LMFDB - Embedded newform 5577.2.a.y.1.3

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:	$0$
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			1.3
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	$-0.566289\pi$
$2$	−0.584778	−0.413501	−0.206750	+	0.978394i	$0.566289\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.65803	−0.829017
$5$	−1.95350	−0.873633	−0.436817	−	0.899551i	$-0.643894\pi$
$5$	−1.95350	−0.873633	−0.436817	+	0.899551i	$0.643894\pi$
$6$	−0.584778	−0.238735
$7$	1.51078	0.571023	0.285511	−	0.958375i	$-0.407837\pi$
$7$	1.51078	0.571023	0.285511	+	0.958375i	$0.407837\pi$
$8$	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	$-0.301276\pi$
$19$	5.09587	1.16907	0.584536	+	0.811368i	$0.301276\pi$
$20$	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	$-0.273583\pi$
$31$	7.26957	1.30565	0.652827	+	0.757507i	$0.273583\pi$
$32$	−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	$-0.554734\pi$
$37$	−2.08160	−0.342213	−0.171106	+	0.985253i	$0.554734\pi$
$38$	−2.97995	−0.483413
$39$	0	0
$40$	−4.17882	−0.660729
$41$	1.03658	0.161886	0.0809430	−	0.996719i	$-0.474207\pi$
$41$	1.03658	0.161886	0.0809430	+	0.996719i	$0.474207\pi$
$42$	−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	$-0.411765\pi$
$47$	3.75225	0.547322	0.273661	+	0.961826i	$0.411765\pi$
$48$	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	$-0.555189\pi$
$59$	−2.65023	−0.345031	−0.172515	+	0.985007i	$0.555189\pi$
$60$	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	$-0.673140\pi$
$67$	−8.47197	−1.03502	−0.517508	+	0.855679i	$0.673140\pi$
$68$	−5.70692	−0.692066
$69$	−0.701611	−0.0844640
$70$	1.72587	0.206281
$71$	−2.31533	−0.274779	−0.137390	−	0.990517i	$-0.543871\pi$
$71$	−2.31533	−0.274779	−0.137390	+	0.990517i	$0.543871\pi$
$72$	2.13914	0.252100
$73$	2.21094	0.258771	0.129385	−	0.991594i	$-0.458700\pi$
$73$	2.21094	0.258771	0.129385	+	0.991594i	$0.458700\pi$
$74$	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	$-0.206661\pi$
$83$	14.5137	1.59308	0.796541	+	0.604585i	$0.206661\pi$
$84$	−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	$-0.530577\pi$
$89$	−1.80966	−0.191824	−0.0959119	+	0.995390i	$0.530577\pi$
$90$	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	$-0.236449\pi$
$97$	14.5085	1.47312	0.736560	+	0.676372i	$0.236449\pi$
$98$	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	$-0.288377\pi$
$109$	12.8818	1.23386	0.616929	+	0.787019i	$0.288377\pi$
$110$	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	$-0.763868\pi$
$137$	−17.2582	−1.47447	−0.737233	+	0.675639i	$0.763868\pi$
$138$	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	$-0.502099\pi$
$149$	−0.161015	−0.0131908	−0.00659542	+	0.999978i	$0.502099\pi$
$150$	0.692276	0.0565241
$151$	16.3107	1.32734	0.663671	−	0.748025i	$-0.268997\pi$
$151$	16.3107	1.32734	0.663671	+	0.748025i	$0.268997\pi$
$152$	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	$-0.329702\pi$
$163$	13.0186	1.01970	0.509848	+	0.860264i	$0.329702\pi$
$164$	−1.71868	−0.134206
$165$	−1.95350	−0.152080
$166$	−8.48728	−0.658740
$167$	14.0271	1.08545	0.542724	−	0.839911i	$-0.317393\pi$
$167$	14.0271	1.08545	0.542724	+	0.839911i	$0.317393\pi$
$168$	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	$-0.262702\pi$
$193$	18.8475	1.35667	0.678335	+	0.734753i	$0.262702\pi$
$194$	−8.48429	−0.609136
$195$	0	0
$196$	7.82183	0.558702
$197$	−7.18370	−0.511818	−0.255909	−	0.966701i	$-0.582375\pi$
$197$	−7.18370	−0.511818	−0.255909	+	0.966701i	$0.582375\pi$
$198$	−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	$-0.880272\pi$
$223$	−27.7784	−1.86018	−0.930091	+	0.367330i	$0.880272\pi$
$224$	−8.28806	−0.553769
$225$	−1.18383	−0.0789218
$226$	7.38419	0.491189
$227$	28.6524	1.90173	0.950863	−	0.309612i	$-0.100199\pi$
$227$	28.6524	1.90173	0.950863	+	0.309612i	$0.100199\pi$
$228$	−8.44913	−0.559557
$229$	4.83459	0.319479	0.159739	−	0.987159i	$-0.448935\pi$
$229$	4.83459	0.319479	0.159739	+	0.987159i	$0.448935\pi$
$230$	−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	$-0.562154\pi$
$239$	−5.99903	−0.388045	−0.194023	+	0.980997i	$0.562154\pi$
$240$	−4.03427	−0.260411
$241$	−12.9290	−0.832831	−0.416416	−	0.909174i	$-0.636714\pi$
$241$	−12.9290	−0.832831	−0.416416	+	0.909174i	$0.636714\pi$
$242$	−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	$-0.281177\pi$
$271$	20.8927	1.26914	0.634570	+	0.772865i	$0.281177\pi$
$272$	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	$-0.659082\pi$
$281$	−16.0666	−0.958450	−0.479225	+	0.877692i	$0.659082\pi$
$282$	−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	$-0.450553\pi$
$293$	5.29670	0.309436	0.154718	+	0.987959i	$0.450553\pi$
$294$	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	$-0.229780\pi$
$307$	26.3020	1.50113	0.750567	+	0.660794i	$0.229780\pi$
$308$	−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	$-0.166571\pi$
$317$	30.8436	1.73235	0.866175	+	0.499740i	$0.166571\pi$
$318$	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	$-0.449451\pi$
$331$	5.75414	0.316276	0.158138	+	0.987417i	$0.449451\pi$
$332$	−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	$-0.425829\pi$
$349$	8.62758	0.461824	0.230912	+	0.972975i	$0.425829\pi$
$350$	1.04588	0.0559046
$351$	0	0
$352$	−5.48593	−0.292401
$353$	16.5793	0.882425	0.441212	−	0.897403i	$-0.354549\pi$
$353$	16.5793	0.882425	0.441212	+	0.897403i	$0.354549\pi$
$354$	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	$-0.634347\pi$
$359$	−15.5233	−0.819289	−0.409645	+	0.912245i	$0.634347\pi$
$360$	−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	$-0.699835\pi$
$379$	−22.8695	−1.17473	−0.587365	+	0.809322i	$0.699835\pi$
$380$	16.5054	0.846709
$381$	5.05085	0.258763
$382$	12.0616	0.617123
$383$	−35.5259	−1.81529	−0.907646	−	0.419737i	$-0.862122\pi$
$383$	−35.5259	−1.81529	−0.907646	+	0.419737i	$0.862122\pi$
$384$	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	$-0.867377\pi$
$397$	−36.4406	−1.82890	−0.914451	+	0.404698i	$0.867377\pi$
$398$	11.0869	0.555736
$399$	7.69876	0.385420
$400$	−2.44477	−0.122239
$401$	13.6597	0.682132	0.341066	−	0.940039i	$-0.389212\pi$
$401$	13.6597	0.682132	0.341066	+	0.940039i	$0.389212\pi$
$402$	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	$-0.279300\pi$
$409$	25.8507	1.27823	0.639117	+	0.769110i	$0.279300\pi$
$410$	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	$-0.294489\pi$
$421$	24.6918	1.20341	0.601703	+	0.798720i	$0.294489\pi$
$422$	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	$-0.241730\pi$
$431$	30.1126	1.45047	0.725237	+	0.688499i	$0.241730\pi$
$432$	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	$-0.571324\pi$
$449$	−9.41670	−0.444401	−0.222201	+	0.975001i	$0.571324\pi$
$450$	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	$-0.525989\pi$
$457$	−3.48691	−0.163111	−0.0815554	+	0.996669i	$0.525989\pi$
$458$	−2.82717	−0.132105
$459$	3.44198	0.160658
$460$	−2.27250	−0.105956
$461$	15.1983	0.707855	0.353928	−	0.935273i	$-0.384846\pi$
$461$	15.1983	0.707855	0.353928	+	0.935273i	$0.384846\pi$
$462$	−0.883474	−0.0411029
$463$	15.9882	0.743035	0.371518	−	0.928426i	$-0.378838\pi$
$463$	15.9882	0.743035	0.371518	+	0.928426i	$0.378838\pi$
$464$	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	$-0.221419\pi$
$479$	33.6023	1.53533	0.767664	+	0.640853i	$0.221419\pi$
$480$	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	$-0.473284\pi$
$487$	3.70001	0.167663	0.0838316	+	0.996480i	$0.473284\pi$
$488$	−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	$-0.609839\pi$
$499$	−15.1124	−0.676525	−0.338263	+	0.941052i	$0.609839\pi$
$500$	−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	$-0.784901\pi$
$509$	−35.2059	−1.56047	−0.780236	+	0.625485i	$0.784901\pi$
$510$	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	$-0.524444\pi$
$541$	−3.56883	−0.153436	−0.0767179	+	0.997053i	$0.524444\pi$
$542$	−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	$-0.450016\pi$
$557$	7.38164	0.312770	0.156385	+	0.987696i	$0.450016\pi$
$558$	−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	$-0.321516\pi$
$577$	25.5485	1.06360	0.531799	+	0.846871i	$0.321516\pi$
$578$	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	$-0.484495\pi$
$587$	2.35936	0.0973813	0.0486907	+	0.998814i	$0.484495\pi$
$588$	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	$-0.422974\pi$
$593$	11.6707	0.479257	0.239628	+	0.970865i	$0.422974\pi$
$594$	−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	$-0.775819\pi$
$613$	−37.7362	−1.52415	−0.762075	+	0.647488i	$0.775819\pi$
$614$	−15.3808	−0.620720
$615$	−2.02496	−0.0816541
$616$	3.23178	0.130212
$617$	−28.2159	−1.13593	−0.567964	−	0.823053i	$-0.692269\pi$
$617$	−28.2159	−1.13593	−0.567964	+	0.823053i	$0.692269\pi$
$618$	1.69614	0.0682286
$619$	−38.4407	−1.54506	−0.772530	−	0.634978i	$-0.781009\pi$
$619$	−38.4407	−1.54506	−0.772530	+	0.634978i	$0.781009\pi$
$620$	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	$-0.390331\pi$
$631$	16.9688	0.675519	0.337759	+	0.941232i	$0.390331\pi$
$632$	−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	$-0.560893\pi$
$643$	−9.64269	−0.380270	−0.190135	+	0.981758i	$0.560893\pi$
$644$	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	$-0.807217\pi$
$661$	−42.2740	−1.64427	−0.822135	+	0.569293i	$0.807217\pi$
$662$	−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	$-0.248183\pi$
$683$	37.1698	1.42226	0.711132	+	0.703059i	$0.248183\pi$
$684$	−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	$-0.598200\pi$
$691$	−15.9632	−0.607268	−0.303634	+	0.952789i	$0.598200\pi$
$692$	−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	$-0.687905\pi$
$709$	−29.6428	−1.11326	−0.556629	+	0.830761i	$0.687905\pi$
$710$	−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	$-0.600365\pi$
$733$	−16.7917	−0.620217	−0.310109	+	0.950701i	$0.600365\pi$
$734$	−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	$-0.655146\pi$
$739$	−25.4629	−0.936668	−0.468334	+	0.883551i	$0.655146\pi$
$740$	−6.74225	−0.247850
$741$	0	0
$742$	0.444164	0.0163058
$743$	−4.81269	−0.176560	−0.0882802	−	0.996096i	$-0.528137\pi$
$743$	−4.81269	−0.176560	−0.0882802	+	0.996096i	$0.528137\pi$
$744$	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	$-0.130531\pi$
$761$	50.5981	1.83418	0.917091	+	0.398679i	$0.130531\pi$
$762$	−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	$-0.656177\pi$
$769$	−26.1333	−0.942389	−0.471195	+	0.882029i	$0.656177\pi$
$770$	1.72587	0.0621960
$771$	16.3441	0.588618
$772$	−31.2497	−1.12470
$773$	0.778578	0.0280035	0.0140018	−	0.999902i	$-0.495543\pi$
$773$	0.778578	0.0280035	0.0140018	+	0.999902i	$0.495543\pi$
$774$	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	$-0.706599\pi$
$787$	−33.9128	−1.20886	−0.604431	+	0.796658i	$0.706599\pi$
$788$	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	$-0.390413\pi$
$811$	19.2236	0.675033	0.337516	+	0.941320i	$0.390413\pi$
$812$	−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	$-0.321945\pi$
$821$	30.4099	1.06131	0.530657	+	0.847587i	$0.321945\pi$
$822$	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	$-0.809379\pi$
$827$	−47.5066	−1.65197	−0.825983	+	0.563695i	$0.809379\pi$
$828$	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	$-0.291922\pi$
$839$	35.2293	1.21625	0.608125	+	0.793841i	$0.291922\pi$
$840$	−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	$-0.396164\pi$
$853$	18.7185	0.640909	0.320454	+	0.947264i	$0.396164\pi$
$854$	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	$-0.507714\pi$
$863$	−1.42374	−0.0484647	−0.0242324	+	0.999706i	$0.507714\pi$
$864$	−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	$-0.103816\pi$
$877$	56.1060	1.89457	0.947283	+	0.320397i	$0.103816\pi$
$878$	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	$-0.122538\pi$
$929$	56.4975	1.85362	0.926811	+	0.375527i	$0.122538\pi$
$930$	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	$-0.369826\pi$
$941$	24.3963	0.795296	0.397648	+	0.917538i	$0.369826\pi$
$942$	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	$-0.718423\pi$
$947$	−38.9960	−1.26720	−0.633600	+	0.773661i	$0.718423\pi$
$948$	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	$-0.669566\pi$
$967$	−31.5859	−1.01573	−0.507867	+	0.861435i	$0.669566\pi$
$968$	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	$-0.518085\pi$
$977$	−3.54984	−0.113569	−0.0567847	+	0.998386i	$0.518085\pi$
$978$	−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	$-0.585430\pi$
$983$	−16.6279	−0.530349	−0.265174	+	0.964200i	$0.585430\pi$
$984$	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.y.1.3		7
13.5	odd	4		429.2.b.b.298.9	yes	14
13.8	odd	4		429.2.b.b.298.6	✓	14
13.12	even	2		5577.2.a.x.1.5		7
39.5	even	4		1287.2.b.c.298.6		14
39.8	even	4		1287.2.b.c.298.9		14

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

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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