LMFDB - Embedded newform 525.2.r.h.499.3

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			499.3
Root			$-1.06407 - 0.614340i$ of defining polynomial
Character	$\chi$	$=$	525.499
Dual form			525.2.r.h.424.3

$q$-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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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	0.0741545	−	0.997247i	$-0.476374\pi$
$2$	−1.06407	−	0.614340i	−0.752409	−	0.434404i	−0.826564	+	0.562843i	$0.809708\pi$
$3$	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	0.962779	+	0.270290i	$0.0871197\pi$
$11$	2.37294	+	4.11005i	0.715468	+	1.23923i	−0.247311	+	0.968936i	$0.579547\pi$
$12$	−0.424653	−	0.245174i	−0.122587	−	0.0707755i
$13$			6.25553i			1.73497i	0.497462	+	0.867486i	$0.334265\pi$
$13$			6.25553i			1.73497i	−0.497462	+	0.867486i	$0.665735\pi$
$14$	−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	−0.983865	−	0.178914i	$-0.942742\pi$
$17$	−5.44602	+	3.14426i	−1.32085	+	0.762595i	−0.336988	+	0.941509i	$0.609408\pi$
$18$	−1.06407	+	0.614340i	−0.250803	+	0.144801i
$19$	2.47385	−	4.28484i	0.567541	−	0.983009i	−0.429268	−	0.903177i	$-0.641228\pi$
$19$	2.47385	−	4.28484i	0.567541	−	0.983009i	0.996808	−	0.0798321i	$-0.0254384\pi$
$20$		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	0.877008	−	0.480476i	$-0.159536\pi$
$23$	4.31341	+	2.49035i	0.899408	+	0.519273i	0.0223998	+	0.999749i	$0.492869\pi$
$24$	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	0.781858	−	0.623456i	$-0.214272\pi$
$31$	−0.829594	−	1.43690i	−0.149000	−	0.258075i	−0.930858	+	0.365381i	$0.880939\pi$
$32$	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	0.781473	−	0.623939i	$-0.214469\pi$
$37$	3.84347	+	2.21903i	0.631862	+	0.364806i	−0.149611	+	0.988745i	$0.547802\pi$
$38$	−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	$-0.714962\pi$
$43$		−	10.2362i		−	1.56101i	0.625150	−	0.780505i	$-0.285038\pi$
$44$	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	0.242965	−	0.970035i	$-0.421880\pi$
$47$	−3.26074	−	1.88259i	−0.475628	−	0.274604i	−0.718593	+	0.695431i	$0.755213\pi$
$48$		−	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	−0.862966	−	0.505261i	$-0.831396\pi$
$53$	−6.23818	+	3.60162i	−0.856880	+	0.494720i	0.00608595	+	0.999981i	$0.498063\pi$
$54$	−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	0.873567	−	0.486704i	$-0.161801\pi$
$59$	0.117410	+	0.203359i	0.0152854	+	0.0264751i	−0.858282	+	0.513179i	$0.828468\pi$
$60$		0			0
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$			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	−0.362439	−	0.932007i	$-0.618056\pi$
$67$	2.15670	−	1.24517i	0.263483	−	0.152122i	0.625923	+	0.779885i	$0.284723\pi$
$68$	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	0.291910	−	0.956446i	$-0.405709\pi$
$73$	10.8182	−	6.24588i	1.26617	−	0.731024i	0.974261	+	0.225421i	$0.0723759\pi$
$74$	−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	−0.888456	−	0.458961i	$-0.848222\pi$
$79$	−0.415579	+	0.719805i	−0.0467563	+	0.0809844i	0.841700	+	0.539945i	$0.181555\pi$
$80$		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	$0.0200952\pi$
$83$			1.14954i			0.126178i	−0.998008	+	0.0630890i	$0.979905\pi$
$84$	−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	−0.798986	−	0.601350i	$-0.794630\pi$
$89$	1.14426	−	1.98191i	0.121291	−	0.210082i	0.920277	+	0.391267i	$0.127963\pi$
$90$		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	$-0.992296\pi$
$97$		−	0.476664i		−	0.0483979i	0.999707	−	0.0241989i	$-0.00770351\pi$
$98$	−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	0.582779	−	0.812631i	$-0.301965\pi$
$101$	−4.14426	−	7.17807i	−0.412369	−	0.714244i	−0.995148	+	0.0983863i	$0.968632\pi$
$102$	6.69141	−	3.86329i	0.662548	−	0.382522i
$103$	−12.3575	−	7.13461i	−1.21762	−	0.702994i	−0.253212	−	0.967411i	$-0.581487\pi$
$103$	−12.3575	−	7.13461i	−1.21762	−	0.702994i	−0.964408	+	0.264417i	$0.914820\pi$
$104$	−19.1409			−1.87692
$105$		0			0
$106$	8.85046			0.859633
$107$	1.87827	+	1.08442i	0.181579	+	0.104835i	0.588035	−	0.808836i	$-0.299902\pi$
$107$	1.87827	+	1.08442i	0.181579	+	0.104835i	−0.406455	+	0.913671i	$0.633235\pi$
$108$	−0.424653	+	0.245174i	−0.0408623	+	0.0235918i
$109$	3.89908	+	6.75341i	0.373465	+	0.646860i	0.990096	−	0.140392i	$-0.0448364\pi$
$109$	3.89908	+	6.75341i	0.373465	+	0.646860i	−0.616631	+	0.787252i	$0.711503\pi$
$110$		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	$-0.740139\pi$
$113$		−	15.4918i		−	1.45734i	0.684864	−	0.728671i	$-0.259861\pi$
$114$	−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	$0.175382\pi$
$127$			11.7996i			1.04704i	−0.852013	+	0.523521i	$0.824618\pi$
$128$	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	−0.766432	−	0.642325i	$-0.777970\pi$
$131$	1.98069	−	3.43066i	0.173054	−	0.299739i	0.939486	+	0.342587i	$0.111303\pi$
$132$		−	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	−0.990514	−	0.137413i	$-0.956121\pi$
$137$	−15.9976	+	9.23622i	−1.36677	+	0.789104i	−0.376254	+	0.926517i	$0.622788\pi$
$138$	−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	−0.395653	−	0.918400i	$-0.629482\pi$
$149$	7.29379	−	12.6332i	0.597531	−	1.03495i	0.993184	−	0.116554i	$-0.0371848\pi$
$150$		0			0
$151$	7.12847	+	12.3469i	0.580106	+	1.00477i	0.995466	+	0.0951165i	$0.0303224\pi$
$151$	7.12847	+	12.3469i	0.580106	+	1.00477i	−0.415360	+	0.909657i	$0.636344\pi$
$152$	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	−0.856016	−	0.516949i	$-0.827068\pi$
$157$	−10.4792	+	6.05019i	−0.836333	+	0.482857i	0.0196828	+	0.999806i	$0.493734\pi$
$158$	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	0.254199	−	0.967152i	$-0.418188\pi$
$163$	−5.82538	−	3.36329i	−0.456279	−	0.263433i	−0.710478	+	0.703719i	$0.751521\pi$
$164$	−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	$0.0112891\pi$
$167$			0.916442i			0.0709164i	−0.999371	+	0.0354582i	$0.988711\pi$
$168$	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	0.725933	−	0.687765i	$-0.241408\pi$
$173$	6.48805	+	3.74588i	0.493277	+	0.284794i	−0.232656	+	0.972559i	$0.574742\pi$
$174$	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	0.997829	+	0.0658544i	$0.0209773\pi$
$179$	7.43805	+	12.8831i	0.555946	+	0.962927i	−0.441883	+	0.897073i	$0.645689\pi$
$180$		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	−0.0472996	−	0.998881i	$-0.515062\pi$
$191$	11.6285	−	20.1411i	0.841406	−	1.45736i	0.888706	−	0.458478i	$-0.151605\pi$
$192$	−7.69180	+	4.44086i	−0.555108	+	0.320492i
$193$	6.23697	−	3.60092i	0.448947	−	0.259200i	−0.258439	−	0.966028i	$-0.583208\pi$
$193$	6.23697	−	3.60092i	0.448947	−	0.259200i	0.707385	+	0.706828i	$0.249875\pi$
$194$	−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	$-0.761986\pi$
$197$		−	19.0881i		−	1.35997i	0.733226	−	0.679985i	$-0.238014\pi$
$198$	−5.04993	−	2.91558i	−0.358883	−	0.207201i
$199$	10.4170	+	18.0427i	0.738440	+	1.27902i	0.953197	+	0.302349i	$0.0977707\pi$
$199$	10.4170	+	18.0427i	0.738440	+	1.27902i	−0.214757	+	0.976668i	$0.568896\pi$
$200$		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	$0.0381664\pi$
$223$			3.57250i			0.239232i	−0.992820	+	0.119616i	$0.961834\pi$
$224$	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	0.0138218	−	0.999904i	$-0.495600\pi$
$227$	13.3591	−	7.71289i	0.886675	−	0.511922i	0.872854	+	0.487982i	$0.162267\pi$
$228$	−2.10106	+	1.21305i	−0.139146	+	0.0803360i
$229$	7.66427	−	13.2749i	0.506469	−	0.877230i	−0.493503	−	0.869744i	$-0.664284\pi$
$229$	7.66427	−	13.2749i	0.506469	−	0.877230i	0.999972	−	0.00748587i	$-0.00238285\pi$
$230$		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	0.949149	−	0.314829i	$-0.101947\pi$
$233$	17.5704	+	10.1443i	1.15107	+	0.664572i	0.201925	+	0.979401i	$0.435280\pi$
$234$	−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	−0.997220	−	0.0745189i	$-0.976258\pi$
$241$	−8.74236	−	15.1422i	−0.563145	−	0.975396i	0.434074	−	0.900877i	$-0.357075\pi$
$242$	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	−0.245378	−	0.969427i	$-0.578912\pi$
$257$	−19.3596	−	11.1772i	−1.20762	−	0.697218i	−0.962238	+	0.272210i	$0.912246\pi$
$258$			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	0.340391	−	0.940284i	$-0.389441\pi$
$263$	21.4862	−	12.4051i	1.32490	−	0.764929i	0.984505	+	0.175355i	$0.0561073\pi$
$264$	−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	0.998787	+	0.0492453i	$0.0156816\pi$
$269$	8.89013	+	15.3982i	0.542041	+	0.938843i	−0.456746	+	0.889597i	$0.650985\pi$
$270$		0			0
$271$	−8.56949	+	14.8428i	−0.520559	+	0.901635i	0.479155	+	0.877730i	$0.340943\pi$
$271$	−8.56949	+	14.8428i	−0.520559	+	0.901635i	−0.999714	+	0.0239050i	$0.992390\pi$
$272$			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	−0.423101	−	0.906082i	$-0.639058\pi$
$277$	2.49714	−	1.44173i	0.150039	−	0.0866250i	0.573140	+	0.819458i	$0.305725\pi$
$278$	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	−0.706983	−	0.707231i	$-0.749944\pi$
$283$	−7.53644	+	4.35117i	−0.447995	+	0.258650i	0.258988	+	0.965881i	$0.416611\pi$
$284$	−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	$-0.802602\pi$
$293$		−	19.8954i		−	1.16230i	0.813796	−	0.581151i	$-0.197398\pi$
$294$	−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	$-0.951475\pi$
$307$		−	5.32151i		−	0.303714i	0.988402	−	0.151857i	$-0.0485254\pi$
$308$	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	0.837904	−	0.545817i	$-0.183781\pi$
$311$	−0.947706	−	1.64147i	−0.0537395	−	0.0930795i	−0.891644	+	0.452738i	$0.850447\pi$
$312$	−16.5765	+	9.57045i	−0.938460	+	0.541820i
$313$	−22.9696	−	13.2615i	−1.29832	−	0.749585i	−0.318205	−	0.948022i	$-0.603080\pi$
$313$	−22.9696	−	13.2615i	−1.29832	−	0.749585i	−0.980114	+	0.198437i	$0.936413\pi$
$314$	14.8675			0.839020
$315$		0			0
$316$	0.407557			0.0229268
$317$	−13.5305	−	7.81185i	−0.759950	−	0.438757i	0.0693277	−	0.997594i	$-0.477915\pi$
$317$	−13.5305	−	7.81185i	−0.759950	−	0.438757i	−0.829278	+	0.558837i	$0.811248\pi$
$318$	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	−0.805323	−	0.592837i	$-0.798008\pi$
$331$	2.01493	−	3.48996i	0.110751	−	0.191826i	0.916073	+	0.401011i	$0.131341\pi$
$332$	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	$0.0248566\pi$
$337$			2.86415i			0.156020i	−0.996953	+	0.0780100i	$0.975143\pi$
$338$	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	−0.440451	−	0.897777i	$-0.645181\pi$
$347$	2.17613	−	1.25639i	0.116821	−	0.0674466i	0.557272	+	0.830330i	$0.311848\pi$
$348$	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	−0.920159	−	0.391546i	$-0.871941\pi$
$353$	−19.5614	+	11.2938i	−1.04115	+	0.601108i	−0.120991	+	0.992654i	$0.538607\pi$
$354$	−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	−0.870505	−	0.492159i	$-0.836208\pi$
$359$	−0.171108	+	0.296367i	−0.00903072	+	0.0156417i	0.861475	+	0.507800i	$0.169541\pi$
$360$		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	−0.424249	−	0.905546i	$-0.639462\pi$
$367$	2.83244	−	1.63531i	0.147852	−	0.0853624i	0.572101	+	0.820183i	$0.306129\pi$
$368$	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	0.768606	−	0.639722i	$-0.220951\pi$
$373$	11.5665	+	6.67795i	0.598893	+	0.345771i	−0.169713	+	0.985494i	$0.554284\pi$
$374$	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	−0.0351693	−	0.999381i	$-0.511197\pi$
$383$	−17.9704	−	10.3752i	−0.918244	−	0.530148i	−0.883074	+	0.469233i	$0.844530\pi$
$384$	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	0.951535	−	0.307542i	$-0.0995063\pi$
$389$	4.13057	+	7.15437i	0.209428	+	0.362741i	−0.742106	+	0.670282i	$0.766173\pi$
$390$		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	0.931892	−	0.362736i	$-0.118157\pi$
$397$	21.5926	+	12.4665i	1.08370	+	0.625674i	0.151807	+	0.988410i	$0.451491\pi$
$398$		−	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	−0.760889	−	0.648882i	$-0.775237\pi$
$401$	3.63461	−	6.29532i	0.181504	−	0.314373i	0.942393	+	0.334508i	$0.108570\pi$
$402$	−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	−0.856287	−	0.516500i	$-0.827234\pi$
$409$	−17.7048	−	30.6656i	−0.875446	−	1.51632i	−0.0191590	−	0.999816i	$-0.506099\pi$
$410$		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	0.950127	−	0.311864i	$-0.100953\pi$
$431$	4.25553	+	7.37079i	0.204982	+	0.355039i	−0.745145	+	0.666902i	$0.767620\pi$
$432$	−2.40657	−	1.38943i	−0.115786	−	0.0668491i
$433$			20.8010i			0.999631i	0.866132	+	0.499816i	$0.166599\pi$
$433$			20.8010i			0.999631i	−0.866132	+	0.499816i	$0.833401\pi$
$434$	−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	−0.705267	−	0.708941i	$-0.749173\pi$
$439$	5.47542	−	9.48370i	0.261327	−	0.452632i	0.966595	+	0.256309i	$0.0825064\pi$
$440$		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	−0.993912	−	0.110177i	$-0.964858\pi$
$443$	−33.3874	−	19.2762i	−1.58628	−	0.915842i	−0.592372	−	0.805664i	$-0.701809\pi$
$444$	−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	0.572886	−	0.819635i	$-0.305824\pi$
$457$	3.19603	+	1.84523i	0.149504	+	0.0863160i	−0.423382	+	0.905951i	$0.639157\pi$
$458$	−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	$-0.963104\pi$
$463$		−	4.97717i		−	0.231309i	0.993290	−	0.115654i	$-0.0368965\pi$
$464$	−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	0.634062	−	0.773282i	$-0.281387\pi$
$467$	6.08133	+	3.51106i	0.281410	+	0.162472i	−0.352651	+	0.935755i	$0.614720\pi$
$468$		−	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	0.741127	−	0.671364i	$-0.234291\pi$
$479$	−4.61478	−	7.99304i	−0.210855	−	0.365211i	−0.951982	+	0.306153i	$0.900958\pi$
$480$		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	−0.204998	−	0.978762i	$-0.565719\pi$
$487$	11.9198	−	6.88189i	0.540137	−	0.311848i	0.745134	+	0.666914i	$0.232385\pi$
$488$	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	−0.999815	−	0.0192154i	$-0.993883\pi$
$499$	−10.7954	+	18.6981i	−0.483267	+	0.837042i	0.516549	+	0.856258i	$0.327217\pi$
$500$		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	$-0.733878\pi$
$503$		−	33.2826i		−	1.48400i	0.670402	−	0.741998i	$-0.266122\pi$
$504$	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	−0.570552	−	0.821261i	$-0.693271\pi$
$509$	9.61002	−	16.6450i	0.425957	−	0.737779i	0.996509	+	0.0834823i	$0.0266042\pi$
$510$		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	0.860679	−	0.509148i	$-0.170039\pi$
$521$	−0.241845	−	0.418887i	−0.0105954	−	0.0183518i	−0.871274	+	0.490796i	$0.836706\pi$
$522$	4.25627	−	2.45736i	0.186292	−	0.107556i
$523$	−5.46760	−	3.15672i	−0.239082	−	0.138034i	0.375673	−	0.926752i	$-0.377412\pi$
$523$	−5.46760	−	3.15672i	−0.239082	−	0.138034i	−0.614755	+	0.788718i	$0.710745\pi$
$524$	−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	−0.985332	−	0.170646i	$-0.945415\pi$
$541$	−8.02177	+	13.8941i	−0.344883	+	0.597355i	0.640450	+	0.768000i	$0.278748\pi$
$542$	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	$-0.802403\pi$
$547$		−	27.2078i		−	1.16332i	0.813432	−	0.581660i	$-0.197597\pi$
$548$	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	−0.253393	−	0.967364i	$-0.581546\pi$
$557$	10.8015	−	6.23622i	0.457672	−	0.264237i	0.711065	+	0.703126i	$0.248213\pi$
$558$	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	−0.760265	−	0.649613i	$-0.774931\pi$
$563$	−13.7102	+	7.91558i	−0.577815	+	0.333602i	0.182449	+	0.983215i	$0.441597\pi$
$564$	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	−0.526505	−	0.850172i	$-0.676498\pi$
$569$	11.2832	−	19.5431i	0.473018	−	0.819291i	0.999523	+	0.0308807i	$0.00983121\pi$
$570$		0			0
$571$	−5.65899	−	9.80166i	−0.236821	−	0.410187i	0.722979	−	0.690870i	$-0.242772\pi$
$571$	−5.65899	−	9.80166i	−0.236821	−	0.410187i	−0.959800	+	0.280683i	$0.909439\pi$
$572$	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	0.0191524	−	0.999817i	$-0.493903\pi$
$577$	21.4889	−	12.4066i	0.894595	−	0.516495i	0.875443	+	0.483322i	$0.160570\pi$
$578$	−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	$0.0260516\pi$
$587$			3.96139i			0.163504i	−0.996653	+	0.0817520i	$0.973948\pi$
$588$	−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	0.387507	−	0.921867i	$-0.373336\pi$
$593$	−5.28673	−	3.05229i	−0.217100	−	0.125343i	−0.604607	+	0.796524i	$0.706670\pi$
$594$	−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	0.999973	+	0.00732860i	$0.00233279\pi$
$599$	12.3922	+	21.4640i	0.506333	+	0.876995i	−0.493640	+	0.869666i	$0.664334\pi$
$600$		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	0.772237	−	0.635335i	$-0.219138\pi$
$607$	14.9829	+	8.65040i	0.608138	+	0.351109i	−0.164098	+	0.986444i	$0.552471\pi$
$608$		−	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	−0.205883	−	0.978577i	$-0.566006\pi$
$613$	13.3363	−	7.69972i	0.538648	−	0.310989i	0.744531	+	0.667588i	$0.232673\pi$
$614$	−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	$0.0560505\pi$
$617$			8.70273i			0.350359i	−0.984537	+	0.175179i	$0.943949\pi$
$618$	15.1834	+	8.76614i	0.610766	+	0.352626i
$619$	−3.57547	−	6.19290i	−0.143710	−	0.248913i	0.785181	−	0.619267i	$-0.212570\pi$
$619$	−3.57547	−	6.19290i	−0.143710	−	0.248913i	−0.928891	+	0.370353i	$0.879237\pi$
$620$		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	0.578058	−	0.815996i	$-0.303811\pi$
$641$	−10.5739	−	18.3145i	−0.417644	−	0.723381i	−0.995702	+	0.0926149i	$0.970477\pi$
$642$	−2.30779	−	1.33241i	−0.0910813	−	0.0525858i
$643$			29.4981i			1.16329i	0.813442	+	0.581646i	$0.197591\pi$
$643$			29.4981i			1.16329i	−0.813442	+	0.581646i	$0.802409\pi$
$644$	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	−0.898130	−	0.439731i	$-0.855074\pi$
$647$	−24.5809	+	14.1918i	−0.966377	+	0.557938i	−0.0682470	+	0.997668i	$0.521741\pi$
$648$	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	0.839469	−	0.543408i	$-0.182866\pi$
$653$	20.1517	+	11.6346i	0.788598	+	0.455297i	−0.0508707	+	0.998705i	$0.516200\pi$
$654$	−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	0.976426	+	0.215855i	$0.0692537\pi$
$661$	17.3580	+	30.0650i	0.675148	+	1.16939i	−0.301277	+	0.953537i	$0.597413\pi$
$662$	−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	$0.136001\pi$
$673$			21.4998i			0.828757i	−0.910105	+	0.414378i	$0.863999\pi$
$674$	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	−0.973938	−	0.226815i	$-0.927169\pi$
$677$	−43.1225	−	24.8968i	−1.65733	−	0.956862i	−0.683396	−	0.730048i	$-0.739498\pi$
$678$			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	−0.918661	−	0.395047i	$-0.870728\pi$
$683$	−27.0717	+	15.6299i	−1.03587	+	0.598060i	−0.117210	+	0.993107i	$0.537395\pi$
$684$	−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	−0.521144	−	0.853469i	$-0.674495\pi$
$691$	12.5797	−	21.7887i	0.478554	−	0.828879i	0.999698	+	0.0245894i	$0.00782784\pi$
$692$		−	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	−0.971254	−	0.238045i	$-0.923493\pi$
$709$	−7.44157	+	12.8892i	−0.279474	+	0.484063i	0.691780	+	0.722108i	$0.256827\pi$
$710$		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	−0.291340	−	0.956620i	$-0.594101\pi$
$719$	18.3084	−	31.7110i	0.682787	−	1.18262i	0.974127	−	0.226002i	$-0.0725655\pi$
$720$		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	$-0.917245\pi$
$727$		−	13.8624i		−	0.514129i	0.966394	−	0.257064i	$-0.0827553\pi$
$728$	−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	0.922150	−	0.386833i	$-0.126431\pi$
$733$	28.3794	+	16.3849i	1.04822	+	0.605189i	0.126068	+	0.992022i	$0.459764\pi$
$734$	−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	0.998318	+	0.0579700i	$0.0184628\pi$
$739$	14.9342	+	25.8668i	0.549363	+	0.951524i	−0.448956	+	0.893554i	$0.648204\pi$
$740$		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	$0.363190\pi$
$743$			49.5577i			1.81810i	−0.416691	+	0.909048i	$0.636810\pi$
$744$	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	−0.799400	−	0.600799i	$-0.794849\pi$
$751$	3.30517	−	5.72473i	0.120607	−	0.208898i	0.920007	+	0.391901i	$0.128182\pi$
$752$	−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	$-0.959310\pi$
$757$		−	7.01509i		−	0.254968i	0.991841	−	0.127484i	$-0.0406901\pi$
$758$	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	−0.959500	−	0.281708i	$-0.909099\pi$
$761$	−6.50438	+	11.2659i	−0.235783	+	0.408389i	0.723717	+	0.690097i	$0.242432\pi$
$762$		−	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	−0.832478	−	0.554058i	$-0.813079\pi$
$773$	−21.3773	+	12.3422i	−0.768890	+	0.443919i	0.0635887	+	0.997976i	$0.479745\pi$
$774$	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	−0.723105	−	0.690738i	$-0.757286\pi$
$787$	−13.6470	+	7.87908i	−0.486462	+	0.280859i	0.236644	+	0.971596i	$0.423953\pi$
$788$	−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	$0.0906125\pi$
$797$			15.8568i			0.561677i	−0.959755	+	0.280838i	$0.909388\pi$
$798$	−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	0.788668	−	0.614819i	$-0.210771\pi$
$809$	−3.92840	−	6.80419i	−0.138115	−	0.239223i	−0.926783	+	0.375597i	$0.877438\pi$
$810$		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	−0.927531	−	0.373747i	$-0.878073\pi$
$821$	−4.01403	+	6.95250i	−0.140091	+	0.242644i	0.787440	+	0.616391i	$0.211406\pi$
$822$	19.6559	−	11.3484i	0.685579	−	0.395819i
$823$	−19.2881	+	11.1360i	−0.672342	+	0.388177i	−0.796964	−	0.604027i	$-0.793562\pi$
$823$	−19.2881	+	11.1360i	−0.672342	+	0.388177i	0.124621	+	0.992204i	$0.460228\pi$
$824$	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	$0.378667\pi$
$827$			53.3872i			1.85645i	−0.372015	+	0.928227i	$0.621333\pi$
$828$	−2.11507	−	1.22114i	−0.0735037	−	0.0424374i
$829$	−14.4223	−	24.9801i	−0.500906	−	0.867594i	−0.999999	−	0.00104627i	$-0.999667\pi$
$829$	−14.4223	−	24.9801i	−0.500906	−	0.867594i	0.499094	−	0.866548i	$-0.333666\pi$
$830$		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	$-0.809618\pi$
$853$		−	32.8905i		−	1.12615i	0.826406	−	0.563074i	$-0.190382\pi$
$854$	−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	−0.0439208	−	0.999035i	$-0.513985\pi$
$857$	23.3994	−	13.5097i	0.799308	−	0.461481i	0.843229	+	0.537554i	$0.180652\pi$
$858$	31.5900	−	18.2385i	1.07846	−	0.622652i
$859$	24.0537	−	41.6622i	0.820702	−	1.42150i	−0.0844589	−	0.996427i	$-0.526916\pi$
$859$	24.0537	−	41.6622i	0.820702	−	1.42150i	0.905161	−	0.425070i	$-0.139750\pi$
$860$		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	0.642379	−	0.766387i	$-0.277947\pi$
$863$	8.80891	+	5.08582i	0.299859	+	0.173123i	−0.342521	+	0.939510i	$0.611281\pi$
$864$	−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	−0.147576	−	0.989051i	$-0.547147\pi$
$877$	−31.9214	−	18.4298i	−1.07791	−	0.622330i	−0.930331	+	0.366720i	$0.880481\pi$
$878$	−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	$-0.794298\pi$
$883$		−	35.7880i		−	1.20436i	0.798359	−	0.602181i	$-0.205702\pi$
$884$	−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	0.967626	−	0.252390i	$-0.0812166\pi$
$887$	36.7178	+	21.1990i	1.23286	+	0.711793i	0.265237	+	0.964183i	$0.414550\pi$
$888$			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	0.511024	−	0.859567i	$-0.329266\pi$
$907$	45.5042	−	26.2719i	1.51094	−	0.872343i	0.999918	−	0.0127763i	$-0.00406693\pi$
$908$	−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	−0.996582	−	0.0826063i	$-0.973676\pi$
$919$	−12.9370	+	22.4075i	−0.426752	+	0.739156i	0.569830	+	0.821762i	$0.307009\pi$
$920$		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	−0.880236	−	0.474536i	$-0.842616\pi$
$929$	−0.888730	+	1.53933i	−0.0291583	+	0.0505036i	0.851078	+	0.525039i	$0.175949\pi$
$930$		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	$0.403841\pi$
$937$			58.4486i			1.90943i	−0.297518	+	0.954716i	$0.596159\pi$
$938$	−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	0.833318	−	0.552793i	$-0.186438\pi$
$941$	−1.90416	−	3.29811i	−0.0620739	−	0.107515i	−0.895392	+	0.445278i	$0.853105\pi$
$942$	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	−0.998621	−	0.0524995i	$-0.983281\pi$
$947$	−47.4955	−	27.4216i	−1.54340	−	0.891081i	−0.544776	−	0.838581i	$-0.683385\pi$
$948$	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	$-0.792596\pi$
$953$		−	37.4426i		−	1.21288i	0.795128	−	0.606442i	$-0.207404\pi$
$954$	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	$0.172090\pi$
$967$			32.0098i			1.02937i	−0.857381	+	0.514683i	$0.827910\pi$
$968$	−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	0.0746266	+	0.997212i	$0.476223\pi$
$971$	−25.7481	+	44.5971i	−0.826297	+	1.43119i	−0.900924	+	0.433977i	$0.857110\pi$
$972$			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	−0.542794	−	0.839866i	$-0.682633\pi$
$977$	−2.71451	+	1.56722i	−0.0868449	+	0.0501399i	0.455949	+	0.890006i	$0.349300\pi$
$978$	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	0.232437	−	0.972611i	$-0.425330\pi$
$983$	37.3400	−	21.5583i	1.19096	−	0.687602i	0.958525	+	0.285009i	$0.0919967\pi$
$984$	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	0.946263	−	0.323398i	$-0.104825\pi$
$991$	6.07758	+	10.5267i	0.193061	+	0.334391i	−0.753202	+	0.657789i	$0.771492\pi$
$992$	−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	−0.154011	−	0.988069i	$-0.549219\pi$
$997$	19.7244	−	11.3879i	0.624677	−	0.360657i	0.778688	+	0.627412i	$0.215886\pi$
$998$	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.499.3		16
5.2	odd	4		525.2.i.j.226.3	yes	8
5.3	odd	4		525.2.i.i.226.2	yes	8
5.4	even	2	inner	525.2.r.h.499.6		16
7.4	even	3	inner	525.2.r.h.424.6		16
35.2	odd	12		3675.2.a.br.1.2		4
35.4	even	6	inner	525.2.r.h.424.3		16
35.12	even	12		3675.2.a.bq.1.2		4
35.18	odd	12		525.2.i.i.151.2	✓	8
35.23	odd	12		3675.2.a.bw.1.3		4
35.32	odd	12		525.2.i.j.151.3	yes	8
35.33	even	12		3675.2.a.bx.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.i.i.151.2	✓	8	35.18	odd	12
525.2.i.i.226.2	yes	8	5.3	odd	4
525.2.i.j.151.3	yes	8	35.32	odd	12
525.2.i.j.226.3	yes	8	5.2	odd	4
525.2.r.h.424.3		16	35.4	even	6	inner
525.2.r.h.424.6		16	7.4	even	3	inner
525.2.r.h.499.3		16	1.1	even	1	trivial
525.2.r.h.499.6		16	5.4	even	2	inner
3675.2.a.bq.1.2		4	35.12	even	12
3675.2.a.br.1.2		4	35.2	odd	12
3675.2.a.bw.1.3		4	35.23	odd	12
3675.2.a.bx.1.3		4	35.33	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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