LMFDB - Embedded newform 5577.2.a.x.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5577,2,Mod(1,5577)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5577, 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("5577.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5577 = 3 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5577.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:	$44.5325692073$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 7x^{5} + 21x^{4} + 13x^{3} - 33x^{2} - 7x + 7 $ x^7 - 3x^6 - 7x^5 + 21x^4 + 13x^3 - 33x^2 - 7x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 429)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.584778$ of defining polynomial
Character	$\chi$	$=$	5577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.584778 q^{2} +1.00000 q^{3} -1.65803 q^{4} +1.95350 q^{5} +0.584778 q^{6} -1.51078 q^{7} -2.13914 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.584778 q^{2} +1.00000 q^{3} -1.65803 q^{4} +1.95350 q^{5} +0.584778 q^{6} -1.51078 q^{7} -2.13914 q^{8} +1.00000 q^{9} +1.14237 q^{10} -1.00000 q^{11} -1.65803 q^{12} -0.883474 q^{14} +1.95350 q^{15} +2.06515 q^{16} +3.44198 q^{17} +0.584778 q^{18} -5.09587 q^{19} -3.23897 q^{20} -1.51078 q^{21} -0.584778 q^{22} -0.701611 q^{23} -2.13914 q^{24} -1.18383 q^{25} +1.00000 q^{27} +2.50493 q^{28} +5.04937 q^{29} +1.14237 q^{30} -7.26957 q^{31} +5.48593 q^{32} -1.00000 q^{33} +2.01280 q^{34} -2.95132 q^{35} -1.65803 q^{36} +2.08160 q^{37} -2.97995 q^{38} -4.17882 q^{40} -1.03658 q^{41} -0.883474 q^{42} -5.48659 q^{43} +1.65803 q^{44} +1.95350 q^{45} -0.410287 q^{46} -3.75225 q^{47} +2.06515 q^{48} -4.71753 q^{49} -0.692276 q^{50} +3.44198 q^{51} -0.502747 q^{53} +0.584778 q^{54} -1.95350 q^{55} +3.23178 q^{56} -5.09587 q^{57} +2.95276 q^{58} +2.65023 q^{59} -3.23897 q^{60} -5.38195 q^{61} -4.25109 q^{62} -1.51078 q^{63} -0.922236 q^{64} -0.584778 q^{66} +8.47197 q^{67} -5.70692 q^{68} -0.701611 q^{69} -1.72587 q^{70} +2.31533 q^{71} -2.13914 q^{72} -2.21094 q^{73} +1.21727 q^{74} -1.18383 q^{75} +8.44913 q^{76} +1.51078 q^{77} -5.54589 q^{79} +4.03427 q^{80} +1.00000 q^{81} -0.606168 q^{82} -14.5137 q^{83} +2.50493 q^{84} +6.72392 q^{85} -3.20844 q^{86} +5.04937 q^{87} +2.13914 q^{88} +1.80966 q^{89} +1.14237 q^{90} +1.16330 q^{92} -7.26957 q^{93} -2.19424 q^{94} -9.95480 q^{95} +5.48593 q^{96} -14.5085 q^{97} -2.75871 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 3 q^{2} + 7 q^{3} + 9 q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{7} - 15 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 3 * q^2 + 7 * q^3 + 9 * q^4 - 6 * q^5 - 3 * q^6 - 6 * q^7 - 15 * q^8 + 7 * q^9	$ 7 q - 3 q^{2} + 7 q^{3} + 9 q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{7} - 15 q^{8} + 7 q^{9} - 7 q^{11} + 9 q^{12} + 8 q^{14} - 6 q^{15} + 17 q^{16} - 2 q^{17} - 3 q^{18} - 8 q^{19} + 2 q^{20} - 6 q^{21} + 3 q^{22} + 4 q^{23} - 15 q^{24} + 13 q^{25} + 7 q^{27} - 12 q^{28} - 12 q^{29} + 10 q^{31} - 33 q^{32} - 7 q^{33} - 28 q^{34} - 4 q^{35} + 9 q^{36} - 6 q^{37} + 16 q^{38} - 10 q^{40} - 2 q^{41} + 8 q^{42} - 16 q^{43} - 9 q^{44} - 6 q^{45} + 26 q^{46} - 18 q^{47} + 17 q^{48} + 23 q^{49} - 39 q^{50} - 2 q^{51} + 10 q^{53} - 3 q^{54} + 6 q^{55} + 16 q^{56} - 8 q^{57} - 10 q^{58} - 2 q^{59} + 2 q^{60} - 10 q^{61} - 36 q^{62} - 6 q^{63} + 29 q^{64} + 3 q^{66} - 8 q^{67} - 10 q^{68} + 4 q^{69} + 20 q^{70} - 36 q^{71} - 15 q^{72} - 20 q^{73} + 13 q^{75} - 10 q^{76} + 6 q^{77} + 6 q^{79} + 20 q^{80} + 7 q^{81} - 10 q^{82} - 30 q^{83} - 12 q^{84} + 40 q^{85} - 6 q^{86} - 12 q^{87} + 15 q^{88} - 34 q^{89} - 12 q^{92} + 10 q^{93} + 32 q^{94} + 18 q^{95} - 33 q^{96} - 16 q^{97} - q^{98} - 7 q^{99}+O(q^{100}) $ 7 * q - 3 * q^2 + 7 * q^3 + 9 * q^4 - 6 * q^5 - 3 * q^6 - 6 * q^7 - 15 * q^8 + 7 * q^9 - 7 * q^11 + 9 * q^12 + 8 * q^14 - 6 * q^15 + 17 * q^16 - 2 * q^17 - 3 * q^18 - 8 * q^19 + 2 * q^20 - 6 * q^21 + 3 * q^22 + 4 * q^23 - 15 * q^24 + 13 * q^25 + 7 * q^27 - 12 * q^28 - 12 * q^29 + 10 * q^31 - 33 * q^32 - 7 * q^33 - 28 * q^34 - 4 * q^35 + 9 * q^36 - 6 * q^37 + 16 * q^38 - 10 * q^40 - 2 * q^41 + 8 * q^42 - 16 * q^43 - 9 * q^44 - 6 * q^45 + 26 * q^46 - 18 * q^47 + 17 * q^48 + 23 * q^49 - 39 * q^50 - 2 * q^51 + 10 * q^53 - 3 * q^54 + 6 * q^55 + 16 * q^56 - 8 * q^57 - 10 * q^58 - 2 * q^59 + 2 * q^60 - 10 * q^61 - 36 * q^62 - 6 * q^63 + 29 * q^64 + 3 * q^66 - 8 * q^67 - 10 * q^68 + 4 * q^69 + 20 * q^70 - 36 * q^71 - 15 * q^72 - 20 * q^73 + 13 * q^75 - 10 * q^76 + 6 * q^77 + 6 * q^79 + 20 * q^80 + 7 * q^81 - 10 * q^82 - 30 * q^83 - 12 * q^84 + 40 * q^85 - 6 * q^86 - 12 * q^87 + 15 * q^88 - 34 * q^89 - 12 * q^92 + 10 * q^93 + 32 * q^94 + 18 * q^95 - 33 * q^96 - 16 * q^97 - q^98 - 7 * 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 $

$2$	0.584778	0.413501	0.206750	−	0.978394i	$-0.433711\pi$
$2$	0.584778	0.413501	0.206750	+	0.978394i	$0.433711\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.65803	−0.829017
$5$	1.95350	0.873633	0.436817	−	0.899551i	$-0.356106\pi$
$5$	1.95350	0.873633	0.436817	+	0.899551i	$0.356106\pi$
$6$	0.584778	0.238735
$7$	−1.51078	−0.571023	−0.285511	−	0.958375i	$-0.592163\pi$
$7$	−1.51078	−0.571023	−0.285511	+	0.958375i	$0.592163\pi$
$8$	−2.13914	−0.756300
$9$	1.00000	0.333333
$10$	1.14237	0.361248
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.65803	−0.478633
$13$	0	0
$13$	0	0
$14$	−0.883474	−0.236118
$15$	1.95350	0.504392
$16$	2.06515	0.516286
$17$	3.44198	0.834803	0.417401	−	0.908722i	$-0.362941\pi$
$17$	3.44198	0.834803	0.417401	+	0.908722i	$0.362941\pi$
$18$	0.584778	0.137834
$19$	−5.09587	−1.16907	−0.584536	−	0.811368i	$-0.698724\pi$
$19$	−5.09587	−1.16907	−0.584536	+	0.811368i	$0.698724\pi$
$20$	−3.23897	−0.724257
$21$	−1.51078	−0.329680
$22$	−0.584778	−0.124675
$23$	−0.701611	−0.146296	−0.0731480	−	0.997321i	$-0.523305\pi$
$23$	−0.701611	−0.146296	−0.0731480	+	0.997321i	$0.523305\pi$
$24$	−2.13914	−0.436650
$25$	−1.18383	−0.236765
$26$	0	0
$27$	1.00000	0.192450
$28$	2.50493	0.473388
$29$	5.04937	0.937645	0.468822	−	0.883292i	$-0.344678\pi$
$29$	5.04937	0.937645	0.468822	+	0.883292i	$0.344678\pi$
$30$	1.14237	0.208567
$31$	−7.26957	−1.30565	−0.652827	−	0.757507i	$-0.726417\pi$
$31$	−7.26957	−1.30565	−0.652827	+	0.757507i	$0.726417\pi$
$32$	5.48593	0.969785
$33$	−1.00000	−0.174078
$34$	2.01280	0.345192
$35$	−2.95132	−0.498864
$36$	−1.65803	−0.276339
$37$	2.08160	0.342213	0.171106	−	0.985253i	$-0.445266\pi$
$37$	2.08160	0.342213	0.171106	+	0.985253i	$0.445266\pi$
$38$	−2.97995	−0.483413
$39$	0	0
$40$	−4.17882	−0.660729
$41$	−1.03658	−0.161886	−0.0809430	−	0.996719i	$-0.525793\pi$
$41$	−1.03658	−0.161886	−0.0809430	+	0.996719i	$0.525793\pi$
$42$	−0.883474	−0.136323
$43$	−5.48659	−0.836698	−0.418349	−	0.908286i	$-0.637391\pi$
$43$	−5.48659	−0.836698	−0.418349	+	0.908286i	$0.637391\pi$
$44$	1.65803	0.249958
$45$	1.95350	0.291211
$46$	−0.410287	−0.0604935
$47$	−3.75225	−0.547322	−0.273661	−	0.961826i	$-0.588235\pi$
$47$	−3.75225	−0.547322	−0.273661	+	0.961826i	$0.588235\pi$
$48$	2.06515	0.298078
$49$	−4.71753	−0.673933
$50$	−0.692276	−0.0979026
$51$	3.44198	0.481974
$52$	0	0
$53$	−0.502747	−0.0690575	−0.0345288	−	0.999404i	$-0.510993\pi$
$53$	−0.502747	−0.0690575	−0.0345288	+	0.999404i	$0.510993\pi$
$54$	0.584778	0.0795783
$55$	−1.95350	−0.263410
$56$	3.23178	0.431865
$57$	−5.09587	−0.674964
$58$	2.95276	0.387717
$59$	2.65023	0.345031	0.172515	−	0.985007i	$-0.444811\pi$
$59$	2.65023	0.345031	0.172515	+	0.985007i	$0.444811\pi$
$60$	−3.23897	−0.418150
$61$	−5.38195	−0.689088	−0.344544	−	0.938770i	$-0.611967\pi$
$61$	−5.38195	−0.689088	−0.344544	+	0.938770i	$0.611967\pi$
$62$	−4.25109	−0.539889
$63$	−1.51078	−0.190341
$64$	−0.922236	−0.115279
$65$	0	0
$66$	−0.584778	−0.0719813
$67$	8.47197	1.03502	0.517508	−	0.855679i	$-0.326860\pi$
$67$	8.47197	1.03502	0.517508	+	0.855679i	$0.326860\pi$
$68$	−5.70692	−0.692066
$69$	−0.701611	−0.0844640
$70$	−1.72587	−0.206281
$71$	2.31533	0.274779	0.137390	−	0.990517i	$-0.456129\pi$
$71$	2.31533	0.274779	0.137390	+	0.990517i	$0.456129\pi$
$72$	−2.13914	−0.252100
$73$	−2.21094	−0.258771	−0.129385	−	0.991594i	$-0.541300\pi$
$73$	−2.21094	−0.258771	−0.129385	+	0.991594i	$0.541300\pi$
$74$	1.21727	0.141505
$75$	−1.18383	−0.136696
$76$	8.44913	0.969181
$77$	1.51078	0.172170
$78$	0	0
$79$	−5.54589	−0.623961	−0.311981	−	0.950088i	$-0.600992\pi$
$79$	−5.54589	−0.623961	−0.311981	+	0.950088i	$0.600992\pi$
$80$	4.03427	0.451045
$81$	1.00000	0.111111
$82$	−0.606168	−0.0669400
$83$	−14.5137	−1.59308	−0.796541	−	0.604585i	$-0.793339\pi$
$83$	−14.5137	−1.59308	−0.796541	+	0.604585i	$0.793339\pi$
$84$	2.50493	0.273310
$85$	6.72392	0.729311
$86$	−3.20844	−0.345975
$87$	5.04937	0.541350
$88$	2.13914	0.228033
$89$	1.80966	0.191824	0.0959119	−	0.995390i	$-0.469423\pi$
$89$	1.80966	0.191824	0.0959119	+	0.995390i	$0.469423\pi$
$90$	1.14237	0.120416
$91$	0	0
$92$	1.16330	0.121282
$93$	−7.26957	−0.753819
$94$	−2.19424	−0.226318
$95$	−9.95480	−1.02134
$96$	5.48593	0.559906
$97$	−14.5085	−1.47312	−0.736560	−	0.676372i	$-0.763551\pi$
$97$	−14.5085	−1.47312	−0.736560	+	0.676372i	$0.763551\pi$
$98$	−2.75871	−0.278672
$99$	−1.00000	−0.100504
$100$	1.96282	0.196282
$101$	8.63799	0.859512	0.429756	−	0.902945i	$-0.358600\pi$
$101$	8.63799	0.859512	0.429756	+	0.902945i	$0.358600\pi$
$102$	2.01280	0.199296
$103$	−2.90048	−0.285792	−0.142896	−	0.989738i	$-0.545642\pi$
$103$	−2.90048	−0.285792	−0.142896	+	0.989738i	$0.545642\pi$
$104$	0	0
$105$	−2.95132	−0.288019
$106$	−0.293995	−0.0285554
$107$	−2.29234	−0.221609	−0.110805	−	0.993842i	$-0.535343\pi$
$107$	−2.29234	−0.221609	−0.110805	+	0.993842i	$0.535343\pi$
$108$	−1.65803	−0.159544
$109$	−12.8818	−1.23386	−0.616929	−	0.787019i	$-0.711623\pi$
$109$	−12.8818	−1.23386	−0.616929	+	0.787019i	$0.711623\pi$
$110$	−1.14237	−0.108920
$111$	2.08160	0.197577
$112$	−3.11999	−0.294811
$113$	−12.6273	−1.18788	−0.593940	−	0.804509i	$-0.702428\pi$
$113$	−12.6273	−1.18788	−0.593940	+	0.804509i	$0.702428\pi$
$114$	−2.97995	−0.279098
$115$	−1.37060	−0.127809
$116$	−8.37203	−0.777324
$117$	0	0
$118$	1.54980	0.142670
$119$	−5.20009	−0.476691
$120$	−4.17882	−0.381472
$121$	1.00000	0.0909091
$122$	−3.14725	−0.284939
$123$	−1.03658	−0.0934649
$124$	12.0532	1.08241
$125$	−12.0801	−1.08048
$126$	−0.883474	−0.0787061
$127$	5.05085	0.448190	0.224095	−	0.974567i	$-0.428057\pi$
$127$	5.05085	0.448190	0.224095	+	0.974567i	$0.428057\pi$
$128$	−11.5112	−1.01745
$129$	−5.48659	−0.483068
$130$	0	0
$131$	15.9772	1.39594	0.697968	−	0.716129i	$-0.254088\pi$
$131$	15.9772	1.39594	0.697968	+	0.716129i	$0.254088\pi$
$132$	1.65803	0.144313
$133$	7.69876	0.667567
$134$	4.95422	0.427980
$135$	1.95350	0.168131
$136$	−7.36288	−0.631361
$137$	17.2582	1.47447	0.737233	−	0.675639i	$-0.236132\pi$
$137$	17.2582	1.47447	0.737233	+	0.675639i	$0.236132\pi$
$138$	−0.410287	−0.0349260
$139$	−5.70544	−0.483929	−0.241965	−	0.970285i	$-0.577792\pi$
$139$	−5.70544	−0.483929	−0.241965	+	0.970285i	$0.577792\pi$
$140$	4.89339	0.413567
$141$	−3.75225	−0.315997
$142$	1.35395	0.113621
$143$	0	0
$144$	2.06515	0.172095
$145$	9.86396	0.819158
$146$	−1.29291	−0.107002
$147$	−4.71753	−0.389095
$148$	−3.45136	−0.283700
$149$	0.161015	0.0131908	0.00659542	−	0.999978i	$-0.497901\pi$
$149$	0.161015	0.0131908	0.00659542	+	0.999978i	$0.497901\pi$
$150$	−0.692276	−0.0565241
$151$	−16.3107	−1.32734	−0.663671	−	0.748025i	$-0.731003\pi$
$151$	−16.3107	−1.32734	−0.663671	+	0.748025i	$0.731003\pi$
$152$	10.9008	0.884170
$153$	3.44198	0.278268
$154$	0.883474	0.0711924
$155$	−14.2011	−1.14066
$156$	0	0
$157$	−14.2192	−1.13481	−0.567407	−	0.823437i	$-0.692053\pi$
$157$	−14.2192	−1.13481	−0.567407	+	0.823437i	$0.692053\pi$
$158$	−3.24312	−0.258008
$159$	−0.502747	−0.0398704
$160$	10.7168	0.847236
$161$	1.05998	0.0835384
$162$	0.584778	0.0459445
$163$	−13.0186	−1.01970	−0.509848	−	0.860264i	$-0.670298\pi$
$163$	−13.0186	−1.01970	−0.509848	+	0.860264i	$0.670298\pi$
$164$	1.71868	0.134206
$165$	−1.95350	−0.152080
$166$	−8.48728	−0.658740
$167$	−14.0271	−1.08545	−0.542724	−	0.839911i	$-0.682607\pi$
$167$	−14.0271	−1.08545	−0.542724	+	0.839911i	$0.682607\pi$
$168$	3.23178	0.249337
$169$	0	0
$170$	3.93200	0.301571
$171$	−5.09587	−0.389691
$172$	9.09696	0.693637
$173$	17.8674	1.35844	0.679218	−	0.733936i	$-0.262319\pi$
$173$	17.8674	1.35844	0.679218	+	0.733936i	$0.262319\pi$
$174$	2.95276	0.223848
$175$	1.78851	0.135198
$176$	−2.06515	−0.155666
$177$	2.65023	0.199204
$178$	1.05825	0.0793193
$179$	17.2723	1.29099	0.645495	−	0.763764i	$-0.276651\pi$
$179$	17.2723	1.29099	0.645495	+	0.763764i	$0.276651\pi$
$180$	−3.23897	−0.241419
$181$	3.70318	0.275255	0.137628	−	0.990484i	$-0.456052\pi$
$181$	3.70318	0.275255	0.137628	+	0.990484i	$0.456052\pi$
$182$	0	0
$183$	−5.38195	−0.397845
$184$	1.50084	0.110644
$185$	4.06641	0.298969
$186$	−4.25109	−0.311705
$187$	−3.44198	−0.251703
$188$	6.22136	0.453740
$189$	−1.51078	−0.109893
$190$	−5.82135	−0.422325
$191$	−20.6259	−1.49243	−0.746217	−	0.665702i	$-0.768132\pi$
$191$	−20.6259	−1.49243	−0.746217	+	0.665702i	$0.768132\pi$
$192$	−0.922236	−0.0665566
$193$	−18.8475	−1.35667	−0.678335	−	0.734753i	$-0.737298\pi$
$193$	−18.8475	−1.35667	−0.678335	+	0.734753i	$0.737298\pi$
$194$	−8.48429	−0.609136
$195$	0	0
$196$	7.82183	0.558702
$197$	7.18370	0.511818	0.255909	−	0.966701i	$-0.417625\pi$
$197$	7.18370	0.511818	0.255909	+	0.966701i	$0.417625\pi$
$198$	−0.584778	−0.0415584
$199$	−18.9591	−1.34398	−0.671989	−	0.740562i	$-0.734560\pi$
$199$	−18.9591	−1.34398	−0.671989	+	0.740562i	$0.734560\pi$
$200$	2.53237	0.179066
$201$	8.47197	0.597566
$202$	5.05131	0.355409
$203$	−7.62851	−0.535417
$204$	−5.70692	−0.399564
$205$	−2.02496	−0.141429
$206$	−1.69614	−0.118175
$207$	−0.701611	−0.0487653
$208$	0	0
$209$	5.09587	0.352489
$210$	−1.72587	−0.119096
$211$	−19.9916	−1.37628	−0.688139	−	0.725578i	$-0.741572\pi$
$211$	−19.9916	−1.37628	−0.688139	+	0.725578i	$0.741572\pi$
$212$	0.833571	0.0572499
$213$	2.31533	0.158644
$214$	−1.34051	−0.0916356
$215$	−10.7181	−0.730967
$216$	−2.13914	−0.145550
$217$	10.9828	0.745558
$218$	−7.53303	−0.510201
$219$	−2.21094	−0.149401
$220$	3.23897	0.218372
$221$	0	0
$222$	1.21727	0.0816981
$223$	27.7784	1.86018	0.930091	−	0.367330i	$-0.119728\pi$
$223$	27.7784	1.86018	0.930091	+	0.367330i	$0.119728\pi$
$224$	−8.28806	−0.553769
$225$	−1.18383	−0.0789218
$226$	−7.38419	−0.491189
$227$	−28.6524	−1.90173	−0.950863	−	0.309612i	$-0.899801\pi$
$227$	−28.6524	−1.90173	−0.950863	+	0.309612i	$0.899801\pi$
$228$	8.44913	0.559557
$229$	−4.83459	−0.319479	−0.159739	−	0.987159i	$-0.551065\pi$
$229$	−4.83459	−0.319479	−0.159739	+	0.987159i	$0.551065\pi$
$230$	−0.801497	−0.0528491
$231$	1.51078	0.0994023
$232$	−10.8013	−0.709141
$233$	13.6237	0.892518	0.446259	−	0.894904i	$-0.352756\pi$
$233$	13.6237	0.892518	0.446259	+	0.894904i	$0.352756\pi$
$234$	0	0
$235$	−7.33004	−0.478159
$236$	−4.39417	−0.286036
$237$	−5.54589	−0.360244
$238$	−3.04090	−0.197112
$239$	5.99903	0.388045	0.194023	−	0.980997i	$-0.437846\pi$
$239$	5.99903	0.388045	0.194023	+	0.980997i	$0.437846\pi$
$240$	4.03427	0.260411
$241$	12.9290	0.832831	0.416416	−	0.909174i	$-0.363286\pi$
$241$	12.9290	0.832831	0.416416	+	0.909174i	$0.363286\pi$
$242$	0.584778	0.0375910
$243$	1.00000	0.0641500
$244$	8.92346	0.571266
$245$	−9.21571	−0.588770
$246$	−0.606168	−0.0386478
$247$	0	0
$248$	15.5506	0.987466
$249$	−14.5137	−0.919766
$250$	−7.06420	−0.446779
$251$	−23.9724	−1.51313	−0.756563	−	0.653921i	$-0.773123\pi$
$251$	−23.9724	−1.51313	−0.756563	+	0.653921i	$0.773123\pi$
$252$	2.50493	0.157796
$253$	0.701611	0.0441099
$254$	2.95363	0.185327
$255$	6.72392	0.421068
$256$	−4.88701	−0.305438
$257$	16.3441	1.01952	0.509758	−	0.860318i	$-0.329735\pi$
$257$	16.3441	1.01952	0.509758	+	0.860318i	$0.329735\pi$
$258$	−3.20844	−0.199749
$259$	−3.14485	−0.195411
$260$	0	0
$261$	5.04937	0.312548
$262$	9.34313	0.577220
$263$	10.1510	0.625936	0.312968	−	0.949764i	$-0.398677\pi$
$263$	10.1510	0.625936	0.312968	+	0.949764i	$0.398677\pi$
$264$	2.13914	0.131655
$265$	−0.982117	−0.0603310
$266$	4.50207	0.276040
$267$	1.80966	0.110750
$268$	−14.0468	−0.858045
$269$	16.5294	1.00781	0.503907	−	0.863758i	$-0.331895\pi$
$269$	16.5294	1.00781	0.503907	+	0.863758i	$0.331895\pi$
$270$	1.14237	0.0695222
$271$	−20.8927	−1.26914	−0.634570	−	0.772865i	$-0.718823\pi$
$271$	−20.8927	−1.26914	−0.634570	+	0.772865i	$0.718823\pi$
$272$	7.10819	0.430997
$273$	0	0
$274$	10.0922	0.609693
$275$	1.18383	0.0713874
$276$	1.16330	0.0700221
$277$	−17.3070	−1.03988	−0.519938	−	0.854204i	$-0.674045\pi$
$277$	−17.3070	−1.03988	−0.519938	+	0.854204i	$0.674045\pi$
$278$	−3.33642	−0.200105
$279$	−7.26957	−0.435218
$280$	6.31329	0.377291
$281$	16.0666	0.958450	0.479225	−	0.877692i	$-0.340918\pi$
$281$	16.0666	0.958450	0.479225	+	0.877692i	$0.340918\pi$
$282$	−2.19424	−0.130665
$283$	−17.2180	−1.02350	−0.511751	−	0.859134i	$-0.671003\pi$
$283$	−17.2180	−1.02350	−0.511751	+	0.859134i	$0.671003\pi$
$284$	−3.83890	−0.227797
$285$	−9.95480	−0.589671
$286$	0	0
$287$	1.56604	0.0924406
$288$	5.48593	0.323262
$289$	−5.15277	−0.303104
$290$	5.76823	0.338722
$291$	−14.5085	−0.850506
$292$	3.66581	0.214525
$293$	−5.29670	−0.309436	−0.154718	−	0.987959i	$-0.549447\pi$
$293$	−5.29670	−0.309436	−0.154718	+	0.987959i	$0.549447\pi$
$294$	−2.75871	−0.160891
$295$	5.17723	0.301430
$296$	−4.45283	−0.258816
$297$	−1.00000	−0.0580259
$298$	0.0941580	0.00545443
$299$	0	0
$300$	1.96282	0.113324
$301$	8.28906	0.477773
$302$	−9.53812	−0.548857
$303$	8.63799	0.496240
$304$	−10.5237	−0.603576
$305$	−10.5137	−0.602010
$306$	2.01280	0.115064
$307$	−26.3020	−1.50113	−0.750567	−	0.660794i	$-0.770220\pi$
$307$	−26.3020	−1.50113	−0.750567	+	0.660794i	$0.770220\pi$
$308$	−2.50493	−0.142732
$309$	−2.90048	−0.165002
$310$	−8.30451	−0.471665
$311$	32.8590	1.86326	0.931632	−	0.363403i	$-0.118385\pi$
$311$	32.8590	1.86326	0.931632	+	0.363403i	$0.118385\pi$
$312$	0	0
$313$	33.2130	1.87731	0.938655	−	0.344858i	$-0.112073\pi$
$313$	33.2130	1.87731	0.938655	+	0.344858i	$0.112073\pi$
$314$	−8.31507	−0.469247
$315$	−2.95132	−0.166288
$316$	9.19527	0.517274
$317$	−30.8436	−1.73235	−0.866175	−	0.499740i	$-0.833429\pi$
$317$	−30.8436	−1.73235	−0.866175	+	0.499740i	$0.833429\pi$
$318$	−0.293995	−0.0164864
$319$	−5.04937	−0.282711
$320$	−1.80159	−0.100712
$321$	−2.29234	−0.127946
$322$	0.619855	0.0345432
$323$	−17.5399	−0.975945
$324$	−1.65803	−0.0921130
$325$	0	0
$326$	−7.61300	−0.421645
$327$	−12.8818	−0.712368
$328$	2.21738	0.122434
$329$	5.66884	0.312534
$330$	−1.14237	−0.0628852
$331$	−5.75414	−0.316276	−0.158138	−	0.987417i	$-0.550549\pi$
$331$	−5.75414	−0.316276	−0.158138	+	0.987417i	$0.550549\pi$
$332$	24.0641	1.32069
$333$	2.08160	0.114071
$334$	−8.20273	−0.448833
$335$	16.5500	0.904224
$336$	−3.11999	−0.170209
$337$	10.9245	0.595094	0.297547	−	0.954707i	$-0.403831\pi$
$337$	10.9245	0.595094	0.297547	+	0.954707i	$0.403831\pi$
$338$	0	0
$339$	−12.6273	−0.685823
$340$	−11.1485	−0.604612
$341$	7.26957	0.393669
$342$	−2.97995	−0.161138
$343$	17.7027	0.955854
$344$	11.7366	0.632795
$345$	−1.37060	−0.0737906
$346$	10.4485	0.561715
$347$	16.3474	0.877572	0.438786	−	0.898591i	$-0.355409\pi$
$347$	16.3474	0.877572	0.438786	+	0.898591i	$0.355409\pi$
$348$	−8.37203	−0.448788
$349$	−8.62758	−0.461824	−0.230912	−	0.972975i	$-0.574171\pi$
$349$	−8.62758	−0.461824	−0.230912	+	0.972975i	$0.574171\pi$
$350$	1.04588	0.0559046
$351$	0	0
$352$	−5.48593	−0.292401
$353$	−16.5793	−0.882425	−0.441212	−	0.897403i	$-0.645451\pi$
$353$	−16.5793	−0.882425	−0.441212	+	0.897403i	$0.645451\pi$
$354$	1.54980	0.0823708
$355$	4.52300	0.240056
$356$	−3.00048	−0.159025
$357$	−5.20009	−0.275218
$358$	10.1005	0.533826
$359$	15.5233	0.819289	0.409645	−	0.912245i	$-0.365653\pi$
$359$	15.5233	0.819289	0.409645	+	0.912245i	$0.365653\pi$
$360$	−4.17882	−0.220243
$361$	6.96788	0.366731
$362$	2.16554	0.113818
$363$	1.00000	0.0524864
$364$	0	0
$365$	−4.31907	−0.226071
$366$	−3.14725	−0.164509
$367$	23.4682	1.22503	0.612514	−	0.790460i	$-0.290158\pi$
$367$	23.4682	1.22503	0.612514	+	0.790460i	$0.290158\pi$
$368$	−1.44893	−0.0755306
$369$	−1.03658	−0.0539620
$370$	2.37795	0.123624
$371$	0.759541	0.0394334
$372$	12.0532	0.624929
$373$	12.3222	0.638018	0.319009	−	0.947752i	$-0.396650\pi$
$373$	12.3222	0.638018	0.319009	+	0.947752i	$0.396650\pi$
$374$	−2.01280	−0.104079
$375$	−12.0801	−0.623815
$376$	8.02659	0.413940
$377$	0	0
$378$	−0.883474	−0.0454410
$379$	22.8695	1.17473	0.587365	−	0.809322i	$-0.300165\pi$
$379$	22.8695	1.17473	0.587365	+	0.809322i	$0.300165\pi$
$380$	16.5054	0.846709
$381$	5.05085	0.258763
$382$	−12.0616	−0.617123
$383$	35.5259	1.81529	0.907646	−	0.419737i	$-0.137878\pi$
$383$	35.5259	1.81529	0.907646	+	0.419737i	$0.137878\pi$
$384$	−11.5112	−0.587427
$385$	2.95132	0.150413
$386$	−11.0216	−0.560984
$387$	−5.48659	−0.278899
$388$	24.0557	1.22124
$389$	−2.67074	−0.135412	−0.0677060	−	0.997705i	$-0.521568\pi$
$389$	−2.67074	−0.135412	−0.0677060	+	0.997705i	$0.521568\pi$
$390$	0	0
$391$	−2.41493	−0.122128
$392$	10.0915	0.509696
$393$	15.9772	0.805944
$394$	4.20087	0.211637
$395$	−10.8339	−0.545113
$396$	1.65803	0.0833193
$397$	36.4406	1.82890	0.914451	−	0.404698i	$-0.132623\pi$
$397$	36.4406	1.82890	0.914451	+	0.404698i	$0.132623\pi$
$398$	−11.0869	−0.555736
$399$	7.69876	0.385420
$400$	−2.44477	−0.122239
$401$	−13.6597	−0.682132	−0.341066	−	0.940039i	$-0.610788\pi$
$401$	−13.6597	−0.682132	−0.341066	+	0.940039i	$0.610788\pi$
$402$	4.95422	0.247094
$403$	0	0
$404$	−14.3221	−0.712550
$405$	1.95350	0.0970703
$406$	−4.46099	−0.221395
$407$	−2.08160	−0.103181
$408$	−7.36288	−0.364517
$409$	−25.8507	−1.27823	−0.639117	−	0.769110i	$-0.720700\pi$
$409$	−25.8507	−1.27823	−0.639117	+	0.769110i	$0.720700\pi$
$410$	−1.18415	−0.0584810
$411$	17.2582	0.851283
$412$	4.80909	0.236927
$413$	−4.00393	−0.197020
$414$	−0.410287	−0.0201645
$415$	−28.3525	−1.39177
$416$	0	0
$417$	−5.70544	−0.279397
$418$	2.97995	0.145754
$419$	22.6067	1.10441	0.552205	−	0.833708i	$-0.313787\pi$
$419$	22.6067	1.10441	0.552205	+	0.833708i	$0.313787\pi$
$420$	4.89339	0.238773
$421$	−24.6918	−1.20341	−0.601703	−	0.798720i	$-0.705511\pi$
$421$	−24.6918	−1.20341	−0.601703	+	0.798720i	$0.705511\pi$
$422$	−11.6907	−0.569092
$423$	−3.75225	−0.182441
$424$	1.07544	0.0522282
$425$	−4.07471	−0.197652
$426$	1.35395	0.0655993
$427$	8.13097	0.393485
$428$	3.80079	0.183718
$429$	0	0
$430$	−6.26770	−0.302255
$431$	−30.1126	−1.45047	−0.725237	−	0.688499i	$-0.758270\pi$
$431$	−30.1126	−1.45047	−0.725237	+	0.688499i	$0.758270\pi$
$432$	2.06515	0.0993594
$433$	30.9402	1.48689	0.743445	−	0.668797i	$-0.233191\pi$
$433$	30.9402	1.48689	0.743445	+	0.668797i	$0.233191\pi$
$434$	6.42248	0.308289
$435$	9.86396	0.472941
$436$	21.3585	1.02289
$437$	3.57532	0.171031
$438$	−1.29291	−0.0617775
$439$	−7.02158	−0.335122	−0.167561	−	0.985862i	$-0.553589\pi$
$439$	−7.02158	−0.335122	−0.167561	+	0.985862i	$0.553589\pi$
$440$	4.17882	0.199217
$441$	−4.71753	−0.224644
$442$	0	0
$443$	−22.5411	−1.07096	−0.535480	−	0.844548i	$-0.679869\pi$
$443$	−22.5411	−1.07096	−0.535480	+	0.844548i	$0.679869\pi$
$444$	−3.45136	−0.163794
$445$	3.53518	0.167584
$446$	16.2442	0.769187
$447$	0.161015	0.00761574
$448$	1.39330	0.0658272
$449$	9.41670	0.444401	0.222201	−	0.975001i	$-0.428676\pi$
$449$	9.41670	0.444401	0.222201	+	0.975001i	$0.428676\pi$
$450$	−0.692276	−0.0326342
$451$	1.03658	0.0488105
$452$	20.9365	0.984772
$453$	−16.3107	−0.766341
$454$	−16.7553	−0.786365
$455$	0	0
$456$	10.9008	0.510476
$457$	3.48691	0.163111	0.0815554	−	0.996669i	$-0.474011\pi$
$457$	3.48691	0.163111	0.0815554	+	0.996669i	$0.474011\pi$
$458$	−2.82717	−0.132105
$459$	3.44198	0.160658
$460$	2.27250	0.105956
$461$	−15.1983	−0.707855	−0.353928	−	0.935273i	$-0.615154\pi$
$461$	−15.1983	−0.707855	−0.353928	+	0.935273i	$0.615154\pi$
$462$	0.883474	0.0411029
$463$	−15.9882	−0.743035	−0.371518	−	0.928426i	$-0.621162\pi$
$463$	−15.9882	−0.743035	−0.371518	+	0.928426i	$0.621162\pi$
$464$	10.4277	0.484093
$465$	−14.2011	−0.658562
$466$	7.96684	0.369057
$467$	32.9225	1.52347	0.761736	−	0.647888i	$-0.224348\pi$
$467$	32.9225	1.52347	0.761736	+	0.647888i	$0.224348\pi$
$468$	0	0
$469$	−12.7993	−0.591017
$470$	−4.28645	−0.197719
$471$	−14.2192	−0.655185
$472$	−5.66921	−0.260947
$473$	5.48659	0.252274
$474$	−3.24312	−0.148961
$475$	6.03262	0.276796
$476$	8.62193	0.395185
$477$	−0.502747	−0.0230192
$478$	3.50811	0.160457
$479$	−33.6023	−1.53533	−0.767664	−	0.640853i	$-0.778581\pi$
$479$	−33.6023	−1.53533	−0.767664	+	0.640853i	$0.778581\pi$
$480$	10.7168	0.489152
$481$	0	0
$482$	7.56061	0.344376
$483$	1.05998	0.0482309
$484$	−1.65803	−0.0753652
$485$	−28.3425	−1.28697
$486$	0.584778	0.0265261
$487$	−3.70001	−0.167663	−0.0838316	−	0.996480i	$-0.526716\pi$
$487$	−3.70001	−0.167663	−0.0838316	+	0.996480i	$0.526716\pi$
$488$	11.5127	0.521158
$489$	−13.0186	−0.588722
$490$	−5.38915	−0.243457
$491$	−10.1397	−0.457599	−0.228799	−	0.973474i	$-0.573480\pi$
$491$	−10.1397	−0.457599	−0.228799	+	0.973474i	$0.573480\pi$
$492$	1.71868	0.0774840
$493$	17.3798	0.782749
$494$	0	0
$495$	−1.95350	−0.0878034
$496$	−15.0127	−0.674091
$497$	−3.49796	−0.156905
$498$	−8.48728	−0.380324
$499$	15.1124	0.676525	0.338263	−	0.941052i	$-0.390161\pi$
$499$	15.1124	0.676525	0.338263	+	0.941052i	$0.390161\pi$
$500$	20.0293	0.895736
$501$	−14.0271	−0.626683
$502$	−14.0185	−0.625678
$503$	11.9190	0.531441	0.265721	−	0.964050i	$-0.414390\pi$
$503$	11.9190	0.531441	0.265721	+	0.964050i	$0.414390\pi$
$504$	3.23178	0.143955
$505$	16.8743	0.750898
$506$	0.410287	0.0182395
$507$	0	0
$508$	−8.37448	−0.371558
$509$	35.2059	1.56047	0.780236	−	0.625485i	$-0.215099\pi$
$509$	35.2059	1.56047	0.780236	+	0.625485i	$0.215099\pi$
$510$	3.93200	0.174112
$511$	3.34025	0.147764
$512$	20.1645	0.891154
$513$	−5.09587	−0.224988
$514$	9.55767	0.421571
$515$	−5.66609	−0.249678
$516$	9.09696	0.400471
$517$	3.75225	0.165024
$518$	−1.83904	−0.0808028
$519$	17.8674	0.784294
$520$	0	0
$521$	−2.84143	−0.124485	−0.0622426	−	0.998061i	$-0.519825\pi$
$521$	−2.84143	−0.124485	−0.0622426	+	0.998061i	$0.519825\pi$
$522$	2.95276	0.129239
$523$	−17.8564	−0.780804	−0.390402	−	0.920644i	$-0.627664\pi$
$523$	−17.8564	−0.780804	−0.390402	+	0.920644i	$0.627664\pi$
$524$	−26.4908	−1.15725
$525$	1.78851	0.0780568
$526$	5.93607	0.258825
$527$	−25.0217	−1.08996
$528$	−2.06515	−0.0898739
$529$	−22.5077	−0.978597
$530$	−0.574321	−0.0249469
$531$	2.65023	0.115010
$532$	−12.7648	−0.553424
$533$	0	0
$534$	1.05825	0.0457950
$535$	−4.47810	−0.193605
$536$	−18.1227	−0.782782
$537$	17.2723	0.745354
$538$	9.66602	0.416732
$539$	4.71753	0.203198
$540$	−3.23897	−0.139383
$541$	3.56883	0.153436	0.0767179	−	0.997053i	$-0.475556\pi$
$541$	3.56883	0.153436	0.0767179	+	0.997053i	$0.475556\pi$
$542$	−12.2176	−0.524791
$543$	3.70318	0.158919
$544$	18.8825	0.809579
$545$	−25.1647	−1.07794
$546$	0	0
$547$	3.50639	0.149923	0.0749613	−	0.997186i	$-0.476117\pi$
$547$	3.50639	0.149923	0.0749613	+	0.997186i	$0.476117\pi$
$548$	−28.6146	−1.22236
$549$	−5.38195	−0.229696
$550$	0.692276	0.0295188
$551$	−25.7309	−1.09617
$552$	1.50084	0.0638802
$553$	8.37864	0.356296
$554$	−10.1207	−0.429989
$555$	4.06641	0.172610
$556$	9.45982	0.401186
$557$	−7.38164	−0.312770	−0.156385	−	0.987696i	$-0.549984\pi$
$557$	−7.38164	−0.312770	−0.156385	+	0.987696i	$0.549984\pi$
$558$	−4.25109	−0.179963
$559$	0	0
$560$	−6.09491	−0.257557
$561$	−3.44198	−0.145321
$562$	9.39537	0.396320
$563$	−35.5383	−1.49776	−0.748879	−	0.662706i	$-0.769408\pi$
$563$	−35.5383	−1.49776	−0.748879	+	0.662706i	$0.769408\pi$
$564$	6.22136	0.261967
$565$	−24.6675	−1.03777
$566$	−10.0687	−0.423219
$567$	−1.51078	−0.0634470
$568$	−4.95281	−0.207815
$569$	−19.6546	−0.823966	−0.411983	−	0.911192i	$-0.635164\pi$
$569$	−19.6546	−0.823966	−0.411983	+	0.911192i	$0.635164\pi$
$570$	−5.82135	−0.243830
$571$	−18.6081	−0.778726	−0.389363	−	0.921084i	$-0.627305\pi$
$571$	−18.6081	−0.778726	−0.389363	+	0.921084i	$0.627305\pi$
$572$	0	0
$573$	−20.6259	−0.861658
$574$	0.915788	0.0382243
$575$	0.830586	0.0346378
$576$	−0.922236	−0.0384265
$577$	−25.5485	−1.06360	−0.531799	−	0.846871i	$-0.678484\pi$
$577$	−25.5485	−1.06360	−0.531799	+	0.846871i	$0.678484\pi$
$578$	−3.01323	−0.125334
$579$	−18.8475	−0.783274
$580$	−16.3548	−0.679096
$581$	21.9270	0.909686
$582$	−8.48429	−0.351685
$583$	0.502747	0.0208216
$584$	4.72950	0.195708
$585$	0	0
$586$	−3.09739	−0.127952
$587$	−2.35936	−0.0973813	−0.0486907	−	0.998814i	$-0.515505\pi$
$587$	−2.35936	−0.0973813	−0.0486907	+	0.998814i	$0.515505\pi$
$588$	7.82183	0.322567
$589$	37.0448	1.52640
$590$	3.02753	0.124642
$591$	7.18370	0.295498
$592$	4.29881	0.176680
$593$	−11.6707	−0.479257	−0.239628	−	0.970865i	$-0.577026\pi$
$593$	−11.6707	−0.479257	−0.239628	+	0.970865i	$0.577026\pi$
$594$	−0.584778	−0.0239938
$595$	−10.1584	−0.416453
$596$	−0.266968	−0.0109354
$597$	−18.9591	−0.775946
$598$	0	0
$599$	9.12181	0.372707	0.186354	−	0.982483i	$-0.440333\pi$
$599$	9.12181	0.372707	0.186354	+	0.982483i	$0.440333\pi$
$600$	2.53237	0.103384
$601$	6.90316	0.281586	0.140793	−	0.990039i	$-0.455035\pi$
$601$	6.90316	0.281586	0.140793	+	0.990039i	$0.455035\pi$
$602$	4.84726	0.197560
$603$	8.47197	0.345005
$604$	27.0436	1.10039
$605$	1.95350	0.0794212
$606$	5.05131	0.205196
$607$	11.5559	0.469038	0.234519	−	0.972112i	$-0.424648\pi$
$607$	11.5559	0.469038	0.234519	+	0.972112i	$0.424648\pi$
$608$	−27.9556	−1.13375
$609$	−7.62851	−0.309123
$610$	−6.14816	−0.248932
$611$	0	0
$612$	−5.70692	−0.230689
$613$	37.7362	1.52415	0.762075	−	0.647488i	$-0.224181\pi$
$613$	37.7362	1.52415	0.762075	+	0.647488i	$0.224181\pi$
$614$	−15.3808	−0.620720
$615$	−2.02496	−0.0816541
$616$	−3.23178	−0.130212
$617$	28.2159	1.13593	0.567964	−	0.823053i	$-0.307731\pi$
$617$	28.2159	1.13593	0.567964	+	0.823053i	$0.307731\pi$
$618$	−1.69614	−0.0682286
$619$	38.4407	1.54506	0.772530	−	0.634978i	$-0.218991\pi$
$619$	38.4407	1.54506	0.772530	+	0.634978i	$0.218991\pi$
$620$	23.5460	0.945628
$621$	−0.701611	−0.0281547
$622$	19.2152	0.770461
$623$	−2.73401	−0.109536
$624$	0	0
$625$	−17.6794	−0.707177
$626$	19.4222	0.776269
$627$	5.09587	0.203509
$628$	23.5759	0.940781
$629$	7.16483	0.285680
$630$	−1.72587	−0.0687603
$631$	−16.9688	−0.675519	−0.337759	−	0.941232i	$-0.609669\pi$
$631$	−16.9688	−0.675519	−0.337759	+	0.941232i	$0.609669\pi$
$632$	11.8634	0.471902
$633$	−19.9916	−0.794595
$634$	−18.0367	−0.716328
$635$	9.86685	0.391554
$636$	0.833571	0.0330532
$637$	0	0
$638$	−2.95276	−0.116901
$639$	2.31533	0.0915930
$640$	−22.4871	−0.888881
$641$	6.00876	0.237332	0.118666	−	0.992934i	$-0.462138\pi$
$641$	6.00876	0.237332	0.118666	+	0.992934i	$0.462138\pi$
$642$	−1.34051	−0.0529059
$643$	9.64269	0.380270	0.190135	−	0.981758i	$-0.439107\pi$
$643$	9.64269	0.380270	0.190135	+	0.981758i	$0.439107\pi$
$644$	−1.75749	−0.0692547
$645$	−10.7181	−0.422024
$646$	−10.2569	−0.403554
$647$	−34.1912	−1.34420	−0.672098	−	0.740463i	$-0.734606\pi$
$647$	−34.1912	−1.34420	−0.672098	+	0.740463i	$0.734606\pi$
$648$	−2.13914	−0.0840333
$649$	−2.65023	−0.104031
$650$	0	0
$651$	10.9828	0.430448
$652$	21.5853	0.845345
$653$	−2.32307	−0.0909086	−0.0454543	−	0.998966i	$-0.514474\pi$
$653$	−2.32307	−0.0909086	−0.0454543	+	0.998966i	$0.514474\pi$
$654$	−7.53303	−0.294565
$655$	31.2115	1.21954
$656$	−2.14068	−0.0835796
$657$	−2.21094	−0.0862568
$658$	3.31502	0.129233
$659$	4.07928	0.158906	0.0794532	−	0.996839i	$-0.474683\pi$
$659$	4.07928	0.158906	0.0794532	+	0.996839i	$0.474683\pi$
$660$	3.23897	0.126077
$661$	42.2740	1.64427	0.822135	−	0.569293i	$-0.192783\pi$
$661$	42.2740	1.64427	0.822135	+	0.569293i	$0.192783\pi$
$662$	−3.36489	−0.130780
$663$	0	0
$664$	31.0467	1.20485
$665$	15.0395	0.583209
$666$	1.21727	0.0471684
$667$	−3.54270	−0.137174
$668$	23.2574	0.899854
$669$	27.7784	1.07398
$670$	9.67809	0.373897
$671$	5.38195	0.207768
$672$	−8.28806	−0.319719
$673$	−10.6688	−0.411252	−0.205626	−	0.978631i	$-0.565923\pi$
$673$	−10.6688	−0.411252	−0.205626	+	0.978631i	$0.565923\pi$
$674$	6.38840	0.246072
$675$	−1.18383	−0.0455655
$676$	0	0
$677$	24.2174	0.930752	0.465376	−	0.885113i	$-0.345919\pi$
$677$	24.2174	0.930752	0.465376	+	0.885113i	$0.345919\pi$
$678$	−7.38419	−0.283588
$679$	21.9193	0.841185
$680$	−14.3834	−0.551578
$681$	−28.6524	−1.09796
$682$	4.25109	0.162783
$683$	−37.1698	−1.42226	−0.711132	−	0.703059i	$-0.751817\pi$
$683$	−37.1698	−1.42226	−0.711132	+	0.703059i	$0.751817\pi$
$684$	8.44913	0.323060
$685$	33.7139	1.28814
$686$	10.3521	0.395246
$687$	−4.83459	−0.184451
$688$	−11.3306	−0.431976
$689$	0	0
$690$	−0.801497	−0.0305125
$691$	15.9632	0.607268	0.303634	−	0.952789i	$-0.401800\pi$
$691$	15.9632	0.607268	0.303634	+	0.952789i	$0.401800\pi$
$692$	−29.6248	−1.12617
$693$	1.51078	0.0573899
$694$	9.55959	0.362877
$695$	−11.1456	−0.422777
$696$	−10.8013	−0.409423
$697$	−3.56788	−0.135143
$698$	−5.04522	−0.190965
$699$	13.6237	0.515295
$700$	−2.96540	−0.112082
$701$	−2.01736	−0.0761947	−0.0380974	−	0.999274i	$-0.512130\pi$
$701$	−2.01736	−0.0761947	−0.0380974	+	0.999274i	$0.512130\pi$
$702$	0	0
$703$	−10.6076	−0.400072
$704$	0.922236	0.0347581
$705$	−7.33004	−0.276065
$706$	−9.69519	−0.364883
$707$	−13.0501	−0.490801
$708$	−4.39417	−0.165143
$709$	29.6428	1.11326	0.556629	−	0.830761i	$-0.312095\pi$
$709$	29.6428	1.11326	0.556629	+	0.830761i	$0.312095\pi$
$710$	2.64495	0.0992634
$711$	−5.54589	−0.207987
$712$	−3.87112	−0.145076
$713$	5.10041	0.191012
$714$	−3.04090	−0.113803
$715$	0	0
$716$	−28.6380	−1.07025
$717$	5.99903	0.224038
$718$	9.07770	0.338777
$719$	32.3389	1.20604	0.603018	−	0.797728i	$-0.293965\pi$
$719$	32.3389	1.20604	0.603018	+	0.797728i	$0.293965\pi$
$720$	4.03427	0.150348
$721$	4.38199	0.163194
$722$	4.07467	0.151643
$723$	12.9290	0.480835
$724$	−6.13999	−0.228191
$725$	−5.97758	−0.222002
$726$	0.584778	0.0217032
$727$	37.9325	1.40684	0.703419	−	0.710775i	$-0.251656\pi$
$727$	37.9325	1.40684	0.703419	+	0.710775i	$0.251656\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−2.52570	−0.0934803
$731$	−18.8847	−0.698478
$732$	8.92346	0.329821
$733$	16.7917	0.620217	0.310109	−	0.950701i	$-0.399635\pi$
$733$	16.7917	0.620217	0.310109	+	0.950701i	$0.399635\pi$
$734$	13.7237	0.506550
$735$	−9.21571	−0.339927
$736$	−3.84899	−0.141876
$737$	−8.47197	−0.312069
$738$	−0.606168	−0.0223133
$739$	25.4629	0.936668	0.468334	−	0.883551i	$-0.344854\pi$
$739$	25.4629	0.936668	0.468334	+	0.883551i	$0.344854\pi$
$740$	−6.74225	−0.247850
$741$	0	0
$742$	0.444164	0.0163058
$743$	4.81269	0.176560	0.0882802	−	0.996096i	$-0.471863\pi$
$743$	4.81269	0.176560	0.0882802	+	0.996096i	$0.471863\pi$
$744$	15.5506	0.570114
$745$	0.314543	0.0115240
$746$	7.20574	0.263821
$747$	−14.5137	−0.531027
$748$	5.70692	0.208666
$749$	3.46324	0.126544
$750$	−7.06420	−0.257948
$751$	−24.9537	−0.910574	−0.455287	−	0.890345i	$-0.650463\pi$
$751$	−24.9537	−0.910574	−0.455287	+	0.890345i	$0.650463\pi$
$752$	−7.74895	−0.282575
$753$	−23.9724	−0.873603
$754$	0	0
$755$	−31.8629	−1.15961
$756$	2.50493	0.0911035
$757$	−33.8373	−1.22984	−0.614919	−	0.788591i	$-0.710811\pi$
$757$	−33.8373	−1.22984	−0.614919	+	0.788591i	$0.710811\pi$
$758$	13.3736	0.485752
$759$	0.701611	0.0254669
$760$	21.2947	0.772440
$761$	−50.5981	−1.83418	−0.917091	−	0.398679i	$-0.869469\pi$
$761$	−50.5981	−1.83418	−0.917091	+	0.398679i	$0.869469\pi$
$762$	2.95363	0.106999
$763$	19.4617	0.704561
$764$	34.1984	1.23725
$765$	6.72392	0.243104
$766$	20.7748	0.750624
$767$	0	0
$768$	−4.88701	−0.176345
$769$	26.1333	0.942389	0.471195	−	0.882029i	$-0.343823\pi$
$769$	26.1333	0.942389	0.471195	+	0.882029i	$0.343823\pi$
$770$	1.72587	0.0621960
$771$	16.3441	0.588618
$772$	31.2497	1.12470
$773$	−0.778578	−0.0280035	−0.0140018	−	0.999902i	$-0.504457\pi$
$773$	−0.778578	−0.0280035	−0.0140018	+	0.999902i	$0.504457\pi$
$774$	−3.20844	−0.115325
$775$	8.60591	0.309133
$776$	31.0358	1.11412
$777$	−3.14485	−0.112821
$778$	−1.56179	−0.0559930
$779$	5.28226	0.189257
$780$	0	0
$781$	−2.31533	−0.0828490
$782$	−1.41220	−0.0505002
$783$	5.04937	0.180450
$784$	−9.74239	−0.347942
$785$	−27.7772	−0.991411
$786$	9.34313	0.333258
$787$	33.9128	1.20886	0.604431	−	0.796658i	$-0.293401\pi$
$787$	33.9128	1.20886	0.604431	+	0.796658i	$0.293401\pi$
$788$	−11.9108	−0.424305
$789$	10.1510	0.361384
$790$	−6.33544	−0.225405
$791$	19.0772	0.678306
$792$	2.13914	0.0760110
$793$	0	0
$794$	21.3097	0.756252
$795$	−0.982117	−0.0348321
$796$	31.4349	1.11418
$797$	26.9305	0.953928	0.476964	−	0.878923i	$-0.341737\pi$
$797$	26.9305	0.953928	0.476964	+	0.878923i	$0.341737\pi$
$798$	4.50207	0.159372
$799$	−12.9152	−0.456906
$800$	−6.49439	−0.229611
$801$	1.80966	0.0639413
$802$	−7.98789	−0.282062
$803$	2.21094	0.0780223
$804$	−14.0468	−0.495393
$805$	2.07068	0.0729819
$806$	0	0
$807$	16.5294	0.581862
$808$	−18.4779	−0.650049
$809$	52.4814	1.84515	0.922575	−	0.385819i	$-0.126081\pi$
$809$	52.4814	1.84515	0.922575	+	0.385819i	$0.126081\pi$
$810$	1.14237	0.0401387
$811$	−19.2236	−0.675033	−0.337516	−	0.941320i	$-0.609587\pi$
$811$	−19.2236	−0.675033	−0.337516	+	0.941320i	$0.609587\pi$
$812$	12.6483	0.443869
$813$	−20.8927	−0.732739
$814$	−1.21727	−0.0426655
$815$	−25.4319	−0.890840
$816$	7.10819	0.248836
$817$	27.9590	0.978160
$818$	−15.1169	−0.528551
$819$	0	0
$820$	3.35744	0.117247
$821$	−30.4099	−1.06131	−0.530657	−	0.847587i	$-0.678055\pi$
$821$	−30.4099	−1.06131	−0.530657	+	0.847587i	$0.678055\pi$
$822$	10.0922	0.352006
$823$	16.1575	0.563216	0.281608	−	0.959530i	$-0.409132\pi$
$823$	16.1575	0.563216	0.281608	+	0.959530i	$0.409132\pi$
$824$	6.20452	0.216145
$825$	1.18383	0.0412155
$826$	−2.34141	−0.0814681
$827$	47.5066	1.65197	0.825983	−	0.563695i	$-0.190621\pi$
$827$	47.5066	1.65197	0.825983	+	0.563695i	$0.190621\pi$
$828$	1.16330	0.0404273
$829$	56.6932	1.96904	0.984519	−	0.175278i	$-0.0560825\pi$
$829$	56.6932	1.96904	0.984519	+	0.175278i	$0.0560825\pi$
$830$	−16.5799	−0.575497
$831$	−17.3070	−0.600372
$832$	0	0
$833$	−16.2376	−0.562601
$834$	−3.33642	−0.115531
$835$	−27.4019	−0.948283
$836$	−8.44913	−0.292219
$837$	−7.26957	−0.251273
$838$	13.2199	0.456674
$839$	−35.2293	−1.21625	−0.608125	−	0.793841i	$-0.708078\pi$
$839$	−35.2293	−1.21625	−0.608125	+	0.793841i	$0.708078\pi$
$840$	6.31329	0.217829
$841$	−3.50384	−0.120822
$842$	−14.4393	−0.497610
$843$	16.0666	0.553361
$844$	33.1468	1.14096
$845$	0	0
$846$	−2.19424	−0.0754394
$847$	−1.51078	−0.0519112
$848$	−1.03824	−0.0356535
$849$	−17.2180	−0.590919
$850$	−2.38280	−0.0817294
$851$	−1.46047	−0.0500644
$852$	−3.83890	−0.131518
$853$	−18.7185	−0.640909	−0.320454	−	0.947264i	$-0.603836\pi$
$853$	−18.7185	−0.640909	−0.320454	+	0.947264i	$0.603836\pi$
$854$	4.75482	0.162706
$855$	−9.95480	−0.340447
$856$	4.90365	0.167603
$857$	47.3032	1.61585	0.807924	−	0.589287i	$-0.200591\pi$
$857$	47.3032	1.61585	0.807924	+	0.589287i	$0.200591\pi$
$858$	0	0
$859$	−40.6908	−1.38835	−0.694176	−	0.719805i	$-0.744231\pi$
$859$	−40.6908	−1.38835	−0.694176	+	0.719805i	$0.744231\pi$
$860$	17.7709	0.605984
$861$	1.56604	0.0533706
$862$	−17.6092	−0.599772
$863$	1.42374	0.0484647	0.0242324	−	0.999706i	$-0.492286\pi$
$863$	1.42374	0.0484647	0.0242324	+	0.999706i	$0.492286\pi$
$864$	5.48593	0.186635
$865$	34.9041	1.18678
$866$	18.0931	0.614830
$867$	−5.15277	−0.174997
$868$	−18.2098	−0.618080
$869$	5.54589	0.188131
$870$	5.76823	0.195561
$871$	0	0
$872$	27.5561	0.933166
$873$	−14.5085	−0.491040
$874$	2.09077	0.0707213
$875$	18.2505	0.616978
$876$	3.66581	0.123856
$877$	−56.1060	−1.89457	−0.947283	−	0.320397i	$-0.896184\pi$
$877$	−56.1060	−1.89457	−0.947283	+	0.320397i	$0.896184\pi$
$878$	−4.10607	−0.138573
$879$	−5.29670	−0.178653
$880$	−4.03427	−0.135995
$881$	16.2234	0.546581	0.273290	−	0.961932i	$-0.411888\pi$
$881$	16.2234	0.546581	0.273290	+	0.961932i	$0.411888\pi$
$882$	−2.75871	−0.0928906
$883$	−33.0296	−1.11153	−0.555767	−	0.831338i	$-0.687575\pi$
$883$	−33.0296	−1.11153	−0.555767	+	0.831338i	$0.687575\pi$
$884$	0	0
$885$	5.17723	0.174031
$886$	−13.1815	−0.442843
$887$	−54.6149	−1.83379	−0.916894	−	0.399130i	$-0.869312\pi$
$887$	−54.6149	−1.83379	−0.916894	+	0.399130i	$0.869312\pi$
$888$	−4.45283	−0.149427
$889$	−7.63074	−0.255927
$890$	2.06730	0.0692960
$891$	−1.00000	−0.0335013
$892$	−46.0576	−1.54212
$893$	19.1210	0.639860
$894$	0.0941580	0.00314911
$895$	33.7414	1.12785
$896$	17.3909	0.580989
$897$	0	0
$898$	5.50668	0.183760
$899$	−36.7068	−1.22424
$900$	1.96282	0.0654275
$901$	−1.73044	−0.0576494
$902$	0.606168	0.0201832
$903$	8.28906	0.275843
$904$	27.0116	0.898393
$905$	7.23417	0.240472
$906$	−9.53812	−0.316883
$907$	31.1937	1.03577	0.517884	−	0.855451i	$-0.326720\pi$
$907$	31.1937	1.03577	0.517884	+	0.855451i	$0.326720\pi$
$908$	47.5066	1.57656
$909$	8.63799	0.286504
$910$	0	0
$911$	53.7300	1.78015	0.890077	−	0.455810i	$-0.150650\pi$
$911$	53.7300	1.78015	0.890077	+	0.455810i	$0.150650\pi$
$912$	−10.5237	−0.348475
$913$	14.5137	0.480332
$914$	2.03907	0.0674464
$915$	−10.5137	−0.347571
$916$	8.01592	0.264853
$917$	−24.1381	−0.797111
$918$	2.01280	0.0664322
$919$	16.3202	0.538353	0.269177	−	0.963091i	$-0.413248\pi$
$919$	16.3202	0.538353	0.269177	+	0.963091i	$0.413248\pi$
$920$	2.93190	0.0966620
$921$	−26.3020	−0.866680
$922$	−8.88764	−0.292699
$923$	0	0
$924$	−2.50493	−0.0824062
$925$	−2.46425	−0.0810241
$926$	−9.34956	−0.307246
$927$	−2.90048	−0.0952641
$928$	27.7005	0.909314
$929$	−56.4975	−1.85362	−0.926811	−	0.375527i	$-0.877462\pi$
$929$	−56.4975	−1.85362	−0.926811	+	0.375527i	$0.877462\pi$
$930$	−8.30451	−0.272316
$931$	24.0399	0.787877
$932$	−22.5885	−0.739912
$933$	32.8590	1.07576
$934$	19.2524	0.629957
$935$	−6.72392	−0.219896
$936$	0	0
$937$	52.5328	1.71617	0.858086	−	0.513506i	$-0.171654\pi$
$937$	52.5328	1.71617	0.858086	+	0.513506i	$0.171654\pi$
$938$	−7.48476	−0.244386
$939$	33.2130	1.08387
$940$	12.1535	0.396402
$941$	−24.3963	−0.795296	−0.397648	−	0.917538i	$-0.630174\pi$
$941$	−24.3963	−0.795296	−0.397648	+	0.917538i	$0.630174\pi$
$942$	−8.31507	−0.270920
$943$	0.727273	0.0236833
$944$	5.47311	0.178135
$945$	−2.95132	−0.0960065
$946$	3.20844	0.104315
$947$	38.9960	1.26720	0.633600	−	0.773661i	$-0.281577\pi$
$947$	38.9960	1.26720	0.633600	+	0.773661i	$0.281577\pi$
$948$	9.19527	0.298648
$949$	0	0
$950$	3.52775	0.114455
$951$	−30.8436	−1.00017
$952$	11.1237	0.360522
$953$	−30.9120	−1.00134	−0.500670	−	0.865638i	$-0.666913\pi$
$953$	−30.9120	−1.00134	−0.500670	+	0.865638i	$0.666913\pi$
$954$	−0.293995	−0.00951845
$955$	−40.2927	−1.30384
$956$	−9.94660	−0.321696
$957$	−5.04937	−0.163223
$958$	−19.6499	−0.634859
$959$	−26.0734	−0.841953
$960$	−1.80159	−0.0581461
$961$	21.8467	0.704731
$962$	0	0
$963$	−2.29234	−0.0738698
$964$	−21.4367	−0.690431
$965$	−36.8186	−1.18523
$966$	0.619855	0.0199435
$967$	31.5859	1.01573	0.507867	−	0.861435i	$-0.330434\pi$
$967$	31.5859	1.01573	0.507867	+	0.861435i	$0.330434\pi$
$968$	−2.13914	−0.0687546
$969$	−17.5399	−0.563462
$970$	−16.5741	−0.532162
$971$	−32.5555	−1.04476	−0.522378	−	0.852714i	$-0.674955\pi$
$971$	−32.5555	−1.04476	−0.522378	+	0.852714i	$0.674955\pi$
$972$	−1.65803	−0.0531815
$973$	8.61969	0.276335
$974$	−2.16368	−0.0693289
$975$	0	0
$976$	−11.1145	−0.355767
$977$	3.54984	0.113569	0.0567847	−	0.998386i	$-0.481915\pi$
$977$	3.54984	0.113569	0.0567847	+	0.998386i	$0.481915\pi$
$978$	−7.61300	−0.243437
$979$	−1.80966	−0.0578371
$980$	15.2800	0.488101
$981$	−12.8818	−0.411286
$982$	−5.92949	−0.189218
$983$	16.6279	0.530349	0.265174	−	0.964200i	$-0.414570\pi$
$983$	16.6279	0.530349	0.265174	+	0.964200i	$0.414570\pi$
$984$	2.21738	0.0706875
$985$	14.0334	0.447141
$986$	10.1634	0.323667
$987$	5.66884	0.180441
$988$	0	0
$989$	3.84946	0.122406
$990$	−1.14237	−0.0363068
$991$	36.4447	1.15770	0.578852	−	0.815433i	$-0.303501\pi$
$991$	36.4447	1.15770	0.578852	+	0.815433i	$0.303501\pi$
$992$	−39.8804	−1.26620
$993$	−5.75414	−0.182602
$994$	−2.04553	−0.0648804
$995$	−37.0367	−1.17414
$996$	24.0641	0.762502
$997$	−2.23772	−0.0708692	−0.0354346	−	0.999372i	$-0.511282\pi$
$997$	−2.23772	−0.0708692	−0.0354346	+	0.999372i	$0.511282\pi$
$998$	8.83742	0.279744
$999$	2.08160	0.0658589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.x.1.5		7
13.5	odd	4		429.2.b.b.298.6	✓	14
13.8	odd	4		429.2.b.b.298.9	yes	14
13.12	even	2		5577.2.a.y.1.3		7
39.5	even	4		1287.2.b.c.298.9		14
39.8	even	4		1287.2.b.c.298.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.b.b.298.6	✓	14	13.5	odd	4
429.2.b.b.298.9	yes	14	13.8	odd	4
1287.2.b.c.298.6		14	39.8	even	4
1287.2.b.c.298.9		14	39.5	even	4
5577.2.a.x.1.5		7	1.1	even	1	trivial
5577.2.a.y.1.3		7	13.12	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:	\( N \)	\(=\)	\( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5577.a (trivial)

\(f(q)\)	\(=\)	\(q+0.584778 q^{2} +1.00000 q^{3} -1.65803 q^{4} +1.95350 q^{5} +0.584778 q^{6} -1.51078 q^{7} -2.13914 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.584778 q^{2} +1.00000 q^{3} -1.65803 q^{4} +1.95350 q^{5} +0.584778 q^{6} -1.51078 q^{7} -2.13914 q^{8} +1.00000 q^{9} +1.14237 q^{10} -1.00000 q^{11} -1.65803 q^{12} -0.883474 q^{14} +1.95350 q^{15} +2.06515 q^{16} +3.44198 q^{17} +0.584778 q^{18} -5.09587 q^{19} -3.23897 q^{20} -1.51078 q^{21} -0.584778 q^{22} -0.701611 q^{23} -2.13914 q^{24} -1.18383 q^{25} +1.00000 q^{27} +2.50493 q^{28} +5.04937 q^{29} +1.14237 q^{30} -7.26957 q^{31} +5.48593 q^{32} -1.00000 q^{33} +2.01280 q^{34} -2.95132 q^{35} -1.65803 q^{36} +2.08160 q^{37} -2.97995 q^{38} -4.17882 q^{40} -1.03658 q^{41} -0.883474 q^{42} -5.48659 q^{43} +1.65803 q^{44} +1.95350 q^{45} -0.410287 q^{46} -3.75225 q^{47} +2.06515 q^{48} -4.71753 q^{49} -0.692276 q^{50} +3.44198 q^{51} -0.502747 q^{53} +0.584778 q^{54} -1.95350 q^{55} +3.23178 q^{56} -5.09587 q^{57} +2.95276 q^{58} +2.65023 q^{59} -3.23897 q^{60} -5.38195 q^{61} -4.25109 q^{62} -1.51078 q^{63} -0.922236 q^{64} -0.584778 q^{66} +8.47197 q^{67} -5.70692 q^{68} -0.701611 q^{69} -1.72587 q^{70} +2.31533 q^{71} -2.13914 q^{72} -2.21094 q^{73} +1.21727 q^{74} -1.18383 q^{75} +8.44913 q^{76} +1.51078 q^{77} -5.54589 q^{79} +4.03427 q^{80} +1.00000 q^{81} -0.606168 q^{82} -14.5137 q^{83} +2.50493 q^{84} +6.72392 q^{85} -3.20844 q^{86} +5.04937 q^{87} +2.13914 q^{88} +1.80966 q^{89} +1.14237 q^{90} +1.16330 q^{92} -7.26957 q^{93} -2.19424 q^{94} -9.95480 q^{95} +5.48593 q^{96} -14.5085 q^{97} -2.75871 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 3 q^{2} + 7 q^{3} + 9 q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{7} - 15 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 3 * q^2 + 7 * q^3 + 9 * q^4 - 6 * q^5 - 3 * q^6 - 6 * q^7 - 15 * q^8 + 7 * q^9	\( 7 q - 3 q^{2} + 7 q^{3} + 9 q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{7} - 15 q^{8} + 7 q^{9} - 7 q^{11} + 9 q^{12} + 8 q^{14} - 6 q^{15} + 17 q^{16} - 2 q^{17} - 3 q^{18} - 8 q^{19} + 2 q^{20} - 6 q^{21} + 3 q^{22} + 4 q^{23} - 15 q^{24} + 13 q^{25} + 7 q^{27} - 12 q^{28} - 12 q^{29} + 10 q^{31} - 33 q^{32} - 7 q^{33} - 28 q^{34} - 4 q^{35} + 9 q^{36} - 6 q^{37} + 16 q^{38} - 10 q^{40} - 2 q^{41} + 8 q^{42} - 16 q^{43} - 9 q^{44} - 6 q^{45} + 26 q^{46} - 18 q^{47} + 17 q^{48} + 23 q^{49} - 39 q^{50} - 2 q^{51} + 10 q^{53} - 3 q^{54} + 6 q^{55} + 16 q^{56} - 8 q^{57} - 10 q^{58} - 2 q^{59} + 2 q^{60} - 10 q^{61} - 36 q^{62} - 6 q^{63} + 29 q^{64} + 3 q^{66} - 8 q^{67} - 10 q^{68} + 4 q^{69} + 20 q^{70} - 36 q^{71} - 15 q^{72} - 20 q^{73} + 13 q^{75} - 10 q^{76} + 6 q^{77} + 6 q^{79} + 20 q^{80} + 7 q^{81} - 10 q^{82} - 30 q^{83} - 12 q^{84} + 40 q^{85} - 6 q^{86} - 12 q^{87} + 15 q^{88} - 34 q^{89} - 12 q^{92} + 10 q^{93} + 32 q^{94} + 18 q^{95} - 33 q^{96} - 16 q^{97} - q^{98} - 7 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 + 7 * q^3 + 9 * q^4 - 6 * q^5 - 3 * q^6 - 6 * q^7 - 15 * q^8 + 7 * q^9 - 7 * q^11 + 9 * q^12 + 8 * q^14 - 6 * q^15 + 17 * q^16 - 2 * q^17 - 3 * q^18 - 8 * q^19 + 2 * q^20 - 6 * q^21 + 3 * q^22 + 4 * q^23 - 15 * q^24 + 13 * q^25 + 7 * q^27 - 12 * q^28 - 12 * q^29 + 10 * q^31 - 33 * q^32 - 7 * q^33 - 28 * q^34 - 4 * q^35 + 9 * q^36 - 6 * q^37 + 16 * q^38 - 10 * q^40 - 2 * q^41 + 8 * q^42 - 16 * q^43 - 9 * q^44 - 6 * q^45 + 26 * q^46 - 18 * q^47 + 17 * q^48 + 23 * q^49 - 39 * q^50 - 2 * q^51 + 10 * q^53 - 3 * q^54 + 6 * q^55 + 16 * q^56 - 8 * q^57 - 10 * q^58 - 2 * q^59 + 2 * q^60 - 10 * q^61 - 36 * q^62 - 6 * q^63 + 29 * q^64 + 3 * q^66 - 8 * q^67 - 10 * q^68 + 4 * q^69 + 20 * q^70 - 36 * q^71 - 15 * q^72 - 20 * q^73 + 13 * q^75 - 10 * q^76 + 6 * q^77 + 6 * q^79 + 20 * q^80 + 7 * q^81 - 10 * q^82 - 30 * q^83 - 12 * q^84 + 40 * q^85 - 6 * q^86 - 12 * q^87 + 15 * q^88 - 34 * q^89 - 12 * q^92 + 10 * q^93 + 32 * q^94 + 18 * q^95 - 33 * q^96 - 16 * q^97 - q^98 - 7 * q^99

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