 - 3 * q^72 - 42 * q^73 - 16 * q^74 - 12 * q^75 - 13 * q^76 - 11 * q^77 - 12 * q^78 - 11 * q^79 + 42 * q^80 + 11 * q^81 - 38 * q^82 - 34 * q^83 + 13 * q^84 - 14 * q^85 + 42 * q^86 - 2 * q^87 - 3 * q^88 + 29 * q^89 - 8 * q^90 + 9 * q^91 + 42 * q^92 - q^93 - 33 * q^94 - 31 * q^95 + 23 * q^96 - 45 * q^97 - 33 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.942842	−0.666690	−0.333345	−	0.942805i	$-0.608177\pi$
$2$	−0.942842	−0.666690	−0.333345	+	0.942805i	$0.608177\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.11105	−0.555524
$5$	3.49194	1.56164	0.780821	−	0.624755i	$-0.214801\pi$
$5$	3.49194	1.56164	0.780821	+	0.624755i	$0.214801\pi$
$6$	0.942842	0.384914
$7$	1.81837	0.687280	0.343640	−	0.939102i	$-0.388340\pi$
$7$	1.81837	0.687280	0.343640	+	0.939102i	$0.388340\pi$
$8$	2.93323	1.03705
$9$	1.00000	0.333333
$10$	−3.29234	−1.04113
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.11105	0.320732
$13$	0.0495663	0.0137472	0.00687361	−	0.999976i	$-0.497812\pi$
$13$	0.0495663	0.0137472	0.00687361	+	0.999976i	$0.497812\pi$
$14$	−1.71444	−0.458203
$15$	−3.49194	−0.901614
$16$	−0.543473	−0.135868
$17$	−7.74735	−1.87901	−0.939504	−	0.342538i	$-0.888713\pi$
$17$	−7.74735	−1.87901	−0.939504	+	0.342538i	$0.888713\pi$
$18$	−0.942842	−0.222230
$19$	−8.43210	−1.93446	−0.967228	−	0.253908i	$-0.918284\pi$
$19$	−8.43210	−1.93446	−0.967228	+	0.253908i	$0.918284\pi$
$20$	−3.87971	−0.867530
$21$	−1.81837	−0.396801
$22$	−0.942842	−0.201015
$23$	−2.63679	−0.549808	−0.274904	−	0.961472i	$-0.588646\pi$
$23$	−2.63679	−0.549808	−0.274904	+	0.961472i	$0.588646\pi$
$24$	−2.93323	−0.598743
$25$	7.19362	1.43872
$26$	−0.0467332	−0.00916514
$27$	−1.00000	−0.192450
$28$	−2.02030	−0.381801
$29$	−8.93168	−1.65857	−0.829286	−	0.558825i	$-0.811253\pi$
$29$	−8.93168	−1.65857	−0.829286	+	0.558825i	$0.811253\pi$
$30$	3.29234	0.601097
$31$	−6.37998	−1.14588	−0.572939	−	0.819598i	$-0.694197\pi$
$31$	−6.37998	−1.14588	−0.572939	+	0.819598i	$0.694197\pi$
$32$	−5.35405	−0.946471
$33$	−1.00000	−0.174078
$34$	7.30453	1.25272
$35$	6.34964	1.07328
$36$	−1.11105	−0.185175
$37$	8.12883	1.33637	0.668185	−	0.743995i	$-0.267071\pi$
$37$	8.12883	1.33637	0.668185	+	0.743995i	$0.267071\pi$
$38$	7.95014	1.28968
$39$	−0.0495663	−0.00793696
$40$	10.2426	1.61950
$41$	1.61240	0.251815	0.125907	−	0.992042i	$-0.459816\pi$
$41$	1.61240	0.251815	0.125907	+	0.992042i	$0.459816\pi$
$42$	1.71444	0.264543
$43$	1.65032	0.251671	0.125836	−	0.992051i	$-0.459839\pi$
$43$	1.65032	0.251671	0.125836	+	0.992051i	$0.459839\pi$
$44$	−1.11105	−0.167497
$45$	3.49194	0.520547
$46$	2.48607	0.366551
$47$	−3.69954	−0.539633	−0.269816	−	0.962912i	$-0.586963\pi$
$47$	−3.69954	−0.539633	−0.269816	+	0.962912i	$0.586963\pi$
$48$	0.543473	0.0784436
$49$	−3.69353	−0.527647
$50$	−6.78245	−0.959183
$51$	7.74735	1.08485
$52$	−0.0550706	−0.00763692
$53$	1.04707	0.143826	0.0719131	−	0.997411i	$-0.477090\pi$
$53$	1.04707	0.143826	0.0719131	+	0.997411i	$0.477090\pi$
$54$	0.942842	0.128305
$55$	3.49194	0.470853
$56$	5.33370	0.712745
$57$	8.43210	1.11686
$58$	8.42117	1.10575
$59$	−8.66125	−1.12760	−0.563800	−	0.825912i	$-0.690661\pi$
$59$	−8.66125	−1.12760	−0.563800	+	0.825912i	$0.690661\pi$
$60$	3.87971	0.500869
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	6.01531	0.763945
$63$	1.81837	0.229093
$64$	6.13497	0.766871
$65$	0.173082	0.0214682
$66$	0.942842	0.116056
$67$	−3.49836	−0.427392	−0.213696	−	0.976900i	$-0.568550\pi$
$67$	−3.49836	−0.427392	−0.213696	+	0.976900i	$0.568550\pi$
$68$	8.60768	1.04383
$69$	2.63679	0.317432
$70$	−5.98670	−0.715548
$71$	13.4818	1.59999	0.799996	−	0.600006i	$-0.204835\pi$
$71$	13.4818	1.59999	0.799996	+	0.600006i	$0.204835\pi$
$72$	2.93323	0.345684
$73$	−14.2256	−1.66498	−0.832488	−	0.554044i	$-0.813084\pi$
$73$	−14.2256	−1.66498	−0.832488	+	0.554044i	$0.813084\pi$
$74$	−7.66420	−0.890945
$75$	−7.19362	−0.830648
$76$	9.36848	1.07464
$77$	1.81837	0.207223
$78$	0.0467332	0.00529149
$79$	−12.8071	−1.44091	−0.720453	−	0.693504i	$-0.756066\pi$
$79$	−12.8071	−1.44091	−0.720453	+	0.693504i	$0.756066\pi$
$80$	−1.89777	−0.212177
$81$	1.00000	0.111111
$82$	−1.52024	−0.167882
$83$	−3.54926	−0.389582	−0.194791	−	0.980845i	$-0.562403\pi$
$83$	−3.54926	−0.389582	−0.194791	+	0.980845i	$0.562403\pi$
$84$	2.02030	0.220433
$85$	−27.0532	−2.93434
$86$	−1.55599	−0.167787
$87$	8.93168	0.957577
$88$	2.93323	0.312683
$89$	3.49530	0.370501	0.185251	−	0.982691i	$-0.440690\pi$
$89$	3.49530	0.370501	0.185251	+	0.982691i	$0.440690\pi$
$90$	−3.29234	−0.347044
$91$	0.0901300	0.00944819
$92$	2.92960	0.305432
$93$	6.37998	0.661573
$94$	3.48808	0.359768
$95$	−29.4444	−3.02093
$96$	5.35405	0.546445
$97$	2.90558	0.295017	0.147509	−	0.989061i	$-0.452875\pi$
$97$	2.90558	0.295017	0.147509	+	0.989061i	$0.452875\pi$
$98$	3.48241	0.351777
$99$	1.00000	0.100504
$100$	−7.99246	−0.799246
$101$	4.01746	0.399752	0.199876	−	0.979821i	$-0.435946\pi$
$101$	4.01746	0.399752	0.199876	+	0.979821i	$0.435946\pi$
$102$	−7.30453	−0.723256
$103$	−8.35920	−0.823657	−0.411828	−	0.911261i	$-0.635110\pi$
$103$	−8.35920	−0.823657	−0.411828	+	0.911261i	$0.635110\pi$
$104$	0.145389	0.0142566
$105$	−6.34964	−0.619661
$106$	−0.987223	−0.0958875
$107$	−0.438376	−0.0423794	−0.0211897	−	0.999775i	$-0.506745\pi$
$107$	−0.438376	−0.0423794	−0.0211897	+	0.999775i	$0.506745\pi$
$108$	1.11105	0.106911
$109$	−5.04229	−0.482964	−0.241482	−	0.970405i	$-0.577633\pi$
$109$	−5.04229	−0.482964	−0.241482	+	0.970405i	$0.577633\pi$
$110$	−3.29234	−0.313913
$111$	−8.12883	−0.771554
$112$	−0.988236	−0.0933795
$113$	11.3993	1.07235	0.536177	−	0.844106i	$-0.319868\pi$
$113$	11.3993	1.07235	0.536177	+	0.844106i	$0.319868\pi$
$114$	−7.95014	−0.744599
$115$	−9.20749	−0.858603
$116$	9.92354	0.921377
$117$	0.0495663	0.00458241
$118$	8.16619	0.751759
$119$	−14.0876	−1.29140
$120$	−10.2426	−0.935021
$121$	1.00000	0.0909091
$122$	−0.942842	−0.0853609
$123$	−1.61240	−0.145385
$124$	7.08846	0.636563
$125$	7.65998	0.685129
$126$	−1.71444	−0.152734
$127$	16.6435	1.47688	0.738438	−	0.674321i	$-0.235564\pi$
$127$	16.6435	1.47688	0.738438	+	0.674321i	$0.235564\pi$
$128$	4.92379	0.435206
$129$	−1.65032	−0.145303
$130$	−0.163189	−0.0143127
$131$	−15.0473	−1.31469	−0.657346	−	0.753589i	$-0.728321\pi$
$131$	−15.0473	−1.31469	−0.657346	+	0.753589i	$0.728321\pi$
$132$	1.11105	0.0967044
$133$	−15.3327	−1.32951
$134$	3.29840	0.284938
$135$	−3.49194	−0.300538
$136$	−22.7247	−1.94863
$137$	5.65682	0.483295	0.241647	−	0.970364i	$-0.422312\pi$
$137$	5.65682	0.483295	0.241647	+	0.970364i	$0.422312\pi$
$138$	−2.48607	−0.211629
$139$	21.1733	1.79590	0.897950	−	0.440098i	$-0.145056\pi$
$139$	21.1733	1.79590	0.897950	+	0.440098i	$0.145056\pi$
$140$	−7.05476	−0.596236
$141$	3.69954	0.311557
$142$	−12.7112	−1.06670
$143$	0.0495663	0.00414494
$144$	−0.543473	−0.0452894
$145$	−31.1889	−2.59009
$146$	13.4125	1.11002
$147$	3.69353	0.304637
$148$	−9.03152	−0.742387
$149$	21.2658	1.74217	0.871083	−	0.491137i	$-0.163418\pi$
$149$	21.2658	1.74217	0.871083	+	0.491137i	$0.163418\pi$
$150$	6.78245	0.553784
$151$	−8.05881	−0.655817	−0.327908	−	0.944710i	$-0.606344\pi$
$151$	−8.05881	−0.655817	−0.327908	+	0.944710i	$0.606344\pi$
$152$	−24.7333	−2.00613
$153$	−7.74735	−0.626336
$154$	−1.71444	−0.138153
$155$	−22.2785	−1.78945
$156$	0.0550706	0.00440918
$157$	1.96933	0.157170	0.0785849	−	0.996907i	$-0.474960\pi$
$157$	1.96933	0.157170	0.0785849	+	0.996907i	$0.474960\pi$
$158$	12.0750	0.960638
$159$	−1.04707	−0.0830381
$160$	−18.6960	−1.47805
$161$	−4.79465	−0.377872
$162$	−0.942842	−0.0740767
$163$	−20.7663	−1.62654	−0.813269	−	0.581888i	$-0.802314\pi$
$163$	−20.7663	−1.62654	−0.813269	+	0.581888i	$0.802314\pi$
$164$	−1.79146	−0.139889
$165$	−3.49194	−0.271847
$166$	3.34639	0.259730
$167$	−1.21018	−0.0936465	−0.0468233	−	0.998903i	$-0.514910\pi$
$167$	−1.21018	−0.0936465	−0.0468233	+	0.998903i	$0.514910\pi$
$168$	−5.33370	−0.411504
$169$	−12.9975	−0.999811
$170$	25.5069	1.95629
$171$	−8.43210	−0.644819
$172$	−1.83359	−0.139810
$173$	−2.13714	−0.162483	−0.0812417	−	0.996694i	$-0.525889\pi$
$173$	−2.13714	−0.162483	−0.0812417	+	0.996694i	$0.525889\pi$
$174$	−8.42117	−0.638407
$175$	13.0807	0.988806
$176$	−0.543473	−0.0409658
$177$	8.66125	0.651020
$178$	−3.29552	−0.247009
$179$	13.7854	1.03037	0.515184	−	0.857080i	$-0.327724\pi$
$179$	13.7854	1.03037	0.515184	+	0.857080i	$0.327724\pi$
$180$	−3.87971	−0.289177
$181$	9.01267	0.669906	0.334953	−	0.942235i	$-0.391279\pi$
$181$	9.01267	0.669906	0.334953	+	0.942235i	$0.391279\pi$
$182$	−0.0849783	−0.00629901
$183$	−1.00000	−0.0739221
$184$	−7.73429	−0.570180
$185$	28.3853	2.08693
$186$	−6.01531	−0.441064
$187$	−7.74735	−0.566542
$188$	4.11036	0.299779
$189$	−1.81837	−0.132267
$190$	27.7614	2.01402
$191$	−6.79478	−0.491653	−0.245827	−	0.969314i	$-0.579059\pi$
$191$	−6.79478	−0.491653	−0.245827	+	0.969314i	$0.579059\pi$
$192$	−6.13497	−0.442753
$193$	−6.80903	−0.490125	−0.245062	−	0.969507i	$-0.578808\pi$
$193$	−6.80903	−0.490125	−0.245062	+	0.969507i	$0.578808\pi$
$194$	−2.73951	−0.196685
$195$	−0.173082	−0.0123947
$196$	4.10369	0.293121
$197$	19.9506	1.42142	0.710712	−	0.703483i	$-0.248373\pi$
$197$	19.9506	1.42142	0.710712	+	0.703483i	$0.248373\pi$
$198$	−0.942842	−0.0670049
$199$	−7.46854	−0.529431	−0.264715	−	0.964327i	$-0.585278\pi$
$199$	−7.46854	−0.529431	−0.264715	+	0.964327i	$0.585278\pi$
$200$	21.1005	1.49203
$201$	3.49836	0.246755
$202$	−3.78783	−0.266511
$203$	−16.2411	−1.13990
$204$	−8.60768	−0.602658
$205$	5.63040	0.393245
$206$	7.88141	0.549124
$207$	−2.63679	−0.183269
$208$	−0.0269380	−0.00186781
$209$	−8.43210	−0.583261
$210$	5.98670	0.413122
$211$	23.9405	1.64813	0.824066	−	0.566493i	$-0.191700\pi$
$211$	23.9405	1.64813	0.824066	+	0.566493i	$0.191700\pi$
$212$	−1.16335	−0.0798990
$213$	−13.4818	−0.923756
$214$	0.413319	0.0282539
$215$	5.76281	0.393020
$216$	−2.93323	−0.199581
$217$	−11.6012	−0.787538
$218$	4.75408	0.321987
$219$	14.2256	0.961274
$220$	−3.87971	−0.261570
$221$	−0.384007	−0.0258311
$222$	7.66420	0.514387
$223$	10.8163	0.724311	0.362156	−	0.932118i	$-0.382041\pi$
$223$	10.8163	0.724311	0.362156	+	0.932118i	$0.382041\pi$
$224$	−9.73564	−0.650490
$225$	7.19362	0.479575
$226$	−10.7477	−0.714928
$227$	−26.3046	−1.74590	−0.872950	−	0.487810i	$-0.837796\pi$
$227$	−26.3046	−1.74590	−0.872950	+	0.487810i	$0.837796\pi$
$228$	−9.36848	−0.620443
$229$	−24.8377	−1.64132	−0.820661	−	0.571416i	$-0.806394\pi$
$229$	−24.8377	−1.64132	−0.820661	+	0.571416i	$0.806394\pi$
$230$	8.68121	0.572422
$231$	−1.81837	−0.119640
$232$	−26.1987	−1.72003
$233$	15.2240	0.997358	0.498679	−	0.866787i	$-0.333819\pi$
$233$	15.2240	0.997358	0.498679	+	0.866787i	$0.333819\pi$
$234$	−0.0467332	−0.00305505
$235$	−12.9185	−0.842713
$236$	9.62307	0.626409
$237$	12.8071	0.831908
$238$	13.2823	0.860966
$239$	−0.265685	−0.0171857	−0.00859287	−	0.999963i	$-0.502735\pi$
$239$	−0.265685	−0.0171857	−0.00859287	+	0.999963i	$0.502735\pi$
$240$	1.89777	0.122501
$241$	−23.8197	−1.53436	−0.767182	−	0.641429i	$-0.778342\pi$
$241$	−23.8197	−1.53436	−0.767182	+	0.641429i	$0.778342\pi$
$242$	−0.942842	−0.0606082
$243$	−1.00000	−0.0641500
$244$	−1.11105	−0.0711276
$245$	−12.8976	−0.823995
$246$	1.52024	0.0969270
$247$	−0.417948	−0.0265934
$248$	−18.7139	−1.18834
$249$	3.54926	0.224925
$250$	−7.22215	−0.456769
$251$	−12.9390	−0.816702	−0.408351	−	0.912825i	$-0.633896\pi$
$251$	−12.9390	−0.816702	−0.408351	+	0.912825i	$0.633896\pi$
$252$	−2.02030	−0.127267
$253$	−2.63679	−0.165773
$254$	−15.6922	−0.984618
$255$	27.0532	1.69414
$256$	−16.9123	−1.05702
$257$	−14.2280	−0.887519	−0.443759	−	0.896146i	$-0.646356\pi$
$257$	−14.2280	−0.887519	−0.443759	+	0.896146i	$0.646356\pi$
$258$	1.55599	0.0968718
$259$	14.7812	0.918461
$260$	−0.192303	−0.0119261
$261$	−8.93168	−0.552857
$262$	14.1873	0.876491
$263$	21.1376	1.30340	0.651699	−	0.758478i	$-0.274057\pi$
$263$	21.1376	1.30340	0.651699	+	0.758478i	$0.274057\pi$
$264$	−2.93323	−0.180528
$265$	3.65631	0.224605
$266$	14.4563	0.886373
$267$	−3.49530	−0.213909
$268$	3.88684	0.237427
$269$	−1.60031	−0.0975728	−0.0487864	−	0.998809i	$-0.515535\pi$
$269$	−1.60031	−0.0975728	−0.0487864	+	0.998809i	$0.515535\pi$
$270$	3.29234	0.200366
$271$	−24.2839	−1.47514	−0.737571	−	0.675269i	$-0.764027\pi$
$271$	−24.2839	−1.47514	−0.737571	+	0.675269i	$0.764027\pi$
$272$	4.21047	0.255298
$273$	−0.0901300	−0.00545491
$274$	−5.33349	−0.322208
$275$	7.19362	0.433792
$276$	−2.92960	−0.176341
$277$	4.46699	0.268395	0.134198	−	0.990955i	$-0.457154\pi$
$277$	4.46699	0.268395	0.134198	+	0.990955i	$0.457154\pi$
$278$	−19.9631	−1.19731
$279$	−6.37998	−0.381959
$280$	18.6249	1.11305
$281$	11.3532	0.677276	0.338638	−	0.940917i	$-0.390034\pi$
$281$	11.3532	0.677276	0.338638	+	0.940917i	$0.390034\pi$
$282$	−3.48808	−0.207712
$283$	4.15294	0.246867	0.123433	−	0.992353i	$-0.460609\pi$
$283$	4.15294	0.246867	0.123433	+	0.992353i	$0.460609\pi$
$284$	−14.9789	−0.888834
$285$	29.4444	1.74413
$286$	−0.0467332	−0.00276339
$287$	2.93195	0.173067
$288$	−5.35405	−0.315490
$289$	43.0214	2.53067
$290$	29.4062	1.72679
$291$	−2.90558	−0.170328
$292$	15.8053	0.924934
$293$	0.185221	0.0108207	0.00541037	−	0.999985i	$-0.498278\pi$
$293$	0.185221	0.0108207	0.00541037	+	0.999985i	$0.498278\pi$
$294$	−3.48241	−0.203098
$295$	−30.2445	−1.76091
$296$	23.8437	1.38589
$297$	−1.00000	−0.0580259
$298$	−20.0503	−1.16148
$299$	−0.130696	−0.00755833
$300$	7.99246	0.461445
$301$	3.00089	0.172969
$302$	7.59818	0.437226
$303$	−4.01746	−0.230797
$304$	4.58262	0.262831
$305$	3.49194	0.199948
$306$	7.30453	0.417572
$307$	−28.1720	−1.60786	−0.803931	−	0.594722i	$-0.797262\pi$
$307$	−28.1720	−1.60786	−0.803931	+	0.594722i	$0.797262\pi$
$308$	−2.02030	−0.115117
$309$	8.35920	0.475538
$310$	21.0051	1.19301
$311$	15.7010	0.890321	0.445161	−	0.895451i	$-0.353147\pi$
$311$	15.7010	0.890321	0.445161	+	0.895451i	$0.353147\pi$
$312$	−0.145389	−0.00823105
$313$	6.44602	0.364351	0.182175	−	0.983266i	$-0.441686\pi$
$313$	6.44602	0.364351	0.182175	+	0.983266i	$0.441686\pi$
$314$	−1.85677	−0.104783
$315$	6.34964	0.357762
$316$	14.2293	0.800459
$317$	14.6815	0.824596	0.412298	−	0.911049i	$-0.364726\pi$
$317$	14.6815	0.824596	0.412298	+	0.911049i	$0.364726\pi$
$318$	0.987223	0.0553607
$319$	−8.93168	−0.500078
$320$	21.4229	1.19758
$321$	0.438376	0.0244677
$322$	4.52060	0.251923
$323$	65.3264	3.63486
$324$	−1.11105	−0.0617249
$325$	0.356561	0.0197785
$326$	19.5793	1.08440
$327$	5.04229	0.278839
$328$	4.72954	0.261145
$329$	−6.72713	−0.370879
$330$	3.29234	0.181238
$331$	33.3092	1.83084	0.915420	−	0.402500i	$-0.131859\pi$
$331$	33.3092	1.83084	0.915420	+	0.402500i	$0.131859\pi$
$332$	3.94340	0.216422
$333$	8.12883	0.445457
$334$	1.14101	0.0624332
$335$	−12.2160	−0.667433
$336$	0.988236	0.0539127
$337$	−19.9521	−1.08686	−0.543430	−	0.839454i	$-0.682875\pi$
$337$	−19.9521	−1.08686	−0.543430	+	0.839454i	$0.682875\pi$
$338$	12.2546	0.666564
$339$	−11.3993	−0.619124
$340$	30.0575	1.63010
$341$	−6.37998	−0.345495
$342$	7.95014	0.429894
$343$	−19.4448	−1.04992
$344$	4.84076	0.260996
$345$	9.20749	0.495714
$346$	2.01498	0.108326
$347$	10.1816	0.546574	0.273287	−	0.961932i	$-0.411889\pi$
$347$	10.1816	0.546574	0.273287	+	0.961932i	$0.411889\pi$
$348$	−9.92354	−0.531957
$349$	16.9472	0.907162	0.453581	−	0.891215i	$-0.350146\pi$
$349$	16.9472	0.907162	0.453581	+	0.891215i	$0.350146\pi$
$350$	−12.3330	−0.659227
$351$	−0.0495663	−0.00264565
$352$	−5.35405	−0.285372
$353$	33.9199	1.80537	0.902686	−	0.430300i	$-0.141592\pi$
$353$	33.9199	1.80537	0.902686	+	0.430300i	$0.141592\pi$
$354$	−8.16619	−0.434028
$355$	47.0775	2.49861
$356$	−3.88345	−0.205822
$357$	14.0876	0.745593
$358$	−12.9974	−0.686936
$359$	−5.01922	−0.264904	−0.132452	−	0.991189i	$-0.542285\pi$
$359$	−5.01922	−0.264904	−0.132452	+	0.991189i	$0.542285\pi$
$360$	10.2426	0.539835
$361$	52.1003	2.74212
$362$	−8.49752	−0.446620
$363$	−1.00000	−0.0524864
$364$	−0.100139	−0.00524870
$365$	−49.6747	−2.60009
$366$	0.942842	0.0492831
$367$	−18.9220	−0.987720	−0.493860	−	0.869541i	$-0.664414\pi$
$367$	−18.9220	−0.987720	−0.493860	+	0.869541i	$0.664414\pi$
$368$	1.43302	0.0747014
$369$	1.61240	0.0839383
$370$	−26.7629	−1.39134
$371$	1.90396	0.0988489
$372$	−7.08846	−0.367520
$373$	−25.5470	−1.32277	−0.661386	−	0.750046i	$-0.730031\pi$
$373$	−25.5470	−1.32277	−0.661386	+	0.750046i	$0.730031\pi$
$374$	7.30453	0.377708
$375$	−7.65998	−0.395560
$376$	−10.8516	−0.559628
$377$	−0.442711	−0.0228008
$378$	1.71444	0.0881811
$379$	−36.9463	−1.89781	−0.948903	−	0.315568i	$-0.897805\pi$
$379$	−36.9463	−1.89781	−0.948903	+	0.315568i	$0.897805\pi$
$380$	32.7141	1.67820
$381$	−16.6435	−0.852675
$382$	6.40641	0.327780
$383$	−2.59368	−0.132531	−0.0662655	−	0.997802i	$-0.521108\pi$
$383$	−2.59368	−0.132531	−0.0662655	+	0.997802i	$0.521108\pi$
$384$	−4.92379	−0.251266
$385$	6.34964	0.323607
$386$	6.41984	0.326761
$387$	1.65032	0.0838905
$388$	−3.22825	−0.163889
$389$	−9.79596	−0.496675	−0.248337	−	0.968674i	$-0.579884\pi$
$389$	−9.79596	−0.496675	−0.248337	+	0.968674i	$0.579884\pi$
$390$	0.163189	0.00826342
$391$	20.4281	1.03309
$392$	−10.8340	−0.547197
$393$	15.0473	0.759037
$394$	−18.8103	−0.947650
$395$	−44.7214	−2.25018
$396$	−1.11105	−0.0558323
$397$	−7.80554	−0.391749	−0.195875	−	0.980629i	$-0.562755\pi$
$397$	−7.80554	−0.391749	−0.195875	+	0.980629i	$0.562755\pi$
$398$	7.04166	0.352966
$399$	15.3327	0.767595
$400$	−3.90954	−0.195477
$401$	30.0943	1.50284	0.751419	−	0.659825i	$-0.229370\pi$
$401$	30.0943	1.50284	0.751419	+	0.659825i	$0.229370\pi$
$402$	−3.29840	−0.164509
$403$	−0.316232	−0.0157526
$404$	−4.46359	−0.222072
$405$	3.49194	0.173516
$406$	15.3128	0.759962
$407$	8.12883	0.402931
$408$	22.7247	1.12504
$409$	2.92991	0.144875	0.0724374	−	0.997373i	$-0.476922\pi$
$409$	2.92991	0.144875	0.0724374	+	0.997373i	$0.476922\pi$
$410$	−5.30858	−0.262172
$411$	−5.65682	−0.279030
$412$	9.28748	0.457561
$413$	−15.7494	−0.774976
$414$	2.48607	0.122184
$415$	−12.3938	−0.608387
$416$	−0.265380	−0.0130113
$417$	−21.1733	−1.03686
$418$	7.95014	0.388854
$419$	8.24319	0.402706	0.201353	−	0.979519i	$-0.435466\pi$
$419$	8.24319	0.402706	0.201353	+	0.979519i	$0.435466\pi$
$420$	7.05476	0.344237
$421$	−0.713317	−0.0347650	−0.0173825	−	0.999849i	$-0.505533\pi$
$421$	−0.713317	−0.0347650	−0.0173825	+	0.999849i	$0.505533\pi$
$422$	−22.5721	−1.09879
$423$	−3.69954	−0.179878
$424$	3.07130	0.149155
$425$	−55.7315	−2.70337
$426$	12.7112	0.615859
$427$	1.81837	0.0879972
$428$	0.487057	0.0235428
$429$	−0.0495663	−0.00239308
$430$	−5.43342	−0.262023
$431$	−38.3428	−1.84691	−0.923453	−	0.383711i	$-0.874646\pi$
$431$	−38.3428	−1.84691	−0.923453	+	0.383711i	$0.874646\pi$
$432$	0.543473	0.0261479
$433$	−3.98585	−0.191548	−0.0957739	−	0.995403i	$-0.530533\pi$
$433$	−3.98585	−0.191548	−0.0957739	+	0.995403i	$0.530533\pi$
$434$	10.9381	0.525044
$435$	31.1889	1.49539
$436$	5.60223	0.268298
$437$	22.2336	1.06358
$438$	−13.4125	−0.640872
$439$	31.2766	1.49275	0.746376	−	0.665524i	$-0.231792\pi$
$439$	31.2766	1.49275	0.746376	+	0.665524i	$0.231792\pi$
$440$	10.2426	0.488299
$441$	−3.69353	−0.175882
$442$	0.362058	0.0172214
$443$	−12.3617	−0.587321	−0.293661	−	0.955910i	$-0.594874\pi$
$443$	−12.3617	−0.587321	−0.293661	+	0.955910i	$0.594874\pi$
$444$	9.03152	0.428617
$445$	12.2054	0.578590
$446$	−10.1980	−0.482891
$447$	−21.2658	−1.00584
$448$	11.1556	0.527055
$449$	2.46911	0.116524	0.0582622	−	0.998301i	$-0.481444\pi$
$449$	2.46911	0.116524	0.0582622	+	0.998301i	$0.481444\pi$
$450$	−6.78245	−0.319728
$451$	1.61240	0.0759250
$452$	−12.6652	−0.595719
$453$	8.05881	0.378636
$454$	24.8011	1.16397
$455$	0.314728	0.0147547
$456$	24.7333	1.15824
$457$	−28.1649	−1.31750	−0.658748	−	0.752364i	$-0.728914\pi$
$457$	−28.1649	−1.31750	−0.658748	+	0.752364i	$0.728914\pi$
$458$	23.4180	1.09425
$459$	7.74735	0.361615
$460$	10.2300	0.476975
$461$	33.1318	1.54310	0.771552	−	0.636167i	$-0.219481\pi$
$461$	33.1318	1.54310	0.771552	+	0.636167i	$0.219481\pi$
$462$	1.71444	0.0797628
$463$	1.89987	0.0882947	0.0441473	−	0.999025i	$-0.485943\pi$
$463$	1.89987	0.0882947	0.0441473	+	0.999025i	$0.485943\pi$
$464$	4.85413	0.225347
$465$	22.2785	1.03314
$466$	−14.3538	−0.664929
$467$	−9.23493	−0.427342	−0.213671	−	0.976906i	$-0.568542\pi$
$467$	−9.23493	−0.427342	−0.213671	+	0.976906i	$0.568542\pi$
$468$	−0.0550706	−0.00254564
$469$	−6.36131	−0.293738
$470$	12.1801	0.561828
$471$	−1.96933	−0.0907420
$472$	−25.4054	−1.16938
$473$	1.65032	0.0758818
$474$	−12.0750	−0.554625
$475$	−60.6573	−2.78315
$476$	15.6520	0.717407
$477$	1.04707	0.0479421
$478$	0.250499	0.0114576
$479$	−27.1839	−1.24207	−0.621033	−	0.783785i	$-0.713287\pi$
$479$	−27.1839	−1.24207	−0.621033	+	0.783785i	$0.713287\pi$
$480$	18.6960	0.853351
$481$	0.402916	0.0183714
$482$	22.4582	1.02295
$483$	4.79465	0.218164
$484$	−1.11105	−0.0505022
$485$	10.1461	0.460711
$486$	0.942842	0.0427682
$487$	−33.9039	−1.53633	−0.768165	−	0.640252i	$-0.778830\pi$
$487$	−33.9039	−1.53633	−0.768165	+	0.640252i	$0.778830\pi$
$488$	2.93323	0.132781
$489$	20.7663	0.939082
$490$	12.1604	0.549349
$491$	6.92051	0.312318	0.156159	−	0.987732i	$-0.450089\pi$
$491$	6.92051	0.312318	0.156159	+	0.987732i	$0.450089\pi$
$492$	1.79146	0.0807651
$493$	69.1969	3.11647
$494$	0.394059	0.0177296
$495$	3.49194	0.156951
$496$	3.46734	0.155688
$497$	24.5149	1.09964
$498$	−3.34639	−0.149955
$499$	25.0512	1.12145	0.560724	−	0.828003i	$-0.310523\pi$
$499$	25.0512	1.12145	0.560724	+	0.828003i	$0.310523\pi$
$500$	−8.51061	−0.380606
$501$	1.21018	0.0540668
$502$	12.1994	0.544487
$503$	−31.2220	−1.39212	−0.696061	−	0.717983i	$-0.745066\pi$
$503$	−31.2220	−1.39212	−0.696061	+	0.717983i	$0.745066\pi$
$504$	5.33370	0.237582
$505$	14.0287	0.624269
$506$	2.48607	0.110519
$507$	12.9975	0.577241
$508$	−18.4918	−0.820441
$509$	−18.6446	−0.826408	−0.413204	−	0.910639i	$-0.635590\pi$
$509$	−18.6446	−0.826408	−0.413204	+	0.910639i	$0.635590\pi$
$510$	−25.5069	−1.12947
$511$	−25.8673	−1.14430
$512$	6.09804	0.269498
$513$	8.43210	0.372286
$514$	13.4148	0.591700
$515$	−29.1898	−1.28626
$516$	1.83359	0.0807191
$517$	−3.69954	−0.162705
$518$	−13.9364	−0.612329
$519$	2.13714	0.0938099
$520$	0.507690	0.0222637
$521$	3.71320	0.162678	0.0813391	−	0.996686i	$-0.474080\pi$
$521$	3.71320	0.162678	0.0813391	+	0.996686i	$0.474080\pi$
$522$	8.42117	0.368584
$523$	−17.0578	−0.745888	−0.372944	−	0.927854i	$-0.621652\pi$
$523$	−17.0578	−0.745888	−0.372944	+	0.927854i	$0.621652\pi$
$524$	16.7183	0.730343
$525$	−13.0807	−0.570887
$526$	−19.9294	−0.868963
$527$	49.4279	2.15311
$528$	0.543473	0.0236516
$529$	−16.0474	−0.697711
$530$	−3.44732	−0.149742
$531$	−8.66125	−0.375866
$532$	17.0354	0.738577
$533$	0.0799208	0.00346175
$534$	3.29552	0.142611
$535$	−1.53078	−0.0661814
$536$	−10.2615	−0.443228
$537$	−13.7854	−0.594883
$538$	1.50884	0.0650508
$539$	−3.69353	−0.159091
$540$	3.87971	0.166956
$541$	−24.3002	−1.04475	−0.522373	−	0.852717i	$-0.674953\pi$
$541$	−24.3002	−1.04475	−0.522373	+	0.852717i	$0.674953\pi$
$542$	22.8959	0.983463
$543$	−9.01267	−0.386771
$544$	41.4797	1.77843
$545$	−17.6074	−0.754216
$546$	0.0849783	0.00363674
$547$	22.6753	0.969525	0.484762	−	0.874646i	$-0.338906\pi$
$547$	22.6753	0.969525	0.484762	+	0.874646i	$0.338906\pi$
$548$	−6.28500	−0.268482
$549$	1.00000	0.0426790
$550$	−6.78245	−0.289205
$551$	75.3129	3.20844
$552$	7.73429	0.329193
$553$	−23.2880	−0.990306
$554$	−4.21166	−0.178936
$555$	−28.3853	−1.20489
$556$	−23.5246	−0.997666
$557$	−13.8294	−0.585972	−0.292986	−	0.956117i	$-0.594649\pi$
$557$	−13.8294	−0.585972	−0.292986	+	0.956117i	$0.594649\pi$
$558$	6.01531	0.254648
$559$	0.0818003	0.00345978
$560$	−3.45086	−0.145825
$561$	7.74735	0.327093
$562$	−10.7043	−0.451533
$563$	−3.01616	−0.127116	−0.0635580	−	0.997978i	$-0.520245\pi$
$563$	−3.01616	−0.127116	−0.0635580	+	0.997978i	$0.520245\pi$
$564$	−4.11036	−0.173078
$565$	39.8056	1.67463
$566$	−3.91557	−0.164584
$567$	1.81837	0.0763644
$568$	39.5451	1.65928
$569$	27.5304	1.15413	0.577067	−	0.816697i	$-0.304197\pi$
$569$	27.5304	1.15413	0.577067	+	0.816697i	$0.304197\pi$
$570$	−27.7614	−1.16280
$571$	−11.8631	−0.496455	−0.248228	−	0.968702i	$-0.579848\pi$
$571$	−11.8631	−0.496455	−0.248228	+	0.968702i	$0.579848\pi$
$572$	−0.0550706	−0.00230262
$573$	6.79478	0.283856
$574$	−2.76436	−0.115382
$575$	−18.9680	−0.791022
$576$	6.13497	0.255624
$577$	36.4041	1.51552	0.757761	−	0.652532i	$-0.226293\pi$
$577$	36.4041	1.51552	0.757761	+	0.652532i	$0.226293\pi$
$578$	−40.5624	−1.68717
$579$	6.80903	0.282974
$580$	34.6524	1.43886
$581$	−6.45387	−0.267752
$582$	2.73951	0.113556
$583$	1.04707	0.0433652
$584$	−41.7268	−1.72667
$585$	0.173082	0.00715608
$586$	−0.174634	−0.00721408
$587$	−30.5450	−1.26073	−0.630365	−	0.776299i	$-0.717095\pi$
$587$	−30.5450	−1.26073	−0.630365	+	0.776299i	$0.717095\pi$
$588$	−4.10369	−0.169233
$589$	53.7966	2.21665
$590$	28.5158	1.17398
$591$	−19.9506	−0.820660
$592$	−4.41780	−0.181570
$593$	−24.2159	−0.994426	−0.497213	−	0.867628i	$-0.665643\pi$
$593$	−24.2159	−0.994426	−0.497213	+	0.867628i	$0.665643\pi$
$594$	0.942842	0.0386853
$595$	−49.1928	−2.01671
$596$	−23.6274	−0.967815
$597$	7.46854	0.305667
$598$	0.123225	0.00503906
$599$	−23.9401	−0.978165	−0.489083	−	0.872237i	$-0.662668\pi$
$599$	−23.9401	−0.978165	−0.489083	+	0.872237i	$0.662668\pi$
$600$	−21.1005	−0.861425
$601$	1.66406	0.0678783	0.0339392	−	0.999424i	$-0.489195\pi$
$601$	1.66406	0.0678783	0.0339392	+	0.999424i	$0.489195\pi$
$602$	−2.82937	−0.115316
$603$	−3.49836	−0.142464
$604$	8.95373	0.364322
$605$	3.49194	0.141967
$606$	3.78783	0.153870
$607$	−7.58111	−0.307708	−0.153854	−	0.988094i	$-0.549169\pi$
$607$	−7.58111	−0.307708	−0.153854	+	0.988094i	$0.549169\pi$
$608$	45.1459	1.83091
$609$	16.2411	0.658123
$610$	−3.29234	−0.133303
$611$	−0.183372	−0.00741845
$612$	8.60768	0.347945
$613$	−25.1894	−1.01739	−0.508695	−	0.860947i	$-0.669872\pi$
$613$	−25.1894	−1.01739	−0.508695	+	0.860947i	$0.669872\pi$
$614$	26.5618	1.07195
$615$	−5.63040	−0.227040
$616$	5.33370	0.214901
$617$	−7.65279	−0.308090	−0.154045	−	0.988064i	$-0.549230\pi$
$617$	−7.65279	−0.308090	−0.154045	+	0.988064i	$0.549230\pi$
$618$	−7.88141	−0.317037
$619$	27.5986	1.10928	0.554640	−	0.832091i	$-0.312856\pi$
$619$	27.5986	1.10928	0.554640	+	0.832091i	$0.312856\pi$
$620$	24.7525	0.994083
$621$	2.63679	0.105811
$622$	−14.8035	−0.593568
$623$	6.35576	0.254638
$624$	0.0269380	0.00107838
$625$	−9.21994	−0.368798
$626$	−6.07758	−0.242909
$627$	8.43210	0.336746
$628$	−2.18802	−0.0873116
$629$	−62.9769	−2.51105
$630$	−5.98670	−0.238516
$631$	12.6174	0.502289	0.251145	−	0.967950i	$-0.419193\pi$
$631$	12.6174	0.502289	0.251145	+	0.967950i	$0.419193\pi$
$632$	−37.5660	−1.49430
$633$	−23.9405	−0.951550
$634$	−13.8424	−0.549750
$635$	58.1182	2.30635
$636$	1.16335	0.0461297
$637$	−0.183074	−0.00725367
$638$	8.42117	0.333397
$639$	13.4818	0.533331
$640$	17.1936	0.679635
$641$	14.1833	0.560205	0.280103	−	0.959970i	$-0.409631\pi$
$641$	14.1833	0.560205	0.280103	+	0.959970i	$0.409631\pi$
$642$	−0.413319	−0.0163124
$643$	3.69437	0.145692	0.0728459	−	0.997343i	$-0.476792\pi$
$643$	3.69437	0.145692	0.0728459	+	0.997343i	$0.476792\pi$
$644$	5.32710	0.209917
$645$	−5.76281	−0.226910
$646$	−61.5925	−2.42332
$647$	46.3072	1.82052	0.910262	−	0.414033i	$-0.135880\pi$
$647$	46.3072	1.82052	0.910262	+	0.414033i	$0.135880\pi$
$648$	2.93323	0.115228
$649$	−8.66125	−0.339984
$650$	−0.336181	−0.0131861
$651$	11.6012	0.454685
$652$	23.0723	0.903582
$653$	7.51510	0.294088	0.147044	−	0.989130i	$-0.453024\pi$
$653$	7.51510	0.294088	0.147044	+	0.989130i	$0.453024\pi$
$654$	−4.75408	−0.185899
$655$	−52.5443	−2.05308
$656$	−0.876297	−0.0342136
$657$	−14.2256	−0.554992
$658$	6.34262	0.247261
$659$	5.51263	0.214742	0.107371	−	0.994219i	$-0.465757\pi$
$659$	5.51263	0.214742	0.107371	+	0.994219i	$0.465757\pi$
$660$	3.87971	0.151018
$661$	4.49436	0.174810	0.0874052	−	0.996173i	$-0.472143\pi$
$661$	4.49436	0.174810	0.0874052	+	0.996173i	$0.472143\pi$
$662$	−31.4053	−1.22060
$663$	0.384007	0.0149136
$664$	−10.4108	−0.404017
$665$	−53.5408	−2.07622
$666$	−7.66420	−0.296982
$667$	23.5509	0.911896
$668$	1.34457	0.0520229
$669$	−10.8163	−0.418181
$670$	11.5178	0.444971
$671$	1.00000	0.0386046
$672$	9.73564	0.375561
$673$	43.6433	1.68233	0.841164	−	0.540781i	$-0.181871\pi$
$673$	43.6433	1.68233	0.841164	+	0.540781i	$0.181871\pi$
$674$	18.8117	0.724599
$675$	−7.19362	−0.276883
$676$	14.4409	0.555419
$677$	33.9134	1.30340	0.651699	−	0.758478i	$-0.274057\pi$
$677$	33.9134	1.30340	0.651699	+	0.758478i	$0.274057\pi$
$678$	10.7477	0.412764
$679$	5.28343	0.202759
$680$	−79.3533	−3.04306
$681$	26.3046	1.00800
$682$	6.01531	0.230338
$683$	24.0834	0.921526	0.460763	−	0.887523i	$-0.347576\pi$
$683$	24.0834	0.921526	0.460763	+	0.887523i	$0.347576\pi$
$684$	9.36848	0.358213
$685$	19.7532	0.754733
$686$	18.3334	0.699972
$687$	24.8377	0.947617
$688$	−0.896904	−0.0341941
$689$	0.0518994	0.00197721
$690$	−8.68121	−0.330488
$691$	11.1661	0.424779	0.212390	−	0.977185i	$-0.431875\pi$
$691$	11.1661	0.424779	0.212390	+	0.977185i	$0.431875\pi$
$692$	2.37446	0.0902635
$693$	1.81837	0.0690742
$694$	−9.59960	−0.364396
$695$	73.9360	2.80455
$696$	26.1987	0.993058
$697$	−12.4918	−0.473162
$698$	−15.9785	−0.604796
$699$	−15.2240	−0.575825
$700$	−14.5333	−0.549306
$701$	43.1498	1.62975	0.814873	−	0.579639i	$-0.196806\pi$
$701$	43.1498	1.62975	0.814873	+	0.579639i	$0.196806\pi$
$702$	0.0467332	0.00176383
$703$	−68.5431	−2.58515
$704$	6.13497	0.231220
$705$	12.9185	0.486541
$706$	−31.9811	−1.20362
$707$	7.30523	0.274741
$708$	−9.62307	−0.361657
$709$	−13.9514	−0.523956	−0.261978	−	0.965074i	$-0.584375\pi$
$709$	−13.9514	−0.523956	−0.261978	+	0.965074i	$0.584375\pi$
$710$	−44.3866	−1.66580
$711$	−12.8071	−0.480302
$712$	10.2525	0.384229
$713$	16.8226	0.630012
$714$	−13.2823	−0.497079
$715$	0.173082	0.00647291
$716$	−15.3162	−0.572395
$717$	0.265685	0.00992219
$718$	4.73233	0.176609
$719$	−46.8731	−1.74807	−0.874036	−	0.485862i	$-0.838506\pi$
$719$	−46.8731	−1.74807	−0.874036	+	0.485862i	$0.838506\pi$
$720$	−1.89777	−0.0707258
$721$	−15.2001	−0.566082
$722$	−49.1224	−1.82815
$723$	23.8197	0.885866
$724$	−10.0135	−0.372149
$725$	−64.2511	−2.38623
$726$	0.942842	0.0349922
$727$	16.2896	0.604148	0.302074	−	0.953285i	$-0.402321\pi$
$727$	16.2896	0.604148	0.302074	+	0.953285i	$0.402321\pi$
$728$	0.264372	0.00979827
$729$	1.00000	0.0370370
$730$	46.8354	1.73346
$731$	−12.7856	−0.472893
$732$	1.11105	0.0410655
$733$	26.3688	0.973953	0.486976	−	0.873415i	$-0.338100\pi$
$733$	26.3688	0.973953	0.486976	+	0.873415i	$0.338100\pi$
$734$	17.8405	0.658503
$735$	12.8976	0.475734
$736$	14.1175	0.520377
$737$	−3.49836	−0.128864
$738$	−1.52024	−0.0559608
$739$	−16.4740	−0.606007	−0.303004	−	0.952989i	$-0.597989\pi$
$739$	−16.4740	−0.606007	−0.303004	+	0.952989i	$0.597989\pi$
$740$	−31.5375	−1.15934
$741$	0.417948	0.0153537
$742$	−1.79514	−0.0659016
$743$	−31.6315	−1.16045	−0.580224	−	0.814457i	$-0.697035\pi$
$743$	−31.6315	−1.16045	−0.580224	+	0.814457i	$0.697035\pi$
$744$	18.7139	0.686086
$745$	74.2589	2.72064
$746$	24.0867	0.881878
$747$	−3.54926	−0.129861
$748$	8.60768	0.314728
$749$	−0.797130	−0.0291265
$750$	7.22215	0.263716
$751$	40.4481	1.47597	0.737986	−	0.674816i	$-0.235777\pi$
$751$	40.4481	1.47597	0.737986	+	0.674816i	$0.235777\pi$
$752$	2.01060	0.0733190
$753$	12.9390	0.471523
$754$	0.417406	0.0152010
$755$	−28.1408	−1.02415
$756$	2.02030	0.0734776
$757$	−10.5609	−0.383841	−0.191921	−	0.981410i	$-0.561472\pi$
$757$	−10.5609	−0.383841	−0.191921	+	0.981410i	$0.561472\pi$
$758$	34.8346	1.26525
$759$	2.63679	0.0957092
$760$	−86.3670	−3.13286
$761$	−21.2871	−0.771655	−0.385828	−	0.922571i	$-0.626084\pi$
$761$	−21.2871	−0.771655	−0.385828	+	0.922571i	$0.626084\pi$
$762$	15.6922	0.568470
$763$	−9.16875	−0.331931
$764$	7.54934	0.273125
$765$	−27.0532	−0.978112
$766$	2.44543	0.0883571
$767$	−0.429306	−0.0155014
$768$	16.9123	0.610270
$769$	15.1444	0.546120	0.273060	−	0.961997i	$-0.411964\pi$
$769$	15.1444	0.546120	0.273060	+	0.961997i	$0.411964\pi$
$770$	−5.98670	−0.215746
$771$	14.2280	0.512409
$772$	7.56516	0.272276
$773$	14.6618	0.527348	0.263674	−	0.964612i	$-0.415066\pi$
$773$	14.6618	0.527348	0.263674	+	0.964612i	$0.415066\pi$
$774$	−1.55599	−0.0559289
$775$	−45.8951	−1.64860
$776$	8.52274	0.305949
$777$	−14.7812	−0.530274
$778$	9.23604	0.331128
$779$	−13.5959	−0.487125
$780$	0.192303	0.00688555
$781$	13.4818	0.482416
$782$	−19.2605	−0.688753
$783$	8.93168	0.319192
$784$	2.00733	0.0716904
$785$	6.87678	0.245443
$786$	−14.1873	−0.506043
$787$	−44.7202	−1.59410	−0.797052	−	0.603910i	$-0.793608\pi$
$787$	−44.7202	−1.59410	−0.797052	+	0.603910i	$0.793608\pi$
$788$	−22.1661	−0.789636
$789$	−21.1376	−0.752517
$790$	42.1652	1.50017
$791$	20.7281	0.737007
$792$	2.93323	0.104228
$793$	0.0495663	0.00176015
$794$	7.35940	0.261175
$795$	−3.65631	−0.129676
$796$	8.29792	0.294112
$797$	−42.3541	−1.50026	−0.750130	−	0.661290i	$-0.770009\pi$
$797$	−42.3541	−1.50026	−0.750130	+	0.661290i	$0.770009\pi$
$798$	−14.4563	−0.511748
$799$	28.6616	1.01397
$800$	−38.5150	−1.36171
$801$	3.49530	0.123500
$802$	−28.3742	−1.00193
$803$	−14.2256	−0.502009
$804$	−3.88684	−0.137078
$805$	−16.7426	−0.590100
$806$	0.298157	0.0105021
$807$	1.60031	0.0563337
$808$	11.7841	0.414564
$809$	19.8867	0.699180	0.349590	−	0.936903i	$-0.386321\pi$
$809$	19.8867	0.699180	0.349590	+	0.936903i	$0.386321\pi$
$810$	−3.29234	−0.115681
$811$	−12.7950	−0.449292	−0.224646	−	0.974440i	$-0.572123\pi$
$811$	−12.7950	−0.449292	−0.224646	+	0.974440i	$0.572123\pi$
$812$	18.0447	0.633244
$813$	24.2839	0.851674
$814$	−7.66420	−0.268630
$815$	−72.5144	−2.54007
$816$	−4.21047	−0.147396
$817$	−13.9157	−0.486847
$818$	−2.76244	−0.0965866
$819$	0.0901300	0.00314940
$820$	−6.25565	−0.218457
$821$	−19.3033	−0.673690	−0.336845	−	0.941560i	$-0.609360\pi$
$821$	−19.3033	−0.673690	−0.336845	+	0.941560i	$0.609360\pi$
$822$	5.33349	0.186027
$823$	−21.2555	−0.740921	−0.370460	−	0.928848i	$-0.620800\pi$
$823$	−21.2555	−0.740921	−0.370460	+	0.928848i	$0.620800\pi$
$824$	−24.5194	−0.854175
$825$	−7.19362	−0.250450
$826$	14.8492	0.516669
$827$	−5.50486	−0.191423	−0.0957114	−	0.995409i	$-0.530513\pi$
$827$	−5.50486	−0.191423	−0.0957114	+	0.995409i	$0.530513\pi$
$828$	2.92960	0.101811
$829$	32.6065	1.13247	0.566235	−	0.824244i	$-0.308400\pi$
$829$	32.6065	1.13247	0.566235	+	0.824244i	$0.308400\pi$
$830$	11.6854	0.405605
$831$	−4.46699	−0.154958
$832$	0.304088	0.0105423
$833$	28.6150	0.991452
$834$	19.9631	0.691266
$835$	−4.22587	−0.146242
$836$	9.36848	0.324016
$837$	6.37998	0.220524
$838$	−7.77203	−0.268480
$839$	10.2087	0.352443	0.176221	−	0.984351i	$-0.443613\pi$
$839$	10.2087	0.352443	0.176221	+	0.984351i	$0.443613\pi$
$840$	−18.6249	−0.642621
$841$	50.7750	1.75086
$842$	0.672546	0.0231775
$843$	−11.3532	−0.391025
$844$	−26.5991	−0.915578
$845$	−45.3866	−1.56135
$846$	3.48808	0.119923
$847$	1.81837	0.0624800
$848$	−0.569055	−0.0195414
$849$	−4.15294	−0.142529
$850$	52.5460	1.80231
$851$	−21.4340	−0.734747
$852$	14.9789	0.513169
$853$	−40.7415	−1.39496	−0.697481	−	0.716603i	$-0.745696\pi$
$853$	−40.7415	−1.39496	−0.697481	+	0.716603i	$0.745696\pi$
$854$	−1.71444	−0.0586668
$855$	−29.4444	−1.00698
$856$	−1.28586	−0.0439496
$857$	41.4107	1.41456	0.707282	−	0.706932i	$-0.249921\pi$
$857$	41.4107	1.41456	0.707282	+	0.706932i	$0.249921\pi$
$858$	0.0467332	0.00159545
$859$	18.5889	0.634244	0.317122	−	0.948385i	$-0.397284\pi$
$859$	18.5889	0.634244	0.317122	+	0.948385i	$0.397284\pi$
$860$	−6.40276	−0.218332
$861$	−2.93195	−0.0999204
$862$	36.1512	1.23131
$863$	−30.9600	−1.05389	−0.526946	−	0.849899i	$-0.676663\pi$
$863$	−30.9600	−1.05389	−0.526946	+	0.849899i	$0.676663\pi$
$864$	5.35405	0.182148
$865$	−7.46274	−0.253741
$866$	3.75803	0.127703
$867$	−43.0214	−1.46108
$868$	12.8895	0.437497
$869$	−12.8071	−0.434450
$870$	−29.4062	−0.996963
$871$	−0.173401	−0.00587545
$872$	−14.7902	−0.500859
$873$	2.90558	0.0983391
$874$	−20.9628	−0.709078
$875$	13.9287	0.470875
$876$	−15.8053	−0.534011
$877$	21.9728	0.741969	0.370985	−	0.928639i	$-0.379020\pi$
$877$	21.9728	0.741969	0.370985	+	0.928639i	$0.379020\pi$
$878$	−29.4889	−0.995204
$879$	−0.185221	−0.00624736
$880$	−1.89777	−0.0639739
$881$	−2.24572	−0.0756602	−0.0378301	−	0.999284i	$-0.512045\pi$
$881$	−2.24572	−0.0756602	−0.0378301	+	0.999284i	$0.512045\pi$
$882$	3.48241	0.117259
$883$	−17.8354	−0.600208	−0.300104	−	0.953907i	$-0.597021\pi$
$883$	−17.8354	−0.600208	−0.300104	+	0.953907i	$0.597021\pi$
$884$	0.426651	0.0143498
$885$	30.2445	1.01666
$886$	11.6551	0.391561
$887$	−3.58048	−0.120221	−0.0601103	−	0.998192i	$-0.519145\pi$
$887$	−3.58048	−0.120221	−0.0601103	+	0.998192i	$0.519145\pi$
$888$	−23.8437	−0.800142
$889$	30.2641	1.01503
$890$	−11.5077	−0.385740
$891$	1.00000	0.0335013
$892$	−12.0174	−0.402372
$893$	31.1949	1.04390
$894$	20.0503	0.670583
$895$	48.1377	1.60907
$896$	8.95328	0.299108
$897$	0.130696	0.00436380
$898$	−2.32798	−0.0776857
$899$	56.9839	1.90052
$900$	−7.99246	−0.266415
$901$	−8.11202	−0.270251
$902$	−1.52024	−0.0506185
$903$	−3.00089	−0.0998635
$904$	33.4367	1.11209
$905$	31.4717	1.04615
$906$	−7.59818	−0.252433
$907$	−5.73095	−0.190293	−0.0951465	−	0.995463i	$-0.530332\pi$
$907$	−5.73095	−0.190293	−0.0951465	+	0.995463i	$0.530332\pi$
$908$	29.2257	0.969890
$909$	4.01746	0.133251
$910$	−0.296739	−0.00983680
$911$	−8.76057	−0.290251	−0.145125	−	0.989413i	$-0.546359\pi$
$911$	−8.76057	−0.290251	−0.145125	+	0.989413i	$0.546359\pi$
$912$	−4.58262	−0.151746
$913$	−3.54926	−0.117463
$914$	26.5550	0.878362
$915$	−3.49194	−0.115440
$916$	27.5959	0.911794
$917$	−27.3616	−0.903561
$918$	−7.30453	−0.241085
$919$	−43.6126	−1.43865	−0.719323	−	0.694676i	$-0.755548\pi$
$919$	−43.6126	−1.43865	−0.719323	+	0.694676i	$0.755548\pi$
$920$	−27.0077	−0.890416
$921$	28.1720	0.928300
$922$	−31.2381	−1.02877
$923$	0.668242	0.0219954
$924$	2.02030	0.0664630
$925$	58.4757	1.92267
$926$	−1.79128	−0.0588652
$927$	−8.35920	−0.274552
$928$	47.8206	1.56979
$929$	16.3467	0.536317	0.268159	−	0.963375i	$-0.413585\pi$
$929$	16.3467	0.536317	0.268159	+	0.963375i	$0.413585\pi$
$930$	−21.0051	−0.688784
$931$	31.1442	1.02071
$932$	−16.9146	−0.554057
$933$	−15.7010	−0.514027
$934$	8.70708	0.284904
$935$	−27.0532	−0.884736
$936$	0.145389	0.00475220
$937$	22.0142	0.719171	0.359586	−	0.933112i	$-0.382918\pi$
$937$	22.0142	0.719171	0.359586	+	0.933112i	$0.382918\pi$
$938$	5.99771	0.195832
$939$	−6.44602	−0.210358
$940$	14.3531	0.468148
$941$	−40.6955	−1.32663	−0.663317	−	0.748338i	$-0.730852\pi$
$941$	−40.6955	−1.32663	−0.663317	+	0.748338i	$0.730852\pi$
$942$	1.85677	0.0604968
$943$	−4.25156	−0.138450
$944$	4.70716	0.153205
$945$	−6.34964	−0.206554
$946$	−1.55599	−0.0505896
$947$	−6.43989	−0.209268	−0.104634	−	0.994511i	$-0.533367\pi$
$947$	−6.43989	−0.209268	−0.104634	+	0.994511i	$0.533367\pi$
$948$	−14.2293	−0.462145
$949$	−0.705108	−0.0228888
$950$	57.1903	1.85550
$951$	−14.6815	−0.476081
$952$	−41.3220	−1.33925
$953$	−8.62127	−0.279270	−0.139635	−	0.990203i	$-0.544593\pi$
$953$	−8.62127	−0.279270	−0.139635	+	0.990203i	$0.544593\pi$
$954$	−0.987223	−0.0319625
$955$	−23.7270	−0.767786
$956$	0.295189	0.00954710
$957$	8.93168	0.288720
$958$	25.6301	0.828073
$959$	10.2862	0.332159
$960$	−21.4229	−0.691421
$961$	9.70408	0.313035
$962$	−0.379886	−0.0122480
$963$	−0.438376	−0.0141265
$964$	26.4649	0.852377
$965$	−23.7767	−0.765399
$966$	−4.52060	−0.145448
$967$	−10.5897	−0.340541	−0.170270	−	0.985397i	$-0.554464\pi$
$967$	−10.5897	−0.340541	−0.170270	+	0.985397i	$0.554464\pi$
$968$	2.93323	0.0942775
$969$	−65.3264	−2.09859
$970$	−9.56618	−0.307152
$971$	−34.3252	−1.10155	−0.550774	−	0.834654i	$-0.685667\pi$
$971$	−34.3252	−1.10155	−0.550774	+	0.834654i	$0.685667\pi$
$972$	1.11105	0.0356369
$973$	38.5010	1.23429
$974$	31.9660	1.02426
$975$	−0.356561	−0.0114191
$976$	−0.543473	−0.0173961
$977$	−21.8729	−0.699775	−0.349887	−	0.936792i	$-0.613780\pi$
$977$	−21.8729	−0.699775	−0.349887	+	0.936792i	$0.613780\pi$
$978$	−19.5793	−0.626077
$979$	3.49530	0.111710
$980$	14.3298	0.457749
$981$	−5.04229	−0.160988
$982$	−6.52495	−0.208220
$983$	−20.9511	−0.668236	−0.334118	−	0.942531i	$-0.608438\pi$
$983$	−20.9511	−0.668236	−0.334118	+	0.942531i	$0.608438\pi$
$984$	−4.72954	−0.150772
$985$	69.6664	2.21976
$986$	−65.2417	−2.07772
$987$	6.72713	0.214127
$988$	0.464361	0.0147733
$989$	−4.35154	−0.138371
$990$	−3.29234	−0.104638
$991$	30.6419	0.973373	0.486687	−	0.873577i	$-0.338205\pi$
$991$	30.6419	0.973373	0.486687	+	0.873577i	$0.338205\pi$
$992$	34.1587	1.08454
$993$	−33.3092	−1.05704
$994$	−23.1136	−0.733120
$995$	−26.0797	−0.826781
$996$	−3.94340	−0.124951
$997$	−47.6634	−1.50951	−0.754757	−	0.656004i	$-0.772245\pi$
$997$	−47.6634	−1.50951	−0.754757	+	0.656004i	$0.772245\pi$
$998$	−23.6194	−0.747658
$999$	−8.12883	−0.257185

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.b.1.5	✓	11
3.2	odd	2		6039.2.a.c.1.7		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.b.1.5	✓	11	1.1	even	1	trivial
6039.2.a.c.1.7		11	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.942842 q^{2} -1.00000 q^{3} -1.11105 q^{4} +3.49194 q^{5} +0.942842 q^{6} +1.81837 q^{7} +2.93323 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.942842 q^{2} -1.00000 q^{3} -1.11105 q^{4} +3.49194 q^{5} +0.942842 q^{6} +1.81837 q^{7} +2.93323 q^{8} +1.00000 q^{9} -3.29234 q^{10} +1.00000 q^{11} +1.11105 q^{12} +0.0495663 q^{13} -1.71444 q^{14} -3.49194 q^{15} -0.543473 q^{16} -7.74735 q^{17} -0.942842 q^{18} -8.43210 q^{19} -3.87971 q^{20} -1.81837 q^{21} -0.942842 q^{22} -2.63679 q^{23} -2.93323 q^{24} +7.19362 q^{25} -0.0467332 q^{26} -1.00000 q^{27} -2.02030 q^{28} -8.93168 q^{29} +3.29234 q^{30} -6.37998 q^{31} -5.35405 q^{32} -1.00000 q^{33} +7.30453 q^{34} +6.34964 q^{35} -1.11105 q^{36} +8.12883 q^{37} +7.95014 q^{38} -0.0495663 q^{39} +10.2426 q^{40} +1.61240 q^{41} +1.71444 q^{42} +1.65032 q^{43} -1.11105 q^{44} +3.49194 q^{45} +2.48607 q^{46} -3.69954 q^{47} +0.543473 q^{48} -3.69353 q^{49} -6.78245 q^{50} +7.74735 q^{51} -0.0550706 q^{52} +1.04707 q^{53} +0.942842 q^{54} +3.49194 q^{55} +5.33370 q^{56} +8.43210 q^{57} +8.42117 q^{58} -8.66125 q^{59} +3.87971 q^{60} +1.00000 q^{61} +6.01531 q^{62} +1.81837 q^{63} +6.13497 q^{64} +0.173082 q^{65} +0.942842 q^{66} -3.49836 q^{67} +8.60768 q^{68} +2.63679 q^{69} -5.98670 q^{70} +13.4818 q^{71} +2.93323 q^{72} -14.2256 q^{73} -7.66420 q^{74} -7.19362 q^{75} +9.36848 q^{76} +1.81837 q^{77} +0.0467332 q^{78} -12.8071 q^{79} -1.89777 q^{80} +1.00000 q^{81} -1.52024 q^{82} -3.54926 q^{83} +2.02030 q^{84} -27.0532 q^{85} -1.55599 q^{86} +8.93168 q^{87} +2.93323 q^{88} +3.49530 q^{89} -3.29234 q^{90} +0.0901300 q^{91} +2.92960 q^{92} +6.37998 q^{93} +3.48808 q^{94} -29.4444 q^{95} +5.35405 q^{96} +2.90558 q^{97} +3.48241 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 2 q^{2} - 11 q^{3} + 10 q^{4} - q^{5} + 2 q^{6} - 11 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) \) 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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