LMFDB - Embedded newform 273.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(1,273)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, 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("273.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.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:	$2.17991597518$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.34292$ of defining polynomial
Character	$\chi$	$=$	273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.34292 q^{2} -1.00000 q^{3} -0.196558 q^{4} -3.48929 q^{5} -1.34292 q^{6} -1.00000 q^{7} -2.94981 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.34292 q^{2} -1.00000 q^{3} -0.196558 q^{4} -3.48929 q^{5} -1.34292 q^{6} -1.00000 q^{7} -2.94981 q^{8} +1.00000 q^{9} -4.68585 q^{10} +0.292731 q^{11} +0.196558 q^{12} -1.00000 q^{13} -1.34292 q^{14} +3.48929 q^{15} -3.56825 q^{16} -6.68585 q^{17} +1.34292 q^{18} +4.17513 q^{19} +0.685846 q^{20} +1.00000 q^{21} +0.393115 q^{22} -0.510711 q^{23} +2.94981 q^{24} +7.17513 q^{25} -1.34292 q^{26} -1.00000 q^{27} +0.196558 q^{28} +6.17513 q^{29} +4.68585 q^{30} -5.78202 q^{31} +1.10773 q^{32} -0.292731 q^{33} -8.97858 q^{34} +3.48929 q^{35} -0.196558 q^{36} -0.978577 q^{37} +5.60688 q^{38} +1.00000 q^{39} +10.2927 q^{40} +0.685846 q^{41} +1.34292 q^{42} +1.19656 q^{43} -0.0575385 q^{44} -3.48929 q^{45} -0.685846 q^{46} -7.19656 q^{47} +3.56825 q^{48} +1.00000 q^{49} +9.63565 q^{50} +6.68585 q^{51} +0.196558 q^{52} -13.1537 q^{53} -1.34292 q^{54} -1.02142 q^{55} +2.94981 q^{56} -4.17513 q^{57} +8.29273 q^{58} -8.97858 q^{59} -0.685846 q^{60} +11.3717 q^{61} -7.76481 q^{62} -1.00000 q^{63} +8.62410 q^{64} +3.48929 q^{65} -0.393115 q^{66} -12.3503 q^{67} +1.31415 q^{68} +0.510711 q^{69} +4.68585 q^{70} -7.27131 q^{71} -2.94981 q^{72} +6.76060 q^{73} -1.31415 q^{74} -7.17513 q^{75} -0.820654 q^{76} -0.292731 q^{77} +1.34292 q^{78} -2.80344 q^{79} +12.4507 q^{80} +1.00000 q^{81} +0.921039 q^{82} +6.17513 q^{83} -0.196558 q^{84} +23.3288 q^{85} +1.60688 q^{86} -6.17513 q^{87} -0.863500 q^{88} -9.88240 q^{89} -4.68585 q^{90} +1.00000 q^{91} +0.100384 q^{92} +5.78202 q^{93} -9.66442 q^{94} -14.5682 q^{95} -1.10773 q^{96} -2.61110 q^{97} +1.34292 q^{98} +0.292731 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} - 3 q^{3} + 4 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 - 3 * q^3 + 4 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 12 * q^8 + 3 * q^9	\( 3 q - 2 q^{2} - 3 q^{3} + 4 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 12 q^{8} + 3 q^{9} - 2 q^{10} - 2 q^{11} - 4 q^{12} - 3 q^{13} + 2 q^{14} + 3 q^{15} + 18 q^{16} - 8 q^{17} - 2 q^{18} - 7 q^{19} - 10 q^{20} + 3 q^{21} - 8 q^{22} - 9 q^{23} + 12 q^{24} + 2 q^{25} + 2 q^{26} - 3 q^{27} - 4 q^{28} - q^{29} + 2 q^{30} - 7 q^{31} - 36 q^{32} + 2 q^{33} - 12 q^{34} + 3 q^{35} + 4 q^{36} + 12 q^{37} + 26 q^{38} + 3 q^{39} + 28 q^{40} - 10 q^{41} - 2 q^{42} - q^{43} + 36 q^{44} - 3 q^{45} + 10 q^{46} - 17 q^{47} - 18 q^{48} + 3 q^{49} + 20 q^{50} + 8 q^{51} - 4 q^{52} - 5 q^{53} + 2 q^{54} - 18 q^{55} + 12 q^{56} + 7 q^{57} + 22 q^{58} - 12 q^{59} + 10 q^{60} + 10 q^{61} + 10 q^{62} - 3 q^{63} + 58 q^{64} + 3 q^{65} + 8 q^{66} + 2 q^{67} + 16 q^{68} + 9 q^{69} + 2 q^{70} - 4 q^{71} - 12 q^{72} - 5 q^{73} - 16 q^{74} - 2 q^{75} - 30 q^{76} + 2 q^{77} - 2 q^{78} - 13 q^{79} - 8 q^{80} + 3 q^{81} + 24 q^{82} - q^{83} + 4 q^{84} + 16 q^{85} + 14 q^{86} + q^{87} - 60 q^{88} - 13 q^{89} - 2 q^{90} + 3 q^{91} - 6 q^{92} + 7 q^{93} - 2 q^{94} - 15 q^{95} + 36 q^{96} - 9 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - 3 * q^3 + 4 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 12 * q^8 + 3 * q^9 - 2 * q^10 - 2 * q^11 - 4 * q^12 - 3 * q^13 + 2 * q^14 + 3 * q^15 + 18 * q^16 - 8 * q^17 - 2 * q^18 - 7 * q^19 - 10 * q^20 + 3 * q^21 - 8 * q^22 - 9 * q^23 + 12 * q^24 + 2 * q^25 + 2 * q^26 - 3 * q^27 - 4 * q^28 - q^29 + 2 * q^30 - 7 * q^31 - 36 * q^32 + 2 * q^33 - 12 * q^34 + 3 * q^35 + 4 * q^36 + 12 * q^37 + 26 * q^38 + 3 * q^39 + 28 * q^40 - 10 * q^41 - 2 * q^42 - q^43 + 36 * q^44 - 3 * q^45 + 10 * q^46 - 17 * q^47 - 18 * q^48 + 3 * q^49 + 20 * q^50 + 8 * q^51 - 4 * q^52 - 5 * q^53 + 2 * q^54 - 18 * q^55 + 12 * q^56 + 7 * q^57 + 22 * q^58 - 12 * q^59 + 10 * q^60 + 10 * q^61 + 10 * q^62 - 3 * q^63 + 58 * q^64 + 3 * q^65 + 8 * q^66 + 2 * q^67 + 16 * q^68 + 9 * q^69 + 2 * q^70 - 4 * q^71 - 12 * q^72 - 5 * q^73 - 16 * q^74 - 2 * q^75 - 30 * q^76 + 2 * q^77 - 2 * q^78 - 13 * q^79 - 8 * q^80 + 3 * q^81 + 24 * q^82 - q^83 + 4 * q^84 + 16 * q^85 + 14 * q^86 + q^87 - 60 * q^88 - 13 * q^89 - 2 * q^90 + 3 * q^91 - 6 * q^92 + 7 * q^93 - 2 * q^94 - 15 * q^95 + 36 * q^96 - 9 * q^97 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.34292	0.949590	0.474795	−	0.880096i	$-0.342522\pi$
$2$	1.34292	0.949590	0.474795	+	0.880096i	$0.342522\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.196558	−0.0982788
$5$	−3.48929	−1.56046	−0.780229	−	0.625494i	$-0.784897\pi$
$5$	−3.48929	−1.56046	−0.780229	+	0.625494i	$0.784897\pi$
$6$	−1.34292	−0.548246
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.94981	−1.04291
$9$	1.00000	0.333333
$10$	−4.68585	−1.48179
$11$	0.292731	0.0882617	0.0441309	−	0.999026i	$-0.485948\pi$
$11$	0.292731	0.0882617	0.0441309	+	0.999026i	$0.485948\pi$
$12$	0.196558	0.0567413
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.34292	−0.358911
$15$	3.48929	0.900930
$16$	−3.56825	−0.892062
$17$	−6.68585	−1.62156	−0.810778	−	0.585354i	$-0.800956\pi$
$17$	−6.68585	−1.62156	−0.810778	+	0.585354i	$0.800956\pi$
$18$	1.34292	0.316530
$19$	4.17513	0.957842	0.478921	−	0.877858i	$-0.341028\pi$
$19$	4.17513	0.957842	0.478921	+	0.877858i	$0.341028\pi$
$20$	0.685846	0.153360
$21$	1.00000	0.218218
$22$	0.393115	0.0838124
$23$	−0.510711	−0.106491	−0.0532453	−	0.998581i	$-0.516957\pi$
$23$	−0.510711	−0.106491	−0.0532453	+	0.998581i	$0.516957\pi$
$24$	2.94981	0.602127
$25$	7.17513	1.43503
$26$	−1.34292	−0.263369
$27$	−1.00000	−0.192450
$28$	0.196558	0.0371459
$29$	6.17513	1.14669	0.573347	−	0.819313i	$-0.305645\pi$
$29$	6.17513	1.14669	0.573347	+	0.819313i	$0.305645\pi$
$30$	4.68585	0.855515
$31$	−5.78202	−1.03848	−0.519241	−	0.854628i	$-0.673785\pi$
$31$	−5.78202	−1.03848	−0.519241	+	0.854628i	$0.673785\pi$
$32$	1.10773	0.195821
$33$	−0.292731	−0.0509579
$34$	−8.97858	−1.53981
$35$	3.48929	0.589797
$36$	−0.196558	−0.0327596
$37$	−0.978577	−0.160877	−0.0804385	−	0.996760i	$-0.525632\pi$
$37$	−0.978577	−0.160877	−0.0804385	+	0.996760i	$0.525632\pi$
$38$	5.60688	0.909557
$39$	1.00000	0.160128
$40$	10.2927	1.62742
$41$	0.685846	0.107111	0.0535556	−	0.998565i	$-0.482945\pi$
$41$	0.685846	0.107111	0.0535556	+	0.998565i	$0.482945\pi$
$42$	1.34292	0.207218
$43$	1.19656	0.182473	0.0912367	−	0.995829i	$-0.470918\pi$
$43$	1.19656	0.182473	0.0912367	+	0.995829i	$0.470918\pi$
$44$	−0.0575385	−0.00867425
$45$	−3.48929	−0.520152
$46$	−0.685846	−0.101123
$47$	−7.19656	−1.04973	−0.524863	−	0.851187i	$-0.675883\pi$
$47$	−7.19656	−1.04973	−0.524863	+	0.851187i	$0.675883\pi$
$48$	3.56825	0.515033
$49$	1.00000	0.142857
$50$	9.63565	1.36269
$51$	6.68585	0.936206
$52$	0.196558	0.0272576
$53$	−13.1537	−1.80680	−0.903401	−	0.428797i	$-0.858937\pi$
$53$	−13.1537	−1.80680	−0.903401	+	0.428797i	$0.858937\pi$
$54$	−1.34292	−0.182749
$55$	−1.02142	−0.137729
$56$	2.94981	0.394185
$57$	−4.17513	−0.553010
$58$	8.29273	1.08889
$59$	−8.97858	−1.16891	−0.584456	−	0.811426i	$-0.698692\pi$
$59$	−8.97858	−1.16891	−0.584456	+	0.811426i	$0.698692\pi$
$60$	−0.685846	−0.0885424
$61$	11.3717	1.45600	0.727998	−	0.685579i	$-0.240451\pi$
$61$	11.3717	1.45600	0.727998	+	0.685579i	$0.240451\pi$
$62$	−7.76481	−0.986132
$63$	−1.00000	−0.125988
$64$	8.62410	1.07801
$65$	3.48929	0.432793
$66$	−0.393115	−0.0483891
$67$	−12.3503	−1.50883	−0.754413	−	0.656400i	$-0.772078\pi$
$67$	−12.3503	−1.50883	−0.754413	+	0.656400i	$0.772078\pi$
$68$	1.31415	0.159365
$69$	0.510711	0.0614824
$70$	4.68585	0.560066
$71$	−7.27131	−0.862946	−0.431473	−	0.902126i	$-0.642006\pi$
$71$	−7.27131	−0.862946	−0.431473	+	0.902126i	$0.642006\pi$
$72$	−2.94981	−0.347638
$73$	6.76060	0.791268	0.395634	−	0.918408i	$-0.370525\pi$
$73$	6.76060	0.791268	0.395634	+	0.918408i	$0.370525\pi$
$74$	−1.31415	−0.152767
$75$	−7.17513	−0.828513
$76$	−0.820654	−0.0941355
$77$	−0.292731	−0.0333598
$78$	1.34292	0.152056
$79$	−2.80344	−0.315412	−0.157706	−	0.987486i	$-0.550410\pi$
$79$	−2.80344	−0.315412	−0.157706	+	0.987486i	$0.550410\pi$
$80$	12.4507	1.39203
$81$	1.00000	0.111111
$82$	0.921039	0.101712
$83$	6.17513	0.677809	0.338905	−	0.940821i	$-0.389944\pi$
$83$	6.17513	0.677809	0.338905	+	0.940821i	$0.389944\pi$
$84$	−0.196558	−0.0214462
$85$	23.3288	2.53037
$86$	1.60688	0.173275
$87$	−6.17513	−0.662044
$88$	−0.863500	−0.0920494
$89$	−9.88240	−1.04753	−0.523766	−	0.851862i	$-0.675474\pi$
$89$	−9.88240	−1.04753	−0.523766	+	0.851862i	$0.675474\pi$
$90$	−4.68585	−0.493932
$91$	1.00000	0.104828
$92$	0.100384	0.0104658
$93$	5.78202	0.599567
$94$	−9.66442	−0.996809
$95$	−14.5682	−1.49467
$96$	−1.10773	−0.113057
$97$	−2.61110	−0.265117	−0.132558	−	0.991175i	$-0.542319\pi$
$97$	−2.61110	−0.265117	−0.132558	+	0.991175i	$0.542319\pi$
$98$	1.34292	0.135656
$99$	0.292731	0.0294206
$100$	−1.41033	−0.141033
$101$	−15.0361	−1.49615	−0.748075	−	0.663615i	$-0.769022\pi$
$101$	−15.0361	−1.49615	−0.748075	+	0.663615i	$0.769022\pi$
$102$	8.97858	0.889012
$103$	4.78623	0.471601	0.235801	−	0.971801i	$-0.424229\pi$
$103$	4.78623	0.471601	0.235801	+	0.971801i	$0.424229\pi$
$104$	2.94981	0.289252
$105$	−3.48929	−0.340520
$106$	−17.6644	−1.71572
$107$	−1.70727	−0.165048	−0.0825240	−	0.996589i	$-0.526298\pi$
$107$	−1.70727	−0.165048	−0.0825240	+	0.996589i	$0.526298\pi$
$108$	0.196558	0.0189138
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	−1.37169	−0.130786
$111$	0.978577	0.0928824
$112$	3.56825	0.337168
$113$	20.5682	1.93490	0.967449	−	0.253066i	$-0.0814389\pi$
$113$	20.5682	1.93490	0.967449	+	0.253066i	$0.0814389\pi$
$114$	−5.60688	−0.525133
$115$	1.78202	0.166174
$116$	−1.21377	−0.112696
$117$	−1.00000	−0.0924500
$118$	−12.0575	−1.10999
$119$	6.68585	0.612891
$120$	−10.2927	−0.939593
$121$	−10.9143	−0.992210
$122$	15.2713	1.38260
$123$	−0.685846	−0.0618407
$124$	1.13650	0.102061
$125$	−7.58967	−0.678841
$126$	−1.34292	−0.119637
$127$	−17.3717	−1.54149	−0.770744	−	0.637145i	$-0.780115\pi$
$127$	−17.3717	−1.54149	−0.770744	+	0.637145i	$0.780115\pi$
$128$	9.36604	0.827849
$129$	−1.19656	−0.105351
$130$	4.68585	0.410976
$131$	18.7434	1.63762	0.818809	−	0.574067i	$-0.194635\pi$
$131$	18.7434	1.63762	0.818809	+	0.574067i	$0.194635\pi$
$132$	0.0575385	0.00500808
$133$	−4.17513	−0.362030
$134$	−16.5855	−1.43277
$135$	3.48929	0.300310
$136$	19.7220	1.69114
$137$	−3.41454	−0.291724	−0.145862	−	0.989305i	$-0.546595\pi$
$137$	−3.41454	−0.291724	−0.145862	+	0.989305i	$0.546595\pi$
$138$	0.685846	0.0583831
$139$	15.5640	1.32012	0.660062	−	0.751211i	$-0.270530\pi$
$139$	15.5640	1.32012	0.660062	+	0.751211i	$0.270530\pi$
$140$	−0.685846	−0.0579646
$141$	7.19656	0.606059
$142$	−9.76481	−0.819444
$143$	−0.292731	−0.0244794
$144$	−3.56825	−0.297354
$145$	−21.5468	−1.78937
$146$	9.07896	0.751380
$147$	−1.00000	−0.0824786
$148$	0.192347	0.0158108
$149$	−5.02142	−0.411371	−0.205685	−	0.978618i	$-0.565942\pi$
$149$	−5.02142	−0.411371	−0.205685	+	0.978618i	$0.565942\pi$
$150$	−9.63565	−0.786748
$151$	−8.58546	−0.698675	−0.349337	−	0.936997i	$-0.613593\pi$
$151$	−8.58546	−0.698675	−0.349337	+	0.936997i	$0.613593\pi$
$152$	−12.3158	−0.998947
$153$	−6.68585	−0.540519
$154$	−0.393115	−0.0316781
$155$	20.1751	1.62051
$156$	−0.196558	−0.0157372
$157$	20.3074	1.62071	0.810354	−	0.585940i	$-0.199275\pi$
$157$	20.3074	1.62071	0.810354	+	0.585940i	$0.199275\pi$
$158$	−3.76481	−0.299512
$159$	13.1537	1.04316
$160$	−3.86519	−0.305570
$161$	0.510711	0.0402497
$162$	1.34292	0.105510
$163$	−17.3717	−1.36066	−0.680328	−	0.732908i	$-0.738163\pi$
$163$	−17.3717	−1.36066	−0.680328	+	0.732908i	$0.738163\pi$
$164$	−0.134808	−0.0105268
$165$	1.02142	0.0795177
$166$	8.29273	0.643641
$167$	−23.5468	−1.82211	−0.911054	−	0.412287i	$-0.864730\pi$
$167$	−23.5468	−1.82211	−0.911054	+	0.412287i	$0.864730\pi$
$168$	−2.94981	−0.227583
$169$	1.00000	0.0769231
$170$	31.3288	2.40281
$171$	4.17513	0.319281
$172$	−0.235192	−0.0179333
$173$	18.0147	1.36963	0.684816	−	0.728716i	$-0.259883\pi$
$173$	18.0147	1.36963	0.684816	+	0.728716i	$0.259883\pi$
$174$	−8.29273	−0.628670
$175$	−7.17513	−0.542389
$176$	−1.04454	−0.0787350
$177$	8.97858	0.674871
$178$	−13.2713	−0.994727
$179$	2.70306	0.202036	0.101018	−	0.994885i	$-0.467790\pi$
$179$	2.70306	0.202036	0.101018	+	0.994885i	$0.467790\pi$
$180$	0.685846	0.0511200
$181$	−23.2860	−1.73083	−0.865417	−	0.501052i	$-0.832947\pi$
$181$	−23.2860	−1.73083	−0.865417	+	0.501052i	$0.832947\pi$
$182$	1.34292	0.0995441
$183$	−11.3717	−0.840620
$184$	1.50650	0.111061
$185$	3.41454	0.251042
$186$	7.76481	0.569343
$187$	−1.95715	−0.143121
$188$	1.41454	0.103166
$189$	1.00000	0.0727393
$190$	−19.5640	−1.41932
$191$	−7.66442	−0.554578	−0.277289	−	0.960787i	$-0.589436\pi$
$191$	−7.66442	−0.554578	−0.277289	+	0.960787i	$0.589436\pi$
$192$	−8.62410	−0.622391
$193$	19.3717	1.39440	0.697202	−	0.716874i	$-0.254428\pi$
$193$	19.3717	1.39440	0.697202	+	0.716874i	$0.254428\pi$
$194$	−3.50650	−0.251752
$195$	−3.48929	−0.249873
$196$	−0.196558	−0.0140398
$197$	1.02142	0.0727734	0.0363867	−	0.999338i	$-0.488415\pi$
$197$	1.02142	0.0727734	0.0363867	+	0.999338i	$0.488415\pi$
$198$	0.393115	0.0279375
$199$	−12.5855	−0.892160	−0.446080	−	0.894993i	$-0.647180\pi$
$199$	−12.5855	−0.892160	−0.446080	+	0.894993i	$0.647180\pi$
$200$	−21.1653	−1.49661
$201$	12.3503	0.871121
$202$	−20.1923	−1.42073
$203$	−6.17513	−0.433409
$204$	−1.31415	−0.0920092
$205$	−2.39312	−0.167142
$206$	6.42754	0.447828
$207$	−0.510711	−0.0354969
$208$	3.56825	0.247414
$209$	1.22219	0.0845407
$210$	−4.68585	−0.323354
$211$	−9.34606	−0.643409	−0.321705	−	0.946840i	$-0.604256\pi$
$211$	−9.34606	−0.643409	−0.321705	+	0.946840i	$0.604256\pi$
$212$	2.58546	0.177570
$213$	7.27131	0.498222
$214$	−2.29273	−0.156728
$215$	−4.17513	−0.284742
$216$	2.94981	0.200709
$217$	5.78202	0.392509
$218$	13.4292	0.909542
$219$	−6.76060	−0.456839
$220$	0.200768	0.0135358
$221$	6.68585	0.449739
$222$	1.31415	0.0882002
$223$	−26.9185	−1.80260	−0.901299	−	0.433198i	$-0.857385\pi$
$223$	−26.9185	−1.80260	−0.901299	+	0.433198i	$0.857385\pi$
$224$	−1.10773	−0.0740134
$225$	7.17513	0.478342
$226$	27.6216	1.83736
$227$	15.7220	1.04350	0.521752	−	0.853097i	$-0.325279\pi$
$227$	15.7220	1.04350	0.521752	+	0.853097i	$0.325279\pi$
$228$	0.820654	0.0543492
$229$	11.3717	0.751463	0.375731	−	0.926729i	$-0.377392\pi$
$229$	11.3717	0.751463	0.375731	+	0.926729i	$0.377392\pi$
$230$	2.39312	0.157797
$231$	0.292731	0.0192603
$232$	−18.2155	−1.19590
$233$	6.76060	0.442901	0.221451	−	0.975172i	$-0.428921\pi$
$233$	6.76060	0.442901	0.221451	+	0.975172i	$0.428921\pi$
$234$	−1.34292	−0.0877896
$235$	25.1109	1.63805
$236$	1.76481	0.114879
$237$	2.80344	0.182103
$238$	8.97858	0.581995
$239$	−10.6858	−0.691210	−0.345605	−	0.938380i	$-0.612326\pi$
$239$	−10.6858	−0.691210	−0.345605	+	0.938380i	$0.612326\pi$
$240$	−12.4507	−0.803686
$241$	8.80344	0.567080	0.283540	−	0.958960i	$-0.408491\pi$
$241$	8.80344	0.567080	0.283540	+	0.958960i	$0.408491\pi$
$242$	−14.6571	−0.942193
$243$	−1.00000	−0.0641500
$244$	−2.23519	−0.143094
$245$	−3.48929	−0.222922
$246$	−0.921039	−0.0587233
$247$	−4.17513	−0.265657
$248$	17.0558	1.08305
$249$	−6.17513	−0.391333
$250$	−10.1923	−0.644621
$251$	27.7648	1.75250	0.876250	−	0.481858i	$-0.160038\pi$
$251$	27.7648	1.75250	0.876250	+	0.481858i	$0.160038\pi$
$252$	0.196558	0.0123820
$253$	−0.149501	−0.00939905
$254$	−23.3288	−1.46378
$255$	−23.3288	−1.46091
$256$	−4.67033	−0.291895
$257$	−4.87819	−0.304293	−0.152147	−	0.988358i	$-0.548619\pi$
$257$	−4.87819	−0.304293	−0.152147	+	0.988358i	$0.548619\pi$
$258$	−1.60688	−0.100040
$259$	0.978577	0.0608058
$260$	−0.685846	−0.0425344
$261$	6.17513	0.382231
$262$	25.1709	1.55506
$263$	20.6258	1.27184	0.635920	−	0.771755i	$-0.280621\pi$
$263$	20.6258	1.27184	0.635920	+	0.771755i	$0.280621\pi$
$264$	0.863500	0.0531448
$265$	45.8971	2.81944
$266$	−5.60688	−0.343780
$267$	9.88240	0.604793
$268$	2.42754	0.148286
$269$	24.6430	1.50251	0.751255	−	0.660012i	$-0.229449\pi$
$269$	24.6430	1.50251	0.751255	+	0.660012i	$0.229449\pi$
$270$	4.68585	0.285172
$271$	1.17092	0.0711286	0.0355643	−	0.999367i	$-0.488677\pi$
$271$	1.17092	0.0711286	0.0355643	+	0.999367i	$0.488677\pi$
$272$	23.8568	1.44653
$273$	−1.00000	−0.0605228
$274$	−4.58546	−0.277018
$275$	2.10038	0.126658
$276$	−0.100384	−0.00604242
$277$	15.7820	0.948250	0.474125	−	0.880458i	$-0.342765\pi$
$277$	15.7820	0.948250	0.474125	+	0.880458i	$0.342765\pi$
$278$	20.9013	1.25358
$279$	−5.78202	−0.346160
$280$	−10.2927	−0.615108
$281$	16.1495	0.963398	0.481699	−	0.876337i	$-0.340020\pi$
$281$	16.1495	0.963398	0.481699	+	0.876337i	$0.340020\pi$
$282$	9.66442	0.575508
$283$	−12.2008	−0.725260	−0.362630	−	0.931933i	$-0.618121\pi$
$283$	−12.2008	−0.725260	−0.362630	+	0.931933i	$0.618121\pi$
$284$	1.42923	0.0848092
$285$	14.5682	0.862949
$286$	−0.393115	−0.0232454
$287$	−0.685846	−0.0404842
$288$	1.10773	0.0652737
$289$	27.7005	1.62944
$290$	−28.9357	−1.69916
$291$	2.61110	0.153065
$292$	−1.32885	−0.0777649
$293$	20.6258	1.20497	0.602486	−	0.798130i	$-0.294177\pi$
$293$	20.6258	1.20497	0.602486	+	0.798130i	$0.294177\pi$
$294$	−1.34292	−0.0783209
$295$	31.3288	1.82404
$296$	2.88661	0.167781
$297$	−0.292731	−0.0169860
$298$	−6.74338	−0.390634
$299$	0.510711	0.0295352
$300$	1.41033	0.0814253
$301$	−1.19656	−0.0689684
$302$	−11.5296	−0.663455
$303$	15.0361	0.863802
$304$	−14.8979	−0.854455
$305$	−39.6791	−2.27202
$306$	−8.97858	−0.513271
$307$	2.56825	0.146578	0.0732889	−	0.997311i	$-0.476650\pi$
$307$	2.56825	0.146578	0.0732889	+	0.997311i	$0.476650\pi$
$308$	0.0575385	0.00327856
$309$	−4.78623	−0.272279
$310$	27.0937	1.53882
$311$	−10.9786	−0.622538	−0.311269	−	0.950322i	$-0.600754\pi$
$311$	−10.9786	−0.622538	−0.311269	+	0.950322i	$0.600754\pi$
$312$	−2.94981	−0.167000
$313$	−27.3717	−1.54714	−0.773570	−	0.633711i	$-0.781531\pi$
$313$	−27.3717	−1.54714	−0.773570	+	0.633711i	$0.781531\pi$
$314$	27.2713	1.53901
$315$	3.48929	0.196599
$316$	0.551038	0.0309983
$317$	−34.0722	−1.91369	−0.956844	−	0.290603i	$-0.906144\pi$
$317$	−34.0722	−1.91369	−0.956844	+	0.290603i	$0.906144\pi$
$318$	17.6644	0.990572
$319$	1.80765	0.101209
$320$	−30.0920	−1.68219
$321$	1.70727	0.0952905
$322$	0.685846	0.0382207
$323$	−27.9143	−1.55319
$324$	−0.196558	−0.0109199
$325$	−7.17513	−0.398005
$326$	−23.3288	−1.29207
$327$	−10.0000	−0.553001
$328$	−2.02311	−0.111708
$329$	7.19656	0.396759
$330$	1.37169	0.0755092
$331$	2.77781	0.152682	0.0763411	−	0.997082i	$-0.475676\pi$
$331$	2.77781	0.152682	0.0763411	+	0.997082i	$0.475676\pi$
$332$	−1.21377	−0.0666143
$333$	−0.978577	−0.0536257
$334$	−31.6216	−1.73026
$335$	43.0937	2.35446
$336$	−3.56825	−0.194664
$337$	−8.21798	−0.447662	−0.223831	−	0.974628i	$-0.571856\pi$
$337$	−8.21798	−0.447662	−0.223831	+	0.974628i	$0.571856\pi$
$338$	1.34292	0.0730454
$339$	−20.5682	−1.11711
$340$	−4.58546	−0.248682
$341$	−1.69258	−0.0916581
$342$	5.60688	0.303186
$343$	−1.00000	−0.0539949
$344$	−3.52962	−0.190304
$345$	−1.78202	−0.0959407
$346$	24.1923	1.30059
$347$	−5.03612	−0.270353	−0.135176	−	0.990822i	$-0.543160\pi$
$347$	−5.03612	−0.270353	−0.135176	+	0.990822i	$0.543160\pi$
$348$	1.21377	0.0650649
$349$	2.84629	0.152358	0.0761792	−	0.997094i	$-0.475728\pi$
$349$	2.84629	0.152358	0.0761792	+	0.997094i	$0.475728\pi$
$350$	−9.63565	−0.515047
$351$	1.00000	0.0533761
$352$	0.324267	0.0172835
$353$	11.2285	0.597631	0.298815	−	0.954311i	$-0.403409\pi$
$353$	11.2285	0.597631	0.298815	+	0.954311i	$0.403409\pi$
$354$	12.0575	0.640851
$355$	25.3717	1.34659
$356$	1.94246	0.102950
$357$	−6.68585	−0.353853
$358$	3.63000	0.191851
$359$	−25.3142	−1.33603	−0.668015	−	0.744148i	$-0.732856\pi$
$359$	−25.3142	−1.33603	−0.668015	+	0.744148i	$0.732856\pi$
$360$	10.2927	0.542475
$361$	−1.56825	−0.0825395
$362$	−31.2713	−1.64358
$363$	10.9143	0.572853
$364$	−0.196558	−0.0103024
$365$	−23.5897	−1.23474
$366$	−15.2713	−0.798244
$367$	−14.9786	−0.781875	−0.390938	−	0.920417i	$-0.627849\pi$
$367$	−14.9786	−0.781875	−0.390938	+	0.920417i	$0.627849\pi$
$368$	1.82235	0.0949964
$369$	0.685846	0.0357037
$370$	4.58546	0.238387
$371$	13.1537	0.682907
$372$	−1.13650	−0.0589248
$373$	−31.8715	−1.65024	−0.825121	−	0.564956i	$-0.808893\pi$
$373$	−31.8715	−1.65024	−0.825121	+	0.564956i	$0.808893\pi$
$374$	−2.62831	−0.135907
$375$	7.58967	0.391929
$376$	21.2285	1.09477
$377$	−6.17513	−0.318036
$378$	1.34292	0.0690725
$379$	−1.02142	−0.0524670	−0.0262335	−	0.999656i	$-0.508351\pi$
$379$	−1.02142	−0.0524670	−0.0262335	+	0.999656i	$0.508351\pi$
$380$	2.86350	0.146894
$381$	17.3717	0.889979
$382$	−10.2927	−0.526622
$383$	19.5212	0.997486	0.498743	−	0.866750i	$-0.333795\pi$
$383$	19.5212	0.997486	0.498743	+	0.866750i	$0.333795\pi$
$384$	−9.36604	−0.477959
$385$	1.02142	0.0520565
$386$	26.0147	1.32411
$387$	1.19656	0.0608244
$388$	0.513231	0.0260553
$389$	17.9143	0.908292	0.454146	−	0.890927i	$-0.349945\pi$
$389$	17.9143	0.908292	0.454146	+	0.890927i	$0.349945\pi$
$390$	−4.68585	−0.237277
$391$	3.41454	0.172681
$392$	−2.94981	−0.148988
$393$	−18.7434	−0.945479
$394$	1.37169	0.0691049
$395$	9.78202	0.492187
$396$	−0.0575385	−0.00289142
$397$	−35.3116	−1.77224	−0.886120	−	0.463456i	$-0.846609\pi$
$397$	−35.3116	−1.77224	−0.886120	+	0.463456i	$0.846609\pi$
$398$	−16.9013	−0.847186
$399$	4.17513	0.209018
$400$	−25.6027	−1.28013
$401$	−29.3717	−1.46675	−0.733376	−	0.679823i	$-0.762057\pi$
$401$	−29.3717	−1.46675	−0.733376	+	0.679823i	$0.762057\pi$
$402$	16.5855	0.827208
$403$	5.78202	0.288023
$404$	2.95546	0.147040
$405$	−3.48929	−0.173384
$406$	−8.29273	−0.411561
$407$	−0.286460	−0.0141993
$408$	−19.7220	−0.976383
$409$	−25.7392	−1.27272	−0.636360	−	0.771392i	$-0.719561\pi$
$409$	−25.7392	−1.27272	−0.636360	+	0.771392i	$0.719561\pi$
$410$	−3.21377	−0.158717
$411$	3.41454	0.168427
$412$	−0.940770	−0.0463484
$413$	8.97858	0.441807
$414$	−0.685846	−0.0337075
$415$	−21.5468	−1.05769
$416$	−1.10773	−0.0543110
$417$	−15.5640	−0.762174
$418$	1.64131	0.0802790
$419$	−18.8929	−0.922978	−0.461489	−	0.887146i	$-0.652685\pi$
$419$	−18.8929	−0.922978	−0.461489	+	0.887146i	$0.652685\pi$
$420$	0.685846	0.0334659
$421$	2.14950	0.104760	0.0523801	−	0.998627i	$-0.483319\pi$
$421$	2.14950	0.104760	0.0523801	+	0.998627i	$0.483319\pi$
$422$	−12.5510	−0.610975
$423$	−7.19656	−0.349909
$424$	38.8009	1.88434
$425$	−47.9718	−2.32698
$426$	9.76481	0.473106
$427$	−11.3717	−0.550315
$428$	0.335577	0.0162207
$429$	0.292731	0.0141332
$430$	−5.60688	−0.270388
$431$	−11.6216	−0.559792	−0.279896	−	0.960030i	$-0.590300\pi$
$431$	−11.6216	−0.559792	−0.279896	+	0.960030i	$0.590300\pi$
$432$	3.56825	0.171678
$433$	4.97858	0.239255	0.119628	−	0.992819i	$-0.461830\pi$
$433$	4.97858	0.239255	0.119628	+	0.992819i	$0.461830\pi$
$434$	7.76481	0.372723
$435$	21.5468	1.03309
$436$	−1.96558	−0.0941340
$437$	−2.13229	−0.102001
$438$	−9.07896	−0.433810
$439$	36.9357	1.76285	0.881423	−	0.472327i	$-0.156586\pi$
$439$	36.9357	1.76285	0.881423	+	0.472327i	$0.156586\pi$
$440$	3.01300	0.143639
$441$	1.00000	0.0476190
$442$	8.97858	0.427067
$443$	−10.4679	−0.497343	−0.248672	−	0.968588i	$-0.579994\pi$
$443$	−10.4679	−0.497343	−0.248672	+	0.968588i	$0.579994\pi$
$444$	−0.192347	−0.00912837
$445$	34.4826	1.63463
$446$	−36.1495	−1.71173
$447$	5.02142	0.237505
$448$	−8.62410	−0.407450
$449$	−15.9143	−0.751043	−0.375521	−	0.926814i	$-0.622536\pi$
$449$	−15.9143	−0.751043	−0.375521	+	0.926814i	$0.622536\pi$
$450$	9.63565	0.454229
$451$	0.200768	0.00945382
$452$	−4.04285	−0.190159
$453$	8.58546	0.403380
$454$	21.1134	0.990900
$455$	−3.48929	−0.163580
$456$	12.3158	0.576742
$457$	8.39312	0.392613	0.196307	−	0.980543i	$-0.437105\pi$
$457$	8.39312	0.392613	0.196307	+	0.980543i	$0.437105\pi$
$458$	15.2713	0.713581
$459$	6.68585	0.312069
$460$	−0.350269	−0.0163314
$461$	−10.7287	−0.499685	−0.249842	−	0.968286i	$-0.580379\pi$
$461$	−10.7287	−0.499685	−0.249842	+	0.968286i	$0.580379\pi$
$462$	0.393115	0.0182894
$463$	−13.6069	−0.632366	−0.316183	−	0.948698i	$-0.602401\pi$
$463$	−13.6069	−0.632366	−0.316183	+	0.948698i	$0.602401\pi$
$464$	−22.0344	−1.02292
$465$	−20.1751	−0.935599
$466$	9.07896	0.420575
$467$	12.2352	0.566177	0.283089	−	0.959094i	$-0.408641\pi$
$467$	12.2352	0.566177	0.283089	+	0.959094i	$0.408641\pi$
$468$	0.196558	0.00908588
$469$	12.3503	0.570282
$470$	33.7220	1.55548
$471$	−20.3074	−0.935717
$472$	26.4851	1.21907
$473$	0.350269	0.0161054
$474$	3.76481	0.172923
$475$	29.9572	1.37453
$476$	−1.31415	−0.0602341
$477$	−13.1537	−0.602267
$478$	−14.3503	−0.656366
$479$	−33.5040	−1.53084	−0.765418	−	0.643533i	$-0.777468\pi$
$479$	−33.5040	−1.53084	−0.765418	+	0.643533i	$0.777468\pi$
$480$	3.86519	0.176421
$481$	0.978577	0.0446193
$482$	11.8223	0.538493
$483$	−0.510711	−0.0232382
$484$	2.14529	0.0975132
$485$	9.11087	0.413703
$486$	−1.34292	−0.0609162
$487$	−10.9786	−0.497487	−0.248743	−	0.968569i	$-0.580018\pi$
$487$	−10.9786	−0.497487	−0.248743	+	0.968569i	$0.580018\pi$
$488$	−33.5443	−1.51848
$489$	17.3717	0.785575
$490$	−4.68585	−0.211685
$491$	−1.03612	−0.0467592	−0.0233796	−	0.999727i	$-0.507443\pi$
$491$	−1.03612	−0.0467592	−0.0233796	+	0.999727i	$0.507443\pi$
$492$	0.134808	0.00607763
$493$	−41.2860	−1.85943
$494$	−5.60688	−0.252266
$495$	−1.02142	−0.0459095
$496$	20.6317	0.926390
$497$	7.27131	0.326163
$498$	−8.29273	−0.371606
$499$	13.1709	0.589612	0.294806	−	0.955557i	$-0.404745\pi$
$499$	13.1709	0.589612	0.294806	+	0.955557i	$0.404745\pi$
$500$	1.49181	0.0667157
$501$	23.5468	1.05199
$502$	37.2860	1.66416
$503$	−12.3503	−0.550671	−0.275336	−	0.961348i	$-0.588789\pi$
$503$	−12.3503	−0.550671	−0.275336	+	0.961348i	$0.588789\pi$
$504$	2.94981	0.131395
$505$	52.4653	2.33468
$506$	−0.200768	−0.00892524
$507$	−1.00000	−0.0444116
$508$	3.41454	0.151496
$509$	−11.4893	−0.509254	−0.254627	−	0.967039i	$-0.581953\pi$
$509$	−11.4893	−0.509254	−0.254627	+	0.967039i	$0.581953\pi$
$510$	−31.3288	−1.38726
$511$	−6.76060	−0.299071
$512$	−25.0040	−1.10503
$513$	−4.17513	−0.184337
$514$	−6.55104	−0.288954
$515$	−16.7005	−0.735914
$516$	0.235192	0.0103538
$517$	−2.10666	−0.0926506
$518$	1.31415	0.0577406
$519$	−18.0147	−0.790757
$520$	−10.2927	−0.451366
$521$	22.0147	0.964481	0.482241	−	0.876039i	$-0.339823\pi$
$521$	22.0147	0.964481	0.482241	+	0.876039i	$0.339823\pi$
$522$	8.29273	0.362963
$523$	−20.3503	−0.889855	−0.444928	−	0.895567i	$-0.646771\pi$
$523$	−20.3503	−0.889855	−0.444928	+	0.895567i	$0.646771\pi$
$524$	−3.68415	−0.160943
$525$	7.17513	0.313149
$526$	27.6988	1.20773
$527$	38.6577	1.68396
$528$	1.04454	0.0454577
$529$	−22.7392	−0.988660
$530$	61.6363	2.67731
$531$	−8.97858	−0.389637
$532$	0.820654	0.0355799
$533$	−0.685846	−0.0297073
$534$	13.2713	0.574306
$535$	5.95715	0.257550
$536$	36.4309	1.57358
$537$	−2.70306	−0.116646
$538$	33.0937	1.42677
$539$	0.292731	0.0126088
$540$	−0.685846	−0.0295141
$541$	−4.97858	−0.214046	−0.107023	−	0.994257i	$-0.534132\pi$
$541$	−4.97858	−0.214046	−0.107023	+	0.994257i	$0.534132\pi$
$542$	1.57246	0.0675430
$543$	23.2860	0.999298
$544$	−7.40612	−0.317535
$545$	−34.8929	−1.49465
$546$	−1.34292	−0.0574718
$547$	−32.5254	−1.39069	−0.695343	−	0.718678i	$-0.744748\pi$
$547$	−32.5254	−1.39069	−0.695343	+	0.718678i	$0.744748\pi$
$548$	0.671153	0.0286703
$549$	11.3717	0.485332
$550$	2.82065	0.120273
$551$	25.7820	1.09835
$552$	−1.50650	−0.0641209
$553$	2.80344	0.119214
$554$	21.1940	0.900448
$555$	−3.41454	−0.144939
$556$	−3.05923	−0.129740
$557$	17.7564	0.752362	0.376181	−	0.926546i	$-0.377237\pi$
$557$	17.7564	0.752362	0.376181	+	0.926546i	$0.377237\pi$
$558$	−7.76481	−0.328711
$559$	−1.19656	−0.0506090
$560$	−12.4507	−0.526136
$561$	1.95715	0.0826311
$562$	21.6875	0.914834
$563$	−34.1579	−1.43958	−0.719792	−	0.694189i	$-0.755763\pi$
$563$	−34.1579	−1.43958	−0.719792	+	0.694189i	$0.755763\pi$
$564$	−1.41454	−0.0595628
$565$	−71.7686	−3.01933
$566$	−16.3847	−0.688700
$567$	−1.00000	−0.0419961
$568$	21.4490	0.899978
$569$	4.41875	0.185244	0.0926218	−	0.995701i	$-0.470475\pi$
$569$	4.41875	0.185244	0.0926218	+	0.995701i	$0.470475\pi$
$570$	19.5640	0.819447
$571$	19.9399	0.834461	0.417230	−	0.908801i	$-0.363001\pi$
$571$	19.9399	0.834461	0.417230	+	0.908801i	$0.363001\pi$
$572$	0.0575385	0.00240581
$573$	7.66442	0.320186
$574$	−0.921039	−0.0384434
$575$	−3.66442	−0.152817
$576$	8.62410	0.359337
$577$	−23.1709	−0.964618	−0.482309	−	0.876001i	$-0.660202\pi$
$577$	−23.1709	−0.964618	−0.482309	+	0.876001i	$0.660202\pi$
$578$	37.1997	1.54730
$579$	−19.3717	−0.805060
$580$	4.23519	0.175857
$581$	−6.17513	−0.256188
$582$	3.50650	0.145349
$583$	−3.85050	−0.159471
$584$	−19.9425	−0.825225
$585$	3.48929	0.144264
$586$	27.6988	1.14423
$587$	26.7606	1.10453	0.552264	−	0.833669i	$-0.313764\pi$
$587$	26.7606	1.10453	0.552264	+	0.833669i	$0.313764\pi$
$588$	0.196558	0.00810590
$589$	−24.1407	−0.994701
$590$	42.0722	1.73209
$591$	−1.02142	−0.0420157
$592$	3.49181	0.143512
$593$	−11.6044	−0.476534	−0.238267	−	0.971200i	$-0.576579\pi$
$593$	−11.6044	−0.476534	−0.238267	+	0.971200i	$0.576579\pi$
$594$	−0.393115	−0.0161297
$595$	−23.3288	−0.956389
$596$	0.986999	0.0404290
$597$	12.5855	0.515089
$598$	0.685846	0.0280463
$599$	42.7324	1.74600	0.873000	−	0.487720i	$-0.162171\pi$
$599$	42.7324	1.74600	0.873000	+	0.487720i	$0.162171\pi$
$600$	21.1653	0.864068
$601$	11.7564	0.479553	0.239776	−	0.970828i	$-0.422926\pi$
$601$	11.7564	0.479553	0.239776	+	0.970828i	$0.422926\pi$
$602$	−1.60688	−0.0654917
$603$	−12.3503	−0.502942
$604$	1.68754	0.0686649
$605$	38.0832	1.54830
$606$	20.1923	0.820258
$607$	26.8929	1.09155	0.545774	−	0.837932i	$-0.316236\pi$
$607$	26.8929	1.09155	0.545774	+	0.837932i	$0.316236\pi$
$608$	4.62492	0.187565
$609$	6.17513	0.250229
$610$	−53.2860	−2.15749
$611$	7.19656	0.291142
$612$	1.31415	0.0531215
$613$	−4.39312	−0.177436	−0.0887181	−	0.996057i	$-0.528277\pi$
$613$	−4.39312	−0.177436	−0.0887181	+	0.996057i	$0.528277\pi$
$614$	3.44896	0.139189
$615$	2.39312	0.0964997
$616$	0.863500	0.0347914
$617$	28.9357	1.16491	0.582454	−	0.812863i	$-0.302092\pi$
$617$	28.9357	1.16491	0.582454	+	0.812863i	$0.302092\pi$
$618$	−6.42754	−0.258554
$619$	25.4868	1.02440	0.512200	−	0.858866i	$-0.328831\pi$
$619$	25.4868	1.02440	0.512200	+	0.858866i	$0.328831\pi$
$620$	−3.96558	−0.159261
$621$	0.510711	0.0204941
$622$	−14.7434	−0.591156
$623$	9.88240	0.395930
$624$	−3.56825	−0.142844
$625$	−9.39312	−0.375725
$626$	−36.7581	−1.46915
$627$	−1.22219	−0.0488096
$628$	−3.99158	−0.159281
$629$	6.54262	0.260871
$630$	4.68585	0.186689
$631$	42.5082	1.69222	0.846112	−	0.533005i	$-0.178937\pi$
$631$	42.5082	1.69222	0.846112	+	0.533005i	$0.178937\pi$
$632$	8.26962	0.328948
$633$	9.34606	0.371472
$634$	−45.7564	−1.81722
$635$	60.6148	2.40543
$636$	−2.58546	−0.102520
$637$	−1.00000	−0.0396214
$638$	2.42754	0.0961072
$639$	−7.27131	−0.287649
$640$	−32.6808	−1.29182
$641$	−7.93152	−0.313276	−0.156638	−	0.987656i	$-0.550066\pi$
$641$	−7.93152	−0.313276	−0.156638	+	0.987656i	$0.550066\pi$
$642$	2.29273	0.0904869
$643$	−17.9572	−0.708161	−0.354081	−	0.935215i	$-0.615206\pi$
$643$	−17.9572	−0.708161	−0.354081	+	0.935215i	$0.615206\pi$
$644$	−0.100384	−0.00395569
$645$	4.17513	0.164396
$646$	−37.4868	−1.47490
$647$	13.8077	0.542835	0.271417	−	0.962462i	$-0.412508\pi$
$647$	13.8077	0.542835	0.271417	+	0.962462i	$0.412508\pi$
$648$	−2.94981	−0.115879
$649$	−2.62831	−0.103170
$650$	−9.63565	−0.377941
$651$	−5.78202	−0.226615
$652$	3.41454	0.133724
$653$	−23.1709	−0.906748	−0.453374	−	0.891320i	$-0.649780\pi$
$653$	−23.1709	−0.906748	−0.453374	+	0.891320i	$0.649780\pi$
$654$	−13.4292	−0.525124
$655$	−65.4011	−2.55543
$656$	−2.44727	−0.0955499
$657$	6.76060	0.263756
$658$	9.66442	0.376758
$659$	21.2969	0.829611	0.414806	−	0.909910i	$-0.363850\pi$
$659$	21.2969	0.829611	0.414806	+	0.909910i	$0.363850\pi$
$660$	−0.200768	−0.00781490
$661$	−39.0252	−1.51790	−0.758952	−	0.651147i	$-0.774288\pi$
$661$	−39.0252	−1.51790	−0.758952	+	0.651147i	$0.774288\pi$
$662$	3.73038	0.144985
$663$	−6.68585	−0.259657
$664$	−18.2155	−0.706897
$665$	14.5682	0.564933
$666$	−1.31415	−0.0509224
$667$	−3.15371	−0.122112
$668$	4.62831	0.179075
$669$	26.9185	1.04073
$670$	57.8715	2.23577
$671$	3.32885	0.128509
$672$	1.10773	0.0427316
$673$	11.3116	0.436031	0.218016	−	0.975945i	$-0.430042\pi$
$673$	11.3116	0.436031	0.218016	+	0.975945i	$0.430042\pi$
$674$	−11.0361	−0.425095
$675$	−7.17513	−0.276171
$676$	−0.196558	−0.00755991
$677$	−17.4637	−0.671183	−0.335591	−	0.942008i	$-0.608936\pi$
$677$	−17.4637	−0.671183	−0.335591	+	0.942008i	$0.608936\pi$
$678$	−27.6216	−1.06080
$679$	2.61110	0.100205
$680$	−68.8156	−2.63896
$681$	−15.7220	−0.602467
$682$	−2.27300	−0.0870377
$683$	4.92946	0.188621	0.0943103	−	0.995543i	$-0.469935\pi$
$683$	4.92946	0.188621	0.0943103	+	0.995543i	$0.469935\pi$
$684$	−0.820654	−0.0313785
$685$	11.9143	0.455222
$686$	−1.34292	−0.0512730
$687$	−11.3717	−0.433857
$688$	−4.26962	−0.162778
$689$	13.1537	0.501117
$690$	−2.39312	−0.0911043
$691$	−34.0466	−1.29519	−0.647597	−	0.761983i	$-0.724226\pi$
$691$	−34.0466	−1.29519	−0.647597	+	0.761983i	$0.724226\pi$
$692$	−3.54092	−0.134606
$693$	−0.292731	−0.0111199
$694$	−6.76312	−0.256724
$695$	−54.3074	−2.06000
$696$	18.2155	0.690455
$697$	−4.58546	−0.173687
$698$	3.82235	0.144678
$699$	−6.76060	−0.255709
$700$	1.41033	0.0533054
$701$	−4.60267	−0.173841	−0.0869203	−	0.996215i	$-0.527703\pi$
$701$	−4.60267	−0.173841	−0.0869203	+	0.996215i	$0.527703\pi$
$702$	1.34292	0.0506854
$703$	−4.08569	−0.154095
$704$	2.52454	0.0951472
$705$	−25.1109	−0.945730
$706$	15.0790	0.567504
$707$	15.0361	0.565491
$708$	−1.76481	−0.0663255
$709$	36.7434	1.37993	0.689963	−	0.723844i	$-0.257627\pi$
$709$	36.7434	1.37993	0.689963	+	0.723844i	$0.257627\pi$
$710$	34.0722	1.27871
$711$	−2.80344	−0.105137
$712$	29.1512	1.09249
$713$	2.95294	0.110589
$714$	−8.97858	−0.336015
$715$	1.02142	0.0381990
$716$	−0.531307	−0.0198559
$717$	10.6858	0.399070
$718$	−33.9950	−1.26868
$719$	−2.30742	−0.0860524	−0.0430262	−	0.999074i	$-0.513700\pi$
$719$	−2.30742	−0.0860524	−0.0430262	+	0.999074i	$0.513700\pi$
$720$	12.4507	0.464008
$721$	−4.78623	−0.178249
$722$	−2.10604	−0.0783787
$723$	−8.80344	−0.327404
$724$	4.57704	0.170104
$725$	44.3074	1.64554
$726$	14.6571	0.543975
$727$	−23.1793	−0.859674	−0.429837	−	0.902906i	$-0.641429\pi$
$727$	−23.1793	−0.859674	−0.429837	+	0.902906i	$0.641429\pi$
$728$	−2.94981	−0.109327
$729$	1.00000	0.0370370
$730$	−31.6791	−1.17250
$731$	−8.00000	−0.295891
$732$	2.23519	0.0826151
$733$	−11.1966	−0.413554	−0.206777	−	0.978388i	$-0.566298\pi$
$733$	−11.1966	−0.413554	−0.206777	+	0.978388i	$0.566298\pi$
$734$	−20.1151	−0.742461
$735$	3.48929	0.128704
$736$	−0.565731	−0.0208531
$737$	−3.61531	−0.133172
$738$	0.921039	0.0339039
$739$	7.96558	0.293018	0.146509	−	0.989209i	$-0.453196\pi$
$739$	7.96558	0.293018	0.146509	+	0.989209i	$0.453196\pi$
$740$	−0.671153	−0.0246721
$741$	4.17513	0.153377
$742$	17.6644	0.648481
$743$	2.30115	0.0844211	0.0422106	−	0.999109i	$-0.486560\pi$
$743$	2.30115	0.0844211	0.0422106	+	0.999109i	$0.486560\pi$
$744$	−17.0558	−0.625298
$745$	17.5212	0.641927
$746$	−42.8009	−1.56705
$747$	6.17513	0.225936
$748$	0.384694	0.0140658
$749$	1.70727	0.0623823
$750$	10.1923	0.372172
$751$	48.6405	1.77492	0.887458	−	0.460888i	$-0.152469\pi$
$751$	48.6405	1.77492	0.887458	+	0.460888i	$0.152469\pi$
$752$	25.6791	0.936421
$753$	−27.7648	−1.01181
$754$	−8.29273	−0.302003
$755$	29.9572	1.09025
$756$	−0.196558	−0.00714873
$757$	−7.43175	−0.270112	−0.135056	−	0.990838i	$-0.543121\pi$
$757$	−7.43175	−0.270112	−0.135056	+	0.990838i	$0.543121\pi$
$758$	−1.37169	−0.0498221
$759$	0.149501	0.00542654
$760$	42.9735	1.55881
$761$	22.3822	0.811353	0.405677	−	0.914017i	$-0.367036\pi$
$761$	22.3822	0.811353	0.405677	+	0.914017i	$0.367036\pi$
$762$	23.3288	0.845115
$763$	−10.0000	−0.362024
$764$	1.50650	0.0545033
$765$	23.3288	0.843456
$766$	26.2155	0.947203
$767$	8.97858	0.324198
$768$	4.67033	0.168526
$769$	−1.67536	−0.0604152	−0.0302076	−	0.999544i	$-0.509617\pi$
$769$	−1.67536	−0.0604152	−0.0302076	+	0.999544i	$0.509617\pi$
$770$	1.37169	0.0494324
$771$	4.87819	0.175684
$772$	−3.80765	−0.137040
$773$	8.10038	0.291351	0.145675	−	0.989332i	$-0.453465\pi$
$773$	8.10038	0.291351	0.145675	+	0.989332i	$0.453465\pi$
$774$	1.60688	0.0577583
$775$	−41.4868	−1.49025
$776$	7.70223	0.276494
$777$	−0.978577	−0.0351063
$778$	24.0575	0.862505
$779$	2.86350	0.102596
$780$	0.685846	0.0245572
$781$	−2.12854	−0.0761650
$782$	4.58546	0.163976
$783$	−6.17513	−0.220681
$784$	−3.56825	−0.127437
$785$	−70.8585	−2.52905
$786$	−25.1709	−0.897817
$787$	11.3889	0.405971	0.202985	−	0.979182i	$-0.434936\pi$
$787$	11.3889	0.405971	0.202985	+	0.979182i	$0.434936\pi$
$788$	−0.200768	−0.00715208
$789$	−20.6258	−0.734298
$790$	13.1365	0.467376
$791$	−20.5682	−0.731323
$792$	−0.863500	−0.0306831
$793$	−11.3717	−0.403821
$794$	−47.4208	−1.68290
$795$	−45.8971	−1.62780
$796$	2.47377	0.0876804
$797$	−21.7795	−0.771469	−0.385735	−	0.922610i	$-0.626052\pi$
$797$	−21.7795	−0.771469	−0.385735	+	0.922610i	$0.626052\pi$
$798$	5.60688	0.198482
$799$	48.1151	1.70219
$800$	7.94812	0.281008
$801$	−9.88240	−0.349178
$802$	−39.4439	−1.39281
$803$	1.97904	0.0698387
$804$	−2.42754	−0.0856127
$805$	−1.78202	−0.0628079
$806$	7.76481	0.273504
$807$	−24.6430	−0.867475
$808$	44.3537	1.56036
$809$	23.7820	0.836131	0.418066	−	0.908417i	$-0.362708\pi$
$809$	23.7820	0.836131	0.418066	+	0.908417i	$0.362708\pi$
$810$	−4.68585	−0.164644
$811$	−21.9572	−0.771020	−0.385510	−	0.922704i	$-0.625974\pi$
$811$	−21.9572	−0.771020	−0.385510	+	0.922704i	$0.625974\pi$
$812$	1.21377	0.0425950
$813$	−1.17092	−0.0410661
$814$	−0.384694	−0.0134835
$815$	60.6148	2.12325
$816$	−23.8568	−0.835154
$817$	4.99579	0.174781
$818$	−34.5657	−1.20856
$819$	1.00000	0.0349428
$820$	0.470385	0.0164266
$821$	−1.10711	−0.0386386	−0.0193193	−	0.999813i	$-0.506150\pi$
$821$	−1.10711	−0.0386386	−0.0193193	+	0.999813i	$0.506150\pi$
$822$	4.58546	0.159936
$823$	−50.7434	−1.76880	−0.884402	−	0.466727i	$-0.845433\pi$
$823$	−50.7434	−1.76880	−0.884402	+	0.466727i	$0.845433\pi$
$824$	−14.1185	−0.491840
$825$	−2.10038	−0.0731260
$826$	12.0575	0.419535
$827$	−18.8009	−0.653772	−0.326886	−	0.945064i	$-0.605999\pi$
$827$	−18.8009	−0.653772	−0.326886	+	0.945064i	$0.605999\pi$
$828$	0.100384	0.00348859
$829$	−4.82908	−0.167721	−0.0838604	−	0.996478i	$-0.526725\pi$
$829$	−4.82908	−0.167721	−0.0838604	+	0.996478i	$0.526725\pi$
$830$	−28.9357	−1.00437
$831$	−15.7820	−0.547472
$832$	−8.62410	−0.298987
$833$	−6.68585	−0.231651
$834$	−20.9013	−0.723753
$835$	82.1617	2.84332
$836$	−0.240231	−0.00830856
$837$	5.78202	0.199856
$838$	−25.3717	−0.876451
$839$	8.97858	0.309975	0.154987	−	0.987916i	$-0.450466\pi$
$839$	8.97858	0.309975	0.154987	+	0.987916i	$0.450466\pi$
$840$	10.2927	0.355133
$841$	9.13229	0.314907
$842$	2.88661	0.0994793
$843$	−16.1495	−0.556218
$844$	1.83704	0.0632335
$845$	−3.48929	−0.120035
$846$	−9.66442	−0.332270
$847$	10.9143	0.375020
$848$	46.9357	1.61178
$849$	12.2008	0.418729
$850$	−64.4225	−2.20967
$851$	0.499771	0.0171319
$852$	−1.42923	−0.0489646
$853$	8.18356	0.280200	0.140100	−	0.990137i	$-0.455258\pi$
$853$	8.18356	0.280200	0.140100	+	0.990137i	$0.455258\pi$
$854$	−15.2713	−0.522573
$855$	−14.5682	−0.498224
$856$	5.03612	0.172131
$857$	4.29273	0.146637	0.0733184	−	0.997309i	$-0.476641\pi$
$857$	4.29273	0.146637	0.0733184	+	0.997309i	$0.476641\pi$
$858$	0.393115	0.0134207
$859$	−42.8072	−1.46056	−0.730281	−	0.683147i	$-0.760611\pi$
$859$	−42.8072	−1.46056	−0.730281	+	0.683147i	$0.760611\pi$
$860$	0.820654	0.0279841
$861$	0.685846	0.0233736
$862$	−15.6069	−0.531573
$863$	18.8866	0.642908	0.321454	−	0.946925i	$-0.395828\pi$
$863$	18.8866	0.642908	0.321454	+	0.946925i	$0.395828\pi$
$864$	−1.10773	−0.0376858
$865$	−62.8585	−2.13725
$866$	6.68585	0.227194
$867$	−27.7005	−0.940760
$868$	−1.13650	−0.0385753
$869$	−0.820654	−0.0278388
$870$	28.9357	0.981013
$871$	12.3503	0.418473
$872$	−29.4981	−0.998931
$873$	−2.61110	−0.0883722
$874$	−2.86350	−0.0968593
$875$	7.58967	0.256578
$876$	1.32885	0.0448976
$877$	57.7942	1.95157	0.975786	−	0.218729i	$-0.0701911\pi$
$877$	57.7942	1.95157	0.975786	+	0.218729i	$0.0701911\pi$
$878$	49.6018	1.67398
$879$	−20.6258	−0.695691
$880$	3.64469	0.122863
$881$	−16.2927	−0.548916	−0.274458	−	0.961599i	$-0.588498\pi$
$881$	−16.2927	−0.548916	−0.274458	+	0.961599i	$0.588498\pi$
$882$	1.34292	0.0452186
$883$	38.7434	1.30382	0.651909	−	0.758297i	$-0.273968\pi$
$883$	38.7434	1.30382	0.651909	+	0.758297i	$0.273968\pi$
$884$	−1.31415	−0.0441998
$885$	−31.3288	−1.05311
$886$	−14.0575	−0.472272
$887$	−4.11508	−0.138171	−0.0690854	−	0.997611i	$-0.522008\pi$
$887$	−4.11508	−0.138171	−0.0690854	+	0.997611i	$0.522008\pi$
$888$	−2.88661	−0.0968684
$889$	17.3717	0.582628
$890$	46.3074	1.55223
$891$	0.292731	0.00980686
$892$	5.29104	0.177157
$893$	−30.0466	−1.00547
$894$	6.74338	0.225533
$895$	−9.43175	−0.315269
$896$	−9.36604	−0.312897
$897$	−0.510711	−0.0170522
$898$	−21.3717	−0.713183
$899$	−35.7047	−1.19082
$900$	−1.41033	−0.0470109
$901$	87.9437	2.92983
$902$	0.269617	0.00897725
$903$	1.19656	0.0398189
$904$	−60.6724	−2.01793
$905$	81.2516	2.70089
$906$	11.5296	0.383046
$907$	20.6111	0.684380	0.342190	−	0.939631i	$-0.388831\pi$
$907$	20.6111	0.684380	0.342190	+	0.939631i	$0.388831\pi$
$908$	−3.09027	−0.102554
$909$	−15.0361	−0.498716
$910$	−4.68585	−0.155334
$911$	5.68164	0.188241	0.0941205	−	0.995561i	$-0.469996\pi$
$911$	5.68164	0.188241	0.0941205	+	0.995561i	$0.469996\pi$
$912$	14.8979	0.493320
$913$	1.80765	0.0598246
$914$	11.2713	0.372822
$915$	39.6791	1.31175
$916$	−2.23519	−0.0738528
$917$	−18.7434	−0.618961
$918$	8.97858	0.296337
$919$	22.6577	0.747408	0.373704	−	0.927548i	$-0.378088\pi$
$919$	22.6577	0.747408	0.373704	+	0.927548i	$0.378088\pi$
$920$	−5.25662	−0.173305
$921$	−2.56825	−0.0846267
$922$	−14.4078	−0.474496
$923$	7.27131	0.239338
$924$	−0.0575385	−0.00189288
$925$	−7.02142	−0.230863
$926$	−18.2730	−0.600488
$927$	4.78623	0.157200
$928$	6.84039	0.224547
$929$	8.42502	0.276416	0.138208	−	0.990403i	$-0.455866\pi$
$929$	8.42502	0.276416	0.138208	+	0.990403i	$0.455866\pi$
$930$	−27.0937	−0.888436
$931$	4.17513	0.136835
$932$	−1.32885	−0.0435278
$933$	10.9786	0.359422
$934$	16.4309	0.537636
$935$	6.82908	0.223335
$936$	2.94981	0.0964175
$937$	−16.5082	−0.539299	−0.269650	−	0.962959i	$-0.586908\pi$
$937$	−16.5082	−0.539299	−0.269650	+	0.962959i	$0.586908\pi$
$938$	16.5855	0.541535
$939$	27.3717	0.893241
$940$	−4.93573	−0.160986
$941$	−25.1819	−0.820905	−0.410453	−	0.911882i	$-0.634629\pi$
$941$	−25.1819	−0.820905	−0.410453	+	0.911882i	$0.634629\pi$
$942$	−27.2713	−0.888547
$943$	−0.350269	−0.0114063
$944$	32.0378	1.04274
$945$	−3.48929	−0.113507
$946$	0.470385	0.0152935
$947$	−21.5787	−0.701215	−0.350607	−	0.936523i	$-0.614025\pi$
$947$	−21.5787	−0.701215	−0.350607	+	0.936523i	$0.614025\pi$
$948$	−0.551038	−0.0178969
$949$	−6.76060	−0.219458
$950$	40.2302	1.30524
$951$	34.0722	1.10487
$952$	−19.7220	−0.639192
$953$	21.0386	0.681508	0.340754	−	0.940152i	$-0.389318\pi$
$953$	21.0386	0.681508	0.340754	+	0.940152i	$0.389318\pi$
$954$	−17.6644	−0.571907
$955$	26.7434	0.865396
$956$	2.10038	0.0679313
$957$	−1.80765	−0.0584331
$958$	−44.9933	−1.45367
$959$	3.41454	0.110261
$960$	30.0920	0.971214
$961$	2.43175	0.0784436
$962$	1.31415	0.0423700
$963$	−1.70727	−0.0550160
$964$	−1.73038	−0.0557319
$965$	−67.5934	−2.17591
$966$	−0.685846	−0.0220667
$967$	−14.5939	−0.469308	−0.234654	−	0.972079i	$-0.575396\pi$
$967$	−14.5939	−0.469308	−0.234654	+	0.972079i	$0.575396\pi$
$968$	32.1951	1.03479
$969$	27.9143	0.896737
$970$	12.2352	0.392848
$971$	−18.3074	−0.587513	−0.293757	−	0.955880i	$-0.594906\pi$
$971$	−18.3074	−0.587513	−0.293757	+	0.955880i	$0.594906\pi$
$972$	0.196558	0.00630459
$973$	−15.5640	−0.498960
$974$	−14.7434	−0.472409
$975$	7.17513	0.229788
$976$	−40.5770	−1.29884
$977$	41.3373	1.32250	0.661248	−	0.750167i	$-0.270027\pi$
$977$	41.3373	1.32250	0.661248	+	0.750167i	$0.270027\pi$
$978$	23.3288	0.745974
$979$	−2.89289	−0.0924570
$980$	0.685846	0.0219086
$981$	10.0000	0.319275
$982$	−1.39142	−0.0444021
$983$	−34.8757	−1.11236	−0.556181	−	0.831061i	$-0.687734\pi$
$983$	−34.8757	−1.11236	−0.556181	+	0.831061i	$0.687734\pi$
$984$	2.02311	0.0644945
$985$	−3.56404	−0.113560
$986$	−55.4439	−1.76569
$987$	−7.19656	−0.229069
$988$	0.820654	0.0261085
$989$	−0.611096	−0.0194317
$990$	−1.37169	−0.0435952
$991$	−45.2860	−1.43856	−0.719279	−	0.694722i	$-0.755528\pi$
$991$	−45.2860	−1.43856	−0.719279	+	0.694722i	$0.755528\pi$
$992$	−6.40492	−0.203356
$993$	−2.77781	−0.0881511
$994$	9.76481	0.309721
$995$	43.9143	1.39218
$996$	1.21377	0.0384598
$997$	44.7090	1.41595	0.707973	−	0.706239i	$-0.249610\pi$
$997$	44.7090	1.41595	0.707973	+	0.706239i	$0.249610\pi$
$998$	17.6875	0.559889
$999$	0.978577	0.0309608

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.a.d.1.3	✓	3
3.2	odd	2		819.2.a.j.1.1		3
4.3	odd	2		4368.2.a.bq.1.1		3
5.4	even	2		6825.2.a.bd.1.1		3
7.6	odd	2		1911.2.a.n.1.3		3
13.12	even	2		3549.2.a.t.1.1		3
21.20	even	2		5733.2.a.bc.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.a.d.1.3	✓	3	1.1	even	1	trivial
819.2.a.j.1.1		3	3.2	odd	2
1911.2.a.n.1.3		3	7.6	odd	2
3549.2.a.t.1.1		3	13.12	even	2
4368.2.a.bq.1.1		3	4.3	odd	2
5733.2.a.bc.1.1		3	21.20	even	2
6825.2.a.bd.1.1		3	5.4	even	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.a (trivial)

\(f(q)\)	\(=\)	\(q+1.34292 q^{2} -1.00000 q^{3} -0.196558 q^{4} -3.48929 q^{5} -1.34292 q^{6} -1.00000 q^{7} -2.94981 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.34292 q^{2} -1.00000 q^{3} -0.196558 q^{4} -3.48929 q^{5} -1.34292 q^{6} -1.00000 q^{7} -2.94981 q^{8} +1.00000 q^{9} -4.68585 q^{10} +0.292731 q^{11} +0.196558 q^{12} -1.00000 q^{13} -1.34292 q^{14} +3.48929 q^{15} -3.56825 q^{16} -6.68585 q^{17} +1.34292 q^{18} +4.17513 q^{19} +0.685846 q^{20} +1.00000 q^{21} +0.393115 q^{22} -0.510711 q^{23} +2.94981 q^{24} +7.17513 q^{25} -1.34292 q^{26} -1.00000 q^{27} +0.196558 q^{28} +6.17513 q^{29} +4.68585 q^{30} -5.78202 q^{31} +1.10773 q^{32} -0.292731 q^{33} -8.97858 q^{34} +3.48929 q^{35} -0.196558 q^{36} -0.978577 q^{37} +5.60688 q^{38} +1.00000 q^{39} +10.2927 q^{40} +0.685846 q^{41} +1.34292 q^{42} +1.19656 q^{43} -0.0575385 q^{44} -3.48929 q^{45} -0.685846 q^{46} -7.19656 q^{47} +3.56825 q^{48} +1.00000 q^{49} +9.63565 q^{50} +6.68585 q^{51} +0.196558 q^{52} -13.1537 q^{53} -1.34292 q^{54} -1.02142 q^{55} +2.94981 q^{56} -4.17513 q^{57} +8.29273 q^{58} -8.97858 q^{59} -0.685846 q^{60} +11.3717 q^{61} -7.76481 q^{62} -1.00000 q^{63} +8.62410 q^{64} +3.48929 q^{65} -0.393115 q^{66} -12.3503 q^{67} +1.31415 q^{68} +0.510711 q^{69} +4.68585 q^{70} -7.27131 q^{71} -2.94981 q^{72} +6.76060 q^{73} -1.31415 q^{74} -7.17513 q^{75} -0.820654 q^{76} -0.292731 q^{77} +1.34292 q^{78} -2.80344 q^{79} +12.4507 q^{80} +1.00000 q^{81} +0.921039 q^{82} +6.17513 q^{83} -0.196558 q^{84} +23.3288 q^{85} +1.60688 q^{86} -6.17513 q^{87} -0.863500 q^{88} -9.88240 q^{89} -4.68585 q^{90} +1.00000 q^{91} +0.100384 q^{92} +5.78202 q^{93} -9.66442 q^{94} -14.5682 q^{95} -1.10773 q^{96} -2.61110 q^{97} +1.34292 q^{98} +0.292731 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} - 3 q^{3} + 4 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 - 3 * q^3 + 4 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 12 * q^8 + 3 * q^9	\( 3 q - 2 q^{2} - 3 q^{3} + 4 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 12 q^{8} + 3 q^{9} - 2 q^{10} - 2 q^{11} - 4 q^{12} - 3 q^{13} + 2 q^{14} + 3 q^{15} + 18 q^{16} - 8 q^{17} - 2 q^{18} - 7 q^{19} - 10 q^{20} + 3 q^{21} - 8 q^{22} - 9 q^{23} + 12 q^{24} + 2 q^{25} + 2 q^{26} - 3 q^{27} - 4 q^{28} - q^{29} + 2 q^{30} - 7 q^{31} - 36 q^{32} + 2 q^{33} - 12 q^{34} + 3 q^{35} + 4 q^{36} + 12 q^{37} + 26 q^{38} + 3 q^{39} + 28 q^{40} - 10 q^{41} - 2 q^{42} - q^{43} + 36 q^{44} - 3 q^{45} + 10 q^{46} - 17 q^{47} - 18 q^{48} + 3 q^{49} + 20 q^{50} + 8 q^{51} - 4 q^{52} - 5 q^{53} + 2 q^{54} - 18 q^{55} + 12 q^{56} + 7 q^{57} + 22 q^{58} - 12 q^{59} + 10 q^{60} + 10 q^{61} + 10 q^{62} - 3 q^{63} + 58 q^{64} + 3 q^{65} + 8 q^{66} + 2 q^{67} + 16 q^{68} + 9 q^{69} + 2 q^{70} - 4 q^{71} - 12 q^{72} - 5 q^{73} - 16 q^{74} - 2 q^{75} - 30 q^{76} + 2 q^{77} - 2 q^{78} - 13 q^{79} - 8 q^{80} + 3 q^{81} + 24 q^{82} - q^{83} + 4 q^{84} + 16 q^{85} + 14 q^{86} + q^{87} - 60 q^{88} - 13 q^{89} - 2 q^{90} + 3 q^{91} - 6 q^{92} + 7 q^{93} - 2 q^{94} - 15 q^{95} + 36 q^{96} - 9 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - 3 * q^3 + 4 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 12 * q^8 + 3 * q^9 - 2 * q^10 - 2 * q^11 - 4 * q^12 - 3 * q^13 + 2 * q^14 + 3 * q^15 + 18 * q^16 - 8 * q^17 - 2 * q^18 - 7 * q^19 - 10 * q^20 + 3 * q^21 - 8 * q^22 - 9 * q^23 + 12 * q^24 + 2 * q^25 + 2 * q^26 - 3 * q^27 - 4 * q^28 - q^29 + 2 * q^30 - 7 * q^31 - 36 * q^32 + 2 * q^33 - 12 * q^34 + 3 * q^35 + 4 * q^36 + 12 * q^37 + 26 * q^38 + 3 * q^39 + 28 * q^40 - 10 * q^41 - 2 * q^42 - q^43 + 36 * q^44 - 3 * q^45 + 10 * q^46 - 17 * q^47 - 18 * q^48 + 3 * q^49 + 20 * q^50 + 8 * q^51 - 4 * q^52 - 5 * q^53 + 2 * q^54 - 18 * q^55 + 12 * q^56 + 7 * q^57 + 22 * q^58 - 12 * q^59 + 10 * q^60 + 10 * q^61 + 10 * q^62 - 3 * q^63 + 58 * q^64 + 3 * q^65 + 8 * q^66 + 2 * q^67 + 16 * q^68 + 9 * q^69 + 2 * q^70 - 4 * q^71 - 12 * q^72 - 5 * q^73 - 16 * q^74 - 2 * q^75 - 30 * q^76 + 2 * q^77 - 2 * q^78 - 13 * q^79 - 8 * q^80 + 3 * q^81 + 24 * q^82 - q^83 + 4 * q^84 + 16 * q^85 + 14 * q^86 + q^87 - 60 * q^88 - 13 * q^89 - 2 * q^90 + 3 * q^91 - 6 * q^92 + 7 * q^93 - 2 * q^94 - 15 * q^95 + 36 * q^96 - 9 * q^97 - 2 * q^98 - 2 * q^99

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