LMFDB - Embedded newform 525.2.r.h.424.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(424,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("525.424");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.r (of order $6$, degree $2$, not minimal)

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:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 15x^{14} + 158x^{12} - 843x^{10} + 3258x^{8} - 4947x^{6} + 5489x^{4} - 1296x^{2} + 256 $ x^16 - 15x^14 + 158x^12 - 843x^10 + 3258x^8 - 4947x^6 + 5489x^4 - 1296*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			424.3
Root			$-1.06407 + 0.614340i$ of defining polynomial
Character	$\chi$	$=$	525.424
Dual form			525.2.r.h.499.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06407 + 0.614340i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.245174 + 0.424653i) q^{4} -1.22868 q^{6} +(2.33443 - 1.24517i) q^{7} -3.05984i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.06407 + 0.614340i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.245174 + 0.424653i) q^{4} -1.22868 q^{6} +(2.33443 - 1.24517i) q^{7} -3.05984i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.37294 - 4.11005i) q^{11} +(-0.424653 + 0.245174i) q^{12} -6.25553i q^{13} +(-1.71903 + 2.75908i) q^{14} +(1.38943 + 2.40657i) q^{16} +(-5.44602 - 3.14426i) q^{17} +(-1.06407 - 0.614340i) q^{18} +(2.47385 + 4.28484i) q^{19} +(2.64426 + 0.0888607i) q^{21} +5.83116i q^{22} +(4.31341 - 2.49035i) q^{23} +(1.52992 - 2.64990i) q^{24} +(3.84302 + 6.65630i) q^{26} +1.00000i q^{27} +(-0.0435726 + 1.29661i) q^{28} -4.00000 q^{29} +(-0.829594 + 1.43690i) q^{31} +(2.34290 + 1.35267i) q^{32} +(4.11005 - 2.37294i) q^{33} +7.72657 q^{34} -0.490347 q^{36} +(3.84347 - 2.21903i) q^{37} +(-5.26469 - 3.03957i) q^{38} +(3.12776 - 5.41745i) q^{39} +1.30782 q^{41} +(-2.86826 + 1.52992i) q^{42} +10.2362i q^{43} +(1.16356 + 2.01535i) q^{44} +(-3.05984 + 5.29980i) q^{46} +(-3.26074 + 1.88259i) q^{47} +2.77886i q^{48} +(3.89908 - 5.81353i) q^{49} +(-3.14426 - 5.44602i) q^{51} +(2.65643 + 1.53369i) q^{52} +(-6.23818 - 3.60162i) q^{53} +(-0.614340 - 1.06407i) q^{54} +(-3.81003 - 7.14296i) q^{56} +4.94771i q^{57} +(4.25627 - 2.45736i) q^{58} +(0.117410 - 0.203359i) q^{59} +(2.50000 + 4.33013i) q^{61} -2.03861i q^{62} +(2.24556 + 1.39908i) q^{63} -8.88173 q^{64} +(-2.91558 + 5.04993i) q^{66} +(2.15670 + 1.24517i) q^{67} +(2.67044 - 1.54178i) q^{68} +4.98069 q^{69} +6.06598 q^{71} +(2.64990 - 1.52992i) q^{72} +(10.8182 + 6.24588i) q^{73} +(-2.72647 + 4.72239i) q^{74} -2.42609 q^{76} +(0.421722 - 12.5493i) q^{77} +7.68604i q^{78} +(-0.415579 - 0.719805i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.39161 + 0.803447i) q^{82} -1.14954i q^{83} +(-0.686038 + 1.10111i) q^{84} +(-6.28852 - 10.8920i) q^{86} +(-3.46410 - 2.00000i) q^{87} +(-12.5761 - 7.26081i) q^{88} +(1.14426 + 1.98191i) q^{89} +(-7.78922 - 14.6031i) q^{91} +2.44227i q^{92} +(-1.43690 + 0.829594i) q^{93} +(2.31310 - 4.00641i) q^{94} +(1.35267 + 2.34290i) q^{96} +0.476664i q^{97} +(-0.577407 + 8.58135i) q^{98} +4.74588 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 14 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) $ 16 * q + 14 * q^4 - 4 * q^6 + 8 * q^9	$ 16 q + 14 q^{4} - 4 q^{6} + 8 q^{9} - 16 q^{11} + 24 q^{14} - 34 q^{16} + 6 q^{19} + 4 q^{21} - 6 q^{24} + 38 q^{26} - 64 q^{29} - 18 q^{31} - 56 q^{34} + 28 q^{36} + 14 q^{39} + 16 q^{41} + 52 q^{44} + 12 q^{46} + 42 q^{49} - 12 q^{51} - 2 q^{54} - 42 q^{56} + 20 q^{59} + 40 q^{61} - 84 q^{64} - 24 q^{66} + 8 q^{69} + 88 q^{71} - 42 q^{74} - 92 q^{76} + 16 q^{79} - 8 q^{81} + 36 q^{84} - 24 q^{86} - 20 q^{89} + 42 q^{91} + 44 q^{94} + 34 q^{96} - 32 q^{99}+O(q^{100}) $ 16 * q + 14 * q^4 - 4 * q^6 + 8 * q^9 - 16 * q^11 + 24 * q^14 - 34 * q^16 + 6 * q^19 + 4 * q^21 - 6 * q^24 + 38 * q^26 - 64 * q^29 - 18 * q^31 - 56 * q^34 + 28 * q^36 + 14 * q^39 + 16 * q^41 + 52 * q^44 + 12 * q^46 + 42 * q^49 - 12 * q^51 - 2 * q^54 - 42 * q^56 + 20 * q^59 + 40 * q^61 - 84 * q^64 - 24 * q^66 + 8 * q^69 + 88 * q^71 - 42 * q^74 - 92 * q^76 + 16 * q^79 - 8 * q^81 + 36 * q^84 - 24 * q^86 - 20 * q^89 + 42 * q^91 + 44 * q^94 + 34 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.06407	+	0.614340i	−0.752409	+	0.434404i	−0.826564	−	0.562843i	$-0.809708\pi$
$2$	−1.06407	+	0.614340i	−0.752409	+	0.434404i	0.0741545	+	0.997247i	$0.476374\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.245174	+	0.424653i	−0.122587	+	0.212327i
$5$		0			0
$5$		0			0
$6$	−1.22868			−0.501606
$7$	2.33443	−	1.24517i	0.882330	−	0.470631i
$7$	2.33443	−	1.24517i	0.882330	−	0.470631i
$8$		−	3.05984i		−	1.08182i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	2.37294	−	4.11005i	0.715468	−	1.23923i	−0.247311	−	0.968936i	$-0.579547\pi$
$11$	2.37294	−	4.11005i	0.715468	−	1.23923i	0.962779	−	0.270290i	$-0.0871197\pi$
$12$	−0.424653	+	0.245174i	−0.122587	+	0.0707755i
$13$		−	6.25553i		−	1.73497i	−0.497462	−	0.867486i	$-0.665735\pi$
$13$		−	6.25553i		−	1.73497i	0.497462	−	0.867486i	$-0.334265\pi$
$14$	−1.71903	+	2.75908i	−0.459429	+	0.737395i
$15$		0			0
$16$	1.38943	+	2.40657i	0.347358	+	0.601642i
$17$	−5.44602	−	3.14426i	−1.32085	−	0.762595i	−0.336988	−	0.941509i	$-0.609408\pi$
$17$	−5.44602	−	3.14426i	−1.32085	−	0.762595i	−0.983865	+	0.178914i	$0.942742\pi$
$18$	−1.06407	−	0.614340i	−0.250803	−	0.144801i
$19$	2.47385	+	4.28484i	0.567541	+	0.983009i	0.996808	+	0.0798321i	$0.0254384\pi$
$19$	2.47385	+	4.28484i	0.567541	+	0.983009i	−0.429268	+	0.903177i	$0.641228\pi$
$20$		0			0
$21$	2.64426	+	0.0888607i	0.577025	+	0.0193910i
$22$			5.83116i			1.24321i
$23$	4.31341	−	2.49035i	0.899408	−	0.519273i	0.0223998	−	0.999749i	$-0.492869\pi$
$23$	4.31341	−	2.49035i	0.899408	−	0.519273i	0.877008	+	0.480476i	$0.159536\pi$
$24$	1.52992	−	2.64990i	0.312293	−	0.540908i
$25$		0			0
$26$	3.84302	+	6.65630i	0.753678	+	1.30541i
$27$			1.00000i			0.192450i
$28$	−0.0435726	+	1.29661i	−0.00823445	+	0.245035i
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	−0.829594	+	1.43690i	−0.149000	+	0.258075i	−0.930858	−	0.365381i	$-0.880939\pi$
$31$	−0.829594	+	1.43690i	−0.149000	+	0.258075i	0.781858	+	0.623456i	$0.214272\pi$
$32$	2.34290	+	1.35267i	0.414169	+	0.239121i
$33$	4.11005	−	2.37294i	0.715468	−	0.413075i
$34$	7.72657			1.32510
$35$		0			0
$36$	−0.490347			−0.0817246
$37$	3.84347	−	2.21903i	0.631862	−	0.364806i	−0.149611	−	0.988745i	$-0.547802\pi$
$37$	3.84347	−	2.21903i	0.631862	−	0.364806i	0.781473	+	0.623939i	$0.214469\pi$
$38$	−5.26469	−	3.03957i	−0.854046	−	0.493084i
$39$	3.12776	−	5.41745i	0.500843	−	0.867486i
$40$		0			0
$41$	1.30782			0.204248			0.102124	−	0.994772i	$-0.467436\pi$
$41$	1.30782			0.204248			0.102124	+	0.994772i	$0.467436\pi$
$42$	−2.86826	+	1.52992i	−0.442582	+	0.236072i
$43$			10.2362i			1.56101i	0.625150	+	0.780505i	$0.285038\pi$
$43$			10.2362i			1.56101i	−0.625150	+	0.780505i	$0.714962\pi$
$44$	1.16356	+	2.01535i	0.175414	+	0.303826i
$45$		0			0
$46$	−3.05984	+	5.29980i	−0.451149	+	0.781412i
$47$	−3.26074	+	1.88259i	−0.475628	+	0.274604i	−0.718593	−	0.695431i	$-0.755213\pi$
$47$	−3.26074	+	1.88259i	−0.475628	+	0.274604i	0.242965	+	0.970035i	$0.421880\pi$
$48$			2.77886i			0.401095i
$49$	3.89908	−	5.81353i	0.557012	−	0.830504i
$50$		0			0
$51$	−3.14426	−	5.44602i	−0.440284	−	0.762595i
$52$	2.65643	+	1.53369i	0.368381	+	0.212685i
$53$	−6.23818	−	3.60162i	−0.856880	−	0.494720i	0.00608595	−	0.999981i	$-0.498063\pi$
$53$	−6.23818	−	3.60162i	−0.856880	−	0.494720i	−0.862966	+	0.505261i	$0.831396\pi$
$54$	−0.614340	−	1.06407i	−0.0836010	−	0.144801i
$55$		0			0
$56$	−3.81003	−	7.14296i	−0.509137	−	0.954519i
$57$			4.94771i			0.655340i
$58$	4.25627	−	2.45736i	0.558876	−	0.322667i
$59$	0.117410	−	0.203359i	0.0152854	−	0.0264751i	−0.858282	−	0.513179i	$-0.828468\pi$
$59$	0.117410	−	0.203359i	0.0152854	−	0.0264751i	0.873567	+	0.486704i	$0.161801\pi$
$60$		0			0
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$		−	2.03861i		−	0.258904i
$63$	2.24556	+	1.39908i	0.282915	+	0.176268i
$64$	−8.88173			−1.11022
$65$		0			0
$66$	−2.91558	+	5.04993i	−0.358883	+	0.621604i
$67$	2.15670	+	1.24517i	0.263483	+	0.152122i	0.625923	−	0.779885i	$-0.284723\pi$
$67$	2.15670	+	1.24517i	0.263483	+	0.152122i	−0.362439	+	0.932007i	$0.618056\pi$
$68$	2.67044	−	1.54178i	0.323838	−	0.186968i
$69$	4.98069			0.599605
$70$		0			0
$71$	6.06598			0.719899			0.359950	−	0.932972i	$-0.382794\pi$
$71$	6.06598			0.719899			0.359950	+	0.932972i	$0.382794\pi$
$72$	2.64990	−	1.52992i	0.312293	−	0.180303i
$73$	10.8182	+	6.24588i	1.26617	+	0.731024i	0.974261	−	0.225421i	$-0.0723759\pi$
$73$	10.8182	+	6.24588i	1.26617	+	0.731024i	0.291910	+	0.956446i	$0.405709\pi$
$74$	−2.72647	+	4.72239i	−0.316946	+	0.548966i
$75$		0			0
$76$	−2.42609			−0.278292
$77$	0.421722	−	12.5493i	0.0480597	−	1.43013i
$78$			7.68604i			0.870272i
$79$	−0.415579	−	0.719805i	−0.0467563	−	0.0809844i	0.841700	−	0.539945i	$-0.181555\pi$
$79$	−0.415579	−	0.719805i	−0.0467563	−	0.0809844i	−0.888456	+	0.458961i	$0.848222\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.39161	+	0.803447i	−0.153678	+	0.0887259i
$83$		−	1.14954i		−	0.126178i	−0.998008	−	0.0630890i	$-0.979905\pi$
$83$		−	1.14954i		−	0.126178i	0.998008	−	0.0630890i	$-0.0200952\pi$
$84$	−0.686038	+	1.10111i	−0.0748528	+	0.120141i
$85$		0			0
$86$	−6.28852	−	10.8920i	−0.678108	−	1.17452i
$87$	−3.46410	−	2.00000i	−0.371391	−	0.214423i
$88$	−12.5761	−	7.26081i	−1.34062	−	0.774004i
$89$	1.14426	+	1.98191i	0.121291	+	0.210082i	0.920277	−	0.391267i	$-0.127963\pi$
$89$	1.14426	+	1.98191i	0.121291	+	0.210082i	−0.798986	+	0.601350i	$0.794630\pi$
$90$		0			0
$91$	−7.78922	−	14.6031i	−0.816532	−	1.53082i
$92$			2.44227i			0.254624i
$93$	−1.43690	+	0.829594i	−0.149000	+	0.0860249i
$94$	2.31310	−	4.00641i	0.238578	−	0.413229i
$95$		0			0
$96$	1.35267	+	2.34290i	0.138056	+	0.239121i
$97$			0.476664i			0.0483979i	0.999707	+	0.0241989i	$0.00770351\pi$
$97$			0.476664i			0.0483979i	−0.999707	+	0.0241989i	$0.992296\pi$
$98$	−0.577407	+	8.58135i	−0.0583269	+	0.866847i
$99$	4.74588			0.476978
$100$		0			0
$101$	−4.14426	+	7.17807i	−0.412369	+	0.714244i	−0.995148	−	0.0983863i	$-0.968632\pi$
$101$	−4.14426	+	7.17807i	−0.412369	+	0.714244i	0.582779	+	0.812631i	$0.301965\pi$
$102$	6.69141	+	3.86329i	0.662548	+	0.382522i
$103$	−12.3575	+	7.13461i	−1.21762	+	0.702994i	−0.964408	−	0.264417i	$-0.914820\pi$
$103$	−12.3575	+	7.13461i	−1.21762	+	0.702994i	−0.253212	+	0.967411i	$0.581487\pi$
$104$	−19.1409			−1.87692
$105$		0			0
$106$	8.85046			0.859633
$107$	1.87827	−	1.08442i	0.181579	−	0.104835i	−0.406455	−	0.913671i	$-0.633235\pi$
$107$	1.87827	−	1.08442i	0.181579	−	0.104835i	0.588035	+	0.808836i	$0.299902\pi$
$108$	−0.424653	−	0.245174i	−0.0408623	−	0.0235918i
$109$	3.89908	−	6.75341i	0.373465	−	0.646860i	−0.616631	−	0.787252i	$-0.711503\pi$
$109$	3.89908	−	6.75341i	0.373465	−	0.646860i	0.990096	+	0.140392i	$0.0448364\pi$
$110$		0			0
$111$	4.43805			0.421241
$112$	6.24012	+	3.88787i	0.589636	+	0.367369i
$113$			15.4918i			1.45734i	0.684864	+	0.728671i	$0.259861\pi$
$113$			15.4918i			1.45734i	−0.684864	+	0.728671i	$0.740139\pi$
$114$	−3.03957	−	5.26469i	−0.284682	−	0.493084i
$115$		0			0
$116$	0.980695	−	1.69861i	0.0910552	−	0.157712i
$117$	5.41745	−	3.12776i	0.500843	−	0.289162i
$118$			0.288517i			0.0265602i
$119$	−16.6285	−	0.558802i	−1.52433	−	0.0512253i
$120$		0			0
$121$	−5.76167	−	9.97950i	−0.523788	−	0.907227i
$122$	−5.32034	−	3.07170i	−0.481681	−	0.278098i
$123$	1.13261	+	0.653911i	0.102124	+	0.0589612i
$124$	−0.406789	−	0.704580i	−0.0365308	−	0.0632731i
$125$		0			0
$126$	−3.24895	−	0.109181i	−0.289439	−	0.00972664i
$127$		−	11.7996i		−	1.04704i	−0.852013	−	0.523521i	$-0.824618\pi$
$127$		−	11.7996i		−	1.04704i	0.852013	−	0.523521i	$-0.175382\pi$
$128$	4.76497	−	2.75105i	0.421167	−	0.243161i
$129$	−5.11811	+	8.86483i	−0.450625	+	0.780505i
$130$		0			0
$131$	1.98069	+	3.43066i	0.173054	+	0.299739i	0.939486	−	0.342587i	$-0.111303\pi$
$131$	1.98069	+	3.43066i	0.173054	+	0.299739i	−0.766432	+	0.642325i	$0.777970\pi$
$132$			2.32713i			0.202550i
$133$	11.1104	+	6.92226i	0.963393	+	0.600236i
$134$	−3.05984			−0.264330
$135$		0			0
$136$	−9.62092	+	16.6639i	−0.824987	+	1.42892i
$137$	−15.9976	−	9.23622i	−1.36677	−	0.789104i	−0.376254	−	0.926517i	$-0.622788\pi$
$137$	−15.9976	−	9.23622i	−1.36677	−	0.789104i	−0.990514	+	0.137413i	$0.956121\pi$
$138$	−5.29980	+	3.05984i	−0.451149	+	0.260471i
$139$	−2.66059			−0.225669			−0.112834	−	0.993614i	$-0.535993\pi$
$139$	−2.66059			−0.225669			−0.112834	+	0.993614i	$0.535993\pi$
$140$		0			0
$141$	−3.76518			−0.317085
$142$	−6.45461	+	3.72657i	−0.541659	+	0.312727i
$143$	−25.7105	−	14.8440i	−2.15002	−	1.24132i
$144$	−1.38943	+	2.40657i	−0.115786	+	0.200547i
$145$		0			0
$146$	−15.3484			−1.27024
$147$	6.28347	−	3.08512i	0.518252	−	0.254457i
$148$			2.17619i			0.178882i
$149$	7.29379	+	12.6332i	0.597531	+	1.03495i	0.993184	+	0.116554i	$0.0371848\pi$
$149$	7.29379	+	12.6332i	0.597531	+	1.03495i	−0.395653	+	0.918400i	$0.629482\pi$
$150$		0			0
$151$	7.12847	−	12.3469i	0.580106	−	1.00477i	−0.415360	−	0.909657i	$-0.636344\pi$
$151$	7.12847	−	12.3469i	0.580106	−	1.00477i	0.995466	−	0.0951165i	$-0.0303224\pi$
$152$	13.1109	−	7.56959i	1.06344	−	0.613975i
$153$		−	6.28852i		−	0.508396i
$154$	7.26081	+	13.6124i	0.585092	+	1.09692i
$155$		0			0
$156$	1.53369	+	2.65643i	0.122794	+	0.212685i
$157$	−10.4792	−	6.05019i	−0.836333	−	0.482857i	0.0196828	−	0.999806i	$-0.493734\pi$
$157$	−10.4792	−	6.05019i	−0.836333	−	0.482857i	−0.856016	+	0.516949i	$0.827068\pi$
$158$	0.884409	+	0.510614i	0.0703598	+	0.0406223i
$159$	−3.60162	−	6.23818i	−0.285627	−	0.494720i
$160$		0			0
$161$	6.96842	−	11.1845i	0.549188	−	0.881460i
$162$		−	1.22868i		−	0.0965342i
$163$	−5.82538	+	3.36329i	−0.456279	+	0.263433i	−0.710478	−	0.703719i	$-0.751521\pi$
$163$	−5.82538	+	3.36329i	−0.456279	+	0.263433i	0.254199	+	0.967152i	$0.418188\pi$
$164$	−0.320644	+	0.555371i	−0.0250381	+	0.0433672i
$165$		0			0
$166$	0.706205	+	1.22318i	0.0548122	+	0.0949375i
$167$		−	0.916442i		−	0.0709164i	−0.999371	−	0.0354582i	$-0.988711\pi$
$167$		−	0.916442i		−	0.0709164i	0.999371	−	0.0354582i	$-0.0112891\pi$
$168$	0.271899	−	8.09100i	0.0209775	−	0.624234i
$169$	−26.1316			−2.01013
$170$		0			0
$171$	−2.47385	+	4.28484i	−0.189180	+	0.327670i
$172$	−4.34685	−	2.50965i	−0.331444	−	0.191359i
$173$	6.48805	−	3.74588i	0.493277	−	0.284794i	−0.232656	−	0.972559i	$-0.574742\pi$
$173$	6.48805	−	3.74588i	0.493277	−	0.284794i	0.725933	+	0.687765i	$0.241408\pi$
$174$	4.91472			0.372584
$175$		0			0
$176$	13.1881			0.994094
$177$	0.203359	−	0.117410i	0.0152854	−	0.00882504i
$178$	−2.43514	−	1.40593i	−0.182521	−	0.105379i
$179$	7.43805	−	12.8831i	0.555946	−	0.962927i	−0.441883	−	0.897073i	$-0.645689\pi$
$179$	7.43805	−	12.8831i	0.555946	−	0.962927i	0.997829	−	0.0658544i	$-0.0209773\pi$
$180$		0			0
$181$	−6.62760			−0.492626			−0.246313	−	0.969190i	$-0.579219\pi$
$181$	−6.62760			−0.492626			−0.246313	+	0.969190i	$0.579219\pi$
$182$	17.2595	+	10.7534i	1.27936	+	0.797096i
$183$			5.00000i			0.369611i
$184$	−7.62006	−	13.1983i	−0.561758	−	0.972994i
$185$		0			0
$186$	1.01931	−	1.76549i	0.0747391	−	0.129452i
$187$	−25.8461	+	14.9223i	−1.89006	+	1.09122i
$188$		−	1.84625i		−	0.134651i
$189$	1.24517	+	2.33443i	0.0905731	+	0.169804i
$190$		0			0
$191$	11.6285	+	20.1411i	0.841406	+	1.45736i	0.888706	+	0.458478i	$0.151605\pi$
$191$	11.6285	+	20.1411i	0.841406	+	1.45736i	−0.0472996	+	0.998881i	$0.515062\pi$
$192$	−7.69180	−	4.44086i	−0.555108	−	0.320492i
$193$	6.23697	+	3.60092i	0.448947	+	0.259200i	0.707385	−	0.706828i	$-0.249875\pi$
$193$	6.23697	+	3.60092i	0.448947	+	0.259200i	−0.258439	+	0.966028i	$0.583208\pi$
$194$	−0.292833	−	0.507202i	−0.0210242	−	0.0364150i
$195$		0			0
$196$	1.51278	+	3.08108i	0.108056	+	0.220077i
$197$			19.0881i			1.35997i	0.733226	+	0.679985i	$0.238014\pi$
$197$			19.0881i			1.35997i	−0.733226	+	0.679985i	$0.761986\pi$
$198$	−5.04993	+	2.91558i	−0.358883	+	0.207201i
$199$	10.4170	−	18.0427i	0.738440	−	1.27902i	−0.214757	−	0.976668i	$-0.568896\pi$
$199$	10.4170	−	18.0427i	0.738440	−	1.27902i	0.953197	−	0.302349i	$-0.0977707\pi$
$200$		0			0
$201$	1.24517	+	2.15670i	0.0878278	+	0.152122i
$202$		−	10.1839i		−	0.716539i
$203$	−9.33770	+	4.98069i	−0.655378	+	0.349576i
$204$	3.08356			0.215892
$205$		0			0
$206$	8.76614	−	15.1834i	0.610766	−	1.05788i
$207$	4.31341	+	2.49035i	0.299803	+	0.173091i
$208$	15.0544	−	8.69163i	1.04383	−	0.602656i
$209$	23.4812			1.62423
$210$		0			0
$211$	15.5876			1.07309			0.536547	−	0.843870i	$-0.319728\pi$
$211$	15.5876			1.07309			0.536547	+	0.843870i	$0.319728\pi$
$212$	3.05888	−	1.76604i	0.210085	−	0.121292i
$213$	5.25329	+	3.03299i	0.359950	+	0.207817i
$214$	−1.33241	+	2.30779i	−0.0910813	+	0.157757i
$215$		0			0
$216$	3.05984			0.208196
$217$	−0.147437	+	4.38732i	−0.0100087	+	0.297831i
$218$			9.58145i			0.648938i
$219$	6.24588	+	10.8182i	0.422057	+	0.731024i
$220$		0			0
$221$	−19.6690	+	34.0677i	−1.32308	+	2.29164i
$222$	−4.72239	+	2.72647i	−0.316946	+	0.182989i
$223$		−	3.57250i		−	0.239232i	−0.992820	−	0.119616i	$-0.961834\pi$
$223$		−	3.57250i		−	0.239232i	0.992820	−	0.119616i	$-0.0381664\pi$
$224$	7.15363	+	0.240399i	0.477972	+	0.0160623i
$225$		0			0
$226$	−9.51720	−	16.4843i	−0.633074	−	1.09652i
$227$	13.3591	+	7.71289i	0.886675	+	0.511922i	0.872854	−	0.487982i	$-0.162267\pi$
$227$	13.3591	+	7.71289i	0.886675	+	0.511922i	0.0138218	+	0.999904i	$0.495600\pi$
$228$	−2.10106	−	1.21305i	−0.139146	−	0.0803360i
$229$	7.66427	+	13.2749i	0.506469	+	0.877230i	0.999972	+	0.00748587i	$0.00238285\pi$
$229$	7.66427	+	13.2749i	0.506469	+	0.877230i	−0.493503	+	0.869744i	$0.664284\pi$
$230$		0			0
$231$	6.63988	−	10.6572i	0.436872	−	0.701190i
$232$			12.2394i			0.803553i
$233$	17.5704	−	10.1443i	1.15107	−	0.664572i	0.201925	−	0.979401i	$-0.435280\pi$
$233$	17.5704	−	10.1443i	1.15107	−	0.664572i	0.949149	+	0.314829i	$0.101947\pi$
$234$	−3.84302	+	6.65630i	−0.251226	+	0.435136i
$235$		0			0
$236$	0.0575715	+	0.0997167i	0.00374758	+	0.00649100i
$237$		−	0.831159i		−	0.0539896i
$238$	18.0371	−	9.62092i	1.16917	−	0.623632i
$239$	11.8954			0.769450			0.384725	−	0.923031i	$-0.374296\pi$
$239$	11.8954			0.769450			0.384725	+	0.923031i	$0.374296\pi$
$240$		0			0
$241$	−8.74236	+	15.1422i	−0.563145	+	0.975396i	0.434074	+	0.900877i	$0.357075\pi$
$241$	−8.74236	+	15.1422i	−0.563145	+	0.975396i	−0.997220	+	0.0745189i	$0.976258\pi$
$242$	12.2616	+	7.07924i	0.788206	+	0.455071i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−2.45174			−0.156956
$245$		0			0
$246$	−1.60689			−0.102452
$247$	26.8039	−	15.4753i	1.70549	−	0.984667i
$248$	4.39668	+	2.53842i	0.279189	+	0.161190i
$249$	0.574768	−	0.995527i	0.0364244	−	0.0630890i
$250$		0			0
$251$	−10.2348			−0.646016			−0.323008	−	0.946396i	$-0.604694\pi$
$251$	−10.2348			−0.646016			−0.323008	+	0.946396i	$0.604694\pi$
$252$	−1.14468	+	0.610568i	−0.0721080	+	0.0384621i
$253$		−	23.6378i		−	1.48609i
$254$	7.24895	+	12.5555i	0.454839	+	0.787805i
$255$		0			0
$256$	5.50156	−	9.52899i	0.343848	−	0.595562i
$257$	−19.3596	+	11.1772i	−1.20762	+	0.697218i	−0.962238	−	0.272210i	$-0.912246\pi$
$257$	−19.3596	+	11.1772i	−1.20762	+	0.697218i	−0.245378	+	0.969427i	$0.578912\pi$
$258$		−	12.5770i		−	0.783012i
$259$	6.20921	−	9.96594i	0.385822	−	0.619253i
$260$		0			0
$261$	−2.00000	−	3.46410i	−0.123797	−	0.214423i
$262$	−4.21519	−	2.43364i	−0.260415	−	0.150351i
$263$	21.4862	+	12.4051i	1.32490	+	0.764929i	0.984505	−	0.175355i	$-0.0561073\pi$
$263$	21.4862	+	12.4051i	1.32490	+	0.764929i	0.340391	+	0.940284i	$0.389441\pi$
$264$	−7.26081	−	12.5761i	−0.446872	−	0.774004i
$265$		0			0
$266$	−16.0748	−	0.540197i	−0.985611	−	0.0331216i
$267$			2.28852i			0.140055i
$268$	−1.05753	+	0.610568i	−0.0645992	+	0.0372964i
$269$	8.89013	−	15.3982i	0.542041	−	0.938843i	−0.456746	−	0.889597i	$-0.650985\pi$
$269$	8.89013	−	15.3982i	0.542041	−	0.938843i	0.998787	−	0.0492453i	$-0.0156816\pi$
$270$		0			0
$271$	−8.56949	−	14.8428i	−0.520559	−	0.901635i	−0.999714	−	0.0239050i	$-0.992390\pi$
$271$	−8.56949	−	14.8428i	−0.520559	−	0.901635i	0.479155	−	0.877730i	$-0.340943\pi$
$272$		−	17.4749i		−	1.05957i
$273$	0.555871	−	16.5412i	0.0336428	−	1.00112i
$274$	22.6967			1.37116
$275$		0			0
$276$	−1.22114	+	2.11507i	−0.0735037	+	0.127312i
$277$	2.49714	+	1.44173i	0.150039	+	0.0866250i	0.573140	−	0.819458i	$-0.305725\pi$
$277$	2.49714	+	1.44173i	0.150039	+	0.0866250i	−0.423101	+	0.906082i	$0.639058\pi$
$278$	2.83105	−	1.63451i	0.169795	−	0.0980312i
$279$	−1.65919			−0.0993330
$280$		0			0
$281$	27.7803			1.65723			0.828616	−	0.559817i	$-0.189129\pi$
$281$	27.7803			1.65723			0.828616	+	0.559817i	$0.189129\pi$
$282$	4.00641	−	2.31310i	0.238578	−	0.137743i
$283$	−7.53644	−	4.35117i	−0.447995	−	0.258650i	0.258988	−	0.965881i	$-0.416611\pi$
$283$	−7.53644	−	4.35117i	−0.447995	−	0.258650i	−0.706983	+	0.707231i	$0.749944\pi$
$284$	−1.48722	+	2.57594i	−0.0882502	+	0.152854i
$285$		0			0
$286$	36.4770			2.15693
$287$	3.05301	−	1.62847i	0.180214	−	0.0961253i
$288$			2.70534i			0.159414i
$289$	11.2727	+	19.5249i	0.663101	+	1.14853i
$290$		0			0
$291$	−0.238332	+	0.412803i	−0.0139713	+	0.0241989i
$292$	−5.30466	+	3.06265i	−0.310432	+	0.179228i
$293$			19.8954i			1.16230i	0.813796	+	0.581151i	$0.197398\pi$
$293$			19.8954i			1.16230i	−0.813796	+	0.581151i	$0.802602\pi$
$294$	−4.79072	+	7.14296i	−0.279401	+	0.416586i
$295$		0			0
$296$	−6.78986	−	11.7604i	−0.394653	−	0.683559i
$297$	4.11005	+	2.37294i	0.238489	+	0.137692i
$298$	−15.5222	−	8.96173i	−0.899176	−	0.519139i
$299$	−15.5784	−	26.9826i	−0.900924	−	1.56045i
$300$		0			0
$301$	12.7459	+	23.8957i	0.734660	+	1.37733i
$302$			17.5172i			1.00800i
$303$	−7.17807	+	4.14426i	−0.412369	+	0.238081i
$304$	−6.87450	+	11.9070i	−0.394280	+	0.682913i
$305$		0			0
$306$	3.86329	+	6.69141i	0.220849	+	0.382522i
$307$			5.32151i			0.303714i	0.988402	+	0.151857i	$0.0485254\pi$
$307$			5.32151i			0.303714i	−0.988402	+	0.151857i	$0.951475\pi$
$308$	5.22572	+	3.25585i	0.297763	+	0.185519i
$309$	−14.2692			−0.811747
$310$		0			0
$311$	−0.947706	+	1.64147i	−0.0537395	+	0.0930795i	−0.891644	−	0.452738i	$-0.850447\pi$
$311$	−0.947706	+	1.64147i	−0.0537395	+	0.0930795i	0.837904	+	0.545817i	$0.183781\pi$
$312$	−16.5765	−	9.57045i	−0.938460	−	0.541820i
$313$	−22.9696	+	13.2615i	−1.29832	+	0.749585i	−0.980114	−	0.198437i	$-0.936413\pi$
$313$	−22.9696	+	13.2615i	−1.29832	+	0.749585i	−0.318205	+	0.948022i	$0.603080\pi$
$314$	14.8675			0.839020
$315$		0			0
$316$	0.407557			0.0229268
$317$	−13.5305	+	7.81185i	−0.759950	+	0.438757i	−0.829278	−	0.558837i	$-0.811248\pi$
$317$	−13.5305	+	7.81185i	−0.759950	+	0.438757i	0.0693277	+	0.997594i	$0.477915\pi$
$318$	7.66473	+	4.42523i	0.429817	+	0.248155i
$319$	−9.49175	+	16.4402i	−0.531436	+	0.920474i
$320$		0			0
$321$	2.16884			0.121053
$322$	−0.543799	+	16.1820i	−0.0303047	+	0.901788i
$323$		−	31.1137i		−	1.73121i
$324$	−0.245174	−	0.424653i	−0.0136208	−	0.0235918i
$325$		0			0
$326$	4.13240	−	7.15752i	0.228872	−	0.396419i
$327$	6.75341	−	3.89908i	0.373465	−	0.215620i
$328$		−	4.00173i		−	0.220958i
$329$	−5.26781	+	8.45496i	−0.290424	+	0.466137i
$330$		0			0
$331$	2.01493	+	3.48996i	0.110751	+	0.191826i	0.916073	−	0.401011i	$-0.131341\pi$
$331$	2.01493	+	3.48996i	0.110751	+	0.191826i	−0.805323	+	0.592837i	$0.798008\pi$
$332$	0.488154	+	0.281836i	0.0267909	+	0.0154678i
$333$	3.84347	+	2.21903i	0.210621	+	0.121602i
$334$	0.563007	+	0.975156i	0.0308064	+	0.0533582i
$335$		0			0
$336$	3.46017	+	6.48705i	0.188768	+	0.353898i
$337$		−	2.86415i		−	0.156020i	−0.996953	−	0.0780100i	$-0.975143\pi$
$337$		−	2.86415i		−	0.156020i	0.996953	−	0.0780100i	$-0.0248566\pi$
$338$	27.8058	−	16.0537i	1.51244	−	0.873206i
$339$	−7.74588	+	13.4163i	−0.420698	+	0.728671i
$340$		0			0
$341$	3.93715	+	6.81935i	0.213209	+	0.369288i
$342$		−	6.07914i		−	0.328722i
$343$	1.86327	−	18.4263i	0.100607	−	0.994926i
$344$	31.3212			1.68873
$345$		0			0
$346$	−4.60248	+	7.97173i	−0.247431	+	0.428563i
$347$	2.17613	+	1.25639i	0.116821	+	0.0674466i	0.557272	−	0.830330i	$-0.311848\pi$
$347$	2.17613	+	1.25639i	0.116821	+	0.0674466i	−0.440451	+	0.897777i	$0.645181\pi$
$348$	1.69861	−	0.980695i	0.0910552	−	0.0525708i
$349$	−12.6307			−0.676108			−0.338054	−	0.941127i	$-0.609769\pi$
$349$	−12.6307			−0.676108			−0.338054	+	0.941127i	$0.609769\pi$
$350$		0			0
$351$	6.25553			0.333895
$352$	11.1191	−	6.41961i	0.592650	−	0.342166i
$353$	−19.5614	−	11.2938i	−1.04115	−	0.601108i	−0.120991	−	0.992654i	$-0.538607\pi$
$353$	−19.5614	−	11.2938i	−1.04115	−	0.601108i	−0.920159	+	0.391546i	$0.871941\pi$
$354$	−0.144259	+	0.249863i	−0.00766726	+	0.0132801i
$355$		0			0
$356$	−1.12217			−0.0594748
$357$	−14.1213	−	8.79817i	−0.747377	−	0.465649i
$358$			18.2780i			0.966020i
$359$	−0.171108	−	0.296367i	−0.00903072	−	0.0156417i	0.861475	−	0.507800i	$-0.169541\pi$
$359$	−0.171108	−	0.296367i	−0.00903072	−	0.0156417i	−0.870505	+	0.492159i	$0.836208\pi$
$360$		0			0
$361$	−2.73990	+	4.74564i	−0.144205	+	0.249771i
$362$	7.05222	−	4.07160i	0.370656	−	0.213999i
$363$		−	11.5233i		−	0.604818i
$364$	8.11095	+	0.272570i	0.425129	+	0.0142865i
$365$		0			0
$366$	−3.07170	−	5.32034i	−0.160560	−	0.278098i
$367$	2.83244	+	1.63531i	0.147852	+	0.0853624i	0.572101	−	0.820183i	$-0.306129\pi$
$367$	2.83244	+	1.63531i	0.147852	+	0.0853624i	−0.424249	+	0.905546i	$0.639462\pi$
$368$	11.9864	+	6.92034i	0.624833	+	0.360748i
$369$	0.653911	+	1.13261i	0.0340413	+	0.0589612i
$370$		0			0
$371$	−19.0472	−	0.640084i	−0.988882	−	0.0332315i
$372$		−	0.813579i		−	0.0421821i
$373$	11.5665	−	6.67795i	0.598893	−	0.345771i	−0.169713	−	0.985494i	$-0.554284\pi$
$373$	11.5665	−	6.67795i	0.598893	−	0.345771i	0.768606	+	0.639722i	$0.220951\pi$
$374$	18.3347	−	31.7566i	0.948063	−	1.64209i
$375$		0			0
$376$	5.76042	+	9.97734i	0.297071	+	0.514542i
$377$			25.0221i			1.28870i
$378$	−2.75908	−	1.71903i	−0.141912	−	0.0884172i
$379$	−28.8968			−1.48433			−0.742165	−	0.670217i	$-0.766201\pi$
$379$	−28.8968			−1.48433			−0.742165	+	0.670217i	$0.766201\pi$
$380$		0			0
$381$	5.89979	−	10.2187i	0.302255	−	0.523521i
$382$	−24.7469	−	14.2877i	−1.26616	−	0.731020i
$383$	−17.9704	+	10.3752i	−0.918244	+	0.530148i	−0.883074	−	0.469233i	$-0.844530\pi$
$383$	−17.9704	+	10.3752i	−0.918244	+	0.530148i	−0.0351693	+	0.999381i	$0.511197\pi$
$384$	5.50211			0.280778
$385$		0			0
$386$	−8.84874			−0.450389
$387$	−8.86483	+	5.11811i	−0.450625	+	0.260168i
$388$	−0.202417	−	0.116865i	−0.0102762	−	0.00593294i
$389$	4.13057	−	7.15437i	0.209428	−	0.362741i	−0.742106	−	0.670282i	$-0.766173\pi$
$389$	4.13057	−	7.15437i	0.209428	−	0.362741i	0.951535	+	0.307542i	$0.0995063\pi$
$390$		0			0
$391$	−31.3212			−1.58398
$392$	−17.7885	−	11.9306i	−0.898453	−	0.602585i
$393$			3.96139i			0.199826i
$394$	−11.7266	−	20.3110i	−0.590776	−	1.02325i
$395$		0			0
$396$	−1.16356	+	2.01535i	−0.0584713	+	0.101275i
$397$	21.5926	−	12.4665i	1.08370	−	0.625674i	0.151807	−	0.988410i	$-0.451491\pi$
$397$	21.5926	−	12.4665i	1.08370	−	0.625674i	0.931892	+	0.362736i	$0.118157\pi$
$398$			25.5983i			1.28312i
$399$	6.16075	+	11.5501i	0.308423	+	0.578226i
$400$		0			0
$401$	3.63461	+	6.29532i	0.181504	+	0.314373i	0.942393	−	0.334508i	$-0.108570\pi$
$401$	3.63461	+	6.29532i	0.181504	+	0.314373i	−0.760889	+	0.648882i	$0.775237\pi$
$402$	−2.64990	−	1.52992i	−0.132165	−	0.0763054i
$403$	8.98857	+	5.18955i	0.447752	+	0.258510i
$404$	−2.03213	−	3.51975i	−0.101102	−	0.175114i
$405$		0			0
$406$	6.87611	−	11.0363i	0.341255	−	0.547723i
$407$		−	21.0624i		−	1.04403i
$408$	−16.6639	+	9.62092i	−0.824987	+	0.476307i
$409$	−17.7048	+	30.6656i	−0.875446	+	1.51632i	−0.0191590	+	0.999816i	$0.506099\pi$
$409$	−17.7048	+	30.6656i	−0.875446	+	1.51632i	−0.856287	+	0.516500i	$0.827234\pi$
$410$		0			0
$411$	−9.23622	−	15.9976i	−0.455589	−	0.789104i
$412$		−	6.99687i		−	0.344711i
$413$	0.0208662	−	0.620922i	0.00102676	−	0.0305536i
$414$	−6.11968			−0.300766
$415$		0			0
$416$	8.46167	−	14.6561i	0.414868	−	0.718572i
$417$	−2.30414	−	1.33030i	−0.112834	−	0.0651449i
$418$	−24.9856	+	14.4254i	−1.22208	+	0.705571i
$419$	−38.1119			−1.86189			−0.930945	−	0.365160i	$-0.881014\pi$
$419$	−38.1119			−1.86189			−0.930945	+	0.365160i	$0.881014\pi$
$420$		0			0
$421$	12.5454			0.611428			0.305714	−	0.952123i	$-0.401105\pi$
$421$	12.5454			0.611428			0.305714	+	0.952123i	$0.401105\pi$
$422$	−16.5862	+	9.57607i	−0.807406	+	0.466156i
$423$	−3.26074	−	1.88259i	−0.158543	−	0.0915347i
$424$	−11.0204	+	19.0878i	−0.535196	+	0.926987i
$425$		0			0
$426$	−7.45314			−0.361106
$427$	11.2278	+	6.99542i	0.543352	+	0.338532i
$428$			1.06349i			0.0514055i
$429$	−14.8440	−	25.7105i	−0.716674	−	1.24132i
$430$		0			0
$431$	4.25553	−	7.37079i	0.204982	−	0.355039i	−0.745145	−	0.666902i	$-0.767620\pi$
$431$	4.25553	−	7.37079i	0.204982	−	0.355039i	0.950127	+	0.311864i	$0.100953\pi$
$432$	−2.40657	+	1.38943i	−0.115786	+	0.0668491i
$433$		−	20.8010i		−	0.999631i	−0.866132	−	0.499816i	$-0.833401\pi$
$433$		−	20.8010i		−	0.999631i	0.866132	−	0.499816i	$-0.166599\pi$
$434$	−2.53842	−	4.75898i	−0.121848	−	0.228439i
$435$		0			0
$436$	1.91191	+	3.31152i	0.0915637	+	0.158593i
$437$	21.3415	+	12.3215i	1.02090	+	0.589418i
$438$	−13.2921	−	7.67418i	−0.635119	−	0.366686i
$439$	5.47542	+	9.48370i	0.261327	+	0.452632i	0.966595	−	0.256309i	$-0.0825064\pi$
$439$	5.47542	+	9.48370i	0.261327	+	0.452632i	−0.705267	+	0.708941i	$0.749173\pi$
$440$		0			0
$441$	6.98421	+	0.469941i	0.332581	+	0.0223782i
$442$		−	48.3338i		−	2.29900i
$443$	−33.3874	+	19.2762i	−1.58628	+	0.915842i	−0.592372	+	0.805664i	$0.701809\pi$
$443$	−33.3874	+	19.2762i	−1.58628	+	0.915842i	−0.993912	+	0.110177i	$0.964858\pi$
$444$	−1.08809	+	1.88463i	−0.0516387	+	0.0894408i
$445$		0			0
$446$	2.19473	+	3.80138i	0.103923	+	0.180001i
$447$			14.5876i			0.689969i
$448$	−20.7337	+	11.0593i	−0.979577	+	0.522503i
$449$	21.8462			1.03099			0.515494	−	0.856893i	$-0.327608\pi$
$449$	21.8462			1.03099			0.515494	+	0.856893i	$0.327608\pi$
$450$		0			0
$451$	3.10338	−	5.37521i	0.146133	−	0.253109i
$452$	−6.57862	−	3.79817i	−0.309432	−	0.178651i
$453$	12.3469	−	7.12847i	0.580106	−	0.334925i
$454$	−18.9533			−0.889524
$455$		0			0
$456$	15.1392			0.708957
$457$	3.19603	−	1.84523i	0.149504	−	0.0863160i	−0.423382	−	0.905951i	$-0.639157\pi$
$457$	3.19603	−	1.84523i	0.149504	−	0.0863160i	0.572886	+	0.819635i	$0.305824\pi$
$458$	−16.3106	−	9.41692i	−0.762144	−	0.440024i
$459$	3.14426	−	5.44602i	0.146761	−	0.254198i
$460$		0			0
$461$	−30.9449			−1.44125			−0.720624	−	0.693326i	$-0.756144\pi$
$461$	−30.9449			−1.44125			−0.720624	+	0.693326i	$0.756144\pi$
$462$	−0.518161	+	15.4191i	−0.0241070	+	0.717361i
$463$			4.97717i			0.231309i	0.993290	+	0.115654i	$0.0368965\pi$
$463$			4.97717i			0.231309i	−0.993290	+	0.115654i	$0.963104\pi$
$464$	−5.55773	−	9.62627i	−0.258011	−	0.446888i
$465$		0			0
$466$	−12.4640	+	21.5884i	−0.577385	+	1.00006i
$467$	6.08133	−	3.51106i	0.281410	−	0.162472i	−0.352651	−	0.935755i	$-0.614720\pi$
$467$	6.08133	−	3.51106i	0.281410	−	0.162472i	0.634062	+	0.773282i	$0.281387\pi$
$468$			3.06738i			0.141790i
$469$	6.58512	+	0.221294i	0.304073	+	0.0102184i
$470$		0			0
$471$	−6.05019	−	10.4792i	−0.278778	−	0.482857i
$472$	−0.622246	−	0.359254i	−0.0286412	−	0.0165360i
$473$	42.0714	+	24.2899i	1.93444	+	1.11685i
$474$	0.510614	+	0.884409i	0.0234533	+	0.0406223i
$475$		0			0
$476$	4.31416	−	6.92433i	0.197739	−	0.317376i
$477$		−	7.20323i		−	0.329813i
$478$	−12.6575	+	7.30782i	−0.578941	+	0.334252i
$479$	−4.61478	+	7.99304i	−0.210855	+	0.365211i	−0.951982	−	0.306153i	$-0.900958\pi$
$479$	−4.61478	+	7.99304i	−0.210855	+	0.365211i	0.741127	+	0.671364i	$0.234291\pi$
$480$		0			0
$481$	−13.8812	−	24.0429i	−0.632928	−	1.09626i
$482$		−	21.4831i		−	0.978529i
$483$	11.6271	−	6.20183i	0.529050	−	0.282193i
$484$	5.65044			0.256838
$485$		0			0
$486$	0.614340	−	1.06407i	0.0278670	−	0.0482671i
$487$	11.9198	+	6.88189i	0.540137	+	0.311848i	0.745134	−	0.666914i	$-0.232385\pi$
$487$	11.9198	+	6.88189i	0.540137	+	0.311848i	−0.204998	+	0.978762i	$0.565719\pi$
$488$	13.2495	−	7.64960i	0.599776	−	0.346281i
$489$	−6.72657			−0.304186
$490$		0			0
$491$	−31.0495			−1.40124			−0.700622	−	0.713533i	$-0.747094\pi$
$491$	−31.0495			−1.40124			−0.700622	+	0.713533i	$0.747094\pi$
$492$	−0.555371	+	0.320644i	−0.0250381	+	0.0144557i
$493$	21.7841	+	12.5770i	0.981105	+	0.566441i
$494$	−19.0141	+	32.9334i	−0.855486	+	1.48175i
$495$		0			0
$496$	−4.61066			−0.207025
$497$	14.1606	−	7.55320i	0.635189	−	0.338807i
$498$			1.41241i			0.0632916i
$499$	−10.7954	−	18.6981i	−0.483267	−	0.837042i	0.516549	−	0.856258i	$-0.327217\pi$
$499$	−10.7954	−	18.6981i	−0.483267	−	0.837042i	−0.999815	+	0.0192154i	$0.993883\pi$
$500$		0			0
$501$	0.458221	−	0.793662i	0.0204718	−	0.0354582i
$502$	10.8905	−	6.28765i	0.486068	−	0.280632i
$503$			33.2826i			1.48400i	0.670402	+	0.741998i	$0.266122\pi$
$503$			33.2826i			1.48400i	−0.670402	+	0.741998i	$0.733878\pi$
$504$	4.28097	−	6.87106i	0.190690	−	0.306062i
$505$		0			0
$506$	14.5216	+	25.1522i	0.645564	+	1.11815i
$507$	−22.6307	−	13.0658i	−1.00506	−	0.580273i
$508$	5.01073	+	2.89295i	0.222315	+	0.128354i
$509$	9.61002	+	16.6450i	0.425957	+	0.737779i	0.996509	−	0.0834823i	$-0.0266042\pi$
$509$	9.61002	+	16.6450i	0.425957	+	0.737779i	−0.570552	+	0.821261i	$0.693271\pi$
$510$		0			0
$511$	33.0314	+	1.11003i	1.46122	+	0.0491047i
$512$			24.5235i			1.08380i
$513$	−4.28484	+	2.47385i	−0.189180	+	0.109223i
$514$	13.7333	−	23.7867i	0.605748	−	1.04919i
$515$		0			0
$516$	−2.50965	−	4.34685i	−0.110481	−	0.191359i
$517$			17.8691i			0.785881i
$518$	−0.484552	+	14.4190i	−0.0212900	+	0.633534i
$519$	7.49175			0.328851
$520$		0			0
$521$	−0.241845	+	0.418887i	−0.0105954	+	0.0183518i	−0.871274	−	0.490796i	$-0.836706\pi$
$521$	−0.241845	+	0.418887i	−0.0105954	+	0.0183518i	0.860679	+	0.509148i	$0.170039\pi$
$522$	4.25627	+	2.45736i	0.186292	+	0.107556i
$523$	−5.46760	+	3.15672i	−0.239082	+	0.138034i	−0.614755	−	0.788718i	$-0.710745\pi$
$523$	−5.46760	+	3.15672i	−0.239082	+	0.138034i	0.375673	+	0.926752i	$0.377412\pi$
$524$	−1.94246			−0.0848566
$525$		0			0
$526$	−30.4837			−1.32915
$527$	9.03597	−	5.21692i	0.393613	−	0.227253i
$528$	11.4213	+	6.59407i	0.497047	+	0.286970i
$529$	0.903660	−	1.56519i	0.0392896	−	0.0680515i
$530$		0			0
$531$	0.234819			0.0101903
$532$	−5.66354	+	3.02091i	−0.245545	+	0.130973i
$533$		−	8.18112i		−	0.354364i
$534$	−1.40593	−	2.43514i	−0.0608404	−	0.105379i
$535$		0			0
$536$	3.81003	−	6.59917i	0.164568	−	0.285041i
$537$	12.8831	−	7.43805i	0.555946	−	0.320976i
$538$			21.8462i			0.941859i
$539$	−14.6416	−	29.8206i	−0.630659	−	1.28446i
$540$		0			0
$541$	−8.02177	−	13.8941i	−0.344883	−	0.597355i	0.640450	−	0.768000i	$-0.278748\pi$
$541$	−8.02177	−	13.8941i	−0.344883	−	0.597355i	−0.985332	+	0.170646i	$0.945415\pi$
$542$	18.2370	+	10.5292i	0.783348	+	0.452266i
$543$	−5.73967	−	3.31380i	−0.246313	−	0.142209i
$544$	−8.50630	−	14.7333i	−0.364705	−	0.631687i
$545$		0			0
$546$	9.57045	+	17.9425i	0.409578	+	0.767867i
$547$			27.2078i			1.16332i	0.813432	+	0.581660i	$0.197597\pi$
$547$			27.2078i			1.16332i	−0.813432	+	0.581660i	$0.802403\pi$
$548$	7.84439	−	4.52896i	0.335096	−	0.193467i
$549$	−2.50000	+	4.33013i	−0.106697	+	0.184805i
$550$		0			0
$551$	−9.89541	−	17.1394i	−0.421559	−	0.730161i
$552$		−	15.2401i		−	0.648663i
$553$	−1.86642	−	1.16286i	−0.0793683	−	0.0494499i
$554$	−3.54284			−0.150521
$555$		0			0
$556$	0.652307	−	1.12983i	0.0276640	−	0.0479154i
$557$	10.8015	+	6.23622i	0.457672	+	0.264237i	0.711065	−	0.703126i	$-0.248213\pi$
$557$	10.8015	+	6.23622i	0.457672	+	0.264237i	−0.253393	+	0.967364i	$0.581546\pi$
$558$	1.76549	−	1.01931i	0.0747391	−	0.0431506i
$559$	64.0330			2.70831
$560$		0			0
$561$	−29.8445			−1.26004
$562$	−29.5601	+	17.0665i	−1.24692	+	0.719908i
$563$	−13.7102	−	7.91558i	−0.577815	−	0.333602i	0.182449	−	0.983215i	$-0.441597\pi$
$563$	−13.7102	−	7.91558i	−0.577815	−	0.333602i	−0.760265	+	0.649613i	$0.774931\pi$
$564$	0.923123	−	1.59890i	0.0388705	−	0.0673257i
$565$		0			0
$566$	10.6924			0.449434
$567$	−0.0888607	+	2.64426i	−0.00373180	+	0.111048i
$568$		−	18.5609i		−	0.778798i
$569$	11.2832	+	19.5431i	0.473018	+	0.819291i	0.999523	−	0.0308807i	$-0.00983121\pi$
$569$	11.2832	+	19.5431i	0.473018	+	0.819291i	−0.526505	+	0.850172i	$0.676498\pi$
$570$		0			0
$571$	−5.65899	+	9.80166i	−0.236821	+	0.410187i	−0.959800	−	0.280683i	$-0.909439\pi$
$571$	−5.65899	+	9.80166i	−0.236821	+	0.410187i	0.722979	+	0.690870i	$0.242772\pi$
$572$	12.6071	−	7.27871i	0.527129	−	0.304338i
$573$			23.2569i			0.971572i
$574$	−2.24818	+	3.60839i	−0.0938373	+	0.150611i
$575$		0			0
$576$	−4.44086	−	7.69180i	−0.185036	−	0.320492i
$577$	21.4889	+	12.4066i	0.894595	+	0.516495i	0.875443	−	0.483322i	$-0.160570\pi$
$577$	21.4889	+	12.4066i	0.894595	+	0.516495i	0.0191524	+	0.999817i	$0.493903\pi$
$578$	−23.9899	−	13.8506i	−0.997847	−	0.576107i
$579$	3.60092	+	6.23697i	0.149649	+	0.259200i
$580$		0			0
$581$	−1.43137	−	2.68351i	−0.0593833	−	0.111331i
$582$		−	0.585667i		−	0.0242767i
$583$	−29.6056	+	17.0928i	−1.22614	+	0.707913i
$584$	19.1114	−	33.1019i	0.790834	−	1.36976i
$585$		0			0
$586$	−12.2225	−	21.1701i	−0.504908	−	0.874527i
$587$		−	3.96139i		−	0.163504i	−0.996653	−	0.0817520i	$-0.973948\pi$
$587$		−	3.96139i		−	0.163504i	0.996653	−	0.0817520i	$-0.0260516\pi$
$588$	−0.230435	+	3.42469i	−0.00950296	+	0.141232i
$589$	−8.20918			−0.338253
$590$		0			0
$591$	−9.54405	+	16.5308i	−0.392590	+	0.679985i
$592$	10.6805	+	6.16637i	0.438965	+	0.253436i
$593$	−5.28673	+	3.05229i	−0.217100	+	0.125343i	−0.604607	−	0.796524i	$-0.706670\pi$
$593$	−5.28673	+	3.05229i	−0.217100	+	0.125343i	0.387507	+	0.921867i	$0.373336\pi$
$594$	−5.83116			−0.239255
$595$		0			0
$596$	−7.15299			−0.292998
$597$	18.0427	−	10.4170i	0.738440	−	0.426339i
$598$	33.1530	+	19.1409i	1.35573	+	0.782730i
$599$	12.3922	−	21.4640i	0.506333	−	0.876995i	−0.493640	−	0.869666i	$-0.664334\pi$
$599$	12.3922	−	21.4640i	0.506333	−	0.876995i	0.999973	−	0.00732860i	$-0.00233279\pi$
$600$		0			0
$601$	43.9866			1.79425			0.897126	−	0.441775i	$-0.145651\pi$
$601$	43.9866			1.79425			0.897126	+	0.441775i	$0.145651\pi$
$602$	−28.2425	−	17.5963i	−1.15108	−	0.717173i
$603$			2.49035i			0.101415i
$604$	3.49542	+	6.05425i	0.142227	+	0.246344i
$605$		0			0
$606$	5.09196	−	8.81954i	0.206847	−	0.358269i
$607$	14.9829	−	8.65040i	0.608138	−	0.351109i	−0.164098	−	0.986444i	$-0.552471\pi$
$607$	14.9829	−	8.65040i	0.608138	−	0.351109i	0.772237	+	0.635335i	$0.219138\pi$
$608$			13.3852i			0.542843i
$609$	−10.5770	−	0.355443i	−0.428603	−	0.0144033i
$610$		0			0
$611$	11.7766	+	20.3977i	0.476430	+	0.825201i
$612$	2.67044	+	1.54178i	0.107946	+	0.0623227i
$613$	13.3363	+	7.69972i	0.538648	+	0.310989i	0.744531	−	0.667588i	$-0.232673\pi$
$613$	13.3363	+	7.69972i	0.538648	+	0.310989i	−0.205883	+	0.978577i	$0.566006\pi$
$614$	−3.26921	−	5.66244i	−0.131935	−	0.228518i
$615$		0			0
$616$	−38.3989	−	1.29040i	−1.54714	−	0.0519917i
$617$		−	8.70273i		−	0.350359i	−0.984537	−	0.175179i	$-0.943949\pi$
$617$		−	8.70273i		−	0.350359i	0.984537	−	0.175179i	$-0.0560505\pi$
$618$	15.1834	−	8.76614i	0.610766	−	0.352626i
$619$	−3.57547	+	6.19290i	−0.143710	+	0.248913i	−0.928891	−	0.370353i	$-0.879237\pi$
$619$	−3.57547	+	6.19290i	−0.143710	+	0.248913i	0.785181	+	0.619267i	$0.212570\pi$
$620$		0			0
$621$	2.49035	+	4.31341i	0.0999342	+	0.173091i
$622$		−	2.32885i		−	0.0933785i
$623$	5.13901	+	3.20183i	0.205890	+	0.128279i
$624$	17.3833			0.695888
$625$		0			0
$626$	16.2941	−	28.2223i	0.651245	−	1.12799i
$627$	20.3353	+	11.7406i	0.812114	+	0.468874i
$628$	5.13846	−	2.96669i	0.205047	−	0.118384i
$629$	−27.9088			−1.11280
$630$		0			0
$631$	−40.1797			−1.59953			−0.799765	−	0.600314i	$-0.795042\pi$
$631$	−40.1797			−1.59953			−0.799765	+	0.600314i	$0.795042\pi$
$632$	−2.20249	+	1.27161i	−0.0876102	+	0.0505818i
$633$	13.4992	+	7.79379i	0.536547	+	0.309776i
$634$	9.59826	−	16.6247i	0.381196	−	0.660250i
$635$		0			0
$636$	3.53209			0.140056
$637$	−36.3667	−	24.3908i	−1.44090	−	0.966400i
$638$		−	23.3246i		−	0.923431i
$639$	3.03299	+	5.25329i	0.119983	+	0.207817i
$640$		0			0
$641$	−10.5739	+	18.3145i	−0.417644	+	0.723381i	−0.995702	−	0.0926149i	$-0.970477\pi$
$641$	−10.5739	+	18.3145i	−0.417644	+	0.723381i	0.578058	+	0.815996i	$0.303811\pi$
$642$	−2.30779	+	1.33241i	−0.0910813	+	0.0525858i
$643$		−	29.4981i		−	1.16329i	−0.813442	−	0.581646i	$-0.802409\pi$
$643$		−	29.4981i		−	1.16329i	0.813442	−	0.581646i	$-0.197591\pi$
$644$	3.04105	+	5.70130i	0.119834	+	0.224663i
$645$		0			0
$646$	19.1144	+	33.1071i	0.752046	+	1.30258i
$647$	−24.5809	−	14.1918i	−0.966377	−	0.557938i	−0.0682470	−	0.997668i	$-0.521741\pi$
$647$	−24.5809	−	14.1918i	−0.966377	−	0.557938i	−0.898130	+	0.439731i	$0.855074\pi$
$648$	2.64990	+	1.52992i	0.104098	+	0.0601009i
$649$	−0.557211	−	0.965118i	−0.0218724	−	0.0378842i
$650$		0			0
$651$	−2.32135	+	3.72582i	−0.0909807	+	0.146026i
$652$		−	3.29836i		−	0.129174i
$653$	20.1517	−	11.6346i	0.788598	−	0.455297i	−0.0508707	−	0.998705i	$-0.516200\pi$
$653$	20.1517	−	11.6346i	0.788598	−	0.455297i	0.839469	+	0.543408i	$0.182866\pi$
$654$	−4.79072	+	8.29778i	−0.187332	+	0.324469i
$655$		0			0
$656$	1.81713	+	3.14736i	0.0709470	+	0.122884i
$657$			12.4918i			0.487350i
$658$	0.411087	−	12.2329i	0.0160259	−	0.476887i
$659$	−20.9852			−0.817468			−0.408734	−	0.912653i	$-0.634030\pi$
$659$	−20.9852			−0.817468			−0.408734	+	0.912653i	$0.634030\pi$
$660$		0			0
$661$	17.3580	−	30.0650i	0.675148	−	1.16939i	−0.301277	−	0.953537i	$-0.597413\pi$
$661$	17.3580	−	30.0650i	0.675148	−	1.16939i	0.976426	−	0.215855i	$-0.0692537\pi$
$662$	−4.28804	−	2.47570i	−0.166660	−	0.0962209i
$663$	−34.0677	+	19.6690i	−1.32308	+	0.763881i
$664$	−3.51739			−0.136501
$665$		0			0
$666$	−5.45294			−0.211297
$667$	−17.2536	+	9.96139i	−0.668063	+	0.385707i
$668$	0.389170	+	0.224687i	0.0150574	+	0.00869342i
$669$	1.78625	−	3.09388i	0.0690604	−	0.119616i
$670$		0			0
$671$	23.7294			0.916063
$672$	6.07502	+	3.78500i	0.234349	+	0.146010i
$673$		−	21.4998i		−	0.828757i	−0.910105	−	0.414378i	$-0.863999\pi$
$673$		−	21.4998i		−	0.828757i	0.910105	−	0.414378i	$-0.136001\pi$
$674$	1.75956	+	3.04765i	0.0677757	+	0.117391i
$675$		0			0
$676$	6.40679	−	11.0969i	0.246415	−	0.426803i
$677$	−43.1225	+	24.8968i	−1.65733	+	0.956862i	−0.683396	+	0.730048i	$0.739498\pi$
$677$	−43.1225	+	24.8968i	−1.65733	+	0.956862i	−0.973938	+	0.226815i	$0.927169\pi$
$678$		−	19.0344i		−	0.731011i
$679$	0.593529	+	1.11274i	0.0227776	+	0.0427029i
$680$		0			0
$681$	7.71289	+	13.3591i	0.295558	+	0.511922i
$682$	−8.37879	−	4.83750i	−0.320840	−	0.185237i
$683$	−27.0717	−	15.6299i	−1.03587	−	0.598060i	−0.117210	−	0.993107i	$-0.537395\pi$
$683$	−27.0717	−	15.6299i	−1.03587	−	0.598060i	−0.918661	+	0.395047i	$0.870728\pi$
$684$	−1.21305	−	2.10106i	−0.0463820	−	0.0803360i
$685$		0			0
$686$	9.33736	+	20.7515i	0.356502	+	0.792296i
$687$			15.3285i			0.584820i
$688$	−24.6342	+	14.2225i	−0.939169	+	0.542229i
$689$	−22.5300	+	39.0231i	−0.858325	+	1.48666i
$690$		0			0
$691$	12.5797	+	21.7887i	0.478554	+	0.828879i	0.999698	−	0.0245894i	$-0.00782784\pi$
$691$	12.5797	+	21.7887i	0.478554	+	0.828879i	−0.521144	+	0.853469i	$0.674495\pi$
$692$			3.67356i			0.139648i
$693$	11.0789	−	5.90944i	0.420852	−	0.224481i
$694$	−3.08740			−0.117196
$695$		0			0
$696$	−6.11968	+	10.5996i	−0.231966	+	0.401776i
$697$	−7.12242	−	4.11213i	−0.269781	−	0.155758i
$698$	13.4400	−	7.75956i	0.508710	−	0.293704i
$699$	20.2885			0.767382
$700$		0			0
$701$	−6.21130			−0.234597			−0.117299	−	0.993097i	$-0.537423\pi$
$701$	−6.21130			−0.234597			−0.117299	+	0.993097i	$0.537423\pi$
$702$	−6.65630	+	3.84302i	−0.251226	+	0.145045i
$703$	19.0163	+	10.9791i	0.717215	+	0.414084i
$704$	−21.0758	+	36.5043i	−0.794324	+	1.37581i
$705$		0			0
$706$	27.7529			1.04449
$707$	−0.736524	+	21.9170i	−0.0276998	+	0.824273i
$708$			0.115143i			0.00432734i
$709$	−7.44157	−	12.8892i	−0.279474	−	0.484063i	0.691780	−	0.722108i	$-0.256827\pi$
$709$	−7.44157	−	12.8892i	−0.279474	−	0.484063i	−0.971254	+	0.238045i	$0.923493\pi$
$710$		0			0
$711$	0.415579	−	0.719805i	0.0155854	−	0.0269948i
$712$	6.06434	−	3.50125i	0.227271	−	0.131215i
$713$			8.26391i			0.309486i
$714$	20.4311	+	0.686589i	0.764613	+	0.0256949i
$715$		0			0
$716$	3.64723	+	6.31719i	0.136303	+	0.236084i
$717$	10.3017	+	5.94771i	0.384725	+	0.222121i
$718$	0.364140	+	0.210237i	0.0135896	+	0.00784596i
$719$	18.3084	+	31.7110i	0.682787	+	1.18262i	0.974127	+	0.226002i	$0.0725655\pi$
$719$	18.3084	+	31.7110i	0.682787	+	1.18262i	−0.291340	+	0.956620i	$0.594101\pi$
$720$		0			0
$721$	−19.9638	+	32.0424i	−0.743492	+	1.19332i
$722$		−	6.73291i		−	0.250573i
$723$	−15.1422	+	8.74236i	−0.563145	+	0.325132i
$724$	1.62491	−	2.81443i	0.0603895	−	0.104598i
$725$		0			0
$726$	7.07924	+	12.2616i	0.262735	+	0.455071i
$727$			13.8624i			0.514129i	0.966394	+	0.257064i	$0.0827553\pi$
$727$			13.8624i			0.514129i	−0.966394	+	0.257064i	$0.917245\pi$
$728$	−44.6830	+	23.8337i	−1.65606	+	0.883338i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	32.1853	−	55.7466i	1.19042	−	2.06186i
$732$	−2.12327	−	1.22587i	−0.0784782	−	0.0453094i
$733$	28.3794	−	16.3849i	1.04822	−	0.605189i	0.126068	−	0.992022i	$-0.459764\pi$
$733$	28.3794	−	16.3849i	1.04822	−	0.605189i	0.922150	+	0.386833i	$0.126431\pi$
$734$	−4.01854			−0.148327
$735$		0			0
$736$	13.4745			0.496676
$737$	10.2354	−	5.90944i	0.377028	−	0.217677i
$738$	−1.39161	−	0.803447i	−0.0512259	−	0.0295753i
$739$	14.9342	−	25.8668i	0.549363	−	0.951524i	−0.448956	−	0.893554i	$-0.648204\pi$
$739$	14.9342	−	25.8668i	0.549363	−	0.951524i	0.998318	−	0.0579700i	$-0.0184628\pi$
$740$		0			0
$741$	30.9505			1.13700
$742$	20.6607	−	11.0204i	0.758480	−	0.404570i
$743$		−	49.5577i		−	1.81810i	−0.416691	−	0.909048i	$-0.636810\pi$
$743$		−	49.5577i		−	1.81810i	0.416691	−	0.909048i	$-0.363190\pi$
$744$	2.53842	+	4.39668i	0.0930631	+	0.161190i
$745$		0			0
$746$	−8.20506	+	14.2116i	−0.300409	+	0.520323i
$747$	0.995527	−	0.574768i	0.0364244	−	0.0210297i
$748$		−	14.6342i		−	0.535079i
$749$	3.03439	−	4.87027i	0.110874	−	0.177956i
$750$		0			0
$751$	3.30517	+	5.72473i	0.120607	+	0.208898i	0.920007	−	0.391901i	$-0.128182\pi$
$751$	3.30517	+	5.72473i	0.120607	+	0.208898i	−0.799400	+	0.600799i	$0.794849\pi$
$752$	−9.06116	−	5.23146i	−0.330427	−	0.190772i
$753$	−8.86361	−	5.11741i	−0.323008	−	0.186489i
$754$	−15.3721	−	26.6252i	−0.559818	−	0.969633i
$755$		0			0
$756$	−1.29661	−	0.0435726i	−0.0471571	−	0.00158472i
$757$			7.01509i			0.254968i	0.991841	+	0.127484i	$0.0406901\pi$
$757$			7.01509i			0.254968i	−0.991841	+	0.127484i	$0.959310\pi$
$758$	30.7482	−	17.7525i	1.11682	−	0.644798i
$759$	11.8189	−	20.4709i	0.428998	−	0.743047i
$760$		0			0
$761$	−6.50438	−	11.2659i	−0.235783	−	0.408389i	0.723717	−	0.690097i	$-0.242432\pi$
$761$	−6.50438	−	11.2659i	−0.235783	−	0.408389i	−0.959500	+	0.281708i	$0.909099\pi$
$762$			14.4979i			0.525203i
$763$	0.692951	−	20.6204i	0.0250865	−	0.746508i
$764$	−11.4040			−0.412581
$765$		0			0
$766$	12.7478	−	22.0798i	0.460597	−	0.797777i
$767$	−1.27212	−	0.734459i	−0.0459336	−	0.0265198i
$768$	9.52899	−	5.50156i	0.343848	−	0.198521i
$769$	−0.822729			−0.0296684			−0.0148342	−	0.999890i	$-0.504722\pi$
$769$	−0.822729			−0.0296684			−0.0148342	+	0.999890i	$0.504722\pi$
$770$		0			0
$771$	−22.3545			−0.805077
$772$	−3.05828	+	1.76570i	−0.110070	+	0.0635489i
$773$	−21.3773	−	12.3422i	−0.768890	−	0.443919i	0.0635887	−	0.997976i	$-0.479745\pi$
$773$	−21.3773	−	12.3422i	−0.768890	−	0.443919i	−0.832478	+	0.554058i	$0.813079\pi$
$774$	6.28852	−	10.8920i	0.226036	−	0.391506i
$775$		0			0
$776$	1.45851			0.0523576
$777$	10.3603	−	5.52615i	0.371674	−	0.198249i
$778$			10.1503i			0.363906i
$779$	3.23536	+	5.60381i	0.115919	+	0.200777i
$780$		0			0
$781$	14.3942	−	24.9315i	0.515065	−	0.892118i
$782$	33.3279	−	19.2418i	1.19180	−	0.688087i
$783$		−	4.00000i		−	0.142948i
$784$	19.4082	+	1.30590i	0.693149	+	0.0466394i
$785$		0			0
$786$	−2.43364	−	4.21519i	−0.0868050	−	0.150351i
$787$	−13.6470	−	7.87908i	−0.486462	−	0.280859i	0.236644	−	0.971596i	$-0.423953\pi$
$787$	−13.6470	−	7.87908i	−0.486462	−	0.280859i	−0.723105	+	0.690738i	$0.757286\pi$
$788$	−8.10582	−	4.67990i	−0.288758	−	0.166714i
$789$	12.4051	+	21.4862i	0.441632	+	0.764929i
$790$		0			0
$791$	19.2899	+	36.1643i	0.685871	+	1.28586i
$792$		−	14.5216i		−	0.516003i
$793$	27.0872	−	15.6388i	0.961896	−	0.555351i
$794$	−15.3173	+	26.5303i	−0.543590	+	0.941526i
$795$		0			0
$796$	5.10794	+	8.84721i	0.181046	+	0.313581i
$797$		−	15.8568i		−	0.561677i	−0.959755	−	0.280838i	$-0.909388\pi$
$797$		−	15.8568i		−	0.561677i	0.959755	−	0.280838i	$-0.0906125\pi$
$798$	−13.6511	−	8.50524i	−0.483244	−	0.301082i
$799$	23.6774			0.837646
$800$		0			0
$801$	−1.14426	+	1.98191i	−0.0404304	+	0.0700275i
$802$	−7.73493	−	4.46576i	−0.273130	−	0.157692i
$803$	51.3417	−	29.6421i	1.81181	−	1.04605i
$804$	−1.22114			−0.0430661
$805$		0			0
$806$	−12.7526			−0.449191
$807$	15.3982	−	8.89013i	0.542041	−	0.312948i
$808$	21.9637	+	12.6808i	0.772681	+	0.446108i
$809$	−3.92840	+	6.80419i	−0.138115	+	0.239223i	−0.926783	−	0.375597i	$-0.877438\pi$
$809$	−3.92840	+	6.80419i	−0.138115	+	0.239223i	0.788668	+	0.614819i	$0.210771\pi$
$810$		0			0
$811$	−55.8410			−1.96084			−0.980421	−	0.196912i	$-0.936909\pi$
$811$	−55.8410			−1.96084			−0.980421	+	0.196912i	$0.936909\pi$
$812$	0.174290	−	5.18642i	0.00611640	−	0.182008i
$813$		−	17.1390i		−	0.601090i
$814$	12.9395	+	22.4119i	0.453529	+	0.785535i
$815$		0			0
$816$	8.73747	−	15.1337i	0.305873	−	0.529787i
$817$	−43.8606	+	25.3229i	−1.53449	+	0.885936i
$818$		−	43.5070i		−	1.52119i
$819$	8.75202	−	14.0472i	0.305820	−	0.490849i
$820$		0			0
$821$	−4.01403	−	6.95250i	−0.140091	−	0.242644i	0.787440	−	0.616391i	$-0.211406\pi$
$821$	−4.01403	−	6.95250i	−0.140091	−	0.242644i	−0.927531	+	0.373747i	$0.878073\pi$
$822$	19.6559	+	11.3484i	0.685579	+	0.395819i
$823$	−19.2881	−	11.1360i	−0.672342	−	0.388177i	0.124621	−	0.992204i	$-0.460228\pi$
$823$	−19.2881	−	11.1360i	−0.672342	−	0.388177i	−0.796964	+	0.604027i	$0.793562\pi$
$824$	21.8307	+	37.8119i	0.760510	+	1.31724i
$825$		0			0
$826$	0.359254	+	0.673522i	0.0125001	+	0.0234348i
$827$		−	53.3872i		−	1.85645i	−0.372015	−	0.928227i	$-0.621333\pi$
$827$		−	53.3872i		−	1.85645i	0.372015	−	0.928227i	$-0.378667\pi$
$828$	−2.11507	+	1.22114i	−0.0735037	+	0.0424374i
$829$	−14.4223	+	24.9801i	−0.500906	+	0.867594i	0.499094	+	0.866548i	$0.333666\pi$
$829$	−14.4223	+	24.9801i	−0.500906	+	0.867594i	−0.999999	+	0.00104627i	$0.999667\pi$
$830$		0			0
$831$	1.44173	+	2.49714i	0.0500129	+	0.0866250i
$832$			55.5599i			1.92619i
$833$	−39.5137	+	19.4008i	−1.36907	+	0.672200i
$834$	3.26901			0.113197
$835$		0			0
$836$	−5.75697	+	9.97137i	−0.199109	+	0.344867i
$837$	−1.43690	−	0.829594i	−0.0496665	−	0.0286750i
$838$	40.5537	−	23.4137i	1.40090	−	0.808812i
$839$	−3.38435			−0.116841			−0.0584205	−	0.998292i	$-0.518606\pi$
$839$	−3.38435			−0.116841			−0.0584205	+	0.998292i	$0.518606\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−13.3492	+	7.70717i	−0.460044	+	0.265607i
$843$	24.0584	+	13.8901i	0.828616	+	0.478402i
$844$	−3.82167	+	6.61932i	−0.131547	+	0.227846i
$845$		0			0
$846$	4.62620			0.159052
$847$	−25.8764	−	16.1221i	−0.889124	−	0.553963i
$848$		−	20.0168i		−	0.687380i
$849$	−4.35117	−	7.53644i	−0.149332	−	0.258650i
$850$		0			0
$851$	11.0523	−	19.1431i	0.378868	−	0.656218i
$852$	−2.57594	+	1.48722i	−0.0882502	+	0.0509513i
$853$			32.8905i			1.12615i	0.826406	+	0.563074i	$0.190382\pi$
$853$			32.8905i			1.12615i	−0.826406	+	0.563074i	$0.809618\pi$
$854$	−16.2447	−	0.545907i	−0.555883	−	0.0186805i
$855$		0			0
$856$	−3.31815	−	5.74721i	−0.113412	−	0.196435i
$857$	23.3994	+	13.5097i	0.799308	+	0.461481i	0.843229	−	0.537554i	$-0.180652\pi$
$857$	23.3994	+	13.5097i	0.799308	+	0.461481i	−0.0439208	+	0.999035i	$0.513985\pi$
$858$	31.5900	+	18.2385i	1.07846	+	0.622652i
$859$	24.0537	+	41.6622i	0.820702	+	1.42150i	0.905161	+	0.425070i	$0.139750\pi$
$859$	24.0537	+	41.6622i	0.820702	+	1.42150i	−0.0844589	+	0.996427i	$0.526916\pi$
$860$		0			0
$861$	3.45822	+	0.116214i	0.117856	+	0.00396056i
$862$			10.4574i			0.356179i
$863$	8.80891	−	5.08582i	0.299859	−	0.173123i	−0.342521	−	0.939510i	$-0.611281\pi$
$863$	8.80891	−	5.08582i	0.299859	−	0.173123i	0.642379	+	0.766387i	$0.277947\pi$
$864$	−1.35267	+	2.34290i	−0.0460188	+	0.0797069i
$865$		0			0
$866$	12.7789	+	22.1336i	0.434243	+	0.752132i
$867$			22.5454i			0.765684i
$868$	−1.82694	−	1.13827i	−0.0620105	−	0.0386353i
$869$	−3.94458			−0.133811
$870$		0			0
$871$	7.78922	−	13.4913i	0.263928	−	0.457136i
$872$	−20.6644	−	11.9306i	−0.699783	−	0.404020i
$873$	−0.412803	+	0.238332i	−0.0139713	+	0.00806631i
$874$	−30.2784			−1.02418
$875$		0			0
$876$	−6.12530			−0.206955
$877$	−31.9214	+	18.4298i	−1.07791	+	0.622330i	−0.930331	−	0.366720i	$-0.880481\pi$
$877$	−31.9214	+	18.4298i	−1.07791	+	0.622330i	−0.147576	+	0.989051i	$0.547147\pi$
$878$	−11.6524	−	6.72753i	−0.393250	−	0.227043i
$879$	−9.94771	+	17.2299i	−0.335528	+	0.581151i
$880$		0			0
$881$	42.1945			1.42157			0.710784	−	0.703410i	$-0.248340\pi$
$881$	42.1945			1.42157			0.710784	+	0.703410i	$0.248340\pi$
$882$	−7.72037	+	3.79063i	−0.259958	+	0.127637i
$883$			35.7880i			1.20436i	0.798359	+	0.602181i	$0.205702\pi$
$883$			35.7880i			1.20436i	−0.798359	+	0.602181i	$0.794298\pi$
$884$	−9.64464	−	16.7050i	−0.324384	−	0.561850i
$885$		0			0
$886$	23.6843	−	41.0224i	0.795690	−	1.37818i
$887$	36.7178	−	21.1990i	1.23286	−	0.711793i	0.265237	−	0.964183i	$-0.414550\pi$
$887$	36.7178	−	21.1990i	1.23286	−	0.711793i	0.967626	+	0.252390i	$0.0812166\pi$
$888$		−	13.5797i		−	0.455706i
$889$	−14.6925	−	27.5452i	−0.492771	−	0.923837i
$890$		0			0
$891$	2.37294	+	4.11005i	0.0794964	+	0.137692i
$892$	1.51707	+	0.875883i	0.0507954	+	0.0293267i
$893$	−16.1332	−	9.31450i	−0.539877	−	0.311698i
$894$	−8.96173	−	15.5222i	−0.299725	−	0.519139i
$895$		0			0
$896$	7.69792	−	12.3553i	0.257169	−	0.412763i
$897$		−	31.1569i		−	1.04030i
$898$	−23.2459	+	13.4210i	−0.775725	+	0.447865i
$899$	3.31838	−	5.74760i	0.110674	−	0.191693i
$900$		0			0
$901$	22.6488	+	39.2289i	0.754542	+	1.30691i
$902$			7.62612i			0.253922i
$903$	−0.909598	+	27.0672i	−0.0302695	+	0.900741i
$904$	47.4023			1.57658
$905$		0			0
$906$	−8.75860	+	15.1703i	−0.290985	+	0.504001i
$907$	45.5042	+	26.2719i	1.51094	+	0.872343i	0.999918	+	0.0127763i	$0.00406693\pi$
$907$	45.5042	+	26.2719i	1.51094	+	0.872343i	0.511024	+	0.859567i	$0.329266\pi$
$908$	−6.55061	+	3.78199i	−0.217389	+	0.125510i
$909$	−8.28852			−0.274913
$910$		0			0
$911$	38.7118			1.28258			0.641290	−	0.767299i	$-0.278400\pi$
$911$	38.7118			1.28258			0.641290	+	0.767299i	$0.278400\pi$
$912$	−11.9070	+	6.87450i	−0.394280	+	0.227638i
$913$	−4.72465	−	2.72778i	−0.156363	−	0.0902763i
$914$	−2.26719	+	3.92689i	−0.0749920	+	0.129890i
$915$		0			0
$916$	−7.51631			−0.248346
$917$	8.89556	+	5.54232i	0.293757	+	0.183024i
$918$			7.72657i			0.255015i
$919$	−12.9370	−	22.4075i	−0.426752	−	0.739156i	0.569830	−	0.821762i	$-0.307009\pi$
$919$	−12.9370	−	22.4075i	−0.426752	−	0.739156i	−0.996582	+	0.0826063i	$0.973676\pi$
$920$		0			0
$921$	−2.66075	+	4.60856i	−0.0876748	+	0.151857i
$922$	32.9275	−	19.0107i	1.08441	−	0.626083i
$923$		−	37.9459i		−	1.24900i
$924$	2.89768	+	5.43251i	0.0953266	+	0.178716i
$925$		0			0
$926$	−3.05767	−	5.29604i	−0.100481	−	0.174039i
$927$	−12.3575	−	7.13461i	−0.405874	−	0.234331i
$928$	−9.37158	−	5.41069i	−0.307637	−	0.177614i
$929$	−0.888730	−	1.53933i	−0.0291583	−	0.0505036i	0.851078	−	0.525039i	$-0.175949\pi$
$929$	−0.888730	−	1.53933i	−0.0291583	−	0.0505036i	−0.880236	+	0.474536i	$0.842616\pi$
$930$		0			0
$931$	34.5558	+	2.32513i	1.13252	+	0.0762031i
$932$			9.94842i			0.325871i
$933$	−1.64147	+	0.947706i	−0.0537395	+	0.0310265i
$934$	−4.31396	+	7.47200i	−0.141157	+	0.244491i
$935$		0			0
$936$	−9.57045	−	16.5765i	−0.312820	−	0.541820i
$937$		−	58.4486i		−	1.90943i	−0.297518	−	0.954716i	$-0.596159\pi$
$937$		−	58.4486i		−	1.90943i	0.297518	−	0.954716i	$-0.403841\pi$
$938$	−7.14296	+	3.81003i	−0.233226	+	0.124402i
$939$	−26.5230			−0.865546
$940$		0			0
$941$	−1.90416	+	3.29811i	−0.0620739	+	0.107515i	−0.895392	−	0.445278i	$-0.853105\pi$
$941$	−1.90416	+	3.29811i	−0.0620739	+	0.107515i	0.833318	+	0.552793i	$0.186438\pi$
$942$	12.8756	+	7.43374i	0.419510	+	0.242204i
$943$	5.64117	−	3.25693i	0.183702	−	0.106060i
$944$	0.652530			0.0212381
$945$		0			0
$946$	−59.6890			−1.94066
$947$	−47.4955	+	27.4216i	−1.54340	+	0.891081i	−0.544776	+	0.838581i	$0.683385\pi$
$947$	−47.4955	+	27.4216i	−1.54340	+	0.891081i	−0.998621	+	0.0524995i	$0.983281\pi$
$948$	0.352954	+	0.203778i	0.0114634	+	0.00661841i
$949$	39.0713	−	67.6734i	1.26831	−	2.19677i
$950$		0			0
$951$	−15.6237			−0.506633
$952$	−1.70984	+	50.8804i	−0.0554164	+	1.64904i
$953$			37.4426i			1.21288i	0.795128	+	0.606442i	$0.207404\pi$
$953$			37.4426i			1.21288i	−0.795128	+	0.606442i	$0.792596\pi$
$954$	4.42523	+	7.66473i	0.143272	+	0.248155i
$955$		0			0
$956$	−2.91644	+	5.05143i	−0.0943245	+	0.163375i
$957$	−16.4402	+	9.49175i	−0.531436	+	0.306825i
$958$		−	11.3402i		−	0.366384i
$959$	−48.8459	−	1.64147i	−1.57732	−	0.0530060i
$960$		0			0
$961$	14.1235	+	24.4627i	0.455598	+	0.789119i
$962$	29.5410	+	17.0555i	0.952441	+	0.549892i
$963$	1.87827	+	1.08442i	0.0605265	+	0.0349450i
$964$	−4.28679	−	7.42495i	−0.138068	−	0.239141i
$965$		0			0
$966$	−8.56195	+	13.7421i	−0.275476	+	0.442146i
$967$		−	32.0098i		−	1.02937i	−0.857381	−	0.514683i	$-0.827910\pi$
$967$		−	32.0098i		−	1.02937i	0.857381	−	0.514683i	$-0.172090\pi$
$968$	−30.5357	+	17.6298i	−0.981453	+	0.566642i
$969$	15.5569	−	26.9453i	0.499759	−	0.865607i
$970$		0			0
$971$	−25.7481	−	44.5971i	−0.826297	−	1.43119i	−0.900924	−	0.433977i	$-0.857110\pi$
$971$	−25.7481	−	44.5971i	−0.826297	−	1.43119i	0.0746266	−	0.997212i	$-0.476223\pi$
$972$		−	0.490347i		−	0.0157279i
$973$	−6.21096	+	3.31290i	−0.199114	+	0.106207i
$974$	−16.9113			−0.541872
$975$		0			0
$976$	−6.94716	+	12.0328i	−0.222373	+	0.385162i
$977$	−2.71451	−	1.56722i	−0.0868449	−	0.0501399i	0.455949	−	0.890006i	$-0.349300\pi$
$977$	−2.71451	−	1.56722i	−0.0868449	−	0.0501399i	−0.542794	+	0.839866i	$0.682633\pi$
$978$	7.15752	−	4.13240i	0.228872	−	0.132140i
$979$	10.8610			0.347120
$980$		0			0
$981$	7.79817			0.248976
$982$	33.0387	−	19.0749i	1.05431	−	0.608705i
$983$	37.3400	+	21.5583i	1.19096	+	0.687602i	0.958525	−	0.285009i	$-0.0919967\pi$
$983$	37.3400	+	21.5583i	1.19096	+	0.687602i	0.232437	+	0.972611i	$0.425330\pi$
$984$	2.00086	−	3.46560i	0.0637852	−	0.110479i
$985$		0			0
$986$	−30.9063			−0.984257
$987$	−8.78953	+	4.68830i	−0.279774	+	0.149230i
$988$			15.1765i			0.482829i
$989$	25.4918	+	44.1530i	0.810591	+	1.40398i
$990$		0			0
$991$	6.07758	−	10.5267i	0.193061	−	0.334391i	−0.753202	−	0.657789i	$-0.771492\pi$
$991$	6.07758	−	10.5267i	0.193061	−	0.334391i	0.946263	+	0.323398i	$0.104825\pi$
$992$	−3.88731	+	2.24434i	−0.123422	+	0.0712578i
$993$			4.02986i			0.127884i
$994$	−10.4276	+	16.7365i	−0.330743	+	0.530850i
$995$		0			0
$996$	0.281836	+	0.488154i	0.00893031	+	0.0154678i
$997$	19.7244	+	11.3879i	0.624677	+	0.360657i	0.778688	−	0.627412i	$-0.215886\pi$
$997$	19.7244	+	11.3879i	0.624677	+	0.360657i	−0.154011	+	0.988069i	$0.549219\pi$
$998$	22.9740	+	13.2640i	0.727229	+	0.419866i
$999$	2.21903	+	3.84347i	0.0702069	+	0.121602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.r.h.424.3		16
5.2	odd	4		525.2.i.i.151.2	✓	8
5.3	odd	4		525.2.i.j.151.3	yes	8
5.4	even	2	inner	525.2.r.h.424.6		16
7.2	even	3	inner	525.2.r.h.499.6		16
35.2	odd	12		525.2.i.i.226.2	yes	8
35.3	even	12		3675.2.a.bq.1.2		4
35.9	even	6	inner	525.2.r.h.499.3		16
35.17	even	12		3675.2.a.bx.1.3		4
35.18	odd	12		3675.2.a.br.1.2		4
35.23	odd	12		525.2.i.j.226.3	yes	8
35.32	odd	12		3675.2.a.bw.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.i.i.151.2	✓	8	5.2	odd	4
525.2.i.i.226.2	yes	8	35.2	odd	12
525.2.i.j.151.3	yes	8	5.3	odd	4
525.2.i.j.226.3	yes	8	35.23	odd	12
525.2.r.h.424.3		16	1.1	even	1	trivial
525.2.r.h.424.6		16	5.4	even	2	inner
525.2.r.h.499.3		16	35.9	even	6	inner
525.2.r.h.499.6		16	7.2	even	3	inner
3675.2.a.bq.1.2		4	35.3	even	12
3675.2.a.br.1.2		4	35.18	odd	12
3675.2.a.bw.1.3		4	35.32	odd	12
3675.2.a.bx.1.3		4	35.17	even	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.06407 + 0.614340i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.245174 + 0.424653i) q^{4} -1.22868 q^{6} +(2.33443 - 1.24517i) q^{7} -3.05984i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.06407 + 0.614340i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.245174 + 0.424653i) q^{4} -1.22868 q^{6} +(2.33443 - 1.24517i) q^{7} -3.05984i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.37294 - 4.11005i) q^{11} +(-0.424653 + 0.245174i) q^{12} -6.25553i q^{13} +(-1.71903 + 2.75908i) q^{14} +(1.38943 + 2.40657i) q^{16} +(-5.44602 - 3.14426i) q^{17} +(-1.06407 - 0.614340i) q^{18} +(2.47385 + 4.28484i) q^{19} +(2.64426 + 0.0888607i) q^{21} +5.83116i q^{22} +(4.31341 - 2.49035i) q^{23} +(1.52992 - 2.64990i) q^{24} +(3.84302 + 6.65630i) q^{26} +1.00000i q^{27} +(-0.0435726 + 1.29661i) q^{28} -4.00000 q^{29} +(-0.829594 + 1.43690i) q^{31} +(2.34290 + 1.35267i) q^{32} +(4.11005 - 2.37294i) q^{33} +7.72657 q^{34} -0.490347 q^{36} +(3.84347 - 2.21903i) q^{37} +(-5.26469 - 3.03957i) q^{38} +(3.12776 - 5.41745i) q^{39} +1.30782 q^{41} +(-2.86826 + 1.52992i) q^{42} +10.2362i q^{43} +(1.16356 + 2.01535i) q^{44} +(-3.05984 + 5.29980i) q^{46} +(-3.26074 + 1.88259i) q^{47} +2.77886i q^{48} +(3.89908 - 5.81353i) q^{49} +(-3.14426 - 5.44602i) q^{51} +(2.65643 + 1.53369i) q^{52} +(-6.23818 - 3.60162i) q^{53} +(-0.614340 - 1.06407i) q^{54} +(-3.81003 - 7.14296i) q^{56} +4.94771i q^{57} +(4.25627 - 2.45736i) q^{58} +(0.117410 - 0.203359i) q^{59} +(2.50000 + 4.33013i) q^{61} -2.03861i q^{62} +(2.24556 + 1.39908i) q^{63} -8.88173 q^{64} +(-2.91558 + 5.04993i) q^{66} +(2.15670 + 1.24517i) q^{67} +(2.67044 - 1.54178i) q^{68} +4.98069 q^{69} +6.06598 q^{71} +(2.64990 - 1.52992i) q^{72} +(10.8182 + 6.24588i) q^{73} +(-2.72647 + 4.72239i) q^{74} -2.42609 q^{76} +(0.421722 - 12.5493i) q^{77} +7.68604i q^{78} +(-0.415579 - 0.719805i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.39161 + 0.803447i) q^{82} -1.14954i q^{83} +(-0.686038 + 1.10111i) q^{84} +(-6.28852 - 10.8920i) q^{86} +(-3.46410 - 2.00000i) q^{87} +(-12.5761 - 7.26081i) q^{88} +(1.14426 + 1.98191i) q^{89} +(-7.78922 - 14.6031i) q^{91} +2.44227i q^{92} +(-1.43690 + 0.829594i) q^{93} +(2.31310 - 4.00641i) q^{94} +(1.35267 + 2.34290i) q^{96} +0.476664i q^{97} +(-0.577407 + 8.58135i) q^{98} +4.74588 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 14 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) 16 * q + 14 * q^4 - 4 * q^6 + 8 * q^9	\( 16 q + 14 q^{4} - 4 q^{6} + 8 q^{9} - 16 q^{11} + 24 q^{14} - 34 q^{16} + 6 q^{19} + 4 q^{21} - 6 q^{24} + 38 q^{26} - 64 q^{29} - 18 q^{31} - 56 q^{34} + 28 q^{36} + 14 q^{39} + 16 q^{41} + 52 q^{44} + 12 q^{46} + 42 q^{49} - 12 q^{51} - 2 q^{54} - 42 q^{56} + 20 q^{59} + 40 q^{61} - 84 q^{64} - 24 q^{66} + 8 q^{69} + 88 q^{71} - 42 q^{74} - 92 q^{76} + 16 q^{79} - 8 q^{81} + 36 q^{84} - 24 q^{86} - 20 q^{89} + 42 q^{91} + 44 q^{94} + 34 q^{96} - 32 q^{99}+O(q^{100}) \) 16 * q + 14 * q^4 - 4 * q^6 + 8 * q^9 - 16 * q^11 + 24 * q^14 - 34 * q^16 + 6 * q^19 + 4 * q^21 - 6 * q^24 + 38 * q^26 - 64 * q^29 - 18 * q^31 - 56 * q^34 + 28 * q^36 + 14 * q^39 + 16 * q^41 + 52 * q^44 + 12 * q^46 + 42 * q^49 - 12 * q^51 - 2 * q^54 - 42 * q^56 + 20 * q^59 + 40 * q^61 - 84 * q^64 - 24 * q^66 + 8 * q^69 + 88 * q^71 - 42 * q^74 - 92 * q^76 + 16 * q^79 - 8 * q^81 + 36 * q^84 - 24 * q^86 - 20 * q^89 + 42 * q^91 + 44 * q^94 + 34 * q^96 - 32 * q^99

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