LMFDB - Embedded newform 525.2.i.i.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(151,525)]

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, 0, 4]))

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

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

chi := DirichletCharacter("525.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.i (of order $3$, degree $2$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 8x^{6} - 3x^{5} + 50x^{4} - 27x^{3} + 53x^{2} + 20x + 16 $ x^8 - x^7 + 8x^6 - 3x^5 + 50x^4 - 27x^3 + 53x^2 + 20x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.2
Root			$0.614340 + 1.06407i$ of defining polynomial
Character	$\chi$	$=$	525.151
Dual form			525.2.i.i.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.614340 - 1.06407i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.245174 - 0.424653i) q^{4} -1.22868 q^{6} +(1.24517 + 2.33443i) q^{7} -3.05984 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.614340 - 1.06407i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.245174 - 0.424653i) q^{4} -1.22868 q^{6} +(1.24517 + 2.33443i) q^{7} -3.05984 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.37294 - 4.11005i) q^{11} +(-0.245174 - 0.424653i) q^{12} -6.25553 q^{13} +(1.71903 - 2.75908i) q^{14} +(1.38943 + 2.40657i) q^{16} +(3.14426 - 5.44602i) q^{17} +(-0.614340 + 1.06407i) q^{18} +(-2.47385 - 4.28484i) q^{19} +(2.64426 + 0.0888607i) q^{21} -5.83116 q^{22} +(-2.49035 - 4.31341i) q^{23} +(-1.52992 + 2.64990i) q^{24} +(3.84302 + 6.65630i) q^{26} -1.00000 q^{27} +(1.29661 + 0.0435726i) q^{28} +4.00000 q^{29} +(-0.829594 + 1.43690i) q^{31} +(-1.35267 + 2.34290i) q^{32} +(-2.37294 - 4.11005i) q^{33} -7.72657 q^{34} -0.490347 q^{36} +(2.21903 + 3.84347i) q^{37} +(-3.03957 + 5.26469i) q^{38} +(-3.12776 + 5.41745i) q^{39} +1.30782 q^{41} +(-1.52992 - 2.86826i) q^{42} +10.2362 q^{43} +(-1.16356 - 2.01535i) q^{44} +(-3.05984 + 5.29980i) q^{46} +(-1.88259 - 3.26074i) q^{47} +2.77886 q^{48} +(-3.89908 + 5.81353i) q^{49} +(-3.14426 - 5.44602i) q^{51} +(-1.53369 + 2.65643i) q^{52} +(-3.60162 + 6.23818i) q^{53} +(0.614340 + 1.06407i) q^{54} +(-3.81003 - 7.14296i) q^{56} -4.94771 q^{57} +(-2.45736 - 4.25627i) q^{58} +(-0.117410 + 0.203359i) q^{59} +(2.50000 + 4.33013i) q^{61} +2.03861 q^{62} +(1.39908 - 2.24556i) q^{63} +8.88173 q^{64} +(-2.91558 + 5.04993i) q^{66} +(-1.24517 + 2.15670i) q^{67} +(-1.54178 - 2.67044i) q^{68} -4.98069 q^{69} +6.06598 q^{71} +(1.52992 + 2.64990i) q^{72} +(6.24588 - 10.8182i) q^{73} +(2.72647 - 4.72239i) q^{74} -2.42609 q^{76} +(12.5493 + 0.421722i) q^{77} +7.68604 q^{78} +(0.415579 + 0.719805i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-0.803447 - 1.39161i) q^{82} -1.14954 q^{83} +(0.686038 - 1.10111i) q^{84} +(-6.28852 - 10.8920i) q^{86} +(2.00000 - 3.46410i) q^{87} +(-7.26081 + 12.5761i) q^{88} +(-1.14426 - 1.98191i) q^{89} +(-7.78922 - 14.6031i) q^{91} -2.44227 q^{92} +(0.829594 + 1.43690i) q^{93} +(-2.31310 + 4.00641i) q^{94} +(1.35267 + 2.34290i) q^{96} -0.476664 q^{97} +(8.58135 + 0.577407i) q^{98} -4.74588 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 4 q^{3} - 7 q^{4} - 2 q^{6} + q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - q^2 + 4 * q^3 - 7 * q^4 - 2 * q^6 + q^7 + 6 * q^8 - 4 * q^9	$ 8 q - q^{2} + 4 q^{3} - 7 q^{4} - 2 q^{6} + q^{7} + 6 q^{8} - 4 q^{9} - 8 q^{11} + 7 q^{12} - 14 q^{13} - 12 q^{14} - 17 q^{16} + 6 q^{17} - q^{18} - 3 q^{19} + 2 q^{21} - 24 q^{22} - 2 q^{23} + 3 q^{24} + 19 q^{26} - 8 q^{27} + 15 q^{28} + 32 q^{29} - 9 q^{31} - 17 q^{32} + 8 q^{33} + 28 q^{34} + 14 q^{36} - 8 q^{37} - 27 q^{38} - 7 q^{39} + 8 q^{41} + 3 q^{42} + 10 q^{43} - 26 q^{44} + 6 q^{46} - 6 q^{47} - 34 q^{48} - 21 q^{49} - 6 q^{51} + 35 q^{52} + 6 q^{53} + q^{54} - 21 q^{56} - 6 q^{57} - 4 q^{58} - 10 q^{59} + 20 q^{61} + 88 q^{62} + q^{63} + 42 q^{64} - 12 q^{66} - q^{67} - 8 q^{68} - 4 q^{69} + 44 q^{71} - 3 q^{72} - 4 q^{73} + 21 q^{74} - 46 q^{76} + 32 q^{77} + 38 q^{78} - 8 q^{79} - 4 q^{81} + 8 q^{82} + 4 q^{83} - 18 q^{84} - 12 q^{86} + 16 q^{87} - 28 q^{88} + 10 q^{89} + 21 q^{91} - 132 q^{92} + 9 q^{93} - 22 q^{94} + 17 q^{96} - 24 q^{97} + 67 q^{98} + 16 q^{99}+O(q^{100}) $ 8 * q - q^2 + 4 * q^3 - 7 * q^4 - 2 * q^6 + q^7 + 6 * q^8 - 4 * q^9 - 8 * q^11 + 7 * q^12 - 14 * q^13 - 12 * q^14 - 17 * q^16 + 6 * q^17 - q^18 - 3 * q^19 + 2 * q^21 - 24 * q^22 - 2 * q^23 + 3 * q^24 + 19 * q^26 - 8 * q^27 + 15 * q^28 + 32 * q^29 - 9 * q^31 - 17 * q^32 + 8 * q^33 + 28 * q^34 + 14 * q^36 - 8 * q^37 - 27 * q^38 - 7 * q^39 + 8 * q^41 + 3 * q^42 + 10 * q^43 - 26 * q^44 + 6 * q^46 - 6 * q^47 - 34 * q^48 - 21 * q^49 - 6 * q^51 + 35 * q^52 + 6 * q^53 + q^54 - 21 * q^56 - 6 * q^57 - 4 * q^58 - 10 * q^59 + 20 * q^61 + 88 * q^62 + q^63 + 42 * q^64 - 12 * q^66 - q^67 - 8 * q^68 - 4 * q^69 + 44 * q^71 - 3 * q^72 - 4 * q^73 + 21 * q^74 - 46 * q^76 + 32 * q^77 + 38 * q^78 - 8 * q^79 - 4 * q^81 + 8 * q^82 + 4 * q^83 - 18 * q^84 - 12 * q^86 + 16 * q^87 - 28 * q^88 + 10 * q^89 + 21 * q^91 - 132 * q^92 + 9 * q^93 - 22 * q^94 + 17 * q^96 - 24 * q^97 + 67 * q^98 + 16 * 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 $

$2$	−0.614340	−	1.06407i	−0.434404	−	0.752409i	0.562843	−	0.826564i	$-0.309708\pi$
$2$	−0.614340	−	1.06407i	−0.434404	−	0.752409i	−0.997247	+	0.0741545i	$0.976374\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.245174	−	0.424653i	0.122587	−	0.212327i
$5$		0			0
$5$		0			0
$6$	−1.22868			−0.501606
$7$	1.24517	+	2.33443i	0.470631	+	0.882330i
$7$	1.24517	+	2.33443i	0.470631	+	0.882330i
$8$	−3.05984			−1.08182
$9$	−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	$-0.0871197\pi$
$12$	−0.245174	−	0.424653i	−0.0707755	−	0.122587i
$13$	−6.25553			−1.73497			−0.867486	−	0.497462i	$-0.834265\pi$
$13$	−6.25553			−1.73497			−0.867486	+	0.497462i	$0.834265\pi$
$14$	1.71903	−	2.75908i	0.459429	−	0.737395i
$15$		0			0
$16$	1.38943	+	2.40657i	0.347358	+	0.601642i
$17$	3.14426	−	5.44602i	0.762595	−	1.32085i	−0.178914	−	0.983865i	$-0.557258\pi$
$17$	3.14426	−	5.44602i	0.762595	−	1.32085i	0.941509	−	0.336988i	$-0.109408\pi$
$18$	−0.614340	+	1.06407i	−0.144801	+	0.250803i
$19$	−2.47385	−	4.28484i	−0.567541	−	0.983009i	−0.996808	−	0.0798321i	$-0.974562\pi$
$19$	−2.47385	−	4.28484i	−0.567541	−	0.983009i	0.429268	−	0.903177i	$-0.358772\pi$
$20$		0			0
$21$	2.64426	+	0.0888607i	0.577025	+	0.0193910i
$22$	−5.83116			−1.24321
$23$	−2.49035	−	4.31341i	−0.519273	−	0.899408i	−0.999749	−	0.0223998i	$-0.992869\pi$
$23$	−2.49035	−	4.31341i	−0.519273	−	0.899408i	0.480476	−	0.877008i	$-0.340464\pi$
$24$	−1.52992	+	2.64990i	−0.312293	+	0.540908i
$25$		0			0
$26$	3.84302	+	6.65630i	0.753678	+	1.30541i
$27$	−1.00000			−0.192450
$28$	1.29661	+	0.0435726i	0.245035	+	0.00823445i
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$		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	$0.214272\pi$
$32$	−1.35267	+	2.34290i	−0.239121	+	0.414169i
$33$	−2.37294	−	4.11005i	−0.413075	−	0.715468i
$34$	−7.72657			−1.32510
$35$		0			0
$36$	−0.490347			−0.0817246
$37$	2.21903	+	3.84347i	0.364806	+	0.631862i	0.988745	−	0.149611i	$-0.0478021\pi$
$37$	2.21903	+	3.84347i	0.364806	+	0.631862i	−0.623939	+	0.781473i	$0.714469\pi$
$38$	−3.03957	+	5.26469i	−0.493084	+	0.854046i
$39$	−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	$0.467436\pi$
$42$	−1.52992	−	2.86826i	−0.236072	−	0.442582i
$43$	10.2362			1.56101			0.780505	−	0.625150i	$-0.214962\pi$
$43$	10.2362			1.56101			0.780505	+	0.625150i	$0.214962\pi$
$44$	−1.16356	−	2.01535i	−0.175414	−	0.303826i
$45$		0			0
$46$	−3.05984	+	5.29980i	−0.451149	+	0.781412i
$47$	−1.88259	−	3.26074i	−0.274604	−	0.475628i	0.695431	−	0.718593i	$-0.255213\pi$
$47$	−1.88259	−	3.26074i	−0.274604	−	0.475628i	−0.970035	+	0.242965i	$0.921880\pi$
$48$	2.77886			0.401095
$49$	−3.89908	+	5.81353i	−0.557012	+	0.830504i
$50$		0			0
$51$	−3.14426	−	5.44602i	−0.440284	−	0.762595i
$52$	−1.53369	+	2.65643i	−0.212685	+	0.368381i
$53$	−3.60162	+	6.23818i	−0.494720	+	0.856880i	−0.999981	−	0.00608595i	$-0.998063\pi$
$53$	−3.60162	+	6.23818i	−0.494720	+	0.856880i	0.505261	+	0.862966i	$0.331396\pi$
$54$	0.614340	+	1.06407i	0.0836010	+	0.144801i
$55$		0			0
$56$	−3.81003	−	7.14296i	−0.509137	−	0.954519i
$57$	−4.94771			−0.655340
$58$	−2.45736	−	4.25627i	−0.322667	−	0.558876i
$59$	−0.117410	+	0.203359i	−0.0152854	+	0.0264751i	−0.873567	−	0.486704i	$-0.838199\pi$
$59$	−0.117410	+	0.203359i	−0.0152854	+	0.0264751i	0.858282	+	0.513179i	$0.171532\pi$
$60$		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	$0.729619\pi$
$62$	2.03861			0.258904
$63$	1.39908	−	2.24556i	0.176268	−	0.282915i
$64$	8.88173			1.11022
$65$		0			0
$66$	−2.91558	+	5.04993i	−0.358883	+	0.621604i
$67$	−1.24517	+	2.15670i	−0.152122	+	0.263483i	−0.932007	−	0.362439i	$-0.881944\pi$
$67$	−1.24517	+	2.15670i	−0.152122	+	0.263483i	0.779885	+	0.625923i	$0.215277\pi$
$68$	−1.54178	−	2.67044i	−0.186968	−	0.323838i
$69$	−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	$0.382794\pi$
$72$	1.52992	+	2.64990i	0.180303	+	0.312293i
$73$	6.24588	−	10.8182i	0.731024	−	1.26617i	−0.225421	−	0.974261i	$-0.572376\pi$
$73$	6.24588	−	10.8182i	0.731024	−	1.26617i	0.956446	−	0.291910i	$-0.0942908\pi$
$74$	2.72647	−	4.72239i	0.316946	−	0.548966i
$75$		0			0
$76$	−2.42609			−0.278292
$77$	12.5493	+	0.421722i	1.43013	+	0.0480597i
$78$	7.68604			0.870272
$79$	0.415579	+	0.719805i	0.0467563	+	0.0809844i	0.888456	−	0.458961i	$-0.151778\pi$
$79$	0.415579	+	0.719805i	0.0467563	+	0.0809844i	−0.841700	+	0.539945i	$0.818445\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.803447	−	1.39161i	−0.0887259	−	0.153678i
$83$	−1.14954			−0.126178			−0.0630890	−	0.998008i	$-0.520095\pi$
$83$	−1.14954			−0.126178			−0.0630890	+	0.998008i	$0.520095\pi$
$84$	0.686038	−	1.10111i	0.0748528	−	0.120141i
$85$		0			0
$86$	−6.28852	−	10.8920i	−0.678108	−	1.17452i
$87$	2.00000	−	3.46410i	0.214423	−	0.371391i
$88$	−7.26081	+	12.5761i	−0.774004	+	1.34062i
$89$	−1.14426	−	1.98191i	−0.121291	−	0.210082i	0.798986	−	0.601350i	$-0.205370\pi$
$89$	−1.14426	−	1.98191i	−0.121291	−	0.210082i	−0.920277	+	0.391267i	$0.872037\pi$
$90$		0			0
$91$	−7.78922	−	14.6031i	−0.816532	−	1.53082i
$92$	−2.44227			−0.254624
$93$	0.829594	+	1.43690i	0.0860249	+	0.149000i
$94$	−2.31310	+	4.00641i	−0.238578	+	0.413229i
$95$		0			0
$96$	1.35267	+	2.34290i	0.138056	+	0.239121i
$97$	−0.476664			−0.0483979			−0.0241989	−	0.999707i	$-0.507704\pi$
$97$	−0.476664			−0.0483979			−0.0241989	+	0.999707i	$0.507704\pi$
$98$	8.58135	+	0.577407i	0.866847	+	0.0583269i
$99$	−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	$0.301965\pi$
$102$	−3.86329	+	6.69141i	−0.382522	+	0.662548i
$103$	7.13461	+	12.3575i	0.702994	+	1.21762i	0.967411	+	0.253212i	$0.0814871\pi$
$103$	7.13461	+	12.3575i	0.702994	+	1.21762i	−0.264417	+	0.964408i	$0.585180\pi$
$104$	19.1409			1.87692
$105$		0			0
$106$	8.85046			0.859633
$107$	1.08442	+	1.87827i	0.104835	+	0.181579i	0.913671	−	0.406455i	$-0.133235\pi$
$107$	1.08442	+	1.87827i	0.104835	+	0.181579i	−0.808836	+	0.588035i	$0.799902\pi$
$108$	−0.245174	+	0.424653i	−0.0235918	+	0.0408623i
$109$	−3.89908	+	6.75341i	−0.373465	+	0.646860i	−0.990096	−	0.140392i	$-0.955164\pi$
$109$	−3.89908	+	6.75341i	−0.373465	+	0.646860i	0.616631	+	0.787252i	$0.288497\pi$
$110$		0			0
$111$	4.43805			0.421241
$112$	−3.88787	+	6.24012i	−0.367369	+	0.589636i
$113$	15.4918			1.45734			0.728671	−	0.684864i	$-0.240139\pi$
$113$	15.4918			1.45734			0.728671	+	0.684864i	$0.240139\pi$
$114$	3.03957	+	5.26469i	0.284682	+	0.493084i
$115$		0			0
$116$	0.980695	−	1.69861i	0.0910552	−	0.157712i
$117$	3.12776	+	5.41745i	0.289162	+	0.500843i
$118$	0.288517			0.0265602
$119$	16.6285	+	0.558802i	1.52433	+	0.0512253i
$120$		0			0
$121$	−5.76167	−	9.97950i	−0.523788	−	0.907227i
$122$	3.07170	−	5.32034i	0.278098	−	0.481681i
$123$	0.653911	−	1.13261i	0.0589612	−	0.102124i
$124$	0.406789	+	0.704580i	0.0365308	+	0.0632731i
$125$		0			0
$126$	−3.24895	−	0.109181i	−0.289439	−	0.00972664i
$127$	11.7996			1.04704			0.523521	−	0.852013i	$-0.324618\pi$
$127$	11.7996			1.04704			0.523521	+	0.852013i	$0.324618\pi$
$128$	−2.75105	−	4.76497i	−0.243161	−	0.421167i
$129$	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	$0.777970\pi$
$132$	−2.32713			−0.202550
$133$	6.92226	−	11.1104i	0.600236	−	0.963393i
$134$	3.05984			0.264330
$135$		0			0
$136$	−9.62092	+	16.6639i	−0.824987	+	1.42892i
$137$	9.23622	−	15.9976i	0.789104	−	1.36677i	−0.137413	−	0.990514i	$-0.543879\pi$
$137$	9.23622	−	15.9976i	0.789104	−	1.36677i	0.926517	−	0.376254i	$-0.122788\pi$
$138$	3.05984	+	5.29980i	0.260471	+	0.451149i
$139$	2.66059			0.225669			0.112834	−	0.993614i	$-0.464007\pi$
$139$	2.66059			0.225669			0.112834	+	0.993614i	$0.464007\pi$
$140$		0			0
$141$	−3.76518			−0.317085
$142$	−3.72657	−	6.45461i	−0.312727	−	0.541659i
$143$	−14.8440	+	25.7105i	−1.24132	+	2.15002i
$144$	1.38943	−	2.40657i	0.115786	−	0.200547i
$145$		0			0
$146$	−15.3484			−1.27024
$147$	3.08512	+	6.28347i	0.254457	+	0.518252i
$148$	2.17619			0.178882
$149$	−7.29379	−	12.6332i	−0.597531	−	1.03495i	−0.993184	−	0.116554i	$-0.962815\pi$
$149$	−7.29379	−	12.6332i	−0.597531	−	1.03495i	0.395653	−	0.918400i	$-0.370518\pi$
$150$		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	$-0.0303224\pi$
$152$	7.56959	+	13.1109i	0.613975	+	1.06344i
$153$	−6.28852			−0.508396
$154$	−7.26081	−	13.6124i	−0.585092	−	1.09692i
$155$		0			0
$156$	1.53369	+	2.65643i	0.122794	+	0.212685i
$157$	6.05019	−	10.4792i	0.482857	−	0.836333i	−0.516949	−	0.856016i	$-0.672932\pi$
$157$	6.05019	−	10.4792i	0.482857	−	0.836333i	0.999806	+	0.0196828i	$0.00626562\pi$
$158$	0.510614	−	0.884409i	0.0406223	−	0.0703598i
$159$	3.60162	+	6.23818i	0.285627	+	0.494720i
$160$		0			0
$161$	6.96842	−	11.1845i	0.549188	−	0.881460i
$162$	1.22868			0.0965342
$163$	3.36329	+	5.82538i	0.263433	+	0.456279i	0.967152	−	0.254199i	$-0.0818119\pi$
$163$	3.36329	+	5.82538i	0.263433	+	0.456279i	−0.703719	+	0.710478i	$0.748479\pi$
$164$	0.320644	−	0.555371i	0.0250381	−	0.0433672i
$165$		0			0
$166$	0.706205	+	1.22318i	0.0548122	+	0.0949375i
$167$	0.916442			0.0709164			0.0354582	−	0.999371i	$-0.488711\pi$
$167$	0.916442			0.0709164			0.0354582	+	0.999371i	$0.488711\pi$
$168$	−8.09100	−	0.271899i	−0.624234	−	0.0209775i
$169$	26.1316			2.01013
$170$		0			0
$171$	−2.47385	+	4.28484i	−0.189180	+	0.327670i
$172$	2.50965	−	4.34685i	0.191359	−	0.331444i
$173$	−3.74588	−	6.48805i	−0.284794	−	0.493277i	0.687765	−	0.725933i	$-0.258592\pi$
$173$	−3.74588	−	6.48805i	−0.284794	−	0.493277i	−0.972559	+	0.232656i	$0.925258\pi$
$174$	−4.91472			−0.372584
$175$		0			0
$176$	13.1881			0.994094
$177$	0.117410	+	0.203359i	0.00882504	+	0.0152854i
$178$	−1.40593	+	2.43514i	−0.105379	+	0.182521i
$179$	−7.43805	+	12.8831i	−0.555946	+	0.962927i	0.441883	+	0.897073i	$0.354311\pi$
$179$	−7.43805	+	12.8831i	−0.555946	+	0.962927i	−0.997829	+	0.0658544i	$0.979023\pi$
$180$		0			0
$181$	−6.62760			−0.492626			−0.246313	−	0.969190i	$-0.579219\pi$
$181$	−6.62760			−0.492626			−0.246313	+	0.969190i	$0.579219\pi$
$182$	−10.7534	+	17.2595i	−0.797096	+	1.27936i
$183$	5.00000			0.369611
$184$	7.62006	+	13.1983i	0.561758	+	0.972994i
$185$		0			0
$186$	1.01931	−	1.76549i	0.0747391	−	0.129452i
$187$	−14.9223	−	25.8461i	−1.09122	−	1.89006i
$188$	−1.84625			−0.134651
$189$	−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	$0.515062\pi$
$192$	4.44086	−	7.69180i	0.320492	−	0.555108i
$193$	3.60092	−	6.23697i	0.259200	−	0.448947i	−0.706828	−	0.707385i	$-0.749875\pi$
$193$	3.60092	−	6.23697i	0.259200	−	0.448947i	0.966028	+	0.258439i	$0.0832079\pi$
$194$	0.292833	+	0.507202i	0.0210242	+	0.0364150i
$195$		0			0
$196$	1.51278	+	3.08108i	0.108056	+	0.220077i
$197$	−19.0881			−1.35997			−0.679985	−	0.733226i	$-0.738014\pi$
$197$	−19.0881			−1.35997			−0.679985	+	0.733226i	$0.738014\pi$
$198$	2.91558	+	5.04993i	0.207201	+	0.358883i
$199$	−10.4170	+	18.0427i	−0.738440	+	1.27902i	0.214757	+	0.976668i	$0.431104\pi$
$199$	−10.4170	+	18.0427i	−0.738440	+	1.27902i	−0.953197	+	0.302349i	$0.902229\pi$
$200$		0			0
$201$	1.24517	+	2.15670i	0.0878278	+	0.152122i
$202$	10.1839			0.716539
$203$	4.98069	+	9.33770i	0.349576	+	0.655378i
$204$	−3.08356			−0.215892
$205$		0			0
$206$	8.76614	−	15.1834i	0.610766	−	1.05788i
$207$	−2.49035	+	4.31341i	−0.173091	+	0.299803i
$208$	−8.69163	−	15.0544i	−0.602656	−	1.04383i
$209$	−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	$0.319728\pi$
$212$	1.76604	+	3.05888i	0.121292	+	0.210085i
$213$	3.03299	−	5.25329i	0.207817	−	0.359950i
$214$	1.33241	−	2.30779i	0.0910813	−	0.157757i
$215$		0			0
$216$	3.05984			0.208196
$217$	−4.38732	−	0.147437i	−0.297831	−	0.0100087i
$218$	9.58145			0.648938
$219$	−6.24588	−	10.8182i	−0.422057	−	0.731024i
$220$		0			0
$221$	−19.6690	+	34.0677i	−1.32308	+	2.29164i
$222$	−2.72647	−	4.72239i	−0.182989	−	0.316946i
$223$	−3.57250			−0.239232			−0.119616	−	0.992820i	$-0.538166\pi$
$223$	−3.57250			−0.239232			−0.119616	+	0.992820i	$0.538166\pi$
$224$	−7.15363	−	0.240399i	−0.477972	−	0.0160623i
$225$		0			0
$226$	−9.51720	−	16.4843i	−0.633074	−	1.09652i
$227$	−7.71289	+	13.3591i	−0.511922	+	0.886675i	0.487982	+	0.872854i	$0.337733\pi$
$227$	−7.71289	+	13.3591i	−0.511922	+	0.886675i	−0.999904	+	0.0138218i	$0.995600\pi$
$228$	−1.21305	+	2.10106i	−0.0803360	+	0.139146i
$229$	−7.66427	−	13.2749i	−0.506469	−	0.877230i	−0.999972	−	0.00748587i	$-0.997617\pi$
$229$	−7.66427	−	13.2749i	−0.506469	−	0.877230i	0.493503	−	0.869744i	$-0.335716\pi$
$230$		0			0
$231$	6.63988	−	10.6572i	0.436872	−	0.701190i
$232$	−12.2394			−0.803553
$233$	−10.1443	−	17.5704i	−0.664572	−	1.15107i	−0.979401	−	0.201925i	$-0.935280\pi$
$233$	−10.1443	−	17.5704i	−0.664572	−	1.15107i	0.314829	−	0.949149i	$-0.398053\pi$
$234$	3.84302	−	6.65630i	0.251226	−	0.435136i
$235$		0			0
$236$	0.0575715	+	0.0997167i	0.00374758	+	0.00649100i
$237$	0.831159			0.0539896
$238$	−9.62092	−	18.0371i	−0.623632	−	1.16917i
$239$	−11.8954			−0.769450			−0.384725	−	0.923031i	$-0.625704\pi$
$239$	−11.8954			−0.769450			−0.384725	+	0.923031i	$0.625704\pi$
$240$		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	$0.976258\pi$
$242$	−7.07924	+	12.2616i	−0.455071	+	0.788206i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	2.45174			0.156956
$245$		0			0
$246$	−1.60689			−0.102452
$247$	15.4753	+	26.8039i	0.984667	+	1.70549i
$248$	2.53842	−	4.39668i	0.161190	−	0.279189i
$249$	−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	$0.604694\pi$
$252$	−0.610568	−	1.14468i	−0.0384621	−	0.0721080i
$253$	−23.6378			−1.48609
$254$	−7.24895	−	12.5555i	−0.454839	−	0.787805i
$255$		0			0
$256$	5.50156	−	9.52899i	0.343848	−	0.595562i
$257$	−11.1772	−	19.3596i	−0.697218	−	1.20762i	−0.969427	−	0.245378i	$-0.921088\pi$
$257$	−11.1772	−	19.3596i	−0.697218	−	1.20762i	0.272210	−	0.962238i	$-0.412246\pi$
$258$	−12.5770			−0.783012
$259$	−6.20921	+	9.96594i	−0.385822	+	0.619253i
$260$		0			0
$261$	−2.00000	−	3.46410i	−0.123797	−	0.214423i
$262$	2.43364	−	4.21519i	0.150351	−	0.260415i
$263$	12.4051	−	21.4862i	0.764929	−	1.32490i	−0.175355	−	0.984505i	$-0.556107\pi$
$263$	12.4051	−	21.4862i	0.764929	−	1.32490i	0.940284	−	0.340391i	$-0.110559\pi$
$264$	7.26081	+	12.5761i	0.446872	+	0.774004i
$265$		0			0
$266$	−16.0748	−	0.540197i	−0.985611	−	0.0331216i
$267$	−2.28852			−0.140055
$268$	0.610568	+	1.05753i	0.0372964	+	0.0645992i
$269$	−8.89013	+	15.3982i	−0.542041	+	0.938843i	0.456746	+	0.889597i	$0.349015\pi$
$269$	−8.89013	+	15.3982i	−0.542041	+	0.938843i	−0.998787	+	0.0492453i	$0.984318\pi$
$270$		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	$-0.340943\pi$
$272$	17.4749			1.05957
$273$	−16.5412	−	0.555871i	−1.00112	−	0.0336428i
$274$	−22.6967			−1.37116
$275$		0			0
$276$	−1.22114	+	2.11507i	−0.0735037	+	0.127312i
$277$	−1.44173	+	2.49714i	−0.0866250	+	0.150039i	−0.906082	−	0.423101i	$-0.860942\pi$
$277$	−1.44173	+	2.49714i	−0.0866250	+	0.150039i	0.819458	+	0.573140i	$0.194275\pi$
$278$	−1.63451	−	2.83105i	−0.0980312	−	0.169795i
$279$	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	$0.189129\pi$
$282$	2.31310	+	4.00641i	0.137743	+	0.238578i
$283$	−4.35117	+	7.53644i	−0.258650	+	0.447995i	−0.965881	−	0.258988i	$-0.916611\pi$
$283$	−4.35117	+	7.53644i	−0.258650	+	0.447995i	0.707231	+	0.706983i	$0.249944\pi$
$284$	1.48722	−	2.57594i	0.0882502	−	0.152854i
$285$		0			0
$286$	36.4770			2.15693
$287$	1.62847	+	3.05301i	0.0961253	+	0.180214i
$288$	2.70534			0.159414
$289$	−11.2727	−	19.5249i	−0.663101	−	1.14853i
$290$		0			0
$291$	−0.238332	+	0.412803i	−0.0139713	+	0.0241989i
$292$	−3.06265	−	5.30466i	−0.179228	−	0.310432i
$293$	19.8954			1.16230			0.581151	−	0.813796i	$-0.302602\pi$
$293$	19.8954			1.16230			0.581151	+	0.813796i	$0.302602\pi$
$294$	4.79072	−	7.14296i	0.279401	−	0.416586i
$295$		0			0
$296$	−6.78986	−	11.7604i	−0.394653	−	0.683559i
$297$	−2.37294	+	4.11005i	−0.137692	+	0.238489i
$298$	−8.96173	+	15.5222i	−0.519139	+	0.899176i
$299$	15.5784	+	26.9826i	0.900924	+	1.56045i
$300$		0			0
$301$	12.7459	+	23.8957i	0.734660	+	1.37733i
$302$	−17.5172			−1.00800
$303$	4.14426	+	7.17807i	0.238081	+	0.412369i
$304$	6.87450	−	11.9070i	0.394280	−	0.682913i
$305$		0			0
$306$	3.86329	+	6.69141i	0.220849	+	0.382522i
$307$	−5.32151			−0.303714			−0.151857	−	0.988402i	$-0.548525\pi$
$307$	−5.32151			−0.303714			−0.151857	+	0.988402i	$0.548525\pi$
$308$	3.25585	−	5.22572i	0.185519	−	0.297763i
$309$	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	$0.183781\pi$
$312$	9.57045	−	16.5765i	0.541820	−	0.938460i
$313$	13.2615	+	22.9696i	0.749585	+	1.29832i	0.948022	+	0.318205i	$0.103080\pi$
$313$	13.2615	+	22.9696i	0.749585	+	1.29832i	−0.198437	+	0.980114i	$0.563587\pi$
$314$	−14.8675			−0.839020
$315$		0			0
$316$	0.407557			0.0229268
$317$	−7.81185	−	13.5305i	−0.438757	−	0.759950i	0.558837	−	0.829278i	$-0.311248\pi$
$317$	−7.81185	−	13.5305i	−0.438757	−	0.759950i	−0.997594	+	0.0693277i	$0.977915\pi$
$318$	4.42523	−	7.66473i	0.248155	−	0.429817i
$319$	9.49175	−	16.4402i	0.531436	−	0.920474i
$320$		0			0
$321$	2.16884			0.121053
$322$	−16.1820	−	0.543799i	−0.901788	−	0.0303047i
$323$	−31.1137			−1.73121
$324$	0.245174	+	0.424653i	0.0136208	+	0.0235918i
$325$		0			0
$326$	4.13240	−	7.15752i	0.228872	−	0.396419i
$327$	3.89908	+	6.75341i	0.215620	+	0.373465i
$328$	−4.00173			−0.220958
$329$	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	$0.798008\pi$
$332$	−0.281836	+	0.488154i	−0.0154678	+	0.0267909i
$333$	2.21903	−	3.84347i	0.121602	−	0.210621i
$334$	−0.563007	−	0.975156i	−0.0308064	−	0.0533582i
$335$		0			0
$336$	3.46017	+	6.48705i	0.188768	+	0.353898i
$337$	2.86415			0.156020			0.0780100	−	0.996953i	$-0.475143\pi$
$337$	2.86415			0.156020			0.0780100	+	0.996953i	$0.475143\pi$
$338$	−16.0537	−	27.8058i	−0.873206	−	1.51244i
$339$	7.74588	−	13.4163i	0.420698	−	0.728671i
$340$		0			0
$341$	3.93715	+	6.81935i	0.213209	+	0.369288i
$342$	6.07914			0.328722
$343$	−18.4263	−	1.86327i	−0.994926	−	0.100607i
$344$	−31.3212			−1.68873
$345$		0			0
$346$	−4.60248	+	7.97173i	−0.247431	+	0.428563i
$347$	−1.25639	+	2.17613i	−0.0674466	+	0.116821i	−0.897777	−	0.440451i	$-0.854819\pi$
$347$	−1.25639	+	2.17613i	−0.0674466	+	0.116821i	0.830330	+	0.557272i	$0.188152\pi$
$348$	−0.980695	−	1.69861i	−0.0525708	−	0.0910552i
$349$	12.6307			0.676108			0.338054	−	0.941127i	$-0.390231\pi$
$349$	12.6307			0.676108			0.338054	+	0.941127i	$0.390231\pi$
$350$		0			0
$351$	6.25553			0.333895
$352$	6.41961	+	11.1191i	0.342166	+	0.592650i
$353$	−11.2938	+	19.5614i	−0.601108	+	1.04115i	0.391546	+	0.920159i	$0.371941\pi$
$353$	−11.2938	+	19.5614i	−0.601108	+	1.04115i	−0.992654	+	0.120991i	$0.961393\pi$
$354$	0.144259	−	0.249863i	0.00766726	−	0.0132801i
$355$		0			0
$356$	−1.12217			−0.0594748
$357$	8.79817	−	14.1213i	0.465649	−	0.747377i
$358$	18.2780			0.966020
$359$	0.171108	+	0.296367i	0.00903072	+	0.0156417i	0.870505	−	0.492159i	$-0.163792\pi$
$359$	0.171108	+	0.296367i	0.00903072	+	0.0156417i	−0.861475	+	0.507800i	$0.830459\pi$
$360$		0			0
$361$	−2.73990	+	4.74564i	−0.144205	+	0.249771i
$362$	4.07160	+	7.05222i	0.213999	+	0.370656i
$363$	−11.5233			−0.604818
$364$	−8.11095	−	0.272570i	−0.425129	−	0.0142865i
$365$		0			0
$366$	−3.07170	−	5.32034i	−0.160560	−	0.278098i
$367$	−1.63531	+	2.83244i	−0.0853624	+	0.147852i	−0.905546	−	0.424249i	$-0.860538\pi$
$367$	−1.63531	+	2.83244i	−0.0853624	+	0.147852i	0.820183	+	0.572101i	$0.193871\pi$
$368$	6.92034	−	11.9864i	0.360748	−	0.624833i
$369$	−0.653911	−	1.13261i	−0.0340413	−	0.0589612i
$370$		0			0
$371$	−19.0472	−	0.640084i	−0.988882	−	0.0332315i
$372$	0.813579			0.0421821
$373$	−6.67795	−	11.5665i	−0.345771	−	0.598893i	0.639722	−	0.768606i	$-0.279049\pi$
$373$	−6.67795	−	11.5665i	−0.345771	−	0.598893i	−0.985494	+	0.169713i	$0.945716\pi$
$374$	−18.3347	+	31.7566i	−0.948063	+	1.64209i
$375$		0			0
$376$	5.76042	+	9.97734i	0.297071	+	0.514542i
$377$	−25.0221			−1.28870
$378$	−1.71903	+	2.75908i	−0.0884172	+	0.141912i
$379$	28.8968			1.48433			0.742165	−	0.670217i	$-0.233799\pi$
$379$	28.8968			1.48433			0.742165	+	0.670217i	$0.233799\pi$
$380$		0			0
$381$	5.89979	−	10.2187i	0.302255	−	0.523521i
$382$	14.2877	−	24.7469i	0.731020	−	1.26616i
$383$	10.3752	+	17.9704i	0.530148	+	0.918244i	0.999381	+	0.0351693i	$0.0111970\pi$
$383$	10.3752	+	17.9704i	0.530148	+	0.918244i	−0.469233	+	0.883074i	$0.655470\pi$
$384$	−5.50211			−0.280778
$385$		0			0
$386$	−8.84874			−0.450389
$387$	−5.11811	−	8.86483i	−0.260168	−	0.450625i
$388$	−0.116865	+	0.202417i	−0.00593294	+	0.0102762i
$389$	−4.13057	+	7.15437i	−0.209428	+	0.362741i	−0.951535	−	0.307542i	$-0.900494\pi$
$389$	−4.13057	+	7.15437i	−0.209428	+	0.362741i	0.742106	+	0.670282i	$0.233827\pi$
$390$		0			0
$391$	−31.3212			−1.58398
$392$	11.9306	−	17.7885i	0.602585	−	0.898453i
$393$	3.96139			0.199826
$394$	11.7266	+	20.3110i	0.590776	+	1.02325i
$395$		0			0
$396$	−1.16356	+	2.01535i	−0.0584713	+	0.101275i
$397$	12.4665	+	21.5926i	0.625674	+	1.08370i	0.988410	+	0.151807i	$0.0485093\pi$
$397$	12.4665	+	21.5926i	0.625674	+	1.08370i	−0.362736	+	0.931892i	$0.618157\pi$
$398$	25.5983			1.28312
$399$	−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	$0.775237\pi$
$402$	1.52992	−	2.64990i	0.0763054	−	0.132165i
$403$	5.18955	−	8.98857i	0.258510	−	0.447752i
$404$	2.03213	+	3.51975i	0.101102	+	0.175114i
$405$		0			0
$406$	6.87611	−	11.0363i	0.341255	−	0.547723i
$407$	21.0624			1.04403
$408$	9.62092	+	16.6639i	0.476307	+	0.824987i
$409$	17.7048	−	30.6656i	0.875446	−	1.51632i	0.0191590	−	0.999816i	$-0.493901\pi$
$409$	17.7048	−	30.6656i	0.875446	−	1.51632i	0.856287	−	0.516500i	$-0.172766\pi$
$410$		0			0
$411$	−9.23622	−	15.9976i	−0.455589	−	0.789104i
$412$	6.99687			0.344711
$413$	−0.620922	−	0.0208662i	−0.0305536	−	0.00102676i
$414$	6.11968			0.300766
$415$		0			0
$416$	8.46167	−	14.6561i	0.414868	−	0.718572i
$417$	1.33030	−	2.30414i	0.0651449	−	0.112834i
$418$	14.4254	+	24.9856i	0.705571	+	1.22208i
$419$	38.1119			1.86189			0.930945	−	0.365160i	$-0.118986\pi$
$419$	38.1119			1.86189			0.930945	+	0.365160i	$0.118986\pi$
$420$		0			0
$421$	12.5454			0.611428			0.305714	−	0.952123i	$-0.401105\pi$
$421$	12.5454			0.611428			0.305714	+	0.952123i	$0.401105\pi$
$422$	−9.57607	−	16.5862i	−0.466156	−	0.807406i
$423$	−1.88259	+	3.26074i	−0.0915347	+	0.158543i
$424$	11.0204	−	19.0878i	0.535196	−	0.926987i
$425$		0			0
$426$	−7.45314			−0.361106
$427$	−6.99542	+	11.2278i	−0.338532	+	0.543352i
$428$	1.06349			0.0514055
$429$	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	$0.100953\pi$
$432$	−1.38943	−	2.40657i	−0.0668491	−	0.115786i
$433$	−20.8010			−0.999631			−0.499816	−	0.866132i	$-0.666599\pi$
$433$	−20.8010			−0.999631			−0.499816	+	0.866132i	$0.666599\pi$
$434$	2.53842	+	4.75898i	0.121848	+	0.228439i
$435$		0			0
$436$	1.91191	+	3.31152i	0.0915637	+	0.158593i
$437$	−12.3215	+	21.3415i	−0.589418	+	1.02090i
$438$	−7.67418	+	13.2921i	−0.366686	+	0.635119i
$439$	−5.47542	−	9.48370i	−0.261327	−	0.452632i	0.705267	−	0.708941i	$-0.250827\pi$
$439$	−5.47542	−	9.48370i	−0.261327	−	0.452632i	−0.966595	+	0.256309i	$0.917494\pi$
$440$		0			0
$441$	6.98421	+	0.469941i	0.332581	+	0.0223782i
$442$	48.3338			2.29900
$443$	19.2762	+	33.3874i	0.915842	+	1.58628i	0.805664	+	0.592372i	$0.201809\pi$
$443$	19.2762	+	33.3874i	0.915842	+	1.58628i	0.110177	+	0.993912i	$0.464858\pi$
$444$	1.08809	−	1.88463i	0.0516387	−	0.0894408i
$445$		0			0
$446$	2.19473	+	3.80138i	0.103923	+	0.180001i
$447$	−14.5876			−0.689969
$448$	11.0593	+	20.7337i	0.522503	+	0.979577i
$449$	−21.8462			−1.03099			−0.515494	−	0.856893i	$-0.672392\pi$
$449$	−21.8462			−1.03099			−0.515494	+	0.856893i	$0.672392\pi$
$450$		0			0
$451$	3.10338	−	5.37521i	0.146133	−	0.253109i
$452$	3.79817	−	6.57862i	0.178651	−	0.309432i
$453$	−7.12847	−	12.3469i	−0.334925	−	0.580106i
$454$	18.9533			0.889524
$455$		0			0
$456$	15.1392			0.708957
$457$	1.84523	+	3.19603i	0.0863160	+	0.149504i	0.905951	−	0.423382i	$-0.139157\pi$
$457$	1.84523	+	3.19603i	0.0863160	+	0.149504i	−0.819635	+	0.572886i	$0.805824\pi$
$458$	−9.41692	+	16.3106i	−0.440024	+	0.762144i
$459$	−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	$0.756144\pi$
$462$	−15.4191	−	0.518161i	−0.717361	−	0.0241070i
$463$	4.97717			0.231309			0.115654	−	0.993290i	$-0.463104\pi$
$463$	4.97717			0.231309			0.115654	+	0.993290i	$0.463104\pi$
$464$	5.55773	+	9.62627i	0.258011	+	0.446888i
$465$		0			0
$466$	−12.4640	+	21.5884i	−0.577385	+	1.00006i
$467$	3.51106	+	6.08133i	0.162472	+	0.281410i	0.935755	−	0.352651i	$-0.114720\pi$
$467$	3.51106	+	6.08133i	0.162472	+	0.281410i	−0.773282	+	0.634062i	$0.781387\pi$
$468$	3.06738			0.141790
$469$	−6.58512	−	0.221294i	−0.304073	−	0.0102184i
$470$		0			0
$471$	−6.05019	−	10.4792i	−0.278778	−	0.482857i
$472$	0.359254	−	0.622246i	0.0165360	−	0.0286412i
$473$	24.2899	−	42.0714i	1.11685	−	1.93444i
$474$	−0.510614	−	0.884409i	−0.0234533	−	0.0406223i
$475$		0			0
$476$	4.31416	−	6.92433i	0.197739	−	0.317376i
$477$	7.20323			0.329813
$478$	7.30782	+	12.6575i	0.334252	+	0.578941i
$479$	4.61478	−	7.99304i	0.210855	−	0.365211i	−0.741127	−	0.671364i	$-0.765709\pi$
$479$	4.61478	−	7.99304i	0.210855	−	0.365211i	0.951982	+	0.306153i	$0.0990419\pi$
$480$		0			0
$481$	−13.8812	−	24.0429i	−0.632928	−	1.09626i
$482$	21.4831			0.978529
$483$	−6.20183	−	11.6271i	−0.282193	−	0.529050i
$484$	−5.65044			−0.256838
$485$		0			0
$486$	0.614340	−	1.06407i	0.0278670	−	0.0482671i
$487$	−6.88189	+	11.9198i	−0.311848	+	0.540137i	−0.978762	−	0.204998i	$-0.934281\pi$
$487$	−6.88189	+	11.9198i	−0.311848	+	0.540137i	0.666914	+	0.745134i	$0.267615\pi$
$488$	−7.64960	−	13.2495i	−0.346281	−	0.599776i
$489$	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	$0.747094\pi$
$492$	−0.320644	−	0.555371i	−0.0144557	−	0.0250381i
$493$	12.5770	−	21.7841i	0.566441	−	0.981105i
$494$	19.0141	−	32.9334i	0.855486	−	1.48175i
$495$		0			0
$496$	−4.61066			−0.207025
$497$	7.55320	+	14.1606i	0.338807	+	0.635189i
$498$	1.41241			0.0632916
$499$	10.7954	+	18.6981i	0.483267	+	0.837042i	0.999815	−	0.0192154i	$-0.00611683\pi$
$499$	10.7954	+	18.6981i	0.483267	+	0.837042i	−0.516549	+	0.856258i	$0.672783\pi$
$500$		0			0
$501$	0.458221	−	0.793662i	0.0204718	−	0.0354582i
$502$	6.28765	+	10.8905i	0.280632	+	0.486068i
$503$	33.2826			1.48400			0.741998	−	0.670402i	$-0.233878\pi$
$503$	33.2826			1.48400			0.741998	+	0.670402i	$0.233878\pi$
$504$	−4.28097	+	6.87106i	−0.190690	+	0.306062i
$505$		0			0
$506$	14.5216	+	25.1522i	0.645564	+	1.11815i
$507$	13.0658	−	22.6307i	0.580273	−	1.00506i
$508$	2.89295	−	5.01073i	0.128354	−	0.222315i
$509$	−9.61002	−	16.6450i	−0.425957	−	0.737779i	0.570552	−	0.821261i	$-0.306729\pi$
$509$	−9.61002	−	16.6450i	−0.425957	−	0.737779i	−0.996509	+	0.0834823i	$0.973396\pi$
$510$		0			0
$511$	33.0314	+	1.11003i	1.46122	+	0.0491047i
$512$	−24.5235			−1.08380
$513$	2.47385	+	4.28484i	0.109223	+	0.189180i
$514$	−13.7333	+	23.7867i	−0.605748	+	1.04919i
$515$		0			0
$516$	−2.50965	−	4.34685i	−0.110481	−	0.191359i
$517$	−17.8691			−0.785881
$518$	14.4190	+	0.484552i	0.633534	+	0.0212900i
$519$	−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	$0.170039\pi$
$522$	−2.45736	+	4.25627i	−0.107556	+	0.186292i
$523$	3.15672	+	5.46760i	0.138034	+	0.239082i	0.926752	−	0.375673i	$-0.122588\pi$
$523$	3.15672	+	5.46760i	0.138034	+	0.239082i	−0.788718	+	0.614755i	$0.789255\pi$
$524$	1.94246			0.0848566
$525$		0			0
$526$	−30.4837			−1.32915
$527$	5.21692	+	9.03597i	0.227253	+	0.393613i
$528$	6.59407	−	11.4213i	0.286970	−	0.497047i
$529$	−0.903660	+	1.56519i	−0.0392896	+	0.0680515i
$530$		0			0
$531$	0.234819			0.0101903
$532$	−3.02091	−	5.66354i	−0.130973	−	0.245545i
$533$	−8.18112			−0.354364
$534$	1.40593	+	2.43514i	0.0608404	+	0.105379i
$535$		0			0
$536$	3.81003	−	6.59917i	0.164568	−	0.285041i
$537$	7.43805	+	12.8831i	0.320976	+	0.555946i
$538$	21.8462			0.941859
$539$	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	$0.945415\pi$
$542$	−10.5292	+	18.2370i	−0.452266	+	0.783348i
$543$	−3.31380	+	5.73967i	−0.142209	+	0.246313i
$544$	8.50630	+	14.7333i	0.364705	+	0.631687i
$545$		0			0
$546$	9.57045	+	17.9425i	0.409578	+	0.767867i
$547$	−27.2078			−1.16332			−0.581660	−	0.813432i	$-0.697597\pi$
$547$	−27.2078			−1.16332			−0.581660	+	0.813432i	$0.697597\pi$
$548$	−4.52896	−	7.84439i	−0.193467	−	0.335096i
$549$	2.50000	−	4.33013i	0.106697	−	0.184805i
$550$		0			0
$551$	−9.89541	−	17.1394i	−0.421559	−	0.730161i
$552$	15.2401			0.648663
$553$	−1.16286	+	1.86642i	−0.0494499	+	0.0793683i
$554$	3.54284			0.150521
$555$		0			0
$556$	0.652307	−	1.12983i	0.0276640	−	0.0479154i
$557$	−6.23622	+	10.8015i	−0.264237	+	0.457672i	−0.967364	−	0.253393i	$-0.918454\pi$
$557$	−6.23622	+	10.8015i	−0.264237	+	0.457672i	0.703126	+	0.711065i	$0.251787\pi$
$558$	−1.01931	−	1.76549i	−0.0431506	−	0.0747391i
$559$	−64.0330			−2.70831
$560$		0			0
$561$	−29.8445			−1.26004
$562$	−17.0665	−	29.5601i	−0.719908	−	1.24692i
$563$	−7.91558	+	13.7102i	−0.333602	+	0.577815i	−0.983215	−	0.182449i	$-0.941597\pi$
$563$	−7.91558	+	13.7102i	−0.333602	+	0.577815i	0.649613	+	0.760265i	$0.274931\pi$
$564$	−0.923123	+	1.59890i	−0.0388705	+	0.0673257i
$565$		0			0
$566$	10.6924			0.449434
$567$	−2.64426	−	0.0888607i	−0.111048	−	0.00373180i
$568$	−18.5609			−0.778798
$569$	−11.2832	−	19.5431i	−0.473018	−	0.819291i	0.526505	−	0.850172i	$-0.323502\pi$
$569$	−11.2832	−	19.5431i	−0.473018	−	0.819291i	−0.999523	+	0.0308807i	$0.990169\pi$
$570$		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	$0.242772\pi$
$572$	7.27871	+	12.6071i	0.304338	+	0.527129i
$573$	23.2569			0.971572
$574$	2.24818	−	3.60839i	0.0938373	−	0.150611i
$575$		0			0
$576$	−4.44086	−	7.69180i	−0.185036	−	0.320492i
$577$	−12.4066	+	21.4889i	−0.516495	+	0.894595i	0.483322	+	0.875443i	$0.339430\pi$
$577$	−12.4066	+	21.4889i	−0.516495	+	0.894595i	−0.999817	+	0.0191524i	$0.993903\pi$
$578$	−13.8506	+	23.9899i	−0.576107	+	0.997847i
$579$	−3.60092	−	6.23697i	−0.149649	−	0.259200i
$580$		0			0
$581$	−1.43137	−	2.68351i	−0.0593833	−	0.111331i
$582$	0.585667			0.0242767
$583$	17.0928	+	29.6056i	0.707913	+	1.22614i
$584$	−19.1114	+	33.1019i	−0.790834	+	1.36976i
$585$		0			0
$586$	−12.2225	−	21.1701i	−0.504908	−	0.874527i
$587$	3.96139			0.163504			0.0817520	−	0.996653i	$-0.473948\pi$
$587$	3.96139			0.163504			0.0817520	+	0.996653i	$0.473948\pi$
$588$	3.42469	+	0.230435i	0.141232	+	0.00950296i
$589$	8.20918			0.338253
$590$		0			0
$591$	−9.54405	+	16.5308i	−0.392590	+	0.679985i
$592$	−6.16637	+	10.6805i	−0.253436	+	0.438965i
$593$	3.05229	+	5.28673i	0.125343	+	0.217100i	0.921867	−	0.387507i	$-0.126664\pi$
$593$	3.05229	+	5.28673i	0.125343	+	0.217100i	−0.796524	+	0.604607i	$0.793330\pi$
$594$	5.83116			0.239255
$595$		0			0
$596$	−7.15299			−0.292998
$597$	10.4170	+	18.0427i	0.426339	+	0.738440i
$598$	19.1409	−	33.1530i	0.782730	−	1.35573i
$599$	−12.3922	+	21.4640i	−0.506333	+	0.876995i	0.493640	+	0.869666i	$0.335666\pi$
$599$	−12.3922	+	21.4640i	−0.506333	+	0.876995i	−0.999973	+	0.00732860i	$0.997667\pi$
$600$		0			0
$601$	43.9866			1.79425			0.897126	−	0.441775i	$-0.145651\pi$
$601$	43.9866			1.79425			0.897126	+	0.441775i	$0.145651\pi$
$602$	17.5963	−	28.2425i	0.717173	−	1.15108i
$603$	2.49035			0.101415
$604$	−3.49542	−	6.05425i	−0.142227	−	0.246344i
$605$		0			0
$606$	5.09196	−	8.81954i	0.206847	−	0.358269i
$607$	8.65040	+	14.9829i	0.351109	+	0.608138i	0.986444	−	0.164098i	$-0.0524714\pi$
$607$	8.65040	+	14.9829i	0.351109	+	0.608138i	−0.635335	+	0.772237i	$0.719138\pi$
$608$	13.3852			0.542843
$609$	10.5770	+	0.355443i	0.428603	+	0.0144033i
$610$		0			0
$611$	11.7766	+	20.3977i	0.476430	+	0.825201i
$612$	−1.54178	+	2.67044i	−0.0623227	+	0.107946i
$613$	7.69972	−	13.3363i	0.310989	−	0.538648i	−0.667588	−	0.744531i	$-0.732673\pi$
$613$	7.69972	−	13.3363i	0.310989	−	0.538648i	0.978577	+	0.205883i	$0.0660065\pi$
$614$	3.26921	+	5.66244i	0.131935	+	0.228518i
$615$		0			0
$616$	−38.3989	−	1.29040i	−1.54714	−	0.0519917i
$617$	8.70273			0.350359			0.175179	−	0.984537i	$-0.443949\pi$
$617$	8.70273			0.350359			0.175179	+	0.984537i	$0.443949\pi$
$618$	−8.76614	−	15.1834i	−0.352626	−	0.610766i
$619$	3.57547	−	6.19290i	0.143710	−	0.248913i	−0.785181	−	0.619267i	$-0.787430\pi$
$619$	3.57547	−	6.19290i	0.143710	−	0.248913i	0.928891	+	0.370353i	$0.120763\pi$
$620$		0			0
$621$	2.49035	+	4.31341i	0.0999342	+	0.173091i
$622$	2.32885			0.0933785
$623$	3.20183	−	5.13901i	0.128279	−	0.205890i
$624$	−17.3833			−0.695888
$625$		0			0
$626$	16.2941	−	28.2223i	0.651245	−	1.12799i
$627$	−11.7406	+	20.3353i	−0.468874	+	0.812114i
$628$	−2.96669	−	5.13846i	−0.118384	−	0.205047i
$629$	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	$0.795042\pi$
$632$	−1.27161	−	2.20249i	−0.0505818	−	0.0876102i
$633$	7.79379	−	13.4992i	0.309776	−	0.536547i
$634$	−9.59826	+	16.6247i	−0.381196	+	0.660250i
$635$		0			0
$636$	3.53209			0.140056
$637$	24.3908	−	36.3667i	0.966400	−	1.44090i
$638$	−23.3246			−0.923431
$639$	−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	$0.303811\pi$
$642$	−1.33241	−	2.30779i	−0.0525858	−	0.0910813i
$643$	−29.4981			−1.16329			−0.581646	−	0.813442i	$-0.697591\pi$
$643$	−29.4981			−1.16329			−0.581646	+	0.813442i	$0.697591\pi$
$644$	−3.04105	−	5.70130i	−0.119834	−	0.224663i
$645$		0			0
$646$	19.1144	+	33.1071i	0.752046	+	1.30258i
$647$	14.1918	−	24.5809i	0.557938	−	0.966377i	−0.439731	−	0.898130i	$-0.644926\pi$
$647$	14.1918	−	24.5809i	0.557938	−	0.966377i	0.997668	−	0.0682470i	$-0.0217406\pi$
$648$	1.52992	−	2.64990i	0.0601009	−	0.104098i
$649$	0.557211	+	0.965118i	0.0218724	+	0.0378842i
$650$		0			0
$651$	−2.32135	+	3.72582i	−0.0909807	+	0.146026i
$652$	3.29836			0.129174
$653$	−11.6346	−	20.1517i	−0.455297	−	0.788598i	0.543408	−	0.839469i	$-0.317134\pi$
$653$	−11.6346	−	20.1517i	−0.455297	−	0.788598i	−0.998705	+	0.0508707i	$0.983800\pi$
$654$	4.79072	−	8.29778i	0.187332	−	0.324469i
$655$		0			0
$656$	1.81713	+	3.14736i	0.0709470	+	0.122884i
$657$	−12.4918			−0.487350
$658$	−12.2329	−	0.411087i	−0.476887	−	0.0160259i
$659$	20.9852			0.817468			0.408734	−	0.912653i	$-0.365970\pi$
$659$	20.9852			0.817468			0.408734	+	0.912653i	$0.365970\pi$
$660$		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	$-0.0692537\pi$
$662$	2.47570	−	4.28804i	0.0962209	−	0.166660i
$663$	19.6690	+	34.0677i	0.763881	+	1.32308i
$664$	3.51739			0.136501
$665$		0			0
$666$	−5.45294			−0.211297
$667$	−9.96139	−	17.2536i	−0.385707	−	0.668063i
$668$	0.224687	−	0.389170i	0.00869342	−	0.0150574i
$669$	−1.78625	+	3.09388i	−0.0690604	+	0.119616i
$670$		0			0
$671$	23.7294			0.916063
$672$	−3.78500	+	6.07502i	−0.146010	+	0.234349i
$673$	−21.4998			−0.828757			−0.414378	−	0.910105i	$-0.636001\pi$
$673$	−21.4998			−0.828757			−0.414378	+	0.910105i	$0.636001\pi$
$674$	−1.75956	−	3.04765i	−0.0677757	−	0.117391i
$675$		0			0
$676$	6.40679	−	11.0969i	0.246415	−	0.426803i
$677$	−24.8968	−	43.1225i	−0.956862	−	1.65733i	−0.730048	−	0.683396i	$-0.760502\pi$
$677$	−24.8968	−	43.1225i	−0.956862	−	1.65733i	−0.226815	−	0.973938i	$-0.572831\pi$
$678$	−19.0344			−0.731011
$679$	−0.593529	−	1.11274i	−0.0227776	−	0.0427029i
$680$		0			0
$681$	7.71289	+	13.3591i	0.295558	+	0.511922i
$682$	4.83750	−	8.37879i	0.185237	−	0.320840i
$683$	−15.6299	+	27.0717i	−0.598060	+	1.03587i	0.395047	+	0.918661i	$0.370728\pi$
$683$	−15.6299	+	27.0717i	−0.598060	+	1.03587i	−0.993107	+	0.117210i	$0.962605\pi$
$684$	1.21305	+	2.10106i	0.0463820	+	0.0803360i
$685$		0			0
$686$	9.33736	+	20.7515i	0.356502	+	0.792296i
$687$	−15.3285			−0.584820
$688$	14.2225	+	24.6342i	0.542229	+	0.939169i
$689$	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	$0.674495\pi$
$692$	−3.67356			−0.139648
$693$	−5.90944	−	11.0789i	−0.224481	−	0.420852i
$694$	3.08740			0.117196
$695$		0			0
$696$	−6.11968	+	10.5996i	−0.231966	+	0.401776i
$697$	4.11213	−	7.12242i	0.155758	−	0.269781i
$698$	−7.75956	−	13.4400i	−0.293704	−	0.508710i
$699$	−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	$0.537423\pi$
$702$	−3.84302	−	6.65630i	−0.145045	−	0.251226i
$703$	10.9791	−	19.0163i	0.414084	−	0.717215i
$704$	21.0758	−	36.5043i	0.794324	−	1.37581i
$705$		0			0
$706$	27.7529			1.04449
$707$	−21.9170	−	0.736524i	−0.824273	−	0.0276998i
$708$	0.115143			0.00432734
$709$	7.44157	+	12.8892i	0.279474	+	0.484063i	0.971254	−	0.238045i	$-0.0765066\pi$
$709$	7.44157	+	12.8892i	0.279474	+	0.484063i	−0.691780	+	0.722108i	$0.743173\pi$
$710$		0			0
$711$	0.415579	−	0.719805i	0.0155854	−	0.0269948i
$712$	3.50125	+	6.06434i	0.131215	+	0.227271i
$713$	8.26391			0.309486
$714$	−20.4311	−	0.686589i	−0.764613	−	0.0256949i
$715$		0			0
$716$	3.64723	+	6.31719i	0.136303	+	0.236084i
$717$	−5.94771	+	10.3017i	−0.222121	+	0.384725i
$718$	0.210237	−	0.364140i	0.00784596	−	0.0135896i
$719$	−18.3084	−	31.7110i	−0.682787	−	1.18262i	−0.974127	−	0.226002i	$-0.927434\pi$
$719$	−18.3084	−	31.7110i	−0.682787	−	1.18262i	0.291340	−	0.956620i	$-0.405899\pi$
$720$		0			0
$721$	−19.9638	+	32.0424i	−0.743492	+	1.19332i
$722$	6.73291			0.250573
$723$	8.74236	+	15.1422i	0.325132	+	0.563145i
$724$	−1.62491	+	2.81443i	−0.0603895	+	0.104598i
$725$		0			0
$726$	7.07924	+	12.2616i	0.262735	+	0.455071i
$727$	−13.8624			−0.514129			−0.257064	−	0.966394i	$-0.582755\pi$
$727$	−13.8624			−0.514129			−0.257064	+	0.966394i	$0.582755\pi$
$728$	23.8337	+	44.6830i	0.883338	+	1.65606i
$729$	1.00000			0.0370370
$730$		0			0
$731$	32.1853	−	55.7466i	1.19042	−	2.06186i
$732$	1.22587	−	2.12327i	0.0453094	−	0.0784782i
$733$	−16.3849	−	28.3794i	−0.605189	−	1.04822i	−0.992022	−	0.126068i	$-0.959764\pi$
$733$	−16.3849	−	28.3794i	−0.605189	−	1.04822i	0.386833	−	0.922150i	$-0.373569\pi$
$734$	4.01854			0.148327
$735$		0			0
$736$	13.4745			0.496676
$737$	5.90944	+	10.2354i	0.217677	+	0.377028i
$738$	−0.803447	+	1.39161i	−0.0295753	+	0.0512259i
$739$	−14.9342	+	25.8668i	−0.549363	+	0.951524i	0.448956	+	0.893554i	$0.351796\pi$
$739$	−14.9342	+	25.8668i	−0.549363	+	0.951524i	−0.998318	+	0.0579700i	$0.981537\pi$
$740$		0			0
$741$	30.9505			1.13700
$742$	11.0204	+	20.6607i	0.404570	+	0.758480i
$743$	−49.5577			−1.81810			−0.909048	−	0.416691i	$-0.863190\pi$
$743$	−49.5577			−1.81810			−0.909048	+	0.416691i	$0.863190\pi$
$744$	−2.53842	−	4.39668i	−0.0930631	−	0.161190i
$745$		0			0
$746$	−8.20506	+	14.2116i	−0.300409	+	0.520323i
$747$	0.574768	+	0.995527i	0.0210297	+	0.0364244i
$748$	−14.6342			−0.535079
$749$	−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	$0.794849\pi$
$752$	5.23146	−	9.06116i	0.190772	−	0.330427i
$753$	−5.11741	+	8.86361i	−0.186489	+	0.323008i
$754$	15.3721	+	26.6252i	0.559818	+	0.969633i
$755$		0			0
$756$	−1.29661	−	0.0435726i	−0.0471571	−	0.00158472i
$757$	−7.01509			−0.254968			−0.127484	−	0.991841i	$-0.540690\pi$
$757$	−7.01509			−0.254968			−0.127484	+	0.991841i	$0.540690\pi$
$758$	−17.7525	−	30.7482i	−0.644798	−	1.11682i
$759$	−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	$0.909099\pi$
$762$	−14.4979			−0.525203
$763$	−20.6204	−	0.692951i	−0.746508	−	0.0250865i
$764$	11.4040			0.412581
$765$		0			0
$766$	12.7478	−	22.0798i	0.460597	−	0.797777i
$767$	0.734459	−	1.27212i	0.0265198	−	0.0459336i
$768$	−5.50156	−	9.52899i	−0.198521	−	0.343848i
$769$	0.822729			0.0296684			0.0148342	−	0.999890i	$-0.495278\pi$
$769$	0.822729			0.0296684			0.0148342	+	0.999890i	$0.495278\pi$
$770$		0			0
$771$	−22.3545			−0.805077
$772$	−1.76570	−	3.05828i	−0.0635489	−	0.110070i
$773$	−12.3422	+	21.3773i	−0.443919	+	0.768890i	−0.997976	−	0.0635887i	$-0.979745\pi$
$773$	−12.3422	+	21.3773i	−0.443919	+	0.768890i	0.554058	+	0.832478i	$0.313079\pi$
$774$	−6.28852	+	10.8920i	−0.226036	+	0.391506i
$775$		0			0
$776$	1.45851			0.0523576
$777$	5.52615	+	10.3603i	0.198249	+	0.371674i
$778$	10.1503			0.363906
$779$	−3.23536	−	5.60381i	−0.115919	−	0.200777i
$780$		0			0
$781$	14.3942	−	24.9315i	0.515065	−	0.892118i
$782$	19.2418	+	33.3279i	0.688087	+	1.19180i
$783$	−4.00000			−0.142948
$784$	−19.4082	−	1.30590i	−0.693149	−	0.0466394i
$785$		0			0
$786$	−2.43364	−	4.21519i	−0.0868050	−	0.150351i
$787$	7.87908	−	13.6470i	0.280859	−	0.486462i	−0.690738	−	0.723105i	$-0.742714\pi$
$787$	7.87908	−	13.6470i	0.280859	−	0.486462i	0.971596	+	0.236644i	$0.0760474\pi$
$788$	−4.67990	+	8.10582i	−0.166714	+	0.288758i
$789$	−12.4051	−	21.4862i	−0.441632	−	0.764929i
$790$		0			0
$791$	19.2899	+	36.1643i	0.685871	+	1.28586i
$792$	14.5216			0.516003
$793$	−15.6388	−	27.0872i	−0.555351	−	0.961896i
$794$	15.3173	−	26.5303i	0.543590	−	0.941526i
$795$		0			0
$796$	5.10794	+	8.84721i	0.181046	+	0.313581i
$797$	15.8568			0.561677			0.280838	−	0.959755i	$-0.409388\pi$
$797$	15.8568			0.561677			0.280838	+	0.959755i	$0.409388\pi$
$798$	−8.50524	+	13.6511i	−0.301082	+	0.483244i
$799$	−23.6774			−0.837646
$800$		0			0
$801$	−1.14426	+	1.98191i	−0.0404304	+	0.0700275i
$802$	4.46576	−	7.73493i	0.157692	−	0.273130i
$803$	−29.6421	−	51.3417i	−1.04605	−	1.81181i
$804$	1.22114			0.0430661
$805$		0			0
$806$	−12.7526			−0.449191
$807$	8.89013	+	15.3982i	0.312948	+	0.542041i
$808$	12.6808	−	21.9637i	0.446108	−	0.772681i
$809$	3.92840	−	6.80419i	0.138115	−	0.239223i	−0.788668	−	0.614819i	$-0.789229\pi$
$809$	3.92840	−	6.80419i	0.138115	−	0.239223i	0.926783	+	0.375597i	$0.122562\pi$
$810$		0			0
$811$	−55.8410			−1.96084			−0.980421	−	0.196912i	$-0.936909\pi$
$811$	−55.8410			−1.96084			−0.980421	+	0.196912i	$0.936909\pi$
$812$	5.18642	+	0.174290i	0.182008	+	0.00611640i
$813$	−17.1390			−0.601090
$814$	−12.9395	−	22.4119i	−0.453529	−	0.785535i
$815$		0			0
$816$	8.73747	−	15.1337i	0.305873	−	0.529787i
$817$	−25.3229	−	43.8606i	−0.885936	−	1.53449i
$818$	−43.5070			−1.52119
$819$	−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	$0.878073\pi$
$822$	−11.3484	+	19.6559i	−0.395819	+	0.685579i
$823$	−11.1360	+	19.2881i	−0.388177	+	0.672342i	−0.992204	−	0.124621i	$-0.960228\pi$
$823$	−11.1360	+	19.2881i	−0.388177	+	0.672342i	0.604027	+	0.796964i	$0.293562\pi$
$824$	−21.8307	−	37.8119i	−0.760510	−	1.31724i
$825$		0			0
$826$	0.359254	+	0.673522i	0.0125001	+	0.0234348i
$827$	53.3872			1.85645			0.928227	−	0.372015i	$-0.121333\pi$
$827$	53.3872			1.85645			0.928227	+	0.372015i	$0.121333\pi$
$828$	1.22114	+	2.11507i	0.0424374	+	0.0735037i
$829$	14.4223	−	24.9801i	0.500906	−	0.867594i	−0.499094	−	0.866548i	$-0.666334\pi$
$829$	14.4223	−	24.9801i	0.500906	−	0.867594i	0.999999	−	0.00104627i	$-0.000333037\pi$
$830$		0			0
$831$	1.44173	+	2.49714i	0.0500129	+	0.0866250i
$832$	−55.5599			−1.92619
$833$	19.4008	+	39.5137i	0.672200	+	1.36907i
$834$	−3.26901			−0.113197
$835$		0			0
$836$	−5.75697	+	9.97137i	−0.199109	+	0.344867i
$837$	0.829594	−	1.43690i	0.0286750	−	0.0496665i
$838$	−23.4137	−	40.5537i	−0.808812	−	1.40090i
$839$	3.38435			0.116841			0.0584205	−	0.998292i	$-0.481394\pi$
$839$	3.38435			0.116841			0.0584205	+	0.998292i	$0.481394\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−7.70717	−	13.3492i	−0.265607	−	0.460044i
$843$	13.8901	−	24.0584i	0.478402	−	0.828616i
$844$	3.82167	−	6.61932i	0.131547	−	0.227846i
$845$		0			0
$846$	4.62620			0.159052
$847$	16.1221	−	25.8764i	0.553963	−	0.889124i
$848$	−20.0168			−0.687380
$849$	4.35117	+	7.53644i	0.149332	+	0.258650i
$850$		0			0
$851$	11.0523	−	19.1431i	0.378868	−	0.656218i
$852$	−1.48722	−	2.57594i	−0.0509513	−	0.0882502i
$853$	32.8905			1.12615			0.563074	−	0.826406i	$-0.309618\pi$
$853$	32.8905			1.12615			0.563074	+	0.826406i	$0.309618\pi$
$854$	16.2447	+	0.545907i	0.555883	+	0.0186805i
$855$		0			0
$856$	−3.31815	−	5.74721i	−0.113412	−	0.196435i
$857$	−13.5097	+	23.3994i	−0.461481	+	0.799308i	−0.999035	−	0.0439208i	$-0.986015\pi$
$857$	−13.5097	+	23.3994i	−0.461481	+	0.799308i	0.537554	+	0.843229i	$0.319348\pi$
$858$	18.2385	−	31.5900i	0.622652	−	1.07846i
$859$	−24.0537	−	41.6622i	−0.820702	−	1.42150i	−0.905161	−	0.425070i	$-0.860250\pi$
$859$	−24.0537	−	41.6622i	−0.820702	−	1.42150i	0.0844589	−	0.996427i	$-0.473084\pi$
$860$		0			0
$861$	3.45822	+	0.116214i	0.117856	+	0.00396056i
$862$	−10.4574			−0.356179
$863$	−5.08582	−	8.80891i	−0.173123	−	0.299859i	0.766387	−	0.642379i	$-0.222053\pi$
$863$	−5.08582	−	8.80891i	−0.173123	−	0.299859i	−0.939510	+	0.342521i	$0.888719\pi$
$864$	1.35267	−	2.34290i	0.0460188	−	0.0797069i
$865$		0			0
$866$	12.7789	+	22.1336i	0.434243	+	0.752132i
$867$	−22.5454			−0.765684
$868$	−1.13827	+	1.82694i	−0.0386353	+	0.0620105i
$869$	3.94458			0.133811
$870$		0			0
$871$	7.78922	−	13.4913i	0.263928	−	0.457136i
$872$	11.9306	−	20.6644i	0.404020	−	0.699783i
$873$	0.238332	+	0.412803i	0.00806631	+	0.0139713i
$874$	30.2784			1.02418
$875$		0			0
$876$	−6.12530			−0.206955
$877$	−18.4298	−	31.9214i	−0.622330	−	1.07791i	−0.989051	−	0.147576i	$-0.952853\pi$
$877$	−18.4298	−	31.9214i	−0.622330	−	1.07791i	0.366720	−	0.930331i	$-0.380481\pi$
$878$	−6.72753	+	11.6524i	−0.227043	+	0.393250i
$879$	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	$0.248340\pi$
$882$	−3.79063	−	7.72037i	−0.127637	−	0.259958i
$883$	35.7880			1.20436			0.602181	−	0.798359i	$-0.294298\pi$
$883$	35.7880			1.20436			0.602181	+	0.798359i	$0.294298\pi$
$884$	9.64464	+	16.7050i	0.324384	+	0.561850i
$885$		0			0
$886$	23.6843	−	41.0224i	0.795690	−	1.37818i
$887$	21.1990	+	36.7178i	0.711793	+	1.23286i	0.964183	+	0.265237i	$0.0854501\pi$
$887$	21.1990	+	36.7178i	0.711793	+	1.23286i	−0.252390	+	0.967626i	$0.581217\pi$
$888$	−13.5797			−0.455706
$889$	14.6925	+	27.5452i	0.492771	+	0.923837i
$890$		0			0
$891$	2.37294	+	4.11005i	0.0794964	+	0.137692i
$892$	−0.875883	+	1.51707i	−0.0293267	+	0.0507954i
$893$	−9.31450	+	16.1332i	−0.311698	+	0.539877i
$894$	8.96173	+	15.5222i	0.299725	+	0.519139i
$895$		0			0
$896$	7.69792	−	12.3553i	0.257169	−	0.412763i
$897$	31.1569			1.04030
$898$	13.4210	+	23.2459i	0.447865	+	0.775725i
$899$	−3.31838	+	5.74760i	−0.110674	+	0.191693i
$900$		0			0
$901$	22.6488	+	39.2289i	0.754542	+	1.30691i
$902$	−7.62612			−0.253922
$903$	27.0672	+	0.909598i	0.900741	+	0.0302695i
$904$	−47.4023			−1.57658
$905$		0			0
$906$	−8.75860	+	15.1703i	−0.290985	+	0.504001i
$907$	−26.2719	+	45.5042i	−0.872343	+	1.51094i	−0.0127763	+	0.999918i	$0.504067\pi$
$907$	−26.2719	+	45.5042i	−0.872343	+	1.51094i	−0.859567	+	0.511024i	$0.829266\pi$
$908$	3.78199	+	6.55061i	0.125510	+	0.217389i
$909$	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	$0.278400\pi$
$912$	−6.87450	−	11.9070i	−0.227638	−	0.394280i
$913$	−2.72778	+	4.72465i	−0.0902763	+	0.156363i
$914$	2.26719	−	3.92689i	0.0749920	−	0.129890i
$915$		0			0
$916$	−7.51631			−0.248346
$917$	−5.54232	+	8.89556i	−0.183024	+	0.293757i
$918$	7.72657			0.255015
$919$	12.9370	+	22.4075i	0.426752	+	0.739156i	0.996582	−	0.0826063i	$-0.0263244\pi$
$919$	12.9370	+	22.4075i	0.426752	+	0.739156i	−0.569830	+	0.821762i	$0.692991\pi$
$920$		0			0
$921$	−2.66075	+	4.60856i	−0.0876748	+	0.151857i
$922$	19.0107	+	32.9275i	0.626083	+	1.08441i
$923$	−37.9459			−1.24900
$924$	−2.89768	−	5.43251i	−0.0953266	−	0.178716i
$925$		0			0
$926$	−3.05767	−	5.29604i	−0.100481	−	0.174039i
$927$	7.13461	−	12.3575i	0.234331	−	0.405874i
$928$	−5.41069	+	9.37158i	−0.177614	+	0.307637i
$929$	0.888730	+	1.53933i	0.0291583	+	0.0505036i	0.880236	−	0.474536i	$-0.157384\pi$
$929$	0.888730	+	1.53933i	0.0291583	+	0.0505036i	−0.851078	+	0.525039i	$0.824051\pi$
$930$		0			0
$931$	34.5558	+	2.32513i	1.13252	+	0.0762031i
$932$	−9.94842			−0.325871
$933$	0.947706	+	1.64147i	0.0310265	+	0.0537395i
$934$	4.31396	−	7.47200i	0.141157	−	0.244491i
$935$		0			0
$936$	−9.57045	−	16.5765i	−0.312820	−	0.541820i
$937$	58.4486			1.90943			0.954716	−	0.297518i	$-0.0961587\pi$
$937$	58.4486			1.90943			0.954716	+	0.297518i	$0.0961587\pi$
$938$	3.81003	+	7.14296i	0.124402	+	0.233226i
$939$	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	$0.186438\pi$
$942$	−7.43374	+	12.8756i	−0.242204	+	0.419510i
$943$	−3.25693	−	5.64117i	−0.106060	−	0.183702i
$944$	−0.652530			−0.0212381
$945$		0			0
$946$	−59.6890			−1.94066
$947$	−27.4216	−	47.4955i	−0.891081	−	1.54340i	−0.838581	−	0.544776i	$-0.816615\pi$
$947$	−27.4216	−	47.4955i	−0.891081	−	1.54340i	−0.0524995	−	0.998621i	$-0.516719\pi$
$948$	0.203778	−	0.352954i	0.00661841	−	0.0114634i
$949$	−39.0713	+	67.6734i	−1.26831	+	2.19677i
$950$		0			0
$951$	−15.6237			−0.506633
$952$	−50.8804	−	1.70984i	−1.64904	−	0.0554164i
$953$	37.4426			1.21288			0.606442	−	0.795128i	$-0.292596\pi$
$953$	37.4426			1.21288			0.606442	+	0.795128i	$0.292596\pi$
$954$	−4.42523	−	7.66473i	−0.143272	−	0.248155i
$955$		0			0
$956$	−2.91644	+	5.05143i	−0.0943245	+	0.163375i
$957$	−9.49175	−	16.4402i	−0.306825	−	0.531436i
$958$	−11.3402			−0.366384
$959$	48.8459	+	1.64147i	1.57732	+	0.0530060i
$960$		0			0
$961$	14.1235	+	24.4627i	0.455598	+	0.789119i
$962$	−17.0555	+	29.5410i	−0.549892	+	0.952441i
$963$	1.08442	−	1.87827i	0.0349450	−	0.0605265i
$964$	4.28679	+	7.42495i	0.138068	+	0.239141i
$965$		0			0
$966$	−8.56195	+	13.7421i	−0.275476	+	0.442146i
$967$	32.0098			1.02937			0.514683	−	0.857381i	$-0.327910\pi$
$967$	32.0098			1.02937			0.514683	+	0.857381i	$0.327910\pi$
$968$	17.6298	+	30.5357i	0.566642	+	0.981453i
$969$	−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	$-0.476223\pi$
$972$	0.490347			0.0157279
$973$	3.31290	+	6.21096i	0.106207	+	0.199114i
$974$	16.9113			0.541872
$975$		0			0
$976$	−6.94716	+	12.0328i	−0.222373	+	0.385162i
$977$	1.56722	−	2.71451i	0.0501399	−	0.0868449i	−0.839866	−	0.542794i	$-0.817367\pi$
$977$	1.56722	−	2.71451i	0.0501399	−	0.0868449i	0.890006	+	0.455949i	$0.150700\pi$
$978$	−4.13240	−	7.15752i	−0.132140	−	0.228872i
$979$	−10.8610			−0.347120
$980$		0			0
$981$	7.79817			0.248976
$982$	19.0749	+	33.0387i	0.608705	+	1.05431i
$983$	21.5583	−	37.3400i	0.687602	−	1.19096i	−0.285009	−	0.958525i	$-0.591997\pi$
$983$	21.5583	−	37.3400i	0.687602	−	1.19096i	0.972611	−	0.232437i	$-0.0746699\pi$
$984$	−2.00086	+	3.46560i	−0.0637852	+	0.110479i
$985$		0			0
$986$	−30.9063			−0.984257
$987$	−4.68830	−	8.78953i	−0.149230	−	0.279774i
$988$	15.1765			0.482829
$989$	−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	$0.104825\pi$
$992$	−2.24434	−	3.88731i	−0.0712578	−	0.123422i
$993$	4.02986			0.127884
$994$	10.4276	−	16.7365i	0.330743	−	0.530850i
$995$		0			0
$996$	0.281836	+	0.488154i	0.00893031	+	0.0154678i
$997$	−11.3879	+	19.7244i	−0.360657	+	0.624677i	−0.988069	−	0.154011i	$-0.950781\pi$
$997$	−11.3879	+	19.7244i	−0.360657	+	0.624677i	0.627412	+	0.778688i	$0.284114\pi$
$998$	13.2640	−	22.9740i	0.419866	−	0.727229i
$999$	−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.i.i.151.2	✓	8
5.2	odd	4		525.2.r.h.424.6		16
5.3	odd	4		525.2.r.h.424.3		16
5.4	even	2		525.2.i.j.151.3	yes	8
7.2	even	3	inner	525.2.i.i.226.2	yes	8
7.3	odd	6		3675.2.a.bx.1.3		4
7.4	even	3		3675.2.a.bw.1.3		4
35.2	odd	12		525.2.r.h.499.3		16
35.4	even	6		3675.2.a.br.1.2		4
35.9	even	6		525.2.i.j.226.3	yes	8
35.23	odd	12		525.2.r.h.499.6		16
35.24	odd	6		3675.2.a.bq.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.i.i.151.2	✓	8	1.1	even	1	trivial
525.2.i.i.226.2	yes	8	7.2	even	3	inner
525.2.i.j.151.3	yes	8	5.4	even	2
525.2.i.j.226.3	yes	8	35.9	even	6
525.2.r.h.424.3		16	5.3	odd	4
525.2.r.h.424.6		16	5.2	odd	4
525.2.r.h.499.3		16	35.2	odd	12
525.2.r.h.499.6		16	35.23	odd	12
3675.2.a.bq.1.2		4	35.24	odd	6
3675.2.a.br.1.2		4	35.4	even	6
3675.2.a.bw.1.3		4	7.4	even	3
3675.2.a.bx.1.3		4	7.3	odd	6

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.614340 - 1.06407i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.245174 - 0.424653i) q^{4} -1.22868 q^{6} +(1.24517 + 2.33443i) q^{7} -3.05984 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.614340 - 1.06407i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.245174 - 0.424653i) q^{4} -1.22868 q^{6} +(1.24517 + 2.33443i) q^{7} -3.05984 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.37294 - 4.11005i) q^{11} +(-0.245174 - 0.424653i) q^{12} -6.25553 q^{13} +(1.71903 - 2.75908i) q^{14} +(1.38943 + 2.40657i) q^{16} +(3.14426 - 5.44602i) q^{17} +(-0.614340 + 1.06407i) q^{18} +(-2.47385 - 4.28484i) q^{19} +(2.64426 + 0.0888607i) q^{21} -5.83116 q^{22} +(-2.49035 - 4.31341i) q^{23} +(-1.52992 + 2.64990i) q^{24} +(3.84302 + 6.65630i) q^{26} -1.00000 q^{27} +(1.29661 + 0.0435726i) q^{28} +4.00000 q^{29} +(-0.829594 + 1.43690i) q^{31} +(-1.35267 + 2.34290i) q^{32} +(-2.37294 - 4.11005i) q^{33} -7.72657 q^{34} -0.490347 q^{36} +(2.21903 + 3.84347i) q^{37} +(-3.03957 + 5.26469i) q^{38} +(-3.12776 + 5.41745i) q^{39} +1.30782 q^{41} +(-1.52992 - 2.86826i) q^{42} +10.2362 q^{43} +(-1.16356 - 2.01535i) q^{44} +(-3.05984 + 5.29980i) q^{46} +(-1.88259 - 3.26074i) q^{47} +2.77886 q^{48} +(-3.89908 + 5.81353i) q^{49} +(-3.14426 - 5.44602i) q^{51} +(-1.53369 + 2.65643i) q^{52} +(-3.60162 + 6.23818i) q^{53} +(0.614340 + 1.06407i) q^{54} +(-3.81003 - 7.14296i) q^{56} -4.94771 q^{57} +(-2.45736 - 4.25627i) q^{58} +(-0.117410 + 0.203359i) q^{59} +(2.50000 + 4.33013i) q^{61} +2.03861 q^{62} +(1.39908 - 2.24556i) q^{63} +8.88173 q^{64} +(-2.91558 + 5.04993i) q^{66} +(-1.24517 + 2.15670i) q^{67} +(-1.54178 - 2.67044i) q^{68} -4.98069 q^{69} +6.06598 q^{71} +(1.52992 + 2.64990i) q^{72} +(6.24588 - 10.8182i) q^{73} +(2.72647 - 4.72239i) q^{74} -2.42609 q^{76} +(12.5493 + 0.421722i) q^{77} +7.68604 q^{78} +(0.415579 + 0.719805i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-0.803447 - 1.39161i) q^{82} -1.14954 q^{83} +(0.686038 - 1.10111i) q^{84} +(-6.28852 - 10.8920i) q^{86} +(2.00000 - 3.46410i) q^{87} +(-7.26081 + 12.5761i) q^{88} +(-1.14426 - 1.98191i) q^{89} +(-7.78922 - 14.6031i) q^{91} -2.44227 q^{92} +(0.829594 + 1.43690i) q^{93} +(-2.31310 + 4.00641i) q^{94} +(1.35267 + 2.34290i) q^{96} -0.476664 q^{97} +(8.58135 + 0.577407i) q^{98} -4.74588 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 4 q^{3} - 7 q^{4} - 2 q^{6} + q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - q^2 + 4 * q^3 - 7 * q^4 - 2 * q^6 + q^7 + 6 * q^8 - 4 * q^9	\( 8 q - q^{2} + 4 q^{3} - 7 q^{4} - 2 q^{6} + q^{7} + 6 q^{8} - 4 q^{9} - 8 q^{11} + 7 q^{12} - 14 q^{13} - 12 q^{14} - 17 q^{16} + 6 q^{17} - q^{18} - 3 q^{19} + 2 q^{21} - 24 q^{22} - 2 q^{23} + 3 q^{24} + 19 q^{26} - 8 q^{27} + 15 q^{28} + 32 q^{29} - 9 q^{31} - 17 q^{32} + 8 q^{33} + 28 q^{34} + 14 q^{36} - 8 q^{37} - 27 q^{38} - 7 q^{39} + 8 q^{41} + 3 q^{42} + 10 q^{43} - 26 q^{44} + 6 q^{46} - 6 q^{47} - 34 q^{48} - 21 q^{49} - 6 q^{51} + 35 q^{52} + 6 q^{53} + q^{54} - 21 q^{56} - 6 q^{57} - 4 q^{58} - 10 q^{59} + 20 q^{61} + 88 q^{62} + q^{63} + 42 q^{64} - 12 q^{66} - q^{67} - 8 q^{68} - 4 q^{69} + 44 q^{71} - 3 q^{72} - 4 q^{73} + 21 q^{74} - 46 q^{76} + 32 q^{77} + 38 q^{78} - 8 q^{79} - 4 q^{81} + 8 q^{82} + 4 q^{83} - 18 q^{84} - 12 q^{86} + 16 q^{87} - 28 q^{88} + 10 q^{89} + 21 q^{91} - 132 q^{92} + 9 q^{93} - 22 q^{94} + 17 q^{96} - 24 q^{97} + 67 q^{98} + 16 q^{99}+O(q^{100}) \) 8 * q - q^2 + 4 * q^3 - 7 * q^4 - 2 * q^6 + q^7 + 6 * q^8 - 4 * q^9 - 8 * q^11 + 7 * q^12 - 14 * q^13 - 12 * q^14 - 17 * q^16 + 6 * q^17 - q^18 - 3 * q^19 + 2 * q^21 - 24 * q^22 - 2 * q^23 + 3 * q^24 + 19 * q^26 - 8 * q^27 + 15 * q^28 + 32 * q^29 - 9 * q^31 - 17 * q^32 + 8 * q^33 + 28 * q^34 + 14 * q^36 - 8 * q^37 - 27 * q^38 - 7 * q^39 + 8 * q^41 + 3 * q^42 + 10 * q^43 - 26 * q^44 + 6 * q^46 - 6 * q^47 - 34 * q^48 - 21 * q^49 - 6 * q^51 + 35 * q^52 + 6 * q^53 + q^54 - 21 * q^56 - 6 * q^57 - 4 * q^58 - 10 * q^59 + 20 * q^61 + 88 * q^62 + q^63 + 42 * q^64 - 12 * q^66 - q^67 - 8 * q^68 - 4 * q^69 + 44 * q^71 - 3 * q^72 - 4 * q^73 + 21 * q^74 - 46 * q^76 + 32 * q^77 + 38 * q^78 - 8 * q^79 - 4 * q^81 + 8 * q^82 + 4 * q^83 - 18 * q^84 - 12 * q^86 + 16 * q^87 - 28 * q^88 + 10 * q^89 + 21 * q^91 - 132 * q^92 + 9 * q^93 - 22 * q^94 + 17 * q^96 - 24 * q^97 + 67 * q^98 + 16 * q^99

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