LMFDB - Embedded newform 495.2.bj.a.442.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [495,2,Mod(28,495)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(495, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 15, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("495.28"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,10,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			442.1
Character	$\chi$	$=$	495.442
Dual form			495.2.bj.a.28.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.665529 - 1.30617i) q^{2} +(-0.0875924 + 0.120561i) q^{4} +(1.11862 + 1.93615i) q^{5} +(-4.16343 + 0.659422i) q^{7} +(-2.68004 - 0.424477i) q^{8} +(1.78448 - 2.74968i) q^{10} +(0.920480 + 3.18633i) q^{11} +(-0.824787 + 0.420250i) q^{13} +(3.63220 + 4.99930i) q^{14} +(1.32131 + 4.06656i) q^{16} +(-1.71765 - 0.875188i) q^{17} +(-4.39439 + 3.19271i) q^{19} +(-0.331406 - 0.0347307i) q^{20} +(3.54930 - 3.32290i) q^{22} +(-1.95998 + 1.95998i) q^{23} +(-2.49738 + 4.33164i) q^{25} +(1.09784 + 0.797627i) q^{26} +(0.285184 - 0.559706i) q^{28} +(-0.810497 - 0.588860i) q^{29} +(0.131006 - 0.403196i) q^{31} +(0.594873 - 0.594873i) q^{32} +2.82602i q^{34} +(-5.93404 - 7.32339i) q^{35} +(-0.771690 - 4.87226i) q^{37} +(7.09483 + 3.61500i) q^{38} +(-2.17610 - 5.66380i) q^{40} +(-0.339428 - 0.467182i) q^{41} +(5.05373 + 5.05373i) q^{43} +(-0.464773 - 0.168125i) q^{44} +(3.86451 + 1.25566i) q^{46} +(1.17495 + 0.186094i) q^{47} +(10.2419 - 3.32780i) q^{49} +(7.31996 + 0.379176i) q^{50} +(0.0215795 - 0.136247i) q^{52} +(4.12294 + 8.09173i) q^{53} +(-5.13956 + 5.34649i) q^{55} +11.4381 q^{56} +(-0.229745 + 1.45055i) q^{58} +(-5.47214 + 7.53175i) q^{59} +(7.40093 - 2.40471i) q^{61} +(-0.613832 + 0.0972215i) q^{62} +(6.96021 + 2.26151i) q^{64} +(-1.73629 - 1.12681i) q^{65} +(-3.05526 - 3.05526i) q^{67} +(0.255966 - 0.130421i) q^{68} +(-5.61635 + 12.6248i) q^{70} +(-2.65487 - 8.17086i) q^{71} +(-0.854195 - 5.39318i) q^{73} +(-5.85044 + 4.25059i) q^{74} -0.809447i q^{76} +(-5.93349 - 12.6591i) q^{77} +(-0.705861 + 2.17242i) q^{79} +(-6.39544 + 7.10719i) q^{80} +(-0.384322 + 0.754275i) q^{82} +(-0.902846 + 1.77193i) q^{83} +(-0.226904 - 4.30464i) q^{85} +(3.23765 - 9.96446i) q^{86} +(-1.11440 - 8.93023i) q^{88} -13.9313i q^{89} +(3.15682 - 2.29356i) q^{91} +(-0.0646171 - 0.407977i) q^{92} +(-0.538893 - 1.65854i) q^{94} +(-11.0972 - 4.93678i) q^{95} +(-2.96200 + 1.50922i) q^{97} +(-11.1630 - 11.1630i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8 + 24 * q^11 - 10 * q^13 - 8 * q^16 - 16 * q^20 + 10 * q^22 + 24 * q^23 + 16 * q^25 - 20 * q^26 + 50 * q^28 - 28 * q^31 + 10 * q^35 - 8 * q^37 - 10 * q^38 - 50 * q^40 - 40 * q^41 + 60 * q^46 + 28 * q^47 + 50 * q^50 - 50 * q^52 + 24 * q^53 - 64 * q^55 + 80 * q^56 - 50 * q^58 - 60 * q^61 - 100 * q^62 - 8 * q^67 + 30 * q^68 + 30 * q^70 - 24 * q^71 + 50 * q^73 - 70 * q^77 - 98 * q^80 - 10 * q^82 - 90 * q^83 + 30 * q^85 - 100 * q^86 + 170 * q^88 + 20 * q^91 + 68 * q^92 + 40 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.665529	−	1.30617i	−0.470600	−	0.923605i	−0.997292	−	0.0735483i	$-0.976568\pi$
$2$	−0.665529	−	1.30617i	−0.470600	−	0.923605i	0.526691	−	0.850057i	$-0.323432\pi$
$3$		0			0
$3$		0			0
$4$	−0.0875924	+	0.120561i	−0.0437962	+	0.0602803i
$5$	1.11862	+	1.93615i	0.500262	+	0.865874i
$5$	1.11862	+	1.93615i	0.500262	+	0.865874i
$6$		0			0
$7$	−4.16343	+	0.659422i	−1.57363	+	0.249238i	−0.881375	−	0.472417i	$-0.843382\pi$
$7$	−4.16343	+	0.659422i	−1.57363	+	0.249238i	−0.692253	+	0.721655i	$0.743382\pi$
$8$	−2.68004	−	0.424477i	−0.947538	−	0.150075i
$9$		0			0
$10$	1.78448	−	2.74968i	0.564302	−	0.869525i
$11$	0.920480	+	3.18633i	0.277535	+	0.960716i
$11$	0.920480	+	3.18633i	0.277535	+	0.960716i
$12$		0			0
$13$	−0.824787	+	0.420250i	−0.228755	+	0.116556i	−0.564612	−	0.825357i	$-0.690974\pi$
$13$	−0.824787	+	0.420250i	−0.228755	+	0.116556i	0.335857	+	0.941913i	$0.390974\pi$
$14$	3.63220	+	4.99930i	0.970747	+	1.33612i
$15$		0			0
$16$	1.32131	+	4.06656i	0.330326	+	1.01664i
$17$	−1.71765	−	0.875188i	−0.416592	−	0.212264i	0.233115	−	0.972449i	$-0.425108\pi$
$17$	−1.71765	−	0.875188i	−0.416592	−	0.212264i	−0.649707	+	0.760185i	$0.725108\pi$
$18$		0			0
$19$	−4.39439	+	3.19271i	−1.00814	+	0.732458i	−0.963818	−	0.266560i	$-0.914113\pi$
$19$	−4.39439	+	3.19271i	−1.00814	+	0.732458i	−0.0443230	+	0.999017i	$0.514113\pi$
$20$	−0.331406	−	0.0347307i	−0.0741047	−	0.00776603i
$21$		0			0
$22$	3.54930	−	3.32290i	0.756713	−	0.708446i
$23$	−1.95998	+	1.95998i	−0.408685	+	0.408685i	−0.881280	−	0.472595i	$-0.843317\pi$
$23$	−1.95998	+	1.95998i	−0.408685	+	0.408685i	0.472595	+	0.881280i	$0.343317\pi$
$24$		0			0
$25$	−2.49738	+	4.33164i	−0.499475	+	0.866328i
$26$	1.09784	+	0.797627i	0.215304	+	0.156428i
$27$		0			0
$28$	0.285184	−	0.559706i	0.0538948	−	0.105774i
$29$	−0.810497	−	0.588860i	−0.150505	−	0.109349i	0.509984	−	0.860184i	$-0.329651\pi$
$29$	−0.810497	−	0.588860i	−0.150505	−	0.109349i	−0.660490	+	0.750835i	$0.729651\pi$
$30$		0			0
$31$	0.131006	−	0.403196i	0.0235294	−	0.0724161i	−0.938602	−	0.345001i	$-0.887879\pi$
$31$	0.131006	−	0.403196i	0.0235294	−	0.0724161i	0.962132	+	0.272585i	$0.0878786\pi$
$32$	0.594873	−	0.594873i	0.105160	−	0.105160i
$33$		0			0
$34$			2.82602i			0.484658i
$35$	−5.93404	−	7.32339i	−1.00304	−	1.23788i
$36$		0			0
$37$	−0.771690	−	4.87226i	−0.126865	−	0.800995i	−0.966278	−	0.257501i	$-0.917101\pi$
$37$	−0.771690	−	4.87226i	−0.126865	−	0.800995i	0.839413	−	0.543494i	$-0.182899\pi$
$38$	7.09483	+	3.61500i	1.15093	+	0.586430i
$39$		0			0
$40$	−2.17610	−	5.66380i	−0.344071	−	0.895526i
$41$	−0.339428	−	0.467182i	−0.0530097	−	0.0729616i	0.781689	−	0.623668i	$-0.214358\pi$
$41$	−0.339428	−	0.467182i	−0.0530097	−	0.0729616i	−0.834699	+	0.550707i	$0.814358\pi$
$42$		0			0
$43$	5.05373	+	5.05373i	0.770687	+	0.770687i	0.978227	−	0.207540i	$-0.0665456\pi$
$43$	5.05373	+	5.05373i	0.770687	+	0.770687i	−0.207540	+	0.978227i	$0.566546\pi$
$44$	−0.464773	−	0.168125i	−0.0700672	−	0.0253458i
$45$		0			0
$46$	3.86451	+	1.25566i	0.569791	+	0.185136i
$47$	1.17495	+	0.186094i	0.171384	+	0.0271446i	0.241537	−	0.970392i	$-0.422349\pi$
$47$	1.17495	+	0.186094i	0.171384	+	0.0271446i	−0.0701524	+	0.997536i	$0.522349\pi$
$48$		0			0
$49$	10.2419	−	3.32780i	1.46313	−	0.475400i
$50$	7.31996	+	0.379176i	1.03520	+	0.0536237i
$51$		0			0
$52$	0.0215795	−	0.136247i	0.00299254	−	0.0188941i
$53$	4.12294	+	8.09173i	0.566330	+	1.11149i	0.979615	+	0.200883i	$0.0643812\pi$
$53$	4.12294	+	8.09173i	0.566330	+	1.11149i	−0.413285	+	0.910602i	$0.635619\pi$
$54$		0			0
$55$	−5.13956	+	5.34649i	−0.693018	+	0.720920i
$56$	11.4381			1.52848
$57$		0			0
$58$	−0.229745	+	1.45055i	−0.0301670	+	0.190467i
$59$	−5.47214	+	7.53175i	−0.712411	+	0.980550i	0.287331	+	0.957831i	$0.407232\pi$
$59$	−5.47214	+	7.53175i	−0.712411	+	0.980550i	−0.999742	+	0.0227186i	$0.992768\pi$
$60$		0			0
$61$	7.40093	−	2.40471i	0.947591	−	0.307891i	0.205855	−	0.978583i	$-0.434002\pi$
$61$	7.40093	−	2.40471i	0.947591	−	0.307891i	0.741737	+	0.670691i	$0.234002\pi$
$62$	−0.613832	+	0.0972215i	−0.0779568	+	0.0123471i
$63$		0			0
$64$	6.96021	+	2.26151i	0.870026	+	0.282689i
$65$	−1.73629	−	1.12681i	−0.215361	−	0.139764i
$66$		0			0
$67$	−3.05526	−	3.05526i	−0.373259	−	0.373259i	0.495404	−	0.868663i	$-0.335020\pi$
$67$	−3.05526	−	3.05526i	−0.373259	−	0.373259i	−0.868663	+	0.495404i	$0.835020\pi$
$68$	0.255966	−	0.130421i	0.0310405	−	0.0158159i
$69$		0			0
$70$	−5.61635	+	12.6248i	−0.671283	+	1.50896i
$71$	−2.65487	−	8.17086i	−0.315075	−	0.969702i	−0.975723	−	0.219006i	$-0.929718\pi$
$71$	−2.65487	−	8.17086i	−0.315075	−	0.969702i	0.660648	−	0.750696i	$-0.270282\pi$
$72$		0			0
$73$	−0.854195	−	5.39318i	−0.0999760	−	0.631224i	−0.985893	−	0.167379i	$-0.946470\pi$
$73$	−0.854195	−	5.39318i	−0.0999760	−	0.631224i	0.885917	−	0.463844i	$-0.153530\pi$
$74$	−5.85044	+	4.25059i	−0.680100	+	0.494122i
$75$		0			0
$76$		−	0.809447i		−	0.0928499i
$77$	−5.93349	−	12.6591i	−0.676184	−	1.44264i
$78$		0			0
$79$	−0.705861	+	2.17242i	−0.0794156	+	0.244416i	−0.982880	−	0.184247i	$-0.941015\pi$
$79$	−0.705861	+	2.17242i	−0.0794156	+	0.244416i	0.903464	+	0.428663i	$0.141015\pi$
$80$	−6.39544	+	7.10719i	−0.715032	+	0.794608i
$81$		0			0
$82$	−0.384322	+	0.754275i	−0.0424413	+	0.0832957i
$83$	−0.902846	+	1.77193i	−0.0991002	+	0.194495i	−0.935234	−	0.354031i	$-0.884811\pi$
$83$	−0.902846	+	1.77193i	−0.0991002	+	0.194495i	0.836134	+	0.548526i	$0.184811\pi$
$84$		0			0
$85$	−0.226904	−	4.30464i	−0.0246112	−	0.466904i
$86$	3.23765	−	9.96446i	0.349125	−	1.07450i
$87$		0			0
$88$	−1.11440	−	8.93023i	−0.118795	−	0.951966i
$89$		−	13.9313i		−	1.47671i	−0.674410	−	0.738357i	$-0.735602\pi$
$89$		−	13.9313i		−	1.47671i	0.674410	−	0.738357i	$-0.264398\pi$
$90$		0			0
$91$	3.15682	−	2.29356i	0.330925	−	0.240431i
$92$	−0.0646171	−	0.407977i	−0.00673680	−	0.0425345i
$93$		0			0
$94$	−0.538893	−	1.65854i	−0.0555826	−	0.171066i
$95$	−11.0972	−	4.93678i	−1.13855	−	0.506502i
$96$		0			0
$97$	−2.96200	+	1.50922i	−0.300746	+	0.153238i	−0.597851	−	0.801607i	$-0.703979\pi$
$97$	−2.96200	+	1.50922i	−0.300746	+	0.153238i	0.297105	+	0.954845i	$0.403979\pi$
$98$	−11.1630	−	11.1630i	−1.12763	−	1.12763i
$99$		0			0
$100$	−0.303474	−	0.680504i	−0.0303474	−	0.0680504i
$101$	12.6404	+	4.10712i	1.25777	+	0.408673i	0.860698	−	0.509116i	$-0.170027\pi$
$101$	12.6404	+	4.10712i	1.25777	+	0.408673i	0.397069	+	0.917789i	$0.370027\pi$
$102$		0			0
$103$	−9.95825	+	1.57723i	−0.981215	+	0.155409i	−0.626378	−	0.779519i	$-0.715464\pi$
$103$	−9.95825	+	1.57723i	−0.981215	+	0.155409i	−0.354837	+	0.934928i	$0.615464\pi$
$104$	2.38885	−	0.776185i	0.234246	−	0.0761112i
$105$		0			0
$106$	7.82528	−	10.7706i	0.760058	−	1.04613i
$107$	−0.964682	+	6.09076i	−0.0932593	+	0.588816i	0.896160	+	0.443731i	$0.146346\pi$
$107$	−0.964682	+	6.09076i	−0.0932593	+	0.588816i	−0.989419	+	0.145085i	$0.953654\pi$
$108$		0			0
$109$	−19.9193			−1.90793			−0.953964	−	0.299922i	$-0.903039\pi$
$109$	−19.9193			−1.90793			−0.953964	+	0.299922i	$0.903039\pi$
$110$	10.4040	+	3.15492i	0.991980	+	0.300810i
$111$		0			0
$112$	−8.18274	−	16.0595i	−0.773197	−	1.51748i
$113$	1.89632	−	11.9729i	0.178391	−	1.12632i	−0.722211	−	0.691673i	$-0.756874\pi$
$113$	1.89632	−	11.9729i	0.178391	−	1.12632i	0.900602	−	0.434644i	$-0.143126\pi$
$114$		0			0
$115$	−5.98731	−	1.60235i	−0.558319	−	0.149420i
$116$	0.141987	−	0.0461342i	0.0131831	−	0.00428346i
$117$		0			0
$118$	13.4796	+	2.13497i	1.24090	+	0.196540i
$119$	7.72845	+	2.51112i	0.708465	+	0.230194i
$120$		0			0
$121$	−9.30543	+	5.86591i	−0.845949	+	0.533265i
$122$	−8.06650	−	8.06650i	−0.730306	−	0.730306i
$123$		0			0
$124$	0.0371343	+	0.0511110i	0.00333476	+	0.00458991i
$125$	−11.1803	+	0.0101588i	−1.00000	+	0.000908633i
$126$		0			0
$127$	−1.03315	−	0.526416i	−0.0916772	−	0.0467119i	0.407551	−	0.913183i	$-0.366383\pi$
$127$	−1.03315	−	0.526416i	−0.0916772	−	0.0467119i	−0.499228	+	0.866471i	$0.666383\pi$
$128$	−1.94151	−	12.2582i	−0.171607	−	1.08348i
$129$		0			0
$130$	−0.316262	+	3.01783i	−0.0277380	+	0.264681i
$131$			14.4532i			1.26278i	0.775465	+	0.631390i	$0.217515\pi$
$131$			14.4532i			1.26278i	−0.775465	+	0.631390i	$0.782485\pi$
$132$		0			0
$133$	16.1904	−	16.1904i	1.40388	−	1.40388i
$134$	−1.95734	+	6.02407i	−0.169088	+	0.520400i
$135$		0			0
$136$	4.23189	+	3.07465i	0.362881	+	0.263649i
$137$	−5.61663	+	11.0232i	−0.479861	+	0.941780i	0.516479	+	0.856300i	$0.327242\pi$
$137$	−5.61663	+	11.0232i	−0.479861	+	0.941780i	−0.996340	+	0.0854799i	$0.972758\pi$
$138$		0			0
$139$	−0.816606	−	0.593299i	−0.0692636	−	0.0503229i	0.552615	−	0.833437i	$-0.313630\pi$
$139$	−0.816606	−	0.593299i	−0.0692636	−	0.0503229i	−0.621878	+	0.783114i	$0.713630\pi$
$140$	1.40269	−	0.0739378i	0.118549	−	0.00624889i
$141$		0			0
$142$	−8.90567	+	8.90567i	−0.747347	+	0.747347i
$143$	−2.09826	−	2.24121i	−0.175465	−	0.187420i
$144$		0			0
$145$	0.233485	−	2.22796i	0.0193899	−	0.185022i
$146$	−6.47594	+	4.70504i	−0.535952	+	0.389392i
$147$		0			0
$148$	0.654997	+	0.333737i	0.0538404	+	0.0274331i
$149$	−0.377177	−	1.16083i	−0.0308996	−	0.0950990i	0.934417	−	0.356180i	$-0.115921\pi$
$149$	−0.377177	−	1.16083i	−0.0308996	−	0.0950990i	−0.965317	+	0.261081i	$0.915921\pi$
$150$		0			0
$151$	0.932668	+	1.28371i	0.0758995	+	0.104467i	0.845279	−	0.534326i	$-0.179434\pi$
$151$	0.932668	+	1.28371i	0.0758995	+	0.104467i	−0.769379	+	0.638792i	$0.779434\pi$
$152$	13.1324	−	6.69128i	1.06518	−	0.542734i
$153$		0			0
$154$	−12.5861	+	16.1752i	−1.01421	+	1.30343i
$155$	0.927195	−	0.197375i	0.0744741	−	0.0158535i
$156$		0			0
$157$	7.32783	+	1.16061i	0.584824	+	0.0926271i	0.441834	−	0.897097i	$-0.354328\pi$
$157$	7.32783	+	1.16061i	0.584824	+	0.0926271i	0.142991	+	0.989724i	$0.454328\pi$
$158$	3.30733	−	0.523829i	0.263117	−	0.0416736i
$159$		0			0
$160$	1.81720	+	0.486328i	0.143662	+	0.0384476i
$161$	6.86780	−	9.45272i	0.541258	−	0.744978i
$162$		0			0
$163$	6.99546	+	13.7294i	0.547927	+	1.07537i	0.984449	+	0.175673i	$0.0562103\pi$
$163$	6.99546	+	13.7294i	0.547927	+	1.07537i	−0.436522	+	0.899694i	$0.643790\pi$
$164$	0.0860550			0.00671976
$165$		0			0
$166$	2.91533			0.226273
$167$	1.88413	+	3.69782i	0.145799	+	0.286146i	0.952344	−	0.305026i	$-0.0986653\pi$
$167$	1.88413	+	3.69782i	0.145799	+	0.286146i	−0.806545	+	0.591172i	$0.798665\pi$
$168$		0			0
$169$	−7.13754	+	9.82399i	−0.549042	+	0.755691i
$170$	−5.47160	+	3.16124i	−0.419653	+	0.242456i
$171$		0			0
$172$	−1.05195	+	0.166612i	−0.0802104	+	0.0127041i
$173$	4.27643	+	0.677320i	0.325131	+	0.0514957i	0.316867	−	0.948470i	$-0.397369\pi$
$173$	4.27643	+	0.677320i	0.325131	+	0.0514957i	0.00826456	+	0.999966i	$0.497369\pi$
$174$		0			0
$175$	7.54127	−	19.6813i	0.570066	−	1.48777i
$176$	−11.7412	+	7.95331i	−0.885025	+	0.599503i
$177$		0			0
$178$	−18.1967	+	9.27168i	−1.36390	+	0.694942i
$179$	2.18633	+	3.00922i	0.163414	+	0.224920i	0.882869	−	0.469619i	$-0.155609\pi$
$179$	2.18633	+	3.00922i	0.163414	+	0.224920i	−0.719456	+	0.694538i	$0.755609\pi$
$180$		0			0
$181$	1.86849	+	5.75062i	0.138884	+	0.427440i	0.996174	−	0.0873933i	$-0.0278537\pi$
$181$	1.86849	+	5.75062i	0.138884	+	0.427440i	−0.857290	+	0.514834i	$0.827854\pi$
$182$	−5.09675	−	2.59692i	−0.377796	−	0.192497i
$183$		0			0
$184$	6.08481	−	4.42087i	0.448578	−	0.325911i
$185$	8.57022	−	6.94432i	0.630095	−	0.510557i
$186$		0			0
$187$	1.20758	−	6.27861i	0.0883066	−	0.459137i
$188$	−0.125352	+	0.125352i	−0.00914227	+	0.00914227i
$189$		0			0
$190$	0.937236	+	17.7805i	0.0679942	+	1.28993i
$191$	−13.3930	−	9.73057i	−0.969082	−	0.704079i	−0.0138398	−	0.999904i	$-0.504405\pi$
$191$	−13.3930	−	9.73057i	−0.969082	−	0.704079i	−0.955242	+	0.295825i	$0.904405\pi$
$192$		0			0
$193$	7.70155	−	15.1151i	0.554370	−	1.08801i	−0.428471	−	0.903556i	$-0.640948\pi$
$193$	7.70155	−	15.1151i	0.554370	−	1.08801i	0.982841	−	0.184456i	$-0.0590524\pi$
$194$	3.94260	+	2.86447i	0.283062	+	0.205657i
$195$		0			0
$196$	−0.495912	+	1.52626i	−0.0354223	+	0.109019i
$197$	9.63624	−	9.63624i	0.686554	−	0.686554i	−0.274915	−	0.961469i	$-0.588650\pi$
$197$	9.63624	−	9.63624i	0.686554	−	0.686554i	0.961469	+	0.274915i	$0.0886496\pi$
$198$		0			0
$199$		−	19.4166i		−	1.37640i	−0.725519	−	0.688202i	$-0.758400\pi$
$199$		−	19.4166i		−	1.37640i	0.725519	−	0.688202i	$-0.241600\pi$
$200$	8.53176	−	10.5489i	0.603286	−	0.745920i
$201$		0			0
$202$	−3.04795	−	19.2440i	−0.214453	−	1.35400i
$203$	3.76275	+	1.91722i	0.264093	+	0.134562i
$204$		0			0
$205$	0.524845	−	1.17978i	0.0366568	−	0.0823996i
$206$	8.68764	+	11.9575i	0.605297	+	0.833119i
$207$		0			0
$208$	−2.79877	−	2.79877i	−0.194060	−	0.194060i
$209$	−14.2180	−	11.0632i	−0.983478	−	0.765254i
$210$		0			0
$211$	6.07815	+	1.97491i	0.418437	+	0.135959i	0.510666	−	0.859779i	$-0.329399\pi$
$211$	6.07815	+	1.97491i	0.418437	+	0.135959i	−0.0922284	+	0.995738i	$0.529399\pi$
$212$	−1.33668	−	0.211710i	−0.0918037	−	0.0145403i
$213$		0			0
$214$	8.59762	−	2.79354i	0.587721	−	0.190962i
$215$	−4.13159	+	15.4380i	−0.281772	+	1.05286i
$216$		0			0
$217$	−0.279559	+	1.76507i	−0.0189777	+	0.119820i
$218$	13.2569	+	26.0181i	0.897871	+	1.76217i
$219$		0			0
$220$	−0.194389	−	1.08794i	−0.0131057	−	0.0733489i
$221$	1.78450			0.120038
$222$		0			0
$223$	−2.22058	+	14.0202i	−0.148701	+	0.938860i	0.794651	+	0.607066i	$0.207654\pi$
$223$	−2.22058	+	14.0202i	−0.148701	+	0.938860i	−0.943352	+	0.331794i	$0.892346\pi$
$224$	−2.08444	+	2.86898i	−0.139272	+	0.191692i
$225$		0			0
$226$	−16.9008	+	5.49139i	−1.12422	+	0.365282i
$227$	−8.17622	+	1.29499i	−0.542675	+	0.0859512i	−0.421753	−	0.906711i	$-0.638585\pi$
$227$	−8.17622	+	1.29499i	−0.542675	+	0.0859512i	−0.120922	+	0.992662i	$0.538585\pi$
$228$		0			0
$229$	18.6401	+	6.05655i	1.23178	+	0.400228i	0.851357	−	0.524587i	$-0.175780\pi$
$229$	18.6401	+	6.05655i	1.23178	+	0.400228i	0.380418	+	0.924815i	$0.375780\pi$
$230$	1.89178	+	8.88688i	0.124740	+	0.585984i
$231$		0			0
$232$	1.92221	+	1.92221i	0.126199	+	0.126199i
$233$	−3.30844	+	1.68573i	−0.216743	+	0.110436i	−0.558991	−	0.829173i	$-0.688812\pi$
$233$	−3.30844	+	1.68573i	−0.216743	+	0.110436i	0.342249	+	0.939609i	$0.388812\pi$
$234$		0			0
$235$	0.954019	+	2.48306i	0.0622333	+	0.161977i
$236$	−0.428714	−	1.31945i	−0.0279069	−	0.0858887i
$237$		0			0
$238$	−1.86354	−	11.7659i	−0.120795	−	0.762672i
$239$	2.59930	−	1.88850i	0.168135	−	0.122157i	−0.500536	−	0.865716i	$-0.666864\pi$
$239$	2.59930	−	1.88850i	0.168135	−	0.122157i	0.668671	+	0.743559i	$0.266864\pi$
$240$		0			0
$241$			25.4119i			1.63693i	0.574559	+	0.818463i	$0.305174\pi$
$241$			25.4119i			1.63693i	−0.574559	+	0.818463i	$0.694826\pi$
$242$	13.8549	+	8.25059i	0.890629	+	0.530368i
$243$		0			0
$244$	−0.358352	+	1.10289i	−0.0229411	+	0.0706055i
$245$	17.8999	+	16.1074i	1.14359	+	1.02906i
$246$		0			0
$247$	2.28270	−	4.48005i	0.145245	−	0.285059i
$248$	−0.522250	+	1.02497i	−0.0331629	+	0.0650858i
$249$		0			0
$250$	7.45411	+	14.5967i	0.471439	+	0.923177i
$251$	−5.03867	+	15.5074i	−0.318038	+	0.978820i	0.656448	+	0.754371i	$0.272058\pi$
$251$	−5.03867	+	15.5074i	−0.318038	+	0.978820i	−0.974486	+	0.224448i	$0.927942\pi$
$252$		0			0
$253$	−8.04929	−	4.44104i	−0.506055	−	0.279206i
$254$			1.69982i			0.106656i
$255$		0			0
$256$	−2.87779	+	2.09084i	−0.179862	+	0.130677i
$257$	2.53487	+	16.0045i	0.158121	+	0.998335i	0.931328	+	0.364182i	$0.118651\pi$
$257$	2.53487	+	16.0045i	0.158121	+	0.998335i	−0.773207	+	0.634154i	$0.781349\pi$
$258$		0			0
$259$	6.42576	+	19.7764i	0.399277	+	1.22885i
$260$	0.287935	−	0.110628i	0.0178570	−	0.00686086i
$261$		0			0
$262$	18.8784	−	9.61901i	1.16631	−	0.594265i
$263$	0.677874	+	0.677874i	0.0417995	+	0.0417995i	0.727698	−	0.685898i	$-0.240590\pi$
$263$	0.677874	+	0.677874i	0.0417995	+	0.0417995i	−0.685898	+	0.727698i	$0.740590\pi$
$264$		0			0
$265$	−11.0548	+	17.0342i	−0.679092	+	1.04640i
$266$	−31.9226	−	10.3723i	−1.95730	−	0.635966i
$267$		0			0
$268$	0.635961	−	0.100726i	0.0388475	−	0.00615284i
$269$	27.0327	−	8.78345i	1.64821	−	0.535536i	0.669860	−	0.742487i	$-0.266354\pi$
$269$	27.0327	−	8.78345i	1.64821	−	0.535536i	0.978351	+	0.206951i	$0.0663541\pi$
$270$		0			0
$271$	18.0744	−	24.8772i	1.09794	−	1.51118i	0.259853	−	0.965648i	$-0.416326\pi$
$271$	18.0744	−	24.8772i	1.09794	−	1.51118i	0.838087	−	0.545536i	$-0.183674\pi$
$272$	1.28946	−	8.14133i	0.0781850	−	0.493641i
$273$		0			0
$274$	18.1363			1.09565
$275$	−16.1008	−	3.97029i	−0.970917	−	0.239417i
$276$		0			0
$277$	13.6871	+	26.8625i	0.822379	+	1.61401i	0.788861	+	0.614571i	$0.210671\pi$
$277$	13.6871	+	26.8625i	0.822379	+	1.61401i	0.0335176	+	0.999438i	$0.489329\pi$
$278$	−0.231477	+	1.46149i	−0.0138831	+	0.0876542i
$279$		0			0
$280$	12.7949	+	22.1459i	0.764640	+	1.32347i
$281$	−8.10210	+	2.63253i	−0.483331	+	0.157044i	−0.540540	−	0.841319i	$-0.681780\pi$
$281$	−8.10210	+	2.63253i	−0.483331	+	0.157044i	0.0572089	+	0.998362i	$0.481780\pi$
$282$		0			0
$283$	9.42432	+	1.49267i	0.560218	+	0.0887297i	0.430120	−	0.902772i	$-0.358471\pi$
$283$	9.42432	+	1.49267i	0.560218	+	0.0887297i	0.130097	+	0.991501i	$0.458471\pi$
$284$	1.21763	+	0.395632i	0.0722530	+	0.0234764i
$285$		0			0
$286$	−1.53097	+	4.23228i	−0.0905280	+	0.250260i
$287$	1.72125	+	1.72125i	0.101602	+	0.101602i
$288$		0			0
$289$	−7.80797	−	10.7468i	−0.459292	−	0.632162i
$290$	−3.06549	+	1.17780i	−0.180012	+	0.0691626i
$291$		0			0
$292$	0.725025	+	0.369419i	0.0424289	+	0.0216186i
$293$	0.360965	+	2.27904i	0.0210878	+	0.133143i	0.995986	−	0.0895072i	$-0.0285292\pi$
$293$	0.360965	+	2.27904i	0.0210878	+	0.133143i	−0.974898	+	0.222650i	$0.928529\pi$
$294$		0			0
$295$	−20.7039	−	2.16972i	−1.20543	−	0.126326i
$296$			13.3854i			0.778013i
$297$		0			0
$298$	−1.26523	+	1.26523i	−0.0732926	+	0.0732926i
$299$	0.792887	−	2.44025i	0.0458538	−	0.141124i
$300$		0			0
$301$	−24.3734	−	17.7083i	−1.40486	−	1.02069i
$302$	1.05603	−	2.07257i	0.0607676	−	0.119263i
$303$		0			0
$304$	−18.7897	−	13.6515i	−1.07766	−	0.782967i
$305$	12.9347	+	11.6394i	0.740639	+	0.666468i
$306$		0			0
$307$	12.4635	−	12.4635i	0.711327	−	0.711327i	−0.255486	−	0.966813i	$-0.582235\pi$
$307$	12.4635	−	12.4635i	0.711327	−	0.711327i	0.966813	+	0.255486i	$0.0822353\pi$
$308$	2.04591	+	0.393494i	0.116577	+	0.0224214i
$309$		0			0
$310$	−0.874881	−	1.07972i	−0.0496899	−	0.0613239i
$311$	12.2271	−	8.88353i	0.693337	−	0.503739i	−0.184419	−	0.982848i	$-0.559040\pi$
$311$	12.2271	−	8.88353i	0.693337	−	0.503739i	0.877755	+	0.479109i	$0.159040\pi$
$312$		0			0
$313$	23.2697	+	11.8565i	1.31528	+	0.670169i	0.963950	−	0.266082i	$-0.0857293\pi$
$313$	23.2697	+	11.8565i	1.31528	+	0.670169i	0.351331	+	0.936251i	$0.385729\pi$
$314$	−3.36092	−	10.3438i	−0.189668	−	0.583737i
$315$		0			0
$316$	−0.200080	−	0.275386i	−0.0112554	−	0.0154917i
$317$	−25.2398	+	12.8603i	−1.41761	+	0.722307i	−0.983896	−	0.178744i	$-0.942797\pi$
$317$	−25.2398	+	12.8603i	−1.41761	+	0.722307i	−0.433712	+	0.901051i	$0.642797\pi$
$318$		0			0
$319$	1.13026	−	3.12455i	0.0632824	−	0.174941i
$320$	3.40720	+	16.0058i	0.190469	+	0.894751i
$321$		0			0
$322$	−16.9176	−	2.67949i	−0.942782	−	0.149322i
$323$	10.3423	−	1.63805i	0.575458	−	0.0911436i
$324$		0			0
$325$	0.239432	−	4.62220i	0.0132813	−	0.256394i
$326$	13.2773	−	18.2746i	0.735360	−	1.01214i
$327$		0			0
$328$	0.711372	+	1.39615i	0.0392790	+	0.0770893i
$329$	−5.01454			−0.276461
$330$		0			0
$331$	−24.6455			−1.35464			−0.677319	−	0.735690i	$-0.736858\pi$
$331$	−24.6455			−1.35464			−0.677319	+	0.735690i	$0.736858\pi$
$332$	−0.134543	−	0.264055i	−0.00738401	−	0.0144919i
$333$		0			0
$334$	3.57605	−	4.92202i	0.195673	−	0.269321i
$335$	2.49777	−	9.33313i	0.136468	−	0.509923i
$336$		0			0
$337$	−30.6340	+	4.85195i	−1.66874	+	0.264302i	−0.918082	−	0.396390i	$-0.870263\pi$
$337$	−30.6340	+	4.85195i	−1.66874	+	0.264302i	−0.750657	+	0.660692i	$0.770263\pi$
$338$	17.5821	+	2.78473i	0.956339	+	0.151469i
$339$		0			0
$340$	0.538845	+	0.349698i	0.0292230	+	0.0189650i
$341$	1.40530	+	0.0462960i	0.0761015	+	0.00250707i
$342$		0			0
$343$	−14.1559	+	7.21277i	−0.764345	+	0.389453i
$344$	−11.3990	−	15.6894i	−0.614594	−	0.845916i
$345$		0			0
$346$	−1.96139	−	6.03654i	−0.105445	−	0.324527i
$347$	26.8957	+	13.7041i	1.44384	+	0.735672i	0.988009	−	0.154395i	$-0.0493430\pi$
$347$	26.8957	+	13.7041i	1.44384	+	0.735672i	0.455829	+	0.890068i	$0.349343\pi$
$348$		0			0
$349$	17.2865	−	12.5594i	0.925323	−	0.672287i	−0.0195201	−	0.999809i	$-0.506214\pi$
$349$	17.2865	−	12.5594i	0.925323	−	0.672287i	0.944843	+	0.327523i	$0.106214\pi$
$350$	−30.7262	+	3.24827i	−1.64238	+	0.173627i
$351$		0			0
$352$	2.44303	+	1.34789i	0.130214	+	0.0718430i
$353$	2.82626	−	2.82626i	0.150427	−	0.150427i	−0.627882	−	0.778309i	$-0.716078\pi$
$353$	2.82626	−	2.82626i	0.150427	−	0.150427i	0.778309	+	0.627882i	$0.216078\pi$
$354$		0			0
$355$	12.8502	−	14.2803i	0.682019	−	0.757921i
$356$	1.67956	+	1.22027i	0.0890167	+	0.0646744i
$357$		0			0
$358$	2.47550	−	4.85844i	0.130834	−	0.256777i
$359$	8.68908	+	6.31298i	0.458592	+	0.333187i	0.792979	−	0.609249i	$-0.208529\pi$
$359$	8.68908	+	6.31298i	0.458592	+	0.333187i	−0.334387	+	0.942436i	$0.608529\pi$
$360$		0			0
$361$	3.24592	−	9.98992i	0.170838	−	0.525785i
$362$	6.26778	−	6.26778i	0.329427	−	0.329427i
$363$		0			0
$364$			0.581487i			0.0304782i
$365$	9.48649	−	7.68677i	0.496546	−	0.402344i
$366$		0			0
$367$	5.41331	+	34.1783i	0.282572	+	1.78409i	0.565293	+	0.824890i	$0.308763\pi$
$367$	5.41331	+	34.1783i	0.282572	+	1.78409i	−0.282721	+	0.959202i	$0.591237\pi$
$368$	−10.5601	−	5.38066i	−0.550485	−	0.280486i
$369$		0			0
$370$	−14.7742	−	6.57255i	−0.768075	−	0.341690i
$371$	−22.5015	−	30.9706i	−1.16822	−	1.60791i
$372$		0			0
$373$	−9.90454	−	9.90454i	−0.512838	−	0.512838i	0.402557	−	0.915395i	$-0.368121\pi$
$373$	−9.90454	−	9.90454i	−0.512838	−	0.512838i	−0.915395	+	0.402557i	$0.868121\pi$
$374$	−9.00463	+	2.60129i	−0.465618	+	0.134510i
$375$		0			0
$376$	−3.06993	−	0.997480i	−0.158319	−	0.0514411i
$377$	0.915956	+	0.145073i	0.0471741	+	0.00747165i
$378$		0			0
$379$	−25.2037	+	8.18919i	−1.29463	+	0.420651i	−0.873710	−	0.486447i	$-0.838292\pi$
$379$	−25.2037	+	8.18919i	−1.29463	+	0.420651i	−0.420919	+	0.907098i	$0.638292\pi$
$380$	1.56721	−	0.905463i	0.0803963	−	0.0464493i
$381$		0			0
$382$	−3.79640	+	23.9695i	−0.194241	+	1.22639i
$383$	−10.9129	−	21.4177i	−0.557622	−	1.09439i	−0.981995	−	0.188907i	$-0.939505\pi$
$383$	−10.9129	−	21.4177i	−0.557622	−	1.09439i	0.424373	−	0.905487i	$-0.360495\pi$
$384$		0			0
$385$	17.8726	−	25.6489i	0.910872	−	1.30719i
$386$	−24.8686			−1.26578
$387$		0			0
$388$	0.0774970	−	0.489297i	0.00393431	−	0.0248403i
$389$	−4.43509	+	6.10438i	−0.224868	+	0.309505i	−0.906512	−	0.422179i	$-0.861265\pi$
$389$	−4.43509	+	6.10438i	−0.224868	+	0.309505i	0.681644	+	0.731684i	$0.261265\pi$
$390$		0			0
$391$	5.08193	−	1.65122i	0.257004	−	0.0835057i
$392$	−28.8613	+	4.57119i	−1.45772	+	0.230880i
$393$		0			0
$394$	−18.9998	−	6.17342i	−0.957197	−	0.311012i
$395$	−4.99573	+	1.06346i	−0.251362	+	0.0535083i
$396$		0			0
$397$	16.0995	+	16.0995i	0.808008	+	0.808008i	0.984332	−	0.176324i	$-0.0564206\pi$
$397$	16.0995	+	16.0995i	0.808008	+	0.808008i	−0.176324	+	0.984332i	$0.556421\pi$
$398$	−25.3614	+	12.9223i	−1.27125	+	0.647736i
$399$		0			0
$400$	−20.9147	−	4.43231i	−1.04573	−	0.221616i
$401$	7.46030	+	22.9604i	0.372550	+	1.14659i	0.945117	+	0.326732i	$0.105947\pi$
$401$	7.46030	+	22.9604i	0.372550	+	1.14659i	−0.572568	+	0.819858i	$0.694053\pi$
$402$		0			0
$403$	0.0613908	+	0.387606i	0.00305809	+	0.0193080i
$404$	−1.60236	+	1.16418i	−0.0797203	+	0.0579202i
$405$		0			0
$406$		−	6.19078i		−	0.307243i
$407$	14.8143	−	6.94368i	0.734319	−	0.344185i
$408$		0			0
$409$	1.80956	−	5.56925i	0.0894769	−	0.275382i	−0.896298	−	0.443452i	$-0.853754\pi$
$409$	1.80956	−	5.56925i	0.0894769	−	0.275382i	0.985775	+	0.168070i	$0.0537536\pi$
$410$	−1.89030	+	0.0996406i	−0.0933554	+	0.00492090i
$411$		0			0
$412$	0.682114	−	1.33872i	0.0336054	−	0.0659542i
$413$	17.8162	−	34.9663i	0.876680	−	1.72058i
$414$		0			0
$415$	−4.44068	+	0.234075i	−0.217984	+	0.0114903i
$416$	−0.240648	+	0.740639i	−0.0117987	+	0.0363128i
$417$		0			0
$418$	−4.98793	+	25.9340i	−0.243968	+	1.26847i
$419$			11.0599i			0.540311i	0.962817	+	0.270155i	$0.0870751\pi$
$419$			11.0599i			0.540311i	−0.962817	+	0.270155i	$0.912925\pi$
$420$		0			0
$421$	−6.36944	+	4.62767i	−0.310428	+	0.225539i	−0.732080	−	0.681219i	$-0.761450\pi$
$421$	−6.36944	+	4.62767i	−0.310428	+	0.225539i	0.421652	+	0.906758i	$0.361450\pi$
$422$	−1.46561	−	9.25349i	−0.0713447	−	0.450453i
$423$		0			0
$424$	−7.61491	−	23.4363i	−0.369813	−	1.13817i
$425$	8.08063	−	5.25458i	0.391968	−	0.254885i
$426$		0			0
$427$	−29.2275	+	14.8922i	−1.41442	+	0.720682i
$428$	−0.649807	−	0.649807i	−0.0314096	−	0.0314096i
$429$		0			0
$430$	22.9144	−	4.87787i	1.10503	−	0.235232i
$431$	6.94552	+	2.25674i	0.334554	+	0.108703i	0.471477	−	0.881879i	$-0.343721\pi$
$431$	6.94552	+	2.25674i	0.334554	+	0.108703i	−0.136923	+	0.990582i	$0.543721\pi$
$432$		0			0
$433$	4.98536	−	0.789604i	0.239581	−	0.0379460i	−0.0354890	−	0.999370i	$-0.511299\pi$
$433$	4.98536	−	0.789604i	0.239581	−	0.0379460i	0.275070	+	0.961424i	$0.411299\pi$
$434$	2.49154	−	0.809550i	0.119598	−	0.0388596i
$435$		0			0
$436$	1.74478	−	2.40149i	0.0835599	−	0.115010i
$437$	2.35527	−	14.8706i	0.112668	−	0.711357i
$438$		0			0
$439$	1.29778			0.0619394			0.0309697	−	0.999520i	$-0.490140\pi$
$439$	1.29778			0.0619394			0.0309697	+	0.999520i	$0.490140\pi$
$440$	16.0437	−	12.1472i	0.764854	−	0.579094i
$441$		0			0
$442$	−1.18763	−	2.33086i	−0.0564900	−	0.110868i
$443$	−2.40922	+	15.2112i	−0.114466	+	0.722707i	0.861980	+	0.506942i	$0.169224\pi$
$443$	−2.40922	+	15.2112i	−0.114466	+	0.722707i	−0.976445	+	0.215764i	$0.930776\pi$
$444$		0			0
$445$	26.9731	−	15.5838i	1.27865	−	0.738744i
$446$	19.7907	−	6.43037i	0.937115	−	0.304487i
$447$		0			0
$448$	−30.4696	−	4.82591i	−1.43955	−	0.228003i
$449$	−11.5295	−	3.74615i	−0.544109	−	0.176792i	0.0240497	−	0.999711i	$-0.492344\pi$
$449$	−11.5295	−	3.74615i	−0.544109	−	0.176792i	−0.568159	+	0.822919i	$0.692344\pi$
$450$		0			0
$451$	1.17616	−	1.51156i	0.0553833	−	0.0711766i
$452$	1.27736	+	1.27736i	0.0600818	+	0.0600818i
$453$		0			0
$454$	7.13299	+	9.81772i	0.334768	+	0.460768i
$455$	7.97198	+	3.54646i	0.373732	+	0.166261i
$456$		0			0
$457$	3.12807	+	1.59383i	0.146325	+	0.0745563i	0.525620	−	0.850720i	$-0.323833\pi$
$457$	3.12807	+	1.59383i	0.146325	+	0.0745563i	−0.379295	+	0.925276i	$0.623833\pi$
$458$	−4.49465	−	28.3781i	−0.210021	−	1.32602i
$459$		0			0
$460$	0.717623	−	0.581480i	0.0334593	−	0.0271116i
$461$		−	5.45336i		−	0.253988i	−0.991903	−	0.126994i	$-0.959467\pi$
$461$		−	5.45336i		−	0.253988i	0.991903	−	0.126994i	$-0.0405329\pi$
$462$		0			0
$463$	15.3996	−	15.3996i	0.715681	−	0.715681i	−0.252037	−	0.967718i	$-0.581100\pi$
$463$	15.3996	−	15.3996i	0.715681	−	0.715681i	0.967718	+	0.252037i	$0.0811005\pi$
$464$	1.32372	−	4.07400i	0.0614523	−	0.189131i
$465$		0			0
$466$	4.40372	+	3.19949i	0.203998	+	0.148214i
$467$	−6.66632	+	13.0834i	−0.308481	+	0.605427i	−0.992248	−	0.124273i	$-0.960340\pi$
$467$	−6.66632	+	13.0834i	−0.308481	+	0.605427i	0.683768	+	0.729700i	$0.260340\pi$
$468$		0			0
$469$	14.7351	+	10.7057i	0.680402	+	0.494341i
$470$	2.60838	−	2.89866i	0.120315	−	0.133705i
$471$		0			0
$472$	17.8626	−	17.8626i	0.822193	−	0.822193i
$473$	−11.4510	+	20.7547i	−0.526518	+	0.954303i
$474$		0			0
$475$	−2.85523	−	27.0083i	−0.131007	−	1.23923i
$476$	−0.979695	+	0.711790i	−0.0449043	+	0.0326249i
$477$		0			0
$478$	−4.19663	−	2.13829i	−0.191949	−	0.0978030i
$479$	−1.51842	−	4.67321i	−0.0693783	−	0.213524i	0.910356	−	0.413826i	$-0.135808\pi$
$479$	−1.51842	−	4.67321i	−0.0693783	−	0.213524i	−0.979734	+	0.200302i	$0.935808\pi$
$480$		0			0
$481$	2.68405	+	3.69428i	0.122382	+	0.168444i
$482$	33.1924	−	16.9124i	1.51187	−	0.770338i
$483$		0			0
$484$	0.107888	−	1.63568i	0.00490399	−	0.0743490i
$485$	−6.23543	−	4.04665i	−0.283136	−	0.183749i
$486$		0			0
$487$	10.6054	+	1.67972i	0.480574	+	0.0761155i	0.392022	−	0.919956i	$-0.371776\pi$
$487$	10.6054	+	1.67972i	0.480574	+	0.0761155i	0.0885527	+	0.996071i	$0.471776\pi$
$488$	−20.8555	+	3.30319i	−0.944086	+	0.149529i
$489$		0			0
$490$	9.12610	−	34.1004i	0.412275	−	1.54050i
$491$	−1.91387	+	2.63421i	−0.0863715	+	0.118880i	−0.850016	−	0.526757i	$-0.823408\pi$
$491$	−1.91387	+	2.63421i	−0.0863715	+	0.118880i	0.763645	+	0.645637i	$0.223408\pi$
$492$		0			0
$493$	0.876788	+	1.72079i	0.0394886	+	0.0775007i
$494$	−7.37092			−0.331634
$495$		0			0
$496$	1.81272			0.0813935
$497$	16.4414	+	32.2681i	0.737498	+	1.44742i
$498$		0			0
$499$	−5.25588	+	7.23410i	−0.235285	+	0.323843i	−0.910290	−	0.413971i	$-0.864142\pi$
$499$	−5.25588	+	7.23410i	−0.235285	+	0.323843i	0.675005	+	0.737813i	$0.264142\pi$
$500$	0.978087	−	1.34880i	0.0437414	−	0.0603200i
$501$		0			0
$502$	23.6088	−	3.73926i	1.05371	−	0.166891i
$503$	−19.0954	−	3.02441i	−0.851421	−	0.134852i	−0.284553	−	0.958660i	$-0.591845\pi$
$503$	−19.0954	−	3.02441i	−0.851421	−	0.134852i	−0.566868	+	0.823808i	$0.691845\pi$
$504$		0			0
$505$	6.18781	+	29.0681i	0.275354	+	1.29351i
$506$	−0.443733	+	13.4694i	−0.0197263	+	0.598789i
$507$		0			0
$508$	0.153961	−	0.0784471i	0.00683092	−	0.00348053i
$509$	1.65845	+	2.28267i	0.0735097	+	0.101177i	0.844189	−	0.536046i	$-0.180083\pi$
$509$	1.65845	+	2.28267i	0.0735097	+	0.101177i	−0.770679	+	0.637224i	$0.780083\pi$
$510$		0			0
$511$	7.11276	+	21.8908i	0.314650	+	0.968393i
$512$	−17.4703	−	8.90156i	−0.772085	−	0.393397i
$513$		0			0
$514$	19.2177	−	13.9625i	0.847656	−	0.615858i
$515$	−14.1933	−	17.5164i	−0.625430	−	0.771863i
$516$		0			0
$517$	0.488562	+	3.91508i	0.0214869	+	0.172185i
$518$	21.5550	−	21.5550i	0.947071	−	0.947071i
$519$		0			0
$520$	4.17503	+	3.75693i	0.183087	+	0.164752i
$521$	7.68839	+	5.58594i	0.336835	+	0.244725i	0.743325	−	0.668930i	$-0.233248\pi$
$521$	7.68839	+	5.58594i	0.336835	+	0.244725i	−0.406491	+	0.913655i	$0.633248\pi$
$522$		0			0
$523$	−6.73563	+	13.2194i	−0.294528	+	0.578045i	−0.990092	−	0.140420i	$-0.955155\pi$
$523$	−6.73563	+	13.2194i	−0.294528	+	0.578045i	0.695564	+	0.718465i	$0.255155\pi$
$524$	−1.74248	−	1.26599i	−0.0761207	−	0.0553049i
$525$		0			0
$526$	0.434277	−	1.33657i	0.0189354	−	0.0582771i
$527$	−0.577895	+	0.577895i	−0.0251735	+	0.0251735i
$528$		0			0
$529$			15.3169i			0.665953i
$530$	29.6070	+	3.10275i	1.28605	+	0.134775i
$531$		0			0
$532$	0.533767	+	3.37007i	0.0231417	+	0.146111i
$533$	0.476289	+	0.242681i	0.0206304	+	0.0105117i
$534$		0			0
$535$	−12.8718	+	4.94548i	−0.556495	+	0.213812i
$536$	6.89134	+	9.48511i	0.297661	+	0.409695i
$537$		0			0
$538$	−29.4638	−	29.4638i	−1.27027	−	1.27027i
$539$	20.0309	+	29.5710i	0.862794	+	1.27371i
$540$		0			0
$541$	−29.7351	−	9.66153i	−1.27841	−	0.415381i	−0.410392	−	0.911909i	$-0.634608\pi$
$541$	−29.7351	−	9.66153i	−1.27841	−	0.415381i	−0.868021	+	0.496528i	$0.834608\pi$
$542$	−44.5230	−	7.05176i	−1.91243	−	0.302899i
$543$		0			0
$544$	−1.54241	+	0.501159i	−0.0661303	+	0.0214870i
$545$	−22.2822	−	38.5669i	−0.954464	−	1.65202i
$546$		0			0
$547$	4.93799	−	31.1772i	0.211133	−	1.33304i	−0.623322	−	0.781966i	$-0.714217\pi$
$547$	4.93799	−	31.1772i	0.211133	−	1.33304i	0.834455	−	0.551076i	$-0.185783\pi$
$548$	−0.836995	−	1.64270i	−0.0357547	−	0.0701725i
$549$		0			0
$550$	5.52969	+	23.6728i	0.235787	+	1.00941i
$551$	5.44169			0.231824
$552$		0			0
$553$	1.50626	−	9.51017i	0.0640528	−	0.404414i
$554$	25.9779	−	35.7555i	1.10370	−	1.51911i
$555$		0			0
$556$	0.143057	−	0.0464820i	0.00606696	−	0.00197128i
$557$	13.0992	−	2.07471i	0.555030	−	0.0879082i	0.127383	−	0.991854i	$-0.459342\pi$
$557$	13.0992	−	2.07471i	0.555030	−	0.0879082i	0.427648	+	0.903945i	$0.359342\pi$
$558$		0			0
$559$	−6.29208	−	2.04442i	−0.266127	−	0.0864698i
$560$	21.9403	−	33.8076i	0.927149	−	1.42863i
$561$		0			0
$562$	8.83073	+	8.83073i	0.372502	+	0.372502i
$563$	−26.1698	+	13.3342i	−1.10292	+	0.561968i	−0.908051	−	0.418860i	$-0.862430\pi$
$563$	−26.1698	+	13.3342i	−1.10292	+	0.561968i	−0.194874	+	0.980828i	$0.562430\pi$
$564$		0			0
$565$	25.3027	−	9.72158i	1.06449	−	0.408990i
$566$	−4.32248	−	13.3032i	−0.181687	−	0.559176i
$567$		0			0
$568$	3.64683	+	23.0252i	0.153018	+	0.966115i
$569$	17.3540	−	12.6084i	0.727518	−	0.528573i	−0.161259	−	0.986912i	$-0.551555\pi$
$569$	17.3540	−	12.6084i	0.727518	−	0.528573i	0.888777	+	0.458339i	$0.151555\pi$
$570$		0			0
$571$			28.7176i			1.20179i	0.799326	+	0.600897i	$0.205190\pi$
$571$			28.7176i			1.20179i	−0.799326	+	0.600897i	$0.794810\pi$
$572$	0.453993	−	0.0566536i	0.0189824	−	0.00236881i
$573$		0			0
$574$	1.10271	−	3.39380i	0.0460263	−	0.141654i
$575$	−3.59513	−	13.3848i	−0.149927	−	0.558183i
$576$		0			0
$577$	3.03825	−	5.96290i	0.126484	−	0.248239i	−0.819077	−	0.573683i	$-0.805514\pi$
$577$	3.03825	−	5.96290i	0.126484	−	0.248239i	0.945561	+	0.325445i	$0.105514\pi$
$578$	−8.84070	+	17.3509i	−0.367725	+	0.721700i
$579$		0			0
$580$	0.248152	+	0.223301i	0.0103040	+	0.00927207i
$581$	2.59048	−	7.97268i	0.107471	−	0.330763i
$582$		0			0
$583$	−21.9879	+	20.5853i	−0.910644	+	0.852558i
$584$			14.8165i			0.613112i
$585$		0			0
$586$	2.73660	−	1.98825i	0.113048	−	0.0821340i
$587$	−5.70952	−	36.0485i	−0.235657	−	1.48788i	−0.767506	−	0.641041i	$-0.778503\pi$
$587$	−5.70952	−	36.0485i	−0.235657	−	1.48788i	0.531849	−	0.846839i	$-0.321497\pi$
$588$		0			0
$589$	0.711594	+	2.19006i	0.0293207	+	0.0902400i
$590$	10.9450	+	28.4869i	0.450598	+	1.17279i
$591$		0			0
$592$	18.7937	−	9.57587i	0.772417	−	0.393566i
$593$	26.6656	+	26.6656i	1.09502	+	1.09502i	0.994983	+	0.100040i	$0.0318971\pi$
$593$	26.6656	+	26.6656i	1.09502	+	1.09502i	0.100040	+	0.994983i	$0.468103\pi$
$594$		0			0
$595$	3.78328	+	17.7724i	0.155099	+	0.728599i
$596$	0.172988	+	0.0562073i	0.00708588	+	0.00230234i
$597$		0			0
$598$	−3.71509	+	0.588412i	−0.151921	+	0.0240620i
$599$	−36.7124	+	11.9286i	−1.50003	+	0.487388i	−0.940026	−	0.341103i	$-0.889199\pi$
$599$	−36.7124	+	11.9286i	−1.50003	+	0.487388i	−0.560002	+	0.828492i	$0.689199\pi$
$600$		0			0
$601$	22.4050	−	30.8379i	0.913920	−	1.25790i	−0.0518905	−	0.998653i	$-0.516525\pi$
$601$	22.4050	−	30.8379i	0.913920	−	1.25790i	0.965810	−	0.259250i	$-0.0834753\pi$
$602$	−6.90894	+	43.6213i	−0.281587	+	1.77787i
$603$		0			0
$604$	−0.236459			−0.00962138
$605$	−21.7665	−	11.4550i	−0.884936	−	0.465713i
$606$		0			0
$607$	16.4492	+	32.2834i	0.667653	+	1.31034i	0.937683	+	0.347491i	$0.112966\pi$
$607$	16.4492	+	32.2834i	0.667653	+	1.31034i	−0.270031	+	0.962852i	$0.587034\pi$
$608$	−0.714845	+	4.51336i	−0.0289908	+	0.183041i
$609$		0			0
$610$	6.59462	−	24.6413i	0.267009	−	0.997698i
$611$	−1.04729	+	0.340286i	−0.0423689	+	0.0137665i
$612$		0			0
$613$	2.37960	+	0.376892i	0.0961113	+	0.0152225i	0.204305	−	0.978907i	$-0.434507\pi$
$613$	2.37960	+	0.376892i	0.0961113	+	0.0152225i	−0.108194	+	0.994130i	$0.534507\pi$
$614$	−24.5743	−	7.98466i	−0.991736	−	0.322235i
$615$		0			0
$616$	10.5285	+	36.4455i	0.424206	+	1.46843i
$617$	25.5598	+	25.5598i	1.02900	+	1.02900i	0.999567	+	0.0294325i	$0.00937002\pi$
$617$	25.5598	+	25.5598i	1.02900	+	1.02900i	0.0294325	+	0.999567i	$0.490630\pi$
$618$		0			0
$619$	−0.537145	−	0.739317i	−0.0215897	−	0.0297157i	0.798086	−	0.602544i	$-0.205846\pi$
$619$	−0.537145	−	0.739317i	−0.0215897	−	0.0297157i	−0.819675	+	0.572828i	$0.805846\pi$
$620$	−0.0574196	+	0.129072i	−0.00230603	+	0.00518364i
$621$		0			0
$622$	−19.7409	−	10.0585i	−0.791540	−	0.403310i
$623$	9.18661	+	58.0020i	0.368054	+	2.32380i
$624$		0			0
$625$	−12.5262	−	21.6355i	−0.501049	−	0.865419i
$626$		−	38.2851i		−	1.53018i
$627$		0			0
$628$	−0.781786	+	0.781786i	−0.0311967	+	0.0311967i
$629$	−2.93865	+	9.04423i	−0.117172	+	0.360617i
$630$		0			0
$631$	−18.6941	−	13.5820i	−0.744199	−	0.540692i	0.149824	−	0.988713i	$-0.452129\pi$
$631$	−18.6941	−	13.5820i	−0.744199	−	0.540692i	−0.894023	+	0.448020i	$0.852129\pi$
$632$	2.81388	−	5.52255i	0.111930	−	0.219675i
$633$		0			0
$634$	33.5956	+	24.4087i	1.33425	+	0.969392i
$635$	−0.136480	−	2.58920i	−0.00541606	−	0.102749i
$636$		0			0
$637$	−7.04889	+	7.04889i	−0.279287	+	0.279287i
$638$	−4.83342	+	0.603161i	−0.191357	+	0.0238794i
$639$		0			0
$640$	21.5619	−	17.4713i	0.852310	−	0.690614i
$641$	7.06172	−	5.13064i	0.278921	−	0.202648i	−0.439525	−	0.898230i	$-0.644853\pi$
$641$	7.06172	−	5.13064i	0.278921	−	0.202648i	0.718447	+	0.695582i	$0.244853\pi$
$642$		0			0
$643$	−28.1018	−	14.3186i	−1.10823	−	0.564670i	−0.198594	−	0.980082i	$-0.563638\pi$
$643$	−28.1018	−	14.3186i	−1.10823	−	0.564670i	−0.909634	+	0.415412i	$0.863638\pi$
$644$	0.538058	+	1.65597i	0.0212024	+	0.0652544i
$645$		0			0
$646$	−9.02265	−	12.4186i	−0.354991	−	0.488604i
$647$	12.2437	−	6.23845i	0.481348	−	0.245259i	−0.196441	−	0.980516i	$-0.562938\pi$
$647$	12.2437	−	6.23845i	0.481348	−	0.245259i	0.677789	+	0.735257i	$0.262938\pi$
$648$		0			0
$649$	−29.0356	−	10.5032i	−1.13975	−	0.412288i
$650$	−6.19675	+	2.76347i	−0.243057	+	0.108392i
$651$		0			0
$652$	−2.26797	−	0.359211i	−0.0888205	−	0.0140678i
$653$	5.37414	−	0.851181i	0.210307	−	0.0333093i	−0.0503921	−	0.998730i	$-0.516047\pi$
$653$	5.37414	−	0.851181i	0.210307	−	0.0333093i	0.260699	+	0.965420i	$0.416047\pi$
$654$		0			0
$655$	−27.9836	+	16.1676i	−1.09341	+	0.631721i
$656$	1.45134	−	1.99759i	0.0566652	−	0.0779929i
$657$		0			0
$658$	3.33733	+	6.54987i	0.130102	+	0.255341i
$659$	−42.1160			−1.64061			−0.820304	−	0.571928i	$-0.806195\pi$
$659$	−42.1160			−1.64061			−0.820304	+	0.571928i	$0.806195\pi$
$660$		0			0
$661$	−19.5844			−0.761745			−0.380872	−	0.924628i	$-0.624376\pi$
$661$	−19.5844			−0.761745			−0.380872	+	0.924628i	$0.624376\pi$
$662$	16.4023	+	32.1913i	0.637493	+	1.25115i
$663$		0			0
$664$	3.17181	−	4.36562i	0.123090	−	0.169419i
$665$	49.4579	+	13.2362i	1.91790	+	0.513276i
$666$		0			0
$667$	2.74272	−	0.434404i	0.106198	−	0.0168202i
$668$	−0.610847	−	0.0967487i	−0.0236344	−	0.00374332i
$669$		0			0
$670$	−13.8530	+	2.94894i	−0.535189	+	0.113927i
$671$	14.4746	+	21.3683i	0.558786	+	0.824915i
$672$		0			0
$673$	−4.94179	+	2.51797i	−0.190492	+	0.0970605i	−0.546635	−	0.837371i	$-0.684092\pi$
$673$	−4.94179	+	2.51797i	−0.190492	+	0.0970605i	0.356143	+	0.934431i	$0.384092\pi$
$674$	26.7253	+	36.7842i	1.02942	+	1.41687i
$675$		0			0
$676$	−0.559191	−	1.72101i	−0.0215073	−	0.0661928i
$677$	2.07893	+	1.05927i	0.0798999	+	0.0407110i	0.493484	−	0.869755i	$-0.335723\pi$
$677$	2.07893	+	1.05927i	0.0798999	+	0.0407110i	−0.413584	+	0.910466i	$0.635723\pi$
$678$		0			0
$679$	11.3369	−	8.23673i	0.435070	−	0.316097i
$680$	−1.21911	+	11.6329i	−0.0467507	+	0.446103i
$681$		0			0
$682$	−0.874800	−	1.86638i	−0.0334978	−	0.0714675i
$683$	25.0400	−	25.0400i	0.958127	−	0.958127i	−0.0410307	−	0.999158i	$-0.513064\pi$
$683$	25.0400	−	25.0400i	0.958127	−	0.958127i	0.999158	+	0.0410307i	$0.0130641\pi$
$684$		0			0
$685$	−27.6256	+	1.45618i	−1.05552	+	0.0556380i
$686$	18.8423	+	13.6897i	0.719401	+	0.522676i
$687$		0			0
$688$	−13.8738	+	27.2288i	−0.528933	+	1.03809i
$689$	−6.80110	−	4.94129i	−0.259101	−	0.188248i
$690$		0			0
$691$	−0.556172	+	1.71172i	−0.0211578	+	0.0651170i	−0.961078	−	0.276277i	$-0.910899\pi$
$691$	−0.556172	+	1.71172i	−0.0211578	+	0.0651170i	0.939920	+	0.341394i	$0.110899\pi$
$692$	−0.456241	+	0.456241i	−0.0173437	+	0.0173437i
$693$		0			0
$694$		−	44.2510i		−	1.67974i
$695$	0.235245	−	2.24475i	0.00892336	−	0.0851482i
$696$		0			0
$697$	0.174147	+	1.09952i	0.00659628	+	0.0416473i
$698$	−27.9094	−	14.2205i	−1.05638	−	0.538255i
$699$		0			0
$700$	1.71223	+	2.63311i	0.0647163	+	0.0995223i
$701$	−10.4715	−	14.4128i	−0.395502	−	0.544362i	0.564106	−	0.825703i	$-0.309221\pi$
$701$	−10.4715	−	14.4128i	−0.395502	−	0.544362i	−0.959608	+	0.281340i	$0.909221\pi$
$702$		0			0
$703$	18.9468	+	18.9468i	0.714593	+	0.714593i
$704$	−0.799189	+	24.2592i	−0.0301206	+	0.914304i
$705$		0			0
$706$	−5.57255	−	1.81063i	−0.209726	−	0.0681440i
$707$	−55.3357	−	8.76432i	−2.08111	−	0.329616i
$708$		0			0
$709$	9.55567	−	3.10483i	0.358871	−	0.116604i	−0.124032	−	0.992278i	$-0.539583\pi$
$709$	9.55567	−	3.10483i	0.358871	−	0.116604i	0.482903	+	0.875674i	$0.339583\pi$
$710$	−27.2048	−	7.28067i	−1.02098	−	0.273239i
$711$		0			0
$712$	−5.91351	+	37.3365i	−0.221618	+	1.39924i
$713$	0.533487	+	1.04703i	0.0199793	+	0.0392115i
$714$		0			0
$715$	1.99218	−	6.56961i	0.0745034	−	0.245690i
$716$	−0.554298			−0.0207151
$717$		0			0
$718$	2.46302	−	15.5509i	0.0919193	−	0.580355i
$719$	4.03181	−	5.54931i	0.150361	−	0.206954i	−0.727191	−	0.686435i	$-0.759175\pi$
$719$	4.03181	−	5.54931i	0.150361	−	0.206954i	0.877553	+	0.479480i	$0.159175\pi$
$720$		0			0
$721$	40.4204	−	13.1334i	1.50533	−	0.489113i
$722$	−15.2088	+	2.40884i	−0.566014	+	0.0896478i
$723$		0			0
$724$	−0.856964	−	0.278444i	−0.0318488	−	0.0103483i
$725$	4.57485	−	2.04017i	0.169906	−	0.0757702i
$726$		0			0
$727$	−25.2212	−	25.2212i	−0.935401	−	0.935401i	0.0626351	−	0.998036i	$-0.480050\pi$
$727$	−25.2212	−	25.2212i	−0.935401	−	0.935401i	−0.998036	+	0.0626351i	$0.980050\pi$
$728$	−9.43398	+	4.80685i	−0.349647	+	0.178154i
$729$		0			0
$730$	−16.3538	−	7.27525i	−0.605281	−	0.269269i
$731$	−4.25759	−	13.1035i	−0.157473	−	0.484651i
$732$		0			0
$733$	1.20620	+	7.61562i	0.0445519	+	0.281289i	0.999899	−	0.0141956i	$-0.00451876\pi$
$733$	1.20620	+	7.61562i	0.0445519	+	0.281289i	−0.955347	+	0.295485i	$0.904519\pi$
$734$	41.0401	−	29.8174i	1.51482	−	1.10058i
$735$		0			0
$736$			2.33188i			0.0859543i
$737$	6.92277	−	12.5474i	0.255004	−	0.462189i
$738$		0			0
$739$	−12.6089	+	38.8062i	−0.463825	+	1.42751i	0.396629	+	0.917979i	$0.370180\pi$
$739$	−12.6089	+	38.8062i	−0.463825	+	1.42751i	−0.860454	+	0.509528i	$0.829820\pi$
$740$	0.0865259	+	1.64150i	0.00318075	+	0.0603427i
$741$		0			0
$742$	−25.4776	+	50.0027i	−0.935313	+	1.83566i
$743$	−20.1411	+	39.5290i	−0.738904	+	1.45018i	0.148368	+	0.988932i	$0.452598\pi$
$743$	−20.1411	+	39.5290i	−0.738904	+	1.45018i	−0.887271	+	0.461248i	$0.847402\pi$
$744$		0			0
$745$	1.82563	−	2.02880i	0.0668859	−	0.0743296i
$746$	−6.34530	+	19.5288i	−0.232318	+	0.715001i
$747$		0			0
$748$	0.651178	+	0.695544i	0.0238094	+	0.0254316i
$749$		−	25.9946i		−	0.949821i
$750$		0			0
$751$	10.6518	−	7.73896i	0.388688	−	0.282399i	−0.376229	−	0.926527i	$-0.622780\pi$
$751$	10.6518	−	7.73896i	0.388688	−	0.282399i	0.764918	+	0.644128i	$0.222780\pi$
$752$	0.795708	+	5.02390i	0.0290165	+	0.183203i
$753$		0			0
$754$	−0.420104	−	1.29295i	−0.0152993	−	0.0470864i
$755$	−1.44215	+	3.24177i	−0.0524853	+	0.117980i
$756$		0			0
$757$	−17.7060	+	9.02166i	−0.643535	+	0.327898i	−0.745121	−	0.666929i	$-0.767608\pi$
$757$	−17.7060	+	9.02166i	−0.643535	+	0.327898i	0.101586	+	0.994827i	$0.467608\pi$
$758$	27.4703	+	27.4703i	0.997768	+	0.997768i
$759$		0			0
$760$	27.6455	+	17.9413i	1.00281	+	0.650799i
$761$	−16.8706	−	5.48158i	−0.611558	−	0.198707i	−0.0131694	−	0.999913i	$-0.504192\pi$
$761$	−16.8706	−	5.48158i	−0.611558	−	0.198707i	−0.598389	+	0.801206i	$0.704192\pi$
$762$		0			0
$763$	82.9328	−	13.1353i	3.00237	−	0.475528i
$764$	2.34625	−	0.762341i	0.0848842	−	0.0275805i
$765$		0			0
$766$	−20.7124	+	28.5082i	−0.748371	+	1.03004i
$767$	1.34813	−	8.51175i	0.0486781	−	0.307342i
$768$		0			0
$769$	−33.4001			−1.20444			−0.602218	−	0.798331i	$-0.705716\pi$
$769$	−33.4001			−1.20444			−0.602218	+	0.798331i	$0.705716\pi$
$770$	−45.3966	−	6.27467i	−1.63598	−	0.226124i
$771$		0			0
$772$	1.14769	+	2.25247i	0.0413064	+	0.0810683i
$773$	5.96974	−	37.6915i	0.214717	−	1.35567i	−0.611021	−	0.791614i	$-0.709241\pi$
$773$	5.96974	−	37.6915i	0.214717	−	1.35567i	0.825738	−	0.564054i	$-0.190759\pi$
$774$		0			0
$775$	1.41933	+	1.57440i	0.0509837	+	0.0565542i
$776$	8.57893	−	2.78746i	0.307966	−	0.100064i
$777$		0			0
$778$	10.9251	+	1.73036i	0.391683	+	0.0620365i
$779$	2.98315	+	0.969285i	0.106882	+	0.0347282i
$780$		0			0
$781$	23.5913	−	15.9804i	0.844163	−	0.571824i
$782$	−5.53895	−	5.53895i	−0.198072	−	0.198072i
$783$		0			0
$784$	27.0654	+	37.2523i	0.966621	+	1.33044i
$785$	5.94993	+	15.4861i	0.212362	+	0.552722i
$786$		0			0
$787$	32.7403	+	16.6820i	1.16706	+	0.594649i	0.926614	−	0.376013i	$-0.122705\pi$
$787$	32.7403	+	16.6820i	1.16706	+	0.594649i	0.240450	+	0.970662i	$0.422705\pi$
$788$	0.317689	+	2.00581i	0.0113172	+	0.0714541i
$789$		0			0
$790$	4.71386	+	5.81753i	0.167712	+	0.206978i
$791$			51.0989i			1.81687i
$792$		0			0
$793$	−5.09361	+	5.09361i	−0.180879	+	0.180879i
$794$	10.3140	−	31.7434i	0.366032	−	1.12653i
$795$		0			0
$796$	2.34087	+	1.70074i	0.0829700	+	0.0602812i
$797$	9.14395	−	17.9460i	0.323895	−	0.635680i	−0.670441	−	0.741963i	$-0.733895\pi$
$797$	9.14395	−	17.9460i	0.323895	−	0.635680i	0.994336	+	0.106283i	$0.0338949\pi$
$798$		0			0
$799$	−1.85529	−	1.34795i	−0.0656355	−	0.0476870i
$800$	1.09115	+	4.06240i	0.0385781	+	0.143627i
$801$		0			0
$802$	25.0253	−	25.0253i	0.883674	−	0.883674i
$803$	16.3982	−	7.68606i	0.578679	−	0.271235i
$804$		0			0
$805$	25.9844	+	2.72311i	0.915829	+	0.0959770i
$806$	0.465424	−	0.338150i	0.0163939	−	0.0119108i
$807$		0			0
$808$	−32.1334	−	16.3728i	−1.13045	−	0.575993i
$809$	16.0484	+	49.3920i	0.564233	+	1.73653i	0.670220	+	0.742162i	$0.266200\pi$
$809$	16.0484	+	49.3920i	0.564233	+	1.73653i	−0.105987	+	0.994367i	$0.533800\pi$
$810$		0			0
$811$	−23.0252	−	31.6914i	−0.808523	−	1.11284i	−0.991550	−	0.129728i	$-0.958590\pi$
$811$	−23.0252	−	31.6914i	−0.808523	−	1.11284i	0.183027	−	0.983108i	$-0.441410\pi$
$812$	−0.560729	+	0.285706i	−0.0196777	+	0.0100263i
$813$		0			0
$814$	−18.9290	−	14.7289i	−0.663462	−	0.516247i
$815$	−18.7569	+	28.9022i	−0.657025	+	1.01240i
$816$		0			0
$817$	−38.3431	−	6.07296i	−1.34146	−	0.212466i
$818$	−8.47873	+	1.34290i	−0.296452	+	0.0469533i
$819$		0			0
$820$	0.0962628	+	0.166616i	0.00336164	+	0.00581847i
$821$	14.6926	−	20.2226i	0.512775	−	0.705774i	−0.471609	−	0.881808i	$-0.656327\pi$
$821$	14.6926	−	20.2226i	0.512775	−	0.705774i	0.984384	+	0.176034i	$0.0563268\pi$
$822$		0			0
$823$	10.4310	+	20.4719i	0.363600	+	0.713606i	0.998246	−	0.0591972i	$-0.0188541\pi$
$823$	10.4310	+	20.4719i	0.363600	+	0.713606i	−0.634646	+	0.772803i	$0.718854\pi$
$824$	27.3580			0.953062
$825$		0			0
$826$	−57.5294			−2.00170
$827$	2.51391	+	4.93382i	0.0874171	+	0.171566i	0.930576	−	0.366099i	$-0.119307\pi$
$827$	2.51391	+	4.93382i	0.0874171	+	0.171566i	−0.843159	+	0.537664i	$0.819307\pi$
$828$		0			0
$829$	8.80126	−	12.1139i	0.305680	−	0.420733i	−0.628348	−	0.777933i	$-0.716268\pi$
$829$	8.80126	−	12.1139i	0.305680	−	0.420733i	0.934028	+	0.357200i	$0.116268\pi$
$830$	3.26114	+	5.64452i	0.113196	+	0.195924i
$831$		0			0
$832$	−6.69109	+	1.05976i	−0.231972	+	0.0367407i
$833$	−20.5045	−	3.24759i	−0.710439	−	0.112522i
$834$		0			0
$835$	−5.05192	+	7.78443i	−0.174829	+	0.269391i
$836$	2.57917	−	0.745079i	0.0892023	−	0.0257691i
$837$		0			0
$838$	14.4461	−	7.36068i	0.499034	−	0.254270i
$839$	7.40356	+	10.1901i	0.255599	+	0.351802i	0.917462	−	0.397823i	$-0.130234\pi$
$839$	7.40356	+	10.1901i	0.255599	+	0.351802i	−0.661863	+	0.749625i	$0.730234\pi$
$840$		0			0
$841$	−8.65134	−	26.6261i	−0.298322	−	0.918141i
$842$	10.2836	+	5.23975i	0.354396	+	0.180574i
$843$		0			0
$844$	−0.770496	+	0.559798i	−0.0265216	+	0.0192691i
$845$	−27.0049	−	2.83006i	−0.928998	−	0.0973572i
$846$		0			0
$847$	34.8744	−	30.5585i	1.19830	−	1.05000i
$848$	−27.4579	+	27.4579i	−0.942907	+	0.942907i
$849$		0			0
$850$	−12.2413	−	7.05763i	−0.419873	−	0.242075i
$851$	11.0621	+	8.03706i	0.379203	+	0.275507i
$852$		0			0
$853$	−22.5965	+	44.3481i	−0.773689	+	1.51845i	0.0794926	+	0.996835i	$0.474670\pi$
$853$	−22.5965	+	44.3481i	−0.773689	+	1.51845i	−0.853181	+	0.521614i	$0.825330\pi$
$854$	38.9035	+	28.2651i	1.33125	+	0.967211i
$855$		0			0
$856$	5.17078	−	15.9140i	0.176734	−	0.543930i
$857$	−21.2860	+	21.2860i	−0.727117	+	0.727117i	−0.970044	−	0.242927i	$-0.921892\pi$
$857$	−21.2860	+	21.2860i	−0.727117	+	0.727117i	0.242927	+	0.970044i	$0.421892\pi$
$858$		0			0
$859$		−	9.31402i		−	0.317790i	−0.987295	−	0.158895i	$-0.949207\pi$
$859$		−	9.31402i		−	0.317790i	0.987295	−	0.158895i	$-0.0507932\pi$
$860$	−1.49932	−	1.85036i	−0.0511263	−	0.0630967i
$861$		0			0
$862$	−1.67475	−	10.5740i	−0.0570424	−	0.360151i
$863$	−31.5320	−	16.0664i	−1.07336	−	0.546905i	−0.174285	−	0.984695i	$-0.555761\pi$
$863$	−31.5320	−	16.0664i	−1.07336	−	0.546905i	−0.899077	+	0.437790i	$0.855761\pi$
$864$		0			0
$865$	3.47231	+	9.03749i	0.118062	+	0.307284i
$866$	−4.34927	−	5.98625i	−0.147794	−	0.203421i
$867$		0			0
$868$	−0.188310	−	0.188310i	−0.00639166	−	0.00639166i
$869$	−7.57178	−	0.249443i	−0.256855	−	0.00846176i
$870$		0			0
$871$	3.80391	+	1.23597i	0.128891	+	0.0418791i
$872$	53.3847	+	8.45531i	1.80783	+	0.286333i
$873$		0			0
$874$	−20.9911	+	6.82042i	−0.710034	+	0.230704i
$875$	46.5418	−	7.41486i	1.57340	−	0.250668i
$876$		0			0
$877$	−3.41955	+	21.5902i	−0.115470	+	0.729048i	0.860225	+	0.509915i	$0.170323\pi$
$877$	−3.41955	+	21.5902i	−0.115470	+	0.729048i	−0.975695	+	0.219133i	$0.929677\pi$
$878$	−0.863707	−	1.69512i	−0.0291487	−	0.0572076i
$879$		0			0
$880$	−28.5327	−	13.8360i	−0.961839	−	0.466411i
$881$	−46.4810			−1.56599			−0.782993	−	0.622031i	$-0.786308\pi$
$881$	−46.4810			−1.56599			−0.782993	+	0.622031i	$0.786308\pi$
$882$		0			0
$883$	4.36822	−	27.5798i	0.147002	−	0.928135i	−0.798376	−	0.602159i	$-0.794307\pi$
$883$	4.36822	−	27.5798i	0.147002	−	0.928135i	0.945378	−	0.325976i	$-0.105693\pi$
$884$	−0.156308	+	0.215140i	−0.00525721	+	0.00723593i
$885$		0			0
$886$	21.4719	−	6.97665i	0.721363	−	0.234385i
$887$	6.95351	−	1.10133i	0.233476	−	0.0369790i	−0.0385999	−	0.999255i	$-0.512290\pi$
$887$	6.95351	−	1.10133i	0.233476	−	0.0369790i	0.272076	+	0.962276i	$0.412290\pi$
$888$		0			0
$889$	4.64858	+	1.51041i	0.155908	+	0.0506577i
$890$	−38.3066	−	24.8601i	−1.28404	−	0.833313i
$891$		0			0
$892$	−1.49577	−	1.49577i	−0.0500822	−	0.0500822i
$893$	−5.75734	+	2.93351i	−0.192662	+	0.0981662i
$894$		0			0
$895$	−3.38064	+	7.59923i	−0.113002	+	0.254014i
$896$	16.1666	+	49.7558i	0.540090	+	1.66223i
$897$		0			0
$898$	2.78007	+	17.5527i	0.0927721	+	0.585740i
$899$	−0.343606	+	0.249644i	−0.0114599	+	0.00832611i
$900$		0			0
$901$		−	17.5071i		−	0.583247i
$902$	−2.75713	−	0.530284i	−0.0918024	−	0.0176565i
$903$		0			0
$904$	−10.1645	+	31.2830i	−0.338065	+	1.04046i
$905$	−9.04395	+	10.0504i	−0.300631	+	0.334088i
$906$		0			0
$907$	13.4148	−	26.3281i	0.445433	−	0.874211i	−0.553706	−	0.832712i	$-0.686787\pi$
$907$	13.4148	−	26.3281i	0.445433	−	0.874211i	0.999139	−	0.0414984i	$-0.0132131\pi$
$908$	0.560050	−	1.09916i	0.0185859	−	0.0364769i
$909$		0			0
$910$	−0.673287	−	12.7731i	−0.0223193	−	0.423423i
$911$	−5.23886	+	16.1236i	−0.173571	+	0.534198i	−0.999565	−	0.0294813i	$-0.990614\pi$
$911$	−5.23886	+	16.1236i	−0.173571	+	0.534198i	0.825994	+	0.563679i	$0.190614\pi$
$912$		0			0
$913$	−6.47702	−	1.24574i	−0.214358	−	0.0412279i
$914$		−	5.14655i		−	0.170233i
$915$		0			0
$916$	−2.36292	+	1.71676i	−0.0780729	+	0.0567233i
$917$	−9.53075	−	60.1748i	−0.314733	−	1.98715i
$918$		0			0
$919$	−1.55222	−	4.77725i	−0.0512030	−	0.157587i	0.922185	−	0.386748i	$-0.126402\pi$
$919$	−1.55222	−	4.77725i	−0.0512030	−	0.157587i	−0.973388	+	0.229161i	$0.926402\pi$
$920$	15.3661	+	6.83585i	0.506605	+	0.225371i
$921$		0			0
$922$	−7.12304	+	3.62937i	−0.234585	+	0.119527i
$923$	5.62351	+	5.62351i	0.185100	+	0.185100i
$924$		0			0
$925$	23.0321	+	8.82519i	0.757290	+	0.290170i
$926$	−30.3635	−	9.86569i	−0.997805	−	0.324207i
$927$		0			0
$928$	−0.832439	+	0.131845i	−0.0273262	+	0.00432804i
$929$	−11.2348	+	3.65041i	−0.368602	+	0.119766i	−0.487460	−	0.873145i	$-0.662077\pi$
$929$	−11.2348	+	3.65041i	−0.368602	+	0.119766i	0.118858	+	0.992911i	$0.462077\pi$
$930$		0			0
$931$	−34.3822	+	47.3231i	−1.12683	+	1.55095i
$932$	0.0865609	−	0.546524i	0.00283540	−	0.0179020i
$933$		0			0
$934$	21.5258			0.704346
$935$	13.5072	−	4.68533i	0.441731	−	0.153227i
$936$		0			0
$937$	−1.04060	−	2.04229i	−0.0339949	−	0.0667187i	0.873384	−	0.487032i	$-0.161920\pi$
$937$	−1.04060	−	2.04229i	−0.0339949	−	0.0667187i	−0.907379	+	0.420313i	$0.861920\pi$
$938$	4.17683	−	26.3715i	0.136378	−	0.861060i
$939$		0			0
$940$	−0.382923	−	0.102480i	−0.0124896	−	0.00334252i
$941$	−1.68653	+	0.547988i	−0.0549794	+	0.0178639i	−0.336378	−	0.941727i	$-0.609202\pi$
$941$	−1.68653	+	0.547988i	−0.0549794	+	0.0178639i	0.281398	+	0.959591i	$0.409202\pi$
$942$		0			0
$943$	1.58094	+	0.250397i	0.0514826	+	0.00815404i
$944$	−37.8587	−	12.3010i	−1.23219	−	0.400364i
$945$		0			0
$946$	34.7303	+	1.14415i	1.12918	+	0.0371994i
$947$	8.63289	+	8.63289i	0.280531	+	0.280531i	0.833321	−	0.552790i	$-0.186437\pi$
$947$	8.63289	+	8.63289i	0.280531	+	0.280531i	−0.552790	+	0.833321i	$0.686437\pi$
$948$		0			0
$949$	2.97101	+	4.08925i	0.0964431	+	0.132743i
$950$	−33.3773	+	21.7042i	−1.08290	+	0.704178i
$951$		0			0
$952$	−19.6466	−	10.0105i	−0.636752	−	0.324441i
$953$	−2.88376	−	18.2074i	−0.0934143	−	0.589794i	−0.989344	−	0.145598i	$-0.953489\pi$
$953$	−2.88376	−	18.2074i	−0.0934143	−	0.589794i	0.895930	−	0.444196i	$-0.146511\pi$
$954$		0			0
$955$	3.85821	−	36.8157i	0.124849	−	1.19133i
$956$			0.478792i			0.0154852i
$957$		0			0
$958$	−5.09348	+	5.09348i	−0.164563	+	0.164563i
$959$	16.1154	−	49.5982i	0.520395	−	1.60161i
$960$		0			0
$961$	24.9341	+	18.1157i	0.804327	+	0.584377i
$962$	3.03906	−	5.96448i	0.0979831	−	0.192303i
$963$		0			0
$964$	−3.06368	−	2.22589i	−0.0986743	−	0.0716911i
$965$	37.8803	−	1.99673i	1.21941	−	0.0642770i
$966$		0			0
$967$	9.49113	−	9.49113i	0.305214	−	0.305214i	−0.537836	−	0.843050i	$-0.680758\pi$
$967$	9.49113	−	9.49113i	0.305214	−	0.305214i	0.843050	+	0.537836i	$0.180758\pi$
$968$	27.4289	−	11.7709i	0.881598	−	0.378333i
$969$		0			0
$970$	−1.13577	+	10.8377i	−0.0364675	+	0.347979i
$971$	41.4379	−	30.1064i	1.32981	−	0.966161i	0.330053	−	0.943963i	$-0.392933\pi$
$971$	41.4379	−	30.1064i	1.32981	−	0.966161i	0.999754	−	0.0221983i	$-0.00706650\pi$
$972$		0			0
$973$	3.79111	+	1.93167i	0.121538	+	0.0619265i
$974$	−4.86416	−	14.9703i	−0.155858	−	0.479681i
$975$		0			0
$976$	19.5578	+	26.9190i	0.626029	+	0.861655i
$977$	−12.9020	+	6.57391i	−0.412772	+	0.210318i	−0.648030	−	0.761615i	$-0.724407\pi$
$977$	−12.9020	+	6.57391i	−0.412772	+	0.210318i	0.235257	+	0.971933i	$0.424407\pi$
$978$		0			0
$979$	44.3897	−	12.8235i	1.41870	−	0.409840i
$980$	−3.50981	+	0.747144i	−0.112117	+	0.0238666i
$981$		0			0
$982$	4.71447	+	0.746699i	0.150445	+	0.0238281i
$983$	56.8388	−	9.00238i	1.81288	−	0.287131i	0.844304	−	0.535865i	$-0.180014\pi$
$983$	56.8388	−	9.00238i	1.81288	−	0.287131i	0.968572	+	0.248734i	$0.0800143\pi$
$984$		0			0
$985$	29.4365	+	7.87794i	0.937926	+	0.251012i
$986$	1.66413	−	2.29048i	0.0529967	−	0.0729437i
$987$		0			0
$988$	0.340170	+	0.667621i	0.0108222	+	0.0212399i
$989$	−19.8105			−0.629936
$990$		0			0
$991$	13.1102			0.416458			0.208229	−	0.978080i	$-0.433230\pi$
$991$	13.1102			0.416458			0.208229	+	0.978080i	$0.433230\pi$
$992$	−0.161918	−	0.317782i	−0.00514090	−	0.0100896i
$993$		0			0
$994$	31.2055	−	42.9507i	0.989779	−	1.36231i
$995$	37.5934	−	21.7198i	1.19179	−	0.688563i
$996$		0			0
$997$	2.22714	−	0.352744i	0.0705343	−	0.0111715i	−0.121068	−	0.992644i	$-0.538632\pi$
$997$	2.22714	−	0.352744i	0.0705343	−	0.0111715i	0.191602	+	0.981473i	$0.438632\pi$
$998$	12.9469	+	2.05059i	0.409828	+	0.0649104i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bj.a.442.1		32
3.2	odd	2		55.2.l.a.2.4	✓	32
5.3	odd	4	inner	495.2.bj.a.343.1		32
11.6	odd	10	inner	495.2.bj.a.127.1		32
12.11	even	2		880.2.cm.a.497.3		32
15.2	even	4		275.2.bm.b.68.1		32
15.8	even	4		55.2.l.a.13.4	yes	32
15.14	odd	2		275.2.bm.b.57.1		32
33.2	even	10		605.2.m.d.602.1		32
33.5	odd	10		605.2.m.e.457.1		32
33.8	even	10		605.2.m.c.282.1		32
33.14	odd	10		605.2.m.d.282.4		32
33.17	even	10		55.2.l.a.17.4	yes	32
33.20	odd	10		605.2.m.c.602.4		32
33.26	odd	10		605.2.e.b.362.4		32
33.29	even	10		605.2.e.b.362.13		32
33.32	even	2		605.2.m.e.112.1		32
55.28	even	20	inner	495.2.bj.a.28.1		32
60.23	odd	4		880.2.cm.a.673.3		32
132.83	odd	10		880.2.cm.a.17.3		32
165.8	odd	20		605.2.m.c.403.4		32
165.17	odd	20		275.2.bm.b.193.1		32
165.38	even	20		605.2.m.e.578.1		32
165.53	even	20		605.2.m.c.118.1		32
165.68	odd	20		605.2.m.d.118.4		32
165.83	odd	20		55.2.l.a.28.4	yes	32
165.98	odd	4		605.2.m.e.233.1		32
165.113	even	20		605.2.m.d.403.1		32
165.128	odd	20		605.2.e.b.483.4		32
165.149	even	10		275.2.bm.b.182.1		32
165.158	even	20		605.2.e.b.483.13		32
660.83	even	20		880.2.cm.a.193.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.4	✓	32	3.2	odd	2
55.2.l.a.13.4	yes	32	15.8	even	4
55.2.l.a.17.4	yes	32	33.17	even	10
55.2.l.a.28.4	yes	32	165.83	odd	20
275.2.bm.b.57.1		32	15.14	odd	2
275.2.bm.b.68.1		32	15.2	even	4
275.2.bm.b.182.1		32	165.149	even	10
275.2.bm.b.193.1		32	165.17	odd	20
495.2.bj.a.28.1		32	55.28	even	20	inner
495.2.bj.a.127.1		32	11.6	odd	10	inner
495.2.bj.a.343.1		32	5.3	odd	4	inner
495.2.bj.a.442.1		32	1.1	even	1	trivial
605.2.e.b.362.4		32	33.26	odd	10
605.2.e.b.362.13		32	33.29	even	10
605.2.e.b.483.4		32	165.128	odd	20
605.2.e.b.483.13		32	165.158	even	20
605.2.m.c.118.1		32	165.53	even	20
605.2.m.c.282.1		32	33.8	even	10
605.2.m.c.403.4		32	165.8	odd	20
605.2.m.c.602.4		32	33.20	odd	10
605.2.m.d.118.4		32	165.68	odd	20
605.2.m.d.282.4		32	33.14	odd	10
605.2.m.d.403.1		32	165.113	even	20
605.2.m.d.602.1		32	33.2	even	10
605.2.m.e.112.1		32	33.32	even	2
605.2.m.e.233.1		32	165.98	odd	4
605.2.m.e.457.1		32	33.5	odd	10
605.2.m.e.578.1		32	165.38	even	20
880.2.cm.a.17.3		32	132.83	odd	10
880.2.cm.a.193.3		32	660.83	even	20
880.2.cm.a.497.3		32	12.11	even	2
880.2.cm.a.673.3		32	60.23	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.665529 - 1.30617i) q^{2} +(-0.0875924 + 0.120561i) q^{4} +(1.11862 + 1.93615i) q^{5} +(-4.16343 + 0.659422i) q^{7} +(-2.68004 - 0.424477i) q^{8} +(1.78448 - 2.74968i) q^{10} +(0.920480 + 3.18633i) q^{11} +(-0.824787 + 0.420250i) q^{13} +(3.63220 + 4.99930i) q^{14} +(1.32131 + 4.06656i) q^{16} +(-1.71765 - 0.875188i) q^{17} +(-4.39439 + 3.19271i) q^{19} +(-0.331406 - 0.0347307i) q^{20} +(3.54930 - 3.32290i) q^{22} +(-1.95998 + 1.95998i) q^{23} +(-2.49738 + 4.33164i) q^{25} +(1.09784 + 0.797627i) q^{26} +(0.285184 - 0.559706i) q^{28} +(-0.810497 - 0.588860i) q^{29} +(0.131006 - 0.403196i) q^{31} +(0.594873 - 0.594873i) q^{32} +2.82602i q^{34} +(-5.93404 - 7.32339i) q^{35} +(-0.771690 - 4.87226i) q^{37} +(7.09483 + 3.61500i) q^{38} +(-2.17610 - 5.66380i) q^{40} +(-0.339428 - 0.467182i) q^{41} +(5.05373 + 5.05373i) q^{43} +(-0.464773 - 0.168125i) q^{44} +(3.86451 + 1.25566i) q^{46} +(1.17495 + 0.186094i) q^{47} +(10.2419 - 3.32780i) q^{49} +(7.31996 + 0.379176i) q^{50} +(0.0215795 - 0.136247i) q^{52} +(4.12294 + 8.09173i) q^{53} +(-5.13956 + 5.34649i) q^{55} +11.4381 q^{56} +(-0.229745 + 1.45055i) q^{58} +(-5.47214 + 7.53175i) q^{59} +(7.40093 - 2.40471i) q^{61} +(-0.613832 + 0.0972215i) q^{62} +(6.96021 + 2.26151i) q^{64} +(-1.73629 - 1.12681i) q^{65} +(-3.05526 - 3.05526i) q^{67} +(0.255966 - 0.130421i) q^{68} +(-5.61635 + 12.6248i) q^{70} +(-2.65487 - 8.17086i) q^{71} +(-0.854195 - 5.39318i) q^{73} +(-5.85044 + 4.25059i) q^{74} -0.809447i q^{76} +(-5.93349 - 12.6591i) q^{77} +(-0.705861 + 2.17242i) q^{79} +(-6.39544 + 7.10719i) q^{80} +(-0.384322 + 0.754275i) q^{82} +(-0.902846 + 1.77193i) q^{83} +(-0.226904 - 4.30464i) q^{85} +(3.23765 - 9.96446i) q^{86} +(-1.11440 - 8.93023i) q^{88} -13.9313i q^{89} +(3.15682 - 2.29356i) q^{91} +(-0.0646171 - 0.407977i) q^{92} +(-0.538893 - 1.65854i) q^{94} +(-11.0972 - 4.93678i) q^{95} +(-2.96200 + 1.50922i) q^{97} +(-11.1630 - 11.1630i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8 + 24 * q^11 - 10 * q^13 - 8 * q^16 - 16 * q^20 + 10 * q^22 + 24 * q^23 + 16 * q^25 - 20 * q^26 + 50 * q^28 - 28 * q^31 + 10 * q^35 - 8 * q^37 - 10 * q^38 - 50 * q^40 - 40 * q^41 + 60 * q^46 + 28 * q^47 + 50 * q^50 - 50 * q^52 + 24 * q^53 - 64 * q^55 + 80 * q^56 - 50 * q^58 - 60 * q^61 - 100 * q^62 - 8 * q^67 + 30 * q^68 + 30 * q^70 - 24 * q^71 + 50 * q^73 - 70 * q^77 - 98 * q^80 - 10 * q^82 - 90 * q^83 + 30 * q^85 - 100 * q^86 + 170 * q^88 + 20 * q^91 + 68 * q^92 + 40 * q^95 - 8 * q^97

Introduction

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